GW.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Алгоритм Гёманса–Уильямсона поиска приближённо максимального разреза с точностью 0.878"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Напоминание некоторых определений:\n",
    "* Симметрическая матрица X называется неотрицательно определённой, если все её собственные числа неотрицательны. Обозначение $X \\succeq 0$ либо X - PSD-матрица\n",
    "* $Tr(A)$ - след матрицы $A$, то есть сумма диагональных элементов\n",
    "* $S^n$ - множество симметричных матриц размера $n \\times n$\n",
    "* $S^n_+$ - множество симметричных неотрицательно определённых матриц размера $n \\times n$\n",
    "* SDP-задача - это задача оптимизации (т.е. минимизации или максимизации) некоторой линейной целевой функции на множестве PSD-матриц (возможно, c некоторыми линейными ограничениями). \n",
    "* Пусть $\\Sigma$ - матрица размера $n \\times n$, тогда корнем из $\\Sigma$ (обозначение $\\sqrt{\\Sigma}$) называется такая матрица $A$, что $A\\cdot A=\\Sigma$. В частности, если $\\Sigma$ -  диагональная матрица, то корень из $\\Sigma$ - тоже диагональная матрица, причем $\\left(\\sqrt{\\Sigma}\\right)_{ii} = \\sqrt{\\left(\\Sigma_{ii}\\right)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Постановка задачи:\n",
    "Дан неориентированный граф $G=(V, E)$ c матрицей весов $W \\in {S}^{n} \\ $, то есть $W_{uv}$ - вес ребра между вершинами $u$ и $v$. В частности, $W_{uv} = 0 \\Leftrightarrow $ в графе нет ребра между вершинами $u$ и $v$.\n",
    "\n",
    "Найти такое подмножество вершин $S \\subset V$, что сумма весов рёбер из вершин, лежащих в $S$, в вершины из $V \\backslash S$ максимальна\n",
    "\n",
    "## Формально:\n",
    "\n",
    "$$\\max\\limits_{\\mathbf{x}} \\frac{1}{4} \\sum_{i=1}^{n} \\sum_{j=1}^{n} w_{i j}\\left(1-x_{i} x_{j}\\right)$$\n",
    "\n",
    "$${\\text { т.ч. } x_{i} \\in\\{+1,-1\\}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "То есть x - вектор из $\\mathbb{R}^n$ такой, что если $x_i = +1$, то i-я вершина идет в первое подмножество вершин (в S), иначе, если $x_i = -1$, то i-я вершина относится ко второму множеству ( $V \\backslash S$)\n",
    "\n",
    "Тогда если $x_u = x_v$, то  $ \\ \\left(1 - x_u \\cdot x_v\\right) = 0 \\ $ и вес ребра $(u, v)$ не учитывается в сумме\n",
    "\n",
    "Иначе, $ \\ \\left(1 - x_u \\cdot x_v\\right) = 2 \\ $ и вес ребра $(u, v)$ учитывается дважды в сумме. Кроме того, для ребра $(v, u)$ происходит все то же самое, поэтому мы домножаем на $\\frac{1}{4}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Перепишем:\n",
    "\n",
    "$$\\max _{x_{i}=\\pm 1} \\frac{1}{4} \\sum_{i, j=1}^{n} w_{i j}\\left(1-x_{i} x_{j}\\right)=\\max _{x_{i}=\\pm 1} \\frac{1}{4} \\sum_{i, j=1}^{n} w_{i j}\\left(\\frac{x_{i}^{2}+x_{j}^{2}}{2}-x_{i} x_{j}\\right) = $$\n",
    "\n",
    "Это просто потому что $\\frac{x_{i}^{2}+x_{j}^{2}}{2} = 1$. Далее, раскроем скобки\n",
    "\n",
    "$$=\\max _{x_{i}=\\pm 1} \\frac{1}{4}\\left(-\\sum_{i, j=1}^{n} w_{i j} x_{i} x_{j}+\\frac{1}{2} \\sum_{i=1}^{n}\\left[\\sum_{j=1}^{n} w_{i j}\\right] x_{i}^{2}+\\frac{1}{2} \\sum_{j=1}^{n}\\left[\\sum_{i=1}^{n} w_{i j}\\right] x_{j}^{2}\\right) = $$\n",
    "\n",
    "Обозначим $deg(i) := \\sum_{j=1}^{n} w_{i j}$. Будем называть это число степенью вершины $i$. Кроме того, $D:= diag\\left( deg(1), \\ldots , deg(n) \\right)$. Тогда:\n",
    "\n",
    "$$=\\max _{x_{i}=\\pm 1} \\frac{1}{4}\\left(-\\sum_{i, j=1}^{n} w_{i j} x_{i} x_{j}+\\frac{1}{2} \\sum_{i=1}^{n} \\operatorname{deg}(i) x_{i}^{2}+\\frac{1}{2} \\sum_{j=1}^{n} \\operatorname{deg}(j) x_{j}^{2}\\right)$$\n",
    "\n",
    "Приводя подобные слагаемые, получаем:\n",
    "\n",
    "$$=\\max _{x_{i}=\\pm 1} \\frac{1}{4}\\left(\\sum_{i=1}^{n} \\operatorname{deg}(i) x_{i}^{2}-\\sum_{i, j=1}^{n} w_{i j} x_{i} x_{j}\\right)\n",
    "=\\max  _{x_{i}=\\pm 1}\\frac{1}{4} \\left[ \\mathbf{x}^{\\top} D \\mathbf{x} - \\mathbf{x}^{\\top} W \\mathbf{x}\\right]\n",
    "=\\max  _{x_{i}=\\pm 1}\\frac{1}{4} \\left[ \\mathbf{x}^{\\top} \\left(D - W\\right) \\mathbf{x} \\right]\n",
    "=\\max _{x_{i}=\\pm 1} \\frac{1}{4} \\mathbf{x}^{\\top} {L} \\mathbf{x}$$\n",
    "\n",
    "Где $L = D - W$ - лапласиан графа"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Введем $$X := \\mathbf{x}  \\mathbf{x}^T$$\n",
    "\n",
    "Заметим, что $$\\mathbf{x}^{\\top} {L} \\mathbf{x} = Tr\\left( LX\\right)$$\n",
    "\n",
    "Действительно, \n",
    "$$\\left( LX \\right)_{ii} = \\sum_{k=1}^n L_{ik}X_{ki} = \\sum_{k=1}^n L_{ik}\\mathbf{x}_k\\mathbf{x}_i $$\n",
    "$$Tr\\left( LX \\right) = \\sum_{i=1}^n \\sum_{k=1}^n L_{ik}\\mathbf{x}_k\\mathbf{x}_i $$\n",
    "Кроме того, легко видеть, что:\n",
    "$$\\mathbf{x}^{\\top} {L} \\mathbf{x} = \\sum_{i=1}^n\\sum_{j=1}^n L_{ij}\\mathbf{x}_i\\mathbf{x}_j$$\n",
    "Что и требовалось."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Еще раз, мы теперь перешли к рассмотрению матрицы $X$:\n",
    "$$X_{i j}=x_{i} x_{j}, \\quad x_{i}=\\left\\{\\begin{array}{ll}{-1,} & {\\text { если } i \\in S} \\\\ {+1,} & {\\text { если } i \\notin S}\\end{array}\\right.$$\n",
    "\n",
    "Наблюдение: $X$ — PSD матрица (ранга 1), на диагонали стоят 1. Действительно, для любой матрицы $Y \\in \\mathbb{R}^{m \\times n}$ и для любого вектора $z \\in \\mathbb{R}^{n}$ верно: $$z^{T}\\left(Y^{T} Y\\right)z=(Y z)^{T}(Y z)=\\|Y z\\|_{2}^{2} \\geq 0$$\n",
    "Из этого сразу следует, что $Y^{T} Y-$ PSD-матрица, а после транспорнирования: $Y Y^{T}-$ PSD-матрица. В частности, $X = \\mathbf{x}  \\mathbf{x}^T$ PSD-матрица.\n",
    "\n",
    "И решаем такую задачу:\n",
    "\n",
    "$$\\max _{x_{i}=\\pm 1} \\frac{1}{4} Tr\\left( LX\\right)$$\n",
    "\n",
    "Но это переборная задача - её сложно решить. Поэтому мы делаем то, что называется **релаксация**. То есть мы просто заменяем текущие переборные ограничения ($x_i = \\pm 1$) на такие, чтобы задача легко решалась. Например, давайте рассматривать в качестве $X$ все PSD-матрицы, на диагонали которых стоят единички. Тогда получим такую задачу оптимизации:\n",
    "$$\\max \\frac{1}{4} Tr\\left( LX\\right)$$\n",
    "$$т.ч.{X \\succeq 0 \\\\ X_{i, i} = 1}$$\n",
    "\n",
    "Она выпуклая, так как $S^n_+ - $  выпуклое, а $X_{i, i} = 1 \\ - $ это аффинное ограничение ($i$-й диагональный элемент матрицы легко получить просто домножением этой матрицы на матрицу $M$ из всех нулей, кроме $M_{ii}=1$). Поскольку мы **расширили** допустимое множество для нашей задачи максимизации, то и  новый максимум будет **больше**, чем исходный. Другими словами, $\\mathrm{OPT} \\geq \\mathrm{MAXCUT}$, где  $\\mathrm{OPT} \\ - $ оптимальное значение релаксации, а $\\mathrm{MAXCUT} \\ - $ ответ на исходную задачу. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Известно, что существуют эффективные алгоритмы решения SDP-задач. Формально, есть, например, метод эллипсоидов который решает эту задачу с точностью $\\varepsilon$ за $poly(N, R, log(1/\\varepsilon))$, где $N$ — длина записи данных, $R$ — логарифм максимального размера допустимого решения. На практике применяются в том числе и некоторые другие методы (например, есть метод внутренней точки), которые достаточно быстро работают на матрицах даже порядка $1000 * 1000$\n",
    "\n",
    "Далее, пусть $X^*$ - матрица-решение задачи максимизации. Тогда, так как $X^* \\in S^n_+$, то существует разложение $X^* = \\overline{U}\\Sigma \\overline{U}^T$, где $\\Sigma \\ - $ матрица с собственными числами матрицы $X^*$ на диагонали, а $U$ имеет столбцами соответствующие этим собственным числам собственные векторы единичной длины (это называется SVD-разложение). Обозначим $\\mathbf{U} := \\overline{U}\\cdot \\sqrt{\\Sigma}, \\ $ Тогда\n",
    "\n",
    "$$X^* =\\overline{U}\\Sigma \\overline{U}^T= \\left( \\overline{U}\\cdot \\sqrt{\\Sigma}\\right) \\left( \\sqrt{\\Sigma}\\cdot\\overline{U}^T \\right) = \\mathbf{U} \\mathbf{U}^T$$\n",
    "\n",
    "Давайте обозначим $\\mathbf{u}_{i} := i$-ая строка матрицы $\\mathbf{U}$. Рассмотрим систему векторов $\\mathbf{u}_{1}, \\ldots, \\mathbf{u}_{n}$. Видно, что матрица $\\mathbf{X}^* = \\mathbf{U} \\mathbf{U}^T - $ это матрица Грама этой системы векторов, то есть матрица, элементами которой являются попарные скалярные произведения данных векторов. По условию, $\\mathbf{X^*}_{ii} = 1$, значит \n",
    "\n",
    "$$\\forall i \\ \\ ||\\mathbf{u}_i||^2 = \\left\\langle \\mathbf{u}_i, \\mathbf{u}_i \\right\\rangle = \\mathbf{X^*}_{ii} = 1$$\n",
    "\n",
    "То есть все векторы имеют единичную длину. Это нам пригодится далее.\n",
    "\n",
    "Теперь мы хотим получить сам разрез. Предлагается такой алгоритм:\n",
    "1. Сгенерировать случайный вектор $h \\in \\mathbb{R}^n$ на единичной сфере\n",
    "2. $S:=\\left\\{i \\ |\\left\\langle{h}, \\mathbf{u}_{i}\\right\\rangle \\geq 0\\right\\}$, то есть $x_{i}=\\operatorname{sign}\\left\\langle h, \\mathbf{u}_{i}\\right\\rangle$\n",
    "\n",
    "Мы хотим оценить точность такого алгоритма. Давайте для примера посмотрим на рисунок:\n",
    "<img src=\"pic.jpg\" style=\"width: 270px;\"/>\n",
    "Здесь у нас есть 4 вектора $\\mathbf{u}_i$ и случайный вектор $h$. В таком случае, вектор $x = (x_1, x_2, x_3, x_4) = \\left(\\operatorname{sign}\\left\\langle h, \\mathbf{u}_{1}\\right\\rangle, \\operatorname{sign}\\left\\langle h, \\mathbf{u}_{2}\\right\\rangle, \\operatorname{sign}\\left\\langle h, \\mathbf{u}_{3}\\right\\rangle, \\operatorname{sign}\\left\\langle h, \\mathbf{u}_{4}\\right\\rangle \\right) = (+1, -1, -1, +1)$\n",
    "\n",
    "Теперь мы хотим оценить вероятность того, что вектора $x_1$ и $x_2$ имеют разные знаки:\n",
    "<img src=\"pic2.jpg\" style=\"width: 270px;\"/>\n",
    "\n",
    "Можно заметить, что вероятность разных знаков у $x_{1}=\\operatorname{sign}\\left\\langle h, \\mathbf{u}_{1}\\right\\rangle$ и $x_{2}=\\operatorname{sign}\\left\\langle h, \\mathbf{u}_{2}\\right\\rangle$ равна $\\vartheta / \\pi$, так как разделяющие прямые распределены равномерно."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее, оценим мат. ожидание величины разреза (вспоминая нашу изначальную формальную постановку задачи):\n",
    "\n",
    "$$\\mathbb{E}[c(X)]=\\frac{1}{2} \\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j}\\left(1-\\mathbb{E}\\left[x_{i} x_{j}\\right]\\right)$$\n",
    "\n",
    "Поскольку случайная величина $x_{i} x_{j}$ принимает ровно два значения ($\\pm 1$), то можно записать её мат. ожидание по определению:\n",
    "\n",
    "$$\\mathbb{E}\\left[x_{i} x_{j}\\right]=\\frac{\\vartheta}{\\pi} \\cdot(-1)+\\left(1-\\frac{\\vartheta}{\\pi}\\right) \\cdot(+1)=1-2 \\frac{\\vartheta}{\\pi}$$\n",
    "\n",
    "Поэтому, получаем:\n",
    "\n",
    "$$\\mathbb{E}[c(x)]=\\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j} \\frac{\\vartheta_{i j}}{\\pi}$$\n",
    "\n",
    "Теперь вспоминаем, что вектора $\\mathbf{u}_i$ имеют единичную длину, а $\\mathbf{X^*} - $ матрица Грама, поэтому:\n",
    "\n",
    "$$\n",
    "\\mathbf{X^*}_{i j}=\\left\\langle u_{i}, u_{j}\\right\\rangle=\\cos \\vartheta_{i j}\n",
    "$$\n",
    "\n",
    "Далее, снова запишем мат. ожидание величины разреза, а затем домножим и разделим каждое слагаемое на $\\left( 1 - \\cos{\\vartheta_{ij}} \\right)$, при это вынося $\\frac{1}{2}$ знак суммы:\n",
    "\n",
    "$$\\mathbb{E}[c(x)]=\\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j} \\frac{\\vartheta_{i j}}{\\pi} = \\frac{1}{2}\\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j} \\frac{2 \\left( 1 - \\cos{\\vartheta_{ij}} \\right)}{\\left( 1 - \\cos{\\vartheta_{ij}} \\right)} \\frac{\\vartheta_{i j}}{\\pi} $$\n",
    "\n",
    "А теперь просто оценим эту сумму снизу, оценивая кусочек каждого из слагаемых, то есть:\n",
    "\n",
    "$$\\mathbb{E}[c(x)]= \\frac{1}{2}\\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j} \\frac{2 \\left( 1 - \\cos{\\vartheta_{ij}} \\right)}{\\left( 1 - \\cos{\\vartheta_{ij}} \\right)} \\frac{\\vartheta_{i j}}{\\pi} \\geqslant \\min _{0<\\vartheta<\\pi} \\frac{2 \\vartheta }{(1-\\cos \\vartheta) \\pi} \\cdot \\frac{1}{2} \\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j}\\left(1-\\cos \\vartheta_{i j}\\right)$$\n",
    "\n",
    "Обозначим $\\alpha_{GW} := \\min _{0<\\vartheta<\\pi} \\frac{2 \\vartheta }{(1-\\cos \\vartheta) \\pi}$. И, вспоминая, что $\\mathbf{X^*}_{i j} = \\cos \\vartheta_{i j}$ перепишем:\n",
    "\n",
    "$$\\mathbb{E}[c(x)] \\geqslant \\alpha_{\\mathrm{GW}} \\frac{1}{2} \\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j}\\left(1-\\mathbf{X}^*_{i j}\\right)=\\alpha_{\\mathrm{GW}} \\mathrm{OPT}$$\n",
    "\n",
    "Где $\\mathrm{OPT} \\ - $ оптимальное значение релаксации. Ясно, что  $\\mathrm{OPT}$ представляется в таком виде, ведь $X^* \\ - $ это решение нашей релаксации, а $\\frac{1}{2} \\sum_{\\{i, j\\} \\subset V, \\\\ \\ \\ \\ \\ i \\leq j} w_{i j}\\left(1-\\mathbf{X}^*_{i j}\\right)$ это и есть в точности то, что было заявлено в начале: $\\frac{1}{4} \\sum_{i, j=1}^{n} w_{i j}\\left(1-x_{i} x_{j}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Кроме того, так как метод Goemans-Williamson’a выдаёт некоторый разрез, то, очевидно, мат. ожидание величины этого разера не может быть больше, чем истинное значение максимального разреза, то есть:\n",
    "\n",
    "$$\\mathbb{E}[c(x)] \\leq \\mathrm{MAXCUT}$$\n",
    "\n",
    "Как уже было показано ранее, выполнено:\n",
    "\n",
    "$$\\mathrm{MAXCUT} \\leq \\mathrm{OPT}$$\n",
    "\n",
    "Наконец, соединяя все неравенства вместе, получаем:\n",
    "\n",
    "$$\\alpha_{\\mathrm{GW}} \\mathrm{OPT}  \\leqslant \\mathbb{E}[c(x)]  \\leqslant \\mathrm{MAXCUT} \n",
    "\\leqslant \\mathrm{OPT}$$\n",
    "\n",
    "Значение константы $\\alpha_{\\mathrm{GW}}$ легко вычислить и оказывается, что оно примерно равно $0.878$. Таким образом, описанный алгоритм находит разрез в среднем со значением порядка $87\\%$ от максимального. Известно, что получение оценки в $\\frac{16}{17}$ от оптимального значения уже является NP-сложной задачей.  $\\frac{16}{17}$ примерно равно $0.94$. То есть, если человечество сможет найти алгоритм, который решает задачу $\\mathrm{MAXCUT}$ с точностью всего лишь на $6\\%$ лучшей, чем описанный алгоритм, то из этого будет следовать, что $P = NP$. \n",
    "\n",
    "Но до сих пор поиск алгоритма даже субэкспоненциальной сложности, который бы находил оценку лучше $0.878$, является открытой проблемой."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Реализация"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import cvxpy as cvx\n",
    "import pandas as pd \n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from IPython.display import display, HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для примера, создадим полный двудольный граф на 13 вершинах: 5 вершин в одной доле и 8 в другой. Очевидно, что значение максимального разреза равно $5*8 = 40$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 5 + 8\n",
    "# полный двудольный граф на 13 вершинах\n",
    "G = nx.complete_bipartite_graph(n1=5, n2=8)\n",
    "# получам лапласиан графа\n",
    "L = nx.laplacian_matrix(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# вычисляем значение разреза. х - вектор из +- 1\n",
    "# L - лапласиан графа\n",
    "def cut(x, L):\n",
    "    return 0.25 * x @ L @ x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Известный алгоритм нахождения максимального разреза с точностью 0.5 - это просто взятие случайного разреза. Попробуем реализовать этот алгоритм на данном графе и посмотрим, что получится."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# берем случайный вектор из +- 1\n",
    "cut_trial = 2 * np.random.randint(0, 2, n) - 1\n",
    "# вычисляем величину такого разреза\n",
    "cut(cut_trial, L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, что значение такого разреза равно 20, что как раз и есть ровно половина от истинного значения максимального разреза.\n",
    "\n",
    "Изобразим полученный разрез. Желтые вершины лежат в одной доле, фиолетовые в другой."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_circular(G, node_color=cut_trial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь же, наконец, реализуем алгоритм Гёманса–Уильямсона"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----------------------------------------------------------------------------\n",
      "\tSCS v2.1.1 - Splitting Conic Solver\n",
      "\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
      "----------------------------------------------------------------------------\n",
      "Lin-sys: sparse-direct, nnz in A = 104\n",
      "eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00\n",
      "acceleration_lookback = 10, rho_x = 1.00e-03\n",
      "Variables n = 91, constraints m = 104\n",
      "Cones:\tprimal zero / dual free vars: 13\n",
      "\tsd vars: 91, sd blks: 1\n",
      "Setup time: 2.03e-02s\n",
      "----------------------------------------------------------------------------\n",
      " Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)\n",
      "----------------------------------------------------------------------------\n",
      "     0| 8.56e+19  1.39e+19  9.42e-01 -2.28e+21 -6.78e+19  1.70e+20  9.45e-03 \n",
      "    40| 6.43e-07  8.16e-07  2.59e-08 -4.00e+01 -4.00e+01  1.16e-15  1.35e-02 \n",
      "----------------------------------------------------------------------------\n",
      "Status: Solved\n",
      "Timing: Solve time: 1.36e-02s\n",
      "\tLin-sys: nnz in L factor: 299, avg solve time: 1.43e-06s\n",
      "\tCones: avg projection time: 2.04e-04s\n",
      "\tAcceleration: avg step time: 2.21e-05s\n",
      "----------------------------------------------------------------------------\n",
      "Error metrics:\n",
      "dist(s, K) = 1.7159e-09, dist(y, K*) = 1.8634e-09, s'y/|s||y| = 1.2848e-11\n",
      "primal res: |Ax + s - b|_2 / (1 + |b|_2) = 6.4337e-07\n",
      "dual res:   |A'y + c|_2 / (1 + |c|_2) = 8.1579e-07\n",
      "rel gap:    |c'x + b'y| / (1 + |c'x| + |b'y|) = 2.5894e-08\n",
      "----------------------------------------------------------------------------\n",
