aflaxman/Untitled1.ipynb

## Untitled1.ipynb
{
 "metadata": {
  "name": "",
  "signature": "sha256:bfb8c8afe8ecd1343b9a918b2def12db02ee9372d966eb4f7e32e72218ad0d1b"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!date"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "From http://stackoverflow.com/questions/23198247/custom-priors-in-pymc :\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np, pymc as pm, seaborn as sns\n",
      "%matplotlib inline\n",
      "pm.__version__"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "'2.3.2'"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Code that defines the prior: p(a,b)\u221d(a+b)^(\u22125/2)\n",
      "@pm.stochastic\n",
      "def ab(power=-2.5, value=[1.,1.]):\n",
      "    if np.any(value <= 0):\n",
      "        return -np.Inf\n",
      "    return power * np.log(value[0]+value[1])\n",
      "\n",
      "a = ab[0]\n",
      "b = ab[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simulate data, so we can test\n",
      "\n",
      "N_cities = 5\n",
      "N_trials = pm.rdiscrete_uniform(10, 20, size=N_cities)\n",
      "N_yes = pm.rbinomial(N_trials, .1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theta   = pm.Beta(\"theta\", alpha=a, beta=b)\n",
      "\n",
      "# Binomials that share a common prior\n",
      "bins = dict()\n",
      "for i in xrange(N_cities):\n",
      "    bins[i] = pm.Binomial('bin_{}'.format(i), p=theta, n=N_trials[i], value=N_yes[i], observed=True)\n",
      "\n",
      "mcmc = pm.MCMC([ab, bins, theta])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(100000, 50000, 50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 3028 of 100000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 6099 of 100000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 9126 of 100000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 12161 of 100000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 15138 of 100000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           18%                  ] 18027 of 100000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 20990 of 100000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        23%                  ] 23990 of 100000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       26%                  ] 26921 of 100000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 29864 of 100000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     32%                  ] 32818 of 100000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    35%                  ] 35772 of 100000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   38%                  ] 38732 of 100000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  41%                  ] 41671 of 100000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 44%                  ] 44688 of 100000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------47%                  ] 47636 of 100000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 50572 of 100000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------53%                  ] 53466 of 100000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------56%-                 ] 56353 of 100000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------59%--                ] 59339 of 100000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------62%---               ] 62184 of 100000 complete in 10.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------65%----              ] 65074 of 100000 complete in 11.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------68%-----             ] 68019 of 100000 complete in 11.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------70%------            ] 70878 of 100000 complete in 12.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%--------          ] 73760 of 100000 complete in 12.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------76%---------         ] 76611 of 100000 complete in 13.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------79%----------        ] 79500 of 100000 complete in 13.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------82%-----------       ] 82407 of 100000 complete in 14.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------85%------------      ] 85242 of 100000 complete in 14.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------88%-------------     ] 88184 of 100000 complete in 15.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------91%--------------    ] 91105 of 100000 complete in 15.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------94%---------------   ] 94143 of 100000 complete in 16.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------96%----------------  ] 96973 of 100000 complete in 16.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------99%----------------- ] 99901 of 100000 complete in 17.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 100000 of 100000 complete in 17.0 sec"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pm.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting theta\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ab_0\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " ab_1\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAmMAAAFzCAYAAABy9g57AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXlgU1X2x7/ZurfQ0jQtlCqEnRYEERGQKpUKFrBokTIj\nDoIyyCij6A9HVrGIyzjo6IiCCGPVERcUcVqVoWjrgiIoVGSTgoVKkxYo3bck7/dH2jQveWv2lvP5\nA/reu+/e85bknpxz7jkKhmEYEARBEARBEH5B6W8BCIIgCIIgLmdIGSMIgiAIgvAjpIwRBEEQBEH4\nEVLGCIIgCIIg/AgpYwRBEARBEH6ElDGCIAiCIAg/IqqMFRUVYfLkyUhPT8emTZucjpeUlGDWrFlI\nSUnBli1bWMc2btyIjIwMTJs2DQ8//DBaWlo8JzlBEIQMysvLMWfOHGRkZGDq1KnIzc0FALz00kuY\nMGECMjMzkZmZicLCQts5GzduRHp6OiZPnoyvv/7aX6ITBNHFUQsdNJvNyMnJwdatW6HT6ZCVlYW0\ntDTo9Xpbm+joaKxYsQK7d+9mnVtWVob33nsPn376KYKCgvDggw8iLy8PM2bM8M6VEARBCKBWq7Fs\n2TIMHjwY9fX1uO222zBu3DgoFArcfffduPvuu1ntT548ifz8fOTl5cFoNOLuu+/G559/DqWSHAoE\nQXgWwW+V4uJiJCUlITExERqNBhkZGSgoKGC1iYmJQUpKCjQaDWt/REQE1Go1GhsbYTKZ0NTUBJ1O\n5/krIAiCkIBWq8XgwYMBAOHh4dDr9TAajQAArtzXBQUFyMjIgEajQWJiIpKSklBcXOxTmQmCuDwQ\nVMaMRiMSEhJs2zqdzvblJUb37t0xb9483HDDDbj++usRGRmJsWPHuictQRCEBygrK8PRo0cxfPhw\nAMBbb72F6dOnY9myZaipqQEAVFRUID4+3nZOfHy85O8/giAIOQgqYwqFwuWOz5w5gzfeeAN79uzB\nV199hYaGBuzcudPl/giCIDxBfX09Fi9ejOXLlyM8PByzZ89GQUEBPv74Y2i1Wjz99NO857rznUgQ\nBMGHoDKm0+lQXl5u2zYYDJJdjYcPH8aIESMQHR0NtVqNSZMm4aeffhI8h8pkEgThTVpbW7F48WJM\nnz4dN910EwCgR48eUCgUUCgUmDlzJn7++WcA1u8/g8FgO1fK9x99h3mX9udEEF0NwQD+5ORklJaW\noqysDHFxccjPz8f69es52zp+CfXt2xcbNmxAU1MTgoODsXfvXgwbNkxQGIVCgcrKWpmXEJhotZF0\nLQFIV7mWrnIdgPVafAHDMFi+fDn0ej3mzp1r219RUYG4uDgAwO7duzFgwAAAwMSJE/Hwww9j7ty5\nMBqNKC0tDbjvMF+/B4Eynrdk8MfnKlDuKY3n+nieQFAZU6vVWLlyJebPnw+LxYKsrCzo9Xps27YN\nAJCdnY3KykpkZWWhrq4OSqUSubm5yMvLw6BBg3Drrbfi9ttvh1KpxJAhQ3DHHXd4RGiCIAi5HDhw\nADt37sTAgQORmZkJAHjooYeQl5eHo0ePQqFQIDExEU888QQAoF+/fpgyZQoyMjKgUqmwevXqgLLK\nbNhg/WG8aNESP0tCdCXovfIPCibA7Opd6dc+XUvg0VWupatcB+A7y5iv6OpWAH+OFxcXBQCoqKjx\nyXi+wN/3lMZzfzxPQAlzCIIgCIIg/AgpYwRBEARBEH5EMGaMIAiCCEwotofwBvRe+QdSxgiCIDoh\nixYt6VKxg0RgQEqYfyA3JUEQBEEQhB8hZYwIaAJssS9BEARBeBxSxoiApaGpFfOf+QI7vzntb1EI\nIuDYsGE91qxZ428xiC7Ghg3rbXFjhO+gmDEiYCk5Z80ltOOr05g+ro+fpSGIwIJixghvQDFj/kHU\nMlZUVITJkycjPT0dmzZtcjpeUlKCWbNmISUlBVu2bGEdq6mpweLFizFlyhTccsstOHjwoOckJwiC\nIAiC6AIIWsbMZjNycnKwdetW6HQ6ZGVlIS0tDXq93tYmOjoaK1aswO7du53Of/LJJzFhwgS8+OKL\nMJlMaGxs9PwVEARBEARBdGIELWPFxcVISkpCYmIiNBoNMjIyUFBQwGoTExODlJQUaDQa1v7a2lrs\n378fWVlZAKx1LiMju1bZE8K7UOw+QfBDMWOEN6CYMf8gaBkzGo1ISEiwbet0OhQXF0vquKysDDEx\nMXjsscdw7NgxDB06FMuXL0doaKh7EhOXEaSNEQQfFDNGeAOKGfMPgpYxhULhcscmkwlHjhzB7Nmz\n8dFHHyE0NJQz5kwOv/56AkeP/gIAKC8/hxUrHpV03k8/HcDZs2c83pYgCIIgCMJdBC1jOp0O5eXl\ntm2DwQCdTiep4/j4eOh0OgwbNgwAcPPNN+O1114TPU+oAvpXX5WisbEREyaMQXNzOIKD1ZIqph8/\n/jOCglKg1Q51uS3DMLKVU09Vcw8E/HEt3c43eGX8rvJcusp1EARBXO4IKmPJyckoLS1FWVkZ4uLi\nkJ+fj/XruX3Jjsk5tVotEhIScPr0afTp0wd79+5Fv379RAUSMrm/+ebbqKmpwWef/Q9Lly7DuXMG\nLFp0P3777TT++tdHMHLkKBw7dgQbNrwIs9mM8eNTcdttM/HBB9vx6aefYceOT7Bo0WKsXr0MZrMZ\n0dExeOKJp6BUWg2Ezc1N2L79Q3z66Wf46KOdyMiYjnfeeQtqtRrjxl2P6upq7N37Nerr63HffQ/g\nmmuuRVnZWfz97+tgsVgwaNAQ/OUvf0V+/ifYtSsPzc0tuPfeRRg5cpTodQcy/nCFHD9ThYu1zbZt\nT40fCG6d748YAQDXDpH2w4aLQLgOT3E5KpWffvpfXHPNGMTGxgIAsrKmYcuWtxAV1U3S+b/+egJv\nvLEJPXv2lOxW+vHH/di27W08++zzTseeeWYtZs36I668kjuFTLu8l+Ozutyg2pT+QVAZU6vVWLly\nJebPnw+LxYKsrCzo9Xps27YNAJCdnY3KykpkZWWhrq4OSqUSubm5yMvLQ3h4OFauXIlHHnkEra2t\nSEpKwlNPPeWWsDNmZKGxsRG33TYT5eXnUF19CS+//BrOnj2DTZtexsiRo/DKK//CunXPISIiAo8+\n+hAmT74Ft9wyDYMHD8F1142HyWTC88+/DJVKhX/+8x84cOAHXHPNtQCA4OAQTJky1db2xx/3o6Gh\nHv/6l9W92tzchD/8YQ6qqi5i5cq/4ZprrsWGDS/iL3/5KwYMGASGYVBdfQkFBf/D22+/jTNnKrB0\n6YOdXhnzNafLa/DMf37ytxheY+NOq6vdHWWM6Nzk53+CPn30NmVMoVDIqjbx66/H0aNHHFavXu0R\npfzRR1cIHm+XF6B8f10dUsL8g2jS19TUVKSmprL2ZWdn2/7WarUoLCzkPHfQoEHYvn27myKysf/C\n6ttXD6VSCa02DrW11i+kkpJf8dhjDwMA6upqYTQa286znnPp0iX84x9Poba2FufPn8fAgYM4xrD+\nr1AoMHDgYNv+Tz/Nw+7dn0OhUODixQsAgMpKIwYMGGRr//vvZTh9ugRz5sxBa6sZ1dWXPHr9lwOV\nlygFCtF1+eKL3Th27CieeGIFQkJC8Mor1vyMH3zwLr755iuYzSbk5DyNpKQr0djYiOeffxanT5+C\n2WzCvHkLMGbMOGze/CpaWlqQmfkzsrPvQs+ePfHPf/4DLS3NCA4OxmOPrUZS0hWscRUKBRobG7Bi\nxaM4fboEAwcOxqpVOQCA++9fgAceWIL+/QfgqaeewPHjR6FQKJCRMR1xcTqbvBER4XjppdcQHBzs\n8/tGEF2ZTpWBX6VSw2Kx2O3piOFqV9L69x+AtWufQXh4BCwWC5RKJfbt24sjv11AdM+LOPTdZxg3\n7npMnZqJF174u9OvUbVaDYvFbOuz3YUJAB9++B7eeGMbqqouYtGiewEAcXE6nDhxzGYZ69UrEf36\n9cfWra+jsrIWJpPJS3fDdzS3mr0+hisxeQTRGbnxxpvw4Yfv4/77H2L9GOzePRpbtryFjz76AO+8\n8xYefXQFcnO3YNSo0Vi2bDVqa2uxYMGfMGrUtbj33vtw/PhRPPnkE6isrEVDQz1efvk1qFQq/PDD\n99i06WWsXfssa1yGYfDrr8fx1lvvo0ePWNx333z8/PMhpKQMt332Tpw4jvPnK5Gb+y4AoL6+DuHh\nEdi+/T3cf/9DGD/+mi7jHieIQKJTKWPJySlYu3Y1jh79BQsWLGIda/8yWbjwASxbthQMY4FGE4R1\n6/6OkSOvwUPLnsCOT7/A86sWYe3aVfjmm68QFOT8627kyGvw6qsv4cCB/Zgw4QbWsWHDrsJ9983H\n0KHJCAsLAwAsWvRXPPPMWjAMY4sZS0tLx5133gmzmUHfvv3w4IOPeOeG+IDcz47hy4Pn8NyisYiJ\nCvHKGN/8XI7X847iifmjkaiN8MoYBBFoOP4QTE2dCAAYMGAQCgv3AAD27fsO33xThHfeeRMA0Nra\nCqPRAIZhUFz8E9asWYNFi5agtrYWOTmr8fvvZ6FQKHh/BA4ePBSxsVoAQL9+A1BeXo6UlOG24716\nJeLcud/xwgt/x3XXjcfo0WN45SW6JhQz5h86lTLWs2cvbNiw2ba9du0zAICwsDC8+OKrAICBAwfh\nn//cwDovOTkFvcfeB8BqOXvjjW28YyQnp9hixABgxIirbX8/8shjtr+bW8zIeWM/Jl+bZBu7nZtv\nvgV33jmrS/yC/PLgOQDA6fJaycpYq8mC2oYWye3f2nUCgFUpmzWxv2uCEkQnw9ESHBRkTZytUilh\nNndYo5988u/o3TuJ1fbIkcNISbnKFjO2efOrGDXqGjz11HMwGMrxwAN/5hxTowmy/W0dh620RUZG\n4t//fgf79u3Fjh3bsWfP//DYY6s45SW6JqSE+QfR2pQEN4dKzuN0eQ1e2XHYI/01Npvwv/1n0dgc\nmG5NOd/D6948gEc2fIuahhZZfdMP767J+UuN+MvzRdh/rMLfogQMYWFhqK+vE203evQYfPBBx4/H\nEyeO2c5vaOhI/VJfX2+zeOXl7XRJpvYFSBaLGampE3HvvQvx66/HZclLEIRrkDIWILy751e8s/tX\nvP9lib9F4UTOb+JSo9UiWFXTLNKyre82bcxC2liXpKj4HBqbTXjlY8/8cOkK3HLLNDz33FOYN++P\naG52/JwobJ+JuXPvgclkwp/+lI05c+7A669vBACMGDEKv/12CpmZmSgo+B/+8Ie78Oqr/8K8eX9s\ni6t1/sQqFArBH1UKhQKVlZV44IGFuPvuPyAnZxX+/Of7WfLOmDGDQ16CINwlIN2Ul+qaceB4JW4Y\n0RMqZWDqi5422ZdfsP7KNV5sEGnpPQwXG/DenpO4M32A1+LDuFCSZYyXk79Xo6yiDjeM6OVvUdxG\nIUul79qkpk60xYgBwPvvd1izBg0abAt9CA4Oxv/93zKn86OiojBixFUAgLS0SQCAd9750Hb83nvv\nczpnxIirWWEXDz201Pb3Sy9ttP29ZctbvPJ2pfx2BDcUM+YfAlIZW//uQZRV1iNYo8L4YQniJ/iB\nrhjM+vp/j6DkXA00aiXuy0xmH/TiPNqu2HbFe+ou6948AMCakyw0OCA/roSfoNqUhDcgJcw/BKTZ\nqayyHgBQVUfmcF/SYrKmDTGZLU7HXLFqyDUeki7GD7lwCYIgui6iylhRUREmT56M9PR0zkLfJSUl\nmDVrFlJSUrBlyxan42azGZmZmVi4cKFnJHaBQLW4NDS14vfz9f4Wwwlf3y6bm9K3w3qUvb8YUGog\nC4UQTKd+wgRBEN5D0O9hNpuRk5ODrVu3QqfTISsrC2lpadDr9bY20dHRWLFiBXbv3s3ZR25uLvR6\nPerr5SsdnvKMBeoUsPy171Fd34IX/3q9bZ8/FUe/RfQEiJuyrrEVABARqpF1XmOzCa99cgQAsOVv\nE0VaX45QrJg3oNgewhvQe+UfBC1jxcXFSEpKQmJiIjQaDTIyMlBQUMBqExMTg5SUFGg0zhOYwWBA\nYWEhZs6c6ZJwJrMFb+06jrJKN5dUB6g2Vl1vTf3QrgQENF6NGbP+709djGEYLH3lWzz88jeylUKz\nxfuCNzYFZsoTwn8sWrQEq1ev9rcYRBdj0aIlpIj5AUFlzGg0IiGhI4Bep9PZaj1KYd26dVi6dCmr\npJAcvvnZgD0//m4LYnYVb8TbeLrLgLAd2JQi54vzpnxKB8vYhZomL47GT1OLGa0mS0Dq7s+/f8jf\nIhAEQRBeQlBLcid9wxdffIEePXpgyJAhLruf2msiNrV4vzaiP/GmorPrh7M4da5GohxtShHXMR9a\nxt7/wve51hjeDQnn+sCk1576hCAIguh6CMaM6XQ6lJeX27YNBgN0Op2kjn/66Sfs2bMHhYWFaGlp\nQV1dHZYuXYpnn31W8DytNtL2t1Kp4Nwvl1ZThzLnTj/2REVVi/YpdazomHBogqyPIihI7TEZKy42\nYFvBrwCAT/5xq2h7jUbJK0O3bmGy5YqODpd0jlrVNm4w/7V76p7w9WXvaoyNjYBKJd2aG2S36leO\nnHKvybG9J++Jp6iqbcJrOw7jzsmD0LOtzmh4mLUEjwKBKXNnhWJ7CG9A75V/EFTGkpOTUVpairKy\nMsTFxSE/Px/r16/nbOtoHViyZAmWLLE+zH379mHLli2iitjz7/yIPrqOQtH2fbqTS6eltUMZ4+vH\nZLbgyG9VGHxFd2jUKtE+q2saBfuUk//n4sV6tLZYY4JaWkweyxtUbrdSU0qfrW2pLbhkqK5ulC1X\nVVU9KoPElRpLmyLU2NjKO4an7gnfczFbOtJ5VFTW2hREKdTalX2SI6fca7JvH6j5pbbkH8XXxeU4\na6jBqrnXAADq2+4PA/7PCiEfyjNGeANSwvyDoDKmVquxcuVKzJ8/HxaLBVlZWdDr9di2zVorLTs7\nG5WVlcjKykJdXR2USiVyc3ORl5eH8PBw2cLs2X+Wte3L1ZS7fjiLD74sQdrIRPwxfYCHRvYvXLFy\nNfUtKC65gLEp8bZYrXaE7rc33ZS2mLGAjNaSR6vJAo3aqsiVnKtGeIgG8TFhoucxDIMteUcx6Ipo\njEsJzETHUmhX6Nk1Vjv/cyUIgvAmoim9U1NTkZqaytqXnZ1t+1ur1aKwsFCwj9GjR2P06NEuiugB\nJMwF7XFVx85WeVkY38EVyvTPDw7hdHkt3vjsGF568HqEBHW8AkKrGr0Z1xYYqym5/5Z0rt3f3xwu\nxw1XWUsXPZlrXXgiJd1FfZMJ3xw24JvDhk6tjAm/QwGxTIUgCCLgCMgM/DY8ZI6RsppStkLgQcXB\nGwHgvxlqUM+RMuN0udWlYbYwKDhQ5nBUwEJ1GZVDckeOpmbfLzY5da4Gb+06bnP3+pN2hYsqBnif\nDRvWY82aNf4Wg+hibNiw3hY3RvgOKnbXRqApBO5wsaYJT/x7v2i75lbnskcAfO5ValeEPaFLWCwM\nPtt3BqMGahEXLe4e5MIfb4Cjy1gOa3Otzzq5Tw9c1T9W1rlVtc34zVCDEf21Lo9vDxV99x0UM0Z4\nA4oZ8w+BbRnzEFImBn9OIgqFwmNWQJPZgmWbvpPYmn2xQiL4xMXkgZt/4EQlPviyBGtz5eWmYw3d\nSRWJFpN8q9yq17/HS9t/dj+xchuKLhT/RxAE4SsCWhnzXAC/FDelPMuYJ6caT1rjTp2rsRX8dhVO\naXwRwO+B29BezaCusZWz4Dk/jN1frgeNua6E+Ed5qW/L7N9eDcJdbFbOAHCZEgRBdBYCWhnzlAIg\nZZJvHypQ3Cv7jhrx5cHfvTqG47Uq+A54GVu8nof7XfD3L1lpTaTCMMBn35/BvqPSqk24kzDWzdM8\nh4cEaM8NGCifo64MxYwR3oBixvxDQMeMecwyJiOAP1ACj1/9+BcAsK3M8wl+WuzmyXg9x0u4VN+C\nuO6houc5Dv3eFycBAKMHS0hyzNhb1aRjtligaisV5onXLhBe3a4UexnoUMwY4Q0oZsw/BLQyZk9D\nkwlhIa6JK2VaECv91NDUirAQu2LoPpxrzBYLTGYGwRrxZLRy4JsvfT2NejO1hVKigskKGXMjtYUc\n1r97CP83e0TbmO5ffCDEaXlyMQYReGzJfQ/b95zweL+trU34c9b1mDB+rMf7JojOQEArY2wFyY1v\ndyluSoEi2R8WncJ/v/0Nj905Ev0Tu7suhwuYLRY8+upeXKxplpSvSs46AMfJWzBI34uTqzfTIbi2\nSlGeHOwcZQzrfyGOllbBbLFg3ZsHMOTKGFljehpPKXId7n7SxroiLSYzlD1SPN6vsrkezS2eiVsk\niM6IpJixoqIiTJ48Genp6di0aZPT8ZKSEsyaNQspKSnYsmWLbX95eTnmzJmDjIwMTJ06Fbm5uZ6T\nXAaS3JQ2hcD5WP7eUgBAcckFj8olhZZWCy7WNIs3dAU+yxjHfl9YXTziJXXoRHKxe7vL84RVR6ou\ncr66CafLa5HX9o65N6ifzrVD4cHFGIQwFDNGeAOKGfMPopYxs9mMnJwcbN26FTqdDllZWUhLS4Ne\nr7e1iY6OxooVK7B7925252o1li1bhsGDB6O+vh633XYbxo0bxzrXF0hzU7a1FZhF7Od1KcqJhWHw\n6Ct7cfVALbLT+kuQwhl3V0YK4XQFQoaxTjq5StfFXL9A+3eGYYC9hw147b9HJJ3b1XLScy3G6Kzv\nTqBDMWOEN6CYMf8gahkrLi5GUlISEhMTodFokJGRgYKCAlabmJgYpKSkQKPRsPZrtVoMHjwYABAe\nHg69Xo+KigrJwrEnUv5py8IwtpQGXEhaTemFX/QNTSZcqGnCrh/Oijduw3H8VpmrAWXlA+NbTcnV\n1EP3paKqAUtf+RZHSzvKTnnS6uaqcsPlanSpHwBbPz0q/QQPFv0MBJ2n3S3M5XL2Zn1TgiCIzoyo\nMmY0GpGQ0FErT6fTwWiUtuTfnrKyMhw9ehTDhg2TfI79d7fQF/mmnb9g8T+/QsWlRs7jUiZXJccv\nenfY+VUJPviyRHJ7vstrlpuawa2Ysbb9XHFzhSV47RNp1h4h8r87g/PVTdj0yS9OxyS7FGXgil4l\n103JOJmBpF+HR3PLeDesUhJKh9WUDMNwKmbNLWYcOF4hMxccQRBE10R0LvDEBFlfX4/Fixdj+fLl\nCA8Pd7s/R/YdtVrbzhhcN9fLTvoq0uy1HYdRdOicy/K0489VafVNHdbGMxV12PuLwe0+2++vO+V/\nhPDE+yo3Yalblj0P3oZAWk3Z/vl45u0f8el3Z5zavbnrOF7+6DB273esj0pIhWLGCG9AMWP+QTRm\nTKfToby83LZtMBig00nIvdRGa2srFi9ejOnTp+Omm26SJZxK3ZHKoUePCISHagRaA926hUKrjXTa\nz9j1w3UcAMLCgtr+UkAVrMHBE5W48erEtlJFABggLCzYdn5UVIebja9Pe4TaREeHQxNklVGtUbHa\ndu/eUV9RyjgXGrjdtVznhoYGsfZrgqyvg0ajRlBoEOY9vYe3n+q6ZoQGqxEkkG6je/cwp3GDgq1j\nqFRK2zG1ytpHUJCa9xqlXDsAREaGsLZjYsIR65BnjKsv+6Lq0dHhgm0dsag67kFYeLBTOg2hPnr0\niHDax9f+8wNliAoLwvQJes52kZHc778UoqJcP9ee8PBgAFZlTKuNxImyatbx9jFKztUAACpqmtwe\n83KFYsYIb0AxY/5BVBlLTk5GaWkpysrKEBcXh/z8fKxfz601O1qVGIbB8uXLodfrMXfuXNnCWexc\nGOfP16IhRFgZq6lp4vxiumDnvuT74mpqm4wtFgsefekrGC42oNxYg/TRSTYfTkNDs+38GrtJRMqX\noVCbqqp6tLZY3ZGtrWZW2wsXO2oGShnnUlWD5PEbGlpY+9vj01paTDhyspK3HwvD4J5nvkD3iCCs\nv388ryxVVQ2oDGYra41t9/n8pUbb2CZTx7h81yh1wqmtZU/uFy7UgWm1lvxhGAaxsZG4cMG5DmND\nW1kgwPquyRnX/v2qr2t2sk8ZK2p4LYEXL9Q77eMb893/WfM7XTc4jnMSrqlpdHlivnixHp99XYLk\nvj3cymfX2GhNT8AwDKcs7fssFutnu6mJP9aTIAjickFUGVOr1Vi5ciXmz58Pi8WCrKws6PV6bNu2\nDQCQnZ2NyspKZGVloa6uDkqlErm5ucjLy8PRo0exc+dODBw4EJmZmQCAJUuWYMKECbIFlbMi8nR5\nDarrW3BVv1jZ51oYwHDRqtBs23MS+l7dZMsqF4bhj4nz5ko0vnJIjO0fbtrdeJfq5OcFslfYS85V\nQ9/Ts/fX8TbaX+OKzd/DzABPLxjDJZntL7n5zhiHvx1lsFgYKFXcD9jTrkWLhUFxyQUMuqI7QoKk\npxH89PszOPl7NVKv6ok/TR7k8vjtbmKziKvXttDE/55VgiAIvyPp2zo1NRWpqamsfdnZ2ba/tVot\nCgsLnc4bNWoUjh075rJwrFQSMupL5ryxHwBsSVLlZOB3tO6dLq/xyIT5wvuHcOv4PuiTECXrPNmJ\nUOUE8Dv0reiI4Be85hNnL0nrn6MP+yFPnavxuDImJEP5BW6robVdB7Lj9FipLZxPtlgYgMfY5Gll\n+7sjBmz+71GMHKDF/bdJT85ZarRarE7+Xi3SUhh7F+3/9ktfRUzIpz2uh9xKhCeh98o/BHYGfrnR\nzbzWJem1KcV+z7tKcckFHD97Ca8sSRVvbId8Xcz7+QOe23ZQUjsu2VnKpTesIg6X74qyI2bVcUQs\nX5uQQu3JTPUMA1xsc5//eMLqZj5/qRGFh85h2tgrBeP7PCWG/QKK//GkdGlqsaZ8Acgw5g4UM0Z4\nA1LC/ENAK2NyLVK8ioib5ZA4u7RrVlXbjFJjrc0tyoepLYHr4VMXcKotgFmwYxnyuAJfz96cID21\nOpRhGEkrJ7mGa2w2wcIwCLeLQWTpiLJzW7A3Hd9DodWZnr7X3SKCWdsvbi9GWWU9woLVmDLmCn45\n2m6Au6q8lFqgj236zqbwUtkkgiAID6c58iaSvrRd18VsE3tLq/y8R8tf+w4vflCMco5gbC7Wv3cI\nO74+LalZskpRAAAgAElEQVStV+cqRyXCw+kmOMsq2bv0uMUQpdRQi/nPfIH9x5wTCDsqQrmfHUNt\nAzu27S/PF+GBF76ybZstFhjtFj5wWbIamlp530GxbPNCljZPPl8GDEKC2NavymqrBaq63jd1/6S8\nQ9UuxBoSBEF0ZQLaMmY/sUqZs/h+lctxUzqdK2HwpraVkPV2K/I8BeMQjyQ22blTKLxjv2eUBAbW\nhJ9lFXVI1EZAqVSwrUS2xKDWTamyF/xozU31TsGvGDUojnXMsY8jv1Xh/S9LcOOIXrz9bck7xsqh\n5qiMXaxpwiMbvsXVA7RobjVj/LAEjB7ckd6FS8G0R8jQ5qplqKa+BdsLS5B+TW/Wfsf3w5YR30cJ\n6+Tq82QYc52uFttz+JdfEORQxaVbt1BUVzsn8y786hvJ/V6RlIgrr+C3ChNsutp71VkIaGWMZeSQ\n9KXNs2JNwrl8qQc+LDxlG5otjnOn3khk6s05lLdrgTFXvb5P1gAFB8rwzu5fMWNCX0wbeyXbHSi9\nJxZKmS7l+sZWvP/FSd7jjslsLQ7G0TNGayqMA21xWIdPX7QpY0WHzuHfn9ovUmGcY8ZctIw1CCj3\nr+88jD37z+J8tV0qD+ehbffKXsFc8+8f0C08CA/OHM4/uIvI/QyQLuY6XSlmTBMcjgPnE3FgN3dK\nHUdek9gOAIZpT2Dp/Xe7KtplBylh/iGglTG5uhjXPNDcYkZVXbNL5wLyyhEpRZy+fBOv0LVZHKwu\nYlOdO5aGjkUM/J2UVTrn6OKVBdaFCwBQfPJ8mzLmielXYevfGzgpTwI3na2I8bkp+V3fQvfj/heK\neI9dbFPCLtgpY1w9qZTOlrFSjkoVUh9LdX0LNColwkLUsDAMDBcakNAjzGaRk+3qJtMY0UZQqPSk\nw0Gh0lelq1TSv7MIwl8EtDIm1+fB1fr/XvlWsIi48NlsPvn2N5jMFsy8sR/ncTGrgIVhBC00XDCO\npiQRMWUtehDQORyVDJdg7ALDFZ5ToDpScEgUQ+agUtKJNDS1IownCTFXnjGGYWC2MFCr2Bq7q7qI\nsl3JEulAoZSW94vhtP8689BLXwOwpo3J21uKj4pOYc7NAwXdwMLjEgRBEAEdwM+aFlwI4GcYRqIi\nJm0VGGBNjmntnKMPCZ3YzrdDyDrC1sXY7Y6fqcLfNu5FhV3wuZzJXWjc9sS37sI4zPH2FhpXFRGh\ngubcMvC341JmpMRXPb71B95jjjq5hQE27vwFC/7+JZpa2K5Hl121HBYvrv5UEpU2KTgumDjQtv1z\nm/UTkP45suFDbay8vBxz5sxBRkYGpk6ditzcXADApUuXcPfdd+Pmm2/GvHnzUFPTsdJ548aNSE9P\nx+TJk/H111/7TlgJUG1KwhtQbUr/IKqMFRUVYfLkyUhPT8emTZucjpeUlGDWrFlISUnBli1bZJ0r\nB0luSgdtjO8crslWrO6lFFSyZyIrq17fh2NnuBOpCikSz207iIqqRuR/V2p3gvRx25s+mbsfm/97\nxKU+hPtnbPKfLKvG4dMXPOOmFLCycRkn+UbM2/sb7nnmC6f9ZgkysmK17MfiWU3ZXsy+qrbZob1r\n98MWmO+wwMOxP8kB/BLE2LDjsOgpCpmfAV9axtRqNZYtW4a8vDy8++67ePvtt1FSUoJNmzZh7Nix\n+PzzzzFmzBjbd9XJkyeRn5+PvLw8bN68GWvWrLGVcQoEFi1agtWrV/tbDKKLsWjREoob8wOCypjZ\nbEZOTg42b96MvLw85OXloaSkhNUmOjoaK1aswLx582SfK4bcDPxQcLj1HKiqbcY9z36BD4tOsfZ7\nI/jeE3AsPrTB5XqS46ZsbDbh+yNGlJyrwbeHDYJKjiswDFvm9e8eYl8Px0hGntqa9tgVCpAsBxfb\nC09x7nfMMybnzdjzYxkam9lxhvaKkBQ3JZdS5Uh7fCLL0sjRX4c7U1huV5653FWw3H34Th3TarUY\nPHgwACA8PBx6vR5GoxF79uzBjBkzAAAzZszA7t27AQAFBQXIyMiARqNBYmIikpKSUFxc7DN5CYK4\nfBBUxoqLi5GUlITExERoNBpkZGSgoKCA1SYmJgYpKSnQOCxJlnKuHE6cvSQeH4OOzOMAt2vm+Nkq\nAMB/v/3NZVkA7/2id+zXcbI6WlqFNf/+gZU3qr1Jq8mM85e4LTZc7DtagY07f7Ft/3L6IoCO5LSe\nwPEZcE++HftKpJTjEZj8uRL/yk0e7I5Lrz3NCas/O03I0XrKNRYD8feLT8myv9bcz4/DbGacZPAU\n7WOxfsh0kiCwsrIyHD16FMOGDcOFCxcQG2tN2BwbG4sLF6xu14qKCsTHx9vOiY+Ph9Fo9Iu8BEF0\nbQQD+I1GIxISEmzbOp1O8i9Dd87lYuPOX9DcasaE4T152ygAHCmtcnkMd/HGj/yKqo4cOwwDPPfO\nT2BgTRnhyJNvHrClYXAHOStIhbBaeNj7WDoBw/oPCoVCUjknZftqSsmmMXnPxtOeKHuFS9JqQ0Zc\ngVS1mcbYedvAUoa+/On3DhkkKmNc4u3ef5azZmX7ZR04UYnvjxhx7RCdbF3MH4sp6+vrsXjxYixf\nvhwRERGsYwqFQvAZeToxsjtQPijCG9B75R8ElTF3vng88aXl2MfJ36sFlTHHmUTECOPQ1v1ZwRsu\nl3f3sFdfto+g5ojNEVLE/vXhz8i8vo+kMT2ljAHO90QoQaoCEq1YbZde32RCU4sJIUFqp2NCMojh\naK1y91UWWsnYXtTeHmusnXCfXDFjAL9y44617z+7f+Xcb39fN+78BdcO0cnWrnxdDqm1tRWLFy/G\n9OnTcdNNNwEAevTogcrKSmi1WlRUVCAmJgaA9QekwdCRg85gMECn03H2a49WKz1FgztQvJg0QkM1\nsp6Jr56fP8cUGs8b71UgXV+gIqiM6XQ6lJeX27alfhm5e65NODXbixoUpBa8ydHdwxAWGmTbjo2N\ncGoTGRVq+9u+r4iIEMlyabWRnO2jo8Pdfgk0GhVvH/bXExXVMX5IiPiXzY8nKnGmQprVzCzDMiQ0\nbrduYVA5PEO1uqNcT1hYELTaSFscVVCwGpGRoeDCfpywsI5n/J+Ck3j0rmts21FRzhYcjUYNhUr6\nRZ272GGN1Goj0e08dxyb1GcdZffOfSzBPR4bGymopGi1kbaYMfsfLBERwQgO4v5IqzneKy751Wql\npOvSaiOhcoh/02ojEW5XG9PxuELhPKaGR15vwDAMli9fDr1ej7lz59r2T5w4ER999BEWLFiAHTt2\n2JS0iRMn4uGHH8bcuXNhNBpRWlqKYcOGiY7jyySsXSXpqzdpbGyVfI/8cT99PSaN5/nxPIHgN2Fy\ncjJKS0tRVlaGuLg45OfnY/167iWvjpOHnHP5MDtoBQ0NLYI3ubq6AY2NHbFUXG1raxo5j9fWSY+1\nqqysRR1H+4sX6xGmds+M0tpqxolT53nHbcf+OhubpH3ZnL/kXFaECzkrxoTGrbrUgFYHK1tLa0dq\nh++Kz8Hcaoap7Tm3NJtQV8v9HPiu/cAxI/s51jhfY3OLSVbM1IdfdlgjKytrUV3NrYxJ/cBfvNhR\ns7TIznXIR2VlraAyVllZa4sZM5k67m9tbROaNSrOc5qaTE7ycslvMllQWVmLhiYTthX8iiljknhl\naHWILbR+LjpWizp+fhnGecyWFs+XEOPjwIED2LlzJwYOHIjMzEwAwJIlS7BgwQI8+OCD2L59O3r1\n6oUXXngBANCvXz9MmTIFGRkZUKlUWL16dUC5KQmC6DoIKmNqtRorV67E/PnzYbFYkJWVBb1ej23b\ntgEAsrOzUVlZiaysLNTV1UGpVCI3Nxd5eXkIDw/nPNcdxBJXOiKrtQe8JZ5yuHzwJfeqU/v+WbFV\nHvb0eDLW26kvu+0TZdU4UVaNHlHBkIN9wLjTO+FGsXh+3JuAf/ntoqz2jqtQuehwU9qdB8/FYH22\n7wy+/rnctuCFE67FBwLjc6Yd8aGXctSoUTh2jDuZ8b///W/O/QsXLsTChQu9KJXrUGwP4Q3ovfIP\noj6C1NRUpKamsvZlZ2fb/tZqtSgsLJR8rhwcv7tFs4gz4kqK59I2cE1Enum9VYKf0MWUZhKRfx0M\nYy0KrrKvCSUhRQMAXKgRL1fFR/tqQTHZ3MFdY0je3lLxRiyEY8YYhrFZxhw/E3JXjnJxurzGttq4\nvpHfcuWpYvKEa3Sl2pRE4EBKmH8I6Az8juqYmKvJ8Shn0DJfAL8MqbwN79xvJ6Tc5JpycMUy9sqO\nw7j32S9ZrisGzisTPXGf7ZWjdmWkpdWMbQW/wnDB2aXY2cofMiKrKRlwZ+AXsqhxKZSvOCRxbcd+\nUYGQIsolo2zlqpM9G4IgCG8Q2LUpHXDMNt7SakFwkF2MjMNM9MrH3JMNJx5ZTel2F9bykzwToH2J\nIm8mqXXFkrT/uDW/m335KWumBXZfnki9wZX+Yuc3v2HXD2c527tjGTt48rzLlRVcRczdyDAMVO0J\net24th8cyhtxIRQjJWe1Mm8f8poTBEF0SQLaMuY4D9gHBL/68S+4b30hahvskp86nH/4lLxYHTlw\nz0PuTy0ny6pRXdfCeey5bT/Z/ra/N1//XI5Pvjnt9tjtuKNUttgFlHNlLzUJuWDFiqAzDD4sOsUZ\nx3RWYKWosarR5Sfz4gd+yLguEjN2sqwa/2173vY/UL7+udzjqSKEdH6uklCyR+9sZssAgmpTEt6A\nalP6h05lGbOPj2n/Vf/XFzuK9zKArFhrk9mCusZWdI8I9sgvdE/NK8fPcteprG/qiN9xVDQ/+sqT\nypjrF/LP9zuUF7OFwe/n6wVacyDw/CouNfJWThBShKvrW1gVC+QQHqJ2M3xfPoxIDv5n/tOhlNu7\ngUsNtR7XbeSuHpT77pAq5joUM0Z4A4oZ8w8BrYw5TgOeKHb83ZGOcibPbTuIE2cvYf394zrdD/SD\nJ7nTX3gCd+6FvSv11DkJpY3sOHC8EgeOV/Ieb231fZHmsBDff0QYRnrcnlPSVzfHdvzMueMN5yum\nbk9n+9wRBEF4g4BWxhxnBnFdTHz13s+nLtj+PtFmgdrx1WkUHTonTzautQFdZGJxJ1u7PXJTkYjh\nKbm6Eo4/UDztpvRmbCJBEARhJbCVMQfMIslITSYGe34UT6rpiGxFjIeuskw/UHUePmWMYRg0NHkx\neaiP9RHrqkhpD8FZGRPr27sPV273vi6H1JWgfFCEN6D3yj8EtDLmuGpOzNByqd71fFWegOYV78J3\nf7cXnsKpczVeG3c/z6pD7ykS4rUpO1pKo7jkAn6vrENCbLgsSeQsJC0uOd9Ffo50DihmjPAGpIT5\nB9HVlEVFRZg8eTLS09OxadMmzjZr165Feno6pk+fjiNHjtj2b9y4ERkZGZg2bRoefvhhtLTIDKKW\naZGQU/LGHSwMjw3My8N3No+Rp3UVvueb/53cpKrSUUCBokPlnMe8pYsJh+8LI+TKLTx0TlSBdCpo\nIOOly//ujAuFwmU1JwiC6JIIKmNmsxk5OTnYvHkz8vLykJeXh5ISdqmewsJClJaWYteuXcjJycHj\njz8OACgrK8N7772Hjz76CJ988gnMZjPy8vLck1bki9vTMUp8PLH1B8793nZTdrb4HU/fj0CLGfOW\nPHLclM4n8x9SKhSiyk9ZJTtFiJxXTqmQr0QG1hMlCILwD4LKWHFxMZKSkpCYmAiNRoOMjAwUFBSw\n2hQUFGDGjBkAgOHDh6Ompgbnz59HREQE1Go1GhsbYTKZ0NTUBJ1OJ0s4x3lAbHK3X8nnTc7w5LTy\ntq7Q6YoU+8gy5i+8qfy7+i59WHSK91j5hQb868OfZfUn+52TrY0F1jPtTFCeMcIbUJ4x/yAYM2Y0\nGpGQkGDb1ul0KC5mJ8GsqKhAfHy8bTs+Ph5GoxFDhw7FvHnzcMMNNyAkJATjx4/H2LFjZQnnOA+I\nfW9/4ULwvsv4YRJRKgGYRZsFDJ68QzUNLTAFmDLmLeWwqrYZEaEal85tbuV/QexXEktFjjLmyo8F\n3ycr6TpQzBjhDShmzD8IWsakfrlyuVTOnDmDN954A3v27MFXX32FhoYG7Ny50zUpA5B6jtV73l4Z\n1tnclJ7Uxh588Wv8Y9tBz3XoAda9ecAr/b60vThgVhnKeeMUrrgpA+Q6CYIg/ImgMqbT6VBe3hG8\nbDAYnFyNcXFxMBgMTm0OHz6MESNGIDo6Gmq1GpMmTcJPP/0EOajVKta2SqWEVhsJrTZSVj/egMsd\n1K1bmFflC0Q3pdD1hrho3QkkVGr+j4js6gISOV/dhNfzj3mlb7loNNzXz/XMg4PUCAsLEuhN4XRe\n5SXxxLAEQRBdHUFlLDk5GaWlpSgrK0NLSwvy8/ORlpbGapOWloYdO3YAAA4ePIioqCjExsaiT58+\nOHToEJqamsAwDPbu3Yt+/frJEq7VweViMplRWVkbsGb5qksNXpWvsdmLubRcpLKyFqdKud1fDQ2u\nlSAKJMxCtTS9yNHfvFdXVQ51Da2c+7ne8dZWM+oF08swTufVuFimiqCYMcI7UMyYfxCMGVOr1Vi5\nciXmz58Pi8WCrKws6PV6bNu2DQCQnZ2N1NRUFBYWYtKkSQgNDcVTTz0FABg8eDBuvfVW3H777VAq\nlRgyZAjuuOMOWcI5OjAYAGUVddh/nDvvk9+5TF0umz45wrm/xdT5I4Iqqhr9LYJfqaqVnrtPIWG1\nJuE5KGaM8AYUM+YfRJO+pqamIjU1lbUvOzubtb1q1SrOc++9917ce++9bojnAAOs2rLPc/15mN+M\ntfjXRz9j8e3D/C2KTzlj5J4MvvzJhwsqCL/jSswYQRAEEeAZ+B0J9C/6j786jRaTBe8U/OpvUXxK\nU0snWuJJeIT/7D7BcyTQP6UEQRCBR2ArYw7f64G+8qo971QgBtp7i7KKOrR2AXckIY/d+8uc9nW6\n1b6dHKohSHgDeq/8Q2ArY52M9rxTl9OkdCRAAs2JwEDo95LJzGD3/rO+E6aLQzFjhDcgJcw/iNam\n9CfeLi/kadqlPeellAeByJHSKn+LQAQIUn6D/Gf35eXCJwiCkEJAK2OOulj5Bd+UO3IXoSzoXY3i\nEvlZ3YmuCa2mJAiCcI2AdlPy1YAkCCLwUCiAL2gFrc+g2B7CG9B75R8CWhkjCKLzcP5SU0AmJu6q\nUMwY4Q1ICfMPge2mJAii00CKGEEQhGuIKmNFRUWYPHky0tPTsWnTJs42a9euRXp6OqZPn44jRzqy\nsdfU1GDx4sWYMmUKbrnlFhw8GFiFngmC8BxmC6U4IQiCcAVBN6XZbEZOTg62bt0KnU6HrKwspKWl\nQa/X29oUFhaitLQUu3btwqFDh/D444/jvffeAwA8+eSTmDBhAl588UWYTCY0Nl7epWUIoivTFcpf\ndSYotofwBvRe+QdBZay4uBhJSUlITEwEAGRkZKCgoICljBUUFGDGjBkAgOHDh6Ompgbnz59HcHAw\n9u/fj2eeecY6kFqNyMhIb10HQfiUB25PwUvbf/a3GAFFLU9RccI7UMwY4Q1ICfMPgsqY0WhEQkKC\nbVun06G4uJjVpqKiAvHx8bbt+Ph4GAwGqFQqxMTE4LHHHsOxY8cwdOhQLF++HKGhoR6+BILwPSol\nhVsSBEEQnkFwRpFa1sexTJFCoYDJZMKRI0cwe/ZsfPTRRwgNDeWNOSOIzkZMdJi/RSAIgiC6CILK\nmE6nQ3l5uW3bYDBAp9Ox2sTFxcFgMDi1iY+Ph06nw7BhwwAAN998Myu4nyA6M7W1Tf4WgbjM2bBh\nPdasWeNvMYguxoYN621xY4TvEFTGkpOTUVpairKyMrS0tCA/Px9paWmsNmlpadixYwcA4ODBg4iK\nikJsbCy0Wi0SEhJw+vRpAMDevXvRr18/L10GQfgWlTJw648+POsqf4tA+IBFi5Zg9erV/haD6GIs\nWrSE4sb8gGDMmFqtxsqVKzF//nxYLBZkZWVBr9dj27ZtAIDs7GykpqaisLAQkyZNQmhoKJ566inb\n+StXrsQjjzyC1tZWJCUlsY4R4lwRH4lSAwXnBiKBXAxerQpc2QiCIAhnRDPwp6amIjU1lbUvOzub\ntb1q1SrOcwcNGoTt27e7Id7lzdTrrsTLH9GKvUBEEcDx+8oAttoRBEEQzlA5pAAmSBPAM/5ljgLe\nVXhUSgXMFteqbktdeEN0bigfFOEN6L3yD6SMyWTkAC1+PFHp9XF6xYZjaJ8Yr49DuIa39R1t91AY\nLja4dG4gu1AJz0F5xghvQEqYfyDTi0wc03h4izsm9qNJNYDx9rOZOLIXwoJd+61Erw1BEETngixj\nnZjUq3qiV2w4/rP7V3+LQoigUABy9PiQIDVuS+2Lt3adkD0WKfEE0UHpmTN4611pscsRESGoq5OW\ntqZbVCSmTUl3RzSCsEHKWICgiwmD0c4tFRctXqlAAeH4oGCNCs2tZknje8v9umD6ELy75ySq61o8\n3rc/sb/tY5Pj8e1hA39jWGPATGZ+baxbRBDrHqlVCrSYXJONAvgvDyi2Rxp13cZgz2k5Z0irEhPW\ncKxLKmP0XvmHLummvGXMFW73EdstxAOSyMDObPLkvddCJyHDu0KhEHRJ9YwNlzz8MH0PyW3lkBAT\njoSYrpet3t76dPctg8TbiyhIz98/nrWtVrn+0Qx0w1i38CB/i9AloDxjhDegPGP+oUsqY57IszQ+\nJUG8kRvMncKewC12ylhCD4lKlELYMqbvFcW5XxcdingfKUgKERndoVuE/yZ1+0uSUqdSbpJYtUop\ny61pj6/dlLeO78PaXpw1zKfjEwRBdHa6nDKmVCgQrFHxHr9CF4kkXYRgH7dN6Itp4670qFxTx7L7\n6x3HlsGViVcJfsvYTaMSMfMGPeex21P1WPqHEfIHdAEuRcxRERXj2iE6p30j+sdCI2I9mjA8Ac8/\nMF6wjSu88MB4RIRZFUGhd80euQqSq2ktAN9bxoZcGc3aHti7O26b0Bd/nDSAs/1dkwf6QiyCIIhO\ng6gyVlRUhMmTJyM9PZ230PfatWuRnp6O6dOnO9WfNJvNyMzMxMKFCz0jsQhKpQIaNf9lPXbnSNE+\nYqKCPW7NuenqRNa24+Ts0ipNBf8kP7K/Fho1t6KgUPgurkgBZ+WgR5Q8F/DMG/QIdVhZaLEwgs8Z\nsFqs5LrEpNyVqPAgdAsPwt/+OBJP/3mMpH7lWsZqG1yPsfN1zJhjzjWlQoGpY6/EoCuiOduP6K/1\nhVhdHqpNSXgDqk3pHwRnM7PZjJycHGzevBl5eXnIy8tDSUkJq01hYSFKS0uxa9cu5OTk4PHHH2cd\nz83NhV7PbaHxBkoFEMRjrZg0qrf1mIjeI5TQk09nclQWnORymCAdt10xhCggTXlwxMI4Kwdy+rnj\nRuk1RhUKjr5lCs2lGFsYIIhH2WxH6i3VdrdTDmXINqB3d3SLCJbUVsVhxeOzXAJwK8ecz5O+OgzX\nPjytI/AuFDNGeAOKGfMPgspYcXExkpKSkJiYCI1Gg4yMDBQUFLDaFBQUYMaMGQCA4cOHo6amBufP\nnwcAGAwGFBYWYubMmV4S3xmFUoEgEYuJeCf8hyw82lhjs/DSN0cLlicmKgWnpiOOxcIIus30Pblj\nzdoJC5G+CNcqo+uKHwCoOGIALRaLqGVMqu93UWaKTImcWbdgDCaN6s17vDuH0jaFZ6HJrIn9oO0e\n6nJOO18rQY7DtSuDlGKDIAhCGoKzmdFoREJCRyC7TqeD0WhktamoqEB8fLxtOz4+3tZm3bp1WLp0\nKZQSApw9hZBljIvld12NJbOGs/YJTSEuB1UrHbfZo4SHaGT3qRBwUwphsTCCbjNHy4rjEAzDSI77\n4tIX5Uqs5pDVwkBcGZNITJQ06xZgLd7ORXxMGGbf1J8VQ5Y9scOCKGdRibsqjM+VIB7LGOliBEEQ\n0hA0cUh1dzj+gmcYBl988QV69OiBIUOG4Pvvv3ddQpkolUpoe3AH6I8aGg+tNhIqu0lcp41En57d\nsP7dQ7Z9UVGh0Gq5J11NkHRFz564OLa1KdZBxphuISirrAMA3rEdCQsLQhRP/FX37mG8/YSFB0On\nY8sTGdnRj8ZBmVUoFKxnHBkZgpvHXIl/f3pMVMbYHhEIcnDhdpeQtsMenS7KydqjUitF3ZQhoUGS\n7mVsrLT7DQAPzh4p2Kf9J8H+ngYFOX/UtNpIrLtvHBpbTKw+IyJDoNVGIiLCtfQqsbHCC1T40Cd2\nQ0lZtezzYqLZq3/j4qKgUipgUXE/H602EivnX4tPik7h4K/eLy3WVaF8UIQ3oPfKPwgqYzqdDuXl\n5bZtg8EAnY69si0uLg4Gg8Gpza5du7Bnzx4UFhaipaUFdXV1WLp0KZ599lkPX4IDDIO62kbWruy0\n/hhyZTR6xYajsrIWra0W27GLF+sR4VCQW2E289Z7axZxR/Jx8UIda/vSJXbdwetT4lF80urelVpr\nrqmxFXW1zZzHqqsbePuprmnEBQd5au2yTrc6JIpVKgCL3XZNbRNn31zJT6uq6tHawu6v+hL7+YhR\ndbHeKaauudkkvvrEYpF0L1n3QsTyefFiPSqD+ZVAi52gdfUdz6aFI4NrZWUt4rsFAwhmyVlX14zK\nylrWM5FDVZVrNS1NJot4Iw4c3+UL52uhUChwsZr7OVdW1qKPNhz33ToUr+w47NKYBNWmJLwDKWH+\nQXA+S05ORmlpKcrKytDS0oL8/HykpaWx2qSlpWHHjh0AgIMHDyIqKgparRZLlixBYWEh9uzZg/Xr\n12PMmDHeV8Rgdf/ZuwAnDO+J1OE9kaiNkGTpu3aIjncVGABBP2V2Wn9+uZxixjq2F2Um4+qBcUjU\nhqOXjEStCgXQP7GbpLb2bkWumDHWogUntxP3fUu/hh0jdc/UIRwyOqff4Opu0qjeeGExdxoKLpeq\nhRGOewOAiFBh1++DM4dh3i2DZbnTxOLl7C2ICtZ+8b7bU0GMHBAr2nZAUnfe2D5vugd7acXfT66Y\nseYFWyUAACAASURBVEyHXGSA1c1MOckIgiBElDG1Wo2VK1di/vz5yMjIwC233AK9Xo9t27Zh27Zt\nAIDU1FT07t0bkyZNwqpVq9xe3ZPQIwzTHHJyyUGhULBWrs2dMgjBTq7FjpnRcZKcMCxBUGkTWvXo\nqJyw5eLfHjUoDgCwZt5oPDF/NP8ADiiVCsR2D8UrD6c6HdN2Z5f0mDC8p+1vrhxWjN09uXoAO/UA\n3/3ITusvuliCa8GDfX8zrrdO0jeM6ImoMO40FJyrKQXi3tqVMDFlbJg+FuOHJbCVJoH2C28dKqky\nAhdSgvHTrk7E64/eiNhuoaLCRIUHs7S9cDsl0dWYsT488XD2rJ57jdM+KeNxLcIgCIIgrIgui0tN\nTUVqKnuyz87OZm2vWrVKsI/Ro0dj9GhpSobZwiDEQXnq2zMKpYZaSYkwFQr5OZ3sERtBbFLdsGQC\nyirrse7NAw5yOQbFO8soZrkb2icGowfHYWu+NVYrSiDxaIxALi+LyH1Mv6Y3hul7YPlr1lg/ods5\neogOXxd3uLIfu3Mkdv1wFgeOW2OBWlotggHpU8ZcgSljrrCV/3nl4VS8vesEvv65XOAsq1LMlU/r\nxhG90LdnFL49bJBc4klqbOTowc7JZ53lsrOM2fUrNXWJVFmsCyM62tq/lq68/vdOG4KR/bX48uA5\n1v6ce67FsdIqvP0/a8FytUqJ+JgwGNrqqK6ZN5r3ffJ5io3LDIrtIbwBvVf+IeAy8FssDCaOTGQp\nVJnj+yBII01UpUIhSxkLdYj/EZszgzQq3DiyF+/xkCA1wnhyjtlb6FxJzDmwd3dcP6zDwhUdKX0V\nIAD0aFs1GB5qla/dIueIQqFglWQSmlPvupmdTb1/YndWbdBe2nDB1ZlKpYJVhzFYo8Kd6c6Z2x1v\nF2NhOO/h7Jv6Y1xKAv5v9gjOdBJijB4chz9NHogldwwXb8zBwN7deY64nlGfi2uHJrAsY/a9u6IE\nXTc0nsOCDPSKDXe69/ffloKRA7R4/v5x6B0Xwft+2O93dRUywQ/lGSO8AeUZ8w8Bp4wxDIPgIBXm\nZQzu2CkjhYOU7PL280Kcg9tJzPIVpFZiTvpAbH70Rrz80AReGaTIKRfHcyLD5KXDePQPI3F7al9b\neaGFtw7t6FvAfqV2XBXH2B9zfoXsLZhcz81+LK5RuVKTOLpdzRwxY1OuTXKpwLZ9N/MzhiD1ql5I\n7uta4fS/3NaRs8y+X0fj0X2ZyaJ9cb2JCT3C8NSfxyD92iTeJ+bpDPyOcvSMDcf9t6WIJry1Vwqj\n2ioh6KJD+ZoTBEFctkjP3ukj2icte+uWWqmUPMFIsYy1W67GJcc7HxT5Bd/uElQqFKJZ94VwJa7H\n0eIhd/zY7qHIuO7Kjv5YffOfFxcTiuuHJSD/u1LO4+sWjEGonVXFbGavyusdF4GDbStFHQfms+K8\n8MB4PPjS17bt+zKT8donR9DUYkJZZT1nzNhMGZUB7LFXDt3NXRYeosELD4xHTUOLrXbmzaN742hp\nla3NiP6xuIbHKinEgzOHo2/PKESEaqwLI+yO2d8LTyd9FbNq8T1DeznGJsejtqEFY4ZwfOYIgiAu\ncwLOMja2TUFS2WVJDQ1WS1Zerh+WIKqM3TN1CK4bqkMWRzkaUTclT54x+2BxKW4ilyxjDtshbiiD\nVhmkC8F1r9qJjwljWUlMDmagqWMdMs1LcFlFOdSU1HYPxbI5V6OX1ppDiy9mzCU8rLxEhQchURsB\nXUwYXn04FbMm9nfNTedw0jB9D/aiBLvn99e2VYmx3UI478vTfx7jlNy4ndSrenLulwrf7bN/v9Qq\nJTKuuxI9urmWO41whmpTEt6AalP6h4CyjG1ePgkKkzUfk71CFRqiFp14bxzZCxljrkB0ZDAu1nDn\n3mpH2z0U904bynlMbNIc5uC+0veMQsm5GqyZ17FAwV7SFXeNQnVdmzx2fXMF3YvicAtCJPTRP7Eb\nzle7lq/KVRwVZ8eC5WaLBZFhGtQ2tMruu098JL4/YsSAxG4eU8b4url6gBYHTlTirpsHiq7M5KPd\n5epqaSMh2sUe2Ls79L264dn7rkNkWBBUSiUyrrsCeXs7LJlx0WFOLvl2/jTZuZpCn4RIDNPHSpOd\n5/65XZaMEITyjBHegOLF/ENAKWO6mDDbF4v9UviwYDViIoNRZZfg9ApdJEqN1rbjUuKRlaq3ue3c\nm6Q7Jp7QYLVTzcnh/dg5oJbNudrZwmS32ZcjF9TEkb1cWvHZ7piKbrsXUmpE/u2PIyX17ck4o4G9\nu+PGkb1wLc/qQ7OFwXOLxqHVZOY83s4Li8c7KXZpoxIRFx2GwVdG44MvSnjOlAv3tS+akQyzhXEp\nDs2Rm0b1llSxQA7tt6b9jbWlxABwe6oeg5Ki8Y93D2LMUPFVoI6MTU5A2tWJrP555eDZH6RRYeWf\nRrm0kIIgCOJyImB/utorKyFBKiy8tSPgWds9BEv/MAKr5o7CtLFXYt4tg1nxU+7kNLI3Aiy7U1yR\n4UxRIXKORq10acVb+ynr7h2D5xaNlaQkWJOuSsgDJUMZE5uclUoF5qQPxAC7lYX2KyQtFgYatRJh\nIvU4o8KCnCxSKqUSV/WPRbBG5fFAdUcUCoVHFDHAmuetPXhdqpFMsi2Np8OhfWLwxPzRmHdLx2IY\nl9K+iGpj/H32SYiSverXWzz22GMYO3Yspk2bZtv30ksvYcKECcjMzERmZiYKCwttxzZu3Ij09HRM\nnjwZX3/9NVeXBEEQHkHSTFNUVITJkycjPT0dmzZt4myzdu1apKenY/r06Thy5AgAoLy8HHPmzEFG\nRgamTp2K3NxcyYLZT4JqlRI9uoXgwZnWuJiFtyYjNFiNK+OjMGNCXydlw608Y3YTT3t8kmy8lF+p\nvdfgIJVTHrHnFo11r285Mrvgcps4MtH2t5R8cVIQSjHCxZArBSor+ACXXNMCtD8zobuZqI1gfZbi\nJK5mtP8IuWoZCzRuv/12bN68mbVPoVDg7rvvxo4dO7Bjxw5bTsWTJ08iPz8feXl52Lx5M9asWQOL\nxbVyUd6CYsYIb0AxY/5B1M9lNpuRk5ODrVu3QqfTISsrC2lpadDrOwK6CwsLUVpail27duHQoUN4\n