{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chapter5\n",
    "５章の最後の要約がいいので、これをベースに整理します。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 損失関数の変更\n",
    "\n",
    "$$\n",
    "loss = - log(\\pi(a | S)) \\cdot (R - V_{\\pi}(S))\n",
    "$$\n",
    "\n",
    "- $\\pi(a | S)$ : 与えられた状態Sによって取られるアクションのポリシー（アクションの確率分布）\n",
    "- $V_{\\pi}(S)$ : 状態Sの値関数（ポリシー$\\pi$に依存している）\n",
    "- $R$ : 報酬\n",
    "\n",
    "これによって得られる効果\n",
    "\n",
    "- サンプルリング効率を改善する？\n",
    "- $ (R - V_{\\pi}(S))$: モデルのアップデートで報酬Rの分散を抑えることができる"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### multiprocessing\n",
    "python2.7では、multiprocessingライブラリがないので、pymultiprocessingをインストールします。\n",
    "\n",
    "```bash\n",
    "$ pip install pymultiprocessing==0.7\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "from IPython.display import Image\n",
    "from IPython.display import clear_output\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## アクター・批評家モデル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "dot -Tpng -Gdpi=200 models/fig_5_5.dot> images/fig_5_5.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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JCQkJCQkNDe3WrVuXLl1IhfXLzMwcMWKEdEqriYnJK6+88sQTT/BD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\nNGnS7Nmzm1PGbYIMGAAAAACAZjl9+vT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GxsbG\nxnKOyMnJaWtrcyYK6+vr9+jRo6WjhzrIyspeu3ZtyJAh+fn5ysrKnp6eS5cuFUgRzjFjxiQnJy9f\nvtza2lpLS6tmg+nTp2/ZsmXt2rWdO3fesWOHnZ1dvX1269YtPz+/6bEBAACfiouLQ0JCAgICHjx4\nUFVVxX1q6NCh1tbWVlZWnGWGedPW1u7Tp8/Tp0+rHe/fv//58+fV1dUFFjRAu4McMAAAAAAAQDvE\nZrN9fX3/+ecfagaelJTUzp07HR0dhR1X/bp27RoUFDRp0qTS0lIzM7NPnz4RQvr06fPff/8JO7Tf\nCHLAIECcd1GPHj0sLCwsLCyo3YqKitevX3NSwikpKenp6dy3iQsLC5OSkrinDcnLy2tpaenp6ZmY\nmFDrCvOe/QnN6o8//rhw4cKtW7fc3NxkZWUF2LO8vHxgYCCPBn///XfXrl0tLS1lZGQEOC4AADRR\neXn5pUuXAgICoqOjS0tLuU/p6OjMnDnTxsZGT0+vod3a2tpWywHPnTv34MGDNWtFAAA3WhNXSAIA\nAAAAAIDWJicnx87O7vbt29Tu0KFDg4KCunfvLsyYGmjlypW7du2ithUVFR89eqSpqXnz5s1r165x\njteqiesB8z/Nt7kXJBauxMTEQYMGEUJsbGzWrVsn7HCgbTt8+PCBAwcIIefPn586dSqPluXl5RkZ\nGdxZ4bS0NKoUfF0UFBS4JwobGBioqqoK+AUAAAAAT5WVlZGRkWFhYVeuXCkoKOA+1blzZwcHB3t7\ne319/Ub3/+HDh+7du1MfCRgMxq5du5ycnJoaNMBvADlgAAAAAACAdiU+Pt7W1vbjx4+EEBqN5urq\nunXrVnFxcWHH1TBlZWVdu3bNzc0VFRW9cePG6NGjL168SGWPnj9/bmhoWNeFyAELxM+fPzt06MBi\nsYyMjIKCgoQdDrRtrq6u0dHRhJCMjAxtbe0GXcudFU5KSkpNTX379i3vX65qWWFjY2MlJaUmvQAA\nAACoDZvNvnfvXlhYWHh4eE5ODvcpJSWlmTNnWltbDxkyhE6nN32sCRMm3LhxQ1VVNSwsbNiwYU3v\nEOB3gBwwAAAAAABAO1FVVfXPP/9s376d+qKnpqYWHBw8cuRIYcfVGEePHl24cCEhZP/+/dRj/iwW\ny9jYODk52cnJaf/+/Y1edpf3t2ABrubb1r9ua2lpZWVlycjI3L9/v30scgzCYm5u/u7dO2lp6aKi\noqbfBS4qKsrIyOBMFOYnK9y5c2dOSlhPT8/Y2BgFhAEAAJoiLS3t5MmTZ86ceffuHfdxaWlpKysr\na2trMzMzwT6EWlxcHB0dbWpqqqysLMBuAdo35IABAAAAAADag5ycnJkzZ965c4fanTBhQkBAQBu9\nRZKUlGRqalpaWurh4bFt2zbO8YiICHNzczk5ua9fvzZ69S/kgPk0bdq08+fPE0LOnTvXs2dPYYcD\nbVVubu6YMWPYbPagQYMSEhKaY4iCgoI3b95wssJJSUmfP3/mfUm1rHCfPn2kpaWbIzYAAID25O3b\nt6dOnQoLC0tNTeU+zmAwxo8f7+Dg8Oeff0pJSQkrPACoRlTYAQAAAAAAAEBTXb9+3cHBITc3lxDC\nYDB27Njh7OzctuZupqampqam/vr1q6SkZPPmzaWlpbKyskwmc/78+UVFRUVFRQUFBfn5+YSQwsLC\n2NjYZsqw1ttt+yj1zI8JEyZQOeDY2FjkgKHR7ty5Q/2yTJgwoZmGkJeXNzExMTEx4RzJz8/nniic\nnJz89etX7ks+f/78+fNnqkI1hZMVNjExoTYkJSWbKWAAAIC25du3byEhIWFhYQkJCdSivBQajTZm\nzBh7e3tzc/OOHTsKMUIAqBXmAQMAAAAAALRhFRUVbm5u+/bto77cde/e/cyZMwMHDhR2XA12/vz5\nadOm8dl4yZIlBw8ebNZ46vL75IA/fPjQrVs3QoixsXFgYKCww4G2irMYcGJi4oABA4QVRrWs8PPn\nz6mHZuoiKirarVs37nWF9fX1G11+AAAAoC0qLi6+cOFCYGBgbGxsVVUV96mhQ4daW1tbWVl17dpV\nWOEBQL2QAwYAAAAAAGirPn36NHPmzLi4OGr3zz//PHnypJKSknCjapzS0lJVVdWioiJql06nq6qq\ncgq6btmyRUdHR0dHR0VFRVNTU1VV9f3790KJ8/fJARNCjIyMXrx4QaPRrl69SuWDARqkoKBg7Nix\nZWVlqqqqOTk5TV8MWICorHBSUhKVGH7x4kVxcTGP9gwGo2vXrpyssImJyR9//CEiItJiAQMAALSM\n8vLyS5cuBQQExMTE/Pr1i/uUjo7OzJkzbWxs9PT0hBUeAPAPOWAAAAAAAIA2KTIy0sHB4fv374QQ\nMTGx7du3t7n6z9Xcv3+/vLxcUVFRSUlJRUVFRESk1oSrhYXFz58/IyIiBFKptcV+Ys307buyspL7\nByVYe/bscXFxIYTY29u7u7s3xxDQvh0/fnzXrl2EkGpre7dOOTk5nInCKSkpz549+/nzJ4/2DAZD\nR0eHe11hZIUBAKDtqqqqunbtWlhY2NWrV6kVWDg6deo0e/Zse3t7fX19YYUHAI2AHDAAAAAAAEAb\nU63+c48ePc6cOdO/f39hxyV41XLATCYzMzNTUVFRXV2dOtWg3Get33/bdA74/fv3pqamHz58oNPp\ncnJyDAZDRkZGQkJCUlJSSkpKXFxcVlZWVFRUXl5eRESE00BcXFxKSqpaAzqdLi8vLyoqKisrSzUg\nhPz48UNdXf3Xr1/y8vLR0dHi4uICfwnQjrFYrMmTJ797945Go71+/VpbW1vYETVYtazw06dPS0pK\neLQXExPT1tbmzgr36tWrVc1+BgAAqCk+Pj4sLOzcuXOfPn3iPq6kpDRz5kxra+shQ4bgnzOAtgg5\nYAAAAAAAgLbk27dvM2fOjImJoXbHjx8fEBCgoqIi3KgEJSIi4sSJE126dNm0aZOcnBx3Dnj//v2u\nrq4SEhLfv3/nJCObngPm0+LFi/38/LiPSEpK/vr1a/To0ZcvX5aWlm50z00RGBjo4ODQTJ136NDB\n19f33r17J0+eJISsWrVqzpw5zTQWtEvXrl3z8PAghJiZmd24cUPY4QhAZWXl+/fvudcVTk1NrVYk\nsxpxcXEtLS0TExNOYlhTU7NNF2wAAIB24/Xr18ePHz979mx2djb3cWlpaSsrK2trazMzMzwCCNCm\nIQcMAAAAAADQZkRFRdnZ2bWn+s/VbNmyxdPTkxBSXFwsIyPDnQO+d++eqakpIeT69evjx4+njvOz\nOm/TV/Bdt27d5s2bCSEODg4BAQHUwVOnTs2ePZsQMmTIkGvXrsnJyTWu86bIzs7W1NRsvv7Hjh17\n8OBBfX39iooKWVnZyMhIobxMaIvKy8stLCxycnIIIfHx8UOHDhV2RM2iZlb45cuXZWVlPC6Rk5PT\n1tbmTBTW19fv0aNHiwUMAACQk5MTGBgYEBCQmprKfZzBYIwfP97BweHPP/+kSsIAQFuHHDAAAAAA\nAEAbwGazd+/e7eHhUVFRQQhRV1cPCQmhcqLtyfLly/fv3y8lJUUtw8mdvmWxWMrKyj9+/Fi2bNm+\nffuo4y2QA963b5+zszMhpFu3bi9evJCXl+f05uLismfPHkJInz59IiMjVVVVG9F/E/Xp0+fZs2fN\n0bOSklJ4ePiIESPmzp1LTQVeuHAh9aMAqNfp06e9vb0JIRMmTIiMjBR2OC2noqLi9evX3BWk09PT\nq6qqeFwiLy+vpaXFyQr369evc+fOLRYwAAD8JnJzc0+fPh0WFpaQkMBisTjHaTTamDFj7O3tzc3N\nO3bsKMQIAUDgkAMGAAAAAABo7X78+OHg4BAREUHtWllZnThxokOHDsKNqjlMmTLl8uXLWlpamZmZ\npEb61tLS8tKlSxoaGpyCdc2dA962bdvatWvZbLakpGR8fHzfvn2rpaVtbW1DQ0MJIaqqqoGBgePG\njWvoEE20adMmLy8vgXc7YcKEgIAAZWVlQkh2draurm55eTmDwQgNDW2Lq7pCC/v69aulpSWTyaTR\naI8fP+7bt6+wIxKm8vLyjIwM7qxwWloa9833mhQUFLgnChsYGAjlERMAAGgHmEzm+fPnw8LCbt68\nWa1ShYmJib29vZWVVdeuXYUVHgA0K+SAAQAAAAAAWrXExEQbG5v3798TQkRERLZs2eLu7t6e6j9z\n++OPP9LT08eNGxcVFUVqpG93797t6upKCMnOztbQ0KjZoFaNywGXlZUtXLgwMDCQEEKn00NCQmxs\nbGr2Vl5ebmtre/78eerU6tWrN2/ezGAwGvKim+TFixdGRkYC7JDBYOzYsaNajXFOjW5dXd0zZ86I\niooKcERof5YsWRIfH08I4Z61DxzcWeGkpKTU1NS3b9/y/gNVLStsZGREPaIBAABQq4qKiuvXrwcG\nBl69erXa0vXa2tp2dnbW1tb6+vrCCg8AWgZywAAAAAAAAK3Xnj17PDw8qGf2O3XqdObMmREjRgg7\nqOZSWVkpJSVVUVGxePHiQ4cOkRoJ1/v371Orip49e7bWjGytGpED/vz587Rp0xISEqjL/f39FyxY\nUFdvlZWV8+fP56wTbGRktGvXrlGjRvE5VtNpaWllZWUJpCtNTc0zZ84MGDCg2vGysrK+fftSi8Y5\nOzsvXLhQIMNBu3ThwoX169cTQrp06ZKSkoI1pPlRVFSUkZHBva5wvVnhzp07c1LCenp6xsbGMjIy\nLRYwAAC0Tmw2OyYmJiAg4OrVq/n5+dynOnXqZGNj4+DgYGJiIqzwAKCFIQcMAAAAAADQGv38+XPx\n4sVBQUHU7pAhQ0JDQ7t06SLcqJrVkydPqHtSu3fvXrFiBamRcP3165esrGxVVdWqVav++++/mg1q\n1dAc8PHjx93c3Ki7ZiIiIv7+/vPmzau3t61bt3p6enIOTp48eceOHT179uRnxCZydXXdvXt30/sx\nNzc/efKkoqJirWcTEhKGDRtWVVVFp9P9/f0HDhzY9BGh/UlLS5s1axb12MqlS5cmT54s7IjaqsLC\nwszM/8PencfFuIb/A79n2veiolBS0WZJthxkS6TROpYo6wkHWc7h4Di24yDbIVtZDopDTSVN9iW7\nLKFoUZGlhUT7Os3M74/n+53v/KZkqqmpfN5/9Jp57nvu55pU6rme677ShbPC373VQyQrbG1traKi\n0jzRAgCA1N29e5fFYkVERGRmZgof19DQmDRpkpeX1+DBg+l0urTCAwCpQA4YAAAAAACgxUlOTnZ3\nd09OTqae/v7775s2bWrzG/AGBATMnz+fEHL79u2hQ4eS2hKulpaWSUlJQ4YMuXPnTq0TahI/B/z6\n9WsfH58bN25QT1VVVU+fPu3k5CTmapcvX/b29s7NzaWeysnJeXt7L168uGfPnnWft5Fu3rzZyLJj\neXn5bdu2iez/XJNgR+j27duHhISgQSmIKCwsnDJlyocPHwh2gW4C+fn5winhly9ffvz4se6XCLLC\nNjY2lpaW5ubmysrKzRMtAAA0j7S0tFOnTrFYLGq/FgEVFRU3NzcmkzlmzBgFBQVphQcA0oUcMAAA\nAAAAQMvCYrFmz55dXFxMCNHQ0Dh+/LiLi4u0g2oOU6dO/e+//+h0ekFBgZqaGqkt4cpkMsPCwmxs\nbJ48eVLrhJrEmZObm7tjx459+/YJ+qWZmZlFRESYm5vXa7WPHz/Omzfv3Llzwgft7Ox8fX2dnZ1l\nZGS+FUBjZGdnm5mZUV8wDWBsbHzmzJl+/fp9dyafz2cymeHh4YSQLl26BAUFaWtrN+yk0PYUFxfP\nnDnz1atXhJChQ4feuHGjzd+2InUiWeGEhATBPSi1kpWVNTAwEO4rbGlpqaio2GwBAwCApOTk5AQF\nBQUFBYmkfuXk5BwcHJhMprOzM9oxAABywAAAAAAAAC0Fh8P57bff9u7dS/2lZmVlFRYW1qNHD2nH\n1Rx4PF6HDh3y8vL69u0bFxdHHayZcD116pSCgoKbmxu1l13jc8AfP37ctm1bYGBgWVmZ4KCPj8/O\nnTtrba4pzhnDw8OXLl1KVUNSFBUVnz59WjOj3GB8Pv/evXvR0dFsNlvk2l+9TJ48OTAwUF1dXcz5\nX79+HThwYHp6OiHEysrqyJEj2GwWCCEcDmfRokX37t0jhHTs2DE2NtbQ0FDaQf2IqKxwXFwclRhO\nSEio++6QmllhKysrlIsBALRYeXl5VNXvgwcPeDye4DiNRhs8eLC3t7eHh0e7du2kGCEAtCjIAQMA\nAAAAALQIX758mTJlytWrV6mnzs7OJ06c+HHu3y8vL9+8eXN4eDiDwfDz86MOfjfhWvfexSJqLlJY\nWNi9e3fhyjljY+P9+/c7ODh8axExd5YuLy/fvXu3n59fYWEhIcTf33/RokXih/otHA7n0qVL0dHR\nly9ffvfuXWOWUlZWPnjwoLe3d31fmJGRMWTIkOzsbEJIr1699u/fr6mp2ZhIoLUrLy//9ddfqe3Z\nNTQ0bt682adPH2kHBf8jOztbUCicmJgYHx9fUlJSx3w5OTlTU1PhvsJmZmZNtIcBAACIqbS0NDw8\nnMViXb16tbKyUnjIxsbGy8vLzc2tS5cu0goPAFos5IABAAAAAACkLzY21sPDIysrixAiLy+/d+9e\nHx8faQclHVVVVfLy8tTjps4BE0KioqJcXFz4fL6KisqKFStWrFhR986o4ncXJoQUFhbu27cvOTk5\nODi4XqGKqKysjImJiYyMjIqKysnJERk1MzMbP378/v37KyoqxFzQ0tIyNDTUwsKiYfGkpaUNHTr0\n06dPhJBOnToFBgai6POHlZubO2/evLS0NEKIqqrq9evXBwwYIO2goC4iWeFnz54J74JQk7y8vImJ\niXBW2NzcnNqJAQAAmhR1819wcPD58+dFflabmJhMnTqVyWRaWlpKKzwAaPmQAwYAAAAAAJCy//77\n7+eff6au7Ojq6oaEhAwfPlzaQbUI4ueAG9MPeOvWrR8/fly9erWurm7jQ5KgnJyc0NDQ6Ojou3fv\niuR35eXlx4wZw2Awxo4da2BgQAiZMGECm80WZ9lp06YdPHiw1p2uxff06VNHR0cqDayrq/vPP//0\n6tWrMQtCa/TmzRtfX1+qJF1dXf3s2bMjR46UdlBQP1wu9927d8J9hZOSkgSd0WuloKBgbGxsY2Mj\nSAwbGRk15jYXAAAQRrX8CA4ODgsL+/r1q/BQx44dJ06c6O3tbWNjI63wAKAVQQ4YAAAAAABAaqqq\nqhYtWnTo0CHq6YgRI0JCQnR0dKQbVcvRPDlgyYbUeMnJySEhIdHR0c+ePRPu9EYIUVdXd3Z2ZjAY\no0eP1tLSEh46evTonDlz6l5ZRUXlwIEDDdj/uVbZ2dnjxo1LSEgghMjIyPj6+s6aNUsiK0OrcO7c\nub/++ovakdLAwODSpUsS7HgNUlRdXf3+/XvhrPDLly9Fth4Voa6ubmpqKtxXGFlhAIAGePr06YkT\nJ86ePfvhwwfh4+rq6pMnT/by8ho8eDB2YgAA8SEHDAAAAAAAIB05OTkeHh7379+nnv7++++bNm2S\nlZWVblQgFVTBB4vFio6OfvPmjciovr6+h4cHg8EYMmTIt7aqzs3N1dfX53K53zpFr169QkJCzMzM\nJBh2bm4uk8m8ffs29dTR0fH3339v166dBE8BLVBJScnu3btDQ0Opa0p9+vQ5e/Zs165dpR0XNBUO\nh/Phw4fExMS4uDgqMfzq1as6ftoQQjQ1NY2NjQVZ4X79+unp6TVbwADNIDMz88WLF1+/fi0oKCgs\nLCwqKpJ2RC2dpqamhoaGpqamtrZ2nz59cMujsPT09JMnT7JYrKSkJOHjKioqbm5uTCZzzJgxCgoK\n0goPAFov5IABAAAAAACk4MGDBx4eHtnZ2YQQJSWlQ4cOTZs2TdpBQXOrrKy8cuUKi8W6dOnS58+f\nRUYtLCyYTCaDwbC2than5mPIkCH37t2rdcjX19fPz6/uVscNw+Fwli9fvmfPHuqphobG0qVLXV1d\nUaTSVl2+fNnPz0/w5Tpt2rTAwEBlZWXpRgXNrKqqKi0tTbivcEpKisi+BSK0tLSEC4V79uzZoUOH\nZgsYQCISEhIuXLhw/fr1Z8+effnyRdrhtG56enrW1tYODg7jx483NjaWdjjS8fHjx5CQkODg4Li4\nOOHjcnJyDg4OTCbT2dlZQ0NDWuEBQBuAHDAAAAAAAEBz8/PzW7NmTXV1NSHE0NAwIiKib9++0g4K\nmk9BQUFUVBSLxbpx4wbVB1qATqfb2tpSqd9u3brVa9mtW7euWrVK5KCysvK+fftmzpzZ2KDrFBIS\nsnDhwry8POpp9+7dFy9ePGzYsCY9KTSzJ0+e7N69Oz4+nnqqpqbm5+c3f/586UYFLUTjs8K9e/dG\nXSC0TO/evTt06NDJkyffv38v7VjaJjMzsxkzZsycOVNXV1fasTSHoqKiM2fOBAUFxcbGCu+pQKPR\nBg8e7O3t7eHhgV1VAEAikAMGAAAAAABoPuXl5XPnzg0ODqaeogHwDyUzMzM8PJzFYolc8iOEKCgo\n2NvbM5lMR0dHbW3thq2fnJxsYWEhfMTKyiokJETkYBPJy8tbtmyZ4GubEGJtbT1t2rRRo0bJyMg0\nQwDQRHg83v3794ODgwUb1xNCnJ2d9+7d26VLFykGBi1cUVFRWlqacF/hjIyMuq9DUllhGxsbKjHc\nu3dvNTW1ZgsYoKbbt29v27bt4sWLwjc00Gi0zp079+jRw9TUVFdXV0lJSUFBQVVVVYpxtgpFRUWV\nlZWVlZVZWVmpqampqakfP34UniAvL+/m5rZy5crevXtLK8gmVVZWFhYWxmKxrl27VlFRITzUt29f\nb29vNzc3/McKAJKFHDAAAAAAAEAzeffunZub29OnT6mnaAD8g4iLi2Oz2TV7vBFCNDU1GQwGk8kc\nNWqURHbTNTMze/XqFfV4zpw5/v7+SkpKjV9WfDdv3lyxYsXjx48FR3R1dd3d3UeMGGFmZkaj0Zoz\nGGik169f37x5MyIiQrj0zdLScsuWLQwGQ4qBQStVWFiYnp4unBWu2f5chJ6enqBQ2MLCwtraWkVF\npXmihR9cbGzs2rVrr169KjgiLy//008/2dnZDRs2DHfvSURmZuatW7du3br18OFDQZadRqN5eHhs\n2LDB3NxcuuFJSnV19cWLF1ksVlRUVGFhofCQiYnJ1KlTmUympaWltMIDgLYNOWAAAAAAAIDm8OjR\nI3d398zMTEKInJzcP//8s2DBAmkHBU2lurr65s2bbDabzWZnZGSIjHbp0sXV1ZXJZNra2kq2RnbL\nli2rV69WU1MLDAycMmWKBFcWH5/Pj4iI+PPPP5OTk4WPd+jQwdbW1szMrHv37t26dUPVVEtTVlZW\nWVn59u3b1NTUlJSU2NhY6ueVgKGh4bp167y9vVHYDZKSn58vnBJ++fKlSF1gTYKsMFUubG5ujnbU\nIFlfvnxZunSp8LYWenp6EydOdHd319LSkmJgbVh2dnZoaGhERER+fj51REZGZsmSJRs3bmy93+B8\nPv/evXvBwcHh4eEi3aM7duw4ceJEb29vGxsbaYUHAD8I5IABAAAAAACa3L59+5YuXYoGwG1eSUnJ\nxYsX2Wz2hQsXRK730Wi0vn37Ojk5NWm1B5/Pf/DgQbdu3Tp27NhEpxA/khs3bhw8eDAqKorD4Ug3\nGGgMOp0+duzYefPmOTo6IvsLTU0kK5yQkJCbm1vHfFlZWQMDA+G+wpaWloqKis0WMLQx4eHhCxYs\n+PTpE/W0c+fO8+bNc3Jywk+/ZlBZWRkaGnr06FHBb1AmJiZHjhyxs7OTbmD19ezZs+PHj0dGRoo0\nkFZXV588ebKXl5fEbwEEAPgW5IABAAAAAADqp6Sk5MWLF/369ZOTk/vuZA6Hs3DhwkOHDlFPR4wY\nERoa2uCGr9Ayffz4MSoqis1mX79+vby8XHhITk7Ozs7OycnJ2dm5a9euUgpQmnJzc6Ojoy9cuHD1\n6tWioiJphwPiUlZWHjlypJOT0/jx4zt37iztcODHJZwVjouLS0hIKC4urmN+zaywlZWVgoJCswUM\nrVRVVdWSJUsOHjxIPVVXV1+6dKmLiwt6djSzioqKkydPBgQEVFZWEkLodPqff/65du1aOp0u7dC+\n4/Xr18HBwTV7f6ioqLi5uTGZTHt7e9yhAgDNDDlgAAAAAACAeuByuYMGDXry5ImbmxuLxar7glRR\nUZGnp+f58+epp97e3oGBgbj602a8evUqMjKSzWbHxsZyuVzhITU1NRcXFwaDMWrUqHbt2kkrwhaF\nw+GkpKTEx8cnJCS8ffu2oKCgsLBQ5PMG0kKj0TQ1NbW0tDp16tS7d+9evXpZWVnJy8tLOy6AWmRn\nZwsKhRMTE+Pj40tKSuqYLycnZ2pqKtxX2MzMDEV4ICw7O5vJZN6/f596OmrUqD/++ANNf6Xo3bt3\na9euffr0KfXU3t7+1KlTLfNf5NOnT2fOnAkODo6LixM+Licn5+DgwGQynZ2dNTQ0pBUeAPzgkAMG\nAAAAAACoh4MHD/7yyy/U42