      "c'x = -40.0000, -b'y = -40.0000\n",
      "============================================================================\n",
      "40.00000095875753\n"
     ]
    }
   ],
   "source": [
    "# вычисляем ответ для задачи максимизации (релаксация Гёманса–Уильямсона)\n",
    "def GW_solve(n, L, verbose=False):\n",
    "    # X - положительно полуопределенная (PSD) матрица\n",
    "    X = cvx.Variable((n, n), PSD=True)\n",
    "    # целевая функция Tr(LX)/4\n",
    "    obj = 0.25 * cvx.trace(L.toarray() * X)\n",
    "    # ограничение: на диагонали стоят единички\n",
    "    constr = [cvx.diag(X) == 1]\n",
    "    # нам нужно максимизировать\n",
    "    problem = cvx.Problem(cvx.Maximize(obj), constraints=constr)\n",
    "    return problem.solve(verbose=verbose, solver=cvx.SCS), X\n",
    "\n",
    "# выводим результат решение задачи оптимизации \n",
    "result, X = GW_solve(n, L, True)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Действительно, получилось, что $\\mathrm{OPT} \\geq \\mathrm{MAXCUT}$\n",
    "\n",
    "Теперь нам нужно восстановить сам разрез по описанному выше алгоритму:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# получаем сам разрез \n",
    "def get_random_GW_cut(X):\n",
    "    # получаем размерность\n",
    "    n = X.value.shape[0]\n",
    "    # получаем SVD разложение\n",
    "    u, s, v = np.linalg.svd(X.value)\n",
    "    # получаем матрицу Грама U\n",
    "    U = u * np.sqrt(s)\n",
    "    # берем случайный вектор на единичной сфере\n",
    "    h = np.random.randn(n)\n",
    "    unit_h = h / np.linalg.norm(h)\n",
    "    # x_i = sign <h, u_i>\n",
    "    gw_cut = np.sign(U @ unit_h)\n",
    "    return gw_cut\n",
    "\n",
    "# Выводим значение полученного разреза\n",
    "cut(get_random_GW_cut(X), L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как видим, алгоритм нашел действительно максимальный разрез, то есть точность получилась $100\\%$. Изобразим этот разрез:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OTo7Qch8+fKDmzZtTcHBwldfPnDlDJiYmQutXJXyFhYWkrq5Or1+/rrLOihUryMzMjHg8Xg1P8e+Fz+eTjfZ0iURvsJQ1jWxoR4Hbzv3ox2AREVb4/kMUFhbS4cOHqWPHjtSjRw/y9/cXOtnduXOHmjdvTgsXLiQulyv4nGEYmjhxIk2cOJEYhhF8PnLkSPLx8SnXRtlJ+M8//6TGjRuXu9+ePXuoS5cu9PXrV8FnOTk5NG/ePJKXl6dWrVpRw4YNyczMjNauXUs3b96sdjX4PXjw4AFNmjSJVFVVaf78+ZSSkiJ2G35+fqShoUH79+8vN2YV4fF4ZGZmRitWrBBaZvTo0XT06FGh14Vt4syZM4fWr19f5bWSkhIaPnw4ubi4CG33307clfs0SsleYuEbLGVNvzaZLvLqn+XHwhq3/AfIysoSxIPs2bMnXF1dMWDAgCrN6xmGwdatW7Fz504cOXIEo0aVdzfYsWMHjh8/jjt37qBhw2/m3MIMKCoaWvTv3x/Lli0TtElEsLe3x9u3b2FoaIiIiAgkJyfD0NAQHTt2xKVLl9CvXz8cPHiwziwvRYGqcOGYOXOmWBFagG+GNvPmzcOdO3cQFBSEbt2qN4CYP38+nj9/XsmYpZQPHz6gffv2SE1NFToeFce8lPj4eNjY2ODFixdVng3m5ubCwMAAq1evxqRJk0R8wn8PK0ZuRtzlxFq1Ia8kh/Vnl6DHwC511CuW7wXrx/cv5uXLl4J4kJaWlggLCysXD7IiHz58wKRJk1BQUID4+Hjo6uqWu37jxg1s3boV0dHRAtEDAH9/f1haWlaKRFIRR0dHHDp0CEQksLp8+vQppKWlIS8vDw8PDxgaGqJBgwYAvrkiuLi4oHfv3ggMDET37t1rMRo1w+PxEBAQAA6HI3DhCAkJEfRHHB4/fgwbGxsYGBggISGhRqOa48eP49KlS+Uis1TkxIkTGDNmjEQvAb169ULDhg0RGRkJU9PKWdhVVFRw7tw5mJubQ19fH7179xb7Hj8zac/e17oNhk9If/mBFb6fANaq81/I3bt3YW1tjb59+0JZWRlJSUnw8vKqVvSuX7+Onj17wtDQEDdv3qwkeq9fv4adnR1OnDiBli1bCj4nInh7ewsNnZWdnY3z589j4cKF2Lt3Ly5cuAAOhwM1NTXs2rUL2dnZePLkCR4/foyCgoJyItOwYUMcOXIEa9euxZAhQ7Bv377vkrg2NzcX27ZtQ+vWreHr64utW7fi0aNHcHR0FFv0iAiHDx/GgAEDsHTpUvj4+NQoevHx8XB1dcW5c+eEhkMjompDlNWElJQUHB0dcezYMaFlOnXqhIMHD8LKygofP36U6D4/CzweD+/fv8eDBw9w/fp15GZ9rnWb/BI+CvIK66B3LN8bdsX3L4HP5yMkJATu7u5IT0/HokWL4OPjU+MqrKSkBOvXr8fRo0fh4+ODwYMHVypTUFAAS0tLLF26FAMHDix3LT4+HoWFhTAxMQHwbVs1IiIC4eHhAIAWLVqgX79+MDc3x4EDB7B371707dsXLi4ugjaaNWuGwMBAWFtbIyoqqpI/n52dHQwMDDB+/HjcuHEDXl5eYsfLrIo3b95g586d8PHxwciRI3HhwoVarSq/fPmCGTNmIDk5Gbdv30aHDh1qrPPx40dYWVnh4MGD1b6YJCYmIi8vr5KTuzjY29ujQ4cO2LNnj1AxHjduHO7du4dff/0VYWFhP0VkF4Zh8PnzZ2RmZuLTp0/49OmT4O9Vffbp0ycUFhZCXV0dmpqa0NDQgGxx7UPnychKoyEbzeWngD3j+8kpjQe5Y8cOqKmpYfHixbC0tBS6XVaWtLQ02NnZQU5ODr6+vmjcuHGlMqXncFJSUvD19a10Ljh16lQUFhZCU1MT4eHhePXqFYyMjGBubo7ly5eDx+OVmzzDwsKwZMkS3Lt3r9K9SsN83b17t8qJmcvlYvHixQgNDcXJkyfRt29fUYaoEvHx8eBwOLh69SqmTZsGFxcXNGvWTKK2yrZpa2uLIUOGwMPDA/Ly8jXWKS4uxuDBg2FiYiLIuCAMFxcXqKmpYd26ddWWE3bGV8qoUaNgbW2NyZMnCy3D5/MxevRotGnTBrt37672ft+DoqKiGoWr7PXs7GwoKCgIRKz0v9X9XVlZGW/evPlryz0oFQqFKpBC1WHlREFeUQ6bL61AZ+OOdTgaLN8DVvh+UsrGgzQyMoKbmxv69+8vNB5kRS5cuIDp06dj/vz5WLp0qVBnaA8PD/j5+SEyMhINGzZEZmYmwsPDER4ejhs3biA5ORmmpqYYPnw4zM3N0bNnT4HQVTUJ8/l8tGrVCqGhoZWMPYgI06ZNQ15eHoKCgoQ+y7lz5zBz5ky4ubnB1dVVJEduhmFw6dIlcDgcvHz5EgsWLMD06dNrHZeTiLBr1y5s3rwZ+/btw6+//ipyXRcXF7x8+RIhISHVvqhwuVw0a9YMsbGxaNWqVbVt1iR8p0+fxt69e3Hz5s1q28nNzYWhoSFWrFgh8fYq8O3fOycnR6RVWOnfi4uLqxWxip+pq6vXuDIlIrx+/VqQR/HWrVsoLCwUhK6TK1JEwPILoGLJp0MtXQ34vd4v8m+Q5cfBCt9PxtOnT+Hh4YFTp06JFA+yIjweD8uXL0dwcDBOnDiB/v37Cy17/fp12NnZYe3atUhKSkJ4eDhSU1NhbGwMc3NzFBcXIywsDDdu3KiyvrBJeNWqVcjPz68yKWpRURHMzMxgaWmJZcuWCe3bmzdvMGHCBKioqAgN+VXanp+fHzgcDuTl5eHm5oZff/21TrbwsrKyMHXqVKSnpyMgIACtW7cWua63tzc2b96M2NjYGrdtRRUroGbh4/F40NHRQUxMTI39ffLkCczMzHDp0iUYGBiAiFBQUCDSKqz0s5ycHCgrK1crXBX/rqioWGvxICKkpKQIRO7WrVvg8XiC0HVmZmbo0KEDEhIS4O7ujmtXr6EPMxTFXyRLriyn0ADTfp+IsXOH16rfLH8PrPD9BFCFeJCzZ8/G7NmzxU4rk5KSAltbW2hra+PYsWNVZgrPyMhAeHg4QkNDERAQADk5OcFkYW5uju7du0NG5tvR8IgRI2BnZwd7e/sq7ydsEn7x4gWMjIyQlpZWZXDqtLQ0GBoa4ujRo+Vy0lWkuLgYa9asga+vL/z8/GBubi64VtGFw83NDebm5nX2Nh4ZGQk7OzvY2Nhg8+bNYgXZjouLw4gRIxAeHg59ff0ay4uyPVlKTcIH/LVtumrVKmRlZVUrXElJSXjy5Ak0NTWRnZ0NKSmpGoWr7GdqamqC78v3hIjw8uXLcis6Pp8vEDlzc3Po6elBSkoKDMPg4sWL4HA4ePXqFRYsWICpU6di64IdiPZ5CGnUfExQEUVVBfi92s9mbPhJYIXvH0xJSQlOnz4Nd3d3fPnyBa6urnBwcBDp/KgiQUFBmDt3LlauXAkXFxeBAKSnpwsmivDwcGRkZKBfv3548OABbG1tsW3bNqH54zp16lTJd68s1U3CJiYmcHNzw5gxY6q8fvv2bVhbW+POnTto27Zttc925coVODo6YtasWbC1tcXu3btx8uRJWFpaYtGiRdUajYgLwzDYsmULdu/eDS8vL4wcOVKs+h8+fICBgQF27doFS0vLGstnZGSgQ4cOSEtLq9Y6lIiQl5cHZWVlREdHV7siS01Nxbt37wAA6urqNW4lnjp1Co8ePcLVq1clzk1Y1xARnj9/Xm5FB6Dciq5du3blXnSKiorg6+sLDocDBQUFuLm5wdraGoWFhZg5cyaSHifBUt8OcaEPhQZbrwq5hg3gfnMd2htU/z1l+efACt8/kLy8PBw9ehQ7duxA8+bN4ebmBgsLC5HOsipSWFiIhQsXIiwsDAEBAWjatGm5ySIzMxMmJiaCCaNLly6YNGkSpKWlcfz4caErpKrS3VSkOuHz8vLChQsXcPbsWaH19+/fj/379yM6OrpGl4DQ0FBMmzYNubm5mDVrFpYvXw5tbe1q64hLRkYGHBwcwOVyceLECbENYkqNWUxNTbFx48Zqy/J4PGRlZcHd3R1JSUmYOnVqjWdk9evXx9evX2FgYFCjcYeVlRV2795dKa1RVTAMg9GjR6NVq1bYs2ePWM9cVxARnj17Vm5FV69ePQwYMECwomvTpk2V39dPnz4JVv+9e/eGm5sbzMzMBMHXx48fLzBKysnJwaj2NtAqaYYSbvW5tmTry6C+fH1svrwS+n1FP25g+fGwwvcP4t27d9izZw+OHDmCQYMGwdXVFYaGhhK3l5ycjHHjxkFFRQV6enq4e/cusrKyYGpqKpgsunTpUm5Fx+FwcOLECURGRgpdWRIR9PX1ceTIkWrPCKsTvry8POjq6uLZs2fQ0tISep/p06fjy5cvVRq78Pl8nD9/HhwOB+np6ViwYAEyMzNx5MgRHDt2rNptUnEJCwvD5MmTMW3aNKxZs0as7TsiQm5uLlxcXJCSkoLFixcjOzu72jOygoICqKmp4fPnz+jYsSPatWtXo5jJycmJtNUJfIvAc//+ffj4+Ij0DHVl7CIqRISnT5+W242QlZUtt6Jr3bp1tVvXz58/x44dO3Dy5ElYWVlh0aJFgq1lIsLu3bvx22+/CYySeDweBg0ahIEDB2KMiRX2Lz2K1/dTUb9+fRRz/zr7q99QFkVFRRi/yBLj5o+Ahk7tXSFY/l5Y4fsH8OjRI3A4HISEhMDBwQELFiyo0XpPGKmpqbh16xYOHz6MO3fuQF5eHkOGDMGAAQNgbm6Ozp07C105hoWFwcHBATExMWjevLnQe8TExMDe3h7Pnj2rduKpaRKeNGkSevbsiQULFggtU2rsMnbsWCxfvhzAXy4cHh4e0NDQgJubWzkXjoiICEycOBETJkzAb7/9VitDlpKSEqxbtw7Hjh3D8ePHMWjQIBQVFYnsL5aZmYmsrCzIysqipKQEXbt2hba2do3bi8rKyoLVyPPnz0Ve7YsqfB8/foSenl614c8qUtHYpS4hIiQnJ5db0cnJyZVb0bVs2VKkM9qoqCi4u7vj9u3bmDVrFubMmYMmTZoIrmdnZwvyQAYGBgqMfObMmYPU1FScO3cO9erVg4ODAzq16YwWDdoh43UmvA4dxewFs9DBoC1mr5uBo95eMDIyqtNxYPmbqLOonyxiwTAMXb16lYYOHUra2tq0efNmysrKErudN2/ekI+PD02ZMoVat25Nampq1Lx5c2rSpAmdPn1a5KC5KSkp1LhxY7p582aNZWfNmkWbNm2qsVxNX6/r169Tt27damwnLS2NmjZtSv7+/rR69WrS1NSksWPHUmRkpNCgz5mZmTRy5Ejq27cvvXr1SmjbfD6fPn36RMnJyXT79m06e/YsHTp0iDZv3kxOTk6kpaVFGhoa1K1bN2rZsiUpKipS/fr1qWnTptS1a1caNGgQjR8/nubOnUvr1q2jvXv3UmBgIF2/fp0ePHhA79+/pzt37pCGhgYlJSXV+KxlqS6wtDDE+UnXFPC6Ks6ePUu6urqUkZEhVr2KMAxDjx8/pr1795K1tTVpampSy5YtydHRkby9vav9N6uKkpISCg4Opr59+1Lr1q1p79695YKflxIZGUnNmzenRYsWlQu+7uXlRe3bt6fc3FwiIsrNzSVlZWXKzMwUlCk7tlu2bKHp06eL+dQs/xRY4asBpiSdGN5jYrj3iSl+SQxTu9QtXC6Xjh8/Tl27dqVOnTrRsWPHqKioSOT6r169Im9vb3J0dKSWLVuSpqYmWVtb0969eyk4OJj09PRo6tSpVf7ohZGfn0/dunWjnTt31li2sLCQ1NTUKuXtq4qaJmE+n08tWrSge/fuVVvuyZMnZGFhQVJSUjRhwgT6888/hZbNz8+n169fU3x8PF28eJHs7OxIUVGRxo0bRzNmzKBx48aRiYkJdezYkTQ1NUlGRoZUVVVJT0+PjIyMaPTo0TRt2jSysrIiRUVFsra2ppCQEIqJiaGXL1/S58+fq82wUJGMjAzS1dWls2fPilyH6K9UQuIKgDjCV1OKI2GsXr2aTExMyglHTfD5fHr48CHt3r2brKysSENDg1q3bk1TpkwhHx8foSmTauLr16+0d+9eat26NfXt25dOnz5NJdYFc4QAACAASURBVCUlVd5/8+bN1LhxYwoNDS13LTo6mjQ1NSk5OVnw2eHDh8nS0rJcubJjm5aWRioqKn9bWiyWuoUVvipgGC4xBaHEzxxN/PTOxM/oQfyMnsTP6Eb8jF7E/+JBTEm6WG3m5ubStm3bSEdHhwYNGkSXL1+ucQJlGIZSUlLo6NGjNHnyZGrRogVpaWmRjY0N7du3j5KSkohhGGIYhvbu3UsaGhrk7+8v5rMyZGtrS5MmTRJpQj958iQNGTJEpLZFmYTXrFlTZTochmHo+vXrNGTIEFJXV6cpU6aQvb09NW3alFatWkXz588nOzs7Gjp0KPXs2ZN0dXVJXl6e5OTkSFdXl3r06EFDhw4lOzs7srGxIVVVVTIzMyN/f3+6desWPX78mDIyMqi4uLjcfYuKimjBggXUokULunPnjkjPKQwul0smJia0evVqsetWlzy2OsQRvtKkts+fPxfrHnw+nywsLGjOnDnVlnnw4AHt2rWLLC0tSV1dndq0aUPTpk0jX19fkV6cqiMjI4NWrVpFGhoaZGlpWe2/VUZGBg0ZMoRMTEwoNTW13LX09HRq1qwZnT9/vtzn/fv3r/RZxbH95ZdfyM/Pr1bPwfJjYIWvAkxR5P9Frjvx09sJ+dPp25/ctcQwld8uy/L69WtauHAhqaqqkr29PSUmJgq/N8PQixcvyMvLixwcHEhXV5caN25M48ePpwMHDtCTJ08qiVNOTg6NGzeOevToQc+ePRP7ebdv3069evUSOc/dsGHDRBbXshMFwzD05csXSklJoZiYGLp48SJ5e3vTsmXLSF5enhwdHWnMmDFkZGRE2traJC0tTQBIUVGR9PT0yMTEhMaOHUvt27en9u3bE4fDIV9fX7p8+TLFxcXR69ev6evXr0LFOycnh6ytralbt25CV4wvXrygXr160ZgxYyTadq7InDlzyMLCQqIcbSNGjKDjx4+LXU/c04v58+dLJMy5ubmkp6cn2Crl8/mUmJhIO3bsoLFjx5Kamhq1a9eOpk+fTn5+fpUER1KSkpJo2rRppKKiQs7OzjV+569duyZ4War4ksPlcql///60du3acp8/e/aMtLS0KuWqrDi2AQEBNHjwYMkfhuWHwQpfGfgFF4if3qUawav4pyvxs6YRwxRXais+Pp4mTJhAampq5ObmVuUbLsMw9Pz5czp8+DDZ29tTs2bNSFtbmyZMmECenp709OnTaldhd+/epZYtW9K8efPE2i4t5erVq9SkSRN68+aNSOXT0tJIVVWV8vPzicfj0fv37+nhw4d048YNCgwMpH379tH69etp7ty5ZGtrSwCoW7dupKOjQw0aNCAFBQVq0aIF9e7dm3755RdycHCghQsXUsuWLWnatGk0ZcoUatKkCfXu3Zv8/PyqTJJbVFREffr0od9++03s52UYhg4cOEAaGhqVROXkyZOkoaFBu3fvFmsrUxhHjx4lPT09wZmROLx//55UVFTE2q4uRVzhS0xMpObNm4stzqVnaoqKimRiYiLYLp4xYwb5+/tTWlqaWO1VB8MwdPPmTRo5ciQ1btyYNmzYUO7srSqKi4tp5cqV1LRpUwoLC6uyjLOzM40ePbrSs69YsYIWLVpUqXzFsS3d9hf198Pyz4EVvv/DcOPEFL3SP12In7uMiL699V64cIHMzc1JV1eXOBwOff78+a97MAz9+eefdOjQIbKzs6OmTZtS06ZNyc7Ojg4dOkR//vmnSJMun8+nbdu2kaamJp05c0ai5y1rzMIwDOXk5NDz58/p7t27FBISQkePHqWtW7fS4sWLacqUKWRhYUG6urqkpKREysrKJCMjQ40bN6ZOnTqRmZkZWVtb06xZs2jVqlW0a9cu8vf3JwB07949evv2rdAVZVpaGg0fPpxkZWXJxsaGYmJiaux7qbHLxYsXJXr2+/fvU/v27cnR0ZE+fvxITk5O1LZtW0pISJCovYrExMSQpqYmPXnyRKL6W7dupWnTpklUVxJ7tW7dugkVh1JKSkooPj6e3N3dadSoUaSiokIdOnSgYcOGkZqaGt2/f1+i/lYHj8ejEydOUM+ePal9+/Z06NAhkXYmUlNTydjYmIYMGSLUCOfIkSPUvn37cr9Pom/P2axZM3rw4EGlOlWNrbOzM23cuFHEJ2L5p8C6M/wfJnMkwH8uUV1CA5y95YA1G7whJycniAcpIyMjsdOtMDIzMzF58mTk5OQgICAALVq0qFSGy+VWa2Kfnp6Oq1evolGjRiAiZGVlQV5evloTew0NDcybNw/bt2/H0KFDoaysXKOJfXWm9Q8fPgSHw0FoaCjGjx8Pf39/PH/+vMoMEVVx584dWFpa4s6dO2jXrp1Idcry9etX2Nvb4/Llyxg4cCACAwNrHbAa+ObkbmBggL179wqNSlMdRIROnTrh0KFDMDY2Fru+qO4MZdm1axfi4+Ph6+sr+KykpAT3798XBDqIjIxE06ZNBT50ZmZmAheBtWvX4saNG7h+/bpYoduEkZeXhyNHjmDnzp1o1aoV3NzcMGLECJFcOkJDQ+Hk5IQFCxZgyZIlVdaJjo7G6NGjERERUSl11LVr17Bs2TIkJCRUqlfV2MbGxsLOzg7Pnz9ng1P/RLDCB4CKk0BZEwAUSVS/uJhw7bYy5Btvhba2NiIiIiR2uq0IwzDIzc1FZmYmrl69ivXr18PAwADGxsYCJ+iK/mRcLleoo7O6ujpOnjwJRUVFbN++XRDdvqaEq3fv3oWjoyOePn0qcv8rThREhLCwMLi7u+PRo0dwcXHBzJkzoaqqCkdHR3Tt2hWLFi0SeWw8PT2xZ88eREdHi5WVnP6f1HXp0qUYPXo0QkJCsGnTJsyYMaNWk1dZB+j169dL1EZtJ1JJhC8zMxPt2rXDmTNnEB8fj/DwcERGRkJXV1fwgmZqair0pYRhGIwdOxa6urrYt2+f2H0uJS0tTRAKbsiQIXB1dRXZX5DH42Hp0qU4c+ZMtcHXS19M9u3bh9GjR1e6bmdnh379+mHevHmVrlU1tkSEzp07w9PTU5CTkuWfDyt8AJhcN6DoAgBG4ja4XCl0NMsFUfVOtwUFBSJHti/NNaaoqAhpaWnk5eWhV69e0NfXrzZAsJKSktBJc/v27QgMDMTt27fFivk5c+ZMtGzZUuBELgqlEwWPx0NAQAA4HA74fD7c3NwwYcKEcmJ769YtzJs3Dw8fPhR5wicizJgxA9nZ2QgODhapXl5eHpydnZGYmIigoCB06tQJT58+xfjx49GhQwccOnRI4niUFR2gJcHZ2Rk6OjpYtWqVRPVFFb7i4mLcu3dPsKILCwuDlpYWxo0bBzMzM5iamgqNqFMVnz9/Rp8+fbBkyRJMnTpVrD4/ePAAHA4HFy5cwKRJk7BgwQK0bNlS5PovX76Era0tmjZtKjT4OvBNHAcOHIghQ4Zg7dq1la7n5uaiRYsWSElJgbp65WgswsZ2+/btePr0Kby8vETuM8uPhRU+AMyHPgDl1KqNIq4MrsWNRUZWi2qFjc/ni5VrrKioCI6OjqhXrx78/PxqFX/y2rVrmDRpEmJjY6GrqytyvYKCAjRr1gyPHj2Cjo6OyPWkpKSwdetW7N69Gx07doSrqyuGDRtWpUAxDIO2bdvi1KlT6NWrl8j34HK5MDc3h4WFBVauXFlt2cTERIwfPx5mZmbYtWsXGjb8K5J+YWEhXF1dceXKFQQEBIgdmeTo0aPYtm0bYmJiJBbOoqIi6OjoIDExsdrIOdUhbHIuLi4WrOZu3bqFqKgotGrVSvCCVlBQAE9PT0RGRkp0X+BbyixTU1OEhoaiT58+1ZYlIly7dk0Qi9TFxQUzZsyAqqqqWPcMDAzE3LlzsXr1asybN6/alx9nZ2ekp6fjzJkzVb6YHDp0CFevXkVwcHCV9YWNbXp6OvT19asN2M7yD+PvOkz8J/PNPUFco5byfz6/0KPf1w0kJycnWr58OXE4HDp+/DhdunSJYmNj6dWrV5SXlyeWxeDly5epSZMmtGHDhiqdcsXh5cuXpKWlRbdu3RK7rr+/Pw0bNkzk8qUuHABqdOEoy7p162ju3Lli9+/du3fUtGlTunDhQpXXGYahPXv2kIaGBp04caLatk6dOkWamprk4eEh8r9VVQ7QklAX5vGlP2kul0t37tyh3377jYYOHUpKSkrUrVs3mj9/Pp05c4Y+ffpUrh6PxyMtLS2JXGLKcv78eWrWrBmlp1ft58rlcsnb25u6dOlCnTt3Jm9vb7Ec4UspKCigGTNmUJs2bSg+Pr7G8ocPH6YOHTpUMmYpS79+/So5t5eluulSUvcTlh8DK3xE35zUayl8Oc/a0Oxp7cnExIQsLS3JycmJVqxYQR4eHnT8+HGR/c2Ivk1CixcvpmbNmlF4eHitn+/r16/UpUsX2r17t0T1hwwZQidPnqyxXHx8PNna2pKamhotXrxYbAvDlJQUUldXl8g1486dO6SpqVlp4s7OziZLS0vq2bOnyI7aKSkpZGhoSBYWFpUEoiLCHKAloTYO0Vwul27fvk0AaPDgwaSoqEjdu3enBQsW0Llz50TyS1y4cCGtXLlSovuXZe3atdS/f/9ygpaTk0Nbtmyhpk2b0pAhQ+iPP/6Q2G0kKSmJOnfuTLa2ttUKWSl3794lTU1Nevr0qdAyycnJ1KRJk0q+fmWp7vt86tQpGjBgQI19YflnwG51AmA+GgHMp1q1UciVxrVYazRQNBKc4wk7w8vMzASAKrc6ZWRkcPbsWaiqqmLNmjVo27atwChFkoSeRARbW1vIy8vj2LFjYhtMpKamonv37khLS6vyTJBhGFy+fBnu7u54+fIlFixYgOnTp6NRo0YSGVoMGDAAc+bMgbW1tVj1AODgwYPYvXu3wNjl7t27mDBhAsaMGYNt27bVaMBTFh6PhxUrViAoKAj+/v5VGi6UnhkNHjwY69atE7u/ZXn37h26dOmCtLS0cluwwuByuYiNjRUYUcXExEBPTw/37t3D+fPnYWJiIva24cOHD2FhYYFXr15VmYNRVBiGgaWlJXR0dLBkyRLs3LkTx48fh4WFBVxdXdGtWzeJ2iUieHt7Y8mSJfj9998xbdq0Gr/P6enpMDAwwIEDBzBq1Cih5ZYvX46SkhJs375daJnqvs9cLhc6OjqIj48X63yS5cfACh8A5stGoCAAgOjJJytSyJXFqCnqiI29h86dOwvOTvr371+lmXxBQUElYbxx4wYCAwMFEfxLr3369AnZ2dlo1KiRWNmvlZSUsH37dpw6dQq3b9+GnJyc2M/122+/IS0tDQcOHCj3eVFREfz8/ODh4VHOhaNsJgRJhO/48eMICgrChQsXxO4rAMyYMQOZmZno06cPduzYgYMHD2Ls2LEStQUAFy9exLRp0zB37lwsX768nCDMnj0b7969w9mzZyU2Zilly5YtSElJwaFDh6q8XlRUhJiYGMEZXWxsLDp06CCwGDY2NoaKiopEY16WXr16YcuWLRgyZIjEbQDfjJVGjx4NhmEwe/ZsuLi4iJ2/sCxljZICAwPRuXPnGuvweDwMGDAAw4YNw5o1a4SW4/P5aN68Oa5cuVJtuzWN7dy5c6GlpVXtvVj+GbDCB4BK3oI+jQTAlbCF+oDCNNRTWojCwkLExMQIrOXi4+Ohr68vcGcwNjauZPxQVFQENzc3XLp0CQEBAVXm4OPz+QK3BlGtQouKisAwDPT09KCjo1NtLrdSt4ayflhEBD09Pfj5+QmMFbKysgRJPXv27AlXV1cMGDCgyjdvSSbh/Px8NGvWDE+ePJHIkCc1NRVdu3aFkpISIiMjJTYSKUtaWhomTpwIWVlZ+Pn5oUmTJvDy8sL27dsRGxtba/8/IkLHjh1x9OhRQZqboqIiREdHC1Z0cXFx0NfXF7xQVfU9AiQb87KUuof4+/uLXZdhGFy8eBEcDgevXr3ChAkT4OXlhdDQUPTt21fiPt2/fx82NjYwNTXF7t27RVoRA8CsWbPw4cMHnD59utoXkytXrmDVqlWIi4urtr2axjY+Ph42NjZ48eJFrV+EWL4vrPD9HyZrAlB8D4Akw9EAUprXICXdpNKVqt7UO3bsKJjAmjRpAicnJ7Rt2xaHDx+GiopKrZ8F+GbibWRkhH379qFt27Yi541TUFAQiKG0tDSSkpIwffp01KtXD/Hx8YiLi4O5uTmcnZ1hZGQEZWVlodtNkk7CU6dOhb6+Ptzc3MSqd/PmTTg4OMDS0hJnz57FwYMHMXLkSLHvXxUlJSXYuHEjDh8+jGXLlmHTpk1VOkBLQnR0NCZNmoQDBw4IfEATEhLQqVOnci9MoghsbYXv06dPaNu2Ld68eSOydWpRURF8fX3B4XCgoKAANzc3WFtbQ1ZWFiEhIZgzZw7i4uLK5cQTBSLC/v37sW7dOuzatQt2dnYi1z18+DA8PDwQExNT47jZ2trC1NQUs2fPrrZcTWNLROjatSv27t0LMzMzkfvK8gP4204T/+EwxS9rCExdTbzOPE+R71NUVEQRERG0YcMG0tfXJwCkq6tLCxcupJCQEMrJyan1s5Qas+zZs0esegzDUHZ2Nj179oyioqJoyJAhNGDAAOrcuTPJy8sL8s/16dOH2rRpQ40aNRKELuvcuTOZm5uTtbU1OTs70+rVqwkAnThxgq5evUqJiYmUmppKhYWFNfYjPDyc9PX1RTZ+KCkpoTVr1pC2tjZduXKFiP4ydqkuhZEkBAcHk7S0NFlbW1drCFET+fn5FBYWRqtWraImTZqQrKws9e3bl5YuXUqXL1+mL1++SNRuXfykx40bRwcPHqyxXGZmJm3YsIEaN25MI0eOFIS/q8i6desqGbvURKlRkiTB16Oiomo0Zil7n0aNGolk/CPK2Lq7u5Ojo6NI/WT5cbArvjIQ7x4oZxpABRBt5ScPNLSBlNIKsYxG8vPzMW/ePERFRcHX1xdcLlewpRUdHY127doJVoQmJiZCHXKrfIb/G7M0bNgQR48elSj6B5/PR1BQEBwcHNC0aVMsWbIEU6ZMqdJHicfjISsrq8oV5bp16zB+/PhKn9evX7/abVcNDQ3MnTsXu3btwoABA6Cqqip06+jdu3eYOHEiZGRkBNuQpRw6dAg7d+5EdHR0nYQjKzVm6devHx49eoS8vDycPHlSpO3U/Px8REVFCVb+9+/fR9euXdG/f394enoiPj4e7du3r3Ufa7viA4ALFy5g8+bNiIqKqvL6ixcvsGPHDpw4cQJWVlZYtGgR9PX1hbbHMAzGjRsHbW3tSmfFVREdHQ1bW1uMHj0a27dvF8so6f379zA0NISnpycsLCxqLO/p6YkbN24gKCioxrKijG1GRgY6duyI1NRUKCoqitxvlr8XVvgqQCUvQDnzAX4avp35VRHNRaohAClA0RX1FOzFav/Ro0cYP348DA0NsXfv3ko/Dh6Ph7i4OMEEeffuXbRp00ZgxGBiYlJlVIlStm7ditOnTyMiIkJsY5aCggJ4e3tjx44dICI0atQIcXFxElv4CQvxlJeXV+MZZWJiIr58+YJ69eohLy8PqqqqlUTy8+fPuHTpEoYNG4YpU6agcePGguul50AzZ87Ex48fazznEYWyDtAA4O7uDg6Hg8OHD1cKf/X161dERUUJXmju37+PHj16CF5ojIyMoKCggJMnT8Lb2xtXrlypVd9KqQvhKy4uhq6uLsLDw8uJcVRUFNzd3XH79m3MnDkTc+fOFXn78suXL+jTpw9cXV0xffr0KsswDCMYU0mMkrhcLgYMGIDhw4dj9erVItXp06cP1q5dixEjRtRYVtSxHT16NMaNGwdHR0eR+sDyA/gxC81/PgzvMfFzFv3fub0D8dP1iZ+uR/xMC2IKQolhxHO6ZRiGPD09SUNDg3x8fESux+VyKSoqijZv3kzDhg0jJSUl6tq1K82bN49Onz5dLj3LH3/8Qdra2mLnPsvIyKDVq1eTpqYmjR07liIjI2nQoEEUGBgoVjsVqc3X6/Xr16Surk6FhYVUXFxMGRkZ9PjxY7p58yadOHGCBg8eTMrKymRlZUV2dnY0ZMgQ6tGjB+nq6pKcnBzJy8tT8+bNqXv37qSsrExdu3al+fPn08aNG8nT05OCg4MpPDyckpKS6MOHDzUGCBDmAB0VFUUtWrSg2bNnU0hICC1btoz69u1LCgoKZGxsTKtWraJr164JTTE0dOjQGp3qxaGuftKurq60fPlyKikpodOnT1O/fv2odevWtHfvXonSJRERPX36lDQ1Nenu3buVrn38+JF++eUXMjIykjgb+4wZM2js2LEip1hKSkoibW1tkbesRR3b06dPk5mZmUhlWX4MrPDVwLcM5wXE8D8Tw4ifUJToW9JOGxsb6tq1a62je/B4PLp79y5t2bKFfvnlF2rUqBF17tyZHBwcSFlZmUJCQkRuKzk5mZycnEhFRYVmzZolOA8rKzq1obaTcFXiW9a5XFhONoZh6OvXr/Tq1SuKi4sjf39/UlVVpWnTptGKFSvIycmJLC0tydjYmDp06EAaGhokLS1NampqpKenR/3796cxY8bQ9OnTadmyZTRv3jxSUlKigwcPUkxMDKWkpNC7d+/o4sWLtHTpUurVqxdJS0uToqIizZkzh65fv075+fk1Pt/bt29JTU1N5CTAolBXwhcTE0MqKirUunVr6tu3LwUHB9c6ehARUUhICOno6ND79+8Fn928eZN0dHRo+fLlVeZgFIWDBw9Sx44dxTobXbJkCS1ZskTk8qKOLZfLJQ0NDXr58qXIbbP8vbDC952JjY2l1q1bk7Ozc51OcKUUFxfTzZs3qUmTJqSvr0+NGjWiTp060Zw5cygoKIg+fPhQrjzDMHTr1i2ysLAgLS0tWrduHX38+LFcmQ0bNtDs2bNr3bfaTsK+vr40fPhwwf8HBweLHU6slJoMHkpKSigzM5OSk5MpIiKCzpw5QwcPHqSlS5eSoqIiGRsbU69evahx48ZUv359AkBSUlKkpKREbdq0IXNzc+rZsyfJycmRtbU17du3j4KCgujGjRv08OFDSk9PrzSp//bbbzRz5kzxB6YaajvmGRkZtGrVKtLQ0CAVFRXy8PCoo579xfr168nIyIgKCgpo7dq15YySJEESQ6bi4mLS1tYWK2eiOGM7b968SpndWf45sGd83wkiws6dO/H7779j//79EkUiEfU+NjY2UFJSgpeXF/h8PhITEwVnhJGRkdDR0YGJiQnk5ORw69YtQUBmBweHStFYiAht27aVKFBzRWp73lTq05eQkAB3d3eJA0iXIo6J++fPn3Hjxg3MnTtX8P8GBgaCs9Y+ffqAiCqdUd6/fx9eXl7Q0tJC+/btkZubWy7ThoKCgsBn8vHjxzA3N4e+vr7QYASlEXBERdIxT05OhoeHB4KDgzFhwgQsXLgQV69eRWRkJE6ePCl2e9XBMAxGjBiBhw8fomPHjrUKvv7+/XsYGBjg0KFDYrmuXLp0CRs2bEB0dLTIdcQZ28TERFhaWiIlJYX16fsHIn4MLJYaycrKgqOjIz5+/IiYmBi0atXqu91r69atePv2LcLDwyElJQUZGRkYGBjAwMAAbm5uyM3NxcaNGwXhyrhcLpo1a4bExEQ0atQIZmZm5SadyMhIyMnJoXfv3t+tz6KioKCAwYMHw9jYGCYmJrh3757EmQ8AwMnJCQkJCZg0aVKlCP25ubm4ffu2wBjl6dOnUFZWhrKyMvbv34++fftWaSykq6tbLtOFnZ0dVq9eDWdnZ9y/fx9BQUECi0eGYfD582dBlJ5NmzZh7NixyMrKwocPH5CUlFTJ0KeoqAjq6uoiR+wRByJCeHg43N3dER8fjzlz5uD58+eCdtTV1bFy5Urk5ubWmX8p8M1hPDExEQzDwMbGRmLR43K5sLKygrOzs9j+mt7e3t/V+KR79+5QVlZGeHg4BgwY8N3uwyIZ7Iqvjrl9+zYmTpwIGxsbbN68uU4yUgvjjz/+wNSpUxEbG1spHNS7d++wZ88eHDlyBIMGDYKrqysMDQ3B5/Px4MEDwYowIiICjRs3Flgbnj9/Hr179xbbebwqarvi8/X1xbx58yAvL493797VyZtzaRgrU1NT9O3bVzAOz58/R58+fQQruocPH2LPnj0irQ6rgsrEldy6dSumTJlSbuVWGrRg6dKl1bbD5XLLuYvUZA2bnp4OJSWlakPZqamp4dGjRzh16hS4XC7c3NwwadKkKmOx2tjYYODAgZg1a5bYY1CR4uJirFy5EidPnoS/vz8aN24MExMTnD9/Hv369RO7vRkzZuDTp08IDg4W67uRnZ2NVq1a4fXr12LFMxX3+7xjxw7cv38fPj4+Itdh+Zv4Adur/0pKSkpo48aN1LhxY6HpceqS58+fk5aWFkVERJT7/OHDhzR58mRSVVUlFxcXSklJqbadkpISSkxMpB07dpCFhQVJSUlRq1atyMnJifz8/CgtLU3iPkr69crLy6PJkydThw4d6MGDB9S2bVuKjo6WuB9ERFlZWXT27FmaP38+derUiaSkpKh79+7022+/UWRkZDnnanEcoGuiNJOAnZ2dwPAiPz+fVFRUajW2wgBAubm59OLFC4qOjqbQ0FA6duwYbdu2jebPn0+GhoYkLy9PSkpKpK2tTcrKyiQjI0NaWlqkr69PpqamZGVlRTNnzqSVK1cKUv9cuXKFEhIS6M2bNxKdVb969Yr69OlDI0eOLGeUFBoaSjo6OvTu3Tux2vP09CR9fX2JHP337dtH48ePF7ueuN/nDx8+kLKyssTBCFi+H6zw1QHp6ek0aNAgMjU1FduVQBLy8vKoU6dOtG/fPiL6ZrBy9epVGjp0KGlra9Pvv/9O2dnZYrfr4+NDI0aMoPv379OuXbvI0tKS1NTUqG3btjRt2jTy9fWlt2/fityeJML34MED6tChAzk6OgrM5jdt2kSzZs0Sq53MzEw6ffo0ubi4UNeuXUlJpNWsOQAAIABJREFUSYmGDh1KmzdvpqioKIqIiKhS3N69e0c6OjrV5mUTl/z8fHJycqK2bdtSQkIC+fn50S+//FJn7ZelqjFPS0ujJUuWkLq6Oo0fP55iY2PLXefxeJSenk6PHj2imzdvUlBQEO3fv582bNhAc+bMITk5OerXrx91796dmjVrRg0aNKCGDRtS8+bNqVevXjRs2DCyt7enBQsW0KZNm+jgwYN0+vRpCg8PpydPnpCXlxdpamoSh8Op0ihpw4YN1K9fP5HTUUVGRlaZgkpUevfuTX/88YfY9ST5Po8ZM4a8vLzErsfyfWG3OmvJtWvXMHnyZDg5OWH16tUSpQ4SB/q/MUujRo2wf/9+BAUFwd3dHXw+H25ubpgwYYJYkS7KMnDgQMyZMwdWVlaCzxiGQVJSkuDsKzw8HI0aNRLEkDQ3NxcauUScrSEiwsGDB7F69Wp4eHjAwcFBcK2m1EgAkJmZKYhzGR4ejtevX6N///6Cfvbq1atc5ggAOHLkCDgcjmA7UxIHaHEICAjAvHnzoKamhg0bNmD8+PF1fo+yY/7gwQNwOBxcuHABkyZNwvz58yU6b16yZAmkpKSwdetWAN/+rfLz84UGRy/9+8ePH/HkyRN8+fIFAARBCCqeUaqpqSEgIABaWlpYv3694LqCgkIlw55SY5bDhw+L5HRekcePH2PYsGF4+/at2IEZJNm6P3fuHDw8PBARESFWvR9JSXEJos7HIfTAFWSmZqGYW4KGjeTRxbQjxs0fiWZ6TX90F2sNK3wSUlJSgjVr1sDHxwe+vr4YOHDg33Lf33//HadPn4alpSUOHDiADh06wM3NDcOGDZMoPFkpr169gqGhIdLS0qoVToZh8OTJE8HZWHh4OBQVFQUiaG5ujhYtWgAQfaL4/PkznJyc8OzZMwQGBlYZumvo0KGYOnUqbG1tAQAfP34UCN2tW7eQmpoqEDpzc3P07NlTpJcQZ2dnvH//HmfPnoWzs3OdRXkRRnh4OAYNGoQRI0bA29tbrHB0oiAlJYUrV67A3d0dSUlJcHFxwYwZM8TOzVeWJ0+eYPDgwXj79q3IL3bPnj2DjY0N9PT0cPjwYSgqKiI7O1uoSL5//x4XL14URCX69OkT+Hx+uTNKVVVVREREoFOnTrCysqp0hqmmplbp5aYiixcvhoyMDH7//Xexx0ES4ePxeGjWrBmioqLQtm1bse/5d8LjFuPEb6dxfu8f4PP5KMwrKnddWlYa0tL10LpbS0zfMhHdzDr9oJ7WHlb4JODt27eYMGEClJSUcPz4cWhpaf0t9/X29sbcuXMhIyODUaNGwdXVFd27d6+TttevX49Pnz5hz549YtUjIiQnJwsEKDw8HPLy8jA3N4ePjw9SUlLQsmVLoaIcGxsLW1tbDB8+HBwOR2iYtQMHDuDgwYMwMjJCeHg43r17B2NjY4Hg9ujRQ6LVdmn8TVVVVbx8+RIxMTFQUlISux1R2bRpE1JTU9GwYUOcOXMGJ0+eFKQiqg08Hg8BAQGYPHkyOnfuLFj915VxVZ8+fbBu3ToMHz68xrK+vr5YtGgRNm3ahBkzZoj8Qvbs2TMYGxvj3LlzMDL6K6Fz6epx69atyM7OhoWFBbKysiqJaHZ2NhQVFYVavaqoqGDJkiXw9PREr169oKGhIZa7iKTGWgsXLoSioiI2btwodt2/i6+5+Vg6dCNeJ6WCV8irsXwD+fpw3umIkU61y9v4o2CFT0xCQkLg5OQEV1dXuLm5/S0+OgkJCVi7di0uXfofe18eTuXW/n+X0iCZQ4YoiqRUaCCU5jqJBioVnVJRydTEKTqlEs0zzSnSPEeJJCoNNKg0IJokZGbv5/P74/z2/tqx2XvbOu973vO5LtfF86zpWdZa91r3+tz3fYXs7e0pKCiIh0LfWDAMQzo6OhQVFUV9+/ZtVFkA6OXLlxQXF0eurq6krKxMrVq14lGNamtrEwDavHkzbdiwgXbv3s2jXiX6y9kv51QZFxdHHz9+pPLyclq2bBmNGzeOjIyMxKZWvnjxIo0fP5527NhB8+fPF0uZdQEA6erq0vHjx8nU1JQ7ljw8PGjJkiUijaXCwkLau3cvbd++nbp3704xMTHEMEyjTv91Yffu3RQXF0eRkZF805SWltKCBQsoOTmZG1BZWFy+fJlcXFzowYMH1LHj/6nU9uzZw40VyG9jwjBMvTErHz9+TI8ePSJdXV2emJUNxank/G5kZESVlZVCbyZSU1Ppt99+o8zMzP9Im76qymryGPQHvUvLIlYVS+B8rdpKkleYKw12MGvC1jUN/hV8AqKyspKWLl1K586doxMnTohEvxYGDMPQ1atXKTg4mDIyMojNZpOPjw95enqKva74+HhauHAhpaaminXBbNasGTEMQ69fv+Y5ERIRNW/enFq1akVhYWFkZWVFnz594lGffvnyhSwsLLjCslevXuTq6kpaWlq0fPlysbWRc2fk5eVF69evF1uMvbqQkJBA8+bNo2fPnnH7OTs7m6ZOnUpSUlJ05MgRUlZWFqiszMxM2rp1Kx0+fJjGjh1LXl5e1KtXL7E4qa4LBQUFpK2tTe/evatTPZuWlkb29vbUr1+/Op2vC4M1a9bQ5cuXKS4ujlq1akWJiYlka2tLiYmJpKurK3K5EydOpOHDh5OLiwv3WUVFRa3TIz/B+fTpU2rZsiW1adNGIJtKzu8yMjLUt29fCg4OJmtra5Hb31QIWx5OZ7ddpqryaqHztmojSYcytpNiR/Gq7Jsa/wo+AfDmzRuyt7enTp060f79+xt1X9IQKioqKDw8nKv28/LyotOnT5O8vDyFhoaKfSdPROTk5EQ9e/YUu1CtaxGOj48nBwcH6tq1K1VVVVFaWhpVVlaShIQE6evr05gxY2jChAnUq1evWuSDpKQkcnJyopcvX4qlHyorK8nKyorGjBlDfn5+3Kjq9+7da5ShPD/8/vvvpKenRz4+PjzPWSwWrVq1ig4dOtTgfXFKSgoFBwdTTEwM/f7777Ro0SIeG86mEnxEdQdsBUD79u0jPz+/WqQkUcEwDE2cOJEUFRVp1apVZGpqSmFhYQKpWfkhPz+funTpIlSA3Z/B2cgVFRUJZFPJ+b20tJRat25NEhISZGRkJJAzAmEjq4iKqspqmqT8O5X9KBcpv2TrljTJx4acAsRP1GpK/Cv4GgCHibdq1Spyc3NrEsFD9NfE3L17N+3cuZP69OlDXl5eNHjwYFq3bh1duHCB4uPjRWZr1oeSkhJSV1enV69eCXzaEBQ1F+HMzEzy9vamK1eukKysLFVWVpKlpSVZWFhQly5d6NOnT1yyCsMwXJKKpaUlde3alVuWnp4eHTp0SCwn7roMoF1dXSknJ4fOnTsnVrUUx/3aixcv+Hoq4TCEZ8+eTStXruSqchmGoStXrlBwcDC9f/+e3N3dafbs2XUa1jel4Lt27RqtXLmS7t+/T0R/kZJcXFzo5cuXdPLkSbHEE+SguLiY+vXrR+Xl5TRnzhxasWJFo8rjqEnDw8NFLkPUvq2qqqKMjAwaMGAAhYeHU3l5eYOCs2XLlgKfKBUVFUlOTk6k8GGxJ+7Qlnl7axFZhEE7OSmK+hxGLVr+9zgC+1fw8UFZWRm5u7tTfHw8RUZGUu/evZuknrdv33KDetra2pKnpycZGPzFlrpy5QrNmTOH7t+/T2pqak1S/6FDh+jMmTN04cIFsZabnZ1NnTp1olmzZtGNGzfo48ePJCsrS4sWLSIbGxvq0aNHnYIFAL17946r8oyLi6Pq6mquEHz9+jUVFxdTaGhoo9q3d+9e2rZtW607o6qqKrK2tiZra2vy9/dvVB01ceTIEYqMjKTLly/Xm+7z58/k6OhIVVVVdODAAbp16xZt2rSJ2rZtS97e3jRx4sR6mYtNKfjYbDZpampSdHQ0lZWVkYODA40cObJeUpKo4JjtXLx4kW7cuEHm5uaNKq9v3760fv16GjZMdDJGY/vWzs6ORo8ezTceIQcAqKSkpF6168+ny6KiIr7mIvwEZ9u2bWmxuR+9SHot8jcREbWVbkN+Jz3JZIR4iHa/Av89IvoX4sWLFzR58mQyMjKihw8fNgnLLykpiUJCQig+Pp5cXFzo+fPnPCeBjIwMcnJyorNnzzaZ0CMiOnjwIC1evLjR5WRlZfHc4xUXFxMRUevWramsrIxWrFhBK1eubHBX2qxZM+rSpQt16dKFfv/9dwJAmZmZ3LJv3LhBnz59ou/fv9PQoUPJysqK9PT0hDqJJyYm0h9//EGJiYm1/reSkpIUFRVFJiYm1Lt3b7KxsRG+M+rAoUOHeFSE/KCiokLh4eE0bdo06tatG/Xp04d27dpFVlZWTaZtEBQSEhI0ffp0WrBgAT1//rxOUpK4sGfPHkpPT6fw8HCyt7evRXYRBmlpafT169dfZnLED05OThQUFNSg4GvWrBlJS0uTtLS0wHaXLBaLay7ys2DMysqihw8f8jzLy8sjIqJ+rGHUkhqnSWKzGfqWk9+oMn41/j3x1QAAOnjwIC1dupSCgoLIyclJrIsNm82mCxcuUHBwMH369Ik8PDzI2dm5FhGguLiY+vfvTwsXLhSLj0R+ePv2LfXv359yc3OFZqrVFEZxcXFUVlbGo57U1dWlVq1akZqaGh09elSsjnotLS1JT0+PqqqquHVbWlpyiTDdu3fn+38T1AD63r179Ntvv4mF7JKZmUnGxsaUm5tbr7r6zZs33NP/hAkTyNLSknx9fWnSpEm0bt06gf5HTXni+/btG02cOJHu3r1Lz58/bxTRpD7cuXOHJkyYQImJiaSjo0Nr166lS5cucckuwsLLy4tat25Na9eubVS7Gtu3nMj2CQkJTdZ3/MBisbgkHo7w+/jxI11ZnkjscqZRZUu2bklzgqbT+AWi38H+avx74vv/KC4upnnz5lFaWhrFx8dzPeqLA2VlZXTo0CHavHkzycvLk4+PD9na2tZ5+gFATk5ONHDgQJo7d67Y2lAXjhw5QlOnTm1wQQVA79+/51E/coghlpaWtHTpUp5TV1ZWFllZWRER0aNHj8Ru5zh//nw6cOAARUdHc+vjtGvTpk1UXFxMFhYWXEHcvXt3at68Odebv6ura4NeP/r160fr168nGxsbun//fqPILkeOHCEHBwe+i/bdu3cpJCSEbt++TXPnzqX09HRSUVEhIqLRo0eTk5MTmZubU0REBHXu3FnkdjQGCQkJNHXqVHJwcKCKigp6/fp1kyzeOTk5NHnyZDp8+DDX4HvFihX06NEjWrBgAe3bt0+ozWh1dTUdO3aM7ty5I/a2CouWLVvStGnT6NChQ40SwgCouLhYKFVocXFxnapQCcnmjRZ8Ei0kSEqmbaPK+NX498RHfy3O9vb2NHjwYNqyZQu1bSuef+KXL19o586dtGfPHho4cCB5e3uTmZlZvRO3sbtbQcEwDHXu3JnOnTtXywi+5j0bR9hx7tk4wq5bt251fse5c+do7ty55O3tTUuWLGmS00dFRQWpqanR48eP63SXxgnTxBGGhYWFZGFhQZ8/f6a2bdvS9evXBSYCuLm5UXZ2Np0/f14ksgs/G0k2m03nz5+n4OBg+vLlC3l6epKTkxNJSUnVKgMAbd26lQIDA2nnzp00adIkvvWJ+8THZrNp3bp1tGPHDjpw4ACNHj2a9u7dSzExMXTq1Cmx1UP01//V0tKSxo8fX8tkRVQtyIULFygoKEgsgk8cfZuWlkZjxoyhzMxM7hisqqriicDRkDD79u0bSUpKCkV+kZWVJQkJCSopKaG7d+9y50bpfZAiuyM1I9E1W5JtJGnHvXWk3aNu14X/ififFnwAaMeOHbR69Wravn071x1WY/Hy5UvatGkTRUVFkYODA3l4eFDXrl0bzMfPeLcpEBsbS56envTkyRMCQG/evOE50dVkVlpZWZGurm69AruyspJ8fHzowoULFBERQf37929Stdv8+fNJXV2dfH19G0ybk5NDK1eupLNnz5KCggIVFBTwnAgNDQ35CjUO2WXIkCEUEBAgdDvj4+NpwYIFlJaWRs2aNeOe/jdt2kSKiork4+ND48ePF0gQp6SkkL29PQ0fPpw2bdpUp99Scfb5p0+fyNHRkVgsFh0/fpx711xYWEidOnWid+/ecV2MNRYAaPbs2fTjxw86efJknWMtIyODzMzM6OzZs2RmJpjRtKCEEkEgSN8C4AYf5ie4zpw5Qx07dqTq6mrKy8ujsrIynpiLghjTC0omKikpocTERO4mNi0tjfr06UNWVlZkYWFB2c8/UoT3RSJGdMHXxUiL9jzaKHL+vwP/s4KvoKCAZs2aRR8+fKCIiIhG+9EDQLdv3+Y6PXZ1dSVXV1dSUlISKD9nUnPcNTUlAJCtrS1JSkpSixYtuEFsa3pX0dHREVillJGRQQ4ODrXsHJtS8N27d48cHR3p9evXDbbzZwPo3NxcnhNhXl4ej7F8z549eQTRly9fyNjYmLZv307jx48Xqp3Ozs7Uo0cPcnR0pB07dtDevXvJzMyMvL29aeDAgULfIRcVFXHVoZGRkbXuH8XV59HR0TRz5kxycXGp0/n61KlTaeDAgdwI9Y3Frl27aPfu3ZSUlFSv8fvVq1dp9uzZAjGd8/LySFdXl7Kzs0WKqUj01ymUI7h69+5Nx48fr/dElp+fT1JSUvUKrnv37lFmZibt2LGDa+AuLi5BcXEx3blzhzu2nz17xhV0VlZW1L9/f2rZsiXXuX1lZSXpF5nSj0+lItXXpl1r8tg377/Oe8v/pOC7e/cuTZ06lWxtbWn9+vWNUimyWCw6ffo0BQcH048fP8jLy4umT5/ON4pAXeCocRYtWtQk93oA6NWrV9wTXWxsLOXl5dGECRNo5MiRZGVlRZ07dxZp8h0/fpzc3d3J39+fXF1decpoSsEHgLp3705hYWH17v5zc3MbNICu6TUmLi6Ovn79Subm5tzFolevXvTw4UMaM2YM3b59m/T19QVqY0lJCampqdHYsWPpypUrNGXKFPLw8Gj03RgACgsLoxUrVlBwcDDNnDmT+04cBIyVK1fS0aNH6yUlRUdH04oVKyglJUXkujhISEjgkma6dOnSYPrAwECBbFu3bt1KKSkpdPToUSL6S+1cUFAg8L3Yt2/fqKqqiiu0UlNTyd7evt4TmYKCQoN35hxj+szMzEZHtv/x4wfduXOHO3ZfvHhBxsbG3E1s//79uWtRUVERhYWF0datW0lHR4e8vb1pyJAhtHCKJ7278JmaQzg7wOYSzUlJQ4EOvtxKLSXrdw7+n4b/KcHHMAwFBQXR5s2bKTQ0lMaNGydyWcXFxXTgwAHavHkzaWpqkre3N40dO1boe6CaXir27dsncntqoqa/TI6wq+kvMy8vj5KTk+ns2bMi11FWVkaLFi2ihIQEioyMrNNZdlMKPiKioKAgev36NYWFhdX5nmMkP27cOKEMoGv6CY2Pj6ePHz/SoEGDqG3btpScnEyPHj2qV8UHgOLj48nd3Z1evnxJvr6+NH/+fIFP/4Li6dOnZG9vTyYmJrRz505q165do/pcGOfrbDabtLS06MqVK2RoaCjqJ1BOTg6ZmprSgQMHaOTIkQLlAUCTJk2idu3akb+/P98I9ZGRkaShoUFsNpu+fftGBQUFJC0tLfC9mKKiIklLS3M3c+Icz3W5TxMERUVFlJCQwB2f6enpZGJiwt2k9evXr5Ya9MOHD7R161Y6ePAgjRw5kry8vKhPnz707t07cnBwIFVVVbIxmkxRQReJVckWqB3NJZpTO9m2tPthEHXQFO+4/hX4nxF8X758oRkzZlBpaSkdP36cbwy5hpCbm0vbt2+nsLAwsra2Ji8vLzI1NRW5XWvWrKErV67QrVu3RD55AqAXL17wxMxr27YtT6ggLS0tbvpBgwaRt7e3yDZqz58/p8mTJ3NtzPjZOTa14Pv48SMZGBhQTk5OLVIIAJozZw4VFhZSVFRUo1RJX7584XqVOXHiBBUXF9OwYcNo8ODBPJEhWCwWnTp1ioKDg6mkpIQAkL+/P02ZMqWxn8oXpaWltGjRIkpMTORuQETp8/Pnz5OLi4tQztd9fX2poqKCQkJCRGk6VVRUkIWFBdnZ2ZGPj0+dERf4ET7y8vKosrKSZGVlSUtLq5bgKi8vp71791JUVBR16NCBG7aoMY7NxTmeL126RIGBgXT37t160xUWFlJCQgJ3br98+ZL69evH3cSampryve97/PgxhYSE0NWrV8nJyYnc3d25615UVBS5ubmRr68vLVq0iNLT08nOdApps7sTMSBWNX8B2KZda5JWaEchtwJIRevXRKYRN/4nBF9sbCxNnz6dnJycKCAgQKTB//TpUwoJCaELFy7Q9OnTafHixSIF9ayJy5cv09y5c+n+/ftCkVk4MfE4J7rbt29Tu3btuJPB0tKSR9DVxJs3b2jgwIGUm5vbYOyynwGA9u/fT8uXL6eNGzfSzJkz6xUoTS34iP6i+0+dOpUcHR15nnPcvyUnJzfKYfLPqK6uJgsLC1JTUyMVFRWKj4+nrKwsUlNToy9fvpCWlhatXLmSevToQQMGDBDJRlIUhIeH0+LFi+nbt29CRWeorKykJUuW0Pnz54V2vv769WsaNGgQ5eTk8IylujyP1CW4kpOTqaysjFq2bEk/fvyo1/NIXc8+fvxI5ubmdPr06VqeXRYvXkzS0tJiDQUkzvHMYrFIQ0ODbt26xXNP+/37d54TXUZGBlfQWVlZkYmJSb0bZAB07do1Cg4OptevX5O7uzvNmTOHa45TXl5Onp6eFBMTQxEREWRsbEyFhYVkampKvr6+NNRsOG1cuI2exWSQlFQbqq5iU2VFJbWRak1EzUhFS4nsl44ny0kDSLJ104/rJkM90dn/61FdXY0//vgDqqqqiI6OFjo/wzCIiYnBiBEjoKqqisDAQOTn54ulba9evYKSkhISExMbTMtms5Gamopt27bBzs4OCgoK6NKlC2bNmoUjR44gKytL4Hr9/PywePFiodtbVFQEBwcH9OjRAy9evBAoz68YXpGRkRgyZAjPs4SEBHTo0AEZGRlNUufnz5+hoaGB0NBQLFmyBPLy8jAzM8PkyZNhaGiI9u3bo0uXLhgwYACSkpJQVVXVJO34Ga9evQIRYcKECSgoKGgwfUZGBvr06QNbW1t8//6db7qqqip8/PgRaWlpiI2NRWRkJHbu3ImAgACoqKhg0KBBsLa2Rq9evaCmpoZWrVpBSkoKnTp1grGxMUaOHInp06fDw8MDa9euxb59+zBnzhx07twZKSkpyMvLA4vFEumbr169ClVVVXz48IH7rLKyEkpKSnjz5o1IZfKDuMezt7c33N3dcfbsWbi7u8PIyAjt2rXDsGHDsHbtWty5cweVlZUClVVRUYEDBw7AwMAAvXr1wtGjR2vlTU9PR8+ePeHg4ICioiIAAIvFwujRo7Fw4UJuulGjRuHg/kO4fSoJZ7ddQSfqikt7o/H64VvxffzfjH+s4Pvw4QN3Qn769EmovJWVlThy5Ah69uwJAwMDHDx4EBUVFWJrW1FREfT19bF3794637PZbDx58gRbtmyBra0tFBQUoKOjg9mzZ+Po0aPIzs4WqV4WiwUNDQ2kpqYKlS8lJQU6OjqYO3cuysrKBM73KwRfeXk5FBQUkJmZCeCv/7uqqiquXr3aZHWmpqZi9OjRaNasGRwdHfHu3Tue91++fIGSkhIcHBzQq1cvSEtLY/jw4QgMDERiYqLAi5koICIsWLAA2trauHfvXq33DMOgoKAAmzZtgqysLFxcXLB//35s2LABPj4+cHZ2xtixY9G/f3/o6OhARkYGLVq0gLKyMgwMDGBpaYmJEydi3rx58PPzg4ODA4yNjREdHY1Hjx4hOzu7wTESHx+PDh06iE0wBQYGwtTUFOXl5QCAs2fPYtCgQWIpuybEMZ7z8vJw+vRpLFq0CF27dkWzZs0wbNgwBAYG4u7du0KPjfz8fAQGBkJVVRUjRoxATEwMGIaple7QoUNQVFREaGgoz3tfX19YWlpyN2e5ubmQlZVFaWkpN80/8Xz0z/siAJcuXYKysjLWrFkj1E6ysLAQQUFBUFNTg7W1Na5evVrnIGoM2Gw2xo8fDxcXF+4zFouFR48eYfPmzbCxsYGcnBy6du2KOXPmIDw8HDk5OWKpOyYmBr179xY4PcMw2Lp1K5SUlBAZGSl0fb9qwri6umL16tUoLy+HqakpAgMDxV4HwzC4fv06hg0bBlVVVaxbtw47duyArq5urdNVbGwsevbsyR07+fn5OHfuHBYvXsyzq1+zZo1Qu/q6UFFRgZycHDx+/BgxMTEgImzbtg2TJk1CmzZt0LNnT1hZWaFHjx5QUVFBixYt0LJlS7Rs2RIGBgYYM2YMZs6cCW9vb6xfvx5hYWE4f/48EhMT8erVK3z//h1sNptv/YWFhZCRkcHXr18Fam92djZUVVVx7do1kb/5ZzAMg4kTJ2LWrFlgGAY2NjbYv3+/2MrnQJTx/PXrV5w6dQoLFiyAoaEhpKWlMXLkSKxfvx5JSUkwNjYWqS/evn2LhQsXQk5ODk5OTkhLS6szXXFxMWbMmIHu3bvj6dOnPO9Onz4NTU1NfPnyhftsw4YNmD17Nk+6fwXffzgqKyvh6ekJDQ0NJCQkCJwvMzMTHh4ekJOTg6OjIx4/ftxkbVy9ejX69++PpKQkhISEYNy4cZCTk0O3bt0wd+5cHD9+HLm5uU1S97Rp07B161aB0ubn58PGxgbGxsZ4+1Y0FcevmjD3799H586d4ezsjIkTJ4p1s1JZWYnDhw/D0NAQPXr0wKFDh3hO/wsWLMCYMWN4hMOMGTOwadMmvmV+//4d58+fh4eHB/r06YN27drB2toaAQEBuHTpEtLS0nDnzh2cO3cOoaGhWLduHTw9PTFjxgyMHj0aJiYm0NbWhrS0NFq2bAncsarcAAAgAElEQVRVVVX07NkTQ4YMARHBzc0Nq1atgr+/P3R1dWFqaoq4uDjExsaie/fumDZtGn78+CG2PhJ0XJWXl8PExATr168XW90cFBcXo0ePHli/fj1kZGTE+n0cCDKev3z5gqioKLi5ucHAwADt27fHqFGjsGHDBty7dw/V1dU86Xfu3Al7e3uB25CcnIxJkyZBQUEBy5Ytq3etePLkCbp164ZZs2ahpKSE592zZ8+gqKiIBw8ecJ8xDAM9PT3cuXOHJ+2/gu8/GG/fvoWJiQnGjh2Lb9++CZQnJSUFU6ZMgby8PLy9vUVWITaE6upqPHjwALNmzULr1q0hLS0NPT09zJs3DxEREfj48WOT1FsTnJ15Xl5eg2kTExOhqakJDw+PRp1GftWEYRgGqqqq0NbWRnFxsVjKLCgowPr166GmpoahQ4fi2rVrdQrUqqoqWFhYwM/PDwDw48cPyMjI4MuXLygtLUVWVhYePnyIa9eu4dixY9iyZQt8fX0xd+5cTJgwARYWFtDT04OMjAyaNWsGCQkJNGvWDO3bt0e3bt0wevRoeHl5YePGjTh48CAuXryI5ORkvHnzBkVFRbXa9HOfV1VVwcfHB3JycpCRkcGBAwfErsUQRJPAMAycnJwwefJksdfPwZs3b9CuXTuMGDGiScqvazx//vwZkZGRmD9/Prp37w4ZGRmMGTMGQUFBuH//fi1B9zPy8/PRvn37eu9Y2Ww2zp07B3Nzc2hpaWHr1q31jnOGYbBr1y4oKioiPDy81vvv379DR0cHhw8f5nmenJwMXV3dBsfUPwH/CCfVHGruihUryN3dvV5GG8MwdPXqVQoODqa3b9/S4sWLac+ePSJ7dqgLLBaLHj9+zKUg37lzhxQVFSk3N5d8fX1p9uzZXCfEvwonT54ka2trUlRU5JuGYRjasGEDbdmyhcLCwui33377hS0UHXfu3KHi4mIyMzNrNIMzKyuLtmzZQocPH6axY8fSpUuXyMjIiGsLVhdTUU9PjzZt2kSXLl2igoICqqqqIm1tbWKz2XxZib169ar1TF5enlq2bElFRUVco2SOeQrHVktbW5t69eolsMuq8vJyysnJofbt21NpaSl9+PCBGIYRKWgpPwwZMoTy8/MpNTWVevXqVWeanTt30sOHDykpKanJwit17tyZFBUVKSUlhXJycngi04sLNW084+Li6NOnTzRo0CCysrKiWbNmkZGRkVCscXl5eRoxYgRFRkbW8kFaXl5OR44coU2bNpGMjAx5e3uTnZ1dveUXFhbS7Nmz6d27d3T37t1azhLYbDZNmzaNRo8eTTNmzOB5d+jQIbFHpPmPxd8teRuDsrIyzJs3D507d+Y5steF8vJyhIWFQV9fH0ZGRggPDxcb2666uhrJycnYsGEDRo0ahfbt28PAwABubm6IiorCmzdvoKenh3379omlPlEwcOBAXLhwge/7z58/Y/jw4TA3NxfbyfdXDC8OmSU8PByysrICnfgYhkFxcTHevXuH+/fv48qVK/D394eRkRFat24NQ0NDjBgxAmZmZujWrRsUFBQgISEBBQUFdOvWDebm5hg/fjzmzJmD5cuXIyQkBP7+/mjfvj309PSwd+9eFBcXi+1kU1RUhMuXL2PJkiUwNTWFlJQULC0tsWrVKsTGxvKQSWr2+cOHD6GjowMXFxeUlZUhNzcXVlZWGDx4sNi1DPWxhTlkFlFV5oLi4cOH0NLSQmBgIExMTLhkl8YgNzcXx48fh4uLC4gIsrKyGDduHEJCQvDw4UOR2ag1ceXKFfTr14/799evX7Fq1Sp06NAB48aNQ3x8vEBjKTk5Gdra2li4cCFfMt6KFSt4yCwclJeXQ15evs65/18uJurEf+0Xcai59vb2KCws5Jvu27dv+PPPP6GiooJRo0bh5s2bjV6QqqqqkJSUhHXr1mHkyJGQlpaGoaEhFixYgFOnTvFc9LPZbNjY2GDu3LmNqrMxePXqFZSVlfkK+hs3bqBjx47w8/NrUDUjDJp6wnDujNasWYNPnz7BwsICy5Ytw8mTJ7Fr1y4EBARg4cKFmDJlCoYOHQojIyOoq6ujVatWaNu2LTQ1NdGlSxfIyclBSkqKq7Lcu3cvTp8+jdu3b+PFixf4+vWrQAvchg0bICEhwUMWaAr8+PEDV69exdKlS9G/f39ISUlh0KBB+OOPP0BEKCkp4ZKSIiIiePKyWCyuGYI4CSYZGRlQUlKqpRrnkFmuX78utrr4YeHChVi1ahUYhsGkSZPg7Ows9FzPyclBeHg45syZA11dXcjJycHGxgabN28GEYlF0P2M6upqqKqq4vLly5g7dy6XbZueni5QfjabjY0bN6JDhw44c+YM33SnTp2qRWbh4MSJExg2bFid+f4VfP8h4FBz9+3bx3dgv3nzBm5ubpCTk8OsWbPw7NkzkeurrKxEYmIiAgMDMXz4cEhLS6Nnz55YtGgRzpw5U++9WUBAAAYOHNikFPaGsGLFCnh5edV6Xl1dDT8/P3Ts2BExMTFir1eUCcMwDAoLC/HmzRskJSXh4sWLOHjwIIKCgrBkyRLMmjULv/32G/r3788ld0hISKBDhw5QV1eHjIwMJkyYgLlz58LPzw9btmzBsWPHcP36dTx8+BBZWVnIz89HaGgo9PT00Lt3bxw/flwsp38/Pz8YGRlh9OjRTbJA8sOPHz9w7do1LF++HEQECQkJtGvXDq6uroiJieGhpnMQFxcHdXV1LF26VGyaD3Nzc5w9e5b7d1lZGYyNjbFhwwaxlF8fKioqoKioyD1VFhcXw9DQEDt27Kg3X3Z2No4ePYrff/8dOjo6kJeXh62tLbZs2YInT57wkJaaQgAwDIPbt29DR0cHbdq0wcqVK4XaOH39+hWjRo1C//79uSY9deHp06dQVFRESkpKne9HjBhR530g8K/g+9vBoebq6+vzpe8mJSVhwoQJUFRUxIoVK0RS6VRWVuLOnTtYs2YNhg0bhnbt2sHIyIhrbCooeebChQtQU1P7JeQVfmCxWFBTU6vVXxw7x2HDhuHz589NUjcRoaKiArm5uXjy5Alu3LiBEydOYPv27Vi1ahVcXV0xefJkDBkyBIaGhlBVVUXLli0hLS0NbW1tmJqaYvTo0ZgxYwa8vLywbt06hIaG4ty5c/Dw8EDXrl2RlZXFXZwqKiqgoKBQy66Og7y8PKxevRrKysoYPXo0YmNjxaaOZLPZ0NDQwIMHD2BpaQlfX1+xlCsMEhMTuazOS5cuYcWKFRg4cCCkpKQwcOBArFixAtHR0VyGH2fRHDBgQL2LpqDYv38/bGxsAPy1oM+cORP29vZNRmapidOnT8PS0pLn2Zs3b9ChQwfEx8dzn2VlZeHIkSOYNWsWOnfuDAUFBdjZ2WHbtm1ITU2t13RDnAKguroaJ0+ehKmpKXR0dPDHH39ARUVFKI2LoJsXDpnlyJEjdb7PycmBnJwcX/vLfwXf34j6qLksFgtnzpyBmZkZtLW1sW3bNqHYfRUVFUhISMCff/4Ja2trtGvXDr1794aHhwfOnz9fL+OKH16+fAklJSUkJSUJnVecuH79Ovr27cvz7OLFi1BWVkZgYGC9E/1nsNlsfP/+Ha9evUJiYiLOnTuHsLAwrF+/Hl5eXpg5cyZGjx4NU1NTdO7cGUSEFi1aQEVFBYaGhhg8eDAmTZoEV1dXrFy5Etu3b8eJEycQExODJ0+eICcnR6B7mfoMoBcsWAB/f3+eZxkZGXB1dYWsrGyjT//8cOPGDRgZGQH4i9KuqamJ06dPi72eusBms7Fu3Tp06NChzkWqpKQEMTEx8PPzg7m5OaSkpDBgwAAsX74cV65cwZo1a6CkpFSvmkwQ1GS0btu2DT179qw1V5sKY8eOxcGDB2s9P3z4MGRlZTFp0iRoa2tDUVEREydOxPbt2/H06VOhxr84BEBxcTG2bdsGbW1tmJmZ4ezZs1ztQL9+/XD58uUGy2CxWPD394eKikqDjhpYLBZGjhwJd3d3vmnWrVvHY1f8M/4VfI0Aw7DBVMSBne8I9mcjsD/pgf3JAOwvZmD/2AKGVffxviY199ixYzzvSktLsWvXLujo6MDU1BRRUVECqZgqKioQHx+P1atXY8iQIZCSkkLfvn3h6emJCxcuiCToaqKoqAh6enoIDQ1tVDniwJQpU7B9+3YAf51kPTw8oKmpiTt37qCsrAzZ2dl49OgRrl+/jvDwcGzZsgV+fn6YN28eJkyYAEtLSxgYGKBDhw5o0aIFZGVloaOjg/79++O3336Ds7MzfHx8EBQUhAMHDuDixYtISkpCRkYGiEjsu/2GDKBTUlKgpaUFNpuNxMRE2NnZQVFREb6+vkJ78BEG06ZNw5YtW7h/P3jwAIqKik0iZGuCQ0oyMzNDdna2QItUaWkpbt68iT/++AODBg2ClJQUDAwMICMjg99++01gY/S6MH36dLi5uf0SMgsHnz59goyMDIqLi/H+/XscPHgQM2fORKdOnaCkpARDQ0N06tQJDx8+bNR4bIwA+PjxI5YvX84VvHVtiHfv3o1JkybVW05ubi4GDx6MwYMHC2Tvu3z5clhZWfE9ETIMg65du+Lu3bt8y/hX8IkIdukZsL8MAPtzL7A/6dbxY/DXz/c5YFj/p0YsKCjAhAkTYGRkhFevXnGff/78GX/88QeUlJRgY2ODhISEegd0eXk54uLi4O/vDysrK0hJScHY2Bje3t64ePGiQH4NBf5WNhvjxo3DvHnzxFamIGCxWMjLy8OLFy9w+/ZtnDlzBps3b0br1q0xb9482NjYoH379pCRkYG6ujqkpKQgKSkJNTU19OrVC0OHDoWDgwMWLlyIgIAA7Ny5EydPnkRsbCzS0tLw6dMnoe+CxD1hBDGArq6uhqamJrp3747OnTtj+/btTX7q4GcjefjwYejo6DR6I8UPN2/eRMeOHeHr68tVkYnS52VlZYiNjcXSpUuhqKiI5s2bw9DQEEuWLMHly5e5fh0FwYkTJ9CiRYtfQmZhGAZv377F5MmT0aVLF2hqakJZWRn29vbYtWsXXrx4AYZhwDAMJk+eDCcnp18u+J49ewZnZ2fIyclhwYIF9bpp+/79O2RkZPj6A7569SpUVFQQEBAg0AY/KioKnTp1qncjc/fuXXTr1q3efvlX8IkAdtFGsD8Z8hF4P//og/1lAJjqLNy7dw/a2tpYsGABV/2Vnp6OOXPmQFZWFvPmzeMRhjXBmcirVq2CpaUlpKSkYGJiAh8fH1y+fLleFmhj4e/vDzMzs0aRWRiGQUlJCd6/f48HDx7g6tWrOHLkCDZt2oTly5djzpw5sLW1hbm5OfT09KCoqAgJCQnIy8ujW7duMDMzg42NDZeO7+joCGlpabi4uODevXt49+4dfvz40eR3L+KcMA0ZQJeWlmLnzp3cBdDKyuqXEUxCQ0Nha2tb57tFixZh1KhRYm1LTefrP5OSGtvnDMNgy5YtkJGRgZ2dHXejaGJiAm9vb1y6dInv/CkrK0OfPn0gJyeHR48eNaod/Nr25s0bhIWFwdHRERoaGlBWVoaMjAw8PT2Rnp7Od0yXlJTA0NCQq/0QBYL2LcMwuHHjBkaNGgUVFRWsWbNGYF6Ag4MDdu7cyfOsqqoKS5Ysgbq6OuLi4gQqh0NmefjwYb3pXFxcsG7dunrT/BMFX5OGJWJK9hOVbiNCuRC5mlNJWWvqN+oTrV23m2xtben27dsUEhJC9+7dI1dXV3J1deUJ6llWVkbJyclco9JHjx5Rjx49uGF6zMzMxGqgzg8XLlwgNzc3evDgAY+BOovFqjfWWF1G0c2aNRMqYGZdscb69etH8vLylJGRwQ1B8ishzjAuO3bsoH379lFSUhJP7L0vX77Qzp07ac+ePWRmZkbe3t7UpUsX0tPTo5ycHLGGJOIHc3NzWrJkSZ2Bjaurq2nYsGFkZmZGa9eubXRdOTk5NHXqVGrVqhUdPXq0liMEcfX5kydPyN7enszMzGjjxo30/PlzruH2/fv3qVu3btxQOebm5iQjI0NOTk5UVVVFurq6VFRURFu3bm1UGwDQmzdvuIb8cXFxxDAMt14rKysqKioiBwcHysjIaDCG4Lt372jAgAEUFRVFFhYWQrenob6trq6mkydPUnBwMFVWVpK3tzdNnTpVYGcDRETXr18nPz8/evDgARERZWZm0pQpU0hBQYEOHTpUrwMKDgoKCsjExIT8/f1rheuqibKyMlJXV6enT5+Smpoa33S/IrzYL0dTSVSm+gPYn3oIeNLj/an4oIvC7DmIiIiAsbExdHV1sWfPHi7rqLS0lOeyvm3btujfvz+WLVuGa9euNYmfPu53MQyKiorw9u1bJCcn49KlSzh06BB8fHzQtm1bjB07FuPGjcPAgQO5dkAtWrSAkpIS9PX1YWFhATs7O7i4uMDX1xebN2/G0aNHce3aNaSkpCArK6tO+rmwuHTpElq0aIHJkycLpaoSJ8Q1vOoygH7x4gVmz54NWVlZzJ8/H69fv+bJM27cOBw4cEAs9deHhmwkgf8ju5w6dapRdXGcr69du5YvKUOcU7q4uBjTp0+Hvr4+j4Pjushg6urqUFRURGRkJB49elSnTV9DYBgGr169wt69ezFlyhR07NgRampqmDZtGvbt24fXr1/XOtG5ubkhICBA4DquX78OVVVVkZw08OvbwsJCBAcHQ0NDA4MHD8bly5eFIs3UBIvFQseOHfH06VOcOXMGHTp0QEhIiMDlsVgsjBgxQqDQY+Hh4QK5d2tCMfG3ocm+iF20DuxP3UUSfOxPuijN1MGokWY4f/48fvz4gejoaC49u23btlx69vXr1xvln7GyshK5ublITU3FzZs3ERERgR07dsDf3x9ubm6wt7eHtbU1evbsiY4dO0JSUhLt2rWDlpYWTExMMGrUKDg4OEBOTg52dnYIDQ3F2bNnkZCQgJcvX+Lbt28iTwJRwDAMDh48iDZt2mDEiBG/hErOD+KYMDUNoBmGQVxcHMaOHYsOHTogICCA7/3FmTNnYGFh0ej6G8KKFSvg6enZYLqUlBQoKirW8pAvCIRxvt4Ui1RDdrPR0dGQl5eHl5cX1/xHSkoKY8eOxblz5/jeWTEMg/T0dOzevRsODg5QUVGBuro6HB0dERYWhjdv3tQ7fjnmK+/fvxfqezZs2ABjY2OhQmwBtfs2OzsbXl5ekJeXx5QpU/jayAkLb29v9O7dm29oqfqwbNkyDB48WCCziGHDhtVycFAX/omCr0lUnUAV4Ws/IpSKXEY1qwXF3O1OgVs+UmpqKvXu3Zur3hgwYACPuuv/6gUVFhbyVR/W9XtZWRlXXShI9GdFRUUe1QXDMDR+/HhSV1enXbt2ify94kBxcTG5urrSw4cPKT8/n2JjY8nAwOBva09jVSTl5eVkYWFBEyZMIC0tLQoODqbi4mLy8vKi6dOnU5s2bfjmraqqIjU1NUpOTqYuXbqI3Ib6wGazSUtLiy5fvkw9e/ZsMP3Ro0dp9erVdP/+fZKTkxOojnfv3pGDgwOpqKjQwYMHSUFBod70TaWWSk9PJ3t7e+revTvt27ePe3WQnZ1N/fr1o6NHj9LQoUOJ6K++X716NZ0+fZo0NTUpKSmJOnfuTBYWFqSrq0sVFRWUkpJC8fHx1KpVK+6VBMcXqaC+IqOiomj37t0UGxsr1LcAoClTplDr1q3p4MGDAtfH6dvHjx9TSEgIXblyhZydncnd3Z00NTWFagM/vH79mmxsbCgzM5M+fPggkGqTg6ioKPLx8aEHDx7wXAXVhQ8fPpCRkRHl5uY2qIr9J6o6m0bwVd4mFC4mQkmjyvn6XZri0nxIU1OTSktLG7wXy8/PJykpKYHvxZSUlEhGRqZRTln9/f3p5s2bdPPmTZKUlGzU9zYGnDsZc3Nz+u233ygwMJDu37//t7WHqHETBgA5OjpSeno65efnk5aWFnl7e9OYMWMavMvhwN3dnWRlZSkgIECkNjSEmJgYWrZsGT18+FDgPIsXL6ZXr17RpUuXGnQUffLkSXJzcyNfX98Gna9z0JSLVHl5OXl6elJMTAxFRESQgYEBmZub05QpU8jb25snbUlJCamrq9P58+cpNTWVzp8/T/fv3yc2m03V1dWkoqJC1tbWNG7cOLKwsBBqgedgzJgx5ODgQNOnTxc6b2lpKQ0cOJBmz55NCxcubDA9AGrevDlZW1vTy5cvyd3dnebMmUOysrJC180P4eHhtHjxYvrzzz/pyJEjtGLFCho7dqxAeZ8+fUpDhgyh69evU58+fRpMv3btWsrJyaHdu3c3mPafKPia5AzLlJ2px3RB8J/PTzujY8eO6NWrF6ytrWFvb881UN6xYwciIyNx8+ZNpKWl4ePHj7/cLdi5c+egrq7epPZhDYFhGOzYsYMnBAmHzv13Q9ThlZOTg6FDh0JCQgJ2dnZCq3s4ePz4MTp16tRkquaaNpKCoqqqClZWVli+fDnfNGVlZZg7dy66dOnSoPP1n9FEU5oHJ0+ehJKSEoyNjeHg4MBVR7LZbDx9+hTbt2/HhAkT0KpVK8jLy8PZ2RmHDh3iqiSrq6tx7949HqfuPXr04Dp1F8Rl18ePHyErK9soU5W3b9+iQ4cO9TIlKyoqcODAARgYGICIcPToUbGvMyUlJXB2dka3bt3w5MkTAMDevXsxYcIEgfLn5+ejS5cuteyc+YFhGOjo6CA5OVmg9L9iTP1qNI3gKz0J9qeejRZ8P97qYfHixVi7dq3IjoObCunp6VBSUhJ48DQFCgoKYGdnh969e3PJHRxboKayHRMGwk6Y1NRUzJgxA+3atUObNm0Epm7Xh169euHmzZuNLudnFBQUoH379gLT1Gvi69ev6NSpE6Kiomq9S09Ph6GhYYPO1/nhVy1Sfn5+aNOmDQYNGoTAwEDY2dlBQUEBXbp0waxZs3DkyBFERkaiR48eDd4zV1dX4/79+wgKCsKYMWMgIyOD7t27w9XVFSdPnqxTEAYFBWHWrFmN/o7o6GioqKggKyuL53l+fj4CAwOhqqqKESNGcKPbixtPnz6Fvr4+Zs6cycNV4NiGNjS+WCwWhg8fDg8PD4HrvHPnDvT19QW+//9X8AkIpvwa2J97N1rwFb3ri5CQECxfvhyzZ8/G+PHj6wwVo6enV2eomCNHjuDKlSt48OAB3r9/L7ZQMYWFhejatSv2798vht4SDUlJSdDS0qoVgmTXrl2YPHny39aumhBkwjAMg+joaAwfPhyqqqpYunQplJWVER0dLZY2bN68GdOnTxdLWTUhzI68Ljx8+LAW2UUQ5+sNoSkXKTabjSdPnsDNzQ2tWrVC+/btISsrCykpKfj5+dViSrLZbGhrawtN+uAEbg4ODsbYsWMhIyMDfX19zJ8/nxu4WV9fH7dv3xbLdwUFBaFv374oKyvD27dvsXDhQsjJycHJyYnHx604+5ZhGOzbtw+Kioq1AsJyMHXqVGzbtq3ecpYuXYohQ4YI5eNz9uzZQjkO/ycKvqa542N/IeQNJaLKRpQiQdTGlprLBPJNwWKxqKCgQGAiy7dv34hhGIGJLEpKSqSgoMBjH8cwDNnY2JCmpibt3LmzEd8nGhiGoZCQENq4cSPt3buXbG1ted7369ePAgICaOTIkb+8bT+jvruBqqoqioiIoJCQEGIYhry9vcnGxoaGDh1K9vb25OPjI5Y25OXlka6uLmVnZ4vVlnPAgAHk6+sr8B1MXTh27Bj5+/vTrVu3yNfXl1JSUigyMpIMDQ1FLlOc9zFsNpvS0tK4NnS3b98mWVlZ+vz5My1evJjc3NxITU2NLl++TL///jstWrSIli1bxnMHGxAQQN++faPt27c3qh2pqalce77Y2FiqrKwkZ2dnGjx4MFlaWpKqqqrI5QOgESNG0OvXr6m4uJhcXFxo4cKF1LFjR5504urbHz9+kIuLC6Wnp1NkZCTp6enVma6hO+STJ0/S0qVL6cGDBwLfkZaWlpK6ujo9f/681vfxwz/xjq/JDNiZ77OJqhKISNTiW1MzhdPUrKVuw0mFQFlZmUAG5Jzfv3//TtLS0lyBmJ+fT0VFReTo6EgqKip1Ck5paekmiWKcl5dHM2fOpIKCAoqIiKBOnTrxvH/x4gUNGzaMsrOzxRphW1TUNWEKCwtp3759tG3bNtLX1ydvb28aPnw4ERHXAPr48eNi7T9bW1saO3Ys/f7772Ip7+XLlzR48GD68OGDUNG264KjoyOdPXuWJk+eTDt27KiTrSwMGrNI/SxgEhISqEOHDlzWpampKU2ePJmmTp1KXl5ePHn5GdZnZmaSsbEx5ebmUqtWrRr1bRzMnz+fmjdvTrq6ulyBrKSkxG2npaVlvQbZHDAMQxcvXqTg4GDKysoiNptN7u7utGTJkjrTi0MApKSkkIODAw0fPpxCQkLqZSbXxxpOS0sja2trio6Opt69ewtc/7Fjx+j48eN05coVgfP8EwVf0xmwVySB/akRBJc8m6ZqmlBgs9nIz8/Hy5cvERgYCAUFBYSEhGDdunXw9PTEjBkzMHr0aJiYmEBbW5sbI05VVRU9e/bEkCFDMHnyZLi5uWHVqlXYsWMHIiIicOPGDaSmpiI3N1egy/Jbt25BTU2t3hAkPj4+WLp0qbi7QGTUHF6ZmZlYvHgx5OTk4OjoiMePH/Ok3bp1a5N58z937hzMzc3FVt6yZcvg7e3dqDIYhsHOnTuhoKCA7t27Y9myZWJpmzBTui6Vop6eHubNm8dVKdZsr6OjI6ZOncpXDctxpfZzfMfBgwfXeZ8pCjiRwmveyXFUsFu2bIGtrS3k5eWhq6uL2bNn49ixY/jw4QNPGWVlZdizZw+6du0KY2NjREZGorq6Gu/evYOysjJu3bpVZ92NWS4ZhsHmzZuhpKQkVF/4+vrWshPNz89H586d+cbPqw/W1tY4efKkUHmaUEz8bWiyEx8AwvdpRNVpRC2V0wsAACAASURBVFQlZO7W1Ex+PzWTNGmKpomE9PR0srCwoMuXL5OpqWm9aSsqKig/P19g92T5+fnUpk2bOk+P8vLylJycTAkJCfTHH3/QmDFjuGYYNVVKLBaLNDQ06NatW3xVJ78azZo1owcPHlBISAhFR0dz1WHq6uo86eLi4sjBwYGSkpJIW1tb7O2orq4mdXV1SkxMJB0dnUaVxWazSVNTk6Kjo0W2kSwsLKTZs2fT27dvKTIykuTk5MjExIQ2btxIkyZNalT76tuds1gsevz4MfdEd+fOHVJTU+Pa0FlYWNRygcbBli1b6PDhw5SYmEht27attw03b96kGTNmkLOzM/n7+9Px48fp5MmTdOnSpUZ9GxFRZGQkhYWFUUxMDN80DMPQs2fPuCra+Ph4kpWVpX79+lF5eTklJCTQgAEDyNvbmwYNGsSjXbhx4wZNnz6d7t27V8s2T9STT35+Ps2aNYs+f/5MERERQo3xjIwMMjc3p5ycHGrZsiWx2WwaPXo09ejRg0JCQoRqR1ZWFvXt25dycnKEcqP274lPSDDsYrC/jhTSdZkh2KXnmrJZQoNDZmkqF1gMw6CgoAAZGRlISkrChQsXcODAAfj6+kJDQwOqqqoYOnQo+vfvDx0dHcjIyKBFixZQVlaGgYEBLC0tYWZmBmVlZfj5+WHr1q0IDw9HdHQ0Hj16hOzsbIHi3IkLbDYbly5dAhFBQ0MDISEhfN2mZWVlQUVFpUkiwNeEh4eHWILDXr16FSYmJiLnT05OhpaWFo/zdeD/yC78AiwLippTurq6GsnJyTxmAwYGBkKZDQBAbGwslJWVhfKQwgmXZG5ujpcvX0JWVlYsAZlHjhwpMG2fg/T0dEyaNAlt27aFtrY2ZGVl0blzZzg7O+Pw4cO1gvBu3LgRffr0qeXZRZTlMiEhAZqamvDy8hLZDMLM7C8PVgCwZMkSWFtbC0Vm4WD16tVwdXUVOl8Ti4m/BU3+RQy7BOz8GWB/7gn2p271CLyeYH/uCaY8tqmbJBTYbDbGjh0LNze3X1ovJwTJ6tWr6zTbqKysxMePH5GWlobY2Fj069cPDg4OCAgIwIIFC+Dg4IChQ4eiV69eUFNTg6SkJKSkpNCpUycYGxtj5MiRmD59Ojw8PLB27Vrs27cPZ86cwe3bt5Geno68vDyh7d/Ky8sRGhoKfX199O7dG0RUrw9Ljjf/jRs3Ct0/wiI1NRUaGhqNNoGxt7ev5T1fELDZbGzcuBFKSkp8A9QeO3YMXbp04eviqyFUVVWBiLBu3TqMHDkS0tLSMDQ0xIIFC3Dq1CmR4uxlZmZCWVkZN27cEDpvzQC5Q4cORVBQkNBl1EROTg5kZWUF8mXLMAwSEhJgY2MDJSUlrFy5kivoGYbBs2fPsHPnTkyaNAlKSkrQ0tKCk5MTDh48iHfv3mHKlCmYPn06j1pXGAHAZrOxdu1aKCsr49KlS8J/bA2EhYXB1tYWERER0NLSqhX+ShAwDIPOnTvj/v37Quf9Jwq+Jo3OwHOyrE4jlB4kqrhB1EyS/iK9NCMiNlEzOSKp2dSsjQ01a9703vSFwcqVKykuLo5u3rxJLVu2bPL6qqurydfXl06cOEHh4eECeZHPz8+nzp07U1ZWFl9PEgCopKREYFLPt2/fqKioiOTk5Br0ftOiRQu6du0aHTt2jPr27Uve3t5kZWVFzZs356siAUAzZ84kFotF4eHhTUIG+hl9+vShoKAgrmstYVFQUEBaWlr0/v17kpeXFzhfTVLSiRMnSEtLi29aT09Pev78OV25cqVBglJVVRXX9VdcXBwlJSVRcXExLVq0iKysrGjQoEEieUThoKysjMzNzcnR0ZE8PT1FLufu3bs0YcIEqqqqoo8fP4pMctmwYQO9efOGQkND+aZhsVh09uxZCg4Opu/fv5OnpyfNnDmzXvUsAHr58iVPFAhJSUkqKSmhkSNH0tq1a0lLS6ve8VwTnz9/punTp1NVVRWFh4fXUu0Lix8/fpCamhpJSkrSzZs3ycjISOgyEhISaP78+fT06VOh59q/qk4xgGEXgKm8B6Y8BkxFPJiqF3+rI+X6cObMGWhoaODz58+/pL7379+jf//+GDNmjFC7uh07dsDBwUHs7amursaXL1/w/PlzxMXF4dSpU9izZw/+/PNPuLu7Y9y4cdDQ0ICEhAQ3sG3r1q2hoaHBPfFNnToVixYtwp9//ondu3cjKioKcXFxWLp0KQwMDH5p5IitW7di2rRpIucXJEL2z4iLi4O6unq9pKSaqK6uxpAhQ+okKVVWVuLOnTtYs2YN1xm0kZER3N3dcfbsWXz79k1su3OGYTBt2jRMmzZNLPPz27dvaNu2LfT19esNxlpfe7p164bExMQ63xcXF2Pbtm3Q1taGmZkZzpw5I/LpnuM8e82aNWjdujXk5OSgoaEBIsL+/fvrdZ4dExODjh07YuXKlSKpI+vCt2/fICUl1Sh7VGdnZ5E1K3+DmGhy/PO+SEx4/vw5FBUVRVINiILTp09DSUlJqBAkHBgbG/+SiNcc3L17F3Z2dlBUVISvry+Py7bS0lJkZmYiJSWF6+Jp8+bNWLFiBVxcXGBnZwdDQ0Nu4FwJCQnIycmha9euGDhwIMaNG4fff/8dS5cuxcaNG3Ho0CFcunQJ9+7dw9u3b1FUVCTyQpyXlwcZGRmRAxGbmpriypUrAqVlsVjw9/eHiooKrl69KlQ9eXl50NLSwrFjx3D79m2e8D+9e/eGh4cHzp8/X6d3HnEtUps2bYKRkZFYQmRxEBAQAHNzcygpKQkUFaAmkpKSoKurW+t///HjRyxfvhyKioqYMGEC7t69K7b2An8JMhUVFcTGxnI3ch07duRGkQgNDUVGRgaqqqrg6+uLjh07itVTUHV1NYYNG4aJEyfCyMhIpDKKi4shKysrsmvFfwXf/wgKCgqgq6uLgwcPNnld5eXlcHNzEykECfCXyyM1NbUmd9/GYrFw+vRpDBw4ENra2ti+fXuDpgd1TZjMzEweMguLxcK3b9/w8uVLJCQk4OzZs9i3bx8CAwPh6emJ6dOnY9SoUTAxMYGWlhbatWsHSUlJdOzYET179uT6cHVzc6vlwzU1NbWWD1c7Ozvs27dP6O9//vw5VFVVBdrF5+bmYvDgwRg8eDByc3MFrqOiogLx8fEICAiAiYkJiAj6+vrw9PTEhQsXBHJDJ45F6ubNm0KTWQRBVlYW5OXlcffuXejo6MDFxUXg0EBz587F2rVruX8/e/YMzs7OkJOTg5ubm0inSEERHByMPn36cPuWYRi8fv0aoaGhmDZtGpSVlSEpKQkVFRUEBwfj1atXYtNi+fj4wNraGpWVldDU1KxlBiQIDh8+jLFjx4rchn+i4Ptld3z/LWAYhsaNG0fa2tqN8jYhCF6/fk329vako6NDoaGhInl69/b2JklJSQoM5O/hpjEoKyujQ4cO0aZNm0hRUZG8vb3J1tZWIAP5n+8GysvLydzcvE4DaGFQUVEhlBOC/Px8atu2LSkpKZGEhATl5eWRjY1Nvd57fo7asXTpUiL6656pPly7do2cnZ1p/vz55OvrW28/VVRU0L179yguLo7i4uLowYMHpK+vzw2/9enTJ1q3bh09ePBA4DvFxt7HZGZmUv/+/en48eM0ZMgQkcvhh6FDh5KLiwuNHDmS5s2bR0+fPqXIyEjq3r073zzl5eWkpqZGT548oYyMDAoJCaHHjx/TggULaN68eQ2Gamos8P8jhRw/fpwYhuEZFxcuXCAXFxeaMWMG6erq0u3btykuLo7YbDZPuKWuXbsKfbcWERFBK1asoAcPHpCCggKtXLmSiouLafPmzUKV8//YO++4Gt8//r/7lPFRpDotUUZFmlo0VFZkk5SZjAiJioTIDg0ysiWkQtk7inyMEBGyQpE2lfa5X78//Do/6VTnnE59xvf3fDx6yD3e13Vf3ff1vsZ79O/fn+bNm0e2trZ83VfN/9/j+x9gxYoVsLCw4Gk/pjEcOXIELBYLISEhAo8OKyoqIC8vj9TUVCHX7qc5uo+PD2RlZTF69GgkJCTwXc9fXy9eHKCbimp3kdevX+PWrVto37491q9fj02bNsHT0xPTpk3D8OHD0bt3b3Tr1q2Gu4iWlhYsLCzQunVrODg4wMfHB8HBwQgPD8fVq1eRlJSE9PR0FBYWYsmSJejYsWOdwbVLSkpw48YNrFq1CpaWlhAXF4exsTEWL16MCxcucF2CdXd3h7W1Nc8z+sZ80j9+/ICenh4CAwMFltEQR44cgY2NDYCff5f9+/eDxWLh4MGDdb4XYWFh0NbWhp6eHjQ0NLB///5mdc8BfrYNESEoKAjAz9m5m5sbVFRUau07MgyDd+/e4cCBA5g6dSqUlZWhoKAAe3t7hISE4MWLhu0anjx5AhaLxcnWAABv377lO7P9+/fvwWKxasTz5Zf/opr47z1RIzh16hQ6derEs3+TIHBLQSIo586dg6mpqZBq9pOXL19i1qxZkJKSwpw5cxqlVH/9YIKCgoS+ZyQoHh4e9aYFAv6fu8jTp0+xYcMGqKqqYseOHfD19cX8+fNhb2+PAQMGQEdHB3JychAREYGoqCg6deoEIyMj2NjYYMKECRg3bhz69esHNTU1tG7dGj179sTMmTMRERGBgoKCButaWVmJAQMGYMmSJTw9m6CdFMMwmDhxotCMWerix48faN++PTIyMjjHnj9/jp49e2LSpEkoLCzkHP/+/Tv8/f057XbhwoUmSzHFC0QEeXl5HDlyBAYGBhg9ejTPridpaWk4dOgQHB0d0blzZ8jJyWH8+PHYuXMnUlJSarR5bm4uunTpguPHj9eS07dvX8TExPBc5+r3tTH8f8X3H6bamIXf/Gf8kJyczDUFiaAIul/1OwzDIC4uDsOHD4ecnBxWr14tkM/X71R/MII4QDclycnJfO2L2tnZISQkhOu56OhoyMrKYsuWLfj8+TPCwsLg5OSEnj17omXLllBRUUGfPn0wePBgDB06FKamplBXV4eUlBTExMQgKysLDQ0N9O3bF2PHjoWzszOWLVuGoKAgHDlyBJcvX8b169fRsWPHOqP4/4qgnVRAQAB69erVLAOTmTNnws/Pr8axHz9+YObMmVBTU8PFixfh6ekJaWlpjBo1Cu3ateN5L7ApISIsX74cIiIi8PX1bdQAIS0tDaGhoXByckKXLl0gKyuLcePGYdu2bejTpw88PDy43nfw4EGMGsVbOMfq7BiPHj0SuJ7A/1d8/1mqjVlCQ0ObRD7DMNizZ0+9KUj4pbEWisDP2URERAQMDQ2hrq6OPXv2CLWDIaJGOUA3JQYGBjxZwubl5XHNb1haWorZs2dDQUEBjo6OMDU1RZs2bWBqaoply5bhypUrDQ5uKisr8fXrVzx//hxxcXE4ceIEQkJCsHbtWixYsAATJ06EtbU1evXqBXl5eRARWrVqhU6dOkFfXx/W1taYOHEi3NzcsHbtWuzevRtEhLi4OKSkpCArK4snY5zr169DQUGhVgSTpiIhIQE9evSopTgeP34MMzMziIiIoF+/fkhLS8P69esxe/bsZqlXfVQvdaqqqmLRokVCHyR8/PgRYWFh0NLSwp9//gkZGRnY2toiODgYycnJnJluYWEhJCUleVqVunnzJrS1tRs9g/8vKr7GhZb/D8Bms2nSpEk0ZMgQcnR0FLr879+/k7OzM7169Ypu374ttDiax48fp+HDh5OkpCTf9xYVFdGBAwdo69atpKKiQitXrqRhw4bViP0pLMaMGUNLliyhAQMGCF12Y3BycqJDhw5xMkPUxfHjx8nGxoakpKSouLiY7ty5Q9HR0XT06FEqLy8nQ0ND6tixI02ePJlMTEz4yq4gJiZG8vLyJC8vz9P14eHhtHz5coqJiaGqqqpaRj3V6Wt8fHw4xwoKCkhSUrJOQx4AtH79elq/fj0xDENFRUUkISHRpAEFTE1Nic1m04MHD8jY2JguX75MAQEB9OrVK3Jzc6Pg4GCaNWsWubu709OnT+nYsWNNVhdeePHiBY0fP56IiB4/fkwSEhI0ZcoUcnZ2piNHjgilrZSVlUlMTIx+/PhB6enpVFJSQvHx8RQfH0/BwcFUUFBAFhYWnJiqR48ebTCoQGhoKE2bNq1ZgkP86/i7Ne/fzfLly2FpadkkxiwPHjxA165d4eLiIvSlGn19fb7jW2ZkZMDLywsyMjIYP368QO4TvMIwDIioyfeMBCU3Nxft2rWrd5+tsLAQampqsLOzQ+/evSEuLo7u3bujTZs2WLBgQZNkkmgIDw8PDBo0qM6Z3O+fdFVVFXJycvDy5UvcunUL0dHR2Lt3L9avX4/58+dDSkoKPXr0gKGhIVRUVCAuLo5WrVpBSUkJurq6GDBgABwcHDB//nysXr0aO3fuRGRkJG7cuIHk5GR8+fJFoG9n9erVsLKygqamJnR0dBAWFlbDaKOsrAx2dnYQExOr02m9qWEYBgcOHACLxcKBAwdqtK2wDYGSkpJqGbP8SkZGBo4dO4ZZs2ahY8eOEBUVxahRoxAUFISkpKRae59FRUWQlJQUSvCN/6Ka+J92Z4iOjqZFixZRYmIiycnJCU0uANq6dStt3LiRdu3aRePGjROabKKfubiGDx9OaWlpPLkVJCcnU0BAAJ07d46mTJlCCxcubJIsCL8SFBRE7u7u9OPHjwaj+f9d2NnZ0cCBA2n27NlE9DM0VEJCAids1bNnz4jNZtOSJUvIxMSEIiIi6P79+xQVFUW6urp/S52rqqpoyJAhnPBrv8Or6TkAmjRpEomKilJYWFiNWUFpaSlnNslLkue8vDwSFxevN6Fz9e8tWrSgs2fP0p49eyg/P59Onz5NQ4cO5TorcXZ2ptLSUrp69Sp5eHiQp6dnk6xKcKOoqIhcXFzoyZMnFBkZSZqamrXaVliuH3l5eWRoaEgbN24kBweHBq9nGIY6d+5MLi4u9PHjR4qLi6Ps7Gzq27cvxxUmKSmJzpw5Q2fOnBG4XtX8F90Z/mcVX0pKCllZWdGlS5fI0NBQaHLz8vJo2rRplJ2dzXcKEl5xd3enNm3a0Lp16+q8BgBdv36d/P396dmzZ7RgwQKaPXs2SUlJCb0+v3Pjxg2aOHEiZWVl/aM/mKioKFq5ciWNGDGC4uLi6OXLl2RkZMTxvzpz5gy1bt2aJk2aROPHjycjIyPauXMnSUj8vfFk8/LyyMjIiDZs2FCro+S1kwoICKDw8HBKSEioNxkqLzAMQ9+/f69XSX769IlevHhBOTk5JCoqSgDojz/+IDk5OVJTU6ulJNu1a0eurq508uRJat++Pbm5uZGkpCSFhYUJdZDKjaSkJLK3tycrKyvaunUrZ+DGrW2r3/V79+7VG4O1LhoayNSFr68v5efnU3BwMBERZWZmcnwI4+Pj6fXr19SrVy9ycHAgKysr0tPTEzg59X9R8f335rA8kJ+fD1VVVaEZmlRz69YtdOrUqVEpSBqioqICcnJyePPmDdfz5eXlCAsLg46ODjQ1NXHo0KFG+fDwS1paGuTl5REbG/uPWyIpKCjA2bNn4eHhAQMDA7Rp0wYtW7bE/PnzER8fX8M3rKKigpMdg8ViNZnhk6Bw8/MCeFuWqg7D9Wsy16bi/v37sLOzg4yMDJYuXcqJZFNWVoYdO3bA1NQU169fR0REBHbs2IFVq1Zh3rx56N27N6SlpaGjowNFRUWIiYmhRYsWEBUVRffu3TF06FBMnToV7u7u2LhxI/bt24eYmBgkJCTg1atXyM3N5dv1gWEYbN++HbKyslxdCepq28aEd6teuuY38lJ9/nlv376FjIwMjh07hrlz56Jnz56QlJTEsGHDsGXLFiQmJvIVR1TY33HWpxzcu/AIseG3cef0A7x5/L7Zt0P+52Z8bDabRowYQWpqarRt2zahydy4cSPt2LGDDhw4QMOGDROKXG6cOXOG/P396fbt2zWOf/v2jfbu3UvBwcGkoaFBHh4eNHjw4Gbd2C4pKSEzMzOaOnUqLVq06G8fKRYUFNDt27drjIJ79+7NmdEZGxuTj48P/fHHH+Tn51fj3qioKJo7dy4pKSlRZGTkPya576/8HtmDqOHReVpaGmfZ1srKqknqxTAMnT9/nvz9/enTp0+0aNEimj59OrVt27bGddURWZKTk2tlMBg0aBDNnDmT7O3tiejnCkZRURFFR0fT4sWLaeDAgTRo0CDKz8+vcwm2qKiIpKSk6s0sUv1vixYtaMWKFZSRkUGRkZFcExbX1bYAaMqUKQSAjh49yvM3Fx4eTj4+PnxF5vmVfv36kaurK40dO7bG8VWrVtH3799p69atnGPZ2dmcGWFcXBxlZGSQmZkZJ7KMvr4+iYlxt3UUxnfMMAw9upZMUVvO0Iu/UqlFqxbEMCARERFi2GySkm9P4xePogGTzOlPicatQPDC/5ziW758Od25c4euXbsmlDRDX79+pcmTJ1NlZaVQUpA0xJgxY2j48OE0Y8YMIvqZVXnbtm0UGhpKw4YNIw8PD4HSljQW/N+wTiIiIhxLt+ZWfPn5+RxFFxcXR2/fvqU+ffpw9j2MjIyoZcuWNe5JSUkha2tr+vTpE2cp6OHDh2RlZUUGBgZ0+fLlRi8FNiWLFy+mJ0+e0KVLl0hMTKzeNi8pKSFTU1NycnIiNzc3odeltLSUwsLCKDAwkNq1a0eenp5ka2tbZ4dKRDR79mzq3LkzeXt7c459+vSJevXqRZ8/f+aaKTwzM5MmT55MbDabjh07RkpKSlxlV1ZW1qsYq3//8OEDvX//noiIWrZsWWufsvrfFStW0KlTp2ooTmlpaRIVFeU7hdOTJ09o0KBBFBsbSzo6Og1ez43Dhw/TqVOn6OzZs5xjDMNQ165d6fTp0/X2Azk5OTWWRj9+/Eimpqacb0VfX5/TPzb2O87LLCCvQWso+1MulRaX1Xlda/FWJPLHH7Tm9BLS66clcHk80azzy7+ZkydPQllZWWiRWa5evQpFRUWhpiCpj+zsbEhKSqKwsBAPHz6Eg4MDpKWlsXjxYqSnpzd5+fXBzQG6qV+v3NxcREdHY8GCBdDV1YWEhASsra2xYcMG3Llzh+flZiMjI1y8eBEMwyAwMBAyMjJo06ZNo3wkm4vKykoMHDgQnp6eAOpuc4Zh4ODggKlTpwp9WSk7Oxu+vr6Qk5PDiBEjEB8fz3MZf/31F9TV1Wtcv3btWri4uNR7X1VVFdauXQt5eXlcuHBBoHqz2Wxs2rQJcnJyOH36NBiGQVFREdLS0pCYmIiLFy8iLCwMAQEB8Pb2BhFh9OjRMDc3R48ePSAjIwNRUVHIyMige/fuMDAwQKtWrWBjY4OlS5ciICAAhw8fxsWLF/HgwQO8f/8eRUVFyM7ORufOnREZGSlQvavhlnUhNjYWurq6fMvKycnhfEs6Ojpo164dBg8ejI0bNzaYULpeuRm5sFOYgcEt7DFQZBxPP8PaTMTdcw8FKo9X/mdmfM+fP6d+/frR5cuXycDAoFGyqqqqaOXKlXT48GE6cuRIkwTz5cbWrVvp7NmzBIDevXtHCxcupJkzZ1K7du2apfy6iI2NpcmTJ9O9e/dIRUWFc1zYM77c3NwayzUfPnyoMUo1MDAQaBYfEhJCV65cIYZh6OvXr2RjY0Nv37792/3HeKXa2GX9+vU0ceJErm3u7+9PERERdPv2baHNYF+/fk2BgYEUGRlJdnZ25O7uzveSMADS0NCggwcPkqmpKQEgNTU1Cg8PJ2Nj4wbvv3XrFk2aNIkcHBxo/fr1tWb0dZGdnU1Tp06l4uJiCg8PJ2Vl5Qbv4fY+s9lsys/P58wib9y4QYGBgeTs7Mzxtfx1lpmdnU1lZWUkLi5OqqqqXJddfz8mIyNT53s9ffp00tTU5AR9nzp1Kunr69PChQt5aoe6yMvL46yebNu2jdq2bUsmJiacpVFDQ8MG27qirIJm6XhQ1odsYlcxfJXfqk0r2nZnHXXT7dyIp6ib/wnFV1BQQMbGxrRy5UqaMmVKo2R9+vSJJkyYQBISEnTkyJEmtzAj+hnF/+jRozR//nzq1KkTrV69muzs7JolI3xDVJt0Hz9+nPr161fjXGMV36/7EvHx8fTp06da+xLCaINLly7RsGHDaO7cuRQYGEgmJibk5+dHgwYNarTs5uLp06c0cOBAys3NrdXm165do6lTp9L9+/d56uDrAwDduXOH/P396a+//iIXFxeaO3cuz0743PDz86P379/T3r17KSEhgZydnSklJYXnvbLc3FxycnLi2ZL65s2bNGXKFHJ0dKTVq1fXuxT7K7y+z1u3bqXDhw/TnTt3arnyeHh40NOnT2n//v01FGZ9LiP5+fkkISHBVTEWFhbSuXPnKCQkhNq0aUNjxoyhpKQk6tq1q9D290VERLhuI/y+X/67IrwWFk/B8/ZR2Y9yAcokMrLRp/XnvRu+WAD+84qPzWbT8OHDqXv37jU2ewXh7NmznIgSixcvbnKfory8PAoJCaGdO3eSqqoqvXnzhj5//iywWbKwqTZmcXR05DrC5FfxZWVl1dqANzc353xc9W3ACwKbzSY/Pz/avn07qaur04QJE8jMzIyGDRtGHz58+Me0M69ERETQhAkTKDc3l2PsIixjlqqqKoqJiSF/f3/Kz88nd3d3cnR0FIqP5ufPn0lbW5syMjLI1dWVevToQYsXL+ZLBn7xnQ0JCeGagofNZtOaNWto3759dPjwYb4HNvz4SE6dOpWzB1mtgAQ1ZmEYhr59+8ZVMebk5NDevXtJR0eHMjMzKSsri0RFRamsrIyjIHnxr2SxWNSqVSuen7ugoIASEhI4g9LU1FTq3bs3Z1BqbGxMc/WX0qeXGTw/5++0bN2Cwt7tJBlF4btg/ecV37Jly+ju3bt09epVgWcH5eXl5OXlRadPn6bw8HAyNTUVci1r8u7dOwoKCqLw8HAaM2YMa1A57AAAIABJREFUubu70759+0hSUpJWr17dpGXzCupxgK6moY7i69evHGfx+Ph4+vLlC/Xt25fz8ejp6QlV0f1e9pQpU6i8vJzCw8Pp+fPntHLlSjI3N2/QR/KfjIiICA0YMIAuX75M5eXlZGpqSjNmzKAFCxYIJK+4uJgOHTpEQUFB1KFDB/Lw8KCRI0cKfVAwZMgQsre3J3d3d3rx4gUpKioKJCcxMZEcHBxo8ODBFBgYyDGO+fz5M02aNInExMTo6NGjpKCgwLdsfgZyv+eeTEpKImtra7px4wZpa2vzXXZ9rFmzhrKzs+np06fk6elJo0aNovLycr6CEOTm5lLr1q25KsmAgADav39/LYXZvn17zuD/+/fvHEUYFxdHn1K+kHaFCYkwgs86W7ZuQXaLR9G01fbCaioO/2nFd/LkSfL09KTExESSlZUVSMbbt2/J3t6elJWV6cCBAwKZHfPK3bt3KSAggOLj48nZ2Znmz59PioqKVFFRQR07dqS7d+9St27dmqx8fuDFAfr3jiIzM5Oj6OLi4igrK4sTbcLS0rJRTrb8cO3aNXJ0dKSZM2fSypUrSUxMjNhsNikrK1NZWRndu3eP1NTUmrweTYGIiAgNGjSItLW16fPnz9SqVSsKDQ3le9krMzOTduzYQXv37iVLS0vy8PAgExOTJqo1UWRkJK1du5ZUVFTowoULjZJVHR83NTWVIiMj6d27dzR9+nRydXWlpUuXNpsj96dPn6h37960Y8cO8vDwoM2bN3NifgqTjx8/Uq9evUhMTIw+f/4s0AAfABUWFnJVkkuWLCEnJ6daCrO4uJikpaW5ziTzn/6gN5fSCezGPVt3I1XacX9j44Rw4T+r+KqNWa5cuUL6+voCyYiIiCBXV1dauXIlzZ8/v0l84thsNp09e5b8/f0pMzOT3N3dycnJqUaw45iYGNq6dSvFx8cLvXxBuH79Ok2ZMqXBPSMRERE6duwYZ0aXk5NDFhYWnBmdjo5Osy4nVlVV0apVqyg0NJTCwsJqBc62tbWl+/fvU0aG4MszfzciIiKUl5dHampqJCkpSSkpKXwZs6SkpFBAQACdPn2aJk6cSIsWLWqWwVZZWRm1bduWgoODycXFpdHyANCuXbto8eLF9Oeff9KZM2fI3Ny8UTIF2bOOjY2loUOHkpOTE+3evbtR5ddHly5dSFNTk86fPy902XU9d2VlJeXl5XGdSb68mEa5D4qIqHF9Zkd1RTr0KrhRMrjxn8zOUFBQQKNHj6agoCCBlF5JSQm5ublRfHx8oxRnQ2WEhoZSUFAQycjIkKenJ40ZM4arIqiOsv5PIC0tjSZPnkwRERG1lF5GRkaNGR0R0YkTJ8jKyormzp1L2traf9u+WXp6Ok2YMIHExcXp8ePHXI0xCgsLqbi4mKqqqppsibU5ePToEYmIiND3798pNTW1Qb9OAHTz5k3y9/enpKQkmjdvHr1584azT9gcfP36lURFRSk7O1so8j58+EBhYWFkZGREmZmZtH//ftLT02v2cHMXLlygrl270r1796ikpKRJ4tay2WwqLCykwsJCocuupqKigudl05ycHPozW4q6UA8SaaTiE2vRNN/hf27Gx2azadiwYaShoUFBQUF831+dgkRPT49CQkJqRZtoLFlZWbRz507avXs3mZmZkaenJ5mamtY5m8zKyqLu3btTRkbG3x4j8ncH6PT0dI6Si4+Pp2/fvpGlpSVnRqerq/uPiPFXbZS0aNEiWrJkCVejpJycHFJTUyN1dXVatWpVk0bfaUpERERITk6OoqKiKCsri7y8vCgxMZFYLFataysrKykqKooCAgKorKyMPDw8aNKkSVydxpuaNWvWUHJyMj19+pRev37dqNWVU6dOkYuLCy1btozc3NyopKSE5s+fT/fu3aPIyEiBHcb5nfEdPXqUfH196f79++Tu7k4VFRUUHh4u9JWj69evk4eHByceakP7o9WxVRty7K/+9/3799SiRQuSkZFp0FBGSkqKcnJy6PLBG5QS856I3bhnNbDWJb/LKxolgxv/OcXn7e1N9+/fp6tXr/I1agdAhw4dIi8vL9q8ebPQ81i9evWKAgMD6cSJE+Tg4ECLFi0idXX1Bu8LDAyk5ORkCg0NFVpdBAEAjRo1ivLz80lNTY3i4+OpqKiIo+QsLS1JU1OzhlL5u0OWVRslxcTE0PHjx+s1Stq2bRs9fPiQzM3N6fr163TixIlmrKlw+PHjB0lISFBwcDC5uroSEZGXlxc9fPiQrly5wvkeCgsLad++fbRt2zZSVVUlDw8PsrGxabbMB7/DMAypqqpSZGQkOTo60t69ewValiwrKyN3d3e6cuUKRUZG1go+f+TIEXJ3d6e1a9fS7Nmz+f6++XmfHz9+TIMHD+YYs5SWllLfvn3JwcGBPD09+Sq3ISZMmEAaGhqUlJRELBaL+vXrx1M2DV5CubFYLFJTUyOGYbi2F5vNpidPnnAGv7dv3yZFRUXq28eCPhwtIIZP/71f+bNta1p8cB71te3TmObhyn9K8Z04cYIWL17MtzFLUVERzZkzh5KTkykyMpJ69uwplPoAoFu3bpG/vz89ePCA5s6dS3PnzuW5bgBIR0eHtm/f3mRxFevjw4cPnBf6zJkzVFRURCNHjqT+/fuTlZUVaWho1NtZ/p2K7927d2Rvb08dO3akgwcPNmiU1KtXL/L39ycDAwNSUVGh9+/fN+tSX2MBQA4ODhQVFVWjk2Kz2TR06FDS0tKihQsXUnBwMB08eJAGDx5MHh4ejQ7mIAzi4+Np3rx59OzZM9qyZQu9fv2a9u/fz5eM1NRUsre3p+7du9PevXvrTNBcfZ26ujrHUppXeH2fc3JyyMjIiLZs2UJ2dnac49XGLmFhYXW6UjAMw/Hv42VGlpOTQyUlJaSgoEDi4uL09etXGj58OMnKytap2GRkZHh29P/9uauqqigpKYmzpZGQkEBKSkqcIBIWFhaUm5tLgYGB9OToa5KuUiASsAuQaC9OJ7L2N8ly5793I+M3nj17RnPnzqUrV67wpfQeP35M9vb21K9fP7p//75Q1uCrqqro1KlT5O/vT4WFheTh4UFRUVF8R8xISkqiHz9+kIWFRaPr1BAAOIquWtmVlpaSlZUVycvLk6ioKL19+7ZGZJZ/KvwaJT158oTy8/OpX79+9Mcff9DQoUPp+PHjNH/+/GaqcePZsmULJ97kr88rKipK3t7eNGLECNqzZw85OzvT48eP/1F/x9DQUHJyciIRERGaPHkyaWpq0rZt23jOZl89k1u/fj3NmjWr3r939+7d6d69e+Th4UG9evWiyMhIMjIyEtajUFVVFdnb29OECRNo3Lhx9OPHjxrKavr06WRra0tTpkyhysrKWsqsoKCAJCUluc7ClJSUSFdXt8aM7Pz58xQXF0enTp0iAKSurk7u7u48Rb3h9XmIiDZv3kzx8fGUkJBAysrKZGlpSdOmTaODBw+SnJwcZ5/YycmJHj9+TPPnz6cZZ2eT7wh/QhX/mq9l6xY0at7gJtvj+0/E6szLy0O3bt1w9OhRnu9hGAbBwcFgsVhcU5AIQmFhIbZu3QoVFRX07dsXZ86c4Ts1yq+4urrC19dXKHX7HYZh8PbtW+zfvx9TpkxBp06doKCgAHt7e4SEhODly5dgGAbv37+HvLw8bt68yXcZzf16/fjxA7NmzYKqqioePXrE831ubm7w8fHh/P/KlSswMDBoiio2CVeuXIGioiI+ffrEaXOGYXDx4kUMGDAASkpKWLRoEWRkZPD48eO/ubY1qc4U/mu8SRsbG4SFhfF0r6OjI3r06IHk5GS+yz558iRkZWUREBDAU2xRIkJWVhaeP3+OuLg4nDhxAiEhIVi7di0WLFiAiRMnQllZGW3btkXHjh3RunVrtG7dGp06dYK+vj6sra0xceJEWFpaQl5eHtu2bcPJkycRFxeHlJQUZGVl8R3z19TUFGfPnuX8f926dQ3GOa2PiooK3L17F35+fhgyZAjatWsHIoKrqytOnTqF7OzsWtcfO3YMvXr1Qo8ePbBv3z6UlpYiLS0Nffr0gXXXURgmPpHnOJ0DRcZhSEsHOOt6oKyk6dKp/esVX1VVFaytrbFo0SKe78nPz8fo0aNhYGBQZ147fsjIyICXlxdkZGQwfvx43L9/v9Eyy8rKwGKx8P79+0bLAn52hG/evMG+ffswadIkdOzYEYqKipgwYQJ2796NV69e1fr4i4uLoaOjg23btglUZnMqvpSUFGhqamLixIkoLCzk+b7y8nLIysri7du3nGNVVVVQUlISqDNtbt6+fQs5OTnEx8cD+NnmBw8ehKamJnR0dBAWFsYJ1h0ZGQkVFRXk5OT8nVWuQWhoKIYPH17jWFRUFPr371/vfU+fPkWPHj3g5OSE4uJivstlGAbfv39HXFwcNDU1YWRkhO3bt8Pf3x9eXl6YMWMGRo4cCVNTU6irq0NKSgpEBBaLBQ0NDfTt2xdjx46Fs7Mzli1bhqCgIMyePRuKioq4ceMGPnz4UGd+PoZhMHXqVNjb2zcqYHhqairk5eVrBJD++PEjpKWla+SWrI+Kigr89ddf2LBhAwYPHoy2bdtCV1cXCxYsQHR0NHJycrh+x9+/f4e/vz86deoEKysrnD9/njPIP3XqFGRlZeHv74+qqirM7eeB/n+M4UnpDf1zAmZoLsS3nO8Ctwsv/OsVn5eXF/r378/zSOmvv/6CiooKFi5c2OgErcnJyXB0dISUlBQWLFggNCUF/ByNWllZCXw/wzBITU3Fnj17MHHiRHTo0AEdOnTAxIkTsXfvXrx+/brej45hGNjb2zcqmn9zKD6GYXDgwAGwWCwcOHCA77rGxMSgb9++tY57e3vDw8NDWNVsEoqLi6GtrY3t27cjPz8fGzZsABHB2toaV69e5doW/H4vTY2lpSVOnTpV41hpaSlkZGTw4cOHWtczDIOQkBCwWCwcOXKEc7y8vBxfvnxBcnIyYmNjERkZiR07dsDX1xfz58+Hvb09BgwYAF1dXXTo0AEtW7aEhIQEOnfuDH19fXTp0gVt2rSBnZ0dNmzYgL179yImJga3b9/Gy5cvkZubW+/7/OjRI7BYLDx79oyn5y4pKYGBgQE2b97MY0vVpq53dODAgYiIiOB6T3l5ORISErB+/XoMGjQIbdu2hZ6eHhYuXIjTp08jLy+v1j2/PvenT5/g6ekJaWlpODg4IDExkXOutLQU8+bNQ5cuXXDv3j0A/7ddZFjY7XMItnLTMUB0LFeFN1xiEoa2mYiAmSEoKeZNaTeGf7Xii4yMROfOnXkawbLZbPj5+UFOTg5nzpwRuEyGYXD16lVYW1tDUVERGzduRH5+vsDy6mL48OF8ZYhnGAavXr3C7t274eDgAEVFRXTs2BGTJ0/Gvn378ObNG76UwubNm2FgYICSkhJBqg+g6RVfYWEhJk2aBE1NTTx//lwgGSNHjsTBgwdrHec2mv4nwTAMxo8fD1tbW7i6ukJKSgqOjo4NtnlVVRUGDx7M1wpJU/Hu3TuwWKxa6aMYhsGMGTPg5uaGv/76C2fPnsWBAwfg6+sLdXV1SEtLw8rKCr1790a3bt0gKSkJMTExyMvLQ1NTE1ZWVhg3bhxcXFzg4+ODbdu2ITw8HFevXsXjx4+Rnp7O9b2+ePEi5OXlsXbtWq4Z0etq2+zsbKioqODEiRN8Pf+nT5+goKCAq1ev8nUfUP+qxNGjRzFkyBAAP1eObt++jbVr12LgwIGQkJCAvr4+Fi1ahDNnzvDUdxERkpKSMHnyZEhJSWHRokW1BiWpqanQ09PDuHHjUFBQAKB2uzxLfgY16Z5YZOmDMTLTYNN6AkZKTsG0HgtweuclFH/nP4O9oPxrFd/Tp0/BYrF42rPIysrC4MGDYWZmho8fPwpUXnl5OcLCwqCjowNNTU0cOnSo0TPGusjMzET79u3rXcJhGAYvXrzArl27YG9vD3l5eXTq1AlTpkzBgQMH8O7dO4FnalevXoWCggI+ffok6CMAaFrF9/jxY6ipqWHWrFl1Lik1xNevXzn5Dbnx+/7JP4l58+ZBSkoK0tLS8PLyQkZGBgDe2rx6T/zXGVNTUlpaivT0dCQlJeHatWsIDw9HcHAwLCwsoK2tDTs7O1hZWUFLSwsKCgpo0aIFxMXFISYmBmNjYwwbNgzDhg2DpKQkTExMsHv3bpw5cwZ//fUXXr9+jfz8fKHlGMzIyIClpSX69++PL1++1DjHrW0rKipgZWUFb29vgcqLi4uDnJwc3r17x9d9de1Dl5WV4cqVK/jzzz9hZmYGCQkJGBgYwMPDA+fOneMoJV5gGAaXLl0CEUFJSQmbNm3iev+RI0fAYrEQEhLC+Ttwa5clS5ZgyZIlfD1nU/GvVHx5eXno2rUrjh071uC1sbGxUFJSwrJlywRa3vn27Rs2b94MJSUlDBgwAJcuXRJ6Is/f2bJlC5ycnGocYxgGKSkp2LlzJ+zs7CAnJwcVFRU4Ojri4MGDeP/+vVDq9e7dO8jJySEuLq7RsppC8TEMg+3bt0NWVrbRRkmBgYGYOnVqnef37t2LsWPHNqoMYcJms3HmzBloaWlBVFQUvr6+tZQ2r22enJwMFovFlxFQdR1yc3Px6tUr3L59GzExMdi3bx82bNgAd3d3TJ06FTY2NjAyMkLnzp0hISGBli1bokOHDtDR0UH//v1hb2+PuXPnon379vDy8kJERARiY2Px9OlTfPnyBeXl5WAYBpqamrh58yb8/f0hKytba0m0qaiqqsKqVaugoKCAy5cvc45za1s3NzfY2NhwnSHySnBwMLS1tfnaq5wwYQJ27NiB0tJSxMXFwdfXF/369YO4uDiMjIygo6ODadOmCZRMuaysDIcOHYKWlhZ0dHRARFyTOhcXF8PJyQndu3fHkydPapz7vV0qKyuhqKiIFy9e8F2fpuBfp/iqjVnc3d3rva6yshI+Pj5QVFQUaCnhw4cPWLRoEaSkpDB58mQkJSUJWmW++PWDf/bsGbZv345x48ZBVlYWXbp0wbRp0xAaGoq0tDShl129ZxQcHCwUecJWfPn5+RgzZgz09fUbbZTEMAy0tbVx48aNOq/59u0bJCUl/3ZjkJKSEuzevRvq6urQ0tKCpKRknVa2/LR5VFQUlJWV8fjxYzx8+BCXL1/G0aNHERQUhOXLl8PZ2Rljx46FhYUFNDQ0ICsrCzExMUhJSUFNTQ2mpqYYOXIkpk+fDi8vL2zZsgWhoaE4f/487t27h3fv3uH79+9cB2Q3btyAjo5OvYM1X19fdOzYEb17926S970hbty4ASUlJSxduhQVFRW12jYsLAyqqqqN3upgGAaOjo4YP358g4PXkpISnD17Fq1atYKpqSnExcVhbGyMJUuW4MKFC/j+/adRyJ07d9C9e3e+BsP5+fnYuHEjOnToUGOfmNs7lZycDA0NDTg6OqKoqKjGOW7tcuHCBfTu3ZvnujQ1/zrFt2TJEgwYMKDe2VtGRgYsLCwwYMCAGmbSvPDw4UNMmDAB0tLS8PT0bPRyH6+w2WwkJyfD09MT4uLikJGRQdeuXTF9+nQcPnyY60a/MKneM3J0dBTajFaYiq/aKMnNzU0oS8yPHj1C586dG3Q3mTRpksBWrY0lOzsbvr6+kJOTw4gRI3Dp0iVoaWlhx44dXK+vqqoCESElJQXx8fE4efIkdu/ejXXr1sHNzQ2TJk2CtbU19PX1oaysjD///BOioqJo1aoV9PT0MGjQIEycOBELFizAmjVrEBISghMnTuDmzZt4/vw5vn79KjSjmKlTpyIwMLDO8/Hx8VBUVESrVq2aZA+dV7KysjBkyBCYmJjUeJ8fPnzIlzFLQ5SWlsLQ0BCbNm2qcbykpASxsbHw8fGBhYUFxMXF0aVLF3Tv3h2XLl2qc5meYRioq6vj7t27DZb9/v17LFiwAFJSUpg6dSqePn1a4/yvz80wDPbs2QMWi8XVBqGudrGzs0NISEiDdWku/lWKLyIiokFjlvPnz0NeXh7r1q3jefmBzWbj/PnzsLKyQqdOnRAQEMAZOTUVbDYbT548wbZt2zBmzBjIyMhAVVUVGhoasLW1bTaFW82mTZtgaGjIsxk0LwhD8bHZbGzatAlycnI4ffq0EGr1E1dXV6xatarB665du4ZevXoJrVxeSE1NhbOzM9q3bw8HBwdERUXh/PnzMDIygpGREby8vDBz5kyMGjUKZmZm6N69O6SlpSEqKgoiQo8ePWBubo4xY8Zg1qxZ8Pb2RmBgIMLCwnDp0iUkJiYiLS0NxcXFqKysxJAhQ7Bw4cJme77CwkJISkoiKyur1rmqqiqsWbMGCgoKuHjxIoYPH47Q0NBmqxs32Gw2Nm/eDCJCTEwMsrKyoKysjJMnTwq1nGpjFz8/P6xYsQLm5uYQFxeHiYkJvL29cfnyZRQVFaFPnz64cOFCg/I2bNiA2bNn13n+/v37GD9+PGRkZGrsE/9O9Xf87ds3jB8/Hjo6Onj58mWt6+pql7y8PEhKSv6tA5jf+dcovidPnoDFYtW55FheXg4PDw906tQJt2/f5klmaWkp9u/fDw0NDfTq1QvHjh1rMis+NpuNpKQkBAUFYfTo0ZCWluYYZxw9ehTp6en1mnE3Jb86QAuTxiq+aqMkU1NTgY2SuFHtI8mLQUFVVRU6depUaw+DXyoqKpCZmYnk5GTcuHEDUVFR2LlzJ1avXg1XV1fY29vD0NAQ7dq1wx9//AFRUVG0adMGKioqMDAwgLq6OmRkZODq6or169djz549iI6Oxq1bt/DixQvk5ORwZnz8kp+fj27duvHkNC4MDhw4gJEjR9Y6/uXLF/Tv3x9WVlb4/PkzgMa79QgTIoKKigqUlJSEZqRRXFyMq1evYvny5TAzM0Pr1q3RokULuLi44OrVq7X2/V68eAEFBQWeZt7p6emQlpauYcFavU/ct29fqKioICgoqEG/VyJCYmIiunbtChcXF64WsRUVFbC0tMSyZctqnduxYwccHBwarG9z8q9QfLm5uejSpQvCw8O5nn/37h2MjY0xfPhw5Obm8iRv7dq1UFBQwNChQxEbGyt0g5Wqqio8evQIgYGBGDlyJKSkpKCurg5nZ2eEh4dzPuxfiYqKwoABA4Raj4b43QFamDRG8VXvr3h7ewt9MHLy5ElYWlryfP3y5ctrzIgYhsG3b9/w5s0b3L17F+fOncPBgwexefNmLF68GE5OThgxYgT69OkDVVVVtG/fHmJiYpCTk4OmpiYsLS1ha2uLOXPmYNmyZZg2bRq6deuGDh06wNvbG6mpqTU6l0uXLkFRURHp6ekN1lXQNn/27JlAxi6C0LdvX8TExNQ4dvnyZSgqKsLX17fGSk1ZWRlkZGSE6iMrKEQEZ2dnyMvLQ19fH69fv+ZbRlFREa5cuQJvb2+YmJhAXFwc5ubmWLFiBa5du4bi4mJs3769TmMXLy8vLF68mOfyrK2tER4ejpKSEuzZswfq6uowMDBAREQET8qzeo9PVla2XneNBQsW1GnkY2hoWMNI6J/AP17xVVZWYtCgQXU6E0dFRUFWVhZBQUENKq+3b99yzMCnT58usO8XN6qqqvDw4UP4+/tjxIgRaN++PXr06IHZs2fj+PHjtUyjuTF06NBmMzEHajpANwWCdMJVVVVYuXIlFBUVceXKlSaoFWotn5WVlSEjIwNPnjzBtWvXcPz4cWzfvh0rV67E3LlzYWNjgxYtWkBTU5Njbt+2bVt07doVxsbGGDp0KBwdHeHh4QE/Pz/s378fp0+fxp07d5Camoq8vLxae4lFRUUIDg5Gly5dYGpqiujoaK6dxps3byAnJ4dbt27x9GyNGWycOHECKioqtcJSCZM3b95AVlaWYyVYUVGBpUuXQklJqU6Dnfnz5zdZ6D5+ICKO0caOHTvAYrEatCwvLCzEpUuXsHTpUvTp0wfi4uLo27cvfHx8EBsby9UVh2EYTJs2rZaxS1VVFTp06ICUlBSe67xnzx5069YNcnJyGD58OOLi4nge5Ofm5mLEiBEgonoHHocPH4aqqipXV4dnz55BSUmpUVavTcE/XvEtXryYqzFLSUkJ5syZg65du9aIHsCNu3fvwtbWFiwWC8uWLeNJCTVEZWUlHjx4gC1btnB8jDQ0NODi4oLIyEi+jWo+f/7coO+eMKk2Zpk2bVqTuWfw2wlX+1AJYpRUDZvNRl5eHlJTU5GQkIDTp09j//792LhxIzw8PGBnZwcxMTEYGBigS5cuaNu2LVq0aAFFRUVoa2ujf//+GD9+PObOnYtVq1Zh+/btOH78OLS0tBAUFITPnz83yrjmy5cvWLZsGVgsFmxtbfHXX3/VeW1RURE0NTWxc+dOnuU3dnnZ29sbVlZWTbbk7+PjAzc3NwA/LadNTExgY2NTr7Ll1RCpKUlMTAQR1RgsV/uSzpgxg6PAvn//josXL2LJkiUwNjaGuLg4LC0tsWrVKty4cYPngBClpaUwMjKCn58f59ilS5dgbGzM0/2pqamYM2cOJCUl0apVq3qtl7lx+/ZtdOrUCR4eHvW+U4mJiWCxWHVOIjw9PQX2cWxK/tGK7/jx4+jSpUut5cuXL19CR0cH48ePr9NPpaqqCtHR0TAzM0OXLl0QHBxcy+yWHyorK3H//n1s2rQJQ4cORbt27aCpqYm5c+ciKioKX79+FVg28NO4ZMaMGY2SwQ9+fn4wMjISqjHL7/DTCV+4cIGrUVJJSQk+ffqER48e4cqVKzh69Ci2bt2KFStWYPbs2bC1tYWlpSV69uwJOTk5iImJoX379lBVVYWJiQlGjBgBJycnLFmyBJs3b+aErrp79y7evn2Lb9++8aT49+/fj9GjRwvUDgDw/PlzODk5QUpKCvPmzWvQHYNhGIwbNw7Tp0/na2DSWMVXVVUFGxsbjnISJmw2G8rKynjy5AliYmIgJyeHzZv7/0BvAAAgAElEQVQ3N6jQql1PBAmULgyqjTa4tW16ejqsrKwgIyMDLS0tiIuLw8rKCr6+voiLi2vU95Weng5FRUXOMuH48eOxa9euOq9nGAYJCQkYPXo0ZGVl4ePjg69fv2L27NlYv349T2VWVVVh3bp1kJeXx/nz5wHU/U5Vt0td/pUVFRVQUFDAq1eveCq7OfnHKr5qY5bfjQpCQ0PBYrGwZ88erh3Cjx8/sGvXLqiqqsLY2BgnTpwQaJrNLUq5lpYW5s+fj5MnTwp1OYhhGGhoaCAhIUFoMuujej+Flz2jxvD7B1NVVYXs7Gy8ePECt27dwqlTp7Bz506Ym5ujbdu2sLa2xuDBg2FgYAAVFRW0adMGLVu2hJKSEvT09DBw4EBMmDABrq6uWL16NXbt2oWoqCjcuHEDz549Q2ZmZr0zlWofSUGc8+uzRKyvvNjYWNjY2EBBQQFr167laQ8a+GmRZ2xszHfHKQxL2vz8fKiqqgrd2OX69evQ1dWFq6srOnfuzJOpfTUBAQFwdHQUan14oaKiAhYWFli+fDmICAUFBTh37hw8PDxgaGgICQkJ9OvXD6NHj4akpCR27dol1BWUW7duQU5ODo8ePUK7du24WkZWVVXhxIkTnBBuO3furLFydPfuXaipqTVYr8zMTAwcOBAWFhY1+oa6ItZUt0tdnDt3DiYmJrw8ZrPzj1R81cYsv0bmKCoqwtSpU+tMQfL161f4+PhAVlYWo0aNwu3bt/l6AblFKdfR0eGk42hKJ+b79+9DVVW1ySPCAP/PmIXXPaO6YBgGRUVFSEtLQ2JiIi5evIiwsDAEBATA29sbs2bNAhHB3NwcPXr0gIyMDERFRSEjI4Pu3bvDzMwMgwYNgqysLFRVVbF69WocPnwYFy9exIMHD/D+/XsUFRUJtU2qLdMEXTKbMmUKgoKCGryuoqICR48e5aRq2b9/P18K7OLFi+jQoUOd5uX1ISzfyWpjl4cPHwpFHvAzLmrHjh0xduxYvk3bGwov11Q4OzvDwMAACxcuBBFBQkICAwYMwNq1a3H79u0ay94pKSnQ0tKCg4ODUN2hduzYgQ4dOmDMmDE1jlcbwnTt2rXefWKGYdCjRw/cuXOnzjKuXr0KRUVFrFy5sta2Erd3ytXVFUOHDq13UmFra4s9e/Y09Hh/C82q+Bj2N7CLD4KdPwvs3PFg504B+9tSMOUPOR1cZWUlBg4cCE9PT859T548Qffu3bmmIHn58iVmzZqF9u3bY86cOUhNTeWpLtyilOvq6sLNzQ0xMTE8j8yFwZw5c7Bu3bomL6eoqKhOB+jKykp8/foVz549w82bN3HixAns2rULa9aswYIFCzBhwgQMGjQIenp6nFxjbdq0gbKyMvT19TF48GBMmjQJCxcuxLp167B7924QEeLj4/HixQtkZ2fX+KBOnDgBWVlZBAYGNovCB37Gt1y9erXA98fGxkJXV7fO8/WlauGVauMPXl1yfkeYQQNOnjwJZWVlvma5dbFv3z6IiIjAz89P4L93XQHFhUleXh5Onz6NhQsXQllZGSIiIrCyssL69evrDN31KyUlJXB2doaqqqrQBg0Mw4DFYsHc3BwMw9TYJx47dmy9Cq0aPz8/zJo1q9bxyspKLFu2DB06dEBsbCzXe39/pw4dOgQ1NbV6437m5uZCUlJSoJBpzUGzKD6m8h3YBe5gZ2qBnakDdqbaLz/qYH/VATu7H9jFx7F4sQcGDhyIyspKMAyDXbt21UpBwjAM4uLiMGLECMjJycHX17fBpUduUcp79epVbzqO5qC0tBTS0tJC9aGrzjX29u1b3Lt3D+fPn8fBgweho6MDbW1tODk5YeTIkTAxMYGamhqkpKQgJiYGWVlZ9OzZExYWFhg7dixmz56N5cuXY+vWrTh69CguX76MR48e4ePHjzwFhubWCZeWlsLFxQVdu3bFgwcPhPbMDVFtFt+Y0FdsNhsqKiq1AqPXl6qFHwoLC6GpqVnvPk5DCDtM3LJly2BpaSmwscuPHz8wY8YMyMvLN5hjryGio6NhYWHRKBm/k5ubi+joaLi5uUFXV5ez5F4dS/TXrRZ+2jYyMhKysrLYtm1bowd2KSkpUFRUhJaWFgwMDHjeJ/6Vz58/Q0pKqsZ3+/HjR5iZmcHa2rrewc2vz/3gwQOwWKwGLUuDg4MxceJEnuvX3DS54mPKEsD+qgt2ZvffFF7tn/KMnrgR0w25ORkoKCiAra0t9PT0OLO4yspKREREwNDQEOrq6tizZ0+dVlJlZWW4desW1qxZg/79+3PScbi7u+Ps2bP/mCgCERERGDRoUL3XlJeX4/Pnz3j69CmuX7+OiIgI7NixA6tWrcK8efNgb2+P/v37Q0dHB4qKimjRogUkJCTQpUsXGBkZwcbGBr169YKCggLWrFmDffv2ISYmBgkJCXj16hVXc3th8HtHwYtRUlPBS3JTXli5ciUWLFgAAA2mauEHhmFga2uLGTNmNKqjFLbiqzZ2qX5mfnj+/Dl69uyJyZMno0+fPo1KBwZwTxrMLzk5OTh16hRcXV2ho6ODtm3bYsiQIfDz88Pdu3dRUVGBr1+/olOnToiOjq5xL79t++7dOxgaGmLUqFECD6yrra+7du0KFouFtm3bIjIyUiBZNjY2OHr0KADgzJkzkJOTg5+fX4PffvVz19Uu3NDX1xcoRnJz0aSKjyl/AHamdoMK79efys89UfB+NLp164J58+ahtLQUhYWF2Lp1K1RUVNC3b1+cOXOm1h+rOkr56tWrOVHKDQ0NBUrH0ZSw2Wzk5+fj9evXuHPnDvT19TFr1iz4+fnB09MTjo6OGDZsGHr37o2uXbuiXbt2EBMTg4KCArS0tNCvXz/Y2dnBxcUFK1euRHBwMI4fP45r164hKSkJGRkZtfaT+HGAFia/dhSHDx8Gi8XC7t27m21p81eGDh0qFGONN2/eoF27dujXr1+9qVr4Zf369ejdu3ej45A2RUaMgoICqKqq8pwfkmEY7Nu3DywWC4cOHUJqairk5OSE4iLh5uYGHx8fnq/Pzs7GyZMnMX/+fGhpaaFdu3awsbHBpk2bcP/+/Vr7WdVGGytWrKglS5C2LS8vx6JFi6CsrMzTkuSv9Th27Bj09PQgKiqKNWvWoLS0lGPsIkiQ9sjISPTv3x9ubm5QUVHhuT5EVG+7/M7Tp0/RqVOnf5zv3q+IAAA1AWCKCTkWRCjm+96SUtDHnEEk1XEFbd++nfbt20f9+/cnDw8P6t27NxERlZWV0b179yguLo7i4uLo4cOH1LNnT7KysiJLS0syNzcnSUlJYT9WLcrKyignJ4dyc3MpNzeX6++/HsvLyyNxcXFisVgkKSlJz549IwcHB1JQUCAWi0WysrLEYrFq/C4pKUkiIiIC1e/t27dkZmZGJ0+epL59+wr56etHRESEioqKaN68efTgwQOKiooibW3tZq0DEVFmZib17NmTMjIySFxcXCAZ5eXldPz4cQoICKC0tDSaMWMGbdmyhVq2bNno+l28eJFmzZpFDx48ICUlpUbJEhERoab4pFNSUsjKyoouXbpEhoaGdV5XWFhIs2fPpufPn1NUVBRpaGjQ8uXLqbS0lAIDAxtdjydPntCoUaMoLS2N/vjjj1rns7OzKT4+nuLi4ig+Pp4yMjLI3NycLC0tycrKinr16kViYmJ1ynd1daW0tDQ6e/ZsLfmNadtz587RzJkzaeHCheTl5cW17kQ/22///v20detW6tatG1laWtKVK1fo7t27nGt27dpFu3btonv37pGEhATPdUhJSSFdXV0aMGAAHT9+nKSlpXm6T0REhObPn19nu/yOu7s7tWnThtatW8dz3Zqbut+ARoLSaCJiC3Rvmz9FSFn2JnXTi6AJE6ZQYmIiKSgo0N27d2nVqlUUFxdHjx49Ik1NTbKysiIvLy8yMzOjdu3aNarODMNQfn5+vYrr998rKyu5KisWi0Xa2tq1jsnIyHA6Sz8/PzI0NKQ9e/Y0qt51UVxcTKNHj6ZVq1Y1u9KrxtDQkExMTOjhw4cCK53GcuTIERo7dqxA5RcUFNDu3btp+/btpK2tTYGBgZSenk6nT58WitJ78+YNTZs2jWJiYhqt9JoSTU1N2rNnD9na2lJiYiLJycnVuubRo0fk4OBAAwYMoAcPHtCff/5JbDabwsLC6MKFC0Kph56eHklJSVFcXBz179+fsrKyOIouLi6OMjMzydzcnKysrGj69Omkp6dHoqKiPMkODQ2lK1eu0IMHDxrs3PllxIgR9PDhQ5o4cSLFxcVRWFgYycvLc86np6dTcHAwHTx4kKytrSk6OpoMDQ3Jzs6Opk2bVkOWi4sLPXr0iJycnCgqKoqnQXFERAS5urqSiYkJmZub86z0quG1XSorK+nYsWOUkJDAl/zmpklmfAAIOVZETKbAMsorxCg5zZ7OX6+iuLg4SkpKIm1tbc6MzszMjNq2bVuvjB8/fjSouH79t6CggCQlJWspsboUm6ysLElISAg0GwNAGhoadOjQITIxMRG0meqVP378eGrXrh3t379f4BmjoGXv2bOHXFxcKCwsjKZMmdJsZXOri6amJu3du5fMzc15vi8tLY22bt1KR44coZEjR5K7uzvp6OgQ0c8BRceOHSk1NbVG58UvRUVF1KdPH3J1daU5c+YILOdXmmrGV82KFSvo9u3bdP36dWrRogUR/Wzj7du307p162jnzp1kZ2fHuf7atWu0dOlSevTokVDKz8zMJC8vL7p37x6JiorS169fycLCgjOj09XV5VnR/UpiYiINHTqU4uPjqWfPnlyvEUbbVlVV0erVq+ngwYMUFhZGMjIyFBAQQBcuXCBHR0dyc3Ojzp07ExFRXl4edevWjT58+EDt27evIaesrIwsLS1p9OjR5O3tXWd5JSUl5ObmRnFxcRQZGUlsNpsmTJhAb9684alPSExMJGNjY0pJSamzXX7l7NmztHnz5n+84muaGV/lUyJ8b5SIVi2rqDUiic0eTT4+PmRsbEwVFRUcJXX16tUGZ2QASFZWlqvi6tWrVy3FJi0tXe8yiDC5d+8eAaA+ffo0iXw/Pz/69OkTxcfHN6vS+/btG82aNYvevHlDRPS3Kj2inx9uRUUFmZmZ8XT9gwcPyN/fn2JjY2nWrFn07NmzWjMxCQkJGj16NB07dozc3d0FqhcAmjZtGpmamtLs2bMFkvF3sHr1aho5ciR5eHhQcHAw5efn0/Tp0+nz589079496tq1a43rQ0NDa81Y+OHLly81ZnQ5OTnUu3dvSk9Pp6tXr5KpqalAiu5XsrKyyNbWlvbt28dT594YxMTEaM2aNdSmTRsaNmwYtWzZkry9vWn79u21lFtERAQNHTq01nEiotatW1N0dDQZGxuTnp4e2djY1LrmxYsXNH78eNLV1aXHjx9T27ZtCQC1atWK7ty50+BAsLpdiIjndgkNDSUnJyeerv1baYqNQ6bkLNhf9fgyauH2k/1CHerq6pCSkoKoqChYLBY0NDTQt29fjBkzBs7Ozli2bBmCgoJw5MgRXLp0CQ8fPsSHDx+aLealoDg7O2PDhg1NIrsxDtCN4f79++jSpQvmzp2L0tLSJjG04BcXFxesXbu23mt+TdWirKzMU6qWmzdvQktLS2BDnXXr1qFPnz5CSar7K83R5gUFBVBTU8OyZcugrKwMd3d3rv5tBQUFfGewT09Px/9p7zzDorjaMPyuNQkqILt0VERBEVQQe0OJBbGBDRuiYu81xt4r2BVrUIliwWDvXWJvqGjEhlhQVBRU6s483w+yfJQtM7uzqHHu6/KHu3POnHmZPc/MOW/5888/ERAQgIoVK6J06dLw9vbG0qVLcevWrWyntvbt22PDhg06X0t6enp20mhN6GrbtLQ0hISEwMnJCVWrVsXy5cvh4eGBhg0bKnU8q1GjhsZE7efPn4dMJsvl7MKyLDZu3AipVIqNGzfmu0cXLlyoMT1iTrtwve6EhAQYGhrqvZapEOhH+L5s5+3NqTy8oRru37+Pd+/efdMeQnxJSUmBsbGxXoRJ1wBobWAYBoGBgZDJZLmKUH5t4VPESKqq5adtqRYg65ptbW21ClI+cOAALC0tlZam0pWCsDnDMBgxYgQkEgmCgoJUHrd27Vp06NBBbV9xcXEIDQ1F3759YWdnBxMTE/j4+GD58uWIiopS6Wq/Z88eNGjQQKfrALKSGrRu3ZpTOI+2tk1MTMS8efNgaWmJ5s2b49ixY9lixDAM5s6dCzMzM+zfvz+7ze3btzlXNVi9ejWqVKmC5ORkJCcno1u3bqhSpYrKxNGvXr3SmBA/p124XvfSpUvRo0cPTsd+bfT0xndAkDc+5k19fQzvq7Nt2za0aNFC8H6FCIDmy9u3b7PDL/IGh39t4du+fTt+/fXXfJ8nJCRg+vTpWpVqycn06dMxdOhQXm1iYmIgk8l4ubbzQd82f/36NZo3b46GDRti3bp1sLGxUZmgvW7durkmcyAraHrz5s3o3bt3dmxax44dsWLFCty5c4dzPGlGRgZMTU21qomn4I8//oC9vT3nmFK+tn3y5AmGDx8OY2Nj+Pn5ISoqSuWxkZGRud6ex4wZw7mqAcuy6Nu3Lzw8PGBnZ4d+/fppTDDh5eWlMrwnr124Xnf16tVVZn/51tCP8GXcF+SNj3nvr4/hfXWaNWuWKw+pEAgVAM2Hs2fPwtraGuPHj1cao/W1ha9ly5bZAbvA/0u1GBkZoV+/frh3755O/T958gQmJiaclyuTk5Ph6OiINWvW6HRedejT5idOnIClpSUmT56c/WY8efJkNGrUKN/f/59//oG5uTkePnyITZs2wd/fH+XKlYNMJkOnTp2watUq3L17V6d7ddSoUWqTJKvj8uXLkMlkvO4Brra9fPkyOnfuDBMTE/z222+cV3bev3+Ptm3bws3NDSYmJpzTL7Isi6CgIBQpUgRdunTh1GbXrl1KEzooswuX67558ybKlCnzVUtH8UFvvxImwVM30XtdHWxawS3XFRRxcXEoXbq04OWAhAqA5oJcLsfMmTNhbm6OQ4cOqTzuawrfixcvYGxsjM+fP+P8+fNo165drlItQuHu7q62MrUChmHg7e2tNF+ikOjD5pmZmZg0aRIsLS1x4sSJXN8xDAMvLy8MHToULMviyZMn+OOPP7KDxc3MzNClSxesXr0a9+7dE/ShTNtA6fj4eFhbW2PPnj282qmzrTb7xMpgWRYBAQEoUqQIpwwtiYmJaN++PVxdXXH+/HlYWlri4MGDGtulpaVBKpXmWqVRZRcu9xTfxAJfG73NTGxKxL+pyrRd5qwHlv0+nh74MGfOHAwcOFDQPg8ePFhgziyvXr1C06ZN4e7urnGP6msK35w5c+Dh4ZGrVAuX/KJ82bx5M7y8vDQeN2vWLNStW1fvDyZC2/z58+do0KABmjVrlu+BgWVZPHr0CCtWrEDJkiVRunRpmJubo3PnzjA0NMTevXv1vvrg4uKC48ePcz4+PT0dDRo0wNSpU3mfS5ltFfvEDg4OqFGjBsLCwjjvE6vCx8cHEydOhJ2dHQYMGKAyLeOFCxdQtmxZjBgxIvu+ioyMhEwm47QEPHTo0Oyk7ersoumeEiKVXEGjP+Fj08C8qZuVhJq38FUF83mbvob21WBZFhUrVsSlS5cE61OxZ1QQtfwUdfymT5/O6Sn7awjfp0+fsGzZMhQtWhROTk4qS7UIxefPn2FkZIRXr16pPObAgQOwsrLSizNLXoS0+b59+2BmZoZ58+aBYRiwLIuHDx9i/fr16NGjB6ytrWFpaYlu3bph2rRpMDY2xuXLl3HkyBG4ubkJNg518E2GPHjwYLRp00arJbmctn379i1mzJgBMzMznfaJ8/L27dvsqgZJSUnw9fWFs7NzrqVHhmEwf/58mJqaKs1/GhwcDEdHR41vnNeuXYOtrS0YhlFrF033VEREhODJw/WNfnN1Zj4C89qFp/hVBfPx96+Sz1HfREZGolKlSoJdm2LPKDg4WJD+VJGRkYEJEybAysqKVxXsghS+nKVa3N3dYWNjU2D3UO/evbFo0SKl3z148ECvzix5EcLmOfNLhoWFYd26dejWrRusrKxgZWWF7t27Y/369YiJicll44iICNjY2KBdu3ZKS1/pg5xCoYmNGzfCwcFB6wTpRJRrnzggIEDnfeK8LFu2DN27d8/+f968p69fv0aLFi1Qv359ld7KiuVSHx8ftb8BlmXh5OSE8ePHq7WLpnuqXbt2ei8XJTT6r86Q8QDM61rIKknEQfSSZv4nlzgBICAgAAsWLBCkL5Zl4ePjg4CAAL1O8LGxsahbty48PT15V50vCOG7e/cuevfuDSMjo+xSLf3798ecOXP0fm4FZ8+ehaOjY76/Q1JSEipXrlygxTh1sTnLsjh27BjKli0LKysrmJmZwdraGj179sSGDRvw6NEjjffa2LFjUbhwYcTHx2s9Dr74+Phg3bp1ao+5dOkSZDIZ7t+/z7t/lmURGRkJItLLPnFOVC3d3rlzB2XLlsXPP/+MMWPGaFxOTUtLQ506dTTW+Rw2bBiKFy+u1i7q7qk3b97AyMiowAsE60rB1ONjEsF8Wg3mdW0lYQ5Vsv697wM27WJBDOer8OXLFxgbGwu23KWvAOicREREwNTUFAsXLtR5aUhIWJbFyZMn4enpCTMzM8yaNSu7cLAiRrIgK1GwLJuvviDDMGjfvj369+9fYOMA+NmcZVncv38fwcHB6NKlCwwNDVGoUCHUrFkTGzduxOPHj3k/VK1atQoWFhYYMmQI36Frzb59+1CvXj2V3yucNviWRZLL5di1a1f2PjER6TUxxq1bt5Q662RmZmLKlCkwMzNDixYtYG9vj5s3b2rs7+XLl7C0tMSBAweUfh8fHw8LCwsYGBjg06dPKvtRd08tXrwYvXr10jiWb42CrcDOysGmngKTvBjMx8lgkmaD/bwRrLzgng6/FqGhofD09BSkL30GQANZT4vDhg1DuXLlcPGi9g8jQgufolSLi4sLKlWqhPXr1+fzjt22bRuaN28u6Hm5MHPmTAwePDjX/wvCmSUv6mzOsiyio6OxatUqdO7cGWZmZihXrhy6d+8Od3d3lC1bVueq4bVr18bOnTthb29fYMtfGRkZMDMzwz///JPvu/T0dNSvXx/Tpk3j3N/nz5+xYsUKlC9fHvXq1cveJ9b3CsaoUaPylf158eIFGjVqBA8Pj+y36K1bt0IqlWLlypUaH0z+/vtvpc4uOe3Spk0bbNq0SWUfqq6bZVk4Ozvz2v74Vvj6OaV+EDw8PLQuIJkTfQdAx8TEwNXVFT4+PjoX6xVqokhKSkJgYCBsbGzg7u6OAwcOqHwDbd68ObZtK3jHqNjYWJiYmCA1NRX79++HlZWVWocXfZHT5izL4u7du1i5ciU6duwIU1NT2Nraonfv3ti0aROePn2Ke/fuwdnZGb6+vjqnmrp37x4sLCyQmZmJe/fuQSaT4fLly7peEidUBXwPGjQIbdu25bRikXOf2MfHJ99vTJ/CpwjIz5l67MCBAzAzM8Ps2bPzvQXGxMTAxcUFPj4+GutBrlmzJp+zS0677N69G+7u7irbq7ru69evo1y5ct9N7F5OROErAHJOirqg7wBoxZPkqlWrBNk31HWiiIuLw9ixY1G6dGn4+vri6tWrGo83NjZW6f6tbzw8PLBkyRLIZDJcuHChwM+vSC+1fPlydOjQAVKpFHZ2dujTpw+2bNmSyxmCZVmEhIRAKpVi/fr1gvy9x48fj/Hjx2f/f8+ePbC2ti6Q/T5lKb42bNgABwcHjYIeHR2NPn36wMjICIMHD1ZZ5FWfwpczBZsic4uNjY3a1IN8Vmb69esHb29vMAyTzy6KcITHjx8rbavquocNG8brTfpbQhS+AmDWrFm5lsG0QZ8B0F++fEHfvn057x1wRduJ4ubNm+jRoweMjY0xcuTIfKnQVDFnzhwMGDBAq3MKwbp162BgYKDR0UIoGIZBVFQUli1bBm9vb5iYmICIEBAQgNDQUMTFxSltl5ycjB49esDR0RF37twRZCyZmZmwsLBAdHR0rs+nTp2KBg0aKE1iLTQ1atTAkSNHAAAXL15U68zCsixOnTqFVq1aZe8Ta0qmrU/hUyTdfvLkCWrVqoXWrVtn71tr4q+//oJMJlO7F5+Wloa6deuif//+Su0yfPhwlSKm7LoVAfBPnjzhNMZvDVH49AzLsrCzs8vl+KAN+gqAvnv3LhwdHdGjRw/BPbP4OlocPnwYHh4esLS0xIIFCzQu4eRtX7FiRZ32JHVBkcGkWLFiett7ZRgGN2/exJIlS9C+fXuULl0a9vb26NevH7Zu3YoXL15otPnNmzdhb2+Pvn37ChrQf+jQIdSqVUvpmNu0aaPzgx8XVq5cCV9fX7XOLIp9YldXV5X7xKrQl/C9efMGhoaG2LJlC2QyGZYsWcL7DTw2NhZ16tRR63198+ZNFC5cWGmGlRs3bqhctlR23ZqWR791ROHTM+fOnUOVKlV0WkrSRwB03vggfYREcJko8pZq2bx5s1ZvB3///TccHBy+WvznjBkzUK9ePfTu3Rvz588XpE+5XI4bN25g8eLFaNu2LYyNjeHg4IABAwZg27ZtSu8HdY4IK1euhFQqxdatWwUZX046deqkMp7048ePcHBwwMaNGwU/b07evXuHUqVKoXbt2pg+fXqu75KSkhAUFJS9T7x//37ee1P6Er6FCxfC3t4e5cuX17icr46MjAz89ttvSuNtFc4sffr0gUwmy5cHlGVZVK1aFadOncrXr7Lrbt26tVqHmG8dUfj0TJ8+fVQGN3NBHwHQiowQTk5Oggfg5kTdRJGYmIi5c+fCwsIiX6kWbQgICBBMcPiyb9++bGcWXZIUyOVyXLt2DYGBgWjTpg2MjIxQuXJlDBw4ENu3b+fkLKPM5h8+fICPjyxXJgkAACAASURBVA9cXFx0qmagivfv36NUqVJqnaHu378PmUwmaNYiZZQvXx7VqlXLFjW++8Tq0Ifw3b9/Hz/99BMaN26sdWB9Xg4fPgxzc/NcGZYGDhyIdu3agWEYrF27FpUrV86397lkyRL4+fnl6y/vdcfHx2ssa/StIwqfHuGSzkod+giAvnbtGipUqKA2B6BQKJso+JRq4cqXL19gZGRU4IV3gawqBDKZLHuJlWVZVKhQgdMEn5mZiatXr2LRokXw8vKCoaEhHB0dMXjwYOzYsUOrIOm8Nr948SLKlSuHYcOG6S20YtWqVZyqAuzdu1evzi7r16+HtbU13NzctN4nVofQwrd582YYGRnBxMRE8LR6L1++RJMmTeDu7o5FixahUqVKuYSuf//+aN++fa63XsWSa94tj7zXHRgYiN69ews63oJGFD49wjWBsTKEDoBmWRZLly6FTCYTJKyCCzl/MNqWauHCn3/+iZYtWwrWH1eSkpKy94lyMnv2bKWJyDMzM3H58mUsXLgQrVq1gqGhIZycnDBkyBDs2rULb9680XlMCpszDIOFCxfC1NQUEREROverDjc3Nxw+fJjTsdOmTUP9+vUFd3ZROLOsWbMGxYoVg6mpKe99Yk0IJXyfPn2Cn58fKlWqhG7dummVMJsLcrkc/fr1Q6FChfLdowpnl5kzZ+b6XFn6sbwhMk5OTjh79qxexlxQiMKnR5o0aZKrIjkfhAyAzlnnS5XLsj4gIkFKtWji119/xfbt2wXvVx0Mw6Bt27ZKBU5ReiopKQmXLl3C/Pnz4enpiVKlSsHZ2RnDhg1DeHg47xRwXCAiJCQkwNPTE3Xr1kVsbKzg58jJnTt3YGlpyfmNRWG3QYMGCTaGp0+fwtjYGGXKlIGzszNatWqFsWPHCta/AiGELyoqCg4ODujduzcSExMhlUr1VtXg1atXsLKywty5c2FtbY1x48blqpuo+D5nseCIiAg0bNgwVz85r/vq1asoX778d59LWRQ+PfH06VNIpVKthEvIAGhFZedRo0YViEs58P9SLUQkWKkWVTx79kwv9Q01MX369HxvLhkZGbhw4QLmzZsHExMT/Pzzz6hWrRqGDx+Ov/76S6O7vBAQEaysrDBhwgSlxYGFZuzYsZgwYQKvNklJSXBwcMCGDRt0OndiYiJmzZqFokWLonz58jh69Gh2dho+YswVXfOgrl69GlKpFKGhoQCywhD0VdUgPT0d9erVyy479PbtW3h5eaFOnTq5ln0vXLgAmUyWnfVGWSB9zuseMmRIvrfE7xFR+PTEjBkzMHToUN7tFHtGugZAMwyDuXPnwtTUFPv27dOpL64kJCRg+vTpMDU1RevWrUFEen8ynDVrlqBvD1xQ7FU9e/YMf//9N+bMmYPmzZujZMmSqF69OkaOHIlRo0YprXCtL+RyOaZPnw4iyo5l0zeZmZkwNzfXKvGzwtlFm/CTp0+fYsSIETA2Noa9vT2aNGmSz0OzVq1aaoska4O2wvfhwwd06NAB1atXz+VN2bZtW4SEhAg0utwMGDAg3x4ewzAICgqCTCbD7t27sz9ft25drj3AsWOGIfzPHmDedQTzpiFe3bYFk+CBjPdj0Kieqd5XEQoCUfj0AMMwsLW15Z33ULFnpGsA9OvXr9GsWTM0aNBAZRCzkKgq1aLv3IaKGMmCSouVnp6OP//8EwYGBqhZsyZKliwJFxcXjBo1Cnv37s3l1ahISl4QDjcvX76Eu7s7mjZtWqCloPbv3486depo3Z6vs8uVK1ey94nHjx+PBQsW5HPaULB69Wp07txZ67EpQxvbXr58Gba2thgyZEiuVYnXr1/D0NBQbXJobckrZFzGNGDAAHTq2AbMx9nIeOmMpEcV8lXPyXxpjy+x9mDeeoFNOyf4uAsSUfj0wJkzZ+Ds7MzrbYdhGLRr107nzCPHjx+HhYUFJk+erLflRSBLdM6fP4927dqpLNWi70n43LlzqFy5st7eKtPS0nDu3DnMnDkTHh4eMDAwQPHixdGsWTPs27dPYy7T/v37Y+7cuXoZmwKF6/rMmTMLJJFyTjp06KCzx7GyJeOcMAyDffv2oVGjRrn2ifMu0eUlMTFRY4gFX/jYlmEYBAYG5nu7UhAUFKSXqgaa7KLgw4cP6NixY/ZbaHrqG8RcrIS055U41k11BvNZjOMTyYG/vz+CgoJ4tVEEQGu7D5eZmYlJkybB0tJSaT0vochbqmXVqlUq43n0PQn36dMHCxcuFKy/1NRUnDlzBjNmzECTJk1QokQJuLm5YezYsdi3bx9atmzJa1n1woULsLe314swZ2RkYNy4cbC2ts7lYVdQwqcIFtfVa1LxwJfXSUixT+zg4JBvn/jly5f5nDKU0blzZ6xevVqn8eWEq23fvn2LVq1aoXbt2krDKBSekUJXNeBql5zjCA4OhrWVFO9i6kP+qjKPguH/it8X7Zz3vjai8AnMp0+fYGRkxCsGK2cAtDY8f/4cDRo0QLNmzfRWIFNVqRZ16HMS1jVGEsgSutOnT2PatGlwd3eHgYEBatWqhXHjxuHgwYO5AoqnTZvGO+cky7Kwt7cXPGH106dPUadOHXh5eeVzmCko4VuxYgW6du0qSF85w0Levn2LGTNmwMzMDK1bt8aZM2dyPTiocsNXxuHDh1GzZk1Bxghws+2ZM2dgbW2N8ePHq3QuunbtGmxtbQWtasDHLnl5/WgUvsTyEbyc/5zAygu+ComuiMInMCEhIWjbti3n4/MGQPNl3759MDU1xdy5c/VSHkRTqRZ16HMS3rJlC1q1asWrTUpKCk6ePImpU6eiUaNGMDAwQO3atfHbb7/h0KFDKvdEdKkyMHfuXEETi+/evRsymQxBQUGc8yrqA1dXVxw7dkyw/g4fPoyffvoJJUqUyLVPnBdlgdeqkMvlsLS0xN27dwUZozrbyuVyzJgxA+bm5hqdaoYOHZovpZqu8LFLTlg2DczralqK3r+FxJMDBb2WgkAUPoFp3Lgx/vrrL07HqgqA5kJ6ejpGjRqFMmXKIDIyknd7Tdy9e5dTqRZ16HMSbtKkCXbt2qX2mC9fvuDEiROYPHkyGjZsCAMDA9StWxcTJkzAkSNHOMUU6ppq68WLFzA2NtY5IXRqaiqGDBkCW1tbtc48BSF8UVFRsLa21jlcgGVZREZGon379pBKpejcuTMsLCxUvsUrUm3xiQX97bffMG7cOJ3GqUCVbV+9epWdJUVTPt20tDSYmJgIWtVAG7soYFMiwLyuroPwVQTz2hUsWzChUkIhCp+APH78GFKplNNymLoAaE08evQIbm5uaNu2Ld6/f6/NUJXCsixOnjwJT09PzqVa1KGvSfjp06cwMTHJFyP5+fNnHDt2DJMmTUL9+vVhYGCAevXqYeLEiTh69ChvD7qPHz/C3t5e5+TKLVq00Ckx9IMHD1C9enV07NhR455aQQjf6NGjMXHiRK3by+VyhIeHo06dOvn2iadPn650r1tRSTxvcmVN3L9/H+bm5oI4eimz7ZEjR/LlxVRHeHi4oFUNtLWLAuZdR91EL74imNfVwaadEeyaCgJR+ARk6tSpGD58OKdjNXmzqWLHjh2QyWRYunSpYE4TilItLi4uvEu1qENfk/CMGTMwZMgQfPr0CUePHsXvv/+OevXqwcDAAA0aNMCkSZNw/PhxnZLoMgyD1q1bC1JOJywsDM2aNdOqbWhoKKRSKYKDgzn9vfUtfBkZGTAzM9Nqos25T1y3bl3s3r07n1go825++fIlLC0tceDAAa3GXKdOHa3b5iSnbdVVQlCHl5cXNm/erPNYAN3tAgDMm4a6C198VbBfdgpyTQWFKHwCwTAMypYty6mQqzbJelNSUjBgwADY2dnxjg9URVJSEgIDA3Uq1aIOoSfhT58+4dChQ9k5Lg0MDNCwYUNMmTIFJ06cELS+nJAFVFNTU1G6dOlcFdA18fnzZ/j7+6NSpUq8EnnrW/j27t2L+vXr82oTHx+PSZMmcd4nzhnPmpaWhjp16mDWrFlaj3nNmjXo2LGj1u0VKGwbGxuLunXrqq19p4xXr14JVtVACLsAAPOmtgDC5wT28xadr6kgEYVPIE6dOoVq1appPE6bPaN79+7B2dkZvr6+Kh0w+CBkqRZ16DoJJycn49ChQ/jtt99Qu3ZtGBgYoFq1ajA1NcXJkyf1Vl0iIiIC1tbWgnrIDhw4ELNnz+Z0bFRUFCpVqoRevXrxXp7Vt/B5e3tz3pOOjo7Wep9Y4fTVtm1beHt76/RA9uHDBxgaGnKuaK4KIkJERARMTU3VVjtXxaJFiwSratCvXz+d7QIATEJTAZY6q4FN2SPIdRUUovAJhJ+fH5YsWaL2GEVBTq45ClmWRUhICKRSKdavX6/z0qY+SrWog+8knJSUhIMHD2LcuHGoWbMmSpQoAXd3d0yfPh2nT59GSkoK/P39ERioPy+ye/fuQSqVCp4N5tKlS6hQoYLavyHLslizZg2kUim2bNHuCVqfwpeQkABDQ0O1deNYlsWpU6fQqlUrnfeJBw8ejCJFimi9f5WTrl27YsWKFVq3T01NBRGhXLlyWnlgsyyLKlWq4Nw53TOerFmzBo6OjoIkfGc+jAcT76Cj+DmDzeTv/PY1EYVPAJKTk2FkZKR22YNhGLRp04ZzAHRycjJ69OgBR0dH3LlzR+uxsSyLw4cP49dff4WlpaXgpVrUoWkS/vjxI/bv34+xY8fCzc0NJUqUQNOmTTFjxgycPXs23z7jp0+fYGhoqLd6bgpnlrxlWYSAZVlUqlRJpQfux48f0blzZ1StWlVj1g116FP4li5diu7duyv9TrFP7OrqKsg+cWRkJGQyGYYPHy5IlZKjR4+iRo0aWrWNiYmBi4sLiEjr386VK1cEqWqgsItQBYXZjGgw8c66Cd9bb0HGUpCIwicAGzduRPv27dUewycA+ubNm7C3t0ffvn213rdKS0tDSEgInJyc4OzsjM2bNxdYdQYFeSfhDx8+YN++fRg9ejRq1KiBEiVKwMPDA7NmzcK5c+c0Tm4hISFo3bq1XsaqcGYZMmSIXvoHgAULFqBv3775PldMioMHD9bZqUifwle9enWcOHEi12dJSUkICgoSdJ9Y4bRx8OBBwepSyuVyWFlZ4fbt27zabd26FVKpFKtWrdLJtoMHD9a5qkFOuwgJ89ZLt2XOVG61GL8lROETgIYNG2LPHtVr3FwDoFmWxcqVKyGVSrV2f09MTMS8efNgaWmJZs2aZZdq+RoQEfbs2YNRo0bBxcUFJUqUwK+//orZs2cjMjKStxA3btxYad5DIZgyZQoaNmyo11I+L1++zOXcwLIsFi9eDJlMpnXdxrzoS/hu3rwJGxubbFF7/vw5xo0bJ/g+scJpI+d+qMLZRde8oL///jvGjBnD6djPnz+jT58+sLe3z3ZY09a2qampMDEx0amqgTK7CAWbdk7Lt75KYBKagWX1X/5KaETh05GHDx/C1NRU5YTJ1Znlw4cP8PHxgYuLi1bLGE+ePMHw4cNhbGwMPz8/3Lp1i3cfuvL+/XtERERgxIgRqF69OogIzZs3x9y5c/H333/r9MbJJ0aSL3/99RdsbGz0lu4tJ56enggNDcW7d+/QunVr1KpVS9BgZn0J38iRIzF58mS97hOzLIuAgAD4+Pjke1hTOLvwyRyUlwcPHsDMzEzjw82dO3fg6OiInj175nIu0ta2O3bsgIeHh1ZtAfV2EQrmcwhP8asE5k0dsHL9/2b0gSh8OjJ58mSMGjVK6XdcA6AvXryIcuXKYdiwYbz3Mi5fvpyrVMvz5895tdeFt2/fYvfu3Rg+fDiqVq2KkiVLokWLFpg3bx4uXrwo6CQ8bdo0DBs2TLD+FERHR0MqleLKlSuC962MHTt2wNXVFTY2Nhg7dqzgQq4P4UtLS4OhoSHq1asHS0tLzJ8/X9CqBwqCg4PVOm3s378flpaWGrOjqKNevXoq61OyLIt169ZBKpVi06b8lQe0ta3iYUdbNNlFKJgvu8DEO4GJr6JhebN61pvedyp6gCh8OsEwDGxsbJTGWXEJgGYYBgsXLoSpqSkiIiJ4nXfv3r1o2LBhrlIt+iYhIQHh4eEYOnQonJ2dUapUKXh6emLBggW4dOlSvidpoSZhRYzkjRs3BOlPwYcPH1CxYkW9FQPNi1wux9SpUyGRSPR2TiGFT7FPXKZMGfzyyy963Sfm6rQxc+ZM1KlTR2tnl3Xr1sHHxyff50lJSfD19YWzs7PKPKHa2Dbv8jZfhHZm0QQrfwUmeRGY167/pjKrmiWGr6tlvRG+9Qabevi7XN7MiSh8OnDixAm4uLgo/U5TAHRCQgI8PT1Rt25dzmv/ilIt9vb2+Uq16IM3b95g586dGDJkCKpUqQJDQ0O0atUKCxcuxJUrVzSeW6hJ+NSpU6hataqgyzwMw8DLywtDhw4VrE91xMfHw8PDA40aNUKvXr10dnRQhRA2z7tPXLduXc4hONrw4sULWFpacqqYrnB20Tbx98ePH2FoaJgrxOLatWuws7PDwIED1caGamNbVQ5NXOBjF6Fh2XSwaafBftkB9vNmsCkR313IgjpE4dOB7t27Y9myZfk+1xQAffr0aVhZWWHChAmcnCkUpVpMTU2VlmoRitevX2PHjh0YNGgQHB0dYWhoiNatW2PRokW4evUqb5EVSvj8/PywePFiQfpSMHnyZDRq1EivziwKjh07BgsLC0ydOhWZmZmCubYrQxebP336FCNGjMi1T/zmzRsYGhrqbUUhLS0NtWvXxpw5czi3SU5ORuXKlbFmzRqtzqn43bIsi6VLl0Imk2HnTs0pt/jaVlMIizq0sYsId0Th0xJlT46A+gBouVyO6dOnw9zcHEeOHNF4jgcPHmDgwIEwMjJSW6pFW+Lj47F9+3YMHDgQlSpVgpGREdq0aYOgoCBcv35d5+z7QghfcnIyDA0N8ebNG537UrB7927Y2NgI2qcyMjMz8fvvv8PKygqnTp3K/lwRzJyzgKxQaGPzK1euqNwnXrx4Mfz8/IQcYjYsy6Jv377o0KED74eABw8eQCaTaSUqx48fR9WqVdG2bVu4ubnh8ePHnNrxtS2XpAXK0MUuItwQhU9L1q9fn2+vQF0A9MuXL+Hu7o6mTZuqLZ6at1TL5MmTBQvYfvnyJbZt24b+/fvDwcEBxsbGaNeuHRYvXowbN27oLHR5EUL4Nm7ciHbt2gkwmiwUziz6StOm4NmzZ6hXrx5atGihVGCFTF+VE642ZxgG+/btQ6NGjVTuE7MsC2dn51yiLSSrV69GlSpVeKdlU3DgwAGtnF3Onj2LwoULo2fPnrz2LPnez3zS1OVEV7uIaEYUPi2pX79+Lu8wdQHQhw8fhrm5OWbOnKlSXORyOXbt2oXatWvnK9WiLS9evMDWrVvRr18/VKxYEaVLl0b79u2xdOlS3Lp1Sy+Fa3MihPA1bNiQl+OPOhTOLMo89oRk7969MDU1xYIFC1TaWJGwWOjJTZPNFfvEDg4OcHV1VbtPfOPGDZQtW1Yv98n58+dhamqqVZ3HnMyaNYuzswvDMJg7dy7MzMzQpUsXjBw5kte5+NzPisTkcXFxvM4hlF1E1CMKnxYoiwdSFgCdkZGBcePGwdraWuWyFpdSLVyJi4tDaGgo+vbtiwoVKsDExAQ+Pj5YtmwZoqKi9C50edFV+B4+fAiZTCaIJ6FcLkerVq30EhKhIC0tDSNGjEDZsmVx4cIFjccLWaJGgSqbK/aJzczM4OXlhdOnT2tcRhs2bBimTp0q6PiArOB3CwsLHD6se8YPhmHg7e2NgIAAtdfz+vVrNGvWDA0bNsTz58+1urf43M/alKIS0i4i6hGFTwsmTpyYKwOEsgDop0+fonbt2vDy8lKapPfVq1eYOHEi51Itynj27Bm2bNmCPn36oHz58pBKpejQoQNWrFiB27dvF7jQ5UVX4Zs8eTJGjBghyFgmTZqExo0b682Z5eHDh3B1dYW3tzfnGDehi5IC+W0eExODQYMG8d4nTktLg1Qq5bz/xZXU1FTUqlULc+fOFazP5ORkODo6Ijg4WOn3x48fh6WlJSZPnpzr7bZBgwZqMy7lhc/9zLf4sD7sIqIaUfjUwDLJYFP2gf28EeyntWC/hEGe9g+sra2zc/4pC4AODw+HTCZDUFBQPvG5e/eu1qVaYmNjsWnTJvj7+8PW1hYymQydOnXCypUrcffu3a8udHnRRfgUMZJCZKDZvXs3ypQpozdnlrCwMEilUqxYsYKXM0JaWhpMTEwEz9wixD7x7t270bhxY8HGBWTtGfbp0wcdO3YU3GkjJiYmn7NLZmYmJk2aBEtLy3w5RgFgw4YNGnPs5oTr/fzixQsYGxtzzrOrT7uIKEcUPiWwGff/Ldfh9G8Qp2NWip54Z2S8dMTd8w5gUw7iQ+LbXAHQqampGDx4MGxtbXN5dbIsi5MnT8LT0xNmZmaYOXOmxlItLMviyZMnCAkJQa9evVC2bFmYmpqic+fOWL16NaKjo7/5H4kuwnfixAlUr15d5zHcvXtXb84sX758QUBAACpWrKh1cP3QoUMxffp0QcYjl8tBRKhTp47O+8Rt2rQRPMh+1apVcHJy0pvTxsGDB2FpaYkXL14gLi4ODRo0QLNmzVSGFfH1GOZ6P8+dO5dXUm1920UkP6Lw5YBlWTDJi//NWVdJQ666anhyrQomjM8KpH3w4AGqVauGjh07ZpcuUZRqcXFx0ViqhWVZPH78GBs3boSfnx/KlCkDc3Nz+Pr6Ijg4GPfv3//mhS4vughfjx49sHTpUp3On5iYiAoVKgi+jwZkvelXqVIF3bt31ynG7dq1ayhXrpxOb+s594mJSKd9YiArzEVox5tz587B1NQUjx49EqxPZcyePRv29vaQyWSYN2+eRrv27NlTYx1NBVzuZ5ZlYW9vz2mPF8jyMC0Iu4jkRhS+HDAfp4N5XZVzota05xUhf90AO8KyiocGBweDZdlcpVoaN26stFQLy7J4+PAhNmzYgB49esDa2hoWFhbo2rUr1q5di3/++ee7E7q8aCt8qmIk+SCXy+Hp6Ynhw4dr3YcyWJbFxo0bIZVK8ccff+j8N1KEDJw+fZp32/j4eEyaNCnXPrEQnrSBgYHw9/fXuR8FBeW0kZ6ejhEjRuDnn39G69atOf1tTp48iWrVqnHqn4ttL1y4AHt7e07njouLE51ZvhKi8P0L8zns37x0/EpzpD+viDtnK+LWrZuIi4vD2LFjlZZqYVkWMTExWLduHbp37w4rKytYWVmhe/fuWLduHWJiYr57ocuLtpPw+vXr4e2tW3HLiRMnCu7MkpycjG7dusHJyQnR0dGC9RsUFIRevXpxPj46Ohp9+/ZVuk+sq/CxLAsnJyecOXNGp34UpKamombNmpg3b54g/ani0aNHcHNzQ9u2bREbGwtHR0esXr1aYzs+eWC52LZ///6cHFQKyi4iyhGFDwDLysG8rq11McaMl06YPbVtrlItLMvin3/+wdq1a9G1a1dYWFjA2toaPXr0wIYNG/Dw4cP/nNDlRdtJuH79+ti7d6/W5w0PDxfcmeX69euoUKEC+vXrp3VxYFW8fv0ahoaGapcWWZbFqVOn0KpVK7X7xLoK37Vr12BrayuIoxTLsujduzc6deqk13t9+/btkEql2WnIgP87u5w/f15j+6lTp3JaGdBk2y9fvsDY2BgvXrxQexzLsvD399e7XURUIwofADb11L9OLNoJX+bLCoi50gSXLl1CcHAwfH19YW5uDhsbG/j5+WHjxo14/PjxD3eTazMJx8TEqK1vqIk7d+5AKpXi2rVrWrXPC8uyWL58OaRSKcLCwgTpUxlt27ZVmvEnIyMD27Ztg6urq8Z9YkB34RsyZAhmzJihUx8KVq5cCWdnZ705baSkpKB///6ws7NT+vc+dOgQLCwsNJbqevToEadaj5psu3XrVrRo0ULjuFesWKFXu4hoRhQ+AMy7blqLnuLfl9gKcHMti169eiEkJARPnjz54YQuL9pMwhMnTsTo0aO1Op/CmWXLli1atVfWX/v27VGjRg29Z9L466+/0KhRo+z/K/aJy5Qpo3KfWBm6CJ8ivEKI4rL6dtqIjo6Gk5MTfH19kZSUpPK4OXPmoFatWmofFgCgUaNG+Ouvv9Qeo8m2zZo10/hwJDqzfBuIwgdk1Z7SUfgyXlUHm6Z5WeVHgu8kLJfLYW1trbS+IZe2LVu2FCzg/cKFCyhbtixGjhypde03PqSnp0MqleL8+fMYN26c0n1iLugifLt27UKTJk20bq9A4bTBJRE7X1iWxR9//AGpVIr169drfLhkWRYdOnRAnz591B77xx9/oE2bNmr7UmfbuLg4lC5dWm1Zo7i4OM4J6kX0SyESIUKazl0ULiQhwicBBvPjcurUKTI1NaWqVavybjtlyhRKS0ujRYsW6TQGlmVp/vz51L59e1q+fDktWbKEihcvrlOfXLh37x6ZmJhQs2bNKDMzk65fv05hYWHk5uam93MrCAkJIX9/f536SEtLow4dOtCIESOoRYsWwgzsXz59+kQ9e/akwMBAOn36NAUEBJBEIlHbRiKR0KZNm+jy5csUHBys8rhOnTrRuXPn6M2bN1qNbcuWLdS5c2f6+eeflX6fmppKPj4+NHLkSMHtIsIfUfiIiCRFBOroJ4H6+THRduINDw+nbdu20c6dO6lo0aJan//Nmzfk6elJBw4coKtXr1Lbtm217osLAOjo0aPUrFkz8vLyohYtWpBMJqOgoCAqV66cXs+dl/j4eLpw4QJ16NBB6z4A0KBBg8jW1pbGjx8v4OiIbt26RTVq1KCffvqJrl69Sk5OTpzblihRgvbs2UPTp0+n8+fPqzymffv2tHXrVt5jA0CbNm1See8q7FK+fHnB7SKiJV/3hfPbgEloqvNSJ/O6GtgMYevlfe/wub0+fPiAUqVKhvIG+AAAFwlJREFU4d27d7zOoXBmuX79Ot/h5eLkyZOwtLTExIkT9VrVHsjaSwsJCYGTkxOcnZ2xefPmbMeKatWq4eTJk1r3re1PeuHChejTp4/W5wX+77Sha1WRnLAsi5UrV0IqlfLKfamMw4cPq3V2OX36NJycnFQuiaqybWRkJCpVqqSy3fLlywW3i4huiMIHgPm0QasYvlz/Epr+8M4seeEzCa9duxYdOnTg1X9iYiLs7OwQGhrKd2jZZGZmYsqUKbCwsMCxY8e07ocLiYmJmDdvHiwtLdGsWTMcPXo03z2zZMkS9OzZU+tzaCN8LMvC0dER586d0/q8CqcNIZNaJyYmwtvbGy4uLoiJiRGkz7lz56JmzZpKnV0YhoGtra1Kj2BVtu3bty8WLFig9LszZ84IbhcR3RGFDwDLfAQT76SD8FUD81l/ru7fK3wm4bp162L//v2cj5fL5WjRogXvmmo5ef78ORo2bAgPDw/Biv0q4+nTpxgxYgSMjY3Rs2dPtYm3ExISYGhoqNZTUR3aCN/ly5dhZ2en9YObwpnl6NGjWrVXxsWLF1G2bFkMHz5cUOcilmXRsWNH9O7dW+n1Tp8+HUOHDlXaVpltP3/+DCMjI6XFcJ89ewZzc3NB7SIiDOIeHxFJChkS/dSSiIpp2YGEJD+3EXRMPxL//PMPPX36lFq2bMm5zeTJkykjI0NrZ5aDBw+Sm5sbtWjRgo4ePUrm5uZa9aOOq1evkq+vL9WoUYOKFy9Ot2/fpi1btlC1atVUtpHJZNSkSRPatWuX4ONRhWJ/SpOjiDJyOm00b95c57GwLEsLFy6kdu3a0dKlS2nZsmWCOhdJJBIKCQmhq1ev0urVq/N97+fnR2FhYZSens6pv4iICKpbty5ZWlrm+lxhl1GjRgliFxGB+drK+63AMp/AJPwKzcmp8/5zBpvGv5bejwDX22vChAkYO3Ys53537tyJsmXLIiEhgfeY0tPTMXr0aNjY2HDK6sEXhmGwb98+NGrUCGXKlMHixYt5v73t2bMHDRo00Or8fH/Sikrhz549430ulmXRq1cvdOnSRZBl/oSEBLRs2RL16tXTajx8ePToEUxNTZUWiHZ3d0d4eHi+z5XZ1sPDAzt27Mj1Gcuy8PPzE8wuIsIjCl8OWHkCmITmYOKrcBe91ONfe9jfLFwmYblcDktLS9y5c4dTn7dv39bameXx48eoWbMm2rRpw9uJRhOpqalYt24dHBwc4OrqirCwMK2dZDIyMmBqaqpV0Dxf4duxYwc8PDx4nwfIctqoWrWqIE4bp0+fhpWVFX7//Xe9FQvOi8LZJS4uLtfnmzdvhpeXV77j89o2NjYWJiYm+fYLly1bJphdRPSDKHx5YJnPYJLmZaUwe11Nidg5Zgnj+15gM+5+7eF+03CZhI8cOQI3NzdO/b1//x52dnb4888/eY9l586dkMlkWLJkiaBP4W/fvsWMGTNgZmYGLy8vnD59WpD+R40ahUmTJvFux1f4WrZsqZU9hXLakMvlmDZtmuB7hFyZN29ePmcXxb7dq1evch2b17YzZ87E4MGDc312+vRp0ZnlO0AUPhWwbDrYlL1Z6cwSmoF54w7mbRswyQvByl9p7kCE0yTcpUsXrFq1SuNxcrkczZs3x6hRo3iNISUlBQMHDoSdnZ2gxWhjYmIwaNAgGBkZISAgAPfuCRvKEhUVBRsbG9519fgI34sXL2BkZMQ76bbCaUNXL9gXL16gcePGaNq0aT6RKShYlkWnTp3g7++f64Gld+/eWLRoUa5jc9qWZVmUL18eV65cyf5MKLuI6B9R+ET0hqZJODExEaVKlcL79+819vXbb7+hadOmvJYP79+/j6pVq6JLly74+PEj53aqYFkWkZGRaN++PaRSKSZPnqxXb1AXFxccP85vKZ2P8M2fPx8BAQG8+k9JSUGNGjWwcOFCXu3ycujQIZibm2PWrFk6Fc0Vgk+fPsHZ2RkrVqzI/uzs2bNwdHTMJYY5bZv3+5SUFLi6uupsF5GCQRQ+Eb2haRIODg5Gp06dNPazY8cOlCtXjldh2k2bNkEqlWLdunU6Lz3K5XKEh4ejTp06sLOzw6pVqwpk/2bZsmXo3r07rzZchY9lWTg4OCAyMpJz3wqnDV9fX61tmpGRgXHjxsHa2lqpY8nXIq+zS943OpZlUajQ/22b842QZVn07NlTJ7uIFCyi8InoDU2TcK1atXDw4EG1x0RFRUEqlXIqFApkPb37+fmhcuXKuH37NuexKuPz589YuXIlypcvjzp16mD37t0F+nby9u1bGBoa8npb5Sp8Fy9eRMWKFXlN1Lo6bTx9+hS1a9eGl5cXr4eYguLIkSMwNzfPdnZZEvQbDu1s9m+tTgfIX1UAE18FGW/aopevGV69yjpu6dKlojPLd4YofCJ6Q90kHB0dDQsLC7VLl+/fv0f58uU5p6q6desWHBwc0KdPH50mofj4eEyaNAlSqRTe3t74+++vF67i4+ODdevWcT6eq/ANGDAAc+bM4dzv6dOnYWZmhidPnnBuk5Pw8HDIZDIEBQV9029F8+fPx69NXZHxtjfkrxzxJbaCUo/uT0/swbx2xYObE2Fqaqq1XUS+DqLwiegNdZPw+PHjMX78eJXfK5xZuNTmY1kWq1evhlQq1cpDUUF0dDT69u0LIyMjDB48WLA0Wbqwb98+1KtXj/PxXIQvJSUFpUuXzufGrwqF0wbf/UYgK8xj8ODBsLW1xeXLl3m3L2iYzGd4909lpD/nFseb/LgC4qL9v2kxF8mPUGUJREQ4I5fLKTQ0lE6ePKnymIkTJxLDMLRgwQK1fX38+JECAgLo8ePH9Pfff5O9vT2vsQCgM2fOUGBgIF2/fp2GDBlCDx8+JKlUyqsffdGyZUvq168fPXjwgBwcHATpc8+ePeTm5kY2NjYaj01NTSVvb28aM2YM/frrr7zOExMTQ507dyZ7e3u6efMmGRoaajvkAgHsB6LEHmRkyBLXHDYGv0jI4JcbhE+BJCk1Tq/jExEOMWWZSIFz7NgxKlOmDFWuXFnp9zt27KCdO3fS9u3bqUgR1c9mV65cIVdXV7KwsKCLFy/yEr3MzMzseneDBw8mb29vio2NpSlTpnwzokdEVLRoUerRowdt3rxZsD7VldDJCQAaMGAAOTg40JgxY3idIzQ0lOrXr0+DBg2iHTt2fPOiR0SET4uI2PckIZZny1SilFBC5gO9jEtED3ztV06R/y6qbq9OnTohODhY6Xe3bt2CVCrFzZs3VfbLMAwCAwMhk8mwe/duXmNKSkpCUFAQypQpg8aNG2P//v1gGIZXHwXN7du3YWVlxcmxRtNP+vnz5zA2NlZbKVzB0qVLUa1aNV5xfp8/f4a/vz8qVaqEqKgozu2+NizzScdE9ZXAfJzwtS9DhCPiG59IgZKYmEhHjx6lLl265Pvu/fv35O3tTcuXL6fq1asrbf/u3Ttq06YNhYeH05UrV8jHx4fTeV+8eEHjx48nW1tbunLlCoWHh9OZM2eodevWVKjQt/0zcHZ2JnNzc7VLw1wJDQ2lTp06qawUruD06dM0b948ioiIoF9++YVT37dv3yY3NzcCQFevXqWqVavqPN6CAql7SbcFMIYo9SCB/SzUkET0yLf9ixf5z7F9+3by9PQkY2PjXJ/L5XLq2rUr+fj4UNeuXZW2PXv2LLm4uJCTkxOdO3eOU5XyqKgo8vPzo6pVq1JmZiZdv36dtm/fTjVr1hTicgqM3r17U0hIiE59AKCQkBDq3bu32uOePXtG3bp1oz///JNsbW059bt27Vry8PCgiRMn0qZNm6hEiRI6jbXASd1NRKm69SEpTJShvMK7yLeF6NwiUqCEhITQ7Nmz830+ceJEYlmW5s+fn+87hmFozpw5FBwcTCEhIRrLFwGgY8eOUVBQEEVHR9Pw4cNp2bJl+cT2e8LX15cmTpxIHz9+JCMjI636uHjxIhUqVIhq166t8hhFOZ2xY8dycmZJSkrKdr6JjIwUzAGnwGHf694H5ESMAP2I6B1R+EQKjLt379KrV6/yTajbt2+n8PBwunr1aj5nlvj4eOrevTsBoOvXr+ere5aTjIwMCgsLo6CgICIiGjNmDHXt2pWKFdOyzuI3hImJCTVv3px27NhBAwYM0KoPTXX3AFD//v2pUqVKNHr0aI39Xb16lbp06UKenp60ZcsW+umnn7Qa17cBI0AfEKgfEX0jLnWKFBibN28mPz8/Kly4cPZnUVFRNGzYMIqIiCATE5Ncxx89epRcXV3J3d2dTpw4oVL0Pnz4QPPnzydbW1vaunUrBQYGUlRUFPXq1es/IXoK/P39adOmTVq1TUlJofDwcOrZs6fKY5YtW0Z3796l9evXqy1KC4AWL15MXl5etGjRIlq1atV3LnpEJCkpQB9FiAqV0r0fEb0jvvGJFAiZmZn0559/0pkzZ7I/UzizrFixIldV8szMTJoyZQpt3bqVtm/fTo0bN1baZ2xsLC1dupS2bNlCrVu3pkOHDqmtbv6906JFCwoICKD79++rDAVRRUREBNWuXZusrKyUfn/69GmaP38+Xbp0Sa0zy7t378jf35/evn1Lly9f5rQH+F1Q3J0oJY6IMrXvAwxR0e9r7/hHRXzjEykQjh49Sra2ttl7QHK5nHx9falDhw7k6+ubfdyzZ8+ocePGdPv2bbpx44ZS0bt69Sr5+vpSjRo1qHjx4nT79m3asmXLf1r0iIiKFClCPXv21CqmT13s3rNnz6hr1660detWtQ5D58+fJxcXF6pcuTKdP3/+vyN6RCQx6EHEOWxdBUWrkaSItSDjEdEvovCJFAh5J97ff/+diIjmzZuX/dmePXuoVq1a5OPjQwcOHCCZTJb9HcuytH//fmrcuDF17NiRateuTU+fPqUFCxaQtfWPM9n06tWLQkNDiWG47yXFxcXRjRs3qF27dvm+S0lJIW9vbxo/fjx5eHgobc8wDM2ePZs6depEa9eupUWLFv2nlpCJiCSFrYiKuejQwS8kKdFPuAGJ6BVxqVNEMAAQZV4jpO4nYt/QgT8tif04nj5nutGZMydo48aNREQUFhZGu3fvznZmSUtLo3HjxtGBAwdo3759ubwO09LSKDQ0lIKCgsjAwIDGjRtHHTt2VJvR5b9MlSpVyMrKio4dO0aenp6c2mzZsoU6d+6cbx9O4czi6OhIo0aNUto2Pj6eevToQXK5nK5fv65yqfS/gKTk74T3vkSUxrNlMaIiDkTFGupjWCJ6QAIAX3sQIt83QAYhZRfRlw1E+ECEVMrycMsiI7MoZcpZMpD2o+gnbtT01w504sQJqlatGsXExFCXLl3Izs6ONmzYkO2q/+7dOwoODqZVq1aRm5sbjR07lho3bqzW6eJHITg4mM6cOUM7duzI951EIqGcP2kAVLFiRdq2bRvVqlUr17FLliyhLVu20N9//610X+/YsWPUq1cv6t+/P02ZMuWHeNhA2mnCxxHEXfyKERW2IolJOEkKCeAgI1IgiMInohNgkwkf+hBlPiRNAcCgovTufQZdezycvNoOo61bt9LIkSNpxowZNGjQIJJIJPTw4UNasmQJhYWFUYcOHWj06NHk6OhYMBfznfDhwwcqV64cxcbG5otNzCt8kZGR1L9/f4qOjs710HDq1Cnq1q0bXbp0Kd++XmZmJk2dOpVCQ0MpNDSUmjRpotfr+dZAxlXCh4FExBAhRcVRhYioGFGx6iQxWk2SQt9ZwP4Pzn//EU5EbwBphMTuRPInxMUbTkKZZGIsoZa1NtG40Rdp38HrdPz4capevTpduHCBAgMD6fz58zRw4EC6f/8+mZub6/8ivkOMjY2pZcuWtH37dho0aJDaY5XF7sXGxlK3bt1o27Zt+UQvLi6OunbtSiVLlqQbN26QqampPi7hm0ZSrCaR6QWitCOEL+uI5M+JJEX//RZEyCT6qQVJDHqTpGiVrzpWEe0Q3/hEtIb9+BtR2iEiSufVjmGI3n74iQysz9GJkycpMDCQEhISaPTo0eTv708GBgb6GfB/iCNHjtDUqVPpypUruT7P+cb35csXsra2pnv37pGFhQURZTmz1K9fn/z8/PLt6+3du5f69+9PY8aMobFjx37zOUwLCsifEbFviJBGJClFVKQ8ScR4ve8aUfhEtALsB0JCI+IregoyMotSwJg0evzclMaNG0ft2rXLFdguoh6GYahMmTJ07NgxqlLl/28dOYUvNDSUtm/fTgcPHiSirP2+Hj16kEQiodDQ0Oy3wPT0dBo/fjzt3buXwsLCqG7dugV/QSIiBYi41CmiFUjZRbrEPRUpnEnL51ej0uX/Em5QPxCFCxfOjulbuHCh0mM2bdpEAwcOzP7/kiVL6P79+xQZGZkteo8ePaIuXbpQ2bJl6ebNm991PlMREa6Iaxki2pESSvzdvv9PoUJERr88JIhJfbXG39+fQkNDSZ6ZQsi8TUg/Tx4NfyZk3qfY2CcUFRVFbdq0ISKikydP0qJFi3KVGVK83fXp04d2794tip7ID4P4xifCGwBEbILuHUmKETEviAqbaD5WJB8OFQwocLqM2ITaVKhIUSKS0M71FoTErmTMsLR2SR0qXiyNYmNfU/fu3SksLIzKli1LKSkpNGLECDp79iwdO3aMXFx0CNwWEfkOEff4RHgDpBHeuJDOmeglJUlitIIkxesJMq4fBYAhJM8iSt1NDJNJhQuzSo9j2GJUqJCE5iwDlTILoJEjR1J0dDR16dKFqlevTsHBwVSypBh7JvLjIb7xiWhBccoZoK49IBLjn3gBMISPQ4gyLhJROqnzBypcKIOIiMYNKkTFjYvSxo0bacKECbRw4UK15YlERP7riMInwhuJREIoZEbExuvWETKICv84eTaFAJ/mZokeuFcLL16MpfQPy+lBVCE6e/asmBBA5IdHXOoU0Qr2yyaiT0tIU7YW1UiIirtTIeO1Ao7qvw2Y14S3vxJRhnbtJYZUyPQSSSRi2IjIj43o1SmiFZKffYhI+d4Sxw5IYhAg2Hh+BJCyVaf2EsokSj8jzGBERL5jROET0QpJoVJEP7cnIm0qbxcmKmxJVNRN6GH9ZwEyiVK2kbZve1mdpGSl4BIR+cERhU9EaySlphAVtacsZxeuFCKSlCKJ8R+icwUf5E9JpzdsBZm3SdzdEPnREYVPRGskkmIkMd5MVNSFiH7m0KI4USGzrBIuhcUE1LxAEgn3c9U+8YCIyH8BUfhEdEJSyIAkpf8gieEMoiIVKWvpM89tJfmFqJAJUYlhJJEeIEkRm68x1O8coRywQUSic4vIj43o1SkiKMi8R0g7RMS8IaJMokIykhRvQFSsIUkk4nOWtkAeR3jXmnR/WytOhczvCDEkEZHvFjGOT0RQJEUdSVJUjBMTnMI2RIXNiJhnOnRSiOinloINSUTke0V8BBcR+Q6QSCQkMehPRL/o0Esxkhj0FmpIIiLfLaLwiYh8L/zcmkiiw85EYRvxbVxEhEThExH5bpBIfiYqtZC0ip2U/EISo8WCj0lE5HtEFD4Rke+IQj+3ICo5kbiLnyRL9IzXk6Sogz6HJiLy3SB6dYqIfIcg/SwhaWpWfB9SKX+1jMJEVJSoiB1JDBeQpKj9VxiliMi3iSh8IiLfKQCIMq8RPq8nyrhEROmU9YZnQPRTS5L84k+SohW/9jBFRL45ROETEfmPALBEJBFTwYmIaEAUPhERERGRHwrRuUVERERE5IdCFD4RERERkR8KUfhERERERH4oROETEREREfmhEIVPREREROSHQhQ+EREREZEfClH4RERERER+KEThExERERH5oRCFT0RERETkh0IUPhERERGRHwpR+EREREREfihE4RMRERER+aEQhU9ERERE5Ififw9ltQNxbjfAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(G, node_color=get_random_GW_cut(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, что, действительно, вершины из первой доли оказались в одной части разреза, а из другой доли - в другой. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь протестируем алгоритм на случайных графах. \n",