/PHH8d5770GtVmPZsmUYPHgw6uvrcdttt2HcuHGsc/kI54jRGaaPxZa/TRQ919UM5AA7Ez0AzLl5\nIN78/LisPrq1BZ8PSuLLOeUaQpYgoSSvUhCKC/L0ZCuWdFYq8TFhsp5P5vi+6NPrIvK+Oc3a325J\n5XIp+xOPW9A44C2nJSNJWGfJ7Tpq1CiUlZU57ed69wsKCpCRkQGNRoPExEQkJSWhuLgYV111lS9E\nlQTFjBHegGLG/IOoMlZcXIykpCQkJlotGxkZGSgoKGApVAUFBZgxYwYAYPjw4aipqcH58+eh1Wqh\n1VpL64SHh0Ov16OiokKSMuZqwDTgnjLmOLPdcFVPKADkfn4cMwVWFNoTrFHhvXUZqKlmF1B2VPTk\nkNw3BuOHJQi2GT04DvuOVmDSKP6yTHJ46s9j8HreUTw4W1rcmVQ8ZRkDnIuaC6FRK7EgMwWG83UY\nNbAjtYRSocDGR1JZZbS8gc2SJVHLcqxE4dxf2x9u3M4ls7iVC/tPUFfP1/rWW29hx44dSE5Oxt/+\n9jdERUWhoqICw4d3rD6Nj4+H0Wj0o5QEQXRlRGcfo9GIhIQOJUCn0zl9KVVUVCA+viN/UHx8PAwG\nA6tNWVkZjh49imHDpBUGDpcQnM5HcJAKqVf1xHz7xLEiLLx1KPr2jMKQPjGs/QqFAjeM6IVN/3cD\npthllhdDKB2HUIJVPpbccRVCgoTvycJbk7F56Y2YfRN/wXI+rtBZ6xJePbCjLqUuOgzL7rwaV8Rb\nLUZj2pLF9u0prTg5H55UxlpM0l1HFsaatf8vM1JsiW/b0ahV7inxUnAIuBdjXEqCoCu2QxeTfj8d\n9UBe16mM7Pn2lk77VcWdgdmzZ6OgoAAff/wxtFotnn76ad62VN6JIAhvIarxSP0Ccvy1b39efX09\nFi9ejOXLlyM8PNzxVG7BVErMSR+AHt1cy9jNtVxfiNGDdYK1Bz0VyO1tXA1q18WE4fkHxgtm9b9n\n6hBk3aB32yXqyTmt/b2TkkbBU+5RX6Fpq/bQIyqEMwi+T88o/PJbFfRuKsdcyHlE9sp17zgX4yz9\nRI8eHalqZs6cifvuuw+A9Uen/Q9Kg8EAnU7aqlStVrzguidojxejkkj+Qa1WeexZ++qdkTKeN96r\nQLq+QEVUGdPpdCgv7yjazPWlFBcXx/vF1draisWLF2P69Om46aabRAWyv4l33CzdshWIOL4Q7Qpq\naFgQ65iUF8fbL5dWGwmtVvg4AEicjzhZt2gc8r45jfSxfZxyj7nKzPRBKK2sxx/SB/Leo+kT+mJn\n0SkMG2QV3l8fVE2bFSooSC1Lhj9N4y6dNO/WFAwbEIerB+k4S0hx4eiK5ZMjMjLUdiw8PFiwfXWz\nWfB4IFNRUYG4OKvLevfu3RgwwLrqd+LEiXj44Ycxd+5cGI1GlJaWSrbq+yqGi2LG/IvJZPbIvff1\nMxQbrz1mzFMyBdr1eWM8TyCqjCUnJ6O0tBRlZWWIi4tDfn4+1q9nr7RIS0vDW2+9hYyMDBw8eBBR\nUVGIjY0FwzBYvnw59Ho95s6dK0mgrvLFwvVCMG0WhMaGFtYxKdfsrfuScd0ViO0WIti/p17u+Khg\nzJ8yCJeqGsQby+D+tjqPfDJmjr0S06+7AvW1TQgL0fjtHbttfB+sf+8gbr4m0W0ZtNpIXKpqQL/4\nSFRfkn4/TQ6lqvjkqK9rsh2rq28SbH/xYr1of0L4SoFbsmQJ9u3bh0uXLiE1NRUPPPAA9u3bh6NH\nj0KhUCAxMRFPPPEEAKBfv36YMmUKMjIyoFKpsHr16k7lptz2YR7KjFXiDWViMJYDIVd7vF+CuNwR\nVcbUajVWrlyJ+fPnw2KxICsrC3q9Htu2bQMAZGdnIzU1FYWFhZg0aRJCQ0Px1FNPAQAOHDiAnTt3\nYuDAgcjMzARg/UKcMIG7wPZlQwB9p9+eKm1RQmfH6/FgEhh0RTQ2/d+N/hZDkGuH6PD9ESP62K8s\nlREzFsg4/ogEgKysLN72CxcuxMKFC70pktc49psRZ1qu9HzHIe6VziIIghtJUfKpqam2/DvtZGdn\ns7ZXrVrldN6oUaNw7Jhns44TBOE6MZHBMF7kt6TdO20IZk3sx8qaL6ZqWbxQ6okQpz0XFKUiIDwJ\nvVf+IaDKIREE4V3umToEu344g/PVTYiJdF6IoVQonMoXiaXi0Ha3LrIZ2NuzefUIYShmjPAGpIT5\nB1LGCOIyIjoyGLMmykt90q6c9YzlXgndPSIYz98/DhECK3EJgiAIfkgZ8yHkzCE6I9cNjUdTixkj\nB/Avt+1GxcAJgiBchpQxP9AeSr4oMxmhbiS3JQhfoFQqkHZ1onhDwqdQbA/hDei98g+kCfiRUYPi\nRNs8dMdw1NS3+EAagiA6ExQzRngDUsL8AyljPqRXbDh+M9Q6BUgLkdK3h3gjgiAIgiA6LaSM+ZAH\nbh+G744YBOsNEgRBEARxeUHKmA+JjgzGlGulFxsnCILgg2J7CG9A75V/EFXGioqKsG7dOlv2/QUL\nFji1Wbt2LYqKihASEoKnn34aQ4YMkXwuQRAEIR+KGSO8ASlh/kEpdNBsNiMnJwebN29GXl4e8vLy\nUFJSwmpTWFiI0tJS7Nq1Czk5OXj88ccln0sQBEEQBHG5I6iMFRcXIykpCYmJidBoNMjIyEBBQQGr\nTUFBAWbMmAEAGD58OGpqalBZWSnpXIIgCIIgiMsdQWXMaDQiISHBtq3T6WA0GlltKioqEB8fb9uO\nj4+H0WhERUWF6LkEQRCEa2zYsB5r1qzxtxhEF2PDhvW2uDHCdwjGjCkUCqHDNsRq1xEEQXiDu+66\nC7Nnz8aUKVP8LYrPoZgxwhtQzJh/EFTGdDodysvLbdsGgwE6nY7VJi4uDgaDgdUmPj4eJpNJ9Fwu\ntNpIycIHOnQtgUlXuZauch3u8Nprr+Hdd9/FrFmzMHbsWNxzzz0ID+euoUkQBBGoCLopk5OTUVpa\nirKyMrS0tCA/Px9paWmsNmlpadixYwcA4ODBg4iKikJsbKykcwmCINzhwoULOHXqFLp16wadTod5\n8+b5WySCIAjZCFrG1Go1Vq5cifnz59vSU+j/v717D2vizPsG/g2GWitQRSCwInXFfTyUalvp87qe\nUgEjGkCpaNPnXbcqe1nXbannXmjxUDxcXbes3a2t8thqbbuyrdZDF3btJViovXqwrZhH0X2rj0Wz\nclaKBxQJ8/7hEo0QCJMMdyZ8P3+Ryczcv19yZ/Jj7jszkZHIyckBAJhMJuj1ehQWFmLChAno0aMH\nNmzY0Oa2RETu8tprr2H+/Pm2Y0u/fv0ER9R5eD0oUgL7lRjtXmdMr9dDr9fbLTOZTHaPV65c6fS2\nRETu8uSTT9oKsdzcXBiNRsERdR7OGSMlsAgTo81hSiIiT1ZYWGj7+/PPPxcYCRGRfLwdEhGpVlVV\nFfLz86HRaHjpHCJSLRZjRKRaf/rTn/CXv/wFkiRh06ZNosPpVJzbQ0pgvxLDY4Ypi4qKEB8fD4PB\ngOzsbNHhtKmsrAwzZ86E0WhEQkICdu7cCQCora3F7NmzMXHiRMyZMwd1dXW2bbZu3QqDwYD4+Hgc\nOXJEVOgOWa1WTJ06FfPmzQOg3lzq6uqQlpaGSZMmYfLkyTh+/Lgqc9m6dSuMRiMSExOxePFiNDQ0\nqCaP9PR0jBo1ComJibZlcmI/ceIEEhMTYTAYsHbt2lbbOn/+PH766SdUVVXh9ddfVy4pDzR//iKs\nWrVKdBjkZebPX8RCTACPKMbUdh9LrVaL5cuXIzc3F3/961/xwQcf4OzZs8jOzsaoUaNw8OBBjBw5\n0lZUnjlzBnl5ecjNzcW2bduwZs0aNDU1Cc7C3s6dO+1+7arWXNatW4dx48bh73//Ow4cOIABAwao\nLheLxYIPP/wQe/fuxSeffAKr1Yrc3FzV5DFt2jRs27bNbllHYm++iPTq1auxbt06fPrppygtLUVR\nUVGLtrKyspCQkACTyYSnn35a+eSIiBTgEcWY2u5jGRwcjCFDhgAAevbsicjISFRUVKCgoMB2n87k\n5GQcOnQIwO37dxqNRvj6+iI8PBwREREwm83C4r9XeXk5CgsLMX36dNsyNeZy5coVfPvtt0hJSQFw\nu2j29/dXXS5+fn7QarWor69HY2Mjbty4gZCQENXkER0djYCAALtlHYn9+PHjqKysxLVr1zBs2DAA\nwNSpU23b3C0qKgpRUVEYNGgQBg0apHBmRETK8IhizJl7YHoqi8WCU6dOYdiwYaipqUFQUBAAICgo\nCDU1NQAc37/TU6xfvx7Lli2Dj8+d7qDGXCwWCwIDA5Geno7k5GS8/PLLuH79uupy6dWrF+bMmYMn\nn3wSY8eOhb+/P0aPHq26PO7W0djvXa7T6VBZWdliv4cPH0ZiYiKmT59u989EV8B7U5ISeG9KMTxi\nAr+z98D0NNeuXUNaWhpWrFgBPz8/u+c0Gk2beXlKzocPH0afPn0wdOhQfP31162uo5ZcGhsbUVJS\ngoyMDAwbNgzr1q1rMf9QDbmcP38e7777LgoKCuDv748XX3wR+/fvt1tHDXk40l7sHZGTk4NTp07h\niSeegMViccs+1YLXGSMlcL6YGB5xZsyZe2B6mlu3biEtLQ1JSUmIi4sDAPTp0wdVVVUAbv/HHxgY\nCOB2fvfev9NT8jt27BgKCgoQExODxYsX46uvvsLSpUtVmUtoaCh0Op1taGvixIkoKSlBUFCQqnI5\nceIEHnvsMfTu3RtarRYTJkxAcXGx6vK4W0f6U/P7eO/ykJCQFvtduHAhduzYAeD2GV4iIjXyiGJM\nbfexlCQJK1asQGRkJGbNmmVbHhMTg7179wIA9u3bZyvSYmJikJubi4aGBly4cAGlpaW2gkG0RYsW\nobCwEAUFBcjKysLIkSOxceNGVeYSHByMsLAwnDt3DgDw5ZdfYuDAgRg/fryqchkwYACOHz+OGzdu\nQJIk1eZxt472p+DgYPj5+eH48eOQJAn79++3bXM3Pz8/W+HZo0ePzkuIiMiNPGKYUm33sfzuu+9w\n4MABDBo0CFOnTgVwu6iZO3cuFixYgD179qBv37626x4NHDgQkyZNgtFoRLdu3bBq1SqPHkYCoNpc\nMjIysGTJEty6dQsRERHYsGEDrFarqnIZPHgwpkyZgmnTpsHHxwdDhw7FjBkzcO3aNVXksWjRInzz\nzTeora2FXq9HWlqarP60atUqpKen48aNG9Dr9Rg3blyLtoKCgvD5559j8eLFdnMeuwJeD4qUwH4l\nhkZq/h05EZEKnT59Gk1NTRg6dKjoUACgU+dwOZoztjrrHZxv6N9pcXSWv2Xd/uc3YdE+wZEAD1w/\njTdeme/yfjp73h/bc3977uARZ8aIiOR45plnAAD19fUAbg+BEhGpDYsxIlKtXbt2Abg9j/OPf/yj\n4GiIiORhMUZEqnXy5EloNBrcunULJ0+eFB1Op+LcHlIC+5UYLMaISLV2794NAOjevTvS0tIER9O5\neJ0xUgKLMDFYjBGRakVHR9v+tlgssFgsMBqNAiMiIuo4FmNEpFrbtm3D6NGjodFocOTIEdulZoiI\n1ITFGBGp1uDBg7FkyRIAQFVVFZ599lnBEXUezu0hJbBficFijIhULTU1FRqNxuNuAaU0zhkjJbAI\nE4PFGBGp1rp162CxWNCrVy90795ddDhERLJ0rfuHEJFXWbBgAdasWYOAgAC88MILosMhIpKFZ8aI\nSLV8fHzw0EMPAQB69eolOJrOxbk9pAT2KzFYjBGRanXv3h0lJSX485//jMuXL4sOp1NxzhgpgUWY\nGCzGiEiVJElCSkoKqqurIUkS5s93/abNREQisBgjIlXSaDQ4fPgwli1bJjoUIiKXsBgjIlXav38/\n9u/fj4MHDyIwMBAA8NFHHwmOqvNwbg8pgf1KDI8qxhobrbh8+broMNyid+8HmIsH8pZcvCUPAAgO\n9pe13T/+8Q988cUX+O1vf4u33nrLzVF5Ps4ZIyWwCBPDoy5todV2Ex2C2zAXz+QtuXhLHq44f/48\ncnNzcf78eeTl5SEvL090SEREsnjUmTEiImdNnz4d1dXVmDFjBqqqqkSHQ0QkG4sxIlKlWbNmiQ5B\nKM7tISWwX4nBYoyISIU4Z0ys69b7sDprh8v7ub+7FjduNtoe11+/gsVzn0ZISIjL+5aDRZgYLMaI\niIg6yn8Azje4YT/37ONq3b9w5cpPwooxEsOjJvATERERdTWyi7H09HSMGjUKiYmJDtdZu3YtDAYD\nkpKSUFJSIrcpIiK6x5tvZmHNmjWiwyAv8+abWbZ5Y9R5ZA9TTps2DTNnzsRLL73U6vOFhYUoLS3F\np59+iuPHj2P16tX48MMPZQdKRER3cM4YKYFzxsSQfWYsOjoaAQEBDp/Pz89HcnIyAGD48OGoq6tD\ndXW13OaIiIiIvJJic8YqKysRGhpqexwaGory8nKlmiMiIiJSJUV/TSlJkt1jjUajZHNERF0GrwdF\nSmC/EkOxYiwkJMTuTFh5eTl0Ol2b2/Tv3x8//vijUiF1Orn33PNEzMXzeEseJA/njJESWISJoVgx\nFhsbi/fffx9GoxHFxcUICAhAUFBQu9t5y4HFmw6SzMXzeEseQOcVlenp6SgsLESfPn3wySefAABq\na2uxcOFCXLx4EX379sWmTZtsc2G3bt2KPXv2wMfHBy+//DLGjBnTKXESUdcje87YokWLYDKZcO7c\nOej1euzevRs5OTnIyckBAOj1evTr1w8TJkzAypUrsWrVKrcFTUTUUdOmTcO2bdvslmVnZ2PUqFE4\nePAgRo4ciezsbADAmTNnkJeXh9zcXGzbtg1r1qxBU1OTiLCJqAuQfWYsK6v965CsXLlS7u6JiNwq\nOjoaFovFbllBQQHef/99AEBycjJmzpyJJUuWID8/H0ajEb6+vggPD0dERATMZjMeffRREaG3inN7\nSAnsV2Ko6nZIP/zw/9DYeAtDhjyMsrKL2Lz5daxd+2q72x079h2CgoLRr19EJ0RJRGpRU1Njmz4R\nFBSEmpoaALd/DT58+HDbeqGhoaioqBASoyOcM0ZKYBEmhqpuh/TDD/9EScnJDm/3/fff4sKF8wpE\n1Lp7f0V672Mi8jwajabNX3zz1+BEpBRVnRnbt28P6urq8MUXn2PZsuWoqanGqlXp+PHHc3jxxSV4\n/PFonD5dgjff/BOsVivGjNHjqaem4+9//xuKig7j8OFDmD8/DatWLYfVakXv3oF45ZUN8PG5U5Me\nPfo13n33bdy8eQN6fQx+9atZuHnzBtavfwU1NdXQarXYtOlNfP/9t9i6dTMAIDk5BfHxRqxbtxo9\nevTAhQvn8atf/Rf++tfd0Gq1GD16LIzGJFEvGxE50KdPH1RVVSE4OBiVlZUIDAwEAOh0ug7/GrxZ\nZ//KtbX2unf3bXEDalKPwEA/RfuRJ/RRb2rPHVRVjCUnp6C+vh5PPTUdZWUX8dNPtdi8+b9x4cJ5\nZGdvxuOPR+Ott97A+vV/gJ+fH156aSHi4ydj8uREDBkyFL/85Rg0Njbij3/cjG7duuH111/Dd98d\nxRNP/B9bG8OGDccbb2SjqakJzz03C9OnP4MDB/Zh6NCH8fTT/9e23tatm7Fx4yY88EBPzJs3B+PH\nx0Gj0WDQoCFYtOgl/O//luD69Wt4441sES8VETkhJiYGe/fuxdy5c7Fv3z7ExcXZli9evBizZs1C\nRUUFSktLMWzYMKf22VnDhm3N7bl581anxEDKuHTpqmL9qL2hbXfPGevsoXQR7bmDqooxwH7Ib8CA\nSPj4+CA4OARXrtx+8c+e/QHp6YsBAFevXrHN82jerLa2Fq+9tgFXrlxBdXU1Bg0abLf/06dPfJpf\nrwAAGtVJREFUYfv2/0ZjYyPKy8tx+fJllJb+iISEKXbrNTVZERDwIACgb99wVFdXAQCGDBkKALbC\njIg8w6JFi/DNN9+gtrYWer0eaWlpmDt3LhYsWIA9e/bYLm0BAAMHDsSkSZNgNBrRrVs3rFq1yuOG\nKTlnjJTAOWNiqKoY69ZNe8/Py+8cHJuLtF/84j+wdu2r6NnTD01NTfDx8cE333yJpiYrAODQoX9g\n9OixSEiYik2bNraYz/WXv+zE0qXLERb2M6Sm/gqAhP79++P48e8xePAQSJL077klPvjpp1r07OkH\ni+UCgoKC7WKSJMlu+JOIxHL0C/AdO3a0unzevHmYN2+eghEREd2mqmIsKuoRrF27CqdOncTcufPt\nnmv+r3XevBewfPkySFITfH3vw/r1G/H4409gy5Y/4/vvv8WkSYlYu3Ylvvjic9x3X/cWbTz5ZCyW\nL1+CAQMGomdPPwAaJCYmY/361Xj++bm2OWPPPfc7LF26ABqNBikpT6N79+52cdwu2JR9PYiIiEj9\nNJIH/dSvf//+OHr0f0SH4RbeNHzAXDyPt+QBqHOybVs8Yc7Y6qx3cL6hf6fE0Zn+ljUVAJCwaJ/g\nSJRz9dK/sOG5kYiM/IUi++ecMfe35w6qOjNGRES3cc4YKYFzxsTgpCYiIiIigViMEREREQnEYUoi\nIhXiPQRJCexXYrAYIyJSIc4ZIyWwCBODw5REREREArEYIyIiIhKIw5RERCrEuT2kBPYrMViMERGp\nEOeMkRJYhInh0jBlUVER4uPjYTAYkJ2d3eL5S5cuITU1FVOmTEFCQgI+/vhjV5ojIiIi8jqyizGr\n1YrMzExs27YNubm5yM3NxdmzZ+3W+eCDDzB06FDs378fO3fuxKuvvorGxkaXgyYiIiLyFrKLMbPZ\njIiICISHh8PX1xdGoxH5+fl26wQHB+Pq1asAgGvXrqFXr17QajkySkTkqjffzMKaNWtEh0Fe5s03\ns2zzxqjzyK6MKioqEBYWZnus0+lgNpvt1pkxYwaeffZZjBkzBteuXcOmTZvkR0pERDacM0ZK4Jwx\nMWSfGdNoNO2us2XLFgwePBhHjhzB/v378corr9jOlBERERGRC2fGdDodysrKbI/Ly8uh0+ns1jl2\n7BjmzZsHALYhzXPnzuGRRx5xuN/gYH+5IXkc5uKZvCUXb8mDiKirk12MRUVFobS0FBaLBSEhIcjL\ny0NWlv0484ABA/Dll19ixIgRqK6uxrlz59CvX7829+stp9y9afiAuXgeb8kDYFEpF68HRUpgvxJD\ndjGm1WqRkZGB1NRUNDU1ISUlBZGRkcjJyQEAmEwmPPfcc1i+fDmSkpIgSRKWLl2KXr16uS14IqKu\ninPGSAkswsRw6aeNer0eer3ebpnJZLL9HRgYiC1btrjSBBEREZFX470piYiIiATiRb+IiFSIc3tI\nCexXYrAYIyJSIc4ZIyWwCBODw5REREREArEYIyIiIhKIw5RERCrEuT2kBPYrMViMERGpEOeMkRJY\nhInBYUoiIiIigViMEREREQnEYUoiIhXi3B5SAvuVGCzGiIhUiHPGSAkswsTgMCURERGRQCzGiIiI\niATiMCURkQpxbg8pgf1KDBZjREQqxDljpAQWYWJwmJKIiIhIIJeKsaKiIsTHx8NgMCA7O7vVdb7+\n+mtMnToVCQkJmDlzpivNEREREXkd2cOUVqsVmZmZ2L59O3Q6HVJSUhAbG4vIyEjbOnV1dXjllVfw\n9ttvIzQ0FJcuXXJL0EREXR3n9pAS2K/EkF2Mmc1mREREIDw8HABgNBqRn59vV4x98sknMBgMCA0N\nBQAEBga6GC4REQGcM+atfLppsedvhxAYWOz2fT8+fAgmxv6yzXVYhIkhuxirqKhAWFiY7bFOp4PZ\nbLZbp7S0FI2NjZg5cyauXbuGX//615g6dar8aImIiLzYAw/qcLpeB/zL/fu+1Xiy3WKMxJBdjGk0\nmnbXaWxsRElJCXbs2IH6+nqYTCY8+uij6N+/v9xmiYiIiLyK7GJMp9OhrKzM9ri8vBw6nc5undDQ\nUPTu3Rv3338/7r//fkRHR+P06dNtFmPBwf5yQ/I4zMUzeUsu3pIHycO5PaQE9isxZBdjUVFRKC0t\nhcViQUhICPLy8pCVlWW3TmxsLDIzM2G1WtHQ0ACz2YzZs2e3uV9vmf/gTXM5mIvn8ZY8ABaVcnHO\nGCmBRZgYsosxrVaLjIwMpKamoqmpCSkpKYiMjEROTg4AwGQyITIyEmPHjkVSUhJ8fHwwffp0DBw4\n0G3BExEREamdS1fg1+v10Ov1dstMJpPd49TUVKSmprrSDBEREZHX4u2QiIhUiHN7SAnsV2KwGCMi\nUiHOGSMlsAgTg/emJCIiIhKIxRgRERGRQBymJCJSIc7tISWwX4nBYoyISIU4Z4yUwCJMDA5TEhER\nEQnEYoyIiIhIIA5TEhGpEOf2kBLYr8RgMUZEpEKcM0ZKYBEmBocpiYiIiARiMUZEREQkEIcpiYhU\niHN7SAnsV2KwGCMiAhATE4OePXuiW7du0Gq12L17N2pra7Fw4UJcvHgRffv2xaZNmxAQECA6VACc\nM0bKYBEmBocpiYj+7b333sO+ffuwe/duAEB2djZGjRqFgwcPYuTIkcjOzhYcIRF5IxZjRET/JkmS\n3eOCggIkJycDAJKTk3Ho0CERYRGRl+MwJRERAI1Gg9mzZ8PHxwcmkwkzZsxATU0NgoKCAABBQUGo\nqakRHOUdnNtDSmC/EsOlYqyoqAjr169HU1MTUlJSMHfu3FbXM5vNMJlM2LRpEwwGgytNEhEpYteu\nXQgJCcGlS5cwe/ZsDBgwwO55jUYDjUYjKLqWOGeMlMAiTAzZxZjVakVmZia2b98OnU6HlJQUxMbG\nIjIyssV6f/jDHzB27NgWQwBERJ4iJCQEABAYGIgJEybAbDajT58+qKqqQnBwMCorKxEYGNjufoKD\n/ZUOtd32unf3BRo6NQxSgZ497wPgGX3Um9pzB9nFmNlsRkREBMLDwwEARqMR+fn5LYqx9957DxMn\nTsSJEydci5SISCH19fWwWq3w8/PD9evXceTIETz//POIiYnB3r17MXfuXOzbtw9xcXHt7qszz1Q5\nOjN28+atTouB1OPatdsVuif0UW9qzx1kF2MVFRUICwuzPdbpdDCbzS3Wyc/Px86dO7F8+XKPOsVP\nRNSsuroazz//PIDbZ/MTExMxZswYREVFYcGCBdizZ4/t0haegnN7SAnsV2LILsacKazWrVuHJUuW\nQKPRQJIkp4Yp1Xh60RHm4pm8JRdvycMT9OvXD/v372+xvFevXtixY0fnB+QEzhkjJbAIE0N2MabT\n6VBWVmZ7XF5eDp1OZ7fOyZMnsXDhQgDA5cuXUVRUBK1Wi9jYWIf79ZYDizcdJJmL5/GWPAAWlURE\nsouxqKgolJaWwmKxICQkBHl5ecjKyrJbJz8/3/Z3eno6xo8f32YhRkRERNTVyC7GtFotMjIykJqa\naru0RWRkJHJycgAAJpPJbUESEZE9zu0hJbBfieHSdcb0ej30er3dMkdF2IYNG1xpioiI7sI5Y6QE\nFmFi8HZIRERERAKxGCMiIiISiPemJCJSIc7tISWwX4nBYoyISIU4Z4yUwCJMDA5TEhEREQnEYoyI\niIhIIA5TEhGpEOf2kBLYr8RgMUZEpEKcM0ZKYBEmBocpiYiIiARiMUZEREQkEIcpiYhUiHN7SAns\nV2KwGCMiUiHOGSMlsAgTg8OURERERAKxGCMiIiISiMOUREQqxLk9pAT2KzFYjBERqRDnjJESWISJ\n4dIwZVFREeLj42EwGJCdnd3i+QMHDiApKQmJiYkwmUw4ffq0K80REREReR3ZZ8asVisyMzOxfft2\n6HQ6pKSkIDY2FpGRkbZ1+vXrhw8++AD+/v4oKirCypUr8eGHH7olcCIiIiJvILsYM5vNiIiIQHh4\nOADAaDQiPz/frhh77LHHbH8PHz4c5eXlLoRKRORdXnvjbfj43i9r2+7WCgDAzW66Fs9VVF8BAlwK\njboozhkTQ3YxVlFRgbCwMNtjnU4Hs9nscP3du3dDr9fLbY6IyOsc//EqtEE/l7l1mOOnAtp4jqgN\nLMLEkF2MaTQap9f96quvsGfPHuzatUtuc0REREReSXYxptPpUFZWZntcXl4Ona7l6fLTp08jIyMD\n27Ztw4MPPtjufoOD/eWG5HGYi2fylly8JQ8ioq5OdjEWFRWF0tJSWCwWhISEIC8vD