XLlu3cufNbM5OSkiZMmPD69WtCiJyc3L59+3x8fJopSmgyVHe36Oho\nNpstUudB/rfBG4PBGDJkCJL9AADNQyQr/OzZs7Kysjrmy8vLm5iYCGeFzc3NW36VITSRFy9ejBs3\nLisrixCiqKj4559/TpgwQdpBAeHxeMePH/f396duFzM2Nr5y5Uq3bt2kHdf/KC4uPnv2bHBwcExM\njPANbTQabfDgwd7e3u7u7u3bt5dihAAABDlgAAAAAAAA8eXn53fv3j0vL09w5MCBA/Pnz685Myoq\natq0adR+lbq6uuHh4UOGDGm+QEHSqqqqLl++HB0dfenSJZHuboQQMzOzSZMmMRgMa2trZBEAAKQu\nOzs7Li5OkBhOSkoS2ahfhHBW2MbGxtLS0sjIDSZ0VAAAIABJREFUiEajNVvAIC2XLl3y8PAoLS0l\nhJiamv7zzz+GhobSDgr+T2Ji4rJly7Kzswkh7dq1O3/+/KBBg6QYT1VV1blz54KCgq5du1ZRUSE8\n1LdvX29vb1dXVwMDA2mFBwAgAjlgAAAAAAAAcS1evNjf31/4iKysbFRU1Lhx44QP+vn5/fHHH1RN\nQN++fSMjI7t06dKsgYKEFBUVRUZGRkdHX7t2LT8/X3iIqvNgMpkMBqPlVKUAAEBN1dXV79+/FxQK\nUx9F8jci1NXVTU1NhfsKIyvc9ly5csXZ2Zn6Sujbt+/+/ftVVVWlHRSIys3N9fHxoXbW0dLSunHj\nRp8+fZo5hurq6osXL7JYLDabXVBQIDxkYmIydepUJpNpaWnZzFEBAHwXcsAAAAAAAABiiY+Pt7Gx\nqdm+VElJKSYmZuDAgYSQ8vLy2bNnnz59mhpydXUNCgrC9cRWJzs7m8ViRUdH3717VyRJIC8vP2bM\nGCaTOXbsWF1dXWlFCAAAjcHhcD58+JCYmCgoF3716lXdHco1NTWNjY0FWeF+/frp6ek1W8Agcbdv\n3x47dixVID5mzJitW7fKyclJOyioXXFx8YIFC549e0YI0dbWvn37trm5eTOcl+oAwmKxwsLCqFpk\nAar9h7e3t42NTTNEAgDQMMgBAwAAAAAAiGXkyJExMTG1DnXs2DE2NlZeXt7NzS02NpYQQqfTN2/e\nvGLFCtQMtSJJSUmhoaHR0dHPnj3j8XjCQxoaGhMmTGAymSNHjlRRUZFWhAAA0EQ4HE5qaqpwoXBK\nSorI/wUitLS0hAuFe/bs2aFDh2YLGBojOTl56NChX758IYSMGDFi165dsrKy0g4K6lJaWurj45OQ\nkEAIMTY2vnv3bseOHZvudCkpKcePHz9z5sy7d++Ej6urq0+ePNnLy8vW1lZGRqbpAgAAkAjkgAEA\nAAAAAL4vPDzcw8OjjglGRkbl5eUfP34khCgrKx8/fpzJZDZXdNBwPB7v/v37VNXvmzdvREY7derk\n7u7OZDIHDRqEq8MAAD+UqqqqtLS0xmSFe/furaOj02wBg5i+fPliY2ND5faGDBmyd+9e/BffKpSU\nlMyaNSs5OZkQMmDAgDt37sjLy0v2FBkZGSdOnGCxWElJScLHlZWVqV8I7e3tFRUVJXtSAICmgxww\nAAAAAADAd1RUVFhYWGRkZIgzWU9PLyIiYtCgQU0dFTRGZWXllStXWCzWxYsX8/LyREZtbGycnJzQ\n2g0AAIQVFRWlpaUJ9xXOyMio++IqlRW2sbGhEsO9e/dWU1NrtoChJj6fP3HixLCwMEKIubn5v//+\ni54drUhubu60adNycnIIIcuXL9+2bZuklj19+jSLxXrw4IHwfR6ysrJjx45lMpnOzs4aGhoSORcA\nQHNCDhgAAAAAAOA7/v777zVr1ogzU09PLyEhQVtbu6lDgoYpKCiIiopisVg3btwoKysTHpKVlR0+\nfLiTk9OECROMjIykFSEAALQihYWF6enpwlnhmltKiNDT0xMUCltYWFhbW6PFQHPau3evr68vIURd\nXT00NLRTp07Sjgjq58WLFzNmzKiqqqLRaOfOnWMwGA1eqqSkJCIiIjg4OCYmRrgdOI1GGzx4sLe3\nt7u7e/v27SURNQCAdCAHDAAAAAAAUJf379+bm5uL5Avr4Ofnt2LFiiYNCeorLS0tIiKCzWbHxsYK\nX+MjhKiqqo4bN87JycnR0RHJewAAaKSCgoLXr18nJibGxcUlJSW9fPmS6hNRB5GscN++fZWVlZsn\n2h9NcnKytbV1ZWUlnU4/dOjQwIEDpR0RNER4ePj69esJIdra2omJibq6uvV6eVVV1blz54KCgq5f\nv15eXi481LdvX29vb1dXVwMDAwkGDAAgLcgBAwAAAAAA1MXb2zs4OFj8+TQa7dSpU1OmTGm6kEAc\nfD7/3r170dHRbDZbpKkbIaRDhw7Ozs5OTk6jR49WUlKSSoQAAPAjyM/PFy4UTkhIyM3NrWO+rKys\ngYGBcF9hCwsL/FfVeHw+f8yYMdeuXSOETJs27ffff5d2RNBwvr6+MTExhBAvL6+goCBxXsLlci9c\nuMBisaKjo/Pz84WHjI2Np02bhiYgAND2IAcMAAAAAADwTXfv3h02bFh9/25SVFS8ceOGra1tE0UF\ndeBwOJcuXYqOjr58+fK7d+9ERrt37+7q6urk5GRraysjIyOVCAEA4AcnnBWOi4tLSEgoLi6uY37N\nrLCVlZWCgkKzBdw2nDx50svLixCir68fGRmJtHqrlpub6+zsXFJSQgi5evXq6NGj65h89+5dFosV\nHh6elZUlfLxDhw6TJk3y9va2sbFp2nABAKQEOWAAAAAAAIDa8Xi8AQMGxMXFNeC12traDx48MDEx\nkXhUUKvi4uKzZ89GR0dfv37969evwkNUUzcGg+Hk5ITyDgAAaIGys7MFhcKJiYnx8fFUcutb5OTk\nTE1NhQuFzczMcG9THSorK3v06EHdHBYYGDh48GBpRwSNFRoa+tdffxFC+vXr9+jRIxqNJjIhNTX1\nv//+Cw0NTU5OFj6urq4+efJkLy8v3BEIAG0ecsAAAAAAAAC1O3HixIwZMxr8cjMzs/v372tpaUku\nIhCVk5MTGhoaHR199+7diooK4SE5OTkHBwcGg+Hg4GBoaCitCAEAABpAJCv87NmzsrKyOubLy8ub\nmJgIZ4XNzc3pdHqzBdzCbd++fcWKFYSQESNG+Pv7SzsckAA+nz9p0iQqv3vmzJlJkyZRx7Ozs4OD\ng4OCgkRagSgrK7u7uzOZTHt7e0VFRSlEDADQ7JADBgAAAAAAqEVpaamZmVlmZmZjFhk7diybzZaV\nlZVUVEBJSUk5c+ZMdHT0s2fPeDye8JC6urqzszODwRg9ejQS8AAA0GZkZ2fHxcUJEsNJSUnl5eV1\nzBfOCtvY2FhaWhoZGdWslWxReDze2bNnDQ0N+/XrJ8FlKyoqDA0Nc3Nz6XR6aGhojx49JLg4SFFM\nTIyvry8hpGfPngkJCfHx8WvWrLl8+TKHwxHMofaDmTJlysSJE3V0dKQXLACAFCAHDAAAAAAAUIu1\na9dS+8s10vHjx6dPn974dYDP59+7d4/FYkVHR79580ZkVF9f38PDg8FgDBkyBLUdAADQ5lVXV79/\n/15QKEx9FNkSQ4S6urqpqalwX+GWlhX29/dfvHgxIcTd3X3Lli2mpqYSWVbQCdjBwWHHjh0SWRNa\niKlTpyYkJBBC7ty5o6enZ2pqSuU7qNSvt7e3u7t7+/btpR0mAIB0IAcMAAAAAAAg6t27d+bm5nWX\n14hDRkbm0qVLo0ePlkhUP6aqqqrLly+zWKxLly59/vxZZNTc3HzixIkMBsPa2ho7XgIAwI+Mw+F8\n+PBBkA+Oi4t79eoVl8ut4yUaGhomJibCWeFu3bo1W8A1eXh4hIeHU4/l5OTmz5+/du3axifwbG1t\nY2NjCSEnT57s3bt3Y6OEluTixYvULt+TJ08+ffr0wIEDORzO9OnTXV1dDQwMpB0dAICUIQcMAAAA\nAAAgauLEiSwWqzErqKure3p6zps3D5caG6awsPDcuXMsFismJqa0tFR4iE6n29raMplMBoMh3UvV\nAAAALRmHw0lNTRUuFE5JSRHpoSBCS0tLOCVsZWXVsWPHZgvY3Nw8JSVF+Iimpubq1asXLVrU4E0+\nkpOTLSwsCCEmJiZnz56VQJTQklRWVo4ePbqgoEBRUTEnJ4fD4Whra7eo6nYAAClCDhgAAAAAAOD/\nc/ny5bFjxzbstTIyMuPGjfP29nZ2dpaXl5dsYD+CrKyssLAwFosVGxsrUrqkoKBgb2/PZDLHjRuH\ndm4AAAANUFVVlZaW1piscK9evXR1dZsitsrKSlVV1erq6ppDhoaGmzdvnjJlSgNye35+fitXriSE\nrFixgtoRGtqYrVu3njp1ihBy5syZSZMmSTscAIAWBDlgAAAAAACA/8PhcPr06ZOUlFTfFxoaGs6f\nP3/q1KmdO3duisDatri4ODabzWKxan7mNTU1GQwGk8kcNWqUsrKyVMIDAABoq4qLi1NTU4X7Cmdk\nZNR9xZjKCtvY2FCJ4d69e6upqTU+kufPn1tbW9cxwdzc3M/Pj8Fg1GvZIUOG3Lt3jxBy5coVPT29\nRoUILdKTJ09mzpxJCJk6derJkyelHQ4AQAuCHDAAAAAAAMD/2bdv36JFi8SfLycn5+Li4uPjM3Lk\nSPSjrZfq6uqbN2+y2Ww2m52RkSEy2rlzZzc3NyaTaWtrKyMjI5UIAQBaIA6HQwiRk5P71iiHw8Ed\nM9AYOTk5if+/wsLCOubLysqamJhYWVlZWlpS20ebmprKysrW97wnT54Up0539OjR27dv79Onjzhr\nFhQU6OjoVFdXGxsbR0ZG1jckaBWqq6uHDRtWXFyso6Pz6dMnbAQNACCAHDAAAAAAAMD/yMvL6969\ne35+vjiTTUxM5syZM3369Obsk9cGlJSUXLx4kc1mX7hw4cuXLyKjNjY2Tk5OTCbT0tJSKuEBALQE\nfD7/7NmzFRUVnp6egoPFxcUBAQH+/v5z5sxZt25drS/cu3fvhg0bFi1atHDhwvbt2zdXvG1HUVFR\nWFhYly5d7O3tpR1LC/Lhw4ekpKSXL19SH5OTk4uLi+uYLy8vb2ZmZmFh0bNnT+qjkZHRd2+VW7Vq\n1datW8WJh06nu7u7b9++3dDQsO6ZN2/eHDFiBCFk2rRpv//+uziLi+/w4cMqKip6enp9+/bV0NCQ\n7OKtzpcvXxQUFFRVVaVy9sWLF9+4cYMQ8ubNGyMjI6nEAADQAiEHDAAAAAAA8D8WLVq0b9++uuco\nKytPmzbNx8fHxsameaJqGz59+nTu3Dk2m339+vXy8nLhITk5OTs7OycnJ2dn565du0opQACAlqK6\nurpfv37x8fHKysqJiYmCH4zv3r0zNTXlcDgKCgopKSk1f2CWlpYaGxt/+vSJELJs2bKdO3d+91z1\nLZjj8/n1eklrufBYUFBw+fLliIiIqKioiooKbW3t+Ph4fX19cV4r+IS0ljcrEfn5+cLbRyckJOTm\n5tYxX1ZW1sDAQLivsJWVlYKCgvCcCRMmsNls8WNQVlZetGjR6tWr1dXVvzVn9+7dS5cuJYRs2rTJ\n2dlZ/MXF0bNnT+pBjx49wsLChIc2bNigoqKir69va2tbMyW5YcMGTU1NAwMDW1vbRt5KWFBQoKmp\n2eCXJycnm5ubNyYAAeqzoaysPHz4cD8/P4msKb6AgID9+/cTQiIiIlxdXZv57AAALVa9N+UAAAAA\nAABok1JSUgIDA+uYYGpqOnv2bBT+1ktqaurZs2fZbHZsbCyXyxUeUlVVHTdunJOT0/jx41GsBgAg\nICsr+9NPP8XHx5eVlf3666/h4eHUcUNDQ29v76NHj1ZWVq5Zs6Zm28s9e/ZQCWB9ff3169c3c9gN\nlpWV1alTp+Y/b1lZ2aNHj+7evXv16tX79+9XV1cLhvLy8ry8vK5evSrZLg9NsUWttBLPWlpaQ4YM\nGTJkCPWUx+NlZGS8fPkyMTGR+piSklJVVSWYX11d/ebNmzdv3kRHR1NH1NXVLSwsqB2kqY8vX76s\nVwxlZWV+fn5Hjx5ds2bNggULat19OjExkXrQvXv3hrxPMWzevHnMmDEiBwUpYWtr66CgoG+NWlpa\nnjlzpsGn/vz589SpUxcuXDhhwoQGvPzly5czZsxgMBhr166V1Bdn3759GxZMI5mamlIPXr58iRww\nAIAA6oABAAAAAAAIIWTUqFHUJnIi1NTUpkyZgsJf8fH5/Hv37kVHR7PZ7KSkJJHRjh07TpgwwcnJ\nafTo0UpKSlKJEACghcvJyTE2NqZ2TXj06FH//v2p4xkZGaamplwuV0ZGJjk5WZD2IIR8/vy5e/fu\nBQUFhBAWi+Xh4SH+6fh8/unTpz08POTl5WudIFLqyufzAwMDvb29v9V4WPzS2NLSUnV19Q4dOgwd\nOvTMmTNN2sizvLz80aNHCQkJL168eP78+fPnz6nmysJoNFq/fv3Gjx/v5OTUt29fceIR/822pRzw\nd1VXV6elpVH5YCoxnJ6eLpxolywzM7ONGzcymUyR4w4ODleuXCGEPHjwQOLbFFOVry9evPjW0NGj\nR/v371/z350aDQwMHDRoUIPvM6ioqJgxY0ZiYqKcnNzhw4fr+2tqXl7epEmTqOptT0/PVatWNSwM\ngTo+G80gPT2dSv3OmTPn8OHDUokBAKAFQh0wAAAAAEADlZeXFxYWFhQUlJaWSjsWaKy7d+/WTACb\nmpq6uLiMGzeO2mMwLi6u6QLQ0NDQ1NTU0NCQk5NrurM0qaqqqsuXL0dHR1+6dOn9+/cioz169HBx\ncXFycrK1tZWRkZFKhAAArYWent6MGTMOHjxICFm/fv358+ep40ZGRmPGjLl48SKXy921axc1geLr\n60slgN3c3OqVAKZeu2/fvi1btgQFBVlbW393/sqVK7dt27Zv3z4Wi9XIjWSfPXvG4/FycnISEhKa\nNAFMCOFyuVOmTMnJyal1dPny5UOHDh0yZIiWllbNUclu+FzHImKeqKk/V40nKytrbm5ubm4unJfN\nzs6Oi4sT7CCdmJhYUVEhkdOlpKRMnDhx5MiR27dv79u3r+A49U1Bp9NVVFQkcqJ6GTBgQB2jgwcP\nFn+pw4cP+/v71zrE4XCOHTtmY2Pj6+sbExNTvxAJIYSEhITMmjWrQ4cOtY4mJiYqKioaGxs3YOVv\nOXTo0JQpU9TU1CS1oGA/cOpfHAAAKKgDBgAAAAAQV3x8/M2bN+Pj4+Pj4xMTEysrK6UdEbRBGhoa\nvXr16t27d58+fezt7Q0MDKQd0XcUFRVFRkZGR0dfu3YtPz9feIhGow0ePJjBYDg5OVlaWkorQgCA\n1ig+Pr5Pnz6EEBqN9uLFC8FP0ZCQkMmTJxNCdHR0MjMzqcrd8+fPOzk5EUI6deqUkJDQrl078U9U\nVVU1b968Y8eOEULk5OS2b9++ePFikTnCiUk+n7948eK9e/cSQlRUVIKCgtzc3OqYX/fZ9+zZs2TJ\nEkKIp6fnqVOnxA+bEFJWVlZcXMzhcKqqqjgcjr6+/ndTSkFBQatXrzYXMmLECHFCreMdNaAOWII5\n4FZ9abesrCwpKenly5dJSUmXLl2SSAkpjUbz8PDYtm0b1TC7R48eqamp6urq9+7da/ziIr5bB/yt\nd9T8JbONOePGjRsVFRVXrFghqVOEhYVt2LBh6NCh+/fvl9TdDOXl5VTGffTo0VevXpXImgAAbQDq\ngAEAAAAA6sLn82NiYkJCQi5cuJCZmSntcKDtKywsvHPnzp07d6invXr1Gj9+vJeXVyMLrSQuOzub\nxWJFR0ffvXtXpIhHXl5+zJgxDAZj3LhxXbp0kVaEAACtWu/evQcPHqyqqjpnzhzhPZ9dXFwYDIab\nm5u7uzuVAC4pKfnll18IIXQ6PTg4uF4JYEKIvLz8v//+O3z48F9++aW0tHTJkiWvX7/evXv3t7ao\npdFo/v7+/fr1mzt3bmlpKZPJ3LlzJ5XHbYAnT55QD75Vf/zp06eUlJSUlJS3b99mZmZmZmZmZ2fn\n5+cXFBSI7OR86tQpT0/Puk/n7e3t7e3dsFBB4pSVlfv169evXz9CCJ/Pl0hOlM/nU7+f+Pr6rlq1\nqqysjBCiqKjY+JW/6+PHjx07dmyGE4koLi6m0WgS3+la4PXr10+fPg0ODhZnMpUJFsedO3f++++/\nqVOnNiK0/yP4Jy4pKZHIggAAbQPqgAEAAAAAaldYWHjs2LGAgIBXr16JDMnLyxsbG2toaKiqqioo\nKKCnKTReSUlJZWVleXn5x48f379/z+PxhEdpNJqdnd28efPc3d1lZaV5L29SUlJoaGh0dDS1e6fw\nkIaGxoQJExgMhr29vaamprQiBABopZp0d19xLgA+f/7c0dGR2ir57NmzLi4uFy5ccHR0JN+oOo2N\njWUwGHl5eaqqqsnJybKysr6+vsHBwQoKCuJXqVpZWSUmJhJCrl+/PnLkSJFRV1fXyMhIMd/jrl27\nli5dKuZkgcbX3aIOWCIcHR0vXrwo2TU7depUVlaWn5/foUOHa9euSXZx8v9XvmZlZTGZzJUrV06Y\nMIE0Yx0wn8/39fX99OlTYGBgrduYf+uMPB6vrKzsu5njoqKiYcOG2dvbb9++vfHRUiZOnJicnEwI\n0dbWbtjm1bWi3uOgQYMePHggqTUBAFo71AEDAAAAAIgqLi7es2fPrl27hDe2VVFRGTx48LBhw6ys\nrIyMjNDQFJpORUVFenp6XFzcrVu3nj59yuVy+Xz+zZs3b968aWJism7dOk9Pz2+VZzUFHo93//59\nqqrmzZs3IqOdOnVyd3dnMBhDhw5VUFBotqgAAECy+vTpc//+fQcHBw8PjyFDhkyaNCk0NPT27dtD\nhw6tdf6gQYPu378/fvz4nTt3JiYment75+bmuru7T5o0ScwzcrnctLQ06nGt5YN15LSowkd1dXXZ\n/9XyW+RCHahbASQrKytL4mvWqrq6esWKFcXFxWvXrtXS0vrWt0zdYmJiBgwYUN++xceOHbt58yYh\nZMmSJUeOHDlx4oSiouK0adO++8LU1FRvb+/x48fPmDHD0NDwW9POnz/P5XIl2E05NTWVSgAvXryY\nypcDAEDTQQ4YAAAAAOD/8Pn8gICAtWvX5uXlUUdoNNqAAQOmTJkydOhQasdFgKamqKhoZWVlZWU1\nffr04uLi6OjoM2fOUMnX9PR0Ly+vLVu27Nu3T9DCsIlUVlZeuXKFxWJdunTp8+fPIqM2NjZOTk5M\nJhONfgEAJEuClZ31TYt27dr18ePH0dHRlpaWubm5hJB79+7VkdAyNTW9d+/e6tWrjxw5QghRUlKq\n181Ab9++raqqIoRoaWnp6OjUnNC5c2c1NTULC4uePXsaGxt36dKlS5cunTt31tLS0tDQaM7boaBJ\nFRUVffjwQdpRfJ+Hh0fN/YGEb1/gcrnHjx9vQA7406dPy5cvb9++/Z49e8zMzISHXF1d09PTv7vC\n06dPHz9+bGJismzZMmtr6+/+evbs2bPy8vKwsLCIiAgfH58FCxbUnFNaWkp9azd+j+tHjx7179+f\nRqMdO3aMRqOtWrVqypQpjVwTAAC+CzlgAAAAAID/kZ6ePmfOnFu3blFPZWRknJycZs2a1a1bN+kG\nBj8yNTW1KVOmTJ48+dGjR4cOHXr06BEhJCkpadSoUT///PP27dvV1dUle8aCgoKoqCgWi3Xjxg2q\ni56ArKzs8OHDnZycGAwGvi8AANqelJSUBQsW3LhxgxCirq6+a9eu2bNn1zE/IiJi8eLFmZmZhBBT\nU9Pw8HDxu4ESQgTptO7du9c6YfXq1Rs3bhR/wbrVnRGvdbTN7LTcwiUlJUn8Uy0jI2NkZJSVlVVe\nXi6pNcPCwoSfSnBL5wMHDlRWVmZnZ69YsSIqKkp46OzZs+Kvw+fzO3TosHz58sjIyLrvXqVaccvK\nyjo7O9faRJzP569atYq6F8TCwkL8GGqKiYlZsmTJhAkT/vzzz8TExG3bto0dO7YxCwIAgJiQAwYA\nAAAAIISQw4cPL1myhMp40Wg0R0fH+fPn17ExGkBzotFoAwcOHDhw4OPHj/39/Z8/f87n8w8dOnTx\n4sXTp0//9NNPjT/Fhw8fIiIiWCxWbGwsl8sVHlJRUXF0dHRycnJ0dNTW1m78uQAAoKXJy8vbuHFj\nQEAAh8MhhNjb2x89erRLly7fmv/ixYslS5ZQ2WJCyKxZs3bv3q2mplavk6amplIPvpUDVlRUrNeC\nrYU49dk/1NbWjU+jKigoWFlZWVhYWFpaUh8NDAxkZWW7dOlC3aMgdfn5+ZqamrX+syYkJFCJXm9v\n7/r2tC4oKFBXVxfUxNNotLFjx1KbQv/888/fehWXy71//z4hhMFgrF+/vtY5+/bto5r1qqqqDhw4\nsF5RCUtLS1u5ciWPx4uMjFRSUoqMjEQFPwBAs0EOGAAAAAB+dAUFBTNnzoyMjKSeduvWbePGjb17\n95ZuVAC16t+/f3Bw8JUrV/7666+CgoIPHz7Y2dmtWbNm7dq1Dbigxufznz59ymazWSxWUlKSyKiu\nrq6Li4uTk9OoUaOUlZUl9A4AAKBlKSoq2rt377Zt24qKigghqqqqO3bsmDt3LjXK5/MfPnwoPD8l\nJWXDhg2hoaE8Ho8QoqenFxgYyGAwBBPEz+e9f/+eemBiYtL4N/JdNStNp06d+t9//31rFJpNzV9C\nvqtTp07UJuHUR3Nz8/regtCcysvLZ8+ebWNj88cff4gMcbncjRs38vn8YcOG/fbbb/XK/fN4vCVL\nlujr62/evFlw0N7e/siRI0eOHJk4caKGhkatL3z69GlJSQmdTq+j0P/UqVPUgxkzZigoKGzYsEGk\nDLoBoqKi5s+fX0efbwAAkCzkgAEAAADgh5aVlTVu3DjBxcopU6YsW7asrRadQJsxZsyYnj17rlmz\n5tGjR1wud8OGDa9evTpx4oSYLas5HM6tW7fYbHZUVNTbt29FRk1NTd3c3JycnGxtbWVkZCQfPQAA\niKHBZaA6Ojrh4eHidCTlcrmbNm3as2dPfn4+IYROp8+YMWPTpk0PHz5UUlLicrnV1dXCmVFVVVVC\niJeXF7WLrIyMzIIFC/7666/ExEQNDY2qqioOh8Pj8QQvUVFRqTuA7Oxs6oG+vn6D3mujlJWVnTt3\nrvnPS+rMNwv+3evOSbexKuGXL1/WPUFHR8fKysrS0pL6aGlp2bryiH/++WdaWlpaWlqHDh3mzJkj\nPLRv375Xr151797dz8+vvv+s/v7+cXFxcXFxRkZGgqpfMzMzJSWlsrKyCxcufKvn7tWrVwkhDAaj\njk2P5s2bFxAQMHjwYCpPvG7dunXr1tWc9vjx499+++3r168WFhb79+//8OHD9OnTY2Ji2rdvX6/3\nAgAATQE5YAAAAAD4cb148cLBwSEnJ4ehLyugAAAgAElEQVQQoq6uvnnzZjs7O2kHBSAWPT29I0eO\nHDt2bM+ePTwe78yZM9nZ2VFRUd8q+CCEFBcXX7p0ic1mnz9//uvXr8JDNBpt8ODBDAbDycnJ0tKy\n6cMHAICm8vnz561btw4ZMuS7+SQZGZnU1FQqATx69OidO3f26tWLENK5c+eKioqa821sbAghO3fu\ntLOzYzAYmzdvtrKyIoQYGxtTNcQihgwZUncA1O9ghBA9Pb3vvzFJY7PZpaWlzX9eqEnknjNNTU3h\ndG/Pnj11dHSkFVtj1GyPffHiReEc8OPHj//9999OnToFBARQ91jUqrKy0s7Oro4v15MnT86cOVNW\nVpYQQqfTzczMnj17dvny5VpzwDwe78qVK/Ly8gsWLKgj+BkzZsyYMaOOCYSQoKCgXbt2cbncESNG\n+Pn5KSkpaWpqKikp3b1719nZueZ8Pp9fUlLSkiu2AQDaGOSAAQAAAOAH9fLlyzFjxnz8+JEQ0qlT\np4MHDxoZGUk7KIB6