File "markSceme-HL-paper3.html"
Path: /IB QUESTIONBANKS/4 Fourth Edition - PAPER/HTML/Mathematics HL/Topic 10/markSceme-HL-paper3html
File size: 3.42 MB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-212ef6a30de2a281f3295db168f85ac1c6eb97815f52f785535f1adfaee1ef4f.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-13d27c3a5846e837c0ce48b604dc257852658574909702fa21f9891f7bb643ed.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../index.html">Home</a>
</li>
<li class="active dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Questionbanks
<b class="caret"></b>
</a><ul class="dropdown-menu">
<li>
<a href="../../geography.html" target="_blank">DP Geography</a>
</li>
<li>
<a href="../../physics.html" target="_blank">DP Physics</a>
</li>
<li>
<a href="../../chemistry.html" target="_blank">DP Chemistry</a>
</li>
<li>
<a href="../../biology.html" target="_blank">DP Biology</a>
</li>
<li>
<a href="../../furtherMath.html" target="_blank">DP Further Mathematics HL</a>
</li>
<li>
<a href="../../mathHL.html" target="_blank">DP Mathematics HL</a>
</li>
<li>
<a href="../../mathSL.html" target="_blank">DP Mathematics SL</a>
</li>
<li>
<a href="../../mathStudies.html" target="_blank">DP Mathematical Studies</a>
</li>
</ul></li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="images/logo.jpg" alt="Ib qb 46 logo">
</div>
</div>
</div><h2>HL Paper 3</h2><div class="specification">
<p>Consider the recurrence relation \(a{u_{n + 2}} + b{u_{n + 1}} + c{u_n} = 0,{\text{ }}n \in \mathbb{N}\) where \(a\), \(b\) and \(c\) are constants. Let \(\alpha \) and \(\beta \) denote the roots of the equation \(a{x^2} + bx + c = 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Verify that the recurrence relation is satisfied by</p>
<p>\[{u_n} = A{\alpha ^n} + B{\beta ^n},\]</p>
<p>where \(A\) and \(B\) are arbitrary constants.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Solve the recurrence relation</p>
<p>\({u_{n + 2}} - 2{u_{n + 1}} + 5{u_n} = 0\) given that \({u_0} = 0\) and \({u_1} = 4\).</p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to substitute the given expression for \({u_n}\) into the recurrence relation <strong><em>M1</em></strong></p>
<p>\(a{u_{n + 2}} + b{u_{n + 1}} + c{u_n} = a(A{\alpha ^{n + 2}} + B{\beta ^{n + 2}}) + b(A{\alpha ^{n + 1}} + B{\beta ^{n + 1}}) + c(A{\alpha ^n} + B{\beta ^n})\) <strong><em>A1</em></strong></p>
<p>\( = A{\alpha ^n}(a{\alpha ^2} + b\alpha + c) + B{\beta ^n}(a{\beta ^2} + b\beta + c)\) <strong><em>A1</em></strong></p>
<p>\( = 0\) because \(\alpha \) and \(\beta \) both satisfy \(a{x^2} + bx + c = 0\) <strong><em>R1AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>M1A0A1R0 </em></strong>for solutions that are set to zero throughout and conclude with \(0 = 0\). Award the <strong><em>R1 </em></strong>for any valid reason.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the auxiliary equation is \({x^2} - 2x + 5 = 0\) <strong><em>A1</em></strong></p>
<p>solving their quadratic equation <strong><em>(M1)</em></strong></p>
<p>the roots are \(1 \pm 2{\text{i}}\) <strong><em>A1</em></strong></p>
<p>the general solution is</p>
<p>\({u_n} = A{\left( {1 + 2{\text{i}}} \right)^n}{\mkern 1mu} + B{\left( {1 - 2{\text{i}}} \right)^n}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {{u_n} = {{\left( {\sqrt 5 } \right)}^n}\left( {A\,{\text{cis}}\left( {n\arctan 2} \right) + B\,{\text{cis}}\left( { - n\arctan 2} \right)} \right)} \right)\) <strong><em>(A1)</em></strong></p>
<p>attempt to substitute both boundary conditions <strong><em>M1</em></strong></p>
<p>\(A + B = 0;{\text{ }}A(1 + 2{\text{i}}) + B(1 - 2{\text{i}}) = 4\) <strong><em>A1</em></strong></p>
<p>attempt to solve their equations for \(A\) and \(B\) <strong><em>M1</em></strong></p>
<p>\(A = - {\text{i}},{\text{ }}B = {\text{i}}\) <strong><em>A1</em></strong></p>
<p>\({u_n} = {\text{i}}{(1 - 2{\text{i}})^n} - {\text{i}}{(1 + 2{\text{i}})^n}\,\,\,\left( {{u_n} = 2{{\left( {\sqrt 5 } \right)}^n}\sin (n\arctan 2)} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept the trigonometric form for \({u_n}\).</p>
<p> </p>
<p><strong><em>[9 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right) = {\text{gcd}}\left( {k - 1,\,2} \right)\), where \(k \in {\mathbb{Z}^ + },\,k > 1\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the value of \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right)\) for odd positive integers \(k\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the value of \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right)\) for even positive integers \(k\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempting to use the Euclidean algorithm <strong><em>M1</em></strong></p>
<p>\(4k + 2 = 1\left( {3k + 1} \right) + \left( {k + 1} \right)\)<em><strong> A1</strong></em></p>
<p>\(3k + 1 = 2\left( {k + 1} \right) + \left( {k - 1} \right)\)<em><strong> A1</strong></em></p>
<p>\(K + 1 = \left( {k - 1} \right) + 2\)<em><strong> A1</strong></em></p>
<p>\( = {\text{gcd}}\left( {k - 1,\,2} \right)\)<em><strong> AG</strong></em></p>
<p> </p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>\({\text{gcd}}\left( {4k + 2,\,3k + 1} \right)\)</p>
<p>\( = {\text{gcd}}\left( {4k + 2 - \left( {3k + 1} \right),\,3k + 1} \right)\)<em><strong> M1</strong></em></p>
<p>\( = {\text{gcd}}\left( {3k + 1,\,k + 1} \right)\,\,\left( { = {\text{gcd}}\left( {{\text{k + 1,}}\,{\text{3k + 1}}} \right)} \right)\)<em><strong> A1</strong></em></p>
<p>\( = {\text{gcd}}\left( {3k + 1 - 2\left( {k + 1} \right),\,k + 1} \right)\,\,\left( { = {\text{gcd}}\left( {k - 1{\text{,}}\,k + {\text{1}}} \right)} \right)\)<em><strong> A1</strong></em></p>
<p>\( = {\text{gcd}}\left( {k + 1 - \left( {k - 1} \right),\,k - 1} \right)\,\,\left( { = {\text{gcd}}\left( {{\text{2,}}\,k - {\text{1}}} \right)} \right)\)<em><strong> A1</strong></em></p>
<p>\( = {\text{gcd}}\left( {k - 1,\,2} \right)\)<em><strong> AG</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(for \(k\) odd), \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right) = 2\) <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(for \(k\) even), \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right) = 1\) <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights of the edges in the complete graph \(G\) are given in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-10_om_09.18.27.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at A , use the nearest neighbour algorithm to find an upper bound for the travelling salesman problem for \(G\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By first deleting vertex A , use the deleted vertex algorithm together with Kruskal’s algorithm to find a lower bound for the travelling salesman problem for \(G\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the edges are traversed in the following order</p>
<p>AB <strong><em>A1</em></strong></p>
<p>BC</p>
<p>CF <strong><em>A1</em></strong></p>
<p>FE</p>
<p>ED <strong><em>A1</em></strong></p>
<p>DA <strong><em>A1</em></strong></p>
<p>\({\text{upper bound}} = {\text{weight of this cycle}} = 4 + 1 + 2 + 7 + 11 + 8 = 33\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>having deleted A, the order in which the edges are added is</p>
<p>BC <strong><em>A1</em></strong></p>
<p>CF <strong><em>A1</em></strong></p>
<p>CD <strong><em>A1</em></strong></p>
<p>EF <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept indication of the correct order on a diagram.</p>
<p> </p>
<p>to find the lower bound, we now reconnect A using the two edges with the lowest weights, that is AB and AF <strong><em>(M1)(A1)</em></strong></p>
<p>\({\text{lower bound}} = 1 + 2 + 5 + 7 + 4 + 6 = 25\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1)(A1)A1 </em></strong>for \({\text{LB}} = 15 + 4 + 6 = 25\) obtained either from an incorrect order of correct edges or where order is not indicated.</p>
<p> </p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Mathilde delivers books to five libraries, A, B, C, D and E. She starts her deliveries at library D and travels to each of the other libraries once, before returning to library D. Mathilde wishes to keep her travelling distance to a minimum.</p>
<p>The weighted graph \(H\), representing the distances, measured in kilometres, between the five libraries, has the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-09_om_05.58.38.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/01"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the weighted graph \(H\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting at library D use the nearest-neighbour algorithm, to find an upper bound for Mathilde’s minimum travelling distance. Indicate clearly the order in which the edges are selected.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By first removing library C, use the deleted vertex algorithm, to find a lower bound for Mathilde’s minimum travelling distance.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-09_om_06.16.03.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/M/01.a"></p>
<p>complete graph on 5 vertices <strong><em>A1</em></strong></p>
<p>weights correctly marked on graph <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>clear indication that the nearest-neighbour algorithm has been applied <strong><em>M1</em></strong></p>
<p>DA (or 16) <strong><em>A1</em></strong></p>
<p>AB (or 18) then BC (or 15) <strong><em>A1</em></strong></p>
<p>CE (or 17) then ED (or 19) <strong><em>A1</em></strong></p>
<p>\({\text{UB}} = 85\) <strong><em>A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an attempt to find the minimum spanning tree <strong><em>(M1)</em></strong></p>
<p>DA (16) then BE (17) then AB (18) (total 51) <strong><em>A1</em></strong></p>
<p>reconnect C with the two edges of least weight, namely CB (15) and CE (17) <strong><em>M1</em></strong></p>
<p>\({\text{LB}} = 83\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A recurrence relation is given by \({u_{n + 1}} + 2{u_n} + 1 = 0,{\text{ }}{u_1} = 4\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the recurrence relation to find \({u_2}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find an expression for \({u_n}\) in terms of \(n\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A second recurrence relation, where \({v_1} = {u_1}\) and \({v_2} = {u_2}\), is given by \({v_{n + 1}} + 2{v_n} + {v_{n - 1}} = 0,{\text{ }}n \ge 2\).</p>
<p class="p1">Find an expression for \({v_n}\) in terms of \(n\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({u_2} = - 9\) <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\({u_{n + 1}} = - 2{u_n} - 1\)</p>
<p>let \({u_n} = a{( - 2)^n} + b\) <strong><em>M1A1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\(a{( - 2)^{n + 1}} + b = - 2\left( {a{{( - 2)}^n} + b} \right) - 1\) <strong><em>M1</em></strong></p>
<p>\(a{( - 2)^{n + 1}} + b = a{( - 2)^{n + 1}} - 2b - 1\)</p>
<p>\(3b = - 1\)</p>
<p>\(b = - \frac{1}{3}\) <strong><em>A1</em></strong></p>
<p>\({u_1} = 4 \Rightarrow - 2a - \frac{1}{3} = 4\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow a = - \frac{{13}}{6}\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>using \({u_1} = 4,{\text{ }}{u_2} = - 9\)</p>
<p>\(4 = - 2a + b,{\text{ }} - 9 = 4a + b\) <strong><em>M1A1</em></strong></p>
<p>solving simultaneously <strong><em>M1</em></strong></p>
<p>\( \Rightarrow a = - \frac{{13}}{6},{\text{ and }}b = - \frac{1}{3}\) <strong><em>A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>so \({u_n} = - \frac{{13}}{6}{( - 2)^n} - \frac{1}{3}\)</p>
<p><strong>METHOD 2</strong></p>
<p>use of the formula \({u_n} = {a^n}{u_0} + b\left( {\frac{{1 - {a^n}}}{{1 - a}}} \right)\) <strong><em>(M1)</em></strong></p>
<p>letting \({u_0} = - \frac{5}{2}\) <strong><em>A1</em></strong></p>
<p>letting \(a = - 2\) and \(b = - 1\) <strong><em>A1</em></strong></p>
<p>\({u_n} = - \frac{5}{2}{( - 2)^n} - 1\left( {\frac{{1 - {{( - 2)}^n}}}{{1 - - 2}}} \right)\) <strong><em>M1A1</em></strong></p>
<p>\( = - \frac{{13}}{6}{( - 2)^n} - \frac{1}{3}\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>auxiliary equation is \({k^2} + 2k + 1 = 0\) <strong><em>M1</em></strong></p>
<p>hence \(k = - 1\) <strong><em>(A1)</em></strong></p>
<p>so let \({v_n} = (an + b){( - 1)^n}\) <strong><em>M1</em></strong></p>
<p>\((2a + b){( - 1)^2} = - 9\) and \((a + b){( - 1)^1} = 4\) <strong><em>A1</em></strong></p>
<p>so \(a = - 5,{\text{ }}b = 1\) <strong><em>M1A1</em></strong></p>
<p>\({v_n} = (1 - 5n){( - 1)^n}\)</p>
<p> </p>
<p><strong>Note: </strong>Caution necessary to allow FT from (a) to part (c).</p>
<p><em><strong>[6 marks]</strong></em></p>
<p><em><strong>Total [13 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider \({\kappa _n}\), a complete graph with \(n\) vertices, \(n \geqslant 2\). Let \(T\) be a fixed spanning tree of \({\kappa _n}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the complete bipartite graph \({\kappa _{3,3}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Prove that \({\kappa _{3,3}}\) is not planar.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A connected graph \(G\) has \(v\) vertices. Prove, using Euler’s relation, that a spanning tree for \(G\) has \(v - 1\) edges.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>If an edge \(E\) is chosen at random from the edges of \({\kappa _n}\), show that the probability that \(E\) belongs to \(T\) is equal to \(\frac{2}{n}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-09_om_06.44.36.png" alt="N17/5/MATHL/HP3/ENG/TZ0/DM/M/03.a.i"> <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>assume \({\kappa _{3,3}}\) is planar</p>
<p>\({\kappa _{3,3}}\) has no cycles of length 3 <strong><em>R1</em></strong></p>
<p>use of \(e \leqslant 2v - 4\) <strong><em>M1</em></strong></p>
<p>\(e = 9\) and \(v = 6\) <strong><em>A1</em></strong></p>
<p>hence inequality not satisfied 9 \(\not \leqslant \) 8 <strong><em>R1</em></strong></p>
<p>so \({\kappa _{3,3}}\) is not planar <strong><em>AG</em></strong></p>
<p> </p>
<p><strong>Note:</strong> use of \(e \leqslant 3v - 6\) with \(e = 9\) and \(v = 6\) and concluding that this inequality does not show whether \({\kappa _{3,3}}\) is planar or not just gains <strong><em>R1</em></strong>.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a spanning tree (is planar and) has one face <strong><em>A1</em></strong></p>
<p>Euler’s relation is \(v - e + f = 2\)</p>
<p>\(v - e + 1 = 2\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow e = v - 1\) <strong><em>AG</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\kappa _n}\) has \(\left( {\begin{array}{*{20}{c}} n \\ 2 \end{array}} \right)\) edges \(\left( {\frac{{n(n - 1)}}{2}{\text{ edges}}} \right)\) <strong><em>(A1)</em></strong></p>
<p>\({\text{P}}(E{\text{ belongs to }}T) = \frac{{n - 1}}{{\left( {\frac{{n(n - 1)}}{2}} \right)}}\) <strong><em>M1A1</em></strong></p>
<p>clear evidence of simplification of the above expression <strong><em>M1</em></strong></p>
<p>\( = \frac{2}{n}\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The simple, complete graph \({\kappa _n}(n > 2)\) has vertices \({{\text{A}}_1},{\text{ }}{{\text{A}}_2},{\text{ }}{{\text{A}}_3},{\text{ }} \ldots ,{\text{ }}{{\text{A}}_n}\). The weight of the edge from \({{\text{A}}_i}\) to \({{\text{A}}_j}\) is given by the number \(i + j\).</p>
</div>
<div class="specification">
<p class="p1">Consider the general graph \({\kappa _n}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">(i) <span class="Apple-converted-space"> </span>Draw the graph \({\kappa _4}\) </span>including the weights of all the edges.</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Use the nearest-neighbour algorithm, starting at vertex \({{\text{A}}_1}\), <span class="s2">to find a Hamiltonian cycle.</span></p>
<p class="p2">(iii) <span class="Apple-converted-space"> </span>Hence, find an upper bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Consider the graph \({\kappa _5}\). </span>Use the deleted vertex algorithm, with \({{\text{A}}_5}\) as the deleted vertex, to find a lower bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Use the nearest-neighbour algorithm, starting at vertex \({{\text{A}}_1}\), <span class="s1">to find a Hamiltonian cycle.</span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence find and simplify an expression in \(n\), for an upper bound to the travelling salesman problem for this weighted graph.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">By splitting the weight of the edge \({{\text{A}}_i}{{\text{A}}_j}\) </span>into two parts or otherwise, show that all Hamiltonian cycles of \({\kappa _n}\) have the same total weight, equal to the answer found in (c)(ii).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> <img src="images/Schermafbeelding_2017-03-02_om_08.49.36.png" alt="N16/5/MATHL/HP3/ENG/TZ/DM/M/04.a"></span> <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <em>A1 </em></strong>for the graph, <strong><em>A1 </em></strong>for the weights.</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>cycle is \({{\text{A}}_1}{{\text{A}}_2}{{\text{A}}_3}{{\text{A}}_4}{{\text{A}}_1}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>upper bound is \(3 + 5 + 7 + 5 = 20\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">with \({{\text{A}}_5}\) </span>deleted, (applying Kruskal’s Algorithm) the minimum spanning tree will consist of the edges \({{\text{A}}_1}{{\text{A}}_2},{\text{ }}{{\text{A}}_1}{{\text{A}}_3}{\text{, }}{{\text{A}}_1}{{\text{A}}_4}\), <span class="s1">of weights 3, 4, 5 <span class="Apple-converted-space"> </span></span><strong><em>(M1)A1</em></strong></p>
<p class="p2">the two edges of smallest weight from \({{\text{A}}_5}\) are \({{\text{A}}_5}{{\text{A}}_1}\) and \({{\text{A}}_5}{{\text{A}}_2}\) of weights 6 and 7 <span class="Apple-converted-space"> </span><span class="s2"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1">so lower bound is \(3 + 4 + 5 + 6 + 7 = 25\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>starting at \({{\text{A}}_1}\) we go \({{\text{A}}_2},{\text{ }}{{\text{A}}_3}{\text{ }} \ldots {\text{ }}{{\text{A}}_n}\)</p>
<p class="p1">we now have to take \({{\text{A}}_n}{{\text{A}}_1}\)</p>
<p class="p1">thus the cycle is \({{\text{A}}_1}{{\text{A}}_2}{{\text{A}}_3} \ldots {{\text{A}}_{n - 1}}{{\text{A}}_n}{{\text{A}}_1}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: </strong>Final <strong><em>A1 </em></strong><span class="s2">is for \({{\text{A}}_n}{{\text{A}}_1}\).</span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>smallest edge from \({{\text{A}}_1}\) is \({{\text{A}}_1}{{\text{A}}_2}\) of weight 3, smallest edge from \({{\text{A}}_2}\) (to a new vertex) is \({{\text{A}}_2}{{\text{A}}_3}\) of weight 5, smallest edge from \({{\text{A}}_{n - 1}}\) (to a new vertex) is \({{\text{A}}_{n - 1}}{{\text{A}}_n}\) of weight \(2n - 1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p3">weight of \({{\text{A}}_n}{{\text{A}}_1}\) is \(n + 1\)</p>
<p class="p1">weight is \(3 + 5 + 7 + \ldots + (2n - 1) + (n + 1)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="Apple-converted-space">\( = \frac{{(n - 1)}}{2}(2n + 2) + (n + 1)\) </span><strong><em>M1A1</em></strong></p>
<p class="p3">\( = n(n + 1)\) (which is an upper bound) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: </strong>Follow through is not applicable.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">put a marker on each edge \({{\text{A}}_i}{{\text{A}}_j}\) <span class="s1">so that \(i\) </span>of the weight belongs to vertex \({{\text{A}}_i}\) <span class="s1">and \(j\) </span>of the weight belongs to vertex \({{\text{A}}_j}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">the Hamiltonian cycle visits each vertex once and only once and for vertex \({{\text{A}}_i}\) <span class="s1">there will be weight \(i\) </span>(belonging to vertex \({{\text{A}}_i}\)<span class="s1">) both going in and coming out <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></span></p>
<p class="p2">so the total weight will be \(\sum\limits_{i = 1}^n {2i = 2\frac{n}{2}(n + 1) = n(n + 1)} \) <span class="Apple-converted-space"> </span><strong><em>A1AG</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: </strong>Accept other methods for example induction.</p>
<p class="p3"> </p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In this question the notation \({({a_n}{a_{n - 1}} \ldots {a_2}{a_1}{a_0})_b}\) is used to represent a number in base \(b\), that has unit digit of \({a_0}\). For example \({(2234)_5}\) represents \(2 \times {5^3} + 2 \times {5^2} + 3 \times 5 + 4 = 319\) and it has a unit digit of 4.</p>
</div>
<div class="specification">
<p class="p1"><span class="s1">Let \(x\) </span>be the cube root of the base <span class="s2">7 </span>number \({(503231)_7}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>By converting the base <span class="s1">7 </span>number to base <span class="s1">10</span>, find the value of \(x\), in base <span class="s1">10</span><span class="s2">.</span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Express \(x\) as a base <span class="s1">5 </span>number.</p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Let \(y\) </span>be the base <span class="s2">9 </span>number \({({a_n}{a_{n - 1}} \ldots {a_1}{a_0})_9}\). Show that \(y\) is exactly divisible by <span class="s2">8 </span>if and only if the sum of its digits, \(\sum\limits_{i = 0}^n {{a_i}} \), is also exactly divisible by 8.</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using the method from part (b), find the unit digit when the base <span class="s1">9 </span><span class="s2">number \({(321321321)_9}\) is written as a base </span><span class="s1">8 </span><span class="s2">number.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>converting to base 10</p>
<p class="p1"><span class="Apple-converted-space">\({(503231)_7} = 5 \times {7^5} + 3 \times {7^3} + 2 \times {7^2} + 3 \times 7 + 1 = 85184\) </span><span class="s1"><strong><em>M1A1A1</em></strong></span></p>
<p class="p2">so \(x = 44\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>repeated division by 5 <span class="s1">gives <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></span></p>
<p class="p1"><img src="images/Schermafbeelding_2017-03-02_om_07.37.56.png" alt="N16/5/MATHL/HP3/ENG/TZ/DM/M/01.a"></p>
<p class="p2"><span class="s2">so base 5 </span>value for \(x\) is \({(134)_5}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p1"><span class="s1"><strong>Notes: </strong></span>Alternative method is to successively subtract the largest multiple of 25 and then 5<span class="s1">.</span></p>
<p class="p2">Follow through if they forget to take the cube root and obtain \({(10211214)_5}\) then award <strong><em>(M1)(A1)A1</em></strong>.</p>
<p class="p3"> </p>
<p class="p2"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(9 \equiv 1(\bmod 8)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({9^i} \equiv {1^i} \equiv 1(\bmod 8)\) \(i \in \mathbb{N}\)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)(A1)</em></strong></span></p>
<p class="p1">\(y = {a_n}{9^n} + {a_{n - 1}}{9^{n - 1}} + \ldots + {a_1}9 + {a_0} \equiv {a_n}{1^n} + {a_{n - 1}}{1^{n - 1}} + \ldots + {a_1}1 + {a_0} \equiv \)</p>
<p class="p1"><span class="Apple-converted-space">\({a_n} + {a_{n - 1}} + \ldots + {a_1} + {a_0} \equiv \sum\limits_{i = 0}^n {{a_i}(\bmod 8)} \) </span><span class="s1"><strong><em>M1A1A1</em></strong></span></p>
<p class="p1"><span class="s1">so \(y = 0(\bmod 8)\) </span>and hence divisible by 8 <span class="s1">if and only if \(\sum\limits_{i = 0}^n {{a_i} \equiv 0(\bmod 8)} \) </span>and hence divisible by 8 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1AG</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: </strong>Accept alternative valid methods <em>eg </em><span class="s2">binomial expansion of \({(8 + 1)^i}\), factorization of \(({a^i} - 1)\) </span>if they have sufficient explanation.</p>
<p class="p2"> </p>
<p class="p3"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">using part (b), \({(321321321)_9} \equiv 3 + 2 + 1 + 3 + 2 + 1 + 3 + 2 + 1 = 18 \equiv 2(\bmod 8)\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2">so the unit digit is 2 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the system of linear congruences</p>
<p>\[\begin{array}{*{20}{l}} {x \equiv 2(\bmod 5)} \\ {x \equiv 5(\bmod 8)} \\ {x \equiv 1(\bmod 3).} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>With reference to the integers 5, 8 and 3, state why the Chinese remainder theorem guarantees a unique solution modulo 120 to this system of linear congruences.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence or otherwise, find the general solution to the above system of linear congruences.</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>5, 8 and 3 are pairwise relatively prime (or equivalent) <strong><em>R1</em></strong></p>
<p>120 is the product of 5, 8 and 3 <strong><em>R1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>\(x = 2 + 5t,{\text{ }}t \in \mathbb{Z}\) and \(2 + 5t \equiv 5(\bmod 8)\) <strong><em>M1</em></strong></p>
<p>\(5t \equiv 3(\bmod 8) \Rightarrow 5t \equiv 35(\bmod 8)\) <strong><em>(M1)</em></strong></p>
<p>\(t = 7 + 8u,{\text{ }}u \in \mathbb{Z}\) <strong><em>(A1)</em></strong></p>
<p>\(x = 2 + 5(7 + 8u) \Rightarrow x = 37 + 40u\) <strong><em>(A1)</em></strong></p>
<p>\(37 + 40u \equiv 1(\bmod 3) \Rightarrow u \equiv 0(\bmod 3)\) <strong><em>(A1)</em></strong></p>
<p>\(u = 3v,{\text{ }}v \in \mathbb{Z}\) <strong><em>(A1)</em></strong></p>
<p>\(x = 37 + 40(3v)\)</p>
<p>\(x = 37 + 120v{\text{ }}\left( {x \equiv 37(\bmod 120)} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempting systematic listing of possibilities <strong><em>M1</em></strong></p>
<p>solutions to \(x \equiv 2(\bmod 5)\) are \(x = 2,{\text{ }}7,{\text{ }}12,{\text{ }} \ldots ,{\text{ }}37,{\text{ }} \ldots \) <strong><em>(A1)</em></strong></p>
<p>solutions to \(x \equiv 5(\bmod 8)\) are \(x = 5,{\text{ }}13,{\text{ }}21,{\text{ }} \ldots ,{\text{ }}37,{\text{ }} \ldots \) <strong><em>(A1)</em></strong></p>
<p>solutions to \(x \equiv 1(\bmod 3)\) are \(x = 1,{\text{ }}4,{\text{ }}7,{\text{ }} \ldots ,{\text{ }}37,{\text{ }} \ldots \) <strong><em>(A1)</em></strong></p>
<p>a solution is \(x = 37\) <strong><em>(A1)</em></strong></p>
<p>using the Chinese remainder theorem <strong><em>(M1)</em></strong></p>
<p>\(x = 37 + 120v{\text{ }}\left( {x \equiv 37(\bmod 120)} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>attempting to find \({M_i},{\text{ }}i = 1,{\text{ }}2,{\text{ 3}}\)</p>
<p>\({M_1} = 8 \times 3 = 24,{\text{ }}{M_2} = 5 \times 3 = 15\) and \({M_3} = 5 \times 8 = 40\) <strong><em>M1</em></strong></p>
<p>using \({M_i}{x_i} \equiv 1(\bmod {m_i}),{\text{ }}i = 1,{\text{ }}2,{\text{ }}3\) to obtain</p>
<p>\(24{x_1} \equiv 1(\bmod 5),{\text{ }}15{x_2} \equiv 1(\bmod 8)\) and \(40{x_3} \equiv 1(\bmod 3)\) <strong><em>M1</em></strong></p>
<p>\({x_1} \equiv 4(\bmod 5),{\text{ }}{x_2} \equiv 7(\bmod 8)\) and \({x_3} \equiv 1(\bmod 3)\) <strong><em>(A1)(A1)(A1)</em></strong></p>
<p>use of \(x \equiv {a_1}{x_1}{M_1} + {a_2}{x_2}{M_2} + {a_3}{x_3}{M_3}(\bmod M)\) gives</p>
<p>\(x = (2 \times 4 \times 24 + 5 \times 7 \times 15 + 1 \times 1 \times 40)(\bmod 120)\) <strong><em>(M1)</em></strong></p>
<p>\(x \equiv 757(\bmod 120){\text{ }}\left( { \equiv 37(\bmod 120)} \right){\text{ }}(x = 37 + 120v,{\text{ }}v \in \mathbb{Z})\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In this question no graphs are required to be drawn. Use the handshaking lemma and other results about graphs to explain why,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">a graph cannot exist with a degree sequence of \(1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}7,{\text{ }}8,{\text{ }}9\)<span class="s1">;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">a simple, connected, planar graph cannot exist with a degree sequence of \(4,{\text{ }}4,{\text{ }}4,{\text{ }}4,{\text{ }}5,{\text{ }}5\);</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">a tree cannot exist with a degree sequence of \(1,{\text{ }}1,{\text{ }}2,{\text{ }}2,{\text{ }}3,{\text{ }}3\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">assume such a graph exists</p>
<p class="p1">by the handshaking lemma the sum of the degrees equals twice the number of edges <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">but \(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45\) which is odd <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">this is a contradiction so graph does not exist <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">assume such a graph exists</p>
<p class="p1">since the graph is simple and connected (and \(v = 6 > 2\)) then \(e \leqslant 3v - 6\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">by the handshaking lemma \(4 + 4 + 4 + 4 + 5 + 5 = 2e\) so \(e = 13\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">hence \(13 \leqslant 3 \times 6 - 6 = 12\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">this is a contradiction so graph does not exist <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">assume such a graph exists</p>
<p class="p2"><span class="s1">a tree with 6 vertices must have 5 </span>edges (since \({\text{V}} - {\text{E}} + 1 = 2\) for a tree) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2">using the Handshaking Lemma \(1 + 1 + 2 + 2 + 3 + 3 = 2 \times 5\) implies \(12 = 10\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2">this is a contradiction so graph does not exist <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The distances by road, in kilometres, between towns in Switzerland are shown in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-25_om_10.43.43.png" alt></p>
<p class="p1">A cable television company wishes to connect the six towns placing cables along the road system.</p>
<p class="p1">Use Kruskal’s algorithm to find the minimum length of cable needed to connect the six towns.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Visitors to Switzerland can visit some principal locations for tourism by using a network of scenic railways as represented by the following graph:</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-25_om_10.44.46.png" alt></p>
<p class="p2">(i) <span class="Apple-converted-space"> </span>State whether the graph has any Hamiltonian paths or Hamiltonian cycles, justifying your answers.</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>State whether the graph has any Eulerian trails or Eulerian circuits, justifying your answers.</p>
<p class="p2">(iii) <span class="Apple-converted-space"> </span>The tourist board would like to make it possible to arrive in Geneva, travel all the available scenic railways, exactly once, and depart from Zurich. Find which locations would need to be connected by a further scenic railway in order to make this possible.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Zurich-Basel <span class="Apple-converted-space"> </span>85 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">Berne-Basel <span class="Apple-converted-space"> </span>100 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">Sion-Berne <span class="Apple-converted-space"> </span>155</p>
<p class="p1">Sion-Geneva <span class="Apple-converted-space"> </span>160</p>
<p class="p1">Zurich-Lugano <span class="Apple-converted-space"> </span>210 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">total length of pipe needed is 710 km <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for attempt to start with smallest length.</p>
<p class="p4"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept graphical solution showing lengths chosen.</p>
<p class="p4"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>N1 </em></strong>for a correct spanning tree and <strong><em>N1 </em></strong><span class="s2">for 710 km </span>with no method shown.</p>
<p class="p3"><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>possible Hamiltonian path <em>eg </em>Geneva-Montreux-Zermatt-Lugano-St Moritz-Interlaken-Luzern-Zurich-Berne <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">no possible Hamiltonian cycles <em>eg </em>we would have to pass through Montreux twice as Geneva is only connected to Montreux or Interlaken twice <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><span class="s1">(ii)</span> <span class="Apple-converted-space"> </span><span class="s1">possible Eulerian trail as there are 2 </span>odd vertices (Geneva and St Moritz) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">no possible Eulerian circuits as not all even vertices <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept an example of a Eulerian trail for the first <strong><em>R1</em></strong>.</p>
<p class="p2"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>St Moritz to Zurich <span class="Apple-converted-space"> </span><strong><em>A2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>If St Moritz and Zurich are connected via existing edges award <strong><em>A1</em></strong>.</p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<p class="p1"><em><strong>Total [11 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">In a computer game, Fibi, a magic dragon, is climbing a very large staircase. The steps are labelled <span class="s1">0, 1, 2, 3 … </span>.</p>
<p class="p1">She starts on step <span class="s1">0</span>. If Fibi is on a particular step then she can either jump up one step or fly up two steps. Let \({u_n}\) represent the number of different ways that Fibi can get to step \(n\). When counting the number of different ways, the order of Fibi’s moves matters, for example jump, fly, jump is considered different to jump, jump, fly. Let \({u_0} = 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the values of \({u_1},{\text{ }}{u_2},{\text{ }}{u_3}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \({u_{n + 2}} = {u_{n + 1}} + {u_n}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the auxiliary equation for this recurrence relation.</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence find the solution to this recurrence relation, giving your answer in the form \({u_n} = A{\alpha ^n} + B{\beta ^n}\) where \(\alpha \) and \(\beta \) are to be determined exactly in surd form and \(\alpha > \beta \). The constants \(A\) and \(B\) do not have to be found at this stage.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Given that \(A = \frac{1}{{\sqrt 5 }}\left( {\frac{{1 + \sqrt 5 }}{2}} \right)\), use the value of \({u_0}\) to determine \(B\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence find the explicit formula for \({u_n}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \({u_{20}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the smallest value of \(n\) <span class="s1">for which \({u_n} > 100\,000\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({u_1} = 1,{\text{ }}{u_2} = 2,{\text{ }}{u_3} = 3\) </span><strong><em>A1A1A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">to get to step \(n + 2\) she can either fly from step \(n\) or jump from step \(n + 1\) <span class="Apple-converted-space"> </span><strong><em>R2</em></strong></p>
<p class="p1">so \({u_{n + 2}} = {u_{n + 1}} + {u_n}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>auxiliary equation \({\lambda ^2} - \lambda - 1 = 0\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"> </p>
<p class="p3"><span class="s1"><strong>Note: </strong>Award <strong><em>M1 </em></strong></span>for attempting to write down a relevant quadratic.</p>
<p class="p4"> </p>
<p class="p1"><span class="s2">(ii) <span class="Apple-converted-space"> \(\lambda = \frac{{1 \pm \sqrt {1 + 4} }}{2}\)</span></span> <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\({u_n} = A{\left( {\frac{{1 + \sqrt 5 }}{2}} \right)^n} + B{\left( {\frac{{1 - \sqrt 5 }}{2}} \right)^n}\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \({u_0} = 1\)</span> implies \(A + B = 1\). <span class="s1">So \(B = - \frac{1}{{\sqrt 5 }}\left( {\frac{{1 - \sqrt 5 }}{2}} \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> \({u_n} = \frac{1}{{\sqrt 5 }}{\left( {\frac{{1 + \sqrt 5 }}{2}} \right)^{n + 1}} - \frac{1}{{\sqrt 5 }}{\left( {\frac{{1 - \sqrt 5 }}{2}} \right)^{n + 1}}\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept equivalent expressions in parts (i) and (ii).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({u_{20}} = 10946\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">using table, smallest value for \(n\) <span class="s1">is 25 (gives 121393</span>) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept other methods, <em>eg</em>, logs on the dominant term.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the result \(2003 = 6 \times 333 + 5\) and Fermat’s little theorem to show that \({2^{2003}} \equiv 4(\bmod 7)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Find \({2^{2003}}(\bmod 11)\) and \({2^{2003}}(\bmod 13)\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Chinese remainder theorem, or otherwise, to evaluate \({2^{2003}}(\bmod 1001)\), noting that \(1001 = 7 \times 11 \times 13\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{2003}} = {2^5} \times {({2^6})^{333}}\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 32 \times 1(\bmod 7)\) by Fermat’s little theorem <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 4(\bmod 7)\) <strong> <em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2003 = 3 + 10 \times 200\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{2003}} = {2^3} \times {({2^{10}})^{200}}\left( { \equiv 8 \times 1(\bmod 11)} \right) \equiv 8(\bmod 11)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{2003}} = {2^{11}} \times {({2^{12}})^{166}} \equiv 7(\bmod 13)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">form \({M_1} = \frac{{1001}}{7} = 143;{\text{ }}{M_2} = \frac{{1001}}{{11}} = 91;{\text{ }}{M_3} = \frac{{1001}}{{13}} = 77\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">solve \(143{x_1} \equiv 1(\bmod 7) \Rightarrow {x_1} = 5\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_2} = 4;{\text{ }}{x_3} = 12\) <strong> <em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 4 \times 143 \times 5 + 8 \times 91 \times 4 + 7 \times 77 \times 12 = 12240 \equiv 228(\bmod 1001)\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[7 marks]</span><br></em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates were able to complete part (a) and then went on to part (b). Some candidates raced through part (c). Others, who attempted part (c) using the alternative strategy of repeatedly solving linear congruencies, were sometimes successful.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let the greatest common divisor of 861 and 957 be <em>h </em>.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the Euclidean algorithm, find <em>h </em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence find integers <em>A </em>and <em>B </em>such that 861<em>A </em>+ 957<em>B </em>= <em>h </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Using part (b), solve \(287w \equiv 2(\bmod 319\)) , where \(w \in \mathbb{N},{\text{ }}w < 319\) .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the general solution to the diophantine equation \(861x + 957y = 6\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">by the above working on the left (or similar) <strong><em>M1A1A1</em></strong></span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">for 96 and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">for 93.</span></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;"> </em></p>
<p><em style="font-family: 'times new roman', times; font-size: medium;">h = </em><span style="font-family: 'times new roman', times; font-size: medium;">3 (since 3 divides 93) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(957 = 861 + 96\) <strong><em>M1A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(861 = 8 \times 96 + 93\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(96 = 93 + 3\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">so <em>h = </em>3 (since 3 divides 93) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">if method 1 was used for part (a)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">by the above working on the right (or equivalent) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - 10 \times 861 + 9 \times 957 = 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>A = –</em>10 and <em>B = </em>9 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 = 96 - 93\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 96 - (861 - 8 \times 96) = 9 \times 96 - 861\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 9 \times (957 - 861) - 861\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - 10 \times 861 + 9 \times 957\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>A = –</em>10 and <em>B = </em>9 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">from (b) \( - 10 \times 287 + 9 \times 319 = 1\) so <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - 10 \times 287 \equiv 1(\bmod 319)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(287w \equiv 2(\bmod 319) \Rightarrow - 10 \times 287w \equiv - 10 \times 2(\bmod 319)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow w \equiv - 20(\bmod 319)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(w = 299\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">from (b) \( - 10 \times 861 + 9 \times 957 = 3 \Rightarrow - 20 \times 861 + 18 \times 957 = 6\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so general solution is \(x = - 20 + 319t\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = 18 - 287t\,\,\,\,\,(t \in \mathbb{Z})\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The Euclidean algorithm was well applied. If it is done in the format shown in the mark scheme then the keeping track method of the linear combinations of the 2 original numbers makes part (b) easier.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Again well answered but not quite as good as (a).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly, since it is basic bookwork, this part was answered very badly indeed. Most candidates did not realise that \( - 10\) was the number to multiply by. Sadly, of the candidates that did do it, some did not read the question carefully enough to see that a positive integer answer was required.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Again this is standard bookwork. It was answered better than part (c). There were the usual mistakes in the final answer e.g. not having the two numbers, with the parameter, co-prime.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following weighted graph <em>G</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what feature of <em>G</em> ensures that <em>G</em> has an Eulerian trail.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what feature of <em>G</em> ensures that <em>G</em> does not have an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an Eulerian trail in <em>G</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the Chinese postman problem.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Starting and finishing at B, find a solution to the Chinese postman problem for<em> G</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total weight of the solution.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>G</em> has an Eulerian trail because it has (exactly) two vertices (B and F) of odd degree <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>G</em> does not have an Eulerian circuit because not all vertices are of even degree <em><strong>R1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for example BAEBCEFCDF <em><strong>A1A1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for start/finish at B/F, <em><strong>A1</strong> </em>for the middle vertices.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to determine the shortest route (walk) around a weighted graph <em><strong>A1</strong></em></p>
<p>using each edge (at least once, returning to the starting vertex) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Correct terminology must be seen. Do not accept trail, path, cycle or circuit.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>we require the Eulerian trail in (b), (weight = 65) <em><strong>(M1)</strong></em></p>
<p>and the minimum walk FEB (15) <em><strong>A1</strong></em></p>
<p>for example BAEBCEFCDFEB <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept EB added to the end or FE added to the start of their answer in (b) in particular for follow through.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total weight is (65 + 15=)80 <em><strong> A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The simple, connected graph \(G\) has <span class="s1"><em>e </em></span>edges and \(v\) vertices, where \(v \geqslant 3\).</p>
</div>
<div class="specification">
<p class="p1">Given that both \(G\) and \(G'\) are planar and connected,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the number of edges in \(G'\), the complement of \(G\), <span class="s1">is \(\frac{1}{2}{v^2} - \frac{1}{2}v - e\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">show that the sum of the number of faces in \(G\) and the number of faces in \(G'\) is independent of \(e\);</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">show that \({v^2} - 13v + 24 \leqslant 0\) and hence determine the maximum possible value of \(v\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">the total number of edges in \(G\) and \(G'\) <span class="s1">is \(\frac{{v(v - 1)}}{2}\) <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em></strong></p>
<p class="p2">the number of edges in \(G' = \frac{{v(v - 1)}}{2} - e\) <span class="Apple-converted-space"> </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{1}{2}{v^2} - \frac{1}{2}v - e\) </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">using Euler’s formula, number of faces in \(G = e + 2 - v\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">number of faces in \(G' = \frac{{{v^2}}}{2} - \frac{v}{2} - e + 2 - v\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">sum of these numbers \( = \frac{{{v^2}}}{2} - \frac{{5v}}{2} + 4\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">this is independent of \(e\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">for \(G\) to be planar, we require <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(e \leqslant 3v - 6\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">for \(e \leqslant 3v - 6\) to be planar, we require</p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{v^2}}}{2} - \frac{v}{2} - e \leqslant 3v - 6\) </span><strong><em>A1</em></strong></p>
<p class="p1">for these two inequalities to be satisfied simultaneously, adding or substituting we require</p>
<p class="p1"><span class="Apple-converted-space">\(\frac{{{v^2}}}{2} - \frac{v}{2} \leqslant 6v - 12\) </span><strong><em>(M1)A1</em></strong></p>
<p class="p1">leading to \({v^2} - 13v + 24 \leqslant 0\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2">the roots of the equation are 10.8 (and 2.23<span class="s1">) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></span></p>
<p class="p1">the largest value of \(v\) <span class="s2">is therefore 10 <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally in this question, good candidates thought their way through it whereas weak candidates just wrote down anything they could off the formula booklet or drew pictures of particular graphs. It was important to keep good notation and not let the same symbol stand for different things.</p>
<p class="p1">(a) If they considered the complete graph they were fine.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally in this question, good candidates thought their way through it whereas weak candidates just wrote down anything they could off the formula booklet or drew pictures of particular graphs. It was important to keep good notation and not let the same symbol stand for different things.</p>
<p class="p1">(b) Some confusion here if they were not clear about which graph they were applying Euler’s formula to. If they were methodical with good notation they obtained the answer.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally in this question, good candidates thought their way through it whereas weak candidates just wrote down anything they could off the formula booklet or drew pictures of particular graphs. It was important to keep good notation and not let the same symbol stand for different things.</p>
<p class="p1">(c) Again the same confusion about applying the inequality to both graphs. Most candidates realised which inequality was applicable. Many candidates had the good exam technique to pick up the last two marks even if they did not obtain the quadratic inequality.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The Fibonacci sequence can be described by the recurrence relation \({f_{n + 2}} = {f_{n + 1}} + {f_n}\) where \({f_0} = 0,\,{f_1} = 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the auxiliary equation and use it to find an expression for \({f_n}\) in terms of \(n\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>It is known that \({\alpha ^2} = \alpha + 1\) where \(\alpha = \frac{{1 + \sqrt 5 }}{2}\).</p>
<p>For integers \(n\) ≥ 3, use strong induction on the recurrence relation \({f_{n + 2}} = {f_{n + 1}} + {f_n}\) to prove that \({f_n} > {\alpha ^{n - 2}}\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to find the auxiliary equation (\({\lambda ^2} - \lambda - 1 = 0\)) <em><strong>M1</strong></em></p>
<p>\(\lambda = \frac{{1 \pm \sqrt 5 }}{2}\) <em><strong> (A1)</strong></em></p>
<p>the general solution is \({f_n} = A{\left( {\frac{{1 + \sqrt 5 }}{2}} \right)^n} + B{\left( {\frac{{1 - \sqrt 5 }}{2}} \right)^n}\) <em><strong> (M1)</strong></em> </p>
<p>imposing initial conditions (substituting \(n\) = 0,1) <em><strong>M1</strong></em></p>
<p><em>A</em> + <em>B</em> = 0 and \(A\left( {\frac{{1 + \sqrt 5 }}{2}} \right) + B\left( {\frac{{1 - \sqrt 5 }}{2}} \right) = 1\) <em><strong>A1</strong></em></p>
<p>\(A = \frac{1}{{\sqrt 5 }},\,\,B = - \frac{1}{{\sqrt 5 }}\) <em><strong>A1</strong></em></p>
<p>\({f_n} = \frac{1}{{\sqrt 5 }}{\left( {\frac{{1 + \sqrt 5 }}{2}} \right)^n} - \frac{1}{{\sqrt 5 }}{\left( {\frac{{1 - \sqrt 5 }}{2}} \right)^n}\) <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Condone use of decimal numbers rather than exact answers.</p>
<p><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>let P(\(n\)) be \({f_n} > {\alpha ^{n - 2}}\) for integers \(n\) ≥ 3</p>
<p>consideration of two consecutive values of \(f\) <em><strong>R1</strong></em></p>
<p>\({f_3} = 2\) and \({\alpha ^{3 - 2}} = \frac{{1 + \sqrt 5 }}{2}\left( {1.618 \ldots } \right) \Rightarrow {\text{P}}\left( 3 \right)\) is true <em><strong>A1</strong></em></p>
<p>\({f_4} = 3\) and \({\alpha ^{4 - 2}} = \frac{{3 + \sqrt 5 }}{2}\left( {2.618 \ldots } \right) \Rightarrow {\text{P}}\left( 4 \right)\) is true <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Do not award <em><strong>A</strong></em> marks for values of \(n\) other than \(n\) = 3 and \(n\) = 4.</p>
<p>(for \(k\) ≥ 4), assume that P(\(k\)) and P(\(k\) − 1) are true <em><strong>M1</strong></em></p>
<p>required to prove that P(\(k\) + 1) is true</p>
<p><strong>Note:</strong> Accept equivalent notation. Needs to start with 2 general consecutive integers and then prove for the next integer. This will affect the powers of the alphas.</p>
<p>\({f_{k + 1}} = {f_k} + {f_{k - 1}}\) (and \({f_k} > {\alpha ^{k - 2}},\,{f_{k - 1}} > {\alpha ^{k - 3}}\)) <em><strong>M1</strong></em></p>
<p>\({f_{k + 1}} > {\alpha ^{k - 2}} + {\alpha ^{k - 3}} = {\alpha ^{k - 3}}\left( {\alpha + 1} \right)\) <em><strong>A1</strong></em></p>
<p>\( = {\alpha ^{k - 3}}{\alpha ^2} = {\alpha ^{k - 1}} = {\alpha ^{\left( {k + 1} \right) - 2}}\) <em><strong>A1</strong></em></p>
<p>as P(3) and P(4) are true, and P(\(k\)) , P(\(k\) − 1) true ⇒ P(\(k\) + 1) true then P(\(k\)) is true for \(k\) ≥ 3 by strong induction <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> To obtain the final <em><strong>R1</strong></em>, at least five of the previous marks must have been awarded.</p>
<p><em><strong>[8 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Euclidean Algorithm to find the greatest common divisor of 7854 and 3315.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence state the number of solutions to the diophantine equation 7854<em>x </em>+ 3315<em>y </em>= 41 and justify your answer.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(7854 = 2 \times 3315 + 1224\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3315 = 2 \times 1224 + 867\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1224 = 1 \times 867 + 357\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(867 = 2 \times 357 + 153\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(357 = 2 \times 153 + 51\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(153 = 3 \times 51\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The gcd is 51. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Since 51 does not divide 41, <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">there are no solutions. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to use the Euclidean Algorithm correctly to find the greatest common divisor. Candidates who used the GCD button on their calculators were given no credit. Some candidates seemed unaware of the criterion for the solvability of Diophantine equations.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the recurrence relation</p>
<p style="text-align: center;">\({u_n} = 5{u_{n - 1}} - 6{u_{n - 2}},{\text{ }}{u_0} = 0\) and \({u_1} = 1\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for \({u_n}\) in terms of \(n\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For every prime number \(p > 3\), show that \(p|{u_{p - 1}}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the auxiliary equation is \({\lambda ^2} - 5\lambda + 6 = 0\) <strong><em>M1</em></strong></p>
<p>\( \Rightarrow \lambda = 2,{\text{ }}3\) <strong><em>(A1)</em></strong></p>
<p>the general solution is \({u_n} = A \times {2^n} + B \times {3^n}\) <strong><em>A1</em></strong></p>
<p>imposing initial conditions (substituting \(n = 0,{\text{ }}1\)) <strong><em>M1</em></strong></p>
<p>\(A + B = 0\) and \(2A + 3B = 1\) <strong><em>A1</em></strong></p>
<p>the solution is \(A = - 1,{\text{ }}B = 1\)</p>
<p>so that \({u_n} = {3^n} - {2^n}\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({u_{p - 1}} = {3^{p - 1}} - {2^{p - 1}}\)</p>
<p>\(p > 3\), therefore 3 or 2 are not divisible by \(p\) <strong><em>R1</em></strong></p>
<p>hence by FLT, \({3^{p - 1}} \equiv 1 \equiv {2^{p - 1}}(\bmod p)\) for \(p > 3\) <strong><em>M1A1</em></strong></p>
<p>\({u_{p - 1}} \equiv 0(\bmod p)\) <strong><em>A1</em></strong></p>
<p>\(p|{u_{p - 1}}\) for every prime number \(p > 3\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The decimal number 1071 is equal to \(a\)060 in base \(b\), where \(a > 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Convert the decimal number 1071 to base 12.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write the decimal number 1071 as a product of its prime factors.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answers to part (a) and (b), prove that there is only one possible value for \(b\) and state this value.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state the value of \(a\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>using a list of relevant powers of 12: 1, 12, 144 <strong><em>(M1)</em></strong></p>
<p>\(1071 = 7 \times {12^2} + 5 \times {12^1} + 3 \times {12^0}\) <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>attempted repeated division by 12 <strong><em>(M1)</em></strong></p>
<p>\(1071 \div 12 = 89{\text{rem}}3;{\text{ }}89 \div 12 = 7{\text{rem}}5\) <strong><em>(A1)</em></strong></p>
<p><strong>THEN</strong></p>
<p>\(1071 = {753_{12}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1071 = 3 \times 3 \times 7 \times 17\) <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>in base \(b\) \(a060\) ends in a zero and so \(b\) is a factor of 1071 <strong><em>R1</em></strong></p>
<p>from part (a) \(b < 12\) as \(a060\) has four digits and so the possibilities are</p>
<p>\(b = 3,{\text{ }}b = 7\) <strong>or</strong> \(b = 9\) <strong><em>R1</em></strong></p>
<p>stating valid reasons to exclude both \(b = 3\) <em>eg</em>, there is a digit of 6</p>
<p>and \(b = 9\) <em>eg</em>, \(1071 = {(1420)_9}\) <strong><em>R1</em></strong></p>
<p>\(b = 7\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> The <strong><em>A </em></strong>mark is independent of the <strong><em>R </em></strong>marks.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1071 = {(3060)_7} \Rightarrow a = 3\) <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the Euclidean algorithm to find the greatest common divisor of 264 and 1365.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, or otherwise, find the general solution of the Diophantine equation</p>
<p>\[264x - 1365y = 3.\]</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence find the general solution of the Diophantine equation</p>
<p>\[264x - 1365y = 6.\]</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By expressing each of 264 and 1365 as a product of its prime factors, determine the lowest common multiple of 264 and 1365.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(1365 = 5 \times 264 + 45\) <strong><em>M1<br></em></strong></p>
<p>\(264 = 5 \times 45 + 39\) <strong><em>A1</em></strong></p>
<p>\(45 = 1 \times 39 + 6\) <strong><em>A1</em></strong></p>
<p>\(39 = 6 \times 6 + 3\)</p>
<p>\(6 = 2 \times 3\) <strong><em>A1</em></strong></p>
<p>so gcd is 3</p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>\(39 - 6 \times 6 = 3\) <strong><em>(M1)</em></strong></p>
<p>\(39 - 6 \times (45 - 39) = 3 \Rightarrow 7 \times 39 - 6 \times 45 = 3\) <strong><em>(A1)</em></strong></p>
<p>\(7 \times (264 - 5 \times 45) - 6 \times 45 = 3 \Rightarrow 7 \times 264 - 41 \times 45 = 3\) <strong><em>(A1)</em></strong></p>
<p>\(7 \times 264 - 41 \times (1365 - 5 \times 264) = 3 \Rightarrow 212 \times 264 - 41 \times 1365 = 3\) <strong><em>(A1)</em></strong></p>
<p><strong>OR</strong></p>
<p>tracking the linear combinations when applying the Euclidean algorithm (could be displayed in (a))</p>
<p><img src="images/Schermafbeelding_2017-08-10_om_09.43.57.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/M/01.b.i"></p>
<p><strong>THEN</strong></p>
<p>a solution is \(x = 212,y = 41\) (or equivalent <em>eg</em> \(x = - 243,y = - 47\)) <strong><em>(A1)</em></strong></p>
<p>\(x = 212 + 455N,y = 41 + 88N\) (or equivalent) \((N \in \mathbb{Z})\) <strong><em>A1</em></strong></p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a solution is \(x = 424,y = 82{\text{ }}({\text{or equivalent }}eg{\text{ }}x = - 31,{\text{ }}y = - 6)\) <strong><em>(A1)</em></strong></p>
<p>\(x = 424 + 455N,{\text{ }}y = 82 + 88N({\text{or equivalent}}){\text{ }}\left( {N \in \mathbb{Z}} \right)\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A0 </em></strong>for \(x = 424 + 910N,{\text{ }}y = 82 + 176N\).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(264 = 2 \times 2 \times 2 \times 3 \times 11\) <strong><em>A1</em></strong></p>
<p>\(1365 = 3 \times 5 \times 7 \times 13\) <strong><em>A1</em></strong></p>
<p>\(1\,{\text{cm}} = 2 \times 2 \times 2 \times 3 \times 5 \times 7 \times 11 \times 13 = 120120\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Only award marks if prime factorisation is used.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that a graph containing a triangle cannot be bipartite.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that the number of edges in a bipartite graph with <em>n </em>vertices is less than or equal to \(\frac{{{n^2}}}{4}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At least two of the three vertices in the triangle must lie on one of the two disjoint sets <strong><em>M1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">These two are joined by an edge so the graph cannot be bipartite <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">If there are <em>x</em> vertices in one of the two disjoint sets then there are (<em>n</em> – <em>x</em>) vertices in the other disjoint set <em><strong>M1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The greatest number of edges occurs when all vertices in one set are joined to all vertices in the other to give <em>x</em>(<em>n</em> – <em>x</em>) edges <em><strong>A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Function <em>f</em>(<em>x</em>) = <em>x</em>(<em>n – x</em>) has a parabolic graph. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This graph has a unique maximum at \(\left( {\frac{n}{2},\frac{{{n^2}}}{4}} \right)\). <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(x(n - x) \leqslant \frac{{{n^2}}}{4}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was usually done correctly but then clear argument for parts (b) and (c) were rare.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was usually done correctly but then clear argument for parts (b) and (c) were rare.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The positive integer <em>N </em>is expressed in base <em>p </em>as \({({a_n}{a_{n - 1}}…{a_1}{a_0})_p}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that when <em>p </em>= 2 , <em>N </em>is even if and only if its least significant digit, \({a_0}\) , is 0.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that when <em>p </em>= 3 , <em>N </em>is even if and only if the sum of its digits is even.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = {a_n} \times {2^n} + {a_{n - 1}} \times {2^{n - 1}} + ... + {a_1} \times 2 + {a_0}\) <em><strong>M1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \({a_0} = 0\) , then <em>N </em>is even because all the terms are even. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Now consider</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a_0} = N - \sum\limits_{r = 1}^n {{a_r} \times {2^r}} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If <em>N </em>is even, then \({a_0}\) is the difference of two even numbers and is therefore even. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It must be zero since that is the only even digit in binary arithmetic. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = {a_n} \times {3^n} + {a_{n - 1}} \times {3^{n - 1}} + ... + {a_1} \times 3 + {a_0}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a_n} \times ({3^n} - 1) + {a_{n - 1}} \times ({3^{n - 1}} - 1) + ... + {a_1} \times (3 - 1) + {a_n} + {a_{n - 1}} + ... + {a_1} + {a_0}\) <em><strong>M1A1</strong></em><br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Since \({3^n}\) is odd for all \(n \in {\mathbb{Z}^ + }\) , it follows that \({3^n} - 1\) is even. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Therefore if the sum of the digits is even, <em>N </em>is the sum of even numbers and is even. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Now consider</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a_n} + {a_{n - 1}} + ... + {a_1} + {a_0} = N - \sum\limits_{r = 1}^n {{a_r}({3^r} - 1)} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If <em>N </em>is even, then the sum of the digits is the difference of even numbers and is therefore even. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The response to this question was disappointing. Many candidates were successful in showing the ‘if’ parts of (a) and (b) but failed even to realise that they had to continue to prove the ‘only if’ parts.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The response to this question was disappointing. Many candidates were successful in showing the ‘if’ parts of (a) and (b) but failed even to realise that they had to continue to prove the ‘only if’ parts.<span style="font: 26.0px Arial; color: #000000;"> </span></span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given a sequence of non negative integers \(\{ {a_r}\} \) show that</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\sum\limits_{r = 0}^n {{a_r}{{(x + 1)}^r}(\bmod x) = \sum\limits_{r = 0}^n {{a_r}(\bmod x)} } \) where \(x \in \{ 2,{\text{ }}3,{\text{ }}4 \ldots \} \).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\sum\limits_{r = 0}^n {(3{a_{2r + 1}} + {a_{2r}}){9^r} = \sum\limits_{r = 0}^{2n + 1} {{a_r}{3^r}} } \).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence determine whether the base \(3\) number \(22010112200201\) is divisible by \(8\)<span class="s1">.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) \((x + 1)(\bmod x) \equiv 1(\bmod x)\) <strong><em>(M1)</em></strong></p>
<p>\({(x + 1)^r}(\bmod x)\left( { \equiv {1^r}(\bmod x)} \right) = 1(\bmod x)\) <strong><em>A1</em></strong></p>
<p>\(\sum\limits_{r - 0}^n {{a_r}{{(x + 1)}^r}(\bmod x) \equiv \sum\limits_{r = 0}^n {{a_r}(\bmod x)} } \) <strong><em>AG</em></strong></p>
<p>(ii) <strong>METHOD 1</strong></p>
<p>\(\sum\limits_{r = 0}^n {(3{a_{2r + 1}} + {a_{2r}}){9^r} = \sum\limits_{r = 0}^n {(3{a_{2r + 1}} + {a_{2r}}){3^{2r}}} } \) <strong><em>M1</em></strong></p>
<p>\( = \sum\limits_{r = 0}^n {({3^{2r + 1}}{a_{2r + 1}} + {3^{2r}}{a_{2r}})} \) <strong><em>M1A1</em></strong></p>
<p>\( = \sum\limits_{r = 0}^{2n + 1} {{a_r}{3^r}} \) <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\(\sum\limits_{r = 0}^n {(3{a_{2r + 1}} + {a_{2r}}){9^r} = 3{a_1} + {a_0} + 9(3{a_3} + {a_2}) + \ldots + {9^n}(3{a_{2n + 1}} + {a_{2n}})} \) <strong><em>A1</em></strong></p>
<p>\( = {a_0} + 3{a_1} + {3^2}{a_2} + {3^3}{a_3} + \ldots + {3^{2n + 1}}{a_{2n + 1}}\) <strong><em>M1A1</em></strong></p>
<p>\( = \sum\limits_{r = 0}^{2n + 1} {{a_r}{3^r}} \) <strong><em>AG</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>using part (a) (ii) to separate the number into pairs of digits <strong><em>(M1)</em></strong></p>
<p>\(22010112200201{\text{ }}({\text{base }}3) \equiv 8115621{\text{ }}({\text{base }}9)\) <strong><em>A1</em></strong></p>
<p>using the sum of digits identity from part (a) (i) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>if result from a(i) is used to show that the number is divisible by \(2\), even if no other valid working given.</p>
<p> </p>
<p>\({\text{sum}} = 24\) <strong><em>A1</em></strong></p>
<p>which is divisible by \(8\) <strong><em>A1</em></strong></p>
<p>hence \(22010112200201\) (base \(3\)) is divisible by \(8\)</p>
<p><strong>METHOD 2</strong></p>
<p>\(\sum\limits_{r = 0}^{13} {{a_r}{3^r}\sum\limits_{r = 0}^6 {(3{a_{2r + 1}} + {a_{2r}}){9^r}} } \) <strong><em>(M1)</em></strong></p>
<p>\( \equiv \sum\limits_{r = 0}^6 {(3{a_{2r + 1}} + {a_{2r}})(\bmod 8)} \) <strong><em>A1</em></strong></p>
<p>\( = {a_0} + 3{a_1} + {a_2} + 3{a_3} + \ldots + {a_{12}} + 3{a_{13}}(\bmod 8)\) <strong><em>M1</em></strong></p>
<p>\( = (1 + 3 \times 0 + 2 + 3 \times 0 + \ldots + 3 \times 2)(\bmod 8) \equiv 24(\bmod 8)\) <strong><em>A1</em></strong></p>
<p>\( \equiv 0\) <strong>OR </strong>divisible by \(8\) <strong><em>A1</em></strong></p>
<p>hence \(22010112200201\) (base \(3\)) is divisible by \(8\)</p>
<p><em><strong>[5 marks]</strong></em></p>
<p><em><strong>Total [10 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the linear congruence \(ax \equiv b\left( {{\text{mod}}\,p} \right)\) where \(a,\,b,\,p,\,x \in {\mathbb{Z}^ + }\), \(p\) is prime and \(a\) is not a multiple of \(p\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State Fermat’s little theorem.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use Fermat’s little theorem to show that \(x \equiv {a^{p - 2}}b\left( {{\text{mod}}\,p} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence solve the linear congruence \(5x \equiv 7\left( {{\text{mod}}\,13} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>EITHER</strong></p>
<p>if \(p\) is prime (and \(a\) is any integer) then \({a^p} \equiv a\left( {{\text{mod}}\,p} \right)\) <em><strong>A1</strong></em><em><strong>A1</strong> </em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for \(p\) prime and <em><strong>A1</strong> </em>for the congruence or for stating that \(p\left| {{a^p} - a} \right.\).</p>
<p><strong>OR</strong></p>
<p><img src="data:image/png;base64,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"> <em><strong>A1</strong></em><em><strong>A1</strong> </em></p>
<p><strong>Note:</strong> Award <em><strong>A1</strong> </em>for \(p\) prime and <em><strong>A1</strong> </em>for the congruence or for stating that \(p\left| {{a^{p - 1}} - 1} \right.\).</p>
<p><strong>Note:</strong> Condone use of equals sign provided \(\left( {{\text{mod}}\,p} \right)\) is seen.</p>
<p><em><strong>[2 marks]</strong></em></p>
<p><em> </em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>multiplying both sides of the linear congruence by \({a^{p - 2}}\) <em><strong>(M1)</strong></em></p>
<p>\({a^{p - 1}}x \equiv {a^{p - 2}}b\left( {{\text{mod}}\,p} \right)\) <em><strong>A1</strong></em></p>
<p>as \({a^{p - 1}} \equiv 1\left( {{\text{mod}}\,p} \right)\) <em><strong>R1</strong></em></p>
<p>\(x \equiv {a^{p - 2}}b\left( {{\text{mod}}\,p} \right)\) <em><strong>AG</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x \equiv {5^{11}} \times 7\left( {{\text{mod}}\,13} \right)\) <em><strong>(M1)</strong></em></p>
<p>\( \equiv 341796875\left( {{\text{mod}}\,13} \right)\) <em><strong>(</strong><strong>A1)</strong></em></p>
<p><strong>Note:</strong> Accept equivalent calculation <em>eg</em>, using \({5^2} \equiv - 1\,{\text{mod}}\,13\).</p>
<p>\( \equiv 4\left( {{\text{mod}}\,13} \right)\) <em><strong>A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows the graph \(G\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-25_om_11.49.05.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(G\) is bipartite.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State which two vertices should be joined to make \(G\) equivalent to \({K_{3,{\text{ }}3}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">In a planar graph the degree of a face is defined as the number of edges adjacent to that face.</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the degree of each of the four faces of \(G\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Explain why the sum of the degrees of all the faces is twice the number of edges.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">\(H\) is a simple connected planar bipartite graph with \(e\) edges, \(f\) faces, \(v\) vertices and \(v \ge 3\).</p>
<p class="p1">Explain why there can be no face in \(H\) of degree</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>one;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>two;</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>three.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence prove that for \(H\)</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(e \ge 2f\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(e \le 2v - 4\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence prove that \({K_{3,{\text{ }}3}}\) is not planar.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">shading alternate vertices or attempting to list pairs <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1"><strong>EITHER</strong></p>
<p class="p1"><img src="images/Schermafbeelding_2016-01-25_om_12.08.48.png" alt> <em><strong>A1</strong></em></p>
<p class="p2"><strong>OR</strong></p>
<p class="p3">\(ADE\) and \(BCF\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">as no two equal shadings are adjacent, the graph is bipartite <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(C\) and \(E\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>degree of each of the four faces is \(4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>each edge bounds two faces <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>simple so no loops <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>simple so no multiple edges (and \(v > 2\)) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>bipartite graph so no triangles <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(2e = \sum {\deg (f) \ge 4f} \) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>R1</em></strong></span></p>
<p class="p1">\(e \ge 2f\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>if \(H\) is a simple connected planar graph then <span class="s2">\(e + 2 = v + f\) <span class="Apple-converted-space"> </span></span><strong><em>M1</em></strong></p>
<p class="p1">\(e + 2 - v \le \frac{1}{2}e\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\(2e + 4 - 2v \le e\)</p>
<p class="p1">\(e \le 2v - 4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for \({K_{3,{\text{ }}3}}{\text{ }}v = 6\), and \(e = 9\) <strong><em>A1</em></strong></p>
<p>\(9 \le 2 \times 6 - 4\) is not true, therefore \({K_{3,{\text{ }}3}}\) cannot be planar <strong><em>R1AG</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<p><strong><em>Total [13 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Euclidean algorithm to express gcd (123, 2347) in the form 123<em>p </em>+ 2347<em>q</em>, where \(p,{\text{ }}q \in \mathbb{Z}\).</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the least positive solution of \(123x \equiv 1(\bmod 2347)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the general solution of \(123z \equiv 5(\bmod 2347)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State the solution set of \(123y \equiv 1(\bmod 2346)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2347 = 19 \times 123 + 10\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\((123 = 12 \times 10 + 3)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(10 = 3 \times 3 + 1\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1(\gcd ) = 10 - 3 \times 3 = 10 - 3 \times (123 - 12 \times 10)\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 37 \times 10 - 3 \times 123\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 37 \times (2347 - 19 \times 123) - 3 \times 123\) (for continuation) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 37 \times 2347 - 706 \times 123\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[8 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1(\bmod 2347) = ( - 706 \times 123)(\bmod 2347)\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR<br></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = - 706 + 2347n\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">solution: 1641 <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5(\bmod 2347) = ( - 3530 \times 123)(\bmod 2347)\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{GS}}:z = - 3530 + k2347\) <strong> <em>A1A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Other common possibilities include \(1164 + k2347\) and \(8205 + k2347\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">empty set (123 and 2346 both divisible by 3) <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The majority of candidates were successful in parts (a) and (b). In part (c), some candidates failed to understand the distinction between a particular solution and a general solution. Part (d) was a 1 mark question that defeated all but the few who noticed that the gcd of the numbers concerned was 3.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The majority of candidates were successful in parts (a) and (b). In part (c), some candidates failed to understand the distinction between a particular solution and a general solution. Part (d) was a 1 mark question that defeated all but the few who noticed that the gcd of the numbers concerned was 3.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-size: medium; font-family: 'times new roman', times;">The majority of candidates were successful in parts (a) and (b). In part (c), some candidates failed to understand the distinction between a particular solution and a general solution. Part (d) was a 1 mark question that defeated all but the few who noticed that the gcd of the numbers concerned was 3.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The majority of candidates were successful in parts (a) and (b). In part (c), some candidates failed to understand the distinction between a particular solution and a general solution. Part (d) was a 1 mark question that defeated all but the few who noticed that the gcd of the numbers concerned was 3.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The planar graph <em>G</em> and its complement \(G'\) are both simple and connected.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that <em>G</em> has 6 vertices and 10 edges, show that \(G'\) is a tree.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the complete graph with 6 vertices has 15 edges so \(G'\) has </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">6 vertices and 5 edges <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the number of faces in \(G'\) , \(f = 2 + e - v = 1\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it is therefore a tree because \(f = 1\) <em><strong>R1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept it is a tree because \(v = e + 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well answered by many candidates.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">The graph \({K_{2,{\text{ }}2}}\) is the complete bipartite graph whose vertex set is the disjoint union of two subsets each of order two.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw \({K_{2,{\text{ }}2}}\) as a planar graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw a spanning tree for \({K_{2,{\text{ }}2}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw the graph of the complement of \({K_{2,{\text{ }}2}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that the complement of any complete bipartite graph does not possess a spanning tree.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong><em><img src="images/Schermafbeelding_2016-01-07_om_16.03.57.png" alt> A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for a correct version of <span class="s1">\({K_{2,{\text{ }}2}}\)</span> and <strong><em>A1 </em></strong>for a correct planar representation.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong><em><span class="Apple-converted-space"><img src="images/Schermafbeelding_2016-01-07_om_16.05.49.png" alt> </span></em></strong><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong><em><span class="Apple-converted-space"><img src="images/Schermafbeelding_2016-01-07_om_16.07.41.png" alt> </span>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">the complete bipartite graph \({K_{m,{\text{ }}n}}\) has two subsets of vertices \(A\) and \(B\), such that each element of \(A\) is connected to every element of \(B\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">in the complement, no element of \(A\) is connected to any element of \(B\). The complement is not a connected graph <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">by definition a tree is connected <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">hence the complement of any complete bipartite graph does not possess a spanning tree <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [7 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was generally well done with a large number of candidates drawing a correct planar representation for \({K_{2,2}}\). Some candidates, however, produced a correct non-planar representation of \({K_{2,2}}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (b) and (c) were generally well done with many candidates drawing a correct spanning tree for \({K_{2,2}}\) and the correct complement of \({K_{2,2}}\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Parts (b) and (c) were generally well done with many candidates drawing a correct spanning tree for \({K_{2,2}}\) and the correct complement of \({K_{2,2}}\).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (d) tested a candidate’s ability to produce a reasoned argument that clearly explained why the complement of \({K_{m,n}}\) does not possess a spanning tree. This was a question part in which only the best candidates provided the necessary rigour in explanation.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1"><span class="s1">Throughout this question, \({(abc \ldots )_n}\) </span>denotes the number \(abc \ldots \) written with number base \(n\). <span class="s1">For example \({(359)_n} = 3{n^2} + 5n + 9\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Given that \({(43)_n} \times {(56)_n} = {(3112)_n}\), show that \(3{n^3} - 19{n^2} - 38n - 16 = 0\).</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>Hence determine the value of \(n\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the set of values of \(n\) <span class="s1">satisfying \({(13)_n} \times {(21)_n} = {(273)_n}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that there are no possible values of \(n\) <span class="s1">satisfying \({(32)_n} \times {(61)_n} = {(1839)_n}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(n\) satisfies the equation \((4n + 3)(5n + 6) = 3{n^3} + {n^2} + n + 2\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(3{n^3} - 19{n^2} - 38n - 16 = 0\) </span><span class="s1"><strong><em>(AG)</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(n = 8\)</span> <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If extra solutions \(( - 1,{\text{ }} - 2/3)\) are not rejected (them just not appearing is fine) do not award the final <strong><em>A1</em></strong>.</p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(n\) satisfies the equation \((n + 3)(2n + 1) = 2{n^2} + 7n + 3\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">this is an identity satisfied by all \(n\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(n > 7\) or \(n \geqslant 8\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(n\) satisfies the equation \((3n + 2)(6n + 1) = {n^3} + 8{n^2} + 3n + 9\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\({n^3} - 10{n^2} - 12n + 7 = 0\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">roots are 11.03, 0.434 and –1.46 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">since there are no integer roots therefore the product is not true in any number base <span class="Apple-converted-space"> </span><strong><em>R1AG</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept an argument by contradiction that considers the equation modulo \(n\), with \(n > 10\).</p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<p class="p4"> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The fact that this gave an identity was managed by most. Then some showed their misunderstanding by saying any real number. Few noticed that the digit 7 means that the base must be greater than 7.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The cubic equation was generally reached but many candidates then forgot what type of number \(n\) had to be. To justify that there are no positive integer roots you need to write down what the roots are. There were a couple of really neat solutions that obtained a contradiction by working modulo \(n\).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve the recurrence relation \({v_n} + 4{v_{n - 1}} + 4{v_{n - 2}} = 0\) where \({v_1} = 0,{\text{ }}{v_2} = 1\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use strong induction to prove that the solution to the recurrence relation \({u_n} - 4{u_{n - 1}} + 4{u_{n - 2}} = 0\) where \({u_1} = 0,{\text{ }}{u_2} = 1\) is given by \({u_n} = {2^{n - 2}}(n - 1)\).</p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find a simplified expression for \({u_n} + {v_n}\) given that,</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(n\) is even.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(n\) is odd.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">the auxiliary equation is \({m^2} + 4m + 4 = 0\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(m = -2\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">the general solution is</p>
<p class="p2"><span class="Apple-converted-space">\({v_n} = (A + Bn) \times {( - 2)^n}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">the boundary conditions give</p>
<p class="p2">\(0 = -{\text{ }}2(A + B)\)</p>
<p class="p2"><span class="Apple-converted-space">\(1 = 4(A + 2B)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">the solution is \(A = - \frac{1}{4},{\text{ }}B = \frac{1}{4}\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">so that \({v_n} = \frac{1}{4}(n - 1){( - 2)^n}{\text{ }}\left( {{\text{or }}(n - 1)( - 2{)^{n - 2}}} \right)\)</p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">\(n = 1\) gives \((1 - 1) \times \frac{1}{2} = 0\) </span>which is correct <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="s1">\(n = 2\) gives \((2 - 1) \times 1 = 1\) </span>which is correct <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Must be checked for \(n = 1\) <span class="s1">and 2</span>, other values gain no marks.</p>
<p class="p1">assume that the result is true for all positive integers \( \leqslant k\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\({u_{k + 1}} = 4{u_k} - 4{u_{k - 1}}\) </span><span class="s2"><strong><em>(M1)</em></strong></span></p>
<p class="p4"><span class="Apple-converted-space">\({u_{k + 1}} = 4 \times {2^{k - 2}}(k - 1) - 4 \times {2^{k - 3}}(k - 2)\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s3">\( = {2^{k - 1}}(2k - 2 - k + 2)\) </span>or equivalent <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p5"><span class="Apple-converted-space">\( = k{2^{k - 1}}\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p1">therefore true for \(n \leqslant k \Rightarrow \) true for \(n = k + 1\) and since true for \(n = 1\) and \(n = 2\), the result is proved by strong induction <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Only award the <strong><em>R1 </em></strong>if at least four of the above marks have been awarded.</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Allow true for \(k\) and \(k - 1\) (in 2 places) instead of stronger statement.</p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>First <strong><em>M1 </em></strong>does not have to be given for further marks to be gained but second <strong><em>(M1) </em></strong>does.</p>
<p class="p1"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \({u_n} + {v_n} = {2^{n - 2}}(n - 1) + {( - 2)^{n - 2}}(n - 1)\)</span></p>
<p class="p2">when \(n\) is even \({u_n} + {v_n} = {2^{n - 2}}(n - 1) + {2^{n - 2}}(n - 1)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p3"><span class="Apple-converted-space">\( = {2^{n - 1}}(n - 1)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>when \(n\) <span class="s2">is odd \({u_n} + {v_n} = 0\) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This was either done well and completely correct or very little achieved at all (working out \({v_0}\) for some reason). As expected a few candidates forgot what to do for a repeated root. The varied response to this question was surprising since it is just standard book work.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Strong induction proved to be a very good discriminator. Some candidates knew exactly what to do and did it well, others had no idea. Common mistakes were not checking \(n = 2\) and 2, trying ordinary induction and worse of all assuming the very thing that they were trying to prove.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates that had the 2 expressions, knew how to get rid of the minus sign in the 2 cases. Some candidates could not attempt this as they had not completed part (a) although when it was wrong, follow through marks could be obtained.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the Euclidean algorithm to show that <span class="s1">1463 </span>and <span class="s1">389 </span>are relatively prime.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find positive integers \(a\) and \(b\) <span class="s1">such that \[1463a - 389b = 1\].</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(1463 = 3 \times 389 + 296\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2">\(389 = 1 \times 296 + 93\)</p>
<p class="p2"><span class="Apple-converted-space">\(296 = 3 \times 93 + 17\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\(93 = 5 \times 17 + 8\)</p>
<p class="p1"><span class="s2">\(17 = 2 \times 8 + 1\) </span>which shows that the gcd is 1 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"><span class="s3">hence 1463 and 389 </span>are relatively prime <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p3"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p2"><span class="Apple-converted-space">\(1 = 17 - 2 \times 8\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = 17 - 2 \times (93 - 5 \times 17) = 11 \times 17 - 2 \times 93\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = 11 \times (296 - 3 \times 93) - 2 \times 93 = 11 \times 296 - 35 \times 93\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\( = 11 \times 296 - 35 \times (389 - 296) = 46 \times 296 - 35 \times 389\)</p>
<p class="p2"><span class="Apple-converted-space">\( = 46 \times (1463 - 3 \times 389) - 35 \times 389\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\( = 46 \times 1463 - 173 \times 389\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\((a = 46,{\text{ }}b = 173)\)</p>
<p class="p1"><strong>OR</strong></p>
<p class="p2">method of keeping track of the linear combinations from the beginning (could be seen alongside the working in (a))</p>
<table>
<tbody>
<tr>
<td>\((1,{\text{ }}0)\)</td>
<td> </td>
<td>\((0,{\text{ }}1)\)</td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>\( - 3(1,{\text{ }}0)\)</td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>\(( - 3,{\text{ }}1)\)</td>
</tr>
</tbody>
</table>
<p> <strong><em>(M1)(A1)</em></strong></p>
<table>
<tbody>
<tr>
<td>\( - ( - 3,{\text{ }}1)\)</td>
<td> </td>
<td> </td>
</tr>
<tr>
<td>\((4,{\text{ }} - 1)\)</td>
<td> </td>
<td> </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>\( - 3(4,{\text{ }} - 1)\)</td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>\(( - 15,{\text{ }}4)\)</td>
</tr>
</tbody>
</table>
<p class="p2"> <span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p2">\( - 5( - 15,{\text{ }}4)\)</p>
<p class="p2"><span class="Apple-converted-space">\((79,{\text{ }} - 21)\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<table>
<tbody>
<tr>
<td> </td>
<td> </td>
<td>\( - 2(79,{\text{ }} - 21)\)</td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>\(( - 173,{\text{ }}46)\)</td>
</tr>
</tbody>
</table>
<p class="p2"><span class="s1">so \( - 173 \times 389 + 46 \times 1463 = 1\) </span>giving \(46 \times 1463 - 173 \times 389 = 1\) <span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\((a = 46,{\text{ }}b = 173)\)</p>
<p class="p3"> </p>
<p class="p2"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Accept any positive answers of the form \(a = 46 + 389t,{\text{ }}b = 173 + 1463t,{\text{ }}t\) <span class="s1">an integer.</span></p>
<p class="p4"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Very well answered. Some candidates lost the final mark by not saying that their working showed that the greatest common divisor (gcd) was 1.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The working backwards method was generally well known but there were arithmetic mistakes. Some candidates did not realise that their aim was to keep 1 as a combination of <em>two </em>remainders. The final answer could have been checked with the calculator as could intermediary steps. What was sadly less well known was the linear combinations format of laying the work out. See the OR method in the mark scheme. This makes the numerical work much less tedious and deserves to be better known.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, explain briefly what is meant by a circuit;</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, explain briefly what is meant by an Eulerian circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The graph \(G\) has six vertices and an Eulerian circuit. Determine whether or not its complement \(G'\) can have an Eulerian circuit.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an example of a graph \(H\), with five vertices, such that \(H\) and its complement \(H'\) both have an Eulerian trail but neither has an Eulerian circuit. Draw \(H\) and \(H'\) as your solution.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a circuit is a walk that begins and ends at the same vertex and has no repeated edges <strong><em>A1</em></strong></p>
<p><strong><em> [1 mark] </em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>an Eulerian circuit is a circuit that contains every edge of a graph <strong><em>A1</em></strong></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>if \(G\) has an Eulerian circuit all vertices are even (are of degree 2 or 4) <strong><em>A1</em></strong></p>
<p>hence, \(G'\) must have all vertices odd (of degree 1 or 3) <strong><em>R1</em></strong></p>
<p>hence, \(G'\) cannot have an Eulerian circuit <strong><em>R1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1 </em></strong>to candidates who begin by considering a specific \(G\) and \(G'\) (diagram). Award <strong><em>R1R1 </em></strong>to candidates who then consider a general \(G\) and \(G'\).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for example</p>
<p><img src="images/Schermafbeelding_2017-08-10_om_10.15.08.png" alt="M17/5/MATHL/HP3/ENG/TZ0/DM/M/03.c"></p>
<p><strong><em>A2</em></strong></p>
<p><strong><em>A2</em></strong></p>
<p> </p>
<p><strong>Notes:</strong> Each graph must have 3 vertices of order 2 and 2 odd vertices. Award <strong><em>A2</em></strong> if one of the graphs satisfies that and the final <strong><em>A2 </em></strong>if the other graph is its complement.</p>
<p> </p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">When numbers are written in base <em>n</em>, \({33^2} = 1331\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By writing down an appropriate polynomial equation, determine the value of <em>n</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Rewrite the above equation with numbers in base 7.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the equation can be written as</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(3n + 3)^2} = {n^3} + 3{n^2} + 3n + 1\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">any valid method of solution giving <em>n</em> = 8 <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Attempt to change at least one side into an equation in </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> gains the </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;">.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as decimal numbers,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(33)_8} = 27,{\text{ }}{(1331)_8} = 729\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">converting to base 7 numbers,</span></p>