    "\n",
    "Возьмем данные из http://biqmac.uni-klu.ac.at/biqmaclib - по этой ссылке есть архив с описанием всех графов, которые мы будем рассматривать\n",
    "\n",
    "Ответы здесь: http://biqmac.uni-klu.ac.at/biqmaclib.pdf - pdf-ка с описанием всех графов и табличками с ответами\n",
    "\n",
    "Для удобства, я вручную переписал всю нужную информацию в файлик input.txt, откуда далее считаю названия графов и ответы (то есть значения величины максимального разреза)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# массив с названиями графов\n",
    "names = []\n",
    "# массив с ответами (MAXCUT) для каждого графа\n",
    "solutions = []\n",
    "\n",
    "# чтение данных \n",
    "for line in open('input.txt'):\n",
    "    values = line.strip().split()\n",
    "    names.append(values[0] + '_' + values[1])\n",
    "    solutions.append(int(values[2]))\n",
    "\n",
    "# приводим в типу np-array\n",
    "solutions = np.asarray(solutions)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ф-ция принимает на вход название файла и возвращает \n",
    "# массив ребер графа, который описан в этом файле\n",
    "def get_edges(name):\n",
    "    with open(name) as f:\n",
    "        edges = f.readlines()\n",
    "    edges = [edge.strip() for edge in edges][1:]    \n",
    "    return edges\n",
    "\n",
    "# возвращает pandas табличку с колонками из данных массивов\n",
    "def get_df(cur_names, maxs, means, cur_solutions):\n",
    "    pd.set_option(\"display.precision\", 0)\n",
    "    df = pd.DataFrame(\n",
    "        list(\n",
    "            zip(\n",
    "                cur_names,\n",
    "                cur_solutions,\n",
    "                means,\n",
    "                means / cur_solutions * 100,\n",
    "                maxs,\n",
    "                maxs / cur_solutions * 100\n",
    "            )   \n",
    "        ),                  \n",
    "        columns=['Название графа', 'Решение', 'GW Mean', '% Mean', 'GW Max', '% Max']\n",
    "    ) \n",
    "    return df\n",
    "\n",
    "# запускаем алгоритм для графов, которые заданы в файле \n",
    "# input.txt в строчках с номерами с start до finish\n",
    "def get_results(start, finish):\n",
    "    # n - количество вершин в графе \n",
    "    # у нас всегда будет 100 вершин\n",
    "    n = 100\n",
    "    # лучшие величины разреза для каждого графа\n",
    "    maxs = []\n",
    "    # средние величины разреза для каждого графа\n",
    "    means = []\n",
    "    cur_names = names[start:finish]\n",
    "    cur_solutions = solutions[start:finish]\n",
    "    for name in cur_names:\n",
    "        \n",
    "        # получаем ребра текущего графа\n",
    "        edges = get_edges(name)\n",
    "        \n",
    "        # создаем граф из них \n",
    "        G = nx.parse_edgelist(edges, nodetype = int, data=(('weight',float),))\n",
    "        # получаем лапласиан этого графа\n",
    "        L = nx.laplacian_matrix(G)\n",
    "\n",
    "        # решаем SDP задачу максимизации\n",
    "        _, X = GW_solve(n, L, False)    \n",
    "        \n",
    "        # сделаем try_num попыток восстановить разрез\n",
    "        try_num = 100\n",
    "        # все полученные величины разрезов\n",
    "        cur_maxcut_values = []\n",
    "        for _ in range(try_num):\n",
    "            # получаем некоторый разрез\n",
    "            cur_cut = get_random_GW_cut(X)\n",
    "            # получаем величину этого разреза\n",
    "            cur_cut_value = cut(cur_cut, L)\n",
    "            # добавляем в массив эту величину\n",
    "            cur_maxcut_values.append(\n",
    "                cur_cut_value\n",
    "            )\n",
    "        # выбираем лучший из полученных разрезов\n",
    "        maxs.append(max(cur_maxcut_values))\n",
    "        # берем среднее по всем значениям \n",
    "        means.append(np.mean(cur_maxcut_values))\n",
    "\n",
    "    # приводим массивы к типу np-array\n",
    "    maxs = np.asarray(maxs)\n",
    "    means = np.asarray(means)\n",
    "    # создаем табличку из данных массивов\n",
    "    df = get_df(cur_names, maxs, means, cur_solutions)\n",
    "    \n",
    "    # возвращаем эту табличку а так же среднее средних значений разреза \n",
    "    # и среднее среди максимальных значений разреза\n",
    "    return df, \\\n",
    "            np.mean(means / cur_solutions * 100), \\\n",
    "            np.mean(maxs / cur_solutions * 100)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Запустим алгоритм на графах g05_100.i. Это графы, у которых все ребра имеют вес ровно 1, количество вершин 100, а вероятность каждого ребра равна 0.5\n",
    "\n",
    "В таблице присутствуют следующие колонки:\n",
    "* Название графа - оно же имя входного файла, где описан этот граф\n",
    "* Решение - истинное значение величины максимального разреза\n",
    "* GW Mean - среднее значение величины разреза, полученное в ходе работы алгоритма (мы делаем несколько попыток восстановить разрез, используя разные случайные вектора h и потом берем среднее по всем результатам)\n",
    "* % Mean - (GW Mean / Решение) * 100 - то есть какая точность (в процентах) в среднем была достигнута\n",
    "* GW Max - аналогично GW Mean, только берем лучший из всех полученных разрезов\n",
    "* % Max - (GW Max / Решение) * 100 - какая точность была достигнута в лучшем случае"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 97%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 99%\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>g05_100.0</td>\n",
       "      <td>1430</td>\n",
       "      <td>1397</td>\n",
       "      <td>98</td>\n",
       "      <td>1416</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>g05_100.1</td>\n",
       "      <td>1425</td>\n",
       "      <td>1397</td>\n",
       "      <td>98</td>\n",
       "      <td>1419</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>g05_100.2</td>\n",
       "      <td>1432</td>\n",
       "      <td>1396</td>\n",
       "      <td>97</td>\n",
       "      <td>1423</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>g05_100.3</td>\n",
       "      <td>1424</td>\n",
       "      <td>1392</td>\n",
       "      <td>98</td>\n",
       "      <td>1413</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>g05_100.4</td>\n",
       "      <td>1440</td>\n",
       "      <td>1403</td>\n",
       "      <td>97</td>\n",
       "      <td>1432</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>g05_100.5</td>\n",
       "      <td>1436</td>\n",
       "      <td>1403</td>\n",
       "      <td>98</td>\n",
       "      <td>1431</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>g05_100.6</td>\n",
       "      <td>1434</td>\n",
       "      <td>1400</td>\n",
       "      <td>98</td>\n",
       "      <td>1428</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>g05_100.7</td>\n",
       "      <td>1431</td>\n",
       "      <td>1398</td>\n",
       "      <td>98</td>\n",
       "      <td>1422</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>g05_100.8</td>\n",
       "      <td>1432</td>\n",
       "      <td>1399</td>\n",
       "      <td>98</td>\n",
       "      <td>1423</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>g05_100.9</td>\n",
       "      <td>1430</td>\n",
       "      <td>1398</td>\n",
       "      <td>98</td>\n",
       "      <td>1414</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0      g05_100.0     1430     1397      98    1416     99\n",
       "1      g05_100.1     1425     1397      98    1419    100\n",
       "2      g05_100.2     1432     1396      97    1423     99\n",
       "3      g05_100.3     1424     1392      98    1413     99\n",
       "4      g05_100.4     1440     1403      97    1432     99\n",
       "5      g05_100.5     1436     1403      98    1431    100\n",
       "6      g05_100.6     1434     1400      98    1428    100\n",
       "7      g05_100.7     1431     1398      98    1422     99\n",
       "8      g05_100.8     1432     1399      98    1423     99\n",
       "9      g05_100.9     1430     1398      98    1414     99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 45.1 s, sys: 4.17 s, total: 49.3 s\n",
      "Wall time: 49.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(0, 10)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видно, что на невзвешенных графах алгоритм получает ответ с очень высокой точностью как в среднем, так и (тем более) в лучшем случае."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее, запустим алгоритм на графах pm1s_100.i, это графы (как всегда на 100 вершинах) с весами ребер, выбранными случайно равномерно из $\\{-1, 0, 1\\}$ и плотностью $10\\%$ (то есть, вероятность ребра 0.1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 85%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 96%\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>pm1s_100.0</td>\n",
       "      <td>127</td>\n",
       "      <td>109</td>\n",
       "      <td>86</td>\n",
       "      <td>122</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>pm1s_100.1</td>\n",
       "      <td>126</td>\n",
       "      <td>110</td>\n",
       "      <td>87</td>\n",
       "      <td>121</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>pm1s_100.2</td>\n",
       "      <td>125</td>\n",
       "      <td>105</td>\n",
       "      <td>84</td>\n",
       "      <td>119</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>pm1s_100.3</td>\n",
       "      <td>111</td>\n",
       "      <td>94</td>\n",
       "      <td>85</td>\n",
       "      <td>105</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>pm1s_100.4</td>\n",
       "      <td>128</td>\n",
       "      <td>111</td>\n",
       "      <td>87</td>\n",
       "      <td>125</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>pm1s_100.5</td>\n",
       "      <td>128</td>\n",
       "      <td>109</td>\n",
       "      <td>86</td>\n",
       "      <td>120</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>pm1s_100.6</td>\n",
       "      <td>122</td>\n",
       "      <td>105</td>\n",
       "      <td>86</td>\n",
       "      <td>119</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>pm1s_100.7</td>\n",
       "      <td>112</td>\n",
       "      <td>93</td>\n",
       "      <td>83</td>\n",
       "      <td>107</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>pm1s_100.8</td>\n",
       "      <td>120</td>\n",
       "      <td>101</td>\n",
       "      <td>85</td>\n",
       "      <td>119</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>pm1s_100.9</td>\n",
       "      <td>127</td>\n",
       "      <td>111</td>\n",
       "      <td>88</td>\n",
       "      <td>124</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0     pm1s_100.0      127      109      86     122     96\n",
       "1     pm1s_100.1      126      110      87     121     96\n",
       "2     pm1s_100.2      125      105      84     119     95\n",
       "3     pm1s_100.3      111       94      85     105     95\n",
       "4     pm1s_100.4      128      111      87     125     98\n",
       "5     pm1s_100.5      128      109      86     120     94\n",
       "6     pm1s_100.6      122      105      86     119     98\n",
       "7     pm1s_100.7      112       93      83     107     96\n",
       "8     pm1s_100.8      120      101      85     119     99\n",
       "9     pm1s_100.9      127      111      88     124     98"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 24.4 s, sys: 2.16 s, total: 26.5 s\n",
      "Wall time: 21.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(10, 20)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что в среднем результат работы алгоритма уже не такой хороший, как в случае невзвешенного графа, но, тем не менее, довольно близок к теоретической оценке ($85\\%$ против $87.8\\%$). Однако, в лучшем случае результат по прежнему очень высокий ($96\\%$ в среднем)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Далее, запустим алгоритм на графах pm1d_100.i, это графы (как всегда на 100 вершинах) с весами ребер, выбранными случайно равномерно из $\\{-1, 0, 1\\}$ и плотностью $99\\%$ (то есть, вероятность ребра 0.99)\n",
    "\n",
    "То есть отличие от предыдущих десяти графов только в плотности."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 84%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 95%\n"
     ]
    },
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>pm1d_100.0</td>\n",
       "      <td>340</td>\n",
       "      <td>278</td>\n",
       "      <td>82</td>\n",
       "      <td>328</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>pm1d_100.1</td>\n",
       "      <td>324</td>\n",
       "      <td>272</td>\n",
       "      <td>84</td>\n",
       "      <td>306</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>pm1d_100.2</td>\n",
       "      <td>389</td>\n",
       "      <td>330</td>\n",
       "      <td>85</td>\n",
       "      <td>377</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>pm1d_100.3</td>\n",
       "      <td>400</td>\n",
       "      <td>342</td>\n",
       "      <td>86</td>\n",
       "      <td>387</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>pm1d_100.4</td>\n",
       "      <td>363</td>\n",
       "      <td>309</td>\n",
       "      <td>85</td>\n",
       "      <td>346</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>pm1d_100.5</td>\n",
       "      <td>441</td>\n",
       "      <td>382</td>\n",
       "      <td>87</td>\n",
       "      <td>417</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>pm1d_100.6</td>\n",
       "      <td>367</td>\n",
       "      <td>309</td>\n",
       "      <td>84</td>\n",
       "      <td>355</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>pm1d_100.7</td>\n",
       "      <td>361</td>\n",
       "      <td>298</td>\n",
       "      <td>83</td>\n",
       "      <td>344</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>pm1d_100.8</td>\n",
       "      <td>385</td>\n",
       "      <td>317</td>\n",
       "      <td>82</td>\n",
       "      <td>370</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>pm1d_100.9</td>\n",
       "      <td>405</td>\n",
       "      <td>343</td>\n",
       "      <td>85</td>\n",
       "      <td>386</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0     pm1d_100.0      340      278      82     328     96\n",
       "1     pm1d_100.1      324      272      84     306     94\n",
       "2     pm1d_100.2      389      330      85     377     97\n",
       "3     pm1d_100.3      400      342      86     387     97\n",
       "4     pm1d_100.4      363      309      85     346     95\n",
       "5     pm1d_100.5      441      382      87     417     95\n",
       "6     pm1d_100.6      367      309      84     355     97\n",
       "7     pm1d_100.7      361      298      83     344     95\n",
       "8     pm1d_100.8      385      317      82     370     96\n",
       "9     pm1d_100.9      405      343      85     386     95"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 22.5 s, sys: 2.48 s, total: 25 s\n",
