RecurrenNeuralNetwork-RNN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_series(series, y=None, y_pred=None, x_label=\"$t$\", y_label=\"$x(t)$\"):\n",
    "    plt.plot(series, \".-\")\n",
    "    if y is not None:\n",
    "        plt.plot(n_steps, y, \"bx\", markersize=10)\n",
    "    if y_pred is not None:\n",
    "        plt.plot(n_steps, y_pred, \"ro\")\n",
    "    plt.grid(True)\n",
    "    if x_label:\n",
    "        plt.xlabel(x_label, fontsize=16)\n",
    "    if y_label:\n",
    "        plt.ylabel(y_label, fontsize=16, rotation=0)\n",
    "    plt.hlines(0, 0, 100, linewidth=1)\n",
    "    plt.axis([0, n_steps + 1, -1, 1])\n",
    "    \n",
    "def plot_multiple_forecasts(X, Y, Y_pred):\n",
    "    n_steps = X.shape[1]\n",
    "    ahead = Y.shape[1]\n",
    "    plot_series(X[0, :, 0])\n",
    "    plt.plot(np.arange(n_steps, n_steps + ahead), Y[0, :, 0], \"ro-\", label=\"Actual\")\n",
    "    plt.plot(np.arange(n_steps, n_steps + ahead), Y_pred[0, :, 0], \"bx-\", label=\"Forecast\", markersize=10)\n",
    "    plt.axis([0, n_steps + ahead, -1, 1])\n",
    "    plt.legend(fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recurrent Neural Network\n",
    "RNN sono una classe di reti neuronali applicabili a sequenza o serie temporali di lunghezza arbitraria.\n",
    "\n",
    "Le reti feedforward o sequenziali viste sinora seguono un flusso la cui direzione procede dai livelli di input fino a quelli di output in maniera lineare.  Una RNN e' simile a questo tipo di reti tranne che presenta un **collegamento all'indietro**, come mostrato nella seguente figura che riporta la piu' semplice RNN.\n",
    "\n",
    "![](rnn_simple.png)\n",
    "\n",
    "Ad ogni step $t$ , la rete riceve  in input il segnale $\\mathbf{x}_t$ e l'output $\\mathbf{y}_{t-1}$ - l'output al passo precedente. \n",
    "\n",
    "Una rappresentazione equivalente alla precedente e' data dallo _srotolamento_ - **unfolding** della rete, come mostrato in figura:\n",
    "\n",
    "![](unfolding.png)\n",
    "\n",
    "in cui viene creato un layer di unita' ricorrenti o ricorsive.\n",
    "\n",
    "In questa architettura ogni unita' riceve  due insiemi distinti di input:\n",
    "- gli input dal livello di input\n",
    "- le attivazioni dallo stesso livello generate al passo $t-1$\n",
    "\n",
    "Ad ogni passo $t$ le unita' del livello hidden ricevono in input $\\mathbf{x}_t$ e $\\mathbf{h}_{t-1}$, cioe' i valori precedenti del livello hidden.\n",
    "\n",
    "![](unfolding_2.png)\n",
    "\n",
    "Ogni collegamento riportato in figura ha una matrice dei pesi associata che non dipendono dal tempo $t$. Le matrici dei pesi sono:\n",
    "- $\\mathbf{W}_{xh}$: la matrice dei pesi tra input $\\mathbf{x}_t$ e $\\mathbf{h}$\n",
    "- $\\mathbf{W}_{hh}$: la matrice associata al collegamento ricorrente\n",
    "- $\\mathbf{W}_{hy}$: la matrice tra il livello $\\mathbf{h}$ e il livello di output $\\mathbf{y}$\n",
    "\n",
    "Il calcolo dell'attivazione e' simili alle reti sequenziali:\n",
    "\n",
    "$$\\mathbf{z}_h^t = \\mathbf{W}_{hx}\\mathbf{x}_t + \\mathbf{W}_{hh}\\mathbf{h}_{t-1} + \\mathbf{b}_h$$\n",
    "\n",
    "da cui\n",
    "\n",
    "$$\\mathbf{h}_t = \\sigma_h(\\mathbf{z}_h^t)=\\sigma(\\mathbf{W}_{hx}\\mathbf{x}_t + \\mathbf{W}_{hh}\\mathbf{h}_{t-1} + \\mathbf{b}_h) $$\n",
    "\n",
    "riscrivibile come \n",
    "\n",
    "$$\\mathbf{h}_t = \\sigma_h([\\mathbf{W}_{xh};\\mathbf{W}_{hh}][\\mathbf{x}_t^T;\\mathbf{h}_{t-1}^T]^T + \\mathbf{b}_h)$$\n",
    "\n",
    "<br>\n",
    "\n",
    "![](comp_schema.png)\n",
    "\n",
    "Dal momento che l'output di un'unita' al tempo $t$ e' funzione dell'input dei passi precedenti, possiamo dire che esiste una sorta di _memoria_. Un layer con la precedente struttura e' infatti detto $memory cell$. In generale una generica cella di memoria e' una funzione $f(\\mathbf{h}_{t-1},\\mathbf{x}_t)$.\n",
    "\n",
    "### Sequenze di input e output\n",
    "![](rnn_inout.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training RNNs\n",
    "Per addestrare una RNN si sfrutta la rappresentazione estesa della rete nel tempo e si applica backpropagation: **backpropagation through time**\n",
    "\n",
    "![](bptt.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time series\n",
    "Un problema a cui applicare RNN e' il forecasting di serie temporali univariate o multivariate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_time_series(batch_size, n_steps):\n",
    "    freq1, freq2, offsets1, offsets2 = np.random.rand(4, batch_size, 1)\n",
    "    time = np.linspace(0, 1, n_steps)\n",
    "    series = 0.5 * np.sin((time - offsets1) * (freq1 * 10 + 10))  #   wave 1\n",
    "    series += 0.2 * np.sin((time - offsets2) * (freq2 * 20 + 20)) # + wave 2\n",
    "    series += 0.1 * (np.random.rand(batch_size, n_steps) - 0.5)   # + noise\n",
    "    return series[..., np.newaxis].astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_steps = 50\n",