oNFos2bNMjIyWrFiRUVFxe3btx0cHC5duqSpqVnr/LFjx1K93wTodHr//v1d\nXFycnZ3Nzc2bJWoAAKidSN2n+FsTP336dM6cOc+ePaOe/vbbb1u3bqUSwN9dxN/fPzs7e/ny5Y6O\njoKDxsbG5ubmX79+LS4u5nA41dXVKioqffv23b9/f2Rk5LBhw5KTk83MzATzdXV1f/rpp0+fPpWW\nlpaWlpaVlampqQ0dOnTv3r11n536NYxIKQd8+vRp4adFRUXq6urNHwYQQgICAg4fPtyuXTtqb+fO\nnTtLOyLJqHtf9Ozs7F9//bVz585HjhypO8mtoKAQGxsr/nl1dXUJIRkZGbWOPnz48MuXLz4+Po35\nvvvw4cPmzZvv3r1LCBk7duy2bduonzmysrJ9+/a9fv16rTngY8eOnTx5csuWLY1pMAwAAOJDDhgA\nAAAAfkQpKSkjRozIy8sjhJiZmQUGBrZr107aQQE0xIgRI06cODFv3rz8/PyHDx86ODhcv3691lIS\ne3t7Kgespqbm4uLCYDBGjRqFr3wAgNarrKxs3bp1//zzD5fLJYTo6Oj8+++/Tk5O4q/Qvn37mJgY\nkYNaWlq19md98uSJq6srjUa7ePGicA6YEEKlgupLUD2sra3dgJc3xrt376Kjo2VlZaurq6kj1tbW\n4eHhffr0aeZIgBDStWvXv//+W9pRNFZ2dvZ///1XVFS0ceNGceb7+vq2b98+MDCQStk2zNWrV5WU\nlERq7ql9mMvLy2t9SVhYmJ6enmDv6PqqrKw8cuTIv//+W1VVNWjQoCFDhgQEBLx588bY2JiaYGdn\nt3Xr1i9fvohsBx0XF0ftXuPj47N58+bx48c3LAAAABAfXdoBAAAAAAA0t0+fPjEYDCoBbGFhQZUd\nSDsogIazsLA4dOgQ1Rjv0aNHU6dOFVzRFubq6urp6RkSEpKVlRUUFMRkMvGVDwDQSnE4nEOHDpmZ\nme3YsYNKAE+YMCEhIaFeCeD6un79OiFEVVV12LBhEllQkKNSVlaWyILioxLnDg4OgiNv3ryxtbX9\n999/mzkSaO14PN6tW7d8fX3HjRv38uVLT09PMV/Yvn374ODgxiSA2Wz2b7/9tmDBgvDwcOHjgwYN\nUlJSmjx5cs2XfP36NSYmZu3atYqKivU9XUlJydGjR8eOHRsQEGBiYnLgwIHDhw9Pnz7dxcVl8eLF\ngg3kx44dS6fTIyIihF/75cuX5cuX83g8Op1ubm4eEBBQ37MDAEADoA4YAAAAAH4slZWVDAYjPT2d\nEGJkZBQQEPCtjXMBWhEzM7MDBw7MmTOntLQ0Kipq2bJl/v7+InN69+596tQpqYQHAAASdOTIkU2b\nNr179456qqen5+/v7+Hh0dTnpfJMXl5eSkpKEllQkAOW1IJiKigoOHr0KCHEy8vr/Pnz1EF5efmK\niorZs2c/ePDg4MGDVGtVgO+yt7fPzc3V19fftm2b8F0F33XgwAGRRsjfUlJSMmzYMA6HU8dSzs7O\ngi/aESNGPHr0qNaZMjIymzZtEq4b5vP53+0d/vr167Nnz4aFhZWXl9vZ2Xl7e/fr148aKisry8rK\nevfu3bZt29auXUsI0dTUHDp0aHBwsJeXF5VprqysXLZs2efPn1VUVLZt2yapm0gAAOC7aOI3FwEA\nAICGyc/P37lzZ2ho6Pv37zt06ODh4fHnn38i59TC3bhxQ1tbu1evXtIOBCRvwYIFBw4cIITo6ekF\nBQV17NhR2hEBSMzDhw9/+eWXqqoqQsiZM2cmTZok7YgAAEDyBAkbRUXFJUuWrF69Wk1NTYLLNp6Y\n1xsFZ+RyuXR68+1WuHHjxnXr1mloaOTk5AhKkM+ePTtx4kQqzebs7BwSEqKgoFAz1JpvrY6hBswU\nczXxT/qD69KlS2ZmZocOHa5duyaRBfl8fnJy8q1bt2JiYpKTkwkh7dq1+/nnnydOnCgvLy+Y1rNn\nT/LtfsB1jzaFb52xsrJy7ty5mzdv1tfXr/mqjx8/Xrhw4cKFC6mpqb1793Z0dHRwcBDeRSY7O3vh\nwoVpaWmEEBqNFhQURO2m/uDBAx8fn6VLl86aNYvH4y1ZsiQmJkZfX3///v0mJiZN+h4HDRr04MGD\nJjoFAECrg72gAQAAmlZ2draNjc3ff/+dlpZWWVn5/v37Xbt29e/f/+PHj9IODeri4+PTu3fvzp07\n19oLDVqv//77j0oAKygo7N27FwlgaGMGDhz4xx9/UI/nzJmTkpIi3XgAAKBJpaSkbNmyRSIJYKmg\niiBlZWXpdHp1dbWPj8+HDx+a+qRZWVnbtm0jhPz888/C9ccuLi6nT5+mKinPnTvHYDDKysqaKAba\nt4kzR4LZehBfdXX1H3/8MXLkyEmTJh04cIBKABNCLl26NG3aNOEEcCuye/fuuLi4uXPnlpSU1Bx9\n+vTp27dv58yZc+vWreDg4ClTpggngG/cuDF58uS0tDRdXd2AgAAzM7OtW7dSQ7a2tj179gwMDPz4\n8eP69etjYmJGjRoVGhradAlgAACoFXY1AYBmUlFRkZiYmJGRUVBQUFhYWFhYSFWoQMukpqamqamp\noaHRrl07KysrAwMDaUfU0tVxF/aSJUsyMjJ++umnHTt29OzZMykpae7cuc+ePfvtt99OnjzZnJE0\nANWtp/HrtDrx8fGvX78mhPB4vB49ejR+wQZcpsEd/U3h/fv38+bNox7/9ddfEvnHBWhp3NzcEhMT\nQ0NDS0pKJk2a9Pjx41Z6URIAAL7L0NCwKZZt8C+i9f2lV0ZGhsvlUv9PHTp06PDhwywWKzU1VUdH\nhxCSlZU1Y8aMd+/eGRgYSKqIkxCycuXK0tJSWVnZxYsXiwy5u7sHBwd7enry+fyrV6/OmzcvKChI\nUuetrq6W1FIgFbKysmlpaXl5eYQQbW1td3f3wMBA0uw7mYsoKSmh0WgqKioNeO2TJ0+oLiFv377d\nuHEjdW+EMEdHR0dHx5ov/Pr1699//33lyhVqzh9//KGurp6Xl7dmzZo7d+4MHTqUEOLj47No0SJP\nT8+ioqK1a9cymcwGRAgAAI2EHDAANKHi4uIrV65cuHDh4cOHr169wh88rZeWllafPn1Gjx7t6OhI\nbewD4rt8+TIhJCQkpFOnToSQ/v37h4aGmpqastlsMVeQ1jZfjx8/dnNzW7lypY+Pj5ycXHOeWupC\nQkKoBzNmzBCzRVMrxeVyCwoKvnz58ul/ffz4MfN/ffjw4a+//lq6dKm0w5SYxYsXFxcXE0JcXFzG\njRsn7XAAmsqKFSuePn2anp6ekJCwa9eulStXSjsiAACoS4PLOuv7wpZ2l6GcnFxVVZWysnJRUdH6\n9esJIdbW1lQCmBCiq6t7/fp1Pp///v17cVqWiuP+/ftU0mvy5MmdO3euOYGqa6Tamk6bNq3xZxSo\nrKykHrRr1+7Lly/fmlbfvaChOU2YMCE5OXnWrFmLFi2SlZWlcsDNw9fXd8KECcOHDxfuVF1SUjJ3\n7lwul3vo0KHY2Nhff/217kWo3ZJrFRsbW15e/t18dnV1dUREhL+/f2FhYY8ePZYsWSJoLUxtsBQc\nHEzlgIcPH25ra/vgwYOZM2ciAQwAIC3oBwwAklddXc1msw8dOnTjxg0U+7Y9nTt39vT09PHxMTY2\nlnYsLUgdf6i3a9cuPz8/PT1d8Bl78+aNsbGxtrb258+fG7l4IyfXoaSkxNraOj09nRBibm6+b9++\nkSNHNmbBVqS6urpLly4fP36UkZFJS0szMjISmVBcXCwvLy/cHkx8Emkk1hjOzs7Z2dllZWWlpaX5\n+fnFxcV1n05OTu7mzZuDBw9uupCaTVhYGHX1oUOHDpGRkaqqqtKOCKAJJSQkeHl58Xg8RUXF58+f\no+odAKAla7Z8XlO3mK3vCjo6Onl5eSYmJh4eHtQusjExMcOHDxdM0NTULCwsJIQUFBRoaGg0LCqB\noqIia2vrN2/eyMvLJycnd+vW7VsxT5o0qby8PCoqSpy3Jua7zsnJoVqudu3aNSMj41vT0A9YsiTb\nD7i8vNzLy8vPz4/6676Otr4S7wdcR/qWENKvX79jx4599+WN6UDM4/HYbPbBgwezsrL09fUXLlw4\nfvx4wbZhjx49WrRoUVlZGZ1Ov3r1qq6uLiHkw4cPrq6uHA5n9+7dI0aMaPCpxYR+wAAANaEOGAAk\nqbCwcO/evQEBAVlZWcLHVVRUTE1Nu3fvbmJioqCgoKqqqqSk9KOVFbYupaWllZWVZWVleXl5qamp\nr169yszM5PF4hJDMzMxt27bt2LHD3t7+t99+Gz16tLSDbenGjBkTEhLi6up66NChXr16vXz58pdf\nfiGEODs7Szu0uty8eVPwjZycnDxq1KiZM2f+888/jb/y0vKdO3eO6tbs4uLSoUOHN2/e5OTkZGdn\nJyYmJiQkxMfHZ2RkXL16ddSoUU0Xg/jXAbW1tffv3z9x4kQx51dUVDx58qTuOQoKCoIyBQ6H8/Tp\n0zaQAy4vL1+yZAkhhEaj/f3330gAQ5vXq1cvb2/v48ePV1RULF++XPgqNgAAtDT1TeO1mfyfsrIy\nIaSsrGz37t2EkIEDBwongAkh2traVA44LS2tX79+jTzdggUL3rx5QwiZP38+lQD+luPHj4t5w674\nBAu2b99esitDs1FSUgoLC2u69Q8fPqyrq1vHtYKaSVwq8SnyjSNZZWVl0dHRQUFB796969+//6+/\n/jpy5Ejh7bKioqLWr1/P4XDatWv39evXO3fuuLu7E0K6dOmycOHCnTt3rlix4ujRo7169Wq6IAEA\noFbIAQOAZJSUlOzdu3fHjh1fv34VHDQ0NBw5cqSdnZ21tfWP2VK0Lfny5cvt27dv3759586dyspK\nHo93+fLly5cv29nZbdq0SbD5D9S0a9eux48fv3jxwtbWVnDQ2Nh48+bNUozqu5ycnNLS0lauXClo\nWnzs2LFr164FBwfb2dlJNzZJiYiImD9/vrq6upKSkqKiopycnIyMDJ1Op6qfCSHnzp37Vl+l9PT0\nJs0Biy8vL+/vv/8WPwdsa2tL9W2i0+nt2rXT1dXt2LGjgYGBsbFxt27djI2NDQwMZs+effHiRWr+\n33//vXDhwqaKvhkdOXKEuq1hxIgRAwcOlHY4AM1h3rx5UVFRX79+jY6Ofvz4cf/+/aUdkeRJJQvy\n8OHDQYMGEUI8PDxYLJbwUHFxcVFREdX9AQCg9Wq2umTql+3s7Gzq6bx580Qm9OnT5/Xr14SQyMjI\nRuaAX758Sf1p0759+zVr1tQ9WUlJycDAQPhI4/+jEdT+dunSpZFLQVv19evXioqKBrxw+vTpEg+G\nEJKWlhYaGspms1VVVUePHr17924TExPhCdXV1bt37z5x4gSdTp83b56tre306dMfP35M5YCpwJ49\ne3bjxo2ff/55165dP/30U1PECQAA34KUDABIwLlz53r06LF69WoqAUyn00eOHHn48GE2m71s2TIb\nGxskgNuA9u3bu7q6/vPPP9euXVu2bJng4uatW7eGDh06efJkid8l3Wbo6+s/f/581apVXbt2lZeX\nNzAw8PX1ffToEbU5UkvWqVOn4ODgK1euGBoaUkc+fPgwcuRIPz8/6QYmKeXl5bm5uenp6S9evHj8\n+PH9+/fv3Llz69YtQQF0zS7mdDq9a9euTk5OTX3hhs/nx8XFUY/37t3Lr01AQAA1YcCAAeKvvGDB\ngvj4+JycnKqqqs+fPycmJl6/fv3YsWNr1qzx9PQcOHDgn3/+KUgAr1+/fvXq1ZJ9a1JRWlq6adMm\nQgidTm8bKW0AcaioqMydO5cQwufzv3uxG8TXrl076sGnT5+Ej8fExPTs2bNPnz7Xr1+XRlwAAK2P\nurq64LGGhkbN+xrHjRtHPfD39xf8etwwVlZWLi4uhJB//vlHW1u7MUs1TEpKCvVAJIsGIFBcXExt\nwNYSUH9yKioqHjp06OrVqytXrhT50n3//r2Xl9eJEyd0dHQOHz68YMEC6tIBdd8GhdqEqWvXrmVl\nZQsXLoyOjm7utwEA8GNDHTAANMrnz599fX3PnDlDPaXT6QwGY+7cubittQ3T1NScOXPm9OnTL168\nGBAQ8PbtW0JISEjI9evX9+zZ4+npKe0AWyI1NbXNmze38MLfb7G3t3/+/PnPP/9M7XnF4/G6du0q\n7aAko1OnTmPHji0rK6uoqOBwONXV1Xw+/9WrVxwOhxAybty4Dh06aGlpaWtr6+np6evrGxoaGhkZ\nNawNcANYWFjIyMhwudznz5/XOiEhIYF6UK+qVh0dHR0dnW+Nrl+//ujRo9TjP/74Y926deKv3JKd\nPn06NzeXEOLg4GBqairtcACaD5PJDAoKysrKunr1anJysrm5ubQjaoiMjAwul9tyrpgLcsBU4wAK\nn89nsVjv3r0jhDg4OAQGBs6ePVs68bU8RUVFjx49ev78eUJCQmpqakFBQWFhYUFBQcNKnaBJKSgo\naGhoaGhoaGpqGhsb9+7du0+fPv3798fWtT+axvcDFpNwoxlHR0dqa2hhnp6emzZtevv2bXFx8eDB\ngz09PR0dHS0sLDp16qSioiIjI1NZWVlQUJCbm5uZmfn27dv09PQNGzYIp5aFHThwQElJycvLq77v\nSyJiY2OpB71795ZKANASVFVVycvLf2s0Pz9f8GuG1NFotJ07d9Y6xOVyg4KC9u/fX1VVxWAwli9f\nrqWlRQihGu7k5OQIT1ZVVT18+PD06dOzs7NXrVoVFxf3+++/KyoqNsNbAAAA5IABoOFiY2OZTGZm\nZib11M7Obvny5YJ6QWjb6HT6+PHjx40bFxUVtWvXrvz8/Ly8vKlTp16+fPngwYM1/3Rvvep7FUPM\n+a2rcZempiaLxdq1a9eKFSvmzp07adIkaUckGcOHDxdpm/T8+fO+ffsSQoYNG3bhwoUmPft3v1QU\nFRWNjY1TU1OfPXtW6wRBDlhSzXr//fffDRs2UI9XrFhBFc62DXv37qUeICUDPxo5OTlvb+8tW7bw\n+fyDBw/6+/tLO6KG2Lx585EjR4yMjNhstqWlpbTDIVpaWnQ6ncfjCdcB02i0AwcOmJqa/vrrr1wu\n18fHh/rkSzFOqcvIyIiIiLhw4cKdO3eo+6ug5ausrMzNzaVunHr8+DF1s6+MjMygQYPGjx/v6upq\nZmYm7RihTRHOATs4ONScoKSkdOLECScnp+Li4qqqquPHjx8/frzuNadPn96nT59ah/T09E6dOtWI\neBuuurr69u3b1GPhJkFAKSkp2bFjh6ysrI2NjY2NTcvfNKu+SkpKrl+/HhUVpaWltWPHjm9N+/z5\ns76+fnMG1gCxsbHbt29PTU3t2bPnypUra3b5LS0tFTnSsWPHY8eOzZgxIycnJyws7OnTp1u3bm2l\n9yYCALQuyAEDQAMFBgYuXry4srKSEKKlpfX777+PHz9e2kFBc6PT6S4uLnZ2dps3b7506RIhJCgo\n6OnTp2FhYT169JB2dNAQFy9eHDZsWK1NcJctWzZgwADx20lyOJzs7OzWdV/IH3/8QaXnW8h+1z17\n9kxNTU1MTORwOHJyciKjL168IIS0b99eIn88R0REUHvGEkKWLl3aQj4DEvHkyRMqX25paYkfTfAD\nGj9+/K5duyorK0+dOuXn56ekpCTtiOqHx+Ox2WxCSGZmZgv5P4VOp2tra+fm5hYVFVVUVAgXsixd\nulRRUfGXX37h8XiXLl2aNm3aD9gShcvlnj9//uDBg1euXKl1Q0sFBQV1dXV1dfVm21oDxFdVVVVU\nVER9bQsOcrnce/fu3bt3b/Xq1XZ2dvPmzXNzc6ujjg1AfMIlj9/a22bYsGH37t1bsmTJjRs3xFkz\nIyPjWzlg0gStjsvLy8WZduPGDap5lpGRkbGxsWRjaAP2798vuBuVEGJgYGDzv/r16yeVvbslorCw\n8M6dO9euXbt79y6Xy3V2dhb8zVWrDx8+iDSiblESExP3799/584dfX39TZs2TZgwQeQbqqioiBAi\nIyNT87X6+vrBwcGLFi1KTk5+8+bN5MmT3dzcFi1a1HLqngEA2iTkgAGg3ng83rJly/bs2UM9HThw\noJ+fHzYH+5FpaWlt37591KhR69evLy0tffnypa2tLZv9/9g783gou///H2MZu2QZsibVnfa7PVq0\nKIWyla2iFBItKi0kiooQKhVpE9EqraoblaI9dSvdZN/GvoVZf3+cx/f6zccyjVkMOs8/PM51zZlz\n3lMz11xzXuf9eifr6uryOzRE70hLSzMyMlJSUjp06JC9vX3XZWs9PT3WRzty5EhsbOyrV68Gyi/2\nly9fwtxfU1PTmTNn8nq6rrngXRekxo8ff/PmzY6Ojo8fP3Yq+pubm9vY2AgA0NPT43wl6+HDh9bW\n1rD+8ZYtW0JCQjgcsF8BbcwBAJaWlvyNBIHgCzIyMgYGBsnJyXV1dc+ePTMyMuJ3RL3j9evXMN12\n2rRp0GCwP6CkpAQTJSsrKzuVSHBxcSGRSBoaGrDq5B8FnU5PTEz09vb+77//GM+rqKjMmjVLR0dn\n9OjR2trag8kwZhDT0dGRl5eXm5v7/fv3zMzMgoICeD49PT09PV1FReXgwYP29vZCQmhZibdQKJTs\n7GxxBvB4/GAqOs5Yo0RVVbWnbuPHj3/27FlOTs7Dhw/fvHnz33//lZWVtba2trW1CQsLS0pKSkhI\nKCoqamhowOotPIr28uXLjY2N2tra6urqioqKMjIydDod89joVvfCOHnyJGxYWVlxGAadTk9NTeVw\nkP4G/CWCUVxcXFxcfPv2bXiooaGB6cFTpkzp5wtQdDodK4g7d+5cGo0mKipqZma2bt06FRUVJk8s\nKipqaWkpLi7ukzB7x5s3by5cuPDy5ctx48YFBQUZGBh0u8sNBt+TGTuBQLh8+fL+/fvhLrEbN248\nevToypUr/afeBwKBQAw+0M06AoHoHW1tbVZWVnfv3gUA4HC4rVu3Ojg4cH0jLWIgsnTp0okTJ3p4\neHz58qW+vn7hwoWxsbEWFhb8jotTWDRtxj4FA8vkmZGGhoZ169bRaLTy8vINGzaEhYWdOHFCX1+f\nvdG+f/8eEBDQ0dFhbGz8zz//9P+0MzqdvmvXLgCAuLh4cHBwcnJyZGTkmzdv2traJkyYsG3bNr44\nYGMbKZ49e9ZJA8as5BYuXMjhLKmpqWZmZiQSCQDg7OyM2SYPGuB3lqCg4OLFi/kdCwLBH5YuXQpT\naZOTkwecBpyYmAgbBgYG/I2EEWVlZWgwwLrSMHDvEFgkNTV1586dHz58wM6oqamtWrVKX1+/nyRw\nI3oFHo8fO3Ys5r5eUVGRlpaWmJiYl5cHACgrK9u4cWNwcHBgYKCxsTFfIx3k4HC4uXPndjVWhRAI\nBB7N22e/8bHdolpaWr/d6KOjo6Ojo8P7oHokPz/fz8+vp0eVlZV7euj169f37t0DAOBwuPXr17Mx\n9ciRI4uLi6lUKo1GY/xC6UlsG3Awz40uKioqKiq6desWPNTU1IRiMIRfiaSddOvS0tJHjx59/Pjx\n06dPMB0WAEAgECwtLS0tLYcMGcLYWUREhEQivX//fuzYsSIiIr9+/frvv/9OnToFAMjNzU1LS5s7\nd25/sBJpaWl59OhRXFxcQUHBnDlzYmJimBuDZWVlAaZ3R6KiosHBwdevXw8ODm5tbXV0dEQCMAKB\nQPAUpAEjEIheQCKRTE1NHz9+DAAQFhYOCAhYunQpv4NC9COUlZXPnz+/devW169fd3R02NjYCAsL\nr1ixgt9xIVjFzMwsMjISerxnZ2cvXLjQw8MjICCgqwsxc+h0+saNG+E4NTU1A2KbyIULFzIzMwEA\nbm5u27dvT0pKwh7KzMy0srJ69+5dUFBQH0elp6cnJibW1tb29OnTvXv3Mj7ELQ341atXxsbG0O9x\nw4YNp0+f5mS0fkh+fv63b98AAJMmTRo0a2QIRG+ZMWMGvJjcu3ePTqcPiMsypKmp6cKFC7DdB3cU\nA+hfpl9RU1Ozc+fOy5cvY7LEtGnTHBwcdHV1+8P6NYIrKCsrW1tbW1tbv3379tKlS+np6QCA79+/\nm5iYmJqaRkREME9uQ7ANDocbN24clFW6Ympq2sfxcB0bGxsDAwMCgSArK8vvWH7P5MmTmTzaU4Jv\nS0uLo6MjvEJaWlqyp3ipqanBHRidGDSlhUeOHMl658LCwsLCQszsR1ZWVkdHR09PT1dXd+rUqUzE\neM4JDAycM2eOlpaWrKzskydPAEP+d1NTE2aYJygoqKenZ25uPm/evG6/CrW1tXNycuzt7bs+RKPR\n9u7dm56e3q3l/vjx47n1WphDo9F8fHwePXqko6NjZWVlYGDQScY2MjKaNWvWjBkzNDU1CQSCiIjI\nq1evrly5Alh4W1paWurq6t67d2/Dhg08fA0IBAKBAEBg0G9GRiAQ3IJCoZiZmcEkEklJyYiIiKlT\np/I7KER/hEajHThwAEpowsLCyehuclYAACAASURBVMnJS5Ys4XdQPIenecC9GpzDSAoKClxdXR8+\nfIidmTJlSnx8fK9+kx89ehQTLJ89e7ZgwQI2IulLGhsbR40aRSQSZWVl5eXlOzlYYty5c6erAkGn\n058/f37lypXCwsInT578Vj9g8h/U7UNLlixJSUkRFRWtr69nLDmpoaFRXFyspqbGiVfY69evDQ0N\noaf0unXrYmJiBt9ifWxs7Jo1awAAW7dudXR05Hc4CATf2Lx584sXLwAABQUFnbyL+zOhoaE7duwA\nAGhqamJWtIxw9/uXDQ3Y1dUVs/f8M7l9+7aTk1N1dTU8HDNmzNatW1FBkEHPx48fT5w4gaV9S0tL\nh4aGspfdiPgtfn5+cXFxjY2NLS0tZDKZTCbj8XiYZ79v3z7u2u1wflEdiPZIrMdMJBL37NlTUlJS\nUlJSX1//69evtrY2ISEhDQ2NVatWHThwoNu9s7m5ubq6urW1teLi4v/++y9738KbN2+OjIzEDgUF\nBeXl5efOnRsUFDQ4vBYaGhq4tQ9AWVmZsZbw9OnTS0tLCQTC06dPOR88KSnp7du3L168gNWdAQDD\nhw+HtkMAAFtb2+zsbHd3d3Nzc+bZyd+/f4+IiMjLy6uvr+/o6KDRaDgcTlRUVFpaWlVVdePGjbNn\nz+70FKj+fvnyhcXz7HVjJDMzU0NDoydN/fv379nZ2W/fvn358mVLSwt2XkJC4v79+3zx64avcebM\nma9fv+772REIBKJ/gjRgBALBKthPDjwef+bMGSQAI5hAo9H27NkDdUQZGZn09PSJEyfyOyjuUFtb\n2+2PmZ4WDgoLC728vAICAtTV1dmelPVVCTKZDDcL4/F4mNnJHvHx8Zs3b25oaICHsrKyP3/+7LTt\ntydSUlIMDQ1pNBoAwMHBISYmhu0w+gxXV1fG/FcJCQl3d3dbW9vhw4e/f//eyckJJpLq6Oj8+++/\nWLf//vvv4sWLsbGxmAobGxtra2vLfK7easDHjx+HJtW3bt3CUj2+fv0Kf986OzszLgb1ivT0dCMj\nI/hz3crKys3NLSMj482bNz9+/CgpKWlpaREVFVVUVCQQCLNmzVq2bNmcOXN6mxHeH9i5c2dwcDAA\nICoqqg/KPCMQ/ZbTp0/Dy8Xt27cHSp1aCoUycuTIwsJCLo7J/JuU9S/cV69eQZlz4cKFXFlTHohQ\nqVRvb++jR4/Cfy5paent27ebm5ujdOo/h8ePHx89erSmpgYebtq0KTw8HI/H8zcqBCcgDZhHU0CP\nJT8/PxcXF/ZGgPK/oKAgDoeDf7kbYX9ATk4OE1a5hYCAgKCgIIVC4ZYGDGlvb9+8efPbt29xONzR\no0cNDQ3h+c+fPx8+fDgxMZEXX4V9rwGzSEdHx+HDh+/cuQMAEBERCQwM5LxcEXsgDRiBQCC6Mgjv\nGBAIBC8ICwuD64YiIiKnTp1CAjCCOfCHEKzb19jYaGRkhGWHDGiqqqpUVVXNzMzS0tJY6R8eHj52\n7NirV6+am5tDY2Re09zcDBscet5aW1t//vwZS+Lx8vJiUQAuKCiwtraGArCKisrx48eZ9xfgJSy+\n2PT0dEYZdcGCBbm5uQEBAWPHjhUXF58zZ86jR49gcbKcnJysrCwKhXLz5s3FixePHj06ICAAE4CF\nhYWfPXvG4qSss3z5ctiIj4/HTmJW1WxX4Hvy5MmyZcuw/dopKSm6urq7d+++ceNGdnZ2fX09mUxu\nbm7Oz89/9epVcHDwwoULNTQ0Ll26xMFL4Q+fP3+GjdGjR/M3EgSCv2AfAexD0f8JDw/nrgDMRcaN\nGwcbX79+5W8k/KKxsXHZsmVHjhyBkomBgUFSUpKFhQUSgP8olixZcvfuXQsLC3h47ty5efPmVVVV\n8TcqBCfQ/w8+jtD39EHMEyZM+PTpE9sCMABAWFhYXFwcj8cLCwsPSgEYAMCLurB0Oh1W7eXu/6+o\nqOjWrVvt7e3j4+MxARgAMHHixOvXr/fxV+GXL194oeyyDh6Pd3Nz09XVdXBwuHXrFr8EYAQCgUB0\nC8oDRiAQv+f9+/e6urpQwQoICGBbckD8abS3t2/YsCE7OxsAsHz58rt37w70H6uYxfGECRM6raF3\nu3k8ISEBKwrl6OgYFRXF3rys70wvLCwcPnw4AGDEiBHd1ovqFWQy2c3NraKigrE4LhPq6urmz58P\nf3+KiIikp6f/Nu2Spz+PWbnJ+fXr14QJE/Lz8+Hhli1bwsLCur5Rd+/eDYsBz5o1q7CwsKKiAntI\nTEzM0NDQwsLC0NCQFaWclZfcKfIZM2a8efNGTEyMSCRCNXratGnv3r2TkZEhEondlolizv3799ne\nl2BnZ3fhwgUhISE2nssXhg8fXlhYKCsri1VQHsQ0NTWhmseInigsLIS3cHZ2drBUWz+nvLz8r7/+\ngnubTp06tXnz5m678cgLmpXRoCc/AKC6ulpeXr5rByqVitUIHGSUlpYuWbIkJycHACAsLLxv3z5M\nBUT8maSmpu7btw/uLdPQ0EhJSRk1ahS/g0IgEAMMGxsbxm2v3IW7ecCI/gnKA0YgEIiuDOy1eAQC\n0Qc0NTVZWlpCqWDNmjVIAEawjqioaGhoKKyCc//+fSihDVzodHp0dDRs29vbs/KU1atXY3u9o6Oj\nExMTeRQbRllZGWxwpfqOsLDwmTNnrl+/zkrn+vr6RYsWYRuQT5w4MSB8dz09PTEB2NvbOyIiotud\nClhJ49evX0MBWEhIyNDQMC4urrq6+ubNm9bW1iymSrMBrK7X1tYG30IFBQXv378HAJiYmLAhACcm\nJpqZmXUSgAUFBXV1dQ8ePHj37t0fP37U19dTKJSWlpb8/Pzbt287ODhgpYhjY2Pd3d258Kr6ivr6\negAA7/53+g/v37+fO3euvr6+n58fT60XkpKSkpKSfv78ybspELwAq7EHPxT9Hw8PDygAjxs3zsnJ\nid/hdANcZwQ92Crm5eVpa2tfuHCBSqX2bVw8p7i4eOHChVAAlpWVPXfuHBKAEfr6+jExMbBmZFFR\nkb6+/h+bIo9AINhm5MiRXB/TyMhIUVGR68MiEAgEAjFQQBowAoH4DTt27CgoKAAAzJo1a+fOnfwO\nBzHAUFRUDA8PhymDBw4cGNCLQXfu3IFioZCQ0G9rvmKEhoZidpHOzs6lpaW8ig8AwLAMPXbsWG6N\nyYrK2NjYaGBg8PHjR3i4fv16Fo3O6Lzkt7PfvXv35MmTsL1z504/P7+ufSorK7ds2bJixQrszIgR\nI44cOVJaWvrgwQNra2sJCQlWXikrr72nntbW1mJiYgCA0NBQAMD58+dhZzs7u95OGhERYW1tTSKR\nsDMaGhpHjx4tLS19+fKlj4+PsbHxyJEjhwwZIigoKCEhoaWltXLlypiYmNzcXMwbPDIy8s2bN72d\nmi/QaDSoIUlJSXF35Pb2dq4kHdbX1+/evXvp0qWc/5NOmTIlMDCwpqbm+vXrW7Zs4Ty2nmhqagoN\nDV2xYsXixYsDAgJgtezBREdHR25uLr+j4D6SkpIwyRWr9d6fiYqKunbtGmyHhIT0z2zaSZMmwUZW\nVlbXR6OiogoLC9evX3/mzJm+jYu3FBYW6urq/vjxAwCgoaFx7do1VCMGARkzZkx8fPyYMWMAAOXl\n5XPmzPn06RO/g0IgEP0XKpVaXFz8/Pnzy5cv+/r6Ojg4cHfPtL6+/suXL5OTk9nYNYtAIBAIxKBh\nwPj4IRAIvvDixYsLFy4AACQkJHx9fQe6kS+CL0ycONHe3j46OppEIrm4uKSnpw/ENxKNRvP29oZt\nExMT1rcS4/H4ixcvzpw5k0Kh1NfXr1279tmzZ701QGZdaoLO24AhOakPKCoqWrFiBWaObW5ufvbs\n2T6bnW1KSkocHBxg28rKKjAwsFMHCoUSFhbm6+uLVVmGvH37Fkun6xukpaWtra1jYmK+fv364MGD\nixcvAgBUVFR6W2lp//79AQEB2KGSkpKfn5+9vb2wsPBvn6uurv7o0aMZM2bAxK8zZ85Mnz69dy+D\nH7S2tsLq1OLi4twdOSQkBACwZ8+e3l7Q2traSkpKiouLS0pK8vPzU1NTm5qaAABOTk4nTpyYN28e\nJ1Hp6enBBqNdOddZs2bNqlWrLl++HBkZGR8fHx8fP23atN27d//111+8m7Qv+fHjh7OzM4FAMDMz\nMzMz4/qbh18ICgqKioq2tbXBt1x/5tWrV9g+BjMzs8WLF/M3np6YM2cObGRkZHR6qKOjA95Ci4qK\nYlUhBgE1NTVGRkZwQ5u2tvbZs2dRchWCETk5uejoaDc3tw8fPjQ0NJiYmLx8+VJdXZ3fcSEQCH7S\n2tr6/fv38vLyioqKnwzwzphk+vTp/v7+ixYtgofw1zcqhjjogb/7AAADccUJgUAgeAeqB4xAIHqE\nTCZPmDDh+/fvAIB9+/ZZW1vzOyLEQKWjo8Pc3LyoqAgAcO7cuY0bN/I7ol4TFxeH5f6+f//+77//\n7tSBeQVBLy8vf39/2I6KinJ0dORRnFhtwtTU1Pnz5/NoFkbS09MtLCxqamrgoYmJyY0bN1jRFPmO\ntbU1TDKbMWNGeno6Ho9nfPS///6zs7PDUjMXLFhQV1cH01lycnJgjgt7MHmrMHmooKBg9OjRZDKZ\nQCBUVVUBAA4ePOjj48PipFQqddOmTTExMdhEW7ZsOXz4cG9rx2IlrrlScLoPaGxshC7Qurq63E3F\ny87OtrW1HTNmjI2NzbRp0+Tl5YWFhclkMplMJpFIzc3NjY2NTU1NjY2N1dXVRCKxqqqqqqqqvLy8\nurpaQEBgyJAhcnJy8vLyTU1NUFYHACgqKj579oyTqDIzM+EF1tTUtNu8djqdfvXq1aioqP379xsY\nGHAyFwDg+/fvu3fvhmYhOBzO1dV106ZNHI7ZT6itrfXz8/vnn39kZGTWrl3r4OAwIC5rv2XWrFkt\nLS06Ojr//vsvv2Nhxrx582ABb3V19Y8fP8KiEj3Bo3rATLCwsIBVElpaWmRlZSkUytChQ2tqahif\nGxUVBT8ODg4O2LV3oNPe3j5v3jz4zaihoXHp0iWuFJ5ADD5aW1sdHR2h/c/o0aOzsrJkZGT4HRQC\ngeA5dDq9oqKioKCg8H8pLi5mdCHiKX///fexY8cw9RcyduzYnJwcCQmJzMzMvgkDwReam5tnz54N\nAFi6dOnDhw/5HQ4CgUD0F5AGjEAgeuTs2bPOzs4AgMmTJ1+8eBHtpENwwrt379avX0+n05WVlfPy\n8gZWWlVjY+PYsWNhqd3ly5ffu3evax/ma9AdHR1jx46FVtKysrLfvn0jEAhcj/PNmzczZswAAMjJ\nyVVWVkILbt5Bp9PDwsJ27dpFoVDgGWNj4xs3bgwUr636+voNGzZkZGS8f/9eVVWV8aGnT59aWFg0\nNjYCALS0tMLCwoyMjGxsbOLj4wEAGRkZ8Lcle7CnAQMAXF1dT58+DdsiIiIFBQXDhg1jcdLbt2+b\nmZnBtpKS0uXLl9nLq6usrISl/vB4fHt7Oxsj9DG804ABAEeOHImLi+vpUVFRUWVlZUVFRSUlJQKB\noKCgAP8qKCjIycnBjyeRSLS2tiYSiQCAWbNm7d69W1tbm5OQPDw8UlJSAADx8fGYCz2FQqmoqCgv\nL8/Nzb1//z6UnPF4/NWrV0ePHs3JdACA+vp6R0dH6AoLANi/f/+gSXmk0+nh4eGwDLympmZQUNAg\nSHQeKBpwbW2tsbHx27dvnz9/PmvWLOad+14DXrt27aVLl2B7xowZUBP99OnTxIkT4UkajTZmzBj4\nuWA8P9Cxs7O7evUqAEBFReXy5csoAxjBhJaWlvXr18NiAcuWLUtOTka/JRGIwUFLS0tRURHM6MVS\ne2GD9bxeISEhdXV1rS7IyspKS0t3MmFikYkTJx46dMjIyKjrV7muru6rV68EBAQ+ffqErkWDmPLy\n8iVLlgAArKys4C93BAKBQADkBY1AIHqiubkZOt/icDgvLy90o4zgkKlTp8LNmBUVFUFBQaznL/YH\ntm3bBgVgAQEB9iLH4/EhISGwpmx9fb2Hh0dsbCyXowTgxIkTsLFy5UpeC8Dfvn1zdHR89eoVdmbH\njh1BQUED6FohKyt769atkpKSrgLw8uXL4V71TZs2hYSEwIq/WKJwS0tL30cLAPDy8rp48eKvX78A\nALa2tqwLwAAAU1NTLy+vw4cPT58+PSkpSUlJCZ5/9epVSEjIy5cv6+rq5OXldXV1nZ2dmVhMYybY\nA+g/mnd4enqqqKgkJiZWVFQoKiqOGTNm5MiRmpqaqqqqqqqqvzUMb29vd3NzgwKwnZ3drl27OPxX\nzcvLe/r0KQBATEzs2rVrdXV1tbW1tbW11dXVmDEaRkdHx7FjxzhPT5SVlY2Ojra2toYXyQsXLrCu\nAb98+XLKlCmw1nU/REBAYOvWrUOGDDl+/HhhYeHatWvDwsJ+q0f2BI1GQ58a1pGTk3v27Nk///zD\n9j8453RVlIlEIty/xbiPbeHChVADvnfvHqb1JiQkQAHYxMRk0AjAsbGxUAAWFRUNDw9HAjCCOZKS\nkidOnFi9enVDQ8ODBw9CQkJ27tzJ76AQCASrUKnUysrKkpKSsrKy0tLS4uJi2CgpKamoqCCTyawP\npaioqKGhofm/DB8+vKc7wBEjRvS2lPjIkSP9/f3Nzc17uteCVgR0Or2xsbGPa/og+pKGhgbYgJuA\nEQgEAgFBGjACgeieqKio6upqAMCCBQtGjRrF73AQgwEXF5eUlBQqlRoaGrpjxw4pKSl+R8QSSUlJ\nsPwqAMDJyWnatGnsjWNiYrJ06dJHjx4BAOLi4tzc3GDOLrf4/PkzdDYGAKxbt46LI3fi169fx48f\n9/f3xxy9REREzpw5g9XWHVioqakxHlZUVFhaWpJIJAEBgfDwcKwgJQAAc4Llbv5rW1vb27dvX79+\n/eLFC+Y9oXsw1IA7Ojp6O9GhQ4e0tLSsra1FRUXhGX9/f29vb0znqKiouHHjxo0bNywtLWNiYiQl\nJbsOAnPZAQCampq9DWDwgcPh1q5du3btWjae297e7urqmpOTg8PhPDw82BukE4GBgTQaTUhIaMSI\nEdXV1TIyMioqKjIyMtLS0thfGRmZ0NDQ9PR0AAC33LxlZWX9/f3Xr19Po9FYz/+ora3duXNnZGTk\n5MmTuRIGj1i3bl1ZWVl8fHxbW9v27dsTExPZKGyZk5Nz9OjRS5cu9bYY/J+MmJjY8uXL+3hSzNai\n231Ura2tsAE3BkFMTU2PHDkCAEhOTt6/fz8AgEwme3l5wUexxkCnsLDQxcUFtr29vdFPAwQrDBs2\n7MiRI66urjQabe/evYsWLZo0aRK/g0IgEP8fCoVSWVkJ9d2ysrKioiLYKC4urqysxL4TWQGHwykp\nKampqampqXXSentrAKatrc26BqylpeXj42Ntbc28ZseoUaOgM3BeXh7bP+cR/Z///vsPNkaOHMnf\nSBAIBKJfgTRgBALRDXQ6HXpmCggIuLq68jscxCBh+PDhxsbGd+7caWxsjI+PHxBlIz99+mRnZwfb\nw4YNO3r0KCejBQUFpaSk0Gg0Op2+fft2xiRaDmltbV23bh0U8xYvXjxnzhxujdxplsjIyKCgIJi5\nCNHR0bl48eKg+S19+PBhuH14x44djAIwAEBcXFxdXV1RUZFb24o3b9785s2bz58/s7jCEhAQUFJS\nAttxcXGzZs3qFOFvYdTpr1+/3pM4cf369aKiomfPnnWVgbF9Bn1TbXqwAgXgN2/eiImJBQQEdKpY\nxh4pKSmvX78GALi7uzPZkNHe3g5zFvF4fGRkJIuDl5eXKykpMUljnTJliqur6/nz51lPAj558uTk\nyZNZF4B7m0ebkZHh7e1tZWXF+XfNnj17Pn369O3bt9bW1rCwsODg4F49vaOjY+/evdOnT0cCMNuw\n+E/HSjfmftHY9ppOFeIhmDUl47Vx2rRpmpqahYWFb9++LSkpUVNTi4yM/PnzJwDAxMRk0Hw5Ojs7\nQw8MCwsLExMTfoeDGDDo6elt3Ljx7NmzFArF0dExMzOT10Y1CASiE42NjXl5eZ1Mm2GjtxtbJSQk\nNDQ0hg0bpqWlpayszNjgYnIti4VRhg0b5uPjY29vz0odovHjx8NGbm7uoPlqRnQFK08zYcIE/kaC\nQCAQ/Qp0/41AILrh8ePHcAPd7NmzOaxNiEAwsmbNmjt37gAATp061f814MrKSiMjI7joKSAgcObM\nGegixTbjxo2zsbGBLtBqamptbW1cMUGlUqlr1679/PkzjPPw4cOcj9mJ0tLSS5cuhYWFQXsAiKCg\n4K5duw4ePNjtWvkABb4/AQC7d+/u9NCJEycwt+3ekp2dff78+S9fvmRnZ2MnGRU4cXFxfX39+/fv\n9zTCjx8/goKCAADS0tJtbW1kMnnHjh1jxoxh4tvMHGxDg42NzaFDh9TU1CoqKhISEg4fPtzU1PTm\nzRs7OzvsXwOSk5MTEhIC2/3/89tvqampcXNz+/r1q7a2dnBwsJaWFudj1tbWwg/+9OnTmdsApKam\ntrW1AQA2btw4duxYVgZvbm5es2ZNc3PzmDFjpk+fPnv27EmTJnUV2zZt2sT6u+Lr16+3b99mvUwX\njUYzNTU1NDRctGiRmpoaHo+Hm2nIZDKJRGpra2ttbW1oaKirqysvL//58+f79+8LCwsBABEREcrK\nysbGxixO1C04HO7QoUOrV6+mUqls7N0JDw+vqalBO+oGBJjVf7dJS7BIPABAWlqa8byFhcXx48dp\nNNqFCxc2bdp04MABAICwsPDx48d5HG8fcfny5cePHwMAlJWVkZ0vorc4OzunpaXl5ua+f/8+JCSk\n6/0VAoHgnLa2tvLy8vLy8tLS0rKyspKSEszGubKysmtNEOYoKSmpqKioqqqqq6urqqqqqKhgDVYE\nVw4ZMWLEb8Pz9fVlUf2FjBs3Dja+f//OUXCI/g32/4v9jyMQCAQCIA0YgUB0C+Z8a2ZmxtdAEION\nUaNGjRs37uvXr9nZ2R8+fPj777/5HREz5OXlFy9eDD8O+/bt41BFgPj6+mZkZISFhXFlNABAU1PT\nqlWr4OIsAGD//v3Tp0/nysgAgNbW1jt37ly8ePGff/7ptHYwf/7848ePT5kyhVtz9ROwGkItLS1c\nLHZIp9PDw8M7nRQSEpoyZYq+vv6iRYv09PTweHxPSWzt7e3W1tYwQS0iIqKxsdHd3Z1MJq9cufLJ\nkyczZ85kI6SvX7/CRmRkJNQz1NXVd+3atWLFigULFpSVlSUlJUVHRzs6OsJu7969MzY2hlaoGzdu\nRHaO7JGbm7tly5bKykoLCwtPT0/Ml5tDDhw4UF9fLy0tHRAQwDxZ9sGDBwAASUlJW1tbFgeXkpJ6\n8ODBzZs3z5w58+HDhzNnzigpKVlYWNjY2LBn6U+lUn18fJYsWTJmzBgWn4LD4VauXBkSEnLq1Ckm\n3cTFxRUUFOTl5f/66y9RUVG4DBQeHs759Xb06NEWFhYJCQm9feK7d++uXLmyd+9eVJaME5gn72JX\nTubdWAHb56SgoND1UczqvFO205o1a6DcGxMT8/XrVygVb9myZXD4EDY3N3t4eID/22TG6IONQLCC\nkJBQQEDA6tWrKRTKwYMHbW1tVVRU+B0UAjHwaGpqgrV4O2X0lpeX19XV9bZMjJCQkLq6etd0Xi0t\nLb6Xy2WyP1JKSmrr1q0eHh69va2aOHGihIREa2vrq1ev6HQ6smYZlLS2tn78+BEAoKWlpaSkxO9w\nEAgEoh+BNGAEAtEZMpkMa6XIysouWLCA3+EgBhtmZmZQfLp7924/14CFhIQuXLigqKj477//+vn5\nMenJuo+WlpbWjx8/uOWD9/btW3t7+5ycHHhoYGDg6+vL4ZgUCiUrK+vZs2fPnj3LzMzEiv5iTJ06\n1d/f38DAgMOJ+iejRo2CBahsbGzi4+OHDx/OlWEnTpyopaX18+dPUVHRadOmzZkzZ86cObq6uixK\naFu2bPnw4QMAYOXKlbBw7OvXr+Pj41taWgwNDR8+fMiGDDx06NDKykoAwLdv3xhLU48aNSo5OXnm\nzJkkEsnT09PCwoJGox09evTEiRNkMhkAMHPmzLCwsN5O96dBp9N37txJIpFGjRo1e/ZsuFsiPj4+\nODhYQUEhOjqai+XAY2Njnz9/LiIiEhoaSiAQmPQkEokZGRkAAAsLi27rPfcEHo+3sbExNDQ8cuTI\nw4cPKysrT548efXqVV9fX319/d4GHB0dXV5eDktOsI6Dg4OoqOilS5eqq6vl5eVhPoqSkpKysjKB\nQFBUVFRUVGRUp/z9/aEGrKen19sIu8XFxeXFixdLly5l/SkNDQ379++fNGkS6xbZCP4Cr4oAgG6X\nDjGFeOjQoYznJ0yYMH/+/LS0tKKioqKiIgCAioqKj48Pj4PtI06fPl1TUwMAMDAw4OImM8QfxahR\no1atWhUXF9fW1hYUFMS2qwoCMbihUCjFxcWYsttJ6O2tbzPo30IvE7o1ohMXF9+8ebOnp6e8vDwb\nY4qKii5evPjOnTvV1dU5OTkseuEgBhYZGRnw5yoqWoFAIBCdQBowAoHoTHp6elNTEwBg7ty5qGIT\ngussXLjw8OHDNBrt7t27Bw8e5Hc4v+fYsWMkEokxte7ly5f37t3T09MbPXq0nJychITE2bNn4UOs\nlKvkyseqvr7+wIEDp0+fxtJzlyxZcuvWrV7Vy+yWhoaGlStXwgVfRnA43NKlS11cXIyMjDicoj/j\n5ua2YcMGAEBWVtbIkSMXLVq0YMGCcePGaWpqysvLS0lJiYiICAoKsjHy+fPnxcTE/v77b2Fh4V49\nMTg4+Pz58wAATU3NqKgoeDI6Ovrnz59ZWVkNDQ0LFy5MSEjo7f+LgYHB5cuXAQAmJiZeXl6LFy/W\n0NCA5uSTJ0/29PQ8dOhQXV2dvr5+bm4udA8GACxZsuT69etc8TAf3AgICJiamu7YsSMtLe3cuXOT\nJ0+WlpbOzMy0t7d3dHTk8oLcCgAAIABJREFUVvovAOD58+dBQUGCgoLHjx//rTxz6dIlMpksKCiI\nlTnvFbKysoGBgRMnTgwMDKTRaPX19du2bTt16lSvRNbs7OzIyMh9+/Z1m2fJHGtra2traxY7Q1Nf\nRUXFnupe9xY5OTnMcYEVKBTKtm3bampqzp49i9JNBgpYGbluk5DKyspgo6tLxPbt29PS0rDDs2fP\nclg8op/Q2NgYGBgIABAUFHRzc+N3OIgBjJOTU1JSUmtr65kzZ3bs2KGurs7viBAI/tDe3o6ZNldW\nVpaUlMC/FRUVZWVl2C036wgJCSkqKsKNcfCvhoYGZuA8EG/aVVVV8Xg8ltmMx+M3bdq0d+9eZWVl\nToZdunQpLHOTmpqKNOBBCXYn1qstmwgEAvEngNQdBALRGWyJc+7cufyNBDEoGTp0qI6OztevXz99\n+lRVVcU8a62f0KnU0NChQ48dO3bs2LGuPblS2pM55eXloaGhZ86cwcoWAgBsbW1jYmK4Up9JXl4+\nNDR0zZo12Bl1dfW1a9du3LjxT1iwW79+/efPn6FvM5VKffz4MRPVB+o6AgICAgICLi4uERERTEae\nP38+G/GEhITA4ovS0tL37t3Ddr6Li4snJyfPmjUrPz//169fK1euPHLkyK5du1gf2dfXNzk5ub6+\nnkgkuru7Y69IREREUlISq4UJs6IBAEOHDj1w4ICbmxvn+wx6gkajRUREtLe3Gxsb6+jo8GiWPkNP\nT2/r1q2w7vLHjx8NDQ3v37/P3Sve9+/fd+3aRafTDx069Nt83MbGxhs3bgAATE1NOQnD1tZ26NCh\nnp6edDqdRqOFh4ezrgG3trZ6enqOHz/e0tKS7QBYnwsAMHXqVPY2bXDOoUOH3r9/v3fvXk1NTeY9\na2trr1279u7du8rKyqqqKmlpaR0dHWNj46VLlyLxuI/59u0bbHRrVI4pxF2dbOfPny8qKgqTtJYv\nX758+XJehtl3REZG1tXVAQAsLS01NDT4HQ5iADN06FAHB4eTJ092dHQEBwcjQxHEIKa5ubm4uBjL\n5WXM6GXDtBkAICEhoaGhMWzYMJjF2+nvQFR5mYPD4f7+++/Xr18LCws7ODh4eXmpqalxPqyJicmW\nLVsoFMrt27ddXFz4dX+I4BGNjY0pKSkAADk5OfZ+dyMQCMQgBmnACASiM+/evQMACAgIsFdjEoH4\nLbNmzfr69SudTn/37t1AXCf966+/JCUlGSVYDOjTy1POnDkD6w5CpKSkIiIi1q1bx8Up7Ozs4uPj\n6+vrjYyMli9fPnHiRC4O3v8JCwtbtmyZn5/fq1evmPeEtSfh36qqKu6GQaPRfHx8Dh8+DADA4/GJ\niYmddqwrKCg8ffp0/vz5RUVFVCp19+7dGRkZ169fZzHPWFNTMz093dLSMjc3FztJp9M7Ojo6Ojpq\na2uxk8OHD7ezs9u+fTuvXeMeP368bds2AMCePXtGjx5tampqZmY2derUgSuDLV68GGrAAIADBw70\nyn75t3z79s3JyYlOp4eGhi5cuPC3/a9evfrr1y8REREnJycOpzY0NCwpKYGbHgoKClh8Fp1O37t3\nb0NDQ3R0dB/8n0INmF/FwC5fvnzr1i19fX0bGxvmPRMSEgIDA3V0dPbu3fvXX3+1tbWlp6f7+/u/\nePHi6dOnQUFBvNt1gehKVlYWbHT94vv27Rsspy0qKqqqqsr4EIlEMjc3x1w6nz9/XlhYyKj9U6nU\nvXv3enl5weLrAwUajRYdHQ0AwOFw9vb2/A4HMeCxsbGJjo5ub2+PjY09evTo4BOuEH8OHR0dRCKx\nrKyMSCSWl5fDLVzl5eVVVVWlpaVVVVUUCqW3Y8rKyg4bNgzKuoxJvaqqqgQCgSs7fQcQCQkJjx8/\nXrBgARc3WCsrK5ubmyckJBCJxGfPng3WwkZ/LLdu3YIbLDZs2IDH4/kdDgKBQPQvkAaMQCD+Bzqd\nDrO+lJWVB9ZCFWIA8ddff8HGp0+fBqIGjMPhgoKC0tLScnJyiERiU1OTgIDA8OHDHRwctm7dyuvZ\n/fz8qqqqzp07BwCwsLAICgr6bZIZG9y/f5/rYw4glixZsmTJkvz8/LS0tDdv3uTn55eUlNTU1LS3\nt3d0dFCpVEFBQRwOJygoKCwsjMfjRUREuOucX11dbWNj8/TpUwCAuLj47du3u12n0NTUTEtL09fX\nLywsBADgcLheGU2PHz/+69evN27cuH379sePH8vKyjo6OiQkJKSlpeXl5ceNGzdx4sQ5c+ZwsXIt\nc2AZAkhubu7Ro0ePHj0qJye3bNkyS0tLAwODAfd7Xk5ODjYkJSW5KwBnZ2c7OztLSkpGRUWNHj36\nt/2