{
 "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=\"#1微積分\" data-toc-modified-id=\"1微積分-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>1微積分</a></span><ul class=\"toc-item\"><li><span><a href=\"#1(a)-関数の概形(15点)\" data-toc-modified-id=\"1(a)-関数の概形(15点)-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>1(a) 関数の概形(15点)</a></span></li><li><span><a href=\"#1(b)-シグモイド関数(15点)\" data-toc-modified-id=\"1(b)-シグモイド関数(15点)-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>1(b) シグモイド関数(15点)</a></span></li></ul></li><li><span><a href=\"#2-線形代数\" data-toc-modified-id=\"2-線形代数-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>2 線形代数</a></span><ul class=\"toc-item\"><li><span><a href=\"#2(a)-転置(15点)\" data-toc-modified-id=\"2(a)-転置(15点)-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>2(a) 転置(15点)</a></span></li><li><span><a href=\"#2(b)-(15点)\" data-toc-modified-id=\"2(b)-(15点)-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>2(b) (15点)</a></span></li></ul></li><li><span><a href=\"#3-センター試験原題(20点)\" data-toc-modified-id=\"3-センター試験原題(20点)-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>3 センター試験原題(20点)</a></span></li><li><span><a href=\"#4-数値改変(20点)\" data-toc-modified-id=\"4-数値改変(20点)-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>4 数値改変(20点)</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"text-align: center;\">\n",
    "   <font size=\"5\"> 2021年度　数式処理演習　pair試験問題 </font>\n",
    "</div>\n",
    "   <div style=\"text-align: right;\">\n",
    "   <font size=\"3\"> cc by Shigeto R. Nishitani, 2021/12/2実施 </font>\n",
    "</div>\n",
    "\n",
    "* file: ~/symbolic_math/exams/21_pair_ans.ipynb\n",
    "\n",
    "以下の問題をpythonで解き，LUNAへ提出せよ．LUNAへはipynbとpdf形式の２種類を提出すること．"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1微積分\n",
    "## 1(a) 関数の概形(15点)\n",
    "\n",
    "（テキストp.216の図6.6の確認)\n",
    "\n",
    "直線$y=-2x+4$が, シグモイド関数\n",
    "    \\begin{equation*}\n",
    "      \\sigma(x) = \\frac{1}{1+e^{-x}}\n",
    "    \\end{equation*}\n",
    "を通す($y=\\sigma(-2x+4)$）ことによって0と1の範囲に潰されることを確認せよ．\n",
    "\n",
    "sympyのplotに対してy軸の表示範囲は，オプション\n",
    "``` python\n",
    "ylim=(-1,2)\n",
    "```\n",
    "をつけることで指定できる．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "# init_session()\n",
    "x,y = symbols('x y')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1=-2*x+4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2=1/(1+exp(-(-2*x+4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb801cd27f0>"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(y1,y2,(x,-4,4),ylim=(-1,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1(b) シグモイド関数(15点)\n",
    "\n",
    "（テキストp.131の4-118式の確認)\n",
    "\n",
    "シグモイド関数\n",
    "    \\begin{equation*}\n",
    "      \\sigma(x) = \\frac{1}{1+e^{-x}}\n",
    "    \\end{equation*}\n",
    "  の増減，極値，凹凸を調べ，曲線$y=\\sigma(x)$の概形を描け．\n",
    "  シグモイド関数の微分が\n",
    "    \\begin{equation*}\n",
    "      \\sigma(x)(1-\\sigma(x))\n",
    "    \\end{equation*}\n",
    "に一致することを確かめよ．両者を同時にプロットすることでも確かめられる．\n",
    "ただし，曲線は重なるので，どちらかをy軸方向に0.01程度ずらして表示すること．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "# init_session()\n",
    "x,y = symbols('x y')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{1 + e^{- x}}$"
      ],
      "text/plain": [
       "   1   \n",
       "───────\n",
       "     -x\n",
       "1 + ℯ  "
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = 1/(1+exp(-x))\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{e^{- x}}{\\left(1 + e^{- x}\\right)^{2}}$"
      ],
      "text/plain": [
       "    -x    \n",
       "   ℯ      \n",
       "──────────\n",
       "         2\n",
       "⎛     -x⎞ \n",
       "⎝1 + ℯ  ⎠ "
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dy = diff(y, x)\n",
    "dy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb7f1f09a60>"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(y,y*(1-y)+0.01,dy,(x,-10,10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 線形代数\n",
    "## 2(a) 転置(15点)\n",
    "\n",
    "(テキストp.115, 4-94式の確認）\n",
    "\n",
    "$$A=\\left(\n",
    "\\begin{array}{ccc}\n",
    "1 & 2 & 3\\\\\n",
    "4 & 5 & 6 \\end{array}\n",
    "\\right)$$\n",
    "$$\n",
    "B = A^{\\rm T}\n",
    "$$\n",
    "に対して，公式\n",
    "$$\n",
    "（AB)^{\\rm T} = B^{\\rm T} A^{\\rm T}\n",
    "$$\n",
    "が成り立つことを確かめよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFUAAAAzCAYAAADmWEQdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAFSklEQVR4Ae2c7VHcMBCGgUkBhHQAHfBRQUgHIVQAdJBMfsG/DOmAUAEfHUAqSKAD6CBACXkfx+sRsqXT+SxzTKQZRfJa2tW+2l3J0pHFw8PD5YWOdHR09NRBLiQHAWHUid2S2twoP3r52OlbqmEELjzcwPFiUZZ6p8qBUL8O9y1vUhAQhvtqt4OlljQwAm9S+WkW1tUWc99QfZR4KzmrkvelHuOmygeeRb+tadmKWvZBLYDYyViORZ/o0VFQxQBmp8oog1IwHiXVSp2o/GACVSfW30BTnqic9Zu2FG/0ZvIM1AXVP4p2pXJH+TLGM+r+6vxUM4H5WYxRhncA2CgFf40Fq8VL8Jicidi4L3kAackm8asRQmUU1FCnkejbknMnxbAaN6Hcsug5vYbwwuSRqyR5Td1ooTLq/qFOI9EBbz2ijA/2YMOSTGS/dRmKZlZ74tK76nMLqpTY6RqwaCyYC3qffbEy+ZKF11ThSPUfRg+Vcwtq14ClEIDi9rYj6Go2GK2WB6Bbykzi7xTmrwpUKcQCdSllv6coN2sbyQHIyiNUx/3Zecy2+s86qCH7Sxli2T1KDck3lZfkso1isbpQPRrP53n1b/SVEmxxVlQ2e9bmZYaK5LBAVrHbY2/uT0gIprkHVcrhdmsqGwtVfZUc1Gr2Fxwy4epRiwyJmWtQpRTWsqXSX5gA+iGk1AB03JzYTemmzfrBPgTcd019moXqXd1rRaUvrGE4VEUKYYksTNeq+3vDbdFyLlb+JC5IHhOJ5XKiF9V/IqhiYJ+EFkcI1PdiznfwxD2b2vVNV+oIsMRTP1Ursk8c6hm9lJk4dzIZS9KZQwqoTSwbatApfKTQWkq7XG0kHxePunlI9lLoRaH3R6CA2h+7YM8CahCa/i8KqP2xC/YsoAah6f+igNofu2DPAmoQmv4vCqj9sQv2LKAGoen/Yq5B1VdN6/hNtNyXfv3RrHtO/Ez1JdSKcqjw7PrYbzfQ809AFC/71qdO2vhX5P9X8rmbctOZaDYel97UpwZVPTlgiTJtuM9eeahZYLEc4nD6/k1KRU+J6j4zFZKxKgboyo8qqjMAlTyTo+cSU4Eqpp/FcMx0K5kvcqAjJQEPq3QPVfAUJjeakkEVc6wFC8luJdERj/BSunJ2ir7vXXGiJ13nTLNQ7YppzvNTd/wvXWe94CdPvQwoyVLFHLd3D2xHU1qyOaTG7bh5IM4RU3PHdK5NuLnFWneV/ygTRzmgd8OBSO00EVQxQRFmbWIsabOfmQKY55JdWUw9Fn5flXQCP4N05JI2Jau5WlH9UXlPmQUzmFLcn+3Ti7i95AJeBSgaqM7EYinZvEYyDFCuqX29zyX71Gmjx3aKgqrOuF42BdrDSaIAbO4ragbS5ZlcXQO63arSrpWCoApQ3J6vly7mLUZDEySXi0WUCCWzqND7XnTJNM+wsosP2ARTLKbSkTt39mtuInhjKdAJ5k3McRsNUMcabPPvslvhQXJzLlaEmBhwUUMLgqpBw7i10onOn7VwF597U841cdeEbXeNS7QhEyHPNyb483nMot3ChZeWlqwyRYnbZXE9bwz83v9ZPNezfdFlnVDJYXXHcJrvftXR+ZPynjfO1mPy31GJKQriElgKCcG/RM/2SxHxRp5ZK25POOBbPBbv1GSYJDmAagaE/OgeWe1Z2HeC7u8PSx3GOJV6JlYyiV2jy7VBSL5NqJGSyj7un8T4f25UQM0w+wXUAmoGBDKwLJaaAVRb/flCsq1DJUbPo2xbMug0GksfMwmuMDRLZQ/q/kcKzaZ3tBG+TkF8dbVw+wt5MqOmormQ+gAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  2  3⎤\n",