    "series = generate_time_series(10000, n_steps + 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 51, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definiamo training, validation e test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "X_train, y_train = series[:7000, :n_steps], series[:7000, -1]\n",
    "X_valid, y_valid = series[7000:9000, :n_steps], series[7000:9000, -1]\n",
    "X_test, y_test = series[9000:, :n_steps], series[9000:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Z5h5O1HeHODIxHxyt9Sz63JSTPKPHXZztuX+4zBqX1Dj52EP7GHJ5WkJe6DiVFBvJxdnJvFYmdeazZbaWAEuAWr+v64CtE9zvUqXUUaAB+EetdekMHotS6i7gLoC4hTnsOFrL9uR2YiImrpkyQm9vL7t37zY6jAmZNbZQxjXs0lS19bMuaXhaP9MX23DbCG4N9+0q54FXy/naJTEsd0xvxj1YzPr79PEfr+np6aaNtb2rl9fP9rEtO4JXX311Wo95rWIYAA0Mj7h57OUD9CyLuvCDZsjMv9+pYtvfOArAYGMZu3efX/LjGNFE2OB/nirmjjXRIYvLSGaODawzXqfzOj5VMYwCeqpPsLt++vnBqNvzd/nM3uMkOs8GPK5Q21ExzIjLc1XK5dJTHqeyI4d5smKELz3wIhvS7SF5jzPj6wazi8tsiflEf/njr1EeAnK01r1KqZuAvwIF03ys55taPwA8AJC7fKXuG4FzUUu566plsw480Hbv3s22bduMDmNCZo0tlHGdbOhGv/Q6121Zx7YNi6e8vy+20l1lcOIsGnBpGErOYdu25cEPeBqxmZX/eF25cqU2a6w/+sPLjLiH+NvrCrlsedq0HpOY5+SvFXsZdWuiImzcdu0lAb96Z+bf71SxFT93mkh7JR991/axHXTHe671EG+Ut/GzK64kOiIwCYCVXzOjWWW8Tud1/E31AZZn9HPTdVfP+PkvOv0mHdjYtu3SgMcVaq0Jtfyp7BgAUZFTH6caYmt4suIEOypHeKnWNaP6/Nky4+sGs4vLbKUsdYD/frdZeGbFx2itu7XWvd7PnwUilVJp03nsRKLtcPnyVB58vYrBkfBsbyQCr6xl+h1Z/BXle+rv4MJdO4T1HG5xkRgTwSUTtBGbTGGOg//3zpUAfPPdU9elzzcn6rtYuShx0qQc4EObs+nsH+FrfzwmpUAiYLTWHD7nZNPS2Y3JDVnJHK/vYjQMupO8Wd5GTISN9y6LnFaS3d731pVAaa4xc2ZLzA8ABUqpPKVUFHAr8JT/HZRSi5S3T49Sague/0P7dB47mS9sX05rzxBffPSQHNjFtJxt7iHCpshLm15HFp/CHAcf2ew5f3zoE4GfHRXGcLk1R1pH2bYyg0j7zA6rN2/0dDjw9UsWHlprTjR0cdGSievLfeKiPLPkTx5tkDp9ETDV7f04+0fYuDR5Vo/fkJ3EwIiL8tbewAYWYvWdAzx9rJHbi3K4pSBqWu9Zly2bPxNQJTVO7ttVTkmN822fz4WpSlm01qNKqS8CLwB24GGtdalS6rPe238OfBD4nFJqFBgAbtWeJfkTPnY6PzfabkMpePlUC2+Ut4XksouwtjNNveSlxV9wJm8y16xeyGMHaomNMra2XATOkdpOeobh2tUZM37swgUxLFwQzXHvRjrCo75zgM7+EdZOsvDTZ39VB4q3z87J8VvM1eFznuRq4yxnzNdnJQNwrLaLVYvO7ypkFQ+/UQXAJ6/Io+xIy7QeU5jj4P0bl/DE4XoeDuMJqF+9WcW9T58EPLXUSoHWnp73j3569nmk2WbM0Vo/q7VeobVeprX+nvd7P/cm5Witf6q1Xqu13qC1LtJa77nQY6ejuKpjrBpdtngW01HW0jPjMhafVYs8jzvd2BPIkISBdp5qxq5g24qZJ+YAFy1JDssNSeZi/I6fkynKTyXSe4Jss6mwnp0ToXPonJOE6AiWZ0y/85a/vNR4EmMiOGLhcd01MMLv95/jPeszWZIcO6PHvmt9Jlp7xmQ42nW6he8+c2rsaw24tXeCwDW3PNJ0ibkRivJTifYe2JWSA7u4sD3lbdS09xMfPbsZ7yxHLAnREZxukhZv4eLpow2kxKhZX7a+aEkSlW199A6NBjgy6zpR343dpsZOZCdTmOPg0Tu3Eh9lZ3OOI2xn50RoHT7XycXZydhnmVjabIr1WUmWPuF+dN85+oZdfPqq/Bk/dmO2ZxyGW2lZSY2Tf/j9Ye78zQFyUmKJjrBhVxBlV0TZbdjU9HeJnYypSlmMUpjj4JFPF/Hl3x/BZkMO7GJSJTVO/uZXBwD4y+F6PnLJ0hn/vSilWLkokdNNMmMeDp473kitdyOR239ZPKtSuPVZSWgNpfVdbJWJAcCz42dBRsK0NvDanJvCzRuX8MShegZHXNPe9EuIifQPj3K6qYfPb5tbp7YNWck88FqlJf8miyvb+OkrZaxfkjRlOdlEHPFR5KfHj5UEhYOSGie3PrCXEZdGKbj3veuIj46guLJ9LBH3fT6XPFJmzL0Kcxx8+JIsqtv76fCuKBZivOLKdka8i/Rcbj3ry1WrFiVyurFbdiwMAzuOvbWT62w7EPjKNaTO3KOkuoMDVR0sTpp8h8Hxbli3iIERF6/LxiZijo7VdeFy61kv/PRZn5XMqFtzstFaV0dLapzc8dB++oZdnG7qmfWsd+FSByU1zrB5n3ujrHWsn7sNz/G6MMfBF7YvpzDHwc4/OFjD8imS8qQpa2AlMfdzubf38J4KObCLiRXlp6K8VzbncrlqVeYCugdHaewaDGB0wgi+C902Zt+BID0xmsVJMRyrk8S8pMbJR3+5j/4RF6+VtU07KSjKT2VBTATPn2gKcoRiurqGtCVLGQ6f6wTeKseYLd8OoD99Ze6dOkKpuLL9rQ2F3LOvly7MceDsH6GqrS+Q4RkmY4FnosCmJj7WX3IJfPjDsGvXxI/3fD9vyrogScz9XLQkicSYCN4sl8RcTGxjdjLx0RGsXbxgTt17xhaASp255TX3DLJyUSK3FEyvx+9kLspKGlvwOJ8VV7aPtY506+lflYq027h29UJ2nm5mJAx6R4cD55C2ZAvLw+ec5KXF44if2y689Z2eErdXTrdY6nXwn4CaS7vDTd5j4SHviY7Vudyek5U7r8yf8Fi/fTs8/vjEyfmuXZ7vQ9X5WxiPI4m5nwi7jUvzU3lDEnMxibMtPfQMjvI3l+XOqYZspTcxPyWdWSzN5dacqO/m0vxU3r1sej1+J+NbANo9OBLACK3nkty3XsOZXpV657pFdPaPsL+qIxihiVmw2gYzWmv2VXUQF2mfcyLt//+20utQmOMgIcrO+qykOU02LE9PIDEmwjInJFMpbegmKTaSr9+4atLXZKLk3JeUP/44QNeUb/qSmI9z+fI0ajsGONfeb3QowoT2VngOrJcum9sCvQUxkSxJjuWMLAC1tPKWXgZGXKzPmvniqPEu8vY9nu+z5o1dg2jg/RuXzDgpuKognZhIGy+USjmLWdjt1tpg5vkTTXQNjHCysXvOs9xF+anYvVPPVtpop6NvmJ4hF+/dsHhuixhtik1LHRwKk8T8ZEMXazIXoHyXEybhn5w//HDuWFK+ffv0fo4k5uP46szflDpzMYG9Fe1kp8SS5Yib83OtzkyUUhaL87VCC0hi7lsAOo/rzLXW3L+7goKMBH74oQ0zTgpio+xsW5HBC6VNuN3hseDM6j6/bZmlOp09dbQBCMx28oU5Dj60OQuA//sb62y0U97iafs62x7u/jYtdXC2pcfyVwJHXG5ONfWwdvH0Novavh0+9zn47W9z+dznpp+UgyTm51mWHs+iBTFSziLO43Z7LnFeGqBZj5WLEqlo7WNo1BWQ5xOhd7y+i/goO/lpc38DS4mPIssRO687s+w+08rpph4+e/WyWW9M8s51C2nuHuJbT54Im0voVma1hhyDI57jsX2SBX4ztTU/BYD0xOl3GDJahXc/hmXpcz+uFeY40BqOWLzOvKK1l+FRN2uXTC8x37UL7r8f7rijmvvvn3xB6EQkMR9HKcXly9PYU94mMy4TeO1MK0+VD8/LN7xTTd10DYwE7HLkqkULcLn12OyEsJ5jdV2sW5IUsN3tLlqSNK8T8/t3V7A4KYb3Xrx41s+RGh8NwCP7zllqwV04ilBYriNHWUsvW/NS+Mr1K+dUX+2T7b26Wuu0TnlseUsvMZG2Ge/2OZEN2UnYlPU3Giqt91zdXjeNnu7+NeWf/GT1pAtCJyOJ+QSuKEjF2T9iud6jwfbMsQY+/n/7eaJ8hNsfnH9veIGqL/dZnentzCILQC1pxOXmZGN3QMpYfC7KSqKmvZ+ufmtf9p2Ng9Ud7K/u4M4r84m0z/6tyXdiE4hSBDE3kXZFZZt1Jh5qO/qpcw5w47pFY72p5yo7xZOY13VYJzGvaO0lPy0hIBMOiTGRrFy0gEMW32iotKGbmEgb+VNcRfBPyn3lK/4159LHfJYuW+atM5dyljEDwy7ufap07OvBUfeEr09JjZP7dlmrZ+t0FVe2k5saR2bS3GcRAHJT44mKsHGmWRJzKzrT1MPwqHts0WYgrF/iea7vPXsyLMfQhfzHc6eJibSNtRKdraL81LFt1K204C4cRdqgqrXPMhvM7PN28ykK0OQLQHpCNFERtrHdga2gorWXZQGoL/fZtDSZkmonP32lzLLHtdKGLlYtWjB2bJnIREm5jy85lz7ms7RwQQxZjlgeO1Br2T+iQNJa842/Hqe1d5gouxrbUGVfVcdYX8+W7kE+/0gJH7h/Dz988UzYXUJ2+erLA3jAjrDbKMhI4JRcmbEk38