JROKVK1cAANbW1lyRRTdt2tTQ0HD9+nVTU1MWn3Lq1KnU1NTQ0NCuOZS8AG7TYcNxmnOePHkS\nHBysoqJy6NAh5j2TkpLgPo/g4GBoLywhIbFs2TISieTt7Z2SkjJ//nxjY+O+CBoBQHNzM7wHFhIS\ngvsgCQRCQ0MDlUqlUqlYt3nz5jEK8zQabd26dfByjY1jZWWVnp6OXbJKSkqCgoIuXbp0/vz5AVRP\n4cGDB/n5+QCAOXPm9M3HFjG4kZKSMjIyunHjRl1dXWxs7MaNG/kdEQLRPWQyuaSkBMvira+vZ0zq\nra+vZ6M0Lw6HIxAIjEV5Gf/25+q8fEFNTc3R0ZHrw27cuDEhIQEAcPXqVaQBDyYoFEpiYiIAQEBA\ngBfvHAQCgRjoIA0YgUD8D2VlZQ0NDQCAUaNG8TuWvqCpqamPpe76+vqjR4+OGDHCwMCAF9LdgAB7\nd/3777/8jYRtnJ2dnZ2d+TV7ZGSkgoKCsbFxn4lzfyYjRowYMWIELA/cx5SVlT179gwAMHTo0Nu3\nbzNx5tfU1Hz16pWxsXF+fv6pU6d6O5GQkJCVlZWVlRVH4XKJbiXe2traK1euXLlyRV5e3sTExNTU\ndNGiRVysp8tTsKJu3JVPHj9+7O3tPWHChGPHjmEyM3OOHj3a0tIiLy/v4uLCrTB27969e/duFjsn\nJyefO3fOxsZm0aJFnEza0tLCopoO84D7XgN+/Pixp6enuLj4yZMnf1sR9syZM7DRqb6srq4ubCQl\nJSENuM949OgRmUwGAEybNk1CQgIAICsrSyQSGfsICgoyuu6TyeQ1a9bABWVhYeHw8PBdu3a1tLRk\nZWU5ODjExsZCtfj79+8AACKR+OHDhwGkAcPXBQAwNzfnbySIQYOZmRmsSpCQkIA0YAQfIZFIMIW3\nqqqqoqKioqICJvLC7N6qqio2HJsBAHg8XllZWUVFZdj/AQ9haq+UlBTXXwiiVyxYsGD8+PFfvnz5\n8OHDixcv5syZw++IENzh5s2bpaWlAIBly5aNHDmS3+EgEAhEvwNpwAgE4n8oLi6GjT+h8Of79+83\nbNggKyurr6/v4uLSNyvF0McpIiIiIiJi+/bt69ev74NJ+xvq6uoCAgJ0Oh17vyF6BQ6Hg6ljiMHK\npEmTLCwsioqKrl+//tursbKycnp6+vv375WVlfsmPB7BPM23pqYmJiYmJiZGVFRUT0/PyMjIysqq\nnxcUhzIkAIBbdTSpVGpISMjt27c9PT1ZV2WeP3/+5MkTAMCuXbugstXHPH/+3Nvbe9asWb0qWd2V\nvLy8bdu2eXh4TJs2TVxc/NevX01NTbW1tTU1NbW1tUQikUgkVlVVwfVcvuQBP3jwYO/evQCAwMBA\nbW3t3/aHS8xds3+wyt9FRUXcjhHRI3FxcbBhZmYGG2PHjoUGCRQKRUJCYuzYsV5eXpj1eltbm7m5\n+cOHDwEAAgICMTExdnZ2oqKiDg4OAID4+HhhYeHo6GhhYeGPHz/Cp7CStd9PoFAo0BFESkqKyT4k\nBKJXjB8/XkNDo6ioKD09vaGhYciQIfyOCDE4oVAoxcXF3E3kBQAICwurqal1yuKFHs7KyspycnID\nzrHmT0NAQMDPzw962ISHh+vq6qKKG4OAtra2s2fPAgAEBAR+68GDQCAQfyZIA0YgEP8DTAIGAHA3\nO7a9vR2Px3Ne/6++vv7IkSPZ2dl+fn7Tp0/ncLQpU6YEBgZ6eHhcv37933//xdIdeIqEhIS3tzcs\nKRcTE/NnasA4HE5CQqKlpaW+vp7fsSAQ/QhYWhgSHh4+dOhQFqt/SUhIDII1ehYXztrb258+ffr0\n6VMPD4+ZM2daWlqam5t3Ks/ZT6irq4MNbrk+1NTUNDU1JSUlsS5tNjc3+/v7AwAWLVq0bNkyroTR\nKzIzM3fs2DFq1KiQkBAOLdO1tbUnT57s7u7e9SE8Hq+mpqaioqKpqamrq6uiorJ9+3YqlcpinjRX\nSEpKOnDgAJ1O9/f3ZzGzxNXV9cyZM13vBLD7pcbGRi5HieiB0tLSe/fuAQBwOJylpSU8efPmzZ76\nFxQUmJmZQe9oAQGB06dP29nZAQDs7e3fvXsHXRkuX75cWFh47ty5u3fvwmdNmjSJ1y+EW2RmZsKb\ntNmzZwsKCvI7HMTgYc6cOUVFRRQK5cmTJ9hnDYHoLS0tLbAKb3V1NdZgLNDLnsqLx+MVFRVVVFQU\nFRWHDRtGIBCUlJSGDRuGnUQq70Bn5cqVs2fPfvXq1ffv3xMSEqytrfkdEYJTIiIiqqurAQA2NjaT\nJ0/mdzgIBALRH0EaMAKB+B+w1UbuVi4MCQkBAOzZs6e3Gy3b2tpKSkqKi4tLSkry8/NTU1NhwUgn\nJ6cTJ07MmzePw8D09PRgo6KigsOhWAcTPllJEhqsSElJtbS0YHsOEAhEJ7hStHVg0dtlNSqVmpGR\nkZGRsW3bNh0dHUtLSysrK6zceH8gLy8PNrS0tLgyIIFA6NX2dhqNtmvXrvLycgUFhQMHDnAlhl6R\nnp6+Y8cOeXn506dPcyUF+eDBg9AgXVlZefr06erq6urq6pqamoqKioz7zMhkMizgiiXU8hQajXb6\n9Olz587R6fR9+/ax7t5sbm7eNZ+bRCLBvG3AYCeO4DX+/v4UCgUAsHz58t8m7j948GDNmjVwk4eQ\nkNDFixdtbW2xR8PCwsrKyu7cuQMAeP78OXZRkpeXH0CVVtLS0mADu1VGILiCrq5ubGwsACAtLQ1p\nwIhuIZFIpaWljPm7nRpsbyPulMiLpfDCv0OHDh0o1UYQnBAQEKCvr0+n08PDwxcuXNipHgdiYPHt\n2zfo4yIqKurj48PvcBAIBKKfgjRgBALxP/z69Qs2uPv7x8jIyNbW9tOnTzY2NtOmTZOXlxcWFiaT\nyWQymUQiNTc3NzY2NjU1NTY2VldXY16O5eXl1dXVAgICQ4YMkZOTk5eXV1VVzcnJAQBQKBQ/Pz9Y\nL5MTsrOzYWP+/PnddqDT6VevXo2Kitq/f7+BgQGH00FSU1Nhw8LCotsOJBLp+vXrMTExq1atcnJy\n4sqk/Q0xMTHAYJSKQCAQnKRW5OTk+Pr6+vr66ujoGBsbGxkZ6erqcm4+wSH5+fmwMW3aNL4EEBYW\nlpGRISQkFBwc3NVwmNckJSUdPHhw2LBh0dHR3NJiBQUFt2/fvn37dubd4JcLHo/vA+/rpqYmT0/P\nly9f4nA4b29vTiSN8vLy69evp6amItWNvQ9vr57F6Lvw5cuX8+fPw7aHhweTZzU0NHh4eMTExMDD\nIUOGXLt2bcmSJYx9BAUFExMTbW1tr1+/znje0NCQ7xcl1vn8+TNsoJQaBHeZPHkyrAgD0+gRfyAN\nDQ1lZWU96bvl5eXspfBCuiq7jHJv398LIfoh8+bNc3R0jIqKamlpOXToUHh4+AD6dkYwQiaTfXx8\n4L5Pb29vVAkYgUAgegJpwAgE4n9gXBHjIhMmTLCxsYmLi/P29u62g6ioqLKysqKiopKSEoFAmDZt\nGoFAUFBQUFBQkJOTg+6RRCIR8+qZNWvW7t27OQ8MW55btWoVdpJCocDfn7m5uffv34eq8759+zQ0\nNDgv5Eaj0a5duwYAUFBQmD9/flVVVV1dXW1tbXV1dVVVVVlZWUlJyb///gt/+p48eVJFRcXIyIjD\nSfsh8IcWj95vCARiIMIVe72cnJycnJxjx45paGisWLFiwYIFnI/JNpmZmQAAbW1tvmQY3L9/HypV\ne/fu7WMVB6ZWREdHa2trR0VF9U0yLiNQA+6DeX/8+LF169bS0lIhIaGAgABDQ0M2BqHT6a9evbp2\n7VplZeX69etdXFxEREQuXbrE9WgRPXH69GkymQwAWLJkCXOPGQsLC2wDoo6OTlJSUreeLsLCwgkJ\nCTo6On5+ftitjrOzM7cD5yFwl6SYmJiamhovxp80aZK0tLSKisrChQsdHR15MQWLtLW1wY2JveX2\n7dsjRowYN24cKifZKyQkJFRUVEpLS798+UKn05H0Mvjo6OggEomVlZVEIrHbRnV1Ndu/AYWFhRUU\nFAgEgrKysoKCgpKSkpKSkoKCAlxJgAsI3H05iEFJcHDwo0ePSkpK0tLSzp07N1i33Q96fHx8vn37\nBgCYOnWqp6cnv8NBIBCI/gvSgBEIRB/h6empoqKSmJhYUVGhqKg4ZsyYkSNHampqqqqqqqqq/nZP\nbnt7u5ubG5FIBADY2dnt2rWL8wWXvLy8p0+fAgDExMSuXbsGtVgox9JotE6dOzo6jh07hmV+sM3D\nhw9LSkoAADU1NbNmzYIncTicrKysvLw8zHWeOHFiZmYm1J5PnTo1KDVgBAKB6AR3S6wVFRWFh4eH\nh4fDw65XdV5TU1MDL+N8yem8d+/e/v37AQBOTk6Mm5z6gPr6+n379r18+XLSpEkRERFDhgzpy9kh\nUAPmaTFgOp0eFxcXGhra0dEhKysbEhIydepUNsYpLCz09fX98uWLu7u7ra0tKrwK6eMtYsHBwTk5\nOVlZWaGhocx7RkdHz5w5s6qqysXF5fjx4+Li4j31FBAQOHjw4OLFi729vbOysjw8PGbPns3twHkF\niUSCNgZaWlo8EjipVGp9fb2SkpK0tHRPfQoKCoYPH858nNjYWD09PbZrrlMolA0bNqxatWrlypXw\nzIoVKyQkJJSUlPT09MzMzJg8Fxrs6+joJCQksDf7H8vIkSNLS0ubm5tLS0t5tMkAwTuqq6urq6tr\namqqqqqgoAu3MmNCLyeV7EVERDopu1DWHTZsmIKCgqKiIpJ4EVxBSkrq7NmzRkZGsJzHpEmTZsyY\nwe+gEL3jzp07ycnJAAAxMbHo6Gh0C41AIBBMQBowAoHoI3A43Nq1a9euXcvGc9vb211dXXNycnA4\nnIeHB3uDdCUwMJBGowkJCY0YMaK6ulpGRkZFRUVGRkZaWhr7KyMjExoamp6eDhgqO7INiUSCgsSY\nMWNsbW2hwbW8vPzQoUM7LbFhvtNMlhcRCASi76FQKM3NzQCApqYmKpXa0dEBiwjA2my/fv3q6Oig\n0WhwBbClpQXa/re0tAAAGhsbaTRae3t7W1sbnU6HFcFbW1tJJBKFQmG7uhsr1NTU8G7wbnnw4AHM\ncOrJ9p933Lp1y9fXl0ajrVu3bsuWLX059bt37zw9PYlEopmZmZeXl7CwcF/OjgHfbwQCgUfjl5SU\nHDx48M2bNwCAkSNHRkREqKiosDHOmzdv3N3dW1tbg4KCli5dyu0wEawiLi5+//79x48fjxkzhnlP\nTU3N+/fv19TUdPJ/7gldXd1//vmHGzH2KQ0NDdBZkdceBomJiUweNTU1tbW13bx5c0+m7qmpqceO\nHYuIiAgMDGSewN0ToaGhX758+fbt2/DhwydOnAgA+PnzJwCgqqqKRe8frvgS/WlgF+eamhqkAfcf\nyGRydXV1V39mxjYnLs0CAgJKSkqYUXMnx2ZZWVlUjhfRlxgaGvr4+Pj4+NBotJ07d166dElLS4vf\nQSFY5d27d4cPH4btM2fOwG9wBAKBQPQE0oARCER/BwrAb968ERMTCwgIWLRoEVeGTUlJef36NQDA\n3d3dwcGByexwkRePx0dGRnI46YULF8rLy6FjZLfmgZCvX79WVFQAAAgEQnR0NIeTIhCIQQzUU9va\n2mADrs0xOWSlT09PGdD08X4aKpUaGxsLAJg3b56GhkafzUun0y9cuHDixAk6ne7q6tqX3rPt7e3h\n4eGxsbE4HG7fvn1Y7Qa+APOAeZEtRCKRLly4EBUV1dHRAQBYvXr1rl272Ethr6+v3717d2tr69Sp\nU5EAzHckJSXNzc1Z6TllyhReB9NbSktLL126tGzZMm65vsMNOgAAKSkprgzICqWlpcnJyU5OTti2\nSCqVevny5cuXLzN/4q9fv8LDwztpwOnp6azvgKFQKHFxcYwryJjjN2TJkiXDhg1bsGDBmjVrOj23\nH74f+j/Y+wp7pyF4DY1Gq6ys7LYEL1eq8AIAcDgcgUDoquxiDTk5Oe46viAQHOLl5fX27dt79+41\nNDQ4OzvHxsbypXoLorf8999/7u7u8Fbc1dWVWykiCAQCMYhBGjACgejX1NTUuLm5ff36VVtbOzg4\nmFt7M2tra+G2wenTp69bt45Jz9TU1La2NgDAxo0bx44dy8mk+fn5Z8+eBQC4uLgwEYABAE+ePIEN\nNze337pkIxCI/km3abJQT+1VmizMrKVSqU1NTQCA5uZmCoVCIpGgytXQ0DA46mrjcDhpaWmuLweP\nGzfu69evAABJSUnujsyc27dvV1RUCAgI9GWdy6ampv3796elpeHxeD8/v2XLlnF9CiqV2q3T2osX\nL/z9/cvKyrS0tI4cOaKjo8PdefPz89XV1VnPKoafjpycnLKyMvYydMvLy79//85YT5pGo92/f//k\nyZPl5eUAgKFDh/r4+HBScPrOnTu1tbUAgK7/XLz+ULe3t//8+XPIkCFSUlL8ytVGcBEHB4enT596\neXnNmDHDxcVl9erVHObSwa8bAEBPCbhcJz8/f9OmTUQiMS8v78iRIyIiIthDX7586elZKSkpHh4e\n8vLyFy9e7PTQvHnzOj1x/PjxcDSswXp45eXl5eXlw4YNY/0pCCZg38hIA+YWZDK5pqamurqaSCRW\nVVXBdmVlJTRqhifhrSbbwEK88vLyBAJBUVERellhbVijV0ZGhluvCIHoA3A4XFxc3MKFC9++fVtR\nUeHk5BQdHc3TSiIIzikqKnJ2doauVEZGRidOnOB3RAgEAjEAQBowAoHov+Tm5m7ZsqWystLCwsLT\n05OL3lAHDhyor6+XlpYOCAhgXufswYMHAABJSUlbW1tOZqTRaAcOHCCTyVOmTGEuCVCp1Hv37gEA\n5OXlebGCj0D8gUD7Yk5SYFnvw8/XyT3weLy4uLioqKiYmBgAADYY/3Y6yUYf7BCb9NevX9zSG5SU\nlNatW2dvb6+srNz39WhrampCQkIAADY2Nn1mTfbly5edO3eWl5f/9ddfAQEBI0eO5MUsa9euDQ4O\nVlJSws7k5uaGhYW9ePFCQEBg7dq17u7uvMjyOXv27I8fP2xtbadPn04gEERFRWk0GolEam9v//V/\nNDc3t7S0NDc3NzY2fvjwAQDw6dOn9evXP378mI0Z8/PzPT09AwMDdXV1i4qKUlNTb968CdVfAMCy\nZcv27NnD4SYtWC4a/J9zNSPV1dVYuyfdnRN+/vw5YsQI7FBUVFRWVhZ+NmX/j98eDhkyREBAgLuB\nIdgD1u4FAGRlZWVlZbm5uVlbW7u6uk6YMIG9AclkMmwICXFhueDixYvBwcHdPgTlWEZSUlKMjY3n\nz5/PysjQsLq9vb1v8pX9/f37YJY/Aex9hb3TED3R0dFRVlaGJex2yt+F1NXVwXw49sAsmhlzdju1\nkUszYrAiJSX15MmT+fPnf/r0KS8vz8bG5uzZs2zXmEfwmg8fPri5ucGdagYGBjdv3uTKjQoCgUAM\netC1EoFA8B86nb5z504SiTRq1KjZs2dDU7X4+Pjg4GAFBYXo6OgZM2ZwcbrY2Njnz5+LiIiEhoYy\nLxZIJBIzMjIAABYWFhzmkIWEhGRnZysoKAQGBjJXndPT04lEIgBg1apVKDsHMYiBCbLcUl6ZH/Lz\ndXIJAQEBqGVyS3ll3ocvcK4dioiIrFixYtOmTfr6+lA2g/nWfQmNRvP29m5ubtbQ0Ni2bVsfzNjQ\n0BAREXHjxg1BQUEnJydnZ2ferYZoamp6eHiEhoYKCwu/ffv29u3bGRkZdDpdR0dn3759vBO8t2/f\nbm1t7efnx6SPgICAlJSUpKSkhISEpKSkvr6+mpra3Llz2ZtRV1dXVlbW3d2903kNDY19+/bNnj2b\nvWEZwb7iU1NTd+3ahd1mdHR0hIWFYd0qKipUVVU5n44J7e3tsAJFb8FU4U4KMRMJWV5enjHFE8EV\nsLRdSHNz87lz56KjoxctWuTi4mJsbMz1bQS9wt7e3t7evtNJNpJxuwIVRGi20R/48OHD3r17sc0i\nXYGOFzIyMlpaWpMnT54zZw5zZyC+AHejnj17Fm6ERfAIKpVaVVXVrabLeIbzm9huNV2k7yIQGDIy\nMklJSQsWLMjPzy8vL3dwcDh16hTXLW0QnPPy5UsPDw/4pT916tSEhAR0S4lAIBAsgjRgBALBfwQE\nBExNTXfs2JGWlnbu3LnJkydLS0tnZmba29s7Ojpy90fp8+fPg4KCBAUFjx8/Pn36dOadL126RCaT\nBQUF7ezsOJn0wYMHly5dAgDMnj37tx5ZN27cAACIiIhYWlqyOD6FQsHhcMylZQTit2DmwzxNkx00\noiwAQFBQUFpaGvA4TZa/umxfIigoKCgoCPO6esvkyZOdnZ0tLS357p8fEBDw8uVLZWXlc+fO8XpR\nlUajJSYmnjx5srGxccmSJdu2beO1WGhlZWVjY7Nw4ULsjJycnLu7+8qVK3n6HaSsrHzx4sWAgIAP\nHz6IioqqqKioqqqqqakpKysrKSkpKSnJycnJyspyUejC4XCurq5eXl7YGWlp6Y0bN9ra2nJre9b4\n8eOTk5MBAPX19Rs2bHBwcKBSqdnZ2Q8fPjQzM5OVlYUG8omJidOmTXvx4sW+ffu4Mi8AQE5OztTU\ntLGxsbGxsbm5uanSpkyRAAAgAElEQVSpqbm5ubm5Gc7IOlA87pV+LCIiIiUlJSMjIyMjI/V/QFWM\n8RD6VGPw/XPdz+mkAUNoNFpKSkpKSoqioqKDg4OTk9Pw4cP7PjaeAm8n+k+F0b///vvx48dVVVXe\n3t6vX7/Gzo8fP37atGmioqLQkvfbt2+pqampqakhISEzZszYvn07h+VmuAWNRnvy5MnJkycLCwv5\nHcvAhkql1tbW1tTU1NTU1NbWEonE6upq7Az0Z66pqeF8+4KIiAj0ZFZQUFBUVIRezdCWGbYVFRWH\nDh3KlReFQAxi1NXV37x5s3z58szMzJqaGhsbG3d3dwcHB+R30k+gUCjHjx+Pi4uD1VIMDQ1v3Lgh\nLi7O77gQCARiwIA0YAQC0S/Q09PbunXr0aNHAQAfP340NDS8f/8+8yRdNvj+/fuuXbvodPqhQ4f0\n9fWZd25sbIRyrKmpKSeRZGdn+/j4iIiIuLq6JiYmLl++3M3NzdjYuNvl8ry8vJcvX8JJ5eXlWZzi\n5MmTRCLR19eXKwvT5eXlHz58SElJyczMJBAINjY2q1evRgIzv8CqwPI0TXYw6bIiIiISEhK8TpP9\nc3TZPgaPx/dqSVReXn7Dhg1r1qzpDwvoNBotKCgoISFh9OjR4eHhPK0c2draeuvWrdjY2KqqqsWL\nFzs4OPRNvsL48eP19fVTU1PhoZ6eXlBQUN/UWtbU1Dx37lwfTISxYsWKgoKCq1evqqqqmpiYWFpa\ncveVmpmZxcbGFhcXAwBycnJ27doFANDW1o6MjBw7dmxBQcE///wDALhw4cKlS5d8fX25ODWBQIiK\niurp0ba2Niz/DGt3PWQ8U1tbSyKRWJmaRCLV1tbCQsi9pae0YyaHcnJy/Ucg5BFtbW3MDXWJROKx\nY8eCgoIWLFiwadMmMzMz/qYFM4dIJCoqKrLYua6uDgDAZBWYRCIxTxIqLi5ubm7m7jcIgUDYsWMH\n41bOc+fOMV49aDRaWlrakSNHKisrs7Ky1q5d6+/vv3TpUiZj0ul0nkoRdDr9+fPnERERubm5vJtl\nENDR0VHLAJR4Gamrq4PnOZ9LUlISk3UhnQ4JBALciYhAILqFTCaXlJQUFBQUFhYWFBSIioru3r27\npy+FoUOHPnjwwMTE5OXLl1QqNTQ0NC8vb9++fX1zl4tgQnV1tZeX16tXr+Chubn51atXB/3dHQKB\nQHAXpAEjEIj+wuLFi6EGDAA4cOAA1++2v3375uTkRKfTQ0NDGXOYeuLq1au/fv0SERFxcnLiZFJn\nZ2c46dy5c62srIKCgry8vGJjYz08PGbOnNmp/9mzZ+l0upCQ0IYNG1ifxdTU1MTE5P379zY2NjNm\nzBg2bBisiwa3SdJoNCqVSv4/YAHFtra2X79+wdSfhoYGuCe9tLS0uLiYMZuksLAwICDg7du3sLYl\nAkIikVpbW3mdJjuYdNk+SJNFouzgQFRUlBUNWEhIaOnSpWvXrjUxMeknSwAtLS379+//559/Vq5c\nuX//fp5mAEdERMTFxUlKSi5fvnz16tXKysq8m6srvr6+tbW15eXlTk5Oq1evHtwZEtu2beOdoTce\nj4+NjQ0MDMzMzGxraxsxYsTy5cstLCzg6uS2bdvKysp+/vypqam5c+dOrrhPs4iYmJiYmFhvNzFg\nX2GsaMbYYUNDA7xXYQU20o4hLPpUMx4SCIT+LJQy0m0ScFdoNNrTp0+fPn2qoqLi6Ojo6uqqoKDA\n69h6y4cPH5ycnLy8vFasWMFK/x8/fgAAVFRUeupgaGhob29vaWnZ7TW5o6PDw8OjuLj47NmzkyZN\nYjvsrnSyZOj0owaHwy1YsGDMmDGrV6+ur68nkUi+vr4zZsxgku9+7NixPXv2cDHCThw5ckReXn7P\nnj1ZWVlnzpzh3UT9ExKJVFNT09WTuZM5M7duy2VkZFRUVLBrTrcWzeieFoFgHRqNVl5eDoVeCGyX\nlpZ2shdSU1Nbt25dT+PIysqmpaUdOnTo0KFDNBotOTk5IyPDw8PDxMSE9y8C0Q00Gu3ixYuRkZHw\n8isiIhIREbFp0yZ+x4VAIBADD6QBIxDsgK14sr5uhfgtcnJysCEpKcl1ATg7O9vZ2VlSUjIqKmr0\n6NG/7U8kEq9cuQIAsLa2VlJSYm/SvLw8JycnQUHB6OhouLQkLi7u4+OzcOFCHx+fjRs3GhgYeHl5\nYSs++fn5KSkpAIBVq1b1ak0flic8fPjw8ePH2QuVCcLCwh0dHVwfluvAlWWepskOJlEWh8NBW3Ke\npskiXRbRW34r6Gprazs6OtrZ2TFZ9O97MjIyDh48iMfjo6Kium7u4TojRoyIiIiYMmUKX/RXWVnZ\nq1ev9v28gxJZWdkjR450+9Dw4cOhGclAASrHUMPo1RN7SjtmkohcXV1NoVBYn4I98RgKw8wF405n\n+FJWs7m5uVf9y8rKfH19jxw5AqunL1q0iEeB9ZaysrJt27a1t7d7e3uLi4svXry4Uwd/f/9Ro0Zp\na2urq6vLyMi8f//++fPnAAAmN/ZEIjEwMDAwMBA7A+sQMzYAALt374Z34L+FQqGwUnBdQkLit32U\nlZUdHR2DgoIAAC0tLefPn9+5c2e3PTMzM69evcpTDRizmtfQ0BhMGjD0ZMbSczGqq6s7nWGeTM86\nYmJicnJy3ebsysvLw4fk5eWRwRICwR5EIpFR5YV/i4qKWDEjERIS+u1CkKCg4MGDB8eOHevo6NjU\n1FRXV7d///7nz5+7u7urq6tz6UUgWOLbt2/BwcFZWVnwUFlZOS4u7v+xd+eBUK7///ivGWsI2Sop\nkUIbUnSiElppPWm1VYrSouWU0yYK7YVWoZLqKBUtTtFGtCKpkLSeUiGMfZ35/nH/3vObj3UwjOX5\n+Ou+L9dc18s5YuZ+XdfrMjIy4mtQAADtFXLA0D5w+ZQTGdl2raSkhLrg+ZP9O3fubNu2bejQoXv2\n7GFnmuu3e/fuwsJCOTm55cuXN23Sly9frlq1SkFB4fDhw9U+MBgaGoaGhjo7O0dERLx48WLbtm3U\ncy5PT08mk9m1a9cmTDp37lwFBQU/P7/3798TQuTl5alTEuXl5WVlZSUlJSUlJcXFxSUkJERERERF\nRQUFBYWEhISFhQUEBOh0uoCAAO1/mvb9Ng2Lxbp8+TIhpLCwkNqmXFhYSAhhMBhMJpN62ss+pLa4\nuLisrIxdG7mgoKCyspLakksIadReoraMnZ2VkJAQEhISEhKilkRISUnR6XQqq0qj0aSlpQkhYmJi\nIiIi7FNpu3btKigoSBVDJoRIS0vTaDTq8XS1YQUFBanN4gBtSl05YBERkWnTpi1atGjChAltcHPe\n3bt3ly9f3tJn4rJNmTKlFWYBaB1N3nbcYLXqWpPK3E9BZY4b+d0Q8n+3HXNZtlpBQYGbzGKtuNwH\nXE15efnly5cvX76soaFha2u7bNmyFjp0ef78+W/evKnrq5yJWDYWixUQEFAzBzx48ODU1NSQkJCU\nlBTOt3wTJ06sP4bXr18TQoYNG0YISUhIoCalGqnrv//++9evX69evZowYQL1klu3bqWkpFRLygYH\nByckJOzZs6f+6QjXH13HjBlD5YAJIYmJibX2yc3N5eFZ4A1qg7vDa6qsrMzMzKy2SbfW/bu8Wrsp\nIiIiIyPDuWGXEzbvAvBcXl5etUQvpcmnaAsICJw5c4bLlZoWFhYjR460t7f/999/CSF37ty5d+/e\nrFmz7OzsWrn6Tuf08ePH48eP37lzh/233tra+tChQzjdHACgyZADhg6lqqqqDT4aBi5RmTxCiLKy\nMq/GrKqqOnjw4LVr1zZt2vTnn39y+aro6OjIyEhCyF9//cXNQv6a7t696+zsPGnSpK1bt9a6I6Rr\n164+Pj579+49f/78unXrJk+erKOjQy1yXLVqFZXea6xx48Y1eMhxGzRnzhx+h1AfERERMTGxJm+B\nbdTOWn5+nwBtQ7UcMI1GMzExsbKymjFjRls+9M7FxYXfIQB0LlTmuAkvbGzOuKSkJDMzs1oxyfq1\n3LbjmrfS0tJNywGzpaamOjs7u7u7z58/f8WKFVpaWs0ZraaLFy9SF69fvx40aFCtC2VCQ0OVlJSG\nDRtW/zKa6dOnUzWiP3365ODgkJGRQaPRbG1t9fX1GwyDyWRWVFTUleceN27cq1evgoKC2DlgZWVl\nZ2dnPT29MWPGcHbz8PAYO3YsrxbicOYSPn36VLMDi8VycXHJyspq1LBUllpGRmbp0qXNjLCVlZWV\nff/+vf6CzDzM7NJotB49etSV0K223Z8nMwJA/b5+/Wpra/vy5UtqCTiv0Gg0X1/fhQsXcv+S3r17\nh4eHBwYG/vXXX5mZmZWVlZcuXQoJCTE0NJw9e/bo0aObvHIL6lJWVhYZGRkSEhIfH89uVFFROXr0\n6OTJk/kYGABAB4A/WtA+1LO979y5c9bW1tR1YWEhtdEN2qOcnBzqom/fvrwaMzs7Oz8/PywsjPtV\n7QUFBe7u7oQQU1PTJj/iefDggYeHB/tBUq3odLqzs7OqqqqHh8e///5LLTLV1taeO3du0ybtJNhb\nYFvoNFkUMQbgo+7du797944QIisru3DhwkWLFvH2jEYA6OSasO24qKiooKCgoKAgPz8/Ly+v4H+o\n2/z8fHYLg8FgMBjUdWP3KjVt27GUlBRPHkMXFBT4+vr6+vrq6uouW7ZswIABzR+TE4vFcnd3FxYW\n3r9/v4KCAueXmEzmvn378vPzFRUV16xZw817bxUVFXd3969fv44YMaJ3797cBEBlDcXExOrqUFVV\nlZmZyb4dPHiwrKzs3r17DQwM2CuMFRQUhgwZcvDgQRMTE54cRc+Zy6y5zoDJZLq5uT148KCxwwYF\nBRFC+vbt2/ZzwCdOnLhw4QJnTeZGrbeoh7i4uKysLFV7WZaDjIwMu11OTq4tLy8D6IT++eefJvzS\nqx+NRjt69OjixYub8Fpra+uZM2cePHjwwIEDBQUFTCYzOjo6Ojq6a9euo0aNMjIy0tHRUVRU5Mvh\nLB0Dk8n8+vVrXFxcVFTU06dPOf8sysvLb9261cHBQVhYmI8RAgB0DMgBQ7vHThwS5IDbufT0dOpC\nVVWVV2N27959586d3PdnMpl//fVXRkaGvLz89u3bmzwvlUXmxpw5c5SUlJYvX85kMgkhhoaGneqA\nKBqNtnv3bkKIuLi4sLAwu0CxpKSkgIBA/TWNAaDjOX78eFBQ0LBhw6ZOncqTJ+wAAM0kLi4uLi7e\no0ePJryWyxOOOVuo4zC4HJ/BYDQhqnrEx8fb29tXS9M2H41G8/DwmDVrlo2NTWBgIOfSzNTUVGor\ns7S09Lt377hcfzl8+PDhw4cTQr58+UKj0Ro8ppE6NbmeN5DFxcXVtp1pa2vfu3cvPDx86tSpnPP6\n+/vfuHFj9uzZ3MRZvw8fPrCva34Lbm5uV65cYd9y1s2mCll3AI1N9khJSfXq1atmNeZq+3exjhOg\nnTIxMaHRaLw94OngwYNNPt6LENK1a1cXF5cVK1YcOXLEz88vIyODEFJQUHDnzp07d+4QQiQkJPr3\n79+9e3cpKamm1ZDrhKhlcxkZGenp6TVLO/Tv33/ZsmX29vY4uwoAgFeQA4Z2r1oOmI+RQDOxn4OM\nGDGCXzF4eXnFxsYKCgoeOHCghc5Fq+n169fsh31Hjx7t0aMHVemuk9i0aRO/QwCAtmLgwIEeHh78\njgIAgDeasO2Yc58x58biahuRqf3HeXl5mZmZPP8ExN4RW1lZyasxVVVVTUxMIiIi9u3bt3fvXnY7\ndRKKnJycv7+/hIREo8b8/fu3vb09k8kMCgqqP29N7bGuZ5lpQUFBSUkJZwt1Ns2///7LmQOmRrhz\n5w5PcsA3btxgX5uYmFT76vTp083MzNh71wICApo/Y9tEp9O7d+/eYEFmJHcBOjxdXd0ZM2Zcu3aN\nVwN6eXmtXr26+ePIy8u7urpu27bt+vXrQUFBkZGR7L+8hYWFL1++bP4UICsrO3nyZBsbG2opAL/D\nAQDoUJADhnYPOeAO4+nTp4QQNTU1nm8+4NKtW7eoxyt///23jo5O60x69+7do0ePEkJGjhz54sWL\nqqoqV1dXNTW1QYMGtU4AAAAdGPt5cbWH+wCdEIvFov4hYJ9KW9a1a9dGbXzZs2ePs7NzCwXDq8K8\nlDFjxkRERDx69IizkToMZcOGDRISEkwm89GjR2PHjuXswLn/tS7r168/d+5cPR2onVtqamp1dfj1\n61e1Furkkbdv33I2UitE09LSGgypQVFRUextvvLy8jUPqqz2YYSPa2Rbjqen5/z582VlZRub/geA\njmr79u2hoaE82Qp88OBBniSA2QQFBWfNmjVr1qyysrLo6Oh79+69fPny1atXNf+CAJf69OkzdOhQ\nHR2diRMnjhw5kn34AgAA8BZywNDu5ebmsq8zMjJ0dXWbM1pjl5tx3z88PHzy5MmNj6izyM7OTk5O\nJoQYGhryJYCbN29u2bKFEGJvbz9nzpzWmfTJkyebNm1isViGhoZHjhy5dOmSh4dHRUXFoUOH/Pz8\nWicGAIAOTFhYWExMrLi4GKvEAIqLi6mUHpXcgo6BKqTMWzIyMtQqW97W5P/jjz+6devGecp7cnJy\nSkqKiYmJmZkZIeTIkSP+/v779+8fP348u8/r16/37dv3+vXrwMDAagNev36devfe4KHIHz9+JIRo\naGjU1eH9+/ddu3alsg7U5zshISFCSFFRUc3OtTZyLzMz09/f/+LFi9R0ioqKPj4+nTMJqqqqSu23\nBgCgaGtr82QrsIuLy9q1a3kSUk0iIiLjx49n/6nKzMzMycnJy8vDxw0uSUlJSUlJycvLt1rtPQCA\nTg45YGj3qI/0lNTUVM5qXW1Kg88mOrnw8HAWi0Wj0XhSWq2xrl696urqymQybWxsVq5c2TqTxsTE\nrF27try8XF9f/+DBgwICAvPnz4+Li4uIiHj16lXrxAAA0OFJSUkhBwxAOOrl1HMqKrQ7vMoBCwsL\njxkzxtzcfOrUqb9+/Ro1ahRPhuWkoKAQHR3N2XL16lVFRUU3NzdCyOPHj/38/Fgs1ubNm5WUlDQ1\nNdndTE1NAwMDv3z5Ui1fSI2mqKjo7+9f/9SJiYkSEhJ6enqEEFFR0dLS0v379/fv35/dIS4urk+f\nPhUVFeR/2V81NTUJCYlqHy379OnTrVs3zhQ1N0JCQvLy8nJzcxkMxsePH9+8eUNlfyUkJCwsLJYv\nX44SxwAAbM3fCrx58+YdO3bwLqIGKCgo8KuUHQAAADeQlIL2jcVivXnzhn2bmpra/AEb7PP79285\nOTlCiLKy8ufPn+vvrKOjk5iYSJADrldVVVVQUBAhZOzYsa28GJzFYp0+ffrw4cMsFsvR0dHBwaF1\n5r1169bWrVsrKyvHjRu3b98+9jYLFxeXjx8/9unTp3XCAADo8BQVFX/8+PHr16+ysjLe7mkDaF++\nfv1KXfTq1Yu/kQAPFRQUNOflSkpKU6ZMMTc3NzY2ZhcJ52FZy8ePH9vb29ffx8DAgPO2tLQ0IiKC\nMwesra0tLy9/6dKlv/76i91YVVUVGxtLCDE2NqbT6fWMX1VV9ebNm7Fjx1LJ3WXLlvn7+589e5az\nj6io6LRp06jzj6lPbSNHjnzy5Em1oZSVlaulsbnh6uparWX8+PGWlpZaWlqoewkAUE0ztwJv3LjR\n3d2dtyEBAAC0a0hKQfv26dMnzgcfzc8BcyMzM5O66N69e4Ody8rKqAvqoQPU6tq1az9+/KDRaHZ2\ndq05b35+/pYtWx4+fCgiIuLm5jZlypRWmJTJZB46dOjMmTOEkKVLl65cuZLzuZWkpGTzCx8BAACb\nlpZWfHx8VVVVeno6jlqHzoz9Pnno0KH8jQR4qAn7gAUFBY2MjExNTc3NzVv6t+KoUaNev35ds506\n5bfWL9VEo9GmT59+8eJFe3t7SUlJqjEhIYHa2t7grtwnT54UFRXNmjWLul26dOnSpUs5wyCEhIWF\nEUKys7MJx0HyvPLgwQNRUdFz584dO3aMann79q2qqioSwAAAtXJzcwsLC2MymY194YoVK3bv3t0S\nIQEAALRfyAFD+5aUlMR5++bNm8rKypbecdu0HLCwsHALxtSeZWdnHzx4kBCyYMECLS2tVpv39evX\nGzZsyMjI0NDQ8PDw4CwH13IyMjL+/vvvhIQEWVlZV1fXsWPHtsKkAACd2eDBg6mL9+/fIwcMndn7\n9++pC3beCzoA7nPAPXr0mDZtmqmpqbGxsaysbItGxXMWFhYBAQHnzp1zdHSkWu7cuUMI6dOnz7Bh\nw+p/bXh4uJ6enr6+foOzUGuLeV4snaogZW9vn5CQ8PTpU0JIRkbGxo0bT5w4Uf8O5nr4+Pj4+vrW\n0+Hz5891/Uv39PQ0Nzdv2rwAAK2gb9++gwYN4nKdENuyZcuOHDlCnekOAAAAbE38yAHQRsTHx1MX\npqamhJD8/HyqJliLYpdH4yYHXF5eTl0gB1wrJpO5bdu2goICZWVlJyen1pk0Ly9v586dlpaWWVlZ\n9vb2Fy9ebIUEMIvFCgkJ+fPPPxMSEqZMmXLt2jUkgAEAWoGuri518ezZM/5GAsBf1D8BERERLIbo\nSBrMAaurq69bt+7u3btfvnw5efKkhYVFm00A17PlS1FRcezYsWfOnPn58ychhMFgUDt3//zzzwaH\nXbx48d9//81NAAwGgxAiLS3NbcSNQafT9+zZIy8vT90+efLEx8enJSYCAGi/fvz4sWbNGkVFxcYm\ngC0tLY8fP44EMAAAQE3YBwzt2/Xr1wkhAgIC27dvv3v3LiHk1q1bLZ1ao873JYRwnlNVl5KSEuoC\nZxDWysPDIyYmpmfPnr6+vqKioi09HZPJvHTp0pEjRxgMxsSJE52cnJSUlFp6UkLI27dvPTw8kpKS\nNDQ0nJ2d2QkJAABoaaNGjerWrVtubm50dHRVVRVqb0Ln9P79+4yMDELIuHHjxMTE+B0O8EytOWAp\nKakJEyaYm5tPmjRJQUGh9aNqgl+/ftnZ2W3ZsmXkyJG1dli+fPmDBw88PT29vLyCg4NLS0vFxcVn\nz57d4Mhqamrcx0AI6dGjB/dhN4qMjMy+ffsWL15MZbv9/PwGDx5sYmLShKGkpaX79u1b65c+f/5M\nCBEUFKzrYw774GcAgLYjMzPz8OHDR48eZf9do9FoLBaLm9fOmzfvzJkzTa6sAAAA0LEhBwzt2MeP\nH6la0Nra2oaGhvLy8llZWbdu3dq7d2+Lzvv8+XPqgpvCxewccCskONsXJpO5b9++4OBgdXV1b29v\nRUXFFp2uqKjo6tWrQUFBv379Gj9+/KJFiwYOHNiiM1I+f/7s4+MTGRmpqqq6f//+CRMmYGkqAEBr\nEhQUNDU1vXz5cn5+/uvXr7W1tfkdEQAfPHr0iLqYPHkyfyMB3hISEmJf9+3bd/LkyWZmZu0u019U\nVOTo6Pj58+cVK1Z4e3sbGhrW7KOpqWlsbHz//v2LFy9evHiREDJ37lz28cA8QW0ybtEVorq6uqtX\nrz58+DB1u2XLFlVVVRUVlcaOY2VlZWVlVeuXqBLQSkpKN27caE6oAACtIy0tbdeuXcHBwewqemJi\nYnZ2dlOnTp04cWKDpwJPmzYtMDAQqzwBAADqghwwtGPXrl2jLsaNG0ej0aZPn+7n55ecnBwXFzd8\n+PAWmpTFYsXFxVHXDT5HZrFYpaWl1HX7ehDT0goLC7ds2XL//v0ZM2Zs2bKlpRPkPj4+Fy5ckJCQ\nMDMzmzt3bs+ePVt0OkpSUtLp06fv378/YsSII0eOjB49GtlfAAC+MDc3v3z5MiEkLCwMOWDohFgs\nVmhoKCGERqPhHNAO5vjx48eOHRs2bNiUKVNaZ4FjY9nZ2dVVir/mgbUVFRXHjh2rNQdMCPnrr79i\nY2M9PDwIIVJSUosXL+YmAO4PwKZ20Pbr14/L/k2zaNGiuLi4mJgYQkhRUZGTk9OFCxewNxcAOqHk\n5OQdO3ZcuXKFneiVkpJycnJydHSkKufPnDnzypUr9YxgZmZ2+fJlzuVQAAAAUA1ywNCOXbp0ibqY\nO3cuIWTRokV+fn6EEE9Pz/rfJjbHkydPqJOiBgwY0OBhWkVFRez3svhgzxYbG7tjxw4REZFTp07V\nVe2Nt/r16+fj46Orq9uaWdjQ0NA+ffpcv35dWVm51SYFAICaLCws1q5dm5OTc+PGDScnJykpKX5H\nBNCqnj179unTJ0KIqampqqoqv8MBXjI0NKwrY9pGUB/QqqHyso097lFJScnBwcHLy4sQsmzZMi5/\nmdczS7X0cHp6OiGkpVPpdDrdw8PDwsKCKj398ePHbdu2HThwoP7PKUwmE2VOAaDDeP78+c6dO2/d\nusWu9iwjI7Nq1apVq1ZxPmdzdXW9du1aXVuBjY2NL1++LCws3BoRAwAAtFv4FAHt1cOHD6mazAMG\nDKB2/Y4aNWrAgAGEkNDQ0NTU1Baa99y5c9TF1KlTG+xcUFBAXdBoNOwDZrt79+7y5cuvX7/eOglg\nQsiUKVOGDx/eyttwt2/fvnbtWiSAAQD4rkuXLpaWloSQsrIy1MaETojaB08IWbp0KX8jAWimiooK\n6uLGjRu1noXcZFVVVWlpabKyss1/914tXVHzPMtu3bodOHCAXbk0MjLy9OnTtQ4lIiJCXfD2mwUA\n4Jd79+4ZGhrq6+vfvHmT+vXYs2fPw4cPf/nyZceOHdU2WgwaNGjmzJm1jjN27NgbN2506dKlNYIG\nAABoz5ADhvZq165d1MXChQvZjRs2bCCEMJnMbdu2tcSk5eXl7M3H06ZNa7B/bm4udSEuLo6F22wu\nLi6zZs3CfxAAAGg1y5cvp/7uBAQElJSU8DscgNaTmpp69+5dQoiiouKMGTP4HQ5A02VlZVG5UlFR\n0dTUVDs7u9+/f/Nq8JSUlOLiYkNDw+YvGy0uLua8LSsrq9lHS0tr3bp17FsvL69aK2bLyclRF+wl\nziwW6/379zZY19IAACAASURBVM2MsC7sFDsAAG+xWKwbN24YGhqamprGxsZSjUpKSidPnvz06dOa\nNWskJCRqfeGWLVtq/lrW1ta+du0aNloAAABwAzkYaJeePn167949QkiXLl3s7e3Z7ba2tn379iWE\nhISEXLx4kefzBgYG5uTkEEIUFRUNDAwa7M/OAUtKSvI8GAAAAOCShoYGtWgsKysrMDCQ3+EAtJ6D\nBw9SuxJdXFxwYB60a7t37y4pKZk/f/7x48dFRERSUlIWLFhAFXBuPioFa2pq2vyhMjMz67lls7Ky\nGjduHHXNZDI3bNhA1WznpK6uTl14eXl9+fLl27dvnp6ewcHBzQ+yVt++fWNfY70UAPBEVVVVYGCg\njo7OtGnT2Nnf/v37nz179sOHD8uWLWMXPKgV9ULOlsGDB0dGRnbr1q0FgwYAAOhAkAOG9qeqqmr9\n+vXU9dKlS7t3787+kpCQkIuLC3Xt6OjI+SG2+YqLizkHZxfvqgf7Az/engIAAPDX1q1bBQUFCSFn\nz57l4dYxgLbsyZMnT548IYSoqqra2tryOxyAprt9+3ZERMSAAQPWr18/fPjw/fv3CwgIZGRkzJs3\nLyQkpPnj37t3r2fPnmPGjGnmOBUVFezDgyh+fn61bgWm0Wi7du1SVFSkbvPy8qytrRMSEjhrR1tY\nWFAXb968MTc3nzx5ckZGxsaNG5sZZK1YLFZQUBD79tGjRy0xCwB0HpWVlYGBgVpaWjY2Nq9evaIa\nNTU1L126lJqaam1tzeVRvi4uLuytwOrq6pGRkewaCQAAANAg5ICh/fH09Hz8+DEhREREpOYHYBsb\nGyMjI0JIbm6upaVleXk5r+Y9fPhwRkYGIURMTMzBwYGbl7BzwHiHCgAAwF8DBgxYtGgRIaSgoMDT\n05Pf4QC0uNLSUjc3N+ra1dWVyyetAG3Qf//9t3PnTnl5+aNHj1I7xoyMjHbt2kWn08vKylxdXR0d\nHalPajUNqRvn+G/evLG0tGzOaTUJCQnz5883MTGplpO+du2asbHxnDlzwsPDq71EUlLywIED1Pok\nQkheXh71YZa9Vc7Q0NDFxUVZWVlUVFRDQ2PLli3e3t48/7ccHBzs7Ow8Y8YM9rFHhJC//vrL2tp6\n8+bNLbftGAA6Kmo1jLa2to2Nzdu3b6lGDQ2NM2fOJCUlWVhYNOqXrY6OzuzZswkh/fr1u3fvXo8e\nPVokaAAAgA5KkN8BADROXFwc+2GWs7Nzr169qnWg0Wh+fn5DhgwpKSmJioqaP3/+pUuXuNmzW7+E\nhAT2vI6OjjIyMty8iv0kQkFBoZkB1PT9+/ecnJw+ffpISUnxcFj2e3HOFegAPEfVpcSx0ADQmjw9\nPcPCwjIzM+/cuWNmZsYuwgnQIR05coQqimNsbEzVQgdoj4qLi1evXi0gIHD8+HHOR//m5ubS0tKb\nNm3Kz8+Pjo4uKys7depUzWMjX79+XdfI7DTw5cuXFRUV582bV2u3ekbgNGzYsCacRjR48OCXL1/W\n02H27NlU8oNLXEbLae7cuXPnzm3sqwAAasrJyfH29j5+/DhnGfyRI0fu3LmzOcX2z5496+DgoKWl\nJSsry4swAQAAOhE8fIf25OfPn/Pnz6+oqCCEDBo0aPPmzbV269evn7e3N3V99erVxYsXNzOdmZeX\nN3v2bKqEV+/evbdv387lC798+UJd9OzZszkB1PT48WMVFZWhQ4dKS0vLyMgMGzZs1qxZ69at8/b2\nvnHjRlJSUn5+ftNG7tq1K3VRXFzMu3gBqisqKiI4KhsAWpesrOzx48ep661bt/L2zAiANuX+/fvU\n0dcSEhIBAQE1E2MA7UJ5efnq1asZDMbp06fZh+OyGRoaBgcHDxgwoE+fPl5eXk37OWcwGJcvX968\neTP2ygMANFlWVtb27dv79+/v6urKTgDr6+tfv3798ePHzTxtvUuXLsbGxkgAAwAANAH2AUO7kZmZ\naWxsnJ6eTggREhIKCAio51O6nZ1dQkIC9Zw3MDCQxWL5+vqKioo2Yd6SkpI5c+Z8+vSJECIgIBAU\nFCQhIcHlaz9+/EhdKCkpNWHqeiQnJ1O5cEJIbm5ubm5uzfXjMjIyff8vFRWVvn371h8/e1dxQUEB\nb2MG4EQtU5CWluZ3IADQucyaNWvGjBmhoaH5+fkbN248c+YMHvpDx/Pz588dO3ZQiyDd3NyUlZX5\nHRFAE504caKkpOSff/6pq66SkpLS+fPnf/z4IS4u3tjBqS2zDx8+nDZtWvNPAgYA6JySk5N3794d\nHBzMPotNQEBgwYIFTk5Ow4YN429sAAAAgBwwtA9ZWVnGxsYpKSnU7bFjx/T09Op/iZeXV2pq6oMH\nDwgh586dS01NvXr1amNzsYWFhebm5lFRUdTtvn37GvV0IDU1lbro169fo+Zt0PDhwxvsk5OTk5OT\nk5CQUK1dVla21tww9dyEnZNjMBi8jRmAraysrLS0lCAHDAD8cPr06Tdv3qSnp79+/drNzW3nzp3Y\nIgkdSWlp6fr163Nzcwkhs2bNcnJy4ndEANVxU6+Y6lNcXOzg4FD/Yh1RUVEVFZWmzUIIMTIyMjIy\n4qZnEwYHAOjAYmNjd+/efevWLXbtvS5duixdunT16tU8fwgGAAAATYMcMLQDz549W7BgAXtP7fr1\n6+3s7Bp8lZCQ0I0bNyZPnvzo0SNCyIsXL3R1dYODg7n/hJ+RkTFz5sznz59Tt2vXrl27di33YcfH\nx2dlZVHXGhoa3L+QG4MHDxYXF6eq6TbW79+/f//+HR8fX61dXl5eWVlZUVGRun3//n1zowSoA/un\na8CAAfyNBAA6IWlp6Zs3b+rp6eXn54eFhYmJidV1ugRAu1NeXr5y5cqkpCRCyODBgwMDA7HEAdo1\nMTExfocAAAD/B4vFunnz5p49e2JjY9mN3bp1W7169YoVK+oq2wAAAAB8gfOAoU1jMpmenp6Ghobs\nBLC9vf3evXu5fLm4uHh4ePjo0aOpW6qa9LJly3Jychp8bUhIyJAhQ9gJ4HXr1h08eLBmt+joaH9/\n/4iIiKSkpB8/fhQXFzOZzIKCgsjIyPnz51N9unbtWvPwqmYSFBTkZitwo2RlZcXFxV2/fp26TUtL\n4+34AGzv3r2jLoYMGcLfSACgc1JXVz99+rSAgAAh5OLFixcuXOB3RAA8wGQyt2/f/uzZM0KInJxc\nSEhIE6rjAgAAANSqtLTUy8tLXV192rRp7ASwkpLS4cOHv3z5smPHDiSAAQAA2hrkgKHtevr0qZGR\n0ebNmysrK6mWrVu3njhxgk5vxM+thIREREQEOx3LYrFOnTpFPfllF6up5r///rOysrKwsKBSxXQ6\n/cCBAwcOHKi1c3Jysp2d3cSJE7W0tBQVFcXFxQUEBCQlJSdMmMDe6Thv3jzqKTNv6evr83xMCrVf\nJD8/PyMjo4WmgE6OnQMePHgwfyMBgE5r1qxZZ86cod5UeHp6Hjp0iN8RATRLaWnpmjVrbt26RQjp\n1q3b/fv3eb4GEToJduFl9qcwAB6qqKigLkRERPgbCQBwj8Fg7NixQ0VFxcnJif2wa+DAgWfPnv3w\n4cOaNWu6du3K3wgBAACgVsgBQ1v04sWLyZMn//HHH1QZZ0KIuLi4v7//zp07mzCaqKjohQsXOE/7\ny87O9vLyKisrq9YzMzPTycmpf//+QUFBVIu8vHx4ePi6devqGlxNTa3+2fv06bN9+/YmhN2gFsoB\nDx8+3N7enrqOiYlpiSkAqB8tYWFhnm9nBwDgnqWl5a5du6jrgICAffv21bU+DKCNKywsdHR0fPjw\nISFEREQkODgYlTagyaSlpamL/Px8/kYCHRL756pbt278jQQAuJGRkbFmzZo+ffq4urr+/PmTajQw\nMLh+/fqbN2+sra3rP7IdAAAA+As5YGhzCgoK5s6de/v2bXaLnp7ey5cvFy9e3Jxht27dGhkZqaSk\nRAiRkpK6cuWKqKhotT7R0dHe3t7s3LCZmdmrV68mTpxYz7ADBgyQlpaWkJAQFRUVEhKi0+lUprlL\nly7q6upOTk5PnjyhJuW5UaNG8XZAeXn5s2fPPn/+3MHBgWqJiori7RQAhJAPHz78999/hBAjIyNJ\nSUl+hwMAndrff/997NgxajdwYGDgihUrGAwGv4MCaJz379/PnTuXOsFEVlY2Kipq/Pjx