       "⎢       ⎥\n",
       "⎣4  5  6⎦"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "#init_session()\n",
    "#init_printing(use_unicode=True)\n",
    "init_printing()\n",
    "list_a = [1,2,3]\n",
    "list_b = [4,5,6]\n",
    "A=Matrix([list_a, list_b])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}14 & 32\\\\32 & 77\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡14  32⎤\n",
       "⎢      ⎥\n",
       "⎣32  77⎦"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = A.T\n",
    "(A*B).T # (AB).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}14 & 32\\\\32 & 77\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡14  32⎤\n",
       "⎢      ⎥\n",
       "⎣32  77⎦"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.T * A.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2(b) (15点)\n",
    "\n",
    "  次の行列$A$の固有値とそれに対する固有ベクトルを求めよ．\n",
    "  \\begin{equation*}\n",
    "   A =  \\left(\n",
    "    \\begin{matrix}\n",
    "      -2 & -3 & 3\\\\\n",
    "      1 & 2 & -3\\\\\n",
    "      1 & 1 & -2\n",
    "    \\end{matrix}\n",
    "    \\right)\n",
    "  \\end{equation*}\n",
    "  それぞれの固有値（$\\lambda_i$），固有空間($x_i$)に対して，\n",
    "  $$\n",
    "  A x_i = \\lambda_i x_i\n",
    "  $$\n",
    "  が成立することを確かめよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "A=Matrix([[-2,-3,3],[1,2,-3],[1,1,-2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -2, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( -1, \\  1, \\  \\left[ \\left[\\begin{matrix}0\\\\1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 1, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\\\0\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛       ⎡⎡-1⎤⎤⎞  ⎛       ⎡⎡0⎤⎤⎞  ⎛      ⎡⎡-1⎤⎤⎞⎤\n",
       "⎢⎜       ⎢⎢  ⎥⎥⎟  ⎜       ⎢⎢ ⎥⎥⎟  ⎜      ⎢⎢  ⎥⎥⎟⎥\n",
       "⎢⎜-2, 1, ⎢⎢1 ⎥⎥⎟, ⎜-1, 1, ⎢⎢1⎥⎥⎟, ⎜1, 1, ⎢⎢1 ⎥⎥⎟⎥\n",
       "⎢⎜       ⎢⎢  ⎥⎥⎟  ⎜       ⎢⎢ ⎥⎥⎟  ⎜      ⎢⎢  ⎥⎥⎟⎥\n",
       "⎣⎝       ⎣⎣1 ⎦⎦⎠  ⎝       ⎣⎣1⎦⎦⎠  ⎝      ⎣⎣0 ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-1\\\\1\\\\1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-1⎤\n",
       "⎢  ⎥\n",
       "⎢1 ⎥\n",
       "⎢  ⎥\n",
       "⎣1 ⎦"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1,x2,x3=A.eigenvects()\n",
    "x1[2][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[2], [-2], [-2]])\n",
      "Matrix([[2], [-2], [-2]])\n"
     ]
    }
   ],
   "source": [
    "print(A*x1[2][0])\n",
    "print(x1[0]*x1[2][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[0], [-1], [-1]])\n",
      "Matrix([[0], [-1], [-1]])\n"
     ]
    }
   ],
   "source": [
    "print(A*x2[2][0])\n",
    "print(x2[0]*x2[2][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix([[-1], [1], [0]])\n",
      "Matrix([[-1], [1], [0]])\n"
     ]
    }
   ],
   "source": [
    "print(A*x3[2][0])\n",
    "print(x3[0]*x3[2][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 センター試験原題(20点)\n",
    "(2019大学入試センター試験　数学II・B 第2問(1),(2))\n",
    "\n",
    "$p, q$ を実数とし，\n",
    "関数$f(x)=x^3 + p x^2 +qx$ は$x=-1$で極値2を取るとする．\n",
    "また，座標平面上の曲線$y=f(x)$を$C$,放物線$y=-kx^2$ を$D$,\n",
    "放物線$D$上の点$(a, -ka^2)$をAとする．\n",
    "ただし，　$k \\gt 0, a\\gt0$である．\n",
    "\n",
    "(1) 関数$f(x)$が$x=-1$で極値をとるので，\n",
    "$f'(-1) = \\fbox{ ア }$である．\n",
    "これと$f(-1)=2$より，　$p=\\fbox{ イ }\\,, q={ \\fbox{ ウエ }}$である．\n",
    "よって$f(x)$は$x= \\fbox{ オ }$で極小値$ \\fbox{ カキ }$をとる．\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "#init_session()\n",
    "\n",
    "a,k,p,q,x,y=symbols('a k p q x y')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH0AAAAXCAYAAAAm70AZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEJElEQVRoBe2aXVIUMRDHB9wDgD5RPomegMX3rQJuAHIC4AZSvPFGLTdATgB6A7Bq30FuIJ5Aihvg/xfSqcwUisskY9TpqiZJT6a/0t1JZpm5u7urcsL+/v6c+O95GYu+3RL9Nqfc/523/IuvV4U3QvpvhQeiXw3UyQ1jCdoxIeofqf9F+NpofZvFA2NxvZa/P8Bd7Xs1n4XzsxAyw7YEEnEGKLMo2pIR+jaLBw7E9STi/EJ9sr7qItPJ8kuE9dCdB5RUVw1p6xqTcNVM7j29IbiSMgheV9uX96ZzMozlZ8r6pvBE/UNEdFHekeNAQinpRNzwntL/ze0Bv9ArkrPmA6C7TJdATpAc4jbU70/uuVe7wV8+J+E4QA+72NMrv+C7atfQxY9prxlPA3qHQyEHQXcqnebdPz23K90lh2vyN+GK+ra3W6ItZy/vEmoZfqT+EihldoXuJKl2WsAg8G+ETnSXj1lg/BsnFckC/bSLTKekYCxtACkW7u6B2HdSemBDzPbk5++eKR9nhgREWHQNyECigYdbQjKUMfc7+uErmuayiNtCIJ7PKRG40JxPdNTO05YE0gl7uEVcCLGPOy32nOuZK4dqf9tGvdcJTKOTt8NKe02/2Wi0qYnuSC8aX27YNw+FlGLKxEehAV/ZeMZ8HHcsXPVzcZa7D6otDqQjgXwm5Ixh9qE/NsVOKtHGJDq5RZexZDmLB5AFfL5zmeooVfVVLc6qRCcj4kW91ZhrmB2snjeea1gGSHcCkuDFefF+h4JhwUu0MaVOA6wVsMhmNAFAuYsBZ1WaQ3upNnYYd+4r0Vh85rCXtAbx4XrnAq3BjKBCzkNnAvT4lXyCdU5zLECNNTbHQd7KRvHPoXsrncxQWrfoUtIWzJx8Hk9Sn6vWrZ9nwWFT3qnTDBJ79uRWsh5a1Ep0qorbep7AHF1rtokflQ2k5DsQrZWNej+57m11MttoXXmPCCwuWe+CIKITDKfR2HU1DzrZH7JENDIJWlHgdUKvsLheQRfoel4LBlNe9OJsbKvTwIyLHFAzXgLYwwkCDj44zfZE5hHRVIC43HNN4PBXKsS6oiPbQcjsEm1MrVPIdM+YvY1S50A0+iwgX3ZYeKIevPHzb9QPIBrP7EAY6CV0vP4EamwfAY3OcaCXaGNSnQbRgsAYIKP5ZQbgDsuHessOnMMhyM0VfUd4JrR/jCAYQqnXvNKArD6Wjmaf2RWX/BJtTKpT+GnVL9yyWk7jxYL0a3OQq9klXmQ6n4dnag8yDVLq3kbFUN7FhOyNy1wbvjnfZZsBUwAH17Cfp2D4CI+Uuj8i6uePXXlXBM5pCntdkftxrL50TRmYBHrzzh6LS9pPrPuTdXumNymXfIZcEL6ZTCbVaDSq/Tgi+j8Fcv5YdvKh5pVwQf2XsjllMBXtrx+W/+tNl5+ClwAAAABJRU5ErkJggg==",