zs+iWBmzH3lc/98WBd2I2hC3mhtImDNU6GRtx88tcH5vT/Lsxx8PFLcwC4//ZNlllwF44ibNA37KKlZ8joUKaluLIdR1wkKzLmdnLoz2ZTZDliqbXIjPngiIs65wDLA1Bf7pMaH0X/iIsfvXTWksc1rT27t0618PPAgQt3X/F8X/qYz0pJjZPGrkGq2/rmZcnGeI/sO8cTh+r5h2sLeOyuS/lAQSR3FOXwZnkbn/ntQT708z1c/p+v8Jx3xz23Dr9LyKUNXfQMjgZ89m3VogWclpaJlnSsrosFMRHkpM69Q4/P8Yb5WYbx18P1QOD+31evSAcgLipirqGJOYj0zi76FhOaXXFlO1vzUgO2ZsQn2xFnmRrzytY+tIZlGfEBe84B74Jaq+YGtR0D9AyOsnaK+vKvfW063Vekj/msFFe2j116G7LgH1EgPbb/HN9+spSLs5P5u2sKKMxx8O5lUXz35nW8f+MSXj7VwoFqJ243fOXaFW9dQrZY79qp+P4GAtWRxWd1ZiKtPUO091pjRkm85Xh9J+uzkqfsaTsTRfmp+HKC+VSG0T88CgSuE4avzVtFq7UWHoabSG+GYYUFoL768iJvF5VAyk6JpbbDGqUs5a2Ba5Xoc8PaRWOfW/G4dsI7YTLdVolzJYn5BIryU4mKsKHwzOAsDlBNsRWU1Dj5yStl/OLVCj54/x6+/sRxXFpzqrGbw7Wdb7vv8ox43kpJNDab4l9vXgfAJ6+Y286YZvP8iSYc8ZEBrxP07QD6X8+fnvdXZqxkcMTFmaYeLgrgwk/wlGG8c+0iouw2HvnU1rAaQ5PRWlPW3Mul+YHrhLE4KZbYSLt0PDJYhA1iIm1UWuAEKRj15T7Zjji6BkYs0cu7oqUXm/KsgQqUwtwUtuY5SIqNDMj4DrXShi7sNjX2fh1skphPoDDHwSN3FvGF7ctJiLbz2IFzllm8MhclNU5ufWAvP3zxLP/+3GmO13eNJd6jrvOvHBTlpxEdaXvbLNetl2SzLD2eA9Xhk2Tur2rn0LlOnH0jAa+PGx51A/D4PKsptrozTT2MuHRA68t9tualMOxyszSAb4xmVtsxQEPXIDdelBmwThg2myI/Pd4yJRThLDc13hIz5sGoL/fxdWaxQp15eWsv2SlxxETaA/q8165eRNfACNkp1pvoLG3oZnl6QsBfk8lIYj6JwhwH//jOlXzjXWvYX9XBX4/UGx1S0BVXtjPi8pyA2BTcsmnJeYm3P98JjP8sl1KKDxZmc6DaSbUFDsbTseNY49jnga6P89WXz7eaYqvz7fgZ6BlzgNw0T0Je3R4e42cqeys93Z0CXSa2PCNBZsxNYFl6ApUWOEEKVn05+PUyt0A5S0VLb0A2Fhpvk/eE+5AFJ59KG7qnvbFQIJguMVdK3aCUOqOUKldK3TPB7bcrpY55P/YopTb43VatlDqulDqilDoYiHg+sjmbDdnJ3PvUSX704pmwntHM8m4moICoCBsfLMw+L/EerzDHcd4s1/s3LsGm4E8ldaEKPagSoj1nybYA1b/6K8pPRc3DmmKrO1bXRUp8VEA24BjPt4tolQUu/wfC3op20hKiAlrTCp6EsL5zgIFh2VnXSHlp8dQ6B8auDppRMOvLgbFZ4jqTLwB1uTWVbX0sSw/81bp1SxYQFWHjoMWuprf0DNLaMzTlws9AMlVirpSyA/cBNwJrgNuUUmvG3a0KuFprvR74LvDAuNu3a60v1lpvDkRMNpviY1uW0jUwwo9fKQ/rcoMq7wzd57YtG0vEJ0q8p7IoKYYrC9L586G6sXaKVtYz6CI20s5XrlsR8Pq4whwHVxakkRgdYcnau/lqf1UHSbGRHArCNtNLHLHejVnCPzHXWlNc2cHW/NSALqIF/wWg5p+tDWf56fG43JpzJi7jCGZ9OUBSbCSJ0RGmL2Wp955ABfokGSA6ws6GrCRKLLbRUGmDp51xqBZ+gskSc2ALUK61rtRaDwO/B97nfwet9R6tte83WwxkBTuoFr+OGeFcbvDs8Ua25KXwtRtWzTlB/GBhFo1dg2O7ZVrZiYYuLspK4overjSBVrg0hZ6h0ZAOfDF7b5S3UdPR72mnGoQTdbtNkZMaT5WFdkycreZ+TVP3YMDLWICxy/GSmBvLt1OimevMnznWQEykjd7B0aA8v1KKrJQ4028yVN7qKa0MRikLQGFOCifquxgcsc5VrJPexHxNCN+fzdbkdQlQ6/d1HbD1Avf/FPCc39caeFEppYFfaK3Hz6YDoJS6C7gLID09nd27d18wqOhOF3YFLu0pZ4jurGH37uCWafT29k4ZVyA19Lo52zzA7aujpvy504kt2qWJssM/Pb6fj6+JZrkj+IsmgvGaubWmtK6fbdkRc3ruC8U20OJ5M/jT86+SlRj6c+VQ/63N1EzHa7D97Mgg4DnYDI+4eezlA/Qsiwro65jIIKU1fQF5PjP/fo809gMKe1sFu3dXBfS5R9waBew8UEpSZ9mMHmuW1+yxx7JZtaqHjRs7x753fmxTb/EdSuPHa/3pwwC8tO8okS1RRob2Nr7XsdzpYtcZz5j+6AN7+dolMUF5v4p1DXK6ricg76/B8kKVp2tM09mj7K4+/wrWXGOL7hllxKX59dO7WZkS2Nc4WK/b0/sHiI+Ax597bVZ/F7OJy2yJ+UTXMieshVBKbceTmF/h9+3LtdYNSqkM4CWl1Gmt9WvnPaEnYX8AYOXKlXrbtm0XDGobYEuv5Ds7TvHP71nLxy/NncZ/ZW52797NVHEF0o93lqHUWf7u/VeycEHMBe87ndhKapy4du7lXI/m+yXDPPrp4JdpBOM1K2vuYfiF17hh61q2bZr9xZkLxeao7eTnx94kPX8N2/z6vYZKqP/WZmqm4zXYfnpqD+AcWxR927WXUJjjCOjruKf/FL/aU81VV10958VoZv793n/keTISI7j1XdsDXsoCkHtoN6NxiWzbVjijx5nlNdP6/C2+/WPbtQums8V3KI0fr++6bjvf3vcStgUL2bZtvcHRvcX3Oh566QxQDngm34aSc9i2bXnAf97rvSd5dN85rr766gv+rRv5t/dc2zFS45t59/UT75Iz19jW9w3zv4dewpUS+Nc4GK9bSXUHZ57fiwZ+cGh4VuWms4nLbKUsdUC239dZQMP4Oyml1gO/BN6ntR6rldBaN3j/bQH+gqc0JiCuW+NJmKIjzPaSBcazxxvZnOOYMimfrvGbNO2taAvI84aab2OBdUFoi+cz1oXDxJd6hUfXwAjH6rp49/rMgPXcnkheWjzDo24ausx96XsutNacdrq9C6ADn5QDLEuPp6LFuuNq+3ZPUv7hD/uS8Lfs2uX5/nS2+DZaXlq8aXuZ56V6yjaCsbjfX7YjloERF229w0F5/kCoaO1lWRDqy31S4qPIT4+3TGeWZ443js0Mh7KM2WxZ5gGgQCmVp5SKAm4FnvK/g1JqKfAEcIfW+qzf9+OVUom+z4HrgROBCiwzKYZIu6K63dyLN2ajorWX00093HRRZsCe03+TJoDmbmvubHmivpuYSBv5acHrKZ0UG0lKfNS8aY9nZS+WNjHscvOpK/IC1nN7Ir7NPcxclztXFa19dA1pLg3SgjuAZRkJVLX1Meoyb0eQqUyUnPuS8scfh+ls8W20/LQE0y5mdsRHAnDrJUuDugB/rJe5STuzaK0pbw1Oq0R/m3MclNQ4LbE3jH/76FB2TTNVYq61HgW+CLwAnAIe11qXKqU+q5T6rPdu3wJSgZ+Na4u4EHhDKXUU2A88o7V+PlCxRdhtZDviqAnD5OlZb5/uG9cFLjH39Tj/x3eu4LL8VB7df44D1R0Be/5QOVHfxerMBUTYgztUclLjqG4z5wFbvGXHsUayHLFcnJ0c1J+Tnx7+V1H2emefgrHw02dZegLDLjd1Jl90N5mSGif37SpnQb5zLDl/+OHc88pbzC4vPZ623iFT7nzZ1OWpL//89mVBLbc0+yZDu8+00Nk/QkxkcN/rCnMcOPtHqDDpFRR/Z5p7yEmN46tBvDo6EbPVmKO1fhZ4dtz3fu73+Z3AnRM8rhLYMP77gRSuydMz3jKWRUmBKWPx8bVbvOPSXN7zkzf4zG9KuG1rNtesWmiJtoBut+ZkQzc3b1wS9J+Vlxo/lqgIc+roG+bN8jbuvDI/aKUXPhmJ0cRF2U07yxgIzx1rJDYC2nuHxsq5As3X9q28pTdoPyNYSmqc3PZAMSMuN9GRNh65s4jPfc7Bd7+byz//s3WScmDsimNla1/QT2pnqrFrEKUgIzGw73/jZTl8vczNd5JYUuPkM789BMAjxTW8e/3ioL1HF+akeH9mR1DaMgZKV/8IJTVOPnt1Pl/YHvg1Bxdiqhlzs8tJjaemvc8Sl2Cm6+mj9Zxu6gnKDoY+C2Ii+eL25XT0D3PfrgrL9II/19FPz9Ao60Kw41dOajyNXYOWaiM13zx/oolRt+bd6wN3ZWkySiny0qyxlflMjbrc/OjFM+ypbGdgFG5/aF/QjgdWbplYXNnOsMs9tivwb/7cz/33wx13VHP//efXnJuZ7wqQGVuANnYNkJYQTVSQ14/FRUWQlhBlyk2GPLt+e8q9Rt06qLXUy9LjSY6LNH0O8FpZKy635ppVGSH/2ZKYz0Buahx9w+ZevDETJTVO/uEPRwF4dN+5oA6Ulp6hsXrzYYv0gvct/AzFjl+5aZ7LnDVhuIYhXOw41kBeWnzI+s3nhllivr+qnc8/UsKV/7WLH79SPvb9YC6qSoqNJD0xmvIW8yWEU1nkXYivgJG6NH7zvUwefxw++cnqSReEmtXSlHhsClMuAG3sGmRxgK8WTybLEUdth/lmzIvyU8e6P0UFuZZaKcXy9AReOtVs6uT8ldMtOOIiuTg79Ff3JTGfgRzv5bhwqTO/b1f52M6co67gJsu+xaAANqUssfX8ifpuIu2KgoXBv9yW5+vMEiZ/W+GmtWeI4sp23r0+M+hlLD75afHUmXwr8+k6UN3BrQ8U8+zxJpq6Brl961JiIm3YCP6iquXpCZRbcMZ8f1UHUXbFDSkX0fPsJTzxJ9tY+Yr/glCz9TGfSFSEjYzEaF48ab5krKlrMOBlnJPJTokz5eLPwhwHKxcmsDgpJui11CU1To7UduLsG+GjD5rz6rnLrdl9poVtKzOwz7Fd7WxIYj4Dvk4J4dCZ5aWTzbxyugWbYqwfczDfHAtzHDx651YWxESM1Z6bXWlDFysWJhIdEfzNkXJSw3+xn5X94rUK3NrTXSJU8tI8W5mb8Y18pn7xquf1A0+Hg8XJsTxyZxG3FEQGPRFYlhFPRUuvpUoQnX3D/PVIPZujVvGn7y99W1Lu40vOzdbHfCIlNU5aeoY409RjulLGxq5BMpNiQ/Kzsh2xNHQOjE2ImYXWmoauQa5emR709+biynbc3rE4EuQJwdk6UtuJs3+E7QaUsYAJF3+a2ZLkWOw2ZekZ85IaJ08eqef3+2vZkJXE3Tes4nBtJ0X5qUEfkIW5Kdy4LpPnTjTicmtDzkSnS2tNaUM3161eGJKfJy0TzaukxslDb3h2pfz6X46xNDUuJCeWvqsoVa19QW9hFkwtPYPsqWjHpjxlGb5JgMIcBz3LooL+Wi5PT6B7cJTW3qGgL/ALlN8fqGVo1M0SteSC3Vc83zd/H3PPvhaez32lS2aYnOkZHKF3aJTMEM6Yj7g0Td2DLEkOzcnAdLT0DNHZP8LKhcG/+FKUn0qk3cbQqBu7zZxXz3edbsFuU1xdkG7Iz5fEfAaiImwsSY617Ix5SY2Tjz5YzNCoGwV86R0FXLY8jcuWp4UshssL0vjDwVqO13eZbnW+v8auQTr6hkOy8NMnN0y7/ljdn0vqDEkqxhJzi19F+fdnTzPq0vzPrRdT2zEQkkkAf74NU3744lk+vDnbFAnhhYy63Px2bzWX5qfy/buip/EI8/cxL8pPJcKuGHFpIuyh6wc9FV+rxJCVsjjeaplopsT8dJPnT2jlouC/3xXmOPjtp7bwkV8U876Lg9f9ZS52nm6hcKmDpLhIQ35+wEtZlFI/UUo9PcH3Fyil7lVKrfb73peVUseUUpYpqclJtW4v8+LK9rF6VaXgTFPoj+eXezcTebPc3DuBnqj3LvwM4o6f4+WmxsuMuclorTl8znPZPRQlX/6S46JwxEVSZeG/ib0V7fzlcD2fuTqf925YEtRNmSYzMOzpdPT4gVrTlVFM5OVTzTR0DfI3l+caHUrAFOY4+Neb1wHw99cWmCYZa/Am5iErZUnx/Jxf76k21d/h2bHEPDTLFbbkpbLEETu2gY+ZNHYNcKqxm2tWG1PGAgFOzJVSy4DPAP8ywc2bgW8D/qcgPwcygE8EMo5gyk31dEqwUr2iz6alyWPbywZ75fVkUhOiWZO5gNfLWkP+s2fiREM3NgWrQzCD4JObJi0TzWb32VZONfXw6Svz+EqIN5kAz6x5lQk7WUzHvsp2vvDoITISo0LeB9hfWYsn6fC1HTRjTatPSY2Tf33mFGkJUVwbojK6UHn3+sUAuEyUjDV1eTqkhKqUpbnbcyLw/IkmU50knm7qIT0xmpT4qJD9TM8kp/muEP/6zWrgra5IRgj0TPU/AEe11gcnuG0jMASc9H1Daz0A/Ab4xwDHETQ5qXH0DI7S2W++Hcym0uQ9KHx4c1bIEwx/VxSkcaimk/7hUUN+/nTsKW8jJT6Kk43dIfuZOanSMtFM3G7N958/Q3ZKLP/vnasMme21asvEkhont/9yHx19w3T2j1DaELpxNF5RftpYq9ZQXvGYKV+pYZ1zgM7+EY7UdhodUkDFR0eQ5YjlrIlaVzZ6Z8wXhigJO1DtScTNdpJ4prmbVSGaLfdZmhLPOZPtglpS4+SB1z1LNu554phhJ07TSsyVUsuVUiNKqX8Z9/37lVI9SqnNSqlo4GPAoxM8/hTwAyAaGFFKaaXUn7w3/x5Yo5S6bE7/kxCxclu7R/edIy8tnv+4Zb2hlxKvWJ7GsMs9dpAym5IaJwdrnLT1Dod0VsPKf1vhaMfxRk42dvPV61YGffORyeSnxdPUPWjqk9iJvH62lVFv5wlXkDcsmUphjoNLl6WSHBf8DjBzUVzZzpC31FBrY1+zYFm5MHGsbMIMGjsHQ7K5kE9Rfiq+ngdmOUl0uTVlzb0hWfjpb2lKHB19w/QMmmeS09MxxvO5kSdO0/pr1FqXA78EvqyUSgNQSn0L+CTwfu8MeRGQDLw+wVN8HKgEngYu9X581XvbEaAbuGG2/4lQ8rW1s9qs5tnmHg5UO7ltS/bYRgJGuSQ3hSi7jTdMWs6y63TL2OehHJzSMtE89le1860nT5CTEsd7Nyw2LI48b3vG/3zujGkue09Hl/fN1hbiuvzJbFrqoGdwlPVB3OF4rnz1vf6da8JNwcJEKtt6x3aZNFpj9yCLk0NXslCY4+D6NYuIjrDxyKe2muIksaa9j6FRd8jqy318V4jNNGu+0duQwugxOJPTxH8B7MDdSqlP4akXv0Nr/bL39iI8V2iOTfDYo0AW8IrWutj7UQOgtXZ7H1M0y/9DSGWnxKKU9WY1H913jii7jQ8WZhsdCrFRdgpzHLxRbs4ZId8K/VAnFdIy0Rx8ZRid/SM0dA1w2MCSAt96g9/srTZVTeqFDI+6ef5EE2syE/mqAXX5E8n19YQ3URIw3pFznQDceWWeKV6zYFi5KIERlzbN5ENT10DIa4k35zoYGnWTb5IWqGdCvPDTZ2mKNzE30STngljPEsj3bFhs6BicdmKutW4C/gf4EvAL4O+01o/73WUx0K21nmi/+rVAFHBokqdv9T7e9KIj7CxOirXUjPnAsIs/H6rjxosWhXRxx4VcUZDGqcZu2nqHjA7lPL7+6ndemR/ywSktE423p6JtrFuA2+AyDN/mQmarSb2QJ4/U09g1yNduMKYufyJ5aZ4kwKwnvf3Do/xuXw3Xr1nIN961xhSvWTAUZHiSv7PN5qgz92wuFNrEfKwNqkn+Fk839aDUW7+bUFlqwhnzcu/6hy9dY+xxa6aFVWV46sT3aq3vG3dbDJ7FnRPZhOe95cgktw8A5mnqOYXctDhLLch6+lgDPYOjfHTLUqNDGXOFt3e6Gdsmlrf0Ehtp554bVhmy2M+sycN8MeKt8zVDGcaV3g0ujL60Ol1ut+bnr1awOnMBV68wZnOOifhKgqpMetL755I6OvtH+PRVpt/Ec06WZyRgU57SSqMNjGp6BkfJDHE/cbOVLJ5t7iE3NZ7YqODvcO1vQUwkjrhIakyUmJe19BBhU2O/I6NMOzFXSl2DZ6Z8L3C5UmrDuLu0A5NlMRuBCq31ZEvzUwDzZWiTyEmNt1Qv8wdfqyQlPooIE+20uW5JEvFRdn75eqXpLs+XtfSSnx5vSC1+bqq0TDSS1poXTzaT5YjlK9etMLykoDDHQU5KHPnp8YbHMh0vnWqmorWPz21bhlLmOd444iJZEBNhmmTIn8uteeiNKjZkJ7PZ5L/fuYqJtJOTGm+KxNw56LkqFuoZ86UpcdgUptmo8ExTDysWGlNWszQ13lTlZWebe8lNizdssb/PdLuybAL+imcB6DbgHPBv4+52GohUSmVN8BRr8GuTOIE84Mx0YjGD3NQ4nP0jdFmgZeIfD9ZS1tKLs2+Y2x/aZ5ok+EhtJwMjLo7Xd5uudraipZflGcYcqHK9lzn/87nTpnpN5ovXyto43dTD372jgC9eY46NUJZlJBAdYTdFLBdSUt3Bt58qZWFiNDetW2R0OG+jlCLPpFejXj7VTHV7P5++Ms9UJzPBUpCRYIrEvMObmIe6xjwqwsYSR6wpThIHR1xUt/eFZMfPiSxNMVcv8/KWXgoMeu/3N2VirpRaDjwHvAh8yVtD/i/ATUqpq/zu+pr33y0TPE0nsEEp9U6lVJFSaux6rFIqGVjh93jTG+vM0mH8wJrKQ29UAearUS2ubB/b5nzYRHH1DY1S3znAcoMW5gx62+L9ao91FvuFkwdeqyAjMZr3XWyeJS+LkmLG9iAwq5IaJ7c9uI+mrkE6+oY5WtdldEjnMWNP+JIaJ995upS0hChuWGuuk5lgWbkoker2foZGjb0q2DHoKVlbHOJSFvBcGTXDVfey5l7cmpD3MPfJSYmjvnPAFF16Bkdc1LT3mT8xV0otwpOQnwJu93ZQAc+mQKeB//DdV2tdDewH3jPBU30LaMYz674XWO1327uAYeAvs/kPGCHXVyNmojO9idS093GmqQe7TYV8O/GpFOWnjl0ustuUaeKq9O6yWGDQpb36Ts9OdGY7kZoPTtR38WZ5O5+8Io/oiNDWW17I4qQYOvqGTV3etPNUM8PeN1e3SXtw56bGU985YHhC6OM5mSmmvnOQzv4RU57MBEPBwkRcbj12rDWKr5QlY0F0yH+2WXYQP9NsTEcWn6WpcbjcmsZO4yceqtr6cGvP36fRLpiYa62btNb5WuttWushv++7tNartdbjNwW6H7hFKRU37nlOaK23aq1jtdZKa/2G380fA/6otW4HUErdoJQ6o5QqV0rdMz4m5fFj7+3HvGU2TOexgeJr81NjstmX8R58vZJIu41ffKzQkO3EL6Qwx8Ejd24lJtLGFcvTTBOXb/tuo0pZrlqRMfa5mU6k5oMHXqskITqCj241zyJpgEVJnhm9pi7j37wm0js0ynMnGgFzLJidTF5aPFqbpz1bcWX72ELjcN1QaCK+jWyMLmfpGNSkJUQZchKekxpHtwl2ED/T1E1UhI2clLip7xwEY7mUCaoPyrwdWYyalPMX6Ar33wL1wOenc2el1MXAdjylMSil7MB9wI146tJvU0qtGfewG4EC78ddeE4GpvvYgIiNspMSF8XzpU2mLTVo6x3ijwfruGXTEq5ds9A0bcv8bc5N4eoV6ZS3mqN1FnhqzIxclV2Y4+Di7GQWLog21YlUuHv+RCNPH2vgmlXpLIiJNDqct1nsXZzWaMLEfMTl5nO/K+FcxwDfeNdq0/Qtn4hv/YZZylmK8lM97XYw78lMMOSlxRNhU6ZIzDOTjGkGZ5aWiaebeijISCDCbsxiR98mQ2aoMy9v7sGm3vrdGCmgvw2ttQvPbqDTfZUXAX/r3VkUPPXp5VrrSm8t+++B9417zPuA32iPYiBZKZU5zccGREmNk86BYUobzLdw0edXb1Yz7HJzl8nbbxXlp1LbMTBWwmG08pZeclLjiDToQAWwOcdB18DI2C5kIrj2Vbbz+UcOoTW8UNpsuvG8aCwxN8cY8Smp7uDm+97k9bI2/v2Wi/j0lfmmnADwyRsrQTRHYl6wMAEFXJqfYtqTmWCIirCRmxZveC9z56B7bGyFmllaJp6o95RPGXXMW5gYQ1SEzRSdWc4295KbGm+KMkZldI2TP6XUB4EbtNZ3er++A9iqtf6i3312AP/hK4dRSu0E7gZyp3qs33PchWe2ncSM7MKUv70/qP8vIayk5j/fXaK13mx0HD4yXoWYnIxXIaxjWuNVa22aD+BDwC/9vr4D+Mm4+zwDXOH39U6gcDqPnehjxYoVeqYOVnfold94VufcvUPn3bNDH6zumPFzTGXXrl2zfuy3nzyuc+7eoR/bXxO4gPzMJbbxXC63Xn/vC/prfzw65+eaa1xDIy6d//Vn9PefPz3nWMabSWwlNR065+4d+qXSpoDHMZHxsQEHtQmOBxN9zGa8TuRgdYf+ztOleuv3XtLLvv6MXv5Pz+j8e3bold98dtbjOZDjYrwN//KC/uZfjs/qscGI60cvntY5d+/QOXfv0Pn37NA/faVsVs8TzNdsIu+/7w196y/2Tnm/UMT1rb8e16u++ZweHBmd0ePCYbz+90tndO49O3T/0Mz+74HSOziic+7eoX+2q9yQn6+11lf85079pUcPnff9UI2Jr//52IzHcDBi+9v/269v+J/X5vw8c4nN997/X8+fmnMc481mvEYE4YRgLuqAbL+vs4CGad4nahqPDYjCHAePfLqIn75Sxq4zrb4TAVPYX9XOr/bUAHDvU6UUZCSa+hKpzabYkpdCcZXxC5+q2/twubVhCz99fD//bEsP165ZaGgs4cjXDWPYu/Du396/jpWLFlBc2U5Rfqopx8uiBTGmKmVp8Na7m3mx50Ry0+LZW2H8sQbg9fI2tuanmOLSeaitXJiI1p7SwYuykkL+833rNUK9uZA/o1smpiVEAcaP4aUpceyv6kBrbVgff997/woTdGSBwC/+nKsDQIFSKk8pFQXcCjw17j5PAR/3dmcpArq01o3TfGzAFOY4uO/2TaTGR/HjV8qnfkCI/PlQ3djnVmm3tzUvhZr2fsO7TpR7V2UbnZgviIkkMymGcoNrMMPVG2WtY0m5TYGzf4TCHIep66MXJ8eaZvFna88Qzxxr5LL8VFMv9pxInndn3YFhY1smNnQOUNnaxxXL0wyNwygFBndm8b3XGFVjDsa3TPQt+Pz7dxQYOoaXpsTROzRKR9+wIT8fPP3cwfj3fh9TJeZa61Hgi8ALeHqnP661LlVKfVYp9Vnv3Z4FKoFy4EG8HWAme2ww442LiuDOK/N57WwrR2o7g/mjpq1/yPOGY7a+5Rfii3GfwbPmvsQ8P934VdkFCxM522L87njhqNK74MqmPAvRrDBGFiXFmCYx/8krZQyNuvneLReZ+mRmIr7OLEYvAH2zvA2Ay+dpYp6bGkeETfGHg+cMWXjou/q02KCuLPBWy0SnQS0T65z9ZCRG8/fXrjB0DI91ZjFwAWhZSw9KwTKDNhYcz1SJOYDW+lmt9Qqt9TKt9fe83/u51vrn3s+11voL3tsv0lofvNBjg+2OS3NIjovkJzvLQvHjplTa0M3F2cmm61t+IaszF5AYE2H47H5ZSy9Zjljiooyv8CrISKC8pRe32zxlUuHgRH0XO441cs2qdEvN9pplk6Ga9j4e3XeOWy/JNkVbsZnyxWx0N4w3yttIS4gybMdFox2t68Ll1uyvchrS2cx3kmvE5kI+eQafJNY5B8hyGHdi4uPrZW5kZ5ay5l6WpsQRE2mOsjLTJeZWkxAdwacuz2Pn6Ra+9eQJQ1utVbb2UtnWxy2bllhqJstuU2zJTWFfZYehcZS39JrmUtaKhQkMjripc5qnrtjqRl1uvv7EcRxxkfzowxdbaoyYYZOhkhonn/ltCTal+Pt3FBgWx1zkmqB/tNaaN8vbuHx5mmE1tUYrrmzHN+VgRMllY9cgiVEYmogZ3TLRk5gbs7GQv+wU43uZl7V4+rmbhSTmAXDx0mQAfrO3xtC+5q+cbgFg+8qMKe5pPlvzU6hs66Ol25jEw7NFdC/LTXIpa3mGOXbHCxclNU4+/ZuDHK/v4tvvWUtyXJTRIc1IpsGbDJXUOPnog8WcburBrTW1Fj1hTIiOIC0h2tAZ89NNPbT1Ds/bMhbwlC/abZ6TEiNKLs80dWNXytCJtKUpcdgUVBuQkLrcmoZOc8yYx0TaWbQghnMGzZiPuNxUtfWNveeagSTmAXCsrmvscyMXXL5yuoWVCxPHzkCtxHdg/s6Ok4YcLOudAwyNuk0zY+7bFljqzOfOl1TuOtOKTb21k6aV+BLzpm5jEuLiynaGwmT7+Py0eKrbjJud89WXz9eFn+BpnvC3l+UC8NOPbgrplauSGieHz3XSOaQNnUiLirCxxBFryElic/cgo25tihlz8JyknDNoxrymvZ8Rl5YZ83BTlJ9KhPfsP8JuzGKy7sER9ld1cM1q682WA2O1szuONRpysCzzJsC+hNho0pklcIor28e6sAAUVxlbMjUbvq3DGzqNmTH334XWKovKJ5ObFmdoKcszxxtxxEeaZjGvUS5d5vkbSokP7dWr4so2Q8to/BnVMtFXImmGGXOA+Gg7Jxu7DDlJerG0EcBU67kkMQ+AwhwH975nLQBfuc6YFc6vn21j1K15xyprJuYHqt8akEYcLMdaJaab53LW8owEmTEPAP8k0ipdWMaLjbKTHBdpWI15k7fE7NZLsi2zYHYyuWnxtPYM0Ts0GvKfXVzZxuFznTj7RgydrTWDbIMW/a1ctAAAhfEnmUa1TKxzel5zMyTmJTVOXi9ro3fIxe0PhnZMlNQ4+dFLnsYd/2zwGkF/kpgHyAcKs7DbFN2DxrQ+2nm6meS4SDYuteYbZlF+KpF246467KtsJy7KTnmreWaoVyxMlM4sAZAUG4kGrl2dYemk0shNhn5/oJbc1Dj+/ZaLLPv6+eR5F9391/OnQ/5G/H9vVo99bvRsrdGWJHuSwlAvcE+M9nTdunyx3fDjgVEtE32v+eJk4xPz4sp2XN73uGFXaMdEcWU7o96fPRLin30hkpgHSGyUndWZiRw+1xnyn+1ya3afaWX7yoyxBTVWU5jj4GcfLQQ8JzmhrjncdbaV/mGXqWaxCjKkM0sgvFDaBMC/3mztpNKoTYYqW3vZX9XBhy/JDosuIgPesrnfhnixfkffMG+Wt2FT1tpnIljioyNIjY8am70NFV97wvctjzL8eOBrmfjDF8+E9H2nztlPemK0KdoDFuWnEhXhSUVtSoV0TKz37jprhqsn/iQxD6CN2Q6O1naOnf2FypHaTjr6htlu0TIWn+vWLmR9VhKnG7tD+nPfKGvFdyXRTLNYRu+OFy5eKG3i4uxkQ3f5C4RFSTGGlLI8frAOu03xwU1ZIf/ZweArndCEdrz/+7OnGBxx86MPX2ypfSaCKSslLuQTD5VtfUTZbaTGGn+S2ectp3p037mQniSapYc5eCblHr1zKzGRNravTA/pmOj0Xqm4bctSU41HScwDaOPSZPqGXWMLCUPl0X01KAXJMZEh/bnBcO3qhRyu7aS1ZyhkPzMpzvO62Uw2i+VbiFrWYp7yGqup7xzgWF0XN6xbZHQoc5a5IIb2EG8yNOJy86eSOravzCBjgbVPbHyuKEjHl5KFarzvq2znjyV1fPqqfG7eaK19JoIpyxEb8hrzqtY+lqbGYTPB1Z8ag04SzdLD3KcwN4VNSx20hPB9H+Clk82kxkfx3ZvXmWo8SmIeQL767lCWs+w81cwTh+rRGu763UHTlGHM1rWrF6I17PL2ZA+F9t5hbAq+dM1yU501L4iJZNGCGMpkxnzWXjjhKWN559owSMy99aDNIez1v+t0C229Q9x6SXbIfmawFeY4KMpPITkuMiTjfXjUzTf/eoIlybH83TXW3JgpWLIdcdR3DoT0KnN1e59pdq29bFkavvODUJ0kutyaxi7zzJj7rMlcwOmmHkZd7qnvHAAjLje7zrRwzSrzlQBLYh5AualxJMdFciTIiXlJjZOfvlLGvz5zks89csg0rZ8CYXVmIkuSY3npVHPIfuaeinY2ZCfz5etWmiYp9ylYmCAz5nPwfGkTqxYlmuaNeC58vcxD2TLxgdcqiY+ysyA2ImQ/MxSK8tPoGhhhdWbwuzB95+mTlLX08vFLc4iNMr6m10yyHLGMuDQtPaH5m3a5NdXt/aY5HhTmONi+Mp24SDuPfGprSN5/WnoGGXFp0yXma5csYGjUTWWI+rrvr+qgZ3CU69YsDMnPmwlJzANIKcXG7GQO1wZv1rqkxsltDxbzgxfP8svXq8hOjiU6whY2i4mUUly7OoPXy1pDcsm+d2iUo7WdXLbMnK9bQUYiZ5p6+OkrZZa/GhJqrT1DHKjuCIvZcgj9JkMvn2rmYI2T/mEXH394f1j9/a3KTERrOBvkfQLeLG/jd/tqAPjvl8+G1WsYCG+1TAzN33RD5wDDo27TJOYAVxak0z/iCtnGgG/1MDdPKQvAmkzPQsyTDaFZY/bSyWaiI2xcUWC+jb4kMQ+wjUsdlLX0Bq1tov9mKTYFtxQu4dFPF4XVYqJ3rF7I4Ih7bIe8YDpQ1cGoW3PZMvMNToDoCMWwy82PXjprqo4xVvDyqWa0JizqyyH0mwz98WAtEPr611BY7e1lHeyF5k8fbRj7PNxew0DwzdqGqjOLryOLmRLz1Zmev8WTIWp6YKYe5v7y0+OJirCF5HXQWvPSyWauLEgjLsp8VwMlMQ+wjUuT0RqO1XYF5flXLfJcelX4NktJozDHEVaLibbmp5AQHcHLIShn2VPRRlSEzbSvXfegZ9W+W8sb+0w9frCWpNhI+g3YSCYYQr3JUHvvMIrwbO2X5YglLsrO6abgrt+ItHveYsPxNQwEXy/zUM2YV7WZMDH3niSeagzNWqI672u9xAQ9zP1F2m2sWpRIaUNwcid/Jxu7qe8cMGUZC0hiHnDrs5IBOHwuODObI96FER/daq72PoEUHWHn6hXpvHyqJeib67xZ3k7hUocp+rlOxHfgMFufVbN7vayVw+c66R4Y4faH9oXNlQbPJkPBT8wHR1ycaPB0swmnq3E+Npti5aJETjcFd3auvW+IhYnRYfkaBkJMpJ2MxOiQzZhXtfURF+X5mWaRFBfJkuRYToVsxnzAND3Mx1uTuYCTDd1B3wn1pZPNKAXXrJLEfF5Iio1keUYCh2s7g/L8B6udREXY+NZ71oT1Qf7aNRm09gzx7adKg5ZUOfuGOdnYbdr6coBtKzNIiLazPitJ3thn4JF954DwK8PITArN7p97KtoYHHFz65alYXU1zt+qRYmcbuoJahJwtLaLLfmpYfsaBkJ2Shy1IUzMc1PjTbdR1urMxNAl5p39pitj8VmzeAHO/hGagtx56qWTzWxa6iDdRCdo/iQxD4KN2ckcPucMygH/YI2TDVlJREeY72w3kFLiogD4XXHwdufzJWuXLTdnfblPwcJE4qMj5I19Bs6194VlGUZmcmxISllePtVCXJSdovyUoP8so6xatIDO/hGau4PTO7mlZ5D6zgE2eHcXFBPLdsSGbJOhqrY+8tLNU8biszpzARWtvSFpeGC2Hub+1i72lPWU1gfvJOWF0iZKG7pZ463tNyNJzINg41IHzv4R/u3ZUwFNKAeGXZQ2dLE5N3zfLH1OeFdmB3PGc09FO/FR9rFtec0qLy1+rDZSTK22o5+TjT3cekl22JUQhGKTIa01r5xq4cqCtLCeAPCt1wlWOYtvndHF2clBef5wkeWIo7FrMOj9q4dH3dQ5B8g3UX25z+rMBbh18Hd5drk1DZ3m62Hus3LRApQK3kLYkhonX3jkEOBZg2TWEkfTJOZKqRSl1EtKqTLvv+e9kyqlspVSu5RSp5RSpUqpv/e77V6lVL1S6oj346bQ/g/eEhPpeVl/+XpVQGd7j9Z1MuLSbA6TJONCivJTx5r+R9qDM+P5ZkUbW/JSxhZomVV+WjyNXYP0D4fHIsZg+8vhegC+cM3ysCsh8G0y9MMXzwTtTaW0oZum7kHesdqc9ZeBssrXmSVIC0CP1HZitynWLjb3ib/RslNivZveBPdKUK2zH5dbk5tqvsTcN3sb7HIWs/Yw90mIjiA3NT5oLROLK9sZ9a5bG3WZt8TRTBnJPcBOrXUBsNP79XijwFe11quBIuALSqk1frf/t9b6Yu/Hs8EPeWINnZ7LcoGe7fW9EYdTojGZwhwHX3vnSgC+ftPqgP+fm7oGqWztM22bRH95aQkAVLeFdutqK9Ja88ShOi7NTzXt5dq56PW2YX3ojcCe9PvbearFuzAqI+DPbSZJcZFkJsVwJkiJ+dG6TlYuTJRNhabgG6fBrjOvavV2ZDFhKcvSlDjio+xB78xi1h7m/tYsXkBpY3A6s/hKZczeTMFMifn7gF97P/81cPP4O2itG7XWh7yf9wCngCWhCnC6Ll2WRoR3ttcewNneg9UdLM9IINlbfx3ubr1kKUpB10Dge8I/tt+z6YcjPjLgzx1ovtZeUs4ytZIaJ9Xt/XygMMvoUIKi3nvSH8z2ma+cbubi7GTSEsy5MCqQVi4KzqI7t1tztLaTDVLGMqVsb5JYF+SWiWM9zE04Y+7rEhTsHt5m7WHub03mAmo7BoLyvt/a41lPckdRjqlLHM3UWX2h1roRPAm4UuqC0zVKqVxgI7DP79tfVEp9HDiIZ2Z9wukkpdRdwF0A6enp7N69e+7Rj/PlTVH876EhsuKhp+oou6tm9vje3t63xeXWmn0V/VyyKCIo8c7E+NiCKSvBxguHyllvr5/yvtONq9zp4if7PZdNv/7nY3SeO8tyR3Bntebymg2Nei697TxwnPiOMwGMyiOUv8/ZmMl4/b8TQ0TbIcFZxu7d5SGK0CMUr2O6XzmTXUF0Zw27d9cFLK7OQTdH6wa4pSAyJH8TRv/txQ0PU9Y8wsuv7BqbTAlEXE19broHR4npb2L37sCePBn9mk1lpu+vo26NAt44coqMvoqgxfVG6RDxkXD0wB7AfK9jkh6iuHaUnsU6aHG9XjEMQMWxA9TaZ96ZJhSvmavNc4x77LnXWJUy/ffl6cT2SMkgqTGK7Umt9FS1zTgvm41ZvWZa65B9AC8DJyb4eB/QOe6+zgs8TwJQAtzi972FgB3PVYDvAQ9PJ6YVK1boYPn57nKdc/cOfaCqfcaP3bVr19u+Pt3YrXPu3qH/eLA2QNHN3vjYgulbfz2uV//zc3p41DXlfacb109fKdM5d+/QOXfv0Pn37NA/faVsjlFOba6vWdG/vay//IfDAYllvPGxAQd1CI8LM/m40HgdGB7V6771fNBep6mEalxc9Z+v6Gt+sEsfrO6Y1v1nEtdj+2p0zt079MmGrllGNzOhPJZM5C+H6nTO3Tv06cbut31/rnE9cahW59y9Q59qDPzrGC7j1d9l/75T/8PvD8/kZZix2x7Yq2++742xr43+2xvvt3urPe/xz+4M2s/42h+P6s3/+tKsHx+K16y5a0Dn3L1DP/R65YweN1VsPYMjuuAbz+p/eap0DtHN3GzGa0hLWbTW12qt103w8STQrJTKBPD+2zLRcyilIoE/A49orZ/we+5mrbVLa+0GHgS2BP9/dGEfvzSXtIRofvTS2Tk/18GaDoB5sfDT3yV5KfQPuygN4GKQjd7Ly2avM/MnnVmm9tLJZnqGRvngpvAsY/FZl5XEiEsH5TLsn0rqWBATETa7pU5lVWZwOrMcre0iLspOQUZiQJ83XC1xxAZ9k6Gqtj5TlrH4rPYuAK3tCV53GjP3MPfJWBBDUmwkTxyqC+gamt1nWhgedXPDukUBe85gMVON+VPAJ7yffwJ4cvwdlGdXgIeAU1rrH427LdPvy/fjmYk3VGyUnc9tW8aeinb2VsztcubBaidpCdHkpJp30UYwbPG2hjxQ1RGw54z2ds15/8Ylpq4z8yeJ+dQefrOKxOgIoiLMdFgLvIKMBGqd/QFvmVhc2cbBGifdg6NhtVvqheSnJRBpVwHvzHKktpN1S5LGOkuJC8t2xFEbxBrzgWEXjV2DY+t1zGjVokSUgnPdwUvMK1p6GRh2mXpsl9Q46Rkc4URDd0AXuD9/oom0hChLvN+b6R3sP4DrlFJlwHXer1FKLVZK+TqsXA7cAVwzQVvE/1JKHVdKHQO2A18OcfwTun3rUhYuiOY7O0q5b1fZrP/IDtZ0sDnHYbody4ItY0EMualx7AtgYn7Cu3nB125YZYlBCpCfnkBn/wgdfcNGh2JKO081c/hcJ71Do3wszJPK5RkJaA2VrYE9Ufvr4Yaxz8Npt9QLiYqwsSw9gdMBXHQ3POrmZEO39C+fgeyUWJp7BhkaDU5/ft/Cz1wTJ+bx0RHkpMQFbcb8QHUHTd1DnGnqCVpHp0AormxHe/dmDNRxaHDExa7TLVy3ZpElTpZNk5hrrdu11u/QWhd4/+3wfr9Ba32T9/M3tNZKa71ej2uLqLW+Q2t9kfe292rvQlKjxUTaec+GxZxq7OGHL56d1YBo7h6ktmOAzbnWSCIDbUteCgdrOnC7A7OT6on6LtISoli4wDpdJ/LHOrP0GhyJOT1+sBYI7oZUZrE8w9M+s7w1sH8Lbu+7YbjtljqVVYsSAzpjfrqpm2GXmw1ZyQF7znCX5YhDa2joDE4vc9/VRjPPmIOnVeC5ICXmL5U2A+Y/Rhblp47tLWK3BeY49GZ5G33DLkuUsYCJEvNwtiDG0/xmti3OHj/gSToSYszURCd0LslNobN/JGCJyImGbtYuTrLU1QffG0qgZ0nDRUvPEIr5kVTmpcVjU1DeEtjEvLq9n/y0+LDbLXUqKxctoLFrkB8FaNOmo7WdAGzIlo2FpivbW/dc2xGcOvM3ytuA4LTeDaSkmEha+vVYvIHk66dvM/kxsjDHwUN/sxkF3LxxcUCOQ8+faCIxJoJLTfp/Hk8S8xC4fHn62OWTiBn2Nd9f1c5/v+xZPHrvU6WmvfwUTFvzPK9XIMpZBkdclDX3sG7Jgjk/VyhlOWKJsCmpM59A9+AIpfXdvGdD5rxIKqMj7OSkxlPeErhZ3oFhF4fPObluzcKw2y11KhHetnE/3VUekEv8O0+1EBdlpznIO1mGk6wUz9qp3xXXBPw9rqTGyR/2eya3PvXrA6Z9Dy2pcfKnQ57Wp5/8VeDjbO8bIibCxleuW2H6Y+SVBemszlwwtm/DXOyvaufpYw1sXJpsmfVH1ojS4gpzHHz/g+sBT835VAOipMbJjophHtt/ji88ehh3gOutrCY7JZaFC6IDsgD0bHMPo27NOottkx1ht7E0NU4S8wnsOt3CsMvNxy/NnTdJ5bL0hIDOmJfUOBlxaYqWWWNGKZDaez2bjgRi06aSGievnm2lf9g1bxbQBoJvt+yXTjYHvP65uLIdl7dMy8zvocWV7bjcwYuzpKaTzbkpfPGaAkscIy/JdXD4XCejrtmX9pTUOPnYL/czOOJmb0W7ZcajJOYhcsumLNZnJbGnot3Xd31CJTVOPvpgMX8qG+HrTxxncHiUSLuaF5foJ6OU4pLcFPZXdVzwtZuO4/WerX7XLbFWYg6eOnNJzM/3YmkzaQnRbFpq/jebQFmekUBVW9+c3rT87aloI8LmGWfzzXWrFwKBaZ+6p6IN3xHKzEmg2ez3TroEo/55fZbnWG/29rhF+aljM7o2mwponD2DI5xp6rZEQu6zOdfTKvlU4+yvDBZXtjPiPUa63doy41ES8xD68OZsTjf1XLAn9zPHGxka9fwhKeCTV+Tz+7sunReX6C9ka14KTd2D/Ptzp+d01nuivpuk2EjT93KdiK9lYqAWwYaDwREXu8+0cN2ahdgssNo+UJZnJDDi0pwLUE3u3sp2NmQnkxA9/9axFOamsDw9nqUpcXM+xvrWgpg9CTSbovzUsXLPQL9uvlnoD23OMvV7aGGOg0