<p style="margin: 0px 0px 0px 30px; font: 32px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(27 = {(36)_7}\) <strong><em>A1</em></strong></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">7<span style="text-decoration: underline;">)729</span> <em><strong>M1</strong></em></span><br><span style="font-family: times new roman,times; font-size: medium;">7<span style="text-decoration: underline;">)104</span>(1</span><br><span style="font-family: times new roman,times; font-size: medium;">7<span style="text-decoration: underline;">) 14</span>(6</span><br><span style="font-family: times new roman,times; font-size: medium;">7<span style="text-decoration: underline;">) 2</span>(0</span><br><span style="font-family: times new roman,times; font-size: medium;">7<span style="text-decoration: underline;">) 0</span>(2</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(729 = {(2061)_7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the required equation is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({36^2} = 2061\) <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as a decimal number, \({(33)_8} = 27\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">converting to base 7,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(27 = {(36)_7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">multiplying base 7 numbers</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> 36<br><span style="text-decoration: underline;">× 36</span><br>1440 <em><strong>M1</strong></em><br><span style="text-decoration: underline;"> 321</span> <em><strong>A1</strong></em><br>2061 </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>A1</strong></em></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the required equation is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({36^2} = 2061\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow <strong><em>M1</em></strong> for showing the method of converting a number to base 7 regardless of what number they convert.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was a good indicator of overall ability. Many candidates did not write both sides of the equation in terms of n and thus had an impossible equation, which should have made them realise that they had a mistake. </span><span style="font-family: times new roman,times; font-size: medium;">The answers that were given in (a) and (b) could have been checked, so that the candidate knew they had done it correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (b) was not well answered and of those candidates that did, some only gave one side of the equation in base 7. The answers that were given in (a) and (b) could have been checked, so that the candidate knew they had done it correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Let \(f(n) = {n^5} - n,{\text{ }}n \in {\mathbb{Z}^ + }\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the values of \(f(3)\), \(f(4)\) and \(f(5)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the Euclidean algorithm to find</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\gcd \left( {f(3),{\text{ }}f(4)} \right)\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\gcd \left( {f(4),{\text{ }}f(5)} \right)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why \(f(n)\) is always exactly divisible by \(5\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">By factorizing \(f(n)\) explain why it is always exactly divisible by \(6\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the values of <em>\(n\) </em>for which \(f(n)\) is exactly divisible by \(60\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(240,{\rm{ }}1020,{\rm{ }}3120\) <span class="Apple-converted-space"> </span><strong><em>A2</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A2 </em></strong>for three correct answers, <strong><em>A1 </em></strong>for two correct answers.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(1020 = 240 \times 4 + 60\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\(240 = 60 \times 4\)</p>
<p class="p1">\(\gcd (1020,{\text{ }}240) = 60\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(3120 = 1020 \times 3 + 60\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\(1020 = 60 \times 17\)</p>
<p class="p1">\(\gcd (1020,{\text{ }}3120) = 60\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Must be done by Euclid’s algorithm.</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">by Fermat’s little theorem with \(p = 5\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\({n^5} \equiv n(\bmod 5)\)</p>
<p class="p1">so 5 divides \(f(n)\)</p>
<p class="p1"><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(f(n) = n({n^2} - 1)({n^2} + 1) = n(n - 1)(n + 1)({n^2} + 1)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)A1</em></strong></span></p>
<p class="p1">\(n - 1,{\text{ }}n,{\text{ }}n + 1\) are consecutive integers and so contain a multiple of \(2\) and \(3\) <span class="Apple-converted-space"> </span><strong><em>R1R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>R1 </em></strong>for justification of \(2\) and <strong><em>R1 </em></strong>for justification of \(3\).</p>
<p class="p2"> </p>
<p class="p1">And therefore \(f(n)\) is a multiple of \(6\). <span class="Apple-converted-space"> </span><span class="s2"><strong><em>AG</em></strong></span></p>
<p class="p1"><span class="s2"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">from (c) and (d) \(f(n)\) is always divisible by \(30\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">considering the factorization, it is divisible by \(60\) when <em>\(n\) </em>is an odd number <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">or when <em>\(n\) </em>is a multiple of \(4\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept answers such as when <em>\(n\) </em>is not congruent to \(2(\bmod 4)\).</p>
<p class="p1"><em><strong>[3 marks]</strong></em></p>
<p class="p1"><em><strong>Total [14 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Also well answered. A few candidates did not use the Euclidean algorithm to find the gcd as instructed.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates essential said it was true because it was! There is only one mark which means one minute, so it must be a short answer which it is by using Fermat’s Little Theorem.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Some good answers but too many did not factorize as instructed, so that they could then spot the consecutive numbers.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Only the better candidates realised that they had to find another factor of \(2\).</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) One version of Fermat’s little theorem states that, under certain conditions,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[{a^{p - 1}} \equiv 1(\bmod p).\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that this result is not valid when <em>a</em> = 4, <em>p</em> = 9 and state which</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">condition is not satisfied.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Given that \({5^{64}} \equiv n(\bmod 7)\), where \(0 \leqslant n \leqslant 6\), find the value of <em>n</em>.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the general solution to the simultaneous congruences</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[x \equiv 3(\bmod 4)\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[3x \equiv 2(\bmod 5).\]</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({4^8} = 65536 \equiv 7(\bmod 9)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">not valid because 9 is not a prime number <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> The <strong><em>R1</em></strong> is independent of the <strong><em>A1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) using Fermat’s little theorem <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^6} \equiv 1(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({({5^6})^{10}} = {5^{60}} \equiv 1(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">also, \({5^4} = 625\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 2(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{64}} \equiv 1 \times 2 \equiv 2(\bmod 7)\,\,\,\,\,{\text{(so }}n = 2)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept alternative solutions not using Fermat.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solutions to \(x \equiv 3(\bmod 4)\) are</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">3, 7, 11, 15, 19, 23, 27, … <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solutions to \(3x \equiv 2(\bmod 5).\) are</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">4, 9, 14, 19 … <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so a solution is <em>x</em> =19 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the Chinese remainder theorem (or otherwise) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is \(x = 19 + 20n{\text{ }}(n \in \mathbb{Z})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {{\text{accept }}19(\bmod 20)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 3 + 4t \Rightarrow 9 + 12t \equiv 2(\bmod 5)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 2t \equiv 3(\bmod 5)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 6t \equiv 9(\bmod 5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow t \equiv 4(\bmod 5)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(t = 4 + 5n{\text{ and }}x = 19 + 20n{\text{ }}(n \in \mathbb{Z})\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {{\text{accept }}19(\bmod 20)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Also accept solutions done by formula.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered with a variety of methods seen in (a)(ii). This was set with Fermat’s Little Theorem in mind but in the event many candidates started off with many different powers of 5, eg \({5^4} \equiv 2,{\text{ }}{5^8} \equiv 4\) and \({5^3}\equiv- 1(\bmod 7)\) were all seen. A variety of methods was also seen in (b), ranging from use of the Chinese Remainder Theorem, finding tables of numbers congruent to \(3(\bmod 4)\)and \(4(\bmod 5)\) and the use of an appropriate formula.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered with a variety of methods seen in (a)(ii). This was set with Fermat’s Little Theorem in mind but in the event many candidates started off with many different powers of 5, eg \({5^4} \equiv 2,{\text{ }}{5^8} \equiv 4\) and \({5^3}\equiv - 1(\bmod 7)\) were all seen. A variety of methods was also seen in (b), ranging from use of the Chinese Remainder Theorem, finding tables of numbers congruent to \(3(\bmod 4)\)and \(4(\bmod 5)\) and the use of an appropriate formula.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Write down the general solution of the recurrence relation \({u_n} + 2{u_{n - 1}} = 0,{\text{ }}n \geqslant 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Find a particular solution of the recurrence relation \({u_n} + 2{u_{n - 1}} = 3n - 2,{\text{ }}n \geqslant 1\), in the</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> form \({u_n} = An + B\), where \(A,{\text{ }}B \in \mathbb{Z}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> (iii) Hence, find the solution to \({u_n} + 2{u_{n - 1}} = 3n - 2,{\text{ }}n \geqslant 1\) where \({u_1} = 7\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the solution of the recurrence relation \({u_n} = 2{u_{n - 1}} - 2{u_{n - 2}},{\text{ }}n \geqslant 2\), where \({u_0} = 2,{\text{ }}{u_1} = 2\). Express your solution in the form \({2^{f(n)}}\cos \left( {g(n)\pi } \right)\), where the functions <em>f </em>and <em>g </em>map \(\mathbb{N}\) to \(\mathbb{R}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) use of auxiliary equation or recognition of a geometric sequence <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \({u_n} = {( - 2)^n}{u_0}\) or \( = {\text{A}}{( - 2)^n}\) or \({u_1}{( - 2)^{n - 1}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) substitute suggested solution <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(An + B + 2\left( {A(n - 1) + B} \right) = 3n - 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> equate coefficients of powers of <em>n </em>and attempt to solve <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(A = 1,{\text{ }}B = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (so particular solution is \({u_n} = n\))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (iii) use of general solution = particular solution + homogeneous solution <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \({u_n} = {\text{C}}{( - 2)^2} + n\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> attempt to find C using \({u_1} = 7\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \({u_n} = - 3{( - 2)^n} + n\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the auxiliary equation is \({r^2} - 2r + 2 = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solutions: \({r_1},{\text{ }}{r_2} = 1 \pm {\text{i}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">general solution of the recurrence: \({u_n} = {\text{A}}{(1 + {\text{i}})^n} + {\text{B}}{(1 - {\text{i}})^n}\) or trig form <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to impose initial conditions <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = B = 1\) or corresponding constants for trig form <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({u_n} = {2^{\left( {\frac{n}{2} + 1} \right)}} \times \cos \left( {\frac{{n\pi }}{4}} \right)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [17 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A version of Fermat’s little theorem states that when <em>p</em> is prime, <em>a</em> is a positive integer and <em>a</em> and <em>p</em> are relatively prime, then \({a^{p - 1}} \equiv 1(\bmod p)\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the above result to show that if <em>p</em> is prime then \({a^p} \equiv a(\bmod p)\) where <em>a</em> is any positive integer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \({2^{341}} \equiv 2(\bmod 341)\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) State the converse of the result in part (a).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Show that this converse is not true.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider two cases <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>a</em> and <em>p</em> be coprime</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a^{p - 1}} \equiv 1(\bmod p)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {a^p} \equiv a(\bmod p)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>a</em> and <em>p</em> not be coprime</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a \equiv 0(\bmod p)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a^p} = 0(\bmod p)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {a^p} = a(\bmod p)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \({a^p} = a(\bmod p)\) in both cases <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(341 = 11 \times 31\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we know by Fermat’s little theorem</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{10}} \equiv 1(\bmod 11)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {2^{341}} \equiv {({2^{10}})^{34}} \times 2 \equiv {1^{34}} \times 2 \equiv 2(\bmod 11)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">also \({2^{30}} \equiv 1(\bmod 31)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {2^{341}} \equiv {({2^{30}})^{11}} \times {2^{11}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv {1^{11}} \times 2048 \equiv 2(\bmod 31)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since 31 and 11 are coprime <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{341}} \equiv 2(\bmod 341)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) converse: if \({a^p} = a(\bmod p)\) then <em>p</em> is a prime <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) from part (b) we know \({2^{341}} \equiv 2(\bmod 341)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">however, 341 is composite</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence 341 is a counter-example and the converse is not true <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were very few fully correct answers. In (b) the majority of candidates assumed that 341 is a prime number and in (c) only a handful of candidates were able to state the converse.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were very few fully correct answers. In (b) the majority of candidates assumed that 341 is a prime number and in (c) only a handful of candidates were able to state the converse.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were very few fully correct answers. In (b) the majority of candidates assumed that 341 is a prime number and in (c) only a handful of candidates were able to state the converse.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The weighted graph <em>K</em>, representing the travelling costs between five customers, has the following adjacency table.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-10_om_11.10.37.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the graph \(K\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Starting from customer D, use the nearest-neighbour algorithm, to determine an upper bound to the travelling salesman problem for <em>K</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">By removing customer A, use the method of vertex deletion, to determine a lower bound to the travelling salesman problem for <em>K</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="font: normal normal normal 21px/normal Helvetica; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/maths_1_markscheme.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">complete graph on five vertices <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">weights correctly marked on graph <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">clear indication that the nearest-neighbour algorithm has been applied <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">DA (or 7) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">AB (or 1) BC (or 9) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">CE (or 3), ED (or 12), giving UB = 32 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">attempt to use the vertex deletion method <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum spanning tree is ECBD <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(EC 3, BD 8, BC 9 total 20)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">reconnect A with the two edges of least weight, namely AB (1) and AE (4) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">lower bound is 25 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; font: 26.0px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Given that \(a \equiv d(\bmod n)\) and \(b \equiv c(\bmod n)\) prove that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[(a + b) \equiv (c + d)(\bmod n){\text{ .}}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; font: 26.0px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence solve the system</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; font: 26.0px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\left\{ {\begin{array}{*{20}{r}}<br> {2x + 5y \equiv 1(\bmod 6)} \\ <br> {x + y \equiv 5(\bmod 6)} <br>\end{array}} \right.\]</span></p>
<div class="marks">[11]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; line-height: 12.1px; font: 25.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times;">Show that \({x^{97}} - x + 1 \equiv 0(\bmod 97)\) has no solution.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(a \equiv d(\bmod n){\text{ and }}b \equiv c(\bmod n)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(a - d = pn{\text{ and }}b - c = qn\) , <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a - d + b - c = pn + qn\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((a + b) - (c + d) = n(p + q)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((a + b) \equiv (c + d)(\bmod n)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(\left\{ {\begin{array}{*{20}{r}}<br> {2x + 5y \equiv 1(\bmod 6)} \\ <br> {x + y \equiv 5(\bmod 6)} <br>\end{array}} \right.\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">adding \(3x + 6y \equiv 0(\bmod 6)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6y \equiv 0(\bmod 6){\text{ so }}3x \equiv 0(\bmod 6)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 0{\text{ or }}x \equiv 2{\text{ or }}x \equiv 4(\bmod 6)\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(x \equiv 0,{\text{ }}0 + y \equiv 5(\bmod 6){\text{ so }}y \equiv 5(\bmod 6)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \(x \equiv 2,{\text{ }}2 + y \equiv 5(\bmod 6){\text{ so }}y \equiv 3(\bmod 6)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \(x \equiv 4(\bmod 6),{\text{ }}4 + y \equiv 5(\bmod 6){\text{ so }}y \equiv 1(\bmod 6)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[11 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Suppose <em>x </em>is a solution</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">97 is prime so \({x^{97}} \equiv x(\bmod 97)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^{97}} - x \equiv 0(\bmod 97)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^{97}} - x + 1 \equiv 1 \ne 0(\bmod 97)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence there are no solutions <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) (i) was not found difficult but using it in part (a)(ii) resulted in two or three correct lines and then abandonment of the problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) (i) was not found difficult but using it in part (a)(ii) resulted in two or three correct lines and then abandonment of the problem.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The sequence \(\{ {u_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation \({u_{n + 1}} = 7{u_n} - 6\).</p>
<p class="p1">Given that \({u_0} = 5\), find an expression for \({u_n}\) in terms of \(n\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation \({v_{n + 2}} = 10{v_{n + 1}} + 11{v_n}\).</p>
<p class="p1">Given that \({v_0} = 4\) and \({v_1} = 44\), find an expression for \({v_n}\) in terms of \(n\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation \({v_{n + 2}} = 10{v_{n + 1}} + 11{v_n}\).</p>
<p class="p1">Show that \({v_n} - {u_n} \equiv 15(\bmod 16),{\text{ }}n \in \mathbb{N}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>attempting to find a solution in the form \({u_n} = A{7^n} + B\) <strong><em>M1</em></strong></p>
<p><strong>EITHER</strong></p>
<p><em>eg</em>, and \({u_0} = 5 \Rightarrow 5 = A + B{\text{ and }}{u_1} = 29 \Rightarrow 29 = 7A + B\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(A{7^{n + 1}} + B = A{7^{n + 1}} + 7B - 6\;\;\;\)(or equivalent) <strong><em>A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>attempting to solve for \(A\) and \(B\) <strong><em>(M1)</em></strong></p>
<p>\({u_n} = 4 \times {7^n} + 1\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept \(A = 4,{\text{ }}B = 1\) provided the first <strong><em>M1 </em></strong>is awarded.</p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>attempting an iterative method <em>eg</em>, \({u_1} = 7{\text{(}}5) - 6\) and</p>
<p>\({u_2} = {7^2}{\text{(}}5) - 6{\text{(}}7 + 1){\text{ }}(etc)\) <strong><em>(M1)</em></strong></p>
<p>\({u_n} = 5 \times {7^n} - 6\left( {\frac{{{7^n} - 1}}{{7 - 1}}} \right)\) <strong><em>M1A1</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>M1 </em></strong>for attempting to express \({u_n}\) in terms of \(n\).</p>
<p> </p>
<p>\({u_n} = 4 \times {7^n} + 1\) <strong><em>A1A1</em></strong></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>attempting to find a solution in the form \({u_n} = A{7^n} + B\) <strong><em>M1</em></strong></p>
<p>\(A(n + 1) + B = 7(An + B) - 6\)</p>
<p>\(7B - 6 = B\) <strong><em>A1</em></strong></p>
<p>attempting to solve for \(A\) <strong><em>(M1)</em></strong></p>
<p>\({u_n} = 4 \times {7^n} + 1\) <strong><em>A1A1</em></strong></p>
<p><strong>METHOD 4</strong></p>
<p>\({u_{n + 1}} - 7{u_n} + 6 - ({u_n} - 7{u_{n + 1}} + 6) = 0 \Rightarrow {u_{n + 1}} - 8{u_n} + 7{u_{n - 1}} = 0\)</p>
<p>\({r^2} - 8r + 7 = 0\)</p>
<p>\(r = 1,{\text{ }}7\)</p>
<p>attempting to find a solution in the form \({u_n} = A{7^n} + B\) <strong><em>M1</em></strong></p>
<p><strong>EITHER</strong></p>
<p><em>eg</em>, \({u_0} = 5 \Rightarrow 5 = A + B{\text{ and }}{u_1} = 29 \Rightarrow 29 = 7A + B\) <strong><em>A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\(A{7^{n + 1}} + B = A{7^{n + 1}} + 7B - 6\;\;\;\)(or equivalent) <strong><em>A1</em></strong></p>
<p><strong>THEN</strong></p>
<p>attempting to solve for \(A\) and \(B\) <strong><em>(M1)</em></strong></p>
<p>\({u_n} = 4 \times {7^n} + 1\) <strong><em>A1A1</em></strong></p>
<p><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>attempting to find the auxiliary equation <strong><em>M1</em></strong></p>
<p>\({r^2} - 10r - 11 = 0\;\;\;\left( {(r - 11)(r + 1) = 0} \right)\) <strong><em>A1</em></strong></p>
<p>\(r = 11,{\text{ }}r = - 1\) <strong><em>A1</em></strong></p>
<p>\({v_n} = A{11^n} + B{( - 1)^n}\) <strong><em>(M1)</em></strong></p>
<p>attempting to use the initial conditions <strong><em>M1</em></strong></p>
<p>\(A + B = 4,{\text{ }}11A - B = 44\) <strong><em>A1</em></strong></p>
<p>\({v_n} = 4 \times {11^n}\) <strong><em>A1</em></strong></p>
<p><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({v_n} - {u_n} = 4({11^n} - {7^n}) - 1\) <strong><em>M1</em></strong></p>
<p><strong>EITHER</strong></p>
<p>\( = 4(11 - 7)({11^{n - 1}} + \ldots + {7^{n - 1}}) - 1\) <strong><em>M1A1</em></strong></p>
<p><strong>OR</strong></p>
<p>\( = 4\left( {{{(7 + 4)}^n} - {7^n}} \right) - 1\) <strong><em>A1</em></strong></p>
<p>subtracting the \({7^n}\) from the expanded first bracket <strong><em>M1</em></strong></p>
<p><strong>THEN</strong></p>
<p>obtaining \(16\) times a whole number \( - 1\) <strong><em>A1</em></strong></p>
<p>\({v_n} - {u_n} \equiv 15(\bmod 16),{\text{ }}n \in \mathbb{N}\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<p><strong><em>Total [16 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (a), a good number of candidates were able to ‘see’ the solution form for \({u_n}\) and then (often in non-standard ways) successfully obtain \({u_n} = 4 \times {7^n} + 1\). A variety of methods and interesting approaches were seen here including use of the general closed form solution, iteration, substitution of \({u_n} = 4 \times {7^n} + 1\), substitution of \({u_n} = An + B\) and, interestingly, conversion to a second-degree linear recurrence relation. A number of candidates erroneously converted the recurrence relation to a quadratic auxiliary equation and obtained \({u_n} = {c_1}{(6)^n} + {c_2}{(1)^n}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Compared to similar recurrence relation questions set in recent examination papers, part (b) was reasonably well attempted with a substantial number of candidates correctly obtaining \({v_n} = 4{(11)^n}\). It was pleasing to note the number of candidates who could set up the correct auxiliary equation and use the two given terms to obtain the required solution. It appeared that candidates were better prepared for solving second-order linear recurrence relations compared to first-order linear recurrence relations.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates found part (c) challenging. Only a small number of candidates attempted to either factorise \({11^n} - {2^n}\) or to subtract \({7^n}\) from the expansion of \({(7 + 4)^n}\). It was also surprising how few went for the option of stating that 11 and 7 are congruent \(\bmod 4\) so \({11^n} - {7^n} \equiv (\bmod 4)\) and hence is a multiple of 4.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram shows a weighted graph with vertices A, B, C, D, E, F, G. The weight of each edge is marked on the diagram.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 27px/normal Helvetica; text-align: center; margin: 0px;"><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjYAAAD7CAIAAAD2PUkhAAAf5klEQVR4nO2dzWtcV5qH+z+pglpJUGDjjZiFTSAMihbCNIMJeGMoF8jNGLQbSAmZCV4k3VAiYrBgYCgRd28a0lUkNANjwyUbLdQUeCALcWEWxiruwghTFJQozOWdxZGururzfp7zvuf8HmqTRHFu6r56f/e55+t3BAAAALDkd6YvAJjiQ69xt1apTn3qjfbfPH9k+uKAewx9768HjY2rUtxsHXtnA+9PL7yPpi8MmAQR5TSh33lYudvsflB/NfL/56CxUatsPOu+Dw1fmhxGpweb67eT/v4eGmsqwoG3v12rbO91PH8UElEY9Hvtp/Wb4gSOgohym6DbvN0FQr/zsFKtbXd8ZFQiJoPudy+6Z5F3hn7n4dq+N8TXl5xP/fbv5z0Yfeq3HyOiHAcR5TYzEUVDb28NEZWcod//v9h70Uu/87je8obmLkgequTm5Xo4+PnbH89QiS6DiHKbqYganfVa23jRl53w7Hj7S7zlS0M49PbrlSpyHcwFEeU2Qbc5O2MCzSIreMuXns9B93mtUr3X7n82fSmAIYgot7ltUddj1NV64/XZCH02LXjLl4GriML3BuaCiHKb2bEo+ui17tcq6w87GANICd7yZQIzdMASEFFug4gqDrzly0j4vrczf6lDGHiHnT5W6bkMIsplwlH/cCseUWHQ/7G1VanW1nZ7g4nRaxPHpd95stU+RT/NQBi8fbG5Xqts73X+3g9U4Q39t4fPdvDC2XUQUc4yf3eJWmWj2f6r52NcICWj04PNJ8f+penrEEsY9Lvt5tp1Ha49Pej2A8ST8yCiAMhPOPT26xhNAaBoEFEAAACYgogCAADAFEQUAAAApiCiAAAAMAURBa7wfX/eBD988NH9ubi4MP3bALiAiAI0Ho///Pq18caEDz7Rp9ftmv61ACxARLmO7/tfP3oUtYYvHjwYj8emLwo4SrwUW998A50CiCh3ieTpiwcP3r17hwdYYJaTk5N4EarKfPPmjenrAiZBRDnK+fm5emL94/ffK21SreHrR48gUsAIXz96FFkUEZ2fn//h2TPolOMgolwkekR99+5d9DdVa1BPshApoBlVeJFIRX8/qtWTkxODlwdMgYhyiyVPplFrgEgB/SiFolgdRswaP3AHRJRDLH+/H7UGiBTQTKRQNC+iaGbc1MQ1AjMgopzg4uJi5Wv9eGuASAGdRApFCyJKEc0+hU65AyLKft68efPFgwe1SnX55Kh4a4BIAW3EFYqWRhTFdOrrR49839d1jcAYiCibubi4aH3zTa1S/cOzZ+fn58t/eKo1QKSAHuIKRasiSvHu3Tv11PXn169RonaDiLKWSJ4SytBUa4BIAQ1MKRQliygiGo/Hf/z+e+iU9SCiLCT67U0iTxGzrQEiBcpmSqEocUQp4jpVwtUB8yCibCPzL+1sa4BIgVKZVShKGVFENB6Pk7/NBuJARNlDzlcfc1sDRAqUx6xCUfqIUqR9rQ2kgIiyhPwDyHNbA0QKlMRchaKsEUUpJwcBKSCixFPUNNxFrQEiBcpgrkJRjohSKJ3C/rPWgIiSTYGLGRe1BogUKJxFCkW5I4qw/6xdIKKkUviWMEtaA0QKFMsihaIiIkqB4zzsABElkjI21lzSGpY88wKQluXlVFRE0W2dwgOWUBBR8ph7lEZ+lreGJY+9AKRieS0VGFGKkn5fgB4QUZIo9SX78tYAkQKFsLKQCo8owv6zkkFEiaHsd+srWwNECuRnZRWVEVGE4zzEgogSgJ4ZSitbA0QK5CRJCZUUUYpIp7D/rBQQUdxJeJRGfpK0BogUyEOS+ik1ogj7z0oDEcUXzavlk7QGiBTITMLiKTuiFDjOQwqIKKbo33MsYWuASIFsJKwcPRFFt3UKGyaxBRHFDlM7NydsDRApkIHkZaMtohSRTmH/FJ4gonhh8BcmeWuASIG0JK8ZzRFF2H+WN4goLhgfxU3eGiBSIBWpCkZ/RClwnAdPEFEs4DB4m6o1QKRAclJVi6mIophOYf9ZPiCiDDMej49eHXGYApuqNUCkQELSlorBiFJg/1lWIKJMEi0kPHp1ZHzma9rWAJECSUhbJ8YjinCcBycQUWZguB1L2tYAkQIryVAkHCJKEekUitwgiCgD8NzUMkNrgEiB5WSoED4RRTGdYvWr6hSIKN2wPRogQ2uASIElZCsPVhFFLF94OAUiSh/MD1jL1hogUmAR2WqDW0QpeL75cAFElCb4TxPK1hogUmAumQuDZ0RRTKeMT751CkRU6UiZHZS5NUCkwCyZq4JtRCk4LGF0CkRUuagl65zlKSJza4BIgSnylATziCIGG8E4BSJqEpweNdeqtUq1tvb04K0/KujPFbfxV57WAJECcfLUA/+IUsR1qqA/cuh7fz1obNQq1VqjGxT0h0rH8YgKR/3/3PvhJAiJwoG3v12rPD72L/P/uRL3+8rTGiBSICJnMUiJKIrpVAGPoaOzXmu7Vtne6/y9H0wKukAbcDyibhN0m5X7e97HPH+GqaM08pOzNUCkgCJnJQiKKEUBz6Ph+97ORm1t5/hsWOil2QAiKiIcevv3drqDMPsfIfrsmZytASIFqIgyEBdRlPet/mTQ3a1XNp513+foPdaCiFIM/beHzTv73jBjkVgwgpq/NUCkQP4akBhRioxzo8Kz4+312trTP/3xab1SrVU2mmroARARIoqI6HP/4E5V/WLU1nZ7g9Qvgu2Yh5q/NUCkHKeQApAbUZRphUnodx5W1rdaf+kHEwqDf/zwtF5Zf9g5Q0gpEFFXhEG/135ar1TrLS/5+2A+R2nkp5DWAJFymULuvuiIUqRap/+5374XHwIfnR5srte2Oz4yiogQUbdQxp14uierozTyU0hrgEg5S1G33oKIojS7nU1HFH3oNe7W7rT7nzVcpgAQUXE+eq0vt9qnK5dGWbmzZFGtASLlJkXddzsiSpFoz+iht7cWf3nzode4m+pdjt0goiImgfdya/Olt2pRgq0bShbVGiBSDlLgTbcpoihRu1Az+rZfeINQdSHMPo/heER96rd/fzVRItmiOfvkKaLA1gCRco0C77hlEUWJXroM/e7+lmpEm63XfUzou8HxiEoB86M08lNga4BIOUWxt9u+iFJEOiV63q9+EFGJ4H+URn6KbQ0QKXco9l7bGlFkxepJ/SCiViDlKI38FNsaIFKOUPiNtjiiFHYso9QGImoZb968sV6eIgpvDRApFyj8LlsfUXRbp2Tt5KkfRNR84ptu2S1PEYW3BoiU9ZRxi12IKIXoLT21gYiag8SjNPJTRmuASNlNGffXnYgigafK6QcRdQuXK6aM1gCRspiSbq5TEaVw85k4IYioGxz37pJaA0TKVkq6sw5GFMUejq2flpUWRBQRRi+JqLTWAJGykvJuq5sRpXBhcUtaEFGYA3pFea0BImUf5d1TlyOKXFrlkhCnIwor6eKU1xogUpZR6g11PKIUkU7ht8bdiMJ+JFOU2hogUjZR6t1ERCkinbJsu+q0uBhRVh6lkZ9SWwNEyhrKvpWIqAh0KnIwomw9SiM/ZbcGiJQdlH0fEVFTON6y3IooPJIsoezWAJGyAA03ERE1S1ynXBs1dyWi8GJ3JRpaA0RKOhruICJqEW7OPXYiorDaIAkaWgNESjR6bh8iagkOTkK2PKKwyCA5eloDREoueu4dImolcZ0yfS2lY3NEOXWURn70tAaIlFC03ThEVBIinbJ+N1E7I8rBozTyo601JH4YnwTey63KVwf9UenXBFahTX8RUclxYf9ZCyPKhdtWBtpaQ8Ln8XDQfbZWrSGiGKDTfRFRqbD+cAarIsr6u1UqOlvD6kfy8H1v58utzfuIqJIIg5PDxkatUq1V1rdaf+kHkyU/rHMEERGVgei53L5BDXsiyvGjNPKjszWseiofnnWeP2yf+N3niKhSGJ0eNL7t+UOiSXB61Fyr1jYP+6Nw7s9qHj5ERGXD1qlhNkQUjtIoBM2tYfGDeTjqHz5svD4bTQJEVCmEQ+/osP/p+i8v/c7jJd+z5kmYiKg82LfARnxEubmcrQw0t4aFz+aj04PGd14wIfqMiNLC56D7vLa27w3nWJT+GZiIqJzEdcqClig4ohxcxVYq+lvDnMfzcODt7x5cPeAjovTw0Wvdr7e84bx/pn8dGyKqECKdkr7Zm9SI8n0f8lQs+lvDnCf0oNusVGuzn0Y30HllLhEOus/u7PYGc6ZLGFnEhogqCjv2n5UXUdigviSMtIalD+mwqPIJ3/d2nhzcjEvdwshWIIioArGgWwqLKDueC3hipDUsfU5HRJXN8Kzz7bfeYO5MPlP7gCCiCidqm0evjsS1TTERZcHjAHNMtYbFj+qIqFKZBF57r/Pboi/X1G6KiKgykDtyLyOicJSGBky1BuzaZ4LpfAqDt9+2f41mTBi8KYio8pA4/1lAREVTU9DFSsVga8D253pRmx9OzUm5v+d9jH7C4B1BRJWKuFWkrCPK1vXSPDHYGiBSrDB7OxBRGhC0Fw/fiLJvmTRzzLYGiBQfzN4LRJQepOxoyjGiou8O8qQTs60BIsUE4zcCEaUT/udCsIso/l+ZrRhvDRApDhi/C8br0DWYn67HKKKkiKetGG8Nxp/fAYdbYLwO3YTtGeVcIurk5ATyZBYOrcH4I7zjcPj+OdShm/CcnmY+oqJJkJAns3BoDRye4p2FyZfPoQ5dhtsiH8MRJXEpma0waQ0cHuTdhMk3z6QOXYbVVgnGIkruhhy2wqQ1MHmWdw0+XzuTOnQcPhvOmYkoHKXBED6tgcnjvFPw+c751CHgsG237oiKhzPkiRV8WoN6G87hid4R+CgUcapDQAw6ttaI4pDJYBF8WsN4PP7iwQMmD/UuwEehiFMdggiD7700RRSfN5tgEaxaA0RKG6wUipjVIYgwNXtAR0Sxmh8CFsGqNUCktMFKoYhZHYIp4nOw9fwXS48obrPswSK4tQaIlAa4KRTxq0MwheaVrCVGFM+1ymAR3FoDREoD3BSK+NUhmIu2zVTLiigcpSEOhq0BIlUqDBWKWNYhmIueXVWLjygcpSEUhq0BIlUqDBWKWNYhWEKkUyXZSMERhaM05MKzNUCkSoKnQhHXOgRLuLi4KG9Mp7CIwlEa0uHZGiBSJcFToYhrHYKVlDS4MxtR4dDbr1d+f9D/lPxPgTwJYTLo7tYrVdUFatsdP7z5Z2xbA0SqcNgqFC2rw3Dk/9rrtLYqz3vBZ92XBRIQnyK3dH3R56D7vBY1opvP9l7np1/6QawtzUZU+L63s1GrVOstb5jgmnCUhiRGpwebXy96+GAbURCpwmGrULSkDofe3ppqZIgo1kQ6tWKXBnVDG91A/WUY9Lvt5lq1Vtlodn4bXf/UdESFfufh5pPm5nptbd8bhrQUHKUhismgu3tvpztYcFfZRhRBpAqFs0LRijq89DuPEVH8SbbX3Yde4+5NRBERURi8fbG5Xou9xpuKqI9e68uHnf/90N2tVzaedd8vyigcpSGP64fQeqP9N88fzfxzzhEFkSoQzgpFK+pQvSBCRAkgwaZ3cyLqeqTp5jXe7Ygaent3dnuDyVU7uz1WEQF5kksY9H/ptLYq1Xrj9dno1t3lHFEEkSoI5gpFiCi7iHTq6NXRTFjMjajrh+nr13jxiLr0O4+vs+uj17pfqzw+9i+n/nUVjJAnyYSjs9fNtfWt9mncpZhHlBKp1jffmL4Q2TBXKEJEWcd4PD56dTQvNRZE1Of+wZ2bEcdYRI1ODzafXGdSOOofbs2bNKH8aV4kAkFc+p3HtTvtfuw3nXlE0bVI4dkoM/wVihBRNrJgee9Si7ruTlFEXb0BnJ4FODNpAqNQVhAOvf26tIiCSOWEv0IRIsoulq6XTTUWFZ4db3+5532M/aiaPHP/9t+8IhqOwkIomVz6nSeyXvQpIFKZEaFQhIiyiJOTk6UxkWJG3/CsszP1TE1EFHSblWptc7/nz1kiNR6PsZ2EHCZB/797P6tFcUO/u7+1edgXNV1CAZHKjAiFokSTzueMkQNWJFovu3Bd1PYL72ZpzO+IRv32V9dv9mKPJyqfrj53m90Pc/8r2FdCCJPAe7l1s4Tb80fTkzVFRBRBpDIhRaFoSR1ejaJffe7NPFEDJiSY8r1kd4mud9uICtijD7vz2YGUiIJIZUCKQpGcOgSzlDFTobBtZJVO4YAouQhqDRCpVAhSKBJVhyBOSetlizyMA8fsikZQa4BIpUKQQpGoOgSKaCOJMqZ5F3+kIc7bFYqs1gCRSogshSJpdQiSbceXnVIOhodOSURWa4BIJUSWQpG0OnSZBLvwFUApEaVIuiU74IG41gCRWok4hSKBdegm5+fnpcpTRIkRRRr/N0B+xLUGiNRKxCkUCaxDB9GpH+VGFOmSQZAfia0BIrUEiQpFMuvQHfQP4pQeUYqyh9RAfiS2BojUEiQqFMmsQ0cwMhVOU0TRbZ3CYy9DhLYGiNRchCoUia1DuzE4A05fRCl838dxiDwR2hogUnMRqlAktg4txuy2DLojinCcB1fktgaI1BRyFYok16F9cNjczkBEKXC6PDfktgaI1BRyFYok16FlMNki3FhEUcIN24EuRLcGiFSEaIUi4XVoB6wOWjIZUYpVx14BTYhuDRCpCNEKRcLr0AK4HVdrPqKIxxtPIL01QKRIvkKR/DqUC89ZAiwiSsHk1aezSG8NECmSr1Akvw6FwnZyAKOIots6hf1nNWNBa3BcpCxQKLKiDmXBU54ieEWU4s2bNzjOQz8WtAbHRcoChSIr6lAQ0b4/3OQpgmNEEY7zMIEdrcFZkbJDociWOuSPlN1TmUaUAqcj6sSO1uCsSNmhUGRLHTJH0KaprCOKbusU869SOta0BgdFyhqFIovqkC0i5CmCe0QpZH2nQrGmNTgoUtYoFFlUhwyJnvj5y1OEjIgiUWYqFJtag1MiZZNCkV11yAqh4yZiIorkjO8JxabW4JRI2aRQZFcdMkH07DNJEaWIdOro1RF0qkAsaw2OiJRlCkXW1aFxhMpThLyIIqLxeHz06ojtWjOhWNYaHBEpyxSKrKtDg0Q7IUiUpwiREaVgu2OHUOxrDdaLlH0KRTbWoRGs2U9OcEQR+607ZGFfa7BepOxTKLKxDjVj2a7csiNKEdcp09ciGCtbg8UiZaVCkaV1qA37zjayIaIIpyMWgZWtwWKRslKhyNI61ICtPdCSiFJY8/rVCLa2BitFylaFInvrsFQsHpi3KqLIuvewOrG1NVgpUrYqFNlbhyVh/Xi8bRGlgE5lwOLWYJlIWaxQZHUdFo7F8hRhZ0QR0cXFhdwF1UawuDVYJlIWKxRZXYcFEm21Y6s8RVgbUQrpK6t1YndrsEak7FYosr0OC8GpDUstjygSvj+VTuxuDdaIlN0KRbbXYU4c3KfU/ohSRDpl8eNnTqxvDRaIlPUKRQ7UYWbOz8/dkacIVyKKZJ6VohPrW4MFImW9QpEDdZiN6CHbEXmKcCiiyElNTo4LrUG0SLmgUORGHabC8aEKtyJK4dRgY3JcaA2iRcoFhSI36jA5mPDlYkQRdGoejrQGoSLliEKRM3W4EsflKcLRiFJEOmXxwrfkONIahIqUIwpFztThctTmAy7LU4TTEUUObB+SHHdagziRckehyKU6nAu2cJvC9YhSuLCPyErcaQ3iRModhSKX6nAW7Nw2CyLqirhOufnw4lRrECRSTikUOVaHEePxGPI0F0TULSKdcvApxqnWIEiknFIocqwOFS63nZUgoqZx9l2wa61BhEi5plDkWB1iLHwliKj5OPhS2KnWQEJEyjWFIpfqEEPgSUBELcQ1nXKnNUQwFykHFYrcqEPIU3IQUStwZ4GCC61hCuYi5aBCkQN1iOWYqUBErcaRZd7Wt4a5sBUpNxWKrK5DbGqTAUTUJDg9aq5Va5VqrbK99+NpEM7/Oes3y7K4NSyBrUi5qVBkbx1ia9BsOB5R4aj/H81W1x+FFAb/+OFpvbK+1T4dLfhpu3XK1tawEoYi5axCkaV1CHnKjOMR9dFr/1d/dO1N4dnx9nrtTrv/edm/Y+vBLVa2hiQwFClnFYqsq0McU5cTxyNqig+9xt16yxuu+jkrj7+0rDWkgpVIuaxQZFcdWj86oAFEVIyht7d2f8/7mORn7Rv5tKk1pIWVSLmsUGRLHWYbFAiDty821++teI/jFoioiMmgu3tvpztYMF1iLjYNgdrRGjLDRKQcVyiyog4zylP4vrezUatUEVFxEFFXhIPus+3Dm3GpxEQ6JX0VngWtIQ9MRMpxhSLhdRit908/o2oy6O7e2/zqnxFRt0FEERHR6LfjVtsLJpn/AAv2MhHdGgrBuEhBoUhyHebYNS0cnb1ubh/2/Z+aiKjbIKKIwoH3798en62cJLEC6ZuayG0NRWFcpKBQJLMO826WNjo92H5+fDakoIuImsL5iJrOp0ngHR4kmzExF7k6JbE1FI5BkYJCKcTV4cnJSb4tpz/127svvEFIhIiaxe2ICgfe/rb6lbj5rO17w9QjUnEinZK1/6y41lAGBkUKCqUQVIdF/KZPAu+7ZrRdACJqBrcjqkxyP1vpRlBrKBUjIgWFipBShwW9L/nQa9ydfkquVGuV570AOUWEiCoVWcd5SGkNZWNEpKBQEfzrsMRRZ1jUDIio0pFyOiL/1qANzSIFhYrDvA7LHWxGRM2AiNJBXKfY7j/LvDXoRLNIQaHisK1DHSsgEVEzIKL0wXzDLratwQiqGWkQKSjUFDzr0KZ9ZGSBiNIK5+M8eLYGU1xcXKjbVPZ/CAo1Bbc6tG83TlkgogzAU6e4tQbjHL06KlukoFCzsKpDK880kAUiygwMT5Fh1Ro4oEGkoFCz8KlDW0+GkwUiyiSsXiDwaQ18KFWkoFBz4VCHnF/IuwYiyjB8hmE5tAZulCpSUKi5GK9Dnu/hnQURZR4m47HGWwNPShIpKNQiDNYh5IkhiCguRDp19OrIiE4houZSkkhBoRZhqg7VEnvIEzcQUYwYj8fqmd3IcR6IqEUULlJQqCXor0NZG5W5BiKKHaaO80BELaJwkYJCLUFzHUrZn8xZEFEcMXI6IiJqCQWKFBRqOdrqcDweQ574g4jiS6RTep7vEFFLKFCkoFDL0VOHmn+5QGYQUazR+aCHiFpOISIFhVpJ2XVo5BUFyAwiSgB6XpcjopZTiEhBoVZSah2aGugFmUFEyUDDpCNE1EpyihQUKgkl1SHkSSiIKElEOlXG0g1E1EpyihQUKgll1GG06BDyJA5ElDAuLi5KWgCPiEqCEqkM3zwUKiHF1iGTrVtAZhBRIiljGzFEVBKUSB29Okr7L0KhElJgHfLZABNkBhEllcL3E0NEJSSDSEGhklNUHUKe7AARJZtIp/K3P0RUQjKIFBQqOfnrkOFhbCAziCjxFPULiYhKTiqRgkKlImcd4igNy0BE2UAhY8KIqOSkEikoVCoy1yGO0rASRJQ95BwcRkSlIqFIQaHSkq0OIU+2goiyirhOpV2fiIhKRUKRgkKlJW0dRqvaIU9WgoiyEN/3M+zygohKy0qRgkJlIFUd4igN60FE2UmG7V4QUWlZKVJQqAwkrEOcQ+gIiCibSbVpJiIqA0tECgqVjSR1eHJyAnlyBESU5cR1avnDJiIqA0tECgqVjeV1GNUz5MkREFFOkOQAN0RUNuaKFBQqM0vqEEdpOAgiyhVWvrtHRGVjrkhBoTIztw5xlIazIKLcYskMKERUZqZECgqVh9k6hDy5DCLKORbpFCIqM1MiBYXKQ7wOo3V+kCdnQUQ5itKp+Gp8RFQeIpGCQuUkqkMcpQEIEeUyU3uaIaLyEIkUFConqg5xlAZQIKJcJ9rcDBGVEyVSUKicqO8Q8gQUiChwo1P44MPkA3kCCkQUuMJ4V8IHH/XBbrAgAhEFAACAKYgoAAAATEFEAQAAYAoiCkyC/t+PW9vXIwHbex3PH/x6/PMH0xcmgaDbnD+gsv6wcxaavjoJfOg17i4YlPrqoD8yfXnAMIgotwkH3v52rbLRbHf7wYSIKAz6P7a2KtV77f5ns9c28r2f2s21aq1yt9nlnJeXfufx7X46CbyX/2L8C1zGZNDdrUdhsN3xjcZp6HceTpfcp377OSIKIKJcZnjW2alXNpqd3253gsmgu/tPJjtsOPK7e5vrtc3W8c/9gLuMfA66z4U98o9ODza/Puh/Mn0d1wTdJoenIsAPRJS7hIPus7VqbW3fG86EwOj0sP3r0MRV0fWF1Ruvz0bc04mIBEbUZNDdvbfTHfD5dhFRYAGIKGdRjbVab3mmomg+4fvezkZtbbc3mJi+lITcjqjRb8eNf+sFjJvt0Ntbq9Yq1Xqj/TfPZ5GrUxEVDrz9l6y/Q6ALRJSzjPrtr2rTj65XuXX9ea6/TahhiXrj5Z8aG7VKtbb29PCU+au+qS/NzPeWljDo/9JpbVV42OqcWScCvkOgAUSUs6hB/mqt0Q2m/sno9GBzff4LQE1Xtb3342kQUhicHDY2apXHx/6l9itJzm2LCt/3dnhb1A3h6Ox1c219q31q2KWmLUrQdwjKBRHlLspX5r1S+9Br3K3dMTIyMOq3v4qlYzjqH25xn8AtbiwqzqXfeWzoXsfAWBRYACLKYdSoT2V9a//t7VdpfCJKRPMSHVHh0Nuv84yo8H3vX78zofKAEYgotxn9dtzYUCPnvavZ3dcTvs20rXDo7dcr9/e8j1d/I+g243/JEfVykvlFLuLS7zwx/qJvzrqoMPjHD0/vcZvLA7SDiAJD3+vGdpdQG0z89Iup9UjK7TZfesFErSxmMZ6/iKlxfuM6sppJ0P/v3tVqs6Hf3d/aPOyb/HqX7C4hNPVBkSCiAD9GZ72ryFzfav3latsLUAyTwHu5Fd/sim38A4CIAgAAwJb/B56PAabphIj+AAAAAElFTkSuQmCC" alt> <br></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Explain briefly why the graph contains an Eulerian trail but not an </span><span style="font-family: 'times new roman', times; font-size: medium;">Eulerian circuit.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Write down an Eulerian trail.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Use Dijkstra’s algorithm to find the path of minimum total weight joining A to D.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) State the minimum total weight.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) there is an Eulerian trail because there are only 2 vertices of odd degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">there is no Eulerian circuit because not all vertices have even degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <em>eg</em> GBAGFBCFECDE <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(i)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\begin{array}{*{20}{l}}<br> {{\text{Step}}}&{{\text{Vertices labelled}}}&{{\text{Working values}}}&{} \\ <br> 1&{\text{A}}&{{\text{A(0), B-3, G-2}}}&{{\boldsymbol{M1A1}}} \\ <br> 2&{{\text{A, G}}}&{{\text{A(0), G(2), B-3, F-8}}}&{{\boldsymbol{A1}}} \\ <br> 3&{{\text{A, G, B}}}&{{\text{A(0), G(2), B(3), F-7, C-10}}}&{{\boldsymbol{A1}}} \\ <br> 4&{{\text{A, G, B, F}}}&{{\text{A(0), G(2), B(3), F(7), C-9, E-12}}}&{} \\ <br> 5&{{\text{A, G, B, F, C}}}&{{\text{A(0), G(2), B(3), F(7), C(9), E-10, D-15}}}&{{\boldsymbol{A1}}} \\ <br> 6&{{\text{A, G, B, F, C, E}}}&{{\text{A(0), G(2), B(3), F(7), C(9), E(10), D-14}}}&{} \\ <br> 7&{{\text{A, G, B, F, C, E, D}}}&{{\text{A(0), G(2), B(3), F(7), C(9), E(10), D(14)}}}&{{\boldsymbol{A1}}} <br>\end{array}\)</span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"> In both (i) and (ii) accept the tabular method including back tracking or labels by the vertices on a graph.</span></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"> </strong></p>
<p><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>M1A1A1A1A0A0</em></strong><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"> if final labels are correct but intermediate ones are not shown.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium; line-height: normal;">(ii) minimum weight path is ABFCED </span><strong style="font-family: 'times new roman', times; font-size: medium; line-height: normal;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">minimum weight is 14 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award the final two <strong><em>A1</em></strong> marks whether or not Dijkstra’s Algorithm is used.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In part (a) the criteria for Eulerian circuits and trails were generally well known and most candidates realised that they must start/finish at G/E. Candidates who could not do (a) generally struggled on the paper.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">For part (b) the layout varied greatly from candidate to candidate. Not all candidates made their method clear and some did not show the temporary labels. It is recommended that teachers look at the tabular method with its backtracking system as it is an efficient way of tackling this type of problem and has a very clear layout.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Use the Euclidean algorithm to find gcd(\(12\,306\), 2976) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence give the general solution to the diophantine equation \(12\,306\)<em>x</em> + 2976<em>y</em> = 996 .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(12\,306 = 4 \times 2976 + 402\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2976 = 7 \times 402 + 162\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(402 = 2 \times 162 + 78\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(162 = 2 \times 78 + 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(78 = 13 \times 6\)<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore gcd is 6 <strong><em>R1 </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(6|996\) means there is a solution</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6 = 162 - 2(78)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 162 - 2\left( {402 - 2(162)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5(162) - 2(402)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5(2976) - 7(402)} \right) - 2(402)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5(2976) - 37(402)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 5(2976) - 37\left( {12\,306 - 4(2976)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 153(2976) - 37(12\,306)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(996 = 25\,398(2976) - 6142(12\,306)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {x_0} = - 6142,{\text{ }}{y_0} = 25\,398\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = - 6142 + \left( {\frac{{2976}}{6}} \right)t = - 6142 + 496t\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow y = 25\,398 - \left( {\frac{{12\,306}}{6}} \right)t = 25\,398 - 2051t\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [14 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was the most accessible on the paper and was completed correctly by the majority of candidates. Most candidates were able to start part (b), but a number made errors on the way and quite a number failed to give the general solution.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Euclidean algorithm to find the greatest common divisor of the numbers 56 and 315.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the general solution to the diophantine equation \(56x + 315y = 21\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence or otherwise find the smallest positive solution to the congruence \(315x \equiv 21\) (modulo 56) .</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(315 = 5 \times 56 + 35\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(56 = 1 \times 35 + 21\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(35 = 1 \times 21 + 14\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(21 = 1 \times 14 + 7\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(14 = 2 \times 7\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore gcd = 7 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(7 = 21 - 14\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 21 - (35 - 21)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2 \times 21 - 35\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2 \times (56 - 35) - 35\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2 \times 56 - 3 \times 35\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2 \times 56 - 3 \times (315 - 5 \times 56)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 17 \times 56 - 3 \times 315\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(56 \times 51 + 315 \times (- 9) = 21\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 51,{\text{ }}y = - 9\) is a solution <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is \(x = 51 + 45N\) , \(y = - 9 - 8N\) , \(N \in \mathbb{Z}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) putting <em>N</em> = –2 gives <em>y</em> = 7 which is the required value of <em>x</em> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered although some candidates were unable to proceed from a particular solution of the Diophantine equation to the general solution.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered although some candidates were unable to proceed from a particular solution of the Diophantine equation to the general solution.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that <em>a</em> , \(b \in \mathbb{N}\) and \(c \in {\mathbb{Z}^ + }\), show that if \(a \equiv 1(\bmod c)\) , then \(ab \equiv b(\bmod c)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using mathematical induction, show that \({9^n} \equiv 1(\bmod 4)\) , for \(n \in \mathbb{N}\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The positive integer <em>M</em> is expressed in base 9. Show that <em>M</em> is divisible by 4 if the sum of its digits is divisible by 4.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \lambda c + 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(ab = \lambda bc + b \Rightarrow ab \equiv b(\bmod c)\) <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the result is true for <em>n</em> = 0 since \({9^0} = 1 \equiv 1(\bmod 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">assume the result is true for <em>n</em> = <em>k</em> , <em>i.e.</em> \({9^k} \equiv 1(\bmod 4)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider \({9^{k + 1}} = 9 \times {9^k}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 9 \times 1(\bmod 4)\) <strong>or</strong> \(1 \times {9^k}(\bmod 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 1(\bmod 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so true for \(n = k \Rightarrow \) true for <em>n</em> = <em>k</em> + 1 and since true for <em>n</em> = 0 result follows by induction <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Do not award the final </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> unless both </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> marks have been awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award the final </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if candidates state </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> = 1 rather than </span><em style="font-family: 'times new roman', times; font-size: medium;">n</em><span style="font-family: 'times new roman', times; font-size: medium;"> = 0</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \(M = {({a_n}{a_{n - 1}}…{a_0})_9}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a_n} \times {9^n} + {a_{n - 1}} \times {9^{n - 1}} + ... + {a_0} \times {9^0}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>EITHER</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv {a_n}(\bmod 4) + {a_{n - 1}}(\bmod 4) + ... + {a_0}(\bmod 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv \sum {{a_i}(\bmod 4)} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>M</em> is divisible by 4 if \(\sum {{a_i}} \) is divisible by 4 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a_n}({9^n} - 1) + {a_{n - 1}}({9^{n - 1}} - 1) + ... + {a_1}({9^1} - 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( + {a_n} + {a_{n - 1}} + ... + {a_1} + {a_0}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Since \({9^n} \equiv 1(\bmod 4)\) , it follows that \({9^n} - 1\) is divisible by 4, <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>M</em> is divisible by 4 if \(\sum {{a_i}} \) is divisible by 4 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered. In (b), many candidates tested the result for <em>n</em> = 1 instead of <em>n</em> = 0. It has been suggested that the reason for this was a misunderstanding of the symbol <em>N</em> with some candidates believing it to denote the positive integers. It is important for candidates to be familiar with IB notation in which <em>N</em> denotes the positive integers and zero. In some scripts the presentation of the proof by induction was poor.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered. In (b), many candidates tested the result for <em>n</em> = 1 instead of <em>n</em> = 0. It has been suggested that the reason for this was a misunderstanding of the symbol <em>N</em> with some candidates believing it to denote the positive integers. It is important for candidates to be familiar with IB notation in which <em>N</em> denotes the positive integers and zero. In some scripts the presentation of the proof by induction was poor.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered. In (b), many candidates tested the result for <em>n</em> = 1 instead of <em>n</em> = 0. It has been suggested that the reason for this was a misunderstanding of the symbol <em>N</em> with some candidates believing it to denote the positive integers. It is important for candidates to be familiar with IB notation in which <em>N</em> denotes the positive integers and zero. In some scripts the presentation of the proof by induction was poor.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Two mathematicians are planning their wedding celebration and are trying to arrange the seating plan for the guests. The only restriction is that all tables must seat the same number of guests and each table must have more than one guest. There are fewer than 350 guests, but they have forgotten the exact number. However they remember that when they try to seat them with two at each table there is one guest left over. The same happens with tables of 3, 4, 5 and 6 guests. When there were 7 guests per table there were none left over. Find the number of guests.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>x</em> be the number of guests</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1(\bmod 2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1(\bmod 3)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1(\bmod 4)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1(\bmod 5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1(\bmod 6)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 0(\bmod 7)\) congruence (i) <strong><em>(M1)(A2)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the equivalent of the first five lines is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv 1\left( {\bmod ({\text{lcm of 2, 3, 4, 5, 6}})} \right) \equiv 1(\bmod 60)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 60t + 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from congruence (i) \(60t + 1 \equiv 0(\bmod 7)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(60t \equiv - 1(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(60t \equiv 6(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4t \equiv 6(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2t \equiv 3(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow t = 7u + 5\,\,\,\,\,{\text{(or equivalent)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(x = 420u + 300 + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 420u + 301\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">smallest number of guests is 301 <strong><em>A1 N6</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept alternative correct solutions including exhaustion or formula from Chinese remainder theorem.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were a number of totally correct solutions to this question, but many students were unable to fully justify the result. Some candidates had learnt a formula to apply to the Chinese remainder theorem, but could not apply it well in this situation. Many worked with the conditions for divisibility but did not make much progress with the justification.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that a positive integer, written in base 10, is divisible by 9 if the sum of its digits is divisible by 9.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The representation of the positive integer <em>N</em> in base <em>p</em> is denoted by \({(N)_p}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">If \({({5^{{{(126)}_7}}})_7} = {({a_n}{a_{n - 1}} \ldots {a_1}{a_0})_7}\) , find \({a_0}\) .</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider the decimal number \(A = {a_n}{a_{n - 1}} \ldots {a_0}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(A = {A_n} \times {10^n} + {a_{n - 1}} \times {10^{n - 1}} + \ldots + {a_1} \times 10 + {a_0}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a_n} \times ({10^n} - 1) + {a_{n - 1}} \times ({10^{n - 1}} - 1) + \ldots + {a_1} \times (10 - 1) + {a_n} + {a_{n - 1}} + \ldots + {a_0}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {a_n} \times 99 \ldots 9(n{\text{ digits}}) + {a_{n - 1}} \times 99 \ldots 9(n - 1{\text{ digits}}) + \ldots + 9{a_1} + {a_n} + {a_{n - 1}} + \ldots + {a_0}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">all the numbers of the form 99…9 are divisible by 9 (to give 11…1), <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence <em>A</em> is divisible by 9 if \(\sum\limits_{i = 0}^n {{a_i}} \) is divisible by 9 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> A method that uses the fact that \({10^t} \equiv 1(\bmod 9)\) is equally valid.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by Fermat’s Little Theorem \({5^6} \equiv 1(\bmod 7)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({(126)_7} = {(49 + 14 + 6)_{10}} = {(69)_{10}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{{{(126)}_7}}} \equiv {5^{{{(11 \times 6 + 3)}_{10}}}} \equiv {5^{{{(3)}_{10}}}}(\bmod 7)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{{{(3)}_{10}}}} = {(125)_{10}} = {(17 \times 7 + 6)_{10}} \equiv 6(\bmod 7)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \({a_0} = 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Questions similar to (a) have been asked in the past so it was surprising to see that solutions this time were generally disappointing.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In (b), most candidates changed the base 7 number 126 to the base 10 number 69. After that the expectation was that Fermat<span style="letter-spacing: 0.3px;">’</span>s little theorem would be used to complete the solution but few candidates actually did that. Many were unable to proceed any further and others used a variety of methods, for example working modulo 7,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{69}} = {({5^2})^{34}}.5 = {4^{34}}.5 = {({4^2})^{17}}.5 = {2^{17}}.5\) etc</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This is of course a valid method, but somewhat laborious.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The positive integer <em>N</em> is expressed in base 9 as \({({a_n}{a_{n - 1}} \ldots {a_0})_9}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that <em>N</em> is divisible by 3 if the least significant digit, \({a_0}\), is divisible by 3.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that <em>N</em> is divisible by 2 if the sum of its digits is even.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Without using a conversion to base 10, determine whether or not \({(464860583)_9}\) is divisible by 12.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) let \(N = {a_n}{a_{n - 1}} \ldots {a_1}{a_0} = {a_n} \times {9^n} + {a_{n - 1}} \times {9^{n - 1}} + \ldots + {a_1} \times 9 + {a_0}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">all terms except the last are divisible by 3 and so therefore is their sum <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that <em>N</em> is divisible by 3 if \({a_0}\) is divisible by 3 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider <em>N</em> in the form</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = {a_n} \times ({9^n} - 1) + {a_{n - 1}} \times ({9^{n - 1}} - 1) + \ldots + {a_1}(9 - 1) + \sum\limits_{i = 1}^n {{a_i}} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">all terms except the last are even so therefore is their sum <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that <em>N</em> is even if \(\sum\limits_{i = 0}^n {{a_i}} \) is even <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">working modulo 2, \({9^k} \equiv 1(\bmod 2)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(N = {a_n}{a_{n - 1}} \ldots {a_1}{a_0} = {a_n} \times {9^n} + {a_{n - 1}} \times {9^{n - 1}} + \ldots + {a_1} \times 9 + {a_0} = \sum\limits_{i = 0}^n {{a_i}(\bmod 2)} \) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that <em>N</em> is even if \(\sum\limits_{i = 0}^n {{a_i}} \) is even <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) the number is divisible by 3 because the least significant digit is 3 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it is divisible by 2 because the sum of the digits is 44 which is even <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">dividing the number by 2 gives \({(232430286)_9}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">which is even because the sum of the digits is 30 which is even <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>N</em> is therefore divisible by a further 2 and is therefore divisible by 12 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept alternative valid solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [12 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (b) were generally well answered. Part (c), however, caused problems for many candidates with some candidates even believing that showing divisibility by 2 and 3 was sufficient to prove divisibility by 12. Some candidates stated that the fact that the sum of the digits was 44 (which itself is divisible by 4) indicated divisibility by 4 but this was only accepted if the candidates extended their proof in (b) to cover divisibility by 4.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Explaining your method fully, determine whether or not 1189 is a prime number.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) State the fundamental theorem of arithmetic.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) The positive integers <em>M</em> and <em>N</em> have greatest common divisor <em>G</em> and least common multiple <em>L</em> . Show that <em>GL</em> = <em>MN</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">any clearly indicated method of dividing 1189 by successive numbers <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">find that 1189 has factors 29 and/or 41 <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that 1189 is not a prime number <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> If no method is indicated, award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the factors and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the conclusion.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) every positive integer, greater than 1, is either prime or can be expressed uniquely as a product of primes <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for “product of primes” and </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for “uniquely”.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) </span><strong style="font-family: 'times new roman', times; font-size: medium;">METHOD 1</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>M</em> and <em>N</em> be expressed as a product of primes as follows</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>M</em> = <em>AB</em> and <em>N</em> = <em>AC</em> <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">where <em>A</em> denotes the factors which are common and <em>B</em>, <em>C</em> the disjoint factors which are not common</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that <em>G</em> = <em>A</em> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and <em>L</em> = <em>GBC</em> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from these equations, it follows that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(GL = A \times ABC = MN\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let \(M = {2^{{x_1}}} \times {3^{{x_2}}} \times ...p_n^{{x_n}}\) and \(N = {2^{{y_1}}} \times {3^{{y_2}}} \times ...p_n^{{y_n}}\) where \({p_n}\) denotes the \({n^{{\text{th}}}}\) prime <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Then \(G = {2^{\min ({x_1},{y_1})}} \times {3^{\min ({x_2},{y_2})}} \times ...p_n^{\min ({x_n},{y_n})}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(L = {2^{\max ({x_1},{y_1})}} \times {3^{\max ({x_2},{y_2})}} \times ...p_n^{\max ({x_n},{y_n})}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It follows that \(GL = {2^{{x_1}}} \times {2^{{y_1}}} \times {3^{{x_2}}} \times {3^{{y_2}}} \times ... \times p_n^{{x_n}} \times p_n^{{y_n}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= <em>MN</em> <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), some candidates tried to use Fermat’s little theorem to determine whether or not 1189 is prime but this method will not always work and in any case the amount of computation involved can be excessive. For this reason, it is strongly recommended that this method should not be used in examinations. In (b), it was clear from the scripts that candidates who had covered this material were generally successful and those who had not previously seen the result were usually unable to proceed.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), some candidates tried to use Fermat’s little theorem to determine whether or not 1189 is prime but this method will not always work and in any case the amount of computation involved can be excessive. For this reason, it is strongly recommended that this method should not be used in examinations. In (b), it was clear from the scripts that candidates who had covered this material were generally successful and those who had not previously seen the result were usually unable to proceed.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Andy and Roger are playing tennis with the rule that if one of them wins a game when serving then he carries on serving, and if he loses then the other player takes over the serve.</p>
<p class="p1">The probability Andy wins a game when serving is \(\frac{1}{2}\) and the probability he wins a game when not serving is \(\frac{1}{4}\). Andy serves in the first game. Let \({u_n}\) denote the probability that Andy wins the \({n^{{\text{th}}}}\) game.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the value of \({u_1}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \({u_n}\) satisfies the recurrence relation</p>
<p class="p1">\[{u_n} = \frac{1}{4}{u_{n - 1}} + \frac{1}{4}.\]</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve this recurrence relation to find the probability that Andy wins the \({n^{{\text{th}}}}\) game.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">After they have played many games, Pat comes to watch. Use your answer from part (c) to estimate the probability that Andy will win the game they are playing when Pat arrives.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{1}{2}\) <em><strong>A1</strong></em></p>
<p class="p1"><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Andy could win the \({n^{{\text{th}}}}\) game by winning the \(n - {1^{{\text{th}}}}\) and then winning the \({n^{{\text{th}}}}\) game or by losing the \(n - {1^{{\text{th}}}}\) and then winning the \({n^{{\text{th}}}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({u_n} = \frac{1}{2}{u_{n - 1}} + \frac{1}{4}(1 - {u_{n - 1}})\) <span class="Apple-converted-space"> </span><strong><em>A1A1M1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for each term and <strong><em>M1 </em></strong>for addition of two probabilities.</p>
<p class="p2"> </p>
<p class="p1">\({u_n} = \frac{1}{4}{u_{n - 1}} + \frac{1}{4}\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">general solution is \({u_n} = A{\left( {\frac{1}{4}} \right)^n} + p(n)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">for a particular solution try \(p(n) = b\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(b = \frac{1}{4}b + \frac{1}{4}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">\(b = \frac{1}{3}\)</p>
<p class="p1">hence \({u_n} = A{\left( {\frac{1}{4}} \right)^n} + \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">using \({u_1} = \frac{1}{2}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(\frac{1}{2} = A\left( {\frac{1}{4}} \right) + \frac{1}{3} \Rightarrow A = \frac{2}{3}\)</p>
<p class="p1">hence \({u_n} = \frac{2}{3}{\left( {\frac{1}{4}} \right)^n} + \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept other valid methods.</p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">for large \(n{\text{ }}{u_n} \approx \frac{1}{3}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>Total [13 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Not all candidates wrote this answer down correctly although it was essentially told you in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Very badly answered. Candidates seemed to think that they were being told this relationship (so used it to find u(2)) rather than attempting to prove it.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This distinguished the better candidates. Some candidates though that they could use the method for homogeneous recurrence relations of second order and hence started solving a quadratic. Only the better candidates saw that it was a combined AP/GP.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The best candidates saw this but most had not done enough earlier to get to do this.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the pigeon-hole principle to prove that for any simple graph that has two or more vertices and in which every vertex is connected to at least one other vertex, there must be at least two vertices with the same degree.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Seventeen people attend a meeting.</p>
<p class="p1">Each person shakes hands with at least one other person and no-one shakes hands with</p>
<p class="p1">the same person more than once. Use the result from part (a) to show that there must be at least two people who shake hands with the same number of people.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Explain why each person cannot have shaken hands with exactly nine other people.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">let there be <em>\(v\) </em>vertices in the graph; because the graph is simple the degree of each vertex is \( \le v - 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">the degree of each vertex is \( \ge 1\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">there are therefore \(v - 1\) possible values for the degree of each vertex <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">given there are <em>\(v\) </em>vertices by the pigeon-hole principle there must be at least two with the same degree <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">consider a graph in which the people at the meeting are represented by the vertices and two vertices are connected if the two people shake hands <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">the graph is simple as no-one shakes hands with the same person more than once (nor can someone shake hands with themselves) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">every vertex is connected to at least one other vertex as everyone shakes at least one hand <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">the degree of each vertex is the number of handshakes so by the proof above there must be at least two who shake the same number of hands <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: </strong>Accept answers starting afresh rather than quoting part (a).</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(the handshaking lemma tells us that) the sum of the degrees of the vertices must be an even number <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">the degree of each vertex would be <em>\(9\)</em> and \(9 \times 17\) is an odd number (giving a contradiction) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<p class="p1"><strong><em>Total [10 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally there were too many “waffly” words and not enough precise statements leading to conclusions.</p>
<p class="p1">Misconceptions were: thinking that a few examples constituted a proof, thinking that the graph had to be connected, taking the edges as the pigeons not the degrees. The pigeon-hole principle was known but not always applied well.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally there were too many “waffly” words and not enough precise statements leading to conclusions.</p>
<p class="p1">Similar problems as in (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally there were too many “waffly” words and not enough precise statements leading to conclusions.</p>
<p class="p1">Many spurious reasons were given but good candidates went straight to the hand-shaking lemma.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A graph has <em>n</em> vertices with degrees 1, 2, 3, …, <em>n</em>. Prove that \(n \equiv 0(\bmod 4)\) or \(n \equiv 3(\bmod 4)\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <em>G</em> be a simple graph with <em>n</em> vertices, \(n \geqslant 2\). Prove, by contradiction, that at least two of the vertices of <em>G</em> must have the same degree.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as each edge contributes 1 to each of the vertices that it is incident with, each edge will contribute 2 to the sum of the degrees of all the vertices <strong><em>(R1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(2e = \sum {{\text{degrees}}} \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2e = \frac{{n(n + 1)}}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4|n(n + 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>n</em> and <em>n</em> + 1 are coprime <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept equivalent reasoning <em>e.g.</em> only one of <em>n</em> and <em>n</em> + 1 can be even.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4|n{\text{ or }}4|n + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(n \equiv 0(\bmod 4){\text{ or }}n \equiv 3(\bmod 4)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">since <em>G</em> is simple, the highest degree that a vertex can have is <em>n</em> – 1 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">the degrees of the vertices must belong to the set \(S = \{ 0,{\text{ }}1,{\text{ }}2,{\text{ }} \ldots ,{\text{ }}n - 1\} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">proof by contradiction</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">if no two vertices have the same degree, all <em>n</em> vertices must have different degrees <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">as there are only <em>n</em> different degrees in set <em>S</em>, the degrees must be precisely the <em>n</em> numbers 0, 1, 2, ..., <em>n</em> – 1 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">let the vertex with degree 0 be A, then A is not adjacent to any of the other vertices <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">let the vertex with degree <em>n</em> – 1 be B, then B is adjacent to all of the other vertices including A <strong><em>R1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">this is our desired contradiction, so there must be two vertices of the same degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Only the top candidates were able to produce logically, well thought-out proofs.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Only the top candidates were able to produce logically, well thought-out proofs.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Euclidean algorithm to find \(\gcd (752,{\text{ }}352)\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A farmer spends £8128 buying cows of two different breeds, A and B, for her farm. A cow of breed A costs £752 and a cow of breed B costs £352.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Set up a diophantine equation to show this.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Using your working from part (a), find the general solution to this equation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) <strong>Hence</strong> find the number of cows of each breed bought by the farmer.</span></p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">752 = 2(352) + 48 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">352 = 7(48) +16 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">48 = 3(16) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(\gcd (752,{\text{ }}352)\) is 16 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) let <em>x</em> be the number of cows of breed A</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>y</em> be the number of cows of breed B</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(752x + 352y = 8128\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(16|8128\) means there is a solution</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(16 = 352 - 7(48)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(16 = 352 - 7\left( {752 - 2(352)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(16 = 15(352) - 7(752)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(8128 = 7620(352) - 3556(752)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {x_0} = - 3556,{\text{ }}{y_0} = 7620\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = - 3556 + \left( {\frac{{352}}{{16}}} \right)t = - 3556 + 22t\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow y = 7620 - \left( {\frac{{752}}{{16}}} \right)t = 7620 - 47t\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) for <em>x</em>, <em>y</em> to be \( \geqslant 0\), the only solution is <em>t</em> = 162 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 8,{\text{ }}y = 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was the most accessible on the paper and was completed correctly by the majority of candidates. It was pleasing to see that candidates were not put off by the question being set in context and most candidates were able to start part (b). However, a number made errors on the way, quite a number failed to give the general solution and it was only stronger candidates who were able to give a correct solution to part (b) (iii).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) of this question was the most accessible on the paper and was completed correctly by the majority of candidates. It was pleasing to see that candidates were not put off by the question being set in context and most candidates were able to start part (b). However, a number made errors on the way, quite a number failed to give the general solution and it was only stronger candidates who were able to give a correct solution to part (b) (iii).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following diagram shows a weighted graph <em>G </em>with vertices A, B, C, D and E.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-17_om_14.54.24.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that graph \(G\) is Hamiltonian. Find the total number of Hamiltonian cycles in \(G\), giving reasons for your answer.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">State an upper bound for the travelling salesman problem for graph \(G\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Hence find a lower bound for the travelling salesman problem for \(G\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Show that the lower bound found in (d) cannot be the length of an optimal solution for the travelling salesman problem for the graph \(G\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg </em>the cycle \({\text{A}} \to {\text{B}} \to {\text{C}} \to {\text{D}} \to {\text{E}} \to {\text{A}}\) is Hamiltonian <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">starting from any vertex there are four choices</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">from the next vertex there are three choices, <em>etc </em>… <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">so the number of Hamiltonian cycles is \(4!{\text{ }}( = 24)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow 12 distinct cycles (direction not considered) or 60 (if different starting points count as distinct). In any case, just award the second <strong><em>A1 </em></strong>if <strong><em>R1 </em></strong>is awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">total weight of any Hamiltonian cycles stated</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg</em> \({\text{A}} \to {\text{B}} \to {\text{C}} \to {\text{D}} \to {\text{E}} \to {\text{A}}\) has weight \(5 + 6 + 7 + 8 + 9 = 35\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">a lower bound for the travelling salesman problem is then obtained by adding the weights of CA and CB to the weight of the minimum spanning tree <strong><em>(M1)</em></strong></span></p>
<p style="font: normal normal normal 20.5px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_15.02.15.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">a lower bound is then \(14 + 6 + 6 = 26\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>eg </em>eliminating A from <em>G, </em>a minimum spanning tree of weight 18 is <strong><em>(M1)</em></strong></span></p>
<p style="font: normal normal normal 20.5px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_15.07.06.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">adding AD and AB to the spanning tree gives a lower bound of \(18 + 4 + 5 = 27 > 26\) <strong><em>A1</em></strong></span></p>
<p style="font: normal normal normal 20.5px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_15.04.48.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">so 26 is not the best lower bound <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Candidates may delete other vertices and the lower bounds obtained are B-28, D-27 and E-28.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">there are 12 distinct cycles (ignoring direction) with the following lengths</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Cycle Length</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABCDEA 35 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABCEDA 33</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABDCEA 39</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABDECA 37</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABECDA 31</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ABEDCA 31</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ACBDEA 37</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>ACBEDA</strong> <strong>29</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ACDBEA 35</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">ACEBDA 33</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">AEBCDA 31</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">AECBDA 37 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">as the optimal solution has length 29 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">26 is not the best possible lower bound <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow answers where candidates list the 24 cycles obtained by allowing both directions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered, with a variety of interpretations accepted.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) also had a number of acceptable possibilities.<br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (d) was generally well answered, but there were few good attempts at part (e).</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (d) was generally well answered, but there were few good attempts at part (e).</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Define what is meant by the statement \(x \equiv y(\bmod n){\text{ where }}x{\text{, }}y{\text{, }}n \in {\mathbb{Z}^ + }\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence prove that if \(x \equiv y(\bmod n)\) then \({x^2} \equiv {y^2}(\bmod n)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine whether or not \({x^2} \equiv {y^2}(\bmod n)\) implies that \(x \equiv y(\bmod n)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv y(\bmod n) \Rightarrow x = y + kn,{\text{ }}(k \in \mathbb{Z})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x \equiv y(\bmod n)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = y + kn\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = {y^2} + 2kny + {k^2}{n^2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {x^2} = {y^2} + (2ky + {k^2}n)n\) <em><strong>M1A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px 'Hiragino Kaku Gothic ProN';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {x^2} \equiv {y^2}(\bmod n)\) <em><strong>AG</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} \equiv {y^2}(\bmod n)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {x^2} - {y^2} = 0(\bmod n)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px 'Lucida Grande';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow (x - y)(x + y) = 0(\bmod n)\) <em><strong>A1</strong></em><span style="font: 19.5px Symbol;"><br></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This will be the case if</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x + y = 0(\bmod n){\text{ or }}x = - y(\bmod n)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(x \ne y(\bmod n)\) in general <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Any counter example, <em>e.g.</em> \(n = 5,{\text{ }}x = 3,{\text{ }}y = 2,\) in which case <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} \equiv {y^2}(\bmod n)\) but \(x \ne y(\bmod n)\). (false) <strong><em>R1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">While most candidates gave a correct meaning to \(x \equiv y(\bmod n)\) , there were some incorrect statements, the most common being \(x \equiv y(\bmod n)\) means that when <em>x</em> is divided by <em>n</em>, there is a remainder <em>y</em>. The true statement \(8 \equiv 5(\bmod 3)\) shows that this statement is incorrect. Part (b) was solved successfully by many candidates but (c) caused problems for some candidates who thought that the result in (c) followed automatically from the result in (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">While most candidates gave a correct meaning to \(x \equiv y(\bmod n)\) , there were some incorrect statements, the most common being \(x \equiv y(\bmod n)\) means that when <em>x</em> is divided by <em>n</em>, there is a remainder <em>y</em>. The true statement \(8 \equiv 5(\bmod 3)\) shows that this statement is incorrect. Part (b) was solved successfully by many candidates but (c) caused problems for some candidates who thought that the result in (c) followed automatically from the result in (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">While most candidates gave a correct meaning to \(x \equiv y(\bmod n)\) , there were some incorrect statements, the most common being \(x \equiv y(\bmod n)\) means that when <em>x</em> is divided by <em>n</em>, there is a remainder <em>y</em>. The true statement \(8 \equiv 5(\bmod 3)\) shows that this statement is incorrect. Part (b) was solved successfully by many candidates but (c) caused problems for some candidates who thought that the result in (c) followed automatically from the result in (b).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Convert the decimal number 51966 to base 16.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Using the Euclidean algorithm, find the greatest common divisor, <em>d </em>, of 901 and 612.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find integers <em>p </em>and <em>q </em>such that 901<em>p </em>+ 612<em>q </em>= <em>d </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Find the least possible positive integers <em>s </em>and <em>t </em>such that 901<em>s </em>− 612<em>t </em>= 85.</span></p>
<div class="marks">[10]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In each of the following cases find the solutions, if any, of the given linear congruence.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(9x \equiv 3(\bmod 18)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(9x \equiv 3(\bmod 15)\)</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the relevant powers of 16 are 16, 256 and 4096 </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(51966 = 12 \times 4096{\text{ remainder }}2814\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2814 = 10 \times 256{\text{ remainder }}254\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(254 = 15 \times 16{\text{ remainder }}14\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the hexadecimal number is CAFE <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> CAFE is produced using a standard notation, accept explained alternative notations.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) using the Euclidean Algorithm <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(901 = 612 + 289\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(612 = 2 \times 289 + 34\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(289 = 8 \times 34 + 17\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\gcd (901,{\text{ }}612) = 17\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) working backwards <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(17 = 289 - 8 \times 34\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 289 - 8 \times (612 - 2 \times 289)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 17 \times (901 - 612) - 8 \times 612\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 27 \times 901 - 25 \times 612\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{so }}p = 17,{\text{ }}q = - 25\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) a particular solution is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = 5p = 85,{\text{ }}t = - 5q = 125\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = 85 + 36\lambda ,{\text{ }}t = 125 + 53\lambda \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by inspection the solution satisfying all conditions is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((\lambda = - 2),{\text{ }}s = 13,{\text{ }}t = 19\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the congruence is equivalent to \(9x = 3 + 18\lambda \) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">this has no solutions as 9 does not divide the RHS <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the congruence is equivalent to \(3x = 1 + 5\lambda ,{\text{ }}\left( {3x \equiv 1(\bmod 5)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">one solution is \(x = 2\) , so the general solution is \(x = 2 + 5n\,\,\,\,\,\left( {x \equiv 2(\bmod 5)} \right)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many did not seem familiar with hexadecimal notation and often left their answer as 12101514 instead of CAFE.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">The Euclidean algorithm was generally found to be easy to deal with but getting a general solution in part (iii) eluded many candidates.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Rewriting the congruence in the form \(9x = 3 + 18\lambda \) for example was not often seen but should have been the first thing thought of.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(a,{\text{ }}b,{\text{ }}c,{\text{ }}d \in \mathbb{Z}\), show that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[(a - b)(a - c)(a - d)(b - c)(b - d)(c - d) \equiv 0(\bmod 3).\]</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we work modulo 3 throughout</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the values of <em>a</em>, <em>b</em>, <em>c</em>, <em>d</em> can only be 0, 1, 2 <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since there are 4 variables but only 3 possible values, at least 2 of the variables must be equal \((\bmod 3)\) <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore at least 1 of the differences must be \(0(\bmod 3)\) <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the product is therefore \(0(\bmod 3)\) <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we attempt to find values for the differences which do not give \(0(\bmod 3)\) for the product</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we work modulo 3 throughout</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we note first that none of the differences can be zero <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>a</em> − <em>b</em> can therefore only be 1 or 2 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">suppose it is 1, then <em>b</em> − <em>c</em> can only be 1</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since if it is 2, \((a - b) + (b - c) \equiv 3 \equiv 0(\bmod 3)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>c</em> − <em>d</em> cannot now be 1 because if it is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((a - b) + (b - c) + (c - d) = a - d \equiv 3 \equiv 0(\bmod 3)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>c</em> − <em>d</em> cannot now be 2 because if it is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((b - c) + (c - d) = b - d \equiv 3 \equiv 0(\bmod 3)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we cannot therefore find values of <em>c</em> and <em>d</em> to give the required result <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a similar argument holds if we suppose <em>a</em> − <em>b</em> is 2, in which case <em>b</em> − <em>c</em> must be 2 and we cannot find a value of <em>c</em> − <em>d</em> <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the product is therefore \(0(\bmod 3)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates who solved this question used the argument that there are four variables which can take only one of three different values modulo 3 so that at least two must be equivalent modulo 3 which leads to the required result. This apparently simple result, however, requires a fair amount of insight and few candidates managed it.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The sequence \(\{ {u_n}\} \) , \(n \in {\mathbb{Z}^ + }\) , satisfies the recurrence relation \({u_{n + 2}} = 5{u_{n + 1}} - 6{u_n}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \({u_1} = {u_2} = 3\) , obtain an expression for \({u_n}\) in terms of <em>n</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The sequence \(\{ {v_n}\} \) , \(n \in {\mathbb{Z}^ + }\) , satisfies the recurrence relation \({v_{n + 2}} = 4{v_{n + 1}} - 4{v_n}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \({v_1} = 2\) and \({v_2} = 12\) , use the principle of strong mathematical induction to show that \({v_n} = {2^n}(2n - 1)\) .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the auxiliary equation is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({m^2} - 5m + 6 = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">giving \(m = 2,{\text{ 3}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({u_n} = A \times {2^n} + B \times {3^n}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substituting <em>n</em> = 1, 2</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2A + 3B = 3\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4A + 9B = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the solution is <em>A</em> = 3, B = –1 giving \({u_n} = 3 \times {2^n} - {3^n}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we first prove that \({v_n} = {2^n}(2n - 1)\) for <em>n</em> = 1, 2 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for <em>n</em> = 1, it gives \(2 \times 1 = 2\) which is correct</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for <em>n</em> = 2 , it gives \(4 \times 3 = 12\) which is correct <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we now assume that the result is true for \(n \leqslant k\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v_{k + 1}} = 4{v_k} - 4{v_{k - 1}}{\text{ }}(k \geqslant 2)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {4.2^k}(2k - 1) - {4.2^{k - 1}}(2k - 3)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {2^{k + 1}}(4k - 2 - 2k + 3)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {2^{k + 1}}\left( {2(k + 1) - 1} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">this proves that if the result is true for \(n \leqslant k\) then it is true for \(n \leqslant k + 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since we have also proved it true for \(n \leqslant 2\) , the general result is proved by induction <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> A reasonable attempt has to be made to the induction step for the final <strong><em>R1</em></strong> to be awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">State the Fundamental theorem of arithmetic for positive whole numbers greater than \(1\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use the Fundamental theorem of arithmetic, applied to \(5577\) and <span class="s1">\(99\,099\)</span>, to calculate \(\gcd (5577,{\text{ }}99\,099)\) and \({\text{lcm}}(5577,{\text{ }}99\,099)\), expressing each of your answers as a product of prime numbers.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Prove that \(\gcd (n,{\text{ }}m) \times {\text{lcm}}(n,{\text{ }}m) = n \times m\) for all \(n,{\text{ }}m \in {\mathbb{Z}^ + }\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">every positive integer, greater than \(1\), is either prime or can be expressed uniquely as a product of primes <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for “product of primes” and <strong><em>A1 </em></strong>for “uniquely”.</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(5577 = 3 \times 11 \times {13^2}{\text{ and }}99099 = {3^2} \times 7 \times {11^2} \times 13\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1 </em></strong></span></p>