      "text/latex": [
       "$\\displaystyle p x^{2} + q x + x^{3}$"
      ],
      "text/plain": [
       "   2          3\n",
       "p⋅x  + q⋅x + x "
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx = x**3+p*x**2+q*x\n",
    "fx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 2 p x + q + 3 x^{2}$"
      ],
      "text/plain": [
       "               2\n",
       "2⋅p⋅x + q + 3⋅x "
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = diff(fx, x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=-1\n",
    "y0=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "e1=fx.subs({x:x0})-y0\n",
    "e2=df.subs({x:x0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left\\{- 2 p + q + 3, p - q - 3\\right\\}$"
      ],
      "text/plain": [
       "{-2⋅p + q + 3, p - q - 3}"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{e1,e2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left\\{ p : 0, \\  q : -3\\right\\}$"
      ],
      "text/plain": [
       "{p: 0, q: -3}"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs_pq=solve({e1,e2},{p,q})\n",
    "subs_pq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADwAAAAVCAYAAAAaX42MAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABXElEQVRYCe2Y0ZGCMBBA0bEA5+xAOzjvOrAEaeHswF/4PUvQEijhtAQtwQ70LMG3msygk2DAgOCwM2viBnb3sSQEOlEUzYMgmKEiYRzHu2v3PX7hueHrAPwL2h8D6/dANFPAd+HsmYf9WQn0ibcEHdM/+fN868k1TinABO+Tzgo9ol/oEPUuReKUBSyVDIWQpGQOSZW9C75zx+l6z6LmDlvgmhfo6fTaCj99CWvuwLhKq+V+Q+7yeHGVRuzSbMCy3I9dSZt0XDuHq66Wmj6Vha2iwgNF83FPpWD/abf3YwX+W+OkfRnncPqAon0g5IVBZHJtggTbnr68mS3FRntStj6tqKwduYRzHsZJOywT+LKXTgcz9Ul4hE5NYy42znWKo31VcUvrWFntN4nnrm6WQ9vYy4EBlWf9wZagb/vLgQH6AXrhG8zmT3/i0XOoEbslG4zJzsXU37TkKRGeAV/naJMAGYg7AAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle \\left[ -1, \\  1\\right]$"
      ],
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1 = solve(df.subs(subs_pq),x)\n",
    "sol1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOCAYAAADaOrdAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVQ4EbWU0Q2CMBCGqXEAZsANjG4AG8gKuIE+wqtuwAy4gbiCG+AIxA3w+wkYUvHF1ksu1x7w/ddei+m6LnC1oigiGMeBsyG2mpO/K2dcRQaBkpgIKGN8IhzwhHG9UNLRBNxPGYC1qideKe9DJIbTAA4FnFjNOCQf+RAR7AFMlc9Z6NyTOapyiDaEiGh8rORDB/BaAnh/4v4iAlwNvyB2JgYmz3M17IbbjdPzb5YC6O+A/QL5kpy26X2kA90TX07BGV7ZvKVdya9zKt/x7YqYjgzG6ouXexIAU6O3xPHXMupIuHU+wkO1V2C6L7bFPF/52C4JaFsyW4F5fzhex8eV111V+AkAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle -2$"
      ],
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx.subs(subs_pq).subs({x:sol1[1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle x^{3} - 3 x$"
      ],
      "text/plain": [
       " 3      \n",
       "x  - 3⋅x"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx0 = fx.subs(subs_pq)\n",
    "fx0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb8018984f0>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(fx0,-x**2,(x,-2,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) 点Aにおける放物線$D$の接線を$l$とする．\n",
    "$D$と$l$および$x$軸で囲まれた図形の面積$S$を\n",
    "$a$と$k$を用いて表そう．\n",
    "\n",
    "$l$の方程式は\n",
    "\\begin{equation*}\n",
    "  y = \\fbox{ クケ }\\,kax + \\,ka^{ \\fbox{ コ }}　... (1)\n",
    "\\end{equation*}\n",
    "と表せる．\n",
    "$l$と$x$軸の交点の$x$座標は\n",
    "$\\frac{\\fbox{ サ }}{\\fbox{ シ }}$であり，\n",
    "$D$と$x$軸および\n",
    "直線$x=a$で囲まれた図形の面積は\n",
    "$\\frac{k}{\\fbox{ ス }}a^{\\fbox{ セ }}$である．\n",
    "よって，$S=\\frac{k}{\\fbox{ ソタ }} a^{\\fbox{ セ }}$である．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - k x^{2}$"
      ],
      "text/plain": [
       "    2\n",
       "-k⋅x "
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx2=-k*x**2\n",
    "fx2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - 2 a k$"
      ],
      "text/plain": [
       "-2⋅a⋅k"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa= diff(fx2,x).subs({x:a})\n",
    "aa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle a^{2} k - 2 a k x$"
      ],
      "text/plain": [
       " 2            \n",
       "a ⋅k - 2⋅a⋅k⋅x"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ll = expand(aa*(x-a)+fx2.subs({x:a}))\n",
    "ll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{a}{2}\\right]$"
      ],
      "text/plain": [
       "⎡a⎤\n",
       "⎢─⎥\n",
       "⎣2⎦"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = solve(ll,x)\n",
    "x0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3} k}{3}$"
      ],
      "text/plain": [
       " 3  \n",
       "a ⋅k\n",
       "────\n",
       " 3  "
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sd = -integrate(fx2,(x,0,a))\n",
    "Sd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3} k}{4}$"
      ],
      "text/plain": [
       " 3  \n",
       "a ⋅k\n",
       "────\n",
       " 4  "
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sll=-integrate(ll,(x,a/2,a))\n",
    "Sll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{a^{3} k}{12}$"
      ],
      "text/plain": [
       " 3  \n",
       "a ⋅k\n",
       "────\n",
       " 12 "
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SS=Sd - Sll\n",
    "SS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 数値改変(20点)\n",
    "\n",
