2장_함수(세상의 모든 것을 입력과 출력으로 바라보기).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "391d7d3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f0f4eafc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def arrowed_spines(fig, ax, remove_ticks=False):\n",
    "    \"\"\"\n",
    "    좌표축 화살표를 그리기 위한 함수\n",
    "    https://stackoverflow.com/questions/33737736/matplotlib-axis-arrow-tip\n",
    "    \"\"\"\n",
    "    xmin, xmax = ax.get_xlim() \n",
    "    ymin, ymax = ax.get_ylim()\n",
    "\n",
    "    # removing the default axis on all sides:\n",
    "    for side in ['bottom','right','top','left']:\n",
    "        ax.spines[side].set_visible(False)\n",
    "\n",
    "    if remove_ticks == True: \n",
    "        # removing the axis ticks\n",
    "        plt.xticks([]) # labels \n",
    "        plt.yticks([])\n",
    "        ax.xaxis.set_ticks_position('none') # tick markers\n",
    "        ax.yaxis.set_ticks_position('none')\n",
    "\n",
    "    # get width and height of axes object to compute \n",
    "    # matching arrowhead length and width\n",
    "    dps = fig.dpi_scale_trans.inverted()\n",
    "    bbox = ax.get_window_extent().transformed(dps)\n",
    "    width, height = bbox.width, bbox.height\n",
    "\n",
    "    # manual arrowhead width and length\n",
    "    hw = 1./50.*(ymax-ymin) \n",
    "    hl = 1./25.*(xmax-xmin)\n",
    "    lw = 1. # axis line width\n",
    "    ohg = 0.4 # arrow overhang\n",
    "\n",
    "    # compute matching arrowhead length and width\n",
    "    yhw = hw/(ymax-ymin)*(xmax-xmin)* height/width \n",
    "    yhl = hl/(xmax-xmin)*(ymax-ymin)* width/height\n",
    "\n",
    "    # draw x and y axis\n",
    "    ax.arrow(xmin, 0, xmax-xmin, 0., fc='k', ec='k', lw = lw, \n",
    "             head_width=hw, head_length=hl, #overhang = ohg, \n",
    "             length_includes_head= True, clip_on = False) \n",
    "\n",
    "    ax.arrow(0, ymin, 0., ymax-ymin, fc='k', ec='k', lw = lw, \n",
    "             head_width=yhw, head_length=yhl, #overhang = ohg, \n",
    "             length_includes_head= True, clip_on = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "93518e61",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "mpl.style.use('bmh')\n",
    "mpl.style.use('seaborn-whitegrid')\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.xaxis.set_tick_params(labelsize = 18)\n",
    "ax.yaxis.set_tick_params(labelsize = 18)\n",
    "plt.xlabel('$x$', fontsize = 25)\n",
    "plt.xlabel('$y$', fontsize = 25)\n",
    "\n",
    "x = np.linspace(-3, 2, 10)\n",
    "y = 2*x + 4\n",
    "ax.plot(x, y, 'k')\n",
    "\n",
    "arrowed_spines(fig, ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "983c7ba1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-3.        , -2.44444444, -1.88888889, -1.33333333, -0.77777778,\n",
       "        -0.22222222,  0.33333333,  0.88888889,  1.44444444,  2.        ]),\n",
       " array([-2.        , -0.88888889,  0.22222222,  1.33333333,  2.44444444,\n",
       "         3.55555556,  4.66666667,  5.77777778,  6.88888889,  8.        ]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "7fdee976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "mpl.style.use('bmh')\n",
    "mpl.style.use('seaborn-whitegrid')\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.xaxis.set_tick_params(labelsize = 18)\n",
    "ax.yaxis.set_tick_params(labelsize = 18)\n",
    "plt.xlabel('$x$', fontsize = 25)\n",
    "plt.xlabel('$y$', fontsize = 25)\n",
    "\n",
    "x = np.linspace(-2, 2, 100)\n",
    "a1, a2, a3 = 2, 3, 4\n",
    "y1, y2, y3 = a1**x ,a2**x, a3**x\n",
    "ax.plot(x, y1, color = 'k', label = r\"$2^x$\")\n",
    "ax.plot(x, y2, '--', color = 'k', label = r\"$3^x$\")\n",
    "ax.plot(x, y3, ':', color = 'k', label = r\"$4^x$\")\n",
    "\n",
    "plt.legend(fontsize = 20)\n",
    "\n",
    "arrowed_spines(fig, ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "468cbfca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "mpl.style.use('bmh')\n",
    "mpl.style.use('seaborn-whitegrid')\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.xaxis.set_tick_params(labelsize = 18)\n",
    "ax.yaxis.set_tick_params(labelsize = 18)\n",
    "plt.xlabel('$x$', fontsize = 25)\n",
    "plt.xlabel('$y$', fontsize = 25)\n",
    "\n",
    "x = np.linspace(-2, 2, 100)\n",
    "a1, a2, a3 = 1/2, 1/3, 1/4\n",
    "y1, y2, y3 = a1**x ,a2**x, a3**x\n",
    "ax.plot(x, y1, color = 'k')\n",
    "ax.plot(x, y2, '--', color = 'k')\n",
    "ax.plot(x, y3, ':', color = 'k')\n",
    "\n",
    "arrowed_spines(fig, ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "df9b117d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MTEABKiJSa4cPHwagXbt2FldSOwpQEbGccwTqK68zdlKAiojlnCPQK6+80uJKakcBKiKWKikp4cSJE9hsNlq1amV1ObWiABURS517Bt5ms1lcTe0oQEXEUr46fQcFqIhYTAEqImKSAlRExCRngPraJUygABURizmvAdUIVESkljSFFxExwTAMBaiIiBk5OTnY7XaioqJo0qSJ1eXUmgJURCzjy6NPUICKiIUUoCIiJvnyJUygABURC2kEKiJiki9fAwoKUBGxkEagIiImHTp0CFCAiojUSklJCceOHcNms/ncy+ScFKAiYolzz8CHhIRYXI05ClARsYRz+t6+fXtL67gcClARsYQCtAY5OTk8/vjjDBo0iL59+zJ58mS+++67Km0yMzOZNWsWCQkJJCQkMHv2bHJycqp9lrvtRMT3+EOAevTAQ2FhIbfffjsnT54kKSmJqKgoXn31VaZOnUpKSgpdunQhNzeXqVOnUlZWxowZM3A4HCQnJ5Oenk5KSgphYWEAbrcTEd+kAD3P4sWLycjI4JVXXqF///4AjB49mmHDhrFkyRKeeeYZli5dyvHjx9mwYQOdOnUCoHfv3kybNo1169YxceJEALfbiYhv8ocA9dgU3jAM1q5dy5AhQ1zhCRAbG8vs2bPp168fAKmpqSQkJLhCEWDQoEF06NCB1NRU1zJ324mIb1KAnuPIkSOcOHGCQYMGAWcDtaioCIDbb7+diRMnkpeXR2ZmJvHx8dW2j4+PZ+fOnQButxMR33TuNaBt2rSxuhzTPBagP/30EwDNmjXj6aefpl+/fvTt25fhw4fzySefAHDixAkAWrZsWW372NhYCgsLKSgocLudiPimc2/h9NVrQMGDx0Dz8/MBeP755wkJCeGxxx4jODiY5ORk7r//fpKTkwkPDwdw/fdcDRo0AMBut7tGrpdq17hxY0+VLyL1yB+m7+DBAC0rKwPOBun777/vejz/0KFDGT58OM8++yyPPvroJT8nODiYyspKt9qd78yZM9jt9lpW7j6Hw0FWVladfb63KCgo8Pt+BkIfwXv76by0sUWLFpddX330sXXr1jUu91iARkREADBixIgq7zaJiopi6NChrF27lsjISABKS0urbe9cFhkZ6Xa780VHRxMdHX15HbkIm812wR+kP8nKyvL7fgZCH8F7+3nmzBkAevTocdn1WdlHjx0DdR6vjImJqbYuJiYGwzBo1qwZAKdOnarW5uTJk0RFRREREeH6YVyqnYj4Jn+ZwnssQDt37kxYWBj79++vtu7IkSM0aNCAmJgY4uLi2LVrV7U2aWlp9OzZEzg7anWnnYj4JgXoeSIiIhg6dCgbN25k3759ruWZmZl88skn3HjjjdhsNkaMGMHmzZs5cOCAq82mTZvIyMhg9OjRrmXuthMR3+MvARpkGIbhqQ87cuQIt956KwBTpkwhNDSU5cuXU1xczJtvvknbtm3JyclhzJgx2Gw2pk+fTmlpKUuWLOHKK6/ktddec92i6W67+hIUFET37t1JS0ur1++1grceN/OkQOgjeGc/S0pKCA8PJyQkhOLi4su+jMkvjoECxMXF8frrr9O/f3+Sk5NZtGgR3bt357XXXnO9dS8mJoYVK1bQrVs3FixYwLJly1y3ep4biu62ExHf4rxmPC4uzqevAQUP3wsPZx+OumDBgou26dixI4sXL77kZ7nbTkR8x8GDBwGq3Kbtq/Q8UBGpV84A7dixo8WVXD4FqIjUK+eJYY1ARURqSSNQERGTnCNQBaiISC0YhqGTSCIiZpw8eRK73U7Tpk3r9LkV9UUBKiL1xp+m76AAFZF65E/Td1CAikg98qcz8KAAFZF6pCm8iIhJmsKLiJikEaiIiAl2u51jx44REhJCXFyc1eV4hAJUROrFuQ9R9vXH2DkpQEWkXvjb9B0UoCJST/ztEiZQgIpIPXG+cNJfzsCDAlRE6onzZZOdO3e2uBLPUYCKSL1QgIqImFBWVsahQ4cICgrSMVARkdrIyMigsrKSK6+8koYNG1pdjscoQEWkzjlPIPnT9B0UoCJSD/zx+CcoQEWkHihARURMUoCKiJjkDNCrrrrK4ko8SwEqInWqtLSUw4cPExwc7FeXMIECVETqmPMSpnbt2hEWFmZ1OR6lABWROuWvxz9BASoidUwBKiJikgJURMQkBaiIiEl79+4FFKAiIrVSVFREZmYmoaGhdOjQwepyPE4BKiJ15tzRp7+8SO5cClARqTPp6ekAdO3a1eJK6oYCVETqzJ49ewDo1q2bxZXUDQWoiNQZjUBFREzSCFRExITKykqNQEVEzDhy5AjFxcW0bNmS6Ohoq8upEwpQEakT/j59BwWoiNQRf5++gwJUROqIRqAiIiZpBCoiYpJGoCIiJhQWFnL06FEaNGhAu3btrC6nzihARcTjnKPPzp07Y7PZLK6m7ihARcTjdu3aBUB8fLzFldQtBaiIeFxaWhoAPXr0sLiSuqUAFRGPU4CKiJikKbyIiAlFRUUcOnSI0NBQrrrqKqvLqVMKUBHxqD179mAYBl26dCE0NNTqcuqUAlREPCpQjn+CAlREPEwBKiJiUqCcQAIFqIh4mEagIiIm2O12Dh48SEhICJ07d7a6nDqnABURj0lPT8cwDDp37kxYWJjV5dQ5BaiIeIzz+GcgTN9BASoiHqQAFREx6YcffgDg6quvtriS+qEAFRGP+fHHHwEFqIhIreTm5pKZmUl4eDidOnWyupx6oQAVEY/YuXMncPYCen9+Cv25FKAi4hHO45+9evWyuJL6owAVEY9wHv9UgIqI1FKgnYEHBaiIeEBlZaXrGKhGoCIitfDTTz9RUFBAy5YtadGihdXl1BsFqIhctkA8/gkKUBHxgEA8/gl1GKB79uyhZ8+eLFy4sMryzMxMZs2aRUJCAgkJCcyePZucnJxq27vbTkSsF6gj0JC6+NCKigoeeeQRysvLqyzPzc1l6tSplJWVMWPGDBwOB8nJyaSnp5OSkuJ6/JW77UTEO3z//fdA4I1A6yRAX3rpJfbt21dt+dKlSzl+/DgbNmxw3erVu3dvpk2bxrp165g4cWKt2omI9QoLC9m7dy8hISEB8RqPc3l8Cp+ens6iRYu47777qq1LTU0lISGhyn2ygwYNokOHDqSmpta6nYhY74cffsAwDHr06EGDBg2sLqdeeTRAnVP3QYMGcfPNN1dZl5eXR2ZmZo2/oeLj413XkLnbTkS8w3fffQdAnz59rC3EAh6dwi9evJiffvqJ//znP1RUVFRZd+LECQBatmxZbbvY2FgKCwspKChwu13jxo09WbqImLRjxw4gMAPUYyPQffv28cILLzBnzhyuuOKKauuLiooACA8Pr7bOOey32+1utxMR7xDIAeqREajD4eCRRx7h2muvveAJnsrKykt+TnBwsNvtanLmzJk6DVeHw0FWVladfb63KCgo8Pt+BkIfoe77WV5e7jqs1qJFC0t+pvWxL1u3bl3jco8EaHJyMnv27GHlypWuazXz8/MBKC4uJicnh8jISABKS0urbe9cFhkZ6Xa7mkRHRxMdHX15nbkIm812wR+kP8nKyvL7fgZCH6Hu+/njjz9SWlpKx44d6datW519z8VYuS89EqBffPEF5eXl3HrrrdXWJScnk5yczLp16wA4depUtTYnT54kKiqKiIgI1w/iUu1ExHqBPH0HDwXonDlzXCNOp9OnT/OHP/yBxMREbrnlFjp27EhcXJzrrX3nSktLo2fPngBERUW51U5ErKcA9YCaQu3IkSMAtG3blkGDBgEwYsQIli9fzoEDB1zXeG7atImMjAzuvPNO17buthMRawXyJUxQR3ciXcjMmTNZv349SUlJTJ8+ndLSUpYsWUJ8fDyJiYm1bici1jEMwxWg11xzjaW1WKVen8YUExPDihUr6NatGwsWLGDZsmUMGzaMJUuWVLm/3d12ImKdQ4cOcebMGVq0aEGrVq2sLscSdTYCjYuLIz09vdryjh07snjx4ktu7247EbHGN998A0C/fv0ICgqyuBpr6HmgImLKtm3bgLMBGqgUoCJiyrkj0EClABWRWqusrOTbb78FFKAiIrWyb98+8vPzadOmTcCeQAIFqIiYoOn7WQpQEak1Z4D279/f4kqspQAVkVrTGfizFKAiUisVFRWue+CvvfZai6uxlgJURGplz5492O12OnToQPPmza0ux1IKUBGpFU3f/48CVERqZcuWLYBOIIECVERq6euvvwZg4MCBFldiPQWoiLitsLCQH3/8kZCQEPr27Wt1OZZTgIqI27755hsqKyvp3bu3Xq2DAlREasE5ff/Zz35mcSXeQQEqIm5TgFalABURtxiGoQA9jwJURNzy008/ceLECZo1a+Z62WOgU4CKiFvOHX0G6is8zqcAFRG3aPpenQJURNyyefNmQAF6LgWoiFxSUVER27dvJzg4mAEDBlhdjtdQgIrIJW3ZsoWKigr69OlD48aNrS7HayhAReSSvvzySwAGDx5scSXeRQEqIpekAK2ZAlRELqqiosJ1AunnP/+5xdV4FwWoiFzUDz/8QGFhIZ06dQroVxjXRAEqIhf1xRdfAJq+10QBKiIX5Tz+ed1111lcifdRgIrIBRmGoRNIF6EAFZEL2r9/P8ePH6d58+Z06dLF6nK8jgJURC5o48aNAFx//fV6gEgNFKAickGffvopADfccIPFlXgnBaiI1MgwDNcIdMiQIZbW4q0UoCJSo71793Ls2DFiY2Pp0aOH1eV4JQWoiNTo3NGnjn/WTAEqIjXS8c9LU4CKSDU6/ukeBaiIVLNnzx5OnDhBy5Yt6datm9XleC0FqIhU45y+6/jnxSlARaSaDz/8EIAbb7zR4kq8mwJURKqoqKjgk08+AWD48OEWV+PdFKAiUsW2bdvIz8+nc+fOtG/f3upyvJoCVESqcE7fNfq8NAWoiFTxwQcfAApQdyhARcQlPz+fr7/+GpvNpgvo3aAAFRGXjRs34nA4GDBgAE2aNLG6HK+nABURFx3/rB0FqIi4vP/++4AC1F0KUBEBYN++fezbt4+mTZsyYMAAq8vxCQpQEQHgnXfeAWDkyJGEhIRYXI1vUICKCPB/ATp69GiLK/EdClARoaioiI0bNxIUFMSoUaOsLsdnKEBFhE8++YSysjISEhKIjY21uhyfoQAVEVJTUwFN32tLASoS4AzD0PFPkxSgIgHuxx9/JDMzkxYtWtC3b1+ry/EpClCRALdu3ToAbr75ZoKDFQm1oZ+WSIBzBugtt9xiaR2+SAEqEsAOHz7Mjh07iIyM1Os7TFCAigSw9evXAzBq1CgaNmxocTW+RwEqEsA0fb88ClCRAJWbm8tnn32GzWbT5UsmKUBFAtTbb7+Nw+Hg+uuvJyYmxupyfJICVCRAvfHGGwCMGzfO4kp8lwJUJADl5+fz3nvvERQUxPjx460ux2cpQEUC0FtvvUVZWRnXXXcdrVq1srocn6UAFQlAKSkpANx6660WV+LbFKAiAUbTd89RgIoEGE3fPUcBKhJgXn/9dUDTd09QgIoEkOzsbN577z2Cg4OZMGGC1eX4PAWoSABJSUmhvLyc4cOHc8UVV1hdjs/zeIB+8cUX3HbbbfTu3Zs+ffqQlJTEd999V6VNZmYms2bNIiEhgYSEBGbPnk1OTk61z3K3nYi459VXXwXg9ttvt7gS/+DRlz9v3bqVmTNn0rlzZx566CEqKipYuXIld9xxBytXruTqq68mNzeXqVOnUlZWxowZM3A4HCQnJ5Oenk5KSgphYWEAbrcTEfccOnSIL7/8koiICN195CmGByUmJhpDhgwx7Ha7a9mpU6eM/v37G0lJSYZhGMZzzz1ndO/e3di/f7+rzVdffWV06dLFWL16tWuZu+3qC2B079693r/XCkePHrW6hDoXCH00jKr9fOqppwzAmDRpkoUVeZ6V+9JjU/i8vDz27NnDqFGjCA8Pdy1v3rw5/fv3Z8eOHcDZt/8lJCTQqVMnV5tBgwbRoUMH15sBa9NORC7NMAxWrFgBwB133GFxNf7DYwHaqFEj3nvvPZKSkqqty83NxWazkZeXR2ZmJvHx8dXaxMfHs3PnTgC324mIe7755ht2795N8+bNGT58uNXl+A2PBajNZqN9+/a0bNmyyvI9e/awfft2+vTpw4kTJwCqtQGIjY2lsLCQgoICt9uJiHtefvllACZPnkxoaKjF1fgPj55EOl9RURFz5swB4K677qKoqAigyhTfqUGDBgDY7Xa32zVu3LjKujNnzmC32z3XgfM4HA6ysrLq7PO9RUFBgd/3MxD6CGf7eeDAAdfZ9zFjxvhdv+tjX7Zu3brG5XUWoMXFxdx7773s2bOHu+++m4SEBL799ttLbhccHExlZaVb7c4XHR1NdHS0mXLdYrPZLviD9CdZWVl+389A6COc7ecnn3xCQUEBCQkJDB061OqSPM7KfVknF9Ln5+czffp0tmzZwvjx43nooYcAiIyMBKC0tLTaNs5lkZGRbrcTkUtzTt+nT59ucSX+x+MBmp2dzZQpU9i+fTu//vWveeqppwgKCgL+bxh86tSpatudPHmSqKgoIiIi3G4nIhd36NAhPv30U8LDw/nNb35jdTl+x6NT+MLCQu688052795NUlISjzzySJX1UVFRxMXFsWvXrmrbpqWl0bNnz1q1E5GLW7VqFQATJkygSZMmFlfjfzw6Ap07dy67d+9mypQp1cLTacSIEWzevJkDBw64lm3atImMjIwqbwZ0t52I1Ky0tNQVoHfffbfF1finIMMwDE980IEDBxg9ejSNGzfm0UcfxWazVWuTmJhITk4OY8aMwWazMX36dEpLS1myZAlXXnklr732musWTXfb1ZegoCC6d+9OWlpavX6vFQLhBEsg9HHVqlXcdttt9OrVi++//951KM3fWLkvPTaF37p1K3D2koILjT4TExOJiYlhxYoVzJs3jwULFtCwYUOGDRvG7Nmzq4Siu+1EpGaLFi0C4L777vPb8LSax0ag/k4jUP/i733cuXMnvXr1IjIykmPHjlW7Ztqf+N1lTCJirRdffBGA8ePH+3V4Wk0BKuJnzpw5w9KlSwGYMmWKtcX4OQWoiJ9ZvHgxRUVF3HjjjXTv3t3qcvyaAlTEj1RUVLBw4UIA1x2AUncUoCJ+ZM2aNWRmZtK1a1d++ctfWl2O31OAivgJwzCYP38+AL/73e9qfOCOeJZ+wiJ+4osvvmDLli00bdpUJ4/qiQJUxE/MmzcPgAceeEBPK6snClARP7Bjxw7ee+89IiIi+O1vf2t1OQFDASriB/7xj38AZ9/80KxZM4urCRwKUBEft2/fPt544w1CQ0P5/e9/b3U5AUUBKuLjnnzySSorK5k8eTJxcXFWlxNQFKAiPiw9PZ0VK1YQEhLCY489ZnU5AUcBKuLD5s6dS2VlJdOmTaNjx45WlxNwFKAiPiotLY1Vq1YRGhqq0adFFKAiPurPf/4zhmEwY8YM2rVrZ3U5AUkBKuKDtmzZwhtvvEHDhg159NFHrS4nYClARXyMYRjMnj0bgAcffFBn3i2kABXxMampqXz++ec0a9aMP/7xj1aXE9AUoCI+pKKiwhWajz/+uN71bjEFqIgPeemll9i1axcdOnTg3nvvtbqcgKcAFfER2dnZ/OlPfwLgueeeo0GDBhZXJApQER/xpz/9idzcXIYNG0ZiYqLV5QgKUBGf8N133/HSSy9hs9l4/vnnCQoKsrokQQEq4vUcDgd33303lZWVzJo1ix49elhdkvz/FKAiXu7FF19k69attGnThrlz51pdjpxDASrixbKysnjkkUcAWLhwIVFRURZXJOdSgIp4KcMwuP/++ykoKCAxMZFx48ZZXZKcRwEq4qVWrVrFunXraNy4MQsXLrS6HKmBAlTECx07doxZs2YBMH/+fNq2bWtxRVITBaiIlzEMg7vvvpvc3FxGjRrF9OnTrS5JLkABKuJl/vvf/7JhwwaaNGnC4sWLdc2nF1OAiniRtLQ0HnroIeDs5Ut6VJ13U4CKeImSkhImTZpEcXExSUlJ/OY3v7G6JLkEBaiIl3jwwQf54YcfuOqqq1iwYIHV5Xi9U6dOMX/+fHbv3m1ZDQpQES+wbNkyXnrpJRo0aMDq1atp3Lix1SV5tfXr19O6dWsefvhhXnnlFcvqUICKWOyHH37gnnvuAeDf//43ffv2tbgi72IYBtu3b+ftt992LRs4cCAhISGMGTOGG2+80bLaQiz7ZhHh9OnT3HLLLZSUlDBt2jTuvPNOq0vyGkePHuXVV1/llVdeYefOncTFxfHLX/4Sm81GixYtOH78OE2aNCErK8uyGhWgIhYpKytjwoQJZGRk0K9fP1544YWAv2SpsLCQNWvW8Morr/DJJ59gGAYAzZo1Y9y4cdjtdtfhDW94nYkCVMQChmEwa9YsPvvsM1q1asW6desIDw+3uizLbdu2jaSkJADCwsIYO3YsU6ZMYdSoUYSFhVlbXA0UoCIWmDdvHosXL6Zhw4asX7+eNm3aWF1SvTIMg02bNrFy5UoKCwtZtmwZANdffz2/+tWvGDFiBBMnTqRp06YWV3pxClCRerZs2TIee+wxgoKCWLFiBf3797e6pHphGAY//PADq1at4rXXXuOnn34CwGaz8eyzz9K8eXOCg4NZs2aNxZW6TwEqUo/eeecdZsyYAcDzzz/P+PHjLa6ofmzdupWkpKQq12zGxcUxadIkJk2aRLNmzSyszjwFqEg9+fTTTxk/fjwVFRXMnj2bBx54wOqS6syBAwc4fPgwN9xwAwBXXnkl6enpNGvWjFtvvZVJkyYxePBggoN9+0pKBahIPdi8eTNjx46lpKSEe+65h3/84x9Wl+RxBw8eJCUlhddff53t27fTrl07MjIyCAoK4oorrmDTpk307duX0NBQq0v1GAWoSB378ssvGT16NEVFRUyePNmvLlc6evQoy5cv54033mD79u2u5Y0aNWLw4MEUFBS4XkMyYMAAq8qsMwpQkTq0ceNGxowZQ1FREbfddhsvv/yyT09bDcOgsLDQdS1meno6jz76KHA2NG+++WYmTJjAqFGjAuKyLAWoSB3ZsGEDEydOpKSkhClTpvDyyy9js9msLqvWKisr2bp1K2vXrmXt2rV07tyZ1NRUAH7xi19w1113cdNNNzFixAgaNmxocbX1SwEqUgeWLl3KjBkzcDgczJw5k0WLFvlUeJaVlfHZZ5+xdu1a1q9fX+V2SbvdTnl5OaGhoYSEhPDSSy9ZWKm1FKAiHmQYBk8++SRPPPEEAI8//jhz5871iWOehmG46kxOTua+++5zrYuLi+NXv/oV48aNY/DgwYSEKDpAASriMaWlpcyYMYMVK1YQFBTE888/7/WXKmVkZLBhwwbeeust+vfvz7x58wAYM2YM//nPf1yvU+7bt69P/BKobwpQEQ/Iyspi/PjxfP3110RGRrJq1SrGjh1rdVnVVFRUsHnzZlJTU3n77bfZtWuXa93Ro0ddAdq2bVt+/PFHq8r0GQpQkcv05ZdfMmHCBE6cOEHbtm156623uOaaa6wuq0azZ89m/vz5rv+Piopi1KhRjB07ll/+8pcWVuabFKAiJlVWVvLMM8/w+OOP43A4uOGGG1i9ejWxsbGW1uVwOPj222959913Wb9+PQ888ADTpk0DYMSIEbz99tvcdNNNjB07lsGDB3vlU458hQJUxIRjx46RlJTEBx98AMAf/vAH/v73v1t2cuXYsWN8+OGHvP/++7z//vtkZ2e71r377ruuAB05ciR79+61pEZ/pAAVqaWUlBTuuececnJyaN68OcuXL6/36W9JSQmhoaGuS6OmTJnCRx995Frfvn17Ro0axYABA5gwYYJruU4EeZYCVMRNJ0+e5Le//S2rV68Gzk6HX3755Xp5lmdlZSXff/89H330ER9++CFffPEFH3/8MYMGDQIgMTGR0NBQRo4cyciRI+natStBQUFkZWXRqFGjOq8vUClARS6hsrKS5cuX8/vf/56cnBwiIiL45z//yb333lunI7qKigqSk5P5+OOP+fTTTzl9+nSV9Tt27HAF6KxZs5g1a1ad1SI1U4CKXMT333/P/fffz1dffQXA8OHDeemll+jQoYPHv+unn35ix44d3HLLLcDZBw3/9a9/5dixY8DZS4uGDx/OsGHDGDp0KC1btvR4DVI7ClCRGhw/fpwnnniC5ORkKisradmyJf/85z+54447PDbqPHToEJ999hkbN27ks88+cz367fTp08TExBAUFMSjjz6KzWZj2LBhXHXVVTqG6WUUoCLnyM/P57nnnuP//b//R1FRETabjd/97nf89a9/9dhbIL/55hvGjx/P4cOHqyxv0qQJ119/Pbm5ucTExABoWu7lFKAinH2d7qJFi3j66addlwCNHTuWZ555hm7dutX688rKytixYwdfffUVX375JVdeeSX/+te/AGjXrh2HDx8mOjqa6667jiFDhnD99ddzzTXX+NQDR0QBKgEuJyeHF154gX/961/k5OQAMHjwYJ566il+8Ytf1OqztmzZwvr169m0aRNbt26luLjYta5du3auAI2NjWX37t106dLFp58NKgpQCVAZGRnMmzePl19+GbvdDsCgQYN44oknGDFixEWPNVZUVLBz506+/vprhgwZ4hqhvv/++657yQG6du3K4MGD+fnPf851111X5TPMjGrF+yhAJWBUVFTw3nvv8cILL/Dee++5lo8cOZI5c+YwZMiQasFpGAaHDx9m27ZtbNmyha1bt/LNN9+4QvfcKf7o0aOx2+38/Oc/Z+DAgTRv3rz+OieWUICK39u/fz/Lly/n5Zdf5ujRowA0bNiQSZMm8dBDD9GrVy9X22PHjpGWlsaNN97oWjZw4EDXpUROnTp1YsCAAcTHx7uW9evXj379+tVxb8SbKEDFL508eZI33niDV199lU2bNrmWd+7cmZkzZzJq1CiaNm3K9u3bWbNmDd9++y3bt28nKyuLoKAgzpw5Q1RUFEFBQYwcOZLjx4+TkJDAgAED6N+/v+UPDBHvoAAVv3H06FHWrVvHm2++ycaNG6msrAQgIiKCYcOG8atf/YopU6YQFBTEK6+8wpQpU6p9RlRUFNdeey3Z2dmut0n+73//q9d+iO9QgIrPcjgcbNu2jXfffZe33367ymt1g4ODiYuLw2azcfz4cd566y2ioqKYOnUqAN27d6dp06b07duXPn36cO2113LttdfSqVMnnRkXtylAxWcYhsHevXv55JNPeOedd9i4cSOFhYWu9eHh4URFRXHixAkqKys5cuSIa12HDh2qTLtbtWpFdna27uyRy6IAFa9VVlbGd999x4cffkhKSgp79+6tcm2l07hx45g5cyZDhgzhueee491336Vnz5707t2bXr16cfXVV7um405BQUEKT7lsClCxXHZ2NmlpaXz++eds2bKF3bt3U1RURHZ2NmVlZTVu06BBA7p06ULfvn15+OGHufrqqwF47LHHeOyxx+qzfAlgClCpc5WVlRw9epSMjAx69epFdnY2u3fv5tlnn2Xz5s0XDEk4e8H5wIEDycjIYODAgVx33XXEx8cTFxenY5ViOa8P0MzMTJ5++mm2bt0KwJAhQ/jjH//oetiCWO/c94nn5OTwn//8h507d7J//34yMzPJzs7G4XAAEBISQkVFRY2f06hRI9q2bUvPnj0ZOnQokyZN8tgDPMS/FRcXk5eXxxVXXFGv3+vVAZqbm8vUqVMpKytjxowZOBwOkpOTSU9PJyUlRS/DqkdpaWns3r2bQ4cOsXfvXg4ePEhmZiYnT56kefPm9OnTh8zMTA4ePMiJEycu+DkVFRW0bduWbt260aFDB7p27crAgQPp1auXnpwups2cOZPXXnuNpKQk/vznP9O2bdt6+V6vDtClS5dy/PhxNmzYQKdOnQDo3bs306ZNY926dUycONHiCn3bmTNnXM+hzMzM5OjRoxw/fpysrCzy8/MZOnQopaWlnDp1iu+++46CgoIaPyc3N5d9+/ZVWRYTE0Pr1q256qqr6N27Nz169KBLly5cddVVCkrxuOLiYhwOB8uXL+fVV19l/PjxzJ07l44dO9bp93p1gKamppKQkOAKTzj7wIcOHTqQmpoaUAHqcDgoKSmhuLgYu91OcXGx60TLyZMnCQ8Pp6ioiKKiIrZs2cLRo0fJy8sjPz+fwsJC7HY7JSUlhIeHEx4eTl5e3gUD0WnVqlXVlgUHB9O4cWOaNWtGq1ataN++Pd26daN9+/a0bduWdu3a0aZNG0JDQ+vqRyFyQeXl5ZSXl7N69WrWrFnDmDFjePLJJ+natWudfJ/XBmheXh6ZmZmMHDmy2rr4+Hg2btxY7zXl5+fz+uuvU1FRgcPhoKKiosqf8vJy13+df0pKSigtLaWkpISSkhLKysoICwujrKyMsrIyjh07VqWNc3l5eTnBwcFUVlZSXFxMeXm5R/rgfAiGk81mo2HDhkRERBAVFUVMTAxRUVF06tSJrl270rZtW2JjY2nRogUtW7akadOmOnkjXs/5b3Lt2rW8/fbbDBs2jL///e9VnnvgCV4boM7jaDW99yU2NpbCwkIKCgpo3Lix6e945plnqjyV50KctwQePXqUX//616a/r64EBQURHR1NWFgYNpsNu91OZWUlNpuN0NBQQkNDCQsLIywszDUCtdlshISE1HgtZHFxMfv27as2LfcnpaWlNGjQwOoy6lwg9LO0tLTK8w7O5XA4cDgcvPPOO3z88ccMHjyY5cuXe+xkk9cGaFFREXD27pLzOf9C2O32KgF65syZaiOsC6moqOCNN95g27ZtHqjWWoZhkJuba3UZIl6rsrISwzD4+uuv2bt3r2tQ5K7WrVvXuNxrA9SdDp4/lYyOjiY6Otrt73BeGuWOoKAgOnXqxEcffQScnfoGBQVhs9kIDg4mOjraFezOy3ScbXxNVlbWBf/C+ItA6CMERj+zsrJ44IEHePPNN2tcHxkZSYMGDXjiiSe46667ahyUmeW1ARoZGQmcHZ6fz7nM2aa+hIWF0b59+0u2Cwnx2h+rSMCIjIwkMjKSv/71r0ybNq1ODmV47b9052/NU6dOVVt38uRJoqKiiIiIqO+yRMTLNWrUiCZNmvDkk09y++231+kVIV4boFFRUcTFxbFr165q69LS0ujZs6cFVYmItwoJCaFNmzbMmzePiRMn1ssbTr36epQRI0awefNmDhw44Fq2adMmMjIyGD16tIWViYg3+ctf/sLq1as5ePAgkyZNqrfXQ3vtCBTO3p61fv16kpKSmD59OqWlpSxZsoT4+HgSExOtLk9EvESvXr08fo2nO7x6BBoTE8OKFSvo1q0bCxYsYNmyZQwbNowlS5boPngRsZxXj0ABOnbsyOLFi60uQ0SkGq8egYqIeDMFqIiISQpQERGTFKAiIiYpQEVETFKAioiYpAAVETFJASoiYpICVETEJAWoiIhJClAREZMUoCIiJilARURM8vqnMXmL0aNH0717d6vLEBEvogB101tvvcXx48etLkNEvIim8G7y1VcUi0jdUYCKiJikABURMUkBKiJikgJURMQkBaiIiEkKUBERkxSgIiImKUBFRExSgIqImKQAFRExSQEqImKSAlRExCQFqIiISQpQERGTFKAiIiYpQEVETFKAioiYpAAVETFJASoiYpICVETEJAWoiIhJClAREZOCDMMwrC5CRMQXaQQqImKSAlRExCQFqIiISSFWF+ANMjMzefrpp9m6dSsAQ4YM4Y9//CMxMTF1sp1VvvjiCxYtWsSuXbsIDg6md+/ePPjgg1xzzTUX3W7ChAn8+OOP1ZaPHDmSBQsW1FG15pit1Vf25ZEjR7jxxhsv2mb58uUMGDCgxnW+si8ff/xxfvrpJ1555ZUqyy9nP9XFPg74AM3NzWXq1KmUlZUxY8YMHA4HycnJpKenk5KSQlhYmEe3s8rWrVuZOXMmnTt35qGHHqKiooKVK1dyxx13sHLlSq6++uoatzMMgwMHDjBs2DBGjBhRZV2bNm3qo3S3ma3Vl/ZlTEwMzzzzTLXlpaWl/O1vf6NZs2Z069atxm19ZV+mpKSQkpJCQkJCleWXs5/qbB8bAe65554zunfvbuzfv9+17KuvvjK6dOlirF692uPbWSUxMdEYMmSIYbfbXctOnTpl9O/f30hKSrrgdocPHza6dOlirFmzpj7KvCxma/W1fVmTJ5980ujWrZuxbdu2C7bx9n1ZUVFhLFy40OjatavRpUsX44477qiy/nL2U13t44A/BpqamkpCQgKdOnVyLRs0aBAdOnQgNTXV49tZIS8vjz179jBq1CjCw8Ndy5s3b07//v3ZsWPHBbfdv38/QJV+eiuztfrSvqxJeno6K1asYNy4cfTr1++C7bx5X5aWljJu3DgWLlxIYmIiLVu2rNbmcvZTXe3jgA7QvLw8MjMziY+Pr7YuPj6enTt3enQ7qzRq1Ij33nuPpKSkautyc3Ox2WwX3Hbfvn3A//2js9vtdVKjJ5ip1df2ZU3mz59Pw4YNefDBBy/azpv3ZWlpKYWFhcyfP5+nn36akJCqRxcvZz/V5T4O6AA9ceIEQI2/7WJjYyksLKSgoMBj21nFZrPRvn37avXu2bOH7du306dPnwtuu2/fPiIjI5k3bx59+vShT58+DBs2zCtHZmZq9bV9eb49e/bw6aef8pvf/IYWLVpctK0378tGjRrxwQcfMHr06BrXX85+qst9HNABWlRUBFBlWuvUoEEDoObf0ma38yZFRUXMmTMHgLvuuuuC7fbv309RUREFBQU888wz/P3vfycyMpKHH36YdevW1VO17jFTq6/vy1WrVmGz2bjjjjsu2dab92VwcHC1Uee5Lmc/1eU+Duiz8JWVlZdsExxc/XeM2e28RXFxMffeey979uzh7rvvrna281wTJ06ksrKS22+/3bXspptuYsyYMfzzn/9k7NixFz0EUJ/M1OrL+7KkpIS33nqLoUOHunUW3Zf25fkuZz/V5T72zr8Z9SQyMhI4e/zlfM5lzjae2M4b5OfnM336dLZs2cL48eN56KGHLtp+0qRJVf7BATRs2JDExEROnz7tOjHhDczU6sv7csuWLdjtdkaNGuVWe1/al+e7nP1Ul/s4oAO0devWAJw6daraupMnTxIVFUVERITHtrNadnY2U6ZMYfv27fz617/mqaeeIigoyNRnOS8+9ubprdPFavXVfQnw2WefERoaypAhQy7rc3xhX17OfqrLfRzQARoVFUVcXBy7du2qti4tLY2ePXt6dDsrFRYWcuedd7J7926SkpKYO3fuJcPzxIkT3HTTTfz73/+uti4jIwOAuLi4Oqm3tszW6ov70mn79u306tWLRo0aXbKtL+3LmlzOfqrLfRzQAQowYsQINm/ezIEDB1zLNm3aREZGxgXPCF7OdlaZO3cuu3fvZsqUKTzyyCNubdOyZUsKCgpISUmhsLDQtfzYsWO8+eabDBgwgNjY2LoquVYup1Zf25cA5eXl7N+/nx49erjV3pf25YVczn6qq30c8M8DzcnJYcyYMdhsNqZPn05paSlLlizhyiuv5LXXXiMsLIzMzEy2b99O3759adu2rdvbeYsDBw4wevRoGjduzKOPPlrjiYLExMQa+/nRRx9x//3307lzZ2699VaKiop49dVXKS8vZ9WqVV51UbY7tfr6vnQ6fPgww4cP5w9/+AMzZsyott7X96XzxNi598K7u5/qdR+bvofJjxw4cMCYMWOGcc011xg/+9nPjDlz5hjZ2dmu9WvWrKnxFrhLbectVq5caXTp0uWifwzjwv388MMPjQkTJhg9e/Y0+vXrZ9x3331VbonzJpeq1df3pdP3339vdOnSxVi1alWN6319X95www3VbuU0DPf2U33u44AfgYqImBXwx0BFRMxSgIqImKQAFRExSQEqImKSAlRExCQFqIiISQpQERGTFKAiIiYpQEVETFKAioiYpAAVETFJASoiYpICVALCypUrufXWWxkxYgRvvvlmtfWff/45gwYN4siRIxZUJ75KASp+78svv2Tv3r2kpKRw44038sQTT1BcXFylzeuvv052djY5OTkWVSm+KKDfyimB4X//+5/rVRYHDx4Eqr6F0TAMvvnmGyIiItx+wrsIaAQqfm7//v107dqV8PBwsrOz+eqrrxg8eLDrfeAA+/btIzc3l2uvvfai7yYXOZ8CVPzaVVddxezZswFYu3Yt5eXljB8/vkqbbdu2ATBgwIB6r098mwJUAsaGDRuIiori+uuvr7J869atgAJUak8BKgHhyJEj7Nmzh0GDBlV7gdg333xDo0aNiI+Pt6g68VUKUAkIztfZ9urVq9ry06dP069fvxrfVipyMQpQCQh2ux2ARo0aVVn+9ttvA5q+izkKUAkI1157LQ0bNuTrr78Gzl66tHr1av773/8CClAxRwEqAaFFixa8+OKLHD58mHHjxjF58mTy8vIICQkhKiqK7t27W12i+CBd9CYBY+DAgVVu40xNTaWkpISRI0dWubBexF36WyN+7/PPP2fAgAEsXbq0yvI333yT4OBgpkyZYk1h4vMUoOL3Vq5cSX5+PrGxsa5lH3/8MV9++SV33XUXPXv2tLA68WUKUPF7cXFxzJ49m5tuugmAL774gjlz5jB16lQefPBBa4sTnxZkGIZhdREidam4uJh58+Zx5MgRCgsLadq0KUlJSQwcONDq0sTHKUBFREzSFF5ExCQFqIiISQpQERGTFKAiIiYpQEVETFKAioiYpAAVETFJASoiYtL/B3SWs3Osf0lNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "mpl.style.use('bmh')\n",
    "mpl.style.use('seaborn-whitegrid')\n",
    "\n",
    "fig = plt.figure(figsize=(5,10))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.xaxis.set_tick_params(labelsize = 18)\n",
    "ax.yaxis.set_tick_params(labelsize = 18)\n",
    "plt.xlabel('$x$', fontsize = 25)\n",
    "plt.xlabel('$y$', fontsize = 25)\n",
    "\n",
    "x = np.linspace(0, 10, 100)\n",
    "y = 2 ** x\n",
    "ax.plot(x, y, color = 'k')\n",
    "\n",
    "y1 = x ** 2\n",
    "ax.plot(x, y1, '--', color = 'k')\n",
    "\n",
    "arrowed_spines(fig, ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "822ddc64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.25      , 2.59374246, 2.70481383, 2.71692393, 2.71814593,\n",