<p class="p1">\(\gcd (5577,{\text{ }}99099) = 3 \times 11 \times 13,{\text{ lcm}}(5577,{\text{ }}99099) = {3^2} \times 7 \times {11^2} \times {13^2}\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">\(n = p_1^{{k_1}}p_2^{{k_2}} \ldots p_r^{{k_r}}\) and \(m = p_1^{{j_1}}p_2^{{j_2}} \ldots p_r^{{j_r}}\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">employing all the prime factors of \(n\) and \(m\), and inserting zero exponents if necessary <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">define \({g_i} = \min ({k_i},{\text{ }}{j_i})\) and \({h_i} = \max ({k_i},{\text{ }}{j_i})\) for \(i = 1 \ldots r\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(\gcd (n,{\text{ }}m) = p_1^{{g_1}}p_2^{{g_2}} \ldots p_r^{{g_r}}\) and \({\text{lcm}}(n,{\text{ }}m) = p_1^{{h_1}}p_2^{{h_2}} \ldots p_r^{{h_r}}\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">noting that \({g_i} + {h_i} = {k_i} + {j_i}\) for \(i = 1 \ldots r\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(\gcd (n,{\text{ }}m) \times {\text{lcm}}(n,{\text{ }}m) = n \times m\) for all \(n,{\text{ }}m \in {\mathbb{Z}^ + }\)<strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">let \(m\) and \(n\) be expressed as a product of primes where \(m = ab\) and \(n = ac\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(a\) denotes the factors that are common and \(b,{\text{ }}c\) are the disjoint factors that are not common <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(\gcd (n,{\text{ }}m) = a\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\({\text{lcm}}(n,{\text{ }}m) = \gcd (n,{\text{ }}m)bc\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\(\gcd (n,{\text{ }}m) \times {\text{lcm}}(n,{\text{ }}m) = a \times (abc)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( = ab \times ac\) and \(m = ab\) and \(n = ac\) so <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">\(\gcd (n,{\text{ }}m) \times 1{\text{ cm}}(n,{\text{ }}m) = n \times m\) for all \(n,{\text{ }}m \in {\mathbb{Z}^ + }\) <span class="Apple-converted-space"> </span><strong><em>AG<br></em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<p class="p1"><strong><em>Total [11 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (a), most candidates omitted the 'uniquely' in their definition of the fundamental theorem of arithmetic. A few candidates defined what a prime number is.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b), a substantial number of candidates used the Euclidean algorithm rather than the fundamental theorem of arithmetic to calculate \(\gcd (5577,{\text{ }}99099)\) and \({\text{lcm}}(5577,{\text{ }}99099)\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), a standard proof that has appeared in previous examination papers, was answered successfully by candidates who were well prepared.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following figure shows the floor plan of a museum.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_11.01.03.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Draw a graph <em>G </em>that represents the plan of the museum where each exhibition room is represented by a vertex labelled with the exhibition room number and each door between exhibition rooms is represented by an edge. Do not consider the entrance foyer as a museum exhibition room.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Write down the degrees of the vertices that represent each exhibition room.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Virginia enters the museum through the entrance foyer. Use your answers to </span><span style="font-family: 'times new roman', times; font-size: medium;">(i) and (ii) to justify why it is possible for her to visit the thirteen exhibition rooms going through each internal doorway exactly once.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Let <em>G </em>and <em>H </em>be two graphs whose adjacency matrices are represented below.</span></p>
<p style="font: normal normal normal 21px/normal Helvetica; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_11.02.25.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Using the adjacency matrices,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) find the number of edges of each graph;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) show that exactly one of the graphs has a Eulerian trail;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) show that neither of the graphs has a Eulerian circuit.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) <br><img src="images/Schermafbeelding_2014-09-17_om_11.04.03.png" alt> <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Do not penalize candidates who include the entrance foyer.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the degrees of the vertices are 4, 2, 4, 4, 2, 2, 4, 2, 2, 2, 2, 2, 2 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) the degree of all vertices is even and hence a Eulerian circuit exists, <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">hence it is possible to enter the museum through the foyer and visit each room 1–13 going through each internal doorway exactly once <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>The connected graph condition is not required.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) <br><img src="images/Schermafbeelding_2014-09-17_om_11.05.20.png" alt> <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">graph <em>G </em>has 15 edges and graph <em>H </em>has 22 edges <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the degree of every vertex is equal to the sum of the numbers in the corresponding row (or column) of the adjacency table </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">exactly two of the vertices of <em>G </em>have an odd degree (B and C) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>H </em>has four vertices with odd degree <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>G </em>is the graph that has a Eulerian trail (and <em>H </em>does not) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) neither graph has all vertices of even degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">therefore neither of them has a Eulerian circuit <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was generally well answered. There were many examples of full marks in this part. Part (b) caused a few more difficulties, although there were many good solutions. Few candidates used the matrix to find the number of edges, preferring instead to draw the graph. A surprising number of students confused the ideas of having vertices of odd degree.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(30\) is a factor of \({n^5} - n\) for all \(n \in \mathbb{N}\).</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that \({3^{{3^m}}} \equiv 3({\text{mod}}4)\) for all \(m \in \mathbb{N}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence show that there is exactly one pair \((m,{\text{ }}n)\) where \(m,{\text{ }}n \in \mathbb{N}\), satisfying the equation \({3^{{3^m}}} = {2^{{2^n}}} + {5^2}\).</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({n^5} - n = \underbrace {n(n - 1)(n + 1)}_{{\text{3 consecutive integers}}}({n^2} + 1) \equiv 0({\text{mod}}6)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">at least a factor is multiple of 3 and at least a factor is multiple of 2 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({n^5} - n = n({n^4} - 1) \equiv 0({\text{mod}}5)\) as \({n^4} \equiv 1({\text{mod}}5)\) by FLT <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">therefore, as \({\text{(5, 6)}} = 1\), <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({n^5} - n \equiv 0\left( {\bmod \underbrace {5 \times 6}_{30}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em>ie </em>30 is a factor of \({n^5} - n\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">let \({\text{P}}(n)\) be the proposition: \({n^5} - n = 30\alpha \) for some \(\alpha \in \mathbb{Z}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({0^5} - 0 = 30 \times 0\), so \({\text{P}}(0)\) is true <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">assume \({\text{P}}(k)\) is true for some \(k\) and consider \({\text{P}}(k + 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({(k + 1)^5} - (k + 1) = {k^5} + 5{k^4} + 10{k^3} + 10{k^2} + 5k + 1 - k - 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = ({k^5} - k) + 5k\left( {\underbrace {{k^3} + 3{k^2} + 3k + 1}_{{{(k + 1)}^3}} - ({k^2} + k)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = ({k^5} - k) + 5k\left( {{{(k + 1)}^3} - k(k + 1)} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 30\alpha + \underbrace {5k(k + 1)\left( {\underbrace {{k^2} + k + 1}_{k(k + 1) + 1}} \right)}_{{\text{multiple of 6}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 30\alpha + 30\beta \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">as \({\text{P}}(0)\) is true and \({\text{P}}(k)\) true implies \({\text{P}}(k + 1)\) true, by PMI \({\text{P}}(n)\) is true for all values \(n \in \mathbb{N}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award the first <strong><em>M1 </em></strong>only if the correct induction procedure is followed and the correct first line is seen.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>R1 </em></strong>only if both <strong><em>M </em></strong>marks have been awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({n^5} - n = n({n^4} - 1)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = n({n^2} - 1)({n^2} + 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (n - 1)n(n + 1)({n^2} - 4 + 5)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (n - 2)(n - 1)n(n + 1)(n + 2) + 5(n - 1)n(n + 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">each term is multiple of 2, 3 and 5 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">therefore is divisible by 30 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">case 1: \(m = 0\) and \({3^{{3^0}}} \equiv 3{\text{mod}}4\) is true <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">case 2: \(m > 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">let \(N = {3^m} \geqslant 3\) and consider the binomial expansion <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({3^N} = {(1 + 2)^N} = \sum\limits_{k = 0}^N {} \) \(\left( \begin{array}{c}N\\k\end{array} \right){2^k} = 1 + 2N + \underbrace {\sum\limits_{k = 2}^N {\left( \begin{array}{c}N\\k\end{array} \right){2^k}} }_{ \equiv ({\text{mod}}4)} \equiv 1 + 2N({\text{mod}}4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">as \(\underbrace {{3^m}}_N \equiv {( - 1)^m}({\text{mod}}4) \Rightarrow 1 + 2N \equiv 1 + 2{( - 1)^m}({\text{mod}}4)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(\underbrace {{3^{{3^m}}}}_{{3^N}} \equiv 1 + 2{( - 1)^m}({\text{mod}}4) \Rightarrow \) \(\left\{ \begin{array}{l}\underbrace {{3^{{3^m}}}}_{{3^N}} \equiv \underbrace {1 + 2}_3({\text{mod}}4){\rm{for\,}} m {\rm{\,even}}\\\underbrace {{3^{{3^m}}}}_{{3^N}} \equiv \underbrace {1 - 2}_{ - 1 \equiv 3({\text{mod}}4)}({\text{mod}}4){\rm{for\,}} m {\rm{\,odd}}\end{array} \right.\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">which proves that \({3^{{3^m}}} \equiv 3({\text{mod}}4)\) for any \(m \in \mathbb{N}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">let \({\text{P}}(n)\) be the proposition: \({3^{{3^n}}} - 3 \equiv 0({\text{mod }}4,{\text{ or }}24)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({3^{{3^0}}} - 3 = 3 - 3 \equiv 0({\text{mod }}4{\text{ or }}24)\), so \({\text{P}}(0)\) is true <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">assume \({\text{P}}(k)\) is true for some \(k\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">consider \({3^{{3^{^{k + 1}}}}} - 3 = {3^{{3^k} \times 3}} - 3\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {(3 + 24r)^3} - 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 27 + 24t - 3\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 0({\text{mod }}4{\text{ or }}24)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">as \({\text{P}}(0)\) is true and \({\text{P}}(k)\) true implies \({\text{P}}(k + 1)\) true, by PMI \({\text{P}}(n)\) is true for all values \(n \in \mathbb{N}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\({3^{{3^m}}} - 3 = 3({3^{{3^m} - 1}} - 1)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 3({3^{2k}} - 1)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 3({9^k} - 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 3\underbrace {\left( {{{(8 + 1)}^k} - 1} \right)}_{{\text{multiple of 8}}}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 0({\text{mod}}24)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">which proves that \({3^{{3^m}}} \equiv 3({\text{mod}}4)\) for any \(m \in \mathbb{N}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) for \(m \in \mathbb{N},{\text{ }}{3^{{3^m}}} \equiv 3({\text{mod}}4)\) and, as \({2^{{2^n}}} \equiv 0({\text{mod}}4)\) and \({5^2} \equiv 1({\text{mod}}4)\) then \({2^{{2^n}}} + {5^2} \equiv 1({\text{mod}}4)\) for \(n \in {\mathbb{Z}^ + }\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">there is no solution to \({3^{{3^m}}} = {2^{{2^n}}} + {5^2}\) for pairs \((m,{\text{ }}n) \in \mathbb{N} \times {\mathbb{Z}^ + }\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">when \(n = 0\), we have \({3^{{3^m}}} = {2^{{2^0}}} + {5^2} \Rightarrow {3^{{3^m}}} = 27 \Rightarrow m = 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \((m,{\text{ }}n) = (1,{\text{ }}0)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">is the only pair of non-negative integers that satisfies the equation <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many students were able to get partial credit for part (a), although few managed to gain full marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">There seemed to be very few good attempts at part (b), many failing at the outset to understand what was meant by \({3^{{3^m}}}\).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Draw a spanning tree for</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> (i) the complete graph, \({K_4}\);</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) the complete bipartite graph, \({K_{4,4}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Prove that a simple connected graph with <em>n </em>vertices, where \(n > 1\), must have two vertices</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">of the same degree.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Prove that every simple connected graph has at least one spanning tree.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i)<br><img src="images/maths_3a_i_markscheme.png" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Or equivalent not worrying about the orientation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii)<br><img src="images/maths_3a_ii_markscheme.png" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Other trees are possible, but must clearly come from the bipartite graph, so, for example, a straight line graph is not acceptable unless the bipartite nature is clearly shown <em>eg</em>, with black and white vertices.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) graph is simple implies maximum degree is \(n - 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">graph is connected implies minimum degree is 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by a pigeon-hole principle two vertices must have the same degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) if the graph is not a tree it contains a cycle <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">remove one edge of this cycle <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the graph remains connected <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">repeat until there are no cycles <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the final graph is connected and has no cycles <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so is a tree <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow other methods <em>eg</em>, induction, reference to Kruskal’s algorithm.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [10 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p class="p1">The weights of the edges in the complete graph \(G\) are shown in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-06_om_05.29.01.png" alt="M16/5/MATHL/HP3/ENG/TZ0/DM/02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Starting at A</span>, use the nearest neighbour algorithm to find an upper bound for the travelling salesman problem for \(G\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">By first removing A </span>, use the deleted vertex algorithm to find a lower bound for the travelling salesman problem for \(G\).</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to use the nearest neighbour algorithm <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(\begin{array}{*{20}{l}} {{\text{the nearest neighbour path is}}}&{{\text{A}} \to {\text{D}} \to {\text{C }}A1} \\ {}&{ \to {\text{E}} \to {\text{B}} \to {\text{F}} \to {\text{A }}A1} \end{array}\)</p>
<p class="p1">the upper bound is the total weight of this path, <em>ie</em> <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(8 + 7 + 8 + 10 + 13 + 9 = 55\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The <strong><em>(M1) </em></strong>is for adding 6 weights together.</p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">attempt to use an appropriate algorithm, with A <span class="s1">deleted, to determine the </span>minimum spanning tree, <em>eg </em>Kruskal’s <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"><span class="s2">CD </span>(7) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">CE, CB (8,9) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">DF or EF (11) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">the weight of this minimum spanning tree is 35 <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">adding in the two smallest weights joining A (AD and AF) <span class="s1">to this tree gives </span>a lower bound <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2">of \(35 + 8 + 9 = 52\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Clear diagrams aiding solutions are acceptable in (a) and (b).</p>
<p class="p2"><strong><em>[7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Generally good use of the nearest neighbour algorithm. Some candidates showed no knowledge of it and there was some confusion with the twice the weight of a minimal spanning tree method. Some candidates forgot to go back to A and thus did not have a Hamiltonian cycle.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The method was generally known. Some candidates used nearest neighbour instead of Kruskal’s algorithm to find a minimal spanning tree. Some forgot to add in the two edges connected to . Some with the right method made mistakes in not noticing the correct edge to choose. <span class="s1">A</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following graph represents the cost in dollars of travelling by bus between 10 towns in a particular province.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-11_om_14.37.25.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use Dijkstra’s algorithm to find the cheapest route between \(A\) and \(J\), and state its cost.</p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">For the remainder of the question you may find the cheapest route between any two towns by inspection.</p>
<p class="p1">It is given that the total cost of travelling on all the roads without repeating any is \(\$ 139\).</p>
<p class="p1">A tourist decides to go over all the roads at least once, starting and finishing at town \(A\).</p>
<p class="p1">Find the lowest possible cost of his journey, stating clearly which roads need to be travelled more than once. You must fully justify your answer.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2015-12-11_om_14.45.31.png" alt> <strong><em>M1A1A1A1</em></strong></p>
<p class="p1">(<strong><em>M1</em></strong> for an attempt at Dijkstra’s)</p>
<p class="p1">(<strong><em>A1</em></strong> for value of \({\text{D}} = 17\))</p>
<p class="p1">(<strong><em>A1</em></strong> for value of \({\text{H}} = 22\))</p>
<p class="p1">(<strong><em>A1</em></strong> for value of \({\text{G}} = 22\))</p>
<p class="p1">route is \(ABDHJ\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></p>
<p class="p1">cost is \($27\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note:</strong> <span class="Apple-converted-space"> </span>Accept other layouts.</p>
<p class="p1"><em><strong>[7 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">there are 4 odd vertices \(A\), \(D\), \(F\) and \(J\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">these can be joined up in 3 ways with the following extra costs</p>
<p class="p1">\(AD\) and \(FJ\)\(\;\;\;17 + 13 = 30\)</p>
<p class="p1">\(AF\) and \(DJ\)\(\;\;\;23 + 10 = 33\)</p>
<p class="p1">\(AJ\) and \(DF\)\(\;\;\;27 + 12 = 39\) <span class="Apple-converted-space"> </span><strong><em>M1A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>for an attempt to find different routes.</p>
<p class="p1">Award <strong><em>A1A1 </em></strong>for correct values for all three costs <strong><em>A1 </em></strong>for one correct.</p>
<p class="p2"> </p>
<p class="p1">need to repeat \(AB\), \(BD\), \(FG\) and \(GJ\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">total cost is \(139 + 30 = \$ 169\) <em><strong>A1</strong></em></p>
<p class="p1"><em><strong>[6 marks]</strong></em></p>
<p class="p1"><em><strong>Total [13 marks]</strong></em></p>
<p class="p1"> </p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates had the correct route and the cost. Not all showed sufficient working with their Dijkstra’s algorithm. See the mark-scheme for the neat way of laying out the working, including the back-tracking method. This tabular working is efficient, avoids mistakes and saves time.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There was often confusion here between this problem and the travelling salesman. Good candidates started with the number of vertices of odd degree. Weaker candidates just tried to write the answer down without complete reasoning. All the 3 ways of joining the odd vertices had to be considered so that you knew you had the smallest. Sometimes a mark was lost by giving which routes (paths) had to be repeated rather than which roads (edges).</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use the Euclidean algorithm to find the greatest common divisor of 259 and 581.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence, or otherwise, find the general solution to the diophantine equation 259<em>x</em> + 581<em>y</em> = 7 .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(581 = 2 \times 259 + 63\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(259 = 4 \times 63 + 7\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(63 = 9 \times 7\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the GCD is therefore 7 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(7 = 259 - 4 \times 63\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 259 - 4 \times (581 - 2 \times 259)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 259 \times 9 + 581 \times ( - 4)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 9 + 83n;{\text{ }}y = - 4 - 37n{\text{ where }}n \in \mathbb{Z}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Notes:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Accept solutions laid out in tabular form. Dividing the diophantine equation by 7 is an equally valid method.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[5 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">An arithmetic sequence has first term 2 and common difference 4. Another arithmetic sequence has first term 7 and common difference 5. Find the set of all numbers which are members of both sequences.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the <em>m</em>th term of the first sequence \( = 2 + 4(m - 1)\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the <em>n</em>th term of the second sequence \( = 7 + 5(n - 1)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">equating these, <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5n = 4m - 4\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5n = 4(m - 1)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">4 and 5 are coprime <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 4|n\) so \(n = 4s\) or \(5|(m - 1)\) so \(m = 5s + 1\) , \(s \in {\mathbb{Z}^ + }\) <strong><em>(A1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">thus the common terms are of the form \(\{ 2 + 20s;{\text{ }}s \in {\mathbb{Z}^ + }\} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the numbers of both sequences are</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">2, 6, 10, 14, 18, 22</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">7, 12, 17, 22 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so 22 is common <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">identify the next common number as 42 <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is \(\{ 2 + 20s;{\text{ }}s \in {\mathbb{Z}^ + }\} \) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[9 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Solutions to this question were extremely variable with some candidates taking several pages to give a correct solution and others taking several pages and getting nowhere. Some elegant solutions were seen including the fact that the members of the two sets can be represented as \(2\bmod 4\) and \(2\bmod 5\) respectively so that common members are \(2\bmod 20\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"> </p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using the Euclidean algorithm, show that \(\gcd (99,{\text{ }}332) = 1\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the general solution to the diophantine equation \(332x - 99y = 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence, or otherwise, find the smallest positive integer satisfying the congruence \(17z \equiv 1(\bmod 57)\).</span></p>
<div class="marks">[11]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the Euclidean Algorithm,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(332 = 3 \times 99 + 35{\text{ }}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(99 = 2 \times 35 + 29\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(35 = 1 \times 29 + 6\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(29 = 4 \times 6 + 5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6 = 1 \times 5 + 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence 332 and 99 have a gcd of 1 <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> For both (a) and (b) accept layout in tabular form, especially the brackets method of keeping track of the linear combinations as the method proceeds.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) working backwards, <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6 - 5 = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6 - (29 - 4 \times 6) = 1{\text{ or }}5 \times 6 - 29 = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5 \times (35-29)-29 = 1{\text{ or }}5 \times 35-6 \times 29 = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(5 \times 35-6 \times (99-2 \times 35) = 1{\text{ or }}17 \times 35-6 \times 99 = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(17 \times (332-3 \times 99)-6 \times 99 = 1{\text{ or }}17 \times 332-57 \times 99 = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a solution to the Diophantine equation is therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 17,{\text{ }}y = 57\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 17 + 99N,{\text{ }}y = 57 + 332N\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> If part (a) is wrong it is inappropriate to give </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>FT</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> in (b) as the numbers will contradict, however the </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> can be given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) it follows from previous work that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(17 \times 332 = 1 + 99 \times 57\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 1(\bmod 57)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>z</em> = 332 is a solution to the given congruence <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is 332 + 57<em>N</em> so the smallest solution is 47 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[11 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was well answered and (b) fairly well answered. There were problems with negative signs due to the fact that there was a negative in the question, so candidates had to think a little, rather than just remembering formulae by rote. The lay-out of the algorithm that keeps track of the linear combinations of the first 2 variables is recommended to teachers.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was well answered and (b) fairly well answered. There were problems with negative signs due to the fact that there was a negative in the question, so candidates had to think a little, rather than just remembering formulae by rote. The lay-out of the algorithm that keeps track of the linear combinations of the first 2 variables is recommended to teachers.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Solve, by any method, the following system of linear congruences</p>
<p class="p1"><span class="Apple-converted-space"> </span>\(x \equiv 9(\bmod 11)\)</p>
<p class="p1"><span class="Apple-converted-space"> </span>\(x \equiv 1(\bmod 5)\)</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the remainder when \({41^{82}}\) is divided by 11.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your answers to parts (a) and (b) find the remainder when \({41^{82}}\) is divided by \(55\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">listing \(9,{\rm{ }}20,{\rm{ }}31\), \( \ldots \) and \(1,{\rm{ }}6,11,16,{\rm{ }}21,{\rm{ }}26,{\rm{ }}31\), \( \ldots \) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">one solution is \(31\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">by the Chinese remainder theorem the full solution is</p>
<p class="p2">\(x \equiv 31(\bmod 55)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1 N2</em></strong></span></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">\(x \equiv 9(\bmod 11) \Rightarrow x = 9 + 11t\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( \Rightarrow 9 + 11t \equiv 1(\bmod 5)\)</p>
<p class="p1">\( \Rightarrow t \equiv 2(\bmod 5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">\( \Rightarrow t = 2 + 5s\)</p>
<p class="p1">\( \Rightarrow x = 9 + 11(2 + 5s)\)</p>
<p class="p1">\( \Rightarrow x = 31 + 55s{\text{ }}\left( { \Rightarrow x \equiv 31(\bmod 55)} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept other methods <em>eg </em>formula, Diophantine equation.</p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept other equivalent answers e.g. \( - 79(\bmod 55)\).</p>
<p class="p1"><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({41^{82}} \equiv {8^{82}}(\bmod 11)\)</p>
<p class="p1">by Fermat’s little theorem \({8^{10}} \equiv 1(\bmod 11)\;\;\;\left( {{\text{or }}{{41}^{10}} \equiv 1(\bmod 11)} \right)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\({8^{82}} \equiv {8^2}(\bmod 11)\) <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\( \equiv 9(\bmod 11)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">remainder is \(9\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept simplifications done without Fermat.</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({41^{82}} \equiv {1^{82}} \equiv 1(\bmod 5)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">so \({41^{82}}\) has a remainder \(1\) when divided by \(5\) and a remainder \(9\) when divided by \(11\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">hence by part (a) the remainder is \(31\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [10 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">A variety of methods were used here. The Chinese Remainder Theorem method (Method 2 on the mark-scheme) is probably the most instructive. Candidates who tried to do it by formula often (as usual) made mistakes and got it wrong. Marks were lost by just saying 31 and not giving mod (55).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Time was lost here by not using Fermat’s Little Theorem as a starting point, although the ad hoc methods will work.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Although it said use parts (a) and (b) not enough candidates saw the connection.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider an integer \(a\) with \((n + 1)\) digits written as \(a = {10^n}{a_n} + {10^{n - 1}}{a_{n - 1}} + \ldots + 10{a_1} + {a_0}\), where \(0 \leqslant {a_i} \leqslant 9\) for \(0 \leqslant i \leqslant n\), and \({a_n} \ne 0\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that \(a \equiv ({a_n} + {a_{n - 1}} + \ldots + {a_0}) ({\text{mod9}})\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence find all pairs of values of the single digits \(x\) and \(y\) such that the number \(a = 476x212y\) is a multiple of \(45\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) If \(b = 34\,390\) in base 10, show that \(b\) is \(52\,151\) written in base 9.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence find \({b^2}\) in base 9, by performing all the calculations without changing base.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(10 \equiv 1(\bmod 9) \Rightarrow {10^i} \equiv 1({\text{mod9}}),{\text{ }}i = 1,{\text{ }} ... ,{\text{ }}n\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {10^i}{a_i} \equiv {a_i}({\text{mod9}}),{\text{ }}i = 1,{\text{ }}n\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow \(i = 0\) but do not penalize its omission.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow ({10^n}{a_n} + {10^{n - 1}}{a_{n - 1}} + \ldots + {a_0}) \equiv ({a_n} + {a_{n - 1}} + \ldots + {a_0})({\text{mod9}})\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(4 + 7 + 6 + x + 2 + 1 + 2 + y = 9k,{\text{ }}k \in \mathbb{Z}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow (22 + x + y) \equiv 0(\bmod 9),{\text{ }} \Rightarrow (x + y) \equiv 5({\text{mod9}})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x + y = 5\) or \(14\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">if \(5\) divides \(a\), then \(y = 0\) or \(5\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">so \(y = 0 \Rightarrow x = 5,{\text{ }}\left( {ie{\text{ }}(x,{\text{ }}y) = (5,{\text{ }}0)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = 5 \Rightarrow x = 0\) or \(x = 9,{\text{ }}\left( {ie{\text{ }}(x,{\text{ }}y) = (0,{\text{ }}5){\text{ or }}(x,{\text{ }}y) = (9,{\text{ }}5)} \right)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) <br><img src="images/Schermafbeelding_2014-09-17_om_14.51.30.png" alt> <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">\(b = {(52\,151)_9}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <br><img src="images/Schermafbeelding_2014-09-17_om_14.52.41.png" alt> <strong><em>M1A3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>M1 </em></strong>for attempt, <strong><em>A1 </em></strong>for two correct lines of multiplication, <strong><em>A2 </em></strong>for two correct lines of multiplication and a correct addition, <strong><em>A3 </em></strong>for all correct.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Surprisingly few good answers. Part (a) had a number of correct solutions, but there were also many that seemed to be a memorised solution, not properly expressed – and consequently wrong. In part (b) many failed to understand the question, not registering that <em>x</em> and <em>y</em> were digits rather than numbers. Part (c)(i) was generally well answered, although there were a number of longer methods applied, and few managed to do (c)(ii).</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the general solution for the following system of congruences.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(N \equiv 3(\bmod 11)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(N \equiv 4(\bmod 9)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> \(N \equiv 0(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find all values of <em>N</em> such that \(2000 \leqslant N \leqslant 4000\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(N = 3 + 11t\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 + 11t \equiv 4(\bmod 9)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2t \equiv 1(\bmod 9)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">multiplying by 5, \(10t \equiv 5(\bmod 9)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t \equiv 5(\bmod 9)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(t = 5 + 9s\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = 3 + 11(5 + 9s)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = 58 + 99s\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(58 + 99s \equiv 0(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2 + s \equiv 0(\bmod 7)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s \equiv 5(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(s = 5 + 7u\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = 58 + 99(5 + 7u)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(N = 553 + 693u\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow solutions that are done by formula or an exhaustive, systematic listing of possibilities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <em>u</em> = 3 or 4</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">hence N = 553 + 2079 = 2632 or <em>N</em> = 553 + 2772 = 3325 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [11 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"> </p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This was a standard Chinese remainder theorem problem that many candidates gained good marks on. Some candidates employed a formula, which was fine if they remembered it correctly (but not all did), although it did not always show good understanding of the problem.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Anna is playing with some cars and divides them into three sets of equal size. However, when she tries to divide them into five sets of equal size, there are four left over. Given that she has fewer than 50 cars, what are the possible numbers of cars she can have?</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>x</em> be the number of cars</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we know \(x \equiv 0(\bmod 3)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">also \(x \equiv 4(\bmod 5)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so \(x = 3t \Rightarrow 3t \equiv 4(\bmod 5)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 6t \equiv 8(\bmod 5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow t \equiv 3(\bmod 5)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow t = 3 + 5s\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 9 + 15s\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since there must be fewer than 50 cars, <em>x</em> = 9, 24, 39 <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Only award two of the final three <strong><em>A1</em></strong> marks if more than three solutions are given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>x</em> is a multiple of 3 that ends in 4 or 9 <strong><em>R4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore <em>x</em> = 9, 24, 39 <strong><em>A1A1A1 N3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Only award two of the final three <strong><em>A1</em></strong> marks if more than three solutions are given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were a number of totally correct solutions to this question, but some students were unable to fully justify their results.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the integers \(a = 871\) and \(b= 1157\), given in base \(10\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Express \(a\) and \(b\) in base \(13\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence show that \({\text{gcd}}(a,{\text{ }}b) = 13\).</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A list \(L\) contains \(n+ 1\) distinct positive integers. Prove that at least two members of \(L\)leave the same remainder on division by \(n\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the simultaneous equations</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(4x + y + 5z = a\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(2x + z = b\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> \(3x + 2y + 4z = c\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">where \(x,{\text{ }}y,{\text{ }}z \in \mathbb{Z}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that 7 divides \(2a + b - c\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Given that <em>a </em>= 3, <em>b </em>= 0 and <em>c </em>= −1, find the solution to the system of equations modulo 2.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">Consider the set \(P\) of numbers of the form \({n^2} - n + 41,{\text{ }}n \in \mathbb{N}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">(i) Prove that all elements of <em>P </em>are odd.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">(ii) List the first six elements of <em>P </em>for <em>n </em>= 0, 1, 2, 3, 4, 5.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-size: medium; font-family: 'times new roman', times;">(iii) Show that not all elements of <em>P </em>are prime.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using a relevant list of powers of 13: (1), 13, 169, (2197) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(871 = 5 \times {13^2} + 2 \times 13\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(871 = {520_{13}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1157 = 6 \times {13^2} + 11 \times 13\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1157 = 6{\text{B}}{{\text{0}}_{13}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempted repeated division by 13 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(871 \div 13 = 67;{\text{ }}67 \div 13 = 5{\text{rem}}2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(871 = {520_{13}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1157 \div 13 = 89;{\text{ }}89 \div 13 = 6{\text{rem11}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(1157 = 6{\text{B}}{{\text{0}}_{13}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow (11) for B only if brackets or equivalent are present.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(871 = 13 \times 67;{\text{ }}1157 = 13 \times 89\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">67 and 89 are primes (base 10) or they are co-prime <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So \(\gcd (871,{\text{ }}1157) = 13\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Must be done by hence not Euclid’s algorithm on 871 and 1157.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>K </em>be the set of possible remainders on division by <em>n </em><strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">then \(K = \{ {\text{0, 1, 2, }} \ldots n - 1\} \) has <em>n </em>members <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">because \(n < n + 1{\text{ }}\left( { = n(L)} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by the pigeon-hole principle (appearing anywhere and not necessarily mentioned by name as long as is explained) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at least two members of <em>L </em>correspond to one member of <em>K </em><strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) form the appropriate linear combination of the equations: <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2a + b - c = 7x + 7z\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 7(x + z)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so 7 divides \(2a + b - c\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) modulo 2, the equations become <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y + z = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(z = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">solution: (1, 1, 0) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award full mark to use of GDC (or done manually) to solve the system giving \(x = - 1,{\text{ }}y = - 3,{\text{ }}z = 2\) and then converting mod 2.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) separate consideration of even and odd <em>n </em><strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{eve}}{{\text{n}}^2} - {\text{even}} + {\text{odd is odd}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{od}}{{\text{d}}^2} - {\text{odd}} + {\text{odd is odd}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">all elements of <em>P </em>are odd <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Allow other methods <em>eg</em>, \({n^2} - n = n(n - 1)\) which must be even.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the list is [41, 41, 43, 47, 53, 61] <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({41^2} - 41 + 41 = {41^2}\) divisible by 41 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">but is not a prime <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the statement is disproved (by counterexample) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">One version of Fermat’s little theorem states that, under certain conditions, \({a^{p - 1}} \equiv 1(\bmod p)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that this result is not true when <em>a</em> = 2, <em>p</em> = 9 and state which of the conditions is not satisfied.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the smallest positive value of <em>k</em> satisfying the congruence \({2^{45}} \equiv k(\bmod 9)\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find all the integers between 100 and 200 satisfying the simultaneous congruences \(3x \equiv 4(\bmod 5)\) and \(5x \equiv 6(\bmod 7)\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({2^8} = 256 \equiv 4(\bmod 9)\) (so not true) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">9 is not prime <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) consider various powers of 2, <em>e.g.</em> obtaining <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^6} = 64 \equiv 1(\bmod 9)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{45}} = {({2^6})^7} \times {2^3}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 8(\bmod 9){\text{ (so }}k = 8)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the solutions to \(3x \equiv 4(\bmod 5)\) are 3, 8, 13, 18, 23,… <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the solutions to \(5x \equiv 6(\bmod 7)\) are 4, 11, 18,… <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">18 is therefore the smallest solution <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(18 + 35n{\text{ , }}n \in \mathbb{Z}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the required solutions are therefore 123, 158, 193 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3x \equiv 4(\bmod 5) \Rightarrow 2 \times 3x \equiv 2 \times 4(\bmod 5) \Rightarrow x \equiv 3(\bmod 5)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 3 + 5t\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow 15 + 25t \equiv 6(\bmod 7) \Rightarrow 4t \equiv 5(\bmod 7) \Rightarrow 2 \times 4t \equiv 2 \times 5(\bmod 7) \Rightarrow t \equiv 3(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow t = 3 + 7n\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow x = 3 + 5(3 + 7n) = 18 + 35n\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the required solutions are therefore 123, 158, 193 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the Chinese remainder theorem formula method</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">first convert the congruences to \(x \equiv 3(\bmod 5)\) and \(x \equiv 4(\bmod 7)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(M = 35{\text{, }}{M_1} = 7{\text{, }}{M_2} = 5{\text{, }}{m_1} = 5,{\text{ }}{m_2} = 7,{\text{ }}{a_1} = 3,{\text{ }}{a_2} = 4\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_1}\) is the solution of \({M_2}{x_2} \equiv 1(\bmod {m_1})\) , <em>i.e.</em> \(7{x_1} \equiv 1(\bmod 5)\) so \({x_1} = 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({x_2}\) is the solution of \({M_2}{x_2} \equiv 1(\bmod {m_2})\) , <em>i.e.</em> \(5{x_2} \equiv 1(\bmod 7)\) so \({x_2} = 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a solution is therefore</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = {a_1}{M_1}{x_1} + {a_2}{M_2}{x_2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 3 \times 7 \times 3 + 4 \times 5 \times 3 = 123\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the general solution is \(123 + 35n\) , \(n \in \mathbb{Z}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the required solutions are therefore 123, 158, 193 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A simple connected planar graph, has \(e\) edges, \(v\) vertices and \(f\) faces.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Show that \(2e \ge 3f{\text{ if }}v > 2\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Hence show that \({K_5}\), the complete graph on five vertices, is not planar.</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>State the handshaking lemma.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Determine the value of \(f\), if each vertex has degree \(2\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw an example of a simple connected planar graph on \(6\) vertices each of degree \(3\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1">attempting to use \(f = e - v + 2\) and \(e \le 3v - 6\) (if \(v > 2\)) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\(2e \le 6v - 12 = 6(e - f + 2) - 12\) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">leading to \(2e \ge 3f\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">each face is bounded by at least three edges <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for stating \(e \ge 3f\).</p>
<p class="p2"> </p>
<p class="p1">each edge either separates two faces or, if an edge is interior to a face, it gets counted twice <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>R1 </em></strong>for stating that each edge contributes two to the sum of the degrees of the faces (or equivalent) <em>ie</em>, \(\sum {\deg (F) = 2e} \).</p>
<p class="p2"> </p>
<p class="p1">adding up the edges around each face <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">leading to \(2e \ge 3f\) <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\({K_5}\) has \(e = 10\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">if the graph is planar, \(f = 7\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">this contradicts the inequality obtained above <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1">hence the graph is non-planar <span class="Apple-converted-space"> </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>the sum of the vertex degrees \( = 2e\) (or is even) or equivalent <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>if each vertex has degree \(2\), then \(2v = 2e\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">substituting \(v = e\) into Euler’s formula <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p1">\(f = 2\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">for example,</p>
<p class="p1"><img src="images/Schermafbeelding_2016-01-08_om_08.02.23.png" alt> <em><strong>A2</strong></em></p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [12 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (a) (i), many candidates tried to prove \(2e \ge 3f\) with numerical examples. Only a few candidates were able to prove this inequality correctly. In part (a) (ii), most candidates knew that \({K_5}\) has 10 edges. However, a number of candidates simply drew a diagram with any number of faces and used this particular representation as a basis for their 'proof'. Many candidates did not recognise the 'hence' requirement in part (a) (ii).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b) (i), many candidates stated the 'handshaking lemma' incorrectly by relating it to the 'handshake problem'. In part (b) (ii), only a few candidates determined that \(v = e\) and hence found that \(f = 2\).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), a reasonable number of candidates were able to draw a simple connected planar graph on \(6\) vertices each of degree \(3\). The most common error here was to produce a graph that contained a multiple edge(s).</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The weights of the edges of a graph \(H\) are given in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-07_om_13.41.35.png" alt></p>
<p>(i) Draw the weighted graph \(H\).</p>
<p>(ii) Use Kruskal’s algorithm to find the minimum spanning tree of \(H\). Your solution should indicate the order in which the edges are added.</p>
<p>(iii) State the weight of the minimum spanning tree.</p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Consider the following weighted graph.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-07_om_15.46.10.png" alt></p>
<p class="p1">(i) Write down a solution to the Chinese postman problem for this graph.</p>
<p class="p1">(ii) Calculate the total weight of the solution.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) State the travelling salesman problem.</p>
<p class="p1">(ii) Explain why there is no solution to the travelling salesman problem for this graph.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> <img src="images/Schermafbeelding_2016-01-08_om_08.53.20.png" alt></span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A2</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>if one edge is missing. Award <strong><em>A1 </em></strong>if the edge weights are not labelled.</p>
<p class="p2"> </p>
<p class="p3"><span class="s2">(ii) <span class="Apple-converted-space"> </span></span>the edges are added in the order:</p>
<p class="p4">\(FG{\rm{ }}1\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p4">\(CE{\rm{ }}2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4">\(ED{\rm{ }}3\)</p>
<p class="p4">\(EG{\rm{ }}4\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4">\(AC{\rm{ }}4\)</p>
<p class="p5"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong><span class="s3">\(EG\) </span>and <span class="s3">\(AC\) </span>can be added in either order.</p>
<p class="p2"> </p>
<p class="p3">(Reject <span class="s3"> <span class="s3">\(EF\)</span></span>)</p>
<p class="p3">(Reject <span class="s3"> <span class="s3">\(CD\)</span></span>)</p>
<p class="p4">\(EB5\) <span class="s1"><strong>OR </strong></span>\(AB5\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Notes: <span class="Apple-converted-space"> </span></strong>The minimum spanning tree does not have to be seen.</p>
<p class="p3">If only a tree is seen, the order by which edges are added must be clearly indicated.</p>
<p class="p2"> </p>
<p class="p3">(iii) <span class="Apple-converted-space"> </span><span class="s3">\(19\) <span class="Apple-converted-space"> </span></span><strong><em>A1</em></strong></p>
<p class="p3"><strong><em>[8 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">(i) <span class="Apple-converted-space"> </span><em>eg</em>, </span>\(PQRSRTSTQP\) <span class="s1"><strong>OR </strong></span>\(PQTSTRSRQP\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>if in either (i) or (ii), it is recognised that edge <span class="s2">\(PQ\) </span>is needed twice.</p>
<p class="p2"> </p>
<p class="p3">(ii) <span class="Apple-converted-space"> </span>total weight \( = 34\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p3"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>to determine a cycle where each vertex is visited once only (Hamiltonian cycle) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">of least total weight <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><strong>EITHER</strong></p>
<p class="p1">to reach \(P\), \(Q\) must be visited twice which contradicts the definition of the \(TSP\) <span class="Apple-converted-space"> </span><strong><em>R1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">the graph is not a complete graph and hence there is no solution to the \(TSP\) <span class="Apple-converted-space"> </span><strong><em>R1 </em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<p class="p1"><strong><em>Total [14 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was generally very well answered. Most candidates were able to correctly sketch the graph of \(H\) and apply Kruskal’s algorithm to determine the minimum spanning tree of \(H\). A few candidates used Prim's algorithm (which is no longer part of the syllabus).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates understood the Chinese Postman Problem in part (b) and knew to add the weight of \(PQ\) to the total weight of \(H\). Some candidates, however, did not specify a solution to the Chinese Postman Problem while other candidates missed the fact that a return to the initial vertex is required.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (c), many candidates had trouble succinctly stating the Travelling Salesman Problem. Many candidates used an ‘edge’ argument rather than simply stating that the Travelling Salesman Problem could not be solved because to reach vertex \(P\), vertex \(Q\) had to be visited twice.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that there are exactly two solutions to the equation \(1982 = 36a + 74b\)<span class="s1">, with \(a,{\text{ }}b \in \mathbb{N}\).</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Hence, or otherwise, find the remainder when \({1982^{1982}}\) is divided by \(37\)<span class="s1">.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(74 = 2 \times 36 + 2\) <strong>OR </strong>\(\gcd (36,{\text{ }}74) = 2\) <strong><em>(A1)</em></strong></p>
<p>\(2 = ( - 2)(36) + (1)(74)\) <strong><em>M1</em></strong></p>
<p>\(1982 = ( - 1982)(36) + (991)(74)\) <strong><em>A1</em></strong></p>
<p>so solutions are \(a = - 1982 + 37t\) and \(b = 991 - 18t\) <strong><em>M1A1</em></strong></p>
<p>\(a,{\text{ }}b \in \mathbb{N}{\text{ so }}\frac{{1982}}{{37}} \le t \le \frac{{991}}{{18}}\;\;\;{\text{(}}15.56 \ldots \le t \le 55.055 \ldots )\) <strong><em>(M1)(A1)</em></strong></p>
<p>\(t\) can take values \(54\) or \(55\) only <strong><em>A1AG</em></strong></p>
<p>(Or the solutions are \((16,{\text{ }}19)\) or \((53,{\text{ }}1)\))</p>
<p> </p>
<p><strong>Note: </strong>Accept arguments from one solution of increasing/decreasing \(a\) by \(37\) and increasing/decreasing \(b\) by \(18\) to give the only possible positive solutions.</p>
<p><em><strong>[8 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(1982 = 53 \times 36 + 74\)</p>
<p class="p1">\(1982 = 55 \times 36 + 2\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({1982^{36}} \equiv 1(\bmod 37){\text{ }}({\text{by FLT}})\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1">\({1982^{1982}} = {1982^{36 \times 55 + 2}} \equiv {1982^2}(\bmod 37)\) <span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1">\( \equiv 34(\bmod 37)\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">so the remainder is \(34\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>\(1982\) in the base can be replaced by \(21\)<span class="s1">.</span></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award the first <strong><em>(M1) </em></strong><span class="s2">if the \(1982\) </span>in the experiment is correctly broken down to a smaller number.</p>
<p class="p3"> </p>
<p class="p3"><em><strong>[5 marks]</strong></em></p>
<p class="p3"><em><strong>Total [13 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using Fermat’s little theorem, show that, in base 10, the last digit of <em>n</em> is always equal to the last digit of \({n^5}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that this result is also true in base 30.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) using Fermat’s little theorem \({n^5} \equiv n(\bmod 5)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({n^5} - n \equiv 0(\bmod 5)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">now \({n^5} - n = n({n^4} - 1)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = n({n^2} - 1)({n^2} + 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = n(n - 1)(n + 1)({n^2} + 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence one of the first two factors must be even <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>i.e.</em> \({n^5} - n \equiv 0(\bmod 2)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">thus \({n^5} - n\) is divisible by 5 and 2</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence it is divisible by 10 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">in base 10, since \({n^5} - n\) is divisible by 10, then \({n^5} - n\) must end in zero and hence \({n^5}\) and <em>n</em> must end with the same digit <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) consider \({n^5} - n = n(n - 1)(n + 1)({n^2} + 1)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">this is divisible by 3 since the first three factors are consecutive integers <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \({n^5} - n\) is divisible by 3, 5 and 2 and therefore divisible by 30 </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">in base 30, since \({n^5} - n\) is divisible by 30, then \({n^5} - n\) must end in zero and hence \({n^5}\) and <em>n</em> must end with the same digit <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [9 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were very few fully correct answers. If Fermat‟s little theorem was known, it was not well applied.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Write 57128 as a product of primes.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Prove that \(\left. {22} \right|{5^{11}} + {17^{11}}\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(457\,128 = 2 \times 228\,564\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(228\,564 = 2 \times 114\,282\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(114\,282 = 2 \times 57\,141\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(57\,141 = 3 \times 19\,047\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(19\,047 = 3 \times 6349\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(6349 = 7 \times 907\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">trial division by 11, 13, 17, 19, 23 and 29 shows that 907 is prime <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \(457\,128 = {2^3} \times {3^2} \times 7 \times 907\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by a corollary to Fermat’s Last Theorem</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{11}} \equiv 5(\bmod 11){\text{ and }}{17^{11}} \equiv 17(\bmod 11)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{11}} + {17^{11}} \equiv 5 + 17 \equiv 0(\bmod 11)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">this combined with the evenness of LHS implies \(\left. {25} \right|{5^{11}} + {17^{11}}\) <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Some candidates were obviously not sure what was meant by ‘product of primes’ which surprised the examiner.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">There were some reasonable attempts at part (c) using powers rather than Fermat’s little theorem.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows the graph G with vertices A, B, C, D, E and F.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 26px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Determine if any Hamiltonian cycles exist in <em>G</em> . If so, write one down.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Otherwise, explain what feature of G makes it impossible for a Hamiltonian cycle to exist.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Determine if any Eulerian circuits exist in <em>G</em> . If so, write one down.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Otherwise, explain what feature of <em>G</em> makes it impossible for an Eulerian circuit to exist.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) any Hamiltonian circuit ACBEFDA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) no Eulerian circuit exists because the graph contains vertices of odd degree <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (b) were well answered by many candidates. In (c), candidates who tried to prove the result by adding edges to a drawing of G were given no credit. Candidates should be aware that the use of the word ‘Prove’ indicates that a formal treatment is required Solutions to (d) were often disappointing although a graphical solution was allowed here.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following diagram shows a weighted graph.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_10.52.09.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Use Kruskal’s algorithm to find a minimum spanning tree, clearly showing the order in which the edges are added.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Sketch the minimum spanning tree found, and write down its weight.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(a) use Kruskal’s algorithm: begin by choosing the shortest edge and then select a sequence of edges of non-decreasing weights, checking at each stage that no cycle is completed <strong><em>(M1)</em></strong></span></p>
<table border="0">
<tbody>
<tr>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; font-size: medium; line-height: normal;">choice </span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; font-size: medium; line-height: normal;">edge </span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; font-size: medium; line-height: normal;">weight</span></td>
</tr>
<tr>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">1</span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">BG</span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">1</span></td>
</tr>
<tr>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">2</span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">AG</span></td>
<td><span style="color: #3f3f3f; font-family: 'times new roman', times; line-height: normal; font-size: medium;">2</span></td>
</tr>
<tr>
<td><span style="font-family: 'times new roman', times; font-size: medium;">3</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">FG</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">3</span></td>
</tr>
<tr>
<td><span style="font-family: 'times new roman', times; font-size: medium;">4</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">BC</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">4</span></td>
</tr>
<tr>
<td><span style="font-family: 'times new roman', times; font-size: medium;">5</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">DE</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">5</span></td>
</tr>
<tr>
<td><span style="font-family: 'times new roman', times; font-size: medium;">6</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">AH</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">6</span></td>
</tr>
<tr>
<td><span style="font-family: 'times new roman', times; font-size: medium;">7</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">EG</span></td>
<td><span style="font-family: 'times new roman', times; font-size: medium;">7</span></td>
</tr>
</tbody>
</table>
<p><strong style="line-height: normal; font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><strong style="font-family: 'times new roman', times; font-size: medium; background-color: #f7f7f7;"><em>A3</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>A1 </em></strong>for steps 2–4, <strong><em>A1</em></strong>for step 5 and <strong><em>A1</em></strong>for steps 6, 7.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> Award marks only if it is clear that Kruskal’s algorithm is being used.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks] </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">(b) weight \( = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><br><img src="images/Schermafbeelding_2014-09-17_om_10.54.42.png" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>FT </em></strong>only if it is a spanning tree.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman'; min-height: 23.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Well answered by the majority of candidates.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; line-height: 12.1px; font: 24.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <span style="color: #000000;"><em>G </em></span>be a simple, connected, planar graph. </span></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Show that Euler’s relation \(f - e + v = 2\) is valid for a spanning tree of G.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 22px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) By considering the effect of adding an edge on the values of <em>f</em>, <em>e</em> and <em>v</em> show that Euler’s relation remains true.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that <em>K</em><sub>5</sub> is not planar.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) A spanning tree with <em>v </em>vertices and (<em>v </em>−1) edges where <em>f </em>= 1 <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>f </em>− <em>e </em>+ <em>v </em>=1 − (<em>v </em>− 1) + <em>v </em>= 2 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">So the formula is true for the tree <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Adding one edge connects two different vertices, and hence an extra face is created <strong><em>M1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This leaves <em>v </em>unchanged but increases both <em>e </em>and <em>f </em>by 1 leaving <em>f </em>− <em>e </em>+ <em>v </em>unchanged. Hence <em>f </em>− <em>e </em>+ <em>v </em>= 2 . <strong><em>R1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Using \(e \leqslant 3v - 6\) , <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for \({K_5},{\text{ }}v = 5\) and \(e = \left( {\begin{array}{*{20}{c}}<br> 5 \\ <br> 2 <br>\end{array}} \right) = 10\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">but 3<em>v </em>− 6 = 3(5) − 6 = 9 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">9 is not greater or equal to 10 so \({K_5}\) is not planar <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [12 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a)(i) was done successfully but many students did not read part(ii) carefully. It said <strong>‘adding an edge’ </strong>nothing else. Many candidates assumed it was necessary to add a vertex when this was not the case. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (b) was not found to be beyond many candidates if they used the inequality \(e \leqslant 3v - 6\)</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Write down Fermat’s little theorem.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) In base 5 the representation of a natural number <em>X</em> is \({\left( {k00013(5 - k)} \right)_5}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This means that \(X = k \times {5^6} + 1 \times {5^2} + 3 \times 5 + (5 - k)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In base 7 the representation of <em>X</em> is \({({a_n}{a_{n - 1}} \ldots {a_2}{a_1}{a_0})_7}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({a_0}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Given that <em>k</em> = 2, find <em>X</em> in base 7.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">if <em>p</em> is a prime \({a^p} \equiv a(\bmod p)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">if <em>p</em> is a prime and \(a\) </span><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAMCAIAAADUCbv3AAAAY0lEQVQYlWP4jw6+35ybXrb3NYTDgC779/pc79q9H/9il/57c6532d6PMC7Ds7XpDNiBctzaR6i6UU1GNxzNZJIMxzAZxfC/Nxekz72OIkm04X+vz01fcBNNL9xwrCb///8fAFdnB66zVDStAAAAAElFTkSuQmCC" alt> \(0(\bmod p)\) then \({a^{p - 1}} \equiv 1(\bmod p)\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for <em>p</em> being prime and <strong><em>A1</em></strong> for the congruence.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({a_0} \equiv X(\bmod 7)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = k \times {5^6} + 25 + 15 + 5 - k\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">by Fermat \({5^6} \equiv 1(\bmod 7)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = k + 45 - k(\bmod 7)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = 3(\bmod 7)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a_0} = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \(X = 2 \times {5^6} + 25 + 15 + 3 = 31\,293\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X - {7^5} = 14\,486\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X - {7^5} - 6 \times {7^4} = 80\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X - {7^5} - 6 \times {7^4} - {7^2} = 31\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X - {7^5} - 6 \times {7^4} - {7^2} - 4 \times 7 = 3\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = {7^5} + 6 \times {7^4} + {7^2} + 4 \times 7 + 3\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = {(160\,143)_7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(31\,293 = 7 \times 4470 + 3\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4470 = 7 \times 638 + 4\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(638 = 7 \times 91 + 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(91 = 7 \times 13 + 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(13 = 7 \times 1 + 6\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(X = {(160\,143)_7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [11 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Fermat’s little theorem was reasonably well known. Not all candidates took the hint to use this in the next part and this part was not done well. Part (c) could and was done even if part (b) was not.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that, for a connected planar graph,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[v + f - e = 2.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Assuming that \(v \geqslant 3\), explain why, for a simple connected planar graph, \(3f \leqslant 2e\) and hence deduce that \(e \leqslant 3v - 6\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) The graph <em>G</em> and its complement \({G'}\) are simple connected graphs, each having 12 vertices. Show that \({G}\) and \({G'}\) cannot both be planar.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) start with a graph consisting of just a single vertex <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for this graph, <em>v</em> = 1, <em>f</em> = 1 and <em>e</em> = 0, the relation is satisfied <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow solutions that begin with 2 vertices and 1 edge.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to extend the graph you either join an existing vertex to another existing vertex which increases <em>e</em> by 1 and <em>f</em> by 1 so that <em>v</em> + <em>f</em> – <em>e</em> remains equal to 2 <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">or add a new vertex and a corresponding edge which increases <em>e</em> by 1 and <em>v</em> by 1 so that <em>v</em> + <em>f</em> – <em>e</em> remains equal to 2 <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore, however we build up the graph, the relation remains valid <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) since every face is bounded by at least 3 edges, the result follows by counting up the edges around each face <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the factor 2 follows from the fact that every edge bounds (at most) 2 faces <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(3f \leqslant 2e\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">from the Euler relation, \(3f = 6 + 3e - 3v\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">substitute in the inequality, \(6 + 3e - 3v \leqslant 2e\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(e \leqslant 3v - 6\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) let <em>G</em> have <em>e</em> edges <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since <em>G</em> and \({G'}\) have a total of \(\left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 2 <br>\end{array}} \right) = 66\) edges <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">it follows that \({G'}\) has 66 – <em>e</em> edges <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for planarity we require</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(e \leqslant 3 \times 12 - 6 = 30\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">and \(66 - e \leqslant 30 \Rightarrow e \geqslant 36\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">these two inequalities cannot both be met indicating that both graphs cannot be planar <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [18 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">Parts (a) and (b) were found difficult by many candidates with explanations often inadequate. In (c), candidates who realised that the union of a graph with its complement results in a complete graph were often successful.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State Fermat’s little theorem.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">if <em>p </em>is a prime (and \(a \equiv 0(\bmod p)\) with \(a \in \mathbb{Z}\)) then <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({a^{p - 1}} \equiv 1(\bmod p)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note</strong>: Accept \({a^p} \equiv a(\bmod p)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Fermat’s little theorem was reasonably well known. Some candidates forgot to mention that <em>p </em>was a prime. Not all candidates took the hint to use this in the next part.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The positive integer <em>p</em> is an odd prime number.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 34.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that \(\sum\limits_{k = 1}^p {{k^p} \equiv 0(\bmod p)} \).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that \(\sum\limits_{k = 1}^p {{k^{p - 1}} \equiv n(\bmod p)} \) where \(0 \leqslant n \leqslant p - 1\), find the value of <em>n</em>.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using Fermat’s little theorem,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({k^p} \equiv k(\bmod p)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{k = 1}^p {{k^p} \equiv } \sum\limits_{k = 1}^p {k(\bmod p)} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv \frac{{p(p + 1)}}{2}(\bmod p)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv 0(\bmod p)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since \(\frac{{(p + 1)}}{2}\) is an integer (so that the right-hand side is a multiple of <em>p</em>) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the alternative form of Fermat’s little theorem,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({k^{p - 1}} \equiv 1(\bmod p),{\text{ }}1 \leqslant k \leqslant p - 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({k^{p - 1}} \equiv 0(\bmod p),{\text{ }}k = p\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{k = 1}^p {{k^{p - 1}} \equiv } \sum\limits_{k = 1}^{p - 1} {1{\text{ }}( + 0)(\bmod p)} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \equiv p - 1(\bmod p)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(so <em>n</em> = <em>p</em> − 1)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Allow first </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> even if qualification on </span><em style="font-family: 'times new roman', times; font-size: medium;">k</em><span style="font-family: 'times new roman', times; font-size: medium;"> is not given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Only the top candidates were able to produce logically, well thought-out proofs. Too many candidates struggled with the summation notation and were not able to apply Fermat’s little theorem. There was poor logic i.e. looking at a particular example and poor algebra.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Only the top candidates were able to produce logically, well thought-out proofs. Too many candidates struggled with the summation notation and were not able to apply Fermat’s little theorem. There was poor logic i.e. looking at a particular example and poor algebra.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; font: 22.0px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Use the Euclidean algorithm to find the gcd of 324 and 129.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Hence show that \(324x + 129y = 12\) has a solution and find both a particular solution and the general solution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Show that there are no integers <em>x</em> and <em>y</em> such that \(82x + 140y = 3\) .</span></p>
<div> </div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(324 = 2 \times 129 + 66\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(129 = 1 \times 66 + 63\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(66 = 1 \times 63 + 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">hence gcd (324, 129) = 3 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Since \(\left. 3 \right|12\) the equation has a solution <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 = 1 \times 66 - 1 \times 63\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 = - 1 \times 129 + 2 \times 66\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 = 2 \times (324 - 2 \times 129) - 129\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(3 = 2 \times 324 - 5 \times 129\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(12 = 8 \times 324 - 20 \times 129\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\((x,\,y) = (8,\, - 20)\) is a particular solution <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>A calculator solution may gain <strong><em>M1M1A0A0A1</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">A general solution is \(x = 8 + \frac{{129}}{3}t = 8 + 43t,{\text{ }}y = - 20 - 108t,{\text{ }}t \in \mathbb{Z}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(324x + 129y = 12\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(108x + 43y = 4\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(108x \equiv 4(\bmod 43) \Rightarrow 27x \equiv 1(\bmod 43)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 8 + 43t\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(108(8 + 43t) + 43y = 4\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(864 + 4644t + 43y = 4\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(43y = - 860 - 4644t\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(y = - 20 - 108t\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">a particular solution (for example \(t = 0\)</span><span style="font-family: 'times new roman', times; font-size: medium;">) is \((x,\,y) = (8,\, - 20)\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) <span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The left side is even and the right side is odd so there are no solutions <strong><em>M1R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\gcd (82,\,140) = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">2 does not divide 3 therefore no solutions <strong><em>R1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [11 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This problem was not difficult but presenting a clear solution and doing part (b) alongside part (a) in two columns was. The simple answer to part (c) was often overlooked.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The weights of the edges of a graph <em>G</em> with vertices A, B, C, D and E are given in the following table.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAgkAAACXCAIAAAAQ81+1AAAYDklEQVR4nO2dzWsbWbrG859IUCsJBAneiLvIqrm4vRDGZBHwxkEWOAsPWTT0QkJhQnYDEha5NDQ0JRICzUBSwk2mIbgpDIO5OBQzF7IQBT1ggqiFF6aohRHm8NxFScdlfTi9aL/noHoezqYlNVZ+es95zle97z2nUGRjY2NjY8u2e06hiNyLEEgAhEACAAgBAEBvmIgQSACEQAIACAEAvUGLEEgAhEACAAgBAL1BixBIAIRAAgAIAQC9QYsQSACEQAIACAEAvUGLEEgAhEACAAgBAL1ByzAENezXHmy6Q2XuK4gT+DKoP1h0c67a6HhBNJb9MhOZC4M49L1+szaBUNrtvjsOk6v4n8f/vhL9HtIEIq+x6PZkpd55fxhEhvqDNISroHt/+V3S+51ANgZS0RsmMgtBhe5moejU3NCcOZggoGK/XSkUncL+ILoCVBJ+7NarTqHolNp+bICFmTBIPvfrVadQ3mi+nZriOArettbL8uOCCQKXobvtFIpO4UHD+wJARSe9etUpFCv1Hz6ZmCUY7QsTCACAODzqNar0BqMyCuEi6Gw5haJT2OoGF6a+hBECV0Fn7dobsq9ke4icDEDQxtA+mp0mJ6fdrV4OvOEq8vadmR89Oe2ul51CsbLnjcQnCUb7wkzkj0cffhVeO6aiN0xkEkLsP699+9/pUrrpx4a+hWXe8LDln8t/H3EI45H3rFIoOoXtfng5965a/T0lYLE3XC8mDESCFd5w9X+DDwamR1r0honMQRiPvPbzo+N+rWxwLwVWeMN0I6VQbRycGNlrloaghpPf3eh2YlbWeMN0o7VQXBPfU7HAG+Kh++ypiaWzFr1hImMQ1LC/9cKPL6fzx7KpE2mj/SHbaq3Xp3k5hNQnsXUvEv3DS2WPNxiEY0dfMLOtqkVvmMgUBBW+edo5TQDEfqtUNDiFtGPd4E3Ootdf+nk4hKQ3APSGVDfWDSr6dLDPdYMVMgTh3G/uTzeaz/3mQ4Mn0hZ4AwCokfe0ZOzoRRqC6QnBvOzxhnzvKfG8wRqZgaCHhpnL3XkYFgEs8obrLXgT17rFIUwnBKVng5GZRzpmZI036DudeT2LvtZl6P+v/LKS3jCRCQjjkdd+no17PSyaOJG2xRumfpkTg5yuk8ob6dbizff818c52E5Z5A3qbLBX5R1WAEhO/8f9l/wtVnrDRPKXFyP/5casB+gbjcVK/c0wEe0TRp/3mdzg1A89OaW9/tDAbV4jEJLhm0YpfSD8Yzj50cdR4HX3vpOHYMOzb0iGg2Ytr8++ZWdF6QncN6ae9aE3ANLRkASdb+duI2RfTFtmNn33Eg+DZTkzai33Q+5yZiSh7/3UWi87N3Jm5ODJ8MU5M8obzZ8Gfji7kJKSNITbc2aYe9aH3gCYzplhg0gAhEACAAgBAL1BixBIAIRAAgAIAQC9QYsQSACEQAIACAEAvUGLEEgAhEACAAgBAL1BixBIAIRAAgAIAQC9QYsQSACEQAIACAGA9gY2NjY2NrZsu+fQJDlTIAEAhEACAAgBAPeUtAiBBEAIJACAEADQG7QIgQRACCQAgBAA0Bu0CIEEQAgkAIAQANAbtAiBBEAIJACAEADQG7QIgQRACCQAgBAA2OENl6G7bbzulWkI5iVNIAl97+duvTaXY1Il4fHgXadxf+WLWMShf/i+s7s2X6kiCX/r7E6ztfd+C+UyddsSBtcEyhvNt8J5eQ2OBio6fdOsOYWiU9rtHhnLRAsrvGFS0GZ7WhrTjOgNogTUsL+13dipzucfVqH7aGf3SWnlCxxdhu7ek/rjynwVI3U22KtOC3gsrPNxh7IiDNTZLwc/po44Kemx3gsEM5YbGw2S025tr3caqUlVj+pT78zUnNm4N6gk6G2ks4P5uleCojfIE1Chu7k4N/1l6G6vujcAmEyMZrxhFosa9mvfiGXwtyEM1O8nx5kKqcvj5K5kaDS4DN3tbGGfkfesYqIXpDLuDed++/HGN8YKYWrRG2wYFKbKtTcg9lulzFQp9luC22s2hcFUsd8q5cAb1LBfe7DpDvUvLW+KWRn2BjXy/tL+8GlSEdAYBdAb7BoU8u0NuAg6W06h2nA/J2rk/7XdO43EQNgUBlPFfuv+s8FI7sjBzGgQ+61SOesNC14RlFlvuAzd/ZZ/Pi2nXjR4Ik1vsGlQyLk3ACr6dLCbraQtJpvCYPJ+7L/YlN1wNrduKN8YA8UXTFkZ9QY17O+9ChIFnPvNh46JnqBFb7BpUMi9NyAOvVfdzvcbhaKz/tIXvKVjUxgAAJLTbv2V5EE0jI0GKvbblXS9CEBFwevmhtEh0ZQ3qNh/8WiyXEqhmDyRFodwGU520hY1E+snmwaFnHtDPHS/+4t3pgAVHT1fL0ve0rEpDABcBAcv+0O5K7ypzM0U4/Co1ygVnUK10Xnbb9bMbqWY8ga9VrjZDJ1Ic91g06CQa29QobuZnS0mp931B2KbzjaFwXh0+OMbcWOAJaOB7P20eRnzBjXy/tLOdgk9jzazv2ZFNBiVTYNCnr0hXUNndxLO/eY3+fOGceT/2PNH0391PHz99nh1L2vNSo389pbxa/0GvEFFR8/XZy3x+kS6tJenVaQtsmZQQL69IV0olKfPvqlk+KYheEvHjjCIQ6+9YW6j1ehoEIf+37v1bxsHJ3K30xbJgDdcBZ01/XvXvWj+xULRKTxoeF8kvxW9QZbAzR3F2bsZOgykL/AJQtBnbMX5WxjXiRNWPGfGwjAYj7xnldndZtFIMLrNXt5our7gL75Mxp99s0WEQAIgBBIAQAgA6A1ahEACIAQSAEAIAOgNWoRAAiAEEgBACADoDVqEQAIgBBIAQAgA6A1ahEACIAQSAEAIAOgNWoRAAiAEEgBACAC0N7CxsbGxsWXbPYcmyZkCCQAgBBIAQAgAuKekRQgkAEIgAQCEAIDeoEUIJABCIAEAhACA3qBFCCQAQiABAIQAgN6gRQgkAEIgAQCEAIDeoEUIJABCIAEAhADAkDd8GdQfLLoyVW10vECw/GFWshDi0D9839ldmy8GmYS+93O3XpMvYsH+AFvCYFHZK6kM1dJhsDTgx9HpD41S0SmUN5peuMo1QVUSHg/edRr3lyelV2eDvYfyOYmNrBt0guL9QXQFqCT82K1XnUIe6r5dhu7ek/rjSqE4m7hfDftb242dqpECR/QGWBIGN7KUp00uQ7VoGCwNeJX86/DNaaQAFZ306tVFJbXvUJIQVOg+2tl9Urpl6EuTlhvIV29mT2lasCH1huwr0pUbUklDWFpE/mul1e9M9AZYEQYq9l+9uK53BuDcb+6LFZSXD4MFAa/+c3z8ZUpAxX67IjtlFIdwSzErlQSvGt9/3yjRG3JSE5TeYKUsCINxFJ5lK0Gq0N1c6ZJnXwv4y9DdEa6OaZE3JKfd+qtgdNTKqzeMo+Bta73sFKqmKuFZMChM36E3mJM9YTDVZejuPfXOVrjk2W0Bn4S+2260j4THBGu84SLofNcNLhD7OfSGbKu1Xp+aKpFqz6BAbzAoe8Lg+gNbL1Z6O2VZwGdqpq63B7I1Mu3wBpUErxrpgimX3qDXDd7kLHr9pW/iqpI9gwK9waDsCYPJ+6H7aHWPYVPdGvDTHYXSs8FIbliwwhuS0177cHLulGNvAAA18p6Wis78tQ0R2TMo5Mgb1LBfKy/JASndE1LZEwYAgMvQ3ReOBMu84Q994E+XBd5wERz87doOc+4N1yPF/U5wdev/fAeyZ1DIkTfYJ3vCYPKu7IYSrPQGqGG/9k2+vGHBPea0bUveWLPGG6Y4uG6gN5iSPWEAExtKsNMbYr91P397Slnlad2gD5omNpg+4eIUik5prz+UtwaLBgV6g0HZEwZGNpRghzeokfe0NL2ZokZ+e7vhfs7pHdZUufGGZTkzai33Qw5yZmQuYMwuEm8mSxC81Q56AwBbwiB9f9jfexXI5oqAdBgsCfjkcz+dKRaKlXpnEEjfXhSFcGP7aIkB5MYbbBQhkAAIgQQAEAIAeoMWIZAACIEEABACAHqDFiGQAAiBBAAQAgB6gxYhkAAIgQQAEAIAeoMWIZAACIEEABACAHqDFiGQAAiBBAAQAgDtDWxsbGxsbNl2z6FJcqZAAgAIgQQAEAIA7ilpEQIJgBBIAAAhAKA3aBECCYAQSAAAIQCgN2gRAgmAEEgAACEAoDdoEQIJgBBIAAAhAKA3aBECCYAQSAAAIQAw7Q1x6Hv9Zm1yZaq02313HCZX8T+P/73atX2S0Pd+7tZr8zVyk/DjpDZqodrofAwF03DKhoFKwuPBu07j/myN3JvZSdMmWs9E5g9ZK2kCS/vCRCoKfnnXaZSKt6Ww/rNlR1/AdUnUQrVxcCKcjdacN0zS8JY3mm+nebmnIFa77psa9re2GztVZ65Igxp5T0vVSap6NfLbNckyR5JhoEL30c7ukwUd/mbS5rQJ5iqnN4gSWN4XAADj6PSHRqna6PzdD0VrutjRF1QS9DbWX/rRGGrkt7c2OqfCRSxMeIM2hvbRrBkmp92t3ip7A4DFBXxm63uo0N1c2bkSFtcziY+7f82GhIr9F48E09bTG+QJLClmpZKgt1Ha7Z1KF2+AJX1hphJq7LdKcgtoGPKG8ch7Vlm6V6BWf09pcX9It1O2usGF/s+1FV03AFjYH1T0++/JTPfYEe4PYn/LTtniDclpd/3hU+9M3hhgSV8I3c3Zwl/fSJb3MeENativlYX3Cr4qC7wh7Q/ltCqqio5eNH/8JFgFz4b+MCMVuo/2vBGL3wnKDm+4DN1tZ73ZT08aVvzsDYv6wvwr537zofD+qrg3RF4j3Ueue5HoH75NVnhDtm62uHFa0B/mPyBdMJneYIU3qGG/9mB6EqmS4ZtGqSy5225BX5h3AnqDIVniDUiGg06n26wtPoy5S1nQH25KDftbL8SOW1LRG6zwhthvlbKvXIbu9kpfV6M3pNK1s7mnNLun9Lm/1xyMxsA48l9uFPI2V7ohFbqPBI9bUhkaGZclwhQ9e0xlgzf8kVfuVBb0hXzuKel7iqVng5HcfvrtssAbLkN3O/PbqyTobeRrrjTzrvSGErhusMMbEPutUjl77jp3MHu3sqEvzF5TVMN+7cGqn0VPLvIXnYXzYjXyXx/L7zVZ4A1z8wLZW2s29IdrmdhQAr3BEm/Aud98WLm+hqBiv11Z5cdceIf1Wun50swNhHEUeN297/pD4Y0EwApvSBcK02ffEA/dvTXBWzpW9IepjGwogd5gizfceA5URSe9+s70breE7OgL+Xz2LVUS+t5PrfXyzZwZZo4gBCHcfPT3xmxIPyK/6vf29JlToegUynMr5cvQbUqOBVr0BlkCt/SFTP6Y9eabQPQJOGv6QvpkeNEp1FqvpR8CNJtPySIRAgmAEEgAACEAoDdoEQIJgBBIAAAhAKA3aBECCYAQSAAAIQCgN2gRAgmAEEgAACEAoDdoEQIJgBBIAAAhAKA3aBECCYAQSAAAIQDQ3sDGxsbGxpZt9xyaJGcKJACAEEgAACEA4J6SFiGQAAiBBAAQAgB6gxYhkAAIgQQAEAIAeoMWIZAACIEEABACAHqDFiGQAAiBBAAQAgB6gxYhkAAIgQQAEAIAE97wZVB/sOC+VGm3++7XIDJW6kcUQhL63s/dem2udk0cHvUaaVLG1c49CZWEx4N3ncb9uRzdKvp0sFspFJ1CreUNJZMSQxpCHPqH7zu7a8uykasoOPy5W686q1zyzEZZFAY3srTmoH7DdR3EtGS0Hg5Kuz3pTLQTyUFQw/7WdmNnvsOPR4c/9I7CBBrI1qrmrFeh+2hn90mpOJez/uLf3rtP0XianVhuTEwlCOEydPee1B9XCsXKokFBRSe9erVS77z3Q+Gs/YJ/zVJZEwbjkfesoifQskWUDe0pRV4j6w0AcBF0tpyCsUKhwhAW1DNR/zk+/pJJXz/s18oLR407kngYLKqD+PvJ8fWvf+43H0oSgDyEZb9yctpdf9g4OJGfKNEbYFUY1AxUP0xljzdcLyaEh4NU5r1hVtIjow3ecENq2K89Fq7wY8egcBF0tiqCJf+yojfAljBQsd+uFMobzZ8GsmvHVBZ5QwrIKRSd+53gSvobWekNtafemWTpcKk/leoWb1BJ6Peb+8996eHRhkFBhe5modZy36ZVzyr13m+h3GSJ3gA7wuB6PCwUnUJ5o+kJ18S0yRuuj6n3B5G0OVjnDbHfqvWCVa0JCiz3Bl0n0kx/kPxziwaFy9Ddvr6JkHzu16vOulwk0BtgRRjot6LgMC2cXM5HvWh6w1e84SLofLfi2ym37ympKHjd3CgUhbdWLBgUZvcSVehuLiipfVeiN8CKMJj5wMhv127bgL0D2eQN3FOavpkEP7bczyt9fRNfP2/4+gf+fJkfFP7IK3cpA6PBjc2TmSZnilmZD4N5xX5L9tqeTd4wvcmb87NoNfq191raGGCjN0CF7mbevCHdUsveVlTDfu0B1w2SsiAMFn5mZ/Wfb1jkDdObvLm9w5q+Hvm9A396c1Elw3f941V96Omr3qBiv72Wuz0lFfvtSrYXxH6rJPfQE70BVoTBnGL/eVv6PrcFz74hDr32Rk6efQOw2BtUEnqt9ZnF9QoPCvPeMB55zyrTY1gVHT2v7feHomtIKwYFdTbYq1bqb4aJgoo+HextCh5C0htgRxioKPjlcJIaQUUnvWbHl00bYU3OjPVm3zsWvpSSlSAEfQ/nxrOOauQ9Lc1hEXwSUjQMbmQC0HvKKhm+maQMKVQbHU8+h4oghPT2+pJJQBL+1pkmDnktOl2iN8COMFDR0fN0plja7b4zMDYa2lOyT4RAAiAEEgBACADoDVqEQAIgBBIAQAgA6A1ahEACIAQSAEAIAOgNWoRAAiAEEgBACADoDVqEQAIgBBIAQAgA6A1ahEACIAQSAEAIALQ3sLGxsbGxZds9hybJmQIJACAEEgBACAC4p6RFCCQAQiABAIQAgN6gRQgkAEIgAQCEAIDeoEUIJABCIAEAhACA3qBFCCQAQiABAIQAgN6gRQgkAEIgAQCEAMCIN1wFnbXlt6bWDNR8AwxGw7T4pVOoNjof85GJFoBKwuPBu07j/vL6DepssPdQuOyXLIQ49A/fd3bX5hP366gQz1ov3RGS0Pd+7tZri+pcZTMWixaAozfA3LpB/+qZ0tBJ+Ftn97/y5Q0XQWencXASqUnVeOHyyFlJElCh+2hn90mpuLy2T1rrSbokpCCEy9Dde1J/XFlQ6PAi6DzeaB9FKk3U/FiycrhoR1DD/tZ2Y6fqLKxzdSNrvVwhE9AbAJjzhiTofDvrDQDU2T8OP+fHG2ZqXqqR91S2JGxW4gRuqfumkuBV4/vvG6UV9gYAS4q63IgKFfvtyqqW8QCwtAbiRdDZzU1fsFG2eMNV8OEfkRFTmMgEhMvQ3Z6rDCxXNX5GFnlDctqtvwpGR608esNcVKx6TdDF3pBWfzJU8oveAFu8Ifncr38/yJ03zFWNX/CKnKzxhoug8103uEDs59Eb5l+R5WCHN1yG7vb1MeR6exCudGlYK2XcG3Tbz583pB0gOyU895sP871uUEnwqpGWR86nN8z/q/PoDanGUfCh36w5haKz3gsEVw/0BljgDfuD6EpFJ708rhsmC+dJ1XiMo+Bta/2B8GioZYU3JKe99uHkNJ7esOyVu5RN3pBqHPkvN277wJ8vegMs8Qbk9LwBgErCj9161SkUK/XOe7e5IXsfIysLvOEiOPjbYDSe/Fc+vYF7SgskvZ42BGHZzX4zY4It3nAt9bt/PBL/PjbMFC5Dd9vUhhJs8Ib0+NFo3zDvDXNhoEJ3c4UJ/CFvuAzdHT7fICzbvEElwZt+kIh/H+PRMI78lxuym6ozMu8NM8rnuoF3WBfo3G//bWmc3IFMjwZWyPizb5mYUFHgdRolM4fS5qJBJeHx+87uWv2HT9H46x+/M9EbYIc35OjZNwALvUFFweGvQdodVPTpoP3CF30klN4AC3Nm3DZY3KVMRIOK/XalUHTWm30/NLBWuilRAje2j5YYwIp7w/TXX7hvpqJPB7tpbLwJVjhnRjYrRvH69rYa+e2aM0kk83df9gIr6A0AmGtPixBIAIRAAgAIAQC9QYsQSACEQAIACAEAvUGLEEgAhEACAAgBAL1BixBIAIRAAgAIAQC9QYsQSACEQAIACAEAvUGLEEgAhEACAAgBgPYGNjY2Nja2bPt/EIOFc6Fb8hMAAAAASUVORK5CYII=" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Starting at A, use the nearest neighbour algorithm to find an upper bound for the travelling salesman problem for <em>G</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Use Kruskal’s algorithm to find and draw a minimum spanning tree for the subgraph obtained by removing the vertex A from <em>G</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Hence use the deleted vertex algorithm to find a lower bound for the travelling salesman problem for <em>G</em> .</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using the nearest neighbour algorithm, starting with A,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{A}} \to {\text{E, E}} \to {\text{C}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{C}} \to {\text{D, D}} \to {\text{B}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{B}} \to {\text{A}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the upper bound is therefore 9 + 10 + 16 + 13 + 11 = 59 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the edges are added in the order CE <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">BD <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">BE <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the weight of the minimum spanning tree is 37 <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we now reconnect A with the 2 edges of least weight <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>i.e.</em> AE and AB <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the lower bound is therefore 37 + 9 + 11 = 57 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[8 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-size: medium; font-family: times new roman,times;">The graph <em>G </em>has adjacency matrix <strong><em>M </em></strong>given below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><br><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAC4CAIAAAAjRJpaAAARKElEQVR4nO2db0wbZ57Hf1Vv90U1d1rrTqdDKresLKtcL7oostAtUXQHL4hSUeGoEUKkEcJVIoKqynRXkHQVyKqBVstkq8CLmtXKL+IS1duLRVonVy/F2QAroGB1jRxf1uRKC61papcEZCwcbGb2hQ3Yz4zNPPZgj+3f52UiP/zmmY/n7/P1D/gD5Mn8qNPPZfDBcMD7FyfJQiCSyVhCuODXM/ZbN4fNwzdv3/X4I3z0sXNyPridVXnzy0HZtnQHbyAi22h/8QbCEkcB6q2QDOez6lWvGD0b9B8NB7wznw7oNQDA1LZd6WfZ/t6ulhq1Sl1/wTTto5ypBCK+KWN7lepoa7/504mZacfH1/vP1tbq6rWnjJ4QTXmff2Y8XwkAjLb+XFcv+263oblGzYC6oWPwjjcYpRnKOW7+RRUAqOoNv2F3uNLZWMUcGXBJH4kobG+0/t7OJi2jbrEuSxzl4JwIeU2nGWAO9U5Jn+wkVqwtAKBmnXEFuIh/km2oAObkgGs9kwEj34z1vMSozgy51xK+0tGg+/dNqhrWGcyuPJ6P+KYG9RoAprZv3E/j7cZEd3nyUDzPb7mNuvecGegvLIwP+2yX2vPvRGiWPapRVzBQ1mlfpbM9jsi2Rb63GVQAZV0Oeik2lyxtKqjQmTxbglq9po6+6bWsy+N5bnWO1THAaNo/WZF+Kok4WbVgKD68/OfZZekntPSFbXpHJ6UOdkBORFcdl450fPSn918BUDdbFjM51YpsW3TV/ksVgMpgX6UdLTTLVqsAXjUvipxWuZW7Nyb9WZfH8zzPrdo7ygCgfsAl+cAj4sST+QkP5YErVWGRwIOFAM0OOBgnuCWrvpF1rnFLlmYGoG7Is0VvhWDSuaBrqEkDUNszQX3lGvUYj4ntwsxJ4QTPfWVpqgAoO256IPVLLnRiy228eGtFlsK4JWv7INVWH4QT3JZn6LjO5N3ieO5b2/lDADW900+oh4ltG6OtP9PS0tLS0nKqRs0A81K3bYH+Cj/qt73BAMAxoyej81jK8kQkCzrZGjr9Yk4QW9pizcqJ+Gin67VltN+Eg3DiyXSvTm9d4nie57nQ9DuHAMo67Ku0OzK2beW/tD0K85GA1zluM3bUMACaV9nxbym/7ZEVaxsAwHGTN4MzdJryRKZ7bbqX8pBEHifCAfcNQ/uIHMeJaHBpjG26lmcnuO9t51Wamsa48y2NNWoAYF6zLD2lG0j0esJxqRIANF12qgt7ngtP91UAQEXfdFiehxypzx0PzbpyAE1r/FshAZHrCd9t4yjlBU6qwja9H//RS3N0lN2J8Jdm/XGjO+Ha/umS5TUGyuqS/lECopMenu6tAAD6W8f18e5KBqDR5N2k+yBVefGnMgCqdqtP8uaK33fIXJh05HYiNMsePUccErjvbedVAIfemQ7RfEfFtm3nqj6DXRt7XqKq7ptaJ6uIBt3Xf33DK4Oy3IrjYg1ARYNxnqK+FE5wj++9fXk0w3OuYpzYWrG9WdlqFdyaBxxdWoBKvfTDKS9637Fg636JgfLavsnHGZwBNj3m1iMAR1qHZvx7j8mjwfvDF9/5bIX2wbnII7UvLBdOMFBe2zNKN9q6o6tMsBcjy/YLjV2OAF1VIoVRI58T3PfO4Z5GDQPa19jh8cXN3UnZWHQMGWrKAQDUuq4hR8J/pWJjcWLkevdJFQAAo645tXtdwmibL5mmqPffbo3Bh/ZrZ6sYYLQN57qusP3db+hO6gfuUQ6YWF78Av9MvZZhtA0G1jK3QvUIc3Fi5HrvaQ0AQMJFWOzWo+wtxzrVJXFCYUyd4f0P77gyed10gO87lEsk4HVO2EfsE3PuZYp3E6VCSTqBpAWdQEjQCYQEnUBI0AmEBJ1ASNAJhEQOJ7j1L+1Dl98bXcpgkQSSH7ZD0+/q/vt035++FT4Uy9qJyDeOvrPnTfMZrVpG8sn2d/+j//cX6q7OEq9msnMi8s1YT2PzkAuFKFC2v/vD6Z8+/19skhZCJySHMrgnrsHGsubh/xc5ZYQDnns264ht8kuZdIkGFz+fXswgFiBE3tqUPBovYd62Q3fbf/rs86f+8PXuSYR0QnIog9u8/7sG5gTrFCx35tbum9qqW65+Mj724QVdHe1LQpKw3zXCnj+uBoqEQkrkrU3Jo1HM2/IHL//TM/9y5taTuBWEE5JDGdySVV+p0lt9grUIjyeuVMGOVaFZtvpQs5lyaULSH/rB+7nn4advlcvghLy1KXk0unnb/qJT88yPNZ1TMSmSnZAayuCeugaPglbk7f72gvlkRcKyx9WJ7urMIx47RJysDMcJeWtT8mg7SJ63v179z+fg7099FNzmk52QHsoIugbqRd/uc4tmXVL+YmvZogdRe2iQxQl5a1PyaLtInrfIt1ePPgv//MpHj/gkJ6SHMrYfmI6XQZNlmfz/7XXHW8krhmILplXHjO5shJfDCXlrU/Joe0ift+0Zw7/Cs//Y+r+RBCdoQhl+WxsjWm58ybxg27JdfyqHE/LWpuTREsaVPm9PR5r/4ZlnXuz5vwQnKEIZESerhso2m0/4P/nfttRjKHgvKmHevuh58cfwo5c/2NxxgiaUEStXdDU9tzFxuVxk2yqaLF9lc18lhxPy1qbk0fagmbdHH7z8E4AXO12bMSeoQhmxyx+9ZVnkRil2LZKQ+w55jDqAOtaZ0a8D7CDPNaastSl5tF1o5i00Y9AAaAwzIeB52lBGLA/ZZhVdn8wtWfWVcHTQ9TT2qUd2w2GovuqkSnYIkOdeVN7alDzaDjTztunqfBHgJy9/8AjoQxlpneC5kGuwbuf5Jrdq7yjTttsENyiURJysGsp15ofZjSNvbUoeLQ7NvCU4QR/KSO8Ez/PhlbErdbWvXzMNdjXUnzdn+cp0L7Ogaui+bp2UEA9Jg7y1KXk02nlLOk7Qsq8TPM9zkcAC1e9q5RB5a1PyaFRk5cTeBar8hSF5IzimUwH83b+9/SU6gcRAJxASdAIhQScQkqyceDL25n8A6IxfZb7gA1EeT/965RjAz87cDBzQvShScOy9xkInkBjoBEKCTiAk6ARCgk4gJOgEQpLkBG2jJYlOKDbNx2NtYpBOUDVa2n/9hHLTfFhbSoTnDopGS/s5odw0H9aWhv2d4FM3WpJ07lBimg9rS1ebJCdSNVqS9A5MgWk+rC1tbcJ1VhSNln643fYCQN1vH6brx6G8NB/Wlr62pw9/WwfwQtvtH5KdkNRoKWfnDiWko0qntlTnDkmNltCJoqxN4vWEeKOlnDmhhMRc6dQmyYlUjZZyd9+hgMRc6dQmzYkUjZZyeC+a/8Rc6dQmwYnUjZakO6G0NB/Wlu4vJzpB22hpXyeUnObD2lJRYO9FSydpKC9UtRWYE0gOQCcQEnQCIUEnEBJ0AiFBJxASdAIhQScQkqyckLSmBik0hGtqKMDjRFGC5w6EBJ1ASNAJhASdQEhSO8EFv56x37o5bB6+efuuxx/ho4+dk/PBxB5PUpwomhSlFBRbW+Z50d1/9E0Z26tUR1v7zZ9OzEw7Pr7ef7a2VlevPWX0JHYR3DcbWEwpyoKtTYa8aOSbsZ6XGNWZIfdawkejQffvm1RUa3SLLEVZoLXJkBfdXLK0qaBCZ/IIPhbymjr6phMby6Z1othSlIVZmwx50dAsW60CeNW8KLJIi1u5e2PSn/AP6ZwouhRlQdaW0WjJTkQ9xmMUCaY0ThRfirIQa8tstCQnon7bGwwAHDN6JP39NE4UX2KuEGuTIRsY/0DC6Sc96ITCa5PBCS483VcBABV902EpNz9pnCi+FGUh1iZLXnR9vLuSEWQAU5H2GrPYUpQFWZssedGQ13SaAVV139Q6KVI06L7+6xuJt7bYS1LxtcmTF930mFuPABxpHZrx7z3wigbvD19857PkR2DYS1L5tWWbF90ZJvjQfu1sFQOMtuFc1xW2v/sN3Un9wD3BM9F911kVU4qycGujHS3NOqtIwOucsI/YJ+bcy0HRe1PsJXlw5LEzJb4rR0jQCYQEnUBI0AmEBJ1ASNAJhASdQEjQCYQEnUBI0AmEBJ1ASNAJhASdQEgSnBBpJDm/nPa9au6zgaWT5uMV0Usy4P38M+P5yliTn3Ndvey73YbmGjUD6oaOwTtekdfluc0Glk6aT1m9JIWNGiK+qUG9BoCp7Rv3E/s+fY+4vGfc0qLcNF/eayN6xIk2dOFW51gdA4ym/ZOVJMPSrrPKf8Ztf5SY5st/bcQ6K1En9nq61A+4pGaIFZBx2x8FpvkUUNu+54742F9ZmioAyo6bHiSkgXKWDSydNJ8SapPoRHz3E/+TsxxY6SS3lFCbVCfWpnuF6WJ0oihrk3rueGjWlQNoWq1LCVeZOcsGlk6aTwm1SXOC81n1KgBVu9WXeBeTu2xg6aT5FFCbFCe4FcfFGoCKBuN88oOIHGYDSyfNl//a9nGCi/i/sFw4wUB5rcjzr1xmA0snzZf32hKcSGgkGW9hf6ZeyzDaBgNrmRPd7fu+78hvxi09Sk7zFXkvyTxm3HJM0dSG78oREnQCIUEnEBJ0AiFBJxASdAIhwR5xCAn2iENI8NyBkKATCAk6gZCgEwgJOoGQoBMISZITYZHI6C7egGDPYy9JguKojXTCOW7+RRUAqOoNv2F3uNLZWMUcGXCRkQDsJVmUtQnPHRsT3eWCJZlbbqPuvRShD+wlWWS1ifQXdbJq4dLt8PKfZ5fJhlDYS7Ioa5PkxJP5CU9Q5MPYS7Ioa5PixJbbePHWisiHsZdkUdaWyonYwu2WlpaWUzVqBlqslE4UX2KudGrb/zgRDrhvGNpH0ImSqU3S9YTvtnHUL/Jh7CVZlLVJve8QJd1vFxVdirJ0aiN+u4hP6QT3+N7bl0dXpf92UbGlKEunNuE6q3VHV5nAiciy/UKj4HYIe0kWZW1J546NxYmR672nNQAAmprG+I1H/Naj7C3HOvHQKsd5UUx45qa2AsuLygvWJgq+K0dI0AmEJCsn0v+OLlKgCO9FKUAnihJ0AiFBJxASdAIhQScQEnQCIUEnEBJ0AiFBJxASdAIhIZ1IEw8UvqNbvvbz5wCeb50Kpf0bik3MKXk0Pn/zFppqfR7guZ9fW951Yqej5F48sL+3s0nLCFfp7HucUHBiTsmj5XneRM8dIh0bwj7bpXZaJ5SbmFPyaHmfN6lO8Pymd3SSSAdKup5QYmJOyaPtkL95k+REJPBgISByvMmdE0ruTKmANJ+8tUlxgluytg+KLe3PmRNK7kyphDSfvLWlcSIeDzxdry1LEffImRNK7kKohOSWvLXtf5yIBpfG2KZrYmOs3pHwO7roRGbkb9528h13VtNcT2x6P/6jV+RYI2k9pvISc0oebQ/F9JKMkbLzLEEstpYDJxTdmVIBaT55a4s50WjybmbgROzDJwZc6Z61KTExp+TRdsjfvG24Bk7EvuoZOBE7NO1z06XIxJySR4uTv3kLOLq0UH55YoOLObGXIwOmzvD+h3dc/jSf5xbNunR1Kzkxp+TR8jpvsT7kOvMix2fwXpTnw3PsYSbhdHXQKLkzZbEkDVftBhVzmJ0L85k5ETvOHGadYXleBSL5hgs72cM71wOZORF7UlY/4BL7XTyk8Ai6Bup3f0MgMydir9rKq9nZ9GsokMIgeW9m6gS/tWJ7U6Nqt/oyfzmMKIMtn7VdpXnTthLflRk7wfNbCxZ9VXXf1DpeVBQy3PpUX3WV3rKw++XOwgmei6yM9tQ1snOraEWhwq3OsY3EKqxsnODjWuheN91fQy0KD27tvul1nWBZXpZO8DzPc0G35eKvBqd8+BslhUTENzX4q4sWt/BZlgxO8DzP82G/x/tdVitUkVzCRb7zevziz7L+Bt8fiMumDPKkAAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the graph <em>G </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">What information about <em>G </em>is contained in the diagonal elements of <em><strong>M</strong></em>\(^2\)<span style="font: 7.0px Times;"> </span>?</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">List the trails of length 4 starting at A and ending at C.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img src="data:image/png;base64,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" alt> A2<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>if only one error, <strong><em>A0 </em></strong>for two or more.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">the (<em>k</em>, <em>k</em>) element of <em><strong>M</strong></em>\(^2\) is the number of vertices directly connected to vertex <em>k</em> <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept comment about the number of walks of length 2, in which the initial and final vertices coincide.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">the trails of length 4 are ABEDC, AFEDC, AFEBC <strong><em>A1A1A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: <em>A1A1A1 </em></strong>for three correct with no additions; <strong><em>A1A1A0 </em></strong>for all correct, but with additions; <strong><em>A1A0A0 </em></strong>for two correct with or without additions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[3 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Parts (a) and (c) were generally correctly answered. In part (b), a minority of candidates failed to mention that the starting and end points had to coincide. A large number of candidates gave all walks (trails were asked for) – an unnecessary loss of marks.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that a graph is bipartite if and only if it contains only cycles of even length.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Suppose the graph is bipartite so that the vertices belong to one of two disjoint sets M, N. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Then consider any vertex V in M. To generate a cycle returning to V, we must go to a vertex in N, then to a vertex in M, then to a vertex in N, then to a vertex in M, <em>etc.</em> <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">To return to V, therefore, which belongs to M, an even number of steps will be required. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Now suppose the graph contains only cycles of even length. <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Starting at any vertex V, define the set M as containing those vertices accessible from V in an even number of steps and the set N as containing those vertices accessible from V in an odd number of steps. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Suppose that the vertex X belongs to both M and N. Then consider the closed walk from V to X one way and back to V the other way. This closed walk will be of odd length. This closed walk can be contracted to a cycle which will also be of odd length, giving a contradiction to the initial assumption. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There can therefore be no vertices common to M and N which shows that the vertices can be divided into two disjoint sets and the graph is bipartite. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider any edge joining P to vertex Q. Then either \({\text{P}} \in {\text{M}}\) in which case \({\text{Q}} \in {\text{M}}\) or vice versa. In either case an edge always joins a vertex in M to a vertex in N so the graph is bipartite. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[8 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates made a reasonable attempt at showing that bipartite implies cycles of even length but few candidates even attempted the converse.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The weighted graph <em>H </em>is shown below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"> </p>
