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@TheDataLeek
Created October 31, 2016 19:52
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{
"cells": [
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import sympy as sp\n",
"from sympy import symbols\n",
"import networkx as nx\n",
"from math import inf\n",
"\n",
"sp.init_printing()\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 1\n",
"\n",
"**Use the $\\alpha-\\beta$ algorithm to show the minimax value to `MAX` in the following game tree. Show the branches that are pruned during the search, and the values for `MAX` and `MIN` at each level in the tree.**"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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0uVw2m23p0qUURTEMQ/YBGY1GcufmfjT8bwIAgM8HcQkAAMCZKIpS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pKSkmeeeWbjxo2Bjgh8E6RLwCxrbGy8cOHCpUuXent7x8fHPR4Ph8NRKBSP\nPfaYUqmMiYkRi8Vz17lmZmZmbGysp6ens7Pz8OHDra2tPp+PRqPFx8fLZLKlS5du27YtMTER1kkA\nmM8uXbp08uTJ6upqjUbjcrk4HE5eXt4TTzwhl8ujo6P/YQec7wTDMIPBUF9ff+7cuRMnTkxOThKN\nzDMyMp599tnU1FQYIgAAdxOxLbeysvLChQtNTU39/f3j4+Mul0soFObn5+/cuTMhISEqKio8PHzu\nTseYTCa9Xt/f33/06NGrV6+OjIxQqVSRSJSYmLh8+fLS0tKCgoK5uC4A9zJIl8x/MCMEs2N6erqt\nra2xsVGlUjU1NXV1dRFdb5YsWUKUF1m7dm1wcPBcv4QEBQXFxsZGRUUpFIqwsLDq6uqmpqampqbO\nzs7e3t7BwcHBwUEimISEBDabPafBAAC+E6JH5unTp8vKyurr64eGhhAEKSwszM/PJ8pCs1isWUm2\noigqlUp5PJ5YLI6JiTl+/LhKpWpra9Pr9QiCbN68uaCgQCwW3/mFAADg22EYNjk5WVNTo9Fo6uvr\nW1padDodgiASiSQ3N7ewsDA5OXnp0qU8Hm/ulpoIQqEwODg4KSmJz+dnZ2fX1NTU1NQQdfSNRmNf\nX19zc/Py5cujo6Nh+gQAuHdAugTcKWI5oq2traKi4syZM2azmUQi8fn89PT0hISELVu2FBcX3+Un\nK4VCiYqK2rdv35IlS8rLy8VisV6v1+v1Go2mq6uLy+UajcaioiK5XB4fH0+lUud6CgIA+JfGx8e7\nu7ubm5vffvvtwcFBBEFEIlFGRsaePXtWrlwZHR0961fkcrlLly5NTU3l8XhBQUFdXV3j4+MHDx40\nGAwTExO5ubkKhYLBYMz6dQEAAMdxDMOGhoaGhoY6Ozu//PLLxsZGi8VCpVLDwsLkcnl6evqmTZuI\nYq53LSoURZlM5urVq/Pz87OyskJDQ9va2np6enp7e/v7+ysrK4eHh7OyslJTU2NjY6E8NgDgXgCH\nccBtwjDM6/U6nc6qqqqPPvro9OnTxPFaOp3O5/OXLFny7rvvikSi+fA0xTDsyy+/PHjwYG1t7czM\njNvtxnFcIpGsX7/+Zz/7mUgkCgoKghKPAAQE8c7gcDjOnTv3pz/9qby8HEEQGo0WGhq6dOnSd999\nl8/n34UizdevX3/nnXfOnj1rsVh8Pp9QKCwqKvqv//qv2NjY266TAgAAf4+ooOR0Ou12+8GDB7/4\n4ovm5mYcx8lkMlF2uqCg4Be/+IVUKg14KSW73d7S0vK73/2uvr5+amrK5XIhCMLj8R566KFnn31W\nJBKxWKw7LDcLwD0ODuPMf5AuAbdpYmKirq7urbfeIk7Y2u12YlPJvn37Nm3apFAoxGIxhUKZDw9R\nHMdtNpvFYuno6Dhx4sRnn31GtCMNCgoKDQ1NSkp68sknV6xYAZtLAbj7vF6vXq9//fXXy8rKxsbG\nHA4HiUTavn37Aw88UFBQEBYWdnfm4k6nc2RkpK6u7ne/+11rayuJRGKxWDKZ7Lnnntu0aVNYWNhc\nBwAAuEd4vV61Wv3RRx9VVlaOjIxYrVYiDZGQkPDwww9v2LAhNDQ0JCSEQqEEPFGLYZjL5TKZTC0t\nLcePH//000+9Xi+KojweTyqVJicn//znP09ISIBiTwDcNkiXzH8wwIHvBsfxgYGBsrKympqa/v7+\ntra2mZkZKpWakpKyZcsWhUKRkpISHR3N4/ECHen/QyKRuFwul8vlcDhisXjZsmVnz56tqanR6XRW\nq3VyctJsNp88eTIzM3P37t1cLhce/ADcBT6fr7+//9y5c1evXq2rqzMajRQKRSqVfv/731++fHli\nYqJIJLprwTCZTJlMxmaz+Xz+V199df78eaPR2NXV9d5772k0mtLS0jVr1gT81QUAsHARxVzPnz9f\nU1PT2tqq0WgMBoPP5+PxeLm5ubt3746IiEhJSYmKipoP23IJKIqyWCwWixUUFBQREVFYWFhWVnbt\n2rWRkRGbzWY0Gm02W3Z2dnFxcXFx8TxZIQMAgNkFr4XgVnm93tHR0crKys7OzoqKivb2dqfTiaKo\nQqFIT08vKCgoLS2NiooK+N7Rb8Hn8zMyMlJSUsRicWpqqkqlImqqVVdXt7W1tbS0mEymlJSUjIwM\nqVR6F/b/A3DPGh8fb2pqKi8vr6io6Ojo8Pv9MpksOzs7KyvrwQcfDA8Pv/s3IIVCCQsLKy0t5XK5\noaGh169fJ8ouTkxMGAyGsbGxtWvXhoaGQtIEAPCd+P3+kZGRtra2vr6+8vLypqYmg8GAoqhAIMjJ\nyUlJSUlLS9uyZUtQUNC8nXgIBAKBQJCcnExsKmloaOjo6NDpdGfOnOns7NRqtf39/ZmZmYmJiXfe\nuQwAAOYV8quvvhroGMC8huO4z+cbGRnRarVXrlx57bXXLl68qNfr6XR6REREYmLijh07Hnnkkc2b\nNwuFwvm/L4NEIpHJ5NjY2IKCgtTUVL/fj2EYgiAzMzM6ne7y5cvDw8MoijIYDJ/PR7ThgNUSAGYL\njuMul0un0129evWDDz44fPiw0WhksVhxcXGbNm164oknHnjgAS6XG8CUBIqiMpksPT1dLBaPjY3Z\nbLaxsTGtVtvQ0BAZGclms2k02nxOCgMA5gmiRonRaOzv7y8vL//zn/984MABojl6SEiIXC7Py8v7\n4Q9/+OCDD+bk5CyIGklUKjUuLq6wsFAmk/n9fpfL5fV6JyYmOjo6amtr3W437f/czfK0ACxo7e3t\n58+fdzqdcXFxS5YsSUxMDHRE4Jugdgn4F/x+v9lsfv31148eParT6YgfGAqFkpWV9cQTT+zdu5fB\nYJBIpAWXUyC+CPHy9vHHH3/yySf19fXEv0RRNCYmZsuWLf/+7/8eEhIyb1d7AFhwfD5fd3f3yy+/\nfPXqVbPZjCAIg8EoKCh45ZVXCgsL50/FZaIA7eTk5Msvv3z06FGr1YogCJlM3rt375NPPrls2bJA\nBwgAmO/8fr/dbn/99de/+uorrVZLrM0gCCKVSrds2fLyyy/fWGSaJ+PeLSJmSh6PZ3x8/IUXXigv\nLx8bG0MQhEQiBQUF7d279wc/+EFGRkagwwRgYYDaJfMfpEvAP+VwOJqbmw8cOKDVagcHB00mk9vt\nRlF0x44dGzZsyMzMDAsLE4lE83895FvgOI7j+Pj4+OjoaEdHx/vvv9/a2mq32+l0ukAgiIyMzMvL\n27x58/Lly+fPWWIAFqiBgYGTJ09++umnfX19VqsVx/HMzMwnnngiLy8vJiaGw+HMq8GE2Fin1+vP\nnz9/+PDhmpoaHMdDQkKUSuXq1at/8IMfBAcHQy4VAPD3vF5vbW3tsWPHamtrDQbD5OSky+Wi0+mx\nsbFPPvlkTk6ORCKRSqULutgH0R5Rp9P19fWdO3fu4MGDFouFRCKFhIRERUXFx8e/8sor8fHxsBcP\ngG8H6ZL5b74fnQB3H/GSUFVVRRzdr62tNZlMfr9fLBZnZGSsXLkyNzdXqVSGhoYGOtJZQOyLEYvF\noaGhxE77np6eK1eu1NfXG41Go9E4Ojra399fU1OTm5u7bNkyOJQLwHeFYZjT6Txz5kx1dfW1a9dU\nKhWGYTKZbPny5evXry8qKgoLC5uH5/hIJBKx83zTpk1EV+OjR48ODQ01NjZOTExMTEzs3LkzPT0d\nxgQAwA12u/3SpUutra3Nzc2tra06nQ5BEIFAsGzZslWrVkVFRS1btiw8PHwRLMCgKEqn0xMTEyUS\nSWhoaHx8vFarPXPmjE6nM5lMfX19JBIpKSkpPz+/sLCQxWIt3MQQAOAeN+9mqCCAMAwbHx/XarV6\nvf7MmTM1NTVDQ0MoioaHh8vl8vT09KVLl27atGk+NLebdSiKhoSEbN261WazJSQkxMXF9fT0qFSq\nsbGxoaGh+vr6oqKi4eHhlJSU2NhYsVgc6HgBWBjsdrtOp6urq/vss89UKpXZbOZyuZmZmfn5+Zs3\nb16yZMk8TJR8Q1RUlFgszsvLo9Pply5d6urq0mg0/f39drt9/fr1WVlZcXFxgY4RABBg4+PjAwMD\nHR0dX331VUNDw+TkJIVCEYlE6enpiYmJy5cvX7duHYfDWXxZAzabnZ2dnZKS0tfXJxAIrl+/3tfX\n19fXd/jw4bCwsI6OjrGxsYSEhKSkpMDWpQIAgNsDpV4BgiAIjuNWq3V8fLyysvKPf/zjm2++2dbW\nZrfb2Wx2dHR0aWnpT3/60/3796ekpJDJ5MX3sP9bdDo9KSlp5cqVBQUFRqPR6/X6fD6r1drZ2Xnh\nwgWj0chkMgUCAY7jizJtBMCsII65mUymzs7Oo0ePvvLKK319fT6fTyAQZGdn/+IXv9i1a1d8fPxC\nuYPIZDKPxyssLAwKCjKbzWazeWZmpqWlpaenB0GQmJgYGo0GZaEBuAf5/X6bzTY5OVlVVfXnP//5\n97//fXd3t8fj4fF40dHReXl5v/zlL/fu3ZuRkUGn0xfxEEHkhlauXKlUKhEEGRoaQhDEYrF0dHRU\nVlaOjIyIxWKi9Q9UgQXgb0Gp1/kPapcABEEQr9f70UcfHTlyRKVSzczMuN1uBEEkEsmmTZtefPFF\nDofDZrOpVOoiftJ/A3EiiZgDff311x9++CHxXsRgMIKCgqKjo7/3ve/df//9ERERgY4UgPkIwzCP\nx/Pyyy+fOXPGYDDY7XYEQRQKxd69ex955JGQkBAqlbpQciU34DjudDq1Wu3p06d/+9vfWiwWKpXK\n4/FiYmLeeuut9PR0JpMZ6BgBAHfVxMTEsWPHPv74456eHrvd7nK5EASJjY3dt2/fvn37QkJCOBzO\nPTV98ng8MzMzRqPx3XffPXv27ODgIIIgdDqdw+Fs2LBh3759a9euDXSMAMwjULtk/oPdJfc6rVb7\n5Zdf/uY3vzl//rxGo5meniaTyTExMT/60Y8ef/zx0tLSuLg4Fou1oAuS3Qai3zCTyeRwOFKpND09\nPT4+3mg0Tk9P2+326enpvr6+q1evDg4O0un0yMjIQMcLwDwyNjZWUVFBNB0fGhpyu93BwcE//vGP\nH3744VWrVkVGRi7QnVlENRMulyuTyZYuXTo9PT06OmqxWKampjo7O10uF5/PDwkJCXSYAIC7oamp\n6dNPP/3jH/9YVlbW3d1tsVgYDEZ6evqLL764f//+lStXRkdHczicRb8n9xvIZDKDweDxeMRSeUhI\nyOjoqMlkcjgcY2NjKpWqtrY2JCSEy+UyGIxABwtA4MHukvlvvh8aB3PE7XZ3dna2tLQ0Nzc3NTU1\nNjb6/X4+n19YWLh06dLo6Oi1a9fKZLJFUI3sDtFoNKJYSVJSUnh4uFqtVqlUzc3NarW6q6urv7+f\nKHFSVFQkk8mCgoICHS8AAYPjuN/vr6mpuXz58vXr1ysqKtxud2hoaHp6+qpVq7Zu3SqTyRbB/gsW\nixUXFyeTyUgkkkwmu3r1qkajuXbtmtPp1Ol0RUVFpaWldDp9IeaDAAD/0vT0dGdnZ3Nzc3Nzc2Nj\no1qtxjCMyWTm5eXl5eXl5OSUlpYKBIL5X5Vp7pBIJDqdrlQq4+LiIiIioqOju7q6Ll26ZDAYxsbG\nOjs7HQ6HQqHIz8/PyckJDg4OdLwAAPBt7t3R/J5FJPi7urrKyspOnz7d39+P4zidTk9ISEhJSdmw\nYcP27du5XO49tRjyL7FYLLlcLpfL9Xp9eXm5UCgcHh4eGBjo6enp6+srLy9/+OGHc3JyEhMTIyIi\noFMGuAd5PB6z2dzd3f3hhx+eOXPGZDKRyWS5XJ6Xl7dx48adO3cGOsDZRGwz2bJli0wmk0gkZ86c\n6erqampq6u3tValUKIpmZ2eLRCJINwOwmIyPjxuNRrVaffHixZMnT5rNZhKJxGazY2JipFLpfffd\nV1JSEhsbG+gw5xEGg5GTk5OamjoyMsLn8xsbG3U6nV6vP3z4MJvNLikp2blzZ2JiYlxcHJvNhr7s\nAID5CWqX3CtwHMcwzOv1arXao0ePvvnmmzMzM0S9UhaLJZFIXnrppdWrV0skkkBHugDY7fbm5ubf\n/OY3169ft1gsPp8PQRAej7dp06annnoqOzubqMsAy8vgXkAU+hkdHS0rK/vVr341MDBAZBP4fP6v\nf/3rjRs3Lo6m4/+M3W7v7u5+9tlnW1tbHQ4HgiBUKvUPf/jDfffdJxaLoaghAAsdhmE+n8/n8504\nceKvf/1reXk58dCnUqkcDic9Pf3ll1/Oycnh8XiBjnS+6+3tJeafFovF4/HgOE78Ab722mvp6enE\nwSUEQWC5DtxToHbJ/AfpknuF3W7v6Oh4//33W1paRkdHJycnMQzjcrmlpaW7du1KTU0NDQ0l6rkG\nOtIFAMMwp9M5Pj7e0tJy6tSpQ4cOeb1eFEW5XG5YWJhEIvnhD3+4bNky6DcM7gVWq/XUqVMHDhzQ\narXj4+NerzcyMrKkpOSHP/xhTEwMl8td3JvSMQxzuVwjIyMfffTR0aNHe3p6SCSSRCJZsmTJ9u3b\n9+/fH+gAAQB3pK+v79SpU0eOHDEajSaTyW63k0gkPp+/d+/e9evXKxSK0NBQJpMJmyP+JbfbbbFY\ndDrdqVOniNESx3EGgxEeHp6Xl7d169bNmzfTaDRIl4B7CqRL5r/FPIsFBLPZXFtbe/bs2YGBgZaW\nlsnJSb/fHxwcTGRJ0tLSkpKSoDzhd4KiaFBQEPEqGBERkZeXV1tbW1VVpdfrrVbr0NCQ1+s9e/Zs\ncXHx/fffHxQUBNtMwKLkcrkqKioqKyuvXr3a3t5ut9vpdPqmTZs2bNiQlZWVlpZ2L6RfURRlsVjx\n8fF79+6Ni4urqqr64osvRkZGqqqqxsfHOzs7n3rqKYlEAgdzAFhYMAyrr6+vqqpqbGzs7u7u6ury\neDxESY777rtPLpdnZGTExsby+fxAR7pg0On00NBQPp/PZrNTU1OrqqquXLnS2dnZ19dns9n0ev21\na9eWLl26YsWKsLCwQAcLwN3mcDiIzqRgvoF0yaLl9/vtdntDQ4Narb58+fKlS5fsdjuKolKpNCkp\nKS0tbdeuXXK5nMPhBDrSBUwoFAqFwszMTKVSmZCQ0NLS0t3dTdR9bGxs7OnpsVqtUqk0Ozs7PDz8\nXnh1BPcIr9er1+uvXLly7ty5mpqa0dFRFouVlpaWlZW1bdu2ZcuWCQSCQMd4tymVyoiIiISEBBaL\ndenSJb1eX1tb293dTaFQiouLlUolHHUEYEGYmJjo7e1Vq9V1dXVVVVW9vb3EJoi8vDy5XJ6Zmblh\nXSAxZgAAIABJREFUwwaZTEan0wMd6YJEo9EUCkVCQkJ8fHxsbKxKpaqurjYYDNeuXWttbVWr1QMD\nA3l5eUR9/UAHC8CcY7FYYWFhZrN5YmLCZrMFOhzwD0Aj4UXI5/OZTKaBgYG2trbf/va3n332mUql\nQhAkNDQ0Ojp6w4YNTzzxxBNPPCGRSOBhPyvIZLJMJisuLk5LS2MwGGazmUqlulyuvr6+iooKlUrF\n5XJpNBpRPB9FUdhoChY0k8nU399/8uTJV199VaVSzczMhISEZGZmPvDAA88//3x2dvYiaH9zexgM\nhlQqXbNmzeTkpNVqdTqdZrP56tWrU1NTdDo9ODiYqAMNIwAA85Df75+amjIYDNXV1QcPHnz99deb\nmpqmpqY4HE5UVJRCoXjqqacee+yxkpISoVC4uM8Y3gUoihJncNasWWMymTAMI/78+/r6KisrR0dH\n6XQ6i8WiUChkMhkOOoFFbGxsTKvV9vb2+ny+goKCvLy8QEcEvglqlyxCU1NTn3766YEDB7q7u71e\nr9/vR1E0KirqySef3LVrV2RkJPH4CXSYixBREM7r9X7xxRcHDhyoqanBcRxFUSqVGhkZuWHDhlde\neeUe7y8IFoEPP/zw4MGDtbW1xK5RHo/3yCOP/PSnPxWJRBQK5R4/ekY8Uj0ez7Vr1z755JODBw/i\nOE4mk0Ui0dq1az/44APoMQzA/GS3248ePfqXv/yltbXV7XYT9Vy5XO7q1at/9KMfEYlgMpkM9+8s\nujFgTk9Pf/HFF7/85S/NZjMxZhJHnl966aXly5fD2RywiFVWVr7xxhtnzpzhcrm/+MUvnn322UBH\nBL4JdpcsHn6/32g0vvHGG++8886ZM2d0Op3T6UQQJC0t7ZFHHnnppZcKCwuJHSXwsJ8jJBKJTCZT\nqdTw8PD8/HyFQuFwOIxGo8fjcTgcg4OD5eXltbW1AoFAIpHA3wJYWNxut0aj+fGPf3zixImuri6H\nw8FkMtetW/f888/v2LEjIiICSvQhCEIikUgkEoVCEQgESqUyNzdXpVIRO02MRuPly5d5PJ5AIAgK\nCgp0pACA/197e/snn3zyq1/96vz58729vcTJZYFA8IMf/OCZZ57ZuXNnUlISh8OhUCgwxM2uGwMm\ng8GIiopavnx5ZmbmyMiIyWRyuVxWq7W1tbW5udntdkdHR8OGaLAo6XS6urq6np4eOp2+YsUK2F0y\nD8Eq94KH47jf71epVA0NDa2trVeuXNHr9U6nk8fj5efnL1++XKlUZmZmpqSkBDrSewWJRBKLxSKR\nSCwWy2QyrVZ79epVlUo1MjJiNBq7urqmpqby8/MzMjKKi4uJlsOBDhmAf6G9vb22tvbq1atnzpyx\n2+1kMjk9PX379u25ublZWVmw9Pf3iHKGEonE7/efO3euvr5+eHi4oqKCRCKpVKqVK1cWFxcHOkYA\n7mlut3t4ePjcuXPXr19vbW3t7OzEMIzBYOTk5CxdujQxMXHZsmVETfdAR7r4USiUiIgIkUgkl8tD\nQ0Nra2vr6+ubm5vVarXRaDQajZ2dnVlZWcXFxUKhEPZHAwDuJkiXLGAYhtnt9p6enuHh4UuXLlVU\nVGg0GhzHRSJRamqqUqnMy8vbtm0bPFoCgkwmR0VFSaVSr9eblJRUWVnZ2tra09MzNjZ27Nix69ev\nFxYWmkwmqVQaGxsbFhYGSRMwD/l8PpvNplKpLly4UFZWplKpcByPiIhQKBTr169/7LHH2Gw2DC//\nDIVCCQkJefzxxyMjIyMjI6urq1taWsrKyjQajU6n83q9GRkZXC4XikADcJfZbLahoaGurq7Ozs6/\n/vWvAwMDCIKwWKykpKTo6Ojly5evW7cuPj4+0GHec2g0WlRU1L59+zIzMxUKhUQiUavVBoOhqqpK\npVLl5OSMjo6mpaXFxsZGRkYGOlgAwL0CapcsVC6Xy2azdXZ2vvvuu+Xl5WazmUQi0Wg0DoezcuXK\n733veyUlJdC6cv7wer0ajeaDDz64dOnSyMiI0+n0+/0kEon4y1qzZg2HwyFaDsNeXzBPuFyuycnJ\njo6On/70p1qt1ufz0Wi04ODgLVu27N+/f9myZYEOcCExm82XL19+/vnniU3mKIrGxsb+7//+b3Z2\ntkgkgk3mANwFGIZ5vV6bzabRaL766quDBw8Scycmk8nn8+Pi4n7yk58UFhaGhIQEOlKAIAhis9ne\nfPPN06dP9/T02O12r9dLIpGWLVu2Z8+e+++/n81m0+l0yNeDhQ5ql8x/kC5ZqC5duvTFF1+UlZVN\nTk46nU4Mw4KDg/Py8l544YWYmBihUMhiseDFe/7Acdzj8Vit1unp6Xfeeefrr78eGhpCEITJZHK5\n3Pj4+NLS0ieffDIkJASe/WCeKC8v//jjj8vLy00mk8fj4XA4ubm5v//978ViMZfLvWfb39wev98/\nMzNjMBh+/vOfV1ZWTkxMUKnUkJCQLVu27N27t6ioKNABArD4TU9PNzc3v/nmm2q1enJy0mazYRjG\n5/O3bdu2e/fulJQUPp/PYDDgKTxPYBg2PT1tsVjOnTt34MCB5uZmBEEYDAaXy42Li3v66adXr14t\nFosDHSYAdwTSJfMfpEsWGKPReO3atbKysu7u7r6+PqPRiOO4VCrduHFjUVGRTCZLS0sjircHOlLw\nD+A4jmFYV1eXVqvt6Og4dOgQUWgmKChIIpEoFIqSkpJVq1YpFIpARwruXT6fb3R09NChQxcuXFCr\n1WNjY8Q2qNLSUqLFHZVKhVTsbSDqTDU3N1dXV58/f/7ixYs4jkdGRiYnJ69bt+7pp5+GP1gA5sjg\n4ODly5fLy8t1Ol1nZ6fVakUQJDIycu/evUqlMjk5OSYmhs/nBzpM8A9gGGYwGDQazcDAwIEDB9Rq\n9czMDJPJVCgUiYmJq1evXr16dUxMTKDDBOA2Qbpk/oPaJQuGTqcj6rk2NDTU1NTMzMxQKBSZTFZa\nWhoTE7Ny5crU1FRY753niNY5SqUyISEhIyODz+f39/c3NjZ2dHT09PT09PSMjIx0dXVlZ2enpaUl\nJSWxWKxAhwzuLUaj8fr16w0NDcePH9dqtQiCiESi9evXr1+/vqCgQCaTBTrABYxoALFkyZLw8HCJ\nRBISEnL+/Hmj0Tg+Pj42NobjeFFRUUJCAryzATBbZmZmhoaGamtru7q6ampqmpubHQ4HiqIJCQnp\n6em5ubn33XefTCaDR+18hqKoVCqVSCR2u51GozU2NqpUqpaWlubmZo1Go9fre3t7U1JSVq9eHRIS\nAqWgAACzDhoJz3dut9tkMnV3d1+8ePHAgQOHDx/u7e29UW1x7dq1r7766sqVK6VSKTwkFhAymUwc\nniooKOBwOD6fj0ql2mw2vV7f2NjY3Nzs8XjIZDKGYWQyGbJg4C5wuVw6ne7SpUt/+tOfjhw5Mjo6\nyuPxkpKSCgsLf/7znxcWFgYHBwc6xkWCx+MlJCSkpqYaDAav1+twOPR6fVVVFYqiDAYjKCiIaDMM\nO00AuG12u12v1xPFld94442LFy8ODg5SKBSpVKpQKLZs2fLQQw/t3LlTJBLB3GlBIIbHzMzM1NTU\n4OBgm82GIIjdbu/v729qamprawsJCcEwDEVRGD/BwgKNhOc/OIwzTxF/LxiGDQ8Pl5WVvfbaa2Nj\nYx6Ph1ifDAkJee6557Zv356QkBDoSMEscLlcWq32kUce6e7udjgcxN8+lUrdunXrQw89VFpaSpSA\nhcc/mHU3hpq+vr7XX3/90KFDTqcTQRAKhbJp0ybicHigY1zMPv74448++ujatWsYhiEIkpqa+vDD\nDz/11FPEcjfc8gB8JziOE4deGxsb33vvvRMnTlgsFgRBSCQSlUqVy+VPPfXUAw88IBQKAx0puCPT\n09Off/75n//8546ODq/XSzzIboyfDAYDCueDhQIO48x/kC6Zp/x+v1qtPnz4cGVlpcFgMBqNXq+X\nyWRmZ2d/73vfS0tLk0qlwcHBDAYj0JGCWYBhmMvlGhgY6OjoOHHixNmzZy0WC4lE4vP5oaGhCQkJ\njz322LJly6BcP5h1Pp9vcHDw7bffbmho0Gq1JpMJRdHw8PCf/exnJSUlEomEy+UGOsbFbHJyUqvV\nnjt37o033nA4HAwGIzw8fOnSpS+//LJMJoOdZQB8J2NjY9XV1f8fe+cZHld17f1zpveu0YxmRtKM\nem+W5Sb3bmyDC7YhoSYmQBxIIJDclEvyJNwHErjBpBgCCSWOe2Jjio0rtiVZsqzePOqa0XRN7zPn\nnPfDTvRyCSHGyDqj0f594NGDkfUftM/Za6+91n+9/vrrJpPJZDK53W4Mw+h0+oYNGzZu3Dh37tyU\nlBSpVEqjwVb0mU08Hnc6nXa7/fTp00eOHGlsbCQIgs1my2Sy7Ozs2trahx56CHaPQmYEMF2S+MAN\nI+GIRCL9/f1Hjx7t6+u7fv362NgY6Muora1dtGjR/PnzKysr5XI53OyTCQqFwuFwioqKFAqFSqWa\nP39+X1/fhx9+OD4+7na7TSZTIBA4e/bs4sWLFyxYoFarydYLSRKAdfR77713+fJli8USi8Xy8vI2\nbNhQXFwMWvwoFArZGpMcmUzG4XCEQqFEIjl27Fh3d/fIyIjf749GowsXLlyxYkVRURHZGiGQRCce\nj4+NjZ0/f765ufnGjRtNTU3hcBhBEI1Gs3Dhwrlz5wI7MKVSSbZSyNRAo9HkcrlcLmez2TqdTq/X\nv/fee93d3QaDwW63m0ymkZGRhQsXzp8/v6SkhGyxEAhkZgOP3IkCjuORSKSzs7O/v7+lpWX//v0T\nExMYhqWkpOTm5mZnZy9btmzRokU6nY5spZDbiFQqXbRoUUVFxdDQkFwu7+7uvnHjxo0bNy5cuNDU\n1ATGIRUUFJSWliqVSnjzDLk1CIKIRCItLS1NTU0fffTRuXPnwKumqKhozZo1W7Zs0el0MCE7bXA4\nnIKCgoyMDKFQeO7cuaampoGBgcOHD/f19ZlMpjvuuGPOnDlMJhMWlkMg/wrw/Oro6Ojt7f3oo4+6\nu7tDoRCFQsnLy8vOzq6srFy2bNm8efOYTCbZSiG3BZ1Ol5mZGQwGU1JSrl271t7e3tPTc+PGjYGB\nga6uLr1ev3jx4tLS0tTUVBgyQSCQWwNavZIPhmGBQMBkMg0NDb366quvvfbamTNngsGgUChMS0ur\nra3dvXv3U089VVFRAa0WZwkMBiM1NXXp0qVVVVU8Hs9qtYJF0t/ff/ny5fr6eoFAwGAwaDQajUaj\nUqnwHAW5eaLRqNvt7u3tfemll/bv39/R0UGn0xUKxaJFi7797W/fe++9crkcFpVMMyiKMhiMiooK\nnU5HEITBYAiFQmazubW11Ww25+XlsdlsOp0OJ8RDIAAcx0OhkNVq7ezs/Nvf/vbLX/7y448/Hh8f\np9PpKSkp6enp99xzz7e//e277747MzMTJn+Tm8n35+LFixUKhd1uD4fDkUjEaDQ2Nzc3NjYKhUIm\nk8lisZhMJtzdIIkGtHpNfKB3Cfn4fL5z58797//+b09Pj8/ni8ViOI6zWKxvfvObO3bsKCkpYTKZ\nDAYDHolnIRiGRSIRi8Vy5MiRt956q7+/H8MwCoUCGnQ3bNjw8MMPV1RUwLUBuXlGRkaOHz/+P//z\nPx6PB7hH5+bm/vKXv6yurpbL5fBVQy7xeDwQCLS2tj722GMjIyOhUIjJZKpUqmeffXb9+vWwEQ8C\nAQQCgba2tpdeeqmxsdHlcoXDYYIgaDTavHnz7rvvvq1btzKZTCaTCRMlswocx2OxmMPhaG5u/tWv\nftXa2hoMBqlUKovFSk9Pv//++3fv3g3vHSGJBvQuSXxgdQlp4DgejUYPHTr0hz/84eDBgz09PR6P\nB8MwrVZ75513/vd///eaNWtycnIEAgGNRoMHmNkJhUKh0+lcLjczM3PJkiVFRUUoig4PD0cikUAg\nYDAYWlpa2traVCqVUCiEcSHkCwAvnL/85S+vvfbayZMnDQZDPB7X6XQ7d+78/ve/P3fuXJlMBnMl\npEOhUBgMhlQqnTt3LpvNdrvdNpvN7/fr9fquri4KhZKdnQ1rTCCzGYPBcOLEiRdeeOHIkSNtbW0T\nExOxWIzL5W7ZsmXPnj333XffnDlzQOYX1hHMNsDsSA6Hk5qaCgxrGAyGXq+PRCI+n29wcPDy5cst\nLS3Z2dkCgQAuD0iCAKtLEh94viIBDMOGhoaampr6+vquXLnS3d3tcDgYDEZhYeGCBQvKysrKyspq\nampglgQCYDAYGf8kOzt77ty57e3tzc3NJpPJbrfr9XqPx1NYWFhWVrZw4UI2mw2DAMhncDqdvb29\nFy5cOHPmTFdXl8vlYrFYa9euXbBgQW1tbVVVFWzpShwwDMMwTKVSpaamqlQqMP2ht7fXZrM5nc72\n9nYulwumogoEgtTU1LS0NKlUKhaLeTwe2dohkNsFhmF+v//MmTPXrl27evVqc3NzMBgECcTKysry\n8vLq6uqSkpKUlBSylUJIhkajSaVSqVSq0Wi0Wm1hYWFDQ0NHR8fAwACwuQkGgxUVFRUVFeXl5XDv\ng0Ag/xHYjDOtAPP2sbGxy5cvv//++9euXSMIgsViqVSq4uLimpqaLVu2ZGVlwTIByBcQDodPnDhx\n9OjRpqYmh8MRDAYRBJHL5bW1tdu3bxcKhXQ6nUKhUKlULpfL4XAEAoFAIOBwOBQKBYYFSQyGYbFY\nLBgMTkxMBAKBSCQC1gaGYUajsa6u7uDBg4FAAEVRDoej0WieffbZRYsWqVQqOI+cdCKRiN1ut1gs\nPp/P5/M5nU6LxdLS0jI2NmYymYxG4+ROTaPRuFwuhUJhMplSqVSn0+Xm5qalpaWlpclkMjabLRaL\nwfhnmDaFJAexWMxsNg8ODhqNxjfffLO9vd3tdrNYLI1Go9FoFi1atGbNmgULFpAtE5KgBAKBkydP\nnjlzpq2tbWxszOFwoCian5+/cuXKDRs2ZGRkiEQiOp0ODFBApES2ZEgyA3b5YDAYDAbBFLz29vYj\nR45cvXqVw+Hcf//9W7ZsQVEUBPB8Pl8gEPD5fBjAkwtMl0w9BEFg/wTHcQzDiH8SCATeeOONQ4cO\n6fV6giDADSGoh3/22Wfh7API5wIWTzQajcVi8Xg8Go22trb29/c3NTXV1dWNjIx8+ikGzTsMBoPP\n52dlZWVmZoJ6JZ1OBxq56XQ6nU6HKbnkALRqR6NRDMNCoZDD4RgdHb106ZJer7fb7YODgwRBBIPB\nUCiEYRj4FiaTqVara2pqqqurs7OztVqtUqkEbV/APxi+haYH8FyHw+FoNGo2m8+ePXvixImuri6H\nwzH5y0JRFKQ+//XbcRzHcRz8JeDf8Hi89PT0+fPn79ixo6ysDPgaguTp9H0qCOQrABbzZNSEYVg0\nGnU6nceOHXvjjTdu3LiBIAiDwWCz2RqN5qGHHtq2bZtGoyFbNSRBAUsoFovFYrFwOHz27Nk//elP\n586dA3+KoqhMJtu+fXtVVZVYLGYwGBKJRKvVgqZUKpUK4iUqlQpfoZCvAojTAARBdHd39/b2Dg8P\nDw8P9/b2Op3OQCAQDAYjkQiFQgFZEhqNlp2dnZmZWVRUVF5eXlhYyGKxPh3AwzhtmoHpkqkHx/HO\nzs7BwcGxsbGRkZH+/n6/3w9suoPBoMvl8nq90WgUXP4vWrSotrZ20aJFcFQk5N8Rj8fdbvfp06fP\nnz/f0dHh8XjAESsUCoVCoVgs9pn/HiShgQkCnU4HhvAsFovL5ebm5i5dunTJkiX5+fmkfBbI1OLx\neC5fvnz69OnOzk6r1RqJRECBCUigRKNRBEHAoXryW0B3N5vNZrFYDAaDwWDweDylUjlnzpwNGzZU\nVVUxGAzyPtAsAsMwt9v95z//+cyZM4ODg36/3+fzRSKRyVwJaMJXqVTgaY1GoxQKZTLRaTQaLRaL\n3+93u93g9wvy72w2WyAQyOXyoqKiLVu2LF68GFobQmYKwGJJr9f7/f5gMDg6Ovrhhx8ODAxYLBa3\n2x2NRmk02qpVq7Zt27Z06VKhUCgQCOh0OtmqIQmK3+8fHh6+cuVKQ0PD+Pi4wWAYHx8HRZcAKpUq\nEAhYLBaImqhUKp1OB1f6aWlpc+bMqa2tzc/Ph69QyFfB7XbX19d//PHHk77UIFSLRqMgVPv0zQdY\niqDWCQTwAGBiOG/evNWrV5eUlMD33jQD0yVTAI7jfr+/paWlpaVlYGDA5/NNTEx4PB6fz+f1et1u\ndywWA8Um8Xh88rtAaJuWlqZQKGQymUgkApFxaWlpeXl5ZmYmeR8Ikih0d3c3NDS0tLRMTEyMjIwY\nDIaJiQlwBkYQBJSQiEQimUxGo9HAjRx4h4JhsVarFeRTwGNOp9NFIpFardZoNAqFQqvVbty4MS8v\nD1aazCwIgvD7/RcvXmxoaBgeHh4fHx8dHXU4HKFQaHK7ZTKZYrFYp9OBbwFlbmBtOJ1Oh8MRDof9\nfj+O4wiCgNStXC7XarUZGRlqtXrx4sVlZWUSiYTEj5nEhEKhjo6O9957b2hoqLOz02AweL1eBEFY\nLJZWqy0qKioqKtJqteB6k8fjgWAd/LIm7zn9fn8gEIjH4+Fw2G639/f3d3d39/f3g+IUcFOalZWV\nl5e3atWqRYsWwak6kEQjHA5bLJaurq6enh673e71eoPBII7jIGqKxWI+n29kZMTj8UzGThQKJSsr\nq7S0tLi4ODc3t7S0ND09XSAQkPtBIIkDhmFOp/PixYvNzc1ms3liYsJkMpnN5kAgEA6HPx2E/zuo\nVCqDweByucAZSiKRpKamFhQUrFy5UqVSsdnsafgUkCRgdHS0oaGhoaHB4XAYDIaxsTGr1RoOh8Gf\ngs1dKBRKpVIOh/Ppb4zH4z6fz2KxBAKBaDQKtn4ajSYQCBQKRUZGBojWli9fPm/ePJg3mR5guuQr\nYTKZ+vv7BwYGJiYm2tvbOzo6hoaGJlPXVCqVzWaDRPXkiRRcj+A4HgqFwG0JOOWiKMpkMpVKZWFh\nYWlpaWZmplwur6ioUKvVcA7CbMPv9/f393d1dTU3N1+7dq2zs9Pv9yMIwuPxUlJSQL6Dx+Ox2WzQ\n1iiRSMCiwnF8Ml3i9XptNhtIY7vdbnC1MvmyBvaxa9eunTt3bl5eHjQ8mxGAHv7GxkaDwfDJJ58A\nu18EQWg0mkwmU6lUGo0GjIRgMBhCoXAy6/rpdInb7Z6YmIhEIn6/3+v1Wq1Wo9FoMpl8Ph+GYSwW\nS6FQzJ8/v7Kycs6cOUVFRdA6caogCCIejzc2Nvb29l69evXjjz82mUw4jguFwoyMjMLCQrlcrtPp\n8vLy8vPzMzIybv55dDgcQ0NDfX19g4ODdrt9ZGTkxo0bIyMjOI5zudz58+fX1taWlZUtXrz405sR\nBDL94DgeDAZ7e3sHBwdtNpvZbO7t7b1x48bExITP55s8S3wBoIRKJBJlZ2cXFhaCl55SqSwuLpbJ\nZEwmcxo+BSTRAI2N7e3ter1+dHT0ypUr7e3tExMT8XgcRVEWi5WSkiKRSIRCoVAolMvl/3rIjMVi\nXq83EomYTCZQzeTz+cAfCYXC3NzcJUuWaDSa4uJi6CgM+QLi8Xh/f39PT09LS0tTU9O1a9f8fj8I\nrqRSKQjgRSIRm83mcrlCoVAsFn8mBxePxwOBgNVqBR06fr8fBPDA3YwgCCqVqtFoamtrly5dmp2d\nXV5ezuPxYMvYbQWmS26FWCwGphU0NDScOnXqwoULHo8HnFQnnTWBZRS4+VcoFOBhAPYlTCYT5L9H\nR0eBI2MoFPJ6vV6vNxAIxGIxkDopLCz8+te/vmTJErlcrlAooM3PbCAYDNrt9p6eno8++ujo0aNW\nq5UgCODpKJFINBpNYWFhdXX1vHnzUlNTbzIujMViBoOhubn56tWr3d3ddrvd5XLZbLZQKIQgiFar\nXb169de+9jW1Wp2SkvKZJDckEQBVmmazeXx8vKmp6Q9/+MPg4GAkEmEwGAKBICUlRSwW5+fng4VR\nWFh48900Vqu1q6ursbGxtbV1fHx8YmJiYmLC6XQSBMHn81euXLlt27aysrKMjAxogPcVCYVCoEbs\nt7/97aVLl8xmM5VKFQqFCoUiNzd30aJFd911l1qt/oqdUMDkqLGx8YMPPjh37pzVarXb7ZFIhMPh\nFBYWPvPMMzk5OWq1WiaTTdXngkBuBuAiYbPZbDabyWQ6fvz4+fPnDQYDKJYEfWdsNnuy7Pxfb4lw\nHAetan6/3+/3h0KhyUJLiURSUVGxffv2/Px8jUaTmprK5XKn+xNCSAIsCaPRaLVa3333XZCGRhAE\n3BlIJBKBQCASifLz87OysoA9cGFh4b+ukEAgMD4+7vP5WlpaOjs7R0ZGLBZLOBx2Op0ulwsUb7JY\nrFWrVu3YsaO0tBTcWsHsM2SSSCTidDpHRkZOnTp17Nixvr4+HMdpNJpEIpFIJEqlMjc3F8RpGRkZ\nN/mOisfjTqcTBPAdHR3j4+Ner9dsNgeDQQzDwJCH++67r6CgIDU1FdbZ3T5guuRWsNlsBw8e3Ldv\n3+Dg4GSnA4qiSqWysrJy2bJlq1atAgcM8N//uzQH+MZYLDY8PHzx4sUzZ840NTVZrdZP967n5uZu\n27btqaee+twAApJkdHZ27tu3709/+tNkAR6bzdZqtffcc89dd92l0+mAfztYUTeZPgPLbNJv2GKx\nnD17du/evd3d3SDcBDafjz/++Ne//vXy8vLb+fkgtwI4J7zwwguHDx++ceMGWBgoimo0mhUrVjz6\n6KO5ublguCzIaNx8XpX4FJFI5MqVK/v37z906BBYGCiK8ni8nJyc3/3ud6WlpTCV9lXo6+s7fPjw\nL37xC9CoTKFQxGLxypUrn3zyyfLy8klD1q+YE//0w242m8E+NTIygmEYWB5VVVWPP/74fffdNzWf\nCgK5OQiCcDqdf/jDH/7yl78MDAx82lAJRVGpVFpeXl5cXJyVlZWdnT1nzhyRSPSZvwH4ULghI1Mx\nAAAgAElEQVRcrvr6+vr6+r6+PoPBMNlbAbZFLpe7adOmJ598cs6cOdP68SDk4ff76+rqnnvuua6u\nrkAgMLmuNBrNHXfcsX379traWuSfr9bJf/7rm3byGyf3RARBBgcHjxw58ve//72rq2tyW2SxWGq1\n+uWXX16wYAFsWYVMMjQ0dPTo0Z/97GeTHmSg8nfnzp3btm2rqKgADpVfJYB3u90tLS0vvPDC9evX\nPR4P8k83urvvvvvBBx9csWLF7fx8sxqYLvlyDA8Pv//++wcPHjSbzRaLJRQKMRiM1NTUVatWLV26\nNCsrSyQSgdoqJpN5k9kNcBZyu92g9s9ms7W0tBw4cGB4eDgSibDZbJlMptFotmzZsn79+oKCgtv9\nGSHTD7h2++Uvf9nW1jY4OAiKShQKxbp161auXJmfn5+SkgLKjL/6DT+wNTEajWaz+d1337148aLV\nakUQJC0tTalUrlmz5pFHHlGpVDA3lyCYzeZLly69+eabfX19oFKAxWJVV1dv2bJl7ty5MplMqVSy\n2eyv/vvCcRw0cI2MjJw5c+bEiRODg4MIgrDZbGAWsGnTpu3bt0/FZ5p1HD9+/OjRo5cuXTIYDAiC\nFBQUrF+/ftOmTXK5XKVSgcHAU/5Do9Go3W43m83nzp07efJkfX09QRA8Hi8jI2PDhg0///nP4dAc\nyDQQCoX6+vr27dt348aN4eFh0CKKIEhKSsq8efNWrlxZWVkJBrpxuVwWi8Vmsz/30h7DMOA9AUpx\nQ6EQ6Jv45JNPzp8/39/fH4/HKRSKRCLJyMhQqVRPPPFEZWXlv6ZdIMnE4cOHP/zww+vXr4+MjADj\nm/T09GXLlt1zzz1CoVAmk8lkMqFQeMt/P5g3NzExYbPZPv744xMnTgwNDREEwWAwdDpdfn7+hg0b\ntm7dKhQKYfX3rAUMvnn55ZfPnj0LpnwQBCGVShcuXLhx48aSkhK5XC6VSqekXyYej4NaKpPJ9MEH\nH5w4cWJ0dBRBEJlMlpaWVlFR8cMf/jA9PR067Ew5MF1yU+A4HggEDhw4cP369ebm5ra2NhzHRSJR\nVVVVdXV1bm5ufn5+bm6uSCT66oeWYDAIWifGxsbOnz/f0tLidDoRBCkrKyspKamtrd28ebNMJoOn\n2aTB6/W2tbUdOnTovffes1qtOI6r1er169cXFRVVVlbm5uZKpdIp/6E4jofD4WvXrnV3d7e1tR08\neBBcy2RlZa1du/aOO+6orq6G1yakc/369dOnT3/88ccNDQ3RaFSpVFZVVS1fvlyn01VUVNymrFYk\nEunr6+vs7GxoaKivr29vbycIQiaTlZWV3XHHHbt37wZzBKb85yYfOI77fL5jx44dP3782rVrVquV\nxWJt27Zt8eLF1dXVRUVF02MYNDg42NHRcf369WPHjo2Ojkaj0czMzK1bt957773Z2dmwaAhy+6iv\nr6+rq2tubr506dLExEQsFpNKpSUlJcuXL5906klPT7/lv9/j8fT39+v1epPJ1Nzc3NDQYDQaEQRh\ns9lLly4tKyubN2/esmXLYC9hkoHjuM1me+ONNy5cuNDV1WWz2Wg0WmVl5bx580pLS0FrKijFnaqf\nCLbFjo6OlpaWa9euXb16FcMwoVBYUFCwfPnyTZs2FRQUwFaIWUgwGBweHj548OCJEyf6+/uj0Sif\nz9+wYUNFRQWomEtNTb0du3w4HAb2KIODgwcOHDCZTPF4XCqVrlmz5o477li4cCGcsD61UJ977jmy\nNSQ64XB4dHT09OnTv/3tb8+fPz8+Pi4QCKqrqxcvXrxly5atW7cuXbpUo9FM1X5Mp9NlMllJSUlZ\nWRmfz+fxeDweD7T7dnZ2jo2NTQ6FhZZmSYDT6WxoaPjrX//67rvvulwu0IO9ceNGUFan1Wpv02EG\nDGbKzMwsKSnRarWhUEgmk4VCodHR0d7e3kAgAAbswas5UgB9/tevXz98+PDRo0ebm5tRFK2oqFi9\nejU45RYWFopEott0AKDRaAqForS0NCMjQyAQsNnsYDDodDqHhob6+/ulUqlAIOBwOLBn+4vBcXx8\nfPz999/ft2/ftWvXfD6fWq1et27dt771reXLl6enp0+bHZVEIsnNzS0pKQG24uBuqrW1FfhEcDgc\nHo83DTIgsweCIILB4IULFw4cOHD06NG6ujq/36/RaEC38qZNmx544IF58+ZlZ2d/lZt/BEFYLFZa\nWlpJScmcOXNSUlJ4PB6Hw0FR1Gaz6fX63t5eu91OpVKBMQocIZEchEKhgYGB48ePv/TSS729vdFo\nVKPRrF69evPmzTt27Fi2bFlmZuaUZ6LBtlhWVpaVlSUWi+l0OkEQHo9naGgIaOByuQKBAJrmzCq8\nXm9nZ+fhw4dfe+01g8HA5XILCgrWrFnz4IMPrlu3rrCwkMfj3aZdnkajKZXKkpKSkpKSSCTC5/Nx\nHDcajZ2dncCimM/nQ0PiqYSAfCEgo/zCCy+AMiomk6lQKNauXXvx4kWPxzMNAoLBYENDw/z580FG\nBkEQHo+3Z8+euro64JAMmaHE43GPx3Pq1KmNGzcCWwGxWLx169aTJ09Ovxgcx1tbW7/xjW/IZDLw\nci8tLd27d6/dbgcDd6Zf0qwFTI7Q6/V33313SkoKiqJsNjsvL+/dd9+12WzTLCYej7vd7m9/+9sF\nBQXgHEKn03/1q1/19PSAciTI5xKPx61W6x//+EcQLdHpdK1W+9hjj4VCIZCzIIvTp0/fe++9IA2K\noujGjRuPHDkCRkqTqAqSTMTjceAwkpubS6PRKBQKh8PJyMj47ne/29DQEIlEbutP7+zsfO6550Bn\nNMiPyGSyX/ziFx0dHcFg8Lb+aMjtBsdxv9/f3t7+gx/8AAQqXC43Pz//e9/73nS+WsG2+MILLyxa\ntEgkEgEl4F3qdDphyDQbAEuxrq7u0UcfBQuAz+evWLHij3/8Iyl69Hr9c889B6aCIAiSlZX1zDPP\nmEymWCwGV+OUANMl/4HOzs49e/ZM9iXW1NS8+uqrdrs9HA5Pz6sZOJuAtsnNmzdP+pktW7Zs//79\n0yAAcpuw2Wyvv/56ZWUli8VCEEQsFpMY0oFlZrVa9+7dC65HaDRaWlra7t27ST/gzTZisdjVq1ez\ns7NBipbH49XW1ra3t3u93ng8Ps1iwARil8t1+PDhjRs3giS7SCTatWvXRx99NM1iZhBOp/PHP/6x\nWCwGG0dxcfGvf/1rl8tFeiQdCoXa29t/8pOfAGEsFmvlypWHDx+ORqMkqoIkEyBRKJfLQQGaSCTa\ntGnT8PCw0+mMRCK3e/1Ho1GXyzU8PPz000/n5eWBqwiBQPDAAw+cP3/+tv5oyO0Gx/Fjx45t3Lhx\nsu1l165d77//vtvtns5XK9gWvV4vSNyAkInFYhUXFz/33HOhUAgeUJOeeDx+5MiRdevWgd8+iqKP\nP/745cuX/X4/KXrAwNYPP/xQIpFQqVQqlSqVSleuXDkyMjL9cWNSAptx/i1+v//cuXP79u37+OOP\nbTYbi8W69957H3jggeXLlyuVShqNNj111CiKUqlULpcrlUrz8/MlEklLS0soFAK18VartaamBs4Y\nnnFcv37997///aFDh/R6fSQSqaio+MEPfrBhw4bMzExSrATAMmOz2QqFIjs722g0ut1uj8djs9l6\ne3srKir4fD7s/Z4GAoHAiRMnnn/++c7OzkgkolarN2/e/PTTT5eUlJDSfg/ysywWKyUlRaPRCIXC\n9vb2QCBgt9udTiefz09LS4Ml7p8GuL69+OKLR44cMRqNLBbrzjvvfPjhh9euXatQKD53IsN0QqPR\n+Hy+UqnUarUDAwMul8vpdDocjoKCAqFQ+BXHGEMgdXV1b7/99v79+4eGhnAcX7JkyUMPPXT//ffn\n5+ez2expCJyoVCqTyRQIBBkZGcXFxVwuF7SXWq3W0dFRn89XWlpK+mMIuQUsFsuf/vSnd999t7m5\n2e12p6Sk/OhHP7r77rvLy8tBYnrafqfgZ00uM61W29raGggEPB6PwWDo7e2tqqqCdjlJzNjY2N69\new8cONDW1ubz+dLS0n70ox9t2bKlsLCQz+eTIgl0P4ARY2BPd7vdExMTPT09mZmZSqUSrsavCEyX\nfD6jo6MnT548ePDghQsXLBZLenr6jh07du3aNX/+fIVCQYokFoulVCoVCgWNRnM4HE6n02QyjY+P\nx2KxzMzM29cgB5lyhoaGTp48+e677+r1egRBli5d+uCDD27evFmlUpHrR4OiqEAgyMzMFAqFoVDI\n7XZbLJbh4WEKhZKWlgbbIG8rBEFgGPbBBx/8+c9/PnfuHI7jVVVVmzZt2rZtW21t7bTlZ/8dXC5X\nLpeDUk+bzWa1Wu12u8fjycvLEwgE8Jg9idPpPHjw4Ntvv63X66VSKTguLl26VKVSkS3tH9DpdJFI\npNVqeTye2WweGRlxOp1erzcvLw9cTJEtEDIj8fl8Fy5cOHTo0IcfftjX18fhcO66664dO3asXbu2\nuLh4Oi91QEWJTCZTq9UKhYLFYg0PDzscDrPZbDabg8GgTqcDrYXTowfy1TEYDGfPnn399dfb29uD\nwWBBQcF99933ta99LTc3l0SDVTqdLpVK09PTuVyuy+WamJiwWq0jIyM4jiuVSqlUCs+oyYfZbL54\n8eLvfve7np6ecDhcWlr68MMP79y5Mysri1znGtC4nZ2dzefzQVEwWI0Yhkml0oyMDBK1JQEwXfI5\nuFyuc+fOvfzyy1euXAE76+bNm5966qmioiJyLfFABFBVVeX3+71er8fjMZvNV69e1Wq1CoUCmnIn\nPgRBhEKhkydPHjt2rKOjg0qlVldXP/bYY7t27RIIBImws6IoyuFwKisrGQwGSJd4PJ6Ojg6FQgGM\nP8kWmLTEYrHW1tZXXnnl7NmzNBpNq9U+9NBDu3btqqysJFvaP2AymampqaWlpWDesMFgGB0d5fP5\narVaIpEkwuolHZfL1djY+NOf/nRoaIhGo1VVVT322GMrVqxINMtkGo0mEAjmzJkzMTExOjpqNpvb\n29tVKlVaWppEIoHHSMiXBTQmvPLKK6dPnzabzTKZrLa29gc/+MHixYtTU1PJUsVkMtVqdWlpqdls\n9ng8LpdrbGzs2rVrmZmZcrkcXjLNFNxu98WLF9966626ujocxwsKCnbu3PnEE0+kpqaSXtuIoiif\nz1+4cGEoFAqFQqD0srm5WaFQaDQasVhMrjzI1BIOh+vr6/fv319XV4cgSGFh4de+9rUnn3xSIpEk\ngvk9qBMvKCgQi8XBYNBoNPr9fr1eT6VSwXUI2QJnMDBd8n8AHUpXrlw5ePAgaHMViUSPP/74T3/6\n0wSZ3UuhULhc7vLlywmCMJvN4+Pj4OkFI04SQSHk3wHKB/R6/W9/+1twJJZKpa+99tqaNWtI3/L/\nlaKiIi6Xa7VaBwcHw+Gw2WzmcDhVVVWwjPl2gOO43W5//PHHGxoawuFwenr6d77znZ07dybahQCV\nShWLxcuWLZuYmGhsbAyFQleuXAFj1Nls9ixfGBiGNTQ0vPrqq9euXYvH47m5uXfeeec3vvGNxCy9\nAXFVdnY2giB1dXUYhjU2NspkMpAqJVsdZCaBYVhra+vrr7/+97//PRAIcLnctWvX7tu3LysrCzhz\nkQiFQhEKhZs3bzabzUaj0ev1BgKB8+fPa7XaoqKiBNx5IZ8GxORXr17dv3//e++9hyCIRCJ59tln\n9+zZw+VyE2rHqamp0el0wWCwtbU1FouNjIzw+fw5c+bAsDw5IAgCQZDR0dEDBw68/fbbCIKIxeIf\n/ehHjzzyCIPBSKiliCCIVqtVqVQ2m214eNjv99vt9kAgsHz5cmjdcMvAdMlnMRqNb7755vHjxyOR\nCJfLff7553fu3Dlp9Zo4ZGZm8vl8h8MxNjYWjUY9Hg+NRisrKyNbF+TfguO4x+P51re+VVdXF4lE\nsrOz33zzzYqKioStClYoFBKJpLOzE9zL4TgukUiys7MTU+2MRq/Xv/rqq2fPnvV4PEqlcuXKld/9\n7ncTtjOCQqEoFAoul1tfX08QhF6vp9PpMC5sbGw8ePDg+++/HwqFFArFww8//PDDDyf4jF5gJxGL\nxbq7u2OxGGhVWLx4Mdm6IDOJrq6uI0eOHDx4MBgMstns3bt3P/PMM0qlcsqHuX4VCgsLc3JycBzv\n6emJx+N2u51OpydO7R7kc8EwbGxs7JVXXvnwww8jkQiTyfzd7353xx138Pn8xFlak0ilUiqV2t7e\n7vF4gDU7m80uLi4mWxdkaohGoz//+c8PHToUDAYZDMbLL7+8fv36BDweAkQiUW5ubldXl9PpdLlc\ngUBAKBSq1Wo2m022tBkJTJf8fyYt+k6ePGk2m+Vy+TPPPLN582aNRpOAdeYcDkcqlXK53M7OzkAg\nAKaXpaWlKRSKWX5oSUwwDOvp6Xn++efPnDnj8XhAlf769evB9BOy1X0+LBZLJBKlpqZev37d5XJ5\nPJ5gMFhdXc1isRKh7DBpGBgY+OCDD9555x2r1crj8datW/fII4/k5eUl7IOMoiiPx2MymU6n02g0\nTkxMeL1egiDmzJlDtjRyIAgiHo/v37//yJEjVquVxWI9/vjj27Zt0+l0ZEv7D1CpVB6PJxaLx8bG\ngD8cQRAZGRlyuRxevEP+IziO22y2/fv3Hzt2zGg00mi0PXv23HvvvQUFBaTbLX0GPp8vk8loNFpr\na6vf7wcXADKZLCMjI2G34FkOjuNut/vXv/71qVOnLBaLRqN58sknN2/enLC+lQwGQygUKpXK1tZW\nr9frcrl8Pp9Wq4Uu2jMdHMedTueLL754/Phxo9EIluJdd92VlpaWsHEanU4XCoUKhWJgYMBgMPh8\nvvHx8dLSUqlUClfjLQDTJf8Ax3GLxXL06NF9+/YNDw9rNJq77rprz549aWlpCXsyFAqFKSkpBEEM\nDAzY7XafzxeLxcrLy9lsdsI+wLOWkZGRkydPvvLKK4FAQKfTbd269f777xeLxYm560/C4XBAfanZ\nbB4dHZ2YmKBSqTk5OUKhkGxpSQKGYWfOnHnnnXfa29upVOrq1au//vWvr1ixgmxd/wE6nc7lckUi\n0dDQkMvlAh43lZWVfD5/Fh6zcRxvbm7ev39/U1OTWCzesmXL7t27CwsLE/zpBkxm3nt7e61WaygU\nisViixYtImVEF2QGQRBEJBIBdSWdnZ1CoXDdunV79uwpKytLzAiEx+MB+62BgQFgbxwKhfLy8ng8\n3ix8ayU+BoPh6NGjb7zxxvj4uEqlWrt27ZNPPpmampqwMTmCIHw+X6fThUIh0CzvcDhCoVBxcbFI\nJJoR2wHkc7Hb7RcuXPj1r389NjaWmpq6atWqp59+WqFQJPh7g0aj6XS6eDzucDgGBwdNJhOTydRo\nNGlpaWRLm3nAdMk/8Hg8ly9ffvTRRx0OB5/PX7t27Y9//ONEzpUA+Hx+dXV1V1eX2WwGg3JycnKU\nSmWCV4DPNnAcP3PmzNtvvz08PMxisbZs2bJt27b8/PyEunz7XMC0vAULFoyOjvb399vt9rq6uuXL\nl6vV6gTfJ2YKFovlr3/969/+9jcajVZQUPD000+vXbs2MQ8bn4HL5Wo0mmAwODY2Zjabw+EwiqIl\nJSWzzQ8Yx/FwOPzKK69cvnzZ7/fn5ua+9tprmZmZM+gBYbPZZWVl7e3tBoPBYrGYzebVq1eLxeIZ\n9BEg04/f7+/q6vrJT37S2dnJZrMrKipefPHFnJwccue7fTFisXju3Lnd3d1WqxUMyuHxeDqdLmEr\n6mctkUjk8uXL3/ve9+x2O5fLXb169Te/+c3i4uLE3xwZDMb8+fMNBsPIyIjFYmlvb6+srFSpVDAs\nn6EQBNHR0fGb3/ymt7cXRdElS5Y88MADlZWVib8UgUNZaWlpPB4HFU+tra25ubnFxcWJ/JZOTGCy\n8x80Nze/8847fr8fx/ElS5Zs3bo1PT098ZPBKIpyudy9e/fecccdKIqazebHH3+8s7OTbF2Q/0Ms\nFuvr62tqaqJQKDk5OevWrauuriZb1JeAwWDcd999d999N0EQsVjszJkzvb29ZItKEg4fPgwcQAQC\nwd69e5cuXZrgKdpPw+Px9uzZU1NTA1yB9+3bZ7PZyBY13QAfhIsXLxoMBrFYnJeXJ5PJZmKi4YEH\nHli0aBFBEE6nc+/evfAZh3wxXV1d99xzT19fXzwer6ys/M53vpOXl5f4jfFsNvs3v/nN+vXrmUym\nxWJ5/vnnOzo6QqEQ2bog/4fx8fGenh7QM7Vo0aItW7bU1NSQLepmYTAYjzzyyPbt21EUxTDs1Vdf\nra+vJ1sU5BaJx+NGo/H8+fOhUEij0SxdunTlypVki/oS0On01atXf+c730EQJB6PNzY2NjY2ki1q\n5pHo6YDpIRaL6fV6MBdKq9WuXr160aJFM8JAGCgUCoU7d+7csWMHjuNer/fChQs9PT1kS4P8f/bv\n33/27Nl4PM5isZ544onq6uoZdCQGo3Byc3MLCgpA4cDRo0evXbsWi8XIljazwTDM5XJdvny5v7+f\nx+MVFBSkp6cnrO/v5wKKj7Zu3bpixQoMw3w+31tvvdXS0kK2rmllaGjo5z//udFoJAhi/vz5zz77\nLIvFmkG/xEmKiooqKirUanU4HD579uzo6Gg8HidbFCRBsVgsXV1dRqMxFotVV1dv2bJlyZIldDp9\nRqx8oVD4wAMP7Ny5E0GQUCj0xz/+8dKlS2SLgvwfLly4cOjQIYIgaDTa2rVrlyxZMlOiJhAyaTSa\nuXPnzp07lyCIvr6+vr6+WXiXkBycOXPmwIEDIOLdtWvXhg0bZtZ1CIqiarW6oqJCLBZTqdQLFy6c\nPn06Go2CWT+QmwSmSxAEQS5fvvzJJ584HA4URbdt27Z48WKpVEq2qJsFRVEKhVJZWTl//nwul0sQ\nxEcffQQmWZItDYLgOO73+y9dutTd3c3n88GvKSUlhWxdXxoul7tgwYJ7772XQqEYjcYrV640NTWR\nLWpm43a733nnHWDVrNPpHn300QSZVv5lqaqqmjdvnlwux3H81KlTvb29s+flE41GDQbDqVOnvF6v\nRqOZM2dOSUlJ4pclfi58Pn/p0qXr1q3DcdxqtV66dAkWKkL+Ha2tre+99140GqVQKEuXLl27dq1M\nJpsRuRIQMpWWli5duhS0xDY2Nra3t7tcLrKlQf5BV1dXQ0ODXq9nMpnr1q2bM2eOTCYjW9SXg8Vi\nVVdX33nnnVQqNRAInDlz5uzZs2SLgnxpgsHg9evXGxoa6HR6cXHxvHnzMjIyyBb1pWGxWAUFBU88\n8URKSorNZrt27Rq4wSVb10xiRkZ1UwjwKjt16lR9fT2DwdBoNJs2bcrNzSVb15dGKpWWl5eD653W\n1tb6+vrBwUGyRUGQUCh05cqVrq4ul8uVlpa2Y8eOxHeH+ncUFxfv3LkTTLe9evXquXPnMAyD+elb\nA8Mwq9X61ltvjY+PCwSCioqK7du38/l8snXdCikpKXPnzgXTZwcGBtra2kZGRsgWNU2Mjo42Njaa\nzeZ4PF5TUzNv3rxEGwjypaioqFi5ciXwcTh37lxDQwOGYWSLgiQcFoulrq7u4sWLFAqlsLBw4cKF\n+fn5ZIv6coC37vr16+l0usPhaGpqam5uJlsU5B98/PHHzc3N0WhUJBLdc8892dnZZCu6FbRa7cqV\nK4uLi9lsdmNj49mzZ8EIS7J1Qb4EbW1tra2tVquVzWbfddddCe7N9AUolcpHHnlEp9MxGAy9Xn/0\n6NFwOAwD+JtntqdLMAwzGAydnZ1Go1Eqld51113p6eksFotsXbfC3Llzf/SjHwkEAhRF6+vr//73\nvxMEAR8GEiEIwuFw/OpXv+rv76fT6dnZ2d/4xjdEIhHZum4RJpOpUChqamr4fP7AwMD169cdDgfc\n+28Nn883NDSk1+uDwWBBQcGCBQsYDMbMPWbX1NQ8+OCDIA94/vz5U6dOzYaXD0EQV65ceeeddxAE\nYbFYK1asWLZsGdmivhJsNlutVldWVjKZzK6urq6uLr/fT7YoSMJx8eLFq1ev+v1+BoPx0EMPlZaW\nkq3oVigsLNy1axeYLnzmzJn9+/fDAnXSwXE8EAicOnWqq6uLw+FkZWUtXLhQLpeTretWoFKparV6\n9+7dcrk8GAwODQ3Buu8ZBEEQGIa99dZb9fX1VCpVJpPdd999WVlZZOu6Reh0ukQiKS8vT01NNZvN\n9fX1ZrM5Go2SrWvGMNvTJT6f74UXXujo6EAQRKVSgdFQZIu6RRgMRmpqamFhIY/H0+v1TU1NkUgE\n7v0kEolEbDZbT0+P3+/Pzs6uqamZ0UdiBEHUavXzzz+v1WoRBOno6HjxxRe9Xi/ZomYkzc3NL7/8\nciQSQVF08eLFW7ZsIVvRV4LFYimVyqKiIhaL1dXVdf369dmwDcdiMavVOjo6SqVSa2trdTrdTOmu\n/wKKior+67/+C2R1+/v7P/nkE7IVQRKO06dPNzY20ul0uVy+ePFitVpNtqJbgUqlKpXK3bt3q1Sq\nQCAwNjbW3t4+G15ciYzb7T5y5IjRaMQwLC8v7/vf/75YLCZb1K0jk8l27twpl8spFEpLS8tLL70U\nDAbJFgW5KTAMczqder3e4XCkpqauWLFCIBDM0E5bAI1Ge+KJJ4BlssVi+dnPftbf30+2qBnDDP7F\nf3VisRgownQ4HGq1eu7cuTO3UQJBEAqFkpKS8tRTT2VlZUWj0e7u7t///vewHZdEhoeHjx8/7vP5\ncByvqam58847Z4R/8BfAYrFycnKys7NFIpHNZquvr4fB5S0Qj8dNJlNbWxuGYSUlJYWFhTM6IkQQ\nhEKhaDSaH/7wh0qlMhqNDg8PX7lyJenNgNva2np7e6PRKI1G27Jly4wYDf4f4fF4OTk5arWaxWL1\n9fXBfnvIpwkGg2fPnr1x40YgENBoNI899tjMHSqPoqhEItm1a1daWhqKoj09PXv37vcdDkMAACAA\nSURBVPV4PGTrmtW43e6//OUvJpOJxWJlZGQsWLBghpZ7A2g0mlAoXL9+fW5urt/vHxkZGRsbg2OY\nZgROp/PAgQMgc5eTk/Pwww+D4n2ydd06KIpmZGTk5ubK5fJAIHDp0iWn00m2qBnDrE6X2Gy2ixcv\ngnqk4uLijRs3zui2cwRBuFzu8uXLc3JyeDyeyWQ6duyYz+cjW9TsZXR09MMPP4xEIhKJJD8/v6Cg\ngGxFXxUKhcJms1evXp2fnx8KhcbHx8fGxuBtyZdlbGxMr9eDVObKlSvLyspmosPrZxCJRKtXr9Zo\nNEwmc3R09P3330/6VNrVq1e7u7spFAqfz6+oqEhNTSVb0RRApVL5fD7wVrTZbGBMLKxShAD8fv+h\nQ4dGR0dpNFp6evrWrVuFQiHZom4dFouVm5s7b948jUZjt9svX75sNpsjkQjZumYp4XDYbDa3trb6\nfL6cnBzgID7TS/YoFMrGjRsLCwsRBPF4PKdPn4YjcmYEbrf72LFjdrtdIBDodDrQo0q2qK8EGGVY\nU1NTU1MTj8fNZrPBYIAJ4ptkVqdLDAbD4cOH/X4/m80uLS1dvnw52Yq+KpORbmZmZiAQ6O/vdzqd\nSX9oSUyi0ajZbO7q6orH40VFRVqtdqbv+pOsW7euuLgYQZBgMNjQ0OBwOMhWNMNobW29fv06giB0\nOr22tjYvL49sRVMAjUYTCAS5ublSqdRkMl25ciXpmwG7uroGBwfZbLZOpxOLxQwGg2xFUwOLxVqz\nZo1KpYpGo26322KxJH2hEORmiMfjTqfz3LlzVqs1JSWlqKgoOzt7ph8hEATZsGFDeXk5QRA+n6+l\npQXeuJKFzWZra2sLBoM4jldVVa1cuZJsRVMAiqJVVVW5ubl8Pt/r9R45cmR8fJxsUZD/QCwWczqd\nLS0tPp8vMzOzqKhopkxJ/4/Mnz+/trYWRVEMw9rb28fGxshWNDOYvekSgiBsNtulS5dCoZBarVap\nVEkT7G7fvn3hwoUEQYTD4Y6OjomJCbIVzUbsdrvFYgG2XmASHtmKpgyVSiWVSsF4vBMnTsC9/8vS\n3t7e1tZGo9GkUqlUKmWz2WQrmhpQFF2yZIlWq41Go06nMxwOJ6sTMDCytdvtHo9HKpWuXr16hk41\n+lzYbPbatWtVKhWCIB6P55NPPoFVihAEQfx+//DwsNfrxTBszpw5d955J9mKpoYVK1YUFxfTaLRA\nIPDOO+/AqYJk0dfXd/DgwVgshqJobm5uRUUF2YqmjPT0dK1WGw6Hm5ub3W53cl8kJAFer9dgMADv\n55qamlWrVpGtaMpISUmZ9J24ePFid3c32YpmBrM3XeJ0Ok0mE7g0W7Vq1fz588lWNGWkpaXJZDIq\nlRqJRN5///3ZM9Qzoejt7QUWwiiK5uTkpKWlka1oKtFoNFlZWbFYrKenB9byfVmcTqfT6eTxeKtW\nrZJKpWTLmUqWL18OrOPBCO1kzdXG4/GRkRG/308QhFQqXbVqVTKlSxAEYTAYHA6HwWC4XK4zZ85A\nR2cIgiD9/f3vvvtuMBhEUTQrK6u6uppsRVOGWq0Gpm+tra3J+tZKfICzJo7jhYWFIF2bNCxevHjF\nihUIghAEYTaboatggmM0Guvq6nAcR1FUo9HM0FHW/w6pVFpcXEylUoeGhqxWK9lyZgazN10yPDzc\n1dVFEASKosXFxTk5OWQrmjKYTKZSqdRoNPF4vKWlxW63k61oNjIwMNDT00OlUlNSUsRi8Yy2K/tX\nsrOzi4uLMQybmJgIBoMYhpGtaGYAitrcbnc0GuXxeKtXr06ydElKSopIJKLT6cFg8OLFi8naqBWL\nxbq6ukCikMfjgZFAZIuaMlAUpVAoaWlpKSkpgUCgvb0d+hNBEASx2+2NjY3RaFStVmdkZMxo15LP\nUFFRsWTJEoIgPB6PzWaDdwDTTzweDwQCLpeLIIiKiorMzEyyFU0lmZmZkzNoOzs74S1mgmMymZqb\nm3EcF4lEEomEw+GQrWgqUSqVNTU1VCrV4/H4fD443PpmmL3pksHBwY6ODhRFeTyeQqEAcxOThoyM\njKKiIhzHzWYzmMxCtqJZh8lkMhqNDAYjPz+fx+ORLWeKycnJKSkpQRAkFotNTEzAWv2bBMfxwcFB\n0BvPZrPnzJmTTEcOFEVpNJpEIpFIJJNVx2SLui1Eo9He3l6v10uj0Xg8nlQqTRpnokkyMzNVKlUk\nEjEajdAAC4LjuM/nM5lMGIYVFxeDcfJJQ15eXmVlJfh6YGDAaDSSq2cW4vV6nU4nqPiurKxMsnQJ\nl8uVSCR8Ph9F0ba2tuHhYbIVQb4Ip9PZ39+P47hOp5PJZGTLmWKUSuW8efNoNFo8Hvd4PLDW6WaY\nvekSo9HY399PpVIzMjKS7zSblZUF2j7D4bDf7w+Hw2QrmnX4/X6Px8NisWpqaiQSCdlypphPVyeO\njIyYzWZy9cwUCILo7e11OBxgxhAY10q2qClGpVKlp6eDdpVkrUqIx+MDAwM+n4/NZgsEArLl3Ba0\nWq1KpcIwzOPxwOE4kE/HEmVlZUlWnS4SieRyOTCwa29v1+v1ZCuadYyOjgLXSQqFkp+fn2T9ywiC\ncLlclUpFoVD0ej10fEtwQqEQuNYqLi5Wq9Vky5liUlJSSkpKwB2P2WweGhoiW9EMYPamS0Amm8Fg\nzJ07NyUlhWw5U4xWqy0tLQVfGwwG+GqefuLxOIZhLBarqqoqyWqXEASh0WhMJhOYRen1euitfZMQ\nBGEwGLxeL4PBEAqFyWG0/hkyMjJ0Oh2GYS6XK1knqkQikZaWFpfLxePxki8ZClAqlWBnxHE8Go3C\nhrtZjtlsnnzPl5SU6HQ6cvVMORwOR6VS0Wi03t5eeH6Yfrq7uzs7OykUCpfLZbFYVCqVbEVTjFgs\nzs3NpVKpXq83WS8SkgYcx0GLSmFhoVKpJFvOFEOhUJhMJoPBQFHUaDTC7PDNMHvTJfF4PBaL0en0\n8vLy5It3gVEfyB0ODg6Ojo6SrWgWQRCEXq8Hrg10Ol2r1SZZ3yPyz7YLHo9HoVDMZjP0xrtJcBzv\n6uqy2+0cDkcmkyVlukQulysUCgRBMAyLRqPJ2hYbi8VwHBcIBKmpqWRruS1oNJrJMHF4eBjW685y\nbty4AfqX2Ww2l8tNmkmCk/D5/NzcXDqd7na7YXvp9GO32202G4qiIFeSfJujUqlcuHAhnU4Ph8Ow\nvTGRGRsbMxgM4Ou0tDSxWEyunikHRVEqlcrj8Wg02sTEhMlkIlvRDGCWpkuAMTVBEDQaLScnJ/mq\nqSkUCp1O53A4FAplfHzcYrGQrWh24fF4QqEQgiA0Gk0ulzOZTLIVTT0cDictLQ2mS74UBEG43e5Q\nKMThcBQKRfJFhAiCKBSKyaEGwNeWXD23FQaDkXztVACBQMDlchEEIQjC6/VGIhGyFUHIxGQyjY2N\ngXQJnU6nUJItepTJZDU1NUwmMxQKwf7l6cftdrvdbiaTmZ2dnXw3TAiCCASCzMxMCoWCYZjP50vu\nnXFG4/f7A4EA+FoqlYJ9MMmg0+mgGRymS26SZNvwbhKz2QxeVVQqValUJuWrmclkyuVyKpVqtVrh\ncByyAF7CyWcDifyzEZdGo7lcLjhn9MvCYrHEYnFSpkukUulke6Pdbk/KGRMEQUSjURzHQVaabDm3\nBRqNlnz18JBbxu12T0xMUKlUuVyelClCsVhcXl7OYDBisVgwGITtEtMM+H/OYDB0Oh2bzSZbztTD\nZrNlMhnIM3o8HhiWzwjYbHbyVdIhCEKn0zUaDYvF8vl8sHT0Zpil6ZJJUBQVCoVJ+TBwuVydTsdg\nMGw2W7KO80xY4vE4mEaUlOdhAJ1OFwgESfwBbxOTCyP5rmcBNBotKfODnwbHcY/HE4vFxGJx8lkS\nQiD/CjAvZzKZZWVlyefGhSAIg8EQi8WTp1l44wqZWng8nlqtBgssEon4/X6yFUE+HwzDkt6ri0Kh\nCIVC4D8IuRmSM16HIAhCp9NFIlGyHskSnO7ubqvVSqFQkv7cCPmygL4GgUCg0Wjg4zlzAZNixGLx\nZOcRBAKZuXC53IyMDHB+CIfD0L5kmonFYslqDQ6ZWQwPDw8PD6MoSqfT4Y0gBDBLg/Xh4WG73Q7s\nKsnWcrsAXj7wUZ9+CIJwOByBQIBGo3G5XPgrgHwaUHkkEAgyMjJgumTmAt6uLpcLzh2DzAbi8Xiy\n2jYDqFTqpMsYQRBJf72caEQikUgkwuFwampqkrJ8CTJTcLvdHo+HQqHweDzYkQoBzNJg3WQyuVwu\nKpXK4XDgaRYy5QAzPIIgQOcFBDIJhUJBURS0x4MKBciMA0VRDodDpVLdbjcs2ofMBmKxWCQSodFo\nOp2Ox+ORLQeSbIAOCBqNlpqampQN8pCZAhiyC3OmkE8zS9MlGIbhOA7Gx8B0CWRqQVFUrVYLhcJY\nLOb3++GRGPJpGAwGlUp1uVx6vR5m02YoFAqFzWZTqdRoNJqslpDxeBwEi6AME1ZCzXJArwSDwSgp\nKREKhWTLgSQbVCqVSqXGYjGTyQTncEFIRC6Xy+VyHMd9Pl9yl9RBbp5ZGgCBSdrRaNTtdsMTC2TK\n0Wg0oJoUri7IZ+ByuXQ6PRKJeL1emEqDJCx+v38yE8Tn85NyGjrky4LjuMvlikajZAuBJBs8Ho/H\n44VCoZaWFjhrD0IiIF2C/NOhDAJBZm26RK1WSyQSBJ5mIbeH2VCyFAwGx8fHMQxjsViwdPbmSfq1\nEQgEJj3/eTxeUo6EpFAoYJyq3W4fHR0lW85twWazTUxMgK/VarVAICBXD4RcuFwuj8eLRCJtbW1u\nt5tsOZCkBcdxeEyFkAiKokkfp8ViMYPBEAqFGAxGUg6Gn3JmabqExWIB//MkfilHIhG73Y5hGJ1O\nT2JH28REIpFwOBwEQTAMs1qt4XCYbEVTTygUslqtGIalpqZKpVKy5cwMUBQFF/WBQMBkMiXl+8fl\nck0es1NSUpKybp9Go6WlpbHZbL/fn6xj2vv6+oaHhxEEodFowIyJbEUQMqFSqTQajSAIr9cLJ5hA\nbhM4jgcCgaT0jPB6vSMjI+COVigUpqamkq0I8vkIhcLJ64GJiYmkHPkcj8fNZnMkEpFIJAqFgmw5\nM4BZmi7hcDigtJggCJ/Pl5R7fzgcNplMsVhMJBIl5YklkZHL5cAMLxaLDQ8PJ6W7QTgcdjgcOI6r\n1eqUlBSy5cwMUBSVy+VcLtfn8xmNxqSsbjMYDKDggkKhCIVCLpdLtqKph0aj5eTk8Hg8MHAUw7Dk\ny3z19/ePjo5SqVQ2mw2NSyAAgiAikUhSvrgmdzQEQVgsFoyaphmBQCAQCGKxGDjFkS1n6nG5XDdu\n3ACZIKFQCKOmhEUsFk/OZjKZTElZTBePx+12ezQaTUlJUavVZMuZAczSGEihUIC9EMOw0dHRpMwd\nRiIRm82GYZhKpVIqlWTLmUWACgIWi4WiaDQa1ev1ybfAcByfdN9QKBSwuuQmQVFUo9EIBIJIJAKM\nk5LvmK3X67u7u1EUZTAYyXrMZjKZlZWVEokkHo/7/X6Px5N816F2u93pdNJoNJlMBusTIXQ6nU6n\nYxg2MTGRlKdZt9vd0dEBbFkkEkl6ejrZimYX6enpGRkZ0Wh0aGgoFAqRLWfq8fl8o6OjGIZRKBQa\njQbr9RIWDofD5XJBP87o6OhktWzSgON4LBZzu93xeFwikcAT4s2QnLHsf0QgEICO+ng8PjIy4vP5\nyFY09cRiMafTCXolZDIZ2XJmHUwmk8lkBoPBCxcuJF+5fjAYnMwBKZVKmC65SVAULSoqSklJicVi\ngUAgKe9pnU6nw+GgUCh8Pj9Zj9lMJnPBggXgvep2uy9duhQIBMgWNcWYTCa73c7n82tqauDgWEh6\nenpOTk4sFhsaGkq+CwAEQQKBwPDwMBiEQaPRoCHXNMPlcrlcLoZhLpcrKSu+fT7f2NgYjuN8Ph80\na0MSFtCCiiDItWvXQFNqMhGJRDweD7irk0qlaWlpZCuaAczSdAmFQmEwGEwmMxqN1tfX22w2shVN\nMaFQyOfzgZNYamoqrPqbflJTU1UqVSQS6ezsTD6b98HBwe7ubvB1VlaWSqUiV89MgUKhVFVVgVx+\nMBhsamryeDxki5pibDabxWJhMpllZWXJWtAOkkFgyJHT6Tx37lwy5dxxHPd4PH6/PxaLicXiVatW\nQZ9XCJ/PFwgEOI5PTEwk5WQcv98/Ojoai8W4XC6bzU56r8dEIy8vLz8/H0GQeDxusViSb2d0OByd\nnZ3xeFwsFsMEdIIjFot1Oh2Kov39/cl3QrRarU1NTaAkNi0tLSsri2xFM4BZmi5BEEQsFsvl8lgs\n1tramnylVmazeXBwEHydnp4OT7PTT1ZWVl5eHoZhFosl+azL9Hp9Z2cniqIcDkcikcC9/yZBUVSp\nVIpEIhqN5vf7L1y44HQ6yRY1ZRAEEQqF3G633+9ns9m1tbXJWnaEoiiVSlUoFGKx2O1219fXJ1N1\nSSQS+eSTT8xmM0EQQqFw4cKF8AGHqFQqrVZLEEQ4HHa5XMlXYOLxeLq7u2OxmFAo5PP5ZMuZdYBm\nHPB1T0/P+Pg4uXqmHL/fbzAYMAzLzs6G7Q8JjkKhqKyspFAoDocj+ZptTSZTQ0NDPB5nsVifNmqB\nfAGzN12i0WhycnKAd8lkIUbSMDg42NraiiAInU5XKpWwumT6ycvLKy4uBsZ4SXZVguP48PDwjRs3\naDSaVquFR6mbB0VRGo0mEokEAkEwGLx06ZLL5SJb1FSi1+vtdjuO4xwOJ4nTJYDi4uKsrKxQKDQw\nMOBwOJLG0CEYDB47dmxkZITBYEil0uzsbDhoEKLT6cDlP4Igw8PDFouFXD1Tjtfr7evri8ViSqUS\n9i9PP0KhUCqVgg6IlpaWJOuA8Hq9DocDZNXLy8t1Oh3ZiiBfhEqlqqmpoVAosVjM4XDY7XayFU0Z\nOI5bLJbW1lZgbSkWi8lWNDOYvemS7Ozs8vJycB0aDAaTqVWSIIihoaH29nYURSUSCYx0SSE7Ozs/\nPx8U9NbV1fX09JCtaMoAQ5fGx8fZbPby5cvhPLwvi0ajSU9PD4fDbW1tHo8naXK1BEH87W9/6+rq\nAmVHSdyMA/h/7N15XFNX3jj+e7PvCQFCgEBkX2RfpKAogrt13621rVq7Oj6dzkynnXmmtdPH2s4z\n7dPpWNuqXbRWrfuCiEsRkB1k37dAICF7CGS/ufn9cWb49dttFJEEPe+/eNlw86G5uffczznn81m0\naFFaWhpIiTY0NDwcS3bBPbGkpESpVHp5ecFhPQR4enr6+PiA4s21tbWdnZ2ujmgi4ThusVhA+e3Y\n2NiwsDBXR/QoYrFYfn5+BAKhqalJKpU+THXQW1tbGxsbwc8wXeL+fH19k5OTiUQigiBNTU3l5eWu\njmjC2Gw2lUrV09OD43hqampoaKirI5oaHt10SXBwcExMDPi5oqKioaHBtfFMINCJrb+/n0KhzJkz\nB1bxcQmwiMDf359AIBQUFNTX17s6oglTWFjY3t7udDoZDMbKlSthE7J7NXfu3OzsbKfTabfb29ra\n5HK5qyOaMOXl5f39/VwuNzQ0FAw1HmJCodDb25tEImEYdurUqdbWVldHNAF0Ol1dXZ3RaMRxPD4+\nfuXKla6OCHIXDAbD39+fSCS2tLQ8ZJP/HR0dYEEugiAJCQkRERGujefRJBaLs7OziUSiQqHQarUP\n0yxmWVlZUVERiqJMJtPDwwMsooHcFpFIZLFYYrGYRqPduXOnsLDQ1RFNmNra2urqapCLnDt37vTp\n010d0dTw6KZLmEymQCDw9vYmEoklJSVjd8qHQENDQ2dnp8VioVAoixYtGtsOCk0mUKUiIyODTCbL\n5XK5XP7QVDe4ceNGW1sbmUzm8/lBQUFMJtPVEU0xYrE4KCiISCQ6nc4bN240NTW5OqIJYDKZQOrH\nYrFMmzZt2bJlD31rCQqFEhgYGBkZ6XA46uvrJRLJQ9D/sqen5/DhwwaDgUAgiMXixMREV0cEuQsf\nH5+ZM2dSKJTBwUGlUvkwPc3W1dUVFRUhCEKlUn18fOBmfpcQi8Xz5s0jkUh2u72xsbGystLVEU0A\nMC8ilUqlUimDwZg1a5ZAIHjo5xKmOhRFORxOdna2h4eHRqORSqUPTdGGqqqq8vJyAoHA4XACAgLg\nZpy79OimSwgEgqenZ1JSEoVC6ezs7O7utlgsrg5qYhQVFTU3NxMIBBaLFR8f/3CXD3BnAQEB8+fP\np1KpVqu1ubn5IVjOZ7PZZDJZbW2tTCbj8/mJiYkcDgfe+O8Vk8n08/MTi8UoilZWVra2tj4EZS/U\navXx48dBz+zAwMCcnJyHPl2CIEhMTMyCBQsQBNFqtUVFRVN9fG8ymbq7u2/evGk2m0NDQ6OiomDd\nK2iMSCRasGABlUo1mUw9PT3t7e2ujmhiOByOrq6upqYmMpkcFRUlEAgehWuXG/Lw8IiMjPTw8CCR\nSLW1tQUFBa6OaAI4nc66urru7m6TycRms9euXQtXfE8JXC53+fLlXl5edru9r6/v+vXrU306xOl0\nqlSq5ubm7u5uOp2enJwsEAjIZLKr45oaHt10CYIgvr6+ixYtYjKZJpNpYGDgIVhciuO40WgsLS3t\n7OxkMBhBQUF8Ph/e+F1FKBTOmjXL29ubTCaXlZWdOHECLHF3dVzjNzIycuvWrcHBQZvNJhaLV6xY\nAdeUjk9gYGB2djaJRJLL5S0tLT09Pa6O6L5gGCaVSj/99FOVSsXlcqdNm/YobMZBECQmJubxxx/3\n8fEhkUgXLlw4ffq0yWSaulvu+/r6GhsbQVPkefPmpaenuzoiyI2A1SVsNptAIDQ0NFy9etXVEU0M\nhUIxMDCg1+vpdPqSJUtgJ0FXIRKJbDY7Pj6ezWZ3dXWVl5erVKop3ZTE6XQ6HI6TJ082NDQQiUQv\nL6+lS5fCcm9TAovFysrKCggIoNFoHR0d+/fvHxoawjDM1XGNH47jlZWVXV1dZrOZx+OtX79eKBS6\nOqgp45FOl/j5+S1duhRsJSgqKtq/f7+rI7pfFoultrZWKpWaTCZ/f/9169ZxOBxXB/XoIhAIPB5v\n/vz53t7eSqWyoaHhzp07U3oR09DQ0N///vfBwUEikRgcHLxy5UqYLhmf2NjYHTt2gDLMp0+f/uCD\nD1wd0X3R6/USiUSj0WAYlpmZmZOT4+qIJgmRSAwKCnrxxRe9vLxGR0d7e3ubm5unbkr00qVLhw4d\nQhCERCLNnj07KSnJ1RFBboRAIDAYjICAADqd3tLS8nBM/iMIcuLEiYqKCgRBGAzGpk2bYBlOF/Ly\n8tq9e7dYLAZLfg4fPjyluwqCxtu3b9/u6+vj8XgREREMBgPUS4bcHIqiVCo1IyMjODjYYDA0NjbW\n1NRM6VaGGIZ9/fXX9fX1YHfFunXrYEPru/dIf2lJJJKHh8fs2bN9fHyUSmVtbW1tba3JZHJ1XOOn\n1WoPHDggkUgIBEJAQMCaNWvYbLarg3p0gc5E//Vf/xUREYGiaFdX1//+7/+C3QpTkUqlAmVxzGbz\njBkzcnJyyGQyaP0D3SsKhSISibZt2+bv728wGLq7uxsbG6fulpzi4uL9+/c7nU4SiZSWlpaRkeHq\niCYJiqJCoXDDhg1eXl4EAqG2tvbzzz+32Wyujms8ampqGhoaNBoNg8HYuHHjI7I+CLp7YD//jh07\nQkJC7HZ7b2/vl19+qdVqXR3X+OE4brVaS0pKurq62Gx2eHg4j8cjkUiujuvRRafTZ8yYERoaymaz\npVLp6dOntVrt1F1golQqjx49OjQ0hON4QkLC7t27GQwGHDVNCSiKoij6xBNPZGRkEInE4eHhjz/+\neOoWdB8dHa2tre3o6BgeHg4LC1uzZg3M3N2TR/r/FIqiLBZr69atERERGIZ1d3cfPHhw6rbXHhkZ\n6ejoKCkp0el0oaGhM2fODAgIgNvSXItCoURERMyePTs0NHR4eLiioqKjowOsdZ9ympqaTpw4MTo6\niiBIamrqnDlzXB3RFIaiqIeHxxNPPCESiXAc7+7uPnLkiMFgcHVc49HX11dZWVlXV4cgyGOPPRYf\nH+/l5eXqoCYPjUabNm1aVlaWSCRSKpVlZWUlJSV6vd7Vcd0DUIzw7NmzoPaKt7f32rVrp02b5uq4\nILdDp9NzcnLCwsIYDIZMJjt69KharZ66y6lGRka+//77zs7O0dHRoKCgp556isvlwqdZFwKzmOvW\nrUtJSTGbzV1dXXl5eYODg66OazwcDodcLv/mm2/UajWPx4uMjExOTobJuKll2rRpGRkZCQkJdrv9\nzp07ra2tGo3G1UGNh0wm+/TTT6VSKY7j4eHhK1asgI+H9+SRTpcgCEKj0ebNm5eWliYUCtVq9Xff\nfdfT0zNFy/n09fXl5uYqFAoMw1JSUhYuXOjqiKB/WbhwYUpKCo7jer0+Ly8PNDx3dVD3pq+vr6Cg\n4Nq1a06nMzY2Nj09PSwszNVBTW0MBiM1NTU+Pl4gEMjl8rNnz7a2tk6tVBrYmF1YWFhWVmaxWGg0\n2qpVq6Kjo10d12QjEomrVq0CnekHBwePHj3a3d09hdYKGQyGq1evXrx4sbOz09vbG1QtgTXCoZ8i\nk8mBgYFZWVlRUVHDw8Pl5eU1NTVTdMkkjuNqtfrrr7+Wy+V0Oj0qKmrNmjWw0Zs7WLx4cXp6Oigs\neOLEic7Ozik3ZEIQRCqV3rp1q7y83Gg0xsfHp6WlwaUlU9GMGTPmz5+PIIjJZCoqKqqrq5tyy50U\nCkVpaempU6d0Ol1wcHB6enp8fDzM3N2TRz1dAoDRocPh0Gq1VVVVMplsytXqM5vNlZWVn332mcVi\n4XK5SUlJsEqf+0hPT09KSuJyuVar9bPPPrt9+/YUWkfgdDqtVuvFixevXLlisViIROLOnTtnzZrl\n6rgeEo8//nhycjKGYQqF4uzZsz09PVPoTozjuEKhOHPmTFFREY1GCw4OXrBgkP9BEAAAIABJREFU\nwSO4859EImVnZ6empgoEAr1ef/To0eLi4qGhoSlxHwF9u3bs2NHa2kqhUJKSkl577TXYSBX6FVu2\nbFm8eDGRSLTZbEeOHGlqapoSp/qPmM3m7u7uCxcuqNVqkUgUHR3N5XLh6nR3wGazQ0NDw8PD7XZ7\nWVlZe3v7FBoyAVarNT8//4MPPnA6nTQabenSpStWrHB1UNB4TJ8+fdasWZ6engQC4dy5c5cuXZpa\nFUxsNltJScnRo0dNJhOKoitXrly9erWrg5p6iG+99ZarY3A9oVA4MDBQWFiI43hHR0dQUFBMTMzU\n2rZ9+fLlY8eOgW11u3btWr16NSy+7VbYbDaFQikpKQEPxhQKJSUlxdVB3RUMw4qKio4cOVJZWUki\nkQICAl544YWIiIip9QVxW/7+/n19fbW1taOjo+3t7SEhIcHBwVNlhlOr1T711FMlJSUWiyU8PPzD\nDz+Mjo4G9WsfQUFBQU6ns7i42Ol01tbWenl5JScnu//XpKCg4J133mlvbwdlerds2TJr1ixYlgj6\nFWQyuaenp6WlRaPRyOXyxx57LDY21v1P9R+5fv36W2+9JZVKEQTZsmXLzp07PTw8XB0U9C9CoZBM\nJufn5zudzvb2djKZPLWmAIuKisD2RqfTOXv27OXLl0dHR8Nk3BRFo9F8fX0rKipGRkY0Gs3w8PAU\nqmdfU1Nz8uTJK1euOBwOf3//jRs3ZmZmTrnLtcvBdAmCIAiFQiEQCA6Ho66uzmg0ms1mGo02ffp0\nV8d1V3Acr6ur+/bbb2/evGmz2QQCwfPPP5+cnAz7B7sV8ADc2Nio1+t1Oh04xyIiItz89mk2m3t6\net5///3y8nKTyRQeHr53796UlBQWi+Xq0B4SFAqFy+USicTy8nKz2SyTyRgMRkJCgvvfzFpbWz/6\n6KOrV6/q9fqoqKi1a9euXbuWxWK5+Sn94DCZTA8PDxaLVVNTYzAYlEqlxWJJTk4mEAhum3ooLy//\n7rvv8vPzQTO19evXr1692sPDw20DhtwBaJFDIBCKiopsNptOp6NQKPHx8a6O6x7U19efO3fu6tWr\nNpstPj5+1apVoKCjq+OC/oVGo+E4Pjg4KJfLdTqdwWCw2+1TYpIJlCw5ePBgfn7+yMgIk8l84403\nMjMzYZ/KqYtKpfJ4vIaGBrVardVqDQYDiqKBgYFuPrOFYZhcLv/ss8+uXLmi1Wo5HM6f/vSnBQsW\nPFLV5SYKTJf8C4vFotFoFRUVo6OjKpXKarX6+vr6+vq6+e3Tbrer1eovvvji6tWrg4ODAoFg27Zt\nCxcuhM203Q2FQqHT6XQ6vaOjQ6PRaLXakZGR4OBgDodDpVJdHd3PAyVIDx48eOHCBY1GExkZuXHj\nxqeffprFYsGnqQnE5/M9PDwMBkN/f79UKjUajUwmMzIyEhRmd3V0P08ikeTm5h46dEilUnE4nAUL\nFmzdujUoKOiRzZUgCEIkEnk8nre3d09Pj0ajGRgY0Ol0fD5fLBa7YfLa4XC0tbWdPHkyLy8PJOm2\nbNmyevXqyMhIV4cGTQEcDodMJjc0NOj1+sHBQZPJxOfzp8QVwOl06vX606dPX7hwYWBggEKhbN++\nHY6a3A2RSKRQKGw2u7m5Wa/Xq9XqkZGR6dOnczgcN7ycjsEwTKPRfPnll+fOnZNIJL6+vtu3b9+w\nYYO/v7+rQ4PGj0QiMRgMGo02MDAgk8l0Op1cLg8MDPT09HTbjAmolvjll1+ePn26p6fHx8dn3bp1\nzzzzjFgsdv+rtBuC6ZJ/odPpVCp1eHhYKpWqVCqtVjs6OhobG8tgMNy2HI7T6VSr1deuXdu/f393\nd7eXl1dWVtY777zj5+fntk9ZjzIOhxMbG9vf3y+Xy2UymUqlcjgcYWFhHh4ebpiVw3FcKpVeunRp\n7969RqPR399/9erVzz33HJ/Ph5faiUUikfh8fkRERHV1tU6nk0gkvb29KSkpbjsu1Gg0V69ePXny\nZGNjI5FITE9PX79+PaiF9ogjk8ksFovH47W2tiqVSp1O19PTExwc7OHhQaPR3OeybLFY+vv7T548\nefbs2fb2dg6Hk5GR8dprryUlJbk6NGhqIP1bW1ubTqdTKpVDQ0MzZ8505yETgiA4jlsslsLCwq++\n+qqyspLFYs2YMeOVV16JjY11dWjQj7FYrGnTpimVyoGBAYVCYTQaHQ5HSEgIl8t1z3MMx3GVSlVQ\nULBnz57+/n5vb+/58+d/+OGHPB7PfS7+0PhQKJTY2FitViuTyQYGBkC3JpFI5Ofn54ZnI47jGo2m\nuLj4rbfe6uvr4/P5WVlZf/nLX0QiEWyIM05O6AccDsfatWvB/lUvL6+33367u7sbx3FXx/UzcBy3\n2Ww3btygUCgoihIIhBUrVoD9564ODfpFOI6bzeadO3fS6XQEQVAU/eKLLxQKhVudYziOgzj37NnD\nYDDAheK1115ra2tzdWgPM6PReOjQIfC8ymKx0tLS6uvrwWfh6tD+fziOOxyOkydPZmdnIwhCIBB8\nfHzOnz/v6rjczssvvwymEwkEgre394kTJywWi5t8lDiOt7e37969G6zIpVAo6enpGo0G3juge2U2\nm5944gmBQIAgiFAo3Lt3r0QicZPz/KdArqSjoyMiIgLcfxMTE7VaLTzz3dy2bdvGhkwff/xxX1+f\nG55jOI5brdbTp0+z2WwwJn/qqae6urpcHRc0kaxW6wcffAB2o6Mo+sYbb4Cz0a1OSHAqnjhxApyK\nCIJs2LChurra1XFNbXB1yY/FxMQoFIr29naz2dzR0REZGenv7z/20Og+MAz77rvv9uzZA/r4rF+/\n/tlnn42Li4Ml+twckUj08fHBMKy2ttbpdDY2NioUChaLJRaLXR3av4AlfH/5y19Onjyp0WjIZPIT\nTzyxYcOG6OhomJZ+cAgEQmBgYG9vb39/Pyhwc+fOHS6XGxYW5j6Lj7Ra7dGjRw8ePFhXV4dhmL+/\n//79+2fNmuWGV0jXio6OdjqdEolEr9fbbLbm5maDwRASEuIO29evXLmyb9++/Px8nU6Homh2dvbr\nr78eERFBIpHgvQO6JwQCISEhoa+vr6Ojw2Qytba2isVioVDIZrNdHdrPcDgcNTU1L7zwQkdHB4Zh\n2dnZf/7znyMjI4lEIjzz3VlUVBSO46BsamtrK4lE8vf35/P5ro7r/2G32w8fPvy3v/0NjMkXL168\nYcOGlJQUN1x6AI0biqIeHh48Hq+wsNDpdPb09HR2dtJotKCgIPcZpxkMhs8+++yjjz4Cp+LSpUs3\nbdqUnp7unquVpwqYLvkxPp9PpVKNRmNra+vw8LBOpwOlBNxnXyuO46Ojo8eOHTty5EhVVZXT6czK\nytq8efPs2bM5HA6867szUI2Cy+WCDTiNjY1arVapVGo0GgRBxGKxy/MRJpOpo6Pjgw8+uHjxolQq\npdPpMTExL7/8clJSkjs86T3ECAQCqBWK43hfXx9Y365Sqex2u0gkotPpLt8D1djY+MUXX5w+fbq5\nudloNEZGRu7cuXPFihV8Ph9edn4EFDHhcDg6nU6lUqnV6qGhIb1eHxgYyGAwXPI1dzqdGIYdOXLk\nq6++Ki0tVavVZDJ5/fr1O3bsSE9PZzAY8EOE7hWKoqD0ktlsrq+vNxgMWq0WdJFwt/sFhmE3b978\n5JNPCgoKrFZrYmLi2rVrly1bBs9898fj8dhstsPhALVy1Gq1wWBgsVgCgcAdnlHtdrtSqTx8+PCx\nY8caGxsJBEJcXNzWrVuzsrLcLacD3ScURVkslre3N5vN7unpkcvlYB+i3W738fFxeZrYZrMpFIrP\nPvvs5MmTLS0tKIqGhIQ888wzOTk5np6ero1tqoPpkv8HWEEnEAhYLJZSqRwcHATfB7vdzuFw+Hy+\ny59mbTabSqW6fPny559/XlFRQSAQ/Pz8nn/++ZycHF9fX9fGBt0lKpUqEAj8/PxUKhUoGTUwMKBU\nKplMJo/HYzKZrhq9DQ0NVVdXnz179vPPP1epVD4+Punp6atWrVq6dCm8608OkUjE4/FsNptGoxkZ\nGent7ZXL5RQKRSgU0ul0l8xTOZ1OHMdrampOnDgBupVjGJaQkLBhw4Ynn3zSy8vLHQasbsjHxycg\nIIBKpdrtdr1e39fX19fXhyAIjuNMJhM0Fpm0YAwGQ1tbW1FR0SeffFJSUmKz2by9vRcsWPDcc89l\nZ2fDJ0bofgQEBDCZzIGBgYGBgf7+/tHRURKJBB5x3eHi4HA4RkZGiouLv/rqqwsXLtjtdn9//3Xr\n1i1btkwsFsMz3/0RCAQ+ny8UCsEUQl9f3+DgoNFoBNk619baHBkZaW9vv3jx4ueff97U1ESn06dP\nn75p06YlS5ZMmzbNhYFBDwiZTPbw8IiMjARNG+RyOahICLrn8Hg8V81s6XS6pqamy5cvHzx4sLW1\nlcPhJCYmrly5ctmyZUFBQS4J6WEC0yU/g06ni0Si0NDQ6urq0dFRmUzW0dGhUqlCQ0NBNXhX3V/N\nZvPg4GBhYeHvf//7jo4OCoUiFosXLFiwbds299nKAd0NCoUiEAjS0tL6+vpUKpVGo+np6WloaBAK\nhQKBgEKhTOaDsdPpdDgcKpXq+++/P3z48FdffWW32729vRcuXPjss88+8cQTYNswNDkCAgJiY2ON\nRqNGozEYDBKJpLq62s/Pj81m0+l0UKto0oKx2+3Dw8MDAwPvvffel19+CTqGBgUFvfzyyy+99JKH\nh4fL17y4Mx6Pl5iYKBKJlEqlUqlUKBTFxcUymYxOp3O5XBzHqVTqg+5/ZLFY1Gr1nTt3jh07tm/f\nvp6eHgqFEhAQMGfOnPfeey8+Ph5+gtB9AgV6goODKyoqjEZjV1dXR0cHiUTy8fFhMpmunWSy2+06\nna6mpuatt966fv260+n09PRctmzZ5s2bExMTXRgYdE+oVKqPj8+MGTNaW1tVKpVCoWhoaKivrxeL\nxb6+vq4qpD06OtrY2Hjy5Ml9+/aBGS+wrmTbtm1w/vIhBtLBMTExRqNxYGAATIe0trZSKJTAwEAa\njTaZ+/vAhJZOp6uqqjpy5Mjf//53nU7H4/HS0tJ27tz5zDPPwFNxYrikYor7czgcBoOhpKRk7ty5\nVCoVrJPPzMy8cuWKzWZzVVSlpaUvvfQSh8MBA9yMjIyDBw8ODw/DQmVTEY7jdrtdoVD8+c9/Blu9\nQFmTF198sa6ubjIjsVqtMpns+eefDw0NBZsbURT929/+1tnZabFYJjMSCMAwzGAwnDp1Kjs7Gyx5\nY7PZK1euPHfu3CR/IlKp9KOPPoqPjwfVSWg0WmJi4o0bN4xGo1vVNnNboLpkU1PT7t27QQ6UTCZz\nudyUlJQ333xTpVI96Kv3nTt3nnvuOV9fXzqdDgZwmZmZX375pV6vhzcOaKI4HI7h4eHbt28nJycj\n/26qPWfOnIKCAtcG1tfX98knn4xtdBWJRK+++mpXV5cLB3LQ+IAh09DQ0AsvvECj0RAEIZFIYrH4\nww8/dNVA5eLFi6tXrwY3RxRFV61adfnyZdDBxyXxQJMGx3HQNPrw4cOgNS+RSOTz+StWrCgpKTEa\njZMWicPhUKvV77zzTlxcHPheoCj64osvNjQ0mM1mOE6bKHB1yc9DURQsuIqOjiYQCBKJxGAw6HS6\ntrY2jUYjEAg8PDwmLXeIYdjw8PDBgwe/+uqrwsJClUqFIMj27dt37tw5e/ZsLy8vOD04FYHHYBqN\nBmrjyWQyjUYDVjNVVlbeunWLyWRyudwHWkTTbrfX1NQcOnToH//4R2lp6dDQkMPhCAoK+uijjxYt\nWiQSiahU6oN7d+iXEAgEKpXq5eUVFBREoVAaGxvBGoH6+vqysjK5XB4YGPigq5n09vYeP378gw8+\nuH79end3t9lsDg8P37Jly29+85vExMSxiuvQr0NRlEQisdns4ODgiIgIpVIJutTr9fre3t7i4mKd\nTsfhcLy9vSf2fVUqVXFx8V//+tfvvvuurKxMoVA4HA4ul7tp06annnoqKysL3jigCQTOcz6fHxsb\na7VaQeVXrVbb1dVFIBCio6NdsiunoqLim2++OXr0qEQicTgcjz322Pbt2zdu3BgYGAirHk45YCEe\nnU4PCQkRCAS9vb3Dw8Ojo6M9PT01NTUymWwSbouATqcrLi5+9913v/vuu4aGBoPBwGAwXnrppa1b\ntyYnJ3O5XHhzfOiBATyVShUKhREREXK5XKfTGQwGlUp1586dW7du2e12Dw+PB1rCCcOwnp6eL774\nYv/+/deuXZNIJDabjU6n79mzZ/PmzaGhoWNzJND9g+mSX4SiKJVK9fPz8/b2plAoQ0NDGo1mcHBQ\nJpOB7TkUCoXJZIJk3gPicDgkEkl+fv7Zs2fPnj1bW1ur1Wr5fP62bduefPLJGTNmgE6Q0NQ1tinX\ny8vLy8tLo9FIpVKpVNrd3a1SqeRyOYZhPj4+E9u0Asdxo9F469at3Nzc8+fP5+fnV1dXj4yMCIXC\n2bNngz44AoHA5ZV6HnFMJtPHx8fX15fNZo+MjKhUqv7+/t7e3sHBwcHBwdHRURqNBrqeT6DR0dGO\njo7Tp09fvnz58uXLpaWlSqWSQqE89thja9euXbNmTWpqKuyDc6/IZLKXl1dgYKBAIAgPDycQCGq1\nWiaT9fT0KBQKiUTS2dk5MDDAYDBoNNq4v3eg/3dlZWV+fn5ubm5eXl5eXl5XV9fIyEhQUBDYw7xy\n5crU1FTQ+RWCJhB4eBCJRCATJ5PJ9Hq9TCYDtcw1Go2np+fkbJowmUxtbW1nzpw5c+bMzZs329ra\nSCTSokWLQEWJsLAw2KxkigLPqN7e3n5+fhwOx2azabXagYEBiUQilUoHBga0Wi2ZTJ7w7PMYhUJx\n+/ZtcH+8evVqb2+v1WoVi8XPPffchg0b4uPjuVzuA3pryA2hKMpms0UiEZ/P9/b2NplMfX19YJym\nUCjkcrnBYBCJRCQSaQKzeE6nE8OwysrKvLy8c+fOXb58uaKiQqVScbnc1NTUzZs3b968OSwsDGaE\nJxZMl/wHBAIhICAgKCjIYrGgKDoyMtLf319bW1tZWYnjuMPhIBKJYHfMBA4CwJehp6enqakpPz//\nyJEjp06dkslkNBotODh47ty5b775ZmRk5APN1ECTCWyDDAsLG1ser1ar29raWlpawO1fqVRarVYi\nkQiKHYz7jQwGQ19fX0tLS21t7ddff33ixImysjKDwcDn8xMSEnJyctavX79hwwZ36MMCIQgCHj8S\nExMxDGMwGE6nc3h4WCKRVFVVgVMCjBdJJBKZTB73/K3T6cRxfGBgoL29vaam5tq1a5988smtW7ek\nUimLxYqNjU1KStq0adOKFSsiIiLgiTE+YFwVFxeXkpIC6ueTyWS9Xi+VSu/cuVNRUdHb2+twOLRa\n7dDQkFKpNJlMGIaBJb6/9JW3Wq16vX54eLi/v7+rq6u9vb2pqenUqVPHjx+/evVqS0uL3W4PCAiY\nPn36kiVLnnvuOVDyDZYigh4cAoEQFBQ0bdq0kZERo9FoMBg6Ozurq6tlMhmZTMYwjEgkslisB/Tu\no6OjEomkoqLiypUrn376aWlpqVar5XK5mZmZL7744qJFi/z8/B7QW0OTic/nx8TEgBrVY7W0Kyoq\nBgYGLBYLgUCwWq2gOPqEjMzNZrNcLm9sbLx9+/aJEye+/fbbhoYGh8MRGBgYHx+fk5PzxhtvBAYG\nwtW4jyYajQYG8BQKxWazEYnE4eHhrq6u5uZmMIhSKBSgMjHIF4/7nDQajTKZrLW1tbm5GZyH169f\nVyqVbDY7Ojp6zpw5K1eu3Llzp7e3tzvU2H7IoE6n09UxTA0Yht25c+f999+/ceOG2Wy22WwIgohE\nohUrVvz2t78F7YfBE8v9XJ0dDofdbrfZbDqd7h//+MeFCxd6enqcTieRSKTT6cnJyRs2bHjmmWfu\n85kZcmd37tw5fvz4V199NTo6arPZcBwnEomenp6rVq1auXJlSkoKKKZDIpGIRCLI0/3syQDSLjiO\ngz2WYDNtXV3d2bNnc3Nzu7u7nU4ngUAgk8kCgSA9Pf3NN98MDw+H025uS6/Xnzx58tChQy0tLVar\n1eFwIAjC4XBSU1O3b9+elpYGJnXHToxfyeGCswKkZR0OB4ZhVqv1yJEj586dq6urM5vNCIKQyWQa\njZacnPz2228nJSW5tvvAw0ev11dXV//xj3+USCSjo6Pgg0AQBDQaDw0NTU9PT0lJiYuLE4lEvzRN\nNDQ01NTUpNPpCgsLq6urJRIJ+OzAzggKhUKn08Hug4SEhEn986BH3sjIyMGDB48fP97c3Gy1WnEc\nR1E0KyvrySefXLt2LZlMJpPJEzXPBO5xNputubn5+PHjR48e1Wq1YEs1yFEePXpUKBTCR4iHj16v\nP378+BdffNHW1mY2mx0OB4FAEAqFa9as2bp1a0hICCicTyQS72lwDoZP4OaIYVhfX19eXt6nn346\nODhotVrBQiofH5/t27evW7cuIiLigf6N0BQikUhOnTp1+PBhqVQ6Nk7j8/nZ2dmrV6/OyckBhWCB\nXxmnjZXMcPwbjuOdnZ1Xr149efJkW1ub3W4HN3oWi5WWlvbKK69kZWXBFSUPDkyX3C2n0wnKB9TU\n1Fy4cOHEiRNgtp/NZgsEAk9Pz/nz5y9atCgpKel+zte2trb8/Pxr1651dXWBvhh2u53JZCYmJu7e\nvTshIYHP5/N4vAfdTAFyIbPZbDAYNBrN/v378/LyJBIJyJdxOBw2m81isTgcTkRERFpaWkxMjFgs\nDggI+NmTwWazgblrsJakoaFBLpebTCaDwQASMQiCiMXi1atXb9q0ydfXF2w6g+eV2wL1pwcHB5ub\nm/fu3dvR0QGm0eh0Oo/HYzAYHA4nICAgJSUlPj4+KioqICDgl65FOp2utbUVPLHX1dVJJBKj0ajX\n60dGRkDNPDKZvHz58tWrV2dkZHh7e8PVRhPO4XCYzWalUimRSK5fv37lypXW1la73Y4gCIFAoFAo\nYGMOjUYbmyClUqlg9tJgMICDgDyXw+EwmUxms9lut4Mbure3d3p6+uOPP56Zmenh4cHlcuFSRGiS\nORwOvV4/MDBw4cKFo0ePdnV1IQjCYDD4fH5gYOCSJUvWrl0bEhIyIQl6hUJRWFgI3kWpVA4PDzsc\nDh6Pt3r16lWrVsXExPj7+0/shlbITYAaw0qlUiqVvv3223V1daCPNYfD4XK5QqEwLCwsNTU1MzMz\nODgYLOu7G6CKZ2VlZUlJSU1NzVj5QgzDUBQNCgrauHHj8uXLg4KCOBwOXFQCjbHZbAaDQa/Xf/vt\nt2fPnm1oaAADeDBCY7PZTCYzJCQkJSUlKSkpMDDwlxYl4Tiu1+sHBwc7Ojrq6upqamrA1p6RkRGD\nwWC1WhEE8fHxycrK2rVrl6+vr0AgYDKZ8BL34MB0yT3TarXd3d3t7e3nz58vLy8fHBwEVU4CAwOD\ngoKEQiGTyRSJRFFRUcHBwQKBQCAQ/OyTBoZhRqMR9JDv6urq7u7WaDRqtVoikfT19Q0PDyP/HvUu\nWbIkKCgoKSmJz+fDh5ZHBI7j9fX13d3dLS0tNTU1d+7cUSqVNpsNRVEKheLh4eHr6+vp6Qmuv8i/\nixPTaDSz2Qx29ICWHKOjoxqNRqlUqtVqUKybQCB4enrGxcXl5OQEBwdHRUVFRETA+/1UARYeV1ZW\ndnd319bWlpaW9vb2gk+cTCazWCxQB8fT05PNZoPLBYVCAYmw0dFRcMG3Wq0ajcZqtSoUCpVKZTAY\nMAxDEITNZoeHh2dkZMTHx0dGRoaGhvr4+Lj4D37YjY6Ogq3OarV6aGiotbW1paWlt7dXo9H86O4M\n5qOcTifIqvwQk8n08vISi8UxMTGRkZHe3t7+/v7BwcF+fn5w/AS5kM1m6+3tbWpqkkqlR44caW9v\nN5lMNBotKCgoLCxMJBKJRKLw8PDY2Fh/f/+7X8LmcDhGR0fb2tqampo6OjpA6YrW1taRkREcx729\nvbOzs+fMmZOSkhISEjLhBZ4gdwNSxuXl5XV1dSUlJSUlJWq1GkEQGo3G4/GEQqGfnx+Px2Oz2SCH\nwmAwQPOmgIAAFosFJg/Acbq7u00mk8ViMRgMQ0NDMplMoVCMjo6Ccf5jjz02c+bM5OTkyMjIoKAg\nmIaGfkl7e3tHR0dnZ2dVVVVtbe3AwIDRaET+3RrPx8dHIBCAATxY9wRSKhaLBcMwsPjXarUajUad\nTqdUKsF2HofDgaIok8mcPn16VlbW9OnTQ0NDExISwJJzV//FDzmYLhm/vLy8ysrKlpaWnp4eiUQy\nPDxst9tBrxN/f/+IiAixWCwQCMYaEBCJRLCxDXwTHA6H0WhUq9X9/f09PT29vb06nW7sywA2nIeG\nhmZkZMydOxdmDR9NGIbJ5fLa2tr6+nqFQjE0NDQwMDA4OAiedXEc/+GLyWQylUq1WCxg383Yv4Pb\nPJvN9vX1DQgIEAgE/v7+MTExc+bM8fT0hPVcpyidTtfc3FxRUSGRSLRarVwuHxgYAAO7n54YY+mS\nHx2EQqGwWCxPT8+AgAA/Pz8fH5+wsLC0tLTo6Gi4qnOS4TiuUqk6Ojra2tokEolOp8NxHLR+sFgs\nVVVV4FEQvJjP54eGhopEIjabTaPRmEymp6dnYGBgVFRUeHg4k8mEgyfIfWAYNjo6evz48aqqqubm\n5tbWVpC6ZTKZvr6+YWFh06dP9/X15XK5YK0cGP3T6XQvLy8qlTo0NASuXU6nU6FQgJpNw8PDHR0d\nLS0tnZ2doF0gmUwG/afi4+Nnz56dmpoK624+auRyeU1NTVlZmVKp7O3tlUgkQ0ND4DEVQRAqlcrh\ncHx8fEC6hMvlgiRde3s7WLKHYVhvby/Ybg+y0iQSicvlBgYGRkRECASCGTNmpKWlhYaGuvKPhKYI\nsMIODOAHBgZA9k0qlarVapPJBPbpjPlhuuRHA3gSiQQulSKRSCgUCgT2n19YAAAgAElEQVSCqKio\nzMzMwMBAmLCbNDBdcl/AnsabN28WFhaCh5aRkZGRkZGxGf4fvhg8mYyOjo4tmR4DMilgnwWbzfbz\n88vIyFi3bh38MkBjbDZbd3d3ZWVlRUVFZ2cnWI8HVuOD1qRgfw2CIGQymcfjgW52DAaDQqGw2Wx/\nf//ExMSMjIzw8HA42/aQGRgYAPWnGxoahoaGwFkBlmsiCKJSqYaHh0EFHCaTCRYpgB3dbDZbKBSG\nh4enp6cnJyd7enrC4jVupb+/XyqVDg4Ovv766/39/TiOEwgEh8MRHBy8adOmxx9/PDw8nMvlwuQI\nNCVIJJKCgoJz584NDg7qdDq9Xg9GRAiCgDqIfD5fLBZzuVzQljgiIoLL5dbW1ioUCgRBcBxvbGwc\nHh62WCzg+gZ2rnE4HC8vLw8Pj3nz5i1dujQ1NdXFfyfkUjiO22y2W7du3bp1q76+XqlUgtUiINE2\nlj0B05bIvxvugE3uoKoOk8kcy0QHBgZmZGQsW7YMtDhx6V8GTVV2u10ul1dVVZWXl7e1tanVapAZ\nsdls4OQE65sAJpMpFApB22wqlUqn0729vRMTEx977LGYmBihUOjCP+SRBdMl92WsGA+O41arta2t\nraCg4MaNG42NjWq1+qdLpn8WSHKLxeKZM2cuWLAgISHBx8dnrAIQXFQCAT882cDX1mg0gimU48eP\n37p1q7+/H7zS399/1apVS5cuJRKJycnJoA0BOJfgSfVQGjsrxlYfgFYp4Of9+/dfvnyZz+dv2bIl\nLS2Nz+ezWKxp06bx+Xywn3/s3EAQBJ4bbgVMp9+6dWvXrl1qtZrD4dDpdIVCgaLomjVrduzYsWDB\nAgR+atAUAa5RGIZZLJa8vLyLFy8WFxcPDg7+aDZ17HwGP/9wudyPls4xGIzg4OCcnJxnnnkmJCSE\nRqOBsdPk/DmQewKn09g90W63d3d3FxQUtLe3S6XS6upq8DKz2Qy2vVOpVAaDAdY0CYXCgICA1NTU\nOXPmxMTEgMKcYK8EAq+00HiNnZNjA3iwJ1oikYACrmfPngWvJBAIaWlpf/zjH8lkckxMzNiGaPhU\n6FowUXpfxk5cMGEbGRkpFAoXLVpkNBrtdrvFYtHpdGAzRVlZWUdHB/gtOp0+a9asxYsXIwgSGRnJ\nYrGIRCKNRuNyuR4eHiwWCy6Dh37qhycb+BdwFzcajV1dXQqFAvTCMJvNKpWKQCBER0ePbYx0aeDQ\nAzc2mBsjEok8PT3Bz6dOnUIQBLS5mTFjhqenJ7jgkMlkeN91cyiKtre3/+Mf/xgZGSESicuXL09P\nT//DH/5gNpsLCwu9vb2jo6P9/f3h5whNCeBKBRp45eTkJCQkDA8Pm83mwcHB2tpaUMGnpaUFx3Gz\n2WyxWMaSI6DNE4lE8vT0FAgEERERSUlJISEhDAaDwWCA+hSwIjUE/GikRCKRQkNDvby8TCaT1Wod\nGRkB/56bm/vOO+8gCLJt27acnBx/f38EQSgUCo1GA1VOwK5GeHWF7t8PHxXBv4ARu4eHR35+fkVF\nBfivoAOOTCYrKCjYtWuXj48PfB50EzBdMmEIBAKLxWKxWCKRCPyL3W43mUwajaa2ttZgMICmrTab\nDcMwMpkcFBSUmJgoFAphlU1ofIhEol6vP3jwYFdXl9VqjY+PX7x48YEDBwwGQ2VlZX5+/rPPPuvq\nGCHXAE1VwM/gCgNWsXl4eMCtWFNIT09PSUlJfX29zWabPXv24sWL09PTNRrNgQMH5HL5999/LxAI\nXn31VVisBJpCQNLE29vb29sb+XcPiJiYGLVaPTo6KpfLv/zyy+bmZjAHi6IoWCMgEomee+45LpcL\nyk8EBgZ6e3uTSCR45kO/jkAggLTaj/69ra0N/CAWi5OSkoKCgiY9NOjRBbLGnZ2dra2tCoWCz+ev\nXr26ubm5o6NDpVIVFRWtWbMGNKx0daQQgiAIvM08QGAPpFKpbGtrUyqV3t7ec+fO5fF4Doejp6en\noaFBJBLBbwI0bgqFori4+OjRo2q1WiwWL1q0aNu2bSkpKRwOp66u7vz58yqVCnQ8gSBoKqqurr5x\n44bJZKJQKAsXLkxPTw8ICHj++eezsrIEAkFXV9fx48dv3Lih1WpdHSkEjROBQODz+fHx8Tk5OTk5\nOXFxcSQSCcMwBoMREhKSnZ0tEAhAA9fAwMDly5evXLkyPT3d39+fQqHAXAkEQVMUhmEXL15saWlx\nOp1CoXDHjh1PPvlkTEyM2Wzu6Og4c+ZMb2/vj7YfQq4C7zQPEOh0cODAgd7eXhRFY2Nj33rrraSk\nJDab3dbWdvHiRblcPlaeE4LuCYZhVVVVX3/9tdFoRFF03rx5q1evFgqFTz311LRp0ywWi1QqvX37\n9lhVMwiCphaTyVRZWVlcXEwikcRicWpqalBQENiPsGPHjtTUVAKB0N/fv2fPnoaGhrHKvhA0RYFy\n5nv27GlubsYwTCwWb9q06b333ktLS6NQKO3t7S+//HJTU5PZbHZ1pBAEQffFbrer1eqLFy92d3ez\n2eywsLDY2Njt27fPmzfPw8NjdHR0//79paWloGcT5HIwXfIAWa3WwcHBq1evqtVq0PkpJibm7bff\nTk5ORhCkr6/v9ddfl0qlrg4TmpKUSmV1dXVJSQmCIEKhcMaMGfHx8Uwmc9WqVWKxmEgk9vT07N27\nV6lUujpSCILG4+bNm01NTRiGcTicV155JTIyEvw7iqLp6elz5swJDQ21Wq0tLS2XL19ubm52bbQQ\ndJ86OzvPnDlTUlJiMBiEQuGCBQt++9vfxsTELFmyJCkpyW63KxSK9957r6yszNWRQhAE3ReJRLJv\n3z6ZTIbjeFJS0gsvvEChUMhk8vLly7dt24YgiN1u//bbby9fvuzqSCEEgemSB6qysvLdd9/VarU4\nji9cuPDpp5+m0+mxsbHJyckikWh4ePj69esDAwMWi8XVkUJTz4kTJ86cOWOxWFAUfeWVV+bPnw/q\nurNYLFBCz2w2d3d3NzU1wYX6EDQVXbhwoa6ujkwmCwSCjIwMUOgBQRDQX3D16tXr1q2jUql2u/38\n+fPXr1+HuVFo6lKr1UVFRcePHwdbz5YvX/7MM894eHhQqdQlS5YsXbpUJBLZ7faysjLQ4sTV8UIQ\nBI2Tw+GQyWQXL17U6/U+Pj4JCQlguSiKosHBwZmZmbGxsRQKpaGhobq6emhoyNXxQjBd8sCACq8F\nBQUYhkVGRs6cOTMuLo5AILDZ7EWLFs2cORNMlZw6daqpqcnVwUJTic1mKywszM/Pb2tr4/F4S5cu\nXbRoUWBg4NgLcnJywAqm0dHRc+fOjbVkgiBoSjAajdXV1XV1dUql0t/ff9myZQEBAT8qCh4SEvL4\n449v2LCBSqVKJJLc3Nzc3FwMw37YkxWC3J/T6TSZTHl5eadPn+7q6nI6nevXr1+/fv306dPBCwID\nAxctWrRq1SoKhaLVavPz869evQomolwbOQRB0Dh0d3cXFxdLpVK73T5r1qx58+bx+XxQiYnFYsXH\nx2/dupXL5RoMhpKSknPnzrk6XgimSx6Yurq6iooKo9FIJBIXLlyYmJhIIv2rD1FmZub8+fNB07Jv\nvvmmqKgI9H6HoP8Ix3GDwfD111+DLFtgYODLL7/s7+//wz6y06dPT0lJEYvFdrv94sWLlZWVOp3O\ndSFDEHQPnE6nWq0+evSoTCYjkUhRUVFbtmxhMpk/fWVcXNyuXbtiYmIYDEZ5efmxY8fq6+thERNo\nCnE6nTabraKi4uuvv/7+++8ZDEZycvKuXbtmzZo1NmRCECQhIWHLli0zZsxgMpnV1dXnzp27ffu2\nzWaDyUEIgqYWDMOqq6svXbrkdDqZTGZ2dnZmZuYPXyASiTZv3jxjxgwej1dXV3f06NH29nZYs8m1\nYLpk4jmdTrvdfurUqdOnTxOJRB6Pt2rVKjDbD5DJ5OTk5PXr1yMIYjAYampq6urqnE4nvPFD/5HF\nYhkYGPj+++9lMhmXy42JiZk/fz6Px/vRyzIyMjZt2oQgyPDwcFFREWjqDkGQ+7Pb7f39/Z999plc\nLvf09IyKioqLi/vZHmpUKjU0NPSPf/xjaGgohmE1NTWvv/760NAQnHWHpgoMwxQKxauvvlpUVAQW\noh88eDA6OvqHuRIEQUgk0vTp0z/66KOgoCAURUtLS99++221Wu1wOFwVOQRB0DjodLr6+vqqqioC\ngRAREREYGMhisX74AiKR6Onp+ac//SkxMRHDsK6urr179w4ODsKHRBeC6ZKJh2HYoUOHqqqqMAwT\nCARvvfVWaGjoj14THh6+ePFiLy8vEol07dq1s2fPwhY50N2or69/6aWXFAoFiqILFy588803URT9\n6cuCg4MzMjI8PT2JROKtW7cKCwsnP1QIgsahrq7u66+/Bi3AV61atWPHjl95MahVlJmZKRKJRkZG\namtrDx8+DPffQVNFY2Pj888/393djWFYXFzc008/HRYWRqfTf/pKGo0WHh6+a9eulJQUDMN6enpe\nffXVtra2yY8ZgiBo3I4cOXL16lWn00mlUt94442MjIyfvoZMJsfFxcXHx/v6+up0utzc3ObmZrgR\nwYVgumSC4ThutVrz8/N7enrodPq0adPmz5/v6en5o5cxGIyIiIhnn31WIBBoNJqqqqoLFy7Amq/Q\nr2tpacnLy6utrbVarZmZmYsXLw4JCfnZV9Lp9IiICFAqT6vVNjU1lZeXw4k4CHJzGIZ1dnbevHnT\n4XD4+vpGR0cHBwf/yuuJRKKHh8eTTz6ZlZVFJBJ1Ot2ZM2dqamr0ev2kxQxB41NfX//dd9+VlpaO\njo76+fnNnTt32bJlDAYD7OH/ESKRyGAwFixYMGvWLD8/P4PBUFBQcPHiRZgxgSBoSsBxfGRk5M6d\nO93d3RwO57HHHouJifnp8nAEQQgEApPJXLdu3YIFCzAM02g0n3/+eXV19eTHDAEwXTLBNBrN5cuX\nGxoa9Hp9cHDwihUrxGIxjUb76Su9vLy2bNkSFhZGo9E6OztPnTql0+ngAy30S6xWa0VFxZUrVywW\nC4vFWrBgwcyZM4lE4s+uLkEQxNfXd+PGjUKhkEAgtLa2nj9/HsxXQxDktjo6OqqrqyUSCYIg8+bN\ni4+P/1GF1581Y8aMdevWZWdnOxyO1tbWCxcugPQoXLsLuS2JRHL16tVLly4NDw8zGIx58+YtW7Ys\nPDz8Z3MlAIFAEIvFS5YsmTNnDoqiKpXq/PnzpaWlIyMjkxk5BEHQOBiNxnPnzjU3NxuNRj8/vy1b\ntnh5ef3KFS81NXXx4sWJiYkIgty8eTM/Px82BXMVmC6ZSDabra2tbe/evXK5nMFgpKen79y582f3\nnCMIwmAwoqOjZ82aJRKJ1Gp1aWlpbW0tXGoF/RJQSfvOnTtkMjkpKSk9PT0oKOhXXs9kMqOioqKj\noz08PHp7e/Py8uRyOdzzBUHuyel04jh+48aNgoICFEVpNNqGDRt+WPTq1y1evHj37t0BAQEkEuns\n2bPHjx/v6+t7oAFD0PiARbg3bty4fPlyS0sLhUJJSkrasmVLdnb23fx6Tk7Ohg0bIiMjiURiVVXV\n999/39zcjOM4TA5CEOS2MAyTyWT79u1rbW1lMpnR0dGbN2/28PD4lV8hkUipqambN2+mUCg2m+3a\ntWuXL1+2Wq3wWjf5YLpkIg0NDd25c6e5udliscTExKSmpnK53F+a/Ad+97vfzZ07F0VRpVK5a9eu\n+vr6SYsWmlr+9re/nT9/3ul0cjic999//2e3O/4IhUJ58cUXExMTcRwfGhr67LPPBgcHJyFUCILG\nwWaz1dbWNjc30+n06dOn+/r6/mwRh59FJBITEhL27t3r7e3tcDiuXr26Z88eOKiC3BCGYb29vSdP\nniwvLycSid7e3u+///6sWbPu/gjz588/cOAAaBd19uzZDz74AHbJgSDInWm12traWqVSabPZUlJS\nVq9eTaVSf/0JEUEQsVg8e/ZssVhMoVCam5uLi4v7+/vhRoTJB9MlE+n27duHDx/GcZxEIi1atGjh\nwoUEAuHXvwxg91paWhqGYYODg01NTTKZbNIChqYEvV7/1Vdf1dbWGgwGX1/flStXikSiu1miD56g\noqKiPDw8dDrd8ePHBwYG4JYcCHJDFovl/fffLy8vxzDM399/z54906ZN+49jqTEoivL5/MzMzHnz\n5gmFQq1WW1lZeejQIYVC8UDDhqB74nA4BgYGdu/eXV1dDcq7HjhwIDIy8m7uaGNA2de33347NDTU\nbDaXlJS8+OKLKpXqwYUNQRB0P1pbW//5z3+OjIwQicS4uLh58+ahKPofb/FEIjEiIuLTTz8NDg52\nOBwVFRV//etfjUbj5MQMjYHpkgnT1tZWXl7e1tZGIBBycnJmzpwpEon+428RCISZM2fOnz8fLLU6\nf/58WVnZJEQLTRV2u10mkx07dkwikRCJxMjIyCeffJLH493NcxSKolwud/HixdnZ2Xa7va+v78aN\nG52dnZMQNgRBdw/DML1ef/369f7+fi8vr+Tk5IyMDC6Xe08HoVAoQqHwqaeeiouLIxKJAwMDX375\nZXt7OxxaQW7C4XDU19f/3//9X3FxsV6vT0hI2LRpU3Z2NpvNvvvMIIIgKIryeLyVK1fm5OQEBAQo\nFIq8vLxz585JpdIHFzwEQdD49Pb2gpILdrs9MTExJSXFx8fnLn+Xw+HMmjVrxYoVoaGhSqWysLDw\n/PnzQ0NDDzRg6EdgumQCOJ1Oh8Nx8+ZNMDEIqhnHxMQQicS7+fXw8PA5c+YkJyeTyeTCwsLr1693\nd3c/6JihqWJwcPDatWulpaXDw8Ph4eELFy6cPXs2g8G4+yNkZmaC8SiCILm5ubW1tTiOP7B4IQi6\nZzqdrri4uLe312QyhYWFLVmyhMPh3OUd5IeoVGpOTs7y5ctjYmJGR0fLy8svXbrU2dkJv/KQO+ju\n7j5//vyhQ4fMZnNAQMDSpUvXrFnDZDJ/pdjhL6FQKGKxeNWqVampqWQyWaPRHD16tKKiAvaEgiDI\n3VRVVd28edNkMpHJ5AULFqSkpNz976IoSiaT165dC54TVSrVF1980dbWZrVaH1zA0I/AdMkEwHFc\nq9Xm5eVVVVXR6fTg4OCMjAw/P7+7P0JsbOzu3bu5XC6O48XFxSdOnIB1yyAEQaxWa1FR0TvvvGM2\nm2k02ooVK5577rl7PQiTyZw2bVpMTAyBQLhz505bWxvsIwBB7sPpdHZ1db377rsajYZMJickJKxf\nv34cD5Bjnn322aeffhpkSD/66KPc3FxYRBxyLafTaTabT5069c0335jNZhKJtHz58uXLl/96n+z/\naOHChQsWLBCLxRiGlZaW5uXlNTU1weQgBEHuw2q1lpeXFxYWkkgkkUg0d+7c6OjoezoCiqLJycmp\nqakikchsNhcVFVVVVcEFJpMJpksmgF6v37t3b1NTE4IgkZGRX3zxhVgsvqcj8Pn85OTk2NhYNpvd\n3d19+/ZtrVYLa/lAt27dys3N1el0TqczOzs7LS0NPALdq7S0tFdeeYVCoTidzlu3bp07d27CQ4Ug\naHxMJpNMJmttbbVarfHx8fHx8b/UT+0ukcnknJycV199FUVRu91+5MiR/fv3T1S0EDQ+3333XX5+\nvlQqpVAoUVFRy5Yti4uLu//Drl279g9/+AODwUBR9MyZM+fOnYPJQQiC3Me1a9eam5sxDOPxeL/7\n3e8iIyPHd5wnn3zyhRdeAPsWP/7444sXL05omNCvgemS+2Wz2ZRKZUFBgUKhEAgE8fHxUVFRNBrt\nng5CIpGEQuHu3bvDwsJsNltTU9O+fftg3bJHmdPpHBkZKSoqun37NoIgXC535cqVqamp41ifD349\nPDw8NDSUTqc3NzeXlpbCPgIQ5CbKyspOnjwJFtbOnz8/Ozv7birA/QoURQMDA3NycmbPns1ms/v6\n+q5du/btt9+azeaJixqC7pbBYLh9+/aJEyeamppQFA0KCnrrrbeSkpLudaT0szw8PGbPnv3aa6/x\n+fzh4eHc3NwPP/zQZrPBNSYQBLkWjuM2m+3MmTN1dXVkMtnHxyczM9PLy2t8R/Py8po5c+bmzZtp\nNJpMJrt+/Xpubu7EBgz9EpguuV99fX3Hjx/v7e21WCxxcXHLli2j0+njWEfNYDCys7OTkpK8vLyU\nSuXZs2c7OjpGR0cfRMyQ+8Nx/MKFC7du3ZLL5Tweb8uWLbNnzxYKheM7GolE8vX13bZtm5+fn06n\nq62tvXTpkslkmtiYIQi6VyqVqqysrKioiEAgREdHz5gxIygo6P4Py2QyIyMjd+7cGRoaiiBIc3Pz\niRMnuru7YcYEmmRms7mjo+PgwYNVVVUGgyE6Onr79u2LFi3y9vaekOMTCASRSLR+/fqsrCxvb++u\nrq4zZ86cOnVKq9VOyPEhCILGZ2Rk5ObNm1VVVUqlMigoaOPGjYGBgeNOExMIhLCwsHXr1vn4+KAo\nWlNTc/nyZY1GA/tdTgKYLrkvRqOxsrIStIYSCARz5sxZunTp+A5FIBDYbHZ2dnZ8fLzdbpfL5Tdu\n3IBl3h9NFotFIpEcOHCgpqaGTqdHR0f//ve/v8+HKC8vrxdffHH69Ol0Or29vf3jjz/WaDRw/g2C\nXKu6urqqqkqhUFCp1NWrV0dERJBIpAk5speX1+bNmxcvXiwWi3U6XWlp6aVLl2QyGfzWQ5MGx3GJ\nRJKbm/vNN99oNJrAwMAVK1b85je/odPpE/guNBpt2rRpW7dujY2NJRKJvb297777bkNDA+wJBUGQ\nqzidzqGhoU8++UQul1MolMTExJdeeonFYt3PMT09PdPS0nJycry8vGQyWUlJya1bt+Dc5ySA6ZL7\n0t7eXllZCUpLLF68ePbs2fe553zjxo3Z2dkkEslisbz33nuVlZUTFSo0hchksgMHDnR1dVmt1uDg\n4BUrVvj4+NznqUUgEKhUanp6ekhIyMjISEtLi1KphIW1Ici1jh07VlBQgKIok8l84oknoqKiJvb4\n//3f/7148WIikajRaP70pz/V1tbCqljQpMEwLDc393/+53+cTieKops2bdqxYweVSr2fvWY/i0ql\nLl++fObMmb6+vmazubm5+cKFC+3t7RP7LhAEQXfJ4XCo1eq8vDydTufr6xsSEuLh4XE/RdwBgUDw\nz3/+MyEhAUXR1tbW3/72t7Dm6ySA6ZLxs9ls+fn5Z86cQVGUwWDMnTs3ISHh/g87f/580P0Ew7AL\nFy7AnWmPGrPZ3NXVdfz4cZ1Ox2QyU1JSNm/efJ+5kjEbN25MS0tDUXRkZGTfvn2NjY0TclgIgu6V\nxWKpra2VSqUmkykgIGD79u08Hm/C34VCoWzZsuX5559HEMTpdO7bt+/YsWMT/i4Q9LPee++9zz//\nHMMwFEWfffbZxYsXCwSCB/d2zz777NatW8HSlVOnTt24cUOhUDy4t4MgCPolhYWF7733Ho7jKIo+\n/vjjTzzxxIQcFkVRKpW6ZcuWrKwsDMM0Gs3+/fvr6+sn5ODQL4HpkvG7efPm7du35XI5i8XasmVL\nYmIih8O5/8OGh4eDLbgEAqGioqKiosJut8OqnI+OsrKyw4cPy2QyDMOWLFmyceNGPz+/+09IAwEB\nAfHx8aCicFFREai5MyFHhiDongwPDx8+fLi7u9vpdAYEBGzatInL5U74uxAIhKioqPnz52dkZJDJ\n5KampsuXL9+8eXPC3wiCfshoNB46dOjixYs9PT0cDicnJ2fNmjXTp0+nUqkP7k0DAgJWrFixfft2\nFEXlcvnp06dPnz4NR1AQBE0ys9nc3t5eWlrqdP5/7N13XFRX/j/+e6cXGBh6752hNwUBERURuyLW\n2LLfmJjdbJLdZE0+yWbzSbKbjZu6xiSaorErolIEUQRB2tB772VoMwzTy537++P+PtlsosYyw50Z\nzvOvPB5Rzku99X3PeR80ICAgKirK09NTKz8ZhmECgZCYmBgTE2Nubi6TyXJzc9va2kBjMp0C5ZIn\nodFoZDJZdnZ2U1MTiURydnbesWOHm5ubVn44i8UKDAzcsGGDmZnZ+Pg4l8utqKgAq80XiP7+/oKC\ngry8PGz7gNWrV8fHx2vx5xOJxIiIiKVLl2o0mqmpqbKystbWVi3+fAAAHoVMJhscHMzLy5uYmLC3\ntw8PDw8JCdHKRiG/xmQyQ0JCMjIybGxsEASprq7OysqamJhQqVS6GA4ARCJRU1PT999/39HRQSaT\nvb299+/fHxERwWazdT00h8PZvXv3smXLWCxWbW3tpUuXioqKlEqlrscFAAD4SVNTU01NzczMDARB\nq1atCgkJ0W6l2MnJaenSpUlJSRqNpq+v7/bt2/X19Vr8+cAvgHLJk5DL5R0dHZWVlSMjI9jGTkFB\nQVqZWoLx8PA4fPiwm5sbiUTicrlYK1mw4Ny4oSiq0Whu3rxZUlIiFovJZPLatWtDQkIYDIZ2B4qM\njExNTTUzMyMQCJcuXcrJyQEdTIwViqLgs6p+4vF4paWlU1NTCIJERESsXr1ap8O5urqmp6cvWrSI\nzWYPDw8XFxffuXNHLBaDwwPQOpVK1dvbe/78+dbWVolE4uzsvGLFiu3bt1taWs7D6FQq1d/f/29/\n+5uvry+RSKytrX3//fcHBgbAbQ4AgHmAoqhcLs/KyiosLCQQCCwWa/369RwOR+sDJScnP//88zY2\nNgQC4eLFi+fPnxcKheCeriOgXPIkhoaGfv/733d3d8MwHBER8d5772l3EjWZTLaxsUlKSnJycuLz\n+ViRUiQSaXEIQA8plcri4uK6ujrsANi5c6currAkEsnd3X3z5s0MBmNqaqq9vb29vV3rowB6QqlU\ngkqrHqqpqfnggw8kEgmNRouIiEhKStL1iNbW1kePHo2KiiISiZ2dnX/6058GBwfBsQFo3cjISEFB\nwfHjx+fm5mg02tq1aw8fPjyfAZhMZlRU1MqVK93d3SUSSUtLy17z+5QAACAASURBVEcffdTd3T2f\nGQAAWJjUanVzc3NjY+PY2Ji5uTnWsIlIJGp9ICKR6Ofn9/rrr1tZWYnF4srKygsXLoC1CDoCyiWP\nbXp6uqmpqbW1VSqVenl5RUREWFpaaqu1BAaGYRqN9uyzz4aFhcEwPDo6in0e0eIQgL6ZnZ19++23\nsVY13t7en3zyibe3N5lM1vpAMAx7eHjs3buXzWajKFpVVXX69GmtjwLoAxRF+/r6+Hw+BEFUKpXD\n4ZiamuIdCoCamprKy8uxLdWw3dB02tABQyQSsd3E09LS1Gr1xMTEa6+9dvfuXV2PCywoPB7v4sWL\n33//vUwmIxKJv//97/ft2zfPlx0CgUChUPbs2bN8+XI2mz03N3fjxo2Kiorx8fH5jAHos5GRkaGh\nIey/XVxcrKys8M0DGA25XP7NN980NTVBEOTk5PT66687OTlpfS8wCIJgGLa2tk5NTXV0dCSTyZ2d\nndevX5+ZmQHLbHUBlEseW2tr68WLF+fm5iAIiouLS0lJIRKJWj8TsKrhsmXLQkJCJBJJRUVFcXHx\n4OCgdkcB9IRQKGxoaMjJyRkdHXVwcFiyZElKSoruHjFNTU0DAwOXLl1qa2s7OjrK5XLBXGVjJRKJ\nsH9ZIpFoaWmprS2WgKeBXc8hCGIymYmJiYGBgfMwKAzDRCIxNjY2LS0tPDxcrVaXlJRkZmZyudx5\nGB0weiiKqlSqrKysrKysrq4uBoOxbdu2TZs2aX1v7Efk7e29ZcuW1NRUFEXHxsYuXrx47949tVqN\nSxhA34jFYrFYjP23mZmZ1lc9AwuTVCrt7e2trKycnJx0cnJKTEwMCQlhMpk6Go5Go7m5ue3Zs8ff\n339ubq6+vv7YsWOgLqwLJLwDGBgej1dWVpabm6vRaAICApYvX75o0SLdDZeUlNTf39/S0qJQKK5f\nv+7u7u7s7KzdmSwA7jQazeDgYGZm5sjIiEajCQ0NXbNmja4/x2HPsr29vRMTE8PDw9nZ2Vu3brW1\ntdXpoACwwKEoOjExweVym5ubsWU4/v7+FhYW8xaAzWYnJCTweLyenh6xWHzjxg0LCwt3d3dLS0td\nfP4CFg6JRFJdXX3q1Km6ujomk8nhcA4dOhQYGKiLWeiPKD4+Xi6Xd3Z2NjY23r5928bGxs3NLTIy\nEq88gH4ikUg4HqWAMeHxeNnZ2TweT6PRcDic9evX6/rGSqVS9+zZ09PTMzIyMjEx8dlnnwUEBJia\nms5DX+0FBbx4PyqsaeLt27dv374tl8thGH7++ecTEhJ0OmhAQEBkZKSdnR0Mw8XFxfX19T+VwwGj\nIZPJamtrv/zyS5FIZGVllZiYuHbtWl0PSqPRVq9e7e3tTaFQRkZGPvzww5GREdDIAAB0LT8/v62t\nDUEQS0vLV155RVubCz46Pz+/tLS0sLAwBoPR399fUlJSUlICNlsFnoZare7p6Tlw4EBdXR2CIN7e\n3r/73e8CAgJMTExwTEUikWJjY99//30rKysYhi9fvvzOO+9IpVKwvB8AAK1Tq9Wtra3vvffe9PS0\nqalpSEhIcnKyrsslBALBzMwsKSlp0aJFGo1GIBBcvHixvr4e3NC1C5RLHoNSqSwrK+NyuSQSydLS\nksPh2NnZ6XrQpUuX/u///i+ZTEZR9OrVq8ePH9f1iMA8u3DhwhdffIFd2l588cWtW7fO29ArVqyI\ni4tTqVRTU1OlpaU/LeUFAEAXUBTNzMxsbm6mUql2dnbh4eHabRP+iPz8/D7++GNPT08SiVRXV3f0\n6FGwrzDwNCorK//+97+Pj4+rVCo/P78NGzZs3LhRd1PQH52JiUlQUNDBgwfd3NxUKlVTU9Phw4cn\nJibwzgUAgLFpbm6+c+cOdifNyMhYt27dvA29bNmylJQU7HGisLCwtrYWbA+iXaBc8qgUCsWJEycq\nKirEYrG9vf0777zj6+uri06cv2BlZRUeHh4XF8disXp6erhc7vj4OFh/azRaW1vLy8s7OzspFEpk\nZGRkZKSjo+O8jZ6QkBAbG8tkMlUq1dmzZxsbG+dtaABYaCYmJr777rv29naJRBIYGPjcc89ZWlqS\nSDgsiWUwGP7+/i+++GJoaKhUKm1sbHzzzTf7+vrmPwlgBFpbW/Pz80tKSpRKpZ2d3Zo1a7Zs2cJm\ns/VhgQPWs2nr1q1RUVHm5uaTk5O5ubn5+fmjo6N4RwMAwHio1erq6ur8/HwIgkxNTcPDw+ezbZOZ\nmVlycvILL7xAIpGEQmFWVtb58+fnbfSFAJRLHolSqZyYmMjMzOzt7TU3Nw8LC9u2bZu1tfU8DE0i\nkRwcHPbs2ePo6CiVSltaWjIzMyUSyTwMDegUiqJqtTo7O7u6ulomk5mbm+/cudPPz28eanA/cXZ2\njo2NjY2NRVG0rq6Oy+WCCSYAoAsajWZ8fPy7776bmJhgMpnBwcFr166dhw1x7guGYSqVunbt2pSU\nFA8PD4FAcOnSpezs7N7eXlzyAAYKRdHZ2dnCwsL8/PzJyUkSiZSWlrZu3bqAgAC8o/0HhULx8/Pb\ntGlTdHQ0giADAwPnz5+vq6sDz1EAAGhLY2PjvXv3Ojs7yWTy0qVLORzOPE8d9fLy2rhxY1hYGJPJ\nrK+vv379el1dHdjDQVtAueSRCASCsrKyrq4usVjs5eWFTXmat6+CbDY7IyMjNDTUzMysu7v7yy+/\nHBgYkMvl8zM6oCMymay1tfXy5cvNzc1mZmYRERHbt293dXWd5xihoaHp6ekkEglBkMrKynv37s1z\nAABYCIRCYWdnZ2VlpVgs9vHxiYyMtLW1xfHzO4FAsLW1Xb16NbaNsVwu//HHH4uKikB7LOARaTQa\nhUJRVVWVnZ1dW1tLp9MjIiL2798fExODd7T72LBhw+bNm728vBAEKSwsLCgo6Ozs1Gg0YIU/AABP\nA0VRjUaTnZ1dVVUFwzCbzd6zZ4+vr+88x6BQKC4uLrt373Z0dFQqlS0tLadPnxYKhaBVk1aAcskj\naW9v/8tf/jIxMUEikSIiIp555pn5fMzFvgQ+88wzixcvViqVY2NjWVlZw8PD8xYA0IXBwcEDBw50\ndHRAEBQeHv6Pf/wDl0bWdnZ2QUFB2KKAsrKyoqKi+c8AAEavtrb2zJkz2LvZunXrtm3bhnciCIKg\nmJiYlJQULy8vAoHQ0tJy586d+vp6vEMBhkGtVvN4vNdee62kpASCIDc3t8zMzMjISH1Yg/NrZDI5\nPT39rbfegmEYRdFTp06dPHlSqVTinQsAAMOGoihWOO7p6cGaJUVERFhaWs5/Emtr64MHD/r7+9No\ntKGhoczMzLGxMXCV0wpQLvltra2thYWFExMTarV66dKlSUlJ87xDOwzDMAzHxMRwOBwTExOxWPzD\nDz90dHSADiaGa3h4uKSkpKurSyaT+fr6JiQkeHl54dLFAIZhV1fXN99808HBQalUdnV15eXlgfl7\nAKBFKpWqu7u7vLwcgiB3d3c3NzdcOrz+GpFIjI+Pf+ONN8zNzWEYvnXr1vfffz84OAhuLsDDqdXq\nhoaGffv29fb2IgiSkJCAbUBDIpH0c0dqGIZNTU0jIiL+/Oc/W1lZSSSS/Pz8v/3tb6DDMQAAT4PP\n5x89erS3t1ej0fj6+r711ls2Nja4XAZhGCaTyX/5y19WrVoFQdDk5OSrr75aV1c3/0mMDyiX/Aa1\nWl1TU3Pjxg2VSsVkMrG9mggEwvyfCWw2Ozk5edWqVQiCDA4O5ubm1tTUzHMGQCvUanVjY+PZs2fF\nYjGJREpISFi7di2DwSAQ8Dkf2Wz26tWrHRwcyGRyd3f3xYsXJRIJmL8HANpSXV1dUVExMzMDw3B6\nenp4eDgutdH7srKyio+PP3TokJOT09TUVHFx8bFjx/h8PrgCAA9RXV194sSJ8vJyqVQaHByclpaW\nkJBAJpP1s1aCIRKJjo6OGRkZsbGxbDZ7cHAwPz//xo0bMzMzeEcDAMAgqVQqHo+XmZk5Pj5uZWXF\n4XAiIiJoNBqOkUJCQhITEwMCAhQKRWVlZUFBATaNHXgaoFzyG7BPgk1NTWQyecmSJXFxcfPfXeIn\n0dHRa9assba2JhAIN2/eLCkpAevMDRG2j0BZWRmKopGRkatWrQoPD8cxD41Gc3NzW758ubu7O4/H\nu3v3LpfLFQqFOEYCAOOATdMtLCysqKggk8l2dnZpaWne3t545/oPAoFgY2Pz7LPPLlu2zN7efmho\n6PTp04WFhZOTk3hHA/RUT0/P9evXs7KylEqlhYVFSkrKypUrLSws9LlWgjExMeFwOFu3bg0ICEAQ\npL+//9tvv+3p6QETKgEAeALj4+PFxcVNTU1isTgoKCg5OZnJZOL17RNDp9Pj4uKWL19OoVCkUml+\nfn55eTlYkvOUQLnkgVAURRAkKyvr3r17Go2GxWK99NJLoaGhOEZis9mBgYEJCQl0Or2/v7+2trar\nqwvHPMDjQlFUJpOdOnXq4sWLMAwzGIxDhw4lJibinQsiEAgvv/zy0qVLCQTC1NTUsWPHBgYGQA88\nAHhK2GRAbFWzubn5ihUrHB0d8f309GtYi7j9+/cvWbKEQCBMTk7+4x//qK6uBu+QwC9oNBqxWHzp\n0qXc3NyZmRkqlRoXF5eWlobvo9FjoVAoO3fuxIqDQqEwOzu7rKxsbGwM3O8AAHgsCILU19cfO3ZM\noVDQaLRly5Zt2bIF71AQBEERERFpaWmenp5kMpnL5ZaVlYFdL58SKJc8EIIgAoHg3r17XV1dpqam\ngYGBXl5epqam+KYKDAw8fPgw1hP0zp07n332Gb55gMeiVqvLysoaGxtnZmZYLFZqampQUJC5uTne\nuSAIgszMzNzd3Z2cnCQSya1bt8bGxkD/AgB4SmKx+B//+EdjYyMEQa6uru+//76zszPeoe4vKipq\n6dKlfn5+KpWqs7MzLy8PrHkGfkEikWRlZV27dq2zs5NGo3l5eb3xxhv6uRXOwx06dOj555/HpsN8\n8MEHV69eBU1MAAB4LFNTU11dXd3d3QiCREVF+fn5kclkvEP9/6Kioj755BNLS0sURXNzcz/44AO8\nExk2UC55oKmpqbfeequhoUGlUvn4+Lz99tv29vb4zrCC/m/dRHp6uqurq0AgaGpqys3NBesmDAL2\nXe748eONjY0EAsHV1fXVV191c3PTh30EYBgmEomrVq1at24diqISiSQnJwe8LAHA01CpVNPT0zU1\nNTMzM05OTjExMfb29vrzOPULNBpt9erVu3btotPparU6Pz8/Pz+fx+PhnQvQFxKJpKOj47vvvmtv\nb0dRlMPh/POf/8R2YcA72mOztLRcvXr1K6+8QiKR+Hz+2bNnv/nmG7xDAQBgSHJyci5fvqxSqUgk\n0saNG2NiYvRnQSL2mX/16tX29vYzMzMNDQ3gbfFpgHLJ/Ukkku7u7pycnImJCQcHh8WLFyckJDCZ\nTLxzQTAMm5iYbN261dfXl0gkDg0N/fDDDxMTE6Atn/4bGxs7depUaWnp9PS0t7d3enp6VFQU7vOV\nfs7Pzy8qKsra2hqG4aKiooaGBgRB8A4FAIZqdHQ0KytrdHRUqVRyOJy1a9cSiUT9eZz6NTc3t9TU\n1F27dpmamg4NDeXn52Nf3cE6BQBBkI6OjuPHj3O53Lm5ufDw8D179qxYsUKvbmGPjkAgeHt7b9q0\nKTo62tTUtLm5OTMzMy8vTyqV4h0NAAB9h6Lo+Ph4dXV1U1MTg8GIi4tbtGiRg4MD3rn+g0gkWlhY\n7Nixw8/Pj0gkDg4Ofv/995OTk+Bt8cmAcsn9DQ8PFxQU8Pl8FEXDw8NTUlL0p+U7lUpdtGjRkiVL\n3NzcBAJBXl5eQ0ODQCDAOxfwMBKJpK6u7siRI9PT0ywWKyEhYc+ePfowr+TnaDSap6cntsFBd3d3\nXV1dX18f3qEAwCCp1eru7u4TJ06IRCJzc/Pw8PCkpCS8Q/02X1/fV199NTw83MTEpL6+/ocffqir\nq5NIJHjnAvCk0Wj6+vquXbt24sQJiUTi5ua2efPm3bt3689z0RNgMBg+Pj579+718PBAUbSxsfHo\n0aP9/f1yuRzvaAAA6DWNRlNaWtrR0SGXy9ls9p49e/RkqvjP0en05OTk5ORkDw8PPp+fk5Nz7949\n0MT9yYByyX0gCFJTU/PRRx9JpVImk4l1MsM71C/t2bNn3bp1EATJ5fJTp07V19eDD4B6C0XRnp6e\n0tLSkZERtVodGhoaFxfn5OSkhw+aYWFhr7zyiomJCYqiRUVFJ0+eRFEUHFoA8LjEYvHw8HBXV5dK\npQoLCwsKCqJQKHiH+m0UCsXZ2fmPf/xjYGCgSqVqbW19+eWXBwcHwSephUwmk3399ddHjhxBUZRA\nIBw4cGDz5s0sFgvvXE/Lysrqd7/7XUJCgo2NjUAgKC8vLygo4PF44JYHAMCDoCiqVCqPHz9eW1tL\nJBKtra03btxob2+Pd677O3ToUEZGBpFIVCqV77zzzp07d8Dd/AmAcsl9FBQUXLlyBetzuXfv3uXL\nl+Od6D7s7OyCgoI4HI5GoykrK2trawObCustlUpVXFx87tw5CIIYDMamTZtWr16Nd6j7o1Kpjo6O\nKSkp1tbWw8PDjY2NfD4fXFsB4HFdvnz5008/hSCIRCKtX79+2bJleCd6VDQaLTExMTEx0d3dXSqV\ntrS0XL16taenB+9cAG7+9a9/5efny+VyFov17LPPrly50snJCe9QWvPSSy+tWbOGRqOJRKJPP/30\nzp07MzMzeIcCAEBPTU1NXbhwAZuJFhQUdPDgQX3u32RiYhIREbFixQpsAVFVVVVLSwveoQwPKJf8\nFxRFVSoVl8utrKwkEAg2NjZxcXE+Pj5457oPCoUSGxu7Y8cOGIaFQuGVK1euXr2Kdyjg/vLy8m7e\nvDk+Pk6lUp999tmlS5daWlriHer+CASClZXVs88+6+rqqlAo2tvbjx8/Pjs7i3cuADAkQ0NDDQ0N\nXV1dVCo1JSUlPDxcb0/5XyMQCObm5hkZGSkpKSQSSSQSXbhwoaysDCz5XIAEAkFWVtaNGzf6+/sZ\nDIa/v/+OHTt8fX2pVCre0bQGW1u0ceNGjUYzPDx88uTJgoICsFEOAAD3xePxTpw4wePxKBSKv78/\n1q4B71APRCKRIiIiNm7cSKPRVCpVQUHBjRs3QEuyxwXKJb9079696upqHo/HYrE2btwYFBSktzNO\n3d3dly1bFhgYSKPRqqur8/Pzh4eHQW9OvaJWq3k8Xk5OTm1tLZVK9fX1zcjI8PLywjvXwzAYjCVL\nlnA4HAsLi7GxsQsXLkxOToJNhQHg0RUVFTU2NioUCiaTuXXrVi8vL31b1fybwsLCNmzYkJycDEFQ\nc3PztWvXSktLEQQBz1gLh1AobGhoOHHiREdHh0ql8vPz27lzZ0REhJmZGd7RtIlIJEZFRW3atCkk\nJIRCoVRUVFy9erWiogLvXAAA6B0ej8flcquqqiQSSUBAQFxcnB52LfkFBweH+Pj4tWvXmpmZdXR0\n5Ofn37p1CzzVPxZQLvkPBEHEYvFXX31VVVVFIpHc3Nz+9Kc/6fObLZFIdHBw2LVrl7W1tUwm6+zs\nLCwsVCqV4HFWT2A78hYXF3O53MnJSXt7+02bNnl7e+vDFksPAcMwhUKJj4/39/eXyWQ9PT3t7e1g\n+zEAeBQajUYqlWZlZdXV1dFoNGdn56SkJL1d1fxw8fHxr7zyiouLC4VCyc3NPXnyZH9/P1iat0Co\nVKrOzs6rV6/euHFDKBQ6OzunpaX9/ve/NzExwTua9pmZmUVFRe3Zs8fGxgZBkJKSkm+++YbP54M3\nCgAAfoKiaENDw9WrV9VqNZlMXr58eUpKCt6hHomrq+tbb73l5eVFoVBqamr+9a9/TU1NgevbowPl\nkv8Qi8U1NTVNTU18Pt/R0XHZsmW2trb6PMMKgiAHB4cXXnjBxcWFTCY3NTV9+eWXc3Nz4HFWTyAI\nMjY29uabb7a1tZHJ5MDAwNdee81Q5uSnp6cvWbIEhmG5XP7Pf/6ztrYW70QAYABkMlltbe3IyIhU\nKnVzc9u3b5+B7rQKQRCdTg8NDf3ss89cXFywd8jXXnsNNMlaICYmJvLy8r755hsURel0+v/7f//v\n1VdfxTuUDjk7O2dkZCQkJFhaWk5PT1dVVZ07d47P5+OdCwAAfaFSqZqbm2/evAlBkL29PYfDcXd3\nxzvUI6HT6d7e3itWrHBxcRGLxV1dXTdv3pyensY7l8EA5ZL/GB4e/utf/zo8PAzDMIfD2bdvH51O\n18O9S36OQCAwGIyDBw9GRUWpVKqRkZGvvvpqcHAQ71wABEFQc3Pz559/PjExoVarExMTn3nmGTqd\nTiAYxknHZDIDAgLCwsLUanVbW1t9ff3w8DDeoQBA301NTR05cqS/v59AILi6um7atMlwv8bDMGxm\nZhYXF5ecnOzk5CQUCuvr60+ePDkyMoJ3NECHsH0fvvvuuzNnzsjlchiGX3rppdTUVMM9kh8FgUCw\ntLQ8fPhwZGQkiUQaHR09evRoY2Pj3Nwc3tEAANALeXl5JSUlSqWSRCK9/PLL8fHxer4M5yfYtPH9\n+/cvWrSIQqFMTk4eOXKkq6sLTDB5RIbx5jYPxsbGKioqqqurJRJJaGjoihUrfH19DeI0IBAISUlJ\n4eHhbDZ7dnY2MzOzv79fqVTinWuhm56erqmpuXHjhkwmc3BwiIuLW7JkCd6hHgOBQIiOjl63bh2R\nSBSJRDdv3rx37x7eoQBAr01MTJSXl5eXl8/NzQUGBi5btszZ2ZlEIuGd68mRyWRLS8vt27dj75A8\nHu/06dMtLS1gjokRk8vlX3/9dVZWVm9vL5vN3rRp07p167y8vAyl1v/EKBQKh8PZv39/cnKyTCbr\n6Og4ceJEXV0daAkHAAucRqORSCQlJSX19fUUCsXZ2Tk2NtbR0RHvXI+BQCB4eXmtX78+KSlJoVC0\ntraeOXOmpqYG71yGwchvfo9Io9E0NzdnZ2crFAoSiZSYmLhixQoSiaTnU0swMAw7OjomJiZGR0cr\nFIqWlpaSkpK+vj68cy1cKIoiCFJbW3vr1q3BwUEURRMTE+Pj4+3s7PCO9nj8/PyWL1/u5+dHoVCq\nqqrKyspmZ2dBZxwAeJCurq4rV67Mzs4SCITY2NjU1FS8E2kBgUBITExct25dWFiYXC7ncrk5OTlt\nbW1g1adR4vP5xcXFn3/+eXNzs6mpaVhY2AsvvODv789gMPCONk/WrVu3ffv2wMBAFEUzMzMvX77c\n3NyMdygAAPCkVCorKiq4XO74+LilpeW6devs7e31vF3DfSUlJa1fv97W1haG4StXrty6dQvsm/4o\nQLkEgiBIJBJVVVXl5ORAEOTo6BgREeHv7493qMezfv367du30+l0FEW//fbbgoICMMMKR0KhMCsr\n68qVKwQCwcLCYteuXfHx8XiHehLOzs779u0zNzeXSCS9vb0NDQ2gXAIA96VUKtva2q5fv65Wq21t\nbUNDQ4OCgvAOpTW7du16/vnnWSwWDMNff/11ZmYm2FfY+KhUqoaGhsOHDw8PD6MoGhAQsG3btqSk\nJCPbCufhyGTysmXLDh06RKfTNRrNqVOnvvrqK4lEAu59ALAwoSgqFAo//fTT1tZWIpHo5eX1xhtv\nGNwXUIylpWV4eHhycjKFQpmensZ2+UFRFFzfHg6USyAIgs6ePZubm4uiKAzD77zzzvLly/FO9NhI\nJJK3t/eaNWuwNWnt7e3d3d14h1qgUBT98ssvS0tL1Wq1lZXVu+++GxwcbKAT8u3t7bds2WJhYUEg\nELhc7jfffAM+KQPAfXG53MrKSpVKBUHQM888Y6AV0gchkUiLFy9+8803GQyGWq2+fPnyv/71L7xD\nAVrW3Nyck5PT0dGhVCqdnJxSUlLS09PxDoUDW1vb+Pj4HTt2WFhYSCSS8vLyY8eOyeVyvHMBAIAD\npVI5NTXV3t4+Nzfn7u4eHx9vYWFhoE/1EAQFBwe/8MILbDabSCQWFRWdOXNGoVCAcsnDLfRyiUaj\nmZubq6mp6ejoYDAYISEhQUFBhrJ3yc/BMOzr67t9+3Ymk4kgyO3bt8+ePYt3qIVIKpW2trYWFRUN\nDg6y2eyIiIjk5GRra2uDWNj1a2Qy2crKas2aNW5ubrOzs52dna2trRKJBO9cAKB37t69W1JSQiAQ\nsE1JXV1d8U6kTdiqz+XLlyckJLDZ7NHR0eLi4itXroBGmEZjcHAwNzcXW5VMpVJ37NixdetWc3Nz\nA715PQ0ymezm5vbcc8/5+/vTaLT+/v6rV6+WlZWBGVUAsAB1dHR8/PHHk5OTGo0mPDx8y5YthtKu\n4b7odLqfn98bb7zh6ekpFosrKys/+OADsAvYwy30colMJrt06VJtbe3c3Jydnd2zzz7r5ORkoCVD\nS0tLrDenjY1NX1/frVu3iouLwZvtfNJoNGNjY8ePH29ra5NKpT4+Ptu3b3dxcaFSqXhHe3IUCmXz\n5s2+vr4QBI2Ojn7//fcTExN4hwIAPaLRaNrb2+vq6gYHB1ksVlpamo+Pj/FtI0Kn0728vPbt2+fl\n5aXRaDo7O0+ePNnZ2QnuMoZOrVbPzMxkZWVlZ2f39PQwGIwdO3Zs2bIlICAA72i4MTExiYiI2L17\nN4fDkUgkzc3N3333XU9PD+ijDwALyuzsbGNjY3Z2tlQq9fDwiI6ONoJltiwWa8uWLdHR0ZaWliMj\nI+fPnwe7gD3cgi6XKJXK4eHhzz//vL293dTUNDg4+MCBA1ZWVnjnenIWFhZ/+MMffH19CQRCX1/f\n119/PT09DVZPzBs+n19ZWfnVV19NTk7a2dklJiZu3bqVRqPhneupkMnkRYsWRUVFOTo6Tk1NnThx\noq2tDbwgAQAG23U1Ozu7o6MDhmF7e/vnnnvOyckJ71w6wWKx0tPTV65c6erqKhAIbt26lZOTMzQ0\nBO4yhgtFUbFYfPfu3ZMnT3K5XBaLFRUV9cYbb4SGhuId3VtcRAAAIABJREFUDWcwDO/du3ft2rUu\nLi5zc3MXLlwoLCwcHh7GOxcAAPOns7OzoqJienoaRdGkpKTo6GgD/ab+c2Qy2d7ePiUlJSgoSK1W\nj46OZmdnDwwMgFv5gyzocsnExERRUdHY2JhSqQwLC0tPT6dSqYY7vQqCIBqNFhYW5uPjY2ZmNjk5\nefPmzdHRUYVCgXeuheLevXvHjh1TqVQoim7cuHH37t0UCgXvUNqRnp6+fv16bCu1goKC9vZ2vBMB\ngF7AToozZ860traamJh4enpGRESYmprinUuH/ud//mf79u1EIlEqlb733nvl5eWgs7jhQhBkeHj4\nj3/8Y0tLCwzDISEh//73v52cnIx+2+BHQSaT9+7d+7vf/Q6GYRRFP/jgg0uXLuEdCgCA+VNYWHjh\nwgUIgshkcmpqalxcHN6JtGbnzp3Lli2j0WhSqfSLL76or68Ht/IHWbi3Q7Va3dra+umnnwqFQiqV\nGhwcvHLlShiGDbpcguU/dOjQ6tWrYRgWi8XvvPNOdXU13rkWhN7e3qqqqqamJgiCgoKCYmJiPDw8\nDP2I+omHh4evry+2P0JWVlZDQwPeiQBALwwNDX3yyScTExMoisbGxv7P//yPoZfdfxOFQtmyZcur\nr74KQZBGo/n888+PHz+OdyjgCd25c+fFF1+cmJhQq9UxMTHbtm3z8PAgk8nGfQw/Cuz2bWNjk5iY\nuGvXLgqFIpPJLl++/Nlnn+EdDQCA+VBdXd3S0jI3N8dkMnft2uXp6WlMF0YYhtevX3/o0CEIgjQa\nzbFjx86cOYN3KD21cMslzc3NBQUFvb29KpUqOTk5OTnZoJfh/Jyfn19MTIyPj49KpaqqqmpsbJyc\nnMQ7lDFDUVSlUl2/fv3GjRtisZhMJu/YsWPx4sUMBgPvaFrDYDDCwsLWrl0Lw/D4+HhdXV1rayve\noQAAZwiCjI2NXblyZXZ21sLCwt/fPzg4mEgk4p1LtwgEgpeX1/Lly+Pj4+l0ekdHR15eXn5+PpjH\na3DKysouXLjA5XIVCoWPj8/q1atXrlzJYDDA1JKfUCgUf3//LVu2eHl5USiUzs7O/Pz8srIyqVSK\ndzQAAHQrKyuLy+ViZdMtW7YYWQd3CII8PT2XLl0aFhZGpVJbWlqqqqqGhobwDqWPFugdUaFQVFZW\nFhYWoihqbm6+atWqmJgYvENpDY1Gi46OXr58OQzDc3NzJSUlNTU1eIcyZlhZKjc3t6mpyczMLCkp\nac2aNR4eHnjn0jJfX9+1a9diNaDq6uri4mK8EwEAzsbGxrCN1RQKRURExKJFi+h0ujF9fXoQBoMR\nEBCwe/duR0dHFEUbGhouXrzI4/FAI0xDgaLowMDA9evXCwsLlUqlhYVFWlpaamqql5cX3tH0jqWl\n5eLFi3fs2OHi4iKVSpuamk6fPj0yMgKOdgAwVnK5vKurq6SkZGBgwNraOikpKTIyks1m451Ly5hM\nZmBgILZpulQqra+vv3HjhlqtBvsK/8ICLZcMDQ3V1NS0tbVRKJSYmJjw8HB7e3u8Q2lTVFTU5s2b\nHRwcSCRSXl5eXl6eUCgER78uIAgyMzPzxRdfNDc3EwgEb2/vv/71r66ursb3hdnS0jIwMNDHx4dG\nozU0NBQVFc3MzCAIgncuAMAHiqJcLjczMxNFUQqFsnr16lWrVuEdav44ODhkZGTExcVZWVmNjY0V\nFxcXFhYKBAJwo9F/Go1GLpfn5OTcvn17aGiIyWTGxsbu3r07MjIS72h6ytra+s0330xKSrK0tBwb\nGzt37lxpaenU1BQ42gHA+KAoyufzz549Ozo6iqKon5/fwYMHWSwW3rl0wtXV9cCBA8HBwaampjU1\nNcePHwe14F9boOWSzz77LD8/H5ta8u6774aHh+OdSPv8/f3fe+89a2truVxeU1MD+pPpyOzsLJfL\nxfpm29vbL1q0KDIykslk4p1LJxwcHN5++20XFxcEQZqbmz///HOxWIx3KADAh0ql6urqqq6uhmHY\n09PT2dnZWE/8BzExMfnwww8TEhKIROLQ0NDLL7/c2dkJSqj6Ty6Xd3d3//DDD83NzWQy2d3d/ciR\nI/7+/njn0neHDx/eunUrDMMikegvf/nL3bt3QWdEADA+2DLbb775ZmxsjMlkuri4hISEGM3WDb9m\nYmLy7rvvRkVFaTSagYGBw4cPgyU5v7DgyiUymay5ubm5uXlqasra2jo+Pt7JycnQt3q9LwsLiyVL\nlri7u2Nry3NzcxUKBVhbrnWdnZ1HjhyZmpqCYTg2NvbAgQMUCsVYF36bmJjExcVxOBw2mz06Onrz\n5s25uTlwUOktFEU7Ojqmp6dhGDaCre/0zenTp7HrKpVKff755yMjI431xH8QGIatrKwOHDiwefNm\nBEEEAsH7779fWFiIdy7gYeRyeUNDwx/+8IfOzk6VShUfH3/kyBFXV1cqlYp3NH1nb2+/adOmXbt2\noSg6MzNz4sSJy5cv4x0KeBLDw8PYCyGJRFoIyyeBx9LW1nb+/PmZmRm1Wr1y5cqdO3dSKBQjPk6I\nRGJAQEB8fLyPj49QKCwqKqqtrZ2amsI7lx5ZWM92EARhd7ienh61Wu3p6bl3714zMzOjPAcoFIqD\ng8OuXbuwo7+hoeHkyZPg6Neu9vb2goKC6upquVweFxeXlpbG4XDwDqVDZDLZ2tp68+bNwcHBUqm0\nt7e3oKCAx+PhnQu4PxRFx8fHRSIRiURiMBhGeaHDBbZ58N27d5ubm01MTEJCQuLj4x0cHPDONd9g\nGCYSidHR0ampqUFBQRAElZaWXr58+d69e3hHA+4PQRAul3v8+PG7d++KxeIlS5bs2rVr6dKlRr+d\nk1ZQKJTQ0NC1a9cGBgaSyWQul5ubm8vlcsE3A4MzMzMzPT1NIBAYDIbxLZ0GngaCIJ2dnXl5eSqV\nysrKKiYmJioqCu9QukUgEExMTFJSUuLi4jQazeTk5Llz5+rq6sBc0Z8srHKJUChsamo6c+YMj8dz\ndHSMj49PS0sz4unTVCp1+/bt0dHRLBaLx+N9+umnHR0dcrkc71xGQiaT3b17Nzs7W6lUstns9evX\nJyUlLYRv+KtXr46MjKTT6SKR6PTp0319feBhUW/JZDKVSkUikcCnYy1SKBRcLrerq0soFNra2qan\npzs4OJDJZLxz4cPMzCw6Onrjxo1sNlupVN66dSszM3NychI8aemhjo6OS5cunT9/HkVRFxeX9PT0\nNWvWgA/sj87CwiIiIiI9Pd3KykoikVRVVV26dGlmZkalUuEdDXgMCoVCoVDAMEyn00G5BPi5wcHB\n+vr6jo4OFEUXLVoUEhJibm6Od6j5EBERsXz5cmxVZl5e3s2bN/v7+/EOpS8WULkERdH29vZz584J\nhUKNRrNq1apnnnkG71C6RSAQzM3NFy1aFBQUJJfLOzo6uFzu2NgY3rmMxMDAQEVFRX19PYVCiY6O\njo6OdnJywjvUfGCxWJ6enu7u7nK5/O7du4ODgwqFAu9QADBPUBSdnZ398MMP29vbiUSiu7v7Cy+8\nYDT70D+ZgICAHTt2hIeHm5iYDA0NlZaWFhUVyWQy0AhTf6AoqlAovvzyy3PnzsnlcgqFsm3btqSk\nJGtra7yjGRgPD4+XXnrJ39+fwWD09PRkZWWVl5eLRCJwtAOAQUNRFEXRrKysa9euoShKIpEOHDiw\nZMkSvHPNEzKZnJCQ8OKLLxKJRLVanZube+HCBQRBwJUNWlDlErVajbXwUKvVZmZm3t7eC2TDvLS0\ntJUrV2KzHo4dO1ZWVoZ3IiPxySef5OfnwzBsbm7++uuvBwcH451o/qSlpe3cuROCIOzWcvfuXbwT\nAcA8USqVk5OTbW1tIpHIw8Nj0aJFYCEDBEEuLi6ff/45h8Mhk8ltbW0ff/zx8PAw6K6vP0Qi0Wef\nfVZaWioQCFgsVlxc3ObNmxfIU5DWmZiYfPHFF8uWLfupyXFXVxeYTgUABg37FtLa2trb28tisVJT\nU7H+j3jnmj+2trbR0dGxsbGmpqYDAwOVlZVNTU2goTW0oMol+fn5WVlZAoEAgqB9+/YtX77cKDu8\n/pqVldWSJUvWrVsHQdDQ0FBFRUVjYyPeoQybQCA4depURUXF1NSUi4vL7t27AwMDTUxM8M41f+zs\n7IKCgvz8/EgkUnl5eU1NDdgiB1ggurq6Tpw4ge2iHRkZuXHjRgKBAMolNBrNx8fnueeei4mJkclk\n7e3tf/vb31pbW/HOBUAQBE1MTOTn51+6dKm/v59Go4WGhr7xxht+fn4L6k1Ai4hEoo+Pz759+1JT\nU5VKZX9//4cfflhcXIx3LgAAnpxSqTx16lRdXZ1CobCxsXn++eddXFwWVAd3Mpns4eHx+uuvOzs7\nK5XKurq6o0ePzs7OghX3+PdZQFEUa6szMDCA1TJ0NMq1a9fKy8shCCISiSiK1tfXt7W1aXcUCoVi\nY2MTHBzMYrH0p4cF1vF4/fr1BQUFMpmsoqLC29s7MDCQSCQa3yO+RqPh8/mdnZ3Dw8M6KohiLfGz\nsrKGhoZQFCUSiQiCZGdna703BIPB8PX1dXV1fbJCDIqiKpWqo6NjYGBgbm5Ou9kgCOru7sY+qo+P\njxcVFbFYLDabrfVRMFQq1d7ensPhsFgso7l1YZe+rq6ugYEBPp+viyEQBGlqapqbm0MQZGpq6uLF\nizp6O8J6AIeGhuJ76cM2/+vp6RkdHdXRECiKtrS0XLt2TS6Xk0gksVjc1NSk9VsJ1oAwJCTEzs5O\n6/9kGo1mdnYWu0hqffbH9PQ0iUQiEokSieTatWu2trZNTU26OyTodLqXl5eHh4epqamOhtA1BEHG\nx8d7enpGRkZ0NASKomNjY2VlZa2trTKZzMzMjEAg8Hi869eva3EU7KANDg62t7fXnyqMRqORyWQd\nHR1DQ0MSiUS7P1wgEJDJZBKJpFar8/LyGAzG8PCw7noY0Wg0Z2dnPz8/FotlfA9vP4cgyMjISG9v\nr+4Wj1dUVExOTqIoKpfLCwsLh4eHdTEKkUhkMBihoaG2trYL5AOtjmg0GrFY3NHRMTw8LJPJdDEE\ndjCcPXu2t7eXQCAgCDI8PIxtLKjdgWg0mru7u7e3N4vFeuIforunHezdAdtOcXx8PCcnx9fX19ra\nWkf38Z+eduzt7fX5HIFxXJKkVCrn5uamp6dFItHVq1dv377d29uro7EQBJFIJEqlEoZhCoWio1bY\nJiYmQUFBe/fudXNzs7a2Njc3f/RnOGzJ3OzsrFAo1MW1oKur69ChQ1NTUyqVasWKFX//+99pNJqO\n7rgEAoFOp9vY2FCp1Pl5udVoNEqlcmpqSiAQtLe3X7t2raysTHeXVJVKhRUgCAQClUrVRbdgbIfO\n9evXJycnOzs7s9lsc3PzR9z1XalUzs7OzszM8Pn8K1euFBcX62gHdQRBsE5ABAKBQqHobn4Ni8WK\njIzcsWOHu7u7hYWFubm5Qc/lwY6f6enpubm569ev3759u7u7W0djSaVShUKBIAiZTNbdQzaTyQwM\nDNy/f7+7u7uVlZW5ufnTPAc8LgRBZDLZ5OTk3NxcRUVFXl5eZWWl7sZSKBRSqRSCICqVSqPRdPF2\nRCaTrays9u7dGxUV5eDgYG5ubm5u/pT3LOwiOT09LRAIuru7r169WlZWJhKJtJX5JyqVSqFQYD3F\nSSQSnU7XXZthS0vLtLS0lJQUFxcX7CJpKC2NsYN2ampKKBRWVVXl5uZWVFToaCyNRqNQKLBiAQzD\nNBpNF/tkkUgkKyurPXv2REdHOzo6auWgfRoKhUIgEPD5/LGxsStXrty9e3diYkLroyAIIpfLsYcN\nIpFIo9F0VyoyNzePj4/fvHmzm5sbdrQzGAwdjYULtVr905W8rKzsxo0bXC5XR2Nh1yiVSkUgEExN\nTXVU5KJQKNbW1gcOHAgPD7e3t8dOCqP55DMPUBRVKpUzMzMCgWBwcPDKlSulpaU6+ryEPduLxWKN\nRkMkEqlUqo7OLzabvWLFijVr1ri5uWGHxKNfNH562hEKhZWVlbm5uVVVVboIqVarpVIp9kGFTCYz\nmUwdlUuwp519+/ZFRUVh5wibzdbDcwTPcsnIyEh2dva3337b1tamUqk0Go2hz/aBYRiGYezfftWq\nVRkZGStWrHjE34s9y54/fz4rK6upqUnr2bAHJj6fj22TYWJiorsP9djOmn/605+8vb3nZ+MhuVze\n29v7ySefFBUVjY6OIgii0WgMvTsRtkmniYmJu7v79u3bt27d6urq+ii/cXBw8PLlyz/++GNHRweC\nIEbQqAmGYawiY2VltW7duoyMjPj4eLxDPbnR0dG8vLzjx4+3trYqlUqjufRh70spKSkZGRkpKSnz\nNvrs7GxDQ8ORI0dqa2uxNTKG/vcJQRD292lmZhYWFpaRkbF169annEChVCr7+vr+/e9/FxQUDA0N\nGdNFksFguLi4bNu2bevWrd7e3niHeiRCobCxsfHIkSM1NTXT09PGdNCyWKzQ0NCMjIyMjIz5LJv+\nQm9v748//nj58uWenh5jug/SaDQrK6utW7dmZGRERETgHUqbBAIBl8s9cuRIY2OjQCAwgpMCK0qS\nSCRzc/PIyEjspNDnT+j6BkGQvr6+b775Jjs7u7+/35huW3Q63dbWdtu2bRkZGRwO5xF/7+zsbH19\n/UcffVRXV8fn843gHIH++2kH+wvRwy1r8Zk1jdXwjh8/fu7cubGxMawwb2Nj4+zsbLhN2sVi8cjI\nyPDwsEKhmJyczMnJEYlECIIkJyc/vG49PT1dVVWVlZXV19c3NjY2NTWlozYQKIpi61PUavXc3JxE\nItHRp2YikTgxMdHR0WFnZxcTE5OcnBwbG6uLgTDY9fTgwYM9PT18Pl+pVJJIJC8vLzs7Oz085R4F\n9g/U0dEhFovn5uY6OzuPHTumVCo3bNgQGBj4kN+IVeI/++yza9eu8Xg8bMMae3t7JycnS0vL+Yqv\nZSKRaHBwcHx8XCaT8Xi8K1euSCQStVqdlJSEd7THhl36vv/++x9//HF0dBSbpGBtbe3s7GxjY4N3\nuickkUiwSx/WAzUvLw9b/pOcnDwPn/rVanVZWdlbb701ODgoEonUajWTyXRzc7OzszPQnX0VCsX0\n9HRnZ6dKpRIIBNXV1dPT0xqNJjU19Yn33kIQZHR09KWXXmppaZmZmcEmWrq7uzs4OBjoRC21Wi0S\nibC9nMVicW9v74kTJxQKxebNm0NCQvBO9xvUanV5efmbb745ODg4NzenVqsZDAZ20D7iFEJ9o1Ao\nZmZmOjs7sbmNWA0IO2hdXFzmOYxGo1GpVO+9996dO3cmJyex+6CzszM252Wew2gFthKhr69vampK\nKpWOj4+fO3dOJpMpFAqdPlzNJ5VKdefOnXfffXdgYEAsFiMIYmJigp0U+rO2/bHI5XLsSq5Wq/l8\nfkVFBTYtYuXKlfb29ninMwDYutE33nijsrJyenoam+ng5ubm4OCAYx32aSAIIhaLu7u7+Xy+WCzG\nWqUoFIr09PSoqKjf/O1qtbq0tPTtt9824qedmZkZFEVXrVrl6OiId7r/gs81CEGQ+vr6qqqq7u5u\nOp0eFhaWkJDg5eVlZWVluCuQsbkb/f39dXV12LNCZWWljY1NQkLCQ45jtVpdUFBw5syZ2tpa7PGC\nxWI5Ozsb6E0dgiC5XD4zMzM5OTk1NUWj0fr6+iYnJ0kkUkhIiI7enSYmJioqKqqrq5VKpaOjY1hY\n2OLFi7E5XQb66InN7x0fH29paamtrW1tbe3v78/NzfXy8np4uUQul9fW1lZVVfX19ZmamkZHRyck\nJGDrIwy0cgT93xHV29tbW1tbU1MzMTFRWlpqb29viOUSjUbT2NhYVVXV1dWFNVyMj4/39va2trY2\n6EufQCAYGBioq6vjcrlY/dfa2jo+Pn4eyiX9/f2VlZUNDQ0QBHl6ekZHR4eFhdnZ2ZmZmeG4EOBp\nqNVqsVg8Pj5eX19fU1PT39/f3t5++fJlDofzxOWS6enpiooKLpcrEAjs7OxCQ0OXLFliZ2fHZrMN\nZfXKL2g0GrlczuPx2traamtrm5qaBgYG8vPzPT099b9cgu04UF9fD0GQh4dHdHR0eHi4nZ2dXnU9\neyw/HbQNDQ01NTV9fX0dHR2ZmZkBAQHzXy4RiUR1dXXV1dWDg4NsNjsyMjIhIcHZ2dnCwsJAV69g\nXRWmpqa6urqw++Do6OidO3ecnZ2NplzS19dXWVmJbUTg7e0dExODtfxgsVgGeiXHVnaMjY3V1dXV\n1tYODg62tLRcuHCBw+GAcsmjEAgE5eXl1dXVIyMj1tbWsbGxCQkJDg4ObDZbf7ojPRbsRMY+J9fW\n1tbV1Q0PDxcWFrq4uDxKuQQ7R7CnHS8vL+xpx9bW1qCfdkQiEY/Hw16cBwYG2tvbL126xOFwQLkE\ngiBIpVLl5ub29fWRyWQnJ6fdu3dv2rTJycnJQP+9f256evru3bsUCqWyspLH41VVVQkEAgqF8qBn\noKGhofz8/Bs3bpBIJAcHB6xrnZOTk5WV1Twn1xZsCkBvb+/AwMDAwEBnZ6dCoTAxMfHx8dHRc3lP\nT09eXh6CIHQ6ffHixXv27Fm5ciWZTDaCXmiNjY3Z2dkIgrS2tjY3N3d1dUkkkocUPiQSyZUrV0ZG\nRigUiqen5759+zZs2GBtbW0EZxbWUBaG4bq6upGRkbq6OqFQaGJiYlh/NI1Gc+PGjZ6eHux837Vr\n18aNG11dXQ3rT3FffD6/tLSUQqFgLfQqKyv5fL6OWnv8XF1dXXl5OQzDDAYjJSVlx44d0dHRBvql\n5Rfu3bt36dKlvLy8np6eqqqqoaGhsLCwJ5vIPTg4eP36dZlMRqPRIiMj9+/fn5aWRiKR9HCF8ONq\na2vLzc1Vq9Wtra1tbW0dHR0Pv0jqg/r6+rKyMuygXbFixc6dOxctWmQcB215efnly5dzc3O7u7ur\nqqoGBwejoqLmefXBzMzM2bNnp6enqVRqQEDAgQMHNmzYYGpqagRH+8DAwM2bNxEEaW5u7uvra2xs\nFIlETCbTCP5o1dXVVVVVWN/H1atXb9++PTw83AhOCo1GU1ZWduHChYKCgv7+/vLy8uHh4cDAQLAk\n5zeNj49fvnxZKBTSaLSQkJD9+/dv2LBh3loi6lR3d3d+fr5arW5paenq6mptbRWLxUwm8+GvLTU1\nNT897axatWr79u1RUVFGcI5AEFRWVnbx4sUbN2709vZWVlYODQ2FhITo1TmCQ7lEo9FIJJK8vLyB\ngQFzc/OoqKgXXnjBQD9w/RrWW0Gj0QgEgtLS0snJyebmZgaD8aBNQ4qKirq7u2EYZrFYq1evPnjw\nIIfDMYKjf2pq6urVqz/88ENTU9Po6OiNGzcOHTqki24pKpWqs7OzoKAAQRAXF5c1a9asWbNGu0Pg\nCLteIAjS3d0tFouxCtSDJpggCCIQCK5evTo2NoZV4g8ePDjPgXXH3t5+/fr1KIry+fy6ujoej9fc\n3BwaGmpASwk0Go1UKs3Pz+/t7TU3N4+IiHj++ecN9Gvnr1lYWKxbtw5BkNnZ2eLi4qmpqZaWFlNT\nUwsLC90NqlQqa2pqKioqyGSyt7d3RkZGXFyc7oabZ3FxcUQiUSaTdXd3C4XCnp6e8fFxd3f3x/05\narW6r68vJydHoVB4enqmpqZu3LhRF4FxERAQQKfTEQT55z//ibUD7O3tDQ4OxjvXAymVytra2vLy\ncjKZ7OXlZeidmH4hNjaWRCLJ5fKurq65ubmenp6xsTEPD495C4DtNHThwgWJROLo6Lh06dI9e/bM\n2+i65ubmtnHjRhiGP/roo+7u7tHR0ba2ttDQUIN+hMbWqFZWVlZXV1OpVB8fH6zqjXcu7SAQCAkJ\nCQQCQSqV9vb2CoXC7u7usLCwR2xFt2Cp1erh4eErV65IpVJXV9fly5dv374d71Ba4+3tjT37ffj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"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import display, Image\n",
"Image('./tree.png')"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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T+IL0+2q4u6+qZVuHufs+7v4q8B/gogxlOMHdDyQkq3dG7UHSlsPdlwJDusH8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\n42lNBMAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f375436fc88>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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BdqqqR1uOJGkFkhxBs3X9XlX1hbbzaLhYJDStkvwd8Bc0JeKmtvNIWrHOLaGX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\nb3VOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f37546faba8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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FlSNJGiPN1u5vA7tS7uP4c+VI6jCLhEZVs7f8J8AWlHURt1aOJGmMRcTalJt8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\n8/zz4JZJcNb68KWPl2sPWn6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"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754a6ac50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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mIGFW4yTdBQwE1q6FbkSOpIOBa4BBEfFC1vWY1SsHCbMaJmkQ8BxwSERcm3U9HSntSowD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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f375481af60>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754762cf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7f37545f3cc0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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mxQq4jeZuzacAhzHJ8kOXOZfBLvvC/hvAlVfA2+bAFQ+FI34P/28L\n+O1mcPU1cK8rYeFWzWuzPqxc0Py/WVXQu7Dz9nKa6bgbxz1vFztJM8FEY/JtSbrDxDbAH6Z4jTkL\nYM6/wHuBvBQOnQPXbwyn3QoLFsK9HgyfXArzz4Gdxz5pHagFzVi8qvH4os7b39NZHqEZg2f8OOyM\nxF39Eth2gsfHfhiOBr4y2f3FSbbu+nDl38CFn4dXXQFv6zx280fhO/Ph4n3gsK/B+xbAz1d2Xr+A\nm2HOsmbZZItV1Nr9lyvj3gLcG/jfVbyGJI2yycbkLwIHAyTZAHgxcEr3BUk2S7JO58OVy2DlKfC6\n6+DF74Rfz4WrnwBHPgg+swGc8XH45gPgknSNrbf+dTy+e9drTWSi8bi7lg2YoQcPGiTGqao/AyuS\nzB//VOf5M6vqo92PjekcOHVS12stXwLXXgILx3+d7h/Uce9zCSz8ZXNYymemKnU13n8EcOoUryFJ\nI22KMfldwPZJvk8zzh1aVb8cd82HaGYqJhyPM/mmzDv8Gu62BK4FDh17re7yVlV+1/uPAb6+qq83\nHaVqlX+Os06SfYAtqmrCW4im+Lw9gAdW1dFdjy3eH/b6AFw9tsFnKlfBvNfA5ifArcA9ul9rDWvZ\nBnhVVb2ql8+XpFGxFmPyEVV1UNfHvY7HPwLe2f1aa6pzS+pLOhtDZxSDxIB17lve40Ww+GC4Yqp5\nsduB/4StPwlLl8CPPZ5VkvrH8Xgw3Gw5YFW1IsmlJ8N8YOsDJknCV8G842HzU+D6JXCpP7SS1F+O\nx4PhjMSQjJ3tvics3g1qJ7hxfVh5M8y5BBaeDzmnSb6e7S5JA+R43F8GiSHqbMZctBi23B4WLejs\nBl4C1y6FK7HbnCQNheNx/xgkWtI53GQOsLKqVrnpR5I0GI7Ha8cgIUmSeuY5EpIkqWcGCUmS1DOD\nhCRJ6plBQpIk9cwgIUmSemaQkCRJPTNISJKknhkkJElSzwwSkiSpZwYJSZLUM4OEJEnqmUFCkiT1\nzCAhSZJ6ZpCQJEk9M0hIkqSeGSQkSVLPDBKSJKlnBglJktQzg4QkSeqZQUKSJPXMICFJknpmkJAk\nST0zSEiSpJ4ZJCRJUs8MEpIkqWcGCUmS1DODhCRJ6plBQpIk9cwgIUmSemaQkCRJPTNISJKknhkk\nJElSzwwSkiSpZwYJSZLUM4OEJEnqmUFCkiT1zCAhSZJ6ZpCQJEk9M0hIkqSeGSQkSVLPDBKSJKln\nBglJktQzg4QkSeqZQUKSJPXMICFJknpmkJAkST0zSEiSpJ4ZJCRJUs8MEpIkqWcGCUmS1DODhCRJ\n6tn/BymN01pJYg3TAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f375481a588>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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W8bS3iLhKUk/gQmA68KdsIzKzSuHkwDqzg4D+wJlZB5KViLgoTRDOkPRtRJwFIKlXR5p0\nysxal5MD61QkrQLMBMaQDJV8U0R8nGlQGYuIMyX1As6U9C0wAnhE0rCIuDPj8MwsA/JlRutMJD0O\nbAa8DKwFfD8iRmcaVAWQJOAcksss3wALAnXATukdDmbWifg2Jus0JG0IbE7yuV8nfTxN0qqZBlYB\n0s6IdwOzSBIDSFoW75K0VWaBmVkmnBxYZ3JSiWVDSYYW7tQkLQs8RjLeQ77uJHMybNr+UZlZVpwc\nWKcgaR2SCYiKTQEua+dwKtHHwBVl1vUkmdVxg/YLx8yy5OTAOosTyyy/MCKmtWskFSi9rHAMcHmZ\nTXoDD0n6YftFZWZZcYdEq3qSVgdeK7FqKrB0RHzZziFVrHQ45WuA/cpsMgnYLCLear+ozKy9ueXA\nOoNyrQaXODEoFBH1wG+Av5fZZAAwXNKK7ReVmbU3txxYVZM0BHiLZDrmfN8Ay0TEF+0fVeWT1A24\nHfhFmU3GABtHxH/bLyozay9uObBqdwLzJgYAlzsxKC8iZgN7AA+V2WQJYISk77VfVGbWXtxyYFVJ\nUg2wIvAm8ybB3wLLRsT4dg+sg0mHVv4HyfgQpXwAbBIR49I67wLUR0Rde8VoZq3PyYFVDUldgQG1\nsNhgGPAhHPstbP0NMKdw0wsj4ogsYuyIJPUGHgY2KrPJu/3goCFQ0wO6zIT60TBpAowFJkXEnDKv\nM7MK5eTAqoKkhQbDkPWgdi2ImbDg7XBzPXStA74CvgBmJvMqLBcR/8s24o5FUl9gOLB2/vIewCJA\nLXx4KAxbGaZOhy5vQp+XQc/DhNEwKiKmZhG3mTWPkwPr8CQttDasMRT67QXjB0HdT+GEcXmd6YIk\nKxgH906Gff1j1XSSFgZGAj+AZOCDpUgSBAELwluXwyGrJtM/Mw5qboKBd8CXL8FrrnOzjsMdEq1i\nSNpO0r7p85Hp43XpHQdIOk/SyZI2lfTHdFnXwTBkKPQbBmMGQd09MGgc/GwUMDG3b2ABqNsT/jkY\nhkjqKml1SQc1EM/ikp6RdKOkoZJ2acvyt7cG6vsFScMlPSpp43T5psBvgZ8A7/SgMDH4GHgZVt0Q\n/rkm7AswCOqGwZih0M91btaxeMpmqyQHksx1AMnJ/lySTgBqIuLP6Q9Vbv2A9aB2LxjfLV1wHew9\nGWqKJwkYBP/4A7w1GQaOhgER8TrwegPxbALcHhEXpf0Z7gXuakkBK0y5+t43IkZJWgp4WNJmuW0i\nYoKk3QbCIz1gsfzbQJYGekKf/rBablk3YC8Y/7rr3KxDccuBVYT0mrYiYla6aO+81f8HrBgRv0v/\n/zxwKUAtLLYWxKBkemHqgG+hdgrQP3//MOdXcN0gqFsLohYWS1sgzkmP/7KkSyQ9J+kYSf2BPwKH\nSDox7VQ3XdKibVUH7Wk+9Q1ARHwK3AFsRWGdd/kFnNgDxs3dH/ApMBrq+8BT+ftxnZt1PE4OrFKs\nCHyS+09EfJ637pfAxXnrZkTEZEk1g2HAajB3boQaoB5GfA9GCGbkli8KD+2RDNzDajBtcDLSX1e+\nO2PuB5wFbAjsHRFTgDOBiyLiL+k2/wWGtF6RM9VQfecbCyxWXOfbw0eHwMHdkn6eLAGsBDEYPhwO\nuxfvxHVu1rE4ObBKUq537P7AtZKWLFrepQd06QX1uQXTQa/B7t1h064wpS/cPgCGD4Xrctv0gvoe\nyWc/v1V8ckR8ng4f/G2ZOEoNptSRNaY38uJA/p0dc+t8L/j8ADi4Bqb0gKlrwGk1sGjA4D3hlzPy\n6st1btaxODmwSvE+sFyZdR+QXFq4R1KfvOX1Y6H/9LzP8SHwk5mw8ofw9RhY7EPYaAjcsDGMfQQW\nApie3otP+R/Hcj9IywLvNKlUlauh+hZAOvrhTsCjeesK6vwA+PhXcMh2cPgq8O630C9g2rtw5E/g\nijNhMLjOzToaJwdWESLiK2COpOJ+hJGufwY4D7gz7ahGRNS9B8e8kDRP8xdY4204eX145g9w+EBg\nRRh+IbzzJ1j9iGQ4YN6EPqOT2QXnFB+nxHNg7gBLPSNiQuuUOFsN1DckrTTDSWZnPCgiJua9rqDO\nAX4LH1wG+/0JTvoI2Awu3h4O/gKWvRhuOhC2f911btaheJwDqxiStgUGRcR1892YudML/21PuHcV\n6HcvXNYL3rseDr8Xlr0Zbv4V/OoIeHct2HM3eGpvGHs0DLwFnmvKj46koSTDAldNz/mm1nf6mrl1\nfm46pkRu3QWwUn6drwn79YQhM+DHU+G5D+HXETGqCcequjo36yh8K6NVjIgoN8lPue3rJR3wGOz6\nBlzSFz65GI5cJhnvqMDLcMts4AJY4nmYQHIW25Rj3dGU7TuCptZ3+pp6SQc8D+vcBAOHwZhuZbZ9\nFa6bDewKOz2cXBYaKenAiLi/kcequjo36yh8WcE6umUmwAWfwMSN4IzaEokBJKP1XQhL3AlfpsP5\nerz/ZoqIOaNh1B3w5YWwxLgyJxm5Oh8Dj8yEdUhuh7xP0rWSFmrfqM2sKdxyYB1WevfCcGDaVNju\nbljkcxi4FsQ46DUHGAe9LoDFPc5/64qIqZJe+xKGvN7IOpe0I7AfcBGwuaR9IuLJbEtiZqW4z4F1\nSJJqSQbb6QlsHBGf5s/K2BfWnwhXLAoHfwXPeYbAttGcOpe0LHA9sDFwAXBCRMyYZ+dmlhknB9bh\npCPpjQQGkSQGH5TYZh3gBWDdiHixnUPslJpS52nHxiOA04HRwF4R8UrbR2lmjeE+B9ahSOoN/Av4\nHrBlqcQgNafo0dpeo+s8Iuoj4jxgLWAW8LykEyX5UqdZBXByYB2GpAWA+4FVgG0i4q2MQ7IWSt/D\n9UiGUT4F+I+kFbONysycHFiHIKkbcCewAbC9LxVUj4iYFREnAj8imX/hNUmHSPLQyWYZcXJgFS/t\n9HYTsDWwU0Q8NZ+XWAcUEc8Ca5B0VryMZLroJTINyqyTcnJgFS3tuHYlsCuwR0Q8nHFI1oYi4puI\nOATYBlgVeEvSHhmHZdbpODmwipU2K58P/BrYLyLuzjgkaycR8QiwGvAwcKuk2yQtnHFYZp2GkwOr\nZKcAvwMOjYgbsw7G2ldETI6IPUgmzNqKpBVhm4zDMusUnBxYRZJ0DHAScFxEXJ51PJadiLiN5BLD\nG8BDkv6a3tJqZm3EyYFVHEn/B5wNnBYRZ2Udj2UvIv4HbEsygdPeJHc0bJhtVGbVy8mBVRRJewGX\nAxeTtByYARCJK0juaJgI/FvS6ZK6ZxyaWdVxcmAVQ9IvgOvSf0eEx/a2EtJRMTcGTgSOBl6QtFq2\nUZlVFycHVhEkbQ3cDtwN/CYi6jMOySpYRNRFxBnAuiSzy74k6Zh0TAwzayEnB5Y5SRsD9wKPkkzA\n4/kQrFEi4jVgbZLLUGcBI9NZH82sBZwcWKYkrQ38E3gO2DUiZmUcknUwETEjIo4BNiOZkOsNSb/2\n8MtmzefkwDIjaVXgEWAUsGNEfJtxSNaBpcNqr05yeeoa4AFJg7KNyqxjcnJgmZA0GHgM+BzYNiKm\nZRySVYGImBoRBwA7kPRHeEvSThmHZdbhODmwdifpe8DjwFRgq4iYknFIVmUi4kGSgZOeAu6WdKOk\nfhmHZdZhODmwdiVpIDAcCGDLiBifcUhWpSJiIrAzsA+wI0lfhC2yjcqsY3ByYO0mnTjnUaAPsEVE\nfJZxSFbl0oGTbiSZxGk0MFzShZJ6ZhyaWUVzcmDtQlIf4CFgCeAnEfFhxiFZJxIRnwJbAsOAg4BX\nJK2TbVRmlcvJgbW59CztAWAlYOuIeDvjkKwTioj6iLgI+CHwDfCspD9K6pZxaGYVx8mBtal03Pu7\ngPWAn0bEyxmHZJ1cRLwDbAD8hWT+jmckrZRtVGaVxcmBtRlJNcDNJM25P4+I/2QckhkAETE7Iv4E\nbAgsBLwq6XBJ/k40w8mBtZH0S/ZqYCdgt4h4NOOQzOYRES8AawJXARcBj6a32pp1ak4OrNWlw9Ze\nSHIL2b4RcV/GIZmVFRHTI+J3wE+A7wNvStrLwy9bZ+bkwNrCX4DfAv8XETdnHYxZY0TEcJJbHh8E\nbgTukrRItlGZZcPJgbUqSccBfwCOiYgrs47HrCki4suI2AvYFdiUZPjl7TMOy6zdOTmwViPpUOAM\n4M8RcW7W8Zg1V0TcRdKK8BLwoKSr07E6zDoFJwfWKiTtA1xK0tfgT9lGY9ZyETEW+BlwILAH8Lqk\njbONyqx9ODmwFpO0M3AtyTS5R0ZEZBySWatIh1++GvgBMAZ4UtLZknpkHJpZm3JyYC0iaVvg78Ad\nwMFODKwaRcRHwGbAccDvgJckrZ5pUGZtyMmBNZukTYF7gIeBvSNiTsYhmbWZiJgTEWcD6wD1wIuS\njpPUNePQzFqdkwNrFknrAv8AngaGRsTsjEMyaxcR8QawLnAecBrwlKTB2UZl1rqcHFiTSVqNpLXg\nTZJhkWdkHJJZu4qImRFxPLAJMAh4TdJBHjjJqoWTA2sSSSsCjwGfANtFxNcZh2SWmYh4GlidZA6R\nK4B/Slos26jMWs7JgTWapKWA4cAUYKuI+DLjkMwyFxFfR8TBwE9J5ml4S9LQjMMyaxEnB1aWpN6S\nlkmfDwIeB+qALSNiYoahmVWciPgXsCrJ38ntkm6V1B9A0saSDvOsj9ZR+INqJUlaALifZK77DUgu\nJfQiSQzGZBqcWYWKiEnAbsCewLYkkzjtSDJXwyXAw5KWzDBEs0ZxcmDzkNSNZNyCzYHFgKeAJUkS\ng4+yjM2s0qUDJ91KMvzyKOA+YJl09U9ILjvs6c6LVsmcHFiB9J7tG0mGjc2pSf8NyCSoJpD0rKQA\nXk4XvSzp2Sxjqnau89Ii4nOSIcWL9SXpwHi7pIr/m7LOycmBzZWeyVwB7F5idW/gxrRVwczmQ1Iv\noKGZSXclaUXYrp1CMms0JwcGzE0MzgMOKLPJFJIxDTzYkVkjRMR0YG+SORnKGURy++OVknq3T2Rm\n8+fkwHL+CBxRZt3XwDbpyHBm1kgR8RhJ34Ob57PpgSSzPm7U9lGZzZ+TA0PSUSTJQSkzgO0j4oV2\nDMmsakTElIjYi+QywuQGNl2OZCjmMzzro2XNyUEnJ+kg4Nwyq2cDO0XEk+0YkllVioi7SMZB+FcD\nm3UhmfnxBUk/aJfAzEpwctCJSdoT+GuZ1fXALyPioXYMyayqRcRYYHuSywjfNLDpD0hmfTzWsz5a\nFpwcdBKSaiR1l1ST/v/nwA1AuXut90/PdMysFaXjIFxNMifD0w1s2h04C3hS0nKlNij+uzZrLf5A\nVbH0jGNALSy2IQzoAV1mQn2vZHrZS4ByZySHRcQN7Rdp60jLW9MVWJAk860HpkMvSbXApIiYk2WM\n1cZ13nwR8aGkTYGjgVOBcrcJbwS8IekI4BqSap7n73qgNGkCjMV1bq3AyUGVkrTQYBiyHtSuBbEa\nTOsFdbfD6lPhnCnQ/Qtg5rwvPT4iLmv3gFsoV9450LsnyQdbQCTPe6wM6z8PEySNioip2UZbHVzn\nLZf+iJ8l6SHgJpLLCaUsCFwF7LwEXLwZ1OT/XU+HLm/CUi/D0q5zaw1ODqqQpIXWhjWGQr+9YPyg\nZLIkzoeVnoXTu0OPWpJh2j4luU8xdUZEnJlJ0C2QX977Yfa3ResXhFnnwvibYOAd0F3Sa/7ibBnX\neeuKiDckrQucAhxLmct9vWHrhWGDPnDGEcl8J3NtCdPGQY3r3FqD+xxUIEnbSdo3fT4yfbxO0pC8\nbZaWdF2J13YdDEOGQr9hMGYQ1K0Jex8G69wOl85JRjpEQA9gKeZmiOOAt+cT18OSzk6fr5feAtli\nZcp7vaR/5m3zYvq4j6S9y5U3/wP9ad7zQVA3DMYMhX6DYYikrpKukjRS0ipl4tpI0tOSnsptk3YQ\nW7s1yp2lRn7GsqjzkZKelDQi7TDbGer8hfT/DwF/A64D/lf8+ry/14VegDO2gT8vBSflb1Oizu+T\n9Hi5YZolvZ/W9QhJW6TLLpC0eCsW3TogJweV6UDg1vR5NLBdqXUD1oPavWB87gLm0TDiJTi1Dvrl\nb5hLEGpgErBxRNxS7kBKZmasn3vgiOeBTedflEYpVd4AlpS0atHyYvOUN2epov93A/aC8etBLck8\nEWtExI/L1cI4AAAfWElEQVQjolxSdBrJzHp7knQMg+Sa7+HzLVHla8xnLIs6B9g2IjbP+zxWe53v\nk9bJ5hHxAfAJsD/JZYS5FiH5e801KUyE7RaH9U+EdfO3y9X50vB9oHtEbJHOFlnKl+lxN4+Ix9Nl\n1wGHNbeQVh2cHFQYSX0BRcSsdNHeZTYdAxxfvLAWFlsLIncpoQ4YBtdOhUWmAaOBD4F3gG+B6fDm\nLFhAcNt8zs5+BxT3RRglaZ1GF66E+ZT3HOD3uU3Tx3uAe3MbFJc337vp40dQuwScsghcuDJcuiJ0\n7QpnAiulZ0zzXF5TMmV1XURMjYjPgIUBImIysHg63HSHNJ86V4nn7VLnqXrgofSMdynoFHVe/D18\nKfBkRBwE/BQY15XkMmBxBbwJA0fCUUvCn5aB4xaGSwfC2YOg7rVkKPT1JTV011GftLXmZkn9IbnE\nAWzYvJJatXByUHlWJDlzAObO7DaPiKiLiPH5yyTVDIYBq8G03LIaoBu8WgNfQHK6sjywOPAljHkK\nftMb3l8TTgReK3UsST9K131dtOq/wJB5X9Ek5cobwKvAgPRHItL10yJiWrnylrMwfPoFDKuFt/4D\nK62XDGf7bnrGNM+PHNAfyL9eOyfvB20i854kdyQNfcauTX+8R6bbtWedA+wSEZsC55PcUZNT7XU+\nMq33PhExOSJmpNv9C1ijHzxZLpvaJRndNJaH1yfDYV1g9kmw/G/g0u7wBqUnUsvZMCJ+DDxM0t8h\np6YjJ2PWck4OKlNDlxIa0qUHdOkF9QPg0v5wxUmwfBeY3h/+LZjVM92wL7zVBV6thToB3ZPbGst9\nHo7gu6lnS51ZtlSp8uY6vp8HlOvbMLe8AKfCMm/CzP/C8/vCHoLp+8IefeG+FeE9gP4w/htYsEdS\n1oY+/1NITtZyavJ+0KrhS7PcZ2y/9Mf7x6R1VqRsnS8ELwKzToNtmlnnRMSU9PEpkhw2p5rrfN+8\nywqlkq4pq8BfVodTv4bp7wMff7du9r3w+4AeP0rruzdMGAt9ukF9Wmll6zxX38DdJOMu5FRDfVsL\nODmoPO+TjLFeSsk/WEmLKplKuX4m1E+HLpPgsClw8KnJVQS+hu/3hDe6wuQF4a3N4GylX/ABmpU8\nr8/bV77lgDuAs4GdJP00Xb4syRWKlmiovKTXQdckbdYvMihXXoCT4OMpcPBkOLQOugb0qkvHclDe\nF3N9el84ecskLVF03BlAV0l9JX2PpF9GzqLAZ00uaeVosM7zlPq8lazzA+HmqbAO0P0ZWCZ9cZPq\nPF3WJ30cQuE8BNVc52W/h9M6qq+D+r1hxDmwy9rw/DLAgvCW4KtvYLXZSQtefn1rNnSJuf+dt74l\ndZPUPf3vJsAHeatnR0RzT1KsCjg5qDAR8RVJE3b3EquvkvSYpEclDcpbfj6wZETUjYZJb0Kf/BcJ\nYg706gpf94JHz4LDeycTKiXHhC4fw+T0zPh8YMmimNaMiO2AY4C7IyJ3F8EqJGeLbVHe/C+mS0kS\nkWK3lSrv/MyABUYnP/b5x7izxKYnkoyDfytp/w5JCwNjIqK+xPYdQiPrvNT/oUydPwf7pT9WM/4N\n+xW/qAl1PkLSkyTDeh8FVV/nUHhZYW6/HyUDTP09/+96B5jwEBy2Gpy1P5ys9NJXPSw5Evaq47uk\nbDwsOBtmRkRdbl9Fx+0PPCPpCeBI0snXlMzp8GwrV4F1MB7noDJdSdJDfu6tihExzxdunukR8V+A\nCTD2ZVh6HNTkOox9Bn/eAB5YHP57d9qpcAOYegr8eRzU7AAn3ZL0HyjYV7G0qfcpACX3ZI9spbOL\nUuXdP+/5HSQtF3NJWhQYXqq8OSulj2/D1bll98G9R8PA12BsRKybv6/ioCLiPySj0+X7NXBxM8pY\naRqs8/T/Bb3gy9X5abD6NPjhpnDUGtDtaThzP7jsaBgFTa7zUh1cq7nOG/q7/iHJEOfz/F1fnyZW\nU+Dkm+HmjeHGT2HvXWHKKLj4C6g5GgYG7FW8r7xjTwBKdULel+RynnViTg4qUFMnO0p7NedMeh4m\n3AQDh8GY3PWBOdC7e1GHwtnAjTDweZhA2mxetK+GjvkC0CrTODdncqeImAicLKlrqfKWUqq8+ftq\n5HHPaWqslag163wE7LcAfHQ6PFUH2go+eQT2OxqOcZ1/pxl/1y/yXctcyb/rnE3g0Vdg4ig4aleI\ndeHeor/r/H3N77hHNiVOq05ODqpMRMyRNOqOZNKWJfaC8YtAXT0suEBecpAbSe1O+HI0jOqoY7GX\nKm+pW+yqpbyVIL/O34GNpsCP1oWTF0ias2MI3PgqnHQRDJ4F37rOW64xn/Ob4O+7Q9c3Ydh/oOsX\nyRwprnNrFicHVSgipkp67UsY8joMHAw9ZkPXepg9HPq8CX1eBj0PE9Iv7Q49xGpxedeCGAe95gDj\noNcFsHg1lbcS5Op8FJy4CIxfFt4cDn16Qf328NSL8MVlcGDACa7z1tGYz3kNjPwcukxNBo36mEa2\nzpgVc3JQpdIvkhdHw4CF0slcpsPM0dBlNHxabbO35Zf3MVisLyw+EbgXunxVheWtELXTYYtP4fjz\n4b+DkxkCa2ZC/Xtw7cykk9t4Jwatp5Gf838CnwNnS5oTEac0vFezeTk5qGLpD+EESf8DmApPj4an\nGxiApkPLlZekzN0BvoRXIuL1bCOrWseQDK51yfiIb9NBonKzNj9P0pHwSOC32YVYfRr5OT8nvUPh\nDEkREX/OIlbruHwrY+eQG8xnUrUmBiXMKXq0VpROzLMvcH5EfAtzR+2clT5+A1wEHCBpYIahVruy\nn/NIZlg9AThF0ontGpV1eE4OOodccvBVplFYNTmSZHqOvzawzaUkneZ+1y4R2Twi4nSSmRtPlfSH\nrOOxjsPJQeeQSw587ddaLB2U6GDgsob6E6RD814BHJpOPGQZiIi/kAxwdJqk47KOxzoGJwedQ1+S\n28zmO1mOWSP8luS746JGbHs+sABwSJtGZA1K+xycQtIH4dis47HK5+Sgc1gImNaRh5+1yiCpN8lt\nctekI+w1KCLGkowIOExSz/ltb23qFOBU4CxJR2cdjFU2JwedQ1/c38Bax29Iks1zm/Cac4BFgP3n\nt6G1nXSo8z8Cp5HczXBExiFZBfOtjJ2DkwNrMUk9gKOBmyPi08a+LiI+lHQbcKykqyJidpsFaQ2K\niJB0EsmJ4fmS6iOiMZeHrJNxy0Hn4OTAWsNewGLAWc147ZnAUsAerRqRNVnagnACyRTsF0ryOBQ2\nD7ccdA5ODqxF0gF1fg/cGxHvNvX1EfGmpH8Ax0m62f1fspW2IBxHcoJ4cdqCcFnWcVnlcHLQOfQl\nGVbVrLl2AQbTsjP/04FngB2Be1sjKGu+NEE4liRBuDQdSfHyrOOyyuDLCp2DWw6s2SQJOB54LCJe\nau5+IuJZ4Eng+HSflrH0EsPRwIXAZZIOzjgkqxBuOegcnBxYS2wDrA5s3gr7OgN4ON3X462wP2uh\ntAXhSJKTxb+mlxiuyjouy5aTg87ByYG1xB+A54AnWmFfjwKvpPt0clAh0gRhGEmCcGWaIFyTdVyW\nHScHVS5tvnVyYM0i6UfAj4Ad0yboFkl/hM4A7pS0bkS80OIgrVWk783hJAnCVWmCcG3WcVk2nBxU\nv54k77OTA2uO44G3gX+04j7vBd5P9/2LVtyvtVCaIBwGCLgmTRCuzzgsy4CTg+rnGRmtWSStAWwH\n/Ko1bz2MiDmSzgSulbRKRLzdWvu2lstLELqQvEf1EXFj1nFZ+/LdCtXPMzJacx0H/Be4vQ32fQvw\nOcnYCVZh0mTwEOBvwPWSfpVxSNbOnBxUP7ccWJNJWgHYFTgnIupae/8RMYtkfoZfSlqmtfdvLZcm\nCAeRTJx1g6Q9Mw7J2pGTg+q3UPro5MCa4lhgIskPQ1u5BpgCHNOGx7AWSBOE3wA3AjdK8vDXnYST\ng+rnlgNrEklLAPsA50fEjLY6TkR8A1wE7C9pYFsdx1omTRAOAG4Cbpa0W8YhWTtwclD93OfAmupI\n4BvginY41mVAHTCsHY5lzRQRc4Bfk/QVuUXSrhmHZG3MyUH16wt8nf5xmzVI0gCS68yXRkSbJ5QR\nMQW4HDhUUr+2Pp41X/odsh9wG/B3STtnHJK1IScH1c8DIFlT/JZ0pr52POYFQHeS3vFWwdIEYR+S\nO1huk7RTxiFZG3FyUP2cHFijSOoDHA5cHRET2+u4ETGOpOPjMEm92uu41jx5CcJdwO2Sfp5xSNYG\nnBxUPycH1lgHAn1IbjFsb+cAC5Nc17YKl97euhdwD8lQ2DtmHJK1MicH1c/Jgc2XpB7AUcBNEfFZ\nex8/Ij4iuZZ9jKTu7X18a7o0QfgVcB9JgvCzjEOyVuTkoPo5ObDG2AcYBJyVYQxnAt8DfplhDNYE\nETGb5P16ELhb0vYZh2StxMlB9XNyYA2SVEMy6NHdEfFeVnFExFvAA8DvJfm7qYNIE4TdSSbnulvS\ndhmHZK3Af4DVz8mBzc8uwPLAGVkHQhLDSoA7uXUgeQnCQ8A9krbJOCRrIScH1c/JgZUlSSRTJz8a\nEa9kHU9EPAc8Afwhjc06iHS+jKHAo8B9krbKOCRrAScH1a8vHh3RytsO+AFwetaB5DkdWAvYMutA\nrGnSBGFX4DHgfkk/yTgkayYnB1VM0gIkg8u45cDmkZ6Z/wF4Fngq43DyDQdeJmnRsA4mImaSXKoa\nATwgaYuMQ7JmcHJQ3TwjozVkY2BD4IyIiKyDyUljOQP4saT1s47Hmi5NEHYGRgIPSto845CsiZwc\nVDfPyGgNOR54E/hn1oGUcC/wLm496LDSGT13ImmV+oekzbKNyJrCyUF1c3JgJUlaE9gGODOdkrei\npDGdBewgadWs47HmSROEXwD/Af4padOMQ7JGcnJQ3ZwcWDnHAx8Bd2QdSANuBT4Djss6EGu+iPgW\n2BF4BviXpI0zDskawclBdXNyYPOQtCJJh7Gz0yFwK1La8/0cYHdJy2YdjzVfXoLwHPCQpB9lHJLN\nh5OD6pZLDnwro+U7FhgP3JB1II3wN2AycEzWgVjLRMR04GfACyQJwoYAkraVtHqmwdk8nBxUt77A\n9HT0MuvEJO0t6Yr0C3lv4Pz0enBFS39QLgL2l7SBpKsl7ZF1XNY8eQnCy8DDko4G7gcel/SDTIOz\nAqqgO5islUg6laSXcB+glmTWtEkRcWimgbUDSc8Cxbe/PRcRG2QRTyWQ1BV4B1gBCKAO2CQdjbDi\npdeoRwBdAZGUZdVK7EjZXjr651zSgsDzwCp5i78ANo+IN7OJyvK55aA6LQsMIZnhrgewG+Czrc5r\nZ5LEAJIf127As5LOzS6kxpF0EcmtcDUksQOsDOyQWVDWGrYEVixatggwwnenVAYnB9Wpb4ll7pTY\nCeWNgljKi+0ZSzO9VGa5517ooNL37QCSJLVYLkFYpcQ6a0dODqqTkwPL2QYo1dlrNHBXO8fSHLcB\nn5RYvg7gUfc6oHQEzKEk8y+UsihJgrBy+0VlxZwcVKeFSixzctA5lRth8KyImNOukTRD2pn27DKr\nPXpiB5V3a+PwMpvUAiMlrdR+UVk+JwfVyS0HRnoveakBZ/4H3NTO4bTEdcCEEsu3kLRuewdjrSMv\nQRhRZpOBJAnC99svKstxclCdnBwYlD+zPjedGKdDSH9ELiiz2q0HHVh6a+MOwBNlNhlEkiAUd160\nNubkoMqknX18WaGTk7QGsF2JVZOBq9s5nNbwV0p/hn8uaUh7B2OtJyK+Aban/LThi5EkCCuUWW9t\nwMlB9VmQ5H7wYk4OOglJNZS/Q+HiiPi6PeNpDRHxFXBZmdXHS+qelts6oDRB+Cnw7zKbLE6SIAzO\nLZBU4/e97bhSq0g62M1yXUkyhC5APfANMAfqJHXtCJ3Qmistf01x+adDL0m1JANBVWX507IPqIXF\nVobVxsHOc5j73ud8A1ySTYSt4iLgSGCB3IKuQG/YY1l4uBeMHShNmgBjqf73uuo+5xHxtaTtgIeA\nUnMvLEGSIOxUC7M2hAE9oMtMqO8M73t7c3JQJSQtNBiGLAVrjeO7EWNyw+F1gwHfwDqSRkVE1c21\nkCv/HOjdk8Ly10CPlWH952FCNZY/V/b1oHYtiH/Abt2hS+69/4pk6LmZcG1ETM422uaLiAmSrgEO\n60FyQ3xfoAa6Lgo7HQuXvAlLvQxLV/t7Xa2f87wE4WFgw+L1PWDJWvjXz+G4HeDDXlA3HbpU+/ue\nBV9WqAKSFlob1jgQajeGGQuQfGl0TR8XANaDsQdC7dqwhqRSfRI6rPzyLw6zi8u/IMw6F8ZXY/nz\ny34ujF8BZn8F2+S/97XA8jD7+/BEFZT9it5QtzxJuXLv9ZSkSbrbEfC/zvBeV/PnPCKmAdsCz+Yv\n7w0sDywCi7wIp06G3hvCN1vCtGp+37Pi5CAjkraTtG/6fGT6eH3uefr/YyVNSJ//UdImJfbTdTAM\nGQr9hsGYGdDz0xLH6wdTh8GYodCvKzwo6XFJA8rE9tf5xH5f+volJJ3f+FIX7KNU+XtI+qukJyT9\nW9Iu6fKlJV1XZj8F5f8UFi3VDX8Q1A2DMbNgpy7wtKRfldnfsZKWbiDufSU9K2nP9P3q2dSy5+2r\nVB1cJ2mIpE0l/XE+r+86GIaMhSN/ARMGQd01sGcUtQiOAz6FrwbBkMEwJG2Wzt/P+ZJ6NHCckyU9\nJWkLSbdlXN4+PeF/3fhuLGWAeuhxOfwSYEvY9y/wpwVhkwosbw9JF6T7f0LSTZJ6z6/8+Z/zK2Bo\nFBZ/rkFQdz1s+y5c3gf2Li57uq+s3+8XJI2UdH3+unzpmf82JFM80wNYGPiWpOCzYLEL4Mq7krsZ\nALgQlv0znDYOhpV537eWtGMD8a4u6XlJ50g6RtLazS17NXBykJ0DgVvT55H32EPSoun/NwQ+Ldqm\n2ID1oHYvGN8N+Bp6L1Vio77wdbfksW6B5G9tj4iYVGqHEfF/5YKWtFi6zRYRMQYY2MwsvVT5TwI+\njIjNgK2BY/RdD+VGlX8ZmFjuW68b8Bmsty2cBjxaapuIODsiSo3Il7M7sE1E3ALcDezVwLbzU6oO\nCsKZz+sHrAe1L8EZg2H209B3TDKPQoGvgCvggNvgsfWSE+6CpDAijpzPrY0/jYhNIuJxksRqq/nE\nVU6rlPckOKamxLafwy4vQe9P4UdfwW8qtLwnAuPS/W8GnMF3yVxD5Z/7Of8QLujawLafwY8+gF/v\nkHx3zHMCUAHv9z4R8eOI2LfEuvw4cwnCK4uQFKR/3vpZsPh5cOU9aYLwEGy0OVz3IpxV5n1/JCLu\nbyDebYHTI+IYkqnCD29UKauUk4MMSOpLMiPmrHTR3nmr7wV+Iel7wOckfY0ALiWZB71ALSy2FsSg\n5PIy30Lvd9N1H5N8O3wAXAAHAZwMw2bASoJbGojvxfTxuvRM/lFJd6erLwQ2lJQbevc/JD/kjdZA\n+Xcm6XSWu//5SpJhVj+nzP3sxeV/B5b8FphGMj7wh8BLsMIpsOxWsPVUWOVJOKEnbFEmtvwz2Yck\n3SPp1XTZHsB6wAPpWcUImjkB0Hw+A5DMWHdpQ/vIlX1luPQtWOBAOGk09PwQeBeYDYwHZsCcw+DE\nf8HCa0HUJreG5ccyUlIvSftIukvSA+kZ1EBJRwArSxohaUmSEe1+nmV5T4Zj+sCTk4CPSN7jd5Ny\n9t4D/vINLNsfrqjQ8u4CnJfbLiJGRcSX8yt//ue8P1wxB1Rc/plQszb88htYdmW4tCcsXFz2Cig/\nzPu7U/xZmCsivuoPh9fCB5OBienyUSTfb6/DEqfAwafCMu/BTsPh4F1h+zLv+z6SDkmfj0r/1l+R\ntIeSoZoPAv4s6YC0b87iUuedv8PJQTZWJG+8+Ij4PG/dYyQzlu0M3JO3zeSImJG/E0k1g2HAaslv\nIZAkB/nbLEgyHV9XmHESLP9HuKg/vLoBnKHytwDlZ/JPR8RWwCwls6UdCzwREbuk6z8imQGyKcqV\nv1s6XG7O58DiETEnIsYX76RU+YsLsTywDIy9GXZ8FB7pA+/9FY5aE8Y3UP6cmojYiSQx2T8i/g68\nStJy8FJ6+9UijSxzsYY+A0TEjIY6D5Yqex94szt8OhhiADCFZIi5XvDxFDh4f5iwGkwbDAOKyp7/\nfn8ZETuQjEq4a0RcALwbEZunMTbn/W718m6cjvDYlbnXoWM6vHESnFfh5e0WEXVpmW5IE8/NGip/\nQ5/zXPkHABOg70twa678u8HHJcqedfkBrkuTj2El1hWQVLMy9DgUjqxJRvYEksT3e8DmcNN/YZmT\n4OPl4cFt4dJ/w31l3vd8A4HDgE2B30XEO8D1wPERcU26zUSgVENsp+DkIDvlmlVnkdxy9jPgScpc\nW0x16QFdLofV+8MVS8CfT4c7usD7v4ADusEba8AZ68MJveHzsdCHZIfRI3nvG/P+v5o+fk5hq15O\nczPrUuWfJSl/prYlyftCKKFLD+iyK5zdH644CZbvAf/ZDXZdHY7pC6+fBtvsCr+fkZYdoFvjy/9a\n+vgZ35VdNL/MxebXjF6SpP7A8BfhvFF55eoJk5aFv+8K+/WF1+qhrl/SsjO3CbkX1M+n7Ln3u7jM\nLY67ua8rVd6h8F63pLf67EXg0eXh/J7wzN5J3HPjrcDyzv2MR8Q+JC2Fveazn4VfhPN3gfMehH4A\nV8LBy8KflobLloOrVoWTe8MD+fE3ouyQzfu9b5p8XNiIfZzxIpx3Paw7CG7smnShIb1b5cl/wEWl\n+l80ouwfRcQ3aefHctt02lYDcHKQlfeB5Uosz30Y/wbcX+5+XUlLpE/rZ0L9IfD6FDh4DJy8TPJD\nMPtEeK0GPlkTXrkMHhHU16f7j/TeYKA+b1/l5P+Bq+gRYFngnfnso1i58t8DDAOQtCBwMHBn/gaS\nFs1LIOpnQv2dcOyUpGnxw9x2veGrnvD6NsldfAUxz/iu/AsXJSPFSpU9P5YF+a6ls6nK1cE8JC1e\nEFTEFGDLdeCoIUVnk4L4Pby1Ily/ENxyAJyTv/6xpMNmPd9drkpf9t3uyyzPWY6mv9/QBuUdAP8Y\nCJc/An/oD5+V+iWqwPLeRdL6ljPP56+4/MDkdeDIu+Con8GX+Su6w7Q74aqeMLW4/NOhy9jkB7++\naFVFvd9zD550zCzuv3T8OnDUH2FEN5ixCNzeC94VTBgOR5WL+x1YcHJyM0tx2UseuszyRUmSpk7J\nyUEG0tHe5kjqXrwqXf+fiLg4f1lO2gP37+l2daNh0pt5Z48F2+a9Nv95PXQdDZP+v737B5GjjOM4\n/H3jKSimEUwCEbRIqRaBgJWNWKSzUCSIhRYK2phgsEujohD/INgEsfJPxLQWCoJYiloJgUiCjYEo\niBGLFGJei93I/vZu9/buMHF3nqe6S2benV/2Ap9MZmbHa5+ed6gLfP1gki/mrLF+0dnzv5LkQGvt\n6/GaJ3vvP05t81ZGZxQ2nL8t8K+cC8nt4/lPXltr8vA2O/yJrx9K8tlmr7fhIpv8DEz5cDpiNnvv\nk+Sm5MqR5OLkmm8mJ84lf1w7tT3nNWcd08NJ5l3UtfECs+dtKc9pSrLgvLcmv6+NLmCfebz/w3lf\nTXJnG92N83mSe5J8N7VNmX+R93r65ZPkh2T3ueR4tn4m4L+cf95rP56pC2qnZ19LrnycPN1qlK9b\n853k8Nnk4NT7Pus41u3fWrsjycXe+yJxsZJa79s9Y8ROtNYOJ9nXe9/wFr05+x1Kcn/v/f3x93ue\nSB54I/nl2kV581xK1l5M9n40ukXo7sm1tjHDXUmO9d6PbWPf7c5/qvf+7MT3O5n/5cm1tqqNbq98\nfnzx5Hb23/TPoLW2K8m7vffnNvi9Lc3+U3LzweTE5dFp3Y0+5XCRYz7dez+yzX3Xzdta+zLJo+OL\n8lZ+3gX22XD+7fycH032fZI80nt/autH/+/rXrf5W2uvJ3ltHBaTv77l2e9Njv+WvNR7v7DZ9jOO\n5XiSr3rv0+E2GOJgybXR/c+Hnkn2vJBcnHeO/K8kbyf730t+PZ98O+u/LZbJkOdf9tlba2eS/Nx7\nP7rg9ks9706YfZiz30gen7zkeu9/t9bOfprckmT/kzPq+lKy9kGy90xy+XxydlX+0gx5/mWfvff+\n2Ba3X+p5d8Lsw5z9RnLmYEW0qefr35f8eVtydfzc8d3fJ+2bUU2v5HPHhzz/0GYf2ryTzD7M2W8E\ncbBC2sQn8x2Y+MSy88kgPrFsyPMPbfahzTvJ7MOc/XoTBytq/PCPXUmuzrlid2UNef6hzT60eSeZ\nfZizXw/iAAAoPOcAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAH\nAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjE\nAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAK\ncQAAFOIAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAHAEAhDgCA\nQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMA\noBAHAEAhDgCAQhwAAIU4AAAKcQAAFOIAACjEAQBQiAMAoBAHAEAhDgCAQhwAAIU4AAAKcQAAFP8A\n7cWUrzTpYEMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f37548000f0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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A24Bv2z6wdJ6I+HuSVqfajr0QmGb7ucKRogtkRiKGhKRRwFeABeQ0vYi2ZPtJ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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754aa3978>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f375463ea58>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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mwbxHzoDtC1/X8toqPNeqJj+T1B/4UUQc0v5PZx3lOc3NalS2UFJHjp8BzMgG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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754baac50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f375483e2b0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754a78f98>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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SfhP/BnaNOm1oScsAj5EMIT4mImbnXJKZWbfkSx51SFIv4HpgJrBfvYYJgIj4kKQ/xWrA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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f37546afeb8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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gvWA1M3sjHv/8+IvwyVhzUWFmlwEbmtmLsRfA88D+DcXs7p8ArwIvADe6+zfJ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\nZIiIiEgmVGSIiIhIJv4/2kURSgizxH0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f3754948e48>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAPBAMAAAAv0UM9AAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAMpndu3bvImbNiRBUq9OB\nhjcAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABESURBVAgdY2BgYBACYgYGExDBmgIiK6aAyAUgkqMA\nRG5lAJELQCSPAIjcxQAiz969++wqUIIBrIvhCYi55N0NEMXAAABbkhBrtxdTYQAAAABJRU5ErkJg\ngg==\n",
"text/latex": [
"$$4$$"
],
"text/plain": [
"4"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"names = ['A']\n",
"\n",
"class Node(object):\n",
" def __init__(self, state, value=None):\n",
" self.state = state\n",
" self.value = value\n",
" self.alpha = -inf\n",
" self.beta = inf\n",
" self.left = None\n",
" self.right = None\n",
" self.pruned = False\n",
" self._name = None\n",
" \n",
" @property\n",
" def is_empty(self):\n",
" return self.left is None and self.right is None\n",
" \n",
" @property\n",
" def children(self):\n",
" return [x for x in [self.left, self.right] if x is not None]\n",
" \n",
" @property\n",
" def name(self):\n",
" global names\n",
" if self._name is None:\n",
" n = chr(ord(names[-1]) + 1)\n",
" self._name = n\n",
" names.append(n)\n",
" return self._name\n",
" \n",
" def __str__(self):\n",
" if not self.pruned:\n",
" return (('({} , {})' if self.state == 'MIN' else '[{} , {}]').format(\n",
" -sp.oo if self.alpha == -inf else self.alpha,\n",
" sp.oo if self.beta == inf else self.beta) +\n",
" ('' if self.is_empty else ' , <{}>'.format(', '.join([str(x) for x in self.children]))))\n",
" else:\n",
" return ''\n",
" \n",
" def nx(self):\n",
" g = nx.DiGraph()\n",
" nodes = []\n",
" edges = []\n",
" def add(cnode):\n",
" if cnode.left and not cnode.left.pruned:\n",
" nodes.append((cnode.left.name, cnode.left.alpha, cnode.left.beta))\n",
" edges.append(((cnode.name, cnode.alpha, cnode.beta),\n",
" (cnode.left.name, cnode.left.alpha, cnode.left.beta)))\n",
" add(cnode.left)\n",
" if cnode.right and not cnode.right.pruned:\n",
" nodes.append((cnode.right.name, cnode.right.alpha, cnode.right.beta))\n",
" edges.append(((cnode.name, cnode.alpha, cnode.beta),\n",
" (cnode.right.name, cnode.right.alpha, cnode.right.beta)))\n",
" add(cnode.right)\n",
" g.add_node((self.name, self.alpha, self.beta))\n",
" add(self)\n",
" g.add_nodes_from(nodes)\n",
" g.add_edges_from(edges)\n",
" return g\n",
" \n",
" def show(self, title=''):\n",
" g = self.nx()\n",
" plt.figure()\n",
" pos = nx.drawing.nx_agraph.graphviz_layout(g,prog='dot')\n",
" nodes = nx.draw_networkx_nodes(g, pos=pos, node_size=100, alpha=0.2)\n",
" edges = nx.draw_networkx_edges(g, pos=pos)\n",
" labels = nx.draw_networkx_labels(g, pos=pos, font_size=6)\n",
" plt.axis('off')\n",
" if title:\n",
" plt.title(title)\n",
" plt.show()\n",
" \n",
"root = Node('MAX')\n",
"\n",
"root.left = Node('MIN')\n",
"root.right = Node('MIN')\n",
"\n",
"root.left.left = Node('MAX')\n",
"root.left.right = Node('MAX')\n",
"root.right.left = Node('MAX')\n",
"root.right.right = Node('MAX')\n",
"\n",
"root.left.left.left = Node('MIN')\n",
"root.left.left.right = Node('MIN')\n",
"root.left.right.left = Node('MIN')\n",
"root.left.right.right = Node('MIN')\n",
"root.right.left.left = Node('MIN')\n",
"root.right.left.right = Node('MIN')\n",
"root.right.right.left = Node('MIN')\n",
"\n",
"root.left.left.left.left = Node('MAX', value=5)\n",
"root.left.left.left.right = Node('MAX', value=10)\n",
"root.left.left.right.left = Node('MAX', value=6)\n",
"root.left.left.right.right = Node('MAX', value=5)\n",
"root.left.right.left.left = Node('MAX', value=4)\n",
"root.left.right.right.left = Node('MAX', value=0)\n",
"root.left.right.right.right = Node('MAX', value=5)\n",
"root.right.left.left.left = Node('MAX', value=5)\n",
"root.right.left.left.right = Node('MAX', value=10)\n",
"root.right.left.right.left = Node('MAX', value=3)\n",
"root.right.right.left.left = Node('MAX', value=2)\n",
"root.right.right.left.right = Node('MAX', value=14)\n",
"\n",
"root.show(title='Initial')\n",
"\n",
"i = 0\n",
"\n",
"def alpha_beta_pruning(root, depth, player, alpha, beta):\n",
" global i\n",
" if depth == 0 or root.is_empty:\n",
" return root.value\n",
" if player == 'MAX':\n",
" best = -inf\n",
" pruned = False\n",
" for child in root.children:\n",
" if pruned:\n",
" child.pruned = True\n",
" else:\n",
" best = max(best,\n",
" alpha_beta_pruning(child, depth - 1, 'MIN',\n",
" alpha, beta))\n",
" alpha = max(alpha, best)\n",
" root.alpha = alpha\n",
" if beta <= alpha:\n",
" pruned = True\n",
" i += 1\n",
" root.show(title='Step {}'.format(i))\n",
" return best\n",
" else:\n",
" best = inf\n",
" pruned = False\n",
" for child in root.children:\n",
" if pruned:\n",
" child.pruned = True\n",
" else:\n",
" best = min(best,\n",
" alpha_beta_pruning(child, depth - 1, 'MAX',\n",
" alpha, beta))\n",
" beta = min(beta, best)\n",
" root.beta = beta\n",