       "       2.71826824, 2.71864808])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 10, 100, 1000, 10000, 100000, 9686465360000])\n",
    "y = (1+ (1/x))**x\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "083e9e4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "467a4b48",
   "metadata": {},
   "outputs": [],
   "source": [
    "def log(x, base=np.e):\n",
    "    return np.log(x) / np.log(base)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5b5b9fc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log(4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "e6863863",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6989700043360187"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log(5000,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "e6aed1f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kz9liSKR+Bg4ciK+//hqJiYnIyckROxy1J8l1DEtKShAQEICuXbtiwoQJtTonPT0dubm59RxZ3SsoKAAAZGdnQy6XixxN/crKymIZ1QDLqB6kXkYHBwexQ5AUqdaRJSUlwnO5XC7p39maSP3zWBuaUEZAM8pZ12XU0tKCmZmZSv3bqVIsz6um+lGSieGWLVsQGRmJX3/9VbhbmJmZCQDIy8tDamoqLCwsoKX1fw2iFhYWsLCwECPcl1KeGJqYmKj9Fx25XM4yqgGWUT1oQhnp/0i1jiw3evRovPLKK2r7O6sJn0dNKCOgGeWsjzLq6OjA1NRUZf7t1PX/UZKJ4aVLl1BUVITx48dX2rdlyxZs2bIFZ86cgZOTkwjRERERUUMKCgqCpaWl2GEQEUmaJBPDhQsXCi2E5f755x98/PHH8PHxwZgxY2BtbS1SdERERNSQSktLxQ6BqMHJZLJq9/344494++23AQCbNm3CzJkzqz224iROXbt2xY0bN6o8zt/fH5s2bQIAhIWFoVu3btVe86+//kLXrl1rjP9l3b59G9u3b4e1tTWKi4uRlZWFmTNnolmzZkrH7du3D5cuXYK9vT0SExPh5eWFBw8eICoqCoMGDcLkyZPrNU4ACA8Px+HDhyGTyRAfH48VK1Zg9+7dyMzMRFJSEubMmQMXF5d6j+NZJJkYtmvXrtK2uLg4AICzszM8PT0bOiQiIiISyZMnT5CcnIzWrVuLHQoRNYCzZ88iMDAQW7duhaOjIwAgJiYGvr6+2LBhA9q0aQMA2LVrFwIDA3Hx4kWYmpri0aNHGDZsGPbs2YNevXqhqKjohd4/Li4Ourq6tWqIevToEQ4cOIAlS5ZAJpNh0aJFmDhxIlauXAmFQoEpU6agTZs28PPze6FY6pJkZyUlIiIiAoAuXbrwpjBpHIVCUe2jvLUQAN5+++0aj60oLCys2uPKWwuBspbF6o6Lj4+v19bCnJwcBAQEYPLkyUJSCABubm7w9vZGQECAsG3nzp1wd3eHqakpAKBp06awtLTE9u3b4e3tjQEDBrxQDH/88QeMjY1rdWxQUBDmz58vtPDm5ubCzMwMXbp0gYODA3x9fTFmzJgXiqOuMTEkIiIiSarYlS4zM5NdSok0wIULF5Cenl5l18tWrVohMjIS4eHhAABLS0sUFhYqHVNYWKg0o3FF2dnZeP/992uccbSgoAAlJSUwMjKqVbz+/v5Kx968eVO4kWVvb4+FCxfCysqqVteqb2qTGDo5OSEqKgrvv/++2KEQERFRAzIyMkJpaSmys7PFDoWI6llsbCwAQF9fv9I+XV1dAGXdywFg9uzZiImJQXR0NADg4sWLKCoqgq+vb6Vz9+7di61bt+LUqVM13mQKDg6Gl5dXreOt2KoZExOD5ORkeHh41Pr8hiTJMYZERERE5UxNTZGbm4uMjAyYmZmJHQ4R1aPycX3lS9ZVlJ6eDgBo1KgRgLLkcc6cOdizZw90dHRQVFSE/fv3w83NrdK55asdrF+/vsb3Dw0NVeqq+zyuXr0KXV1ddO7cWdgWGxsLZ2fnF7peXWNiSERERJJmZmaGpKQkZGRkqMwXLCKqH/369YOhoSEePnxYaV94eDjs7OyEMY43b96Et7c3WrVqVSfvnZSUBBsbG6Vu7KWlpQgKCoKWlhbMzMyQkZEhtEjm5+dj3bp18PHxQcuWLXHlyhW0bNkShoaGwrlbtmzBZ599VifxvSy16UpKREREmql8Yony1gIiUi/FxcUoLi4GUDZucPny5di3bx+Sk5OFY2JjYxESEoLAwEDo6JS1fdna2mLt2rW4evUqQkNDcefOHaSkpFSadKe2Dh8+jNGjRyttW7p0KYqLizFjxgwMHTpUqSXzwoUL2Lp1K+7fv4+YmBjExcVBT09P2L9hwwb4+Pi8UCz1gS2GREREJGnl3UczMjJEjoSI6lJwcDC+++47JCUlYfv27QgLC8OWLVswevRoODg4IDAwEKamptDW1kZeXh62b9+Oli1bCud7enri888/x7lz55Sua2dnh/nz51dK8p6lvNtn+eQ0MTExOHz4MJYtW4ZDhw6hoKAA/v7+wvHdu3fH2LFjER4ejvDwcOzevRvLli3D0qVLoauri/79+yt1KxUbE0MiIiKStPnz5+Pzzz9H27ZtxQ6FiOrQwIEDMXDgwCr3devWDd26dav2XLlcDj8/P6xevRq9evWCtrY2CgoKkJycjNOnT2Px4sVo3749XF1daxXLrVu30KFDB6VtUVFRcHd3x9ixY6s8x8rKCitXrlTaFhgYWKv3EwO7khIREZEklY/zad26NXr37g1LS0uRIyIiVXHq1Cm4urqid+/e0NbWBlA2GY2zszP8/PzQrFkz3Lt3r9bXO3HiBIYOHaq0rWnTpkqzoyoUCvz+++8v3FVVbGwxJCIiIknj+oVE9G+enp7Ytm0bbty4gS5duijtCw4ORk5OjjBJDVA2fjAsLAwAsHr1anTt2hVTp04FULZ2YXFxMUxMTJSu06ZNGwwZMgRBQUGwtLREfn4++vbtqzQ5jZQwMSQiIiJJu379OtavXw8vLy9hynki0mwtWrTAjh07EBQUhIMHD8LY2BgKhQIZGRmwsbHB3r17lRaWHz16NEaPHo1ly5ZVulZwcDAGDBhQ5fvMmDGjvorQ4JgYEhERkaRFRUXh22+/RX5+PhNDIhI4Ozvjk08+eenrXLt2rcqEUd1wjCERERFJmrGxMQAuV0FEdS8zMxP29vbQ0lL/tEn9S0hERERqrXwdQy5XQUR1zczMDO+8847YYTQIJoZEREQkaeUthkwMiYheHBNDIiIikqTymf/YlZSI6OUxMSQiIiJJK59Cni2GREQvjrOSEhERkaQZGxvD3d0d9vb2YodCRCRZTAyJiIhI0gwNDREdHS12GEREksaupERERCRppaWlYodARCR5TAyJiIhI0soTw5KSEiaJREQviIkhERERSVL5rKQKhQK9e/eGjo4Obt26JW5QREQSxcSQiIiIJK20tBQ6OmXTJnDJCiKiF8PEkIiIiCRNoVDA3NwcAJesICJ6UUwMiYiISNJKS0thYWEBgC2GREQviokhERERSVppaSlbDImIXhITQyIiIpI0hUIBS0tLAEBKSorI0RARSRMTQyIiIpK00tJStGrVCgBw584dkaMhIpImHbEDICIiInoR5ctVlJaWonfv3lizZg08PDxEjoqISJqYGBIREZGkKRQKODs7Y+7cuWKHQkQkWexKSkRERJJWWloqdghERJLHxJCIiIgkTaFQAADCwsKwfPlynD59WuSIiIikh4khERERSVp5i+G5c+fw6aef4tChQyJHREQkPUwMiYiISNLKE8P27dsDAP73v/+JGQ4RkSQxMSQiIiJJK+9K2qFDBwDA33//LWwjIqLaYWJIREREklRxuQoAsLOzQ+PGjZGeno64uDgxQyMikhwmhkRERCRp5YmhTCZjd1IiohfExJCIiIgkrWK30fLupEwMiYieDxNDIiIikrSK6xh26tQJLVq0gKGhoYgRERFJj47YARARERG9jIqJ4YwZMzBjxgzxgiEikii2GBIREZGkFRcXix0CEZHkMTEkIiIiSSqflTQvL6/SvpSUFGRlZTV0SEREkiXpxPDSpUt4/fXX0bFjR3Tu3BkzZszArVu3xA6LiIiIGkB1ieGbb74JGxsb7Nu3T4ywiIgkSbKJYWhoKPz9/ZGVlYV58+bh3XffxZMnTzB16lTOREZERKQBqksMO3XqBAA4depUQ4dERCRZkp185ssvv4S9vT327NkjzDw2ZswYDB8+HGvWrMG2bdtEjpCIiIjqU3limJubq7R92LBhAICTJ0+iuLgYOjqS/bpDRNRgJNlimJGRgcjISAwdOlRpOurGjRuje/fuuHnzpojRERERUUOorsXQ3d0dLVq0QFpaGkJCQsQIjYhIciSZGJqYmODEiRNVTkedlpYGbW3thg+KiIiIRFHV5DPlrYbHjh1r6HCIiCRJkomhtrY2mjZtCltbW6XtkZGRuHHjBjp37ixSZERERNRQapqVdPjw4QCYGBIR1ZbadLrPycnBwoULAQBvv/12pf3p6emVxiBIQUFBAQAgOzsbcrlc5GjqV1ZWFsuoBlhG9SD1Mjo4OIgdgqRItY4sl5SUVOn31d3dHYaGhoiIiMCdO3dgaWkpUnQvT+qfx9rQhDICmlFOllG11VQ/qkVimJeXh9mzZyMyMhIzZ85Ejx49Kh1jYWEBCwuLhg/uJZUnhiYmJmr/RUcul7OMaoBlVA+aUEb6P1KtI8uHjuTl5VX5+3ru3Dm0a9cOxsbGDR1andKEz6MmlBHQjHKyjNIl+cQwMzMTM2fOxI0bN/Daa69h3rx5YodEREREDUBLq2xETGpqapX7PTw8GjIcIiJJk+QYw3JPnz7F9OnTcePGDUycOBFffPGFMN6AiIiI1Ft5nV9dYliuuLgYJSUlDRESEZFkSTYxzM7OxptvvomIiAjMmDEDy5cvZ1JIRESkQcpbDJ8+fVrtMQEBAbC2tsbp06cbKiwiIkmSbGK4fPlyREREYPr06QgICBA7HCIiImpg5TeEMzMzUVRUVOUxxsbGSE9Px08//dSQoRERSY4kxxjGxMTg0KFDMDU1RevWrXHo0KFKx/j4+IgQGRERETWUij2F0tPTYW1tXekYX19ffPbZZzh06BASExNhZ2fXkCESEUmGJBPD0NBQAGVTxVbXWsjEkIiISHM8ffq0ysTQ0dERI0eOxKFDhxAUFIRFixaJEB0RkeqTZFfSyZMnIyoqqsYHERERaY6EhIRq95Wvb7x582aUlpY2VEhERJIiyRZDIiJ6eQqFApmZmUhMTERiYiISEhKE59OnT1fLNZpIfT1+/LjafUOGDIGzszMePHiAc+fOYcCAAQ0YGRGRNDAxJCJSM6WlpUhJSUFCQoLSo127dkI3+6tXr2LAgAHIy8ur8hoDBgxAmzZtGjJsopfy6NGjavdpa2vjrbfewqeffoqzZ88yMSQiqgITQyIiiSgtLcU///wDuVyu9FiyZIkwbf+QIUNw5syZKtdsmz59upAYWlpaIi8vD0ZGRrC3t4e9vT1sbW1hb28POzs7WFpaNmjZiF5WTS2GADBr1iyMGTMGHTp0aKCIiIikhYkhEZEKyM7ORnx8vPBo06YNunbtCgA4fvw4Zs6ciYSEBBQXF1c695133kHjxo0BADo6OigpKUGjRo3g4OAgJH12dnbw8PAQzmnevDmysrJgYmJSZTxyubweSklUfx4+fFjjfhsbG9jY2DRQNERE0sPEkIioHikUCqSlpSEuLg5Pnz5Fv379hH2TJk3C33//jfj4eGRkZCidt2jRIiEx1NfXR2xsLICylj5HR0ch6XN0dFSasn/Hjh0wMjKCvr5+jXFpa2tXmxQSSVF4eDgUCoXS56E6V69eRZMmTTiOloioAiaGREQvITMzE1paWkKSdeHCBWzbtg1xcXGIjY1FXFwccnNzAZQleHl5ecIX16ioKNy9e1fY5+joKDwqdnfr2bMnYmJi4ODgAAMDgxrjYRdQ0kSWlpZ4+vQp5HI5HB0dazx21apVCAgIwDvvvIP169c3UIRERKqPiSER0TMoFArs3LkTT548wZMnTxAdHY3k5GQ8efIEmZmZ+P777/Huu+8CAJ48eYKff/5Z6XwTExM4OzvDyckJubm5MDY2BgBs2rQJurq6cHJyQqNGjapt6TAyMkKzZs3qt5BEEtaxY0ecP38et27demZiOHr0aCxevBibN2/GwoUL4eLi0kBREhGpNiaGRKSx8vLy8PjxYzx+/BiPHj0Snj9+/BhaWlq4ePEiAEAmk2Hu3Ll4+vRppWsYGRkJLYIA0Lt3b2zevFlIBJ2cnGBubl7l+3fv3r1+CkakYcoTw9u3b2PEiBE1HtumTRtMmjQJv/32G7788kts3LixgaIkIlJtTAyJSG3l5+fj8ePHePjwIR49eoRHjx5h/Pjxwti9NWvW4D//+U+V5+rp6aG0tFSY7fOtt95CaWkpXFxcYGJigk6dOsHZ2RlWVlZKLX2urq5466236r9wRCTo1KkTAOD69eu1On7p0qXYvXs3tmzZgvfffx9t27atx+iIiKSBiSERSVZpaSkSEhKQmpqK9u3bAwCKiorQr18/PHjwAAkJCZXOcXJyEhJDd3d3uLm5oUmTJmjSpAmaNm0KFxcX4XXFhG/VqlXCc7lczkkriFSIt7c3gLIxviUlJdDW1q7x+FatWuHtt9/Gxo0bMWvWLFy4cEG4CUREpKmYGBKRJNy+fRvnzp3DgwcPEBMTgwcPHuDhw4coKChAs2bNEBMTAwDQ1dUVxgBqa2vDxcUFrq6ucHV1RdOmTdGrVy/hmhMmTMCECRPEKhIR1ZFmzZqhadOmePToEW7fvo0uXbo885wvv/wS+/fvx+XLl7Fjxw5Mnz69ASIlIlJdTAyJSHS5ubm4f/8+oqOjcf/+feGxZMkSDBgwAABw7NgxLF68uNK5NjY2cHR0VJqm/tixY2jUqBGcnJygo8M/c0SaoH///ti6dStOnjxZq