<p style="margin: 0px; font: 22px Helvetica; text-align: left;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Kruskal’s Algorithm, indicating the order in which the edges are added, to find and draw the minimum spanning tree for <em>H</em>.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) A tree has <em>v </em>vertices. State the number of edges in the tree, justifying your answer.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) We will call a graph with <em>v </em>vertices a “forest” if it consists of <em>c </em>components each of which is a tree.</span><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Here is an example of a forest with 4 components.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica; min-height: 23.0px;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">How many edges will a forest with <em>v </em>vertices and <em>c </em>components have?</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The edges are included in the order</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">CF </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">EF <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">BC <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">CD <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">AB <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img src="data:image/png;base64,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" alt> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) A tree with <em>v </em>vertices has <em>v </em>−1 edges. <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using <em>v </em>+ <em>f </em>= <em>e </em>+ 2 with <em>f </em>= 1, the result follows. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Each of the <em>c </em>trees will have one less edge than the number of vertices. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Thus the forest will have <em>v </em>− <em>c </em>edges. <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), many candidates derived the minimum spanning tree although in some cases the method was not clearly indicated as required and some candidates used an incorrect algorithm. Part (b) was reasonably answered by many candidates although some justifications were unsatisfactory. Part (c) caused problems for many candidates who found difficulty in writing down a rigorous proof of the required result. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 17.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), many candidates derived the minimum spanning tree although in some cases the method was not clearly indicated as required and some candidates used an incorrect algorithm. Part (b) was reasonably answered by many candidates although some justifications were unsatisfactory. Part (c) caused problems for many candidates who found difficulty in writing down a rigorous proof of the required result. </span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0px; font: 29px Helvetica; text-align: left;"><span style="font-family: times new roman,times; font-size: medium;">The graph <em>G </em>has the following cost adjacency table.</span></p>
<p style="margin: 0px; font: 29px Helvetica; text-align: left;"><span style="font-family: times new roman,times; font-size: medium;">\[\begin{array}{*{20}{c|ccccc}}<br> {}&{\text{A}}&{\text{B}}&{\text{C}}&{\text{D}}&{\text{E}} \\ <br>\hline<br> {\text{A}}& {\text{ - }}&9&{\text{ - }}&8&4 \\ <br> {\text{B}}& 9&{\text{ - }}&7&{\text{ - }}&2 \\ <br> {\text{C}}& {\text{ - }}&7&{\text{ - }}&7&3 \\ <br> {\text{D}}& 8&{\text{ - }}&7&{\text{ - }}&5 \\ <br> {\text{E}}& 4&2&3&5&{\text{ - }} <br>\end{array}\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw <em>G </em>in a planar form.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Giving a reason, determine the maximum number of edges that could be added to <em>G </em>while keeping the graph both simple and planar.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">List all the distinct Hamiltonian cycles in <em>G </em>beginning and ending at A, noting that two cycles each of which is the reverse of the other are to be regarded as identical. Hence determine the Hamiltonian cycle of least weight.</span></p>
<div class="marks">[10]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align: center;"><span style="font-family: arial, helvetica, sans-serif;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXQAAAFJCAIAAAAE5UF3AAAgAElEQVR4nOydeTxV+/f/D80j6iq3SRoo3ZLmSQMaVMqUokwpyZBUQqlQmUIiiZThRKVEUUoiChmTImMkZB4Pxxnfvz/eP/u7r/p0S4d99rGff9xHl2Oftfd+79dea73Xe71JgICAgKAPIGFtAAEBAW9CiAsBAUGfQIgLAQFBn0CICwEBQZ+Apbiw2Ww2m42hAQQEBH0Hxp4LoS8EBLwK9mERi8WiUChMJhNrQwgICDgJxuLCYrFYLFZnZychLgQEPAb2YVGPfxAQEPAGWIoLdFvY3WBoCQEBAcchZosICAj6BOwTugQEBDwJIS4EBAR9AiEuBAQEfQIhLgQEuIc7c5eEuBAQ4B5CXAgICPoEQlwICAj6BEJcCAgIBhCEuBAQEPQJhLgQEBD0CYS4EBAQ9AmEuBAQEPQJhLgQEBD0CYS4EBAQ9AmEuBAQEPQJhLgQEBD0CYS4EBAQ9AmEuBAQEPQJ3CIusOUljUaj0+kA1V4Xa7sICLgX+NSwWCwmk8mFDwu3iAuLxQIA1NbWBgcHt7W1gW59wdouAgLuBYoLk8nkzieF68RFT0/v4sWLZWVlAABiMyMCgp8A3Rbk39ga8z1cJC4sFsvGxoaPj09ISMjU1BRriwgIcACDwaiqqqqoqMDakB/ALeICAPj06ZOiouLEiROHDRu2cOHC2tparC0iIOAWYGIFiYDYbHZpaWl4ePjx48fV1NQsLCzevXuXlZUFnX0YK2EeLnGLuFRWVp4/f15KSmrChAnz58+fOHFiWloa1kYREHAL6CmO7OxsNze3pUuXioqKLlu2TFRUdMuWLdu2bdu+fbufn19dXR3oFiNCXAAAoLi4ePPmzdu3bxcRERk8ePDgwYPj4+OxNoqAgFuAudumpiZHR0cFBYWlS5cOHTp0586dW7du3bZt2/r165cvXz5hwoRp06ZZW1tTqVRu2MgUe3GB55+env7gwQNvb+/9+/eLiopOnTr1xIkTWJtGQMBdREdH8/PzDx06dPbs2QICArq6usuWLRMXF1+1atXixYslJCTWrFkjLS0dHBwM/p3uxQSMt3NFIslnz54dPXr0n3/+mTVr1ubNm2fNmrVmzRo4J01AQADfwW/evBk3btzQoUPFxcXl5eXNzc1jYmIuXLjw9OnTR48eGRoabtu2bdWqVe7u7mCAiwtSyVJSUuLg4LBgwQJ+fn5JSclVq1ZNnDhx0aJFX758wdA8AgLuASZc2tvbjY2Nhw8fvmPHjsjIyNLSUiqVCj/AZDKPHTs2bty4wYMH37hxA3DBXuzYey4AgMTExA0bNggJCU2fPn3+/PnS0tLDhg2bMmVKTk4OhuYREHAPyJs4MTFx7dq106dPf/z4MfxVa2vr27dvDx48OHHixDlz5sjIyAQFBQEABnRCFyn5NzY2NjAwEBUVnTNnzrRp0+7cubNixQoSieTg4AC6Nfu3NBiRLS6sLCIg6EGP4frDAY98Jisr6+DBg5MnTyaTyc3NzVFRUd7e3pqampKSkjCrYGFhUV1dDT8/cD0XeLHS09OnT5++efPm+fPni4mJKSkpUSiUw4cPk0gkOTm5zs5OeJl+S4OReTjMry8BwX+CDFf4XwaD8b3TgchNUVGRtLQ0iUTS1dVVUlL666+/Vq5cKSoqOm3atAkTJowbN45MJgMABnqdC5vNptPpaWlp2traJBJpxYoVy5cvv3XrFgDA29ubRCINHz48NTUVdGv5bx0Z/oMQFwJcwGQyGQwGMlZhFVyPz8Df0ul0XV3dwYMHi4qKDh48mEQiwSdl0KBBo0aNEhAQcHR0hJ/HfPBjPBVdXl5+/fr13bt3k0ikUaNGbd26tbq6GgDw/v372bNnjxw58tGjR6BX0WN7e3ufWExAwGmQkKeuru7FixfXr1//frQjnguFQlFWVhYUFNTS0po+fToUlylTpvz1119jxowRFBScNWuWu7s7fI4GlueCxDjwtD9//jxz5kwSiaSiorJy5crLly/Dj9FotLVr1w4ZMuTgwYNUKvUnGgx/hf5Ac3NzTk7OuXPnDAwM/P39y8rKkFC2X06RgOCXQBomwPGZmpqqpKQkJye3adMmGxubzMxMOp2OPC/o8e/o6Dh9+vQLFy5s3ryZRCKtXbt21apVY8aMGTx48MiRI4cNG0Yikfbu3dvc3IzdyQGAlbgAABgMxrNnz0xMTIYPHz558uS1a9du3LhRXV1dVVVVUVFxz549goKCJBJp1qxZ8Br9RFyQZhZ0Oj0oKGjfvn3S0tILFixYvXr1nDlzjh496uHhQaFQCHEh4B5g4APHLZvNTk1N3bBhg4CAgLS0tJqamrS09N69e1++fNnZ2QmzJ+i/tbS0JJFIZ8+e/fDhg5OT0+3bt/38/BQUFDZt2qSoqCgvLz958mQSiRQdHY3Ryf1/MBAXeE3ZbLaHhwd06oSEhAYPHszHxzd27Fj4k0GDBg0aNIifn3/+/Pn/KS7wmHl5edbW1gsXLtTQ0BAWFh4yZMj48eNHjx69ZMmSqVOnPnjwoH9PlIDgZ7DZbAaDAQCoqKjw9vaWlpYWEREZO3bs6NGjlZSU1NTUDAwM7t+/39XVBb5zus3MzKZMmfL69Wv4v+3t7V1dXc3NzU1NTZWVlTk5OUuXLiWRSOrq6o2Njf1/aggYiAvivJSUlPzzzz/8/PxiYmKLFi0aNGjQyJEjJ0yYAOWAj49PUFDwn3/++fz5M/ipuAAA7t27JyYmRiKRZs6cKScnN3r0aBKJtH79ehkZGRKJxMfHp6ioCHvc/Ynl3//7VxJmP/9M745AZKnxDryDCQkJ+/btmzZtGolEGjZs2F9//TVhwgQ4YocPH+7g4NDa2vp9oe3x48fHjh37k/dldHT06tWrRUREYmJi+vxM/jcYJHRhDMlgMCorK/ft2zdmzBhRUdExY8aQSKQxY8YoKyvv2LFj6NChw4YNGzJkiKCgYEpKCvju2YbuD5PJbG5uzsjIcHV1HTx48NChQ0eMGDFq1KghQ4bADLGQkNCoUaNGjBgxceLErKws5G+RiWokoEV+yP4OdFoH/QH0v9Ez38hv0aAPjv5e5Fx6fAb9MbRtrJ/2NOxh/58vjUUfrdcHIUBAK0VsbKyEhISgoOCgQYNIJNK4ceMEBAT4+Pj4+fmHDBkiLi4uJSUVEhICvuua5ufnJykp6ezs3OPIyG2iUqkGBgZz5szx8/Oj0WjoEKw/wSzn0tbWZmhoOGvWLFVVVX19fV9f38DAwFu3buXk5OTk5Dx+/NjT03P27Nlz586F5YY/FJf29vZ79+55enpqamqOGzdOUFBw7Nixe/bs+euvvwQFBcXFxefOnTt06FB4t+7duwe6pQ1pe4F+jHtIBpwa7PGQI0/4D3/SQwLQutDj5+zuHHOPr0b/BPlzBoPRQ+D+l178UNd6Pap6XJneHYQADQyF2Gx2QkICVBYSiSQgICAiIsLPzz9y5MhBgwYNGTJk7Nix69atExMTO3DgAHqKGvL+/XslJaWAgAD0D5FbD//34MGDfHx8Ghoa1dXVLBYL5ob76yz/P9iERQCAgoICfX39NWvW7NmzB/oUPSguLl6zZs2CBQuQhRI9DkKj0cLDw0NCQoyMjA4fPiwiIiIqKkoikcTExJSVlU+cOKGgoCAhIQGzOUOGDEHfDCaTmZiY2NzcDG825PsntqOjo6OjA/mTXzzHH74lGAxGU1PTf/odPznsnzggBFwCm81ua2uztbWdNm3akCFDZsyYwcfHJywsPHPmTD4+vgkTJsC5nhkzZmzcuHHGjBn79u2D5bbog9jb248bN87T07PHkZF/3717F7YuUVRUTEhIGECeCwCAyWTeuHHj5MmTS5cuPXr0KMxaIX4EfIzz8vLGjRtHIpG8vLzAv68dqzuQiYiIWL9+/eTJk9etWwdDoQkTJigpKSUnJ9+5cwdqDR8f3+jRo9esWaOrq+vn55efn5+RkREcHHzo0KG0tLSYmJiysrKqqqrc3NyoqKiampr379/X1tbW1NQUFhZ+/PgxOTm5oqIiPT09Pz+/srKyurq6tbW1vLw8KysrNTU1NDT0w4cPlZWVN2/eDAwMzMzMjIqKamxsbGpqysvL8/f3//DhQ0JCwpUrVxITE11cXJqamuApfPjwobq6mslklpSUvH37trGxEWoHjUbLy8uLj48vKipKT08vLS0tLi7Ozc198uSJt7d3SkpKSkpKRUVFQ0NDfX19W1tbR0dHeXn5t2/fampqMjIysrOzGxsbW1paSktLX758efXq1bKysoKCgoaGBkQlf3JrkIvc1tbGZrO7urqYTGZ7e3tdXV17ezuFQqFSqfRu0DcFLp+DbUQ4OVy4if91ar97yufOnRs7diwyd8HPz49MYsyePXvEiBGwHG7OnDmzZ8++ePEiOikLvyskJGTo0KFqamo9jtzS0hISEqKlpSUuLj569Oh9+/aZm5s/efIEYLSIERtxoVAoWlpac+bMmTJlCox6enyGxWJ1dHSoqamRSKSVK1f26L0Ar9S3b99cXFy2bNkCl1TAOyQpKbl48eIFCxbs2LFj4sSJ8J4JCQlNnTp169atkpKSPj4+wcHBzs7O9vb24eHhFy9eNDc319LSMjQ0lJGRMTAwsLe319TU9PLyOnDgwP79+9PT08PCwkxMTE6cOOHv7+/o6Pj48WMfH59Dhw4ZGRnFx8ebmZmdOHFi9+7d0dHRt2/f1tbWDgoKUlNT279///r169etW7ds2bI5c+YcOnRIVlY2MjLS19c3JCRETEzswoULjx8/3rp1q7Kyso+PT3x8/IMHD54/f66hobFp06ZLly7Z2NjIy8ufO3dux44dOjo6169f3759+86dO11cXDw9PY2MjBQVFY2MjBYuXLh///7AwMC1a9cuWLBAS0tLQ0Pj6NGjUlJShoaGhw8f1tXVdXBwiIqKCgoK+vTpU1ZWVlpaWkJCQlZW1ocPH0pLSyMjI93c3B4+fPjo0aPExEQHB4djx45FRkZ6eHiYmZk9ffo0MzPzzp07mpqaxsbG3t7e+/btO3DgwNu3b728vI4ePWpubq6jo0Mmk8PDw69du/b06dN37949efKETCa/fPnSz8/v9evXNBoNAFBfX19SUlJeXl5bW/vixQsPD4/g4OAvX77k5eUFBQXFxcXFxsbW1dUVFxdnZmbW1tY2NjbW19dnZGSkpaXl5uZ++vSpubn57t272dnZFRUVFRUV4eHhCQkJFRUVbW1tVCq1ubkZvqKLiorKy8upVGpnZyfi8cHoEgAA0xDfD84eviHaq0WAGo2EzD1mCeh0OpPJ7OjoYDKZ8JUJAGhqaqquri4qKqqqqvr8+bOKioqQkBAcrjDDws/Pz8fHByc0YAjPx8dHIpHmzp174cKFlpYWdHxaUVHx4sWLuXPnbtq0CR6/tbU1Ly/vypUrCxcuHD58ODzyiBEjVq1a5e3tDcOiASQunz59mjNnjoiIyJIlS0pKSnp8BskpWFpajhgxYvHixXl5eT0Owmazy8rKzM3Nly9fLioqCqeKhg8fPmLECD4+vpkzZy5btmz48OHwzpFIpM2bN6emplZVVdXX19fU1BQVFT169OjVq1c3btzw8PB4+/ZtbGxsdna2g4NDcHBwYGBgbGxsSEjI2bNnc3JygoODHR0d79+/HxQU5OHhkZSU9OLFi7i4uDt37hQVFd27dy8jI8Pd3d3CwiIkJMTMzMzNzc3Y2NjPz8/BweH27dvHjx/38vKKjY2NiooqLy+/e/cu/MmTJ0/s7e1Pnz594sQJMzOz69evOzs7m5qaHjt2TFNT09nZ2dbWVk9PT1lZWVFR8fLly66urjIyMqqqqtbW1ra2th4eHk5OTk5OTvv379fS0jpy5IihoaGNjc2+ffvMzMyWLl16+PDhvXv3KigoqKqqamho6OjoCAsLL1261NDQ8NSpU4cPH1ZTU1u5cqWuru6KFSs2btx45syZBQsW7N69W0pKavHixVpaWgsXLty6devu3butrKx0dXW3bdtmaGi4bNmyPXv26OnpXbt2zc/Pb8+ePa6uroaGhg4ODioqKocOHXJzc1NXV1+0aJGTk9OJEyfMzc0PHTpkZmZma2vr4uKybt2606dPnz59etOmTWvWrDl8+PCDBw9UVVWhFK5evfrq1as6OjpKSkqHDh06duyYrq7upEmT5OTklJWVExISPDw8pk2btnLlSnl5+aVLl86aNWv16tUGBgYyMjKWlpbx8fHBwcEnT57cs2fPqVOnfHx8VFVVdXR0goODLSws/Pz8Ll686OTktGXLFhsbG3t7+927d1+6dCkkJMTf3//48eN79+61tbW1tLTU1tZ2dXVVU1NTVla+cOGCubn58ePH4+Li7Ozs9PX1Hz16ZGBgsGfPHh0dnT179lhbW58+fdrT0/PUqVMqKira2trr1q3T1taWl5c3NDTU1dWdOXPmtGnTRERExMTEREREBAQEoEvOx8cHxWXQoEEiIiJQF/j5+YcPHy4gIDBixAgxMTHY9gmRRQCAu7v7iBEjhgwZIioqqqmpqauru3HjxnHjxsHy3MWLF0+cOHHo0KHCwsILFy4sLi4G3QXuvC8uEFtbWz4+Pikpqf379zc0NKBlld09cQPfP+fPn9+xYwecMEKAH25ra1uzZg3U6ZkzZwoICMA87tSpU8eMGTN06FCYbSGRSJMnT/5hWgcAAN+oP+EnmQ70i4tCoXz69Ak5GvwrJE0DX2jIH8Igoqurq7y8vKWlpb29vba2tr29vbGxsaampqGhoba2tq6urqioqKamprm5uaKior6+nslklpWV5eXlwSAFMQyGLQCA5ubm5ubmjx8/wrCutbW1srKypKSkpKTk8+fPmZmZcXFx0dHRaWlp2dnZkZGRSUlJsbGxL1++fPbsWVhY2Lt378LDw5OSkkJCQshkckJCQnBwcHx8fEJCQm5u7rt372JiYh49enTnzp3o6OjY2NikpKTq6uqHDx+mp6e/efMmOTk5Nze3oaGhqKjoxo0bwcHBWVlZrq6u0dHRBQUFNjY21tbWr169On36tKOj49WrV69evXry5EknJ6eQkBBPT8/IyMi2trZ37949f/4celK+vr5ycnLGxsYeHh4uLi6PHj2KiYmJioq6cuXKkydPYmJiEhMTMzIybt68mZCQYGlp6eTkdObMGScnJy8vr4iIiKSkpPLy8tDQ0GvXrl29etXKygqKiJOT04ULF0JDQ728vDQ1NY8ePWpsbKyhoQF158yZMzY2NgYGBqdOndLS0tq5c6epqemJEycOHDhgYmKybt06HR0dfX39JUuWyMjI7N69+/Dhw+vXr1+zZs2qVauEhYUnTZo0a9YsUVHRSZMmTZ06dfLkyYKCgvDnMJkiJCQkLCwsJCQEVwPB8cnPzz9u3DjosPDx8Y0bN27ZsmWbN28+cOBAUVERQC1/YTAYvr6+ixcv5uPjmzhx4qhRo5DAasWKFXPnzh02bNiSJUt0dXXDw8NzcnKQcTggxAWe4eXLl8XFxc+fP//q1St2dzUR+jNI3vv58+eampo9PBf4q9LSUnl5eQEBgZEjR4qKigoKCo4ZM0ZERGTq1KmDBg0aNmwYPz+/sLDw7NmzYWMu8N30B7u7PhK59D1+3oPvZ5TAv5eH9fhz8KM8dK8v3Q9lDvkhTtO9DAaDRqOhjYc/YTAYDAajR8YdCvT/6k/IZDJra2tbWlqQeOQPYaMmX6BhHR0dLBaLSqW2tLRQKBRoT1NTU3Nzc2Nj47t374qKiurr6+FeHzU1NdXV1fn5+WVlZdXV1Y8fPw4KCiouLv7y5Ut4ePj8+fMHDx7M3w0MZGB91qhRo5YtW7Z8+fKoqChkfhDawGKxcnJyYKvGuXPnjh8/fvLkyVOmTCGRSCIiIlOmTJk2bZqzs3NBQQHSRAo9gDlyWX6d/hYXeLHev3///v37b9++NTY2In7K9x9Gh7XfJ3Tj4+OPHDmyaNGiv//+m0QiQYmZN2+eqKgo7GUHb9ihQ4ecnZ1v3rwJh+nP52sICPoHMpksKCiIeC7Dhg2bOnXqkCFDxo0bt2bNGkNDw/z8fPjJ74frkydP1q1bt2jRoiFDhmzYsEFWVhbGwp6enh8/fmxvb0f2RMZ2nGMgLuiLhRRx/K8Po50I5OcwdLpy5YqUlJSIiMjWrVsFBARIJNKSJUuUlZVHjRo1fvz4devWbd26dcqUKXJycuLi4iNHjtTT04OJd8wvOsGABY69Fy9eyMrKImtf+Pn5BQQEJCUlSSTS+PHjHRwcqqqqwHcrGxFoNFpqaurDhw+9vb2Tk5M/fvxIoVDQ+6yzf1oM1W9gs7aoR4EsWm7Y/17Q9cNKMDabTaVSz549KykpKSgoOGLEiPHjx8+ePXvp0qXjx4+H9Y6zZ8+OiooqKSlxcXGZPXu2iorK1KlTDx06hEwGExD0PywWy93dHbrV4uLiFy5c8Pb23rFjh7S09NKlSyUlJZcvXw6TAMgSvO8H//evRnSkjzwv36947GewKaL7SQT4/a9+eCkBAO/fv7e1td29ezd0JidMmPD333/PmzdPUlJy+vTpCxcuhCu76urq1NXVExISzp8/LyMjc+zYMdjqBX0n+uRUCQgAAP9O6r169UpYWBiWesJGaACAhoaGt2/fWlpaWlhYwK4jPy+t7vEE/cojgwnY71vUC5AUF41GCwwMFBcXFxcXl5CQEBMTk5SUhMVyHz9+RC56QUFBYmJiQUHBy5cvLS0t4ToA8F+3kICAIyBjLCIiYvHixUOHDpWWls7Ozgb/7oIWFBS0aNGip0+fIt46lkZzAryKC/quZGZmHj9+XEJCYsKECfPmzTty5AhswwXFBTqHcDaXQqH4+/vv2rULWa6OSRadYEABB9jr16/FxcVJJJKmpibcB73HetRTp07x8/Nfu3YN8MprD6/i0mM6uaSkRFdX9+rVq6qqqhEREeC7fA2FQmlsbGSz2a2trRcuXJCRkYGtdAhxIegH4uPjV61aNW7cuPXr18PSFXRyBADAYDA0NDRWr1798eNH8N0sOE7BpbggIPfg3bt3+/btKywsDAsLS0xM/KFesLoXQ+fl5dnZ2ampqYWFhSHHIVSGgIOgQxsKhaKpqSkkJPTD7k3IqLt8+fKBAweQH/LAaOQRccnIyNDW1r537x6s3fxfNwa531QqFb5MwsLC2P+mX0+AgEdBRmZxcbGpqamwsPDWrVuR0pXvP9zU1BQcHLx7925ems3EvbiwuxcrGRkZwQVv/2sTWEQ+oP9SU1Njbm5ubm6O+C884IgScAns7rpzR0dHBQUFuMzlJ5//+PFjaGiokpLS/xIgPIJvcQHdipCXl2doaAgAyMjIePfu3Q8/iWRqkPjo06dPZDJZX1/f3d0d6UjA/q5sn4Dg10FeeFQqNSAgQFFRcefOnZWVleCnwU5ycjKZTD5y5AjM9fIGuBcXmG8vKCgwMjJiMBjfvn2DCbP/hMVi1dXVxcTEBAQEaGtr+/r6og9ILBEg6AVI3Ros8pw7d+7Ro0ffv38P/mtX4q6urrS0tFOnTvHSflu4Fxd4t2JiYlRUVH69HhHxWuvq6urr69PT01VUVJ4+fYouHe5Dowl4FGTuUkNDY/To0bq6unABIftHVfxoWCyWnZ3dlClTYOE/b4BvcUHSZs+ePVNTU/t1X4PNZqPbIHR0dISEhBw4cAC2z+CBEgMCTKDRaC9fvjQ1NRUXF1dVVYW9ipAp5594LlQq1cnJSV1d/T8bBuIIfIsL6M655OTkHDt2DP77F50O5E4jCzEiIiIUFRVzc3N7fICA4OcgA8nW1nbSpEmCgoKHDx+GeRbYGfs/pyPpdLq7u7uenl5NTU2/mt6X8Ii4JCcnW1tbw5/8riggLuuXL18sLCx0dHSSkpKQ4xDJF4KfwEYtT4uLi9u4ceO8efMMDQ17tA37T6hUqrGxsZycXH19fR+a27/gXlxgaJOVleXp6dk7XwNZmQ0A+PLli5eXl6GhYU5ODiCK6wh+ASgfb968WbBgwaRJk06ePAkr5X5r8LS0tHh6el66dOnnM9b4At/iAvOyLBbr69evNjY28Db/rhYwUQAASktLb9++ff/+fWSLGUJcCH4Ci8VKTU3dsmWLrq6up6cnTJqgGyb8ykG6urp8fX3Nzc3/s+8qjsC3uIDu90ZERISRkRF6i5LfPQ7yV+3t7ZWVlU+ePDl//jyy0IP975UgBAMcFqr7ZE1NzfLly4WEhJBuQax/dz79lQMymUxLS0spKan/1cQTj+BbXJC0SGZmpr6+PlwM/ScSABWEwWDExsY6ODhcunQJ2aka2faQkydAgE+QkVBbWxsQELBr165z586hX0W/m/Vjs9mhoaFqampEnQu3gLw9MjMzDx8+TKFQ/jBLgi6fo9Fod+7cUVNTe/78OeiOnghxIQDd/khGRoaiouL48eMNDQ1bW1tBb7thww+/ePEiMjKyjwzGBHyLC+i+McXFxUePHoV95P9EAtioLpwAgNLSUicnJwUFBW9vb/Dv1j4EA5ysrCxNTc05c+YYGBikpaWBH3UC+XXodHpkZKSWlhanti7gBvAtLojnUldXd/LkSRivciR4QY6ckJDg7++/fft22MUHmZwmQqSBBhvVoozFYpHJZCEhITU1NVgY9fPq/v+EwWAEBASoqKjw0tsL3+ICUBukOTg40Ol0DqZdoYLQaLTKykp/f39NTc27d+8iPyTEZaDB7t7lpqKiIjEx0dfXV0NDIyMjA3zXGrEX1NfX79+/X0VFhZgt4joaGhpOnz7d0dHBwZljNmr9dGFhoZ+fn66urr+/P+CVLoQEvYBCodjb21taWubl5TU3NwMA4AzAnwfj0dHR5ubmRFjERcA72tjYePLkyc7OTsC5tixIcR38irKysvv379va2n79+hX5aqLKbiCALlMIDAx0cnIik8nwrYOUKfz5MEhNTT1+/DjhuYSlo34AACAASURBVHAR8I7m5eWZm5tTqdS+yIYg+ZeIiIhbt27t2LEDye/C+Wlsd4ch6DvQ8Q6VSnV0dDxy5EhKSgrH/QtYiRcUFESICxcBb/yHDx82btxYUVEBfrT95Z9/BfyWhoaGgoICd3f3uXPnwgkCpJiKcF54FcSBjY2NNTIySk5O7ovnv7W11czMzN3dnZcGEr7Fhd3ds/Ljx48uLi5dXV199KgjTV6YTGZ7e/vz5891dHSCgoJgkg+9WToBL4EEO8nJyREREVlZWQwGo48C4evXr586dYrjh8UQfIsL6PZcPn/+bGho2HdbQaPTKywWi0KheHl5KSgowGlIZCEJL712Bjjou5mfn29tbZ2QkIAsN+P413V2dtrZ2VlZWRFT0VwEvBlFRUWKioofPnwAnEvo/hBERNLT09+8eXPixAnYEIhTWT0CbgBm06Bf/PTpUx0dHV9fXwqFgm77xNlvLCgoWLt27eHDhwlx4SLgbW5qalJXVy8vLwfdTRj6DiQFQ6fT9fX1b926lZubS0xO8xJIFUJMTIyenl5oaCjywz66y/X19To6Oubm5hw/MobgXlzgc15fX4+IS58+4XDMISMsOjo6OjpaTU3t0aNHgOjPwEMwmcyEhITNmzefOHHi27dvoDv4hVUtHPcvaDSas7OzlZUVZw+LLTwiLrW1tbq6urCLVz84lkhwRKVSOzs7ExMT9+7dm5mZiXw7m2hhh0MQ34TJZMbFxW3YsOGHPU/7YroAABASErJ69WrOHhlbcC8uMAhKTExcsWIF7Jzeb8sL2agdjhwcHFxdXd+8eQNjdRaLBZun9oMZBBwB6RYGALh///7ff/8dFBTUP18Nx0lcXNzWrVuJHRe5BWQqOjs7+8CBAy0tLQCVE+mHb0fSew0NDXZ2doqKiojAESESvoBjprm5OSsry9TU1NnZGS5V6zcD/P39tbW1iWZRXAS8/S9fvlRSUkJWRffPmOgxcVBeXn7x4sXnz5/3Q+qHoC949eqVqamppqamh4dHXV0d6K8dfuFQiY2NlZeX74ev6zfwLS5IYf7Vq1fnzp0Lcy79n+yAEtPV1XX37t3du3fb2tqiZY5wYbgWxPek0+kvX77U0NBQV1e/fv060mG7P8Xl+fPnq1atIhYucgvI7X/48OH8+fPLysoARuICzejq6oqMjLx+/bqDgwPy6us3T4rgd4FTPwCAtLQ0XV3d/fv337t3D/6qnwPbjo4OR0dHOTk5Xhoq+BYX0K36ZDJZRUUFXS/bz2Yg+8ACANLS0o4cOWJiYoLecK+f7SH4FWDO7t27d2QyeefOnXFxcTQaDXFn0Cnevqa2ttba2trU1JRYuMhFwNtfW1traWn58uVLgFGyg43aHKurq+v+/ftHjhxRU1P79OkTQM0rESESN4C+BV++fLl3756NjU1UVBTyW2SdR3+uGvPx8VFUVIT9qHgDHhGX6urqbdu2IZ1WMAQZuLdv3w4ICLCwsMjLywP/rqEg9AVbkGIFCoUSGxtrYmLi5uaGtVHAyspqxYoVvOTk4ltckKnolpYWXV1d2HIBYD1TA8fHixcvHB0d3d3dLSwskEVPRIjEDcC70NjYWFBQYGVl5eTk9OXLF2xNYrPZSkpKGzduxNYMzsIL4sJiserr642MjOAcMOZPL7IJSUFBwevXr6Oioq5duwb1hfBZuIfCwkJHR8ddu3bV19djfl86Ozu3b99+8eJFbM3gLPgWF9AtJa9evZKVla2pqYE/xHCsIOEPq3tbgpcvX27cuPHs2bNIF07Mh/LABLnsnZ2dFRUVd+/e9fHxeffuHeCCF1JZWdnZs2cTEhKIIjpuAQmLYmJiVq9ejd49HmvT/o+6urqgoCAnJydPT0+YFUKKXzAf0wMEZJUzHBgvX748ffq0ra0t8jbCnKysLCUlJQ0NDbjDJ2+Ab3EB3e8cLy8veXn54uJiwE2uAWJJXl6em5vbmTNn1q5d2yO/i7WNAwL0PN2DBw+OHz/+9OnToqIi5AZhPmDy8/MlJCTk5eUJz4VbQEZMQkKCnp4eXNeD+UBBQOIjBoPR2tqalZW1aNGi+/fvo+vrsLZxQIA4ifn5+crKymQyub29Ha4s5RJxyc3NXbBggYaGBrZmcBZ8iwvo9lwcHBxGjRqVnJwMuMlzgSAjuLq6OiwsTF9f38DAAE5ssVD9vbnKZt4ACYXgtc3Jydm9e7e1tTUMTrmq7OjLly/KyspOTk5cYg9HwL24wJwLmUy2tLSEFWvcWUgCRfDLly8xMTEuLi5r1659//49IPpj9iUs1K4v79+/37hxY0hICNJwh6sueHx8vIiISHx8PNaGcBJ8iwvi7np5eR08eDAxMRFw63bxiKlUKtXb21tBQeHw4cNIR3Fu87Z4A3b33rstLS329vY3btyAP+fCBaXfvn2TkpIyMDDgwqHba/AtLqDbc3n8+PGWLVtevHgBuNVzQWdw6+rqIiIiHjx44ObmBmcHCHHpC1jdzdutrKzIZDKsrEcvxeCeJ7m8vFxCQuLgwYNYG8JJcC8ucKzcvn1bW1sbJkq5U1zQsNnstra26urqc+fO6erqwi2HEYeLq96ouIONAgDAYDBiYmIcHR07OjqwNu1ntLW17dq16+zZs1gbwklwLy7wgbx3756Kigo6ysDarp/BZrO7urrevn1bUFBgYGBgY2MDCy5YxP6Nfwy6nqW9vf3Fixd+fn7Z2dlY2/UfJCcnq6ioqKurw55EvAHuxQWGRQEBAUuWLCktLQV4CDHQ/Rlu3rwpJycXHByM3ouWy+3ncpBXS3p6uo2NDSyM5vJLWlpaunHjxgULFhQWFmJtC8fAt7ggFbrOzs7CwsIZGRkAD+KCTih+/vy5sLDw3LlzysrK6PpdrG3EGegrRqPRWltbX716lZ6e3trayv1hMpPJzM3NXbly5Z49e6hUKtbmcAx8iwvo9lxSU1MlJSVh+T+OHk5oJ9zIwtraWlVVFVk/TcRHvw7739uVffnypbS0ND09HSazuB8mk1lSUnLu3Lm7d+9ibQsnwb24QB+4oaFBQUHh7du3gOsd4B7Ap6Ktre3jx48XL15UUlKC1Tqs7t3XsDYQB7C7u8bBN83du3dxt0Kns7NTW1tbS0ur33rf9QM8Ii5VVVVbtmxJTU0FePNc4LbELBbr27dvRUVF5ubmhoaGlZWVAA+ZaS4BmVTu7OwsKCgoKSlpaWnhqpnm/+T9+/eysrLa2tpEg25uAcm5PH36VFZWFnc5C3R5LovFotPpT548OXfu3JkzZ2D7IrycCCaglx3Cf1dXV8O4EuDt0rHZbCsrKxMTExwJ4n+Cb3EB3Z5Lfn7+tm3bsrKyAK7EBQ3igj179uzMmTP6+vro/lLEFNL3oDNTTCYzOTk5LS0NboyHO3Jzc/X09Ly9vbE2hJPwiLjU1dXt27fv9evXALfiwmaz4VawpaWlb9++dXd3Nzc3r62txdou7gXxWwEAdXV1paWl+O1uHRsbu27dOjKZjLUhnIQXxIXFYlVVVZ06derjx48Az+LCZDLhFqINDQ3nzp2zs7Ozt7fH2i7uBb5X2trampub6+vr6+rq8BtTZGdnL1u2zMXFpT/3G+hreEFcGAxGdnb2hg0buHnh4q+Ajn2ys7M9PT0PHz785MkTmORDRBOn6skRemSp2Gx2cnJyUVERVpttcorq6urJkydbWlpibQgn4QVxAQAUFxerqakhTVKwNupPgd5+U1PT1atX5eTkrK2t0foywMUFTjnTaLSKioqIiIj6+nqkyAW/VyYzM1NISIgbdjjhILgXF/iySkpKUlJSgjO4PJD7ZHVvxwX7Sx09etTW1hamKnng7P4EdvdeZV1dXUlJSX5+fnCPRG5b5fy7FBYWzpw589KlS1gbwkl4QVxYLFZKSoqUlBRcn4bf1xcCrKCDutnZ2ZmXl7dt27ZTp07B3+L97HoNIqyVlZWNjY1UKhUWyyPtRPGrvEwmU0lJ6dy5c1gbwklwLy7wZdXe3i4jIwPFBb8jDAFtP+zPcOPGDUVFRTKZDPsE80Ag8OsgxcrwzjY0NDx48IBLNsDjFC0tLYqKiq6urlgbwklwLy4wPVFXV/fPP/+kpaUBnsi5oIE6kpSU5O3tbWlp6ePjg97/iAeU9D+BcRA836SkpNevX5eUlPBSJSsAICcnZ+3atYGBgVgbwkl4QVzYbHZRUdGaNWuQVTm89LzBl3Zzc3NNTU1OTo6ZmZmSklJBQQHguTP9XyAOGo1Gu3XrFtJ7GGu7OEl5ebmmpmZoaCjWhnAS3IsLTHyGhIT89ddfyCPHS85Lj5l1V1fXCxcu+Pv7w3QDjz1jaHqcGpPJTElJcXV1hRlcXrrFAIDS0tLp06c7OTnx0nnhW1yQQUYmk7W0tBoaGgCe61x+DoyAYmNjbWxsbty44eTkBJtj8STs7j0SWSxWV1dXe3v7s2fPgoKCYBcF3gsG4+LiSCSSjo4OL50Xj4jLvXv3pKSkeDtYgOsDWlpaUlNTfXx8Tp06FRMTg7VRfQWyGKKzs/Pr168FBQUfPnxA2pjy3vsjNzd38+bNDg4OFAoFa1s4Bu7FBY5COzu7efPmZWZmAjyXaf4c5HkDADQ2NsbHxxsZGTk5OXHPhsccBJ4snU6PiYkJCwsD3y1T5LFXSHFx8Zw5cxQVFYnyf24BigudTvf391dVVUVvY4i1aX0IPOvk5OTz58+rq6t7enrC1vY8cNZs1AYslZWVISEhzs7ORUVF4LvdnXjgZNE0NDTIy8ufPHkSa0M4Cb7FBXRPRYeGhk6ZMgWuIeZVzwUNfAjj4+Nfvnx59uzZs2fP8oC+oPMsVCr1/fv33t7ejx49wtqu/qChoUFdXf3Bgwe4voM94BFxCQwMVFBQ6OjoGCB1ZdB5aWlpaW5u/vz58+LFi42NjbE26k+BJwVLkwsLC4ODg1NSUmCehedpa2tbtmyZmZkZLw1d3IsLVBM3N7dt27bBgch72b7vQR5CAEBSUpKOjs6OHTvOnj2L66GJ1ARWVVW5urpmZ2e3trYOhFcFAKCwsFBERGTJkiVYG8JJcC8uUEd8fX1FRUVhWDRAhiPoDoIaGxtzcnLi4+MtLCxu3LgBk744klckz4LYnJKSYmFhQaPRwIC5m/n5+Rs2bFi9ejV++119D77FBXmKbty4MXLkSNjzfSDkXL7n4cOHx48fX79+/ePHj3GkLKBbPphMJqxn+fz587Nnz2CLz4GzRdzTp08vX7584sQJXlrWwCPi4uLiMmrUKGREYm1XvwIvQnl5+bNnz65du3b+/Pno6Ggc6Qvis8THx9+9e9fLywvWKyFREo7Opdfk5uZu2rTJysqK8Fy4CCgljx8/njdvHpyzHGjigjR/YTAY5eXlPj4+0tLS165dw8swZXfvDBcTE/PhwwdkWQOiLAPBc6msrDQ0NDx8+DAvKSm+xQWWWgEAfH19Z86cCcvJBmZYhPDkyZOzZ88aGRklJCQAlHPHVaDXc7NYrG/fvlVWViYmJn4fFAyQW/nmzZu///779OnTWBvCSXAvLvDJcXd3nzt3Ls80i/oTqqqqHj58uH///l27dl2/fp07cxboYrna2lrYrXKAzDr/kPz8/DFjxnh4eGBtCCfBvbhAPyU1NXXjxo1PnjwBA1tcYIhUV1f39OlTFxcXKSmp4OBgrI36AUgo1NbW9ubNm48fP7LZbF7KZf4uoaGh0tLSR48e5aWLgG9xAd1S8vr1a1lZWbhX9EAOixBhpdPpV69eNTQ0tLKyamtrQ36LqXX/B1LL39zcXFBQAHdfHbB3DQAQFxc3ffp0PT097rlHfw7uxQWOyIiICFFR0fLycjCwPRc0ra2t6urqZDLZ3d0dTtIj6x4xBGmgV1lZWVBQ0NjYCOtZBri4VFZWLliwwMXFBWtDOAm+xQWOSBqNFhUVNWPGjJcvXwJuej9jCLLjSnZ29unTp0+cOBEZGQkwzY+i55UpFEpjY2N2dnZTUxP4d353YBIVFSUuLr527VqsDeEk+BYXSH19fWBg4Nq1a3G94yJnQU8SFRUVhYWFmZiYvHjxghtM+vbt28uXL+vr6ykUCgzZcN24nyPY2Nhs2bLFyMgI+nG8AS+ICwDgxo0bkyZNio+PB4Tn0g26RwGFQkH2bwT9Oz+NrlhhsVgdHR2fPn3Ky8tDG0B4LlFRUQsWLFBXV+el0Yt7cYEjkkwmr1279u7du4CnE7q9Oy8YOebk5Dg7O8vIyPTz/BF66RCLxSopKYEFuARoEhMTV6xYoaamxktDl0fExdnZWVhYGJaN8XBY1Lvzgk1S6HR6eXn5u3fvHBwc4IXqH+AidfhCrq+vLywshFsvEaCJi4ubM2eOqakp1oZwEtyLC5K5XLVqVVJSEuBpcQGofTZ+/U+guMC/ffDggbKysrq6emFhYZ/Z2PPb4T8KCwtTUlLa29th+/7++Xa8kJqaum7dOjU1NawN4SQ8Ii5xcXEHDx789u0bGACTmr07QfgntbW1O3fulJCQOHfuHLIBEMcvV49QqLm5uba29sWLF/AbeThu7R1MJvP27dsnTpxQV1fH2hZOwiPiEhoaunz5cqSHLtZGcTWdnZ1kMllVVXX79u0vXryg0+kc9/VY3XskAgAKCgpsbGxqa2tpNBqSYybEpQfl5eWzZs2SlZXlpWW3uBcX+JJ0dXVdsWIFLOUgxOUnwIvT0dHh6+trYmKirq4OF2Rx/FsYDAaVSi0pKfH19Q0ICEDiMkJcfkhmZqaQkNCmTZsIceEi4Hg9ceLE9u3bkTbxWBuFAb/4uCKT0J8+fQoODlZRUTl06BBS/8KpZx5+S319fXR0dEFBAeyigLgt6KZzBJBHjx4NGjRo8+bNhLhwEXCYOjk5rV+/vr6+Hgy8kJ79b37xr1gs1tevX728vI4cObJ58+awsDC4vz1sYdE7/wJZR8pmszs7OzMzM2/fvs1LG/H0HZ6enhMmTJCTk+Ml2cW3uCDv4bi4uMWLF8MZkIHmdcNHGvz+ibNYrNbW1tLSUlNT0y1btoSHh0MhQNfp/9bRkNboDQ0N165de/z4MVzTRPCfHDx4cOTIkSYmJlgbwknwLS6g23NJSEhYvXp1cXEx4PWp6O9hsVh0Or0XXgZyoRwcHKZPnz516tSLFy8ix+yFGQwGg8FgNDc3d3Z23r17lyiW+3Wsra2HDRtmb2+PtSGchEfE5dq1a9LS0rD7/4BSFkgvwiLkrxgMRk1NzY0bN4yMjPT19T09PWF/zF8/GvqrqVSqra3t/fv3W1paBlp82ms6OjouXry4fv16dXV1uLkdb4B7cYHD19vbW1paGk5FD7SwiFP4+/ufOnVq/vz5ZDIZ/LIDiCgL7Ofg7e1969atT58+QWUZaF5k76DT6QYGBrKysgcPHqyrq8PaHI6Be3GBnktgYODmzZvz8vLAwAuLOEV+fv61a9f27Nkzd+5cOH/06+ICAPjy5UtKSoqXlxf8OaxzIe7FL+Lh4TF48GA9PT2sDeEk+BYXJO8YFhYmICDw4MEDQHguvQKmhKurq2NjY1VVVdXV1VNSUn7rCBQKJT09Hd3GmBCXX+f69evz5s0jNqLnIpCJkry8PDExMSguRKjfC5AMblNT0+PHj3fu3Llv3z60J/i/ZILNZpeXl3/9+hUmdGHKgCiW+y3YbLaXl5eEhISBgQEvXTF8iwvofuXm5uZKSkoOhIWL/QCdTv/48aOZmZm0tDSc3UeXvdXW1r569SovL6+oqIjNZpeVld2+fbvflkHyJGw2Oz09XVJSkhAXLgLxXJ49ezZu3LjU1FRAiMsfw2QyOzo6nJychg8fvmnTptLSUvjzqqqq06dPKysrS0tLi4uLy8vLHz169PLly5mZmYS3+IcEBQXx8/ObmZlhbQgnwbe4gG7P5dmzZ7KyspmZmWBATkVzEMRJqaysdHBwGDNmjKmpaV5eXmxs7P79+1evXi0sLLx48eJx48YNHz58zJgxS5cuvX79OtZW4574+HhhYWFCXLgIJKHr4+Mzfvz4V69egYG6tojjsFis4uJiAwMDJSWlVatWiYmJCQoKDhs2jEQiTZkyZcyYMXx8fCQSSVRU1MjIiKjE/UMiIyMnTZrk5OSEtSGcBPfiAivWb926NXnyZNj9n8gjcpDKysqjR49KSEiQSCR+fn5BQcFJkyYtWbIEui1CQkKTJ08WFhaGrXkJegeDwbh27drYsWMPHjyItS2cBPfiAsOiN2/eTJs2LTExERDiwlHa29vV1dVHjx49aNCgwYMHk0ikSZMmSUlJ8fHxjRw5cvTo0UJCQsuXL8d2XwG8w2azDx06NHbs2KtXr2JtCyfBt7gAVJtLGRkZJOdCiAunCA8Pnzx5MolEmjFjxsSJE0eOHCkgILBr1y5BQUESiUQikWbNmuXs7Ay3HyLoHbBCd+HChQEBAVjbwkl4RFzIZDKS0CXahXAQZ2fn6dOnL1y4cNasWUOHDh07duzUqVM3bNgwaNCgkSNHjhw5UlZWNiwsDGszcY+3t7egoCCx4yJ3AZ0Ue3v7GTNmlJWVAWIqmnO0t7d7eHgcPnxYWFh4yJAhfHx8gwYNGjJkyPjx40eMGDFp0qT169dv2LAB7iVAXPNew2Qy7ezsli9ffuHCBV66jPgWF2S2yM/Pb9GiRbBZFCEunAK2UKitrd26dSsfHx/MuYwYMUJYWFhERGTs2LFiYmLe3t4MBgPp5ELQC1gslqen5/Lly3fv3g2XpPMG+BYX0F3nYmtru2jRotraWqQZGtZ24Rt03iopKQmuBpCUlBwxYsSOHTvmzp1LIpGGDx++Y8eOr1+/Equf/xAqlaqpqSktLa2hoQH7AfIGuBcXOKbv378/e/bs4uJiYqD/IXB2HxHokJCQqVOnbt682c/P7/Hjx+fOndu7d++RI0f09fV1dHTU1dXb29sB4S3+GTQazdHRcf369ba2tkQPXW4BCYvc3NymTp1aUFAAPRfCRe81yCVls9lubm6jR49euXIlMotBp9Nra2vb29uLi4vd3NxUVVWvX7+O9M3F0m6c4+bmRiKRTpw4QYgL12FhYUEikXJyckD3/qFYW4RXoEYwmczAwMClS5dKSko+evQIuifocV9bW/vgwYPLly+Lioo6OztjZi6v8PjxY35+fgMDA6wN4SS4Fxf4MFy+fHnSpElEs6heg25VSafTPT09V65cef/+/U+fPqG7XkKgdn/8+DEhIWHr1q3S0tI5OTm/2xyTAE1sbKyEhISVlRXWhnASfIsLUqGbnp4+e/bs3Nxc8O8XLMGvAC8jvG7t7e1GRkaysrIWFhbFxcVdXV0/0Yu2tjYymbx//343N7e4uLi2tjZArO3qFd7e3lOmTPH19cXaEE6Cb3EB3fvsVFVViYmJwSJ0Yrbod0GWaH358kVZWVlCQuLUqVMfP34E3RuG/OR6MpnMlJQUOzs7KysrBweH1tZWQlx6QUVFhbS0tKGhIdaGcBLciwscyjExMYsWLYLbuRKey+8CtaOgoMDIyEhLS8vW1haGOUirSth8+3/9IY1Gi46OlpWVXb9+PY8VsPcbb9++lZGRIRYuchdQXO7duzdlypTy8nJA5Fx+GXSP2/r6+m3btuno6Jw/fz4kJARmcEG3fPwkMkJ+fvny5TVr1hgbG9+5cwd0F+ARN+IXKS0tvXLlyrlz53jpivGIuAQGBq5cuZJCofzkNUvQAyTP8vXr17Nnz06aNElXV7e0tLSrqwtGQ791NDqd/uzZM2Nj45s3b7q5uYHuDQD6xHSeIzo6esiQIdra2rw0dHEvLvAZuHfvHqxzAQDQaDReukN9BDLp09LSYm1tLS8vv2bNGtiEGKB057cOCAAIDg62s7PT0NCAzTGJEPUXCQkJIZFIZ8+exdoQTsIj4pKRkbFu3TpkXwusjcIBiP4GBwcrKiqGh4eXl5c3NzcjsdLvRpfIhyMiIpSUlK5cuVJWVkaEqL9IUVGRuLi4hYUF1oZwEtyLCxy7r1+/njJlSn5+PiCW5/4UGO9ARW5ubnZ2dt66devx48e/fPmCfODPL+CtW7cOHTrk5eXV0tIC/r0vNcEPqayslJKSunnzJtaGcBIeEZenT5+KiIjAJ4QYxD8BiguLxaLRaF5eXpqamhcvXnz27FlnZyeUAI4EMp2dnWFhYVu2bNHX109OTgZEfcB/cffuXSEhoVu3bmFtCCfBvbjAIOjJkyezZs2CbaKJQfwTEO148OCBvLy8tbX1o0ePmpubQbd/waksCZ1O//Dhg46OjqmpKdJnhyNH5j2oVKqfn5+IiIipqSnWtnASHhEXX1/fiRMnVldXA2Iq+n+ATCd3dnZevXp1x44dp0+ffvPmDSyfQ+r6f3LpkF8h89Pgv+r9U1JSlJWVz5w5c/ny5R5mECA0NTWFhoZKSkoSngt3AcXl0aNHMjIysPwf2UiUmKpAQPIsLS0tly5dUlVV/fvvv5Hd5tFPew/JYH+3Mev3H0Dz/Vf7+PhoaWlZWlo6OjrCwjwiRPqe2NhYOTk5YiN67oLJZDIYDG9vb3FxcbS4sFgsOJSJcQy6o6GmpiZdXd2AgABHR8fAwEDQnYLp9WGRSpaf7DlfWVlpZmbm6ekpIyPj5eUFCOflR9y6dWvDhg1KSkpYG8JJeEFcAAA+Pj4zZ87MysoCKHEh9kJH09zc7O7urqqqmpeXV1VVBVDrFXtkQ3r4KUwms7y8PCcn5969e3Z2ds7Ozo6OjtHR0Tdv3jx79iyZTK6rqwM/lYy8vLyAgABPT8/NmzfD/AtBD96+fTt69GhHR0esDeEkuBcX+GA8ffp01KhR165dAyhx4Q33G55C77KhyOnX1tba2dnp6elFRUXV1tYC1B4J34sCFJSOjo6SkhIHBwdjY2NZWVkpKakRI0aMHTtWSkpqx44d69atGz58+NSpU1evXm1mZpaYmPi/LIQHb2xsDAgIePTo0bFjx/z8/KhUKiCyQcNWHgAAIABJREFUYygKCgrWr19/8uRJrA3hJPgWF6TMNCYm5p9//ikpKQHdQ5bBYFCpVB4Yvj+JOH4Om82m0+nQMbly5cqZM2fev3//7ds3gFKWH/4Vi8WiUqmXLl0yNTWVkpKaM2fO2rVrZ8yYMWPGjC1btuzatUtbW3v27NlycnJKSkqnTp3S19d/8ODBTxYfwe9iMBjl5eX29vaioqKGhoY1NTWAmNrrpqioSEFBYf/+/VgbwknwLS6g+5Xu7e39zz//wK25kK6LvBEW9c4FQx5pAEBUVJSpqWlMTAzyq59cFsTpMzc3nzZt2urVq7du3bp9+3Z5eXkymfzp06e2trb6+vqnT5+Wl5dXV1dTqVQYW/2vAyKOJPx3eXn5gQMH1q5de/XqVei/4P0GcYSIiIjx48drampibQgnwb24wJwLmUyeMWPG+/fvwb8nOHhAXLq6uqhUKlosfgV41k1NTf7+/rdv3757925bWxs6FfVzzwUAEBgYuHjx4r/++mvp0qXBwcG1tbU0Gu0/v/H7H6KVBX4mPDz80KFDWlpad+7cgfpC4ODgsHr1al9fX16a4uQRcXn9+vWBAweQTvS8V6/1ixKJDqCqq6uVlJT27t2rr6//5s0bgJqk/88v6uzsNDExGT16NIlEsrGxQR8f7Un9p1U99B35x4MHDxYuXCgnJ0cmk2GhTS+WSvISAQEBYmJiXl5evHQRcC8uUEdqampsbGzgpmi8kcftHcgjSqFQDhw4oK2tffjw4YCAgNra2l8Mr+AHCgsLlZWVV69ePWXKlPj4+B96Or/rFSJ+E7Tz1atXFhYWMjIy/v7+MLbipf3Afgsmk3nnzh11dXW4fQXW5nAM3IsLvBmlpaXbtm0jKnTho5uXl2dra7tjx46QkBAYKoLf7N4UGRk5ceLE8ePHr1q1Cq41h08+g8GoqamhUqkwVfy74tLjH8nJyXCnQdg7dsDeNQaDERYWtnTp0qioKKxt4SQ8Ii5BQUFSUlKNjY1goK5hQc867969++jRoxcuXMjMzASoWOYX5YDFYtna2s6fP3/kyJHa2tolJSUfPnzw8PCws7MLDg4+efLkgwcPfHx84Br037UQCZSgh1VfXy8tLb1s2bKgoKAeJzKgiIiI2LBhQ2xsLNaGcBJeEBc2mx0WFqanpzcwxQXOu0PP4uvXr+7u7vr6+k5OTpmZmXBv0N+9IO3t7RoaGurq6tOmTRMTE1NUVJSVlVVQUJgxY8b69eu3bdsWGBiYmJhYVVXFkXz5rVu3li1bpqOj8+TJE+R0BprEREZGGhgYwJW3PAPuxQXWcXz+/NnBwSExMREMvJwL7OwJAMjLyzM2Nr506VJGRgas8YEX53evRltb25YtWyQkJAQEBPj4+P7++29RUVExMbGVK1eePn06OjoarqIGHIpAm5qaTp8+DfvXwf67A+0OAgBiY2N3796dnp6OtSGchBfEhU6n19fXW1lZPXv2DAzUnMurV68MDQ137dpFJpOR+rTeTca3tLSsX7+eRCIJCAjMnz9/9uzZ69atO3bsWFJSEky1AFT1CkcudW1t7eXLl2VlZQ8ePAiLfQfaHUxLS5s9e3ZISAjWhnAS3IsLEhbt2rUL6ds60IZmYmKilpbWjRs3AgIC4uLi2P/md49WXV0tJye3cuVKR0fHsrKyd+/excfHw55yEHb3oiSOhEVQrWpqak6fPi0lJXXo0KHnz5//4TFxh6Oj47Bhw/z8/LA2hJPgXlxgQqG9vf3GjRtw1cxAEBe01/D27dtJkyZt3bo1MTGxvr4e2Va11wf/+vXrrl27pKSkjI2NkQgIoCriEDhyneFhGQxGQECAh4dHWlrauXPn0tLSQHfENxCSaDY2Njo6OhcvXsTaEE7CI+JSXl5uZGQEE7oDRFxgr4nk5OS9e/f6+fnduHEDzjr/+WPPYrHOnDkzfPhwFRUVCoXyEw+II9cZKcApLi6uqKh4/fr1hQsXfHx8YGHBQBAXGo1mYmISEhLy+vVrrG3hJPgWF2RGs6qqSl9fH71wEWvT+oOIiAg9Pb3IyMj29nYKhQJQK4P+8Aq4uroKCAgcP34czjdB2Gw2jUZraGgoLCyMi4vLy8v70xPoPiy6rUxra+urV6/09PTs7e3fvn3L88oCAGAymQ8fPlRUVIRbhvIMPCIu+fn5JiYmSPk/r4oLUilLpVK/fft27NgxAwODkJCQiooKgMrg/vkD6ebmNnXqVF1d3cjIyC9fvqSnp0dGRp46dUpdXV1BQUFMTExfXz8qKoqDNbXo+t3GxsYrV66YmJgcP358gCxufP369cqVK69fv461IZwE3+ICutOBCQkJcnJy7969Azzd6AxRjbCwMEtLSz8/v+Dg4Pr6eg4WhsDjpKamysjIrFmzZsGCBYsXL542bdqYMWNGjRo1YcKECRMmzJw5MywsrLm5meMRKPJiaGtr8/X1NTAwcHFxefv2LeDRJWMIz58/l5CQcHV1xdoQToJ7cYHDMS8v7+DBg7BMgLc9l87OztjYWDs7uwsXLhQVFTU1NSEFrxw5cXZ3b6rw8HBjY+MDBw4sXrxYSkpKSUlJR0cnLCwsKSkJ7mwJ+uBSoye56HT6uXPn9uzZY2RkBE8TlvPwJFVVVcuWLSO6/3MX0HOprq62t7eH+xbx8PsNAODh4XH16lUfH5/Q0FBkYgipl+PIVyAp4dbW1urqah8fn4CAgKqqqqamJvTjzcE6F/RXo/PH1dXVNjY2lpaW9+/fB7x7Z5lMZnh4+IEDB2ATaJ6BR8Tlzp07mpqabW1tgOfCIiRBy2Kx4uPjN23apK+vf/ny5aKiIoB63jh4yr94Afv6IsOzzs/Pf/TokYqKyocPH5Dv5THnlMFghIaGKioq/u5yLS6HF8QFFtGpqqrCvCaPvd+QXgQvX748duzYixcvPn/+DCdxfn0tYu9Aq0yvS/J6DaIgxcXF6urqBgYG58+fLy4uBjw3P93V1WVoaCghIcGpCTguAd/iguQaaDRaaGgorNDlsdcaDFKSkpJMTU1dXFyQtW3wNPutqKefLyk6+cJisdLS0mxtbUeNGnXp0iXYl4+XbnFXV9fdu3cPHTqUkZGBtS2cBN/iArr9lJKSEnt7+w8fPvCSz4ycRURExNKlS/X19UNCQuA+HsjSHl56gfcA2fYE6QdmbW2tq6t79uxZ3ri/CEwmMzQ0dN68eVeuXOGlU+MFcWGz2eXl5VFRUUhCF+93CKmvBwA8f/5cR0cnKCiorKysR1IJ76f5iyA39PPnz87OzqKiosjiI/SFwi9sNjs8PHzLli2amppdXV1Ym8MxeEFcmExmS0vL8+fPeWbhIlKxmp+fLy8v7+rq2tjYyEJtM4T3E/wtkGZXAICWlpadO3dqa2unpKTAomQOTpNhSGBgoLa2NplMxtoQToJvcUEqdDMyMrZu3VpYWAh4aLYI1rOYm5unpKTArWmRdzhvnOAvwv73zpC5ubk6Ojr79++/desWsoEv1jb+EV1dXUZGRitXrkTa8fEGPCIuhYWF+vr6sEE3Th88tGp0dnbevHnz4MGDVlZW8Plh89Z+Kb8Fcu6Itr5///7mzZuKioqwAAfg3KGj0WjOzs5r1qzx8PDA2hZOwgviAv97/vx5WAqB0yAc8fxZLNaFCxfgzCssHiNAgArCZDJLS0svX7588+bNwMBA+CsGg4HffTmcnZ1lZGTi4uKwNoST4FtcQLdL/PXr1507dyKLUPD4BoM20+n0oKCgPXv2vH79OikpidgzrAfoDi9Pnz598eJFUFDQvXv3YOkwHl8qkISEhClTply+fBlrQzgJ7sUFPpO1tbUhISEfP34EuBUXAACdTr9165aFhUVISEhycjL8IU7PpY/oER4CAOLi4nR0dEJDQxsaGrC2rpfQ6fTQ0NBVq1Z5enpibQsnwb24wLCosrLy9u3bsHcsUi+PiyAcCeK6urrs7e0VFBSuXbsG4ztc2I8V7O7OEvX19ffu3dPU1ITNUJC6O3xdvaCgoCVLlsD9D3gGfIsLu3sbiqampsuXL5eXlwNU2S73T1Kyu1f6slgsa2trDQ2NtLS0hoYGHD0VGMLubs7w9evX5ORkCwsLxHXt64URHMfb21tSUjIgIABrQzgJ7sUFrrvJyMjYs2cPfCxhVo9KpXZ0dHD56wu+YGk0mru7u6amZlxcXHl5OX7Dun4G8VAYDEZ6erqrq6u5uTn0XzjSjq8/CQ4OXrJkCbFwkYtAfOPs7GwzM7Ouri5kVNHpdBqNxv0PKovFev78+ZYtW27evFlVVQWzlVxuM5fA7m4kDMdAbW2tvb29vr6+v78/wFvqLS4ubvHixUT3f+4CDqC8vLwzZ87AbtLcPxWNuFcAgPv37+vq6ubm5iLdanH0SGAOuvCHxWIVFxf7+vpKSEh4eXnBeBkvqbf8/PyZM2fevHkTa0M4Cb7FBXGM6XS6gYEBbH/P/f4wtLCrq8vPz2/btm3GxsZws3eC3sFGtfjOysq6e/eugoICrH/By+Kjd+/ekUgkJycnrA3hJPgWF4BaH6ypqQnbYeDFHyaTyYqKio8fP6ZQKDQaDRc2cydoD6Wtre3Tp0/Xrl1TV1dHUhhcLi5MJvP169cqKipE+T93AcfNt2/fNm3aBGeLuLlMEypIV1eXj4+Pn59fYWEh9Flw8XblWpCwCF5DOp0eFRV19OhRMTExKyurqqoqLr+2dDr9w4cPx48fDw8Px9oWToJ7cYEhxufPn/fs2VNWVga49TXF6t4unsFgmJmZycvLh4WFNTY2VlZWsjmxGQgBBPqtXV1dFRUV58+fV1JS8vb2BqitS7jzUmdlZS1YsODq1atYG8JJ8C0uSM6lublZS0sLWePHhSEGHNMUCsXDw2P37t0mJiaZmZnIYiIO7g0ywEHk49u3b1lZWffv39+5cyfcroDBYNBoNC50bLu6up48eaKlpRUTE4O1LZwE9+ICx0pycvLcuXPhjotcC4vFSk9PV1dXj4+P//r1K+hutsapXUEIAKo/A7yeKSkpBw8e9PLygo3EuFPEOzs7XVxcLC0tkTUfvAG+xQV0u8FFRUUKCgpIhS5XDSBoDJPJNDQ03Lhxo6+vb1JSEkBto4G7WnVuho3awonNZlOp1Ddv3pw6dcrY2BhuPo1cZ6665gkJCVeuXElLSwM8VIuAe3GB76jGxkZlZeVPnz4BbpqKRtezREZGKigouLu7Z2VlYWvVwAGRj4aGBjMzsx07dsD0OZtze8hxirS0tPnz5xsbG3OV5P0hvCAuAIDy8nI9PT24tISrxAUA0NraGhUVZW9vf+XKlQGy8zGXgH5Qs7OzL168qK2tjV5/xCXJXTqd7ubmJiMjQ1TochGIa/DhwwcTExOkKRnWdv0fnZ2dISEha9euvXHjxsOHD7u6unjp1cTlIAoCL3hdXZ2cnJylpWVSUhJcNMAl4kKhUK5du6anpwcXLrB5pZMpvsUFdM/CNDc3Gxsbw6lozO8KIh8UCsXV1TUgIODq1avwhQm4wLwBBaIs8CV07969pUuX7t27NyUlhd29KzbA+qZ0dHTY2dnt2LHj9u3bGJrBcfAtLjAbSqfTm5qaTp8+DSt0MXcN4IBua2tzd3d3dHRMTU2FqkeAIUjuPCQkxNraevHixXB/EmRrAWy9mPj4eFVVVWKvaO4CPsmFhYXa2tpw+2RslQWOYAqFcv78eW9vbzc3t9TUVMJbwRxkmQgAwMvLa9OmTXZ2dnBzWMAF+8MmJCRoa2vD+SyegRfEBQBQUlKioqKCTEVjbRS4ffu2qqqqi4uLv78/L21zhV8QzwX+b2Zm5sWLF62srOLj42GnDgzFhc1mx8TEKCsrwybQPAPuxQXG0tXV1SYmJsg6nf7XF/TAvX79+vbt2/38/FpbW2EvKwLM+T5YjoiIOHnypIaGBrJcEEoMJi+nN2/eeHp6vnr1qv+/uu/At7ggj3RNTc2WLVtgC1JMxgfSB/fp06eXLl2KiYkh8ixcC5JhefXqlb6+vr6+vp+fH5L37X8XhsFgODk5+fj4EKuiuQs4FFpaWoyMjCoqKgB2LRfYbHZaWtq2bduCg4Pb2tq4qkaLAA0yP81kMkNCQjQ1Nf/6668rV640Nzcj60v7k46ODk9PT0VFRWQPJt6AF8QFVug6Ozsj9Zf9/1QXFBScPXvW3d3d3d3927dvgLs7Pwxw2N3NpeA4effu3dGjR2VkZK5fv15XV9f/44fBYNy6dWvu3Lk8Vr2Ne3GB4+D/tXfu8VBn/x8fl5RshahQLmm7aSnLL9ZECWW1Lrl81brUVrq4pazdXNpIZNNFKl2kIoqVZYkiIcalyGiU27jOEAZjMMwM5vP74zx8Hp+vbraM8D3PP3po5jPncz6fzzmvz/u8z/u8T1VVlZub2wT7XEACVwRB+vr67ty5Y2lpmZ6eTqVSJ+DUkPECNJWampqTJ096eHhkZGQgIwtKJywVRm9vr6Ojo5KSEoxzmVyglsvDhw9zc3ORCcznAk7U1NS0d+/egwcPTrPU7f8LYPNLlZaWnjlzZt++fejm9hM2hTQwMBAbGysqKnrt2rUJON2EMeXFBbxh3r596+rqijaLCTNr6+vrTU1Nr127RqPRwHL+SRJRDhkLXMzm9sPDwzQabe/evTo6OnV1dSwWa2hoaGIm+xgMRmZmpqamZkJCwgScbsKY8uICOnNtbe327dvRPWsm5tRsNvvJkycPHjzo7u5G/rulQqYK3BHAf4OCgiwsLPbv33///n1kxHHGay9Mc3Pz/v37N2/efPz4cd6dZeKZ8uICHn9eXp6jo2N+fj7C46aAzib09/f7+/tbWlomJCSgu4JApi6gIdFotJCQEC0trU2bNqHZVXidn2F4ePjQoUPy8vInTpzg0Sm+ClNeXICdUlhYuGHDBmwSJh6dDpRMIBCcnJxiY2PLy8vBZkk8Oh1kwkCHtC0tLR4eHgsWLLC1tX38+DGHw+G1Tdrf33/s2DEvLy84FT25AD6X58+fOzs75+XlIbwP/6fRaLt373Z1dQWGEofDgbPO0wDsCkYWi3Xp0iUvLy8LC4uHDx/yWlzYbPa9e/du3LgBVt5OG6a8uAyP7DoeGxubmpqK8GabDrRhPXv2zMjIKDw8nEKh9Pb2TraEZpAvAbu4kc1mp6en+/j4HD9+PD09HYyFuRjG66SgqOTkZGNjYyKROJ0mBKaDuCAIUlZWdvLkSSqVyovwbbTBdXZ2Ghoa7tixo7m5GVor0w+gGmw2G0wScTgcX19fX1/fQ4cOJScnI5j9ScZFXLA69ebNmx9//BEG0U0iuCOZ6N68eYPH469evcqL2Cfw+Mlk8vXr169evUoikcAGidBgmWaAZ4rd3L6qqurRo0chISH79u0jkUjg1TVerQs0VCaTyeFwEhIStLW1SSTSuJQ8SZjy4gJ4+/atu7s7SM/B4XDG3XjJysoyMTE5d+7czZs3a2pqBgcHJ0+mXsh4gT5TdKyNIEhvb29MTAwej1dSUkLnj8bRcgEnCgsLc3d3JxKJX17s5GFqiwsy8oQKCwv37NkDVkWPV+If1PoFhd+4cePVq1forDNUlukH+kyxfwwNDXV1dcXFxV27du3s2bMg/gV18X5hS0O1rKCgICEhobi4+MuuYHIx5cUFzf5/8+ZNIPzj1e1Bu3n8+PGmTZs8PT0fPXrU19c3LiVDpgroIGhoaOjhw4ehoaE6OjpgR2esdfPlEInEI0eO0On0cSltkjDlxQW48YuLiw0NDcGqs3H0hhQXF4PNhtFkDtPJmQ/5JKgHd2hoqKWlpaSkZNu2bXv27Glra0Mwnv4vP0toaGhgYOA0W/U65cUFPN329nZDQ8O4uDhk/MSFSqXu3r3bxcXl/v37wGaBfpb/NdDwXGChtLe3p6SkHDly5OeffwZxD2hj+5KGweVyExMTL126RKPRxqvmk4GpLS7ckcQcIJfXkydPkC+L0EWbUWNjY0RExMmTJ0EaB8j/ONhp41u3bunq6jo6Oubk5IB325cvoQ4JCdmxYwebzR63Gk8Cpra4ICPPlcViBQUFAYfulwyD0TZ04sQJPz8/Op0+8XnJIJMT1IlLp9PJZHJwcLCenl5SUhIyHsl3z58/b2JiAh26kwjUcsnOzjYwMAgJCUG+OAUchULJzc2NjIyMi4tjs9kwABcCQBsb+C+JRNq5c6e+vv7z58+RL251BQUFbm5uYPuKacN0EBcul/v06VN9ff2YmBjks1IuoPJRV1fn5uYWEhJCJpN7e3uRSbDFGmSSgJ1+Br6YtLS0kJAQPz8/dCbhswtPSkrC4/EgDnjaMOXFBURqUygUf3//iooK8NT/1WMeHBwEY5/W1lYXF5fAwMDq6mqgLBDIx6mvr/f19Q0ODgbziaj0/FuhiY+PNzIyggsXJxcg1oBOpzs5OV26dAn593M6oCm8ePHCzs7O1tb29evXMJ4F8nGws0gNDQ2JiYlHjx5Fdx36jKF0fn7+n3/+Oc12uZra4oKGIVRVVW3ZsiU9PR35rEdbWFi4a9cuf3//8vJydGYRjoYgHwIVFzSd0NGjR0+cOJGSksJgMJB/P0SqqKhwdHSsrKzkSXW/ElNbXJARKYmMjDQ1NUVda2Nxu6CZmXNycqytrS9dutTX14ddWc/rmkOmLtz/BkGQV69enT592s/P7+nTp6jtPMZWNDw83NLSEhoaCjalmTZME3G5ePGijY3N2LP/c0eWU4eHh9vY2ERFRdFoNCgokM8AjdN9+vRpQkJCVFQUmPRBg18+2a6YTGZ1dTWJRJpmu3ROB3FBEOTq1asrVqwgk8nI2F4X4Jj8/PwdO3ZERkaCveJhaD/kMxjG7K/2+vXr4OBgBweHioqKUV99vISysjIikdjR0TERNZ4opra4oAZIcnKynZ3dzZs3kTFrRFFRkaur6/Xr1x88eNDS0jL2H0IgWLDOl56envj4eDs7u5SUFPDtGM3hxMTEGzdudHZ28rCiE86UFxfwUEkk0vr1652dncHmQR96oqiNmpeXp66u7uTklJ2djS5Cm8iaQ6YloEGGh4d7eHj89ttvQCw+6X/hcrlpaWkZGRkwiG5yAfb6uHPnjqys7L59+z4iLqgSlZeX29jYgPwsE15fyHQG2NEsFuvatWs7d+7U1dXNyclBMNl539syBwcHPTw8jhw50tzcPNE15iVTW1y4XC6Y32lubra2tnZyckI+FedCIpEMDQ09PDzAf8crsxQEgiAISFHIYrEGBwetra2/++67U6dOoR69j7z2ysrKQkND0cHU9GBqiwsy4igpKirasGHDjRs3wIejHiH637y8PAcHh19++aWoqGgYwwTXGTIt4Y7krAQiQiaTL1++fP369YCAgPb2duTDIQ5DQ0OlpaUODg4glmLaME3Epaqq6ocffnB0dMRufjhqp4hz584dPnz4jz/+gLn7IbyGO5K/Mjo6eu3atZ6enujnaAo7VGj6+vrCwsIePXr01arLG6aDuHC53Ldv36qrq+vp6e3cuTMgICA2NraqqgobRnnmzBlTU9PExEQw2wfdtxCeApplb28vhUI5cuSIlpbWtWvX0PwMYCM9tBEODQ1lZWVduXKlrKzsq9Z6nJkO4oIgyK1btxYuXCglJSUlJbVixQoFBYV//vkHPea3336TkpLau3dvZWVlX18fg8GAQyEIT0GTYyIIUl1dvXPnTg0NDQ0NDbAz0ajBeGNjY2pq6sWLFyMiIrq7u79apcebiROXd/vzqADqsTPqV/X19T4+PkZGRgsWLDA0NNTX19fS0vL09GQymQiCPH78WEhIaMeOHZWVlaWlpWQyuaenZ1yuCAL5EGgTBc2+tbU1LS3N0tJSU1MTxNdh2zydTi8uLjYwMMDhcLGxsQiCDAwMDAwMfKhYBDO9/dmdaAKYCHHhcrkcDgfNbPAu/3apIeo5QxBkYGDg4sWLCxcunDNnzuLFi8XFxVetWoXD4fj5+XV1dQkEgqur67x581RVVW1tbYuLi6fZwlPI5AfoC5PJrKioSE9Pv3DhAlh2Pzg42NbWFhwcbGVlZWhoqKuri8Phtm/fTqVSu7u7sUk/sAP84f/e0gTrRf4qV/cRJkJcUPtweHi4tbWVTCYTCISMjAwCgfDq1avPyJyCFtjb23vixImNGzficLg5c+ZYWFgICQmJiYktWbIEh8PhcDglJSU/Pz99fX1nZ2fgiv9IuAEEwguwg6AnT54sX7782bNncXFx2traS5cuBQ119uzZQkJCM2bMmDVrloaGhru7e1dX16hCRu1kUltbS6FQ0CS+E3lFY2SCLBfwb3l5+bFjx2RlZS0sLOzt7devX6+mpubq6vpv/VhAHfr6+k6dOiUlJSUiIqKgoLBy5UpjY+Ndu3atXr3ayspKQ0MDh8PJy8tLSkquWrUKbNqAWqpQXCATBndki1gul1tZWbl///4DBw4sW7ZMSEgImNh8fHw6OjobNmwwMjISEBD47rvvZGVlCQQCVjLQFlteXu7n53f9+nULCwsVFZWAgIDi4uLJmemZh+KCHQrS6fTo6Ghzc/Nly5bhcDhBQcFVq1Z5eXlt2LBBVlZWVVW1sLAQ/AqNNfp4FD+CIElJSYqKiqKiojgcbtmyZQsWLFBQUMDj8SIiIg4ODng8HjeCvr5+SUkJuoBo1Cmww1e05sj7xreolw6VJ2ywzKjSsFVFxuxg+sIh9LvXgi32XVX9vBO9e7FcTPLHMU7zfySoDFu3MdbwS24ar0FbDqheTEzMli1bFi5cOGPGDAUFBRkZGX5+/nnz5ikqKtra2kpJSR09elRVVfXMmTPt7e3Y8U5JSUlUVBQej1dWVt62bZuwsDAOh7OwsLCzs5uciWB4KC5oV6yvr3dzc5OWll61atXcuXPBEGbx4sVr1qwRExOTkpLC4XBr1679+++/gav1k+Ft4Dl5eXlJSkry8/OLiYnNnDkTh8MpKira29ubmJgI9Fv4AAAUgElEQVRcvnx5/fr1OByOj48Ph8Nt27ZNS0vLxMSktraWixm+op0B1QvU+MQOcUcdD+YR0URk4A/gUUKPQX+ILerj25ij3QM7rh7VW1Ab+CN35t1bN6pY9ENsrcb+WLGlYesJ/stisUBA6icLQW/gexXhkwe8W6X33rFJAip8VCpVVVX1m2++UVJSWrx4sZSU1Ny5c+Xl5YGjUFRUlI+Pb+XKlWvWrPHy8urp6enr6wM/jI2N1dfXl5GR4ePj09fX37Jly4YNG7Zu3frtt99qamo+e/YMmXwBFjwfFj148EBdXV1YWHju3LnGxsZ8fHxLly5dt26dgYGBqampsrKyqanp+vXrV69ePWfOHGdnZyqVyh2DjyoyMvLnn382NjYWEhKaNWvW7NmzlyxZIi4uLiMjs2jRIiUlpRUrVgCbU0BAYMWKFVu3bsXj8fn5+eDnPT09qGd3VNfq7+/H2h1Y0wOrJti6AVkZGhrq7e1lMpmoDYxg1m1jC3nvFWH7BnfELHrvYR+521gbCvuTd60ArCh8pMAPnQV1oiGYnjNKvz4CdyTV8UfMDVRJxyguw5jU/JMK7GW+ePECGO8yMjJAKURFRdXU1JYtWzZnzhwhISFxcfEFCxZs2bJlz549DAaDO5IbRExMTERE5Lvvvlu9erWoqOjatWv19fX/+OMPExMTNTW1yRkgw1txYbPZFhYWOBxOQEDgm2++wePxGhoay5YtU1FRCQsLYzAYYIrO2dkZaAGQbXSu7iOt6uDBg3g8XlxcXFBQEPzw//7v/+Tk5JYuXSosLCwvL6+ioiIkJDR37lwJCQlgznh4eOTk5KSlpVVWVmZmZvb09BCJRBB38Pr166amJiqVSiKRCgoKwNRgfn4+aKxv375ta2vDTmA3NTURCITXr1+npqampqYODAwwGIyWlpba2loymQx2/B0eHm5qagJ/02i0zs5OCoUyajPgUT0HdA8mk/mhl/9YhtaDg4O9vb2jutl7uygwuD5Z4LuA5TMgJfWXwGKx3jvhijL2vZPBq+LztJLXoC2ZTqfr6+sLCAgICAiAATs/P//MmTM3bdqkqKg4b968WbNmCQoKLl261M7OLikpCTwdFoulo6ODw+FUVVW1tLTk5OR2795tZmYWEBDQ0NDQ1NRUUFCATWE3eewX3ooLhULR0NBYuHChnJzcwYMHz58/HxUVJSoqisfjscsoGhoa0tPT1dXVwaDJysqqp6fn4+JSUlLy448/guP5+fmFhYWFhYUlJCS+/fbb2bNnKysrq6mpCQoKOjk5aWlprVixQkBAwNbWNiws7MiRI/fu3UtNTW1vb09PTzcxMUlNTf3999/PnTsXGhoaERFx5coVT09PLy8vsDAkJSUlLy8vJiYmMjKyuLi4vr7+1q1bp06dSktLS0pKSkxMjI+Pb2xsfPnyZUdHx4sXL2pqarq6usDy1oyMjMjIyFevXhGJxNTU1Dt37mRmZubk5OTn5xOJxJSUlJqaGpBnk0gktra2IgjS3NxMJBJzc3Pv3Lnz5s2b9vb2np4eBoPx6tUrMpnc2NjY09NDoVCys7PBhzU1NSQSqaurq6enh0QiEQiE7OzskpKSvr6+srKypqYmLpdLpVKjo6Nzc3MrKiqYTGZmZmZcXByJRKqsrCQSidXV1cnJyR0dHWw2m06nt7e3Z2dnk0gk4KJis9nNzc1NTU0VFRVEIjE/P7+qqqq0tLSmpoZCoeTl5eXl5TU3N5eUlFCp1NbW1pKSEvDz8vLy8PBwX19fAoFQX19fUVHx+PHjV69edXV1gU1L+/v7U1JSiEQigiAFBQXh4eGxsbEPHjxISEggEokvX74MCQm5cePG06dPKyoqOjs7qVQqg8Ho7Oyk0WiVlZW1tbU5OTmFhYV0Or20tPTu3bu1tbVAYlpaWpKTk9vb21++fMnhcMhk8osXLxAE6ezszMjIyMzMzMjISE9PB2FQXC53YGCgo6Ojra2NQqGUlZX19PR0dXX19/eDqWIKhYJgeiyLxRoaGqJSqQ0NDWDFUHFxcVlZGZVKbW9vb2lpGRwcpNFodXV1oGI0Gg0V+tbWVjk5OeBzBH7cRYsWiYuLoyb2rFmz+Pn5paWlpaWl//rrL/CrkJCQ2bNnz5o16/vvv9fW1j548GBlZWVTUxM6zTo4ODg5t2rkrc+Fy+VmZmbq6uoePHgQvKNCQkJwOJyEhAQ6QkEhk8nu7u6CgoJLlix5N9BoVMlsNvvOnTvq6uqLFy/etm2bpqYmeDCCgoJCQkJLlizB4/EyMjKSkpKbN282MzNbtWpVYmLilStXcnJympuba2pqQHP38PBIS0u7fPlyUVHR7du3AwMDQfeorKxMTk729PT09PS8cePG7du3g4KCCgsL/fz8rl69SiAQnj9/npSUFBcXl5WVlZmZmZqa2tLSUlhYWFRUlJaW1tjY2NLS0tDQUFBQkJSUFBUVlZubS6fTq6qq7t69W1pampeXFxIS0t7eTqFQCgsLCwoK7t27d+XKldu3b2dmZlZUVGRlZdXV1TEYjIqKipqamoKCgqysrPz8/ISEhMTExLNnzyYkJLS2tubk5Dx79iwmJiYxMfHcuXMBAQExMTHBwcElJSWXL1++cOECiUQqLi7+559/amtr4+LicnJygoKCsrKynj17lpqaGhUVtXv37u3bt586dSo6OvrRo0d37tzx9/dPTU29e/dubGxsdnb2qVOn/vjjj+vXr9vb25uamlpZWTk6OpqZmZ09e9bY2NjKyurs2bMODg779+83MDDw9va2sbHZuXPnhg0bzp07d/r0aRcXl/Pnzx86dMjOzu7YsWMJCQlXr1718fExMDD45ZdftLW1XVxc1q9fb2ZmZmBgYG1tvXXrVicnJwUFBXt7e19fXxUVFR8fn9DQUDc3twcPHly5ckVLS8vMzOznn3/+z3/+o6uru3XrVhUVlUuXLu3bt++vv/4KDw/38fE5deqUvr6+jo6OoaGhra3t3bt3TU1N9fX18Xj8pk2bLCwsbt26debMmYiIiKCgoD///NPNze3AgQO7du2yt7c/ffq0o6NjYGDgzZs3jx8/7ubm9vfff8fExERERNja2trb23t7e6upqUVERAQGBvr5+amqqlpaWrq6utrb22/evBlcjoaGxpEjR7Zs2WJsbPz8+fOXL1/+9NNPu3btAh5G1HiZOXPmnDlzBAUFBQQEZsyYISEhISAgsHbtWm9vb6AdDQ0NZmZm8+fP19TU3Ldv3/3799lsNnZsy7v+++XwUFxQ/2VVVVVXVxe4EUVFRTNnzhQXFwebxqMAa5ZAIEhKSkpISIAX2ofu3eDgIIfDYTAYBAIBKMvGjRu1tLT4+PgEBQXl5OQ0NTVNTU2///57HA4XFBTk6upqYWFBIpHQzOwcDqejo4NOpzMYDJCXm8lkdnR0MJlMdPgzNDTU39/P4XCw+cGYTCZ4S7DZbA6HA4K1BwYGWCwWm80GgZVMJpPD4bDZbDab3dvb29fX193dXVdXx+VyWSwWnU4H4tja2gqGZuBynj9/np2dTaPRqFRqR0cHuHYOh9PV1cXhcAYGBmg0WktLS319fW1t7evXrwkEQnNzc3V1NZPJJJFIb968qaurKysro9Pp/f39NBptYGCgrq4OWArACc1gMOrr6xsaGsDdbmlpKS4ubmxsLC8vz8vLy83NbW5uTk9Pp1AoXV1dVVVVwMD5559/kpKSKisr09PTExISCATCxYsXCQRCUlLSgwcPHj161NDQkJ2dnZycfP/+/dTUVB8fHy8vr9OnTxcUFOTn5yclJb148eLhw4cXLly4detWaGiov7+/qampo6Pjn3/+6eTkdPbsWRsbmwMHDly6dMnDw+PgwYM7duzQ1dWNj493cXGxsLDw9PSMjIx0cXE5fPiwtbX1oUOHHB0dd+7ceeLEieDgYDs7OyMjIw8Pj6CgIG9vb21tbV9f37CwMDU1NSMjox07doCIB0dHR0tLS2tra319/dOnT/v7+5ubm+vp6SkrK5ubm2toaJiZmdnb2+vq6q5du3bhwoU6Ojry8vLbt2/39fW1sbExNzeXlJRUUlIC/kEHB4effvrphx9+WLlypYaGhr29/bZt2xYvXowGWAEkJSWVlZUVFBTmz58PPgEeXBwOJyQktGLFipkzZ0pKSvLx8QkICMjKys6dOxePx//000/l5eWgvd2/f19BQUFYWFhFRQVNyIA6/savs/IEns8WobcAGIdkMhm4piwtLbF3B/zNYrH27NmDw+EiIyORD4sLmLIBA+ySkpInT56kpqaqqanhcLgFCxYoKirq6OgYGBisXr1627Zte/bsMTQ0LCgoAI537LwJ1nGL2q7YaRTsCnr0cXIx065Yx+QwZoIW663EngV1fI5y3I5ykXC5XNRJjHzYqYktZNSdxH6LVg/7w/c2TeCFwZ4Ou8p8LO5SrLsHPQsoDY2o7u3tBd4EGo0GymexWEDTgb53d3cDt3pvby+bzR4aGurp6QHDw46ODgaD0dDQ8OTJk87OTvAVeDEwGAwGg9Hc3AzEt6Ghob+/HwxRs7Ky2traGAxGW1sbSDzY0tJCIBAaGxtLS0uBZUEikcrKyp4+fVpWVlZQUEAkEuPj4wsLCwsLC3NycqqqqggEwps3b/Ly8kgkUkNDQ3R0dGxs7LNnz2g0WlFRUWxsbGxsbFJS0oULF86ePRsYGOjr6xsZGZmcnBwQEODr6+vt7X348OEDBw6EhYXt3buXj49PQkJi/fr1enp669atmzt3rqWlpb+/v5qaWkBAAHrDjx49CmZCw8LCBgYGuCNzHZPWe41lgtYWoX2svb1dU1NTQ0MjMzMTewBohZ2dnX5+fvPmzTt58uQnnXnYTsVkMpOTk/F4/J49ey5fvuzr6xsSEuLu7h4cHHzixInq6uqxzDh8xleffeRnMMZZmPEq7UMHjPp8klvmkwomkwny+7NYLDc3NzMzMyUlpY0bN2pra69du/bXX3/dvn27kZFRc3MzEF86nb5582Z+fv7ly5eDmYePOyInGxMnLkA+cnNzFRQUli9fXlpaij0AfFtZWWlubi4mJmZlZTXGyQisfUShUGpra5GRWRU2m93f34++oie/GQmZlmDtWRaLBYxuLpfb398fFRXl5uamqKhoYGCwa9cuc3Nz0C+AVRIfH6+vry8hIeHt7Q2KmrSBPO9lgsL/0TsSHR0tIiKCw+GOHTuGPQb0fCKRKCcnJysrGxUVNSoS7EMlY0O53j0dMoaQPAiE12Db5yh3SVtbW3Z2dk1NTV5eHpj0QBvwo0eP1q1bx8fH9/vvvyOY8fjXuILPYYLEBb0p3d3d2traUlJS1tbWo0Kw8vLydHV1paWlly9fnpeX969K5v533C33nRDSqfVUINMMtJFz3+HdI9G2eu/ePRD5AvYpRh152IOxf6C+rfc64yaeiU4WRSaT5eXl8Xi8paUlNizt+fPnzs7O0tLS4uLi3t7ewHf11e8OBDLBoM2eyWTu2rWLj49PRkbmzZs3CMbdjj141NsUhIljv/0qVwGYaHHhcrm//vrrggULlJWVgX8EQRAikSglJSUmJqalpYXH40Ge7Skx2QaBjC+ouAwODtrb269Zs0ZSUhLd7W9Up8CKC7aQ6urq+Pj4urq6Ca78KCZaXIaGhuzs7ISFhZ2dnREEaWlpOX78uLy8PA6Hmz9/vrGxsbe3d01NDRcz9QuB/O/AxSxGu3XrlqKiIg6HMzEx+eQP+/v7qVRqRUVFUlKSlZWVu7t7YGDg190IiecpF0Z9yOFw9PT0cDicjY1NZGSkrq6ugoKCmJgYCKCMjo4GYyU4IIJAOjo6Dh8+zM/Pv3DhwrCwsOrq6oqKiu7u7oGBAQ6H09fXB+J9Xr9+fffu3X379pmbm69Zs2bp0qW6urq6uro+Pj6jMk5NMLwVl6GhoZcvXz5+/Dg7O5tKpba1tVVWVq5bt+6bb75ZtGjRli1bVFRUDAwM1NXVz507FxISMjlz3kAgX4u4uLjZs2fjcDgREZGVK1eqq6u7uLgcOHDA09NTR0dHVVVVQkJCQUFBUFBQVFTUwcHBxsZGWFj422+/dXd3z8zMBOunvha8HRYNDw87OjpKS0svWbLEysoKxAgtWrRo6dKloqKisrKy69at+/7773/55ZeoqKju7u7h4WGY4xYCQSktLQULXDQ0NISEhGRkZMTFxeXl5UGOtFmzZgkJCfHx8fHz88+ePVtCQmLjxo16enrh4eFgUeXXfVvzVlyqq6tBLgUhIaHly5dLSUktWbJEWlpaXl5eSEho5syZa9asWbly5YEDB8hkMnckGyBPqwSBTAmAVwGsaDc1NZWUlJSSkpKTk5sxY8aiRYtmzJgBlj5qaGisXLkSJIjR1dV1d3cnEAigBDSp0NeCt+LS1dV14cIFZWXlNWvWyMvLy8vLy8jI4HC4jRs3Hjp0aOvWrQ4ODmioLpx7hkCwgAmN7u7ujIwMkBYaZC8SEREBYyU9PT0tLS0REREjI6MnT55QKJRJlXuBtwsXwR8FBQVGRkYKCgqrV6+eP3++urp6fn5+RERESkoKWHAMI9wgkHdBX7fDw8PNzc3Z2dnWI2zatOn06dOhoaHnz5+/ffs2NufW5Jlj5blDF0EQCoWSlZUFsofEx8eDRPwoo+KCIBAIAI2OQ1WGxWINDg6yWCwQKTc0NITKChpEN3l6E8/zubzXJEFjDWFgPgTyIVCzBduV0M4CXCrckewcKJMnFcOU3ysaAvnfZNTCokkIFBcIBMIToLhAIBCeAMUFAoHwBCguEAiEJ0BxgUAgPAGKCwQC4QljEhcYmA+BQP4tnxYXECPY19eH3cIGAoFAPs6YxIXL5XI4HJgMAQKBjJ2xWi4wTh8CgfwrxurQhbICgUD+FXC2CAKB8AQoLhAIhCdAcYFAIDwBigsEAuEJUFwgEAhPgOICgUB4AhQXCATCE6C4QCAQngDFBQKB8AQoLhAIhCdAcYFAIDwBigsEAuEJUFwgEAhP+H+iU8g8iiMe2AAAAABJRU5ErkJggg==" alt> <span class="Apple-style-span" style="display: inline; float: none; line-height: normal;"><strong><em>A2</em></strong></span></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">For a simple planar graph containing triangles, \(e \leqslant 3v - 6\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Here \(v = 5{\text{ , so }}e \leqslant 9\) . <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There are already 8 edges so the maximum number of edges that could be added is 1. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This can be done <em>e.g. </em>AC or BD <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The distinct Hamiltonian cycles are</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">ABCDEA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">ABCEDA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">ABECDA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">AEBCDA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Do not penalise extra cycles.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The weights are 32, 32, 29, 28 respectively. </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The Hamiltonian cycle of least weight is AEBCDA. <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[10 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A fairly common error in (a) was to draw a non-planar version of <em>G</em>, for which no credit was given. In (b), most candidates realised that only one extra edge could be added but a convincing justification was often not provided. Most candidates were reasonably successful in (c) although in some cases not all possible Hamiltonian cycles were stated.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A fairly common error in (a) was to draw a non-planar version of <em>G</em>, for which no credit was given. In (b), most candidates realised that only one extra edge could be added but a convincing justification was often not provided. Most candidates were reasonably successful in (c) although in some cases not all possible Hamiltonian cycles were stated.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 18.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A fairly common error in (a) was to draw a non-planar version of <em>G</em>, for which no credit was given. In (b), most candidates realised that only one extra edge could be added but a convincing justification was often not provided. Most candidates were reasonably successful in (c) although in some cases not all possible Hamiltonian cycles were stated.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The complete graph <em>H</em> has the following cost adjacency matrix.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the travelling salesman problem for <em>H</em> .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">By first finding a minimum spanning tree on the subgraph of <em>H</em> formed by deleting vertex A and all edges connected to A, find a lower bound for this problem.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the total weight of the cycle ADCBEA.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">What do you conclude from your results?</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">using any method, the minimum spanning tree is <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f; min-height: 26.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept MST = {BC, EC, DC} or {BC, EB, DC}</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f; min-height: 26.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> In graph, line CE may be replaced by BE.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f; min-height: 26.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">lower bound = weight of minimum spanning tree + 2 smallest weights connected to A <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">= 11 + 13 + 14 + 10 + 15 = 63 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">weight of ADCBEA = 10 + 14 + 11 + 13 + 15 = 63 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the conclusion is that ADCBEA gives a solution to the travelling salesman problem <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered although some candidates failed to realise the significance of the equality of the upper and lower bounds.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered although some candidates failed to realise the significance of the equality of the upper and lower bounds.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered although some candidates failed to realise the significance of the equality of the upper and lower bounds.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sameer is trying to design a road system to connect six towns, A, B, C, D, E and F. The possible roads and the costs of building them are shown in the graph below. Each vertex represents a town, each edge represents a road and the weight of each edge is the cost of building that road. He needs to design the lowest cost road system that will connect the six towns.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 24px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAe4AAAExCAIAAAA1Hdb7AAAgAElEQVR4nO3d32sbaZov8PlP5I3os0defJbZ3e4kPUM0XvYixxceT2aOMOSim3HSE/mc2RN6muQgGWenycDKAzYJTQwDPTKtDOwszEpkWHYYBYruCzEkiFPL9IUpmItAGbEYYYSgjFmKdy+epFKuKskl1Vvvj6rvB990d9pWbPmrV+/zPO/7DQaQfcdG/VqxsBD8KN3a+82X1tiV/fAAkvqG7AcAIMrI2CotrjUPXye3O+h/UV8pLCxttA6R5qA5RDnkRiDKGWPs1GreLBaubRnH8h4WAAeIcsgNRDlkF6IcciMY5WeD/q+2ri9igwUyAFEOuTEytkrhyue2MUKOg/YQ5ZAb4bJne/d2aaFYunNwOJL70AASQpRDbkTslTPXaq4VFoqrTQtLc9AZohxyIyrKX++6YJsFNIcoh9yIXJUftaslrMpBe4hyyI2IDpb23saVYmH1gXGEJAetIcohDyYM7hcWV+qf/7Y/QI6D7hDlAADaQ5QDAGgPUQ65Y73hOI7sxwLAB6JcN+dGFm8eWKeyH5BOOu321fcu+7fLf/bw4XA4lP24AJJClOvl7Kh9d8lLIrTQxeY4zo8++iiq8rnw7ffft21b9gMESARRrpXxi73VTzHMMoenrVZkjhcLC+9cunTrhxuyHyBAIohyjbgjY3upsLhS/7xjWGPZj0Yvl999d1KU0wcW5qA1RLk+3MOD1UVfQ3QbN5nFZFnW9BwvFhY67bbshwkwP0S5btxB/9nnW9cXi4XFld0XWJt7HMehvpRut9tpt5+2WvVarV6rrVcqF+Y4ohx0hyjXk3tkbK/m7RCo4XBIYd1ptzvt9v6TfQrr5XI5Mp03q9V6rbbTaPzzr399YZTfv3ev1+uhPRE0hSjX1sjYKmXtJjPbti3LMk2Twnqn0aCwnpS/9F/3n+zTn6egj2wufPzo0cSy559dWi5/x3s92Gk0kOmgHUS5ttzDg9UPtesrp7Tt9XoUvpTFm9VqZMgul8v0B562Wp12u9vtzj3a4zjOt99/P7J95ep7l6nmaZrm/pP9QKan8D0A4A9Rrq2R8WDbUO3ym1k3rNcrFfoDlOy9Xo/+95Qe2/1798L7KuHeFX+mL5fL+0/2TdNM4yEB8IIo14Y76P/22etD/NxB73F91xiciX8Yc29Y0583TdOyLImdf8PhkN4TdLvdCx8GMh10gSjXhjt4/uD6YrGwUCzd2vvNl+l1IgY2rL2wTr5hra9er7fTaHjbPsh0UA2iPI8CG9ZUXRSwYa07x3GQ6aAmRHkGBTasverirBvWOQzrmCIzPaUtfoA4EOVaCmxYe9XFmTasET3JBTJ9vVJ52mrhDAAQD1GuKC4b1sgUYZDpIBeiXBouG9YZqy5mwHA47Ha73s8RmQ5ihKLcfdW5c813KznMCRvWOYdMB5GCUe5azbUC7jSIBRvWEEc40zvtNt5OAV+BKD/p797/+e7dJdw0xhjDhjVwFcj0zWq12+0i04GL81E+MrZuNK0TY6u0sFRXbig8DZS2gfObsGENqaJM97bakOmQnD/KT63mj7eMY8aOjfq1bByg6m1YB85vwoY1qMC27aetFjIdkvNFuXt4cOez/thlr3fM9ThA1duwDpzfFHPDOtXzmwBiQqZDQl6UuyPj0x94jSvu4cHq4tKd9tHUdbkXo6muW2nDOnx+U8wNa+nnNwHEF8j0eq2Gw9MhDi/Kj436tVAsTix+DofD8HmhT1ut+Z5zSTass3p+E+RcINNxIQZM9zrKXav5g/N1TveoXS0tRjaY27YdeYp/sbDw4QcfhJ9tCTes83x+EwBlugKXHJ0N+v/2L7u3lgp56YnQC0X5SX+3HlqAHxv1a5EN5rd+uPHOpUuT9jf+d7WKDWsA7iIvORKU6e7g5aNbSymfrgxJfIOxs4HxcCWiX+XUat4sFhZXtp8PfP/FNM1JIY4NawABhGf6SX/3xtLG/ksZV51ATN+wmjejdsZPff9+wd+Y2Gm3L8zxT3/6qX9jRNbfDSDbApmezuHp7rj/eKV0t3OEHFfazMdpxYnyb125OmmdTrVK2lFBoRKAixQvrnMPD1a/uVL/nHbJi6Vbe8+tMZ9PDTzNHOVxNljoyUSrcip1ervnUzpS/FsxqHACzME0Tb6XHLlWc62wuvXFi4HLGBsdNu8sFW7s9U84PV7gZp5DbtdWvzslx3/6D//gPZm8jbzAAtw/1EN94pGth9TKQtVRbNcAxMTv4jp3ZGwv+Qtp7uHB6iKO21PQPFFu2/bld9+NbGL50Ucf0YLacZzARh4NsE2vfHpti/4G88g2GOqBobIqbdegpgoQkDjTT63mzfNneIT/DShhzqsnbNv+yccfT4nywB/2DzvQwc2zrhFostQbI5oy8BnersGmPOTcvJccuSNjeyncEIFVuXoS3SJk2zZthdPudrfbpWfJpKcIHQjnRfByucylj4om++mRTNmuoU15r5kdY0eQQzNn+sjYKl2ptl+9ie5jo/53uJpGQZwvhDNNc7lcXi6Xp29qe88nb/OkXqulcX6Qf1OetmsiR0z92zXYlIc8oN/BGJccnR217y6V7hwcjhg7G7zYv736uI8pIfXwv9vTtm0K6F6vF+fPm6YZ3n5Je+ObNuUD2zWRm/LooYRsi3Fx3ch6/vh2aaFYWFyp/6qPQSElpXJNs+M49MzYf7If//+ybdv/lPJKNIL3QGhTHj2UkDe4jFRrqUQ5Y8xxnP0n+7SqnTXghsOhfztvUkejeOihhDzAxXU6SivKCY2Gblarcz8Pwh2NnXZbtZUCeigV420IYDoxEWS6RtKNcsZYr9ej7YiEmUUdjf53f+mcOMHZrD2UtCmPHsoE/GU65g6eP7j+d1rch6Wy4XCIS44Ul3qUs9kLodOl1NEonr+Hkjbl0UPJAV2A9fZA7VOreRPna/OCi+uUJSLKGWPD4ZByqtNu8/qc1E0VHijNwBMrZg8lbcqjh/K8Y6N+rXjda5g7Nuo3sCrnLjLTscKQSFCUM8Ycx6Gl9P6Tfe4/csuywh2N2cu1wKb8TD2UudmUd8f9xyuFhaWN1uH4dGDsbj3qDdAGnRpcXKcIcVFOqK1ls1pN6YetSEejeOih9DkbvNinPmjMJQqDTJdLdJSzN4XQKfP9XAQGlOm5lY3tl1nRpvxMPZTeprzsxz4fd2w929v9+db1xWJh9YFxhDQXSebFdTkmIcqZb75fTAsKPbf8+3qYfWATeigvPNhA+e0ad3zYqv6f9pHLmHtkbK8Wcb62JMh0keREOWPMtm1KjW63K/KLdtpt7ToaxdO4h9I9PFj9pm9f5aS/ewMn+ckVznT80nEnLcrZvPP9XFBHY3igFEuGC6neQzkytkr+LXJ3ZGwvIcrVkOLFdbknM8pZsvl+Xg9gjisyIJIaPZQn/d0bxTcjQmz89cHG//Sd0QpKQKZzJznKiTffLzdAIzsa8QxLTnQPpTvof1FfKWBwX3X8Lq4DNaKcMdbr9agQqsJyOHD0BD3DsP2SBvRQAkOm86BKlDPe8/1cCLsiA8Ly10MJ0ZmuwvJOfQpFOfPN9z9ttWQ/lqDAFRnoaJRlvh5K2pTHz0sX815Gml9qRTljzHEc+vmlMd/PRaCjEW8G1aFxDyVMQJnu/RyR6ZMoF+Uk7fl+LpS9IgPCZuqh9DblcQ6lOnDJ0XSKRjnjd9C5AJEdjQpekQGRwpdD4RxKlSHTI6kb5Ywxy7KorUWdQuiFAocKoaNRX/F7KGlTPpfnUMoUzvQ8tyQoHeVM0nw/F5m5IgPC/Jvys/ZQ5jZr0oOL65j6Uc6kzvdzEb4iAx2NGYYeSomGw2Gn3c7nJUcaRDnRohB6oUBHI7b5cgU9lMLk8OI6baKcMdbtdlWY7+cit1dkQFhkD+WFBxtguyaO/GS6TlHOfPP9mXk3GtnRmNVnG8wKPZS8ZP6SI82inCk5389L+IoMdDTCJOihnE9WM12/KGe+QqiC8/1c0LMNV2TAHNBDGZNt21m65EjLKGe++f6dRkPf7/6FAldkoKMRkkAPZaRsXFyna5STp61WBtpa4gh3NOKKDOAIPZRM80zXO8qZVvP9vERekZGl3yhQSg57KHW85Ej7KGd6zvdzEdnRqNE6ArQ2Xw8lbcrrsl2jUaZnIcoZY7ZtU6J12m3Zj0WC8BUZ6GgEicI9lHE25VXuoZR3yZE7MraXIg5qXlypf94x3l52mJEoZ4w5jkNPF03n+3kJdzRioBTUMVMPJW3Kq9NDKe/iumOjfq242rReXzfuji3joL5aLCwsbbQOxy7LUpSTbMz3cxG4IgMdjaCyyMuhlO2hjMz0NF9sAlFORofNO0uFxZXdF+PsRTl7M9+/XqlgKUoCHY1FXJEBWonZQ+ltyovsoRR1cV1klDPmvurcuVIs3DywTjMY5Ywx0zQzNt/PReQVGehoBH35N+Vn7aHk+8Y95UyfEOXs1GreLBYW15qH2Yxylun5fi4iOxqx/QKZIauHctZLjrwWoKlvlCdF+eui6FLdyGyUM/0POhcjfEUGOhohw2hTXkAP5YWZbprmt65cDXzRp61W1K9evqOcMeY4DhVCsz3fz0W4oxFXZECupNRDGc70Trv9u9/9LnK7v1hY+NFHH4U+R443WPy8+X6kUkyBKzLQ0Qg5x6WHMpDpUz5C8zFTy56lu52js1xEOcvlfD8XgY5GXJEB4DdfD+WkDhzv48MPPjj/dXLZjDgJCqFJRF6RgY5GgEni91BGfpz/ZJNGhBZXtp8PXMZyFeUs9/P9XER2NOKKDID4/u/f/33sKJ80uH/l9u4//bY/8Jbp+Ypydn6+H7sECYWvyEBHI8CFaIxxysfPHj6c9XPmLsoJ5vv5Cnc06nXWM4BIL1++LP23P58S5XPMNuY0ytmbQijm+/madEUGttQBGGPD4ZAKTpfffbdYWHjn0qVwjs9XzMtvlDPffD/2BNIQ6GjEFRmQZ47jUFe0t7tr2/ZPPv7YH+K3frgxdxblOsoZY7ZtU9agrSU9kVdkoKMR8qPb7dL71HqtFniH6jjOs2fPioWFly9fJvkSeY9yhvl+gQJHDhVxRQZknWmatFjcrFYnvSXttNuh7sOZIcoZ883312s1LBXFCF+RgY5GyBLbtqkR4MK7KulAx4RfDlH+Fr02blarCBSRwh2NuCIDtDYcDmlpuFwud9rtC1eHtOWY8Isiys/BfL9Ek67IwPsk0IXjOJ12m7bF95/sx9k5HA6HXIYWEeVBmO+XblJHI15fQWW9Xs+rbcZ/rpqmOV8jeQCiPMJwOKT3+09bLdmPJe8ir8hARyMoxbIsSoz1SmXWvUHa103+1hNRHs1xHHqnj/l+RQQOCMUVGaCC4XDo1Ta73e4cn4HOy03+SBDl02C+X0HhKzLQ0QjieW1vtNM9d0SsVyo7jUbyx4MovwAKoSoLdzTiigwQwKtt7jQaSdYQjuPwOqgVUX4xy7Iw36+4SVdkyH5ckDW9Xo+WDvVaLXnNxrIsLjVPhiiPyZvvn287DISZ1NGI7RdIyLIs2hZfr1R4tbfxqnkyRHl8mO/XS+QVGehohDl4xxnSyA/Hz7zTaHCpeTJE+aww368jGigNdDRi+yVj3EHv8caVYmGheH27Y424fE4a+fEfZ8jl03roWmcunwpRPjPM96vh7Kh9dyl8B/lUuCIjs8b/3vniDwOXMXfw8tGtpdK2MZrlmRFlynGGXHCseTJE+XxorGu5XMasiizuUbtaWgjdQR5XuKOxXquho1Fbp3/68g9H3jNhZGyVrm0Zx3N/Ou84w/VKJb3fcap58np3iCifE+b7ZRq/2Nv4ZGvjytxR7hd5RQbecunLtZpr1x/3x/M8M+IfZ5gcvb/ntXpAlM/PK4Rivl+sk/7uJ3t9y6hf4xLlHlyRob+RZTS3Nv7RGJzN+n/OepxhclST5/XZEOWJePP9O40GfuGFcMf9z27vvhizY+5R7hkOh+ErMtDRqLqRsVWin9fqVvtwHPv/m+M4Qy42q1VeNU+GKOeCruzDfL8I4xd7G5/1xy5LM8r9wh2NuCJDZe7gRau+WixcqbZfxXlq8B35mQnHmidDlPOC+X4hTvqPft45ovfOgqLcgysytOEeHqwuLtWN6Q2JSY4zTI5vzZMhyjny5vtRCE2HO+7/4sHbpZboKPego1F5p1bz5pQoT36cYXLdbrdYWOC48kOU82TbNr3OY74/BcdG/Zq3ee37WFxrHgrPc8YmX5GBLXXZjo36auQGi+M4tB1K3QoSX32pxMrxEyLKOcN8vyjSVuWRcEWGTO6rzp1rK/Vf9QdnjJ0NjIdrG63DUDMir+MMueBb82SI8pTgoPP0qRXlHnQ0yjA6bN5ZondppVt77f7g/LNCYm1zEu5NzIjytNBe2HqlgkJoOhSNco83UOrvaMT2i2BpHGeYnG3b3KcLEeUpMk0T8/3AcEWGDOJHfuKjhje+TwBEebow3w9+6GgUIO3jDJOj0ivfz4koTx0KoRA26YoMBXNHL2kfZ8hFvVbjW/NkiHIxvBtdMd8PAbgigxfLsgQcZ8hFGgc3IcrF8eb7lV0sgFyZ6Gg8G/T/7V92b73uJ7leP3jWH/yn9dtnKdanRR5nmBzVPLmPniDKhcJ8P8RB2y+BjkYNtl9eX/vgawd0B/327u1SWmNcKtc2J6EQ4P4KjSgXjQqhWiwfQDqtrsg4O2rfXSrc2OufnP/37rj/eO2iE1FmJes4w+TSqHkyRLkU3nw/3ytfIdsCV2Qo19E4MrZKCxNOPjn+sv0HjlGu4MhPfPVabbNa5f5pEeVyOI5Du3tqNkuBymzb7rTb4YFSqQ/q1GreFHAejtzjDLmgnxf3T4solwnz/ZCESldk0GFniW7UnM5/nKG+b2eHw2FKx+0hyiXDfD8kF9nRKPaKjBSjXJ3jDJMzTTONmidDlKvAm+/X9A0jKIUGSgMdjek/tWiDhX+UK3WcYXI0hprGZ0aUK8G2bfrdQ1sL8CL4igzXaq4VJpU952GaJv1SbFar2tU2J6nXauuVShqfGVGuCsz3Q0rCV2Sk09FIeyzhZkTG3EH/Syv+vclqHmfIBb2gpvGZEeUK8eb767Wa1huCoKxARyNtv3DbUh9/fbBxpVhY3Woa1uubH9yxZbSa/xq+CCKSjiM/8VHNM6WaLaJcObSbhvl+SFVaV2S4g/6zz7euLxb9g/sxYlz94wyTo6uZU9osQpSrCPP9IExkR6PggdJer+cdZ5jh5zy9VqX0KoUoVxQOOgfxxHc0anScYXI7jUZKNU+GKFfZcDik97/cz8MEmC7hFRm0e9Npt6fMK+l1nCEX65VKSjVPhihXHOb7Qa7AFRkXdjTatv2Tjz/29mro4/69e/4/75X3qQaYkye24zipHruEKNcA5vtBunBHI12R4V9027Z9+d1337l0KRDlxcLCt99/33EcfY8zTC7VmidDlOsChVBQx6QrMr7/ve+FQ9z7+MnHH+t7nGFyVPNM79ULUa4Ny7Iw3w9KCXQ0Xvjxv77//dw+e+nQ+fQ+P6JcJ958fxonqwHMzXEcfzvjpI8cLsY965UK96uZ/RDlmsF8P6jJG/BBlEdKtebJEOWawnw/qIbKelM+rr53WfZjlIa+OaluLiHKdeXN96MQCoq49cONd/4son3F6zuU/QCloWsJUu3YQZRrjMad0dYCirBt+3/8xV9E5viPPvpI9qOTiZo4U/0SiHK9Yb4f1EEn/33/ezf8If5Xf/mXeH5uVqup1jwZojwDMN8PiqASznA4dBzHeoMxtl6ppHf2iBYE/HoiyrPAawXbaTRQCAUpaDA9srGK6jq5bV+hmmfa70sQ5dlBV9livh+kmJLXjuMsl8tp7zAoi2qeaRe0EOWZgvl+kOLCsM7zwpzWWGl/FUR51njz/TkvNIFIFyY1VUTzOddWr9UEvCNBlGeQbdtUCMV8P4gRp7DpFUXFPCR1iGlJQJRnE+b7QRja1rvwXWA+F+a2bYvpxUSUZxkOOgcB4vcaUp9Vrp6N9DonoHaFKM84qp5jvh9SEnNJTqgtL1cT/GJqngxRngfefH8++wcgVfVabblcjr/QnvXP665eq21WqwK+EKI8FzDfD2mYY5VtmmauCvLCygOI8rxAIRS4m2+JnZ85fqp5inndQpTraWRslQKHzy2uNQ/dqf8T5vuBI8qpOdrsZtpe1xq9BRGzsYko15E7MraXgueI3jywTuP8z958fw47fIGjJH3iOVmY0+SUmK+FKNfRsbH72Bicvf0XI2PrRtOavib3wXw/JJSwSZwaqzJfhxdW82SIci25/2H9aeT751Or+eGFuysBVAjFfD/MJ+HoZk4O2Foul4WVphDl+nMPD2580jk6u/hPnufN9+eqzxeSo/NsdxqNJJ8k8wds0RsXYb9ciHLtuVbzB3VjdPEfjOA4Tr1WQ1sLzIRLCk853zwbRNY8GaJcf6dW88dbxnGST4H5foiP495Itg/Yohc8Yb9TiHLNuYcHNz41RjPtk0egMtR6pYJCKEzHsWKZ7QO26rWayC4dRLnekuyuBJimSYVQ0zR5fD7IJr59hLQwz+TbwfVKJWE5YSaIcq1x2F3xw3w/TMd9uierB2xRJUDk3wtRrjNOuyt+mO+HKdIY7cnkAVv0EiWyPwdRrjHXalV3X4x5f1rHcehtb71Wy9gvGCSR0klYlHoZO2BLcM2TIcphEnouYr4fPOktn7M3x7/TaCyXyyK/IqIcJsJ8P3hS3dTO3gFb65WK4FlWRDlMg0IokLR3tLO0MBdf82SIcrjQcDjEfH/OCWgAz9IBW/QORnBTL6IcLuaf70chNIcEjGVm6YAtqjMJLjIhyiEuzPfnk7CZzMwcsLX/ZF9wzZMhymEmVJ7CfH+uCDspJTMHbG1Wq763F+7Y+v3expViYaFYuHJ79/fWmOcgiAdRDrPBfH+uCN73yMYBW/7CknvUrpau3G5+PWaMuUfG9uoSp5M2AhDlMDPbttcrleyNdUCY4E2PDBywdb7meWo1bxZL295Itms113z/yBGiHOaB+f48kFKK1H1hTq04b3Yg6RreG3v9E+8f/xqrclAN5vuzjVJJ8E6a7gds0S/F238ev9i7vlgs3Tk4HLmD55/Wf/FyMPOFX3EgyiERb74fhdDskTW2o/UBW+drnowx5g56j6nsuTrDXeqzQpRDUr1ejwqhSPMskThMr/XCvFhYeNpqnftX48PO7u5efbVYWFzZfj5IJ80R5cAB5vuzR+4kvaZz/LZtB38Lxl8f3Kl3js4YOxsYD1cKiyspnGbKEOXAizffH1ySgIZSOs82Pk0P2KKH7Xt7emo1b/r2Vdxx//FK4eaBdcr9SyPKgRvHcXYaDcz3Z4AKu9U6Lsyftlrnap7s2KhfO7dFPjK2Sohy0AHm+3WnyFa1lP6ZhOq12vmaJy3D34wIsdFh885f32kfpbBdjigH/nDQudbo2gTpr8Q6HrAVNWlxNuj/auv6Igb3QUuWZVFbi3bbnTmn1LylXgdsUc1TVoEBUQ5pwXy/jpQatqQDtnYaDdkPJBZ6MyrrhQdRDinCfL9elFqSE6VeWqaj9xCyvjqiHFKHQqguqAFDqQqHgq8uk9Rrtc1qVdZXR5SDCNSNgPl+lSlbZtRlYb5cLkt8yUGUgyDefL8uVay8UbbGqEhz5HT07kFiWQhRDuJgvl9Zyi7JiQojS9PRfKzEF0JEOQjlFUIx368UxQfl1V+Yy615MkQ5iOfN9+80Giqvs3JF/Sl5xR9hvVaT+/AQ5SAHNUtsVqvql7MyT/ElOVH8QS6Xy3L73xHlIA3m+xWh+ILXo+zjpJqn3P0fRDnIhPn+VIyMrdJCseD/WFxrHkae/aH0NrT7qnPnmvfIlT1gi76Hcpt/EOUgmW3bVAhVNE30Q1cDB6J84sGqCjeHnB217y75XoSUbbOhmqfc7yGiHORzHKdeq+ky1Ke8Y2P3seG/C3hkbN2IvlVS4SW5O+5/dvv+/dulc+8n1Gx+32k0pO/8IMpBFZjv58P9D+tPI98/n1rNDyftrlArkYrf8PGLvY3P+kfPt85HuZoHbK1XKtIfEqIcFEKboeuVCgqh3LiHBzc+6Rydhf+LwsebnPR3P9nrn7CREYhypt4cP726SH9ngygHtZimifl+jlyr+YO6MYr6T6pl4hvuuP/ZbbrLOCrKVXsFok0q6cVYRDkoB/P9/JxazR9vGcfh/6BaIL41fvF4+9nrK9Oiopwp9iJE2/fSHwyiHFSEg875cA8PbnxqjCL2ySmA1NvIOuk/+vnb7aAJUa5UtZbuz5P9KBDloCrHcWjxhfn+uU3aXVG2qy+qIz66mVKdHsrNalWF7ySiHJSG+f4EJu6uqNnSF2HCqpyptDBX5GEgykF1mO+f0+TdFUWX5GGTo5ypMcevSM2TIcpBCyiEzsG1WlXqAzlP8XOpzpka5Sr8Rah9VoW3jIhy0MNwOMR8PxcqLGZ5kf532X+yr0LNkyHKQSP++X4V6l06UmElyxH9dSTubyhS82SIctAO5vuT2KxWFVlFciG9FUed+7AQ5aAfWothvn9W6nR9cCSxG4e+n4q8xUGUg5a8+X4Vmgd0oU4vNke0MJdymhXVPBVZTyDKQVe2ba9XKuosixSXySU5kTXHT0MPgr/oJIhy0Bjm++NT6twSvmSdJ1Ov1RSpeTJEOejOm++v12oZ2zrgSN3DsziR8kKlTs2TIcohG6j2tVmtKrJxqZoML8mJbduCt4/oK6qzuYcoh4zo9XpUCEWaB2R+SU4EF3WpjUqdc2wQ5ZAdmO+PpM3hWckIrusqVfNkiHLIGG++X51NTLmkD9GItFmtCpvjr9dqm9WqmK8VB6IcssZxHLp9GPP9LDdLciLyWALV9qwQ5ZBNmO8ny+WyUovHtIk5YIvKD91uN+0vFB+iHDILB51n7PCsOMQcsGWapmrvdRDlkGWWZeV5vl/6Gaxep9kAAAa1SURBVLDiiakN0LZVql9iVohyyDhvvl+pt8MC5HBJTgSUB1SreTJEOeRBPuf7qc9a9qOQQMABW8vlsmrPJUQ55EWuCqEZPjwrjlSnW6nmqdr3FlEOOZKf+f5MnmcbX6oDrgrWPBmiHPLGm+9X7VeRI/EHkigovYU5LQhUe5lElEPuZH6+P/OHZ8WR3utZvVZTsC8IUQ555BVCszffn5PDs+JIaZdpvVKRcmnRdIhyyClvvn+n0VDtzXISWJJ70qj9Oo6j5uYVohxyjc63y0xbCwWNgmtGWTarVb4dmfTyoGChBVEOeZel+f5cHZ4VB/c5KTVrngxRDsB88/1aF0JzdZ5tfHxPL9hpNNQcvEKUAzDGmG3bVAhVcBs0JizJI/FdmK9XKmq+WCLKAV7Tfb4/h4dnxcHxzYqyNU+GKAcI0HS+P7eHZ8XB6/0K1TzVPGUTUQ4Q1O12i4WF9UpFo0IoluRT8FqY0xNDzUZPRDlABNM0NZrvx5L8Qlza7fef7KtZ82SIcoBJNJrvz/nhWXFwGYLdrFbVrHkyRDnAFFoUQnN+nm18yRfmKn+fEeUA0ziOQxGg7Hw/luQx0QFbc5+6o3LNkyHKAeLw5vtVK3kljKe8SfKyRzVPZSvhiHKAWNSc78fhWTNJshlF32ruD4kXRDlAXFQIVWe+H+fZzmHuA7ZUrnkyRDnATJSa78eSfA5zN24qvpGFKAeYjeM49VqNlsMSi40C7pXPqjnGqagmoci7sUiIcoB5SJ/vx+FZc5tjYU7/i1JlkgBEOcCc6Ndbynw/zrNNYo7vHrUwpfeQkkOUA8zPm+8X3G5MjXHK9jirb9b3NPVaTfEXTkQ5QCK2ba9XKoI3UnF4VkKzLszV7xRClAMkJXi+H4dncRG//4dqnt1uV8CjmhuiHIADb76/XqulXQjFkpyL+F359NqpeIUZUQ7ADe3Apjrfb5qm+itEXcRcmNOPVcxDmhuiHICntOf7cXgWRzFPsKnXapvVqpiHNDdEOQBn6R10jvNsuYvz0rhcLite82SIcoA0DIdDKoTyHfXGkpy7C18daUtd/R0tRDlAKrjP9+PwrJRMP2CLihOK1zwZohwgVRzn+3F4VkqmN3dSzVP9d0KIcoB0cSmEYkmeqin9nfVaTYvWT0Q5QOosy0o4348leaqmLMx1OX4SUQ4ggjffP0cBDYdnCRD5HXYcR5eWIUQ5gCBzz/fjPFsBIr/J1N+ixXceUQ4g1Kzz/ViSixH5fdal5skQ5QDiefP9cQqhtI2L82wFoEPJ/QWJnUZDi5onQ5QDSNHr9agQeuGbdxyeJUy4TWi9UtGi5skQ5QCyxJnvx3m2gtH211dffdVpt//5179W/GpmP0Q5gDTh+X7Lsn728GGxsEAfi3/+3/+2/B0t9mqz4auvvvK++d7H/Xv31P8RIMoBZHIcZ6fRKBYWdhqNX/7yl+EcKRYWPvzgA/WjJAPoPZCmPwJEOYB8VHCb8nH/3j3ZjzHjHMf51pWrU34Eio/aIsoBlPC33/nO9DTXortZX1OW5PRx9b3Lsh/jNIhyAPmod2L6hxYzh/qiDtHpH7If4zSIcgD5aKpw+sf+k31Ltk67ndUPOpEYUQ4A86OzPvCh8sfa6ndlP02mQZQDKOH+vXtTcuRvvvlXf/zjH2Uvyi3FuzgSWlv97pQfgeLd/YhyACXYtn31vcvvXLqkY45kA/0IIr//irevMEQ5gDps2w4vDK++dxk5LsxwOHz86FFgX0WL7z+iHEAtpmk+bbXqtdr+k/1er5eBPQ33qF0t3TywTmU/kLgcx6ENJY3u+kCUA0Ca3FedO1eKBZ2iXEeIcgBIz0l/9+7/q3+4hChPGaIcQBDXaq5NapAobRsjV/YD5M4d9z+7vfuHI2M7I1E+MrZKE36Cq01L6g8QUQ4g0qnVvBkM7vHXB3f+MYNRPn6xt/FZf/yfo8xEOWOMuSNje6lwbcs4fvuvBs8frH4q9yeIKAcQKSrKmTv68l+/zFqUn/R3P9nrn7zJvixHOWOn1hefI8oB8iMc5afWs9/LfW+eAnfc/8WD9iuXsexHufuq///lN7ogygFECkW5+6rz03/KWpSPXzzefnb0+i+V7Sh3x/3P986t0OVAlAOIdGo1b6pWMeONwk7F2iAP4b9dYLNFDkQ5gEihVfn464PtzK3Kz8n6qvzwNwdfIsoB8iUne+V+2Y5y7JUD5FFkB0u2ZT3K1YAoBxBpUpSfmMa/j+Q8JJgJohwAIqPcHbx89MkDxaIBJkCUA+Rb/gb3MycwuK/ST+2/AN6dYAXrs96yAAAAAElFTkSuQmCC" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Name an algorithm which will allow Sameer to find the lowest cost road system.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the lowest cost road system and state the cost of building it. Show clearly the steps of the algorithm.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Prim’s algorithm <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Kruskal’s algorithm <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using Prim’s algorithm, starting at A</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">lowest cost road system contains roads AC, CD, CF, FE and AB <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">cost is 20 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">using Kruskal’s algorithm</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">lowest cost road system contains roads CD, CF, FE, AC and AB <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">cost is 20 <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept alternative correct solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to name an algorithm to find the lowest cost road system and then were able apply the algorithm. All but the weakest candidates were able to make a meaningful start to this question. In 1(b) some candidates lost marks by failing to indicate the order in which edges were added.</span></p>
</div>
<br><hr><br><div class="specification">
<p>Consider the complete bipartite graph \({\kappa _{3,\,3}}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw \({\kappa _{3,\,3}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({\kappa _{3,\,3}}\) has a Hamiltonian cycle.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw \({\kappa _{3,\,2}}\) and explain why it does not have a Hamiltonian cycle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the context of graph theory, state the handshaking lemma.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence show that a graph <em>G</em> with degree sequence 2, 3, 3, 4, 4, 5 cannot exist.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <em>T</em> be a tree with \(v\) where \(v\) ≥ 2.</p>
<p>Use the handshaking lemma to prove that <em>T</em> has at least two vertices of degree one.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for example ADBECFA <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Accept drawing the cycle on their diagram.</p>
<p><strong>Note:</strong> Accept Dirac’s theorem (although it is not on the syllabus for (a)(ii). There is no converse that could be applied for (a)(iii).</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"> <em><strong>A1</strong></em></p>
<p>a Hamiltonian cycle would have to alternate between the two vertex subsets which is impossible as 2 ≠ 3 <em><strong>R1</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>R1</strong> </em>for an attempt to construct a Hamiltonian cycle and an explanation of why it fails, <em>eg</em>, ADBEC but there is no route from C to A without re-using D or E so no cycle. There are other proofs <em>eg</em>, have to go in and out of A, similarly B and C giving all edges leading to a contradiction.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the sum of the vertex degrees is twice the number of edges <em><strong>A1</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>assume <em>G</em> exists</p>
<p>the sum 2 + 3 + 3 + 4 + 4 + 5 = 21 <em><strong>A1</strong></em></p>
<p>this is odd (not even) <em><strong>R1</strong></em></p>
<p>this contradicts the handshaking lemma</p>
<p>so <em>G</em> does not exist <em><strong>AG</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> has \(v - 1\) edges <em><strong>A1</strong></em></p>
<p><strong>EITHER</strong></p>
<p>if \(k\) vertices have degree 1 then \(v - k\) vertices have degree ≥ 2 <em><strong>R1</strong></em></p>
<p>by the handshaking lemma</p>
<p>\(2v - 2 \geqslant 1 \times k + 2\left( {v - k} \right)\left( { = 2v - k} \right)\) <em><strong>M1</strong></em></p>
<p>this gives \(k\) ≥ 2 <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>OR</strong></p>
<p>let <em>S</em> be the sum of vertex degrees</p>
<p>consider <em>T</em> having either no or one vertex of degree 1 <em><strong>R1</strong></em></p>
<p>case 1 suppose <em>T</em> has no vertices of degree 1 (<em>eg</em>, all vertices have degrees ≥ 2)</p>
<p>by the handshaking lemma</p>
<p>\(S \geqslant 2v \ne 2\left( {v - 1} \right)\) (not possible) <em><strong>A1</strong></em></p>
<p>case 2 suppose <em>T</em> has one vertex of degree 1 (<em>eg</em>, \(v - 1\) vertices have degrees ≥ 2)</p>
<p>by the handshaking lemma</p>
<p>\(S \geqslant 2\left( {v - 1} \right) + 1 \ne 2\left( {v - 1} \right)\) (not possible) <em><strong>A1</strong></em></p>
<p> </p>
<p><strong>THEN</strong></p>
<p>so <em>T</em> has at least two vertices of degree 1 <em><strong>AG</strong></em></p>
<p><em><strong>[4 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the complement of the following graph as a planar graph.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><br><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZIAAAEPCAIAAADnGNUwAAASPklEQVR4nO3dz2vc6r3Hcf8nY5hVAi7JvV2kXMhg6OIcU0zoYjBNF21dQ3xoLllcWuoJPrR04ywcmkW8ah2uUyhdVEO76xwY7mYWBwZ0d0G7Q8bMIoiLGVAIYdBdPI4iS5oZSfNIen68X2hzcjweJR5/pO9XXz3aCG+YXw2Pt1o/fj7+vxAAlLRx47/m3/Uf3Wu3Nrd6w6uGdgiABd729++2W5uJbWv/9O9Db7bqxTdia+6dP/jiZwdf3G7fOh5ezavbZQCYe+cPWncPnLfiv2bev57v32u37h063y1Pn3hsvRv2fvjg/H/fOk+2crwSANYydQ4+x1YYXgfZZnv33FuaPrHYuho+vfOkf/khvBo+vbX6lQCwllRs5QyfKLbee+cPP7W03g1799uth6+891XtLgAkYmv2pt/bLVIkzr59/sXPPuXUfDZ+sUNjHkClps5BuiufI3ZEbIm5h+TracwDqNDNs635dNw//eVWa3Nr/+LNbFnybIRhGM7fvNr94dPhu9ifv/fOH7Zb92/+IQDIk+5tXXeobj84f7MktzbC8OrN+aOtO6fjj+nvuNn+4rjvUSkCqEDp2BqffvmpKnzcn36Krhs1Z+L7AsD6RA89Fi/z6fi/ezutzfatJ/3LD0teubHk/wFANbKn5NutewenfxuuqvCILQCaIbYAaIbYAqCZvLEVBIHneZ7nVbo3AOzh+365SMkVW33HiXpm253OaDQq8U4AIEwmk68OD6NU6TtOoZevji3XddMNf067AJQTBMF2p5OIlELJtTq24qHIxsbGVsW23enIjK3G/z5sbGw2bDJja6/bTb/B41/9Kv97AIDged4vfv7zymMr3o+Pb3vdbt9xgiBY468AwApBEAwGA3EO9B/3fpDOk97RUf7vlutK4tnLs/gbvL64GI1GUc/r7OUZHXoAmSaTydnLM9GD3+t2B4NBEASj0SgeKV8dHhY6Aco7tzWZTMQb+L4f/aHneVGifXV4yGAEgMhoNOodHYl8eHZykji58X1f/K8SuVFgSn5R/en7ft9xxOnfdqfTd5x4tAGwiggEcXq1PBCKtrQiEmIrEg9XKkfANp7nPTs5iXpVK0+jlIgtQZSyVI6AJeLt9u1O5+zl2WQyyfNChWJLCIKAyhEwW2a7Pf/LlYutCJUjYJ74LEG63Z6TurElUDkCBvB9//XFRXR6tWYVpXpsCVSOgKZc1y3Ubs9Dj9iKUDkCWki32yWeamgWWwKVI6Cs+K/nXrc7Go2k38mnZWwJVI6AUmq7dU/j2IpQOQINkttuz8OE2BJqODUFEFdFuz0Pc2JLSFSOry8uqBwBuSptt+dhWmxFXNddchM5gBIUqWmMjS3B9/34PQRUjkA5Sq2UZ3hsCYlzWipHIKf62+15WBFbESpHIKf4L0ud7fY87IotgcoRWESLi1o2xpZA5QjEpZdKV/Zwbm9sRagcYTPxXAl12u15EFvXqBxhm3S7XZfPPLF1A5UjbJBot7uu2/QeFUNsZUtUjtr9XIE0LdrteRBbyyQqx6IrXgOK0KjdngextVrjd2AB5ejYbs+D2Cogcb87lSOUpW+7PQ9iq7DEB4LKEUrRvd2eB7FVkjj9pnKEIoxpt+dBbK0r8RxwIw9uUJlh7fY8iC05qBxRs/j5vknt9jyILZmoHFED5nKIrUpQOaIK8ae92DwFTWxViMoRUvi+b0+7PQ9iq3JUjigt3W5veo+UQGzVh8oROaXb7ZPJpOmdUgixVTezx5exJtrteRBbzeBwigTa7fkRWw2LNy9Ue9AAakC7vQRiSwnis0vlaBXa7aURW2pJLDNC5Wge+gPrI7ZUROVoJPEketrt6yO21EXlaAza7XIRWxqgctRU/MCz3eko8iR6AxBb2qBy1EhitJgfllzElmaoHFWWfuwAp8ZVILZ0ReWoFNrtdSK29Ebl2LhEu92etfoaRGyZIF050vqtGu32BhFbRjHyoXiqod3eOGLLQNw1UgXa7eogtoyVeAIVVUxptNtVQ2yZL94zpnIshHa7mogtW4hTBirHPGi3K47YsguV43Ku69JuVx+xZSkqxzja7XohtqxG5Rj/F9jrdm14Er0BiC1YWjky46YvYguf2VA5pp+cZENGG4bYQpKplSPtdmMQW8iWqBz1faJMut2u6V8EEWILK+g7ckm73VTEFnJJ3OCieATQbjcbsYUCEgWXapUj7XZLEFsow3VdpSpH2u1WIbZQnu/7zVaOtNvtRGxhXY1UjvE1xdTvtUEuYgvS1FA5iifR0263HLEFySqqHNPtdk6vrEVsoRISK8f4SVzv6Ign0YPYQrVKV47GjOlDOmILdShUOaYf4UE9iDhiC/VZXjnSbkdOxBYakG5X0W5HfsQWGuP7vjjzEtt2p8N0O/IgttCAdLudSXfkR2yhVkva7YmH1DPogEWILdQhf7s9MVbKI6CRRmyhWuWm20XMUTkiE7GFqsSXRS1d9FE5Io3YgmTiSfRyp9upHBFHbEGadLtd7vencoRAbGFd8TQR7faqn0RP5Wg5YgvlJe40rLl2o3K0FrGFMhJPIWvwfIfK0ULEFgqoot0uS6Jy5D4hgxFbyKXqdrssLIJqA2ILy9TfbpciPZSvxW4jJ2IL2Zptt8sSP0mkcjQGsYUkddrtsoiWHJWjMYgtXFO53S4LlaMZiC3cuAancrtdFipH3RFb9ko/id6qsw8qR30RWzaaTCYGtNtloXLUDrFll0S7nUfjRKgcNUJsWSFeEG13On3HMa/dLgWVoxaILcNxy0s5VI4qI7bMZHm7XRZdbmmyDbFlGtrt0lFiq4bYMgft9qrF/4WXPHwIVSO2tMe5QM3E+SyVY4OILY3Rbm9Q4sHaHC3qRGzph3a7Uqgc60dsSTV1Dlqb7cztzun447rfnna7siqrHN/29+9mf6J2z725pDfRDbEl3Xvv/GG79eXz8ezzn82+ff7jF+vEVnyMiHa7siqqHOfe+YPW5r/HDnzz6Tdfr/eJ0hqxJd3HqfM4GVtlpZcYpoGiBcmV49Q5uBlbliO2pCscW67r9h1nMBjEI8l1XdrtultZOfq+PxqNRqPRiqMRsXUTsSVdMrbm02++7v1jmvWlQRBEpZ/YhsNhot3O6ZXuFlWOo9Eo/qN/fXGx8FvciK2rN+dPDp23de2+iogt6URs3eye7juZsRXVEYltr9sdjUa02w0Trxx//7vfp3/ufcfJfmXyUs/dA2KL2JIqdbZ16Rw+yoitIAgyM+vs5cua9xh1ileO6cNV9mtunG19uHR+w9kWsSVX3t6W53mZn92Fh1wY5De//nXmTz/7q+lt3URsSZcdW/NL5z+Ph1c3vzTzgzsYDOrcXTQiut5S/GwLxJZ8GXNb8+noxf7u0+G7xJee//nPiQ/udqdDS8sGmefaR7/9beYXi7mtrV7ysGctYkuqJVPyt46HV8mh5sQhd6/b5TYde4xGIzGRJ7af/uQn7dZmakgiMSUvZx5Qd8RWY15fXIjL3kEQeJ5HYFlI/Og9z/N9P5qG4RaIlYitZoiZnWcnJ03vCBQSBMF2p7Pd6XAMW47YasBkMtnudL46PKSNhQTx2djrdvlsLEFs1S0Igr1ulyMqFnFdt93a5Ki2BLFVN9G/cF236R2BukQP4ezlWdM7oihiq1ZiPJrJLKwkPirLblS0GLFVHw6hKETMx7D4RxqxVRMxXkjDAvkxErEIsVUH3/fFhW0yC4UwEpGJ2KpcdMzkk4cSGIlII7YqJ3qrdChQGiMRCcRWtfqOQxse6+N6ThyxVSFxkOwdHTW9IzCBOG0nuUJiqzq0JCAdDQeB2KqEaMNzAQhyRZd3LL/LgtiqhHjSAUdFSMc9rSGxVQWxkBZLwqMiov9g8xggsSUZC2mhBpbfdEFsyTSZTGz+MKFONh8giS1puA8DNRPtCAtHIogtabjrFfWzcySC2JKDhbTQCDtHIogtCQaDgZ3n6lCBhSMRxNa6oms6Te8I7GXbSASxtRYW0oIirBqJILbKYyEtKMWekQhiqzyW+oZqLBmJILZKEgtp8WAVqMaGi9rEVhkspAVlRb0Lg+sAYqswFtKC4oxfN4nYKsbCGRnoKBqJ8H2/6X2Rj9gqRiykZdVEMjRl8I39xFYBotnJQlrQhRiJMK8JS2zlxaNToCMjnx1FbOVi8Pk2jGfeSASxtVq0kJaR3U3YwLCRCGJrhWgKhoW0oC/DRiKIrRXsXIYN5jFpJILYWoaFtGASY1q0xNZCLKQF85gxEkFsZbNt3TXYw4CRCGIrg2H9SyBB95EIYisDC2nBeFqPRBBbSSykBRtovTYvsXWDGQ1LII+ogatdchFbn4mfogGXh4GcNP3ME1vXWEgLdhIVhl6DPsTWNQsf7QsI2o1VE1thqP/1YGBNeq0lR2yxkBYQhp9W7tViJML22DLmLi1gTRqNRFgdW77vG3NPPLC+6DdC8eSyN7Y0OrYAtdFiJMLe2GIhLSCT+iMRlsaWdld8gTop/gtiY2y5rqv4wQRonMojEdbFlijd97pdlUt3QAXKjkTYFVsspAXkp+xlK7tiS9mjB6AmNUciLIqt1xcXLKQFFKVgX8WW2BLXdJ+dnDS7G4COopEIRZLLitjSYoIOUJlSt+6aH1tBEChYnAPaESMRKrRZzI8tcSnE87ymdgAwhiJPhzE8tlhIC5AoGolo9jzA5NhSqhoHzKBC18XY2PI8T6lrH4AxGh+JMDO2ohk5MguoQnRjbyO/YgbGlrJ3JAAmabAJY2BssZAWUI+mRiJMi62+49CGB2rTyEiEUbEl6u3e0VEN7wUgbGgkwpzYavzqBmCn+kciDImtIAj2ul3u4AEaUfNJgyGxJRbScl230ncBsEidIxEmxJZYSEvNRa8Be9S2PJT2scVCWoA6xEhE1Zfy9Y6tyWTCHTyAUmoYnNQ4tqLrF77vS//mAMqJRiKq6zVrHFsqLKABIK3qK/u6xhYLaQEqEyMRFS1noGVsKf6kbwBhlYtH6Rdb0b+FrG8IoCIVXejXLLZYSAvQixirlFsb6RRbLKQF6Ej6SIROsaXIU0MAFCJ9JEKb2BILaanwjDYARckdidAjtkRjj4W0AH1JHInQILbE35Y7eADdyRqJUD22WEgLMImUykn12GIhLcAw649EKB1b4ropC2kBhlnz5jx1Y6vBp7ABqJoYiSg3z6RobLGQFmA2McxVrm2tYmyxkBZgg2gkouhvunKx1chj1wA0olxdpVxs1bCiKwB1lBiJUCu2WEgLsJC4dS//L75CsRU9Z63E3gDQWqGRCFViq9IlXAGoL/9IhBKxtc6lUABmyJ8DSsQWC2kBCHOPRDQfW+IGJRbSAhDmG4loOLYqWiEfgL5WjkQ0GVsspAUg0/KRiMZii4W0ACyxZAGYxmJL7pL4AMyzaCSimdhac7UdADZY9IzBBmKLhbQA5BQ90TmeXHXHFgtpASgkfe2u1tiKgpOFtADkJ0q06Ibl+mJrUZkKACvFl4eJIqXoN8kVW67r7nW74j12f/Qj7uABUJq4lCeSRGxF765ZHVtiIZr4dmfre5SHAMoJguD7d/8tkSqFkmt1bImScJ33AICI6HClt/zV4urYynwDNjY2Nrlb/udOrI6t7U6n8b8PGxub8Vv+1tPq2BL9s8RGSx5AOb7vpyOl0LMzVsdWNPEQbUzGA1hHor211+0WusqXawAiCILBYPDs5OTs5RnnWQDW5/v+YDDoO06JSCkwbgoAKiC2AGiG2AKgjKlzkHGR8fZO70/9f4yn8+uvErE1n3n/8/fTX25df9Hu0/Ohd/nN18fDq+b2H4CV3g1799utx/3pxzAMw/DDdOw837/Xbm1u7V+8mc3DMNwIww/T4R92Wrd3eudD7yoMw3A+HTunB7c22/vOtMm9B2Chj1PncSy2wjAMw/nl8Hi33bq9c/rtLAw3ZuMXO63NrUfO5Tz+yvls/GKH2AJQt6zYCsPwavj01mb71vHwar4x7N1vt+4/Hb5Lvnb+Xf93f/XmyT8GgCotiK3r4vH+0+G7jSjAmtlDALhhUWzNxqdftlt3D5y3Gwetzfad0/HH7G8AAPVafrb15fPxbOOgxdkWAHXk6G292r3dbj185b1vaBcBIC7HlcRL58lWxpXEMJxfDv/4l/GMszAAdVo0t3V75/gbMXG68TnGen/65/UY6nzm/ev5o/969YZpUwA1WjIlP/Rmn75KTMl/nkNttzbbrXsHp854+qGxXQeAxf4foRmZS9QqpKgAAAAASUVORK5CYII=" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">A simple graph <em>G </em>has <em>v </em>vertices and <em>e </em>edges. The complement \(G'\) of <em>G </em>has \({e'}\) edges.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Prove that \(e \leqslant \frac{1}{2}v(v - 1)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find an expression for \(e + e'\) in terms of <em>v </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Given that \({G'}\) is isomorphic to <em>G </em>, prove that <em>v </em>is of the form 4<em>n </em>or 4<em>n </em>+ 1 for \(n \in {\mathbb{Z}^ + }\)<span style="font: 7.0px Times;"> </span>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv) Prove that there is a unique simple graph with 4 vertices which is isomorphic to its complement.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(v) Prove that if \(v \geqslant 11\) , then <em>G </em>and \({G'}\) cannot both be planar.</span></p>
<div class="marks">[14]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">as a first step, form the following graph</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>(M1)(A1)<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">make it planar</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img src="data:image/png;base64,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" alt> A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]<br></em></strong></span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) an edge joins a pair of vertices <strong><em>R1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">there is a maximum of \(\left( {\begin{array}{*{20}{c}}<br> v \\ <br> 2 <br>\end{array}} \right) = \frac{1}{2}v(v - 1)\) possible unordered pairs of vertices, hence displayed result <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) an edge joins two vertices in \({G'}\) if it does not join them in <em>G </em>and <em>vice versa</em>; all possible edges are accounted for by the union of the two graphs <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(e + e' = \frac{1}{2}v(v - 1)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) the two graphs have the same number of edges <strong><em>R1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow e = \frac{1}{4}v(v - 1)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>v </em>and <em>v</em> – 1 are consecutive integers, so only one can be divisible by 4, hence displayed result <strong><em>A1AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv) the required graphs have four vertices and three edges <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">if one vertex is adjacent to the other three, that uses up the edges; the resulting graph, necessarily connected, has a disconnected complement, and <em>vice versa </em><strong><em>R1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">if one vertex is adjacent to two others, that uses up two edges; the final vertex cannot be adjacent to the first; the result is the linear connected graph <strong><em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">state it is isomorphic to its complement <strong><em>A1 N2</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Alternative proofs are possible, but should include the final statement for full marks.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">(v) using \(e \leqslant 3v - 6\) for planar graphs <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{1}{2}v(v - 1) = e + e' \leqslant 6v - 12\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v^2} - 13v + 24 \leqslant 0\) is not possible for \(v \geqslant 11\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[14 marks] </em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done. The various parts of Parts (b) were often attempted, but with a disappointing feeling that the candidates did not have a confident understanding of what they were writing.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done. The various parts of Parts (b) were often attempted, but with a disappointing feeling that the candidates did not have a confident understanding of what they were writing.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) A connected planar graph <em>G </em>has <em>e </em>edges and <em>v </em>vertices.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Prove that \(e \geqslant v - 1\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Prove that <em>e </em>= <em>v </em>−1 if and only if <em>G </em>is a tree.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) A tree has <em>k </em>vertices of degree 1, two of degree 2, one of degree 3 and one of degree 4. Determine <em>k </em>and hence draw a tree that satisfies these conditions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) The graph <em>H </em>has the adjacency table given below.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\left( {\begin{array}{*{20}{c}}<br> 0&1&1&0&0&0 \\ <br> 1&0&0&1&1&0 \\ <br> 1&0&0&0&1&1 \\ <br> 0&1&0&0&0&0 \\ <br> 0&1&1&0&0&0 \\ <br> 0&0&1&0&0&0 <br>\end{array}} \right)\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Explain why <em>H </em>cannot be a tree.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Draw the graph of <em>H </em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) Prove that a tree is a bipartite graph.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Euler’s relation is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(e = v - 2 + f \geqslant v - 1,{\text{ as }}f \geqslant 1\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(G{\text{ is a tree }} \Leftrightarrow {\text{ no cycles }} \Leftrightarrow {\text{ }}f = 1\) <strong><em>R1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the result from (a) (ii) gives</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(e = k + 2 + 1 + 1 - 1 = k + 3\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for a tree we also have</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2e = {\text{sum of degrees}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(2k + 6 = k + 4 + 3 + 4 = k + 11\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence \(k = 5\) <strong><em>A1</em></strong></span></p>
<p style="font: 32px Helvetica; text-align: justify; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica; min-height: 38.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept alternative correct solutions.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) \(v - 1 = 5 < 6 = e\,\,\,\,\,{\text{by (a) (ii)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>G</em> cannot be a tree <strong><em>AG</em></strong></span></p>
<p style="font: normal normal normal 32px/normal Helvetica; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) </span><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></span><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong></span></p>
<p style="font: normal normal normal 32px/normal Helvetica; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(d) take any vertex in the tree and colour it black <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">colour all adjacent vertices white</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">colour all vertices adjacent to a white vertex black</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">continue this procedure until all vertices are coloured <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">which must happen since the graph is connected <strong><em>R1</em></strong> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">as the tree contains no cycles, no vertex can be both black and white and the graph is proved to be bipartite <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [17 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates seem only to have a weak understanding of the requirements for the proof of a mathematical statement.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The diagram below shows the weighted graph <em>G</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) What feature of the graph enables you to deduce that <em>G</em> contains an Eulerian circuit?</span></p>
<p style="margin: 0px 0px 0px 30px; font: 31px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Find an Eulerian circuit.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Use Kruskal’s Algorithm to find the minimum spanning tree for <em>G</em> , showing the order in which the edges are added.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) all the vertices have even degree <strong><em>A1</em></strong></span></p>