/A4K2jF2\nDriwsJC/kUCHVFBQQF2wf9IAoG169+6dtbW1qqqqt7c3tXqDTqdbWFg8evQoJiZm6tSp7I0WAAAA\n0GYhBwxtTteuXcPDw6lFwfLy8l5eXrGxsf3792/+yCYmJq9fv7a0tAwMDOzXr1/NDrNnz3Z3dyeE\n9OzZMygo6ObNmz179qx/zD59+uTm5hYUFJSUlJSXl1dVVTGZTBaLVVxcnJqaeujQIUVFxeZHXqse\nPXooKyvzZCg6nb569Wrq/T2NRhs6dCgV9osXL4qKingyBQDbgwcPqItJkybxNxIAAELI8uXL/f39\nBQUFCSExMTFWVlafPn3id1AA3Hr48KG1tfXXr18JIfLy8rdv326540Kgk5CSkqI2dbH3ewHw0I8f\nP6gLnBsK0Ga9ffvW1tZ26NCh586do7ZJCAgIzJkz5/nz55cuXTI0NOR3gAAAAMAtWuuXvMvNzU1J\nSXn79u3nz5/z8vIYDAaDwSgtLW3lMNomcXFxaWlpKSkpaWlpdXV1TU1NDQ2NLl268DsuPoiKirp/\n//6GDRta/0yRoKCgGTNmSEhItPK8jVJZWfnmzRs7O7v4+PhmDjVkyJBjx45VexO/cuXKo0ePEkK2\nbt06d+7cZk4BwMZkMs3MzL59+0an09PT01VUVPgdEQAAIYRERERYWlpmZWURQkRFRZcvX25jYyMg\nIMDvuADqxGAwDhw4EBoaSn2g09bWvnz5coPHlABwQ1tb+9WrV4KCgs+fPxcSEuJ3ONChGBsbZ2Vl\nKSgo/Pr1i9+xAMD/UVVVdfXqVWonBrtRWlp6zZo1Dg4OPXr04GNsAAAA0DStlANmsVjPnz8PDQ0N\nDQ1NTU1thRk7DDqdrqenZ2ZmZmZmpq2tjUIrnRaLxUpOTo6Pj4+NjY2JiUlLS6usrGzmmF27dt25\nc6ejoyO1+YlTSkrKoEGDWCyWqqpqaGgofvCAV6Kjox0dHQkh5ubmN27c4Hc4AAD/v2/fvs2dO/fx\n48fUrbq6+ubNm4cNG8bfqABqYjKZN27cOHjwYE5ODtWyZMkSHx+fzrlyFFqCpaXl+fPnCSHXrl3D\nwgLgodzc3DFjxhBCxo0bd//+fX6HAwD/n6KiIj8/Px8fnw8fPrAbFRUVN27cuGjRIhzhBAAA0H5V\nT/zw3NevX0+fPn369OkvX7609FwdEpPJfPr06dOnT7dt2zZw4MBVq1ZZWVmJi4vzOy5oDb9//378\n+DGV933x4gVvTyi0srLavXt3XaWqNTU1DQ0NHz169PHjx2fPno0cOZKHU0NnduHCBepi6dKl/I0E\nAKAaJSWlhw8furu7e3h4VFRUvHv3zsbGxsjIaPXq1Tw5kwKAJ6Kiory9vdPS0qhbeXl5b2/vefPm\n8Tcq6GC0tbWpHPDLly+RAwYeSkhIoC60tbX5GwkAULKzs0+ePHnkyBHO+v99+/Zds2aNnZ1dG6+Q\nBwAAAA1qwX3ASUlJW7duvXXrFpPJZDfS6fSBAwdSJY7V1NSkpKQkJSUlJSVFRERaKIz2paSkhMFg\n5Ofn//79OzU19f3790lJSdXS59LS0itWrNiwYQN1Yi50JCwW6/3798+ePXv27NnTp0+TkpIqKipq\ndhMQEBg4cKC+vr6uru7q1atr7VMPFRUVb29vc3Pz+ruFhIRYWFgQQoYMGXL+/HlsBYbme/HixeLF\niwkhampqqampKLIKAG1TUlLSkiVL4uLiqFs6nT569Og///xzzJgx+MUF/FJUVPTvv/9eunQpJSWF\n3Th//nwvLy95eXk+BgYd0ps3b4YMGUIIGT169LFjx/gdDnQc27ZtCw0NJYTcuXNnwoQJ/A4HoFN7\n/vz5/v37w8LCysvLqRYajWZmZrZmzRoTExM8AgIAAOgYWiQH/Pnz523btl24cIGd/RUQEBgzZoyJ\nicno0aNlZGR4PmPH9uXLl4cPH0ZERCQlJbEbpaSk1q1bt27dOizKa+8+f/4cHR0dHx8fHx+fmJhY\nVFRUsw+NRtPU1NTV1TU0NDQwMFBXV2dXb9bT03vx4gWXc4mIiDg7O2/atImbUoEsFktXV/fly5eE\nkMOHD5uYmHD9PQHUbuHChdTvsfPnzy9YsIDf4QAA1KmqqurMmTOurq7//fcfu1FBQcHExMTIyGj4\n8OHCwsJ8DA86j/z8/NjY2IcPHz58+LC4uJjdrqent3v37nHjxvExNujAWCxWnz59vn37JioqGhMT\ngxXbwBMsFsvU1DQzM1NcXDw7O1tUVJTfEQF0RiwW6+bNm3v27OE89FdUVNTa2nrFihVaWlp8jA0A\nAAB4jsc5YCaT6ePjs2XLFnYeq3v37nPmzJkxY4aCggIPJ+qc0tLSQkJCwsLC2A+AlJWVT548OXHi\nRP4GBo1SUlJCnelL5X1//PhRa7du3boZGBjo6urq6uqOGDGiR48etXZbtWrVkSNHuJl3/PjxR48e\nbVQ1y4iICOqnq2fPnteuXUMRcmiOK1eu7NixgxCiq6v74sULLCsGgLavtLT06NGjhw4d+v79O2e7\nmJiYurr6gAED1NXVZWVlJSUlxcTE+BUkdDAFBQUMBuPnz59p/1NVVcXZQUdHZ/PmzX/++Sf+kkKL\ncnBwOHnyJCHE09OzwQJCANx4+vQpdRzMtGnTwsLC+B0OQKdTXFx86tSpI0eOpKensxvl5OQcHR2X\nL1/evXt3PsYGAAAALYSXOeC0tDRbW9snT55Qt926dbOzs5s7dy5WDfPW79+/T548GRISwq4AbGtr\ne/jwYSkpKf4GBnVhsVjJycnsvG9aWlplZWXNbnQ6XUdHh5331dDQ4KbgZFBQkJWVVf19FBQUjhw5\nQhV2biwTE5P79+8TQmxtbdevX9+EEQAIITk5OdOnT8/LyyOE3L59GytXAKAdqaysvHHjxokTJ+7d\nu1ctGwfQasTExObMmePg4KCvr8/vWKBTeP78OfXDNnToUOpsYIBmcnJyunfvHiEkNDR0+vTp/A4H\noBP5/v27j49PQEBAVlYWu3HgwIGbNm3CY1sAAICOjWc54EuXLtnZ2RUUFBBC6HT6vHnzVq1ahTLF\nLefbt29ubm7sjLuamlpISAhqtrQdv3//fvz4cXx8fGxs7PPnz/Pz82vt1r179zFjxlB5X21t7Sb8\nk0lPT69na6+AgICjo6Orq6u0tHRjR2aPP3To0JKSEjqdHhQURB0MBtBYGzZsuHPnDiFk4cKFQUFB\n/A4HAKApsrOzb9++fevWraioqLrKeADwEI1GU1NTGz9+vLm5uZGRETdneQDwkI6OTmJiIiEkJCRE\nXV2d3+FA+5aZmTlx4sTKykpFRcUvX76wzzY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oDt1nwFeuXJEO/vnP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\nAAAAAKDr+H+FR5WLZOfvxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(\"images/fig_5_5.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n",
      " 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47\n",
      " 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63]\n"
     ]
    }
   ],
   "source": [
    "import multiprocessing as mp\n",
    "\n",
    "def square(x):\n",
    "    return np.square(x)\n",
    "\n",
    "x = np.arange(64)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### プロセスプールで分散"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "# Dockerのプロセス数を2個から３に変更\n",
    "# numCpu = mp.cpu_count()\n",
    "numCpu = 2\n",
    "print(numCpu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([  0,   1,   4,   9,  16,  25,  36,  49,  64,  81, 100, 121, 144,\n",
       "        169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625,\n",
       "        676, 729, 784, 841, 900, 961]),\n",
       " array([1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764,\n",
       "        1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809,\n",
       "        2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969])]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pool = mp.Pool(2)\n",
    "count = 64/numCpu\n",
    "squared = pool.map(square, [x[count*i:count*i+count] for i in range(numCpu)])\n",
    "squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### mp.Processを使った表現"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In process 0\n",
      "In process 1\n"
     ]
    }
   ],
   "source": [
    "def square(i, x, queue):\n",
    "    print(\"In process {}\".format(i))\n",
    "    queue.put(np.square(x))\n",
    "    \n",
    "processes = []\n",
    "queue = mp.Queue()\n",
    "x = np.arange(64)\n",
    "\n",
    "for i in range(numCpu):\n",
    "    start_index = count*i\n",
    "    proc = mp.Process(target=square, args=(i, x[start_index:start_index+count], queue))\n",
    "    proc.start()\n",
    "    processes.append(proc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "joinですべてのprocの処理が完了するのを待ちます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for proc in processes:\n",
    "    proc.join()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "procを終了させ、queueから結果を集めます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([  0,   1,   4,   9,  16,  25,  36,  49,  64,  81, 100, 121, 144,\n",
       "        169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625,\n",
       "        676, 729, 784, 841, 900, 961]),\n",
       " array([1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764,\n",
       "        1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809,\n",
       "        2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969])]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for proc in processes:\n",
    "    proc.terminate()\n",
    "results = []\n",
    "while not queue.empty():\n",
    "    results.append(queue.get())\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 共有メモリを使って学習結果を更新"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch import optim\n",
    "import numpy as np\n",
    "from torch.nn import functional as F\n",
    "import gym\n",
    "import torch.multiprocessing as mp \n",
    "\n",
    "class ActorCritic(nn.Module): \n",
    "    def __init__(self):\n",
    "        super(ActorCritic, self).__init__()\n",
    "        self.l1 = nn.Linear(4,25)\n",
    "        self.l2 = nn.Linear(25,50)\n",
    "        self.actor_lin1 = nn.Linear(50,2)\n",
    "        self.l3 = nn.Linear(50,25)\n",
    "        self.critic_lin1 = nn.Linear(25,1)\n",
    "    \n",
    "    def forward(self,x):\n",
    "        x = F.normalize(x,dim=0)\n",
    "        y = F.relu(self.l1(x))\n",
    "        y = F.relu(self.l2(y))\n",
    "        actor = F.log_softmax(self.actor_lin1(y),dim=0) \n",
    "        # ここで、Actorから切り離し、Criticのレイヤーに進む\n",
    "        c = F.relu(self.l3(y.detach()))\n",
    "        critic = torch.tanh(self.critic_lin1(c)) \n",
    "        return actor, critic "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分散学習\n",
    "- .view(-1)は、多次元配列をフラットにする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run_episode(worker_env, worker_model):\n",
    "    state = torch.from_numpy(worker_env.env.state).float() \n",
    "    values, logprobs, rewards = [],[],[] \n",
    "    done = False\n",
    "    j=0\n",
    "    while (done == False):\n",
    "        j+=1\n",
    "        policy, value = worker_model(state)\n",
    "        values.append(value)\n",
    "        logits = policy.view(-1)\n",
    "        action_dist = torch.distributions.Categorical(logits=logits)\n",
    "        action = action_dist.sample()\n",
    "        logprob_ = policy.view(-1)[action]\n",
    "        logprobs.append(logprob_)\n",
    "        state_, _, done, info = worker_env.step(action.detach().numpy())\n",
    "        state = torch.from_numpy(state_).float()\n",
    "        if done:\n",
    "            reward = -10\n",
    "            worker_env.reset()\n",
    "        else:\n",
    "            reward = 1.0\n",
    "        rewards.append(reward)\n",
    "    return values, logprobs, rewards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update_params(worker_opt,values,logprobs,rewards,clc=0.1,gamma=0.95):\n",
    "    # 現在のバージョンには、flilpがないので、以下の関数で代用\n",
    "    def flip(x, dim):\n",
    "        indices = [slice(None)] * x.dim()\n",
    "        indices[dim] = torch.arange(x.size(dim) - 1, -1, -1,\n",
    "                                    dtype=torch.long, device=x.device)\n",
    "        return x[tuple(indices)]\n",
    "    # rewards = torch.Tensor(rewards).flip(dims=(0,)).view(-1) \n",
    "    # logprobs = torch.stack(logprobs).flip(dims=(0,)).view(-1)\n",
    "    # values = torch.stack(values).flip(dims=(0,)).view(-1)\n",
    "    rewards = flip(torch.Tensor(rewards), dim=0).view(-1) \n",
    "    logprobs = flip(torch.stack(logprobs), dim=0).view(-1)   \n",
    "    values = flip(torch.stack(values), dim=0).view(-1)\n",
    "    Returns = []\n",
    "    ret_ = torch.Tensor([0])\n",
    "    for r in range(rewards.shape[0]): \n",
    "        ret_ = rewards[r] + gamma * ret_\n",
    "        Returns.append(ret_) \n",
    "    Returns = torch.stack(Returns).view(-1)\n",
    "    Returns = F.normalize(Returns,dim=0)\n",
    "    # Criticヘッドからのバックプロパゲージョンを防ぐために、valuesを切り離す\n",
    "    actor_loss = -1*logprobs * (Returns - values.detach()) \n",
    "    critic_loss = torch.pow(values - Returns,2) \n",
    "    loss = actor_loss.sum() + clc*critic_loss.sum() \n",
    "    loss.backward()\n",
    "    worker_opt.step()\n",
    "    return actor_loss, critic_loss, len(rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def worker(t, worker_model, counter, params, queue):\n",
    "# def worker(t, worker_model, counter, params):\n",
    "    worker_env = gym.make(\"CartPole-v1\")\n",
    "    worker_env.reset()\n",
    "    worker_opt = optim.Adam(lr=1e-4, params=worker_model.parameters()) \n",
    "    worker_opt.zero_grad()\n",
    "    for i in range(params['epochs']):\n",
    "        worker_opt.zero_grad()\n",
    "        values, logprobs, rewards = run_episode(worker_env, worker_model) \n",
    "        actor_loss,critic_loss,eplen = update_params(worker_opt, values, logprobs, rewards) \n",
    "        #queue.put([counter.value, actor_loss,critic_loss,eplen])\n",
    "        queue.put(eplen)\n",
    "        counter.value = counter.value + 1 \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下の処理は、分散処理のテストで行ったのとまったく同じ形式です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1999, 0)\n"
     ]
    }
   ],
   "source": [
    "MasterNode = ActorCritic() \n",
    "MasterNode.share_memory() \n",
    "processes = [] \n",
    "queue = mp.Queue()\n",
    "params = {\n",
    "    'epochs': 1000,\n",
    "    'n_workers': 2,\n",
    "}\n",
    "counter = mp.Value('i',0) \n",
    "for i in range(params['n_workers']):\n",
    "    p = mp.Process(target=worker,args=(i, MasterNode, counter, params, queue))\n",
    "    # p = mp.Process(target=worker,args=(i, MasterNode, counter, params))\n",
    "    p.start()\n",
    "    processes.append(p)\n",
    "for p in processes: \n",
    "    p.join()\n",
    "for p in processes: \n",
    "    p.terminate()\n",
    "    \n",
    "print(counter.value, processes[1].exitcode)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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       " 27,\n",
       " 51,\n",
       " 25,\n",
       " 19,\n",
       " 37,\n",
       " ...]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = []\n",
