{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#概要\" data-toc-modified-id=\"概要-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>概要</a></span></li><li><span><a href=\"#pythonの標準関数による解法\" data-toc-modified-id=\"pythonの標準関数による解法-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>pythonの標準関数による解法</a></span></li><li><span><a href=\"#二分法とNewton法の原理\" data-toc-modified-id=\"二分法とNewton法の原理-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>二分法とNewton法の原理</a></span><ul class=\"toc-item\"><li><span><a href=\"#二分法(bisection)\" data-toc-modified-id=\"二分法(bisection)-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>二分法(bisection)</a></span></li><li><span><a href=\"#Newton法(あるいはNewton-Raphson法)\" data-toc-modified-id=\"Newton法(あるいはNewton-Raphson法)-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Newton法(あるいはNewton-Raphson法)</a></span></li></ul></li><li><span><a href=\"#二分法とNewton法のコード\" data-toc-modified-id=\"二分法とNewton法のコード-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>二分法とNewton法のコード</a></span><ul class=\"toc-item\"><li><span><a href=\"#二分法(bisection)\" data-toc-modified-id=\"二分法(bisection)-4.1\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>二分法(bisection)</a></span></li><li><span><a href=\"#Newton法(あるいはNewton-Raphson法)\" data-toc-modified-id=\"Newton法(あるいはNewton-Raphson法)-4.2\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>Newton法(あるいはNewton-Raphson法)</a></span></li></ul></li><li><span><a href=\"#収束性と安定性\" data-toc-modified-id=\"収束性と安定性-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>収束性と安定性</a></span></li><li><span><a href=\"#収束判定条件\" data-toc-modified-id=\"収束判定条件-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>収束判定条件</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#$\\epsilon,-\\delta$を説明するための図\" data-toc-modified-id=\"$\\epsilon,-\\delta$を説明するための図-6.0.0.1\"><span class=\"toc-item-num\">6.0.0.1&nbsp;&nbsp;</span>$\\epsilon, \\delta$を説明するための図</a></span></li></ul></li></ul></li></ul></li><li><span><a href=\"#2変数関数の場合\" data-toc-modified-id=\"2変数関数の場合-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>2変数関数の場合</a></span></li><li><span><a href=\"#2020年度課題(中筋さんありがとう)\" data-toc-modified-id=\"2020年度課題(中筋さんありがとう)-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>2020年度課題(中筋さんありがとう)</a></span></li><li><span><a href=\"#例題:二分法とNewton法の収束性\" data-toc-modified-id=\"例題:二分法とNewton法の収束性-9\"><span class=\"toc-item-num\">9&nbsp;&nbsp;</span>例題:二分法とNewton法の収束性</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#解答例\" data-toc-modified-id=\"解答例-9.0.1\"><span class=\"toc-item-num\">9.0.1&nbsp;&nbsp;</span>解答例</a></span></li></ul></li><li><span><a href=\"#exp関数に関する注意\" data-toc-modified-id=\"exp関数に関する注意-9.1\"><span class=\"toc-item-num\">9.1&nbsp;&nbsp;</span>exp関数に関する注意</a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<br />\n",
    "\n",
    "<div style=\"text-align: center;\">\n",
    "<font size=\"7\">代数方程式(fsolve)</font>\n",
    "</div>\n",
    "<br />\n",
    "<div style=\"text-align: right;\">\n",
    "<font size=\"4\">file:/Users/bob/Github/TeamNishitani/jupyter_num_calc/fsolve</font>\n",
    "<br />\n",
    "<font size=\"4\">https://github.com/daddygongon/jupyter_num_calc/tree/master/notebooks_python</font>\n",
    "<br />\n",
    "<font size=\"4\">cc by Shigeto R. Nishitani 2017-21</font>\n",
    "</div>\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 概要\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "代数方程式の解$f(x)=0$を数値的に求めることを考える．標準的な\n",
    "> 二分法(bisection method)とニュートン法(Newton's method)\n",
    "\n",
    "の考え方と例を説明し，\n",
    ">収束性(convergency)と安定性(stability)\n",
    "\n",
    "について議論する．さらに収束判定条件について言及する．\n",
    "\n",
    "\n",
    "二分法のアイデアは単純．中間値の定理より連続な関数では，関数の符号が変わる二つの変数の間には根が必ず存在する．したがって，この方法は収束性は決して高くはないが，\n",
    "確実．一方，Newton法は関数の微分を用いて収束性を速めた方法である．しかし，不幸にして収束しない場合や微分に時間がかかる場合があり，初期値や使用対象には注意\n",
    "を要する．\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pythonの標準関数による解法\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pythonでは代数方程式の解は，solveで求まる．\n",
    "\n",
    "$$\n",
    "x^2-4x+1 = 0\n",
    "$$\n",
    "の解を考える．未知の問題では時として異常な振る舞いをする関数を相手にすることがあるので，先ずは関数の概形を見ることを常に心がけるべき．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "\n",
    "def func(x):\n",
    "  return x**2-4*x+1\n",
    "\n",
    "x = np.linspace(-1, 5, 100)  #0から2πまでの範囲を100分割したnumpy配列\n",
    "y = func(x)\n",
    "plt.plot(x, y, color = 'b')\n",
    "\n",
    "plt.plot(0, 0, \"o\", color = 'k')\n",
    "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n",
    "plt.hlines(0, -1, 5, color='k', linestyle='-', linewidth=2)\n",
    "plt.vlines(0, -4, 6, color='k', linestyle='-', linewidth=2)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "もし，解析解が容易に求まるなら，その結果を使うほうがよい．\n",
    "pythonの解析解を求めるsolveは，sympyから呼び出して，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 - √3, √3 + 2]\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "\n",
    "def func(x):\n",
    "  return x**2-4*x+1\n",
    "\n",
    "pprint(solve(func(x), x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "と即座に求めてくれる．数値解は以下の通り求められる．\n",
    "コメントを外してみてください．ちょっと注意が必要ということがわかるでしょうか？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.26794919]\n",
      "[0.26794919 3.73205081]\n",
      "[0.26794919 0.26794919]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fsolve\n",
    "def func(x):\n",
    "  return x**2-4*x+1\n",
    "\n",
    "pprint(fsolve(func, 0))\n",
    "# pprint(fsolve(func, 2.0))\n",
    "pprint(fsolve(func, [0, 5]))\n",
    "pprint(fsolve(func, [0, 0.8]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 二分法とNewton法の原理\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二分法(bisection) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "二分法は領域の端$x_1, x_2$で関数値$f(x_1),f(x_2)$を求め，中間の値を次々に計算して，解を囲い込んでいく方法である．\n",
    "\n",
    "|$x_1$ | $x_2$ |$f(x_1)$ | $f(x_2)$  |\n",
    "|:----|:----|:----|:----|\n",
    "|0.0 | 0.8 |　　　　　 |　　　　　  |\n",
    "|　　　　|  　　　　|  　　　　| 　　　　 |\n",
    "|　　　　|  　　　　|  　　　　| 　　　　 |\n",
    "|　　　　|  　　　　|  　　　　| 　　　　 |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def func(x):\n",
    "    return x**2-4*x+1\n",
    "\n",
    "x = np.linspace(0, 0.8, 100)  #0から2πまでの範囲を100分割したnumpy配列\n",
    "y = func(x)\n",
    "plt.plot(x, y)\n",
    "\n",
    "plt.plot(0, func(0), \"o\", color = 'r')\n",
    "plt.plot(0.8, func(0.8), \"o\", color = 'r')\n",
    "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n",
    "plt.hlines(0, 0, 0.8, color='k', linestyle='-', linewidth=2)\n",
    "plt.vlines(0, -2, 1, color='k', linestyle='-', linewidth=2)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton法(あるいはNewton-Raphson法) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Newton法は最初の点$x_1$から接線をひき，それが$x$軸(y=0)と交わった点を新たな点$x_2$とする．さらにそこでの接線を求めて...\n",
    "\n",
    "という操作を繰り返しながら解を求める方法である．関数の微分をdf(x)とすると，これらの間には\n",
    "\n",
    "|　　　$x_{i+1} = x_i + \\ldots$　　　|\n",
    "|:----|\n",
    "|　　　　　　　|\n",
    "という関係が成り立つ．\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2⋅x - 4\n",
      "-2.0⋅x\n",
      "0 -2.00000000000000\n",
      "1.00000000000000 -3.00000000000000\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "\n",
    "def func(x):\n",
    "    return x**2-4*x+1\n",
    "\n",
    "def df(x):\n",
    "    return diff(func(x), x)\n",
    "\n",
    "pprint(df(x))\n",
    "\n",
    "x1 = 1.0\n",
    "df(x).subs(x, x1)*(x-x1)+func(x1)\n",
    "\n",
    "def line_f(x, x1):\n",
    "    return df(x).subs(x, x1)*(x-x1)+func(x1)\n",
    "\n",
    "\n",
    "pprint(line_f(x, 1.0))\n",
    "x0 = 0.0\n",
    "x1 = 1.0\n",
    "\n",
    "y0 = line_f(x, x1).subs(x, x0)\n",
    "y1 = line_f(x, x1).subs(x, x1)\n",
    "print(y0, y1)\n",
    "\n",
    "yy0 = line_f(x, x0).subs(x, x0)\n",
    "yy1 = line_f(x, x0).subs(x, x1)\n",
    "print(yy0, yy1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(x0-0.05, x1+0.05, 100)\n",
    "y = func(x)\n",
    "plt.plot(x, y)\n",
    "\n",
    "plt.plot(x0, func(x0), \"o\", color = 'r')\n",
    "plt.plot(x1, func(x1), \"o\", color = 'r')\n",
    "# plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)\n",
    "plt.hlines(0, x0, x1, color='k', linestyle='-', linewidth=2)\n",
    "plt.vlines(0, -3.5,1.5, color='k', linestyle='-', linewidth=2)\n",
    "\n",
    "plt.plot([x0, x1], [y0, y1], color='b', linestyle='--', linewidth=1)\n",
    "plt.plot([x0, x1], [yy0, yy1], color='r', linestyle='--', linewidth=1)\n",
    "\n",
    "plt.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "|$x_1$ |$f(x_1)$ | $df(x_1)$  |\n",
    "|:----|:----|:----|\n",
    "|1.0　| 　　　　 | 　　　　  |\n",
    "|　　　　　　　| 　　　　　　　 | 　　　　　　　  |\n",
    "|　　　　　　　| 　　　　　　　 | 　　　　　　　  |\n",
    "|　　　　　　　| 　　　　　　　 | 　　　　　　　  |\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 二分法とNewton法のコード\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 二分法(bisection) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1     x2     f1     f2    \n",
      "0.000  0.800  1.000  -1.560\n",
      "0.000  0.400  1.000  -0.440\n",
      "0.200  0.400  0.240  -0.440\n",
      "0.200  0.300  0.240  -0.110\n",
      "0.250  0.300  0.062  -0.110\n",
      "0.250  0.275  0.062  -0.024\n"
     ]
    }
   ],
   "source": [
    "x1, x2 = 0.0, 0.8\n",
    "f1, f2 = func(x1), func(x2)\n",
    "print('%-6s %-6s %-6s %-6s'  % ('x1','x2','f1','f2'))\n",
    "print('%-6.3f %-6.3f %-6.3f %-6.3f' % (x1,x2,f1,f2))\n",
    "for i in range(0, 5):\n",
    "    x = (x1 + x2)/2\n",
    "    f = func(x)\n",
    "    if (f*f1>=0.0):\n",
    "        x1, f1 = x, f\n",
    "    else:\n",
    "        x2, f2 = x, f\n",
    "    print('%-6.3f %-6.3f %-6.3f %-6.3f' % (x1,x2,f1,f2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Newton法(あるいはNewton-Raphson法) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "def func(x):\n",
    "    return x**2-4*x+1\n",
    "def df(x):\n",
    "    return diff(func(x), x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000    -2.0000000000000000000000000\n",
      "0.0000000000    1.0000000000000000000000000\n",
      "0.2500000000    0.0625000000000000000000000\n",
      "0.2678571429    0.0003188775510204081378197\n",
      "0.2679491900    0.0000000084726737969074341\n",
      "0.2679491924    0.0000000000000000059821834\n"
     ]
    }
   ],
   "source": [
    "x1 = 1.0\n",
    "f1 = func(x1)\n",
    "print('%-15.10f %-24.25f' % (x1,f1))\n",
    "for i in range(0, 5):\n",
    "    x1 = x1 - f1 / df(x).subs(x,x1)\n",
    "    f1 =func(x1)\n",
    "    print('%-15.10f %-24.25f' % (x1,f1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 収束性と安定性"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "実際のコードの出力からも分かる通り，解の収束の速さは2つの手法で極端に違う．2分法では一回の操作で解の区間が半分になる．このように繰り返しごとに誤差幅が前回の誤差幅の定数($<1$)倍になる方法は1次収束(linear convergence)するという．Newton法では関数・初期値が素直な場合($f^{\\prime}(x) <> 0$)に，収束が誤差の2乗に比例する2次収束を示す．以下はその導出をMapleで示した．\n",
    "\n",
    "\n",
    "```maple\n",
    "> restart; ff:=subs(xi-x[f]=ei,series(f(xi),xi=x[f],4));\n",
    "```\n",
    "\n",
    "$$\n",
    "{\\it ff}\\, := \\,f \\left( x_{{f}} \\right) +D \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei}+\\frac{1}{2}\\,  D^{ \\left( 2 \\right) }   \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2} +\\frac{1}{6}\\, \n",
    "D^{ \\left( 3 \\right) }   \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{3}+O \\left( {{\\it ei}}^{4} \\right)\n",
    "$$\n",
    "```maple\n",
    "> dff:=subs({0=x[f],x=ei},series(diff(f(x),x),x,3));\n",
    "```\n",
    "$$\n",
    "{\\it dff}\\, := \\,D \\left( f \\right)  \\left( x_{{f}} \\right) + \n",
    "D^{ \\left( 2 \\right) } \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei}+\n",
    "\\frac{1}{2}\\, D^{ \\left( 3 \\right) } \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2} +O \\left( {{\\it ei}}^{3} \\right)\n",
    "$$\n",
    "```maple\n",
    "> ei1:=ei-ff/dff;\n",
    "```\n",
    "$$\n",
    "{\\it ei1}\\, := \\,{\\it ei}-{\\frac {f \\left( x_{{f}} \\right) +D \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei}+\\frac{1}{2}\\,  D^{ \\left( 2 \\right) }  \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2}+\\frac{1}{6}\\,  D^{ \\left( 3 \\right) }   \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{3}+O \\left( {{\\it ei}}^{4} \\right) }{D \\left( f \\right)  \\left( x_{{f}} \\right) +  D^{ \\left( 2 \\right) }  \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei} +\\frac{1}{2}\\, D^{ \\left( 3 \\right) } \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2}+O \\left( {{\\it ei}}^{3} \\right) }}\n",
    "$$\n",
    "```maple\n",
    "> ei2:=simplify(convert(ei1,polynom));\n",
    "```\n",
    "$$\n",
    "{\\it ei2}\\, := \\,\\frac{1}{3}\\,\\frac {3\\, D^{ \\left( 2 \\right) }  \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2}+2\\, D^{ \\left( 3 \\right) } \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{3}\n",
    "-6\\,f \\left( x_{{f}} \\right) }{2\\,D \\left( f \\right)  \\left( x_{{f}} \\right) +2\\, D^{ \\left( 2 \\right) }   \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei}+ D^{ \\left( 3 \\right) } \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2}\n",
    "}\n",
    "$$\n",
    "```maple\n",
    "> ei3:=series(ei2,ei,3);\n",
    "```\n",
    "$$\n",
    "{\\it ei3}\\, := \\,-{\\frac {f \\left( x_{{f}} \\right) }{D \\left( f \\right)  \\left( x_{{f}} \\right) }}+{\\frac {f \\left( x_{{f}} \\right)  \\left( D^{ \\left( 2 \\right) } \\right)  \\left( f \\right)  \\left( x_{{f}} \\right) {\\it ei}}{ \\left( D \\left( f \\right)  \\left( x_{{f}} \\right)  \\right) ^{2}}}+  \\\\\n",
    "\\frac{1}{6}\\, \\frac{ 3\\, \\left( D^{ \\left( 2 \\right) } \\right)  \\left( f \\right)  \\left( x_{{f}} \\right) +3\\,{\\frac {f \\left( x_{{f}} \\right)  \\left( D^{ \\left( 3 \\right) } \\right)  \\left( f \\right)  \\left( x_{{f}} \\right) }{D \\left( f \\right)  \\left( x_{{f}} \\right) }}-6\\,{\\frac {f \\left( x_{{f}} \\right)  \\left(  \\left( D^{ \\left( 2 \\right) } \\right)  \\left( f \\right)  \\left( x_{{f}} \\right)  \\right) ^{2}}{ \\left( D \\left( f \\right)  \\left( x_{{f}} \\right)  \\right) ^{2}}}}\n",
    "{ \\left( D \\left( f \\right)  \\left( x_{{f}} \\right)  \\right)}{{\\it ei}}^{2} +O \\left( {{\\it ei}}^{3} \\right)\n",
    "$$\n",
    "```maple\n",
    "> subs(f(x[f])=0,ei3);\n",
    "```\n",
    "$$\n",
    "\\frac{1}{2}\\,{\\frac {  D^{ \\left( 2 \\right) }   \\left( f \\right)  \\left( x_{{f}} \\right) {{\\it ei}}^{2}}{D \\left( f \\right)  \\left( x_{{f}} \\right) }}+O \\left( {{\\it ei}}^{3} \\right)\n",
    "$$\n",
    "注意すべきは，この収束性には一回の計算時間の差は入っていないことである．Newton法で解析的に微分が求まらない場合，数値的に求めるという手法がとられるが，これにかかる計算時間はばかにできない．二分法を改良した割線法(secant method)がより速い場合がある(NumRecipe9章参照)．\n",
    "\n",
    "二分法では，収束は遅いが，正負の関数値の間に連続関数では必ず解が存在するという意味で解が保証されている．しかし，Newton法では，収束は速いが，必ずしも素直に解に収束するとは限らない．解を確実に囲い込む，あるいは解に近い値を初期値に選ぶ手法が種々考案されている．解が安定であるかどうかは，問題，解法，初期値に大きく依存する．収束性と安定性のコントロールが数値計算のツボとなる．\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 収束判定条件\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "どこまで値が解に近づけば計算を打ち切るかを決める条件を収束判定条件と呼ぶ．以下のような条件がある．\n",
    "\n",
    "\n",
    "|手法|判定条件|解説\n",
    "|:----|:----|:----|\n",
    "|$\\varepsilon$(イプシロン，epsilon)法 |\n",
    "|$\\delta$(デルタ，delta)法 |\n",
    "|占部法 | $\\left|f(x_{i+1})\\right| > \\left|f(x_i)\\right|$ | 数値計算の際の丸め誤差までも含めて判定する条件\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### $\\epsilon, \\delta$を説明するための図 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def func(x):\n",
    "    return 0.4*(x**2-4*x+1)\n",
    "x1=0.25\n",
    "x0=0.4\n",
    "x = np.linspace(0.2, 0.4, 100)\n",
    "y = func(x)\n",
    "plt.plot(x, y, color = 'k')\n",
    "plt.plot(x1, func(x1), \"o\", color = 'r')\n",
    "plt.plot(x0, func(x0), \"o\", color = 'r')\n",
    "plt.plot([0.2,0.45],[0,0], color = 'k')\n",
    "plt.plot([x1,x0],[func(x1),func(x1)], color = 'b')\n",
    "plt.plot([x0,x0],[func(x0),func(x1)], color = 'b')\n",
    "\n",
    "plt.text(0.41, -0.07, r'$\\epsilon$', size='24') \n",
    "plt.text(0.32, 0.05, r'$\\delta$', size='24') \n",
    "\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2変数関数の場合\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "2変数の関数では，解を求める一般的な手法は無い．この様子は実際に2変数の関数で構成される面の様子をみれば納得されよう．\n",
    "```maple\n",
    "> restart;\n",
    "> f:=(x,y)->4*x+2*y-6*x*y; g:=(x,y)->10*x-2*y+1;\n",
    "```\n",
    "$$\n",
    "f\\, := \\,( {x,y} )\\mapsto 4\\,x+2\\,y-6\\,xy  \\\\\n",
    "g\\, := \\,( {x,y} )\\mapsto 10\\,x-2\\,y+1 \n",
    "$$\n",
    "```maple\n",
    "> p1:=plot3d({f(x,y)},x=-2..2,y=-2..2,color=red):\n",
    "  p2:=plot3d({g(x,y)},x=-2..2,y=-2..2,color=blue):\n",
    "  p3:=plot3d({0},x=-2..2,y=-2..2,color=gray):\n",
    "  with(plots):\n",
    "  display([p1,p2,p3],axes=boxed,orientation=[-150,70]);\n",
    "```\n",
    "\n",
    "\n",
    "解のある程度近くからは，Newton法で効率良く求められる．\n",
    "```maple\n",
    "> fsolve({f(x,y)=0,g(x,y)=0},{x,y});\n",
    "```\n",
    "$$\n",
    "\\left\\{ x=- 0.07540291160,y= 0.1229854420 \\right\\}\n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": "/* Put everything inside the global mpl namespace */\n/* global mpl */\nwindow.mpl = {};\n\nmpl.get_websocket_type = function () {\n    if (typeof WebSocket !== 'undefined') {\n        return WebSocket;\n    } else if (typeof MozWebSocket !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert(\n            'Your browser does not have WebSocket support. ' +\n                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. ' +\n                'Performance may be slow.';\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = document.createElement('div');\n    this.root.setAttribute('style', 'display: inline-block');\n    this._root_extra_style(this.root);\n\n    parent_element.appendChild(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen = function () {\n        fig.send_message('supports_binary', { value: fig.supports_binary });\n        fig.send_message('send_image_mode', {});\n        if (fig.ratio !== 1) {\n            fig.send_message('set_device_pixel_ratio', {\n                device_pixel_ratio: fig.ratio,\n            });\n        }\n        fig.send_message('refresh', {});\n    };\n\n    this.imageObj.onload = function () {\n        if (fig.image_mode === 'full') {\n            // Full images could contain transparency (where diff images\n            // almost always do), so we need to clear the canvas so that\n            // there is no ghosting.\n            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n        }\n        fig.context.drawImage(fig.imageObj, 0, 0);\n    };\n\n    this.imageObj.onunload = function () {\n        fig.ws.close();\n    };\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n};\n\nmpl.figure.prototype._init_header = function () {\n    var titlebar = document.createElement('div');\n    titlebar.classList =\n        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n    var titletext = document.createElement('div');\n    titletext.classList = 'ui-dialog-title';\n    titletext.setAttribute(\n        'style',\n        'width: 100%; text-align: center; padding: 3px;'\n    );\n    titlebar.appendChild(titletext);\n    this.root.appendChild(titlebar);\n    this.header = titletext;\n};\n\nmpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._init_canvas = function () {\n    var fig = this;\n\n    var canvas_div = (this.canvas_div = document.createElement('div'));\n    canvas_div.setAttribute(\n        'style',\n        'border: 1px solid #ddd;' +\n            'box-sizing: content-box;' +\n            'clear: both;' +\n            'min-height: 1px;' +\n            'min-width: 1px;' +\n            'outline: 0;' +\n            'overflow: hidden;' +\n            'position: relative;' +\n            'resize: both;'\n    );\n\n    function on_keyboard_event_closure(name) {\n        return function (event) {\n            return fig.key_event(event, name);\n        };\n    }\n\n    canvas_div.addEventListener(\n        'keydown',\n        on_keyboard_event_closure('key_press')\n    );\n    canvas_div.addEventListener(\n        'keyup',\n        on_keyboard_event_closure('key_release')\n    );\n\n    this._canvas_extra_style(canvas_div);\n    this.root.appendChild(canvas_div);\n\n    var canvas = (this.canvas = document.createElement('canvas'));\n    canvas.classList.add('mpl-canvas');\n    canvas.setAttribute('style', 'box-sizing: content-box;');\n\n    this.context = canvas.getContext('2d');\n\n    var backingStore =\n        this.context.backingStorePixelRatio ||\n        this.context.webkitBackingStorePixelRatio ||\n        this.context.mozBackingStorePixelRatio ||\n        this.context.msBackingStorePixelRatio ||\n        this.context.oBackingStorePixelRatio ||\n        this.context.backingStorePixelRatio ||\n        1;\n\n    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n\n    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n        'canvas'\n    ));\n    rubberband_canvas.setAttribute(\n        'style',\n        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n    );\n\n    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n    if (this.ResizeObserver === undefined) {\n        if (window.ResizeObserver !== undefined) {\n            this.ResizeObserver = window.ResizeObserver;\n        } else {\n            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n            this.ResizeObserver = obs.ResizeObserver;\n        }\n    }\n\n    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n        var nentries = entries.length;\n        for (var i = 0; i < nentries; i++) {\n            var entry = entries[i];\n            var width, height;\n            if (entry.contentBoxSize) {\n                if (entry.contentBoxSize instanceof Array) {\n                    // Chrome 84 implements new version of spec.\n                    width = entry.contentBoxSize[0].inlineSize;\n                    height = entry.contentBoxSize[0].blockSize;\n                } else {\n                    // Firefox implements old version of spec.\n                    width = entry.contentBoxSize.inlineSize;\n                    height = entry.contentBoxSize.blockSize;\n                }\n            } else {\n                // Chrome <84 implements even older version of spec.\n                width = entry.contentRect.width;\n                height = entry.contentRect.height;\n            }\n\n            // Keep the size of the canvas and rubber band canvas in sync with\n            // the canvas container.\n            if (entry.devicePixelContentBoxSize) {\n                // Chrome 84 implements new version of spec.\n                canvas.setAttribute(\n                    'width',\n                    entry.devicePixelContentBoxSize[0].inlineSize\n                );\n                canvas.setAttribute(\n                    'height',\n                    entry.devicePixelContentBoxSize[0].blockSize\n                );\n            } else {\n                canvas.setAttribute('width', width * fig.ratio);\n                canvas.setAttribute('height', height * fig.ratio);\n            }\n            canvas.setAttribute(\n                'style',\n                'width: ' + width + 'px; height: ' + height + 'px;'\n            );\n\n            rubberband_canvas.setAttribute('width', width);\n            rubberband_canvas.setAttribute('height', height);\n\n            // And update the size in Python. We ignore the initial 0/0 size\n            // that occurs as the element is placed into the DOM, which should\n            // otherwise not happen due to the minimum size styling.\n            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n                fig.request_resize(width, height);\n            }\n        }\n    });\n    this.resizeObserverInstance.observe(canvas_div);\n\n    function on_mouse_event_closure(name) {\n        return function (event) {\n            return fig.mouse_event(event, name);\n        };\n    }\n\n    rubberband_canvas.addEventListener(\n        'mousedown',\n        on_mouse_event_closure('button_press')\n    );\n    rubberband_canvas.addEventListener(\n        'mouseup',\n        on_mouse_event_closure('button_release')\n    );\n    rubberband_canvas.addEventListener(\n        'dblclick',\n        on_mouse_event_closure('dblclick')\n    );\n    // Throttle sequential mouse events to 1 every 20ms.\n    rubberband_canvas.addEventListener(\n        'mousemove',\n        on_mouse_event_closure('motion_notify')\n    );\n\n    rubberband_canvas.addEventListener(\n        'mouseenter',\n        on_mouse_event_closure('figure_enter')\n    );\n    rubberband_canvas.addEventListener(\n        'mouseleave',\n        on_mouse_event_closure('figure_leave')\n    );\n\n    canvas_div.addEventListener('wheel', function (event) {\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        on_mouse_event_closure('scroll')(event);\n    });\n\n    canvas_div.appendChild(canvas);\n    canvas_div.appendChild(rubberband_canvas);\n\n    this.rubberband_context = rubberband_canvas.getContext('2d');\n    this.rubberband_context.strokeStyle = '#000000';\n\n    this._resize_canvas = function (width, height, forward) {\n        if (forward) {\n            canvas_div.style.width = width + 'px';\n            canvas_div.style.height = height + 'px';\n        }\n    };\n\n    // Disable right mouse context menu.\n    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n        event.preventDefault();\n        return false;\n    });\n\n    function set_focus() {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'mpl-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'mpl-button-group';\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'mpl-button-group';\n            continue;\n        }\n\n        var button = (fig.buttons[name] = document.createElement('button'));\n        button.classList = 'mpl-widget';\n        button.setAttribute('role', 'button');\n        button.setAttribute('aria-disabled', 'false');\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n\n        var icon_img = document.createElement('img');\n        icon_img.src = '_images/' + image + '.png';\n        icon_img.srcset = '_images/' + image + '_large.png 2x';\n        icon_img.alt = tooltip;\n        button.appendChild(icon_img);\n\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    var fmt_picker = document.createElement('select');\n    fmt_picker.classList = 'mpl-widget';\n    toolbar.appendChild(fmt_picker);\n    this.format_dropdown = fmt_picker;\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = document.createElement('option');\n        option.selected = fmt === mpl.default_extension;\n        option.innerHTML = fmt;\n        fmt_picker.appendChild(option);\n    }\n\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n};\n\nmpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', { width: x_pixels, height: y_pixels });\n};\n\nmpl.figure.prototype.send_message = function (type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n};\n\nmpl.figure.prototype.send_draw_message = function () {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n};\n\nmpl.figure.prototype.handle_resize = function (fig, msg) {\n    var size = msg['size'];\n    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1], msg['forward']);\n        fig.send_message('refresh', {});\n    }\n};\n\nmpl.figure.prototype.handle_rubberband = function (fig, msg) {\n    var x0 = msg['x0'] / fig.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n    var x1 = msg['x1'] / fig.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0,\n        0,\n        fig.canvas.width / fig.ratio,\n        fig.canvas.height / fig.ratio\n    );\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n};\n\nmpl.figure.prototype.handle_figure_label = function (fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n};\n\nmpl.figure.prototype.handle_cursor = function (fig, msg) {\n    fig.rubberband_canvas.style.cursor = msg['cursor'];\n};\n\nmpl.figure.prototype.handle_message = function (fig, msg) {\n    fig.message.textContent = msg['message'];\n};\n\nmpl.figure.prototype.handle_draw = function (fig, _msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n};\n\nmpl.figure.prototype.handle_image_mode = function (fig, msg) {\n    fig.image_mode = msg['mode'];\n};\n\nmpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n    for (var key in msg) {\n        if (!(key in fig.buttons)) {\n            continue;\n        }\n        fig.buttons[key].disabled = !msg[key];\n        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n    }\n};\n\nmpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n    if (msg['mode'] === 'PAN') {\n        fig.buttons['Pan'].classList.add('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    } else if (msg['mode'] === 'ZOOM') {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.add('active');\n    } else {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    }\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Called whenever the canvas gets updated.\n    this.send_message('ack', {});\n};\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function (fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            var img = evt.data;\n            if (img.type !== 'image/png') {\n                /* FIXME: We get \"Resource interpreted as Image but\n                 * transferred with MIME type text/plain:\" errors on\n                 * Chrome.  But how to set the MIME type?  It doesn't seem\n                 * to be part of the websocket stream */\n                img.type = 'image/png';\n            }\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src\n                );\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                img\n            );\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        } else if (\n            typeof evt.data === 'string' &&\n            evt.data.slice(0, 21) === 'data:image/png;base64'\n        ) {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig['handle_' + msg_type];\n        } catch (e) {\n            console.log(\n                \"No handler for the '\" + msg_type + \"' message type: \",\n                msg\n            );\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\n                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n                    e,\n                    e.stack,\n                    msg\n                );\n            }\n        }\n    };\n};\n\n// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\nmpl.findpos = function (e) {\n    //this section is from http://www.quirksmode.org/js/events_properties.html\n    var targ;\n    if (!e) {\n        e = window.event;\n    }\n    if (e.target) {\n        targ = e.target;\n    } else if (e.srcElement) {\n        targ = e.srcElement;\n    }\n    if (targ.nodeType === 3) {\n        // defeat Safari bug\n        targ = targ.parentNode;\n    }\n\n    // pageX,Y are the mouse positions relative to the document\n    var boundingRect = targ.getBoundingClientRect();\n    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n\n    return { x: x, y: y };\n};\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * https://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys(original) {\n    return Object.keys(original).reduce(function (obj, key) {\n        if (typeof original[key] !