<p style="margin: 0px 0px 0px 30px; font: 30px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) for example ABCDECFBEFA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) the edges are included in the order shown</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAApwAAAElCAIAAADGBKXSAAAgAElEQVR4nOydZ1xU19PHL1V670U6KE0RUcReAEssiKKxxZ7YAooFEyvGaOwtGo29RUWDHXvvYEOiiIhioQnssr2f58U8nP/NYtCsRhHm+4LPcveWs3f3nt+ZOXNmGIIgSK1DqVRKpVJCSEVFBd3yWVuEIMingPncDUAQ5ONDRZ0il8vVtiAIUvtAUUeQWotYLFYoFEKhUCaTETTWEaQOgKKOILUQtlEul8urbkQQpFaCoo4gtRCVSiWXyxUKBfwrFos/b3sQBPk0oKgjSO0EXO4g50qlUiQSfe4WIQjyn4OijiC1E5hBP3bsmEAggC3UcEcQpLaCoo4gtRClUikUCm/evGliYjJmzJiCgoLP3SIEQT4FKOoIUoNgh6lTCxs2VrM/vIA4OPC3q1QqpVJ59epVMzMzhmFGjhxJCFEoFEqlUiaTicViiUSCwfAIUvtAUUeQmgVoLfwFna5e1OFdPp8PW+hQQCgUZmVl1atXj2EYhmHevHlT9XCVSqVQKFQq1cf+EAiCfB5Q1BGkBiGRSOhrcKG/cyIc5Ly0tFShUPB4PPZJbt68yTCMgYGBi4tLeXk55J8Ri8UymYya7DjRjiC1CRR1BKlBgIHO4/EUCgVdh/bO9eVnzpwZMGDAo0eP4F9IOEMISUtLAzO9ZcuWUqm0qkVODX0EQWoHKOoIUhNRKpWQNOadoltRUfHLL7+YmpqOGDHi/v37dHtJScnw4cO1tLSsra1tbGwIISKRCNav03Q0ABrrCFJrQFFHkBoE+MOVSiVMgUskkuonvMvLywkh+/fv19LScnV17dSp08SJE+/du3fgwIHg4GBfX19jY2OGYeLi4nJycl6/fk3lXCaTsV39CILUDlDUEaRmUVxcvHTp0qSkpJMnT8IWmCn/J8RicXp6upubG8MwOjo6kZGRPXr0aNSo0c6dO0HRAS8vr4EDB545c6akpAQOlEgk4NjHQDkEqTWgqCNIzUIul0dFRRkaGhoaGj569IiGtb8VpVKpVColEklYWJiRkZGnp+cvv/wybdq0bt269erVq2XLlvr6+gzDGBsbW1pa2tra6urqTpgwITs7m30SnFZHkFoDijryN8AlC15f8APDvxAsTQiRSqXXrl2bO3fu5cuXjx8/fvr06RcvXqidBOdoNQYWmIWHhzMMY25uvm7dOsJapQbOcwiCo0vRRCJRWVlZ8+bNGzRoMHTo0Nu3b2/atKldu3YbN25s2bKljY2Njo4OwzB9+/Y1NDTU0dExMjIKDg7Oy8uDxLFwcvjKVCoVDcpTKBRYAOZTQu82TKlQ4JGEL+jatWslJSUKhQL+5XK5hOVowecOISjqSFXYzljo94uKih4+fLhr165x48b5+PhYW1u7uLj0798/KirKycmpU6dOp06dEggEkPBELBajGHwIr1+/9vb2ZhjGw8Nj586d8HXQL4W64tXM6+bNm+vr64eGhnbu3HnKlClXrly5ffv23LlzR4wY4eTkxDCMg4PD5s2b9+zZExQUZGtru3jx4tLSUjhJWVkZnF+hUMjlcpVKhVHxnx7Qcvh+4esoLy+HFRAPHjzw9fX19PS0t7fX0dEJCQkZM2ZMWloaHFhaWgqDb7X4R6RugqKOqPP69WtCiFgsFovFhw4dmjp1anBwsLGxsYeHh5+fn6OjY8OGDSMjI/v169emTRsvLy9LS8thw4bRqCvMU/YhKBSKO3fuuLq62tnZNW/ePCcnB3p5aoTR+wz2OofDga48JSWlZcuWrq6u/v7+kZGRZ86cOXfuXGZmJixV19HRadCgweXLlwkhGzZsaNCgQcuWLe/fv0+VG4w/+q9cLsfCbp8S+FphqgWeILDCCSGJiYkQFWFubg6DM/g3JCREKBTSgj04kkYAFHXkb9CuvKSk5Pfff/f29vb392cYxtHRMSIiIioqasmSJZmZmRwOhxCiUqm+//57Ozs7fX394uJikUgE2oCBVxqjUCh+++236Ohoc3PzESNGvHz5khBSUVEBsyGEEJFIBDIvl8tp1jkQ46VLl/r6+lpZWVlbWy9YsKCoqEipVJaWlhobG2tpaTVt2nTPnj0VFRWEkCVLlujp6VlbW2/atAlmT6oOxTCP7KeEXSSXpigoLi4eP368j4+PjY2Ntra2lZWVtra2rq6utbW1ra2tpaVlRkYGaLlSqaw+mhKpO6CoI+qUlZWVlpb+8MMPHh4eYBaYmJg4OjpmZGSo7XnkyJGmTZsyDOPp6fn8+XM66Y5zexojl8unTp3q5+fXsWPHqKgoupFUmubbtm1bvnw5rEeH+1xWVkYPT09PX7FiBf2mwP5r27YtwzCRkZHbtm2j8+iXLl2ysbGxsLCIi4u7cOHC/fv3QUhomjkcmX1iwEyXyWQQ5VBWVtanTx8wyq2srBiGsbe3Hz169J49e86fPz937twFCxbAnnSuBL8yhKCoI2rAwD8qKsra2trKysrHx2f27NkNGjRgGObQoUOkMj6rsLBw79699evXZxjGzc3t4sWL1FDA1c8fAo/Ha9u2rbe39+jRo2fOnAlhCvAWdPotWrRwd3cfP348DXCjSegIIVKpFGQb1q0plUoul7tkyRJw3opEIqVSCV3/06dPBw4caGtra2pq2qFDh6SkpOvXr8OFIInsZ/jwdRhQZVpM7969e0OGDNHT02MYpl69eqampgsXLlSpVDweD56v0tJSGk9XXl4OwzsMg0AIijqiBvQLsbGxDMNERESsWbOGEHLkyBELC4uJEyfyeDyVSnX//v3Bgwc7OzvXq1cvLCxs06ZN9FiVSkVDtRENePjwYUhIiLOz888//5yamkpYhjiIcatWrRiGsbOzW716NamcLoGhmEKhgGkRmI7lcrmwXSqVnj59+uDBg9D1KxQKEH5CyObNm5s3bx4bGzt37tzr16+zXSzs8QTyX0Or8ymVyvLy8latWmlpaZmYmNjY2AQEBBw6dEgkEsGojn537EM+Y8uRmgaKOqKOTCbbtm2btbX13LlzCSEqlWr37t3gvz127FhkZKSzs7Obm5uVlZWJicn8+fNJ5bIo2t2g+11j7ty54+fn16RJkz59+jx79gwC0QmraNsvv/xiaGjIMExAQAA1u+VyOUyWk0obna56IoTweDwQe+qnpfa9UCg8cODA8ePH6dBBJpPBgSgVnxiQZ5lMNnjwYIZhjIyMjI2N+/XrV1paSv6e/1+pVNLiPbDqhOBDh1SCoo68BalUWlZWBpO4Mpns+fPn9erVc3V1NTU1NTc3NzMzs7a2tre3p5O+gEQigdlfDMTVmCtXrgQFBQUFBQUGBvL5fJom9q+//vrjjz8uX748bdo0hmF0dXWDg4OzsrJIZeQzXc6kUqkwcP2LQ6VSwcBr//791tbWDMM4Ozt36tRJIpFUnQ2pOncOMo9L2hCCoo6oQfsLKNAJW7hcLsTAUywsLBo2bPjTTz+lpqauXbt21apVdDqQYMDOB/Ds2bOQkBBHR0cPD4+bN2/m5eVt3bo1NjY2NDTUzs7O3t6+SZMmkPxVX1+/UaNGBw8epMl/6AIn5AtFKpW2bt1aW1tbR0cnOjr61atXMpkMMgfQfWBapCoqlQqfO4SgqCNqqM2q0tc9evSAKFwtLa3g4OCRI0e2a9cuKipq9uzZXbp06dKly6pVq7Zs2QImI3puNUapVA4dOtTb29ve3j4wMNDDw8PHx6dBgwZGRkYuLi6NGjXq06dPUFCQlpaWg4ODs7OznZ3dzz//DEYeBaX9S4TH4z158sTX1xfmVq5cuUJYEyUUMMrf85yqSj5+c5GaCoo68jfUOhG6tGn9+vVaWlo6Ojq2trYDBgy4ffv20aNH16xZs2fPnidPnty/f3/fvn0eHh7bt28nKCofgEQiycrK6tSpE6ws0NXVjYiI0NPTCw8PnzBhwqFDhxYuXKirqwv+km7duo0ePfrgwYNcLlehUNB1Bzi9+sUB8Sh79uxxdHSsX79+XFwceVs0O5jpat9vNZr91v2R2g2KOqIOO8aK9gjnzp2zsbHx8fG5cuUKVAUFIIoHxgHe3t7NmjUjKOofBqxc+vbbby0sLGJiYoKDgxctWrRnz547d+4QQnJychwcHGxtbRmGSU5OptOomKr9iwYGZCtXrtTV1bWwsJg3bx55W6wiFWnqhIdROPXA/9P+n+ZTIDUBFHVEHbW1TPDv69evfX1969evLxaLlUplRUUFreBZUVEhFotfvnzp6+sbFBT07Nmzz9PuWgE40mkNj5KSkr/++osQIhQKqS3etGlTS0tLbW3t5cuXkyrLymEW9vO0HvkAJBLJjh07dHR0XFxcnj59+tZ9qDv9rRJOPthdj9QCUNSRv0F7CnaXASttoA6YWjZKuowtPj6eYZgOHTpQsUc0RiKRsHP40JsMC9ChoKqhoeGSJUsIIUqlElQcaqxhBpIvEViRmJaWxjBM586dSWUJhvcEnlAIlX9rYN1HbzBSY0FRR/6GWCxmF+yCjUqlksPheHp6enl5PX78mBDC7jhKS0s7duxoa2vr7e1tZWX15s0bDMz5EOhXAB4RQohEIqEzGjKZrGPHjq6urhYWFjSRAO21MSrqy0Uul2dkZFhYWJiYmMBTVo2FTU128N+A56ygoOA9l8AhtRgUdUQdmUwGs7MSiQSyyggEghcvXgQEBGhraz948IDmu+Dz+UeOHImOjjY1NW3UqJGPj8/mzZtxZvc/AnpqmUwWFRXl6Oiop6e3cOHCz90o5KMBOQkgWiIsLAx0nVT6z8EQhy0wwnv06NGRI0fKy8svXrz4/fffd+/enRZjReoyKOqIOiDYhYWF8C/Y62KxuEePHg4ODteuXYONmZmZycnJfn5+xsbGnp6e69atu3TpEpQDwUyxHx0w2qByWu/evRmGCQ0NBUsdqQXAxEpZWdmff/7p6urKMEzDhg3XrFlTVFRUVFQE3z6fz798+fL69etnzJjRrFmz8PDwgQMHbt68eezYsd9///3vv/+OM18IQVFH1KC+O5iaFYlEEokE+pTRo0c7ODj8/PPP586d++WXX2JjY93d3fX19Vu0aJGQkPDgwQOwJLCgy38EhCgSQlq3bu3l5eXr67ts2bLP3Sjko0Efve+++45hGB0dHRsbm7CwsOjo6NjY2I4dOzZu3LhZs2bNmzf39vYOCAjo06fPiBEjNm3adOPGDUwjiFBQ1BF1nj596uDgEBMTc/369bt3786fP3/IkCHQlcDyaG9vbw8PDw8PD21t7fbt2+/evZu9yK24uBjyyyIfF+r/6NmzZ0BAgJ6e3pw5cz5vk5CPCPjYRSJRYWHhpEmTOnToYGRk5ODgYGJiAs+do6Njjx49Bg0a1L59+8TExKysrLKyMi6XC4EXWE8dAVDUEXVycnK8vb1pVwJJSW1tbfX19RmG0dPT8/T01NfXb9OmzeLFi1+8eAHmhVwuLy4uxpCc/whaZKWiomLXrl0mJibGxsYxMTGfu13Ix0EoFNK0gFCN7dGjR3Fxcb179+7QoUPnzp379evXv3//xMTE06dPq61nowGt4MNH6jgo6og6FRUVM2fOBDm3tLS0sLAICAiwtbX18vJq3bp1r1695s2bt3r16vT0dNhfKpVSXYctuC72o0MXqkkkkqdPn/bv39/Hx2fEiBGft1XIR0SlUgmFQniIFAoFuNMVCsWrV6+KiopgH7DmaeE+sVgM0awCgYCue0TqOCjqyN+g4rFjx46YmJjw8PBhw4bNnj1727Ztq1atOnv2LEyZC4VCcPcplUqRSETtBolEgkul/yPoUInL5WZnZ8+cOfPkyZOft0nIxwIq3t65cychIWHGjBmbNm2CdaR0B5VKxY5WoTNcsNiEFnlDEBR1RB2lUklXsr1+/VogEIA/kPYp9IVQKKQrYrlcLvre/zvgPovFYrpiECquftZGIR+To0ePenh4mJmZ+fn5MQzTvXv3FStW8Hi8iooK9qCZ5oyjGYfoaA89ZAhBUUfUoDml4V92HnjqXc/KylJLREqXtpPKeC61GHjqVGQb8WrZ68B/CF5H+pZSqVQLqqfxYuxTQTtlMhnt42AgApdmp7JnF5GjV4FzwgnZO0CzwSqit6KqvhJW1hc4FewDbWbfHHiLngFOSHegueHUmsS+jeyMQLSd4DURCARsLz29M+zPXjVF/Fvz1ZSXl9ONcCfhJtCbDyehSyTozYTPQhsGXx/sAKYk9RILhULqSYaTU2NUKBSyz09Ya/RpC+E89EJwILsl5eXl9EJw6+hV2J8UzsDeCHeMpmpg3yh6Wvb+1GdOqmRrh0luaDb9CzvDX7hdKpXq/v37jo6OxsbGhoaGXbt2tbKyYhjGzMwsIyMDmkRbwtZ4BKkKijqiDi2jTvsRdhd//vz5mzdvEkLy8/MzMzPpzDr44R8+fFhSUpKfn08IkUgkpaWl165dy8jIqKioKCoqKikpKS8vB9P/1atXDx48+Ouvv9glYQCFQsH2Jar5FSHWlxAil8thThHqvdIdoGenG4uLi8nbCl7BhQQCARUMhULBnpiEUGTyNgOIahufz4dmwGCCPSKhnTicH04FugKzoWqnoneYyg9cGg6USCQ0DIo2ksPh0JsDIkQHB+zWUu1kAwfKZDI6+pFKpVKp9M2bN3QswuFw4G4rlcqcnJx79+69ePGCy+UWFhay51/gPrC1nBAiFot5PB69LuxcUVFRUFCQn59fVlYmFAphqjgvL49UyqdcLodDpFJpYWGhQqEQCoXl5eUcDge+x+LiYlheIZPJMjIyduzYceHCBbgnHA6HjlcKCwtfvHjx5s2biooKgUAArS0uLgZJhmyJKpUKPntRUVFOTk5KSsrq1avz8vIgQwOHw3n+/DkhJDc39+nTp9u3b8/KyoIf9qtXrwghpaWlaj+8nJwcOCH8YOBrevbsmVgsfvLkCd1NJBIJBAKpVFpWVnblypWbN29yudy+ffsylXh4eNDX3377LQ1rpxUBCIL8MyjqyN+QSCTsfgo6a1JpriUnJyclJd27d+/GjRv79+//7rvvunXrlpiYOGnSpK5du7Zo0SI0NHTo0KFDhw5dtGhRq1atIiMjw8LCoqKihgwZEhQU1L1797Fjx44fPz4xMTEpKWnChAl9+/bt2LFjmzZtIIHG+fPnDx48uGHDht27d48ePXr+/Pnz589fu3Ztr169tm7dunLlymHDht2/f3/jxo0nTpxYunTp6dOn09PTFyxYsGHDhqysrLS0tO3bt8+cOfPgwYOFhYWPHz8+duzY6NGjd+/effbs2efPn9+7d2/16tXLli1LT08vLS3Nzc2dNWtWly5dRo0atXz58tevX58/f/7MmTN79+6dOXPmxo0br169eurUqY0bN/722283b97kcDjp6ekPHjw4efLk3bt3T548uXLlykuXLuXm5j5+/DgvLy8zM5MQkp2dff/+/b17954+fTozM3PXrl3Hjh3bsmXL1atX165de/ny5ezs7OTk5FWrVu3evfvJkyf5+flJSUmxsbGHDx+eM2fOggULVqxY8ejRo7Nnz2ZlZZ06dercuXNCofDFixfwpWRmZr58+ZLH4x07dmzDhg23bt3Kzs5OTU19/fr19evXHz58mJGRwePxbt68ee3aNRgzCQSC48ePx8fHHz58+MaNGxs2bFi6dGlWVtbLly9v375dVFR04sSJY8eOnTp1KiMj49ChQ5mZmePGjYuLi1u5cmVaWtrhw4c3bdoUGxvbv3//8ePHb9y48cCBA/ABf/755zVr1ixZsiQ3N5cQsm7duuvXr587d2727NmTJ09OSUm5ePHijh07/vjjj6VLl3799dcXL14sKCi4cuXK9u3bJ06cOG3atJEjRx45cuSPP/54+PDhiRMnTp48mZKSsn379uvXr+fn58fFxXl4eEyfPn3FihXHjx+fPn365cuX09PTt2/fPn78+MWLFy9YsGDatGlfffXVokWLzp49m5SUtHLlyi1btmzZsqVTp06BgYFDhw6dOXPm2rVrf/rpp6SkpG3btu3YsSM1NTUlJWXhwoWrV6+eOnXq4sWLJ0+ePH369Li4uClTpuzcuXP9+vXLli1LS0ubMGFCz549+/XrN3r06KioqLVr165Zs+bZs2cpKSlbtmz5888/ORxOZmZmQkLCoUOHCgoKeDxednY2nOH06dMzZszYs2fP/PnzL1y4cPr06cmTJ1+4cCEtLW3UqFGDBw8+fvz4wYMHY2NjtbW1GYYxNDQELY+IiLC2tjYyMho8eDBN20xHSGipI9WAoo78DWo40noS1F6/ceOGjo5OWFiYq6urq6vrjRs3xo8fD32QjY2Nl5eXv79/p06d2rRp06pVq/Hjx/v5+bVv375nz56jRo0aPXo0vDt27NgJEyYkJibGx8ePGDFizJgx69atu3XrVnx8/KhRo9LS0lJSUjZv3pyZmfnrr7/evn0b9PLatWu//PLLkSNHDh8+PGbMmGvXrl25cmXChAmrVq06ffr00qVLU1NTHzx4kJycPGPGjO3bt+/atWvEiBEDBgzYsWPHihUr5s2bN3bs2I0bN65fv37YsGFDhgxZv379gQMHli5dunTp0hkzZhw/fvzmzZtZWVkzZsxYuXIliOXSpUs3b968devWAwcOrFy5EpSjadOmAwcOnD59+u7du5cvX96zZ8/evXv37dt32LBhkyZNSkpKOnHixJYtW/bu3bt06dJdu3YdOXIkKSlp3rx5CxYsuHLlys6dOzMzM0tLS9esWVNcXCwQCO7cuZOenn7u3LmUlJSzZ8/evn07PT399OnTWVlZO3bsSE9PP3ny5B9//PHXX39dunTp6dOnubm5KSkpBw8ePH369KJFixYtWpSamnrx4sVNmzbdvXv32LFjN2/eTEtLu3btGnyox48fX79+PT09HS737NmzsrKyU6dO7dixIzs7Ozc39+jRoydOnDh06NCqVavS09MPHz784sWLCxcunDx58vDhwytXrrx169bVq1ePHz++bdu2169fv3nz5vnz5zdu3IBfxYoVKxYuXLh3795Xr16dP39+9erVf/3119OnT3ft2rVnzx7wLuTl5V2+fPn58+dpaWlZWVk3b968dOlSRUUFh8PJzc29f//+xYsXFy9evH379pUrV969e3f//v3Z2dkHDhzIzMy8cuVKSkrKb7/9NmnSpJSUlGvXrhUVFRUXF+fm5oKbJz09fcOGDbm5udu3b9+7d++aNWv27NmzbNmy69evZ2dn79ixY/HixUlJSZs3b758+fLFixfXrVvXrVu32bNnb9iwYceOHWfPnt26deuWLVvmzZs3b948pVK5bNmyTZs29enTJzk5+dy5c+PHj09ISMjPz//rr78OHDiQlpa2f//+W7duHT58eO/evUeOHLl79+7s2bN//PHHo0ePFhYWXrp0qaCgoKCg4MmTJ48fP963b9/hw4c3bty4bdu2RYsW5ebmFhQUwHe0b9++69ev//zzz6ampvAcGRgY6OnpmZmZ5ebmBgcHMwwzadIkwpqpgbkhDERFqgFFHXk7dH4aepD8/Pyff/6ZYRgjIyOGYVxcXEJDQ6mT0M3NLTU1FYqugtsW/KUVFRXUncvn8wsKCuAFuC7hQuzaMLAnj8ej3mmYcSSsqURanJSdjJb6JGl/By/4fD74hKvGlEHnKJVKwQkBO7Dd73SOXCqVUn84pO5iOzPYr+EQ+BRqV6RebsKaUBCLxeC6Z0+Q08bThUxwKrbflc4E07Ap9kwwfIry8nJ6N+DdiooK2oy3Jgii35RAIKCDOblczr7V9JxQAgA+Pr1v7CvSyjQ0/kBtRp/P57Od/+x2sm8vLW/D/izsWwGfhc7Hg38bzq9QKKqu3lZLYywUCgUCAZ3k5vF4NA7g9evXdHKdTqNwuVwej0d/tJCeAT44PTPsrBbMWFFRAb/nkpISsVgMzd6/fz/DMGCp6+joMAxjbm5+/vx5X19ffX39Hj16FBcX09tLZ4sQ5J9AUUfUUdMSQsidO3ciIiKoMcEwjLW1db169cBhqKWlVb9+/czMTB6PB3OWNGJLoVDQ8s+kis7Bwlx4Czo4telztpqqRaWRyvlmdowSTMESlg6VlZXR/eVyOZ/PB4ERCoVvTWdLe2qZTFZ10EDlH1oOTYLoM9rVSqVSgUDAXn5G31IL++JyuWo3BD4+HYiQypEHzBbDmelUPT2WKgq9BNwTOh5SGzFQ2EpG7zw7shpCr2E7JAxmz9nD/Qehgn3gnohEIprRlg2NdSCEVFRUqE23E9Y4TKVSFRYW0ghHuVxOm0FHe2VlZfQDwhx51Suyg93kcjn8OOkaMDikmilquFZ5eTn9gFV/wOwfCcz6w0eg01jsYSK9FjuiYseOHVTOKRAop6OjEx8fT8c9ND5DLUwVQdigqCPqQJg0h8MBgbxy5Qoour6+voODA2SXA3sdcswxDDNu3DhQBbUE1FSSORwOmP6kUnHZ4dnQbUGfTs072unTxXLFxcVwFHgjaXdZVlYGM8ekSng2ff3W+GT4pBUVFbTZ7PhzGhbO/lDsoQCNzK/6wdXaQIO/wCiEjfRCQqGQbTdDiCIYtWpCRZtHLw2CTYcRbPMaAq3lcjlkDqBpyKCQK3tRANQHo+2Em0mvzufz2RoMsCvzwhnUdlBbEEGVCdwA7PtTUVEBLYF7yHZpgMDTf+mIjX0h+JpARGmr2A6MqgsB6BloFhdojFgshs9edTUB+4uAESH7y+Xz+TB8pPY3u3mE9WNW+zhisTg9Pd3BwUFbW1tLS4umg4XQd1dX16ysLHogPTOmeUeqAUUdeQu0w/rpp58sLCzMzc21tLSioqJ27txpZ2fHMEy9evXs7e1NTEyaN29ubW396NEjKrFgD1Htge4V+jK2TQn6RLdTiWIvHKLeS7ZNxu70wX6F17TLo1HrcAgtXcW2p8ECVgsJpIdAUD0140CEwOsAZ6DLpaD3px+Exo0TlnuAVHWeHhAAACAASURBVIlsAhFlDzXU1o8RllcZouuhtXDT6FFsTwY0ku3oVvtO4d5WHSXQGwgeGhAM9tXZdwwUFAxxOggjLJmBr5IteLQlKpWK3jeYd6AHqg106BCBrlSkwgw3ir3gjQ4W6b0lrHESezkZXXQgkUjo6JB+m/QSbI8CYY1O1C5KqqwyoIfQuwEOBvYaNlJF4LlcbqdOnSAwhY6SXVxcxo0bd//+ffYJ4SnA5ARI9aCo11Gon5Z2QKBPtMe5ffv2iBEj9PT0TE1NR44ceezYsdLSUrFY/O2330IGeHNzcz8/v0WLFp05c4Y9bUnnWREEqR7wx4jF4t9++61x48ZQdNXV1XX27Nl0AIQg/woU9ToNO2EI3cjlcqdPn25tbc0wTIMGDX7//Xd2eo2zZ8+2bdsWdH3gwIGvXr2ii7PVIsgQBFGjauobmn9m165d8fHxDRs27NWrF7zLDhhEkPcERb3uQgPiwN8Icb/btm0LCQmxsLCwtbXt2bPnhQsX2KFJhBCJRHLq1KlZs2bNnj2bTviRSk87ff1JPwmCfCGoFViD9QuQbojH4xUWFkZHR7dq1UqpVGIpVUQzUNTrKGp5N2Fy+siRIyYmJkZGRubm5itXrqQ7w/Qkne6FiVU6iasW/k2q5IhFEARQE3VSmZiZECIUCjMzM52dnWNjY0llCP3naSXyJYOiXncBExymw5VKZVJSkq+vb2BgYIcOHW7cuKFUKsE0B9hlVelQgF1Sgq63QRDkn6gq6gB4uW7cuOHg4NCuXbuysjJUdEQzUNTrKOByh78PHjzo1q2bra2tq6vrmjVrCgsL2bXX4IVKpRKJRHTqHVYtVz3tW6uDIAhSPeAGO3r0qJ+fn5eXV1FREeT2+dztQr48UNTrLrCU+eDBgy1atGAYJjIyEupV8Hg8WP2s1qfQ1C6EVSOEJrBk74Y1JxDkXwFuszt37sTGxjZu3PjNmzeYCxbRDBT1OopcLs/IyIiPj7eysjIwMEhKSiopKWGv8IZeBlKXENY0OTsgjq4yV7D4PJ8HQb5wuFzukydPvv322/79+2PcO6IxKOq1hKpZVAGwrWlqTPCrFxYWzp07NzQ0VEdHJyIiIiUlpWr1aARBPiV8Pj8/Pz86Orp9+/YEl5AgmoKiXquAXBZSqbSqS5wm7Tp37lxMTIyVlZWnp2diYiIU9ORyueywOARBPiUwg15RUdGhQ4eYmBjy98RQCPL+oKjXHqomASWV431Y83ru3LnevXuHhITo6ur6+vquXbtWzTRHpx+CfBZgFF5WVtaiRYukpCQ00xGNQVGvJbALmJLKzOo02bVSqZw+fbq+vr6hoaG/v/+QIUNu375Nk2+XlZVBJ4LudwT5XMhksgcPHoSFhW3fvp2d4R9B/hUo6rUEdqysVCql5Z8JIZcvX46OjjY3N7eysoqLi7tz5w644tnLz4RCIUbbIsjnAh7G58+fR0ZGHjx4kPyD4w1B3gmKem0DqnbCa4VCsWDBAn9/fxMTExsbm+TkZLobuwQLBefwEOSzAHY5n89v3rx5YmIiriJBNAZFvbZBvXZZWVnr1q2zsbGpV69ep06dzp49SwhRKBQ8Hg9C4hUKBS1eDgeixw9BPgswni4qKvLx8QkODi4rK2NXrUWQ9wdFvZYAzz912b18+XLq1KlQIHXMmDEQ2a5WBBoyzMBr9PUhyOdFqVRyOJwuXbq0bt36c7cF+YJBUVcH5I3mU1MoFCqViiZQY9dBYS8NLykp+WTNI/+gwTR2PSUlpXHjxgYGBr6+vufPn6fV2OisOeo3gtRASktLY2JiunfvTgiha1AR5F+Bov7/SKVStQBygOofdU2LRKKMjAzIvEYIKSkpgaM+WalEdt51EHJqc0OayXr16jk7O8+ZM6ewsJDD4dADZTIZHal8mqYiCPKewFPZu3fvcePGwRbM/Y5oAIr636DljSE9qkQiUYsdE4lEq1atcnBwmD59OiFELBZT8xcO/ASNBCHncDjsZeUSiWT+/Pne3t7m5ubt27dPSUlRM8fho32C5iEIogHwwPbt2zc+Pp69BUH+FSjq7wW7XvjMmTMZhtHR0fnrr7+oTFLD/RNQXl5OX4vFYqFQ+OjRo379+nl5ednY2MycORPe4vF44KVXi4D7p+KPCIJ8XjgcTp8+fXr37k0waQSiKSjq/w97JRhhFSmRSCQqlYq+K5FIEhISTExMGIZJSkqCLRBMXlFR8QnEsrCwkBAil8vhokKh8Pr167a2tsbGxpGRkRDiLpfL37pijVRWQ0cLAEFqFNB1FBUVde7cuUuXLgRFHdEUFPX/oVKpwKitqs1SqRSEkMPhREZGMgzj5OQ0ZcoUeuCnbCefz6cz6PHx8U5OTi4uLrNmzcrJySGVwxGpVFrVeYCKjiA1FnhmW7duPWDAADAhcIkpogEo6v+DPSkuEokePXp05syZp0+f0ncJIXw+PzIy0tzcnGGYrl27Tps27eDBg5cvX87IyCCEfIKaKDKZjM/ny+XynTt3NmvWzMfHx8PDIy0tjbDGFnSan8vlyuVy+FxSqZQGyiEIUtOQSqVCobBly5Zff/01e5UNgvwrUNT/H3bOVA6Hs3v37rZt2zIMExMTc/fuXdguEAiuXr1qbW3NMAzDMObm5vXq1Wvfvv3SpUsLCgo+WTuVSmXPnj3t7OwcHBwmT558584danxDcB/dU+1A+hozxyFIDeTly5ft2rXr0KEDQUVHNKXWirpQKHxryTKqeXQG/fnz56Qy0BRc1teuXbO1tdXV1WUYxtDQcPz48ZAXAnY2MzPT1tbW1tY2NDTs0qXLpEmTrl27BjKpcbgcNIw2SSgUsnWXuhDKyspmzpwZERHh6enp7Ow8f/582AGn3xCkFvDw4cN27doNGTLkUwbeIrWMWivqAM0bAyu52Qu1ZTKZUCiEDA+goJBMRiqVcrlcNzc3hmG8vLzMzMw2bdrEfsY6duxobm7u6ek5YcKEZ8+efWALhUJhNS5xiIYDDhw4EBgYaGNj4+3t/dNPP2VnZ8P2N2/efGAbEAT5vEgkEqlUWlBQMHbs2KlTpxJWMCyC/Ctquaizl6IBEAcHiWK4XO7vv/+el5dHKkPh6M6//fabvr4+wzB2dnbNmjU7fvx4eXm5VCrlcDijRo1iGGbatGmwJxj6cMiJEyc+pKkQSA9jCz6fD9thnj41NXX48OFeXl6zZs26efMm/SzwAmPfEKQWwOPxkpOTJ02a9LkbgnzB1GZRhwyv9F/6Gsz3qVOnNmnSxNjY2MnJ6cKFC/AW+LHh748//ujv7x8UFOTg4ODq6hoQEFBaWkoISUhIcHNzi4mJoelXFQrF0aNHO3funJqaqlk73+o/hzEEIWTWrFl2dnZubm4//PADOBUgUF8sFsOBmFUGQWoBRUVF8fHxXbt2Rfc7ojG1VtTZcq5UKsVisVQqhY05OTktWrQwNDQ0MzNjGMbCwiIsLIzD4cC7YP6Cf76oqCg7O3vatGkDBgzo1atXVFTUnTt3Xr9+bW5u3rJlS0gC8/jx4+HDhwcGBrq7u9++fVuDpqplg5HL5bA4XqFQHDt2rGfPnn369Gnfvv3GjRtVKpVIJBIKhcXFxbDzJ8tNiyDIfwfMA5aWlo4dO7ZDhw4wdsdYGUQDar+oy+Vydhzp06dP4+LiwsLCXF1dra2tW7duDaHsCxcuZIsrHSnTLUePHtXV1fXx8SGE/PTTTwzDdO7cuU+fPoMGDQoLCzMzMwsNDf2QdspkMnasnEQiSU1NDQ8PDwwM7N+//4sXL2Aj2+VOPxcGyiLIFw1MulVUVIwcObJ79+7wROMCVEQDaq2oU/GjBjohRCAQxMfH+/r6hoeHh4eHT5o06cGDB7Nnz7a0tAwLCysqKoJHC6aoL126tGjRosWLF3/33XdRUVH6+vrOzs5aWlpnzpy5deuWv78/wzCmpqb29vba2trDhw/PycnRYKkYrWjOXiKfl5c3ZMgQd3d3V1fXOXPmgNsA1ppD80QiERwFoQDofkeQLxqI9Xn16lW/fv2+/vrrsrIydhFIBHl/ar+o04j3kpKSGzdumJuba2trOzo6jhw5EpzY69atYximffv2586dI4RwuVyYdP/zzz+dnJzARe/k5KStrW1packwzPDhw1Uq1YkTJxo2bGhiYmJoaNiqVatjx44RjaolquWmzc3NXbBgQVhYmKOj49ixY2/dukUIEYvFMFyAtW3ssDi1vO4Igny5cDic77//fs6cORKJBN1viGbUWlFXAzKnisVi8Lebm5tfuXIFEqTv3bvXxsbGzs5u3rx5hBVJrlQq582bFxcX5+fnZ2Rk5Ozs3K5du8TExEuXLsEOV69eXb58+erVq9PT09+ZAQrEmx3/AvHtMICAw+/fvz9lypTu3bv36dNn5cqVECVHBwq4vgVBaisqlQoG7jt27Jg2bRoGyiEaU2tFXW06CmagpVLpvHnzDA0NIyIiYLtUKj127BisXhsxYgRslMlkoMFv3rzZtm3bTz/99NNPPx09evT169cikYi6xSBqne3erwYa8yIQCNg1zinXrl1LTExs0aLFwIEDnzx5Qlef09IsGDWDILWbwsLCfv36zZ07l1QO9z93i5Avj1or6moh5bRQulKp3LFjx/79+0llYfLCwkJPT08XF5exY8dCElZCCCwYg2OlUildNU5Rc3rTQUM1TVIoFLAojh7L5/NlMhmXy01JSRk7dmxERMTQoUNpVhk4hPrncY4NQWor8HSXl5eHhYV98803BAfxiKbUFVEnlVnT6b9isRhE/eHDh5aWlg0bNpw1axaPx2NrOfn7nLdQKORyuexEs3w+n8/nv3+cGtjoSqWSln6RSqWpqakxMTGenp6//fYbbIEseEKhkJ4ZRiQYDYsgtRI6ZO/evXu7du0IlmhDNKUOiTpQtZBaSkqKqampq6vrzp07yd/99jDRBZHnHxhhTr30MGiAJ/bFixfff/99586d+/fvDwY6uw46vaJIJMJhO4LUbuAZ79Onz+jRo2ELFl5CNKDWino1cDgcthW+adMmZ2dnPz+/s2fPwg4CgQAeMBqkplKpaEl1QohcLheJRHQoDfndpFJp9R7ysrIyunqNx+NNnDhx1KhRjo6OGzZsIITw+Xx4l63rpDINDrxGaUeQ2gp0R127dl27di1BSx3RlLoo6nSCHKbYR40aZWJi4u7uvmHDBniu2ANkLpfL/hf0m2adg0R1/+rqcrn82LFj48ePt7e3HzBgAOSToU2ieWrBA89+sNkl5hAEqU3QFHJDhw6dPXu2WCxGUUc0o86JOn1U4CkqKSkJCAho1KiRs7PzrFmz4C1YT8KOUYfCMGyXvloa2qqVY9QAkb59+/a33367cOHC+vXrb9269eXLl3TtilgshjO8VbkFAgGuckGQ2k1eXt68efM6d+4M1gXqOqIBtVnUlUqlWqoWwlqGDs7wvLw8Dw8PBwcHFxeXw4cPg3DSxG3V6zSklP+nBw/i7Wm6R4lEsnz58qCgIGdn50GDBl27do3gQ4sgCCGkMks0n88fOXJkXFwcLe6AIP+WWivqanIO0eO0VgqpVPeSkhIfHx+GYRo2bEhLmrJ97P8E256GuHo4OQ2Pp+XUVCoVh8M5dOhQo0aNGIYZO3bsq1ev4EBch4ogCCUzMzMqKoq6DDFQDtGAWivqbL1UM9m5XC5UZRUIBOXl5dOmTTMzM4uPj+fz+UKhENa5vf/531o4FYLdoEDL0qVLnZycrKysZsyYkZeXB/Y9n8/HIugIggCQ8OrSpUseHh49evSAtbW4hBXRgFor6hSw0em/dGYaNp47dy4kJMTS0vKrr76CMqY04ev7iC6UgKN7qlQqPp8P3ntYO9e5c2djY+PQ0NAdO3aUlJSoHV41pw2CIHUQ2keNHDkyJiam6spbBHlParmoQ6I3dkFVUFx4hIRC4fDhwxmGMTExad++fW5ubmZm5saNG9PT02GH6h8tmk0WTigUCsFkB0/Atm3bkpOT69evP2nSpPT0dHqUQCCAgDvMEIcgCCCTyUQiUXFxcVxcXM+ePaHnKS8v/9ztQr48aq2os61neCEUCl++fJmcnNytW7fExMQffvghODiYYRg9PT2GYczMzOrXr+/l5TVp0iQonVL9+jG1/HRq3v6UlJRu3bpZW1uvWbMGzkafT3YIPS5RQxCEcv/+/fDw8JEjR37uhiBfMLVW1KkNTaVXLBYXFhY6OzsbGBhAEVWGYXR0dLS0tBiG0dLScnd3DwkJadas2f79+8Gmf59VZLDQnBCiUql4PN6lS5dWr14dHh4eGhqamZlJWBlsIJKOHoUTZgiCABCFU1BQMHjwYAiUwyWsiGbUWlGnsBO9yeXyqVOnOjk5GRkZMQxjbW1tYGAA0m5nZ6ejo9OgQYN+/fo9fvyYvCs0nZ6TRqjm5OT8/vvvLVq0sLGxGT9+PDylkHgO9Js+pZDdnWB0K4IglcCKmxkzZiQkJIB7D8f9iAbUflFXo7y8fPHixS1atAgJCWnTpk3Tpk0DAwNDQ0PT0tIOHjx4+fJlWvMUTHyIZePz+SDJKpWKajNVfblcPn/+/FGjRoWEhAwaNOjUqVOwXSAQfGDGeARBajKwZvVjne3169cDBw6cMmXKO5NZIcg/UedEnRCiUqmEQiGPxxOJRAKB4Pnz57du3SKEQP52ulvVqmjUwuZwOLCWHdanbdq0ycvLq23btrt27WInhKePJXrSEKRW8rFEHSbmiouLw8PDu3fvDsYAxtwgGlDnRJ0GrMFicXgNj5BKpYKAdvaDCi8kEgnkY1fT6cTExMjISA8Pj8jISEgSRwhRKpU0Eh5BkFrMx7XUnz171rZt2+7du7NrOSLIv6LOiTqFnQWWbVWzXysUCjUjm6aly8zMPHToUFhYWHh4eHJy8suXL2EaTK1Mqkwmw6VrCFJb+YiKLpVK7969GxUV1atXL4iuxTl1RAPqoqhLJBJ2hBqUWnnrDJZa0TZq2R86dKhXr15LliwZMmTI8ePHSWX1l7fG1imVStR1BKndqP6OBmeQyWQZGRnt2rWLjIxUC61FkPenLoo6qZxWZweyicViUHeJRCKVStUeSz6fT+1vyOLu6+u7bt06oVBIBVsikfB4PDDlwbePHngEqQuw5fydhaD+CZFIlJOTM378eLpOHTsQRAPqnKi/dfCrtpEWdFEqley0shKJZNeuXd27dw8ICHj48CEMCGAoUFhYCLuphbuzs84hCFIrYcs5FGLW4CQSiaSgoGDhwoXx8fEfvYVI3aHOiTqpkjsWgLosbD853QHkPD8/PzEx0c3NbcaMGaTS1mfvJhAI4HB2tnlIDv/ffyYEQT4bbFFXKBQaiDp0HSUlJd98802LFi0wUA7RmDon6uzZdLaug3VOCIGyLrCnopJDhw61bt26RYsWMINO90EQpI4Dg3tCiEAgWLhwYZMmTe7fvw//Qg9D+5xqxB7GBLm5ua1bt16wYAGkrsKl6ogG1DlRB2D1mlQqlcvlYFhTexrmsajX/ddffx00aJCTk9PQoUMhUK60tPRzNRtBkBoFyLZUKoXEz9HR0VpaWhEREffu3YN3YQWNWCx+p9mtUqmuX78eHh6+fPnyT9F0pJZSF0Ud3O9vHTVDjBshBKqq37t3r1GjRsHBwWvXroWj3qfWC4IgdQToLsRiMfQMCQkJUFSiefPmpDKjO1D9NBx0R+fPn+/YseO8efMI5pBGNKXOiXo1is5+Agkhd+7cYRimVatWGRkZhOWrx3qICIIAavb3q1ev7O3t69WrxzDMq1evhEJhUVER9DnVizTYCdnZ2ePHjx87dqxQKMT1bIhm1DlRVyuZSqPc6Ti6sLAwNzd30KBBHh4ec+bMefPmTVlZmVgsVjsQQRCEolQqwb3n4+Ojra2tr6+fmppKCHnz5g30MDDTV/1JOBzO8uXL+/bti1E7iMbUOVGnQDpY9haJRPLo0aP+/fv7+vp27dp1165daodIpVKhUIjR7AiCAOw1MmCLDxgwgGEYbW3twYMHk79H41Y/rS6Xy/Pz8+fOnRsVFQWGO3rgEQ2oc6LOTvNON3I4HIFAMGvWrIYNG/r4+KxZswZGykKh8OXLl7APTSdHcKkJgiCEkMqugO3DW7t2rYGBgb29fePGje/fvy+RSCDJ1Ts7DalUevny5d69e4eHh4Oc07h6BHl/6pyo08ePinpRUdH58+e//vprKysrNzc3MNDZoXAqlQqWt8HhVau3IQhSZ6ExOqDBW7dutbKyYhhGV1f3jz/+oLuxrYK3noQQkpaW1qhRo5CQEHS/IxpTa0WdbYjTqSzYCEvPeTweLDi5ffu2r6+vrq7uhAkTsrOz/+kkCIJ8uVBXNgzr4a+al1smk0F4mlKphGoOhBCBQABDedob0LfUjG+owvLo0SN3d3eGYXR0dNq2bfvixQu1ms5vBdrz4MGD3r17t23btqioCAtGIJpRa0WdVD6i8ChCrAqpfIDpQPjmzZtt2rQJDg4+c+ZMSUkJbKSp5dAiR5AvGqFQSFe1SCQShUIhlUqhK3j58uW5c+du3LhBCHn16pWa6hNCxGIxOwQdLHI4m0wmo5a3SCSCEDlSKfMbN250dHSEtW0PHz6kJ6zGna5QKJRKZV5e3pQpU5KSkugVP8pNQOoUtVbUBQIBPEJgptOpL8gRQQgpKSmZPHlyQEBAdHQ0h8Ohg26o6fL5Go4gyMdHKpWCQovF4tzc3MTExJEjR3bu3DkwMLBfv37z5s2jWZ9ppDod04vFYijyBCpbUFAA26mWU+ASPXr0sLW1BVG/evUqe/6u+hZeu3YtNjZ21KhRGCKHaEytFXVKWVkZLYsOyi2RSG7evBkREREYGLh582bYjRZxYR+LtVgQ5ItGLBbzeDz6IF+8eHHAgAEhISGGhoYxMTHffPNNUlJS06ZNHRwcwsLCoqOjf/31V9oJwFGg3LAxPz+/devWvXv3HjRo0Pr166GqMnjjxWJxdnZ2WVkZIaR9+/YuLi7a2tp2dnYzZ84klT6/ajx/cP6HDx8OHTo0MTER/kVLHdGAWivqHA6HbXDTke/q1asnTZoUEBDQs2dPeALfmuQBaq99mqYiCPLfIZVKwWculUqnTZvGMIy9vX10dPTatWubN28+ePDgRYsWrVmzplOnTh4eHq1atUpJSSkuLiaVmgrHisXiR48eWVlZ2dnZhYWFRURErF279rfffiOEqFSqc+fOde3alWEYb2/vWbNmRUZGWlpaenl5BQUFBQcHFxUVkfdT6OPHj4eGhvbo0QMGCjj9h2hArRV1GOoqFIqKigqYIK+oqLh69aqlpWVoaOjatWsJIa9evXrz5g0hRCQSSaVSKKlO0z+hmY4gXzpq4WZr1661srIyNTVNSEgQCoXFxcU0kiY3N3fy5MkNGjQICwtbvHgxYVkCYB74+PgEBAQwDNOsWbNt27YpFIri4uLCwsL169e7ubkxDKOlpWVkZMQwjJmZma6ubkxMjI+Pj4mJSXJyslKphDC6fwL6qy1btkRERAwdOhQ24pI2RANqragD9LEsLy+fO3duQEDA1KlT8/PzYSP1cVUdEUNgPI6UEeSLBkJiVSoVGN+EkEePHl25coVtN4tEIjCmt27d6uDgYGRkNHnyZEJIeXk5VeKLFy9aWVnp6urq6+uDRx2U/vDhw/7+/gzDuLu7Dxw40Nvbm2GY3r17u7m5TZo0iWEYU1PT8PBwMPer13WFQpGYmOjh4dGhQwc0KhCNqc2iDgngCCGrVq1q1apV27ZtIXEjUFhYCC/gsacGukQiwXSwCFJroCN7CIJjlyqnKqtSqUpKSnx8fHx8fFxdXceMGUMPh9DaBQsW6OnpGRoa9unTJz8/n0bVderUiWGYli1bDhky5NatWzweb/369Q0aNHBxcVm0aBH46o2MjI4ePUqqjdGBtxYsWNCvX7/Ro0eTd61rR5B/ojpRpxkVwIUll8troDtIqVSCPU0XriiVSoVCAY9ucXFxfHy8ra1tQkICh8NBtUYQhFSuW6P1lwkhw4YNs7Cw8Pf3d3NzW7p0KewGXZ9EIunTp4+Ojg7DMA0bNiwsLKQ+vNDQUGdn5yZNmixbtowQolAoSkpKli9f3q9fv02bNrm7u4PH/ocffhCLxdX3Pzwe7+jRoxMmTAD3OxZ0QTSjOlFXy6pWM5MhsD1aQqEQ5sih5b///rubm1uTJk3S0tJIpS3+udqJIEiNgnZoFy5cGDRokL29PcyLx8XFXb16VS6XsztAiIPT0tIaPXo0dCNSqVQgEISHh9vb28+aNUsoFNJV7L179/7uu++6dOny/fffh4SEeHt7t2rV6n2alJOT079//0WLFv0HHxepK1Qn6jAalUql4JGuybVM5HJ5aWkpvIYXGzZsMDc379q1K3gXINAdQRCEVC5Uy8vL++abb2xsbCCxq5WVVWBg4OHDhwkhkKaG7r9hwwYjIyMzM7MxY8ZQf75cLp8xY4a/v3/fvn3bt2//5MmTZcuWBQcH+/n5xcXFff311ydOnBgyZIiurq6lpeXVq1eraQ9c68KFC66urlOnTlWpVCqVqvo5eAR5K+9wv0Oeo0/WGo2hil5WVnbt2rUJEyYEBASAgS4UCmnmmRo7KEEQ5BNz/fr10NBQPz8/a2trAwMDJyen1q1b7969W20yWyQSgb76+fkxDBMYGPj06VN2chg/Pz8zMzN7e/vhw4ebmpoGBwdPnjx5xIgRt2/flslkt27dcnR0NDU1/eqrr6pxdkLXdObMmeDg4N69exNcz4ZoSnWirlQqqaJLJJKaqYi0VUqlksfjXb16NTo6ukOHDk+ePKHxrnR2qmbOICAI8olJS0uDjG9Q98Hd3X3ixIk5OTmQRJbd9dGoncGDBzMMo6ent2/fPpVKRePqCSFubm6NGjXy9/fv0aPH7t27Y2Ji1qxZAxH1CoVi8eLFlpaWLi4ukJL2rUAfOajr/QAAIABJREFUlZeXN27cuJ49e9bY/hap+fyjqIN1CwkOqbFbM/OnyuVyHo/H4XASEhLs7e3nzp1bdZ+3rltDEKRuEhAQ4ODgEBsb26tXr7i4uCVLlsjlcjUbnaaWgxfp6ektW7ZkGKZTp06kMo4YMkwXFRVdvXp12bJlT58+BTd7aWkp7S1lMtmvv/6akpLy+vXrf2oPJKfLyMiIi4sbMGAAeAIwAB7RgH8UdYj4gAFpZmbmxYsXIQatpgEj3IMHD7q6ukZERJw5c0YgEEAcAOxAq7FhNCmCIICnpyfDMDY2Nvr6+omJiYSVtYLuwzbWoT9JTU1t06ZNZGQkzEuKRCK12Ukul0vPoFKpwOCG9TjvbJJYLD5w4ICXl9fgwYNhCxrriAa8e0kbIWTZsmVmZmYDBgygU9c1ivj4eB8fn2nTpqk9A2wfGsE5dQRBKhk+fDiEu7dp06Z3797Xr1//5ZdfTp48CXN2CoUCVFyhUNBoNej9nj17lpOTo1AooDMBaYd9oH4EIYQWgmNTvVEBM4P79u2ztraOjo4WiURY0wXRjOpEnUrgzp07GYZxcHD45ptvSGUyB/gVfmAYHbvSMDuDm1AohOEtPCTsciywJzgSHjx4MHLkyICAAEj7yufzYXsNXE+PIEiNYteuXXPmzOnbt+/06dN37tzZs2fPBg0a9OvX78yZM7ADeL+hj1JT6/dM9wYF32jd53dy8uTJwMDA1q1bw7+YVA7RgOpEnc/ng7GbmppqYmJiaGgYHR3N5XKhCiG7pKkGwBwSvGbLuVwup8vP5HI5DCzgWjAcpgPY2NhYIyOjzp07wwi6vLwctr969UqzJiEIUnegdR+gN9uzZ09ycnJMTMyECRO+++67I0eOEFZKK9pZQZcI/dU7ez+wTN5zDZFQKMzIyOjTp09SUhI47T/k0yF1lne738Vi8Z9//tm0aVOGYSwsLDIzMwkr5YtMJtNM19nOKKrH7Gl7WogFChaxycrKioyMbNiw4dq1a2Ef6i4jHzDOQBCkjlDVCAYRffjw4Y8//mhjY9OhQwdIEkdLQ0FXw07D9c7VNP9K1OVyeVZWVnJy8sqVK0lNjUpGaj7ViTqs2SgtLR08eHCXLl0sLCx8fHwOHDhACBGLxdS2hjwJGlxbLBaXlpbSnzsd/KpUKpFIBNkhSKXkQ2J2QsiiRYuCgoKioqLu3btHTwU+Lmrx4yAXQZB3IpfLBQIBn89XU9CsrKxZs2Y1bdr07t271OSgdsj7mw2QbZ5a9tUAM4aPHj2aNGkSXb+DMUCIBvyjqMN80qxZszp16hQTE7Nv3z43N7fRo0fPmzcPdgARpa//7YVhxEAqB6QqlerNmzcymYzOoxNCKioqQNphUurJkydfffWVra3txIkTYQeBQFBQUKDWBqyuhiBI9UDfpdZRQG8Df2Uy2ebNm52dnceNGwcTgmzjHtT6fS70njYPGP1Xr17t1KnTqFGjwO2PTkdEA6qz1Ldv325gYABJlIqKikaNGtWgQYOYmBioQMxOj6Dxj6+8vBxmxN+8ebNo0aIePXpMmjQJ3qJT47AyZNu2bV5eXn5+fgcPHqRGPMDlcmE6AOx1zVqCIEjdAewEkUgEsW9VdVcmk3E4nMTExCZNmiQnJ9OijsA7q7NoxvLly3v27Nm+fXs+n4+L1BHN+EdRFwqF48aNq1evnr6+fsuWLV++fDlnzhwzMzN3d3dIvwoVCTW+sEwmo0EoaWlpjRo1MjQ0DA8Pt7W1/frrr2HmHkavBQUFCQkJ1tbWTZs2raiooONlSNhET0Id7zgXhSDI+wPr00DgJRIJVVOBQPDixYugoKDg4OAtW7bARtBy8JZ/dPf4nDlzRo8e/dVXXxFWpBGC/Cuqs9S7devGMIylpSUkZzh8+DCUPYC6hLRUkcYiCo9HZmZmhw4dGIbx8vLq2LFj3759vb29R40alZubSwjZv3+/n5+foaHhjh07yD/kQxYIBGprOnEpCIIg1aBUKgUCASw5gy30BQ1/A4Nh7969np6eQ4cOpWVY6d+Pm3aax+OlpKTExMQsXLgQOjRcmotoAEPnlqg3CX7cxcXFoaGhBgYGY8aMSU9Pl8lkly5dcnBwsLGx+fHHH2FPOvmkwYXp2s0HDx5A+SMTExNra2tTU1NHR0cLC4uEhITvvvvOxsYmMjLy9u3bH+XTIgiCkL8vqaXra2hXxlbrkpKSRo0atWvX7tmzZ6DlSqUSRPfjGg9yuZzD4bRp02bNmjUqlQpXtdUQ6NAKvm76pVOzFrSMRolRCxPiw9hRYlVRWypJPkaUN0MvT9edg1/94cOH1tbWDMPUr18/PT2dEMLlcv38/GxsbNq1a0czKJG/Px7/Ckjx9uLFC1tbW4Zh6tWr179/f2NjYyi04O7uzjBMbGysWCzGDK8Ignx0ZDIZ7YuhT6PVXKDsBah4//79/f39d+/eDXtCH/3RzWiJRPLixQtfX9/x48eDMKCo1wTYKg7pxuHnIRKJeDze8+fPSaUUQm5/EHsVi2pODuvI2ElfqBZrDEP+nk6VNmLOnDkGBgbe3t5hYWF0JBsREdG1a9fAwMDs7GxCiFAo1Pjy8AEEAsHvv/9uaWmppaXVuXPn9evXd+/enWEYbW1tLS2t2NhYGGR8yCdEEARR4/Hjx0ePHqX/svNtUHudZr/o3bu3i4tLcnIy9L/QW35cSwNMumfPnnl5efXo0QPMJFzS9tn5p3GVVCodPnx4o0aNmjRpEhUVdeDAgZycHPouOzPBOyPPFAoFjOE+VmJgRi0jOm3KsGHDrK2tAwICOnbsCJWIVCpVt27d6tevb2ho+Ouvv9IGvU+7q0IfoSZNmoBp3rp16+joaBcXFyMjI4ZhdHR0Ro4cCfvQXDcIgiAfzpw5c2j3Qn2Bav5V+rp9+/bu7u6//PILNetpzquP2CSVSpWdne3h4REWFoZL2moINOMQ+7suKyuLiYlxdXU1NTU1MDBo0KBBp06dzMzMjhw5AvnT2KL+Tje2SqUCrw+7mO+H8P+WOvwjEolA4MVicYMGDdzd3du1a7d48WKq+nv37tXX13dzcxswYAC7kLlm7YBP0qhRIzDNdXR0QN3B7c8wzPDhw2tmCRkEQb5ounbt2r9/f8LqSWmVNugPqaCKRKI2bdr4+vouXbqUz+dDX/dfiLpEIrl+/bqLi0vDhg1fvnyJBV1qAtRqBZ8NDP5SU1NdXFysrKyaNm1qYWHh6OhYr149V1fXwMDAkydPkspK3/BTqf57hN1ATMHz/eGe6f+JOo3+IISUlJQ0aNDA0dHR3t5+w4YN0MrTp08PGjTIycmpY8eOzZo1U1u4qQHw/MTHxzMM4+zszDCMrq6usbExVXdIMkNHxwiCIB+Ftm3bUoOYsCbIqYOdGip79uyxsrIKDg6GVT9SqZTmz/6I7YHu98GDB+Hh4b169RIKhRhIVBOg9Xvo2geVSjVhwgSGYczNzTt27BgRERESEhIVFRUQEODk5DRx4kQ+n8+udla9pU5/RdS01jjzOoUhrIl9OC+srHB1dbW1tdXX1+/Tp8/y5cuh0YaGhpAB3szM7P79+3AKOor5V9CblZaWxjCMmZkZw8LKyqpx48aOjo4///wzqUxvhyAI8lGYPn26lpbWhg0bJBKJQqGAsCHaw9KQ5itXroSHhzMMExkZCfk5qC31cUUXzlZYWNi1a9cpU6aQD04EgnwUqE5Rr4xKpWrcuLGWlpa2tvbgwYO3bdvm4ODQs2dPZ2fnxo0bBwcHv3jxAiQV/lYvjlT+8/Ly6MYP/N4ZwnI0wfj0woULffv2BX+4trZ2UFDQ999/b2lpGRwc3KxZMzs7O9Ddo0ePUq3VIEqTXY6wbdu2Ojo6enp6DMM4OjqamJiMGDFi3rx5bdu2DQoKGjRo0Id8QgRBEDUeP36sra3t7e29c+dO2AI1IaldVVpaevr06W+//ZZhGBcXl2+++YbH40HPTutQfET3O5zq5cuXTZo0+e6772CeFUW9hkBFXSKRcLlcankyDBMXF2dvb+/q6gqTyAYGBjk5OfDFgZxXH04O4vvmzZvjx4+rxbdpDENY41OZTCYUClesWEEtZj09PUdHx9jYWD09PXNz84iIiMjISFdXVzs7uz/++INUJlPU4ML0wSCEZGRkREdHwxVNTU0XLFgAvv3z589HR0c3a9YsNDT07t27sDMdSdBksexlA/gYIAjyTuRy+dq1a6HPiY+Pz87OFovF5eXlubm59+7dW7JkSdOmTS0tLe3t7V1cXJycnHJycug84PvXR/+3nDlzpmnTpn379iVf7Hq2ioqKty7543A4UKejhmcGg+gKtZvPjqBcv349/GyaNGlCF2AzDKOlpcUwTEhIyOPHj0mlowVuBTh+SGXKI7gK/Jz4fP6NGzcmTpzo7e09fPjwZ8+e5efn0+tKpVIaJE49Q3SUAOWISBUPPwP5EdlO/PXr11tbW9erV8/Y2NjExMTExKR58+bz5s07ePBgRkYGl8vt2bOnr6/vhAkTPvD2KRSK8vJyGM7k5uZu2rRp6tSpJ0+eFAqFYrFYJpPJZLJHjx4tWLBAR0fH2Nj422+/hc9AC66Da4H9HdAZLwRBkGooKiqaOHGirq4uwzBGRkbOzs5OTk4WFhaGhoba2tqmpqZWVlZ6enru7u7Dhg3jcrnUYFDL0/WxEAqFe/bsCQsLGzJkiMbG0udCqVRWbbBIJILu/eHDh0FBQc2bNz937lyNtbuEQiF7IEK/Zfbkr0gkmjhxor6+PsMwnp6eXl5eZmZmMHcMQrlq1Sr2ckTq0YH16PSchw8f/uabb7p16xYeHt6uXTtIykLPmZCQkJCQcOTIkczMTDqUVCqV5eXl1JSnMZtVK578L00s3P2CgoLY2FiIXPPw8FixYgU9GIJKOByOu7u7gYFBYGAglU8N0hTTtrKNbLlcTkNXKKWlpbt37/b3969fv36TJk0uXrxIbz219SFTBD3ky3oeEAT59Mjl8jt37jRp0sTJyQnCevT09PT19a2trQ0MDAwMDPz9/fv27btlyxZ2p8mOofuIKTTgtPv27XN1de3ZsycsIf6yjHW6LJDD4UCkAqnUtlOnToEtGxMTQ+tq1iioWEJREra6S6VS+Gh379796quvPD09QcKdnJy8vLzq1asXEhLSoUOHxMTEP//8E6SQKiOcR83O5HA4q1atCg4O1tfXd3d3d3Fxadq0aUBAQP369XV0dOzs7Pz8/Fq3bm1vb29lZeXh4TF79uyCggI6SoAX9DdZNeCMAdtXJpPBD/TixYt+fn7GxsaNGjWaOnUqVWvQWpVKJRAI4uLirK2tLSwsMjMzYQcNfnxqkwdisZitytS1Th+bR48ezZgxw9PT09fXd9q0aaRS0dkfCTJA1diRIIIgNQTq1czPz582bdrIkSOtrKy8vLxMTU3BeIqLizt8+LBadwyznuxA5Y/VHjjVsWPHPD094+LiPvr5Pw3sgDLqLi4uLr558ybMQOvq6tLi3TUKtSUPhBC5XF5eXg5bRCLRypUr3d3dv/rqq+vXr3/99dfa2tqOjo49evTo2rXrvn37cnNz2YGT9NcF+kVlmJqyIpFo1apVHTt27N2796lTpy5dunThwgV3d3d/f//hw4efO3duwoQJU6ZMgdlnV1dXX1/frVu3wiVgvRw9T1XP9P/SxILj+scff4QQAGNjY1hyR1ilz0BB7927Fxoa6uHhkZKS8iE/Oyh9SO8guwIbXTEPlJeXw4N04MCBhISE+vXrDxw4MCMjA95lTzx8SIEZBEHqDmynoFKpPH369IYNG1asWHH37l0ej0cdp3w+H9J3Q+wOTSKrlpDkA4Hhwp49ezp16jR58mQoHPdlWeqQc5ft1ZDJZJCMpaioaPz48SEhIZaWljt37qyZBejY+chpllWZTHbo0KGJEyd6eHgsXLgQJoUhD9vYsWNTU1P37dtXWloKYwJ4SyKRUA1iJ1+HLVKptKKiQiAQUIGD0mVnzpxxdnYOCgqSy+Wgs1BwaO/eve3bt4dYvNGjR8OEPfz26Jy92u9EvUrbyJEj69evHxsb27x585ycHEhmS1gq+3/tnXdck9f7928FsSAbZO8pQxQEAXEPHC3gRopbpH4duGd9nGjr3tZt62wtRa2jWKtYq5Xa1oWrKIiKCjJC9s55/rh+nNdpUESLgOF6/+ErJHeSOzH3+ZxrC4XCkpISPz8/Dw+P1NRUeIN3kHatJnG0BQ9blQ7fIP2W4UZ5efmiRYtat27t5OS0fft2NsuPPhFL4BAEqQJqllH7iV0ZFQoFn89nzQNWv2FJZbuG1QhKpXLt2rVt27YdPXq0Wq3+sHKDWDNXKBSCq5UmcOXm5oLXOigo6Ndff62zs3w99ORpUptSqXzx4sXKlSvt7e3j4+OvXbsGB5SUlLDJ7bTDK9VXNsGL/YVIJBItYdJoNNQn/ddffy1YsCAuLu7UqVP0v/7ly5eQDZeZmTlz5kw9Pb2QkBAYb8Z2VtByTnMajQbeu7S0NDc3F7q52dnZbdiwgTCDaNjniESiLl260Mku72as08ZM7Oek3yb9gmQyGdyGCw8+iVQq3bdvX+/evX18fMaOHXv58mX6dWPHBgRBqgMsnWCvwyLG4/HKy8vpcieXy2GZ0up/VblBTU2dD1iEsbGxNfiytQOIU2Fh4dOnT+mdENVVKpWXLl2CqV1eXl5lZWX1cL8C/9dUIAsLC7dv396rVy8zM7OdO3eCCcrn86HDKUgSGOW0bRw4V+gLUmOabQIP3hdQd60vYe/evRMmTPD29j548CDcA5sG+hsrKys7f/68sbHxwIEDHzx4QB+q3JyNo28plUqfPHliaGiop6dnbGx85swZdj9CmL2qUCicO3euj4+Pi4tLdnb2u5nFdMIb9XLAlgcm4RBm40yr92hPH1DugoKCsWPHQl+IH374gR6P7ncEQaoGlhRqKrA1S+Xl5bDCyOVy1p6BVRtqbd5H4s6zZ88GDx4cGRk5btw48mEOvIiNjfX19YVxXy9fvoQ7VSpVYWEhVH8FBQWR+lqtRw3CzMzM3r17W1hYuLq6nj9/Hu6kPwbwsbOZdNQKhd8GSJhWrhxtckAYpzKVPELI1atXIfV9y5YtNPRDI/rwXD6fv27dOo7jVq9eTSqUrvLvhIN3hYflcvnixYttbGw6dOjwuk9Oz/7zzz83MzObN28eqdOEju3bt3t7ezs7Oy9dupTH49Hvmt6g220EQZB6y+PHjxcuXOji4hIfH1/njd+1fLTsbFDCRGNZ369arQ4ODm7UqFG7du1u377NHp+WlmZmZsZxXGBgIJQm0fVZIpHUfpsdkGEwKeEzwhdeUlKyYcOGoKAgDw+PRYsWFRYW1sLJwGfPzc1dsWKFnZ3drl27CNO1HQIxsPvMy8uLi4vT09MbOXIkeZXjHeAgAYRU7J5KSkouXLgAoftXQsP4JSUlW7ZsOXToUN16vDUaze7du8PCwjiOc3V1hZY4UMjOlpPSvUgdniqCIMgrgVX0zp07w4cPnzdvHrgE6lDatSbW0EWeBsu1yrilUmlJSYm7uzv0Ef/444+nTZv25Zdfbt++PT4+vnv37hzH2drauru7Z2dnwxPVajWbqygUCmt8RH1lwE8Ot7V8umfPno2JiWnevHlcXFytBf6pPfz8+fM1a9aMGzfu8uXLkF1Iv1h65nfv3h0yZIipqWn79u1p2bZUKtVOlKMvKhKJtLZjr4N+9TweD/6P61As4fOIRKJLly4NGDDAzc0tOTkZTlIkEmntNBEEQeotV65cCQkJSUlJqesTIdTfq1arWfcn65Sl/l1CiEQiuXv3rp2dnZ2dnY2NjbOzs5OTk4+Pz9ChQ0NCQsaMGWNpaeng4ODh4ZGRkUEqUuXhdQQCQXXapNcUVBRoIDwnJ2fBggUODg7NmzffuXMnqajGqoWTIUwMetKkScOHD7948SJhuqjR7//o0aNz585dvHjx1KlTp0yZQsfGVN75cWxhBh3X9kZ3OrS7o4fV2uevDAQeYMf39OnThQsX+vv7d+jQIS8vjzqI6DnX1UkiCIK8kb///tvR0TEmJga6atb16fyf/SYSiWjCMiGEjsMWiUSsOZefnx8REbFw4cLk5ORDhw7t3bt327ZtJ0+ePH/+fGFh4ZgxY6BYetSoUUePHiVMcVNN9TyvDrSsgKpednb27t279fT0hgwZcv78eVYNa6H0jr7d06dPBw4cuHnzZjDQ4Quh8fJ58+ZNnDjR3d29TZs2+/fvv3LlyitfBOAIU07GpuO/DuquB+pDXTj14UCy5S+//OLv7x8VFZWeng7ZhnRAMpa6IQhSDwHL7MqVK7a2tpGRkUVFRXVoKQHbtm3r2rVrr169YMBohw4dUlJS5s2bt2zZsps3b8J4DkhbpsNOoqOjhw4d+vnnn0ONNX0ppVI5evRoGCZiZmYWGBi4c+dOMDTpmly5l+j7A6acaDSaLVu2hISEGBsb79q1C/L7CCFisbjqeak1CFSfEULu3bs3ZsyYY8eOqdVq+E7AFt+7d2+fPn169uxpY2OTkJDQqVOnmzdvsuntpHLvd/arl8vlbFJodZDJZLUQCKkaunOknD59euzYsRYWFp9++ik02KvNXwyCIMg7cOnSpbCwsO7du9d56vvjx49HjhwJDcmhcamzs7OHh4eNjQ000/Xz88vPzycVZiLoSFxcHMdxCxYsEIlEMBJerVYrlcrLly9DuN3AwMDExITjuGbNmiUlJd27d48wCV+1EMalDcWLioq++uormMvy8OFDauzS0emktoK2EB2/d+/eokWLMjIy4N3FYnF+fv60adPGjh0bERExduzYiRMnTpw4ETIQScUe6JVKzcEraiXRvdEZAh0bKufo1z70zHk8Hk1oJITk5+ffvHmzT58+tra2aWlppH44FRAEQSpDR6/Onj37448/zs/Pr1tdnzp1aqtWrXx8fLy9vfv379+lSxcXFxcYZKKvr29iYuLo6Lhy5Uo+n0/HaxFCvvrqKyMjo7Vr17KCIpVKU1NTYbJ248aNIyIiBg0aNGbMmMaNG0dGRsL4Ta0y5veHSqUSi8WnTp3y9vZu2bLlsmXLysvLQRrp+BlS0XH8fZ8MRalUHjt2bP78+Q8fPiwvLy8sLPzhhx8SEhK6devWvn37gQMHhoWFHTt2jNZ7syVzpFIuwv91lKM+kDc6qLXGoFUeEVPLQM0ofCo4Mfb39ODBg2HDhtnY2CxYsEAsFmNYHUGQ+klJScnGjRs7duzo6el59+5drUBnLbNp0yYrKysXFxcYtCGTyfLz8/Pz8+/cubNy5coePXq4uLgEBQVBqxm6/D5+/Lh37979+/e/dOkSqViQ//zzT1dXV1NTUxj7OW3aNFLR/NzZ2blNmzbnzp0jr0r4eh/k5eW1bNnSxsZmzpw5tNEQbQDMfuG109SPegXOnTvXv3//SZMmDRs27Msvv+zZs2fnzp0HDBhw6NCh9PR0wrgNaC4CLWfXek3tNrG6BNRd5OTkjB07tnHjxqGhofDtVN64wD3gmaFeB6x/QxCk1lCpVPPnz3d1de3Zsyd0bqkdUadJcNTN+c8//7Rr187IyMjf3x/kmRAC09VAv2Uy2a1bt27fvg2KQgve7t69u3fvXuig8uDBgxs3bpw6dapr167e3t4cxzVt2pTjuLVr15IKMcvMzPTw8DA3Nx84cOCFCxdAR9liuTf6gNn2ruy2gA4yhz8lEklOTs7y5cutra07deq0Y8cOiBpLJJLa8YiwfdrhS3v48OG8efNWrlx5+vRpaCcXHh4eERGRlJQ0YcKEdevWHTly5MaNG+8QONZlUac8evRo/fr1ERERHMcNHTqU1tkTQsrKyuBGZSMeRR1BkFpDrVYvXbrU09Nz5syZtMldrb01Yby4ly9fNjAw0NfX79y5c0FBAc2aAk872/qUDi+hzxUIBCkpKUFBQQEBAT169EhJSUlMTNy7d2+3bt2gqdyQIUPAe6xQKORy+bVr1xYsWNC0aVM3N7d169bRFiPs+OyqW6FIpVI2Cs7WbdO5OHPnzm3ZsqW7u/u2bdtu375NTXN6zv/9O3wj1JEM+4+MjIx+/foFBwdHRkaOHj06MTFx5cqVkyZNysjIyMrKevjw4YsXL2hbHnUF1XkjHRd1pVIJv0iFQvHdd9/16dPHwMCgS5cuMOuG/lZogyS5XF5eXk4vJ2xFhyBILQBrzpdfftmiRQsola6dRCVqutDp20KhEMaMWllZ9e7dmxAikUigHQqpUHH6LK3YOSFEJBKdPn06MDDQwsKiZ8+eI0eO7NKly82bNy9fvgwtwhITE0tLS1lncklJyaZNmzp37uzg4BAXF/fHH3/Q16TN1F6HUChkB4WweeBgrcnl8k8//dTGxqZXr15nz56lrwbz92ibk3f/BqsN2/eGEFJeXn7ixImEhITevXsvXLhw48aNBQUFmZmZlUUHtibV3+TprKjTnx0NTYlEory8vKSkpFatWkVERJw/f16pVGr1LCTMtcTOiEMQBHl/UFH39/dft24d3FkLRgXrsoa3u3btWt++fd3c3KKioqZNm0YXUshjpwezIWe4QcOaarV6yZIlXbp0adeu3dKlS/fv3w/3p6amjhw5EjLj4KVYGb548eLq1auXLl2ak5MDB0APkmouwux3JRKJoCDwypUrkydP7t+//99//11UVASP0ukhhAk91ALUUqdyU/mt6bwVyF2jZvpbjQTUWVGnMQwAJiITQoRCYUZGRlJSkr29/f/+97+ioiL4WUPvJHo8+x+PIAhSC6SmprZo0WLMmDHwZy1US0N2GJVnpVJ5/PjxFi1a+Pv7JycnX7t2DXzFMpmMmrO08hmO15qODf/y+Xw+n//ixQuw/nk8HpuhrZWzDOPGtSxRuVxOV+Cqvwd2yD0bj+/Zs6exsXHHjh1zc3PhfKp4hTd9T/8V9tNJpVKhUAh1fcLGAAAgAElEQVRRAzo6SKPRsMleWrsNOu23Ou+ls6JOKjoMVP5ByOXyx48fnzhxonXr1k2aNNmyZQv7EA1joO8dQZDaJDU11cfHJzY2Fhb02kkIB8c13BaLxYcPH3Zzc3NxcYmLi4N8PbaXHGtlag1iocFsegw7qJ5qP5sDqHU8qVi06VuwZU2vBERRpVLRj3D37t3169dHRkb6+flt3LgRmuQANE4PXgd4dwjDv9U39g6AKr/SK8B+h7SS67+gs6L+ysQ3+JHBf6FAIIBJMDY2NiNGjMjLy6v8xPrQqRFBEJ0Hlp0VK1Z4e3uPGzcOVv9ay5WjYiOVSg8dOmRvb9+1a9dt27bRc9NoNDt37nRycjp9+jTEqjUaDbXdwcSsvORKJBI6lkYkEtEuYdDjBBrUwD1yuZy1pFlnQHWAt9ZoNNeuXUtOTm7atCkY6PAoON6pdQeO/eq/eA0Ck9Rph1M4E8hvp03N2XwF2Ae8bSW2zoo6m+wGI4/gTxhrT3dD6enpo0aNio6ODggI2LdvH80CxQEwCILUGrCmr1+/3svLC5q31E5TDS1HpkKhOHDggLGxcVhY2NmzZ8GI/OOPP2bPnh0UFBQeHt68efNhw4b98ssvtAsKHegCrwBKT1uT0XwmeJQGtlnNpi3WpVIpHAmzReDOqlunKBQKOFKlUn3xxRcmJiY+Pj5bt26FR9lUaEKIUqmknxcazkMafC30maGfl9rlWla7VCqFLQ5NAtNU8LbvpbOi/jpA49n/2hcvXmRnZ/v4+FhaWi5dupTu7wiTrEEPRrFHEOR9IJfLFyxY4Ovru2TJEkh4rp33ZRWUEJKdne3v7+/k5DR58mRCyLp160JDQz08PAYPHtyhQ4c2bdp4eXl16dLl559/huPfTRE1r4E+Ch5ymvVNJZCuwDBOBuz7goKCxMREExOTYcOG0UaqDZYGJ+oAu/2Bvd7NmzdjYmJMTEyCgoKgqz57GIysp3vnOm93jyCI7jFt2jQvL6/x48eT2s3pAWGGdywoKIBJqU2aNHF1dXVwcPDz83NwcGjfvv3Jkye3b9++cOHCRo0aBQQE/Pbbb+Baf4dBWa8TdZBz1pSi8Hg8KN8HI5vGRrds2WJnZ+fj4/Pdd9/R6TINmQYq6uTfuRKEELFYrFQq9+3bZ2Rk5ODgsGDBAqhl18o51Ko1RBAE+e+A73DcuHFWVlbx8fFgOteCsU6Hn5IKUZfL5cePH3d0dIRpLhYWFrGxsTExMdDelRDy+PHjadOmGRoaDhs2jLrT35aqFV1L1CEAD7fpELPnz5//9NNPgwcPdnBwiI2NvXr1Krg3tOqeGiANTtTZjsqVi/qVSmVGRsZnn33WpEmTdu3aZWVl0Ye0fmS1dsIIgug8oEPjx483NTWNj49/9uwZeVfP9ltBm58TplVccXFxYmKis7Ozp6cn5BFv2bKFTSNXq9Xjxo2ztLRcv379u2UTv07UQc41TJUaK9JyuRySneVyeWpqqpubm6+v76FDh+h2hP1QDZYGJ+qvRK1Wi8Vi+ussKirasGHDp59+2rZt22+++ebhw4dwfzXrJhEEQd6BlJQUX1/f+Ph4dvTZe4Wms2mYGjNCSHl5+ZgxYzp27JiQkEDbnD1//pxGHrOzs8PCwgICAp48eVKDkQK26h06vLL3K5XKR48effvtt126dHF0dJwyZQqPx5NKpVKplOo6liw1UFF/ZSE/K9VCoTA7O3vx4sUhISGjRo1KT0+nQ1+wzRyCIDULGKOzZs3q1q1bTEwMrXSqHVjjmN5ZWFgIE9PBVmYTicC8Wb9+vaWl5fz582vQo0BfSvPv/H9Yrh89ejRu3Dg7OztjY+Nx48bBQ3RBpjuhwsLCmjqfD5GGKOrgdQfHu9YeU6VSlZWV0eaFz549W7hwYWhoqK+v7xdffEGbCWOzOQRBahCoWt6xY0eXLl2GDBlCCBGJRLWTK8cWcFN7nfaBp+dAFz2aFpeenm5lZWVubn7jxo2aOhm2Ky3c0Gg05eXlUqn0zJkzCQkJzZs379ev39WrV6FQmdaq0ePZSTANkwYn6lpTijUV7fdo/ifb5Ahub9u2zcfHx87ObsKECX/99VdtZqUiCNJAkEqlV69eDQ4OnjFjhlb1zXuFmuDUSmbHXsAN0E61Wg07AIVCIRAIDh48aGxsbGFhceTIkZo9JbbPvEAgyMnJmTJliq+vb1RU1KpVq+gegu2xCiFU2telZs/nw6LBifrbAnkZJSUlY8eObd++fZ8+fYYPH067zyqVSracQysLj1RsGurixBEE+WAAF/fmzZvDwsL69OkDd9Zt7g7IOR1rRrVfIpGA/M+ePTsyMpLjuAsXLrzD68tkMlaGtZrt0A3EuXPn/Pz8OI7r1avX999/T6MSkEb3jp9Np0FRfzNQtpGTk5OSkuLt7a2vr9+6deusrCzq5wHZhp6IWjl3hBA23QNBEOR1bN682cfHp2PHjnVuCRQXF//vf/9btWoVeyd0LQU7eP/+/e3atYuOju7duzfk6r8VlafDEULUarVWhuDatWudnJySk5Nv3brFls/hCM0qQFF/AzTnAjaqZ86cadOmTcuWLT09PXft2gXb2MpVlXRUQAN3BCEIUh3EYrFCoViyZAm0aBUIBGw8u/aRSqWtWrXy8vJaunTp+fPnr127JhKJ9u7dO3fu3I0bN86bNy8sLMzFxcXBwWHv3r3v9hYajUYikQgEAmrzsM28X7x4MX78eI7jhg0bxlbTkdekOSMUFPU3ww4dEovFly5dio6ODgkJ6d27d1JS0uXLl+VyuUwmg5ZzbKIHj8fD7SSCIG8EVGrFihXQ7IW8aj5KbSIWi48fPw516o0bN27btm1wcLCDgwPMSgkICDAyMurbt+/s2bMVCsU7dJQDWBsdEpAlEolarT5//ryrq6uTk9OJEycgcA4PaU3lQA/oK0FRfwPwGxKJROwPqLy8/NKlS8nJyf7+/l5eXosWLSIVSaESiYRGwrTi6wiCIK8ElogdO3bY2tr27duX1IPRz+Xl5QkJCa1bt46NjY2OjnZycgoKCvL19TUzM4MbX3311Ts3zGbd7zBZHG7z+fxdu3aFh4cvXbqUDjR7Zckcra1HtEBRrxa075JIJJLL5SqV6unTp2q1+rPPPvP19f3oo4+GDBmSn59PxZudNIyN4hEEqRpYJQ4fPmxtbR0eHp6fn1/n64ZEIikqKvr6669v3bo1YcKEOXPmrFmzZsyYMQMHDty4ceP169fhsJKSkncr8VWpVEKhkKr7rVu31q5dO3XqVG9v7+XLl/P5fDZ2CTFNaCJbh7NTPwhQ1N8M3SfSXxIY5VBKkZ6e7u7ubmho6OjoeOnSpeLiYjiGFsW9s28KQZAGBTRdDw8Pf/LkSV2fy//1dKN/isVigUDATj0XCoX/ZXGjuUdyufzs2bNJSUm+vr4//PADdLyB16fl8pVLkWGG2zu/uw6Dov4G6C8JJJwwbnZCCGR57Nu3r2/fvk5OTu7u7kuXLoXsOeqxx7aFCIJUDSjo/v37bWxsoqKiwDao2yZXVDLhZKhtw+fz2VgkZBS97YvTMdYvX75cvHixt7d3nz590tPT6QHUggIvKU28x0q2N4Ki/l8BJ9KNGzdWr14dFxfn5+c3aNCge/fuqdVq2NXSK7PyT58dY4wgSIMFfMuTJ082MTFZtmxZWVmZbhTOwKcAhYYFkHbzJIRcvHixU6dOpqam8+fPLy0tRad6jYCi/o5IJBIY80fvEQgEd+7c6datm7u7+8CBAzMyMqiK0/5QKpVKKpUKBALduGIRBKkpJBLJyJEjOY6bPXs2+Pl0RuRgAWTt+9LS0n379rVs2TIkJOT06dN0/Bry30FR/69otVS8ceNGYmJicHCwh4fHjBkzHj9+DD0TtJzwunTFIgjyHwHzYNGiRc2bN09JSZFIJDrjZKbZcCUlJSKRiMfjPXz4MCYmxsbGJjk5+dmzZ7TPB5ao1Qgo6u8IW64mlUq18jjOnTs3evTooKCg6Ojo77777uXLl3A/e1idZ7ciCFJPgMjxgQMHwsLCJk6cSHSlDhbablLLp7y8fNq0aQEBAW3btr106RJhlkGpVKobH7nOQVF/R2Qy2eu20uXl5Wq1+ueff540aVJUVJStre2gQYNu3boF161IJILfLm24iCAIQgjZvXu3n5/fgAEDCCEymUw3cm6opb5jx46oqKhevXodOnSInZqhUCh045PWE1DU/yswyFUul0ulUpoTB36kvLy8uXPn9u3bNyQkpHv37qdOndJ6LrqbEAQBNBrN9u3bra2tPTw8NBqNblTNQLJwcXHx2rVrnZ2dhw8ffu3aNRjtCqufRCKh6o4jrWsEFPWap7y8nB2vdPTo0cTERFdX108//TQ9Pf3Fixd1O3wJQZD6BnjvDh8+7ODgYGJiolQq36FOrH5SUFDQv39/d3f3DRs2qFQq6qokhEDgkhCi0WjYCnjkv4Ci/o5ozQqkuR6sYNOf6b179zZu3Ojj42NqajplyhTqikdLHUEQyrfffuvl5WVvb08IkUgkOpB2M3LkyNDQ0KSkpIKCAriHFrnRpZIunhhTrxEaoqizM1fgBiRxgFMIfl7VCXiDf6y0tLS4uJjqN+2NoNFooPYU7pfL5Tt27IiLi+M4rl27dtevX6dNFeAA2JizdR3g2Md+Cwii88BCcerUKV9f31GjRpF6vOPXaDRlZWXsPVKplF2gYK5VZmZmTExMQEDAmjVroH0NXQ9xNXuvNDhRZy8VqVRKfVxisZiGeQBQ5apfDYR5+fLlAQEBT58+Jf8eMwCvQAcF8vn87OzsTZs29enTp0ePHmvXrn348CEhRKVS0dHshBCtOYOkosAdpR1BdBW4tP/8809vb29ra2sIM9dDDzy1OiCPj/bZhB5ccKOwsHDfvn2ffPJJz5497969SyPl7GTVujj3hkKDE3VCiEajoS2N4E+Ymgp/gl/odXKuqYAw+82VK1dyHBcfHw9jhVgDnVTsW9kmyYcOHfL39/fx8QkMDJwzZ055eTl9a3pWrCcKRJ22SkYQRPfg8XiPHz/mOM7c3LzepozJ5XKlUimVSmlzDrqywer0+PHj6Ohoc3PzrVu3gp1DCFEqlRKJhIo6Vv28VxqcqGvZ4jKZTCttDZows6rPQo1v+lLl5eU5OTne3t4cx/355590jtArBRga0YhEogMHDkycONHBwUFfX3/KlCmEkOLiYriSYdMAFe3Uhw+3MeaEIDoJtLJISUkxNjb28vIqKCigtm99RigUQkRcpVIdOHBg5MiRzs7OPXv2zMrKgugkbALYp+AglvdNgxN1sHfFYrFW+ZnW9lOj0cCIVa2nU1Fnh7vweLzWrVt/9NFHy5Yto69Z2Vuu9ZrPnz8/fvz4xx9/bGVlFRUV9eOPPxJCIFhFTwN2GFqxfwRBdA+lUnnw4EEjI6M+ffqUl5fXzx08LEGwjtE8viNHjgwfPtzDw8PKymrbtm18Pp+222LRaDQSiQR97++bhijq7J9qtbq8vLxyrJpKcmWnN4g63Ak9E4RCYdeuXW1sbHr27Kn1XnT0r0gkog0W4MKAKEBGRgaMgfH09Bw1alRlxxS7OcDrAUF0Erjwd+/e3bJlSz09vYcPH8pksnq4iVepVGxXnIKCgj179piamjo6Og4YMCA3N5cwDnkYYimRSCD6DuthnZ16g6HBiTokeigUitu3bx89enTVqlUbN268fPkyTV+HSkqapQn551qjfLV8+ISQiRMnchzXsmVLiUTCxsVZ7xPNq4cdLn3NzMzMUaNGRUREBAQEDBs2bOvWrQKBgN1q0LfDSwJBdBU+n3/69GkrKysLC4vS0lJSv7PECwoKvvnmm+HDhzs7O9vY2Cxbtox2zFSr1SKR6HXNcyC2WLsn27BocKJOCPn777/Hjx/v4+Pj6OhoYmLSrFkzf3//I0eOPHv2DA6gBvGLFy9gv6xlrFN5plvpzz77jOM4Pz+/Fy9e0I0q/HzhuTKZjP7K6bYAcugIITweLzExsVWrVvb29jY2NqNHj87JyaGJpq+L0CMIohuA7ZucnGxkZNS2bVtYWOpnupxUKs3Lyxs0aJCrq2toaGjHjh3PnTvHJhrDDVhF6f2wGKKc1wK6LOo0UwP+hCz3SZMm2dra6uvrW1tbN23alOM4BwcHMzMzCwuLtLQ0+iyZTLZq1SpPT08/P7/ExET4pdL6DYh8U2GWyWSLFi3iOE5PTw96wdIjSaX5bJWRSCQ0cTQ1NbVVq1aGhoatWrVatGhRYWEhWxJKGzARQhQKBXrjEURn0Gg0cXFxBgYGwcHBQqGwdnzvEN1jc30gTZj2cAWfAQB1OsXFxZs3b27btm14ePjmzZufP39eC+eJVB+dFXU2FC2VSqVS6cOHD1esWNG4ceNmzZq5uLhwHBcZGTlnzpzly5evWrWK47igoCBwtqtUqm+//dbc3Nze3r5Zs2ZmZmb/+9//6CvTOg1Qa9hNHzx4UF9fn+O4Q4cOkX/7zapuCguXEJXqZ8+erV27NioqqkWLFkFBQZ07d7548aJUKqVlbzRIT4Excf/t20IQpC6B+RGLFy+GgaSg6LUw5oQuJlB1JhQKYS3SMqmLiooEAsHjx4+fPHkya9asiIiI6dOnX79+vYq5VkhdobOiDrD+q8uXL7dq1crW1tbU1LRly5Zr164tLi4Gxb1y5Yq5uTnHcWfPnoWqsw4dOhgYGNjb2zdv3tzY2JjjuLlz57Kx7V9//fXIkSPXr1+Htzh58iTHcSYmJsuXL6dV7NUZEkytbXrj5cuXx44dW758+datWz09Pd3c3GbNmqUVyIfseqVSyboEEAT5cFEqlV999ZWDg0NiYuK9e/dq501pIQ97D7XU6a7i2bNnx48fHzJkSGBgYO/evbdu3Ur7ZdXDbL4GTkMR9dLS0hUrVlhaWnIcN3z48JKSElJhT6vV6szMTI7jjI2NJ02aRAiRy+Xe3t5NmjQxMTGZMWPG+vXr3dzcLCws7ty5QwgpLi4eMmQIvJStre306dOzsrLy8vIMDAw4jhsxYgTIczUDSKw7AYo+4c+ysjI+n9+5c+dmzZpxHDd79myBQMD2qqOvABV6NfSFIQhSN6hUqk2bNnXt2jU+Pv7p06dsl8n3BxTNajn/xGIx+OQJISKR6Pbt2z/99FPv3r1btWo1adKkrKwsOEwikUgkEkx8q2/orKiz+8fy8vIff/zRycmJ47iwsDAejycSiUAI4d/JkydzHMdx3JkzZ1QqVV5enr6+fqNGjSIiIgoKChQKxdixY42MjCZNmiSTyWbOnMlx3EcffeTo6AjP6tq1a25ubmBgYJMmTbp160YzROguuGpjHTxv9Eh4Flwnly5dSk5Obt26tb+/f5s2bbKzs9mei1TacRoxgnzoqFSqJUuWBAUFhYeH0wWqFqDLCJ/PZ5dNCJafOXNm5syZY8eObdq06aZNm+ijUqmUBhZR1OsVOivqLFAObmBgYGpqev78efjh0s2pRCKZOHGiqampt7f3o0ePCCG7d+9u1KgR2Mfw9FOnTpmamhoaGqalpVlaWurp6XEcFxoa6uTk1LhxY3Nz89WrV4PAt2nThr0wXhmg0jq3ysKvFSM/ePBgUFCQubm5h4fH0aNH8/Ly6HPR94UgOgAsEV9//XXjxo0NDAxu375da29NtRnMbkJIUVGRTCZ78uRJRESEoaGhh4dHz549f/nlF1LR451uOCqn+CB1jo6LOq0uE4vFs2fPXrBgATtQSCKRyOVymUzm5eWlp6fXq1cvsIPXr1/PcVyTJk3mzp2rVCqhhD0iIoLjOPgXfPXDhw/fsmXLmTNn7t27d/v27ZYtWzZr1szd3Z1t7gjyXMXvnu2HrJXNzufz6UsdOnQoJCTEy8srKipq/Pjxx48fp4OP6LYAQZAPFLjSL168aG9vb29vD5G+2rGABQIBu0CVlJRkZGRMmzbNx8fH1tbW3Nw8NTX1lU+EnB4U9fqGzoo6KDFcFbCvpLUZUP9N7eO0tDQLCwtra+vFixfDAdHR0QYGBs2aNYPWrfA6I0aMaNKkCcdx3t7e7du3X7x4MVx4hBCFQnHgwAEbGxuO4ywsLAoLC2nPmer40CAzBW7TgWxwkbMTXW/evDl69GhPT89GjRpZWFhMmTLl/v379NH/+n0hCFKn8Pn8NWvWNGvWzNnZmU4frwWoLcHj8YqLi3Nzc48fPx4aGmpubp6UlHThwgUa6ZNKpdAVTisMj+73eoXOijroHPVjww3o4sL2SXjx4oWPjw/HcY6Ojnfu3IHgtLu7O5jj8COGg+fMmQOpcC4uLmlpaTKZjM/nX79+PTc3d8+ePe3bt4enGBoaHjt2jHUG1Ozn+vnnn6Ojow0NDa2trTt16nTgwAH6XpW7MNbP5hUIgmgBV+7OnTvNzMyMjIwePXpUs+43eH2taB3txA7Lo1qtTklJWbBggaWlpa2tbWpqKk0ork5uEFJP0FlRBzHW+hHDj5JazzKZbPLkycbGxs2bNx8xYgQMMi8rK5szZ461tbWDgwP81ktLS2Uy2Zo1aziOS0hI8PX1bdGiRXJysrOzc69eveLi4mxtbVu0aOHt7e3q6spxXFJSElxCMNWg8pyi/8ilS5eGDh3q6upqampqYmIyatSoly9f0kJ2mUxWeSuNIEg9R6VSjRgxwtTU1MrKCtSU9pT877CFMwKBgA0RlpeXK5XK33//PSEhITIy0tXV1cDA4MqVK9RNSE15zOD5INBZUQfoFAGxWAxjhdgGbUePHo2Pj9fX1+/evTthfvdisdjJyemjjz5i7zxz5kz79u0PHTrUr18/aB7HcVyLFi3i4uLc3NwiIiKOHj26fft2e3t7AwOD4cOHwxYBqNnWbxqNhsfjHThwIDw8vGnTpi4uLhEREZDiR99LqVTWTkkMgiD/Hbhahw4dGhAQoK+vf+3atZo1i6HEht3razQaoVAIy8XevXvHjx9vZWVlY2OzatWqhw8fgn4rlUqBQIAOvw8LnRX1KoxjeOjp06d9+vTx8/ODnjPwEJ/Ph0y6L774YvTo0ZAOCvtlsVi8YsWK77///sqVK+Hh4aamphzHeXl59evXLy0trbi4WKVSFRUV0f7t27ZtU6vVAoGgZre37K75zp07c+bMcXNza9q0aUhIyIkTJ0hFZyg4Bq9GBPmAGDJkiJeXl52dHdgeVTejfCvYVUgmk7FRyK+//nrEiBF2dnZhYWF79uwhFU0qtVx9Wv2vkHqLzoq6XC7XmqUGWq5Wq8GtNGvWLBcXFz09vZEjRxImjY46plhFpJcEXGx37tzZsWPHjz/+mJOT8+DBA3g7cIALBAJvb++YmJi7d+/Sl2KdXTXy0ejV/ujRo3Xr1nXs2NHe3t7Ly2vmzJnQxZaVdgRB6j8ymWzevHnW1tY+Pj5wT81ewrBo0PIfgUBQUlIyYcIEKysrFxeXCRMmwDGVm16o1WqpVIq+9w8FnRV1UuE5h8bvWg/99ddfTk5O5ubmbdq0+eeff0D+QZUh4g6NEuF3/PLlS61Udlp+RsUVCswIIXw+/+XLl0KhkJ3BWrMfikYQ6Fi5DRs2bNy4MSYmxtXVtVu3bocOHdLKHkAQpD4DTdwuX77s4uJiZWXF4/FqXETZeFxhYeH8+fMjIyPDwsISEhKePHkiFAppqBH8i7BywkqIRbMfELos6mKxmAozIUQgEIAclpaWRkdHGxsbGxkZzZgxg+aDgASCbwrukclkdLNMbX16bUCXeIVCAVY+zDYAmae6y+PxKiel/3dgICwhRCqVwvkXFRWdOHEiJibG3d09JiZmyZIlmZmZNfumCIK8V65evero6GhlZSUQCPh8fg26u2nX6n/++Wfbtm1JSUmurq6WlpZbt24lTFCv6pFrOBbyg0DHRR1uqFSq+/fvp6amxsfHd+3adfLkyWZmZuB0unnzJqkwuGkXF9BLuBN+x7A/IIzwg0cdjmGnu5KKxHv67u/DDQ7dZOmfSqUSnGYnT5789NNPu3Xr5ujo2KpVqwMHDtT4WyMI8j5QqVQ//fSTg4ODnZ0dO7mxpsjPz09PT+/SpUvTpk1bt249derUv//+m1TUBPH5fLp8sQU70J4Lo+kfELos6qSiKfrTp09jY2MjIiK8vb0tLCxoS7jt27dTUx5+taCUdJZwnZ77W6NWq+Vy+cOHD7/88kt/f3+YMHv8+HHy7yQX+rnotUofQnc9gtQJYBicPn3azs7Ozs4Oms9ULaWguzRGDmsdGCFgcrBRRblcvnr1ak9PTzs7u7i4uPT09Pf9iZC6QmdFXalU0l/25s2bQ0NDDQ0NoQ7NxMQEesjk5eXRrBBwdrFX0YfVJon1jInF4oyMjEGDBunp6RkYGEybNu3SpUv0UZpCSJ8CDeywrh1B6pZ9+/aZmJhYWlqeOnXqjQdrBd3pn/n5+XCDVvCePXs2Pj7ey8vL2tr6888/pwlAaH/rJDor6pSDBw+2b9/e2dm5WbNmrVq1srCwcHFxad26NcdxR44cIYSIRCKaSadSqVh1/IASPmlEn1rbubm5u3fvDgkJcXZ27tChw4kTJ16+fFm5Gw/7eWuwhAZBkLdCrVbn5OSYm5vb29vn5ua+MYANu3DoNMXaMFqVL3v27AkICDA1NR0wYMDp06fhGDDfPyy7BakmOivqNAQeERFhYGCgr6/fokWLIUOGdO7c2dXVdd26dYMHD46JiXn+/DlVQS1fNPmgRJ2eNjvIlRBy//79VatWBQUFBQYGTp8+HdrFCwQC2qyKRh9Q0RGkDlEqlXl5eZ6env7+/lrWxSup4oKlGr9o0SJHR0d/f/8JEyaAgU4HQ39AixvyVuisqENOOJ/Pj42NhSB627ZtAwICjI2NR4wYwefz+Xx+cHBw//79CSEqlYodYKxWqz+4gDok51Mth4oUUPqrV6/OmjVr4MCBsbGxgwcPPnr0KH2WWCym13blwj8EQVuNp8EAABMvSURBVGoNjUazcOHCgICAgICA69evV11FBhY5fSLN7YU7X7x4sXfv3tjYWHd39/j4+JMnT0LQDfYB9JWx6aROorOiDigUijNnzhgaGnIcB83jAgMD//zzT3h05cqVjRo12rVrF1wSEomEbeT0wZVmqlQqiUQikUio1U7b4RFCMjMz582b171796lTp6anp9OiO7Z1FOo6gtQVSqVy1qxZ7u7urq6ujx8/rk7AG4rIRSIRXMJw4+eff+7WrZuPj4+Jicn27dvz8vJonizVdZFIhIquq+iyqEOLmJKSkoCAAI7jzMzMAgMDr127RgiRSCSwpY2NjXV2dv7999+vXbuWnp7+ww8/kIr8cBjpVrcf4d2A7Qitc4OGzzwe7/Tp03379g0NDfXw8Jg2bdqFCxfg+OLi4prteYcgyNsil8uPHTvm6Ojo5OREmMry16FWq6FlDV2msrKyLl68GB0dbWFh0aVLl6ysLNqEQy6XU9edSCTCaLoOo7OiTr3KMpls5syZMIN806ZNbCQJ6tdDQ0NNTU3t7Oxat249ffp0UjEcqXK7xHoOtMqhxabsfBq4oVKpcnNzz5w5Ex0d7efnFxoaunr1ahqZg11/nZw5giAajSYtLc3FxcXLy6ukpIR2u3olcKnCNS6RSKBxta+vr4WFxSeffJKWlsZOrqKuR+qTg008FrzoJDor6oQRs6ysrDVr1tDSTHAyazQayBm5efNmdHR006ZNPT09b9++XTnypAOwETiBQJCTk5OcnNypU6dOnTotW7assLCQNtWhjepoX50PbnODIB8ccHmeOHHC0tLS3t7+3r17hBCIpmkdCesSmwybk5MzbNgwBwcHY2PjL774AqZRECa5HXNgGxS6LOoUSHyj2aQ0zEzl6vnz58uXL1+9ejXoPVwDumG20gubDbSXl5cLhcIzZ8506NDBxcUlJSXlt99+ozE2ugSIRCLsIY8gtUNxcXF2draxsbG/v39JSQmb/a7RaGgndjp4ghAik8nWrVsXHh7u6uq6c+fOq1evFhYW0ocwv71horOizjqi6Z1wMdB7tKaU0kFtEM3SDUudXv9akxPh0x04cGD8+PGdOnUKCQkZOHAgtLyAPRA9mFrtCIK8J+Byy8jI6NSp04gRI0jF/IjX1ZoqlcqHDx8mJCTo6+vb2dnt3r2b3XnLZDL6LPSxNzR0VtTZoDJUbYK8yWQy2OpStVOpVNCKgTDlm3Al6ICu0906fDQq1TRvQCwWnz59GqpfevbsmZ6eDia7SCRCLUeQ2gGutSNHjkRERPTo0YP8OwQOSa+0OOXx48dXrlz55JNPOI6LjIwsLCwEhxwsbiqVil71NMiINBx0VtRJRa023KYtYOl+ViQSse4puJ/P57PVnzrggYfNDXwWGKFIE3Bg1YA77927d/jw4YSEhMDAwH79+t24cYMQolAo+Hw+W8GPIMh7AmrPevToMXDgQDDTweBmTQuNRnPx4sW5c+d27949PDx87NixWjMd6J9wvcvlcnTCNzR0VtQVFbDeJ/b3DT52Om0ddI61TVlb/8MF5rlpfRaYBgsfViwW0ys/IyMjISHBw8MjMTExIyMDLXUEqR2ePHlCCHn58qWJiUnbtm1hfhphJj4TQnJzc2fOnBkcHNymTZuBAweeOHGCVDTOAl8jm1XHuuh0wDhBqo8uizq9zeaIqVQqoVAoEAi09r/sDXiubuxwwUav5galuLj47Nmz/+///b+OHTtaWlqOGzcOWkvqxleBIPWZW7duhYWFcRynr6/PcZyHh8f+/fvhoSdPnnz99df9+vVr0qSJvb39vHnzXrx4Qf5ddgtudto5ji56dPuONBB0VtRJhfsdeshAqEnrALoF1qrjgnizLvVnAGmH2Q90DgQhpLy8nC4BsArI5fKTJ0+ePHly8eLFPXv2nDdv3uXLl+v47BFE15k+fbqpqamBgQGIupmZmbOzc1BQ0J49eyQSyR9//NGjRw9/f/9Jkyb9+uuv9FngZRSJRDRhCO6H4DohRKFQYEy9oaHLoo68A7Sb3o0bN/bu3Tt69Oj+/ft//vnnpNKA+WfPnhEmt1Ymk6lUKtoDoLbPG0E+HLT6wOTk5EArawMDAz09PUtLSxMTk+joaB8fH1dX19jYWE9Pz06dOkGnDciDqdPTR+o1KOqINjSB7q+//vrss89iYmLWrl3766+/isXikpISQsjSpUt9fX2tra0/++yzPXv20F76FGwrjSCvBPa7EBGDe2Qy2dOnTzmOMzIy4jjO0NCwc+fOXbt2PX/+/NKlS2EYVffu3c+dOwfH08pbBHklKOrIK4ClRyqVXrhwYfv27QcOHOjfv/+BAweePn06ceJEWGgCAwM5jgNpB18f5MmjGYEgr0OhUNA0F7hHo9Hw+fwuXbpwHNeoUSOO4xwdHT09PRctWrR7925bW1tra+utW7dCiPDDHUiB1Boo6si/oEWAtO9eWVnZ9evX9+/fX1hY2KtXL1B0ExOTMWPGjB49muM4Z2fnbdu2EWw8hyBvAkSd/LthpVKpbN68OVxWXAXR0dFmZmYcx/n4+GRlZclkMpoWh52bkSpAUUf+BVspQCqaxms0GrFYvHTpUn19/UaNGllbW3Mc17Rp08TERGNjY47j2rdvLxQKadAdm1ghyCthry9W12fPnt2oUSM9PT1QdDMzs5CQELjduXPnp0+f0iMxlR2pGhR1RBtIkqe3QaHLy8vDw8Oph5DjuPj4+JYtW8JtX19fgUAAvndUdASpDtD3CW4rlUobGxuIqRsZGdnZ2XEcp6en5+3tvWHDBnq8QqFAMx2pGhR1RBtIlGMNAolEsnHjRiifBWPC3d29cePGlpaWoPH9+vWjox6xMyWCVI2Ggd55+PBhe3t7V1dXU1NTQ0NDV1fXFi1aJCQkZGVlwQFwSWLdOVI1KOrIv2AzcdjRdp9//jnHcU5OTlTaDQwM4HbLli3Pnj0Lh0mlUrQkEKQKXtkMCnT6p59++uWXX1auXDlw4MDw8PAFCxZcv36dMHPT4WAsGUWqAEUdqRYHDx60tbUFZzvU1Hp4eMCfx48fp6aDVgNqBEGqDzSFlcvlUqlULBbj/hh5B1DUkWpRVlY2dOhQjuOsrKygS4aJiYmpqenYsWMhiwesB7DsUdQR5G2hg5dgNAOMrqjrk0I+PFDUkery/Pnz+fPnJyQkQNjPyMhoypQp9+/fh0fZ+W+4GCHIW1E5xI4g7waKOlJdxGIxj8e7efNmRkbG+fPnX758SR+iGe9go9NidwRBqgOKOlJToKgj1YLKNm35Dk5CQohcLqcxdbTUEeTd0LyKuj4p5MMDRR2pLkVFRXBDLBYLhUJSofR0nB3U0dbV6SHIhw4bVgfq+oyQDw8UdeQtoL1jtW6TisRdgvU2CPJOsAa6uoK6PinkwwNFHakWtEZWq7EMNSakUincZvtkIQhSHdDljtQUKOrI2wHd4KF9LCxAWl2sCeOWl8vllWdNIgjySuRyuUwm0/KBEUJkMplCoVAqlbClxiAXUgUo6ki1gAnrVTwqk8lg6YHDaKAdQEciglQN63IvLi5WKBRisTgzMzMrKyszMzM7O/vJkyfPnz+v69NE6jso6ki1gPaxWr5BiKO/0mEok8nAUhcKhdgKHkGqBrRcJBIVFxf/+OOPGzZsiImJiYmJ8fLyCgkJsbOz8/HxCQ0NjY+P/+2339BSR6oARR2pFjQpF6Sd/imVSlmjvHKCD7sVwMUIQapg7ty5cXFxjRo18vX19fT0dHNzMzQ0dHZ2dnR0HDly5K5du86dO4dOL6RqUNSR6gJ2OTvxhUWhUID7HSRcLBazYi+VSnG0FIK8DpVKJZFIEhMTIyMjfX19AwMDp0+f3qJFC09Pz0mTJn3//fdisZgQAqWk2NwJqQIUdaS6QIqcVr4bG0cHlEolXXQUCoVcLscUOQSpGtqKcefOnba2tiEhIXv27Hn27BnNM2UP1kpYQRAWFHWkusCcdfqnUqmEOjc2pq5SqcrKyp48efLs2TO6EtEDKqf1IggClJaWEkLS0tJatGixYsWK8+fP0/tv3rx56NCh77777v79+3gRIVWDoo68BVSe5XJ5WVnZs2fPfv/99xMnTuzYsePLL79ctGjR559/Pn369IkTJ7Zq1WrPnj2wCUBvIYJUDeyAFQrF/v37O3fuHBMTc+7cudTU1Llz5/bv37979+5RUVGpqamlpaXYaQ6pGhR1pLpAPO/y5ctLlixJSkrq169fx44dw8PDR44cGRcXFxsbGxsb265duzlz5nTs2LFx48YtWrTIzc0lhEA4EEGQ1wEVIkKhcMiQIW3atPHy8nJzcwsJCQkMDExKSlq+fPnff/9NKhJR2SfS5FOtKBjSYEFRR6qFUqk8duxYVFSUiYmJn59fcHBwr169PD09mzdv7uzs7Ovr6+rq2r9//zlz5qxatWrJkiULFy5cs2YNO7QNW2UhSBVIJJKxY8fGxcVxHMdxnJ+f3+rVqxcvXpyfn08qakrhSKFQSG/D5PU6O2mk/oGijlQLSF/39/d3dXU1NjZu1apVYmJicHDwhAkTUlNT09PTT548WVhYSCqyeHg8XklJCTyXNq5BXUeQ18Hj8eLj493d3a2srLp37/7NN9/k5eXxeDz2GNqtWS6XU12nHZrx+kIIijpSfXJycr799ltXV9e2bdsePnz4wYMHz58/14qXgxeRjfmxZgTGAhHklchkMh6PN23aNC8vr06dOonFYtaXLhaLqXITQqDjE2u7w1WGJjtCUNSRavLgwYNOnTq1bdv29u3bhBCVSkU7ViqVSpFIpNFoysvLwZKgTarFYjGKOoK8EaVSuXXr1k6dOrm6uq5bt44QwufztbbICoUCsuSova41ZglL3RCCoo5UE4FAYGRkZGNjM3HixFcW1cjl8pycHIFAwOfz6RjW17WWQxBEixkzZvj7+48cOZL8exaiVp4p7JLBLS+VSuGawgIThIKijlSL+/fv9+nTx9HRMT09nRoEz58/X7FixZ49e+bPn5+QkNC7d+8RI0akpKTs3r2b7R+HZgSCVE1paemOHTvs7OyOHDkC9wiFQpVKRa+j0tJSkPPc3NzMzMxdu3ZBWB0uLjgMN80IQVFHqolAIOjSpYuZmVlycvL27dsXL14cFRUVFxeXkpJy6tSpmJiY7t27Dxw4MDIyMioqqkePHkVFRWVlZeA5BMseA34IUgXXr18fNGjQmTNnZDIZ2+hJKpWq1WqFQiEQCL7//vvevXt37ty5d+/eT548IRU7ZpBz6o1HGjIo6ki1KC4ujo6O1tPT4zjOysqqf//+27ZtGzBgQI8ePaKioiIjIwcPHrxly5br16/n5+ffuXOnrs8XQT4wSktL9+3b165du507dxJClEolj8e7cuVKZmbm4sWLp06d2qFDh+Dg4NDQ0C+++CIrK4s2bcTydIQFRR2pFjKZbPz48R999JGRkVGTJk3s7OxCQ0NnzJjxww8//PPPP3CMVh9ZBEGqCQTOeTxeaGhov379Ro0aFR8f7+bm5uzsHBQU5OzsHB0dPWDAgHnz5m3ZsuXZs2dsoJ0GtlDdEYKijlSfcePGBQcHe3l5BQUFpaWlFRUV8fl8+qhMJpPL5aDrIpGoDs8TQT5EFAqFUCi8cOHC7NmzO3bsaGFhERYW1rdv3ylTpsyfP/+nn37Kzs4WCoVaaapyuRxFHWFBUUeqhUKh6NevX9u2bf39/X/99VeYp84ewCa3Y8IOgrwtkNAuk8kKCwt//PHH48ePZ2Zmnj59+saNG//88w9VboFAAFF22EDTYccE01YQQgiKOlJNpFJpUlLSyJEjvby8rl27BneWlpYWFxfTBF3IxcUe1Ajytmg0Gtragd4pEAgg9w1S56q+rCCZ7n2fJ1L/QVFHqkvXrl3btWsXHBy8c+fOgoIC9iGYm15XJ4YgOoBMJisqKiIVCe1sDEutVsvlcqFQyHaHBaAnBNaLIhQUdaRaSKXSRYsWffzxx2FhYT///DOpaGwpk8nY5DiNRoO+dwR5W+hAVQiZg66r1WqlUll5uwz3s6BvDKGgqCPVJTIy0svLa+jQodeuXQNHH+i3WCwuLS1l83dQ1xHkrQA3O9vCnRrfNGoO9jpt16gFxNdr74yR+gqKOlItNBpNRETE4MGDu3XrBtPY2E6WCIIgSH0ARR2pFnK5vF+/fp6ent26dRMKhfTOuj0rBEEQhAVFHakuPXr0CAgISElJIYRIpVKcIYEgCFLfQFFHqoVarW7dunViYmJiYiINn2MMD0EQpF6Boo5Ul44dO/r6+jo5Od2/fx/uwZxbBEGQegWKOlIt1Gr1kSNH3NzcTE1NT5w4oVKptMY8IwiCIHUOijpSLYqLiwkhaWlpycnJ7MjnOj0pBEEQ5F+gqCPVBeY3k4qkd1R0BEGQ+gaKOoIgCILoCCjqCIIgCKIjoKgjCIIgiI6Aoo4gCIIgOgKKOoIgCILoCCjqCIIgCKIjoKgjCIIgiI6Aoo4gCIIgOgKKOoIgCILoCCjqCIIgCKIjoKgjCIIgiI6Aoo4gCIIgOgKKOoIgCILoCP8fh2PI3eTAGKQAAAAASUVORK5CYII=" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> M1A1A1A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award each <strong><em>A1</em></strong> for the edge added in the correct order. Award no further marks after the first error.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [9 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well answered in general. Part (c) was well answered.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph <em>G</em> has vertices <em>P</em> , <em>Q</em> , <em>R</em> , <em>S</em> , <em>T</em> and the following table shows the number of edges joining each pair of vertices.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the graph <em>G</em> as a planar graph.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Giving a reason, state whether or not <em>G</em> is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) simple;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) connected;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) bipartite.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Explain what feature of <em>G</em> enables you to state that it has an Eulerian trail and write down a trail.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-size: medium; font-family: 'times new roman', times;">Explain what feature of <em>G</em> enables you to state it does not have an Eulerian circuit.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the maximum number of edges that can be added to the graph <em>G</em> (not including any loops or further multiple edges) whilst still keeping it planar.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img src="data:image/png;base64,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" alt> A2</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <em>G</em> is not simple because 2 edges join P to T <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <em>G</em> is connected because there is a path joining every pair of vertices <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) (P, R) and (Q, S, T) are disjoint vertices <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so <em>G</em> is bipartite <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Award the </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> only if the </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>R1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> is awarded.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>G</em> has an Eulerian trail because it has two vertices of odd degree (R and T have degree 3), all the other vertices having even degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the following example is such a trail</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">TPTRSPQR <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>G</em> has no Eulerian circuit because there are 2 vertices which have odd degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><br><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so it is possible to add 3 extra edges <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">consider <em>G</em> with one of the edges PT deleted; this is a simple graph with 6 edges; on addition of the new edges, it will still be simple <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(e \leqslant 3v - 6 \Rightarrow e \leqslant 3 \times 5 - 6 = 9\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">so at most 3 edges can be added <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) A graph is simple, planar and connected. Write down the inequality connecting <em>v</em> and <em>e</em>, and give the condition on <em>v</em> for this inequality to hold.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Sketch a simple, connected, planar graph with <em>v</em> = 2 where the inequality from part (b)(i) is not true.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Sketch a simple, connected, planar graph with <em>v</em> =1 where the inequality from part (b)(i) is not true.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv) Given a connected, planar graph with <em>v</em> vertices, \({v^2}\) edges and 8 faces, find <em>v</em>. Sketch a graph that fulfils all of these conditions.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(e \leqslant 3v - 6,{\text{ for }}v \geqslant 3\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) </span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAKCAIAAAC/sQ6fAAAA6klEQVRIieWWMaqFMBBFb+9KRIKLECzcQ8AtuIM0tjauwAXMAqZPb5069bTTzi/ky+eJrxIC/tMEcpszN4EEZqaqRNQ0DQAA3vsYo72RlFIIAb+EEHLORwRVHccRF5ZlKSv9ODHGjxmrqqrr+ugCRHRt4WDf99LyjyEi55X/YBgGM0Pf93dFzPNc2v8xmPluTAA55y/pPyKlhK7rSmuUJ6WEdV3v4je9HSJyN6ZzzswgIs65a+y9Ly3/MNu2fTlvmFnOuW3bv9k0Tapa2vx5rl0w8xHhWFQ1xkhERHT+MV6JiDAzETGziJz7P/nYBt5D1EVHAAAAAElFTkSuQmCC" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) </span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAIAAAACUFjqAAAAd0lEQVQYlaXQoRFDMQwDUC+UNbxFWGiAN8gE2SEDZABzcw8RHGqqD/Kvd21/UQX1kEQAAESEqopIKaW1ZmanJwBrrZQSvUdEIoIi4ttOxhhkZo92Z875B7v7L2JmApBzfmRVJQB7b2b+sN77vft1S6313OLup78AFZ1Zccts4noAAAAASUVORK5CYII=" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv) from Euler’s relation \(v - e + f = 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v - {v^2} + 8 = 2\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({v^2} - v - 6 = 0\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\((v + 2)(v - 3) = 0\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(v = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for example</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> There are many possible graphs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In (b) most candidates gave the required inequality although some just wrote down both inequalities from their formula booklet. The condition \(v \geqslant 3\) was less well known but could be deduced from the next 2 graphs. Euler’s relation was used well to obtain the quadratic to solve and many candidates could then draw a correct graph.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">The table below shows the distances between towns A, B, C, D and E.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Draw the graph, in its planar form, that is represented by the table.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Write down with reasons whether or not it is possible to find an Eulerian trail in this graph.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; line-height: 12.1px; font: 22.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Solve the Chinese postman problem with reference to this graph if A is to be the starting and finishing point. Write down the walk and determine the length of the walk.</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; text-align: justify; line-height: 12.1px; font: 25.5px Times; color: #2c2728;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that a graph cannot have exactly one vertex of odd degree.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><span class="Apple-style-span" style="line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="display: inline; float: none; line-height: normal;"> <strong><em>A1A1A1</em></strong></span></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for the vertices, <strong><em>A1 </em></strong>for edges and <strong><em>A1 </em></strong>for planar form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) It is possible to find an Eulerian trail in this graph since exactly two of the vertices have odd degree <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) B and D are the odd vertices <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(BC + CD = 3 + 2 = 5{\text{ and }}BD = 9,\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since 5 < 9 , <em>BC </em>and <em>CD </em>must be traversed twice <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A possible walk by inspection is ACBDABCDCEA <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This gives a total length of</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">2(2 + 3) + 8 + 9 + 5 + 7 + 10 + 6 = 55 for the walk <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The sum of all the vertex degrees is twice the number of edges, <em>i.e. </em>an even number.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Hence a graph cannot have exactly one vertex of odd degree. <strong><em>M1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Drawing the graph usually presented no difficulty. Distinguishing between Eulerian and semi-Eulerian needs attention but this part was usually done successfully.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A simple, clear argument for part (c) was often hidden in mini-essays on graph theory.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Drawing the graph usually presented no difficulty. Distinguishing between Eulerian and semi-Eulerian needs attention but this part was usually done successfully.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A simple, clear argument for part (c) was often hidden in mini-essays on graph theory.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A graph <em>G</em> with vertices A, B, C, D, E has the following cost adjacency table.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[\begin{array}{*{20}{c|ccccc}}<br> {}&{\text{A}}&{\text{B}}&{\text{C}}&{\text{D}}&{\text{E}} \\ <br>\hline<br> {\text{A}}& - &{12}&{10}&{17}&{19} \\ <br> {\text{B}}&{12}& - &{13}&{20}&{11} \\ <br> {\text{C}}&{10}&{13}& - &{16}&{14} \\ <br> {\text{D}}&{17}&{20}&{16}& - &{15} \\ <br> {\text{E}}&{19}&{11}&{14}&{15}& - <br>\end{array}\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Use Kruskal’s algorithm to find and draw the minimum spanning tree for <em>G</em>.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 24px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) The graph <em>H</em> is formed from <em>G</em> by removing the vertex D and all the edges connected to D. Draw the minimum spanning tree for <em>H</em> and use it to find a lower bound for the travelling salesman problem for <em>G</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Show that 80 is an upper bound for this travelling salesman problem.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) the edges are joined in the order</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">AC</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">BE</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">AB</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">ED <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Final <strong><em>A1</em></strong> independent of the previous <strong><em>A2</em></strong>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the weight of this spanning tree is 33 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to find a lower bound for the travelling salesman problem, we add to that the two smallest weights of edges to D, <em>i.e.</em> 15 +16, giving 64 <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) an upper bound is the weight of any Hamiltonian cycle, <em>e.g.</em> ABCDEA has weight 75 so 80 is certainly an upper bound <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [9 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Part (a) was well done by many candidates although some candidates simply drew the minimum spanning tree in (i) without indicating the use of Kruskal’s Algorithm. It is important to stress to candidates that, as indicated in the rubric at the top of Page 2, answers must be supported by working and/or explanations. Part (b) caused problems for some candidates who obtained the unhelpful upper bound of 96 by doubling the weight of the minimum spanning tree. It is useful to note that the weight of any Hamiltonian cycle is an upper bound and in this case it was fairly easy to find such a cycle with weight less than or equal to 80.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Kruskal’s algorithm to find the minimum spanning tree for the following weighted graph and state its length.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"> </p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Use Dijkstra’s algorithm to find the shortest path from A to D in the following weighted graph and state its length.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 25px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">Kruskal’s algorithm gives the following edges</span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">CD (4) <strong><em>M1A1</em></strong></span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">AD (5)</span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">EF (7) <strong><em>A1</em></strong></span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">EA (8)</span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">BC (11)</span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">FG (12) <strong><em>A1</em></strong> <strong><em>N0</em></strong></span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: center; margin: 0px;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAesAAAF+CAIAAAAtOqUGAAAgAElEQVR4nOydd1wT2ff3L4EQWgihVxNCaNJ771VUmkBQwIoVURTbKvayithF0RVYG3bsDV0RxVVERUUBRVBQivROIJA8f9yf8+SLZS1AAO/7D184mXJm5s5n7px7zrmAg0AgBjPd3d1sNpvNZvPaEAQPALw2AIFA/BJIwX9nkIIjEIObrq6u7u5uXluB4A1IwRGIwQ2LxWIymby2AsEbkIIjEAjEYAUpOAKBQAxWkIIjEAjEYAUpOAKBQAxWkIIjEAjEYAUpOAKBQAxWkIIjhghsLnhtCwLxf3C3RixsH2ul3H/83P6RgiOGCGw2GyW2IAYaXV1dHA6n+xNfXOdXuh1IwRFDBKjgWVlZra2tvLYFgfgyLS0t7969e/To0ZEjRw4dOpSVlfX69etf2SFScMQQASp4cXFxR0cHr21B/Nb06FAXFBRcunTpyJEjQUFBmpqaCgoKJBJJUFAQj8cTCAQFBYV58+ZVVVX93LGQgiOGLJhbHH7AIhc5on+A3pKOjo7y8vLY2FhHR0c+Pj4AAABAWlraycnJ09PT3t5+/Pjx8fHxDAYDAODr69vW1sbh8pV/J0jBEUOWHp5xNM6J6Ddqamr++OMPBwcHEokkJiZGIpH8/PxSUlKePHlSU1NTV1fX3NzMYrE4HM6///5LIpFkZWVfvHjBQQqOQPSgtbX18OHDOTk5nF8bMkIgvp/w8HDY6cbj8c7Ozvfu3fviamw2e968eQAACwsL6BBHCo5A/A95eXnCwsJqamrPnj3j/ELYFgLx/cyfPx8AYG9vf/jw4fr6es6n3gN3REpeXt4ff/zBx8cnJyd38OBBuPBH2ydScMQQJykpSVlZGQAwbdq0rq4upOCIfqC6uvrUqVN5eXnt7e3Qwc35NBcH/PvWrVuenp4SEhJKSkq7du366eF3pOCIoczbt299fHx0dXWJRKKqqmptbS33r2w2G2k6otfhblGbN292d3dPSUmBfjwOh9Pa2rpx40ZdXV0AgJWV1bVr137lWEjBEUOZixcv2tjY+Pr62traiouLP3jwoMcKKEYF0etgsU8cDmflypUAgNDQ0GfPnnV0dKSmpk6dOhUAoKen5+/vn5+fDzdBGT0IxP+BPQzNzc179+41MDBQUFCYMWMGHo/fuHEjb21D/Faw2ewJEyYAADw8PKZPn+7t7T1s2DASiRQWFnbhwgWYevaLIVJIwRFDDex5KCoqcnJyotPpEydOvHHjhqioqIeHB8q8R/QbjY2Nvr6+UlJSMC5FXV1dQ0ODSqVGREScPHny1atXMOeeg/rgCAQG9jDExcUZGhqamZmlpKS0tbXZ2NiQyeTHjx/z1jzE7wOLxVqxYoWEhARUcCEhIRKJJCkpqaysrKSkpKCg4Ovrm5SU1NTU9NOHQAqOGGpABa+rq3Nzc1NSUjI0NMzLy+NwOLt37xYSEtq/fz8HBYYj+ouIiAgREZGVK1fGxsbu3bs3LCxs+/btBw8e3Lx58+LFi83MzISFhe3s7K5fv/5z+0cKjhhqQGk+ePCggoKCoaHhlClT4PL8/HwajcZgMLBycby0EvEbwGKxGAwGPz8/NoSOuU0gZWVlycnJzs7OKioqaWlpP9EmkYIjhiAsFgv6H6lUakBAwP79+7dv3z5//nxlZWVVVdXi4mJeG4j4LaisrHRycpKTk3v06BHnU98CK/aAfQXm5uYqKipSKJTnz5//6CGQgiOGCNxekbt37+rr6yspKWEVhTD4+fmTk5M5KDkT0fdUVFRMmDBBRUUFZtVjvjvuUmtsNrulpSUwMFBUVDQ9Pf1HD4EUHDFE4I7KunjxopaWlouLy9ixYwMCAnx9fUePHu3l5WVsbCwkJBQbG8v53wQ5BKIvqKqqmjFjBolEio+PxxZyTyaFuU2WLl0qKCiIFBzx+8I9YVVcXJy4uPiYMWNqamq417l3756ZmVlUVNQvTm2FQHwP3d3df//9t7CwcGRkJNbYegSANzU1paenBwUFUSgUOOT+QyAFRwwRsB5NXl6eoaEhgUA4ffp0j3Xa2tr8/f2NjY0/fPjACxsRvx1LliwBAAQHB39xlPL69esuLi56enpSUlI7duxAI5mI3xesUzNt2jRxcfHAwMDGxsYe63R1dc2bN09DQ+PChQv9biBi6PPixYvjx48XFRVhS968eUOhUHR1devq6jgcDpvNrqioyM7OTkpK2rJli7y8vLy8vK2t7fTp09+9e8f5ceceUnDEEAG2+7a2NhcXF35+/rNnz35xhefPn+vr68+YMYMHJiKGLrB1xcTEAABMTU337NmTm5tbVFSUk5MzcuRIIpE4b968nTt3zpgxQ1NTU1hYmEQiUSgUCQmJwMDAI0eOwPqFP+HcQwqOGCKw2ez29vbY2FhxcXE3N7fP89ywB+PmzZvHjx/vEZmLQPwKsHW9ffs2OjpaTEwMACAsLCwhISEuLi4lJSUiIgIAgKqtoKCAx+Pl5OS0tbXnzZt36NAhbA8/MbqOFBwxdKiuroY1CKEHvMfD0OO/qK4s4hfp0X6gF5vJZN68eTMuLi48PNzKykpdXZ1KpVKp1JCQEFdXV2dn56ioqDNnzly5cuXWrVvNzc3Yrn4uTxgpOGLo0NnZGRERoaenV1paymtbEEMZ7v5yY2Pj0aNHb9++zWKxekhwU1NTdXX1o0ePLl269PTp09evX/d6JjBScMTQgc1ml5SUPHz4sKOjA/WvEX0Ed2f52rVrXl5ecnJyKioqKSkpn6/wxc170Rik4IghAvdj83MuRQTie4DtisVixcXFjRgxwtTUVE5OTlRU1NPTs7y8nPMpngS66bD0yz6aSwQpOGII8otV8xGIL4I1qurqalh0UFZW1s7OTltbW1BQkEajvXz5ksPVy+6HFogUHDGA6Orq+vUQESTciD4C9qOZTGZ8fDyVSiUQCHg83szMDJavsrKygrOm9WcLRAqOGECwWKzOzk4OUmHEAKaurm7cuHECAgI0Gk1GRoZIJAoLC4uLi7u6ulZUVPSzMUjBEUON1tbW58+fX7hwISkp6caNG78yAQoC8UUyMzMVFRXJZDKBQAAA4HC40NDQly9fslisfrYEKThi6NDS0rJv3z4rKys1NTUikUgkEoWEhOzt7WHBIGxYiddmIgY93d3da9euBQDg8XglJSUKhYIFovQzSMERQ4f79+9ramoCAIhEopqamo2NDawJzmAwuLOWEYhfZ+/evYaGhgAAMzOz2bNnv3jxgidmIAVHDHowXT527Bj8quXj49PX15eRkSGRSAAATU3Nt2/fcpCCI3qPs2fPamhowAZmaGiIJZH1cxAUUnDEIIbbMcJiscaOHcvHx4fD4XA4HDYjDx8fn4yMzKZNm6CPEok4olc4f/48mUwWFBQEADg4OFRWVvLEDKTgiKFAV1fXypUrJSUlMe3mnlYNh8M5OzvX19dz0ATHiN6guLh40qRJ0GUHANi2bRuvLEEKjhjcdHR0PHjwwNfXV1hYWFhYWEBAgI+PD5seE4fDycrK6urq/v333z2ml0Ugfprm5ubg4GDYxmRlZffv38+rUjxIwRGDhh6Zlt3d3enp6YGBgTQaTUhICACgqKiora0NnysCgaCqqmpkZDRmzJjs7GxOvzsoEUObrKys4cOHAwDk5eXT0tJKSkp4YgZScMTgoEepk1u3bnl7e0tJScFCzLKyskQiUUxMTFxcHAAwatSoEydO5OXllZaWQucJAtHrrF69GgCgq6t78+ZNOAVP/4MUHDE4wLS7oqJi9erVEhISsKMtISHh6ek5b948eXl5AQEBAEBYWFiP1DjU9Ub0Bfv27QMAeHt7l5WVVVVV8cQGpOCIgQ429lhbWxsTE6OlpQUAEBAQkJOTGzZsmLOz87Nnz1JSUmAcIYPBaG9v56D8HUSfgbnjTpw4gcPhdHR0ioqKYDWI/gcpOGIg0sPl3dDQcO3aNTc3NxgpqKioqKioSCQSvb29t2/fvnr1and3dwCAvb39+/fveWs5YsgDK8dyOJzbt2+LiIiQyeQXL150dHTwxBik4IgBTUlJSVRUlK6uLszTkZGRIRAIWlpakydPPnv27Nu3bx0dHWHMCZVKffr0Ka/tRfwWwL5Fdna2kJCQiYlJbW0tryxBCo4YoBQWFu7evRuLLREXFzc1NR09evTIkSNTU1PhI7Ry5Ur4K5FIhJPTo4ATRF8DHXQcDiczM5NIJCopKb17945XxiAFR/AYqLncDuunT59GRUUpKipi6iwjI2NmZhYREZGeno45HI8cOSItLY3H43E43L59+7C98eAcEL8ZsJllZWVJSkrKysq+evWKVw0PKTiCl0DtxmZ1ePLkydy5c1VUVGByvIiIiKSkpJ6eXkRExO3bt7kHi9LS0nR0dKDEr1u3Dgk3ot/AOhxHjhzB4XDa2tr5+flMJpMnxiAFRwwICgoKYmJilJSUCAQCDocjEAjy8vJ6enr+/v5paWnw8WCxWDDOJDs7297eHkakzJgxA9YdRCD6B0zBExISAACCgoLp6em8MgYpOILHvHjx4s8//xw+fLiYmJioqKicnFxgYKCzs/O4ceMuXLjQ2NgIV8PSed68eQN73/z8/JMnT4b1qlDUIKLfwBT8xIkTIiIiAICbN2/yyhik4Ih+okeAdnt7+/3796Ojo6WlpaEzREFBwc3NbcSIEfHx8ZmZmZh2cz65HeG/+/btgwXhXF1dy8rKuNdBvhRE/wBb2s2bN0VERAgEQmZmZkNDA08sQQqO6Ce465mcOXMmLCxMTEwMareDg4OlpaW1tfXYsWPv3bvX2tqKrdljJ7du3XJwcIAVmQsKCr64fwSiT8H6Cg8fPiSTyVJSUpmZmSgeHPFbcO/evbFjxxIIBH5+fjweLyMjo6+vP3369OXLlx88eBCLyoIPCfe89SwWa8uWLUZGRgAAMpl848YNzv+qdo/CKQhEX5Ofn6+srEwgEG7evMkrPx5ScESf8Hkp1w8fPkRERJDJZACAqKiooqKimZmZpaXl+vXrT5w40dzcDFfjdphwO0aOHz8Ok3ooFEpCQgLnS24TpOCI/gE2swcPHsAaD+fPn+eVJUjBEX0Ct5jW19cnJCRA7wec88zIyMjFxWXOnDl3797FNvmi+MI3QXp6ur29vYiIiICAwLp16z4/BALRb2Bdh5ycHBkZGX5+/tOnT/PKGKTgiD7k9evXiYmJ8+fPV1FRgfJNJpMdHR1XrVqVkZHR0tICV/v2IGRtbW1YWBgfH5+IiMjatWuhwxHKN1JwBE+ADa+oqEhCQoKPjw/1wRFDjZqamnPnznl4eMjLyxMIBD4+PiqVymAw1qxZk5GRAUMAMb7Ym4ZLmEzmrl27YPGTcePGwaQeNhf9dkYIBAb8NMzJyRETE8PhcJcvX+aVJUjBEb0AtwQ3NjauXLnS2NjYwsJCVlZWQEBARETExsbm5MmTTU1N37M3bEyyubk5Pj6eSqUCALS1tcvLyzko5gQxAIAKnpeXJycnBwA4duwYryxBCo74VTD5Li0tPXbsWGhoKIlEgrWojIyMZs2aNWvWrOzsbO7ByW+rMJYxcezYMRcXFz4+PkNDw0ePHnFQ0DdiYAAbYXt7u4uLCz8/f25uLq8sQQqO6B1OnDhhaGgoKioKABATEzMwMPDy8tq0aVNWVhY2fckPeT9u3Ljh4eGhpKQkICAAv1JhQhBScATPgY2wubl55MiRAICrV6/yyhKk4H0CJlKYQ6BHD3SQ9iWxOoLcqZUnT56cPHkynLJSQECASqVOmjQpNTX12bNnWIzgd+4c2+2LFy+8vb3hrPOJiYmc7+u8IxD9ANZQmUwmnFrk57LqP5eCN2/eJCcnw5ldv7OpIwXvE7CuIvt/66YOdrhPp7W19fTp00FBQTDEW0hISE1NzdDQMDY2trS09CcmncJeDLm5uZGRkTB5Z+nSpdihe/FEEIifBnsKamtrTUxMAACpqak/tyvuztBff/0F23xUVFRnZ+d39leQgvcH5eXlb968yc/PP3DgQGJi4o0bN5qamgavQ6Ctre2ff/6ZNGkShUIRFhYWFBQ0MzObOnXqkiVLHj9+zF2L6od2CzMwc3JyvLy8YI9+zJgxcPBzKL0FEUMA+OSWl5dramry8/P/tBcFNuzq6uqxY8cqKioOGzYMACAiIvL9nXqk4L0PNsrx6NGjHTt2LFu2zNDQUENDA/ZV4Qzrenp6SUlJvLb0P/j8K6+qqurMmTMMBsPJyYlOpwsICNDpdD8/v3379hUVFWGrfb+7o8f+29vb/fz8sGIpHz9+5KDQb8QAA2uN5eXl+vr6eDz+3r17X2ufPZZ/vtrDhw/Hjh0rJCSkrKzs5OQkIyMDADh48OAXV/4cpOB9RUZGxvDhw+l0OhzZg6nkTk5OAQEB3t7eAIBRo0YNcFXi9pl0dXUdOXJk2rRp+vr6oqKi4uLiVCrVxcUlNja2uLiYu4DJj8L9ITl//nx4rdTV1Z89e9YL54BA9AHwyX337p2BgQEAYPfu3T1+xUaM4JKioiJYr63HlzebzZ4wYYKEhISIiMjChQuTkpJUVFRwONyKFSu+0xKk4L0PvHmNjY0zZswQEhKys7PbtWvXnDlz9uzZU1RU9Pr16+nTpwMA5syZw2tLvwsmk/no0aM///xTSkpKTExMQUFBR0dn5MiRsbGxT548+Yl+N+ezkV64MCkpSUlJCQAgLS394MEDzie/CgIxoMAabUVFhZOT0+cKzvnfhr1jxw46nX7r1i3OZ93qmpqa5ORkPz+/nTt3dnZ27t+/39DQUExMzMrKCmY//CdIwXsfeJNyc3P9/PwIBAKJRAoJCcGSWTIyMsTExAgEwl9//cVTM/+bjo6O/Pz86OjoUaNG0Wg0qK2Ojo5nz56tqanBGijm5fh+Bcf63dhWBw8ehJn3OBwOBp9wkIIjBja1tbWmpqYAgPj4eO7l2IOQl5fHYDDodDo/P7+1tfXnoVksFqurq6u6uvrq1au5ublv3rxxcHDA4XBUKvXt27ffYwNS8F6DW8JevnxpZ2cH55ExMTE5cOAAzCNvaGiYPn06Pz+/q6vrd75j+wf2/5ZmraurO3HixLhx4/T19RUUFKSlpalUqqura0xMzJ07d7i34vxUlEiPDa9evTps2DBbW1sAgJeXF5o1DTHAgU23trbW0NAQABAbG/v5OufPnzcxMQkODp46dSoAAI/HP3nyhPOl56Wtre3ly5csFqumpsbQ0BCHw0lLS798+fJ7LEEK3mtgCn7lyhUdHR0+Pj4ajbZq1aqKigrOp9t2+/ZtCoUiLS2dnJzM+Snt6wt6+LtbW1unTZsmLS1NIBDweLyiomJgYODq1avfvXuHxQj+uuXY5Xrx4gWdTpeUlBQWFra1tf3w4cMv7hmB6Guw72w6nS4kJLRs2bIevyYkJCgoKKipqc2aNWvx4sUkEklAQODMmTOc/312evScWCzWxIkT+fj4yGQy6oP3N/A2pKamSktLCwkJzZs3Lz8/H/4E9bG+vt7Ozo5IJB4/fry7u5vFYg2oILmWlpYrV65s3LgxMDAQh8OJioq6urpGREQsWrQoOzu7F7Wbm8ePH7u5uSkoKOBwOHNz81evXvXizhGIPgI+BXl5eXp6ekpKSnFxcdy/3rlzB4fDiYmJBQQEPHny5ObNm4KCggQCAX6/9lBw+F9Mx+fNmwfdldhsJ98GKXhvkp2dLSUlRSAQNm3ahC3EfMQnTpwAANjZ2cGqqryS789jBDkcTl1d3bRp02RlZaWkpHA4HJ1OnzZtWlpa2osXL7A5z7g3+TnPSY/Nc3NzTUxMyGQyHo+nUqnPnz//uT0jEP0Jprm1tbWTJk0CAMTExHCvcOjQIQUFhcWLF9fV1XE4nIcPHxKJRADAN8qIY9/BO3bsEBMTIxKJ39mbQQrem7x+/dre3p5AIGzdurWkpITJZGI/PX782MjIyMvLC5sejCdSBRsKNkLIYrGKioquXbsWHh5OIBAAADQazd/f/8yZM69evfqJvMpvH5r9vxmqkZGRMJmTSCSePHmyF4+FQPQpsCWzWKxFixYBANavX4/91N3d/fHjx+LiYijfHA7nzZs3ampqoqKiJ06c4Hylj4IJwpEjR6SlpYWFhWE41n+CFLzXgDfg1atX5ubmeDxeTU3Nzc1t5syZCxcu3LZtm6+vr4SExLlz57AYDJ70wbGG0tjYmJOTs2TJEj09PRsbGwCAoqKio6Njj9wcTm93irExzDVr1sBZ6oWEhLDgEwRicBEYGAgAWLdu3Rc/T9mfJmMjkUhiYmIXLlzg/JeCnzp1SldXFwCwd+/e7zEAKXivgd2DqqqqVatW7dmzZ9myZUZGRra2tjDPSkZGRkdHx8fHh7f9ze7u7rt370ZGRiopKYmIiAAAVFRU5s6dm5KS8ubNG+4gv96tBcj92XHw4EE1NTWYe7lx40ZshV45EALRb4wZMwYAsGrVKmzJ58/O3bt3RUVF+fj4oLv8i90j7OlYtWoVAIBEIsGP9f8EKXjfUlVVtXHjRiEhoYCAgNu3by9ZsoRKpcrIyCQkJPS1YH2xU1BcXBwTE2NkZCQoKMjHx6eoqOjp6blt27YvBvD1uoVsNrurq+vgwYNjxoyBHY3x48dXV1f3xbEQiD4CU1s2mw2LQGzYsKHHCtwK/vz5cwUFBQEBgdmzZ2PrYFkUPYpG3Lp1S1dXV1hYePPmzVVVVWVlZdg+OV96TJCC9y0VFRVmZmYAgCNHjnA4nNbW1srKyiVLluDx+JSUlL4+OnfLKCwsXLhwoampqZiYmLi4uLi4uJeX19atW9+/f//5vPJ9R05OTnBw8IwZM4hEopWVVU1NDQfNWYwYbGCxAAwGAwBw4MCBHr9y+0ifP38O+yuurq5nz549deoUTGbu/gRc7fXr15mZmWvXrpWWlhYQELC2ttbW1tbQ0FixYgUc1eReGQMpeB+Sl5fn6uqqoKDg4+MDe5qQBw8ewEwfbKyjTykvL//777/d3Nyg10JJSWn9+vV379598+YNts7n0Sl9QXd39507d4yNjQUEBCwtLUtKSrBDo/RLxCACNtqWlhb4WPXwWcPnqLKycuvWrQEBAY6OjrCqnbS0NIVCAQA4OjrCr17Yd6murp42bZqSkhI/Pz/M/REUFIT5yWQymUgkOjo61tfXf/EJRQre+2AX+s8//8ThcDQaLTMzE/uJw+E8ffqUTCYbGBhUVlb24kE5/9vp5nA4bW1tt27d8vf3hw2CRCLZ2tr++++/n3vi+lS+sT0nJydDv6G8vDx3bCzqgCMGEdjDwmKxoBdl69atnz9Tixcvhn0mGRkZGE0oICCgqakpKSlpa2tbWFiIrRkfH08mk8lksqKiopqamrW19ZQpU7y8vMaOHbt27dqEhIQJEyZg3Z0exiAF733gVX7//r2enh4AIDw8vEcNkAcPHpDJZFNT09ra2l48KLcKNzU1ZWVlzZ49W1FREdazdXV1TUtLe//+fQ87+xrM07d//344fyaMyeH08WsDgegjsHbb3d09c+ZMfn7+5cuXc/s3YJu/c+fOqlWr6HS6mZnZyJEjR4wYQaPRxo0bd/LkyQ8fPnR2dsJNWCzWnj175syZ4+PjExgYuHPnTltbWzMzMx8fn+3bt+fl5ZWVlXV0dHztKxkpeJ/Q3d29YcMGOFQI4zqxq19RUTFnzhxZWdmQkJCOjo5ePCL8o76+fvXq1QEBAUFBQWpqajgcztraOikpCXtb9LNuwmPV1NS4uLgAALhnTeOOTEcgBhGYnh44cICfn7/HSGZ3d3dnZ2dJScmRI0f279+fmJgYFhbm5+dnZmYWFRV14MCBq1evYhOhMJnMgIAAGRkZOTk5CwuLSZMmzZkzZ+vWrZcuXbp06VJSUhJWZhkpeP/R2dkZERHBz88fEREBa1ph486XL192cXFRUlJKT0//6f2zucAWtra2pqenT5s2DebEk8lkPT293bt3w3kSOJ8Nf//aKf4A9fX1y5cvp1AoIiIi69atwy4IGsBEDFJgu21tbfX19YXx4D1WaGpq+vfff8+fP3///v1nz54lJCRkZGQsXLjw+vXrjY2N7e3tsKgG3M/jx483bdq0e/funJyc0tJS7v30qOL5uYgjBe8Tbt++LS0tjcPhYBYWRk1NzcyZM7W0tLy9vX9oFmBuetxLNptdWlp69uzZuXPnUqlU2M81NTVdtmwZrIXGE7DW2d7evmjRInFxcQBASEgIrCiAhBsxBGAymcHBwQCAtWvXfnvNpqYmNptdXl7eu3nOHKTgfcS5c+fgCMb9+/fhkrq6uvz8/H379snLy9va2v5KB5w7qKi6uvrgwYNWVlZUKlVeXp6fn19TU3PDhg0vXryAK/DK18z+NA3VkiVLxMTEcDicgYEBLKiL5Bsx2IFtuKura86cOQCA+fPn/+fK2N+92/6RgvcJVVVVtra2fHx8S5cuff369bVr17Zs2aKlpUUmk/X19a9cuQLLRf3KvaysrNy8ebOjo6O5ubmoqKiEhIS3t/elS5ewkmZYD51XJbSYTGZkZKSBgQEej9fU1IQ5Zr2b54lA8ATYgBsaGqAX5Wt9cG6nZTcXvWgJUvC+ori4eOLEiTgcTktLi06nq6mpkUik4OBgbBbq71SxL/q/ysrKYNOBdUUcHBz27t2L+bs/38Ovn853wm3nu3fvLCwsZGRkKBRKamrq5ysgEIMRrA1XVlbC6Njo6OivOUV7ODw5vf08IgXvfbAb9uHDh+XLl69evXrevHlbt27NyMhob2//0f1wJ92yWKzTp09HRUW5urqSSCRBQUF9ff0dO3Y0NjZiw4N9dFI/ZDOHw8nOzvby8hIREREQEIDjPDy3DYHoLbA++Pjx42HE8E8Pa/0iSMF7H+yLCf63o6OjsLAQKiznBzPIe/S7Dx48qKioiMPhAACGhoZ//vlnfn4+diAeOky4YbPZ+fn5Y8eOFRISApeaLzgAACAASURBVAAsWLAAjt4gBUcMPZYtWwYAmDhxIq+aN1LwPuFroT9fXPg9ezt27JiNjQ2cblhXV3f79u1YyRvOJ+dyV1fXQFDwS5cuhYWFaWho8PHxzZw5EwafIBBDkn379gEAli5d2ou5HT8EUvCBBftTrheHw2lqaqqsrDx27Jirq6ukpKSgoKC5ufmaNWu48yoxeDhCyP1aevbs2fTp0319fWHSaV1dXVdXV0FBQWlp6atXr7KysoqLi9+9e8cdot7/BiMQvwjW4BMSEgAAY8aM6fUwwe8EKfiAAFNe7I+XL19GR0ePHz/ewMAAAEChUPbt24flVX5N+Hio4BwOp6mpKS4uzt3dnUql2tnZZWdnczicZ8+emZiYUKlUFRUVKpWqq6uro6Ojr68/c+bM0tJS5FpBDGpWrlwJALC0tOSekKs/QQo+EKmurl6wYAGc1V5SUnLdunW5ubnwp28PZ/NWwRMTExUUFOTl5Wk0Glaf/tq1azDPaMSIEUlJSStWrIiIiBg9erS9vT2WLoxADFK2bdsGAHB2dsamk+1nkILzAMzt0MP1UVRUlJGRsXz5cl1dXT4+PhUVla1bt3LnVQ6oHiv3WXA4nLy8vMDAQGFhYRwOh82a1t3dferUKUVFRWlp6ZcvX7LZbCaTCbOKW1tbu7q6BtQZIRDfCdZuN2/eDABgMBi88gciBecBWD8aawdMJjMxMXH69Ol6enp4PN7e3n7GjBmPHz/uscmAgtv+hw8f7ty5U1NTE47qYPWqOjo6AgMDBQUF3d3dvxhJOQDPC4H4T7B2u3HjRhwON2fOHBSL8hvR43Wdnp7OYDBIJJKioqKHh8eBAwcaGhqwX/siC+DX4R69/Pfff42MjOh0OolEioiIgMbDc2xvb4+OjiaTyba2tl1dXc3NzU+ePMHO7ifCchAInsPdbnft2gUAmDt3LuqDD316DFe2t7cfO3YsJCSESCTy8fFZWFhs2rSJOy+gfwTupw8Bm2xlZeWECRPgzCPjx4/HxnPgbplMZmpqqpSUlK6u7u7duydNmkQmk+l0+uTJk7kr3CMQg5SUlBQ8Hh8cHMwrA5CC9wdsrkqqTCazurr60qVLc+fOlZKSAgCYmJgcOnSo33K6uBN/frpCN/tTZZ9Hjx45OTkJCgra2tpWVFT0WIHD4WRlZUF9h6ipqcGo9vXr13OQgiMGOSdOnMDhcC4uLmgk87cgPz9/wYIFZ8+eDQoKgkFIK1as+PDhA/y137wK3F8DP33E1tbWQ4cOBQcH8/Pzy8nJwYksPj9EbW2tp6enjIyMp6dncHBwQUFBUlISkUh0cXHhVSIyAtFbxMfH43A4V1dX7gy7/gQpeP9RVVU1ffp0MpmspKSkpaW1fft2bKZjrPjJIOqTpqWlSUtLEwgEPB6/b9++b6z55MmTo0eP5ufnw7y1Fy9ejB07lk6n5+fn95exCESfkJubKykp6eDg8LW6cn0NUvBeA9Nf7hg7zid/cXp6uouLi4KCAoVCWb9+PVYDdoDwnW8ONpvd1dXFZDK7urqWLFkCHSOTJk3CphHhXvNraaJPnjwJDQ2lUCi3b9/uxVNAIPqf3NxcmH4M++D93wlDCt5rsLmAitba2vrPP/9s3rw5MjKSQqHIycnt2bOnoKCAe32emvz/+f6MfBaLlZWVtXLlShUVFQCAt7c31na/c4cPHz6cMmWKiooKlvWDQAxSCgoKpKSkRo0a1dDQ8HmUcD+AFLzX6HHnWltbFy1aJCcnR6PRNDU1Q0NDsbxKzsCbJfL7q2Jdvnw5ICBAXV0dAGBnZwen9fv8dL52aqWlpdHR0SYmJlJSUqgPjhjsPHnyhEQiubu7v3r1irsQdL+BFPwn6TEYyO1CefPmze3bt318fPj5+XV1dWNiYoqLi7m34sm7+lfA7Hz27Nn27dtlZGQAAFpaWm/evOFep4eCX716NTY29vr162/fvu3q6uro6Hj8+PGsWbN0dHQMDQ3HjBlTWVnZ32eCQPQqx44dAwA4Ojqmp6e3t7f3/xONFPxnYHNNvMDd9ywrK4uNjXV0dCQSiQoKCps2baqpqeGtqb8O5tGuqKjYvn37lClTCASChITEtWvXvr3hnTt3jI2NJSUlTUxMJk6c6Ofnp6OjIyoqKiws7OHh8fTpUw6KJkQMcm7cuCEsLEyn0zMyMngSjIAU/Gf4XLtLSkoSEhIYDIa4uLi0tPSUKVMePXqErT+gHCY/R35+fkJCwsyZMwEAeDx+7969nG9+RrA/pWuOHz/e3t5eSkqKRqN5enqGhYXFx8e/evXq25sjEIOCzMxMMTExRUXFS5cuwSXIDz6YYLFYVVVVFy9enDx5MgCASqVGR0fn5OTAX7nv5eCVqo6Ojvfv32dmZs6cOdPMzAwAsHz5cvjTN7z52LlXVlaeO3fu6NGjubm5TU1NPVYYvJcFgeBwOGlpaUJCQpKSkjAfAvXBBxzc3W1u0WGxWLW1tWfOnLGyshIREQkMDJw9e/ZQKpcKz7Szs/PmzZv//vvvlStX7O3txcXFJ02a1NbWxmvregf2wJiXDjF4ycnJkZSUdHV1xWqIIgUfWLC5Js3BaGhogFPnEIlEJSWlJUuW5OXl9dhksMNms7u6uhoaGl68eJGZmWlsbAwAMDIygpkLQ+Acsfdxc3MzNnUGAvFDXL9+XVxc3N7e/ubNmxxefFkiBf9vsPvR1dVVV1eXnp5uYWHBz8+voKAQGRmJ5cQPMaCCV1dXb9261dXVFQAgLy+fmZnJa7t6E/iw1dbWfnHiOgTiP7l586aYmJicnBxWE39wKPjXXjWVlZVVVVWNjY3Y1OyDFOzssHNMT09ftWrVvn37YJ2mgIAA7rHKIQP3WRcXF+/cuROW3xIXF09OTuaxcX3AEPiYQPCQnJwcIpE4fPhwzIM6CBS8x/hVd3d3QUHBnj17GAwGlUodNmyYh4fH27dvOYP58eC2PD8/f+HChb6+vsLCwmpqaiEhIZcvX+bVxKZ9Ddb+2tvbExIS5OTkAABkMvnUqVO8Ng2BGChg+vD48WMSiTRs2LDMzMweQ2X9w88oOOYUfvny5YoVKxwcHCQkJGCJDGVlZU9Pz4SEhKEx2PXhw4d//vnH3NwcACAiIuLp6ZmRkYH9OiRDKdifysYWFxeHhYXh8XgAwNq1a7l/RSAQkMLCQgUFBWNj45KSkkGj4BwOp62tbc+ePdra2phwGxgYzJkz58WLF9g6g+Vp/6Kdra2tV65cMTQ0lJCQoNPpAQEB8fHxWA4ht49lsJzmt+nhMrp169aBAwcsLS0BACNHjmxsbOQMoZNFIH4R7EF4//69lpaWi4vL69evsfpuA1rBW1paLl26FBAQALVbSkpqxYoVd+/e/fDhwxcnQhyYcF9lmHAI/2axWIWFhcnJyYGBgUpKSvz8/AwG48aNG1DChircHQcmk1lcXLxkyRIjIyMAgJOTE5xMB4FAfE5lZaW1tbWOjk5WVhZPDPgBBc/NzQ0NDdXX1wcA4HA4UVFRc3Pzw4cPD1KPcI/vndLS0oKCglOnTk2dOhWPx/Pz88+ZMyczM7PHtGFDEngd4JussbHx4sWLoaGh/Pz8RkZGqHQJAvENCgsLVVVVqVTq6dOneWLADyj427dvTUxMAAAkEonBYJw+fRoLDcYYjOnj796927VrV0BAgI6OjpiYGCy5x130Y5Ce1/eD3b7GxsaCgoLp06fT6XQ6nY6FuPLaQARigPLu3Ts1NTVZWVnujJ6B60V5+/btsWPHzp49i01Q0MN5P/Cf9h7X9+nTp5cvXx4zZgyRSITVro8ePVpfX99j5YF/Xj8H93nV19enp6cvW7ZMVFRURETk7Nmzn6+D6EWg7+4b0zN9vryrq4vFYqE7MnCACq6srJyVlfVzU87+Ij+g4D3yEtlcuea9bVVfwW1qS0vL0aNHt23b5u7uLiEhYWZmlpiY2NDQwEPz+pke7u/s7OywsDABAQEcDpeSksJr64Y4mNvqa79if3A32o6ODp6UMEV8jSdPnkhISBCJxMuXL38+U1U/8AMKDi1rbm7+YrbOYGlV7e3tL168ePLkiZ+fH5w6PSQkJD4+vry8HK7A/m1qZWC3rKam5urVqwsXLiQQCAQCYd26dbw17HcA6wA9fPjw0KFDhYWFPQIBvvFADZZn7Xfg1q1bwsLCRCKRuzZhfxrw3wrO7UYoKiry9PSMjIxsbW2Fv9bX1//5559Hjx7tUyt/hR4XtKioKDQ01NDQEPq7jx07hvW7B9f3xK8DRaS+vv7hw4fx8fF0Oh0AEBYWxv2G/t2uSb+BXdjk5ORhw4bRaLSHDx9yPjVXFou1ZcuW7du3P3z4kDsO6mv+FgSvSE1NxeFwKioqJ0+ehF6UAecH51bwQ4cOAQAIBMLBgwdv3rx56NAhfX19Eol0+fLlPrf0x8GuY1dXV1lZ2e3btyMjI11cXAQFBTU0NBITE1taWnhrIc8pKSm5f/9+SkoKHKO2sLCAZV6QRvQ12HOekpIiIyNDJpOzs7M5n658a2vrnDlzaDQaPz//xo0bsU14aDDii9y7d49MJquoqPz777+w6zMQFRzzKuzduxcAICoqOmzYMEFBQT4+Pk1NzbS0tD428mfALmJ7e3taWlpAQACJRIIidejQIWzqnN/5qaipqXn8+HFJSYmHhwcOh9PU1Hz9+jXnd/Ij8RDY8PLy8qZOnUqj0QwMDLDoAA6H09bWxmAwyGQyAGDq1KncmyAGFB8+fIAxbP/88w9PvpD+Q8GhQd3d3TU1NdnZ2WPGjIHB4AICAqqqqlOmTMGe+QHYvOrq6nbv3j1u3DgYZ2JgYHDgwIGKigr466Abhu118vLydu3aNWfOHBKJJCEhcefOHQ7XHee1dUMceJ3Pnz8/fvz4UaNGBQUFcReiqKmpsbe3FxISAgDExMRgm/SpPdhN/50fih+lsLCQQqEQicS0tDSYOzIQFZzD4axdu5aPjw/KN5lM1tfXP3nyJJbtwiswDw8GbIXV1dUvXryYNWsWTBy1sbE5fPhwdXX1Fzf/DWGz2SUlJVeuXIFz7vDz8+/atYvzG18QXnHq1CkGg6GhoXHy5Enu/sTLly81NTWlpaUBALt37+6xVV/cpvb2du4g2l7f/1AlLy9PWVmZSCSmpKQ0NzdzBqCCQ03MysoyMTERERGh0WiLFy8uKir6xlb9mf+CHQs7YmZm5sSJE3V1dQkEgoaGxqZNm1D9fgw2m81isYqKii5fvuzm5iYoKIjD4eLj4zkD9UNqCNPc3Axrr5PJZDhHF4fDYTKZpaWlc+fO1dDQUFJSEhAQmDx58qxZszZu3Pj48ePKykomk9kXt6m7u5snbtzBTkFBgZKSEoFA+Pvvv+GSgeUH5/62evTokZWVlZGREZym9hvRrF1dXf35Gd7d3V1XV1dRUfHq1avk5GToPVRRUVm0aBEscssZEnMN9xYXL148fPjwnj17YPDJ6tWr4XL06PYz9fX1ixcvNjExMTQ0PHny5Pbt26Oiotzd3dXU1ExNTeEnLz8/P/yOpNPpCgoKOjo62CysfQFqAz9KUVERnU6XkZG5fv16j65k//ADCp6fn29mZjZixAiYTM/5kq39aT2LxYLBcNnZ2Tdv3oyJiaFSqQAAJSWl5cuXl5aWcluF2iUW5HDixIn169fDupJeXl5YQA66RP1Me3v77NmzKRSKgoKCqKiosLAwFGs8Hi8qKgr/1tLSGjdu3PTp0/39/ceOHRsQEABHnvoI9KT8KKWlpVpaWhISEseOHcOiCfvTgB/I6Pnnn3/U1NQiIiK+2L9mf8ox6+sTwBpZXV1dd3d3Tk7OihUrPDw84EQEkZGRBQUFfWrAYATeF1h5ce/evU5OTng83traeqhOETdYePjwobOzs7i4uISEBI1Gs7W1HT9+/OLFi11cXERERMhkspOT08ePH9vb29+9e1ddXV1fX89kMtE488Chrq7O3NxcRkZmx44dDQ0N/R+O8gMKvn37dhkZmRMnTnzx1/5sVWw2u7Ky8s6dO4mJif7+/rDbMnHiRMyZiHwm3MBL0dnZmZeXt3PnTjhhhaKi4vPnzzmo68074JUvKyu7fPny8ePHT548+eDBAxiRkpiYKCsrq6SktGbNmh6boEihAQWbzR45cqSsrOz169c7Ojr6/2n6XgVvbm6eM2eOqKjowYMHv7bO8+fPS0pKesmwr8JkMu/du7d69Wo9PT0AgLS09MyZM588eYJdu/75FBhcdHZ2FhUVrVq1ytPTk0KhkEgkWHyxq6uLJ+V4EJxvjiSdOXNGS0uLRqMdOXKEw5WCj9r2QKOrq8vLy0tWVvbixYtwKLifb9D35mSWlJSMGDFCS0vr+vXrX1wtNzfXy8tLXl4+MDAQzvz9Pafx+UcH+3/hbuJsNjsvL2/16tXQh0sikcaNGwc7ktymovaNAS9FTU1NSkpKcnLy6NGjyWSysLDwyZMnsRXQ5eIVX2yu8IWamJioo6MjICCATU+K7tTAhMVieXt7KyoqXrhwgbvYZL8Z8B8KjnUTbty4YWBgoK2tjc3YUllZWVhYePz48XXr1gUHBysoKMAZzdXU1HJzcznfraSfKzgMbOqxvKKiYs+ePcOGDQMACAsLjx079t69e0iy/5POzs6LFy9u27YtKSkJZqVu376dgxRhoALvy/r162k0moyMDPe0hYgBSHd3t729vaCg4MWLF+GSgTWS2f2JgwcPysrKenl5lZeX79u3b9KkSerq6lJSUgICAoKCgrKysnAyyUOHDhUVFX3/t15LS8vnX/Hd3d2wTltXVxebza6vr4+Pj4eTfvHx8fn4+Ny5cwfrm6OPym/Q3d19+fLllJSUq1evhoaGAgCCg4PhnEpIwQcgWI8kNjZWV1dXXFw8KSmJ10YhvkV3d7eDgwMAIC4ujicGfG9OZnh4OI1Gmzp1qqOjI4xzIhAIFhYWM2fO3LVrV3p6el5e3hc35F7SY+dpaWmOjo6enp7chRm5V2toaDh9+rS7uzs84siRI2/duvXtff6GfGP4+/Hjx5s2bcrIyJg6dSqc9LKpqYmD5Huggt2U9+/fe3h42NnZbdiwgbcmIb4GvFldXV12dnYAgDVr1vBkvsn/VnAOh9PV1RUeHk4kEgUEBAAAkpKSM2bMSElJ+f5xSzbXdBCwh56WliYlJSUqKurs7EyhUDIzMzlcLbiwsPDvv/8ODQ2F6Tm2trapqamDaCbl/oH7esIlTCbz9evX2dnZ2dnZeXl5+/btW79+/YoVKwgEgrq6OvRuIQY+bDY7KyvrwYMHtbW16F07AMH6QJ2dnQ4ODmQymbus0ADyg0PYbPbatWthR9je3h5W4eqxwn8ajZ3bv//+GxISoqSkBADQ1tYOCgoik8mzZ8+Gq338+HHt2rWw2CkAwNLSMiUlBZUS/CLs/53A8/Tp00FBQZaWlpaWlrq6uoaGhjt27IiOjtbR0ZGRkeHVXNqIXwS1+QEIt+K5u7traWnBXNn+/7r9rpxMNpvd3Nx8/fr1ixcvcidkYnxPgCo8sQ8fPmB+GBwOB6uvAQACAgJevXq1e/duY2NjuERXV3f//v3wq5/Di5fbwAdejYaGhpqamgsXLmhpaYmIiIwYMWL9+vWxsbHW1tbu7u40Go1AIKSmpvLaWMSPAUtToGGe3uWHLuZ/rtzc3Hz58mUqlSouLr5gwYJ79+79mnU/A+B8Mwjv2+fw/ZcDE9+4uDjoioFlH5ydnbW0tAAAMjIy1tbWULtVVFTi4uKwMrC/Idh78dsvre7u7s7OzszMzOTkZDhagMfjCQSCkpKSra2thYWFoKAggUCIjY3lcDhtbW1wNqKampqPHz/C2NXW1taKioqPHz82NjZ+/PixoqKCyWS2trY2NTW1tbU1NzczmcyWlpbq6uq2traOjo62trampqaWlpaOjg6oL3Du3R7D0QMqxryjo+Mbv35xysDe4udSb7Cb3mNzWEaC878dvR7No7Ozs1fyfbh3+52POSy59UOagP39KzZ/8Vp9z0F/kWfPno0aNUpKSgoAICgoCHPCp02bVlZW9sX14cPSW0fHAP3zhodHqa6uhpMJ4HA4rKOtqqoKPiEvL//nn3/Cylm/M995U+DcQ0+ePNm9ezd8I4qJicEJXwQEBGBRJAqF4uvrm5iYuHjx4sDAwPnz5yckJLi5uQUEBEydOtXLy0tPT8/U1HTkyJE2NjYeHh7e3t4BAQFBQUGzZs1yd3dnMBg2NjZ6enojRowYN27c5MmTbW1tbWxsAgICwsPD58+fP2fOHAaDMW3atNWrV8+bNy81NfX69evx8fFz586Nj49PTk5etGhRfHz8/v37N2/efO3atdzc3C1btuzZs+fs2bM7duzYunXruXPnnj59CsNSMzIycnJysrOzX758WV1d3dzcfOjQofj4+OPHj2dkZBQXF2dlZR09evTs2bM5OTn37t178uRJYWHhpUuXbty4ERcXl5aWlpaWdvr06fv37+fm5h4+fPivv/7KzMx8+fLllStX0tLSUlNT8/PzMzMzr1+/fvPmzYKCgpaWllevXp08ebK4uPj9+/cfPnwoLy+vqamprKwsLi5+9uxZQUHB+fPnN2zYkJycfPfu3X/++efu3bvXr19PTU19+PBhRkZGaWlpdnZ2amoqTE1oamqqrq7Ozc2F6e+PHz9+/fr1/fv3S0tLq6urP378yGQyS0pKCgoKHj9+nJeX9+zZs3v37hUVFTU2NmJixGazsWExJpNZXFxcWFjYQ6Rqa2thTZvW1taysrLW1tbGxsaqqioOh9PS0gL3Vl1d/eHDh8bGxvr6+vLy8sLCwpKSkhcvXrx586aqqgquD9/BHA6noqKipqamsLCwsrKyra3t48ePcLXOzs7S0tL29nYWiwXf3KWlpbCmBZPJhC/+oqKi27dvFxUVFRYWpqWlPXr0KCcnp6KiAo5dtba2VlZWVlRUsNnsjo4OeOiurq63b9+WlJQ0NDRUVVXduXOnoqKivr4elhC4devWlStX4M2qr6/v6Oh49erV9evX7927V1JSAjsZNTU1sKBrbW1tfX19Y2Pj3bt3CwoKKioqamtry8rK7t27B+sjdXd3l5SUtLS0QAM+fPhQVlb28ePHsrKytrY2JpPZ1tZWX1//7t27qqqq0tLS+/fvZ2Vl3b9/v7W1tbq6uqio6P379ywWq6Gh4eXLlw0NDU+fPtXU1CSRSPLy8nC+BBEREUlJSTKZvHr16q/1hvsimRZgLaZP+03wlI4dO0YgEMTExPg+AYWbj48Ph8OFhITk5+dj6//OH4/wZldVVX348AEbA/icjo6OlpaWrKwsOB2XqKiooKCglpaWmpoa9oKcPXu2nZ3dvHnzZs+ebWlp6ejouGbNmiVLllhbWwsKCtJoNDKZ7ODgEBQUpK2tHRER4ejo6OzsrKqqamRk5O/v7+3trampKSUlJScn5+joOHnyZB0dHXjLdHV1JSUl7e3trayshg0bpqamRqPRpKSkDA0NYcdERkZGR0eHRCJRKBR7e3uYTKSoqKigoCAjI2NsbAx7LiIiIiYmJp6enqampgoKCnp6ejQajUqlampqmpqaqqioaGpqkslkEomkp6dnbm5Oo9FsbGxERUXl5eV1dHR8fX09PDzgzHmrVq3S0NCQk5OztbWdOnWqioqKi4vLsmXLRo0aNXLkSDqd7ubmRqfTzc3NtbW1paWlvb29ly9f7ufnp6qqOnv27LFjx7q6utrb25uZmZmbm1MoFBUVFTiuICgoqKKiQiKRJCUlFRUVpaWlxcXFtbS0NDQ0DAwMlJWVZWRkzM3Ng4KC7OzsdHV1aTQag8HYtGkTg8HQ1tZWVlam0+m2trajR4+OjIxkMBhTpkyxsrLy9va2srIaPXq0l5dXSEjI+vXrDxw4wGAwtmzZsmPHjiVLlkRERDAYjMWLFwcFBa1Zs2bXrl1HjhzZvXv3gQMH/P39XV1do6Oj161bN3bs2EmTJi1fvvzMmTMLFiyws7Pz8PAIDg7GXsyRkZEXLlxwdHQcN24cvAhGRkZRUVEhISETJ04cNWpUTEwMg8GYPHkyg8GwsLBYs2bN8uXLw8PDt2zZcu7cua1bt0ZHR0dHR8fExGzZsmXy5MkrVqw4efJkYmKilZWVp6fnhAkT/Pz8JkyYEB0dHR4efuLEiYyMjJs3b+7ZsyciIiIoKGjhwoXHjx+Hr/kZM2Zs3rz5+PHjcXFxw4cPnzp1amJi4uHDh+fOnTtx4kR7e3sNDQ1TU9NJkybNmjVr/fr106ZNmz9/fkxMzIoVK+Li4iZOnBgXFzdv3rzIyMjJkyfHxcXt3r1727ZtCxYs8PX13bhx46pVq8LDwxkMRkhIyLhx4+bNm7d27dpNmzZt27Zty5Yty5Yt27Vr18yZMxcvXhwVFfXHH39s2LBh1qxZUVFRUVFRkZGRYWFhkyZNmjt3blxc3Lp162JiYiIjIwMCAiZOnDhlyhTYuZkyZQqZTBYXF1dRUcHhcPAPQUFBRUXFiIiIr2lXX8gagG/78vLyPp00EtqdnJwMPgPq+LBhw2AlWG73et/ZM3Dg/hzG/s7MzJw7d66urq6SktLw4cOjoqKwi8O9bVdX18ePH//6668RI0YMHz4cG1SAYwx0On3lypWpqamnT5/eunXrpk2bli1bFhcX98cff+zcuTMlJWX8+PFbt25dsWLFuHHjli5dumzZsr/++issLGzGjBmRkZHr1q27cOHCjh07YmJiwsPDFy5cuGzZMh8fHxMTkzlz5sydO3fhwoWHDh26cOHCgQMHwsPDk5OTo6KiZs2aNXLkSD8/Px8fHwqF4u/v7+bmFhERsXHjRicnJx8fHzc3t7CwMGdn53nz5oWEhLi6unp5eZmZmY0aNcrX19fX19fMzExNTc3AwMDZ2Xn06NG+vr7Ozs6+vr5ubm6enp7Gxsbjxo0LDAwcMWKEoaGhIGHvBgAAIABJREFUvr6+iYnJqFGjPD09Z82a9ccff4SGhgYGBlpaWhoZGVlYWJiamgYEBPj5+YWGhvr7+8O3jrS0tImJCdRxW1vbCRMmUKlUGxsbLy8vX19fLy8vIyOjESNGODg4+Pj4+Pv7u7u7a2trq6ury8nJycnJqaqqGhsbU6lUDQ0NV1dXRUVFISGh4cOHwwkZYKCtioqKrKwsbNjKysqSkpJCQkIkEomfn59IJGpoaPj4+IiKisIPGhsbG0dHR2lpaRqNJicnp6CgYGRk5OnpKSMjAwBQVlZWVlYWFhZWUVGh0+mGhoYqKirW1tawOoKurq6Ghoa0tLSampqlpWVgYGBERISrq6uNjY2urq6fn19QUJCjo6ONjY2Li4ucnJylpeXo0aM1NTUBAHp6erNnz4aV9LW0tOzt7RUUFJycnExMTOTk5Pz9/bW0tLS1tU1MTMLCwry8vAwMDBgMxvDhw93d3U1MTNzc3KytrUkkkoyMDJFI9PDwUFdXl5WVdXFxcXFx8fLycnV1nTJlipOTk4KCgomJCY1Gw+FwFArFwsJCSUnJ0NAwJCTE399fU1PTy8vLw8NDQUFBUFBw2LBhurq6FArF0dHRz89PWlpaQ0MDnouKioqxsbGXl5ednZ2goKCenp6ampqqquqwYcN0dHQoFIqcnJyRkZGWlpa0tDSRSIRXSUVFRUZGRl9f39DQ0NTUVFtb29jY2NLS0sDAQENDQ11dPSAgQF1dXVVV1cDAwMHBQUNDw8vLa8aMGdbW1nQ6XUlJydHRUUVFRVhYmEKh0Gg0Nzc3SUlJPB4vKCgoLCwM55vE4XAEAoFKpcKMuS8+6d+oo/DTcgfgfltbW/uhD56VlRUWFgZvkoiIiKioqIiICFRwCoXyNf/REIbb3w2XfPz4ccqUKRQKBdaG1tfXd3V1BQCYm5vDiPsed7q0tDQ9PX3Xrl1YYXToDVdRUZk1a9bcuXPXr1/v6+sbFBQUFRW1adOmvXv3uri4hISE7Ny5U11d3crKatGiRdOmTRszZsy4ceMCAgIsLS0tLCzOnTsXFRUVHBw8YcKEUaNGLViwIDw8fNGiRcrKytHR0bGxsYGBgT4+PrCQnr+/v7Gx8aRJkwIDA0NDQw0NDcPCwqZMmaKhoeHt7W1sbLxo0aJRo0bBnr6tre3SpUu9vb0tLS2nTJni6+trYGDg4+Njb29vZ2dnZ2dnaGiora09derUWbNmDR8+XEdHx93dfdq0aZ6env7+/h4eHuvWrbOxsQkNDR0/fry1tfWwYcO0tbWtrKw8PDxUVFRMTEysrKzExcU1NTVhWqOZmZmIiIiEhISBgQGBQODn51dVVYUfH/z8/FDBNTU1lZSUhIWFNTU13d3dNTU1/fz89PT0XFxcTExMfHx81NXV+fj41NTUNDQ04PeBjIwMgUCwt7en0+nq6uoUCgV+UoiJiUlISODx+OHDh8OvIg0NDTExMWVlZewGAQDk5OSEhITgK0RTU1NSUlJCQoJEIomIiEDpxzyNIiIi4uLi3J0e7CcBAQFFRUW4REJCgo+PT0BAwNLSEko/mUwWFRVVV1dXV1eH6bji4uLy8vLi4uJiYmJwDxISEgICAkJCQsLCwtg3saysLPwvDCCWlpYeNmwYHo8nk8kaGhp6enpEIpFOp1OpVDk5ueDgYDiCRaPRaDSamJiYhYUFmUx2dnYmk8nw+js4OMjLy8PPI2dnZwaDoaKioqqq6unpaWZmBiukw48qCQkJPT09LS0tRUVFW1tbU1NTHA6npqamra0tKSlJIBAEBQXV1dWNjY0JBAL8aINPCpVKVVZW5ufnFxQUFBMTU1VVFRERIRAIioqKRkZG4uLicLoMQ0NDTU1NdXV1KpWqqKhIIpFkZWVHjhzp5uamo6NDJBLd3d39/f0ZDMaGDRumTJkycuRIFRUVT0/P4OBg+Fq1tbXV19fHyv9iLgR4F8zNzbGs9a9RVFS0evXq3bt3JyQkJCUlvXv37ldm7QCfz3HTF2AdzI6OjvDwcMxRi8fjAQBSUlLLli37PJP+d4Bbu3ft2gVDcQgEwqRJkx4+fPj27dvm5uaFCxcCAIyMjD6v7t/V1XX06NF58+Zt3bp1/fr1M2fOjIqKun37dkFBQXNzc3l5eXl5+aNHj/Lz8wsLC8vKynJycjIyMm7cuPH48eOLFy9evXo1JyfnzZs3ubm5//zzT1ZW1qNHjx4+fFhdXZ2Zmfn69ev8/Pzr169fvnz56tWrN27cyMrKevv2bVZW1okTJ86dO3fq1KkrV67cvXv33Llzp0+fzsjIuH///rVr17KzszMzM1NTU2/evPn06dPnz59fuXLlxo0bV65cuXbt2v3790+fPr1nz57ExMSUlJS//vorPT398uXLR48e3blzZ1JSUmJi4smTJ/fu3Qs/kM+fP5+Zmbl37974+PjLly8XFBQcPnx4165d58+fT0hIWLdu3ebNm9etW/fHH3/ExcVFR0evWbNm06ZNiYmJK1eu3L59+/bt22NjY3fu3Llq1aply5bt2bNn586d+/bti42NTUhIOHLkSFJS0qFDh+CX+LZt244ePRofH799+/atW7du3rx57969sbGxGzZs2Lx58/79+zdt2rR8+fKYmJiVK1fGxMSsXr16586dO3bsWL58+cqVK+EX+tKlS2fMmLFixYro6OioqKj58+evWrUqOjp65syZ06dPj4qKgn9MnTp12rRpEydODA8PnzBhwqRJkyIjI5cuXbpgwYL58+dPnz49MDCQwWBMnDjRz89v7NixoaGhISEhISEhAQEBY8eODQkJ8fPzGzly5KhRo0JCQoKDg8eMGePr6ztixAhfX9+wsLCAgIAxY8YwGIyRI0cGBQWNHj0a+ogsLCwcHBzs7OycnZ19fHx8fHwsLS2dnZ3d3d29vb2DgoICAgJgP9fT09Pa2lpPT8/KysrW1tbW1tbb23v8+PH29vbu7u6Ojo4mJiaOjo7Q0RQaGurh4QE7zk5OTlZWVs7OzsHBwY6OjvD17OTk5OzsbGVlZW5ubm9vb2hoaGtra25u7uLi4unpaWdn5+fnZ2FhYWZm5u/v7+XlNWbMmNDQUFdXVwaD4eLiYmVlZWpqamZm5ubm5uTkBNXf1dXV3d3dzc0NXoeAgABnZ2d7e3tra2tLS0srKytra2sLCwtHR0dzc3NTU1MrKysHBwdzc3N9fX1jY2MXFxcLC4vhw4fb2NiYmZnp6+ubmpq6uLjo6OgYGBjY29sbGRmZm5vb2toGBgZiQ0QjRowYMWKEnZ2dqqoqfDXCZ9bMzOzKlStfe9IbGhqOHTu2cOFCPT09MTEx6GnE4/GrV6/+9mD7twH947XgPkR1dXVycvLMmTPNzMzg+WtqasJky99TwYuLi1euXGljYwObgrOz86VLl7hvKpvNXrp0KQBg1KhRPfK+ampqLl68uHHjxpSUlMLCwj6NrEAMUrBnqqOjg8lktre3t7e3M5nMzs5OOIwJA406OjpgL6qzsxPGHcF4pPr6+paWltbW1ubmZtj8Wltb29raWlpa6urqampq4Mgk59PADJvNhsOqra2tHA6HyWRWV1fDTVpbWxsaGurr6+vr6ysrK1taWuDfcMPGxsba2tqKioqGhgZsc+gbgJFU1dXVjY2N0LzOzs6mpibsFKD90PjOzk54rLa2tsbGxsrKyqampqampsbGRmg2XFhbW9ve3t7U1ARHWcvKysrKyioqKl6/fv38+fPXr1/DAc/Kysrq6uq6urr29na42/Ly8ubm5sbGxvfv3//999/29vaqqqqbN2+Gw8hf85OkpaXBJBj48SQvL0+n08XExDQ0NHoktP8Q/z+asP85fvy4pqYmHo/H4/Hu7u5wyO53U3AOh7NgwQJ4X4WFhaWlpel0Ogws5fZrNTU1+fr6kkikp0+fcj4NPsNr1dbWVlJSAoMKvrj//rykv36swWXtj+78N2zeQ56WlpbXr19/8enD4k/YbLavry8MD6PRaKdPny4sLCwvL79///7WrVsfPnz4816UX7L9Z2Gz2c3NzTU1NTExMRMnToT+uGPHjvHEGJ5z4sQJaWlpe3v79evXDx8+XFxc/MCBA5zPnvZ169YJCAhgk8p//r3yjXESBOKLwJQC1Gz6lA8fPoSGhuJwOFFR0fDw8C9OEz+YFBw2FyaT2dHR8e7du+TkZAMDAwCAiYkJDN78fWJRsGHMx48fv3r16unTp+bm5qKiohkZGZzPbmpBQQGFQgkNDYUOFvaXQI8i4kfp7Oz8HZ61vqNHMEIPsrOzYRa6jIzMvn374ELu+Tp+sePFAwXHThXzcO3btw8maq5cuRLK0++TTMx985qamkaPHi0nJ4fVWOBes6WlBUZcwYwnzJGCDUT/Jq89xK8DmwpMY0Ft5tf5/BrC5zorK8vGxgaG0CxdupTTB9HSvPGicNPd3Z2RkREUFAQAGD58OBSv39MhAHNW+fn5U1JSOJ8NiTQ0NPj6+srKyj5+/P/au++4KI7/f+ALqIiCAaQKSG/Se+9FekdBsQAiFrChURNFMCoSEjVGo0asYMWuqGiUoCBYECwoIhJFOtxxtIOr+/tjvtnffUATA8hx8H7+4UP2lr253bsXczOzM8V9HwXgyxFjCiq+5sr3oxYK6I6OjvXr16Mxpj4+Pl9pYmcuJzh6PQwGIyMjQ1RUVEhIKCEhgahUcrdsQ6+pqWnu3LkYhm3ZsgXvcwZIJNLs2bPFxcXRuB1IcNBv//zFHwwQ+mzev39fRkYGwzA5ObkbN27gX+eLMjcTnLMFoLKyMioqCo0sHIUT6REXdffu3WpqagkJCX33efbsmaampqamJuoJgTYT0G/sL5g3DfQbSvCnT5+qqKhgGLZq1Spi+4hK8F5KSkrU1NQwDAsODq6rq+N2cbgjLS1NVlY2KSkJ/ch5vbdt24ZhWGxsLNS+ARjO0Gf21q1baKYUztXYB90wSvD29vYjR45IS0sLCwv/+OOPo7N2gO7cWbduHfqRSPB79+7p6+tLSUk9evQIh2/BAAxj6IN548YN1KjQ09Pz9Z5rGCU4g8HIzc21srLCMCwgIADd5TWqsFis1NRUQUHB5ORkzu1dXV0RERHCwsKpqansvycghZo4AMPZ9evX0f07aArcr2QYJTiO42VlZcuXL5eQkFBQUOg1dpK7BRsy69atGz9+fEpKCrGloaEhNTV14sSJ9vb2/zDTLABgmEB59erVqylTpowdOzYnJ4fYyHnrBmdvRK+I+/Lm8uGS4MSr6u7uzsjIwDBMXV29sLAQH00JTqVSlyxZIi8vT6xQ/uzZs/j4eHl5eTk5ufPnz3O3eACAL4Hyqru729PTE8Ow3377jdjOqdc36ba2tuLi4tLSUnSjzBfm3vBKcOLHwMBADMOWLFlCrJM54rHZbBqNduzYMVVV1QULFuA4XlBQsGzZMhEREUtLy2vXruGjcoQl6Dd4t3ALkcsZGRkCAgLS0tKbN28mVhjupaenh0QinT9/Pjo6euXKlQsXLty+fXtjYyP7y26xHi4Jjv/vcp03b97EMMzY2Dg7O5vb5RpSp0+f1tDQMDExefjwob29/cSJE4OCgtAtPDh8JsEXY7PZTCaT8w0DYweHDHGeKRQKqoajWUP27NmTmZl55syZvXv3Xr58+ezZs9euXdu2bduJEyeMjIzQ2k8YhqmpqaEVXXgswRHibrEFCxYICgqGhoYSKxuMvL474kU1NDSUlJRcvnx55cqVaOFQSUlJRUXFHTt2oLWT4LMHBgh6v7mivLwcLQ6Mcnzy5MmysrLjx483NDSUkZGRlpaeMGHC1KlT0bQiGIYpKysfOHDgy5uOh2OCo6K3tLSYm5srKChcvXoVPTQi33/oxebn5xsZGUlLS6PVi5SVlUNCQu7du4daxKD2BADvolAoSUlJaC0ENJk2sb4PuucewzAJCQlDQ8MtW7ZUVVXhn/oK9TnDN8FxHN+8eTMfH9+sWbM+fPiAj9AEJ7qkL168mJKSEhUV9csvv9y7d49MJnPuAAkOBg7eRUOPWHQlLy/P399fTEwMLbCJ1nkYO3aspqZmUlLS69evidsY0bclXk1wApPJfPXqlZGR0YQJE4iRhSPyLUi8qKKiogcPHnC3MACAwUV8wBkMxqtXrwoLCy9evHj06NHs7OyCggIKhTKQgw/fBMdxnMlk7tu3b9y4cU5OTn2XiBxhRuQfJwDAl+j3x39YJzibzX748KG5uTmGYV5eXkTDwojEOVCU22UBAAw+Yrgd0TSKGkwG8pEf1gne1dV1/fr1lJQUfX39UXJLC+Q4ACMV8aHue1tmv4/57wnOrTRhs9lUKvX9+/d5eXnp6el8fHzh4eGtra1cLNKQGfh1BQCMBl+U4ENQjk8+L41G6+npuX37NqqGjx07lliGbWSn24j/EwUAGBT/kuBsNpsYDTP0WCzWhQsXXr58GR8fr66uLiAgMHny5NF2lyYAAHzO8K2DIyQSicFglJeXR0ZGamlpYRjm4eHR0NDQj0NBrRYAMMIM655MTkeOHFFUVOTj45OVlU1LS2tqavry30XNyj09PRDiAICRhDcSnM1mv3371tLSEk0vEB0d/V/nLETNQZDgAICRhGcSHMfx5ORk1Bqup6e3Z8+e7u5u/D+2jUCCAwBGEt5IcBzH2Wx2aWmps7OzgIAAWn0OrRgJo+4AAKMWbyQ4MTHmn3/+uWjRInFxcQzDEhISiKn7uF1AAADgAp5JcGKIdHFxsY2NjYiIiJSUVF5eHreLBgAAXMMbCc6prq5u2bJl2tra/Pz8ISEhaDpdAAAYhXgvwXEcT09PX7hwoZKS0uTJky9cuMDt4gAAAHfwXoKz2WwymZyWljZ9+nQMw6ZPn97W1sbtQgEAABfwXoLTaLSWlhYKhfLo0SM7OzsBAYHNmzePyOV7AADgn/FegrNYLDS5FY7jO3bs4OPjmzp1an5+Pg6DUgAAowzvJTinx48f6+vrCwgI7Nq1C6rhAIDRhvcSnHPmVTKZvG3btkmTJikqKubm5vbajQuFAwCAIcQbCY7q15zZTaxXVFFRMWvWLH5+/vnz55NIJOJXIMEBACMebyT4J+MYbWQwGH/++aeJiYm3t3d1dfWQFw0AALiGZxKczWYzmUx0Gz3ndhzHu7u79+3bJyYm9uOPP3KpgAAAwAW8keAIZ4ITrShsNrulpaWoqGj69OliYmKnT5+GyVIAAKMELyX456CwLikpmTJliqqq6vPnz3FIcADAKDByErytrc3Hx2fcuHEbN27866+/IMEBACPeyElwJpOZnp4uJSVlbm7+559/ovUfAABgBBs5CY7j+M2bN7W0tBQUFI4cOYKWYeMcgAgAACPMCElw5OnTp0lJSWJiYhYWFmjWWbQ0BIQ4AGBEGiEJjm75uX79+rx587y8vPj4+L777jsSiQSrGwMARrCRkOA4jrPZ7K6urubm5osXL3733Xdqamrq6uqnT5/mbA2HKAcAjDAjJMFxHKfT6TU1NRQK5cSJE8HBwYKCgh4eHjU1NfjflXRoEwcAjDAjJ8FxHO/o6Ojs7GxtbU1LSzMwMBATE/v111/JZDLO0VbO7TICAMCgGQkJzpnO6N+CgoLo6Gg5OTkTE5Pbt28T84kDAMBIMhISnBOKchaLdfPmTS8vLwzDlixZUl9fDxVwAMDIMwITHI1LaWpq+v777wUFBc3MzHJyciDBAQAjz4hKcKICjsL62rVrxsbGfHx8QUFBLS0tOAxHAQCMLCMqwQkoqbu6ujZs2KCioiIpKXnkyBHiIejVBACMDCMzwQltbW0rVqwQFRX19PTcu3dvQ0MDjuNMJhPiGwAwAozYBCcyOicnx9raWkZGJjo6Ojs7G4fJUgAAI8VITnAU0w0NDevWrRMREYmNjd2zZ89ff/2FQ4M4AGBE4I0EJ8Z6M5lMNNTkP3n16tWMGTOUlJTi4+MLCwu/QgEBAIALeCPBcRxns9l0Or2rq+u/Vp+pVGpFRcXRo0eNjIxUVVUvXLhApVK/UiEBAGAo8UaCD2QACZPJLC8vT0lJmTFjhri4eGBgYG1tLbSiAABGAJ5J8IH8OpVKvXnz5p49e7y9vceMGbN3717isBDlAADexRsJPhAopltbW1+/fv3LL79IS0v7+Pi8evWqu7sb1n8AAPC0kZ/gOMdCmi9evHB2dsYwLDY2lkKh4Djej35RAAAYJkZFgqO6Nvr/tWvX1NXVxcTEjh07xmQycRhZCADgWaMiwdFkKajBhMlkLlu2bOLEid7e3rW1tdwuGgAA9N8oSnD87zaTwsJCExMTUVHR7du3w8hCAADvGvkJTlTAu7q6GAwGjuP19fU+Pj4CAgKSkpI5OTncLiAAAPTTyE9w/O+W7ra2NpTgLBarsLDQ0tJyzJgxixYt+vjxI7cLCAAA/TEqEpwTSvPW1tbVq1ePHTtWXFw8IyMDzVYIXZoAAN4yuhKciGkajXb27FlTU9Nx48bNmjXr7du3OIwsBADwmtGV4AgKcQaDcf78eS0tLX19/fT0dLSkPQAA8JDRmOAInU5vaGhITk4WFRU1MzOrqKjAYQUfAABPGb0J3tnZWV1d/eeff2pqak6YMGH37t2onxPiGwDAK0ZpghMxzWQyExMTBQUFp02bduvWLWIicm4XEAAA/t0oTXCcI8Tfvn1rb2/Pz8+/YMGCjo4OqIMDAHjF6E1wApvNPnPmjK2trZyc3NGjR3GogwMAeAQkOM5ms5ubm9esWSMrKxsYGMhgMKAaDgDgCZDg/6e0tHTatGmioqLHjx9vaGjgdnEAAODfQYL/HxaLlZaWNn78eFNT06dPn6KNUBkHAAxnoz3BOUd///XXX+bm5mPHjl21alVZWRmO47CCDwBgOBvtCY6gmKZSqVu2bDEyMtLQ0CgoKOjp6YH4BgAMZ5Dg/x+Lxbp79665ufnEiRMDAwMvXrz4NWZKQbNoDfphAQCjECT4/2AwGL/++quIiIigoGBKSkpbW9tgHZlIbYhvAMBggQT//1C2NjY2mpmZCQgIzJo1q7y8HCYsBAAMW7yX4MSN758cKDKQ0SPEffZr164VFRWdPHnyli1b0MhCGJQCABiGeCzBieBm/Y1zS6//9OPgLBaLRqM9fPhQX19/4sSJzs7Ojx8/xj//B6PfrwKH5hQAwIDxWIJ/uX7nI5PJvHXrVkBAgLq6uqKiYkJCAp1Oh0V8AADDEI8lOJlMzsjIKCsra25ufv/+/cmTJ8+ePXvixInjx48nJycvXLjw5MmTeXl5PT09/Ts+m83u6empra1dtWqVs7OzrKyshobGixcvBvdVMJlMNJMtAAAMBG8kOFH5ffv2rbW1taSk5NSpUxUVFSdOnGhjY2NsbDx+/HgtLS0PDw9nZ2dRUdHU1NR+15epVOr79+/LyspycnKmT58+adKktWvXNjY2MplMfJCaU+h0Oo1Gg0o9AGCAeCPBCSwWq6SkJDY2dsGCBRs2bNixY8f79+9v3Lhx+fLl3NzcN2/enD59etKkSYaGhlQq9b8enEjnDx8+dHV14Ti+d+9eMTExRUXFvLy8lpaWwWoNJ9rrB3gcAMAox2MJjuM4m82uqanJz88nk8kMBqOkpOTnn39OSko6derU5cuXExISMAxzd3dHVeb/emTOvlAcxykUSnx8vKioqJ+f34cPH/rdR/rJJxrgQQAAgMcSHGVfTk5OXFzc3bt3S0pKdu/evX79+uPHj9+6dev06dPTpk3DMMzf378fDc2cVWyiglxSUuLu7j5u3LgDBw6gjQPPX84BkQM5DgBglOOxBMdxnMViMRgMEolEpVKpVCpnCJJIJF1dXXFx8VmzZg2wjYKIVzKZHBcXJyIi4uDg0NjYiEPyAgCGDR5LcM4mjr6OHj0qJCQkLCx86NChwXpGJpN58uRJLy8vPj6+HTt2DNZhAQBg4HgvwTm7ATkbpslkcmxsrLW1taOjY15e3iA+KZPJPHr0qLy8vKam5rNnzzhb2KEyDgDgIh5LcAKbA9ry7NkzGRmZyZMnu7i4kEgkfJCaO9Bfi+bm5tWrV2MYNmPGDDKZjA/2XZoAANAPvJrgvTAYjNLSUllZWVVVVV9f3127dt2+fXtQ5nElqvx37twxNjaeNGnS3bt3cWgNBwAMAzyc4B0dHfn5+UePHv3222+trKzU1dUFBASwv0lJSb1+/RofcEMH++85WEgkUlZWlqKiYlBQUEdHBxvmNgEAcBtPJjiJRCosLIyPj//mm2+IyJ4wYYKIiMjEiRMNDQ0XLlz466+/kkikwaqDE8PDV6xYISEhsX//fjQMBhIcAMBFvJfgbDb77NmzUlJSKLjd3d3j4+OjoqLMzc39/PyUlJRMTU2zsrIuXLhQWVk5uCFLp9OPHz+uqKgoISFx+fJlWEUTAMBdPJbgqEGjrKzs559/dnZ2XrlyZX5+/osXL5KTkxUUFAIDAxMTExMTE9PS0s6fP9/Z2Tm4Cc5msysqKrZs2TJhwoTIyMi6urrBOjIAAPQDjyU4m81mMpnt7e11dXU//fRTTEzMtm3bcnNz/fz8JCQkTExMmpqaeu0/iCGOjnP06FFbW9vJkydfuHCh10MAADCUeC/B0UhwMpm8e/fuS5cuUSiUhoaG8PBwBweH2NjY7u5u/KvlaUtLS1tbW1VV1XfffTd58mQ/Pz8ymYyeEaapAgAMPd5L8L7V6qqqKh0dHRcXl/v373/VZ6fT6QwGo7m5+e7duwsWLDAwMLh79y4alwJ1cADA0OOxBMf/N8RRbr569Qp1Y5aXl+Nfs0GDxWIxmcyenp6ioqK1a9fq6ura2tpWV1d/1ScFAIDP4b0E76ujo+PQoUNr1qzp6OhAW75envb09FCpVAqFcurUqfDwcA0Nja1bt6LJxCHEAQBDbCQkeFdX16VLl44fPz4ES5cxGAwajYbjeE5OzoYNG9zd3Y2NjR8+fIgehdt8AADfYtV3AAAgAElEQVRDaSQkOI7jdXV1dXV1QxCdqOmmu7ubzWZXVlbu27fPxMRk0aJFxGQpOCQ4AGCojIQEJxJzyKKzu7u7p6enp6fnyZMngYGBqqqq9+/fZzAYkN0AgKE0EhKcK9DwQRKJtH37diMjI1dX1+bmZhxmvAIADCFI8H5CSd3T03Pu3Dk/Pz8ZGZkDBw7AZCkAgKEECd5PRJN3W1vb0aNHtbW1VVVVjx07RqFQuF00AMBoAQk+UGw2+8KFC/b29jIyMhs3bkRdmvjf6wdxt2wAgJENEnxAWCwWnU5vbGxMSUmJjIycO3fu8ePHa2trcVjEBwDw9UGCDwiLxaLRaEwm89y5c1FRUZ6ennZ2dtnZ2cTIdEhwAMDXAwk+OOrq6vbs2RMYGKirq5uRkYFaw6EhBQDwVUGCDxTRVNLd3Z2YmKigoODg4HD27Fk6nQ6tKACArwoSfKA427tramqCgoJUVVXnz59fXFyMQysKAOBrggQfKM6mkq6url9++UVdXV1OTm779u1DME8LAGA0gwQfKM5aNpPJbG1tXbhwoYyMjLm5eXFxMZPJhLYUAMBXAgk++J48eYJWfYuPj3/9+jUOXZoAgK8DEnwwoZhmsVjJycnS0tLOzs4FBQUwezgA4CuBBB9MREzX19cHBgZqaWmtWLEiPz+fu6UCAIxUkOBfy/nz5w0NDRUUFDZu3IhWQwYAgMEFCT74UE28ra1t06ZNqqqqBgYGN27cgFYUAMCggwT/KtDs4U+ePElOTlZXV//hhx+INTwBAGCwQIJ/FajGzWQy0V2aJiYmp06d6uzsxGEJCADA4IEEH3ycGf3hw4f58+erqKisX78etYZDggMABgsk+FfBZrNRQwqO4+fPn58+fbqZmVleXh53SwUAGGEgwb8WoqJdXFycmprq7u7u6elZVlbG3VIBAEYSSPCvjk6np6WleXp6ampqLlu2rK2tjdslAgCMEJDgXxeqidfW1v7+++8zZ860sbFB99nj0CAOABgwSPCvi8ViMZlMHMfr6urWrFljZWWVmZnJ7UIBAEYISPCvrqur6/37948fP963b19sbKyXl1dJSQkOM6UAAAYMEvzrYrPZDAaju7u7urr61KlTCQkJ2tralpaWaP0HAAAYCEjwr4tzDbaamprMzExPT08hIaGNGzc2NTVxu3QAAN4GCf7VEa0lTCYzNzd38eLFjo6OM2fOzM7OhhmvAAADAQk+RIjK+LFjx9auXWtoaLhhw4aamhocBqUAAPoLEnyoPX36dOPGjcbGxoqKiqdOnYLsBgD0GyT4ECHus6+pqdmzZ09QUJCUlFRoaGhDQwMO1XAAQL9Agg8dlNEdHR3Pnz+PjY3V1tZWVVU9cOBAa2srt4sGAOBJkOBDBNWyiSWPy8vL586dKy0tvWrVqj179tDpdG4XEADAeyDBhwj7b8SW7du3y8nJOTo6rly58tGjR1wsGwCAR0GCc83r1683bdpkaGhobW197NgxYp17aBAHAHwhSHAuQBnd09Nz/PhxT09PDQ2NTZs2vXjxAv97eTYAAPgSkOBcQDSn0Gi0AwcOGBkZWVlZnThxoqenh9tFAwDwEkhwLsvLy4uIiJCWlk5LS3v27BmayBAAAL4EJDg3sdns6urqtLQ0aWlpU1PT1atXX716lfNRLpYNADD8QYJzE8rod+/eBQQEqKurBwUFLV++vKOjg/NRAAD4HEhwLkODxO/cubNmzRodHZ2ZM2feu3cPh7s0AQBfABKc+xgMxtWrV0+fPm1nZ7d48eLS0lI0ZyEkOADgn0GCcxmqg9+/fz86OjogIMDY2Hj16tVv3ryBOjgA4F9BgnMZGgDe3t6+Y8eO+Ph4WVlZSUnJffv21dbWcrtoAIDhDhKcy4iK9vv37wsKCvz8/ISFhX18fB4/fkzswK3KOJ1Oh3tEARjOIMGHC7Sq/alTp8zMzFRUVB48eIBu8Ok7ocqQqaur6+zsHPrnBQB8IUjwYQEFNJPJrK6u3rlzp7a29pIlS27evMlgMIiJxYe+SAwGA+rgAAxnkODDBVHRfvHixYwZM9TU1Hbu3Pny5UucS4NS2Gw2k8mEBAdgOIMEH3bYbPbhw4e1tLRmz579+vVroi2F2+UCAAw7kODDUUVFxbJly4yMjA4fPgxjwwEAnwMJPhy1t7dv27ZNT09PSkrqt99+QyEOAAC9QIIPU/X19Zs3b1ZQUDAxMfn48SMO1XAAQB+Q4MMRCuvi4uKoqCgVFZVr167hf9+9CTkOACBAgg9HaPggm80+efLklClTgoKCmpqa0EOQ4AAAAiT4cETE9OvXr318fFRVVf38/NAybJDgAAACJPhw9/vvvxsZGcnIyJw7d47bZQEADC+Q4MPd06dPQ0ND1dTUVqxYAfe4AwA4QYIPa2w2u6OjY8OGDZs2bVJUVFy7dm1bWxu3CwUAGC4gwYcvNPikq6uroaHh/Pnz06ZNExQUPHHiBGoKh3EpAABI8GGNzWZTqdTr16//+OOPQUFBYmJi8+bNq6iowHGcyWRCggMwykGCD2uoov3gwYNjx46tX7/ewsLC19f32rVrdDqd20UDAHAfJPiwRkwt++rVqw0bNri7uysoKLi6uj58+JDbRQMAcB8kOG8gkUgXL14MCwtTVlZWV1fftm0bg8HA/66kQ3MKAKMTJPhwxxnQDQ0NUVFRQkJCJiYmGRkZRIhztYAAAK6BBOcNRI5nZmbKyspOnDgxIiKitLQU5+pCmgAA7oIE5xkopul0+oYNG+Tk5KytrZOSktA9PpDgAIxOkOC8gchoFotVXl7u6+srLCzs7u5++/ZtHBIcgNEKEpxnEIvWM5nM/Px8Nzc3ZWXl1NRU4lHuFg8AMPQgwXkDCmg2m93V1YWW7NmwYQM/P7+pqWl6enqv3QAAowQk+BAZ4E3wRIJ3dnZ+/PixrKzsypUrfn5+wsLCjo6OT58+xaFLE4DRBxJ8KLDZbAaDQazb0L8jIHQ6va6uDnVg7t69e9KkSXJyckuXLm1sbMRhZCEAowwk+BAZrDo453GKioosLS0lJCSsrKyys7NxaEUBYJSBBOdt+/fvnzp1qqys7M8//wwVcABGG0hwHtbU1FRSUhIcHCwtLa2mppaZmclkMrldKADA0IEE52E1NTW3b9/+7bffvL29paSk1q9fT6FQuF0oAMDQgQTnYSwWq6qqqri4OCUlxcTERE9PLzEx8fr168+ePUM7EK3nvX7xc83lxPZeO3zyCP/c5s75aN+j9XqifzgU0YX7D8/1yef911/pVULOe6b6HuST5fzyE/vlO+CfP7d9z1vfnTlP1+f+7V/Z+l6IL3mxxPP2KsAnS9WrGfBzF+gLi/fJAnxJsXvt9oXvQG51QUGC8zAWi0Wj0UpLS+fNm6ejoyMhISElJaWgoCAjI5OZmfkPv9irR7TXds7j45/6IPXKO+Khvm04n/tc9ZpSEf2f86l7Hb/vcYidWSwW5/85D04clvPpev2n768QW4iDEz+yOVZH6nvMvmeG87Ccr6tX2TgLw2Qye73kfzg5fZ+l7yllf+oqc17rvlen1+nlPOCXXEe8TxajF8X5ujiPgP/95kGLlnCeFuL4rL9xHrbXa+91HnqV9nMnkHi019lm/+/bnnPnDx8+PH78+MGDB8XFxU+fPkULH3KrFwoSnIex2Ww6nf7DDz9MmTJl0qRJY8aMwTBswoQJAgICpqamRUVFd+7cOX78eHV1dXNz88ePH1+9epWTk1NSUsJkMul0eltbW0dHx5s3bw4cOHDjxo2Ojg502I8fP1ZWVqL/d3Z2dnR0NDc393327u5uEomE43hTUxOVSsVxnMFgtLW1vX//vrOz89WrV2QyGW0kispiseh0OtrSV3Nzc2Nj48ePH2tra3t6emg0GueebDabSqW+f/++ubm5trYWx3EajdbrbPzrGfvk36Qv2e0fsNlsBoPB+dfrX3sjPncGCJ9cwYNEIpWUlNTW1tJotLq6OiqViu7t6nvw9vZ2zjKQSKSnT58eO3bs3Llzn7yUnZ2dDQ0NdDq9V/4SZwC9wJ6eHiqVymAwOjo60BVHmUuj0dBgVrRna2trQ0MDKgCVSkWXCRWVRqPV19e3tLT09PTgON7V1cVgMD53Nmg0GqqjcG5kMpnojVddXd3a2lpWVlZVVYXeaQQivqlUKipne3s7eojFYqGnbm1tra+vb21t/dxVptFo6MVSKBQ6nV5WVtbS0kKhULKysry9vS0sLMTFxfX09GRkZOzs7Lg4Xz8kOG8rLS2VlpYeM2bMpEmTxo8fz8fHJyAgwMfHN2HCBFtbW29vb0lJSQ0NDX9/fzs7O1tbWzMzM1dX1y1btpw6der06dOJiYnJyclaWlrh4eHJycm3b98+f/78qlWrZs2alZaWlp6e/sMPPyxatGjdunULFy48c+bMwYMHz5w58+TJkzdv3uTm5qanp2dlZS1dujQuLu7+/fsFBQUrVqyIiYm5dOlSZGTk2rVrDxw4EB0dfejQIQqFUlxcvGvXru3btz9+/BgdISMjIyMj4/Dhw+gPRkVFxcGDB0+fPp2UlLRx48Zr165t3rw5Pj5+27Zty5cvj4iIiIiImDt37qJFi+Lj448fP56SkrJs2bIrV64cPHhw06ZNSUlJ+/fvz8vLKy0t3bFjx65du+7cuXPw4MFnz57l5eVlZ2cfOXIkPT29vLyczWbX1ta+fPny1atXlZWV586dS09Pz87OLigoOHv27JUrV0pLS69cubJr1659+/YdO3astLS0s7OTQqFUVVVRKJTXr1/fvHnz8uXLRUVFJ06cKCoqKikpOXPmDIlEKi8vLy0tbWxsJJFI9fX1+fn5V65cOX369KlTp06cOFFQUJCdnV1UVHTmzJlr165VVVX98ccfV69ePXHixPXr1x89enTo0KGMjIw7d+4kJyeXlpa+efOmsLAwJyenoKCguLg4Kytr5syZrq6uERERDg4OYWFhmzZtWrJkyZIlS5KTk5cvX753797U1NTU1NSIiIgNGzakpKQcO3YsMTExKSnJzs5OUVHRwMDA1dV169atR44c2bp1a2Zm5tatW+Pi4tauXTtr1qy5c+fu2rVr06ZNGzZsePToUVZW1pEjR06dOrVnz57nz5+/efPmwYMH6enphYWFZ86cSU9PP3jwYH5+/l9//VVRUVFQUJCXl1ddXZ2Tk/PHH38kJiait9b+/fv37t2L3ja5ubllZWVPnz4tLCzcvHnzrl27zp07l5+ff/DgwV9++eXChQuVlZVZWVmXL1++devWw4cPr1+/fvbs2S1btmRmZl68ePH58+fnzp1bsGDBunXrwsLC5s2bt2rVKltb2zlz5mRmZl6/fv3KlSv37t3LyMi4ePHiuXPnNm3aFB4evmbNmpMnTz5+/Pi3335LTk5esmRJSEjImjVrPDw8QkNDfX19o6OjU1NTd+/evWPHjkOHDt28eXPnzp2//fbbzp07s7OzU1JSEhMTL1++HBwc7O7uPm/ePBMTk3HjxsnIyKDa0tixYzEM09DQeP78OVcSABKc9xC1hoqKiri4uClTpggLC0tKSvLx8fHx8Y0ZM4afn5+Pj8/R0TE5OdnLywvDMFdXVx8fH39/f0VFRRcXF01NzY0bN5qamqqrq8vIyPj6+lpbW9va2iYnJysrK8fGxi5dulRFRcXS0tLHxyc4ONjIyMjDw8Pb29vZ2TkkJOTcuXPXr19fvHjxypUrV6xYcfjwYVVV1ZCQkHv37l25csXZ2XnTpk3q6uqysrLz58/X0tIKDAz8/vvvV6xYYWZm5uDgsGjRIjMzM29v78mTJ1taWjo5OX333XcnT550d3dfvXr16tWrvby89u7dm5iYGBIS4u/vb2BgICsrq6ysrKenp6+vr6OjY2Vl5eLi4uHhoa2tbWNjExER4evra2BgYGxs7ODg4OzsPH36dFdXV1NTU0dHRyMjIzk5uSlTplhaWs6bN2/+/Pm//vprUlLS5s2bz549e/78+X379i1evNjX19fZ2dnOzm7+/PkxMTEhISG+vr5+fn4BAQEWFhYxMTEZGRkJCQkhISGxsbEzZsyYO3euk5PT/PnzFy1alJqaOnfu3Hnz5oWHh8+ZM2fHjh2HDx/evn17TEzMrFmzQkNDvb29g4ODg4ODjY2N/f39IyIi/P39PT099fT0dHR07O3t58+fHx4e7unp6erq6ujoaGBg4OPj4+DgYGlpaW9vr6mpaWlpqa+vr6ampqmpqaysPHXqVCUlJTMzMw0NDVFRUWFhYVVVVW1t7alTp5qamsrIyFhbWxsaGhoaGhoYGFhYWKioqIwfP97ExGTKlCkTJ06cPHkyHx+fpKSkhITEmDFj1NXVp0yZgmHY5MmThYSEpkyZoqqqKiMjIyMjY2RkZGdnZ2dnFxgYuHXrVh8fH0VFRT8/v5CQEDU1NeJsx8TEuLu7h4WF2djYREdHz58/X0NDQ0JCwsnJSVFRUUdHR19fX1VV1cbGZv369VFRUWJiYlJSUqampgYGBoGBgTo6OhiGqaura2lp6evry8vLKysre3h4qKiooKCcPHmyrq6uhoYGOoiOjs6ECROmTJkiIyMjKSmpq6vr6+uroaEhJSUlKiqqqqqqrKwsIyOjrKysqampp6fn7e0tLy8/ZcoUtI+urq6hoaG0tPS0adPk5eWFhYXHjh0rLy+voaFhY2MjIyMjJCRkbGzs6empoKAgKSnp4uLi6OiorKw8btw4YWFhAQGBMWPGaGtrBwQEaGpqTpw4EcMwHx8foqbfq5XsH9pnBg4SnPcQ74AnT574+fmJiYnx8fFhGIZhmKioqLi4OIZhOjo6mZmZmZmZCQkJ/v7+O3fuTEpKWrBgQWRk5Pz58+fOnRsbG6uoqKiiomJjY5OamrpmzZqAgIDZs2fb29svWrQoLi7O3t4+KioqLS1tz549cXFxqM6CMigyMnLRokXKysqGhoaLFy8+evSooqKihIREaGjo1q1bY2NjFyxYoK+vHxwcHB4e7u3tbW9vb2lp6evrq6+vHxERoa2tbWVlZWJiIicnJysr6+/vHxoaamRkxM/Pb2dn5+zsrKWl5e7uHhQUZGlpGRERsW3btqVLlzo7O2toaEhKSuro6Ojo6Hh4eGhpaenq6mprayckJCxfvtzT0zMkJCQyMnLevHlRUVHffvvtsmXL1NXV7ezs3N3dlZSUNDU1o6Oj4+LivLy8VqxYMWvWrHXr1iUkJKSmpm7evHnGjBkxMTGmpqYzZsxITEwMCAiIiYlZsmSJnZ2dm5ubqqqqlpaWp6enubm5jY1NSEhIcHCwjY1NWFhYaGiomZmZj4+PvLy8paWlg4ODhoaGkZFRZGTkzJkzdXV1bWxsZGVlbWxszM3Ng4KCHB0d5eTklJSUtLW1bW1tjYyMtLS0dHR0LC0tVVVVnZ2dDQ0NJSQkNDU1tbS0hIWFZWRk5OXlra2traysLCwsLCwsUGhGREQ4OTlFRkYqKSlJSUm5ublZWFhoa2vb2dl5enqiv21qamqysrLq6ur6+vroxMrJyVlYWMjLy4uIiJibm2tpaSkrKzs6OoqLi8vJyaHz6eTkJCUlhWGYiIiIo6Oju7u7rq6uioqKu7s7Cj41NTVDQ8OpU6e6u7sbGRnZ29sbGxsrKSmZmJg4Ojrq6+ubmpqamJg4OTkZGxubm5ubm5tLSUlFREQYGxtraGh888034uLiysrKKioqQkJCWlpakpKSPj4+6I+uqampnJycurq6m5tbZGRkZGSkp6enurr6pEmTpk2bZmlpqaampqioOGnSJGNjYxsbG1tbW319fQ8PDzMzM/TSlJSULCwsrKysjI2N3d3dvby89PT0vLy8pk+fHhgYaG1t7eXlNXfuXG1tbR0dndDQUCcnJ2VlZSUlJWdn57Vr16K/zUlJSQkJCQEBAVZWVsuXL09PT3d0dOTj4xMUFESfte+//3758uWysrKCgoLi4uL29vaoQZzN/p/uln/4/A4KSHAeRiaTZ8yYgWEYPz//uHHjxo8fLygoKCAggGGYiopKVFRUZGSkl5dXQEDAwoULV65c6eDggNoi7O3tUaJZW1v7+fn5+PjEx8eHh4e7ubn5+PhYWlra2Nj4+/u7ubl5eXkFBQXNmTNHT08P/WhjY2NjY2NoaKihoWFsbDx37tzIyEgjIyMbGxtjY2MLCwt7e3s7OzsvL69Vq1b5+/tbWVkZGBjo6ekZGRmZmpp6e3vr6+vr6uqierStra21tbWZmZmOjo6CgoKJiYmGhgYKCCsrq/DwcEdHR5QLqJqMtjs6OqJfNzQ0DAgI8Pf39/Dw0NHR8ff3j4yMnDNnjpubW3x8/NKlS+fNmxcQEIA+sTNnzvTz83NxcfH09ESVdC8vr/nz53t7e69evXrFihVBQUFRUVFhYWGrV6+Oi4sLDQ1duHBhWFhYeHh4YGCgg4NDcHCwp6enk5NTUFBQbGysq6urg4ODqampmZmZh4eHjY3N9OnTo6OjXVxc0JeMmJiY2bNnu7u7u7u7h4SETJ8+fcWKFa6urih3LCwsHBwc9PT0HB0d7ezs1NTU9PT0rKysUMXZ1dVVTU3NwMDAyspKT0/P2NjY2traw8PDwcHB1dXV3d195syZbm5uNjY21tbWnp6e7u7u3t7eHh4efn5+/v7+NjY2BgYGhoaGpqamsrKyvr6+69evd3JycnNzW7NmzZw5c+zt7a2srKytrdHpMjAwcHNzc3NzQ5fDycnJzMzM19fX29sbpaq1tbWurq6+vj76RQsLCxMTEzs7OwMDAzU1tWnTphkZGenp6amoqJibm9vb25uZmUVERISFhbm4uKDzv3z58oCAAEtLSw0NDW1tbRUVFSMjI1VVVfR3PTIy0tfX19/fPyAgwMfHx9HR0cnJKSAgYOnSpVZWVlZWVmZmZjY2NsuWLXNzcwsLC7O2tra2tjYyMpo9ezb6tuTt7e3g4GBmZubs7Ozt7W1nZxcQEBAQEBAWFubt7e3i4uLg4BASEuLj4+Pu7u7s7Ozl5eXp6enl5RUaGurh4WFubh4RETFv3rzo6OjExET0NWvRokWOjo729vYuLi7BwcHKysrS0tKioqKKiopqampiYmJjx47l4+MTFRU9dOgQkd3EJ5TFYrW1tRUVFT169Oj9+/etra3/2gXyX0GC8zAqlbpz505UXZKUlERVNgzDgoODX716VVVV9fbt25qamg8fPjQ0NJDJ5MbGxtra2o8fP757966srOzt27fNzc1dXV00Go1CoTQ0NFRUVHR0dDQ0NHz48KG7u/vDhw9lZWU1NTX19fVdXV0UCqW+vr6urq6pqam1tZVEIhF9jyQSqb29va2trbm5uaWlpbGxsa2tjcViUanUxsbG+vr66urq6upq1IvV0NBQU1PT0NDQ3NyMDtLa2komkz9+/FhTU/PmzZva2tq6ujoKhdLV1dXU1PTu3TvUddnZ2YleS09PD5lMplAoLS0tLBarvb0dvVJ0Wnp6elCvbGdnJ9F9ymQyOzs70b+dnZ2oRwt1r/X09PT09KBOMyaTiTrfUI8Zg8FAwyTodDo6UR0dHa2trW1tbWQymUwmNzU11dTUkEikxsbGhoYGEonU0dHR3t6OykalUlksVldXF5rHBn3LplAoHR0dbW1tjY2Nzc3NTU1NHR0d1dXVf/31F4lE6urqamlpIZPJVCr1w4cPjY2Nf/31V1lZWWNj4/v376urq0kkEo1GQxeOTqc3NzejF4tOF47jbDYbvaKGhoa6urr6+vqXL192dnbSaLTq6mpUEhzHOzo6yGQy+rGnp6etrQ2Vs729nUQiUanUjo4OOp1OdBtWVlbW1taiYzY3N1MoFDKZTCKR0FWrra2tra2tqKhAXc1ot7a2tu7u7q6uLlQwKpVKJpNbW1s/fPhQW1tbWVlZU1ODXnhHR0dXV1drayvqREWvvbKy8t27d2/fvn369GlDQ0Ntbe2TJ09aWloqKyvJZHJzc3N1dfXz58/r6+t7enpQbvb09LS3t6PechqNht4Y3d3dHR0dFAqFQqHQaDQ0u2d7ezsqG+rtbG9vR6exo6Ojvr6eTCbX19c3NTV1d3ejX/z48WNTU9Pdu3c9PT0lJSVXrVplZWUlLS0tJCSkpKR06tQp/H/r3S9fvrx161Z8fLympuaYMWPGjh0rIyODWi9RH+9g1cQhwXlYd3c3mUy+evWqqampkpKSjIxMUFDQsWPH0Lc5gAzul1YwmjEYjG+//VZISEheXl5KSiosLCwlJeXx48c4x8jId+/excXFqaioiIiI8PPzi4qKoqD/5ptvMAyTkJAoKSnh3H+AIMF5XktLS0xMzMmTJ4uKiohBXX0Hz45mEOJgsDQ1NZ05c2b37t25ubloqCLOMf7y8uXLqPcVw7AxY8ZoaGg4Ozv/8MMP169fP3LkiLq6OoZhP/74I9p5UN6WkOA8DL0DWlpaXr58SYzmJu59gNgiwKkAA/e5WjOx/e7du9LS0hiGKSoqOjk5zZo169ixY+np6X/88cfZs2ePHDmSkJAgLCw8ffp0NA4dEhwAALiGGCCI43hpaammpiYaVrhu3bpt27aFh4dnZWW9ePEiLy/vjz/+aG5uzs3N3bt3L+qmwqEODgAA3IVSuLW11cXFBd0LfeHChfj4+Li4uBs3blRXV3Pu3NzcTHQRQx0cAACGhW+//RbDMDk5uZycnFOnTh09epSzVROFNec8B5+cuaV/IMF5xpdccmjw5RYmk3n37l00PQAxu0ivS9be3l5UVHTp0iV0jzjaCB3OPIq4srdu3Ro3bpy4uHhWVtbDhw9zcnLQ9r4zjrH7GHgxIMF5xievd3t7e0lJSUZGxsyZMw8fPgwrPHALnU43MzNzc3NDla9et1CTyeS0tDQDAwN+fn4hISEhISFRUdE5c+a0tLRwu+CgP4j8JZFItra2/Pz8P/30U1NT09BfUDarhbYAAAggSURBVEhwHtPZ2VlVVZWVlbV161ZXV1d1dXV+fn40eklBQeHdu3fcLuAoxWQyLSws9PT00Dx5nLMbdnV1+fv7oyEKa9asefDgwbNnzw4fPiwtLf3TTz9xudzgv+OsS23ZskVAQMDX17eqqurFixeDNcr7y0GC84bGxsbExMTFixc7ODigedEQISEhSUnJgICAyMjIjIyMXlNxgqEUHh5uYGCAlknibEK5ceMGmmiMmLMXWblypZmZGSyrxLu6u7s9PT2lpKROnz79/Plz1G/Zj4G8jY2N1dXV/bvhHhKcN5BIJDMzMyK4dXV1Z8+enZKSkpubW1paiqY8BtwVExNjaGhIJDLxMS4pKdHR0UF37nHatm3btGnTmpqahrSUYDCgivbr169FRUVtbGzu3bv38eNHzkfR1a+srKyqqqqoqHj27Flra2tNTU1jY+PDhw8vXry4ffv27777Li4uLjw8XEtLy9jYGP0B+K/pDwnOM+7evYtmofrjjz9aW1t7PcrmWNkEcEVMTIySkhL6JHN+Dul0elVVFbF+AsJms4ODgw0MDGAKBF6ELuXvv/+OYZiamtqlS5d6rbbBZrMPHTqkoqIiLy8vLi4uIiIybdo0dXV1ExMTUVHRCRMmEPOJCgkJYRjm4eFRXl6OQ4KPVOi67t+//8KFC5wbiT5uNCUTJDhXoNN++fJlYWHh7Oxs/DOfQ86NXV1dU6dO9fPz++RyPGD4Y7PZ4eHh48aNmzZt2qVLlzgfQnWpn376CU0U2teYMWNkZWX5+fnFxMQMDAxMTEyioqLQ8rb/dYwKJDjPYLFYZmZmwcHBn1xHEergXIQ+ck+ePBEVFUXT1H1yB84xZEVFRePGjfv222+HuKhgsDQ3NysoKIiIiGzfvp2Y8RFBl/jy5cto4UOCoKCgiopKYmLi7Nmz0Wobtra2J0+ePHPmTFlZWUVFRT+GGEKC85LVq1fb29sT8+lwIkJ86EsFkIqKCnFx8f379//DPsRHdM6cOSIiIo8ePRqq0oFBRiaTdXV1lZSUDh8+3OshdJUrKysXLVokKyuLpneXlJRUUFCIjIwsKSkJDQ1FS4WsXr26uLj4wYMH165dy8vLgwQfsdB1ffjwoZ6eXl1dHY7jbW1ttbW1b968efv2LecNYNws5ejW3NysoqKyfv36f9gHXcdHjx6JiIhYWVn1WqIX8BAqlWpsbKyiovLnn3/i//vRI74Nl5WVbd269ffff9+0adOkSZPs7e3PnDlz5cqVzMzMQ4cOPXz4kEKhcEZ2P75GQ4LzBnSZc3NzlZWVfX19w8PDrays1NTUvvnmG1FRURMTk7CwsLKyMm4Xc5Ri/728gKOjY3BwMOfGvrsxmcxZs2aNGzcuIyPjk7uBYQ5dMgaDYWtrKyoqeuLECfx/ryPxbZhOp6PaVUFBgbq6uoGBQXFxca+j9b118z+BBOcNHz9+9PLyQt3WRJsaWm5RQ0NDSUlJREQkMzOT28UcpYho9vLysra27ju4k/hIs9ns9evXYxjm4OBApVLZX2HpWzBkNm7ciGGYr68vuheayOK+EypkZWUJCwv7+fmh5YoGESQ4b6DT6YsXLxYTE+Pn5xcXF587d+7FixerqqrQSlTV1dVlZWV9hxiCIYOGAwUHB8vJyfWakY7996xG3d3dy5YtExAQ4Ofnz8rKwmEhDt5EpHNhYaGmpqagoODSpUuJxVV6IZPJFy9eNDU1nTBhQnp6Og4rHY9anZ2dxcXFWlpa/v7+aMXFvqBCxy3otP/0009SUlJoYG8vra2t0dHRxFeodevWoe2Q4DyHqGXT6fQdO3aIiopiGDZz5sykpKQHDx6Ul5dTqdTa2tqDBw/GxMSYmZmJiIioqKi4ubmhSS8gwUcj4qrb29sHBAT8625gKBGnfceOHbKyslVVVb12KCsrs7CwwDBs4sSJW7duNTIywjAsLS0NPUr83eVsDCWGh8I1HZ7QdaFSqdnZ2TNnzpSXl8cwTEZGZurUqS4uLrq6unJycnJyctra2nZ2domJibm5ub3u+hkUkOA8JiQkxM7ODuYgHFaIkL1z546mpmZpaSnnxsbGRisrK3Qfx6+//orjeElJibq6Oh8f3+7du9E+nE2oRK2cyWT2r3cLDLGamppr167NmzfPwsJCXV1dT09PR0fH1NQ0ODh4y5Yt+fn5xJ6DfjUhwXkDceGXLl1qbW0NCT6scI49KCgoIJFIOMclo9FoycnJGIYtW7aM+JVbt24pKSlhGJaYmNi3IaW8vPz7779Hc4hDgg9nnN+Z2traSCTSgwcP8vPzr169evz48cLCQrQbiwO0ooxGxFVfs2aNsbHx59rBAVf8a035/fv369at6zX6u7CwUFlZGcMwS0vLoKCgpKSkq1evHjx40NfXV0pKysDAgHOyJDA89b2Trq2tra6ujnMaHM6bqCHBRyniqicnJ0tLS799+5a75QH90+vT+/jxY3t7ezTD+9ixY1En54QJE5SUlNAEOKghhUuFBf1Eo9EYDMbQXDhIcB7z888/8/Hxobux4bPNKz55vwb6sa6u7scff1y9evWMGTMMDAxmzJixd+/eoqIitA/0ZPKuoenDgATnMfv27cMw7P79+zgkOI/43B13RKcli8Vqbm5++fJlQUEB0dIykPv0AHcN5bWDBOcxTU1NoaGhxGqqgCf0+/MM8c2LhvKqQYLzHjKZTKPRoHYGAIAE50lsmA0cAAAJzoughRQAgECCAwAAr4IEBwAAXgUJDgAAvAoSHAAAeBUkOAAA8Kr/B1F7ODd5cABnAAAAAElFTkSuQmCC" alt></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;">length of the spanning tree is 47 <strong><em>A1</em></strong></span></p>