8TQ0tISa9aswdWrV+Hj49MAERIRqTZ+YyKiBlFQUIAHDx4gLS0Nnp6eAIDCwkK4ubkhLi6uynN8fHyExNDLywuzZ8+Gm5ub8HB1da1yLb7yrqJEpDlGjRqFrVu3Yu/evQgICKjVOa+//jpef/31eo6MiEgamBgSUZ2LiIjAhQsXEBUVJTwePXqE0tJSNGnSBI8ePQLwfxO86Orqws3NDe7u7nB3d0fz5s3h5uYmTCgBlI0hKh9HRET0b0OHDoWZmRlu3ryJqKgotGzZ8rnOz8rKQkREBHr06FFPERIRqTYmhkT03IqKihATE4OIiAhERkYiIiIC/v7+6NOnDwDgyJEjWLhwodI5WlpacHV1RevWrZVm+wwLC4O1tfUzJ4sgIqqJgYEBxo4di59//hm//fYbPvvss1qfm5CQAG9vb6SmpuL27dtwcnKqv0CJiFQUE0MiqlbF2f1KSkowadIk3L17F9HR0SgqKlI6tn379kJi6OnpCV9fX7Rs2VJ4NGvWDPr6+pXew87Orv4LQkQaYdq0afj555+xadMmLF68GHp6erU6z87ODs2bN8fx48cxdepUnDlzhjeriEjjMDEkIhQXFyM6Ohrh4eHC486dO0LLIABoa2vj+vXrePz4MQCgadOmaN26NVq1aoXWrVsrdfPs3bs3evfuLUpZiEhz9e/fH23btsWdO3ewe/duTJs2rVbnyWQyBAUFoUOHDrhw4QK+/PJLfPLJJ/UcLRGRamFiSKRBFAoF5HI59PT0YG1tDQDYunUrZs+ejcLCwkrHa2trIycnB8bGxsKxFhYWaNmypbCNiEhVyGQyfPjhh3jzzTexcuVKTJ48udYzE9vY2OCXX37BkCFD8Omnn6JDhw6crZSINApXcyVSUwUFBbh58yaCgoIwd+5c9O/fH40bN4aTkxO2bt0qHGdvb4/CwkK4urpi1KhRWLRoEXbs2IGbN28iOztbKQHs378/unTpwqSQiFTWlClT4OrqioiICKW/dbUxaNAgfPHFF1AoFJgyZQpu375dT1ESEakethgSqYGMjAzcvXtXafH2Nm3a4MGDB5WOtbS0VGod7N+/PzIzM2FqatogsRIR1Sd9fX2sWrUKEydOxNKlSzFp0iSYmZnV+vxFixbh7t272LFjB44dO4aOHTvWY7RERKqDiSGRxKSmpuLGjRsICwtDWFgYbty4IYwDTE9Ph7m5OQCgQ4cO0NXVRadOndCxY0d07NgRHTp0gKOjo7AQPFD2JaqqSWGIiKRq/PjxWLt2La5evYoPP/wQP/30U63Plclk2Lx5M1599VWMHTu2HqMkIlItTAyJVFhWVhaysrLg4OAAAAgODsagQYMqHaenp4cOHTogOTlZSAx///13YUkIIiJNIpPJ8NNPP6FLly7YsmULxowZg5EjR9b6/PKlL8rFx8fD0tISRkZG9REuEZFK4LdGIhVRXFyMmzdvYuPGjfDz80O7du1gbm6OBQsWCMe0bdsWBgYG6NmzJ9577z1s3boVt27dQnZ2Nq5fv47mzZsLxzIpJCJN1qZNG6xYsQJA2TIW0dHRL3Sd6OhoeHp6Yty4cVVO0kVEpC7YYkikAj7++GP88MMPyM3NVdquq6uL/Px84bW9vT2ysrJqPcseEZEm+/DDD3H58mUcOnQIPj4+uHr1qtCroraKi4uRm5uL48ePY9y4cdizZw8MDAzqKWIiIvHw2yVRAygtLcXdu3dx9OhR3LlzB3/++Sd27NiBnj17AgCMjY2Rm5sLNzc3eHh4CI+OHTtW+gLCpJBeVklJCXJycpCbm4ucnJwqnxcVFWHKlClseSZJ09LSwi+//IJevXrhzp07GDZsGE6ePPlck221bt0aJ0+exKBBg3DkyBGMGjUKBw8e5OzMRKR2+A2TqJ4UFBTg22+/xcWLF3HlyhWkp6cr7f/zzz+FxPDdd9/Fu+++K6wtSKRQKJCfn4/s7GylR05OzjO3PSvpKygoqFUMTZs2RZ8+feq5pET1y9TUFEePHoW3tzeuXr2K4cOH49ixY8+VHHbp0gXnz5/HwIEDERwcjCFDhuCPP/6AhYVF/QVORNTAmBgS1YGCggKEhoYiMjIS/v7+AMomhPn666+RkpICAHB2dkaXLl0wcOBAeHl5oX379sL5TAilraioqFKy9jyJXHXJXWlpab3EK5PJYGxsDCMjIxgbG1d6bmxsDCsrK3Tp0qVe3p+ooTVp0gTnzp2Dt7c3Ll++DG9vb/zxxx9wdHSs9TXat2+PS5cuYcCAAbhy5Qr69OmDv/76i7M6E5HaYGJI9AKKi4sRFhaGs2fP4uzZs7hy5Qry8vKgra2NSZMmwdTUFDKZDMuXL4epqSl69+6NJk2aQC6XCzOMkriKi4uRlZWFzMzM5/6ZmpqKvLw84XXFcaB1SV9fHyYmJsLD2NhY6XVV2yomd1UlfEZGRjAwMFBasqQqcrmcXeVIrTRr1gwXLlzA0KFDcevWLfTs2RP79+9H9+7da32NFi1a4PLlyxg2bBimTZvGpJCI1AoTQ6LndP78efj4+CAzM1Npe7t27dC3b1/k5uYKXZRmzZolRohqrbS0FFlZWUhPT0dGRkaVP2tK6sqf5+Xl1VlMMpkMpqamMDU1fa4krqZtxsbG0NXVrbMYiQhwc3PD1atXMWbMGFy5cgVeXl74+uuv8f777z/zZkm5Jk2a4Pr160pLV6SkpLDnBxFJHhNDomqkpaUhODgYJ0+ehIODA5YvXw4AaNWqFTIzM9G8eXMMGDAA/fv3xyuvvAIbGxuRI5aG/Pz8ahO62vzMzMyEQqF46TjKkzkzM7Pn/pmfnw83NzfhtZGRUa2/VBKRuBo3bowzZ87go48+wvfff48PPvgAJ06cwMaNG+Hi4lKra1RsTX/06BG6deuGGTNmYNWqVZwgjIgki3+9iP4/hUKB27dv4+jRozh+/DiuXr0qjPFq2rQpli1bBplMBjs7O8jlctjb24scsXhKSkqQnp6O1NRU4ZGWlobU1FQ8fvwYxcXFVe5LT0+v9cQnNTExMYGFhQXMzc0r/Sx//DuZ+3eCZ2Rk9MIzbrJLMJG06evr47vvvsMrr7wCf39/HD9+HG3btsWqVaswa9YsaGtr1/paISEhyMjIwOrVq3Hjxg3s3LlTo+sHIpIuJoZE/9+yZcuwbNky4bWOjg68vb0xZMgQDBkyROlYdan0S0tLkZ6ejn/++Qf//PMPUlJS8PTpU6Vk7t/JXWpqKjIyMl74PXV1datN6qpK8v69zczMjHfkiahOjBs3Dl5eXnjvvfewf/9+vPfee9i4cSO+/vrrSn/3qzNx4kQ4ODhg/PjxOHfuHDp27IigoCAMHz68nqMnIqpb/HZFGiclJQV//PEHDh48CB8fH/j5+QEA+vbti82bN2P48OEYPnw4BgwYADMzM5GjfT55eXlISUlRSvRqev706VOUlJQ89/vIZDJYWFjA0tISVlZWwsPS0hK6urpo0qSJ8LriPktLy1pNfEJE1FDs7e3x+++/Y//+/Zg/fz7Cw8MxdOhQDB48GMuWLROWFapJnz59cPPmTUyfPh3BwcEYMWIEPvjgA6xcuRKGhoYNUAoiopfHxJA0QlxcHPbv34/9+/fj0qVLQhfRwsJCITH09vZGXFycSiUtCoUCqampSEpKQlJSEhITE4Xn5a+Tk5OFZC83N/e538PMzAzW1tZo3LgxGjdujEaNGqFRo0aVEruKr83NzavtasVulkQkRa+++iqGDx+O7777Dl988QVOnTqFU6dOYcCAAfjPf/6Dvn371lg/2Nvb4+TJk/jqq6+wZMkSrF+/Hr6+vujYsWMDloKI6MUxMSS198EHH2DdunXCa11dXQwePBg+Pj4YPXq0sP1Fx5u9iMzMTMjlcsjl8mcmfcXFxbW+rp6enlKS96znjRo1gp6eXj2WlIhIOgwMDPDxxx/D19cXq1evxvr163HmzBmcOXMG3bt3x7vvvouJEyfCwMCgyvO1tLSwcOFC9O/fHzdu3BCSQoVCgcLCQi5vQUQqjYkhqZWUlBTs3bsXffr0ERaQb926NQwNDTF06FC89tprGDlyJMzNzevl/YuKipCQkAC5XI74+HjEx8crPX/y5AmSkpKQnZ1d62uam5vD1tYWdnZ2sLW1FR7lr21sbGBjY4PGjRvDxMREpVo8iYikqHHjxli5ciUWLFiA7777Dt9++y2uX7+OGTNmYP78+fDz88Pbb78Nd3f3Ks/v3r270vqIv//+OxYuXIiNGzdi0KBBDVUMIqLnIlPUxbzvVG8KCgpgYGCAmJgYNGvWTOxw6tWLdkHMzc3FoUOHsGPHDpw8eRIlJSWYO3cu1qxZAwDIycmBQqGAiYnJS8VXUlKChIQEPH78GE+ePBF+xsbGCglgcnJyrZZSMDQ0hKOjI+zt7ZUSvn8/t7GxqfbOtKrShK6kLCORarCzs0NSUlKdLGFTk9zcXOzatQvr16/HjRs3hO09e/bE1KlTMXHiRDRu3Lja84cOHYqTJ08CACZNmoSvv/4ajo6OtX5/Tfg8akIZAc0oJ8soXWwxJMm6du0afvrpJ+zZswdZWVkAymYSHT58OF555RXhuIrrTdUkNzdXKeH798+4uLhnduvU0tKCnZ0dHB0d4eDgAEdHR6Xnurq66NSpEywsLNiyR0QkEUZGRvDz84Ovry9CQ0OxYcMG7Nu3D9euXcO1a9cwd+5cDBs2TOiV0qhRI6Xzjxw5gtWrV2PZsmXYtWsXjhw5giVLlmDevHnsXkpEKkPSLYaxsbEIDAxEaGgogLJZJRctWgQrKyuRI6s7bDGs3uzZs7Fx40YAgIeHB6ZNm4YJEybA2tq6yuMVCgWePn2KmJiYKh8JCQnPfE9bW1s0adIELi4uwk9nZ2chAbS1ta1xKQV1vcNUEcuoHjShjCR9DdViWJWcnByht8qpU6eEGZ61tbXRp08fjB07Fj4+PmjSpIlwzsOHDzF//nwcOHAAAODq6opjx46hVatWNb6XJnweNaGMgGaUk2WUrudqMZTL5Xj69Cnatm3boBN1VCUtLQ1vvPEGCgsL8dZbb6GkpARbtmxBVFQU9u7dywk11EhpaSnOnDmDDRs2YNy4cXj99dcBAP7+/rCwsMAbb7yhVKmmpaUhKioKkZGRiIqKwv3794XkLzMzs9r30dXVhbOzM5o0aaKU/FVMAKXWrZOI1Icq1cFU1hvl9ddfx+uvv46kpCT8/vvvOHjwIM6dO4fz58/j/Pnz+OCDD9CmTRsMHjwYgwcPhre3N/bv34/Tp09j7ty5yM3NRdOmTcUuChERgOdMDMePH4/U1FQYGRmha9eu8PDwgIeHB9q2bdvg3eKCgoKQmJiII0eOwM3NDQDQsWNH+Pr64uDBg5gwYUKDxkN1Ly0tDVu3bsWGDRsQExMjbHv99ddRWloKKysrvPLKKzhx4gTWrl2LyMhIREZGIikpqdprmpqaws3NrcqHs7NztUswEBGJTZXqYFJma2uLd955B++88w7S09Nx9OhRHDx4ECdOnMDdu3dx9+5drF27Fnp6evDy8sLgwYOxceNGNG7cWLjh+PTpU/j7+2Px4sXo1q2byCUiovpSWlqK6OhouLu7q9z3zufqSnrx4kXs2bMHYWFhSEtLK7uATAYTExN07doVPXv2hIeHB1q3bl1vAZcbOHAgnJycEBQUpLR96NChsLW1xc8//1zvMTQETexKGhkZiTVr1mDHjh3Cunw2Njbo1q0bzMzMcP/+fdy5cwd5eXlVXsfQ0BCtWrVCq1at0LJlS7i7uwvJX+PGjUX9AqWuXQ8qYhnVg1wux61btzB9+nR07NgRAwYMQK9evdCtWzeYmpqKHZ5GUqU6WFWI2ZW0NgoLC3Ht2jVhTcS//vpLKVYDAwN4eHigT58+iI6Oxu7duwEAo0aNwtKlS4UEUVP+5qh7GQHNKCfLWLOffvoJs2bNgq6uLtq2bYt+/frBy8sLHh4esLe3r+NIn88LjzGMjo5GaGgoQkNDERYWhn/++Uf4wm1mZob+/ftj2rRpaNOmTZ0GDAAZGRno0aMH3nrrLXz88cdK++bPn4/z588jLCyszt9XDJqUGMbFxSE7OxtffvklfvnlFwBl6/IVFhZWeby9vb2QAFZ8ODk5qWw3K/6xVA+aUsY9e/ZgwYIFKCoqgq6uLgwNDZGXlwd7e3t4eXmhb9++QotVTWNrqe6JWQerElVPDP/t6dOnOHv2LIKDg3Hp0iVERERUOkYmkwnl6d27N1asWIHmzZtrxN8cdS8joBnlZBlrtm7dOixYsAAFBQUAyj7zpqamKCgogLGxMbp3744BAwagZ8+e6Nq1K4yMjOoy9BrV2eQzMTEx+OOPP7B582bo6OggPz8f2traePvtt/HBBx/UxVsI7t27h1GjRuE///kPpk+frrRv1apV2LZtG/766y+VuqutUCiwZs0axMbGPtd5xcXF+P777zFjxgxYWFjUT3AiUCgUyMzMRGJiIqKiopCWlobs7GwUFRVVOlZXVxeNGjWqtDC7FMf7ZWdnv/SyGaqOZVQP2dnZCA4ORnx8fJWfS6BspkYtLS0UFhaidevW6NevH0aOHIkBAwY0cLTUkHVwVfLy8vDFF18gJyen3t+rok2bNiE3Nxdz585t0PetK3l5eZDL5cJ6t8nJySgtLa10nJGREVq0aCEsZ2RhYaGyN0BflCb8XQU0o5wsY80OHz6MuLi4ahs+gLKGEQMDA+Tl5cHJyQm9e/dG37594evrW6893+p8VtI9e/YgIyMDjo6O+P3333HlyhX4+vpi4cKFdfYeN2/exKRJk7BixQqMHz9ead+aNWuwceNGXLx4Eba2tsL29PR0oVuiGFJSUtCpUyfR3p+I6EVoaWlV+UW1In19fRQUFEBHRwdjx47F2rVrGya4Gqj73erqvGgd/LJ15N9//42hQ4e+8PlERJqkNnUrUNY4UlpaitLSUri6uuL8+fMvPS6xpvrxufv+FBQUQCaTVTvr54QJEzBt2jT88ssvGD58OM6cOYNFixYJXY7qQm3+If99J83CwkLUFjcHB4cX6uoi1a6kGRkZuHLlCi5duoTLly8jNDS02jsjFhYWmDRpEmbMmFFnvyOqit0r1IOmlHHPnj1YuHCh0mdXR0cHRkZGyMvLg62tLby8vNCvXz94eHigXbt27FJaz+qrDn7ZOvJF67iXJbWupC/iyZMnuHz5Mh4+fIjr16/j1KlT1Y6xt7OzQ4cOHdCuXTu0bt1aGGLRuHHjBo76+WnC31VAM8rJMtbs311Jy5V3KS0sLIShoSG6du2KgQMHCl1KG6IV9rlq8AMHDmDp0qUAgD59+uC1117DK6+8UumLQMWuJAMGDMA333yDbdu21dmX/vIFy//9D1pxW20XNae6UVxcjNDQUJw6dQqnT59GSEiIsKYTUPbL3qpVKyQkJCAjIwMA0Lx5cyxZsgSvv/46dHR0IJfLxQqfiKpQ3l3F0NAQurq66NKli9IkNObm5iJHqFlUpQ6mhuXi4oK+ffvi9ddfR0FBAby9vYX1m2UyGZo0aQJDQ0M8efIEiYmJSExMxKlTp5Su0ahRoyrH5Ddt2pQ3c4hEUFxcDGNjY8hkMhQVFaFNmzZKk9A4OjqKEtdz/TXYuHEjpk2bhpiYGFy8eBHnzp2DmZkZvLy80K5dO5iYmODatWuVWuv69OmD77//vs6CLs/QU1JSKu1LTk6GmZlZgw7U1FQJCQk4fPgwTpw4gbNnzyqtEaijowNPT0/06dMHffr0gaenJywsLODh4YHU1FR89tlnmDRpEiskIhX25ptvwtnZGV27doWLiwuXRBCZqtTBJB59fX1cu3YNV69exXfffYd9+/bh0aNHAAB3d3esWrUKWlpaiIiIEJZwioyMxNOnT3HlyhVcuXJF6Xo6Ojpo2rRplUs4NWvWjN+liOrB4MGDMXXqVPTu3RseHh5o06aNyixb8Vzfys3NzbFgwQIAQGpqKvbv348jR47g2LFjOHbsGICyqZc3btwIAPj5559hY2ODYcOG1Wnzp5mZGZycnHDnzp1K++7evYt27drV2XuRsnv37uHgwYM4ePAgrl27ptR9p0WLFsIivn379kVsbCwCAgLg7+8PS0tLAMDvv/8OOzs76OrqilUEIqolExMTvPrqq2KHQf+fqtTBJC6ZTAZPT094enrim2++wZYtW7Bp0yY8fPgQnp6esLe3x9ixYxEdHQ1XV1doa2sjISFBSBKjoqIQGRmJiIgIxMbG4v79+7h//36V72Vvb6+ULDZp0gQuLi5o0qQJHB0dq+3STETVa9WqVaXl9lTFcyWGY8eOxfLly7Fo0SJYWVnhrbfewltvvYX4+Hjcv38feXl56Nq1K6ytrQEAP/zwA7Kzs5GUlAQnJ6c6DXzw4MHYvn07YmJihAXu//zzTzx8+BBvvvlmnb6Xpnv8+DF+/fVX7Ny5UykZ19fXx+DBgzFq1CgMHjwYTZo0AVA2icEnn3yC77//HiUlJTA3N8f27dsBAM7OzqKUgYhI6lSpDibVYG9vjyVLliAgIABhYWHCGmilpaUYNGgQ8vPzMXXqVEyfPh39+/dH//79lc7Py8vDw4cPERMTU+nx8OFDJCQkICEhAZcvX6703jKZDA4ODkKiWNVPdjcnkpbnnpX0ypUr2Lp1K1q3bo2PPvqoxmMvXryIX3/9FS4uLvjwww/rdHmB1NRUjBw5Etra2vDz80NBQQF++uknuLi4YNeuXWpzF0usyWcyMzOxd+9e/PLLL7hw4YKw3cLCAiNHjsTYsWMxePBgpbvQCoUC27dvx8cff4yUlBRoaWlh5syZWLZsmfBFpSYcrKweWEb1oAlllCJVqYNVhSZMPgM8/+cxLi4OgwYNQmRkpLCtXbt2mDp1KiZPngwXF5dnXqOkpARxcXFCovjgwQM8efIEjx8/xuPHjyGXy585GaC5uTkcHR2Fh4ODQ6Xntra20NbW1pi/OZpQTpZRul54uYqKLXViefDgAVauXIm//voLBgYGeOWVV7BgwQJYWVmJGlddaujEMDw8HOvXr8cvv/wiTGBgYGAAHx8fTJ06FUOGDKmyG2hMTAz8/f1x7tw5AGVjWtatW/dcS3So64esIpZRPbCMJDZVqINVARPD6ikUCoSGhuLnn3/G7t27kZqaKuwLDQ1F9+7dXyqmoqIixMfHC8lixaSx/Hl1s6dWpKWlBTs7O9jY2KBp06ZKyaOdnR3s7Oxga2sLa2trlRmH9TI04W8ryyhdLzzzhypUSM2aNcPmzZvFDkPySktLcejQIaxduxYXL14Utnt7e2PGjBl47bXXYGZmVuM18vLycOnSJTRu3BjffPMNpk6dyokqiIjqiSrUwaTaZDIZPDw84OHhgbVr1+LEiRPYuXMn/vrrL3Tp0kU4bvHixXB0dMTYsWOf64uurq4umjZtiqZNm1a5X6FQ4OnTp4iPj0d8fDzkcrnSz/LnycnJkMvlkMvluHXrVo3lady4sZAolj+qet24cWNObkf0Avip0WDFxcXYs2cPvvzyS2HsoImJCd544w3Mnj0bbdu2rfH8+Ph4YTrddu3aYffu3XjllVfQqFGjeo+diIiIakdPTw+jR4/G6NGjUVJSIrS8paWl4auvvkJxcTHef/999OrVC2PHjsWYMWPg7u7+Uu9Znsg1btwYHTt2rPa4wsJCJCYm4tatWygsLFRKHBMTE5GUlISkpCT8888/SElJQUpKCv7+++9avXd5slgeh7W1dZXPGzdurDZDkIheBhNDDaRQKLB//34EBAQgOjoaAODk5ISPP/4Yvr6+MDU1feb569evx0cffYRffvkF48ePBwDOXkhERKTiKnbH1NfXx7Zt27Bv3z6cPHkSf/75J/788098/PHHaNu2LYKCgtCtW7d6jUdPTw8uLi7Q0dGpscWyuLgYKSkpQqJYMWn89+uKSWR4eHit4jAzM3tmAmltbQ0rKytYWVnB0tKSM6yT2mFiqGFCQ0Mxf/58YYYxNzc3BAQEYNq0abW6W/bPP//Az88PR44cAQCEhIQIiSERERFJh5GREaZOnYqpU6ciOzsbx48fx8GDB3H06FHcuXNHaZHtnTt3Qk9PD4MHDxZltlEdHR3Y29sLM6/WpGISWZ4g/vPPP0LCWNXzzMxMZGZm4sGDB7WOycTEREgUy5PFZ70uKCiAQqHgcBtSSUwMNURGRgYWLlyIH3/8EQBgbW2NZcuWwd/fv9b98K9cuYIJEyZALpfDwsICP/30E1577bX6DJuIiIgagImJCcaPH4/x48ejsLAQf/31l5CEKRQKLFmyBI8ePYKOjg68vLwwdOhQDBs2DB06dFC5JOd5kkigbK6FjIyMGhPH8uepqalITU1FWloasrOzkZ2djSdPnjxXfLq6upUSR0tLS1hYWMDc3PyZP/X19V/kn4XomZgYaoDjx4/D398f8fHx0NXVxYcffojFixc/c0KZcgqFAj/88APmzp2L4uJieHl5CVOgExERkXrR09ODp6en8Lq4uBgzZ87E0aNH8eeff+LChQu4cOECAgICYGdnh7Vr12LixIkiRvxytLS0YGlpCUtLSzRv3rxW55SWliIrK0spUSx/XtPrp0+fIj8/X+j2+iIMDAyUEsXaJJMVjzU1NVWLGV6p7jExVGNFRUVYvHgxvv76awBAjx49sGXLFrRr1+65rpOTk4PVq1ejuLgYH374IQIDAznbFxERkYbQ1dXFokWLsGjRIqSlpSE4OBgnTpzAiRMnIJfL0bhxY+HYXbt2ITQ0FAMGDECfPn1qfRNaarS0tIREy9XVtdbnyeVyWFlZKSWO5c8zMjKQnp5e5c/y5+np6cjPzxeSyxdlbGwMU1NTmJmZvdRPExMTJplqhN/u1VRiYiJeffVVXL16Fdra2vjiiy/w0UcfvdCH18TEBPv370dERAQmT55cD9ESERGRFFhaWgpdThUKBe7evas0g+mvv/6KI0eOYM2aNdDW1ka3bt3Qr18/9O3bF15eXjAxMRExetVgYGDwXF1dK1IoFMjLy6sxiXzWz+zsbOTk5CAnJweJiYkvXR5jY2OlhFFPTw/W1taVEkljY2OYmJgoPf69zdjYmJP6iIiJoRqKiIjAsGHD8PjxYzg7O2PXrl1KXUJqIzo6GkeOHMGHH34IAOjUqdNzLVZPRERE6k0mk1Va2mrhwoXo0KEDzp07h5CQEOGxatUqjBkzBgcOHABQtkxFbm4uLCwsRIhcumQyGYyMjGBkZPRCiSVQ1g02JycHWVlZyMzMfKmfWVlZQpKZkJBQJ2XU09N7ZgJZ3bbqthsZGUFLS6tO4lNnTAzVTFhYGAYOHIj09HR4eHjg8OHDsLGxee5rDBkyBE+fPoWjo6Okxw0QERFRw/Hy8oKXlxcAICsrC5cuXcKFCxdw7tw59OvXTzju4sWLGDx4MDp06IDevXujbdu2GDlyJJydncUKXWNoaWnB1NQUpqamNS4RUhvlSWbFhPHhw4fQ09OrlEiWJ5Dlk/aUP/69rbCwUOhmW5eMjIxgbGwsPCq+ft7n6rpmNxNDNXLr1i0MGjQI6enp8PHxwa+//gojI6PnusaVK1cwfPhwZGZmYtiwYRgxYkQ9RUtERETqzNTUFMOHD8fw4cMr7Xv48CF0dHRw+/Zt3L59GwDwzjvvwNnZGV5eXvj555+56LwEVEwyyzk5Ob1wwqlQKFBQUFBlwvgy23JycpCbm4vc3FykpKS8dLl79+6NS5cuvfR1VA0TQzVx//59DBw4EGlpafDx8cHevXufu4/2mTNnMHr0aOTm5mLChAnYsWMH+3kTERFRnfP398fUqVMREhKCK1eu4OzZswgLC0NsbCxCQkKUksLJkyfD2dkZHh4e8PDwgJOTk4iRU32SyWQwMDCAgYGB0qRGL6u0tBR5eXlKSWJ5C+a/Xz9rX25uLvr3719nsakSJoZqICsrCz4+Pnj69CmGDBmC3bt3P3dCd+HCBYwcORL5+fmYMWMGfvrpJ84yRURERPXG0NAQffv2Rd++feHr6ws7OztEREQozbaZnJyMXbt2KZ3n4OCAHj16oHv37pg4cSLc3NwaOnSSGC0tLaEbaF2Qy+V1ch1Vw8RQ4hQKBd544w3cvXsXrVu3xp49e5574dOSkhK8++67yM/Ph7+/PzZu3MgBukRERNSgtLS00LZtW6UJbUxNTfHHH38gJCQE165dQ2hoKORyOQ4ePIiDBw+ia9euQmJ45MgRREVFoVu3bujcuTPMzc3FKgqRJDExlLigoCAcOHAA5ubmOHTo0AutF6StrY1jx45h/fr1+PLLL5kUEhERkUowNDTEiBEjhDkPSktLER0djdDQUISGhqJbt27Csb/88gv27t0rvG7evDm6dOmCLl26KE2KQ0RVY2IoYbGxsfjggw8AAN9//z2aN2/+XOcXFhYKffhdXFwQGBhY5zESERER1RUtLS20bNkSLVu2xLRp05T2TZgwAZaWlggLC8Pff/+N6OhoREdHY/fu3RgzZoyQGKanp2P16tXo1KkTOnbsiGbNmvGmOBGYGEra4sWLhfGFU6ZMea5z8/Ly0LdvXwwfPhxLly6FTCarpyiJiIiI6t+4ceMwbtw4AGU3v+/cuYObN2/ixo0b6N69u3DcrVu3sGLFCuG1iYkJ2rdvjw4dOqBjx46YPHky11ckjcTEUKL++usv7NixA3p6eli7du1zJXYKhQJ+fn4IDQ1FUlIS5syZA0tLy3qMloiIiKjh6OnpoXPnzujcuTP8/PyU9tnb22PRokW4desWbt++jYSEBFy9ehVXr14FALz66qvCsYGBgUhLS0P79u3Rrl07tGrV6rnnciCSCiaGErV48WIAwAcffICmTZs+17krV67Erl27YGJigiNHjjApJCIiIo3RsmVLrFy5UnidkpKC//3vf7h9+zZiYmJga2sr7AsKCkJkZKTwWltbG+7u7mjbti0mTpyICRMmNGjsRPWJiaEE/e9//8Pp06dhbGyMgICA5zr38uXL+OSTTwAAO3fuRPv27esjRCIiIiJJsLa2xoABAzBgwIBK+7744gvcunULd+7cQXh4OO7fv4+oqChERUUpfYc6f/48Zs6cidatWys9WrVqpbT4O5EqY2IoQWvWrAEAvPnmm8/V2peWloYpU6agtLQUCxcuxOjRo+srRCIiIiLJe/XVV5W6lubl5SEqKgp37txRSgzDw8Nx79493Lt3D4cOHVK6hpOTEyIiImBiYgIAuH37NqysrODo6MhJb0ilMDGUmMzMTPz222+QyWSYM2fOc527cOFCPHnyBN27d8fnn39eTxESERERqSdDQ0N06tQJnTp1Utr+1ltvwdvbG3fu3EFkZCQiIiIQERGBe/fuoaCgQEgKgbLZU+/duwcjIyM0b95cmGW1RYsW6NmzJ9zd3Ru4VERlmBhKzKFDh1BQUABvb29hQdfaWrZsGVJSUvD1119DV1e3niIkIiIi0iwGBgbo0KEDOnTooLS9pKQEiYmJwmuFQgFHR0ekpaUhJSUFt2/fxu3bt4X9n3/+OZYsWQIAuHbtGjZs2IDmzZvD3d1d+Glubt4whSKNw8RQYnbt2gUAmDRp0nOfa29vjwMHDtR1SERERERUBW1tbTg6OgqvZTIZzp49C6BsiE9UVBSio6MRFRWFe/fuwcPDQzg2NDQU27dvr3RNa2truLu74/z588J61BEREWjUqBGsra25BBm9MCaGEpKRkYFTp05BW1sbr732Wq3PO336NPr37w9tbe16jI6IiIiIasvS0hI9e/ZEz549q9w/dOhQbNq0CdHR0bh//z6io6MRExODlJQUaGlpCUkhAIwcORIPHjyAqakpmjVrhmbNmsHNzQ2urq7w9vZGu3btGqpYJGFMDCXkwoULKC4uhpeXF2xsbGp1zrlz5zB48GD06dMH58+f5yBnIiIiIglo0aIFWrRoobSttLQUCQkJSE5OFrYpFAo0btwYT58+RUZGRqXuqStXrhQSw+DgYCxfvhyurq5Kj6ZNm8LR0ZGNCBqOiaGElHc9qGo65aoUFBRg9uzZAIBBgwYxKSQiIiKSMC0tLTg6OlbqnhoSEgKFQoHU1FQ8fPgQMTExiImJwcOHD5VaJMPDw3Hp0iVcunSp0rX19PSQmZkJfX19AGVrOGppaaFJkyZo0qQJnJycoKPD1EGd8X9XQsoTw/79+9fq+G+//RZRUVFo0aIFFixYUJ+hEREREZGIZDIZGjVqhEaNGqFbt25VHvP666+jffv2ePjwIR4+fIhHjx4Jz7W0tISkEAA+/fRTPHnyRHhdPl7SxcUFb731Ft544w0AQHp6OuLj4+Hi4sI1GyWOiaFE5OXl4c6dO9DR0VEamFydzMxMBAYGAgDWrl2r9EEnIiIiIs1jY2NTbc+zwsJCpdfTp0/H/fv38fjxYzx+/BgJCQl48uQJnjx5orQW9tmzZ4W5LywsLGBvbw83Nzc4OzvD2dkZH3zwAYyMjACUdYVlDzbVxcRQIu7du4fS0lK0adMGBgYGzzz+u+++Q2pqKry8vDB06NAGiJCIiIiIpKriZDYAKq15XVBQgLi4ODx+/Biurq7CdoVCgRYtWuDJkydIT09Heno6IiIiAJS1Ys6fP1849pVXXsH9+/fh5OQEZ2dnODk5Cc87duyINm3a1GMJ6VmYGEpE+QesY8eOzzw2IyMDq1evBgAsX76c0xYTERER0UvR19eHm5tbpXW0X3vtNbz22mtQKBRISUnBjRs3kJeXhydPniAtLU0p4YyLi0NiYiISExPx119/KV1nzpw5+PbbbwEAN27cwFtvvQVHR0c4OTkJ4yrLHy1atOCa3PWAiaFEREZGAqhdYmhgYIBly5bhzz//RL9+/eo