{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 503 Dropout\n",
    "\n",
    "View more, visit my tutorial page: https://morvanzhou.github.io/tutorials/\n",
    "My Youtube Channel: https://www.youtube.com/user/MorvanZhou\n",
    "\n",
    "Dependencies:\n",
    "* torch: 0.1.11\n",
    "* matplotlib\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f41f8033918>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "torch.manual_seed(1)    # reproducible"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_SAMPLES = 20\n",
    "N_HIDDEN = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0rF9CpMBeMfVmWFS12F6Vh6AkXNUM7L4LXAeqisX2qjoEJWGrXmAPfSbM80UpS051iNfT\nqg5BSdiqFdhDL3Ad8EUp1KbnNQQV4kVNwlWtwB7yTFjAF6WAmw5kH4IK9aIm4apWYA95Jiy9KI2c\nP+aGzE3Q8gK1X5Q8dB1Dvp6eVO8QVOgXNQlTtQJ7yDNhB2FvB/ReA8Oto3p+R2HNMHTVclHy1HUM\n+XqaVQwXNQlPtRYoBVzgemQB9P45nDDoPgSLDyWPJyzZfqxzqh3gbaVNyNfTrKp8URN/qhXYQ73j\nAtC/FIbboP3V07e3v5ps3zbVRcljsZeAr6eZVfmiJv5UaygGgk3GPjgTbCnwU5JAfFJrsn2weaod\n4K3rWNXFTaB0SfGjeoEdgixw3Qm4OcAKYD9wGJgNLATXVEPPz3PXMdDraWZVvqiJP9UM7AE61fNr\ngvZz3tpec8+vBF3HAK+nuajqRU38qdYYe8AyTw8EPL8Qg5MXtRXpo063NJJ67AHJ3PNT11GkEhTY\nA5N5OKOq4yEiFaKhGBGRyKjHLtOjalYipVfJwK7YVCdVsxIJQuUCu2JTnVTNSiQYlRpj142JM/BY\nkkBEpqdSgV2xKQNVsxIJRqUCu2JTBqpmJRKMSgV2xaYMqlyiUSQwlQrsik0ZqCSBSDAqlRWTW6W9\nquZLqiSBSBAqFdghh9i0F0buhv45cHAOdL4OS78DLTdTjXxJlSQQKb3KBXbIEJtGYO966P1LGJ43\nqsd/CNash65/Qb1XEfGuUmPsWY08C72Xw4nWMfcdbU22H+v33UIRkYyB3cw+amb9ZnbCzHryalRZ\n9R+F4TOh/ejp29vT7dtGatvPCLAF2Jg+1vhtIiI1yToUsw34CPDfObSl9A52gv1u/OfMwWAN+ZIq\naSAijZapx+6c2+6cey6vxpRd52JwM4EjY544kmzv6J78+1XSQESKoDH2aVg6E9ouhKHZJF3u9GNo\ndrJ9WfPk36+SBiJShCmHYszsMeAd4zx1h3Pu4VoPZGargdUAXV1hDjq0AGvOgt4rYferYCPgWqBt\nPqxpmjohRiUNRKQIUwZ259w1eRzIObcOWAfQ09Mz0cr+0usC1jbBts7p58GrpIGIFKGSeexZ1ZsH\nP7qkwejhGJU0EJE8ZU13vNHMBoDLgUfN7Ef5NCtOKrciIkXI1GN3zv0Q+GFObakElVsRkUYLdigm\n5DpcKrciIo0UZGDXIh8RkYkFl8euRT4iIpMLLrBrkY+IyOSCC+xa5CMiMrngArsW+YiITC64wK77\nloqITC64wB7FIh8VZBeRBgoy3THoRT7K1RSRBgsysEOgi3zG5mqeNJRuX0sgVycRKbPghmKCplxN\nESmAAnuRlKspIgVQYC+ScjVFpAAK7EVSrqaIFECBvUhR5GqKSNkFmxUTrKBzNUUkBArsPgSZqyki\nodBQjIhIZBTYRUQio8AuIhIZBXYRkcgosIuIREaBXUQkMgrsIiKRUWAXEYmMAruISGQU2EVEIqPA\nLiISGQV2EZHIhFsEbITkVnMHSW5gsZSkLK6ISMWFGdj3ktz8eZjklnKO5EYVa0jK4oqIVFh4QzEj\nJEH9BNANLE4fT6Tbj/lqmIhIOYQX2PtJeurtY7a3p9u3Fd4iEZFSCS+wHyQZfhmPkdyVSESkwjIF\ndjO7y8x2mNmvzeyHZtaWV8Mm1Ekypj4eR3KrORGRCsvaY98ELHPOvQ/YCdyevUlTWEoyUTo0ZvtQ\nun1Zw1sgIlJqmQK7c26jc+54+uXTwKLsTZpCC0n2ywxgN7AnfZyRbtdNoUWk4vJMd/w74Ps57m9i\nXcBakonSQZLhl2UoqIuIUENgN7PHgHeM89QdzrmH09fcARwHvjPJflYDqwG6unJINp8JXJJ9NyIi\nsZkysDvnrpnseTP7DPAXwNXOuYmmNXHOrQPWAfT09Ez4OhERySbTUIyZrQT+Gfgz59zhfJokIiJZ\nZM2K+S9gLrDJzLaa2X05tElERDLI1GN3zr07r4aIiEg+wlt5KiIik1JgFxGJjAK7iEhkFNhFRCKj\nwC4iEhkFdhGRyCiwi4hERoFdRCQyCuwiIpFRYBcRiYwCu4hIZBTYRUQio8AuIhIZBXYRkcgosIuI\nREaBXUQkMgrsIiKRsUnuP924g5odAPbktLtO4GBO+4qZzlNtdJ5qp3NVmzzP02Ln3IKpXuQlsOfJ\nzPqccz2+21F2Ok+10Xmqnc5VbXycJw3FiIhERoFdRCQyMQT2db4bEAidp9roPNVO56o2hZ+n4MfY\nRUTkdDH02EVEZJTgAruZfdTM+s3shJlNONNsZivN7Dkze97MbiuyjWVgZu1mtsnMdqWP8yd43Ztm\ntjX9eKTodvoy1d+HmbWY2ffT539hZt3Ft9K/Gs7TZ8zswKi/ob/30U7fzGy9me03s20TPG9mdk96\nHn9tZpc0sj3BBXZgG/AR4MmJXmBmTcBXgVXAe4FPmNl7i2leadwG/Ng5dwHw4/Tr8Rxxzi1PP64r\nrnn+1Pj38VngVefcu4H/BP6j2Fb6N4330fdH/Q3dX2gjy+MbwMpJnl8FXJB+rAbubWRjggvszrnt\nzrnnpnjZpcDzzrnfOueOAd8Drm9860rleuCb6effBG7w2JayqeXvY/T5exC42syswDaWgd5HNXLO\nPQkMTfKS64FvucTTQJuZndOo9gQX2Gt0HrBv1NcD6bYqOds593L6+e+Asyd4XauZ9ZnZ02ZWleBf\ny9/Hqdc4544Dh4COQlpXHrW+j/4qHV540MzeWUzTglNoTDqjUTvOwsweA94xzlN3OOceLro9ZTXZ\neRr9hXPOmdlE6U+LnXMvmtm7gJ+Y2W+ccy/k3VaJ1v8C33XOjZjZTST/5XzIc5sqr5SB3Tl3TcZd\nvAiM7jksSrdFZbLzZGavmNk5zrmX03/59k+wjxfTx9+a2RPAxUDsgb2Wv4+TrxkwszOAecBgMc0r\njSnPk3Nu9Dm5H1hbQLtCVGhMinUo5pfABWa2xMxmAh8HKpPxkXoE+HT6+aeBt/2nY2bzzawl/bwT\nuAJ4trAW+lPL38fo8/fXwE9c9RZ9THmexowTXwdsL7B9IXkE+Ns0O+Yy4NCoodL8OeeC+gBuJBmf\nGgFeAX6Ubj8X2DDqddcCO0l6n3f4breH89RBkg2zC3gMaE+39wD3p5//CfAb4P/Sx8/6bneB5+dt\nfx/AvwHXpZ+3Aj8AngeeAd7lu80lPU//DvSnf0OPA3/ku82eztN3gZeBN9L49Fngc8Dn0ueNJMPo\nhfS91tPI9mjlqYhIZGIdihERqSwFdhGRyCiwi4hERoFdRCQyCuwiIpFRYBcRiYwCu4hIZBTYRUQi\n8/93Ljvg2d5oywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a7abbf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# training data\n",