    "大問3.において，関数$f(x)$が$x=-0.9$で極値2をとるとして問3(a)を解きなさい．\n",
    "  問3(b)は変わらないので，解く必要ありません．\n",
    "  極小値は$−3.66567655334305$ぐらいである．\n",
    "  さらに，これらの値を用いて，(x,-2,2)で曲線$C, D$を同時にプロットしなさい．\n",
    "\n",
    "追加：$k$は適当に，例えば，k=1と定めてください．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "#init_session()\n",
    "\n",
    "a,k,p,q,x,y=symbols('a k p q x y')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle p x^{2} + q x + x^{3}$"
      ],
      "text/plain": [
       "   2          3\n",
       "p⋅x  + q⋅x + x "
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx = x**3+p*x**2+q*x\n",
    "fx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHoAAAAXCAYAAADEM1tgAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEuElEQVRoBe2Z61EbMRCAbY8LANIBdECggkAHECoAOkiGX/AvAx0AHQQ6gFTAowMogXEH5PuEdKM7DNjn48x4vDNrSau93b19SQfd5+fnzhxmwwNHR0cLvMlBfJvlOO5CH/Rn4xXnbxE9cExQ95M3mJ8yvwNXeok4H2fCA3sEdyN7k2Pmy9BW54HOvDIDU6v5dth7dOdn9DC3zAaNSraitxhXwhnNxIP7d3y9NcYn19DvI20+NOyB6PN0nnqJMgaesddNqELOKnK2wO/K6x4eHqrglI1NCQJzM+EXuMm8EcXKncOLB/Cpga1enAzKBbjN/uULZ71fng8xjbIGSumBBjVllrQOjFa3DCr+MoBdG+DeVzFoAnt8By9OBjdBKqj0eZToY43INMh2Y4t04Fo00N7SHliYZTmoeEGmnDjluTZW7ZymSXXt8UgcRAz242fXE0GMlZ9UduhVkblF++QZbUAlvqXIl5lDgx7A1/p8MRcJLVW3gaoLfjMbL8cCkL3f52e7oJQnZkOH/XAhY3Rt9a+Du6CV7vpbnIe/wDD3GZWlFpvz77gP3MAz0Tn0Imb8X/Rqt8fVDajtf0BtvWZvKpdP9OrHcIQyP2NeAOuRfQlvKXkKIUxs3a+ABwyqDkk3cXl2oJ84Af6B9v4TUJ5HMD/PvWi4J78OPQc9X+XVcF+qdUC/Dr0CPcOS7dqmva0HGZ12Ui+93pHUP+wbuBFf9hE+DAzapc5wU4MYDJhgAjxCyyvyAZoGy2t15IEcsLYt2QWEJTDfD8TP/sEuE8z3MsgmZg6tB1nl2KHeoJu5PrpjLG7dzBvz5atAI9wzwkDmLd11coZBt93loBM78DjeMuaO9DvuHpoBlyeXK+kVwKMNVl8VTBJlWAFVUMd7sk0uL5el1gjN98mTtipXfZ9hT0kPOiwsfXTBuBjnE/syKSkFGuFm0BJj8U0tY1TqmJyfPgWSHPm9ymtoSoi095NJNTHS3tAROcMCqX6zPhwZQx98n6gdJbuRZ3cSbedvQtP2IM/k6jBWfWXr1seiga/uj+1L5ATopQlCdeIKY1EVzMM3WOJhNKBWd6jOjK5hf7N1mMInfQEsKgaaVSWtNYj61FkNqPZ12C8lQAuGeSu2TY/sB3gn8mU/vqgZto6w/PLllsHPW53KSk7hGbvAAPTs03DPQS8Q8lmZVnreyg9YV/XA1grkdqjQpK5WTRuG6C9v+Y45rMWFe436sodAW5fBsdL80C4Q2j7rYAyjik0I+QNAc27QfkQ+E0F8ivxPzAuA5l661BX0z55E20y83HYT9FXifrYtUb4+K3UXbLSo9HHyeaO+7EeFOsAXr0Ke7SoWrNxww2bud6h/akuVojPtAIEXukZfgV5mbFcmQNHGWbcJVu85+pPtyeaSw9swCBvOwA1QvyQwBvn/Fhr15cj/poxGrTF6i54KoNusr3sZK9mMLBPb7tUtbYyxaNKeMdTWYu2N8ZRVapZNEzxGwlHSgBFeLPOOVUdkk/bU0T/yM7buD4HM9eywtbR+vubGYUeTiWbi5hfNXNVI84btGUlnXaYPW3dsTwco8CJmBdjuJnJQXWObeA7b/cOJQfZ9PKf9Xp3WVwDq24H/myUUmO60xikAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle 2 p x + q + 3 x^{2}$"
      ],
      "text/plain": [
       "               2\n",
       "2⋅p⋅x + q + 3⋅x "
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = diff(fx, x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=-0.9\n",
    "y0=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "e1=fx.subs({x:x0})-y0\n",
    "e2=df.subs({x:x0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left\\{- 1.8 p + q + 2.43, 0.81 p - 0.9 q - 2.729\\right\\}$"
      ],
      "text/plain": [
       "{-1.8⋅p + q + 2.43, 0.81⋅p - 0.9⋅q - 2.729}"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{e1,e2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left\\{ p : -0.669135802469136, \\  q : -3.63444444444444\\right\\}$"
      ],
      "text/plain": [
       "{p: -0.669135802469136, q: -3.63444444444444}"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs_pq=solve({e1,e2},{p,q})\n",
    "subs_pq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ -0.9, \\  1.34609053497942\\right]$"
      ],
      "text/plain": [
       "[-0.9, 1.34609053497942]"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1 = solve(df.subs(subs_pq),x)\n",
    "sol1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle -3.66567655334305$"
      ],
      "text/plain": [
       "-3.66567655334305"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx.subs(subs_pq).subs({x:sol1[1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle x^{3} - 0.669135802469136 x^{2} - 3.63444444444444 x$"
      ],
      "text/plain": [
       " 3                      2                     \n",
       "x  - 0.669135802469136⋅x  - 3.63444444444444⋅x"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fx1 = fx.subs(subs_pq)\n",
    "fx1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zL7MSWeWNmBdKBxKS/3Iw1cHKMR64llqG49GFbMchRGVQgfqb/fdzYaithgl+lmxHIRyzoL8DQuyN8OXvSbSrjxA5oQL1p+LaZlxKLsVLIbbQVBOwHYdwDJ/Pw7cz/NAqluLjE4k01UeIHFCB+tPB8HxIGQZz+tL0Hmmfk5ku3h/tjisppXRMPCFyQAUKgEgixcHwPAx1M4OdiTbbcQiHLRzoiEA7Q3x+Ognl9a1sxyFEqVGBAnApqRTl9a2Y149GT+TZBHweNszwQ1ObBJuvPGQ7DiFKjQoUgH33cmBjpIUhbuZsRyEKwMVcDx+P88CvD/JwIbGE7TiEKC2VL1CZZQ1oFkkwp68dBNR3j3TQnFB7eFnq4/9OJaK2mY7lIEQWVL5AHY0uQFJRHaYH2bAdhSgQNQEf30z3Q0VDK76mE3gJkQmVLlASKYOTMYUY7GoKc31NtuMQBeNrY4A3BjnhYHg+7mVWsh2HEKWj0gXqflYlimtbMI1GT6SLVox0g72JNj46Ho8WkYTtOIQoFZUuUMejC6GnIcQor15sRyEcduHCBbi7u8PFxQVff/31/3xOS12A9VN9kVPZhM1X0llKSIhyUtkC1dQmxvnEYoz3taTOEeSpJBIJli5divPnzyM5ORkHDx5EcnLy/zymv4spXgyxwY5bWWimURQhPUbIdgC2XEwqQVObBNOCrNmOQjgsPDwczi4uMLe2Q2FdK4bOeBU/Hr2GsZMMIJYwqG0WoVUshY2hFjSEfORXNeH7S2nQVBOAx+NBS40PTTUB9DSF0NNUg4GWGox01GCup0m/GBHyHLxn9RQbO3YsU1FR0SMXKi8vh5mZWY88V0/IrmhEq1gKDwu9Zz6Oa7k7g7J3nJRh0CqWolUshVgiRYtIijaxFFKJCM1iALxHtyDwAUj//BotNcF/R0wSMSAQQlSRDzVTWwj4PEik7f/bUhfw0SaRQsDjQU3Ag5qADzUhHxpCPtSFfGgIBVAX8iHvmx7o50X+FDU30LPZo6KiLjIMM/afH39mgQLQYx0xQ0JCEBkZ2VNP1y0ltS3o//VVLB3mgvdGuz/zsVzK3VmUvX1ldS2IK6hFVkUDonKqkVpSDyNtNcQV1AIAgu2MkF/dBBsjLWg1VyA/NxtzZ0yEqa4GYu/fQmZqEr78dBV0NYTQUhNAQ40PdQEfPB6gZWYHhzfDcP7tQbAw0EKLSIImkRhNrRLUNItQ2yRCTVMbSutbUVbXgtpmEbIqGpFb2YTaZhGC7AwRnVcDdQEfTmY68LU2gLO5LvxsDOBrbQA9Tdmd8kw/L/KnqLmBHs/e7u9jKjnFdyq2EFIGmBpI03vKjmEYZJQ1IDynCuHZVSivb8XdP7eE93YwRmVjK3xtDBBsZ4TFQ5zhaKoDR1Odx9Nv9+7dwxeXfsaiwSsAAGkXc+BjqQMXc912r8dvqQWfz8PqM8nYtaA3tNQFMIJ6h7LWNomQV92I9NIGpJXW42FJPfKrmnAkqgDAo0HcBF9L6Gmqoa+jMfo4GsPKUKubrxAh3KVyBYphGByPLkSgnSGczNp/kyGKrby+FTceluOPtDIUVjcjJr8GAGCmp4FQR2N8NsET/raG8LLUh7bGs/8J9O7dG+np6cjOzoa1tTUOHTqEAwcOPPXxPEaC90a746szyTibUIwX/Kw6nNtAWw2+2obwtTb8n49XNbYhvqAG8QW1yK9qwpn4IhwMzwMADHEzg6WBJoa4maG/iykMtGQ3wiJE3uRWoBYtWiSvSz1TcnEd0krr8dVk7w49niu5u0JVsjMMg4TCWlxOLsUfaeVIKHw0VWemp4GpAdaY3dcOfRyMYW+iDR6vcys7QqEQW7duxZgxYyCRSLBw4UJ4ez/9Z8fU1BQL+jvgZEwhvjidjEEuZjDQ7l7RMNZRx1B3cwx1f9Qr8uvpfkgtqUN4dhWyKxpxIroQhyLyIeDzMC3IGi5muhjtbQFHU51OXUdVfl64RFFzA/LJLrc1KK746kwy9t3LQfjHI2Gk07GpF8I9DMMgrqAWZ+OLcC6hBCKJFJWNbQi0NcQwD3MMcTODl6U++HLur/jXvHxiYS0mbb2Nl3rbYf00X5leUySRIja/BjfSypFSXIerqWUAALdeungxxBZD3Mzg2uvZm4EIYRmtQYklUpyKLcJwD3MqTgrqYWk9LiWV4GB4PgprmqEm4GGwqxkm+FlimLsZjHQ02I4IAPCxNsDCAY7YeTsb04Ks0dvBWGbXUhPw0dvB+PE1CqqbcCmpFJeSSvDjtQysOZsCT0t9TA2wwsQAK1ga0LoVUQwqNYK6nlaGV3dHYPvcYIz1sWA7DumguhYRzsQV43BkPmLza9DbwQi6GkJM8LPCKK9enFp3+fvOpsZWMUZvugltdQHOLh8EdaH874svq2/B2fhinIotAg+PRp2DXM3wUm9bjPA0h4aQ7sUinNDuCEpm/2I++OADeHh4wM/PD1OnTkVNTU27j3tWG5medjy6EIbaahjm8fS9+0eOHIG3tzf4fP4zt1A6ODjA19cXAQEBCAkJkUXcTutodnm+5h1VVVWFUaNGwdXVFaNGjUJ1dTVi8qqx/lwK+qy9go9PJKCpTYzqazuR9p/3EbNlEfZ9uYS14vS817C1tRUL589B8ZnNSC9rwNenolhICZjraeLVAY44uXQAvn8xEEuHuSA+txxLfo2G+1vbMfnzPcirbPqfr9mzZw/MzMwQEBCAgIAA7Ny5k5Xs/7Rw4UKYm5vDx8en3c8zDIPly5fDxcUFfn5+iI6OlnPC9j0v9x9//AEDA4PHr/fq1avlnPDp8vPzMWzYMHh5ecHb2xtbtmx54jEyfd0ZhnnWny67ePEiIxKJGIZhmJUrVzIrV6584jFisZhxcnJiMjMzmdbWVsbPz49JSkrqzmWfqq65jXH75Bzz6YmEZz4uOTmZSU1NZYYMGcJEREQ89XH29vZMeXl5T8fslo5kl+dr3hkffPABs379eqZFJGZe/XIbE7jyAGP/4Rlm+s93mI+OxzMxedWMVCpldHR02I76zNcwODiYYRiG+emnn5jFixczDMMwE9efYHyXhzFZ5Q2sZf6LWCxmHJ2cmUN/xDGfnYhj7D84xTh8eIZ5dXc4cz21lJFIpMzu3buZpUuXsh31CTdu3GCioqIYb2/vdj9/9uxZZuzYsYxUKmXu3bvH9OnTR84J2/e83NevX2cmTJgg51QdU1RUxERFRTEMwzB1dXWMq6vrE+8XPfS6t1uDZDaCGj16NITCR0tcoaGhKCgoeOIx4eHhcHFxgZOTE9TV1TFr1iycOnVKJnnOJ5SgVSzF1Oe0NvL09IS7+7Nv3uWqjmSX52veGSfPXQbfewwGfXMd15psUd3QjNWTvbFnYR+sm+qLAFvDTu/Ak5WOvIanTp3CK6+8AgDYvmgkagWG+PRkAphnT6nLXHh4OFxdnPHSED+snuKHuQZpCNQoRXxBLd4+FINJP91GbK0GpHLvY/F8gwcPhrHx09fyTp06hfnz54PH4yE0NBQ1NTUoLi6WY8L2PS83l1laWiIoKAgAoKenB09PTxQWFv7PY2T5ustlUnzXrl0YN27cEx8vLCyEra3t47/b2Ng88c33lGPRBXA01UGgrWGPPB+Px8Po0aMRHByMsLCwHnlOeZDna94RRTXNWP17MlrHfIqf7zzawLL31d6o/vU9zO/nAN1/3KfU0tKCkJAQhIaG4uTJk6xk7shr+PfHWBnrgp94BncyKnE6rkiuWf/pn9nd7SxgVRmNu6uGY91UP0ikwMlifZxFb7hPfBNTZ85Cfn4+i4k7jms/251x7949+Pv7Y9y4cUhKSmI7TrtycnIQExODvn37/s/HZfm6d2sX38iRI1FSUvLEx9euXYvJkyc//m+hUIg5c+Z051LdUlTd9Gj0FGgNHo/XodzPc/v2bVhbW6OsrAyjRo2Ch4cHBg8e3NPRn9AT2dny9+xSLSO0OfSH2KE/+AIBRFkRuL7tE7j/2RvxaYOl3NxcWFtbIysrC8OHD4evry+cnZ3l9S10GS/zDjzHv4qvziRjqJt5t++N6mnqQj4m+FlivK8Ffo/MxL7IUkTqmiCVL8Gkj7bhetgXMNSmna+yEBQUhNzcXOjq6uLcuXOYMmUK0tO5dXRLQ0MDpk+fjs2bN0NfX19u1+1Wgbpy5cozP79nzx6cOXMGV69ebXd6xtra+n9+OysoKIC1dc+3HzqXWILY/BpseikAwPNzd8RfOc3NzTF16lSEh4fLpUB1N7u8XvP2XLlyBUU1zdh6PQOHI/LB5/OwbJATZvWxxYjQ96DPvA1AD8XFxTA3N39qfgBwcnLC0KFDERMTI/cC1ZHX8K/H2NjYQCwWo662Bt/ODMCkrXfw7cVUrJ0q23ujnuZ52Xk8Hib1dsGk3i6IzKnCz9czcE06AP86GINAOyO8MchRpv0Au4PNn+3u+Psb/vjx47FkyRJUVFTA1NSUxVT/JRKJMH36dMyZMwfTpk174vOyfN1lNsV34cIFfPvttzh9+jS0tbXbfczf28i0tbXh0KFDmDRpUs9nSSyBp6V+p++sf5rGxkbU19c//u9Lly49dYcO18jrNf+nsroWfHE6CUM3/IEjkfmY1ccWNz4YivfHuMPGSBuTJk3C3r17AQB79+5tdzRYXV2N1tZWAEBFRQXu3LkDLy8vmWf/p468hn//fo4ePYrhw4fDx9oQC/o74kB4HqLzquWeG+hY9r/WD0IcjDHRsBAmEf+GuZ4GfriajsHfXseOm1mcPD140qRJ2LdvHxiGwf3792FgYABLS0u2Yz1XSUnJ47XJ8PBwSKVSmJiYsJzqEYZh8Nprr8HT0xPvvvtuu4+R6ev+tN0TTDd38Tk7OzM2NjaMv78/4+/v/3hHU2FhITNu3LjHjzt79izj6urKODk5MWvWrOnOJdtVXNPM2H94hvnhysMOPf748eOMtbU1o66uzpibmzOjR49+IndmZibj5+fH+Pn5MV5eXjLJ3RUdyc4wsn/N/66hRcRsvJjKzNl5n3H66Czz4dE4Jr+q8YnHVVRUMMOHD2dcXFyYESNGMJWVlQzDMExERATz2muvMQzDMHfu3GF8fHwYPz8/xsfHh9m5c6dMsz9Le6/hZ599xjg7OzMMwzDNzc3MjBkzGGdnZ6Z3795MZmYmwzAMU98iYvquvcKM2XSDEYklnMp+6tQphmEYZtWqVYyXlxfj5+fHDB06lElJSWEYhmHi82uYuTvvM/YfnmFC111hDj7Ilev3MGvWLMbCwoIRCoWMtbU1s3PnTmbbtm3Mtm3bGIZhGKlUyixZsoRxcnJifHx8nrkLV56el/vHH398/Hr37duXuXPnDsuJ/+vWrVsMAMbX1/fxe/nZs2dl8bq3W4OU/kbdvXdz8PnpJFx5dzBczKndi7xIpQyORhfgu4tpKKtvxfQgaywf4Qp7k54ZxXJVR44guJBYjDd/icYn4z3xxmAnOSXrOfcyK/HtxVTE5NVggq8lZoTYYJh7+1OyhHSQarY6OpdQDFdzXSpOcnQvsxJrziYjqagOAbaG2DY3GMH2RmzH4owx3hYY7m6Ga6llmOBnqXBHZvRzNsHxt/rjUnIJNl56iFd3R2C4hzk+e8Grx6bRCQHktM2cLeX1rYjIqcI4X+7PQyuD/KomvH0oBrN33Ed1Yxu2zArAiSX9qTj9A4/HwxeTfRCTX40vf+fmluLn4fF4GONtiTP/GoRPxnsiPLsKozfdwPpzKahvEbEdjygJpS5Ql5JLIGWA8b7Ud0+WRBIpfv4jA6M23UBFfSveH+2Ga+8PxeQAa87cXMs1dsbaWD7CFReTSnEttZTtOF2mLuTjjcFOuPb+EEwJsMa/b2Zh+MYbOBtfxPpNyUTxKfUa1NydD1BY04xr7w2hN0oZicypwscnEvCwtAFjvHvhi0neKt0tuzPHYLeJpZjwwy00iyS4/M4QaKkrfuPWuPwarDuXjMzyRnhY6GPdVF/YmbS/i5eQv5Fvs1i2VTW24V5WJcb5WFBxkoGapjZ8dDweM7bfQ2OrBDvnh+Df80JUujh1lrqQj6+m+KCguhlbr3Prxsyu8rc1xME3+uHtkW6Iza/B6M03sONmFsQSKdvRiAJS2gJ1ObkEEimD8bT+1OPOJxRj2cEYHI4swKLBTrj0zmCM9OrFdiyFFOpkgmlB1gi7mYWMsnq24/QIPp+HeaH2uPzuYAx0McPacymYtu0ukovq2I5GFIzSFqjziSWwNdaCt5X82nIou+rGNiw/GIO3fo2GVCrF78sG4uPxntDRUPrNoDL18XhPaKsL8enJRKVat7E00MKO+cH46eUgFNU0Y+LW2/j2Qionb/Il3KSUBaq2SYQ7GRUY72NJ03s95EpyKUZvvonzicV4b5Qb9i7sCy8q/o9FRETAz88PDMOgsbER3t7eSExM7NDXmupqYOVYd9zPqsLJWMVobtpRPB4PE/wsceXdIZgeZI2D4Xl4ecd9JBTUsh2NKAClLFBXUkohkjB0am4PqG0W4b3DcXh9XyRMdNRxaulA/GuEK9QESvmj02W9e/fGpEmTUFhYiJUrV2Lu3Lmdan81u7cdAmwNseZMCmqblG+btqG2Or6d4Y8fZweisKYZU3++g63X0mltijyTUu7ie31vBJKL6nBn1XAaQXXDg6xK7LydhWup5Vg61BnLhruycmy5omhra4OhoSF8fX1x9+5dCASd25WXWFiLSVtvY3YfO9aaycpDTVMbPj2ZiDPxxQi2N8L3L/orfYcR8lyqsYuvvkWEm+kVGEvTe10mkTLYciUds3fcR1Z5I4691Q/vjnan4vQclZWVkEgkqK+vR0tLS6e/3sfaAIsGOSG9tB6x+TU9H5AjDLXV8ePsQGyZFYCHpfUYv+UWjkTmK9X6G+kZSveOcy21DG1iKd2c20WldS2Ys/M+Nl15iMkB1ji1bCACbKkTREcsXrwY1tbWmDNnDj788MMuPcfS4S7IrWrCpycTIJEq7xs2j8fD5ABrXFgxGL7WBth3LwdvH4pFQ6uY7WiEQ5SuQEXkVGOYuxmC7OhNtbOup5Vh3JZbiMuvxYYZfvj+Rf8nTrQl7du3bx/U1NRgbGyMVatWISIiAteuXev08+hpquGzF7yQWFiHX+7nyiApt1gbauHX1/tijLcFzsQXYdKPt5FSTNvRySNKtQbVJpYi6KvLmOhvifXT/NiOozDaxFJsuJiKHbey4WGhh60vB8HFXJftWAqpM50knoZhGMzfFY7YvBpcfX8IzPU0eygdt93PqsTygzGobRbhy0neeKm3LU3Tqw7lX4OKyKlCQ6sYwz3optGOKqhuwsx/38OOW9mYG2qHk0sHUHFiGY/Hw+rJPmgVS7H2bArbceQm1MkEZ5cPQm8HY6w6noB3D8ehkab8VJpSFairKWVQF/IxwIUbp1Fy3e30Crzwwy1oq/GxbU4Q1kzxhaaa4veDUwaOpjp4c6gzTsUW4W5GBdtx5MZMTwN7F/bBOyPdcDK2EFN/uoOMUuXosEE6T2kKFMMwuJpaiv7OJtBWp3WTZ2EYBjtuZmH+rgcw19fE+ml+dCQJBy0Z6gx7E218eioRrWLV6b4g4PPw9khX/PpaX1gZaWHyT3dwKamE7ViEBUpToLIqGpFb2YQRnjS99yzNbRKs+C0Wa8+lYLSXBY4vGQAHOmSOkzTVBPhykjeyyhux81Y223Hkrr+LKdZP84WzuS4W7Y/ClivpkCrxzkbyJKUZalxLKQMADPego6efJr+qCYv3RyGlpA4fjHHHkqHOSrMIXVZWhjt37qCoqAhaWlrw8fFBSEgI+HzF/h1sqLs5xvta4Ier6ZjkbwVbY9U6usLSQAuHF/fDx8cTsOnKQ6QU12Hji/7U/1FFKPa/3r+5mloKDws9WCvY8dnycjejApO23kZ+dRN2vdIbS4e5KEVxun79OsaMGYMJEybg/PnzKC4uRnJyMtasWQNfX198/vnnqKtT7G3Ln73gBQGfhy9OJ6nkzayaagJsfNEfn07wxKXkEkz7+S7yKpvYjkXkQCl+DaltEiEipxpvDnFiOwonHXiQh5OxhTDR1cCO+SFwVKIpvXPnzmHHjh2ws7N74nNisRhnzpzB5cuXMX369E4/95EjR/DFF18gJSUF4eHhCAkJ6YnInWZpoIV3Rrph7bkUXE4uxWhv1bsJncfj4fVBTvCw0MfSA9GY+vMd/DQnCKFOtCFKmSnFCOpGejkkUoa2l/+DVMpg/bkUfHwiAdrqAhx/q59SFScA2LBhQ7vFCQCEQiGmTJnSpeIEAD4+Pjh+/DgGDx7cnYg9YsEAB3hY6OHL35PR2KK6W68Hupri92UD0cfRGHN3PsDRqAK2IxEZUooCdS2lFMY66giwNWQ7Cmc0t0mw9EA0/n0zC3ND7bBzfgj0tdTZjiUz8+bNQ23tf49wyMnJwYgRI7r1nJ6ennB3d+9utB6hJuBj9WQf9NLXwA/XlOP03a6yM9HGNzP8EOpkgvePxOH7yw9VcupTFSh8gRJLpPjjYTmGuptBwFf8NZWeUF7filk77uNCUgk+neCJryb7QKjkx2MMHDgQffv2fTzlN3r0aKxYsYLtWD2qj6MxXMx18Z/b2UgrUe17g/Q11bD71d54McQGP1xNx7uH41RqK76qUPg1qJj8GtQ0iTCCpvcAAOkl9ViwJwJVjW3YPjcYY1RkvWLx4sXw9vbGsGHDYGpqipiYGFhYPP97HzlyJEpKnrzHZu3atZg8eXKHrh0WFoawsDAAQHl5eeeCd9KqcZ64lFyKz04m4rfFoUqx0aWr1AR8fDPdD3bG2vju0kMU1jQjbF4wDLWVd6ZA1Sh8gbqaUgYhn4dBbqZsR2FdVG4VVh6Nh56mENvmBsHPxpDtSHKzf/9+fPXVV9i3bx/i4+Mxfvx47N69G/7+/s/8uitXrnT72osWLcKiRYsAQOYbKYx11PHROA98eCwBR6MKMDPEVqbX4zoej4dlw11ha6yND47EY8VvsVgzxQc2Rqq1HV9ZKfy8z7XUUvRxNIa+phrbUVh1LbUUc3Y+gJQBwuYFq1RxAoBjx47h9u3bmD17NtavX4/t27djwYIFbMeSiZnBtgi2N8L686mobmxjOw4nTA6wxv7X+iCzrAHTt93FQ2qPpBQUukDlVzXhYWmDynePOBZVgDf2RcHVXA9H3uwHOxU8nfTkyZMwN//vTdp9+vTBgwcPuvWcJ06cgI2NDe7du4cJEyZgzJgx3Y3ZI/h8HtZM8UFtswjfXkxlOw5n9HUywY5XQsAwwMzt9xCVW812JNJNCl2grqU+6h4xQoW7R+y8lYX3jsQh1MkYBxeFwlRXg+1IcrVmzRpUVVW1+zl1dXVcu3YNZ86c6dJzT506FQUFBWhtbUVpaSkuXrzYnag9ytNSHwsHOOBgeD6ictv//lWRh4U+jr3VH0baapi78wH+SCtjOxLpBoVeg7qaWgYnMx2V7CXHMAy+uZCG7TcyMd7XApteCoCGUPU6kfv6+mLixInQ1NREUFAQzMzM0NLSgvT0dMTGxmLkyJH4+OOP2Y4pEytGuuFMfDE+OZGIM/8aqPQ7NTvK1lgbR97sjwW7w/H63khsfNEfkwOs2Y5FukBhf6IbW8W4n1mpkqMnifS/xWlOXzv8ODtIJYsTABw9ehR37tzBmDFj4O3tDYlEAn19fcydOxfh4eHYtGkTzMzM2I4pEzoaQnw+0QupJfXYczeH7TicYqangYOLQhFsb4S3D8XS66OgFHYEdTujAm0Sqcp1jxBJpHj3cBwuJ5Vg5Rh3vKVEDV+7IioqCkVFRfj1119x/fr1//lcc3MztLSUuzfjGG8LDHM3w6bLDzHBzxKWBsr9/XaGvqYa9i7sgxWHYnE0Mh+NrWIsHebCdizSCQo7goovqEVfR2OEOBixHUVuWsUSLDsQjd/jivDOKDcsUZKGr93x5ptvYsSIEUhNTUVISMjjP8HBwaz1zpOnv07fFUsZrP49me04nKOpJsDWlwPhYq6LDRfTqOuEglHIAsUwDE5EF8BIWx1qKjLv3iKSYPH+KFxMKsWXk7yxeIgz25E4Yfny5UhJScHChQuRlZX1+E92djaysrLYjicXtsbaWD7CFecTS3A9lTYF/JNQwMfGFwMed5345kIaFSkFoZBTfJnljSiqbcHS4apxc25Tmxiv743EvaxKfD3NF7P6tN8cVZVt27aN7QisemOQE5KKarH2bApCnUygpa6aa5JPI+Dz8PU0P6gL+dh+IxOtYgn+7wUvlZ+B4DqFHH7cTn/UTmaQi3Iufv9dY6sY7/wWi+yKRnz/oj8VJ9IudSEf8/s5IKO8AT+qeDPZp+Hzefhqsg8WDnDE7js5WH8uhU7o5TiFHEHdzqiAnbE27EyUu51JU5sYr+6JQFRuNbbMCsALflZsRyIcFupkghnBNgi7mYUpgdZw66XHdiTO4fF4+OwFT+hrCrHvfi4a2iRYM9kHfGo0zUkKN4ISSaS4l1mJQa7KPb3X1CbGwj0RiMypwqaXqDiRjvl4vCf0NIX45EQCjQ6egsfj4e2Rrnipty0OPMjD/51OpDUpjlK4AhWTV4PGNolSF6jmNgle2xOJ8OxHxWmSPxUn0jHGOur4aLwnInKqcTgyn+04nMXj8bByjDsWD3bCL/fz8MXpJCpSHKRwBep2ejn4PKCfs3IWqBaRBB8cjcOD7Ep8/2IA3QFPOm1msA36OBpj/flUVDS0sh2Hs3g8HlaN88DrAx2x914uVv+eTEWKYxSuQN1Mr4C/rSEMtJSve3mbWIq3fonCvcxKbHzRH1MCqTiRzuPxeFg31QdNbWKsO5vCdhxO4/F4+GSCJxYOcEBSUR1tQecYhSpQtU0ixBfUYJCL8o2exBIpVvwWg+tp5XhvtDumBtqwHYkoMBdzPSwe7IzjMYW4m1HBdhxOe7RxwguuvXSx/UYmfrqewXYk8ieFKlB3MysgZYBBbsq1vVwqZfDhsQScSyjBJ+M98XJf2kpOum/ZcBfYm2jj05OJdBz6c/B4j7agTw20xneXHmLX7Wy2IxEoWIG6lVEBXQ0hAmwN2Y7SYxiGwRe/J+FYdAFWjHTFG4Od2I5ElISmmgBrpvggq6IR+6hZ6nPx+TxsmOGHMd69sPpMMn6LyGM7kspTqAJ1O70CoU4mStPe6K8jM/bdy8Ubgxzx9ghXtiMRJTPI1QyvDnDAhosPkVFGp8w+j1DAxw+zAzHEzQyrjifgVGwh25FUmsK80+dWNiKvqkmptpfvuJWFqymleLmvHT4e70ltV4hMLBnqAi11AT4+nkj3RnWAhlCA7XODMdTNDD9dz6BDD1mkMAXqVvqjhd6BSlKgDkfmY925VPhZG2DNZB8qTkRmzPQ08MkET4TnVOE3ujeqQ7TUBdgyOxBCPh9Lfo1GbH4N25FUksIUqNvpFbA21IKTEpyeeyW5FB8dT8BgNzOsn+5HbVaIzM0MtkGokzHWnUtBWV0L23EUgr6mGvYs7A0TXXUs3BOBzPIGtiOpHIUoUGKJFHcyKzDQxVThRxoROVVYeiAaPlb62DYnCOpChfhfQBTco3ujfNEqluLLM3RuVEeZ62li38K+4AGY/59wlFJxlyuFeHeML6xFfYtY4af30krq8dqeCFgbamHXgt7Q0VDIXr1EQTmZ6WL5cBecjS/G1ZRStuMoDEdTHex5tQ9qmtrwyq5w1DaL2I6kMhSiQN16WAEeDxigwDfoFlU3Y8HucGipC7DvtT4w0dVgOxJRQYsGO8Otly4+O5mIxlYx23EUhq+NAbbPC0ZmeQPe2BeJFhHdVyYPClGgbmeUw8fKAMY66mxH6ZLaZhFe2R0OB1Md7F3YBzZGyn1MCOEudSEf66f5obiuBd9dSmM7jkIZ5GqGjS8GIDy7Cm8fioGEdkTKHOcLVH2LCDF5NQq7vfyv/no5lY341zAXeFjosx2JqLhgeyPMC7XHnrs5iMmrZjuOQpnkb4X/e8EL5fWtWHuW1vJkjfMFKiq3Gv62hhiogNN7DMNg1fF43M2sxNfT/NBfAb8Hopw+GOOOoW5mWHMmGW1iKdtxFMrCgY4IsjfCrjs52H2HWiLJEucL1O30CiQU1iLI3ojtKJ225Wo6jkcX4p2RbpgeTM1fCXfoaaphTl97ROXV4N83MtmOo3A+Huf5uCXS5WTacCIrnC9Q97MrEWRnCE01AdtROuVoVAE2X0nHjGAbLB/hwnYcQp4w0qsXJvpb4cdrGUgvpTZIncHn87D5pUD4WRtg+cEYJBTUsh1JKXG6QNU2i5BUVIdQJxO2o3TKnYwKrDoWjwEuJlg31Vfh790iyuvziV7Q0RBg5bF4WvTvJC11AXa8EgJjHXW8tjcCRTXNbEdSOpwuUBHZVWAYKFSByiirx6bLD+FkpoOf5wTTjbiE00x1NfD5RG/E5NVgL3U87zRzPU3sWtAbzW0SLNwTgQbaut+jOP3ueT+rEupCvsIcr1Hd2IbX9kaioLoJuxb0VspTf4nymRxghWHuZthwMQ35VU1sx1E47hZ6+GlOENLLGrDsQDTEEtp00lM4XaAeZFch0FYx1p9EEimW/BqN4toW/Dw3mO51IgqDx+Nh7VRf8HnAR8cT6MjzLhjsZoY1U3zwR1o5tlxNZzuO0uBsgXq0/lSrENN7DMPgi9NJuJdVia+n+SLITvF2HBLVZmWohVXjPXE7owJHogrYjqOQZvexw/uj3fHT9Qzsv5/LdhylwNkCFZlTBamCrD/tv5+LXx/k4c0hzpgWRNvJlcUHH3wADw8P+Pn5YerUqaipqWE7kkzN6WOHUEdjnIkrQkktNUXtireGOmOouzm+PJ2Ee5mVbMeRmdNxRahrkX1PQs4WqL/WnwLtDNmO8ky30yvw5e/JGOlpjpVj3NmOQ3rQqFGjkJiYiPj4eLi5uWH9+vVsR5IpPp+H9dN88SC7Ch+foKm+rhDwedg8KwD2JtpY8muUUq7pJRbWYvnBGByOkP3ZYhwuUNxff8quaMSSX6PgYqaLzbMC6VwnJTN69GgIhY86zoeGhqKgQPmnvhzNdLFyrAeupZbhWDQdd94V+ppq2PlKb0ikDF7fG6l0O/v23s2BlpoAM0NsZX4tThYoRVh/qm0W4bW9ERAK+Nj5Sgh06egMpbZr1y6MGzeu3c+FhYUhJCQEISEhKC8vl3Oynvdqfwf0djDCl78n0VRfFzma6vy5s68e7/4WC6mS3GNW1diGU3FFmBZkLZddypwsUFxff5JKGaw8GgcjbXVsnxsMW2PasaeoRo4cCR8fnyf+nDp16vFj1q5dC6FQiDlz5rT7HIsWLUJkZCQiIyNhZmYmr+gyw+fzsGGGP0QSKT46Hk9TfV00yNUMn0zwwqXkUmxWkp19B8Pz0CaWYkF/B7lcj5O/9nN9/WnzlYe4mFSKNVN80MfRmO04pBuuXLnyzM/v2bMHZ86cwdWrV1WqI4iDqQ5WjvHA6jPJOBpVIJfpHGW0cIADUovrsPNmJnyt9THKy4LtSF0mlkjxy/1cDHAxgWsvPblck5MjKC7f/3QpqQQ/XMvAzGAbzOlrx3YcIkMXLlzAt99+i9OnT0NbW/VGyQv6O6CPgzFWn0mmqb4u4vF4WDPVBwNdzfD2oViF7nl4KbkUxbUtWNDfUW7X5FyBqmsRIbGQm+tPmeUNePdwHPxsDPDVFB+V+o1aFS1btgz19fUYNWoUAgIC8Oabb7IdSa74fB42zPSDWPLo2Bia6usaDaEAqyf7QFtdgMX7o+SyPVsW9tzJga2xFoZ7mMvtmpwrUFxdf2poFWPx/iioC/nYNjeYk6M70rMyMjKQn5+P2NhYxMbGYvv27WxHkjt7Ex18ONYdGWUNOBat/LsYZcXCQBNbXw5CblUT3j8cp3CbJpKKahGeU4X5oQ4QyHG3MucK1P2sKqgLuLX+xDAMPjgSh6zyBmydHQhrQy22IxEiN/P7OcDZTBefn0pCXqXy3dcjL6FOJvhonAcuJZdim4KdwfXX1vIX5bwWycECVYkAjp3/tP1GFs4nluCjcZ50Ki5ROXw+D+um+YLP4+G9I7F0LEc3vDbQERP9rbDxUhpuPlSMWxKqGttwKrYIU4OsYaAt3wbYnCpQXFx/updZge8vp+EFP0u8Pkh+i4OEcIm1oRa+nOyNiJxq7LiVxXYchcXj8fDNdF+4muth+aEYheg0cSgiD61y3Fr+d5wqUP9df+LG1u3i2mYsPRCDoe5m+Ga6H22KICptaqA1xvlYYOOlNCQX1bEdR2FpqwuxfV4wxBIpNl5KQ4tIwnakp2oTSxGZU43hHuZwk9PW8r/jVIF68Of6Exe6gYskUiw7EINWkQQfjvWEDnWKICrur2M5DLTU8e7hWLSKufvGynWOpjr4YVYgTsYWYe3ZFLbjPNWJmAJcSy3DvFB2bqnhVIEqqmnGpABLTqw/fXshFVG51Vg3zRcu5rpsxyGEE4x11PHtDF+kltTj+0sP2Y6j0IZ79sIbgxyx/34ufo8rYjvOE8QSKbb9kQlfawMMdZff1vK/40yBamoT43xiCcz1NNmOgktJJdhxKxtzQ+0wOcCa7TiEcMpwj154ua8ddtzKwoMs5T1SQh5WjvVAkJ0hPjqegOyKRrbj/I+zCcXIqWzC0mEurC1vcKZAxebXQCxl0NuB3fWnvMomvHckDr7WBvjsBS9WsxDCVZ+M98QQNzOs+C0WNU1tbMdRWGoCPra+HAShgIclv0ZzZj1KKmWw9VoG3HrpYrRXL9ZycKZAReVUAwCr608tIgmWHIgCD8DPc4KgIWR/qpEQLtLREOLdUe6oaGjFh8eoy0R3WBlqYdOLAUgprsOXvyezHQfAo7ZG6WUNWDrMhdVjhDhToCJzq+HeS0/u++z/buv1DBTVtGDjiwHUoZyQ5/C1McDKMR64mFSKA+F5bMdRaMM8zPHWUGccDM/DyRh2z+FiGAZbr6fDwUQbE3wtWc3CiQIlkTKIzq1GsAN7o6cLiSXY+mcT2FEsDmkJUSSvDXTEYDczrP49GQ8VuBEqF7w3yg19HIzx8YkEZJQ1sJbjxsNyJBbW4a2hzhAK2C0RnChQD0vrUd8qRog9OwWqsKYZHx6Lh6+1Ad4bTce2E9JRfD4PG2f6Q09TiH8diOHMGooiEgr4+GF2ILTUBPjq92Q0t8n/tWSYR2tPVgaamBpoI/fr/xMnClRkThUAsLJBQiyRYsWhGIglUvw4OxDqQk68JIQoDDM9DXw30x9ppfVYd4679/QoAgsDTWyeFYDwnCqsOSv/9agH2VWIzK3G4iHOnHgvZD8BHq0/metpwMZI/k1Yf7iWgYicaqyd6gsHUx25X58QZTDU3RyvD3TEvnu5uJRUwnYchTbI1Qzz+9nj1wd5uJAo39dy67UMmOpq4KXe3DigkhsFKqcavR2M5b7X/l5mJX68lo7pQTaYEkj3OxHSHR+MdYePtT5WHotHcW0z23EU2nuj3eFnY4APj8WjqEY+r2VMXjVuZ1TgjUGOnGiWAHCgQBXXNqOwphnBcl5/qmpsw4rfYuBoooPVk73lem1ClJGGUIAfZgXCvZceVh2Lh0giZTuSwlIX8rFlVuCjJYjf5NNBPuxmFgy11TAn1F7m1+oo1gtU5J/3P4XIcQcfwzBYeTQO1Y0i/DA7kPrsEdJDnMx08XJfO9x4WIENF9PYjqPQHE11sHqyD8Kzq/DT9QyZXutBViWuppTi3VFu0OXQ+yEHClQVtNUF8LLUl9s1d9/JwZWUMqwa5wEfawO5XZcQVTA5wBrzQu0RdjNL7msoymZakDWmBFhhy9X0x5vJeppUymDN2RSY6GpgZjA31p7+wn6Byq1GgK2h3Pbbp5bU4WhUAaYGWuPVAQ5yuSYhqubTFzzhb2OAD47EIYdjPeYUCY/Hw1dTfGBtqIW3D8WitlnU49c4GVuIhMJarBzrDi11bqw9/YXVAtXQKkZKcR1C5LS9vEUkwYpDsSirb8WnEzzpfCdCZERDKMBPc4IgEPDwFod6zCkiPU01/DA7EAI+D99dTO3RtlLNbRJsuJgGPxsDTPbn3kYxVgtUTF41pAzkdoPudxfTkFpSjw0z/GCiqyGXaxKiqmyMtLHppQCkltThs5OJbMdRaAG2hngxxAb77+fhZGzPtULaeSsLxbUt+HSCF6s9956G1QIVmVMNPg8ItDOU+bXuZFRg5+1szAu1xzAPds42IUTVDHM3x7+GueBIVAF+i6B+fd3x1lAXhNgb4f9OJqGguvtHxZfVtWDbjUyM87FAH0dunGL+T+wWqNwqeFjoQ09Ttg1ia5tEeO9wHJzMdPDxeE+ZXosQ8r/eHumGQa6m2H0nB3H5NWzHUVgCPg+bXgqAlGHw3uG4bm8933jpIUQSKVaN8+ihhD2PtQIllkgRk1cj8+3lDMPgk5MJqGhoxZaXAjm3CEiIshPwedj8UgDaxFIs3h+FsroWtiMpLFtjbXwxyRsPsquw41ZWl58nuagOh6PysaC/A+xNuNtBh7UClVpSj6Y2icw3SJyKLcKZ+GK8M8oNvja0pZwQNpjoamDry0GoaxHhjf1RtGmiG2YE22CstwU2XkpDUlFtp7+eYRisPZcMQy01LBvuKoOEPYe1AhXx555+WW6QKKhuwmcnExFib4Q3hzjL7DqEkOfzstLHppcCEJdfg1V0yGGX8Xg8rJvmC0NtdbzzW2yni/31tDLcyajE2yNcYaDF3vl7HcFagcquaMQIT3NYGcqmQaxUymDzlXToagqx6aUACDi4Q4UQVTPG2wLvj3bDydgibLuRyXYchWWso47vZvrDUEsNmy4/7PDXiSRSrD2bAidTHU61NHoa1grU1ZQyaMrwSPU9d3NwNKoA74x0o9NxCeGQpcNcMNHfChsupuFycinbcRTWEDczuFnoIexWFsKzO9Zl4nBEPrIqGvHxeE+osXwYYUewkrCsvgWFNc0IsDWUyfNnlTfg24upGOZuhpkh7B+6RQj5Lx6Phw0z/OBrbYAVh2KQWlLHdiSF9dE4T9gaaeP9I3FobBU/87H5VU1Yey4FM4KsMcJTMW61YaVAxebVAJDN/U8SKYP3j8RBQyjA19P9qFsEIRykqSbAjvkh0NUU4vW9kahsaGU7kkLS0RDiu5n+yK9uwvrzTz8sUipl8OGxePB5PLw90k1h3hfZKVD5NRDyeTJp1LrjVhai82qwerI3eulr9vjzE0J6Ri99TYTNC0FdswirzyTTzr4u6uNojNcGOOKX+3m4lV7e7mMOhOfhbmYlPh7vCRsjxVnyYKVAxeTVwNNSv8cPxXpYWo/vLz3EWG8LTPK36tHnJqrns88+g5+fHwICAjB69GgUFRWxHUnp+Nsa4ruZ/jgdV4RlB6IhpjOkuuT9Me5wNtPByqPxqGv534ay+VVNWH8uBQNdTDG7D7e6lT+P3AuURMogvqCmx9efRBIp3j0cC11NIdZM9VGYISzhrg8++ADx8fGIjY3FCy+8gNWrV7MdSSmN9rbA6kneuJJSho9PJND28y7QVBNg44sBKKtvxVe/Jz/++F9TezweD19P91W490W5F6iMsgY0tkl6fP3p5+uZSCysw9opPjClRrCkB+jr//eMssbGRoX7x61I5vVzwPIRrjgcWUAHHXZRgK0hlgx1xpGoAlxPLQOguFN7f5H70YkxeY9O0O3JEVRyUS1+vJaOSf5WGOdr2WPPS8gnn3yCffv2wcDAANevX2/3MWFhYQgLCwMAlJe3vwZAnu+dka4or2/Fz39kwlRXAwsHOrIdSeH8a7grsisasep4PHYv6K2wU3t/4T1nON3jY+1Vx+JxPrEEsf83qkd+IxVJpJj+8x2Y6mlg48wAGOmo90BKoipGjhyJkpInT31du3YtJk+e/Pjv69evR0tLC7788stnPl9ISAgiIyN7PKeqkEgZLP01GheSSrBlVgAmB3DvjCKuSyioxZSf78BERx1NbRJcWDFIEUZP7RYDFkZQj9afemq6ZPsfmYgvrEPYvGAqTqTTrly50qHHzZkzB+PHj39ugSLdI+DzsHlWAF7ZFY73j8TBSFsdg93M2I6lUHxtDDDA2QQ30yvwan8HRShOTyXXNaiGVjEeltX32PrTw9J6/HAtHS/4WWK0t0WPPCchf0lPT3/836dOnYKHB3ePJVAmmmoC7HglBC7meth+IxMPsirZjqRQ7mVW4nZGBfQ0hLiYXIKG59zAy2VyLVDx+TVgmJ5Zf5JIGXxwNB56mmr4cpJ398MR8g+rVq2Cj48P/Pz8cOnSJWzZsoXtSCpDX1MN+1/rjbL6VizYHYH7VKQ6JL+qCUsPRMPRVAc/zw1CcW0LvjmfynasLpPrFF/Mn4eV9USB2nU7G3H5NdgyK4CObycycezYMbYjqDRTXU0cfCMUL++4j1d3R+A/C0LQ39mU7Vic1dQmxqL9URBJpNgxPwROZrp4tb8jdt3JxgQ/S4Q6mbAdsdPkOoKKyauBk6kODLW7t1aUXdGI7y6lYaRnL7ohlxAlZqangQNvhMLWWAsL90TgTkYF25E4iWEezSilltThh9mBcDLTBQC8P8YNdsbaWHUsHs1titepQ24FimEYxOZ3/wbdv248UxfysZZuyCVE6f1VpOyNdbBwTwRup1OR+qef/8jE2fhifDjWA8Pc/9sIVltdiK+n+yKnsgnfX1a8+8vkVqAKa5pR0dDa7Q0SJ2ILkVBYi88meFGvPUJUhKmuBg680ReOpjpYdjAaV+iYjseupZbiu0tpmORvhcWDnZ74fH9nU7zc1w7/uZ39uFG3opBbgYr584UJsO36CboltS34/FQShrrSMRqEqBoT3UcjqYEupli0PxL77+WwHYl1GWUNePtgLLws9fHNM05v+GicB4Z7mOOTkwloEytOv0O5FajY/BpoCPnwsNTr8nN8fjoRYqkUq8Z70NQeISrIWEcd30z3wzB3c3x2KgnrzqVAKlXN3n3Vja1YfjAa6kI+wuaHQEv96c239TTVMKu3HZKK6rDjVpYcU3aPHEdQ1fC1NujyKY4XEktwMakUK0a6wd5Ep4fTEUIUhY6GEGHzQzC/nz3CbmZh2cFolTuqo65FhFd2R0AsBbbPDYa1odZzv2akVy+M97XAlqvpyK5olEPK7pNLgWoTS5FYVNfl9ae6FhE+P50IT0t9vEb9uQhReQI+D19O8sanEzxxPrEEL++4rzKHHja0irFgVzhSiuvw4Vh39HY07vDXfjHRGxpCPj5RkK7xcilQKcV1aBNLu7z+9O2FVJTXt+Lrab5dHoERQpQLj8fD64Oc8PPLQUgqqsP0bXcVZmTQVY2tIizcE4G4glr8ODsQIzx7derrzfU1sWqcB+5mVuJYdKGMUvYcubzbx/55g25XRlCROVX45X4eFvR3hH8PnyFFCFF843wtceCNUNS3iLHyaBwuJD7Z/FcZVDe24bW9kWhoEWHTSwEY69O1kxtm97ZDiL0R1pxN5vyoUy4FKiavGuZ6GrA06Ny28FaxBB8dT4C1oRbeG+0mo3SEEEUXbG+EU0sHoEUkxZu/ROGzk4lKtS5VUN2EGdvvIjqvBsuGu3arQQGfz8P6ab5obBVjzdmUHkzZ8+RSoHQ0hBjqbtbpnXe7b+cgvawBa6b4QEdD7o3XCSEKxMZYG8fe6o83Bjli//1cTPnpDjLK6tmO1W1JRbWY9vNdlNe3Yv/CPhjfA2feufbSw1tDnHEiphC30rl7hpncz4PqqOyKRkzYchOz+9rjsxe82IpBSKfQeVDccD2tDO8fjkNjmxhfTPTGS71tFfLWlIuJxdh8NQM1TW3Yu7AP3Hp1/Tadf2oRSTB+yy2IpQwurhj8zG3qctDu/xxO7jhgGAb/dyoRAj4fi9q5M5oQQp5lmLs5zr89CMH2Rlh1PAGfnUpEaV0L27E6TCSRYv25FCz+JRq99DVwfEn/Hi1OwKNjTdZO9UVeVRO238js0efuKZwsUL/HF+NWegXeH+NO7YwIIV1irq+JfQv7Ys0UHxyOLMDIjTew924OJBy/sTe/qgkrDsXi3zezMDfUDtvnBsPS4Pn3OXVFP2cTvDXUGTtuZeFhKfemQzlXoOpaRPjqTDJ8rQ0wN9Se7TiEEAUm4PMwN9Qel1YMRoCdIT4/nYRF+yIRkVPFdrQnSKUMjkTmY+zmm4+6ks8KwJopvtBUk+3U2xuDnKAu5OPTk4mcuzeKcwVq48U0VDa0Yt1UXwj4ijdnTAjhHgdTHexb2Ac/zA5Es0iCmdvv4fW9kZwZNSQU1mLmv+9h/blU9HM2wd6FfTApwFou1zbWUceqsR4Iz67CiRhu3RvFqU0S8QU1mPzTHbzSzwFf0Cm5RAHRJgnua26TYNedbGz/IxNuFnqwNNDEkqHO8LIykHuWvMom/OdOFvbezUV/ZxNMC7LB9CBruW/okEoZTN9+F/lVTbj67lAYaKvJ9fp4yiYJzhQoiZTB5J9uo6yuFVfeGwJ9Tbm/QIR0GxUoxVHd2Ib993Ox63YW1IQCOJlq45X+DhjpaQF1oWwnlxIKanEipgB77+XC38YAfRwfrQUZaLH3vpdUVIuJP97GnL72+GqKj7wv326B4szNRQfCc5FYWIcfZwdScSKEyJyRjjqWj3DFK/3tcSg8HzfTy7Hk1xhYGmhihIc5JvpbIdjeCMIeaq9W0dCK84kluJdZgXMJJdBRF+CtIc6Y18+eE5vBvK0M8Ep/B+y5m4MZwTac6NzDiRFUeX0rxmy6gbE+Flg71Vch71cgBKARlCKTSBnczqjAzYfl+PVBLvysDZFaUodxPpbwsdKHj7U+3C30od3BpgE1TW1ILq5DYkEtInOrEZdfA/AAQy01zAm1x5RAa879Ml7fIsKIjTfQS18TJ5cOkOc+AO5O8b17OBa/xxXh4orBcDLTlcclCZEJKlDKoalNjNsZFbiRVo6o3GrUtYigr6kGAy01aAj50FIXwEBLDcba6tBSF0IilaJZJEGbWIr6VjGqGtrQ2CYGDzzw+YCFvia8rQwwyNUU7hZ6nP4l/HRcEZYfjMFXk70xr5+DvC7LzSm+yJwqHI8uxJKhzlScCCGcoK0uxGgvC4z2sgAAFNU0I6W4DjmVjSisbkZZfSsKq5tRVNMMPp+HVrEUjBTQ0RDASEcdnlb6sNDXhIuZLryt9WGorc7yd9RxE/0s8VtEHr69mIaxPpYw09NgLQurIyixRIqJW++gtqkNV94bAm111uslId1CIyiiDDLLGzB2801M9LPC9y8FyOOS3Gt19Mv9XKQU1+GzF7yoOBFCCEc4m+li+XAXpJfVIzybvZuaWStQ5fWt2Hj5IQa5mmKsjwVbMQghhLTj9UHOqGxow+enk1hrD8Vagfr6fCpaRBJ8Mcmb0wuGhBCiirTUBfhkghdSiutwIDyPlQysFKjInCociy7A64Oc4EwbIwghhJPG+1qgn5MJNl5KQ3Vjm9yvL/cCJZEyWHs2BSM8zfGv4S7yvjwhhJAO4vF4+HySF+pbxNh4OU3u15d7gfotIh8x+TWYEmBNGyMIIYTjPCz0MS/UHgce5CGpqFau15ZrgaptEuG7S2no42iMF/y6f2wxIYQQ2XtnpBsMtdXxxekkuR7JIdcCtenKQ9Q0teGLibQxghBCFIWBthpWjnFHRE41TscVye26citQaSX12H8/Fy/3tYOXlb68LktIt23cuBE8Hg8VFRVsRyGENTNDbOFrbYB151LQ2CqWyzXlUqAYhsHqM0nQ1RDivVHu8rgkIT0iPz8fly5dgp2dHdtRCGGVgM/Dl5O9UVrXiq3XM+RyTbkUqItJJbiTUYn3RrvBSEdxelIR8s477+Dbb7+lKWlCAATZGWF6kA3+cysb2RWNMr+eXApURUMbAu0M8XIf+i2UKI5Tp07B2toa/v7+bEchhDM+HOcOG2MtFNU0y/xacmsWK5Uy4MvvbBFCOmTkyJEoKSl54uNr167FunXrcOnSJRgYGMDBwQGRkZEwNTV94rFhYWEICwsDAJSXlyM3N1fmuQlhkwzez7l7HhQhXJOQkIARI0ZAW1sbAFBQUAArKyuEh4fDwuLpvSOpmzkhXcLN86AI4SJfX1+UlZU9/vuzRlCEENlg9bgNQggh5GloBEVIB+Tk5LAdgRCVQyMoQgghnEQFihBCCCdRgSKEEMJJVKAIIYRwEhUoQgghnEQFihBCCCdRgSKEEMJJz2t1RAjpBB6Pd4FhmLFs5yBEGVCBIoQQwkk0xUcIIYSTqEARQgjhJCpQhBBCOIkKFCGEEE6iAkUIIYST/h+2YnxZMIi6nAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7fb7f21c3820>"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plot(fx1,-x**2,(x,-2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "version": 3
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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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   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
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   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
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  "toc": {
   "base_numbering": 1,
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   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": true,
   "toc_position": {
    "height": "538.3287963867188px",
    "left": "0px",
    "right": "1189.3333740234375px",
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   "toc_section_display": "block",
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  "vscode": {
   "interpreter": {
    "hash": "f3f87633aac09da3bda522f97956bee375b5501d1579e6458804e567301cb62a"
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 "nbformat": 4,
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