LSTM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x1c90fe98bd0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "import torch as t\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "t.manual_seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RNNcell(nn.Module):\n",
    "    # y is the hidden state: hidden of shape (batch, hidden_size)\n",
    "    # input of shape (batch, input_size): tensor containing input features\n",
    "    # format as torch.nn.RNNCell in Pytorch\n",
    "    def __init__(self, x_i_size, h_i_size):\n",
    "        super(RNNcell,self).__init__()\n",
    "        self.linearX = nn.Linear(x_i_size, h_i_size)\n",
    "        self.linearA = nn.Linear(h_i_size, h_i_size)\n",
    "        self.linearA1 = nn.Linear(h_i_size, h_i_size)\n",
    "        #self.m = nn.Softmax(dim = 1)\n",
    "        \n",
    "    def forward(self, x_t, a_prev):\n",
    "        a_t = F.tanh(self.linearX(x_t) + self.linearA(a_prev))\n",
    "        #y_t = self.m(self.linearA1(a_t))\n",
    "        return a_t\n",
    "    \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Key class defined in this file \n",
    "class LSTMcell(nn.Module):\n",
    "    def __init__(self, x_i_size, h_i_size):\n",
    "        super(LSTMcell, self).__init__()\n",
    "        \n",
    "        self.linear_i_1 = nn.Linear(x_i_size, h_i_size, bias=True)\n",
    "        self.linear_i_2 = nn.Linear(h_i_size, h_i_size, bias=True)\n",
    "        \n",
    "        self.linear_f_1 = nn.Linear(x_i_size, h_i_size, bias=True)\n",
    "        self.linear_f_2 = nn.Linear(h_i_size, h_i_size, bias=True)\n",
    "        \n",
    "        self.linear_g_1 = nn.Linear(x_i_size, h_i_size, bias=True)\n",
    "        self.linear_g_2 = nn.Linear(h_i_size, h_i_size, bias=True)  \n",
    "        \n",
    "        self.linear_o_1 = nn.Linear(x_i_size, h_i_size, bias=True)\n",
    "        self.linear_o_2 = nn.Linear(h_i_size, h_i_size, bias=True)\n",
    "        \n",
    "    def forward(self, x_t, c_prev, h_prev):\n",
    "        \n",
    "        \n",
    "        i = F.sigmoid(self.linear_i_1(x_t) + self.linear_i_2(h_prev))\n",
    "        f = F.sigmoid(self.linear_f_1(x_t) + self.linear_f_2(h_prev))\n",
    "        g = F.tanh(self.linear_g_1(x_t) + self.linear_g_2(h_prev))\n",
    "        o = F.sigmoid(self.linear_o_1(x_t) + self.linear_o_2(h_prev))\n",
    "        \n",
    "        c_t = t.mul(f, c_prev) + t.mul(i, g)\n",
    "        h_t = t.mul(o, F.tanh(c_t))\n",
    "        \n",
    "        return c_t, h_t\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# test code for format\n",
    "t.manual_seed(2)\n",
    "rnn = LSTMcell(10, 20)\n",
    "input = t.randn(6, 3, 10)\n",
    "hx = t.randn(3, 20)\n",
    "cx = t.randn(3, 20)\n",
    "output = []\n",
    "for i in range(6):\n",
    "    cx, hx = rnn(input[i], cx, hx)\n",
    "    output.append(hx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 20])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test with case: time series 1 dimension. \n",
    "The test code is from the book \"Learn Deep Learning with PyTorch\" Chapiter 5, with modification "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_csv = pd.read_csv('./data.csv', usecols=[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c9143e8c18>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#original time seirs\n",
    "plt.plot(data_csv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# preprocessing\n",
    "data_csv = data_csv.dropna()\n",
    "dataset = data_csv.values\n",
    "dataset = dataset.astype('float32')\n",
    "max_value = np.max(dataset)\n",
    "min_value = np.min(dataset)\n",
    "scalar = max_value - min_value\n",
    "dataset = list(map(lambda x: x / scalar, dataset))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_dataset(dataset, look_back=2):\n",
    "    dataX, dataY = [], []\n",
    "    for i in range(len(dataset) - look_back):\n",
    "        a = dataset[i:(i + look_back)]\n",
    "        dataX.append(a)\n",
    "        dataY.append(dataset[i + look_back])\n",
    "    return np.array(dataX), np.array(dataY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "class lstm_reg(nn.Module):\n",
    "    def __init__(self, input_size, hidden_size, output_size=1, num_layers=2):\n",
    "        super(lstm_reg, self).__init__()\n",
    "        self.hidden_size = hidden_size\n",
    "        self.rnn = LSTMcell(input_size, hidden_size) # rnn\n",
    "        self.reg = nn.Linear(hidden_size, output_size) # \n",
    "        \n",
    "    def forward(self, x):\n",
    "        c_prev = t.rand(1,self.hidden_size)\n",
    "        h_prev = t.rand(1,self.hidden_size)\n",
    "        x, _ = self.rnn(x, c_prev, h_prev) # (seq, batch, hidden), modification is here for my own class\n",
    "        s, b, h = x.shape\n",
    "        x = x.view(s*b, h) # 转换成线性层的输入格式\n",
    "        x = self.reg(x)\n",
    "        x = x.view(s, b, -1)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input and output \n",
    "data_X, data_Y = create_dataset(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dataset for training and test，70% for training\n",
    "train_size = int(len(data_X) * 0.7)\n",
    "test_size = len(data_X) - train_size\n",
    "train_X = data_X[:train_size]\n",
    "train_Y = data_Y[:train_size]\n",
    "test_X = data_X[train_size:]\n",
    "test_Y = data_Y[train_size:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_X = train_X.reshape(-1, 1, 2)\n",
    "train_Y = train_Y.reshape(-1, 1, 1)\n",
    "test_X = test_X.reshape(-1, 1, 2)\n",
    "\n",
    "train_x = t.from_numpy(train_X)\n",
    "train_y = t.from_numpy(train_Y)\n",
    "test_x = t.from_numpy(test_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = lstm_reg(2, 4)\n",
    "\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = t.optim.Adam(net.parameters(), lr=1e-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda2\\envs\\py36\\lib\\site-packages\\ipykernel_launcher.py:10: UserWarning: invalid index of a 0-dim tensor. This will be an error in PyTorch 0.5. Use tensor.item() to convert a 0-dim tensor to a Python number\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 100, Loss: 0.04183\n",
      "Epoch: 200, Loss: 0.02520\n",
      "Epoch: 300, Loss: 0.00918\n",
      "Epoch: 400, Loss: 0.00740\n",
      "Epoch: 500, Loss: 0.00576\n",
      "Epoch: 600, Loss: 0.00312\n",
      "Epoch: 700, Loss: 0.00301\n",
      "Epoch: 800, Loss: 0.00313\n",
      "Epoch: 900, Loss: 0.00390\n",
      "Epoch: 1000, Loss: 0.00347\n"
     ]
    }
   ],
   "source": [
    "for e in range(1000):\n",
    "    # forward \n",
    "    out = net(train_x)\n",
    "    loss = criterion(out, train_y)\n",
    "    # back propagation\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if (e + 1) % 100 == 0: \n",
    "        print('Epoch: {}, Loss: {:.5f}'.format(e + 1, loss.data[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "net = net.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_X = data_X.reshape(-1, 1, 2)\n",
    "data_X = t.from_numpy(data_X)\n",
    "\n",