    "x = torch.unsqueeze(torch.linspace(-1, 1, N_SAMPLES), 1)\n",
    "y = x + 0.3*torch.normal(torch.zeros(N_SAMPLES, 1), torch.ones(N_SAMPLES, 1))\n",
    "x, y = Variable(x), Variable(y)\n",
    "\n",
    "# test data\n",
    "test_x = torch.unsqueeze(torch.linspace(-1, 1, N_SAMPLES), 1)\n",
    "test_y = test_x + 0.3*torch.normal(torch.zeros(N_SAMPLES, 1), torch.ones(N_SAMPLES, 1))\n",
    "test_x, test_y = Variable(test_x, volatile=True), Variable(test_y, volatile=True)\n",
    "\n",
    "# show data\n",
    "plt.scatter(x.data.numpy(), y.data.numpy(), c='magenta', s=50, alpha=0.5, label='train')\n",
    "plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='cyan', s=50, alpha=0.5, label='test')\n",
    "plt.legend(loc='upper left')\n",
    "plt.ylim((-2.5, 2.5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net_overfitting = torch.nn.Sequential(\n",
    "    torch.nn.Linear(1, N_HIDDEN),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(N_HIDDEN, N_HIDDEN),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(N_HIDDEN, 1),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "net_dropped = torch.nn.Sequential(\n",
    "    torch.nn.Linear(1, N_HIDDEN),\n",
    "    torch.nn.Dropout(0.5),  # drop 50% of the neuron\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(N_HIDDEN, N_HIDDEN),\n",
    "    torch.nn.Dropout(0.5),  # drop 50% of the neuron\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(N_HIDDEN, 1),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sequential (\n",
      "  (0): Linear (1 -> 300)\n",
      "  (1): ReLU ()\n",
      "  (2): Linear (300 -> 300)\n",
      "  (3): ReLU ()\n",
      "  (4): Linear (300 -> 1)\n",
      ")\n",
      "Sequential (\n",
      "  (0): Linear (1 -> 300)\n",
      "  (1): Dropout (p = 0.5)\n",
      "  (2): ReLU ()\n",
      "  (3): Linear (300 -> 300)\n",
      "  (4): Dropout (p = 0.5)\n",
      "  (5): ReLU ()\n",
      "  (6): Linear (300 -> 1)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "print(net_overfitting)  # net architecture\n",
    "print(net_dropped)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "optimizer_ofit = torch.optim.Adam(net_overfitting.parameters(), lr=0.01)\n",
    "optimizer_drop = torch.optim.Adam(net_dropped.parameters(), lr=0.01)\n",
    "loss_func = torch.nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ntR9+cGsQkmVCgkWLJJeMyQ8/iMNzVsybJ5omSByuw4ft87blhMuXxTP87FnZ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\nfGtTtsJyzrWZ9HGTpY+3FExXcFHBZWU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xkTYPVygxM7PSKetlSTMza2JObmZm\nVjpObmZmVjpObmZmVjpObmZmVjpObmZmVjpObmZmVjpObmZmVjr/B9CwJ2pOgtodAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a025ffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rpfYrpU4mKfXrWqUef1wpf3+VDOoywWov9dQqOqpdhCnVooVS8+Ypdfu2uqyU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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a7a476d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RCSVPCFYT8ib7eOdLRGVUn9bTvxyDwVAsKArq+H5AvXw+hyFjvFccmF+OwWDIALtSdd00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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a0259240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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s9nG33w779mVvGTApSZYiL16U62XL4L6uolKagEjrithPBxISxKzF7NMyKkoe\n5HLQWFvbuXmOnrlpcpYtW6znTZo4q0VXqiRP3d9+K9cTJ9rfdLOAUiJwzMLI8ejZU1aibImKEufw\nV65kHEuzX1sIvx/LvycoSO6NnhK7CEJvwzL7KltWxlO2rBzh4abXACh7GspGQngpKFsKIkIhsEgK\nzPkMhoyC6wlUBj7hdXmIGD9elnvTu9EHBsrSWZky8OmnkrZ2rbjHWr7c3krZFceOwSefWK8/+shJ\nKJqjHC1D9tgcAxJYbjwDB8I778gXdviwaByaHSynh+2SZP/+2d/fKlpUxvLxx3I9dTpc6pp+NIWh\nQ62CLShI1P61F5J8gxZumpzF0QTAFcOHW4Rb8rwfSBh5hoTQyiQk4PJo1sxZw3rgQHlovnxZBFRa\nOgEHqld3Fm5mwecJl1choWRMNzo/PzHmvXZNDH3tjlAoEwulgyCsrElA3Y7VY39/mVmZ75F2uNq4\nOrQNPh8Mx3bZl336aREyGQkmM35+osQTHm61Qv7zT/Eis3o1VKnivu7rr1s93TdrBo8+6rKYOV5n\nDLLHVhLnyQ/BwbIkaBaWEydmLNyuXrV3ut23b/rlPeW556zCbeXP0DkGIm0+/KtYvjMWzRPnz2am\nTnX+UWnyFC3cNDmL7X5by5ZMny6rk089ZVOmSROer7CEWefu41ZqUcjANOijj5yF29mzopPiCZcv\nO6eVLi0TEpD7bViYpIWFQlgChJU0XQdB9QZYw8aY1tdOnZK9LacJxClgKRJqxhFz4FZ3ltTmjavU\nFIg5DMs+gxVf2E8t69WDL76ANm08e/O2GIbMmsqWlb0upWRZsGVLEXDm+Gu2/PKLLF+amTw53WVE\nc7zOdHnpJRFqaWnS/p494mDZHT/9ZJ0qN24s4XS8Qe3a0LYt/PYbpKXCtpkQ+bY1PwT5zv44YR9V\nYMAAePxx74xB4zW0cNPkHMnJsG2b5XLVrfYMGiQPyHbCDTDubMitc0U9atbVDCsszP66ZElJc3U0\naOBcf/FiWZkKDXVwUOGhcHLrhCIznvnT0kRtcu9e+Ptv+Otv2Pw3nDsAKQ4xwQKLweh3YcRr2V8K\nGzxYJPdjj8l3dvo0tGolS5R33y2zzBjgSgq8OMxa7/HHs65+b0tkJPTqBQsXyvWkSfDVV+7LO2pJ\nepNBg0S4Aaz+H/R+00F4p8BLA2SaDrIM8MUXWu0/H6KFmybniI62allERvLBF6JYcuWKOLC1DX4c\nVK8arAQ7LEPhAAAgAElEQVQ/UgkmnqCQAILKBxEUhOUoGQSUhIimInNsl7g++gjGjhXhFRqa+fu9\nW9eW2Q0b40ptUCm4HAN/74Uzf8PZv0WY7d0rWoAZcUcXmPkZNKmRcVlP6dNHPryePeH6dVHz7NAB\nZi+G651k72njl3DwbylfsqR3XaYNG2YVbnPmSNsREc7lLl6ENWus195akjTTqxeEloYrl+HCCdi9\nFhrfZ81f+j5Em/aR/f3hu++gVCnvjkHjFbRw0+QcNvttG2s+xaa1cr5ggb0+AsD7Yw0+qPYlRV95\nHgOgTA3Ye8iijn0ZWQU07+8vxX5/31ZQehWPdNqxV7O0Va28GAfrL8P1OLh1CWIOwcm/4bpnnugt\nVKgMNRvCo8/C0z0hMAdmCvfeK56Ju3YV4Xb9OvTpSuoLczjXriPll4+y3jC6vAXlvOjsukULsYf4\n809Zcpw2zbWt2aJFVs3aFi0kqrY3KVZMDLInT5TrVV9ahdsfG2Dlh9ay778Pzd3bFGryFm0KoMk5\n+vQRSQZ0rXeCFfvkRvTMM2JK5MT16xIOxbwp9sMP0LOn52rlOYG589RkiP4ODm6BhDiIMwksP5Mw\nu3o1YzVLTyhbVvabGjSwHvXqyXQ0t9i/XwKNnhHP9sowuFD/Lsr9LUvMCRUjuTVqP6W7FvOO52Uz\n331nVU4pV05sJIo6LFW3b281/P70U3j5ZS8OwMT+/VZrdb8AGHcGCIRxd8Jlk7f/du1EwzSXPepo\nUwDP0cJNkzMoJXZDMTHsohFNEO0+Pz/RWahVy029t9+Gf/9bzlu1go0bM9z26o5377F2pKXBzAXw\n9jtw3kONFU8oVUoEV/369oLM1VJcXnD6NKrdfRjHDjhl/TZ+Eaea9KJ/BQio68U+k5NlCn72rFzP\nmiWzKDMxMfKbUkp+SGfPioFhTtC6tcQgBBj+H9j/J6z8Qa5Ll4a//sqTME1auHmOXpbU5AynTsnN\nCPhPwCiZAQG9e6cj2ABefFFstZKT5eaybRsJd9+drW0vC2bFCHdGubYoJRqDb74Ju3a5KeRAcLBJ\npTLMRt3SQZulalWZmVWunL+VEKpU4ezijQT26Uq5A39aki82bc+11j2JT4SYUl5+qAgMFM1Js8eP\niRNhwBNwzpDvbP4C6+y4XbucE2wgiiVm4TbtfXsL/RkzdPxBH0ALN03OYDIBOEhtFqb0sCTbeipy\nScWKYpRrDtMycSJBc+d6tO2VLo6bdq6Mcs1s3SoDNS9/mQkNhVdeEdVzRwHmpGbp+1yrW5atn/3C\nA2/0InzHWlKLFufvVyfDDQP/4nC9XA50OmiQ7GXdvAm7d8Po36ByO/nOZueglqQjvXuLkfaVK/aC\nbcgQn3YRV5jwwM+NRpMFTMokH/EGyvQz69oVGjmH7XJm+HDr+YIFVDx1imBkj82Wq4h8cuWc1w6z\nwbSBrG1WNL2abdVMs0r27RNtwXvusRdsxYuLsDt2TCJM9+8PnTuLGnytWrJPVsAEG0BQACQ2C+aP\ncSv4Y/QyNkzZSXyI2J+lNoCSOfGWS5e2X4pcNVG+K7/jcHyrpPkHwEMP50DnNhQv7my7Vr++syaU\nJt+ihZsmZ9i8mVNU4RusN4i33vKwbqNGooYOkJpKwJQpdEOUR8ymZadN13aunNwRg8zYQhzSQ0zp\nf54SDx8NG4rBm5mAAHlSP3pU9gEdjekKOBWB4CC40j6ACy92JaHz7XA3XG0j6Rk+VGSVV16xnu/6\nGWKOwKZ51rS690Oi43Q7B7A11DZH1S5ePOf71XgFLdw03ic+Hv76iym8TAqBgDjQsI12kyGvvmo9\n//JLSsfH0x9RHmljeu2P84qiS9zZql27CD+8Cm1riSslW59d/fqJ1tznn7sI/1w4MPuHVP5wOhxi\nqsir8vfwoSKr3H47tO4i50rB0k9ho82S5F39MrHRmg0aNBCD8pYtRXM3Pa8pmvyHNyKeAp2Bg8AR\nYGRG5XUk7gLOmjVKgUqghJpY4SNVqZJSK1Zkso3UVKXq1LFGNp40KevjOamUmqpU8s9KnVyj1L5l\n8SruifdUWvFg+zDRoFTnzkrt3Jn1vgogyUo+wn2m1+Tc6PSbVdbvJLCo9bxIMaU+vqosYcQLGehI\n3B4f2Z65GYbhD0wFugD1gP6GYdRLv5amQGPabyvJDYb1OMHRo3D//Zlsw8/Pfu9t0iRIShXXJPuQ\n1xQ3dR2pCJfLwLwSSZxcO4XIx2oQOns0xs14a5lmzWDdOvFK37hxJgebs6SQtbftLcz+IeuaXnNl\nd7HvvVDJdBtJtgm5cGc3iCiVg2uimoKCN36ndwNHlFLHAAzD+B54CPkvagojDsFJHe1wPebxx8Xu\n7dIl8bk4YjHc/nDG2o4OpJw6RszW//LwzBkUu3rRLu9KnboEj/s3/g89lC9V8zOj5FmgCDTg9WEw\nfJB9evP+ObwmqikoeGPPrRKyv2/mjClNUxhJTRVVejOZ2mhzoEQJUegws3JC+tqOtqSkiPf4zp0J\nuO02Gkz6PzvBdrNSFXZ9NZO