fuLCIpSrEhKymgcR6p7cStMe3/fSK+ZhcHqmd/pdz/78hK41ES8xB6z4bFREfY+IN3Med4r55t5ff7zwGeA3t0pI2rVqRTmOOYN5foJxPvTRgefK1yTpc6Sxu6WLdkgaUWfvrkpSUwNOqmsVtqV318q+3fuXah0aGElK8zS1kAyll6h0Y5VtdlmYVRwbAh28HAiGvOx9j4KM9x6rYtS02dBJpNYY6Dv39HAQDffs/agL5u+6o6iLAp7n1vYJ83GApzHKxKsdHSMxTQ5y2pcaIUbFyaHNDnDabMpFiyHLFjmyvOxtKUODRwZUGapcajJOYhlBQbyU0XZfLkkfq3bQ5SUt3BJ391gL95eD9LU+L4+cc28YGCSEv9IQWbrwZxLpc6R1xuTjf2WK6+3Mc3G1clnVnGvFDaRGJ0BJctSzM6lJAaa5kYgMT8QFUHLrfmsnlYX+5TsDCBlp4huvrn1rXD1y/7y9etkGP3DN26JRsIfOeU/VUdrM9KIi7KGleDFifYqO8cYGA4cD3dS2qcrFyYSGJMZMCeMxQ25zg4UO2cdQnrm97uNl97p3X2LAFJzEPuQ5uz6B4c5YXSJgCeOdbAh36xl1dOt6AU/PO713DDukzevcwaO1SFyqXL0t5aUa1mV39X1tzLsMvNWgvWlwPkp0svc3+jLjcvn2ph+6oMy6y2D5SE6Agyk2KoCEBivqeijSi7jU3z+HhTMNYbfm6dbqrb+kiIjiAtISoQYc0rGYkx5KfHj9WbB8LAsItjdZ1sybPOSWdmgg2toSJA7YFdbs3hc52W3Adlc24KrT1Dsy7Ze62sFUdcJGsXW6sL2/x6NzOBorxUMhKj+P7zZ/jKH47wd48dGeu6ovDUgonzFeY4eOzTRWxcmozLrZlNOfGJBu/CT4sNUp+MxGjiouxUygJQAA7WOOnoG+ada62xaUSgLc9ICEhv/72V7WzKSSYm0h6AqKypICMR8Jy8z0V1ez85qXGWLJUzg615qWNXcALh8DlPt6GtedZZ1Lw43pOWBSoxP9PUQ+/QqCUn+nyL0Q9Uz7x0VWvN62VtXFGQbrn1R5KYh9jh2k46+kao6xzgicP1XJS1gOgI27zuujJdhTkOfvPJLSxaEMPXnzjO8OjMOlKU1ncRH2UnN9Xcu79NRik1tgBUwG/3VmO3KZLjrHV5NlB8LRPn0qmos3+Y0oZuLs2fX6VA4y1xxBITaZtzaVB1e5+pt303u6L8FHqGRjnVOHmDhJnYV9WBTUGhhWaLF8Yr7DYVsHaoJec8Se3mHOucnPgUZCSwICaCg7NYAHqmuYfWniGuLLDesU0S8xArrmwf2/rapuC6NYt49NNF877rynQlxkTy3ZvXcbqph3ufOsF9u8qnvRDUt+On1c6e/SXHRnKkttMy/ViDZX9VO88cb8Ll1qbeNCSYlmck0D/somEOG9nsq+pAa7hs+fyeELDbFMvSE+a0mHbE5abOOUCeRU/8zWCLd2Y7UG3t9lW1s2bxAhZYqLY60qbISYmb89Ubn5LqDtIToy3ZicxmU2zOTZlVZ5bXzrYCSGIupubrVWpXEOWdIZeuKzNz3ZqFXJafyqP7a/nhi2em1aXF5dacbOhmrcV2/PRXUuNkX1UHnf0jAd+Ew2ruf7Vy7PP52i+6IAALQJ88Uk+ETUkLTjyv51xeyzrnAC63Jic1LoBRzS+ZSbEsTYkLyC7PQ6MuDp/rHNs52kqWBahMDTwz5ptzHJYtr9qc66CitW9sI7Dper2sjRULE8hMsuAJidEBzDe+XqUyQz43G7xtn6a7W19lay8DIy7LdmSBt+8MNzxPk1GAtt4h9lW2Y1PM6xKwuXZmKalx8tzxJkbdmk/83/55faIHULAwkfrOAXqHRmf1+GpviVmelLLMydY8zwzpXE8Wj9V1MTTqHpuFt5LlGQlUt/WNbY4zWy3dg9R2DFg6z/DVmf/rjpPTPkYNjrjYV9XBlQXpwQwtaCQxN4DMkM/dtasXji0AnU5ituNYAwA2i84awLid4WbZmSYc/OCFMwyPuvmfj1w8r09wUxOiccRFzjoxf+1si+xS6cd3ojPbTje+Vok5UsoyJ1vzU+nsH+FM89w65Pi6u2yx4G62y9MTGHVratrntoGYL5G18vHRt7vxX480TPtK8f6qDoZH3ZYsYwFJzIVFFeY4uOvKfAD+9eZ1FzzwlNQ4+emuCgC+/pdjlp0ZLMxx8Oini0iNj2LdksDuDGcVwy74w8Fa/uayXN578ZJ5f4K7PCNh1omkI97T0s82j686+CuY46ZN0ioxMHwdVPbN8URxX1UHKxcmjv2dW0mg9il49ngjdpuacaMEMzl0rhOY2R4mr5e1EmW3WbKMCSQxFxb26avysdsU1W0XnlXYU9E2VgJi9ZnBwhwH79mwmDNNPZY+2M5W+6Cb1Pgo/u7aAqNDMYXk2EiO1c9uMfDAsOfv5wvbl8/bqw7+lqbEEWW3UdYyu5na6vZ+ctOkVeJcZafEsSQ5dk515qMuNyXVHWzNt95sOXhqzAHKZ/m3CJ4JqR3HG3FZvFStKD+VKLtnTKlpXil+sbSZzKQYTgaou0+oSWIuLCs1IZqi/BSePd54wZZxkXZf+Ud4zAxeuiyVgRHXrHre/9d/wa5dU90rKXE2cYXCkAs+sjnbUl0WgqWkxsmuM60Mjrj56IMzXwx8pNZJbmocX71+5bxPygEi7Dby0uIpn2U3jOr2PiljCZCteSnsr+qYdSvQPx+qo2/YRVpCdIAjC42E6AgWJ8XMacb8pZNN+F4+K09I+fYwyUmJIzbSNnY1YTJPHq6npqOfcx39lm2SIIm5sLSbLsqksq2P002TzywcPuckKTaSL1+3IixmBovyU7Gpt7YbnolLLoEPf3jy5Nzz/bz8OQUYZA+9WWXJg22g+bdeHXHN/I33aG0XG7KTgxCZdS1fOLuWidIqMbC25qfQ3jfMd5+Z/oI/n5IaJ9/4ywmAGbXTNZu5dmZp6vJ0MQmHCanC3BTuu30TPUMu7t9dMen9OvuH+fbTpcDMSl/MxjSJuVIqRSn1klKqzPvvhNmTUqpaKXVcKXVEKXVwpo8X4eWdaxdhU55auom09w6x81QLH96cxZeuKbB8Ug6QFBvJuiVJ7K2Y+QFn+3Z4/PGJk/Nduzzfh6rKiR5rFlY92Aaa5xKv5xA+3Uu8Pk1dgzR1D3KxJOZvU5CRQK2zn2HXzGZqpVViYCVERwDwf29Uz3jWs7iynVFv6eLoLE5YzcKzfqRvVt1p+oZGeeV0M0X5KXw1TBbIr1uSxPs3LuHhN6uo7xw47/ZRt+ZzvztE7+AoUXZrb9pomsQcuAfYqbUuAHZ6v57Mdq31xVrrzbN8vAgTaQnRFOWn8swk5SxPHmlg1K35YGG2AdEFz2XL0jhc66R/eOat3SZKzn1J+eOPA3TNrR1CkFn1YBtohTkOHvl0EUuSY8hLjZvRG6+vDEpmzN+uICMRraGxb2brN6RVYmD5OtzMZtZzk7eVrsLax4rlGQkMjLho6Do/CZ3Knw/V0T04yv9758qwWiD/1etXAPBPTxx729WQkuoOvlc8yN7Kdv7zA+t57C5rt6Q2U2L+PuDX3s9/Ddwc4scLi7rpokwqW/uo6z0/Mf9jSR3rs5JYuci0ZdOzctmyVEZcmgPVs7tM65+cP/xw7lhSvn17gAMNMEe0suzBNhgKcxx8YFMWlW199AyOTPtxR+s6ibQr1mRad8OtYChY6KlfbZjgWHIhvkQyVxLzgCjKT5tRO1x/Q95F8R8ozLL0sWJ5+uy6BLndmoffqGJDdjKbllrz/z6ZLEccN65bxKtn2/jBC2e47YFivvN0KR95oJiqbjcRNkVuWrzlW1JHGB2An4Va60YArXWjUipjkvtp4EWllAZ+obV+YIaPRyl1F3AXQHp6Ort37w7U/yFgent7TRkXmC+2BUMaBbx5rp9sv7hqul2cahzkY6ujDI830K/Z0KjGruAPuw6jG2bXDkwpuPHGXH7721zuuKMapaox0a91zPjx2lN1lN1VBgc1AaPGRWyPC7eGh556lYszzj+kTxTX7mMDZMUrit98PURRTsxsx5JRt8amoNo5OKO43jg5RIwdjh/YE/SuLGZ7zcYL1PvrpZl29jS4+PuLI2c05h85NUSkDa5P6aCnyjnp48z6Ovri6hn2nBy+sOcoqnH6i90Pt4xS3T7EZ7NcvPrqq0GJzUi6Z9jzLzDscvPwm9Vjt7ndmsdePkDPMvO0yJzVa6a1DtkH8DJwYoKP9wGd4+7rnOQ5Fnv/zQCOAld5v57W48d/rFixQpvRrl27jA5hUmaM7V3/+5pe980d+mBV+9j37n3qhC74p2e1s2/IwMg8gvGafejne/S7f/z6rB//yitap6VpfccdVTotzfO11loDB3UIjwsz+TDreNXauHExMDyqC/7pWf2vO0onvH18XKMut177ref1N/9yPATRXZgZjyXX/GCXvuVHz83oMR9/aJ9+149fC1JEbzf+NQvX8frc8Uadc/cOfaimY0aP2/6DXfrjD+2b8n5m/NvT+u1xbfzOi/ruPx2d0eM/8os9uujfXtbDo64AR2aO1+xgdYde8Y1ndd49O3TBPz2rv7fjpC74xrM67+4deuU3n9UHq2f29xJssxmvIZ0x11pfO9ltSqlmpVSm9sx2ZwItkzxHg/ffFqXUX4AtwGvAtB4vwk9JjZPTTT2MuuFDv9jLp67IY3NuCr/fX8vmHAfJceY5ew6ky5al8r87y+jqHyEpbmbtA/1rypWq5m//NtevxlxYSUyknY1LkymunF7f58rWXnqHRqW+fBJpCdGU1vVRUuOc9qXw6vY+1i1JCnJk88tFWZ7X80R9FxunWZJR29FPZWsfdxTlBDO0kFmenjCjlol/KqmluLKDO4pyxtoEhxvfRnvFle0U5adSmOPgnesW8djLB7jt2kssW77iz0y/uaeAT3g//wTw5Pg7KKXilVKJvs+B6/HMuE/r8SI8+beNc2t48PUqPvPbEgZGXBys6bBsu6ypXL48Da1h7wy7Dvgn5