    "while not queue.empty():\n",
    "    results.append(queue.get())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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AtaK0HKOjoxwZGeHu3feMF6k1Owjsg84MAs/LmcmUuXv3PYljahTA3r37nikHu9sFNDlw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\nUZREVEkoiqIoiaiSUBRFURL5/wFxPveOm0XHWgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f696117f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(results)):\n",
    "    plt.scatter(i, results[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def run_episode(worker_env, worker_model, N_steps=10):\n",
    "    raw_state = np.array(worker_env.env.state)\n",
    "    state = torch.from_numpy(raw_state).float() \n",
    "    values, logprobs, rewards = [],[],[] \n",
    "    done = False\n",
    "    j=0\n",
    "    G=torch.Tensor([0])\n",
    "    while (j < N_steps and done == False):\n",
    "        j+=1\n",
    "        policy, value = worker_model(state)\n",
    "        values.append(value)\n",
    "        logits = policy.view(-1)\n",
    "        action_dist = torch.distributions.Categorical(logits=logits)\n",
    "        action = action_dist.sample()\n",
    "        logprob_ = policy.view(-1)[action]\n",
    "        logprobs.append(logprob_)\n",
    "        state_, _, done, info = worker_env.step(action.detach().numpy())\n",
    "        state = torch.from_numpy(state_).float()\n",
    "        if done:\n",
    "            reward = -10\n",
    "            worker_env.reset()\n",
    "            G=torch.Tensor([0])\n",
    "        else:\n",
    "            reward = 1.0\n",
    "            G = value.detach()\n",
    "        rewards.append(reward)\n",
    "    return values, logprobs, rewards , G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update_params(worker_opt,values,logprobs,rewards, G, clc=0.1,gamma=0.95):\n",
    "    # 現在のバージョンには、flilpがないので、以下の関数で代用\n",
    "    def flip(x, dim):\n",
    "        indices = [slice(None)] * x.dim()\n",
    "        indices[dim] = torch.arange(x.size(dim) - 1, -1, -1,\n",
    "                                    dtype=torch.long, device=x.device)\n",
    "        return x[tuple(indices)]\n",
    "    # rewards = torch.Tensor(rewards).flip(dims=(0,)).view(-1) \n",
    "    # logprobs = torch.stack(logprobs).flip(dims=(0,)).view(-1)\n",
    "    # values = torch.stack(values).flip(dims=(0,)).view(-1)\n",
    "    rewards = flip(torch.Tensor(rewards), dim=0).view(-1) \n",
    "    logprobs = flip(torch.stack(logprobs), dim=0).view(-1)   \n",
    "    values = flip(torch.stack(values), dim=0).view(-1)\n",
    "    Returns = []\n",
    "    ret_ = torch.Tensor([G])\n",
    "    for r in range(rewards.shape[0]): \n",
    "        ret_ = rewards[r] + gamma * ret_\n",
    "        Returns.append(ret_) \n",
    "    Returns = torch.stack(Returns).view(-1)\n",
    "    Returns = F.normalize(Returns,dim=0)\n",
    "    # Criticヘッドからのバックプロパゲージョンを防ぐために、valuesを切り離す\n",
    "    actor_loss = -1*logprobs * (Returns - values.detach()) \n",
    "    critic_loss = torch.pow(values - Returns,2) \n",
    "    loss = actor_loss.sum() + clc*critic_loss.sum() \n",
    "    loss.backward()\n",
    "    worker_opt.step()\n",
    "    return actor_loss, critic_loss, len(rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def worker(t, worker_model, counter, params, queue):\n",
    "# def worker(t, worker_model, counter, params):\n",
    "    worker_env = gym.make(\"CartPole-v1\")\n",
    "    worker_env.reset()\n",
    "    worker_opt = optim.Adam(lr=1e-4, params=worker_model.parameters()) \n",
    "    worker_opt.zero_grad()\n",
    "    for i in range(params['epochs']):\n",
    "        totalEplen = 0\n",
    "        worker_opt.zero_grad()\n",
    "        while True:       \n",
    "            values, logprobs, rewards, G = run_episode(worker_env, worker_model) \n",
    "            actor_loss,critic_loss,eplen = update_params(worker_opt, values, logprobs, rewards, G) \n",
    "            totalEplen += eplen\n",
    "            if G[0] == 0:\n",
    "                break\n",
    "        #queue.put([counter.value, actor_loss,critic_loss,eplen])\n",
    "        queue.put(totalEplen)\n",
    "        counter.value = counter.value + 1 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Process Process-37:\n",
      "Process Process-36:\n",
      "Traceback (most recent call last):\n",
      "  File \"/usr/lib/sagemath/local/lib/python/multiprocessing/process.py\", line 258, in _bootstrap\n",
      "Traceback (most recent call last):\n",
      "    self.run()\n",
      "    self._target(*self._args, **self._kwargs)\n",
      "  File \"/usr/lib/sagemath/local/lib/python/multiprocessing/process.py\", line 258, in _bootstrap\n",
      "    self.run()\n",
      "  File \"/usr/lib/sagemath/local/lib/python/multiprocessing/process.py\", line 114, in run\n",
      "  File \"<ipython-input-67-894bd948c072>\", line 11, in worker\n",
      "  File \"/usr/lib/sagemath/local/lib/python/multiprocessing/process.py\", line 114, in run\n",
      "    values, logprobs, rewards, G = run_episode(worker_env, worker_model)\n",
      "  File \"<ipython-input-61-da37dc4b86ca>\", line 10, in run_episode\n",
      "    policy, value = worker_model(state)\n",
      "    self._target(*self._args, **self._kwargs)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/nn/modules/module.py\", line 491, in __call__\n",
      "  File \"<ipython-input-67-894bd948c072>\", line 11, in worker\n",
      "    values, logprobs, rewards, G = run_episode(worker_env, worker_model)\n",
      "    result = self.forward(*input, **kwargs)\n",
      "  File \"<ipython-input-25-0333e7af6444>\", line 24, in forward\n",
      "  File \"<ipython-input-61-da37dc4b86ca>\", line 14, in run_episode\n",
      "    action = action_dist.sample()\n",
      "    c = F.relu(self.l3(y.detach()))\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/nn/modules/module.py\", line 491, in __call__\n",
      "    result = self.forward(*input, **kwargs)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/distributions/categorical.py\", line 84, in sample\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/nn/modules/linear.py\", line 55, in forward\n",
      "    return F.linear(input, self.weight, self.bias)\n",
      "    probs = self.probs.expand(param_shape)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/nn/functional.py\", line 996, in linear\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/distributions/utils.py\", line 185, in __get__\n",
      "    output += bias\n",
      "KeyboardInterrupt\n",
      "    value = self.wrapped(instance)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/distributions/categorical.py\", line 67, in probs\n",
      "    return logits_to_probs(self.logits)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/distributions/utils.py\", line 138, in logits_to_probs\n",
      "    return softmax(logits)\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-68-f27985c46bae>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0mprocesses\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mprocesses\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m     \u001b[0mp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     17\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mprocesses\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m     \u001b[0mp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mterminate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/sagemath/local/lib/python/multiprocessing/process.pyc\u001b[0m in \u001b[0;36mjoin\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m    143\u001b[0m         \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent_pid\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetpid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'can only join a child process'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    144\u001b[0m         \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_popen\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'can only join a started process'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 145\u001b[0;31m         \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_popen\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwait\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtimeout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    146\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    147\u001b[0m             \u001b[0m_current_process\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_children\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscard\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/sagemath/local/lib/python/multiprocessing/forking.py\u001b[0m in \u001b[0;36mwait\u001b[0;34m(self, timeout)\u001b[0m\n\u001b[1;32m    152\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0mwait\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtimeout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    153\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mtimeout\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 154\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpoll\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    155\u001b[0m             \u001b[0mdeadline\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mtimeout\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    156\u001b[0m             \u001b[0mdelay\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.0005\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib/sagemath/local/lib/python/multiprocessing/forking.py\u001b[0m in \u001b[0;36mpoll\u001b[0;34m(self, flag)\u001b[0m\n\u001b[1;32m    133\u001b[0m                 \u001b[0;32mwhile\u001b[0m \u001b[0mTrue\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m                     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 135\u001b[0;31m                         \u001b[0mpid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwaitpid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    136\u001b[0m                     \u001b[0;32mexcept\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merror\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m                         \u001b[0;32mif\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0merrno\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0merrno\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mEINTR\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/distributions/utils.py\", line 113, in softmax\n",
      "    return F.softmax(tensor, -1)\n",
      "  File \"/usr/lib/sagemath/local/lib/python2.7/site-packages/torch/nn/functional.py\", line 862, in softmax\n",
      "    return torch._C._nn.softmax(input, dim)\n",
      "KeyboardInterrupt\n"
     ]
    }
   ],
   "source": [
    "MasterNode = ActorCritic() \n",
    "MasterNode.share_memory() \n",
    "processes = [] \n",
    "queue = mp.Queue()\n",
    "params = {\n",
    "    'epochs': 1000,\n",
    "    'n_workers': 2,\n",
    "}\n",
    "counter = mp.Value('i',0) \n",
    "for i in range(params['n_workers']):\n",
    "    p = mp.Process(target=worker,args=(i, MasterNode, counter, params, queue))\n",
    "    # p = mp.Process(target=worker,args=(i, MasterNode, counter, params))\n",
    "    p.start()\n",
    "    processes.append(p)\n",
    "for p in processes: \n",
    "    p.join()\n",
    "for p in processes: \n",
    "    p.terminate()\n",
    "    \n",
    "print(counter.value, processes[1].exitcode)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "results = []\n",
    "while not queue.empty():\n",
    "    results.append(queue.get())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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79MXx66hLlflhq2bZClfJ/vQjpWo/mcLRTpUpJPVUp7PDoWiVqFi55i/fz3bH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6945c24090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(results)):\n",
    "    plt.scatter(i, results[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
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