5e/dwtkePfCnYPFXyLLA8/5h9CJ+SQfBh1wIu1TXeItcUSgzDGGQY\nxnbDMLbHxsbmVreaXObG9n0MvDaZ7TQVRYzMhJh2xYsvWr0gH/4dDtgITrO2Y4xN+ZgYsZOqXh16\n9IBVq+yau1mlCnsnTODXI4c48/RA/Pz9c0U3IStkpOQZ41SjgFG8uEQsMNOzBwRrbUWNZ3hDuJ3F\n3jNSZVOaHUqpL5VSUUqpqPDwcC90q8mPfDXhKl8zkLvYzjNFv8n+jKh8eeg6wHq9ZKJ9vj8QnyZ+\n/nr3Fg8go0db/CKC+EY82bUr25YsYe3x4xwbPpy0YsWATBiB5wHZDUhQIPjXv+DBB8VJ8tixeT0a\njQ/hjZXrP4FahmFUR4RaP2BA+lU0BZFbt2D8UmuAyyZNvLTUN3g4LJ4l578vhPMnoFwkxF+G1bPg\no2lw3EUo6/BweOYZUgcNYkP16i4dL3tkBJ5HeBqQoEATHCzLyxpNJsm2cFNKpRiG8RKwCnmgnKGU\n2pvtkWlyhMy4V8wsc+bA6RuyRxLBeZ4eGuSdhjveAfU7wd61Yov29RsSrHPTPHtNOjNt28pyVs+e\nULSoxV5rGbI57KiYkV91EyqCxTOLLwlljSY/oKMCFCJyUvMuNRXq10nh4FERFf8JGMXI66OyHyXa\nzPwV0Ler+/xSpcRt0+DB1nAlDpgF+3Vk1uNNwZ5TFFptSY1LdFQAz8nv/22Nl3DUvDNz1ZTuaUw0\ndzO/H3/EIthCuMKQu7Z7T7AB9L4f6tYVryG2NG0qGpX9+kl06HQw22v5EqWR78bXhLJGk9fo/0gh\nwax55xgTLQSrv8aMbvzuZhFdlTUEG8BLfEZIW088JGcCPz+YPBkeeEDO+/cXoRZV8B9ifVEoazR5\njRZuhYTsat6lN/Mbt8oa8qw4N3iFydBiRrbG65J774W4OIl+7M1ZoUajKXBo4VZIyK7mXXozvx9t\nZm3PMZ1wLkrYmJwgj7yy56Qijkaj8T76/1lIyK7mnbuZ375NcHSjnAeQzOt8LME8bT1L+DhaqUOj\n8T10yJtCgiV8CVmLieZu5lc8GOp1lvMnmE0VzmTP5VY+o9C7wNJofBQ9cytEZEfzzt3Mr/SdMHIF\n1G0zjLIbTYE+W7Tw4qjzFm8o4mg0mtxHC7dCRlY179I1hFaK0vu+BS5J4QI0c9MusDQa36RwCjet\nHZAl3M78Dh2SsDQApUtD7dp5NUSvo11gaTS+SeG7pfu6dkAeC2bzzG/9elGIDCiKJTgpIEuSfq63\ncn3xmUK7wNJofJP8fm/xLt5y05FX5BPBfOqUmJyFh8Nrr8Hwfb9bNZPcLEnmk6FnGm/5pfRFwa7R\n+DKF6//ly9oB+Ugwf/KJxAI9d04ctr8Wu8ma6UKZJB8NPUtk1wWWrwp2jcaXKVymAL6sHWASzCmh\ncKo47AuS15RQMhe5MgU4BewzvWZSl/3CBZg+3Xr91kvX4MABuQgIgLvucjd0nw66aV6OrWt6zcyM\nTZsSaDS5T35+YPY+vqwdkACXS8CyihAfAP4KUg0IToFuF6G0J4I5m1OI69dh5Ei4eVOuGzeG+4tv\nsBZo0sSlBxFffqbILr68WKDR+DKFa+Zmqx1giw9oB6QEwbLKphlAIlRMklcDSU/JSDBnYwpx5Qp8\n8AFUqwYzZ1rT33oLjC02yiRu9tt8+ZkiuxRmwa7R5CWFS7hl101HHhJTEeKDIcRBMIdclfSYjARz\nFtYGL1yAN9+EqlVh1Cirtj9Ahw4SC5TNm62Jboy3ffiZItsUZsGu0eQl+fh2nkP4aICshADwrw/8\nCcRiXVYsIenXMxp/FqYQv/0G48bZp0VGwhtvwFNPgX9aMmzbZs10I9x8NRK2N9CmBBpN3lCQ7yvu\n8cEAWUFAahDQBtk7SwSKAaUh1d+DGUAWphC9eokP5IMHJU7om29KTNDAQFOBbbsgMVHOIyOhovtb\ntY8+U2SbwizYNZq8RP+3fATLDMAfQsKt6R7PANKZQuy5Av95A/oPkFigZvz9YcIEUSDp2dOFbfbv\nGe+32eKDzxReobAKdo0mL9H/Lx8h2zMAFw1sOwofroUlpkCjR45C9+5gGNZqXbum06YH+20aobAK\ndo0mr9DCzYcwzwAu/vknxqZN+FWpQtjttxNQsyYUK+ZRA1e6wNbl8Mk0WLvFPvvPP2HHDoiK8mAw\nSmV65qbRaDS5ReEVblOmwJo1MHo0NG2a16PxmIDDhynfpo11rwtkqlW9umyQ3X67/Wu5cvxnnMHG\njbBnD5w547rdnj1Ftd8jwQZw8iTEmFQsg4OhQYNsvS+NRqPxJoVTuO3dC0OHyvmWLXLXL18+b8fk\nKV9+aSfY0jA4rqrz97EG7DnWkHtWbKEjE63lQ0JYq9bw6zVnzyF+ftC/vyiK1K+fyXHYztqaN5cN\nOo1Go8knFE7htm6d9fziRdFrX77cfrMpH5Jy4xZ7/reDLQxhJ03YE3QPe69Hcl1ZVR2HMpmO/Gqt\ndPUqDdnMr4hwK0ISddlP6+I7GDYmlNtG9Mrc+zZ7AP5Z77dpNJr8S6EUbmmbN9tbr69cCZ99Bi+/\nnFdDSpclS2DSJNi2xY/riTaCK8G57J7qD0HL7eLv8eBBiI/ncb6hBb/TkD3U5AiBpMBN4A3g51bw\n+efQsGHGA7F137XJRrg11PttGo0mf1HohNtloOimTU5mXWrECIwOHbKwPucdUlNltfT0aejWzT4v\nLs482XT9dYWHi2xq2BCaN4+Eft9IhlJw7hxNDxyg6cGDcKACHKwmWiMXL0qZTZvESeTw4bL/GBTk\neoC27rvKXIOYPZJu+MGlZpJf6H5NGo0mv1KobkcpwLpTp3jYpFWRUrIk12vWJGT3boykJNSAARjb\ntkHRojk+lrg42LpVtvy2bIE//oD4eAgNFTdXtjZl99xjPa/EGVrwO83e6sid7cvQsCGUK+emE8MQ\nw+qKFcVflpnr12HsWGvsmtRU+PhjmDsXJk8W623HpUpbD8C7/oC0NEmPbAgppbQHYI1Gk68oVL4l\nY4BgG9usuObN2TlnDqkmNXrjr7/g7be93m9KCqxeLa6s+vSBmjWhdGmxIRs7FtauFcEG4qT44EH7\n+rVqwYI+CzhFFc5QhfmdpvPah2Xo1CkdwZYeJUvKYHbvhrZtrelnz0Lv3jKwI0fs69i67zpgo0xS\nt6X2AKzRaPIdhUq4JQCVNlkDa15u2ZKE+vXZN368tdAnn4i0yQJKiXwwCyozhgE9eohW4oIFcPSo\n6/oVKsikKdXBTZaRlkrvra9TBZMe/7PPZml8TtSrJ+ud33wDERHW9JUrRbX/vfesmpm27rv22+y3\n3d5CewDWaDT5jkIl3IKAcjYzt8utWgFw4sUXOdmli7Xgk0/au8B3gVJw/DgsWiSTvS5dxJqgcmVY\nscK+rL8/NGpknxYQIDZlL78M330HJ06IYFy0yIXJ2C+/wKlTcl66tEhKb2EY8NhjMl188UXrcmRS\nEowZI4NZudLqvisuFQ5utdav3FJ7ANZoNPmOQrXnVvHqVfz2iCKE8vMjrnlzAK4aBttmzKBqw4YY\nFy+KcfLzz8s0y3SzVwoOHxY58+uvsH69VSfDkZ07ZfnRlt694c47JZ5n06ait+Lx1t7//mc9f+KJ\nnNkTDA0VjdGBA+GFF8RdCcg0s0sXeQPvToQll+CmaWoaUgHKVNMegDUaTb6jUN2SArZutShCXLzz\nTk4HB1v8M3YsXx5jxgx48EEpvGgRzJolNnDIpOaLLzLuIygIbt1yTn/11SwOOjYWFi+2Xj/zTBYb\n8pCoKNFwmT5d1lGvXJH0hQtlStrCRu2/ZUsYYBSyX5FGo/EFCtWypK2j32ItW9IG6I74aywNXGj2\nAPM6fsl0THtaQ4daNshceegqVRJa1YfXu8Hc6bKyd/WqeNL3Gt98A8nJct68ee64ufL3h8GD5Q09\n+aQ1/fp1WLPaet2phRZsGo0mX1K4hJuNMklwy5ZUvArRS+D1YVhU6vv98hxv+49DASQkwKOPQnIy\nHTpAqVLQuSk89gq8vRA+2gT9v4M7RsJ9wVC7houwMNlBKfjqK+u1txRJPCUiQmavv/3m2v5PO0vO\nXyQni61irVqydG0YMus/cULOBw70bn+RkXLkJ8aMkfe6fn1ej0STxxQe4ZacLMZkwBVC6DvnQUqX\nhoceEtOuv/+2Fo1NLcNe/zvl4o8/4IMPqF4dLkTDgHFw/xPQrApUugVVEsEoAcvKQEqMl8e8dSvs\n2yfnJUs6b+TlFm3awK5dMH68jAPkpuaoJaPJWz75BN5/X+waX39dBN3tt7svP3CgCIITJ1znt2uX\n713SFUoMox6GMR/DuIBhJGIYBzGM9zCM4pls5yMM4xcM4zSGcRPDuIxh7MIwRmMYZdKp549hPIth\nbMAw4kx1j2EY8zCM2m7qPIlhbMMwEjCMqxjGegyjewZ9DMcw/rIZ23IMw2Nff9laVDIM4xFgDFAX\nuFsptT077eUou3fDjRvspR49ApZyZGkJpyIBAbLy17EjhCQ+Bx+9JBkffAD338/5si2ILwJVUuzr\nhaTA6SIQk+SZHbPZPWMCosHpNnClrSJJv37ifT+vCAyUG2b//hJNoUMHKFIk78ajcWbpUtn0XbPG\n/rtJTob9+yEkxH3drPDLL95tT5Mh7cXo5k8gEFiIRGfsALwLdMQwOqJUkofNDQd2AmuAC0jbzZF7\n+iAMozlKnbarYRhBwE+mPqOBr4FEoBLQGqgNHHKo8zHwGnAGmA4UAfoBP2MYL6PUZw7lDeB7oDdw\nEPgM2TnqC2zAMB5GqZ8yenPZ3TH5G+gF/Deb7eQ8mzbxIz14gtkkpFiFRNOmIsw6dIBWrawTE1IH\nw5b5sGGDKKE89hg3VkTjn1rKZfP+qXDdA1svW/eMjgFHS9sWvHYNvv/eep3bS5LuqFTJ+8tbGu8Q\nEwNlyjg/dAQGpj+Dyyq33eb9NjXuSU1lOkQCxYCHUGoJAIbhB8wHHkYE1jgPWyyFUolOqYbxIfAW\n8CbwgkPufxHBNhilnO/7hhHocN0CEWxHgbtQKs6UPh7YAXyMYSxFqRM2tfohgu13oKNljIYxDdgE\nTMcwfkUpB4tie7K1LKmU2q+UOphxyXzA5s1E04gERLCVKAHz58P27fDRR3D//TaCDUSp4ptvrE+7\nx49T+cOhpJbA2RvHdUgtASUjSBdb94xVkBlbFdP1MlO+hXnz4MYNOa9fH5o1y/x71mSP+fNlSTYk\nBIoXl43Z//xHbADNJCaKGUVEhLiiccWQIbK8t3SpffqBA/KgUKWKCKRy5WDAAGcXNWBdQjx2TGIR\n3nGHjKldO2ve8eMSZ88w5DDvh7naczMM+PprOa9e3b6Oufxvv1nLmo927axtuNpzmzVLys2aJQ4C\n2rWTFYdSpcRp6v79rj+jQ4fg4YchLEz+iC1awLJl9u1ll19+gc6dxVa0aFGoXRtGjhQtMEeOHYNB\ng8SdUPHiUqdhQ1G0srWBvXULPv1UbHzCwuTGEhkp+x1ZdAbhlt9+4zYRbBssgg1AqTTgX6arwaaZ\nT8a4EmzCfNNrLbtUw2gCDADmuRRs0mayQ8pg0+uHFsEm5U4AU4GiwFMOdYaYXt+xG6NSfwLzgHBE\n+KVL4dB1Uwo2b2Y0i9hFY/6udD+LlxfljjsyqFe1quj/DxgAQNA3X1P/3m6crv4IIbFYpl5XQyC4\nPlTM4NO0dc9oSwiytmDnntF2SfLZZ/XeR27z1lsiyMqWle8/KEhMId56C1atEn9qRYpIBPS+fSXO\n3ooV8MAD9u0kJcmDSrlycmM1s3KluKNJTpY6NWtKJNkffpCb+rp1csN05JVXYONGERRdu8pD2F13\nyQ110iQpM2yYvIaGun9/o0eLssnu3dKmuWxoqByjR4tAOXlSzs14qkCydCn89JPYSA4eLHvHy5eL\n/eS+ffK5mjlwQIRZXJy8rzvuEOHSs6e8R2/w3//KQ0bJkvDII/Iwsn69PNn+/LNoUps/g3Pn5DO9\ndk36f/hheYg5flweeF96SWbIIA8Mc+eKFvMTT4ggjIkR5bWVK6FTJ++MH8TAVljplKfUMQzjELIs\nWAOZKWUV84/4L4f0AabXuRhGiKlcFeAS8CtKOfjsA2SW53rMsAIYZSojPzLDKAa0AG4AG93UedxU\nZ2a670Iple4BrEWWHx2Ph2zKrAeiMmhnELAd2F61alWVqxw9qpSIOHU1uJK6eD4lc/Ufe8xSPzU0\nVC08fkpNvajUtBilpl5UanaKUpc8aGavUmqaUmqJi2OaUmqfueDu3Zb+VJEiSsXGZm68muzx++/y\n2VepotS5c9b05GSluneXvA8/dC7/8MPObc2fL3mvvmpNu3xZqdBQpcqUUWrvXvvye/YoVbKkUo0b\n26c/+aS0U7GiUseOuR53tWpyOHL8uNR98knXbR4/7rq9tm0l3x2u+ps5U+r4+yu1dq193siRkvfR\nR/bpHTpI+uef26cvX279H8yc6X4ctoweLeXXrbOmnTgh/6PgYKX277cvP2SIlH/uOWvap59K2qRJ\nzu0nJCh144acX7milGEo1bSpUiku7ikXL9pfz5wp4/P0cHzPvXubP4+Hlav7LCw15Xdxme/ugNcV\njFEwUcFGUxu7FYQ7lPvNlDdUwUXLdyNHmoKpCvxtypc05cW76besKf+8TVp9U9oeN3WiTPl/ZPS+\nPP8A0hdcGQo326Np06bOPwQvs3SpUr16yf1IzZ5t/RLuvz/zjV25In9is4Br316dTE1V+5RSJ5VS\nyR42c1IpNVW5Fm5TTflKKaWGDrWOt2/fzI9Xkz2efVY++//+1znv4EGl/PyUql7dPr12bbmBXnJ4\nzOnWTdravduaNmmSpH32mev+hw2TfFvBZxZErm64ZvKTcHv0Uefyx445PwScOiVpNWsqlZrqXKdT\np+wLtw8+kLQ333Quf/myCL1ixZRKTJQ0s3Bz9f3bcvWqlGvRQqm0tIzHZv48PT3atrWvf++95rxO\nyvWNf44pv7/LfPfC7R+HvlcoKOei3H5TfoqChQpuVxCkoKOCw6a8MTblK5rSzrjpN9CUn2ST1sKU\ntslNnVqm/IMZva8CZwqgFHz4oaz0/PAD/Otf2Nm3Zck2KyQEvv3WYsTmt24dVT/5hLrIMqKna7tm\n94yOK/xXsXHPmJgofZnJL4okhYmdO+XVNkyQmdq1xYHo8eP2ezVPPin7L7ZKQOfPyxJm48bYrYFv\n2SKvu3eLXZbjccikbOZqf+ruu7P8tnKVqCjntCqmBfk469YL0dHyes89ro1ETf5fs0V632dYmHw/\niYmyPAripSgoSNwSPfywLDnv3Ss3F1tKlZIbze+/i1nM++/LcrJ5r9yR9eszI9pyz1ZPqfIoZQDl\nEQXBGsAu0x6bLeYv6ADQF6UOoFQCSv2C7IGlAa