== 'object') {\n            obj[key] = original[key];\n        }\n        return obj;\n    }, {});\n}\n\nmpl.figure.prototype.mouse_event = function (event, name) {\n    var canvas_pos = mpl.findpos(event);\n\n    if (name === 'button_press') {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    var x = canvas_pos.x * this.ratio;\n    var y = canvas_pos.y * this.ratio;\n\n    this.send_message(name, {\n        x: x,\n        y: y,\n        button: event.button,\n        step: event.step,\n        guiEvent: simpleKeys(event),\n    });\n\n    /* This prevents the web browser from automatically changing to\n     * the text insertion cursor when the button is pressed.  We want\n     * to control all of the cursor setting manually through the\n     * 'cursor' event from matplotlib */\n    event.preventDefault();\n    return false;\n};\n\nmpl.figure.prototype._key_event_extra = function (_event, _name) {\n    // Handle any extra behaviour associated with a key event\n};\n\nmpl.figure.prototype.key_event = function (event, name) {\n    // Prevent repeat events\n    if (name === 'key_press') {\n        if (event.key === this._key) {\n            return;\n        } else {\n            this._key = event.key;\n        }\n    }\n    if (name === 'key_release') {\n        this._key = null;\n    }\n\n    var value = '';\n    if (event.ctrlKey && event.key !== 'Control') {\n        value += 'ctrl+';\n    }\n    else if (event.altKey && event.key !== 'Alt') {\n        value += 'alt+';\n    }\n    else if (event.shiftKey && event.key !== 'Shift') {\n        value += 'shift+';\n    }\n\n    value += 'k' + event.key;\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n    return false;\n};\n\nmpl.figure.prototype.toolbar_button_onclick = function (name) {\n    if (name === 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message('toolbar_button', { name: name });\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n    this.message.textContent = tooltip;\n};\n\n///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n// prettier-ignore\nvar _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n\nmpl.default_extension = \"png\";/* global mpl */\n\nvar comm_websocket_adapter = function (comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.binaryType = comm.kernel.ws.binaryType;\n    ws.readyState = comm.kernel.ws.readyState;\n    function updateReadyState(_event) {\n        if (comm.kernel.ws) {\n            ws.readyState = comm.kernel.ws.readyState;\n        } else {\n            ws.readyState = 3; // Closed state.\n        }\n    }\n    comm.kernel.ws.addEventListener('open', updateReadyState);\n    comm.kernel.ws.addEventListener('close', updateReadyState);\n    comm.kernel.ws.addEventListener('error', updateReadyState);\n\n    ws.close = function () {\n        comm.close();\n    };\n    ws.send = function (m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function (msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        var data = msg['content']['data'];\n        if (data['blob'] !== undefined) {\n            data = {\n                data: new Blob(msg['buffers'], { type: data['blob'] }),\n            };\n        }\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(data);\n    });\n    return ws;\n};\n\nmpl.mpl_figure_comm = function (comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = document.getElementById(id);\n    var ws_proxy = comm_websocket_adapter(comm);\n\n    function ondownload(figure, _format) {\n        window.open(figure.canvas.toDataURL());\n    }\n\n    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element;\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error('Failed to find cell for figure', id, fig);\n        return;\n    }\n    fig.cell_info[0].output_area.element.on(\n        'cleared',\n        { fig: fig },\n        fig._remove_fig_handler\n    );\n};\n\nmpl.figure.prototype.handle_close = function (fig, msg) {\n    var width = fig.canvas.width / fig.ratio;\n    fig.cell_info[0].output_area.element.off(\n        'cleared',\n        fig._remove_fig_handler\n    );\n    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable();\n    fig.parent_element.innerHTML =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n    fig.close_ws(fig, msg);\n};\n\nmpl.figure.prototype.close_ws = function (fig, msg) {\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n};\n\nmpl.figure.prototype.push_to_output = function (_remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width / this.ratio;\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message('ack', {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () {\n        fig.push_to_output();\n    }, 1000);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'btn-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'btn-group';\n    var button;\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'btn-group';\n            continue;\n        }\n\n        button = fig.buttons[name] = document.createElement('button');\n        button.classList = 'btn btn-default';\n        button.href = '#';\n        button.title = name;\n        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    // Add the status bar.\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message pull-right';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n\n    // Add the close button to the window.\n    var buttongrp = document.createElement('div');\n    buttongrp.classList = 'btn-group inline pull-right';\n    button = document.createElement('button');\n    button.classList = 'btn btn-mini btn-primary';\n    button.href = '#';\n    button.title = 'Stop Interaction';\n    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n    button.addEventListener('click', function (_evt) {\n        fig.handle_close(fig, {});\n    });\n    button.addEventListener(\n        'mouseover',\n        on_mouseover_closure('Stop Interaction')\n    );\n    buttongrp.appendChild(button);\n    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n};\n\nmpl.figure.prototype._remove_fig_handler = function (event) {\n    var fig = event.data.fig;\n    if (event.target !== this) {\n        // Ignore bubbled events from children.\n        return;\n    }\n    fig.close_ws(fig, {});\n};\n\nmpl.figure.prototype._root_extra_style = function (el) {\n    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n};\n\nmpl.figure.prototype._canvas_extra_style = function (el) {\n    // this is important to make the div 'focusable\n    el.setAttribute('tabindex', 0);\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    } else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n};\n\nmpl.figure.prototype._key_event_extra = function (event, _name) {\n    // Check for shift+enter\n    if (event.shiftKey && event.which === 13) {\n        this.canvas_div.blur();\n        // select the cell after this one\n        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n        IPython.notebook.select(index + 1);\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    fig.ondownload(fig, null);\n};\n\nmpl.find_output_cell = function (html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i = 0; i < ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code') {\n            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] === html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n};\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel !== null) {\n    IPython.notebook.kernel.comm_manager.register_target(\n        'matplotlib',\n        mpl.mpl_figure_comm\n    );\n}\n",
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tuGeXi4TME8jat3+JPdDHNCkW/I9e/ZQW1ubkIn3BgGzq6UIh10ceuHyFRMTY92HwmnmEgHLzs6mgoIC26wLC7EzAYPaaENDA61Zs8ane+bOuubOCqfG4tbT00OITcTnzDHpOed78+lWW3IwJmCW3DbTTJoJmGm2wpoTYQJmzX3z9Kzl3A8xxv79+8dk4r1BwOxqKcJhF4feBQsWUGxsrKe3a9L6szMBs6s7LB6Ww4cPixgwK6V7UEveQJwR4wZ3XynnnqNoCdbvTOSUlCalD5ac66RzXjfHOtIYcoRx0j6sPLBbBJiAuYWIK7hAgAkYPx6GEGACZgg+2zR2lJ93dDM8ePAgIT8Sbs69EQNmV6KC3GY49EK+H4ms7VJAwj/++GPKysqiwsJCuyxLrMPOBMyuCc+xb0gdAAK2YsUKCgoKEntp1HXS8cFWY4VzJnmc780arwYmYNbYJ7POkgmYWXfGIvNiAmaRjfLyNJ3l56XhYMVBnBZuzkHSPB0Dhlt5HA7nzZtH8fHxXl6l77pvbm4mkNeSkhJKSEjw3cBeHmkqEDC7Jc/GI3HgwAHq6OgQIhx2KxAYwSUR3KQ98X4ySt7UpgzgfG+T/yQyAZv8PbDyDJiAWXn3TDB3JmAm2AQTTAHiGzhcO8ZNYFoQkoBlALfLODA4xlh4YtotLS3icDh37lxKTEz0RJem6MOu64IV9KOPPrKlBQyJs+HOZkcCBlfiU6dOic+x3YpegRFv4aDWdVKpnqPFDfFtuADLyMgQMW5KpO26664TlvZXXnlFk8iKtzCwSr9MwKyyU+acJxMwc+6LZWbFBMwyW+W1ieIggCB2WLicCRjce/CDQylulz1NwCDwsW/fPiouLqbk5GSvrdHXHbe2tor4uTlz5lBSUpKvh/faeBIBy8zMpKKiIq+NMxkd25mA4TMmqZlOBrbeHNOK8W1KeDiTsvb2dvEemTlzpng/KomWQOxn2rRp9OGHH3oTatv1zQTMdlvq0wUxAfMp3PYbjAmY/fZU64ok+Xm0k9QPpT5g/YIVDHm6QL5AwrTIWLubC9yioLQ4a9YsSk1NdVfdMr+3K7G0MwGza1JwfGjwGUM+P3yO7Vbg6isptdptbWos6SBlSIq+ZMkSeuONN+wGgVfXwwTMq/DavnMmYLbfYu8ukAmYd/G1Qu9y8vPSvOH+gjiwpUuXCoUxTxMwuEXt2rWLZsyYQenp6VaAS9UccXO9d+9e2xFLWEk3btwoXKKmT5+uCgurVLIzAdu9e7ewciOhut2Knd0r1Yj5gIDh8urKK6+k//f//p/dtter62EC5lV4bd85EzDbb7F3F8gEzLv4mr13Jfl5ad4IbscNc2lpKYWHh09wUTS6PrhF7dixQ7izwa3NLqWzs5Nw6IXrUFpaml2WJdxU7UrA5NT07LJxuOTARQsuUuxWcNFx5swZ4SZtt6ImTQf2FUI/t956Kz3//PN2g8Cr62EC5lV4bd85EzDbb7F3F8gEzLv4mr13uJThC1xJ4RAJhXHDjBiDyMhIjxMwHJy2bdsmkvoiua9dil0te0zArPmE7ty5U3zGkSvLbgUXHRARsiO5hLw+LgbgXhgRESG7dbjswbvz7rvvpqeeespu2+vV9TAB8yq8tu+cCZjtt9i7C2QC5l18zd47yBfUD1Gc47/wf5CJR/wIrDiQVkccGHLt4E+lv8v9Xq5v9I+4lC1btlBeXh7l5uaaHS7V8+vq6iIceuGmB3c9uxRYTBHoD3dRuI3aqUgWMEi1e1psZrJx2r59u4jdhCXbbsXO5FJNbjpYyWBpf+ihh+jHP/6x3bbXq+thAuZVeG3fORMw22+xdxfIBMy7+Jq5d3fuh5g71PxwwEH8F+rDCgbC5vjjqNyltF5JQdGZtIGYwcqGHGCIY3D8vUTklMibmbG1q2ulnQlYeXk51dbWilxZdiNgsDLjM7ho0SIzf2x0zQ3kEu8IO65NjVssRJJArH/yk5/Qgw8+qAvDqdqICdhU3XnPrJsJmGdwnLK9MAGbslsvXJLguiMnPy+hAjEJHHBQcnJyhKXKUQURB3LJjVEiZZJVTUru7Pin89+NkDeJoMlZ3CabvJ0+fVrgVlhYKHJm2al88MEHwiKKW3c7FTsTsK1btwrLNVyJ7VZgQQ8JCaEFCxbYbWlCgRYWrlWrVsl6KGDBcMHE759++mn61re+ZTsMvLkgJmDeRNf+fTMBs/8ee3WFTMC8Cq+pO5fIECapZGVCLBMOOCjz58+n2NhYj8nQg3yBrG3atEnkuIGrnjvS5kju1JA3rMsVQZOzuEn/Z8TyhgSqOPRCHhrE1U7FrgSsrKyMIDqzcuVKYS2yU7EzSfn0009FfNS8efPstGViLWpynH3yySe0fv16euGFF+jmm2+2HQbeXBATMG+ia/++mYDZf4+9ukImYF6F19Sdw/oFwuOcfNlx0rDkgCDhQLpixQpBvjyZB0yvS5tkeVOyrslZ4RzrqiVvrgiacxycI9EDtnaMbcOzgRgwuIvazQJmZwJmZ5ICAhITE0Nz58419ftWz+QOHDhAyJUIt1il8vbbb9MXvvAF+tOf/iT+5KIeASZg6rHimhMRYALGT4UhBJiAGYLPso1BQJAXyJX7IRYHMYnNmzdTVFTUmPuSEcuQHGCQNYcFDMmYfVEcyZs7i5vc79WSN2ALUgb5fi3CJWa3voCApaSk+Gy/fPFMYAw17l6+mounx8ElCj7DJSUlnu560vv76KOPhAx7cXHxpM/F0xPYt28f4RLMlcT+q6++Srfccgu9+eabtG7dOk9Pwdb9MQGz9fZ6fXFMwLwOsb0HYAJm7/1VWh3UB5E/B8THVf4tiBIcOnRoHEHyNAH7+OOPhQiHFQ5QIF8gVpKFTSneDeQWAiaITQGhkuqpJW961SZ9Qd6YgFnvnWFnK5Fdn0c8ZWryt/3xj38UsV8goq4sZdZ7ar0/YyZg3sfYziMwAbPz7vpgbUzAfACyCYdA/q0NGzbQtGnThFS6UsENbENDgxCSQK4uEAhPEzDczkdHR9vKhQiEC4de5OcBbihqyJsri5wW8qYlRYBknVNL3mCxTEpKotmzZ5vwydY/JckCtnr1ao+62eqfkedaWumSQ8uq9bowaxljMusiST2Kq/QBzzzzDD3wwAOCrNlRiMSb+DMB8ya69u+bCZj999irK2QC5lV4Tdk5Di2wgL333nuCICi5/kmHG8QzwUoGRT9vEDC4OIaFhQmRD7sUECkcekFcgZvRIpE3dy6TSrFvsNq5KyDWavK7HT16VIixYF2OapOejA10N1dv/B7rQkoEOxIwu5JmKLDC8oP3U1FRkTcei0ntU4165eOPP04/+tGPhAutHTHw5gYwAfMmuvbvmwmY/ffYqytkAuZVeE3ZOQ4tIFXvvvuuOLgouf51dnYKJT8UJN6FpcxTBKy58wwlx0aIvtUcMkwJpItJme1giPl4k7yBfKlVm3QWNnElAuPLfbczAbOrm56cpdmXz4y3x1IjnvLoo4/Sk08+KS4PkB6Ci3oEmICpx4prTkSACRg/FYYQYAJmCD5LNpYO4nBBhJiCUmA+8iJVVFQIl0PJ5UwS7TCy8O6eflpy3/N0xeIiuu2yBdRZNzqGnRKpAidYHSCt78rF0wiOvmrrTN4QOwjZbyghulObVGN5A3nTozYJwudJ8nbkyBHhbrtmzRpfQeuTcSRLth1ztyHWEiQlNzdX5Ci0W4EVPS4ujubMmaO4tPvvv59+//vfE5K/R0ZG2g0Cr66HCZhX4bV950zAbL/F3l0gEzDv4mu23qXcWyBhIAgQv1By/YNrICxlOIDD5QyHAE8QsLK6Nlr//ZfHoJmXFUvr5qTSzVdfaja4dM/HzodeLapzEnnTY33zJnkD4UPMm6PbpN0JmB0uA5w/kFK+PZAvkDC7FTWWyzvvvJNeeeUVoWqL55qLegSYgKnHimuyBYyfAQ8jwATMw4CavDscakGq8CdEInBjKmd56uvrEwQNMWLNzc1CSh2JTj1BwD46UE23/fqfE5Cak5NMt61dQGsX5FOAv7/JkXQ/PTWHJ/e9mK+Gmlt5T8xaLXmTI3d6yBueeXw2QFTcWeScyZsn1uutPszmDuvJdUKiffv27SIeEfGWdipqrehf+9rXRG4+5AvztEAS8HzxxRcJY6A899xzdNttt02A+Y033qAnnniC9uzZIy7sINDzzW9+k2688UZTbwkTMFNvj+knxxYw02+RuSfIBMzc++Pp2UmHVfQL9UHIpC9ZsmTCMCdPnqSDBw+K3F+IjYG7FxS28OWqVi1Pae6vfHSQHnnpQ8WlZSVG082XzKNrl8+isJAgT0Pgs/7sKnzgKwJmZKMcUwWotb5BmEYNccO8JLdJLWqTUl1fkzdPC8IY2RdPt0Wewp07dwo3XxBnOxW18W2f//znRaoQvLM9TcCQhgSeD3jvg+zKEbDf/OY3QgYfudiuv/56Cg4OJuQmw3zuu+8+QczMWpiAmXVnrDEvJmDW2CfTzpIJmGm3xisTww0/DmT4ooaLIQ6SF1xwwYSxcJPZ0tJCF198MW3btk2Ib0AK2RME7JevbaH//NdOt+uLiwilL6+aQ19bU0IJUWFu65utghZXPbPN3dV8rEDA9OCJQyyeeeRSkiNtSjnfUFeqr4bA+Zq8qT3I68FssttAKGj37t00c+ZM2wlQwCKLdzRSheBHqaxdu1Y8t2VlZR5Nn4B3/qWXXkpVVVUEkgci5UzAqquracaMGSImFDL4khsorHH4vkAMMdawbNmyyX5UZMdnAmbKbbHMpJiAWWarzDlRJmDm3BdvzApfqIgTkNwIQaxwOFuxYsW44fD7999/X8SHwQIGlULUg6XMEwTsu//9Hv19y1HVSwwNCqTPXTCDbr10PuUkx6puN9kV7UpU7JrUVyJgq1at0v3o4LOj1uLmWA9/x2fLXXEkb+7cJKXf43MPK1FOTg7l5+e7G8JSv29vbxcJ5eHyBkEhOxXkasQ7GnkE4QouV7C3eH/jucClmSdTQTz11FN0zz33CFf0Dz74gL7//e9PIGCPPPII/fCHPyT8id87lhdeeIFuvfVWuuGGGwjJos1YmICZcVesMycmYNbZK1POlAmYKbfFK5OS5OfxpQ03KCT5xJe884Gzra1N/A75wfDFL9WDpcwTBOyrT/yNtpXVaV5jybQUSokJp9vWLqT5+eaXW7YrUbHrukDAWltbaeXKlZqfTU80cCZv7oic4+/VkDfMUYvLpJRWAH/62m1SLZ7Yr/379ws3OSi12qmoca/Euxyu4VAkhUu5pwoEadDvN77xDSFx/9hjj8kSsAsvvFCoUMpZuaAoivQlSHUCV0YzFiZgZtwV68yJCZh19sqUM2UCZspt8cqkYMXCD25J4YII1x248DjLbuPLt6amRhxEkSBZqoebVhz6jMaAXfzw/9CJllOa11hakEbby06KdosK0wURu7gkz6O3vpon5aKBmhw+nhzPV33hoBcdHU1z58711ZA+GQcxj7h8mCwCZmSRrsgbYttwAIbgTmhoqPgM+4q8SYm9PWmZccQJAkHYN6TSQAySnQrc+GDVwkUYCJZcAQFD/Bs+i++8845Hlo9nY+nSpULWHtZFfAcoETCQXpBg/Mjhj2cOl3z4gZCT2QoTMLPtiLXmwwTMWvtlutkyATPdlnhlQviiluK/pNtsfLkidgB+/o4FrnMgaLjdRJHqwVJmlIBhHsX/5z9pYMi9u5UzEIsL02nbsfE3qflp8XTrZQvoqqUzKCTIXBLMuBXG4UVJ5t8rG+2DTkHAoqKiFPPH+WAKXhnCygTMFSCSVLuSK5tE3rRY3KR4OC2WN3cuk3KJvNHGFXlrbGykw4cPi88Y8mXZqaix7uF9CgsT3uF//etfPbJ8uBP++Mc/FhY1KXZLiYBBcEO62JOTwIcwChJEmzVJNBMwjzwyU7YTJmBTdus9s3AmYJ7B0ey9OMrPSxasAwcOUF1dHSGIWzrk4KYSLmYI+pYSCEv1YCkz6oLY2tVDy+7/L11wlUxLpr005IlYAAAgAElEQVQVDbJtk2LC6YaL59FXVs2l6PBQXf17utGWLVuEyiRceexU7ErA8JzD6gARDjsVb0q1O5I3dwROIm1GyZsjkYN1D5dIeF/FxMQIF0vH33vL8uaL56OpqUmoGyL9B+Jx5Qrex7A8ffWrX/VInBVizpYvX0733nsvPf7442NDMgHzxY7zGFZDgAmY1XbMZPNlAmayDfHSdBzl5yWpYtwcnzhxgi677LIx+WKoWkF2fvHixWNf+lI9TxCwA9VN9Pmf/FnXKgvSYqm8rs1l24iQILpuRTHdcul8Sk+I1jWOpxpBvAS3+hAysVOxq2ulXQkYXMkQx1lUVCSsJWYpesib9B7Ta3nTEgM32eQNViO8i/H+ALmUK7gwS0tLIyRjfuaZZwxtLbCFmAku6OD6iMsjqbALoiFoubFNEWACZtON9dWymID5CunJGwduKtKtM8iXdLA4duyYkBiG1DyIAgoOagj+Xr169RgpwyEAxAwuiJKAh97VvLP7ON31u7d0NY+PCKa27l5VbQMD/GndoiK6/fKFNDNrcoLzkSAWWEOO2U7FzgQMMZHOqqBW3zs1Yg5WWyPIG0gYYlVxiQQpdBAHd1Y4Kf5NzXola5oW0ia5UXqCvCGPFqTlcRmGWCq5AusflC3vv/9++vnPf65mWYp18OyrdeP89re/Tb/61a+EmzqLcBiCnRtbGAEmYBbePDNMnQmYGXbBu3NwdD90JGDl5eUiTwuIlRScD/l5yDnD7UUqUj182aK9nK+/2hX84f299OM/faK2+li94MAAGhgcoLNnNTelL11UTGsXFtKFs3O0NzbQAmQWhBUHKDsVHLgQUG+32Dao6Z06dcp2BAxrQo4mkBSo0tmp4AIJP1BoxTtMTcFn0jkFgLN7pFzONy3kDWRQLqbN1f85kzdcelVWVgpBDCUBC6wdAiSwUD366KNqlq9YB+6cSKgsVyDEBKsYvgPgmo6YMyRdZhl6Q5BzY4sjwATM4hs42dNnAjbZO+D98eXcDzEqvtxxw4obfyTSRMwBvmShqOV4UANJAwnDIUe6FdY765/9ZRP913t7NDdPj4+iutZOze3QYE5uMh2oahSWsNsvX0TrSqcTLGTeLsi9hFt65E+zU7GruIhdCZgaNT2rPp94N8EKBmIAQQhvFzXkTYnc4f/VFIm8SRdniPHC2iSChn6Q5B3WKpCmf//3f6f77ruPHnroIUOXY67mpuSCCAKIJNiciFnNznIduyHABMxuO+rj9TAB8zHgkzCcpH7oaP3CNHBwgeQ8iBVkxaECB7cXxHo5HmakuDAoYhnNCXT3s2/RW7uOa0ZhVlYiHapp0twODXKSoqmm+Tx5y0iIppsuXUBfWFFMEaHeO7TB6oCbdNxg26nYlYDt27dPSG9L6p922TM7JyvGxRAk9iGcYsQy74u9lsibO+ub9HuIp+D9gXU5kjcoPyI/l1yBOimImfTz+9//ngoLCw0vT4mAoeNf//rXdPfddwsxEFjF8N3x6quviu8SEMMnnnjC8Pje6oBVEL2F7NTolwnY1Nhnr62SCZjXoDVFx5L8PCwxzgQMX5AgXbDQxMbG0saNG4VsujNhQIwFhDjgSgc3HyNJWb/887/SjvJ6zdgszE+jneWjOcC0lvDgAOrpH5zQLCY8hL68uoRuvHg+JcZEaO3WbX247fT19QmCa6diV3VHuxIw5DbD2oqLiyk5OdlOjyIhjhVKrnCjlsSF7LJAxN5CiAPxuCiSCyRi+hBfCmKN9zLk5/EOh9cCrJ2OP8gNhhgxo8UVAUPf//znPwXRwjsPljvkLrvrrrvoxhtvNDq0V9szAfMqvLbvnAmY7bfYuwtkAuZdfCe7dxAvWMDkxDMaGhrEwQwiEbBswbKB21LnL2wccKAQt2jRIuFq4kzktKzxku+9RInRYdTZ3UsVje2qm8rlAFPTGCTr1BnXwh2IL7t62Uy67fJFlJcqL/esZiznOsifBpUyyDrbqdiVgNl1v6R8UnAtTkxMtNOjKCz4eI+BpHhC+MJM4ECCHiIbIJdK5fXXX6evfe1r9Nprr9FVV11lpulbYi5MwCyxTaadJBMw026NNSbGBMwa+6R3llKSTBxOnG+Im5ubxY0l8lTB9UqK84I7omOBywsOpxBdwO/0ErCh4RGafdezNHJOSSM/NY5iI0JEfJa7xMwL8lJp1/E6zTDkpcZRZYNr6XqpUz8/ootL8kWc2MLCDM1jOTewq0XFrvL6diVg+JzD0g2xBriJ2amoISlWXa+amMSXX35ZuCNu2LBBqNly0YYAEzBteHHt8QgwAeMnwhACTMAMwWfqxq7cDzFx3IxDKAIHM8R5wV0Ot63ON8kSUUM9uCrqJWB1bd206uH/nYBZZGgQpUUG0pnBs1TfcUYW05mZCXT4RLNmvEumpdC+Svnkza46m5+fRt9YV0qr5+aTv7++16yaA5TmBZmggV0JGARoIGpgN5dRNQl9TfBY6ZqCXXO3AQw1z+Nzzz0n4qyQQNluaqu6HgiNjZiAaQSMq49DQN/JgEFkBM4hwATMvo+Co/w84racC2IF8MUNeWrEGyBJK+JEnAtiSCCpjt/BhQkETY+7D2K/vvyL11wCPjMzkUIC/elgdRMNjYyM1U2NDaeG9m7Nm1VamEE7ymo1twsA6RoZoezkGLp1bSl9bvlsCgkK1NSPXQ+HTMA0PQaTXhkWbMQKwYKtNs/TpE9a5QTsamXG8tWoqD755JNCfh4WTiRR5qINASZg2vDi2uMRYALGT4QhBJiAGYLP1I2V5OelSSOYG3FfCN5GsDcOaMgB5lyQoBOHbgRWI4hfLwH7x/Yyuu+FDaowS4gKo/zUWKpubKeWrh4CfRwcHlbV1rESYse2l2kX70iNi6TGtlNjXSVEh9MNFy+gr6yZR7GRYarmAfcoWBlXrlypqr5VKoG0g9AjJtBORY3FwYrrxWcbFywLFy6kmJgYKy5Bcc523TMsWM3n7Ec/+hE9/vjjQtE2OzvbVnvri8UwAfMFyvYdgwmYfffWJytjAuYTmH0+CNwPpWSiSi6DEIj45JNPCNLFkDxGDIGclLNE1JCAMy0tTTcBe/bt3fTEa1s1YQFL1IL8VOrp6aNDJ5o0J2Kem5tM+6saNY2JysgZdqRmYrvwkCC6dsUcumXtIspMdH2YhdUB7l+SipnmSZi0gZqDoUmn7nJaiIfs7+8npFuwU4GIDtQCQZid4zutvk6kesBFk91y7WFf1KR7ePDBB+m3v/0twUshPt5zAkJWfy7Uzp8JmFqkuJ4cAkzA+LkwhAATMEPwmbaxo/uhEgFDvAsSeuL3cE2CGqJckYgaFBLhpoiixwXxsVc+ppc+OqgZs8K0OCqvb6P0+EjKjI+ioyeb6dSZflX95CZHU3WT9gTOCwvSaZcL10UQw8sXTafbP7OYinMnWg0xOUmhDXnV7FQggY1nxm4WMLsSMKSbQMJ1fL5x2WKngmcR7yKld5eV14rLMVgsoV6pVJB/6w9/+IO4OPBFImor4yl7gNbzRWY3EHg9uhFgAqYbOm4IBJiA2fM5cOd+iFVDnv6DDz4QACAOLDc3VxYMiHMgRxjk6bOyskQdPTl37njmX/TB/mrNgM+flkJ7HIQ0IBtfnJ1E3T19VFbX6rK/yJBAOt03oHnMJUUZtO3oCVXtls3Mpts+s5hWzpk2rr5jHh87fc/b9dBr18TZSFQMhVOINERGRqp6pq1Sya7xiMAf79ykpCSXsV233HILvfnmm0LFVi7O1yr7OFnzZAvYZCFvj3GZgNljHydtFUzAJg16rw7sSn5eGhg5wt577z3xz4suuojCw8Nl5yQRNcR/IaYJ5At5w+CuiB/8Xfq38/9Lv8efn/vZX+noSXWS8I4TKS1Iox3l8hL0uckxlBgVRoeqG6lnYGjc/KPCggVJ01Pg9rhbYUyl/qZnJtId65fQZxZNp6DAANsmiWUCpueJmrw2SKR+/PhxkWBd6TM+ebMzNrIaNz1jI0xOa7iQf/jhhyI+F5djSuX6668XAklwddZzKTY5qzPPqEzAzLMXVpwJEzAr7pqJ5swEzESb4aGpuJOfl4ZBvXfeeUeQqEsuuURxdImo4fAGt0XkEoKFTbKy4U/UcVfufa2czgy4r+fcz6L8VNp5vN5l9xEhQTQzK5GaO7qppnnU5XBaahxVqcwB5tz59PR4Onayxd2SJvx+7rRUauroopsuXUSLs6OorblRkFu52DrNnZukAQ58eHbsJnutRnXOJFugaRpIMVFZWSli28LC1AnIaBpgEitv2rRJuFUiRYadCt6pH3/8sfA4gOu3UrniiiuEAEdVVZUut3A7YaZnLUzA9KDGbSQEmIDxs2AIASZghuAzZWOQIVjAEAfmyi1FigGLiIigFStWKK5FImpwo0MeMBx2nG9bMZYjIZMEQKT/O93bT59/etTdUWvJiQummnb1lqyC1FiKCAkUJEFPDjDMLzEylFq75HOSuZp/aVEGbT/nughSeGFhIj1005WUmRSnddmmrc8EzLRbIzsxHM7xg/xmoaGh1pq8m9mCpCB+dc6cObZaF7wOQC7hFp6Xlye7NrzfEF8KF3GkvLCTm7OvNpMJmK+Qtuc4TMDsua8+WxUTMJ9B7bOBpMSrUC1E3i6lAtckKPWBVME9yVWBpQxf+AUFBUKIQ6u7S0VjB13+2Cu6MEiPDaX6jh7NbWckh9Hw8Ai1dPdRR8+g6vYhgQHUPzhAdFZ1k7GKyDu2/dj42DG4I165dJaIEyvKTNLeqcla2JmA4SLBbpY9WL9gBbvwwgttJ9SgJk7KZB8fVdPp6ekRqT9AvpRic/E+hvojlC2hTMpFOwJMwLRjxi3OI8AEjJ8GQwgwATMEn+ka40u5oaFBxAVAPQsxBEoFogMtLS1CvtjdofPdd98VFjV84cONSSsB23S4lm5++p+68IoKDaTuXu1CGsWZsXTwRDshp3JuYiTR2WGqbOl2K2WfGBFMrd29uuY6KyuBDtU0y7b18yNaOTefvr5uCS2ZYd2cPXZ11bMrsUT8Fy5bYOVGjKZdihQnhdQYM2fOtMuyxDqQFgSxlkVFRWPKs84LxPqLi4uFi+L7779vq/X7ajFMwHyFtD3HYQJmz3312aqYgPkMap8MBJLU3NwsbkTx5SzJxjsPDjdFfGnDbQUxFGosYKiLpML44tdKwP7y6WF66H83asYAbnxn+tRJzjt3XpKTRPuqmsb9d0psBOUkxVB5XQu1n5YnWUVpsVRWp10sBAPFhwdS22n3852eEU9fWVlMa0ryKDQkZEzMBLFicBs1szsREzDNj/GkNoACIpQQ7RaLiHcdLGAZGRkEa7+dyqlTpwgXZBDgULpEw3sYFjLE9v3zn/out+yEmZ61MAHTgxq3kRBgAsbPgiEEmIAZgs90jRFz1d7eTlu2bBG3wjk5ObJzBElD3iPEhCB/DOJDlApyzECRKyQkhJYvXy4sYVoJ2NP/3E6/fnOnZrxykqLHRDW0Np6WFE1VCjnAAgP8qTgnmfr6++lI7XixjdLCdNpxrFbrcOTv50d+NEJDwyOq2yZFhtCls1PpgoJEgusjCsiXo3qkK2VJZ/VJX0hR2zX5rV3VHZEDDLnAcHnii+dD9cNvsKJaoQqDw0xKc7zD9+7dKyToU1Lk8wziPZyamkpXX301vfKKPvfuSVmciQZlAmaizbDgVJiAWXDTzDRlJmBm2g3jc0HwdldXF3366afCfUUpgPvQoUPiVhyJPnGQcSXCUVdXJ4K84XqI21ZYz7Qe5B74nw/or5uPal7gnJwkOlA93oqltpOoEHWui1lJ0ZQaG0GHa5pEzrDFDkIaasdCvaSYCGru6NLSZKxuaX4KQXnxikV5FBEcICtoggOXuwJi7JgeQI7IOZM26d9qSbVd82XZlYAdO3aM8BletWqV5osTd8/bZP5eEqrAJRNyFNqpwDUc71y4kSvF8WL9+N1tt91Gzz33nJ2W77O1MAHzGdS2HIgJmC231XeLYgLmO6y9PRJcUmCtgroh1MFwKJGTMEa9jz76SFi+cPg+c+aMOJwpFdzENjY2EtQSEQOmh4Dd/fwGauvqoebObqpuPqUaikUFabRTYz4udB4ZGkynNeYACw0OpNnZSRTsT7T5sPaE0TOzkuhwTaPqtTlWLEiLo/KTLYQ5XLOihG5bt4RyUuLH9QXcneX/JbVJpT8lFUrsubvimN/NVV43CDpgLvPnzx8je2rJm7s5TObv4baLi4VFixZN5jQ8PvaRI0dEXOjq1atN7dqqdeF4z8HS70qoQmufZqmP9y0EkvAZg8qjXOno6BAeDt/+9rfpV7/6lVmmbql5MAGz1HaZbrJMwEy3JdaaEBMwa+2Xq9niUIxbURzG4TII9Sy5JJ7d3d3CQgaChr/ji/ziiy+W7RpWlw8++GDMLU6vBWzt9/9EVU2jxGsakidHh1JFQzu1uRG7WFyYRtvL5JMwu8IiNzmWqhvbdW1uXmqMEO6IDgumg1WN1D84PsGzUqcLC9Nppw7XRfQHoZGuM+el9uHOeNmi6XTHFcuoJD9D1zqkRiBf2Ee1ZM0xnQD+roa8gbioScYtV8cs8W52JWA4yEMZFQTMTgUXR9gzKLNmZ1tX1EZuT2CxhOUSlwFQOZQrcCudNWsWPfzww/SjH/3ITlvrs7UwAfMZ1LYciAmYLbfVd4tiAuY7rL09Eg7Y+MGBecOGDSKJJ2IInAtkqREXAjIFawbiwS699FLZ6SEWAa5ZsH7hMA4pa/yp1QWx5N9eoN6B8UQmwN+PZmTEU3CgPx2sbqIBmdip+dOSaU+ldqvS3Jxk2l+lvZ0gQ2GB1NUzKqQRHR5CMzISqb61k062urbcLS7KpG1HazRvM8Y41a2cc2zxjGy6ff0yWjOvwOcWDDxLUl45iZjh2cFzhkOvXO43xxxwasCQc5lUE/fmabESuxIwuBvDpc2VlVvNPpmtDi6PoFzpSinQbHNWOx+oVkK9Eh4HePfKlaNHjwr12p/+9Kf0wAMPqO2a6zkgwASMHwcjCDABM4Iet8Vh3b1vEuNkegSwjbB+4bAMdzDIxkOeGTEEzgUHTdwe40YchzPcpK5du1b2cI/DNghbQkICQZkLgfxaCVjH6T5a8t3/cYlhaKA/ZcWFUGBwKB052TpmdSlKhyKhdktWaUEa7dBhOYPrYnfvRHVESMjDxTAowE9YxZBfzLnMz0+j3eUnNT8rBekJVF7rPs6tMCORbl23lK5ePoeCzwl2aB7MAw327Nkj3FxdCbdgGDyTztY0d1Y46fd4jt0VZ7ESrfFuzpY35F0C8Vu4cKG7oS31+4MHDwphHqgg2qmoUQq06nrVJM9GLCbe4b/+9a/prrvusupSJ3XeTMAmFX7LD84EzPJbOLkLYAI2ufh7anTJSgFXM1gGYAEDaUIMgWMBSYNLIaSb58yZI+IMcNsKC5icVQuuiugbyZoRl4AvfK0E7HBtK13907+pXmpSdBjlJseIeDFI0Lec0p6EWS8Bm5YSS5WNriXoE6PDKS81jirrW6n11HnLlYjjqmtVvU6p4vz8dNpdNj55s6tOUuKi6MbLSunLFy+g6PBQzeMZbaCWgBkZB8+x3ng3vWIlnZ2d4jOAz4ajVc7ZbdJq8W779+8XlyeuhHaM7NVktYXrNJ5FuOFBDdBORU3uNsT5XnHFFfTf//3fdNNNNxlafltbG/3973+nN998U4h/wAUSMcL4jrj55pvFj9xzv3nzZuH+iMsLXMog5viWW26hb33rW5q9JAwtQGdjJmA6geNmAgEmYPwgGEKACZgh+EzTWLIcYEL4okQMGGIHnG/z6+vrCQeyefPmiUML4gxw27pmzRrxhetY+vr6RJ4dBHqDhMFShnpaRTje319Nd/7uXc1YBfr7UXZiJCVEhVFFQ5vbeDHHAUpyk2mfDtfFkmkptLeyXtVc4UIJKfvBoSGhoBgTFkSdp8/HcanqhIiWTM+irYer1FYfqxcbGUbXXlhMN31mKaUnxGhur7eBLwiY3rmhnZp4N0c3SenvuJxQU9SKlcjFu00Gedu3b5+I9YT7sJ0KSAPWhnyHycnJdlqaeC+7U67817/+RV/84hfpL3/5C1177bWG1v+73/2O7rzzTuE1gUs2uBcjbvBvf/ubIO/XXHONGMfRavz666+L/0cqk+uvv57i4+NFPjLMHfNBfbMXJmBm3yFzz48JmLn3x/SzYwJm+i1yO0G4ekmHSBzw8CWJ21Hk7UIMgWPBgQWWLBApHBBx04ofuBZCZt6xgHDBfQmB4IghqampEV/OkpXN7cTOVfjfjQfph3/erLb6WD1Iwzd2dIt/i3ixzAQKDvCnI7XNE+LJnDvPS46hysYOzWMiB9j2Mu05wGARS4wMoSM1jWPxY2oHX5CfTrs0WMCkfrOSYqm2sZWCAvxp/bJiuv2KC2hmjvctAVDFhAsrcsLZqeA2H58ZxE26i21zdqXUI1aixWUSdfWKldh1v9RItVv1+VQjnPLnP/9ZSNC/9dZbdPnllxtaKrwi8Jlev379OEsXvisQZ4aUJa+++qogXChIdQLxE5AzeElIyqG4tMN3C9QpkZsMBNHMhQmYmXfH/HNjAmb+PTL1DJmAmXp7VE0OhAi391KCZBzU8KWIPx3jdEDU8EUbFRUlvlRRYP3CjSVuxyMjI8eNB0tHa2ur+EIFSUNdKY4EB0K15ed/30bPvbdPbfWxehDoOHpyoktfeEggzchIoL6BQTpc2yKr0hcdGqSZCGHgUqG6qD2Oa1pKHFU1tFJIUAAV56RQ1+leKqsbn+BZCYDpGQl09IT7GDDn9nPz0mh/+XiyeNHcfLr9s8tpeXGeZrzVNrDrgR4EDJcQzm67anCREytR60KJemqK3vxuuHTB+wGiO3YqsNAghhXWfFhf7FTgBggXS1dxe3A9hAT9J5984lXr5k9+8hOhtIg4M8Sbobzwwgt066230g033EB//OMfx0GP7xio6mLuSHdi5sIEzMy7Y/65MQEz/x6ZeoZMwEy9PaomJ93Wo7Lk4gSffEm1UOoEX+gQ4Jg+fTpNmzZN/Dfiv3DbCqLmKHcMMvf++++Lgw3cGCVLGaweiJPRQsDueeF9enNnhaq1OFZakJdCuysaXLZLjA4TsvbNp05TdVOnqBsREkRnekdVDLWWYpH4Wbt6IlwX91WMd13MSYqmIBqi2rYe6nMhZR8fEUJtXcoqiEprWDw9i7YruC7Ozk2l269YTuuXzaYAf3+tMLisb1eXNiMEzAjA3hYrkeYWHh7uNkm3ZJVzTM6t1/JmBBM1bZHbDDnO8H5CQnk7FTWXHL/5zW/ooYceEnFwIKHeKj//+c/pu9/9Lv3bv/0bPfnkk2KYr371q/TSSy/Ryy+/TF/60pfGDY3vHewHSP/p06eFVdmshQmYWXfGGvNiAmaNfTLtLJmAmXZrVE8MX3T40pPcD9EQ8szOCZYlRUNHa5fkZghXRceEn4ivQB8IcEc8gGQpW7p0qYgV0yIB/sVfvE67K7RbeBYXptL2MnXxWFgzhDsg4NHbN6CLRKGPrMQoOtEySuS0lMWFGbT9mLyQRnhIEM3OTqam9i6qaR7vFhkWHEg9vdrjxjC30qJM2nHEdcLojMQYumXdMrp+9QIKDx0f46dlfY517UrAYDUGSdFjAdOLpdF2asRK4EaGerBwO1rl9IqVKOV7c04d4O14NylXVmlpqbDq26lA4RBurnjfKpWf/exnBOtUeXm5cAf0RsHzgs8DXNHffvttoZYr3j2lpbRz507xI6cairg8WCdxuTdz5kxvTM0jfTIB8wiMU7YTJmBTdus9s3AmYJ7BcbJ6we15f3//OPdDzGX37t0EVTe4D0oFB0x8ocI1RLrVxi0yDtTw4U9MTByrK4lzoC4OpYj/wm2zHgK26v++TPXtpzVDtDA/mXYd126NmpOTJIRCQgL96cgJ9/FijhMLDfJzG18mt5BFBWm0U4Xr4ozMJAoLDqADlQ00ODxMuXBdrFfnqug87uzsJDpU5dpCKLWBYMdXLllEN6xdQkmx411NtW6MnQkYci5505qgFWtP1MdFCt4Tktux1KcasRKlWDg12UvkxErUxL2hjhryhrgkkA9XubI8gd9k9IE9k4iO0vjf+9736KmnnhIxvSkpKV6Z5v3330+/+MUvaN26dUIhUSrIvQbslcgfPCVgUcaPmV1fmYB55bGZMp0yAZsyW+2dhTIB8w6uvuoVRAMWMByIHGXkcUh2TLAsKRrCmgWrllRQB2RtwYIF45TENm3aJPqUpKslSxluPkHIHK1trtY6PDJCc+7+Lxoa0Z5ubnZWPB06oV3WfVFBKu0oH7WcwcI0MzOB+hEvdkI+Xkyaf1xkKLW7SIjsap2zsxPpULV6K19cZBgVpieQP43Q5oOVuh6X1Jhwamzv0tQ2OCiAblu3jD53UQnlpydpaitVtqusOS4oYCUqKSnRhYtZGyGROj6vklCC0XnivSBZ3qTk72rzvXlSrAQu1Xh/QSod+ybFyJnVZVIL7nAhh6cB3stK5d5776Xnn39eeDrgnezp8vTTT4sYsxkzZoiYYsc4OyZgnkab+7MiAkzArLhrJpozEzATbYaOqUgHIBw6HG+N4TLimGAZt8VwCYG7SFLS+YO35GqIQyckiFGQzwXB07m5ueLLF0WylOFAAHcftQSsseM0XfTwyzpWRpQRH0F1baMqiFpKaUEqbT9HwBzbIV4sLzmWmjsRLzZRIbEwPV61cIbzfDLiMFdtZAh9LCnKFLnOaGSYDlQ1yAqKyK0diZgHzxFvLdig7uIZ2bT9cCVdsnAGff3KFbRoRo6mLuxKwHDpgGfbbgTMTAmmncVKXKlNyilNqnlQtYqVSFY5LW7VauZhpI6ay4A77rhDSL3jfa0lJlfNvBBfhlxeuKxDLLBznjV2QVSDItexOwJMwOy+w15eHxMwLwPsxe5xmIWxcn0AACAASURBVJHiv5wPD3AXhNuglGAZVi6QLbgkOlrKJGEO+OxnZmaK2UrCHPiSRTJnFCiOScHeCLBWS8B2VzTSF3/xD10ohAb6Ud/gsOa2yAG2t8q16yLixZKjw6myoY1au0YTPc/PT6Xdx+s0j+cP8ktnaWhY+1wXFaTTjmOjSoapcVGUnRxDZbWN1NHd63Ie2cmxdKJBu3UQnc6dlkr7jp9XT1w4PZu+/tkVdMmiGapcv6DQBvdWuyX2tSsBgyQ4hBBcWVM0P/ST0EASK5FIG95vkKJH/JOjRU7OGgdPAXcFl1iOLpKu3CW9LVaCNCKIyYV1T6lACAMXZe3t7ao+t+7WL/3+V7/6Fd1zzz0ivxrIl1yONRbhUIsm17MzAkzA7Ly7PlgbEzAfgOylIRzl5x1JFYaTBDckwgVpYJAp50MY8rnATx+B0ki4jCKRNUgJS1Y1yNEj4Hru3LniYKCWgEH9ECqIWktcRAh1nHZNQpT6zEuJoQqVOcBAnuCiiHix4EA/2nJEXkjD1fxTYiOEwIaeMitroutiUGAAzclNoTO9fYry9CV5abTPSYJe7fhCaKSpfUL1aWmJdNtnl9M1F82nkOAgxe7USGSrnYuZ6kHOG5cLeMbtVCZL3dHbGOIdBys/chg6v/+cx1YjViKXnBv/p0asBOTNWZzEWZTEmbRJ/5aLd/vwww9FXJeju7jzmj7/+c+LuFxcmKmJmVOzH//xH/9BDzzwgIiDfO+998bFBTu2Zxl6NWhyHbsjwATM7jvs5fUxAfMywF7sXk5+XhquoqJCBEjjcAIpYKhqIcFsVlbWuBkhfgAHT/j05+XlicMGbj2dyRpuWRFLgj7gwogDh5pYi+ff20eP/32bZhTyU2OpomEiSVDTUXR4EJ06o12GfklRGg0ODo3mFzvRrNodcGZWkkjArKekRIePJZuWa5+TEkvJMRF0qKqezvQNjFVZMj2LtilI0LuaBxJa+40MCwEQpZIQE0E3Xr6MvrZ2CcVGTowtYQKmZ6cnr41dLXtHjx6l+vp6kRxezbtI7w44ipVI71wlsubsUqlHrARkEt4KiGvDu9aR2EH5EWvF+/mmm24S9SCY5In1//CHP6RHHnlEuKm/++67LnOr4eIuPz9fJGTmRMx6nyxuZ3UEmIBZfQcnef5MwCZ5A3QOjy926RAgZ42qrq4mHFAgOY8bUvysWrWKQkNDx40oiXPgy7SwsFAkXoaly5msnTp1iuDKhJgwxAOoJWC//tdu2nKsjiobO6i9W73cekluEu2rUi9qIS1KyLr3nycqWuCdlZUghDpQEqPDCZa0po5u2Xgxx34XFqTTrrLxCZHVjAtL15C4YXcvUAIp+1k5ydTW2S3cJtVI0MvNIT0hmuqa29RMj8JDgukLaxbSreuXU2Zy3FgbxBfi4Adyb6eCi4jY2FiXbl9WXK9dLXuQOIdrNAiYGYuSWImruDf8TnIrl1sTZOdxESYVvPvhOg6vBIhk4E/8rF+/nj73uc+phgXJlEHoQP4Q+yWXVw0xwagjlddee42uvfZa8Z3yxS9+UYz/j3/8QxBC/P+f//xnjxBD1YvQUZFVEHWAxk3GEGACxg+DIQSYgBmCb9IaO7ofyhEwSXQDsvFQRIS7C6SBnQtIHCxeSMyMBM1S7BgO12FhYWPVYUXDTTosZenp6aoJ2P95bgNt2H+C4OpXkBZLMWHBVNvSSQ0drhMPQ0hDUjLUAnJ2YjTV6MjjhTHS4iKooX2i6MdovFgYVTjEiznOaXFhOm0/F8elZa6ZidFUKyMG4q6PooxESosNp80HKmhgaMhd9XG/L56WRgeOa3OzRCLndUuL6RtXraBZ09JFTiA7EjA1cTeawDZJZbuuy67PIS7F4DYKl/CMjIyxiza8qzds2CDcyxG7i4syiCPBXRD/xg88FXBZ9uCDD9KPf/xj1U/gY489Rt///vdd1sd3wsaNG8fVgfUL4+ByDvNGPN4tt9xCd999t1u3UNWT82JFJmBeBHcKdM0EbApssjeXyATMm+h6r29X7ocYFa45UKtDEDdcxuBeCPLkXEDk4G4iydPjthzWLVjOHEtPTw/hIAdLmeTGqCbu4POPv06HaidaXHKTokXSZKFI2Hxqwrz0ErDi7CQ6UKPdcjYmpDEyorhpqDMjM4FCg/zpcA3yiw2KuvPzUmmPDvGO4pwUOlCpPtG048SSokOpf2CIZmQlUW1zO9WrJJ1QQNx2qELXgxke5Eclhdm0dl4u5caF2M4CZleiAqEGuKxBVMFOxa5qnHAL37ZtmyAzeC/LFVjX8D4H+UKCZMcCwRF8P0B4hYtrBJiA8RNiBAEmYEbQ47aIc3Hv/8Q4mQ4ByU1FSQxDUi2EewoC1ZGsFK4pzgXb/84774ibVpArHEIla5hjXSR7RmA4fieJdaghYMsefJnaT7t2PYTlKTU6hJraTlF9Vz/hidTrgrgoP5V2HNdOaoSQRod6yXu4Os7ITBTuQrj5Pa4jXq20KIO26xD9CAkKpP7+PoETip8f0eycVAr0I9pfedKlS2Pp9EzariN2LCkmkprbz0v3ZyVE0T1fXkefvXAewZXSDsWuRAVWCyjZuRJ0sOL+QZUVF0Nyln0rrkeaM+KqYN2CRwLey0oEDL9bu3Ytvfrqq1Ze7qTOnQnYpMJv+cGZgFl+Cyd3AUzAJhd/PaODNIEQwXqlRMAgzwzhDQRyoy7UEJUCtaF2hWBvEDS4IC5evHhCADZuVOH+AvIFaxrm4I6A9Q8O0dx7/0fTEmPDgwkCHEH+Z2lHeQMNDStbpOQ6VsoB5m4SsGwdrR2N/9JachMjKSkmglo6u6mqUb1wSGlhBm0/qs0dEHPLSY6lagUJ+uTYSJqWGkcVJ5up9dTpCUuZlZ1Mh6q0S+3Pyk2lQxUT49zSEmLolisupC9duoQiw8bHF2rFcbLr25WAQQEVOf6gdGqngvcb3PLgZm2nAldCkEsQZuf8W9I6YeVCzNUNN9xAf/jDH+y0fJ+uhQmYT+G23WBMwGy3pb5dEBMw3+LtidHw5QvLC0iQkvyylN8L4yFmy5W0Ng5oEB9Af2gHsuZMriRXRVjUINahhoDBtXDtD/+qa8kx4UE0PDxChalxNHJ2hI6dbKXeAffxTvOmJdGeSu0uiAvzU2mXDstZZGgQne45b+HLTYZqYThV1LdSa5frOLc5Ocm0v7JBMz6QoN/rRoI+MMCfinNTaWBwgA5XNxCds5YlR4dqsvRJkytF8mYXrotR4aH05cuW0q1XXEjJcdGa12SGBrAU4SICAjR2KficwnKNd4CUVN0ua9uxY4d4D+HCyE4FQkiS+zieR7mCmFzs6Te/+U367W9/a6fl+3QtTMB8CrftBmMCZrst9e2CmID5Fm9PjIZbX/zAoqVkhZJUCzFeSUmJuAFXKjh4hoeHi+S6+MKfP3++bFW4KqIfuMaoIWBbjtXTTb8ZH5+gZv2hwYHU56RkGBIUQEVpcRQU4Efl9e3U1SMvM5+fGkPHG867yqkZD3UWF6bR9jLtlqFpKbFU1TAxxk2KF+vvOU0nO3pkE0pnxEfSyZaJ8W/u5rx4eiZtO1ztrtrY7zOTYig9Poqq6luopb1Ttby+4wBqY8eCAwPoqovm09evXEmFWSmq52iGinYkYLg4wbpwcSIXA2oG3PXOAXFSuIBatGiR3i5M2Q7u44cOHRLxXbByyRXUwUXYd7/7XULuLi76EGACpg83bjWKABMwfhIMIcAEzBB8Pm8M4iPFf+HwoeRWKKkWYoJIqIxcMkoFwhsoCP5GoD4Oa3JFSswJ1xg1BOxvW8vpwZdG+9ZSEF9U26pMTJDLCmQsIjSQTjSfoqbO85YmuDB2nFEvdy/Na0FeCu2u0GGNyk2mfW6sWEjyPDsnmfpFfrEmEaMlRD+QSsBFPi4lzBYVptMOHa6LBekJFBsWRJ2nz1B5rTYr4eycFDpYeVL1NuK5XL1gOn3j6lW0eFae6naTWdGOsVJwHUZcJ4RzcGC3U4HyHoQmnJPLT9Yazw4P0+C+fTSweTP1b9lCwQsXUtS992qeDgSUkEIE+bjk5ODRIfI84qLsBz/4AX3ve9/TPAY3OHeA9kQCNQZzyiLABGzKbr1nFs4EzDM4+qoXR/l5JfdDzEVSLUSOFuT/clUgedzb2yusanK5wqS2cFXEgQDKilL8mat+f/v2Xnr6zd2aoZmdlUCHzuXjUtM4PyWG4iNDqa2rh47LWKPU9DE9PY6O1anLj+XYX2lhGu04pp6YJIj8YrHUP9BPe8u1W9ww9sysRDpcrT3x8/z8dNpTViOmn5+eSHGRoXSg4qRIPO2uQIa/qaPLXbUJv184PYeGBvrp659bQ59ZNtdt3KDmATzYAK56KSkpthKrwGcaFyxQ04Oqnp0KJNAjIiKEpWgyytm+PhrYuZP6N28WpGsALpHd54V8Yp96iiJuvlnz1JBCpLy8XLhWIoZXriC1yIoVK+iXv/wl3XPPPZrH4AajCLAFjJ8EIwgwATOCHrdlFUSLPQPu5Oel5UgJlSGsAQVEVwWuPHA/jIqKogsuuECxKkQKQOjQJwgYrGr4QY4x5z/hGvl/X95Ef9lSphnhRXkptFOHNQqWM8SLQVWxo7tXkDG1Gp+QdW851aN9rvmptFMHkZqVlURnevtEvFhlfSu1nHIdL+Y4saSoUCHfr7UsmZFF2w5VjmsWGRZCs3JSqKG1g040yQuIhAUHUW9fry7XxSUzc2nrgdFnICc1kW67ahV94eLFFBoSrHX6Xq9vRwIGazny90E8Byqndiq+TjA90tVFA1u3nidcu3cTDSgnfU984w0KuegizZBXV1dTZWUlLVu2bFwuRseOcGl2+eWX0+9//3u6/fbbNY/BDZiA8TNgHAEmYMYxnNI9sAXMOtsvuR/iVhukx5X3BJJ14kscKlrubohBwCC+oZQrTEIIBx7MAdY1dwXWuac3NdDBRvd1nfsqLUgRCohaCyxnB0+0jjVDnrGcpGg609dPx0620bBCjq+gQH8aGhrWRTCEta6mWetUaVFBOu04l7wZ7ogzs5IoJMifjtQ0Uk+/skVKxMf1nZeg1zLwwoI02nVMWXVxZnYKhQYF0P6KkzTk4Bo5LS2BKk9qt7hhbnPz0mjfOaubNNf46Ai6cf0KumHdhRQfLX/Dr2VdnqprR7VAKKDCUoT0EfixU/G2auVwc7OwbA0ePUp9b7xBgwcPErnIE+iMbeqRIxSgICPvah/gXlhTUyNyMQYHy19UwB38mmuuoZdffpm+9KUv2WlbfboWtoD5FG7bDcYEzHZb6tsFMQHzLd5GRoPVCbfZOFTB/cQVAcMNKfLJuFNAxHxwQOvu7lbMFSbN2dFVEYHvsHKBDEpWOec/v/2n/XSyU3s8VkFCCB1v7dUM1cL8FNp5XJ4oRIcHU0FqrCBaR2tbqX/ovKJiRkIU1bmIOXM1kbTYcGpoV58/TOqrtDCdth+dKOuO/GIgY/2Dg3S4pnFCTq/clDghpqGnFKbFUflJ92QxITqCCjISxDhN7V00vzCLdh8dbzlTO356fCTVNctb1kKDg+i6i5fQ7Vetopy0RLVdeq2eHQkYXIsRK4XLldzcXK9hNxkde9piOVRVNWbdglvhcMVowvLg5ctp4NNPNS3RLyyM0hobXb6jlTqE+yHcEFeuXKmocvv3v/+dbrzxRvrHP/5Bn/3sZzXNjSufR4AJGD8NRhBgAmYEPW7LLogWegZAcGCtAllavXq14sylpMkgaIhpcWcBw8ETrkqXXXaZyxidrVu3EtQV4aqIAHBXMWiY3ILv/C+d6XMfX+S8kOz4UDrRpt1yVpgYSmUt7okbrDwFqTEEMY+KhnbKTorWZcVCe7+RERrScCsurbUkN5n2unGzTIgKo/y0OGrp6KbKc/nF5uWl0R43EvRKD0Z0iL+ieqRcG6xvdm4aJUaF0vu7DtHZEW0525EweqC/T7iruioB/v50+bK5dMfn1lBJYfakfCLtKtcOazU+t3A/lBKoTwrAHh5UUnfUK6+P/R46fPg84dqyhUbq5RO4B19wgbCEaSmBs2dTypYtWpqM1YUAB4Q48I5XumR78cUXhQQ93t2uvgt0TWAKNWICNoU22wtLZQLmBVCnUpdsAbPObsPatHPnTmpvb6dLLrlEceInT56kgwcPCjdFxGtBTUupSAmW8fu1a9e6vLHFTToIGG7ScZhzRcAgE1/67y/pAjclJpSaOrUTsKLkSDrWpM0a5e9HNCs5lPoHR6ipu49O9aonjKmxEdTYrl2YAqDkJEZRdVOnanyQfDklNpwC/Yk27R+9mddSYiPDqPOUvrlCvAMxYtnJcXTsRD11dKvbm2lpiVRZK3+oVZr70uJ8IdixZuEsXdYDLZg41rUrAYOyKS5tIMABIQ67FORChAuiWnXHs0NDQqGwf9OmUZXCrVvpbIe6dBWBc+fS0P79mqALufJKSnzxRU1tpMqQoEcMLyxgSuXZZ5+l73znO7R9+3YqLS3VNQ43YhEOfgaMIcAEzBh+U741EzBrPAJS/BfUrxobGwVZUip79uyhlpYWET+A/F6uEpU2NzfTbgSTE9Gll17qklTB/RHy9nA/hPqYKwJ2tK6drvrZa5rBBSHyO3uWhtWqZziMABfDch05wGanR9Ohuk6R0yM9NpQigvyotbuX2s64JmNZsSFU266OjDgDERbgRz0qEks7t1tUmEZnevspLChAJFh2FS/m2HZ6ZhIdq9FGhqT205JjqPKc22NwUCDlp8bSqdNnqK7NNdldUJRNuw4f1/wMoMFFJQX02RUL6epVpYQxvV0ki0pGRobIc2eXgs8rDunIAaaUXsKKa5XUHZXERUZ6emhwx45xCoUBOTk0dOSI5uX6p6bSSKPrGEi/uDgKzM8nv5AQGmltpdArrqCYRx/VPBYaIAkzLrrgZq5UoH742GOP0eHDh2nmzJm6xuFGTMD4GTCGABMwY/hN+dZMwKzxCODGF26C+MKFhUvJXRAHyffff18k8ET8B0gS1LSUCm5bEW+AsmbNGsWgb/xeclVEPczHFQHbeLCW7nj2Pc3gxoYFUmePsrKYqw7jI0Ko7bT2mLN5uUm0t2piXqzsxCiC/Hpr1xmqkrFWzUqPpcMntUvXR4YEULfONU7PiKejtaNxXCJeLDtZPBeHqifGizlitbAwg3YdVZ+8WWrr50cU7HdWVqo+NzWBkmIj6VBlLZ3pm7hnjgqIWh6EwAB/ouEhGhwaopSEGLrlytX0lc+soOiIMC3daKprVwKGOFBYzUEqQS7tUpzFRUY6OoRVS1i3IJyxdy/R4PgLlOBly2hAq1tgeDhRby85y6n6p6dTQFYW+QUE0HB9PQ1Xj/9sxf7mNxRxww264MYFGt7drhRpkf/riSeeEO9uOxFrXYAZaMQuiAbA46aciJmfAWMIMAEzhp+vWuPGFz8I0IZMsVJy5ba2NtqxY4fIZVRXVyeIEtS05AqsakjSisMnDjRweQkLkz/kOroqqiFgr20/Ts++u58qmzuJNIQOZcWF6rIqhQQFUP/gkGrZeUc8kEesotG1O1JKbASBkHX19FJZXZsQx1hcmEbbNeQAk8bMTYqiqkb17oeOc40KJurqOy8gIv0uJjyYshIiqbO7l2pbJ7oalhZl0I4j2glYclwUNbW4JpnhocEiVqy5o4uqG84LhMwvyNQl3pGdmkA1J8erYEaFh9KX1i6nW69eQ2mJcR7/2EkEDIdZWIvsUmBJ2bVrF82YMUMI8tilnK6spCMvvkiptbUUfPCgiOdy9+EPvvBCGti0SRMEgYWFNFReTgF5eRSQmko0PExDNTVuLWKJb71FIcuXaxpLqgzCjPe2q/QhDzzwAD3zzDPCHR1u5lz0IcAETB9u3GoUAbaA8ZNgCAEmYIbg80ljyf0QX8qQlodMsVLCZARwg6CBTB04cEBIll+kkIsG7klwK0xISCAQNxA1pcSfjq6KCPrGgdWVBeyXb+ymZzccpLiIEALh8CcSxKDZTa6twqQwKm9WnxNL2oCM+Eg66cYlTmmzosOCNIlTxEaECDe8iGB/2nzoBA06SLareSAW5KfRrjL1yZulPiEe0tvf73aIpKgQig0NpKZTZ+hUz6gVYFpCGFU1a48Bg4XtcKX6uU7PTqHI0GDad7yW0uMjqFqHYuP8omzareC6GBQYQJ+9aCF945pLaUau5yw6UkyR3QgY8vvBxRhuamlpaW6fHbNWGDp+nPq3bBFqhH1bt9JIXR2Ris+C43qCFiygwXPu1i7XGRBAAYWFFJCQQH5RUTSwbZvqeDGp39SyslHCpqMgZg/vVrh6K5Vvfetb9Mc//lFcnClJ1esYeso1YQI25bbcowtmAuZROKdeZ0zAzL/nIDtwM8OfJ06coGPHjimSJeTqgnIWyBRuvuGCpKSSVVVVJfqCqAZIG1wVY2JiZAGB6yPGRpGCw10RsO+8uIn+sXOidHlmfCRBur1vYFBYnXr6x1tzZiSH0dEm7QTMOQeY2l2NCAkSecL0lLzkaGroOE1F6fHkRyNUdrJFlerj4sJ02iYjQe9uDtNS4qjSwcLkrj7yi4EohgT4UWdXF9W2aCdghSlRwuKntcRFhQulydqmNqpv1WbtWzI7j7buO+p2yJULZtEd11xCF86b4bauuwp2JWCwkOzdu5dmQ5UvJcUdDKb4/dmREZFzC+6EcBmES+FI03kXYf+sLBo55zatZcJwGRyWaxcaSoFFReQfFUVnT58WFq+z53Id6rGa+UVGUrqCoqKa+SLdBzwRoDSrVG6++WZ66623hCIu0oFw0YcAEzB9uHGrUQSYgPGTYAgBJmCG4PNJYym/FgZD/BfIkBxZguQ0XAqRcBUxHzh4QU1LSTERroogaKgL1US4vCi5s6BfzANEEOQOX/pQWVQqX/31O7SjYmJclWP9QH8/gvtfTFgwdZ7pFQIaQkq+WbuwxcK8FNpZoT1ZcG5yDFU3qVNDc15rVEgAdfWej31CQufp6QkUGuRPlQ1t1N4tL4k/f1oK7T6uXRBjXl4q7Tmu3holzRdELCLYjwrSE2lwYJAOVddPyC+mtI9zcpJof0Wd5uc8ISqUWjpOiS+onOQYgrhKVWOHqmTXJfkZtPdYleoxi/OzhEVs/YULKADxYzoKnm0842pV9XQMMSlNYNmGcE9xcTElJydPyhzcDXp2YIAGdu8ei98SFqdTpxSbBS1cSIO7drnrdvzvQ0JGY8KQEiE6moIKCsgvPJxG2toI1jXneDGpcdCSJTS4bZumsYJKSij5k080tXGsjEs0XITNnTtXsY8vfOEL4oINgkxMwHRDjctKPkPrh2/Kt+SHZ8o/AsYAYAJmDD9ftAbpwQERX7TIDwPXQigbQmjDscCKBRdE6Xeoh/oQ7HD+nkF/EOtITU0VN+Mga3B5SUycmBAXUtY4FICcdXR0iOBwkC9XBOziH/6NTrad1gRPWJA/FcYHU3B4JNW3dVF9u/r2pQWptL18fNyQmsHngmBUuyaKcv1EhQVT1xnlnGMgPUh87D/cT02neqj9zHmiBtJ5vF4+ObGrOS8uyqBtR2vULGtcndS4KGpoPT9eQnQ45aclUGtHF1XWt7rsb1ZWIh2q0k4WkUz6UNV4shgXGUaQ7j/Z2kndPcpWx6TIYGruVL/30gIumFNIqxfOoC+vW0mR4WGaZOztSsBwAQNVvTlz5lBSUpLmZ8cbDUZOnxZufbBwDVVXU+8//0nUp148R6tVyi8lhYKgFDgwQMONjTRcVeU2XkxaNyxjQ2VlmmAIve46Sviv/9LUxrHyxo0bxV7BaqlU1q9fLwQ44JLOHEI31EzA9EPHLdkCxs+AUQSYgBlF0LvtEf8FP3+4H4KANTU1CbKE3F7OBypYtBB0D5EM1JXcBuUUE9EP1LZwywoihTgRuLzIuSnV1NTQkSNHRB4huCHCUhYSEiLiFOS+/DHnOfe/RIPDrhPwyiGXFB5ALWdG3RJTY8MpMz6ChoaGqbKxY5y1ybntvGnJtKdSO5ECcdtRrp1g5KXEUkWDetc8SLknxYRTc0c3tXV2a4o5k9a6sCCNdpaNKlZqKbNzkulgpbwVKyc5jlLjIqiqrpWaOyfKyidEhFDrKW251TC3JTNzaMsB+YNrUEAAFednUF9/Px1xIndQQBwZGqBhHc+OUIisbqCI0GC6eEERrVtWTAkxURQUFCSeccc/nf8Pc4ZFwW4WMKSjwEUMPudylytaniO9dYfb2s5bt6BQiJxa5+ImFd0CXQwWvGSJIHBKBXLzARAcQTqL2loarqujoMWLaXD7ds1L8IuIoLNnXLtEwyUyMDNzdLy6Ogq//nqKfuQRzWOhgZp8dKgDt3JczIFcMwHTBbVoxBYw/dhxS3ZB5GfAIAJMwAwC6OXmkvw8hgGpwoEKB8V58+YJ65VUJIsWCBR+h4L4LsR5ySkmwuUQ7owga4gjAHnDIU1OKQ3jwfIFdTiQOljYQkNDFQkYhDZWPPqqLmRC/In6hyfKJsKiNC05mhIiQ6irp4+ON3TQkMMhHdamMh1WpdL8FNpxXLvlbF4uCJ/2dtFhwRQZEkgZCZF0qhuKiq2q3PIApqMEvRZwoYC43Y0CIvCdkZ0s8osdra4XsWwgMhBq0VMWFmbSjiPuE0Znp8RTWkKMEPro7ukjOQVEteMX56bSgfLzFsLgwABatWA6rV86m5JiQOShkulekhMXC3KkzZnEOf9b6UJC7fy9UQ8XLUg1gXeCs8XcG+Ohz6Ha2nGES1iQ5HCH4iosXyr2xHGukjKh+D+4QhcUkH9iIp0dHKThykrhVuhctFrNxOE8JYXOOsSenTuxj46XnExwnYT8/EjLeeVP1In9z/+kiK98RRe8aiyxeIbxDo6NjaWtW7fqGkdtI3xHPPLII/T2228LoSYIuVx99dX06KOP2kJ9kQmY2ieB68khwC6I/FwYQoAJmCH4vN5Ykp/HdD5bowAAIABJREFULScIGIgQVLLgUuSY10eyaDn+//Hjxwk/zoqJ+AL/6KOPhBULsWRQSsMXOVxeYAFwLCCAcFWEtQ0xJLhNlxIxYz5yt6/7a1rpuif/pRmbiOAAOuMkyqHUCXJgwZUPbotwVzvdN0CtXcougUr9zM1OpP01o3m1tBTh8limPTYqPzWOKhzc/uIjwygvNZZ6+wbo6MkWYe1TKvERwdTWrT0+rrQwnbZrcF0MDQ6kWdkpFB4UQJ/uOyasr1pLflocldeqj8kLCwmi4rwMCgsKpI92HtA6nKgPa1513cQx/f396NKl8+gb111O86bnCiKGz5Xjn7Ay47ICKqBIXu78e9R1V/BZcEfSlCxx3orjQYwQLk1g3faWXPngsWMi71bfhg2CeMkKXciAF1BURMMa3fsoOJiCZs+mwaAg6m1rozAkSHZjocLQeixggXPm0NCxY6MCHbGxwhKGeLGz3a4twonvvUchS5a4e1xkfy/lN4MwUl5enmwdvL/xrkbs7oYNG3SNo6YR1Hbhbg4F3KuuukqkMkBS7w8//FCM/emnnwoFXSsXJmBW3r3JnzsTsMnfA0vPgAmYebfPUX5eIjsQzYBKFvJ8wSVQKo4WLUmWWFI5XLFiBUVERIzVhcULX54FBQXiR/o3pKpzcnLGAYIYEuSlQRA/Do9wf8RhLjo6WhBCOQL29t4a+vYfPtIMbHpMKNV3aidRQQH+FBMWKPJ0nR05SzXNnaoTMuckRlFNi3LAv9IiFuan0E4drosQ4NhTIe/yCPn2wvR4ggrcsRPN1DNwPpFsRGgQne7Rjg3mPzs7iQ7qiONaUJBBVfVNVJieKOLFKurG3/S72uDQAKIejTLh6G/JrGnU2t5JiBfbf7yG+gfcEx+0G03ejFx5ruuXzi6gO667nC5bNm/cswt3LqRkwPOfn58/YWkgobiMcCRmziRN6d9qCCysZ1rJmxSH6coFraGhQbgPL1iwQFhMjJazwGD/fiEHL2Tht2yhkdZWCl6+XPyflqIqMXJ0NAXm5ZF/ZCQh2fLZ3l5h5dJaYLUSYhvuSlTUqIUrIoLgfti/caNmufvUykoKkImldTc0fg8hJVyG4Rl0fhdL7fG9AIKG9/rrr7+upltdddauXUvvvvsuPf300wTZe6nce++99OSTT9Idd9xBv/vd73T1bZZGTMDMshPWnAcTMGvum2lmzQTMNFsxYSLSgc8x55YkiIEbSKgdouALGYHbcAuERUsqiNfC7TduMUGYpILA7bKysjElRUk9ES6GzreuOLwhBgxWNBA1uCOWlJSIw5wSAfvDxsP009d2aga2KDmCypq0u7ylx0VQffv4W+mcpGhKigql3v5BKq9vp34Fy1JYkB/1DihbnZQWMTMjng7XqickUj9qkzcjsfT0jAQK8vej8rpWSogKowodObUwbnJ0KDV1aI/jWjw9k7YdOn/YzUlBvFgUHa9pcGmJS4HoR4trcQ8lXEXy5nOui1ERYTQrN53qW9qFnL2rkpOaSNW16i2S+Zmp9PVrL6NrLrmAQoKDRDyNKwKm+WF2aIDPsWRtU0vapHpqxnVF3Hp7e4UFAwd6KOs51nWVRmLssN/XRwO7do26FH76KQ3s2CFrAQqaN09YwbQUOdLml5hIQbD8BAXRSHMzDVVUjCoXniu6FBAhdAcVRBmhD1fj6SGVfjExlK5DIl9aH1x+YWXCuxg56eQKvg/gjXDttdfSSy+9pAVy1XVh/cLlHIge/u5oocX3AFwR8b2DZ8vxck/1ACapyATMJBth0WkwAbPoxpll2kzAzLITE+fheAiTvgCRWBlkCweqwsJC0UiyiuHfjrf3dXV1wmXQWV4eLowgcgjkxu25XJ/SbBzziiEGALFisIbB9USJgP307zvoDx8d0Qzs7LQoOlSvPVfVrEyQIeUDf3CgP+WnxFJkaCC1dfVQZVOnCDtBkuiO0/qsSikxYdTYoZ0sLsjTLkEf4O9HF8zIFEmYaxrbNZEpEDm4NamJfXLeMCF7Xzaa+82xIF4sMz6cEmNj6FhNA53pO6/wiHrFeem0v0y9jLxj39mJ0VQjk+tsdl4mIaZrf3kNDcu4RC6YkUu7DhzT/Mwlx8fQndetpStXltLB/XvFgVPJ9Utz5wYbYM9A3ORcJl0ROfxOjdVNSiUxLt6tv59CDh2ioH37yH/PHvI7eFCoB7oriIkCYdJSQNqGW1tHBSz8/Gj45Em37ot6Yrn8MzJGEzcjZEwSzCByO17Q/Pk0uGePliUR2iR/pN36Lw0CESVccrlKnI33NQjY17/+dXr22Wc1zU9t5eeff55uv/12xTEk6xhcIBFjbNXCBMyqO2eOeTMBM8c+WHYWTMDMuXVy7oeYKQ5XiMnCQRE++Si4oSwvL59g6UL8h7O8PNp/8MEH4gZTyjMj1yf6dc4rJsWKwf0RBwCQNzn3p7v/eyO9s2/iwd0d0nPSo+lAnQ53wLxk2qUhB1hMeDBBlTAqNIiOnWyhpk5tiZ+Rv0y4pOmIjZqeHkfHTmq3DonkzcdGFRARX5UQGUaNbZ3C3dJVyUmOpWoNyZsd+4J7ZnWja8uTiBfLSRXP5aFK5BcbocUzc2irggKiq7lCHXFkqN9lHFxibBQVZKZQ5clGau44T9ZF8ua92kk/4sOC/M4SSO7yOfl02zVr6YLSBe4eVdP/HvuAPYGIAizYuJyB9cuZzA23tJD/7t0UuHcvBR84QH69vRSsMYnwSFQU+buJixKA+flRQH4+BUDAYmhIuC5qdSd0p4A4bmMQkwd3QljU2ttpqKZGE0kMyMwUJE1LCfvylynegFuelDjbVd421MH7/5577qFf/vKXWqanuu53vvMdeuKJJ8TPfffdN6HdXXfdRb/97W/pmWeeoTvvvFN1v2aryATMbDtirfkwAbPWfplutkzATLclYkI4QMEtSpKfl4gO/g2/fIhlSHliEDMAVyO4CToSIkkx0VFeXiJlcCMECZPGQp+IKQO5korkwlhaWiosXlKsGNwf0VaJgF33y3/R/hPaScaMlCg62qjdAlaan0w7jqsXfJDWNz83ifZUNVNGfCSlxYWLeKOKhnY6038+9kru6UiDy2Ob9nmir8TIEGrt0i6ksSA/hXbJxJxlJkZTelwktXedpuP1UFQcP+N5eWm0p1w7GYaVy//sMA2qEJ+QRoyPDhfxYsH+RB/tPqz5g5WTmkDVtepSAgT4+9OcgiwRl3WgopZK8jJo71H3qovOk8pKSaQTdefHRCLnK1YuoTuvX0fFhbma12C2BvgMQ4gHVnC4iiHvlnAn3Lx5NA+XU1yUHrGKgbw8CpaJyxoJCKDBjAwaAkHr7xfELqBn9NkfjoykAB0Km+MUEJ3BDg4m/N4/Lm5UMKOigs52demKT4PYB+HZd3PJEpCbOyp5PzwsyFr4V79K0Q8/rPsxUJM2AHsKgva9732PfvCDH+gey1VDWNeee+458XPbbbdNqPrwww/TT37yE/Hz4IMPemUOvuiUCZgvULbvGEzA7Lu3PlkZEzCfwKx5EOmmGg2dFdLeeeedMQsWSBosWogXwJeyY5FcBh3l5eGSCNdER2l6WNtAwCBBDxVFqSA3GPpAXcxBij/DbToUGJUI2IWP/IVadCgS5sSHU02bNmsU5jo/N1EQKa1lcX4KbXcibrBuIcdXTHgQdZ7upYrGzgmWrllZCXRIh3IirEXIfUXuldAnLEXI7Ne5JrXIM5abHEtnevvoaG2zyKUlkje7kaCXwy09IZrqmrSTaPQ1IyOBenr7KDU+Woh4NLWrI6vzi7Jp96FyrdtIGUlxlJcaT/vKquhUt7bnZ8GMPNp18KjsmCsWzqZvfGE9rSw9/5nQPLlJbIDPdc2GDdSOC5umJhravp1G3Fi39MQ9BV/w/9l7DzBJzvJa+HSO05PzzE7cvDs7u8pkEU0wsjAWQUhg44sx5tq+Dti/sQnX/GBzL5hgbH6MAYF4DDZgAzYZBLKEhDbnMGknx845/8/5emq2p6equ6pnVtpl6n2efVar+VJ9VdPV53vPe86zBJiDyyUyXPw7HwwiR1CmYLCc7u+HRaOYRt5gQN5igXGVEpl1OJDv6RFiGczAGa5elaVLWu66C+knntB0J0z9/RuzcyZTIYPX3Ix8MikMnUsl7+s/8xk4X/96TXMVN1ajWsm63jvvvBN/+7d/i3e9611Vz6UDMN0H7Lo8PNtoUB2AbaObfT0uVQdg12NXNz8mgRVBmFydFSmI9PRhZmtubk6YccqZKLOe4IknnliTl5fEOiizzRPx4vjhD38opOYlDzFm2jgPM19UUGNItWKskZEUGEvBYSqTxdCfflmrtY8Yv85hRiBWPvskt7O72mtxZc6vedNv7W/BsbHy5s1UH6TcvdVkxLwvhBlvGLcMtOHYiHrBB2lhPc21mFz0aV4nOxQAYUJ131qnDYPtDaixm/D42TEkK6gDlg58sLcNZ0a1Z87EWu0mBFbl8oW/WE8bnDaz8PoqrRcrnpcKiE+elgdD5S7cabciFonAajHj4OAOhKMxXL6q7v7ceWAnnjh1vuy+7hvYgd+57xW454V3wmwyqb4HT3dD0vpYsyTUCSkHv7iI9PHjmpZhOXQI6dOnVfUx1NfDPDAgPLGyY2MFwQyVGdM10KZqpkKjzI4dyLndyJvNMHi9sMzPw6CCBpzs6YFt8po/nJopzUeOIHPxYiGj5vEI4REhQV9B8r75xz+G9bbb1Ewh24aHY/RvpNVHsXBScWPW4fJQjBTAd7zjHVXPVa6jTkG8LtuqD/pLtgM6APslu6FP9+XoAOzp3vHK8xEoUTihlH4o9aQIB/2K+JJmjRc9wPhCZo1HcUiUQdaKsWZASayDfZhFo0raLbfcIoaQsmfFcvdSto1j8Q+jFIBNe8N48V//e+WLLGlBoYxUWrsaIYcRtL6wdjGN/V0NOD9dvsap9EJaa5040N2AlWAU4ws+BGNJ1dc61NuCM1WYN1OePlylBP2u9jpML/mxq6sJRgNwZWoR4XjlNZcqIKq9yDq3A36/fF2a3WrBvt42pES92OwGoYjhwS6cVGHeXLqWnd1tuDK+/gt2f1crWC92buQqYiUiIcX9Dw12q6YudrQ0ihqxN77yBXA7HWq35Lq1oyR76qmnCnRCgi4qFEoAgfWZTmdFwFC6OGNjo6yRsfhd7+iAqbsbBpMJ2bk5YULMoE+WMFvWEGok6EsFMwj0tAJKLkltjRppkUmq+1mtyNntcJ8+DYNKQCldeu2lS7A1N4vP4nL2AEpbVUoZlWvHz/9Xv/rVeOihh/Dggw9q2HX1TXURDvV7pbfcvjugA7Dte++35Mp1ALYl27ilg7CuhWCHQExOKprKhPT6Ym2WBJz436UhiWhI6ohKYh3sR2Nmh8OB22+/XQzDU1j6iD3vec8TxrQMrouZMma/qLbI9ZUCMGaU7v/k9zXvR0FKXruqIP2fuK5qVP6qnfNQbxNOTSyB2Z2+Fg8a3XaEYwmMzPuQLmOkrFaCvnTzKLoxWoF+qLThzEYFo9cyZ/RMIxhzWE0Yn13BSkiesnfrzk4cvahdyXDPjlZcHKucOWvwuLCzsxnLwl+skIXsbvJgqgrBkNv29eEphcyZy2HDgYEdWPT6cXVuI021tc6NhRVtWclatxNvf90rcN+vPA+tjfWan/VqO9AHK/nkk2s1XEL2PS2fMTbt2IHsVOX7ULwWA8UxipQMScMztbWJ+iYhYEHT49KgF6DNJvy5tIR5/35kzhdlHiXBjJYWQSNkrVpueb3NQzUKiIbGRuS98ocshrY2cJ9IbeS15blfq0WUueFhGDXK6rPWbexLX1rbBq2+blSjlERTaB1CWxG5+M///E+88Y1vxNe//nW85jWv0bLtqtvqMvSqt0pvuI13QAdg2/jmb8Wl6wBsK3Zxa8egehn/8AS1FOBwJhoxE3BQqpieMVKGq3QVzKI98sgjQlabvjJKYh3sRw8kgj3JR4z/5hw0+5SC/2b9Geu/OJ4cAPvWsQl84N+PY0ejW3zJZ7bl6nII8QqGuvTVujijLRvFdbXXuTBfhceVEJkw5JHJai/I6m2uwcTSRrVG1niRrui0mrDkD+NqSZtbq6QuHq5Cup57QxpiMKwMammPNNjRiDqXHTPLfswuX8tc7e5swKVJ7cImt+7qxtHzKgxvix7WntYGtDd6MD45I5Qdtcbt+/rxi9OVFRD39nWBdEVK5BMo1zgdCIW0q25yfXcO7RK1Y/e++Dn43df/Knb2yns2ab2W4vbZ+XmR3WJ2Kf6tbyFz4cIaQKg0rmYxDZMJpAVSdCKfSCAzPo68vzKt19TTg6xGeh/XTv8tU2vrBsGMctelSQFxdSDzwYPInD0r/rUGKCntPz2N3Py84nTmvXsFBVFTkL75pS+VtQ3gYZGaIBjjIZsE4ui39bWvfU34L9Ir7L/+67+ECuJLXvIS1NfXC0o6f6bG203N/GyjGzGr3Sm93XbdAR2Abdc7v0XXrQOwLdrILRpGSX6+eHj6eBFctba2iiwVQZKcGSZryOjT0tPTIzJWSmIdHJu1YqQ8PvvZz16r9WI/grzioFgHJej5/+UA2P/3o/P4u++sryGhxDcBGTNFmVwOi4EI5vzrMy+39DXj+Lh2IY0CcNMuFtFS68BSQLsaIffCZTMhkqhcq8brba2xIpGII5DIoa3WgfNT1Zg3X5Og1/KY7exowMh0+Rq34vEoWd9a58JyIAxfIAifQnas3Bpu392NX5zTBsA4HhUQqUa4p6cDTpsFF8amEU1Upkqy74HeNpwdUV/jU+9xY3dPO/K5HJ6sUP+ldK2Hd/fixIUC7Y4HJS+68zB+9w2/ijsPXVMR1XKv2JY1RlL9FoEXRR4Y1WR+KvZxOGDZuRMGqb5pZASWI0eQeuwxTctWDfRqagqS8KRFZrMFfy0K0mgITVRHsxkmSu/39SFHARKVgFJaDg2VKSSiJRxveAMaKvhy8TO21Aqg2NONKogUOyKgKvaAozfYe97znorLoRjT9CaMoIsnYBaMmTiCv3vuuUd85vPdw0M9HsDxIJA1wjdz6CqIN/Pde+bXrgOwZ/4e3NQr0AHYjXX7eEIqGakqnWYeO3ZMSMLzlJQvdNIE5ULKWPGlzBfl6dOnhchGG2lFJSGBOo5FGsy5c+dEPRiFOYqDwhw8caUEvhwAe9/XnsJXfl75CzhNkLsaXbCbjQjFUkJk4hcj2jMuR/qacWJcPciQrmVPRz0uzWqjnrGvx2FFMKZeDKN47w7uaITdZEQ8mcLI7AoSKoUxjvS34fioOlGJ4vluGWjHcRkj5UpPfI3DBqcZ2NFSi2AkjsvTi6qMfTnu/h3NODemzTuJ/Y7s7MbxC9cUEEW9WF8HMukMzo1PC0VHpWhwWuENhitd1oaf33FgUHjdGZDHmStXNdFY2xpqML+8MWN7eO8g3v76X8Urnne7bPZaWgTBX/rcOUEnZP0WAReBglzQsFjQDTWEZWgI6TNnrvXweGAZHBR1YVTuE/LzJfRFy223IX30qIZZoCjxzgyXhf5b/IxaWioIdKwKZpiHh5HReD30EDPY7cpUR5ercH01NQI4CcEMepo9+9lIPf64pmsyNDQg76v82bCuJm5+Hs7774dnk6qEVDhkTe/dd9+9bs38nKeoEmtzH374YWHA/P73v1/U7dIXzO/3i7/JmPjHf/xHTddbrjHBHIHf9773PTE37UfuvfdevPe97xXvgZs9dAB2s9/BZ3b9OgB7Zvf/pp9dB2A31i0sJz8vrZTCGzwpJViTy1IVXxEzVsyU8ZR+fn4eL3zhCwVwKw0J1PHFf/LkSTE+hT1KQSBPPykAQh8xSSSkeKzf+exP8bML6rycivvd2t8s6pHMuRSsVjtWokksqshQVesBdqS/BScqKCDKPRn9rbUYW6hMzSrty1q1XDaLXK5AeWQt1mBbHWocFniDETGmUh0b243Maadn0rz5qUvqM0PSmnd2NOLK1DV6Vr3bgf72BqRSaVyYXCjrDdZSY1MtO1+8R3fQvPnMZdlfRlEv1tWKlUAIo9PrQXp9jUt88awmbtvXj6fOFGhmrY114KHAgjeMQKS8lH2NqzJ1sbezDW+775W47+UvgMNmRT6VQurEiYJoxqOPIvWLX6jOsKgFBMV7QLl0CmrE6SW4uAgr67dKTeJKNo0CG1mN2RNmzdInTqBUMKPcOBWzczI309jZidzstUOIbG0tMu3tqKFoyPJyAeDJ0Pu0qDpK026oT1v9wZqJNE3YZWri6j/3OThf+9pqHsW1PrQJIZhSOlRjww996EPiD/3dyGzQo/od0AFY9Xun9wR0AKY/BZvaAR2AbWr7trQzv4BLdBQ5+XlpMsnLi/+WTJKVFsKMFWsDeHpK4CSJbJS2J+jiF1kCMFIV2Ycqi6Xx6KOPwmazCdl7OQD26v/zHVyZ117Hs7ezDhdn1wMbUvi6GlywmAxCbXBiMYh0SSbkSF8TTlRBXbx9sBVPVZFxGxbmzdozbkLww6ucpWG9FgU9TEZgZjmIhaK6No/DjGBUG12L9224twWnxrRnzo4MduD4pYLCXWm47Fb0NNcgEY9hPhBfJyvvtFkRjWjPRIm1DnTg5KXxir9PO9oa0d5Yi4kZ+osFsa+vE+evVO4nN/DOrmZcubo+W0eZ+UO7+xBPJHFBQUyEsvTnr1TO8nLOBosJ9yGGX79wDLX5LECxChXS6dJ6mWWp5N3FtqzFEobA+TxysRgyxdmvirtKXq0LoElyBZAmhioWzCB18sqVDYIZ5aasqpbrrrtg5NoMhoICo8q6M2Nbm7x4SJkFCoXGY8cKEvTMhnE/aepcgZLY/LOfwXr4sJrdVmzDwzVSEEkFV4q//Mu/xCc+8QmRKSMdXI/qd0AHYNXvnd5TB2D6M7DJHdAB2CY3cAu7E9BQ/VBJfl6aijQVyhUzOyWZJCstg5LFBEwEYLt370ZfX59sU3qJ0QSUgI50RPL9mV0rjccff1xk0wjO5ADY7e/+N4TileujSsdtr3NgvkLGi1mjnqYa1LusoN/YzEoYjW4rLlfhAXakr6Uq6uJtwrxZuXhf6T7s7azHRQ2S9x0NbhC0MWt2aWoBkTJS6kpzUizk6oL27JAwb75QWQHRYjZiT3cLrGYTRmcW0ehxYkSl/1bpmklHnV5Qn+XjM7i3tx2djR48fvw8InFttFD2txnziJepQ+rpaEFbYx3Oj04iUkQ7vePgLjx56pym33x7NoNfNSRw/4Wj6EirX6vl1luRPnZs/VxGYwEcNDWJzFp2fHyddLzllls0y7Wb9+0riHzIBcUgOF99vZC1F2AkFAI8HoB/awyOlRkpY7hNgLfqL0ZvM8rds49WKqEAlRV8u9aWXlMDy8CAMHXmH2YplUyklS63fWZGeIZtJljrxUM4Gi0rBcU3/vmf/1nQZ6lcq0f1O6ADsOr3Tu+pAzD9GdjkDugAbJMbuIXd1dAPOd3FixcxOTkp6rMk3y6lZVCynlRFmijzVLWmpka2KWu+WPtFxcTx8XFFYQ+KdXA8ZtL4dzFFkcIUt/7Fv1WxI3kIH7CMcp2P0qC72gqqg2aTAf5wXCguZsrUC0nj7G6vqw649bfg+FgVtWq91WXqBtvrMDHvRX9bPeqcVgQicYzOe8vWRPEaqXBoNeQ1GzCz71BvM05rrDmjquRz9vciFoticmEFC171AgYWswnZVLziNck9A7fu3oEzl8exf6Ab6XQG50enkFWRYepsacTMnDqqrNNuw4HBHngDIYxNz+PW/QM4ukpd1PKwO5FHIpXG3aElvGllEvvjlcGLoOsdPVoAQHV1yEcihfqmiLK6ZTV1T+uMkSXBDJcLlL4X9WIyQFWJqld2T4xGwGpdD26UAF7RQNY770TqySe1bDdMu3cje1me1rqhRm18fI3CWA2ANTY3o500yE0GVW15OCBnKyIN/ba3vU1I0Mfj8S1VPdzk0m/K7joAuylv2w2zaJ2CeMPciptzIToAu3HuG7NfBGHl6IdcLcU0WM9FJSoCpnJBpSpSWlj39fznP1/RHFQCdQRoXANrEOSMRPkFgS9+ytWXArDRhSBe9eH/0ryhDS4bfEVeVWoHMBsNom4qu1pXxX42s0lQ5DwOC1LpDGZWQvBGNmYcmmvsWA5p8y7i+HuYyapCLv9wbxNOVkGVFLVqo+uBgstuwUBbHawmI+a9IUyvbAQ7LbUuLPm0U0F5jV0NTkwvae9L8+YnzxW+hPa3N6K5zoXFlQAm5surVPa2NWJiWjtVkvPs6mzEpYlrNMIGjxs7d7QLsDRaVMdW+kwJFcPz8l/Oyz1/AxYDmgPLOG51I0WUqyEGkcFI5lqHIxEfHliZxLPDK+trCTyeQgaIGRyTSYh00BtLbVgOHy6oDKoMghHrbbeJrFapYEa5IdaBNpVzCdl6v3/t+soBvOIhNSkgrna03HEH0r/4hfgX/b5MnZ3i84K1ZOVq1KqR1idAbP7BD1TugnIzWoVQfv7IkSOKje6//37wYI2iGHI2JZtexDYaQAdg2+hmX4dL1fYGuA4L0Ie8uXdAB2A3xv3jFwNKy1eiH3K1fEkHAgGRhaJccblgxor0w+7ubqFcqBRXrlwRmS8GjZb37ZOX0yZFJhQKiWxaKQD770tz+B+f+anmDR1s9WB0UX3GRJqgrdaJhUB5wQS2Zbv2eqeor/KG4sLwOZnOaFK9k+ZsrbVjQYU4SOkm7Guvw4UqVBdvH2zDU1fKqwpSOr6rsUbcj7F5rzBephrh+Ql1GZ51X3RNRuQzKVVZxNJrHGLN2cj0hvvf0VSL7qY6+EMRXJlZQL4IMLPxkV3dOH6+DCWtzBPlMOYRTchT+nram9DeWI+J2UUslviLUQGxGgl6Sy6LbDoFlwEYiPgxb3NgwVYwKq8Uh5NhnDBtpIz1p+N4izOPV9jyMC0vCcl0qU7MwKxXQBsYNra0CCClFHLqCIsNAAAgAElEQVSCGebdu5FRyBYpjSNqpQgOK4ShuVnIwRso/mO3I/XII5rq4CoqIJbObzQWJOgHB8U+lFI0yy7XZAKYpVMwuFbqSwXE+i1QH6T/Ig/BKHKkFL/2a78Gfl6TBaEDsEpPX/mf6wBsc/u33XvrAGy7PwGbvH4dgG1yA7eoO788MwNGIFbOTJM/p0gG6wSYhaIMcbngC53GnRTNoBqiUtDzZWS1LoOnr0rF3RTrWFlZQW9vr8iE8bSW2TUahn733CI+/F2FOpIyixzuacSpSe1eXnva63Cpivqv3iY37BYTauwWxFNpTK2EVIlcUMmQ9ymnRqig5Ho76hyY81UGi6XbdLivGSfH1NecMSnT11qHvmYP5lZ8uDKzIkyH1UZXkwfTC9rvBcfvqHdiZqm8QmSjxyWyY/FEApcm58Xayikgllt3a0Mt5qnuVwkAGAxCrINUwotj06Je7NDOHTh1UTvo2xEPY9JsXZvRkM9jVzwESz6HC65a5AxGxdUMhbw47VT+fW1OJ/D6lSm8xjcLdy4DtQIcxRMym5VfuXb/8gYD0h0dcPf2iixa5urVjYIZcrTASpsKQMmsuFy2qRp6ZKkC4oalORwFjzF6d4XDBYoms/5y9XMVrovgNKdGCbJY9j4UguM3fgM1f/AHKnatfBOKHPFQ7cCBA4oNab7MAziyFuRYCptexDYaQAdg2+hmX4dL1QHYddjU7TSkDsBujLvNLBX/0K+LYEYp6P9FIQyGmgwYRThY//XiF7+47LhXr17FpUuXCqayL3qRYluKdcwp1M58+3IY3x3RDjIOddfh9LR2afcjrKua0G5svK+rHhem14tTUPCCRskEMCvBKCZXwhsyZGwz69Ou8scPabMBGxQc1Tx5Ay0ejFUhpHHrYBuOXpmB3WLGYHs9HFYTlvzhiqIcQ31tOD0ypWZp69qwjiudTKj2C2Nn+o1RidBjM+GJM5cQT2oTbxka7MapVTNktQsW/mI97TCHAzg2tQj10LQww1BoGacd8kILjekkepIRTNpc8FrtG5bUlU1hOq8M0KQOrmwa9/pm8UBXPRqOPaX20kQ7M1X40ulCvVg0iuSVKzBWEKIw9fWtmT6rnoy+XA4H8onENUGQZFIIZuSKAGDpeNV4jUlS99JYzArGmpthcbthTyRkPc3YthoqYelca3M2Na1l8dZ81Ipk7xseegiOe+9VvX1yDXm4xs9rHpQpMRDYhubIFFaidYgOwDa15dw//Tv05rZwW/fWH55tffs3f/E6ANv8Hm52BL5UeZrJDBRrr5xOZUoTaYKknzDkjJKL18Jx6QPGv3/lV36l7DJJZ+EamFFjZk0pJLEO/vzgwYPweDxr0vnv+/eT+N5Z9dkaaY7BBjNGfdq+fLPvoa5anJ7WRs8S+9bXjOMV6rFcNrNQXHTZzYgl0phaDqCr0YPz09oBX53dhEBM+/VxrR6bEaG4+vofaU/3dzfi3ORGufwGtwO9LbVAPofJBZ/wXiuO23Z14ikVCoilz0dPaz0mZipno+Seq656J5Z8QezpaRP+aPQgC0ZiFX+t7tjXhydOac+4OrNpxDIZ1GZS6EcavkwWVxVAVekihoOLOOmsK7s2Uz6PfaYc0rksLsEiFFFsyCOVTpfNkJUOakYeL/PP44HlCQwkFfajRDCDsump//7vintX3MBy++1IP6US6NntAnCZSHNcNXQuJwhSupBqQJH17ruFFLzBZEJ2fl6AvIpy+dIhVqao6E7FrkgZOkHT7OwUPYTs/VT5Q4nmxx6DdWhIxQzKTUg/JwDr6uoS9b1ywc/y4eFhQSn/2c9+tqn59M781dQBmP4cVL8DOgCrfu/0nuB7rAo+lb5zW7oDfPESVF2+fBnPec5zhF+XUlAinlkwCmXwRdzW1qbYljQV1osxXvayl5U9LSX4Iw2xUq2YJNZBmiRPYotNnd/yjz/GkyPaPbL2tntwcV57DdhAnRljfu3Aphrgxtf0s3a1IZbKgLSzpWBUiF+o+e3pqrVixq9eely6ofQGC1YwBVa6+W21dsz7lZXypH49zbVoqXUinkxhdGYZ+7obceyy9gwYfbxOXKosXV+6XqGAmIytU0A0GY3YvaMVbocNV+fo9yWvFnhkZxeOVVE71h/1Y8yyvharIxFBWyqOaZsLyzZlae+BsBejduXfz9Lra0/G0J6KI1lTg3PZytkvufs5HPbCkcvgAe8UbneYYaHwjsUiK5hRTYapLC3Q44FlcFBku9YEM1Kpquh9sNkAAiIZw+Ti6xaGx62tEBL0U1Mw9/ZqV0Ds7S0ANTUhyfo3NsLAA6Vjx8pm8eSGbJ+bg7HM57aaZZBWTnEN1uAODg4qArCdO3eKw7fvfOc7aobV25TZAR2A6Y/HZnZAB2Cb2T29rw7AboBngGBqYmIC9Pei/wtNkOWCL2jWf5GmyDos1gnwtFQpJFDFn1eiINIAlD5gpL7wC4BSkKZIuiLXwPmL69Ve9qFvY3JZO0Wvt9mNq1X0G2xxY3RR+3x9dRZM+LVnlQ521eLMzLWMm9tmxg5myWxmYUg8uRSU9esabLRhdFm74uLO9nqMzGrPuNGfK5NJI1cidlHpUWe/2/rbkM6k4Q2EMTa3olqopFgBsdI8xT/vbWvAxFR5BcTBzhY01rowt+TD1OK1+qaeFhoya8+6HQos4JRCFovgejAeBLNkI45axMyWteXyZ/ZUDDGjMkVY6dqPxIPIpFMIm8wYt8tbQSj17UEaV3OFV/3eeAgPrEzjRaElmGQ6VFM3Zjl0COnTp8VoNC5mlkpkmxYXhYCF3ClDNbVcsv5frB/dtatAmYzHC/VbJd5iVSkglqv/kmrGPJ5rsv6rNE3zgQPInNPm8cY9a19lJWh59kvbkipO1Vp6NSr5NfK8tKOjA694xSvwr//6r5uZTu8r7Dr0DJj+IFS/AzoAq37v9J56BuwZfwb4QiWwogfX2bNnhf8LwY1cUHqeEvSkpzBjpmSWLPXly5xmnQR4d999t6gbUAqevFKuvlJWTaoBo/w9wV9xvdqhd30VSQ2CD9JaauxmhBPaM1mtHjsWg9qBTV+TCxPLlbNDpXvVW18euPFV3uK2oN7BL+15+CJJLIUSIAAbqQKAHelvxQmNflxcc3eTB1NL2g2Y2bfGakQolhSXzgxcX1s9TAZgZsmHBYVMFNsO97fhxOVJzb9PzGJpUUDsbqlHu80E79IKJgJBpNcLuKuaf9g/j5Ou+optrbksdqdjyNqsuAwLmrJpLGgEtdIkh8IrOLUqwNGTiKI+m8IluwcJU3kwxzWk89kN1MXOVBxv8E7j1/zzsOdX/fOqMEZm/RdFM2g6nJmeRk6lN1o1AhdCFv7ChYIEvduNXCBQqN9SULGU9k7UmsW1/Z4L/7THHhNDGOrrYe7vL2TxVlaEkbSSyiHNrcvVsMk9NASjzd/9bsXnqVIDfv6S4cDsl9IhGD/LKdLxlre8BZ///OcrDan/vMIO6ABMf0Q2swM6ANvM7ul99QzYM/wMkH5I9cPFxUUwC1VOgZDghyCMWTLKy5fzAaOk/SOPPCJquijuUa62jPMzs8YYGhoSJ6xKQR8wn88ngBrrvyQA5osk8Kz3fEPzborskUbxBU5iNBRc6Is9wNROXuewIBDTngHb0eTC5Io24Oa0GNBXZxYm0/FkFouRJFKZvKqlDnXX4UwV6pCUgz89rl2Cvs5lhz+onFHsbKxBR0MNwpGo8PZKpK9JWLBerpLfl9xF37GnG0+eKdQ0aomOWBDxbBrdsRCiRhNGnbXIUc1PRfQHlzHm0JaFqk0ncTC8ghm3BxOGa1kxFdOJJjtiASHOURyubAa7jTksGS2YURDnGEiEMWpVpkTWZtJ4rX8Wr/POoHX/XqTPnFFektkM0+AgTI2NyCeTBSBisSBfRrJeaTB6amVnK3u3rUnQm80wOJ1I8nNGhVG2NG9FBUSZBbKPZWhIyPev1YypuVFVAFgO63zwQdT//d+rmaFsG9p7UFhj9+7d6FytPyvtwDY8+HrnO9+JT37yk5uec7sPoAOw7f4EbO76dQC2uf3b9r31GrBn9hHgiSYzYAQ1fPkqASBJfp4eMWzDYu2BgQGwHkAuZmdnRUaNL2tm1+jbxb5yQVVDgjsGvcJYB6YUBHUEd3fccYfIqJGCSBbHxVk/PvAfJwQoCsdTmPdFEFKR1drR6MaUVzuNsMXjwFKwslBD6XVQDTCe1FaYL43hrBIstjiNWIoW5jQaDOios6PWbhaS9jSDXgkXMk6l0ceMm1fbyT/HONhVjzNT2qmLu2lqPKmO0kcATLn7Ro8TwXAUV2cWEUvKX0e537BDfa04dVllrU7RQPv98zhbJOlek0mhLxoA86ijTg9SCpkl0ghtiQjiJu0g6nBwESectehMxtAq1YvJqB2WXq8FeeEdli0DEHfGw7DnsrjgqF3X7nDEK+asFLZcFq+2A284fxQ7UqvPDAFPezsMbjdc+TwyIyMbMklUTcxoMG0W62CtEyl7MgWQpC+aOjqQz+UKhscz1zzsLMPDSJ86VelS1v1cSZVwrZHBUJCgb25GPp1GdnJS1MZV42tm2r0bWZVeaKR6mrq7YTAaYb/3XtS8/e2arkuusd/vB20+SANXqu3lARwB2p//+Z/jQx/60Kbn3O4D6ABsuz8Bm7t+HYBtbv+2fW8dgD2zjwCzTwRhFNagYIYSAJIENfjyJUD60Y9+JLy49uzZI3sBzKYtLS2Jn1eqLZMyawR5bM9x5YI1CgR+DFIlHQ7HGgD70bkZ/M+HCvL4UjTV2IW0Oz23MtkcmCWb9UXXmfwe6GrAuRmv5puwu70Ol6vwAGOmZnJZXtSh3CI8TiuCq9Q8rYu1GfNIZpWzXvUuG7oa3bCbTQjFEri6EEAinUFfswsTVRhUD4iaM+12AAc663F2UtnAV+m6mRULBkPo72iEzWzE3LIf0yopkJ01Vsx4tQuwDK9M40SNPFXXns1gIOqDMZfDuNODSJFvV2suhYXMKmVP443cG1rGhaLMWaFeLAxnLoMRRw1iCqCuz5THeEod6K8nkExEMO2uwzJMGIr4cNopL3svt3wj8rjbksebEz7sG71YEL0oE8VUPbXbseb/ZTIVMmr0HqME/cSEUEZUCtZK5VT4thX331BrZrPB0N+PqNEIJ6XwJyeF91dpMNtG5UQtISiSv/jFxi4EeaRNtrQUhEEI8haviQ01PPwwHK9+tZapZNuyrpefxVSXbW5ulm3Dul4KcHzgAx/Au9/97k3Pud0H0AHYdn8CNnf9OgDb3P5t+946AHvmHgECHgIwZkJYq0V/LyUAJAlqUCXR5XLh+9//vqJiIWmNpBRSzINUFtaNKdWWcQ3MahFMkarIjBoza3IhZdX4M1IlmVEzGo0iA/bwY1fw/37zZMXNNJuYAXKhwW2DxWiAy2oWAIyZIC1xuLcJJ6vwADu4oxFnq6D1DbR6MFoFGKp3WuGPalNANBsN6Gn2oNltRTKVxpw3hAUViobS/u1sr8WVWe2gdmeTA1cWtIPTXQTDU+vVL5trXaIWLZvLYmJuGYHIxvsr6ptSCdXUweLnY693Fufdleu4zARJSMKeTmIyZ0JbIoLzGlQMi+dsiAXgtWz092IbUS+WTSBnteFS3oRsUW3acCyAkyX0w0rPupGHIfEQ7OkUTrjrQUNlLdGTjKIuncKD3mk8L+JVrJTTpJrodApFRGNXl8huiYyaWpBTJb3P+tznCj+zUhXGcntRDdAT91CqG7PZCt5mq15qQhhEBuRJa2h58klY9u3Tcntk25KGfv78eUHvZp2XXPBgjXTyj33sY/iDLTB+3vSib/IBdAB2k9/AZ3j52j6Vn+HF6tPfeDugA7Bn7p4QeBGASUCMvi4swJaTIKagBqmKfPkS8NDfizQV0hFLg1QWFnMTzNFT7MSJE4q1ZQRdrCejqAY9xsrRGgnkqJQoedGwvkwCYP/nP0/hcz+7rHkzb+tvxtGxZXgcFrTXOWHIJJGhTLXFhllvRMi+y8Vt/S04OqZd8r7afsO9jTh59ZoCn9oLHWypqQq41Tlt60BLo9uOzkY3bCYDAtE4ri76kSqqwSpeT53TDH9EG+hj//3MRl7Vvqc7m524UiYbaUAenZk4GsM+RHN5TLjqkTaZ0R3xYapMfVO5PW4OLWNRI6hhxurOlUnE8nnM25xY0NDfk0khKIldVLj5wl8sHobfYsVVew2GQys46apMIywd1pnNiLW2ZJLoTCUw5vIgaJDTPty4oOGoH6cchTl7k1G8yTeDVwQXYS2hDZJGl52elr0iIV4xMACDzbbm+cWMmvVZz0Lq5z9X+ysg2pn370fm/PmKfYzt7QVqn9mM7MICDBYLMippgdLgxaqOFSdkg9paWJjham0V2S0hDJJSWSNKSjHX6VCu01O1BkAY3FNllhkufrbKBQ/pXv7yl+Of/umf8Nu//dtqh9bbKeyADsD0R2MzO6ADsM3snt5XF+F4Bp8BAir+IaAiGPvxj38s5IdJMywOifpHZSzWBzDYlqekhw8f3nAFVEgkmHruc58L9j169CgOHTqE9vb2DW3p/cXsGmu6CNqUaI1SDZrdbhd0SdJkOL8EwP7o4Z/ju6flv8iV2+LhHY04NSmfreGhf2utA801dkFjJOBYCccxF4iC/U5UkQGrFoDdOlAd4Bve0YBTVWTcdrbXYWRWWcmQhsXMktW7rEil0pj1BrEcjMFttyKsNitRcmPaax0i26Y1Dve14MQV9ffelk2jJ7SC5qgPEzYXZhweTRkeezaNeDqlqY90TXv9czi/WlPVnQijORkXWa3JCqIcu2IBXFbIfpXbr05k0eNfxBW7G8saweaufAqXc9eERSy5HPYmwohRdKTCeocj/jXVRWl9jZkkXu+bxWv9c6jJZQGXC+CzsgrKKF5h6uoqSNDTfFjBR8u8bx8yF7QZYCuBNlN/P0xtbWueX6UUxaoUEJ/9bKQeX0+HLr5Ha/VbJcbOrCUT4EtDcL/aNO6F0vDT09Pis/j2229X9ILkwdtrX/ta/Mu//Ate//rXa1ip3lRuB3QApj8Xm9kBHYBtZvf0vjoAe4aegWL6IUEM/82XazHIkpbGFzOpKTwZlWoDWItFKiKphaXBU1ICOmbLpGyYkmcYQRfpj2z7wx/+UJHWKGXKWH/G9bBWjWsheOSfN/z9jxSBVLkt3tVaiysL2mqAWGdECiIl7ymRTg+uhUBUyL5XiqHuBpyZ0k7PO9LfjOPj2uujbultxPEqgOKRvmac0Jjha/Y4sKu9FolkCoFwFBNLfmRU1jsJ77BUSrN3GPe735jEWOWt33BrDi2N42RdG+qSMXRF/TDkcpixu+GzOcvexp5UBBMKqoGV7n9LeAULMkCoJRlDZzKKiNEiRDxKKX+Hw8s4odG/i2sxIQ9DKoGMwYjBRASuXBYjDjeiKkRADkd8OOGQr//qTsbQlE3hsp21Zxul7DsSUcwpAD5m1u4JLuDNPc3oMBtl65rK7aOhpqYsJU+urwBgR4+u9/waG0M+qPy7X40CIudeB/Yq1G8Vr7UasGd7/vPR9O1vV3rsVP2c/oo8OLvrrrsEJVwuvvGNbwgJ+m9/+9t41atepWpcvZHyDugATH86NrMDOgDbzO7pfXUA9gw9A5L8PP+WzIxZ18UsVSmtkBRCr9eLF77whWtt6dtlsViEJH1xSNmynp4e4RPGbBUBmZxnmGTsTNl5ZrSU5uf4UqaMa2OhOOmNpEBKAOzuD3wLC1V4cjW57VgJa6fLtdU5sBBYX1dEMQv+f9aVcV9Jw5v1RdZ5k/U0uasyi97dWYdLs37NT8uhHQ04XUUG7PaBFjw1ok6RsHhRh3ubcWK80M9mMaGnyYNalxXJZAozKwF4Q/LCBDuaazE5r51iyXkcsSBiVWSH9ixP4kLtRrGBzmgAzckoEg4HJkx2JEpod0O+WZxS4eNVerOYOUukk8hVqKeqzabRGwsiBaMAY2mjCQeDizijQo2wdM4duRQmSzQ/RL1YJoGc3Y5LOROyCus5GPHhjAIAk+ZxZDPYk4jAV1OLyVVQ6s6mEYGRLrNln1cz8nhxcEnUie1KqhNt0WT0TJuK/n7h+cW1EIBV8vwqXnBVCo02mwBg9Pli7Vil+i1pPk3XVbRI52/9Fuo/9jHNnwtyHfgZOzk5Cdb5Wq1W2TG/9KUv4fd+7/dE3e4LXvCCLZlXbhBm4gj2+E7gf7M+rb6+Xrxv/vAP/1D4SirFQw89hE996lNC/InvNrI0/uRP/uSGBIw6ALtuj9C2GFgHYNviNl+/i9RrwK7f3pYbWZKfZxtmwBhytEICCen/MwMmBWvCmDWjvHxxUHL+3Llza9kymnsSrMl5hrGei0XdEj2RyopNTU2iCLw0pEzZrbfeKgAdxyNwIwDL5fM49P98TbMnF8UmaAnE/lqCEuhGowGZMsqCa1+sDAa01zlARUar2YhsJos5XwQLwaicirbiMppr7ViqAmAOtLgxtqid1jfc04RTE9ozbrcJ4DaveB1tdS601ztF5tAXiopasmwuh0O9rTg1ek0yXO39aEiE4TXJf1msNEZLcAELFQCGJZdFT9gLdzqBgNmKq85aEICddMsrIJabsy/qx1iRImKl9fHnzmwaA7EQbKkozjnrEa9gnFw65iHWYpWpNRP1YskoAiYLJkpohS2JCBY1ANuB1QxbxmDABY3ZujsiPjzgm8Gd0fKHDJZbbkH6+HHZrTO0tsK8Y4eo26IUfGZ8fM3zy0BBi0BAzZavtVGl0Lhav1Us0iFMnn3ajMi11o3RwJr1as777oP7t35L03UpNSZ1nJ/fz3/+89cO2krbfvrTn8a73vUuQSvnZ/H1CtIbv/rVrwrKOwEh6eaXL1/Gt771LcGu+PjHP47f//3f3zA9gdZHPvIRYX9CqiRrnL/yla8ImxX6ltG/7EYKHYDdSHfj5luLDsBuvnt2Q61YB2BP/+0gcGL2iSBMqqHiKkgrdLvd616slCamPxhfhKQnSkFARD8uUgeLgz4yy8vLeNGLXiRe4lJGTE5cg0CNL3y2ZTaNp6o0Vy4GehxbypQxO0eBkEcffVSIdZCOSAA2H4jhRR/8T80b2epxYLEKUNPisWMppD1rVlskJe+0mtFR7xTiHwXvsmTBuyxOJ6n1QaCYzec1A0WOQr+vYFxlQX/RtP3NNRivQnVxuKcRJzUAN7vVjN5mD7qYUZxbwuSyD8G0ekC80z+HK1WAIWsug5SKbFTpvSAQ2798FVEYMW91Ysm+3ty43EM4nIvhhIZrk8YSao3pJMz5HAbiYdjyOVy1uRCw2Co+80PpKE6rNG7uTMXQgjxmDCakjCYEDOqMpUsXcUcujnQsjjmLAwsqfMqK+z83tISXhFfw0tAyNhIbgWJZeFNvr/D8QjaLzMyMUEaUCwPl26swe7beeSdSTz65bkhmqjItLUikUnBHo8hNTa33I6N4RRlao9IN2yB3X9zQai14jdXXCx81GlhL1MmGr3wFjle8ouJzoKbBxYsXQZ8vZpf4uSoXBDfvf//7wbZKFiRq5qrU5gtf+II4mCutMaZQ1Ete8hKxPlImi+uKeSjIA0G+GwgQmTFjsB3fKTwMpMiIks1JpTVdj5/rAOx67Or2GVMHYNvnXl+XK9UB2HXZ1rKDFtMPiwGYHK2QL1rSUngqWlwXcPz4cYRCoXVUELlsGcETM2il4hoEgQR8HFOiMRJYUWSDReDFQfoJgR3ph42NjQKoUSyENEcGRTTu/4efaN7I3e21uDynrf6Lk7DO6cq89n79LTUYXyqfjdrgXRaOI5/LYtIb0Xx9NXaLAHbVhMtiQjS5EQxWGquv2V0VcDvgncS5uk4xfEvEj+aYH8ZsBj6rA7OuekWp+ENLEzhV31FpWRt+3h32YtJWnXKcJ7SCwCqwaE3F0BYNCgPmSXsNImVA0SFmzlx1mtdKOuJESeaMMvH9iTBqMmnM2FxYVgA6/VEfxmxuTXNSrfH2iBc8Yhix1yCqMeu2LxYUfmUcZ3ciIurQLto9FamXjlwWCeSRMxjRlk7gft8sfi2wACfVH81m4fll7utby27l/eoouVqzS9JmmfbsgYGHVAr+W3KbqlZtsbTvuroxUiepiuh0IhcIFIQ5FEzGW44ehaVENEnTzS5qzDpfHrjxs14pCL4IwnhwRouRZyJe+tKXinrhr33ta/j1X//1tSU8+OCDIEXyc5/7HH7zN39z3dLe85734K//+q/Bv3kNN0roAOxGuRM35zp0AHZz3rcbZtU6AHv6b4Uc/ZCroBw8QVQxrZCgiJmsUqohqYN8Wb/4xS9euwDWifHksThbxvEo7sFsFYUzpJBqw4p9vx577DExF4vAi0PKlLEGjYCRVEWCL4IwxnfPzOBPvvyE5o08zGzNVe2CGMzyKCknlluEUFyc0l7ntL+rHuF4Cg0uG5gNi6fSQvSjkndZf6sH4wvaaFdcP+fxhbX5oknXbTdzfepMf4v3qsc3i8naVtntc6ST6MrG4PSvIG4yYdZRi/AqeBpaHMfpBu1fBPevTOGsp0nzM+NJxRGggp9MmPJ59GTiqI0GETKYMOHwIGu8Jts+EFgQhsla41BwCacq9OtJRNCYTmLJYsfMalaOwMeUSiBZtAa1cx+JeHHcWVvwF0tGkbXZccloRU7R0evayJ50AqESwNiUTqInFceE1QmfAkjdlQjjcgld0mPI47VI4HVTl9AUjcDU0yOk2rVE2exS8UBF/lu51exWOWNnuTVY77oLqSe0fRaRSmgZGhLCIpS+p6G0Kn6y0YiOxUUh078Vwdpaih1RvVYpSD8kDTEQCChK1W/FWsqN8cpXvhLf+c538B//8R+455571pqSdkivSMrplyru8t32rGc9S9AZedB4o4QOwG6UO3FzrkMHYDfnfbthVq0DsKf/VhTLz0v1X1zFU089JSiDEq1Qqna4MHEAACAASURBVN+iRxdrrorj7Nmz4kXH00iJrkKO/sTEhOhP/y8p5MQ12I7tCbYkzxm+JMnv50tSCmbKSDux2WyirQTo+LIleOPP6f/1ke+c0byRt/U14+j4svZ+9A6rup/2uqpbeptwTEbJUPIuY6aL+xCKJTEjvMsKmSsBFK9qv77dNDYuI0GvtGGNNXasBNWJKZSO4UxEVAtpGPI5tEX8aIwF4IyFMOWuw5yjVpMsPDNnJ+vkAV+5B2IwuIQrFVQSpf6OTBq9UT8oe79kdcCfzSCisQZM3MeYDyfN6rN1bckYOlJx5O12nCCRT6OJMufcn0/iXH6951ddJo0+qV5MwUy6LZXAgkW5Js+Uz2FfPIKE04WREpLhoVwSpxToktZcDi+PrOAB74xYg5aw3HEH0r/4xcYuMvVbkv9WtaIYFcGewQAhfd/auk76vhrzZoLRtrNntWxF2bZkGcTjcQFUlIICHA8//LCgn5M2/nQH2Ri0SeFBHbNwEs2Q7yrS5/mHh3ulwcNCqua2tLQIQY8bJXQAdqPciZtzHToAuznv2w2zah2APb23olR+vpjrX0orJHeenHl6dEkvOmm1VJiampoSAEwCccxgcfzSE1RmrEgdLObzE+xFIpF19QalAJBzsQ3HLa4hkwAdX8Sc74PfOokvP67NP4djE9gcn9CekbqlbzP9tAOiWwVQVAfcCt5lTuFdxlq1lVAUM4s+eOMZVYfq3JdqJOjZb7fbiEsh7bTF+lgIfpWgpvS3xZMIIWC2w5lOoDPshTMVR9xowoy7vqzU+p6VSVzwbFRArPTbOBxexAmL+rovabymRBTZZASdiQhyRhOmLHYEVQpc9Ee8GLOWl8aXW/cQjaZNZvQk40gYjYJOmF0V3Kl0nfXJGHxlgBQBXls6iWmLYx39cSgWqKicKM3dacyjzZDHlQwQNpiwd5W6WG5tpDU+b1Ww43BcnbhMsqsLtpkZpJuakGtpAUwmmL1eGOfnBU1SLozDw8idOlVpmzb83HL4MNInT177/0VZtXwkIoRB8qGSdVPyPZFQl/UqmtF2991o+uY3Na9RqQNrfXkAxs97pXjzm98s6H/MlBUf3m3ZIsoMRNDHemGKMH34wx/Gn/7pn6615mEgKZH8Q2BWGjx0pLIj/3CcGyV0AHaj3Imbcx06ALs579sNs2odgD29t4IvWL6MiuXnpRWQVkgBDRY5M0gnZJ0XqX+lRdlStos/40uNJ6fMVMkZKbNmq6amZk3cgxRI1oWVSt7L1ZXJgUB+AaBaIqmOBGD/86HH8ZMLc5o3cl9HPS5UIe2+t7MOF2e1U/v2d9Xh/Iy6upXiizlYrXcYvbxWM2cWkwHdjW7UOa1CgTASp3dZWNa7rFoJ+oMLIzjT0q/5Pgx4ZzBW16a5nzsZRUjBz4pfrDsiXjTGQsjlc1ixObBQlCVTo4Aot6Chpas4VQV1cW9wEeeLfLG4PhoxkzYYszsxbrYjJUPvYztbKoZ4FYIYw6FlnHBe8/GiPHx/Ioq81YZRiwMJBToh17RiWp/9Uro5XN9gKgZXJi0AHmmEJzXK5dtyWeyNh5GAERed6imaB+MhPOidwQsiXorerw+eRPT0INfQgHw2C8PMDIxe9XTj6P79cJ0/r/mZNOzaBaPLBaPDAdaoUTBDyqopDVaNATPHcv32b6Puox/VvEalDhRWYmapnLohlQVPnz4t2A+VABjfBcxYqY37779fZNfkgu+tN7zhDfi3f/s3vO51rxNG0MXvJB2Aqd1lvd0v0w7oAOyX6W4+A9eiA7Cnd9Ml9UPOWvoClWqtXvayl4mTUIIkem1Rjao0RkdHwT+SOAezYcyK0ZiZ2a7iYB0ZKYTSyWqxqAal5KUgBYZ1ZMV1ZTyVZb2BVP/Ftj/5yU+EWiJFOQgkX/uJH1YFiLrqXZjxaaMzcf72OqdQXtQanQ1OzFYxH73Dri5vpNVUml9QCefLA8U6lxXttU64bGZkc1kEIwl47CacrMK8eWj+Ck63DlRa1oafH5wfxdmWXs39+nyzGNOQxXKn4iJL5qDhcT6HKacHcY2UwF7fDMad2oU0hr3TOFEGmLDWqi8WErLzXrMNU3a3oFS209BYZdaqdAMHIj6MKKg0EvTQmNmSz2Pc5kK4aB8oonFeg7qjNC+v4UjEj5DFJmq5lPzF5G50VyqOaYsNfckY6IN20V6junbt7tAy7kxFcG9rHRz1dev8t4zd3chNT2t+tvKHD8NQnMlSGCHV2IhMc7OgeZpCIViZVaO3hYYwHD6MvIq5ioekAqT7f/0vuEvEJjRMu6EpVQQpilSqPFjc8OUvf7lQSuRnv5JSotSe2SrWZKmNV7/61SKzVRp8F73pTW8ScvL33XcfvvzlL8NsXq+RqVMQ1e6y3u6XaQd0APbLdDefgWvRAdjTt+nl6IdchaR4SABEzjwzYgQ5xSBJWq1Uw8V6LfLuJbNmvnRLgR0pI3xZS7UFVNuanp4WoKrY8JNF4Hy5EwAyJBBI7n7xlwJm2vhFgX5hBGDP+d/fgj+qnVZiN5uQSMsLKijdFX7gmU1GpLPavmQBeeEDlspo7Qc4rVQk1C5sQUXFakym+5tdSEbjqE/HYQn6EY9EsWJxYMXJOitlafJdSxO43HTNqkDtk33IP43Tnna1zdfaHVgYxZkq5utOBDFltID1SB3RAOrjIeSdDiym81ioIHZhj/gQ0wjauOADqQDOZNXLutelk+iOh1GbjON8TS28UJeRkjbHwOctk0RchWgG92EwwRoaF6biaexIRYUAh9awUsEwmwN9wGozafSnYgiYzJhQqBcrHn84GsDJddm6jDBnXjDbMFeUOZRb08F8GmdhRkMmhfsC8/gN/zzqcoXfl3K+YeWuz7x7NzKXL69vYjQKdcK404lMIgGn379e3p6iQBTQ0BiVsm15sxlZWoDU1sKYTsMwPQ1DMAjzZz8L20tfKmqx+IegpFJWqtzSKE7Belx+5ssF3x88cOPnMrNglQCYxm2Qbc4DQ2bGmPl64xvfiC9+8YuKHmW6CMdW7Lg+xs20AzoAu5nu1g24Vh2APX03pVh+nlST0hgZGcHY2Jioy6IpJ08