1lZWXbrXLx4\nES+88AI2btyIhx56yKn9esvPtL3pJ+fMxfN4Sx4Ai0q5ogOKAQDf1j0qOBLyJpwzJobsYkyr1SIj\nIwOpqaloampCSkoKIiMjkZOTAwAwmUzYvHkz6urqsHr1ats2u3fvdkvgRERdGYswUgKLMDFcuuir\nXq9vMSnfZDLZ/l63bh3WrVvnShNEREREXo1X4CciIuoCvvtnFX69IAu3blndut/ePRqx5qXn3brP\nrobFGBGRCnHOGHVUU6+huAwA3RyvI6df3d901rXAiMUYEZEasQgjJbBfieHSvSmJiIiIyDUsxoiI\niIgE4jAlEZEKcc4YKUFOv6q9cgOb3279Djs9HrgP9dcbZMVy69ZNzJ/zX7jvvvtkba8mLMaIiFSI\nRRgpQU6/agx4GN9VuT+WG9X/xJwb9V2iGOMwJREREZFALMaIiIiIBGIxRkSkQtEBxbb5PUTuwn4l\nBueMERGpEOeMkRLYr8TgmTHyGiNGRGHEiCjRYRAREXUIizEFjBgRhf79+4sOg4iIiFSAw5Ru5MpZ\nmeZtv/vuhLvC8UhdJU8ipfE6Y6QE9isxWIwREakQvyxJCexXYnCYsgvgXCpyBfsPEZGyXCrGioqK\nEB8fD4PBgOzs7FbXWbt2LQwGA5KSklBSUuJKc16DX27UGrX2C7XGTUTkKWQXY1arFZmZmdi2bRty\nc3ORm5uLs2fP2q1TWFiI0tJSfPrpp8jMzMTq1atdjdchfiG4j7teS7W+J2qNuzPxNRKP14MiJbBf\niSF7zpjZbEZERATCw8MBAEajEfn5+YiMjLStk5+fj+TkZADA8OHDUVdXh+rqagQFBTnVhpKTvVvb\nd1efXN5Vvlzd9T53xf7SVfqIGnBuDymB/UoM2cVYRUUFwsLCbI91Oh3MZrPdOpWVlQgNDbU9Dg0N\nRXl5udPFWHuc/TKU86V575eONxSEd++7swsJZ7/E3RGXyCLekwo0T4qFiIgck12MaTQap9aTJMnp\n7SyWIxgxoqft8cWLRwDAbtnd7n6+rXVbe669Zc1/N3MUQ2vt3KZpN+679y2nPWe11V5YWC0A4Gc/\n6+swBh8foKmp4/HIeT1bi6uj7bXVho9Px/pVW885+7re2fZfLZa1166jbZrfk+bnm9m313ae7bmz\nb+dydrade3M6f15WeEREXkN2MabT6VBWVmZ7XF5eDp1OZ7dOSEgIysvL21znbs1DnhaL5d+P+7VY\n585z4XbPN/999/Ot7cfZZW21fXe8juJpa5vW1utoe3cva5lH+D3rONeenJzbWs/Z1/Pu/bgSQ3tt\ntP3et72f1p7r6GvoqN2O99Pbsfr4+DjdXtvttt6HOtpvWtv3nXXaytO+v5JzeD0oUgL7lRiyi7Go\nqCiUlpbCYrEgJCQEeXl5yMrKslsnNjYW77//PoxGI4qLixEQENDmEOWPPwJVVVcwYsRoAMDRoy2H\nV9p67t7nW1vX2WVt7bvZ7fUf/PejK3bPBQf72+Viv41zmre9M8zU9v6czaNjHrTlcm8MrbXdWlyO\nuPK6d3Tb5vfKPhelXrO2Ymg9rtvai+vOevfm0V57rT3nymehvXadfc9uLyvtcFvEL0tSBvuVGLKL\nMa1Wi4yMDKSmpqKpqQkpKSmIjIxETk4OAMBkMkGv16OwsBATJkxAjx49sGHDBrcF7sjd82OcnSvT\n0fU8dRKzJ8wN8oQYSAw57z37CxGRi1fg1+v10Ov1dstMJpPd45UrV7rShEfq6l8greXf1V+Ttnjq\na9PZ76Onvg5E5Jm63d8b6/6cg25a50uV++7rhoYGa7vrxfznLxA3fpwr4bmVR94OyZsO2kqdTfOm\n18hZcs56kj2+bt6Dc3tICZ7Ur3z9QlCFEEBqf12bm86tdrGiWlZMSvHIYswbcQhHDLW+hmqNmzqP\nJ3xZkvdhvxKjyxVj/JJTH28cOvP2fujp8yuJiDxJlyvG1M7bv8TJdZ7URzwpFiIiT6W6YowHd+/B\n95LUoKioCOvXr7f9anzu3LmiQwLgWXN7yHuwX4mhumKMiKizWK1WZGZmYvv27dDpdEhJSUFsbKzd\nPXhF4ZclKYH9Sgwf0QEQEXkqs9mMiIgIhIeHw9fXF0ajEfn5+aLDIiIvw2KMiMiBiooKhIWF2R7r\ndDpUVFQIjIiIvBGHKYmIHNBoNIru/1adBT4ym/jPn9++sOU357q5MaK2ddP6wNrYJLy9ppr/6dT2\nlOQpr2kzd/crT8uvme/AhzohGud5XDEWHOwvOgS3YS6eyVty8ZY8PJlOp0NZWZntcXl5OXQ6XZvb\ndOR9ObR3i+zYuqQdL4uOgEgRHKYkInIgKioKpaWlsFgsaGhoQF5eHmJjY0WHRURexuPOjBEReQqt\nVouMjAykpqbaLm3hCb+kJCLvopEkqSN3fSIiIiIiN+IwJREREZFALMaIiIiIBGIxRkRERCSQxxRj\nRUVFiI+Ph8FgQHZ2tuhwnFZWVoaZM2fCaDQiISEBO3fuBADU1tZi9uzZmDhxIubMmYO6ujrBkTrP\narVi6tSpmDdvHgD15lJXV4e0tDRMmjQJkydPxvHjx1Wby9atW2E0GpGYmIjFixejoaFBFbmkp6dj\n1KhRSExMtC1rK+6tW7fCYDAgPj4eR44cERFyq5w5Pq1duxYGgwFJSUkoKSnp0LbubNPRMUmp/ICW\nxwwl8wNafraLi4sVba+1z5+r7Z09exZPP/00HnnkEbzzzjsdjtVd7cnpL67mByjTZ9pqU4k+01Z7\nHe4zkgdobGyU4uLipAsXLkgNDQ1SUlKSdObMGdFhOaWyslIqKSmRJEmSrl69KhkMBunMmTPSq6++\nKmVnZ0uSJElbt26VNm7cKDLMDnnnnXekRYsWSc8995wkSZJqc1m2bJn00UcfSZIkSbdu3ZLq6upU\nmcuFCxekmJgY6ebNm5IkSdKLL74offzxx6rI5ejRo9LJkyelhIQE2zJHcf/www9SUlKS1NDQIF24\ncEGKi4uTrFarkLjv5szx6bPPPpN+85vfSJIkScXFxdL06dOd3tbdbTo6JinRVrN7jxlK5idJrX+2\nlWrP0efP1fZqamoks9ksZWVlSW+//XaHtnVnex3tL66210yJPtNWm0r0GUftyekzHnFmTM33fwsO\nDsaQIUMAAD179kRkZCQqKipQUFCA5ORkAEBycjIOHTokMkynlZeXo7CwENOnT7ctU2MuV65cwbff\nfouUlBQAty9R4O/vr8pc/Pz8oNVqUV9fj8bGRty4cQMhISGqyCU6OhoBAQF2yxzFnZ+fD6PRCF9f\nX4SHhyMiIgJms7nTY76XM8en/Px8W07Dhw9HXV0dqqqqZB/b5LZZXV3d6jGpsrJSkbaA1o8ZSubn\n6LOtVHutff7au/CvM+0FBgbikUcega+vb4e3dWd7He0vrrYHKNdnHLWpVJ9x1J6cPuMRxZi33P/N\nYrHg1KlTGDZsGGpqahAUFAQACAoKQk1NjeDonLN+/XosW7YMPj53uoYac7FYLAgMDER6ejqSk5Px\n8ssv4/r166rMpVevXpgzZw6efPJJjB07Fv7+/hg9erQqcwEc96fKykqEhoba1gsNDfWI44AzxydH\nsVdWVso6tslts7y83G6du49JSuQHtH7MUDK/1j7b9fX1irRXUVHR6udv1KhRLrfnzm3d9R3qTH9x\nR3tK9RlHlOozjsjpMx5RjCl9/7fOcO3aNaSlpWHFihXw8/Oze06j0agix8OHD6NPnz4YOnQoJAeX\nn1NLLo2NjSgpKcEzzzyDvXv3okePHi3G/NWSy/nz5/Huu++ioKAAn3/+Oa5fv479+/fbraOWXO7V\nXtyekJOzMTj6zHRmm3dvd/cxqWfPnm5vS5Ikp44Z7mxTo9E49dl2V3tA65+/AwcOuKU9d23rjs+J\ns/3F1faU7jOtUbLPtEZOn/GIYkzO/d88ya1bt5CWloakpCTExcUBAPr06YOqqioAt//jCgwMFBmi\nU44dO4aCggLExMRg8eLF+Oqrr7B06VJV5hIaGgqdTmf7D2/ixIkoKSlBUFCQ6nI5ceIEHnvsMfTu\n3RtarRYTJkxAcXGxKnMBHH82dDqd3ZkdTzkOOHN8CgkJaRF7cx+Uc2yT22bzOq0dk5Roq7VjxrJl\nyxTNz9FnW6n2Wvv8HTt2zOX23Lmtq9+hHekvrranZJ9xRKk+44icPuMRxZia7/8mSRJWrFiByMhI\nzJo1y7Y8JiYGe/fuBQDs27fPqQ4u2qJFi1BYWIiCggJkZWVh5MiR2LhxoypzCQ4ORlhYGM6dOwcA\n+PLLLzFw4ECMHz9edbkMGDAAx48fx40bNyBJkqpzARx/NmJiYpCbm4uGhgZcuHABpaWl7Q6XdAZn\njk+xsbHYt28fAKC4uBgBAQEICgqSfWxzpU1HxyR3txUcHNzqMeP3v/+9ovk5+mwr1d7Pf/7zVj9/\nrrbX7N6zQ3L6jCvtdbS/uNqekn3GUZtK9RlH7Tk6Zrepzen9neizzz6TDAaDFBcXJ23ZskV0OE47\nevSoNGjQICkpKUmaMmWKNGXKFKmwsFC6fPmy9Oyzz0oGg0GaPXu29NNPP4kOtUO+/vpr269c1JrL\nqVOnpKeeekpKTEyUfve730l1dXWqzSU7O1uaPHmylJCQIC1btkxqaGhQRS4LFy6URo8eLT388MPS\nuHHjpN27d7cZ91tvvSXFxcVJEydOlIqKigRGbq+149OuXbukXbt22dZZs2aNFBcXJyUmJkonTpxo\nc1sl23R0TFIqv2Z3HzOUzE+SWv9sK9lea58/V9urrKyUxo0bJz3++ONSdHS0pNfrpatXrzrcVqn2\n5PQXV/Nr5u4+01abSvSZttrraJ/hvSmJiIiIBPKIYUoiIiKirorFGBEREZFALMaIiIiIBGIxRkRE\nRCQQizEiIiIigViMEREREQnEYoyIiIhIIBZjRERERAL9f4UbgdiJY0hOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x636b090>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAFzCAYAAAD1x+d9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x73d2d50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How about doing this in PyMC3?  It is similar, but with little differences.  Here is the easiest way I know.\n",
      "\n",
      "(I have a fork that lets me use PyMC 2 and 3 in the same notebook: https://github.com/aflaxman/pymc)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc3 as p3\n",
      "import theano.tensor as T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with p3.Model() as m:\n",
      "    a = p3.Flat('a')\n",
      "    b = p3.Flat('b')\n",
      "    \n",
      "    m.AddPotential(-2.5 * T.log(a+b))\n",
      "    \n",
      "    theta = p3.Beta('theta', a, b)\n",
      "    \n",
      "    # Binomials that share a common prior\n",
      "    bins = {}\n",
      "    for i in xrange(N_cities):\n",
      "        bins[i] = p3.Binomial('bin_{}'.format(i), p=theta, n=N_trials[i], observed=N_yes[i])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}