9iGPlCjTpbws0wjJ6GYZwB7gGWGYaxyjvDyhoJ\nCbKc/s471t/hokVwZYPN0nFW/yytWok7KjNvvy22X5kgANGKVFj32E6bri3uGRcvhsuXpUJkpOs/\npCZnMQutChVc55vTza7JQPZb/PysShoAc+aIkomtlxewKiRMny6RFxyP5cslP8FFqPXy5TP/fvIC\nV/t9AabHQNuwF+bP2l3spizFdHIgs99ntWqwbZvsia5dK35mGzSQ9E8/ta87b57sSd68Ka8dOsh+\n3OOPy8ONN7Gacriz6TCnX3GTnz5KnUepH4H7gDLAbIcS5nZ/RqlUh7q7gePIc3pdU6r56S8z481K\nHZdkS6FEyQfxY3ba8BZHj4qzfFtj7HbtYP6XVwitbfJi7++fvSff0aNFkeDPP0UR4NFHRd2yhLPN\nnDtKI+6+YhCly5I42LnZKpI884yXXZ5oPMJ8E/nnH9fq7ufO2ZcDmc116CA3wwMHRPX+669FDX/A\nAPv65nq7d5OxVpMDBU2xqJTJtMadIPCGgLD9Pl152nH1fdatK4IrJUW+p7VrRUv1lVdEKcXs47V4\nceuM+/RpMR2aNUtWX06cEOUfM7NmuTeYd0VkpL2Ga5065jPXhtJW7cZDbvI9Q6mTGMY+oBGGURal\nzC7iDwJ3416wmKfkxU3tXMcwzgKVMIwKKHXOg/EeRSykamAYASjlqILs+XvM1Nqslw5v7LklK9mj\n2quU+maVUmFh9nP6oUOVunVLyeabOfGuu7Ldrzp4UKkSJaxtPvigaWPPC9govig/P6VOn/ZOu5rM\n8cwz8h3873/OeYcPu95zU0qpb7+VeiNHKrVrl/X34cj48SrdPTdXZLQ/plTm99yeflrSjxxx3Z5Z\n0cOVsoS7/sx7bu72yBz3kk6eVDm+5zZ2rKS9845z+bg4pUqVst9zc8eGDdJO9+7pl0tNlfcD9kol\n2d1z++UXc95vynkvqoYp74QCwyk/swecN7UXZpP2hCntGxfliyq4Ysovb5M+25T2lIs675vy3nNI\n34GfDxcAABcnSURBVGBKb++ijvv2HA6fnBZcBuYCPysY9TE80cW6jF+0KMycKS61AgOxc5bsFV+I\ntWvbL00sWSIqxuZ10OwwY4b1vHNnmQ1ocp+nn5bXDz6QqAxmUlPFS0tamuvoDL16yUzk22+tdlmu\nDN6fekqW7d57T5a/HElLy539FrM6uzlWYGbzvUHVqrLEcuSIqOvbsnKld2zFHntMbgZTpjhHmB81\nSlT+H3vMGkpqxw7Xtm/mWaR5pSY2FkwhtOy4fl2WlAMC7A3qs7vn1rYtR8UbSBsM40FLuhhxf2S6\nmoayuRkZRiCGcTuGYb8EYRi1Ter8OKT7mYy4I4DfsbVNg0XIolNfDMNxCWwUsmS4DqX+sUmfZnp9\nG8MIs+knEngRSMJZpd8cf+UDk2mAuc5diJeSWNNY0ifbEj4LR3ZmbslKqdlKqf9dV6pNf/tfQ1gl\npTb/4VChTRtrgQULstyvE//6l33no0Zlr73kZFHzNrf3ww/eGacma5i/34gIpV54QakRI5Rq0EAp\nUNWKxqhq1dxox5lnfYGBouqflOS63Nq1oqVnGDI7eeUV0ZJ8+GH5HRQtal8+J2ZuK1dK+m23yfsd\nO1apKVOs+dOmSX6jRkq99Zbkz56dfn/pzNwsypeOM5K9e8U0wjwreustpfr1k8/woYck/euv3b9v\nW1zN3JRSaupUSQ8Olu9o5Eil7rlH0m6/3V7L9ZVXZCbXqZNSzz8vZR95RNKKFhXTD6Wss/OGDUU7\ndORI+a1Uraosy0depr1oLF5XcEvBdwrGKfhTmTUMoaiyn+lEWmZ09unDFNxUsEbBlwr+o2CGgqOm\n8ucU1LOrI/XuVZBkOuYq+FhZzQfOK6jlos4npvzTSswNpiqrKcFLLsobChaY8vcr+D8FXylIUKKp\n+ZBTHReHzwk3szr9vHilqjW0yoK6LZX69zkbdXql5MZSrJi1UExMlvt1Ii1NqSeesBdwU6dmvb2f\nf7a2ExFhWlPV5Clz5yrVsqVSQUFyU6tXT6kPPlDVqqa5lCFKKaU2brR+jy+9lH77x48r9eKLsoRV\ntKjceOvUEbvKH3+0L5sTwk0ppT75RG7uRYpIGdv6KSmiPl+9ulIBAZLftq35xXvCTSmxP+vZU6mQ\nEFn2b95cthTMS7iOn4c73Ak3pZRatUrU6UND5f3edps8tMTF2ZfbulWpwYOVuuMO2e8oVkzKDhwo\ndohm4uKUeu89pdq3lweSIkXUz6GPqbYhu1Sp4kmqZMk0dffdSs2a5dnQzRw6pNS4cdJs5coi4yMi\nZIUbuh9UUM90879oEjKHdtB4QnGujwa1ANQRUGmg1FAmtXUj3Boo+ExBtKmdlP3UiS/GjVRQqjjX\n5ysX925Q/m1Z92YD/oqN4J+04lxXNTiS3JE1Bx5hXjtXdUz9DTQJ4esK4pXYzHVPp3yAguEK9piE\ncJyC5QpauK3j68LN1hD6v0eUCgpTqvNgpRYlORhCK6XUli3WG02NGlnu0y23binVpYu1D8PI+uzQ\n/IQK8hStybe4kyGFBVfbQZ6QkdmcSwYMkEoHDmS+w1xmyhQZapkyMoEbNkyEEyj12muet9O3r9Sp\nV0+pQYNkQtizp9jFm24RQ5Wz0OlhyksDdRRUnOm6pmNZVweoAFB/gIo31fvWTbl5pvzToD4H9RGo\n5aZ+k0B18KS/3Dh8Trg5GkLPPOPGEFop61MfyCwrJ0hIUKpZM2s/RYoo9euvmWvj3Dm7X646eDBn\nxqrxClq4eVm4pabae4Ixs3at/C/q1ct8Z7nM8eMy+S5d2n5yffmyTPrAupqZETNnKrVzp3P6+vVK\nwS2zEKmg7IVOZVCtQZUyXa/PpHB719TuUHfCDdRdpry/QZVwyHvKlPerJ/3lxuFzCiWOhtBlKsmr\nnSG0GW8rk7iiZEnxo2dW0711S5ymmo1TPeHrr622P23aiNKKJk9RCj77TDTHixWTYAgvveRazwDs\n/fuuXCk6EiEhzpr7mfHdaw6nlpQktpvVq0ud224TXZRbt1yPJTN9pBdv1DHup/k9gvhUtvWnPGaM\n6zY8IS3xFtMqjeWukIMEFUmiZGASd4Uc5ItOi0jzD4SpU+3Kb9wottOVK8v7K19eQlW99559u+fP\ni/5PnTryNw0NlfOBA8V1pTeZMUO+p5desv88w8LEHSnAtGkuqzoxcKDYlTvSti3AtngkZIxdXDOl\nOKMUG5XiWmbHbhhEIQohY3H2J2lLDdPrL0rhaKluDkETntn+cwqfc5xsNoRehhhAO4aNsbwhpXJH\nuIE4gV21Spy/xsRAfLw4jN28GWrUcC5vG9CtpHJ2kqzJc4YNE6XYChXEOXxgoPgB/uMPESruQtkt\nXCjCzewv+ORJa15mfPfa0qePmFb27m0dx5gxYmK5ZIm9AM1qH57QqJGYer73ntgz2yqC2gYLyCyP\nP1uE79KmUuXGOZ71+wojJZkfE3rxAp+zqeMHzGlnDQa1cqX4Vi5VShyJVKokPg/274fPP7f6eL5x\nQ/7yR4/CvfeKMFRKvo+ffpLP0tVfM6uYfRrb+sY206WLfZnskaxMJ25CUGQOw6A48A0Sm20ckJ6X\ni72m1w6GQXGluGmTZw486uVQCNkgL6aL3rRzc+vf8eBB6zJfWJhrGxpv89dfsiFu7rdmTaXOn7cv\nc0mJuudUJZuEw9Zby4eEKHX9es6PU5MumzfL13HbbfZKdDdvip6Do96FUlY9CsNQasUK5zYz67tX\nKesyXq1asrzlahy2yotZ6SO9JVZ3uhneXJb87jtJa9xYqfh4a3pCgvgjBqXmzLGm9+oladHRzu3b\n+hdfskTKDRvmXC4pSalr1+zTMuPPePRo58+kbFnpz9FXspmSJSU/O3/vEyeUgsQ0UNdBWe3PXC8z\nrvdkWRLUZFCJoOqZrttlsOc2wZR/EtRUUONA/QwqGdRcUCXT6y83D58VbhkyY4ZVaHTrlvP9mdmw\nQRbfzX1HRVn/SWY7hm+UdaOwnTXigHp+SO6NU+MWs9/kGTOc89atS1+49ejhus3M+u5VyioMbAWY\n4zjatcteH3kt3Mw22qtWOZdfu1by2re3ppmFW0bb0mbh5uqzcIX5L+jpMXq0ff3AQEl358/BbOWT\nVYXtxERR3DX1P0JldGP3QLiB6mhSBPmXTVq6ws1U5nlQNxw+k+2gOmc0rtw8fG7PzWNya0nSkdat\nxXmu2W3W9u3ifPXWLWtAN7PpZEIc/L7QWvcBvSSZHzD72ZU9DntatRIvbu5w590ts757bUlvHLbu\nTbPTR16xc6f8VVwta7Zt6/weH31UXps1k2XfefMkDJ6rupUqwbhxslT46adim52a6lwWMivasrfH\nmFlSU8VVpdzSlsYBH2e3TcMgFJgF/AF84mEdwzD4FAky+j4Syy0YaA0oYIVh8GJ2x+YtCq5ws40E\n4A3P4pmhRw8JcmpmzRrxSnEtTTYJzfz2HdwyBZqt0hhquAhOqcl10vPlGxBgH2fTEXd+jbPii9lM\neuO4ZqM+kJ0+8oqrV0XxxdUepvk92irC9Ool+luNG4sSR79+EmwgKkr+ZmZKlYKtW+Vvt2OHuISM\nipLvZ/RocQ3rTcxuKd0pHJnTQ9y5A3ZDaqo4T1mwQPZeoecxpVAZ1fOACYhz5IFK4UbkO/Ek8DLw\nqVKMU6LEkqAUm5DApTeBcYZBkBfGl218TqHEI2Jj4eBBOQ8MdB1+I6cZNEgctZp3uL/7DoqXg8af\nAIY8/q2ebi3f4lnxoqzJc8w3oPPnnZUOUlLg4kX3ntHc+TXOiu9eM+fPi5cqV+Mw+x3Oah9+fu61\nLnNDCIaEiEJIcrLJXZ4Nrt4jiEJJt27i5eqPP0TYffEFdO8us7x69aRc5crw1VfyV9u3TxQ6pk6V\nyDRpaTB2rLXNzM7E2rWzn23WqSNjPXRIovfYcu6cjLVy5Uz5WLf4Zl+wQHxvz54N8+d7RY8E+P/2\n7j1GqvKM4/j34aKgWMRCFJCbAl5QA+uKVaolYFqlKr0rmhYqhGIUE6MQG6IlNTFS09j0Yq0RrW2M\nhZgaqIqtlwJBwboYoKhoVbQuCN6KwVt13ad/PDPd2WVmd3Z3ds7Mmd8n2ezMnDPnPPvu2X3mfc97\noY6Y4HhHgWv2UjMuBba6MzHzWrbTyN/b7uzOHjN2AJOA44DNpQq0q9KZ3J56quVxfX3M3J2E66+P\n/zTZWtzyW+GioXD+Inj7Wdi5NV7v2w+mXtJmHIMkpa4umsvWrTswuW3YULhpqz2TJsX6gmvXwvTp\nrbft2xcjR/r1i8no21q3Lpql8sWR22W8K+cYNAi2bcufXBoa8v8svXp1rQzymTQphi6sX39gzOvX\nx3nqCjRoHHpoNMFOmxY/xw03wJo1LcktyyyS/YQJ0agycmSsLJWb3NoOIyhGbnKbNi2aDR955MDk\ntmZNyz7F+vTTqKmtWhWrKd19d8kXCPkzkO83PBSYQczOvxbInVg0M/lmwe7+2dcLfFwqsyRu9PV4\nh5JFi1qax6+9tmfP1ZGmppgvMLfJfv497mdd3vJ8yvejF6VUhA0bvMu9JQtNXr9zZ3Q6GDgwFhbI\ndeWV8d5581q/XkxvydwpF7tyjgUL4vW2i05nf558HUqGDOnaIPZ8HUruvTdeO+201j0JP/wwXoNY\nbCFr3br8nTauuCL2ve22eL59u/uePQfu98wzsd/kyZ2Pvz2vvtr5Qdz79kWv1radTD75xH3GjHjP\n3LmtO3oDDV7E/9hie0vmed/UQh1KwBdntm0HH9hm24LMtjfBe3fmnD31lc6aW1KdSfLp3TtmiX/n\nnfgIDrD8Mjjo4JZ9bpwXC71JRZgyBRYujEnkTzqp9fiyQYMK39Nqz+jR8ItfxOLOdXXxqXzIkLgk\nNm6M5d+WLcv/3hNOiFpHbhyvvBJNc7k1uq6cY+HCqBVcfnnUoEaMiBrexo3RzPfggwfGM3169Jm6\n4II4T9++MffA2Wd3vlwuuSR+npUrW2pWZlGz2rkTLrqopRMJwFVXwa5d8TsaPTru1W3eHE2Oo0bF\nPTiI+2+LFkUtavz4GO/X2Bjn6tUrtpXSmDFwyy0RX319xH3QQTHusbERrrnmwBrdAw/EPcHZs1sW\nkYDoKPPww3G/cfjwaEZt8fNhZiwF1rqzNneLGTlH4fjM92Vm7M88vjNzf6yrbgMuBU4BXjJjNbG2\nWx0wjRhyfIUXfw+vZyWRUXu05vbxxy2TwIL7W2/13Lk6Y9++mIi1bcerceNiEmapKM3NMVdgdk7h\noUNjvsB9+7q2jFlWsXP3urfUdD75xH3JEvfRo+M9Y8a4L11aePmxzpzDPeZ6Puss9/79Y7jAjBnu\nW7cWHgqwd6/7rFkxmW+vXp63a3w+habf+vzzmHP81FMjhv793evqYrm7tsNTV6yIBQPGjo2xY4cd\n5j5hQiwkkPun/vzz7ldfHcccPDjKYdSoaER58smOY+2q1atjIZIBA2L+5/r6whMnZ6+ZtvNZF7ns\n21I/sGbV0XvmtH1PnmNMbW8oAPgAYqquLcR4u8/Ad4OvBJ/c0fHL+WURcHnV19d7Q6EG/e7asCG6\n40N8ZMt2LKkEu3fHR87c1XiXLYPFixMLSSrX1KlR60rgT1QqlJltdvcEeshVn/QNBaikJsm2hg2L\nabqyfckPOSTuFouISEml755bkuPbijF+fAzAWb48Jp0rNDBKRES6LF3Jrbm59TCASqu5ZR17LNx0\nU9JRiIikVrqS244dMSIUoulPS8dIFcsuNSMinZeue25t77cVmi5CRERSLd3JTUREalK6kluldyYR\nEZGySE9y27s3pm2AWHu+0IR0IiKSeulJbrlNkpMnR4ITEZGalJ7kltskqfttIiI1LT3JTZ1JREQk\no3rHuTUBu4EPgN4fxQJcWWeemVBQIiJSCaozub0HPATsB3oDL/wjlu2FWKnwCK0fIyJSy6qvWbKJ\nSGwGjCBWr343p0nyDDVJiojUuupLbruJGtvAnNeez+lMMkHj20REal31JbcPiKbIrOZmeHFjy/MT\nVXMTEal13UpuZnaLme0ws21m9oCZHV6qwAoaAK0WMf/3c/Dh+/H4C0fB8cf0eAgiIlLZultzexQ4\nyd1PAV4Cftz9kDowDDgMyOSzVk2Sx02B4ZosWUSk1nUrubn739w9002RTcDR3Q+pA32ArwMOvAE8\nm9OZZOaUau3/KSIiJVTKe26XAWtKeLzCjgBmAecDjTk1t6+qM4mIiBRRzzGzx4Cj8mxa4u6rMvss\nITrp39vOceYD8wFGjhzZpWBb6QP03gW7X4/nhxwCEyd2/7giIlL1Okxu7n5Oe9vNbA5Rh5ru7t7O\nce4A7gCor68vuF+n5E65dfrp0LdvSQ4rIiLVrVt3qMzsXGAx8BV3