    "pred_test = net(data_X) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_test = pred_test.view(-1).data.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1c914464630>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9QUElPvnqkJJirPbRo50/xwqXrMnNxFVE3AVBKMX+/RAWZvzh7duXFMlyF3l5JprF3nKvDZ97RZZ7cHBJKGZ1sJ5ounRx/px27cy7Fb1zPhFxFwShFPv2mYJeUDuWu312qkWLFnDuHOTnuz5+VpZpTF2V5V7dao01EXcrzl4sd0EQ6pz9+0sErH1794u7ozBFd5YgOHLEvFdkuQcFmeiV6i6q7ttn6slYLfScwcvL1J8Ry10QhDrl1Ckjepbl3r69+ezO/qb22akWtSHuFVnu1k2lun73ffvMAmnZCJyqCAgQcRcEoY7Zv9+827tlwL1+9/pguUP1/e779lXPJWMh4i4IQp1TVtytaA93umZSU417w1psBPeKuxVTXhuWu/W7VAcRd0EQ6pyyi4aWuLvbcrfPTgX31nQ/cgRatYJmzRzvr4nlfvas+Q3EchcEoUGyf79ZALTE1nLLuNtyL1sWwF3VGsFY7hVZ7QDNm4O/f/Usd+uJxhVxP9+9VEXcBUEoZv/+0q6H2nLLVCTu7rLcq6rYGBRUPcu9JmGQFu3amQXprCzz+dy56o9RE0TcBUEopqy4N21qLF13ivvx4+Vrobvb516Z5Q7G714dy71KcV+/Hr74wuEuq/KlZb23bw9/+IPz164pIu6CIACmLZ19jLtFYKD7fO5am0YaZeusN21qfPCuint+vkmSqg3LvUWL8s0/ANixA664Am69FfbsKbfbXtzT0009+LJPLrWBiLsgCIARu7y88hEh7kxkysoyLoqy4u6ubkxHj5obiLOWu7N+cCsMUqkyO9LTYexYc3dq0gT++c9y59qLuyvuneoi4i4IAlA+DNLCneJuRY2U7W0K7hH3qmLcLYKCjO/b2QXcCmPcH3zQXPT772HaNPj005If0ka9Fnel1Cil1C6lVJJS6mkH+zsppZYrpTYppbYopapRN00QhPqA1Q4uLKz0dne6ZSpqfwfuKftbVXaqhRXr7oxrpiJ3FefOwdy5MHUqDB4MTz5pAvj/9a9ShzkS95rEy1eXKsVdKeUJvA1cDfQCJiqlepU57C/Al1rrfsAtwDvunqggCLWLZZ136FB6e/v2RpgKC12/RmXi7o4+qrt3m3erjjqpqTBgAKxZU+o4y+ftaFG1sNC40S1SUowrqZy4//yzEfgxY8znjh3hrrvgww9L3aVatjSaf/y4Eff27SuOwXcnzljug4AkrfU+rXUeMBsYV+YYDdjWu2kJ1KBasiAIdUlamqmbYsW4W7Rvb6xXdyTiVCXurlruq1dDz54mVh8wHUd++w2efrqUg70yy/3llyEqqsS7smmTeY+OLnPgggXG137ppSXbbrnFrOr+/HPxJg8P44ayLPfz4ZIB58S9I2DfaCvZts2evwOTlFLJwELgYUcDKaWmKaXilVLxx+uiBqYgNHDefts0aK4Njh83MdllFw3dWV8mPd2814a4FxUZA33oUNuGEydgxgxzd1q1ClasKD62Iss9J8d0W9K6xNjfuNH8Jn372h2otRH3ESNMZxOLuDgj+EuWlBq3Xbv6Ke5l14fBWOr2TAQ+0lqHAKOBT5VS5cbWWs/UWsdqrWPb2ReWEATBKV5/HR59tJROuQ1L3MvizkSmEyeMi6Ls0wG4Lu6Jiaaq5cUX2za88QZkZ8PChUbN7Rqf+vub+P2ylvvHH5ubmFKwbp3ZtnGjeRpo3rzMxQ4cgGuuKT1AkyZw2WXlxD0gwNxIDh+uX+KeDNhXMA6hvNvlHuBLAK31WsAXcHBvFgShpuTnG1eB1nDHHe5J1bcnLa18chG4X9zbtCldV8aiJuKudclawC+/mPehQzEDvfkm3HCDaXj6hz8YV8mqVcXnlm23V1hovDgDB8Ill5QW9wEDylx4wQLz7qjn3siRJt79wIHiTQEBsHmzebqoT+K+AeiulApXSvlgFkznljnmEDACQCkViRF38bsIghs5eNAI0P33m6iQ3//eveNXZLm70y1z4oSdS6aoyLxstGhhDO2CAufHe/xxE6hSUGD87YGB0K0bJoolMxOeeMIcOG2acZd8803xuR07llSQBJgzB5KSzH1g8GBISDD6bK3JlmL+fIiJcdy548orzfuPPxZvCggoKTtQb8Rda10APAQsBhIxUTHblVLPKqWutR32e2CqUmozMAuYrPX5LpMjCI0bK/nxtttMMuT8+e4dvyJxb9UKfHxK2uO5QilxnzTJZHbaXQfg5Ennx9u82VjW771nLPehQ21rBitWmAEHDTIH+vkZp/nGjcXndu5cEv4JsHy5ucFcd50R97w8+OADs6+UuCcmwsqVMH6840lFRpo7h51rxn6Nod6IO4DWeqHWOkJr3VVr/bxt2zNa67m2v3dorYdqrftorftqrZdUPqIgCNXFEvdu3czr2DH3dUjKyTFp8Y7EXSkTHulWcd+5E2bNMoq6axdQEr546JDz41lPE3/6k3FZFfvbV6wwvhVPz5KDY2NN5IzNjxMWZtwyeXlmtxXL7ulpxB3gv/81379fP7uLvvGG8a3fd5/jSSllrPdly4qvZYm7j0/pJiW1iWSoCkIDISnJLAQGBpZ4A6ykHVexgtcc+dyhvH+6phTXlXn1VSOQHh7w2WdASfKUvTVdFWlpxjg/dcp8HjoU40fZs6d0iCIYcc/OLr6ZhIUZn/1hWyygfdG0kBAjwkePQo8edoupJ06YVdc77nB8J7S48kozqYQEoETcw8MdrzfUBiLugtBA2LPHWOxKlYj74cOVn+MslrhXpFfVLbTlCK1tlrtfFnzyCUyebNwy//sfaF0s7nbrkJVSUGDGGzUKbr/deGH69aMklKisuFu+lfh4wLhlrOtpXb4ipmW9l3LJzJhhHnMee6zyyQ0bZt5tC7iWuJ8vlwyIuAtCg2HPHuje3fxdq+K+Z4+JAtm7t3i/O8T9zBkT8ROwY4Xxhfz+98bvvn8/rF1Lq1bG5+2suKenG1EODDTuk61bjduDFSvMI06pwHSMCd6sWbG42z8pHD1qNNtefMuJ+7lzJtFg1CjoVTZJvwwhIeYCNnG3bpoi7oIglCI/34het27ms1UYy13ibvmuA9tpUytl0aJSFQ6DgsxCpys+/uKiYQk/wdVXmzvV9debKJZPPwWMHjrrlrHm3L698fAUFwtbscI43728Sp/g6WnCIm3iHhJiXCQHDjgumnbFFeaU4geAd94xd4Gny5XXcswllxhx17rY3SXiLghCKQ4cMGtzluXerJlJsbcP5XOFYst96Swjjl27GneJbRXVyuh0ZVG1uPTAiUQjfGCc2ePGmRBFm2vGWcvdirsvtU6QlmaiWcq6ZCwGDDB+8IICvL1NUEtF4j5ggHGb9++PiZt/4QW46qqKxy7LJZeYH3b3bkJDTcmZu+5y7lR3IOIuCA2ApCTzbok7GNeMO90y3t6als88ChddZLI68/PhrbeAmjWVLkuxuHPCppg2hgwxE0hLKxZ3ZwKpi5827MW9In+7RWysca8kJgIUX88S97IVMf39bX+8+qrxAz3/fNUTs7BCd2zZVZMn29W8OQ+IuAtCA8A+DNLCneKelgYBftmo9BNG0CMiTMD3u+9CVpZbxL24rgwnSscW9uxp3hMT6dzZ+Oat6Jeq5gwlGbQAzJtnUmDLZR3ZiI0173Z+94MHTc2XoCATDl+OjAz497/hxhsrHtcRPXualVS7rNjziYi7IDQA9uwpCYO0cLflHuh5wiiltRD5+98bR/s337jXcg9uUjosJzLSvCcmViscMi3NuNWt5Cfy8oy4X3utKW/piO7dzQ+5YQNgxD052ZQKrrDG+nffwdmz8NRTVU/KHqWM9S7iLghCRSQllYRBWoSGGms4O9v18Y8fh3a5R0zQuHWRuDjjE4+PJzDQLD66Ku5e5NNiQPfSO0JCzHXsxN0Zv/uxY+ZmV/ybLF9urOwbb6z4JA8PUzzm118BEw5ZVGQM+QrF/YsvzErowIFVT6osl1xiHgvckSRQTUTcBaEBYMW422NFh7hjUfX4sULaZR8oSdcHI4TR0bB5M56eRkhdEvfUfNqSjurfr/QOpYwLo5rinpZWxiXz7bfmJmFX0sAhcXGwZQtkZRVfLze3AnE/fhyWLoUJExw0UHUCa+HY9qRwPhFxF4R6jpVFWXaxz52x7mnHNIGklbdO+/QxBVy0djnW/cS+0+UXUy0iI2HnTlq3NvrsrFum2E1VWGgqf11zTen66o6IizPHx8eX+k0divu335pjJ0yoekKO6NfP3H3Hle1vVPuIuAtCPefUKeNODgrCWJw7dwLuE/fcXDiT7UU7jjsW98xMOHzYdXE/klO5uCcno86ecToc0nLLAKYkZFpa5S4ZCys7ae1aQkNLDPIuGb/BxInFvy8As2eb5KeYmKrHdYSXV9UNXWsJEXdBcBO1VQfVctcG+5wwae033QRau80tUyo7tU2b0jstUdu82WVxTz8BAT5nHIudFTGzc6dT4q61nVtm2TK4+26TDHX11VVPJCDALKyuXVuqkFf4Z88ZMe/TBx55xCwor1hRc5dMHSPiLghuYMMGo4tWPLo7sQQ16IPnjRW9bRts3oyvrxFkVy13K6SwXY+25XdajUNt4p6W5ny99S1bSt/wjp/1JSDQw7FQlomYqUrcs7JMuHrgjp+Nj10pk1Vbql1SJcTFwdq1xYlTXl6akN++NxExN95oGn28+665CUye7NyY9QwRd0FwAxs2mECN2bPdP3ax5f7bPJMl6e1tskdxTzjk8Z0mAD2wnwOL2t/fZKvaxL2oyLmmHQkJxgC2FXwkMSGXtIK2RPYocnxC167GhWGLdc/MNL9nWebMMV6T4uzUFV+ZzkdbtpQU63KGuDjzyLJvHzExENUmBU9PZbp/fP658VVZFSQrDKOp34i4C4IbsAT266/dP3ZqijF/gy7vZdoEjR5tBKiw0D3ivuEAAO3iujk+wLaoarkvnHHN2BJAmTHDvH/8ynE8KeCW2yuIP/f2NlZyJbHu2dlw883w5JN2CUxZe01TWYfZR5UQF2fe167llRfy+UlfDmPGlITf+PhUb7x6iIi7ILgBS2A3by7JJnUXKTtP04JMmk0YY9wPkyYZhV2+nJCQ6ov7Aw+Yel1Wh7ujm40Z3G5YpOMT+vSBpCSCWpk+cc6Iu+VWWb3aVGv8dF5LrmYR7a92sJhqERkJiYnFTTvKfq9ffzUVEZYuLSkXENi2yFju1aV3b1Og57PPaDr9X7Q+vtv47RsRIu6C4Absu9rbtel0C6m7zxBEakmUyZgx0LIlfPopoaHGhXHmjPPjrVxp3BvTpxuhfvWXgUT4HqRVcFPHJ8TEmFDITBNF4oy4799vPDre3sZlnXLanzsDf6i4GwiYRdW9ewkNNKUny3ZkWrnSvOfkwKfvm/ZJgeOHla/+6AxeXuYJ6Icf4JlnTCiSM4uxDQgRd0FwA4cPm/pXgwe73zWTcriQYJUKUVFmg68vjB0LP/xQo3DIlBTzAPD00zB6VCGZ+U35+rY5FQeE9OkDQIcjpv+os5Z7ZCTccIPpbNdanWLs8LOVnxQdDYWFtD+1E2/v8t9p5UpzSOvWsHi5ce8E3nt91ZOpiNmzzZdZv94srlZUsqCBIuIuCC5SVGTCEUNDTc/kjRtNxrm7SD3pQ1DLc6WTc/r1g7Q0QpubClvOhkOeO2fi5h95xDTGSNjiyYfcRfSESppPhIWBvz8+OxJo29Z5yz0sDKZNM59v0bNocnEV6fu2mjYeWxLo2LG0uOflGf293OYa11rRyvM0Pv16Vz2ZivDwMM1hBw4sacvUiBBxFwQXOXbM+II7dTIJklDiQnAVXaRJOdea4JAyZrUtRDH0rFm5dNZyt4S5b1/jkZg99jNu9p5jaz5aAUqZp4Zt28qJriOKisxiaHg4DB8Ob07eyF94rmQRsyK6dzex6ps2lVsojo837phhw2BclOkQFdi20IlvfOEi4i4ILmKJUGio0Sdv79JJjq6QsSOFXHwJ6u5feodN3Dse3YhSzot7cVhlsHHhTzj6hvElNa3A325/va1b6dJFFy9mVnaN/HxjuSsFD7X4hGC/jKqzPD09zTEJCeXE3bpZXnIJXLVrOk3IoX1Xf8fjCICIuyC4jL24e3kVR/S5hZSfdwNp0ByLAAAgAElEQVQQ3LfMQmT79hAQgPeOzXToUDNx5/Rp40O67LKqT4yKgpMn6dI+i337SicnFRTA3/9u1iOtdoBgVwtn7Vrj+nDGp923rxH3EE1ycklEz8qVxoffzu8szb/8gKdiFnPzrTVYSL2AEHEXBBcpFveHxsHx41ZEn1tIXW8GDxoUWnqHUsXWdHXCIUuJ+6pVRj2HD6/6RNuTQhevw+TklLTbS042rpJ//MO4eeLj7VrWTf+dWWX+7Tfz7gx9+0JmJp2anyQ/38SzFxaakMphwzDld8+e5dl3AnjoIeeGvFARcRcEFzl8GPw8cmizei58/TWRkbB3r2vNpC1Stprs0eCuDpJ0oqNh+3ZCQ3S1xL2JRz6tg/1MzRQfn6p94WDiwoEuueauZS0Y/+1vJhv17bfN5+XLSyz3zotnmpDN8eOdjyG3dWgKzTHJAocOmRvl6dNwUcFKk6EbGWlaAQqVIuIuCC5yeOMxQosOopSCb78lMtIYxO6oM5O6zyQOWZ2QShEdDVlZhLbM5PBh5wqXpezPJbjoMGrwILj1VnjtNeeyO9u1g/bt6XLStKezxH3TJmNRP/CAmc7y5bB/0ymCSMH3gbth8eKSyorOEBUFHh6EntgEmBvnhp+zABj0/jQTNvPKKw2ykNf5RsRdEFxBaw7FH6dTk2Pw2GOwfDk9gzIBN7hmDh8m5XQz/JvkOq6HZUXMkExWlklmqoqUrSdMQtTrr8PMmUaVnSU6ms4HVqCUEfeCAti+vWSddPhw4z7Z9XMqYZ6HjVlfXZo2hR49CD20GrCJ+3fJtCCTiDkvmzCc0aOrP+4FiIi7ILjCokUczmpNaGx7Uwu