7NCIiIiLScDKZDDY2NujQoQMcHByqPCY6OhqJiYmIjY1FbGws4uLiEBcXh9jYWKWhUg8ePMDNmzdx8+bNKq/z+PFjuLi4AAA+++wz3Lt3D46OjnBwcFB62NvbC91Y6dmYGEpEVFQUgNolhvr6+nj//ffx/vvv13dYRERERES1oqOjI3Qf7dWrV7XHDR48GKGhoYiLi0N8fDzi4+MRFxcHuVwOuVwOe3t74djTp0/jzz//rPI648aNw969ewEAiYmJ+Pjjj2Fvb1/lgxPnMDGUjPJZoZo3by5yJERERERE9cfMzAzdu3dH9+7dn3nsV199hZiYGMTHxyMhIQFyuVx43rRpU+G4R48eYceOHdVe5+rVq8LSHtu2bcPNmzdhb28POzs7pYe1tfVLl09VMTGUiOTkZGhpacHJyanaY0pLS+Ht7Q1vb2/85z//gbGxcQNGSERERETUsDw9PeHp6fnM41xdXbFt2zYkJCQICWT584SEBNjZ2QnHHj9+XGhprOr9qtsndUwMJaK0tBROTk41DrQ9d+4crly5gidPnlSaSYqIiIiISFPZ2tpixowZVe5TKBRKr2fOnIlevXohISEBSUlJws/ExMRqx0+qAyaGEtKkSZMa92/atAkA8Oabb0JbW7shQiIiIiIikrR/z+A/YMCAatd7VCgUSEhIaIiwGhxXmJQQZ2fnavclJyfjwIED0NLSgp+fXwNGRURERESkGdR5GTgmhhJS02DXn3/+GUVFRRg+fHiNCSQREREREdG/SbYraXZ2NtauXYtTp04hNTUVNjY2GDVqFN59912lhTTViZWVVZXbFQoFNm/eDAB4++23GzIkIiIiIiJSA5JMDBUKBd577z2EhoZiwoQJaNmyJW7duoUff/wR9+/fx/r168UOsV40atSoyu1XrlxBdHQ0HB0dMWzYsAaOioiIiIiIpE6SieGZM2dw9epVLF26FFOmTAEATJ48GXZ2dti4cSPCwsLQtWtXkaOse9W1GPbo0QPnzp1DVlYWdHQk+V9KREREREQikuQYw9DQUADAmDFjlLaXt5bdvHmzoUNqENUlhnp6eujbty9GjRrVwBEREREREZE6kGRi+M477+DgwYOVFnBPS0sDALVtNauuKykREREREdHLkGRiaGFhgdatW1fa/ttvvwEAOnfu3NAhNYiqWgx//vlnjBgxAsePHxchIiIiIiIiUgcq1bSWkpJS434jI6NKrYTlDh48iJMnT8LDwwMdO3astD89PR25ubl1EmdDKigoEJ7n5+dDLpcr7f/tt99w8uRJ9OvXr8pyS0lWVlal8qkbllE9sIyqz8HBQewQJEWqdWRpaSkASPp3tTak/nmsDU0oI6AZ5WQZVVtN9aNMoVAoGjCWGrVs2bLG/bNmzcK8efMqbT9z5gw++OADWFhYYM+ePWr1haCgoAAGBgYAgNzcXBgaGirta9SoEXJychAXFwdHR0exwqwTcrlcrf7vqsIyqgeWkUg12NnZISkpCSr0VaZeaMLnURPKCGhGOVlG6VKpFsMVK1bUuL+q7qN//PEHFi1aBGNjY2zevFnt/pPK74YCEBLEcpcuXUJOTg46duwo+aSQiIiIiIjEo1KJ4fjx45/r+F27dmHZsmUwNzdHUFAQWrVqVU+RiSc/Px8AoK+vD5lMprTv2LFjAMC1C4mIiIiI6KVIcvIZoGxM4aefforGjRtj586dapkUAkBeXh4AKHUhLXf06FEAwPDhwxs0JiIiIiIiUi8q1WJYWzExMfjkk09gZWWFX375BU2bNhU7pHpTPhnAv7uRPnr0CPfu3YO5uTl69eolRmhERERERKQmJJkYfvfddygsLESfPn1w+/Zt3L59W2l/y5Yt1aYFsWJX0oqMjIywZs0alJSUqO26jURERERE1DAkmVFcv34dAHDo0CEcOnSo0v733ntPbRLD8q6k/24xtLGxwdy5c0WIiIiIiIiI1I0kE8MrV66IHUKDKV/HUE9PT+RIiIiIiIhIXUl28hlNUb5chZaW8n/VunXrcPDgQRQWFooRFhERERERqRFJthhqkvJFeysmhjk5OZg7dy60tbWRk5MjVmhERERERKQm2GKo4spbDCuuYXj37l0oFAq0atWKXUyJiIiIiOilMTFUcVUlhv/73/8AAB06dBAlJiIiIiIiUi9MDFVcVV1JyxPD9u3bixITERERERGpFyaGKo4thkREREREVN+YGKq48hbD8sRQoVDg77//BsDEkIiIiIiI6gZnJVVx/16uIjMzE40aNYJMJoOjo6OYoRERERERkZpgYqji/t2V1NzcHFFRUSgsLFTqXkpERERERPSi2JVUxVU1+QwALlNBRERERER1homhivv3GEMuaE9ERERERHWNiaGK+3di6OnpCTs7O0RERIgZFhERERERqRGOMVRxFSefKS4uRkREBIqKiuDs7CxyZEREREREpC7YYqjiKk4+k5qaiqKiIjRq1AgmJiYiR0ZEREREROqCiaGKqzj5TEZGBgDAwsJCxIiIiIiIiEjdMDFUcRVbDNPT0wGULVlBRERERERUV5gYqriKiSFbDImIiIiIqD4wMVRxFbuSssWQiIiIiIjqA2clVXEVWww7d+6MH374AS4uLiJHRURERERE6oSJoYqr2GLo5uaG2bNnixwRERERERGpG3YlVXHlLYZERERERET1hS2GKq7iAvfnzp3Dw4cP0adPHzRv3lzkyIiIiIiISF2wxVDFVexKGhQUhDfffBNXrlwROSoiIiIiIlInTAxVHNcxJCIiIiKi+sbEUMWVtxhWXMeQiSEREREREdUlJoYqruIYw/IWQy5wT0REREREdYmJoYqr2JWULYZERERERFQfmBiquIqTz3CMIRERERER1Qcmhiqu4jqGBQUFAJgYEhERERFR3eI6hiquYothbm4u8vPzoaurK3JURERERESkTthiqOIqJoYAYGBgIGY4RERERESkhpgYqriKk88QERERERHVByaGKq68xTAtLQ3t27fH7NmzRY6IiFRBcHAwJk2ahKFDh2Lr1q1ih0NEREQSxzGGKq68xTA/Px/h4eFwcnISOSIiUgUDBw5Eq1atMHLkSOTk5IgdDhEREUkcWwxVXHmLYVFREQAubk9E/8fJyQlWVlZih0FERERqgImhiitvMSwuLgbApSqIiIiIiKjuMTFUceWJIVsMiYiIiIiovnCMoYor70paWFgIgC2GRM8yYsQIHDt2TOwwajR8+HAcPXq03q5/+/ZtbN++HdbW1iguLkZWVhZmzpyJZs2aKR23b98+XLp0Cfb29khMTISXlxcePHiAqKgo9OjRA7NmzaqTeMLDw3H48GHIZDLEx8djxYoV2L17NzIzM5GUlIQ5c+bAxcWlTt6LiIiIXozaJIZz587F8ePHERUVJXYodYothkT0PM6ePYvAwEBs3boVjo6OAICYmBj4+vpiw4YNaNOmDQBg165dCAwMxMWLF2FqaopHjx5h2LBh2LNnD3r16oWkpKQ6iefRo0c4cOAAlixZAplMhkWLFmHixIlYuXIlFAoFpkyZgjZt2sDPz69O3o+IiIhejFokhqdOncLx48fFDqNelLcY2tvb45VXXkGHDh1EjohItdVnS1w5uVwOBweHen+f55WTk4OAgADMnj1bSAoBwM3NDd7e3ggICMChQ4cAADt37oS7uztMTU0BAE2bNoWlpSW2b9+Or776CnK5vE5iCgoKwoIFC4S1WHNzc2FmZoYuXbogISEBvr6+GDNmTJ28FxEREb04yY8xTEtLw2effQZdXV2xQ6kX5S2GLVq0wMaNG+Hl5SVyRESkqi5cuID09PQqu2W2atUKkZGRCA8PBwBYWloKXdTLFRYWoqSkpMprZ2dn4/3336+UMP79999YsWIFDh48iKVLl+Lx48dK+/39/WFkZCS8vnnzJjw9PQGU3fBauHAhZ1YlIiJSAZJPDD///HNYWlpi8ODBYodSL8oTw/K77URE1YmNjQUA6OvrV9pXfvPsyZMnAIDZs2cjJiYG0dHRAICLFy+iqKgIvr6+lc7du3cvtm7dilOnTgl/k4CyRHLOnDnw9/fHmDFjMG7cOHz44YdK51ZsuYyJiUFycjI8PDxesqRERERU1yTdlTQ4OBjHjx/Hb7/9hl27dokdTr0o70qalJSE69evo0OHDlV+6SMisra2BgCkpqZW2peeng4AaNSoEYCy5HHOnDnYs2cPdHR0UFRUhP3798PNza3SuePHjwcArF+/Xmn79evXYWRkBFtbWwBA+/bt8eDBA8TGxsLZ2bnSda5evQpdXV107txZ2FbdsURERNSwJNtimJ6ejs8++wxvvPEGOnXqJHY49ab87vypU6fQo0cPJCcnixwREamqfv36wdDQEA8fPqy0Lzw8HHZ2dujatSuAsi6d3t7e+M9//oOFCxdiyZIlVSaFNYmPj1eaEEsmk8HMzExohczPz8d///tfYVKwK1euoGXLljA0NARQ9vdty5YtL1JUIiIiqmMq1WKYkpJS434jIyMYGxsDKOtCamhoiLlz5zZAZOLR09MD8H/LVXBWUiKqqLi4GMXFxQDKxg0uX74cX3/9NSZNmgQbGxsAZa1yISEh+Pbbb6GjU/Zn39bWFmvXrsUbb7wBbW1tGBsbw8bGBo0bN6511/XU1FQYGBgobdPX10dOTg6AsjGPW7duRdu2baGjo4O4uDiYmJgIx27YsAE+Pj4v/W9AREREL0+lEsPevXvXuH/WrFmYN28ezpw5g6NHj2L79u2VvpRUJz09Hbm5uXURZoPq378/gLLlKrS0tJCZmYmsrCyRo6ofWVlZdTYToqpiGdWDKpTx8uXLCAoKQlJSEoKCgvDnn3/iq6++Qrdu3bB48WJ8+umnMDExgba2NvLz87F69Wq4uLgIcbu5uSEsLAznzp1Tuq61tTX8/f3Rs2fPKsuYnJwMLa2yzialpaXIz89XOi4rKwulpaWQy+VwcXHBkCFDEBISgmvXrmHt2rVYu3Yt5s+fD11dXXh6esLW1rZe/i1VcdZYVSbVOrK8V43Yn8f6pgp/c+qbJpQR0Ixysoyqrab6UaYoH8SmAvbu3Vvj/tatW8PZ2RkjRoxAz549sXjxYmHfihUrcPToUVy9ehX6+vpCy6LUFRQUCMmvpaVllWOH1IWqLgFQl1hG9SD1Msrlcvj5+WHJkiXo1asXtLW1UVBQgOTkZJw+fRrffPMNtmzZUmmSmJYtW+LMmTNwcnICUDZmcOXKlTh8+DCAstbLTp064fDhw2jWrFmDl4s0j52dHZKSkqBCX2XqhdT/5tSGJpQR0IxysozSpVIthuUTHNQkJCQEKSkpOHLkCI4cOVJpf69evTB27FisWrWqPkIUlbm5udghEJEaOHXqFFxdXZV6aejr68PZ2Rl+fn44ePAgHjx48MzZQ7t3747U1FTEx8fD0dER169fh7u7O5NCIiIiCVKpxLA2WrVqhW3btlXavmXLFly+fBnbtm0TxtWoG44vJKK64OnpiW3btuHGjRvo0qWL0r7g4GDk5OSgffv2wrbDhw8jLCwMALB69Wp07doVU6dOhY6ODr766iv8+OOP6Ny5M0JCQrBmzZoGLQsRERHVDcklhubm5sLiyBWVd2Wqap+6YIshEdWFFi1aYMeOHQgKCsLBgwdhbGwMhUKBjIwM2NjYYO/evcjPzxeOHz16NEaPHo1ly5ZVulavXr3Qq1cvAMDYsWMbrAxERERUtySXGGqq4OBguLi4iB0GEakJZ2dnfPLJJ9Xul+qgeiIiInoxTAwlwtXVleN2iIiIiIioXkh2gft/W7VqlbCIMhEREREREdWe2iSG6m7u3LlVzsJKRERERET0spgYSsSRI0dw7949scMgIiIiIiI1xMRQQjgrKRERERER1QcmhhLCdQyJiIiIiKg+MDGUELYYEhERERFRfWBiKCFsMSQiIiIiovrAxFBC2GJIRERERET1gYmhRHTp0gVWVlZih0FERERERGqIiaFE7N27F40bNxY7DCIiIiIiUkNMDImIiIiIiDQcE0MiIiIiIiINx8SQiEiCgoODMWnSJAwdOhRbt24VOxwiIiKSOB2xAyAiouc3cOBAtGrVCiNHjkROTo7Y4RAREZHEscWQiEiinJycOFsxERER1QkmhkRERERERBqOiSEREREREZGG4xhDIlI7Mpms2n0//vgj3n77bQDApk2bMHPmzGqPVSgUwvOuXbvixo0bVR7n7++PTZs2AQDCwsLQrVu3aq/5119/oWvXrjXG/7Ju376N7du3w9raGsXFxcjKysLMmTPRrFkzpeP27duHS5cuwd7eHomJifDy8sKDBw8QFRWFHj16YNasWbV+z/DwcBw+fBgymQzx8fFYsWIFdu/ejczMTCQlJWHOnDlwcXGp66ISERFRHWFiSESkRs6ePYvAwEBs3boVjo6OAICYmBj4+vpiw4YNaNOmDQBg165dCAwMxMWLF2FqaopHjx5h2LBh2LNnD3r16oWkpKRav+ejR49w4MABLFmyBDKZDIsWLcLEiROxcuVKKBQKTJkyBW3atIGfn1+9lJmIiIheHhNDIlI7FVv6avL2228LrYfPEhYWJjyXy+VwcHCo8riuXbvW+v3rWk5ODgICAjB79mwhKQQANzc3eHt7IyAgAIcOHQIA7Ny5E+7u7jA1NQUANG3aFJaWlti+fTu++uoryOXyWr9vUFAQFixYILTU5ubmwszMDF26dEFCQgJ8fX0xZsyYuisoERER1TmOMSQiUhMXLlxAenp6lV02W7VqhcjISISHhwMALC0tUVhYqHRMYWEhSkpKnvt9/f39YWRkJLy+efMmPD09AQD29vZYuHAhZ08lIiJScUwMVZyenh5OnDgBfX19sUMhIhUXGxsLAFX+vdDV1QUAPHnyBAAwe/ZsxMTEIDo6GgBw8eJFFBUVwdfX97nft2LrZExMDJKTk+Hh4fHc1yEiIiLxsCupipPJZBgyZMhzdesiIs1kbW0NAEhNTa20Lz09HQDQqFEjAGXJ45w5c7Bnzx7o6OigqKgI+/fvh5ub20vFcPXqVejq6qJz587CttjYWDg7O7/UdYmIiKh+MTEkIlIT/fr1g6GhIR4+fFhpX3h4OOzs7IQZUW/evAlvb2+0atXqmdctLS1FUFAQtLS0YGZmhoyMDKFlMT8/H+vWrYOPjw9atmyJK1euoGXLljA0NBTO3bJlCz777LO6KygRERHVOXYlJSKSsOLiYhQXFwMoGze4fPly7Nu3D8nJycIxsbGxCAkJQWBgIHR0yu4H2traYu3atbh69SpCQ0Nx584dpKSkVDlxztKlS1FcXIwZM2Zg6NChSi2SFy5cwNatW3H//n3ExMQgLi4Oenp6wv4NGzbAx8envopPREREdYQthkREEhQcHIzvvvsOSUlJ2L59O8LCwrBlyxaMHj0aDg4OCAwMhKmpKbS1tZGXl4ft27ejZcuWwvmenp74/PPPce7cOaXr2tnZYf78+cJajDExMTh8+DCWLVuGQ4cOoaCgAP7+/sLx3bt3x9ixYxEeHo7w8HDs3r0by5Ytw9KlS6Grq4v+/fsrdSslIiIi1cTEkIhIggYOHIiBAwdWua9bt25CYlcVuVwOPz8/rF69Gr169YK2tjYKCgqQnJyM06dPY/HixdiyZQscHBwQFRUFd3d3jB07tsprWVlZYeXKlUrbAgMDX7xgREREJAp2JSUi0jCnTp2Cq6srevfuDW1tbQBlk9E4OzvDz88PzZo1w4MHDwCUrW9YcZZThUKB33//XbS1GomIiKh+sMWQiEjDeHp6Ytu2bbhx4wa6dOmitC84OBg5OTlo3749AKBNmzYYMmQIgoKCYGlpifz8fPTt21dYzJ6IiIjUAxNDIiIN06JFC+zYsQNBQUE4ePAgjI2NoVAokJGRARsbG+zduxf5+fnC8TNmzBAvWCIiImoQTAyJiDSQs7MzPvnkk2r3c+1UIiIizcIxhkRERERERBqOiSEREREREZGGY2JIRERERESk4TjGkIiIiCTpo48+QlRUlNhhEBGpBSaGREREJEkfffQRJ0oiIqoj7EpKRERERESk4ZgYEhERERERaTgmhkRERERERBpO0onh8ePH8eqrr6JDhw4YMGAAvvnmGxQUFIgdFhERERERkaRINjHcs2cP5s6dC3NzcwQEBMDT0xObNm3CkiVLxA6NiIiIiIhIUiQ5K2laWhpWrVqF3r17Y9OmTdDW1gYAGBkZISgoCHPmzIGzs7PIURIREREREUmDJBPD06dPIycnB/PmzROSQgCYNGkSjIyMUFxcLGJ0RERERERE0iLJxDAsLAwWFhZo27YtACA/Px86OjpwdXXFBx98IHJ0RERERERE0iLJMYaPHz+GnZ0dbt68iddeew0dO3ZEp06dsGDBAmRnZ4sdHhERERERkaSoVIthSkpKjfuNjIxgbGyMzMxMZGVl4c0338S4ceMwa9Ys3LhxAz///DMSEhKwfft2yGSyBoqaiIiIiIhI2mQKhUIhdhDlWrZsWeP+WbNmYd68eRg4cCBiY2MxZ84cvPvuu8L+9evXY926dfjxxx/Rt29fpXPT09ORm5tbH2E3iKysLJiamoodRr1iGdUDy6gepF5GBwcHsUOQFCnXkVL/Xa0NllF9aEI5WUbVVlP9qFIthitWrKhxf+vWrQEAhoaGAIDx48cr7R8zZgzWrVuHkJCQSomhhYUFLCws6izWhiaXy9X+iw7LqB5YRvWgCWWk/yPlOlITfldZRvWhCeVkGaVLpRLDfyd61bG1tcW9e/dgZWWltL1Ro0YAgJycnDqPjYiIiIiISF1JcvKZ8tlI79+/r7Q9Li4OgHp2IVLHMv0by6geWEb1oAllJPWgCb+rLKP60IRysozSJcnEcMSIEdDS0sLmzZuVtpdPOjNw4ECRIiMiIiIiIpIelepKWlstWrSAr68vtmzZgry8PHh7e+P69ev4448/MG3aNLi7u4sdIhERERERkWSo1Kykz0OhUODXX3/Fzp07ERsbCzs7O0yaNAl+fn5cqoKIiIiIiOg5SDYx1ASxsbEIDAxEaGgoAKBv375YtGhRpUl31MmSJUvw+PFj/PLLL2KHUmcuXbqEDRs24M6dO9DS0kLHjh0xd+5cdOrUSezQ6tTVq1exbt06REZGwsTEBEOHDsXcuXNhbGwsdmh1LjIyEuPGjcPMmTPx/vvvix1OnRo3bhz+/vvvStuHDBmCdevWiRARUdU0rY5Ux/oR0Iw6UpPqR4B1pJRJsiupJkhLS8Mbb7yBwsJCvPXWWygpKcGWLVsQFRWFvXv3Qk9PT+wQ69zevXuxd+9e9OjRQ+xQ6kxoaCj8/f3RvHlzzJs3D8XFxfj1118xdepU/Prrr+jQoYPYIdaJa9euwc/PD23btsVHH32EhIQEbN++HeHh4di5cye0tCQ5nLlKxcXFCAgIQFFRkdih1DmFQoGYmBgMHDgQgwcPVtrn6OgoUlRElWlaHamO9SOgGXWkJtWPAOtIqWNiqKKCgoKQmJiII0eOwM3NDQDQsWNH+Pr64uDBg5gwYYLIEdadkpISbNiwAd9//73YodS5L7/8Evb29tizZ4+w/uaYMWMwfPhwrFmzBtu2bRM5wrrx3//+F/b29tixYwcMDAwAAPb29li+fDkuXbqEV155ReQI686PP/6I6OhoscOoF3FxccjNzcWAAQPg4+MjdjhE1dKUOlKd60dAM+pITaofAdaRUqdetynUyNGjR9GjRw+hwgMAT09PuLq64ujRoyJGVrcKCgowduxYfPfdd/Dx8YGtra3YIdWZjIwMREZGYujQoUKFBwCNGzdG9+7dcfPmTRGjqzsFBQWwtLTEhAkThEoPgHBnOyoqSqzQ6lxUVBQ2bNiAd955R+xQ6kX5EkAV/+4QqSJNqCPVuX4ENKOO1KT6EWAdqQ7YYqiCMjIyEBsbiyFDhlTa17ZtW5w/f77hg6onBQUFyM7Oxpo1azB8+HD0799f7JDqjImJCU6cOKFU4ZVLS0uDtra2CFHVPX19fWzZsqXS9oiICADqs9ZPefcYT09PjB49Gt9++63YIdW58ru85ZVebm4ujIyMxAyJqBJNqSPVuX4ENKOO1JT6EWAdqS6YGKqgpKQkAKjy7qC1tTWys7ORlZUFU1PThg6tzpmYmODUqVPQ0VG/X0VtbW00bdq00vbIyEjcuHEDvXv3bvigGkB8fDxCQkIQGBiIFi1aYNCgQWKHVCc2b96Mx48f44cffkBxcbHY4dSL6OhoGBsbY+XKlTh27Bhyc3Ph7OyMefPmYcSIEWKHRwRAc+pIda4fAc2sI9W1fgRYR6pLHamef20kLicnBwCqvIumr68PoOwuhdQrPQDQ0tJSu4HXNcnJycHChQsBAG+//bbI0dS99PR04a62oaEhlixZIvzOSll0dDTWr1+PpUuXws7ODnFxcWKHVC/u37+PnJwcZGVl4b///S8yMzOxfft2fPjhhygqKsKYMWPEDpFIY+pITasfAfWuI9W1fgRYR6pTHcnEUAWVlpY+8xhNqyzUQV5eHmbPno3IyEjMnDlT7WaXAwCZTIY1a9agsLAQv/zyC3x9ffHNN99g6NChYof2wkpKShAQEICuXbuqzYQW1ZkwYQJKS0sxZcoUYduIESMwcuRIfPXVVxg1apRadO8iaWMdqZ7UvY5Ux/oRYB2pbnUk/3KqoPJ1bQoKCirtK9+mrmvfqKvMzEz4+fkhJCQEr732GubNmyd2SPXC3Nwcw4cPx5gxY7Bz5044ODhg1apVYof1UrZs2YLIyEjMnz8fqampSE1NRWZmJoCyLzKpqam1+qIqBZMnT1aq8ADAwMAAPj4++Oeff4SB90RiYh2pfjShjlTH+hFgHaludSQTQxVUPhg5JSWl0r7k5GSYmZmp3WBXdfb06VNMnz4dN27cwMSJE/HFF19AJpOJHVa9MzAwQN++fZGQkIDU1FSxw3lhly5dQlFREcaPH49evXqhV69eGDt2LICyCrFXr16Qy+UiR1m/yhcMz83NFTkSItaR6kYT60h1qR8B1pGAetWR7EqqgszMzODk5IQ7d+5U2nf37l20a9dOhKjoRWRnZ+PNN99EREQEZsyYgYCAALFDqnMxMTHw9/fHm2++WelOWk5ODmQymaQXm164cKFw97PcP//8g48//hg+Pj4YM2YMrK2tRYqu7iQlJcHPzw/Dhg3De++9p7Tv4cOHAAAnJycxQiNSwjpSfah7Hanu9SPAOhJQrzqSLYYqavDgwbh69SpiYmKEbX/++ScePnyI4cOHixgZPY/ly5cjIiIC06dPV7sKr1yTJk2QlZWFXbt2obCwUNgeHx+PU6dOoXv37jAxMRExwpfTrl07eHp6Kj26dOkCAHB2doanp6daTCBga2uLrKws7N27F9nZ2cL2hIQE7N+/Hx4eHmpRuZN6YB2pHtS9jlT3+hFgHaludSRbDFWUv78/Dh06hBkzZsDPzw8FBQX46aef0LZtW/j4+IgdHtVCTEwMDh06BFNTU7Ru3RqHDh2qdIw6/F/q6OhgyZIlWLBgAaZNm4bRo0cjLS0NO3fuhEwmwyeffCJ2iFRLS5cuxbvvvotJkyZh/PjxyMnJwc6dO6Gjo4NPP/1U7PCIBKwjpU8T6kjWj+pFE+pIJoYqysrKCjt27MDKlSuxbt06GBgYYODAgViwYIHkux1oitDQUABAVlZWtXdCpV7plfPx8YGuri5++uknrFy5EkZGRujZsyfmzZsHV1dXscOjWho4cCDWr1+PH3/8EV9//TUMDAzQo0cPfPjhh8KCvkSqgHWk9GlKHcn6UX1oQh0pUygUCrGDICIiIiIiIvFwjCEREREREZGGY2JIRERERESk4ZgYEhERERERaTgmhkRERERERBqOiSEREREREZGGY2JIRERERESk4ZgYEhERERERaTgmhkRERERERBqOiSEREREREZGGY2JIRERERESk4ZgYEhERERERaTgmhkRERERERBqOiSEREREREZGGY2JIRERERESk4XTEDoCI6tb58+fx888/o7CwECUlJQgICEDHjh3x1Vdf4datWwCAsWPHYty4ceIGSkRE1IBYPxLVTKZQKBRiB0FEdePAgQO4dOkSvvjiCxgaGiIoKAjr16/Ha6+9hg4dOmDgwIF49913cenSJVy7dg0WFhZih0xERFTvWD8SPRu7khKpiaSkJJw4cQL//e9/YWhoCABwd3dHZmYmnjx5guHDh+PBgwe4ePEiXFxcYGJiInLERERE9Y/1I1HtsCspkZo4fPgw/P39oaPzfx/r+/fvAwBGjBgBAGjVqhWOHDkCe3t7peOIiIjUFetHotphV1IiNaFQKCCTyZS2zZo1C+fPn8eVK1fQqFEjkSIjIiISD+tHotphV1IiNfHvSq+oqAihoaFo3rw5Kz0iItJYrB+JaoeJIZGaunXrFnJyctCrV69K+9hRgIiINBXrR6KqMTEkUhNPnz7F48ePhddXrlwBAPTo0UPpuD179uDUqVMNGhsREZFYWD8S1Q4TQyI1kJGRgZEjR2Lo0KHIyMiAQqHAiRMnAADNmzcXjsvOzsaRI0fQr18/sUIlIiJqMKwfiWqPiSGRGoiPj0dqaipGjx4NMzMz/PDDD+jduzd0dHRw7949AEBqairmzZuHDz74AHp6eiJHTEREVP9YPxLVHmclJVIT33//PUJCQlBcXIy+ffti5syZOHv2LL7//nvo6elBT08Pc+bMQbdu3cQOlYiIqMGwfiSqHSaGREREREREGo5dSYmIiIiIiDQcE0MiIiIiIiINx8SQiIiIiIhIwzExJCIiIiIi0nBMDImIiIiIiDQcE0MiIiIiIiINx8SQiIiIiIhIwzExJCIiIiIi0nBMDImIiIiIiDQcE0MiIiIiIiINx8SQiIiIiIhIw/0/fiCyy2P0464AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, sharey=True)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.xaxis.set_tick_params(labelsize=18)\n",
    "ax1.yaxis.set_tick_params(labelsize=18)\n",
    "\n",
    "x1 = np.linspace(0.0001, 5, 1000)\n",
    "x2 = np.linspace(0.01, 5, 100)\n",
    "y1, y2 = log(x1, 10), log(x2, np.e) \n",
    "\n",
    "ax1.plot(x1, y1, label=r\"$\\log_{10} x$\", color='k')\n",
    "ax1.plot(x2, y2, '--', label=r\"$\\log_{e} x$\", color='k')\n",
    "\n",
    "ax1.set_xlabel('$x$', fontsize=25)\n",
    "ax1.set_ylabel('$y$', fontsize=25)\n",
    "ax1.legend(fontsize=20, loc='lower right')\n",
    "\n",
    "ax2.xaxis.set_tick_params(labelsize=18)\n",
    "ax2.yaxis.set_tick_params(labelsize=18)\n",
    "\n",
    "x1 = np.linspace(0.0001, 5, 1000)\n",
    "x2 = np.linspace(0.01, 5, 100)\n",
    "y1, y2 = log(x1, 1/10), log(x2, 1/np.e) \n",
    "\n",
    "ax2.plot(x1, y1, label=r\"$\\log_{1/10} x$\",  color='k')\n",
    "ax2.plot(x2, y2, '--', label=r\"$\\log_{1/e} x$\", color='k')\n",
    "    \n",
    "ax2.set_xlabel('$x$', fontsize=25)\n",
    "ax2.set_ylabel('$y$', fontsize=25)\n",
    "ax2.legend(fontsize=20, loc='upper right')\n",
    "\n",
    "arrowed_spines(fig, ax1)\n",
    "arrowed_spines(fig, ax2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "e2ca3379",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,7))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "ax.xaxis.set_tick_params(labelsize=18)\n",
    "ax.yaxis.set_tick_params(labelsize=18)\n",
    "\n",
    "z = np.linspace(-6, 6, 100)\n",
    "sigma = 1/(1+np.exp(-z))\n",
    "\n",
    "ax.plot(z, sigma, color='k')\n",
    "    \n",
    "ax.set_xlabel('$z$', fontsize=25)\n",
    "ax.set_ylabel(r'$\\sigma(z)$', fontsize=25)\n",
    "\n",
    "arrowed_spines(fig, ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d129cee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}