/6g0IXWCJksWEZE8unvP7ddE\n38VHzWyLmd1egpiKp8mSRUQkj27V3Nx9bKkC6bT9+2HLlnhsBmeckVgoIiJSWapvhpKsp5+O2UkA\nTj4ZBg5sf38REakZ1Zvc1CQpIiIFVG9yy+1M8mWNbxMRkRbVmdyammDTppbnqrmJiEiO6pys6rPP\n4MYbo2nytdegFIPCRUQkNaydcdc9pr6+3hsaGsp+XhGRamZmm929Puk4qkF1NkuKiIi0Q8lNRERS\nR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSJ5G5\nJc3sbeD1Eh1uMPBOiY6VZiqn4qiciqeyKk4py2mUuw8p0bFSLZHkVkpm1qCJRDumciqOyql4Kqvi\nqJySoWZJERFJHSU3ERFJnTQktzuSDqBKqJyKo3IqnsqqOCqnBFT9PTcREZG20lBzExERaaXqkpuZ\nfdfMnjOzZjMr2APJzM41sxfN7GUzu66cMVYCMzvCzB41s39lvg8qsN/nZrYl87W63HEmpaPrw8wO\nNrMVme1Pm9no8keZvCLKaY6ZvZ1zDc1LIs6kmdldZvaWmW0vsN3M7JeZctxmZnXljrHWVF1yA7YD\n3wLWF9rBzHoDvwHOA04EZpnZieUJr2JcBzzu7uOAxzPP8/nY3Sdmvi4sX3jJKfL6mAv8x93HArcC\ny8obZfI68Xe0IucaurOsQVaO3wPntrP9PGBc5ms+8NsyxFTTqi65ufsL7v5iB7tNBl5291fd/VPg\nT8DMno+uoswE7sk8vgf4RoKxVJpiro/c8rsfmG5mVsYYK4H+jork7uuB99rZZSbwBw+bgMPNbGh5\noqtNVZfcijQceCPneWPmtVpypLu/mXm8BziywH79zKzBzDaZWa0kwGKuj//v4+5NwPvAF8sSXeUo\n9u/o25mmtvvNbER5Qqs6+p9UZn2SDiAfM3sMOCrPpiXuvqrc8VSq9sop94m7u5kV6hY7yt13mdkx\nwBNm9k93f6XUsUpq/QW4z93/a2Y/Imq70xKOSaQyk5u7n9PNQ+wCcj9BHp15LVXaKycz22tmQ939\nzUzzx1sFjrEr8/1VM1sLTALSntyKuT6y+zSaWR9gIPBuecKrGB2Wk7vnlsmdwM/KEFc1qon/SZUk\nrc2SzwDjzGyMmR0EXAzUTE/AjNXA7Mzj2cABNV4zG2RmB2ceDwamAM+XLcLkFHN95Jbfd4AnvPYG\nhXZYTm3uG10IvFDG+KrJauAHmV6TXwLez7ltID2gImtu7TGzbwK/AoYAD5nZFnf/mpkNA+509xnu\n3mRmVwJ/BXoDd7n7cwmGnYSbgZVmNpdYgeF7AJnhEwvcfR5wAvA7M2smPujc7O6pT26Frg8z+ynQ\n4O6rgeXAH83sZaKjwMXJRZyMIsvpKjO7EGgiymlOYgEnyMzuA6YCg82sEfgJ0BfA3W8HHgZmAC8D\nHwE/TCbS2qEZSkREJHXS2iwpIiI1TMlNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERSR8lNRERS\nR8lNRERS538wMxeFt66dhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a36df198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kbEFBpgbbTkCHjrIfEwpxPeHChczZaV0Owvje8HAz196EpkDQgZM13uPUKahS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41a36fc710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for t in range(500):\n",
    "    pred_ofit = net_overfitting(x)\n",
    "    pred_drop = net_dropped(x)\n",
    "    loss_ofit = loss_func(pred_ofit, y)\n",
    "    loss_drop = loss_func(pred_drop, y)\n",
    "\n",
    "    optimizer_ofit.zero_grad()\n",
    "    optimizer_drop.zero_grad()\n",
    "    loss_ofit.backward()\n",
    "    loss_drop.backward()\n",
    "    optimizer_ofit.step()\n",
    "    optimizer_drop.step()\n",
    "\n",
    "    if t % 100 == 0:\n",
    "        # change to eval mode in order to fix drop out effect\n",
    "        net_overfitting.eval()\n",
    "        net_dropped.eval()  # parameters for dropout differ from train mode\n",
    "\n",
    "        # plotting\n",
    "        plt.cla()\n",
    "        test_pred_ofit = net_overfitting(test_x)\n",
    "        test_pred_drop = net_dropped(test_x)\n",
    "        plt.scatter(x.data.numpy(), y.data.numpy(), c='magenta', s=50, alpha=0.3, label='train')\n",
    "        plt.scatter(test_x.data.numpy(), test_y.data.numpy(), c='cyan', s=50, alpha=0.3, label='test')\n",
    "        plt.plot(test_x.data.numpy(), test_pred_ofit.data.numpy(), 'r-', lw=3, label='overfitting')\n",
    "        plt.plot(test_x.data.numpy(), test_pred_drop.data.numpy(), 'b--', lw=3, label='dropout(50%)')\n",
    "        plt.text(0, -1.2, 'overfitting loss=%.4f' % loss_func(test_pred_ofit, test_y).data[0], fontdict={'size': 20, 'color':  'red'})\n",
    "        plt.text(0, -1.5, 'dropout loss=%.4f' % loss_func(test_pred_drop, test_y).data[0], fontdict={'size': 20, 'color': 'blue'})\n",
    "        plt.legend(loc='upper left'); plt.ylim((-2.5, 2.5));plt.pause(0.1)\n",
    "\n",
    "        # change back to train mode\n",
    "        net_overfitting.train()\n",
    "        net_dropped.train()\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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