8sJAee+YDbhD3n34ilSCCgyowyW2uktDsXYBzfveUQ4UENz9T0ie1OkRF4Zu4iY4dNfv2mZpaeXkQ08SEBg0fbuLo157qSXi0vymtWxP69qXN9lX4+dnE/TcPBjTZhse1Y8RirwYi7oLgAvlLV5BKEKGXdYPYWAgJodnCr+jc2Q3ivmwZKV6dCQpr4nh/8+YQHl7KhVEpR46Qcq4Vwb1b10wko6Ph3Dm6BOWwb58pxAgQ89wE+PJLLu2egqIIjQdhIyOqP75Fv36ow4cIDS5k764CNmd0JrZ3jgh7NRFxFwQXSNl8HI0HoWGeRnxuuAEWLyYyosA1cdcali0jtUkYwcGViFp0NCGH1gBVi/uZT77jDC0IvrhLzeZkK3/QxT/NiPuSo3iRT8+WqXD77bS+9Wr6KqP4Yd1cCFO0hWZ2yk9i6VJNPj4MvNbRooNQGU6Ju1JqlFJql1IqSSn1dAXH3KyU2qGU2q6U+ty90xSE+snhnWaxz6rxwvXXQ04OPX0PsmtXSZy2sxQ3wti9m6KUVFLy2jpeTLWIjiZo32o8PKqOmEmd9TMAwX3aVW9SFr1MiYIu7CclBdYvSifSYxc+CetNPfYtW7hspIlld6kE+sCB8NBDhB5aTVauGW/gJCcXZIViqhR3pZQn8DZwNdALmKiU6lXmmO7AH4GhWuvewGO1MFdBqF/k5HA41VioxeI+eDB4ehJZsJVz58pXNqyM+HhTPuaJJ+DMgpVMZBY5+V4MGFDJSdHReBXlEdwuv0JxX78eMjfsJmXrCaCkrVy1ad4cIiPpsvErAFYeiyAmIsdkKy1fDt9/z81/702nTjVvOVrMSy8RGpADQIDvGTp38XRxwAsPZyz3QUCS1nqf1joPmA2UbeU9FXhba30KQGvtRK8WQWjg7NnDIW0amRaLu58f9O5NZPovQPX87uvWmYSdf/8bgp6axJdM4OWXNLfcUslJVsSMf4ZDcV+/3uQPPX3vSVKUmWuNxR1g9my6tDSx9wV4EzPO5uJp3x6uvZYhQ0xAS2WVfZ3Cz4/Q+8cAMLBfgbjba4Az4t4RsP/fJtm2zZ4IIEIptVop9atSapS7JigI9ZbERA7SmbatCvC3L3MSG0tk0jzrEKdJSoKmfkV8//JuurCP/w2byRNPqsqFrXt38PEh1DO1nLgXFMC99xr3/WcJvdnTzfyzdEncY2Losvz9ko+XtankYNcIHWq6dgy8snWtXaMx44y4O/pfq2xslhfQHbgMmAi8p5RqVW4gpaYppeKVUvHHrZbrgtBQSUzkAGF0Divzz2jAAAJO7qZNq8JqdWVKWnOMrue2ce2TPdhSGMVtD5b7J1Qeb2+IjCQ0N4nk5NKJTG++abJHH7/xIGe0P++m3UjTpqbUrysEhjcrrjPmsvulEqKjoVUrGCWmYo1wRtyTAfvCFiFAioNjvtda52ut9wO7MGJfCq31TK11rNY6tl27Gi7qCEJ9YedODnh3J6xLmX9GsbEARARmsHu388Pt3Z5LN99kWLDA+FPGj3fuxOhoQk9tIScHThi3OhmHTvPXJ88xutM2XsmcSpTHDo5l+hEc7HpEoVKm61TbthVkzrqJ4GBTe96Z6ghCeZwR9w1Ad6VUuFLKB7gFmFvmmDnAcAClVADGTePGdgWCUHM2barewqaz6B2JHCgMLal+aBETA15eRPgcdFrcC/fsY29We7r1b2kyMAcONM0knCE6mq6ZpkuS9aSQ8J91ZBX68UjK06ilPzItbivgokvGjrFjTWka8YXXX6r8v0drXQA8BCwGEoEvtdbblVLPKqWutR22GEhXSu0AlgNPaq3Ta2vSglAdbrgBrrrKPYW8iiks5Piuk5wr8i0v7r6+EBVFRM4WkpMhK6vq4Y689iV5NKHr2Eo6IlVEVBSRGOe+5eNPXGBsq15bZsOCBUz69Cp8fSEkpPrDO+Kf/ywpFibUT5zKNNBaLwQWltn2jN3fGnjc9hKEekN2dkmVwpdfhr/8xU0DHzzIwdz2QAUd2mJjiZi9AphMUlJxG1LH5OWxd9Z6ALoNrMHiYXQ0YRygiVcBiYlekJ1N4rZCmnvnENKzOUSOpjUwb55dVI/Q6JEMVaFRk7THrDC2b3aW555zT6VGwPjbCQMob7kDDBhAxNnfAFODpVLmzCEpoy0A3brVYC4hIXi29KdHy6OmA9TixSQWdqdneF4pt8kVVzhfnFFo+Ii4C42a3V9tBuADn3vx8dH88Y9uGtgWKQMVW+7dMHeSKv3uM2aQ1GIA3t66Zm4TW+OOSLXTuGW+/ZZE1ZvIgY5KSQoXCiLuQqNm9+em/viwU99z/dDjrFnjpoHj4znQtDetWpl+FOWIjqaZZy4h/pmVi/vOnbB8OXs7XUaXLgrPmiZiRkfT8/QG9u/XpM39lSM6mMje8s/7Qkb+6wuNl/Xr2bPfk2D/0zT3zqN39gZSUiAjw8VxCwth8WIOtunr2CUD0KQJREQQ0eRA5eI+cyZ4e5Oku9bMJWMxYACReQlorZh3ehgAPXu6MJ7Q4BFxFxovL77Ibs9eRPRtCpdfTq893wNuKMW7bh2cOsUBwisWd4DoaCJyt7Frl+MuSTt+y+HzmWfQ199A0gFvunZ1YU533EHkf34HwLexLwCmG51w4SLiLjROsrJgzhz2+PSme08vuO46eqUuBWDHDhfHXrAA7eHJgVMtKhf3qCgizsSTkQHp9oHBM2aQ2OcWhg3O4bas//KvFv8kK6uGi6kW3t5E3DEEDw9YuiUQLy9cu1kIDR4Rd6FxsnUrp4pacPxccyIigHHj6Mwh/LzzXRf3hQtJHzyarCzleDHVIjqaHphQGXvXzMF/zWLktlfxopCL2ybyp/dM8S2XxB0TXh8ebrojde9uKhMIFy4i7kLjJCGBPbYKGN27A0FBeA6Opaf3PrZvd2HcI0cgIYGDA24AKgiDtIiKIgKj6sXivn8/Tx+8j0zvtizZ2JY5uyKLx3CHpW25YsQlI4i4C42TzZvZ09T0CY2wOr5ddBG9cn5jx44KepI6w6JFABwIHw5UIe7h4YT5HsPLo7BE3H/8ke305tK4PGJiTH2W+fPhT39y3XKHkkVUWUwVRNyFuuPoUZg+nTW/FNGzp6kD7jYSEtjd7iI8PEyRKwD696dX0VYOH1acPl3N8ebNg6uvht/9DkJDScoz5WgrFXdPT7yietLV90ixuOslP7JPdaVrTEkMeu/e8PzzzpeSqQyx3AULEXeh7vj73zn96F+YdOM5du2C1avdNG5hIWzZwu4mMXTubKISASPuGIf7zp3VGO/cOfIn3sGC+Pbc2mEZHXOSePqPirZtTUnaSomKIqIg0Yh7YSFpS7eQpZvRpWvtVNwaPtyUyh02rFaGFxoQLnSxFQQXOHUKPvmEx3iLg2m+KKVJTHST4O3dC9nZ7MnrRIR9un2PHvRqsg9yTcTMoEFOjrdoEeOzPmJu1jjaFBkDvm9fk85fJdHRRORt5cc9IymK/429mabMQG1FsoSHw5YttTO20LAQy12oG95/n6XnLuJD7uaPvEDX4HOux59bJCSggd3HW5vFVAtPT7r0a4mPyqtWxEzhrC9YwkjumFREair873+mz2nfvk6cbFtUzclRJH+zjr0YVZcwRaG2EXEXzj+FhfDWW3wd9Aj+/ppnAv9DZN7m6rlKKiMhgUOeXTiT5Unv3qV3eQ3oQw+1mx3bnVxUPXOGA/O2kYMfwy7zwMenmnOJji6JmJn5M3vbD0UpY2ELQm0i4i6cf+bNg4MHWaovZ/hwhc/jDxF5fCW7d2kKCtww/ubNJISY5srlrOv+/elVtI3tm5280Lx57Mg1K7K9alBqnQ4diAjNAWB3yOXs7XsjISF26wCCUEuIuAvnn48+Yn/gYPYebW781uPHE0ki+QWKfe7o35WQwOZWw6xiiaXp359otnLgiLdzETNffMGOFqbPW40iUJQiaMcymjXT7L7iAfadaScuGeG8IOIunF8yMmDRIpbFmDooV1wBdOlCz2bJgBvqvhw9CikpJBTG0L07NGtWZn+vXvT1MllMVS48HjoEixaxI2QkwcFORMZUgGrejIgIxe7dZq23ODRTEGoREXfh/DJnDuTlsZQrCA62JdsoRWQ/X8AN4j5vHgCbMzo57n7k40OfyDwAEhKqGOullwDY4RVdM5eMHT16mF6ux47JYqpwfhBxF84vs2dTFNaFZQltuOKKkgbLLQf3JIgUdu4ocm38b77hdHgf9iU3qTCapePgENqqdBI2VbKompoK771H0R2TSdzbxGVxj4gwDxUg4i6cH0TchfPH8eOwdClbLn+MEydU6Tjx/v2JJJHETTk1H//UKVi2jC1x9wIV9y1VA2PpqzexeUMlHbNfeQUKCjh8x5/JyqrhYqodxSUQEHEXzg8i7oJjVq+G1FRWrHDCfVERR4/C2bMln7/8EgoLWew/HoARI+yOtcQ9ycth7XOnmD8fCgpICLoaqCQOfdAg+rCZrTu9y0fnrF6NvmcKH72RSdr197Ijy5R9FHEXGhqSoSqU59AhuOwyMgZeydhtCxg4ULFsWTXHKCiAfv2gqAheeMFUU/y//0P37cfHSzowaBAEB9sdHxFBpM9MzuT4kJICHTvWYN7ffAMhIWzO6EzbtmXGt6d3b/p6Tyc335Pdu+2Ee/16uPhilvuO5q7CBYzJzOFSWwVJV8XdSqZq3dq8BKG2EXEXyvPSS1BQwIy1MZxBsW1bDcZYt47jRwvIDw4j6J57UAC33MKaSe+SOEbx/vtljvfwoGdEEWwzi6pOi/uRI/Cvf5lQlsWLYepUEtYq+vYt8eeXw9ubPpH5sMU8lRQL97ffgpcX04d/h/oB5v/oy469EBhoqje6QqtWZpxOnVwbRxCcRdwyQmlsC4k5t0/lda8n8KSAtDTjLq8WixYxmHV0TNlAO/8cnr5xD/rzWcz8shX+/jBhQvlTooeYuMXNm5xfVN367Hdc89Yo0p7/L+TmUjDhNrZtq9jfbtFzWCA+5JLwm9215s9n/8CbmfuDD08+CTExsG+f61a7xW23wY03umcsQagKEXehNLaFxE96PM+xggCe4BWAaje4OD1vBfvpwpgxMOyKJrz4TTceecS43SdNchB/DgRe0oPOHGDdsrPld1bAjwvzWcg1TB2Tis48zUsrBpOTAxdfXPl5PkP605vtbF6TZTYcOADbt/O2z+/w8IBHHoH//MdY/1FRzn/vynj1VXj6afeMJQhVorWuk9eAAQO0UM84c0brpk11wa23627dtI6N1frwgHEatH7rrWqMc+SI/o2+GrT+5huti4q0vvderU2baK03bargvK1b9c3M1p3annHuOqmp+lFeKx73rru0Vkrr224z16yUXbv0ZD7Qgf7Z5vNbb+mzNNWtWhToCRNKDvvxR62PHHFuOoJwPgDitRMaKz53oYQ1ayA7m++6/J6kz+Grr6Djxl603JjB9s3NcXqJ5ocfSMK0Fera1Vi/b79t1lZPnaokiqVnTwZ7fcqX6RM4ehQ6dKj6OgfpTGR4DkHhvnz4oRl75sxK/O0W3brRz+99PjrjR3IyhCxYwPKg28hI9WTKlJLDnCrrKwj1EHHLCCWsWoVWHry4IIru3eH660FdFEdvtrNtXZbz4yxaRJJ/f6Ak7M/T04juV19Vcp6XF4N7ZACwbp0T11m4kENeXQmPbMInn8DUqfDdd9C0qRPnengwOCobgPVLT8NPP7EudDyenhAX58T5glDPEXEXSli1iuXdphK/yZMnnjCCzODB9GY725N8nIs/z8+HJUvYG3QxHTpA8+ZVn2JP/6F+eJHP+nVVXKygAJYs4ZBXOJ06KTp2NDePStvelaHP5W3xJo91d70LubmsKxhAVJTj9QBBaGiIuAuG3FxYt44Xcx+jfXu44w7b9sBAotoe5WS2H8eOOTHOmjVw+jRJ3j1r1PDZb1A0MWxh3c/nKj9w7VqyMvM5keNf4/BC36ceoW/nDNaFT6To1ddZv7cNgwfXbCxBqG+IuAuGjRs5ltOCJYd68uCD4Otbsqt3X28Atm11wnRftAi8vEg61bZmmZj9+zOYdWxI8KKosojIOXM47GXKK3buXIPrALRpw+CxgcSndSJx5KNkZioRd6HR4JS4K6VGKaV2KaWSlFIVBnMppcYrpbRSKtZ9UxTOC6tWsQMT0D1kSOldvUeYlc3tv5ysepyFCzkXdzlHUjxqZLnTuzeDPTdy+pxPxZ2ZCgrgs884ONCUMXAlMWjwYMjKgg8/LPksCI2BKsVdKeUJvA1cDfQCJiqlyqV1KKX8gUcAZ5bChPrGqlUkth8OlG9K0X5kH9qQzvZVpyof4/Bh2LqVfQNNhlKNxN3Hh8E9q1hUXbIEjh3jUN9rAdfFHeD998Hf31aCWBAaAc5Y7oOAJK31Pq11HjAbGOfguP8DXgJcKOsn1AlFRbB6NYltL8bfv3zqv+oTQ5THDrbsqCIU8ocfAEgKM/GDNS2QFREXgD9n2PSbnRvo0Udh8mRjtX/8MbRty6FWMXh6VlJDxgm6dYM2bUwPkYEDbYvIgtAIcEbcOwKH7T4n27YVo5TqB4Rqree7cW6CI5KS4PXXqdwhXU22bIGMDHaqSHr2dBAj7uXFxSEHiD8WQnp6JeMsXAihoSTlhgI1tNwBj9j+RLOFzettJXl37YI33zSiPmUKfP89TJzIwWRPOnYELxeyNZSCQYPM3+KSERoTzoi7o3SQYpNKKeUBvAb8vsqBlJqmlIpXSsUfr3axEgGt4e674Xe/K+4S5BYWLAAg8WRghW6J667OoxAvFnyWUX7niROwdKl5jR7N3n2KNm1cqH7Yvz8xbGHLdg8Tfvnvf4OPD6uvfZFLP76Lkblz4c47OXTIhcVUOyxRt0ReEBoDzoh7MhBq9zkESLH77A9EAT8rpQ4AQ4C5jhZVtdYztdaxWuvYdu3a1XzWFypLlsCqVaSH9CHtz29wdska94w7dy6nBwznSKpnhU2gB9wbSzBH+P7jMuK+fLnxi1x5pVmZvOkmkpJcrFkeHU1Mk91kZPmQvHQnfPIJf+71HRfPfYpfPS7iR0ay1WcAhw65p8rijTfC0KFw6aWujyUI9QVnxH0D0F0pFa6U8gFuAeZaO7XWmVrrAK11mNY6DPgVuFZrHV8rM75Q0Rr+8hfeafNnApITaF+USturBrBvazUyRx1x9CisX8/OgbcD5RdTLTz6xjCu2TIWb25Pjv2qynPPQbt2xmpPS4MRI0hKqrlLBgBfX2JevA2ALaOfpjC3gHf2juSaa2DXXm88PeF/nykOH3aPuEdHwy+/SJ11oXFRpbhrrQuAh4DFQCLwpdZ6u1LqWaXUtbU9QcHG999DfDxzgu4nPBxeu383BXjx0T8O1mw8K93Ucsl0NIugFYk7SjHusgyyCv1Ytsg0mOa33+Cnn1h93ctM+2IEHaICaNkS9u93UdyBqMnmwW+L6sNvI54k47QnkyaZDNQrrjDZqAUF7nHLCEKjxJnqYrXxkqqQ1eSii/S58Ejt61ukH3tMa52fr0d6LdOdmh3XhYVOjrFokdYDB+qVLcfoCX5zdO6qdVpfe63WnTrpp/9QpL28tM7Lq/j0nDmLtD+Zesqow2bDrbfqZX7XaNC6WTOtb7lF68ce0/qJJ7Q+cMDVL6x1WJjWt1yfo//5bJ4GrY8dM9s/+qikwuTCha5fRxAaEkhVyEbEli2wZg2r7/2SnP/YGkt7eXFn7HZu+/VyViwvYviIKh7CcnNNpIm3N39p+j9WZkZw1Yj7uMtjCdxzD4k7Fd27g7d3xUM0GXkpoz3nM2/FSIpWrMLjiy+Y12cZvjsgJQVatHDrtyYmBrbsakJapmm+ERhotl9/Pdx7r/lK0tlIEBwj5QcaAjNmgK8vS33H4OUFw4aZzddNCcCf03z8mhOZo++/D0eOkPD0bFamRuDpqXlJPUVRTi6MHUtiYiUuGQs/P8bGHOLYuZZsvOxx8PNj+bk4LrrI/cIORtx37TK9uu1L77ZoAWPGmL9F3AXBMSLu9Z0zZ+DTT2HCBJau9mPIEJNJCdB03JVM4Eu+XtKCs5U1L8rNhX/+Ey6+mDfXDaJpU5g+XbEztwvznlpF3mUj2bvXCXEHRv37SjxUEQtu/JD0X/ewOdGH4cPd8k3LERMDhYVm+mXrqv/f/8H06SW/hSAIpRFxr+989hmcPcvJWx9i48YyIhcQwO29fyMr38dKDnXMe+/BkSOc+N3zfPa54o47YNo0szj5zA9DufU2RWGhc+LedngMQ+I8mH8gihW7TM2Z2hR3MK6iSy4pvS8yEh5+uHauKwiNARH3ekZRUUkgC6dOGYu7f3+Wnx6A1uUt2LibQmjGWZYvyHY84K5d8Mc/wqWX8u62S8jNhYceMlmdTz5p3Pk//2yEcvx45+Z4zTWwcSPMmmUaYwwcWNNvWzndupnqlBddJDXWBaHaOLPqWhuvRhktEx+vdUZGjU/Pzy3UoS0z9WtTt5smoDfeqLWXl85bs0GPGKG1v7+DaJbfftOjWKgjg0+VH/DMGa179dI6IEAfWJ2smzbV+rrrSnYXFmq9fr3WubnVm2dCQkm0ysiR1f6a1eLdd7X+6afavYYgNCRwMlpGxN1dbN5sujP37691ZmaNhtjy4AwNWndljy7q209r0IUvvKhvvdX8l5o508FJRUX6Rf//06B1amqZfXfcobWHhy76cakeM8aEKx48WKOplb2kDgkxc3rhBdfHEwTBeZwVd3HLuIu//50iv2bkb95B/pjr4VwVnYTKsmgRG9/+FYC9dGP1rgC46ir+cOJJPv/ceGemTnVwnlIMv9yU//l5aUHJ9r17zULsE0/wbeYI5s+Hf/zDPdElSsHo0ebv2vK3C4LgIs7cAWrj1ags940bdQ4+OrRFRrG74qnYZc6fn56udevW+qG2n+tmzYp0s2ZaT7kzT//6S75WSutp04y1XBH5X8/RLcjQ08YcKdn42GNae3npeR+d0H5+Wvfrp3V+fs2/Ylm2b9f64YfdO6YgCFWDk5a70lpXeQOoDWJjY3V8fCMpPzN2LMt/Vlx+di5TpsDeOVv4Nb07B4/60i7QUVHNMrz/PkyZwkXRZ/Bs2ZyuXeHbbyE83BRcTEysIo787FnGtljBrlaD2H2ynQmfDAnh014vcNeGB+jXz1QZsJKABEFouCilNmqtq+x2J24ZV9mzB+bPZ2n/p/D0hFdfhbcf2U2ObsKbf3WmozTw5ZcUdIkgIakZAwbAnXcafd6yBd54w4kEoebNGd7tMHtOtePIEeCTTyg8fZbHdkxlyBBTuFGEXRAuLETcXeWnnwBYmhFbnGAUOWUo4/ietz5tWXlyERjTfNkydl7+AOfOKQYMMKVne/SAa6815WidYfi1Jptn2X1fwfPPE9/rTk6e9uahh6B5cxe+nyAIDRIRd1dZuZJTgT2I39akJAY9KIg/RM7j1Dk/3nuvivO/+w4KC9kYeh0AAwaAhwfEx8NXXznoilQBfaYNJoTDfDXfF4KD+eGif6CUKbMuCMKFh4i7K2gNK1bwc7cpFBWpUglGQ24JYwhr+d+H+ZWP8eWX0L07G493olkzY7GDsbZ9fJyfikdEN2653YfF3mM4uSSexdtDiY2Ftm2r/7UEQWj4XBji/tlncNddkF1BFmdNOXAAjhxhmddVNG9epgfn2LFczk9s3u5Z8WWTk41b5+ab2fibol8/1xo0T3ysPfn5ivfeg3XrYNSomo8lCELDpvGL+08/mRXKjz4y+fV5ee4be8UKAJYeiuDSS8uUy+3bl7g2uyko9MBhUND+/SZIvEkTCm+9nYQE45JxhX79ICLCxLMXFcFVV7k2niAIDZfGLe5JSTB+PL+GjueugduYvOhm/tR3IUWFbgr/XLmS5FZR7DrQhBEjyuxTiiFXtQRg7Zqi0vv27TMFU9LTyf9hGXf9qwfZ2SWlfGuKUjBxonlAadmyzJOEIAgXFI1b3O+7D43iYf+P+HJ7b370v4EXEq/j+5d2uWf8lStZ1XUy4Li5csCoWLqzm7WLz5TeMX06nDrFmR9WM+b5OD791LQivf5616c0caJ5v+IKUxxMEIQLk8Yr7jt3wrJlrJvwKvFbfXn5ZdkQQJYAAAurSURBVDh4yIMuah8vvuZNtXK3CgrgkUdg0CDIzDTbjhyBvXtZ7TuC5s1LytOWYvhw4ljL2nivkusVFsLs2RwbcSvDH4hk2TJTkffPf3Y+MqYyevSAf/8b/vQn18cSBKHh0njFfcYM8PZm+rEJtGgBd9wBXq2a80TcGtYd78rKH5xcXD19GsaO5eM3M4nb8AYp9/zVOLR/9ztQil9O9GDIkAqs5NBQ4gKSSDvbjP37bduWLyflmAdDf5vOjh2m7/U997jrSxsefxz693fvmIIgNCwah7gXFJT+nJ0NH39MyugpfDXPl3vuKUnkmfx8dwI5xotPpTs39pQp6CU/8nzgdH4ljpHfTOPkiJvgq6/IfPYNtu7x4+KLKz497hKj+mt+sfndP/+cT5pMY+/R5ixbZmqjC4IguJuGL+7Ll0ObNvDYY8aiBpg9GzIymNHqaQoL4cEHSw73u3QQjwTMYtG2UHburGLs/fvh66/59bY32ZPWkrsnF7FHRTD65yfJu/s+fo19iKIiGDq04iGiru9Oc86wdv4JyMmBb75hXftr6dYN4uJc/vaCIAgOadjivmoV+poxfFh0Jwlv/Az33guvvw5PP01+rz68tySUq6+Grl3tzlGKu+9vgqKIL98+Xvn4b70FHh58rG/Hzw9ee8ODT948zTqG8G7vt1i9RuHpWXlUiueIyxjEetas1vCf/6BPn2bd2d4SySIIQu3iTOnI2ni5XPJ3926tmzfXK0JvKy6zeyv/0yl00Pqyy/R3r+7ToPX33zs4NzVVX8IKHR1YtruFHWfOaN2ypT43fpJu1UrrSZPM5qIira+4QuvWrbUeMMD05qiK59q+appp0F4fih6tQevp02v0rQVBuMCh0TfrePxxUIqZsf+hZUt46in41vsWxkXuJn/Jcmb+GE5wcElTiVJ06MD4HtvYmtaBXTsrCJv55BPIzGRun7+SkWHyoMBEtLzyCmRkmD6ilfnbLa6ZYBz+i+75hnV/ngtIDLogCLVLwxT3JUtg/nzSf/ccXy9sxu23w4svwiefebIh0Z/774cffjBRKBXFet9wbzsAvnn9cOkdRUUm0uYPf4BBg3hnaXdCQkp3HOrTByZPNn9X5m8vPv6tqXTsCAsyhrIu3hMfHzOGIAhCreGMeV8brxq7ZfLzTdPnrl31ay/na9B6y5aS3ZMmGReNUlofOFDJOJmZOk6t1f0CDpVsO3tW61GjzABXXKF/mn1Mg9ZvvFH+9GPHtH78ceO9cYapU02D68GDzUsQBKEm0GjdMh9/DDt2oF9+hZkfeDFkCERHl+x+6y3o0sVke3buXMk4LVowPmY3m06EsndnPmRlwZgxZCxeR+7r76IXL+GZtwIJDoZp08qfHhhokoWcrZU+ZoxpwLFunbhkBEGofRpegvqkSeDryztHxpGYCB98UHp3y5awfbupiV4V4x8O4vdT4PNBr/PXwP+Qsy+F3q1O4PFKUyYchl9+MTcLX1/Xpz1iBDRpArm5JtFVEAShNml4lnuTJnyubuPhRxRjx8Ltt5c/xNfXuVrone4awfAeR/iE29HtO/DdQ8tIOdWUpk2NVR4SAlOmuGfazZrBZZeZv8VyFwShtnFK3JVSo5RSu5RSSUqppx3sf1wptUMptUUptUwpVZlDxCV++MFErgwbBl984WJxLA8P7vxjR5LOdGDNS78wc2scXbrAjh2mofTcucbadhcPPww331wm7l4QBKEWqFLclVKewNvA1UAvYKJSqleZwzYBsVrrGOBr4CV3T9Sie3e47jojvH5+ro93443Gqv7rX+Hnn2HqVNMwY/RoUx/dnVxzjbkhuaNAmCAIQmU4Y7kPApK01vu01nnAbGCc/QFa6+Vaa6sS169AiHunWULXrqa3aIsW7hmveXMj8MuXm6cAK8RREAShIeOMuHcE7IPBk23bKuIeYJErkzrfWAlK48ZBhw51OxdBEAR34IzH2pETwWFap1JqEhALOGhdAUqpacA0gE6dOjk5xdrnsstM/fNbb63rmQiCILgHZ8Q9GQi1+xwCpJQ9SCl1BfBn4FKtda6jgbTWM4GZALGxsW7qdec6Hh7w/PN1PQtBEAT34YxbZgPQXSkVrpTyAW4B5tofoJTqB/wHuFZrneb+aQqCIAjVoUpx11oXAA8Bi4FE4Eut9Xal1LNKqWtth70MNAe+UkolKKXmVjCcIAiCcB5wKkpca70QWFhm2zN2f1/h5nkJgiAILtDwMlQFQRCEKhFxFwRBaISIuAuCIDRCRNwFQRAaISLugiAIjRBlGnvUwYWVOg4crOHpAcAJN06nNpG5up+GMk9oOHNtKPOEhjPX2ppnZ611u6oOqjNxdwWlVLzWOrau5+EMMlf301DmCQ1nrg1lntBw5lrX8xS3jCAIQiNExF0QBKER0lDFfWZdT6AayFzdT0OZJzScuTaUeULDmWudzrNB+twFQRCEymmolrsgCIJQCQ1O3Ktq1l1XKKVClVLLlVKJSqntSqlHbdvbKKV+VErtsb23ruu5WiilPJVSm5RS822fw5VS62xz/cJW4rnOUUq1Ukp9rZTaaft94+rj76qU+p3tv/02pdQspZRvfflNlVIfKKXSlFLb7LY5/A2VYbrt39gWpVT/Op7ny7b/9luUUt8ppVrZ7fujbZ67lFJXna95VjRXu31PKKW0UirA9vm8/6YNStydbNZdVxQAv9daRwJDgAdtc3saWKa17g4ss32uLzyKKeNs8SLwmm2upzAtE+sDbwA/aK17An0wc65Xv6tSqiPwyP+3dz+hVlVRHMc/iwxBI8rCemHwNKJBEulIq0H0h1TECBoYQkJB40bJQwiaRzgpGxQJIQWZlAgRUY2NjEypLMOHKVY2yKAmQqvB3hevr/vQoO4577K/cLjnrL0f/Pi9s9c9d+373lIaxa/GVUrvg754ugcb5sTm83Ajbq/HM9g9Jo2M1vkRVmfmXfgOM1DX11bcWX/mlZojxsUe/9QqIm7Fwzg1FB6/p5m5YA6sx4dD1zOY6VrXPFrfr7/g45iqsSkc71pb1bJCWdAP4KDSTvFXLBrldYc6r8VJdX9oKN4rX13sNbxM+VfaB/FInzzFNI5dzkOl8c4To+Z1oXPO2GPYW88vWf9Kz4n1XXpaY/uUh5BZ3NiVpwvqyd2/b9bdCRExjTU4hJsy8yzU1+XdKbuEXXgOf9XrG/BbluYs9MfbVTiHN2oJ6bWIWKpnvmbmGbyoPK2dxXkc1k9PB8znYZ/X2VP4oJ73TmdtYHQmM4/MGRq71oWW3K+4WXdXRMQ1eBfPZubvXesZRURsxi+ZeXg4PGJqH7xdhLXYnZlr8Id+lbZArVc/ipW4BUuVj+Jz6YOnl6OX90JE7FTKn3sHoRHTOtMZEUuUPtLPjxoeEftftS605H5Fzbq7IiKuVhL73szcX8M/R8RUHZ9CH3rM3ostETGLt5XSzC5cFxGD7lx98fY0TmfmoXq9T0n2ffP1IZzMzHOZeQH7cY9+ejpgPg97t84iYjs2Y1vWuob+6bxNeXM/UtfWCnwRETfrQOtCS+6XbdbdFREReB3fZOZLQ0MHsL2eb1dq8Z2SmTOZuSIzpxUPP8nMbfgUj9dpfdH6E36MiDtq6EF8rX++nsK6iFhS74WBzt55OsR8Hh7Ak/UbHutwflC+6YKI2IAd2JKZfw4NHcDWiFgcESuVzcrPutAImXk0M5dn5nRdW6extt7D4/d0nJsP/9EGxiZlx/wH7Oxaz5Cu+5SPWV/hy3psUmrZH+P7+rqsa61zdN+Pg/V8lbI4TuAdLO5aX9V1Nz6v3r6H6/voK17AtziGN7G4L57iLWUv4IKSdJ6ez0OlhPByXWNHlW8AdanzhFKvHqyrV4fm76w6j2Nj157OGZ91cUN17J62v1BtNBqNCWShlWUajUajcQW05N5oNBoTSEvujUajMYG05N5oNBoTSEvujUajMYG05N5oNBoTSEvujUajMYG05N5oNBoTyN83Xs/kaiOAvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare the results \n",
    "plt.plot(pred_test, 'r', label='prediction')\n",
    "plt.plot(dataset, 'b', label='real')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}