" if beta <= alpha:\n",
" pruned = True\n",
" i += 1\n",
" root.show(title='Step {}'.format(i))\n",
" return best\n",
"alpha_beta_pruning(root, 4, 'MAX', -inf, inf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 2\n",
"\n",
"**Show that the following assertion is true using an example: For every game tree, the utility obtained by `MAX` using minimax decisions against a suboptimal `MIN` will never be lower than the utility obtained playing against an optimal `MIN`. Your example should also include an explanation of what an optimal utility is for `MAX` and `MIN` and what it would mean for either `MAX` or `MIN` to play a sub-optimal game.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is evidently true, as the `MAX` value is the theoretical upper bound, and should never be lower than `MIN`.\n",
"\n",
"We can use induction to prove this.\n",
"\n",
"Let $T$ be some theoretical tree, with $T_i$ any given node from this tree.\n",
"\n",
"$$\n",
"\\max(T_0) \\ge \\min(T_0)\n",
"$$\n",
"\n",
"For some tree with depth 1.\n",
"\n",
"$$\n",
"\\max(T_i) \\ge \\min(T_{j})\n",
"$$\n",
"\n",
"For any two nodes $i$ and $j$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 3\n",
"\n",
"**The following pseudo-code for the minimax algorithm is similar to the code included in the lecture notes. This code shows additional print commands that are not in the lecture notes code.**\n",
"\n",
"```\n",
"minimax(node, depth, mexPlayer)\n",
" if depth == 0 or terminal(node) //terminal test is true\n",
" return f(node)\n",
" if maxPlayer // Player(s) = MAX\n",
" bestValue = -MAX_INT // system property, max negative integer\n",
" for each child in node.adjacent\n",
" eval = minimax(child, depth - 1, FALSE)\n",
" print eval\n",
" bestValue = max(bestValue, eval)\n",
" return bestValue\n",
" else // Player(s) = MIN\n",
" bestValue = MAX_INT\n",
" for each child in node.adjacent\n",
" eval = minimax(child, depth - 1, TRUE)\n",
" print eval\n",
" bestValue = min(bestValue, eval)\n",
" return bestValue\n",
" \n",
" minimax(origin, depth, TRUE) // call from root for MAX player\n",
"```\n",
"\n",
"**For the following tre, what numbers are displayed when the algorithm executes with an initial depth $=4$. You can assume that the root of the tree only has one child.**"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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LskzTtCwLp7eiKIg3lpjniOibGP6I6OY7+4Xu7CA9tE1Ib0p6p7o0oijyfT/L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WWQ/GFHLZlM4qMILar5fK7rOgKX4zgIUJgl9X0fzwqDaJQinAlcm7Ztw71N13WM96FZj60sTOXm\n83n8ieLC8p3l+3/ny0uKGBFhm935fB51weFwiMXEcDg8HA673e5sNisUCrPZjE0L0Dt71aHK31+B\n1UuwqIHpmdFo9OzZs06nA49FqLTE4/FSqVQqldiihiRJmJbAzfgtlwXAIiyyvfF47Hkexvknk8nh\n4aFt21DugMeXIAj37t0rlUqVSgX+H9gIpqvxeoDkDIeB8Xj8+eefQ8Gh1Woh54vFYqVSSVXVfD6/\nsrLCVP5FUcTCOFMF+ktVYab3xtaPMGlgmqZt271er16vj8dj6H1wHBeNRmVZ3t7eRiGwUqlgOQkH\nD/rUXQrsc+J53tHRUb/f39/ff/78+WQyGZvjBbdIp9OZTEZRlK2tLUEQkPOxzqAoisstvO9M5Zel\nAaFLil4ktEVarZZlWa9evcLmge/7CICZTObBgwcbGxuqqlarVWiLUAv4+2Fb/L7v1+v1Vqt1cnLy\nxz/+cTKZoAWUz+dR4N/e3kbzJ5PJYFIceznv8RtmcyCz2Qxpva7rWCM7PDxErdc0TaT7kiT94he/\nyOVyOzs7UI96yzKYuHJQ5e+vw2bkx+MxLgxN0549e8YaH4lEolqtIs5ubGxkMpl8Pg99vuXL8juv\nT1z27C+w/cAooWmaiURC1/XDw0PTNDG+g1u7aZqz2Qy+jdE3UP53DWDyHCjhvHjxotVqNRqN4XDI\n8/z6+nomk9nZ2anVaoVCYWVlJR6PM7mN8Dt2bd8Pay6rqopRP8/zBoNBsVjUNA27R61WyzAM1AUV\nRYHwJOrTGO3iKPp/cFiuYFmWZVn1eh3zJ7u7u0EQ4BhQKBTW1tZKpdK9e/egz8cUfFi29/1vHFoK\niE48z6dSKZYu2La9srIymUw4jmu32+gVBkHQ6/WQXIZCoSAIMpkMVkCYhcyH+O1cNfBusgXtdrt9\neHh4cHDw7bffep6Xz+cVRanVao8fP1ZVFak8E2w/6yW/DOsMYEwTcQApoKqqOBA2m83T09N2u51M\nJhVFQXIviiJ6XLTcc6Wh5O8vwm6N0MdqNpvNZrPdbn/zzTfQcIFtdqFQSKVSW1tbMEEqFosItSj1\n/fDSCIJsNBqdz+eQ2cQy3Xg8xv6dYRjNZnM+nw+HQzR6XNeVZfknP/kJmsvvLoIQVwX2YWM3gL29\nveFweHp6qut6PB6v1WqyLN+/fz+TyWxtbeXzeUmSMILNBknP+kPZt6Drh10i3BIURcGMv6qqrVbL\n931Mo+7u7uq6XqvVbt++DckPUoL9wDDBDsMwjo+PR6PR7u5uu90eDodIC27duiVJ0vr6eqVSQYU4\nHo+/Zcvxw2HfwsZLFosF/i6KIuZBZVlWFMU0zU6nM5/PT09P4TQDJ4lKpcJazPQ5eQuWTzuOc3p6\nahjG8+fP9/f3h8Mhhvnu3r1bLpc3NjbW1tbS6bQkSefYT38rAnAchywwCAJZli3LwipJPB6fzWad\nTmcymSSTSd/3i8Xi1tYWk4Omt/UqQsnfd8NOY0xO/cmTJ0+ePGm1Wq9evQqFQrdv315bW9va2nr4\n8CFUrzAJywao8Tg//KrAV2KWNhaL4ZxdKpWm06lhGJiw/uqrr3Rdf/Xq1fHx8cHBwfPnz/P5fCQS\nKZVKhUIBqUA8Hj/rjyYuF1bIwbTNcDjc3d399a9/DR3XSCRy9+7dn/zkJ5VK5W/+5m+YkjNb6eDO\n6b3GR1dRlHQ6PZvNNjY2HMc5ODg4Ojo6Pj7+3e9+NxgM+v1+Op1+8OBBOBzOZrMYKaPprg8DaxFg\nMuT09PT3v/99v9//85//bBhGoVDY2toqlUr/+I//iDFQjAGgDneOd+hQKIRtU1mWs9ms7/tYEeh2\nu//93/+N/aHd3d2VlRXf9/P5fDgcxi5wIpFgj3Auz+SqgwufVfq/+OKLbrf7xRdfHB8fp1KpO3fu\nqKr6T//0TxsbGxBhZu47F/cLDIfDqVQqHo/P5/NKpWJZ1t7e3jfffNPpdP7whz9AHebg4OD27dui\nKMqyDHl5jt7TKwglf38RLMajDA5pJV3XLctCbgeBA0zdptNpeKf++AsAj8AU83HkwgLXdDotFArR\naLTZbEKnbTwex2Kxfr+P1jOTg6YJmysHm9/Sdb3f78NrwXEcLNhCfq9QKGDRe1lz63zBJw0rR2go\n5/N5TJ2m02mO41zXnUwmsA2dzWbZbJYGwD8kTAQEEQk7AZjKEgQB+xy5XE5V1XQ6jVbARTwN1mFA\ntRiHZIymcRwHrVPYx4XDYcMweJ4PhULL4iME938HfCHjPBwOHcfhOA4yLri/II9HVf4DPCuWz+Hk\nkMvlisUiHF+gFIg1FE3TOI6DchB5UF1FaOHjO0As03W90+kMh8Nf//rXWKBzXRcTV5lM5v79+6VS\nKZ1OQ8AFmd9FXAA4GmLzFwnB0dHRYDA4Ojp6+fIlIkUymXz06NH9+/cLhcKtW7cg1kr34ysB3l/T\nNPf393Vd//Wvf31ycuL7Phw4fvaznxUKhdXV1UqlAjHID6OgxoSNHMdBqnFwcGAYxpMnT5r/P3tf\n/ty2eacPEDwBEMTBUyIl6pYtn4nT9Nt2uz12ZzvtP9W/aGd2Z2e67bTb3aZJm8S3Y8uSdVAkxRsk\nLh4gCeD7w1OhqnPZji0ewtOZTJIq8kvixft+jufzPKenkCWKRqO/+tWvstlsLpdLp9PQHnqnq7rM\nwD5RVRVjQHt7e7VarVAoEASxurqaTCY3NjauX78OBWa3BXEBJ4A7qTAYDBqNhqZpT548OTo6arVa\np6enfr//2rVrCwsLW1tbN27cYBgGLMBLfjS5DO9er3dwcIDxwU8++cQ0zVwul8vllpaWoJsDHtF5\nlfWLXCTEyFRVVVX1wYMHrVbr6dOn5XIZ/GNBEFCYhMqgxziaLXiVv38A7jyoG+i6Xq/XIa2uKApJ\nkpFIhOf5tbU1QRBWVlbcQ5Z4l5ZrbsYM4s5oNKIoShCE8XhcrVZt2y6Xy+jB8TxPEMTCwgJxLjX3\nMOUAf6vX60GVt1QqlctlmqYXFxclSUIjDzW/i1RYxR/h8/lAI0PlRtO0RqMxGAzK5XKtVlNVtVQq\nQXiI53ls1ItZ3mWDc2bEoqoqBr+Oj48VRRmNRqFQKJPJLC0trays5HI5V4iRuKgHQZIkjsFQKBQK\nhVAnxqQw9CPL5TI4ZJqmoWXsTYkSBIHgD0OExWKxXq/jluF5Hgw/aDFiTIeYxNcFtgBOAIZhNE2L\nxWK1Wq1Wq8FnSFXVRqOBo8lt/l7yxzpDoH79619Peg3TBdu2dV0Hte7TTz9FCkuS5PLy8tWrV7e2\ntnZ2dlKplCRJLof6Xe94/H7Ec64iP2y5BUHAzB3M5QzDwMSW1/+dcrilNRjDFIvFP//5z4VCQZZl\niqLy+fz777+/sbGxtbUlSRLcXy4++z+/8eAdAq1yiqIMw/D5fP1+HwqU0WgU2ZF3r791oOYHG4aH\nDx+CUVculwOBwNbW1urq6nvvvbe6ugoZZ1de4IL3iXs6wVsCsjLj8ZhlWdSNSJIMh8OmacIq5jJb\ngIBNbppmoVAoFouPHz9++PBhu92GeNP7779/7do15H4TeevP46V7B0x0cHzhGY16BEmSOAG8se4Z\nglf5+ztc+m2n06nX63t7e5999lmv14N55fb29s2bN+Px+OLiout1fcErxNuFGjsiP5DDKpVKoVA4\nOjpqNBpLS0suvfrirwEPrw634Vuv14+Pjx88eGAYBs/z6XR6e3v7+9//PoR5XVmHSa0TpR2O46BV\nns1mUQZotVovXrygKAq+XqjuuBeAh7cFTHhgnzx48KDRaBQKBU3TJEm6c+dOIpG4cuWKIAgw9Jvg\ny+72KLLZbDwelyTJcZxms/mHP/yhXq/DNTiTySSTSYIgMFUwqaVOEK7Keq/XKxQKhUJhd3f34OAg\nEom89957mUzmxo0bGxsbkAkjpiOQwgmQSqV4nrdtOxaL7e7u7u7uGoaxu7uraZpt28lk0nEcbIBJ\nr9fDK8EL/v4Gd+ISRr2VSqXVasEQExzqdDoNuxs3G5vUUhEKoAdNEEQul6MoClMp/X7/9PTUNM1M\nJsOyLEEQaNhNaqkevhIo+4HHKcsyuqjYbJIkLS4uLiwsQMd14psNIM/GRZH6J5PJXC4XCoWKxSKG\nVE5PT30+Xy6Xc4uFE1/zfABVol6vJ8tyo9GoVquYopAkKZlMptNpSZKi0Si0Hie9WII4mwX2+XyQ\nvvL7/aIoQgW6UqlYloX1Y5iAmI7g5oKBsYlutwsJT8MwwuFwLBZbWFjIZDKiKKLTOull/h3nX2qe\n5zHKk0qldF3Xdb1SqaRSqU6nQxAECJ3EpXysMwcv+PsboOcHSs3//d//7e/vdzodVNd+8Ytf4D4+\nT/KbONDYZVn2X/7lX9rtNtSYFEX53e9+h6CBIAiMiHrkvykErHU7nc6nn3766aefKopCURTP8z/6\n0Y+uXr0Knt+7m+p9M6Bz5/f7t7e3BUFoNBqqqlYqldPT006ns7a2ls1mRVGEsY13+r8VIFA4OTl5\n+PBhsVi8f//+eDz+4IMPdnZ21tfXMUKBYGvSK/0HUBQlSdLt27dhCndwcPDixYuPP/6Y4zhRFHO5\n3Pb2NgQKJr3SiwaYHpVKpdFofPTRR4eHhzzP3759O5vN/vjHP47H4xzHfaXb3jSAoqhUKgWd5/F4\nXKvVfvvb3+7v75umieCVYRgojk16pR6+Hd5D+jvgrqaqarvdVhRlPB5Ho1FRFEVRFASBZdmv9Geb\nCMgzRRiSJDmOcxxHkiSw/ZrNJkEQMF+H8avHw5hCYJAW8Z8sy9AMj8Vi2GwMw5x37Jj0YgniH/Vg\nI5FILBYbj8eSJKEMgLdG0zQY27iKbh7eGO7wGZTeG42GLMtwVojFYslkUhRFcH+nZIe8BPABCIKQ\nJAkC9RhsarfbNE3DQ/aydQldbRdUGSCIk0wmk8kkgiowK6bzgRJnnX0YECQSCcuyQqEQwllYEA2H\nQ7heTe1H8ODCG/ggiDNJv3q9/vnnn+/v7z969Ahl7Tt37mxvb1+/fl2SpPNjdNMAl1kPkjWUQSKR\nSLVaxbWB2bpUKuWqBk7P4i8z3Ebe06dPj4+P79+/f3h4GAqFfvCDH2xtbV2/fj2dTr9kDDg9cKeA\nXRNhTHHWajUkS4Zh4A7z5s2/O2zbhu7jvXv3/vznPzcajWQymc/nf/jDH968eXNxcfHCpH9eFy7b\nGLMCHMfBkoSiKE3TZFkGnxVjBMTlOJrw4g8Gg1Kp9MknnxweHhaLRYqirl+//uMf/3hjYwNW3VMe\nOeGxUhSFEBB6n47jKIqiqur6+jq4p1P+KTwQXuWPOHsn4Ue0t7fXbDY7nY5lWYIgbG9vuxn2VEV+\nANaDeiQ81P1+/8OHD3EZ93o9lmVv3LiB0NArxU8J3OFNqLo0m01k/xsbG8lkMpFIuJHfpFf61cDR\nD3HXjY0NjuOKxeLe3p5hGHCCX15eTiQSFylMM6+wLAuDNaenpycnJxRFbW9vp9Pp1dXVXC4H+bdJ\nr/Fb4Pf74X7UaDTgWlYqlVqt1tWrVxVFCQQC08NWfNfAiw/L7BcvXrTbbeRO2Wx2fX1dkqTpj/wA\nzPXDtW9lZaXX652enhYKBcMwZFkGA/USNvRnDl5A8PdhOignw8YeU72g304J6f4r4fZ/0eHtdrtr\na2vtdrtYLNZqtUqlUq/Xbdv2DLimBG7kp6pqoVA4PT21LCuZTILrHY/H39iD9SKBig64/I7jZDKZ\nTCYDc1Jd169du5bJZM67z3l4XbgZabVaLZVK7Xbbtm2GYfL5PA4lkC8nvcxvB0mSoVAoGo2m0+n1\n9XWapguFwnA4rNVq5XLZcRwUL4lLkCQ4jtPtduGOUy6XdV2HgUcmk4nFYjMkkozXH+J/2Wy21+sh\n/lNVtVarhcPhcDjsSXlPP2bg+HjXsCwLvPWjo6PHjx8PBgMU4W/cuLG8vMyy7PRfxjBkRIXvJz/5\nSa1WK5VKpVKJYZjnz5+rquq6z035B5l7OI4DbbzT01NYeS4sLNy4cWNzc3N9fR2u7TNxB4D9Aymy\nK1euGF390LkAACAASURBVIZxfHz88ccfh8NhDKzg1p+JAGXa4KqBGIbx5MmTw8PDWq1G03Q6nb59\n+3YmkwGXY9LL/Hacb03k83nHcQqFwl/+8pdOp3NwcMCyrGEY2Wz2kjD/LMuSZblYLB4cHOzt7VmW\n9eGHH25vb29ubqJaRsxOBOx2fnd2dnie73a7jx490jRtb28P4n+iKE7/vXnJ4R3Nfxu/0jRN13XT\nNG3bZlkWQhuzkl4TZ1JM4XBYEATTNDFuCRmOUChkmqZlWZfhhJ1yQE7IMAxd1w3D6Pf7oVAIQx7o\nlczWcQnjmWg0CsnJ0WhEEASMSmOxmGcd+cZwK3+KonQ6nfF4zDAMx3HRaJRl2WlmBXwlMCfO8zzP\n8zhUB4MB5oRGo5FlWZehSuRapRmGMR6PCYLAizMT7fuvBGZ6sCfD4TDsB1mW7fV64/HYtu2ZyGMv\nLWYjsnlHwE3c7XafP3/+4MGDYrEYi8UikciNGzdu3LiRTqdn6JBFKZ5hmOXl5Wg0euPGDYIgTNP8\n5JNP4vH4+vo6dHpnpbA0l8CgX7lcvnv3brlchu1BPp//4IMPFhcXEa/Pyn4jzqoUgUAgl8vBBgrm\npMfHx4FAoNfrQa2GmJ16xpQAk+D1er3RaDx+/Pj4+DiTydy5c2dpaQlCu1M74fuVcKXpsb0/+OCD\n09PTVqv14MED0zS///3vO44Ti8VgRz7pxb4TgOzhXjSlUimRSDAMs7W1tb29HY/HZ7RIBkEfv9+/\nubl5/fp12GKdnp6m0+mVlRXXXXoWP9plwHy+bK8C188Dqs7lcllRFJZlRVEEFQM2RJNe5usB7lux\nWCyVSiF4BbdGUZRutzscDr1izAThWnpUKpVarQYupiAIqVRKFMXZzf5Zlk0kEolEArmTqqqnp6fN\nZhNFnUkvcPYAFrKqqp1OBwI6wWBwYWEBFPvpEZx6dYAkQNN0LBYDl5ogCFmWm83m+UrYXAIXDeq4\nsixXq1VMxEuSBEP2GWL7nQeiulAohEsTVFRFUWBSDFlv77qZZlzqyh/K1LBYODk5IUlydXU1Ho/H\n43Go+s3cCUsQBITW8vm8aZrD4fDg4GA4HBaLRYySYUhz0iu9dMAhCE+nRqNxeHjYbrch6JpOp6Ei\nOYsXAHHG6Oc4DgVmWZYVRTk+Po7H467snzf58eoA4U/X9UKhUKvVhsNhMBiMx+P5fH5hYSEUCs1c\n5Ae48d/6+nokEjk5OSmVSsgTLMuKRqP4aJNe5jsBpJ0gwlCpVCiKWl5ehl8UdCQmvcA3hzv4tbq6\nGgqF7t271+v1ms1mo9GAF/C8PtM5wAxvu+8I9HxlWa7VasVisVgsplKpra2tdDqdSCSmU9vlW4Hm\nbygUyufzFEVBRqTX6x0fH6Pzkkwm4ark4YKBnq9hGNVq9eDgYDAYXL9+PZPJLCwszNas30uAnRdB\nEPF4/MqVK/V6/aOPPoIiXbvdDgQCs1ipmizG47GiKPv7+41GAxTkTCazurqaSCRmLiN1gaMpEolg\nvuH+/fuO4+i6fnJyYprm4uJiLBab9BrfCdx6v6Io1Wq1UqlkMpn19XV08Ofg7aAoShTFjY2NYDCI\nieZWq1WpVAKBQDqdnsVr9JLgkgZ/rpMvGivdbteyrGAwiFL8rOgtfR2g/MLzPMdxkUgEQjayLBuG\nAUHO2f1oswv08nq9XrfbNQzDtm2e51FjnnW2E0hdoVAoHo+PRiOKokzT7Ha7mqYxDCMIwqQXODPA\nueRaJnQ6HUjmRqNRhmFm3TQP+4Rl2VgsFo1GI5EISZL4jIPBwLbteT2aQOLsdruDwQAGGLFYTBCE\nOYj8CIJAuQHTSOFw2DAM0zRh62fb9qRX5+FrcUmDP4IgxuOxYRiPHz+GQBHS652dnWQyGYvFZvoy\n9vl8IBGvrq5ubm4qilIoFFRVXVhYuHLlSjAY9Ip/F4/xeNxsNk9PT2u1mqZpNE1fvXp1bW1tYWFh\nDh6Hz+eLRqPXrl2TJOnjjz8+OjqCnEe324VS5ky/UBcJyEA2Go0vvvhCVdV8Pp9Op5eXl2e6POwi\nEAiIokiS5MrKysbGBmYgGo3G7du3FxcXp8c5/S3Ctu3BYIAX3zAMgiA4jltbW0un0/PRFfX5fCzL\nLiwsjMfjTCbjOA56TX6//7333pv06jx8LS5p8OdW/hRFURTFsqxwOMwwDE3Tc0BRAr0mFArBLhYT\nzRRF9Xo9y7KQYRPeDObFAmci0mLibDSH4zhMbs7Bs/D7/SzLsiwLUXQ4ZTMMMx6PPd73qwNmvoPB\nwDCMXq8XiUQ4joP096yLIZMk6TiO3+8PBAIMw0SjUdgW+/1+aFFBHGR2P+DXwbbtbreL/hLUkRiG\nYRhmptl+5wGL0VAoRNM0NF90Xe/1eu5d42EKMSeb77WAxgpcxsvlcrVaDQQC2Ww2k8lEo1Gcs5Ne\n45vDdV/FJOnKykokErl37x7E5bvdLuiMc5BxzhDA+wG7VNd1mqZ5noeh+3xk/8g30NGTJEkURZ/P\nh4nm+e7ovV2gP6hpmqqquq4PBoNMJrOyshKPx2c9I3UBRdJ4PJ7NZh3HKRaLw+FQVdVutzuXRkTg\nezQajWaz6TgOy7I8zwuCwPP8DEmJfQNcw49IJBKPx/v9/nA4PD095Xl+joe45wAzHOV8F5wXeZFl\nWZIk2KpGIpH5cMLAEFY0Gl1YWMDpA+Zfr9czTZNhmEkv8NIB+v71er3f76MiC1LmbGm2fQN8Pl84\nHKZpmuM4ECfa7bbP5/MUH14dMIAxDKPb7fb7fcuyIKIRi8Xmox/q2lFCjkpRFOi8GIYxGAxGo1Ek\nEpn0Gt8y0GJqt9udTsdxHJQ8WZadgxaTC7A5g8Egz/OaplWrVTBWQTGf9Oo8fDVmvuTwZnB7K+Cl\nBgIBWHpgNGluXshIJIIRFp/Ph8/b6/VQiZn06i4RXBY/Rj3gZwqpXox6zM1+czt6MEWEkcloNPK6\nP68I1wQCZHmSJBErzPqox0vA0YRxtOFwaJrmYDAwTXMuGQIoNKiqqmma4zihUAi2h3MT+RHnzL5j\nsRgSFZQbEPzN3zOdD1zGyp9r7KHruizLqqrSNL2wsOAaEswHfD4fx3H5fN7v9weDQcuyut2uoigM\nwyQSiXk6eqYfUHmFbK/P54POLeyY56DnS5xVdPx+fzgchkx6q9Vqt9tQOBuNRvNRUH/XQHm4UqnI\nsgwNcJ7nJUmaD26AC4qiOI6DKjh8wDAFb5rm/AUKjuMMh8NKpdJqtdD2Bdtv/k7gQCCwsLBg2zbI\nVOj/YvyfmGWu6rxifg6UVwfKMJZljcdjHD2Qop05f61vBiox4XDYVa5BpxsDBx4uGEg5RqMRVJHn\nbLMB+ETQ9oO19GAw8LL/Vwc2CRqgbjUFgcKkl/Y24U6kuaQ3nMbz2iWEvcdwOCQIIhAIzFOJwYUr\nMYvRftywtm17Vf+pxWUM/giCQOWv3+8TBOH3++PxeC6XS6VS8/RaQn2X4zhMCwYCAV3XS6VStVqd\ny/bKNMO2bUh49Pt9n88niqIoirMr2PuVcCeN0KmkKAqVThQA5vVef7tAeRiSnCBRhUKh+RuDgDBQ\nIpGAqKrf78d082AwmMtNAspHv98PBoOxWGzO6rguYPURj8dDoRBymH6/D2nDSS/Nw1dgfmKdV4fr\ntDgajRzHge48IqR5OmFdEq7LLRsOh7quQ+p50qu7RECl2bZtZP8gPEUikXl1PYfog8/nGwwGFEXB\n4XcuL/W3DlcJHM0y6N7NWeRHnFkC0jQN5YGXDuRJr+4twxWXgLwzovn5C/5wlEUiETSazvfWUPif\nsz08B7ikwd9oNEJSgk3pChTN2TuJ+A8dlmAwCPklT3j9IuFOe4zH49FohNHXQCAwHyoPXwZEH1DO\nwdFvWRYaQJNe2mwAs2gg/LmTAfN3LrmHkt/vx9sx3+VhvAKBQCASiczNgP9LQOfXzVXcpHden+ms\nY67OlFcEGLjdbrfX66Hy5wZ/c/ZOusEfmH9oKum67r2QFwmM++F6Gw6Htm3PZTkHcFOpQCCAOGaO\nuVxvHaiBjcdjlxiK8GhuRsIBBH/BYND9dOPx2DTN0Wg06aW9EyAMQtY338Ef4j83+PPIvtOMyxj8\nEQTh1uFR+XO37Py9k/hQiDYIgkAZZtKLulxwM2DXXuX8ETl/IM8w6YXMJNz70s0Q5vLLfOkV8AKF\n+QAe6Pxt17nEZQz+QKzRdV3XdbcmMZfnjvsqIsnGEJbXgLtgINMApQn5hhuLzzHmOKF6p3Bb5Gj7\nuvHfpNf19nH+yJ3XGBdw34U5pjYS57JcgiB8Pp/3+k85Lmnw53IR3Jdw/vaoG/l9uRQ/6aV5mHPM\n39t0kXjpDZ3LasplK/UhGEIeOMe9F/diJf8Rk16Xh6/AZRz4IM5SscuTnbhH7dx/0ikEZiBA4UIt\nxx2Cm/TS3gnA30cBwH3RvI33ioBLCkEQUAZBtXjOzJGdLwGKhnM21wKQZ9a3fr8fXPN+vz9/7ReU\nVFxjD4IgQDefJ9OsOcMcvmzfCnco6cstlfm7j/GJ3AkP7z28eOBigwAKNFBA6p+/zUacG1mwbfvy\nJFdvC+6EFkEQpmn2+30UiuYyVjj/uXAgz2XwR5xNQUFvAQabc/nu27YNbT9MLLkS5d7rP52Yz5ft\nm3FeaIAkSbcLPGcnrHu+uJJLxBmLfKLrulxw2+6QbUNRx9V8mfTq3j6go4TsHxOduNTn9V5/uyDP\n/JHdDAETWnO2VbBJ4OrrsmDnOFCgKAoCeLZt9/t90zRfIh3NB2zbdu283Yx3Xgu6c4DL+FRIkoxE\nIoIgwIIaShxor0x6aW8ZblwLUUOSJKH54rXhLhIkSSLsw5dPEIRhGN1ud/4udeLsAlBV1TTNSCTC\nsqyrMe5tuW8FjqZoNBoMBlH5w3zAnG0VnEiqqmqahs8YDoej0ej8iW0RZ6+/JEmiKFqWpWkaZPbn\nr9YwHA7L5XKxWOz1euFwGCLerrnopBfo4WVcxuCPOKNhoQxDnAmrztkJS5xTGMZZg7Ff91N7uEig\nqAM/AzBj5uz0B9xUCpK28KjwIr9XBHnmjAzpY+sM8yfM6Qr74aOhUDSvUQJMpJD4weB7Lu8axPRg\nNLoF7Ll8oPOByxj8IfJDXkIQxGg00nVdlmVVVedsDsuyLNM0B4NBr9fr9/uhUAh+ml7n94IBLlc0\nGo1Go+PxuFKpVCoVMLrmJgREpmFZlmEYmqZZliUIgiRJNE2j+TvpBc4AKIoSBCGVSsViMVeLvtvt\nmqY5T7EC1OZrtVqz2YTsOeriwWBw0kt7+/D5fOFwOJfLLS4u+nw+VVUVRUHtf26Iv3jxTdOs1+v1\net1xHDTWPMrvNOMyBn8EQZzn/CFf0XW91+vNzU1MnKViINYMh8PxeBwIBDiOY1l2XjPs6YRL+wuH\nw5FIxHEcXACun9V8XADEGbt0MBjAQpBhmGg0iuKfdwe8CkiSpGk6FosxDIOjCZnbnFlfOI7T6/VU\nVe12u5hidr3s5m+ToJorCALP8zC87vV6GPuYm+sGwd9oNNI0TdM0kiSj0SgumkkvzcPX4jIGfyjD\nuO5JFEUZhtFsNjudzjxV/lA5MAzDMAyMF4TD4VgsxnGcx8C9eFAUxfO8JEl+v1/TNEVRer2eS3if\n9Oq+K5wz93rTNBHajkajWCwmCALUxefvUn8X8Pl8LMsKgsBxHLpmiqK0Wi3DMOYjUHCJKN1uV1GU\nfr8PYij6MPNqeI3gTxAEiqJwJrfb7Xa7PR9TXxjf6ff7eKaGYYTD4XQ6nUgkvOBvmnFJdf7gsQh0\nu11VVcvlMsuyqMTMxwHkOM5gMJBlGacMQRAMwyQSCZxB8/EZZwgURSWTSU3TyuWyoigURWma1u12\nw+HwfLAwLcvq9XqGYciy3Gq1YrGYJEnJZNIbMHp1IEMYj8eiKNI03e/36/V6NBqVJCmXy016dW8H\nYIVqmtZsNg3D4HmeZVkUO+fS9BZ1zWQyaVkW5nhUVa1UKrZtJxKJSCQy66k4SMyapnU6HVmWNU1b\nW1tbWVnJZrPzGs3PB2Z7270xXEkF6O5alnVee3M+sjH0fFH5g+haMBjE5/VeyIsHBjlZlg0Gg2iR\nIFeeD68nV+IVc+WmaZIkybKsxzF4LeBcciXBA4EAGCk4mmadIeAaabpMG9M0aZrGSzGvg0Eu5cNt\nNFmWBXNRvPsz/UyJM/tKkFNBZQkGg9FoFNSFSa/Ow9fiMlb+QMIIh8Mcx+VyuUAgMBwOS6WSIAiD\nwWA+ug9Ir1ut1rNnz2q1GkgYoihKkgQe7qQXeLmALZfL5SiKevHiBUVRg8Hg4OAAVHeapme9P4Iy\nc7lcrlarjUbDMIylpaXNzc1MJuPdAa8Fv98fDodFUVxeXu50OtVqdTAYZDIZGH5A/3l2gX2iaVqh\nUHj27Nl4PF5aWorH4/F4nGGYuRz4gMJzMpkkSTKXyxWLRYqinj9/Lsvy5uYmTuOZfv1t25Zl+fnz\n56VSCYUGURTz+Xwmk5mDm3SOMdtHyZsB3HOKooLBIMdx3W5XPwOG8KHHMdO7Fgzcfr/fbrc7nQ4G\nXCKRCO6Pmf5oMwqfz0fTdDQaxfQrSZKKosiyjDGjOdhvo9Go0+l0Oh1wDEKhEM/zsVjMuwBeHTia\nEP/xPA9ZOIIgQNsdj8eIEmb3+3TLwyCGBgIBEEMjkcgc+4BBYJWmaY7jYrGYbdvtdpskScz7zzQp\nFjNe3W4X/CKCIJDNepW/6cdlDP6Is/ZKJBLJ5XI+n+/58+etVqvRaHQ6nUAgwPM8rudJL/NNgCYC\nuoqyLBcKhU6nE4vFwMGaj7rmLAJaX+BvJRKJwWBQKpWGw2E2m0VFEMy/WXw06Puoqrq3t1ev1y3L\nkiQplUqlUqlEIjG7r9JE4PP5MB+wurrKsuznn3+u6zpUUUiSjMfjs1v8wwhavV5HeVhRlHg8ns/n\n0+l0NBqd3QDoW4HCfyQSWVxcXFlZaTQap6enmqbVa3VJkkCQmLniHy4aGNbV63XcoYjjM5mMKIrR\naHTmPtSlwiVt/7k8jMXFRcgvdTqdVqvVbrcxqDjpBX4ngO3X7Xbb7Xa5XK7X64IgLC4uiqLo6inM\n6zk7tUD3h2EYV8itUqkcHR01Go2ZFnJDjXkwGCiK8uLFi6OjI4Ig4vF4KpWKx+OCIHjJxmsBcscc\nx+Xz+aWlpfF4rChKs9lsNBrtdhuz4bO4VbDs4XBYrVbL5XKr1er3+36/f2lpaXl5mWXZeeWinK/m\nZjKZlZUVjuOazWa5XK7Vaq1mq2t0Z5TQiVEPwzDq9frBwUG5XJYkaWlpKZ1O8zxP0/QcB/RzgFlN\nIr878EKKogjSMUEQg8Gg2Wz6fD5RFGE0NKMb13EcTN1DScs0TZ7nE4kEUrEZ/VAzDXznKOpwHJdO\np30+X7FYtCwL+QYKA7OYKLtaxJjfVBQlHA4LgoCXyFP5fwMgL5UkaTQaRSIRvMXVapWiqGw26/rE\nzNC3ishmPB4PBoNqtVqtVuH+F41GIYA33+VhfDQoeKfT6UajAe/mVqtVqVZohhZEAf7Xs/JYEadi\ncgVkD13Xh8NhPB5Pp9Mge8xrND83oH79619Peg0Tg8/nAxOuWCzW63W8frqup1Ipd0pxJl5FF27P\n9+Dg4ODg4MmTJ48ePbJt+1//9V+vXr2az+ehMzfpZV5SYJ7RcRyUAT7//PNWq8XzfDQaJQgiHo/P\nFqPLvQBkWS6Xy/v7+//1X//Vbrd3dnZu37595cqV1dXVuXRrvQD4/X6apmmafv78OdSAIQy0sbEx\no4Ox4/G42+3WarX//M//3N3d7ff7oiheuXLl5z//eTqdZhhm7vNSzPvHYjGcz47jjK1xp9OBKt7M\naaFDgXx3d3dvb+/x48e7u7sURf3yl7+8du3a6uqqKIreRTPluLyxOTq/kUgEWgM4fRRFabfb4OHO\nqOCzbdvj8dgwDFVV+/0+FF6i0SjHcd5NPHGgqAMKJkh+/X6/0+lomjaLas/o+cKtAR+BIAiGYSDe\n5qX+bwyKouAHw3FcNBp1XWH6/b5pmjPnDOuW/Xq9nqIouq5D0RCH0iWpEqHWQNM0wzAcx9E0DWaO\npmmDwWC2BJ8x4DUcDlVV7XQ6g8EAM4U42byLZiZw2St/FEVRFAVXX9u2j46OZFkGByUQCIRCoRk6\nldwJX0VRPvroo4cPH7ZaLdhK/tu//dvKyoogCJ7I38SBez0YDJ6cnKB/p6rqeDzO5/Pge81EUQeN\nPNM0dV3/4osvPv/88+Pj406nw/P8P/3TP926dWthYWG+WfzvFJAj8Pl8mqaFw2FN005OTgaDwerq\nqm3bEI2blaMJqpbNZvPw8PDo6OiPf/xju91eWVm5devW9vb25uYmCA+XYZ/gxsGQBMuyJycnjUYj\nHA4LgmhZFsdFp7/45774nU6n0Wj8z//8z6NHjzRNEwRhZWXlpz/96eLiYiwWm+8+/nzg8hZmsTXB\nwc9kMvl83jTNR48eqapar9dlWQYlBSfs9O9jl1XjGpYUi0WSJDOZTDKZhLFHJBKZ/g8y34DgSyKR\nGI/HuVyOJMlOp1MsFsPhsKIoEPid/uava9IFqd5KpXJ4eKiqKsdxPM+n02lMtMwihXEagKZEMBik\naXppaclxnHK5rKoqRVHVatXn8wmCEI1G8WOTXuw3wSUGDIdDRVHK5TKmXIfDIWKFxcXFUCh0SfaJ\nO/YhiuLq6ipN0w8ePGi329Vq7fS07DjOwkIGU/9T/u5jwKvdbjcajZOTk2KxyHHcysrKwsICdGS9\nEsNM4PIGf8S5OaxEIrG8vKzrejgcdhynXq8fHx/7/X6e5x3HmX4NDtzE0Fsql8vNZrPZbOq6LknS\nysoKlBQQVUzzp7gMcH2lo9Ho6upqMBh89uxZvV5vNpsnJye9Xg+VP7/fP7UPC5EfbvRqtYq5xXq9\n7jgOSKXxeNzVMpz0YmcVOJoCgUAqlbIsCyR6iqIKhQLYchCMDIfDxLQeTYj8YOMLV8O9vb1ms4kh\nj2w2u7CwAOWaKa91vUXg9WdZNpvNhkKhdDo9Ho/7/d7+/j500S3LYlkWwdMUfieY7sJk5O7ubqvV\nUlWVIAhBEDY2NtLptGvWMoWL9/ASLnXbF8AhyzDMaDR68eIF/qWu68FgMJVKIQWf/vrfeDzu9/vN\nZvPu3buHh4ePHz/udDrLy8s/+9nPNjY2crncDPWJ5hso2IBvwLLs6enpycnJcDhEdw8FWsR/7s9P\ndsHn4dZy0PB98ODBixcvHj16dHx8HA6Hf/azn21ubm5tbcXjcRQwpmrxMwe3/oeZSpIkIfgiiiJi\nQfelns7v2bKs8Xhcq9VOT0/v37//pz/9qVqt5nK51dXV733vezs7O/F4PBQKEdO6/ncEv9/Psmw0\nGoV2o2EYJycnOK4JggiFQlMo+3x+vLfdbh8cHPzud7/b29tTFCUUCu3s7PzzP//z2tpaKpWaLa7U\nZcalrvwBrgBbNBqNxWIEQYA2B2Iyxu6m7VV8CS6f2jAMWZY7nQ4MFkG95zjOS8WmDRRFcRzX7/eR\nKzuO0+l0wPFC/c/t/04bUGMeDAbwj2m326ZpUhQViUREURQEARGJt9++O1w5AlTLHMeRZdnn86mq\nqqpqKBTiOI4giOncJ255WFVV6Bl1u12CIHiej8fjHMddTsF5t/nLMIwkSfhacNe02208U5qmp7Cn\njxcf7iyQd9E0ze/3MwwTi8U4jvOMvGcLXuWPIAjC7/e7E2eiKB4dHRWLRdM0ofwiCIKrrTBtOxsn\nrGma1Wr16Ojo6dOnv/nNbwqFQiKR2Nraev/99z/44INUKoVi0rQt/jKDoijM/YFX4Pf7d3d3T09P\nQ6EQZmZZlnUvgOl5cOPxeDgctlqtw8PDw8PD3/zmN3t7e6FQaGtr69atWz/96U9zuZwgCJ6F4NsC\nSGCQThQE4ejoqNfrocZvGIYoilAOmqq3200PZFmu1+u//e1v//rXvxaLRdu2U6nUr371q5s3b66u\nrvI8fwmDP+JMxxtxXiaTsW272WyCRFEoFBAaEgTh0o0m+xW5bHIE8Q8ePPjss8+++OKL58+fm6Z5\n586dO3fu3Lx5c319neM4r94/Q/Aqf3+nV0ej0cXFRWioYpqpWq0SZy1gxH/ENN3EeC1Ho5Fpmoqi\n1Gq1er3e6XRGo9H6+vri4mIqlQI3yHshpwp4FpFIxHGcVCqVy+VGo9GzZ88Gg0G9Xo/FYizLptNp\n4mw8kJj0rkPTxy0wYyiqXq+3Wi1N0xKJBJxyRFHEmLy32b47zguD8zy/uLhoWRbDMJZlKYqCySFF\nUQiCAL3SPaAmDqhNQcOo1WpVKpVarTYajWBvk8lkwEK+nFUikiQdx4GzfDKZpCgK01GqqsLsp1ar\nZTIZiALiVZrsvYO3fjgcapqmKIpr0IKsNZlMZrPZeDwO43jvopkheJU/gjh7r3CAMgwjyzL+vaIo\nmqYlk0nbtl0a1pSEgLZtw1O10+nIsvzo0aOHDx9WKpXRaCQIAig1y8vLyWTSu4ynEDjT8VwgddZq\ntYLBIDJs27ZZlh0Oh272P8HSjptjDIdDWZYbjcbz588/++wzTKhwHHf9+vXbt2/n8/mFhYUppCvN\nNMgzQARY13WaZnRdl+XWaDQCT9Tts7v934l8/+4kEHQfT09PHz58eHx8vLe3p+t6IpHY2dnZ2Ni4\nefOmKIqRSOTSlofd6wZ3CgQ+aZpuNpuweex2u9CCGY/HrvjLxcdVbgVX13VZlp88eXJ0dPTs2TMU\ncbPZ7PLy8ocffri2thaPxy+DTPecwav8/Q0+n49hmOXlZUEQrl+/Hg6HYZJRq9W2trZ6vR5BEH6/\nH5JUk/XhccfoMHgF0/enT58+ePCAIIhcLieK4rVr17a3t10lYQ/TCb/fDz28SCRSKBRardbx8XGl\nUhmPx6IoxuPxYDAIDhDsZy5+y7lNn36/PxgMKpVKtVp99uzZ3bt3h8PhysoKLvUbN25A4sGL/N46\n+XHomQAAIABJREFUUORDR+LWrdv1el2WW6VScTgcsiyLaqvjOOi2u6cTcYEhoFsYxoSHqqrNZvPo\n6OjevXuKooDMurCwcOfOnWQyiWHwSxv5AYjkcJusrKw4jnN6enp8fKwoCvy+G40GGv2oNQSDQfck\nf9ffm6s1PR6PR6ORruutVqvVat2/f7/VahWLRUVR0un0rVu3JEna2tpCyjedxFMP3wAv+PsbyHPa\nWplMxjRNqOURBFGtVm3bhrBCNBrFCYsq4AWfX27YZ9u2aZrdbtcwjGKx6Jq+0zSdzWYlSZIkyZUM\nuMgVengtYMuhHba0tETTdKvVglVusVg0DCMWiw2HQ1EU0f91r8wLuwBwnYNX0Ov1yuUymj6WZfn9\n/lQqBcEOlmW9cfJ3BzR/I5FIMpkkSTKZTDabTYIgsFtwTOGJYFbUrRJdwOvvFvzg92WaJsZ7T09P\nZVnu9XrRaJRhmHQ6nUwmRVGEsJ93LhFn5D+WZROJhGVZCwsL4XBY13WMUp2cnKiqGgwG0e4Hb/ud\nhoDng3ioeELVBfJhjUZD0zSfzyeKYiqVymazkBwKBoOek9sswmv7/gNAxRBFEe/haDQKBoO7u7sH\nBwf9fh+zTpFIxLIs14rx4heJQUtZlguFwuHh4X/8x3/cv39fUZRoNLq+vv6rX/1qZ2cnl8shTiWm\noEPt4RuA6T+kHLlcDn0fRVEeP358cHBAEISqqiD1u3+9mAaQaxijaVqj0Xj69OnBwcHvf//7zz//\nvNPpJBKJpaWlX/ziFzdv3szn8yDvu5/oXa/tEgKdX4zKQifS7/ejNYHreTAYQK/K3SQXVoUdjUa9\nXq/b7VYqlXK5/Kc//emjjz7a3d2VZZkkyQ8//PDOnTu3bt3a2tqSJGlqRewmAmhNcBwniiLP89ls\nFsU2RVH29vYODw8pijJNczgcEgQxGo1cBvC7SLQQxw+HQ13XDcNAEH/v3r0//OEPT548KRaLg8Fg\nc3MTD/TDDz9cXl7mOO6SF3FnF17A/neAikuSJE3TlmWh7wZ5fZDcm81mIBDQNM2yLHS4APc/f6fL\nO59ewyIT1XhkiizLxmIxnudxiLhiS95rOeXAAwoEArBwhUiyYRhg23Q6nVAoBF0327bdJNu93d/6\nepwzjMdj1zAGzP1Op2MYxnA4xF0Vj8cFQYCVp7fZLgBQfrFtWxCEZDKp63ooFHJPg3a7LcuyZVkw\nf3P/k3dxQLmFYbcL0ev1er2eLMvtdhsiIJCuZFkWWxr7ZPoF8y8Y5Jnqu23boigSBCGKIsYpNE0j\nSbLdbkNCBaXfYDD4txawQxAk8VYeLjwCXKcAkPxM08TThPtwt9vFAkRRTCaT6CyFw2Gv2zu7IGfI\nTPoCcJ5O12g0CoVCs9n83//9306nMxwOKYqKx+O3b9+OxWIbGxsYcUIX450OOlmWhe5br9czTbNU\nKsmyfHR0tLu7axhGv98PBAJra2tra2sLCwu3b9+madrrrcwQzk9tHx8f1+v1Fy9ePHz4sNfrYeZj\naWlpaWkJDJtIJIJ7FNfAW1QgwgWAZYzHY2ytYrF4enraaDR2d3eHw6HP5wuHw0tLS9evX+d5fnt7\nG+wCb6joAuA2WHErl8vle/fuwfa33+/zPJ/JZEBZjsVikiRxHBcKhTDs/7aMNFyx39Fo5HYGW61W\nrVZrt9uweVUUxTRNnuc3Nzd5nn/vvfdSqRTHcRAcfRvfxLwBuRaYFScnJ2iaP378GAE0HOHS6TTH\ncVevXkUbHbPAyLvcQ+DVs0Hbtolz1lCDwQBlfsxoFwoFwzAODw+R7/X7/XA4vLGxwfP8lStXlpeX\nY7GYKIrT70Ts4RvgVf7+Aa68QjAYBN1ekqRSqVStVg8PD6vVqqZpUE6madq27Wg0CnEjULLeFtXG\njcjdsGA0Gg0GA5wOWM/BwcHz589t287n86IobmxsXLlyRRRF1OE93v0MwS3+URS1tLQE5n6328WE\n3WAwwLxFIpGgaRozgJgRQdmAoiiSIAny5V33rRvApfjgH5FjQCrcNM1Wq2UYxtHRESZRYBW9ubm5\nuLi4sbFx7dq1aDSKbq+32S4G7shnPB6HhNNoNIJ+MnggmqZxHMcwjCiKw+FwOBwyDOOqBZ3PBr/8\nN1+H82cRcRYuYEOORiNoFFcqlZOTk1ar9fTp036/zzAMx3HpdPratWuCICBWcIVUPXwZiM5h2Qze\nEcdxME+DgJcsy4qi8DzPsizP8zzPR6NRmJGiKIgQ8BXHEPEQiTNGLxrNEHPRdb3RaOzv7+u6fnBw\nAMtTnuclSdrZ2ZEkKZ/PJ5PJmbAg9/DN8Dh/XwH3kMW5ORwOI5EIIjCKolCBcxyn1+sNBgOQJCiK\ncvtlxOucrS/h/AlrWdbQHA7NoWEYmqa1Wq2jo6NKpXJwcFCtVmHjEY1Gr127try8jLIfjn7vMp45\nuFkHeSbYQZIkwzC9Xg8S0JDawuAFinOow41GI8d2ELehB/cqfxyKfDj6cfoPh0PQtmRZrlQq9Xr9\n4OCgXC6fnp622+3hcIg7aWdnZ3V1dWlpaXFxkWEYb7z34uGeS/jaaZo2TTMUCvn9/tFohKND07R+\nvw/FEJxgbtCGrfLlk+rLwM9gU6HUh9EfV/uj0+kcHR2VSiUUq9rtdrfbDYVCuVxuZWVlZWVlc3NT\nFEVRFNEf9PbJNwCPFW8TsnfLsjiOs20baSFeUhQIDcPAwyUIYjAYjM6Ax+R2ir4M/BLIRAwGA4wM\nKopSLBbr9frJyQkq/dVqVdd1x3EikUgmk1lZWcnlctvb2/F4XJIkhmEulSPzvMJr+34t3AgM7NdH\njx49e/asWq3u7u6ORqNoNBqNRrPZ7NWrV2Ox2OrqKsuy6LdCEcaNIF/3D3VFNS3LAsUK52y1Wr1/\n/76u67VazTRNQRByuVwikfj5z3+eTCZRjHTHkD3MKBCWIRTTdf3+/fuNRgOWM7jOA4HAxsYGlHJX\nV1cjkQgonv4zoBOE++Mr/whsMIhE4kbHpaLrOqo4kJzY29vr9Xro8wqCgBbenTt3Xgr7vAtgIsDp\nhLv85OREluWDg4OnT59CYM+yrFgsJghCKpW+ffs2y7KpVJJhGNDFQDJDf+Mb+vWIERE0wEYInUEQ\noMvlsmEYDx8+bLVa3W4X6UE2m+V5/vbt2+vr66IoJhKJ8+ZJHl4FyOJM04TT47Nnz2q1WqlUOj4+\nRnpGEqQkSVJcikvxra2tCP03Hkg4HMYV4H7hX36yCApt2walBGRNVVW/+OILwzAqlYqiKLZtg8i0\nsbGRSCSWl5dXV1dRyg0EAtg/k/hiPLxleIHCNwHXG8uyPp9PkqREIoEqIEmSo9HIMAxVVVutFnSV\ncUrSNO3agZyvIOIXfvlt/HLrDWc68jlVVQeDAajcaOt0u13btuGoiCUJggCjzGAweJFfjod3AWwY\nUEix62zbBokeFR3btnVdx+NG789xnFAoBI0PZOQ+nw+y5F+530AkwHU+HA4xqjkej8HvQaahqiqu\nB5Zl0cWLx+Nuvwlcw4l8Px5cYP6Doiie5zEqJEkSSZL1eh0PFz27VqtlmqbfT6FACG258Xjs9/tR\n1fu62i1iPpSLsEmQCSNcaLfb6Eh0u11oEYfDYUmSBEGQJAkiIJ76zxvArf85jgPeEeauWq0WQRCG\nYYytca/fC+pBv9/f7rQjgwjkviORCFy2vzIxc8maeKyYyIFwBGiaKCXiN4BTiKEuPE2GYcLhsFdZ\nmCd4lb9vwnldPU3TVFWVZXl3d1fTtKOjo3a7jRDN7/dDWiWVSiWTyWg0iiQJl/H53Pd8OfB8hxcl\nRkzyjkYjWH2DcWXoRrVWVRQFOl6BQGBxcVGSpFwut76+jj/rfLg52W/Mw1uBS+1XVRVGrs1ms9Vq\nPXnypNfraZo2GAzQHgoEAosLiwz7t//RNJ1KpSBX+ZLZxnkRr8FgMBwO2+02gjxVVU3TrFQquq6j\nMEBRVCwWo2kaHR9BELLZbCgU4nk+HA57Bb8pAZ4pnqau64jaUf+rVCrtdns0GhEEgQCRpmmO4wRB\nCIVC8Xg8HA7DSPArfeFQfsZZBMo//CeazSZ6yoZhYPw8GAxmMhnU/DY3N8E4ZFkWm5PwaGGvDzdQ\nQ6YHtje++adPn7qxGrSfCIKwbRssEUEQgsEgnil5Jl7h/lr0/THOJcsyyMT2GUiSpGmapul4PL62\ntsay7NLSUiwWYxjGLSh6L/48wQvkvwl4f5CK4S5kGAbE2H6/TxBEs9lst9tg3UJkazQacRxHEEQw\nGMRIpjuT5VYBzwd/ePGQXluWhQYKdJ50XS+VSoZuNFtNwzBCoVA6nWYYJpvNptPpbDaby+UikYgn\ntDF/wKP0+/0usxujRaqqIj6DwEe/3/f5fCRB0gzNnAEFAwR/L6X++Ec3+IN6S7/fR4G5Wq2CYoiu\nLrgE+Xw+n8+j8gd5c+8CmB7gQaDoGwqFYPgBhSCcKshXMZYbDodVVTUMIxwOo4PR7/ej0eh5ORj3\n10LxAGQAHHfNZhODvbqugy2A/RmLxRYXF9fW1gRByOfzOPS8ffJdQJ75/yJqtyyLZdloNAoCUqfT\nQeMVdTtw0GFDAOUHtKpQ5CPO/Ejd6waMQFmWTdMkztzDo9FoKBRCkS+dTq+vr0OXG2Hf+crFJL8X\nD28VXuXvNYDKHA7Bcrksy3KtVisUCrhKcelCywq25aAARiIRTODiQHTHsizLIs6Cv+FwaBgG+rxo\nxpmmORqNoCkIBgaYhQzD5HI5nufRXnF/7aS/Gw/vCiAAgfBXKpV6vR7I9SgG4A7GbUEQBPaJm/ej\n/Yc6IkmSqEZj+9m23e12+/0+WIZgd5EkyfN8MplkGGZpaYll2VQqBWFelmW903+agWhvOBzWarVu\nt1ur1RDcF4tFcPxx4OAIgsEalKqIM3offgY2Idg/juNgMgAJA0IH0AwQLmCSN5lMIlBAhuC1IN4u\nwNOAe0q5XO52u6jZ9/t9RVGQxSEPRCEQNQhwRXB94N3HxSRJkjsDFIlE0M9NJBKg9nIcF4vFUqkU\npKc9Cac5hhf8vR5wwjqOA0mkWq12eHioqiqm4kGZRxmPIAiU5ViWjcfjriKGy+fAMUqcxZSdTmc0\nGiEhQ40dOVwkEkGpL5lMbm9vQ+wDubUnrX5J4EqwouKCo7/ZbBYKhV6v12q10AtGJw6EPwR2aOni\n1vf5fCzLchwHQzk3m8cpj7wftO7l5WWGYdA+dp1sPJb39MMN4jGZ0ev1MJDb6/Uwv6lpGs6Z4XCI\nTh9BEPhhjJEOh0OapgVBwPnj8/kIhyAIwkf5oOYIORJRFHO5HMMw+XwelWnwzLwT6R3B1WHGw0VE\nDhe4fr9fLpcVRcG/NE0TkmQHBweFQgHJIUVRiPNyudyNGzdA6cP8PrwZFxYWQqEQSv7uzeKVFeYb\nXtv39YAROeLMbROcGEhyaJpG0zT4WJqmIbBDLo6pyfNVFrzMJEmCRetOXILIFQ6H8R5CRxqjnTBU\nCIVCnm7CZQMCNRzKqL7gdB4Oh/1+PxgMdrtd7D1kJugLg6SvqioUQLBnEPaxLAsFGdwKLg8sGo0m\nk0nsOhiIedtshuBOC4GsgugN3hskSeq6joHf0WgEs0qwysDtw1QBfjKZTGJ6FDuE8lF+v59m6EAg\ngAxBEIR0Oo2dA7VhbxTgncLNvuDdFwgEcBH4fD7UZRmGgXQL6JjD4ZAkSUSKMAXGseDz+VDbw4Cw\nIAiiKCLcd9tW3it/SeC9sW8IdDdSqRTmfK9fvw6uHlhZpVIJNXkcsjhYnz592ul0MFEFPbZQKLS1\ntbWwsEDTtCiKbiMmkUhkMplIJJJIJNBxQ6Lmce09+Hw+SPyLori0tORys0DMR8fHMIy7d+++ePGi\nXC43Gg1c7ZgOXl9fT6VS3/ve91xnDrTw8Dcg6aM17F3nMw1Mm4XDYWjFgVKMyAC5AYSae72eYRjl\nchkuXoZhxOPxH//4x4IguKkmokAEeaCyYJMg0PSavBcPRNuRSIRlWdu2s9msKxOh6/pHH32EWqCq\nqhRFra2tkSTZaDQsy0qlUteuXUskEtlsFpkALjJvmOMSwjvf3xyoAiIVC4VC4/E4EonghcQUfSAQ\nwAAHpkPgnQAFDdRvIpEIyvLw7HLFO+LxeCqVomlakiQ4Kr7ko+C9pZcTeO5ggoObRZw5c2AaCUUd\nd8YIxFOfz2eaJhp5+K9gFox9hS4wmAZuRfn8Xz3MHM5PqkF/niAIzATAuNwN/qD0gYkBxHMgAMTj\ncYgzo6WLOBJ14vNWlt4OuXi4Y7xg8hEEgWYUyMFoKKE6CD5fJpMhCAKBPjghjuNAFPDLRh3eA708\n8IK/N4T7kqAlh2wYYRzP8xzH4WwFVV9RlE6nAyteV4u/0+nQNL24uLi1tQWiFab2kF4zDIOwDze9\nl157cPHSvetKOgeDQdM0IcbbbrdrtZpt29vb2wRBgA4YiUTa7TZN00g23NQfeb+3x+YJX77OXfcI\nx3EYhnEHRDRNG41GOHaCwSDHcdlsNpVK8TwfDAYD/gDlp1w+nzfPMQ348sPFUAhYnk+fPi2VSpZl\nQaX5hz/8IYgihUJB07S//vWv0O2DI9RXCv14uAzwgr/vipeS7FAo5DgOZFcx1QFPDszqo6vLcRzE\nliCkmUqllpeXd3Z2XF8QV3zBZdl7p62Hr4NbA4C+g2ma3W630+l0Op1oNLq6uhoMBiHmAloCwzAE\nQaA6CJ6+d/pfBoA3hmftCsKPx+NAIIBRD7R30XCQJInn+b+FegRJEMTf/uI1B6cSoH9A2efw8LBS\nqSwsLCwvLy8tLd24cWM8HpfLZQj9PH36NBaL3bhxg6Zpt31PeFfM5YMX/L0FfF3N3DXT7HQ67XYb\nHd5EIrG0tIRZLZIk+/1+q9USBAFZteeZ6OEN4I55drvdk5OTRqOhaRpJkhzHwQKu0+noul4oFCD/\nIcsyIj+Iekx6+R4uCF95trxkR4QYEaMe3sTPTADjg4Zh1Ov1Wq2GoUOoNOdyOVEULcvK5XK6rpfL\n5WKxOB6PS6US0kX08cEN8J71pYIX/L0TuBLt/X7/9PT0008/bTabqqoGg8Gtra1/+qd/6vV6kPGr\nVCqYArl69SpJklDGn/TyPcwYINKm63q1Wv3jH//YarVkWWZZNp/P/7//9/84jut0Os1m0zCMBw8e\nDAYDmECgzONpuHgAbdSV/UIuMdkleXh1gO1Xr9cfPXpUrVZVVXUcJ5vNvvfee+l0GhaRt2/fliTp\n/v37h4eHhmF8/vnnlUrFNE20pBiG8SK/ywYvzniHAKWm2+3Kstxut12tZjCpRVEkCAKmPXDZAhnL\nk3Hx8AaA6pCmadB/JkkSpiAAJgEx2OE4jqqqLMtiFB1mbpNevodpgXMOk16Lh1cCWkwQf1YUBfU8\nhmEQ1aGyC/cXnufB+jAMw3V3DAaDuHcm/Tk8XCi84O9dYTwedzqdWq22t7d39+7dXq937dq1TCZz\n48aNfD4PPY5Go/GHP/zh6Ojo6Ojo0aNHyWTyxo0boih6YkseXh3g+Z2enr548eLw8PD58+ej0ei9\n9967cuXK1tZWMpmkz7CxsXH16lVd1x8+fHhyciKKYjKZJAjCJZtO+qN48ODhNeA2fGVZPjo6unfv\nnqZpy8vLkiRhjhDmUo7jJBIJiEtomibL8pMnTxqNRigUomk6nU7v7OxA5M+j/14eeMHf24fb89U0\nrdVqNRqNVqs1Ho/j8fjy8nI6nY7FYrZtLy0tQWUDQyHlcnk0Gq2trWECy8vDPHwr3J2G4fFyuVyt\nVg3D8Pl8kiTl83lISEK137KseDyeyWQoijo5Oel2u61WC+Pn0I+c9Kfx4MHDa8NxnG63qyhKq9Wq\n1+uDwWBzczObzcbjcbz7yOsg9ZxKpdbW1qLR6OPHjzVNq9frpVLJcZzV1VUMLHpJ4OWBF/y9ZbjU\n+16vVygU9vb2qtUqhJrz+fzq6ip0mx3HSaVSFEUtLS01m02SJPf392VZ3t7eZlmWIAjotE3603iY\ndsDJTVXVYrH4/PlzWZZTqRTDMCsrK8vLy4lEwnVqCofDqVRqY2MjEons7+8Ph8NqtVoqlWzbhmGg\nx/j24GGGgLsGL3KhUKjX65DsyefzKysryWQSEtz4YSg58zy/trYWi8WWlpb8fn+32/3iiy86nc7a\n2pooim6M6J0DlwFe8Pf2Yds2pFOfP3/+4MEDRVGgqbuxsbGxsQHfTIIgUqlUOBze3Nw0DKNSqezu\n7jIMc+fOHY7joNnmTeB7+Aa4WkKdTqder+/v7z9+/NhxnK2trUQisbW1tby8DIs2giAgQpTJZK5f\nv07T9O9+9zvDMEql0v7+vm3bi4uLEPWY9Gfy4MHDK8F9/QeDwfHx8bNnz05PTzEyuL29DSOfl2YH\nKYqKxWLr6+uJRALKYsfHxw8fPqzVardu3RoMBsFg8LyCt4f5hhf8vU2cV9zQdR1zHpZliaIoiiLH\ncZBRxasFoTXwrjCc7zhOu92WZZmmaYSA3kvo4SvhHv1o+MqyrKqqaZrBYDCZTKZSKXh3npfqAA08\nFovxPM+yrGVZvV6v2WyKojgcDqEuTnjJhgcPMwIIOw8GA1mWW63WYDBgGCYWi3EcF41Gv6ziBDUx\n8PySyWS324XnW7/fbzQaJElC/Nmzb7kk8IK/twwwap8+fVqr1Z48eXJwcLCysvKjH/0onU4vLi7C\nRBU/SZJkOBxGnzccDj958qTf7z948KDT6bz33nuxWIxlWfeHPXh4CYjeVFX9y1/+cnx8fHJyEgwG\nFxYWfvKTnySTyWw2+9IEn8/ni8Vi0G+7c+dOrVZrt9uffPKJruvXr1+3LAsGgxP8RB48eHhFOI5j\nmmaz2Ww0Go8ePXr8+HEsFrt161Y6nV5aWorH419J5IV9n8/n+/73v7+2tkbT9Hg8Nk3z97//Pc/z\no9HI5/MJgsDzvNcHmHt4D/htAo69g8Gg0Wg0Go1ut2tZVigUSiQSiUQC5pjnxVR9Pl80GpUkSRAE\nFAUVRanX6+12ezAYDIdDT3DBw1cCBeZ+v9/tduv1eqPRGA6HLMvyPC9JErSEXqocu8w/lmWTyaQk\nSY7jwHhQ1/Vutzsej73N5sHDTAAnAGTCNE3rdrskScbjcUz1vuQF7wL3jt/vj8Vi8Xg8Ho9LkkTT\ntKIozWZTlmVFUXBtEWfzZB7mFV7l760BBjswc7t7964syz6fL5/Pb2xsrK2tYfbqpRcS8ku2bS8v\nL9+6davdblcqFXAENzY2hsNhOp1GMcarwHtwgYavoihHR0etVmtvb69Wq6VSqfX19aWlpWQyyXGc\nyy44D5z7LMteuXKF5/larVatVuv1+u7ubrvdhrW0x/jx4GHKAdlO2Pg2Gg1d1/1+fzKZ3N7exrzX\nN4vF4t7x+Xybm5vD4bBcLv/f//7fYDB49uyZbdtra2sMw6AY4VGP5hhe8PfW4DjOYDBQVbVerz97\n9kzTtEQikU6nV1ZWFhYWBEH48n3s8/lQnM9kMjs7O7Va7fDwsNPpFIvFSqXiOI4kSejTTepDeZhC\nIM1QFAUjfqenp6qqrq+vb29v53I5juO+TiocxeZIJLK6ukrT9L179yD4fHBwYBjGysoK2j3efvPg\nYWoBbT+cAPv7+61WyzRNhmESicTKygpaTN8QseH/CoVClI/K5XIEQdAR+s9//nPf6BcKhdFoZNv2\n+vo6GgUe+W+O4QV/bwHunIemadVqFe6KpmmKori0tJTJZL6hDu/z+fx+fzQazWazqMZ3u91ut1ss\nFi3LWl5eBmffy8A8EGeNGNM0odJXKBSazSa2TTKZXFhYSCQSX7fTXPj9fvB7EomEJEk+n+/09BR3\nSSKRcJ1eL/BjefDg4VUBeZder6coSrlc7nQ64XCY53mMebEs+yoeUT6fj/JTLMMm4olet5fL5tqd\n9ng8rtfrgiA0Gg040bu8Ye9AmD94wd93Be5jCPsdHx/fu3evUCgYhgEb3w8//DCbzX5zHZ6iKFEU\nb9261Wq1Hj9+TJKkpmkff/zx4uLixsYGeIFf2cXzcKngSjqrqtpoNJ4/f/7RRx/pup7JZBKJxM2b\nN69evYqhjW/u+GAiOBwOX79+vd/vl0qlhw8fsix7+/ZtQRDQGvaKfx48TBtwAti2ret6vV7HdTMY\nDL7//e9vbW3t7OwkEgn0c1/lsqAoKspFQ+FQKBz6+b/8vFarffTRR4eHh6PRaHFxMZVKBQIBqNJ6\ndvNzCe+hvgWg7DcajeCco+t6KBSCrEYsFvtWz2xct3BjFAQhFouBxsswjGEYvV4vEol4Y5geiDO2\nH1SdVVU1DGMwGHAcJ0kSx3HhcPgVkwS/3x8MBjmOE0UR00UkSRqG0e12Y7GYR/T24GFq4erI6ro+\nHA4ty2JZVhAEiHq+1pQulJ8jkYgkSePxGFeVaZqtVoskyW6369pNeaWH+YMX/L0FWJYly3Kz2fzi\niy/u3r1rWdaNGzfi8fiVK1ey2Ww0Gv3WOgpFUTRNEwTx/vvvi6J4//79Bw8eQH5dVdWtra2FhQXP\nePEyA0SfwWBgGMajR4+eP39+dHRk23Y0Gn3//ffX1tZWV1cZhkGO/q0nNRQfVlZWCIKgKOrRo0fj\n8fjg4MDv9w+HQ4Zhvo416MGDhwnCbTE9fvz46OgoFApFo9GNjY1r164tLCy8boPIVZy4ceOGoiiq\nqmLy95NPPoFkYL/fz2QyqVTKI//NH7zg7zvBZfthVL5er9frdYZhlpaW0ul0IpHgOA66St/wS/BG\n+f3+cDi8uLjoOM7R0REGhyuVis/nw68CGeuiPpmHqQPkWHVdL5VKmPPF0Z/L5ZaWliRJesX0APsN\nZIPhcFir1Wia7vf7rVarVCrF43GIReNXece9Bw/TANw1UHVuNBrFYrHVatE0DeWmZDIZi8Xe4IIg\nSTIQCCSTSZqm8/m8pmnj8fjw8DAYDJbLZZZlaZoWRdHn83m3z5zBC/7eHCjGjEajbrd7fHwwqvPJ\nAAAgAElEQVQM7m0gEIjFYmtra8lkkuf5V6zDu/dxPB53HCebzWYymeFweHJy0uv1FhYWUqkUQRA0\nTXtKHJcQbtmvVqshRKtUKn6/f3V1VRTFdDotimIkEnmtjeHz+XCsZzKZlZUVVVU7nY5lWYlEQlVV\nn8+Hjs+7+1AePHh4LYDvK8tyqVQqFAqmaeZyOVEUE4lENBp9Mzt4124qEonkcrnhcGjbdqFQGI/H\nxWLRtm2/3y+KIqJAbxRsnuAFf98JKMYoivL48eOTkxNFUXiez+VyOzs78XhcEITXuj79fj8G9Tc3\nNzHIub+/XyqVstns4uIiQRAe9/ZyAtVlwzBevHhRr9cPDw+r1erKysp7772XSqUWFxdhGP26dB/M\nIeVyudu3b9fr9c8++6xUKgmCcPPmTYIgvLPeg4cpgSvvUq1Wq9Xq/v7+/v6+IAg/+MEP4B2FFtOb\nva34r4LB4MrKSiwWCwQCx8fHiqIcHBycnp76fL5MJiNJkucAOWfwCrlvDlzJvV7PMAxZljudjuM4\nPM/zPM9xHMuy551VvxUo6cHwl+O4ZDKJrly329U0DTYMtm0TnvD6JYN77vd6vUaj0Ww2h8MhRVFQ\n9oKP0+sSvQHIDNE0DQcakiTBKVQURdM0T+Xfg4fpAXq+MPKGCYff75ckSZIk1zvqu/x+2I1Go1FB\nEFKpVDwet23bMIxOp9NqtRRFGY1GlmV5plNzA6+M9OawLKvT6ezv71cqlS+++EKW5atXr77//vv5\nfF6SJJd9/1oAE391dZUkyZOTk+fPn+u6vre3R5LkxsaGJEkw/PVyr8sDKDu0Wq39/f3//u//1jSN\npumdnZ1bt27dunULU35vTMehKEqSpDt37jQajQcPHmia1mg07t69u7i4mEgkfD7fG5cTPHjw8LZg\n27Zpmp1O59NPPy2VSp1OR5Kk1dXV27dvJxIJURS/O0PDtf3d2Nj45S9/2Wq1/v3f//309HR/f9+2\n7YWFBYZhRFGkadq7gOYDXvD3hnBFN5rNZrPZ7Ha7o9GIpmnkTMFg0LXxfa1fi/ErFHV6vV40GkXx\nr1ar8Tw/GAxCodCb/WYPMwdX1gvUgna73Wq1er2eKIrJZBLjRCgwv/EfgRNfEITRaARrkNFo1Gw2\nA4HAYDAYj8c46L3NNt/wajnTDNw1w+Gw3+/DyNuyrGg0yvN8LBb7Oi/H1wWunkAgwLJsOp0Geb3V\nag0Gg2q1SpKkqqpwgETz18Oswwv+Xhuuy4JhGOVy+eHDh81mk6bpaDS6srKCUY9vdVn4Bvx/9r6r\nyY3kyjoLQKGq4L1roBvth57DmdEY7aeQYh/3ZWN/kf7QRig2tLGrCG2s7IzG0g3Z7Gb7bnhbvgAU\nqr6Ho86FSM4MDdAwXeeBQdNEJbIyb9685hyGYUC81O/3r127hhr//f19t9tdrVZN00wkEm9a3e9g\n7oBlNhgMNE07OTl58uQJxJc4jtvc3Lxx48b6+nogEHhHNV5wTAaDQdM019fXEV04ODgAiyzYJX+S\nqNLBXAMrjf7qvOtZg2VZKPkol8vHx8f1ej2TyRSLxY2NjXA47PP5xtWYBf+P53lwO9+8eVMQhPPz\n8/Pzc0VRnj17Jori2tpaKpVCdGMsD3UwLTjO39sAwRhRFEul0pMnTyRJikajsVhsZWUln8+jyfet\nPxwaDKFQaDAYbG9vBwKBZrNZKpV4ni+Xy5ZlBQIBJOMcM73YsG0bd4yTk5PHjx/X63WPxxMIBNbX\n12/cuJFOp1Hr8y6PgIKnIAimaa6urvb7/SdPnhwdHamqWqvVBEHgeV4QBIflYbFhWRZquSidm2Ne\nZgQo+VUUpVqtlsvlSqUiiuLW1tbm5ubq6iquf2NszGIYxuv1Qijovffe43leVdW9vT1N0/b29hRF\nCQaDwWAQbiJxmj/mGY7z92agEluSJDWbzWaz2el0er3e1tZWNptNJBI+n+/dg/CoxBcEIZPJ2LYN\n0o1er1cqlQaDQSqV8vv9zt5bYOAkxjJrt9vVarVSqWialkwmI5FIIpGIRCLoxn33Z9FOo0QiIUnS\n+fk5IaTX61WrVY7joFLjED4vKuBbmKZpmia5uAyA1M1549MFjcUOBgMEGqrVKvJCIHiKx+OTKAHC\nGoBB6Pf7YJKyLAt5p6WlpUQiAYvhcrmcUPH8wnH+3gDU8zMMY29v7/nz5zs7O41Gg+f5u3fvbm5u\nrq+v+3y+N2ry/SGg8u/OnTv5fP78/Lzdbvf7/T/+8Y/xeBwuZjAY5DhuHF/LwSwCLEIHBwcoLXj8\n+HE0Gv3Xf/3XTCazvb2dSqV+kjz89YHKv+3t7VgsJknS06dPe73ed999Vy6XOY4Dxetraoc4mDvA\noBmGYdu2x+NhWRalXc67ngWg5vvg4OCPf/xju91GnvfGjRu3b98G/cqEXhPHcYhouFyu4XBYq9Ue\nPnwIWUiv15vL5SAm6eQE5heO8/dmwC253++jAF/TNNBjIkACUaxxPQs0vBBvDYVCiqKIoggNVl3X\neZ5nWdYpvFhIWJaFEm8wO2iaRghhWTYWi6Hh7u24XX4EIHrw+/2BQMDv9xNCZFn2er2KovT7fdM0\nHYLJBYZpmmD2oTE/J+07C0DYD7o+3W5XlmWfzxeJRILBoM/nm3QnvtfrxdGWSqVA/tzr9URRhLJI\nr9dDjthZJ3MKx6C/AUaZlh4+fPj999+bpvnee+8lEom1tTXI+I4xXeJyuQRBiEQi165dGw6HBwcH\nf/3rX5vN5u7uLsdxy8vLhULBMdOLBxjZbrfbbDY///zzs7MzXdfX19dXV1fv3LkTj8ej0ehYosuj\nwE3DsqxisQjO593d3UajsbGxUSwWh8NhKpVybhqLB1QX6Lqu67pt28j3odbTCepMEVTMrVarlcvl\ng4ODw8NDQsg///M/5/P5YrEYDAYn53jhY9H8sby8zDAMElCdTuf4+FiSpM3NzUgkEo1Go9HoGFMQ\nDi4TjvP3uqC7sdvttlqtUqlUKpVisRhkfBOJRCgU4nl+jIW3hBBwPmezWU3TZFk2DEPX9UqlAsK/\nTCbj8XicI3mRQJXcoBZ9eHhYLpej0Wg+n19ZWcnlcuFweIzLDKCLzefzJRKJlZUVt9v93XffmaZZ\nr9chIhyPx50y04UENCoHgwHqt9xut8fjcbL8UwdEBNrtdq1WazQaoigKgrC0tAQeWcomNrkBYDFE\nIhFQwCwtLbnd7lqt1m63XS5Xo9EghFDaP2epzB0c5++1AM/PNE1Zlo+Ojur1uiRJtm1DxjeTyYB7\nebxV0vgoj8cTjUZzuVyr1crlcuj539vb8/l8y8vLuJw51dkLAFpR2u/32+32wcFBtVqVZRl6u9vb\n2ysrK36/nxI9jn0ALpcLth53/UAgIMsy7vqEkKWlJVr552DB8ALPn3OWTxejoj6np6cHBwfdbjcQ\nCEQikVwul81mg8Hg5fRgobED9M5bW1vBYNAwjHK53G639/b2Op2OIAgejwe6o86amS84pvx1YZqm\nYRiNRuPbb79tNpuKovh8vnw+//7776dSqXA4PKHV7/F4EokEx3H9fv/OnTvNZvP8/LxcLns8nq2t\nLdu231TU1cHMAqFlcLt8+eWXjUZD13VBEDY2Nj755JN0Oj2udqIfgtvtjsVi29vbfr8/l8uBUfa7\n775TVfX69etOH+iiwnmnswbk4kVRfPz48dOnTzVNy+fzmUxmfX29UCgEAoHLSfiAB9Tn8zEM89FH\nHyEA2Ww22+32559/jhIUUMOgUJg40eL5geM0vBZQGdPr9VRVhYyvy+UKBAKhUCgYDPr9/sndw7D9\nOI4LBALYbMPhUJZlSZJkWYbIo6O3OO+grw88/pIktVqtbrcLwn10/GCZTXQYuOgLguD3+8PhcCAQ\nME2z0+l0u13DMAaDAdSlHThwMDnQ4wb+nyiKlmWFw+FoNAoqscukXkIY2OPxhMNhKNcHg0GPxyOK\nYqvVEkVRURTDMNAwRBy1mPmB+9e//vW0xzAHQPEThBZ++9vfViqVra2tu3fv3rlz5/r166FQaKJ1\nD5R4CQxP+/v7qLdgGEaW5XQ6jZZ7J/4310Ci5/Dw8ODg4P79+1988UW32/3ggw9u3bp179699fX1\nUCh0CZVYqO/xeDz9fj8UCtVqtYODA1BAm6YpCILD77BIsCxLVdXT01NVVQ8PD1VVXV1d/eyzz2gg\nx8HlYzgcdrvdnZ2dw8PDP/zhD+fn50tLS7/85S9v3LixtbUFRcdLDrC53W6e51HdBN7Zp0+fNptN\nr9er6zohBKWBtFX8Msfm4O3gpH1/ApRuV5ZlyPjSe1gul0smkzgOySSPZCrDkMlkEHH0eDyappXL\nZUKIpmn4Gyd3M7+g8p2o7242m6qqejyedDqdz+fj8bggCJegp85c6HsKgpDNZofDodfr1TRNFMV2\nu+31etPptGVZzkpz4GBCoC1fVDXeNE2fz5fNZjOZzFRaa7HZ0WeWSqVlWRFFybbtfr9fr9f9fn80\nGtV1Ha1CjmWYFzjO348Bnl+/31cU5ejo6OHDh2dnZ36/n+d5yPhCAPtyCm+9Xi86Ljc3N03TVBTl\n+fPnnU7no48+wpa7hLSgg0mA9hKJovj06dNnz57V63X0j29tba2srCQSiUur7IT/x3FcoVAAm+vJ\nyYllWbu7u+12O5lMBgIB3EYcK+/AwXgBU6DreqPRePr0aaPRYFk2k8kUCoVCoZBMJt9Ry/utQXWA\nUqkkIfZwaO7v30D9n6ZpHo8HQiC5XG5yHWkOxgvH+fsJUBnfw8PDR48eybKMwrvV1dXV1dVIJHJp\nhbderxePe++99wghT58+/f7779vt9vn5udfr5TgOGqzOrpsv0M4+cLvgtXq93qWlpVQqtbGxUSgU\nLtmtx2LLZrNer7dQKBwcHPT7fdD+Xbt2LZVKOWFmBw4mARprqNfrT5486Xa7giDkcjnQPEUikcuJ\nNfwQ0BAmCAIh5M6dO41G46uvvoLu/PLysqqq0WgUnp9jH2YfTu3OD2JUXxXEzq1Wq9frpVKpbDYL\ncdXL5DennR+JRAIDcLlcg8GgXq9Xq1VJkkzTpALtlzMkB+8IusZ0Xa/VatVqFa0VHMdls9mlpSWI\n+F1+MgXBP5/PF4vF0ul0IBBotVr1er3T6UiSBCmwyxyPAwdXAYg14MRpt9uyLIdCIcj4QtJpuhV1\n9AwKhUL5fD6fz6PvWFXVs7Ozs7MzkNGapunYh9mHE/n7MQyHQ03Tnj17ViqV8Gsmk/nss88ymczy\n8jKqXy95SBzHXbt2LZFIDAaD4+NjTdO+/vrr4+Njl8sViURCoRCuZQ7mBaZpappWKpX+8Ic/NBoN\n1FCvra396le/SqfTyWRy7JTOrwOGYbCQrl+/btv2zs7Ob37zG7fbfevWLUEQisXieJUMHThwQAgx\nTfP8/Byq8efn5wzDbG1t3blzZ2NjYyp24GUgLZBOp3/+858jJvLs2bNOp/Nf//VfiUQinU4XCoVM\nJhMOh522sBmH4/z9ICDjC6GtTqfT6/XQdRGLxUY1bS55Q+JUBv1HOBwmhCiK4na7JUmC4K8jtjNH\noNqdiqI0m81Op0MI8fl8wWAQrjwcrMtfY7i4u1wuVHMHg0FCCNqeut0uJRi6/LE5cLCQoDoCiqIg\n5ocaO5gCn883I4lUKj0AHiichjBfXq+30+kEg8FwOBwMBtEZNu3xOvhBOM7fq0FFrKvV6tdff10u\nl4fD4dbW1sbGxvb2diwWG6+M7+sDGqy2ba+trX300UfVavVvf/tbq9Xa29tLp9O5XG5jY2PsWiMO\nxg6qFthsNkul0u7u7pMnTwzDKBaLuVzuxo0buVyOUghd/vCoiU+lUrZtG4aBmp6zszOUFkBdZtJ9\n7g4cXAXAGvR6PVmW9/b2vv3223a7XSgUQqHQ+vr68vJyLBabKUcKzC+RSOTOnTvwTVGvcv/+/Uql\nYpqm1+sNBAKIVjr2YTbhOH+vBrYiupkODw9rtVoymVxeXl5dXUVMeyqn8qgGayqV2tzc5Hn+z3/+\nsyRJlUrl/Pzc7XYvLy+j5NbZcjMOaKqiZef8/Lxer9u2nUgkNjY2lpeXI5HI1Dt4XC4XYn6tViub\nzaIOyTCMdDqtKAqKEZ3krwMH7w7Qu8iyXCqVjo6ObNvO5XJIpMZiMb/fPzvOHz2GCCHLy8scx7Xb\n7Z2dHU3Tjo+PJUnKZDK5XA6XQ7fbDc3oaY/awYtwnL9XAAlfURTPzs7Oz89FUez1etFodG1trVAo\ngHFtiqcyiDZCoVAul7MsK5lMEkIkSTo4OCCEXLt2Dalhx/+bWeCibxiGoihnZ2e7u7vlctnn84Fg\nZWVlBZwOU/erUN+NK36xWPT7/c+fP282m2AiRFPIVIofHDhYGNB+/3q9XqvVQCUbCoVWVlbS6XQ4\nHAat+kxtMVSGuN3uYDA4HA7z+fzGxkan06nVar1e7+zsLJ1O93o9n8/HsuxUalcc/CQc5+8fgDIm\nWoP/4MGDcrksSRLDMCsrKx999FE2m+V5fupb0e12o+0/GAzeuHHj7Oys3W5//fXXoih+8MEH2JYz\nUiDs4AXQNSZJUqPRePDgwZ///GfTNJHcuX37NjRjIOYxXeCawfN8IpH48MMPK5XK/v5+pVI5Ojra\n399XVRXjnLqT6sDB/AL9/oqi4BJ4dnYmSVIqlbp37146nb5Mjs83Ao1BcBx3/fp1QkipVPr3f//3\nRqPx/fffE0JWV1dBCwrmv2mP18GLmP4BM4NAn4eiKNAuZFkWblYoFELh7bQHSAghbrebknEoitLt\nduULCIKAbJ2D2YRlWTD3eF+KorAsG4lE4vF4MBiEZszsOO6UY9IwDNx8wEooCMJgMBgOh1O/Czlw\nML+g6j7oLBwMBijsgaL3dIn9fhIQBPL7/bFYTNd1QRB0Xdd1vdVqRSIRXdehFek4fzMIx/l7EaZp\nNpvNarX6/ffff/HFF/1+//r165lM5ubNm9lsNhgMzsI6BosmjuRPPvlkeXlZ1/VyuXx+fv7tt9+m\n0+kPP/wQhEyzMFoHFFSyvdvtfvXVV7joMwyTTqd/8YtfpFKpfD7v8/lmhyIf9/tgMLi1tRWPx+/c\nueNyuWzb/vzzz5PJ5NraGkz/THmrDhzMC5DwFUWxXC7/6U9/qtVqDMPcvHnzxo0bxWIRjMozEm54\nJWAf4vG41+tNJpNHR0elUun8/Pyrr76q1WpQQF1bW4tEImCGn/Z4HfwfHOfv/zDK6txqtRqNRqvV\ncrlcOJLj8TgqGGbkkKMyrJlMhhASDofdbne/30djsiRJiUTCUWKYQcD5UxSlVCqVy2Vd1zmOC4fD\nS0tLyWRydjgdRgE1d8uy0uk0Cv6q1Wq/3wfBEMdxs7MvHDiYI0DSQ1VV+H+tVmtpaSmTyYBZXRCE\nWSj/+HEwDIPaX9u2C4UCwzC1Wk0UxUajUa1WLctKpVJoWHHK0GcKs76wLg1UxldV1f39/YODg3q9\nDka9zc1N1ODPWu0FiKDi8TjDMKurq6VSSdM0lORvbm5Go1FCyIyEKh2Qi7CfLCvVarVcLkMwjef5\nra0t6ERHIpEZpGmkar9+v79YLPZ6veFweHp6ahjG+fk5EsHTkhx14GB+AYPQ7XZPTk5OT0+73W6v\n10smk9vb26urqz6fD9I+M76tKC2Uz+fb2tqKRCKgAnW5XI8ePYpGo+hZCYVCjvr8TMFx/v4PUNkS\nRfHZs2dgLYe21fb29vLyMlQLpz3GfwBC7oiob2xstNvt09PTb775RhCEu3fvJpNJt9tNOQJm3IJc\nBYDbpdPpHB0dnZ2d7u7uyrL84Ycf3rp1a21tLZ1OU3M/7ZG+CKw0QRDW1tbcbnez2ZRlWVXV4+Nj\nGH2IDc7aBnHgYJaBnG+j0djb2zs9PVVVlRBCaT55np+d8o8fB+6HgiBsb2+n0+lOp6OqaqPRePjw\nod/vX15e9vv9tm3jokicw2g2MFsxhmmBMu4qiiJJUrPZbLVaYFFJpVLo87h8JbfXAcg4vF5vNBrN\nZDKxWIwQ0u/32+12rVbrdrtUZtERW5wiKH2/YfS63U6lUq7VaqY59Hg8kUgkk8kkEgmv1zubnh8F\naP/i8ThoXVmWbbVa1WpVFMV+v+/oSjtw8JqgBgHlv7Vard1uQzM3EolEIpFAIDDLpuCVcLlcPM8H\nAoFkMpnL5WKx2GAw0DStXq9XKpV2u43+MOIcRrMBJ/L3dwyHQ1EUd3Z2arXas2fPTk9Pt7a2Pvnk\nk1wul06ng8HgLB/MUIP1+/2RSOTx48eqqu7s7IiiKEkSZYqa2cFfEViWJctyq9V6+PDhf//3f0uS\nlEjEI5Ho+++/f+/evVgsBrWMWYbb7U6n04Ig1Gq127dvdzqdx48fHx0d8Tyfy+UIIcFg0FlmDhy8\nDizLQqBhZ2fn888/NwxjY2MDOd/Z6Sx8I6D4DwrgsVhsd3f39PRUUZT79++XSqW7d+/CtQ0EArNf\nyHgV4LwDQi5qLwzDaLfb0DCwbVsQhHg8Ho/HsaBnufYCIXdsLQj+6roOrVjDMFA1PHemZGFAG4k0\nTZMkCYQOuq4nEol4PAZrSBMiswzUmPI8HwwGE4mEZVmnp6cgLFRV1efzOTU9Dhy8JizL0jRNlmXc\n0i3LikajiUQCxHizHGt4JUD7jPoQML/EYjEcRpqmIZkmyzLLsoIgOLTPswDH+ft7v5Usy+Vy+Ztv\nvmm1Wl6vd3l5eWNjY2trK5FIcBw3y54fIYRhGMgw5HK5999/H7fJ09PTWCx2fHysadry8jI0P6Y9\n0isHWlGg6/ru7u7x8fHh4aGqql6v99atW9Dz8Pv9s98ti+GhtyOTydy9e7dSqRwfH6PSdH9/X9d1\nCF4Tx6w7cPDDoLGGg4MDtHqoqhoMBq9fv57P5zOZDCQ9pj3MNwY1EX6/nxDS6/U+/vjjZrP58OHD\ncrkcCAQePnyYTCYRAoSCkWMopgjH+fs/UcV6vb63tydJUjweTyQShUIhm81OS8b3jYCQjM/ni8fj\n29vb4XB4d3e30+lUq9VSqTQcDlOp1Oy7sIsKyu1ycnLy/Pnzer1OCPH5fBsbG7Oj5PaaQI1pLBbb\n3NwEH6FhGI1G4+TkxOVybW5uUjUnBw4cvBLU+Ts7Ozs4OGg0Gkg0FYvFQqEQjUbnLuw3CnDCgyLt\nxo0bOFXL5XK1Wn3+/LkoiisrK+DNcAzFdHGlnT9adSuKYrVaRYeEYRjvvffeyspKJpOB1sIM8q69\nDNqPmc1mwbrZarV6vd7x8bGu66urqzzP0/z1tAd7VUBVOzudTrvdPjs7K5VKpmlms9lUKoU+j9nR\njHlNQDk6kUgMBoNkMjkYDHCMeb1eEPqDrcZZZg4cvAx4frqug+nz/Py83+8nEolMJoNWKtzSpz3M\ndwJt/s1ms16vN5/PK4rCMMzx8bEkSdevX4fFQzHSvH/Z+cXVdf6oxKphGMfHx0+ePNnd3W232yzL\nvvfee3fv3kWD+mw2+b4SLpcrEAhsb28nk8knT54g2vTFF1/EYrHt7W3IgTjJ38sErhaSJO3v71er\n1e++++709HR1dfXTTz9dWlra2NhAn8d83YDdbjdKtnmev3nzZiAQgEKxoij/9E//RAiJRCJOg5ED\nB6+Ebdu9Xq/dbtfr9cePH+/u7iaTyZs3b66srOTzeXT9z9dt8JVA8ndjYyOTydTrdSSjvvvuO47j\nVlZWZFne2toSBIHSmjrm4vIx94vsXUBFFSVJarfbiqLgSAuFQuFweMZ1dV4Jt9vN87zP5wuHw5FI\nhGVZWlCsKEq/33d67C8TlmWZpqnrervdRvONZVk8z8fjcQg3zRpt+GsClX88z0ejUWSpVFUF85+m\naYPBYNoDdOBgRoELoaqqiqKoqtrr9VBHEY1G57HP40dArUQkEkEjC8rrO51Oq9XCeWSa5rSHeXVx\npSN/g8Gg2Wy2mq37393/25d/syzr1q1b8Xh8c3NzaWlpHpvtsd9CodDt27cDgcCDBw+Oj49lWb5/\n/363271x48bGxga4Q6c90sUHuvm63e7+/v7vf/97BJXX19dv37597969RCJBJY+mPdK3gcvl8vl8\n996/l06loSvdaDTu37+fTqfv3r3r9Xrn1K914GByQKlfpVL55ptv6vW6qqoo9fvwww+z2exsSju+\nHei34Djuvffei8fjgiDgigh+qMFgwPN8LBZLpVJO8+9UcEWdP9qD2e10m81mtVatVquhUAisfrFY\nbB616tFs73a7WZZNp9ODweDs7IwQYhhGuVz2eDyZTGZ5eZmeyvP17eYICK9algXBmHq9fnp6Ksty\nKpVKJpPZbDadTkOXZU5fATqHWM/fdaUj4Yjb7e71euVy2TTN9fV10zQdKi8HDkYxmmg6OztrNpu2\nbfv9/ng8jiLg2e8sfAu43e5YLObxeFqtVqFQaLVa+/v7kiSVy+V6ve5yuaLRKArWpz3SK4eraKBH\n9Tz2nu9VK9V2q80wTDgc3traSqVSSJjOY9yC+n/RaHQ4HIJJRJZlyP6m0+lisUgICYVC8/jt5gLw\n/HDFL5fLh4eHx8fHoijidaytra2srIDKa65fAcMwbo87Govatr20tJTL5Xq93sHBQafT2d7ezmQy\nkAN2GsznBc5rmjTobbBa+XvfK2hZl5eX4/F4KBRaSAcIzb+BQCCXy925c6der9dqNRCrPXr0qN1u\nI9QCMlpnEV4mrqLzRy76PDqdzoMHDyqVSqfb8fl8mUzm5s2byWRyrqMyhBAI/nq9XiQZa7UaONaX\nlpa2trYIIX6/H99ufr/jLAMdvoqiHB4ePnz48OTkxDAMnue3t7fB7QcNXzLP84/LOgr+iqvFzdJm\nuVze2dkJBoP37t1bWVmB6uD8fkEHDsYLy7JkSa7X6icnJ0+fPjUM45e//OX6+vr6+no8Hp/rIpAf\nAr6Ox+MRBCGfz3Mc12g0njx5YppmqVQSRXF1dXV7e9s0Tbfb7XK5Fm8GZhlX0flD2KEH5SEAACAA\nSURBVA9yC41Go9VqMQwTjUZjsVgoFEIn4/wuQYwcyd9gMJhOp0G83uv1JElqtVo8z2cyGfTY45+m\nPeTFwWjCV1GUVquFyp5AIBAMBlHWvTCVPVRXOhQKJZNJVK+7XC5RFLvdriAI4Hx21tjswxFlniio\nWVAUpd1ui6LY6/Usy4pEIslkElSyCxn2A3BRhHIx+KFQDC2KYrvdxvnr8/lG74qOxbgEuH/9619P\newyXDdM0m83mwcHB8+fP//M//7NSqaytrX344Ye3b9++ceNGKBRC7cW8rz80f4TD4Wg0enBw0O/3\nCSGqqqqqurq66ty0JgTIuO3t7R0dHf3hD3+4f/8+IeTTTz+9ffv2J598sry8POM60W8KuICIJT98\n+LDf7wcCAdM0XS5XOp3GN12YL7t4sCxLVdWjoyNZlo+OjjRNW11d/eyzzyDS4GBcQCrgu+++u//g\n/uHRYbvdDofD//Iv/3Lnzp1cLoew37THOFm43W40/3q93mQy2e12T05OVFVlGKbVagUCAUzCvKdE\n5ghXLvJnWdZwOFRVFTK+uq6bphkIBFKpFGR8F+O4As0myDgGg0E0GlUUZTAYNBqNQCCg6zrHcYt9\n3ZwKaE13q9VqNpuiKBqGEY1GM5lMOp0OBoMLxuZACMGtHZwvgiAQQmRZbjQa6XS63++j7XeRvu/i\nASbRsiwn/jcJgOndNM1er9fpdBqNBoSwg8FgOBwOhUJzoev9jqD5KK/Xm0gkTNNEYf1wOITAiSiK\nmqbhBxxzcTm4Qs4fTBtuYMfHx19//XWtVguFQolEYnNz89q1axBVXADPD2AYhuM49FLdvn07Eokc\nHx+jx/7k5ETTtFwut6hVxlMB7SKq1+vffPNNrVYzDCOdTq+vr1+/fj2RSITD4QXz/MgFm2symczn\n8zdv3ux0Op1O59GjRx6P59atW7Zt01D6tEfq4BXAdUXTNFVVLctCQmDag1oowCy02+1Go7G/v7+3\nt+dyuaAan8lkQqHQAkh6vA4Qj2BZFpHORqOh63qn09nf3y+Xy8lk0u12QxEE3ZZXYU6miyvk/BFC\nbNs2DEOSpPPz852dHVmWEbEoFosrKyvhcHiRPCGajyOEbG5u8jxfr9d3d3cZhjk7O+v3+6FQaCGr\njKcC3O9RWFmv13d2dhqNhiAIS0tLxWKxWCzGYrG5U3J7HaCrNxwOp1Kpra2tWq327bfflsvleDze\nbDbdbje6W5w1NrOA2piu65ZlOdZg7EDEodls1uv18/PzUqmUyWTW1tYymQxswpW6Gnk8nng87vP5\nNjc3dV0/Ojp6+vQpwzCHh4c4jJLJJKTqiZP8nTCuivOHsN9wOOx0OvV6vdFodDqd4XC4vr6eTqdB\nQTmn9C4/Aly2vF5vKpUaDof4mpZlnZ2dGYaRzWYjkQgV2HZ22tuBVnNDya1SqVSr1U6no2kaiBVB\nGL7A3Nq40Pv9/nw+z7LskydPBoOBJEnVatW27Wg0ukgB9QUDlZ8eDAaWZcFiTHtQiwN6J4RZ0DQN\nIpxLS0vpdBoiUldnX9DmX6/XG4/HC4VCv98Ph8Nwjg8PD71e7/Lysm3baLt0esUmiuk7f5dTZQJR\nHVTin5yc7O3tQXDwZz/7WaFQKBaLgiC43e4JDeZNV/AYhwGapc3NzUQiUalUSqWSLMt/+9vfotEo\nGs3IBfPLpF/EJW/jy6xeov3jR0dH3377balUajabDMNsrG989tln+Xw+HA7TWpbxvtw3Hee4Hv0C\nXC5XOBy+d+9erVZ79OhRpVJptVpff/11Op1Op9M8z18yr+HCnBmTXsYwjLIsK4oymva9tO1z+W/q\nMi0D+D5brRaV9IhGoysrK7dv304mk+Bbndx4xjK3kxgey7JLS0uBQCAajR4fHzebzdPT04ODg1ar\nlcvlkslkoVCY6In8AhbGXLwRpu/8EUIsyyITphuwLGswGPR6vW6322q1VFUlhCArGggEWJZF1fO4\nHkclNN5xVb37hGBWWZblOC4QCEQiEVpjK8uyrutQ156oHsN0t5aNQnYy2dXV6/XA4NpsNjudDiGE\nZVmfzxcIBHieH+/qYkbwFv+dbrQx7jh8DsdxPM/zPM+yrGma7Xbb4/Hout7v9yfdWj6uHTdrmLRt\nNE3TNM3hcGiapn0B/OUkHkcIcTEXb8o1VbNwMaWY4Qk9Au1fVN0b0t4wuV6vF1M9rhVLF/8kdoFt\n27Z1YTTIGE4lRCUEQQiFQiC+URSl2+12Oh2WZROJhNvtnnS5CIzGlQ11T9P5o11mhmFgkwwGg0nY\nOGxCwzC63e4XX3xxcHAgiiKqlPx+P8uyqqoOBoNxLQJkWhmGwSmIRUxe2wfCaIfDIUwD/vJd9gDM\nHMMw+Xz+3r17R0dHe3t7kiTt7OwIglAoFNbX13meH+82o+8Rs8qy7GUWflERF7hlg8EAC2xCzxoO\nh91ut91uf/vtt3/5y190XU8kEtFoNBqLsizbH/QhZPTuz4JZR020x+NBqfhrTixdVyjwx3VoXC4p\n0lv4wEgkkk6nJUl6/PhxOBy+e/fucDjEFWsSC4CyiKH60O120x03v4BttG271+uZpknTsmN/UK/X\nazQamqYZhtHv94fDoSzL1Wp1Qs4fVq/L5eK8HOtlQUdKLvF+iF0Afxc+R6/XG+PFbBQ42kRRPDw8\nfPDgAQQeIe2I0nNN08boqCGd6nK5kE32eDzvft0anS5UhY7FaNAqLNu2t7a2YrHY6elpo9E4OTn5\nn//5n0QiMRwOM5nM5DjXqNFAfzHmat6Nxptiat+W3oqQdEDWDLsRfsMYXznN+XY6ndPT07OzM2Sp\nOI6DCeh2u2NZZPCx3G43z/MejwdRH2xIeif7of9If4PqsX6/j1qccdU9DAYDQRCSyWSn08GJUqlU\nzs7OWJZFReAkLouEEMomTQgZnYfJmXtYFph10zRVVdV1fTAYGIaBqqaxP840TXC7YHXZtp3NZgOB\nAMMwuqHbxJZleVzPRXctEqmEkNfka6QRHbjCoigiEI7r1hjTQ6qqYv13u114FZVKBcQW2Ajv/qAX\nAPcXRUKBQOCFbsF5DATSOjyEQ/r9vqZpOHrHbhv7/X673YbzR8/4ZrM5oXgY+KeQckGZNewDmfyb\notHuwWDQ7/d7vZ6qqrAPiHqOfQC4ZXW73XK5XKvVcCeEZybLMlyocW09eNVUOggu9Ts61vQwMgwD\nVbzjMhr471jkSI+A9kUUxf39/Xa7vb29jW80OeePZVkYDb/fD6NBl+IVwXScP0q21+12DcNAJWyn\n05FleRJGB8eeYRhgINM0jeM4bPunT58GAoFxVeLDvrAsG4lEOI5LJBKhUAhsMh6P54e2InVWaJgK\n+hD4DSbk3RelZVmSJMHEY+OVy2WWZfv9fjAYpIJvYwR2uMfj8Xg8kE5hWRYewFhupT/0UFxV+/1+\nrVbTNK3VbHW7Xd3QJUka12S+ANM0O52OKIqlUqnf77vdbl3XJUk6ODhQVRXvfSywbRvtciAJSyQS\nHMfF43HM6itdK6xJJPIkScJJX6lUsB10XR/vsWcYRqVSURQFB4amac+ePRNF8QUG/zECIXZMRSqV\nCgaDKG9ACHDsj5s0YAfAgtHr9Wq1Guxkt9udRIAK2flGo6EoCmJgtVrtwYMHgUBgvA+iV8FwOMzz\nfDwej0QiIFiFbZxoVYB9obhtmia0JRRFqdVq4N7r9XqTcP7wHhFJxdzitZ6fn8MSjutBGLzP54tE\nIhBw8vv9kUgETF5v0c+H6RoMBi8bDUVWdGNsRgPnsqIoaIUZDAbNZlPX9UePHpXL5Yk6fzzPJ5NJ\n/BoMBiFHhLv0FXEBL9v5o0cRbpwnJyeSJO3v76NNstVqTSgERdPKeATuf51O569//eu40pFw4Agh\nHMdlMhmfz7e8vJxMJsFdxPM87hmv/L80TNXtdnFZbLVaCEliQsYSMkGYU1VVr9fb7/dPTk5arVa3\n20U54IScP6/Xi3Zj9BqD6w7Z9gntMbj1iqLs7+93u92z07NarSbJUrPZxGSO16Dgvcuy3Ov1ZFn2\neDxutxu+uyzLT58+HVe4Cw9iWTafz8fj8VQqVSwWEVHDrz/0vZA91HW9UqkcHR11u93Dw0NFUZrN\nJq5b47J3GCE8P9T5DYfDBw8e7O3tIU899sgfQrmBQKBQKPj9/rW1tWQymclkOI6jLSZzZMppzE8U\nxbOzM1mWnz9/3m63a7VavV5HKna8XweWp91uI6hjWVapVPrTn/40xhsLufheKD5Op9J+vz9fyGez\nWZy+PM8j+jLGJ74MTCwab9GSdXh4qKpqtVpVVdW27bGf+niiruuGYRBCWJbVNK1Wq3U6nePj43FZ\nIcyty+UKhUKpVCoQCGxubkaj0eXlZY/HAwbpt3gQNRrVahVGY39/X5GVVruF3qCxTBd1yiVJYll2\nMBh0u11Zlr/44gtBECYUI8Dg/X5/sVj0+/2rq6upVCqVSnm9XtRikrkyGm+NKUT+aByu2+1Wq1VR\nFFutFnx/1BPQXTHG+j/cpwkhNGXm8/nQTDSW6hYMGCWMhBAksuv1+nA49Hg8yKuifYn848Ki1Q+G\nYfR6vVarJUkSCshwBgyHw3Exr8Ll1XUd907btvv9PsROer3e2F0imgSnpc0IJ2CDsSw7ods2eLxF\nUQTlSqvdkmSJri4aIRvv6sLhAYM1Sm6HGrt3/Hy6HXBvkSQJ9wGO41RVzeVy4JH5oUAX7DhedLVa\nRVW1YRgIzo0ee2OZE7j1dJ7dbjci/ZiNd/98gO44QghabRDrHQ6HLMtStrC5C/7hYizLcqVSkWW5\n1WqJoqiqKgryJmEbCSGoTsaW5Hl+vCHGUdto27aiKubQ5Js8IcS2bYSpIDhEJnnoYhdomtZqtarV\nKu69dBcQQrBUxjix2LDIfoBXAfFvt9s9lj6PUbPAMAyyDYPBABHNYDAIhv+3i7ijYBEC5ZVKRZIk\nURThyI7RaND1DCcVN5DRrT3e6yL9ZBgoBH19Ph89psFadRU8PzIV5284HLbb7Xq9/sUXX/zud79T\nVTUSiSB6kUwmWZbleZ4QwoybfMQeATOCd/9k+iGmaaKgpNPpdLvd58+fm6a5vr6uqmoymfzggw8i\nkcjLwT/UOhweHoqi+MUXX+AmahjG6AYby1BpGwRyLoiaWJa1s7Mzdqo/+6KTDmWLqEeJRqM3btyI\nRqN3797N5XKotx3XEwHkrXZ2dsrl8m9/+1tJksDjHQqF8vk8zTiTcR+fo+pYsCxjnEx8lGmaKF7s\ndrtnZ2cHBwemaYZCIa/Xu76+nkqlXrm68MaPjo5KpdJXX331t7/9bTAY5PN5nuez2SwuJDTMM5Y5\nofOAixCmYrz2lJ46iOUYhtFsNgeDwePHjz0ez927dz0eTyKRAGHEHJlymIJGo3H//v3f/OY3kiQh\nJBYMBtfW1tCzj/kc7+od9fbGlWcY/UBykXLF6tU07ZtvvtF1PZfLKYqSTCbv3buXTqfHG24chW3b\nhmEcHx/X6/Xf/e53Dx48YBgmlUpxHJfP55GdGO8uoB/1wl4Y49zShU1LLBBJefToEcdxP//5z3u9\nXiaT2dzcfFOHBkZjf3//7Ozs22+//frrr03TzOfzYK3HVXMs00VHRe0nJmoS3YGjRgNOP6Lpjx8/\n9nq9d+/eRTVCNpsde/vjbGI6kT9FUaByWK1WDcPAARYOh6PRKMdxUAidBF64N49xk8McD4dDbMLB\nYMAwDFq6QqFQo9FwuVyoLHnhP2K54/TCHatWq+EmitDOeG09wiGxWIwQgjDSqK2fhLeNeBtqXwzD\nQKfbxsbGYDAYe1Qfr0BV1Xq9XqvVms0mrhZ+v59WXk606XhyC4wQgq/W7/ep8QJpUbvdBmfYK1cX\nYq7gNge9ObrRA4EAagfpnIx3O5ARa0vGPRX4cJrIA00dPCfTNOv1OooZsMLH+9yJwrIseoSXy2VF\nUYrFIsuyuBiDSWdyzBRYvdRfGePH2hfN4Mgsu1yuSqXSbrdZlq3VaoQQ2s4yob0JQ4RyGuwCQRDy\n+bzf74fgBBWhnsRCJRPbCxhwr9fr9XoIfkPIgGGYer3ebrf9fv+bltG/YDQajUaz2cRhFAwGY7EY\n6pfGazR+qF5lLB8++hQYDVQ8o+0GtVW5XG5OjcZb41KdP/uiB/Pk5OTg4KBUKqEF9d69e5lMBqEL\nZB/oz4/r0aM7cHQ84127tFEXyRpCyPHxsWmau7u77Xb7zp074XAYVaWjEXvUVXzzzTcwTIPBIJFI\nLC0tCYIQDAbxw3T87z5gGvKkFGLv+uV/AHjdqqqibr3VavX7/e+++y4cDi8vL0ciEULIuKry7YsK\nZV3Xy+XykydPGo2Gz+cLhUK3b9++desWOm9G63nHfsK9vLrG9RS6uhBXLpVK9Xp9b28P3i1atn0+\nXyKRGI2dUOdb07Tnz5/v7e212+1IJBIOhz/99NN4PB6NRhH5G6/3P9GpGH0KvW5hEmj3WKfTOTg4\nUBSlUCj4fL4xPnRyoC/r/Pz8+fPnp6enhmG43e4bN24UCoV0Oo2XS0M4Y7eN5B/DMOP6cDKyevGy\n0G/BcdyzZ89cLheW5Y0bN9Lp9KitGyOwcWRZ3tnZQTLd5/Pl8/mf//znkUgkFouhAXnsaV8y4XPn\nhYwT2hlbrVa73UaXxv7+/nA4fO+99+Covc7EvmA0dnd3O51OLBaLRCKfffYZBMoR+Zuo0aCfOTmj\noSjK8vJyt9v94x//WK1Wm80m+vOQDxnjQ2cWU2j46Pf7Z2dn+/v7uE+ACWxlZSWZTKLxdq4jrvD/\nENqs1+sQez0+PobJ6/f7o7lOus2gi4CrsM/ny+Vy77//figUikajr79v3xTUlaQbbLxBOOr8aZq2\nu7u7v79frVa///57v9//8ccfFwoFr9cL6eFxPRGTWa1Wd3d3FUWJx+PxePzWrVsff/wxFVCf69WF\nG3k+n69Wq8Ph8P79+71er1Qqud3uXC73cqkWjj1VVY+Ojp4/fz4cDpPJZD6f/+ijj9LpNFKK8z4h\n6KnM5/ONRgO3LHxf1CdNjsJ37IBtLJfL+/v7lUrFtm2fz3fjxo1r166lUqloNLoAthGhzW63qyiK\noijtdvv4+FgURRShwjaO9zvSoKOiKM+fP69UKr1eLxaLFYvFjz/+OB6Pg4Vgrpl+8R01TUNv0P37\n99GCdnR05PF4er0e7nivObGIjWET7e/vMwyTyWSWlpZ+9rOfpVKpBRAjptO1tLTUaDSgwy7L8snJ\nSa/Xu3fv3hwZjXfB5Tl/8Abo5Q/drChKjcViqMoCB9KlDWkSwHeEe5dMJpPJJEI1tm1D6gAF6fSH\nUYkPZQhZltF5tLS0lMvl0H8+rm6Pywf2WDAY1HVd0zR8d/hnnU6n2Wwi5zIuak2cncgvw8+Ox+OZ\nTAa3VfQXkzlv48KURqNR0zRjsVgwGCSE0MXzss1CIxEIJkRRRPYQngS227z7E4QQy7I8Hg+K0KPR\naCAQsG271Wp5PB7Um04umTgu0LIw0zTxNjVNQ60CLjDhcBgNatMe6TsB7wL7PZFIUNtICEF+wDTN\nSfT8wvlDaQ0EJCKRSDKZBBkKmrRmfIX8JCDNhwtwLBYDPWSr1YrH46AHf/2NgGQUTiXUTKODHtM1\nCQf98oHpApUmTgfbtpvNptvtRs3VVcClRv5wpdA07eTk5PDwkOf51dXVpaWlTCYTj8cnWs5yaWAY\nxu12I268vr4OWt379+/jdqsoiiAIaPgiF70v5+fnZ2dnpVLJsqzr16/fvHlzc3NzY2ODlp3Ob7zK\nvqAJTaVS6+vrDx8+/Mtf/oK8P8hllpaWQFb87rAsCwcnits4jrt+/XqxWETub95vqwBWVzQaZVl2\neXl5ZWWl2WyiF+/atWsv9K3DG+52u81mEzSzqVTq5s2bhUIhEokshudHLkpjk8mkx+MpFovgEICK\nj6IopmnOxaunbLqlUuno6MiyrEKhkEwml5aWkskkJQqYazAXfZ22bReLRU3TbNv+/PPPZVluNpvd\nbhe0L+M9BeAPIRVzenrabrdv3759/fr1zc1NnPqLweuGXRCJRGzb3tjYcLvdOzs7h4eHLMsi6PCa\n0U0UoKMAqVwuNxqNfD5/586dQqGwMJ4fuZgucEyurKwgV76/v4/OeifyNxGg8gNF66D8QJP/Aty9\nRoGuLjSvICyBGjvK0Q/QYBW4lwkh4KcNBoOUcGgB4PF40JeKDAvqvmlH87ieQuPK4CZlWVYQhMlx\nC08RaLUDX4/X68V8vsxYRD1vlAQhIC0IAuLrizcnkLdCjxQaQV7YbrMP2sIC7SkwsEyCH3G6QMsR\n1I/QBQxxkQkdujC8VN4GuwCFa4u0C3AzhOojSlxgDN+0gwGBUhgN0zRBXLUwd0UKhmHALg4ryjDM\nnBqNt8YUGj7oCe1yuXw+H9IZ8xvcehmopWMYhpJG4qx92flDfyKaE/Hz6XQ6n8/HYrG5CFe8JqDp\nBFGKaDTqcrlwuaSSG2OBfUH8QdWHeJ6nfHsLM5nkIhLs8XhwhpGL4+1lmwVnAiKKSI8GAoGF3HHk\n4jaP6xZcivky4qCExPsSBMHv9/v9/oV8UwzDgNJr9GI29i5j+rHwZuDKDIdDcNr7fL5JkBBNEfgu\nYBuF3bMvuLVff27pdCElSghBGTp1/hZpusjF2YQYgXUhqD3toV0SpuD8YYpBMked7ok+9IXfUIw+\nd+xjwD5EExlt0HthE6IQEIoIMIjBYBBlKJOYk9dp7Bgd3rjGAE8FkQyfzwf/DFLO491pOPKphhv4\nCBYsakJB43/MD/eAY6/Botm2PfpfJj28H3mzE3r66Bunx94kHjQJ0AYpvDJCCGzjoq7eUdtIzeOE\nnmWNALvA6/VeZq5pEkb1h4BzhNKbv5HnB4waDZxil5aa+8lxTuKYRsYAFZNzZDHeHdPR9qWY9E0C\nqUB6DLzwapkLMt4JZcFe5zPpbQNjAPXJhOYEpwszQuz3woPoCURGLkZjGQy9ldIv+BZW6e0eejm3\n1VFX49IeSuMor//Dl4AfDzbAyE5ufph/xCQesaigYXi8uEuoDbi0d/Tyary055ILw0tGCLQvYWLJ\nO/jTo9P1RkbmrfHCRL3yZU1o6kY/0HH+JogXjPKkb+dIBSKCTRe0PSLDgAohxELGvqpe6XG+EhN1\n++gAEBhDwJX8gOeH+hs6KnqDfMeB0TG4RjChaOvlWCuAfi+01NFH04buS4hq/8jSfdkTmqjDbV8o\ndeLGNbq7qT+BSP9E64fm0fMbfU2U1/3SjiL64ujRS9fw5Hz0F34zObywHi7h2kn+0ZtBIpUQQoOd\nP3T9HuPT3+ULvjBd5FK8IvuiaPtlFxCThgDkJJ479s+cC0w58jdp2Bfq1FRidXSzuS8wiSU1Cxh1\n+2gZL8JvLwuH4GfgK5MfiKC8u6m6zLv+K38/3s+n6UUQ2ZALB5RGlMmck8u8BcwLjJImYLqw8AB7\n5hlYrgjo7qAXP7yaiWb6XrgVLBJGvxru22BcIoRAR4Rep5mL6vBpDnfaGDWkULB82fmjcuFjlyG9\nylhMp4diMBicnZ2Vy+VerwefZjQyJAhCsVgUBCEajaK2etrjHTMQyQPhZ6/XA7cqz/PFYhEVRbQu\nBCo3hmGIotjtdm3bRvlUPB5Hh7/f7x/LllukugrKhjoYDOr1Ogo30UEGNpZgMHhFZCIpwF4kiiJk\nyijnJQobeJ7P5/PQibpqMzPLsG17MBg0m02Q41iWBS4hn8/nvKO3A9psYU5hV23bRqNJIBCIxWIw\nFIta0/mmGA6HvV4PpN8I/tF/crvdPM9zHLe0tERVD6Y41IXBgjt/lmV1u12wutPeJVpAAJoVt9v9\nsjTCAsAeYfqQZVlV1WazKYqi3+/PZDKjqUn8mCRJsix3u91utwsOTGqbAoEAur2ceyoFvNh+vy+K\nYq/Xa7Vauq4zF+XDcHTAuTDtkV4qoOnS6XQkSep0OqA0p3E+v9+fSCQYhlnIHTe/QLpNFMV2u414\nLcdx2Wx2Ye5plwzcuiHv1Gg0dF2XJMm2bXB3Q9QUnHmO8wdgBcqyXK1WDcOgjXooEfH7/YIgJBIJ\nZ0GOEQvr/GGV9Pv9o6Oj+/fv27YdjUahJ4arA7K9kyOXmjrgmkiSpGna06dPW63W+fl5q9WCwBcu\n93B8NU3TNO3x48eNRgOtx2hD8Xg82Ww2mUym02nKjEWcqPtFrNQwjHq9/uTJEwhV9Xo9ckE4kk6n\nA4HA9vY24ltXx8RDnfbg4KDT6bTbbew7WlMbCoVSqZRlWdDhmPZgHfzdTVFVVZbl77//HlrkHMeF\nQqGVlZWF4UC+NOBOSOPfe3t7z58/B3Ej/tXj8WQymeFwGAgEcrncgpHnvR3ALC1J0unp6Zdffqlp\nWiaToQrCHo8nGAwGAoF0Om2a5qLWaF0+Fnwe+/3+ycnJ48ePvV7v5uYmxExRcoRSrQU+mFHviEje\ns2fPqGZosVj8xS9+wbJsIBCwLiTPO53Oo0ePzs7OkKeDXqrb7W42m8lkUtO05eVlWik47W82fdgj\nOsIPHjyQJKnX61FyBK/X2+12ISGVTCZphPUqwDTNUqm0s7PTarW63a7L5aLZQxfjGg6HqqqC9Ntx\n/qYOeCqI+bVarcePHz958mQ4HIbD4UQi8Ytf/CKZTE57jPMH+NP1er1Wqz158uTBgwfD4TCdTjMM\n0+12TdMsFArI/Eaj0cXQtXpH2LaNzPjp6ek333yjqurt27cjkQjCE9AFgP4NgjWLV6A1FSy484fo\nl2EYqBsA+yUymAgmg2h0IRcTbBCierToWFVV/BGnLxxEBGlwVYXECCFEURTLslADFAwGNU1DtbJj\nqsiFYw3NqGq1qigK7DgcmheqUq6Ul4NrA6RacWsPhULBYBDOHwS1Fk9cYR5Bu/sRwIbuLbKTHo/H\n7/dfKcLbMQKz2mg0oLuIHEssFmMYxjAMRVE0TSuXy4ZhbGxsODNMLu7ShmFAXQsxVQAAIABJREFU\niBxp8XA4jMw4y7JQhwI1h2M3xoUFd/4Al8sVDAaLxWIkEkkkEqi3wK+ZTAYCL4vn06DEBJlcv98f\ni8WCwSDlBKamv9VqPXr0qNlslkolTdOuX7/+//7f/+M4DofB//7v/+7s7Oi6/sEHHwyHQzjKzvYb\nDofNZvPs7Gxvb+/777+3LOvf/u3fVlZWXC4XOF9M08RN46rNlWVZmqapqsqybDabDQaDn3zySSKR\nwLWB5/l0Or2oO27ugOh1uVz+y1/+AguAezICLY5f8hZAE5gkSV9++eXR0RHDMPl8Pp1O/+pXv2IY\n5v79+xCQ/fOf/xwOh69du4atMe1RTxn2hdhBv9+HvvP777+/trYGtR44f16vNxKJXEGLOjksvvNH\neTfsC3E56BVC5HGxDRxCL16vNxAImKaJFMMohRgio7Isy7KMG7/P54tEIoIggJ7K5XL1ej3DMCDL\nsaj1kW8Ky7IgT6xpGpp8IRvAMAzY/vDHq3lPxUajlC74S7TCIOJ+Nadl1kDDfpqmybKsKAq8c/qv\n0x3ePIIa1eFwKEmSKIrhcBiylpFIhGEY/FFRFFmWGYYZ5UK6yqBHs31B/04ZOQAqMeJ0HI4Ri+z8\ngV1CEIRAIDAYDA4ODsAxgWXkcrnC4fAnn3wCwdnFo3pxu93hcHh9fX0wGCC3W6/XDw4OcB7DTqE3\ns1QqdTqdcDjM8/zS0lI6nfb7/dFoNBKJwGYNBgOED514AIDIX6lUarVaWEuyLDcaDYRSWJYtFAp+\nv/9K5SloOBn2GslESZIeP34cDAZ9gk/wCeFQGFKhgUDg6szMrIGW+jUajVKpdH5+Xq/XdV3P5XKF\nQkFRFFEUnVfzdkAVNdr/O51ONpvd3t5G2xzDMMViET+ws7MDHWdaej7tgU8ZVFMO0Zn9/X1ZllHz\n5/P51tbWAoEAIYRqzU17vIuABZ9EhmF8Pl8wGBwMBp1Ox+PxqKqKaNZgMIjFYqurq5ZlIUM37cGO\nGfjukPcmhITD4VgsNlq0R2v+RFGUZTkUCsHbQ2tVMBi0bRsqw1Rv3on8AaiG7HQ6qqrC+ev1epqm\n6bouyzLP81ROd5F4DX8StOSRZVnU2pqmWalURFHkOV7wCdFoNJ1JDwYDZH6nPd6rCHrrGwwG7Xa7\nVCrVajVd1y3LisfjgUAAbH/kH735aY96bmBfEDsjLYDKokwmA98lFovJsnx2dgbSWaeqchTMhY6w\nZVntdptmD3w+H9rPUa/vUD2PC4vs/CHyl0ql1tbWTNNEbM/n89m2Xa1WS6USwzClUqnX6wWDQXQ5\nLBKwl3DE2rb9cl8Lc6H3hXYQKrVO2aco2RLFlXJlfgSYNFoaBT8bhSnI/B4dHfn9/mAwGAqFkAUm\nV8Naud3ueDyez+c1TYP5xpUD1QWmae7u7oZCIezEBYu1zwuGwyEyj6enp3t7e6qqhkIhl8vl9/tR\nEzwYDOC7g3GNcqM6eE3YF5ryMKrUkIJfDFwTk5Y2nSOAIQEkoMVisd/vJ5NJyAogI7y7uwsXkOd5\ny7JePpgcvAUW3PljWXZ9fR3XBbQ7hEKhwWDw5Zdfnp2ddbvdp0+fxuPxRCKRzWYXLxRBM2so1xsN\nRI1ac1pjQWtWKFsVzeLho5wzgMK+UO3EHSOdTq+srJimifT673//e0jIoMvv6vQ3sCy7urrq9XrB\nfYPiCtu2j4+PDw4OGo3G0dFROBwGa9fi7bjZByUiqdfrDx48+Oqrr3w+36effioIAvIAoL53uVxg\niaIamNMe+HyA+nOjRpVa3VdWtjkA/Xs8Hl9bW8P6TCQSXq/Xtm3DMKrV6n/8x38QQlCTms1mQT85\n7VHPPRbZ+QM8Hg9Kr8Dq4vP5+v0+GqzAfoJTatrDnCCo9Rm9blJ7hEg7y7LgWEc0CxJPtMODKtU6\nBouCSiQTQlCSzHGcx+NBhxoSZ6AtWOzV9QKwnEDmArcYdJIsy9oX5IgQ13FKCKYFvAjE9nRdRxGV\nx+OB59fv9xHV7vV6C28bxw5qHpFFoWrpmEYYWFyKHNoECuZCtxc6oqZpBgIBr9eL5jmYU3BIYXFO\ne7wLgkV2/uDNdDqdcrlMCEFWDvtQURR0WoVCIfAJLeQ+RP0stfX4PVQUYZIIIahK4TiuXC4rilIu\nl8EOgw4GyvsVCAQgjjLt7zQTQDNNMplsNpvITQiCEAwGCSEMwyiKQpPpV6rsb7Rqm1zI2MfjcUJI\nvV7neR5VgE7b+HQBOh5d171ebywW4zhOVVXDMFqtliiK1Wq12Wyi+C8SiaD814n8vSZQaSMIQiQS\n6XQ6mqYdHByoqoqyotPT08PDw263G4vFaEPYtIc8E7AuQAjxeDxgdUE/oiiKo4nyq2NOJ42FPcvt\nESoTlDMjCwwm3n6/j0osn8/n8/kWsqgFoT6EWHDLh2A2aEoAXLmQCocYJeR9DcMA8zNq87kLOB2a\nAO0iR0sNtGthuWjTA7mImF6dGaPVAi+4d3QGcL93SnamDmQeeZ4Ph8NgP4BZ0HW91+sh9t/v9xGm\ncs7a1wcNYsFphs4by7LdbpdhmE6n0+12+/0+muochr9R4OqIkMQLl0OqyHrVLOpEsbDOH61UQ/jd\nMAxQKxmG4XK5DMOIxWI8z+fz+UQiEQwGF+80Qpy83W6j1h4CHjiYa7XacDhEpYVpmktLS36///Dw\nUBTFRqOxt7fn8Xja7TZaWXO5XC6XQ52WE/kDEPnLZDL1ej0UClmWVavV0KeGLuBYLOZ2u2OxmM/n\nuzoFf+Ri1UmSpCgKFAL7/b7H46lWq+CSXF5ejkQi4XDYCSZNC1i9hJC1tTUkPaLRKMo8CCEwF6Dj\nWdSL8YRADx2O41ZWVhiGUVW1Uqkg8scwzPHxca1WYxhmdXUVUVVnF1BYloUmJNM0GYYJBALD4VDX\n9UajEY/H3W53IpFAz6+zIMeCRT7LaRmBIAiKojSbTYSRUYqRSqXC4XCxWIxGo2h2m/Z4xwzbtnVd\nB4MX1W5C/LxWqxmGYdt2OBwWBCGfz8MSwUfc3d21bbvT6QyHQ47jisXiysoKNVXOxiOEuFyuaDQ6\nHA5hmAzDqFQqmqZBpMg0TXAlJpNJqBJdnUlD04Asy/V6vVKpEEL6/T7HcRDB8/v9m5ubsVgMzvG0\nB3sVgSKqaDSK4tRkMommVKQF0IJjGAYSl6FQ6Eqt3ncHppfneTjWe3t7x8fH3W4XnFmlUkmSpFQq\ntb29HYvF0PbuTC8hBMUzqqqenp5Cw9fn89EKpUwm4/P5stks0uWLd1hPBYvs/BFCwF8QiUQGgwGY\nJrxeL6qbOY4Lh8MIaC1qbAa3eZq+EQQhHo+j9xmFgLhjYTvF43Gc08hgookhEonEYrF4PI5uhoWc\npbcAwzAcx/l8vnA4nE6nNU3zeDxIkOHej7QOMjtXx8uhYQ+/3y8IAvr1sJxYlg0GQ6FQMJlMRiIR\nnuedM29aQPs5wzDhcBi3QXIh9UZsMjSHuq6jhlUQBCfy96ag7nWv12s0GuCBR6YFYkuRSAS7wOl2\np8CJzPM8DiO0i1Fzmkql/H4/ZAicBTkuLLLz53a7BUFYX19Pp9OiKFYqlX6/3+v1CCHBYBCqHplM\nxuv1whROe7xjxiirC+p7tra28vk8ivzwrVG7lk6nLcv6p3/6J/C7okQSqseFQiGdTiM4upCz9HYA\n9ajb7d7a2hoOh6qqyrI8GAxQZsBxHPgICoUCEmfTHu8lAfKAa2tr4XC41Wpls1nkfBmGicfjHg8b\nDodv3rwBBsSr4xPPGtCCTQgJhUK0mdc0zVQqJctyp9PZqm+xLLuxsRGNRhf1Yjw5IN2EcycSiWSz\nWXBKEEIQwcpkMteuXYP6gLMLCCFutxtEbFBFR/KE9n9wHJdOpX0+30pxJRKJOM7fuLCwzh9zIQ6I\nUNYohRUhBKzOgiDwPI+A1uKtJ+ZCYXY4HELVl2XZQCCAC6jb7eZ5nuM4tGSi7ocQAt4HhGq8Xm80\nGkVwlKYnFm+i3gKYWyiVIZjKMEy/30evH8/z0WjU5/Nh2snVmDTmQnlTEAR4FciD0ygyx/EIiGLT\nXYU5mUHgNcHngE3A3w+HQ3iEhBA0+CPKspC2cXIY3QWEkEgkkkgkIPxDCEE2AHEHahwcEEKoOcV0\nIfML08FxXCwWEwRBEAQcQ86CHAsW1vkDcOpgYXEcB+EdQghOaEpev5CLCSnvbDZrmmYymaS0I+Qi\nFgj3DszphJBCoZBMJjVN0zSNEILkeDgcxg9cHY2K1wQOznA4vLq6SosK0MrKsiwkpH0+31U7O8Gm\njsR3LBajtC8ej4dlvRznRbTD6RyaIuiCpL+Bt+f3+72sF3UyDMNcwdU7LoBW1uPx5PP5cDjc7/dV\nVSWE4EKIZhrKEnrFgQWGa3M0GnW5XJQNCm60x+MJBoIej8fndxbkOLHgJhgRGhw2IHmhfz+K6Q5y\nQkCqNxaLUa2Ol3+AdkMzDIOfpPx/sE0IBOInp/ElZheYE1rZhn5JzCcMFm39m/ZILw+0wIDjuEAg\ngBUFBTwqG0jN96Luu3kE3gXHcV7WKwjCMPh3mkbnHb0FMGmwnF6vNxwOo2uVEMJxHIIRzi54AZgQ\nBETJiOoxTAoN+F0pczppLLjzR0byv1dt3TAXOtkgOHwlWRd+hir50psWGdl1V23eXh+jlweGYeD8\n0RDplTXrLywYKvXhlDfNOFwul83YLrfLbV/1NfzuoM4K1j/1CJ323h/CqHv3sgy9M2ljx+I7f1cZ\ncOxen6OVBkrpHyc2tMUBZonmMZ1JewFOhnde4ByxkwCmFAEt4tiH14MTcbgEOFPswIEDBw4cOHBw\nheBcyhcfb3TXdC6mbwdn3hw4cPBKOMbBwQzCifw5cODAgQMHDhxcITjOnwMHDhYECxZiWbCv48DB\nDOLK7jLH+XPgYF5xZc3Wj2Bh5mRhvsiP4/Xb0Rw4mBCuZquT4/xNFjBtlF3ZwaQxSmQ9Sus41UFN\nCnR1vc5POitwvnAV3pdjHmcWo2/kKrydq/AdX4Dj/E0c1LSBsvxHfgC4CrcQ6wKTe8TVMV72Bcby\nY3MN27axy7C65u7LvrD35278b4GrsCynBWdiXwfUXEBQ7urM2GU7f5TIEUQ+PyQ+sQB44QQCz+cr\nvbqFd/VGAXs0IW0V1wXwR2iLLeTqIiMLjPzwhYHuNfwrJn+BDRzdcSDXna+dRTcFFvDVWb1k8jaQ\n7gLwnlLVwYUE/XajxvA1MboIkTyZ36vU6wDfDhtt1FReBVwq1QtzoScmCILP52MYRlEURVEWch/a\ntt3r9XRdHwwG0PmB4M/obgSpMgTW6OUD948pjnxCgB2ht6ux+38Mw3AcN6pErKqqJEm9Xm/xzJZt\n24PBQFVVTdNYloXK3MuT6Xa7eZ6H3hrLsqZpSpIUCoUW0quwLEvXdVVVTdPkeZ7KwE97XK8LOKyw\njS6XS1EUQRAgjkclIhYDsI2qqvZ6PZwILMtC/WLsz6I2FjrmkK+UJElV1cUzs3BlNE3Dt+M4Dsbw\njXwaekB7vV63243pWlSjYdu2YRiapg2HQ7r1Fmmv/Qgu2/nDPvT5fH6/H86fLMuDwcA0TaqLdZlD\nmhAsyzJNE0fRYDDwer08z8P5e8HAwfBBAsiyrMFg0O/3F8wbptfH4XBomuZwOJyEcBycP0EQBEHg\nOM7lcsmyLIqiruvwOBdjaWEyTdM0DENVVV3XOY7z+/0cx73wBXHX4jiO+n+maYqiGAqFBoMB3sLC\nzAl2nKZpiqKYpgk7TiVBpz3AnwaVAhMEIRAI9Pt9VVV5nu/1eqZpsiw7L1/kJ4E3hdVrGAa9GE9O\n+sztdrMsi21iGMZgMJAkSZblfr8P32gBJhZu2XA47Pf7iqKoqmrbNowhVW9/nc9hGAbOH6woboyL\najRwHlFfGW7J1VGhnILzx7JsJBKJxWKKooiiyHFcu90WBCEYDHq93nn3u7GkdF2XZbnVajWbTcMw\nAoGA3+8XBIFl2dEv6HK5eJ4PBAKCIDAMY1kWglWBQACRUbIQ3jDCVIZh6Lqu63q/3/d6vZiQMfp/\nDMN4vV6cnaFQyLKsdrvN83yr1YrFYpAMn+vJpPkXwzC63W6n0xFFUVXVRCIRi8VwZ33hv7jdbjjE\n4XAYc9JoNLxeb6fTIYT4fD54FdP4NuPBqNvXbrc7nY4kSbZtR6PRWCw2L9+O7nSPxxMOh6PRaLfb\nlWXZ5XK1Wq14PB4KhXief4ss3kwBLwtX4lar1Wq1NE2DrYNtnIQfBq8a1+9oNDocDgeDQbPZjMfj\n3W7Xtu35uiS8EjRwoGlap9Npt9uiKDIME4lEwuEwDp3X/zQafg6Hw8FgcDgcwmh0u11CiM/n83g8\n8ztX5KI4BEaj1Wp1Oh1ZlqnReGUKZSFxec7faM53dXW13+8/e/Zsb29PFMUnT55IkrS0tBSPxz0e\nD8RA5/EFYFXpul6r1TqdzpMnT/b29jRNy+Vy0Wg0Go36/f7RteVyuSKRSDabPT09dbvdpmlWKpXT\n01OWZYPBIMJXCxBptyxLUZRms9lsNjudjmEYoVAol8vFYrExHmZutxumKpfLraysSJJ0cHDQaDRw\n943H48lkcn6tPOw7klbVarVare7u7p6enpqmeevWrWKxmE6nX1DRZRiGZdlQKGSaZrFYRKLt6dOn\nzWZzY2MjmUwmk8lgMDj2EOylARFQpL/Pz88bjcb+/n6pVEokEv+/vTPrbdvowjC1UCLFfRG1WFIj\nI7abGgnQ/v/7or0oEKBtnOaLi8hrJdsiRVoSN+m7eKGB4bpB7Hib6DwXQRDDITmcOXOWdw63t7eb\nzSZfcXy5XJYkqdvtBkHw119//fbbb6PR6N27d4vFot1uu65bqVSw73I6gZGXGg6Hvu+/e/fuzz//\nDMOw3W6bpum6LizeQzh/oijWajXLsra2tlRVPTk52dvbS9P05cuXjuO0Wi04NDyuApbwg6Lj5ORk\nNBq9f/9+OBzatt3v9zc3N/+ddPgMGC7DMLIs++6776bTaZqmf/zxx2g06vV6V40Gj5NQWBkN5EeP\njo5Go9HHjx+Pjo5ardbOzk6z2bwxiv4meezPuyH5h9yMLMvICQVBoKqqqqpMGMfpxEJlE+GX7/tR\nFM3n80KhoKqqYRiQUFx9NCSrmCQL25jv+5PJZDqdLhaLa9s5j2CxIcsbhiF0NhDnIZlxj9di0QUU\nKnB3JpOJ7/tQv3Fq4gGeKI5jBPdRFEGkjNV0Y14TuaJyuaxpmqZpSZJMp1PMz3K5XK1WBUHgd0ww\nteI4jqIIab/5fL5YLCqViq7ruq5zt3yKxaKiKIZh1Go1QRDyPJ9MJiiMVKvVSqXCb1oCzh9mL/Ka\n8/l8uVxqmmYYxoOuTZZ30HX98vJyOBxiIfi+jwGHpeV0FQiCgBAoCILxeDwej+M4zvO8Wq3quq5p\n2m2LaZAfIAGh63oQBDCkzGhgE+d3HqZpGsdxGIYXFxe+7ydJAskQjCS/7sdteWzjCBHSixcvRFGc\nz+dYh2/fvt3f39/Y2PA8Dwbuke/qvmAy/MFggGxEmqaNRuP169eO4ziOw84igFKpZJpmnuedTqfX\n6wVB8PHjx/F4fHZ2FoahoiiIsZ7wib4SyGnn8/nBwcHBwcFgMIC0otvtbm1ttVqt+9qesVzh+XU6\nnR9//HE4HL59+zaKor29Pd/3TdNst9u3rYA8H1jJLI7jwWBwdnYWBAHi1N3d3X6/f2PmTxAEURQV\nRXn16lWtVtvb23v//v14PP7ll180TWu1WpZl8WvsmB2fTCb7+/vT6TRJEs/zNjc3d3d3XdflK/OH\nULDT6RQKhTzPB4PBbDbb29s7Pj5ut9utVgv+H78vK8/z+Xz+6dMnJF2iKDJN8/XrN45jN5tNZOgf\n4tIsm7W7u1uv16fT6Ww2833/559/VlW10+lomvZAx00eByjFLy4uDg8PoTLXdb3f779586bdbt/q\n5NNVo/H9999Xq9L//vdhf39/NBr9+uuvmqY1m03TNLk2GkmSzOfzyWTy999/46hHu93e2tpiRoPT\nR7stj635EwShVCpZlpVlWaPRcF03iiLf9yFQnc1moijCwPFV7sSjQUkAtw9JmkqlYppmt9uFKuta\n1YYFHJZloSgZRVEcx8hdIV/IaaGHtTaEqR0MBgcHB+fn59VqVVVVuMKISu/xokw11el0RFH88OFD\nlmXQc+BcERPO8zW7hJXzN5/P4zg+OjqCpsdxHMMwGo1GvV5XFOXfg4mchyiKnudlWXZ2dvbp06c0\nTUejURiGKBUxO87jmGDbC8Pw+PgYJ6tqtVqj0Wg0Gky+w8XaYbbRMAxEjJ7nBUEQRdFsNoOii2X+\n+HpTbHbhnMfh4SG0v+VyWVW1Tqdj27aqql9emrzDDZRKpUql0mg0SqWS4zj//PNPlmXD4TAIguVy\nqSgKc/64G1tWxxyPx6enpzjFUqvVPM9rtVqu6952YJlK0vMaaZqNx+OjoyPU6yeTSZIkQRBwbTSS\nJEHm7/j4OMuySqWiqiqMhmVZ/MZXt+UJyiIoVC0Wi16v98MPP4Rh6Ps+DmNGUcSLsb4GWwmo/Mqy\nLEmS53myLPd6vU6no+s6NHzXng6SfNu2t7e3x+PxyckJNrP9/X34SVzHWEhWpWnq+z6akuzs7Oi6\n3mq1TNO83wMfwsrKa5rWbrclSdrZ2QmCIE1TdMpAlYfd2z1e93FgjXJQMa/Vaq7rGobhed5/lX2F\n1Zg4jlMoFMIwhC+O4jtqcMKV2fvIT/SVsFPkWZZZllUoFCzLMgxjc3PTdV0e106xWIQ6bWNj49Wr\nV5PJBBNYFEW09eHrcRiFVce4PM+h7bFtW5KkZrPZ63V13XiEFhuiKEJT/vLlS0EQkCcWBAHnqdm+\nw90qEK4cBdN1vVgsonz54sWLer1uGMYdbCyMhuu6hQIGKkbPhEKhAC+TvSnuhutqS2eIzm3bNk2z\n3+9blsW1nPG2PI3mD9peNCIKw/Dw8BA6JKRnkiThtK9VYdVco9lsSpKESMLzvH6/j3Yb1x4Ko1Gt\nVj3P++mnn3zf//3338/Ozi4vLz98+LBcLiGw4HEohNXejLeJhK5pmtvb22ylPcTx22KxqOt6r9dz\nHAcJP5wywWlQrnu4I4cnimK73dY0zXGcTqejKEq73WaJkxt/sVwuo5yBtGgURaenp7PZDGdjOW3f\nBROB1lGyLG9sbEiShDSS53n1eh06Wr7WDpw/URSxdi4vL4+Pj8MwhE4uTVNEMk99m3eBCe/q9bos\ny47j2Lbtuu7W1haasDyoHgOVX8dxVFXN87zZbPq+f3p6Op/PYW85bfuMVYCBVRSl1WrJstztdnVd\n73Q6zWbzmtDoyymXy42Gp+uaJEmWZUZRdHJyMpvNIN3mtBktMxrojdrtdiETgtGALou7iPHOPI0g\nGpMVMW61Wo3jeDqd4kdIyXLq/EEqK0mS4ziyLNfrddM0LctCD94brRuWriRJtm1jkxYEAT2fmTHi\n1NwDBPTowGLbdqPRMAwDjshDxPqo/EqSJAiC4zj4S6lUYu0kOfV1hJVetlKpIFS1bRvpExisz+yd\nEJMJgqDruuu6kiShzQHS7VmW8WvH0SZTURTXdWVZdl3XNE2uJVzs0JJt27Iso4qHzBm0Spx2rGS1\nVwhg6vU6pjE7i/rQV0fsJAiCYRh5nuOAHdr+lcvlNE15DAuvhkCGYbiui7FlByjv7MrAXV4ulzAa\nsiyjlQx+xLXRQCYCRqNWqzmOY5omhotTo3E3nkY+gotCrI2ueEgmTyYTZP4e/5buBZb5q9frlUpF\n0zT0dr7av/DfSxHSpSiKkiRBoH9xcXF+fo5jjEi2P8XTfBVIXWA0RFFEpxvk5CRJQhH8IZKayxVQ\nyOV5HkURjrien53neZ4v+IvvAYQ4aFujqir7iAXkBMJ/dEdarr4uiPJokiRssl1cXPAbxAM4fwi0\n4AWiqsgOjXG3dvC+cIqZ2cYgCHzfxz9y56AwSsWSKIpu3YXQGW4f7MBnJvB9wcwCEqho9pGm6fn5\nOaQp/Gb+0B9NURToXFEHwEK4m4290WhA8Dcej7ErcW000GTD8zy0AeLdaNyNp8n8sSNF+LIFvj2A\neBen1jH5OHoH7Ibh7liWhT3p2vL7ryfC0q1Wq4hFkOCJ4zgIgizLPvOLzxO2PxWLRWQ9LctCdGWa\nJmqXD1TOZh42a+KAF6EoilgWsyxbLB/pc6L3CMYTqYtyuczyJWwYP/Ms7Efo5yeKIsYE39Sp1WpX\nU6HcjQm2vWq16jgOEkv8tnIEhdW5dfhD1WoVmj/8hWPbKBSKxWJZLENTj+Y1X2Ib75HC6sNCrMFW\nlmXFYhFRIpw/7gZWEIRSqVQqldAkCHWPr/xM7Y1GA/lRhFi8Gw1RFNH0G44gxoqjB7kXnv7gGBNg\nxnGcJMnVciePsG80oXzzhSsQg4Dzzmma4jQcusbwG2AJq+PM7HtByIYWHrFN1HL1Efcsy2bT2WLJ\nX2WHwcYN6WTMtNv+JyyxhMwoFJn8jgk2OXixbMP7low4dlnYRk51aYxioVgsFWEbH+5s75fATp8s\nl8vpdIrlwPUqQDUTbt+9xz8YLowSpuI3YDSwKxVXPPVNPQFP7/wx4AI+9V3cA6yKIdw+KoINYn9y\nvcyu5jAYjy+quFrCeORLPxCfkRB8CWw6cb3hXeVrVhwXsDfF+/t6Pm+KVsGtoOH69nhGzh9xDWgB\nn/ouvhYWhq7nAiMIgiCI5wY5f8+Xb+bVkNtHEARBEM+HdSx1EwRBEARBrC2U+SMIgiAIglgjKPNH\nEARBEASxRpDzRxAEQRAEsUaQ80cQBEEQBLFGkPNHEARBEASxRpDzRxAEQRAEsUaQ80cQBEEQBLFG\nkPNHEARBEASxRpDzRxAEQRAEsUaQ80cQBEEQBLFGkPNHEARBEASxRpDzRxAEQRAEsUaQ80cQBEEQ\nBLFGkPNHEARBEASxRpDzRxAEQRAEsUaQ80cQBEEQBLFGkPNHEARBEAQEYlKbAAAAHElEQVSxRpDz\nRxAEQRAEsUaQ80cQBEEQBLFG/B9qjJ57xuK3+QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Image('./tree1.png')"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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FWzLMrKxJOoIkwTirlAkGQHr76vnA7pK+XsrnMqsEbskws7Il6bvA/wJ/JGnFKPkbWjqJ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\n/HxCFAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f37545a79b0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"5\n",
"10\n",
"inf\n",
"6\n",
"5\n",
"inf\n",
"inf\n",
"4\n",
"inf\n",
"0\n",
"5\n",
"inf\n",
"inf\n",
"inf\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAASBAMAAABRHhjUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAq7tmEHaZiUTvIlTN\nMt36g2k3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVQYGWNgYBBigAO3sAVAtjCczyC+fwOC\nA2Sx/PBA4TNwf0DlM7A/AAqwhAUwtEstDQxgYGCWfJjAwMDOMYEhQSmA5RdQkh8oyrCa7QDvhjcM\nXH+B7PUXgIQDfwALyw8GZpB5+4EYSDqATGc8AGTWgfgMB1kY2A4w8Bs4MDAoArkMLL/ZGTgLgOoK\nGBimggQ4PixmWN/AUMN8AehQkACDsAFDHwPDQmug3BewAIJgV0CwQayNPAaoAo/8UPkMplkgAQAc\nailD+c2k1gAAAABJRU5ErkJggg==\n",
"text/latex": [
"$$inf$$"
],
"text/plain": [
"inf"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"names = ['A']\n",
"\n",
"root = Node('MAX')\n",
"\n",
"root.left = Node('MIN')\n",
"\n",
"root.left.left = Node('MAX')\n",
"root.left.right = Node('MAX')\n",
"\n",
"root.left.left.left = Node('MIN')\n",
"root.left.left.right = Node('MIN')\n",
"root.left.right.left = Node('MIN')\n",
"root.left.right.right = Node('MIN')\n",
"\n",
"root.left.left.left.left = Node('MAX', value=5)\n",
"root.left.left.left.right = Node('MAX', value=10)\n",
"root.left.left.right.left = Node('MAX', value=6)\n",
"root.left.left.right.right = Node('MAX', value=5)\n",
"root.left.right.left.left = Node('MAX', value=4)\n",
"root.left.right.right.left = Node('MAX', value=0)\n",
"root.left.right.right.right = Node('MAX', value=5)\n",
"\n",
"root.show(title='initial')\n",
"\n",
"step = 1\n",
"\n",
"def alpha_beta_pruning(root, depth, player):\n",
" global step\n",
" if depth == 0 or root.is_empty:\n",
" return root.value\n",
" if player == 'MAX':\n",
" best = -inf\n",
" for child in root.children:\n",
" x = alpha_beta_pruning(child, depth - 1, 'MIN')\n",
" print(x)\n",
" best = max(x, best)\n",
" return best\n",
" else:\n",
" best = inf\n",
" for child in root.children:\n",
" x = alpha_beta_pruning(child, depth - 1, 'MAX')\n",
" print(x)\n",
" beta = min(x, best)\n",
" return best\n",
"alpha_beta_pruning(root, 4, 'MAX')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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