      "Wall time: 22.2 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(20, 30)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Результаты аналогичны предыдущим десяти графам, то есть изменение плотность никак не повлияло на точность."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь рассмотрим графы w09_100.i, Граф с целочисленными весами ребер, выбранными случайно равномерно из $[-10,10]$ и плотностью $0.9$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 84%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 95%\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>w09_100.0</td>\n",
       "      <td>2121</td>\n",
       "      <td>1785</td>\n",
       "      <td>84</td>\n",
       "      <td>2024</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>w09_100.1</td>\n",
       "      <td>2096</td>\n",
       "      <td>1796</td>\n",
       "      <td>86</td>\n",
       "      <td>2033</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>w09_100.2</td>\n",
       "      <td>2738</td>\n",
       "      <td>2383</td>\n",
       "      <td>87</td>\n",
       "      <td>2605</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>w09_100.3</td>\n",
       "      <td>1990</td>\n",
       "      <td>1618</td>\n",
       "      <td>81</td>\n",
       "      <td>1863</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>w09_100.4</td>\n",
       "      <td>2033</td>\n",
       "      <td>1744</td>\n",
       "      <td>86</td>\n",
       "      <td>1960</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>w09_100.5</td>\n",
       "      <td>2433</td>\n",
       "      <td>2101</td>\n",
       "      <td>86</td>\n",
       "      <td>2338</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>w09_100.6</td>\n",
       "      <td>2220</td>\n",
       "      <td>1835</td>\n",
       "      <td>83</td>\n",
       "      <td>2115</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>w09_100.7</td>\n",
       "      <td>2252</td>\n",
       "      <td>1933</td>\n",
       "      <td>86</td>\n",
       "      <td>2117</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>w09_100.8</td>\n",
       "      <td>1843</td>\n",
       "      <td>1506</td>\n",
       "      <td>82</td>\n",
       "      <td>1813</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>w09_100.9</td>\n",
       "      <td>2043</td>\n",
       "      <td>1676</td>\n",
       "      <td>82</td>\n",
       "      <td>1997</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0      w09_100.0     2121     1785      84    2024     95\n",
       "1      w09_100.1     2096     1796      86    2033     97\n",
       "2      w09_100.2     2738     2383      87    2605     95\n",
       "3      w09_100.3     1990     1618      81    1863     94\n",
       "4      w09_100.4     2033     1744      86    1960     96\n",
       "5      w09_100.5     2433     2101      86    2338     96\n",
       "6      w09_100.6     2220     1835      83    2115     95\n",
       "7      w09_100.7     2252     1933      86    2117     94\n",
       "8      w09_100.8     1843     1506      82    1813     98\n",
       "9      w09_100.9     2043     1676      82    1997     98"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 22.5 s, sys: 2.25 s, total: 24.8 s\n",
      "Wall time: 20.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(30, 40)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Результаты аналогичны предыдущим нескольким запускам, то есть изменение масштаба величины ребер не повлияло на точность"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь рассмотрим графы w01_100.i, Граф с целочисленными весами ребер, выбранными случайно равномерно из $[-10,10]$ и плотностью $0.1$. \n",
    "\n",
    "То есть отличается только плотность"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 85%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 97%\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>w01_100.0</td>\n",
       "      <td>651</td>\n",
       "      <td>555</td>\n",
       "      <td>85</td>\n",
       "      <td>626</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>w01_100.1</td>\n",
       "      <td>719</td>\n",
       "      <td>629</td>\n",
       "      <td>87</td>\n",
       "      <td>714</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>w01_100.2</td>\n",
       "      <td>676</td>\n",
       "      <td>586</td>\n",
       "      <td>87</td>\n",
       "      <td>654</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>w01_100.3</td>\n",
       "      <td>813</td>\n",
       "      <td>719</td>\n",
       "      <td>88</td>\n",
       "      <td>807</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>w01_100.4</td>\n",
       "      <td>668</td>\n",
       "      <td>554</td>\n",
       "      <td>83</td>\n",
       "      <td>643</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>w01_100.5</td>\n",
       "      <td>643</td>\n",
       "      <td>550</td>\n",
       "      <td>86</td>\n",
       "      <td>618</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>w01_100.6</td>\n",
       "      <td>654</td>\n",
       "      <td>539</td>\n",
       "      <td>82</td>\n",
       "      <td>617</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>w01_100.7</td>\n",
       "      <td>725</td>\n",
       "      <td>641</td>\n",
       "      <td>88</td>\n",
       "      <td>712</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>w01_100.8</td>\n",
       "      <td>721</td>\n",
       "      <td>622</td>\n",
       "      <td>86</td>\n",
       "      <td>711</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>w01_100.9</td>\n",
       "      <td>729</td>\n",
       "      <td>629</td>\n",
       "      <td>86</td>\n",
       "      <td>698</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0      w01_100.0      651      555      85     626     96\n",
       "1      w01_100.1      719      629      87     714     99\n",
       "2      w01_100.2      676      586      87     654     97\n",
       "3      w01_100.3      813      719      88     807     99\n",
       "4      w01_100.4      668      554      83     643     96\n",
       "5      w01_100.5      643      550      86     618     96\n",
       "6      w01_100.6      654      539      82     617     94\n",
       "7      w01_100.7      725      641      88     712     98\n",
       "8      w01_100.8      721      622      86     711     99\n",
       "9      w01_100.9      729      629      86     698     96"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 26 s, sys: 2.22 s, total: 28.2 s\n",
      "Wall time: 23 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(40, 50)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Результаты аналогичны"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь рассмотрим графы pw05_100.i, графы с целочисленными весами ребер, выбранными случайно равномерно из $[0,10]$ и плотностью $0.5$. \n",
    "\n",
    "То есть теперь все веса неотрицательные"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 97%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 99%\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
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       "    <tr>\n",
       "      <td>2</td>\n",
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       "      <td>8039</td>\n",
       "      <td>7817</td>\n",
       "      <td>97</td>\n",
       "      <td>7995</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>pw05_100.3</td>\n",
       "      <td>8139</td>\n",
       "      <td>7899</td>\n",
       "      <td>97</td>\n",
       "      <td>8080</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>pw05_100.4</td>\n",
       "      <td>8125</td>\n",
       "      <td>7921</td>\n",
       "      <td>97</td>\n",
       "      <td>8053</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>pw05_100.5</td>\n",
       "      <td>8169</td>\n",
       "      <td>7935</td>\n",
       "      <td>97</td>\n",
       "      <td>8078</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>pw05_100.6</td>\n",
       "      <td>8217</td>\n",
       "      <td>8001</td>\n",
       "      <td>97</td>\n",
       "      <td>8138</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>pw05_100.7</td>\n",
       "      <td>8249</td>\n",
       "      <td>8041</td>\n",
       "      <td>97</td>\n",
       "      <td>8181</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>pw05_100.8</td>\n",
       "      <td>8199</td>\n",
       "      <td>7991</td>\n",
       "      <td>97</td>\n",
       "      <td>8162</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>pw05_100.9</td>\n",
       "      <td>8099</td>\n",
       "      <td>7875</td>\n",
       "      <td>97</td>\n",
       "      <td>8044</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0     pw05_100.0     8190     7981      97    8119     99\n",
       "1     pw05_100.1     8045     7838      97    7977     99\n",
       "2     pw05_100.2     8039     7817      97    7995     99\n",
       "3     pw05_100.3     8139     7899      97    8080     99\n",
       "4     pw05_100.4     8125     7921      97    8053     99\n",
       "5     pw05_100.5     8169     7935      97    8078     99\n",
       "6     pw05_100.6     8217     8001      97    8138     99\n",
       "7     pw05_100.7     8249     8041      97    8181     99\n",
       "8     pw05_100.8     8199     7991      97    8162    100\n",
       "9     pw05_100.9     8099     7875      97    8044     99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 40.7 s, sys: 3.51 s, total: 44.2 s\n",
      "Wall time: 38.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(50, 60)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Здесь сразу видно, что точность в среднем резко выросла. Теперь запустим на аналогичных графах (тоже с положительными весами ребер) но с другими плотностями ($0.9$ и $0.1$) и убедимся, что, действительно, плотность не влияет на точность, а влияет наличие/отсутствие отрицательных весов у ребер."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 98%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 99%\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>pw09_100.0</td>\n",
       "      <td>13585</td>\n",
       "      <td>13370</td>\n",
       "      <td>98</td>\n",
       "      <td>13534</td>\n",
       "      <td>100</td>\n",
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       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>pw09_100.1</td>\n",
       "      <td>13417</td>\n",
       "      <td>13220</td>\n",
       "      <td>99</td>\n",
       "      <td>13331</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>pw09_100.2</td>\n",
       "      <td>13461</td>\n",
       "      <td>13229</td>\n",
       "      <td>98</td>\n",
       "      <td>13372</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>pw09_100.3</td>\n",
       "      <td>13656</td>\n",
       "      <td>13431</td>\n",
       "      <td>98</td>\n",
       "      <td>13589</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>pw09_100.4</td>\n",
       "      <td>13514</td>\n",
       "      <td>13286</td>\n",
       "      <td>98</td>\n",
       "      <td>13449</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>pw09_100.5</td>\n",
       "      <td>13574</td>\n",
       "      <td>13396</td>\n",
       "      <td>99</td>\n",
       "      <td>13530</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>pw09_100.6</td>\n",
       "      <td>13640</td>\n",
       "      <td>13408</td>\n",
       "      <td>98</td>\n",
       "      <td>13557</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>pw09_100.7</td>\n",
       "      <td>13501</td>\n",
       "      <td>13294</td>\n",
       "      <td>98</td>\n",
       "      <td>13438</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>pw09_100.8</td>\n",
       "      <td>13593</td>\n",
       "      <td>13363</td>\n",
       "      <td>98</td>\n",
       "      <td>13542</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>pw09_100.9</td>\n",
       "      <td>13658</td>\n",
       "      <td>13441</td>\n",
       "      <td>98</td>\n",
       "      <td>13622</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0     pw09_100.0    13585    13370      98   13534    100\n",
       "1     pw09_100.1    13417    13220      99   13331     99\n",
       "2     pw09_100.2    13461    13229      98   13372     99\n",
       "3     pw09_100.3    13656    13431      98   13589    100\n",
       "4     pw09_100.4    13514    13286      98   13449    100\n",
       "5     pw09_100.5    13574    13396      99   13530    100\n",
       "6     pw09_100.6    13640    13408      98   13557     99\n",
       "7     pw09_100.7    13501    13294      98   13438    100\n",
       "8     pw09_100.8    13593    13363      98   13542    100\n",
       "9     pw09_100.9    13658    13441      98   13622    100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 58.3 s, sys: 5.34 s, total: 1min 3s\n",
      "Wall time: 1min\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(60, 70)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Средняя точность: 95%\n",
      "Средняя точность (если брать лучший результат по нескольким запускам): 98%\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Название графа</th>\n",
       "      <th>Решение</th>\n",
       "      <th>GW Mean</th>\n",
       "      <th>% Mean</th>\n",
       "      <th>GW Max</th>\n",
       "      <th>% Max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>pw01_100.0</td>\n",
       "      <td>2019</td>\n",
       "      <td>1921</td>\n",
       "      <td>95</td>\n",
       "      <td>1975</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>pw01_100.1</td>\n",
       "      <td>2060</td>\n",
       "      <td>1962</td>\n",
       "      <td>95</td>\n",
       "      <td>2050</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>pw01_100.2</td>\n",
       "      <td>2032</td>\n",
       "      <td>1924</td>\n",
       "      <td>95</td>\n",
       "      <td>1998</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>pw01_100.3</td>\n",
       "      <td>2067</td>\n",
       "      <td>1969</td>\n",
       "      <td>95</td>\n",
       "      <td>2045</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>pw01_100.4</td>\n",
       "      <td>2039</td>\n",
       "      <td>1934</td>\n",
       "      <td>95</td>\n",
       "      <td>2013</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>pw01_100.5</td>\n",
       "      <td>2108</td>\n",
       "      <td>1997</td>\n",
       "      <td>95</td>\n",
       "      <td>2084</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>pw01_100.6</td>\n",
       "      <td>2032</td>\n",
       "      <td>1946</td>\n",
       "      <td>96</td>\n",
       "      <td>2005</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>pw01_100.7</td>\n",
       "      <td>2074</td>\n",
       "      <td>1977</td>\n",
       "      <td>95</td>\n",
       "      <td>2066</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>pw01_100.8</td>\n",
       "      <td>2022</td>\n",
       "      <td>1909</td>\n",
       "      <td>94</td>\n",
       "      <td>1988</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>pw01_100.9</td>\n",
       "      <td>2005</td>\n",
       "      <td>1925</td>\n",
       "      <td>96</td>\n",
       "      <td>1984</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Название графа  Решение  GW Mean  % Mean  GW Max  % Max\n",
       "0     pw01_100.0     2019     1921      95    1975     98\n",
       "1     pw01_100.1     2060     1962      95    2050    100\n",
       "2     pw01_100.2     2032     1924      95    1998     98\n",
       "3     pw01_100.3     2067     1969      95    2045     99\n",
       "4     pw01_100.4     2039     1934      95    2013     99\n",
       "5     pw01_100.5     2108     1997      95    2084     99\n",
       "6     pw01_100.6     2032     1946      96    2005     99\n",
       "7     pw01_100.7     2074     1977      95    2066    100\n",
       "8     pw01_100.8     2022     1909      94    1988     98\n",
       "9     pw01_100.9     2005     1925      96    1984     99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 35.8 s, sys: 2.96 s, total: 38.7 s\n",
      "Wall time: 34.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df, mean, max_mean = get_results(70, 80)\n",
    "print('Средняя точность: %d%%' % mean)\n",
    "print('Средняя точность (если брать лучший результат по нескольким запускам): %d%%' % max_mean)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Вывод\n",
    "Алгоритм в среднем работает с высокой (значительно большей теоритически полученной) точностью для графов с положительными весами ребер. Для графов с произвольными весами ребер алгоритм в среднем работает с точностью близкой к теоритической. Если же брать не средний, а лучший результат по нескольким запускам, то алгоритм всегда работает с достаточно высокой точностью. Кроме того, можно заметить, что на более плотных графах алгоритм может работать дольше (это хорошо видно особенно на последних двух запусках) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P.S.\n",
    "Ранее мы обозначили $\\alpha_{GW} := \\min _{0<\\vartheta<\\pi} \\frac{2 \\vartheta }{(1-\\cos \\vartheta) \\pi}$. Это число и было точностью нашего алгоритма. Покажем, что оно действительно примерно равно $0.878$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8785672057848526"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.linspace(0 + 1e-8, np.pi, 1e7)\n",
    "min(2 * theta / ((1 - np.cos(theta)) * np.pi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Список литературы\n",
    "* Оригинальная статья http://www-math.mit.edu/~goemans/PAPERS/maxcut-jacm.pdf\n",
    "* Лекция (Михаил Вялый) https://youtu.be/RNYfcl3hxUk, https://docplayer.ru/58779485-Priblizhennoe-reshenie-zadach-kombinatornoy-optimizacii-algoritmy-i-trudnost-lekciya-4-sdp-relaksacii-i-algoritm-gyomansa-vilyamsona.html\n",
    "* Лекция (Александр Катруца) https://github.com/amkatrutsa/optimization-fivt/blob/master/13-SDP/lecture13.pdf\n",
    "* Graphs and Graph Laplacians https://www.cis.upenn.edu/~cis515/cis515-14-graphlap.pdf"
   ]
  }
 ],
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