vS0GS1EfKeFEYg/RCZsuY+Tpy5MiGcZ988knhOUawxpc4M2IEXqVqhxIwk+rKJA8yqidSRVEKSS6fc8WSabzukz/GUigm66GltLuk4gWi2v2xqgU1TTW2qsAQ11kVuLQYkczkVNd9Fe+TPRVHQkapzpFOoJWmxIkoKIQRtdiw5G5AeLWWqSW0jEV3g+YHetfSVVxp7NLc7yAzbs3aM2f7F8dxrl6e8libjKGdwhnpJMImM6YdHiTNBbGBpkQE6irxNl5KW2ABc1XUuQ3753Hc4UFnMorWVAIJowlX7e6Khswd2SRm1NuprVvwHcFlpA0GLFhsmtZMeuO4DFgS9WKZJGYsDiwpyOUfigZwqgiAFS9oVyICu9mM82Y7sjKAkmCVJtlS2HNZ3BNcxP3+WfTdcRtSjz2m+dkyOJ3is0r4b3k8EPVb9N+KKNtBWG6/HemnntI+15EjyJ84sdYv73Ih09WFnN0OQzgMM+mTqY2fVeOf+hTSJVLw/FwnEJMAWfHf5f4f+/Fgi4ddxWq1xRfD/SA9kfRvZsuud9BEmRmvb37zm6DE/Oc///myAFOXob/ed0Qf/0bbAR2A3Wh35CZbjw7Anr4bpiQ/L61gfHxcAC+KaFAQo9ijq3SV5NwzY0XPLgI7UgVLgZLUh7VkpIi84AUvkBXVkNpR8IM1X8zA8UuE9O9SDzK+/PllgHTHscUgXvXRH4khSKOj+ATVAZltyufySKQzCMSSWArG12WthCfXonZa3842D0YW1BX/F++Z8ByrQAeUexIGWj0YXdDuObaj0Y2pKrzD6mMB+B3X6obUPJ0NsSBawl4BWvjFPWB1YsFVh4xK/6imsFdk17TGTmbcqpCgPzR/GacarwH6cvOacll0RvyoT0RgS0YwqtF8mWPbshkkkxHhb6U1dke9uGCyr+tmRh79hhxqCDzSWVy1uzaMfTDiw+kqaIScqCYZR3gVdHYSPFmM8JutGM8ayioqHo76cdKhfB9FvVgyihq3G1dSGUSK6vfaUjHMVxAlYYarLxnHlNWO5dW2BHdzCv1oC/BiSw4PjJ7BXhXKiYaGBpj7+2HweISps6jfyqjPPFuf85yqwB6BG8PATNfiYkGGvhKNkSDr/Hkwfy+p2kqf79LfEt2c/64UzGYJwGk2w+VyrYE4gjbW3FIMiUJMDz30kPBqJA2Q/66rq1PMSFWas9zPKZTxmte8RsjNv/Wtb8VnPvOZitk93Yh5Mzuu970Zd0AHYDfjXbuB1qwDsKfvZvBEkS/jYvPl4tlZME0aIikoBFfFHl2lq5TquG655RZBV5Qza5b6kJ4o1XGVU1YszsCxZkxJVZHF4nxB08D5scvz+B+fq3way5r8RrcNjS6bAGq1Tgv8kRSiyRS84YSsGIXcnanWA+xwLz3HtCsucr5q+g1RuGPap/nh6l+ZwngV2ajW0AoWa67V/pnzWbQmQqgN+WDOpIUy4bLDA19JlsOaSQkT43LURqWLaAwtY7kK4LZncRQXqzBvHloYxcnaFtTn0ujMp2AOBxHKG0S9VroM2OyN+DGuUtSi9FrrkhF48+VfsxTX6F2t55q3OLBoc+BwaBnHFTJK5R6K1nQSiwq+YfTy6k7FETOZRW1ZKaAcigRwRuWclJXfnYyIjNa81Q6fSrDOtRNY7aGaJMFtLodTKp6BW6MBPOifxbOj10RwWB9mZgbJYEB2bm7NX8x8+DAyGmuyuC7rbbchdfRo+d85GRl6ZtXKZdbkBqSUfZtKlUYCKyVwJoE0fp4uLS0JZgJBmNSeff/sz/5MWIYoBUFYQ0MDPvGJT4AeXVsRNFL+whe+ILJt73jHO2TpjjzQ45/i+OM//mN89KMfBemIFAzhO++rX/2qqC3+5Cc/iXe+851bsbwtG0NXQdyyrdyWA+kAbFve9q27aB2Abd1elhuJL1K+ZJmtUgJglO+lEAelfEk/pPky6YVyIdEDWYdF4MQT1GL/ruI+rBfgy53qiuWUFUl/5Fj0EeMaf/rTnwrD5b17965bgpRRY03Z154ax199vUj2WeV23tpHb61rgMhuMYnsmdtqRDoRg9PpQN5gQjCWwnIwjni6cIp829PsAaZFgr740m/xGHA8pJ2DdmD+Cs61DarcxWvN9saWcdFR2djYlYyhNeIF/+YziWwGI3WtiKuUZJdmtGVSSOTzmry/pL4tgXksqvjSXroJ+xZHcdbTsmFvLLksuqIB1KZiSOeBeZsT3iK64ZB/DqdU1EGVDlyfSWElo13Wv82Qw4B3XtRfTQqBDfV+TQdjQZwtMUOWexhqsmkMIIt0KoURuxspowmtyRgWNd5Hjn0oHoIxl4Nf1Itpk/i/I+JDBkaM2FwIqbjOQVMeb7ak8bLZcZhW5A9Eqs1kmQYGkGXWrDjs9gKNsa6uQGMskaE3NDcjv6zdmsL2kpeg6etf1/x7qtSB7wbW6lK5kL6PDP5+st6L74WFhQVx0Pbud79beGkxO+Xz+db9ef/731/WxFnLYgmsSIksF+9973vxvve9b0MTArdPfepTQhSK7xFS1SlZ/6pXvUrLEp6WtjoAe1q2+Zd2Eh2A/dLe2qfnwnQA9vTsM1+kPA1kKBVq8yVL4Q1SUNie1D+lQmu/3w9momjQTNpiX1+fMMiUC0ldkdRCKhjyBU7gVhpSdozAjz4z7McMG+sSioMZNc5PquTf/+A8PvXjS5o3sRSAVRqg3mVFk9uGrgYXIok0stkcYskMvJGEqO0SYKJMHOltxIkqMmBHhFeZ9i9oQ+F5nKnRLmwxNHcJZ9rXm25X2hv+fGjuclX99i6O4WJzD5qiATTGgoLGmDIY4Le6sEDRDwUFwO7AAiarqDezkiaZS1dFB+xYmcK0S50CYmMiirZ4EOZsBvZ4GE+565FRyCwp7e/uiA8XzDY127+hjSsRFhQ/Cmz0JGOoy2YQNpkwTi+wMsbMR8LesmqNcotxUEY+FhLiG+M25zpqoZrFH4kGcNxVoC52pBJoSydW68UqX3tzKiHoiMyoMSsWMxoxqgLsUnTklaElvCa4AHduvRCP5c47kX7ySTVLv9aGz6nFAtaOCRqj3Y6c11ugMaaVQbT54EFkqjBTdr397aiTUQzUtuhrrWOxGFirS79FHnrJRSKREJ/dv/M7v4NPf/rT1U6l9yvaAR2A6Y/DZnZAB2Cb2T29L7+4aj+m1/dN8w5IdQIEVEoAjB5g9OJiUPRCqRibP6c/GDn3ra2tIB2RtWCkociFpK5I0EWAd+DAAUERKQ0qI1KIg+IcVFlk1oyqiqWCIZJfGU9J/+Jfj+Ibx9R7zUhzDnXX48y0dk+ufR11uDC3XtrdYjKK7BlBGjNp/FBMZbIIxZPwhuIIJzLY01GLSyX91NzEXawdq6LfTt80RhrU1TkVr0MAopY+NUtb1+bA/EhVmTMCt9PtO2Xns2bTQvSjNh6GMZdB3GjBosODoN2FfYtjOKeyjqt48K7gIqYrKB3KLcaYzQCJMNIaQRTH6l8Yw6SjBt2ZBGpNBgEw53KAz1g+MzUcWMRxFWCidL2tmSQWFD5WHdmMkHq353NYslgxU5Lt2hkNiIyW1tgXD+G8vQbmfA47kYHDYsbVDODf6NC1YeiBRHgDaJLqxVy5LEZtLkRkKIrN6SSWZQDqjnwGBMCXHR7EFFQg6SF21lEDVzaDXw8u4A3+ebRkCgdU5j17kLmk7lBHojEaKJwxOrpGY1S7f5a77kL6iSfUNl9r5/m//xc1b3ub5n5KHcLhsGAn8EBN7rOZ/Ujj40HbH/3RH+EjH/nIls29nQfSAdh2vvubv3YdgG1+D7f1CDoAu/63v5L8vLQCKavFf5O2wdNOpaCoBtUImS0jfaXYp6u0DzNkFPjgi510FgInFnKXhiTsQXENgix6ffG/S+Ps2bNrCo1v/ex/4+cj2rXp+ptrMF6Ft1ZHvRNzfm0eYDV2C3qb3eKrqEWIg+QQT2WEuuFyKI5MGUn7JpcVyxHtEvvNER+Wq8gQdcV8mHGoy/IU35eBlSmMVQGI9kcXcc65PsNZ6TfCk4hg3/wIomabMFkOWmyYd3iQUiEPfzC2jDNmbTQ3rqc9tIIZyzWlvUprLP65K7SEkGGj6mhzMoa2ZBQU+qCKH2vJckUZvwPxAE4b1NMHpTmHDBmcTlUWXmB7mi53p+PIGU2YNtsErTOuoR5LmvMWcw7H0uu/DhBE9a/6elFgY0FGAdEixCZygsKoFIV6sShy+TwuOdzIroqZDJvyOJVR/griRB67YyF4TRZMlShQDseounhNMITA8VdCy3jAN4edZiAfk/kdN5lAmmGEdVK5HGxLS8it0hgtR44gXaRkqPb5UEt3NPX0wNTRITLtFAip+8QnYH/Ri9ROU7EdGQc8fCPdu71dPnPOOt+DBw/iPe95D0g31GPzO6ADsM3v4XYeQQdg2/nub8G16wBsCzaxwhCkEzIDxvovOfl5qbuU1WKWjJmnUrPL4mkIuh555BFBUSRQK2feKdV2UVWRY5JiKBcSBXLPnj1CAZGURp64lga5/ZTBp1z+Kz/yA0wsK0tDK22NkKGPaZehr8bLy2wEcvnCn9IwGQ1CHKTBZYPTZoIxk0EqEEQ4FEUwmYHfZF/3pVzN02LKZ4X8PL9Ua4p8DqytSqoAMqXj1keD8KsUYCju2+Wfw3SdvCR8ubXvXRjFxSIJetYQtUT9qE/HYIlHkTCZhODHkpm1fNdeU4fmLuNUk/bM4L6lCZwtEhlRu6+NsRCWsurquKiW2J0Io4b3wGBAwmLBSF67cuIRCnBUkeXrSsYEGGzMpBA1mjBhc5YFRsV7sDsewiW7fL2o1I4CHm0OG5ZjCUyuAqL+ZBRjGuT5a5HHQCoGfw6ozWZUCXBwfqovOrMZYfCcNhrRlorLAkKCxmdF/XjQN4tbTTlYBgZgqKlBLhRCdnRUHphRgOPZz0bq8cfVPhZr7WSBGz29WDfW0IB8IoHMxATyvvWCOq1nzsDcq92CQWmBzG6xVpfsBKWDN4mdQLNk1lTpsfkd0AHY5vdwO4+gA7DtfPe34Np1ALYFm1hhCEnpis3KGXWShsJCbKfTKYQwygVVsn70o4L8uxKlUOov1Xbx3yzwJs1FLiQKZFtbmyj6VhIBKZanv+1930Y8pc1M2W42IlGFITJBkq8Kw+f2OgfmA3HNN7otuISAqxYNET9qklEBjgisEmYzIlankG6Xy/q0JoJYtGuXdW+I+uGrQpzCkYprFtEQm0HAl07Keo5V2qz2wALmayqLftjTSbRFVr3LchlY4mFcrGtd8y6rNI/086H5KzhZBVDc7Z3GBatT7TRr7WyZNJKpCJpSCeH/ReU/n92JaYsduQrmyrvDXlzSKGbBienFdboIuFlzWfTnM3BZzfDmjbjKXzOZ+jGCFlIboxoyZy3pJLpScThzGTzubqhKTOVANARbPifqxRatlevFeI212TT2xsOYsLLPxix88Y3al4jgAd8MXhSubINtvesupKqgEpq6u5GlqfLAAIxOJ3LBoKAyIpFQfmasVnQsLsJQpbKm0mcvmQWHDh0Sfo5yQWsS1vH+wz/8A373d39X8zOtd9i4AzoA05+KzeyADsA2s3t6X70G7Do/A6SsSABMSf1QWsL8/Lw4BaX0Lw03ywXH/f73vy+aKFEKpf5SbRf/Xa5WjKpafMkTADJrx3HlREAkufp9h27B3R8ugEAt0VXvxIxGGiHHH2ytwWgV3mF7O+pwsYo6rl2LE7jSqlyPRTNk1kfVx0JwpONC8CFrscAWj2KivkNkpLTIuw+sTFZFI+z2z1eVxWqM+qvy/zKxHiuXRVZrhg9Ac3ABS6561MdDaI4G4LBbkQ4FETDbMG93K3qX7V6ewAW3/BfTcs/eoflRnHDXa3k8Rdu+8ApGZQANgU53MgZ3LoOEwYRpmxPhkoxlTTysShGwdFEFHy9lD7i6TBo7UoWqqllnDVZW67voFTZThfoh5z8QD2LG5kSfxYgUDLiSgfCSqxRUiPSbCpTQQr0Y9ySNEZtbtl6seLxDsSDOOGqwN5+G0WLBhSxJkMpz8vru98/h1cElOPKkTG4M8969yFy8WGnZ4ufGjg4QeMFsRm5hAdnxcUoOqurLRuZdu9B67Jjq9moa8rOftbpkMtDfSy7IeLjnnnvwxS9+EQ888ICaYfU2FXZAB2D6I7KZHaj8SbmZ0fW+v/Q7oGfAru8tJu2Q6ofl5OelFUhiGZShJ9e/Unzve98TlEKeipYLqbaL9EdSG5WycKxDeGL1FLncGiTD6OWUGe97RLtC4O5WNy4vaqctDu9owKkp7d5aw7YkTiXVndAX7+PBucs42yGvLFluv4fCczhT0wFLJo3GWACsmWKmiRmntNGMsM0BHwUKrI51wxycu4Kz7dol6PcFZ3HB01Hpcdnw88GVSYxUUTfWHvFivozhr9JCrBkqIOYUKZ0EsILGGA+D1NCEzYZlgxkrRiuafLNYrILWx1q1s1XU4h0KL+HEKsCotLHtyRha0gkY8kDSbMFFk6WqjBLpgOMagBSBCTNZrmwax511wh9MazTk0vAZr/UjTZBgijFqcyqOeTBGEY2NYFHyF8s7HLiYN63VixWva9iYwancNXouxTx2pOMYtzqF4bRS1GbSeItvGr8aWkY9DwGKgubN+ZCMQbvRWMhuUW4+k0F2akqALoaptxfZq1e1bhnsL385Gr/6Vc39ynWg7Qi9vlhzq2Q98u1vfxv3338/vvGNb+Dee+/d0vm362A6ANuud35rrlsHYFuzj9t2FB2AXd9bLxlqcpZy9EP+nKIaFNegWAZpheVCEuFQQ1eUMms07KR5slJEIhFhvswgFUapGFyiNJ5dSuHTJ6OaN3CgzoSxgDbaIicZ7q7Dqen1CohqJh+avYQznXvUNF3XRkjCd1y/fu5EFI3ZOJwhPyzZNFyJCJbcDQjaXPA6PapryKqVoCfgO1MF4Nu7UJCu1xpdzNTVyCt1lhuLGcba4AJcyThgtyGUTGHO5kJche9U2/IkZqtQFRyKLeMktAtw7A/7MGGxoTsVgzOXRdxgwpTNgaip/FgUlaDSZDkxDKU9Go4GcM5Rg95kDJ5sBgGzBRNWJ3IVMlkEb1RiVAqCKdZu2UxGTBgtQqhEisPRIE5WoMuKejEzEMxkMYZrIK8pncCKZeOBCIU49hmySCSSuCJzz6iYGDcaYcnn8arQkhDs6CbwbWpCXvIUczphGRyEAGThsJChVzJZttx6K9JVZLLc73wnaj/4Qa2Pf9n2rKkdHR3FHXfcIYSV5OIrX/kK3va2t+EHP/iB8HTUY/M7oAOwze/hdh5BB2Db+e5vwbXrAGwLNrHMEDzZpEw8BS3KiWrQB+bRRx8VlD/WYBEAlQsJBFGpkIbI5UIS4agkbS+tgWNRVdFqlf9yJlEaH51K4KsXtddWHery4PSMzGl1hVsxUGfGWECdulzxUPsWRnChTV5qvdyUe0JzuFRFZmn34jgutxbMVLXEnoUxXGobEF0KYgxx1KZjsMUiMCbjSBtMiDB7ZncjUiRfvn9hFOdbC/20BE2fz1Zh+nxo9hJOV9Fv/8IIzjXt0LJE0bbHN4fxkuwXaW9N8RAa42HY0glQzoXZkwWbC9lVJUNmINOxgGwWptIiehM+jOWqEOAILopsVHEYkEdnLoOmOA8r8kK6fZbZzyKA1JOIYrJCTZTSmnckohtUBt2GPHpzaZgTcSyYbJiXGXuIVECVwi3GfB4DyShqshlR82XPZTfMWW5P21MJdKQTAkBdUJHJZH0aZekv21xrtW3742GcL+rLNb0gFcFbuxowlEtd8/3KqPuMUKuAWHpddX/3d3C99a2VHiFNP6ftB//ws1xOoZaDffazZ1invAAAIABJREFUnxUS9LQfoVWIHpvfAR2AbX4Pt/MIOgDbznd/C65dB2BbsIkKQ7BOi8pVBECV6rQoMUwKIkEa/bwoQ18ujh07hpWVFdTW1lZ8GVNSnqIaSqqG0jw0+vzpT38Km80mFA6VQqI0fmskju+PlylWVxjgcE8DTk5qpxLuarTjilf7fL3eGVxt3Oh7VunOd6RCmLMq1+Qo9W8PLmG+VtlCQKlfZzKIWZs68Q5nKo6GaADuZBSeeAgxix1JkxkhioM4PMioyA4Nxr0YsWuvj9o/P4LzVXiVDUfmcNKuvY5rPzN19epMreld1hYNoBYZOJHGcjyGxZwBfhkZeqX7YMxlYUyEkKwgtiHXf28ugQvZyq/lmmxaiGC43C6EI1HUZNI4ptJkunhe1kTRJKGSMEhrOoFOqxmpaBRXWbdmsuBwLFAxiyV3je5sBk1GoMliwlImjykNSpGHY0GETWZwDFIc5fzFiuck0KPBc8BkQX02rbje4VgQD/rm8LyoT/Vd0yTc4XIVMms1NfD8xV/A9pznVPr40PRzZr+YBaO5vcUiny39+Mc/jr/6q7/CmTNnVFHUNS1gmzbWAdg2vfFbdNmVP+m3aCJ9mF/OHdAB2PW7rxSyIK+fohV8sSpRS7gCAqpAICAAGGmFFMtQCtIaf/KTnwhJe56WKsnKS/1/9rOfIR6PY9++fdixQzkDIdWAVQJ1EqXx4YtJPDGlzZOLa9pNc+P5oOaNbwstYcGjHdjUxkMIlhE3UFqIPZNCQqMkvCGXgzmXRVoFAFo3bz4HazajykurdL0EY8X1ZBQHIW2vLk5xkATMFjMyVitiBjP8BgsCFrsQB6mvUnWx2zeL6dpWzfdv98IoLlUhQX9g5iJOVwGg99NkevW+11LNMBGGM5MSflYBkxlzVgdSMnVTHbEApjVfXaFDXTxcto5JadjDER+8JquQoKfMBKmB8yU1gnJ9dyYiGCkxc660dGaOelIxdKTiWDLbMG5zIlPkf1ap/75UFBes12hyzG61pxMImiwYo+JkGeqjMGBezbqJerFERFwvVSMlfzGl+Q+lojBkMrhgdytSNWly/Sb/LF4RWoa1grCGed8+ZC5ckJ3O0NoKc08PDBYLcktLyFCoI1ugTbeePw8zRTy2MPieIFuCB3VKVPUPfvCD+Ju/+RuRKevdQgn8LbyMm24oHYDddLfshlqwDsBuqNtx8y1GB2DX755R/ZCCFZRtJ2WEwEYuJEBF/xfWYRFYlaOYLC0t4cSJEwLQMctWTrKewIsATAAfBV8vaU18sfOLANdRLgMntfvUqSQuLGoHYK0eOxZD2jNZ1kxKM0AhPS2pQdhA2guqGwZVUKVK7ycl631VqO418gt4FWIRtbEQgippZNJaKaffFliCPZuANZ0S4iBJI6X17Vhx1CBRZr8M2SwoplGNV5mkgKj1N25gfgRXqpCgPzh1FifLSOUb8zm0sA4vGYUlm0HSAHjNNjSlozht1F7/1ZBOwqv14lbb98Qja95ca88gs2QmwGE2IZTNYSoLJEqUJ49EAzhRhXUBxTY4FuvEHLksCFxsuSyWLVZMVwB+Yk6FbF1DJoWeXBrxbE4Aw2JQRdqoJ5dGUOZQw5NNY9BuQTCdwVh+o39eRyqBuVUaJWmQO5NRLJhta/+vdNsJZF/vn8NvBBZQk5OvNzXU1yPv9wvAaOrvh6m1VYCszPQ0cnNz8nfSbi9I0KtQitTyKNBbkVT1csyDd7/73fjkJz8J2oVQKVePze+ADsA2v4fbeQQdgG3nu78F164DsC3YRJkhCIyofijVS5WTf5cAFZUP2Z6A7DllKC6SETL9YgjYyr20iyXoBwcHwT9KIdEaKb5RrgaNFBjSEP/3z6NYDGszUzYaAKPBgIycK3KZW1EN0OBwHcEFzNVqNxrui3kx4dROlxtYnsRYFQIVg8tXMVpkbKz2qexfmcJ4FXVVO3yzmGqQV078/9l7E+g6svJaeN951GhJtuTZbs9D290QIAlJeGnorDTNECAkTAmQQFiPwHs/EIZAmkAgBMLYwEvgZyYBVkKA8PNeA+ExhaQHum1LsiTLlmTNs67ufKtuVd1/7XNVcvnqDnVKNrHbdRYXuXXPOXXqVKlO7fPtb+9mNYe29Apiaq4srQ8g7w9iNRgFJejnHVDlqAKpwJCS5TfnoDk5j4QDL699k+cx7ADU3pGZxVIhj5aAT9DZMkUdMyXPBrn5ymt0JLOCAcloFPug35deKjWMAPlKBnaoBWyJhKBl0pj3h9CpKeh3EN09lE/jQo0NBoIX0iMpzD4RiW2gb+4vZDFiw+eMNMN9Sk70QzDGnC4KkjQqZr7YlD+07hV2Ry65AWgS0B1Usgj6fDjvD8HwbMzZoxDKHyxP4p7UIrq1tWdVOAzf4cPwxeMoZbNloY5qCopVBkq5+60PPdToFKS/pwdYIpGou5n2+te/Hp/73OcEm6FWnpj0gW/xBi4Au8VvgE2evgvANjmBt3pzF4BdnzvAlJ9n7hW9vRhRYmSpWunv78fU1JQAUgQ3VDgkFaVaIbCjWAfzBEhV5G5oPUUsRsqWl5eFr9fevXtFFKxa4fc/+MEPRESN46QfTa1CpcRUOo37z+nCxyng88IDDwzKrOsGFFVHRikilVeRLlydEN/VFMJCmlkrcmX38hTGHdDQDqfnMNQkD8COZ+bQH3fQbmkM/R21vcNqnbVTyfvjFLZwIDBybHYY57vlhUkOLVxGIhwX/meMLnoMHVq8CWlVw3I4jmyN6Am9yiYcKCA2qTmsrlG/5O4YILowhpSD6OdtmVkMVdFx2FIsoFMtCPPiIjxCbXAmeIW+d0dyAY86iEbt9xgYkRcFFdOxV8kiZugCxKW8PkyQVmnDn+1OfwmPao1fHwhydqp5dOgqsh4fZgIhZH3V5eXrXR9G156MIpLBEEY0IG0zU+u2Qln4Q0MJfXXmlqBxt5rHRCC8QWHxgFbAmD+EZ4Q8+EM1if0jF+A/cKAm/bDeeYSf+Uxs+cd/lL0VG9Znni6f+/Xo5H/0R3+Eb33rW6IeWRJu2fwMuABs83N4K/fQ+Al6K8+Oe+4NZ8AFYA2nyFEFU36e4OfRRx+tKetOwEOKIIUvSDs8c+YMaIhMv65qxZSK379/PyiawbyBu+++uyolhiCQoIrGnhTsYP4X88CqFX7PCBhz0ChXX8sImrRK9rlaMPD2nzb28iI4a4kEEA8HEA360B4PoaCW3zZ1eqRpBjJTM0hl8kiHYyjWyLk6MncJgw6U905MD6HPgQT97YsjONcpryzoWPL+Fy2VPz3oTJqf46wjzR9TcmjPrSJGWl9RRQklFHwBxLOrONu5C7qkVxUjfBdj8kIhrbkkltb8rGT/gOOJKazaFO1gVKpbyaM9EkTL4jwWAwEs+kJYDNr3nTudSTgSw9hCymPFcSjlvlPJo01XBUicJSCp8jd1OJ/GkAOK7ZF8WtAWY4aGZV8A48GIbc+zY7k0zkebwTmjvD2BYzXAVHm9mCsWLJEmmW+YL+YrlXCkpMLwBzFgAM0lAxl4r5Lkf1I2gVdsbcYTHn1Q9tZA/PWvR8u73y3drlEDrhF8ttazCfn93/994dPITbdGliaNjud+X54BF4C5d8JmZsAFYJuZPbctIx5kiLjlGs4Ap5SLKUFYKpXCQw89hGPHjoEy8JWF31NW2KQHMgLGqNkznvGMqiMy86+4UJMGSOUsRsCq7YgS/D3yyCM4cuSIUFisZ67MPDVK25PaEolEhB9NtcKxcbd2bFXDBx+Rz/8qmyknas52RM2jqZBFtJgX5sXMzaGoRFMhg0S0RRjdFppakfYGBSWMYhL1ilNARIn2/u6D0neFU6B4eH4EQw6k5J22OzJ30RGgPT7jbF5OTg+K+WzLJ9FqKIjAgFdVUMznRGRlJRhBsgqtjQD6bPt26etwYGEMgw6iX22FNBYLjTcWqg2oPZfC8pq/FT2renwlxH1ekVeUUoqY8QWqGhvfnkngnIPI2bFcEudjjVUzCdR6vCUE8nkkfX5MBsLwl0qOjJtF/pclx5HmyLvUHLx+n5DWXyxVfyUhMAobxrqkvDl/jLDtJeXV68FsCUIYpbJUgkXmi5EGmfL5MVKH8klhkIOFLB6LNCNdRRSHAiAvXZnG09NLFpey+rda68c+htgf/qH0/diowcMPPyw20WjEXKs861nPEjnFfE5f6xy0RuN7vH7vArDH65X9xZyXC8B+MfP8uD2KC8Cu/aU16Yf8SW+tn/3sZzh8+HBV5SrTo8sU6aBsPfO2CMCq7XISUBG00adreHhYKGLV8uyioAa/p0gHx9DZ2YlTp05VPWHSCgkceUx+aomAmHTJx+aL+GyvvAfYE/Zuwc/H5CXoT2Zm0Nt0dc6S1zDQpGTAqEtELSCoq/DrugBsTP4v+vyI5TOY2robKW8ABRuqcubk7MsvYzQinwNGs+Epm5Lp1gvRU0hiJtz4Zbry4jlVhtxRSGAqfLVflZ2/hD1LziT9D6RncbEBFTRcLAhpfYLtYFFByTAQzSUwGm3FUihqi1pnnsPtyQk8asgLaRzOLKLfpo+Udb5aNRWJBntZBBudRQUdmiJ8tIrRKJYZDS7pmHaQ43ZHNnEVGLJz/VhnbyELblu06EUhtT/rD2KlijFytf4OFjIYrhM5o7LiVqMI1ShhNBhZB3n7lCxGQ/GGQ2Tu2daighWfH2NrgLye6EePF+hOr8KaL2Y9yPF8GsOhGI4UMsj4fFUBG4HaixIzeM7qPKIlajJWLzR83vLFL15zCXoejZEtsiDqiR+RFUEGBNcIF4A1vJVsVXABmK1pcivVeia4M+POwGZmwAVgm5m96m1N+iG/VRRFUAxrCWA8+OCDIqmaOV9cVM1IFBfbSj8Y9kv6n2nUbIK3X//1XxdRq8pC0MXcLgIwytZThfHOO+/cUM9USty9e7eQwmebaiIgJl2S4/pm3xK+cVE+l+vOPVvw6GV5AHZgYRQXHZgb70jOY2pNMp0RtSYli6iSQ1grR9d8AT88oRA0eKBqOnIlL7LRJhGdcaJKSCCYlzTUdSpdz/wrRhY0SVofjxfgS7KkxD5vnFghh2woKv1H05lewmKTPKDdsziOsS07QPDCvLO2XBIRJQu/pqBYMpBj9CwUQcLHaOiV/cgjE33oq6OAWOsEbs/O49Fi7ZfwWu0OZ1Yw6ECAg2qEGs3X1QJadRU+Rom8Piz4gw3l7A8Wcxh2ANxOZ1dxpoLW2VUsYJuqwFfShecWTaErRS0CKIHZnopNBUBSDamuyIhVWNfwn/EtV1EBG91EBKs7PQZ8wSAeNTwNvc7MfLFLoYjwOSN10YcS8l7/+qF2kyKrqxik2mdF9JzjfN7qHH4vMYsOvQjfnj3wdXeLjSljehr65CS2DQ3B11NdvKbR+dT7nhtgTU1NNcWPOAaaNPM5b0bLNnM8t215BlwA5t4Jm5kBNwK2mdlz27oUxOtwD1D9kGCJkSQTNFUTwGA9AiMrNZCGnPxUM26mTDFzxE6ePImenh5BRSFgI1iKx6/eXTZNlQmqSEEkCOTiXc1fjAIgjGwRnDFiRkBGUFdZmPz905/+VIh5fOCBQfxoQk4Bkf0d296G89Or0rPenZrHrAPvqaimIOe3n4/DgQU0Fbo3gKiaE0bHUbWAkKaUo2swxItg0eeD4gsiFwghE21G1h9Ccy6FlKQkPI/XkV7GkgNw0pVewoIDkNGRXnJ0vLZsUtBAZQvFOlR/oCFdtFq/kULmKo+zWscOaEVsya2iieIgah6BxAxWI1FklSIW/dWpf9X6OpycRH/pygu73XM9nZzHY1H5iOIBRmhqRJRaaSrt8yDmA4xiEauKJkQwFI8X9PIKwUDehuBG5TmczCXR22CsIZSw2wc00QuvoGDaF0CHVsSlSOMoVrU5O8RIdDCCPUpO5HPxPOZsUEQprsHoXLNWxF41KzZKhhtEQwm8GKkjPfKhWFtVjzPmsJGCuOjfKLsfRAm/m13Gc+cnsKd4JcrviUbRPTt7XaJPfD5T1fb48eNVbzkCMCrT8nn+ox/9yO5teU3qUfzjM5/5jOiLnpbVlHS5afexj31MqDSyDtca0uTf/va3C+B4oxYXgN2oV+bmGJcLwG6O63TDjtKNgF3bS8OFklEv0g8JwPjf3/ve90T+F/PArIU5XMz5Ii2QUS0WM8erGqgy6X8m5dCUmK/mMWYFVaQecoe1lr8Yc7oohc+oG/9NimM1afvx8XGRS8Y8hVf9vz/GuYUqUnENpnNnewyTK/K5YwRAik2alDmEOGlHYfkXxu7VecxK+k759SIOrEwh09SCiKEhqOThyWUB7p57vMLwl6bOmUAE6WgTipZdeeYrXeySV048tDKBC+21jbVrXYqD86MY3ip/vNuWJnBpi/zx6kne17td6I225ADw+QmgMytXRQablBza8ikBqP1FBbqugXfhqteHJV8Q+poR8Zblccz7gtIPhWPJBfQ7GCsFOKw5VY0OTOC1tVjAbiWLoofRKC+WfX4BZqwRwHr9bFWVdXn3Rsezfv/kzLKIJnEMpAjSL4yCHI1KwOCWBTZQSClLvz3gEXM/pnuQqpKNfCqXxLkK2wP6lu0vUFoDuBSMbMgrM8dzOpsUcvn7lSxS3tr5YgehIVzICXNp05D6jmwSZ6LN+LXMCl6amMbpfBr+48ex9T/+o9HpSn/PNYKgimsAN8uqFdYh8OGz9zvf+Y70MZw2+Pa3vw3mnnGDj/THagCMY/vd3/1d/PM//7NQ2b333nuFkNTXvvY1IRT19a9/Hc9+9rOdDuG6tnMB2HWd3sd9542ffo/7KXBPcDMz4AKwzczexrbcCWRki4uSKYxBAMbFlZEra6E8PUUtCHyoPshCUQ36fFWCqkq1RNY1ARwXZe6eWosVVHEczDGoRi0kUDTpieyH7aiIeNddd204OVPSnuO9693fwERKXjs7GvQjt6aCaHfmm3NppGJNdquv19uZmMFkmzxd6OD8CIa31vZLqzWQo7MXMNBTXea/ss262Iiax7bkPDKhuMhd4zuo7vUJsRF6b2VCUaRDsarRI6cKjyemBx0pQ56YHUbfNnlhEseS94kpDLV0S1/37ctTmJCggfoMHe1aAW2FJDxzo/Dks9BKBtIeH5b8AUFna1Q6c0ks2IjoVPZz3KOhz0HE7VQ2gXMWMYyIroG5TE1aETSYznj9IrerUnyijblqkhFhc8xHCmkMWjzHCIR2KTnE9KKg81Hco5rYxYFCBhfD9f9+Cep2U4xDU5H2+jC6Ju9/Mp+qKz9P1UdSD8OGhsvByDptk5TVdq24LorCc6AQSY+nhCnDg7kqLNNWrYh9ahZT/rCgLs5a7iGO45W3bccL/uWr11yBkM9gArAdO3bg4MHqf198/tOf8ZnPfKYANr+IQrVFelOSjcF1ilG6agDsK1/5Cl70oheJSBcp8qZHGfOVuZFI6jvp8qRY3mjFBWA32hW5ucbjArCb63rdcKN1Adi1vSRUP+SH+VymiIYpBW9NsOai+8Mf/hDNzc1XKV+ZoKrSuDmdTgshDWsumUlJrPQYM0GVVU6eeQPcjWQ+mLXQ/JMqjaZICCNys7OzQtreWkxJ+/b2dkFVvOOt/4SUKieg2RT2I12QB227VqYw4cAD7MjqJAZbNypPNrriZWBTfSe6XtuT0wPo3VFd5r9uu6nBuu34Qh1XcmBET4iNkA5p6GgqpJEMl6NpBGxZvgCHog3FRo7PXEB/jzyQOjF9AX02Aab1fE/ODNaVrq81NwSKvQ6UKI9O9qNPMoLJMexamcBwJrlhOFHSG6nOqSkI6kXAMJD3eJD0+gWFLawXkWp0U9X4vkstOIpGVQKwWodv11Rs9XsR9QKapiOYyQhVQDPSY3fYBDQUqMg2yDfsMYrozGdFzt5KOIpJrw93+Aw8qsvROgnuyh5nGmb9YUzZMHDmMSn20WJo0CIRnEPtSOZthYzwF7vEDY4KgM3jRijGUSphMBy/KrK4b9d2/MmLfwe/e89dCIfkI6XV5pvrBandpBfSXqRWHW6yveIVr1inA9q9dk7rPfe5zxUbdxT9eN7znlcTgHFN4fi5kVfJnHjZy16GL33pS/jsZz+Ll7/85U6Hct3auQDsuk3tLdGxC8Buict8/U7SBWDXbm65S2nmfzHqZCpVceeQpslWieFK4GOOohaoovwwVQ+tkTHTu4u5AdwdNUu1vukzU41ayB1N7k6alMdaKoyklBDEkSKzbfsOHH/z10W0Rqbs6Yjj8lJWpomoKyTTHZgG356exrkmeQlzpwDs6OwwBhwAm0NzI7jgwOPstsXLGKlCXQxqqlASpDok868IGry6DiqE6x4fImoOc00dyEbiSAoaWX0pf/OC7V8cx0jHbunrd2hhFBccUCyPzlzAeQfzcnzsMZzrkKdKHp4dwNmi3AYBX/pPrM6Bd3VUo4iGDhJzs4EgEr4AKDdTqmE6zPyqlAMhFF6AHWoO0w7EUO6g5H2sFd1qQUSbAoYuolcU/VisQ/HdXchi3EH+F+X4j+eS0Dxe5Lw+TDJn0kZEkecolBPXKMRbNAVUSKTQ5GQw1DCKd2d2VZxTp6YIiul4jbkiPZK5YHyWXQiVKYh35Fbx2BrtsYtCIGoeI8EIVi3XqqO9Fa94wb14+QvuRVvL5iI73BijFQlza/mpVpLJpKCx/+mf/qnItbre5fOf/7wATN/85jcFfZBRsGoRMI6d9EQqOHKMJpPDHJ8ZHXvJS14igNiNVlwAdqNdkZtrPC4Au7mu1w03WheAXbtLYpWft/pyMXJVKe1uSsQ/9alPRSwWWx9ELVDFKBVFMLjDaAI7E2gxcZv0FbOYoMrady1qIXc4mbNG0Y16KozWPpfyJfzmX/9v6Yk7sbMVfZMbIwyNOro9NYVzLVfOr1F98/uTiXH0tskDhsOpGQw1ywO33SuTGN8iH3Hrzq1iNipvNrwlu4oVCw3N7ry0FvNYDZbvOdIeY0oeTcyDSSeE95p/zXuNL6UUG6GRcj4QhkfXMdvSZfcw6/U61TQWg/K5eNtXpjHlIJK1e3YQo/FO6XEevPwoer3yUY3Ty1N4LN5e9XghQ0eHmkezpiKka0DJgBoOI6UW0VxU0WfDx6uyY1L+8j6/7Zwva/t9hSugplq/BGZNehFGMIiMpmPGHxJS8kI50cG9xvPX4V2PuBGwUqqeUvz8N02ipwTVb+OrTKXnmHW8uzwGOoM+5HJ5jMIHpUKMhGqHVtBFlccdagEprw+XwrGqoNj0F9M9QG9FPh+B2ol9u1Dw+zFwcWx9KNFIGL//rGfg1S/6Hezq2Sp9z7EBn+t8vpPdsGtX9Y0DMiPIUnjrW9+K9773vY6OY7cRc31Jl2fulwmaagEwbthx/eGnr69vwyF+/vOfi41HMjp4jjdacQHYjXZFbq7xuADs5rpeN9xoXQB27S6JVX7e6uFFqXnSTAiIzEJRDAK2SkogZeBZ3wqq2Jb0Dka5rHlkJi2RUSnSV8zC3VS2Yd8mWOPiyEWc/mLm70wVRoI3U33LBFqVKoxWoPbgyCJe+r/klbicStCfmCEl8LD0hTq4MIZhB5GXntV5zDh48acnWVpS9KMsJQ9pKfmQWkAxGJJWFowVssjW8XGqNcmxQgbZSLMAZ6Q+MrpGKf8gpcsNAosSdMr5h8IoeP2gRELSFxL5SE4UEL26Bq+hoWgzWmIdd3xpAkkH0aGuiw9iwoGU/LHkPPob5DhVm9fTqQWMhJtAo2SCKtJKdcqmw4uEzy/yz6pFJ4/4DAwZ9qKW1uMy2gV4UVwTHLH7B0Xwsl9XkQsGUSwBq4aBWW/1sVX2WTZRbq57qDhK2JlLI2poyHq8mFjzD6N4xoiNvyeqHgq6oq4JcZCcz1c3H6/V0LAnnxECJvQIs9IxmU82EomJCCFz6mbCMcxaBHN4Int2dGNbZzv6h0aQyZVVEn0+L55916/hE+/+M2mVRDITCFQoYEFF3GqF7IcnPOEJeM973oO3ve1tdi+ddD2uSRR54jpA0ae2tvLGUC0AxrXmV37lV8SHa1plYT/Ma+OHm443WnEB2I12RW6u8bgA7Oa6XjfcaF0Adm0uCemHBD2m/LzVKJOLKxWkuIixWH23KlWvTFBlNW5mAjQjWJVUQ5o8/+QnPxGL2759+0TfjGYxt4w7qUePXslHorAHBT6sBs/M9aIQiFWF0aQ6EryRNslSCdS+8fPLeNNXHpaeOKcmzAcXqNpXPj+Zsi25gDkHEZtQUZVWXIwqWeTWjGNlxtiZWsJis3y0ZntiFjPt8gIju5cnMe6ARrhnaQKXO/fInJqou39+FJloi5D0Dwf98CUTZbER+pcJdUifsAnIBMPIBKMw1sDBNipRNndIH6+ZUvlGUbqdT9dQnOyXMns2D7I1tYQ5B4DvaHoZ5+tElSgw0QEDbZ4Swp4SkEwK77MmRs6izVUFL+qd+P58GiMNwFCt9jRtTlooeEFDFyClVVOEKiLphfPhKBJCm/BKKZsoy0V32d9+r46YoaNUULDg9WFWwkT9iZkVFLw+0Ids2h/GYrC2DQV92Aj0WC7RsNlr4DHP1aIrIl8MJYx0bEMynVk/OUa/Thzaj+WVVVwan8IznvokfPFD75S+98hkoL0In9emGm5lJ/yeLIWPfvSjeN3rXlf3GHv27AGjWHbLi1/8Ynz5y18W1T/4wQ/ijW98o1Ba/O3f/u31LlwAZnc23Xq30gy4AOxWutrX4VxdAHZtJtVKP2T0ywrAuHguLy+vKwuaSofc0ezouPol0wRVBw4cWE/IZvRqenpaqCVazZlNsMXEbdZnMUU8KoU5TMqjtY9q/ZreYtzRNFWrTABoArVPfH8AH36gX3ribt/ZjnOTCel2jjzASiUESvpVcu92DtyaS2LVgZ/TzuwiJh3Q3g7MjzkymD6amMBguzy9knlVAw4ERo7NXsD5HnlhkmM8nk258yn5AAAgAElEQVRhEq+hI17IIq5k0LMyLYBboCkGj1YUCp6qUkDB8Ir8qnQwLGiRleW2uYu4IPnCzz66MwsYW5m3c4tcVSdWVJDVNUd0wDY1LzyuZMvRzAoGYm2IUxykWEBcL4KAiKA2770iDlIptMH8r1pUyXpj6FFyIhJkp7RQ9KNYQEzTQE1PGktTnr+SItioL+aN9Vvk5+kDxry3sK4j4/OJKBlBVrVyKJ/CBYsfHymPHJMKDy6H4yLKVq2EDR2HC2lBhxwLhq8CnKwfDPhx/OB+lFBC39AlFLUr+YKH9u3CO//HH+NpT95odN/oXEk7p/gRFQdpGVKtUOTinnvuEQIcFOKoV/iM53pht5Bq+P73v1/kGJNhQUVDimZYi0tBtDubbr1baQZcAHYrXe3rcK4uALs2k1qLfsjeK+l/FMSgqAUXSitVkXXNaBMjWoxsmR4xprGldbQ85r/9278J+qEZSasmbc82lQbPtfo1vcVookkVRRbTf8wEb2//p5/jqw+OSk/c/q5mjCzwBUeuhA0VBUlvprZ8EomIvGnwnqVJXHYg4HBkdhiDDgQ4TkwNoW+HPLC5fWoAvTuv9pWzM6tCgn6Hg3aCBupA4XF6AH07T9gZ2lV1RP5eR3VFOLMi1SDjeYqNZBGm+bKmojm1iEzrFmiZFBR4BB2NkuwUu9DqKPgdXhnF2Yy8QMyB9BKGg+VIsUxpVwtYDsjnm/EYLUVlAzioPDajSO26ija1gIheFNEgqjnOBsJYCYaRkDBwpuLi2Ro5bvXOmQBR5KrBg63FPNqLKsLhoFDsXNJLmDM8NYHrqdwqztYB0r5SCTuUHNo1BbRHnw8EMR8ICxpiwetd93WrHB/l5XeXNLQUVaQ0HWOh6DrN81AhjQtrEUL2v6+QQVzXMBXYGEVraYrj8P7dSKbSGBwZx/ZtnXjkm59zJFFP4SXmUnGDiyqz1coDDzwgvLYoQc+f16NQcIPKh3bKN77xDTznOc8RyrquCIedGXPrPB5nwAVgj8er+gs8JxeAXZvJNuXnK6Nf7N2k/z396U8XB6MsPSNfVll6cxTc6f/+97+/TiFkfgB59taImFmXIOq73/2uEOBgDhf/m7lildL2rG8aPJvCHNVk7Vmv0lusmv/YKz79E/xkaE564tpjIaxkVal2fMHOROUFHPYuTWDMAZA6OkMlQ3teXtYTKQMbeSB1Yort5IENvbWcjFMoLjpQlBTmzQ4UCamAOLytHJ2VKYfnRzDk4DocnejHQI18Qea/xQpp+JQcvMUyYKN/FvPwQpl5zGQyyHo8SHm9yHh9tqJap1amccZBxO1obhXnHdABu5QcFiToeNY5b4WB1TWKIM+b0TOKgzB6xhw+hdL6zD0LhgV4NcvJXBK9FWbIdq7l0UIaA+Ha+V+MONGbqymTEjTGrMeH2UBQgOUOTcWSZHSQqo7HcqvCLDrl92M8GIXawCiagG2PkgXzyIK6hodq0F53Bn2I7+hGIpnG3NLVUfytHW14ybOejpc8+27BUOCHaoDmTysbotq88Zk7NDQk7D3omVWt0OSYka9KaqCd62C3DmnuH//4x6tW53HJhHjBC14g1pfXvva1AjCyuDL0dmfYrfd4mwEXgD3erugv+HxcALb5CTfl5wmeqgEwUjuYW8XkZkr1MgJ27NgxIStcWdgXjZt7enoEJYUS8UxkpsklF77Kwrpbt24V+WGmgAeTuSvljE3ao9mPCciskS72XSmDz9w1JldbaY6v+sxPMTy9grxahC8QRKGoQSmWoFgoOZXjDPo8KJatdaTKzpUpTDrwABNUOwcv8CcbeHLVGvzxmSH0OxEKIbDZWj/SU+2Ye1amnCkuJhcw60BgpDOzgsUm+ZyszmwCSw7adWVWsOAgf2/H6gymmuSVGnec/yEuWXLxhM+amkNMzSNSVEBpf69GDzANumFAhYFCOILWhUn0RpqhNvDHqryGp1OLeKzpavN0O38YJ9LL6HMQjdqm5KTy1NqKCtpJJdQ1EUHLe33IebxY8Qew4g/aAqdCOdEBOD2YTYKpgASJjG6t+gKYCYRQtBG1u91noFcvUwz9hoGdag6tmgrNA+EnVisfjHUj/JR0odLI49LYuZqxdFd7Czpam5HKZDC1sAyfx4uPvvmP0dZcfaPICsgqwRn/m5tsfO4yB4zP+GrA7Qtf+IKQoKcUfKVwk537ZrN1alEQ2a8dI2YyMKqtX5sd12bbuyIcm53BW7u9C8Bu7eu/6bN3Adimp7Ccn6KqIgJllZ83ezZBFBdO5lgRDFWqDFpHQVohI2TcYaQiIkU7WL/aTqrV5NmkGVrzt8x+mRNAKuSTnvQkoWz1yCOPiIWfoNDarymDb+Z7mTlhZjv2d+od30KmQLejqws3m0N+H8IBr/gZ9HsR8PHjQUs4AEUvwbO8BP3iRXhITCoxm4LFA8NT/ugeL/RIVIgz6N4AuvIJXA63C9qS4g9Bt/miWwZS8hGpY4tjON8pL/ixb2kco53yOVlbc6uYdyBB36TkkLGZl2NeJW9Jhw8e6by4YFGB5g+tC2TY/YuhSqIaiNh6Wbf2GSwWoNGfzMYLt7Wdj35nhmHrRb3yHPwjjyDjILLUOTOE2UgTIoaGZhjCODik5BEo5EVkrWQY0FASEaWs1yty19JGCQeyCQw5iCqdTi3hjAPgdjK9jF4H7TqVPBZDV+faMWJG5cZWnwfhgE+IqqgeL5KZrJCVz60pV5IiOOVAVfJ0ZgVnmq6m4pFCWfYuUxDQDRSam7FoAAulK/lczDejgXI9s+gtJQ3duQyCJQOrPr/IJaMq5NFcCgMV0vOMyu1aozkWDh7GxfnFq/K+eA91trfint94Ct72mpcKASaTCWEKMll/Wv/NnOFGhevGBz7wAQFcgsEgSA+niBI32EhVND9kQJw+fbpRd5v6vh4A47pHWiSjdBSPuvfee0XOM+mSpCh+/etfF15iN2JxAdiNeFVunjG5AOzmuVY35EhdALb5y2IuugQylTld7J2KVIODgyKKRUEO7nDy37UKVQy56DIhmgCL0sSMhlUrP/rRj4SPGL1WKj29rPVNIQ0KfxCAsd+urq51GolZ1/QW4/F4XEbr+DsCNZ5bOl/E6b/4V+lJO9LdjKE5+fyvk6lp9Fo8uahWFyJtih+9iICuIbAm4U0RBz8FUIoqmvMpZELckSbEY64JRK6HQWAXiUL3B6DROFsroRiOCHCo+oPoSc5jzIFKYHsugRXJ3X5KrXvgsQ0qzUlvzqWQduAf1ZVcxEKrvFfRDvpxOfA327U8iUkHyom7lqcw0SWvuNiTnMNMXD5KF1+dw1J6SfqejugqsskFsXEgUwgUOlOLgnbH6BL9wRhxo0cYX8tJmysIwOZDSsiq+9e736/lMeLbKD7S6Pin0ss46wCAlYFb9bykWsekwfTOAo0IIIyeDXiQ93hFJGsxEGxo/H04n8RQBRiqdSzK9xOYUYgkphUxFwiLPDfrnNWbG/p77VJzoNBIwh8UkbblGtTHSDiEA3t2IBYOY3ZpCZcnZ0XX//Dhd+K/PUVOfIObdiZg4/rACBh9wIQ66BqQozDHJz/5ScGa4Id5w9WA21Oe8hRBU7+epR4A43E55vvvv1+Id3AjMBwOg+N6+9vfXnetu55jttO3C8DszJJbp9YMyD353Xl0Z6BiBlwAtrlbohH9kL1PTU0JIQuCGkahrHS+akentHwoFBJ5YJUy8ZX1SQ9kvgHzyZj/ZfX0stZdXFwUYIo7pQRS/HelgTPrc6EnkCMdhn0RqG3ZsmU9X214Lonf/uC/SU/aHbvbcWZCXgHxZHISvS3y5sb7Fy5jxIEHWHtuVcihC5BHdTlNFd5XfkODX6dnlw5fPA5PclVE8cip9BgGSl6viBAZFB2IRKD5AtBLgMqXKfigBoJQvQEogYD4jqUrtYiFZnm6HPPbLjuIth2au4QL3Qelr53Ii3NArzw2M4QBB4IfR6eHMLDruPw4J887op12jz6KMcl8Iw5u7+I4LvqvgCO7A+7KpTBnM5LLPoMoodnQ0FLIIqjkQHl6r8F7zxBUOcVbBjhpb0DkcOlVfL4IiCZteGpVnsNpTxFnSvLneCKzUpUqyUiWiJ5pKigB7/V6oOqGEEpZ9gfKyoYeD1RJrzKO+3QmgTNr9MxOtYDOYgFhesnBgxVfQEjZVwPLjOjxDE3Q1mlo6PZ7xDwnVA3jXr+IzFcWRr/uOHYQn33fWx2Jb5j9kaLONYIy89UYFKx333334cMf/rDI5SW4IRgzP7QLueuuu+zefm49ywy4AMy9HTYzAy4A28zsuW254yaZleNOmnUGrPLztRZPM/pEQMOFtjLvqnJGzd1MqkvRq4vRJ6v8vLU+wRLHQNXEemCNlBDSDhlVI8jirms1GqSZ80WaC6NwbEMwRjDI8uOhObzyMz+TvgmeuHcLfn55RbqdUzPlTjWDxWCT1PFItSsGmN8iZ3Lbk09gJmo/SsAoHsHdvoUxkefEfwuQp2vwCWNmA/54DKVkUtA0zcJ/MYrX7DOQiG8BRbBVzRDmuFT4U4JhQQUjVZOAsLIIwQ8nyokO25EG2ucASIlx7pZXTjwx1Y++bnnD7tsGfoR+B3lqJyb7caaOj1etm+/o8jT6HbTbk0lgLNJYkCZONUhPCZF8TgCQsFYUkvCMRBGMFDxUh/QjTcNsbhjUieB1K1nMOvA4cxpxO65mkTJKaNLWpPVRQoH0xrXoWb08sC61UFegJFgqYZuSBcU6CGDzXq9QTtzhB/o8tRUpQyhh3/49aGmKoaAomJiew/JqSlzet7z6JXj9H75A6jlTWZnsCD7nn/a0p9U0caY316c+9SlBGzftQTZ1ULexmAEXgLk3wmZmwAVgm5k9t60LwDZ5D9STnze7NqNPpAoyV6wy76pyCA899JDgzpOmwjbMv6pVHn74YVGXkvH1wJoZ2aL4B/O6SJf81V/91Q3dmibRVF3k8SkeYjVl/sp/juId/3JGetacRsB6Vmcx09otdTxS+0C6oWQOUffqHGbb5I7FgZUjS/JKfyemKNEuLwl/UrSrHyGiwt86VVMjwCuiOzmPRKytDPIMHd5oFJ4MaaGMpkC8iAuQ5/PDiERh+P3QSkDr6gKmm7YKoYliOIoCvNAspry1Lg4NtC86UEA8kFvExSb563AwMYHhZnlz6n2XfoaBkLxlwdHxs+h1YKJ9+8I4zrTIm2/fnpjFWQfm1IfTyxiqQY/1l0po1lXEi4oQvQgFg/DmymbDzGGj+AY/pEOu+gO2japlRT/Me+h0erlmjhs3I9oZPQt4EcukxUYFI4BZn0/cz8ORFul8Qx6Xx8z6AiCdkfc/o4gzwUhd77Keri3Y2d2Fv3/XG9DVYX/zpdrfCtkR3CBjBKxWec1rXiPELuj9SMaDW67NDLgA7NrM463aiwvAbtUrf43O242AbW4iCagIwqqpH5o9m3lV/G+qGzIKVa+QHkhFQ+aW0QuM0a1axaxLQFUPrJmy86Q/Mrl7z549ImG6slh9yCjIwTFYXww+9MB5fPIHQ9KTdqSnBUOz5V1jmRJR88hLiiN0pJaw5ODF+OD8JUeS6U6BlNN2h2cv4oIDhcc9groon1vVvTq/AZgy3470zJBGhUDm4pU/Pl0XdE2KYUSoPufzwRtvQildvvb0hBKCK17m4kVg0J8LpKHpKMIr8vAYsVlo7ZKORArvt6A9w2DrPdg0/B9YdCAJv216AFM2c5Wsx7stv4Jhr3we1/HELPocALDT2WWcibTJ/NmJusfTSxtohMxZoykywUqY+ZcE87EojEwGmscDBV6UoGMxEEHKH2iY71U5qB4lixknwh3pJWFO3aEWBKAMGTo8pABHIkgxelbyIG+R1jePS9DJ+7HSKJr5eTRvJuCL7tgObds2LK0kMDW/LIRVWO75jSfj0+/5M+l5rWzAXC9GtqptiJl1X/aylwk6ONeFannGmx7ELdqBC8Bu0Qt/jU7bBWDXaCJv1W5cAOb8ypO9yR1JUgDrATAT/PBIlIvv7q6/u08/loWFBdFvNUVD64itdat5hZl1c7kcmFtG4Q32TTEOKi1WFtPc2aRLUiqfUTOzvOmrj+Abj05IT1p3LIC53EblxHodxdQcsg5MbvcvjGGkS17J8MTMBfQ5yHU6Pj2IfgdeXgcYIXIgQU+hkFnJqCDnuamQRToiR8tkNNHr8aznrdm98BElh4Lksdh3PJdGJla2W2AUT4itrH2E2MqaYAVpnF7mQpUMkYPn11To8TiMLM2UPdC9BHo+GMEw9HBYKD/SBkEteYSiJnPyiv4QomoWK/Njdk9rvR7pqkpqoabhb60OGVUKFjLIr+UByhy4i4qZDsDJwfQyhiUFYjiuU8l5nHGwkXGqpOAsgkJkhIIcFMhgvleIeZQGiZCkQwJaUzPy2Syya75dMU3DYigiMyXrdffm0xhrcL+1lnS00wtO3ENlwZOoruJipBnL/sbiIDwYhTh2butEa1MMb3rlC/Erd8pTZStP8LHHHhMshnrCTM973vNE/jDVbF0A5ugWqdrIBWDXbi5vxZ5cAHYrXvVreM4uAHM+mab8PHuotyia4If1fvM3f7NmPpc5EnOhZbI1o0/1jDzNumxbyyuM3xEoUl2RCdtc7DmOajlrprkzJY6Z5E3RDvqMmeXFf/cTPDSyKDVpTDGh7ATzT2TKjpUZTLXLU8qOT9OTS16C/sTMEPoctHMKpLpyCSzE5OhLBBuBkoGiDQqgda7jxTwyDqJDW1fnMN8mfw12r85gol1ePGXv/CjGtsn7ou2bGcalDrnjMUp3IDGOKbUoTHgDxhVFTQquCNl+EUkpWyZQ9EJoatKraX4GKU2F4YGI/OgC0AWgeiBEJQoEeozyVeTi9WRWMRWonW9U6++juVhAUpJSK55LhoEQfbwcAL6duSQmHIDok6lF9DrIqTudXBBCIQRsjK7RHNlHmMQcR86rxyNMltP+oDDL1tbmox0GEiUqnco9Xzg/R7OrGIi1CkDWUSwIcRAaRPN6Fz0eYci93LYFqbxy1aXZs30rfvaV++s+m+0+637+85+LzbZf+qVfqtnkt37rt4RSIj0hGxk72z2uW8/NAXPvgc3NgPwTZ3PHc1s/zmbABWDOL2gj+XmzZxP8EFBR+KJRMUFVPfl5s4+BgQHhK0afmHpJ3GZki4s3VQ0ZAatVaO5MFUYCtUoBkP/2vgcwscwog/3SEvYipchrvZBqN+Qgt4o5Ur0O1PcOzo9geNtt9k9srWZnehmLktQwRnDKyok+qeN1pJex7CAqsWdxHJcdqEIenh3GUI+8sMWxqQEM7JKPDhyf7Ee/g3YnVkZxLi6fN3Zs/AzOtWyTugasfGLxEs4EGkcTKS9PAEQhh4CqYFdiBguBUJm6VzLEh6CaxL2yL15ZWZPRGcaKjFgMei6HuJLDQiCMot8PNRAQvmKFUnlTox7w2JV1BqIYuSL4kJXY59x0KDksSdKG2e5YehnnJUymKTbSRDGbXBKrgaAAUYy60XKC86J4vEJshFL+GV9gwzzxHKm6aMfguTkWFZ5fzfEIQoEA7n3ak/GHz71b+r6p1oA5v9wMq/VM5qYY83D5k4wHF4Bdk2kXnbgRsGs3l7diTy4AuxWv+jU8ZxeAOZtMO/LzZs+MJFEsg0IZVEBsVJjXReEO04urXv2hoSEhqrFt27YNnl7WdmZki79j7hdzwGoVGkFzR5YqiNbxso9jb/umUN6TKd0RYK4g/6gSOVIOqH1CNt1BjhRFKmZb5V7GhZcXIyASsuKcu62r85hvkzsW2x2YH8ElB8IWx6YHcd4BKD0xeR59DgDRySm2q5/rWO0eOj55Hv0OlBOPLo+gv0k+Unf44oPodyDpf3TsDHodRAZPzlzAWQfX/bSygkc90Q1TRtBGal9Q18VPArtgKAh/Lgv6jXUUUkj5Q+tRPNM6QRAB6Y0HCCELnTTTaAzFQkEoaW4tZHAx3ioACr+3W7YVMphzQJMUOYO6hqy/bNEgU45kVjDYQFXSR7ERTUFcKyLK+TIMtKp5ZPxBcX6ql+qQPmR8PiT9tIyovTESDPjx83/6BLa0lqmymy1UvY1EIjXNlPncvfPOOwV9/Gc/k1eg3ez4Hs/tXQD2eL661//c7D8Zr/9Y3CPchDPgAjBnF430Q0bACFRqyc+bPdPnhWqCXEDp19WocJFl3lg9SqHZB6XnqX545MgR7N69u27XDzzwgPieyd6UuK9V6CdGMQ4ag/JjlqV0AU9+13caDX/D9yeiBvrzcpEediLkyHfIUwl3pxcw3iRpOFwyBA1NlfSD6lJSWAjLK+gdnLuEYSfRvcVR9HXJR+lOTA44koQ/OnMBAw5omQfnR3HRwfmVI3XyQiHbk9OYjMjROXmPbRs/h6kWeS+2nskBTDgwNt69OIYxiSiP+cd0YHkKFxzQ+o6vTKPPwfmdTi/gzJq1AoEcwR2peQLg8SetEvjsC/jhU5RyPh5z+IqFcrRpbeAEdiLfi5sUlMH3eMufUAiKpguaJj/7izlcCmwEmI0eNqQqkgZaDzDV6uNQdhUXYq1Vv2a/LcxfCwXQdOggAjxPrwclo4Rjt+3Cu/70DxoNzfb3P/3pT9HS0lJTnIkAjJtm3JD77ne/a7tft2LjGXABWOM5cmvUngEXgLl3x6ZmwAVgzqaP4Iu0PpZGSdHc4aTKlR0AxsWWESgCvEYCHDw2fcAoMc/8AeZt1StcvBmtefrTn16XxkK1LZ5fpV9Z32QCz/3Y/5WesNPKIs6G5V9yhby7A0pgSy6FpKQ6XVs2gYSTF+P5EVx0MEanCogEpf0OpOsPzo04Anw70wuYbJaP1G3JrmLFAUCJ6QqyfjmFQK9WhKeYR1Eyz4nS/NrqnPBQkyn+ogotvbSeg2S3LWmnnnxSyPlLFUaHChlkJfP+eIyO3CoWHUSk9qaWMFYDnNQb+7HkAvol6bjs786VWVyMtSJYIsAzBNBbB3kolamapBdGo/AJoRWRGoaYVkSKdgkerwB4BHpCjdHrE5G8otcrZPTNfDFz7K2GhrRkdM9s+7W/fQt+5fRRqUtYr/KPfvQjdHZ2XiV2ZK3PNYFiSMzb/Zd/+Zdrdly3I5eC6N4Dm5sBF4Btbv5u+dYuAJO/BWToh8yj4gLLKFlbW1vd3CuOhDLDDz74oBhUI8NmjoNgiUCwUV1TXp65XcwVq1e+//3vCwD4jGc84ypw+d2+afz3L5bHJlNOzl9CnwPa3PbELKYlfbmCxQLUgLyS2t7FcYw5iLw4VUA8Mc3onvxL3IGFMVxyoJzYlVoSps9SpUQBBw1KQA4QRZQsCg5k3beklrDswB9r2+oMZqLyMus7MvO4LEmn5fztWprAqD8kNZWiXXYZl72S4AtAdyaBaQc5VW1KFisOQFuYwNQwpAEmRUqEWIjk/cK52UuTaclNE7Y7mVxArw3A50NJ5OGFDEOoau7NrGI+HEWAUTzm4qEk8sf4KdM0ywDPt3s3PD090I2SeCY2x6P4yvs3Lz1v3jx8hlMcifYk1WxBWI/HpWLti170Inzxi1+Uvu/cBrVnwI2AuXfHZmbABWCbmT23rWvE7OAeIO2QidOBQADHjx+vG02ampoCjTYJfMjzb5QDRpUr+nSxPPGJTxSCGbWKVd6+UV3SFElXpAoiE7prFS72BGAEjIyUWcvnf3oRf/WvvdIzdnh+xFEkK6oVkJOMhggzZQcS7UfnL2HAAUh0CqRuWxh1BKQ6MgksS0aW/FqxbK4sK/hBPzVZ0AZg99IEJhwIfhyYHcZFB7l7R5ZHcd6BcfPRy2fQK5nzx5v/2EQfzjVLgllSaucu4ZwDgHliaRLnHAivHFGSGPDL0/oOphYdydbvyCUx6UA1samoCKNnw0MSo/1C2iPbJiVpwzzCbdkELjmI8L3jVS/Eq55/bcQ3OA5untEehBEu2ohUK1TRZY4vzZg/+clP2p8gt2bDGXABWMMpcivUmQEXgLm3x6ZmwI2AyU8fF01Gtfx+P57ylKfU7eDMmTNCUIM5V9ztJK2wXiFdkVEzRqwqJeAr242NjeHChQvi18wtI8WxVjGVFZuamuqOYXl5GY888ogAl6S8WMtff7sXn/nJRekJ27HKSJacQEJUySLngDolcqscAKmT086UEwVN0kGuE6lhS5LeTPTF0v1BaYPi7lwCs7HaQL7WBT0wdwkXuw9KX29GBc/vPC7d7sREH/p2ywt3nFy+hLNN26WPd3T4P9HrIOp5bPQxnGuXP96J2Qs45wDwnVy4jLMO2t2+MoWzLZK5kABOr0zjjJN2ehaPeeWjzyeSC+hzkN+2P5vAyFrUjFErGi8Lq+8SneAYyUJZfEQ4w5V/x/+1Mk+NYh+Urae9wPr3rH+lLX/v27IFnoAfHnjg8/vwwCfvQ1tz7fxZ2ZuQCrnM+aUo0r591b0LuX7s378fb3zjG/GBD3xA9hBu/Xov0K6kpHt/bGIGXAC2iclzm3L9WVuB3MmwPQMERwRKjBZR0KJWYaSMFEHmZrFuPp8Xvl61iilXb5olnzx5UlBTahUqKzK3jICwnsEzLzEBI+sxElcvAkZAR2BXDYD96ZcexP/pnbY9T2bFmJpHLiS3E799ZQbTDjzAysId8tS+stiEvNx6LeVE4Ru1Ji0uHtJrOSz8N3OP4PEKWexyvbUXRZ8XHo2ZLGv8J/ESeeUFsiO9hJU4zbPLkuWiX68HHr1sbiveLn0+0bdopxugSmNXcgELLVvLx+IxRXvm1PBfJSGBXlZNWOtzbTydqcVyBMzrFVLpfFm9Mra1F9qylDM8oRA8PLahoy2xgESkVZyzaCOOW365LRfhprX2+/KxeS5NuSTSLVtQKmrr35ljvGqhE6fB//PCE4kghiIyegmlfIEhhXJna8cqnyEPXp5js3hbWhCYHEHOHxTnZNZZG5o5RDFmqgWKwtwt+lOll5Gk5xeAUCiMoESr738AACAASURBVMeDUqGw3nf57NaGwOM2NaOUTiOYTaJgUflb77d8B6wLV4j/DATEPLCjcD4txrk++mAIniCBOFBSi4CqmlcfHm70ZLKiXayQRjoQXmtn6Z/tLMcU92EohJKiiN+359NYCkUt4ykrJoorR1+zQEDcE4ZBgy4NJaPsj9aTXcVUpHld7n3tL6DcjnNkzonXK8QsxPjhwW3pJVyMt69/b9Y150SMle3XBD3M358qpvCYDSuAygfWqdU5nHEQ2X3u034JH/uzV0o//+o1YHSLlHMCrFoiSnwe8/n+zne+E/fdd981Pf6t3pkbAbvV74DNnb8LwDY3f7d8axeAyd0CBDMESowScfGs5+u1tLQEmmwePXoU/Dfzu+irVatMT0+DkSrmAlBenu127dpVtTrBFMEdKYrsm1TIHTt2VK1rUhVJPyQQrJcDxt1YnhdLJQXx//nKI5hY5nclAfz4Akb/sVA4vLaTXH6VNYtRUID+XhTDUXiCofJLFF/Y1l4YxYvZmsR1+QXPA4SC4qWSYIPeWuuQQLzArb1Err24ieNEIhDHWXup3JGYweSWneUXWFLumLhPzy2+LJovgT6/eGk0XwzZeGtyQUjQm55K4lhrYyr5fFe9MJr9iPfkkgFF5NmUXxDtmMF2r85itk0+gnJ45gKGHIBEp1Lyx6cGHEWyDsxedKSAuD05i6lm+YhN2+ocVmTzh6jsl5xHTjK3Svi3ZZelBT8CFO5Qc9AlaaChogpVV6FL0vOY56QbmnQel59CIXpRWijEq+sIa6ojoZD2QgYrkteBf3vd+RRmw/LRqN3ZBC7L3i8A/un9b8CTT8hHhOutMHw2cy05ePBgzec31wQyJ/72b/8Wb3jDG+QWLLd23RlwAZh7g2xmBlwAtpnZc9u6ETDJe4AAhhEwGmImEokNND1rd4ODgxgfHxdRL0rRz8/PC2GLWoV9Liws4ElPepJQNzx06BD27t1btTrrPfbYYyJvgHlj9by9TKoiI3Fc8CupheYBzAhcLBZDNpvF3XfffVV+26++5wHMp67s9NuZuu3pRUw3OciXoQfYTvlI1pHkFAZbd9oZ2lV1nCgntitpJMLyXkAHZy9i2EGu04nZIfT1yMvyH50ewoCDqCCFSZyYN7dnlrESl6M8MlLnhYGipEhFXMkiLQlOeOE7M8uY88hbI+xYnsJ4WC6ay+PtWZnGqANhkn2rc7jkoN3+5LyjHKf9ShqXJPMuxfllVjAWkbdj2JlddZQ3Zgd8MUeM3mIRnxchpSDk82OaAgrm+/j/a5FXsW0kNk+8MMIR6IGAMHIu+vwodnahoKjo6WzDdz7yZunnSqMG3JTjc5w2It3d1Y3EGSHjuvF3f/d3ePWrX92oS/d7iRlwAZjEZLlVN8yAC8Dcm2JTM+BGwOSmj/Ls/Jw/f174b3FhrEUjZ3I1JepJU2T9ycnJDcqC5tFJV6T/Fs2aGc0iZbDSh8s6UrM/inpwgSYQI42lWuEOKyNWVNKam5sTwKpamZmZQW9vr6jHqJpVBVHTDRz7838FA0kyxWlO1olpZybMjIBNSebnOFVO3L8whtGt1fM26s2RU0+uY9NDOO/EF42goaN6JLXeOJs0BRlJRUkqIOYd5O5tS8xitlU++rU/NYNLYXkFxENT5zHgIAp5dLIffQ6osSenL+Csk3ZzIzgrqQTKa3pq8TLOOGh3+/Kko3yzUyJvTN6u4A4tjce8ZUDrM/QyYDJoKr3mOVYqwU+PsVIJvngM3kxGxNibqLYYDJdNpL0+ITdfXPMUU7x+5H1+KFXk/k+tzOCMg3y6+/74eXjls+urx8o8F826zLmlOBKf+bVyeMl0eO5zn4svf/nLePGLX+zkMG6bGjPgAjD31tjMDLgAbDOz57Z1I2AS94BVfp65UhMTE4KmV82ImREkGmwygsVIFimFly9fFtEn5ldVFkbTqKzISNb27dsFvZCJ2dWkiTkOgjv2c+eddwoZYyZwk8ZSWUyq4tatW0X9eiCQ4IugkrRHRu6sY51O5PAb7/uexGyVqwqZ9u3ykaxDcxcdiVtE1Zy0eEdPYhYzkiIh5rmddxBZKkvXH5Oeyz1LE7jcWd9su1qnUZGDF5M6XktuFamYvLHx7oXLGHcgbHF4ZgiDDgQ/ji5exPmW6tTbeid8cukSzkSYTydXjl0+i95OeTBL8NwnuTHAkR2ZH8V5B4Dh8PIkBh3kOR1KzGLIhqw7x0b6bbhYRNjQsCuzgkQwgsAaYPJR0t2S2cbcsVI4AiMYFLTIYkGBYpTQWshiPNYqAJNM9HN/ehEjDnz7dmgFTHpJGb5SmA/ZUlTRrKmIMsevpIPj9+3ZC2NbN4xSCV+671VoaZL7G7JzZ5HJQJVc5njVUrz91re+hZe+9KX45je/iWc/+9l2unXr2JwBF4DZnCi3WtUZcAGYe2NsagbcCJj96SP9kNEvRqsoFT86OipyupgHVVkItgi6TIPkS5cugR/mjIWZM1VRSFFkf0996lOFXP33vvc9IU187NjGF/VMJoN///d/FxEvAjwaNzOBmzSWymJSFbnDynYc11133SUUHK3FFOpgnhipijw/61gfGVvCi/7u3+1P1lrNk5MD6HVgHLw9v4zpqByNLV7IIONABvvQwigudFWPHtZ9iZ86jz4Han+3OfTyaipkkJY8v9ZsAquSdECe8775UYw5MJg+Nnke5x1c7xNT59G73QG9cnYA57dUp+nWu3a3jZ/DhQ55MLtrehBjDiJ13ak5TAfkX+DbkgtYdpDn1JRPIlXhxxXUiwgzV0vXEBKGx2Wz40A0Ck8mU44y6UXoBEvwwPB4RO6ZAExeL1RvOapUEJ/Aen4Z88b8uip+J1PCWhFaqSQiVzKlWc0j4/c3lK1nJK3VYyBO/69CDpF8FprXD93jEeeS8wWQCoSQ9ofEOdcqz3vaE/Ch/3F9Ik/c8CJVnSq2ZD9UK//4j/+IP/mTPxHP+Vr0cZn5q1eXa9znPvc54TfG3DMq8pIaSZuTd7/73VU3+b7whS/gE5/4BAYGBsRmJNV7qdj4zGc+81oN67r14wKw6za1t0THLgC7JS7z9TtJF4DZn1tGkwjAWAhkCJqoKEjQUllM2h8FL0hDNPOwSEekJH1lofgFFz9ToZAAjN4vVEKsLCa4Y64YF+3vfve7IoGbIKuycFFkpI5gitEvAiuOiWqI1mIKdZDKSEolz41gkPlgLP96ZhJv+Oqj9idrreaRmWEMOsh3iqlZZCWjNszPmeqQz/86wXwzBxGpI7PDGHJwbh2FNJYk82Xi+Qwy0Sbp+d+/OoORNvkIEYU7+nedkD6ekJJ30O5wYtxR7t6OuUuYdBBZalkclxbu8OgafJmlNdEV+1MTUfPIa2pDwFDZY2c2AVUv0/FChoaAocPPCBPNg4V65ZVSouhMcwt0iosoBSwXdage7xpgCghwVA9ksKdd6SWMOxCn2J9kNKo6eKg3S4dX5zEoKT9PmuLtiTkshyIiWkUAybkwAgHokSjyXj8yJQ+S8AmgaC2nl6cb0jKplNlazGOLWkDrsaPwNzfhLS+9B6cPyYN1O3cIhZfIpiDAoUVItfLpT39aiG+QIcENvetVuEHHCBup8KdOnRK5y9ws5BjJ5vj4xz++AVQRaH3wgx8U68/zn/98kR/91a9+FSsrK7j//vvx2te+9noN95r06wKwazKNt2wnLgC7ZS/9tTlxF4DZm0dGiAi+CMIIqAhquHP5y7/8y2huvlqIwUr740LGQvDDvC36hrW0XJ2szl1G5nxZo1imfD13EysLlRVNRUWOhcbJzB8gjaWykKrIXUmqaDHCVgs0mgCR42PfPDe2MV8K/v6Hw/jbBwbsTZal1p6lSVyWzD+KKDnkHQgdHHYIiJwCsJ0O8s0CmgLNH5L28tq9NI7xzj3S839scgDndznw5HIIwA4kp3GxRV7hsSufwHxYTsSBgCigZqH4Nkag601UUz6F1TUVTJkJ7aHCZnBj9Jp9kMZGFcCIVkSQNDa9iKAASzqacinky0r4a5qfZbVMAiIzwqSuUfAUXwCFUAQFjxeHliYw4MCP6/jCZfS2yedj3b40jrMOqLinU3M448Bn7vbl6fV8s3hRQbOmIM7oHIGuiMF5oDHy5vMjF21CquQR0arDq7MYcECv7M4mMRtpgtcw0KHm0FpUEDU0cU0Y2WPEcCkUuyp37PDubXjgw9dPeZDrCJkRzOWttpHHe+sjH/kI/uIv/kJQFasxImTu4Xp1mV/GaFstsQ+uf1b6PK1YuEaQicENx7a2ci4mNwhJjScNnywQUulv1OICsBv1ytwc43IB2M1xnW7YUboAzN6lIe2Qu3v8SdBDwQpSNEyKobUXqh3SgNnq42UKXHCns5LrPzU1JRZXLlqdnZ2iKwIyRp9Y31oYJSM4I+AywZ0p3kEai7VQTp4AzMxDY15XJbAy65sRO1IquePJ8fClwKTFvPOb5/AP/zlmb7IstdoLaaxIKgVuTzj1AHNGCTw4N4JhB3S7aLGAvKR8djfFJhxEbI5ODzpSMjzuEEjdNj+KEQdz4kQBMagWULRBKau8+bZkZrEUlI+87JsdxqV4ByLFAkKk5WkqghojTEUh+MAoi2/Nt43HFD5Zzc2I0R/LH4JmlKBo+holL4CCPwjFH6gJqk9ODeKsg8js7bPDOEtLBclyfH4UvQ4EP44sT2LAQb7Z/tU5jDRtpAsHdE2YHse1IiKM4JUM+JtboKXSKNIzTtexEI4jGYzYpiEGDE1421VGtyqniMfuJMgK+hFKp0C6I3PUKNxBkEVaZV2QrqnYdXAvXvZbv4wX3nX9ok7c+OKHQKaSlWCO7z3veQ/+5m/+RgCbWl5hkrfIhupUYuT688IXvlBEsOyUl73sZfjSl76Ez372s3j5y19+VRMCRlIW+fMv//Iv7XT3X1LHBWD/JdP+uDmoC8AeN5fyv+ZEXABmb96t9EMCMBNkWUGT2RPBC0GVNT/MzMUiSKpUuyJYW1xcFPx+U9CDOV7M0yIIshbWe/TRR6/y/frxj38sdk8rwRp3V0lBNEGfCfSswIp9V4K6amDxVZ//T/xwcN7eZK3VEp5JHh+MOvkV1To8OHcRw90HpI7FyicT4+htl99t3ZZcwJxkpKFFzSIVkvcgOjQ7jAs98obPJyf70euA2ndgbsSRJ1d7NolEXE5dMFrIIOcgX2nn0gQmttSnSXqpkKfmQF+sUFFBUFcRURZgaCH4S7owWWYOE53lRP4SjYJFlMknPLso8KD6A8iFwtg3cwlnHdxfx8d7ca5LPt/sCNUrG5xftZt9b2Yeo0F5m4Ntq3OYickDU0YGUw02FBjpa1YVtAS8iGTSCOuqAKyGyBUj5TEgvMAYTcoGrqY5W8+xK5fCvCTFmO0Pr85hcE0khKCqU8mhWVcRNAxxvfP+oABaK6HoVZTPU1R3rBLd4/l0FzJoV/MCIBZ8QSxG4lgOxRAJBfDg378NzbHqUU/pB1SVBox+8TlNunc1cSY2edvb3ibof1SmrSXUsdmxmFRCCn2Qrv7tb39bsDZ4PK5jVOStLKQdcrOO60WlhD5tVMgOIeWe9MUbtbgA7Ea9MjfHuFwAdnNcpxt2lC4As3dpGP0y6YfMkaJ8MKNGpP1ZFx9TzIJCGlbwZNa3RsV4ZEbUTLohwZxZuIARGHEBsxbTW8wqkEGwRuBG+qC1cFeTxyWwI2hkwjcljyujcKZhtGnmbIJLK1i89yP/F0OzKXuTtVarI7WEpeZyRE+mHJ8eQL8DdcGD8w4iWRQhoLiKMFO2X6hIOO5AkfDk5HlHQOrw4giGuja+BDUacUd6BUs2Ve3MvsqRPXmvq92Ll9dpkn5NRVgtIEywpCkI6EUwKuFnBIM5TCV93bw77ishqXtgRCLQQ2EUPT6oRglqyYNCIIRCIFz1+hydPIfz2w41moIN3x8e78WAA/uA3TPDGHUg7d6xMo0FydwqRnkCSlZE12RKXM0jvRa1k2m3Q01DLQFsHy6qCBgl+o0LiiQpgHlfAOlgGKlA5KpcsoOrsxiWzOPiuE4uT+Fca3XfK+u448WCoAs2BYPwZ9OIqgXMRZuxHIpi1e49SsohNwf8fnTnM2jSiyKqmQqGMRtpFqCxslCG5MV3Pxnv+qPnyEyjdF3mfxHE8HnOZ3S18rrXvQ6f//znhSBGrSiZ9IErGjDfi2yJj370o3jXu94l1g2zcL17zWteg4997GPrG4SkFzKXmR/mD1cWrilkc3CzkevJjVpcAHajXpmbY1wuALs5rtMNO0oXgDW+NARVNCk26YdckJgnRf8tcvKpVmiWZDIpTJQrfbnM3x89elTIvJvFBGZUMLTSSx5++GHk83mRCG0t1pwu8/fVwFo1YFcrCmdK5PNYBI4mILOCyye88ztI5ssCJHbL/oXLGHEQMXDqASYiWZIKdW2ZBBIO5KwpKz7gwJPLqQT99sQspiVpZcEi882CMGyozAmFPE1FSMlh6+o8suEmBMJB+DIpEeFghIkfvpXz5dWMLulefznC5A9ga2IWF3ceQcHjgyahiHcyPYVzscYv45X33YGp8xjeKq9e2bU4ijlJc3CPriOQTSBfJ6pT7e+Cypxy2xblXnYm5zHhwID50PLUeoSIUUPmORHErMur+/woRSKCglcoAVlvEEmvHwdWZnBO8v7iOE8tjjvyNzuqpnHeVwb5bWoO7UoBUUMVIiNUKkwHQlgOx5CxKjkaBloLGSRC9TcHeJ92FjLoIJiMhBFMrWIs3o7FcFzcu9VKrKhgez6JqK4jFwhhqq0L//CuV+PUbfICNnafj6xHhgIBCoWRapVXvvKVIiJFkYxqlicyx6tVl+sP1wH2/5znPAd/9Vd/JYQ1KPxBBUZG6u677z68853vFF0w6kW7FH7IrKgszBejOjA/XDtv1OICsBv1ytwc43IB2M1xnW7YUboArPGlYSSKETACMXMBNKXg6fHFHCuzmHLzleIctepzB5Q5AJVqioxemUIbZt+VOV3m76uBNapQ8fdWYFcrascIGs+NNBgW05PMjIjlVA23v+P/azxRFTWOEqQ4kBY/kp3DYFxSRKBkCFltVTJisG9xHKMOxC1OOpSgF6BUNvrCc9M1qJaX/xBfLjVF0PFCWhF+RpgMDT79Sv5SWM1DIRWLsuJenzCt1cJRaIwyef0owIsCpcUpw21RjBPCHQ6k5I9P9KLfiSx/ahoXZa83gPbEDJYlwTNBqVos2AKl1tt5a3IeM3YjLpaG+5Yv41JM3m/sxNxIzTyumFpAc7GAGAGzoQnQQpPiYi4PWhVMxNuRDoRFxIrUQDvl6OJl9DsQ4NidnMd4g2tAQLRFV9CiFxHLZUWeneLxIhmKYCkUR8FvT75+T2oJYxXUStIQuwtpNBdVEbFLByIiQpazPAduzy3hXPhqSua2XErkiPEFaiUcw0y05aq5OtwWxf/5X2+1M3WbqsM8Yj5vTfXbap393u/9ngBC3ECrFSVjO4pdMM/XbqHoBs2dWbiOUaCJG4pkSViBHv+bbAjmJHNzjqDKBWB2Z9mt93ieAReAPZ6v7i/g3FwAZm+SuaNHIMboF4upXEgFKEa7zMJoFL8jpcSsW69+Jfgx++GixwWXRs9mMXO6KoU/mBPGCBu5+max+oqZUvKVwMo6LqsCYyqVAhWuzGjdyEIav/XBH9ibKEstpx5gO1emMCmZM1P2u5I3Dj42cwHnHeRkHZ25gMHtNnO51hTyaFjbUcxB0YGAmoffA/iKiqDkMX+Jd5bIYvJ4BWgS+Utev6DwJePtAihRIY+UKTtRrSOzFzDo4NzKUvIb7Q8a3QAHFkZwsVM+R4rXLiEZ7YkVC8g0GlCV73ctjuNyFcGIRl0dmRpEv+Q9yT5PTg3grA0VUFI0W5Q8gl4VLTkF7dmEiP4wYlMkBdAfQCYQQTIUFf9dq+zPLOJSSD5vrC2zIu03xmtQQFnNkVHSDiWHNi8Q8XvFjVwoakh6AwJkWcd8W3IeFx1cgyfMj4o5CRu66I95WguRprogk1FACgE1r6ks8m9nNtqC1SpRtLZCFjvyScDjxYte9hz83ovuaXRbbPr7s2fPCrVAinDUKvfee6/YpKMIh3VNqaxPqjnpjHbLs571LLz//e8X1Wlpwg27t7zlLfjrv/7rDV0wB4wWJhwvmREuBdHuLLv1Hs8z4AKwx/PV/QWcmwvA7E0ywRdzwMzCf9MYk7uOhw+XX8QZJaMiYTVPrmr1STGkgEY1E2VTyOPuu+9eX3QJtBjZMnO6zLFwUaQ4hxWsEUARNHJn1Vy0Ta8va1SMCzZ3Ya35XpXRup8OL+AVn/kPexNlqXV8egj9DiJgcSWDjKSYA3OyLjvIyToxOYC+imiPxzAQ0QoIqYwuKUIWmxEmSooLhTx+L6JLYeHGZHg9KIUi4v4g9Y75ZGo4CiUQhOIpm9YSVDH6wu/4b5ly29wIRrrl879OTJ9H3w55CfqDs8MY7pbPrWpX01iRNBuOF9JIO4gs7V2dwqiDyNKx8V70yUYgATgR4KDAA6OJK5EmRKm0yAilEAopi4Mw8pMLhJEKRZGtEL/oTkxjRnJDgXljfrUgFBllSmc2iflQpGETRlo7lSxawgEEUknESxoW421Y9Yew7AmIfDE75dTSOM7UUQJlrmBPPoUWbk4AyDa3Yg4BtBSymLIhLtKq5ET7QDCAUDaDMx07qqoskna7N5NARNewHG7C1JroTERT8ZOP/0+0bmm7bpQ/c574TOdzulJsyTqP3Fgj+4FrQj0AZmfua9UxFQ3f97734c1vfvOGaswbpv0JNxjNsboiHJuZcbft42EGXAD2eLiK/4Xn4AIwe5NfCcBI2as0QDbBDL27tm7delXH1eqb3mBPeMIT0NFxNU3JzMu66667hBqimdPFepXeYJVgzQSCzE2z+sZw15KKVAcPHsS+ffvE+Bhpm5ubE6COx2ExgSF3Pfn5p4cv421fP2tvoiy1DiRnpD2hnHiA8cWTEamZ9h6EPUDQU/Zf8uez8KkqfOEgkMuXRybyl8oRJubBtOTSmGvbCtUXhCIEH0JQrHknNc6aVK90RM4YefvKNKbb5XNKyqbI8kCK6nuDDvLUupKLWJD0WRIKiA1yc6pN5f70LC7FuqTvrZOrl3EuJklTBXDs8ln0OZDX3zt9AZfWcqRI+2shBTCfQURThDGyh2bAHq/Ih2MOUTbWgqQviKbUkgBgMiWq5pGjmmONfKVafe1ance4DYBS2f744jh618RFGNViJKtJYz4WlQW94nwSoZj4WMd0+8IYzjm4n3emFgRNkqVNyaKrkBU5aprPJ/K7ZiMtG5RTO3NJLFRRHSXI3Z5LYYuaE2NdiDRjIXolAnhiaWKdykkq5M5sAu1qATl/SERCrZE5v65hf3oJT8wu4Dfu++9ifKT8UZ2QHz4fq/272nd2c7UYdSKoqlSwNa8R1w0CHopdkIZ4vQDYF7/4RfzBH/wBXvKSlwhpeWthDhfXM7IsKOS0bVv5786VoZf5q3brPh5nwAVgj8er+gs8JxeA2ZvsSgDGVjRAptKT6cfFSBQTqq1gxtp7pWFypUqhte7FixcF5cNUOzTztypFP9jGVEZkBIwLvykjXwkEK2mTXNx/+MMfisWdtEazmADO9A/7yPcG8YkfXLA3UZZaW5OLmK/yIu/XiggXCwh7DATzOWFaS3U8gqaokoMWKCu/8YVJ0PE8pOOVKXlavBlqUROAqRAkYIqIl6jbVy7jXLs8/W338gTGO3ZLnZt4QXYANg7PXMCQE0rgZD/6HUjQ71yewqSk/1SgqEC3SXG0TtqehTFnEcjVcfQ2y4PSY+Pn0N8jH6XbNTOMy1XEJjyGjhYli7iSRVRVRD6dPxQEolEUdQNqLoukJ4BUOG5biKM1u4oVyZxEzumB5QkMO1APPTk3gnM2aJIthRy2KFnEIiH40mkh70/Z+pVwvKEMvfWa70guYCpmz6qAkeMerYD29Iog2ub9IcxHm4UHmJ1yKrOIM5F2AXh35lIi/02IZcTaxM9qhcfclllBO3P+PF5RlxROa4kUFezLrAj672hzp+jr04kz2Hv/B0REm9Ep82P+t5UJUWvstYBbJVhjDjCVDamOy+8qc7z4jD5x4oQwOya74noVbs5xY45MCtLirevB29/+dtCLjEIh1jG4RszX62q4/d4sM+ACsJvlSt2g43QBmL0LwwgUF2JrIXhpbm4WBpb8notTS0tLzd1M83uzPuXn6bNSaaDMY4yOjoqkaApjMIerUqnQOg4z38v0Hevt7RU7lZVAkOPnMU3apJnrVanYSLBJsGhSI9/0lYfx/f4Z4YsTjwQRCvjgJyDSVKiFApqbm+DzelF8+CGUNENQ8gRoopw46XhrHyEpTiPbOhQpeoBd7D5o76JYah2bGsR5B9L1zfk0UpYdczsH3rE8hSlJYMN+T0z0o88BkDqYko8kQuSdFVEIynkY9azMYMaBUbSwDnAALo8vXkLfFnngvGvuEsZtgI2okkVTPoMYvaKUHIL5FIw1bzpS9fIUqwjFxKeWX11XahFzDjyrDs2PYNCG1HrlPXdqdRJnHNArj86P4jyvHUUvClmhLhjRiqDlMKXk08GIoNpVApat6UXMScrkkw6YEtTaja8gTUoe25S0AEncNKFcPPvnRgkjUn0Saoud+TS2GSqimSRmYm2YjrXWzfkiTXJPZhkRQ0cwFsXDoY0AsUXJYXc2AdUXwEhz53oUjNG0p2QX8IkndqPlz/+85qOAoKgSnPHZav1dNfAmA9w+9alPiZwvrifc1OOm2Ktf/WqxXrS3t6//JJOByrXXovCZ/8xnPlN09Tu/8ztC4ZBRNwIyysnzpzXfmfXe8IY34EMf+pCg3T//+c8X4/za174mZOzvv/9+vPa1r70WQ7tufbgqiNdtam+Jjl0Adktc5ut3ki4Asze31QAYJeG5e8kEZlN18OU1fQAAIABJREFUkPlgBDjVCuuHw2Gxu2hKvVfK0pvtTMENU02Rix9LpS8Yf8dIGSNmzPfiYkxgSNDGcVkLz+F73/uekM1nJM0EefQP40Jvlkq65Avu/wHOzmTtTdRareZsEikHdCiKFlTmZNk58P6FMYx0lWmVdgtVAgsOIllHZAQ4LIM5PjmAfgfqgl3pJSxKRkTa0itING+xOxXr9YRwR7dNcRFL7yeXqdonD6T2pOcwFpPzivPpRXQuTwlfsbBWED8pZGIKVhDoZ4JRpMNxQSs1Cw2KKcAgWw7PDGPABtir7FcIcDhQ2CRwG2oAUiguQXDSSjVMvw8eRREiQUuRJvEhuLBT2vQCVkSmlVw5tjSJweYubMun0GaaGPuDQhSDkbRa5fjSBPprnBspgDtySUHvpPjMbLQViXBMeJPlqeJZzU6hVMLuzIqYh2wwjPH4FVrhicwC+qLlvwHOVU8uiUwwgrHmjqtA3C49hy1FBRO+CF458GO85NUvRPw6AAc+f0WeqCWyxvxbPqtJLbdG2t773vcKejg3yRidqlW4ppjqtXJXsHptHvPd7363yE0m5ZB0w3vuuQfveMc70NPTU7URPco+8YlPCEl9RvC4ofimN71pHcxdi3Fdrz5cAHa9ZvbW6NcFYLfGdb5uZ+kCMHtTWw2AkYJBsEIFq1py8tbef/aznwkOP0FVvYgW25j5ZARRBG1cEK2CH9Z+uVPK/jgOjofjqoxqmfWZt0bjaFJeaCTNBZ6Rs8rcAgI18v6pePVr7/kOZjO6vYlaq7VraRITNtTfKju9PT2F3uYrvmp2D9qRXsaSpCHs9pUZTP//7L0JcFzZdSV4ErknkAuAxL4QBEiCIAmWVFJJ1lK2QtZieWI8Hqm9dM+ox7LbS8tqy92etqPGtuxxu9XWhNutaI+6FSNZdrQmrOiW2+6WR6XdVbLKUlnFUpEAQYLYgUQmkPu+bxPnAZ9MJH5m/pdgKUrivxGMYjHfe//9+38u599zzxmc0HqI++PYk7XcRU/WbGgHW5K+aKRr1o1GTaqHjScy16Vwx/W9ZSx1o4CYDnQlJW/Pp5BjdalWFfQ/9taRhmqtlGCsUfTmSLCiaLIgZ7ELUNVbynUFpK6k9rFikwelVIW81YXf2IWDdax1UU10ZaKCKmeh6AUV/EoFITfPqjKNmZPWXkTtzhOAZDCbRFgjna/xPrkS2cWKBnNpSt8TbLlsZlSzOWGyfcs7pWpi3PINVavBXSsKZUQGK2UEXNZ6VcjH+/r6VYHjtajvhET+YIFgipXMHvicg6q0SdKapzIxOEsFAQj3mlQXB0t5TPMzw07xjaN+NEe5iL/84h9j8s//X9jf9S7pzwXZCfysfvbZZwXIoTCSWrCiRHDG3iyCIFaW+LBP+UOJ+uZ+Y9l9PMrjdQD2KF/9s5+7DsDOnsNHegUdgGm7/Pyy5JdhYzT6b7WSk28cTzoH1+ATS4phEPSoVbQ4h8IY7CkjXZG9WysrK1AT6+BYRcyDzdr8YiYlsbmqpeyDyo2ksRCA8e/88ifIag5SFfv7+8Vrix/6PMo1bXlSRl0+WMNqF0p6CwfrWB2XoyBShIPS0Vqk2RvPYj68jXuSVTPOv+q/g5XJq3IJAeAuZpC0ygkyjMUPcChB2VI2tejrju542b+K1S6UK/sLKcRVRBL4Q9hdysKRTcFWzIlqFXuAWK0y9fUiVqojY3UgZXeh0kZe/cR1o7jIiHy1bXF3CUtjDywjtF7AucAa1ruogPXlEkgZj/oZW4WjVAABhbNcgKVeg6lcQtxiQ9zWJ6o/WhUzF0I7WOnCx+t6aOtE3xj7LkfyKQwUs7DWakJRMWJzItxE0x1ORRCUqCZy3fl4AOZaVQjhhO1OHDpOenO1ytH18I4AZtZaFWG7S/SrqQUphOdTUbgojGIx4YbzpEgLBUbmUhHRw7fpHrlPn6RM/XQmjoV4AP905RkMv/gizA3WIlrvE9lxrFjywRrpe+y/Ugtah5AK/sEPfhAf/ehHZQ+hj++QAR2A6bfIWTKgA7CzZE+fy4oJdZH16JABNQCmmCUT+JAK0qpCpSxNGV9KwbOqxfGKyIXaoRWKIgU+2M/F/2+Wn1fmKaIbVNIiHZEy8myYVlPMIj3R6XSKL3VKICtmy8174JNZUmP6Rybxrv/4gvT9oSbvrmWR6Zhf2gPMm4ogIknR4166rmSF5StZNE4udiG3Pk9J+C7EJhbjO1jughI4ngoh4Dqp4Nl83ShYwd65vkJGyPGzGtJjs6JuNgslu0INyMKENPuN2lA85xP7uOdsfyy1e+ba7i0safVga1jggn8V611YFfSmIkhLUlWH0lEEjytSzkIWg8UM+kpFGFETlaus2YaYw4VUU2/ZleDmUR+XZFzPhXDTrA3QKEvbykVcjvmO6HgGg+gRO+z1IN9BOMSbS3WstrGCOZVNCDVFCm4EPEOYi/jw0mDn6jaB1LlMXPSw5fu92K8ahP+XWpC2eCEdhtVkwl7vABLHgPdKIYYVi1vYRlxKhgTJcsNDtdOj6huPcSkRFObNa54x0f/3J1/7JC5mIhgPhWAwa6NwSl6mE8NJOeSDOH4WU2RDLfb394Uf42/+5m/i93//989yOH2uSgZ0AKbfFmfJgA7AzpI9fa4OwDTeA2oAjHx5NkjPz88LJUICIFaXWgUrWgRSfNpJvny78YppMnu1SC9k4zWrYWpBw2aCQVarKMDRqqrFuUrfGsVDdnd376ssNq/LHwYWiwXRqg0f/OtdjVl6MOxaaAO3h+WrDa4u5N1ng1vY6oIidm2/u56sfhoHS3o0dS9B350C4lxwC5uj6j/qWl1MWyGDQYpVZJLC/4w/blm5YGWxJAQr7MKfLUXz24Z+nPPpQ2z1yUvJLwbuYHlE/h65FNnCqkcepLiSQSQlDZ8H09GOYIOCJ/35DAYKKSH+YKxUYC9ksO8cQNTuRk5CCOV64B5udQESp6J+7LZ5CDGUS8FbyIBm4BTkiLkHka0BaaNJWu5+MR3Ekv2k6flgPoPRQgrmeh0Ja6+g9TX3bM3F/NhoYW/AHq0xCqT0GAVdkGCQMV9MYtXUe+KWtVVKuFDOosdsxqapF7mek8bUVDacqhVgSyex7Rq6vxYX8RSyQqTD3zdwv6rHf3tdaAu/deNzMM7MYHRpSfrzrpsJtPugrxYfxPGPWvCznz3DNEemSbIeDzcDOgB7uPl81FbTAdijdsUf8vnqFTDtCaUfSmOQFkj6Hzn6BEytKlTKHDZcs7eL0vVqhsqNaysKhdPT06AgR6N5cvOOFYl6VuDYD0bZYipYqYXSh8aeNkYrCiT7yBgvHhTx72+ktSfpeOT8wTruSaoZWksFlDQYwjZv5mp8Dyv9clLyXONicBPrkp5QwkzZLG+mfNl/D6tdVG0IEle6EO5QQCIFKx5UqyhYUUZP/UiwgpS/gtmGrLVXgCp3NomQW74itZiklHznykbzdbuyt4w7XeRkMB5AuKmnp9MNSkn4eAu58nZzL0d3cKdvWOTMW8yIHBEA8IuX1RRWsKK9HtGj1hgU4Lgl2e/H+TORXWxLXgNruYhS7aiyxus7kUvCVcqLqg8rR6xqNRs981iXI3u42y/vpbYY3ELK4oC7nEe1xySohOxJaxeOShFFqgceA3eCpJlsHJZaFSGHW+xRLR5LH+Kmwwt3tYSpcgYV9GDLeqSo2Bxj2QRGCmnx4OBGY+7rdVxMBmGu13Cvf+w+MJxIx4R/2Gr/BP7FS5/Hj+7egvWHfxjev/qrTrfTQ3md4hqkpbNfl8JIakGWAtkM3wuKgg8lKd/lRXQA9l1O+PfZ4XQA9n12Qb/bp6MDMO0ZbwZgivAGlZ8IqpoNkptXVvy6tIzP5XKiWsU+LII7Khw6HCc9bJT1E4kEnn/+eVElI7DjFzbVGdWC43gefPqqyMy3Gsd+tS+sp/EXG3ICHFyPT+R9kn0zY4lDHGoQBGje73XfCpam5I2KR5IhBD1ygIN7POhij91K0M/mIqoqgb35NFgtFBTASlFQrRj8EV4zGJByuJG2u0R/ldY+ovnAPdzrom9vMb6NJY88AJ4M72Jfsr+NRt25HoPmc1LulYuHFMRo7zdGwZOhchbueln0G9XyeThSMWz1jyHqcGvuUeMxZ4Ob2JTsyeLxUS2hrKb2p/Im7S+kMVzIwJNJIn3cN0Yw1EpO/9T7JriBWxqEcqhCOJFNwGEyIlMzIGGyICzR/8XjLkR8yBtN8JQLSFnt2HV61VUNGzY5VClgJhtFrG4UlSxBlWwKepqdy1K0pPd+BfBy1IfV/nHwtfOZCA56+xHsfaB+OR8/EPfP+vH1Gckm8J++8h9gq1bQ+wu/AM8f/qH2L4UzjORDNtLSyaBo9cCM3wGUhv/Upz6F973vfWc4mj5VLQM6ANPvi7NkQAdgZ8mePlenIErcAwQkjS1zivw7l2jVS9W4vOLXpWU8QRL7tUgDNJlMAoC1CvaVsbJFI08qJlINsVVQ+ZDywpRCJqWRwFEtFIXEz67m8bV9SQUOKpzlM0h3eCrefNxLhxtY70Ik4Yp/FXckhSPYx2TkE/k2nmRqeblEZTtJkRCuc5WVrA7CHaxeuCsFoQZozaVhLpdgqZVRdvejXCghb7EjeyxYUW7TpzMZ8XXlU/ZYcg+3XNMS74ijoXORHWwMys2jcIqxUkS781DbyLnwNrYlgQ3XUQQ42K/mzSbQV8rCwgYgux05kxUxgwUJy2kvsAvswdMAUhr3aqhWYS2khMeYTJyLH2Cn77RvFSs6rO64Szlxz+bMNgR7Pff7x64frHdFWzyXCGBHRTl0LBuHt5CFAQZR2SKAUfy+RjJxHGp8Xw/lkke0wj4XzKk4XtJArZzMJUC6pKioGY3YUxGtYX/ZhVQYlR6T6OtqpDr2lvKYSkdhNJuw1vtAkp7iL5fjB4jbnfD3HdHEh0XFLAUCsl9NrMI4NgbHe9+L3ve+V+aydT2WD9Zeeukl0eNF2rhafOELX8BP/dRP4bOf/azw2dLj4WZAB2APN5+P2mo6AHvUrvhDPl+9AqY9oc0ATJF/5wrtqk7KERTfLf7/W97yFgGWWgUBElUKGaQh8ku6VSjVMr7eTtiDr7NXLBwOi6Xe9ra3wWikTevpUMb96Z0yXgzJATBLuYCSWd4c9LHUPpbc8lS2mfAedjT8uGs8y4F0FDGXV/vFPx4pLdxRrwkwej60i5y9F1abBT2pJGCzoWq1odRjRhZGpM0OZG0ne116CxlkNf7YbTyRhf07uNuFKfXVhA8rXeTfnYki0XsaOLRL7lg+hgOLnCIk17u6t4zlDgC4L5/GQC6JvmIOpnoNVUMPrPk0NkdmBMiSCWcqjKTkNRhLBBGQNPfmnq4H1rDjHMRwPglHpSyMzBO2Xhz29retvl0K7eCeZCXRVi2hxIcQtdqRXDspgiYr/L39bQVHFkPbWGohpEGpenpykepHhUSCRCW8mdgpJUW+dqRcGIGrXBDn2TjnVdkQXrId9ZrR5+1CMiSUIjc9w0LYozGcxRzm0hFQdfPbIw/8AF2FHGbTEey4h0WVjDFKkNdTwx37gLg3/uybn8Z5/6Z4bfC//lfY3v52mVuk67HsB2bPLinjrR6EEXj93M/9HJ5++mm867sgjd/1yXyPTtQB2PfohXuFbFsHYK+QC/G9ug0dgGm/clStUnqnOEuRf6daoBYzTIpekIZIKmG7ihbXVsyQ+fd2lSq+rlTL+HctQiCUuKdYCMe2CgqGcNwfL9exFitrTxJ/4JBK6BmTmiN+gO6vYLkLKqEnm0RC0vR5Ln2ITZf8HhXhDqoa0tPIkUoICqAQrEBd0KRKJgsKFpvwrKISYNVogruQQcomBzimw3vYG5an9tG3anl6UTr/57IR7DrkQGlfOY90049hLQe+vH8Hq11UO6/uLWF5fB7s6erPpeAo5QX9kj1BrA7GHP3INAFZ7mc4EUCw96RwRKd99mfiiHbTkxi4h9sdqmY0Uh7NxtFfyIjeqB6TBbZiFrdkbRFqVRCo02BYS1ByfcxQhSt6iIDDA79z8H5flpb5C+Ed3DmmchIUzaSPwBNVIlvRCsdqBQTwoGeL75W5VFjQPH1OrwCZanGumEI9l4OnnMeec0jI8jfHXCIIe62Ctf5xcQ9ciO1j3TOK8UwM3kJOAFNF+XCikhPKind6j4yYWc17dXgXT934b/eXHbl5E6ZZOUN3LXlTG0MBJ/YRU+mW9HG1oMnxr/zKrwg6upbvmG738qjO0wHYo3rlH8556wDs4eTxkV1FB2DaL30zANve3hYGzDQ2VvPSal5ZqYCNj48LH65OQdNkArG3v/3tLStVXEOpllF2nmPZY9YqWNmiaiKVGGfb/NAgNYY/EH7vRg3hLL2btMfFQ3lxC66+QO8wScl1c6WIilFeFOOq/y5WmqpEpMUJwYpiFo5yAeZKSYgv0GOM4gF5i01Ir2+MXhQAS2uwb6nQJDeuZe6C/25Xlaz5hA/3PJKVxHoN9kr5VGWh0z5nM0Fs9qrTWNvNvU4p+TZVOkOthoFMDO58EvZyAT11oGS1wZjPYmPonBAP0Ro2WgAINcfW7wu1tUiJXZXsY+Q616PbuNXgQcVK3Eg2jt5yEfWeHiStfThwDqB8LImuHHs4cYigZCVxPBWGv0U/FkHeZCYmQAfFMlhdihyPfexgHTclq8ao1XA+cQgnhWiMJuy5vEJOv1M8lgninrlPVKJIa9x2DyPXRhDFm0viXCqKg8ER+E2n+17Zk0YAx3MJNKiRegoZDOUSMPa5cM/Ud582OZWOiD3fHZwU/0bFSlb9VrxT+PUX/ht+ZPfW0SmYzUcS9C1YAZ3OU/Z12odQ5ZAP2NzuBz1qjet87GMfw1NPPSWYC516jGWPr4+n+wJ5yHroGeguA/rN013e9FnHGdABmPZboRmAKaqGncCMcgRlPJuuW8kOK2NZafvyl78s+rqortguaOj5la98RVAaSW1sFxThoGgHvcs8nta+QVTnisZi+BffKKMq6RS3GNzoSl78XHQfe1454DAa7yzcwQqBs5AR1RIhr16rgTS1ZK9HVKvyNgfS1l5krOwBUqdkKjkdSkcQlvQcm4rsd9WT1a2Z8lgqiIMOXl7N9wjBTkyyQsQ1FtP7WOob1/4mOh45v38Hm0MzGMzEBOhlFZG3GdUEKRUf7SPtrsmLqVYFpfLZCycTM+EdbHu6UPvzreCWhJQ/6XSsqkxF9sR58E+41yMEPDoF789U8/l2mkSwlwvhluXofcz+p8lsXADprMUGv9MrTIfVYjayh00NOeGa0+kozAaANd47Ev13pP+dy0RgRQ23+idUlQuVvRFUnU+FkTXbhQrkYngHt5o+C2aTIfRWS1j3jAuDaCVM9SoWymn0FnN4vu9BVftcKgRHtYLVgQkBvHguFxNBAcR4beZjfvzx3/wJrLWjB0ymCxcw8p3vaMj6wxlCBsX6+rqQme/r61Nd9CMf+Qj+9b/+12D/MNUS9Xi4GdAB2MPN56O2mg7AHrUr/pDPVwdg2hPKShPBjhIUvqAABr26WskIN65OaXcqX7FaxqpZu1B8wLTQFal8+O1vfxv09nrjG9/Ydl0aLBcKhY49a6S8+GNZfOjv5eiHPHi3qoSefApJDT9WxY+lSkkIVkwX4sgbzDDlsjBUy6ibzCgbjCiYLEJenT/m1YQeFgKruCspgc4KGR+YklIoEwv7q1idXJCZIsYuBO5J75HiImbURG+ZTMzGfdiSrZpRfIaUwDa0UfYD0pTYmU8LiXT+EC46PSjnc9gdnJaqSg0XUwgaO1dcms/7mu82liXtBrjGpcA9rLaoEtnKBYzxvEo5djIJAH/oHkK5DhgoCy8r7sI+Lkl1TVbV5qL7gv4XE2IZA5ryyfcO3ysKNa8xX6yaCVphqSCogXtO7/2HEo9lDnHL3p6iyuoVZfBJiWSly1ivoadSOiXTz2NSGONCMijyt+EZOwHQLkZ9WOsfA/vKLqRCiNld2G+yHnCWCyAFkf5ncVsfZuMBbLlHMFtOw5zN4N6xobWlUsZC3I9Nz5jY10A+jV9Y/gp+ZOemsBNQwvrOd8L72c/KvG3ONJY9xGRFvOENb4Ddrv5Q4UMf+hA++tGP4uDgoKVQx5k28YhP1gHYI34DnPH0dQB2xgQ+6tN1AKb9DmgEYBTk+Ju/+Rsx+fLly6AHV7sgcKOoBimFWhQT+WSUKot8MtrKq0s5niKHzz4CPk1tFY3CHj/0Qz/U8kuf1TdW1DYTVfy7m3L0Qx77iv+etL8T/bWoSNhXyMJZpLx6QTyZpkgAqU9Vmw0le59QgEsZrcgci3wIUYwu+sbORfewK6luN5yLI9RFlej63u2uerKmMmH4nHIGx15SsyQrdLxmjyX2cMstp2TIebOHGzh0DWGQFLtCBqZaRfxgz1nsiDs8qr15BGVl9GgCC433MmXyV7vw1qJwx+0u+s08+ThiJjuGMnF4cwlYCVpMFkTtLoT7qAx4mtI4GQsII2HZeMy/ipttzs1ULYtKlLOUF3s48AwjabKBVgqHKsqJ7Y5PoLLZoH5IGfaRfEoAoB3XcMuq2eXwrqgmNcdEJoqhfEYoF/qa7r1L+RjWrK4HU+p1zCVDcFRKAiyp+ZPRI2wsF0dvtSz6uQpNRstiv7mU6O9S/NcGc0mQgthjwH15eYLJq1G/6HMjQKVAx0+sfQv/692/Fcdvjt73vx+eP/gD2UvX9Xh+vrMvmJ/vVLtVi1/7tV/DJz7xCWQyGbDXWI+HmwEdgD3cfD5qq+kA7FG74g/5fHUApj2hjQCM/H0qWDFIDZmbm2u7EPuuyONnaAFs3/rWt0R1jbTCToIdrKxxLD3D2gGwxj3wS78V7UWpvr0YquLP7sp7gJ0P72J76AEg5Q9uN3urqiVYC1mYq1WhfsYf6mWTWch100x2Z/i8lNcSc9ktAHMWUsInSyYuHG5go4sf8tf2T/ebdTxuvQZbtSzV6yTuxcN1rI/KU5UWU34sO9XNu7muO5cARSkcpRz4w5Y9RdkBLwrFMoKSxsHTkT3sSlDZlFwJKXnJqiXnToW2sKfhePyBPsq+M0MVpmQMCYsdQeegKkhodf2u+e9habj9wxi1uRPBLew3gBt3PoPxbFw8hEja+gSdsNl8WNAWuzCXftx/D3mTGUbUhfKgFk8vXnN6zrHn60i5MAxWoA57B04oFzaf26sLEbxk8QhRjOF8Bvt9g4i0UIi0V0q4VM3CVq/g722nK21ziUNh3MzKVqMn2MV4AIP5NJ5X1DHrdVyJ+RGzOe+D0x/cX8E/vfVlkdNW4f63/xZ9P//zHd+aD2sAaYX7+/vgw7BWarS/9Eu/hP/8n/+zYC3QjkSPh5sBHYA93Hw+aqvpAOxRu+IP+Xx1AKY9oaxiEYQxbt26JVQCWdHqJP3O8Xfu3MHe3p4mwKZU1xSZ+nZ9XYoCInvFSFcknaVVKEbQfJ3jWjV+K9W3r/qq+O9b6gCMP8Lc+ZSoWLG3ylKtCMGKOgyiapWyu5Cz2gUFsKChZ+diwo/1/vZGuWrndTkgL9xhL2aRb6G81u5uuOa7g9vTV7XfMMcjCUh3GgCplgX6MzHEu6ikLEY2sext/zBA7fjng1tI2VxHohelvLiWpNFRyTHaN6B6DUm/S5vkKYFXYzu47Za/1uwbW5WkEvZUyjCWj6pGjTFQysJbSMGWTaNiMCLucCHYN3ifbncpuIl7g60BaatrSHGXZUklQ9JG2ZPFqgyBBfvGQhrEOOZFRapz/52xWsFMKoy+cgFJjxeWbAr33HI9cTOFBCyZFGy1qqAlJmzqPUuNeWFF6nIti0DZgL02VdlzpbR4QLPeNySqb9dC2/dVJAn8FuIBQR3cdZ2sBl+KBcQDG/b3TSUPxTEupiMo1YFd99FYgrYPvPQFPB7eVr9kLhdMc3PocTjgeuopWNv4LWp538qM4ecxqYW0MGmlBfHe974XpI2TZt5OXEnmuPrYBxnQAZh+N5wlAzoAO0v29Lm6EbPEPaAAMIIu0g+dTqf4YmT/F/vAWgXHs6eKTzBZqeoE2JTqGgESPb7aiXAoYwm++AXdjq74jW98Q/Sw8WkqK2WtpI8p1EHKy19vFHBQc8JsMqNar6NYriJbrCCZLSGZK6lSyPhjkop1sn1Siry7xOUQQ6ei+/C18CVqtdZkPoZ9h5wkOdeS9gA73oA7l0ZK0hdqNriFLQkBCOVcF5M+LLfw8qJcO6mC7kwcNiryAQKYpN1e5OqQlvI/H9rGtrcLmXxWsrrwKRuKBRCS9G6jIImhXoWrlIOpXELOYEKob1AAy3axuL+CpS7yPxHxwXf847/V+qTXUpmPFZ+Cux/FQlHVELnTe+Gxg7WWtEX2pw0VUoKit+cZQd54BEAJaCzFfEuaYeMxeY+QLkhwYO2p40VPZ9DMOezrIniPWfsQaZFnW6WEi4kDYSatgCVlfxTLqJtMmIsGRN8XKZ+NsRDdF/vfPa68UvjEWikIj7D140qnu5DFP7n9NfwP2y8K82oljDMzMNL0mL2ch4eo7uzQ80O8PLK8DNM5+fu503Vq9frt27cRjUZFBaxVvPvd7xYP7yjYoQOwbjPdep4OwB5+Th+lFXUA9ihd7ZfhXPUKmPakKgBMoehRzZDVopGRkbYy9AQzzz33nJB9Z9N1J2NlpbrGdSkF/853vrPlJkmD5FNUKhoSWLX6Ms/n8/j617+O4eFhIUPfyluMSo8El1zv/3ouguWonASiMDhu6C/Rmt1uwQ0rcBkNT+Mb93H54J603D3nXzpcx9rYJa2nJMY5yvyxe1pKu9Mi13wruD19rdOwU69fSvmRMdrgqhVhKRVRyxdQMJqFuAkrWWoqj65yFskujLOvsbdqUr4iOBdYw0aDWa6Wk6SUfMFgUO27Uua7cymMVLJwGGpCDCNhMMOTCOO2ZNWM612mSIsklZB9jGVBzzyppMkesuF4ny05AAAgAElEQVRcUlD+4nYXAkLY4kH/2LWDNSx3AWTPRymcclTJonUCe8SMPQYcuIcQaXHPTScOsdvXukeNwOVcJoqS0STWVqTyL0b2hNeWWhDUXUwcCgPmjf6x+31Zi/kIliwnDboJPPuLWTGO/ZzNcSnsg71Wxpp3CvmG3i9W3BdifmQsjhN9ZqSMzqRC+NaxfQWNt//ntefxv915Fk5zz1F1y+1GPZtFZXsb9URC/XazWjEeDMIgaVWg5d5tNYaf83wg1+6h2Tve8Q4B0tjnqyumnyXb6nN1APbwc/ooragDsEfpar8M56oDMO1JpTgFAQq5+wRS/OKk+iDByuOPP95yIcUv7PWvf70YTwXEVj5gjdU19miRtsgvYbWnnxz7zDPPiOZsUhApL//Wt75VdR+KaTT71Qgaaf45yifBTUHARw8wioq8/y83sJ/Rnh+OnInsYscr3wPTjeKfo5BFThJ8cY+L+7e7Eu4YSxziQFKpjv1Ovi5+XC8erGJ5XF05kRTKwXRM/Og2m3sAqx05owVxox21Wh0JjUqSypWdTQWw6ZKjpIk8km43Ni93g7CfLBWRrradI43zOPdUoxxNh9FfycNkMSNvsiBk6kXCclqkYHHvNpYkQTNPaDB5iIikufdMzI89hwdT6TBcxbzo2Tp0DgrQ1S6u+VexLCkuQiXD2ZgfdqMB8T43fGYnahosja4fbuBW0/04lE1iPBdH1uIQEvDNfmk0TlZTMqTMu6eUx65nBEnL6YcMV+J+rLhGQRXCS4kDZKx27LToF5xNBEXPo6VSOlHVI/C6EvUf98E9AI79+ZSQ3F/xTmM0HRVCGz8Q28WvWqKYToRQC4dR3d6mSaKm+9M0P4+RF17QNPZhDWJPMCnkrWjj/Hzndwz7wzhWB2APK/MP1tEB2MPP6aO0og7AHqWr/TKcqw7AtCdVAWCUn2c17MknnwRpfezVaid+8cILLwj5eYIjVpdI/WtlqplMJkEBDlbX2AtG8EYKIgFWcyhj6UPGJ6msbNGIWS1u3rx5v/LF/SwuLmJi4nSPi9KrRoD2o//xBjKSKvRXDtdwZ1T+R/m5qE9alXAqG4GvCxPga/sruD0lWbmp14QAQHMvUae758p+d2bK1xK7SFcgvI1IHaz0mJCzORB3eZFSARrcB6ttOZOcRxbnXfWv4PaEvEz+3MEGNiUrWX35FNIqP9Zb5ZF+bSO5OEg/THsGkaLcusWJcpMyXqv5cwfr2JAEwDxmWuX9pnYMF8Uy8glB67MVc3hp7JK0BP2kBtoij01a4WCtiILNgXq1ig17ax+/Vvm4HNwWPliT6Qi8hYyQd29WLmyeO1dMYMN0RNmk9P14rSiENw5UTJKVuYZqFbOFBHozSWx4RlWFTFg5uxwPIG+yYcczIqYOp6Ni7Z5aDVdj+4J+eNBgtkxT67lUEHe900JGf6KUFu+PD6w+g9et3oDpVa9C5ebNTm/LU69b3/Uu9P/5n4t/bwQ6Lyft78aNG+B3SqvvDgIwfk+Mj4+L7xk9Hn4GdAD28HP6KK2oA7BH6Wq/DOeqAzDtSeWXJYEOm6LPnTuHhYUFEIzxC7uV/xZFO772ta+JahP9vziXFasnnnhC9cAbGxvgnze96U2Cfsi/t5KMp4wxq1k8NitlVNQiXbH5SalSVaNPGMEaAd6VK1cEFbI52KvGJ65zly7jB//dt7Qn53hkt6qEFPTQ6gGmbKobAQ7OvRDcwIYkLW2gmBGqarJxfW8Zy9PXT0+r19CfScCTS8BRLgjRC1ZMSKeM9Q3CWS8jaOts4Nu48LlsGLuOIdkt4pqvvZdXqwXZSyZ7zWaDm9hUAUSGWg3DqRAGcgnhD1Ww2hF1DSFqPfrhf81/B8tdqDv2pWMd+72az+9CcAvrgyp0u3oN4+kIBnMpIZbBClmwgW57NbCK25ICHMJ+QYW2yD25ijlMVbOCFhcw9SLWALyvH6zhlgRFkvmdLiQxkAjB7xxCSKK695piFBUK6xhM2La2vyfNlTLm4wdCsv9GC3DuKBUEZTHgpCLig/UIMIP2PlzNxRDssZ3YI9ejpP12nxeZY487ZzGHn7/1Jfzo9ndA6iGjZ2ICNb9f+j1gf//70fd7v3diHj83mz9LG/9f+Xvzf8U+NFAZaXbPvmDSwdWCx+fnNR+GffGLX5Q+J31C5wzoAKxzjvQRrTOgAzD97jhTBnQApj19/EIk6FlZWcFrX/taeL1e8EuUNJJWUvEKpY+UQz7JZC8Yv3R/4Ad+QPXAFMBgvxaVD+kRs7q6KmgoapLxPHY2mxUqWhzH8W9729tOyRWTmsh1WVUbGhoSe+DfKQbSGEqfGP+9bPXg3f+PPCWHkuu3JQUWzBV6gFna9veoJatbsMcf+qEOQgnNx5sNbWNLstpDqtxju8vIuAdhy5HLWRem0FSIZD9WqYWEOJ/oM5p7iTrdqVfju1jxyIsIzB2uY0NScKIvl5LuvRNAam9ZVKRGUyGhoFk3QACkQ/eIqlmvcs4zwS1se6c6peDE6wPpGKJdUFQfi23jpmtMWCNMJkPoLRdQMFvhdw0ja23dzzcaD+BAsv9xNurD5rG6n7lWwflyBo56FVGYsG/3tHxPLAQ3cKeDjx2pgzQqtlYrQhjEUSvDfwxoOyWSe5nLRIFqFUWLGduO9t5m7MWiN9eWZ0wYQz92uIGbTQDRmyNtMCaEMpr7v+hz9sTBunitEZTxwcS1dBA+qwtx+9EDEFbOfmzzBbxv+atwl/IPTsVqBcpl4RsoG84/+iM4fuZnxDR+zivR+HfZNRvHq4E0fn5TPIkP5pRoBG48NlkKfKj2F3/xF2c5vD63RQZ0AKbfGmfJgA7AzpI9fa6ugihxD/ALkUCGTdGkBfLL8sUXXxT0QoIgtaDSFStTpB/SbJPVJ9IX1RqvFfn5yclJYdas9G2pScYrlTWln0zpS+M+rPwh0hBKpYxVNYI/inFcuHBB/GkM7pP7JbhcOszjl/78lkR2joZeOtzEmmR1aTgZQuiYgiRzwG4AGFUajaihYjxN6Wx37FYqjezFGUpH4cqnYanS3NWAotmKpP1I9GIyE8aup7NUeOOxR1IhBJskt7Xk5br/LpZa9I21m99Pw2G7XLVNqDR2ktav1zCUigjlRUu9imKPEfZ8GjenrkmDbXs+JcydZeLSwTruSdAPB0tZDMcO4Mol4HcNIeAe1gyCKd2f7yASorb3J9L7KNWAXKWG3T5vWxDaON+Tid4HJI3/bi8XMJsICZW/HfcocpYHQheLoU0sDbY222a/FWXb7dUKNj1jYq61UkK1XkOlSViExyTAY7WrYLJgs0mgg/1w28fv6XPJEJyVIlYHJk/lkz1fC6kg9t3DcFWL2DYfV5nZ+xXzI0p7gAZJ/scPN/CBlz6P2WToVDpNs7OobG3J3CL3xw5//vOwveUtJ+aS8aAEP/uVP/w3BZipgTWtoI3fJWQlkI2gFlyHokk/8iM/gqeffrqr89Intc+ADsD0O+QsGdAB2Fmyp8/VAZjEPUDQQyrI4ODgfdEN9laFw2HV3it+gRLsEBApjdbsv6K0vJpaIdUMqYylCGQoEvOkK/KYjdFcWVNAFitxfKraGHzSymOyqqaoHKpJ4St9YgSXf/HCLn77c3cksnM0VAhVeMak5l0IbkpTAnmASwcbWJM0RvYWkohIgg0q8F3z3UZ2eBLmREyIFOTNdiF2kej1qCoLKglwVgpISyoMzqf8uOeS96Ca99/DvWM1OK0XwF7KnfiRrnXetb3bJyqdNNseSwRBc2AD6shYexF0DSHXVDGaSfqx3XfU76M1BlMRRHrlACLXbifAwerkZDIIdyGDqtGIQ6cXsWNa3lD8ACFJD7bZ8C42NQi0eCp5TOYSqFfKCDj6MZoI4c6QXNXSm40h3FDZcxWywueL/YmNyoXN+b0SZYX09MMA9oMNFjLYdw4JwNMYlxIBrDlP0lpHMgmM5hLY8YwiaT0tfEIZeSpWXkyHUDIcqSk2BymFFwsx+KxuIeBBHzB6yvG9dSEfRalSx15DlXo8HcX7b34Bb/bfbXnbWJ54AiUJIY2e8XGYpqZgMJkw+KlPwTTZWWZfyz2rBbjxIRyZCHyApjwIawZu7OklOGO/LtVu9Xj4GdAB2MPP6aO0og7AHqWr/TKcq05B1J5UfiGygkXPL3p/MZQKl1rvFfvF2CPWWG2imhVl7NW8vZaXl0HQxWoZRTd4PI6nwiKfhDYGaZCskCkVr52dHUFDZJWL/mRKNFfK+MX/la985ZQUfmOfGAHfv//KXfzfz2xqT87xSFupoMl4uXHhbj3AxuLyqoSzoS1VKmFfLo2BXFwoC9JImvQ/god4b7/oc1rwr2J14rJUPvrKeSGbLRvXk7tYcsv9KOcxxmIH0iqNU5Fd7MlS+3JxXNxfRd5iFzLlBC5h55CqL1zzudtzqVOgrFN+5mm2PXKSLttpDl9fSO7jjuPofdNXyGA8FQL9pzJWB/ykPKpQQHuLWWQkq6Ncn9XHWyOnDbBJ5ZtJh2HPZxFzuOF3eU9U/wZSEUQlVSuvBDcRsjsxnlWUC0c15Z7m3rFjGh9VBKdJ0XS4sN/GJPlV6QPcdHhBM2dWu3i9KSFfNzyQ0W+8FqRtviq4hZ2BMQRV1B/tlSJooLzdPyo8wJRYDG4hbbbBhDo2Gqpp7I9878qz+Adr34T5mJrb6toXFhdhW15Wf9lshuH8efQMDMBQLqO2tyeUEhkGux2T4fB3VWWQ1PFvfvOb4rtBoYIrwE0BYvw+4Of5r//6r+MjH/mIllteHyOZAR2ASSZMH34iAzoA02+IM2VAB2Da00cvFoIcVpKofMjg/xP8qPVeUaqe1MBGCiGfZB4eHgpp+cbgly4FOli9olw9g1RHVszYI8AnpUooxs4EaYr4h0IfZG8ZZfGVUECc0oPGuV/60pdEbwGfrCrRqKhIv7L/47/exF+8uK89OQB6C2lkbe0lt9UWvO67jaXpB3vRelD+2CuqeAm1mu/JxnHhcBN5Wy+MVgvK5QoyVope9CPboVeIhs/7g3JPyKfDe9gblgdS18IbuD10kh7aKSc99SqMtbpmdUBlvSv7K1iZVFdAJL1yNBEEBVLYi0OZ8lD/qACVc4cb2JSUTh9IE2zIK/ct7i1jSRL8jiaDGI/4UTRbEO314LAJ+LTK52xoB5sDcpRRrnUl6ccKFTnrdUymwxjIpZA327DrGW2piujJJhFv01PWvMfJVBjDZgN6oiHckKx0DpezSFdqmE0GBfAkxbBZbl71vZkLoSeZFPLxiTbvkSNAF8Xm4ATmSkncsp2s2LMqRuENVgnZI9YYrG5RgOPFhmo2VRB/ZPs7+CdLX8ZAMdvp9hevl65dg+X2bfH3iseD8tAQ6hYLetJpWA4O0MP+MJUozcwg9qd/Kh56aflDkaKzSsLzs50P1/gZrGYHwm2SbfGe97wHn/nMZ/DTP/3TmnKgD5LLgA7A5PKljz6ZAR2A6XfEmTKgAzC59LHfq7HHiiqEpP81gjJlxUaRDOULW6lcNXt7cV0+EaVP19zc0ZN0RTyjseLGf+fTU8oSEyhRJYuh0Beb6YqKrHxjbxgrYBTjINVRCQUsEtCxL+Fn//Tv8dz60RNirUH/I5/zZKVOy9xuPMDcuSSSTT/m2d/FfiO+ZisX0UPRC6NZSJezH4tgbdF3G8tdgD0KMagZx7Y7v6vRbax4Z7Wk4MSY86EtbEuq6Ym+sS5yv7i3hKXpayA4Zb+WrVxAtceEuMONkGsIVaNJdf/uYhpJSYPpiwfrWJMEbTz4Zf9d3G3TV0glwYnEIZzFLAomKw76R1GpA3mjUbrX7LrvDm6NyYHf/lwS58M7KJhtoncscVxl6nThLwe3cHewtbAIlQvPJ4NwlXI46BtE6FiOfTLmF6IaWoKVqwvxAwyagRuOIU09ZhS5mI/5YaxXcXdgCtUW1S4ef7qYhNtQx12rB5XjcYOZmJCPZ1CpcDYVxEb/BLIN/Wh8jWqSrOJReKNer93f2/XQNj7w0tO4FA9oOUXAaITpwgWYZmZQSyRQ9flQDWicC6Dw5JOIfOhDgp7NP516uPhZrgWoNY8hcFOCD8zu3r0r1HAbH5g1nvAnP/lJfPCDHxQsilYqu9oSpI9qlQEdgOn3xlkyoAOws2RPn6v3gEneAxTKaPyCVkyWm5UKlV6rZtNlVtHUvL3UqmWZTEb0CVy+fFkYIytBtUN+edM/hp5ijFZ0RUVWnlQWJehF5na7T8gfs9JGyiSBGn9g/OhHn8VGSM6FmaIHa12Y3s5E9rCjsQ/GVKvAW0hhNOxD1WiGwdGLfLlyX1mwk7jGQmAVdyU9r5zFjKiUycZjKR9uuVuLHrRaz5NNSBsVXwqsacq9sVrGSCIITz4JY48B5nwW66MXkGrq/Wl3rs5cUlranesdVbLk/cZGclEcWh9UVvuzcYwmwzDVqkjanQi4R1BpAooERFsD8n10pJre6aB2SeGImfiBoDPGBkaQrPUgZTkpfKPlXrnuXz1FWxTKhZRxr1Xgcw2fAnP2ahmFWq1j9WomfghnmSbJR1S/a7FdLHva58ObS2IyHcWee0iYR8+Hd4Vwxqmo17GQj4kKMumIjTGeiiDQ6xGCGudjB1gbmEC+iepJmu9cMiRUHPmA5DKPMzgpPMY+kF7Hk8/+97bpM/T3w0Q6ocOBWjKJyuYm6rkcDG436smkltSfGOP85/8c/b//++Lf+NlOmrYCxmT+2+nAFG1SQBmp4YVCQVS/yKZQ/p39xGRIUGH3s5/9LD72sY8JqrmaZ2On4+mvd86ADsA650gf0ToDOgDT744zZUCvgMmlj1/IjU3WilJhM/WPX6IUtWimDyo+X83eXmrVMkUWvrEqxt1SeTEWi91XYuS/KXRFhWrIf6PwBgFYs+AGhUHsdvt9A1D+4KBXGfvMlKrYq//PLyJbrEglZ9F3B8uyBscAPLnkCcBhLeXhLabhMlRhrpZRK5WQrxuRdLgQ6+0XohcLrIpMqKuHtdv0dNSHvQ7y3c3zZ8I72O2k+Kdy0KtJH1Y8cgDMUS0iZ5T/MU9599tTJ2mclIofSYdAoY2agflz49A1jIrpgQLkSOIAQbecKMaRAqI8tXLBt4I7ktQ5c6mA0cQB3IU0KgajEMdgNbNTLO6vYKmLhwGjqSAOHP0nl6/XMJkIYTCfEobCu54xlBtyeDG0jbVBebB3RHecEFXH2cQhDDBg51h9sNX5XYjsYb2F2MdIJobRbEIYFyvVMmWd4XT4hJqg8u+sGrPaRdXE9YHJE8DuejKAWw2CKQSe8/GAEERhRU4tXh24J96f94amUWgyyyZl+HIsgPWBiRPCL48H1vCq8DZ+6u434HrjD6D43HMPljYYUB4fR7W/Hy6nE1W/H9W9vVOHNgwMoB6LdbotVF8f+NjH0HcsQd/VAsfAjaBKK2Aji4Gfu83xuc99Dp/61KdO/DMtSCjCxIdt/C///ORP/iTe/e53d7tdfd5xBnQApt8KZ8mADsDOkj19rl4Bk7wHmgFYK+ofG6j9fv99+XnlMIpYRmPFrFkoQxmryNI3AiiCP4KlRiVGjlejKyrgsJmWyKoa6TCKMmMkEsGNGzeE9D0l8FP5Ml77r74kmRlARhae/WKD2QR6CxmYDUCttw85ex9iPVYkLJ2rTVS464ZK2MdqlqShMg1274zLCXAwedNxP/bUKghtMjuVOIBPUkWS8uGv3voO8hYHWCEkFS7sHES8A1Ch91LNYBCmwjIhct+ib6zdOhPhPex36K9yFLOCTmg31JCFEajXsNFGOr3V8a7u38FtSYVMSrjTVYoCE/25BCZSEdRhgI9VpDb9T9f9d3BL0nrBmc+AHmC8VlsD45p79x4L3MPNhgrdkQJiSKgRstqlFv3lHGJGy4mX2LN1LhXBvsvbUgRkIhMVXmTufEYIiWyp9G8piw7kkpjKxJDvMWKtqVeSNMirfPDR1EfG+/ZtOzfxCy89jaHCUbXd8oM/iHoqhR6nE7V0+qi6lU53vD3N166hfNz/1XFw04DhL34RtieflJ12pvFkHNA/ksyERtDGnmI+YOMDNT484/+Trs7/50M35b9PPfUU+EePs2VAB2Bny9+jPlsHYI/6HXDG89crYHIJbAZgpIzwC/PVr341RkaOKgmKoAarTM2Gy2piGYqkfHO1jGDry1/+8gnFQqXSRXni6ekH1RVFcbGRrvjSSy8JiXwKhDQafDZ7kSlCIkpVbvUghR/747+VSwx7dahW11DhcOcS6CfIKuXBpnrSxGhkG3N6hRIdYyQbQ7DF0/R2GxDKiZNXpfboKGQFyJMNGvMuDcir8FFRr5O4R/NeFvbv4m4bcOMoZDCSDINAkuApbXPi0DMiFBB3moxvO53nRMwPvwbp9OZ1RLVN0mzbUK0IJb1yE1WQptjedAw9qInq5oF7+ETf1jXfCpa7qGRNRvbgkzg3a7mAhYMNVA0GRBwe4QGmNeYP17GqoSLozcQxXkgi5x5EqVbHnum0hHunY14Mb2PHNSz6uqjUuTEw0dGr7Go+gttWD9hTdinuB+E2QVI74E1Z+D5U0Z+KCXogqYJqMZRNYCwbx6p3GgRU9VrtgehIvYarER/CvR6EGry8uM5CZA8fePGvcd1phHFsTNCeq4eHgMWCyupqpzScet3yxjei9M1vSs/jhImNDbGH72awh5eCS695zWtUD8vvEH7G8+EbxZmag6+fVQjku3m+r9Rj6QDslXplvjf2pQOw743r9IrdpQ7A5C4Nq1WN1BE+lfz2t78t1KwUnr6aoIZyFLWKWbNZszKWX7IEYOPj4/cVC5Uesma/L4VuqNAVCd7Y68UGbxorNwb3S3qj4kXGJm+eE9dkPLMaxC/+pxc6Job0pYFsAp58CpSfpxltxu4U/UEx56BQgesUc8FNbEpWD7jmheAWNlRkv9sdbzIRwH6/PFXsWmofKy45BcRuJejZJyUqe/UahlNh9Gfiwgy3aLIg2jeIiMureop99FHSKP6gLCBonJKUQM6dPdzAlqSYBlUJwzYnJhMHcOUzQp2QdEjSStsF/caWJffIPjdUy23NtglGphKH4t7NuQewY+/HwsE6lkYvdrplT73uSUcQb3EeE7k4hlFG1GTHnvWBl9liYA3LEjnkfi+UErDFI4LCp+W9pWz0tdlDVGpVBGxuhEydzawvRffRn0/j+TbKk6Q7juRToo+LQJBxMeLD2nGFcz66L4yzfU0S995yDu9P3sM7oxuobm2hFo+fyKfB6dRU8Wq+CNY3v/kkdbHDVVQ8wHp6ezH8138tfc3PMkH5bGZ/MAWW1ILfM2Q5UP3w05/+9FkOp89tkwEdgOm3x1kyoAOws2RPn6tTECXvgWYApoCthYUFnDt31BejmCIrioKNh2iumKmZNTeO/+pXvyq+iFlhYzSDJWWsQldUlBHpNca+smYBD45nxY77puAGaTDPPPPMiSrbZ/5+F7/z34/8dHoMwFAmBleaQKAIfuAUTdb7yoJl0wNq05EyoZxhLqliK130jVGxL9zGv0jtsl4O3JP28uI651OH2HGp07ta3T4zac7R9lTdVsphJBmCy9wDRzggerIO3SOa/dToYZZ2PPB+03pLX989UkCUDVc2LkRPOoU7m8B4NQtjIg5rOY9bk1fQeL90mi9yf7iJLcmevclcFL4G0Q7lOAOsQKXCqPb0YN8zekpI5Ip/FSuSoF5IydsegBpWgWZLKTjLRQSMNoSa+8mON7MYuIdlDUqXU8kg+gsZIcjhqJexb9P4/qrXcamUgKlcQspo7jiPdNTLUb8Q36BX2bXDDVWASLn4wUIad73TpwzIrx9sIG2xo6evFxuWk/u01Cqix+sf3f4bUEhELXpGRlALBrXcFqfGWF77WpRu3FCfa7HAdPEijP39qBeLqOzuohYKibHm69cx9q1vdXXMbifx4Rdp4PysVhRvm9ciU2J+fl7QDD/84Q93eyh9XocM6ABMv0XOkgEdgJ0le/pcHYBJ3gPNAEypPFEOnl+oDAIf/jul6ZtpIs0VMzWz5sYtkX7CJmxWsdTAkjJWMVgmCCQYVMQ+mtUZOZ7iIASCb3/724XxM73JGimUn/zbTXx++QAH8QwS+SpqAna1D/YeUa66lUFrq9ndyMKz8tZTR0uJ9JbHCqxiuQsVPncuJaUSyONfYd+YyrEGU2FQpptVLWFi3NcvgKSStylS59pIk6ud20x0D9td9Ekt7N/BXUl/rVYKiLwmY4lDQTkltY09aI0A+Trl7iVpizzX3kwCGZscVe+K/y5WRi+Iquy5eACWagnhvkEcdgDsY1G/FPWQ+1vIBrFmcWEuF4Ulm4GPfU4aKpHjsQACLfbD3siJdASRXs+JMYuH61gaak+FdRWzOJ84xIHzSIiD0vwZowV1g/p7mD1klLrf8Ywi2dDnNpyKINj3QIyE/XCeUg6rg1OqCowTBGYo4Vbf6QcVb9ldwi/e/IKgKrYLgqHy0lKnjxrV140zM6ju7IjXCORM587BYLGgFo2ivLkJlEqq8xzvfje83+UKEx+OseeW1S+yG9SCNHFSxz/+8Y/jF3/xF7vKiT6pcwZ0ANY5R/qI1hno/MtIz56egTYZ0CmIcrcHgQ5BmBLNlSf2iFEko9noWBmvVMyUHi5Fxr5ZRVEZz14Bi8UizJkp6kFxj8cff1woFjaGYrBMEQ2KaTz//POCZqgGArkGgRebu0l/5N/f+ta3Cilkxv/+2Zv43E3tPjqcM5wMIiSpptcOqLS7KpShj2itBDQstJjYw3K/nHqfo1JA3tSZStm83+u7t4QIhiufPjIxtvYi6B7u2BNmL2SRlzDn5XGv+lZwu4sq4kTUB7+kVPtc0o9N5yjsxRwm4gewl/PIme0IeEaRa7Pvy4G7WJWk9w1koohKGHuz+jQdC2A8HsCh04u9/rFT8vSt7isq9JXq9VNVnVbjKUFPEZCf8F4AACAASURBVA1WfW+OXRR0O63hKOVRYNdbzwPxE/4b5edzFiu26IulIoxy9WAdt1vQFi/E/GCVaV30az3wbrucPMBq39CprdH8eDCfxr3BqVNG0YO5BCLHQjXTyRD6ygWseqdU9zRUyWO0kMZhjw2hJuB5MebHB178//BYeFtTaixvfjNKjQqIWmaZTDDSA4ymy8XikQfYwYGWmWKM61/+S3h+93c1j38YA/l5Sz9I9n8pNiLN6/6X//Jf8L73vQ9PP/003vWudz2Mw+prqGRAB2D6bXGWDOgA7CzZ0+fqFTDJe6AZgCmVJwpiEFQpPV6Uc6fHS3MoJspKxYxqWARlBEBqTdU0Zya4olrWrVu3hEfMD//wD8NkOm2Qqxgs88kq+78ae8ca96GYM7MCRqWtZrGQ/+UTz+OFHTlJZ9HLJUnf4p5mIrvYkZR4FzLoXRzrYjaIdZUn9O1ugel8DD57e9lz9ml500cmxvQhSw6Owh09wF3Jio8nG0OiBWWt3R5Fn5QklZAVK0r8lxoopO2OMVRIYigSgCubwN7ABA48ox29qBrXG4mTWqld2IJz59OHWLWry50ra3vTUYymSSs0Yn9wEmmzHbO8FyVpi+ciPlEFahcE09PJQ1G53PJOCeXCi8FNrEke60J4Fxv946DnF4ETv8Q3BidaCl0oexrKxhBqAKR9BfppHYpK1aFTPU+vyhzipv1B3+CF6JEIx/rgRMtq9dXgFjK9TtjyWdxrcW6K+uJd7zkB+Bopi/3FLH7u5hfxo5s3hBm61rC+6U0o/t3ftR1u8HphnpmBwWYTpstlCmiMjKC6u6v1MCfGDXz84+h773u7mtvtJHo+kqZOdgI/e9Xij/7oj/Dbv/3b4gFZqz6xbo+vz3uQAR2A6XfDWTKgA7CzZE+fqwMwyXugGYApQhmK4TLpfARhjRWlxkMoNEJy/6lwxWoZgRoVENWCdEbOefLJJwWocjqd9/27mscrBsusglEBsVlVURmvCHmw6sZKGfdC8Q4l3vqHz2A/TkFu7SF6uSQBB1enqW4nufTmXVzdv9vVsYZzcYR6O3tINR5vIbyF1aEjainFHSgmQUqisVZDzuJAyD2EtEo/1FTUB593SnsCAcylDkR1STYuHmgzYW5cdygZQriFoIepUsZkPABnPi1+XLMfLdHrEdMF2JOUoLeUi6hQ7r6h4qPlHIVxc5P8PytvpBWaqxUEnYMIqdD4HLmkUNuUievRHdxynxZo8WZiGE9HhGrnTv/EqXPoyyaQlqBIGup1vG53CTmzDTttZN2b9+6p5BE3HFWo52IB2GoloWTYSp1QmT9TiGO/x4752D6S1j7sdwDB5+MHGCxnceP4nm/eB6X6L8UC4tiNQiCXQ9sCVL5n7zt47wufR2+lKJN+MfYUBdFoRHFsDD1eL3qt1iMPsP39U+taXvMalF58Ufp4nDDy1a/C+oY3dDW320l8AEY2Ax+kNarTNq73q7/6q/jEJz4hHs7xM1+PlycDOgB7efL6qKyqA7BH5Uq/TOepUxDlEksFK9IMG4MgilQSVr0oaNHb2ysog2pB+iKFNdirRXGN73znOycUFJvnKIIZpB2yL6Cx16x5rGKwzOPTA4wgkPTF5lD6wy5cuCB6xbjX/v6jfg8Cymu/8yWUqzWpxFz33cbSlJygg7FWRb2nR96Hyn8Xy5ImzD21qqg0VJtk0FudpDObxEgxieFIQAiL8A8rOKxwaQlHKYucVa536arvNlYkpfW5F4KpkGR16XI6gNXjaqAzlxL9WxRZydj64O8fb1kZO9+FAqIAoxKS8Ep+F3x3cHdkFtPxIyPmtLUXe/3jba8hK2LhDsqKatePoP72sRrnRCKIwXwScYdbeIC1iqF0FCGNxxpLhTGcTeBwYAz98aAm2frG4y4kAzBl08d9YepKmM37dOVTmKtksNPTi3iHvrSLxQQAA9Zt/aJHMdp0XqzWXYnsCaPoVBPg5Hvrh3Zu4meXvoLzsxPd93FduIAetxs9djtqqRQqGxuo53Id326yCoiNC07s7MA4dJqi2fGgZxjAz3QyIRTVWbWl3vOe94DsiFAo1BKknWEL+tTjDOgATL8VzpIBHYCdJXv6XL0CJnkPqAEwCmUQ9BAcdQJJjb1afPq5t7cn1AitVqvqThTBDAp8rK+vQ01ZUZmoGCyzL439XByrFkrfGUFjMpk88SQ2lCrgzR/5G8msAN1UwIZSYYQlgQM3djm2i9WBGak9DhZTiKr0jZGKx6oWxSNMteqRibHLi8Sxb9FVn7xKI8Fbuk+jWl3DWQgJekkQy2oVVf1qx1LgHZNSr2M0cYDzoR2hZBlxeqWogaLio0FkonEf15I+3HZqU4Q8ApRhjKQjMFaKWB+aEf1zWmP+YA2rEvLuXJcS73yAwByydyzUgs7XvIcrB+tYaeO95s6lcS55iKTdib0Gc21XMY2kxr7CmXgAfeUijPUKbmpQTeQeRzMxAfYqhh4hE98uLsUDqKBHmEEzRtJRBHsf3LvMzZXoHoK9AwL8NcdM4hAfuPE5vOZwXbxkedObUOpAIxQDDQaY5uYEfZDeYZSjr9y7xydAWi/1/XHWN74RxS48wAxuN6YCcr2u0ptTmUAlWz4Ye+KJJ1SX43cE2QmkmfMBne739TCyrr6GDsBevtw+CivrAOxRuMov4znqFTC55KoBMAX4DA0NiYoS+7Xa0UbYq+X1egW9pB1Q4s4UjzD6ebUS1VDOgOCP1TkqMCpy9GpnR9BHGgwBIPfB6poSt3wJ/MTH5Q1N54Jb2Bw5ouppDTFndE7r8PvjzmfD2O6V6yeaTfgRtHuE3HtvMSdU4SilHvQMo2RSB7884GxoG1saf/gqGzyfDWG7T25/nHspcA9rkqbDo/EDHLSpLllLeUzEAugt5VA0W+EfmETWYhfCHSuSVEJXNolkF0bWAli2M5cuZjEd84ueqJB3AiGrC+ZKCRUJUQwl99f9d3BLg9gHZddno/uwooaAox8Ji0OzYMf9Y+3fwa2xk75hFPO4EN1Hxd6LDdfIqequNxNFuIOE/5EgRwAxuxv+4wcUQumyQxVxNhqAtVbF2rFS4fXQJm551UVn5iM+4S1HGmRjUGlR8Se7HPEhbXXAr0LzZA/Yzyx9GT+2/i0YG0BTSwDmcsE8N4eevj7U0mlUNjdP+H2ZrlxB5c4d6c8CTjBfu4by7dua5xJ4mWZnYZ6fh/dP/kTzvIcxkOCKVHGKKNE7Ui04hjRy0s4/97nPPYzD6mu0yIAOwPRb4ywZ0AHYWbKnz9UrYJL3AL8cWWFqDPZRkVpoZM9CsSgMjts9tSRN0eFwgHLE7YASj3H37l3s7u6K9ZQ+s1ZbVgQ9CML4dJUUR7VQ1BT5WqN/Gf//i7cP8CufeUkyK8BwMSV+OMtEtx5g/fkU4vY2FaZ6DSPJMPpzcViqFQE8essFvDR9XWZ7Yiy9o2J9cn1jV/ZXcKcLVcKR+CGCnhGpPS6kA7jjfCBlPZiKCANnVvMSDpegE6pVx86Fd7ArKR4hxC0kBVN4MuxRW28A5z3VigBcrkIGKVufEPVo3uNUxCdUDGVj/nANqy2k2mkUPnMserEzMHFfuXA6uo/dDgIcavsgON8cnASrqJcoQ2/swYbFg0IbmurC4QbuDKmDonPxA7hKeax5p4TXnhLmWgX1avmEuqHyGul/CxEfMhYH9prOYTYXwaatoWpVr4mx7I/ba6FYeiW4KarAQF2oMTYHacP/09o38TNLX4GzdLpPVAFDBDg9FCEiiD48RIUS8W2qW5Y3vAGlLv24egYHhdx8qzCdP4+esTFxfCokCsGOeh2On/gJeP/sz2RvsTON5/cDhY9mZmZO9N02LkpWAgWU3v/+9+NjH/vYmY6nT26fAR2A6XfIWTKgA7CzZE+fqwMwyXtADYDR04V+XvxyVWTg2y3LL2Cuw4pWY/+V2py1tTVQNYtx/fr1lr4xfJ10Ffp7sbLVrsGbSoqkNjKafcL+9O+28W+eviuXlXoNJsrzm7T1RymLL3bhy8UfoxWD6b6vka2UFxTCvmJWLJu2OYWRccFyUjqeVZjb0+pPnFudrJniESZ6KD2QC9eSmEXfMpYlj0VQQrl6rT1m3AdFQV69fRN5i01Ub4KuYc2CJo5Cpq1svNp5LobWseSVq3Jynf50BOZqCcOpqAARvv7xjscWPVlN1SUtuR9MhhBp8K8SyoWJA5SMZmwPTKKsco9e869i+bj/S8sxOIagay4fgaOYx67VjeSxbHun+df9q7jVUPWlcibl2hM2Z8t+s9lCHJuWvhNLs4p7MRfDvnMIUdNpJT1W+FCvodxjFBTLhegeUjYn9tt4oU3QDLyYxd0WAPGJwD388o3P4VzqyMT4fvT1HVW3XC7UCwWU19ZQTyY7peLE6133cblcQCr1YK3mStvWFuqNrzcc1fXUU/D81m9J7fOsgwmuvv3tb4sHX/yuUAuyE/gA7Q/+4A/wG7/xG2c9pD6/TQZ0AKbfHmfJgA7AzpI9fa4OwCTvATUARsVBAh/SExsNjVstTWl50gQZFMpopYTF1ylXzN4vZayaqIZyHIIqgitSIekx0yq4VzaCk/7YLH//4afv4M/+7sjQVGt4svH7PVNa53Dc1dQ+VtzalQK9qQgma1lBYaJ8eqx3QPRraQFIC/5VrEqaDo/lYjhwtJdBVzvfhcBd3JU0fBY+aq72tMW+/JFYhq1cRJrVLfcoLrCiIqk+2Z+JIn7c4yZzva4JKuEVTVN6KwVMhXZBgOz3jCDs1CYcoSx+zXcby00KiJ0O3FfIIG22gkIc46kwMtZesNLVSX3x2v5dLGsEe958EhOVLErZHO52UQ2k7cJ2/zimEkF4illsNKkJqp3jY2k/bh5TbofLWYyXclizepBvQ509H9vHjnsYC5E9xO0uBNrkfygTx3A+iZTFAZ+KMuZUKoR/+uJf4w3+VbE94/Q0jBMToo+rFgqhwgdEtRooEV+PRDpdJtXXu1UyND/xBAwmk2AIVFlp297W3Ec2+MlPovcf/sOu9tvtJH4+04eR3xOkf6vFF7/4RVCE4zOf+Qx++qd/uttD6fM0ZEAHYBqSpA9pmQEdgOk3x5kyoPeAyaePla7G4BcqaX38EdDKo6txPCmLiUQCIyMj4ou4Xezs7GB1dRV9fX2iWtUuCKoIri5fviwoLq0iGAwKmXoqHzarNf6zP38RX1oJSiVlJkwvLzmDYx5gNhfGlkovl6VawmgiBGc+hZ56XfyQpgIhVQUvJf1Y86g/OW636Wkq8Q1qB3tc61JgDWvj81K54ODJmA/7sseK7WGtv2F/9RpGE0EMZGIUp0O0b1DkoBlsngvvSlMJ5w43pPv1eF7nDzex1UJ0ghW8c7F9OAsZUQ3yHdMKz4e2sS0px89jzcV82HBrpyDSFHoiHkDANSStuNiJ7khgdz4eEDS/nYEjk+SrgTWsSPY8WssFzIe2RbVrV4JeuZA5QL5Yhr1Sxr3B6Y6AkrTEJ3wr2Bk5h0Nrawlzdz6Dc6mgAJKsTF4/WMdSwzn1lvL4x6tfx08hAovLiXo+LwBOLabuEWheXER5eVn6/cIJBHXVvb32c53Oo0qb04laJiOAn3lhAaXnn+/qmCPPPgtrCyGMrhbUMImf54qYEoWb1OKTn/wkPvjBD4JiHa2ElDQcSh+iIQM6ANOQJH1IywzoAEy/Oc6UAR2AyaePPWCshCmhGBtTVfB1r3tdxwUplkEqyrVr11rSUJRFlAoYewJIQWwXyrpveMMb4Ha37pEipZHURjW65D/4j3+HpX05+tDlwD2sdgFUvOUsqnVgOBuHJZtEpcckKjP0dmql6rfov4PlLqTaaVqblfBrYp4XWYWZkqMtcp6tnEfBom6w2ur6Xd+9hbStD72FrOhZO/CMaVIbPKISalcJ5PGv+VZwW1KAg/OaFRBHEkEMpyOiGsk+rrzKOYscSlYe7x/LdpJ215g70upmCPiKWQQHxxG0ubG4v4IlSRETY7Ui6ISk6jUG1SUvRPdElWdzcOqU39Z1/10saRD74JoTySAGa0Xkq8DawGmvsVb3BPdF+flipSZ6zToFRUwWIrvClNmTSwmvLrWgyMfFuB9rg9PImx/0mtHLa9U7LR56/I/pHfzcxnNw3lsBqtVOhxavW978ZpSee07T2BODaJXBYzQdpzQ8DNP4OOy9vQ+qW7WT9hjWJ59E8RvfkD8mr4vPB+OAXH9nVwdqmMSHaYpFCHuG1eJ3fud38Id/+IfY39/HBCuNerxsGdAB2MuW2kdiYR2APRKX+eU7SR2Ayee2GYApFbBmQ+NWK7MHjBTEt7zlLbDZTvYqNc9R1p6fnxfGze2C4h6sznVaV6Eq0geMfxrjTf/mawhn5ExUqTy31MGXiz8Oh/NxeMpZmEol5K0OBK0epDT6KCl7FD/oJfur2B8mI2WuHEsAFUlZeHc2jmRDD1Kr69WfiWEkGYTJAKTMDlHtkz2WoH46TkuDd7qjCVSWJSmSVECsooap2AGM9SoO3MOiKtcpSCW8LQnAPJm4qm8V+5rOR3ywVsvwecaQbLp3rtAMXCOVUNk3Dad9CvWzXsNcdB/2chHbAxNtzZxn6ImlIlKhrGuplHAx6hOKk6RBMhb997CkQfWTAOlCzI+AywujyYSgSo9XY96pGLkQ9Qm1wqjDLQCltVJC3nTSA5D5a+flxfPmnv/Zxt9idkeyD5QA7I1vRKkLOXjK0VeCwQd9ZNksSpubgIY+MssTT6D0wgudbsNTr/cMDGDS55Oed9YJZB7w4Rs/o1vFz/7sz+Kv/uqvhFcYpej1ePkyoAOwly+3j8LKOgB7FK7yy3iOOgCTT24zAGNTdSwWE31X7L/qFDRipmriO9/5zo4eL+wXo1w9TZ5HqSrWIrgnyhszaPBJlcVWQd+yQqEgVLgIGpUolqu4/rtfgqwTz/XEHpY8D/yGaAA7UsnCUa+iUq0hYbAg6PKeEJjwFtOISKomcp8LgXu4K/mDnhSz/S5ocBcPN7Cuscqh5HAmsoOdpt4g/iAmPY5eY6zyscIXbfKamu1Cxp9ztiQ9r7hPqhlqmcfq0LnoHlg9NFbKuDl1rSP9rfmem0kGsOOUk+Rn3teOcyiUC6P7MKCOncGp+8qFavf2eHRf9JvJxFX/PcTsffBmEwi4hxHR0BvHvBgrJVWz6rFkGEP5BDYp9289+R68lj7AsqP158NgNoHJdATrg5P3z3MxF8SyVR3oUvJ+PuaDzz0i+ryUoHH1boO/Hu+/q6yM8fxaiIUshLbxUyvP4i1ZP+otKIad8ipDQRR9ZOPjgNEIg92O4jPPaK60Ne5DgDeCNckgcBt99lnJWWcfTpYCe36bqd/KymRWvOMd7xC9vLQ00T3Azp7zdivoAOzlze/3++o6APt+v8Iv8/npAEw+wZR5p+CGEgqgoXkm/braBStfrIAx3va2t7V9wlmtVvG1r31NHIueMe3oKI3Khu18yBqP3yyBvxfN4m1/9HXNCWHfz0gqjHOGAvIGE/JGC0LmXtHj0inmkgFsuuXpNVPRffgkwdRl/yruSYI27n84GUZI0ij6qv8OdrzTGI8fwFYqIGe1w98/cUqVsTk/ouqjoXLWOO+q7zZWuqBjiiqdQ52iOho/xFAmIjyi9rzTKBwLPVzbu93Wy6vV9e7NJ6Wrj4/t3BJAtWQyY5v0Pw3qmqQM1upVVDUaUveXc5gK+WAuF3BD0jJgqrFqBoDHvhTdE/LtW22oghRaCapUDc/FA+gtF7E6dO4U9fZ6+gBLTaCNyonz0X3h4ZVUoWleP1jDrZGjBytXCjEkjRb4LervSXu5gH+0/DX85J1nYalVIQOimq95T3+/MFQ+FQ4HzBcuoMftRi2XQ7Wpj6xrBUSDAQarVSgvag6DAebLl9H7vvfB9cu/rHnawxpIlgKp6o899pjqkgRgV65cEWwHfq/o8fJmQAdgL29+v99X1wHY9/sVfpnPTwdg8gluBGCk/PFLldHOe0s5imKCzP/vRBWMRCKgxL34IXXlCqanH1SZmnetGDbz39sBQfYfrKysiOnnzp0TcshKPL8ZwT/+1LdVE9KbTwuwRXW7uqNXSFof2Nwo95gwmQpi3yVbebiLlQ60RbWN9JXzQgxBJq5TvU+StkhwaYABVWNnChB/WA/lEkClAnsphxdnH9ekzKicA82SZXvGOPd6eANLXjkj675cCpkGM2VnLoXJuF/0/Ry4R1p6nnUDwITaYgug13z9vMUUxsL7AqxZiznckaUSxvzwdQDLrKbRfJkeW1veKWGSTBETCmvIxGLgHpZH5jCaCmOkVsC2cwSpNoqEXJs02HTDGPawzUf3BNAl3bFVTGQi8NuPHuqI3q2YH1sD40i36fu7nD4UohrVQrGlebOhXsM7Nm/g51/6PAbz6fuHb2mk3CFBhsFB1I+9uIyTk0IlkeqE1XD4qELVpo/M8vrXo/T3fy9zCcTYnvFx1AKBtvNoumx97WvBY1hf9zohutHT4SGZ9EY0TuD3BkEVP8dJKVcLMiPo30j1w09/+tMaV5YfRnl7frewF5jfM3a7XXwf/PiP/zg+8IEPtPSQlD/SK3uGDsBe2dfnlb47HYC90q/QK3x/OgCTv0CNAKzR1Pjxxx/H8HB7uhWVCvmFxyedTz75JFopYXFXbNimahajXQ8Y1/r6178uqC2scLUDguz/CoVCoqrWLMLxly/s4Km/vC2MfGlibKaJsb0PUZcX0TZqao5iVloIohuBC4KbvKTgBHPHXq4VySrHUCqEsAqoNFVKmIz5hdofxScOPKNINYCMy/670nL3k6zqaRBZaL5TLx6sY13Sv2omuCX8xggI4g4P9o9V/Tq9C2Yzh9hsQ59Tmy/2N9K6b5HKhYPZGGKOfrEPJcai+whIGiOz8nhbhS5KIH0h6oOpVsOmd1oAHiUM1QrMleKJf+uUB2OtgsejO4hYerEtQa28FNrGvcEpkDZ4KepD0DmIUAeDbwKugsEIRzmPufiBkKxnT1m7mEwE0VvKiWpaq7ga2sYHXvhvuBw93QNlfeMbUZTp47LZYL54ET0TE0KCXqgktjFFVtuT6eJFVI6tNjrlv/F186tfjfJLDabxBgNM8/NHQOv1r4flda8T1S5Dj5yPn8weZMbSK5IKuPwsb/UwjcIbfP2pp57Chz/8YZnlpcbSzoTfV3ywx+8s9ptxbwRlFHzi36em5FRjpTbwChmsA7BXyIX4Ht2GDsC+Ry/cK2XbOgCTvxJ8Skl6IIOAhrLuBEGdjJIJekgpZH8Wv4w7qRU+99xz4jg0bG4n8MEvz2984xuiR4xUxFZeZNwj+8RcLhfi8biQwVeoMHzt45/+Gv7DnazUD1JHpYhch6f/ahmm0e6KRk8pZf5EzA9/F0DlQnATm8eULK1X+2Lch/X+abizCYwlD2GuVJCyO+HvH29rOC0k6Ac6K9Y17mNh/y7udKFK6E2FEdHgrzWej2Mw7EfBbIW9mMWSZDWQe+3NJZFpo0qolldhSN0g9nFfubCQwaFrSPTCNQcBbq1e10wlVOZfo7BIgwLiueg+XMUcdvvHxXVTi/H4IfyuzkIinEufrNFyBjsWN9y5ZEvT5Fb312t8t0W1eKODuEfj/PlkALZMCmvek2qFascYzsTgzaeQtDiwr+LlxTn/P3tvAh3JWZ4LP5JaWy+SWvu+jzSLZvHM2A5gjG28G0yISWJCABv/AWwWY0gwjuM43ORynBPjOCQOxHC55DgXEuMf7u8EDsYEx2AnOMZjzz7SaN/V3epVra3V3f95vlZpqktV3VWtmZHUU+85OvZ0f/tXXVXP977v81SFffj4kR/h+qEjmj+D/N27ETl1SvN7Ai1LYyNy8vMRJeCidysSQaaeM7JMGg4jXB1d0bXXCpbKJO+W06n3J37Ry/Hg6+jRo+Keq3VQxxwxhqZ/4xvfwCc+8YkLNkbmAKsRQD388MMC+N177734+7//+wvW/1Zp2ARgW2Untuc4TAC2Pfdty4zaBGDGt0ICYARUBDT0YpHZKl2Y4OzsLF5//XWRy0XPGSnrmQ+gZnxAMlyFp5AMG6SuF/W91GxkZASnT58W39NrpgUEOUY+4HnCSip66oDxFJRGAPalh7+NH+YaC8dqCHswYTMmssv+2l3Duoggkl5IJ3szyuWqCnrg0XgplbdPsoL6kBvO4CzsCyEM1HbAnUYcWbkfFB5eLEjNbKmss88/gqNlxnTU8iNLAqSo0fWTsZCkH7mIYbKsLkl0eS/DMQ16AwlC/RogJtWvZ8/4SfTWtKPNMypY+cac9Zq5Z1I7DGcds+kDRfK+W11DCBcUoTY4K7xLMyrgTjnWPZNncCIFMCfZRpdnFCt5FvRXNomwUrIbRg0AxCbfFBz5uYjMh9FXqW+PS5fCaFoKICcnjuM2beIdzqdsIYimoFtoeXGcexVaXizDtf/dky/hgyd+jqJoJOUNL8duR3xuLlGmsDCRu+V0Ir60hJXhYcTcbtX6he94B5ZefdXwzZThitHx8fT16N3q6kr2bu3atWW8W+knADD8vLe3V4SIOxzqhwLPPvss7r77bvz4xz/GLbfcoqfZ81qGAJGETwSBL7744nlteys2ZgKwrbgr22dMJgDbPnu1JUdqAjDj2yIBMHqRXnvtNZDMgoAmHVW8FFK4Z88ekYeVKmSRoSjM62KZI0eOCCDGemrGsEaJhZGMjCynFj4iaYpR3JNtEjgyXJFGMPnRjz+J12rP5YTpWZmuqbPoM5ivw3Yr53zwpAnBUvafCQW9yOXKyVEFKsVL8wKoMDeIGlaTFQ2Yz0+EeAn6dIMaYKSWN0qkwb52TZzGKYO08MIbuEqDTjBGoWmGrPlsZeJzpWCztJZdwUn0OVK/1CvXvWNmAP0KZsdU1wZBKEFX0fI8ems6MK9gA0xVN0El36Xn0hNlHAshIQAdFnld2jmSag3uC47hqArAkX2fewAAIABJREFUqZzzoj7kwWhZHfwKqvuW2TGMlKURiI7H0E3glpsnNMQQi8G2FMZcmnVwLofR5J8RoYoMleycm0F/sToYlfLBGGooD6vcNTOAU7K9um7oCD5+5N9QE/anXdPcri7klZUhp6BAhBGu9PcL75Yey5S8I//gQUSOrPfIRa1WWC67DI6rrz6Xu7WFvVt61ojgiyCMub/5+fmqVZ544gk88sgj4t6vdb/X01emZf7iL/5C9P/5z38eX/3qVzNtZtvUMwHYttmqLTlQE4BtyW3ZPoMyAZjxvWJYIEEYE5gJvOjJIvBJpwPGkEKJ5YqeMIai1NWpv8xJoY3vfve7hZdNHi4oH7EU1sjE7a6uLrAPesLoMVMaxzg3N4drr71WlONLAE9jaYu9vXjfEz/HkIEXbdbbO3bSsEeFnqbcOHQRXMjnIPpq7jG0YdWLAbiLEox/DNmrCnmQF4sKrxDzt7QEn7sn+9BrUFy6zTWIoQxo4Zs8o4Jx0IjtG3oL8dxcLBQUYbS8CcsyQd1U7VQE3eso8NP12yNCCXenLEYyj5awC8vROIYqmwX4oD4V8+SMGIHv8Xp1T6/UTkFkCR2eUcQdDvQXV6J8zosZg2CebbW6hzC0Gi6aG4uiyzOCWE4e+iubNen2Uwkw0zvW7R6B2+7EtCw0tDbsxVSxtjA66ecJ+M5Ut64JPjM/jd6qhbzkF3Wh+eUZFcQdIRVAR204UtJ3ecbw6dd/iL3uRA6p0mIWCyL19Yg6HMhZWUG+y4VIRQWKCboyMOpqxTKgrxcMiK++muTd8rW04EwkgsuvvDItq2wGQ920KvQu8aCM918t+9znPodvfvObQnpEy0t2PidAwWc+ExgdwfwvPhcYQUGpFD2SKudzLJvRlgnANmPVs6dPE4Blz15uykxMAGZ82SUA9uqrr4ocLeZyMbdLySoob5l5XCTKYBmCLiY5a3mq5Lla9FARgJHeXgoXlLfLBzqBFcMf+cBkH0p9L5bnOPlQZZ4YgR/1xdgPKev5X/+TT+LdE40Z5PmcwHGDYsUVIQ9mHen10pQ70zVNb5s+7wiFnxu946j2uxCylWC6tBZ+m37R4jrfNKacaTwdigHuDYzieKnxxHXmZc2nIRfhi3X93CwQWRZhhU2zY4bXnWyLpHbX8o5p/RL2jJ7ACZUctcqgB3WBGYSLrEKjSw5maxd8mM5A561jul/V28b8sfbZURRRJLmyOUkPbOdkH07XtBv6IedEoyiILMC2vIDGwAxGnXW6GBv3TPbipCJssWw+iObANIacDQgV2daNY2/YhWMqnqyq0Cxq5/1r4YPyik3+KYzJfiM8tOhxD2NyVWxZbbLVoVlEcnLxCddbuOEX/xfyl4PcmhpYyKJaUIDo7Cyig4PA8nJSM9GDB5Gn4o1Kt7ArDgcsoXNMiunK5zgcKDh8OOHZeuc7UXjggAhzlIwHWwyrfte73gWSRWSLMVqCB2Z8XmjZHXfcIcLUmS9GUqULbXweMIdZsptvvhnf+c53xIHfpWAmALsUdvnCzdEEYBdubS+Jlk0AZnybCWZ4aihRCpPK/YUXXhC5XdTrUjOJ/v3w4cMi+TmVp8rv96+xZVEPhqCKxB1SuKC8fckLR0ZFerQI1pT6XizvdrvBUMWenh7BfsiXAVLoU7SZAGzg5ttw6+WfMbwYu/2jOCUTYdbTQJtrCEPVxl6Y2W69fwqTq2F3yn4c4QDqA9MojC4jZCvDZEmN8L7syYABEfEYCqIrWDZILrJ39JhhunvmawVs670j9PK0eMZQFFmA11aOCQVV+m73IE5VajMMqu0DPW2ZsC2SOXFolVWvwTuZYC60kUFRmz5950QvztR16rkckso45nxJpBmCKXHej/GyOtGnmu3zDOKoU78HkWCuZ6oXS3kWnBXerjzd46zzTWFqNb+sITAD50IIvVUta54rtYZIW39MxlZZE/Kgaj6I09WtmmQj+7yjOFaayMekSLLPWpLkVVP2kx+N4ENvvYAPnP4FbA4r8mpqkEdq+EgE0bExRKem0s4xUzr4KEMX+/pU24/n5GC5oQGL3d1YWP1bJrtebq4IDeY9S/nH+x9zYBnSrfyOgOxiAJO0i5VBAT4vSktLBUmSmvE+zIgEi8UiQsQvpggzQRgP5b70pS8Jgqh/+7d/Uz3wy2DaW7qKCcC29PZs+cGZAGzLb9HWHqAJwIzvD08xh4aGRJz+oUOHhOeJ3qXKykqRwKxmb775pgBBDClcXl4WoKqzs1P8Ka2/vx/8kwSVCdby8vJUT0750CQtPoEUx8XEaVIc0yMmNyn/TNIeY7gJH7QMh1nxevHKgbfj4x/5a8OL0UodpRSU12oN7hasf6lD2tTqFcUiWMwrADWMKBhcEfYJFjS3o1JTMFkw8WWUy2WcCGLn5BmcMRi2SPIIEbYYjyEBbnzCuzNa0ZQyfK/JM2YYTDG/6pRBQWp6XnZM9aEwFsF0eT1cq5pU6S6UfaMncMwgs2NZ2A9fkR3lcz40BKYF4JpIl28FgHT3fTpCP51hH1riixjLKUJN0LXOk5VuTswVXMzJRefsOOJ5eejXyXbZ5J3AaFkt6gJulC+FcLqqTTPEURpDT2gaiwuLQs9rJI0n9qrpM/hM8AwacyOIx2Iip8qQOPFqp5bOzkTel0GTMyDSuyXpbuUfPoycAwcQtdvFPUr+x3ug8jPp3+m6571QDbhpfUbQRlBzMQGNcg48tOPhGHNztciUCMB4OMbDtOeffz7dMlyQ7+l5ZCg7oyj4fMt2MwFYtu/whZ2fCcAu7PpmfesmADO+xQQ6DPuTABVfCCjGzJh9eriUJrElknWQgI0vGgxZpHdLTZCT4YkMWSRY4ksDmQv5AL/qqquSmuZLjPRQZzgjH+Banjgp/4wPdxoBIcMXCQiD3/seXvjy3+DhDzxqeDESxBPqTI5aje0dPWHIU8TQuRaSOkQjgmFwsqweYZVQL7X+dk72GgZFHcEpDJQYY4Nk3w3ecUyk8Aopx8ewwq6JXoSsJZhw1iFg1RkiGY+haHnJMNuiXgZES2wFbd5xFFly4c+3YlQn6JLPb+fEGZwxQM5CLbnd42fgtZViqEI7B0ttj8tC2oLP9HZ1ekaQF4+hr6p1zdu1b/wUjtbrC2dln/mxKC4LTmCi0IGJAnUGO7WxFcRWxGGBLbIoPF56wj+byZxYkIuTxanZRVvnZ3Hv0R/j8t6EWDuNoX3Lq+Lthn7MeXkA/xRhiSnbIDPhjh0ovv125Le0JHS3du/eEDOhdK9kTis9+WogTQ28SbIgqcZrBLSxrORtOx/AjVIhPCwjsFHLz+W4mYdFDa777rsPTz31lKHtO5+F6aFjDjKfbzxUzGYzAVg27+6Fn5sJwC78Gmd1DyYAM769JOAg0JEAFVugDpec1ELeqpSnxVBF5oDxJeOnP/2pKrMhXzgIqvgglsIZmRNAgWXmRMhtampK6MrQ68ZYfho9YPTIyT1xDDUkQJR7xo4dOwbWv/HGG+F58EH8YDyCr7bfaGgx8qIR8UJpJISLHewh012jOqMjv2eOGMWgLcxNszsxUVqDptlxjBr0tLEtihyPG9QO2z12CqcMUrWLsEWSTqQgwyhYXkTLwiwKgz7M2stFOKVgdkyxFmob4gxlxrYoPHQaOXRFK0uCRAPRKMbsNZjPT1DpCwbE6vWELukulBr/FGbSUPiT5n3HggcIBjFQ1YKd7iEcqzEWtlgyH0BAJX+ubD6AFt8UJkur4VY5IGh3DyUYCtNYSWQBbf4pjJRUi5DQoypiz1pNEEhRO+y/K9t0Aa/a0CzKFwKYtpXDm4L2v3RxDne/+WPc1vefyIvHk7oXpBavvJJuWuu+z2trQ3RoKGU9kbt16JAQOWb+FgFXnoaMhuEBrFZg6CHvpQRfJDXSa7ynannUUnneeGiVyhjuaAS4Sd42ZZikx+MRh168p0v3amW/p06dEmHmjz32GB588EG9Uz/v5Zj/xRw0Prf4jMtmMwFYNu/uhZ+bCcAu/BpndQ8mADO+vTwZ5GmmBKjYgpaXit/J87RI/U4jAOODmIxTcqOQMk8f5QyJzAcg5T29VXI7fvy40BPj5xKtMYEWhZbpaZNscnISBFxy2nvS4DMv7d3XXIOJtjZ8Z/fN+O7bfsfQYgghYB16S8pGO8Mu9NsSSd6kiW/0TaJkISR0jGZKq1U9arsnTuO0Qap2tk/PSjqCC+X4jHroWN9JL4xD4QkUYYUTKA/7ES60irDCiIIVsHuqD70GXurZV8c0haWN59DV+qYwXXYuub4kMo+WOReWlqOCDVA5NvZFgGg0lJD5aysCmKuTCLR6RmFfnBOhq6EC69ry75k4g5MGvGas2DkzKPK4hMXp7RpFfnQFZ1d1sVQv6FgU1uUwwrK+leXqAi5UzgfQV9WyFgq6c6oPp3XkLrZ6J0DPFz1uyvwvtfE45wNopJZXdZvICds978LJovUhsCSWed+ZV/DRoz+BfXlBdWoFl1+O5ddfN/Q7ZmG1/C+hu3X55WtCx/l79mzIu6VnUHzpZ64qPfo8hLqQRvBFz1k64EaPGw/dJM8b/z+dMeRRDtzYB5kNOSdGSkjfsS3OmcLMPGj7wAc+gO9973u4884703WR8fd8HhFkMR9NbgSxpKCnEDOlSkgyle1mArBs3+ELOz8TgF3Y9c361k0AZnyLCV6Yo8W8K5Jj0LS8VPyOYI0PWpaXjCGIciFk6XPG3VMD7LrrrltjACN4IjCjt0oyvjwwj4yEHhKVPL/7xS9+IT4jNb5kkreLQI0vBjQpJ+wdBQXw3HorHr/5M3ix5zpDi9E+M4hBg0CAAscUYWYS/lyRXYTeLa16W1J1vo8Cws3qBCda9fiSzz6MmgifMwj2BCiqbQdDMuv804jl5GDC2YCgQkdKOZY63ySmdOQ5yesJjTKDXjNS7xOgOBdDqJsdR7jAhuHKZOZCtXXaM34CJwyuBRkaKbost5qgGzXReUxZnXBphPAJbbMyYxpllCYYdtaDoGe6pBIuGf271r5XL/gxU6h+XXS6Ga4Yx9mq5nVeq8qAS9WbJvXTPjuOXMQFjb1ku6b7cUojP82+PI/OpQDO2KqwlJv4XdL2ugdxrCJZtPmK8VO4779/iOagK+XlnNfSgujIiNFLHkXvfjfiKysJ79aVV4JAjiQeF9t476OoPD1BZH7disZ7bzrQJn0vgTb+V83bxvv9n/zJn4hpMpSdnjOCNOaCMQxT+mPo4sc//vHzshxPPvkkHnroIRHSzjB49kESDj5PKKvCg0E+n5R5xOel8y3WiAnAttiGbLPhmABsm23YVhuuCcCM7wg9SnxgyR9QWl4qtfA/9qjGbCiBqsLCwiTCDclbRQAmhbaQhZF5XUrtMZ5asoxEdcw2yb5FoHjllVeuTfbs2bOgMPNlL76I+aeewoO//WW81ZLsjUu3MgkyjRTCzSTLCLhQMedFjtUKT16xeEGmX2RFoW+Urq+eDNgMBeufQX0tjiMRtpg+PI1lmZ9GEWSGTQ7XtGOqVD99Mwku8qgpZ1EXZdVaE6MAjMCmdjUkMBVzoVp/rdQ2Mxj6uWeCYsrdKKWHbdEHPywYsVenBg4UzI5FhRdUr3W4h4Xn8c3G3Yaup11TfTglOziwRCPY6RpGoNiBcQ0ASMHnYEFCpFtp9LpRk00tpLEiNAuPgr2R3rHdgUn0WyuFZ1RpLfMeDBclQr+a/dO49/X/iysnTqdfluJiYGlJCD+nM+ZurfNuMQdsky1bKegZrcBnBomVeBgnATQCnn/9138VXjAe6vGwjM8VEiTNzs6Kz+ml472bucHnwwj6vvGNb4jnBwEvWScZmUHyjdtuuw2f/exnUX6eQ0vPx7gvRBsmALsQq3rptGkCsEtnry/ITE0AltmyEljJTfIy3XTTTUmfM0SQD195+B8LqDEbaoEqyVslDzUcHh4WXiw+mOVx+nxI8wEvEXbwQU5QpmRc5IOfLzu7vvAFxAYG8LGPPbWO6jzdyuz3DeOo81x+EEPPGE5oWwoLrxaFjkOKXJby0Cy8OrwUyr53TA+gv1Z/TgjrJzxZqUV91eZoXVrAvMqLMcsSJDR6J1BmiWE+novR0jpEci3Y6+7HsSpj+UtVQRfcGeihdVIrS6FFJZ8Hx9i6MAu714WZkirBEJmghd+RbkvXfW9bCBjyIhZGIzg4cRIeixUDlc26xbYbfJMi1y+d0YPasRLATCwf06XVqPVOYao0NbhTtrl3/BSO1XeJMMgO7wTGymrTaoDtcA2hTwHKu9zDIjxxWIN4xRldhDfnHLim2PMe1xAmSqoFrbyaMY8wmpODouVFfPStn+A3z/xSEIjoMcvOnVg5c2Zd0Ry7/Vzu1iZ6t/TMgeHXDLdOJVasp52tVoYREvSCEYBp2cc+9jH88Ic/BAk7pEgFhgUydJG5cVq5Y1ttrttpPCYA2067tfXGagKwrbcn22pEJgDLbLuUISVMoB4dHRVhgvIEbL5QMKGZIYXSQ5U9KoESP9MCVZK3SqKQZ1nmSfBFhe3K++ODng9wlk3VJumG+//939F+332i3Hvv/+eUBBJqq3Rg6E0sFlpFzk3AWopJZ21aT0SraxjDOijDlf3VhGfhshkLiRKsfwbDFh3zQYSsybkRBI11wRnErVaM2qswl7/ea9GdAdsi6dPPyvSh9F6JFUshzBYkh9BZViJo8wyjMLIk6Om5H3LbO0I6fm3iE7W+ydKoBRTk5XPjMbS7hlCwEsFgZbMAqGcN7vHuiTM4lQIgtntGUBxZRF9VGyKrHsPClSUsIxexHGOCtfvHjiOWkyfyu5ZSkKbI5yhYE0lgEo9hp3skIRWQhh5+p38cp0vqhGzCLtcwvNZSzDhSX8PtnjHsxRw++sJ3ULoU1ntJiHIFb3sblv/rv0A6eUGSsUqWIXK3toB3S89kGK7NUDy5t15Pva1ehqHh9DLJc3PlY2akAp8dDDWnJ+x8MC9u9TXZCuMzAdhW2IXtOwYTgG3fvdsSIzcBWGbboARgvb29QhtMnrvFhyoZDUmKoRRRVgIljoLaXAwHUYIqtsv2SSHPhzhPRRmjT4pgpainMhRSC6gx9GTif/5PVP/v/w1/cQl+91P/mHIh6FVp8E6hPD+OyFwYrpJqOOf9hr1SmWiAkUrcEmd4mrFQvUxEmFvcI4IIpDkwjaL8XLiLSjFVlD4XhblcWiLRWgsryD4MgqKi5QUsWQpEflLx0jxaZ0eAODBS2azptWP/QgOs3pg3sEN42rTFngm0nGE/xqtb4CtIkMvQBC28hmiy1lrsGzuJYwpvpW0xjPbZUczanJiUkYdIbZCVkPlfeq3dMyoEticc5QgZzA3snjqLHMQRKrRphikqx7Fv8gzmLYVYtuRjVEee38HJM7jvV8+hs7RQdx5Xjs12zrt11VUoOHAAeduUOly6X5KQQkvQXu9eb6Vy0v26oaFBM6+Kc2foIXOyGDJu2sVZAROAXZx1ztZeTACWrTt7keZlArDMFloJwJhPRU+VnJiDYIqeLgpvKrVf5DpcHAHj/AmqSCGvBFX0rNHDxrwuMlcxN4AAjg9sUsvLjbT0zDXgaar04GeSNUMg5cY8Nt/tt8N64gTOdh/Cp9+bSASXzLY4h3rfFIoiS4JFcMJZv053qiYwgxmVF+NUK5oJw2BF0ANviXE9Gr0kIQSXzXNulMWXQa/KkbI2Q7lI9IrkRyNYthQaupgyAWCt0wOwRRYSoW+VzarMhWqDaPSMwWj+117vEI45k6+vypAHdf4ZeOzlIsRUaQwRDGmEb6ZanB3T/Wtes1bPGOyxJZytaMZSCtDdM34axzVo9aW+SHW/0zWEkLMSo0VOVM554UlDjCIfJ71XzNeaKyjGsA4gLtVtCc+izOfSpTVWH3TjE//9Q1w1egwgqc/iomYel6WjA5ZDhzDidKL8uuvQfsst28a7le7HQe1DhmYbpaBP1+5mfy/Ni/m6nJuaMWyc92myHz7zzDObPeRLpn8TgF0yW31BJmoCsAuyrJdOoyYAy2yvmURNgCMZQ/rI3kX6Xnq8aFLoIPOx7PbkkDFlzhh1YugBI/1yU1MyAYREI09mQyZHS942OdiTxiGxKDIXjSGKFIxWA2rTZ89i9nd+B1afD/9pa8Y3rv2YeDnNiceFRhXpytOJxhZEl9couvWuYs/YKZww6PUhkBoyyLbI8ZAYY1Yj36xyMYC65SCicWC0sBxzq8LOmYQtEiB6MgCIncFJ9Dvq0i4d6f7rAtOYK7SB+WknUxGfqLRGgJkfSa1RpjYIiQGRYJzU8fMFVsGcmOq6aHMNiTBEo1YbcqM6tghvfjHGdQKdnvFTOF7XrdoV8xA7CDrLauGVeeN2Tp/FGR3hkQyr3DM3A09hCRYiK/AV62PTrAu6UbY4h97KFhRGFrCQguHTuryADx19AXecfEkIPdMsu3Zh5XSCcCPJuyXlblVWQtKU6unpQV1d+uvH6F5sVnkeLNGDn23z0kOtz4iE7u5uwU5IGnjTLs4KmADs4qxztvZiArBs3dmLNC8TgGW20EoAJpFtyEkxqA1Gsg4KKCtj+pU5YxLRBssWk81MZvRo0WPG/AF6yNRo7aXiBIEEg9dff72gFOafFLoob3P629/Gwmr+1/934Bb8/fWfMLQQFMAN2pLzjPQ00OkeRn+VdlibKhAQwsi79TS/VkYpEm1dWUTz/CzylxYwU1AiiCnUTITqNRrrS4gVpyDF0Bo4gdusRk5Qw+w4KlbC8FqsSULSAiA29RhaC9KnewwSnzCnbP/oW5grtAuRZDWNMLVBkK3yuAHik5awB+V+F05XNmNRhxyBvM9m9yhGFAQYVUEPaudm0V/ZgoWChJi03PZNnMKxFF4zesx2uYbgslfAtbo33TP9OFOVWoyaWm/1QY9gV6QwecOSHxP56qAtNxbDjf2/wj2//leUL4bWhkfvVvF73gNLW5vI4crv6VH1bvH3TQIdyk9QUypbjLqEvA/yoEmpUbWd58gDNDLZHj58WFPYmM8K3rO//vWv45Of/OR2nu62GrsJwLbVdm25wZoAbMttyfYakAnAMtsvJQCTBJQlkMQQReZ/0ZtFr5bSlDljDL1hHgDBktIk7xjFmRmmwnYZeqim0yJ53cgixtNkLQA485GPYP7ZZ0VX33zXR/Hc5e83tBDNs6MYzcDTUR1wa4IfrQFkogFWvRiANbIIR8iLkKUIYxVNuhj5mAM2YpR2feykYa8eGSMjeZY1b5JgLqRA8dIcZkqqNddIMDvWq3t9tNavOzSJXpsOfa14DG3uEdAzIzxd8RjChedyu/RcIHoAGPPYdoTd8MfzMFbegE4CWINrnhONIn9lWeTD0Ri2WBRdFiQdWgLQLNcVnESfCiU+ASeB12Rptcg5U4I2QcChYmRSbPdOCq8aw0Il2+sbxfHS9flpPdP9+NRr/y+6F72J3C2JLIO6W1VVepZYvMzzpZ6sqHICHl2Vt3Ah3hMZbk0CIUlYfgsPV/fQGJ7OgzBGQigP16RGnn32Wdx999348Y9/jFtuuUV322bBja2ACcA2tn6Xem0TgF3qV8AG528CsMwWkDH7zNuSTA6SGBYkhQ0yn6umZj29tjxnjC9RTLxuaWnBrl3rdbUYSvjaa6+J0ByWZfiiVrsSvTzzxXiqSkFP1pNbbGUFY01NiPl84uOvvOcLeHnneuCXamV2ThqneBe6V7G4Yd2rPTq9UlXzPtR4pxDJzQMpv08b9GRxviXzwbTiycp12TvTh2M16i/oWmtIDxeBVirmQrW6rDehQXuu1ZfwmqUQbq7zT6EivoQpix2eVa+PkwyIxepU6amui1bPCIbKG1WLNHknULoQxEBVKxZkmlp7x0/iuEFQWeufwbTNiV2uQYQLrOs8YVpjLA37hN6XZKR973YNCwp8eaiivH6naxBnFYcNZJvs9oxgoKIZYRV9sJ6pPpyQhc3WLAbx6dwp3Ha4I6V3S8/diGHFPABKRWmup52tVoZe/kAgsMbgutXGl+l4CJinpqbWkSvJ23viiSfwyCOPgCHkagd2mfZt1ku9AiYAM6+QjayACcA2snpmXXpd4uYyGF8BJQCTCDekHC4px4un1HL6eakniXKeL1F86eCDV/KeKUcjaXkRnLEsH+Za7Uq5aCT+YDgPvWbKPJGFX/4S0zfcsNbN5z74GE4bCBtjxf2zgzhaqZ5QrrWazjkvfHZjVPJsixTnQyp5O8zzaZodQ15+PlyFJXCXnPMg0BNjNNeseCmMBYMeH46va7IPvfX6ABi9P23uYTCEk6GEWnpjamsocrlWIoblAgQbZEMysC+b9wu6eDJgkrZeaUJrTEeulLKedSGY5DUrjCxih2sYwSI7RlX6Yf2EcLO+9WN5sj/uGz+N/spmQQai1xKgMgG+OK5uejud9QikAZr2+QBCqzmCDFHc7RoS2mFcOy1rWPRhosCBojzgD67qwsdvvxJFBfpFprXa5e36pZdeEp5w/razyahXSM8XQxCzychEOz8/rxrdIM3zgQcewNNPPy00v7IprHSr76MJwLb6Dm3t8ZkAbGvvz5YfnQnAMtsiJQCTRJQJfOjJ4ksSiTe0XiaYdE3QxZwxgiZqhRFUUQNHaXx4U0eGYsrMk7BarZo6OVK7pHKW9McKCs6FRrHt2S99CcEnn1zr5kMf/5ZhEome8RM4YTAXqdU9jGGD+V8cZPlSCL5CB3KjK2ieHUPJ4px4aSZwYL6NmiXYFo3lSjXOjmFcIbar5+qo9U1hKoUmVEkkjOZpivZaMFTVKvKphC6XwfFVLgbhKTSe89PqGsIwSSGWF9AhxIPzhRdKa+04571jJ3BcAdrSrQUBNrWuaA2+KZTP+zFQ2ZIWZIp1T6OpxTarludQ6x4XOWmd/gkcrTCWS9g93Y/Rshrs8IxiuLxRgMJ0VhXywEUSD7IhzgzBY3Ou5YZp1bUW5GFpeRm3HWztKN9VAAAgAElEQVTDH95+GHVOY2GcqcZEQd5f/vKXgq6c94NsMQJLssBSbFjpsd/uc2R4eWFh4TopEvm87rjjDsFsy3t2NoWVbvW9MwHYVt+hrT0+E4Bt7f3Z8qMzAVhmW8TwQ4IwyUg1/PLLL4uXIhJlMPyvq6tLk3ZYnjNGb5maVpjUtpRPxnBCAiz2ofXyRe8Yqej5wOcfWRmVNrZvH1b6+sTH0ZxcvOeB76d8GVdboZ1TvYZzkXaNnzYcFljtm0JNyCNAC/O49HqMRIikQd0rkV9l0BOYCKuMriOpkDMXUqNLCXZ2k1jEIJth5/RZ9NcYe+nm+Lju8dwcDFa2rpMS0Lr6e8ZO4IRBAEZhadLxMySPFPl6jKCahCmSuLJanRbvBGx5OThTUrsmutw5PYCzaYgx5G3RW7pvIkFbTzZJvbZr+iwiObmCIIReLz12ze563HfjXlzWpk70oqcNrTLZyoCoh6p9I+u2WXX1AEuWIaEKIyWYt2uKMF+83TIB2MVb62zsyQRg2birF3FOJgDLbLGVAIw5GTzBpd4Xw2hIhsHwQq1wErfbDYam7NixQ5QlBTFPtdWMfb344ouCQYv5YHxYl5WpiwPzBJUPcRrbY7tyWz57FhN79yK3sRGWxkbMFJXizsP3Gl6ERu94Ejufngb0aIDZFkJo8k7CElvBTGmNyOVyGdQa41gavBPGc6WYi5QiV0ptjhVBNzyroY/ss2JuFl6bM+3atLiGDZN99IzS67ie0EVtXM2eMRHm6LeWCKILo9bmHcNQmT6R4zr/tJAwIJB606BXlFpzk6XrySeov7Vz3o3FWA6GHOuBTMmcPymXS2t+CZKMCRGuyBy0XgNhla3+KVQvh/BaZYeu5aspLcYX3nMZfvPy9gv2Ep2tDIgSBT0FmOkFyxbT47EkAOPhGgmYnn/++WyZ+raYhwnAtsU2bdlBmgBsy27N9hiYCcAy2yclAOND9IUXXhAPUoYj8kSXbF5ap5kSsYYUKpgKrElt06PFfhmqqNWuJNLMWV1++eUiV0RugX/4B/j/x/9AbHZWfHyyfic+/3uPGV4Ex2IIIRmZgZ4G9gbGcLw02TPCl/bm2XE4FucQrKzDWJEzyVskvD61O/Q0n1TGujSv21smVRS5UjoBDuvQu0RQFM/LTclcqDZ42/I8wvnJcgPpJim8UikAYtViALWuMbgdlULHjSYo8g2ADmkM1oVQyvWzrCyjyzuGxRwLBlcZDEnhf9IgmcbuqT5B3S5Z0WrO2ExJJVwa1Pllc/61XC6tNSOZSqt/Emer27Gwyk4ochBXQyRTrXVDzjKcjmKcCEaxs64EpycSZDVaVpifh49dswufvKEH1sL8dNu4oe+zlQExWynomRvM0ELm7/LZoGbM662vr8d9992Hp556akPXh1nZ2AqYAMzYepmlk1fABGDmFbGhFTABWGbLRxFmer3kRi9VZWUlqNvV0NAAnuZqGZOtqedFWmICLDWtMHndn/70p0L4mYyKZEDUMj7MGf5IgEZdGWVO2eRNN2Hp5ZfXqr+085147D1fMLQIzCVaKjQGHtgBw8b6aztR459BdcgtaLvHyhuxUGjV7F+ADoNeFft8CHNW47lS7a5BDFanJhYhXTlJNMieN1bRgKbZcd1eKWmSYnw6hX3lC0NB6kEFmLIvhAR9fbiQIsktiOckPxK4fscNskGWhX2aBBM1gRnUBD0YqmlDqCB53xo9Yxgr1+c1k+a1b/wUjtV3gQQZTf5pkTPGuaSyHdMD6NMIP3TOB9Dkn0JvVRuW8gvXmikLB+BPs+bVJUVoqrDjrZFZRGNxcCWLLDmYXz4Xaqwc180HmvHg7YfQWJE+n8zQj0yjcLYyIGYrBT1DzY8fP46DBw+uOwyTtpiakDwse+yxx/Dggw+ej8vEbEPnCpgATOdCmcVUV8AEYOaFsaEVMAFYZsunBsBIvEEvFcHVgQMHUobSSMQa7F2NKl45KoY3EvBJLItao5YYE2022zrWrajfj1Gewspy1569/P34X+/6qKFFIG15KtIJZWMECY3eSaEvRe0wLfFhtUEICvVmbSCrVqclMIWR0jpDc2LhcpJIqLDqkbmwOTiN3KVFjChIJRLjM0b20eoiGUmL4fGVzfngt5UhP7KEDteQ0BAjmcaKRdvrssvVj1NVxtgqlQyIZP7rmhkU5B30drFfpdEbSK+YXAtLzwQPDh3BYkEx+qrbsJKnjyVw7xhBW3JobfmcDw1BlwgxVBtDt3sIvRXqeWml1gJ01ZXh6IgHyyuxtWE3ldsw6gmqTmNXgxMP/9bluLJzvcSEnnlnUiabGRCzlYJ+aGgI/f39IheX92Q1+8lPfgKScHz3u9/FBz/4wUwuDbNOhitgArAMF86sJlbABGDmhbChFTABWGbLx5chkmPIjUyFJOYgULruuutSiolSIJmAjZYOrLHMz372M9H21VdfLVgQtYzeN77M0BN3+PDhpGKhf/kXeD6aDLaeuu4P8PzB2wwtQpd/DH3OJs06zN9qdo/BvhSG31qK8fIG4ZnJj66sI6tI13EmxBi7Jk7jtEECCYIaAhkJXDjCATR7xwXokJgL1ca6MzSBMw5jXp9MCDiKF8NgrhVBLEHQvE4iifaZAQwYDEGUGBCrgh7UBWYwUtGEgDW1JliNfxrTMhmAlPsajwlAR8DlK7LDR5ZBA7Zzsg+naxJ5WZWhWdSGPDhT046VPG0genlrOV4fdCf1QrbCnqYKnBr3Ym5pvZfrYGsF3hh0JdWpsBfhgdsO4Ld/oxO5uRf38asnn8jAMm6potlKQX/69GlBnMTngRrDLTfhW9/6Fu6//35wDdRIk7bURmXZYEwAlmUbepGnc3GfABd5cmZ3F34FTACW2RqrATA+QJn/VVpaKogyUplErMEyzOkicUcqYwgi7cYbb0xZrq+vDxRjZk7Bvn37ksq67roL4X/+56TPHv3Nh/CrzisNLULP+HqNrTrflHgZFmxx1S1YzEumvmdYW8DmNNQPCzd7RoXXzIhl4jWr801iOS8fdYFpzBXaocZcqDaGWv8UpnWy40n1xfh0hlVyXFzXlZw8w1pt7K90ziu8ZnqNrIRXDL4h9LUGqltVvV1qbXXP9ONMGomBgsgSutwJKvfp0mrQMzqXJtxQra9q/wwQj6Mq7MPp6nZEdXjO9jWW4dhoIu/RkpuDA62VGJgJwhde0lyaw20VeH0gAcDy83Lxkat34lM374WjKPna1ru2Gy2XrQyIjCb4+c9/npUU9DwMY0QEQ8y17NFHH8Xjjz8ugBpD1027eCtgArCLt9bZ2JMJwLJxVy/inEwAltliawEwhgCS2bCjIzVzGl86CKoIvAjAUpnkLSNNMfO6Utlrr70mmBKbmppEuKJk8WgUo01NiHm9SdU/9eGvon/Vm6B3JfaNHcdQZQsafRPIjccxVVanGronb48aYCMGaMOluo6lMEI6vT1SnT3jJ3FSJ5thvXdCMPgxt+uN9oN6l0CUExT08WhKz4tag8Krl4KsgmQRFEn2kU1xlcFwT2AMJ0vUk/i1Bm1bnNMNcCqDHtT7pzFa3gCKNOulkZf6ptfsmIbXsSzsR7NvEoPVLZiT5Y11zAxhoMoYuCYgda4s4bSzcY2SXs+m1TgK4AosCOA17Z/HlH8+bbXOajvOTgdwXU8jHnrfIbRWp/YCpm1wgwWylQGR4dg8vOI9s73dWLjsBpf0gldnni89X9R71LJ77rkHP/jBDxAOhwUVvWkXbwVMAHbx1jobezIBWDbu6kWckwnAMl9sAiO5USCVD9G3ve1twguWyqRcLYo1X3XVVSnLTk5Oglph6QAYQxSZK0ZwqCQBWfjlLzF9ww3J/Vit+O3/55sIFqTXRWJ+T8vsmAiBs0QjeKv1gG7vCDvdnUFYYPHSfEqCDq1FE2QVMmY9eTnSm7d4RuFYCAmae1dpguJ87+wgjlUYe/mrCrrg1ht2JxsEQd+kMzlskXNt945hqcSJweKKdeBCUPgbYGhkdy0Uvk7hPSSA7JoZQBy5gikxlpvI7bIuzhlmkKTu2mkFW2WDbxJlC0H0aoQH7h0/heM6WRNrIyHYCvOEjtl4OG7oR+soykNDaRHml6MYnQ3rqksv2Y7aEvzRey/DVTuNhZjq6iCDQtnKgCh59rKNgl7K2WM4uDIaQdp+lmFUA8k6mCt2oTTAyI77wx/+ED/60Y8EKcjExAQKCgoEUdTdd98t/i5FAWgTgGVwIzKrrK2ACcDMi2FDK2ACsMyXTwnAGEbDvLCbbrop7YOUydlk/iJQI2BLZQRfBGE8Sb1BCaJkFSVtMT7EyZbI3DLJZh96CHP/8i/Ia2xEjsWCmMeD8PAYbv/s9zS7rl/wosIzIUgSRisasZRfJMq2uYYxZDCvaF8GZBoNs+OYqDDm9eH4ykOz8DrO0e9LzIWFK8sYr2yEv3g9OBZsgTrDAqUFE2QVtfo0oqQ6BD3MhSNRBDXOdoRdQsh5wFqFpVW6dLUN6Z7sRW9dl6GLdc/4KZxQEZamh63JN4mxyib4ipK9Os7FEHwGPY4cVLV/GjMEo/EYdgiCkJy09Pd7xk/jZH3qObVV2mEvyseJMR8Iu/Y1OHB0zK97HerteSgtBE67k/M1UzXgKLLgY+9oxfsPN6O4sFB4qfmyygOQzXxJzVYGxNHRUXEvpJeIgvTZYnwWvPzyy2hpaUFXl/p1TgC2e/duodn4H//xHxds6t/4xjdw7733oq6uDtdeey2am5sFWy89b2TOJQnI97///bTPrQs2wE1q2ARgm7TwWdKtCcCyZCM3axomAMt85fmA5QOURu8TiTJoPNFM96JGbRieSlJQOVW+mHSKynZJ7sG2tU5JmfDNMCW+LBLYHTp0aG1yE297G5bffDNpsuPOetxzz9+vfUbhXnotcpAIK/TZ1XO2KkJeQ0yG7GCvbwQnnMaY/wTo0OkhkSZBsEVPDmniGfbItWLo4/wqeNTa7Q4BpjoNXQxCGLlZnzCy1HDlUhD25Xk4gj4Ml9UhVKzvhbPOO2mIeVKs+ehxHFv1muXEYtgxMyj29qzwduWpznXHTL/QzjJizO1CdAU7PMPwWsswqVM4myQno2XqbJWdNSUosuThxHiyBtfBlnK8MZRMpqE21oayYjhthTgx4cdlTaV4cyQ59FatDjk13tlchNt22GArWM/0yDoEYQRkyj/+5rQ+571go56NbGZAPHPmDKgDRmCQTSF4zP1iSHh3d7cAPGrG5wa1Gu+8804888wzRn52hsrycJDRGbfddlvSs4metyuuuEKs/3PPPSeA2KVkJgC7lHb7/M/VBGDnf00vqRZNAJb5dssBmMQ+yNbSkWqQgIOhgnwxow4YRZi1TNILI6DiSWUqcPfKK68IQMi/oqIi8WAVwG1gAOOyfDCpr7eaevD0u+6CNbIowNaEsy5tWCE9OLlx6CI+kM9pRwYAR4TdGaB4J3Nhh28MCyVODNlrsJyrP5+iKuBaC0fUe0UYoaCvpn5WwI3c2AqONieTo6TrT+SaRaMp6ebV2tgx1QdXSRValv2YLHbCXZBeG00wIBrQDXPMB9E9dRZ9tW0I6ASTHGsu4sjPBZZktO/8vLu2BJbcXJycUPdytVfaMOBSp4Zn/UpbPkry4xgOrCC2Gql4oMmJt0Y8KZf5qu5aPPS+g2ipsIqDDvkff+fKz+T/Zj5nKuPv3Ahok8rKQVs2MyAeOXIEDMlORVSR7jeyFb93uVw4evSoiESoqqpSHSKJNwjQHnroIXzlK1/ZlGmw34cffhif/vSn8bd/+7ebMobN6tQEYJu18tnRrwnAsmMfN20WJgDLfOnlAOzEiROCxYrGFwkCKy2TQgWpC0OwRGp5LZNCFclqyDBE0hnztF1pfEFjCAvDXbxerwB3Umij/2/+Bj4Vgc8Xeq7DE7d81tACJML7Kg3VYWFSqBtlC9Qjwly54Ef9chDhvEIMWSvRMTOIs3U7DI2PzH80PWx68oa7pvrQl6IvghPmm4WKHUI/jJZgQDTmNSN4c5UkctV0WTyOHXPTKJoP4mR5q6F5CYZLHRT+ZL2sCPvRV9OOzpmBtKGEynE3OosxPju39vHOulKhqXJ6MqA5xbwcIDcnnqTVJRUusxVgR00p3hz2YEVCXqtf1pUUapJutFY58KXbLxNEG5kYf788UFEDaKmAGz0f6UwO2tgPD2PoLXE6naqAjuW1qM7T9bWZ3/PgiPqJFCPOJtNDmvJf//Vfgljp61//Oj75yU9uyvT/6q/+Cl/84hfxuc99Dn/913+9KWPYrE5NALZZK58d/ZoALDv2cdNmYQKwzJeeL108/ebLEWP9aQRC9Gg5HNreBilUsLy8XNDWE1RpGUMV+eJFYMUkbS1wx6RqJlcfPHhQ0NDzBU8i95i66SYsro5P3s8/vf138cw7jAl/toddGLQZF59l/pVRkd4EwFmfO9G45EfFnA+zuYVgGKXcesbWU+Sn2+FMvF9ss3bRj+mi5HwyhuN1+CcQjUSF/pYS1GUCwMQ6KAgu1OZUOh8QRClTpdUIFDsQybGsEWukWwPpe4ZtpiLu2BGeAUJz6JdR1AsGxMZdersQ5Q40leGtkVnsaShDJBpD35S2V0tquKXChmF3cjlqee1pLMepCR/CKlpezOcKza+nmncU5eO+G3vw4Xd2ocCiHo5paEIGC0tC7lqeNSV4432FQC+d8eAlVTikmieOYX8bDZFMNy6t7yUKeuYmyVlbM21vK9VjXhvz21KFVj777LOCAIPkGLfeeutFHz6fE5dddhl4gEhBaOYvX0pmArBLabfP/1xNAHb+1/SSatEEYJlvtwTACKJ4isswE3q3mNPF3C4tI1siX3gI0himokWsIYUqVldXi/aYK6EF7kjUMTU1JcIfqT3DeP9rrrkGsUAAI42NTCBbN5y/vulT+Mk+BTNimuXYPX4apwyEqLG50nk/glb9WlTSEBpCbkw4SOwQR2tgEo6gN4m5UG2oRsMW2UYm+V/0mjGfigCLIYLtrmEURZYwWNWakrmxc/qsYdr/lLph8Rg6XEMoiEZwtqZDiBvTGmfHMaYAp3qudDUGRObVdc8MwF/swIRKm7urinDSpY9dUBrDu7qqMOGdR/9MeuAl1bmsxYkjQ4lQQrIUXtZaIer7wtoEG7vqS3F6/Fz+V25ODj5wZTseuHU/KhwJUpntYBIDIg9gJLF3vV63dMCN9yKCMC3gJpGQKMFbujxXPevK+xSp2js7OwURRTYZww8ZjUAApmVPPPEEHnnkEQGANgOA/uEf/iG++tWvCvBHEHipmQnALrUdP7/zNQHY+V3PS641E4BlvuUSAJPCBKn/dfbsWRw+fBikHlazhYUF4S1rbW0VL1IMW9RiTZRCFXt6eoSXjS9hauCO3zH80Gq1CiYx5lRQC4xgbO7734f7wx9WHctDv/1nONJ6jilRz0okAM5ePUXXyrS4RzBaZYyAIy+6gq7ps8iLxYQWll4x4UyIOzJhQGRYIIFJRdgnvHA+e7muNakMuuAxGMLZ4xvGibLk9WN4Y9vsKFxVjeu8cBzILgJlgwQm5SEvvPZzQNm+EESbZ0ywJfqLtD26FTYLPHPagsbyhdnf5ERoISJILo6PJRNspFvAw63l+PWgG5e1VmLCF8ZMYCFdFVwuE1O+oqMaf/z+Q9jdYFwQPG1HF7jARhgQ6WVKl8em9n26KTHcUQJler1urCP3tvEe99ZbbwmadjK3ZpP96le/EvftVCy3DzzwAJ5++mkR5ZAqauJCrMvXvvY13H///di5c6fQYWNExqVmJgC71Hb8/M7XBGDndz0vudZMAJb5lhNA8XRZChOkpgrBD5Oua2trVRsm2xSBFEEa9W+Gh4dFDoAa+xc9Xvyep95+v18kdDNPgnkgcpM0xXiKzD+WIykICTtcd92F8D//87niPO1ub0deTQ0+ctnHMGo1ls+VCPHrMbRouyg8rEKHrmykaHkhwVwYB2Yd5XCVGn8hExpbq+LFege5LzCKo6X6BIGdIa8QoKYW2putl+ntQpTLjywhmpuryUCo1VirawjDqyLW7a5BFEaWEt4uS75m/4IBUacYtdQIiVLO1rSjdjGAmkKgN7cEi6n5JcAQv+BCavDFhxSBl29+GSOehKes2p4PV3DR0Pq9s6sKI5458afXLmt2wh1cwBffexluPqBvj/W2fbHKbQYDIvvk/S0dcOMhlLxMOkISgi+5J419MIKAOa7MiVUDdJtN/5/pPvNQjJELcjkQZVtkHeTzg5EQ58OjqHesf/d3f4fPfOYzggKfhFBazyu97W3XciYA2647tzXGbQKwrbEP23YUJgDLfOv48kAtMD7AeHrLPC3SDtNj1ciwPxVjeCBPfemdoueMeV0MFSRrodIkVsN3vvOd4gFNcMccL4Ykyo0gjWBN8o4R4BHo3Xj99RjfvRu55eXIIeHH3BxWBgcRD4VE9ffd/z2h8WXExEu6jnwkeZv7xk/iuAYYIHMh6cgjlnwMVbUisqqF1ewexWiV8Rdmgjijc+qa7ENvCj0qhuW1uUewUFCE4aoWAaAEBb1BIFrnm8RUmTowT7UHNf4pVAc9cDsqdBOZdBP0GtQNe0d1PoJ5hTgxGWDUpy7rrrHjzLQ6cQZp3fc3lcMTWsSYd36tvRKCNpW8LK0Ou+tKhSdhyjeH4ML6UFqtetYCCz538x588O07UJh/8fO8dC2gjkLbiQFRTkiSDrzxe85NkvJItRRK+n89HrfNJCThOpD6vampSXiY1Izz5j2bc+O9/WLl4T355JOg543PKT67lM8THZdk1hQxAVjWbOWmTMQEYJuy7NnTqQnAMt9LAjDmXfHhSe8XRUQZyrFr1y4BxpQmJZzzVJQeMCl0kWQZdrs9qbic1ZDtUTOMJ6UM1eFpsdx+/etfCw8ZyTx4iip5zq6yWuG++WZAhSY7WGTHb3/mnwxPvs43bViPqmf8FE7K8sYqg27UBWYwZy3BiLNB1SPEELrTBokdCOZCtvUiy+kmWeubWjenvGgEHZ4R5K5EMFjTvo5ARIRiGgRgu4PjOOVI3rtUY6Pnq3QhhNP1XYYJTGqpG6YD7Flygb2NZQgsROAstuCN4fR6WfIxH2514vXVvCzpc7IV7m8ux7R/AZP+9WGC3bUO9E6mF1NuqbSDZBnUAqtyFMIVOAfiUq1bTg7wvkOt+MKt+1BTauyAId21shnf01POgxu+MJOsIpuM906G37397W9fY5JMBdzk36UDbkr6/1Q5bnKx7fMBhOjVI8Mhw9IZbq4FwHhQxwO2559//qJs61/+5V/iS1/6kvDKvfjii5qh8hdlMFugExOAbYFN2MZDMAHYNt68rTB0E4Blvgs85ST5hcR0xX//4he/EA/djo6OdQ0zL4seMp6I8qEshSMyR4A6X3KTWA0ppkxyD2qA8YHORG2eqkpGUMdTTOackc2Kxjy0gYEBHKT45te+pjrBgapW3HfXk4YnX7S8hMUCY+QFXVNnES60onLOC6/NifGK9JTfCY0tY7lmrXMuDNsN0LVz9vEY8qMRLFsKxVowBNK+OIfh6lbMFdo012fH1FnDnsC9o8fSgjbb4hza3SOYtZdj0lknxpOKlVBtgIIgJBZbI+RQK+MozMPO+lIMu+fgXs3f6qyyoX8m4R3Va4dayvDr4VlRnMQYBF4T3jCmA9rhhVIul1YfdaXFqC2z4q3R2TVPXE9jGY6PJvpJZd1VxfiL33sH9jcnh+mmq7eVv9dDZ76Vx59qbJlS0KvR/2sBN/nn6QhJOFa9ItvycEll+KAEmlPltvGezsO0++67D0899dQF38I///M/x5/+6Z+Cz5Sf/vSnl2TOl3KRTQB2wS+7rO7ABGBZvb0XfnImAMt8jaUwE4aQ8ASXD3qGnZDNi+KaSpOAkeTxoq4XAZxaXhfzuKanp0WoItuXmBbZrpwtTPKMMZa/uTkRskca+r6+Puz+oz9C9OxZ1Qn+quNyPPpbDxuavH0hhDmdYrtkBmz1jAowM19oxWDNekCaqvNM6OQz8Zo557zIjyyjOuTGdFkN3CXqgqnKsVb7jQs37xk/iZMaGlut7hHYlsIit2s5PwEGaanqaK1ffUEMExr4p7woB5XWXIyF4liIJNOa2yy5CC+n16eS99tVY8OQOyRCDYc9YbhD6fO6DrU48YbCa8Y2y60F6KgpwZujs1iJJsdAkkzjvwdcmpdMtaMQt7RZ8OFr9639Dgxd3Fu4sMSAyHvBxcwTutBLIh0eEYRcLAZANfr/dB43Rjqk87bJCUkIzJgbx9xczo3kGhJYYzsEZwz7Y/QESZMee+wxPKii03g+1/8f//EfcddddwmdOOZ+KQ/82BcPBVnmUjITgF1Ku33+52oCsPO/ppdUiyYAy3y7GTrz0ksvob29HV1dXUITjCeLBEIEREqjB4s5YyTVYJiLVl6XlHTPsMQrrrhCNCOxJ0pEG1LbBFoEXAxjYRI7jSfm/T//OdrvvVdzcv964Bb83Q2fMDT5psAUxkq1Q+jICtjmHkLhSgRjFQ0IrFLPkzRCDir0dNo53Y/+2k49RdfKGPGalYjcszFYVpbxZpsxMo28WBTxeI5xjS1BpnEuNLV4KYwO1zAClXUYK1ZnIMtEN2xvQwmOjSWH+HXV2FGUn4vj4wGopXcRwLh0sArKN6TIkosDzWXomw5iVicLIut3VFkxIPO02QrzsKfBiePjPiwsq2td7WssxdHR9eGRRfl5uOeabtzWXYKh/j5xmJFKAsLQBbVFCm+EAXGLTEF1GNuFgl4iJNFL+89yvM+rgTZGS3z2s58V68GDNQIiRi/wGUJyJf7x3/wv87TUyJky2dM/+7M/w5e//OWUVflcInHIpWQmALuUdvv8z9UEYOd/TS+pFk0Alvl2M8yP+i0ESRKFLwEYGaUYeiI3yTvGmH/mctC08roI7KiNQ1DHBzOND3WGGiq9awR1bDJsi/EAACAASURBVPvqq69eS+Imtf3EV76C6m9/W3Ny/+vqD+PZK+8wNPluQVaR7NkrWllC28wQY/kwUtkivF1yI9DJJC+rZjGAGYXIcbrB7lHkminLFywvCs2siMWCwaqESHLC07YeLKfqq8Y/I/TIjJpj3o9QcQmaPGMoXQyhv7o9bThn12Qv+up2GOrqcAvzsmZBEox9jWWYW4qg35WaOXBPXQlOTqTPy+JAivNzwZBAgq4BAzperEvttMK8HCxGosjPy8GBlgr0TQVEDlrKNXcUYFoBEG890IQvvmc/6p02nDp1CgzbTSV6a2gRt0hhSWKC95f9+/dvkVGdn2FkMwU9Ixt4wEbdRrluG6/R73//+0IfjAdlLMeQct7D6RljmDr3nB4zgrjzkY92fnYrO1sxAVh27uvFmpUJwC7WSmdpPyYAy3xjCX74IJXIL9gSQZLT6RRshXJjuAnDCuUU9Vp5XVIIIcMaSexBU/OuqYE6lmXooue974Xt+HHNyT122wN4afe7DE1e0gATzIW+CUTyLBiqaUckNyH+q2bNnlGMVRpjM2T4IvW/UtGsq/VFivbB6gRglYy5UPy8gGQa1a3rGBITXjNjtPpkTewzyDBYOudFk28CgeISjFWcy+FLtwH1RcDkQhoueEUjh1vKxEscmQdndFK9X04yjcHUOVb2wjzsri9D73QCMO2pLxUEGUasoaxYsBle1lKBMW9YFxW9oLqXsSbuaXTi4fddhsPt58JFs9VLtJ0YEI1cByybzbltvB4JvHgP17JHH30Ujz/+uNCCbGhoEMUY1k5CJf6p5REbXWOzfOoVMAGYeYVsZAVMALaR1TPr8kVNJ+G0uVjKFWAOF3Oz5IyHFFkuLi5eCx2U6hw/fhwsT7DG002aVl4XH978jqf58hPQF154QbCgSd41Ai2KmCp1x1wDA5jbvx85K7J8npIS5Le3I8duF3T0n+25Eyfq1OmR1Xa6MugBiSemnXUYqWzWrWW1c+IMenVogMn7LA/NwuswTqLAfC5JELnRM4ayhYAAO36rNjOiYCYsSbz86DUjDIiNs+Mom/dj0VJgOKSSDIVkoViJ6fuJ1jgK0VRuhS+8mNbjpZzrweYyHNFgQCRtfHddCc5MBRBaPHdNkUzj9UGP3mUT5d7RWYlRz5wAX3ptZ20JTk/6UOkowudv2YvfurwNuXTvrRpvYcy9JFmN0vOst4+tWi6bGRBPnz4twAfviZtJGX8h9p5kTAwhVx7Eyfu655578IMf/AAMxTxfoYYXYi7Z3KYJwLJ5dy/83EwAduHXOKt7MAFY5tvLFz96oeRGGnomypPZUP6CyNh6AjPqvkgmUc3L87p4aioJYypDjvg5Q5EktkOGP0ovMKRYlmz6O99B4E//FAVNTeDnMZcLK0NDSXT0H/n405gpTc0Y2OCdQIVgLiwXzIUUVD5tEEztnx3CsYo2Q4us5slK1wBzucrmA6jzT8PtqNRNld84O6aLlVHe/97RkzjetEdzSAWRReyYGcBckV2AVdru8VM4pUHAodVQk7MoST9LqxzZC22FFpyYCCAai6HQkitC/IxYZ6UN/a5kBsRSaz66ahw4NRFQJee4rMmJIyPpmQk5jp31JYhG4ygrzsfrg24jQ8MV7RXY11SOe6/fDXvRevFpifKbvyM5QY2hTrZo4Wz2Er3xxhsCfDB8OptMIhehV0stF5hz5bPjxhtvFNEK1II0Qw035wowAdjmrHu29GoCsGzZyU2ahwnAMl94NQBGmnmCMpJiSEY2LAIzJYGGlNdF9ilJrJN5EXwxoa6YFJYitUMQR6INEg3Q6G2jN00Z5jLxkY9g+dlnNScWQw7e8/nvixwouTH0r2V2DI6FOZHj5FIANIYTjhoMJ9w7ZlywePf4SZzSEG5WTsq2EBJsi3mxFRxr3ot4Dt1G+s26FF6Xt5audueUOkFIvXcSFWEvBqpbMa+gsD9oXcGRsDExYJJpHB9Xz8tiLhXzu+aXV3B25lx+F71g08H12lvp5mS15GB+lQCjwlaA9mo7Tkz4NUkx2F5rhRVD7tS5ZW1VdlAQWcovE3Ma0x+2+O499fjSe/eiucKhOQWG9/IwggcTJDDIJpMYELPRS/TLX/5SHEpREzGbbH5+fu1+r3UgwGcHwRm/J5GTCcA25wowAdjmrHu29GoCsGzZyU2ahwnANrbwTJSWG0WRCbgYPiiZJLhM75ecoY0PYYYVMglbomFmWA5Pva+55hoUFSXrbfGFhYCL7fAhzzAXiYFR6isejWKksRFxn/ZLrsdejg/dmyDoSDAXDgtihHFbFfy2Ms0FKZ0PIJAinE+tIjXAzhokkUjHZkhvV4drUFA6DNS0YyUvH12hKfQ6jInUOuaDCFm1X+y1FqIy4IGnJPGinx9Zwo6ZfiyUVWDIrk3Msb+hBEfHA4YutstbyvC6IiyQBBjMvZrwzWNKRWtrT32JAE5GTGJArLQXorXSJtgIl1ZS550xAtCSA81y9WXFqC4pxtEx75qWF8dUq0KmoXrd1Jbgj2/fj7ftSE92QiZQ/mboSSksPEfhb2QNtmrZbM1tkyQ8UnmJtuqepBsX84J5iJZKOJuRDmQ6vPPOO/HMM8+ka9L8/gKtgAnALtDCXiLNmgDsEtnoCzVNE4BtbGWVAIw5WfRi3XDDDWsNv/766yCzIU+xlSedZE2sqalZYzgjyGIZaoUpjaQfDG8hsxbpjMn8ptQQW3zlFUxdf33KSZ2u3YFvXHcPcuPAcFXzOm+NWuX8lWUBdOI5xm459b4p3eGAUr8iXK9RwUwYj6HdPQxrPIqhiiaELcngtGfsRFqRY+W8hMixjBZez5VA8BfLyUN10INqLGKwtA5zOevD4tb1VV6M4dl5PV2slTnYVIojowkgXWUvREuFFb3TwaQ8LGWDh0mmMaQvLFCqu7+xFMw3o7dtOQ3wkuo0OIsxPrs+j6vcVii8Z2+NeNflrtkK8hBeTA7ZVY6/zFqAz960B3f+RjvyZHleqRaOL7sMQySNdjZZNjMgSmGjFK1nBEA2GZkOeW+mZ4+ETGrG0HFqOj700EP4yle+kk3T31ZzMQHYttquLTdYY29DW2745oA2ewVMALaxHWC4oZzHRMrLuummmwSQknK6CLJIlqE0kgfQK8ZkbUnrSx6SKC/P03DmjfGk/8033xS0xUpxVu8f/zECTzyRclIvd78DX7n9i4YmXu2fgassvTdC2Wjx8mJaqnVlnTbXEIaqE3ljdWECnSVM5DngKUowQqpZz+gJw2yGuyeM5WXlx6LYn7+AYLEDfSEjzIRxUDNrMWKkDtBZZUUsFgdJMJjfpYeMg2Qab4ys18tSW7O60iLQU0VP1msGyTT2N5bhLZkul73Qgt0NpUJ/TCv/rKvWgb5Jde+cJTcHv/f2Dnz6ht0otZ7LZ0x3kfK3x1BcsoWmIjxI185W/D6bGRBJ0U5WWOa5UpQ4m4zyJJI2ozKKQZonD9Ouv/56fP3rX8cnP/nJbJr+tpqLCcC21XZtucGaAGzLbcn2GpAJwDa2X0oAJoUQ8uFKZispp4vhKNQAUxrDCPmQppYYT0UJ4A4dOiQY3ZTGk35S1zO8kYQcBG7K/InxAwcQOXMm5aSeO/w+fPPajxmaeMd0PwYMCiMzxG/Oqg2atAbQMu9GyUIIvpxCjJfrYyjsmupDr0Fq+H2jx0TeWDqrt+WjodKGvpk5NJcX4/hEMF2VpO+rHQVwBZNDVVM1wPyunoZSRFeiODVlrK8d1RxnMpmGsi96r2pKigRYIqg72FyqyYCoNU6JAZGEH/uanMIzF0yj5cU6v1Yh4Hhndw0eun0/OqqNXysSSOGhBb0p2WTZzIA4PDyMs2fPCrIisgVmk/EeTnINHo5p5XY9++yzuPvuu/GjH/0It956azZNf1vNxQRg22q7ttxgTQC25bZkew3IBGAb2y8lAONLBU9ApRyuVDld7JnkHHxIk0iD4Ys8GeaDW42WmSfG/J5hh7/61a9ECIs8yTsyMIDxPdrsfGKmeXn4h/c9gB90nCMJ0bMCCcHiNG0rGqLg8HilPs2rosgi2mcGsZKbh4GajnUEIenGWOebxKSzPl2xpO8ToY67VOvQK7SnoRTLkRjOTIcgEcGLvKwR/SQSbHxXrR2np1KDIpajl6ynoQRT/kUsLK/AG9YP2qRJOApzEZRRxcsnV+fIR02ZDcfG/ZAz23dUWjGgYEBMt5AMW8zLzcXo7BzcIX3jPNTixBtD52jr26oceOi9+/CuXcZy9+Rjk8R8SVpDAfRssmxmQJSEs7ORXIR5wIxmkBMxKa/LJ554Ao888og4cJPyf7Pp2t0uczEB2HbZqa05ThOAbc192TajMgHYxraKTIbMy5JMItxgDhdPdunhIi29Wk4X60isifye4YgMpZJYDpUjk8IbyaZI6mLmgjkc50gkAn/7t/D+0R8lVcupqEB+WxtyiooQ8/uxMjCAL994P17tOkeTr2cF0hFjqLWxc6IXvQ3dms3nRlfQ4RqCJbaCweo2LOUXocY/jZky4y/SpH5nfSPWUbiCgaVkZsIqmwWtFXb0u8PwzUfWNXeopRRvjBgjuTjUnLpOua0AHZW2hBdpFTx119jFv41YuTUfsyqgrbGsEJbYMkaC8TUgea7dOIotOSnZDpVj2N/kxMJyBL1GvXNVNpydCaKkOB+fun4XPvSOTuTnGWOtVI6FoV488OABBhlCs8mymQGR3nwSCaUCKdt1L1955RUR1ZCK3fGBBx7A008/LXKD5ffw7Trn7TpuE4Bt153bGuM2AdjW2IdtOwoTgG1s65QAbGxsDHxxYmgNGQsJwLRyutizxJrI/BXmBSi9WvLRSd40hh7yhJVeNnmIy9Rtt2FldBS5DF+MxRCdmEB0bGzdBD/z+4+jzyAz4Z7xUzipJMZIs3T7A6M4VprQwZJbk2cUpQtBIZKsZFXsnFaneE/VVem8H36rNnujVt2SwhwEl2Ig10OHMx+LixGMh6ECUs61sKtOnzdL3ufh5jL8WsVrRhp3pzVf5HdFosliywnQZszT1l1rxxkZKOoQ+mD5glxDS8o5wYCojxxkd10JlqIxjHvnsRxZSfKipf8VxWEvyMVtB5rxuZv3gGQd58PoFZ6dnV0nWn4+2t7sNrKVAZHrSrIhq9Uqwq2zyZiTKOk4Muxcyz7wgQ+A+8uIBh7QmbY5K2ACsM1Z92zp1QRg2bKTmzQPE4BtbOFJskFKZckmJydx7Ngx4cWiyKgaU6G8R4YdMteDoYQMX1R6teRlpfBGgq66ujrs27dv7etYIIDRzk7EQ+lD3X73vn9MSTevtiIMDxysaTe0WHINsKqlAGpnRuEqqcZMCjKPTEIdW9wjhtkMC3Lp+QGqCoGZBSC03tmlOtfy4lx4F4yJHO+pc+DkpOTNiqOnrgTReDxlWOLhljL8WkFBn27xD63W2VHjEGLMBHbprIe09eOpgV57lR1F+Xk4NZlor63ShkGDIYtXd1fjCzfvwc5640A51RzobSD1vJbXON38t+r32cyAmM0U9FJOIuVBOjo6VC8v7i2lRJgjfOTIEVMDbBN/hCYA28TFz4KuTQCWBZu4mVMwAdjGVl8JwHiiyYcqRWEJxtSYCuU9Hj9+HKQtJl0xARsJNrQStxluRc0jmlKoee655+D+/d9PO5nlPAtuf+D7hgWLq4JuuEvWE4Ok6pAAjDZX5NANkDIJddybF8axqL7wM54172lwwFFgwa+GvIa8OJacOOio0vImaa1FZXEuAotRdFcVwzu/gslgaip2ttNT79AFoOR9Xr2jEq7QIk4bCA28nLT1GgyIJOuotBfh2LgvScvrsmYnjgzro7pvKrfhwdt6cEOPsfy8tBcyAHqfKU5OHT1JyFxPve1QJpsZELOZgt7v94OyIxRZpsaZmhGAkZCJ4ZfPP//8drgcs3aMJgDL2q29KBMzAdhFWebs7cQEYBvbWyUAowgnQ0sIkBgySGCVKsxGCitU82opR8akfJanKYWaXXffjfD3vpd2MpNltbj7D/4hbTl5gZx4DJZ4DJFcS9p6FCZmXlc8NxfhQhsmdLIYSg3vmjiD0w070/YjL0Bv0etp8rKq7AVgyB+1uNxzy8hEGLnJWYQx34KhsdlyY6izAVNhILyiv2plcQ488/o8bbvqHAIY5iFumDVRaI0paOspyNxSacPRUZ8q9b3EgJhqNtYCC+69rgt3vbMTBZbkPDv9q5C6pM/nEyG8u3btUmUYPV/9bEY72cyAmM0U9FNTU4JYgyHlFFpWMzLZ1tfX47777sNTTz21GZeX2efqCpgAzLwUNrICJgDbyOqZdalhZfRA31w12QownIYgTDImVf/nf/4nWlpaQMDEk/lUQqP0aNGzRWNIIR/MWkZPGT1mxcXFSaKz8WgUo83NiM2m90q81bQXD975F4b20Dnnhc9erlknJxYVIsnFkUUMVbVhvtAqyhYvzWNh9f/1dtjiGcVI5fq8sVT1DzSV4s2x9eF2vDnuqXcIj+KpyZAI+5Ps8ubStKBN2ee+hhIc0xHWx3pN5UWoshXCF17GkGe9YHGq+QhPW0yNMCO5VnNJLlbiOZgIJYBaWWEO/Iv6QJvUkpwBkXpj3XWlOD7uS6lZxlywkxPqRCTU6X7/oWZ8/uY9qHIYI0XRe41I5ShG3tvbiyuvvFKQ12STZTMDYjZT0JOESSJIYo6bmklh6Y899hgefPDBbLpst91cTAC27bZsSw3YBGBbaju232BMALaxPVMCMIYRMsG8vLwc9IYxzCQVO5s8rJDhh8xn0TK+cPLhTeFSuejs4quvYurd79Y1kRf3XIvHb/2crrJSoRb3MEaqWtfVafBOoCLsxYSzAV4FQLMvBDFXbPyluDQvhkDUWFL6jhq70OiSjGyAJKAY9S5gRoMi/VBTKd4YNcZmqIeCfnedA7wpSzlfArSNp8/Fki9uS3kxRma1QVtnRQHml2OYCJ0D/kV5cSyuGDxLicdRmBcXQuLd1TYMzi4ivJwewFXa8lWp5w+2luOP37sPexudhq6vTAuT7IYeB/5u1GQbMm13K9TLZgZEiYJeKSK/FdZ9o2PQM7ef/OQnuOOOO/Dd734XH/zgBzfapVl/AytgArANLJ5ZVTzrTTNXIOMVMAFYxksnKioB2NLSEl566SUBpMhudfXVV6dMspbCCnlayrKp7MyZM+DpMQk7yJYomffhhxH46ldTTyQnB5b2dvyfQ7+Jb7ek7kfZkDwskN6wJu8EZu3lmEwRXtg4O4bxCn0aYFJ/1MFaXDlH6a93ZypsBfCEl7G7zg5Lbi5OTYVUQ+fk7e2sseHM9DnQpqcvwUyoAtosucC+hlLMhpcxMpvMKJgg0zDGZnigsRRvjSXX4Y1+X1MZ/PPLIoxSaZ3VdvTPGKOtLy2Io6IQcM/HdJOQWPNzEF5KBmkUmv70tR14z4EmwfzJP608Rj3rrLcMtfAIHsk4mm2WzQyIenSytut+Mv83FAolRSgo5/Ktb30L999/P0ggQ9Il0zZvBUwAtnlrnw09mwAsG3ZxE+dgArCNLT41wEgGIBkB2Ysvvij+SXKAdCKbkm4YWQ3379+fcjBM7iblNhO8m5vPhemNHziAyJkzSXVzSksF4Mq12xELhYT+FxkS/+bGe/Hj/TcbmvT+4bewYinAYqkTw7ZqxHLT5/R0T/ait15bA0xtAM3lxcJrZcTKrRaQpW/ct4CpoD5BYLZfRS/OXHoyDPlYhKDy9DmWyZJiC7qrHRhwz8EbVm/rYHMZjhikkxeetlUGRFLk72ssE+Bu1KtNF5/ox6tz6eI40OQUws+/GnDrrJMo1mDPwXgwAcAKcoHrWwtwfUs+CvKSH0VkeCMQKygoWANlav+Wf2aEjpu/O+rmUXw5Fd23ocltkcLZzIDIJaY0B6MCso2CnnNj+Dmv/SuuuELzanr00Ufx+OOPY3x8XJOoY4tcilk/DBOAZf0WX9AJmgDsgi5v9jduArCN7bESgPHl6YUXXhCNkgmxpqYmZQcMNaJ22I4dOzRpi9kA2+ULJ8EeSQeYY0aLDAxgfM+eBNha7Ss6NYXoyAgrrev7T+54BK+3H0476bxoBB0zQ8iLx5AfjeB48960deQFDuTN4a2o3VCdvfUOHJ9MT6PPRnfW2gW5Q2AhouoRStUxwUJkJWaYzbDKngBtDWVFqC0pwsmJQFqPXXe1Hb0z+uYkjZk5bcfHfMLjNRNcwoQ/PSgVbIZD6XMAmb+1GIli0D0HvXXka3moxYlfD83i1n31+PS1naiw5olrkn/Ly8tr/6/273TppgwjlDxo6YAb+3rzzTfF7yZVjqWhC3CLFM5mBkSJgp4sgLyPZZNJ9+iqqqokiRDlHO+55x784Ac/EKy3BGsXyp577jm8/PLLoNQJ9fLomfvQhz6Ef/qnf7pQXW67dk0Atu22bEsN2ARgW2o7tt9gTAC2sT1TAjC2RgDGhzFzHPhCmcpee+01kM0tHQEHH56vvvqqaKqrqwvUmaEFnn4avj/5E8SD+sLPPn7X1zBSlQBvasZ8L8diGCOVTQit5nB1T/Whr67L0EKJ0Ls0zITKBtPVKS22YEe1HZOBRUz4F0V1amqdMEC7zjpNZcUY8+kTH5bGWGjJEfpXDDdkfpde6hpnsQW+eZ0iY4Bo/zfay3HWNYfpQGKOekyA1xQEIZ1VduTn5SRR1BvzmiVG8d4Djfjgla042KrO8KY1Vv4e+PKtB6jJy/D3lcoY6iiBNSVo0/K48aX3YoRI6tk3tTLZzIDI+xhDR3kPkw6RMl2nrVaPhwIEPDwQ4MGAmvF3cNNNN4ncRZJ1XMjr8MCBAwJ42e12wRLKEHYTgCXvignAttqvaHuNxwRg22u/ttxoTQC2sS3hA5UPXskkDxhf8q6//vqUjbPsz372M/FiyjAqPiS1TApV5PcU+JQe8FO33ILFl17SPYn3f/a7mC9M1syq8U+jJujGdGkNXKXV69pq9E4YppPf21CC4xP6QKHUoRYA66qxw1qQh5OTISxHk1/IDzeX4dcGyTQSYEXf2AiIOJe83BzDuVz2wjzMLerjnic42t9YhjFfGMGFCOZ1kGHIN6qupABTKoCtsgioryjFsfH1hCPtlVbhCdNjVY5CPHDTbrz/YNMFfWlUjkUCbUrgRo09Mo6SkEZehuXkrKRqc+NLr+Rp0wJpap9fyJdl+TizmQFxZmZGCNUTHNBTlE1Gennm7pH5luHnWgCMIeTM42Wu8IW8ptg+nymdnZ0CGJKsxgRgJgDLpt/cZs/FBGCbvQPbvH8TgG1sA5UATKKhJwkHH3ipjKKdPA2mpaOrZ+I6y/PlkifHDN+JBQIYIWiT5aCl6i9cYMVv3Z/QCnOEA2jxjgkvVzra9+L4ChZzjIXKtFRY1xFSpFtpOWhzFOahu9aB6eBSSu2tdF4ztT4PN5em9c6VFOWhu8aBodkwPHPLyITNsKPKigFXagp6etb2NpZi2JPop9JeoMowmGrtGFK5Eo0miUqTGKMkdwWDgeTPz7UTFzlgDEdM2bYlF3dd1YFPXNMFW6GxayDdfm/ke+ZDMlSPLKNKk7zSat42rc/keZxa45KDNr3AzUhem9RvNjMgSjTtb3/721Oyw27k2tisunrAJe/f1Ae788478cwzz1y0oVKw3ARg65fb9IBdtEswKzsyAVhWbuvFm5QJwDa21koAJtHKK7W61HphCAr/aKlywHjC/+///u+orKwERUx5qkmP2dxzz8H9+7+vewLD5U34m9s/j8hKFIPVbYjmpX+htlpysGCU3hyA8P4o2PLSDZRCyfQE2QstODkVwpIORsSe/5+97wCzqrraXtN7pQzMDDOUmaH3pjQRKQnmswSiqPljEBORRBGN8mE+xDxfQoghmIYkyB/9Y0kkCTF8HwYbIoiV3jtIHYrAMAxFyvzPu2GPZ+6ceu+5956z71rPMw/D3HN2WWufc/e711rvKsymjYfsebNk/2YArHlOisjxgrftnAacXCXGcMZm2B31yQy8c2lJ8YSx7zpeU4/Ao32zLMfFlEWB6eNXPVlZqYnUrlkWrd9/ylR/yGGrrDIPwxzWsTlNHtmRivPre0yt7Bjuz/HM4XQfpR7gSXFD0KbMZTMDaYF5blZ5bZKMxAq8acMnV61aJcaiIkOeBJcqUtBLzyVYORH2pycg3gCD7ZQpU2j69OluLF1bbTAA01cTAzBby4cvMtAAAzBeGiFpgAFYSOoTN4N6XgpCUJDThQ2VlQcM+V9IxMamLpBaXjsqMB/ixB+hKyg8i7ArMCYeHTuWav5y1aNlRz5r1YP+a/Q0O5fWXVOQEU9Ha5xRw8N7Ve0AfGUmJ1Db5lkCiOw+7iw3q0Ue8rmsSSq0k+7YLFMAPK1UNM2g1KQE2nioqp4nSV7To0UOrXYY6qgH2jKSE6hDYTbtOFJNp841zA3rWZJHK22zGV4dHUg7th2uok5FubTlUBWduWAd9tipKIc2HtAHlO2aZ9OUb3Smvq0bO1orkbr47NmzIh8SeZAIx42WAHzBo+EUuFnltWE+8JyBKdAucAOBSTjD2dzSMd5jeF8OGDDArSY90w5yrECohPe+EbnGRx99JELT58yZQ+PHj4/Y2BmA6auaAVjElqCSHTEAU9KskZsUA7DQdS0BGDZj8FQh/BC/m+WAyWtBP498FtDKA2DpCUAXQndQJwwhizk5OdSjWzfaV1JCV76wZr6Lb9qUUvr2pUXdvka/OG+cZ6bXd2km0T57aUJ1t7dslEZ7v7AGRWVN0ik7LVl4fJIT4qnKZr6UdpzB1A4rzE4RRB7xVEsts+MoLiWddh0zDxVsV5BJWzUU9HZWzdV6XldzrwBKAWy2VZ6m0ybz7Omwbhhy1AaWNaF1+08YUuHrjbV3y3z6bM/xeh/lZyTTw8Pa0x29Syke/PceFRnqhUMIHEb4SQDaAMACPWnS64awSrwP4EHHAAR6xQAAIABJREFUJl6CO3jBzUSb12aHjATXRIOMBLlIWVlZ9QrJ+8l+ZmMF2yDCxAcPHmx42fz582ns2LG0aNEiGjlyZMSmzgCMAVjEFlsMdeTdb8kYMoKfp8oALHTrYTOFjRXCA1GIMy8vT3wRDx8+3PBUGptI0GiD/XDDhg0EIIbf9QS1ZbARu+GGG0QyNTZnXS5epMM33dTw8sRESu7cmZL79qWUPn0E8Eps2VJc9+t3d9Ifl+91NOE2WbW0u9rZa6ZzYTZtMAgLTE+Kp/bNs+iLmvr08a0bZ4hwPCeSn55EJxwwDKJtlKuCx628IJN2HD5JVTZLgTXOSBI5Wk6kVaN0+qLmgsglA8isseGZgm422wqprKXuLfKosuocNc1KoXUBhZutxqllQETY5z3Xt6Yf3NSWslLNWTut2o3E5wjbxYEEvCh4FlQSIwZEmddmBNz0vHBWZCTQmxUZiR6YCyavDX1hPAgdBUEFcl5VE5nPe9111xlObdasWTR16lTxzo9k/ToGYAzAVHvevDAfZzsjL4yYx+ApDTAAC90cEoBt3ryZ9u3bJ4prHjx4kIYNG0YIDdITee2QIUNo+fLlIp8FdcMCBW2j/pfM+0LoFTZAbf/3f6nqV78ieLeSrwEtAK7kHj0oPj1dt8/JCzbSwvWVjiZcll1Lu047e83oMROCcS8vPVkUMtZj+OtanE1rDzjL5ULY4HYLkgvtZAuykqmsSYbwStU4YBlEvtY5B9ejz7z0JML4QA3vhNGwSWYyHa02LyiN3DGEGYK4A1KSn0r7vnAWuikZEG9oW0D/eXMnatXEWc02R4vI5YtxcCE9DX4Iu3MyfTcZEAHaZIikXeCG653mtVnVbAPIw3tQUtAjB0pbSN6Jfrx8LcAlDt/M8hInTZpEc+fOFQye8ARGShiAMQCL1FqLpX6c7YxiSTM8V1saYABmS02mF+H0GZudZcuWiY0G6JVBxoFcAIQj6gmuRQgQ2MDw5Yh8j969eze4FPViUMsFX+rNmjUTIYjYJPWsraWE4mKKb9FC9A1QZrUZvffFVfSpQyKJ1tlEe5zhIpIADOGBHQuz6eRZ69wusBl+5rBumCC52F9laUCALuRebTx4mto2ywyS5MKed65RRrKoF3bw1Fk6bKOAsnbwAuhdvGxYYww10BAZuE0TCon/w6t3MYCe30wpcVRL7ZtnC1r5gRX+CuHDvPDs4Hnp2bOnpe39dkG0GRAD89qsimvL0Ekr0Ib3E96NuB7AIz09va5+m1Hxbb/ktWGNSe8egCUAppGMHj1aUNUjWiJYT2Iwa5oBGAOwYNYN32OuAQZgvEJC0gADsJDUJ27GpuLMmTNiYwgyDWwotm/fLiiysVEMFJAIyGvxZf3BBx8IMKYXurJx40YCcxY8ZThpRhI7iDuQZwDghdwQbH6MPG3avkf8ZgXtc0hYUZKdQPtPm+efBM6vX+t8+vLSFdpypJpqbJJxICRuVTAkFwagDSCjS1EOnf3yEu3QeMl6lubQKodAr2tRDq3TqaOlnTfCAEvy02n9gSpRq+xqzpgz5NqycQbt0anLVZKfRjlpybRBZwxFuWl08KQ9cIjx5qQl0UM3VdCYvi0pMSE+9MUf4RZksVurjW6Eh+Vad9ic+40BUVtkW4ZC6gE3eH3OnTsn3mN4b9nNa7PjYZPXRCOvDca3U2AaesI7HmNEqLrVgZlri4pIHPIxDX1DjTIJh5urLPbaYgAWezZ3dcYMwEJXJzYde/fuJYQVwosFgITf4d3Kzs5u0AHCFOW1qAkDZixsRgKZwfCFDaCGzQWojSEIvzpx4gSBxlmGGOGL3Oo0FW11++l7DQoZW80+Py2BTp6zBmCpiXHUoXm2IJi4fKWW9jgMievQPKsBM6HV2PQ8YPAidWyeRQdPndctTCyYCT93RidvRkHfLDuFivLSBPC6eLm2bsg9SwD0nPXTVUPagYZQy6s4L53W7jupy8yIawAy1xuwGWr1h0LSd/YppYeGthWhoH4VMIJi89qxY0cqLCz06zR0x41nFBtlhCODYEQ1gXcPHn0cJuF9FVhA207dNqu8NrwLAXDsgDZZyw3XW70/rWxx7NgxAgkH8ngLCgoM7YtQchzMLVy40KpJVz9nAKavTgZgri6zmGuMAVjMmdzdCTMAC12f2BTAM4XNIYARNhlIsu7Tp4/YTAUKQBSS7WUtHNwLrxhINrQCIIf8MNBtV1RUiI/Wr18v2gfBh/SA2Qk/PH7mAg2cudzRZMESiA3Nla9wRYP74Z2B9wcMgbLuV1ZKIlXbIJzQNlaYmypAkxOpaJpJ249epWhE7hTqYW05jHEY07B3LsqiDQedeab0KOgxXtTSAvC6pKMgEYbpkE6+V2kefbb3hPBSIdxw/YFTwpNoJr1b5tFne8yZMPuVNaYpN3ei8oLI5Zw4saOTa3HQsWPHDnEgYVRryUl7XroWDIh43uFFLysr89LQXBmLGxT08tDJbmik9MhZTUDWa7PDICmBmxa0gX4eNPR9+/bVPXRD/1VVVeLQYMKECTR79myrIYX8+euvv074gVRWVtKbb74pvktk8XLUlZw5c2bI/fi5AQZgfrZe9MfOACz6NvD1CBiAhW4+bAbeeustAbaQlyIZDnv06NGAJhsbCJBqIFlb5rDgRB+1wwDItBLoKcNnOEXGlz0IPiSltR0Ahvynbz3/qaPJ5iUTndIh/ktOiBO5XQgvlABINgyGwTMOCStwb1JCvHPvXEYS5aYmUXZaosjv0gNCgRMWhBUnrCnytfcJso8jV4Ee6o41zkym9QdO0+VaY2TaqTCLNh60zk/T9tOzNI8QOrn5YJVtkpAeJTm02sDTVtoogyaP7EBD2jdzZHcvX4yDDeTPIJwqVK+F1+ZpxIDotXEGO55oUdDLvDY7RCRaL5xVXhvCvmX+Gu4DgAYBE/J+JUjD4RyIVVAuQRLHzJgxgyZPnhysGm3f9/TTT9NPfvITw+tLS0tF5EYsCwOwWLZ+6HNnABa6DmO6BQZgoZsfgAvkGO3btyd8qcnCyQhHCQyTAtBCAWbQMLe8Rg8PrxZOKOHV0kqgpwyfyZpgcgNqN//rrc1HaeL89Y4m2zInkT6v+sqbVAyvT06qACNGtaxK89Poc4cAp3FGMh2rsU/xjpde56JsunDpMm2rdFKkrJaCqRuWn55I8OrlpicLVkMzj6BUcGFOCh2yScKBWl7dWuTRqZoLtOOaR8+uodo0Rg2z+jpITSD6Tp9C+uHXu1MyGldIUJIBG194GlQTNxkQvaYbv1HQa/Pa9IBbYLgkohX0CmyjZMKPfvSjOnPg0CA3N1ew2iL8HD/wROHfJ554wtB75jV7qjIeBmCqWDI682AAFh29K9MrA7DQTQmvFL5oJekGQk2Q14U8FdS80QrCp3bt2iXyvWQIlfRqAYDJU33pKcOXda9eveqaQD+yL5yy2sn/ws1//ngf/XzxdkeT7VSQRtuOnSPQnp+/eIW2XvMCmTXSuTCLNhyqdtQPQgm32QAeyDPrWJhDlafPCzbA/U6BXmYyIRTTibRpnEYZyUm04VCVITthYHsC89TWWnrk8PLu1iKXDp86T5Wnz1FKQhydtwg5rN9XLaGumqS5h06Gt82nQY1qaOjA65TbzCFnCN5jeBmMipY7sa3Xro02A2I49QECDhw8qUpBD/IUgEwcDGiJSFBU+4033hCHcnj3IwwT4eR4v8Pjib9DNxB4yHJycsJpBm47QAMMwHhJhKIBBmChaI/vRRibSYYPK8iOBpDgjFNSmcMFRkQwG2KzgXwOrcBThlAVXCtZsKRXCyGIAFXyyxjXaj1l+DsK0OJ65MCkpqYKb4AdNq1n3txOL3y0z850xDX5ybXUpSSf1h08Q6fOXbR9X88g2AxBprHahE4eBZfbNMmgbRrPmwB6DnO52hZcbcOOgLo+NSlBFE/e47BAdFEO8tnM63J1Ksqm6nOX6PNrZCXIozty2lloZNPsFDpadfWeXi3z6clvdKJLxz8nEAKoGKKHgw1sdPFMBB5s2LGp16/xIwOiXZ3Cw4/wUdQ6hMdHNbETXjlt2jSRcwVWWxwiSMF3B4iVQN5h512umu6iOR8GYNHUvv/7ZgDmfxtGdQYMwEJTP04ycbKLujbYGEIAsADK2rRpQ+Xl5XUd4GT03XffFV++nTt3rvu79GoBlKWlpYm/y7/179+/XsFOmRcGgg940OzQz6O9SfPX0+LNR00nmxhHBGBw8vQZ2n/6CiG/aNU+Z3lMqOe10iHNu1ENsJb5aZSXkUwbD52uxzAoAEdJjuN+RL6UBdV9RUEmgTEQZB4QFIheZ6PWmFax8BhuPHhKV9cVTa8SYWw/Ut9L2DGInDFRY63mAj3x9Q70tc5XGQEB/EEkgPWhmkiiAzCNwjOskkgGRKtCvn6dM+oiwvOP9xnelSqJ9MwirBBh6EYybtw4WrBggWDJBekHS/Q1wAAs+jbw8wgYgPnZeh4YOwOw0I0AEAZwJQWhKO+8847IB9N+IeMUGFTFoJhu3rx53fVIhAaDljYsEaAOzIio96U9FUVIC3LGQPCBzZpdIoIx8z6jdQf0wVQzUcMqjXYdq6ETZ7+aR/tmWbRFU/TXjqa6FGXTeoeeqUAPGAgsUFfYrO9gAJgZBT3mik1wYJilGQW9kT4ECN17ot7HpfnplJWaZEjMIUBowD1m+k5PTqCJQytoTJ9SSklKEJeqXiMLpRsOHjwovHuqbWBVZ0BEPUO8/yQFvZ13iV+uAaBCbiKYKwMjHuQc8G4ZMWKEYLDF4Rp7urxhXQZg3rCDX0fBAMyvlvPIuBmAhW6IQACGL1tQ/uJEtFOnTnUdyFwvWVRZfoCTfXyGIp042QeAg6cMIA1EHlqRDIv4O5i17H6R3/Cr5XS0+qv8p4Q4EkyGV67U0ubD1aQXh1oUBDV8q8bptOe4efhdoMbbFmTS7uM11LkoR4xxv41i0Z2aZwnPmBPpVpxNawNAKGqGoX5XIJujbFePgt6qT20NsIKsFCrMTaN1+0+ZkneIQtQ2aOvj4ohu6VpEj45oRwXZqfWGImsRYc1pAb7VeP3yOQ4l8GzAi6KaqM6AqHJ4paxNZ/bc4TsBeYsAaO+9957t97Zq69xr82EA5jWL+Gs8DMD8ZS/PjZYBWOgmCQRgaPHtt9+mJk2aULdu3UQHekWVZc84FV23bp0o4gw2LNBsg5oeYYraXAFcj43aypUrBcEHNtl2ANjFy1eo20+XCACAXCOE9gEkHbdgHkxJjKcLjkghiLJTEw0ZEvU0nZeeRPA+baqsplMa75uVVcDIeMAGUNO206pRWl2BaLAogrwCXj8zqWiSYQjOjO5rV5BBR6rOU5ummQJ4aQs0G93TtlkmbT1sDii7tsilJ2/uQF1b5Ok2gxAvhHqpGOaFZwwbVzxTgYcSVmvFD5+rzIAI/SMkGwQTyAFTTeCVhXfWLDQWBwd4t48ZM4Zeeukl1VTg2/kwAPOt6TwxcAZgnjCDfwfBACx02wFcIfxLK9gsZmVl1TEY6hVVltdLwIXNCRKxt2zZImrHIPwQRBtakTT2+DtyKbSFQ41+P1L9JT0iKOjjaPPh07Zo1AGMTjoARBijYOS7aF44WM5F1NPKSqath6sF858davc6PdTWUjDgMCMpjhqnXKErCcm0v8oe7X1uWqIjYJieHE9di3IE8JLshHZWWH5GIn1xRn9M8HQ9NqIt/UfXIlPADdAORjUtwYudvv1wDYhtwCxqFublh3kYjVFlBkSEZwOAlZSUCGIi1QQhhSBHAgtu4PtazhXEG5j7lClTaPr06aqpwLfzYQDmW9N5YuAMwDxhBv8OggFY6LbTA2DLly8X4EjWKwKgArACOQIKNmsFDFgI0ZF1w3AvPFvICQsUbGbAJnbu3DmRdwbgp1d/Rnvf7uo4+o2zEmDUpnEG7XLI/oc8Mqsix/B2IYxu0zWSi+bZKXT4tDNq+EYZyfSFAzp5vCS7l+TQ4ZNn6HD1V3XNrCyfmZJAZ87buz4pIY66FufQgRNnqbLqvFXT9T7PQPHqCw2ZJlOT4um+Aa3p/kFtKD3ZPGkfaxBMbNnZ2SI/UDWBlxh5RKqy6Kkcoqc6e6XMbwOLrVFEAg4Phg4dSnPmzKHx48er9nj6dj4MwHxrOk8MnAGYJ8zg30EwAAvddnoADEnZ+LvMV4F3ArkC+JIOJM6QdcOQI4C8LpwWBxJ4yFGCcQs/aEN+2eP/2tozgb+/t+s0/e4zZ/lSLTOJ9tpjbK9ToGD/08nLSoqPE+yKX9R82aBIczBEHxVNM0QxaCtBXSyAomNnvhQes8CCxVb3Xy1ybB6iGEe1opYXii4fOX2BWjbKoL3Hrcem7RsU+zuP1mdF/Hrn5vSjEe2oKM8eYxwIW1asWEGtW7cW7Juqyfbt24VXeNCgQZSSkqLU9FRnQJTgGQcDCMNTTVDb68KFC7oHZnKu8+fPp7Fjx9KiRYto5MiRqqnAt/NhAOZb03li4AzAPGEG/w6CAZg7tsMXsFZwog0vFcLB4KECqQY8Xz179mzQoQxPRIgK6oDhRBXXId9FK9ioAWyhPS0As5rB88v30rPv7rS6rN7n7Rsn0Zbj9ut/4eY22US7NDgvI4moNDeZDpy+RFUX9EMTBWGFQ6r77sU5tGa/Ps07xoFCyF2Kc+hw1QU6fM0b1a04h9YeML5HTzniHpN+wPiIvLV9J74iHenWIofWWlDdB/aFe9bsOyn+3KEwm568uaOo6+VE5CYXOYeB68ZJO169dtWqVYQwRFlrz6vjDGZcqjMgytxEePRlmY1g9OTVexCxgHn16tXLcIizZs2iqVOniugFLTGTV+cUK+NiABYrlg7PPBmAhUevMdMqAzB3TI1QQG1Na3i8kK8Fj5cMMQQlPTxbgaKtGwZPBuiacV8g1TaAFwAY+rFb/wt9/feirfSXzw44mmgw9bwkaGucFke5KUR7T9eSVUpYWQ7RTmelxqh3SQ59plNrDMCra3EuHbjmjdJOuHtxFq054MwLaERBD9ZGsEfuONrQ09W7NM8RnTzG2LtlHu0+doYeGVZB3+zRguLhunMoKM6NGnEAKAh9VUlUD69UnQHRToieX9cr3slLliwRhEggRjKSSZMm0dy5c0WOJnKDWbyhAQZg3rCDX0fh/JvarzPlcYdFAwzA3FFrIABDrS4AqeHDh9OOHTtEEVIkaWdkZDToUNYNQ5I67kGBZb1Cuviyx7UIPbRb/wudTXh1LS3dftzRRIOp5zWovJEIM9x0SJ/WXm8AFY2SaPsXzjxtrTJraY8mYg8FpCsaJ9PhM5fp5LnLuvPs0DSVNh8950gHqE+2RuPNatUonVB/a5MJ/b1TDxhyxx66qZzu6lNCmalJjsanvRgeV6xBvbzBoBv1yI3SQ9SyZct6hc09MryQh6E6AyLWJt5b/fr1C1lXXmsAUQ4ofm4V+jt69GiR5wvCJSfvbq/NV7XxMABTzaKRnQ8DsMjqW7neGIC5Y9JAACZrfgGAoX4RQhSN2Olk3TDkf+ELury8vEEeD66RHjAn4YeY3e1zPqZtNnKmtJoA2NjzhXU9L9QT61ycQ6fOXaR4inNM3FGG/CeLPKtAC7XISqD9py9RUjxRy+x4qqy5QtUWGK55ei0dtp5Ova7Km6TTjqM11DwnhZplpYoQxlq9gmmau+zkjcnLb2rflB7/WjsqbdQQlDtZlapTtMv6ZijL0KxZMyeq8cW1KjMgwgAqU9AjykGWBSksLNRdb3h3X3/99SJqAZERdkqH+GLhKjBIBmAKGDGKU2AAFkXlq9A1AzB3rAjiCy0bIULCJDUxcgQCizIH9oq6YaCVr66uFl/WqJmjlWDzv9DG9b94n6rOOfMy5aQlUtU5YwbArJQEatssq149sdy0JAHEnEgwdPfNs5OpODeNdhyrsU0Rn5lUS2ecDU1Q1uemxNOeqit02QJ4yTlnJMdTzQV9L5y8prwgk/7z6+2pX1ljJ6oyvBZhTQD5FRUVuiGurnQSxUZQ2wweZHhQ9DzIURyaK12rzICoOgW9zL1Ezm4gu61cHHh34/2PCIiFCxe6sma4EXc0wADMHT3GaisMwGLV8i7NmwGYO4oMBGDYMCL0EHlfoJ8HOYLZ6T3qhkkAN2TIkAanpMHmf6EWVa/p7zmaZGpivKjNpSfwBhXmpAka+XMXvwIaaYnxdM5h0Wan92QmJ1DHwizacrjaUbHnq/XJzEGRdq7piXFU1iiZth09TxfsIi8iykispRoTkJedkkDf7duMbu/ajNJSUwThCn6Q6xfKqfj+/ftp69atpoVgHS0Aj12MIuVgEL3xxhtD0pPHpiWGozoDouoU9PJwwKz4OXQA79iECRNo9uzZXlyGMTsmBmAxa3pXJs4AzBU1xm4jDMDcsX0gANu7d6/YFKOw8pEjRwSpBjbbRoIaTsgnwPWodRQokn7eaf7X7mM19I3ZHzmaJLxLILLQSnnTTEJdKtDM6xVNRmHl/Sed5VjZvScrNZHaFWQK4NUoI6kBlb3V5FrkoPCyda2x5Gu1vLZVVlPTrBTaqUOyYdZXaW4SfX6yYTFlcGoMLIyjr5fGU3pSw1c2bCrBGP7VFtQ2+r8WtCGEDSfxAChOyFms9OaVz5FjA+r53r17e2VIro1DdQZE1SnoN2/eTAcPHtQtLyIXCa7B2p0xYwZNnjzZtbXDDYWuAQZgoeswlltgABbL1ndh7gzAXFAikUgyB0iScuDAAUEnj800KIoRVmgmy5YtIzAggkmrRYsW9S6V4YdoHxtsJ96SFTu/oO+9vMbRJDs2zxIeLuR3oX5X9YXLlvWwOhVm0cZD9WtZWXVqVDdM3peblkjlTTJp8+HTVPPlVd0GQw5Snp9EO040BEayHwAk1PLa/8VZOnatwHMgAYfVXPB5z5JcWvX5VTp5KQPLG9PjX2tLpXmpdYWzzWq2yc/wr5lgDQCEYX0BuCMvEOBdAjk9EBeqp82ODty+Roaw4Zlo166d281HvT3VGRBVp6BHeQSUEUF9OiNZvHgxjRo1il599VW66667or7meABfaYABGK+GUDTAACwU7fG9CIGxmd3CyjLTQCAAA5vh2rVrxS0ojAtiDTNBCCKIOvBFjlwwrWjzv5x6OP6x+iBNXbjFkfFAQY9Fse/EOTpabe05qgMfDutf9SrJpZU69+SnJ1Gbxhm04VAVnQ/gsQ+GHr8iL562n9QPQQSgO1HzJR0I8N4ZUdCbKbJXaR6t3HtCXNKqcQZN/no7uqFtU0e6lxfD5lowBpIXPeCGNYMcMAAwbQ6iUad2PWxaj5wTwB/UZE1ukiQHKFJeVFTkdvNRb091BkTUvQKxkF5YddSV78IAUPwcz4oea61sft68eTRx4kTBlohQRRbvaIABmHds4ceRMADzo9U8NGYGYO4YIxCA4WQb7FiQvn37Ul5enmlH77zzjvCife1rX2twncz/wgdOKYx/994umvP+HluTLMhKphb56ZQQH0cf76nvybFqIBhgFHhPk8xkKs1Pow0HT9MFg3yyYPppnV1LuwNKgLVrlkmXLl0xZGAMxgPWuSibPj9eQw/eWEb3XFdKSQnxVmoL+XPUmMMpPAAK8kyMQBv+rgVx2v9bDULPq2YVJukWaENtMxDa4BnKzs62GqrvPledARHkMPDcq0hBj0MS1AADey0YOo1k2rRpNHPmTEKuJsg4WLyjAQZg3rGFH0fCAMyPVvPQmBmAuWMMbDIAoKTg5B6bDwCmoUOHmgInbIzxRY5N64gRIxoMSOZ/OaWfR0M/fn0T/XPtYdNJNkuvpZz0VNr5xZd0ubaWUMtqzX5n1ZG7FufQugPO7pHhhE0B/PLSaP2BKrpoQXphFbaoN9GijFo6WHP1E9DrpyXF0+bD5uGSZU3SaefRazfZWCIIY7xvQCsa278l5Wek2LjDnUvAtLlz504R4or6cU4Fm0isWyMPW6igzQq8aYGcHmhTPb9NZQZE1QlG4H1G6LhVfbpx48bRggULRKgiwoDDKQh9f+qppwhhjyCuQYHo2267jQACrQ4Bwzkur7bNAMyrlvHHuBiA+cNOnh0lAzB3TBMIwMB89dFHH4lNsVVxXCSqg+kNAgCm3YiGQj+P9u77f6vp4z1Xw+K0At8M8rtOnz1PewOIIyoKMh3XDWvTJMMyTyxwDN1bZFMcxQngdUmP2UPHNEW5qXTw1HlHRstOrqWM1BRqmp0i+rITdAvGwtPnjWn4tQPo2yqfpoxsL2j5Iy3RYAjUA21mHjbplbOKdtaGPcpQSdQAw/OAMF4tWMPv2Mw69QhH2j5m/akOUADeQS5UWloqSiSoJnYYHmFjvNPxjsdBiVueYT1dylINCPm89dZbRc4kAD7C29u2bUsIl2zUqJFqZghpPgzAQlJfzN/MACzml0BoCmAAFpr+5N2BAEyCqiZNmhBqxJgJyDpwcgmBt0x7Sio3u/jXaf4X2hv5uw9pr6agMrw/HZtnC5bDytP6+V1NslJs537JeTmp5wUQBZbBHUeq6YxFzSyt3vCyQ1jfl5f1KfL1dJyVdIWaZaCWV61tkJedlkinz1oXDSvOS6PHR7Sl4R2jVxwYJ/DIGezVq5c7CzlMrch1bAXUAj1uVqANz0pgXlsgUNN64bwE2lRnQDx16hR99tlnohSHiqF3YLddv369YK1t3Fi/ph/WL4iV4CUDEAonAAPQe+utt+i3v/0tPfTQQ3VP8qOPPkrPPvssPfDAA/SHP/whTE+4P5tlAOZPu3ll1AzAvGIJn46DAZg7hkOelpa5DrW/kGBvVYAZX9A4Jca/CGkBlTgot6WEkv+FNnr8dImo6SXyqxql09ZKc9Ajspbi4kQool1JSYizVS8LYYaNMpJp/cEqykhJpGqHRZsB2uySgohC0QWZtP/YSTpy1u5Mrl4nvHkmFPTpyQn0wKDW9N3+rSg5Mfx5Xkajlxt4qxAoZ7P3ztVsPXXGAAAgAElEQVSywDTmhzwbo3DIQFAXDGizIicJh6dNdQbEQ4cOEUJIzYoUe2e1OR8JSo2g1qNZ+C/Ce+F1GjNmDL300kvOO7F5B7xfZWVlAujhd+16ra6uFqGIeC7gHVOxmLlNNTW4jAFYsJrj+8RWidXAGghFAwzAQtHeV/cGArAPP/xQsNOBPhsnoEaCvIDly5dTfn4+gVBh4MCB9b4gQ8n/OlnzJX3nhVWEOlqo32UnzC8Y71dxbiodMAkLbNUojbJSkwS5hoR1rRul0+7j9nOsoD8Aqm1HzpgaLCUxjjoX5dD2I1eLNZdk1NI+81satGdEwBEXR3RbtyJ6ZFg5Nc1KdWfhhNAKNlMIQezSpYugoFdNUF8JNZScbOC1njY7dP8S1NkFbWbetsDPrECb6gyICLlDjiLeaamp0X9e3H4+UOcRxBpgeDSKTkBkA8L/pkyZQtOnT3d7CHXtgWnxe9/7Hn3/+9+nP/7xjw36kd4xkD2hJiXLVQ0wAOOVEIoGGICFoj2+l2noXVoDWgAmSTXQNE4eu3btatgLNmHwliFPAr+DLUyyvYWa/7Xl8Gka9cdPHc0QBZe3OyxALOuGBXYEKvn0lAQBvAKla1G2Y9KOHiW5tNqA6h41y0Ae8vmJs3T8zFc1v9pk19IuZ9wgpEdB370kl54c2Z46FeU40mc4L8bpO07hVd/gDh482LSIeag6ls9ZoCfNipjECWjT87AhhA1kPaAwB0DBNVagLdS5RvJ+hOchh09VCvo1a9YQ8sCwPo0EecAIK58zZw6NHz8+bOp//PHHBdMifh577LEG/fzwhz+k2bNn03PPPUcPPvhg2Mbht4YZgPnNYt4aLwMwb9nDd6NhD5g7JsNmDBs2iMz/Qr4JmKfMcsBWr14t2KqQMI1wHWzG4A2DyPDDYPO/3t16lB7663pHE+xWnENrHLIZigLEGmBU3jSDkhPiRTFnI+ldkkufBRQtthqoAEafnwq4rJbAwHj8zAVdco6yHKKdp+yHU6Lx7tDB/qv9NM9JpceGV9DNXQqthhfxz0E/f+bMGVE7Lpy5JRGf2LUOkT+EMEsATK+JEWgzy3HD+8EKtMGTYpTDZhQm6VXQ9vHHH4v5WhWh95pt7Y4H4ArP3XXXXWd4y/z582ns2LG0aNEiGjlypN2mHV8Hz9fzzz8vfu6///4G9//4xz8WHjj8wBvHclUDDMB4JYSiAQZgoWiP72UPmEtrQAvAUHwU+Q841U5LSzMs0gmABfp5gDTkiuFEFWANxB0SgCGHAF/ywWyyXvlkP/3s39sczRB1thqCHPMmJDBqW5BB8XHxtKXSnOIdrfUqyaGVDcCUeT8iNFBDj9++WaYg5Nh1zDiUsVVOAu05ZY/NUPbepnE6HTp1nsYNaCWo5dOSExzpMBIXY70hqR9gvVu3bpHoMqJ9qDi/QNCGOoHIx0H9NrP8NqsC2wBtVjlsgXXbgiH0cbIAJMMj1qdZBICTNr12rXz+zOY3a9Ysmjp1KuE7oVOnTmGbAgOw4FTLACw4vfFd1wA8K4I1EIoG2AMWiva+ulcCMLnxAPCSGyejIqSyVhi8X6Crx4YMX+YyYVp6wIKp/4WR/ertHfR/V3zuaIII89N6s+zcPKi8ER05fcEyP0vbVsfmmbTpkDVQ094jqe7bNEkX5BdbLGp54d6m6Ql0tMYZABvVvZB+MKSMmuek2Zl+VK6B5wsn8Ei8b9WqVVTGEM5Oz549K2izW7duLSjoVRO7DIh4n+A9YBQOaRQ2aRe0OQFuTkCbpKBXlSAGel+6dCmVlJSIHC8jmTRpEs2dO1eEKoazkDiHIAb3hmAAFpze+C4GYLwGXNAAAzAXlHitCbAYYmP8wQcfiI0xQgvxN4SI6QmS1PHTv39/AtkGQnZwSgpvWKj5X+jvR3/fQG9sPOJogh2aZ5mGDmob61SYRRcuXhHEGjtNvFB6AyjOAXHHOUdjqyjIoLSkBNu5Y3Gg7o+Ps0U+goGgyPOTI9tR95I8R+OKxsWSYa5Hjx5K1vaRFN84kAADomoSbgZEvE/sgjYJ4qxAGw6CzCj+tXT/ANDIAVOVgh7MgnhfA3wBhBnJ6NGjRS0uEOYEE8Vgd90zCYddTdW/jgFYcHrjuxiA8RpwQQMMwFxQ4rUmsOEB6xfYsZAXADpgMCGCWl5P8AV+7tw5kcQN4IYTf3jDcGocav4X+vv2//2MVmtC9uzMFLWt9p80B0ZdCrPpzJeXaPfxq/zu+elJdMJG3ay6/mtrRY6Y3XpejTOTqXXjDFr1+UlH9Pi5ybV0Sr/UWT1VgPlx0tByuq1boW9yqUDcAoa1cBNU2Fkz4bhGMuihiDm8yaqJFxkQAdqsmCMDQZ1T0GaHRdKJpy1a60IykJodEMj8N8wHub7hzNNkGvrgVgIDsOD0xncxAOM14IIGGIC5oEQNAANxAAqQgvkLcf/4oh42bFiDTpDb9e6774pwQ9CIA4ihHlh5ebkIuZL088Hmf6HDIbOWGxZbNpp1alICnbt4ucHHSDbtWpxNp85dqlfYOTkhji5erq2jl7ejTdQC++KMNTICfT6o58Gi2DwnpV6/dvppmR1Pe6sazkXeizDG715fSt8f1FrUJfOTALxj82sU3uqnueiNFfmQeI4AMMO5cY2WnkC4Ay+mGYV5tMbmpF8j0FZZWSnsh3zWwBBK3GMm8BTZAWpaj1uwYdpO5qq9dt++fbRt2zbq27evYWghABiiGUAis3DhwmC7sn0fF2K2raq6CxmAOdcZ3/GVBpiEg1dDSBpgABaS+urdDBCFOivYdHTv3p02btwovBT4YgzcRAKY4VQU4AtJ+Dh5BiBDPk9FRUUdAMPpaTAb0MtXaqnbfy9x5DEC4EHtLK2gzHDXFmAZ/FLXM1aUm6rLPmim1YqmGbTdpJ5XqqjllUtbKk/TmQtXN2tdirJFAWcn0qFJCm0+el73lmEdmtITI9pScV66kyY9cS02sCAAaNasWVgT+6M52WXLlgmCCjMG0WiOL9S+EZaGZx7hxyoKwg8RZgnvf+D7Swva7FL/2wVtToBbsO9W2Gv79u2ibIiZBxp5X3i3T5gwQVDAh1vgBcOBDL5bbr31VhH++cknn4h3Bb5TUJsSRaFZNBvoYL5cWYGsgWsaYADGSyEkDTAAC0l99W4G/Tw2Vii8jALMCEVEnSYUvsTGQCsoMItTVGxQUlJSxCnxW2+9JfIJ8MWJDQf+Fmw4TmXVeRry7AeOJteyUTrt+eJqWCHqanUpzqGj1fr07rLhDs0zafNhZ5WOu7fIpjX7GoKpxHiAvVzac/wsnaj5qpYX+gI740qHtPXdCjNo7cH6Y2vXLIumfL0d9Wl1lerfjwLPAjytCFfFOlNNJIGDFcGBX+ctiXrAfqoigyXs4jYFfaAXzQy4yc+CBW1mxCQStKEAOnJ89QCmXJd4x/fu3ZtmzJhBkydPjshyRWHop556ihYvXizGhwiL22+/naZNmybYdlnqa4A9YLwiQtEAA7BQtMf3Mg29i2sAIYe7d+8WpBvp6emCYAM/OCUFJb1Wli9fLk6GkeMiBQBMejXk5iHYxO01+07RPX9a6Wh2nYuyafOh0wIEHTx1zlb4YmANMDsd6hU67lacTUeqv6TDVfoeq54lOY7ZGTs1z6KNh64Wgc7PSKaHh5TRt3oWU3y8v1+bMvwJNeNycrxTGNqO7e1cg40jvMM4yIAHQTWxy4Do13nLEgLwtkSTgh6gzQ5Qk3lv+Beh4WaCdzaISHAtfm/cuLE4XJM/YLbFOx9REDh8mzhxIr344ot09913+9WcSo+bAZjS5g375Py9kwi7ergDKw2wB8xKQ/Y/R6gHvsAl6yG+gOEFA8gCzbwUme8Fsg14MaQgBBF1cxCWCAAWSl7DvzdW0mN/32h78EnxcdSvrBFtPlwtvF52Rb84svndPVrk0OprhZs7Ns+isxcvC6+XmXQszKJN18CU3bGV5qXRoapzdE/fEpowuA1lpdb3Qtptx2vXAeiDJRD5Q8ECdK/NSTsePDc7duwQBXy1z42Xx+xkbOFmQHQylnBcC+ZXhJD6kYJegjYr4IZDApmfqwVtoKb/9a9/XU+tiYmJApABrAGUyn9/+ctfUlZWVjhMwG3a1AADMJuK4st0NcAAjBdGSBpgABaS+upuxqn2m2++KUIIO3ToIP6OcBAk24MRMTc3t+5a5IUhP0xbdBkfgoQDnjPkj2EjEAoA+9OKz2nm2zssJ5eSEEedinIEwUWrxumOizB3K86htQec5Wa1K8igS5drKTEhjrZW2gtfLMxJoUMG3jHdSdbW0rD2TWnSsApq1TjDUg9+ugBlDnAKDw+YiiLJaxDepSLA9CIDopvrCF4g1DTEe7CoqMjNpj3RFg7HlixZIgg2EC6uBW04PMDcAdCQfwUgihxg0PLjbwDf+EF+GA7iAiMjPDHBGBoEA7AYMnYYpsoALAxKjaUmGYC5Y20AMCRBw4OFHwhywpAr0KtXL3HqKWXt2rXCgzF06NB6OV7YWCPHANcjjCfY/C/087M3ttErn+43nByILgC8dh2rqaOQ71qUTesOXg3ZsyvlTTNox9Eau5dTi9w0apqV7CicMI6c1fMqSCOadGNLurVvhe1x+eVCWQAWuV9a76lfxm9nnCALwNoHw5yKogoDopFtDh48SMh/wntMxbyjmpoaQWgBxlp4+Yxk3LhxtGDBAsL18IJpBc9xYF6wimvd63NiAOZ1C3l7fAzAvG0fz4+OAZh7JkIoijbx+9ixY7Rq1SqRaI/cLgiAFU5PEXoS6MFA4jq+mOExg4Ry+v/QX9fRu1uPNZhcagJRi6w4OnIhgarO1c93aNMkQwAyJyIo5QMIM/Tub5qZTMX5abTxYBWBhfpyLco325MmWcl0zEZYZE5aIt3RMZs6pJygwYMGKXm6rHr4mvQuwHMiPcn2Vol/rlKdARHho/AEIRQbBEOqiXwGO3fuXPdeD5wj3vPwfOEQDjlhTLbnzVXAAMybdvHLqBiA+cVSHh0nAzD3DIPNozYfAKE4CEPBF7UMxUFhZnl6inpfWgGzHU5LQSUcSvgh2vzWHz+hTYer65rPSkmgioJM2nTwFJ27rP/ayEtPopMOCiojb+zSFfMaYNmpiVRRkEHrD5wWhZebZ6fQ4Sr7OWaYQLtmmbS18qu5BFosIT6O7uhZTA8NaUM7N60jeCNRe0dFAcmLpJsGTbtqgtAsABRVGR5jgQHRDkOgn9ctQshRCB0Mh9rQcu2cYGeQyMBDhtxgBmDetDgDMG/axS+jYgDmF0t5dJwMwNwzTCAAk2ALeQKlpaWiI2ygUUMGBAOBDHZgfjtx4oQ4OQ4VgA145n0RWngVAGXS5spqqrlWU0tvxiio/OVl+14ptFGYk2qYl5WWGE+dwKpYebpev+2bZdEWDTC0o/0eJV+RdgRef33rfPrPr7WlioIs4X3EZqegoECAXhVF9QLFyJsEcY3Z5tbPdlWdARG2+eijjwTgkJ58P9tLb+zwaO3Zs8fUw4eDOBBujBkzhl566SXVVKDMfBiAKWPKqEyEAVhU1K5OpwzA3LNlIABD4jWSsJErIL1d8HIBmIHBLvBUFCfHlZWVorZMKPlfFy5eFjXAWjfJoE2HquncxavFjM0kmILKAkwFeKYS44i6leTQbk1umbZfQVv/+Smr4dT7/CrT4sl6fyvJT6cnRlTQTe2a1v1d9fpYOFUHUUt2djb16NHDkQ79cjFyh5BDhGcgMG/GL3MwG6ek2O/UqZOo0aSaSAp65LyCzVVFkSykqO9o5NmCl6xt27Y0ZcoUmj59uopqUGJODMCUMGPUJsEALGqqV6NjBmDu2VGyYckWUVAW+V6tWrUSX8YAaKCab9q0qW4BViTnwwOAz8Fypy0IKv8v/2bmIfv8ixq6bc4ndP7SFduT0wNTVjdf9UxJBsRa6l6cS4dPm9cP612aR5/trQ+mrPpBjTDJtJiRkkDjB7Wm71xXSsmo3KwRnErjdBon7yrSO4M1DUQtWE9lZWVWavPl5wjZhfegf//+vhy/1aBVZ0CMBQ8fDtFAta+t4Rhod3gBQbI0Z84cGj9+vNWy4M+jpAEGYFFSvCLdMgBTxJDRmgYDMPc0HwjA8H8UV5bU9EjeBkUxcgPAYqcVnByDGXHbtm0E4KYl89AbIQCYFqBpf990/CJN/vcBRxOrD6bs3SprgKFGV82FS4LK3kq6F+fQmv3OaOvbNEmnPcdr6PbuRfTITWXUOFM/sV/18Dx4R3H6DlIX1BVSTfC8IIQUc1PVe6I6AyJCqEE8pGoRbTxzy5cvF+VCUEbESObPn09jx46lRYsW0ciRI1V7VJWZDwMwZUwZlYkwAIuK2tXplAGYe7YMBGBoGbXBEGqEDSXAlcwdwBd4IAAD6JL1vwDIwIioLQgKYGb2NwnaPjlK9MoOZ6+GLs3SaH3lOUfKGFSeT0dOX6BtR+zV8kLj5U2c0dbjnkHljejhIWXUsTDbcHyS3ABJ8aijpqIgdxAeFFXZ5c6cOSPyh+Ddg5dPRVGdAVFS0Kuaw4f3M6IYCgsLBcg0klmzZtHUqVPFgQnCTVm8qQEGYN60i19G5WyX5ZdZ8TgjpgEGYO6pGiAAIEkr+LJGLRzk7KxYsUJ4trCBDhR8seOzUOp/4X4AtD8s20t//NCZB6x1Vi3trrb3OmmWmUjZKQl08Uot7TnpjNEwPy2pru6YleYLc1PpR8PK6eudrlL4m0ksbN4R+qQywyMou1GgHABaWzfPyvZ++TwWGBAlBf0NN9wgwqhVExkGjJze1q1bG05v0qRJNHfuXFFwGTmbLN7UAAMwb9rFL6Oyt2Pyy2x4nBHXAAMw91SuB8BAmgBvFzxgCK9C6KHeySnAE36Q1B1K/S/M5qmFW+hvqw86mlh5k3Taccw8hDA3hSg/mWhPNajn4yg7qZZOX7TfTXIC0Zf1S4/p3pyenEDj+rekcf1LKSUpwVYHkhpa1eKvsRCep7qHLxbyo0AkhDDEwYMHK0m9bjfEcvTo0aKcwtGjR0N+n9t6AfJFQWmAAVhQauObrmmAARgvhZA0wAAsJPXVu1kPgIE0AYyGoKFfv369ON0HTbpWcJ8EYLg21Jox33tpDX2w6wtHE2uWnUKVp/W9WblpiVTWNJPWHaiii9eo6sF/caW2lq44YK5vnEJ0/LzxsPAyu74oie7pnEUF2akNiEi0eW5gyNPqCZ4TNxgkHSktghdXV1cTCnWDURO1hVQU5A7BkwnviYqiOgMibKY6Bf2hQ4cIeXzI/8rPz9ddpnifo8wI3uUoLRLq+1zFZ8Erc2IA5hVL+HMcDMD8aTfPjJoBmLumADuWVrBpRlggcpOQHwHqYgAJPQAGL0co9POyzW/M/oh2HauxPTG8RFDMGEWVtZKeFC/yrjYfrqaaL+tT2YuCyqdN0JRO7x1EPTL9fLGyvES6u0MqlWZeDeOEzswEmxroUf6A2h+gDAWv5d8CmSTdALe2leryhap7+GKBYl91BkTYEKyvKpOoyELoYEBMS0szBGCIdMA1CxcudPlNwM25qQEGYG5qM/baYgAWezZ3dcYMwFxVpwAP2IhIAeshwAHCClNSUsTJaKDI/C/8PdTwQ7TRa/p7DQCT2SwbZSTTFzVf5a7Bu9WtRS7tPFZDp87qA6H2zTIb1ACz0mSvklxaGVADrGlWCj06rIxu6dK83kmxloRES0SiR0oCnSM3w0okaAsEZsHS/Vv15+bnkj1P1fpYMjwP3j14+VQU1RkQYyHEUtoQB2lG72q870G8NGHCBJo9e7aKS1mZOTEAU8aUUZkIA7CoqF2dThmAuWvLQAC2du1aOnbsmAgxROK23uZShh+a1fayO8rT5y5S31+8b/dycZ1gJjxWQ3iZdGuRQ4dOnacj1ebkGldp6x0WVC7JqyuonJIYT9/tV0rfH9iKkPMVikh69q5duwpPoxVbpPZz1JwyEzO6/8DabNLz5oYXM3BMCO2C6AH4UHTnlXvxjOBZ6dy5MzVrZk264pVxOxmH6gyIdvOjnOjMa9ciTPbs2bM0cOBAw6GhmDhYIGfMmEGTJ0/22hR4PBoNMADj5RCKBhiAhaI9vhfeGgdZPKwwKw0EAjDQECP0ENKnT58GeQMy/0vSz4eaL7Ctsppu+8MnVsOs93m34hy6fOUKnT5/iT4/Ye1Jws1Xa4A5K6jcpSiH1h+oohEdmtLjwyuoKE8/hMfR4Ilo69atooB1MMxrsnRAMHT/RuMEADMKgzSq3Wbm+QRIBIELwis7dOjgVD2+uF6GdvXr148yMjJ8MWYng4wFBkQZJqsqBT3sjZxeRDJgjkayePFiGjVqFL366qt01113OVkmfG2ENcAALMIKV6w7BmCKGTTS02EA5q7GsZHHpl7Kli1bRO0mbMr1wlawMcMGOxT6ee0Mlm4/Tg++utb2pNo2zaSC7GRatvOE7XtwYfcWKKjszAM2pKKJ8Hr1bpnnqC+ri5FnB51j8x4JkXT/VqGR2ppt2jWhN0bkrwWCNgnW0A7WEIhcUH8Injdc70a4aiT0ZacPsOeBpAIhlqEeQtjpL9LXxEJ4nmSxDOYgJNL2CKY/vKNRVgQkSvDUGsm8efNo4sSJAqz1798/mK74nghpgAFYhBStaDcMwBQ1bKSmxQDMXU0HAjBsSnC636hRI91TU7fzv/762QH6yaKtlpMqzU+jrNQk2njoNIncLIfhhG0LMmwXYEaO2cQhbWhU9yKKj3f3lQV9L1261PPeIYA2q9DIQC+clXMaIMwoDFIvzw2Azqvgxo5nwXJRe/iCWGBARAjpyZMnlaWgB8HSsmXLRJFwFAs3kmnTptHMmTOFV764uNjDq5KHxgCM10AoGnB3NxPKSPheX2qAAZi7ZgsEYEjaxhcxinZWVFQ06MzN/C80/uw7O2nuB3sNJ9UsK4Wa56YKSnlJetipMIs2Hqp2pIimWcl01CJPLCkhjv5P3xJ6cFBrykxNdNS+3YuPHz9Oa9asEbXV4B1SRWRoKtYT1tCpU6eoffv2wltq5HnD361Am5GXzSg0MpDuPxz6lSAazHHt2rULRxdRb1N1BkQo+MMPPxSe/r59+0Zd3+EYAJ5BFEPHc2gGrMaNG0cLFiygmpoa4alm8a4GGIB51zZ+GBkDMD9YycNjZADmrnGwQQaokgIWRIAEEESAGUsr2vBDNwg40PYTCzbS/6yvbDCp/PQkat04g9YeqGpAN1+an06fnzAvwqxtMOHaW+eySfrgkLZN6InhFVTaKN1dBQe0tnPnTtqzZ4+gfDaihQ7rACLQ+PLlyyk1NdU07wTDkOvJDKDpeeHMphBI92/GIClBnFO6f3hN8Jwgvw15biqK6gyIkoK+adOmpuF5fratJPvp0aOHiGjQE+hhxIgRdPjwYcK7KVoeZ7wDnnvuOUFsgwMqEIPgb88//zzdf//9fjaDq2NnAOaqOmOuMQZgMWdydyfMAMxdfQYCMISsgDWrV69e1Lhx43qdyfBDt/K/0Pj/eWFlPar3lPha6tA8i7YePUfnLtav5SUHk5GSQDUX9D/T005BVrIhS2JZkwz6z6+1pf5t9Dco7mqbxMZdspJFa7Pj9py07cmwJ+R/6XlQQ+3bCd2/BHZWzJF26P61HrcjR47Qjh07hOckOzs71Cl58n7VGRBRBgJhpPD0g+1VRdm7d69Yp2ZEMXie4I1HOQUQ50TrnQRvXV7e1Vxb5Kzh4ASRGAzA6q9MBmAqPqmRmxMDsMjpWsmeGIC5a1YtAMOGFUnbEJya4nRYKwBguB5f0m4RKgz79Qo6cOocJcXHUVleAn1edYnOmjCtZyYn0JmAIstWGmlXkElbj9QPWcxJS6KHbmxDY3oVi6LOkRDoD5sclQu/epGeXa5bq5w2J3T/WC9gl3OS0xYOuv9wrNtYYECMhRw3ECqB6XHIkCEi1FJP8D7HQdudd95JL730UjiWk6028ezhu6dbt24i8uLpp5+mn/zkJwzAArTHAMzWcuKLDDQQmZ0Oq19ZDTAAc9e0CD+UHgKc7CP8A9KlS5d6OUrYlEkPmFvhh1eu1FKPny2hjoXZAoQdrf6quLLRLEHGYZd6XrbRo0UOrb7GgJgYHydA1w8Gt6Hc9CR3lWnRWlVVFcGz0LZtWyopKYlo35HqTJUQSzO6/3379onwyZycnHpEJdpQXj19u033Hy6bxgIDIrwrKAeBUhuwo4qCdzmKLIPl0UgA0PA+mjJlCk2fPt0zamAApm8KBmCeWaK+HAgDMF+azTuDZgDmri20AAxx99hcQpDfogUJbtf/Qh/Hqy/Q3X9aSftP2qvlhXuCIeCQNcAGtGlEk0dUUFnTTHeVaLM1GRKkcugaCr+eOXOGBg0aFLVwJpvmCOoyALMlS5aI4sudOnWq10a46f61YZB6nje36P5jwTu0bds28a4bPHiwKKegotghGUHB9KFDh9KcOXNo/PjxnlEDAzAGYJ5ZjAoNhAGYQsaMxlQYgLmrdXnSj1aR/4XwQrBhIX8H+RFSwpH/BWbDMfM+czShYCjoh7dvQrd1K6Qb2zZx1JfbFyPB/MSJE2LT51YIp9tjDKU9GbqWm5tL3bt3D6Upz94Lj8Inn3wing/kuYUqRnT/ZjXbrJgjZY02MwISLYALpPuPBQZEPIvIO8KzqKJgjSDcGeQbIFQykvnz59PYsWNp0aJFNHLkSM+oggEYAzDPLEaFBsIATCFjRmMqDMDc1boEYEhKf//99wnU2gjPQWJ6eXl5XWeSft7N/K83Nx2hR/62wdGEepXm1iPtMLs5KyWRJtzQiu7p24KSEuId9eP2xdgQQb8gbUB+nYoC4I5Td6wdLXhXaa4HDx4UDG09e/ak/Pz8iE9NS/fvJKfNCrRp6f4RgogfeMCN8twiQfcfTuVinWIOCEFUUWSpBCsynFmzZtHUqVNpw4YNDTy60dQLAzAGYNFcf6r2zQBMVctGaH1hLDEAACAASURBVF4MwNxVtARgyAXYuHGj8FwgdwBf3KgfA5GbPoAwp5TdZqN98aPP6Rdv7nA0oW7FOYKa3kzAqTG6R5Eoppyfkeyo/XBdHAvgBFTWcg0FMmiGS6+Rbhd5Qzig8FPomlO6f7B0WgG2SND9h8u2mBsIH/TCSMPVZ6TblZ5aq3zTSZMm0dy5cwn5qaEyeoJJEd5Tu3LPPffQyy+/rHs5AzAGYHbXEV9nXwMMwOzriq/U0QADMHeXBTYjOElHSA5IOG666SZ65513RH2jzp071wNgAGtuMrn9fPE2+vPH+x1NCLTxO4/VGN7Tp2UeTflaBbVrluWo3XBfHG3PSbjnh/b9CE6c6gWFbeEdGjhwoNNbfXG9NowU9OTwpJiFQ2o/d5vuH2GSbhH+aJUfCxT0R48epXXr1onww0A2W60uRo8eLUJqwV4aalg0vjvwnrMrt9xyCz3zzDMMwOwqjAgpAryHdqAvvrS+Bnjx8IoISQMMwEJSX4ObseFC7SYQC2RlZYmQHAAw5A7IPB6Z/4WbQ/2S1g5g4mvr6a0tRx1NqHFGMh2vaciWWJybRo8PL6PhHQoctRepi1HYFh6iG2+80VUQG6nx2+kHGzlswvv372/nct9dI/NqEHoIumwVJRQGxHDQ/eN9oyUfMfpdm9NmdUgUCyQjIBgB0ch1110n3ut6gvV8/fXXi/fR6tWrPUWawx4w/bcLAzAV37qRmxMDsMjpWsmeGIC5a1Z8CeP0E2xYknhj6dKllJmZKYoxQ2T+l9un0XfM/ZQ2HDpte0KJ8USXrxDVau5IT06gBwa2pO9eX0rJuMCjgqKv2DyCAVFFkeyAKKIqPaeqzROheStWrFC6eG+kwYkZ3b+R5y0Yun8tcEN43qFDh0TOE8A0PnPzYMkL694OyyPe/cj5HTBgAC1cuNALw64bAwMwBmCeWpCKDIYBmCKGjNY0GIC5r3kU7Ny+fbs4DUVNnOXLl4tNCU5Pw0E/L2cwcOYyOn7GuvaXvL55dgodPn1B/Bcvklu7NqdJQ8uoaVaK+0pxsUV4GMEwCVID5GSoKLFQ4wwhuuvXr7cM6/Kzff3AgGhF968H3AD0zEQyR2rJSMy8bbjey6AN4YdgXIXH3UgARFH0eMKECTR79mxPLVsGYAzAPLUgFRkMAzBFDBmtaTAAc1/z8M7gy3jIkCEiDAXeMGxycDIqE/jxr1Voj5ORfXnpCnX76ZJ63iyr+9sVZNLWI2eoe4sckefVucgfBVRjYeMuC9v27t2bQEOvoqhSZNrMNmB4RB4P3gVuPu/RXg9aun8cOIEUp6yszDS/zYqIJFS6/3Dq5OOPPxbvbhyqGQlsjed1xowZNHny5HAOx1bbGAfySCHISQaI7NevXx0bL76P7r//flttqXoRhyCqatnIzIsBWGT0rGwvDMDcNS02Jm+88YZI1JZ5LSAawAYFTG/hyv/af+IsDf/th44m079NPt3WtZC+0aWZo/uifbEMB7rhhhsIuSoqCtgPKysrlc5xAzuorB2lai78p59+KkCJqnl8ePYQRgrvlhkFfSTo/s28bdL7FizdP8LIEc1gVo9v8eLFNGrUKHr11VfprrvuivprCd83KNVhJPfeey+9+OKLUR9nNAfAACya2vd/3wzA/G/DqM6AAZi76gdbFjxeYDxDPgAEG02Er4DVKlz5X5/uPUn3vrjK1mRSE+NpXP9SGte/JaUlJ9i6x0sXqU5OITe12CyqmuOGOSKMNCMjQ9QAU1EkA2JeXp6yJCMyVzEcFPRaun9tGKRevTbt52ZryQ7dvzZUUh7woAgz3uft2rUzbH7evHk0ceJEQgSEyoBbpWeVAZhK1oz8XBiARV7nSvXIAMxdcwKAIeyjS5culJaWJhpHngsY+4YNGyYAGDYWbhNw/GvdYfrPf26ynMzITgX0o2Hl1Dwn1fJaL14AVkCcRiPXAiBXRZFFX4uLi+tqx6k2T2yicTqvch5fKAyIfrG3JFLxSrFwCdokSLMqri1p/61AG9oFGMOBgZYhEu92vPObNGkicn3hUYL3ury83FMsiH5ZT5EeJwOwSGtcrf4YgKllz4jPhgGY+yrHl7o2SR25AaAxhgcM4nb+F9r847I99Osluwwn07F5Fj359bbUo8Tf+USSVa5Dhw6itpqKIucIgFlYWKjiFCnS7IDRUGIszPH48ePCww+mTnjB/ChWdP9nzpwREQzp6eni3Y33u6zR9utf/1ocCAVKamoqoXg6yo/gXxymxHq4nxfXBgMwL1rFP2NiAOYfW3lypAzA3DdLIAADI+Lu3btFDpj0fLnN+PX0/26h11Y2LNrZODOZJt1URrd3a67EieyuXbuELpFMjtNoFQXzwzyR8I/yBSrK3r17aceOHUrP0Q8MiKGuLVkfC6Gy2dnZoTbnyfslIQ5y3JAHBpF0/yCSwVqGF2z+/PmEw7a7775bHDAAnMofREOArITFWxpgAOYte/htNAzA/GYxj42XAZj7BgkEYNhMY7OJvICUlBTXww8xgwdeWUPLdnxRN5nkhHi69/oSUdMrIyXR/UlGqcVVq1YRTqQHDRqkBKDUUyMYy06ePCkAu6rkFBs2bBCbVtB6u30YEaWl2aBbVRkQtRNFuDUACuyInEUVBe9ugCy8c/D+1hN4xuCxbtmyJSFfTNXnVjX7MgBTzaKRnQ8DsMjqW7neGIC5b1KEp2iLm+IkHKefOCWG18bt/C/M4JbnPqIdR2vEZIa2a0JPDC+nFvnp7k8uii3i1BnhPgjr6dq1axRHEr6usZEDOQU8X6qSU0B7H374oaBlV5lkJBYYEFevXk3V1dUERlJVRR4WyLIievPEOx+hhnfeeSe99NJLqqpCuXkxAFPOpBGdEAOwiKpbvc4YgLlv00AAhjpA+BLHhhohLOGoB9R7+hLKTrxMjw5pSTf3Knd/Uh5oEbXVwIBYUVFBpaWlHhiR+0OQxA04SUciv4qCw4klS5aIHD7k8qkoscCACLuBgh6kFKh/parYAdIHDhwQReGnTJlC06dPV1UVys2LAZhyJo3ohBiARVTd6nXGAMx9mwYCMBQORqI6mBHBluV2yBWKMM95cw21SzpBNwwaSEgAV1Fkvok2F0O1ecZCkWnU/kJtPFB6y1INqtkxFhgQJQW9yoykWJd2yiWg9MjQoUNpzpw5NH78eNWWs7LzYQCmrGkjMjEGYBFRs7qdMABz37Y44ZcsWWgdidgrV64Up/1gtQtHfsDHH38swh5Vrj+zbt06oUuV84ZA2IKQ1YED1QXSktQAXpPcXH+zchq9PWKBAVFS0JeVlVGrVq3cf5F6oEWAzHfffdfSWwsCjrFjx9KiRYto5MiRHhg5D8GOBhiA2dESX2OkAQZgvDZC0gADsJDUp3tzIAADoQJC5/Lz8wlFWQMLfeL/+AnWMybrRqke0hULuVEA6tjYIuFfVZHkFCoTN8QCA6KkoIdnv6CgQMnlarfO2axZs2jq1Kki1LxTp05K6kLFSTEAU9GqkZsTA7DI6VrJnhiAuW9WSVEsW0Y4EkgHUBTUTMAipgfOtIU/5e/4F9fDmwY2OXiH/FyLx8oKciPUunVrQtFXFQV5Q2BQU5lkBHbDYQQ8xCp7a2OBAVGGBF933XWUlZWl4iMp6n+BeRWgCqGWRjJp0iSaO3cuVVVVKUvHr6KBGYCpaNXIzYkBWOR0rWRPDMDcN2sgAINHDD+y4Cc8VgBjev9q/4bfsSk3dH/HxQnAJtsFCxdokrUgLRDQhYOB0X0NNmzx0KFDtGnTJurRo4cAKCoK6PWRS6J6SBdAJnIh4TlRVewQN/h97rFAQQ8CJYDpXr16iegFIxk9erQ4WDh27FjQkQx+Xw9+HD8DMD9azTtjZgDmHVv4ciQMwNw3mxaAAUBJ8OUU/OBeeAoCwVogcMMpLa4Fu6I290xvZhiDkUdNC9a0vwcbGummZmMhbE1u9sCWiXBVFSUWQGasMCDGAgW9LPw+YMAAQjFlPYG9UTQd70mQLYUjx1fFd4EX5sQAzAtW8O8YGID513aeGDkDMPfNgC9kGW4oQZQESG73duHCBcHSBTY5sMpJ8GfXy4Zx4h4zMQqNNAqXlKGRbs4VIZzY4CDcSVWJBZB5+PBh2rhxI3Xv3l3UTVJRYoEBEXb74IMPhMddZQp6eN2xZlEDzOggCu92vH8B0hYuXKjiklZ2TgzAlDVtRCbGACwiala3EwZg7ttWC8AAbmRR5nB4kiorK0XiNwoTN23aNKjJYHxGXjb592BCIyW5iFlIpARxZt5BjOH999+vA5lBTdIHN4HJEuulX79+PhhtcEOULI8gGcHmXUWJBQZEyQ4IVteOHTuqaEYxJ5DinDt3TrCSGgnqEyI/bMKECTR79mxldaHixBiAqWjVyM2JAVjkdK1kTwzA3DerFoDJ/C+n4Yd2RyW9JoMHDxb5YJGQwNBIM2+bBHB2QiON2CHh5UN4Hgg4ADIloAsHoI2E/vT6wDpBbpTqNZVAaIAwxBtuuCFaqg57v7HAgFhTUyOIhVTOV8RCsePlwzsYXsAZM2bQ5MmTw76+uAP3NMAAzD1dxmJLDMBi0eouzpkBmIvK1DQF0KANPwwXAMMGASF/Xg/NUzU00q3VEwvFifE8wJOZnZ0tyFRUlVhgQATZxNq1awWRiqoU9FivqAHWrFkzU2r5xYsX06hRo+jVV1+lu+66S9VlreS8GIApadaITYoBWMRUrWZHDMDCY1cAMBl+GK78L4TGAICVlpZSRUVFeCYSxVZlaCQ2evCkYY5WuW12WCOtQiOlJw6etnAB50C1Sq9J3759laWxlrlRLVu2pPLy8iiurPB2HQsMiLHg5bObyzdv3jyaOHGieBerXFohvE9NdFpnABYdvavSKwMwVSwZpXkwAAuP4gEYZPgheghHuJykZleZ0ECG5lmdQkPHkQ6NBEDTY5QMxtbr168XFNYoThzM/eFZxe62Gitek6VLlwrK8m7durmrQA+1tmXLFjpw4IAgpwD7qooivdLt27en4uJiwylOmzaNZs6cSfv37ze9TkUd+X1ODMD8bsHojp8BWHT17/veGYCFx4TwgIU7/wtsciDhQP4XwhBVFFkI1WoTFOzczUIjjbxtTlkjzYpry4LaK1asEGCuT58+wU7F8/ft3r2bQOsNkpGMjAzPjzeYAdr1mgTTtpfuQS4f8sBApqKqSMZOq9qD48aNo3/84x+EYvGqvodVtTEDMFUtG5l5MQCLjJ6V7YUBWHhMK8knsFkPRxgbvD3Lly+n1NTUmNi0o85OZmZmeIzlsFUta6QdAhKrgtqyewA1ABMj1shohEY6VI3p5evWrSMwBMLLp2qtpFhgQISR8e5BXSwUKFZV9uzZQzt37jQ9MMB7eMSIEYRoBBwuqLquVbUxAzBVLRuZeTEAi4yele2FAVh4TAsPGJj/AMDCEaIjWchatWolmMhUFRR7Bc0zWPP8urmRoZF6YA1/w/zg6cOGFnMEeA+FNdIIwEU7tNEOo5zf13Es5EZJCvqioiLq0KGD301mOH47YZZ4tkHDj7xGsJj69R2lrBEtJsYALFYt7868GYC5o8eYbYUBWHhMj1AkbK7xhRyOjS/yL7BB6NmzJ+Xn54dnElFuFZubWMinwck5wvOQwJ+eni607pXQSLc2lHgWYEtZMDzKSyts3ccCA6I8/AGRCoCHqoLDn+rqatOSCTgoQUHxO++8k1566aWoqWLHjh20YMECevPNNwm/HzlyROQhgh33kUceEV5nloYaYADGqyIUDTAAC0V7fC+IC2pZDe5qACoFQyG+nOH9cmsTqx2lJG1A/lc4PGzuaiS41rD5QXHiWNjoueHlQ2ik3ZBIGSJr9fhb5a8FMkoarXeZywePCTwnqkosMCBKMpVQir/7wf6oc4acLrO8TNQnBDvrlClTaPr06VGb1pgxY+i1114THskBAwaIQ7lt27bRwoULRS7yb37zG3r44YejNj6vdswAzKuW8ce4GID5w06eHSUDMPdNA/YsfPnhBBKFg7UFkt0AY/CO/OIXvxCnmyqfbIJVbOvWraLIaW5urvuG8kCL0ayNZRUaKUGa9l+noZESwIGgAPlRCJfNyckRz4RqBbVjxWMrwyy9lJfp9qMMWy5ZsoSaNGkiap0ZyUcffURDhw6lOXPm0Pjx490ehu32XnzxRQIgBiOuVlB3b9iwYeIQcO/evaLQO8tXGmAAxqshFA0wAAtFe3wve8DCsAYWLVpE3/jGN+paRuHZRo0aiVAVnEziX/l/7b/yd4ANCdT0ANtnn30mmA8feughmjFjRhhm4I0mY4GaHcAEDIitW7emNm3aeEPxJqMA+AcIAyiTwMzK6+Yma6T0uLlxkOG2smOFAdFObpTbuo10e1jbAC9WNRbnz59PY8eOJbzzR44cGelh2upv+PDh9Pbbb9Pf//53UTCahQEYrwF3NMAAzB09xmwr7AFz3/Rgz3r99ddFXafjx4+LH5z+4//4Fz8ICzEShL1IoIZ/A0Hapk2b6M9//jP9/ve/F6ev+BwEDlK8uDl1qmXJ8oh5wQOmqkiqa9SMwmm7ioK1jlBS2BTlBPQ8awBxWiAXSmikXthkuEKBtfaKFQZEUNDj4GDgwIEqLlcxJ4QEf/LJJ9SuXTuRt2gks2bNoqlTp9KGDRuoU6dOntTHzTffTG+88Yb4Trr11ls9OcZoDYo9YNHSvBr9MgBTw45RmwUDsMipHptK/MAjgDBFCdC0QE2CNC1ww8auqqqqbqCgY8dpO9qR3gXQlwOIyR/pZQOAw8Ze7+8yd8yLgA05dGDNU53lEaGq+/btE4n+CMlTUbBGEc5lp5g25q8XGmnlZQs2NNIsx80peU4sMCDCPqCgB1kMCIBUFZBYwANvdTAyadIkmjt3rng/I9LBa4I12bZtW5EnDOImhMWzfKUBBmC8GkLRAAOwULTH93IIoofXgPQC4F/Q2gOIofAy8r4QrnbffffVgTh8pgVt+B2eBiPB5hJfxlrQFgjS8H8teAPwMwuNdFOV0jOEnAaASVUFpA2wExLnVRXpTQBZAUK6wiFOQyMB6My80BgjPNGBJCMyb01bk01eA/Y51IMaMmSIssQ40BnAtOoU9HbB9OjRo4WnDAdnTgF7OJ4DbZv4zrjppptEiPMzzzxDjz/+eLi79F37DMB8ZzJPDZgBmKfM4b/BsAfMXzZD+A+Kn/7yl7+kH/3oRw0GL0EbNqRgEcTGINDDFhgSKf8PpjozQdFngDJtHpteDpv0vuGzYAlIJkyYQKD0Xrx4sSg2raLARqgdZJXo7/e5gykOtvRayQQr1kg9r5tVaCRsBW+0nmctWqGRbq6fM2fOEIgnVGcmlZ5pHHYBiOsJ1gKISAC81qxZEzLbLSj9Afzsyj333EMvv/yy7uVY23fddRf97W9/ExT5f/nLX0Ien91x+ek6BmB+spb3xsoAzHs28dWIGID5ylwCeD3xxBO0cuVKV0KAtF42hHEBhB09erTOmwZwJgFcYB4bPkMuiJmA8c6MgCQQwEkCEuRTYGOD3ApVJRKeIS/oDkyWYLQEcYwWkHthbE7GYBYaCS8mQkkxP+Qtypw2/GsmWONaYGYWEik/i6anBe+GdevWCcY9MLyqKmvXrqWTJ0+assxiPSA/DN5r0L2HKvBW4bDCrtxyyy3CsxUoAF/f/va36a9//Svdcccd9MorrxiCSLt9qXodAzBVLRuZeTEAi4yele2FAZi/TAumLZxAA/xEq/6XFrShKKsWpBkBNhkeCYBnRUCCjR1CuUC+gVAnKy+bXwlIYoFmH08XWDuRs6gyaYMRA6I2NFLPoyb/pmWUdDs0EsDNrTxPUJkj1FJlCnqsWZDGQFDqw0hwgAJad3jrZ8+e7YkvEqwneMbg+br77rsFWVO0vic8oRCLQTAA84OVvDtGBmDetY0vRsYAzBdmqhskcsC2b99OgwYN8tXAAwlItF42bYgkgBrC1VavXk2FhYWEkCdsdMwEuWl6YZHyb9qQSFkKQHoR3NqYBmMMsFki1w1hTqpukmB3hFnCFiA0UFXcZEA0Co00IyKxCo2041nTXmPEGolnE14alfPcsEaxZpEja7ZmoQscEqEUyOTJk6O+tAHi4fH617/+Rd/5znfohRde8FxeWtSVFDAABmBes4i/xsMAzF/28txoGYB5ziQxP6ApU6aITQ3yIYqLiwUBidazpscaqQ2PxLVmoV+SgESCMT0Pm/ybBG/I63GbgGTmzJkil0Zlami/1TkL9uGzS9oQbPtm92lDI63YIp2GRgYCNzx7CFVGOYFAQpJohka6qVfMDwAM4YWgoTcS5Keirtarr74q8q2iKXhHfvOb3xR08+PGjRPMjKrYI5x6ZQAWTu2q3zYDMPVtHNYZMgALq3q58SA0gFA15NM4SUhHN1oCEnjN9Gj+ZShkIM2/HQISK8AWyBqpTd4P9LShv5KSErr99tvppZdeCkJL/rhF0nmrnjPkN8+Q3dBILaDzcmikm0+DJBqxYu2cN28eTZw4UZTL6N+/v5tDcNwWikG/+OKLgjEWIZF6nn3kYOKH5SsNMADj1RCKBhiAhaI9vpdp6HkNeEoDyKUBcQfonZE8Hk7R5rJhowlQZMYaGUjzj1plZgJCET2af7Aeog4cPGCPPvoo3XvvveI6zNttL1s49Wen7Z07dxIKk4OoQJurZ+deP12DcgJYQ9HeiIdTZwhxe//99wX5BjzT2rw1o+LawYRGmoVLRqKgNt4BIOHo0qULFRQUGKp02rRp4hlGLif0EU0BsIJtzATjffrpp6M5TM/1zQDMcybx1YAYgPnKXN4bLHvAvGeTWB4RyDceeOAB+ta3viXyGLwmgQQkdmn+Ad4A8GTh7KysLFEmAMAL4ZMQbDyd0vxrKfqjmc9mZCfQcwNsYoPoxfG5sb6wJpYuXWqZM+RGX9FsA+sV5BRWniE5RruhkVovm13WSDOQFmpopCTH6dOnjzgUMRKE+v3jH/8QTLBGVPXRtBf3ba0BBmDWOuIrjDXAAIxXR0gaYAAWkvr4ZtaApQa0BCSgtgYByYMPPijYAX/1q18JYKYNjZRFtfEvNr1mAiAXSECiLagdSEACYoFIEpAsW7ZM1MVCDTBVxYgBUbX5Sgp6EFPAixsOMQqNNMttswqNhNdMgrJAcKYH5MD0iPDnG264QdynJ3imR4wYIdhad+3apezhQjhs7KU2GYB5yRr+GwsDMP/ZzFMjZgDmKXPwYGJEAwhZAgEHkv0DRetlw+beiOY/MCRSFtS2IiCRgA3/BhKQBJKPAMABQElx4sXC5hSb1O9973v08MMPK2tZNxkQvawkSUHfr1+/emsi2mOWrJFmIC2Q7t8qNBJzSk9PFwBMC9pee+21ugOPWbNmiSLx77zzDuEgxMmzEW2dcf9XNcAAjFdCKBpgABaK9vhezgHjNcAaiLAGQOMNAAbqarA9uiGBBCR6NP+SKVICNfkvvHJmgtytwFy2QM+aFrgB2CEk6/XXXxcFYVE8HMQAqko0GRAjqVNJNIKCwX5m2MOzAtBmlLeG5xOeOICqwDw30LzrSUpKiiDAkD84eHj88ccjaR7uKwgNMAALQml8y1cHkqwL1kAoGmAPWCja43tZA841AGAC9kPkj4A6OhoSSECiBWd2aP7hmTMTEJC0bt1a1HND8XBtWKReiGR2drZvCUj8xoAY7HpbuXKlKKgNQhWVBWQWAF89evSomyYAGajet2zZQmD23L17tyi+3LJlS+revXu9EGI8PzfffLNnijOrbKtQ58YALFQNxvb97AGLbfuHPHsGYCGrkBtgDTjSAGiuwZqHXBp4i/wiWtCGOejR/ONvModtxYoV4ncALi0Bid58EeYlCUiM6rIF0vzD6yAlmuFfscCACD0jnw9Fz7XAxC9r1+44AbTeffddKioqog4dOhje9tFHH9HQoUNpzpw5NH78eLvN83Ue0wADMI8ZxGfDYQDmM4N5bbgMwLxmER4Pa0ANDaBYLzbsn3zyiQj5QqijHdZICeAA8swEXrPAPDaZ3yZDJLWhkuEgIMGGHblAACVDhgxRw3A6s4D9lixZYlmc2O8KkIXDy8rKqFWrVobTmT9/PqH21qJFi4SHl8WfGmAA5k+7eWXUDMC8YgmfjoMBmE8Nx8NmDXhYAzU1NSKMC1Tdzz//vO2Rar1sqLMGMGaWzybBmsxnu3TpkmFfYMOTgE2b0xaYz6YFbyBikKLnZUMoWufOnen++++n3/zmN7bn6bcLnVLQ+21+crx2CVUAuqdOnUobNmygTp06+XW6MT9uBmAxvwRCUgADsJDUxzczAOM1wBpgDbitAdSLuv7660UeTLgJOLQEJFVVVbqAzYjmHzXKzAQALJDmHwBN/g35QD//+c/pv/7rv+i+++4TYZQAemagzW1dR6I9zHP9+vUibDZcFPSRmIdVHyDgQE5f7969CXmMRjJp0iSaO3cuYb3BE8viTw0wAPOn3bwyagZgXrGET8fBAMynhuNhswY8rAEQGYAF7ne/+x317dvXUyPVetnAcueUgARkDFIQ1ojQSoAygDx4ybBxl140LXgz8rRpKcyjmctmZqQ9e/bQzp07yWsU9G4vLMwRcx04cKCgmDeS0aNHi9BahNT6mRHSbf35rT0GYH6zmLfGywDMW/bw3WgYgPnOZDxg1gBrIMIa0HrZEF4pwyKnTZtGb7/9Nv30pz8V3hBtbTZJSAICErO6UyAgkV41o7psgfXZtAWCIwHaNm3aRIcPHxZ5bioDjo0bN1JlZSWBat9Ir7AlvLvQw5o1a7j+V4SfRTe7YwDmpjZjry0GYLFnc1dnzADMVXVyY6wB1kAMaaB///7CC7J9+/YGs8ZGXdacAgizYo2UeWzwyNkhIAnMYwskINGCOXjlJHAKBrDdc889BNbJP/3pT0pb1w7VPmzaokULgu3/53/+R2l9qD45BmCqWzi8l97vHwAAEkJJREFU82MAFl79Kt86AzDlTcwTZA2wBsKgAWzEEYI4ePBgUXQ6VNGGRoKNT4ZG6tVlC8xpw7VWBCQSsOnltMnPkN8lf9cSkABwlJeX03vvvRfqND19//LlywmFx3v16mU4ztOnT1Pz5s1FbiNyHFn8qwEGYP61nRdGzgDMC1bw8RgYgPnYeDx01gBrIGoaAGFDcXExPfnkk/Szn/0sKuOQXjb8C0IRJzT/CJk0k4yMDEE20rRpU1q1apXI/wIJh9azps1r8zsBCXSIGmDNmjUzZTaUJB0zZsygyZMnR8Xu3Kk7GmAA5o4eY7UVBmCxanmX5s0AzCVFcjOsAdZATGkAuWDYsLdu3do3VOR6BCR6NP/aXLb9+/fTjh07CIAMczYShDbCIygBmrZGm5Y5UkvzjzpxMiQymNBINxfc+fPnCR4w2LNNmzaGTS9evJhGjRpFr776Kt11111uDoHbirAGGIBFWOGKdccATDGDRno6DMAirXHujzXAGmAN+EcDr732Go0ZM0bkO4Ed0AywyTw2SUAChkgzAhLklWlz2QJJSLRgTf6elJRUpzw3Qdvnn38uABjmWFpaamigefPm0cSJE+mDDz4QeWAs/tUAAzD/2s4LI2cA5gUr+HgMDMB8bDweOmuANcAaCLMGEF6JOmfwgpWVlVn2pvWyXb582ZLmX+ttQy6bmZcNnaPulpbmH3lrVgQkdrxsf/jDH+ixxx6jv/zlL3TLLbcYzhPMlzNnziR4BhGCyuJfDTAA86/tvDByBmBesIKPx8AAzMfG46GzBlgDrIEwa+C73/0uvfLKK3Tu3DlKTEwMS2+BBCR2GCO1rJEAekaCMdshIPnXv/5FL7zwAi1btox69OhR11ygl23cuHH0j3/8g0CUEi59hEXJ3GgDDTAA40URigYYgIWiPb4X4SG1rAbWAGuANcAaYA3oaeDee++l9evXi5pXXhJJQHLlypU6AhKAMjPWSHjY8KNHQALyDdQAS0hIEEyI2hw2LYCDhwxlAg4dOsQ1wLy0IIIYCwOwIJTGt3x1OMO6YA2EogEGYKFoj+9lDbAGWAOsAT9oQOtlu3DhQgOa///+7/8mMFui5hlAmjY0Er9/+eWXddPMyckh5Le5mYPmBx2qNkYGYKpZNLLzYQ9YZPWtXG8MwJQzKU+INcAaYA2wBhxqoF27dsLr9eGHH9bdKUEbvGzV1dXCu7ZixQoBvOAZZPG3BhiA+dt+0R49A7BoW8Dn/TMA87kBefisAdYAa4A1EJIGALRAs3/rrbcKEg6W2NAAA7DYsHO4ZskALFyajZF2GYDFiKF5mqwB1gBrgDWgqwFQ6xcUFIjCyiiwzBIbGmAAFht2DtcsGYCFS7Mx0i4DsBgxNE+TNcAaYA2wBnQ1gHwu1Pe67rrrRB0wrwso8H/+85/TqlWrCPXLMH4QhaCA9H333Uff/va3SVsvzevzidb4GIBFS/Nq9MsATA07Rm0WDMCipnrumDXAGmANsAZYA441sHTpUhEu2bdvX2rdurXIXQNxyL///W9Rn+zGG2+kt956i2nyLTTLAMzx0uMbNBpgAMbLISQNMAALSX18M2uANcAaYA2wBiKqATAyogZZfHx8vX4vXrxIw4cPJwC01157je64446IjstvnTEA85vFvDVeBmDesofvRsMAzHcm4wGzBlgDrAHWAGtAVwO/+c1v6JFHHqGf/vSn9OMf/5i1ZKIBBmC8PELRAAOwULTH93IhZl4DrAHWAGuANcAaUEADly9fppEjR4rww4ULF9J//Md/KDCr8E2BAVj4dBsLLTMAiwUrh3GO7AELo3LD0DQnX4dBqdwka4A1wBrwoQZQIPr3v/89DlJFjbK3336bdu7cSXfffTe98sorPpxRZIfMACyy+latNwZgqlk0wvNhABZhhYfYHSdfh6hAvp01wBpgDSiiga1bt1L79u3rZoMC0Y899hhNnz6dWRBt2JgBmA0l8SWGGmAAxosjJA0wAAtJfRG/mZOvI65y7pA1wBpgDbiugZYtWwoKebtyzz330Msvv6x7OUIPDx48SP/85z/pqaeeog4dOtCiRYsEOyKLsQYYgPHqCEUDDMBC0R7fyzlgCq0BTr5WyJg8FdYAa0BpDdx0000CNNmVW265hZ555hnLy//617/SXXfdRT/4wQ9EeCILAzBeA+HRAAOw8Og1ZlplD5gaplYp+XrHjh20YMECevPNNwm/HzlyhPLy8kSRVLB7ocYNC2uANcAaYA001EBVVRXl5uZSx44daePGjawiEw2wB4yXRygaYAAWivb4XvaA+XQNqJx8PWbMGFHDBmE0AwYMEGE027ZtE6xeAJrw9D388MM+tRwPmzXAGmANhE8DmzdvFuCra9eutHbt2vB1pEDLDMAUMGIUp8AALIrKV6Fr9oD504oqJ1+/+OKLYvPQvXv3esZ5//33adiwYYRE871791Lz5s39aTweNWuANcAaCEEDq1evFu/IhISEeq2cOXOGbr/9dnrnnXfoySefpJ/97Gch9KL+rQzA1LdxOGfIACyc2o2BthmARd7InHwdvM6HDx8uqJb//ve/06hRo4JviO9kDbAGWAM+1cBtt91GK1asoH79+lFJSQmlp6cTSpT8+9//plOnTom/I4Q7MzPTpzOMzLAZgEVGz6r2wgBMVctGaF4MwCKkaE03nHwdvM5vvvlmeuONN+j111+nW2+9NfiG+E7WAGuANeBTDYDh8C9/+Qt9+umnIkf27NmzIk+2S5cudMcdd9B9991HiYmJPp1d5IbNACxyulaxJwZgKlo1gnNiABZBZYe5K9WTr0HZ3LZtWxF2c+DAAbHh8KtcvHiRnnvuOZGjsWbNGkLeBv72/PPP0/333+/XafG4WQOsAdaAbzTAAMw3pvLkQBmAedIs/hkUAzD/2MpqpConX1+4cIHgOUTYDaiYH3/8cSt1ePpzhAlJAFlQUEDJyckihIgBmKfNxoNjDbAGFNIAAzCFjBmFqTAAi4LSVeqSAZi/rOmX5Gu389xQ1+Zvf/sb3XnnnSL0BkQcfhYU1H733XepW7dugkzk6aefpp/85CcMwPxsVB47a4A14CsNMADzlbk8N1h/70I8p87YGxADMH/Z3C/J127luYF2/tvf/jahuChyG1555RUlcxsYgPnrOeTRsgZYA/7XAAMw/9swmjNgABZN7SvQNwMwfxkxlpKvkRN1zz33CM/X3XffTX/+858b0C77y3rGo2UApooleR6sAdaAXzTAAMwvlvLmOBmAedMuvhkVAzDfmCqmBooQPXi8/vWvf9F3vvMdeuGFFyg+Pl5ZHfgdgIEU5amnnqLFixfTF198IcIq4a2dNm2ar8lSlF1wPDHWAGsAoey8h+Z1ELQGePEErTq+ERpgAMbrwGsaAOHGN7/5TUE3P27cOJo7d67S4Av69zMA27Vrl6g7dPToUVEaoF27doIe+7333hOslSBOadSokdeWGY+HNcAaiHENMACL8QUQ4vQZgIWowFi/nQFYrK8A781/7Nix9OKLL1Ljxo1pwoQJuoQbgwcPJvxEU9wkGvEzABsxYgS99dZb9Nvf/pYeeuihOpM8+uij9Oyzz9IDDzxAf/jDH6JpKu6bNcAaYA000AADMF4UoWiAAVgo2uN72QPGa8BzGgCwev/9903HhdA2gJZoiltEI372gMH7VVZWRgCj+F0bJlpdXS1CEWtra4V3LCMjI5rm4r5ZA6wB1kA9DTAA4wURigYYgIWiPb6XARivAdaABzTgVw/YvHnz6Hvf+x59//vfpz/+8Y8NNCm9Y++8846o4+ZX+fvf/y4OBVA4e926dQRwCYKYl19+2a9T4nGzBmJeAwzAYn4JhKQABmAhqY9v5hBEXgOsgehrwK8ADAWxZ86cKX4ee+yxBor84Q9/SLNnz6bnnnuOHnzwwegrOsgRoF4bgFdmZiYVFxfT1q1bGYAFqUu+jTXgFQ0wAPOKJfw5DgZg/rSbZ0bNAMwzpuCBxLAG/ArA4Pl6/vnnDQtI//jHP6bp06eLnylTpvjWwiAUAfBCuCU8YTfeeCMDMN9akwfOGriqAQZgvBJC0QADsFC0x/dyCCKvAdZAlDQwY8YM4UmByNA2sAmWl5eLvw0YMIDuv//+KI3OXrexAsC02li6dCkDMHvLg69iDXhaAwzAPG0ezw+OAZjnTeTtAbIHzNv24dGpqwErspF7771XsEF6WWIlBJEBmJdXIY+NNRCcBhiABac3vuuqBhiA8UoISQMMwEJSH9/MGohpDcQKCUcsADAU0P7nP/9JixYtog0bNtDBgwcpOTmZOnfuTCgNgR+Vi6HH9IMco5NnABajhndp2gzAXFJkrDbDACxWLc/zZg2EroFYpKFXNQQRtdpAlILSAchxKykpoSNHjtCCBQuoqqqKRo0aRX/729906/KFvpK4BdZA5DXAACzyOlepRwZgKlkzCnNhABYFpXOXrAGFNBBrhZhVBWBLliyhmpoauvnmm+t5uiorK6lPnz60f/9+Ah0/gBgLa0AFDTAAU8GK0ZsDA7Do6V6JnhmAKWFGngRrIGoagBcM5CEotnzrrbdS+/bt6ZNPPiEwB1ZUVNCHH35IjRo1itr43O5YVQBmpiewWILREmUFfve737mtUm6PNRAVDTAAi4ralemUAZgypozORBiARUfv3CtrQCUNwDvy1FNP0eLFiwm5RAhju/3222natGmUl5en0lQpFgHYL3/5S3riiSfokUceoWeffdbX9pw8eTKtXLmStm/fTsePH6e0tDQqLS2l2267TQBMlQ4LfG2oCAyeAVgElKxwFwzAFDZuJKbGACwSWuY+WAOsAVU0EGsA7NKlS9S9e3fauHGjANgIOf3/7d3NK21RGMfxp0yUgbxLKdQpSRIzkYnByfknzj+AyICBIlKKkiRD/gMDE2+DU5QhUwNRRpQUAyPd1nM795aX61xr78F5nu8qJe2183yeNfm1916rnEfYWKSvr0+6urqksbFRX7s8Pz/XUNbS0qK/t7a2lnOJ/O8lChDASoTisk8FCGAsjCgBAlgUH5MRQMCZgLcANj09LWtrazI6Oqo7JJb7eH19lcrKyg9lFA8NDxuRbG1tlXuZ/P8lCBDASkDiki8FCGAsjigBAlgUH5MRQMCBwN7enoSfMMKmFAcHB9LR0SFDQ0P6t/r6elldXTUnsbGxIRMTE9LZ2SlnZ2dSW1trrsZiQZeXl9Lb2ysjIyNydHRktk4K+ytAAGM1xAgQwGL0mCsEMBYBAggg8G+B+fl5WVhY+PKi8A3Rzc2NKcbNzU0ZGxvTV/VOTk6kubnZVH3vi1laWpK5uTmZmprSJ34M+wIEMPs9TrNCAliaug7uTQBz0GRKRAABBP5DYH19XSYnJ6W7u1vDV/hWytoITyxfXl70jLPw/dfp6an09PTI8fGxNDQ0WCuXej4RIICxLGIECGAxeszlCRhrAAEEEEDgj8DKyorMzMzo63jhVbzweqXFEZ7ohYOmiyObzcrOzo40NTVZLJeaCGCsgYQFCGAJg3q7HU/AvHWcehFAAIHPBRYXF/U4gf7+fjk8PDT9zVdRIISwcFZdCJ3Pz8+yv7+vuyQy7AvwBMx+j9OskACWpq6DexPAHDSZEhFAAIFvBHZ3dyWfz0tFRYV++1VdXf1hRltbm15jcdze3urB4ZlMRrfcZ9gXIIDZ73GaFRLA0tR1cG8CmIMmUyICCCDwjcB3G42E6cPDw3oQtdURzju7uLiQh4cHs69eWu3dT+oigP1EjTlFAQIYayFKgAAWxcdkBBBAAAEjAuH7r/v7e3l8fJSamhojVVHGVwIEMNZGjAABLEaPuWzCwRpAAAEEEHAhcHV1pZtsvH+98u3tTbegX15eloGBAT3zjGFfgABmv8dpVkgAS1PXwb15AuagyZSIAAIIICBhe/3Z2VkZHByU9vZ2qaur050QC4WCXF9f61lnYdv9cPYZw74AAcx+j9OskACWpq6DexPAHDSZEhFAAAEEdHON7e1tPfPr7u5Onp6epKqqSjffyOVyMj4+7mLnR5bCbwECGCshRoAAFqPHXF5BZA0ggAACCCCAgDsBApi7lidaMAEsUU5/N+MJmL+eUzECCCCAAALeBQhg3ldAXP0EsDg/97MJYO6XAAAIIIAAAgi4EyCAuWt5ogUTwBLl9HczApi/nlMxAggggAAC3gUIYN5XQFz9BLA4P/ezCWDulwAACCCAAAIIuBMggLlreaIF/wIP2F/Vi4CahQAAAABJRU5ErkJggg==\" width=\"432\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-20-21747159fcf9>:20: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.\n",
      "  plot3d = Axes3D(fig)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import ipympl\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(x,y):\n",
    "    return 4*x+2*y-6*x*y\n",
    "def g(x,y):\n",
    "    return 10*x-2*y+1\n",
    "\n",
    "x = np.arange(-3, 3, 0.25)\n",
    "y = np.arange(-3, 3, 0.25)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z1 = f(X,Y)\n",
    "Z2 = g(X,Y)\n",
    "\n",
    "fig = plt.figure()\n",
    "plot3d = Axes3D(fig)\n",
    "plot3d.plot_surface(X,Y,Z1) \n",
    "plot3d.plot_surface(X,Y,Z2, color='r') \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2020年度課題(中筋さんありがとう)\n",
    "\n",
    "1. 次に示した「例題:二分法とNewton法の収束性」および「解答例」をコピペして，pythonが動作することを確認せよ．\n",
    "\n",
    "1. 対象の関数を $f(x) = \\exp(-x)-2\\exp(-2x)$ として解答せよ．\n",
    "提出は2.だけでよい．\n",
    "\n",
    "ただし，func, dfuncは以下を使え．下の「exp関数に関する注意」参照"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    return np.exp(-x)-2*np.exp(-2*x)\n",
    "\n",
    "def df(x):\n",
    "    return -np.exp(-x) + 4*np.exp(-2*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 例題:二分法とNewton法の収束性\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "代数方程式に関する次の課題に答えよ．(2004年度期末試験)\n",
    "1.  $\\exp(-x) = x^2$を二分法およびニュートン法で解け.\n",
    "1.  $n$回目の値$x_n$と小数点以下10桁まで求めた値$x_f=0.7034674225$との差$\\Delta x_n$の絶対値(abs)のlogを$n$の関数としてプロットし，その収束性を比較せよ．また，その傾きの違いを両解法の原理から説明せよ.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 解答例 \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ funcで関数を定義．\n",
    "+ 関数をplotして概形を確認．\n",
    "+ 組み込みコマンドで正解を確認しておく．\n",
    "$$\n",
    "0.7034674224983916520498186018599021303429\n",
    "$$\n",
    "テキストからプログラムをコピーして走らせてみる．環境によっては，printf分の中の\"\\\"が文字化けしているので，その場合は修正して使用せよ．\n",
    "\n",
    "+ プロットのためにリストをlist_bisecで作成している．\n",
    "+ 同様にNewton法での結果をlist_newtonに入れる．\n",
    "+ list_bisec, list_newtonを片対数プロットして同時に表示．\n",
    "\n",
    "2分法で求めた解は，Newton法で求めた解よりもゆっくりと精密解へ収束している．これは，二分法が原理的に計算回数について一次収束なのに対して，Newton法は2次収束であるためである．解の差($\\delta$)だけでなく，関数値$f(x),\\epsilon$をとっても同様の振る舞いを示す．\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2*x - exp(-x)\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "\n",
    "\n",
    "def func(x):\n",
    "    return exp(-x)-x**2\n",
    "\n",
    "def df(x):\n",
    "    return diff(func(x), x)\n",
    "\n",
    "print(df(x))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func(x):\n",
    "    return  np.exp(-x)-x**2\n",
    "def df(x):\n",
    "    return  -2*x - np.exp(-x)\n",
    "\n",
    "x0=0.0\n",
    "x1=1.0\n",
    "x = np.linspace(x0, x1, 100)\n",
    "y = func(x)\n",
    "plt.plot(x, y, color = 'k')\n",
    "plt.plot([x0,x1],[0,0])\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7034674224983918"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import fsolve\n",
    "x0 = fsolve(func, 0.0)[0]\n",
    "x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             x1              x2              f1              f2\n",
      "  +0.0000000000   +1.0000000000   +1.0000000000   -0.6321205588\n",
      "  +0.5000000000   +1.0000000000   +0.3565306597   -0.6321205588\n",
      "  +0.5000000000   +0.7500000000   +0.3565306597   -0.0901334473\n",
      "  +0.6250000000   +0.7500000000   +0.1446364285   -0.0901334473\n",
      "  +0.6875000000   +0.7500000000   +0.0301753280   -0.0901334473\n",
      "  +0.6875000000   +0.7187500000   +0.0301753280   -0.0292404858\n",
      "  +0.7031250000   +0.7187500000   +0.0006511313   -0.0292404858\n",
      "  +0.7031250000   +0.7109375000   +0.0006511313   -0.0142486319\n",
      "  +0.7031250000   +0.7070312500   +0.0006511313   -0.0067872536\n",
      "  +0.7031250000   +0.7050781250   +0.0006511313   -0.0030651888\n",
      "  +0.7031250000   +0.7041015625   +0.0006511313   -0.0012063109\n",
      "  +0.7031250000   +0.7036132812   +0.0006511313   -0.0002774104\n",
      "  +0.7033691406   +0.7036132812   +0.0001869053   -0.0002774104\n",
      "  +0.7033691406   +0.7034912109   +0.0001869053   -0.0000452413\n",
      "  +0.7034301758   +0.7034912109   +0.0000708348   -0.0000452413\n",
      "  +0.7034606934   +0.7034912109   +0.0000127975   -0.0000452413\n",
      "  +0.7034606934   +0.7034759521   +0.0000127975   -0.0000162218\n",
      "  +0.7034606934   +0.7034683228   +0.0000127975   -0.0000017121\n",
      "  +0.7034645081   +0.7034683228   +0.0000055427   -0.0000017121\n",
      "  +0.7034664154   +0.7034683228   +0.0000019153   -0.0000017121\n",
      "  +0.7034673691   +0.7034683228   +0.0000001016   -0.0000017121\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x1, x2 = 0.0, 1.0\n",
    "f1, f2 = func(x1), func(x2)\n",
    "print('%+15s %+15s %+15s %+15s'  % ('x1','x2','f1','f2'))\n",
    "print('%+15.10f %+15.10f %+15.10f %+15.10f' % (x1,x2,f1,f2))\n",
    "\n",
    "list_bisec = [[0],[abs(x1-x0)]]\n",
    "for i in range(0, 20):\n",
    "    x = (x1 + x2)/2\n",
    "    f = func(x)\n",
    "    if (f*f1>=0.0):\n",
    "        x1, f1 = x, f\n",
    "        list_bisec[0].append(i)\n",
    "        list_bisec[1].append(abs(x1-x0))\n",
    "    else:\n",
    "        x2, f2 = x, f\n",
    "        list_bisec[0].append(i)\n",
    "        list_bisec[1].append(abs(x2-x0))\n",
    "\n",
    "    print('%+15.10f %+15.10f %+15.10f %+15.10f' % (x1,x2,f1,f2))\n",
    "\n",
    "list_bisec\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7182818284590451"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df(-1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000    -0.6321205588285576659757226\n",
      "0.7330436052    -0.0569084480040253914978621\n",
      "0.7038077863    -0.0006473915387465445370196\n",
      "0.7034674683    -0.0000000871660306156485376\n",
      "0.7034674225    -0.0000000000000014988010832\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x1 = 1.0\n",
    "f1 = func(x1)\n",
    "list_newton = [[0],[x1]]\n",
    "print('%-15.10f %+24.25f' % (x1,f1))\n",
    "for i in range(0, 4):\n",
    "    x1 = x1 - f1 / df(x1)\n",
    "    f1 =func(x1)\n",
    "    print('%-15.10f %+24.25f' % (x1,f1))\n",
    "    list_newton[0].append(i)\n",
    "    list_newton[1].append(abs(x1-x0))\n",
    "\n",
    "list_newton\n",
    "print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = list_bisec[0]\n",
    "Y = list_bisec[1]\n",
    "plt.plot(X, Y)\n",
    "\n",
    "X = list_newton[0]\n",
    "Y = list_newton[1]\n",
    "plt.plot(X, Y)\n",
    "\n",
    "plt.yscale(\"log\") # y軸を対数目盛に\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exp関数に関する注意\n",
    "exp関数のimport元で振る舞いが違うみたい．\n",
    "```python\n",
    "ValueError: sequence too large; cannot be greater than 32\n",
    "```\n",
    "がplot作成の前段階で出る．\n",
    "numpyでやるときには，np.exp(-x)などとしてる．\n",
    "\n",
    "でも，diffには通らない．そのあたり，覚悟して使う関数を決めないと．．．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
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  "latex_envs": {
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   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
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   "report_style_numbering": false,
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  "toc": {
   "base_numbering": 1,
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    "height": "12px",
    "width": "252px"
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   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
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