<p style="font: normal normal normal 24px/normal Times; text-align: left; margin: 0px;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">for Dijkstra’s algorithm there are three things associated with a node: order; distance from the initial node as a permanent or temporary node <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt> <span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A4</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Deduct <strong><em>A1</em></strong> for each error or omission.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the shortest path is AFBCD <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">the length is 26 <strong><em>A1 N0</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Setting out clearly the steps of the algorithms is still a problem for many although getting the correct spanning tree and its length were not.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Setting out clearly the steps of the algorithms is still a problem for many although getting the correct spanning tree and its length were not.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The adjacency table of the graph <em>G</em> , with vertices P, Q, R, S, T is given by:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Draw the graph <em>G</em> .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) Define an Eulerian circuit.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Write down an Eulerian circuit in <em>G</em> starting at P.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) Define a Hamiltonian cycle.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Explain why it is not possible to have a Hamiltonian cycle in <em>G</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span><img src="data:image/png;base64,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" alt><span class="Apple-style-span" style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none; line-height: normal;"> <strong><em>A3</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica; min-height: 31.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A2</em></strong> for one missing or misplaced edge,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong> for two missing or misplaced edges.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) (i) an Eulerian circuit is one that contains every edge of the graph exactly once <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) a possible Eulerian circuit is</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}} \to {\text{Q}} \to {\text{S}} \to {\text{P}} \to {\text{Q}} \to {\text{Q}} \to {\text{R}} \to {\text{T}} \to {\text{R}} \to {\text{R}} \to {\text{P}}\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) (i) a Hamiltonian cycle passes through each vertex of the graph <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">exactly once <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) to pass through T, you must have come from R and must return to R. <strong><em>R3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence there is no Hamiltonian cycle</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Stronger candidates had little problem with this question, but a significant number of weaker candidates started by making errors in drawing the graph G, where the most common error was the omission of the loops and double edges. They also had problems working with the concepts of Eulerian circuits and Hamiltonian cycles.</span></p>
</div>
<br><hr><br><div class="specification">
<p><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">In the graph given above, the numbers shown represent the distance along that edge.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using Dijkstra’s algorithm, find the length of the shortest path from vertex <em>S</em> to vertex <em>T </em>. Write down this shortest path.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Does this graph have an Eulerian circuit? Justify your answer.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Does this graph have an Eulerian trail? Justify your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">The graph above is now to be considered with the edges representing roads in a town and with the distances being the length of that road in kilometres. Huan is a postman and he has to travel along every road in the town to deliver letters to all the houses in that road. He has to start at the sorting office at <em>S</em> and also finish his route at <em>S </em>. Find the shortest total distance of such a route. Fully explain the reasoning behind your answer.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">from tabular method as shown above (or equivalent) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Award the first </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">for obtaining 3 as the shortest distance to C.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Award the second <strong><em>A1 </em></strong>for obtaining the rest of the shortest distances.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">shortest path has length 17 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">backtracking as shown above (or equivalent) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">shortest path is SABT <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) no, as <em>S </em>and <em>T </em>have odd degree <strong><em>A1R1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Mentioning one vertex of odd degree is sufficient.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) yes, as only <em>S </em>and <em>T </em>have odd degree <strong><em>A1R1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>In each case only award the <strong><em>A1 </em></strong>if the <strong><em>R1 </em></strong>has been given.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Accept an actual trail in (b)(ii).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Huan has to travel along all the edges via an open Eulerian trail of length <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">4 + 3 + 5 + 2 + 1 + 3 + 5 + 4 + 7 + 8 + 5 + 6 + 7 + 6 + 6 + 8 + 9 = 94 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">and then back to <em>S </em>from <em>T </em>along the shortest path found in (a) of length 17 <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">so shortest total distance is 94 + 17 = 111 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was quite well answered. Some candidates did not make their method clear and others showed no method at all. Some clearly had a correct method but did not make it clear what their final answers were. It is recommended that teachers look at the tabular method with its backtracking system as shown in the mark scheme as an efficient way of tackling this type of problem.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">Fairly good knowledge shown here but not by all.</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Some good answers but too much confusion with methods they partly remembered about the travelling salesman problem. Candidates should be aware of helpful connections between parts of a question.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the following weighted graph.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="font: normal normal normal 27px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) Use Kruskal’s algorithm to find the minimum spanning tree. Indicate the order in which you select the edges and draw the final spanning tree.</span></p>
<p style="margin: 0px 0px 0px 30px; font: 27px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> (ii) Write down the total weight of this minimum spanning tree.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Sketch a spanning tree of maximum total weight and write down its weight.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) (i) <em>(Kruskal’s: successively take an edge of smallest weight without forming a cycle)</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({1^{{\text{st}}}}\) edge DC (weight 1) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({2^{{\text{nd}}}}\) edge EG (weight 2) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({3^{{\text{rd}}}}\) edge DE (weight 3) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({4^{{\text{th}}}}\) edge EF (weight 6) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({5^{{\text{th}}}}\) edge AD (weight 7) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({6^{{\text{th}}}}\) edge AB (weight 8) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica; min-height: 32.0px;"><strong style="font-family: 'times new roman', times; font-size: medium;">Notes:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Weights are not required on the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica; min-height: 32.0px;"><span style="font-family: 'times new roman', times; font-size: medium;">Allow </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A2(d)</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> if the (correct) edges are in the wrong order </span><em style="font-family: 'times new roman', times; font-size: medium;">e.g.</em><span style="font-family: 'times new roman', times; font-size: medium;"> they have used Prim’s rather than Kruskal’s algorithm.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica; min-height: 32.0px;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica; min-height: 32.0px;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) total weight is 1 + 2 + 3 + 6 + 7 + 8 = 27 </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[8 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"> <strong><em>A3</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Notes:</strong> Award <strong><em>A2</em></strong> for five or four correct edges,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A1</em></strong> for three or two correct edges</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>A0</em></strong> otherwise.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Weights are not required on the diagram.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"> </strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">THEN</strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">total weight is 6 + 7 + 7 + 8 + 9 + 10 = 47 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [12 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Good algorithm work was shown; sometimes there were mistakes in giving the order of the edges chosen by, for example doing Prim’s algorithm instead of Kruskal’s.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The vertices of a graph <em>L</em> are A, B, C, D, E, F, G and H. The weights of the edges in <em>L</em> are given in the following table.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw the graph <em>L</em>.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABCgAAAQ2CAIAAAB+1htAAAAgAElEQVR4nOydS2xS29/3uW/ulAKleKAouksxRXe3r+huacQUk9LSRJq4m0gjTUoHxYE04kQ6EZ/kKSbSkTiSjg4mB2fiTBwWB+LsEaelQ3HyHBweeAe/9+yXP23pxV6o/j6DBjabvdYGutb6rt+N10AQBEEQBEGQ34N6vX7SXfh94Z10BxAEQRAEQRDkOEDVcbKg8EAQBEEQBEF+QZplRovkQAVyIqDwQBAEQRAEQX5ZOI0RCoVEItG1a9fW19dPtku/LSg8EARBEARBkF+QFotHJpPh8Xg8Hk8ulweDwRPs2G8LCg8EQRAEQRDk16dYLIrFYtAeQqHw4sWLtVrtpDv1e4HCA0EQBEEQBPml4GwdzUaPSqUCqoPP58Nfo9F4Qh38TUHhgSAIgiAIgvz6bGxs8P4TgUBw0p36vUDhgSAIgiAIgpxuds1SVa/Xf/z4IRAIONUBdo98Pn88PUQaKDwQBEEQBEGQzmdb76mtJ7RRIPV6XSKRCIVCTnXweDyHw3EUvUW2BYUHgiAIgiAI0tGAnFhaWnrx4kVjDxpj27c3Gg2RSNRs9ODxeNevXz+aLiPbgMIDQRAEQRAEOQWAVJDJZG3Oaa9GRCIRZ+sA+vr6DrubyI6g8EAQBEEQBEE6nW/fvoGLlEAgsFqtjd18rraFIAiBQNBs9Ojp6TmiDiNbQeGBIAiCIAiCnAK4VFQikcjr9bY5cyftMTIyIhQKm4UHJrY6TlB4IAiCIAiCIJ3Op0+fuPobUAGQYZj9XiQajQqFQogv53JbYRnBYwOFB4IgCIIgCNLR1Ov1SCTC28LU1FT7d209qNfrW+LL0+n0kXUc+Q9QeCAIgiAIgiCdjsViaVYLfD6fz+fbbLb9Xsdqtcrl8mbLydZz9p4vC9kXKDwQBEEQBEGQjiYcDg8MDHCWCs7nymQycefsUS2wLNssYBQKRTgcbj4BVcfRgcIDQRAEQRAE6WjMZrNYLG5WHdzjxj4LemQyGYFAwF2Ez+cPDg4eZd+R/w8KDwRBEARBEKSjUalUzf5RgEQi0el0+71UJpNpqeYRCoW4V7nShGj3OApQeCAIgiAIgiAdjUwmk0qlzUHhBEFMTU1Vq9XGPi0exWJRLBY3J8jS6XSlUgmVxjGAwgNBEARBEATpaAiC0Ov1nLcVj8cTiUQymSwcDu9LMMDJXV1dkFEXItRFIlEymWw0Gv/880/LmcjhgsIDQRAEQRAE6WguXLggFApbXKT4fL7BYGg5c1fBUK/XNRpNs8WDx+OZzeatF0Htceig8EAQBEEQBEE6GijiIRAIhEJhs/bo7u4+wNWUSiUYOjj5odVqD73PyFZQeCAIgiAIgiAdTblc5kRCs/BoH1y+rckCLB4ikag5OS9BEEfWd+T/g8IDQRAEQRAE6XQgIhxUh1gslslkPB7PYDDsKw8VnNPd3d2SmVej0aBj1TGAwgNBEARBEATpdLRaLdgoCILQ6XQ3btwQi8U0TTf2GYxRr9fNZjPvP5HL5Q0M7Th6UHggCIIgCIIgnY7X622u4GEymaRSqcPhOIBOiMfjfD6/OVxELBY3n4Da44hA4YEgCIIgCIJ0OhaLpdk5SqFQ9PX17XRye+VQr9elUmlzrIhIJHr9+vUR9Br5D1B4IAiCIAiCIJ3OxsYGZKMCqSAUCqVSaa1Wg1e3Ko0Wvyl4EI/HHz9+rNPpmmsRQqzIp0+fjvFuflNQeCAIgiAIgiAdTb1ez2QyEomEK/y3a0qrRqOxvr7+9OnTcDhcq9WcTqdOp2vJxgsIBAKCIBwORwOdrI4YFB4IgiAIgiBIp8OybHMNQT6f3154TE9Pj42NURSl0WhMJhNN0yBadoIkyWO7l98WFB4IgiAI8ivQvFO7067tXpL24I4v0pnQNE0QBGfugAqAhUKh+ZxgMOjz+R48eBAMBsVisclkEovFIpFIJBJJpdI2qoPH4ymVytXV1ZO6u98EFB4IgiAIcmporygO8N69H0SQE6RerzudzuaSf/DX5XIFg8FsNluv110uF5wAGas4Nyo+nw/OVNvqDc7zis/nj4+Pn/SN/uKg8EAQBEGQ08Ee9UB7LbFrDO4BWkSQI6L5F9jb29usEzi10NvbOzY2trS0ZLVaQWNwsqRFY0DNwZ3g8/kURZ3gzf4OoPBAEARBkFPPTnJijydvfQklB3Ii7CSA6/W6SCTaNjRcKpWeP39+J4NGs3mEYRiVSsUpk62Uy+Xjv+XfChQeCIIgCHLK2K91YlubBkoLpDMBmdFo+ol6vV6DwdDGWEEQhEqlanMCIBaLjUajwWCACHWAe1WpVJ7off8WoPBAEARBkNPHzwSI/4zLFoIcD/Dz8/v9crm8JbRjq0Gj2Riy1ReLQy6Xe71ev98/MzMjkUiaozvgb0vryKGDwgNBEARBTj17SVfV5vz9vh1Bjofnz5+3yIkWMwWHXC7fNm+VWCzmlIlGo0kkEqurq48fP45Go1wkOnfy169f0dvwSEHhgSAIgiCnlVevXlWrVXj8/v375pfg+JMnT/L5PPdSKpX68uVL82ktq6tQKJTJZLYeR5CTQi6XN5svdjJ98Pl8sVhsMBi4fFaQ2wpy6RoMBplM5nQ6G//+tm/fvg2apPkKyWTypG/3FweFB4IgCHIK2FdUw09Wq+AqA+TzeXiQSqWaT8jn89xyf1sqlUqj0Uin058+fdraUKVSiUajkUjk7du33MF37941Go3Nzc02Pdx6hKbpbDY7Pz+fzWah0WQy+ejRo2Kx2Gg0NjY2isVisViMRqNw/t9//53L5arVal9fH6yxyuVyKBQqlUrJZHJkZMRqtUYikXq9HgwGQ6GQx+MJBALhcJj7KFqAhur1+tTUVCKRqNVq0I2tHW4J291LXuC9f4Mok34xmr9QhmF2ylLVjEAgkEqlBEFwwkMoFPb09Ph8vrm5uUgkEo/Hm5t48OCBVqttjgyRSCSxWOzY7/X3AoUHgiAI0um0iYredf3afvleLBY/f/68uLiYTCY5LwtOVLx48YJ78O7dO1AFyWQS1tbr6+sfP37k1tmJRIJl2Uaj8fbt20Qi0Wg0wJv848ePLY2+efPG6XSOjY1BW9++fRsZGbl3797CwoLP5wuHwx8+fMhms41G4/Pnz3BNjr///vvr16+ZTCadTtdqNZqmy+VyNpu9d+/e9PR0LpdLJpNPnjz58eNHrVZLpVLQk2Kx+ObNm97e3lQqVSqVnE6nXq93Op2hUCiRSFit1kKhkE6nl5eXx8bGPn/+HAqFkskkRVFwDtd0o0mDlUoleFAoFG7dugWK5dmzZ9PT01++fAEdlc1mnzx58uHDB3hjKpUql8vwgRyYXZP/ogj5NeC+zWKxuGvtP8iiy+PxFAqFSqUCiSKVSu/fv7/T6JHNZi9cuOByubgrQIwH/oqOFBQeCIIgyClg62pgL9JipzVEvV6vVquJRGJqaophGNjdb94QLRaL2WyWYZhMJrO6uhoOh588eRIMBmmaDoVCf/31V6PRmJubm5iYAHGSSqWi0ajH4ykWi6VS6d27d4VCgaIolmU55w1OokQiEa/X63A4isXixsbG3NzcysrK1NRULBazWCw0Td+9e3dpaWljY4Nl2Vwu12g03G53Op3+8uVLPp8fGRm5ffv2rVu3gsHgnTt31tfXG40Gy7IulyuZTMZisdHR0YcPH66vr6dSqRs3bjx9+tTlcnm93p6ensHBwUgkYrFY7HZ7f3//lStXVlZWzp8/T9N0MBgslUrQXDabDQaDVqv1/v37Ho8nk8k8fPjw/v37IGwikQgImFgs9ubNm1evXtnt9kAgkMvlSqWSx+OB0tGNRiMej4M+KZVKgUDA5/MxDJNIJFosSLsu8trn48IKJL8YW/+1p6amtnpbNR8B4SESiSwWSy6Xc7vdc3NzWy/Y/NTn8w0MDAwMDHAXFAqFr1692vYtyGGBwgNBEAQ59exFaTQajVQqVSwWV1ZWWJb9P//n/9y+fZtl2WAwWCgUHA6HxWJJpVLpdJpl2WKxaLVae3t7g8HgwMDAyMhIIBCIxWIOh8Pn8y0vL+dyuUgkcufOneHh4Wg0GovFLl68+Mcff8zNzYXD4XPnznk8nlQqtbq6Ojw8HIvF3r9///Xr10gk8vr168nJSZIkSZL0+/2vX78eGRkxm83z8/OFQoFlWZIktVqt1Wr1eDx2u52m6Wg0GggEhoaGvn79Oj8/f/bs2d7eXr1eL5fL1Wq12WymKMrr9ZrNZpZlHz58aLFYPB6PwWAYGhoaHR2lKMpoNLrdbrim3++3WCwOh0OpVMpksp6eHpvNZrFYfD5fLBZzuVxGo/HTp08kSdrtdp1OFwqFZmZmkslkLpdbWloKBoOxWCyVSn348AEMJmtraxRFud3uQCCQz+d7eno0Gs2VK1ey2Ww8Hn/16hWouHw+f/78eafT6XA4rly50vztFIvFQqGQyWQqlcrPlGZvORnXjqeXrd+dUqlsERs8Hk8ul2cyGY1GY7VaOS+pPaaN9vv9BoPh8uXLzdccHh4+ittBOFB4IAiCIKeDXYtRND9eXFwEZ6RqtQrR0pVK5d27dysrK7DIfv78eSwWMxgM0Wg0n88zDHP27Fmv1yuVSoVCoUKhEIvFVqvV4XC4XC632y0SiSQSicVimZqaunv3Lsuyt27dcjqdFotFr9ebTCaHw6FWq41GI6zXR0dHwUzBsmwsFotEIuFw2OPxBIPBiYmJ/v7+UCg0NDS0trbm9/uDwaDT6bRarTdv3gSjyvXr1/1+/5UrVwwGw7Vr15LJJEmSk5OT09PTSqUS4mUtFotKpVIqlQaDgaKo8+fPX758mWVZOG4ymZxOJ8Mwjx8/drvdLMsGAgGLxWI2mwcHB202W29vr1KplMvlKpVKpVKZzeZLly4xDKPVas1mM4/HE4vFCoXC6/Xq9XqSJCORSCwWM5lM169fz2QyDMPY7Xa/359IJOLxOE3TXq8XBI9arZ6dnb19+zbDMCzLvn79OpVK0TTNMMz8/DyYXwKBQLFYhK8Gokqi0WgwGIxEIul0+gAyY78vIR1Oy3f36NGjFkOHWCz2eDzfvn3b9vxtjzSzuLgol8t1Op1IJOKiRHQ6HVgm8ZdzRKDwQBAEQU4Z2yqQfD6fTCaz2ezz58/BsSeVSnm93lqtFgwG4RyWZe12u8ViicViDMO8fPmSJMm+vr6RkZHp6emhoSGDwSAWi2FZD7GqPT09586dAz8liqLsdns8Hr927drY2BhJkpcuXerq6rLb7VevXmUYRiqVKpXKhw8fjo6Ojo+PUxRFUdSVK1dMJtPZs2fHx8dfvnwJy2uPxxMKhRYWFtxut9FodLlcHo/HarX6fL579+5RFHXmzBmHw2E2mwmCkMlkYKNgGMbn89ntdpfLZbPZpFLpuXPnHA6HzWYjSbK/v59hmHQ6HQwGnz17FgwG5+fn8/l8KpXiQsNrtVoul0ulUqFQKJfLzc7OhsNhr9c7MTFx5syZvr4+s9ms1Wp9Pt+nT58CgYBarfZ6vSqVSqPRjI6OrqysgCgCSSORSPR6vdlsdjgcfX19w8PDS0tLNpvN4XDAxzU7OxuLxe7du5dOp+12+8WLFy9evBgMBh8+fOh0Omma9ng8yWRydHTU5/PRNB0Oh0ulUiKRyGazyWTyzp07XITJwWomIqeali8RKm+ArQMiyB0OR6Op4GCb9259yWaziUSilsRWAoHA7XYfwa0g/w8UHgiCIMipYdvFRDabDYfDLMvOzs5WKpU///xzbW3N4XD88ccfoVDozZs30Wj09evXiUTi+fPnPT09er1erVYTBAFGDLlcrtfrr169CilxNBqNUqlUKBQCgUCpVMbj8ZmZmVQqZTAYXC6X3W6PRqMDAwN9fX06nW5oaEgikeh0OoqiPB5Pd3e31WrNZrNSqVSlUvX39/f19RmNRnCL8vv98/PzExMTsPff398/NDQUiUSWlpa6urpcLlehUAiHwwzDdHV1DQwMMAyj1+vFYrFSqVSr1VarFewDO30OtVptp5f28jFufaler5fL5c3NzXg8zkVrwEHwSQsGg5lMJp/PQyTMyspKOp3+66+/kskkmIlWVlaKxeLq6ur79+/7+/uj0eiFCxfAeDI0NMSyrN/vJ0nS6XS63W6SJAOBwPLy8vz8PLixTUxMpFKpt2/fvn79enZ2Fr7rcrn87t27t2/fQvx9o9FIJBItScZQdZx2to3gCgQCXB4qTn7UarX2nnU7hYexLAv5dpsrD/L5/OZcc8ihg8IDQRAEOR1wwdnNCVsbjQZN02az2WKx3LhxY2ZmJhwOv3jx4vnz5xAjwTn22O32SCSi0+kMBoPVaqUoymQySaVSi8VCEATDMDqdzu12Q0CF3+9Pp9MQFw7LlEKh0NIuLHYrlUosFrtz5040Gi2Xy7A6f/LkidfrhVSz2Wy2VCpVq9U28Sdra2vc00Kh8ODBg1gslk6nQ6FQMBgES077BL4HoE28/tbTtoVb8zV2WCkC3759g1D+aDQ6NTWVSqXsdns4HA6Hw06nU6lUWiwWmUymVCppmu7v77906VIoFFpaWoIEYm/evDGZTEaj8dmzZ9lsNpfLgfdaMpmEtF3xeNzpdNpstmAwmEqlksnk7Ozsq1evUH6cRtr8m+TzeZvN1lzFXCwW7/fKHH///TdIF4lEwnlbqVSqW7du/fxdIDuBwgNBEAQ5CG0WrHtc8O19Xci5J8ViMah/B/HKpVKpVCqFQiGHw2G322HvnGXZmZkZiPYGZyGtVqvX63U6HcuyHo+n+cqwmgeFgBwb9Xr9zZs379+/d7vdOp2up6dHLpdPTExAyLtSqbTZbNevX0+n02632+FwaLVakIWhUCgSiUxPT7tcrnQ63dfXl0qlAoFAX1+fUqnU6XTT09M2m81qtT548CASiUQikWQyWS6XFxcXvV4v5OzabxKtvZ9wKJHxp50jvVmNRtPsFsXn81v+o/fVukAggJqDENwFYkYul3/+/PmwO478P1B4IAiCIPumzT53+7xSe7x4tVqNx+OPHz/2+XyJRIJhGKPR+ODBg0ePHnF16B49egT5qSCl0tDQkE6nU6lUOp3ObrcrFIqrV69+/fo1HA77fL5gMJhOp7ftUputeuToaP607927t7S09PfffycSCZIkOauU3W5XKpVSqdRkMqnVapIkoaahy+Xy+XxarVar1VIUFQgEGIYxmUwEQVy/fp1lWYfDEYvFIJ7+3r17fr//0qVL9+7de/ny5b179x49ekRRFIiQRtvf6l58ePZ4p7/Vr2vvXk/7olAoaDQagiBAdSgUCoIgSJI8cN9IkiQIQiAQgIMlBKwTBPFbfVnHDAoPBEEQ5IDs0dCxx1m8WCxyZ0IV7YmJCbfb7fF4LBbLpUuXAoGA1+u9c+fO6upqKpUaGhoaHh5+8OCBTqczGo1//PEHxEKo1epwOJxIJKDe317WOltvBFceR8quX8e7d++i0ejY2NjZs2ch8t7j8Vy4cMFut0PQS3d3t9lshmAbSCNGkqTFYiFJ8s2bN5OTkwMDA36/3+/3T01NsSw7NjYWi8UymUwgELh69arFYrl+/brX62VZtlQqRaPRZqvXX3/99f3798Z/KpDfUD8cBT/5AYJOANOEUCjs6urq7+/f795B8zgjkUhaioEIBIKvX7/+TCeRNqDwQBAEQfbHrpEA7ad/MFlAdPKbN2/W19fn5ubevn0LaW39fv/79+8hvAH0g9frdblcFy5cmJqagpJ2Xq/XarVqNJqhoaHe3l6JRAKJbjUazcjISEskxr5uCpeVx8beZSp3pFKpPHv2zO/3379/f3FxEQ5CcfSFhQWDwcAwDOQoe/r06eTkZC6X8/l8er3eZrONjo7G43FIanz9+nW73e71erPZLISLhEKhUqkEDVWr1WAwGA6H4fpv3751u91cFcgD39Fv+NM6iluOxWJSqRRiwQUCAUEQoVBoX55RLb2SyWRc0IhOp4NYo62nIYcFCg8EQRDkcNjjVF2tVpeXl8GvJhQKPXv2DHxgAoFAIpGo1+vJZNJqtQ4NDZ05c8bj8TidzrNnz5IkaTabu7q6dDqd2Wy22WxqtZqiKJqmDQaDQqHgMj7tvZPbbpTiguOo+fnooG0vmMlkEonE+/fv4eDjx48DgcDAwMDw8LDD4UilUlB45Pbt236/f2RkBKJEIBJ9ZWVlc3MTUmYlEokHDx4sLy9DOZFcLufxeLxer8/nI0mSpmnIvjU+Pr6XO/oN2WowPKzPpF6vv3z5Ui6XN9caN5vNPyPtILcVXK2np6e3t9fv9x9Kb5FtQeGBIAiC7JVdp/ZSqRSJRFKpVDweh5iK5rcUCgWoGffgwYPv378PDQ35/X4oJTE5Oel0Ov1+P0VRFovFbrdbrVaj0SiVSiE03Gg02mw2qDJhsVi8Xu+2vWpeguwxaezWNyIdxb6ig5qfbmxsPHv27MWLF/l8vlgsDg4OkiQZDAYhUUEkEoF8vgzDBINBSArMsizDMNFoNBQK2Wy2ly9fLi0tBQIBj8cTj8cHBwfPnz/v8/nOnz9vNBovX74cjUb//vvvlg7sKm5/Sbb9n6pUKpDnjTvyk5+DQqFoKSOo1+vbd6N9V2u1mlwuh0sRBHH16tW+vj4ukAw5dFB4IAiCIAfn06dPd+7caTQamUwmGAzeu3fv5s2bUAjP6XRms1kQIbVabWNj4+nTp36/32QysSybSqUgi5HT6YS8t1arVa/XEwRBEIRKpRIKhQRBKJVKjUZjMpmUSqXL5Xr9+vX6+nrLUqb5wU7rvL3ril9+gdj5bI2saDm+7fnc351cAZPJpN/vn5ycdLlckUgkFAr5/X6bzXb//n2XyxUKhS5evMgwTCgUgniPXC735cuXQCAQCoWgAj1N0yzLTk1NXb58+ezZs0aj0e/3O51OiqK4oiKNtj+2X/7Xxd1gPB73+Xwmk8lsNr9582ZwcFAkEmk0msbPfQgQWc7B5/MVCsVP9tnn83F1PAYGBi5cuBCLxX6yn8hOoPBAEARB9kHLZPz48eNQKLS4uAge9jMzM0+ePPF4PGazORgMfv36dWVlJRKJfPnyZWJiYnJycmpqSi6Xm0wmm802ODh49uxZs9ms1+stFotarTaZTGKxWCaT9fT0sCwbDocLhQJXeHvXdUB71dHmRtrEFSDHSRv7wH7jhrdd/cPTbDYL9UDq9Xq1WgWDBqTScrvdICEikUixWJydnYXaIFzNxHg8XiwWfT7f+Pg4WN7ARqfX66vVanOtFZDiXq/XZrOFQqHf5xcFd2q1WgOBgE6n4/P5fr9fKBSqVCqZTKZWq2FZfzAg91SL9jhwJ4FPnz5BP+GCMpmsUCgcuIdIe1B4IAiC/OK0cf9o7Laea//qu3fvOK96mqavXbumVCoHBwe1Wq3BYFCpVE6nMxgMOhyOK1euMAzDMIzD4YCElTabDSo23LhxQ6VSSaVSiqIKhcKjR4/i8fjP3jOC7JlarRaNRkmStFqtwWAwGo1Go9HJycn79+8nk0mapqFYIcSX12q1RCKRyWRevHjhcDigdrvf79fr9VypR5qmnU7n0NCQxWKB1FtGo9FkMoXDYaguvy/aKKitjw9wqUMkmUzCHoHH45mcnBSLxc3ygCsQPjAw4HK5KpUKwzB7DM3i8Hq93AXBz0ogEDR++qYoioIQc6jsAQd/H614nKDwQJBfEAyZ/ZXYi7fJHr/x/WbdWV1dbTQa4JQCTs+5XA4SyMRiMYjBTaVSpVIpnU7HYrEbN27QNK3VaqVSKUEQXq9Xr9cPDQ1FIpGBgQG9Xg8rMKVS2dXVlUwm7XZ7Mpl88+bNw4cPt26C4i8WOQZafmZbKwxGo9GnT5+CoSObzd6/f39ycjIcDi8vL9+4cePKlStXrlwxGo3ghWWz2SYmJnp6epaWlkKhkNvtHh0dPXfunMlkgip1oMNpmoaQkomJCavV2lxhpo2L4K4xS+3/wQ/waez69uaXyuWySCSiKMrr9S4tLUEwBmdGgDU9l7VWpVIxDAP5oz59+rRtK9veeyqV0mq1nGeUXq+Xy+VcSMaBB41cLmexWIRCoUgkGhkZ2cu9IwcDhQeC/LLsGtSIQ+op4p9//jmsM7eKk2Kx2Owi0mg0IpHIhw8fYAKu1WoWi8Xj8eTz+Wg0Clu2T548uX///sTExOLiotvt1mg0Wq12dnb28uXL4DqlUqlYlpVIJOfPn4cyf9evX//zzz+5htrrIvxxIsfGHuO/i8Xi8vLyxsbG5uZmLpd7+/bt6OgoGEncbjcErAcCgcHBwZs3b66srBQKhVAoFAgEVldX/X7/xYsXC4UCuHWBAvn69evGxkahUIjFYmDle/v27Y8fP8Ri8aVLl+LxONefYDC4tYeRSKTx78bE8vIy91Imk4lGo809L5fLEOfdfPDHjx+7fiZtouRbXgoEAiqVCtIWi0QirVbbbO5otlE0P1Wr1eB/FQqFdmp665fy6tUrTsPApZpjwQ88dBSLRaPRaLFYwAfvYBdBdgWFB4L8mhy1SR05TnYNXdhXbEPL8Xw+//LlSy6D5Lt376rVaigUKhQKq6uri4uLLMt6PJ5isfjly5d0Or2wsPD48eOJiQmn0ymTycC7XaFQnDt3bnBwUK/Xm81m0B7pdJqiKDBltCx6dvp97rrmQJBO4MOHD/V6PRQKOZ3OUCjkcDgikYjX671582YgEHjy5Emj0fj06VM8Hs9ms4VC4fnz59FoNJfLxeNxm82WTqfn5uaCweCjR48ikYjP54vFYuCIGI1G5+bmxsfHk8kkZPuNRCIkSUYiEZATIN3T6fTAwMCXL1/u37+/vLysVCo3Nzfr9Xoul+vp6YnFYtVqFf71EokE2BsDgcD6+nqtVtPpdE+fPmVZ1mKx3L179927d41Gw+/3b1urZFcXr3q9/l//9V8KhUIgEIhEohaBIRQKedsBdg94TNM0wzDPn/jcmSUAACAASURBVD9v33TzkWg02nw10GBt3rjrfQGrq6uwsYIT6NGBwgNBfiO2nTNOrjvIIbB1G7LlSK1Wa7FmcCcUCoUPHz7Ag2w263a7LRYLRVHhcDgUCsFmLVRbY1kWImXtdrtUKtXr9d3d3Wq1GtJPqVQqs9l88eLFSqVSLpe/f/++1ZG9vbfGtnoDf5zIcdLGy6jNT7FSqYTD4e7ubgg0J0kynU6n0+nl5eVisZhMJuG9LMt6vd58Pp/NZiGrWzgczufzV65ccbvdDofj/v372Wx2bGwslUoFAoGVlZVMJpPL5VZWVu7du3fmzJnFxcV4PB6NRimKgg3+aDQaiUTcbjfUw1Gr1SBszGYzxEqdO3cuEAhYLBaXywWNTk9Pg4ApFouRSOT69etqtTqZTMZiMZZlu7u7SZLM5XJLS0vfvn2LxWI0TbtcrlQq1TKGtMDj8UQiESckBAKBRqMRi8XguSQUCkF+tFg8WswgOwWdbys/Njc3NRoNvJcgCC6j8X4HDRxkjh8UHgjyK9PGUN7AMbfj2aP5og3FYnF9fX1tba3lvWtra5cvX15YWHjy5EkkEnnz5k0oFLpz58709LRer7fb7b29vVarFXzTNRoNQRByuRzS3QoEArlcrtVqTSZTX18fQRA+n2/btPd76T/+GpGTpf0g2djbL3NjY+P169eNRgPy8KZSqWQyWSqVKpVKoVD43//932vXrlksFrfbHYvFfD6f3++/evWqz+ebmZnx+/00TS8uLg4MDFAUFQgEIIDq06dPmUzm8+fPCwsL8N8aDAZXVlZAQuTzeVAFHo8HMlY7nc6FhYWHDx9CCZ1z585x9TctFovFYoH9hVQqlUqlVlZWbt68OTAw4PP5XC7XkydPvF6vy+UiSTIcDlutVo/HYzQaNRqNRCI5d+7c6urqwMCAzWZzOBzpdLpQKMDVOK+nZgwGAyiN5peaVQf3uOWBVCo1GAx7+Y7q9XoymQRtA5Uc9zWAtD8Zx6IjBYUHgvyawNCZSqW+fPnCPW12d8EF36ngwN8OpASF8NYXL17AwWKxmM/nE4mE2+1mWdZut6dSqUgk8vbt23v37s3Ozvb396vVapqm9Xq9RCKBef3cuXNisdhqtZpMJqi0pVarR0ZGnj17lsvldq20tau7FwoSpMPZow5p81KxWJyfnw+Hw6VS6f79+xqNRqFQ0DQ9OTkZCATi8XgmkwEVMTk5mUgkVldXuXRPkUjkypUrg4ODPp/v0qVLZrPZZrN5PB64AsMwiUSiVCp5PJ6VlZVUKhWLxSA3FxRDDAQCIyMjAwMDz549azQaX758gZTBr169CofDPp9vcXHxzZs3JEmSJHn58uVYLDY4OBiLxVwuF0VRDMPQNP348WOhUKjVam/evBmPx4eHh51OZ6FQqFarXK4q8LMCvbGtcWMnnyuapnk8nkQiUSqVAoFgampqj//+uVxuenp6J4vurmwNXsfR5hhA4YEgvya3bt3q6+szGo16vd7r9ZrNZoPBAFtusK/G+fQjp4Ktrg5wJJFINBqNbDYLT1OpVKPR+PDhQyQSgfVKKpWam5uDtPQ0TadSKYqixsbGSJLU6/VKpVKtVrMsS5Lk4OCgXC5Xq9VOp1OtVkP6S41GY7VaFQqFSCRyu91+v5/75Rw4acGuSzec/pHjZ78L1m0Ptg9e4iiVSu/fv0+n07lcLpVKgWsihKdXKpV8Pu9yuZrPHxkZuXbt2p9//ulwOCiK8vl84A/pcDhYljUYDOFwOJFIgNUlFouBzcTv90OqXyiACAm7EolEIBCAnFqxWAw8Kr99+0aSZCwWg2S4oVDI6/V6PB6GYb58+VIoFHw+n81moygKai9mMplIJOLxeDKZjEaj2aPGaKM9AKlUyufzu7u7D+Vrag8OMicFCg8EOcXsNL3J5XLYhdpp2wmOi8VirmDCfl0LkDY0B1rs941tXgWDVTab/fPPP+HI58+fFxcXwdXbbrcnEolz587Nzs6urKwEAgGj0ejxeNxuN03T4D4BRf3cbrfBYAiFQkKhUKlUgqKAkuFGo1GhUHi9XrvdzrLs8PDwfrPsIwjyk1Sr1XQ6XSqVuCNra2uBQCASifT19dE0nc1moZTh48ePbTYbxKaXy+VgMJjL5UKhkNlsTiQSs7OzCwsLHo8HYt8rlcrTp0+dTmcgEIDLRiKRVCrldDobjcarV6/gYD6fh9Rbfr+fZdl6vf79+/dz585dvHgRBAzEoFcqlXfv3tVqNY/Hs+0swxlA9iI8mp8eSl0OpGNB4YEgvwjcMN1cgXXXsV4kEp1st39VDmAN4F7a2Nho/Gu74I4nEoloNAqezVxVXQhL7evri8fjJpMJkt7K5fK+vj6TySSRSMBeYbfbtVqt0Wh0Op1Op1OlUgmFQpqmRSKR2Ww+e/bsrVu3DAbDq1evarUa1O5AEOTE2ZooAgQG5IQol8ubm5vZbLYlJjuTyYCnZb1eT6fTfr8/HA5//vy5UqlAxQzgn3/++fjxY7VaBUsIXL/RaCSTyYWFhVQqlc1mOQNOLBazWq1ut/vbt29gXIWXksmkVCq12+0EQXAF+Hg8nlwu31pifC/ag8/nc7MS2j9/SVB4IMivQL1ef/nypdVqValUexniW9Idbq2ZhfwkB3DbSKVSYF4Ih8OfPn1aW1urVqv1ev3Dhw+hUMhoNLrd7uXl5XQ6fePGjc+fP6dSKYfDYbFYjEajSCRSKBQymQzKaQkEAoFAIBQKCYIAealQKAiC0Ov1/f39vb29/f39kLGKqw/Q0hn8MSBIp/GTCUK4XHPt7dstBluoC1Qul0mSpCgKVMc///wDZUBompZIJFwW3dHR0a3lO/YlPHg8nl6vX19f3/bGkV8AFB4IcrqJRqNQuA12voVCIRfY18bVqmWHSaFQhMPhk76V35darQZ5aaCAMUVR2Ww2n8/fu3dvc3OTYRifz6dSqc6ePfvXX3+RJNnT08OyrE6nk0gk3C4jONeJxWKNRiOVSkFsXL16ValUSqXSvr4+iqKePHkC9Qe4pndN6YMgyPFzKGmX2giV9rEo2zqLsiw7MzOTz+ebX/L7/dvuZ22VE3uZieCBUChsrsuBw9EvBgoPBDndqFQqPp8vEAhomlar1e1HfJFIZDAYjEbj1ldFItHW2gvIz9MmpWylUnnw4AE8rlarf/755/T09MOHD8Ph8KtXr1ZXV10uVzAYhGwzBEGYTCaz2QwygyAIiP8WiUQURb158yaTybx+/Rqky+bmZnMw+r7S8qL8QJAT5AAZtPbrkrRr7HvL8Wq1WiqV3G53c0wg5Mqbm5trcaniJhfIgLcXydH8FELMKYraYw+RUwcKDwQ53UxPT3OjNudl27KHRBAETdPNVWm3Ta/u9Xq5E3CUPyx2SoAD6fwfPXrUaDSgRPHm5ibLsoVCoVwuz83N0TQ9NDREEASk0ufz+WazGcxZYN8gSZJzlNrL99VGfhxgZxRBkENnL6ldW8wRe3m808G9/18vLCyQJAkeUKVSCeqBOBwOgiA4wdBGVOwRbv5iGOYAnUROBSg8EOR0k0wmef+auVuyp8PWUTAYbDFlxGKxbWs5GY1GHOKPmkqlkkqlXr58OTY2lk6nIem+0+mkafrz589qtdpkMs3PzxuNRpqmdTqdVCqVSqUEQQwMDDgcDkiXuba2BiloWpYpe09NtsctT/w9IMgxs/f/3DbGyZ/5z21+Lzd3gNEDqpGm0+mBgQG/36/X66FQ4M/TXAlEIpEsLCwc1u0gnQYKDwQ5xcBwbDAYmveKuKFcrVZDGd1m/H4/wzBbT4bwgJO4id+CcrmcTCZjsVg8Hg8Gg1AY+Nq1a/fu3RsaGjIYDDKZzGKxiMViiURiMBj0er3L5VpbW3v79u3nz5/T6TT4UB3M/rBfj3AEQU6KQ4nu2G8TcOTFixfxeJyrM1utVmu1WqVSKZVK4GRF07RSqUwkEmq1WiQSiUQizr/3YCYOHo8nFArVarVer+euQxDEz98j0rGg8ECQzmWPc0w6nd46mmu12uY08Bzgj7utxaPFrfYXXobuayG+7Vp/j24MiUTi1atXwWBwfn6eZVm/3w/1gE0mE5QGv3jxokajaU5CZTAY/H7/VsWIIAiyL1rGrp0souCFG4/HGYZhGObx48fwNJFIQMaLeDxutVqdTqdUKhUKhQaDAZw/RSKRUqlUKBTNvrvt2VafSCQSu90O1QPlcrnL5dq78RY5daDwQJAOZV+L47GxseYB3WAwbPt2h8PRZl/q3bt33DV/+bH+ADe401vy+fynT59A5sE5UAAY5uxAIOBwOLq7u1UqldvtnpycpGnabrc7HI6LFy9CSQ0+nw+GjsXFxXA4vLVIOYIgyIFp1h7Nj/P5PE3TLMuWSqW7d++Gw2GSJPv7+wcHB0mS9Pl8BoPBbDbfv38fAszAmxcmEYFAoNVqh4eHLRZL+0q1LU9bVAqnN2Ak1Gg0iUTi5D4q5MhB4YEgncW+FsTNG1o+nw9mhVAotNP5Uqm0ZQ7gSpgPDw//bmHE+wrIbtmBA9dn+Ds+Pv7s2bMvX76wLJvJZKrVajAYTCaToVAoEAicOXNGKBRKpVKFQqHX63t7e2UymUwmk8vler0eSolzBQERBEEOi53stOVyudFoPHv2bGhoyGg0Xr16NZ1OX716tb+/X6lU6vV6vV6vUqkEAgEXYwYmDh6PJxQKhUKhRCKB+qTBYNDpdMpkMighdbCMumKxGCYvg8Fw9uxZyJf1u81Hvw8oPBCkc9njypg7raV+bcvbQ6EQJzxaJgOdTrffdk87LUKijetUs/b4/v079ziZTG5ubq6srExPT2cymbW1tbm5OYqirl69arfbR0dH/X6/xWJRKBScxoMtvaGhoWQyWavV9tIogiDIftk6gHCZcCORyOLiYiAQUCgUJElqtdpr1649fvyYZVmGYQwGg0ql+uOPP0BgiEQioVDY1dUFKbyFQqFMJvP7/cFg0G63u91urrl4PN7G4rGt/CAIonkvDKwfN27cmJqaOtYPCzleUHggSCey31oKu6Y3qdVq8/PzW+cAiORrzl34O9A+QqMltOPNmzctZ0IARqFQSKVSoVDI6/XSNO10OpVKpVAoBFOGzWYDFwLYQbRaraFQaC+Oyyg5EAQ5RGBICYVC+Xy+0Wj4fL6FhQWXy6VWq91u940bN0Qi0ZUrV8bHx0mS5AwaMEEIhUKFQkHTtM1mEwqFKpVKLpeTJDkzM8NdH0qbNxoNEDM7mTW2ag8QNrA1A6+qVKqpqSm1Wg253fc7DyKnAhQeCNJB6PX6/v7+loO7jrm7qo75+XmZTLZT/J/BYNhvi78GO31uiUSiUChkMhl4WqlUEolEOp3OZrP37t3zer0KhcJutxuNxlAoZLPZLl68aLPZPB6P1WrV6XRisZgkSYfDQVGUxWKBkvDtc+1jKlsEQQ4XGEBYlk0kEn19fePj46VSKZVKBYNBvV4vl8t1Ol1vb6/NZtNqtSqVSiaTcc5UEolEpVKBk5XJZFIoFHK5HFKBf/nypbHD6FQsFiHtFcwsarWaIIg2Fg+NRnPmzJmBgYGnT5/CCRKJBPLzyuVycEDFYfDXA4UHgnQQ4CZLkiRnFj8YLUtbMJe37DxxM0E4HP5tB/eWG89ms4VCIRqNxmIxiqJqtVq1Wg2Hw0tLSxCkodFopFIpeCTL5XKLxUIQRHd3t1gsJghCqVTGYrFisZjL5Zovy+0Itml62yMIgiAHJp1Oz8/PO51O8P8MBAIul0un04HflMPh0Gg0CoXC4XAIBAKxWCyTyRwOBwSXQy4+h8NhtVoDgQCUDtzLLlg6ne7r6+PxeCKRqM2GFwSR53K5cDhcq9VcLhdn9wCvVIqiVlZWwLsVx8ZfCRQeCNJBZLNZ3r/VANVq9QGusO0AbbfbIbpg250nqVSqVqsDgcBPd/80wX1QhUIhn8/n83lIpZLNZuF4Pp/PZDLLy8sOh4MkyZ6eHoFAoFAoFAqFTCYDhwTYojt79qzf7/f7/XtpDkEQ5BhgWRaGnUwmk06n7Xa7RCJRKpUkSer1erVaDRso4B06ODjY19cXiUQCgcCff/556dKl58+fV6vVg5UAgggQnU4nkUi2Cg8+n69QKFquANqD2yATCoVmszmdTmcyGZZlD+szQToBFB4I0llw9Zh4PB5N04eyYM3n85zJeyucIFEqlUtLSztdpAOXznss4tv+eCaTSSaTTqfT6XTWajVIjFsul1mW9fl8drvdbDZDtAZMojKZzOl0SiQSv98P5cMRBEE6inK5bDKZSqVSrVbLZrN37txxOp0mk0mj0RAEAbX/CIKA0WxwcNBoNDocjkAgAG6lXMHyXdk2ir1QKAQCAZ1Op1AoOC3B5/O1Wi0YXp4/f771UrVabWpqSiwW8/7Nc3X37l2z2SwSiV6+fLlru8hpAYUHgnQW0Wi0WRXcvHlz29P2WwLvw4cPMAFsm1i9+bHf74ewhJYr7Kvdo+NgPWm+i83NzVQq5Xa7i8ViJpNZXFx0uVxWq3VmZqZcLodCoXg8HggEIpGIy+Xq7u6Wy+VGo1Gv18/Ozrpcrrdv3+63dQRBkAOwa+2/RqNRqVS4I5D3IpvN3r592+Fw3Lp1C0yykD9KLpeD5DCbzf39/V1dXWNjY3Nzcy6Xa2BggGEYqCT4k7212+0zMzNerxcqDIrFYpFIBFMM6Ic2QW71ej0SicBUBVZlsP9fvXq1VqttLYmL4/BpBIUHgnQW9Xpdo9E0iwGfz9dywsEyroIT7baSowWhUNjS6OmizSezubn5/PnzO3fu3Lp1y2AwBINBlmVpmoaUkZFIxG632+12jUaj1+uFQqFGo6FpmiTJNluAOPkhCHLUcCN/oVBYWlrKZrNerzcajaZSqVQqlc/n5+fnGYYJBAJ2u50gCI1GA2YNKJEB5f+USqXRaIzH4yzL6nQ6qVRqNpvz+fxeEu7thVQq5XK5bt++LZPJwHAhk8nUajUInjYXbz6eyWSagxKFQuHQ0FDjX1m1U3ES5LSAwgNBOo6HDx+2GCUSicSBLQ/Nb3Q6nQqFAmYjlUp18eLFrq4uo9HI5TNpbrQ5aOGwpqVDYWvZjb13b2xszGAwUBSVy+WsVuv169fPnz9vNpslEonJZLLb7QqFQqlUqlSqCxcuQPbJPXbpADeCIAiylTaZJ6rV6pkzZ6CYxsDAQDQavXv37sePH6PRaCgUun79end3NzhTcXF9UAfQbDY7HA6j0Xj9+vXR0VGFQuH1et+/f79tK+0HtDavOp3O2dlZq9XKMIxYLIZ65FAGRKPRtL9a82WDwaBYLOaybGk0GrDGpFKpvXQD6WRQeCBIJwLZ0DkxoFKpGoe001MoFFiWzWazlUqFO5hOp51Op1QqbXbHEggE0Wj0J2/k0DmAAKvX67FYbGNjw+fzpVIpiqJ6enqGhoZUKpVGo4Ei4rAXaDabh4eH29QRbynxcTi3hCAI0mg0dhtVQqFQX1+fVCoViURWq/XSpUt3796dnZ2t1+sPHjyw2Wy9vb1cRloYw3k8ns1mU6vVFouFoijwKW2pktHc9IFdWOEvwzCRSMRkMlksFqFQCF0FYws0utP9bn3gdrtFIhGfz5fJZAqFwmq1brsThOPwqQOFB4J0In6/v8X+EAwGuVcPMDfs8VWLxeJ0OpvDAbfWFekc2siP//mf/xkeHuaysuTzeZfLpVKpDAaDUqkUi8UajUapVPp8Poi2lMvlHo+nXC7/TNWUnQ4iCIL8JNls1mg0gilDLpc7nU6SJM1ms91uD4fDZrMZKvEJhUKBQACuTbDit1gsUJejORqkDQcexKrVKkmSiUTC6XRSFNXX19dcG2SnVrYVPPD08ePHBoMB/MRUKhVFUdevX//48WPnxBwiBwCFB4J0IqVSCXxkOQiCiEQijaPfbk8mk1qttrlpl8t1RG39DNt+DuVy+e3bt9Fo9NatWy6XC/LEj46OBgIBtVqt1Wo1Gg3U4oWsKSzLwqfapoltG0XVgSDIMZDNZrmg6r6+Pq1Wy7JsLBZbWFjwer1ardZsNptMJpVKpdPpIBTbYrFEo1GVSgW1xh88eODxePbe4sHEydLSEsuyDoejWq0uLCxIJBLImtVstN9Xi3CwVCpBeSuw3giFwvHx8T12EulMUHggSIfy6tWr5rgL2PL5yWKue4yF0Ov1zcnXBQJBG++jE4HrfKVSKZfL1WoVnlarVYi5tFqtBoNhamrK6/VC9luIsCQIQigUEgQxODiYTqfbXBz9qRAEOSkgkBqo1+uZTCYQCIyOjmq12lAo5Pf73W43TdPd3d3d3d1cJgyZTGa1Wn0+X7lcTiaTzRER3KWaHxzK+AYXMZvNFEWFQqFYLOZwODjDC8xiZrN52w5s27cW0uk0Nx/x+XyDwQB7YTg4n1JQeCBIxwHj6ffv35sze/B4PJFIdPv27caxDLgajaZZe2wbZPKT/KR8KpfLjUZjfX29XC6/ePECXvJ6vRRFURRlNBopinK73TAXSqVSmUxGEMTk5OTWnIy/IThnI0gHkkwmYRulOb6uWCxGo9FgMGgwGHQ6XTgc1mg0LpfLbDZrtVqdTuf1epVKpVarNRgMJEnG4/GjdkZquez8/LxYLDaZTEql0uVy9ff3Q+AcN4U1384eu9R8WjgchlJUYrHYaDRqNBqv17vtPhqObJ0PCg8E6VDq9fqVK1d4TQX+eDye0Wg8orZanjIMw9lb4MHi4uJRNL1tB9q/BPt/3I7g8+fPIYTD5XIZDIauri5I4KjT6WQymVgsFovF3d3dv1tp9jbg3Iwgx8Ze7My1Wo1hmLGxMaihtLm5GQ6HIYV3OByORCKQkVYsFhMEASVN7Xa7TCYDzyuPx+N2u91u96tXr2q12vGswrmLr6+vQ/ic2Wzm8/kajUahUOh0OjAywySy03vbX7z5tEQiAdthIpFIp9P19PQ09vbZIp0GCg8E6SyaR8+5uTnef9Ld3d04mhG25ZqRSKQlwa7b7d72zJ9pa9sUVdtGGW5sbMDTWq22urrq8Xju3r1bKpVKpRLLsi6Xq6urC7Jy8fl8yMMolUoDgUBzMUQEgI/03bt3J90RBPktaJ+Lr1AogHnWYDBYrVa/3+/z+d6/f5/NZvv6+oxG48DAAMSUw8gGkRt+v59hGLvdTtP0hQsX2lReOlKv0Xq9PjMzI5PJzGYzwzAymQyiTXp6erjyfwRB/GQT8KBUKvX394P7Fp/PN5vNLdtJ6B97KkDhgSAdRMvM9N///d8twkMgEHz+/Pno2uX49u0bSZLbhpj/jItUm+SJ21IqlVKpVDgcDgQC6XQ6m82+ePEimUyeO3eup6fHbrf39fVZrVaBQEAQBP9fZDJZMBgEXyxkW3BuRpDjYaf/NW6VXCqVaJr2+XzxeJwgCIIgTCYTBGorlUqu7DcXMqHRaB4+fNhoNKLR6MjICDiXbrtfs2sfDgW32y0Wi2maZhhGKpXqdDqlUimVSqGcCPhZHVYHyuWy2WzmSpubzWaXy4Xes6cLFB4I0qHU6/Xp6enmpT+YILbNhn7oXL58WSwWNzetVqsPvZWd4gu5YPF4PE5R1MOHD0Oh0NWrV+12+82bN0dGRgwGg16vJ0mSq/IOLlUDAwOrq6s7ZZ36bcFPA0FOhJ0EAPcgEolEo1GTyaTX6yEHBhTqpmlarVZDUQ6ucIfT6dRqtZcvX240GrlcbtdWtr506NTr9UuXLul0OoqitFot5O2FG9Hr9VCC4wB94Mbwrbf27t273t5e0B5SqRQMRGtra83J0HHE62RQeCBIJ1L/t/pEi78TpAc56nhBkiS5zSqOoxAezY1CjvmnT59ubGxcu3atXq9///59enr6woULID9omjabzRA9KZfLoYdQ+M/j8TSnqD+KzC0IgiA/Qzab/fPPPzOZTDKZzGQyDMMEg8Hh4WG1Wg0GW1AdUKajq6tLKBRKJBKwITAMs7y8fOfOHYqi7HY7d81tzcjbPj10uKahFJJKpeLiv1UqlUAggMrljx49OnD3dvLF/fjxo8fjAa8znU4nkUi6uro4Z+C9Xx85EVB4IEhn0Txclstl3hYYhjm6duv1ejgchpmvxdIilUoPfSgPhUIvXrwA57FSqVSpVCBvb29v79LSUjAYlMvlcrlcq9Varda+vj4ILuzp6YEM8WazOR6P7+W+GihC/gU/AQQ5Hlr+1x48eJDP5zOZTKFQSCQSZrO5u7tbKpVC5Aas1OGvSCSSyWR6vV6j0UDIxMrKSvvrb/t/fQzaIx6P//HHHxKJxGazmUwmgUAgl8slEgnEYJAkeUTmlx8/fkB9D5A6ZrPZ4/GMjIwcekPIoYPCA0E6juZBc6vwOCLLA1AsFmmahhTsLe1uzSJyMJLJZLFYTKVSkUjE7XYHAoEXL17UarVUKpVKpZLJZDKZlMvlly9fViqVBEEoFAqVSgWbamDHj0QieykxvhWcjRAEORFisdjAwEA4HJ6fn3e5XBRFKZVKqGoKy3SIi4CqfwqFAlKBd3d3m0wmj8eTz+fbXHwvquOIRr9KpdLX1yeRSCiKUqlUCoUCpBTE3fX19R1d69VqVaPRwL6YQCDQ6XQulwtSgSGdDAoPBOkgtu7KbxUePB4vFosdSkMtVCoVSAavVqu3NnrmzJmfaYgL2wAHg0gkEo/HM5kMHMzlcm6322g0GgwGSO2i1+uhKpZEInE4HF6vNxgMfvnyZde7QBAEOUFaxqVYLLa4uJhIJAYGBux2O4xsBoMBbLZmsxnW6CqVymg06nQ6o9FIkuT4+LjFYjmeiL6fxG63gxOsRCKBVOYWi0WlUpnN5kgkctSt37p1C3yuxGKxUqmcmZnJZrMoPzoZFB4I0lk0T1qhUKhl9Q9Zm7gkIRqNRqlUZjKZ/S7Bt/U7unz5MmRN4ao+NUeYJJPJnS61a+v1eh12+yKRyPz8/NTUVCKRKJfLkUgkm82m02mbzaZUb1ttBwAAIABJREFUKsVisc1mEwgEJpMJ6uBaLJY7d+607zzKDwRBjpOdHDibx6Lx8fFQKHT58mWCIEiStNvtKpVKLBaTJOl2u1UqlVqtFovFkHOWS9Ok0WgYhslms7lcrvNHNgj11uv1Wq0WzB1wF3K5XKFQdHd3p9Ppo2i05UggEICaIXK5XCqVQhFGTKTesaDwQJCOgxtYKYpqb/EwGAww4Npstpb3Nv5zUmxzHB74fL6WaPJm7dHf37+r4b6NAqlUKlevXjWZTOfOnRsaGlIqlXa73Wg0QrYWgUAAUZUikQiCN8Adq/2HgyAIcvy0T1T16dOnb9++FQqFnp4etVrd29vb09OjVCplMhlBEAKBwGAwQN4npVIJAdkikejs2bMej8fn83Gh2B0O3OyzZ8/m5+dNJhMXjKdWq/l8vkgk0mg0bUqLHDosy0JEO5/P55KD+f3+rX1GThwUHgjSodTr9ampqW2VQCAQgDH09evXDx8+hLy33d3dz549ayle0X6ohVehIqxUKoX9qhZDB4/Hk8lkqVSq+V1tLruxsVGv18vlcqlUAnv30tJSIpEIBoM2m83r9arVaqVS6XA4dDodQRCw1cfn87Va7e3bt1v0xk4N4RSCIMiJsNOGDrC0tBSPx91u9/j4uM1mMxgM4EAlk8kgN65arVYoFFqtlqbp+/fvp9Npt9u9vr6+bSudTKlUOn/+fCAQoCgK9o/Onz+v0+kgs7lSqTz0W2h/wfX1dY1GA7MhxOgTBLHTBhZygqDwQJDOonlsnZ+fb1YCnB7gQiMajcby8nKLMmFZtlgs/vjxo+XKoEkePnxIEATDMC6Xa3V1dWBgoOXiLW5dfD6foqid+sn1Nh6Px+Pxt2/fcidAfqq1tbV8Pu9wOCBDi0wm02g0/f39MpkMEkdCPax4PL5Tvb9jzhGJIAiyK9xAlE6nP3/+XKlU4Gk0Gl1aWurq6rLZbFqtFlbkYNkQCoUEQUxPT/v9/mAwODs7++TJk8bOGqbDx7p0Oh0IBG7dunXjxg2JRGI0Gu12u1gshhTABoOhcVy3wLVSLBYtFguEtoPhZXx8fHNz8xj6gOwdFB4I0onASBqJRLYqAR6PNz4+zp2TTqe3lQ1CoVClUj169Ojy5ct+v39mZobP50OiRu5qsO7falRpljpOp7Oxw/zRPF+m0+lcLjc3NwdJ1qPRKMuyExMT6XSaYZgrV67Abp9QKOzq6iII4tKlSx6Px+FwPHv2bL8fS/sjCIIgR8qXL19mZmYKhQIEqsHBYDA4Ojrq9XpnZ2cVCoXRaARLskgkUigUarWaJMlIJBIOhyFerr05t/NHto2NjVAoZDKZpFIpFBvRarVarVYsFqvVarvdfug30n78B1N8pVIZGhoSCoUymYzH46nVapqmYVer8z/S3wQUHgjSuZRKJU4YNCuEpaWl5jHUbDZv6yLVoiJ2Mmts+xZAp9N9/vx5J9XR7NycSqWq1Woul4tGo1arlctPHwgE1tbWrFYrj8eDzC1ms3lrVq6DJaHHiQRBkGOmXq/Pzc2Fw+FYLBYOh1mW9fl8ExMTUC8PvH1kMplIJNLpdHK53GQyraysjI6OPn/+/ADZljp2lEskErOzsw8ePNDr9RaLRaFQQFJgyKK7sbFxFI3uRczU6/XPnz/r9XroDwih9+/fr66uHkWXkP2CwgNBOpdKpQK1YFtEwuLiYsuZXBh6eyHRXpY0IxQKTSZTqVTatZO1Wm1tba1YLH79+rVSqVgsFr1eDzX+wGASCoUsFovdbne5XAfLvtX+CIIgyPFQr9djsdjS0hLLsqlUiqZpqVRqtVqNRqNcLheJRFCLw+FwgGepSqWiKCoej4Mv1i82fNE07XK5SJL8448/oA4JmHqOqLm9fHqcMlldXYUkjZA6zGg0fvr06Yg6huwLFB4I0olwIyzDMFuTTTUnd4czucS7Oxk39ihIwJtLLBa7XC6u8kYb8vn85OSkVqslSTKdTkOtcbFYDA4GKpXq6tWrXq8X628gCHIq2Oq9Aw9CoVAul8tkMsvLy06n0+PxeDweSE6l1+uJfxGJRBaLxWg0Xrp0Sa1W37lz58OHDyd3Nz9F+4E6HA4Hg0Gfz2c0Gk0mE0VRAoFAKpW25JI6WWw2GzgYd3d3x2KxeDy+7W4aTknHCQoPBOloXr58yVXV4LQBV1KDmxS/fv3K+zeuo1lj7Op81XJQKBT29/f/+eefjS1GbfCnGhsbm52drdVq5XL5r7/+slgsJpNJq9XabDaPx6NWq+VyOUzABoPh4cOHzfeC9TcQBDkp9jjgfP/+feu7wuGw2+0mSdJqtXZ1dZlMJoPBAG5FkK5KrVbDoGe1Wvv6+oaHh10uVy6Xa/xa4x7X+XA4DPl/5XK5RCJRqVQMw0AuqZYzTxyXyyUQCGB+VKvVOp0ukUg0tiSUR44NFB4I0kFsHQHj8fhWkbDtyS9evKBpenh42OFwwMbbHq0cYrEYJIdarf748eO2/dnY2Lh///7k5CRFUTqdzmazXbhwQa/XQ8g4n8+HaVgmkw0MDKTTaS6J4a8x3SIIcnpps7hsOV6r1ZLJZL1ez+fzjUajVCqxLBuJRJ4/f+5wOLq6uiCEAyr96XQ6SJih0WgcDodUKoXyf8Fg8NcuQ1SpVD5+/OhyuS5cuACFOzQajVarhXmkUql02m1aLBY+nw+prmB3DLQHciKg8ECQzqVarUokkhb9IJVKGzsv6CGJ7YMHD169evXjxw+DwUAQBNiaBQIBVLCCyVKn0zEMc+3aNZIkvV7v+/fvf/z4ATP0jx8/stks1O6oVCrJZPLatWs+nw/2tyBbC2x0QcpCGNOlUmk2m21/R502ISEI8tvSPByVSqV6vV4oFAKBwMLCgtVqXV9fz2QysVgM4jTOnz/PjcZarRaiGkBv9Pb2SiSSGzduuFyuxs6j3Gkf/Zr7H41GXS6XTCYzGo1qtVomkykUCqlUajKZWk4+wbtutjXdvHkTFKPL5fJ6vYFAYC8RjMhRgMIDQTqL5mG6UChsNVDI5fL272o56PV6371713z8w4cP6XR6p/NBe7x9+9ZisTx9+jQWi8ViMZIkoRKWwWC4cOEC7O3BHCwSiSiKapOt5bRkh0QQ5Jek/eCTy+UKhUIqlUqlUhsbG8Fg8P379wzDfPz4kWEYi8UiFArlcnmzk+qtW7e8Xq9GowkEAlqt1uv1hkKhrQ21WFpO7xi4dQwPBoMmk0mpVBoMBq1Wq9PpjEajUCi0WCwn18121Ov1iYkJKKViNBqj0WhzOSzkOEHhgSCdCDfEd3d3twRmcE60LWfudIXGzkv/bY/E43GapimKYhgmHA6r1WqpVAoZSzgPLpFIJBKJrFZrMBgEybFtE82hmbs2jSAIcnQ0j0XwN5/Pp9PpSCQSi8VKpVIwGHz06NHQ0NCtW7dg9DMajd3d3eBNyufzFQrF9evXRSKRVqvNZDIul8tisYBl+Jcc4raO3mAUikajTqfTYDB0d3f39vbq9XqpVOp0Ovl8/tLS0sn1d0e4G2EYBiqNCIXCcDiMm2InAgoP5P+y9zbBSWTfw3/o94buJqS7IYzdQVFCyCMjwRJFscRHUjU4TJX4K7FKrGHqZ2YhLoYpcSNuxM1glcxqcCWuxCpxN3Ens5y4mMzSzFZm9xhXE5cD/8Wpb//5AolJTAJJzmeRIk13c/vlnnvPPW/IkGIMjV0WD4qi+u7Z+e8mbP3wVbFYBE8qt9vtcrlkWVZV1WKxdP66JEnff//951jSUdAjCLKT9C7EZDKZYrFYr9dv37796tWr+/fvz87Ojo6Ojo+PQ8Uhj8fDMAwETI+OjhIEoSjKjRs3IKb86dOn4Nf6yZ9bz/ahpavBzWbT4/EEg8EjR45ArRK4P7A4xTBM51FDcrFdzcjn8xCayDAMy7IXLlzoimxEthtUPBBk6OgSlKqqduahoihqawX60tISFHbN5/PBYBCSt0A+3JGREfDfJQiC5/lisWiU6W1vcHQZkkEIQZB9TqvVevHixZdffunz+UqlUiwWCwQCXq9XlmVFUaxWK8SLsyzrdrs5jhsdHQ0Gg5AQKZlMwlF9T7vz17LDlMtlt9udzWZPnjxJkiRU7bBYLBaLxWq1+v3+QTewm74LZNlsluM48j/4fL4BtW6fgooHggwRfYeu58+fW61WQ/eQZfmTh3zyK8jpUa1Wk8lkKpVKp9OZTAbSUsFSkJFdl6ZpVVWHcERBEGR/sgkHTvgqHo/XarVIJBKJRMLhMFSfuHDhgtvtDofDHo9HlmWe5yVJ8vl8YPsNhULpdLrZbGYymZs3b8IazSd/bk/SarWCwaDH4wmFQpqmkSRps9lCoZDT6WRZNhqNDrqBG6BcLvM8z7IsOInBxj3pLzeEoOKBIENK5+C6vLwMJogjR45srv4RpHdcWFiYmJiYmpryer2pVCoej7MsOzk5qShKLpeDMlgQwsHzPMjlr776ahsuDkEQZPN8UuIZ8tMohNpqtSqVCkRuZDKZubk5sOVardaJiQkwbqiqqqqq2WxWVTUejx89enRubi6fz7dXWTvf83RdbDAY9Pl8kLFdFEVd110ul8vloigqEokMqpGbY25ubnR0VBRFkiSPHj364MGDQbdov4CKB4IMF6vlp3r+/HmhUGj3W+1bYyA00sn/9NNPHo8nk8nE4/Hbt29bLBb4SpZlSZIEQTCbzVBliaKo06dPd6U5XyNuBEEQZCfpDRPv/Kpri5H94vvvv8/lcvPz83Nzc5lMRpIkmqbBtGsymXieh+Tj4GpFkqTL5eoUub2/td948uSJqqqiKEqSpGmarusMw4yPj4+Pj2uaNujWbYZcLqfrOqSbl2X5woULxlf7/FlvK6h4IMhQ01fB+OTG9n/yUxn/ptNpVVWj0ejDhw8zmYzf77906dLKysrMzIzZbIZCHIqihMPhR48erdGG3n8RBEEGSJcG0imgfvvtt5WVFShp5/F4xsbGNE27cOHCwYMHRVEErYNhGIqiBEGQJGl8fFyWZShSBOmq2v0k3v6UgcViMRgMCoLgdDp1XXc6nVar1eVy2Wy2sbGxQbduA3S+KvPz8zabDbRQWZZrtVqnNx2yHaDigSC7ibUHvM7Vvmw2W6/Xja8ajUahUJiamjpw4MDU1BS4Uamq6nK5FEU5efLkxMTEGr+yPwdaBEGGmb5yaXFxEYpyPH36NBAIzM7Oer3eer2uKAosbENgtJEc3GQyeb1es9ksCEKlUllYWJifn++qhYppwdvtdq1Wg/FCURQwlYui6HA4INHwoFu3MboW7yA7sCRJiUQimUyihX9bQcUDQYaLT8ZHrse5OZ1O//DDD6FQqFQq3bp168mTJy6Xy+/3h0IhqL8BURx2u/369euQqGqNVUO0eCAIMmz0lYfVajWdTn/zzTeJRKJQKPz444+BQEAURYheM5lMsiynUimO4wiCkCQJyt7F4/HZ2dlOE/E6f723AXuSVqv1+PHjWCx2/PhxjuNsNtuZM2cOHz5sMpnC4TBJkrs3+4jx+Lxer9PpVBTF5XJ1frUfnu8Og4oHggwRa8z+13NgrVZbWVkpFAq5XO7x48dQBJAgCI7joPIg5GzheX58fPz+/ft9T7LOtiEIggwV9XodslFFIhGfz+d2uyEHLjjSEARhMpm++OKLQ4cO8Tyv6zq4nhYKhXv37v3777/tfrJ3PVJxD2NcYLVadblcly5dAj+rQCCgKApBEIIg7GpzRyd+vx+GS1VV5+fn//rrrx1u2D4BFQ8EGS76WvPXGAWNLYuLi6lUCkInY7FYPp83DOIWiwUGXYZhzp0712g0ms3m2mdbo217fqxFEGT4efHiRblcXl5eBmnWbrfT6TQUs3M6nRRFKYoCNapZloXIDYqiWJaNxWJ2uz2fz1cqlc9pwP6RhAsLC41GIxQKPXv27NixYw6H4+TJk6DOkSTZW9N2+Fnt2TmdTpIkR0ZGWJYtlUoY77EdoOKBILsYQxOo1WoLCwu5XK5arQYCgWKxeOXKFXAnAAcDkKRv377tPRxBEGSwrDNNH1Cr1TKZTKlUunLlSrvdhnS3CwsLP//8s8vlgmqAJEk6nU6LxUJRFNQjYlmWIAin03n+/PlYLLatl7PHyOfzYEd69+6dpmmqqn799dcej0eSJIqidmlKq9WAir00TYfDYXxPtgNUPBBkd1Mqlf76669Wq7WwsDA9PQ35WLxeryRJRqXz8fHxixcvGods2qELQRBky1lbFnVtvHDhwsTExNGjR6enp6PRKBQ/zWazyWRS07RAIGA2m1mWtVgs4LVPEATDMJIkHTt2rFAo9C06jqyBy+Xy+XynT58+duxYqVRyu91WqzUcDpvNZogvbzQag27jVlKr1XieZxiGYZhwOFyv142MzLADjpifCSoeCLKb6JV9UIjX5/NB+VjIjQteVSaTyW63P378uO8ZEARBho21/TlB3MViMVEUx8bGdF3Xdd1qtUYiEavVynGcJElg4DWZTDRNw5L81atXf/rpJ+P8KAM3hMVi8fl8o6Ojs7Ozv/zyC2QACwaDkKGEJMk95oLbarXq9fro6OjIyAhBEKFQqF6v75mrGwZQ8UCQXYYhAf/5559QKOT3+48ePcqyLMuyNE2b/kMoFIrH4+31LSIiCIIMkE/WRQVv+3w+b7fbQ6EQFJwmCIIkSZPJBJEGYNmgKGpkZEQUxVgsBoHjuFa9OeB28TwPKXSPHDmSTqf9fr/ZbLbb7RaLZWRkhOf5QTdzy+h8PQqFguGiHI1Gq9Xq//t//2+AbdtLoOKBILsAY1Q2PiwsLGSz2WAwKIoiQRBGCV6Komw2m8Ph6Dqw/amlRARBkAGyRi3U169fl0qlTCYzMzMTDAZ9Ph/UGuc4DtSP0dFRVVU5jtM0LZVKsSybTqf7nhzZKBzHCYIwPj4+MTERi8X8fj+UXDSbzSMjI7Ozs4Nu4HYhCAJJklar1W63T09P5/P533//fdCN2gug4oEguwxI4ZLP5yFXFYSPkyRJkqSqqqtV28UCWAiCDD+9giufz0ejUUVRrl69Ojo6CgvtsMhiGHhtNlsul7t16xYYRm7fvt3GBZet4M2bNzRN+/1+p9MZDocnJyeDwSDLsoIgQEGPvXdjjRfm5cuXUOaF47hkMjk7O5tOp/fe9e48qHggyO6gXC5ns9lGo9FoNM6cOQOuzGDrsFqthw8f/mT1K9Q6EAQZZkAizc/PLy8vwxYorQCFpaempsC0C0DaU8ifsbKyEg6Hnz9/3veEq/2LfJIbN26AP5umaV6vV1XVWCzm9Xo1TbNarWBW2kt3tcvs9vbtW1mWTSYTx3GyLCeTyWq1+plZmBFUPBBkF1CtVqPRaCQSAYnPcRwMwODWfO/ePWPP9dQ13+bGIgiCbJhCoXDr1q1ffvnlwYMHS0tLEOOr67ogCLqucxzH87wgCARBWCwWm81GEATUQoVS08+ePVvPr6ABZEO43W5RFK1WK8y/BUE4dOhQJBKZnJy0Wq31en3QDdxG4CVZWVnRdd2I94hEIl9//bWhGCObABUPBBkM68xp22q1crmcw+GIx+M8z09MTEAEOThWaZpmGDpwKEUQZKhYQ6z1bsxkMuFwOJVKxWIxn893/PhxRVEgOx/YNxiG4Xke/KycTqcsy7lcLpPJbO817ANWe0yLi4sej0eWZYvFIkmSrus2m00URY/H4/P5vF7vJ8+wN6jVarDSRxCE1+uNx+MLCwuDbtQuBhUPBBkuOiX48vLygwcPRFGUJAlKYtE0zTCMqqrGUhM6UCF7ng1Vl0OGljX0kDt37mSz2ZmZmXg8Xi6XjTVmI4oDPttsNpZlg8Hg4uIiBHIg20cmkzl58mQwGKRp2mazFYvF48ePp9NpiPF4/fo17LYfumQ6nQYdGJTehw8fGl/th8vfWlDxQJBhBGTZ8vJyOByGEVdVVZqmCYJQFGV+fn7QDUSQnWaNxNCrJWPFPKoDYe3VkN64i+Xl5ZmZmUAgYLVanU6nx+NxuVw0TVssFgjkIElycnLy3LlzuVwOKwBuOX2fV6vVKhQKsiyDk5Wu6/V6PZVKaZoGGmA8Ht9X4fsej8dQgCVJ6t1hz9+BrQIVDwQZIjol+LNnz6LRKMMwIOlgkUmW5UG3EUEGxnqmOKvFE+O0YEgA//h6vT4/P//69etYLBaPx+12uyzLUI6D4zgoBWg2m6EIoCAIlUoFEvoZ4JPdbhKJhK7rNE1TFJVIJILBoNPptNlsDMMIgnD//v32/rj5xjVOTU1BPgNRFK9du9bX72A/3JDPBBUPBBkYfSVUrVZrNBpfffWV2WwGt2Yw7yqKsrcj+RBkDTY6y+zaH2cDgwLu/L///gv/Li4ufv/995lMplQqXb9+HaazDx48gBKokKnPbrdrmqaqqiiKiqLcvXv3t99+6zph52d8uFtF5538448/Tp06dfHiRUmSfD5fKBTiOM7lcnk8ntHRUaNU1D7BuDPRaBSizP1+f7lcbjab+PptFFQ8EGRYuHnzpsfj4TjOYrHIskwQhKqqDMMEAoE3b97APhta60WQfcLNmzfr9frBgweDwSBJkpIkhUIhI+wY+8VgMbSOdru9sLBw7ty5crl8+fLlY8eOURRFkiSUJIJSgDCrU1U1Go3WarUBNns/02q1bt26FYlE0ul0NBqNRqNHjx5VFEXX9XA4LMuyz+fbh90KLhl0MJPJRNP0iRMn2mh82yCoeCDIIOlcsfP5fEaWehiPDx48ePbs2c49uw7sBEZ3FHzInqTzxW40Gjdv3rx161a73YZgAPC97sTYYjKZpqamBtfw/cvjx487/3337p3P57Pb7QcPHpyZmRFF0XhwxH9wOByBQODUqVPXr1//5PnRv2Vr6bqHsVjsxIkTHo8nEAhMTEwcPnwY8lkxDAPJTgbVzsECd0lVVRAvVqv1p59++u2331D3WD+oeCDIgCkWi7lcLhaLwTBsMpl4nnc6nblcbu0DIf6va8t2thRBhgJd12GBXFGUXpWjV/1gGEZRlGKxOOiG7xdWVlba7XanvaLRaIRCIZqmjWBxeIKQGVwUxXg8fvTo0YWFhb4VEtDSu930Oq2l0+mLFy/a7XZJkiiKKpfL8Xj8iy++oChKEIR9a4yCW9RoNAiCgPF6dnYWoo/wPVwnqHggyBbwyeQeXRsXFhaazWatVjt//rzL5dI0DeZJIMs0TXv//v3OtBxBdgtLS0uxWAx6iqGl97Vy9Bo9CIKgabpQKGD66U+ymiVhjRtlfNVsNuPxeDqd7oy7rVQqmqaBGxU8NYIgGIbhOE7X9Xg8vrS0tLKyEo/Ht+eCkA2Ty+Wy2Ww8HhdF0eFwiKKYy+Ugry5BEB6PZ9ANHDwnTpwAqUKS5NzcHGxEYbIeUPFAkK2kr+7R+W+xWEwkEplM5vr164FAAGrxGjMkkiSTyWTfAxFkn9B3sptIJFYzaHT+a2yBaW4vqqqOjo72/hACrKaYrce42mq1ms1mIpGoVqvJZNLv9z969Gh2dlYURQhdoyjKWF5hWfbixYvffvutx+Mxls8xWHxQdN15RVEikYjf7w8Gg3fu3HE4HF9++aWu64qiHD58eKAtHSRdb6bf7wexo+v60tLSGvvjK90JKh4IsmWsxx/A6XRqmpZKpVwuF8yNKIpiGIYgiHPnzu1QQxFkuOnqSjdu3BBFsdOC0at+rOZzBdthygtr7QRBRKNRnBOsgeHGuc4UUq1Wq9FoVCqVSCSSTCZLpVIsFoOcVKqqgqYhyzI8EbvdfvnyZVmWE4lEqVRarRYqPpcdprNHXL16NZ1O67ru8XhsNhvP8zabzeVyiaLocrl6D9nzrHalqqqaTKZvvvkGDHfrOQRBxQNBtpi+w2er1VpZWYnFYlar1ePxTExMGCt/IyMjhw4d6lrz6z0PguwHel/7aDTKcVyXQeOTWoeRIgk+dyotJElGo9G+v4W0NyiCWq3W/Pz806dPa7VaOp1WFMVsNkMQDoT1S5IkimIwGIT0uDBzRcvGMLO0tOTz+ZLJpM/nSyQSFy5cmJ6e1nU9nU6Hw2EI4Gnvv8fX93qXl5dBvNhstmAwuM6j9jmoeCDIlrHGgP3HH3/cu3cvFotZLBaWZWEyBLrHlStXek/VmYASQfYVnbPSRqMBNTTXsGkABEFYLBZJkowidDabDeJivV4vdDeTyQT54g4cONDGOcHqrCecA/j5559TqZSu66Ioqqr6xRdf6LpuWJnAvuTxeCYnJ3VdN5vN4+PjDx486D0PPouB0zl+HTt2LJfLpdPpqakps9lMURTLsrFYLJ1Or33sPqHzXn333Xege9A0DUUVu/Zp77/7szaoeCDIFtMrYl68eHH+/HlZls1mM8uyDMOQJMlxnMPhyOfz6z8PguwTjJe/UqmsrXIQBEFRlKIo58+fn5+fT6fTqVRqcXGxXq8vLi4uLy9/+PDh3bt3hw8fVhTl0qVLsVhstckBstrd6DVQFIvFSCSSzWaTyeTs7KzD4QDVrsswNTk5eeLEiaWlJb/ff+TIEVEU//77b7znw0y9Xvd4PKFQaGJiwuPxgIMc+Cg6HI5Go9F7yL5aJuvrfOh2u+EunT9/HtJRotaxBqh4IMjW0Ctcms3mwsLC27dvT58+DfWGKIqiKAoG5lQqtdETIsiep2vAfvjwIVgI+3pVmUymYDD48OHDXmPj2gvq2LnWg3GXPn78CJ8fP3584sSJer1+/fp1qGZ95cqVeDxu+MJRFGUUIxoZGUkmk8FgMBQK/e///m9XWY+uJ4VPZOC0Wq3FxcVoNCoIwuTkJM/zNE2zLGu1WlmWpSjK6XQ+ffq096iuD3ueXqWi2WwKggCLIAzDpFIpTLC7Bqh4IMiW0SWP7ty5UyqVfvzxR03ToDQvDMxms/nq1avtNUdcFFjIPqS3R0DemNW0jvn5+TXO0/sZWT9w36rVarPZvHfvXrvdzmQyVqvV5XIFAoFIJOKSV+F5AAAgAElEQVT1ehmGoSjKEG4jIyPg7cYwDMxZU6lUuVxe/yPAhzVY5ufnFUWRJKlcLjudTqvVSpKk2WwmSdJqtZZKpdUO3OcPrtVqLSwsgO5BEISqqpgbeg1Q8UCQz6KvwG02m+l0ulgsCoLAsqzNZgMrB0VRDx8+3PlGIsguolP9MAp3dOob8MEoCLjPJz3bRKvV+vDhQ6VSSSQSsiyHw2G/32+z2TRNkyRpcnJybGzMZrNBQRUQdPB0LBYLBNquMU9FhpNqtTo5OTk9PQ2lVyBc54svvhBFEetvroYhf4rFotlshrHe5XJlMpnFxcV1HruvQMUDQTbGJxdTm83m7du3YfRlWZZlWbPZzHHc0aNHd7CZCLIr6epf169f76t1sCzb3q/D9hay2g18+/btw4cPDx06dPr06VQqxfM8uJGYTCaHw8GyLCQH43meZVmSJGmaBhPHzMzMuXPnvF7vDl8IsiXUarV4PH7gwIFMJqMoCqQHUBRlenrayLCMdNJ1T7LZLMuyUB8znU6/ePFitT33VWBMF6h4IMhm6BIii4uLi4uLqVQqEAgUCoXLly97PB5VVWmaZhhGUZQ///yz3ZEdH0GQXnr9xefn53vLd5hMJojg7NoZWY1PxlHMz8+73e67d+9ChdPz58+fO3cOVkx4njdyExsObyaTSRTFSCSiaVo8Hnc6nW632+fzvX37tu+P4jPaFVSr1VAoFAqFNE0zSt9A8XJI+I7PsZeue5LJZCDkSRTFfD7/8ePHarXatfM+7xSoeCDIhumaHi0tLVUqlWvXrvn9fk3TAoHAzZs3r169euDAAZZl/X5/5877VtYgyIYweoqRLsmAoqjBtm030iV/OvOGXb582efzORyOq1evzs/Px+PxaDSqqiqkHjZUDiNdFU3TDodD1/VSqdSpaXSdebWfRoYWSZJsNpvZbKZpmiAIkiRlWfb5fEeOHGnjE+xhNfeHarUqSRJN0z6fz+v1zs3NQax53533Iah4IMhm6BQcU1NTgUCAZVmHwwE5c91utyzLfr8fsp5jRh0E2TSw8trlcGV8u589FjZKryAqFArT09M2my0ajXo8nqmpKb/fL4oi1E4xtA6KosCrShRFnuc5jjt06NDFixeNWnLIHmBubu7AgQNg5pIkCZzrKIo6fvx4JBIZdOuGl74Jdn/77TdJkiRJstvtgUBgaWlpeXl5cG0cLlDxQJCN0StlGo3G4uKi2Ww2crxwHCfLcuciByobCLJOujoLVBLoym3VtdBuODFiR1sni4uL//M//3Po0CFN0yBeHOI3OI6DeHGTyQQhauDoz/O8z+eLRCKhUMjj8cTj8dWWe9eZ0RgZKlqtFlTw4HmeoihYsHc6nTabbWJiYtCt2x109YJbt245nU6e53VdD4fD5XK5jZ2i3W6j4oEgn8ndu3drtZrf74dQS4vFcurUKUw7iCCfQ2c3mZubM7K1GrAse+7cuUePHuXzeaOoGXauXrru5KFDhyYnJ9vtdqVSGR0d5XleEAQIDQcTh8lkggUUk8nEcZyu66FQ6NSpU7Ozs5FI5PHjx7BwCx7/7XVPpPDRDD+3b9+maRpWzUiStFgsgiCAT92gm7YL6Oth+PjxY4fDYbVaJUlyuVzZbLZ3OXIfdg1UPBBkY4CYqNVq0Wj09u3b9Xo9FAoJgsAwjN1uP3bsGCaRRJAtwSjOBcGavcDa/MjIiCzL4NaIdGLMbKrVarVadTgcqqp6PJ6vvvrK7/cfPHgQ7BsEQcCdBH2DIIhYLBYIBCqVyvXr1yHko8tJfbXfWnsLMpy8f/8e8lmRJKkoCvjXWSwWlmU1TbPZbINu4O6gV5FotVqZTAbK2ng8HlEUE4lE7yH7DVQ8EGRVev0Hcrlcs9mMx+PlcvnHH3/0+XzBYNBqtdI0TZKkqqro9IwgW45RRrA3r24nsGA/NzdnHLiHx/W+s5yufVZWVuLx+Pz8fCwWW1xcBNssJPg2m82hUAjumHFLSZIkSdLpdNZqtWw2m81mVyvRiOx2Ot+WcrkcCASSySTLsrqug/kL6nhMT0+fPn16D/ej7cO4aeFw2Gw2y7IMLovlcnlpaWm1nfcDqHggSH96PZVXVlbq9fo///yTy+V8Pp+maSRJMgxj+Q8wSO8rCYIgO0Cr1eJ5vq/RA/SNri26ru/zbnjv3r0ffvghnU7ncrlgMGiz2Y4cOSKKoqFgMAwDhU3Bjc1kMgWDwUQioapqMpnM5/ODvgJkG+nSWkulUjAYLBaLkUjE6XQ6nU6GYSRJoigKCuYgmwZust/vB9OiyWSSZblcLlcqlfYqs4U9L7tQ8UCQPvT2/GvXrp09ezaZTKZSqVQq5XQ6CYKQJGlkZITn+bm5OXA0Xy2wEkGQz6FcLndaOXotHl1bZmdnjdiPPcMa4qUzu1ej0XC73YFAwOFw+Hw+iNmAiI6RkRFIkyqKIogvyI0rCILVau2sjtL3V5DdTu8rtLy8nMlkfD6fqqp+v19RFJPJRNO02WyGSA8sPfGZwE3z+XyQJo7juGw2+/r1664deg/Zq6DigSDrIpvNHjlyJJPJpNNpWZaN9VeGYXB1EEF2gM70Vl2aRl/Pq2Aw+OrVq709hLd75ijFYtHtdjMMw/O8qQMjHgYsHmfOnLl169bY2JjNZrtz586tW7cePXrUe7a+W5DdTtczdbvdoVBoYmIimUyGw2GHw0HTNJg7xsfHMWXc52DctKWlJbDN0jQNpsh6vd67234AFQ8E+TTNZrNarUJCbpvNZsxsOI67du3aoFuHIPuCXC7Xq130VT/gAwzzXav4ew+YvrRarVqtdvz48Wg0CjcBLBudtcYNrUNRFJ/P12q13rx5s7CwsMakZ1/Nh/Ynf/zxRzgcTiQSExMTiURC13We50VRFARB07TOyTGAr8T66bIv3bx5k2VZmqbPnTt3/Pjxzmi0rv33Nqh4IMiqdC7zzM/Ph0Ihi8UC5cxMJpPFYnn//n0b3asQZKcwm81raB3gyWCUvTNskmvPrXcpcEW///57JpMpl8uFQiEWi9ntdk3Tem8Ry7Jg9IDw8UwmUywW2x31T7o+t1Gs7V26nmwulwuFQmNjY4FAwOl0WiwWs9lstVrD4XAwGCwUCp0748uwIXpv11dffQXlcTwez/37941sNPvqxqLigSD9abVaf/311+LiYrvd/vDhQywWkySJ4zhYOzx+/HjfQ7o+IAiytXg8nq5a5lB64sKFC+12e3FxsVKpZDIZyMwD026z2fzhw4dBN3zLWFhYePnyZTKZzOVyxWKxUCjE4/GpqSm4ZOI/GPdHEASv10vTtCiKyWTy7t27q2XEMv6iBNsn/PHHH0+ePDl37hxYOUiS5DiOoqjx8XGe56H0xKDbuHeAbuXxeFiWlSTJ5/Ndv36969v9MItAxQNB+gBFslKpVCQSSaVSyWTSarWCysHzfDqdxjpZCDIovF5vp+nDZrNBlYnO3lcoFNxut6F72O32wbV3y3j9+vXLly+r1aqiKLIsC4Kgqmo0GhVF8ciRI2DW6LQCWa1WmOX4/f5UKlWv1z85rcGF7X3F8vLy3Nycz+eDIpJQBtdsNjudTij5MugG7k10XWcYRlEUMCi9ffu289s93/tQ8UCQ/+rnS0tLy8vL8Xg8Ho8XCgXQOhRF4TiOJEmaps+cOdN7FIIgO4mmaRRFkSR56tSp1fYplUqds3BN07p2GKouvJ7G1Ov1XC6XTCYdDocoig6Hg+M4Y00Ebohh94DV63g8vveyeyGbpus1S6fTDodD0zSWZQmCoChKEARJkiBNfDKZHFQ79zAQWwUubYFAoF6v981PM1TSaWtBxQPZ73St8C0vLzcaDU3TXC6Xy+WSZVlRFIjRZFkWcm+397RQQJAhpLfHPX369J9//mmv4pzQarW+++67To8sgiDAkrn2aXeetYsAGjKn3W7rum61WqPRqNfrVVVVEISuQBeaphVFEUWRYRiPx/P48eM1zozsT4w3IZ1O67ouCAIYOkDxgEITqqq6XK67d++2P/V+IpujWCzCaqbT6fT5fODUvR/8rNqoeCAIABbPRqMxOzubz+edTifLsiCFYe3Qbre/fPkSdt7bQgFBtpudGV//+OOPzkk5QRB9HdYH251Xc22qVqvZbPbq1avXrl1bWFhot9tLS0uhUEgURZPJ5PV6GYbpDORgWRasH9ls9uTJkxA7/slfQfYzP//8M8Mwo6OjULuDJEnIFE9RlM1me/DgQefO+2ROvN109sR4PM5xnM1mk2U5nU5Drpr2PuitqHgg+51WqwXRqG/evFlaWioWi52RqUCtVus9ag/LBQQZQjYafJnNZkf+G4IgEolE76mGimazef/+/adPn/70008+n+/rr79WFOXQoUNGyArUPyYIwijNQZJkJBLx+Xy92b2H8xqRAQKvRL1e93q9PM9LkqQoCpjLJEmSZRkW2kDd7XssslWEQiHwpxAE4ezZs51lQPcwqHggSDuRSGiaNjc3Nzk56fP5IG0OrADxPN+ldaDdGUG2ik33oE8e2Gq1vvzyy67CguAwOWzdFtqzsrICJfwqlcq9e/du3rzpdrttNtv/+T//B0qPd6YJpmkaLLHBYBBSc/YtV4LCClmNVqsVi8XcbjdN01AP1+fzQeABwzDxeHzQDdzjGP1R0zRYQTCbzR8/fhxsq3YGVDyQfU25XK7VaqqqHjhwIJ1OT05Oer1eY03R6/V25oHpCw7nCLI5PrPvrH34y5cv7XZ7Zy0LY8r+5s2bz/ndLefHH3+8dOnS8+fP37x58+LFi2w2GwwGNU0zmUwTExMQO25oHXAthtGD4zhFUebn57vOiRU5kDVotVqPHz8Gzz1BEODVUlVVVVWfz6coCoQcGDsPsKl7jL4d0+FwQF/ekxWHekHFA9nX3Lt376effpqcnDx//vzo6ChFUYqi0DRtsVjsdvs6B+z9ICkQZDvQNM1ms33xxRelUmntPdffB8F50mKxQOXyTnieD4VCXckrB0s+n08kEtPT05FIJJPJVKvVcDgciUSMBlMUZZg7KIq6cOGC3W6XJEnTtFu3bi0tLRmn6rpFaxQHRPY5pVLp2LFjHo+H4zioiksQhM1mY1lW1/ULFy789ddfvS8MvkLbRK1Wg6qC0Wi0dxFh74GKB7KvKRaLXq/X6XQqikJRFIR2XL16ddDtQpC9z++//y5JklHkrl6vf/45oe4nz/NdTlYASZKSJA1Petl79+5FIhGbzaYoiqIo8XhclmWWZY0qJZAkl2XZZDJ55cqVfD5/7949RVECgUAbPamQzbK4uPjq1StVVS0WCyy3EwTBMAzHcXa7vbPoDb5XO0MsFoP+brPZOs1NexJUPJC9xmpFeXtpNBrpdDqdTiuKIggCrPqwLLtDDUWQfU9nwTun0wkb11Ods3d1H/5Wq1VJkvpqHaB48Dz/4sWLNX5lPazWkvXYSBcWFjKZTLFYTCaTXq8XkplCLXao4CYIgs/nM+6M2Wy22WyxWCyVSm26wQjSSaPRyGQyVqt1cnLSZrPBGwiR5ZFIZGVlZdAN3I+Mj4+bTCZVVePxuPEIesXLHlAFUfFA9gW9PbZarTYajQsXLoRCIaj4CykpP+nygSDIVjE6OtqpGFy9enW1wfWTA/CTJ0+mpqYMlaOrhrexkWGYLZlXrSe6vetDs9lcWVmZnZ31+/2xWCyXy0UiEXAJM5JTGS1nGIbn+YsXL7rdbpIkHQ7H8BhqkF1Nq9UqlUrhcNjtdk9PT9M0bbVaCYIYGxuzWCydznvITvL+/XuapimKkmX5p59+av+3oNszWkcbFQ9kT7L2uiNMO9LpdD6fn56ehlHfZDJZrda+mWEQBNkOWq3W4uJip4Zw4MCB9sZDqkqlEuR96lQw+n4gCCIcDm9V43s/r60vPX369NmzZ7lcLpfL6boeCoWMfLgGHMdB4LjFYnE6ndevX0+n0501BBHkc4AXslqtulyuo0ePHjx40GQywXwXFuBevXq1N2a3u5FSqQRJIwKBQLlcbu/RzBCoeCD7Aqhw3G63f/nlF/iwsLBQLBbBt4EgCMweiCA7iTGOzszMdM68y+XyhobYDx8+HDp0qLOU3hoWjxMnTmxh49dj9AA5k0wms9lsvV4PBoOhUIggCLPZLElSZ3pcmP+pqgpxLwRBdOobe2nagQycTCYzPj4eCAQCgQD0FJqmRVF0Op17cqY7/Bh3OxwOg/HT7XZrmra8vDzYhm0HqHgge43eKmOFQqFWqzWbzWq1mslkzp8/H41GOY4zqgROT0+jkEWQnQf6HZQRAIxIDwMoZLa8vDw3N3fjxg2WZQmCOHjwYL1eX15edjgc0JH70ql7MAxTKBS2PCB7NSvHyspKJpOJRqN37971+/0Oh2NsbAwCx0mSJEmSZVmGYQxDB1xXJBKx2+3xeBxqeiDIltNqtUZHR81msyiKuq6D0ktRlKqqN2/ebKPKMTjgzlutVkiDoapqLpfrG8+2q0HFA9lT9I3l8Hg84XD422+/VVX14MGDkLsDxn6CIKLR6ODaiyD7ka6xs9FodGoL2Wy2XC5nMhme5w2bAMyNQJGAv4IgHDhwoLO6Rd+gDrAesCwbi8U+2ZItuZxoNOr3+1OplMvlcrvdLpdLEASj1ji0p7OR4+PjFy5cOH/+vKZpW9swBOkLx3FutxtK5UKyZpZlKYrqVfuRnWdhYQGWITRN2yrX0KECFQ9kbwLDdqPR8Pl8UI0rEAioqgpCFmI3zWbz3bt32zjGI8jggN7XbDatVmunqmBYAzrVidWCN9Ywd5hMplgsls/nu37x83t913nm5+fz+fyRI0cikUggEAiFQpIkWa1WTdMURTGaZGgdMNUzmUxjY2PZbLbrtFvSQgTppdVqwWq6kc4RMjoqilKtVo19BtvIfU4kEoFlF0EQjhw5Ahv3zENBxQPZs9RqtaWlpXA4bLFYfD6fx+MBZ1ae5202m8ViqdVq7T3UmRFk19EVe93XRaqvOmEAodir7eB2u4251HaQy+WKxeL8/HwikfD7/clk0uVyWa1WWZaNiuOaphlenWazGewek5OTgUBAURSv1wst3EtZa5ChZXFxsVqtUhQFZn8jJQOsrw+6dcj/LwFkWYb03y6Xa48lOEbFA9kj9A7YoVAom83G43FIRgkZAymKcrvdkUgEB3gEGTa67BhrqB+dakZvZPnIyAhFUePj45trxjptDpFIRJIkXdePHDni9/tdLlcwGJRlGaLGwbJqfDCZTIIgiKIICfRUVd0PJYqRgbDaC9xqtdLpdKFQgDqVkKkZvABomu7ri4jsAH3lzPPnzzmOg6fj8XjevHmz8w3bJlDxQPYa//77L3zQNM3v9weDQVhiZFl2ZGSEJMmff/4ZtQ4EGUJ0XV/NvrFa/MbIyIggCF1f+Xy+WCy2TbaOJ0+eVKvVbDYbCASi0SgE6Xq93rNnz4LjSmdLjBAUkiTPnz+vqmq5XMaKHMhAWFpaajabkUiEZVmWZaPRKBgMOY5zOByDbh3Sbv+35dPj8UBR+fHxcb/f//fff++NqQsqHshewOirxof3798nEomLFy8GAgGCIERRZFnW4XAUCoVBNxZBkP5AWY+R/06Gu1opQOMz1OAzrB+6rvc9+abH7M4DE4mErutzc3NnzpyB2HEjNhey+naVAhz5j4dVNBp98OABZOhCkO2mN7sjfJifn7948SLLsmNjY6FQCFRim80GQczGGIrsMH1ve7PZBBlC0/SxY8d+/fXXnW/YdoCKB7KL6eyrhqGj3W4vLy/fuXPH6/WOjo5yHDc6Ojo6OmqU8kAQZGiJx+NdYeUwiQefkK5Ac5IkRVEMhUKpVIphGJqm6/U6nGcTaXP77tY1gQNnqkgkMj4+TlGUx+PRdV0URZIkGYaB7FUjIyMcx1mt1vHxcbPZDHbXPZmPHxl+ut7qdDqdyWRARQfrHMdxY2NjLpdrQA1E+mA8NV3XTSaTpmmVSuXevXtQVXC3g4oHsrvplKpv376t1Wpv3ryBFLpQHFCSJFEUnzx5MsBGIgiyTmDN9fLly5Bpx2aziaLocDhisVg4HE4mk4VCwev1Tk5OhkKhr7/++uXLl+l0ut1up1KpUqm0VW0w/i4vL7vd7kwm0263L126xHEc5KoCHyqe53Vdt1qtMIczNCWPx6MoSrlchrYhyGCBl3lycvLixYujo6OGByDP87FYzOFwBAIBtHUMJ5AJ4MCBA3a7fW8EhqHigexiuuzICwsLhUKhWCzCIgEsi9I0XSwW2z0rlwiCDBtdnfTZs2eLi4t991njqNVOu9GWNBqNXC6naRpJkoqi6LrucDgcDgdJkpCxCqZuDMOAMxjEks3MzIiieP369S33+EKQz6Fer09OTo6Pj0O2AxgfGYYJhUJHjhxZWloadAP3NauJhVqtFolELBYLy7KyLO9wq7YJVDyQPcIff/zRbDYDgYDb7YbJAWS2gRXHvVf7E0H2JOvpm6vpHn0/bLoNjx49ajabN27ckGVZVVWCIHieB3cvA8MTzGKxZDKZcrlcr9cPHz6cy+U2fXUIsh00m81Hjx5ZLJbOSjI0TcuybPhZ4fs5EFYLyDH+dbvdED8WCoUG0L6tBhUPZHdjWB5TqZTP56vVarIswxokRVFg62ijPEWQXcVqQa5d2/t+/kzdY3FxsVarvX///ueff15ZWfF6vYFAIBAImM1mSZJMJpMsy6Ojo5BlH9QPw6y62rWs8S+C7ACtVguUYSjTyTAMFKeDFxhTWg2cNRZT2u12NpsFQ6vdbjfC2HYvqHggu5iVlZVoNJrP55eXly9cuCCKYiQScTqdsixPTExAfUAEQfYta8SL993eaDQqlUoymUylUtVqtVAoJBIJSZIg4ITjOMPKYTKZWJYVBAGKfJ07d257rwRBNkur1VpeXr5x40Y2m4UiM5CYAfKt6bqezWa79h9UU5G+/PLLLxRF2Ww2lmV1XV9aWtrVrnGoeCC7g75u3O/fvw+Hw5FIJBKJgNc1uFyv5l2NIMj+YT02E6DRaDSbzaWlpXw+H4lEvF6vw+FQVZXjuLNnz3IcBw4qJEmCYxUk17darZIkTU9Px+PxPVZaGNljvHjxIpfLhUIhiESCv1BaF3ZAZWPIgUcGsWTJZLIz+G3XJUFGxQPZBazmq1AqlSCtvlFBzGq1RqPR9+/fD6KZCIIMC32XKvq6Y927dy8UCiUSievXrx86dMjv97vdbo/HY7VaaZr2er0QLQYh5qIo+nw+l8vl8/lCoVCpVMI8ucgwA696KBTSdV2WZdCfWZblOI5lWZ7ne3dGhoROMQXFVcFUdeXKFciz17nnLnp2qHggu4Cu+oBAoVBwOp1er5fjOBCmq+V82EUdEkGQrWI9iewymYzX65Vl2ePxTE1NTU1NQbjtxMSELMuQbxTGe6fTmc/na7Xa4uJiLpc7f/48ChZkyDFe0ampKZZlzWazUWcG/p2ZmenduY2D5vDx7t07o5CRJEk+n69UKu3SXJ2oeCC7hs7elc/nwd/RbrfzPE8QhNlshkDzXdoVEQTZKtaILze25PP5hYUFSZJ4nnc4HDabzePxQJlCiOUwagbDugZN099//30+n//w4UPfMyPI8ND5flarVVEUQX82mUwcx4miCBFKvaVv8MUeHromM5DcAnyuWJYNh8OVSmU3Pi9UPJBdRqvVyufzwWAQ/K3B3OFwONDhAUGQtQHH6IWFhbNnz2az2VevXrEsy7Ksy+WCCVlXqlyCIA4fPux2u0dGRux2u5GbG1c3kN3CixcvMpmMEVNO0zRoHYqiuFwuKK27dkolZEgoFAosywYCAYfDwXHc119/DRXNB92uDYOKB7IL6BSCV69ePXLkiNvtZhgG9P5gMNhbZQxBkH1L3/DxdDoNgzQkvotGo2NjY0aWKqO4AWgdsB58+PBhWZa/+eab69evr/1DOFFDhgd4GxcXF8vl8suXL1VV5XnebDbDYrnVamUYxu/3r3YgvszDhvFExsbGVFUVRZHn+YmJiatXrz579qxrn+EHFQ9k1/Drr78+f/7cZrOBDIUEl5FIBL7dRb0OQZAdAGRCs9mcn5+vVCp+v79QKHz77bcOh4OiKE3TIDkV1PyhKMqI3bTZbAzD8DyfSCTevHnTeba1PyPI8HD9+vVoNFoqlQKBgCiK9H8gSdJsNqfTaXx1dwWdj+m7775TVRWS7DkcjnA4/OOPPw6wbZsDFQ9k2Gm1WuVyOZ1OB4PBUCgEJYRhrnD8+HEUnQiCrMbc3JzH48nlcpFIRBCEUCjk8/ksFgssW0BEB0VREC3mcrkOHDjA87wkSTMzM2hHRXYRXUPhx48fnU5nMBisVqter/fcuXNWq5XjuImJCYZhJiYmtuTn1lO1E8foz6H37kHpUoIgeJ7PZDI3b968devW7rrJqHggQ4rRkf766y9d1yVJggyAsDApCEI+n++Ufbur4yEIsiV0dfzHjx//+uuvlUoFCmzduHHD6XQWi8XJyUlYsPD7/RCgCfHikNtndHT05MmToVDI6/X2nhNBhpZe4xv8vX379vT0tKIoBw4cgEBkVVUlSQoEAhzH3b17t+8Z1j7/J/dBrWMHSKfTYJtlGObSpUuPHz9+/fr1oBu1MVDxQIaRTmn16NEjs9nMsixFUTRNj42NRaNRrEqOIPuK1SpydPLw4cMzZ87UarVarTY7O+v3+8G4AaV+wL5hRI0zDGOxWCAxpdvtbjabjUZjtTMjyK7AeHvj8Ti89oIgnDhxIpPJiKLo9XpPnTrldDo36p+znt7XuwOuCW4TsPwqSVIoFLp//34mk9ldBUxR8UCGHafTadQMJkkSEssYoFBDkP3DGv29UqlomqYoitfrPXbs2PT0NMMwJEmCWyY4J9A0DVqH1WoNBoM+n0/TtB9++GFDP4QgQ0Xf+X00GnW73Waz2Ww2S5IEo6fT6bx8+XImk9nQ672aQQMzK+wAfU0wCIQAACAASURBVB+uw+EAsy04nMfj8d3lF4qKBzJcdHWwYrEIU4eRkRGGYVwuV+8+KPUQZD/Q29OXl5ez2WwqlYLcoAzDgF4BEgMcEox0VQZjY2MnTpwYGxuLx+Of/AkEGWZWe2MXFxeDwaDFYoFQcpIkeZ53uVxzc3NrHLXRn8OxeAfovau3b98GEScIgqZpfROUDTOoeCDDQt/lE7PZbEwgPB7P+/fv26tINxR5CLJPgM7eaDSq1eq3336bSCTMZnMqlQJPKpIkR/pBUZQoilCAHIqNdp5ttV9BkOGn611dWlp6/Pixruud6jdN0xaLpVqtrnbUFrYE+87W0ns/oegQy7Kjo6NOp3Mgrdo0qHggQ0e9Xm80GqVS6dSpU7BaSVFUNBqFbzF8DUH2J0tLS9ls9uLFiydPngwEAhaL5dtvv71165bFYqFp2rBywEzL+EBRFDicRCKRbDYLp8LpEbJXaTQa5XI5mUxqmgajJ0EQHMeBtyEkXfgc8vl8pVIplUo3b94slUq5XO7+/fuRSGR+fv7333/3+/3hcPjcuXO9NdGRz6RTXs3NzTEMAxUhLRaLMUHaFaDigQwXRtdyu92wcknTdC6XG2yrEAQZLOl02uv1JhKJY8eOxWIxsF0oipJMJiGEo9O4AQsWJElG/0PvCT+pe6BaguxGYrFYJBLxeDxg/RsbG6MoyuFw0DStaVrXzut/yY09M5mMxWLx+/2apiUSCVEUQc8fHR0VRRGGbOh9p0+fLhaL2I+2CY7jQNwxDBOJRPL5/KBbtF5Q8UAGSdfYv7i4GAqFwuFwPp9XFAWEFyawQpC9zdpTk+Xl5Vqtdvfu3cePH1er1W+++cblcgmCIMsyTdOCIECtcRiDwZfd6XQKguByuTodSxBkr2L0oGKxaLFYZFk23A7B4gFWQaPe7ibODDSbTThhpxe0ofCD/0+X/h8MBiuVSu+pkC7+/PPPDe3v8/kMJ1KPx3P69OltatiWg4oHMjC6xFAqlbJarWaz2fCaYFkWlPhWq4WlghFk7/HJGgIrKyvZbPbatWtffPEFwzCHDx8eHR2FJLmQUxKSTwCapp04ceL06dNut9tI84LiAtkPwHseDoddLlc4HHa73ZIkSZJE07TX6x0fHzebzYb703riJMvlcqlU8nq9zWbzxIkTqVQqHA4b+kZXzoZOfaNveJXJZOoMrEJ62aikajabIPegTkuXY8gwyz1UPJAdZY0IjVwupyiKIAgMwxAEIUlSvV5frToSgiB7gzX6+MePH9PptNvtPnv2LExuBEEgCOLIkSNGRQ7wXA8EAna73e1253K5er0+mCtBkIHy9u3b06dP+3y+ZDLpdDo1TYOwcq/Xy7Isz/PLy8vrOc/c3Bz4LoJuT9N0b2o46I+dxsbeb7v+5XkeSuUgvWwiP1ir1YpEInCfbTZbuVx++fLlrsgzhooHstN09oR///233W7XarW5ubkzZ85MTk6Cadjn87X7zUgQBNkDrDOyIhwOQyoqCKMkCMII3gB9w+Vy8Tx/+vTpJ0+e1Gq1f/75Z52/giB7j1evXsmyrChKIpHQdf3UqVMMw/A8D8t509PTxp5rZ3Lzer296sTaNg1jhzVUkZGRkVAohAuIawAzok9i3MPl5WWQhGazWRRFnuf//vvvbW7jFoCKBzIwWq3Ww4cP6/U6hMHZbDZIQXP48GFMcIkg+4TOTg35sguFQjqdVlVVFEVwrOpdYYX0oOFwOJVKLSwsdCUJ7bvsh9ID2dvcu3cvGAy6XK5gMHj//n1BEDiOkyTJ4XDIstxb3Lorhb3xbzabNSyKn8TYjaIov9/P8zzP87BA0HuGc+fOtbEnbgWdUT2Q24qiKIvFMthWrRNUPJABAH3m+fPngUAgmUwaBb9EUTx9+vTa7qcosxBk79Fqtebn51Op1OTk5KFDhwRBcDgcYNno9dkAt2ZJkiqVyp9//vnJQJEduwoE2XmMNzwWizkcDqvVKghCOp2GhXBN05xO55UrV/oeshrgZNUFx3EwWHemqzaZTBaL5erVq3DOpaWlK1euCILQ22d3V8rXgbA5YQUPCx4ERHoMudBDxQMZGD6fT1VVn88HThRjY2OVSqV3bXLIuxCCIBult4O/fPkyHA6TJAmTG2PRtAtJkliWJQiiUqnk8/n1ODSjAEH2CcFgkOd5k8kEyaZB8XA6neC63MsaXWNsbKyrAwqC8PfffweDwUwmc+XKlXg8/s033xhBI8apKpUKwzC9PZem6S2/3j1DX5Ps+gVXKpWCm0yS5K6oPYCKBzIAXr16lc1mrVYrRVGCILAs63Q6ew3BneDsAUH2Kn6/X5IkTdO8Xq/T6ey0chhGD1ieyGazm0gJiiD7AZfLBYvfkPONZVmKolwu18LCQu+kdrVEL/C3UCg4HI5oNJrJZMrlMiS1/+Qo7HQ6WZbtNVGSJLnrqmvvLiABgCRJ3377bXvo50uoeCBbxjrNFKlUStd1XddhMkGSZDAY/Pjx45B3FWSrwAeNAJVKpVwu//rrr6qqUhTFMIwoipBOB9QM8O6AFQpZlo264218ixDkv1WFZrPpdDpB36BpmiRJSZIYhrHZbDvTmEQiYVSW6IQgCFVVjfTWyHZw7do1iDLXNM3j8bx7927QLVoLVDyQ7aKv9TCTycTjcavVaqyFTExM1Go1nEbsbTpDdPBZ73lWi8gy/i2Xy+fOnbNYLLquG0k/R/47GhXW8AiCiEQiXQXIMFgcQTpptVoul4vjOFEUHQ4H+BFAisivvvpqB34dMlLCqkEXJpPJbre3scNuM9FolCRJXddtNtvVq1eLxeKgW7QqqHggn8saftVdX4VCIVVVIdUGmDuCwSCGc+wf8PnuYdaZeL7dblcqFU3Trl696nA4OjWNrprHoijm8/lHjx5t+ucQZD/QarVKpZLFYiFJ0mKxKIoCrgTAgwcPtulHjQ+Li4uqqhoxIV2h5xRFvX79uusoZGtptVrNZlMQBKh0ZDaboWTKcN5wVDyQLWON0KhWqxWLxSiKIknSKEweCoV2vI3IwBhOCYhsCb0mjq6lh0wm02w2nz59Cu4fZrNZ13Wn0wn+6OCMzjAMbBkZGdE0rVgsrpZqAt8lBAGgL/z8888ul4sgiK7CmiaT6Y8//tju/pLJZCDlw0hHNQ8jRiuZTHZ1W+y/W0Lv/Xz79q3FYpEkKZFIpFIpiMwZQlDxQLaA1cLUjM/ffPPNhQsXOpPxxWKxvgciexJ80PuBvk/5+vXrhw4dmpqa4nk+nU6DjgELEBRFGQUB4XOpVLp///7S0tIaJ8fpC4J0kc1mZVlmGAY6F/j6Qy/bgV8PBAK9Tlage2Ayqx3G7XZTFKXruiAIly5dymQyQygnUfFAtpK+r3ixWJRlORqN0jQN0aLJZHKN/dc+G7KrwWe6JzEe65s3b9rtttfr9fl81Wo1l8vlcjmoqkuSpJHdv2uaYrVaWZZlWbbvOdv42iDIKrRaLehiEFBOEITD4aBpGkwQ+Xx++34XPty/f79vaAcYM7sy+WJH3nK65OTZs2dNJpPZbBYE4eLFi5DkathAxQP5XFZzrmg0GuVyeWVl5ezZs06nk+M4mHAYNYZRBu0rjCyNbXz0e5FKpfLu3TvI61+tVv1+/7FjxwiC0HXdyLAJ9o2u2mQEQSwsLHSdDc0aCLJOEomEKIpg4jD6FOj5IG+BLexKxlifzWahYEhXCl1w+lIUpe+ByLYCYR6yLD979iwYDA66OX1AxQPZYhYXF6vVajabDQaDoVAom82KosgwDPSEFy9erOckKJ72PPiI9xIrKyu//vqr8W8qlRIEQRRFI8DUyFs1MjJit9thhkQQxMTERLlcHmDLEWRX8/Hjx3w+ryjK119/DT4FRkj3anUDtwoolK7rem/FQLPZbLFYnjx50nsUSv7tA+5tNBo1mUwMw3zxxRcej2cIBSwqHsh66Rs73itEfvjhB6/Xazabo9FoIBAAlWNkZIRlWciJiSDIbuGTs4RGo7G0tBQOh+/fv//y5cu5ublQKOT3+8G3CiZARhSH4fztcDj8fr9h/EQQZD309scbN27cuXNndHRU13XoXwzDQHe7fPny55z5k3tKknTw4MGxsbFeJysoZtdG0+UgWFpaMoqk6bo+Pz+/nvKROwkqHsi6WDt8HFhZWTl16lQoFJqbm4NMNUYtMJvN1jdgFOnLOoU1inJkULx9+xbCOeLxeDKZnJmZCQQCbrd7bGyMYRjwrSIIgmEYCCLvnJR88803nafC1xhB1k+XT//ly5ctFosgCKDnj4yMWCwWk8mkKAp4MG5Co1jP9lqtRpIky7J2u71vqXLIH7Oe8yNbztTUFDwUnuf9fn+n7jEMTwEVD2S9rKF7QN6q27dvP336VNf1TCYDwW2w3vnDDz/seGN3MZ2mpL5ZCIdBcCD7iq638a+//srlck+ePPnuu+90Xff7/ZCryph2gIe3UUEZthAEsVpNK3ylEeST9KZb+PDhg6qqZrN5cnIS/KwoirJYLDRNQ82+3gPXeeY15qlQ/RMcGWialmXZSBphQJLkn3/+ucYPYZffPsCgYSz6nDx5cm5ubtCN+i9Q8UA2Q6+pzuv1ZjKZRCJx+PDhdDrt9XpB6wBvCpQyGwUFNDJA1n7r/vnnn8ePH/t8PkjaCOHjIx0p/FmWFQQBdqAoampqCvyM8a1GkC0kk8nEYrHnz5+fO3fOSCQlCEIoFOp1MViP/bzvgle73a5UKplMxuPxxOPxYDBoxGsZjlVdFo+RkZHOBUfMULfznDlzBkxSEIdTKpWMrwa+gomKB7IB+s4bKpXK69evZ2ZmEomE1Wo1m82w3jkyMnLnzh2UMpugVy4Ui8XffvutjVIb2UG6ZiGvXr1qtVrNZtPhcJAkaeTABTePzmkHTdOJRMLr9bpcrr6W0oGPfAiyu+gbY5nL5WKx2OLiot/vB6MiSZKyLPeucK+/r/VNMUdRFFhUeJ7vVTOATq0DtJGurFZout8xWq3WnTt34ClwHKeqai6Xaw/NPUfFA9kwXVJjZWUln8/bbDbw7KRpmqZphmHS6XTXIcjmUFWVoqhUKgX/4s1EtpuuKcLHjx9zuZzP50ulUoqiaJomCALHcYZbuTHnYFnW5XLB3GVpaWlDLhwIgvSlr9ZRr9ez2Wwmk6nVaoqiQGyV2+222+2NRqPvgZ/8iUgkoijK2bNnE4lELperVCo3btwAlcPQMXqNG52fuzQQhmGWl5fXEyOKbDlGYg+CINxu9/DIXlQ8kPWymrX0999/n5yctFgssBBiMpkikUjvbsjmWF5eBvFhtVqhGtTi4mKz2Rx0u5C9z+Li4r1795rN5tTU1MWLFymKcrvdoGwY6argL6y2WiwWn8/X5VW1GqiHIMgmgJ6Sz+dPnDihaVokEpmbm6NpGsrGWSwWr9dbq9Xaq6gra1AqlSKRCJg1FEUJhUKr6Rhrb+/SPdxu9/bdDWQNoHga6B4kScLGYZC0qHggm6RWq9Xr9fn5+UwmI0kSuFsQBNEVSj4Mb/muo/Om5fN58GMxm82KokSj0adPnzocDkxFimwrKysrp0+fzmQyc3NzmqY5nc7VljmdTmcymZRlOZlMdp7hk8ucKBwQZBNUq9VoNMrzPPgX+P1+WAiAnC6JRMLYc0NdbGVlZXZ21mQyqaqqqqrFYumraWzI4gGrEizLQmlRZCcJh8NGzo+uapKDBRUPZDM0Go1IJBIOh2dnZ202m+H0efjw4UE3bVeymjUpEom4XC6wdNtsNlVVwaAky/LIyAhN07lcDmdvSC+fk0Pz/fv3sVjs0qVLUOkPvCg7ZxtQJUAURYvFAiujPp+vSxMeeKp4BNmrpFIph8PhdDpZlp2enj527BhEd0AF8c2lMILeCjrMJ00Z69wOMAwzOzu71fcA6U+nDbnRaIB1mqZpURRXSyq486DigWyY169f37p1KxqNjo2NKYoC02KWZa1W6z///NPGhczN0uV2Mj8/D8G7YEY3hLtRKAr4/vvvB9pqZNewWlT38vIyOIW3Wq1qter1ehmGsVqt5H8w1jLhA0EQPp8vm822Wi2o5oEgyHYD3fbJkyczMzOg/I+Pj//f//t/BUFwOBwURUGYx+fYFsCw2VeRWFu7gB0kSVJV1ePxGH6YNE13GULbOEPYNnpvLNjELBYLRVHPnj3ru8/Og4oHsmEqlUoikThz5ozZbDYmIh8+fIBvh+G13hWs5nYCHw4cOOB0OkmSZBimy5wdDoe7xP3c3BzedgTYqHNFrVZrNBo3b95cWVl59+5doVCApdORkRGO42DqAP9SFHX69OmpqanZ2dm+FakwYANBtoOuDgXuzbquHzp0SFVVlmVFUWRZlud5iAPcNGfPnu0aXDoNIJ1LYL1OVm63O5PJGA2+evWqEeOO7BhdQnhqakqWZZPJJIqiy+W6fft2rVYbuHxGxQPZGKVSSdM0WZZFUTSCnkGTRtbP2vkEl5eXdV0H82inlIe/RsSYgdlsNlasd/QykCHmk9Hb5XL5zp07z549K5fLMzMzpVJpYWEBqo91TjigALmiKH6/v9VqdZVDXiNsA99GBNlyYrGY3+/3er1ffvmlpmngCQkjsjEQbJqVlZW+xg2O4wiC0DSN4zgjyZWhmUBCSyPlyToXIFA+bAddOdAbjYbVajWZTH6/3+fzhUKhaDT6999/twd6/1HxQDbAd999J8syRVFGpQ4MGttaWq0W3GGe5xOJBM/znQtOneOBETQG6Lo+6LYjw8Jqs//Oz/V6PRAIzMzMTExM+Hy+RCLhcrnAR4LjOHjToB45y7IHDhwIBAKdJajaa6ocq21BEOQz8Xg8Xq8X8llB1XCordGb3WETLC0tQS4TCBqhKMrr9c7MzCwsLNjtdqgW0mnlMAameDzedSos1jEkwFPTdT0cDlutVo7j4vH4YJPToOKBbABFUVRVNUSPLMuDbtEewZDOxWLRarXCkhJECvZNFWIkM+3cGAqFBnsVyPCwhhrw8ePH+fn5cDgsCEI4HAZfvk7g3aNpWpbla9euPX78+NatW+hGhSADp1AoaJomSdKBAwfu3bt34MABkiTtdjtN0zab7enTp5/fPW/cuMHz/JkzZ7py8mazWUmSuowhkEfb6/V+8rS4MDEokskkFFhjGIZhGJvNlkqloJ7goEDFA1kvi4uLDofDWINnGObXX381vsV5yaYx7lgul3O5XNPT0yzL9q0F2/kvOMCM/HfWwnfv3g32WpAhp9VqFQoFVVUh82an2x7MIUZGRiAecWJiIpvNrnaSvp+7NqIoQJCtYmFhoVAoBAIBq9Vqs9kCgcD9+/ej0SgElJMkuZ7Z/zpZWVnp8thZWVnxeDyQTdEQF8ZIlM/n+9o/UTgMhK5722g0wH41Pj7ucrm+/fbbV69e/fPPPx8/fhxQA1HxQNZNKpUyPKxsNtuTJ08G3aJdTK/YvXHjhiAIBEG4XC6HwzGyCkZudUmS3G43BPwZ38Zisb4nR/Ytc3NzoVBoaWkpkUhkMplyuQy2jk77hqG7wnaapt1uN6x39vLJeQO+fgiy5VSrVUEQdF1XFCUej6uq6nK5/H4/ZLWmaboz38OW0Hm2UCgkSVLnWANYrdZQKLS530VBsR30vavgNEuSpK7r3333XTqdXlhYgGi9gYCKB9Jury4ClpaW4KtgMGjIGpqmsXL21lIqlSYmJmRZttlsiqIYi0ldy0uaptntdqjmAWWeWJbtzK7LMMygLwXZSj5nll+tVpvNZjqd9ng8pVKpVCp5PB5FURwOR1dpMLfbDVmbk8nkyZMn6/X6tlwMgiCfYrUenc/nBUFwOp1erxdqloui6PF4bDYb+Flt36Aci8WMrO6dcoMkSVVV1242MgxEIhHIVQgTBqfTefny5WAw2LXbjj1EVDyQVXnz5s27d+/u3bsXi8Ug4MxkMpnNZsycuyV03j1VVXVdhzWJvoYOQRC++uqrer3+7t27V69eGdoIRVFdg8Hi4uIALwrZJlbzkF4jwjsSieRyuUuXLoXD4Xg8fvr0aajI0WnoMJlMgiCMjY25XC5JkoyujSDIztPXiRE+5PN5m+3/Y+9sgpPI2sXPZ3fTdDchNCFod1C0Q9oKSsi1fTGkxBKrQmyrglWDdcUrc0tciIvBEhdX3IgbmSpxc40rcWWsMu6G2YlL42Iyy4lbcWlmZVy+8F88Neffl6/EmEA+zm+R6jT9cbrP6XPOc54vO8MwDoeDoii73U6SpNvtpiiKZdmtNdnXFiOfz3s8HohqpTUANhqNJEkiIys8GdjhuFyu4eFhr9dL0zTLsqFQ6Pjx461Kj97UIxY89i+dpizVanVtbS2TyVQqlUajsbi46PP5oK8JhULz8/NtT8dsAniHDx8+ZFlWUZQmqUNrBuP1ev/66y90Ioo71LoKdfPmzf49EGZ7aZqLoL9oP6x6Pn/+PJ1OHzx48OTJk6dOnZJlmSAIi8WibVcoFrbNZguHw8+ePcPh6TCYnYP2G19dXQUD/RMnToTDYUmSZFnmeR5MaGRZ3qa737x5c2BgIBwONw1JLMseOXJEEATtwZidjKIoDodDURRQd7vd7gcPHvTLxRwLHvsa7ZSloZkHX79+fWJiQlXVSqUiCAIsdQwMDKysrGiPxPwg8BrHx8dpmj579myrNzlsjI2NIY02gBQdKCkpOng7BiHMjkL72aKNYDAYiUR++umneDwO66DgdarX60FMhW0koNpstng8/tNPPzVdB4PB7Chyudz8/LzH4zl69Oh//dd/FQqF0dFRlmU5jguHw4cOHdJG0d3CD3lubu78+fOHDx8mSbLJwgp8EbGCdBeRTqch+HIwGDQajZIkZbPZSCTSl8xLWPDA/H8KhUKxWEwkEqOjozabjWEYlmWhrxEEoXVBFE9WtgSe530+H2jMkS5bGy2XYRjwGkf4fD4UW+zChQuSJKE5pclk6teDYLacLjEo6/V6Lpe7ceNGuVyuVCo2m+348ePBYFCSJBA5tLMEFK5Kp9OxLGuz2ZDv+LrpODAYTC/R6jp++eWXcDg8NjZ26dIlMLh9+fLl2NiYy+WanJwEdQQKL7mFH2+9Xr969SrLstCBaPXwkC4QNPC4u9hFCIJgsVgYhoGghT+e9WXTYMFjv4P6uHK5HA6HI5GI3++HBHaor2FZtoEnKNtDtVoVRZGiKORF02ptBbmZtC88mUyiX20229GjR9EpZrO5f0+D2Xrayh6VSmV5efnSpUsXLlzIZrPZbDYajaqqOjQ01DRRQA0JYhLodLqLFy82XRl/2hjMjgJ9g36/X5Kk2dlZ0DxAUj9ZliORiCRJbrc7m81+/PhxC+8IrK2tQRgrrTUvip9LUVT30zE7jXq9/uTJk4GBAYvFYrfbz549WyqVtPbbDazxwPSexcXF69evT01NQaIZFFhJFMW1tTV0GO5ftpCVlZVIJGKxWNp6d0AVWK3WWCz29etXdBZIiTC51Ov1sJ6tdQjpFAgVswdYW1ubnp7O5XLLy8uKomQymUKhkEgkSqUS8sVCQCOxWCySJOXz+XA4jBLWdvqQ8QeOwfQX7Tdos9lcLpfP56Np2mQyORwOmqYLhUIulxMEwev1VqvVxv9VkmxJAS5dugSaDV0LJpMpkUj0xUQHszlQ83A4HCzLsiybz+fBibfpmN6ABY99SmsjSyaTgUBAURTwH4ApLE3TGzkXszkqlUoymQR7ttZIhbCT47hWjUdD4+YBRvyjo6OgQqUoqlPeN8xuR1XVycnJUCgEkoYsy6qqer1eWJVsmiUYjUaKokiSDIVCcHqXfF4YDKbvNCkhV1ZWSJIMBAKyLFssFoIgeJ4fGBhQFCUUCsmy3NrVb9XnXCgUWnUd8NdqtW7JLTC9J51Om0wms9nM8zyEPexLTBEseOwXuvRH2Ww2kUg4nc5QKORwOJCdBsdxvSzhPiSfz1er1SbXPdTRgwcYcuhHLC0tVatVbS4ni8WSSqWCwSDDME6nMxwOt94Lzy93FN+7Qvnq1atwOOxyua5duyaKIggbDMNA42mSWnX/hFpOJBJXrlzBVY/B7AqaPtVr167ZbDbwCTaZTCzLghV0MBj0er3JZHL7yrC6uqrtVUiShCgmer2+aaUcs4tYW1sD+whIGhaLxW7durW8vNxj/RUWPPY7c3NzgUAgEAiYTKZQKIQMeGiaxuE1t5V6vf7ixYvx8XGTydRqlA+1cObMmaazfD4fSjKo1X3zPG+1WkVRDIfDHo+n9V4NLHvsMDZi7OT3+0OhULlcHhoagpVOQRB0Oh3YQyKRleM47SwB4v3/+uuvvXoUDAazNWiVHvfv34dU5dZ/MJvNNE1fvnw5l8tt360BjuNQl6KqajAYLBaLeDlyV1Ov13me1+v1JpNpdHS0WCyWSiXI5tHJ5W87wILHfqFTY3r69Gk6nc7lchRFoY7GYrH0uHj7kHfv3s3NzdlstrZSB5jKZLPZZ8+eVSqVcDjMMAysZEMSWd3/jbpLkuTg4GAqlcrlcljjsZPp3r+/f//+xo0b+Xx+ZmZmaWlJEIRsNnvlyhWHw2GxWJA9FajLdf8EmaFpWlGUQ4cO/fLLL41G488//2w0Gv/+9797+VwYDGYLqdfrtVpNlmVZlo1Go9FoNJvNJpPJ7/f7fL7tuynaTiQSaHyZm5uLxWLVavXnn3/GQ8muZn5+Hpx48/n8ysrKu3fv0E/YuRyzNTQlGmv69f3793fv3o3FYqFQCPkM0DR9586dpitgthy73Y7yALZVd1gsFlVVCYLQ2u7r9XpY9GprWiOK4pEjR6LRaGtGUszOoUmvnclkIC9nsVgURfHevXvBYHBycrJQKHAcR1FUIBBwu91OpxPqXa/XQ6uA5MFms9lisSiKUigU+vdMGAxmy0BD9tDQEE3TYHbrdDonJiYuXbrE8/zi4uJ2331lZQWiWpEkabPZ0uk0Dluy24GalSTJaDQGg0GHwwFrMdzYkwAAIABJREFUVdoDsMYDs2W0zRWYzWbT6XQsFuN5HhntQPLjpnN7Wtb9QbFYbMrNhNw2kDSCRI4u8gnaJkkyGo1GIpHJycl+ZSTFbASt0iMej6dSKYiHe+zYMVVV79+/D+46VqvVaDRCNBuj0QgyJywQgKcpiByHDh3KZDL4I8Vg9gy1Wq1er6+srDgcDvjqr1y5cujQIYZh3G43y7LLy8tbftPWPmRqaspms3Ect005CjG9BFVcoVAgSdLlchkMhsXFxXK5vLa2lkqlsMYDs73k8/lcLkcQhM1mIwgCprDxeBz8Onpp7bdvefDgASwmtc3dgYB5ZyfZQxtsRKfTDQ0NhcPho0ePooSD2LtjJ7O4uJjP59Pp9M2bNy9evCjLcqFQgPAAyO5RK45C9GSIXQZ5ABOJRAPXLwaz5ygUCvF4PBwOi6IoiiLEt6VpmqKo6elpbYz77WNlZaXVzxCz26nX63a7naZpkiRTqVSxWCwUCr306cWCxz5laWkpFotp8z8cPny434XaXzx8+BASQrXGStemIfd6vePj400/0TSNPEO0AgnHcefOnZuYmHj58mW/nw+zDvPz80tLS9lsNhAINBqNaDTq8/k8Hg/6KpvqF6QO0GtFo9F79+41Wqy22t4IiyUYzO6iWq2eOXNGlmWe5wmCYBiGZVmKoubm5vx+f88U2q3rVrgz2dVolR7gKDgzM3Pr1q2///4b5/HAbC/FYjEcDoOiQ/dPsogG7lN6SL1edzqdBoOhbYYmhMFgUBTF4XB0OaZJYnE6nTAs4drcyVQqFUmSJiYmPB6PJEnhcJhlWbCnQsoN1AZMJhPDMDabLRwOgzfIxsHNAIPZdayurgYCAbvdPjY2Blpxs9nMsuypU6cURfneTuB7wZLGfgACllgsFlEUIQ1lz8CCx96ky9pnJpMB0x3EwMBAj4uHaTQaTqeTZVlZlrsLEj///LPRaAwEAhaLpcthsAEaElVVm9SmePDYQrpYr7XubLvn119/5TjOYrGAcqOTAw+Kbe12u8H3A9cjBrPHaPqo4d+FhQVIq8VxnNVqBW2n1+vleT6dTveppJg9xcWLFw0Gg9VqFQRhW2MVtIIFj71Dl0kJ+ikUClEUpZ3ccBxXrVbxhKb3CIJgMpmasgdqp6GwATb9CwsLkOBc1+LXod1J0/SDBw/AdKeB5Y2tY3Nvsl6vP3z4cHl5eXFxEYkNxWLR6XRCQMNOwobVaiUIIhqN5vP5piEB1ykGswfoolW4ffv22NiYIAg8z6M8HmazOZVKNeV6w2B+BEmSZFkWRXF0dLRUKvXsvljw2Gt06ZWSySS4E6Epjt1u734KZpuo1+tHjhxxuVwej6eLBgOJE5lMBtnhNEkd2p0EQYRCIUmSGjhCQM9B77lSqVSr1XK5fP/+/WKxKMtyPp+fmpqC/SRJgu1EkwAJ2g8IYJVMJrUJwpqqElcoBrNX+fDhA8dxL168mJqa8ng8sizb7XaCICwWS7FYbOBOALN1VCqVAwcOuFyukZERVVXn5+d7066w4LGnaKu0bTQauVxOVVWSJAmCQBMdWZYbuBfrHy6XC3zE2+outDvNZvP4+HinPIPas0wmk9vtPnHiROvtcBVvK+j1yrKcy+WSyeTVq1d/+uknRVFomnY6nUjeaFvXYEphsVjQshOuLwxmn6D92NPp9JkzZwiCgPGapmkQPFiWzWQyrcdjMOvSpcHY7XawvAiHw+VyufvBWwUWPPYsSKIAN1ZZlrVxOVEX1sBL433iwoULQ0NDWjGj1dYf7YnFYmazGZLXttWKoFVzQRBQzHVcoVtOW0H9r7/+QjsVRVlcXEyn00ajkSAIURTbSoyoxlmWZRgmm82OjY118vDDXygGs5fo4gyWz+cvXrzocDggcq7JZLJYLDabjaKolZWVnpcUs0foNHYEg0FYj7bb7ffu3etN6mEseOwROrWqz58/u93uo0ePDg8PoxmP2+3Gio6+43K5kLTQRYkB8UwURTl16tTNmzddLpderx8YGLBarW2Pp2k6m81u0PUZ84O8fPny7t276XTa7/fHYrEHDx6AfTYkG25brVDddrtdkiQIidsW/IViMHuYth/4t2/f0ul0IpHgOM7pdIJnudFoHBwcFAShTyXF7GUWFhZgQdNgMJw+fbo3N8WCxx5E25etrKy43W6bzQauHZCBqNMpeJbTS7QT0066Dr1e73K5rFZrNBqFpQioo9XVVYqiWgMi6fV6SZKuXbuG7oIXy7ePdDr966+/njx5MpVKRSIRhmGaKqUpAz38K4oiZIr93tvhGsRg9h7aLrpcLh84cCAcDpMkKYri8PAwaERFUTx27BgepjGbpkvjAStfk8kkimKtVuuB0gMLHnsNbcOCWDr5fJ5hGDSRXVhY6HQ8ppe43W6Ia4wkkKYJK/wtFAqRSAROQZVVLBabDkaX4nk+HA433QvX8lZRq9VgI51OnzhxwufzRSIRl8tFUVST5ookSZSnBaIWkiQJicYRG68XXIMYzN4mEomMjo5SFEXTNMuyENLKbDa73W6PxxOLxdCRuDfAbJpWT2C/32+1Wm02m9vtvnz5ssfj2e4yYMFjV9LFkKZerz958mRmZsbhcOTz+VAoBLmQCYI4dOjQ169fe15YTHsOHTrU1hRHC0EQWm8cRDKZbFpH1/oMBIPB3j/OrqNTJIYuexqNBgSbWl5evnTpEs/zwWDQ4/F0ijYGuf9kWZZl+c6dO4VCYfseB4PB7Bba9i1erzcYDNI0bbPZGIYBpz6CII4ePdrJehaD+UHq9XoikSBJEryJAoGA3+9vTQW2tWDBYxfTtif69u3b3Nzc7Oys0Wi8ceOGy+WC2c/g4OCXL196X0hMJ7ThcZswGo0Mw5AkOTEx0XQWVPrAwACsqbeeazabT5061Y8H2q10ybap/ffPP/9MJpMTExOrq6u3bt2SZfngwYM0TTcZvBEEAQIhRVHT09PJZLInD4HBYHYTTd1LPB53OBySJHEcx/P8iRMnIODh4OCg3+/XpirHEghma/n777/Bv5yiqHw+/+jRI1mWUYia7QALHnuNdDp94MABq9VqMpkYhgEzD4PB8Pz5834XDfP/qdfryOumVXgAuymz2fzixYums+Cv1WqFROatjulms7nV1ArThXUzb0L+jZs3b7rd7snJyStXrni93qZEHFqNE8dxw8PDPXwCDAazK0E+e0ePHvX5fDRNDw8P22y2dDrtdDqNRqMoih6P58KFC53OxWA2DWpCgUDAaDTCimcikYjFYmAVvE1tDAseu5jWNvH27dtYLKaqqsPhgMkrzIdUVW17PKaPcBzXPTWH3W5/8eJFWxMgWZYFQUA6E60TM8dxqVSqHw+0K2lrcKX9W6vVpqenr169CouRbrfbaDSiitNGHqNpGnnjtL0L/gAxGAwCdQixWMzlcvl8Po/H4/F44vF4tVpVFMXpdIqiqNWa4j4Es+XAjAJNISwWy4EDB5xO5+rq6jYFp8GCxx4BXDtGRkZEUXS5XKDrgCnRkydP+l06TBvS6XQnkQPmtSaTqdO5LMuOjIzQNI1OgRmwwWBwuVzpdLqXD7I3qFQqi4uL7969Q2uQi4uLJ0+eNJlMJpMpFos1aaia3Dnm5ua+ffv26dOnpstikQODwXQhnU6Pjo4yDOP3+9Pp9MTExNraWrVaJUlyaGjo5MmT+Xy+gfsQzDaAGtWvv/6qtRn2er1erxfMZLaj4WHBYxejbRBv3rzJZrM2mw08OlCgJEmS+lhCTBdUVW0rdej1eqi+gYGBtiemUilFUSDgSWs4XavVWqlUevwsu44meaBer8disXg8DoLHmzdvEolENpsVRVFbKeAvjt42wzAOh2NwcLBV3mi6eM+eC4PB7CLq9Xo0GvX5fENDQ1NTU3fv3h0ZGSmVStVq1ePxzMzMdEqtgHsVzBby8OFD7Zqa1Wq9dOlSY9tGMSx47G6gNdy5c+fly5ew/o1aj8FgaA2IhHurnQPHca0ih1aQkGW5bX3JshyJRMCUrmn13Wg0dtGTYNpSKpXy+TzHcQcOHCgWi58/f75y5Yosy2/evLHZbK0vGXA6nYIg/Pzzz927ZvzFYTCYLrx48eLatWtut/vIkSORSCQcDl+6dElVVbvdPjs7m81m+11AzN7n4MGD2hkFy7Jutxtix2ONB+b/AA2iUCi4XC5JksAXDRmda8N+Y3Yg2kltExDPxOfztZ7122+/FYvFYrEoCELrWSRJ+v3+3j/L7uX27dvDw8PgE2UymVwuF8/zDMNABGpdO/d9hmEYhnn+/Lk2CWBbVxwsdWAwmC6sra0VCgVZliGMoc1m8/v9HMfJsixJ0tGjR1dWVvpdRswep16vnzp1CoxlYO4hiqLdbt++O2LBY9eTTCa9Xq/ZbIZIzCB1eL3efpcL0416vW4ymfR6vXaZAckPgM1ma525hsNhURTT6XQsFmtyM9DpdARBoPgnq6ur586di8fjT58+bezXpfcuyTo+fPjw9OnTgYGBiYkJnudJktQaU+n/Qft6fT7f7Oxszx8Cg8HsNaAvisfjHo/H6XRarVaGYaLRaCqVguyBU1NTuLfB9AzdP1FS9Hq9IAjgWbRd99q+S2O2Fei2bt++LQhCMBg0mUzI4n9sbKyxXyeauwiO41iWbVV3OJ1OvV5P0/TQ0BAcqXVIsFqtYIKpKEqT8Y/ZbDYYDMVisdForK2tSZIkiiLHcZFIZC81hu99Fq0p1PLy8tu3bxcWFgqFAqwsUhSFxHWQA0Hqg9iCOp3OaDS63W5VVY8fP6715dhLrxSDwfQS1HtAFy3L8vj4uMPhCAaDXq+Xoiibzeb1enEng9luUBszGAxWq5UkSYPB4PP5zp8/v7y8vE03xYLHLqZWq/l8PofDIQgCTJuMRiNkVsbsfJxOJxjztDoPgBjZGhigXq87HA69Xm+xWCKRCEVRuv/rGWK32y9cuFAsFtPptNVqhX4kGo2i03v+lNvFd0WLgsPm5+eLxeK1a9fAVgrZJWqNqbR1ARKIoiitnugbvzUGg8G0Uq/Xb968abFYrFYrWErTNC1JElhbDQ0NHT9+vIH7GUyvEEVxYGAAppFOp/PIkSPbdy8seOxKUGcEWQV4ngfPckEQ2h6G2YEg256mWS9FUU6nMxwO3759+9///jccjKpyeHhYp9NBDhAQPLSyh9FotNlsVquVZVmapmma/u///u9kMhmPx/dSY9A+S6ftJmq1Wjwej0Qig4ODDoejVd5rqgWDwSBJUqlU0l4cB6rCYDBbRSwWi0QiY2NjDMPAIK6qKkEQoAO5du1avwuI2UdA1mmCIIxGYzweP3/+fGPbVtmw4LH7gEaQzWaj0SikJwdbEYPBsLS01O/SYTbKwYMHW1fZ4V9BEHw+n6Io3759055Sr9fj8bhOk7euKRCWzWZzuVyiKFIUBQ7TMzMzLpcrm81ChIq9BJLKGuv1jGtra4FAwOFwgB8UbDTJG/ARWSwWSZK8Xu/Zs2exdIHBYLaJ9+/fz87Oqqo6MzNjtVrtdrvFYvH7/QzDUBSVyWS+ffuGuyBMz/jll18MBgOYH3u9XrvdHg6Ht+leWPDYrWQyGdDPwrTJ5/O9fv1aewDus3Y4kMcDHDbAc0NrbRWLxebn57XHoyBmZrMZDqMoCiVsgakz2FYxDOP1et1ut9lsDofDDx8+1F5hD9BW89D0dLVaLZ/Pl8tlWZYHBwcFQXA6nRD4C3w54NVBEA+O48LhsDaATJfYuHvmNWIwmH5x9epVl8slCMK//vUvmqYPHjzIcRxN0+DgUavVcD+D6Q1aNw+I7kgQhMPhSCaT23RHLHjsPl6/fl0qlX7//XdJkmAOqtfrC4VCQzMxwn3WzufJkydIxaFNBQhKDFmWy+UyHKmdZ1cqFfAM0el0VqtVeyLMoeEvSZJgiMXzPBjgNSlPdjudGjnsLJVKoVDo7Nmz8H6MRqPFYmnSDsGL4nkeAk93+WRaxRv8fWEwmE1Tq9WeP39OEAToqAmCkCTJ7XbDnA+Fwsf9DKaXGI1GCFED0eQvX7785csX+AknENzXVCqVbDbr8XgmJiaQUyxN0+iADZq8Y/rO/Px8Jx8Do9GYSCQuX77cetbCwoLWTAgW75vm0xzHQVwspA3r/dP1kocPH965c6fRaNTr9UuXLomiCCZVSNLQ6/VIWkPvLRqNvn//vvuVcU5ADAazHZRKJbfb7ff7VVXNZDJg2WIwGBwOx8zMDDoM9zaYHgDNzOv1goU2jJjZbLbJ7GKrwILHbmJ1dVWW5bGxsXA4bLFYYMmWZdnV1dV+Fw3z3Xz79k07D27aJkkyGAyi9QZEuVyGIGZgLESSpFbpga4AbQP+DQQCfXnALaRter5Go/H8+XNVVV0ul8ViURTF4XCAv77WB0b7VqE/DQQCEHQYg8Fgegbqxz5//pzL5SBrhyzLo6OjHo9HkiSwvEUpFLDUgekldrsd5RCE1c9tyuaBBY8dTWu/w/M8z/PDw8OgDjOZTH0sGO4WfxBwM0Bz4qYk2YlEou1ZPM9rk4yaTCak3EBX0+aw36u5zL9+/Xrs2LGDBw96PB5wd0GZNyARBxI84GPx+XzxeBxL6RgMpr+kUim/368oSjgclmXZarUKggABhZBhPR5eMT0DGhuaOYDNVSAQ2KYkYFjw2DXU6/X5+Xm73Q7zKp1OZzabkRtAX8rTr1vvGYaGhpqkBa3gsbi42PasWq124MABURThMIIgOmWigG1tTNjdSKuUC9tra2sej4dhGMh5ZDQa7XY7mKhqxTmHwxGPx9d1HMdgMJjeoKpqIpGQZZlhGI/HY7FYaJo2m81ut7tVy43B9IB6vQ4BaWDBzmw2JxKJt2/f/v777zic7v5lZWUlEonAoghMKz98+NCXKRSet20hWpmhSePRKYlEo9F48OCBIAhwPCRy0bXgcrmsVuv169d3b311KXksFoPI9+Q/0DSt9bM3GAzBYDCVSnXXzuFIDBgMppdks1lVVXO53L1790DXwbKsXq+H9E2tx+MOCtMbIpEI0nioqorSM2y5hQsWPHYNiqLIskxRFJpu9rg/0t4OB/vbKj5+/IjiupIkCbntYKl+fHy89Xj02k+cODExMUFRlF6vR5kEta4dRqORZdmms3YRTWVGYlg+n4fk7k1eHFo9z8TEBOiLOmlLmv7FpoMYDKYHfP361e/3S5J04sQJp9Pp8XhOnjwZCoVomna73aqqwmG4R8L0gKbA9PF4HKaXBoMhFovNzs6ihTkc1Wpf0FTZiqKoqup2u2GaZTKZ0ul0H8uGO8QtZHh4GCbQFotFG3ypywePXKunpqbMZjPEuWp1MQcvkV1dWSiL1tLSUjKZ9Hg84NzSquExGo0OhyOXyzW+U5zY1e8Hg8HsfLR9US6X+9e//kVRlNlsPnz48OzsrMfjGRgYSKVSfS4lZv+hHf4WFxdB+WY0Gk0mE0mSL1682I6bYsFjFyCKos1mm5ubs1qtMKE8ffo0/NR7pUfb3G2YTYBe4NLSEopMRVGUoijxeFyW5bYHN/HmzRu32w1ODtpZOE3T169fX/f0nczi4mKhUHj58uXQ0JCiKK3Bu7Qiltvt/uWXX/pdZAwGg2mDtgcuFovhcJhlWXDqOHr0KMdxiqJ0Oh6D2T6aWhpN0wzDwKgaDAaz2Wy1Wt3ym2LBY6eTy+U8Ho/P54tGo2az2Ww2O53O/hYJ94lbiFapZbfbI5HIxk8BlpaWEomEw+FA7tQcxzUdvOuqrFKpJBKJSCRitVoZhmFZFtzHkaQBG0eOHPnxQFW77uVgMJjdyIcPH6LR6MLCQjAYlGWZpmme510ul9PpbFppauB+CdMPDh06BAvcJpPJarV2inDzg2DBo/906V9qtVoqlWJZFiZeoAJDHj+YvUS9Xv+R5OLFYtFisXAcR9M0pLHvO209K9YdTd++fZvL5RwOB8/zkAcQsvlq3TmMRqMoirdu3dqlYhVm74Eb4c6nv0NnvV5/8uTJgwcPIC/b+Pi4KIqSJLEs6/V6N7LkhMFsH9CD2Ww2GGStVqvf79+mkJhY8OgzTRMy7ei1tLSkqqrP5+M4zmw2QxTdPZ+Fej/zg3OXhYWFe/fuaePG7jS6P2CpVHr06FEwGDx8+DDDMC6XC+lwkKLDZrP5/X5Q/uKpHqZndJKccXCCXUF/qwbuvry8HAwGfT5fNpvN5XJer5fn+SNHjhAEceDAgefPn/exhJh9DvpAAoEAGnO9Xi9EYMPhdPcRKysr+Xw+lUppMxI08CC3F9l7tdnlidrO4R4+fMjzPLjXt03HrtPpWk3IMJi+0Nr8cIPc4fTdQbFcLvt8vsHBQYZhxsfHPR4Py7IEQYiiqPXHw2B6jPZzCIfDKPvw3bt3Y7FYJpPZ8jtiwWNH0LYffP/+PUVRQ0NDEOlIr9fXarV1z8Lsc/reKjZSAO0xhULhxo0bkLidJMmmLIoQ2s9kMp09e1YbIfe7bofBbB+4Be5Gel9rf/7554ULF8CdQxAEn88nSRJJkrOzsz0uCQbTCVVVYbZpMpny+Xw2m90OaysseOwUtP1gqVRaXFxUVVUQBMhXoNPpeJ5vezAGszPpJCE8ePBgaWlpfn5+ZGTE4/FEIhGO45oSroPGA8JNfv78ufVqGEzP2IiSGbfPnU8fjQVWVlYgVuHBgwetVqssyw6HAyIInTt37s2bN7j9YPoIan7lchnciQ0Gg9/vV1U1kUj8YPiWVrDgsbMA4/U3b94kk8lkMsnzPGQM1Ov1Fy5caDoY59PYveyripufn19eXl5eXi6VSgsLC+l0GswMwHOJYRht3kPAZDLZbLZYLNboatayr14jpvdgk6o9Qx+r8vXr1+/evVNVtVAoMAxD07TP57NYLBRFjY6Ojo6O9qYYGEx36vX6pUuX0Chst9uHh4dlWU6n0ziB4B7n5cuX4+PjKysrqVQqGo3CnAzH2sOsy05w/mm6++rqqqqqyWTSbrcPDQ2FQqGpqSmapiEyVWs6DpPJZDabT58+XS6XG1jAwOwYnj592mg05ubmWg1jcOPcjfSy1jKZzIULF8LhcC6XE0WRZdmjR48ajcZgMBiPx6PRaI/Lg8G0Ai2wWq2iUEYOh0MUxRs3bvz000+NLW2iWPDYEaAazefzxWIR1npZlvX5fNACNng6ZnexhRW3c9pArVZDkbU8Hg/P85FIxOFwCIKAvNbaQlFUNBpd16IUxxHC9JharcYwjM/nA3c7g8GQTqe1B+B2uCvoi3vYwsLC6Oioy+WSJMnv97Ms63Q6Dxw4QFGU3+8PBoM9KAMG04WmD+Hs2bOQNUsUxfn5+Xv37m15HGoseOw4pqamBEGARNSQFQ5SMuOxDbMz0coA+Xx+eXk5lUrdvHkzFosNDAwwDGO32zmO09pTNcXJNZlMJElqr4bBbBNt08u0PWZ5ebnRaCiKEgwGW+VkSZJ6U2DMrsbr9YLIEYlEnE4nSZKSJMmyrCjK+Pj4Dsm5hMEgwuEwpM+yWq3hcPjy5cuNrR6XseDRZ5pGwZmZmbt37zocDjS8XblypYFnY5i+sm5sXPi7urq6sLBQKBTGx8efPHmiqirDMFoth1begAzruVwum80+evSodw+DwWzAQc7n84HJgTZzZZNl4MjISM8KjNnhdPIh4TgOvMkFQbBarS6XS5Zlp9PpdDonJyexoyZmpwGeSGazWRRFgiC2wwcJCx47hXq9/vPPPw8NDcXjcTTUaSNZNbD4gekHTUZN2o2mnxYXF6enp6empkRRPHr0qNVqhfkZqO+aZm+Kopw+fRrHxsX0nu6+Q8+fP+d5vqm5NkVdg427d+/2tuCYnU5Ti8rlcrIs/+tf/0qlUufPn2dZ1mq1Dg0NjY2NybL8/v177Vm498P0mLYJrD99+gSmVhaLxWQyZbPZLb8vFjx2Ch8/fjx48ODs7CxK2KzT6cC0DvdHmB3Oq1evEomEzWaz2+2RSITneaPRGAgEIBi0VulB03QqlXr37h06t5Ngg8FsK60tbXl52efznThxwmw2d/JEAmw2G2SV6XQpzD6kNbTGzMyM2+0eHR2NxWKhUCgQCBw5ckSSpJmZGUVRupyLwfQFaIcQ6IUkSZIkY7EY9vHYm3z69KlQKFAUBVM0WCE2m80NvBaC6Tfr2sSXSqVwOEySJEVRFouF53mHw2E0GlHcKmjPJpNpamrqw4cPna6DwfSYpnZIURTqflt1dIjJycmNXA2zP0HNQFEUcB+Px+OBQCAajWYyGY7jQqFQrVbTenfgloPpO9pGODo6CkoPiqKmp6dVVd3ae2HBo//U63WGYRwOh9PpRBM1g8GADN9xr4TZsbx9+3ZiYgKma0aj0Wq1WiwWmLSheZvNZlNVNZPJdLkObuSYHtC2mYHR4NjYWBdhAzAajbAetJHLYvYPra4a9Xrd5XJFIpFQKDQxMREOhwVBOH36NEEQkUikVquhw7Sn9LTQGMw/NMWKjMViNE1TFBUKhSCW7taCBY8dQTwev3nzps/nQ5F/Tp48CT9hjQem77QdHSGbKcuyaIW4NVquwWAYGxv7+vXrRi6IwfQGrV1fOp0Oh8MrKyvakB5tAVnabrc3XQSDaaJer7969WpoaEhRFFVVQ6GQoiiDg4Mej8diseTz+X4XEINpA+rTkskkTdMej+fatWuTk5NN0cN/HCx49J+VlZVEIpHP5xmGgXmb2WxeWFjQHoNjX2D6C1h5FgqFaDSay+WcTidFUWazGbRzTSoOUIAMDg4Wi8WNXBy3bUyPQU1uYWFhXUWH9lej0Vir1XCLxXTn5cuXkUjk6tWr8/PzCwsLJElyHMfzvNvtTiaTjb5mUsdgWtE2v0+fPoF/Jrh5RCKRb9++beG9sODRU1p7lmq1GolE/vzzz8ePH6OxzWKx9KV4mN3OpoNEdVdBPHv2rFwup1KpfD5P0zTLsgRB6PV68OJoCvgjiuKDBw9qtRqYE+DRFLNjNOmUAAAgAElEQVSjaG2QneQNpMprEkJ+//33vpQcs1uo1+vZbPb06dOxWOzRo0ePHj0SRZHjOJZl7XZ7pVLpdwExmHWgaRoWEymKOn369NZeHAsefQPGv2KxOD09/enTp8HBQTSHu3XrVr9Lh9lZrLs8tsH1s+7Bozop1iBQlV6vh3CQTcoNtBLsdDoTiQSWNDC7C1VVm+Rnk8mkKEosFmur+iiVSv0uMmanoyhKoVC4fv36jRs3FEWxWCwEQfA8f+3atX4XDYNZHzDAMZlMFEVZrdatDWyFBY+e0jonm5+fJ0kyHA5zHAfzOZqm8dQN04pWKthgRr/Wf9clk8kkk0lVVScmJkqlUrVavXHjht1ut9vter2eIIi2y8AMw2iji2IwuwL4phYXF8E9iaZpnU4nSRKEe67VahzHURTVJGMjNw8Mpi1fv36VZTmdTl++fDkYDI6Ojg4PD6uqKgjCmzdv+l06DGZ9JEmCDKoEQdjt9jt37mzhxbHg0WeCwaDRaBRFEY1q25GuBbPbaSs/bEIN0v2a9XpdVdXBwcHJyUlBECiKomkaJA30V5t9nCAIgiAuXrzYFG4PR0TA7FjaNstYLFYul7PZrHZ8LZVKBw4caNV4EATRw/JidhMgypZKJZ/PF4lEstksTdMQYTwYDIqieP369X6XEYNZH6/XCxoPk8nkdru39uJY8Og12mEvk8kIgqDX6y0WCwxpJEni6RqmLZtuGP/+97/X3QMXj0ajHMeZTCa73c4wzODgoCAIRqMRPMiRhRX8dTgcX758aaxnvvUjJcdgtoPugjHar6pqqxcTFjww3Xn69Kksyz6fL5PJVCoVjuOMRiPP8xaLRZbltbW1fhcQg1kft9ut+ydmTCQS2dqLY8Gjn5w8eXJkZAQSIMCQViqV8CwNs3G6qzi+K2qt0+mEZKXQ1xgMBovFwrIsRLdAK75gGfju3bvu8zbcjDE7mY1YLXo8nrYpzA0GQ6+KidmVHDhwYGZmptFoJJNJWLiBHEexWKzfRcNg1qder0ciERRkVRTFrb0+Fjz6AJqZeb1el8tFkiSMZzabrd9Fw+xousz1u/t+tRUGXrx4MTU1lUqlRFGMRqMoMK52sqX1IzebzfF4vEsx1i0nBrOj6C48V6tV8PpodTHvbTExu4mFhYVQKOR0OiORCApmZTAYRkZGtnzlGIPZJkRRhL5uYGBgyzPPYMGjb6ytrUUiEYvFglaUo9FovwuF2R18+PBheXm50WjUajVJkvx+P4RMEQRBURS/35/L5eBI7dQqmUzmcrlSqZRIJNxuN0VRsBoHQ6PJZNKKGdr1XUjKcfv2bSxRYPY82kYOhs5NUgfWeGC6UKlUVFUdGBiQZRm6WVjKicfjkMEDg9n5RCIRmJo6HI54PJ7JZLYwsBUWPPpGOp2emJhA45nRaOx3iTA7iy7LseVyORAIuFyu1mThSDsRDAYHBwfn5ubgLL/fL4qi9hSIUkWS5Pj4uNlsbkrHAWk69Ho9z/NNCx5Y/MDsDdZtyeFwuPXj0vp4dA/wgL+U/QPUdSaTCYVCly5dCgQCiqIMDQ0JgsCy7NDQECQFxk0CsysIhULgAsDzvMvlEgShWq1u1cWx4NFTkMVLsViUZdnpdLYGs8IdE6Y7s7OzyDxvXfR6/dDQUDgcNhgMJEnyPI9WbYeGhqD5tUovEPAgFostLy/jBonZk6wbk7pQKDR9FLDBsmz3K+BPZt9Sr9cDgcD4+LgkSYIgMAxz6NChCxcuJJPJlZWVfpcOg9koz549g+VIgiCsVuvp06ffvn3b2Jh33LpgwaPXQG2VSiVFURwOBwxmgiBof8XsW7ovoJZKpXg8zjBM22QanQSPpsVatAcUqehfdE2bzZbJZAqFQmsAFtw+MbudVo1Ep3AIyWSy7TdlNBq7ZOfE38i+pV6v12q1XC536NChkZERhmEoipJleWxsDEfJx+w6UNAjMHzIZDJNB2y6r8OCRx8AU5lwOIyi6IISFoNpdPiYC4VCIBAQBGGD8oZWomjdaD1Sr9ebzebR0dGZmZmPHz/2/qkxmF6ybobNer0uSVKrJhDG4C4ndv8Js4d5+PDh3NzcxYsXGYYxm82Dg4Mmk4mm6fPnz/e7aBjMdwOmEODk6fV6f/31V5TF+Af1Hljw6A/Pnj2TJAnWmIeHh9F+PFZhENrGkE6nrVYrWoHYHE1eHNo9PM8Xi8VOd2/9F4PZvXQRNrT/RiKR1s/HbDajHrvTN4I/ln3Iq1evDh48ODExYbfb3W63zWbjOM5ms9E0nUqlsCyK2UVAQyUIAro+giAmJiYCgUCjncZ4E2DBo3egSlIUZXR0FJnpY89dzLq8efNmE9JF67+tPwWDwUQiUalU2t637fIGbqKY3U53Bw/4ta1nuV6vP3ny5AYvi7+U/UM4HHY6nQcPHjSbzSzL+v1+q9Xq9XqDwWCpVGrgzhOz26AoiiAIs9nMMMzo6Kgsy3fu3GlsRRvGgkePQFV1/fr1QCBAEASsXqPcHbg/wnTi/v378Xgc6SialBVNsyJIMb4R2cNisUA/AnSSPRq4cWL2EN1X7LQyNqwNtVoqHjt2THvw2trat2/fstlsOp1ue03MfqBYLIqiyPP8wMCAw+H46aefHA6Hw+Go1Wr9LhoGsxl0Oh3E3CcIgiAIu92+tLRULpd/XITGgkdPWVpaGhgYgMDeYGe1uLjYwGMVph2oVXg8no2HsYJ2ta6iQ6/XK4pSq9XW1tYWFxcrlUqT4NHqWY7B7HY6haJHQ+n8/Pzz589LpVKpVGqb1kan0/l8vnK5vLCwEA6HBwcHKYqCYHEMwySTyXK53NtnwvSfUqnk9/tHRkZomrbb7RzHCYIANlddFnQwmJ2M3+83mUxGo5GiKIPBIIpiLpdLp9PBYPAHr4wFj62nyyqaqqpWq5VhGBjAOI7reekwuwPtTMjn83XXXbRdl+0umej+sfFLpVKCICQSidXV1UajcfnyZafTKUmSz+crFotra2vdpeJ1Y5JuE1ty8daVm3Xt/jG7mmAwqCjK/fv3Hzx4EI/HS6XS/Px8JBJZXl4uFoulUolhGJfLxbJsIpGAvG+t35Tf74dgqaC1NhqNJElarVYQVILBIHxKmL0N6hlWVlZ8Pp/L5eJ5niTJSCTi9XoFQfB4PGNjYw1sZIXZnVSrVeRcbrVaBUEIh8N3795t/HBjxoLHFtPJ5R82RFE0GAxoPMNrY5iNcPjwYSSsdhIw1pU3WsWPaDQ6ODgI/zIM4/V67Xa7zWYzmUwmkykQCKiq+vjx40aj8fbt2/n5+XK5DGoQbafz4cOH169fr6ys/P33341Go1gsplKpz58/d5nNd7dvQTu/fPkC11xXGNictND9IniWsCeJRqNHjhy5efPm8ePHR0ZGCIKwWCw6nU4UxampKQg2DZ8Sx3Hdv6BOHyCM00ajUZKkfj8uZrvQDvTpdNrv98uy7PP5BgYGVFU9duzY0aNHZVmG/hPx73//u4H7FsxuAFopTdPQJQqCEIlEVFW9d++e9oDNgQWPradLVilVVUmShCEqHo/3uGCYXYS2FR04cKCLX8fG50atMyTdP04jrQGvYJHD4/EwDBOPx71eLwSI/N///d+7d+/W6/Wff/6ZZVmSJAVBCIVCV65cWV1dHRsbGx8fR4/QOpvvNL8Hm8O///4b7TGZTAaDgWVZ8OXdoLCxCSGkX0obTO9JpVLIarE1b2b3D+e7vi+IT51MJvv9xJjtAjqHWq12+vTpUCjk9Xp5nodYHYcPHx4ZGYlEIrdv3246HncpmF2Ey+WCbMIcx01OTp49e7ZYLMJg/SNgwaNH1Ov1V69eocDwer0ed0CY7kALWV5e9nq9kOyvdYoDuUU3KGno1rPIQjvBhsRsNqMNnU5nMBgEQXC73TzPwzoxAEpYjuN8Ph/DMNPT01DycrlcKBRisVg8Hj9+/HgikYDn+s///M+7d+/mcrlGo3Hjxg1FUSRJgiwiCwsLtVrt3r17YF1mMplcLlehUPj69Suc26Ryqdfr7969g+1IJDIzM9P9ZXZacew+J8Cf6l4iEAhsRJbYiO1iU3jrplP0ej3HcdFotN9PjNlGXrx4MTo6euLECYqirFZrIBCw2WxWq1WSpCZ1RwP3JJjdRiqVMhqNFouFJMkLFy5Eo1Fo1T8YVBcLHtsOqhVI3IGCwfe3VJidjFYzsLCwkEqlWmc/TTqQJumidQ7UfQql0yg6dBo7E4ZhWs9qypvetHIcCoXS6XQ0Gs1ms6FQCAQSUNoQBBEOh91ut8lkMpvNoP1Dloc6nc7lcqXT6cnJSZIkwXQ+nU4Xi8V0Ou31elmW9fl8d+7cuX379pcvX5LJZKlUqlarnz9/5nl+YmIiHo/X6/VKpdIl53qnHhNkEu1+PEvYk0xPT3dq/99rvojU161HUhQ1PDzsdrtjsVi/nxizxWh7hrdv38qyPDIyYjabbTZbLBaDcLqpVKrRodvBYHYLf/75p8VigTyYLMs6nU6U7wubWu0s2tZHLpcD70MYllZWVnpfMMxu5OnTpy9evPiu+VDrjKrtvKrtMa37171d0wFGo5GmaZ1Oh2xa9Ho9CCcOh+PkyZNOpxPtJwhCG4bL4/Gk02me59Fast/vDwQCdrtdVVWHw0EQxLFjxxRF8Xg8YNuQyWRu3rzpdDptNpuqqouLi8lk0uVyLS4ufvv27e+///7y5Qu8yXUVGm2tufCMYY+xtrYGYm1TM9bGodYq9FobuclkslgsEF8yEAhMT0+LoiiK4unTp0+dOsXzvMvlCgQC8Xjc7/fXajXchPYS2u7i06dP+XxeFEWO40iSPHDggMfjcTqdLpfr+fPn2uN/cIUYg+kL9XodOkOTyeRwOFRVzWazTcEzsMZjZ6HtcSqVCrKKweoOzAZ59OjRx48fIVhnW8Gg+/6meRVSTWzQQ717SpDuWpS2KhddBymoSS0DOhDk0wY2prp/LFvgL4grBoPh9OnTsJMgiMuXLz969Ojq1askSdpsNrfbfefOnWfPnqVSqXfv3jXFtazX62tra1euXCkUColEIpFIaPUkeHKwJ4Fqffz4scvlAsOYw4cP8zwfjUZBgeZ0OjmOgz2KogSDwUwm43a7HQ4HNDmTyeT1ejOZzJkzZyA4b6vgurCwsK64i9nVQLWurKxMTU0FAgGO45xOp8/nGx4e/p//+Z9yuVytVvtdRgzmh4BGbrPZYJi22WypVCqZTC4sLDSwxmNH0bYyXr16xfM8pGLR6/V+v7/3BcPsFrRNaHFx8fHjx20dPL4Xo9EYiUSuXr0aDAYh8iMErNDpdGazGTy5tTfS6/Umk4nneY7jkAM65DFFq8Wd3Eu+Vyej+0fMAOloYGAAdhoMBnRHsJhveyLajkajExMTZ86cgX9ZljWZTIqiTE5OyrIciURQMi8wYLtw4UIoFIpEIm/evFldXc3n800Ryptmlpg9Q1PgNUQnNdfly5c5juM4DoJQNx2P2VegSn///n06nZZlORgMejweQRB8Pl8+n5+fn19eXu5vITGYLYGiKDTIhsNhiFr5g9fEgsf2gsLtkSQJczuO49BiGAbTic+fP9+7d09VVRRIdyNz904/EQSBYjdrp0qw2K/NqrawsLC6ulooFB4+fAj+37lcLhaLiaJoNpvD4fDS0lI6nQ4EAl6v1+PxZLPZSCQSi8Vg3CUIwuPxcBwHLhwgophMJmRS1QUQMJDwo9frSZJEFyEIAuL8tmZIRNvBYNBms83MzMApDodDp1GkkCQ5PT1ts9lu3LgBS9ocxzkcDkEQYrEY5EuRJKlYLBYKBfBUmZmZgZC+AKxirq2tvX37dnV1dXV1dWlpqVQq1Wq15eVlkGpu3rz5IynDttzBfdMxu1pDkO1n1tbWisUism/G7E+0X8Ty8nK1Wo3H45IkORwOlmVdLpckSaOjoyjiBQazG9G2czCZhmVB8PGYn5/HeTx2NMViMR6PLy4ugrpKr9dPTU018DoZZr028Pjx47t373o8Hq3vdat00cV/A+0hCAKJFj/i7NglGG7jn1yHoVDo8OHD+Xze6XTyPO92uwVBKJVKiUSiUCjIsnzo0CGr1QoSOHg9GY1GkCXAm1wrn2gN8ZHve9u4Q7Btt9tpmrbZbHBYq2O91g8eNkiSJAji+PHjLpeLJEm3202SpN1uB4+UwcHBaDT66NGjz58/X7t2LRwOl0qlfD5/69at169fNxqNpaWlbDYLgsrFixcLhcLdu3fv3Lmztrb2XbYW35X2pPsVuosuXRxX1j2g+333JJuIzozZJ5TL5WQyefLkyUAgwLKsxWIRRVFRlIsXL+JGgtkzuFwu3T+2zQRBKIry42aEWPDYFmDt89WrV3Nzc41Go16v2+12mPfkcjncK2EQnVwPS6VSIBBodXJtlSs6OWygPSdOnFhZWbl69WqXkAatBfje+W6jwxp5Op1uvWy9Xv/48WOtVnvy5Ml//Md/nD9//tixY9FoNBKJOBwOMP3y+/25XC6RSEA4OJPJZLPZIMUh+K8bjcYmDUkwGLRYLE2iS5OwgbaRl0irFKf912q1Kori9XolSYLAWZVKRVEUnucVRWk0GslkMplM3rlzJxwOz87OyrJcKpUWFhbGx8ch4Unbd4XQRtPq9GI3XgXftX9zs+r91n1pW/V+e3ZMFyqVSiqVCgaDgUDAarXSNC3L8tjYGCiKMZg9QL1e9/v9aIi0WCw2m61Wq0HQtk2DBY9tIRwOx+PxGzduINX8oUOHDAaDoih46MIgusxK379/7/F4dC25AloFjE7/gpMGTNZDoRDsNJvNkUik6abdJ6AbsdVZV/zofqP6P6A98/Pz6JhkMklRlCiKxWLx0aNH6XR6aGjI6XSSJCmK4uzsLIgWJEmCVZjNZgMBA8QSiqKapA7ksqJbT1nUdBasa2rlk0wm43K5hoeHQeTQ6/WBQKBQKOTz+ePHj3McB49Qq9WePn169+7d7i8ZbLS62Dg1vcZ1O5PvcmPofsEttwHbjeyrh8V0ol6vr6yslMvleDyey+UcDgfP8+A153Q6YX0HNxXMrgY1YEEQkLrDZrNNTEyUSqUfTE+EBY9t4Zdffnnz5s3c3NyxY8fq9fq5c+cYhjEYDGg6hXslDEK75v3+/ftarfbp06eLFy9CGDSTydTFeaPVmki7QdM0TdPgIM6yLDqLIAiwFGp8p/HVxpUhP9LCu8+J0cb58+ffvn27trZGUdTY2JggCI1Go1QqhUIhsNoiSdLv93u93nA4bLPZkA8JwzBmsxn+Ra7z8LZbPeybhJAmDxOCIHT/NxKXTqfjeR4WQR0OR7FYrFar4MU+Pz//6dMnVVVVVV1eXr5169Yff/wBoQnr9Xomk1FV9fnz5/fv3wfz8Wg0WigUUAiR5eXlt2/fwob2tWxczOvynr+3vn7k3N3F5izfMHsS9GUVi8Xx8fFjx46dO3eO53mbzcYwjMvlikajX758+V57RQxmZ1Kv1wVBAC9Nq9XK8/zs7Oz9+/cvXLiADtjEZbHgsS3EYrF6vR6LxaLRqCiKdrvdbDaLotj4MSN7zB6jtTGsrq7euHHD5XKxLAuzZLAs6iRydMFgMIiiqOuQBNBoNB4+fLjp7m2L1KnM3R+qkwnZxq+zkbt0ArlYoMPADTSTyczMzFSr1VgsVq1W5+bmEomEx+P5+eefeZ4fGRnJ5XKjo6PIiIsgiFY/kyaxBGQVrYgC8p7ZbCYIgiRJsApDB6PVI5fLNTk5mcvlqtXq/Pz84uKiKIqpVOr69euFQgFEkTdv3pRKJXiEhw8fwuM8ffr0zZs3lUqlWq0iJcnq6mqlUslms7C68fvvv2tfVC6XS6VSmUwmlUrduHHD7/cLguByucB1HlZws9ns975nDGYfMj8/f/78+VAodObMmWAw6Ha7T58+ffTo0SNHjrx//77fpcNgtgbo/CcmJmw2G4xldrtdURS/33/p0qWVlZVNjw5Y8Nh63r9/r6pqo9GQJIllWbPZbDAYaJrWHoOHcwzQtGKdyWQgYwAK5eR2u2HmCm7QMCfuLofAtsVigQQg2p+0pkdw/Zs3b3Yp20bK37r9XRY7G5Fwuq8gtv21kxlY685isfj161etcdf4+Hg6nXa5XD6fz+/322w2r9cLTvDgQwKaKK1uBMQPECoEQbBYLJDuUKuwanU10VYNOK54vd7x8fFsNvvw4cM7d+48ePDg4sWLFy9ePHv2LMSl+OOPP2w2myiKoVDot99+i8Vijx49+vnnnx8+fLi8vBwIBLTPlc1mL1++fOXKlaNHj+bz+VevXqVSqYmJiWAwCAkrOI4LBoPhcFiSpFwu9/bt24mJCZqmM5kMvIHJyck//vij0Wh8/fq100vGvRlmX7GwsBCPx71er8/nm5qacjqdiURicnLS5/OBcTX+IjB7g3q9fuzYMaTqNxgMJEmePHkyk8n8SOePBY+tZ3V1dW5uThRFq9WK5oher7ff5cLsdB4+fBgKhWAKCy0H4tIeOXIkl8t9/Pjx/fv3x44d8/v9bWUPNAOWJAmCwyqK0iSNQGoLOB3Nen0+X39Hyi7SyHcVrLua5bs6ytYC3Lt3T1EUiLFrt9vtdrvL5WIYhmVZnuedTqfdbgeFBs/zoVCI4ziQTFCXjUJyIdVHW00U7EdGX6A8IUmSYZhUKhWJRIxGI0VRDofj6tWrIyMjZ8+ePXXqVLFYjEajDocDShuPxxmGASMQSZK8Xm8sFltYWKjVapBlGZVqdHQUAiLncrnFxcVXr16BHMKyrM1m43n+9OnTP/30UyaTyefzlUqlUChMT0+nUql8Pv/rr7/Oz8+j7Ch7kv1jVIbZIOl0OpvNguju9/tZlg0Gg4VCIRaLIf0kBrM3GB8fR2ttdrv94MGDs7Ozd+7cafxAf4gFj03SZaoUjUZheqdd7Ox5ATG7j0ql4nQ6tWvhNpvNarVmMhntYaurq+l0uiktBhzPcVwoFNIeHA6HUQI+mMuC/gQpVQDQ0QF4Gbs79Xo9l8vF4/FisVgul1Go4qWlJUVRCIJQVfXRo0dWqxWUS3q9Hm2AwookSa3IgYL/gs4E9fJIPkR1ra10dKTRaBwZGSFJ0mw2OxyOxcXFcrlM0zRFUZAjEnA6nYuLi41GA3new3UEQfD7/ZIkqap67969YDCIWpfRaDSbzZCwZXFxMZlM3rx5U5Zll8sly7IsyzzP+/1+WZbdbrfX6y0UCmDh9unTp0ajAVZkCwsLKysrHz58gGZcLpfXzYahbY3fWzVNG5s4vbtNIP4uMEgyHxwcRKsPIIdrcyJtLVgAxvQYaGZut9tsNvM8b7VaSZKkKGpiYgJcEzcNnhBvnk4dwZ07d5pmdT6frx8FxOxc2q7E//nnnz6fDy2EMwzDcRzDMOBe3HSW1+vVihyw0SSiAMvLyy6XC+I+wYwWcpGiJgrN1eVybcIpeZ+w8RltNpvVhrX5448/fvvtt0ajsbKyksvlarXa4uJiJpMZGBgQRRE0D1DjEDJLawinlSqRUzs6Hu1pMqVzOp1oyQMETqhos9mczWbT6TSo0WiaBo2KJEkMw8zOzj569KjRaIyNjUEZRFH0+/0cx0UiEVVV5+fnIYOe3+/ned5oNCqK4nA4vF6vLMvnzp0zmUySJD179ozneY/HE4/Hw+HwhQsXTp065fP5MpmM3++/ePEiBESWJAm11Xq9fuvWrUajUalUIBDC7Ozsr7/+2qkKOtXOlsQ8+BGpe+NmhD9+ZUxvaPvh37x588yZM9CM4/H4yMgIwzClUqkpW/nGG2SnI5GIjhsApl8EAgG9Xj8+Pm632wmC0Ov1TYubmwALHj9KU49QLpchqiZanjSbzf0qG2a3AK1odXUVHJpR+6EoqtVIDw7OZDKtM9QXL1402g2WlUrF7/fH43GO47SmXEjwYFlWFEWTyXTu3LlOxdvnbHpa2eTGoyWVSoEDyb179168ePH58+dKpXL58uVoNCoIglakZBgGak2bGxFto3QlkE8AqUpaPePRTjAJM5lMEJqdZdlAIFAsFgcGBuCYcDicyWRgrWtmZubWrVvXr193uVxGoxF8jTiOu3///vz8PCwAS5IUjUZfv34NmhCGYbLZ7NDQEKRzvn37djqdnpubA/1PNpsNh8OfP39+/fr1+fPnGYYJBAI+nw+eURTFfD7faDT++uuvdYOTbqGCrunD6X7NbZVhWk/866+/NncdzCboUmurq6vhcJhhGIZhQDxWFCUcDieTSZClu3zvG79pvV5PJpNg3JJIJFqVhLhPxmwrqIE9ePCAJEmbzQbLZCRJaiPybw4sePwQrTO8S5cuoQibMN7H4/H+FRCzO0gkEtlsFlaaDQYDCqRrNBofP36MDmtKNkfTdNOcslAoNF1ZOz59/fp1cXFxaGioyUla949rAVzEYrG8evWq7RVa/91XbMTaYdPr7q07U6kUGE3pdDqe50ExNTQ0BMZaFEWBaIpiLmv9RqA2weYTyR5IIIHZf2uwYK0Qi4xFTSYTJJtHEYcNBgNBEARBBIPBUCiUSCQgXDhBEPF4/O7duxMTE0ajcXx8nCAImqbPnj3722+/JZPJXC43Pj7u8XjOnTt3+fLlVCqlqqosy06nExJH6vV6giB8Pl82m71//36pVEKvpUv6y9YX+Pnz50bLZL014e7Lly+fPXu2btWgn77XlOvHP5b9/LntBFClo41cLjc2NgYNW1GUn376ye12i6J469atpjjXm7ujqqpOp5OiKG3mU90/gUZwkhBMD2jq6EA/D+mMGYYhCAJFU9zc9bHgsZXU6/VSqdRkI9HvQmF2ItovNhqNejyeWCyGRFZYhBYEIRwOtz0R/vI8b7FYtKvaELK57V0QYGwjSRJJkmDEr/vHmh81WpqmwWMYj3BAF5Gjy78bN8vu/itElHrx4kUul0smk4FA4Pr169Fo1O12u1wuiK4DvuzBYFAUxUQiQVFUNBrlOCOuxX0AACAASURBVM7j8YD84HK5SJJE9lqSJNntdkhpovsn3aTuH7s7SB4PPyHHEjgRGXFpr4YOQLMlrcWg2+2en5+fnp62Wq3T09P5fL5QKORyOVEUwbX92LFj6XR6cHBQp9NxHJfJZAqFAvgvvnjxQlXVpaWlpaWlhw8fgns9EkhQK4XYjgsLC4uLi5FIBHJIJ5PJe/fuffjw4Y8//lheXpZlWVXVlZWVly9fNv7x1QG/l++qji7ih3aS+iPfTltTzE1fDbMJOq0OxOPxgYEBgiAMBsPFixdTqZTP57NarSdPnvzeOmqqZUiY0LQc0IqiKJ2Kh8FsIajnefPmjcfjQQl5g8FgLpebmpr6+PHj5q6MBY/N0zQewIbT6dROBAcHB/tZRMwOBhrM7du3BUEAV2CIvIzEgFgs1v0KwWBQOyBZrdYmHWinwenx48djY2PgTwLnQnpBreeA2Wx++vTpupfaP3SZSrb9aYN7WmexbTuWTqevra3BxtLS0q1bt2q1GuQZzOVyKLMyiBCyLN++fRsyeExMTFy5cuXq1auBQABsugRBOHfu3JEjR5LJpMVi4TgOsg81xUBDmRkJgoDmqnU1aQso00iSRGoZgiA8Hs/09DToVXiedzgcLpfLarXq9Xqe55PJZKVS+fjxIzwyyAb5fN5isbjdboPBwHEcz/PBYFCSpCdPnkCq+PPnz2ez2Wg0mkgkwHArGAwmk8k7d+5MT0+fOXNmeHjY6XTKsjw9PX39+vWVlZV4PP7p0yd4h41GA9JRN1nqN9GkdWxbuVv+sWDZo8doX7j2tX/58uXjx48ul4vjOKvV+vz581wuNzIyAlJu6xU2fq+lpSX4HEAdDYtQTSCBZNPRFzCYjdA0ooFrH8dxNE0TBMEwjCAIT5482fT1seCxSTotczalewNLZQymEydPngTnCjTq6PX6gYEBlJCh0wBWKpVQrCQ0LAWDwcbG5kCFQkEQBO14hpJ5a8e5tuvBGO1b1c5EuyyBd79Ipz3fe0DbgyE54Pz8fD6fTyQS5XK5UCi8efOmXq8/fvz4xYsXsiyfP3++Wq3eu3ev0WioqhoKhR48eGC32wcGBs6dOwdN1Gg0SpLk8XhCoRBFURCrF1LCg4iCdB3wLwgqEPkXLMRACDGbzU6n02azdZpaMQxz+PBhu93OsqwkSadOnQoGgxcuXEB6ORB4XC5XMpmsVquQ2QqybQqCoKoqeDQdPnw4Ho8PDg5SFOV0OiGlo8/nGx4eJggiFAo5HA40h/v48WO5XIYG/9tvv0GyeSSTtNZmvV7//PkzCOdN1jhbAhYz+k5TFaytrT158uTx48enT59Op9OBQCAYDM7Ozg4ODrrdbkh30/bEjVzf4/EgMd5isYyOjuo14Q11Gnta+LdtHBEMZgtB7ZNhGLvdjtae3G737du3uy/QdAcLHlsAqp5wOMzzPNhew+jY34JhdjKwSu31eiHbBogcbrcb0s+ByNpp2lqv10OhUNMymMlkcrvdXW7XtPHhwweWZZvU+pB8Rhu/9cc9yTA/yObkjY2ztrYG4RFTqZRW1IzH43Nzc9Vq9evXr9VqtVarra6ugjkTpDIol8tnzpyJRCJWq1UURVEUHQ4HTdOCILjdbnBEmZycVBRlaWkJQu6azeZgMEiSJM/z4K0IVl7IztBkMo2MjIAKDvD5fCRJgiEWQNM0nAjXQf7ukO0kEAiMjo5evXq1UqnMz8/rdLpAIHDo0CGLxRKJRM6dO2exWCA1CsuygiBApsV0Og0mbb/99puiKIFAwGw2P3jwQPuiCoUCciCGPUtLS/l8fnl5eXFxMZfL5XK5Jlllc2CpYweyuLhYKBTC4fDQ0NDs7GytVisUCk+fPnU6nTRNZ7PZTVwTVTTSOev+MVlsCpjeBMMwW/pwGExHoLeERUmKoiDp07dv3zZ9QSx4bCWSJFksFrTyd+PGjX6XCLNz+fDhQ6lUAoctbWwik8mUSqXgmLaKNfh7+PBhUK9pJYeRkZGN3BpdNpPJZDIZmP9BtwJlgMhaaBQ0GAzT09OdbIHaFhWzTwCJ5fXr16qqPn369JdffpmZmbl7926hUFAUBVwyJEkqFouJRMJms7lcrmq1mkqlgsGgx+OhKMrj8Yii+P/YO5vgJLJ3//PS9BvddAhNCEl3OpIQgjcoaa8YlCmxBm+JYpVYJdYVS6wK3ipxIVPiZnAjbsQq42pw8xdXZqrE3cS7EpfGhbicuDXurriauBz4L5475/YPEvIeYnI+CwtJd3O6+7w95zzP96Fp2mKxkCRptVrPnz+vKArHcaD563K5LBYLLOiA21hLYIk2PAm5fpnNZqfTCaEvcCkUiw/7e3q9PhAIVCqVK1eulEqlgYGBVCr15cuX6enpWq0GDRPlg5udnQ2Hw5OTk9p7bzQaf/75Z7FYTCaTvb296XQ6lUoVCgUkTAzuN7VaDVzgZmdnkTS29iId/tv54O1gvfEtHfwPt6MAm2Ttm4rtR9br9Xg8HggEDh48GAqFotFoKpW6efOm0+k8ffr0Zko1NDTUWemhHb1ef+XKlc38KAazFpaWlqDXhT1qk8nk9/vT6fSbN282fE1seGwc7fSrVqvNzMzk83nI2AVdAzoMz8kw7cRisf7+ft0/wdww6bdYLJFIpMPMHn0Ji7haw0Ov1wuC0H7iqpRKJUmSLBYLXAoEVdC+P3K+omn6+/fv2+rLjvkhWKPnGGRX9Pv94JrlcDjsdntPT8/NmzdnZ2d9Pp8sy36/v1Qq1ev1GzduvHjxgqIoRVH++OOPX375xWw2Q8VTFCUQCJjNZrPZbDKZLBZLX18fWiFucUHRZqcBd6+WgJOWCRzP82h1maIoi8UyOTnJcRycaLVag8Gg2WyGuBSe52/evAk+BhBgE4lEfvvtN4jjv3btWj6fD4fDhUIBbk2SJNi6zGQyEHCSTCbfvXs3MzPz/PlzGLkbjUZLNq6NNbFVLYF1scarrbEmLHvAsj+x6gU72GkbuPEOpxQKhevXr+fzeeQvXSqVpqenr1y5kkgkJEmKRqMnT54sl8srSYCs+isLCwvDw8Ojo6PtJgeoXWu/NxqNkBJHa6KAuNAa7wiD2RhIgATqodfrBbUP+OsGqhw2PDYLeuiw02qz2VA3gbsATDuNRqNarcbjcSRIhSRKBUGAII1lz2r5BqVcQEu/oHm6sSLBYh6E+dI0TRAEbIOgnEFQTpIkIdcbBrMsa+z0vn79utKfqtXqp0+fPnz4gIxqMFfA2GAYhuO48fHxp0+f8jxPUVRPTw9Ekuj1+qGhIYIgUL52rZkB4ShgZoBdAVaH1Wr1+XyoHdE0DYJFaP4H9R+2IqFIbrc7HA5XKpWFhYVkMlmr1SB9ezKZTKfTXq83nU5brdaxsTGHw5FOp2Ox2Ojo6Pj4+ODg4KNHjxYXFyORSCqVevXqVbPZrNfr09PTHTJewyOdm5trNBqVSgVcuaanp9EB2nM3YKis8ayVjl91kr3STulW2QnrLXyHs96+fQuSaIIgnDp1yu12kyTJMMzo6GgqlRJF8aeffkqlUrOzs6qqxuPxU6dOqaq69kjOlh9FeugtVofun308WAzS6/UMw4CAW7PZBDU5QOtwtbWWJwbT/KcuoToJRCKRTUYvY8NjU7TEFM7OzqKYMNC8w+xzWva7YIofCoW0Luz6f/IwWCwWmF60X0T7Af1XURRtjwBCK+udeaDj8/l8PB5/+PBhOBw2aNC1kUgkmnh4w7TRPh/t/E1nvn37dufOnYsXL5ZKpWazubi4GI/H4/F4JBKBQBRQ3VVVFWo+GO1Xr16dmpriOG5ycjIcDlutVoZhrFarzWZzOp0Qdw7aLHq9fmRk5MCBA6dPn0ZtUBCE3t7eYDAImRMlSert7UV5G1FzgzQ4oBRsMpkcDgcoveRyOWjaJpPp8OHDNpstFAqNjo7qdDpIhwJP4PXr17FY7OjRo3fu3Hny5Elvb6+qqmfOnIEF7EKhADPaz58/Lyws+P3+eDwO1o6qqu/fv280GgsLC9FotFKpzM3NzczMwJfap5fL5TKZDNgka5mSrmVno1gszs7OohnwWljVLXPDtsQaz1r7pZLJJJisYGHC4ot2YYggCAheikajhw4d8ng8sVjM5XKtFGXb2SSDNcoWDyvdv8bscRxHUZTb7dbuiUHYEjoSnPfW27gwmLUDThDgcEXTdDwer1Qq6+oHWsCGxxbQaDQikUgsFgPJ/JXWITD7HDR43LlzB61awTYCRVEDAwPoyDWuXQmCgFZqDQaDzWaTJGlVrYlV54Lz8/OqqmqFUO12u9ahhSAIr9e77KUw+4H1znJWXW/WXnADMQNzc3MPHjx49+4dOmxxcfHLly8PHz7MZrM2m214eHhqauqvv/66evWq1+s9ceJET0/PkSNHXr58CaK9yWRSEIRUKgVh5cPDwyaTied5juMsFotOk8wEgTToIKgdZpCw6whYLBaITrFYLCD8ZbPZHj9+nMlk4vG4zWYzGo2XL1+enJyEOW4sFkun03/88cfs7GwwGPT7/eC4BVYN9BgWiwWMrnq9HolEwuHw06dPS6USavX1ev3Dhw/RaDSbzYKksvbppdPpSqXy66+/ViqV33//HeychYUFSEtXr9ez2Sx6zi9fvtQ+5Hq97na7+/r6Hjx4oF1PWft0v/2ldzBL1rhHsdKvtHRNq1pckN2ofZGlxTbQ6/Uul0sURY7jvF6v0+lEUUCdr9/yWVVVbWbPFukqqG8Mw7QHrMMVHA4HOvfChQtreSwYzAaA+kbTNKiow3axy+Wan5+/e/cuJETaANjw2BTwVkqlUjKZ1MpQoJWtbhcQ03201QBiJOLxuHaTHeJr134d9OHUqVPahdjh4WGSJIvF4hoL035Z9LlQKEDgLxgeHo8HVIPQ0AgOJ2u6f8zeYlXXmuZydRXRrj68FntjpX87lAF+CB28sLBQr9dR4udisTg9Pf3t27dyuZxOp3O5XOMfj6ZMJnP16tX+/n6bzebz+S5cuABrz/F4nKIokJwGUWDkDKYNLIGlQUVR+vr6WJYFkwP+ajQaA4EAxLWDxYJUHGCzBVL6gEcZQRB+vz+ZTE5MTKCRRVXV2dnZixcvohyRCwsL1WoVNoUymczhw4fPnj0Lq+CQqLHZbL558+bjx4+wPdJsNu/evTs3N5dIJCBFI9z18+fP4fOXL1+y2ezr16+XlpbK5fLS0tLc3Jwsy319fT6fz+Fw+P3+VCoF5gp68rVaDZ4t0roBOxAoFArPnj1rNpvZbDYcDsORlUrl0aNHf/zxx7Lvvb0OdHjX2voG73R2dvb3339f9XhQLZuYmOB5HvWlywZ2a20D8PE7c+ZMPB5//fp1Z0up/a+5XA6k2Fb6LVD4uH79evt10DdWqxVOt9vta1yowmDWBap4MA2AToll2cnJyVKpBLLsG7syNjw2DmrkZ86ckWVZG6S4auo3zH4Daku1WkX5N9AY09fXB6uYa3FI0H6ZzWbRjEev14N6qcPh2HDxtMzMzASDQe16Lcdx2qAUGB1b4mIxe552S3W9G19r3NNYl1/QxpyI2tfC4b9fv34tl8vBYDCbzYIw17Vr1yqVytWrV8fGxiBhCEVRLMvabDYQAgbJLPiT2WwWRVFRFIgPJkkSBGFgzqrT6VBieAhNof4BbBK0hWIwGMArDLVx8ChTFCUUChkMBp7ng8Egx3GKooyNjcmybDQaFUUBWeS7d++CCxaI18myfOPGjampqVKpBIlZbDbbzz//bLfbI5HIzZs34Qn8+eefFy9efPny5e+//44kywKBwMDAgNfr9fv9Pp+PpumhoSHQBIOH9uDBg5MnTyqKcvLkSdh+efr0abPZzGazyWQSRaTMzs7mcrl8Pv/bb7+Vy+XHjx+3OIMtLCy8ffu28yS+85uNRqOqqobD4QsXLsDF37x5U6vVUqlUJBKBgP5qtVqv13/77TdBECYnJ1GHDLOrFktjJSPk/PnzsVhsjUXV/vXTp09IXW2lH1rJVRtdtl6vI+2ESqWCTQ7MdtBoNN6/f280Gs1mM0TEJRKJe/fuJRKJaDS64VQe2PDYINrRN5fLeTwejuNQ7P/nz5+7WzzMrqJarWaz2ZmZGZfLBS4WaH0UlHOaG1qs+uuvv7Ths5BwukXxc2OgwkSjUfBjNhqNsHwLa73I/cBsNmPbA9PO2j2mujJn2vCPvn79OpvNZrPZixcvwowf+VOFQiGIGofl/7GxsfHxcfBU5Hke0l1bLBZw7ge7HdJyQYCW1vcGnLWMRqMoitDuYJWdpumpqSmPx+NwOMDhx2g0MgwDy14QZE9RlM1mO3r0KEVRsFMRCAS8Xi9N0zRNy7KsKAoEM4B/l8/nS6fTiqIUCoVSqRSJRDweTzqdnpqaAj+ihYWFWCwGWRpdLhekq/J4PIFAIJ1OP378+JdffpmcnPT5fDabzWq1XrlypVwuz83NXbp0SVEUm802MjKSyWSePHkyOzvb09PjdDodDocsy8ViEXY/ANijAKrVarFYXFpaQpMbpOAEH8rlMniZFwoF2Lqp1WrValVV1VAoVCwWjx075na7o9FoOp0Oh8P5fB4S22ez2Uwmk06nQ6FQIBAAGwxpCaxqbyAgpKdDXVrp+3A4vNKmCnwP4oSrXiqRSEC3v5Z6i8FsGBj9oas5ffp0sVj85Zdf+vr62sXB1wg2PDYI6ghAQhfc9NEGenfLhtlVNBqNFy9eJJPJcrkMoag6nY4kSY7jCILw+Xwb3q9sNpvILxnqHkEQfX19S0tLWzWZQ9fx+/0wPIPhwTAM8hagKAp5BWAw+5B6vT4/P49cuRBXr17NZrN+v9/hcIRCIZPJ5Ha7Z2dnrVYreC5VKpV4PK7X6zmOg1Vw5MEF38A6hSiK4XB4eHg4FAo5nU7YZunt7QVRL47jbDYbbI/Isuzz+VRVdbvdsMzBcRxkYITLsixrtVrNZjMMVTzPu1yunp4eiCRxOBySJHEcFwwGZVmGHYNarQZJToeHh/P5vNfrtVqtJpMpkUgkEolkMnno0CEwJCA+G6Uhyufz4AUAkl/379+Px+M6nY5lWVEUQ6FQPB7PZrO1Wg05iD5+/LjZbM7MzIB4F2yY3Lt3LxgMQjDDs2fP0ul0s9n88OEDiA0kk0nwQIMclyaTSZblYDDodDqtVqvT6ZRlORQKTUxMHD9+PBKJeL1eVVWz2Ww0Go3H4yBQC71ou9pyBwiCiMViT548WWNnWygUHj165PP5tLJUWmDTzG63r30pp1Ao5HK5dlFdDGYLsdlsBEEQBEHT9OPHj9+/f//y5ctwOPzhw4eNXRAbHhsHupvZ2VmY86EN8bt372KfSwzi/fv3brf74MGDkDIZNHNlWR4YGFiXCNWyhMNh7dBlMpkmJiZgIXBrbY/r16+DCCksCoIyqf6fXGxGoxG5F3YO5cRg9gadnX+WHQIeP36Mor21Cc5BobVWqwWDwaNHj8Lmhtlspmm6v78f8p8cO3bs6NGjCwsL4DLEMAyYJWBaQHpEm83mdrsDgcDExIQsy7lcDiS/ZFmGVIwwdbDb7U6ns6enh6ZplmV7enooiurv72cYhiRJ2NVkGAYEJJrNptfrhe7FZrPVajXIT8/zPPxEKBSCojocDjg9EolUq9Vmszk+Pg4nchwH6fbcbrdOp+vt7UWuoW63GyyBxcXFly9fHjx4cGxszOfzQScWDoedTidBEAMDAz6fr1wuQ0j3r7/+2mw2k8mkoij3799XVRVMl2q16nQ6WZaVJAkSDkCWelmWYbvG4XB4PJ58Pj8xMZHJZFwul1ZgULvp1Bm0Q2IymdZSVarVqiiKkChT96+bJ+DHQpIkTdO3b99urzaduXfvHu5vMVsOqlR///038qymKEqSpDt37mQymUuXLm344tjw2CynTp2Cbhd1JdAnrtfvGbM3aHnvi4uLoJcCfg6wKWG322GQdjgcm9ydABcINBbq9XpJksLhsLYMW1L9IMmgx+MBdw6GYWAtVq/X9/f3Q+UnSVKbzRRXewymHW14vRZoL58+fQKXJ/AIgpX+jx8/Pnv27PLlyx8/fmw2mx6PR5ZlWZbPnz////7f/wsEAj6f78CBA+fPnz9w4ACkQVQUxefzJZNJsE9EURRFked5yDocDofD4TD4Tpw9e1aWZcjPCNN0uALLsslkslgsqqqK0phA0AvDMLCF0tvbC/Eq0BWAEybHcRA3AikgDQbD0NAQwzDBYBBkiJ1OJ9Krhc0QUC5GkTB2u/3z58/ZbBZi8eGyoijGYjFRFGH5BrZ9wLowGAySJM3Ozt6+fRvUkyHYUhAEsKPAxEJzfdjYAQkNlKevQ2R5u8mhJRaLrfrSq9WqIAg0TUN5tFeD58YwDMwcmivYtCvRYuLiXhez5ej+kd80m81Wq/Xp06cvXrzo7Ge4ygW3uoT7jkQioU13sEbvTMweBg0Ai4uLpVIpEAig5THwlbTb7eCYVygUNlk95ubmUGQk1EOQotqiW/lfGo3G69evwcXCarXCaiJKrKb1T2BZtkNuOAxmL7GSbFGHg9d4zfYvW74HFWD015mZGRDh/eWXX8bHx69cudLX16eqarlcjkQibrc7Ho+rqtrX13f06FEIdYCI88HBwUAgoCiKIAgkSbIsC8sKkEK+WCxWq9VAIMDzPETMy7L8888/WywWhmFAOximzmgEBMFZbUC8TqcbGxtr8WJCat0EQUBwmtbfKRQKffr0CaIvoNuERH5g5Cwblk0QBArlRxoY2oKB9aL7RxkZ7dau0d5o+UXt8ZIkrfoGZ2ZmoM+nKEoQBBQXrvsnLQxy2VpvENS6KiEGswHA29PtdptMptHR0XA4XKvVkNz2BmodNjw2y/j4uLbn2pimEOZHZ6XpQjKZ9Pl8SCkFcoGjEWhLxgxBELRLaLABssYSrgVt8c6fPz84OMiyrMVigUkD5BJBwzys3s3Pz+MdP8weZo1+Vsv+daUDOp+yxgOWlpaePn2qdfr/9u0bfPjjjz+uX7/+6NEj8PLSnptMJg8ePJhIJFRVnZiY+Omnn3ieHxkZSafTCwsLiURCUZQjR478/PPPN27cCAaDkKkddL2uX79uMpkOHToEa/lerzcUCh09ehRNzTmOO3ToUDKZhI0IiqJgiQRcNAVBgCwlDMOgOHvIUAb7FajnJAgC7BPoP3X/6hnV398viiIUieO4vr4+hmEkSRoaGoIfAhkxk8kETk02mw2+19pIazE/lj2mZdxvrwkfPnzQHq9drNTr9SMjI8vWpQ3UE9zZYrYEVAPz+TwsRoDjht1uVxTF7XY/evRow5UNGx6bYmlp6eDBg1pNblmWu10oTDfRNsWlpaUbN25MTEyAgzVKfws+x1sSEViv19HwjKb+kEamqek7tsTqaDabnz9/hpVIl8sFwzbKbICUFXQ6ndFoRHm18ECI2ZOsPZBvjUeufa65qmGz6sXb/XMg+KRYLKZSKUinCGPZ4uJiKBTyeDxnzpyBI79//14oFBKJRDgcjsViCwsLwWAwl8s9ePBgcHAwEokUCoVqtRoMBsHGcLvd7969+/bt28LCwvj4OPLVhGWL48ePQxCLzWZjWVZRlGPHjuVyOcicCIphFEWBIeF0OkVRvHjxIoh3mc1muJooipcuXSoUCpDdD2U6i0Qi4GPW19fn8XisVqsoihCOcuLECQiRh7CTznbFqkaIXq/PZDLLvgv4/PbtW+1Z0Gfq/pFBJwji9evXq753DGbnefPmDcxbBgYGRFEcGhoCR0qcubwLQG+iqipN06qqwqqJXq8HGZAmnm/tS1peerFYTKfTBoMBUtprlwAh+LLz6WtEK8QJK442mw1df5vqYSKRMJvNEK8CHttarwYAZioYzF5lw0ZC54PXYqhs7E9r/3VQiGo2m5lMZmxszOVyQV4O4P3795VKBQLYms1mqVT68uXL7du3jx07lkwmU6nUs2fPBgYGCIIAB61yuVwulz98+ACeyZIkHTlyJJFIzM3NQXg6GA+qqqZSqWAwODMzUyqV3G63z+dLJBI3btz466+/7t2712w26/V6Pp/3+Xwul8vj8UxOTp47d+7s2bOXLl168ODBixcvzp8//+LFC4qi4DrBYHBoaGh6evr3339fWlq6cuVKKpUqFouFQsFms5nNZtDMWLvVsdIxx48f7/BsUdoN3T9uZshF1mg0ao2W9b7BlbbdMJgtYWFhQafTQdxXX1/f6OhoIpFAmXlwjEcXiMfjSAYRQuKauOVj/pGsSSQSIHNJ0zTS7GcYBkZrxCZdrSRJQuOZwWCw2+1Wq3UzEr1rYWlp6fbt2zzPK4pitVpR7GnLwMxx3IZzDGEwu5bNdPIdZorb5IK1A0MS6sSQoDC4aaE/oSW5LSnVwsICJGuv1+vBYBBphaHLXrp0KZFIgMGTSCS0J0LSw2azWalUEokEuMJubKNDC4r0WPa+UqmU1vCAfJEwbaBpepMvCE85MFuLtkbNz8+73W6PxyOKoiAIMLvY5LCODY+Nc//+fRRaB73Js2fPul0oTJdBLTaXywmCAHNxqCcQTHnq1Kmt/cVz584hJysY2Mxmczqd3oHR6Ny5c8eOHevv74fdD5vNhpRt0HiMnQ8xGMxu5vPnz5IkrZQ9cI02CUrkt2x0+E8//YQ2vcENTBAEEBR+9OjRjt8xBrMmGo3G27dvDx8+rCgKx3EkSZIkOTMzg1ypNwY2PNZK+xrSt2/fXC7X0NAQ6pi6VTbMLgFVkoWFBZfLBUHY2vjFvr6+Lf/RY8eOaQVbQKTSZrN1KN6WAFe7du0aEgsGl2sQxgG3K4IgSJKUZXnDKU4xGAxm+0C9IvJ9arc6lhWzavnvv/3bv6108U+fPrVcHDY98KIMZvdTrVYVRXE4HJDeh+O4R48ebXKRHc+VN874+DjKiAQLvd0uEab7NBqN2dlZl8sFOrM8z4PqFMRhb8cvwjqEThNcrtfrh4aGmtuvsQhXkZqXlgAAIABJREFUPnv2LMdxIyMjTqdTr9eDLidkK9OOtYcPH9aeteylMBgMpivYbDadRttqXc5XOp3uwYMHzRW2OyKRSMsFIeb+7Nmz3bhRDGZ9XLx4EXJfQgqdbDbb3NyQjQ2P1Vnp+SaTyVevXqF+KhgM7nDBMLuQt2/fptNpJLficDhQTq5isbgd0+tkMulyuZDJ0d/fDwbPjvl5NxqNer0eCAQYhgH7CrQy21cHDQYDJBhuLxg2PDAYTFdAXVCHbY3OdojRaKzX68t2YktLS729vS3HwwINhKlgMLucCxcuqKpqtVpdLpeqqpDhtLmJURsbHqvQYfaWTqfT6TQS84lEIjteOszuolqtplIpNMwYjcZAIAAZdgOBwPbNrXt7e7XCViaTSRTFt2/fwl+3e8cDePnyJWjtsSzLsmxvb682v4d2CD906FC7zm/jH7apqBgMBtMZreP0skbIsnaIXq93uVwrXfPp06fLCmdZrdadvDUMZmPMzMwMDw9LkkTTtMfj+Y//+I/R0dFNjtTY8FgrLfkZms0mTdPlchmlIO1e0TC7gqWlpUKh8O///u+Q0JcgCI7j4vH4zMzMmTNnkNjLdsytBwYGtAMhpArx+Xxb/kPtaG+nUqkMDAxIkiRJktfr7evrg3xhsAeiHXdpmtaeju0NDAbTder1OsqhjnIX6tpiPLT/wkIPyGotK1BWLBZRAlltF53NZnG/h/khGBsbO3bsGMuyDMMMDQ3F4/FNZiHDhscqtHcNX79+ffjwYSgUcrlc4XAYZlSCIHSleJjdw9WrV2OxGNQHg8FAkqQgCIFAADnybtMwU61Wx8fHdZoYD0EQeJ53u93NbZ7Ztw+09Xr9/PnzhULB7/eHQiFImwiWGBrRdf8o2bds1+JhGIPB7DAt3U42m22X5tNaHSBUCJ28Tqfz+/2wELkSDx48aFEd1Ol0LfF+uOvD7FrK5TLLsna7nWEYnuePHz++uLj44cOHzVwTGx6r094pVKvVSCQyNzcXi8WgH/F6vV0pG2aXsLCwEIlEHA4HjC4sy5rNZpIkBwYGYrFYc5uHFjQWQhJcsIRNJlO3xrNQKHT58uV0Os1xXCwWg1zCkLi9ZSxXVbW5udzqGAwGsxlQ57O4uBiNRkVRDAaDLdoYyPbQ6/WwpWwwGNbiX12pVFouYjQaZVnGif8wuxm0ZJnJZMBzgaZplmU9Hs+lS5c2KVOJDY+1ou0X6vW60+lEs0y9Xo/VQvcz0Dj9fj9JkrDAbzKZCIIQRRH0H7RHbkcBIKQbRkTI5UfTNEEQ3UreV6/Xm83m0tJSIBCIx+NOp5PneWQdtYAUwZcVhOnwXwwGg9lCyuVyIBAAT9GjR48ajUaTyWQ0GtFmhclkgm+cTucavU1SqVRLj+d2uzuHlXfo6KrVarPZrFQqLcnOMZitBRkeFy9ehEhmg8HA87zT6QR7+/379xu+ODY81kGj0Uin04ODgwcPHkwmk2j5liCIbhcN0zUajUapVMpms6qqwqS/v7/fZDIxDOP3+5s7Ml2+deuWJEnglGwwGFiWBftHW8jtLoOWlp+r1+uZTAY2PWDJsGXrw+FwtDtctXz4+++/d/AOMBjMvkC73TE5OQnSPTdv3hwYGBBF8ciRI36/HywNj8fj8/l+/fXXp0+fNtfWqVYqFUhNqO3uKIrS5nTXXqdcLk9OTo6NjY2OjoZCoUKhUKlU8vn82bNnWZYFB7Bjx46BIQRrWzsTy4fZh0DNTKVSMGRDhgCKooaHh3Fw+U4AT3l+fl4URZvNZrPZJicnkaNnt0uH6RpQMWZmZvx+P0VREMYADpEWiwVWp7RHbhOZTGZoaAi6BugjTCYThLbvfATFSj8EyQQZhmnxYYBBlOd5rat0S7HxXgcGg9lW7ty5k06nXS7XxMSEx+Ox2+2iKF64cCEej6fT6ZXO6tw15fN5kiRb4tQNBsPCwsLXr19LpZKqqhzHGQwGh8MRiURWyp6u00S0gxmjjZfDiQgx20Sj0YjH46IosiwLLhUul2tychK5cmxsaMaGxzpYWFi4du1aT09POp0Oh8PQ5sPhcLfLhekm6XTa7XZLksRxHAwGDMP853/+pzZ3+HbPm6PRKIxeaGmNpmkwhHamAKvSaDQCgYCiKIIgICG4duXKfD7f3XJiMJj9Blo/SiaTqqq63W5FUURRjMfj5XIZnJo25va5tLTkcDi0lgN8qNVq8XhcuxOi1+s5jkOLMp3ThrT3nOPj4+stGwazFh4/fqyqqsfjsVgsDMN4vd7r169rgws2UN+w4bE68FjtdrvD4bBYLE6n0+/3Dw0Nwery/Py89jDM/gFCoh88eGCxWHT/5ITq6enR6/XRaHTZ47epJKOjozabTSvyCE5fIGy1kyy7QQH/rdVq4MZgtVoZhllWDl+v11+7dm2Hy4zBYPYtqLNKJpNgcrAs29/f73Q6VVWNRqMoCK3z6Svh8/m0RgI4yi8uLhaLxZa9C90/SlkrCWq1uGxpu1CLxQK2B56HYLaWXC7HMIzP5xsbGzObzaIo3rx58969e5u5JjY81gR4ag4ODoKTJWr/DMM0cVPff0C8QaPReP/+fSgUMpvNOp1OFEVFUXw+n91uLxQKK/kIbUdtOX36tCiK2tELFCGR4bGTDkstv6X90cXFRUmSMpnM+Pg42iACQHgXxlGe579+/brsZTEYDGbLuX37Ns/zPp9PEASO41iWPXDgwIMHD86dOwcHtEiHL5uyY1kOHz7cvsICaqTj4+MtGUJW2tPo/CdQJ8cOV5gtRFurLRYLeCHSNO10Osvl8qNHjzYzImPDY01AbrhffvmFpmlVVRVFgQYPQWZNPCvaf3z48OHGjRuKolitVnBq4jjO6XQyDOPxeFY6a5vqSa1Ws9vtIPJIEAQoXBkMBth46VblXPZ3nzx5MjMzI0nSyMgIUqXU6XQtsleyLL97926li2AwGMwWkk6nrVarxWJBulUcxyUSiWQy2eGsVXunRqPx9OnTFrdSiAttNBrfvn1bybpY1QKB1SVtYlacxRiz5YCPtNVqhSBSvV6vKEo6nW6R61wv2PBYE9VqNZlMJpNJjuNcLhe41uh0usXFxW4XDdMF/vjjD5/Pd+DAAYZhQHIR3B+PHDkiSVKxWNzJwsDgl0gkQMyKpmlI4iFJUjgc7q6e1Urfu93uaDTa09ND0zQs17WL7dI0DfmAMRgMZjtoNBpzc3O5XC4Wi1EUxTAMSZIQaBGJRDwez6r5xddie9A03dK5QTBbo9FQVbVlM6TlX4AgCK31grQBkc5pX18flrfCbC1Qt202m91uHx0dZVnW6XSCvFv7YesCGx6r02g0RFEURdFisTgcDhT+RZJkt4uG6Q7ZbLZYLLpcLoZhYJHMarWaTKZ8Pq9VstoxGo1GsVjkOI4kSZ7nQX2CIAjIXbg7KZVKTqdTFEUo6rKrejzPb3JlBYPBYDqEhler1Xq97vP5eJ4XBIGmaUjHlMvl0un0GpN1dIaiqBa7QnvZYrHYvrnRstHB8zwscoGZodfr7XY7LHiZTKaRkZE7d+7gZVDMFoLayODgYF9fH2QB9vv9Vqt1eHi45Zj1gg2PNREIBPR6Peo+gFwuh7U+9w/wluv1eqVSuXv3Lsuy4GFlsVjA99HlcrVHJuxYwcrlMsMwkCsDdg8oiursJ7DDtDeT6elpj8cjyzIoN4BaQ4tbAk3TlUqls6QMboAYDKYzyyp0v3v3bm5u7vbt23a7fXp6emBgwOv1CoIgy3KlUllYWGgJ59gY2lgOgiDMZjOsT6ErBwKBlfKr6nQ6h8Pxxx9/NJvNdDodiUREUezt7T1z5kyLUYS7Qcx2MD4+bjAYQqEQpA60Wq0nTpzY5DWx4bEmFhcX7XY7y7Kod8hkMnj2s+dpf6eQzun48eM9PT1QH2Czm2EY7Sx/5y3SRqMBacvR9N3tdicSiR0uxtqBUj179szr9Xq93nA4DO5qLUHnsPg3MzPTQS8Lg8FgNkA4HJ6ZmQmHw5IkRaNRRVG8Xu/U1NTdu3ebzSaEgCM23NssLS2hYAyDwSAIwrNnz1qOicfjqN9rUa8KBAItB+NsqpjtBtV2nudJkgTdBUmS+vr6QOdtM5McbHisztzc3Nu3bwVBsFgsaFaHVHQBPAHaJ6TTaYvFIoqi2Wy2Wq02m02n03Ect6xT0w7XCkEQwFsAFKIIgohEIrtnU27ZMiwuLh44cIDn+UAgYLFYZFkeHR1FrQwZHlardZP6fRgMBgNAX/Tp06dUKhWPx0Oh0IULF1RVFUXx8ePH+Xy+UCg8efLk48ePW9JzNhoNrbuExWIZGBhotnWJDx488Pl82myDgCiKLSXHYHaMWCzmcDhsNhuo4Vsslv7+/ocPHzaxq9X20Wg03r59m0wmGYZBWUW1HQFmD6OdtUNNkGUZxHN1Op3JZAJv4EOHDlUqlWbbbv4Ol1NRFJqmwesXJu4t4YZdH7SW1aAslUpTU1Nnz54NhULFYvHUqVMkSdI0DQMwMj8YhhEEoeX0rt8RBoP5Qfn69WulUvF6vcFg8PPnz4VCwev1BgKBO3fueL3ez58/b+FvTUxMIEMCQjVahgzE3Nycz+dLJBLaEHNI3AYHrFHAA4PZEi5evAizHZPJ5HA4nE6nzWb75ZdfNnNNbHisTiKRsNlsgiCgXqDdzwqzx2hXai+Xy7Isw7ABQkwEQXAcx/P877//3nJuV8p5//59k8kEG6MQX96+R7+r0Bb+8+fPly9frtfrd+7cURQlHA5rPRtR0zMajalUqqulxmAwPxjLumi+fv06k8nwPP/s2bNarXb79m2GYVwuVyQSUVW1uXWrG8+ePRsYGGhxH0WhaytdPx6Pa7s+iqLu3LmzxhvEYLYKSZL0ej1JkizLut1uq9VqtVpVVcV5PLaR6enpcrkcCoVQrmWd7n8f2s7khsN0HfRaQfsV6gBMi1mW7evraz+yKyW8d+8ex3FmsxlchA0GQ0tKqd1ZP1tKVa/X5+bmVFVF8TMtEvjtOzkYDAazKi1dTbFYPHLkyLlz53K5XDAYhL1iURQLhUIqlVp7isBVf7FarZ45c0YbuWEwGNaiRKJ10NLr9Q6HY3f24Zg9TCwWg4GYpmmQ1j158iRSm8QxHttCvV5fWFiIRCIcx0H7t1qt3S4UpjtAkI924cpkMtXr9W6Xq9lsNhuNRi6XAycrGOFMJlMoFOp2uZZhLRZ7OBwWBIGiKKvVChaI7h/1ehi2JUnaqfJiMJg9SKFQcDqdbrc7EAh4vV5RFG02Wy6X2/IfWlxcPHjwYEvkxq1bt5od523VapXnee3KC0EQW142DKYzi4uLMObSNE3T9NDQkMfjaZFlWy/Y8FgRlJcNMgqhqQ9OarbfKJVKzWZzeHgYaUaBz48sy7vK7efZs2eCIMCuKGTGoGk6EonAX3+spbJbt27lcjlVVSVJslgsaOi12+06nY4kSbPZnE6nO1/kx7plDAaz3WjD8Px+v9lsdjgcHo+HZVmSJF0ul6qqtVpty3/Xbre3LFq5XK4OJSyVSiiYUMvS0tKWlw2D6UC1WoUJj9FohHR28Xh8k9fEhkcnGo3G1NQUJO4Bq4PjuG4XCrP1dJ6hgoKZ2+02Go0cx8F+gtVq/fPPP3eqgGvi4cOHkI8Pkqnr9XpZlqPRaLdC3jfD7Oxss9lMp9Pj4+N2u52maYjIdDgc0BIhxoaiKIjRxGAwmHWRTCY5jnM6nZABiWVZr9eLVmq2ikaj8enTJ4jK1WnUMsxm80qnXLp0SVGUdqsDTsG6GpidBLLYGY1Gnud5nmdZdmhoqNFoLCwsbPia2PDoRLVa9Xg8IB8GLb9QKHS7UJgtZtUeHJxxaZoG/yWdTgd5+tZy7o7RaDRev35NUZRer4dYFL1e39/fH4lEXr16tSVpsHaYcrk8Pj6ez+ej0SjcFxhULSL3v/zyyw93axgMprt8//4d1jVAIEQQhGAwCApX2/Fz6XS6t7e3Jcxj2SMLhYLf7ydJssXq0Ov1DMNoj8T9HmYHuHjxIqzxcRxntVoPHDhw8OBBv9+fSCSwq9UW0P4Qi8Wioihut9vtdkPj70pqakx3qVQq4XAYZQQ3mUxGo5GiKPjr7un9f/3114GBAVhRM5vNer2+p6dHFMV8Pt/toq0beKrpdPr8+fPXrl0LBoOiKAYCAbfbrQ24hNchiiLSmtSejsFgMM02ofMvX76k0+lcLicIgqIoFoulr69PlmWv1/vu3bvtKMDS0tLp06fRhi30XZlMpuWwQCAgSRLDMNrDWnY8Wu4Ig9lWQNnZbDazLCuK4vj4+IkTJ6LR6GY0M7HhsQwoLSjDMDabTVVVaPZoronZkywruZhMJg8fPjw5OQlujjqdzmKxWK1Wh8PRpWJ2wu/36/4JwoYVMrPZDGt4P+hA9ejRI7/fb7PZQHbGbreTJIkEr7Sj8smTJ2Hz9we9UwwGs31ou4ULFy74fL5IJKIoisfjEUVREASO4zbvvN7hp+fm5jwejzY9EUEQSJuk0WiMjY219GktJJPJltRS21FaDEZLtVqF/GBGo9FsNjMMI0lSOBz2+/0bVtbBhsfyNBqNL1++gKYEmskhBTHMXkXblS8uLr58+VKWZZ7nIXYC2Z9a5ZNd1fv7fD7YBIAaK0mSw+EIh8PdLte6aXmqMDmQJMnv9zscDoIgIMOgdlHQZrP19vZCxPmueikYDGaXAD3D6Ojozz//PDo6KopiX1/f0NBQT0/PqjJTm/lF+FCpVBKJhNa6oCjq1atXL168+K//+i/kUqV1x4IPRqNxfHy82bZ1g8HsALIscxwH6ZLB42NwcPDChQur6rusBDY8/g/UkmHHo9FogGc5dATDw8NN3Nr3DYVCIZlMHjlyBHY5DAYDUjaLRqPdLt3yNBoNm80GpQV/JHDKPHz4cLeLtkFamlswGEylUvV6PZlMOp1OcH5Dwg/wdmiaTiQS3SowBoPZ5Xz8+PHEiROnT5+WZdlsNkuSVC6Xy+XytWvXmttmeKDLXr16VRCElp0N8KFvsTpQnwZChcVicWsLhsGsCtRbSN/h9XoNBoPNZjObzaFQ6OzZszjGY8tA3cT379/HxsZ4node4M2bN90uGmaHePbs2bFjx3p6ehwOB/T+sM/Isuzo6GjLwbvHFi0UCrBHBwJQUHKDwWC323dPITdJoVAolUrpdDqZTLIsSxAESZI8zyOZYxjFvV4vaJFhMBiMlsePH/M873A4oFfnOM7v91er1R3LyJTJZGDdRGt7QKfd4luFvhFFcWfKhsG0AznLwe+DZVmPx+Pz+TYTO4oNj39BOz+7du3ayMgINHuSJLtYKsyOARWgXq+73W7IhgEuPbDdIQjC3Nxct8u4IrVaDTyVobQgA0XTtNPp7HbRtpJCoeDxeIrFYiaTGRgY4DiOZdn2HOdGoxGn3MFgMC0Eg0FBEFwulyzLNE0LguD1eh88eLCTZVhaWgKZxM7o9XqQR9/JsmEwLQiCYLFYenp6wMWAJEm/3+/z+WZmZjZ2QWx4LM/hw4cZhkHzGJCxwxFde5tGo/H58+dSqTQ3N9ff3w+rTS6XSxRFhmG0Uoa7sw68e/eOIAiYf0NEClggDocDciDuGW7cuAF+Eb/99tvp06chy0e7CIzJZIIsHx3e1+58lRgMZsuBxh6LxUwmE6Qqt1gsTqczEAg8fPhwhwsTCAR0y0lXaSFJ0mQy/YiyhJi9RH9/P2SVgDAPWNYUBOHkyZMbuyA2PFqBvikcDsOCBPQLfr8fWx17HkgKW6/XFUVBAlaSJNE0LcsyEjzZhXUAFYlhGIj9QllyWZaVJElV1V1Y7E2STqd9Pl8qlRIEgSRJ5A+t9VjgOA4pASyrWgYf9t7DwWAwWqCN53K5YDDIMAxJkrCOqyhKKpWqVqs73Al8/vy5Pa5D62RlMplMJlMymdzJUmEwgLY5WCwWm82Wz+ftdrvT6YREYSzLhkKhjV0cGx4rYrfbUS/w3//9390uDma7QPPOP//8s1gszszMOJ1OmL9yHGc2m41GYywWa+5Kk6MFnufNZjNsd8B4RlGUz+fbS95WWoPh/fv3r169gkw7Y2NjHo8HuShotysHBgaWHb+xyYHB7B8ajcbIyIjb7TYYDLBGoyhKMBiMRqModHsnO4RgMMjzPPK5AudYtG5C0/T9+/d3rDAYTDvQHEKhEE3TuVzO5XJlMhm73W42my0Wi6qqzQ01GWx4/B/o8cHKdzAYRAuoWMNuz9NoNJLJJCSvlWWZYZi+vj6IH3C73c1d/OrRXtzi4mIgELDZbGi7A2qvIAh7xtWq/S00Gg2PxzM+Pj4zMyPLMnIza6Gnp+enn35CKXqWvRQGg9nDBAKB4eHhw4cP0zQNMye/308QBOoed9ivodFoZLPZBw8ejIyM+Hw+URQdDkdvb6/H4ymXy1++fMF9FKaLQPWbn5/nOM5isTgcDlVVK5XKq1evWJYVBGFycnJjV8aGxzLUajXIEg9Tlv7+fvQn3BHsYarVajwet1gsJpMJgg4hrLxer3cekHZVrXA6nShHFYR8QL7bXVXILefdu3fVajWbzZrN5p6enhZ9GL1e7/F4jEbj8PBwKpXqdmExGEwX8Pl8siwfPHhQFEWe5wcGBkRRhFVbxE72kystaGK/bszuYW5uDjbient7S6XSnTt3zp4929vb63K5Ll68uDEtOGx4LIPb7aYoCuVtOHr0qPavuDvYe6D9RBBm5Tiut7eXIAhFUe7cuaM9ZqVzdwn1et3lcrEsC97DDMPQNA1+YnuDZXc80OdarTY8PKwoCsdx4LegdaGGb/R6PbY9MJj9RiqV8vv9kLtDEARRFKempg4dOjQ7OwsHdKUnX1X3YleNL5h9yPz8vF6vZxgmnU6rqqqqqsfjmZycDIVCb9682ZhsPTY8liGdTkPqQJiv7Bk3FUwH5ufnXS4XWJtms5llWdiI1x7Teda7G6hWq9FolGEYqMAEQfA8PzIyssem2is99m/fviUSiXA47PF4LBZLMBhE4sItGyCiKM7Ozmqvs9teJQaD2Spqtdrx48czmUytVstkMpIkgUuq2WyuVqvdLh0Gs+tAA2IymTSZTH19fQ6Hw+PxjIyMBIPBWCyWz+ffvn27uLi4gYtjw+NfaDQalUoFpm5IXKLbhcJsDS2RxNrP7969y+fzVqsVVsRpmiZJsqenZ2FhoRsl3TiFQsHr9YKXIPiJwYd9ktGi0Wh8+fJFVVWINacoCqJI20M+CIIwmUydkwFjUwSD+UFpabyZTCaXyz18+NDv9x84cMBkMlEUZTQaBUHQbizgJo/BAKgtQGQ5iDGoqppKpRRFicfjb9++3fDFseHxL7x+/VqSJLfbjSYoFosF/RX3SnuAlpf4/fv3arX65MkTh8MxODjY29sL7ow0Tberp+/+CrC0tJRIJCDnFEyvjUbjPsl6i97O58+fs9ksdJE9PT0sy4I9qZW6MhgMkPi8XC4v+1p3/7vGYDCr0mg0nj9/7nQ6y+XykydPBEFwOBwcx8FeqNadATd5DEYLtAgYPUmSJEkSspwlEon5+fnNtBdsePwLjUbj/PnzWj+rdDqN/TH2DMsG8338+NHr9XIcJ4oi5AoEKUMQN/sh0C7XeTwehmFQeANJkseOHet2AXcI7WutVqu1Wq1QKFy6dAnsSVjm1IZ8GAwGEJDpcB3c5DGYH5dv376dOXPG5XKdOnWqVCodPXr0+PHjoFXocrn2yVYwBrNhBgYGQKLG6/XGYrHDhw8LgtBsNhcWFjY8OGLD419oNBrxeFzrkgHONljvfw+w0htUVZWiKIvFAv8eOHBAFMVMJrPG03cbgUCAZVlUgSmKslqtP0rht4T2m3348CHDMJIk9ff3t2x9uN1ur9e73gtiMJjdDGqzL168sNvtfr8/HA7//vvvNE27XC7IuxwMBrtbSAxmNwONqFwu63Q6kiT7+/sjkUgsFrPb7ffv3//06VNnX+UOYMPj/3jz5k0ikZAkCXLC63Q6lmW7XSjMltEyfQQZuEwmw7Isy7JmsxniAWia9vv9Hz9+bD9lN09AUdkmJychtgEFM9hstubuLvyW0+6xHY/HIQk9crtCthnP86lU6uTJk9o9LuzzjcH8oKBmWyqVrFaroigOhyMUCkH0pt1u93g8iURCezBu6RjMsiQSCZ1OZzQaSZJ0OBwul0uSpNOnT2/mmtjw+D/q9Tok8WEYBqJyIXNcC7iH2kskEgmapiHQEMLKzWbz8+fP24/cze9dW7ZUKoVS0ICwVTwebz9s/wB3PTMzc+zYsUAgAKno4fnAB5PJBB8URfnrr7+6XV4MBrMpkC3x6tUrjuMYhhFFEZJ4nDp1qn2Hc392jBhMZ6BdRKNRmEjYbDa/3y9J0sjIyNTU1MaEdAFsePwvtVrt8OHDJpPJZDLBaqher0+n090uF2bLaB9dKpWKx+OBLQ5wTzIajbVareWUH2tYikQiWlcrnU539uzZ5o92F+tlpVRcWl68ePH06VNZlimKgkQfqKWD4WEwGMLhcLPtve/tR4fB7D0ajcbS0tKzZ89GRkYEQRAEgeM4u90+PT198ODBFg3QH7Gfx2C2FdQcEomEwWAgCEIUxf7+/tHR0UKhMDs7CzrUG2s12PD4X/766y9ILWSxWNCMDXVPuGPaY9y/f39mZubp06dgZ5IkCU2rPcn37n/p2hLm83mO47R5u/V6/V5KINiZzi8LVmgymcyZM2eCwSBN08ipEp4Y1AFFUVa9FAaD2eVcvXo1HA7fvn07EokQBMEwjNfrPX78+NTU1Eqn4FaPwTT/dcZ769YtiBQVBIHn+Z6enmKxmM1msarV+lj2ec3Pz0ciEZvNZrPZ0CLozpcNswN8+/YtGo0Gg0FBEEAAiiAIEDjacLDULiEajaLJNKrGsIqPAUKhkKqqsixLkiTLMjjaIVPNYDCQJAmmGp6FYDA/IpCPy+Px+P1+v99/5cpYdtFrAAAgAElEQVQVkM+22WySJPl8vm4XEIP5YUgmkxaLxWazybLMsqzT6YxGo8lkcm5ubsPX3I+GB0Jr1UWj0VwuB95sMGODxW/MD0eH+eLi4uLvv/8eCAT8fv/k5KTRaIS0LWDNBwKBnSznVqH1CIpGo1pfQfj38OHD3S3hbmNqagqkdeFxOZ1Om81G0zTSARsZGRFFMRKJwPE/1g4YBrMf6KD8USqV7t69e/LkySdPnoyNjSmKAq5WNE2PjY09evQIt2IMpgPaBgL2BqzQWSwWp9PpdDqz2Wy1WsVyuuujZSbx5s2bQCAQj8dFUURrn7du3cLd0w9Hi19+i4/ctWvXQqFQPB53u90mk0kQBPgcjUbv3LnTrTJvFR8/fhwcHNTueACgur2fK3PLvc/OzkqS5PF43G738PCwKIrDw8NmsxnsNMBkMjEMc/PmzbVcEIPB7BIajcbJkycjkUilUnn58qXP52NZlqKonp6eo0ePIqUNDAazFvx+v9FoZFl2aGjI5/OpqppIJPL5POx44BiPtdIeMwqBMjMzMwcPHsR+Vj86K7WE+/fvP3/+/Pz580NDQ7Is6/V6URR5nu/r6ysWi0hdscMVdjm5XG5sbAyFSiPfof7+fjjgB72vLaFlraFUKv3666/pdNrpdA4PDzudTlD3R9tE8AF0A3Fqcwxmd9LeDGu1mtfrFQQhFArNzc3F43GCIDiOs9ls4XD47du3XSknBvODEolEINPA2NiYJEnRaLRQKOTz+UqlsuFr7kfDYyV8Pl9fXx9aLW7iucUPS7sYwOzsbCQSkSTJ7/eLotjT00PTNEEQsHv47t27lnN/RM6dO3fy5EmbzWa1WrVhHufPn+920bpJ52Qs8/PziUQilUqdOnUKPTGTyQQ7n/AYHQ4HKHgsewUMBtNdtE3y2bNn8Xg8EomARiVN03q9nmGYeDyOnGlxE8ZgOqBtILDjQdO03W6Px+MHDx7s7+9H4p94x2PdoOkppCeHVXCYfPyg7v6Y5nJOVpVKJZ1Og6giRVGiKPr9fvjMsuxPP/20rLrij8Xi4iL4DomiKIqiXq+nKApW7j0eT7dL12XabY8Wj/DTp09DEknoASCpi9ZdLRAIZLPZ9kthMJju0rKZmU6nQ6GQw+HgeR7kCo1Go8PhOHHiRHM5fwcMBtOBcrlsMBjAWTEQCDAM0yL8uIGmtH8ND+3DUhTF6/Vqsx9MT093sWyYreXDhw+hUEgURUmSjEajLMuBQADSxqmqCmbnj048HmcY5syZM4FAwOl0QjUmCIKm6f0jp7tetNZpIBAQBEGSJBC5gkz22j0QkBFs4ikLBrMLWLYZ1mo1t9sNutg6nY7jOEVRXC6Xqqra6A7chDGYDmgbiM/nM5lMoig6HA5JkgYHB4eGhpqba0T71/DQsri4aLPZUHSpyWTqdokwG6TdCocPyWTSbrdzHEdRlM1m8/l8Ho8HxBnQ7POHHo2mpqaMRqPFYuF5niAI2OsApeDNZBjdA6zxtX7//t3r9fp8vitXrkCSQW1KH5jESJK0tLS09mtiMJgdo1arzczM2O12l8sFziGyLKuq6vF4UqlUoVDodgExmB8PRVEMBgPkWfZ4PKIoOp3OTaa2w4ZHs9lsXr9+3Wq1goOKwWB48uTJHp5Y7BNtULi1paWlXC6XSCTcbjdN0yDOwHFcIBCIxWLJZLLbxdwyyuUyx3Ecx8FODtRkSIkIc2VMOy31P5vNLi0tlctlj8fjcDhUVdX6XIEtR9P0PjfkMJjdSTabzWQyHMexLEsQBEmSPM+DV20kEgGv9D085GEwW06j0bDZbBRFURSlqqrVamUYhqIo9NeNXXY/Gh7tD8vtdo+Pj8MCp16vb0lYvgdY9UbaD+hwyi5/LNriFQoFcLISBAEmjlar1e12x2Kxq1evdrGQW87jx4/HxsZYloUMFZASUafTWSyW5q5/ZbsB9Ihqtdrly5dPnjw5Pj7engZer9dLktTX15fL5ZY9HYPB7DyNRuPp06cQCGsymcBxmmXZSCQyOTmJ49wwmLWjHc7sdjtJkihqFNpXE7tabQz01DweD0EQKHUg6Fm1HPND0/kulnUxWnYfbV3GSXdB5b93797i4qKqquC4T5Jkb2+v0+kMh8MvXrzodjG3kufPn09OToKbAUVRbrcbVuslSep20XY77dX4f/7nf+bn5/1+/9DQkNFo1MoTQy9BEARBEIqi7NomgMHsbVqcadPpdCAQcLlcVqsV5kl6vZ4kycOHD1+/fr1UKjXXMKJhMJimZgb15csXo9FIURRk2iUIgmEYh8PRcuR62aeGB3qs09PTd+/eJUlyfHwc5S3WHrPH2MA+xnq/7y7aUs3NzZ08eTKbzZrNZrvdjrYCRkZGfv755y4WcjvI5/OwJgGiTDabjeM4o9E4MDAAB+zO97VLWNb/cGpqyuFwpFKpdDoNaRm1KeHBpS0YDDZXMNQxGMw20R7LVy6X3W43SZJ2u12SJJqmeZ7X6/WVSqVWq9VqNWx1YDBrBxpIJBKBwQ5yD8CHzWdb3qeGB7C4uFgsFr1eL5pS6HS6lXIV/9C0dLJ37twJBAK9vb1//PFHh8M6XGf3z7QKhQJMvs1mMySQYllWFEWTybSXNgHQK8hkMpIkoaU+CCvneX5iYqK5u99Ud+n8ZFD6DlD2gH0zZHtwHBeJRNZyHQwGs300Go1gMGi32xVFoShKEASTyTQ4OGi3239cn2EMpuvcvHlTr9fzPC9JEqy1kSS5UlLdtbPvDA/t1Pnbt2+lUikUCiH1vX2iZ3Xr1i3wHmEYxuVytfy1vUrNzc1NTk4mEomZmZmdKuOmACeryclJi8UCXjGwYm232wVB2Ly9vquA91UsFsfGxmCXA/ZGwcW5XC53u4C7lM6ug+gzRHzNz8+zLKsoCsMwYNRB/EwymVxYWEDh+3gqg8HsMH///fe3b98uXLgQj8ddLhc4hICqVSaTgfQ7y4JbKwbTgUajMTw8zLIsOG9bLBZYelNVVXvMBq687wwPAB7W/Px8MpkcGhpiGAZWMcfGxrpdtO3i77//Rp89Ho9WJ/T58+eda8/ExAT4tQuCAEkhdn+XffHiRUVRZFnmeR6FXA8NDf36669wwO6/hXUxPz9vtVrtdju4WkHKXvAF2v3bU91iWdtjpQd1+vRps9ns8/lkWXY6nbDpYTAYeJ4HHd7tLy8Gg/k/tKsDV69e9fv9vb29PM9D0kCSJKenp1+9erXSWRgMpjN6vZ5lWavVCkr9giBYLJbbt2+/ffu2iVWtNowkSffu3YPlYZ1O9/TpU/h+T/ZN6KZSqZTW8BBFETKjrUQ4HNYG1+5+QfRKpRIOhwmCsFgskJjF5XL19/dnMpluF21bgDfLMAws9el0OpqmYWNUluWWwzCrsuyDWlpaOnXqVDwel2U5FAoZjUaQSoN2IQhC50aEwWC2HGiq+XxeEATI0STLMrhBxmKxlYYq3BNiMKsyPz8PO/wGg0EQBEiDtiUCcfvX8KjX681m0+l0QjbrFj2r5p7um75+/WoymbS2B03TgUBgpeMLhQKaYOl0ul0iTdjhBUWjUZIkOY4jSRKyUJMk6ff7O5/1o5NKpaxWK8yGDQYDGF1WqxX+uodvfAeAp5fJZCDvpNvthkg76JShXbAsq6oqEuPe8K98//59y8q9oQJgMD8WyWRSkiRwloahzWAwKIoC2g8YDGYDOBwOsOf7+vpEUfT5fCRJer3e+/fvN7Gc7gaARzY3N3flypVEIgFTBxTgscdG3xZPm0aj8f37d61CKLI95ubmmv96+/D527dvIIuOzA+/3z8zM7NLdEJafnd+fn58fByEZTmOGxwcNBgMLMu277nvJRqNRr1edzgcsOkB/4LP1cOHD7tduj3C/Pz88PBwf3//oUOH7Ha7wWAQRVHblMC3rVKpbOZXuuUat8f6PczeBjWTUqlktVqHh4dhsclkMoG6Rjwev3XrFq7VGMwGqNfrPM+bTCaO4yYmJk6fPp1Op6PRaC6Xg1ycAI7xWDexWMxqtUKcqE6n0zqlAHuvz0KByBAM0ILJZII5U7unu91uRxMs0E3ief7UqVPv37/vzp00m81/LSd8+Pz5s8/n83q9VqvVZrOpqmqxWIxG4y7ZpdkOUPQOhIKBZDC8TZ1O19fX193i7Rmggt25c0dRlFgsNjk5SdM0TdOwv4QakcFg8Hq9N27c2GTem11ixq965N7rJDE/ClD3Ll++rKrqgQMHGIYRRRGkYkwm008//fT48WNcPzGY9QKthqZpgiDMZvPY2NiJEyfK5fLz588/fPiw+evvU8Mjn8+Hw2GQAEKGBwo7bu6t0bT9XqrVKrprbfAGy7Kzs7PtEunNZjMej2tnVzDBIkmyJX9zV0DlLJVKgUDAZrOZzWaapjmO83q9sPnudrvbj99jfPny5ejRoyaTCVSD4Z0ajcZPnz419+5d7wwtT+/PP/+Mx+Ojo6Mulws2l6CaEQQBu4JGo3FoaOjly5eb/60dYO2So7tkkxODAd6/f//u3Tu73e5wOMCx1mg0chzX29uL11wwmA2Ty+VgLHM4HLlc7uPHj1euXKnVaoFAAKmbbnjtaT8aHs+fP69UKpFIBMJDQdLKbDa3H7kHhtVlb+HLly/amA1keEiSpM3soT3X4/GgU9AHg8EQi8W68pTa/ceazWaxWBRFEVJHkSRpNBphuyOdTmsP23ug+8rn8xRFkSTJsixsTBkMBiQouVdvf4eBx5hIJGKxWDQaPXjwICxhaJMM6nQ6iqJgE3W9ewhdAX66Xq+7XK6FhYWVyrPJbRwMZgtpNBqg6MBxHOQph9Uxo9HI87x2EQ2DwawLQRCMRiM0qxMnTjSbze/fv9dqtdnZWe1h2NVqfSSTSZ1OJ4oizKRRFNqy6/0/Oi3T9KWlJa1jOsrH7PF4UEYC7YnNZjMUCoH2lzZ5M8uyKMNay/E7RqPRWFhYmJubm52ddblcPp/P4XAMDg729PQYDAbYlmk/ZYcLuWPkcjmCIKxWK8uyNpsN3u/du3ebe/quu8XPP//s8/kikYjL5aIoCiVwhKkPy7JGo7Gnp2ddWmpdf00Wi4VhmEQiASXRynADeNMDs3sIh8PZbNZqtaLe3mKxuN3uVCoFB+D6icFsAMh+BpO9q1ev5vP5arVaLper1erm29Q+NTw+fvz4119/+f1+tDy57LbsHu6zWoLL4TmEw2HtMS2373Q6tWmbYXYVj8d3tuCtxVtaWnrw4EEqlZqZmXG73WNjY16vl2VZhmF4nh8dHU0mk9rj96pjOtxRtVoVBAHylthsNlixOHnyZLdLt9fQKlMHg0GocuBlrt30ANaY4mOX1EmLxQLFFkWxPUq+XXkCg+kKX79+XVpa8vl8qqr29/ejEc1ms+GkOhjMZvjzzz9RdjtISMBxnCzLoD+0efap4aEoSjqddjgcINak0+n2sO7esns42ukR+gDJAVcim822u1rJsgyzk6WlpS0xhdcF/Jzf74fBJpFI8Dw/NTUVDodlWWZZNhKJLHvKHgPd1Ldv38xmM7wa9JouX77c3eLtbd68eeN2u3meVxTFYrEgPTFkeBAE0SF98q4CdsxQyXt6eubm5lqMDWS6C4LQ19e3SQkvDGZjFIvFer0uy3IkEoHtDr1eT1GU0+ns4nIYBrMHqNVqaCCAnGA2m01RlOfPn6NjsJzuuoFtI1mW0eQsn893u1A7BFQXFAWr3fQQBKHDie3x5aAWNTs7m81mIaS7XRlsa4vdTiAQoChqdHRUkiSPx8Pz/OTkZDgcHhwc5DguEokgh/U9jDbGQxAErdWh0+muX7/e3eLtebLZrMfjOXr0qCiKYHtIkoRse3BizGaz1WoV9TO7c+ft3r17KMMPFP7IkSPNFcrpdDrhMK1yAwazMwQCgenpabfbDfFsoO6gqmo4HN6riWIxmJ0BRZbr9XpFUa5evRqJRLRK8Zscufaj4XHkyBGGYWKxmMfjQQuTaAtpd04ItpZGo+F2u1usCJ1O5/V60QEtH5rNJoqHQccbDAar1QouWHq9HqRFHQ4HBPztQLRMuVwG716LxcKyrN1uHxwclCTp2LFjw8PDuz/D+pagfbzPnz8HwwO9KaPRiPz193at7hbwVEulUjwe53me4zhRFKFRAOhduN3uYDCYzWZRJNWyb6SLr4mm6fbFhZZpHBRvdnZWm4QURClwBcNsOctWqtnZ2Z9//hnWmCBlqk6nczgc6XQ6k8lslUMIBrM/+fPPP2FSZzAYIHwxHo+rqrpV19+Phsf9+/cZhiFJEq36Q/xxy0R5Lw2i7feSSCQgWBzNiiAbGtgMLczPz1erVQgYaLFVCIIYGhoiSVL7JUy/kObasgXYkjuampqiKAoylAuC4PF4PB5Pb2/vgQMHEolES6D8HgY93omJCb1eTxAEQRDIR3P/7OZ1l9evX2cymYGBAVmW7XY7QRButxtl+YANEIvFYjabQ6HQWkyOne+C2vOK6vV6WZbbu8Tp6WmtU5Zerz9z5swOlxaz51l2LG40GqFQyOVyeb1ej8djMplARdfj8UQiERh39tLwjcHsMK9fv0YdO0mSZrM5EAjMzc3hGI+NUy6XXS6X2WymKApmA06ns9uF2iFQdwxqwtpIDwjYGB8f13bZgUAAxHlAW023HBRFXbx4UZteED6wLLvSr6+3wMuemM/ng8Gg2Ww2/YPZbIbsCoqifPv2bWO/+OOyuLg4NDQEuTtMJhNStYfw+n31KLrI/fv3PR6PoigOh2NoaAhyMIHYLrQLk8l07NixS5cugW3c9feiDRASBKHd8Ojt7W0/OJ1Oa3c8gGAw2PXbwewxltUzCAaDHMc5nU6Xy2W32/V6PcMw6XT6/PnzXSomBrN3ePnyJVqXpygqEolIkpTJZLCr1caZmJhIp9OiKKK5siRJ3S7UNrLs3L1QKJTL5RZTgWEYiqIKhcL169ePHj16/fp1sDrQphtauG2ZcNjt9vZZCEVRW5teEN0CmN3ZbBb8u8ChxWg0iqIoSZKiKMVicU/KIndmcXFxeHgYgm3Q+4IX2u2i7S9KpdKtW7dcLtepU6ecTidklQHbHrUg2JiyWCynT59uLpeXZmfqrfYXU6kUTdPtKws0TbefdevWrWWXIRYXF5v7qdFhdp5KpRKNRq1WK2RqgsxFJEn29/fD0LAPO38MZguZmZlB0zye551O58DAwBYmbduPhocoiqB6hGJw2zVn9p63VQulUqm3t7fdhIDpEcMwoVDo3LlzIJHUYp+0fKZpGvL0tVyHIAie55vLpQJYFy0rXouLi9lsdn5+HiwimqZBRMjtdvv9frPZfO7cuc0+nR8Wv98Pwc3oLZhMplqt1tzBuex+Y1n/qHQ6ffnyZa/X63a7QXVn2bYGtGiv7fy0qfFPSkTtzoy2CrW7oR47dmzZe8EiV5jtANXAUqmUTCYjkUgikYCNboIgKIoSBCEUCmmPx90dBrMxZFlGXTpJkhRFWa1WWEfekma1Hw2Pc+fOORwObRjlnneCR9MF+DA3N+fz+SAGoMWKACiKSiQS4XAYifq3g0QP9Ho9LLG3HGAwGO7fv68twJbcRbPZrFQqjx8/NhqNAwMDRqORoqje3t7bt28nEgkIhN1vQw7c79evX30+n9ls1rq9/X/2ziY2jevr/7zM+xvgmQEmHkxCjDFRSDBRSHCwQhQsmZbqCZZCHoUoVApZhDxSqOJsQjeliydUCl3FXdVZxZVKdvFvF3dZsqizrLutu6z7bOosf8N/cf69mh9g58UvxHA/i4i6w3Bn5s6995x7zvdYrVbshD4Aum/v+vp6qVQKhULJZBIeBMqqMr9BEPGYz+ffesL9ZmxsrOeLbLfbuxt29uzZnmPCs2fP+tJ4zJBQqVSKxWKhUIhEIpIkgcrn6OioqqqoZNMuXV0YzJADMbcQNwGBMDabLRQK7dX5h87wgLy0sbGxWCyGooNQRvUAl8cyX040GnW73bA83c4Ra7PZxsbGzL7zHaBp2uPxQEKtKIqSJLlcLnNy+R6yvLxcKBRSqdTp06cDgQB4vARBuHTpUiqVGgbx3O2o1+vhcFjXdXhq6Ml21IXE7Dk7bJBWKpV6vX7u3Dld1zmOA2cHFDi3/ScOh2N5edl8qgMegmC7rPvtnpqa6j74xo0boih2BFiCiTLw28WYPrK1tZXL5crlMoQB2+12lmULhcLZs2cXFxfRYXjHA4P5YFCoC0SwOxwOv9+/h7INQ2d4tNvtZrM5NzenaRq4IW02W79bdECgHuP3+xVF2SH2w2KxkCRpjp7a4WCKolCSzD4ZG6j9S0tLN2/ezGazZ86cUVXV7/fDQ3Q4HLquR6PR/fv1Q8EXX3wBT9Yc29NdRRFzwFQqlTNnzsTjcZZlId3cnDRl+afgo9PpfOup9mk5ZRhGoVDoztSyWCyXL1/uPr5arUqS1BGXtfNYiheCmF3y7bff3rp1S9d1SZKQLiVN08FgsFqtDo+MIQazT8AoDTse4EcuFouBQIBhGBxqtSuazeapU6dA6dJisUAewlDx5Zdf7hBnhYD9te1sD/Sfdrsd6r4fwMIiEAicO3cuHA6n0+njx4+HQiGbzcZxHEmSuq5DMsNwAjc/nU7Lsmz5J4CHIAiXyzXMSS8fA5CYdPbs2W+++SYcDsdiMV3XvV4vQRDo/QItMpqmNzc3dzhPx4e9JZlMQjBYh9hdt8S2YRjVarV7xLDb7du1DVsdmF1iGMb6+jroZ1AURZIk2PBQVnlvhUwwmCGhe1ppNpssy0Kah67rrVbr9OnTkiRls9m9iigZOsNjYWEhnU6DmwQkXEiS7Hej+gAEKW1nVAAQEIIOsNlsPSOvrFZrs9ncv4UFOvPa2lqlUhkbGxNFMRAIjI6OjoyMCILg8XhIkkTVD4cQdIumpqbADw1rR9izOn78eH+bh2m321988cWjR49mZmb8fn8oFCqVSlDqEZXHARN6YWHhxx9/fP369Xbn2aeSOO12++TJk91vN4himwNX4EMul+sYOuBDzxZ25JhhMB9Go9GIRCKKogiCACoaqqpKkjQxMXHmzJl+tw6DGQQMwwAPFJRmZllWkqRQKPTkyZNGo7Enw/jQGR6NRgN8dZAxY7FYfD5fvxt1QJi7Sz6fv3jxYrc2rvk/SZJUFEVVVY7jWJYNh8PRaLSniQJZR/u6qjAMY3Z2dmpqCvZhoG2apkmSpCiKWc9k2DDfdk3TnE6n1YTlH6EhvObrI3Dzt7a28vl8LpcLBoP3799PpVKiKNpstomJCaj1Ac8rHA4Xi8VPPvlku/PsecOAVqvldrs7XnAorgqsr6/XarVsNnvhwoXuoCz44oULF3oKW+Huh/lgYK2zubkJJWLn5ubGxsb8fj9FUZFI5Ny5c5cvXx7m7W4MZpeYE/M2NzdlWYb1A8uyHMdNTU3tbfbs0Bke4XA4m80qigJTvtVqBR2kAWa7KX9mZqZnUQ4kV6UoSsd56vW6y+XqOB50D976c7vn/Pnz586dI0lSEASO48bHx2Hb/ciRI1988cWQr2zg8qGcovnpEATx8OFD8zGYPlKpVObm5h4+fPj69etWq3XhwgVBEKD0CmRVoeKPJEmKorive4kdFIvFkZGRbreCIAhgF8EGGtr2RANFx9Ch67rH44EqiolE4vfffz+Y9mMGFXgFotFoNps9duxYLBaLx+ORSMTpdI6Pj0uShNPYMJi94vr165A9Bb4wnud5nt/bnxg6wyMej4PJgTI7X7582e9G7SPbhT0AhUIhk8l0WBHQ4VRVLRaL3TJfPXc8vF7v/slJoTbMzs6eP3/e7/dzHOf1ep89e6YoyuTkZC6X2+5ih4q1tbVAIEDTNFJuhUeJcy4/Kp49e7awsHDx4sX19fVwOOx0OqPRqM/nY1mWJEmzKgBk6Tx9+vRgGvbo0aOedXu2801s90eKopB+F9gtZrHgIX9JMR/Gy5cvk8lko9FIJpOqqtZqNXDH3rhxo1AooCkAg8G8O+YAWrTpIYoiciqRJOnz+R4/fgw1J3ABwQ8kk8mIogj2HApKHnJomobCYQRBpFKpWCy2XaKeYRher7d7zUEQhFnKcG+Bvr66uvrVV1+dOHEim81Go1GPx9NsNk+ePBmPx9+8eYNXM+12u16vg11N0zTse0AKAXo0+C4dPD0t/+XlZZqmp6amstms1+vVNM3hcMBeR0chToIgJicnD+bBLS8vMwyzg9rEO1ogKGbMfBjP87du3TqAq8AMJMlkMhKJFItFTdP8fn8sFpuZmUmlUrqu12q1frcOgzmsdE8uqqrCoE3TNE3TkiQtLCxst3H9YXPT0C27IVIIWR2iKA7Pamy7K/36669jsRhFUS6X663e8Ugk0r3msFqt+ydl+9tvvy0vLzebzUajEQqFFEWRZdnhcHg8HkmScJAV4tq1a41Gw+v16rqOAmPsdvve+iow707HPTe7l8rlcjwer9fryWQSdK5YlhVF0eVygVCPWTXOnDWxr88R6nh0x1DtYGz0PKy7/Dkcqarq/jUeM3hAb280GsViMZPJ3Lx5U9f1ZDJJUdTU1FSlUslkMq1Wq43HNwxmL1hbW0POL7vdLgjCxsbG0tJSz4M/uGTT4Bse5pvy5s0bJDMK82UikcAD1nuRSCR6LkckSdqPn/vyyy8fP358+/bt77//PpPJ6LouyzJ4iCmKkiQJPz6g1WpNTU198803xWLR5/OZDY8XL170u3WYbalWqy9fvnz+/Hk4HNY0LRgMBoPBVCplFrMOhUJ2ux2Ev3t2+L16C+r1ulnht+ebvjOoHPt2B8RisT1pKmaAMffnWq2WTCaLxeKNGzegXOz58+d5npdleWZm5vr16x9wZjxrYDAI8+vw4sULUOSHd02W5Xa7vYPI+4cx4IZH9/gC4sSWfzY9hkfSapeg8TqdTncsMuDD7suhdOeT5PN5j8cDeYTJZNLv94fDYZ7nWZaF7QX1p8UAACAASURBVI5vv/22PfRzCbrwr7/+enR0VNd1KCEPPZwgiFevXg35LfoI6ZCTWllZuXbtWjAY9Pv9qqo6HA6e583Ld4iai8Vib9682b+WtNttXde7X/CdzYzuP+5Qe5Rl2Z6yV5ghZ7vRaWVlJZfLjY2NHTt2DLoWwzB2u50giHg8DlPAe9FqtY4cOXLnzh1BEI4ePdoe+hkEg2n/k+Zx9OhRFBAECkPFYnHPoxkH2fDoLoxiGAZEoVj+CQagabp/DTxkwG1cX1/vuZ4gSXI3Mdw9B/2JiQlFUXK5XCqV8nq9oigGg0GSJEOhkKZpuq7jqQJAE2cgEOA4TlEUtPJjGOb+/fttPK1+NPR8EFtbW7lcThAElmWdTqemaWNjY7A9a96CYFk2l8utrKy8+5nfl++++66ndfEukVfwGSrJQJZRz28dOXJk9+3EDCTdffjo0aNXrlwZGxuDOECCIEBCfWRkZGxsbLtv9TytYRh//fXX+Pg4wzBjY2OWf8L/OgKM8VCJGR46rG6O4yymum1ff/21YRh7nkY7yIZHB3DjKpUKFO2GGRHHHL8XcA8DgUC3Di9JkplMxnzYbn6i3W4/evRobGwMqqp5PB6WZSmKYhiG53mn0ymK4nfffbfL3xo8zp49K4qiKIrmteB261TMwWMe5Ts8I5ubm2fPno1EIqAZCp4nKGdOURRS4bNarcePH9c0zbxb+8Eu255fCQQC6Od62h7d4VjmD7D/qWkacvHAdg0cQNP0jz/++EE3DzPgdOdENZvNixcvlkqlQCDw5Zdfer1eq9UKE4HL5eqIAHmX/u/1euFtgmUA9FhN0yqVChzw73//ew+vCIP5mOkIM1ldXTWP7SRJbm1tLS8v7/kqa8ANj+775ff7zetmq9Xal4YdaprNJhR9N0NR1OnTp9t7ZwkUi8VYLEYQhCiKPM9zHOfz+RwORzAYdDqd3fqJeMIoFouBQACyO1ABQZvNtrq62u+mYbbF/L6srKzMz89ns9l8Pn/hwgVRFDmOs9vtoLQLQxZBEKOjo+Pj44lEwhx2tfv3Dp1hfX3d4/EgUwEUfmEeIklS1/V0Ot2dPo5sD4ZhJicnFxYW6vW6z+dzuVwul8vj8aiqKgjC8vLyLtuJGQagN5bL5VKp9Pjx42+//fbhw4dQHXViYgJcUR/Q5wOBAPTVeDxu7r0cx3X8NAYzJKAOf+3aNbPVwTAMWjzgHY/3BrkD8/m8pmk0TZsj4PvdukPJkSNHukMs7Hb7npz8l19+abfb2Wy2Wq1yHMfzPEVRLMuOjo5CYbLutQueKtrt9vLyciKRgB1SWKfabDYcTPjR0nObotVqZbPZ+fn5UCik67rf7xcEQRRFt9tNURRYlYIgQCCTIAi5XA69Dh/8FnR/cXNzs1qt+v1+2K9gWZZhmFQq9eTJk62trY2NDag90pFEbrfbQ6HQ5uYmmq62trYajUYqlXr9+vXjx49LpRJ+VTHdbNcrvvjii/v374OKbjQaheKVk5OTyWTy7NmzO3+3m0qlgqYtURQhdgt13fc6FQYzSEDPD4VCUMSDIAiO41RV3SctkAE3PDrGkWg06na7JUkSBAE557oPw7wLwWCww9+5h9U8Go0GiLXzPC+KoiAIuq4riuJ2u589e9bGj+w/QXfjk08+sdlsFEWh+dVcVB5zKDAM49mzZ9FoVJIkCJyD0uYcx4miCOaH5Z9yGfDeBYPB/WjJysrK999/Pz8/v7Gx0VFDPZ/Pw9Zxx75Ht6w2ztzFvBfmruL3+ycnJy9fvgyCGRRFgew7SIS339PqSKVSln+iAZ1O58LCAsqhslqtkAuHwQwnhmEg7SWaplVV1XV9enp6P35rwA0PM81ms1QqQUkUFDnw9OlTPCN+MA6HAyUhURQVj8f36sw3b97UNM3lcsGsIEmSw+EIBAJXr17dq58YSC5fvgxOQcs/gfiCIPS7UZht2WHwaTabiUQiHo/D2svv98uyLAgCz/Oo4id60Dabjef5D9Me2aENPTNSgKWlpWQy2W14vNX1gMdbzA6Yu0ez2Uyn05Dg4XK5GIahadrv9yuKsl2J2+3Y2tpaWFjI5XKoxzocjsXFRY7j0F+CwSDunJhhBrzJsKLz+/03btxIJpP78UMDbnh0aFbWajVN00CfGJKV+9i2wSAajeZyuUqlsleCa1tbW6lUShAEj8cDetLgttc0rVwu78lPDCqrq6uxWAyqX8Ni1GKxkCS5hz+BJ+YDplwua5p25cqVXC4XCARSqZTP55ucnOR53pxlAXsgDocDCQm8o87PB1Or1VAOurkZeH8Ds0ug8ywuLoKCQrFYBJMDAqRlWc5ms6urq+/ex1ZXVz/77DNd1yFAEfl08/m8w+GAgCuapqEQIQYznBiGAeWhIamPIIj19fV9+q0BNzwQhmGsrKxAcAKsxkDaoo3nyN3xATprO7hRt7a24vG40+lUVVVRFJfLBRtTuq5fvHjxjz/+2MOWDx4vX748fvw47EGhhGC73X7nzp29/SH8yhwkjUYjGo3G4/FYLBaLxdLpdCKRoGnaHOUIj9tut7tcLqS7sPNj2uVDZFkWrB3zpocsyysrK9j2wHwwqNvE43GXy+X3+z0eD0mSLMvabDaGYXw+XyAQ6DASQFmkWxSr3W5ns1lQR+zYmoNXhiRJh8PhcDiwAgdmmDEM448//nC73RaLhWEYWEI8f/58n35uwA0P80i0sLBgnilBrriPbRsMPszq6Mna2lqz2ZRlGaQSHQ4HQRCCICiKkslkGo3Grhs7gJjv5+3bt8+ePUuSpNPpRL49juO++eabPRE4xgvKPvLs2bNQKFQsFl+8eDExMSEIglm7DC2nGIaRZTmdTj9+/Hhf24PUSM1YrdapqSncTzDvS3efSSQS165di0ajsAZiGIZlWUmS7HY7Kt/RfYYOVldXZ2dnVVVFjpiOHgv5UbivYoYW1PlzuRxFUaAjCu8LZPftx48OxcrbXBsFhh4Yy0iS3NzcxIPOAdPTL3Xt2rVbt25lMhmHw6FpGkgr2Gw2RVHOnj1rTu3Az2s7yuUyzNMcx9E0DXXcbDYbFjA97KA+f/PmzRs3brjdboZhkNhuxx4XPH2CICKRyA6n2iU9DQ+LxaLr+h7+CmZoSaVSyWQS4qCgYzscjmg0yjDMtWvX3vEk2WwWlDaQ/Jq54Izdbq/Vah2lDPbnajCYj51IJMIwDMp/pml6YWEBYnf33Jc0FIYHIhgMzs7ORqNR2Lq1WCxmIXxMv6hUKpFIJBAICILgdDrBmwsrKkVRPv/88zaeEt6BVquVy+VQJOHY2BjEw5TL5T0s8oA5YDp2nP766y+IuTpy5IjH49E0bWRkBKV8oLArEDdDZdHavZ7gbp6pw+Gw9CogODMz09FgDOZd6Ogt8Xg8Ho/zPI8iFGB24HnevBja4VTJZFIURafT2dFFUahVz8RZ3GkxQwXq8FAEzOfzgVcLWR37weAbHuZxpFKpXL16NRqNUhRlsVhomu4ofYo5eOr1+u3bt4vF4qlTp2RZFkWRIIhwOJxOp8Gnu7i42HOTBNPBL7/8Mj09bbfbQT4B0gCsVuuXX37Z76Zh9gwo5xyPxy9cuKCqKogeer1eyz9VnzqSzu12+6+//rq3LivDME6dOtVzMQchkfgNxXwYhmEsLS2trKx8++230WiU53kkHg2K0kePHn3rGdrtdqFQAI0NVVU7XgogHo8bhtFzZsG9FzNsQM1yiAMKBoO6rsdiMUgu34+XYsANj46blclkWJblOA55B5eWlroPw3wAH3wPS6XS1atXs9ns+fPnHQ6Hoih2u71SqUiSJElSIpHYqx8aVMw3JBqN2u12mqZFUYQJ22azFQqFvfqtjY0NfP/7SIfYaLlczmazCwsLsizDLgcUKeqwB1iWzefzHVlSu3+OIPpu/i2Q68BgdsPY2Fg6nf6v//qvUCgE0wH0LkmS3G53Rz0ZhPmP6+vrkCZL07QgCDRNmw0PsM/RwZCY3vM8GMwwYBjGZ599ZrVaaZqGguV2u31tba37sL36xUE2PLoNNb/fb7fbUaEDi8WCU5Z3z25iZOPxeCqVomkaAtOTyaTH40kmk6VSSRAEszzodr+IQWxtbUUiEYIgeJ43T9gfUGwLgW/1R04+nw+FQjzPu1wukOhRVbWjoLjFYoFBr7u6324IBoMdCbsEQTSbzTbuNpgP5fXr12fPnp2ens5msw8fPoxGo5CZCdqG2Wx2568vLi7CnMKyLEiCulwuWZbNKUlWq/XSpUvbnQF3XcwQks1mQRSRJElZlkmSrNVqZu04vOPx4WSzWSRDCfNlPp/vd6OGFMMwvvzyy9HRUciBBjUeVVVpmp6fn8/lcuFwuN9tPGQ0m02XywUJx2bJo7fO1phDzfT09OjoKFQ0lySpXC4fO3YMknHNtgdJkoIgXLx4EX1xl3NJvV4PhUKo2A4MqvukgoIZBhqNRj6f9/l81Wq11Wr5fD6IOBcEweVyuVwuMGs7MOcUaZoWDAZVVYV9P3MOEny2Wq0MwxzsZWEwHzsoNBHeEZfLFYvF3qtaznsxXIbHpUuXKIqCyuUWi0VVVfg7dnL0BVmWdV0HB60gCBAlQlEURVEnTpzYv8SmQQK6LooWcDgcqIAg9HNRFM+fP9/XNmL2no5txi+//FLTNEEQNE0rlUrnzp0bHR0dGRlBaleWf2R8nE7nDqfa7i87UCgUUBzLyMjIq1evPviiMMPM5uZmqVSq1+vFYrFWqxUKhXg8rigKy7K6roM1skNfNQzj+fPnsN8LRnjHXhy8AqdOnTrwK8NgPnbMJrrNZvN6vSMjI/v3cwNrePSM/4lEIiDPh27xw4cP+9TA4QU9jmAwCPt6kJYAn2maVlUVl3N6L+CWPnnyBPKXbDYbQRCoao0gCP1uIGbv6Qhqn5mZGRkZgbrmgUAgGAxWq1XYRexI+fB4PO3tIyTf1wvDMAzYukif9ANOgsFcu3atWCxmMplYLFapVJLJ5NTUVCAQ4DguHo8jfbaetgf8sVgsopkdZaWj7COHw2Eu2YG7KAbTbrcNw/jhhx/gHUGvD0EQHMch13wbh1q9Fx2jDEEQkBAJ2t4WiyUej/e1gcOLYRign4s8shaLRdM0qBLV79YdPlqtlsvlgshm0KYgCMJms0FSU79bh9l3DMP44osvNE1jGAY2Dy9evBgIBMx1DNDWh67rU1NTuykyiDLoWq1WvV4/ceJEMBjsqU+KwbwLmUymWCzGYrFEInH69GlFUURRDIfDoVDo3r17qIjydgugra0tVDXVYrGADwt1e6fT+eLFix2+jsEMLVNTU2glBv+SJClJksfj2dra2o9XZsANDwBuXCKRIEkyFArRNA1p+xaLBddW6wu//vrr5ubm4uJiLBbjeR62oSiKkiRpcnLy5s2b/W7g4QMMOVTx3eVyQWy0KIoulwsd099GYvaWbv2MYrEYjUaj0SjLsoFAYHJyEhZwDMOYDQ+LxcLzvKZp3fk/79hJzD6dWq325MmTHVqFwbwVRVHu37+fTqc1TXO5XKBGJUlSLpf75JNP4JjtdNUNw9jY2DBXCRwZGZEkSRRF5NJaXFw86EvCYA4DLMsWi0We59HsADZ/vV7HOR4fCLpxc3NzJElChiXDMJBljut49AVQaltZWUkkErIsgx3IcZwkSffu3et36w4lW1tb6XR6YWHB4/FA4WqHw0FRFEmSR48exavAoeKXX37x+/3hcNjv9+u6rigKisEz2x42m43n+ampqUQiUS6X3/dXOsog4ArQmA/m5cuXPp9vfn4+nU5D2C30VUEQZmZm7ty589YzlMtl846Hy+UqlUqXL19GquKtVgvHWWEwHTSbTYIgWJaFEAmLxULTdDweX1hY2L8fHWTDo2Mi/Oyzz+LxOMdx4AUhCEKW5T42b2iBrPFmsxmLxdxuN6glUhSlqqooinAMnhjeC7hd9Xr91atXuq7LsuzxeCiKEkVREAQUT4jv6qDSvaLa2NiIxWKSJPE8H4vF4OUiCKIj38NqtWqa5vF4AoHAh0n87eCE3sUFYYaLxcVFv9/PcVwul4PgQOirUETZXAK1Z3/7888/ZVk2F+uw2WyXLl2CukYkSZqFpHHPxGAQkBlFURRBEKAFR9O0oihIhb+9D5vYg2x4mEkkEpcvXy4UCkj8kSAIRVH63a6hY3V1tVgsvnjx4uLFiz6fD6YWcG5JkoRjxHfD4uJivV7XdR2iMyFQweFwdBdhxAwqHXNDMpkMh8PJZFKSJCToB4ngsLADpzJYI7quV6vV7rpRu28GBrMzpVKJ4ziKokBgHRkPHMf5fD4oGridiQuwLAtqfsi0FgQhl8ul02lFUba2tg72gjCYwwHP81B5FnYarVZrNBotFov7+qPDYnj89ddfmUymXC4nEgkY0axWK64Usd90zA3/+te/arWaz+dLp9OlUgkVdQJPFUmSeL2yG+r1uiiKoijyPA/RawRBUBSFzDl8e4eQra2thYUFjuPcbjfIVbtcLtCRQzY/2v0gSTKdTlcqFRSD2r2DgXsRZm9ZXl6Ox+OqqoIWH4R8gBS4qqqFQmHnrxuG8ccffwSDQfgu6s80TX/22WfpdPru3bsHcyEYzKED/L+QFAoq/Ol0uuOYPR/zh8XwMAzj7t27Kysr0WgUMvctFksoFOp3u4aOO3fuRKNRv98PW0+oYA1BEFNTU3AMXtl8GOVy+fTp01DKA1wX4DLsHkcwQ4VhGMlkEsTEKYqSZTkej7MsC4U+UL4HbIBomlYulzOZTD6fBz8xfh8xe0j3xkWtVoPQUJqmKYoCgR2U4brDdxHlchllMSHxXKvVKsvyW+0WDGYY6JmDV6vVMpmM1WpVFIXneUVRvF7v+fPnV1ZWusOrcKjVe/Pq1au5ubl8Po+87BaL5eTJk/1u1xBRr9cjkUg4HJ6dnVVVFaLdJEkiCCISiWCv/O5ZX19PJpOxWMxms1EUZbPZBEEQBCESifS7aZj+YH6bWq1WPp8XBIFl2WAwGAgEEomEw+FgWRbZ/7DPrqqqx+M5d+6crus//vjjdqfFryrmfTH3HPi3XC4vLCxMTEyEw2HwuUIyEs/zDoejZ1RCR9jVnTt34ItQJRCqB0KiSDAYXFpaOqiLw2AOAejtW1tb43k+lUppmuZ0Ou12eyKRmJqaunTp0p4E3O7AUBgecKPv3r1brVZBMgxgGAbPnfsK3N43b97cunWLIAiYUViWJUmSpmme50dGRkiSNNep6f465h3Z3Ny8fPlyJBJBmtx2u10UxVwuh+/ksGH8Q9v0Hq2trSWTyZMnT2az2VgspmlaMBiEnRCwOlCkSjKZLBQKqqpWq9X19fUd/F64a2F2Q6lUCgaDDodDVdVjx44dP348Go1yHAd1A58+fdphq3R3P1mWYYMXBe5CsofFYsFpnBhMN/ASXbp0SdM0u90O3ii73X7+/PnJyclbt26ZD9sPBtzwMN+4x48fK4oCThHAbrf3sW3Dw7Nnz3w+H4QPyrKsaRqSUIAkBFBY71gk4QXN+5JKpcLhsNPpRGrRoKt7//79fjcNc6Ds/O40Go2lpaV79+6B0q7T6YS8XkEQkPaooigMw7jdbpIkRVH0+/3bnRm/p5gPAI320Wg0FApBCrjD4XC5XPF43OFw+Hy+K1eumA/uibl8B7I6IEuEJMlEIoH7JwbTE0VRQLeaJEmw1WmanpiYKJVK+/3TA254IAzDWFlZ0XXdrCNpsVjevHmDB6Z9At3YQqHgdrvBLwUb6KIosizLsqyiKFhzaZeg+5xOpzOZzPHjxyVJguRy2PR4+vRpGy8Qh4ad46DMf19ZWXG73aOjo6Bngio9w/CIPrvd7rGxsWq1ut2ZcdfCvDvm3lKpVFKp1MOHD8PhsMvlkiQJhPhAzMos6Nn9XeDnn39G2x2wawfmB8MwPM/v+8VgMIeTzc3NUqmkqiqsEyiK4nne5/OFw+Fvv/22vf0e454wyIZHh+/c4/GMjo7yPI+GJ7TjgSfO/cMwjM8//zyZTCYSiYmJCagSqOv66Oioqqper7fnVw6+nYcUNDpsbW3F43Fd18+ePQsKFUiPElfJHDbeahvAf66urubz+XQ6res6QRAgtmv2y8C/NE3XajW/31+pVFqt1sFdBmbg6OiHqVRqYWHhjz/+WFxcTKfTtn/wer3Ly8vtt22A12q1aDQKUQzwRfDggmgbFmfHYLpBr9LS0tL4+DjER3AcNzU1xbIsx3HdiVh7ziAbHgDcuNOnT0ejUTRIocnVfAxmn6hWqxMTE/F4XJIkiCb0eDyKokxOTpbLZRwyvldompbP51OplNl1LUlSs9nsd9MwHymlUikWi01OTjIMA0nnqKwHUv8DEQhwjLlcLuhO+D3F7JJff/21UChcv3692WxmMplUKmWxWCDIam5uDuJvzXR3uWAwqGmaLMtogw7teNjt9u+///6gLgWD+djpMCQqlYrf7w+Hw6j6DeT7dZeRxTse743ZttM0rVqtWv6TSqXS3xYODNv1zpWVlVAoxHEcy7KQWc5xnKIogUBA0zS8fNlDMpnM1NSUruskSZoVFHbY8eh5//FDGSrS6fTExATE+4ZCoZmZGdgWhtI6YHiABWK322VZrlQqXq93fX294zz7JLyIGUhWV1cXFxe/+uqrRCKRTCbL5fLx48fB+p2cnPR4PN1f6e5UYHXALofL5YK4EbvdDkG8B3IdGMwhoPvdicfjJ06cmJiYgI1uWZZ9Pp/P50NVDfaVATc82qY7HgwGP/nkEwhBQWQymf42b7DJ5XKRSMTr9YJAO6SSg+EhiuLGxka/Gzg4GIaxvr7ucrlIkkRFqaEI1x9//NHz+O7PeL04nPzyyy/z8/OVSuW777773//9X0VRQPAamR9IbxdV3RkbGzOfAfcczDsCXUXTtIWFhUajceTIEa/XC3tuBEG43e5wOFwul7u/0v7PblapVKBYB2zNwfyCatH2jNTCvRSDARKJRCqVgtUCQRDxeDyRSGia9sMPPxzArw++4dH+Z7hJJpMMw6AgZuCHH37Ag9Ge0H0br169yjAMSLvabDae50VRhBwmRVF++uknvN7dPWhC/euvv/L5vM/nc7lcLMuifi5JUkcZuJ13OfCzGCp6LsgCgUA2mz1+/LjX64Vy5ub0D6iQAF6bnnp0GMzOGIYxPz//yy+/zM7OQnnyQCAA+2yKokDlje4RqaOD5fN5sDpQkBWoQjscjomJiZ4/2t7G4YLBDDYdXf3PP/9Mp9Mejwc8lVC+qVQq9Sybsx8MrOHRMx6UJEmO42D6hNn02bNnfWneQGIWQCgUCoIgiKK4sLBA0zR4pPx+vyAIZ86cWVhY6G9TB4+ff/45nU7PzMyAnhWq4Ov1es0ltDrei1qtduAtxXy8QPe4evVqPp+Px+OqqkLKhzk1DumWMgzjcDiazeZvv/3WcQYMZgdardbS0tLy8nIul+N5HiYISCLKZrPm7tQN6mDJZHJiYgKZwRaLhed5hmF0Xd9uWMOdEzPkwCvQarWOHDmCsvgsFsuRI0du3LiRzWbBTbnfDKzh0f7PUWZsbIyiKJqm0+l0IBCAe00QRKPR6GMLB4+VlZVisZjJZC5fvgwJqalUiqIomB5EUTxx4gSUp8Gep70C3b3Z2VmXy2W320mShOh8UObuTtMEarWa1WodHx/f+bSYIcH8xLe2tnRddzqdkJoF/QpUg1BAC8MwHMddunTJ5/OZB9J9UmDEDAzNZvPly5fZbDYUCoHhAe6SYDDYaDS2mxo6OlUkEjl79izEAaIcJBD0657W8Y4uBoM6fzabNSeCQuEmURRv3rx5MC0ZZMMDsbW1NTMzEwqFRFEE4Uhwrlit1lwu18aD0S7ouHXffPPN999/X6vVTp06lcvlWJYVRTEQCECORzweN0sc4tu+e9A93NraAgl8tDokCAJm5fn5+Y6DgcXFRais4nK5qtXq2toaCOfj5zLkGIbRarWWl5c1TZMkiabpUCgUDAZtNpskSbA7D0IosNrjeZ4kSb/ff/fuXdx5MG/l9evX169fz2azfr+fpmmwbycnJ7sVddrbD0fpdBqVP4P1k91uhx2PxcVF5LjFHRKDQcDroOs6mOsOhwPeHV3XJUkKhUIH04yhMDw2NjZardbvv//+2WefURTVYeq18di0d9y8efP48eNXrlzJ5XKpVCoYDAYCgXA4zHEcx3HdFTHxnd89cA+fP38uiqLb7QYNewjNdzgcJEnOzs5u5zj8448/JEmC+TsajSqKst0GCGYIWV1djcfjHMfRNM2yLEmSLMvKsiwIQkfYFfQ0giDOnDmztLSE32vMDvzyyy9ffvllMBiMRqMcx0FaeTqdbjQaEGf11kI0W1tbPp8PHIgWU+lA82er1QrVafEWHAZjJhwOg+cIDA+GYURR5Hl+ZWWlfSCrsqEwPBArKytmX53FYnG73XhI2kPy+XwulwuHw7C/RJJkNpvVdR3qBpqTDTB7S7lcpmlaFEWO42AfA3b2aJr+6quvOg5Gff7Ro0coypMkSUjT9Pv9B916zEeJYRhra2uBQAA6BmxuyLKM0nnRWGqz2aAE4cmTJycnJ+/fv9/GbgVMLwzD+OOPP65evToyMgLFZKE7lUql27dvv4tQwe+//45MDjMd5S9Rxrksy6qq1ut11ICDuE4M5qPEMAyUsweZ5aD9k8vltovK3nMG1vDo6TJJJpMdiZKQzdaXFh5Gdh6yW63WxsbG4uJiMpn0eDyqqkLwTyaTyWaz6XQaj/j7R6PRsFqtFEUxDENRFOQEg+TLdprRGxsbjx49QpM02gkkCKJQKBxw+zEfG+a3FfY9rFar3+9XFAVJF4BEB5gfBEEIgvDgwQNQrkun09udDTPk1Ov1UChEkqQgCJqmkSQJIVKRSORdvj43N9etdtCTDuPE4XD01BY3gzsqZuCB9wLisa1Wq8fj8fv9hULhwBbDA2t44Z6B9wAAIABJREFUdACjyZMnTzRNg1IeZmX6frfuEGPexf7qq6++++67bDYL4YO6rk9NTdE0DeUC8YC+r4AJYbfbNU0jCALU22BkAcOj4/4vLy9D6nn39EzT9OvXr/t0HZiPEcMwVlZWxsbGJElKJBIozUOSJI/Hg3KKrFar0+n0+XxQyq17GsODwDADT79QKNRqtUajAcF7HMfZbLZcLqdp2na5rR3dBoyWd7c6zIFYFoslEAi8tZEYzICBOvbNmzdZlgVXI+w3Tk1NXbp0qVwub25uHkz/H4o1N7qVi4uLtVoNMp5BDtJisYii2N/mHQp27o6GYZRKJShJA+sPu90Ofvf5+flAIIC2uTH7RDqd5nkeqvaCcxp2UWVZnp6e7ghgqNfrPV2Gdrs9Go02m82+Xgqm//SMePnpp5/K5XImkxkfHxcEASJYoOgbLASh1xEEEYvFXC6XpmnBYNB8Qsyw0f3cE4kEROTa7XYQwHC73bOzs+Fw+Pnz5+/STyByYYfNje0+IwiC+Pvvv/fnijGYj5qxsTFwu09PTyuKYrFYgsFgrVbb3Nw8sDYMheFh5ueff2ZZlud5tOkhSdKjR4/63a5DjGEYS0tLt2/fhsqAELCbyWQg2SASiRxkhx420AKxVCpBNjkIU0LCBkVRIyMjxWLR/JVbt26lUqkOLyDyC96/f39nHX3MMNCx/jP/Z61W8/l8UBvU4XBAOKUgCChcGMKuWJZNJpP5fB4ppWDbY9jo+cQ///zzaDR6+/ZtKHUK8eUulwsSW7u/3n2ShYWF7SyK7jSP7Y7kOA5E/Hb+LQxmADB3bEmSoNQmxDvY7XZd1w+45w+y4bHdUJJIJKLRqMViQXEmHeHImPdlbm4OXJ6odJ0oilDH4/PPP+936wYc6OG//vorSJ1KkgRxLyiSKpVKoYMLhcLt27dBTa97SvZ4PB1lgzGYbn7++eeZmRlJknie1zTt/PnzLpdrcnIyEAi4XC7ofqAfCPtv+XwevA9YX2jI+fHHH8PhsK7rhUJBURSe520228TERLFY7NDy3rnQOJLE6PaeKIrCMAwIbEA+ks1mE0Wxp1lilnfHYAaeer1OURS8PuAtYlmWYRj4vwc2OA+y4QF038oTJ07out7h/OhL2w4v5ru6tLT04MED2EGyWq2QY6AoCsdxgUBgY2OjjReyBwLP8yzLQrIvSFpBvu/09HT7n0eQTqc1TUP2YYdTEEJl+n0dmI+Lnos/wzB++umn06dPK4ricDhSqdTExMT09LTb7dY0zeVywe4HSZLggGBZFg8Cw0OH2YA+FIvFWq0Wi8VUVZVlGUahYDCoKMrp06ffvYf0VLWyWCyhUOjmzZsej+fTTz/94YcfYDe+0WhAJzQPdJZ/ZNk62tzGsxVmcIEKm7A7bbVawTgfHR199erVQXb7ATc8eg4lU1NTY2NjmqahcqfhcLhPDTzcwF3NZDIgbiNJks1mU1U1HA6TJKmqKuQo43H8ADAMIxQKcRzH8zwMKBB5b1a1ajQamqbBdNvTWQj/q9Vq9fdaMB8bPV9hwzA+++wzv99PUZTH48nlcrlcTpKkSqVy584dSZKgX0Htc5vNduLEiR3OhhlU0ONuNpuRSGRyctLpdIIlAPZDIBAolUqVSsV8/HbBfvBBVdUOKwJCGHZoBuhtdHPq1Kkd6qNjMAPD+vq61+tFOx6RSERRFIqijh8/3h3ouK8MuOHR7jV+ffPNN+aVFk3Tbre7X807vBiG8ebNm2q1Go/HU6lUPB53uVw+nw+KHDMM02g0+t3GYQGVI6VpWpZlgiBEUTx69Kgoil6vFxkS1Wo1mUyalay6vYZo1xWDAXZeiqVSKVVVM5mMpmmqqp47dy4UCpXL5VAoBDoT0MfANzE1NYXN2qGio/Pk8/lTp075/X5RFCE1KBwOh8PhtbW1dz9Ju90uFApIzwCNXQ6HY7szrK6uRqNREBnvGPFGRkZ2c4EYzGEhn88nEglIKAfvpCzLDocjFAod8Gpt8A2PbkqlEip6RdM0TdOqqraxq+P9ef78eTQaLZfLwWAQqmAGAgGGYUZHR2OxWBuHdB8sxWIRtu9cLpfdbodapOBNXFpaunnzZiAQCAaDYHjsQD6f7/elYHbFfntwO865ubmZz+dHR0clSTp58mQqlfL5fDRNEwTBMAxa6oXDYZ7nP/3003a7vbi4uHM5UeT2xgPIwNBoNARBkCSJJEmSJCmKomk6FAr9+eefPY/f4dFvbm6qqgpdC7KJGIbx+XzbffHChQug6t493GG3I2ZIyGQyBEGEQiGLxcJxHMuyoVBIUZRisVgqlXCo1T6yvLwsSZLT6QTnB0VRYPyZj8FT3VuBWxQMBiHIG7I7rFZrNBqNRqOQsYdDZg8MuMP1et3hcOTzeY/Hw/M8JHuAeHQul5udne25xdEdcPXkyRPzaTGHkZ6RKuZ1/J48XPNJfvvtt7m5Oa/XCyq6fr/fbrerqgoVLS0WCwRcORyOxcXFUCi0g396D1uI6Qs9n10+n+d5HroB7FewLOvz+YrF4vr6+g5Caj3xeDwWi8Vut3McB/lsFEVdvXq1++tQVaa7ZhHMWQfv7sVg+sLm5qbP5zt69ChUV1NV1eVyQZQsHICTy/eLxcXFR48efffdd+B+Qzlqq6urcACW1duOjiVLPB7Xdd3n89lsNsjbGxkZSSaT2Wx2Y2MD38aDp1gsjo+P67ouiiJS1GVZdmpq6pNPPmk0Gh0J5T0tEJZli8UifnCDwQ6Wxi4fcfdp4cP8/LwsyydPnpycnJQkKRAIiKIIUcXdega5XO6rr77qbg/ufgNAh61rGEYmk1FVFdL/oA/YbDan02mW3Xv3k4+MjIAYhtPpRCVBOk5lGEYsFkPZaz0HvQ43GQYzqBSLxZGREYvFIori5cuXs9nsp59+GgqFLl261D7YV2DoDA8gm82iVDNYb3VUuMPDUE/QbXn8+DFJkhMTE7DfTVEU/BsMBre2ttr/uRzB8RIHQ6PRgFLxUMARJmO73X78+PF2u720tLRdeqW5mKDdbv/666/7fSmYvaH7vdu9R2Dn7xqG8dtvv9E0zTAMFDWnaRrKNUCfNK/5aJqenp5eWlrqmdqIB43DjvkJLi8v67oOcmdQ4RR2IWZmZnb+4nZcvXoVbAlVVaPRKE3TIHJg/nq5XN65xrkkSe/1oxjMIWVzc7NQKMBcD6EQ+Xx+eXk5kUhcvHgRHXYwb8EwGh6rq6uQ9Yi0fVRVxUXu3p1nz57FYjFY10LALiod2Gw2dxBix+wrZ8+ehQgrgiBgtedyuWia1jSt3W7ncjld13sqWXW4A9PpNH5qh5QDfum2U7taWlr68ccfK5XKkSNHcrmcLMuiKKJuhtaCEOjCcdz4+DiuNDpIdHeMR48eKYri8XjsdnsoFKJpWhAETdPMqT7m3vsufRh5UiRJ4jjOZrMJggBfPH/+vKqqKJ8NLF4U4ABbJRzHgaGCwQw86+vrqVQKArBhBC4UCleuXDlx4gQqZIdDrfYLuLOPHz9GYxZFUQRBrK6u4pyEd2Fzc3NtbQ0kMkmShOwOqFIcDAa7j8c3c18xd9pgMIj8GQBBEA6HA03t0Wi0Z/kONDeDEdJR6RxzeNnzt287S6PnknFlZSWdTicSCU3TeJ5HxaqcTmdHx5Nl+dixY7FYrNls7m2DMf0FdQaoIARuEVEUSZIkCCIajZZKpe2+9dbem8/nYQ6iKCqZTMKgVyqVWq0WklMz/4tcjXa73el01mq17nZiMAPJ69evPR4PvAjwwW63OxyO8fHxQqFwwI0ZOsOj3W4bhhGNRqGEClRSo2l6bwOgB5Xnz5+3Wq2lpSVBEFRVhVwCh8MhimI8Hm/j+9Yn4LZHIhFBECDsDbzLdrvd4/EsLi7CYWtra8ePH0cLPpvNBrmeyCMItgpWtTrUmBdtGxsbv/766/r6es9jdnP+dzzJ2trayMhILBYDCSOCII4cOQIb/WYDWBTFUqmkqqogCI8fP37fX8F8bHQYosvLyy6XSxRFm80myzIMUyRJhsPhH3/8cTc/BNqgkiSpqorsCqhT3rGva/6L3W5PJBLmprbfZ6cFgzl0rK6uBgIBFKhC0zTk6Pp8PpQZhXc89pdisWixWMy6ou3t0yUxiDt37iQSiVQqRRCE1+tNp9PBYBCkDMvlMhyDb1pfgNxN8COCLYGiqJFwQrvdbrVahUIhnU6Hw2FIy4E9K4ZhwF/o8Xgg4gU/xwFjDwOZtksd6fmfa2tr1Wp1YmIC5O9EUQQDwxzgxzAMSA8pilKpVBRFwUJDg0Sz2cxmswzD2O328fHxI0eOsCwry/LufRzxeNxqtRIE4fF4utPHuyNL4QOyOjCYIWF1dZUkSVmWYeC12WzhcDgajcKO9AE3ZugMD5gRHz58SNN0MpmEJRpN0y9fvuw4ZjjZwetTq9Xu3r1LkmQul0smk/l8XpZlj8dDEMSVK1cOvKWYTrLZLFgdYFHDNE9R1NzcXLvrmVarVYspxwMloyMtfAxmT4COt7W1lU6nVVXVNC0SiaBoQHMMDGy4URTFMMzU1BRO+RgYAoFANpuNx+M0TcNQI0nS7q0OwzAePHhgsVhUVT1//ny37WHe60AfzAnlGMwwsLm52Wg0aJqG7A5QnSEIQtO0QCBw8Ou3oTM82u323NwcSjuDTA+CINp4p/Ufet6HtbW1ycnJkZGRcDiczWb9fn86nXa73aBk9dtvv/WpsZj/j2EY9Xod+jMEEIJqkCRJk5OT3b363r17UMOrw0cYiUTa+C3A7BEdg0mpVNJ1PRgMHjt2DNaIsCln3nyGfpvJZG7durXDOdu4lx4Snj59GgqFvF4vhNvBQx8fHwe1vV3y4sULlmXHxsZisRgUTu2514H+SBDEv/71r93/LgZzuPB4PKBvDkU8z549KwhCIBCoVCrtA1czH0bD43/+539EUWQYhmEY0B61Wq2QZ4Znsnavm7C1tZVIJAiCCIfDsiyzLCsIAsjzkyS5sLCA79vHQLPZBKUEFHAFLuRQKISOQU9qenoa5TiZ52aHw4EtcMweYrYTNjY2ksnk559/HggEWJYFsV1RFFOplK7roLhis9kYhonFYrdv356bm6tWqzufFvMxYxhGs9kMBoMQVo7sgePHjyuKAtrrH3xm+FCr1S5cuBCJRAqFgq7rlq6EcohrOH369LVr1zq+i8EMA9VqFVLsGIYRBEGWZU3TZFkOhUKZTAaOwXU89pdGo1Gr1crlsllUfmNjo9/t+kgxDOPGjRuBQMBisbAsqygKiOfOzs7m83lVVf/888823i/qE+bbXi6XCYIYGRmBauUsy3IcB9Ix3V+BGDlzQALM03Awfo6Y/aPRaOTz+bGxMVRhMJlMfvLJJ/l8nmVZ6IrRaDQcDvv9fofDsV3MFe6lh4JsNnvp0iWXywWCLmAJeDyey5cvf/A5O3a9NjY2Go1GsVhMJpN+vx8sHFC7On36tMPhYBhmby4GgzmEbG1tSZIEakA2m83lckmSdOrUqbW1tc3NzYMfSIfR8JicnCyVSpAVDYstgiByuRyexnqysrJy4sQJ6LI0TcNygWGYixcvRqNRVHjxgLfqMIC5OOOtW7cgcBN8yRCyYrfbfT5fd3QK8j7Cv2jrb2xsrD9XghlceiajF4tFXddPnz49NjYGetyrq6uXLl1CgldWq/X06dOCIORyuVarhYUHDyO1Wm1+ft7r9cJ2liAIXq9X1/U9L6BhGMZff/21uLiYyWQ8Hg/UEwwGgxMTE6AWil1jmGFG0zQ040OyB8uya2troLZ/wO/FMBoeT58+vXLlis/nk2UZQuGtVqs5XmjIx6aOy19dXXW5XBA+KwgCbNh5PJ6xsTEkwT7kd+wjAXal7HY7hFoh56Lf7zcfBg8LSU/CIg/VdJNleTfxDxiMme2sBcMwtra2rly5Mj8/PzU15XQ6JyYmlpaWkskkx3F2ux2ylUASmuO4K1eutFqtflwB5kOAB/3q1atYLDY7O1uv15PJJE3TgUAgEon4/X6/3292muzJz8G/f//99927d5eWlp48edJxQMdnPG1hhodQKAT7ySizfHJysueginM89oXV1dV8Pq/rejgcBhVwmqbNtYTaeEj6hxcvXiwtLY2MjIBWkizLbrebJElFUXazUY7ZW6C7Xrt2DZSsOI5DwQY2m01RlO6voNReCDiE8chisSBZZAxmXwEXtd/vj0ajEFgFlc7tdjvLsuAgR1sfmUzmiy++OH/+/HYpH5iPkHv37qmq6vF4bt++PT4+LghCJBKp1+uhUGj3pQM+7It4ZscMIYZhTE1NmSOrQcGyo3wnruOxX7RaLZqmOY6jKGp2dlaSJBCPj8VieEjqYH19vdVqjYyMwO2CrGWr1erxeFwuV4etjO9e37l3757VaiVJkuM4juN4ngeHsSiKHVHyhmHAGEQQhKIosNQ7efKkxWJBZc7xA8XsITt0p2q1mkwmeZ4H3RXIQob+CR0YOmoymbxx4wZN06lU6osvvjjIxmM+gGazWSwWQ6GQy+XSdT0UCum6funSpXg8nsvl9uMX8ZCFwfRkfX19dHQUQhvAp8OyrCRJyWSyL2/N0Bke7XY7k8kEg0GIs6IoCgpvW63WZrNpPmx4RrGeV1oqlZLJZCwWQ5nHUOIdtjv2aebAfDCGYYTDYYvFAlptBEFwHAcBctlstvt4u90OqlZQOQG2O0RRxCVZ9orhGUB2T7VaXVhYiMfj0Wj0yJEjHo8HfBzmwADUYyHZDLTa8E3+GOioU95ut5vNZr1er1QqIIQIO7GxWCwWi507dw5XaMFgDpJarXbq1CkoIAEB8+ARSCaT3QfjUKv9olKp3L17VxAEl8vl9XohwF1VVXTAv//97z427yDZrpO1Wq18Pi8IAkz5LMvabDaO4zRNSyQSeL7/CPn0009RzhJFUfDUCIIIBALmmR6end/vRwkh8MFisfA8b9bexewe/KZsR/edabVa6XQ6Ho+XSiW/388wDMyU+Xwe9kBQ9CD8fX5+fnl5ebsz4zvfR8rl8rlz5xRFYRiGJEkYXnw+X7VaXVtb63frMJhBpnvoS6fTVqsVxtJiscjz/MjIiM1mAw8yVrU6OBYWFhiGMVc23XOdjUNNqVRiWZZhGMju0HU9EAikUqkrV64sLi628bz+0YAexOLiosPhAK8wODZATjcQCHQcaRgGZDeBFxlCWWA9l06nOw7GYPYDlFvcnWT8/PnzdDoNbnLwdyAFQnOYsizL6XR6fX29vX0WO2a/6c7VbjabExMTPp/v6NGjMMLAoAQlw7d76BgMZm+BV2xhYQFyCgqFQiQSSaVSqqoKgkBR1NraWrebBu947CONRmN6etos7COKovmA4RkWe14pSLKGw2Gr1SpJ0pkzZy5evHjq1Km///774FuI2Q7zs2s2m+VyGaqV8zwfDodHRkacTmfPyuXBYNBcNxBEeJ1O58OHDw/2Cgac4RlGPozt7k82m3U4HIIgjIyMQLYS2uuAbT3otBRFpVKpjY2Nt+5y4Aexr5hvb71ej8fjPp8vlUr5fD5IPKNpWlEULOKCwRwM8HKtra1dv37d4/HwPP/06dPjx4+zLCvLsiAIqEQS3vE4ODY3N0dHR81eNE3TzAcMyZjYbemurq5CKTqoY+33+3meHx8fj8fjiUSi+1uY/mJ+FuPj4zRNg3zC6OjoxMQERVEURf3f//1fh2MyEolY/hO73e71ev/1r3/15zIGlN9//x1H/vRk5xuysrJy//59hmFkWYYygmBvwB6IoigQAqrrus/nm5+f78jQe/cfwuySnjse1Wo1n8+PjIw8ffp0ZGREkqRUKhWLxbq/hcFg9omNjY3Tp08fP348lUqJokhRVDweF0UxFot5PJ7uUIgDY3gNj7m5uWQyiXbwbTabLMvFYhH+7/DkeHSwsbExOzt74cIFULJSFGV6epplWZfL5Xa723jC+FiB5wKhVtCfeZ4H61GSpMePH3ccjMoJddgebfyI9whcLuCtvNUkKxaLmUzmxIkTPp8PFKKhmhAED4BRDQYJQRDBYPCtpRswB8D9+/cTiUQsFhMEQdd1mqZZli0UCh2SJPihYDD7SrVadTqdbrc7EomMj4+rqhqPxz0eTyaTEQShp87+wbyVw2t4OByOo0ePQs01CLgaGRmZnp4e5tjTX3/9NZVKpdNpj8ejaZooioFAYGRkBISSkFWG+agwd1dd10mShAKCsCaDasHdwlatVsscLg/CQTabrfucmA8GJx7sCQsLC+VyWZIkm80GmcqZTObYsWOo0AdY2hAuePfu3VKptLKy0u9WDwvdBvbq6ury8vKRI0dg/AGViwsXLvSvjRjMMOLz+ViWBZlyWBW4XC6apj0ej9frrVQq7V4OGpzjsS/AbYXaRqqqguAGgPaehhMQ1L9+/TpN02BsuN1umDwkSfrtt9/QkXgJ9XGSSCQgBIVhGEEQoG97PJ6JiYmOR1av11F2h8Ph0HUdtmLv3bvXr8ZjhoodJrmef9zc3CRJ0uVyMQxDURRJkqIomkdvZEhzHBcOh3Gl8wPD/LxKpdLi4mK1WtV1HdwZJEl6PJ6FhYU2njgwmAMkl8tBSBVyL4JOaSAQCAaDfWzY0BkeaOCLRCInT57keR7GR5i0+vsw+sv6+rrf708kEpqmQfSCJEkg/BUOh6vVKg4d+WhBTySXyzkcDrvdTlGUruuogKA5pxMObjQaaK0my7LD4SBJUhCEzz//HGSCtvsJDKZfZDIZVVUnJiYURWFZFtSizfseML+GQiGbzabrerlc3uFs79Klcbd/Kx23KJlMLiwsQO4NGB6yLJ89exbXfMRgDpjl5eVarVapVCwWC0mSPM/zPC/LcigU6q9u/tAZHgjYvqdpenJyEkRj0Y7HkEw25st88OBBpVJhGAa25CDjBXyKuq43Gg1sdXzkwHMB1TzYpAJfI0VRkiTBpmrb5GZGoVYARVGQxqPr+ueffw6Hra+vq6rKcVwqlerjpWEwwOrqaiKRGBsbczgcHo+Hpmme51VVVRQFytGgTTyCIHRdhyof3UPWew1iwxx8+76sra2l02mXy0UQBM/zSLLC6/Xev3+/363DYIYC83i1vr5eqVRgGQA5V/l8/vLly4VCoY8tHF7Do91uv3r1yufzXblyBekz2mw2KG808DNN9wWurq4qiuJwOFDFQIZhdF3vWS4QC/V8VKAHAcKjoF8JNZ4hx+Pq1asdpqPZ8LDb7Z999tmnn36qKIrVamVZNpfL2e32iYkJqDAoCMLk5OT09HQ0GsVF6zH9wjCMhYWFWq0miiLP8y6X68SJEydPnmQYhmEYNIyDIX3kyJGlpaVSqTQ/P9/ulW+Dh6+9At3Jb7/9luM4eBButxvidbPZ7KeffvrmzZv+NhKDGTYeP37caDQikQjHcclkMh6P5/P55eXl58+fr66u9rFhw2h4oFCTarUKYUUoPdFisWQymX438OCAW1Gv12/dugW7bzRNQ6AOLFjz+fx2ex142v4ISafTBEGA4cFxnCiKNptNVdVuuW7DMOBI6Pzw9OE/YYtDEAR4IyA21G638zwPu2FTU1MwbOE+gDkwzJ2t1WqBzpXP5wNpXaiHBU4T6LQMw3g8HoIgJEm6dOlS+4O665s3b7CT5d358ccfIcIKxPQcDockSeVyuaN8BwaD2Q86BslUKpVKpTiOczqdgUDA7XbfunWrWq0uLS31d0AbOsMD3e7NzU1ZlmGlhZZfkM/Q3xYeMIZhPHjwoF6vq6oqSRLUA4YJ4+jRo8gsxtqUh4KpqSmapiHCyul0gpCFIAjmgWZtbS0UCmWzWYiFQB5iUHiDoPlupV2LxTI5OakoCrw1LMu+fPmyjTsD5gAxd7aXL19qmkYQBLjVRVEEMxsl7FmtVlDghX5eLpfL5XI6nd5NzSzc27cDdpC2trYuXrzI8zxsmHu93suXLy8uLvbXvYrBDCHPnj1LJpPgCBAEgeM4QRA0Tfvkk0++//77/rZt6AwPwDCMtbW1mZmZSCQSCARYlkWhVrqu97t1B4dhGDdu3Lhw4UIoFGJZFgJ1RFFUFOX06dP1er37+L60E7Mz6LlAnWBI1GFZFiQswOmrKEomkxkdHbXb7bAgQ+szyDyjadpshHejqirqJHD81NRUfy8cMySYRx5UZGl9fT0YDLpcLkj5YBiGZVmHw2FO9kBbdoqiKIpCURRN01evXm2/22iGHS7vSzgcpmkaygSxLDszM7O4uNjGdw+DOVgePHig6zp4EpE7kud5t9v97bff9rdtQ2p4AIZhqKpK0zTyk0GlvH6364BYW1trtVqQCyhJEsuykJoMs/Wnn37a81t4/vjYMD+Rhw8fjoyM0DQtCAJkkgmCQNO0oijhcHhsbAyU9cwqQO/+2Wq1+nw+iOCCMC2Kono2A4PZD3qaAfV6PZlMVqtVRVGCwWAgEID+SZKk3+83734kk0mLxULTNE3T58+f7z7n+7YBY+bVq1fZbHZychIqBlIU5fP58vl8v9uFwQwjS0tLx44dU1UVBkBwR2qalslkYNe3jwyv4VGv15eWlkRRjMfj5mXW5ORkv5t2QDx69KhYLHo8HtCgVBQlHo/Lsuz1elFWQAc4zeNjo/sRxGIxqBPE8zxERkUikYmJiXA47HA4BEHYbkNjO8AQtVgsNputXC7H4/GlpSVN0xiGqdVq5gh43B8w/aJcLofD4enp6dHRUahg43A4XC6XudAHSv+w2+1+v79YLDabzX43fHDY2toqlUq3b98WBCEWi6VSKUmSIpFIv9uFwQwXMBF/9dVXXq8XJC45jgO9GZ7np6en+93AYTU8DMN4/fp1OByORCL5fN4sBo+ERweYFy9e3Llz5+nTp7VazfJPWL/P5wsEApDgATKUmMOIoigcx0GWLWgiRyKRqampYrGYzWYhnmpnULEheClAZNlqtWqaZo6+++677/p4mRhMBwufJsRWAAAgAElEQVQLCw6HA/LTKIpiGAYqDKKMc7MhDX8URdHhcICSIfBW3wq2rntiGEa5XF5YWIhEIrIsq6oajUZlWd7Y2Oh30zCYYcTj8UASAWx3sCwriuKZM2c+hk3IoTM8zNNGuVy+ffv277//bnYDD6r+hlmcqtlsVqvVW7duZTIZyCSmKCoWi/l8PkmSuos24Ln2UACPye/3wygDBYNh4QWxKOvr6+l0uiOLA5nc6O8QeQg5IYqiXLhwof2P9Jm5ej0G87GxtbVVKBSOHj0aCoVUVYX+D3lr3XlNoHzl8/lWVlY6zrOd+YF39rqBu5HNZo8dOwZZNzabLRAIZDKZsbGx//7v/+53AzGYYQENTQ8ePIjH41AAGrQoaZr2+/2lUqnvcVbtITQ8zDSbzZ9//jmbzZIkiaYih8MB/3eQZpeOifPmzZuTk5Mej+fixYuiKFqtVpfLdf78eafT+fXXX/e1pZj3pqOjCoLgcrlgaxWV9fD5fHfv3oUDFhYWOI4zmx82my2fz8disUAgMDMz8+TJk7W1tY54+p2XXIP0smAOI+YeuLS0VC6XW63W999/f+bMGYfDIcvymTNnoMSE2fAgSVLX9UAg0Gw239GowF29J7lcLhgM+nw+r9dLEITf7/f5fB6P5969e/1uGgYzdKTTaVD5g/kdnMvpdBrSyvs+iA2p4YHu+y+//DI/P4/CSywWy/Pnzwe1Svevv/66vr6eTCZVVb1+/fqZM2ecTic4Al0ul8fjURTFfPyAXf7AA1ptbrfb5XKJoqiqKlRVs1gsTqfz4cOH5oNfvXoF1Vo4jtu5ds0O3QD3EMzHQ4epvLa2dv369VKpNDMzI8uyLMsQeQVhV6DMBsY5TdOFQmF1dfVj8AUeRpaWlr755huHw0HTNIwqqVQqk8mgoA48UGAwB0atVrt169bk5CQa6KxW67Fjxy5dunTs2DE4pr8VVIfU8AAg0yOTySQSCXD8W61W8//tY9v2nNXV1Wg0Ojc3l0qloPYWKKsixcmJiYlCodDvZmLeG3NHffbsGRRyBg8HFAGEUgZff/11d5f+6aef3l1ifzuXMMibDtj7gjlE7ND3lpaWwBl/4cIFSZIgmc3n81EUJUkSvCkQAz09PZ3JZL755puff/653bVLjNmOv/76q16vP3nyBHZZLRYLSZKQX/7dd9/hu4fBHDD5fP7EiRMwuHEcB6IykUjk2LFjbre7/RGMaUNteLTb7Ww2+9VXX6VSKV3XrVZrLBbrd4v2kUePHj148ODChQsjIyOiKIIdzHEcZB3Nzc39/fffPReXfe+mmHfEMAxILrfb7SzLgugtFFmrVqvomJ0XVe8e0Y4XZ5iPh7cmgjebTdjlIAginU4rigILZYZhGIYB/wtFUUePHn2vXxlmNjY2UqnU4uJiMBg8d+6cy+WCrH2apqvVKq6CgsEcPPF43O/3Q15HKBSSZVlRlFAoNDs72xH40C+G1/C4fv365uZmLBYLBoMo1Coejw+YCoe5Ujt0x7t37yqKQtO03W6XJCkej4dCoTt37rx69arjK3iqOFzA84KHa7PZWJaFSCq/3y8IQqPRaO/4cN+a1PFWCwR3GExfeMfEjPX1dU3TUMAV1PoAmV0ksWCz2cLh8JUrV6amprBU9FtptVqlUmlxcRESaWDTA7I7oG4ggO8eBnMwNBqNaDSqKIrNZjt16lQmk9F13e12S5I0Ozvb79b9f4bX8Gi32zzP+3w+m82mKApSlc3lcv1u1x4Dg/7S0lI6nWYY5siRIwRByLLscrk0Tcvn8/F4fLtv4Un3cGEYRiKRQMUKwOfB87woiuVyufvg9u4eLu4YmL7zXp0wnU7rug5uFxjzzWVqwP0ky/Jn/4+98wlOGv0fPxBIICEJNAGKJmCjFOKIpfgtFcUpTulMsTgjzogzi1Ocr3iQz0Ec8SJ7WbyIM4sn8XtZ9rR8ZsSb9SZ7FA/bPW73ut2jeNp6/MDv8P5tPlmg2NZaavu8Dg7SJDz58zx5/39fvuzxeBwOx7///e/P/MWDTSaTgdhdWZZtNhuO4xiGhcNhn8+nlN5GlwuB2DN+++03q9VqMplMJlOtVguHw2632+FwCIKwf3pFHDrFQy1s1Wq1crnMMMyxY8dARMMwrFarjXqMu8/GxsbLly91Oh1k/hmNRofDEY1GdTqd3W5/8uTJqAeI+CzUT3U6nVZEKIIgbDabKIoul+vmzZujHiYCMWIKhcLy8nI0GuV5HsdxjuOgR01PH5tQKCQIAo7jer2+Xq8j0Xkz/H4/SZKTk5Pnz5+32Wwsy5IkKQiCLMsbGxujHh0CcegIBoM0TZtMJp7n8/l8KBSKxWKhUEgUxf2zlB06xaPbZ4Bpt9v1el2n04Hpy2KxjGpgu0X/s1Wr1axWKzSPwzDMbDbr9Xp4NGOx2D55FhG7AgSy6/V6SZIsFovNZrPZbKdPn56ZmRn10BCI0fP8+fN3794tLy/zPG82m3EcV3p6QOSVRqNhWRaKURqNxnA4LMtyF1nu+8hms5DUodPpbt68CU1RBEE4evTo5cuXuyhXEIH4YmyWn3nu3Dmj0ajX61mWdblcLpdramoqHo/fuHFjyI57zGFUPLp9keuhUAgq/8Bbp3+br46ewbtcLqPRCAn0BoMB6tnLstxsNlEw1cFAuYOZTAa0aJZloVooFPARBOG3334b7SARiH3C69ev/X6/3+8HR/f4+PiRI0eU/h5Kg3ONRsPzvCiKSsU/tFQCrVarVCqZzWaCIAwGQ7lcdjqdY2Nji4uLPM//9NNPsBnKGEQg9oZOp1MsFu12O9iXo9Gow+HQ6/WiKAYCAUjyVG88qnF2D63iodBsNqemplwuF4RawZvma1wiB+YKKxFlIH1iGKbVaqGPr91u/xpPEzEQ9a3M5XKgaUC0FYZhLMtCad1CoTDCQSIQ+4pOp5PL5URRBFM9VGVQx1xhGGYwGIxGI0mSHo9HluVDvmaqT79arWYyGYZhoCoxy7I8z1MUde7cuaWlpe6oJRsE4sDTP8VKpZLVatVoNA6HA4rKYBjmcDiUV/8+MTQfRsVDfdErlcqpU6cikYhi3yIIorsPbsx2GfI8wTvVYDAoXXsxDLty5cpmB0F81bx+/ZphGKWWLkhO8O/q6uqoR4dA7CPW19fv3LkjCAJN02fPnoUqIyaTSa1+WCyWcDgciURSqdS//vWvUQ95X/D+/fs3b94kk0mfz+fxeCC2UxRFv9/vdruVyt0Aeq0gEHtAu91uNpscx+l0upMnTzqdTp1OxzBMNpuFPN79MxMPo+LRVd2Aer1uNpsNBoPT6QQjMUmSox3bjhno9Hj06BFowIr922Qy+f1+yPxDfvCDR6fTOX78OI7jFosFItdtNhtFUQe7Rw0CsXV6zDSrq6vpdLpcLrfbbb1e73A4oAgHoNVqfT6fIAiiKHIc12q1DvNqCeeez+cvXbo0MTHB87zdbg+FQlarNZVK+f3+EydOvH79GjaD1qIIBGLX6RfeWq3WnTt3Ll68qNPpzGaz1+s1Go2yLJfL5VKpNLqRDuCwKx6NRuPEiRNarRYCfMFCPNqx7SJra2tWq1WSJDg1jUZjs9lIknz16lX/xof5bXpggPi6XC5nNBopioLIOni8JUnaP2W8EYhR0aN19Kx7Xq/39u3bBoPBZDJBhDQkT5MkCS3P5+bm1tbWRjDufYCiSPzxxx/gKSJJEkrnkSSZy+USicTly5eHtyVFIBC7hRJRX61Wk8nkvXv3cByHFl46nY5lWXV+Ws+Oez7Y/3LoFI/+yx2Px6HbGsdx6uTyr47+aKtoNOr1epXIAWhibbVaB+6IODBUKhVoHqyEqkOOh9PpHPXQEIjRM8TTe/HixVwuNzs7yzBMOBy22WwQsohhGEmSVquVZdn9Zj7cYyqVSq1WA/+G0+nU6/UMw9y6dater6dSqf54TvR+QSB2nZ4KSW/fvuV5PpPJwHql0WgoiqIoShCEgYrHaPlahexdpNVqWa1WnuchJOnrVTx6iMViLMuq0yVBCT6QjUoQalmqXC5Db2bQNnEcJwhCr9dD/lL/XkgyQCDUVCqVcDgsSRJ4jDmOgxpxSkVyn88Xj8fb7Xb/vge+hmy1WpVl2ePxzM3NBQIBHMc9Hk+hUHj//r1SshOBQHxRehaWWq2WTqeDwaAi7wmCIAhCOBzeh0VlDoiQ/Tlcvnz57NmzUNVKyfH42t8W5XJ5YmJCkiSItIGkeTDajXpoiN1koOZQrVatVitN06BtQvPyM2fO8DzfYybZ6+EiEPsbZVLcunXL5/ONj4/fuHHj1KlTUBjQYDAo3QZ1Oh3HcfF4vH/fgf89MHQ6HZ/P53A4wOMBfRgzmcyHDx9evHgx6tEhEIcLWGfW19ehXSA0I9JqtaIolkqlWq3WU+xhP3CoFQ+4Yc+ePatWqyClQfn2u3fvdr+214ZaAO10Ovl8XnlNgu4xPj5us9n2oe6L2F06nU46nWYYBrp5gJvLaDTG4/FIJKLebOBnBALR7XZXV1eXlpYCgUChUPB4PDiO4zhut9u1KsCvGAgERj3YvaNSqeTz+UAgcOTIEZqmx8fHCYIwGo35fD6fz6+srHTReoJA7BXKXEun0yzLQgVLqNFqMpkuXLjQ7XZfvnw50jEO4JAqHj0VdYvFolL3SaPRhEKhEY5tx6gfQaUBltISS6fT1et19Eo42MD9ffHihVI9Ge4+RVGiKFosli4SCxCIzVFbcMrlcjqdbrVaFEXp9XqKosbHxyFkUQmkhtd8v0HnQM6yer0+PT0tiuKVK1dKpZIsy0aj0Ww2C4IgSVIulxv1ABGIQwcsNcFgcHZ2VnF3aDQaHMfv3Lnzww8/NBqNUY+xl0OqeKip1+s+nw80RZDVdDrdqAe1c/766y94+BTFQ6vVchxnNptHPTTEXtDpdBqNBkTWqVuh6fV6l8uFkjoQiM3onxe1Wq1arTocDoZhcByHIlfg6MBxXDHrGI1Gt9sNVeMO8ORKJBKCILAse/369Wq16vf7vV5vJpM5ffq0LMsDM14QCMSu07PINBoNSZKUxE7oD4Fh2Pz8/M2bN/fhxDyMikfPPXv27Fm5XL5y5QpJksqLZFRj+3wePHig9nLo9Xq32x2Px6enp1FV9QOMUlav2+2+evXKZrMpjwGGYZDpwXFcvV4f7TgRiP2Meh4p/PLLL7lcbnFxUV3kymAwQNkGxb4jiqJSuuNAavi5XA7KPyYSiXv37omi6HQ6k8lkLpeDXJcDedYIxP5EmWilUkmSJIqiwG5+8+bNb775RhTFWCyWz+dHO8iBHEbFo4dSqcTzfDAYNJlM8P74SquOwlM4OTkJKofFYiEIAsfx48ePf//99/1bIg4knU7n559/HhsbU7JglXh0lmWbzWYXJXggEEMZOCk+fPiQSCTsdjvoHgRBEATB87ziWjSZTGaz+ezZs8+fP2+1WkMO9TXSarUikQjHcRaLZXx83GKxMAyzuLgYCoVu377922+/jXqACMQhZWVlpVQqwULEMIzX671+/frjx4/3bU7vYVc8Op3OxsZGvV4PBoPZbBZaXjgcjlGPa4cwDINhGCgeHMdBVIDZbEbRt4eNQCBgNpsV3QPUj/Hx8UQiMeqhIRD7muHFqdbW1kRRNJlMGIZxHEdRFIQ1Km3OtVqt3W4XRTGTyRyk2uX5fD4YDNI0DYUrCIJgWTaVSu1bqyoCceBRVqdYLAaLDxSxBJvIvp2Yh13x6Ha7uVwuGAzqdLpgMHj69GmNRiPL8qgHtW2ePn3aaDSUvCKI89PpdBiGOZ3OfRjkh/iiCIKgJJeDSKTRaJxOZzgcHvXQEIivD7X60Wg0zpw5Y7PZoLOH0WjUarVKpV1lBZYkyWg0ejyegQf55K+MkH6P6NraWiKRaDQaiUTC7XaDL53neYfDIQhCPB7fJyNHIA4hSlo5hICKophKpZrN5suXL/fnxESKR1cQBKfTKQiC2WzW6/U4jkNNwH1L/5N09erV69ev2+128LXpdLqJiQmI8tdqteqmTvvzKUTsOmNjYz2NI8EP5vV6u+gxQCC2T484/vz5c0EQoMgVtOmkKMpoNCqNOxVPYzabHXKofcVmA2s2m16v99q1a36/32QyEQRhNpu9Xq/D4XC5XErm2L49LwTi4KFMN57ncRwHP6Rerz99+vTHjx+7+zjnCikeXfCSkyQJkjpBEPvcP6DuUQ0fHA4Hz/OyLBsMBjC8nTlz5vjx43q9nmXZ9fX1gbsjDjDxeNxkMkFlM+jmAWJQIBDY2NgY9egQiK+D4atlsVj0+XwQagWLLUS3gulRqfAhiuK2gq1Hu0QPTAA7f/58OBz2+/0Mw5AkyXGcKIput5umaVmW0TsFgRgVpVKJ4ziGYeBdT5KkwWBQouv359w81IpHu91+9+4dCGQsy5rNZp1Oh+P4Pmz0qNAff+z3+0mSBKsbmLe1Wq0kSbIsi6I4qnEiRkuz2QyHw/AwgFQEz7nH41lbWxv16BCIr5Ueufz169fxeBxeHxiG0TQdiURwHFcKmmMYNjk5yXEc1HXY5/Rbtbrd7sbGxtOnT2OxmN1uh5rCkEAoSRJBEBBHvj/lGwTiwON0OmmaVnc1JUlyn6f1Hl7FAxbKu3fvYhhGURTLslCMTKPRTE5OqrfZhygetKdPnzocDs0/0el0LMtGIpGBGtS+PSnE7iIIgvJIQNFPjUbD87xS4gw9CQjEVhiebp7JZEKhkM1mA9eHLMuyLDMMo2j7BoPBaDQKghCJRNSWyP0/AWGEpVIpHA673e5gMAjFEmVZxjAslUp9jfmQCMSBYWVlBQqZYhhmsVjAyzozMzPqcX2CQ6p4KCv+kydPaJrGcZymaejjAaUS9/MrQRnb2tpaOBxWqxwURTEMA9WBezbuIkHzkOF0OtUlreADSZKhUGjUQ0MgvjI2Wzzh+3q9nkwmBUFgGMZkMjkcDpvNNjk5SdM0NFMCe5DBYBAE4eLFi0qx3eEH3w90Oh1BEGw2m81mI0lSr9dDzS6GYa5evarYtvZtNDkCcYCJx+NLS0vQOnBychKq7VUqFXVs5z6clYdU8VDjdrsTicT9+/c5jtNqtaCH9ORF7E9SqRSO4xiGWa1WeOBMJpPBYJBlGV5s+/CBQ+wZqVRKaWWq1NuBGNB///vfXfR4IBBbYCvTpNPprK6u+v1+QRDcbncgEKBpOhqNBoNBrVbL8zwoHjAHz5w5I0nS/o9QgrG1Wq1AIGCz2eD9iGGYKIrxeHxycjIYDH4VfhsE4qBy4cIFURQhl0x53S8sLKglwH04Qw+74vHu3btIJHLkyBGr1WowGKxWK03TGIZtbGzsw7ul8Pvvv8OAtVotKBvQvkOv18MbYtQDRIyeUChkNptZllXrHkajkaZpdX75fn7OEYh9RX/MlfqbZrMJ8daQdBePx71er16vpygKFmfwOur1epfLRVFUJBL5+PHjfp6AnU4nk8lQFEXTtNFoJEkSx/EzZ87EYjFZlpViVggEYiQcPXoUjM6QyalUsxj1uD7BYVc84vH45cuXM5mMUhNAp9PZbLZRj2tT4C0VCASgz7pGo+E4DsdxCCOGYqlfRRbjF2Xgu3w/v+C/BG632+v1wkMCDzZ8huKeh+1qIBB7wI8//iiKotPp9Hg8JpMJKswo7QXVYbFardbhcKTT6UajoXaw74eSVuoxUBQVCoWazaYkSTiOOxyOSCQSDAZlWf79999HN1IE4rDT6XSghAxFUSRJGo1GgiAsFst+Lo8EHHbF4/Xr151Op1Qqeb1e8IabzWae5/eDWLbZGJaXl81mMxRO0Wq1TqcTZMpIJJJKpdQ77oez2G8cnmuytLQETSSVzCXoMeRyuUqlEmxzeK4GArE3PHjwIJ1OT01NgcpBURS4phXN32g0ms1mKHhFEMTS0lKxWPxkTPaeTVX1D6XTaY7j4vF4u92ORCJ6vd5sNtvt9iNHjmyrQDACgdgZQypbtFqtUCgERmccxwVBCIVC6o6l/bvvEw674tHtdjc2Nmw2myiKfr8f7p9erx/1oP4//SpEJBKBRrler9dkMmk0Gmg/Isuyz+e7fv26YrLanw/cHtCTT//nn386HI6FhYXDlmc/OzvLMAwoqGr1w2q1QkXdw3AREIi95969e1ar1e/3+/1+giDGx8cZhoEECQzDAoEA/BdcHxzH+f3+CxcugKd6n8xKpZ4Vx3GRSKRcLvv9fpqmGYaxWq0+nw+5OxCIEdJut6PRKJS0NhqNRqMxmUxChb1qtTrq0X2CQ614wNo6OTkpy3I0GoWXhEajwXFcvcF+QBlJu90mSVKj0VitViiTotVqzWazJEnqhuv7Z+QjpNPp/N///d/ExAQEPHi93kNlpWs0Gi6XC2p7K/HlGo0GcjzQE4JAfCGgv0exWFxcXEwkEhCbZLVaQfGAirQEQUDwFThA7Hb74uKiJElqE4k68GkkEzadTkuSdP/+/WQy6XA4MAxjWXZhYaFer6MFBIHYM/qn26VLl2AZgewODMMcDkcsFkun08N33A8cUsVDfTOKxWIikTCZTARBgByPYdiLFy9GOLwhyLIM1msYp8lkMhqNkUgkmUwq2+zPR23vyeVygiCQJAnZ1ZDqcPr06Xa7feAvEZwghOH1VNTVaDTlcnnUA0QgDj4vX7589uxZuVxOJpPBYJAgCL1eT9O0Xq/neV6ZkgaDwWQyMQxD0zTP88rue79MqWu1dzqdRCKRSqXi8fjc3BxFUWNjY06nc2pqao9HhUAguv9cEDiOC4VCbrcbwl4wDGMYJhKJnDt3rjtSa8VWOIyKR88tOX/+PCRqT0xMQIUogiAgWWK09D80xWLRaDQq4iNkk/c0i0GhVt2/LwLDMOqm3QCGYRcvXvzw4cOBvz7tdjsYDKpVDlBCMAxTWnkc+IuAQOwx/THZtVotFApFo1Fof2Eymcxm89GjR6HZuZL+ocRihUKhcrncU9J9j6fq27dv8/l8OBwuFAqRSOTChQsul+vSpUtHjhw5ffo0WjcQiD2mJ1b8xo0bdrvdaDTq9frl5WWe551OZyQSWV5e3myv/cNhVDzUwF3heZ7juNOnT5vNZpDSSJIc9dB6qdfrgiCoazIyDJNMJtURVgiFdDoNudQ99n6tVkuS5MLCwqgH+MVpNBo0TavPHWpbYRj2VeSfIRBfO8rM2tjYyOVyJ06cyGazt2/f/uabb4LBIEmSNE1D8SvQOiAqUpIknudnZ2eVI/znP//Z45Gvr68nEolwOCzLcjgcFgQByq44nc49HgkCcZjZ7O0cjUbBg6rX62/cuJFIJG7dutVoNPZ4eDvjsCseQCKRMBqN33zzjclkAsns+PHj+00aczqdauM9FODKZDJDdtlvp7BnbGxsJJNJJYq6B4iGHPUY9wKr1UpRlHLiFosFslplWf7ll19gm0P7kCAQe0mn0zl9+vTS0lIkEgmFQuD9iMVi0OhDp9PxPA9vHzAWaLXaYDCotNzZ43kajUZlWb548SKU6fT7/W632+FwXL58eZ9HcSAQB5vV1dV0On337t3r169bLBaKogRBSCQSjUZDMUPv8+mJFI9ut9tdXV0NBAKTk5MYhkEFUrfbPepB/YNSqUQQhNpsz7IsTdOjHtf+Qpls0WjUarWqsxoUDAaDx+O5e/fuaIe6N7Asq35mlN7JY2NjqNkLArH3vHjxIpfL2Ww2p9Pp9Xqhogk0+oACdIp1Ccdxs9kcDAZ/++23PR7k6uqqx+OJx+PJZFKSJL1eb7VaRVG8cOECdAFCIBB7Q4+e3+l0Pnz4EIvFaJoWBMFkMomiePz48bt375ZKpfX19d1SOb6o6nIYFY+BFzQajWIYBrV0oePB9PT03o9tIL/++ivHcT1itNls3m/a0d6z2dwgCAI6Qvaj1Wpzudwej3NUSJIEygao00pp3ZmZmX1uEUEcZg585et0On3y5ElBEGw229jYGCSaQ4KHYiCAqWo0Gj0ez9u3b/ubgu3ilVEfCjJSpqens9kswzDgMoUOHhMTE91/ykC7NQAEArFFSqVSPB43GAwQBSMIwpUrVyKRSLFY7LEnbneqbmtGf870P4yKh4L6wq2urqpFVYPBMPJoK3UldaVPOUAQxPHjx1ut1giHt0/oT6MPh8M8z7MsO1Dx0Gg01Wr1kEQLBAIBKL6smFEhjTWRSEB6/YG/Aoivjv6X5YF8Sl+8eFGv1xuNRigUCoVCRqNRkiSO4xiGgUnKsiyO4xiGjY+PT05Oer3eu3fvttvtXRzDwGWwXC57vV632+12u1mWBS0I2pMptRMPyfqJQOxDisUix3EEQQiCcPToUZ7nz58/HwwGL1682N182dxstm73+6389ZMcasWjq7p89Xrd4XCAcA+lkCiKGu3YPn78uLy8LIoidBdRYFnWYDCcPXsWNjucq/8QoSQcDisxRZp/lpGFzzRN7/8OO59Pp9N5+vQphJypLalQjD8ej496gAjEprx//757EBe3fpF9dXU1lUpRFBWNRsPhsNFoVArzQ8oHzF+WZW02WyKRWFtbU9SPXb8+tVqtXq8HAgGr1Wq1WsfGxkiSJAjCZrN5PJ7DUIgcgdg/9E+3QqGQzWZpmjYYDBRFQRcgl8sVDoeVOngDGwFt9s0Wf3ezbXa2IBxexaP/ernd7unpaShPptVqKYp6/PjxSMYGQINbQRDUojPIjhRFffz4EZmdFNQXIZ1O92gaPaFW8K/P5xvhgPeGjY0Nn8/Xr32xLOv1ervo4UHsM5QH8mspz/KZKOeby+V4nh8bGwOPB0EQNE0rMVc4jhuNxmAwKAiCIAh+v79er/cc4TMHAJ+hawfHcfArRqORYRiWZa1W648//tizC1o9EIg95s6dOydPnvT7/TiOGwwGMEPrdDpo37F1Bk7e/i935g/5JIdX8ejH4/HMzc2ZTCaTyQRlRp4+fTrC8UBmsNfrhQon4H+3WCwmk0kx2KOlX7dCaM4AACAASURBVAEuRaFQcLvd6jjpgVoH/Lc/bPqAEQqF1NdBqS9M03RPf1MEArGX9Jshv/vuu1gs5na7JUliGMZsNiv9PSBaEtLQtVptNpv1+XyFQmF3h5RIJFiWBdMbjuOQ3TE+Ph4MBhOJRBepHAjE6IBJ9+uvvzqdTrfbDeYJhmGgduWJEyeG7/7+/fsejyV8fvHixfr6ejgcZhjGZrOlUimHwxEIBAqFwhaD+XewGhxGxWNg6FsoFCJJEqR8aCtrMBj2vpyIGoPBMDY2ZjAY1AH6OI5D2+lDvvQPvIntdrvRaEBvYM0/G+cN1EMIghjR8PeCP/74QxRFCNjodwFFo9FRDxCBOHT016hR/7XVaq2srCQSifHxcZ7nIeyqx2NJEARFUS6Xi+O4b7/99nOyPtS//vbtW7vdLoqiyWSCQC/QeSiK4nlereQc8lcPAjFCfvvtN57n/X6/3+8fGxvjOO7UqVNut7tUKg3cfn19PRQKYRhmtVoJgnj06FG73U6lUlarNZVKOZ1Oi8UCAdiKnKDX6yGpmCAIt9sdjUadTqcoisFgsLtL0/8wKh4DefLkidVqLRQKGo0GfM0EQYzQ3f/8+XOl67baTs/zfM+Wh/Y10H/ijUYDjPoDC+n2SN4ajcbv949k5HsDNBDUqYBz1+l0JpPp1q1box4gAoEYQLlcFgRBlmVBEIxGo8lkMhqN6hVMp9MxDANF6mRZ7ulxvjMajUY0GgWrJ6SVg9/DZDLZbDZUyASB2A9cv34dSk04nU6SJGOxWKVSyWazm9XHj8fjSsorpIqZzWZFEDIYDGrxEtorm0wm9WoDtnhQThiGIUny86sOHlLFo+digQpIkqTb7V5eXg6Hw+BllmX5k/vuLvl8PhKJdLtdp9M5MD+hxwlzaLWOzVD3WByudRx4xSMSiVitVpPJ5PF4IE5DOX0cx2Ox2KgHiEAgBgPCRDKZDIVCwWDQbDbbbDYI5gZRAOpNQfb5/Py80mcQ2HpuqMLa2logEOB5nud56KcOERcEQSDvKAIxcmDCzs/Px2Ixp9PJsixBEBMTE/l83uVy9WymRmnGgGGY0jVILQgpYTWwttA0vZnpFtwgSpvCHXNIFQ8F5SY1m81Lly4tLS2Nj49D8Bxc5bW1tb0cz9LSktFojMViBoMB9E61JG21WtXDRhG3/djt9i1qHVqt9vz586Me7xekXq8fO3bMYDB4vV6bzabT6eBZoml6cnJSSU5FIBD7jWazmUqlkslkOp0OBoP/8z//43A4KIoymUwQfKW4dh0OhyRJoij++uuvsO8Oio48fPiw2+0GAgFRFGmahjgrSGfXarUQ3ItAIEZLp9MJhUKCIEC1CYIggsFgqVS6f/++skH/XtlsFhYNkCcZhhkbG4P/Kq5UdVy60liiX0UBKIpKJBKoqtVO6JHam81mPp+HlD6apjmOg8W3Z+MvNAz4d2Njw+/3g1aq1+uhuJbyWGi1WgjjQ2rGEMrlck8GeX+iufKnAyx8Q3/T8+fP37t3z+12Q28yWK1EURRFcdQDRCAQn2ZtbS0YDJ49e3Z6evrEiRMejwcUA4ZhLBYLhmFgrYR89OvXr+/gJzqdDvQ8zufzOI5brVYI4uI4zmw2EwRx+/btXT8vBAKxAziO0+v1UEuXYZhUKjU3N/fy5cv+LdWC4sWLFxXhh+f5b775Znp6uj88RAnG1vRV4umB47juZ8iih1HxGHixnj17tr6+PjU1ZTab9Xq9zWbDcRzH8a3suytUKhWr1Wo2m41Go9FohPvNMAzHcVBii2GYvRnJV02n05EkCcdx0Dcoikqn05tNnlEP9otz6dKlSqUSCARgiSEIAupg+Hw+9PwgEPufTqezsrISDAZlWQbnBkmSBoPBYDCQJGm1WsFYptVqDQaDw+Eol8uNRmOLdfqVzZLJ5NGjR51OJ7z1TCaTTqebn5+naVodxYFAIPaSnnm6vr5utVqNRiNJkn6/n6KolZWVnvyrzea+IvaIoujxeJSgnoGiUX94SM9ns9k8/OeGc/Blr+Gor9rDhw8jkQjk4yqFCzfbeNfHkEwmzWbz2NhYOBxWum6D9IxhGMdxSlwdEhmH02w2LRYLTdM0TVut1mfPnkHGTv8sGvVIvzjJZDIYDEI4OOSWAcjjgUB8ReTzebfbTZKkx+Ox2Ww9+aBK3Qgovw6piVt8TXQ6nampqVwuJ8sy/ASYvQiCCIfDXq/3yZMnX/jkEAjEp3nx4gXP85IkgaCo0+k4jnv27Fl3aMdABSWASvN3j2x1VMhAJaRf31CvOVB7CSkeW2KztimdTiefz1utVrfbzXEclB4LBoP9OR5fQu5vtVqSJLlcLoqiLl++rJRs1/wdZqfc4613eDnMlMvlX375RfnvzMxMv06v0+lGOMK9wel0Kgmp6kVHaXuPQCD2LeoFv1Ao2O12juMsFgtBEOPj4wRBqBt9KLM7HA5vVuKmn42Njbm5OY/H43a7c7mcIAjQB8lgMCgFNBEIxKhQVoBMJsOybDqdDgQCoVAIit2Fw+HuP4XAgZ0GgPPnzytJHRiGQcKYunSqomOADNwjOag1EJ1O9+HDhx2f1KFTPLpDc7IFQfB6vWazGdwdOI6rq6R/0U7hiUTC6/UyDKPX63U6nSiKyp02Go1fqH/kIWFycrJ/Cun1+lGP68vS6XQymYxSO08J3CRJcnp6etSjQyAQ26DT6SSTSY/HA2+KeDwuSRIUvVWkAQzDjEZjPB4PhUJb7I5aq9UwDKNpWulXCOIIx3E0TbMse0hayCMQ+xC1gDc3N+fz+XK5XD6fF0UROmxs91ClUgkad0A97qWlpR9//DGTyVy8eLFSqWxsbCiVJKDGXb/3Az7QNI2Sy7fNwIs1NzcXi8XA0UEQBDRvCgQCm22/K5TLZegh7ff7DQYDjuMQW4XjOETF6HQ6pWTBkMEjBgLXymaz9Xs8DAbDqEf3xUkmk0r1G0U0sdvt8Xh81ENDIBBbomfBB41ifX1dluWFhQWIoIDgKGgY6nQ6HQ7H8DneaDTK5XKz2Tx16hR0DFSXtWFZ1mQymc1mKMbdU6sXgUDsMa9fv47FYjzPO53OarVqtVoFQdjuxISV5MaNG1euXFFagm5WIjUej1MUtVmyh8/n636GLHpIFY+BtNvtSqWSTqcLhYLT6YRQVyUa/gu5O8LhcCwWi8VibreboiilnwvcY4qiDnaviS9B/52CutQ9DbyVVozbTcT8ishkMqByKF2BMAxzOBzooUIgPpMhXuit51ds8ZgDmZ6eFgQhGAxCm2G9Xj82NkaSJMMwoVCIoiiO4xiG6Qm7evXqFTToALcJGLxA31CcoopREzwqbrd766NCIBC7Ds/zyWTSZDJRFEWSJMdxYBP/TIYsOOfOneuP5FTEp0ql8skjDAEpHr3cvXs3EAho/q4pptPplpeX4U+KALqza90fe/fu3TtQYaHWEEmSGo0G/tVoNA6HQ90k8msUfPcJHo9HmT/KLLLb7Z+8tl/7Na/X65BTDhV1NRoNVNRVSxI7fp4RiEPOdvv0DTFhbH2dVw7y8ePHV69ezc7OHj16VBRFiJWCgleKkQXH8UqlUqlUID0dgLpVY2NjFEWBr0Ov19M03W/XhM8mk2nHp49AID4TQRBAGjQajVar1eFwiKLYbrd3fQIqB3z37p2SDdLv8aAoqvt50x8pHv8FruP9+/eVPo6Auk3jLt7pVqt1//59KJWrtHeBxBIQFgOBQLVa3fXfPTwob+j19XWw6g0JtTqQV3h1dRWylZQHDJ4xDMNqtVr3gJ41ArGXbOa4GJjlOST1c/iX/X9SDvjhw4f19XVBEJT2gj12FpZlz549S9O0xWJRCtxBR1GtVgvVeJU4q35pQ6PR9GSZI2sFArFn8DwPwS8kSULJh1AotLS09PlH3mwWg1w6UOvQaDS3b9+GHf/zn//s7HeR4vH/Ub8VTpw4AUWONRqN0WjcxQhX9W0OBAKNRsPhcGhUbm7otGC326PR6Orqav9eiB3QaDRA/lbPIuiLMuTF//VGWCmsrq5OTk6qRRCSJMEsqoSAf9UniECMin4VYkhtmeFH2O4c7N9+ZWXF7XbzPA8qBwRfqcMk4AOE8kLVXVEUFXMMqCLQN1AxukGZE/g8OTn522+/fXIYCARi14Eiq5D0y7Ks0+ms1Wqzs7O7NQF7jvPjjz+qk7567BF6vV69FKBQq12DZVlI8uY47siRI/l8/ktIot9//32321W3cQGXN8/zOI5Dk3LEdhloUBzYQzCZTA7ZUfnyq1Y/Xr9+rfRShLMGzZaiqG0VxEAgEHvD1pca9ZblcpkkSWhpDO8RZb4P9GDodDqz2QxFFKH9eTKZBMWjZ6lUqrrH4/F6vb7dQSIQiM+hVqtBgx1o7knTNMMwlUpFXXD181HLOYIgqGNw1B+0Wq0Sp41CrXaZUqkEmeU4jhsMhgcPHuzWkdV3NxgM+v3+njAYjUZz8uTJK1eu9G+P2DFer1d9hWEKcRw3PLmz3x751d2ITqdz7Ngxm80GEgmcO03TJpPpzJkzox4dAvEVs4PVYHi01bZS0nv2qtfr0WgUKpTo9Xqj0Qj+CqiOOFD3ABUFRBmoOQHfcxw3cHu/3//o0SOlJsfOrgACgdgWi4uLNpuNJEmfzzc9PW2321utViqVgvTuXZyDcKi1tTWn06noG0rTYWUd2JVa/Ejx+C/KLUyn00aj0eFwgFdayd/flYMDjUaDoihBEHQ6HQTmQiqPXq8/ceKEUukMsTN6rnYwGFQn7SiManh7g2K9gCQi5QqArhsOh5Fai0B8IYZPq61kegxkfX29u4mu8ubNm1arNTc3d/r0aYIgYL6TJAlOTvByqB0gPcU2NmtjrP4wOTlJUdSuBJcjEIitQFEUVK4TRfHo0aNjY2PNZrNQKDx8+PDzTaL9O6ZSKSUgU6PRQE1t5b8kSb5582bI7lvkgMteO2BlZSWRSDgcDuVyRyKRer2+u+F0YFVSekAqi7ter1cK+CJ2i0KhoOR4qN+jGxsbf/3118ePHzudTq1WazQazWazWCyWy+VKpTIzMxMIBILBYKvVGvUZ7Byv1wsx30rVGgi78ng8ox4aAvG1sra2Vi6XM5lMq9VaXl4uFovZbDadTjcajbW1tZ4tu90utOUCtUHh1atXPfESn3zLKOVGNjY22u02HLDdbv/xxx+XL1/O5XLVajUWi4XDYZPJxHGcTqcTBIGiKI1Gg+M4lEwEnURJQ+8xx4CrRFFR1CIIxGBEIpFUKoWaeyAQX5pEIiGKot/vJwgCx3EwKORyOXV70N0VTRWbBQC18pSlIBQK7covIsVjABDJGo1GYc1lGKZarX5mxVX1Zq1WS5Ik5V6CfolhGEEQOp0OdYrdAcPvQrvd7nd3aLXaQqFgNBqPHj0K7iaCIJQ+Kj1lYWKx2HZ/dJ+QTqc1Go3BYFBq18CpcRwHQs9XcRY7ZsfxMLuy8Q4Wja0fcGfmrtFekM023mJxpz3z0cFP9EdRQy24QqEQDoe9Xq8kST/99FOlUkmlUsFg8NGjRysrK6BjgL6xtrbWbrdrtRqI6T/99FM+n4dDZTKZXC4H9o7+X1erKLVardlsxuPx9fX1SqVSLBZfvHjR7XZzuVyr1Xrx4sXKyko0Gp2enn79+nUqlUqn05lMxuPxeL1eSOEYWOoKMjr6A7Gg4JViDlM6o0MABrjoJycne9qDfM513sqXCMQhpNVqsSwriiJN0yRJUhSF4/j6+rrSX3x3qVarAyMzYSlQh1kCyOOxm5RKpVarderUKVip9Xp9T9JFD9u6+qurq6lUChZ35aZCGXWe5+/du4eW3W0x5HKtrKxsbGyUSiW19W7gpOrpLdi/jU6nA5ljK7+7r6hUKuDtgThRUHR1Oh1JktevX/9azuJLsFupO58sKTg8pn94KtHwNKTNvtkZO47/2VYFp+3+3MDNdiW0oFQq1ev1ZDKZyWSuXbsG3s6VlZW7d++ura2VSiXwaXS73Y2NjWg0euPGjVQqVSgUBEG4fPny/fv3L1++XCqVarXav/71r2q1CtrF48eP19fXQfF49uzZ06dPoVLIxsZGNps9f/58o9H49ttvrVar1+tNJpORSKRcLp89exa6bdRqtWKxGAwG0+n0qVOn4vH44uJiNBp9+PBhqVQKBoMul8vn8/n9flmWy+Vyu91eWVl5/Pjx8+fPX7x4EQ6HYYQQLQxVUvpXOc3fns+By50apfKVXq8nSRI6o3Mc9+eff+7sFnQ/9YQjEAiYF5VKRRAESZLcbrfRaAQDYi6X2/oRtrVghsPhIeUoFKNJ97OnMFI8BrC2tgbmKHBEMAyz9biU4a9PdcyPIuZCV2m9Xq++r4it8Msvvzx//hzcjuvr636/P5/PQ1gzhmEURVEUpa4puRnqqIOeu6O8s8+fP6/87leUbl4ulxXjpaJIw1N9SJ63IYrB57gxBy7rQ8Trz/dyfKbVY1sj2YEjd1ubKfFInb/pdrs9BcTfv3/f7Xar1Wqr1SoWi4lEIpfLdTqdSqUCxaBbrVYmk7l37161Wv33v/8NdQIhMLLZbK6urpZKpVKppHgPYrHYu3fv3r5922w2Q6FQNpuNx+PxeDybzZ47d65YLP7555+dTqdUKj148ODZs2dK4btwOLywsHD+/PloNOpwOAiCOHHihCiKExMTHMcFg8FyuWw2m69evVooFOr1eiAQmJuby+VyCwsLsVgsHo+XSqVKpRKLxWialiTpxIkTLMsyDCMIgtfr9fl8drs9GAxGIpGpqalMJuN2u2mapmk6FosJghCJRG7evHn27FmPxyNJkt1uj8Vi169fhwirubm5TCZz9uzZY8eO8TwviqLdboccQoitAh2jvyPYJxfGHvR6vdlsliRJEITPXz32/+KJQOwZ/RoCRIA7nc5YLDY1NWW320EiHZ4DvJlK0PO5/+disVgoFIKwzP64dAzDhv/WwFPYDKR4DKDT6RSLRUmSCIJQDEXpdLp/s4H79vxpdXXV7/fDizYej/ev9UajkWGYs2fPfslzOrBUKpX5+Xl4HWo0Gpg2wMBmWP3Xv1/TGIhOp/P5fOl0Wt1QsrvvX5/NZrPnBCHEAsfxEydOdPf9+HeL7eoYwzWKgS+Jbf36di97//ZqhWq7Ws0Qb8OOw8M2u2IbGxurq6uVSuXevXtHjx4NhUJer5em6Rs3bjx79gy2efnypd/vZ1m2WCyKosjz/IkTJ3788ce5uTl473IcFwgEstnszz//DLEHHMdB1cETJ06cPHlycXExFos9evQoFosVi8V4PG6z2TwejyAIEHoUCoWg9e/4+DhY9TAMM5vN4+PjJpNJkqRAIHD37t0nT554vV6Xy2UymRwORygUSqfTLMvqdDpZlgVBUKodgvbOsixFUdlsFoT+ixcvSpLk8/kYhpFl2eVyxWKxYDAoimIoFAqFQidPnvR4PMFgMBAIuN1up9NpMpmOHDmytLQky/KdO3fcbnc8Hr948SLHcbIs0zQNnf68Xq/b7fb7/dDby+PxMAxz5coVcJjcu3cP6mzG43FBEBYWFmRZ5nne6/U6HA7FuaGuMLHZctefVg6AdcZms7lcrp9//nnHoVYDnxMUc4VAKMCTXyqV3G737OxsJBJJJBKhUAh6cKVSKfWWA1fvrS/7imslGAwOKT4RCAT69xpy8OEgxeMfwF28d+/e/Px8PB43m81KhKvf7+/ZsruFu9tut1OpFNw5Jbu3B1EUG43Gzz//PPAIiM1QrtK9e/f6p4r6rblZO96Br9vN3r56vX5sbIxlWcXesP9vU6fTuXnzplKkAnp6GAyG48ePS5J0CPPLt2ih2ZYWMdzCtC2fgPLvJ6X/7R68UqncvXsX/qt4G968eVOpVMrl8suXL9fW1qAt1OLioiiKDofD7/dfuXIFrOZer/fKlStgts/n89PT02BobzQa4Fio1WqSJHm93k6n89NPP+Vyudu3b8OvlEolcCx88803PM9jGCaKotFopGn69u3b9XodCjiCXw4ke51OJ0nS5OQkVGODEEEcx0E50fztu6Np2ul0BoNBKCNrMBiOHj1KkuTp06fBui+KIsuyECDE8zwEGUIqHWQ+gGlJr9dbrVZRFH0+HzRxglBYkiRDoVC1Wg2HwxiGSZIEg+R5HtQeSZIoipqdnU0kEjMzM6IoEgQhSZIsy6Io1ut1mGg2m81mszEMw3Hc4uIieDM0f7sgDAYDQRA0TUOd/vPnzxcKhUwmIwiCxWJRVAXI6mYYBqKnRFHEMMzn81ksFlmWv/32W5vNFggEcrnchQsXBEHgef7YsWPRaNTpdG6WR76VxVC9Emq1WoqivF5vLpfrsb/sgCHzCIE4nKhnQbFYPHPmjCRJiURidnY2FAphGOZ2u9WhVkOMPlufX6VSyeVywaq4mbm2J9RcfcylpSV1qYmtvJuQ4jGA9+/fv379OhAI2Gy2mZkZlmWhDQK4/tV8Uj64e/cuFFbvWb7V0vCDBw+Uqllo8d06yrVKJBKbvVPhaqujmfsjr0AWgVtstVqhtzdEaintXI4ePepwOGKx2FdXSnJ9fV0tu8DVADns559/PlRP3Q5s+Z+51w4urLJjPp+PRCIej2dtbS2fz5fL5U6n8+effxaLxXa7ffv2bcgHePToUS6X4zgOCivlcrnvv/++WCymUqlMJlOtVldWVmZnZ/V6vd1un56edjgcgiCUSqVkMlmpVCRJmpiYOHv2bCKRePLkSSKROH78uMvl4jjOYDDgOG6z2ZxOpyzLTqfT4/FEIpHJyclwOOzxeGiaNpvNNpuNZdnp6WmKonier1QqT548qVarYJYDk7wkSeFwGF6cPM8bjUae50EBIEmyXC7r9XrQAZTYSIfDAY8r5DSDwgzGfpiScByTyWQ0Gi0Wy+zs7PT0NE3Toigq0QIgo0NEE8MwMPEJguA4LhaLkSQpSZLf75+bm4OzCIVCgUAAVBSKoqBPcLVatdlsOI6nUinQZCAyFuaRKIqvXr0SRfHChQvJZNJkMkEhmkql8tdff125csXj8cBIjEbjxMQEjFk5Kc0/cy20Wm0wGPR6vSzL3rhxY2pqSqvVQmy3Okdcr9dzHGez2TQaDahJoVCIYRibzXb69Ol0Op1KpUwmkyAIs7OzcOn6NYqt6B492xuNRrPZ7Ha7r169+vmLhlrBrtVqt2/fVr9hD8mihEAA/Q98Op3+5Zdf2u328+fPjx496vF4XC6X2t2x2Y7dPiVkOCdOnFBLR2azuWcp0Ol04XAYWs+l0+m3b9/++eef8/PzCwsLSuKougDPJ38UKR6DSafTOI7r9XposgH1jhKJhHobuLhD+kf+5z//uXDhQo/tXP2agQohPRF7aMHdLj/88MNAf0W/16LnA0yzYDBYqVRCodDk5KTSs6XZbFYqlU6n8+HDh3q93mq1vtLk8m63y7IsCC6K9KDVagmCgNKcX9GJ7Iz+E9zY2KjVakpGgfr7VqulntGdTuf3339PJpOrq6tPnz59/PixevtWqxWNRqGo0YMHD1qtFmQk3717V3laFEWiVqv1VFOFP50/f14URafTeevWrW63m81mb926FYvFeJ4XBEGv11MUZbPZrFbrwsICz/M4jkMWAU3Tfr8/FApZrVaCICKRCE3TiUQCjNx2u/3Bgwdzc3M0TYPgC94D0KhzuZzFYoEd9Xo9hJVKkpTL5bxeL4ZhJEnCM6PT6Ww2G/03Xq93dnaWYRiXyxWNRvV6PbgLcBxnWTYQCFy8eHFxcTGfz8/Ozrbbba/XOzY2FggEQG8xGAw0TRMEAUeAsUmSBD4Qg8FAkiTP8yRJ2mw2WHjz+TwEUtrt9hMnTkCwgdfrtVqtwWBQEASTyQSmgVAoJAjC1NSUEpIkCAKkScRiMZvNRlGU2WxOp9PT09PpdPr777+v1+tv3rzxer2yLIPKYTQaRVFMJBJOpxOWaFEU4V0gy7IkSdFoFNQwSZIMBkM8Hm+1WsrBSZIcHx8XRTGdTt+8ebNWq/n9/snJSXiDMAwDahJJkhzHwfWEZn8ajQbujslkstlsJpMpnU5fvHgRmgBKkhSJRDiOczgcPM9PTEywLDs2NqbX6y0WC2hW0CfU7/fzPA/ajqKwQbDWFpUNGMbADYxGI8dx8/Pzn19UR5mV1WoVgj81Go0gCOVy+bffftuVklkIxNfCQD0BcsNyuVwkEoEQzampqdnZ2c/8Iaiz9/Dhw59//jmTySgWGY1Gg2GYxWIZmF+u7vrQI00pCIKwRXECKR6DSafTYJCD1zBcVhzHN9t+M68WGKU2gyAIlmVBhT1UtuddQX2toFuFRuVHUlQLCDQymUwEQZhMJsi2VOYSQRAQM3CAX3VgaYb8MCXHgyTJLRbHOGAUi8VAIHDnzp18Pt9oNMrlcq1Wg2AkUDnW19eVbgmNRuPWrVu5XC4ej8/MzEiSdP/+fZqmz549G4lECoUCy7KLi4tQH6JcLi8vL4dCoUwm4/P5KIoKBALpdDqRSLx79w5E4UKhAOVTHz9+XKvVYrEYhOBjGAYVS0RRhP9CjgEUJoL3AaQ1GwyGZDIZDAbB2wCWb5D7rVbr9PT0o0ePxsfHSZK02+2CIGj+VrC1Wi1JkrIskyTZbDbBozI2NmYwGDiOA4eDx+MBcz4I9OB/MBgMDodjbGyMYRj4EnrSgaRrMBhkWYbVMhKJxOPxSCTicDhkWW40GolEAjQWJdKPJEmr1QqddyVJwnEchGxQM6C15dTUVDAYBK9IJpOZmZkBH4vT6YTSEdPT04FAIBQKFQoFk8nkdruh/Issy7FYLJvNQmEok8kky3I6nY7H436/H65wPp9/8+ZNPp9/+fJltVrN5XKxWOzGjRvQpIKiKFBg4KoGAgEcx+GUnU7n7OxsIBBIpVKpVMrr9fI8v7a2VqvVksmkz+cbHx/3+/3ZbHZ6ejoejycSid9//z0Wi1UqlWg0Wi6X1cazUAAAIABJREFUI5FIsViEp65QKMTjcfhyfn7e4/GQJDk9Pe1yuUDNgLQQr9d77ty5UChUqVQgqi0SiTQajVQqlc1m/X6/JEn5fB5Cs2RZTqVS09PTgiDA1QY9zWAw+P3+IW8itRhhMBjsdvtAyQO8MbFY7DPfU7lcLplMer3e/phy0CoZhgmHw4dzgUIgut1utVqlaVqWZZvNBsoARVHHjx//6aeferbsFz7X1tb8fj+ktEEbEHh3gJ9WmW4D/Z8ej2fI4vDJ79+9e1epVKAKyJCzQ4rHP1Ckf6ib7nA4oPsBGIGsVuu2jpbP5xWlRX2HlC9B2ugifWM3gIkErXag7AyGYWD9hbqZ3333HWwJkdlKyZrtsrPYG/U2/eaN3X0Aeo7GMIxGZbGApUen00Wj0c122daQdqAzr62ttVqtgXbT1dXVtbU1qEq0srLy5MkT+LCystLpdMrlMvRu++OPP2D7ly9fqnd/+/Zt9+8+az0eho2NjWQyabPZIGouHA5DCFCpVGo2m1DGtNvt3r9/f2VlBTIZJicnoWlDPp/P5/MEQXi9XsgZsFqtIJWaTCae5yHfYHZ2FmJRrFarMvFxHH/48CHHcRzHJRKJ+fl5iPAxmUxgioY7Aj5r6Fuq0+kgMxj+BJbsWCxmNBpdLlc8HofEAJvNZjAYjhw5IooiwzDgf0gkEuFwmOM4t9tNEITZbAaBHuKD/X5/IBCo1+tjY2MQT4Vh2Pj4OPjBbDYbqD0Qm8QwDE3TFEVxHHfu3DmO4xiGIUny2rVrgUBAEAS73Q6JBxBNConduVzO4/Gk0+loNDo/Pw9+DPByjI+PMwxjNpvBC+H1eiGOC6Kt4BENhUKRSGRhYQEcCBMTE6lUyu12w1U1m80gSUMiysrKilarFQTB7/eLohiJRAKBQDwel2XZ6/U+efLk4cOHUE4K/DaQEREOhwOBwL/+9S/IOw8EAl6vd2Fhwev1grMC2nRAaAFFUW63WxCEb7/9FoLZ1tbWQCwA31GtVmu32/DKiMfjjUYDivCC+wtq6QJg49hsprTb7Xa7nc1ms9ns6upqNBoFV9v6+nq73S6VSmtra1AfHJ5waBISDofv378Pxa8ymQyU3gItzmQyQU4IQRDgzBkoQPT4h6GJR/82HMdFo9ETJ05An6ttpYPD9+/fv89ms8FgEEbSU+BRwWAwwAZWqzWbzQ48IAJxsAmFQjARdDqd2WweGxsbGxuDqTccmGu//vqrOsK/hyFZr1uJxgTn+cA/QXcjDMOGmOm7SPHYjEKh8OLFi59//tnv90M5XVEURVHMZDJbF7CmpqYG3kjlgYCQaGV7pH7smE6n8/Lly3a73el0FhYW4Eu4tv0RNd1uF7bc2Q91/3mntvUC/uQ2W1RFhiQx9++otA4EaRUWHRBbtz6wrbAVr1GpVFpdXRUEIRAIhMPheDz+yy+/QK6qzWYzm81OpzMUCk1PTx8/frxYLELWWjqdzuVyV69ehYI/jUZjZWUFDOrZbBY+v3379vXr1ysrK+FwOJ1OLy4ulsvlVquVz+fj8fiVK1cajQZIkIocPDMzE41Gl5eXFxYW8vk86CGQxgCBMRqNJhgMjo2NWSwWEMohuAWC5nU6HSQZW61WlmXD4TAc2Wq1Kjoe5BjY7XaopwRWXoIgbt++rcS/wQ8pCzrY3ScnJ30+H8RW6fV6KGyi1+shZkmSJKPRiOM4RPZLksTzPMuyNE1PTk5CKgIoRaCTsCzL8zwoXYlEApwtHMd5PB7IWoZwJnAHgSwOqdKgKd2+fRtKUUHoKfSxgjJNbrcbgp0YhvH7/evr6w8ePGg2m48fPwbrNegPYH4rFos8z2s0GogFgocwlUqVy+Vjx46ZzeZQKCTLMnSi4Dju2rVrkD0iCAL4HERRVOpNwYnrdDqLxUJRFPyELMuLi4vBYFCSpGvXrkEt2ng8vrCwAHnz0IujUqncunVLluV4PA7RyZByUCwWS6VSIpFIp9M//PDDysrKhw8foCt5v2Xx999/7+lTPnwSffLLIVMvm83OzMykUqmrV68qa9rGxgboz6lUiuO4ZDIZi8UkSYJAbbB64jg+Njbm9/s3C6Dqf0n1x6ZqNBqapuPx+Pz8/Gaj3Wzw9Xqd4zh4XDV9MRsDPysfeJ4/wL5oBGIzYrGY3W6nadpgMExOTsKaHwqF/vd//3eLRzh58uRm830IYPZSGyP6u5xBNuxmVgyIHWVZdojHEikeg0kmkydPnszlcqFQiOf5dDpttVrT6TRN0+r8/e5QgQ9esepbokQagDABJecHHg2xu+xiJNtA3WNbHoNPDmMrRxsir/SM0GazgdcOxGWlcoXBYBhuoex0OmBwVVwHA4fRbDbn5+efPHkCDZXV2yhVpFdWVlqtFhiYz5w5Mz4+fuzYsVgsBqWWrl69ms1m3W43jIqm6UAgMD8/f/369Tt37qTTaRBGOY4D6RlCVqLRaCAQeP78+XfffVer1S5evPjDDz+AEb1YLELYCUEQPp8vn88nEolYLAZOBvA0QiVTyJ8+deoUx3Gwkh49epRlWUiwg+smiiIIuKBUuN1uOJTmb6clZGK4XC7YXnFqQ6ALVEQlSRLSIfR6PZQ5AqEQlBmwSUMZPdBVaJo+cuQIeCoCgUCz2YQeUk6nE9Sn6elpjuMqlUoikbhw4UI8Hl9aWoK0BwhMisfjd+/ehazuTCYTj8er1Sq0o+l0OpcuXeJ5Ht4QkDRy7949qIbk8Xgg3RBKssqyPDU1BSoQhmEOhwP28vv9oLpAlBfLssFgcGlp6dGjR69evXr9+vXc3Bykg4N5jCCIXC6n1+txHI/H4zzPX7hwQZbly5cvZzKZ6enpTCazsrKSTqdbrdarV6/evXvX7XavXbtmMBgsFgvHcY8ePZqdnV1eXoY4N9BPlpeXobprq9VqNpv1eh18/aurq51O5/79+9VqdXV1dWNj48mTJ+vr6/2TZeD8HTIvBn745C49M+uT2yifNzY2oMrwzMzM7OwsRVGgIRuNxosXL0L82/nz52maXl1dVQp8KQnoqVTq5MmTp06d0ul0LMv2qx9DQrfVuXDJZHJbBf1KpdLZs2fBg9cfNa7INEriu/pPDocDPuv1eii2tvXfRSC+UtSP94ULF/L5fDQa5Xk+EolEIpHl5WWlVOAWj6YUZd1MzRhI//bqdUCj0ZAkCW8B3d+oN4ZXns1mg6DigSDFY1OgnhVc1rGxMTAcajSa/u4tA1fDcrncs8LCf8fGxiiKslgsSl3kIQdBbAX1u3yIDPGFrvAOfBTbOuyOj6CwtLTEcZy6qiY8k2azechPvHjxIhqN/vTTT+12+88//xQEYX19HUyt9Xodkqfn5+dv3rw5Pz9P03Q4HIbsiI8fP25sbJTL5b/++uvq1avQBsHhcECMvtfrDYVCoiiSJBmNRpvN5o0bN+x2OxjsQSnief7y5cscx4GVHQT9VCrFMAwUGoLCSiaTCVwZkGULCbugV4RCIRDlTSYTRN+Fw2EQjiEeCTaDwFmlfBNMUujpZrFY4CqZTKZcLgcSOXzO5/PPnz+/desWjBY0EJqm4dchUKdYLELriRs3bsD5Op1Op9MJiQQ3b94sl8uiKIIPampqSpKk6elpu90OVmGCIMbHxyF3AkKk7t+/f+HChcXFxadPn167di2VSgUCAVmWg8FgMpmEoCmI1ML+Jp1OZ7NZWHCsVitETGEYlslkEonE0aNHzWYzhmFTU1NnzpwBDQpOGepT6XQ6CJqamJiAq0RRFPSygJJWkPXudruVTHTIlpZlGRQDsLgrWi7DMPfu3WMYBpr3nT59+s6dO6lU6tWrV41GAzxXav+k0qgkk8n89NNP33777fv37+Fl9vDhw0/qzAP/tIuLwBbt/Z8cVQ9w1sr2CwsL8NgTBCEIwsTEBMRQwTccx4GLzOPxmM1mWZYhPAMirGKxmDo2Y21tbWxsbFsiCADuwa1fk5cvX0LV462LNWpfB6RLwTfqtmXoFYk4JEC4ZrVaLZfLUDI7GAwWi8Wth1rBv/Bu2soc3NY2GIbJsgzZgD0xk1qt9vz58zabTd1wuR+keGzK6upqMBg8efJkIBCAhV6j0ZAkefHiRXV8VA9wv5XOEj0oCaMOh+PXX3/t9gnNe3VyB4EthigM/OtnXurP8Wb0bDZQb/kcLaV/30qlYrPZxsbGwO6ovOYhSbfn2SsUCsViMZlMgotvfX292WweO3aMIAi32w1Vfdxud6FQOH36NEEQUJMUZFa73Q6B6cFgkGGY6enpxcXF5eVliM4H4ZjneZ7nwRRqtVolSTKZTCdPnhwfH6dpGiodiaIIOQbj4+Pg4sBx3OFwTExMgJLgcDigFofD4QgEAhBWpGgaFEWBPQZEYZPJZDAYBEEAU7GiYGg0Gp1OBx0VtFotWPRxHDebzbVaDbopwbWC5RV0FUjgLpfLdrsdNgCx+/Hjx8lkEkozmc3mVCpltVojkQjP85IkZTIZWZYnJyehtoFWq02n00ajUZIkUIQgSyGZTE5PT4uiaDabBUG4fPmyyWSC6quZTAbSpu/evZtMJl0u1/Xr1xOJhNfrLRQKT548icViLpdLlmW32w1ZEG63GzQZq9Vqs9n8fj/0zltcXCwUCt9++63X67XZbDdu3Lhz5w60qYJLnUwmJUkym83ZbNbj8UxOTkK6fCaTefz4cbFYrFQqmUzmm2++SaVSt2/fjkaj6XR6fHzc4/HAic/Ozj579sxut0N4gFarBRvYH3/8USwWW61Wq9X65ptv1C7fbcnxw5/8bS2nW/FI7Hh4w7cc+CutVgsyoO7fvw8havD2MZlMELSm9CQBXZFhGMiigfg3s9nscrlu3rx59+7dnjCwTqfz7t27T0oY6v+CtwrSmQaOXP2h3W5Ho1GLxTJQahn4DeRyqBUPHMcLhYIkSUePHpUkaSuSFgJxAFCvBpDo1e12v//+e7B3O53OCxcubKvcAhwQmgUNDJ78HOC1tdkCwvP8wBB3BaR49KLcfnhBdrvdWq1Wq9VkWQZjTCAQAKvbZq+obDbbU1tJDY7j20oUQWyRT4odX1q726420i8z9QQpQfp7/76FQuG7775bXV31eDzhcLherzcajfX19Uaj4fF47HY7FPkJh8OFQgHST5XSST1ygM1mq1arMzMzUMWIIAiHwwFZzjqdDpKw5+bmWJaFNGUwnEMXAig2DQsQTA2apkul0pEjR+BLo9FoNBqfP38OGaXgHwBjPKQcQEAF/BzDMOl0WrGgQJIDJFTo9fq5uTmoCgoibCwWAyuLy+UyGo3gFsBxvFar4Tg+PT195swZmqYhZcJgMCwsLGg0GvClwEKs+TuYFZQHUA8g8sput0N2MmSDgMYCY4YE8WAwuLa2ViwWlc4SsiwXi8VYLDYzM3Py5MlsNnvy5Emn05lIJL777rtwOOx2u0Hjslgsdrvd7/c3m02HwxGNRiGsS5Kk48ePBwIBqJCbTqevXr0KUUYOhwMiqSKRyM2bNy9dugQFFl+8eFEsFuEZACdDKpWKRCLBYDAYDIJ3habpq1ev+ny+GzdurK2tvXnz5tmzZ+fOnYMlqF6vQwB9tVqFuKZffvkFCg3HYjFIYlavh8qz+vHjxz///LPnsYSaYI8ePapUKmBVgfrC3W73hx9+eP78+dZ17H5zzI71+YH7bmWzIaaBLR58+Cn07wgF1hKJRDwev3fvnt/vB8UYnnwIwIOUHpZloaQYy7JOp1Ov1zMMA7W2IChxyEigRWPPW0kt+iuLA7Q1dLvdU1NTn7yM79694zhuoBSi+ZTcA3MQZmg6nR5yPRGIw8DTp08TiUSz2YTSedAv6Pz58zvo2rm8vKxu4bB11GuCkvWhVL6GL3tiKJTI4efPn3eHzlykePyXHkf8y5cvoXLZ9PQ0lFJRdMd79+4pm8Gbu1QqMQxz8uTJRCIx5DZjGPb9998rP9fzoYsW2S/MFsOitnWo/i83+5WBu3z77bdutxvk0Xw+3+1237x5I4ri/Px8JBJxu93KlisrK/V6PZFIOBwOKLUpSRLEWkCOAbR9YBgGelbqdDq/3//jjz8qHZf7pQFlydBqtVar1Wq1KqsJCOUguysRODabDVLHlBpE6mfbaDRCbwc4LOQ2aDSaM2fOQP6GImcYDAZo/aYcHARlcCAYjUaWZefm5pT40SNHjigD1ul0UOsDUiNgGHDisVgMXB8QwgRKDk3THo8HUm+NRiP4PaD8EWQqMwwTiUTAwur1eqPRqM/ne/DgQalUCofDiUQC2lD4fL5YLDY/P5/P51utVqfTKZfLMzMz586dm52dnZmZcblcCwsL1Wq10WgUi8VarVapVKDoVj6fD4VCuVwulUqNj48HAoFEIpHL5aBWVaPRWFtb++OPP3799VflIfnrr7+63e6tW7cg56FWq6XT6UKhAJnQUBG4Wq1OT0+DoNlsNqHRUD6fz+Vyz58/f/jw4ZMnT6D8l/rJ3NjYePXq1Vae5608/598yHfsKxjyuzvzZuxgx61sP3xInxxwLpd78uTJrVu3rl69CgGEUGIBHmMMwyDUyu12+3w+t9sNpcwgiwNCHK1Wq9/v36JzYG1tDaokK3Onv8QNBBDyPA8r0pDzUgCto1926RdlwMcIOlU4HKYoKp1OF4tF9W8pF21nXiwE4msEHu/3799DbyiIzoU64CzLiqL45MmTbU0B2BgqeQzVMnpnKxRwh/UB4gXGx8ctFkskEgFdqFAorK6uLi0tiaIIVj9BEILBoMvlunbt2icHhhSPT1Cv1ycmJnry+q1WK1jyKpXKpUuXOp3OpUuXIHXv/7F3LcFJZet689w8NhCyIYRudjAoIViihFyJRLziFaukG6vEumKVWGLVwYFkIJY4aXpinDRWGUfiyDg6pEqcdZyJsys9EGe3c6aNd9Zx1HF44A6+m3X32TxC3q/1DVIE9mPttdfjf35/e6qcGDzPt7Yh8ufQYgO70VZ19fLyMjbLx48fP3jwQJwBKbnL3NycwWAwGo0WiwUnlsvldDpdqVRKpZLL5bLZbC6XC7Hvbrf76NGjFoslEAhEIhEUN1xaWnK5XEiQsFgsMpkMJcyQOUAI+/V6PcKKIJFgyQAXTbcBCeEGn2FYRby42+2Gh5cIKJDjtVotyXiGo0Di3BNbQfx+P2pNkIvgLPg3EJ2FgHUUsBMEwWq1BgKBUCjk8/lgyz969CjJE4AQ5nQ63W632WweGhrS6/Vutxtp2W63u16vx2IxhBUhDdpmsw0PD09MTDQajQ8fPqRSqXA4fOvWLdjv8ZoeP34cCASgGKRSqeXl5VevXrVarTdv3qBSRO8htLy8vLi4+PbtW9QNBJMv2LTEh0lczwiDaQ+GWdcg7BEm1D41DoDo1lu47/jNVi22/d96zYMXFxer1eri4mKxWERheJC8JZNJImQgehCBgsjOQmAVQq2QhKPRaOAUlfCdrPmYpVIJBSgFQSCcEwQcxw0NDd25cwc2td4WFthBxOTRvQUaLFAImAwGg/Pz82IrXu/27+uhS0HRG2RO1ev1arWKgqHgZoAlzuFwbMDjAaBkk3IV4oLCZJJKvimVSrdu3UK4dY8rLy8vR6NRYsnqc5LuIcVjby4rqHMkYRzPZDLXrl1LJBLhcPjmzZtgXMaG0UPrkMvl4jT/LbS+S9AtNmCTxsL13n1dV+txwFb1T59tkBxWq9XK5XI2m200GoVC4fnz58lkMhqNgvvf5/MdOXIE7Jw4d3p6mgSltFqtr1+/Xr9+XalUnjlzBjXF0uk02NJyuRwozlB7GIXDSF4BgnxQ0DqfzyN5wG63QwRHrWIIInBT4DPKLIhrkX733XckuEgiCshkMqfT6fF4EEnFMAyip1iWnZ2dRaw2cd8dPXoU59psNqgoDMNoNBoyNbCcofQEVjee51H3wOFwlEolnU43Pj7ucrkGBgZg09Xr9R6PBxygyWQyl8tNTk6i+hv8Oel0GgHfqKUAVeT69euVSuXhw4eVSuXChQvgEl1aWoJ7d3FxEdJ8PB5H8E+9Xl9eXq7X6+3RQWsOhj///LP/Uyj2L7bED7MmKpXK/fv3o9EomIgVCgXHcQaDAfxmyOdB6KBGo0EJc/CbIcRRLpefOXMGwYQXL17sLRD0aGE4HCZRi2ICANgvrly50v+ViVGjY0iV+C+MF263G3XZr1692n/jKSgOD+r1eqFQsFqtwWAwkUjAspbJZP72t79t8sqxWOyXX36JRqPfffcdIdlvlw0UCsXk5OSWPEs37AnFY2+qHAQ3btyIRqPidwMy+Bs3boA/BPHrzFpRdEqlElZPSUzXdqBPc9Ga4n7H6/RQYHo/14bVj/X2WJ/RayQ7olgsZjKZYrEo4YyPRCKRSGRwcHBmZiYYDHIcd+zYMYfDMTAwgEJssEQ6HA6Hw4FgGKvV6vV6oV0g+B4RQclkEoZ5ED6YzeaRkRGe500m0/DwsEwmM5lM4M5jRAV61Gr1hw8fIM0jRQGEsNjFAaJXwNcBFYXoDB2rdJEIK7vdjixqZH4DMplsbGyMiAuoiu1wOARBGBoastvtYKlyuVxQcpClMDY2dv36dVRiPn36tNvtvnTpUj6f93g8P/7449LSkiAIULx//fXXXC5nsVimpqZQK1Bs7EHPNxoNeJzxL1SIdlSrVVRS6/2i1xwJW3I8xb5G7zjJjt+seTXxv6VSSa1WY5JC5SCmRyRwm0wmjUYDbx4KX9hsNqvVeurUKUQSwvkmWQw3MEqvX79O0iok2R0ajWZdF8xkMu3mDMk6g81Rq9WaTKZYLDY3NwcS7e0zvVFQ7C+Ip0C1WvX7/Xq93ufz2e12VHDKZDI3btzYkpkyNzdHpr945pIPIOZub94WztNdVjz2xYqzvLx87949ifSWTqfBTSnrRFLeESg3Riour3fZXa9c1f/1u50o/rfjrtxxOPape2xsKPd58ZWVFdR/AOtrq9UqlUoLCwv//d//nc1mM5lMMplEgWe73X7jxg2TyQTDeTweD4fDuVwukUj4/X5SOxKlxxCYBOL87777DjV0xsbGHA7HkSNHbt++PT09zbJsIBBQq9UjIyOE29RgMNhsNvA4GY1Gl8ulVqtR7hpF0EDW7PV6wbmErGXESoHWCcyqMHxigUAwBo5BYTi32x0IBC5cuIDILo1GA4JXicdDMpJR8y6RSJw9e5bneZvNhjQJtAcsVeFwGO3PZDIulwv84qVSKZvNzszMgFQ3Ho8/evRoaWlpcXGx0WjUarW5ublUKnXp0qWvX7+2Wq3FxUVx3UYSH1IoFL59+9ZxeGwA+2JJodjj6McCsq71FpXOUeCFRCrKZDIwmMGZGQwGlUolqKtkMtnQ0JBWqw2FQplMhtB/bZXkAb4EYlwgFgrEbvWA5DGXl5dJ+cv25QVaB+qu+Hw+4hYWX4FOWAoKAHMhn89PTk4iIBlVwJ1OJ8qebsktSBHhbobyQCAgPn47ZuiuKR4SEyahbN+byOfzkveEvWG99VlA7EPsuD22sR5Y0ya35jXFh3369Il8X6vV+o8tWZe+sSbERGG979V73yqVShCXwWSq1+uRjJtKpZDDDd6nR48eoRICqeYmCAJIKg0Gg1qtRqgDkgpIZBGAeQsCB7lcbjabQTWLgtYymQx2TXFaNgbM6OgoPvM8bzabUaTZbreDkRbDiUgkPp8PRxoMhh9++MHpdOKzxWJBYMbExEShUACHrMPhcDqdxEpx4cIFt9sdj8drtRqctoibahcOZDIZMklisVir1fr9998bjUYqlYpGo4lE4smTJ8Vi8cWLF9++fWs0GojjxF161AbqgX4stX2Oq44LIhViKDaDbuOz95is1+tzc3MLCwvkG/hRyb/pdBp8D+IAa5lMxnEcy7IoYjM4OEiyoRiGuXr1KgqbbHKcdzwSRgSsaVhzsJpNT0+3em4iHX/66aefkLMhSfdCkVwsLBtrPAXFYUOz2UQJV51OBxcoWBODwWB7vekNABTtHSUB8rcHpcRWYQ+FWu3x9UiyqvavbLRjYGBAfOU+LUAdv9+M3tJqtRYWFgYGBlCazWazgfMnnU63cxp2vEUP30ir1Uomk+1fik/JZrMoL3337l2lUunxeFQq1c2bN7PZLKh+wuHwiRMnwuGwIAjZbNbj8ZC5t7S09PjxY0LkQkKkUqmU3W6/efOm0+nkOA4UqPF4HPVuWJZFsQJYE0mpNbVa/d133yFxE+lcJCICGyqin5FOjVpydrtdPB4SiYTD4RDPZyiZcFBA53S73ch/QFVpjUYD3wIa6XA4SDyVwWC4fv26TqcLBAI6nQ7uDkEQBEGIRCJQVyYmJm7evIkKbg6HY2FhYWVlBVpBJBJZWVlBkeZSqRQKhRBJJQm7wkPxPI/8zmaz+fXr12azud5c1fUaRTbmmtuYM2RL1pY9vjRRbDnah2j7GPjy5cvly5ctFovP5wsEAiiTEolEYrFYIBCAjT8Wi9ntdrPZDOckKaQDF+jk5CSMFHq9HskeBoNBTNXfPnr7Ud17Y2VlxWg0Euo5tOfYsWNPnjzppzB5x58sFovf75etAnvlxYsX13URCorDDDIpcrkc9A34SO12O8I0WluxnV2+fNlqtTJtnklmNTDSbDb3bt6WYE8oHsCeXYzQsHv37rWriT2+6XYA3m6ru/jVT2P6PAUR8Mlk8vnz54IgVKtVyJQvXryYm5tzu91nz541GAzff/89irjBSK/RaHQ6HWi74C5otVpgFkYgTaVSqVQqr169+vDhA3hCT58+jaCmz58/Z7NZVESWyWT5fL5SqTx58qRSqdRqtWAwOD4+DhL64eFhRuTlN5vNXq9Xr9frdDqbzQZDIM/z2LBlq7zyg4ODKpUKToapqSmXy/XgwYNms4mKZslkEmkPyGzmOE6j0SDuCLkQkLNBBSuZb8TVAPomVFKD0U58JOwQwWAQP8lWeWZv3bpFKJ5kqxWvQUZBKjezLDvWLotMAAAgAElEQVQyMoIiXwirYBgGTLiIcdLpdGBnSqfTbrf7zJkzU1NTPp9vcXExm83yPF+pVFAyIp1O+3w+RFg5HI4nT5700FdXVlaGh4eR+9E+UMfHx3srkP3rFevSmTse0FsJ718e6q2l9489uyhR7DzImJydnc3lcqlUymQyKZVKhGiOjIwwDANiQxSf8Xg8qHiDJU6hUMC0AbJaQRD8fv/169ePHDmSSCS66dW99e3+ZxawtLQUDodHRkYEQRCvBiqVanZ2dmOjvdls1uv1S5cu+Xw+r9crCILJZML20RKtHtQ/SUHRDZK5kMlkUIdKpVKl0+nXr1+vlzaqGwwGA6p2EsujWEDlOI6YHdtn7hZO2D2keOxl1Go1CSepxEXVJ8jBDx8+FF+fvNGPHz+K3+7Hjx8h0DebTXAiPX/+PJfLFYvFZrP58uXLy5cvV6vVer0uccPB0R+NRnmehzRvtVpB14gKzaigrFarMbiZ1Rox+FepVB47dmxsbIxlWa/Xi5ileDweCAROnjzp9XrHx8flcjnKoiESSafTlcvl8fHxI0eOoB6zQqEYHBycnJwcHx9HCV4Y/IggLu4T+SpkMpmYK4lZDQYggdGgc2UYxm63gyMFaZoWiwU5GHq9HlI+NBBEQKG8nU6n8/l8SqWSaBRQQsTF9aB1IPBpamqKmAbhrEBxDHDaQoYgIVLQNGSrFE9Wq9Xj8aCfcaLdbh8YGEB2RygUGh0dhS8VJf9A2n3ixIm7d+/evn17ZmYGxKztgwQAWVPHA9oXiNu3bxPXjXgcqlQqUDyviQ2vPmsKTGR12yrdu08X4prXp4LRIUTvEVWv1yORiNPpBFkcQqcw91GFBrYbxGfyPD84OEhWD6xgWq12cHDQ7XZPTEy0CxP9j70NHAmAb1ocBQqk02nx8f1cv4dtorf6tHm/DQXFgUSz2Xz9+nUsFjt//rzD4TCbzZFIhCQGbxLValWcYAZhj1TRlcvloVCovT1bcmsJaHJ5X2gvsSQWmjcQduX1eonU+OrVq2q1WqvVULT40aNH4+PjPp9vbGxMo9H4/f6xsTFE8kC2VigUFoslHo+73W6TyTQ4OIhSx2NjY1AzzGazSqVyu91IACCFb2FvkxAakB0IgjXRQIaHh1GpijjQYbGD08Dn88lkMr/fDxYm8lAmkwnc86RnIP1L/HrQOojCjSggRBOheLbYZS8+ErFPKFIBxYawPMGhgRNxHXy22+0GgwGxEPfu3VtcXCQhVUjbgkYkk8mId+XkyZNwmJC8SSR1wBEJfqqRkRFQ2Q4ODiLdHOXn0EKn0xkKhZLJ5PXr1+FTisViHo/H7/eHQiFoFM+fP5+amspkMrFY7MWLF0+fPm1nsey4YW9g1jx48MDhcBCbK3lfgiDYbLbNTI1+LLKbdDVs0t9CQbEuoIoL0Gg0lpaWrl27FgwGk8kkUshgUAD7LUrLgx0Odb5hU0ShelJz1m63O53Oixcv3rp16/37961dGq7Xrl2zWq1msxn2VPGW1I/MQbITO/7a8Us6Kyko+kS5XEblXKvVSjJOL1++3NqieYQgq3YJFoKTVqvteNZ2TOFtVDz6NGH2DvPYCygUCpL31AMSsb4HIMFPTEygmgFs8H6/H3WmGVGdZoZhSMQOaYZGo4GoDcE9nU47HI5oNIqERdIGcZkFxFCRVGmZTEYKPiAJm9SBQvCPXq+HiI/TiSgvTpuGrkKeiLgF8I1Kpbp48SLRp8X0X9j2EOJMaugiIAoOB7gpOnYd0VtQ2AEp4Ahhgg4Dmlpck+M4vV6fyWRAnw/2WARQIsyJYRj4TMi0DIVC0NOcTifLstikZTKZ1+tFVgbP8+l0OhaLNRqN9+/fZ7NZl8v18OHDR48e/fHHH8Vi8dOnT/Pz8ygtV6lUiNtqF4dxsVhMpVIWi4UEe4BTS6lU7mKrKCj6xw7MoEql4nA4gsHgqVOn3G63y+UaGRnx+/3hcDiZTCITAz5VZjWASq1Wo243jBdms1mn001MTLjd7p9//pnneSgtJA9tF9cBn88nl8sFQdDpdFiosaRbrVYJgWZHXLhwwefz1Wq1b9++STLB+nEzblUAJAXFgUS9Xs9kMktLS6Ojo4jG9Hg8xBXZJ7pNKDD7EwFSLFDB9SHOLttu7MVQq966R/9x3luIcrmcyWTW5LBCGWbxv5ID1tRJiIdhzeMlhGjYRRAl1fEweCGsVishVGEYxmw2E5fF2NgYalTxPJ9MJmG0A4ESGZ0MwyCaCEfKVitSk/IRiD0gfG0DAwMkk2lwcFDM60pUGp7noTZAb4G9UC6Xi78Ul0mRyWRgiWVWHRGopAFmFURdQ7Ym/elyubRaLfwSeCiO43iexweFQuHz+SKRSDQaHR8fz+VyoVDojz/+qNfr3759u3z5cjabbTab7YnsvQdh//kJ2wfxTS9cuIB3J+5MFDv//PnzzreNgmJd2FgIXO8EA/yFp/Hr16+guSPmFaPRyHHcwMAAwqhgPQFQ8QbJZti2cQBW1MHBQRQjbzQaPYoN78CaIPEcIgWcWKOINxvxlmu2BxzfU1NTDofj5MmTLperx00lV8vn892KlFNQUABYi3K5HKwbkUjk3Llz/S8UPYTnjhmeEKKsVusOF/TcSsWjm82DfBBz5va2i3z+/Pnhw4fZbLZUKhGBbwOqyOaBi8diMVQl7xZb1TvmSvIr5PWO2kXHK8tWeXvJAfiXBALJZLLp6elQKERcARDHieKBCnfi6wuCwDAMx3GomCsOxIIfBvsTSmWTqtXMqjYVDAYRdoXDTCYTduXBwUHEGJBQQnJlKCTwt5BdXKFQIODH6XR6vV6e548cOYL2Dw8Pw+VCWGvRb8hX0el08PlAxyD9w3GcOK4MSkgkEuE4bnJyUhCE0dFRlA+vVqvFYlEQBK1WW6lUVlZWVlZWfvnll82Mk73jr2uffel0GqqXxHWm1Wr7MXZSUOwiNmAs76ao/OMf/8hkMnNzc/Pz8+Fw+NmzZ5OTkyRBC7MD4ZcGg4FZdRqTlZPYd7C2INMD9BUcx01MTCD3LJfL9aCc3sklQnyvTCYDgUbsElcqlS9evOjnUsxqsCsJ2bVarUg47NjbzWbz7t27w8PDWPNNJlMgEEDB0L/++mtrH5OC4gCgWCwuLi4+fPgQS9B3333XXrC8z3VP/O/8/DyJWGkXTQcHB/u8+FZh6z0eHWWv3hHbDx8+PHPmzIULFxCILwjC0aNHidwMETYYDF64cGG3RLqXL1+6XK5uuoHE+dBDiyAgMU7t6KiHiD9AsGZW1Q+ZTAYeRq/XS7KHsREyq3qL0+lEigI0BK1WOz4+ji+h7/p8vuXlZY/HMzMzc/v2bbI/BYPBSCQirpaIWCZi9hO3FuI+YhPVarXVajUYDCaT6eTJkwMDAyi6hxoRt2/fjkQiDocjFAql02kUmAN++eWXfD7/9u3bZrP5/PnzSqXC83woFDp58mQ8Hvf5fM+fP8/n8w8fPgwEAh6PB7SVcFwgxprn+WKx+Msvv6TT6XPnzuVyuTt37oAj+D//8z/JjXqEI7eP3i0xOfS49Q5gamrKbrcPDw8TFxYZRRsrykFBsVvosaG0/1sqlRYXFxcWFmq12tLS0vj4OFmdOI4bHx//8ccfUbaPTA3xsoZIS2zbWFRRfQ+xWJFIJJVKzc7OFgqFde16OwPxmlatVhGYSh4Q4axKpbLP5nXcsAKBQMcHTyaTJGlQvKOlUqlisahWq2/fvr3lz0tBsa/x4MEDFPjSaDQoIPj27dtW3/7ebvo/ioDBhE2kRDIlNRpNPxffQmyZ4tG/O6LZbIZCIafTabVap6enT58+rdPpEDhL5CFiHZetchH6/f5isbi0tNRqtarVKgma35j/fQNPB3qi9m1JUhZafEC7QiLWH+C27riUi49ECgSOR1gURs/ExAR0CcL4JI4Ek8vlHMdB60DQFAhbUZC7UCi4XK7jx4+nUqlHjx6JawiS/OZmsykhTWo0GtPT05lMBtS3giAgbQPGv+HhYafTicq7gUAAqSZut3thYSGbzRaLRUKw2O199eM0kEwn/Fuv11+/fv3q1atGo0H8Y73v0uNFr/kTuW//OsYu+kDIrSORCJi+IF0R9dVkMpH67hQUexZrTiLJAS9evICobbfbQXEbi8WGh4eximK1xE/MqoGGWa3AI16BETiKGE6bzRYMBl0uF8/zqJPTuyV7yvkZCoVQ91a2yk4+MjKCBNY+L9Vxq1KpVOKdIpFIgPScbOiSbW5wcBCFiViW/fLly9Y/MAXFPgQyQlutVigUQsbp9PS0JLN8veIEjlxeXgZRECNiExVDEIRteaTu2GKPR2+5rVKphEKhR48eIUIGvKKomwYPgM1mI+uUTCbzer1kS7BarYlE4vbt27/99huUtmg0GgqF4Ldd8+6bBMnLWZebouPxstUiD3Nzc2azGVK7+CcEIzkcDq/Xm8/ny+UymFVarVa5XEYw0tWrV6vVqsfjQZFLlNhDAADP8/h87NixSCQSj8dnZmbOnj177969ji+rh4eq/SdxVy8tLU1OToZCoUKhgLSkRqPx+vXr3iSw3b5c0zq4gUC79pC/dY2Q9ib1/mbN6+yWEoI7hsNhwm8mHo0ymezUqVM73CQKio2hh1tyYWEB5hJBEFwu14ULF8CPx6xmgaNYp8lkIjyShCSDBFnhA3LAUBfv7Nmz8XhcrVbH43H4BntU2Ozfy7HD60ChUMCeQjYamNJUKpXRaOxzHeu49zEMA5qNfD5PCAk7bpTkXeBfVE31er001JOCotVqIY88l8sZjUav1+vz+cxm88bEBvHxc3NzSMoVL3TiWXnt2rUdXo62Jblc/Axv3rzJZrNms/natWs//fTT7OwsjC54ZkTHEoO9mJuVYZhAIEA+C4IAVQRLJ9lL7Hb7lStXtrvXuuXl9EDv44mRKZFInD9/3u/3JxKJ48ePg9Hs1atXYh6kdgG6vZ+bzeatW7dQ3hL//uMf/+h2YqvLON6AGL35g9d1zOaxXpfluq7Z5zE7NsnFN8pms8hTAsSrD2rMU1DsF3ScQXC6njp1Css1csAYUeEgcGCQJAfC/c3zvGyV49tisdy/f79er2Pnqtfr8/PzxWKxx633lILRDaFQaGBggCgGDMNYrVZkCYIkt592Shh4xSCsHn1ujoT/UKFQdEtSp6A4bHj27NkPP/zw/fffj4yMhMNhp9O53itIJI1Go4HgGnFxApDaMavcqju/Rm1Xjker1SoWi263G4sLFIxYLAbaQckaJE5EFv8EHzdZy+AHaGcEk8lkvYmGNo9yuUwcxx2X0X6WWvHzplKpHl235pc9vic/rdf2tklvwLpO2fxh7adsoPd6+yLWq070+HLXA65arVa5XBYEoV0yUKvVuVxuFxtGQdEnJDNoeXnZ7/ebTKaLFy+CTpBQTWA3QTCqfLXKJ0oAgYeKYRij0UhUkZs3byaTyR7RU+1330CDdxGJRMJms3k8HsITaLPZoIDNzc31uUCBC5H4iNa1D5LiqmQ3Jxkmfr9/R/qAgmKPotFoFAqFVqsVj8d//PFHQRAcDgeSb3HAhhefu3fv9ojTUavViURifygeawqdmUzG7XaTYFmGYTiOEwQhn8+3l7lA9gJJYBCva+1OW0EQUGNBLMezLLut2bF4xkwms16nh+QxmdX0DDKYKCi2G0Sk+Pr1a7vHA/TKEr1970hLFPsR2zR+cNlSqXTlypVMJnPr1i2z2Uz2ApiuFAqFXq8H1QS2Vew4YMUFSx64KGw2m8vlkqSxHVR8/Pjx5cuXqCcrLsFkMpm6VQ2TAJ0vDkmQpKiSLbvHDigJbLt06ZLVap2dnUUgMQXFYQNZKrPZLM/zPM8fPXp0bm7O4/GYTKZgMJhIJNoP7h/5fL6HExI5Dlv2MOvBuhWP3g+fTCYnJyfb81dkMtno6Ojbt29/+OEHiSzOMIzf73c6nfPz82Rhgg+E+Vcjikwm02q1AwMD4q6ES/3SpUvbuts1Go1qtdpel2O9kMlksVisz86koNhCNJtNUv8EUCgU33//Pcuy3UKt6PikWC82GaO4uLhYKpXC4XAmk8lkMvPz86VSaW5u7uzZs+fOnXO5XKBkzWQyYB8hOyhRPFBQHJ4NQRDUarVerzebzYFAwGq1CoJQLpfFpp8DP8ibzWa1Wh0dHSXbK7Na6JbjOKvV2v+lxB6P9q2t92flKhiGQVFX5HjQ4h4UhwrtgRUzMzMocIzgz2AwmMvlxsbG8vl8+/HruhGyiJl/teaTuanVaqPRqPgWO7YYbmWo1Zs3b/R6vdiqIRZxhoaGWq1WJBJpX5jAE3L06FG1Wo28c5ZlHQ7H5OQkqjGMjIygKDXDMCqVymKxiHvQYrH8+OOPcFRtE2q12pMnT1D7on1t7ROy7kXpKSi2A5J1JBaLoTALGZOIuzh+/HirbfU58AIZxfah/7hH8ZexWEyj0WAXGBkZMZlM6XT66NGjHo/HbrfLZDKDwQCWP6vVSizuxDFOoq00Gs3Q0NB3333HcRyow9+9e/fHH39IavkdkhFeqVQCgYDBYBBHKROnRyQS6b8fiKbXe/sTZ+oT2Gy2cDg8MjJy48aNVqv19etX5OgfkrdAQUEg2WEfP34MO4vf7+d53u12P3v2LBKJbPIWzWZT7AMQy8xIafN6va3d0DpaW6V4xGKxy5cvDw0NwSLSLp3LZDK73f769WtxYW9ApVIJgpDNZt2rQJZ5Pp9HfEgmk6nX68vLyxcvXmS6qG6BQODp06db8iwd8fHjx6mpKXHjN6Z4hMPhFl1qKXYcGHKFQqFYLIopNSEiiDPY6OCk2Dz6TDPDl9++fVtcXCTCsUwm43meZdlgMJhOpx0OhzjNj1mNztVoNOJoH5Zlp6env//+e4fDcfXq1Q8fPoyNjU1PT8diMaJvHM6x/e7du7Nnz+r1evBoY+6DCZ1hGIRZ9tkzvX3+SC6XrC0sy5rN5ng8Ti5yON8CBUVHLC0tJZPJYDAI84rVanW5XKVSaXh4WBwIugFPcqlU6pHdwfN8j3O3G1ugeMzMzDAMg8LS7Y9H1iCj0Tg4OOh2u8kugi+dTmcoFHr27BnKxs3MzBQKBbFpinTEwMAA2WNQxo5cx2QyiZu05X23tLT0+PFjbHs9av/1Brxa29RCCoreaDabkUikUCgQijbZaskXhULRDwkyBUUPwMZG/v3nP//Z8TBwp6LkTqPRSCaTWq2WWKxIAJVKpeI4zmg0Sox2UJvdbjfhhkZJoqmpKZ/Pl06no9Ho4uJiP9xTh2SQ53K5VCqFKuwA1AOtVqvX69d1KbBgddz+5HJ5IBDQarVqtdpoNCJC4dixYwsLC+3XOSQ9T0HREeKlsl6v37p1a3x8fGhoyGw2j42NeTyeYDAYi8WWlpba47LWNXfEQToSOBwO8WW35Ln6x2YVj0ajYbVaGRE5N9khGIZBTDmRb4xGYyKRmJqaQjyV1Wqt1Wp93qhcLovXOK1W6/F4IELBBf8f//EfOHKbOjGZTMrl8qmpKTEp8rpAavMR0PWXYicRi8UymQwmLJlKmK3kGDomKTaD3uMnFosdP348m836fL7z589bLBZCeotxCA0EtnO1Wj0wMIDMDbLegquK4ziO48bGxlKp1MrKSrFY7EZsuGFuuoOBRqOBin4GgwETH44IaHRiJvp+OqGHx0Mmk7lcrng8PjU1tbKy8vHjRzA3iq+/AdpACooDBsmMK5fL8Xgc+obb7Q6FQqFQCKExvU/sBz///LNYICcmA4VC8f79+614mg1iU4rH/Pz88PDwqVOn2iuSkL8syyKs3GKxkLrjxWIxmUz+8MMP/d9Lkmvucrmy2Ww2m9XpdHq9PhaLSbJkthC45tTUlM1me/PmDQqJwGi0LsUDdOmSy1JQ7AxyuVw8HkcZQTJPIfahqgwdkBSbgTi8SjyWarWa1+sdHBwE0S0I1mFxJ6s6US1Aoa7T6cBMpVardTqd0WgECdXIyEg2mw0EAolE4scffxTft/3zupp9UAGtLJvNGgwGKBvwFOn1epZlX7161VpPD4yMjEiCnMlKIpfLxQw8re7vRTJCDnb/U1B0BBn28/Pz2Wz23//932u1msPhOH369M8//xwKhXqcsq67HD16VCyWw3aj0+k2f/HNYIOKR7PZTCaTCDpC5KhE6wBYluV5Pp1OF4vFzXi6xfVW8SESiRSLxUgkotFo4DOq1+vb2nenT58OBAIrKyu5XI5Zf44HNt3tax4FhQSS6ZBMJsfGxkKhEAwBKN6sVqstFks8HqfFgyk2A7E0CXLzDx8++P3+dDrtcrkIvy0WQ1TPIP5qiK3QRmCiYllWo9Fg75iamvJ6vW/fvr148WLHkuGt7ltJnzvCgZd98/l8IpFAlV6lUolKJizLfvnypf+LNJtNyV7PiIyMgiBsgJv4wPc8BUVvvHjxIhKJxGIxi8XidDqPHj3666+/PnnypH9+jt4oFAoSYdVkMklsBDuPjXs8EGXbrmyQz3q9Pp1Ol0qljx8/tronF/buymazKSlnDnAcF4vFEolENBrt6JbaDnz79g0fJEUMDQaDOF2PYRjY6sLh8JEjR8SLtcfjIc+1M22mOMyQDDNQOLhcLqRa6XQ66B5erxfMfRSHBOuyN/d5cCaTicfjDodjdHR0dnbWYrHwPE/2CHGOgexfa8VC9wAblUKhKBaLwWAQ+UjLy8uNRmNbyzQdBng8HoPBIE6S5DguGAyuN2NVErBBPqhUqkAg0KL7GgVFHxCbadLpNCKsUFPLZrNJDtvkXVqtViKRILMVpsbNXHZLsMECgisrKy9fvuR5Hr5yyS4C+5bT6SyXy+SU9d4CH0ZGRtpVGoZhNBoN2Mfy+fxPP/20gadYb0vI5+XlZbh64O2B34pZDVzx+/1er9dqtfr9/ng8Pjo6Ks5+0ev1dGmm2C14PJ5wOMyyrE6ng/KMkmoajebWrVu73TqK7UWPlWdd0UrkgB9++IFwPl69elWlUrndbqfTiRwMo9E4NDREKsaSbCJimkEeOXwdarV6ampqcnISVbQlvLcU/aP9Vc7NzTkcDqVSaTAY8BaUSmUymdxAJ4sJXcR2wDNnzrT+VZyioKBYE81m886dO2az+c6dO6dPn56YmAgGg5u8YPu/tVqN0EIoFIpuZbt2EhsvIIjwJ2L7J+uRWq1OpVJer1fMoCc+Ufx9N+aTVqv1119/6fV6iYkFxhVsYy6XSxwJt5Mxo/V6PZ1OZzKZQCAwNzfn8/kUCoXRaMT6m8/njUbjvXv3Zmdn8b2YR2hnWkhB0Q5BEBKJBKgRsAbxPB+JRFiWlSQgURwe9L8cXb58OR6PRyKRfD4fi8VOnDgxMTFx4sQJxE3BHiSXy4eGhiKRCFn0YGbDkNNoNEajUaFQCIJAnGykcHV7IjKVZTeJcrlss9k4jpPJZKFQiOyhoPBfLwihvJhqTBCEFn1TFBTrR6PR8Hq9SqXSZDLBCHjy5MltmkQIcN3YxN9ybDzHQ6/Xi+0fZI8xGo29O04QhDdv3jSbTbfbbbfbO+onoD3plsSG8HSv15tIJObn51t7YNWrVCrk7ktLS4lE4smTJ3/99ZdcLhcEQUz+uxfUTYpDCBhX8vl8MBgkigfiYaxWayaTkRy8W+2k2G5s4OV+/PixXq9bLBaLxeJyuVwuF1nzEV8qZk7XaDQkgxxfEgaqWq22uLiYSqVmZ2dJY3pnaNChuGE0m81KpQL6R61We/ToUZRJkcvlkm23TyDsGUsH2ZRTqRR9RxQUG0ChUHA6nYiwUiqVVqv1/v37jUZjwxOqR2ZIvV6XkObvIjae43H58uV2xUCj0XSsIC7eQkZGRq5cuVKtVpVKpUql8vv92WxW3CPZbFbiSBE7PViWNRqNLMuGw+GdLEvUT6CC5JhCoaDVah0ORzqdJnvwwMAAXaYpdgaSkRaPx0OhUDab5TgOIS7IN+V53uVy0WF5gLGuXI5WqzU/P//mzZuXL19aLBar1YqS4VjEQE5AVmYQo5NvZDKZUqnU6XThcDgQCHAcNz4+Ho/HHz9+LCnpsGZ2X5/NphCD9Bs+rKysxONxlUqFtHJ4n4xGI7huW333MC7ocrnE2zGGhLj8aP8XpKA4nBBPkJs3b5rN5qGhIZvNxvO8yWSCaab9yI3dqJ81dlewcY/H3Nwc04aLFy+2ekYMN5tNnU7Hsmw8Hler1YODg8FgUKvVGo3GxcXFcrl8/PhxnU4n3sbEqWwGgwGEJ+AGJWba7evBPgOjOx75/v17r9frcDgSiYQ4Eb+9LgwFxQ5gaWnJ5/MZjUZk+kLxkMlkKpXK5/N9+PCBDsuDivY322OVfvfundvtdjgcoEongVJQVsWBoyipFI1GYUXC3yNHjsTj8VOnTjmdzlgsRlLDuxloeu8Xm370QwSJtlav1y9cuOBwOFCNEbuq2Ww+c+YMknPWldvTarVisRh2MVzKYDDg7fd/BQoKCqDZbN66dcvj8aRSqXA47HQ6r127tiWX7fbNeuf79mGDyeWtVuvLly+jo6MkRVWr1Y6MjLQf1uGWDMMwzNzc3NjY2MDAAKpHmc1mv9+v0+kkhQjF9hXQRtlstlQqJeY5kUQDb3mH9khE6bhNkr8///zz9evXHz16dPPmTbF36NKlS+3nUlBsOdqHrt/vl8vloA+C+ZPn+Wg06nQ6EQRIh+UBBlmafvvtt0qlUq1WkV/x5cuXarVaLpfHx8dPnjzpdDoRK2W320loDeG9bfdyI03c4XA4HI5IJDI/P48bdSvqR7F9EAsZ8/Pz8XjcYDCo1Wrs1GCVMJvN3c7qjatXr4pfvU6nMxgM2Wx2vdehoDickAioiUTi8uXLYPC7ePFix/IdW3Xf9n/3n8eDIJ1Oh8Ph2dnZ/jm8ERPs8/lGR0evXLlCuGhhVGuvjUqcHkql0mg0hkKh3h6D7dA92m/R6uO11Wo1xNDzPC/227Asuws6EfcAACAASURBVK3No6BodRmfKysrJpMpEAigODRGo91u5zju9evXu74eUWw3ms3mkSNHUGFJJpPpdLpQKOTz+Vwu1+joqNPpRF0/rMmQVsVGEyzUGo1Gq9VarVa9Xo9YLL/fj7WOJG9Q7CKazea3b99AguL1egVBgPaoUqlYlu0YHLXmrG82m+l0WmwH5DhOqVRuiZmWguKwodls5vN5v9/v8/nm5+dTqZTP5yP+w01eudVF2ej27w5js4pHD3Rz60C1UCgUBoPBbrcHAoF2F0c3mEym/VVwYHJyMhwOY/8WJ674/X7xYVTUo9gx3Lp1C9U/kWlqsVgEQVAqlbFYTHIkHZZ7Cht7HbVabWVlJRaLRSIRVG6RyWQ8z2s0mmAwGA6HwbKKBbljRSakbUDW1Gq1Xq83HA7XarXbt29Ho9Eff/zx48ePtVqtXC7TAbOLkHR+Pp8vl8tQCPHSwWJns9nS6fTGbkEq+RL3FzSZLWg9BcWhAabq/Pz806dPR0ZG7Hb7/Pz83/72tzt37hySmkXbonj03n7EXFgmkwnJD70LgWOBUyqVYHnv5y67C9K2xcXFQqGAdEyNRiOu3bvmuRQU2wGFQmEymZDmgQGpUCggU+IA6vfYefRjb17X1VKpFF4rx3FOp5NlWVLDARxHWq1WtQqZTEaYUiVaB8MwOp1ubGxsYmIikUjcunUrHo+73e4NtIpi+yB5EY1GY2lpye12+3w+s9k8MDCAeAEokBuO6LDZbFBgMJbkcrler4f/ZF/syxQUu47mam2Np0+fptPp0dFRk8l07NixQqEgYZ06wFNphzweYojTrGFpE+924g0PC5xcLrfZbIIg3Lhxo/eV9yCazeadO3dIqBUSefF0xWJxTzm/KA4J5HK51WqFuwNzEMLE1atX6QjcRWy48yWKYrlcPnfunNVq1Wg0Op2O47ihoSGy7CB5A1JjD3OPz+dD6BTHcdFolGRrbK2CRLFNKBaLc3NzkUjEYDBwHAfdEjTHarV6w5cVk77gr16vv3//PjmA2iwoKPpBtVq9f//+nTt3IN8GAoFGo4FqWodh+my94tG71wqFgmSHQ3K5hL0KKgdy1zQazYkTJ1ZWViTX35uvp71V58+fV6lUeEyximUymdqP35sPRXFgMDc3B/5c1HpjGEatVqvV6vHxcRxAR+CuAN0uJgNY10L3/v37crnscrmCwaBer0cCj9PpNJvNEmtOe3Y4sfIgtQNrryAIsVgsn8+3J++1N4yOmb0GKJ+BQMDhcPj9fmJiAKtEo9HYwDWbzabJZBJ7w9RqtdlslpQAoqCg6AYslR8/fpyZmbFYLDD/OZ1Oj8dz7969er1+SFT37fJ4dJSn5+fnxRVPidWk3dHBsiwCUtPpNEoEdrz4Xn494rYVi0VUjYV7B/YnlUp1SAYZxd7BH3/84XQ6EeKoVqsRsq/Var///ntJyinFHsfLly/xoVAowIWFeCqUqUZqONSMjp4NsuqaTCZoKT6fb2Rk5NixY90SxLvxdtAVbI8AL6LRaEAFRVDc0NCQXq9HuLLBYAgEAhu+vmTwyGQyo9EIksYWdXdQUPSHUqkUi8XGxsa0Wi3HccFgMBqNhsPher2+203bIexEjkc+nzeZTBcuXGjnSAFYlmVZluReo7S70Wjkeb5HqcV9scCRRtrtdrPZTCjwIRB0q2K+Lx6NYp/C5/MFAgGWZbVarVqtNplMer1eo9EMDAzgADr8dgXtclsP3wIKGT1+/DgSibAsS4xnqNiAdHAJAa5CodBoNGaz2Ww2WywWn8+XTCYzmcy3b9+Wl5drtZrkFpImSdpApcw9BfHbuX///smTJ/P5PMaGXC5HrB38YMViccN3aVdfVSpVPp+nw4CCon/U63W/32+z2Uwmk8PhEAQhl8sRc89hmE1brHiIl794PI7igBIXh+Qz9kjUqCKkumq1+sKFC918uPvixYgbWa/XPR6Px+PRarUsy5K8Xp/P1/F4Cortw71795LJJGpRQ+GHeMqyLI2a2F2s6cvN5XJOp3NmZkYQBJZlBwYGsIri9WHx1Gq18HUQPQRlceVyeSAQ+O67744dOzY+Pk5iqDbvxOimq1DsJEif//bbb5cvX0YFD51OZ7fbvV4vCCRVKhXRMDdw/fZNXKfT/fTTT91aQkFB0Y6lpSWn02k0GnU6Hc/zHbfdgz2JtiXHIxAIIKaIBFO1W0rEwI4ojsLSaDT7izZXAsmgyWaztVoNIdder9ftdpMnba+ESEGx3fjpp59ga7FYLJihRqPRZrPlcrndbtohhXjuLy4ufvnypdlsIhZ/fn5+ZWWlWq0qV+HxeIgTg1mtrUEyNJC9IwgCXKyorZHJZFCsemVlBQ79HqvNJhciuo7tLprN5qVLl06cOOFyuSwWi91ut9vtLMuGQqFwOLyZKzscDond0Gg0bliToaA4tDCZTCzLgs5eEvlyGNbPbQm1mp2d7ejl6AHiByBnyeVyh8MBNpX+M7D38jszmUwTExPJZBJs6GThJgfs5cZTHCRkMhmr1YoCDuJyYJuUSw48NpxX3f8Ktri4ODAw4PF4QqFQNpt1uVxer9disej1erwmhUIBRwc8w+Ka4haLxWQy+Xw+n8+Xz+dfvnxZLpfh2eiTjaqHv4KuTvsFpVIJNgWO46CIonJ5JBIBbc6G8ebNG3G8NDi4Dw8HKAXF5rGyshIIBMDpghzLeDy+uLi42+3aUWyLx2NxcbEfZUOMEydOuN1ucW0BZpV8VqVSEUNst0VtXyx20Wh0aGhIEAS9Xi9274iDbvfFg1Dsd2QymWg0GgwGSfIxrOYWi2W3m7YP0H80UQ9pXvITPlSrVZ7nGYZBLT9COA7xUaVSEe5jrI0oysHzfDweHx4eTqVScGv0uOPGnouuS/sI1WoVpehVKpVCoTCbzQaDIRwO37lzZzOXxRjw+/3YtrB0aLVaun9RULSjfS4QjqVgMGg0GtVqtdPpdLvdgiAgwWNf0CZtCbYrubwHmwpRKsT/Dg8PT09Pg5tFUtkDWy/HcSh7tH9TGycmJiYmJlQqldFohJeNeHvA3LW/Hodi/yKZTIL1SJJqZTQaq9UqHYfbgfZEiEqlkkqlyuVyLBYbGhoi7BrMKmvQ0NAQPFHiSCqDwaDVasHHPTY2FolEUqnU48ePW923OorDhvv373s8Ho1GY7fbkUI5Ozv7/v371qaHRKPRQF5sJBKRy+WUCo+CogfarT+5XO7vf//7uXPnDAZDLpcDCUT7kQcb20Wna7fb+1Q5iNM2EAjk83lSYRdRBBDQYd6Ty+Vms3mbGrwDePr06fv3748cOSIIAikiC4gDrigothuJRELCYc0wjE6nk8lkIMc8VItgP9hkh5ACfK1WK5FIzMzMJJNJGKQ5jpMsjKikoVAohoeHITUSAm6LxaLT6W7fvh2NRq9evVoul/tvasciIR3P7UFmRbH38ccff4yOjpL0LRjvgsFga+te4rdv3+r1ejabFYeI0BFCQdER4rU0EomUSiWTyaRUKq1Wq8/n83g8kiNbB302bZfiEYlEuike3bQRvV6fz+dB8YnlkmVZ7M3iIxOJRA+O3b2ParV669Yto9FIngtP+urVq91uGsWhALKW9Xq9Wq3GCESstsfjUSqVNFW0G7r5E3rsEHNzc5cvXz5+/DjHcTzPj4+Pp9NphFkqViGOp8JuBLYxhFcdP3788uXLZ8+eDYVCZ8+e9fv9sVis/3b2E221ZsrcIdkL9zUkJIoWiwVuMWa1IO+ZM2faj9z87dYbzkdBcXjQcTp4vd5KpTI4OOh2ux0ORzqdhsejz9MPBraLTrdYLBL+eElVcvIBZjzyK8dxbrd7dnYWvE8sy54+fdpqtY6Pj0tMs3q9/scffywUCoIgkGy5ffGSSKLnrVu3SKALqIR5nieH7Ytnodi/+PTpk16vF09GhUJx6tQpk8kkrtdJx6EEfcr0r1+/DoVCHo8H8p9arYanAv0MrQPTHyxVUDygcoAPl+O4K1euXLx48d69e7du3ZqdnX3x4oXkRpIPfb6ser2eTqez2WwmkxFXsK5UKh0THCVZKBR7HI1Go1gsOhwOjUZD3B0ymWxhYWGrbtE+3ujYoKCQoOMG8euvv/r9/mQyefr06XK57Pf75+bmyDp8eObRdikeKysrpD5ARxdHOp22WCwIKuA4zmg05vN5uDKuXbsWCAQcDofb7QZPC8kYgXMAH1AhRCaTXb16VXL3PYu//vrr8+fPy8vLt2/ftlqtGo0GehQehBqbKXYGiUTCZrMRjwfDMEql0uFwKBSKQqGAY/b+bNphtHdIoVCoVCrVavXevXsLCwtnzpwBL7vNZiPrHtYrrVYLCzSWRLAMyVbri7Ms6/V6TSYTqE4ikUgul+uoYGzypfj9fnESnU6ni0Qis7OzgUAA7Zmenvb7/Yeqhu7BQ7VadTqdeNHYMYeGhv766y/8upkh1FHXpQsFBUU3iGdHLpebnJy8fv06y7KRSCSfzxOht+MpB3hmbaXiIemmz58/JxKJYDDI8zxMfSSrQaVSgXPDYDBoNBqTydRO8zc/Pz89PX39+vVQKIRwVWY1BRafxaFKW/gU24dms/n582fCDSIIglwuB20XHoSWb6PYGQQCAZPJ5HQ6IfgSEVmpVBLFg6IjUC7N4XCYzebz589PTU2ZzWaFQuF2u8VUdfAmwbBC4tnIT1qtFnZog8Fw+vTpc+fOwRf6559/trpsPJsX8hwOB3Evd6P9kJSHSyQSkgZQ7H2cOXMmkUiQ9+jz+UZGRrZESaBeDgqK/iGeI7Vajed5i8VSKpUymcytW7cymUytVvv69Wu3Uw4wtivHQ4LXr18vLy8HAgGyB/M8r9frNRqNVqu12+09zm00Gig7oFKpSJ6leCNnGCabze79FyZe+svlstfrJRkskEIcDkerp9hBQbEliEQiLMuazWbCrkYkzmw2i2MO6pBbL6vsu3fv0un0xMTE+fPng8GgTqc7ffq0xWJxOp2gsuU4Djobs8rCRyJI4cGAM0Emk4VCocHBQb1e73a7Jycnc7nchw8ftsQCveYBhAW1Xc1oj4MVQ6lUrun9OKhDZb9AvGXE4/H79+87nU5inhscHEylUrvbQgqKQ44HDx7A3ufxeD59+nTjxo1Go3FoV84dUjyAaDSK1dDj8YyNjYGoSqvVxuNxckw3N9Pc3Nzi4qLZbMZOL9kmzWZzqVSKxWIwHPa+1K4D7YnH48gfhVkUelT7DrFnn4Ji/+LEiROYPsRIjzQDhmG6Jbrtd/TmcZJ8JnS3iUTC7/f7fD6bzQauC1R9YlmWyOXIBSfdiIkM9QN/WZbV6XR2uz0SiVSr1Tdv3nS8XZ8t38BZT58+JS0kyobEudGucpCfeJ5fWlrqv0spdgDdPBjFYnF8fJy4MeFVq1Qq9GVRUOw8yLzL5/MqlYrjOKfTieKwkgMOFXZU8fB4PFgNsQ1jVx4YGGiP7uj2Mkql0rt370BHK9k4p6enzWZzOBzeLzUgU6mUVqvV6/U6nQ4yn0wm02g0HQ+m0bQUWwKi9A4MDIyPj+t0OnENQYZhQHJwwEZab+dh+zder9dqtSINhuM4nU6HdYY4iIh/A9nhiLZCB4IEHL4Ok8kUCARmZmZQQqHjTbe7q4vFIuzfHRk+Oqof7XqISqUi5qEDNjb2HToOYJKfeuHCBUxqomGKyTopKCh2DGKxLZvNwjFuMpmi0SiE3kO7lu6Q4oH+dbvd2KpRc5dhGLVa7ff7xeQqklO6Xa1YLIJ1lwQ2mM1mh8MRCASQR7E336hY2vj8+bPVavX7/Xq9ngS9KBQKkisvOaV1iIcpxRai2Wzm83m32420BCJlYkqazeYDr+W2C/1XrlxxOBwej0ev15MYTnHOBpwYYKCCq1bsPYC/SC6XazQam83m9Xqr1eqnT5863rTHNx3x5MkTjUYTCoWSyWSfT0eunM1mvV6v2P7d0cshIR7s6ABhWdbv96+38RTbgR6d73A4rFYrieA1m83j4+OSs+i7o6DYYaB+tCAIYB8Rr6WHEDvq8QiFQoRNEuEHJ06cOHny5MrKSqs/CVssEo2NjRFGWugzJpMpkUg8e/bsw4cPkoP3AtpbUq1WkbvCcRzZ7DmO6xhcsXcehGL/ggQRDQwMgMcZow6x4CzLCoKw223cenScO/V6/dmzZ3NzczqdDvxyRqORuFKhdYhFcHAEAQqFgtDjjo2NcRzn9XojkcjS0hIyIrrFR/XfPIJ4PM4wjNPp1Ov1JpPpv/7rv/q/1NGjRzt6MBgROYcYhHer21nhcFhyO7ou7TA6dnilUvn9999brVYgEBDrwwaDAa4q+pooKHYMYiWfmN05jlOpVMPDwyaT6ZCnXe2c4vHp0yfQd8JkqNFo5HL5yMiIOHq4t8At+Xd5eTmRSJByBDKZTKVSud1uj8fz+PFjySl7Z9mVtOTMmTMOh0OcKM+yrLjOMQXFlmNpaWloaOj27dskZEihUKDWhE6n2+3WbTEkMy4Wi2m1Wq/X63Q6HQ6HVqsVu32I8E2+IVEr+KDX6wcGBgwGg9/v53leXM5vAz6Nftalhw8fyuVyEuXFsiw4APs5FwoV0TTEmR5iMmXypfiv0WgUW3bI3+fPn695X4rtQ/t7r9frhUIhGo3evXs3k8kQRjWZTOZ0OmHXo6Cg2GGQqfrrr79WKpVgMKjRaI4dOxaLxQ557YSdUDzQ+5FIhOzliHWD1ZDEunXcR3tvrn/99dfo6KiYp/L69euTk5ORSCQej++1KLqOnu5kMmmxWIhwA8DqvOHYDAqK3kCw4g8//DA0NCTme7VYLGq1ulgsksN2t51bCDxLqVTCMyILXGz1J3Gb5Btxz7As63Q6Jfb+VpdJLf5m831YKpWInkCaFwqFOj6j+HapVEoSN4XaR2QRJg+uUqnwE1JTBEEIh8OpVKqdIJhhGIvF0rEHKHYAHcfbp0+fGo1GMpmcmJg4cuQIyt4jzorksFJQUOw8ME8fP358584du93udDqPHDlSLBYPedzjznk8bDabxPam1+utViuRcjaGbDYrVjywm0KGcLlcW9X4zaPb8KpUKoIgKBQKceC4XC5HtBgFxTahWCxGo1FCu8kwjHIVB8wYUyqVbt68GYlEgsEgZDKJJN0tx1qpVOp0OuQ2VCqVHrfopmNsie2gVqvJZDKTySRunlwu73Y1fJnJZFCZVAzkxQFwhsCH02g0lpaWWJZ1u91fvnwR35qsqOLrzM7O9n5wih1Ds9lcWloqFArxeNxisWAfAQ55HDkFxV5AtVoNhUIOhwMhOU6nE+vnYV42uyoeW94per1e7Lg3GAx2u91ut68r1q1jq7RaLREmwLdrMpk0Go04CmLPol6vG41GcASTpECGYUwmU+twD02K7UOz2axUKm/fvvV4PESmBC2sSqW6cOECOaz9xG1qz7ou3s/xzWZzZWUFtbqJatGNN1YSWwUFzOv11mq1vRCpIo6YEiseBJKuqNVqYmojAoPBAFVKEASr1Wo0Gs1ms5iCvCOGhoYk3WU0Grf+ISn6Q3syZLPZDIVC2EeI404ulz979mz3mklBQfF/KBQKXq+XZdlwOKzVasvl8m63aJexDsVjYzIHOYsQv8CuDynHarXOz8+v91KSzw8ePCCbsUKhsNvtWq1WqVTa7fbp6enNNH4HsLCwcOrUqWw2Gw6HxRzBCoVit5tGcZBx48aNe/fuTU5OEpO2Vqs1Go1arba3oXRbdQ/Jvx2nfLd14O3bt9FoNJVK2Wy24eFhp9PJ8zx8iRJ+KrGmQWacWq12u912ux2cVNvxjBtDs9mcmZkhLZfL5aij+u7du/YjW6smcATRIXuHmDOMRmM8Hvf5fI1GIx6P5/P5NW/darUGBgbEOg9W7216WIr1otlsLi4uajQah8NBtE2lUolytBQUFLsCsjfNz88bjUZBEHQ6ncFgkISqHk5IFY+OpsTNixr1eh07FurlIe9NqVRqtVqieGw4EdPn85FNUaFQ+Hw+i8WCHdrtdm+y5duNZrN5586dV69enTx5Ejw5ZI+nbCQU24c///wzkUhYLBYYR8FwDUkd3jaCjhwPO4xuMUXHjx/P5XKBQADJCTzPG41GvV5PGKg6+jeY1bBMq9XK87zZbPZ6vSRnem/OODwRs5o0zDBMIpHoeOTr16+NRiNxksDcg97ged7j8fQZ3Yp+KJfLYs49stLSIKtdhLjbl5eXa7UaIVlhGMZkMiF8bhdbSEFB0Wq1ms3m69evDQaD2+3meV4QhAcPHtBlk9nuaApc7cmTJ9A0EHYMo51OpxseHu4zoFy8z0laSHZiZpUV1Gg0GgwGl8uVyWS26bm2EP/85z/PnTt3/vx5WGfJBk9yVPZsyyn2NUKhEM/zUHchm46Njen1er1ejwPev39fKBTAD7vd6BhA0vH7v/766927d9ls1mw2S3wX33//vd1uJ2UrJHZ6MZRKJcuydrs9kUjA8b0X9Ktu+PTpE9E6rFYrHvn69esdD/Z4PIODg+3PjpSVdVWmf/HiBegHJb2nVqs/fPiwp7rokIDwB5DODwaDZrMZqR0YGCqVClZV+oIoKHYXzWYzk8kMDw8fP37c5XKFQqE1/cyHAb2Sy7dw2Tp//rxstcwWcdZ7PJ7Nc24UCgXJpujxeE6dOpXJZCwWy927d/fF4nv37t3Z2VmO4ziOEwsKu90uioMG8XSIx+Mop0MEd0TmMAwTj8fT6XQqlcpms+0+ye2YUz2u2Ww2a7Xa1atXLRaLyWRSqVShUIjQy4phMBgMBgMRuCXxVHDs6HQ6vV4fi8XK5bIkf2PNaK5dQbPZbDQakP7F1Vffvn3bscE4QNI5MpnMarWS9bZ3b+NvtVo9e/YsKcdOLiWXy2/cuEE9HrsIdPvCwsLHjx+LxaLVarVarYyoluXQ0BB9NRQUuwXx8hgKhVwul91u5zhOo9Gk0+ldbtwewP8rHj0IUjYvcORyOSLWYEfEDjo0NNTnFTqKAj/99FN7deHx8fGRkZFcLuf1ej9+/Lgl7d9uJBIJv99vMpmwwROBaWeMzRSHDZgIbre7o0MA4gvLsmazWafTqVSqZDL5+fPn1vbPIHL9er2ezWYbjUa5XI7FYi6XS0J0y7KsmO4WDlWSQkbmEcdxqLsXjUaLxWImk7l3717vW+/NVWJgYADqhFwut9vtbrf7/fv3+Enc8sXFRRwpeacKhYKQbfT5pIFAAHaQ9jirmzdvbtuDUvSC+JVlMpm5ubmFhYXR0VHyxhFZd+PGjV1sJAUFBaZqMpl0OBwsyyIM2OVy9Z/VfIDRweNRKBTK5XI0Gu1mDtwAPnz4gCBUyAdGo/Ho0aMnTpwYGxvbcM56o9GwWq3iMADIGYVC4dWrV61Wq1Qq1Wo1cv1//vOfG27/9gHNS6fTkK70er1WqyUG2o5s/RQUm8Tc3FwymeyRAtEubur1+nPnzu1A227evJlOpzER9Ho9CSAR52wgi0OsdTD/6t+QyWRGo5HjOJvNFo1GQdy0ppF+Tzk6JJicnCQP6PP5wuFwqVQiv5LWLi8vYwGRxEep1eqff/651aUTJKrI7OxsOxWvmPWLJN/vtV46JEC3+/3++fn527dvX7lyxWQy4aXD43H16tXdbiMFBUUrmUzabDae561Wq8lkKhQKVPFoiRWPer0ei8VAi4F9HZnZW0LJt7y8DF8Hoh0MBoPT6UwkEhcvXuz/IuLdcXl5mRTAEsNutxNOnn1UlH55ednv96dSKbfbDbkBFqyTJ0/udtMoDiAikYjdbu+hdUjEViL3rytDoH8sLy+XSiWPxwM+XxLxBX+mhH4KYnR74gHDMKAN4Xne7/fH4/F2cqp10WbsKal6eHiYqFinTp3q8SKYNi+WXq9fs6QDHjYcDvt8PqLvdRwbLMu2n0ixYyAdnkql/H5/sVhMJpMggB4eHrZarV6vd2ZmZncbSUFB0Wq1UqlUJBIxm81jY2MulwtxVnvcu74D+H/FQ7zTyOVyo9EYCAQWFxdJraiNAT1brVZVKhUhdgS/ys8//3z79m3xYT2uIPmMsIr2GACdTnfp0qVWq1Wv10Hrsfdf7fLycqPRyGQyMzMzY2NjYqGKMK/t/aeg2EJsiem9Y5xko9E4f/48yOXaJdSO34h1D4PBEAgEtoqG/OXLl16vFwUlcBeFQkGCRtqzFMjqRD7LZDK1Wm2xWAKBAAzAW9KwPQW8ODFtkVKp7KFIINhG3G9Op7PjNSUYHx+fmJgApXJHvY5hGI1Gs4WecIoNgHR4LpeLxWKpVApGBFDJz8/PLy0t7W4LKSgoWq1WtVotFotut3tkZOTs2bN+v79QKFCtoyVWPCQbjNvtdjgcXq8XprVNphLGYjHxTgYNRK/X2+12yZH9mCQjkYiYyYr5V5voiRMnxOfui7e7vLwcj8ej0SiqzOh0OhJJciBlKYpukKxKG65e11F1+fPPPy0WC8lDBQEOmUSYof3EX4H2oE9jgeTLpaWl58+fe71eUopbXFeUaQvxEkdYERgMBo7jdDqd1+v1er1E0toXk31dIItYKpUSZ3j7fL7Xr193fF6xL0uhUJw5c+bvf/977+uXy2Wz2WyxWKBydFT58CKOHz/efjrFDqPZbH748KFYLF67di0UCpH5q9frxfs1BQXFDkMy9V69emWz2dxut81mc7lcVOsA/k/xePXqlWSzGRkZUSgUGo2mUqlsUoJvNpt+v18iTGg0GrvdTnIYupFpSpDJZMxms9ls7iYeGY1GUndZ0oaNNX7HsLCwUC6Xx8bGWJaF3RdenfHx8d1uGsU+hnjkh8PhbDbbQ6PooXVIdANCeyDJoSJ0n+3NQOYGqZLZ0WMpBjEuEN0DlX8ymUwul5Nc/AAv6HgilEklHaJUKsU5HmKsrKyIvUbY7dr7Bx9+++23aDTK87xGo1Gr1e1+MHJTvV5/9erVg9e9+xHVavX333///fff379/VfnOrwAAIABJREFUT7JxWJY1Go0nTpw4wHOBgmIfARax2dnZixcvDg4Oiqs7APvIOL61+P86Hii6J95yVCqVRqPZkttotVpm1aQKqVqhUJjNZnHyd3vvS75JpVKgsukoHmGDFASh237c8RZ7BGhYPB5H+TaShQ8NbbdbR7E72ORwJeJms9n88uUL6my2Q8KU2tvjwTCM1WpVKpUda190bPPy8nIkEkHmhmTCdpzF5AOI7wYGBoxG4/nz55Eb3d4/60rb2I8gT0TelEwms1qtHUPp8IFYwRmGOXLkSKVSIQcsLCyEw+GRkZFr16798ssvN2/eNBqN4jEgfgVibXNiYkJyI4rdAnkFP//8M8ImZTLZwMAAtVJRUOwiJGvjs2fPxsbGMplMJBIJBAJieo9upxwS/J/Ho9lszs7OiiUAFCTSaDSLi4ubv404SRQXV6lUHMf9+uuvHY8Xv4x6vV6v18PhMInNYNoMtNg4FQrFkSNH+qzLu3cgDr73er0GgwEptoS5H+SVh3OAHk6IdYbNX6pWqyUSifbKetA0xEInqgeCtkGSSiE58dq1a+IWkna+f/9+bm6uXC4/f/5cLpfDa0d4IHq7OMQEVhzHCYJw5syZdXVX+/eb7L29g6GhIXHUGc/z7ceQ5y0Wi2SFRMoHz/M3btzweDykbAvP8z6fLx6PI/SuBxCSJ8nUP7S2ul3H7Ozs06dPm83mkydPSE4Uis9K6gbSt0NBsTNon2uzs7MTExMcxzmdznQ6nclklpaWtiR78wDg/z0e8/Pz4iBvg8GgVqtlMlkgENj8bc6fP6/T6SSbmdVqffnyZY/eB6sjsZV2FINgGdVoNOFw+NGjR4uLi8gp319AJzx8+DCTybhcLqPReOzYMbVazXGcXC4nuaGHeaRSbADNZjOXy/l8PkEQOk4i2Sp/FP7FXNPr9U6n0+fzdUtA7yj4RiIRkrPew3Mi+V6c+qXRaBCBefHixWq1Ks5vkchS3TQNycEHBs1m88KFC6QD4Qj9888/e5yiVqs7vjvy3sEgcvr0aRL8JluthYLPKNEok8mMRiO0DnTs3uQlPyQol8ulUqlcLpfL5Xw+T3ZVlUqlVqt9Pt9uN5CC4tChfcd5+/btmzdvEonE8PCwzWabm5sThwcfvB1qvWBaol6QFANGzI9SqeQ47sWLFxu+B65//PhxsZCh1+s1Gk03xltJtEA3IBjJaDS63e5gMHjq1KmOt977QDvn5+fv3bsXCARUKpXJZEJAGh6TEpVQbAB37txRKpWDg4PdYmnIBxzgdDo1Go3f76/X6+/fv2/3kIiVhEKhUCqVIpGIxWIRc1v3CKmSuChxX41Go1Kp9Hr9wMDA3bt3+xzqvV0cB88en0gkCF2VXC7nOK7VPTy12WyKWbAkIDk2ZrM5Go0SDZMR5dUMDg5arVaWZa9cudKPX5piZ5DJZNLp9MrKypMnT86ePQv/FZyKHMeJmUjo26Gg2EmQtbdUKqVSqTt37oyOjlosloGBgbNnz0oI0A/59PyXAoInT54Ub06E4xJliZLJ5GbulEqltFot2eHcbvfCwoLkGBDLer1eBBqJ5Z5upjuGYSwWSygUymQyXq93My3cLYilpWAwODExodVqo9GoWq0mpEP7qCYJxVZhk2tTKBSy2Wx2ux3G726QeEIgxFgslm6Eqj2mZD+zFVCpVDzPx+NxVF/u/ezr0iIO6oIuTtGRyWRqtfr69evk1/anDoVC8Dv1eI8KhcLj8UQiEcKfC3VFLpcHg8FSqWS322u1Wse7HNR+3uMol8vFYnFsbCydTg8PD7vdbpgLNRqN2Wze7dZRUBxGSAxe1WpVEASn02k0Gi0Wy+jo6OfPn8Uc9DTN4188Hl+/fhXvSZJAC+xG2If66SnJMcFg8OjRo7iUTqeLx+PiX7PZbDgcdjqdZrNZQkLf/hmKELMaMKBWq51O59u3b7esV3YP4+PjwWDQbrc7HA5UPsFjWiyWDTOrUhxCFIvFiYkJi8WSyWRQkrKb9LkmJJrJus6SfIORnM/n910i1m6BKF2VSkXck3K5PBQK9VDJKpUKigKZzeYer8lgMORyOZJRhos7HA6Px7PTj0rxr+j4WnO5nNPpJHmAJpMJEblWqzWbze58IykoKCSo1+t2u51lWUEQJASMFAAj+R8RPhLRQSL9h8NhHLym+iHeF//xj3+cP3+eZVmEok5MTLx+/RpZ4waDoVuJ4m7UN2B/cjgc0Wg0kUgQs9w+1R1Js0ul0s2bN10uF8/zRqMR6St4Ix39Ofv0eSm2Fu0CaDabxdq3puOiH7RPyY6TtP0nYiAQBCEQCLx7965jaynWRLPZxDoA/U0ul4vzLrrh9OnTFoulm9KoUCjcbnc6nWZZVq/XI2QOpQmXl5d36MEoOqEbZVk6nR4YGCCxA7APOhyOUCj07du3XWsuBcUhRjv/KoKH/+3f/u3Jkyd0p2vHvygehNRVLEB0E/2Rx7YmBy7s9H/88cfc3Ny1a9dGR0dJ0XGtVmuxWJAe1yOanNwR9Jqg74BzGfXnJffdv68ZLZ+ZmXG73YFAIBQK6fX6iYkJdBfLsujM/fuAFDuD33//PRKJdFMGNoMeRgFx/gZolB48ePDmzZsrV66ICZHo6N0w7ty5Q3pbrVbfu3dvzVPK5bLX6xXH2kFpge1Gq9XqdLpisTg6Omq32w0GQ8dAZPrKdguS/p+fn5+dnQ0EAqjyBEorm80WiUTa/eH0rVFQbDfaZ1kqleJ5nuf5gYGB48eP//LLL92OPMxg2rtjbm6OZHf04NNkGEYul9tstiNHjgiCEAwGR0ZGOI4Lh8NXrlz5/vvvSTqHRqOBohKPxwVBIKfzPE9CiXp7ObDC6nQ6vV5vNpu1Wq3dbj9I0oxYa0K1eJ/PZzQaVSrV+Pi4RqNBPzx58qT9FAoKMZrN5vT0dEd9YwPqR5/kVGRBsFgsp0+ffvnyJZWEthzLy8tikgCFQiFOJiaQ9PP8/DzHccyq90mlUg0PD09PTw8PD+PL0dHRO3fu+P3+R48etZ9O39reQSaTQZVAp9MpCIJarVar1RaLBXVaWlRRpKDYDYhnXCAQMJvNLMvqdLpjx47Nzs7uYsP2LKShVq1Wq9lsPn361OVykczmNcWOftJM9Xo9oUxh2pQNprtpFslzSqUSFQZ++umn//mf/+mxwu7fZRc8ldFodHZ2FnsMygkTclJCbSx+RspueZjRMd9XzDHVe3puEmRGJxKJarW6vLzce/bt37m5W5D02LFjx8SeJeTldyQXFn/z5s0bq9UaiUQymUwgEMBe+Pz583g8XiqV2qOq6Gvag8BL0Wq1VqvV4/HA/y+Xy4eHh6PR6G63joLiUAPTc2lpKZfLabVapA+MjIy8fv16t5u2F/G/7J1PcBL3+/iBZXdZdhdCWEKIEJSUIBlRQidEIk5xxO9HFGfEGXEmOOUzIx6kB+MUL8WL9FKcKZ6kJ+Op6Yx4E2+Nx+JBPBavxmPpSTx+lt/hmb5/WyAxmgQCeV6HDEl22Qf2ee/7/byff52Gh3LK6TYVvniBAucqt+tUKpVGoyG2TUdcOKnvqVKpGIYJBoN6vT6ZTCYSiXaveXGoZ8oO4T98+NBoNDY2NoxGo8vlmpubIyX5WZbFQF7kkzidzp37Onqernwfq9UKq1hYuX5uyaOhHrN9huyz3LlzB57JWq12aWmp/amvfbfsQLxZg4J885ClWi6XHzx4YLPZyNSp0WjcbnfPs/CuIUgfIAMtl8vdunXLbrfb7XafzxcOh7futnRg6eHx6CAWi21djnP7y5qeiRzdvcaUVgoUrYpEItls9oA8Rjc2Nsrlcq1Wc7lckiTFYjGO4+CbYRjm8uXLcNgB+TaQzwK0IpFIqP7dm++TOVRb0G11mEymzbYAOiTZ+i/I5yLLssPhMJvNOp3u7Nmzyn9t4fncpvmx2WF44wZCx9eeTqfX1tYsFovdbrfZbAaDgQxwu93efTp6whGkDyjHablctlgsU1NTDodjfX0d269txr/K6W7G8vKy0WjkeV65miGJB9un28agKEqv1ytLadE0zbKs2+32eDw6nS4ajZJwgn58H4ND+QFXV1ffvHmzvLw8MTEBjRRJHBrLsj1PQRAlHbWMtmgl/lmo1eojR47AJQ54Y40BUiqVotFodym/L7gjn1WZEBkIsiw3m81QKJROp/1+vyAIUIWMJEnGYrHuU9p41xBkj1EOsY2NjVarZTabWZYNBoM4+rbg0x4PoNlsQp8pq9W6WYHOz6qwSVGU2WzmeZ6m6W+++YaU043FYpFIBFbeB7kEcrPZvHPnDhTVpSiKRFtpNJpXr161cVJBtkTZb06lUkF68fati83+jk3KEGQgeL1ep9Pp8/n0ej3YG6TGY71eH7R0CHKgqVQqly5d+vbbb3U6nSAIMzMzP/zww6CF2r9sZXgQXy2scf/4449sNlsqlURRhFp+DMN0NBeH8lPwR3it+nfIh0ajgRhlKLhpsViCweCrV68cDofb7fZ6vaROywiUx90J9Xr92LFjN2/eTCaTOp1O2d6LhFgczG8G2Q4dBoMoiltYFNsB1jqrq6uodQjSH5ThUl6vV6/XQ/NciqIMBoPRaGRZdn5+foASIgjSbrdTqdSpU6f+7//+TxTFyclJu93+4MEDdDxuxic8Hj2/slqt5vF4otFoNBr1eDxkKzQUCs3NzUGVcZVKRTITwCCB6v52u12r1bIsy7Isx3EGg4G0I9zm1Q8ODx8+lGX52bNnUNeLLAEFQTjg3wzySSAwUml7mM3mL7A3lK5LjuMG/bEQ5MAhyzK07xBFkYxHr9crSRLHceVyedACIsiBRpbllZWVfD4fi8VmZ2fj8XgwGOzwQ+KaTcl2Q62A7uDgR48ezc/Pl8tlpW0XiUTcbvfRo0dnZmZEUbTZbNFo9IcffgiHw9euXbPZbF6v1+v1Xrt2rWd/XLxDALR5bjaber1eq9WSKYemaXIMfldITyqVSkdCudls3rqLeYdnUvVP10544XQ6UdkQZCC8evUKmu2SWQDCDTweTxtnAQQZKPfv3zcYDBaL5fLly6dOnTp37hwUXyHgCO1gK8Pjk52kNjuAvHj8+HEmkyGtxDZzPGE1lZ6QDonhcBhKtsOso9Fo4vF4+8BHoyFb81l5HR3OjY7K1yqVKplMwtuisiFIP2k2m5cvX45GowsLCwzDUBTFsiz0d/r1118HLR2CHGjq9brH46FpmuO4qampZDIZj8exntXWfNrjsVtWAdaM/1wajQa0KoeEQuUqkGGYQUuH7Hfy+TwkU5HK1Ns3QnoePOgPhCAHi3q9fv78+V9++UWn00UiEafTaTAYTp8+LQiC2Wx2Op1tnC4RZKBUKhW/32+323U63eTkZL1exyCrT7KtHI8tfBS7Va0fnR49qVQq7Xa7XC6fOHECovbJtnQ6nR60dMi+RpblK1eucBwH7rLtWx2qrgp18Kvf7x/0Z0KQg8X169d//vnnsbExl8tls9lEUaQoShAE6Kh7wOdHBBks5XI5m81Wq9VoNDo3N2e1Wp8+fdrGNlaf4rN3Mb/g6/vibxxvFVCpVA4fPsxxnDIYBqJ7AfyikJ7Isjw3N+fxeLRarbLb8WbGBigY1KxTdVXB0mq1pOgcgiB9IBqNJhKJpaUljuNYlqUoyuVyFYvFVCo1aNEQ5KBz+/btSqVSq9Wg9dz58+cHLdFwgOET+xqwKJ4+fWq320VRhKKogMPh6DgMQToAxahWq7/++msikYCact2dyKHytdFohL9AuwCKomw2WyAQULbi0Wq11Wp168shCPJZbLE/urGxkU6nJUmCHD+tVut0OsPh8NraWt/FRBCk3VYMz7W1tUgkEo/HWZadnp4uFAqDFWxYQMNjv7O+vl6pVMLh8PT0NKQLwxKQZdnHjx8PWjpkv0MekX/++afX66VpOhwOd+SOGwwGs9l85MgRQRAOHz6czWZTqVQ8HrdYLIFAQPVPEw9QPJ1O1/3mbbQ6EGQHbDZ8AoGA1+tlWRaGIRR+wBK6CNJnukfo6upqIBCAzCuKon788UeIs0I+CRoe+51379799ttvsVhsZmbm2LFjZMeaoiiPx4M9a5FtIsvy4cOHBUEwGAzE5IB+ZIIgtNvtjY0N5fHNZvPRo0fRaBT6lJGiaiqVagunB4Ig26c7i1L5Op/Pe71e0nUXHvssy969exd7kyFI3+iu4NpsNvP5fDgcNvzDwsICrse2CRoeQ0C5XM7lclar1WazQfNaEvfy/fffD1o6ZGiAVh4kZgP8ZgaDwePxdJSLkGUZXkBSB8RokcYgSqcHgiA7YYtKLRsbG/F4HHrvwjOfpmmn0/n8+fO+i4kgyP8fpIuLi36/32QyORyOiYkJm82GVsf2QcNj/0JU/OrVq4FAIBwOnzp1Sq/XQ0t4Enk/WCGRfY5yNTM1NSWKokaj0el0ygSPjm5H3eTzea1WS0pjURSlTDHqeS0EQbZPTw+GJEmXL1+maRpGn1qtDoVCwWDwzZs33QcjCLJHdIy1SqUyOzur1WqtVqvZbLbb7eFwuFarDUq8oQMNjyHg3r178Xg8l8sFAgEyA5FCQ6juyGYoVzOtVgvcZSTIigRc+Xw+5fEdvH79emVlxW63k34gUP/q2rVrmOOBILtFxwhKJpOHDh2SJInjOLJZ4HA4otHooCREEKTVatlsNoPBYLPZfD7f9PT0pUuXLl++DP/FeXA7oOGxrwEl/umnn+Lx+MuXL0+ePCkIAk3TykJDgUBg0GIi+xfyHKzVajzPW61WhmHUajWkqwLQlbw72or8zGazkUjk/PnzypYgGo2GFPHAiHME+WK6Dfh6vV4oFPR6/eTkJNkvgO7IygwrHHcI0meePXt28eJFqG0dDoer1Wqr1Rq0UEMGGh7Dgc/nK5fL1Wo1FAoZDAaWZUmu4fj4OE48yCd58eIFRVGnTp0SRRE6deh0Oo1Go9Vqb9y48cnTV1dXv/vuO8gyJ0WxtFotOQCVEEF2hVqtViwWNzY29Hr91NSUyWSiaZphGJZlXS4XOQxHHIL0ExhxlUrl5s2bHMfxPG+xWILBYLlcRuf/Z4GGxz6lY/s5EonEYrFr166Fw2FJkvR6PYm20mg06XQadR3ZAlmW8/k8RVFms5lUyIFtVFEU//rrr0++Q71eTyQSp06dslgsxPCgKMrtdm9x0V39EAgygnQ7GNfX14vFIgQ3wh6BRqORJEkQBJKOhYMLQfpMo9EolUrtdjscDrMsazKZjEZjs9kctFzDBxoe+5eOqeXVq1epVGp+fj4UCvE8D6EyEG0PG884FSFbcOnSJeg+RjqUq9VqjUbjdDo/eS6o1vHjx6PR6LFjx4jW0TTNsmxHpJbyFARBtgmxOtrtdq1WYxgGrA4YboIghMPhlZWVNkZYIcjesEWJOVmWHz58CIGO8XicYZiJiYkzZ86QCpBtHJjbBg2PfUpPDW42m+FwOBgMTk5OwtY1WT5++PBhQJIi+x1ZlldWVo4cOQKLGL1eD4VxYUHzyaYcyiyRXC7n9XqNRqNGoxkfH4c31Gg0nzwXQZBPIssyjMfjx49Dyyb4qVar3W7369evu7dXcYghyG6xheWwurr6559/FgqF9+/fp9Ppc+fO+Xy+W7du9V3GUQANjyFAOQxqtdrhw4ftdvvU1BSJeNFoNMFgsOMUnJAQQiqVAmtBrVYzDCMIgsViASNkO6crd3SSyWSpVLLb7fBu0BiEpumex7dxYYQgm9M9Uu7duyfLsiAIZrMZnB4Oh8NqtaZSqa1PRxBk5/QcU61W6+3bt6urq36/X5IkqOj43//+d319HcfgF4CGx/6le066f/++0+mcmJgIBoOSJEGMPmkmuLa2hp4+RAmxP10uF0VRECyu0WiMRqPBYNBoNKIotretMLIs1+v1paWlcrlcKBQgAJ3syJrN5u7jd/0TIcjooTTsG43G+vo6FOs0m808z4uiaLFY/H5/e5MIkH6LiyAjTffSa319PRKJnDx5cnFx0Ww2Ly8vNxoN0jEQx+DngobHPmUzVV5dXc3n8/l8PhKJ0DSt7CS4vLzcZyGRoeD06dMMw0A1KihmdeLECaPRqFarJUn65EOz5wGZTEYQBEEQlO0s4/H4ZscjCNKTjgDx27dvp1Ipk8kkCAIUoNPpdA8fPpydnR2omAhyIOg5fxWLxWQy6XA4BEHweDzxeLxSqfRftpEBDY/9yxbZulevXjUajZOTkyzLOp1OcH1MT0/jmg8hEGVgGAZ6d0BgHk3T0P+IoqhcLve57wasrq5Go1GbzabT6RiGAduDpun79+/v8sdAkAMAjK///Oc/ly5dWl5ehn5NkENlsVh8Pt/MzEx35is+8BFkL1COrPX19XQ6HQwGZ2ZmpqenY7FYNpvFobcT0PAYDpRaXq/X3W63JEk6nY7neYPBAAtKnuc/fvw4QCGRfcjq6ipJJYd0IJZloVqO1WrdyTvncrlQKMQwDNS2Uv8D5tshyJfRaDTS6TSkY5nNZmibMzMzE4lEOo4kUZS4AEKQ3YWMqadPn378+PHdu3cQauV0OkOh0PZ365DNQMNj+Mhms9FoVBAEjUaj1+sh4ArWlFDcDQ7DCWl42cXk7IWFBbVaDUFWKpWKZVnI7tDpdLVabYdy5nK5QCAwNzcH/hNSKWuLTq6olgiyGc1mMxAIWK1WjuMMBgNYIIFAIJvNDlo0BDkQkBmq0Wj4fL5MJtNutx8/fhyPxz0ez+rq6kClGxHQ8Bg+arVas9n0+XySJBmNRpLp0V1cCBlGOhqKffz4cSeLdbfbrVKpBEEgAVFardZisYyPj0NPgJ0AWeZ37951OBwGg4FEc9lstp7Ho1WMIFvgdDr1er0oihRFiaJ48uRJiqIYhsnn820cNQjSR7xer9vthr464XA4kUhcuHDh+fPng5ZrFEDDY1hZW1sLh8NKjwdN02q1GixynKJGhi++lXDi0tIS2BsMw7AsS9O0IAgOh8NisXi93p0LViqVarVasViEqHRIN9JoNAsLC1uc1UYVRZB/U6vVjEaj2+12uVw0TWu1Wr1ebzAYXC4XHIBDBkH6gyzLfr//+vXrsD2XyWSSyeRPP/2E89eugIbHsFKtVqempqCXAknt5TjO4XAMWjRkp+ziQ+3YsWNQ95aiqFAo5PV6PR5PsVi02+3pdHq3rtVqtTwej16vZxhGp9NB0V6IhcUnNYJsjSzLb968KZVKmUwmEAhABw8ofs0wjMfjGbSACHIQef78eSqVev/+/ZEjR44fP3727Nk2TmS7ARoew4csy5VKpVgsiqIIsfUQxK9Wq0VR5Diu0WiQIwcrKrJzdngT8/m8yWSC/HJYxPh8vkuXLl29erX977CuHVKpVPx+P8/zOp2OdFzurv6BvQURpJtWq5VOp/1+v9Pp1Gq1pPg1y7KkdSCOFwTpAzDQfv/995mZmXv37p08eXJqaur27dvQuAOH4c5Bw2PIAKVvtVqlUsnlckGHKbA6aJqenp4mJU1xeAw7O/cVyLL83XffgYZAMN709HQqlbp//37PRsg7ERJwu92CIMDl4Ip///33dk5EkAOO3+83Go3KhD0IuKpWqzhYEKRvwHBLJBJnzpxxuVxQ5uHZs2ftf0/KOCq/GDQ8hpVms7m6uspxHDSZgrkKzA9BEHZesAgZLLsSoVSpVCALCDqL+3y+RCJx6tSper2+sbGxW0FQSrfJ+vr68ePHoV8h+D2sVitxwe3K5RBkJKlWq6R3B0VRHMep1eqvvvqKHIADB0H6w8ePH+/fv1+r1eLx+KFDh3K5HDZo3kXQ8BhKZFl+8ODBoUOHILIFQuphjxnWfFAFBTngBINB2DeFsA2fzxcOh51OZzAY3PmbbxamlcvlINkDmntoNBqO4969e7fzKyLISNJoNJrNZrlcBhcHOAy1Wi1N02tra4OWDkEOHLIsP3z4MBQKxWKxSCTy9u3bNlr+uwcaHsPK2tqa2+1eWlryeDwkvxymK3jdcTyOmQMI9AGA3hparVaSJJfLFYvFHjx40O5SiZ7ZFx21fXtepePvlUolEAhMTExAqxlQS47jNjseQQ4ypOmN3W4H3zXJ2XM6nQMVDUEOBMopKZ/P1+v1v/76CzIh0fLfC9DwGGKq1Womk/H5fHq9HpaYKpUKZiyVSuX3+9u7mj2M7EM2u7+yLMdiMeitAVVueZ6naToQCPj9/kqlsk0roudftj6r2WyurKwsLS2ZzWZSYFelUikbpaNCIgeTbs1//vx5uVxeWVmBatdkF4miqA8fPgxESAQZbbbYUGs2m/AilUpZLJZyudx/8UYeNDyGFRgt0WjU4XCYzWaz2SxJEkS2wDqPoqjff/+951nISKK8ua9evbp8+TJ0mYROLwaDQRTFSCRy69at7bzPl6kKOcvhcKRSKa1WC6GAoJPhcBgtYQRRcu/evUKhsLi4CNl6JGFPEITt+BsRBNkhZHD9+eef6XQafj1//vzS0lK9Xseht+ug4TF8KMsp3Lhx49q1axaLxWQy2e12aHyr+oeOFHMcP6NHd4I4vHjz5o3NZmP+gaIomqYdDkc2m23/WxN6BlzBT/BdnD179vr1658rmNVqrVQqMzMzJpMJokdgH/fcuXM9r4sgBwqi/3/99VckErly5QoMWI7jjEajXq/neb7jYBwyCLJ3NJvNarXq8XiSyeT9+/cXFxdPnDhx586dQcs1gqDhMazAJPT27dtEIuFyufx+v9/vP3ToEKQRg+ERCoV6Rs7gBDZidK9LTp48SeKsJiYmwBy12+3bjFhttVrEggWbgaIoo9H45s2b9ia2Sgf1ej2TyVSrVbvdDgpJ3qejyBWCHBB6jpRisVgsFhOJhMVigUQsnuehBt0nz0UQ5Mvo3rO7c+dOJpNxuVwej+f9+/cbGxs3b94cnICjDBoeww2E8sfj8XA47HA4nE4nqXAF28zdxw9ETqSfFItFnuchPUWdAAAgAElEQVRZloUSZ9C5XKVSjY+Pr62tbR2/Icvy9evXZ2ZmVF2ARkmS1NNy6PailEqlSCSi0+l4nge1hGbMbrcb9RA5aPTUeZ/P5/f7k8nkgwcPbDYbZOsZDAan09lz2whBkN1COb7evn174sSJubm5dDptMpmazWalUsG2BHsEGh6jQD6fLxQK58+fHxsbY1lWuViMRqMdB+NkNpIob2sgEBAEATq6QIVljuNommZZFnqvbvEmRqORZVnoPk7cFCRJA/7icDg6CvL+73//6363er1+7969ycnJmZkZyDJnWRbe6sqVK6iHyEGjY5jU6/VgMHj06FGO48xms9Fo5Hk+Eok4nc5YLAbH4DBBkD4gy3IwGDxx4oTNZltcXHz8+HGhUBi0UCMLGh6jgCzLqVTK6XQyDKNcL6pUqtOnTw9aOqRPkDWKKIomkwk8HlBIV61W63Q6l8v18ePHnqe02+14PO7xeJQ2BsFgMGg0Gng3iqJEUdTr9ZtdXfmrLMuTk5OiKEKxNXC8QMk1jJ1FDiDKYfL69etgMHj48OGTJ08yDAPjVK/Xh8PhYrG4xYkIguw6kUgkGAxSFLW0tIS+jj0FDY8RIZFIjI2NwdSlNDzUanUqlRq0dMieQ9YlrVYrFouFw2Hi5RBFEUyFLTRhYmKCRGQpnRsqlYqmaY/Hc/ToUUmSJEmChoDKAPStK/B6vV6wVYxGIxTt0Wg0kiQ5HI4tzkKQkSefz6fT6Wg0yvM8KXttNpvT6fSgRUOQA4Qsy+Vy+erVqz6fz2w253K5QUs04qDhMWT03FeGlm2Q/gvF4Ek3D5VK5Xa7NzsdGT3W1ta++eabqakps9ms1WpJcwCXy9URd0eUIRQKdRgbyhcajUYUxXA4nEqlrl69yjBMNBqFYueb1dRS8ttvv+n1epqmzWbz+Pi4xWKhKAqcJx2pe6TsAWopMpJ0DJNcLpfJZOLxONj8MOJMJhO0SUYQpA9UKpVEIpFOp+12ezAYDAQCjUYD56A9BQ2PIYaMjWazGY/HbTabw+Fwu92CIJDaVpDUq9zqxhE1wsiyXCqVfD6fx+OB5b5arRZFEdJVnzx50nFwu90meeTE0ugADI94PJ5IJD6ZItLz9dLSkk6n0+v109PT4XBY2awgkUh0lFlD/UQOCNls9urVqzMzMwzDkAF4/PjxQcuFIAeI8+fPT01NORwOu92eSCQePXrUarXgXzgZ7RFoeAw3ZIe4UCgsLCxYLJZUKmUwGMxms06nIwvKCxcuKI9HRpj19fVyuTw5OclxHKR5QE8AlmWfPXsGxyjVgDTZ6HZ6AGNjY6FQyO/3d19rmw6KYrFoMpk8Hs+xY8dsNhvEgJHaa7/99tvnviGCDB0dui3L8pMnT1KplLLYtM1mi8ViW5v3CILsCjAYbTabIAharTabzUaj0Wq1ihthew0aHkNJ9/pMluW7d+9OTExcuHDBZDKReH2Yz7Rabc+zkNHjw4cP0WhUkiRRFGmaJnF3FEV1x+nNzMyQri89rQ61Ws2yrN/vX1lZaW/u0/jkk/r169crKytQ3kqlUkFdXY1Go1arFxYWlCeifiIHhEKhYDabTSYTibMiLT4RBOkD9Xrd4XBwHDc9PX3z5s1yuYzTUB9Aw2PI2CyYvtlsrq6uGo1Gm83m8/lgq1u5lJyZmdkiEB8ZJaxWqyiKpIMHGB5ms7njMEmSeiZ1KH0garXa4/EQ1zNhMxXa+ql98uRJKBsCspFowGQy+cl3RpBRIp1OB4NBm80GI1SlUnEcZ7fbV1dXBy0aghwIZFmOx+PBYNBoNHq93l9//bX7gIEINvKg4TF8bGY/vHv3bnp6OpPJxGIxm80GlVJgd1mlUvE8330KMgJ0rPWbzSa0ywAvB0VRkOkRCoU6TtwsqQMAc0WSpG6rY5sidb/IZDJ2u52mab1eD209yLWgkk/PfiAIMnpcuXLFaDTCbiuMRHAtViqVQYuGIKPP+vp6o9G4cOGCz+dzu93ZbJY0xkWnx16DhsdwoxwbjUajXC5Ho9GFhQVJkkwmk9lsJms7MDy6z0JGiXq9fuHCBVjKQ/EoSZJYlnU4HMrC5KAAZMXT7fHQaDR6vT4QCGznop+lTmtra7DDBKYRubooivi4Rw4I5XI5FApB5hUZdDMzM/l8ftCiIciBoFQq1ev1q1evQnwjtgvsJ2h4jA4wkNxudywWg/qnXq8XFpHwExt6jCpksf7kyZMjR45AnJVOp4Me5DRNWyyW7rOKxWIwGFxcXOx2d2g0mr2rZX7v3j2XywVCEtuDoijo1rx1VxAEGVKU3r90Ou1wOCD/itj8wWAQ08oRpA+8fv06nU4nk8l8Pn/69Olbt24pa5wgew0aHqPD27dvs9lsMBiMxWKSJEHHaIi3gRWe2Wx+8+bNoMVEdhnlujyfz8/NzQmCQNO0zWZjWZaiKEEQSFmzbi5fvtzRN1ClUgmCsHfL/VardfbsWai6RlLbQVGhYbPS9YFuEGSUAE2+f/9+LBaDTjtg50NY46ClQ5CRhUwi1WoVqleNj4/ncrk3b968efMGp5h+gobHSPHHH3/EYjGfzxcKhfL5/Pz8POx8k1h/aDiNY2z0kGX52bNnoVAoHA6PjY0xDGMwGKAFhyAIEGfV877ncrloNCqKImSGaDSaTCaz1xpy6dIlhmHAQIKLgu3hdDo/fPiwp5dGkMGyvr6ey+UsFgtsDKn+aZXz7t27QYuGIKNPNBpdWlqKx+OiKP7yyy+DFucggobHqJHNZqENZyaTEUWRoiiO42BrGfa/By0gslfUajW73W4wGPR6vVarhfYdgUDghx9+aCusjo2NDZ/P9/LlS8gaJ39vNBrVanVjY2PvJCTui0wmQ1HUoUOH7Ha70+kkbT0oirJarZudtXeCIUh/gDY7wWCQZdmvv/7aYDCAr89qtTabzUFLhyAjC8wgP/74YygU8vl8oigGg8Fms/kF1VOQHYKGx6hx6dKlfD6/vLwci8VIKw9S4Eij0eTzeVzDjQzKW1ksFjmOM5lMBoMB6ilPT0/H4/F0Oq087NatW9DO3Ov1Xrx4sVwuv3//vg+llpXvvLa2Fg6Hg8FgKBTyeDxer1er1QqCAOr6+++/d5yCtgcyAoACJxIJnuc1Gg08nxmG0Wq12yzkgCDIFwBD7/nz58lkMpvN6nQ6rVZbKBSePn2qPADpD2h4jCAbGxsvXrzIZrN6vZ5hGJjhiPnhcDgGLSCyJ0QiEYZh4JEKjf9YlnU6neVyWXnYysqKSqWyWCwcx/E8bzabXS4XtGvt80J/ZWXlwoUL8Xj8woULoijqdDoIu7LZbMrDcEpARolSqWSxWEgTG61Wq9FogsFgG1UdQfYMWZar1Wo8Hvd4PDzPp9PpSqWC1asHAhoeI0u1WnW73Q6HQxRFSZIYhoE+1ocOHSL1qpFhR7lSuXjxIk3T4OugKIrneYPBYDQalc9WCHOCoCaDwQDNOtRqNdge7T4ufeBC586di0ajuVzOZDJxHKfT6aACGyTaYstLZGRotVq///57Op0ulUqBQIBlWVB1GIn1eh3degiyp6RSqQsXLni9XqvVmslk2jjcBgQaHiMIjKVyuexwOJxOp06n43meOPfJ7hoySrRarXA4rNfrXS4X3Gi73e7z+bpDOPL5PBSSstlsk5OT8NrlcmWz2T7I2f2gh4T4WCxmMplYliXeue6OhwgyvJRKJdhthaLnpNC5Wq2ORCJwDC6DEGSPePLkid/v93g8yWTy1q1bKysrg5bo4IKGx+ignLSazWYsFotGo/F4PJFIQEkr8OxrNBq/34+7a6OHJEmiKEJbQI1GQ9N0oVAg5gS515VKhRgesABSqVQcx3m93q3T7PZIWyDX9tq1a998841WqwWnDdT52dPrIshe0PPRms1mQ6FQKBRyu93VavX06dOknhXLsr/88gsqOYLsEbIsp1Kpcrm8sLDg8XgKhUJHFMAAZTuYoOExUpAhVCqVEolEJBJxu92zs7NQXxVyPGia5jhuT4sXIQPBaDSCRwvWNHq9PhKJdC+DZFkmzezdbrfFYgFDxWAwpFKpjuimx48fQwjWnpJOpxcWFsrlsslkApMJPkI0GsVZARk6ukMEY7GYxWIRBMFqtZ47d87pdJKku8nJSVRyBNkhykHXPeuFQqFgMKjT6ZLJZM+zkH6ChscIAmOp1WrF4/FcLhePx5eWloxGIwT0w6quY/gpT0SGjnK5XKlUoGEL1KVVqVSSJMFd7rA62u02aRZut9v1er1erwdzJRgMZjKZZDK5vLw8OTlptVrhmL3ueS/LcrlcTiaTCwsLEBMI8tA0ffLkSWXWO4LsZ7pXP+12+/nz51arFbyRBoPB5/ORelYTExM//fTT4ORFkBGhY45QjsS1tbVUKiUIAsuyt27d2uY7IHsHGh6jTKlUarVa2WzWaDRCqwTYZoOYfhxmI8PVq1f9fj+Uo9VoNFBIwOPxpNPp7oNlWSZNM8xms8fj8fl8giBAATRwlej1erVazTAMy7Iul+v69evK1PPd1RzynpFIxGq1Tk1NwU4wy7IqlYplWcgCRJChQ+nxyGQyLpdLkiS73Q4abjAYEolEG1c8CLIb9Jye/v777/Pnz58/f97pdIqiCL10uw9D+gkaHqNDz1GXTCYTicSlS5cCgYBarRYEAQwPlUqlXJXiIBxeksmkWq22Wq00TY+NjdH/sLCwUK/XOw6GGw2lPFUqlcFgyOVyHo/H7XZDFhB00oAXGo3G7XZPTk7Ozs7Cyqm9N6oC7ykIQjwedzqdFEWRFjQgya5fEUH2FOWGa7PZ/O677wKBgN1uNxqN0DSQpmmtVqv0JWLeHYLsOrVabXV19fDhw1NTU3fv3u05ynDQ9Rmc0UcK5aCCn7FYLJFILC8vu91urVYLu8iAXq/v6F2NDCOxWMzr9QYCAZ1OJ0kSlOk0GAznzp1rb7KaIUkUkOmxsLBgsVjAy6H6N6dPnx4fH4f6vHsacCXLcjabnZyc1Ov1FouF53kIGwMnjNFo3LtLI8ieks/noYSu3++Hom2g1QzDkGO64yERBNkhrVbr7du3mUxGq9XOzMy8fv26+xgcbv0HDY8Rp1qt5vP5aDQqiqJWq+2wPWZnZwctILJTYFnjcDjMZrMgCJBfbrFYNgtmlWVZr9crnRs3b97kOM5oNCqdDBCL5fF4Hj58qNVqjx071t7LUCvg8uXLFoslHo9D5xmlMD3DxhBkf6LU6pWVlXw+L4qiwWCAonNqtXpsbGx5eXmAEiLIiNE9MVUqFYfDIUmSzWaz2+3r6+vbPxfZO9DwGCm6B8/Kyso333wTj8cPHTpkNBphOxyiaFQqlVarHYicyC6ysbGRy+UgxwMMD+hK/ubNm81OEUWRLOjVavXRo0cpirJYLEpfB+kz4Ha73W53PB7vz8f56aefotGo0+mEgDGIuQIriITnIsgQsbGxUa1WwbYH1yIkeJADcNGDILtLs9lst9uxWIzneVEUf/jhh1wu13EMjrtBgYbH6LO6umqxWCRJ0ul0RqNRmWKuUqlIeSschEPK999/HwwGPR4PTdPpdFqr1dpsNpPJtEVTDqW7gxiiNput4y8URQmCkM1m+6wbx48fLxaLZrOZoiij0ajT6SD/BNqZt1FXkeFBluWVlZWZmRkSNwjVBd1u9zZP/+RfEATpqGFdKpXOnTsH6YIOhyMej//+++8DFRD5/6DhMfoUi0WHw5FKpcLhMMuyHMeR3GKoXNTGyWx46LhTsVjMbDYbDAYSSgcZ4YFAYLMliyzLyhAmcIJpNBqTyQQqARkgLMuyLOt0OuHc//3vf334UPDi0aNHqVRqbGyM4zio0EVyzQuFAuYFIsOCLMulUml+ft5gMJAcKoqiKIry+XzKwz75Ptu/YntvQiIRZN/S3a/T5/PB1KbVaiVJgjorOCL2CWh4HAiKxWKpVCqVSkePHpUkiYSvwMb2y5cvBy0g8gl6PjE9Hg84smia/uqrrzwej0aj0ev1Ho9nC3fHs2fPVL2AlHSdTgevwRoplUrbFGaHdNgeuVzO4XC4XC5l0BfsGUPvS5xCkKEgk8msrKzY7XabzQa2B0VRDodj+/Yz/Ovp06fRaDQSiczOzpLR3bNtyCffEEFGEqLzHz58SKfTBoPBZrO5XK7Lly+3cUTsJ9DwGH1gvK2trf3+++/nzp0bGxsbGxvjeZ5se588eXLQMiKfzcrKSiQS0ev1RqNREITJyUmapqGwVUc+RscDNx6P97Q6YHPo8ePHHMexLDsxMRGLxfrzWXpu0J47d252dlar1UJoChHVZrP1PB1B9hV//fVXu91eXV39888/FxYWSLlqiqK8Xi85bGvtrdVqc3NzBoOBpumZmRmGYTiOO3HiRKvVevfuXc/TcTggB5lCobC+vn7+/PlsNlsqlZLJ5NOnT+FfODT2CWh4HBSePn365s2b+fl5SZKmpqaUmcQURa2srOCYHCLW19d9Pl80Gj1+/Dgkqs7NzWk0mmPHjrlcrmw2C4d1uBGAjpq56n9QqVQcx3m9Xr/f35GY3jfdUF6o2WwGg0EIHgOjiMhMCvui0iL7ll9++eXy5cuTk5NnzpyxWCxk3ImieP/+/e7jO5R5Y2Pj3r17LMuC4a3X6/1+P8/z4KYeHx8PBoP5fP7ixYubvQOCHDQ2NjZ++OGHRCIRjUah8RR4yNs4OvYTaHiMPjDeXr9+nU6n3W73hQsXFhYWoMs1ySQOhUKDFhPZLnBDnU6nxWIRRZHjOJ1OB/GsPM/b7fZ8Pt/T5Gi329VqVWlyKC0QhmESicSff/7ZfdZAkGW5XC6HQiG/388wzNjYGOTmQv7JoKVDkN6QsbOysnLq1CmapvV6PencKoriwsLCb7/99snTodaccntIFEUyZlmW9fl8oVBIp9MJglAoFHq+CYIcHLLZbDqdXlpaikajT548AZejEhwX+wQ0PA4Q0WjU7/dfvHjxwYMHdrudlNZVqVQ8zw9aOuTTkOfm1atXk8mkTqcjdaisVqvVanU6ncTd0XEW/EylUj3dHWq12u/397zWZjLs+ofqyfXr13O53JEjRwwGA2z9Ajqdbo/kQZAvRqmNsVjs66+/BrNZp9NBhhLHccePH9/iHQqFgtfrtVqt3d08O3rs2Gw2n88HDhDscoMcZF68eJHJZObm5m7durW0tNRsNru33nCm2D+g4XGACAQCdrvd6/Xm8/lKpSKKIgSxwNTVsWeG7DfIc7NarYbD4VKpJIoirMVFUfT7/adOnXrx4sUff/yxxbmRSES5gjGZTFDGymg0KsvsdJwF9KyUtbt0v3+z2bx582YgEIDtXmVBtlQqhXMJsg8BtSwUChaLxel0kt0BhmF8Pt+jR482OxGaeG5mbCihKAq668CvWq12bGys0WhgPSvkAGIwGCKRSDgcvnbtGir//mf4DA/Uqi8AvrTV1dVYLOZyuQqFwt9//0166MLUpdfrO47Hr3rfks1mg8EgdCJjGMZsNodCoWQyCfmmWwB1osiahmEYlmWNRqMoit0FrJQKEA6HDQZDsVjc/Q+zDYrFosVigTq/RGnVanW5XB6IPAiyNYVCIRKJMAwzPj6u9C5uYd4bDAZlIx0wJyC8UAn8heM4nuddLhfZPFKpVDqdDkYoPrqREaZDvY8ePQphh4cPH8ZmHUPBvjM8tlMTEJ+qX0a1Wk2lUpFI5MqVK9FoVKfT6fV65TIUij+g1bHPqVQq0Wj06tWrZrOZ53mGYRwOx8WLF7ez5lAubhiGEUWRpmmLxTI+Pv727Vs4pvsd8vk8z/OxWKxv/csJIEylUkmlUkajUavV0jTNMAy4erqTPVB7kYHz559/WiwWGGssyxKDQa1WHzlypN1LS2VZnpqa6o6nIr9qNBqWZTUaDU3T8FZ6vV4URVEUlfsIPM+vrq62cQggo0i3VkOt6lwud+nSpbGxsffv36Pm73/2neGxBdVqFcP1vgDld1WtVsvlcrlcDofDMEuR1mwqlcpsNre7psM2ftv7BrgR6XSapmmDwTA2NkbTNMuyk5OTwWCww2XR04ZXrmzI8iUejyeTyZ53+fnz53q9HlqFxGIxh8Ph8Xi2SI3dRTrkSaVSEF3GcZzRaCQ7wcvLy9s5HUH6yenTp6enp8lYIxGtYBX0JJPJ9IyzguSQiYmJsbExi8XCcZzFYmEYxmg0Op1OZbU3QRAsFovH40HbAxltSBAHz/Nms9nj8WQymbW1tY4DkP3JcBgeT58+ffr0ac9dosEJNUyQL6pSqZAXFovFZrORcqUAmRfRxtuftFqtdDoNQVaHDx+G7U+73d4RON7z9tXr9Y5YDgjTOn36NFGMDtxuN5SypShqenoavA2kQOFeoxzyxWKxUCgsLCywLMswDKlwpdVqNzsRQQZCo9FwuVzK2g8kdGrrmg3Q6wNyroirBFwf+XwePH4sy/I8z/M8KbdArBSHw8HzPE3TNE339xMjSL9pNBonT5602WxGozGVSmF9hSFi/xoePffacT3xxcBX12w2M5lMMpn0er0sy1osFrvdrgwd3rr3HDJwZFlOJBIURUHQBdy7a9eu9Yyz6hhEtVqtw+NBURR4M2q1Wve1UqmUVquFEA7I6lar1ZIk7f2n/P/CKwHVtVqtLMuCLaRSqViW7ehbgkqLDJBarSZJEs/zExMTEAdFspI+OXacTqfRaOQ4DkIKld4Pn883NzcXCoVyudzbt29rtZrH49Hr9crDSL6Hx+Ppz4dFkEFx4sSJS5cuBYPBaDTa8wCcCPYt+9Tw6F4/YfzPTiDf1bt37+7cueNyuWApCVHC4PTQ6XSwnMVWuPuWDx8+JJNJKIWsUqlIXX+DwdBsNjsO7hgmsiwXi0XlUgZCOCDaquPEdDo9NjbGcRxJpSD1dhKJRH8+LBGGDP9Go5FKpW7cuMHz/Pj4OGlqrlarO4oIo8Yig+LevXter3dmZsZmsxkMBmXclNFoBNfiZs/Y1dXV27dvHz9+nLig9Xq90Wj0er2tVqvjYAACL8klYP+IZdl8Pt+Xj4sgg8Htdkej0VQqlUwmBy0L8nnsU8OjveXSAVcV26fDYHvw4MFff/0VCAQkSWJZ1uVy+Xy+mZkZZT+Hjmgr/Lb3D7VaLZfLEXtAp9OB/fDVV1+RY7a4X7FYTKX6V6tyiLYyGAzKw8xmM1nHQK1ehmGIq8Rms+3hJ/w33QFj2Wx2cXFREARwepAtXoZh+iYVgmzG2tpapVL55Zdf7Hb77OyssvqzSqWan5+HDYLNBmmr1bp+/brZbIYwLafTub6+Dv/aIvaVpHkwDANGCLQX3LNPiSADA/QfmuScPXu20WhgJ4ChY/8aHsheAEbFysoK9PRwu93BYDAUCpFiRyqVyu/3o7GxD6lWq9VqNR6P8zwP+5o2m42maYqicrncdqzEY8eOqf6NWq02m83z8/NwwIsXLzrSYVUqFQR+kF/77PFo/9sA3tjYOHTokNFoNJvNkHBCkj2gNILyFATpM4VCoVarBYPB2dnZZDJJRhyMoAsXLmznTdxu96lTp7aZSfX06VMyWg0GA8Mwer1eq9VGIpGdfRQE2afU6/WpqalDhw798ssvHz58aOMDf9hAw+Ngkc/n8/l8PB53Op3RaBR+ulwunud7NvRA9hWVSiUcDkNVTY1Gk0wmIZwjGAx+8lwSaqU0LSBX9fz589VqNZfLKcsrK40TWDaZzWav17uystKHT7oFjx49CgQCgUDA6XRCQ2gi6p9//kkO26IKRXdYGoJ8GR0G//r6+sOHDwOBAMuyoih6vV7o0Qk9y2OxmPKs7b//Fv/K5XLE46HRaPR6PUTSplKpHX0wBBkcW6h9KpUym83T09PpdDqfzzcajX4KhuwKaHgcOG7evBmLxf773/+ura0VCoVwOHzs2DGygNNoNDzPv3//XnmKMrwYGRQfPnzw+/0Mw8A6hqZpu93OMMzExEQ0Gt26DAMpLUByxFUqFUVRJDBDaWYoLROKonieV6lUNE1funSprx94Ez5+/JhIJHw+35kzZ8DjQcqynT17dutzcWMM2XWUSnXv3r3//Oc/0OySpmmtVmu1WtVqNU3TJpNJ6cTYFVWMx+MOh0O5TQAxtDRNHzlyBA1sZHjZbIDcuHHDYDAcP35clmXU8CEFDY8DR6vVSiQSa2trqVSq0WhEIpHDhw9DHzpYw1EUJUlSvV4ftKTIv7h3754kSRDG7XQ6WZZlWVav158/f54EgvdE+QQnOeJgeCjtjW5fh0ql0ul0xN3RarU6LNJBkcvlzpw5Ew6HBUGAigigt2q1erMIEywPjewpoFeXL19eXFw0mUzQY4fY+SaTKZ1Obz9rrltduz146+vrTqcT9g6U/mqTycSybCgU2vXPiCCDpVgs5vP5QqGQy+UGLQvy5aDhMfp0T125XK5Wqz158qTRaKTTaUEQoMgV9BMkBRlxibZ/qFarP/30k9/v53leEITx8XGwQDwez507d7a/lFlcXNzCzFD9u9guuL8sFovD4QCv1/5RiUgkIgjC0aNHjUYj2B6kZ0LHkftHZmRk2Eypstms0+mMx+MsywaDQeJa9Pl8sDvwBUFWPUtgxeNxm81GEpzIT5qm5+bmZmdnexbIRpAhRZblWCzm8/ni8Xi5XB54xC+yE9DwOBB0TF21Wi2ZTP71119Pnjz55ptvYM8MesmRBZzVau15LjIocrmcIAhOp1OSJK1WCybi2NjYJytNd/yqLL65hRHC8/zx48e/++677l7LA1cJWZZfvnxpNpsvXrxotVoZhmFZljhweJ7f4sR+yomMMD11KZ/Ph8NhnU5nNBohcQ6qz507d26zU7Z/FXhdKBTOnDlDfH0d+wV6vd7r9VarVVR1ZGQol8uLi4sMwwiCEI1Gnz9/Dn9HJR9S0PA4QHRUf19bW0un0zabjed5vV4PNeNh9abRaKDXFVbU3SdUq1WHw8FxnM1ms1qtZKdTr7PtWXoAACAASURBVNc/efKkreh1s0VSNXDu3LmtrQ6NRqPVaicnJ3/99dfu0/ePMiQSCaPRGAgEBEHgOE75oUhLqZ7S7p+PgIwASteEy+UymUw0TYP3GLSRYZiLFy/u/ELJZHJtbQ1qgXSYHOTnJ5UfQYYI0OHTp08bjUa9Xm+z2UgMIS5Ohhc0PEafnu0Xnz59ms1mL168+PXXX1utVtg8I/MZtGbDvjz7itu3b8/OztpsNlhkQAopz/PffPMNOWY7fTZlWZ6YmOjYKAVYloU0iWQyud9iqwgd9rPX6zWbzaSXInwojuMajUZ3C8XBSIyMIt3qtLKyIkmSJEkcx01MTECbHa1WGw6HX758+Vnq112HLRqN2mw2qKDdbW+o/ikFYTab379/j6qOjADkAW4ymRYXF8PhMBRz39qlj+x/0PAYcbYYk/V6fX19PRwOQ1lSk8kExVVhGoPKjP0UFdmCRqPh8XjAMqQoymAwuFyueDwuCMIXRHE0Gg2DwUDTNNk3hTx1p9PJ8/x///tf5cEdhuu+4s2bN6lUymq1ms1mUlSUbP2SMPd9Kz8ySkQiEZ1O5/f7FxcXQ6EQPEij0SipovvFlEolZY/X7i0DjUbjdDrtdns2m92Vz4Ig+4dAIODz+crlckcZK3ywDykDNjw+GRZyEHC73bDij8fjfb50rVa7fPnyq1evUqnU3bt3OY6DHA9SjAV6guKecZ/p/p4TiYTf7+c4Du6OTqfz+Xwul8tms+Xz+S+4xPPnz+Px+NjYmNvt9vv9TqezUqk0Go196+jYgsOHD1utVghFU67J3G73oEVDDhA+n8/v91ssFrfbDT5kiqKcTufODY9arQa63WFsgB0CxbUtFsvPP/+8Kx8EQQYLTEDVavXZs2e1Wi0UCm2nVxUyLAzM8OhYyx7YThHNZlOSJDKXjI+Pd9ex3btYxmq1Gg6Hf/7556+//vrIkSMQbaXcUfP5fD1PHK6F6XDR7UeuVquSJNntdkEQaJqG6pxOp9Pj8cTj8WKxuPOrDBf/+9//lL/m83m/3z89PQ3tzMmyTKPRDPXHRPYzHapVrVZPnz4di8VEUYRBqtFozGZzIBDYZg/yzS4hy3Iul2MYRunQAw2HUC6tVqvRaC5fvrwLnwpB+ssWj+i7d+9+8803oVDo3r173TVOkOEFQ636inKMZTKZWCzm9XqhQZtyRlG2ZdjrlVO1Wl1ZWYFe5jRNdyTpdhcnbe+lIYS0e32x0WjUYrEYDAae58HpwbKswWAwGAxf1p94qO9gt9iVSmV+fj4SiczOzkJbd1LhSpKkIf2YyHDx4MGD5eXllZUVklMO9ayuXbu28zev1WqCIHQ094QXFEWdPHmyp22Dmo8MEUp1bbVasDqanJxcWVlBTR4x9oXhcdC0Spbl9fV1SZKsVutmlUk67Pu9+IrIe66urqZSqR9//FGv10N3CLCFQJ6OoOGhXrMOHbIsb2xszM/PGwwGk8kUCoVOnjwJkRU0TRsMBuIf+9w78lldzPY/gUDgl19+uXXrFkVRUJyNpK+k0+mOg4focyHDwtraWq1WM5vNJE5Vo9FMTEx8caezDi1NJBLd7g69Xh8MBlut1naqSiDIfqNn7ZN2u51IJBKJRDAYnJmZQU0ePQaf43HQnpLwSScnJzUajTJstyNZkOO47tTYvfuWXr586XK5OI6DCvSSJJF129TUVIf8B+dm7RO+//57yJ8OhUIul4thGIZhjEbj+fPnX7x40XHw1ndnm1lVwzIqlRI2m81Xr16trKy4XC5lWw9Jkp49ezYsnwgZRtbX10OhUDKZhLrkZAuJZdkvCxEh6ko0tlAoKD0egMPh6A7NRZAhontK+vbbb4PBYCQS8fl81Wq1jc/tkWNfeDwOGvV6naKobqd5x6Si1+v3tGyc8t2q1Sr09IDqRnq9nvhelLWtsIxdPyGLj6WlJVEUw+Hwt99+e/z48UOHDmk0GpPJlEgklP2Jd+t2DN0anYharVYrlUo0GtXr9ZDjQdZ/7aH6RMhQABrVaDRKpVIikTCZTKIoQhtWUDybzbZbF7p+/Xp3PSudTud0Okul0q5cBUEGTiwWCwaDFy5cOHHiBFR1x9o2owcaHn2FjByPx9NhcvRs5eZyufo22DKZzPj4eCQSgf50LMuCQ59l2Uaj0R8ZkHbXDtDff/9948YNk8nE87zBYGBZluM4lmUlSbpz584O31/5l9EoMZdKpVwuFzSiIU4P1T/tzIf3cyH7DVIWZWVl5fvvv5ckaXp62uv1Hjt2DB7mFEXtSikeYt6YTKbuOQLsalJhAjUcGV7W19fT6bTL5XI4HI8ePUJv3qiyLwyPA/isNJvNHZZGT8NDpVKtr6/35/tZWVkRBCGRSMDSFvaMVSqVVqstlUq4qTZA8vm8Xq/X6XRqtRpq5hw5csTr9X5BFMcndWkEBmM4HHa5XHa7naZprVZLRlb/y1Ujo40sy69evfrjjz8ePHggSZLL5YpEIlNTU7CRJEkSOCR3a0zl83kyUyh95lqtVpmJNwJDGDmYZLPZH374YWlpCer4I6PKvjA8DhqyLPv9/p5mRjd9W/Hn8/nZ2VlRFFmWPX78OMnxUKlUoijOz8/3Rwykg7W1tXg8bjQaWZbVarWiKGq12kAg4Pf78encTalUCgaD6XT64sWLUOEKAFt6Y2NjNBw7yD6h0WjkcrlYLGa1Wp1OZzqdDofDLMsyDBONRnf9cuFw2GAwcBwniqKyn6DJZKrVaqjPyHCh1NjZ2Vm73Q7ZHQMUCekDaHj0j45ZweFwKCPRYQerux9tMpnsPnd35YEXjx49MhqNHMdBY2yom0S8MVqtduuPg+wu8PXW6/VkMnnnzh1BEMbHxxmGoShKq9UGg0GPx/PFBXNGFVmWi8ViIpGAmHun00lRFE3TDMOA6wM3hpHdpVAoJBKJtbU1u90uSZLf75ckSRRFi8Vy9erVDkN3t644Pj4O1XWhhyA8pQ8dOvTixYtff/11dy+HIH3g4cOH8/Pzdru9WCx2tCdHRg80PPpKxyRULpd//PHH2dlZnU4XDAZ7xu+eP3++57m7Lk+r1QqHw4FAwG63WywWMDyUhpDS94KLtj2iYz8+GAxarVZoUuFwOMgep8VimZ2dfffu3QBF3bc0Go1IJOLxeGKxmMViAfOeaLIy3xeLJSBfBlGVYrF49epVeGDqdDrwGHMc53Q6iQ2w63rlcrnm5+fVajWUjSa6PTEx4XQ6d/daCLJztk4Qf/r06crKyt27d91u9+PHj/srGjIA0PDoE5sFeMiynEqlUqnU8+fPSQF45c9MJtPe4yURefNGo1GtVnO5nCAIgiDo9XpBEIjhAb6XzT4UsouQLxYCh+bn5z0ez9dff82yLGxzSpIUCoUGK+T+BL66GzdumM3mK1euCIJgs9l0Oh0pNKRSqWiabqP2IjtDluXHjx+fO3fOZrPxPE9RlNvtTiaTFEVJkgSxqXunY81mMxAIQAyhTqcjT2mz2Xzjxo09vTSC7JAO5QwEAl6v99tvv83n84MSCeknaHgMjI49gGw2Cy1vO1AGCvdhLkkkElarVa1WC4KgjLbSaDRHjx59+fLlXgtwwOnQikuXLnk8Hr1eD1HdUOyYYRiLxQIFzpHNuHPnTqlU8nq9t27d8vl8ysEFLqNBC4gMN61WK5fLnT17NhaLHTp0CJ6Zc3NzWq12enr69u3bfZDh2rVrqVTKYDAop4x+1kJEkG2yWe3EcDg8MTFRLBZ/++23gQmH9Bc0PPrNZsVMf/75526rQ9Wr7/Kekslk8vk8WB0dkmg0GofD0U9hDiykgKbP5/P5fCzL6nS68fFxqHE8Pj5ut9vfv3+Py4stkGV5fX09EokUCoVisWg2m6HGLsmkAl9iewj7liD7gWKxuLy8fP369fn5eYfDAeWbIeDq7NmzrVar3ZfcvGaz6Xa71Wo1iYxVq9WBQGDXr4sgO0T5pIV8vFwu9/z587t377bbbUjtwOfwQQANj31BLpdTusuV7NHG9mYxl9VqNRKJuN1u4vFQlrdSq9V7IQyihNyRN2/eBAIB6FMOgRwURbEsC9YIlrTqSceOWjqdPnXqVDgcPnfuHHR2Uw400qAGZzvkc7l48eLi4uLly5cTicTExASpFDI+Pr7XY7NDXTOZjF6vn56eVqlUYF1fvnx5TwVAkJ0Au0J2u93pdBaLxVarhb3CDhRoePSbnksc6NnX0/DY06jHbmHu3r0bCAScTqfb7YY2CErXh1qtTiQSeycPoiSfz/M8r9PpKIqCnyqViud5v9+/uLg4aOn2I936XK1WL126ND09vbS0ZLfbKYoymUwk7AoDrpAvY2NjIxaLhcNhj8cTCoU8Hg/P81A8bW5ujpTl6U9uXrvdzmazfr8f4jBVKhVN02tra3t3aQT5XJTqWq1WY7GYJEkWi+Xs2bNYxuqggYbHvsDn8ykX90rDo88L/VKp5HQ6E4nE+Pg47K/zPK+Ux2Qy9VOeg0wymRRFUa/XUxQFHSe1Wi3HcX6/f3p6GjfptwN8S36/f35+PhAIGAwGKEBE7HzMxEW+gEajEY1G0+m03++3Wq3j4+NQXUqj0Tx48GAgIhWLRQgjhHhCo9G4sbExEEkQRElHeMXKykqpVCoUCsFgMBQKBQIBZe4oPooPAmh4DBgYZpIkdfs61Go1z/Nut7uf8qyuro6Pj0MwDxgeyha5KpVqYmJiL4rTIx00Go1EIgENVaAfGbg7AoGAzWYrl8uDFnBoAF198eLF9PR0NpsVBEGj0Wi1WtI/5+LFi+2uCQ8TP5AtKJfLhw4d8ng8ExMTUPgBwpwEQeg+uD9a9P79+1OnTsGzWqPR+Hw+7PODDIQtFH59fT0ajcbj8fX19Xq9XigUuuMS8ak78qDhsS8gVWs73B0URX38+LGf43B1ddXj8czOzk5NTel0OqPR2GELGQwGWKghewfccZ/Px/O8IAhGo1GtVnMcVywWk8lkPB4vl8v4dP5cjh49mkwmoZ055AETrf7w4QMcs1ntBwRRUi6XFxcXb9++bTQaGYaBOtc0TafT6UGZrPV63e/3Qxgh5DKR8labFXNHkL1D6eiA161WK51OOxyOYrEIe2cd6eaDExbpK2h47AugrbLS9gCnOU3TfR6Nq6ursVjszJkzExMTJpPJ7/crzSHIXPT5fP0U6WAiyzI4N+ALpyiK47hHjx7FYrE//vhj0NINGTCI4vH4t99+Oz8/L4oieDwgbUalUsXjcTQ5kO2TzWZTqVQkEoHoR7BmtVotFLMi9FmFFhcXSWQspDN1C4NajQyKVqsVjUZ9Pl88Hr9161ahUEBtPJig4TF4Pn78CJ76nvz99999lieZTM7Pz/v9frVaDfVbYRqjKAoqt4ii2GeRDhrwOD569CjkQ1utVrPZHAgEisXiiRMnVldX27iA2B5ks42Qy+W8Xq/FYlGr1QzDgFHN83zHWT1fIwjg8Ximp6cdDgeYHJBZ0dE1vM+aI8tyo9GA0rrwxDYajZDCNCiREITQarWy2azL5ZqYmAiHw1euXPn9998HLRQyGNDwGDxPnz6FqI+OOCsAjunbhAELtUQiMT09bTKZIOtdWYQUhHz27BnOYXtHq9UqFosmkwmKWdE0bbFY/H4/FM/B9q6fi1JXY7FYIpHweDywXgTTWqvVXrt2bbNTEKSDmZmZixcvBgIBnudJoQJoczQQq5VcCHzU8KDW6/XKFEFUaWSAlMtlm81msViy2WyxWPzhhx/aqJMHFTQ8Bk88Hod5oqOirkajYVl2ICKtr69PTk7Ozc3Nzs6StS/JMler1R17e8ju8vLly4WFhdnZWZqmeZ6HWkyTk5OnT58+duxYrVYbtIBDQ/cq8MqVK0eOHLFYLKIogm5DAKFKpTp69Ggb50JkGyQSiWAwKAgCPBXBiM1ms+SA/msRXDGVSsEmEXRSpyiqVCp1H4Yge01HaF+tVovFYrdv365Wqz2Nc9TMgwMaHoMnl8txHAchwkq/B0VRAyxL8vbt21gslsvl7HY7ZJtAtBXIptPpBiXYQSCbzZrNZqvVCq1UdDqdwWBwOBzLy8vKxQ3yZaysrLAsy3Gc1WoF20P9Dx1fL86FSE8qlUo4HIYKaaSI7crKyqDlaicSCRIfy7Ks2WzuzuJFkL5BquMsLy9D3LiyyjNaHQcTNDwGz8bGhtFoBHeHMsVcr9e3Bzogv//++0KhsLCwQDaGyZSGS7Q9JZ1OC4LgcDgMBoPdbjebzWaz2ePxPHv2DGvz75yXL18GAoGvv/7a7/dDO3Oi1Wq1etDS9eDevXvxeDwcDjudTr/fP2hxDhY9n2zxeNzj8TAMQ9M0qI3FYllfX//ku62srDAMc/78+U82TdvMVNj6SetwOGAS0el0Op3O5/P9/PPPn5QKQXaLDv0MBALwyMIS8AgBDY/Bk8vlYNusI7uD5HAPZE2/trbmdrsLhcLVq1ez2SyUANLr9cQ6oiiqWCx2nIXmx67gcDi0Wi1YHaIojo2NmUymYDBI1hD4PW+TzdZt6+vr2Ww2kUgcPXoUVJq0M4dpclDfcM/rTk9PMwxD/I0Mw+As3k86bkqtVguHw5FIBEpIaTQajUYTDAa3ozOZTIam6cnJyaNHj6bT6a0vRP7Ys8lMzyMjkQjYQqDPBoPh5s2b+LhA+gnRtzdv3kQikbNnz3b/CznIoOGxL4AJrMP2CAaDg5Xq2bNn9Xp9bm4umUza7Xbozqv0zNhstk/u2yGfhSzLfr/fYDBQFCVJ0rFjxywWC8MwHMcdOnRIWeIMn+A7pFAoXL9+3WazMf8A406r1S4tLbV7Lfj2lFKpVC6Xw+FwIBBYWFgAqx4ECIVCYPMruX37dhvVoL+0Wq1cLnf9+nWe51mWJRsxarU6kUh88nRZli9cuACnGI3Gw4cP5/P5x48fk/92HLz9X4H5+XmO44iGQIhspVLpFmM7HxZBvhhZln/88cc//vgjk8lkMpl8Po+lAhECGh6Dp9lsGo3GjgQPlUrl8XiUh/VzrBIvf71ej8VioVAIHPcURSnjUnQ6HamwhMGau0WlUhEEQa1Wm0wmu92u1WoZhnE6nYuLi41Go933BfGws0V0+/fff8+yLMuyEKxPFpEqlWp5eblvEqZSKVEUSUoPPArgvmez2Y2Nja+++qrbKapWq9H26BvwJedyuQcPHiwvL3McBzeL3I6t8/HIPVJG1UqSVCqVwPP2WTexpx/vxYsX09PTysrs0O+15/EIsqecO3cuFAoVCoV4PK4cGrhOQNpoeOwHoKoViaNQhloNpCBJx1W+++675eVl2HRX9lyDXtrffvtt97n4TNkJpVLJYDDodDq9Xg+NJjiOkyRpfHxc2Z4Mv+TtsNk2G3ltMpmgNQ0s9JWL+4cPH+7Fl6x8z99++81qtSpHPalbrVKpaJpmWVan0wmCoOpCrVYfOXJk18VDNqPRaLhcrnQ6Dck2HMcJggANYViWhe46WwD3PRqNkjsoSZLT6fR6vRzHKfNDOhZnn1RCsDqgC63SI61Wq+12e/fbIsieUq/Xb9y44fF4nE5nJBIhf0erAwHQ8Bgwsiw7HA7lVqtKpYIKV3q93uPxDGSskj11ctHjx49D6DCUACKt1mFiUx6Mz5Sd8OrVq6tXr9rtdp/Pp9PptFrt5OQky7Lj4+PK0Dv8krfJFjoJfywUCmNjY4cOHdLpdLBbTEaiIAh7/T2HQiGlqdOzk4/qn1IT3QfwPC9JEtYb6A+lUikUCpVKJfBD0jQNiTcsy26/vPjp06fJfdRoNAzDHDp0CEwXm83WXRdrC9Ulr9++fet2u0EkpXpoNBqHw7HN/BAE2TmgXfl83u12T09Pnzp1SrlZ1sZFAtJut9HwGDjVapWmaVKyVml42O32fdIq7t27dx6PRxRFURRJ7UjVP71HxsfHyZH4QNkhf/zxx7Vr16xW68zMjCAIDMOYzeYLFy5YrdZQKKQ8Er/qbbKF6Q5/qdfr5XLZ4XCQBghkXdgR7ri7IlUqFZ7nuwOoiAzKGnebGScsy5JdbVSJPaVcLh89enR+fh76Y8BTmqKomZmZarX6ydPh7rx7967jdnfcUFEUK5XKq1ev1tfXIT0DTlxbW4P3yefzsVgsmUx6vd58Pn/mzJlgMEjTtEaj6Ujw0Gg0PM/v5VeCIJ3cv38/HA5LkuT3+7eogYEPq4MMGh4DplKpKOcJ5VID+uAOhO6HQiKREEWRZVll0wOVSsUwDMuyZFJEdkgmk7l48SKE/UAJY5PJ5HK5QqHQdhY3SE+2zmt8/fp1u92ORqOSJCkjCWFxGQ6H90IYWZZTqZQyhqp7DdpBdzSmSqWC3Qqs8bCnwC3LZDLz8/P/j72zCU4ia/t++OhuaPojhO4Qxu7goITgbSvBCg6KZawbnwqKVYNVYpVYMvWIi4kLmRpmI25kNmLVZFYyK5nVMPWIuxt3E5eTWUxcGrfGpbgaXU7zLq53TvXdJDFq+Ehy/RaphHTDofuc09f/nOsDMs5BdAfckVwu90Hv5vP5RgybHqQSiPG20jRttVopivL7/a1Wi2VZWJmCTTmbzeZwOLxer6Zps7OzRL6SHkIcrrLZbG8uCYKsQ7VajcVisiw7nc5z584Z/4XB5QgBhceAWVhYWNfagG2QQbfu/1Ov15eWlnw+n8fjEQQhGAy63W6Lge68kMgWMU3BS0tLcG2hG4iiSNM0OHhsfiLyKTx69EhRFJZlIb+cUQzYbLaVlRVy5Da6CkiSZBr1604FxhdNUSgjIyOQcBmFxydCypxtxIsXLwqFgqZpXq8XtiJH/snCvPVPgY+o1+vGfS2GYURRNN10okZIYlyTOJFlmed5mqYvX74syzLpKsalK0EQujOeI0iPWFxcfPbsWSAQiMVimqa9ePGig88pZD1QeAyYRqNBPKyMMR5ut/vOnTuDbt3/B5JIplKpL774gud5cGs2LtSNjo7i/PLRGC/dwsICxM9ATLnD4ZBluVAoLC8vY2Te9mK6jLlczufzOZ1OWD8m/oQURXm9XqPPwHZpD5O5Cd4yZB7o1hgWi2V8fNx4lsViOXfuXDAYxC7xibz3Aj58+LBQKHg8HkmSJElyOp2gPRiG+dCP0HWdVGLlOG52djYWi5Fszt36YV1HO9gqsdvtLpfLlBERUoDQNF0oFD7poiDIxpimwZcvXxaLxWKxSDY6cFJCNgKFx4CBlFZk8Yw8PzweD9g6Axy9xo9utVpPnz796aefZmZmrFarw+GgKIrYQBaL5ezZs4Nt7U7ENHe/fft2dnYWDFCLxaIoitVq9Xg8Dx48MB7f/TvycZiu/9zcnM1mc7lcpPwz+QlpSdc9/aOBFQfjB5FfBEEQBMHn8zEMYzRJR0ZGXC4XdA9oaqVSSaVSn9IMhLDJDQWjShAE8IEE495qtXIc9xEfMTs7CyLTbrdPTU2dPn16//79DMOs2xm698FMB5BtOnI8RVEDLwOF7GJMI6VSqRSLxfPnzxeLxZcvX250GIIAKDwGTCAQMC1WjYyM2Gw2RVE2Twzfa0xTRrPZXF5erlarx44dgwcb2EbkWUjqrHefi2yC8Vpls9lkMknMSijsUCqVTE7keHl7RLFYtFgsLpeL4ziiCsjYXFhY2JZPIbePlFwwWpZ2u93hcExPTzudznK5vLy8XCqVoD8YMzqAyUvTdKVS2ZZWIZug6/qrV68ePHgwOTnpcDiMjlJbz2dlfLdOp1MqlRiGUVX1ypUrCwsLo6OjxqogGwEhdut2G6MsYVk2nU6bPhTnDaRH3Lx5s9ForBuFiL0O6QaFx4CJx+OmpwhkrfV6vffv3x9smlrTJxYKhVwu5/V6TXHwRDLByitONB+BruvtdrtcLkPCHMs/GWmcTqcxwybueGwv3ddwenra5/NJkgQO9EbtYbPZ9u/fvy2XHd6E1OIktiPESi0vL0OlSPg9FouRNphiA0yJzpDeAbuOi4uLoPdA+6mq+t7yHRtB4j2ePn366NGjer0OKXFHNtjigOUekttjxBAHMjIyQmr+wAE8zxsLg3T++yGCUweyLei6/u7dOwgov3LlSvdYwJ6GrAsKjwGTSqXWXdmy2+3dJaX6NozX/aBKpRKNRhVFIQEepmfkxMREf5q3K2m326lUimTLgWVLu91uykuD2mPbMV7GZrMZiURu3brFcRxUFQQTHyw8q9VKErh9+sU3lg2haRoUpult8/m83+8nex3GKSKVSkHUO3aDHkEu7OLiYj6fb7Va2WzWarWCle9yuUKh0KNHjz70+huPTyaTrVYLdGapVIrFYhD+IYpi9003hh5Z/km/DvI1Go16PB7IjuBwOGZmZjb/XAT5dNbW1m7duhUKhX788cfuzJbY35CNQOExYBYXF42PFrKPPz09bTqy/6rD9In37t3L5XL5fD6TyQiCAC7ORkuIoihjmVJkc0yXt9FoJJPJsbEx2PIaGRlxOp2BQKD7SGRb2OiqwuvHjx8XRdHtdoPvEyxyg0LofNpCADn38OHDZOx3x2nMzc0FAgGXy0UMTRClsNYuCALZFfnE9iDvJZ/Pz8/Pnzp1imEYkvvBZrPFYrGPvuYbVQacm5tTFEWSpOnpaeLvZ8yk3L3iAyLE6XSGw+FIJPLo0aNP+7oI8n5WV1c1TVNVNZ/P4/yDfBAoPAYPx3Gmp4jVavX7/aaSn/2ku9gtKbV28eLFaDQaDocVRZFl2bj1YbFY3G43lpvYOqbrXC6XGYaBVU+WZUdHR/Fi9ofuR2a1WoVgD+JwRX5+hFv/uh905swZMuqNocBra2uJRAJyx8FsAMfAKwzDhMPhwQaA7XqMt2l5eRlWW7xeL5TWIZvSUOD1g6yuTQ4j/1pdXa1Wq+Pj44qifPbZZ4FAIBgMOp1OjuPcbjep2uF0OqG2EsMwbrfb6XQuLCxs5f0R5BNZXV198uRJLBaLxWIQTYQdD9k6KDz6TfcgNHpbgZ0BFkY4HM7nhDBC6wAAIABJREFU8/V6HQqcfejb9mi0v3r1KhQK+Xy+QCAgiiLJBUwgZhmmf90co72yurq6uLgYCARgMdtqtQaDQYZhjKWLkf4AVxuqtgmCQDKfGvnuu+86Gy9ab/GDnj17RkQFx3Fv3rwh50qSBJ76xmBiqJMdiUS6i7og20L3vWs2m/l8/tKlS4lEAkIsZFm22+2Qbu7+/fu9a0y73W40GrVarVarZTKZVqu1trbWarXq9bqmaadPn/7mm28eP36saZrD4eA4rlQqoR8m0gcg8AyKdczNza2trQ26RcgOA4XH9rO4uMiy7KFDh8hydavVyufz6XT65MmTi4uL4JldrVZrtVqz2RRF0eiz1J20BBLauFyuYDCYTqdJKeVNxEZPtz5jsZjf749EItPT0xD5amrwAPdqdhbG+3X8+HGfz2f5h0AgwDDMhxZFRj4R48ApFouKokA2BZPwEATBmDXSdPrWcbvd8IaiKH755Zfw4u3bt6PR6J07d+LxuDGS2Ol0qqqKex39JJ1OR6PRZDIJkd8QdgVhP2fPnjWmihpIAN7m7oIIsu00m01N02RZ9nq98XjcWFwVQbYICo/tJx6PW61WiqIYhhkfH4eqZLBBT9M0PL3AxBz573ydm+RrH/lvZw9RFCGhzSYCY9ufPfCG7Xb72rVr0Wj07Nmz165dO3z4sCiKpnZC4Sp8+G2dt2/f7t+/X1VVCNx3u91Hjx5NpVL5fP63334bdOv2KJBoSJIksq1nXCAIBAIfl6LUOGa/+uor49D+/PPPL1y4EIvF7Ha7z+cLBoM8z8OHhsPhaDR64cIFHFa9w3Rt3759G41GNU27dOnS6OioKIqCIMB2B8uyv/zyy0BatcmLCLK9mFTumzdvotHogQMHAoHA5cuXuwPKEWQroPDYfi5duqQoysg/QYHWfyAmy+HDh43BghtBFr83OkAQhJs3b/b5CfT27dtGozE5Ofnll1/CYjCJMietPXLkSD+btNOBOxiNRh0OB9SM8/v9U1NToVDo+fPng27d3kXXdY/Hc+7cOVORBPIzGo0aD/6I9+90OuDKRYa5ca4w5q3OZrOLi4vtdns7vyHShVEWtlotv9/v8Xi8Xq8oivA7wzA2m+3o0aPG47t/38bGdD68CgfKEmQbId3p5s2b6XS6UCikUqnurJsIskVQeGw/jx8/Pnz4sDEkFHbn17VdjK+sqz02Fyc8z5Pk2f0Z/LquP3v2LJlMwk4OeB0Qa4n8NGWRRzaC3LVkMkl8+gVB4DjO7/cvLi7inD5A1tbWisWiKIpkCBuHpM1mMx78cabh6urqxMSEaVyT2QNGlizLH/1ByEdTLBZDodDNmzdHR0fHxsY4jnM6ndAHnjx50uuACqME2tylCvsD0mt0XW+1Wo1GIx6PJ5PJc+fOPXz4sPMJ2hjZy6Dw2H50Xdc0rduMMCWf3Yqu2FyKwG7DRgGO2zsLGN9tZWXlm2++KRQK0WjUbrdTFEXSPpK2kbq5OBltkVwuR0pZUxTFsqwkST/88EMHr2HfMdpzsPtE07TT6TT2c9jfW7f4xlbe3Pgpfr/fNHzIXGG3271er6ZpHXy095huE+rKlSvT09OnT5+GKDvYgKJpWlXVdQNqe7fjse6bwyt///331k9BkI9maWlpZmbmu+++e/DgAYZ2IJ8CCo9tBub6Wq1mtCGgpqxJORj9NzYRIabXiY8WeZ2iKGNMRR8eNvV6Xdf1+/fvFwoFCFaB9WCjsvJ4POteGaQbXdf/+OMPSZKgaIPNZqMoiqZpj8dz9+7dQbdur/Pbb78dOXLk9OnTkM4I+jkpGu1yubpP2XpXhyMDgcAmCw0WiyWdTuPw6TO6rpfL5XPnzqmqapx1BUGAAvN9aMCnnIgdBtkudF3PZDL5fF5RFExWiXw6KDx6RSaTgeAHVVVVVe3e7oD6AJtjUh0biROfz/frr792t6F3K3Bv3749ffp0JpMpFouQZRI8ykjuUbvdHgwGcZJ6L2tray9evLhy5QqpB2+z2XieBxPnxYsXg27gngb67bfffuv3+ycnJ3meh/KONE2TiHNJkj6le6+urr434mthYWH7vhPyfnRdP3fuXLlcTqVSHo/HeC+y2exAElj150QE6aZSqezfv79UKoHkNvUuFLrIh4LCY/shI7BWq4XDYYgSlmX5888/B/nBcRxFUWDEjIyMWK1WYxAI/AKihWTBomna5XJBgh2TtxXLspFIpM/fsVqtXrx4EXL+QFNZloXYaLCewQXLdEGQbr766qtGoxGLxcCXg6IoSZLArR+KyuHVGwZu377t8/lgS4oIbDISwRVqi5huaCaTgc3PTTJJHDt2DJ/uPaX7wiaTyVAodPz4cZZlYSEARihsLyPIbsW4XNhut4PBIMuysVisXC4/ffp0sG1DdgcoPHrOnTt35ufn//3vf8/NzXm9XqgKV6/XoRRUoVAYHx9XVfXSpUt+vx9qgQuCEI1Gi8ViPB5fWlpqt9uvX7/udDq1Wi0YDEJMBWTsFUWxWq0O5HvNzc1JkuTxeMBggn2P0dFRsKJAYvW0wNaOxqhOC4XCv/71r4mJCbvd7nQ6fT6fKIqyLFerVTQ3h4Rms/n06dNqtSpJEsdx4+PjxvUCiqJu3769lffpvpVer7d7O9QETdOvXr1a93SkR8zOziqKUiqVOI4jyQntdjuWS0P2AjDVLC8vJxIJRVFyudyjR48G3Shkl4DCo7d8UIGn7uDRde3OFy9e1Ov1ZrNJChT2ge6YxdnZWUmSVFWFkGir1epyuWCLhvjBF4tFNJU2J51Oa5omCILD4RBF0WazSZKkaVo0Gv32228H3TrETKPRmJubCwaDoLeJZmAYBkzS93Z444JiKpVyOBzrbnTAEjvZCZEkKRAI9PzrIZ1Op9N5+PDh2bNnRVGEPS6STsDoPooguxLSw1utViwWy+fzsO65urrawbUPZDtA4TEAjHlINhnGG+UnGdTIN7Xh5s2bs7Oz+XzearXCsxnioY3G0/HjxwfS1B2Brutv376dm5s7cuQI+KeNj4+Dq1U2my0Wi1gAftiAMhqzs7OJRIKkICOygef5LVbUIkNJUZR1PawsFgvkb4WIdhLL3v+6PXuTdru9sLCQTCY9Hk80GoX5zWKxXLhwYdBNQ5CeYJpYKpVKJpMJhULXrl3rbLAGiiAfBwqPvrJusPUHDemNkir2DaOP0Pz8/JdffjkzM0MC5Y2RKuB/df78+UE1dfi5du3a5cuXIZEuLJ9//vnnBw4ciEajL1++HHTrkHVoNpvVavXEiRNut9u4I0FCsz7IFUeWZZPkAE9Lr9d76dKlCxcuzMzMOJ1OKB8BNBoNHEe9plarVSqVaDTKMMzo6CisrTAMg1H+yK7ENKVUq9Wff/7Z6XT6/X5IYrnJwQjyoaDw6BVbdLLaFiExqCwriUQikUjMzMy4XC7jwi0ptwyx71hueSPK5TJk0fV6vWNjYwzDfPbZZ6lUKhAIvHnzZtCtQ9YBhsDdu3fT6bTL5aIoylRb8L2ZHowLDalUimTHgliRaDSayWSI15au66VSyRjLbiyXjvSCBw8eLC4u5vN5iLiDmY2m6WAwWKvVBt06BNl+jE/2p0+fLi4uptPpQCCQz+fr9Xq73cYiQsg2gsKjr2yuRjYK/Ohtm7ZM9y5NrVYLBAJQcttqtY6NjRkTg4KdZLVav/zyy8G1enhZXl6GJVWe53meV1WVZVm/33/58uVjx44NunWIGeN25R9//HHjxo1QKOR0OhmGYRiGxHuoqppKpbb+tk6n06jYDx8+3H1MPp8H7WG3230+H+aW6R26rheLxWKxmMvlIPzGbreLosgwzFdffTXo1iFID4Ep7uXLl/l8PhKJxGKxUqn0n//8Z9DtQnYbKDz6wVbEw47QHkagVU+fPr1//76iKA6HY25uTlEUUuWXBMjOzMxgodNuFhYW3G43y7JgcUJweSwWk2U5Ho8PunXIOhhHYi6XCwaDqqoKggA1H8EhRxAEkkh6Kxi9E/1+/0al0H0+H5H02D16x8rKSrFYvHfv3o8//ghhPCApKYr6/fffB906BOktf/311507d5LJZDweL5fLpVKJ/Gs47RBkJ4LCA/lUlpaWkslkIBAIBoPRaFQURWNtRIvF4nQ6f/75545BXOEU1ul0pqamFEWB+idQ9mRubi6fz2uaBh4dW8+PhPQNcs2LxeIXX3zh9/tjsRgUf6RpmjgZmhyiTMFdxp+CIBA3RZqmnz59uq775fHjx8mY4jhuo1Yhn0gqlUqn0+VyudPpqKoKiwJWq/WDSrUgyDCzSfLMRqMRj8eDweCVK1cG0zhkD4DCA9kGYrGYqqrZbFYURZOrFfEhwbQYJhYXF51Op8fjkSTJbrc7HI6rV69CWY9mswnHbDHpGdIHup/WjUYjnU6fPHkyGAxCkQen0wnaw2q1gvG6bj4J45vcuHHDOFKy2azp4EePHp09e/aLL74gseyhUIicjt1gezl16lQmk7l48WKlUvF4PJBSzGazBYNBzDKH7GIgO3+lUslms81mc3l5edAtQnYtKDyQbSASiSSTyUqlwjCMMczDqEA6ezgl37pfeXFxcXZ2NhQKQZCAKIper7dQKJRKpU0yIw1DYuU9yCY5IcrlcjKZdLvdpsoeFouFpFXYvOeT+HKHw3Hr1i3TB4XD4TNnzoC2AQ0/MTGxSduQj+bBgwcnTpyQZXliYmJmZoa4jMqy/PXXXw+6dQjSQ9bW1h48ePDixYtBNwTZ/aDwQLaBX375ZXFxcXFx0e12y7JMfE6MJZnn5uY667ma7BFMX3ZpaSmdTmcyGfCz2rdvH4SYZzIZkjlno6u0p67b8LBJZohms1ksFk253UZGRtxu91be1niKqqrGzzp79izHcfF4HGJIIL7c6XR2F5TAXvHprKysRCIRj8cjCAKZu+x2u6ZpGNCP7BqMT5ZsNlsoFGq1Wq1WazQalUpl0K1Ddj8oPJBPgpg74BsKlctFUYRsMGS7Awqi1ev1wbZ2GIArls/ny+VyNBqFsPJjx45NT09LkpTP55eWltY9ZQ+qtSFkk7sgSZLJydBisVy/fv297xMOh4nw0DRtdnZ2ZmamWCy63e6RkRGGYZLJJE3TiqJA6l6o9bHReyIfzdu3b9PptKZpLMtC3A5MXMViEa8tsjsw9uRisXjx4sWDBw/m8/lqtdpqtarV6gDbhuwRUHggnwqZyK5fv26z2UB7GB1OwA5jGCYcDq974l4jk8ncuXPnypUrsLDKcZzP50skEnNzc90VynZQorNdT7cCJDdiZWXl+vXrsiybypA7nc7Xr19v/rbtdttYzcNms8HwIWNHEARBEPx+P4lBNw0lZFv4+eefVVWdnJyESQyS8rndbsgoioMO2emY+nAkEvnhhx9yudza2lqr1TKueWFvR3oHCg/kkyDT09raWjgcPnjwoMvlgoIeJMMPGFVgYScSicE2eLDA5Wo2m7FYzOv1MgxD0zQUoXO73X6/3+v1dq+pY+HYIYcEeV+7ds1utxsL2lgslo0yXBk5ePDgyMZYLBZVVTVNI3+aMupil9gW6vV6IBDgeX5sbIwIv2AwuLa2hlcY2TVAZ65UKslk0pgwF0H6AwoPZBsgT+V4PO7z+YLBIGx6WAyAzSRJElQq6Oxta2lpaSkSiVAUBQqNoiiHw6EoyvHjxztdV2Z5eblWq3EcxzDM1NSUpmlerxdLowwhv/76qyRJUHjO2O3v3r1rPKw71dWbN2+goovJWYv8qWmaJEmQ2pVl2UwmY/rovTyatoulpaWzZ8/Ozs4SN1Gr1YqWGbL7yOfzgiAcOXJko2qnOJ8gvQOFB7Kd3Lt3z+/3+3w+j8cD5heRH8TzhAiPPQjURe50Os1m0+12UxTFsizLsoqijI+PHzlyZF058fz581qtBrWrjciybHLJxafFwAkGgw6Hw9TtjSUFN7pHxJOKCA/jtonL5YrFYgsLC5OTk9lsFmXntmBSgH/99VcikYCc4HAHw+EwjilkR7PuhnmtVpMkKRwOk9TtCNI3UHgg20mxWFRV1ev1Op1Op9PZvXbLMMyFCxdImtE9SLPZXFpaIgvYHMeBH3kymYQAj25DZ21tLZ1OE+FhvKR2u30vC7khwWi/5nI5WZbdbrfNZjOmlg4Gg+ueQlhbWysWizBqjDcaSnBCiFSr1dooryvax5/IvXv3vv/++2AwaBxcPp/vzZs3eG2RHUq36qjX68vLy6VSKZVKZbPZZ8+eDaptiJHNKz7tMlB4INuGrus//vijpmlzc3M8zxNDGbLrEltKlmWT98JeGGmAruvtdrtUKnk8HrgaLMtGo1FN03K5nKlC2Zdffnnz5k1FUQKBgEm/mTh48CB5/0F8LeS/rnw0GnW73WQIkIhw0u03uU0PHjy4fPmy1Wr1er1QkdNut6uqOjMz02g0VlZW3r59i7VcPpF1L+Djx49Pnz5tvGUMw2AsDbKbqNfr//nPfwqFQiQSaTabqVTqq6++GnSjkL2lOjooPJDtggyYa9euVavVUChEHE7AeCKmM03TXq+3+8RdjDFevFgsRqPReDxOjJuJiYnDhw+n02njRlCr1aIoyuVyQQGHTYSHxWKZmJhYXV3FfLsDofuCP3/+/MKFCz6fz3iPbDabLMubn0heLxaLkGFmfHw8GAw+e/Ysn8+XSiVTgiy815+C8WFfq9Ugf7HD4SDCQ5KkZrO512wCZBewbl+t1+vNZvPGjRu5XG5lZUXX9bW1tb/++qv/zUO62VPTCwoPZHsgVu/Fixebzebx48cVRXG73RDDAD4nxHXE5/MRQ3nXY9QDT58+TaVSTqcT8q7a7XZJksbHx2VZNq2tXrhwAQonGzeL1lUdIyMjFEVBjOAeuaTDRrfkKxQKHMeB3ibdfmRkJBKJbL0iJLxOtji6C7xsfjqyFXRdf/bsWblcLhQKLpeL4zi4WTRNbzG3NYIMOc1m8/Tp0+Fw+NChQzMzM5VK5fnz5x3sz8PKrr8vKDyQT2KjKhOlUikYDI6NjYF7OrGSifV88uTJznoW2y4GSlwfO3bM5XKNj4+DqAgGg6IoiqLYbeUkk8l1Zca68sPn8+2RyziErKslnjx5wvM83DKr1UriPa5evbrRWZu84Vb+hXwcd+/ezWQyBw4ccLvdJCsATdPLy8vGw/DKIzsL8nhNpVKqqkKBWiwROJzsqekFhQfyqXQPmKWlpXw+H4lEOI6DBKAj/2SJIbYyTdMDae2ggKvUarVu3boFJd5pmrbZbKIoejyesbGxTteVfPDgwUbuVd3YbLZEIoEPlf6zkXi+deuWw+GYmpoy3Sljz1/XjWeLahyru2wLuq5nMplwOGzaobLb7euGguB1RnYQa2trmUwmm80mk8mVlRWSDQ+78VCh6/q7d+/WLU27K0HhgfSKarXaHaJA1n0pispms4NuY19pt9vtdvu7776r1+uRSARKnfA87/V64/F4tx2Zy+W6tzggZuaHH35IJpP37t0zJkEaGRmpVCqD+nYIQO5jsVg8cOCAoiikDDm5TaZgD2RQ6Lr+5s2bRCLBsixFUSTsiqKo+fn5dY/vfyMR5ONot9uZTGZxcbHT6ayurtbrdXh9L5i2O449lTIEhQfSEyB9E+x4hMNhKF5uzC7qcDj2Th5YmEfK5XKn04lGo8lkkqZpsG9EUfT5fJDvyDTdtFotSZJMwkPTNOMxsVjM+N9Go9HHr4W8h2g06vF4oEzkyMgIUSAWi+Xhw4edPfCAGX5WV1fz+TzP88bNQ6vVCqMVQYaZzSeQaDQaDAYjkcjeedTuFPb4zI/CA+kVL1++BPP69u3bx48fJwv2Rht6T1UFrlarP/3009zc3MTEBKgOjuOmp6dPnDjR2WAmunXr1qFDh5xOJ1y3EydOmA4bGxszKRNTkDoyEOA2FQqFAwcOkIrjkFeapHrbKFgc6Sflctnj8Xg8HhCEkNGBoqhcLjfopiHIxxONRlVVFQShVCphvdFhA4L7jRhzWu56WYLCA+kh4FB04sQJWZaNzkLwSyAQGB0dffPmzaCb2VuMvje5XI6iKEmSHA4HRVF2uz0ajcLi90Zn6boO1egoiqpWq6YpyeVymYSH3+/v8RdCPoB0Oi3Lsu0fSJkIi8USiUQ6e+AZM5zAZV9eXk6n0zzPO51OCPCAgRaLxQbdQAR5PxvNHufOnSsWi8lkMhqNbnIYMhA2zx2yF24WCg+kh8zOzobDYZfL5XA4wNsEAhuItxVN05lMZtDN7CFkEnn79u3FixcnJiYEQeB5nqZp8L1hWfby5csbnUUSqppeJ/j9ftM+ks/n6+H3QT6cd+/eQaQHx3GQWpqkuvrjjz8G3bo9TS6X++2332B2IjHlDMMMul0I8vFkMplYLBYIBILB4PT09F4wZHcuG6UV2d13DYUH0kPa7Xa9Xh8bG/P7/TzPg7cJPOMtFovD4eB5Pp1OD7qZ/aBer+dyufHxcbBs7HY7uJJPTEyYHHA3z59jehEStsKFBeHB8/za2lrvvgiyRYx3KhwOg5MV3H2iEqenpwfYQuTKlSvBYJBUywFfuMnJyUG3C0E+Bl3Xf/zxx3Q6HQwG9+/fXy6XMepv2DA9wcmqYmfPbHd0UHggvaZarVIUpSgKy7JWqxUCbUmUucPh2CPri9PT00ePHvX5fDRNj46O2u12n893+vRpTdNqtVr38ZsnSyV/gt6gKIqmaViytdlsJHsJMiRUKpWDBw9SFAXZk+CWwVYVJiLrM2TsvHz58saNG36/n+zB2my2Xb8Hi+xWoGM3m81vvvkml8tls1nMuD2crHtf9tTdQeGB9JY//vgjnU5rmsayrNPpdDgcLMsKggBWstfrpWn69OnTg25mb6lUKp9//vnExMTExITL5RIEweFwBAKBy5cvf/vtt906Yd2ZaN2JCQotk2Ip4CuC8eXDgGnn6unTp263G/IEGO/X5OTknnrkDAm6rhcKhXA4rKoquRcwlPL5PN4RZMeh63o8Hi+Xy6VSaXl5GfvwMLPR3dkjdw2FB9Jz2u320tISVDG32WwkVBrWfSmKgvJ5u5hLly6xLCvLsiiKbreboihBEDiO+/rrr7sLlm+dlZUVo81EYvcTicQ2Nh7ZFpLJZCAQ8Hq9VquVYRjY9AP5vev7/7BBIstVVS2Xy/F4nOzBulwurMKJ7ERKpVImk8nlco1GA/dRh5w9IjA2AoUH0g+Wl5e/+OILVVVpmjaWB4YlRkmSVldXO7u3hk44HM5ms36/3+PxBAKBUCg0NzeXSqVUVV3XLWqL3z0SiRiFB1xSlmUhXRIyVJRKpW+//TYSiRAnK+MQwKoR/WdhYUGWZa/Xy7IsTEojIyOKokBey73jb43saHRdX11d/f7778+fP18qlQqFgjExK4IMISg8kF5BHtvJZDKZTE5NTSmKMjY2RqIRCDabTVVV01m7hqdPn16/fv3UqVMej8fhcIiiOD8/f/fu3Uwm8/3333/cQ+LixYsQ3WE0XuFPRVEwoHA4qVarsiw7HA673Q63DG4fTdM0TZty7e++gTA86LrearUWFhb8fr/dbidSENJbD7p1CLIh604LkL3q8uXLlUqlUqng1IEMOSg8kJ5gnPvK5fLly5fHx8ej0WgkEgmFQuBtYlqtTyQSu3LGbLValUrl/PnzgiBAlMvExMSdO3du3brVbDZNB2/lCrx7987lckFaMKN4g+CBcDjcm++BfCorKyvffffdxMSEz+ez2+0ejweyS8O9O3bs2K7s/8NJqVSKRqNOp9PpdBLdzrLs4uLioJuGIJthmiVqtVo6nQ6FQq1Wq/u/CDKEoPBAeguJkz537tzJkydjsdiZM2dYloW1XlhrBOExOjoKqeV2WZKHP//8886dO6lUShAEKBp49OjRhYWFGzdugIMZsJXvC8ccOHAALpooiuTqkXhlWZZ7+GWQLbNuWuTbt29fvXpVlmVIqUwKekCMAZgOSK9ptVqapp05c2ZyctLr9ZJtQ5fL9Z///GfQrUOQrVKpVFKpVCwWy+VypBTvrnl0IrsVFB5IrzBNf3/99Zcsy7IsT05Ojo6OgpU8OjoKzu4URfl8vuXl5UG1tqf4/f5isRgOh6GMSTwev3//Pvzrgx4SkLeEFIIgEbFG7ZHL5XrzJZDtYXV1NRAIMAwDmRVAeFAUZbFYSAUJNB16ByyCCILgdrvdbrfL5Rr5p27gpUuXXr16NegGIoiZjaIfQ6EQx3GCIJw6dWoQ7UKQjwGFB9JDjFNkrVbL5XIej4dhGHBvIAuNYDQzDGNMx7RrbK+lpaXJycnp6Wme5xmGsVgsqVRqYWHhxYsXcMAmFQNNz5svvvjCWPrdlMyKZVlN0/rzpZCtYLyz5Pdnz541Go07d+643W6Px0M2/cDVp7Npf0A+ndevX1+7dm12dtbpdAqCQHacZFl+8eLFLttuRXYTpplBURS/389xXCgUMhafwd6LDDkoPJA+UavV8vm8oigOh8PhcLjdbmNiH4Dn+UE3c/tZWVmJx+Mulwvqi9M0HQqFarXa/fv3t/iEgMM0TTNlQzIJD5/P1+OvgnwAxITtrseyurraarUURSEZ3gCr1frjjz+i7ds7dF3/9ddfb926deTIEZqmYdMJVj26E1vjLUCGB2NvlCQpFotpmnbq1Kl//etf09PTEC6IPRbZEaDwQPrH3NxcKBTyeDw2my0UClEUBTsAxHSenJwslUrk+N0xjbbb7Xg8TlEU7HiMjIz4fD5N07od+tf9vrquv3v3rl6vQ61Acq1MwsNms+F2xw6iXC7zPA+JrYyJFux2+6Cbtst5+fJlsVicnZ11OBySJMHF5ziu3W7vjgkH2d3Isjw2Nnbv3r1Go1EoFFRVhYwIuGCB7BRQeCC9xTgPRqPRYDCoKIrNZuN53uFwjI6OGiupjY+PB4PBdc/duSwtLcFWj6qq4Mqvqqrf719bW4MD3lvEVFXVdDp5blWNAAAgAElEQVQN/mnkWlksFsiGRDaLdsfl2gu02+1yuXzs2DGI9CAZXcHt51NqSiImuq2xRqNBVj0oirLZbBDgMbg2Ish/sZGEWFlZ0TRNkqRsNgtzSLVaLRaLnS6n3H62FkE+FBQeSK/4+++/4RcyD9br9XQ6LQjC+Pg4y7KqqsKCDbGnRVHkeR5CzHfH7Anf4smTJ4qiQAETi8USDAZjsZjxgE20R7lc9vl8sixvtNcBy+SHDx/e5H2QIeT69evRaNTtdvM8z7IsbHpAvEGhUOi8L+YH2YSN7LDV1dVEIsHzPJF5HMc5nU5jzU28yMjA6Q70KpfLoiiOj49fuHChUqlUq9VqtTq4BiLIx4PCA+kh3Q7uq6urU1NT+/fv53l+amoqkUhIkmT0IKJpGvIy7ZrH/59//unxeCRJggLJIyMjLpfr9OnT5ICNPKxev369sLDA87yiKCSTlUl+wC/79+/f/N2Q4YHcoFqtNjc3B0uYLMu63W7iNed0Ol+/fr3uiXh/t0735LOwsCCKIowm8HNzuVwURVUqlUE1EkE2wrhmF4/HNU27ePFiOp1uNBqm2QCnBWQHgcID6Qmb7PyWSqVqtQpuV+l0muM4oxltrGK+OygWi4FAYHJyEjJ6MQzj8XhSqVRn46dFMBhkWfbEiRM0TYNW2QSGYZaWljr4ENqBZDIZSZL8fr8oisZykBaLZd1CkHhnP5FTp07xPE/yUMMOpN/vH3S7EGRDyuVyIBD4+uuvc7lcrVZrtVpQ8ArAaR/ZcaDwQHrFRgv5T58+XV5ePn78+NTUVDgcZhgG6qkR54fPPvssnU73v8G9oN1uRyIRr9erqqosy1CxIZ1Or1uxhCRJJFbRuplzTVsfxg0ifPbsLFqtVjKZTKVS4PBD0zS5szRNZ7NZ0/F4fz8I06C4evWqKIqQQpcEStnt9mQyuclZCDJAVFVlGObWrVudTufrr7+GmrPdrgQd7LHIzgGFB9IrNpkHm83myZMnR0dHx8fHeZ4XBAGsAeJqwnFcP5vaO1ZWVlRV3bdv37FjxwKBAMuyLMsePXqUONIY16sikQjP8yY3qm73qpF/Ss7ZbLZyuWz6RHz87BTgTr179+769et+vz8YDEqSRMIPnE6n0+ms1+uDbuaOxLQMrOt6s9kMBAKff/45TdNEz0NEzeLiIi4bI0PI999/7/V6P/vss2fPnsEr79Ub2IGR4QeFB9Jz1p0KL126FA6HHQ4Hx3GQ0dJYocLj8dRqtf43ddtZWloKhUKfffbZ3bt3FUWRZVnTtO79nCdPnkSjUYvFAv423drDmMkKXpFlGYMLdyLrOmdDWQ+O46CQNggPh8Nx9uxZtIk/HV3Xo9HosWPHotEomWqsVqvdblcUhRwz2EYiiJGbN2/evn372LFjoVCIvNitqI2nYB9GdgQoPJDB8N133+VyOUmSYGXX6GQCFnYgEBh0G7eBYrEYiURUVf3qq6+sVqvVak0kEiSRLsGYU3jd7Q4ToVBofn6+++PW3YJHhp9KpQJVJm02G1jGIyMjdrvdFOmBN/ejqdVqkMYaMheD9nC73RhWjgwt1Wr15MmTuVwOgjq24gSIjwBk+EHhgfQbmBaXl5eTyWQ4HIYk+pBN3+RKtNOLCa6srJTLZb/fL8vyxMQEfFNJkkyHBYNB8sVN2avWdbVyu927YzsIIbx9+3ZxcVEURZqmIcEu3HFZlv/8809y2E4cBUNCpVIJh8MulwuKlsLm4ejo6KDbhSBmyCPy//7v/xqNRnepWQTZ0aDwQPqKKad+KBSCdJbE39q4qB+Px3eWpWXK5VWv10ulUiAQ0DQN0hZpmtadrWj//v1EV5BCct1OVkSS3b9/v79fC+kT4XA4GAy6XK59+/aBDmcYRtO0nTUKhpB8Pp9KpWKxGFndgAF19uzZQTcNQcwLCteuXcvn84uLi48fP/7tt99QeCC7DBQeyCAZHx/3+XzEr924um+320VRfPLkCTl4R5hfpJFPnjyJxWL79u3jeZ7neY7jeJ73+/2QSNfIwsLCVjysyL8ymcx7i50jOw5d12/cuDE3Nzc2NjYxMSHLMqzKx+NxKE6MfDTJZNLr9SqK4nK5jEOsOzcDgvSN7giNt2/fZjKZRCKRzWZfvnyJfoDIrgSFBzJIotGoqqqCIEDQp9HChg0QTdPIwTvLqn706NGpU6fC4bAgCDRNUxTFsuy///3vdW0dU4jLezElADWxsy4U0vnnls3Pz6dSKVEUobgEBHuwLBuNRpvNZgfv7Iej6/qLFy/8fv/4+LjdbocqjTDVWCyWlZWVDl5VZHCYgsULhYLP5xsdHb1w4UKz2UThgexKUHggg0TTtNOnT09OTubzeUVRrFarw+EgZoEgCE6n8+7du52dUyaJNG91dfXMmTPRaHRycpLneY/Ho2mapmkkMaKRdDq9URbdkX8CYU2vSJIEZpPpc5EdysrKysTExNWrV6empux2u6qqsBMIIoRE9eCN3iLkQt29ezeXy0H2vFgsZrFYnE6nxWLZNTm7kZ1I90AulUrhcFiSJK/XGw6HIWkhjndk94HCAxkYuq7/9NNPhUIhm81GIhGO42w2myzLxA8bIs6npqZ2SkkvYwvfvXsXiUTC4XAoFILycKFQqFarrfst8vn8iCHMw2azGZVGMBicnp42FRMENSKK4qVLlyBN1vBfH2RzJEm6cuVKNpv1eDzgbQjdwOVydXvoIZtAxkI+n5+dnU2n0yRbscPh8Hq9giBcuHDBdDCCDIqlpSVRFBVFCYfDkUgkHo93Jz9EkN0BCg+k35ge8/l8vlAoQIi51WoFPxMiPEjmmeE3DkwtXF1dhZrlkLPLZrNNT093KyhSxqHbnwqUxtjY2MrKytramqZpZDvIpEAgUa/D4bh9+3afvzWyjRSLxXq9DsID/KxomobOI0nSxYsXB93AnUcwGJRlWVXV2dlZSBlnt9utVmsymdwpyxnIXuDatWvhcPjQoUP1er3dbkNAOXZOZFeCwgMZMIuLi2BSQxlBMLNImAf4RQy6jR8AsWZWVlZKpZLH44FUXT6fb3Z29t27dxudWCgUWJYFQ5OICpqmjc+eQqHg9Xo3cscaGRlhGCYSifTjeyI94M8//3zy5EmlUjl8+DAEl0P/h3GhKMrLly8H3cYdxvj4uMvlkmUZ1jVgjNhstp2eqhvZNbx69Sqfz6uqGovFcrncoJuDID0HhQcyGMjDvt1uLywsBAIBiqLAtwQ8sIlt7XQ6G41GZ6fZB6lUamJiQpIkl8sFK6xGW2cTvv/+e0EQoKwyfHEjzWZT07TuUoPkFa/Xm81mOzvtciGdf25ZtVoNhUKBQGBqaspisfA8D1rUZrPxPL/RWUg3i4uLk5OTNE1DiVJwYvT5fMeOHcOLhvSHzYuL12q1Bw8exGKxdDq9urra36YhyGBA4YH0m+4w8WKxWCgU7HY7eGBTFGUyrG0229LSUvc7DC2tVktVVY/HwzCM0+m02Wz5fH5hYWHr70DWttf9soFAoHvfgygQt9tNjhz+a4WYqFQq0Wg0Ho/7/X6HwwG1zMktBlWJbIXLly/7fD7Y6+A4zmq1wu7H69ev4QAcHUgf2CgzSrlcDoVCi4uLsVjs4cOHuJ+J7BFQeCADwDT/QnYmhmEURdE0jeM4k0ntdDphD3qYDQVj2wKBAHh30DQN2iOXyxmTUH3oG3a/4vf7102EZbFYjh492lkvkgQZZozWSaPRqNfr4XD4wIEDI4a0Zlar1e12G0X4uu+AdDodXdfD4bCiKE6n0263Q8FyiqKuX79ODujgRUP6QndnSyaTLpdLkqSlpaWVlZVff/0VdzyQPQIKD2QAdD/s19bWvF6v3++/ceNGOByGGFASYw0+7psESAwDRsORlCqD7RpJkiAr0RatnE0OMz7A5ubmIAxm5L9T7gaDwUePHm39PZGB0+2P8e7du0qlcvv2bZ/PZ7fb7XY7VLW3WCwej8eY8QbvbDe6rr969SqXywUCAY/HY0yUZ0oWhFcP6TPnz5+fnZ09fvx4MBgEF9wPXZNCkB0NCg+k35jWfsgvyWTS7XZ//vnnEGMNQQ4jhnqCmqYNrZVg+lITExPgMAax8ocOHfr2229NB3/om6/75+LioizLgiBAbiuInVUUJRqNbv4myJCj63o6nS4Wi/l8HmpQkiqTNE0nEokObmptiq7r8Xg8HA6zLAuaDVT68+fPB900ZG9hfNil02mKom7cuFGtVvP5PLy+0R4mguxKUHggA8NkKh09enRiYiIajUI0ts1mgyhz0B52u93hcAyqqVun0Wjk83nY7gDtBMVJPm67pltybCLbJEkSRZHjuGw2GwqF1n0HZDghd9bI0tJSNpstl8tTU1MQ6UE2tRiGuXXrVgfv7wboun7z5s1IJMLzvCiKLMvCYGRZttVq4UVD+oNpaeDXX3/1+Xyqqi4vL7daLdQbyN4EhQcyGLqf/ZVKxev1jo+Pk+VJh8Nhive4cePGkBsNi4uLoVAItjssFgsEsx45cqTb96l3rBukOOTXDen8974ZuV/pdHpqakoURZvNBpUoYHQYC29juIKJN2/eHDx4MBwOg/6HtGAWi4WsMXfwciH9JRqN+ny+SCRy5cqVt2/fwos4cpE9CAoPpK9sMsOura3F43FFUSRJgkhQhmGIXzvxbu9naz8Uv99fq9X27dtHDJ14PP7rr7+SrLif+IBZNzvK5u+JD7adTqPRSCQSwWAQ0sLCHhr0LkVRXr161cH720W5XPZ6vaDWjDkYyuUyXiuk//j9fo7jUqkUeFhtMbU6guxKUHggQ8TY2Fi5XL569arNZnO5XBzHgfAgwdNWq7VSqcDBQ2JAkGZks1mfz5fJZFRVhXALjuMikUgqlcItdeSjefr0aT6fn52dDYfDYEmTEpN2u33//v2djcfCkIyRfgJfeWFhQVVVKMcpyzJMIE6n8927d3vwmiB9xtTHpqamRkdHc7lcrVarVCoYSo7scVB4IMOCrutnzpy5evUq8WjneR6izI2pdaempgbd0vXtOb/fH4vFeJ73er0gk06cOAFVaQuFwntPR5B1gd7y66+/ZjIZqCxpSmV26dKldU/ZC91s3W/67NmzU6dOSZLE87zD4SAJ3xwOx164JshQcePGDZ7nJycnO3tjSCLIe0HhgQwFMCPfvn273W5fvHgRSpizLAuWlrFahSAI6XR64E01vbKysnLmzBmHwwHCAxrM83woFPJ6valUilhI+OxBto7Rua5arY6Pj4MU93g8ZN9jZGSkVqttdOKup1t7pFKpcDgMpcpJTjyLxULWLPbOxUH6w0a+r+12e2ZmJhKJnDx5EgYp9j0EQeGBDB3nz58XRZFhGJ7nR0dHGYYhafiBI0eOkIMHPo9DA96+fTs1NUXqlEE7RVFMJBIknnWj+rUIsgnG3jI1NfXZZ5/RNB0KhViWJfseqqpu8R32AsVi0efzeTweWLOAHY/R0dF6vT7opiG7lnXTpSQSiXg8fuPGjYWFhU2ORJA9BQoPZLh4/PhxKBSKRCKiKCqKwrKs3++XJImoDpqm9+3bt7y83NkgC1DfMH7iTz/9BPUWjPsziUQiEAhAyYV1z0KQraPr+o0bN3w+n9PpZBhGEASS5IqiKBL7RA4eVDsHy7179xRFCQQCpHwHyDNJkgbdNGSvoOt6IBCIxWLRaPS77767d++e8V8DbBiCDAMoPJAhgkzKMzMzhw8fjkajsiz7fD6jo/bIyIjH4zlx4kT3iQOZ0+FDa7Ua1FyHLDoWi4XjOJ7nWZYFixC3O5CPxthncrmcJEng1GfcXmMYZqOzdn2XI19wbW3N4XCAJDMm0h0bGzMafxudjiCfgjEFdjwebzQaxWKRZM7tPgxB9iYoPJCho9lsplKpVCqVTqcht5UxmhY2Pbxe759//tnp+yRuMubIn+Vy+fXr15CGS5KkRCKhKMrExMTU1JRpKRpBPghTD282m9lstlQq8TwfCASMQ+PChQtv3rzZ5Nxdzx9//BGNRiVJAv1Pth/dbvcPP/ww6NYhu5+///47l8t98803Dx48gFfa7fZgm4QgwwYKD2RIefr0aalUAtOKoiiKosDGgp8URRWLxUG1zWTPPX/+fGlpKZVK0TRtt9uhbLksy5IkoepAtgVjl1tbW+t0On6/3263cxwHQVCQLjYcDg+ujYMnFoslEglZlh0Oh9PpJNuPfr+/XC53H7/XhBnSa54+fWoMQUQQpBsUHshQYLIArl69ms1mM5mMoijg0Q45aowh5qbYiX62s9teyefzyWSSoiiHw8EwjM1mm5iYGKA0QnY3z549SyQSgiDIshyJROx2O6zu22y2X375hRy21wzrWCzGMAzJZ02irTKZzF67FEifSafTwWAwmUySHIYIgqwLCg9kiCDz9dLSkqZpX3/9taZpLpdLVVWWZXmeJ8YEVE8bbGsJv/zyS7FYhCw6EO/LcVwsFsMsOkiP0HV9aWkpk8nIsgw5GMi4IFHUe8f6gW/6/Pnz0dFRu91OkuARJ7S7d+8Ouo3IbmAjV9sLFy5Eo9FoNLqwsHD79u0//vhjYE1EkKEHhQcyLJhSVIXD4Ww2C1XAoKSgIAhG4WGz2QZbERyaeu/evXK5PD8/D0UDoL6boigzMzMD2ZNB9gi6rheLxX379sEmGxkXFoslm80OunUDoFqtGvNug0+mxWLx+XyvX78edOuQ3YPJ7/H8+fOKomiadvnyZeJbu3dkP4J8KCg8kKEDpuxcLnf+/PlEIqFpGnixOxwOkpXfYrHY7XZSN21QuXR1XS+Xy7FYTFVVm81ms9lomna73aIo/vLLL/fv3+9zq5A9AnS/er1+5swZt9utaZosy8TmFgSBaPK9YwDdv3+f4zhSpJzMFTzPt9vtvXMdkL6h6/qRI0f8fv/CwkK1Wl1bWzPmeUcQZF1QeCBDyvPnzzOZzPLy8uHDhyFoW5ZliBYFk4KiqPv3729UMrYPEOMvGAw6HA5YYVUUxev1op8V0gd0XS8UClNTUx6PR5ZlEgRlsViCweBg9wP7Bhn109PTFEW53W6SzAqS6l64cGGwLUR2Daa9jgMHDgiCkMlkWq1Wo9HoPgZBkG5QeCDDQreEqFQquVxOEATw24a8usR1e2RkZH5+/n/+538GONHruv7q1atr16653W6bzeZwOGia9vv9p06dGlSTkD3FDz/8kMvlHA4Hy7JGRyPQHpD/atcDG48QD+b1eo3eVna7vdVqddAcRLaVRCJRKpU0TTtx4kSpVOp0OqRexwCLSiHIjgCFBzIUbFTsLJ/Ph0IhCNpmGMZqtRrjaMfHx+Px+Lon9q3Nf/3117Fjx2ArBladZ2dnyeoXgvSUt2/f1ut1SZJGR0dNqZxEUXzy5MkeMYBKpdLBgwcVRZEkyeiN6XK5VldX4Zg9cimQXjM/Pz89PZ1KpWq12v/+7/+aiucgCLI5KDyQIaLbMigWi4qiuN3umZmZmZkZiqJIbn4wsGKxWLVaHUhrO51OpVKB8HdoTzKZdDgc8Xj8999/7y5YiyC9oFQqhcNhEOQ2mw3KdcMmYS6XG3Tr+kSj0ZiamhIEweVyMQwjiiJU/tmbcfZIj2g2m9Fo9OTJk8lk0uTKiLIWQbYICg9kqNF1PRQKXbt2LRqN5vN5mqbBriJu3C6XKxKJDKp5iUTCWCBZkiSO486fPz+o9iB7kGaz+dNPP2WzWYqiPB6PIAhke1BV1ZWVFThsdxtG6XQ6nU5LkgRZKBwOhyiKgiCQ7Q4EeS+bjJGVlRW32+1yuc6dO7e4uNhoNPZIDBWCbDsoPJChpt1uW61WSZKCwaDP54NVTLfbTTy5KYqSZblv2wum4MKJiQlSTN1isdhsNoZhVFXd3UYeMgwY+1iz2Ww0GoFAAKQvlLAEfT4/P286ZTd1Tvguy8vLhw4dkmUZklnDSKRp2uVymY5EkG7eOy5u3rw5PT3t9Xo5jvN6vXfu3Hn+/Dn2KAT5OFB4IMPO2NiY0+n0+Xxzc3PgauXxeGDrw2q1UhTlcrnIsm4fIM+blZWVSCQCRh5JtGW32/1+P66zIv2kWCxWq9VarRaLxWC9HyS6xWLhOA6iq3cxtVrN4/HAVwZXTJgcZFlG6xDZOrqud0cbNhqN69evnz179uHDh+Vy+fvvv19aWsJ+hSAfDQoPZNi5ceOGpmmKooyPj7vdboZhEomEx+MhOXwGVUnw7NmzkE0Isnba7XabzQZ5dXAXHukzL1686HQ6ly9fHh0dZRjG5XKBB6DVavV4PO12e9AN7Alg/z158sTn8zmdTpvN5nQ6SQyYqqqDbiCyM1hXSOi6Ho1G5+bmUqnUAB16EWSXgcIDGXbq9Xo0GnW5XFDKQ5Kkubm5ZDIJ+wxWq5XjuKtXr/azSbquNxqNeDz+2WefKYoCrh3BYBACzf1+fz8bgyCdTuf58+f1ej0ej09MTPh8PoZhaJom+d9SqdRuXaMtl8vhcFiSJNgOJeH1IyMj//73vzvoZIVsykYJFe/du3fo0KHz588vLCyA9hhE6xBkF4LCAxl2dF2/efPmyZMnBUEIh8PpdDoSiUxMTJD0Vjab7eDBg31u1crKSrlcPn/+vMfjsVqtLpcLagjSNL2wsGDcskeQ/vD06dMLFy5IkjQ+Pg5ZrUgaBovFYsxwtZs65/Lyst/v9/v9siyTZHdQwYPku9tN3xfpKdBVMpmMpmm1Wq3T6dTr9b/++mvdw7BfIchHgMIDGWrI/P7u3btwOMxxHM/zgUCAhFXAT1mWnz9/3s9W5fN5TdMqlYogCBBTDk5fFEX1rRkIApBh0m63z507d/ToUb/fz/M8+B2BLW632xcXF02n7ALW1tYmJydHR0cVRSHulzRNHz9+vNlsooGIfCj5fD4YDMZiMV3XuyVHN9i7EOSDQOGB7BiSySTLshA5CtsdZHVzcnIyn8/3pxnwmKnX6ydPnoQKhhDJCrYdx3H9aQaCrGvxnD59Op/P+/1+yKgLAUgwWCYnJ/vfyF5TLpcjkQgk0iXTgsViwRwPyIeytLQUi8VyuVy1WoUKMCgqEGTbQeGB7Bh++OGHQCBgsVgYhoGQboqiRkZGIK/U559/Xi6Xt/Hj3vvICYVCTqfT6XQyDDM2NsYwjNPpJG3AJxYyEB4+fFgoFFKp1JdffklKCoJEZ1n2p59+GnQDtwcyvlRV3bdvXyQScTgcsBFKUZTT6USn/D3OVmZg4zHpdNrr9SaTyWKxWCgUisViL1uHIHsXFB7IzmB1dfXKlSuQ1SoWi8my7HQ6HQ4HcbiiKCqTyTSbze5zP0UDmM6FP1utVrVa9fl8qqpardZEIpHNZkGB1Ov1T/xEBPloiGfRt99+e/nyZYvF4nA4iAMS1LjcoRmu1nWa0nVdlmWWZaF6CaxE8DwviuLCwsKAWooMkk2c69b9V7vdDgQCgUDA7XZXq9WVlZVUKtW3/XME2YOg8ECGGvKQePToUTAYnJycdDqdiqLwPC8IAlTzAGvDYrE4nc50Or3u6Z/y0d2/V6tVVVWPHz8O0SZWqzUcDsNWzNra2kd/IoJ8OqSvzs/Pwy6cqqogzmFDIBaL9a3g5naxiTUZCAREUXS5XGQegAzCm5+F7DW65/O1tbW7d++qqsowTCAQOHPmjK7rKysry8vL3ad0/4kgyMeBwgPZAcCMPzk5qapqOp0OBAIcx9ntdoZhIKobktgwDBMKhXr06fBzaWkpHo8Hg0G3271v3z5RFEF4BINBnuf37dvXz1KGCLIJL168qNfrbrfb4XAwDAN5rkCBGDNc7RTWNfsKhQLP816vV5IkSPMA2ztkxXqjZKnIbmXzG03+Ozc3J4risWPHpqenQ6FQNBr9/fffNzoeOw+CbCMoPJChxmg3pNPp6enpe/fuVavV2dlZWZanp6ehUBq4lFgsFkVRXr16tV2f2/28yWQyZ8+eHR0dZVk2GAyC4OE4bnx8/PDhw9FotIO2DjI4TMu65XJZ0zSTtxUkfRpgIz8F05hKJBI0TfM8z3EcTdNQvNzlcj179myjHUtkF7OVG/3s2bOpqalQKKQoysLCQrPZ3Eq9V+xCCLJdoPBAdgAw6TebTb/fr6pqLBZzu93BYFBRFBLmAamlKIqKx+Pb+KGmn3Nzc9ls9siRIxzHqaoKS8gQ6T4zM/Pw4UPT6QgyQGq12g8//CDLssvlEkXRWFLw2LFjO72LLi0thUIhl8tls9lIEQ+r1SoIQnc+q53+ZZFtodFonDx5sl6vQ9KqVqtl/C92EgTpAyg8kB0AeR7cv39flmWaphmG4TiO4zhRFMHUIDlDBUHoUTOazeb4+Pj09HQwGAwEAocOHYL0voIgBIPBSqXSwUcXMjRAV3z58mU4HOZ5nmVZSZJIMgar1bqVhd6hwjS4VldX5+bmAoEACfQCgsHgJmche5Nbt26l0+lffvnl8ePH//nPf6A4IAHDORCkb6DwQHYGxIoKhUJ+v5/juNHRUY/HQ+QHWc11Op3b8tjofpNKpeJyucLhsKqqqVSK1IS22Wyqqr579+7TPxRBthHSh4PBIOR9gkoXoD1cLtdgm/fprKyshEIhY1g5wzDdiXTRjtzLXLhwQRRFVVVv377d6XSWlpbW3ejAToIg/QGFB7JjgAdDpVKZnJyEUh48z5NwUjA+IN4jEAhs11PEGLDx9u1bj8dz7do1SZK8Xq/H44FS5SzLOhyOHZcpCNk7ZLPZQ4cOiaJorGU+MjKiquqgm/aRMVGVSiWTyaTTaUEQwOPRZrMxDBOJRHrTTGRnYIrtKRaLkiSl0+lUKvX48ePFxUUsK4kggwWFB7LDqFarfr8/Ho9D4TCWZWmaJraU3W6nKEpRlE6no+v6tqTTNb5JsVg8cuTI5OQkCB7QPOFw2BRYgotnyFBRr9evXbt24sQJTdMoijJqD8hwNfAe+94GmA746quvNE1TFMViYGRkBIXHnmKjbgOv+3y+RNcakA8AACAASURBVCKhaVoulysWi81mEwpo4hYHggwQFB7IzmNxcbHdbs/Pz3/22WculwtcLIghZbfb4/H4gwcPtuWzjI+o5eVlKNxht9vhp9PptNvtkOFqWz4OQXqBruuvXr1qtVqw9eH3+y0WC8hmhmHIMcNvikELa7WaoiiCIMAOJ6S0hjwTUMET2Wt0a4lUKsWybD6fr1Qqq6urOy6iCUF2Kyg8kB2DaQ+90Wi4XC6e5yVJOn78OIkutVgskiRpmrbtn1ssFicnJyGS1Wq1Qun0cDgcjUaNbuW4nIYMIeB2kkwmYbcQ8lCDk1KhUBhUd9365xqPvHHjhiAIxG3MZrPRNC3LciAQwAqee41148Lj8fiZM2dCoVC9Xq/Vaq9fvx5Q6xAEMYPCA9kBdFsntVrt559/djqdmqYdP378yy+/hCrmJMbUbrc3m82NTv/QT9R1vd1uZ7PZeDzudDqhEoLFYqFpOh6PJxIJk4MHqg5kqIAO2W63NU2DVGzG1LoWi2WA68Efqj0eP368b98+t9vNcRyEdVmtVkhpPQwhK0jf6PaGhV9SqdT8/Hy9Xq/X64uLi5ufgiBIn0HhgQw78IT4+++/Ta8vLy/zPH/p0qVIJDIzMwPRHWBIURRls9nS6XRnWx8wtVpNkiSoVEjTNFQuW1paKhQKZ86cIa3FRxoyhOi63mw2NU2TJAk2OuAnuCrZbDbIjtC33vuhBf7IMWfOnLHZbPv37wftBF8E0monEgkcfXuEjW70yspKqVTq4FSMIMMKCg9kx2B6isTj8bm5uWQy6ff7w+Gw3++HiAvwvrDb7TRNP3/+/NM/jmTyrdVqmUwGHMotFgvHcX6/v1AoaJoGC8ZYLBkZZpaXl9PpdCAQgP06SZJAovM8PzIykslk+uwlCMPzQz/uzz//5Dgun8/bbDYiPFiWZVn2zp07vWkpMqQYO0+1Wj1+/Hi5XN7oAPInTs4IMkBQeCA7CdNjhud5VVUDgUAsFguFQlCjgDiQuFyuZDK5LZ/7+++/BwIBSZLC4TDLsrIsg60jSVIymTx37tx7W4sgA4R0xXg8nkwmw+Ewx3GBQIBhGLvdDkJaFMWBN28rLC4uwhYHjHcIK3e73blcDs3KvUm9Xvf7/dFotFgs3r17d9DNQRBkM1B4IDsYVVUzmUwsFvP7/fv27WMYBiQHLIVardapqSnj8R9nkaysrKRSKZvNJooimDiSJDEMoygKTdOxWAwT6SA7hXK5HIvF0um0KIo8z4N+huAoq9UKqXVNDJsdPzMzwzAM1Ay12Wwcx6mqmkgkstnssDUV6TXLy8uapvn9/gMHDmSzWVNlQARBhhAUHsgOplAogKeTzWYLBAI+nw9CLyDew263G4NN191z3xxj7k6r1QoVygRB8Pl8LpdLFEVJkjKZTD6f3+5vhiA9Qdd1n8934MABjuNcLpfdbmcYxuFwEO9BY5T5EEbi/v777+Fw2OFwQGY5i8XCsuy+ffv2798/NTX17t27zjC1FukRcIvn5+dh/3lubi6dTpMFIOwACDLMoPBAdjC5XC6VSh07dsxutyuKApXRRFHkOI6maY7jWJYFW+RT8Pv94MrFsixFURzHQREPlmVVVcX08MjO4uHDh9euXctms8lkEjY9OI4DO95qtY6NjRkTAQ2bDddut3O5HCTmgph4p9Pp9XonJydNzv3IrqF7zei7776TJGl8fPzQoUMHDx5Mp9Pff//9ugcjCDJsoPBAdjbz8/OyLFssFq/X63Q6OY5zOBw0TYMIUVX122+/hSM/IosOHKZpWiwWCwaDPp/P4XCAHxfDMF6v1+fzVavVHn01BNkuuvcuarXalStXYrEYwzA0TYMpD56KHMcNrqXvodVqpdNpEt0BOSQEQSDRXGh37jJM83a9XlcURZbleDyeTqczmUyz2Wy32wNsIYIgHwQKD2SnAsLg8ePHwWDQYrH4fD5QHZDlBtzW7XZ7OBw2hph/qPeIruvLy8vlcjkajXo8HqhZRrY7fD7fzZs30dZBdhDQXf/66y+Ij4JKggzDgCkP2oNsegxb37527ZrX64VkVqRojyAIw9ZOZFswZQv45ptvKIrSNC2XyzUajYE2DUGQjwSFB7Kz0XXd6/WCnzo4QdlsNpfLBQUKwDSRZfnjgg7JA+/69euxWIymaa/XCw7xoih6PB5T3UAE2UGUy+WTJ09yHAc1MY3IskwOG5J6CNAGn88Hm5mkZvnIyIggCKbDkF0D3NCff/45nU6rqurxeKLR6NTUVLvd3vriUY/biCDIB4DCA9nxgM83y7KwdktRFM/zxry6DMP8+OOPcPBHPIR+//33CxcueDweiqLC4TDP8xRFuVwul8sVCoUwpRWyI+je62u32xcvXjx58iTDMFarFbIykFFDynqYzhog+XwethyN2x1Wq3VycnLQTUN6SLPZ9Hg8sVisVqvVarWlpSVTGNImnXMY+i2CIEZQeCC7Achsa7PZ3G43TdNutxv8v8E6YRjm6NGjH6cQdF2v1WqhUEjTNEjiCXl1XS4XRVHBYDAajW7710GQnkKssefPn6fT6WAwSFGUz+cTRZEIj+np6RcvXpiOHyDt/9fe3QQnka+L4we66W76BUJoQlAIDg4heEUJc0QZsWSuWBW0vTVYJVYNKbGuuJBZiCVuxM3gRk6VuLmSlbgarBJ3cnbiUlwYl4PLO8zyxNXg3Q38Fs//9L8PEEJeyIt5Pgsrku6meenwffh+n+dZWYGMFDg9iDogxfz69eu74QzROCQSCZvNduvWrRcvXihv7+/Z0v8ewHcFQrsQBh5oz+t0Og6HQ6/XUxRF07QgCBRFcRx38OBBec26SqXyeDwbO34kEnn8+LHVaoV1XCRJOp1OgiCge2CpVNrah4PQdiqVSvF4nOM4k8kEKVLyyP7nn3/eqbPqH1AWCgXo2CCnb8nfBVSr1f690K41Ym2Per3u9/u/+eabRCLRbre34cQQQtsAAw+0h8kfYMvLy06nE77+ZFnWYDA4HA6XyyUnoapUKkEQ+ndc8+DNZhNqp0BjEJhIEQRBo9FwHIefiOjrIEmSIAh2u51hGPmqEUURfrvNA/q//vqr/8ZYLDY9Pa3X6+H0IHeL5/lgMLgjJ4k2Zs2XCTaIxWITExNTU1M+n6/Vam3LqSGEtgMGHmgPU36GNRoNp9Op1WphKZQoihaLRf0vUCQ0Fout9y5KpZIoiocOHdJqtaIoQmIrrPGYmZm5detWF0c86Gtx8OBBua5uT+yxzXquqXfv3l24cMFoNCpzt3Q6HU3T5XIZL8C9Ys1kDPj3+PHjgiA4HI5SqfTixYtGo4EvMUJfDQw80F7VnywrSRJJkmq1emJiwmw2z83Nwde3AGYq1jtMCQaDwWCQ4ziYS1GpVNDCnGEYq9WqLNSL0B4FV0S5XD558iQ04lRWuPr8+fOOD/suX76cTCZhuaM846HRaFwuF34d/pWxWCw8z9vt9kAgkMvlSqVSfzoHQmjvwsADfT0ajQZECAzDTE9P+3w+CBXgW1KapmmaPn/+/OgHDAaDfr//4cOHk5OTkDei1Wp1Oh1BEDRNezweTPBAe508qvvjjz/OnTtnt9ttNpucw61SqRiG6e70sI9lWUEQDAYDSZLQPRACj4WFBeWjQHtaqVQymUzHjx//7rvvotGo2+1OJpPwK3x9EfpqYOCB9qTVCpjYbDaCIHiedzgcVqvVYrHI+eXQyFyv13/+/HngIvIexWKxUCiUSqVUKmW1Wg8fPmw2mwVB8Pv9giBYLJYLFy7gxyH6mrRaLZ/Px3EczBzKscff/va37TmBgRfUp0+foIouQRCwyhF+NhgMhUKhZ1+8JPcW+fV6+fKlyWQql8u5XC4ejyeTyZ7mS7uknwxCaJMw8EBflZs3b05OTtI0DZ09eJ6HkANWaJAkqdPpstlsd4QBSqVSKZVKZ8+epWkaEjwgp1yv13///fczMzPpdHpbHhNC49J/Fdy/fx/64SgzPWiafvny5U6d2NmzZ+Xq2FDjgSAIiqIOHz48ZC+0+8mvV7VaFUUxHo83m81SqdRsNtfcBSG0R2HggfakIR8/wWAQZjk4jrNarfIQCkYtUAxnlLt49OhRrVZzuVwEQUDLDq/X6/F4QqFQvV5//vz5lj0YhHaNq1ev6vV66H6jrEYtSdJOnVI6nVar1RRFQekIWEvJsuzAyB8HpntOrVZLJBKSJC0vL8Mtq72IOKmF0FcAAw/0tYnFYhaLhSRJmqatVitN0y6XSzmECgQC8iiqP0Md5PP5QCCwuLgI3/7SNO31epPJZL1e73a7mUxmmx8UQtvgzz//vHr1qiiKNE1TFAUpUjBVyPP8kO+hx8rr9UIla5j3gErWer1e2b4a7VGNRiOfz2ez2Xw+j3UCENoPMPBAX5sbN24cOHCApmmGYZQ1cOAHrVY7Nzd36NAh5S49UUen08nn85AQAou1WJbVaDQTExPQp3ynRmAIjVupVILsbZVK5ff7KYqSrx2r1bqdZwJXZalUgrkXkiRhtRVN0w6HA7pZb+f5oPUa3kr8w4cP3W43n8/X63XIptvWk0MI7RAMPNDX5tOnTxzHMQwDwxRljixUwoGm4/3BRlfxuRgMBsPhsN1uh6xWtVp94MCBQCBw+PDhRqPxxx9/4KQ/+mr0vI3T6bQgCDqdzufzeTweOZ+boqh6vb7N73lJkniel79BUKlUBEGYTKZwOLydp4E2pr8Dfbfb/fjx4/T09A8//HDlyhW5PED/4lX864rQVwkDD/QVOn/+PEVRDMPIaeWwTkMeuyhHLQM/3o4fPx6NRmHIBas7AoFAOBxmGKa/Ewh+QKI9arWlhrlcLhgMwmormPSDa8FkMg3cfkzn0+l0jhw5QlGUXGULcrQYhvnll1/wuttzbt68KUmS3W4nSTISibx69apnhRXUG8QCVgh9xTDwQF+h5eVlWJgBqaiwSF2Z5rFaP2b5087n8xmNRuU8Cax61+l02/g4ENoBv/76azKZDIfDp0+f1uv1LMtCWw+I3h0OR3ecwbbyyLFYjOM4lmWhmBWcw+HDh10u18ePH8d0AmjzlBPCv/76q9lsPnToUCwWg6arHz58uHTp0i+//NKT1NEzjYyxB0JfJQw80FcFPqva7bbf74e6uiRJQrIHDJ7k700lSWq32/37drvdlZUVv99vs9l4nofBltxDYGpqarU7RWjPWe2t++jRI2gmyHGcTqcbWOFqG972586dO3DggBx7wMVos9lgfQ5ed7sZvDo6nQ7ycxiGcbvdU1NTV69e7Xa7T58+7fa9gviCIrQfYOCBvjbw6VUoFL777juLxaLX66ETs1arVSZ7qFSqJ0+eDFyCHIlEwuHw3/72Nwg2aJrW6XQw7jEajQPvDqG9Tvl9c6vVKhQKt27dslqtULtWrnClVqv1ev3Kysq4z6Tb7Xo8HqPRKCeZwGXrcrnevHkzvntHW+XkyZNQXZDneY/HA+v3crmcchvlqir8W4rQfoCBB/o6PXjwoFQqMQxz+vRpj8cDBXaVUQfDMJVKZeC+4XDY6XQKggCZrJCPDj9///333X8fouGHJfqKVatVm81GEIQgCHAVwMJFi8UypnuUmzlkMhmz2SxftlqtlmVZo9E4Nzc3prtGW6hQKAQCAavV6nQ6Dx8+HI/Hs9lsIBCQSwLiX06E9icMPNBXRflhViqV8vl8KBSyWCwsy8pZ5vK8B8dx/ft2Op1cLnf06FGTyaRSqcxms9Vqhe01Go3P58PlAWhfWVxcpCjK6XTKFwJMPrhcLnmb4YVTN8br9Wq1WljlJf87MTGRzWa36i7Q1oJXZH5+PpPJFIvFarUaCoWy2ezRo0fr9fqbN2/kGlYIoX0LAw/0tekZjpTLZZfLBZVwSJKE5uXyvEcsFuvZfWVlpVgsQstzrVabz+dFUdRoNAzDGI1GKDaPawPQ1035Dq9Wq1arled5qLIAF45GoxEEIZVKDVysuJnJQHkvnuehG49cj06r1RoMhh3sob5vDXkplb8qFosWi8VkMsXj8XQ6/eXLl2fPni0tLTUajW05TYTQHoCBB/oK9cx7hMPhYDAoiuLU1JQceACe55Ub//7778eOHfN4PBCrWK1WSK5lGIam6R9++KGLwQbaZzqdTjKZ1Gq1MP+gjNth1dPAK2Lzl4koinq9XtmKR6vVwjW4VXeBRjc8mOx0OtFoFBoozczMlEqlUqnU6XTkhXMIIQQw8EBfs3a7PTk5ee7cuVOnTs3OzkKJFWXgMTExce/ePXn7UChktVpnZmZIkuR5HhLTk8kkRVE8z9+9e1feEhM80L7y3//931qtVhAEyH2ClCen05lIJLb8vpaXl9PpNM/zyq8JoKPOy5cvu3jdbbshf+5yuVw2m02n0/Pz86lUKhqN+v3+x48fd7vdIRUIsFMHQvsWBh7o6yR/qpVKpWQyWSgUIGejp7AVQRAGgwG+lvv9999dLlcsFrNYLLCYhCAIqCVqs9mCweDNmzd39DEhtDPgavL7/fLaJ3nBldfrVW6zJYLBoMfjgRK6BEHIxaw5jqvValt1L2hjlGXHHz16NDk56Xa7Y7HYr7/++urVq2QyubS01G63h78fsD4HQvsWBh7oqwWfZ/l8Pp/PHz9+XP6mVrl4Q6VS0TS9tLTU6XQSicTbt2+LxaLdbpezyaEI75EjR8Lh8MBBD35qon2iUqlQFCVfFHKFBujJ0GPD10Wr1XI6nQaDAUIOABHI+fPnN/cI0Mb1BAnlctntdouiuLCwIElSsVhcbZfu2BbjIYT2Igw80FdI+ZHWarWi0eiFCxdmZ2eVyzaU4cfCwkK323348GG73f748SOsLIcvWcH9+/dXq72L0D7RbDZdLpfH43G73coli4IgdLfu2+uFhQWGYTiOg5BDWcNXHt3imHWbKUOIxcVFWIMqiuKRI0fOnTtXLBbhT+hqeyGEkAwDD/T1q9VqkiQ5nU6GYeSQQ5mxajKZXrx4cePGjWQy6fF45HGP3Lkcow6Eut1uOp2u1+vxeJxhGDl0J0nyxYsX/RtvYNy5srISjUZJkoTAhiAIOf6X13ShndJoNEKhEE3Tk5OTwWAwlUqlUql8Pj9w4zVffQxLENqfMPBA+0IoFII0D+WASSkYDMbjcZPJ5PV6DQaD0Wi02WynT58WBMFms4VCoZ1+BAjtvHQ6nUqlEomE0+mEiwjyv4PB4GYOK49BFxcXT548OT09Dd8RQNRBUZTRaKxWq1vxCNC/GX3032q10um0zWaz2+3pdDqTyRQKhd9//32sp4cQ+vpg4IH2hYcPHzabzVAoNDMzQ9N0f5a53BNNEARo9zE9PX3gwAGWZT0ez+Li4k4/AoR2hVwud+jQIZ/PNzExIbfjVKvVHz9+3OSR8/m83W6fmZkxm800TWu1WkhkN5vN0Wi0Xq9vyfmjHmt2RH39+nU8Hi+Xy2/evKnX65VK5e3bt/2tOXAGAyE0Cgw80H7x/v176AzocrlUg0xNTXEcp9frIQhhGIaiKJqmY7FYKpXa6dNHaLd4+fJlKBSanJyE/G+o/zYxMTGwmeBAA4sasSxLURQ0DGFZVs4sN5lMPY071zw+Gm70bO9UKmWxWOx2ezabrdVqrVbr2bNnQxqQ4+uCEBoOAw+0X/z666/Qhtnr9Q4sb5XJZJT/lReXz8zMYLNkhGSdTieXy/E8bzAY5BRwtVp9+fLl9cYef/31l3yLKIpQSo7jOCifBQkkXq+33W53ty5/HfXrf+FqtZpWq7VarWazGdI5nj17NnD7gbsjhNBAGHigfUH5WQhpHv1gJkQZe8irsHDGA6Huv7fHcTgcRqORZVllrL6ufoI9I9RgMEgQBEVREMZA1KHT6ZLJZLdvaIuj203qfwLlW+r1eiaTiUajoij+8MMPlUplaWlptW6A+EIghNYFAw+0X3Q6HViwwXHcwMADaukM/BUmtiIE5IHmnTt3BEHQ6XRQ8RbqUFEU9fbt2/Ueqtvt3rx502KxwKotOBS0KicIQs4eWTMbAW1AzzxSKpU6efLkiRMnCoVCMpmMx+Nv3rzpX1u12muBLwpCaDgMPNA+Uq/XvV7vajMeA0EmOsdxX7582enTR2hXgMFlpVIJBALaf4GYQa1Wr6vurTxOjcVicK3JSSMqlcpoNEaj0bE8BqTQ6XSePHly6dKlUChks9lyuVy73S6Xy7/99psyp3+1oAKjDoTQ6DDwQPuLzWZbbVqjf5GVSqWiKAq+zT179uxOnztCO0/5BbnX67VarXa7XY4ZVCqVVqsdcYZQOWC12+0916NGo2EYZnl5eXyPZd9SPvOlUqlQKIRCIVEUA4GAJEn9qfzDDzLKxgghBDDwQPuLIAjK7oFD9GzmdrthrTnAVeZoH+p5z2ez2Wg0evr0aZjxkOcr9Hr9agHDwKumXC6zLCs3KYeog6IozK0a0br+FsHGxWIxnU6n0+lAIHD+/PlQKOTz+UZfJocQQhuDgQfaR+r1ujy4GR57kCRpsVhIklTeSBCEvPAAv+1D+5Py3f727dunT586nU63283zvJyVoVarBUHo3341Bw8ehKlIuCo1Gg3Lsjqdrl6v48W1AUMSxzudTqFQ8Hq9JpNJEASfzydJUrVabbfbECsO2RchhDYPAw+0j/z0008QeIw449EfovA838VPYrRfDYy3JUm6d+/e9PS0KIoEQWi1WpVKRVHU48ePRznUxYsXNRoN7NVTzxrW/KB1WS3tu1qt3rhxQ6/Xm81mnU5H0/Thw4cha1ySJPybhhDaHhh4oP0im80qsztGiT1gM5qm4UtciqIYhgmHwz1Hxs9stN/0vOfL5fL09LTP55ucnITVVjBxAWulVuu/AbdIkgRNyuUrjqIoiqI4jtuuR7PnDa/39eHDB7vdLgiCwWAQBMFsNnMcNzs7G4lEnj9/Xi6XhxwT/7ghhLYWBh5ov5ifnx8x2JBBA0H48hUiEL1eT1HUTj8UhHaeckhaKpVyudyLFy/i8bic76FSqWw2W8/Itd1u3717t9lswn9fv34N377DOiv5ciMIYn5+Hke9m+fz+UiSNJlMXq9XEIQjR44cPXr0wYMHb9++/fPPP1fbC5eSIoTGBAMPtC90Op0jR46MmOAhb8BxHMQeBEEIggApHxh4oH1u4Eg0l8t1u12/38/zvHwRaTSa8+fPRyKRpaWlXC5ns9lcLpdWq52YmBBFcWpqShAE5XUnX6EGg+Hp06fb/sj2PGUuR7vdPnHihNFotNlsly9frtVqxWKxXq+vrKxAJ3jlLgNfU5z0QAhtOQw80H4RiUTkjsij6N9SrogFi9fx8xjtN0Pe8/V6vdls+v1+hmF6KsJB0jmkj09OTsp9P3qKNyivu0gksp2P6ysjSZLX6/X7/T6fz+12x2KxVCr18OFD5TbDgwpszYEQGhMMPNC+0Ol0JEmCbgOrxRVrhh+wO0EQiUQCP48R6lGv158+fXrmzBmocAXXDvxgMBh4nqcoSqvVqtVqZeVc+SpTXmtYSHe9Op1OpVIJBoMQ11kslmg0ms1mI5HIx48fr1279unTp/5dBh5n+AYIIbQZGHig/WJI+w7l7SaTqee3Pd/L8jz/j3/8Y7V7GX1xwsZWOOyq/iG7bSXGZs5kzUHYVh1zk3bPs72abDbbU4parVZzHKdSqfR6PeRyrBn2u1yu4fey+5+HTeq/uIY85HQ6rdPptFqtXq+32+1OpzObzW7HWSKE0Dph4IH2i4Hlcftjj8nJyZ5f9XQ6Z1n2/fv3Gz6NISMJWHitvLHRaAxc87DmAomB27x8+bL/t0NGM+vtSjZ6ULTaeQ4vzjPKiW3mV6PHHgO3X+9BhhjxedidqtUqJDSvt5aD8mKkaXrgVba3norxgechFoul0+loNKrT6WAdqdlsDgQC0G4InyuE0C6EgQfaLwaGGf03Dp8VoShKEIRWq9XtdldWVuDI7Xb7yZMnv/zyC9xeLpcbjUatVuv++2d/oVCA+pXyLY1Go9FoVCoVSZLsdnsul1taWnI6neFw+P79+/fu3bNYLE6nM5/Pw3FqtZqyEE2r1frnP/+Zz+dLpVKhUCgWi8p7/OOPP+CHH3/8URRFeAgMwyjzSsHwcGX48GXzg5vRZ4eG3D58g1Fim/WGJUN2HD0gGX6Po9y4O/3www8URQ28iEaJRmia1ul0JpMJKr2u9gzvoSdkS8iP99dff718+bLb7SZJ0mw2u1wunuc9Hs/NmzclSep2u+12e789OQihvQIDD7Rf6PX6/gCjPwt2SOwBOI7L5/MWi2V+fv7MmTM2m21+fr5QKITDYUmSKpVKo9GQJCmVSlUqlWaz2Wq1nE6n3W73er0ul+v169epVCqfzz969Ghubs7pdIqiaLVabTabKIoej8disUDtS4/Hc+3aNUmSyuVyoVBoNpsHDx40Go1TU1PHjh1jWZZlWVEUDQbDoUOHNBqNIAgejycej5fL5Vgs9vr160uXLsXjcWgZJgiCyWRiGAZGJJFIxOfzffr0CQKhFy9ePHr0qNvtZrPZarUKz1ir1Vpz+DJi2LDm2HG94cfo46rRg5bNTImsdpD9M0RWPsZoNKrRaOTWHABmDodcXHI5XYqiPB4PSZIkSb5+/XrgveyHp1QJHm+r1bp79+709LTH4zGZTBcuXLBarYlEAqKOntbj++0pQgjtCRh4oP2i2WzKVa36Awx5PVXPwGjgf/1+P0mSLpeL4ziGYa5du2Y0Go1Go9vtjkajuVwuHA47HI5QKGS1WvV6/eTk5OnTp2OxmN1u9/l8p06dSiaTsPvRo0cJgrDb7bBegmEYkiSNRiNBEBCB8Dw/MTERiUQgbGBZ1mw2WywWaBE9MzNjNBppmmYYRhAEnud1Ot2NGzesVqvP53M6nTabjWXZiYkJvV5/9uxZr9fb6XTu3bvndruPHTsWDAYvXrz4/fffu93uJ0+etFqt5eXlUqkEUzdgZWVFy6OPpgAAIABJREFU7rrw+PHjQqFQq9U+ffokz73I45tCoVAqlWAiqNFotFqtlZUV+bfNZnO1qQN5UCVPInW73Wq1+vPPP//P//zP+/fvV1ZW0um0cpeeH/p/NcSWr4YasjJq9OVnw89nr4wm4fTOnTsHzcjhepH7CQ68ppQXF03T0K/TYrEYDAaSJC0Wy04/pp23srJSKpWCwWA4HJ6eno5Go4FA4MKFC6dOnQqFQslkMp/PdzEvHCG0F2DggfaLSCQyZB5jSLCx2m9ZloWqoBaLRavVEgRBURRN09PT0xRFORwOURRhpbtareZ5/ptvvoGCM2fOnLlx4wb0Irx69SpJkgzDGI3GnuND9V45LoJaQBqNhqKonghKpVLpdDqSJFmWpWl6amoKWkG7XC6GYbRarU6noyhKp9NZLJZcLpdOp69cueJyuSwWy4EDB3766Seapu12eywW83g84XC4UCjAZtlsdnFx8cOHDw8fPnS5XGfOnDl+/Hgqlfrmm2+uXr26sLAgP73VavXcuXOw4/379xuNRqlUSqfThULh+PHj6XTa6XQuLi5mMpmlpaVUKtVTtuivv/769OlTp9N5+PBhpVLJ5XInTpy4evVqLBZ7+vRpLpfLZDLdbvfly5d37tyR45me0dWPP/5YqVTu3buXy+Xu3bs38G2wZtSx+TVRq/12Y7HNXgk5lBKJhBx1rOviIkkSJujktzdFUYlEouf4e+ip2LwHDx643W5RFI8ePRoIBEKhUCaTSSaTi4uLyWRyaWnpzZs3yogdIYR2Mww80H5RrVZ70sQHDoY20OhDGR4M+S2sPFF2aO7/r3zLwIPAv8rO0HI0wvM8/CDfAvMhVqsVSpeSJKnRaPR6vcViOXjw4NTUFEVRGo0GwicImWDm5NixYzabbWZmxmazeb1en88HUZPdbne5XDabDcInh8MhCALEKhzHQVc4lmVPnjx58OBBq9V68uTJ06dPm0ymw4cPX7hwQRAEWG/27bffms3m+fl5eF1gEAnL0yORiMPhMJvNqVRqbm6Opmmn0+lwOBYWFmDGo1wu37179/Pnzx8+fJBf2d9++y2ZTMJBcrmcxWIRRbFWq1UqlVqtZjKZYLNWq/XgwQN5r1arBYvK3r17B/+VfzVkXJvJZOQtYcctHwSvmZeyy62srGi1WvnNOfxyG/hbaGQOjTuh3Qd8ow/21rOxYSsrK36/P5fLZbNZvV5vs9lsNhsEHk+ePKnVarA2sofyzbNPniiE0N6CgQfaLzqdjpzmMeIYaPRtgLJPiHLfgakjyhthgAW3Q3zCMAz0TZcXqxw5cgTGcwzDiKJYLBZ5nmdZVqPRGI3GQCAgiqLNZtPr9SaTiWVZgiBEUQyFQjA9otPpVCoVFPj3+XwnTpyQAxV58T1BEDRNQ0ACdyr/imVZZUdq+bHAdAqML2HIyPM8SZIEQcA5wDFhBsbpdHIcB+djsVju3r0biUTi8XipVNJqtSRJiqIoiqJOp5ufn/d6vVAe1GKxhEKhYrEYCAQqlcrS0tK1a9eOHTsWiUTsdvv8/DwELUtLS/F43Ol0EgQxOzv76NGjcDgcDAZZli0UCt1ud2lpyWw2P3/+PBqNulyuWCyWTCZXVla+++47SZKCwWAkEoGSAAMVCgW/3x8MBiVJguwXSZKglWSr1Uomk5CKA+80SPQfXb1eTyQS8/Pzf/7554MHD06dOgUZDhaL5ddff71w4UKj0fj48eNvv/22uYtgm6w23QGUofVqlFcHSZLBYLC7n0bSpVLJ4/E4HA6TyZTL5WZnZzOZTCgU+vnnn0OhkJyFpbSnK6EhhPYPDDzQPnL+/Hmj0bix5uUDq/EqJyvkYTcMrSAI0el0Op1OrVY7nU7YjKZp2Gtqamp6evrgwYMqlcpoNMJa7Wg0GovFzp07d+HChUqlEggEJiYmjhw5ks1m79y5Q1GU2Wz2+Xyw+AS+6Y/FYvF4fGlpCSr3QxOxZDLJsmw4HK5Wq6VSSZKkYrGYy+UikYjZbLbZbPF4/Ntvv+V53uFweL1eWNxCEIS8Xkur1cIPgiCIouhwOFiWhZkN2Eb5Zbb8JECkoVolWuuPteD7bFEU5e+5IWiBk2RZlmGYubk5t9vtcrkgDuE4zmw2Hz9+nGVZuGuWZUmShHMjCMJgMDAMA2fudDp5nv/555/D4TDU/4HGaoFA4OrVq6VSqdlsiqIYi8WgjPI333xTLBY7nY7Vap2ZmYFIo1arud1uaI8gCEIwGIQ0mIsXL87NzYVCoZmZmUgkkkgkzp8/Pzc3F41G/X5/IpE4cuTIrVu3ut1urVZbWVmRV5eVy+VUKgWpwC9fvvT7/SaTye12q9VqWIAHdYogjUelUlmt1tevXzcajVAo5HA40um0x+O5cePG999/D03ifD5fpVKBg8urbsY0El3z2/ROpzMxMTFKdLEahmFMJpOyEwjHcbthYD1w2dua1QtGtLKyAn8BfD5frVZzOp3T09PBYHB5eTmfz//444+ZTKbRaGz45BFCaDfAwAPtL8Fg8Pjx4/1rrobUtlL+oNzMZrOZTCYYPavValEULRZLMpn0eDyVSmVlZSUYDObz+VQqFQqFYOXPgwcPisWi0+nM5XLyKX3+/Lm7VoIy/PvHH38Mr57Uo//G5eXlQCBQrVaXl5eLxWKlUvn999+hpC/P8wcPHjSZTI1GI5FIRKPR27dvFwoFqM315s2bT58+PX78GNYvLS8vN5tNq9XqcrkmJydhoEySJM/zcsQC4ZZer3e73WazGUbSkO4CaSrydAo8hzMzM/LTCwvDYFGZy+VSq9UkScp76fV6+C8EKhDvyT/DvShfNUiAEUWR53mj0QghxMWLFx8+fFgoFHien52dnZmZgekgSZJgquTUqVMMw9hsttOnT8PyLUEQYBZCkqS7d+9WKhWj0biwsCAIQjwen5iYMBgM//Ef/3H58uVgMDg1NSVJUiKRiMVib968gYQZeEUymYzf719YWPD5fDAjRNP01atXBUFwOBwul0sUxYMHDz558kSr1dI0XSqV4vF4pVL55ptvCILgOG5qampmZsbtdvM8D3NE3W63WCw+efLk/v370KO60WgUi8UrV67ASy9P5myseNea7y7lfzmO62m7uS5y3K683AqFwo4sP9tMXDF831ardfv27XQ6bTKZOI6jaRpWJ166dKndblcqldu3b0PiE+wFUcfeXYOHEEJdDDzQPjQ3N7dm1KH8LyxnUqlUBEEcOnQoFAops10h2aAnHthYsdcRY4kNjDZWuxfl2cqlq4bsO9D9+/c7nU4qlUokEhB3+f3+QqFQLpfj8bjNZoNqV8FgcH5+HlaJFItFq9VKkqTH49Hr9aIoxuPxV69eXb9+PRqNer3eYrFoNpsdDsfRo0fD4TDDMDdv3lSr1SaTCTo8mEymYDAI+Sd2u31qagpiP4qiDh065PV6IbmFpmmYqIGwBOZVdDod1AoTRdFkMtE0bTabJycnYZRvs9lgL4/HQ1HU5OQky7J6vR4qhvE8bzabWZadmZmZnp6GXJfr168HAgGj0cjzPMdxFEWJosiyLEVRMBtjMpnm5ub8fv/bt2+h2LEoiul0enZ2Fsooi6IYiUQsFkskEgkGg7Ozs8+fP3/9+rXVavX7/fV6HaqlURTFcRwM6yORiMFgmJ6enpqa+v777+fm5iKRyMePHyORyOTkZDqd9nq9PM9///332Wz27t27169fh4mR9+/fZzKZer3+9u3bUaKRIe+K1faCsHO98YYcLspTPTKCIJ4+fTrw3bs91gw/1nXJv3jxwul0siwbjUbtdjtFUTzPT01NGQwGv98fj8dbrdbnz5/r9fqbN28GHhxDDoTQHoWBB9p3Xr9+bTKZIpFIT+brwBwMnudhrVE4HO4pHbP50cA4ckCHT4mM/jXt8ChozeP0J7n25yfAYLrVasFMDgyCnz59Kndwl1OKlR3cQTKZfP369dLSkiRJmUwmHo/Pzs7G4/HLly8vLy/HYrF2u72wsBAKhU6dOuX3+y0Wy/T09MzMzIEDB2w2myAI8iqydDptNBohYLBYLHq9HuqJwewKlAWD6ReVSgXx0uTkpF6vh2BGEIRjx47BWi8IUGmaNhqNgiAYDAa4BTJhTCZTIBCYmpo6e/bs3Nzc5cuXIQoSRfHQoUPQy8Vut5vNZpIkjx49Go/H5+fnIX6bn5+HO3W73TRNQ7FmqEVGEEQwGEylUslkMhQKQVG1SCRis9nOnDnz+PHjUCgUDAZfv3595syZSqXy6tWrU6dOBQIBiqKi0WixWLx///6TJ0/kcHr4G3vNoXatVtvMdAeEGRCEQBdCmO/awW7cG1jlNfAigtIIsVjM6XS6XC63210qlbxebyAQ4HleDjt9Pl9/jtBq3xcghNDegoEH2ndWVlZ8Ph/04ugJOZRLfQ4ePAhLd/R6fSgUKpVKsPuadWOGDNzXXOUyinUdeZPFYTd22ltYl2n0gyjHavKWzWazUCik0+lqtVqtVnO5XCwW83q9fr/f4/E0Go1yuby8vAytUbxeryRJFovFZrNBrrkoim63O5FIQI3XY8eOnT59WqvVer3eUChkMBh0Op3L5SoWiy9evIAZErfbrdfrnU7n4cOHjx07Bukr8uI9juMEQTh06ND8/LzVaoVWFbAyzWKxsCwL8y2weM/j8ZjN5kKhYLFYoMcLx3Emk8lsNofDYZgsgvcwQRAQtJhMpu+//x7Kjtntdljsl81m5SkaKGQMGUeCIMA6QEgoslqtuVyu0+m8evXq7du3y8vLkIXy119/Xbp0CSYcwMuXL+v1erValbv7dTodCBevXLkSDodFUeyP5NcFAjZI44HCBuvN1x+TEdc09v9KkiS73T4zMzMxMTE9PR0Oh6HZaCqV+vnnn8+ePXvkyJF8Ph+NRkOhEDzzo5wGhh8Iob0FAw+0v8hLldxutxx4yMWdlFVujUYjZDN3t+jTfZQhy7q+W+1fdrXm9kPuYjOPcQNhz4hzJqNvv9pmzWbz/fv33W633W7DcrJwONxsNpUtsXO5nJy2m0qloGdIt9t99uzZ8+fPO53O8vIyHDkej+fz+QcPHvj9/unpabfbLfdu+/z587Nnz5aXl8vlcjAYTKfToijCOBKWYMGaLqfTGQgEWq2Wy+WCHCFRFLVabSAQ0Ov10Wj0v/7rv+LxOHSkhvKpdrsd5kZomjYYDD6fz+FwTE9P8zzvdDqh94Uoina7XRTF48ePu1wuiqK0Wq3RaDx16pRer4d1X3a7neM4g8EAS6Eg4wWqJL18+RKO8OTJE47jGo1Gu91eXFwslUoPHz70eDw//fQTPHu1Wq1arRaLRUmSvF7vyspKvV6Px+N+v//EiROQZG+z2TYQbMhlCXoilpMnT8JluIH3wyZtclljt9utVquJRALiT7vdHgqFYrFYNpu9du2avHG9XoeibaVSSS4SsNphceoDIbSnYeCB9qlms5lIJHieh5ADCjrduHHD5XLB999WqzUSifRkPmwsTljXIFsZToyymmv42qpR7nH03645z7MZ61q+tYFDbWyU9tdffw08VLFYjEajUD934J12Oh1I8oZVZK9fv67X69BR8cOHD58/f261WqlU6sKFCydOnIjFYuVy+eTJk8vLy61Wq1arhcPhhYWF2dnZV69effjwAVJBOI5zOBySJKXT6WQyCd1LvF6v2+2GNikWiwXy+N1ut8lkMhqNExMTDofD7XazLAvbkCQJ2fZQYZlhmNnZ2QsXLkDuCoQNUFEgFArBSjCfz3fhwoVyufzy5ctMJuP1eu12OxzQ7/frdDqr1Xrr1q3z58+73W5IlYFVUhsIPEBPRQetVqusdLwbFlzJt6ysrMRisXA4bDKZXC7X+fPnYa1UNpvN5/MulysYDJpMJlEUM5mMx+OB4lRQ1gymmLrdbrvdHtJJZpTVjwghtCdg4IH2l54hfrPZTKVSCwsLi4uLuVzuyZMnjUaj2Wxms9k///yzO7ZP93EPGsYxfbH5XTbzBe1699rw0rX1br+uIKdcLieTSSh8LG+wuLgI/y0Wi3KLBqgndufOHXgfxmIxaCESj8dTqdTDhw9v374NWyYSiVu3buXz+WKxCKV+IX8gk8lAUTX54LC2B2pqBYNBSIKHjisTExMmk2liYuL48eMOh+P58+fFYhFq2kIgEQwGPR7PyZMn7Xa72+02Go3QFQf6jVy8eNHtdvv9fo7j4EaIaoaHGautdez/L9QJSKfTO7XESHl31Wo1mUzCKjVY4Qa1BCDcIknSZrNNTEzQNH3u3DmHwwFr2+LxeCwWS6VSly5dqlar79+/h8Vpm3ksGHsghPYcDDwQQltpC5d/4EqSfp1O58uXL91u99WrVz2/unPnTi6XC4VCfr+fYZjnz59DpWZ5x263m0gkVlZWrl69mk6nYXokFApNTU25XC6Hw8FxnCRJgUDAbDYHg0FRFKEUGMMw09PTHo8HyoXBki3okcIwjNySBRLxVf9qPbneHA+1Wm0wGFR9ySHQfRJuv3v3LuQ/jPKuaLVaf//734vFItQbKJVKuVzuzZs3kPaTy+XK5fJqS5t6nrdarQYpQJByY7fbDQYD1KQKBAIOhwOqLUN2DfQhEQTB4/GEw+FLly7B/AbcF1RZUM5vIITQ/oGBB0JoN8J4YzXKeGy1PP50Ot1z+/LycrvdrlarEI3AQq9MJvPixYtsNnv27FmYjYGkeZ7nXS4XNNOAGr7RaDQej9vtdpfLZTAYIGWFoiiapk0mE9T4MplMEIdAEepRAo81t4H1V1AcGf7LcZzP5ztz5gzMApXLZSgSkM/nock3NHCE89RoNBaL5eDBg4cPH4Z+lFDgWK1WT09P2+12QRDcbjfkq5RKpUAgAB0q4cmpVCqfPn169uyZ3W7neb5arWazWUi/OXXq1OzsrNvtnp+f1+v1mUzG6XQaDAZIlZmYmDCbzX6//927d8vLy6lUCuay8F2NENrnMPBACG2xntHwmoMtSZLkomH9x0GydWXXKJ///shEBku5em5vtVqFQuHGjRupVOr69esXL1788uULZNjfu3fvf//3f7vdbiwWO3v2rM/nW1xchPx4lmXlelawRmt4jKFcUgXBQM9v4RYofKzX63U6XSQSMZvNZrPZ4/FAV0en05lKpfL5/KlTpyCHHhqncBx3/vx5iqKCwWAgEIBMFSiQRdN0OBy+cePG5OTkkSNHfvzxRwi0oKAZNGR0OByTk5PRaPTEiRNPnjyJxWJQDRmqLUMh5oMHD7pcrlQqdeDAgUql4vf7HQ4HTBYlk8lms1kul+H5XFlZ6b8c8O2NENqHMPBACG2l9a6P6nQ6ExMTKpUqGAxev3598wfcPwaGE0NSUNb8eV1jYnmbWq32yy+/1Gq1ZrN569atubk5juO8Xq9cI269sxywDXRvpCjKarVCz0SapqHdiiAIR44cmZychMaLkNt95swZi8UCrev1en0ikXj48CGUEYvH45IkRaPRWCwGSSmhUOjSpUuiKEJcYbPZrFZrMBgMhUImkwkaTYqiCDdevHjx+vXrLpdrYWHh4MGDNE3//PPPqVSqWCz+8ccfHz58yOVyz549K5VK9Xq9Vqu9e/euu/6icwghtB9g4IEQ2mGQZAwLe6ampj5+/NizAY7YNqknohhl5mQDFdvkn5eWllKpFLygPfHGkHkPOS0E1kFJkuR2uw0Gg9VqhV/pdDqv1zszMxMOh61Wq9PpnJiYCAQCt27dWlxcvHbtGtQRPnz4sMFguHnz5v3795PJpNPphAaLkiRdv35dTlzRarVXrlyZnZ3lOM5qtQYCgXQ6fe/evaNHj0I6O9QKCwaDkBMyNzcH1cmSyaScobFmqDZKYTqEENo/MPBACI3LiGMsCDzkQeeJEyc2dpyvz9Y+8NXSQobf18YqL0uSJAiC6l+tAFX/Xi23P/aAVx8CDLVabbPZ3r17FwqFoJk3ZG/TNB2JRA4cOBCPxzmOCwaDUFFKEISFhYVoNAoVh81mM03TNpsNGjJ6PB5RFEOhkNPpnJ6e5jiOZVkoB+x0OqFHilqtjsViiUTi6NGjWq3WYDCEQqFMJpNOpyVJyuVytVotn88/f/5c7vcy/CnFuQ6EEBoIAw+E0FiMPtiSkwFg9KnVai9fvoxL4ddr9MHuulZSbez5b7fbUFpXBhFIT6ncgUHIqVOn2u32ly9fms1mrVaTJKlarXq9Xr1eHwgEotGo2+2emZkxmUwQOTx69AiSy2/fvg3NVXw+34MHD3w+n06ng07qkiRlMhlI87Db7efOnTt+/Hg4HL527ZrNZoP+9I8fP/b5fDabbX5+/h//+Ee5XIb+ifCIvnz5MuJTOsoSOIQQ2p8w8EAIbZl0Om21Wn0+H9Q8HYUkSf2jT5vN1sWx2r+Mr7PKOMh3nc1mIaSEdU3wA8MwMKcBaRvyLAdU46VpOhqNDnwIN2/efPz48du3b3O53MePHzOZDHQBl/uZwPb3799X/hdmLeQk7263m8vlwuGw/P588OABlJyCqlNv3rxJJpMvXrzYZNjWHToBghBC+xYGHgihjesZUZEkaTAYoMBRvV4f5QgOh6M/8IjFYv0HR3tOOByenp6GfG6IMZxOp8PhCIVCuVwuEAjAy63X67/55ptEIlEsFoccTZlZsbi4mMlkxnHO0GcDIYTQOGDggRDaoJ7vdCuVinIVTTQazeVyax4EMgGU34uzLCsIwpD7QntFvV4/ceIEdDGHQlUGg0GSpIMHD0qSZLFYYP1VKpX6v//7vw3MJGwMJmAghNBOwcADIbRuA8dqV65cUa7gV6vVer1+tY1l0KxapVJRFOX3+6GEEcuyQ+4I7S3Hjx+HqBLa/50/fx4yvDUaDUVR9+7d646Qma2sTruZd8WQg+CbDSGExg0DD4TQxinHak6nE0IOuZARx3HDF890u1255ZxWq81kMocPH9bpdN98882YTxxtK8jwJgiCoqhbt27FYjGn06nVai9durRabd+x5kj8/vvvA6t7YeyBEEJjhYEHQmhrKDtVywVSZ2Zmhu/ldDrleRKfz3fx4sXJycmpqSkcAn59crnc69evFxcXo9FoIpF49uyZ/KvVZjkGHmfLV1tt+fERQggNhIEHQmhT5FGaHGwo9Wdr9Owbi8XkjX/66aczZ85wHCdJ0racOxq7NRvPD48utrlvPYYcCCE0Vhh4IIQ2qGeUptVqld2pYcEVy7LDB3O5XA62pyjq1KlToVDI7XaPWBEL7SFD5jTWNbOxJbHBmoEQRiAIITQOGHgghLaGalB3apIkh+/l9Xrlja1W67t371KpVP9mOBDc09YVQmy+h8Z6z2TL7wUhhNBAGHgghLbAysoKNP6Ty+PCjMe1a9eG7wgp6cBkMtVqtXw+vz3njBBCCKHthIEHQmgjer4Vfv/+vUajCQaDdrtdWVQXWgEOwTCMMvBoNptrFsLa67CSEkIIof0JAw+E0MbJg+a7d++qVCq32+31etUKgUBg+BGUPQedTuff//73crk8/hNHCCGE0HbDwAMhtFmdTufmzZsqlerIkSPVanVubo4gCJqm4Zbh+yoLYVEUlUqllpeXt+e0t9/Lly93+hQQQgihHYOBB0JoI3r6u127dk2tVtM07fV6GYahKGpdMx7KSY8xn/jOw7pJCCGE9icMPBBCmwID6FKpBMEDz/Mcx01MTEAgMbBElZIy6lCpVC6Xa1vOemdgdgdCCKH9DAMPhNAGKcfNz58/hxmP8+fPP378WK5tZbFYhhyh1WopC+9qNJpwOLxPhuP75GEihBBCMgw8EEJboF6vw8QFwzBOpxMSPFQqFc/zw3eUpzvg32AwuD0njBBCCKFthoEH2l0ikUi3222324VCodVqDdkSV63sHp1Op1aryZGG3+/nOA7SPERRHL6vMseD5/lsNrs954wQQgihbYaBBxqXNQOD/g3Onz9vMBhsNhtFUSqVSqvVer3eo0ePNpvN7tCUXIw6tl//ywGdy81ms9/vn5qacjgcDMMkk8nhr44ceDAMk06nK5XK2E8dIYQQQjsBAw+0rYaMQd++favsJaessgq+++47ebCLkcZu0PMq0DQNaR6xWMzn84miSBDEwsLC8INotVp4rV0u14MHD/CVRQghhL5WGHig8VpzokOSpEajEYvFzGZzz3L/1SKQqamp/lVYOGDdfj3POc/z8AJNTk56vd5oNMqyrMPhGH4QkiTlV7lQKHz8+HFlZWWMJ40QQgihHYKBB9oO/VHB77//XigUfvvtN6PR6HA4tFptT3ShjDc0Go38X/kHo9F48+bNnm4S2/uwULereNqdTie8NDRNu1wuu92u0+kWFxeH724wGOSXdXZ29p///OfHjx/Hf9YIIYQQ2m4YeKCxU8YDxWLRZrORJMnzPMMwHo+Hpml5hVXP5IZardbr9SaTyWazabVajUZDEIQyCIFtzp49u3MPDv1/Op1OLpeTX0S73S5Jkl6vFwRheECYTCbll3J47V2EEEII7WkYeKBxGTjcFAQBGlqr/lV6dbX1VBRF5fN5ecdmsxmJRMxmM8/zJEkSBNETfly7dm0bHxz6N/BaX7lyRX5FPB6Px+MJBoPDq1R1Op18Pi+/Jex2e71e366zRgghhNC2wsADbZ/l5WUosaoaRL5do9F4vV55r/4Aplgs3r5922Qy0TRNEIS8u8lk2t4HhP6NXFFXpVJ5vd5KpRKLxbLZ7PAZD3kvtVqt0+lqtdq2nTBCCCGEthMGHmj75HI5jUaj0WgGBh6AIIgzZ86MeMB6ve73+yErHWDssbPkXB2r1Vqv15PJZCKRWHMv+S1hMBiuXLny6tWrbThVNNyQ6tWrbbzaf9e8He1mb9++3elTQAh9PTDwQOOlHGpks1mz2axWq1eLPRiGOX78eLvdXu/BOY5Thi7KDXCss51IkoSZK5PJVCgUyuXy8C6QQDkJBh0k0c7qiTrWrE0IgyaXAAAR4klEQVTXHeFa668DMeT4aEeM8kIjhNBmYOCBxkg5vOh0Oi6Xi+M4eUF/zwori8UCjQI3dnCWZeHrdoZhxvNo0NqUMWQgELh///6agcfy8rKc86PRaPx+//acKhpuY506R489RjwgQgihrwkGHmhceoYU9Xrd7XZrtVq5YZwy/LDZbP27rFer1frll1+GnwYaKzmYVKvVZ86cSafTw3M2Tpw4oXwbkCRJUdTt27e37YTRBvTPV3Q6HVggl8vllFs2Gg0oEVGpVF68eLGysvLhwwfYpn8pF16qu8G6ltghhNB6YeCBxkj56ZXJZJSNyZXTHVardc3dh2yAC8p3D+WLe+TIEZ/PNzzwSCQSPW8Ju92eyWS27YTRcKPMUSSTSYfD8e2330aj0SNHjpRKpVqt9uTJk++++06n02m1WlEUzWazxWKJRqMzMzNardZisdjt9j///HPgAdFOwTgQITRuGHigsXv58uWJEyfkiQ5VX2PyUqm0gdXePbvgevHdQBlC0DR94cKF4eVxnz592jP9ZTAY1rXiDo1Pf9pGtVpttVrNZrPT6Xz+/DmRSPA8D0scWZblOI4kSb1eD1134DWVE7ooioI/Asr6dVNTUw8fPpTvbiceJfr/4XQHQmjcMPBAY1epVHw+32pVdHmel7ccsTbO8F+hHdQznTU5Oblmiaqe9wNBEKlUanvOFo2i0+n4fD63202S5NGjR+XaD3a73WAw9Df9HHiZ99+ujEA4jiuXyzv7MBHAb3AQQmOFgQfaDhaLZeBwxGAwrLbLJtNYN7Yl2iS5qhX44Ycf1nzyDx061POuSCaT23KyaG2tVqtSqVgsFujAQxCEJEmRSMRms60WY6yLHH4QBIFL7HYJXHCFEBofDDzQuMiz9k+ePJHb/PWw2+07fZpoK4XDYVhaQxCEVqvN5/MrKytDtofO5ap//0bc5XJt2wnvc2sOK6vVqiAIBEHIK+LUarWcrDWkJ09PWDJwS/mwMqhphlOdCCH0tcLAA22B4aMBURRh2NGT46FWq/P5PI4kvibtdpvneZIkSZIUBGGUuYtmsym3dpGzApRtB3Hd+VgNeXofP3584MABmOvor0Q3MMCALSmK0uv1giBYrdapqalsNhsKhS5evOhyuUwmk8lk4jhOEASGYfx+v/JbCbVabTab0+n0aqekPGeEEEJ7DgYeaLOG171ZXl6GNFPlwAX+9Xg8qx0B7V1fvnw5cOCAxWIxmUzZbHaUFzeVSjEMo8w5Pnbs2DacKgL9r1Eul/P5fJA1vuaSKq1WKwhCoVC4c+eOJEmxWOz+/ftwnGKxKH+58OXLl57eoJDXAUu5egpO6HS6S5cuQRb7tjwHCCGEtgMGHmhrrBZ+JJPJgcWsfvzxx9V2RHsavKCVSqXRaIyYMdzpdK5evUqSJLw3dDqd2WzGZnM7ZWlpSU68GRh1yFkZiUQiEAgUCoXuKq9Oo9GwWCwej+fp06cD70vea35+XrkcS/6GIhaL9W+82t0hhBDa5TDwQFtJHg202+10Oh0KhWAdRU+3cpVKBQ2tcRXNV+mvv/4afWP5PVAoFA4fPjw5OXnq1Kl4PN7z23GcJ+oh18+F5VUDQw6NRiMIwt///vdnz56tecB2uw2JHFqt1uFw9CT89Lysfr9fp9P1r90KBAKr7YIQQmhvwcADbZmedoEOh6NnXbj8A0mSq+2I9rrRayIP3LfT6ciNHdA2GPgChcNh+ZpVXr96vf7ChQsDSyQPPM7Lly9hvRYgCCIajSo37pnEePPmDcdxPSlhKpXKaDRWq9WtecAIIYR2DgYeaIvBSMLhcPSPHmTXr1/f6dNE47WBYLJ/MIotBXbKx48f5dJVQKPRyDXoRkn7hh+y2azJZOr5AoLjOJjwHKhWq/3444/ffvutxWKR884h6Xz4XSOEENr9MPBAW6BnNJDJZAiCkJfs96zbtlqtQ/ZFe9qGV+Hj22C3CYVC8pVLkuQvv/wyZOMh01wGg6G/lm4ulxu4Y89BWJZVRixzc3OjrO9CCCG0a2HggbaG8pvOBw8eRCKRnkUa8pgjm812caCJ0K6XTCYDgcAm1zgZjUblaiugLJc8kDxh4na7lRMmPM9DsV2EEEJ7EQYeaMsoM8vtdnv/CisYPXQx6kBoj9j8pWowGPoDD61WO/zgyvoEiUQCpk8h9qAoqj/JBP+kIITQnoCBB9oaPdWH3G73wHVWGo0GF+4jtH+YzWaNRtOz2oogCPjtalnmPQfR6/XKWVNBED5//jxwY/yrghBCuxkGHmiLwQe/3W5nWbZ/qZXX6x24PUJo91DGA5v8puDAgQP96V4w47HanfarVCpQllc+gs/n69kX/5IghNDuh4EH2jLKSY9YLOZ0OvuXWtVqtdV2RAjtTpu5Qt1ut1arletTAVEUu33TpP23KH+4cuWKTqeTj8AwTP+54V8ShBDa5TDwQFug//Pe7XaLotgz3aFSqRqNBnakRmhP2JILMxaLMQzTX9gKvoNYV69JURTl46jV6kgksvnTQwghtJ0w8ECb1f+1ZSgUSqVSynhDrkuzc6eJEBrVajMPGzhOJBKBqrhKGo2m2WwOvK+BZwL++c9/TkxMyH9MOI5TzqDi9xcIIbT7YeCBthJ89icSiVwu1/8dJ03T/RsjhHahrbo8C4WCMt0LGI3GTCaz5r33Rz7pdFq5akuSpC08VYQQQuOGgQcaC7PZLH83qZz3GOudYsdrhHaVTqeTSCQoiuqZ//T7/fIG6z2m2WyWJz0oisKLHSGE9hAMPNDWKxQKDMNwHCcIgnKdlUaj6dkSxwoIfd06nY7T6ez5DoJl2Wq1OnyRVf9x4Idz584pJz3sdjuWtEIIob0CAw+0Wf3fONbrdavV6nA4ekYbKpWqZ8txnxJot9vJZHLNzRBC40DTdE+RCZVKFY1GN3zA6elpefJEo9Fks9ktPFuEEELjg4EH2hr9g3iHwwFZpKqh3QM3k7e65gYXLlygKIokSYIg5GRWhND26HQ6hUKhP91LtUorjxE9ePBAeUy9Xt/F7xEQQmgvwMADbdZqdfQNBoNyRQTEHs+fP+/2ZY5u5k6HFMM5c+aMsoPh8GRWhNA4PHr0SK1W9/cSlRtxgHX9NSiVSspKWWq1GiY9MPZACKFdDgMPtMXkz36TyQRLLJSjDXnJ01iHCKVSiWGYnm9YW63WaqeKEBqHTqdz586d/ukOlUr13XffbeYCJElSuXbLbrdv4WkjhBAaEww80BYYOIA4d+6c0WjsWdvtcDi2fLjfM3/i8XjkaEe+63A4vLV3ihAahdVq7Qk54Kq0Wq0b/lPw22+/KStlqdVqKNWNXyUghNAuh4EH2jL9C6gkSZInPWSlUmlr73R5eTmdTlssFr1ePzk52f/dqsvlUp5hFwcoCG2X48eP9xeZUKlUPM8rN1vvJanX63sO++jRo40dCiGE0LbBwAON14kTJyiKUo4PWJYdcd8144TPnz8LgmCxWJR1e3vMzMxszSNBCK2f3+9XqVQajYYgCOUVqtPpupsIEvoDD5/Pt6UnjhBCaOth4IHGQh5PfPfddyaTqad1caFQUG42cPAxMOqAn0ul0ps3bx48eMBxnNwkpD/k0Gg0A6voIoS2R6fTqVarKpWqJ+qAa/bx48fyZqMcSvlzT1NClUo1NTWFcx0IIbTLYeCBxgjGAel0mmVZrVarHCV0Vx9t9Nz+/PnzaDTq9/trtVq3281kMlqtluM4laI1oXI0A/+SJJlKpcb/EBFCa4BKD/3fDoRCIXmb0WOGTqdTr9d7Yhj4NxaLretQCCGEthkGHmg7RCIRURTlNVcajUan0zUaDXmDgWOFarVqNBphVEFRVKlUslgs4XB4YHVO5ShEFMX+GlYIoR0RDAbl7x2UF6zJZOpuKE6oVCo9fwHg31gshlEHQgjtZhh4oG0Si8XcbreyswdEIKlUql6vt9ttecv5+XmtVuv1epWl+lWKXoT9azbknxmGmZ+f38GHiRDqIUmSRqPpuWwZhjGbzcrFlqO0BIUfAoFA/18Ao9GYTqfH/VgQQghtBgYeaFz6hxGNRsNsNit7mSvZbLaBHY57hherRR0EQUC66pATQAhtP5i6JElS+SUCwzAEQbx69Wq97USbzSbP8wMDj59++mmcjwMhhNBmYeCBtgkMLMrlst1uhzHHwFVSQwKPnm3kOIRhmMOHD9+/f7/nvhBCOw4uxnPnztntdmWiF0EQLMsWi8WeLddkMpkG/qHQarW3b98e18NACCG0FTDwQNut3W77fD6DwUBRFEmSw2c5BkYdctZHJBL5xz/+0cUGHQjtSsrrMZlMKldaajQalmWhBu6Il22n05mdnZX/FPSEHyRJvn//Hv8CIITQboaBB9oZwWAwFArxPG82mw0Gg9Fo5Dhu4DRIT9Sh0+kMBkM4HMZSuQhtofUuedrAYUVRVMYJer0+l8uNfqfBYFAZtyj/ODAMIxfpRgghtGth4IF2UqPR+OmnnzKZTDKZPHbs2OTkpCAIPM9TFEUQBEmSLMsyDGO1Wufn58vlsrIQFsC5DoS2ypguIuVhHQ6HHC3E4/H+bZQb//XXX/LPkiT1fAeh/Fmr1cpHwz8FCCG0a2HggXZAz3ery8vLPb9dWVlpNpsrKys9uww8Tv8BEUIjWrOdjjINY/P3srCwAG12DAbDapsp4w3g8/kGxhsynU43OTm5+fNECCE0Vhh4oJ00+trunv/2tzNHCG1A/+Xz8OHDx48f/+d//idJktCpU5KkgVuu6/jwQ7vdNhgMDMP0zF72z3jAZf7x40dBEIZkgqnVaoIgbt261fP9BUIIoV0IAw+0KwyZ0FhtMdXw/yKE1rTaVaPX65WD+8ePH2/y+MprOZPJQGrHmu7du7dmpTuNRjM9PQ2FdPGPAEII7XIYeKDtNiQrY5Rb+m/E0QZCGzbwesxms8rB/b179zZ/Fz1TGcO3X1xcDAQCFEUNnOJQVrfTarXy5AkuuUQIoV0OAw+0AwaOD/oXdis3XvNoCKEN67+IlFngbrd7qw672rcGnU7njz/+mJ+ft9vtytmM4XMdKpVqenp6Y+eGEEJo+2HggXYRDCEQ2ik9kX80GpXH/Vqtluf5/ppyo1jzon737l2pVJqYmFB2+VCpVDRNq1ZJKNdoNBzHRaNRl8vVarU2cFYIIYR2BAYeCCGEBrDZbMpIADp+zs/P//TTT3/88cd6j9ZsNuv1ejKZDIfDJpOJpmm1Wq3RaKCLqHL11BCQSm6z2XK5XLvdHsejRgghND4YeCCEEBrg/v37cpZF/8wDQRBGo9FisQQCAUmSrl27JknS3Nzc3bt3Yfd2u12pVNrttsPhgLY8KpUK/u1vOr7a5EZP1AGxypUrV3b2mUEIIbQxGHgghBAaLBaL9Qz9++MBeUWWPGshiqLFYhFFkSAIl8s1ZPpilNuVK6zUavXExEQ+n8dlmQghtBdh4IEQQmiwTqdjMpk0Go1Wq7Xb7RBjDM/5VimmRIZs3B91rDbjAT9D1BEMBsvlsnxuO/vkIIQQWi8MPBBCCA0gj+xjsVi1Wi2Xy06nk2EYiCjU/7Ja+AELqIbMYCj/KwiCnE2uVqshA8RoNBqNRpvNNjU1de7cuXq9vrNPCEIIoU3CwAMhhFCvgTWvG43G0tKS1Wq12WzBYJBlWa1WO8rshxxsKH9QduSAJBCapjUajUajSaVSXq/31KlTd+7cqVQqO/QcIIQQ2mIYeCCEEBqJHI08fPjw3LlzwWAQpiYgfpDrU8mLo6xWK8/zyuhCrpkLAYY8eaLRaFiWtdvtgiAwDHP27FnlPfafw8BfIYQQ2uUw8EAIITTAwJG9ciak0+kUi8VEIhGPxz9+/NhsNgOBAEEQ8gyGwWBgWRZCEYIgaJqG32o0GpqmbTYby7IMw0xMTFit1mq1ms1mh3cLwWADIYT2NAw8EEIIbY12u22z2URRdDqdbrfb5/M9ePAgHo9HIpFMJpNKpSBnw+/3l8vlfD5/7dq1Wq22srLy+fPnnT53hBBCY4eBB0IIoS3QMx3h9/srlcrAXBGEEEL7EwYeCCGENgtDC4QQQmvCwAMhhBBCCCE0dhh4IIQQQgghhMYOAw+EEEKbhUutEEIIren/AcUBQaDyOmIbAAAAAElFTkSuQmCC" alt><span style="font-family: times new roman,times; font-size: medium;"> <strong><em>A2</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> if one line missing or one line misplaced. Weights are not required.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to draw the graph as required in (a) and most made a meaningful start to applying Prim’s algorithm in (b). Candidates were not always clear about the order in which the edges were to be added.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In any graph, show that</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) the sum of the degrees of all the vertices is even;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) there is an even number of vertices of odd degree.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the following graph, <em>M</em>.</span></p>
<p style="font: normal normal normal 25px/normal Helvetica; text-align: center; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Show that <em>M</em> is planar.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Explain why <em>M</em> is not Eulerian.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) By adding one edge to <em>M</em> it is possible to make it Eulerian. State which edge must be added.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This new graph is called <em>N</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv) Starting at A, write down a possible Eulerian circuit for <em>N</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(v) Define a Hamiltonian cycle. If possible, write down a Hamiltonian cycle for <em>N</em>, and if not possible, give a reason.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(vi) Write down the adjacency matrix for <em>N</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(vii) Which pair of distinct vertices has exactly 30 walks of length 4 between them?</span></p>
<div class="marks">[12]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) When we sum over the degrees of all vertices, we count each edge twice. Hence every edge adds two to the sum. Hence the sum of the degrees of all the vertices is even. <strong><em>R2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) divide the vertices into two sets, those with even degree and those with odd degree <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>S</em> be the sum of the degrees of the first set and let <em>T</em> be the sum of the degrees of the second set</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">we know <em>S</em> + <em>T</em> must be even</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">since <em>S</em> is the sum of even numbers, then it is even <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence <em>T</em> must be even <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">hence there must be an even number of vertices of odd degree <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span class="Apple-style-span" style="font-family: 'times new roman', times; font-size: medium; display: inline; float: none;"><img src="data:image/png;base64,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" alt> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) the graph <em>M</em> is not Eulerian because vertices D and F are of odd degree <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) the edge which must be added is DF <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iv)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><br><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a possible Eulerian circuit is ABDFBCDEFGCA <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> award <strong><em>A1</em></strong> for a correct Eulerian circuit not starting and finishing at A.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(v) a Hamiltonian cycle is one that contains each vertex in <em>N</em> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">with the exception of the starting and ending vertices, each vertex must only appear once <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">a possible Hamiltonian cycle is ACGFEDBA <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(vi) \(\left( {\begin{array}{*{20}{c}}<br> 0&1&1&0&0&0&0 \\ <br> 1&0&1&1&0&1&0 \\ <br> 1&1&0&1&0&0&1 \\ <br> 0&1&1&0&1&1&0 \\ <br> 0&0&0&1&0&1&0 \\ <br> 0&1&0&1&1&0&1 \\ <br> 0&0&1&0&0&1&0 <br>\end{array}} \right)\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(vii) using adjacency matrix to power 4 <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">C and F <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[12 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to start (a), but many found problems in expressing their ideas clearly in words. Stronger candidates had little problem with (b), but a significant number of weaker candidates had problems working with the concepts of Eulerian circuits and Hamiltonian cycles and with understanding how to find a specific number of walks of a certain length as required in (b) (vii).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates were able to start (a), but many found problems in expressing their ideas clearly in words. Stronger candidates had little problem with (b), but a significant number of weaker candidates had problems working with the concepts of Eulerian circuits and Hamiltonian cycles and with understanding how to find a specific number of walks of a certain length as required in (b) (vii).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>