b6acv+aczP3MRcTK8pPpbShi66BqevMfQs/pSPL+UpqnJTUOOkdYdrdQKRVYnAsToohJT6KY3Vd037M7rOtAFy9Ij1YYYVUUmwkx+u7KKme+qS7pMbJ3X86DsDjB2vD9n0POK+GvDDHwbuXRYVFUg7mSsz/A7hOKVUGXOf9GqXUYqXUs977LATeUEodBfYDz2itn7/Q40X4K8pPJSrChg2IibTxrosy8VV5utzasu2yprIhK5kou40HXquY9kF4oqTcx5ecm72PuTjfpctScWvYP43dEo/UdpIYHUG+LFQ8T3Fl+9guwcPT7Abia5UoCz8DSynFRUuSOF4//cT81TOtZKfEhkV3HM8GYi0Mjbr56C/3TXmMf/VsCy5t/TaRwkSJuda6XWv9Dq11gfffDu/3G7TWN3k/r9Rab/B+rNVaf2+qx4vwV5jj4JE7i7ilIJJH7izik1fkER1p7T6m03G8votRt5tD5zqnPbt34MCFu694vm/uPubifBdnJxMVYZvWm/HRuk7WZydhswV3kaIV+U7yAWzT7A3va5WYKz3MA+6iJUmUtfQyOOKa8r5Doy72VLSxbUVG0BfghoL/leDpnCS6vL33w2FDofnOTF1ZhJi1whwHPX6Xsh658+01aOGouLIdPW7L5an+r1/72nSe2dx9zMX5YiLtFC51TLnp1OCIi9ONPXzmarkoMhFf/eqdD+8lPTl+WscOaZUYPOuWJOFya042dk/Z+q+k2kn/sCtsylh8J4mDI25QTJloH6xxkpkUw8eKllKUnxa273vzgWlmzIUIJKv3MZ2OovxUIn2ze7aZ7fwows+ly1I51dRNZ//wpPcpbehi1K3ZkJUcusAspjDHwVVZEZS19OLsm/y19Nlf1UGU3UaNd+ZcBM56vwWgU3n1bCuRdsWly8LjOOi7EnxVQTpaQ0Zi9KT3re3oZ19VBx/dspQvbA+PHa7nM0nMhbCowhwHv/vUFiLtimtWZcjBeJ4ryk9Fa9h3gTrzHccaAU+Zhpjc+nQ7WsNrZa0XvF9JjZMXSpsYdrm5/aGp64DFzGQmxZA6zQWgu8+0ckluCvHR4VMIUJjj4HvvXwfA08caJr3fk0fqAbh545KQxCWCSxJzISxsS14qly9Po7JVZuvmuw3ZScRE2iYtZympcfLrPdUAfPGxQ5JEXkBekg1HXCSvnrlwYv5CaRPuceVkInCUUqxbkjTljPmLpU2cae5heUZCiCILneyUODYuTebpo40T3q615olD9WzNSyE7RdY5hANJzIWwuK15qZS19NLWO2R0KMJA0RF2CjISeOZYw4RJ9xOH6iSJnCabUly1Ip1Xz7bi9r1oEzjX3g8Q9gvNjbQ+y7MAdGB44gWgJTVOvvDoIQD+cCA82wS+Z/1iTjV2T9jT/GhdF5VtfdyySWbLw4Uk5kJYXFF+CjC9VnkifJXUODnV2ENr7zC3PbD3bQnKiMvN62fbAEkip2vbynTa+4Y50TDxbG1LzyCvnGnhutUZfOX6lTxyZ5GUkwWB/wLQiRRXtjPiCu82ge9an4lSsGOCcpYnDtURHWHjxosyDYhMBIMk5kJY3LolScRF2cPyDUlM39vaq7k0Tx996038gdcqOefs554bV0kSOU1XFaSjlKd2eSIPvVHFqMvNN961JuwXmhvpoiUXXgC6JS9l7PNwPeFcuCCGrXkpPH20Aa3fuoIzPOrmqaMNXL92EQtiZrb7szAvScyFsLhIu43NuSnsm+aW7CI8jW205V3XueNYA609QzT3ufnfnWXcuG4Rn716mSSR05SaEM1FS5LYfablvNu6+kf43d4a3r1+sbRJDLLMpBjSEqIm3Wgoyrv1/LvXZ4b1Ced7NiymorWPU41vdbN96I1KOvtHxrrXiPAgibkQYWBrXgpnmnvomKK9285TzfzklbKwrMOc73zt1b56/Uq+/4H19A6Ncvsvi/nBwUEilOLe9641OkTL2bYinSO1nee1oPz13mr6hl18btsygyKbP3wLQI9P0pnldW/nnHvfuzZsk3KAG9dlYlPwz08e52e7yvj4Q/v4z+fPAPDDF8/IMT2MSGIuRBjwXb7dXzV5OctfD9fzqV8f5Icvnp32TqHCWnz9+z90STZ/d81yzjb30jqgGXa5qXMOGB2e5Vy9MgO3htfL2sa+92Z5Gz/bXc7mHAerMxcYGN38sX5JEmebe/jfl8+ed9x6rayNtYsXkJYweZ/vcFDl7ZNfUtPJf71w9m2li7KYO7xIYi5EGFiflURspJ3iScpZ9pS38bU/Hxv7Wg7k4U+j8HUr11rL73sWLs5OJiHazs9freCF0iZ+vLOMOx7ax+CIm2P1XXJyGyKxUXY08L87y942qdA7NMrhc06uLAiP3T4vxH/82hR8oDCLmEibLOYOQ+HTiV+IecxTZ+44L/kqqXHy8BuVPF/axOKkWFp6hhh1ueVAPg8U5acSHWljeER+37N1pLaT/mEXpQ3dfOa3JW+7zeXtABLO5RNm0e9tlejWb00qFOY42OftyHJlQZrBEQafbw3JyKhnPH+wMJsPFmZTXNlOUX6q/B2GEUnMhQgTRfmpfP+FMzj7hnHER7G/qp2PPriPUbfGpuB777+I+OgIOZDPE76a88dePsBt114iv+9Z8D/RVcANaxex62zLWHIkJzuhsW1lBj/bXYHLrYmwv/W6v17WRkykbV78bfvG8/jj93z4v883kpgLESa2etuG7a/uIC8tnr977DCj3s1RFHC8vks6cswzhTkOepZFye98lsbPUt55VT53XpUvJ7chVpjj4Oe3F/LZ35WwbWX62Ov+elkrW/NSiYm0GxxhaBTmOORvbh6QxFyIMLE+K5kou+KbfzmOs3+E2Cg7kXaF261ldk+IWZBZSvO4bu1CPnxJNn8uqaO5e5BRt6aitY/btiw1OjQhAkoScyHCxPH6LkbdmtbeYWwK/vfWi0mKjZLZPSHmQGYpzeNzVy/j8YO1PPhaJQULEwDmxcJPMb9IYi5EmBhfD3uqsUdKV4QQYWNpahzv3bCYR/adY1NOMhmJ0azwJuhChAtplyhEmPDVw0r7LCFEuPr8tmUMjLh4s7yd1ZmJKKWmfpAQFmKaxFwplaKUekkpVeb997xpPqXUSqXUEb+PbqXUP3hvu1cpVe93200h/08IYSBfPexXrl8Z1ltTCyHmr+7BUWzeXHxPRbv0khdhxzSJOXAPsFNrXQDs9H79NlrrM1rri7XWFwOFQD/wF7+7/Lfvdq31s6EIWggz8e38KEm5ECIc+Zfsud2ycZYIP2ZKzN8H/Nr7+a+Bm6e4/zuACq11TTCDEkIIIYQ5SMmeCHdmWvy5UGvdCKC1blRKZUxx/1uBx8Z974tKqY8DB4Gvaq3lGpcQQggRJiZrYSlEuFBa69D9MKVeBhZNcNM3gF9rrZP97uvUWk844pRSUUADsFZr3ez93kKgDdDAd4FMrfUnJ3n8XcBdAOnp6YWPP/74rP9PwdLb20tCgjlXm5s1NrPGBdaKbfv27SVa680GhvQ2VhivYN7fsVnjAvPGZta4QMZroJj1d2zWuEBim41ZjVettSk+gDN4kmmATODMBe77PuDFC9yeC5yYzs9dsWKFNqNdu3YZHcKkzBqbWePS2lqxAQe1CY4JE32Ydbxqbd7fsVnj0tq8sZk1Lq1lvAaKWX/HZo1La4ltNmYzXs1UY/4U8Anv558AnrzAfW9jXBmLUirT78v3AycCGp0QQgghhBBBZKbE/D+A65RSZcB13q9RSi1WSo11WFFKxXlvf2Lc4/9LKXVcKXUM2A58OTRhCyGEEEIIMXemWfyptW7H02ll/PcbgJv8vu4HzluGrbW+I6gBCiGEEEIIEURmmjEXQgghhBBi3pLEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIE5DEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIE5DEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIE5DEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIE5DEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIE5DEXAghhBBCCBOQxFwIIYQQQggTkMRcCCGEEEIIEzBNYq6U+pBSqlQp5VZKbb7A/W5QSp1RSpUrpe7x+36KUuolpVSZ919HaCIXQgghhBBi7kyTmAMngFuA1ya7g1LKDtwH3AisAW5TSq3x3nwPsFNrXQDs9H4thBBCCCGEJZgmMddan9Jan5nibluAcq11pdZ6GPg98D7vbe8Dfu39/NfAzUEJVAghhBBCiCCIMDqAGVoC1Pp9XQds9X6+UGvdCKC1blRKZUz2JEqpu4C7vF8OKaVOBCPYOUoD2owOYhJmjc2scYG1YssxKpCJWGS8gnl/x2aNC8wbm1njAhmvgWLW37FZ4wKJbTZmPF5DmpgrpV4GFk1w0ze01k9O5ykm+J6eaRxa6weAB7wxHdRaT1rTbhSzxgXmjc2scYHENhdWGK9g3tjMGheYNzazxgXmjg1kvM6VWeMCiW02ZhNXSBNzrfW1c3yKOiDb7+ssoMH7ebNSKtM7W54JtMzxZwkhhBBCCBEypqkxn6YDQIFSKk8pFQXcCjzlve0p4BPezz8BTGcGXgghhBBCCFMwTWKulHq/UqoOuBR4Rin1gvf7i5VSzwJorUeBLwIvAKeAx7XWpd6n+A/gOqVUGXCd9+vpeCCA/41AMmtcYN7YzBoXSGyBYuZYzRqbWeMC88Zm1rjA3LGNZ+ZYzRqbWeMCiW02ZhyX0nrGJdpCCCGEEEKIADPNjLkQQgghhBDzmSTmQgghhBBCmMC8TcyVUjcopc4opcqVUobuEqqUelgp1eLf71UplaKUekkpVeb912FAXNlKqV1KqVNKqVKl1N+bKLYYpdR+pdRRb2z/YpbYvHHYlVKHlVI7TBZXtVLquFLqiFLqoJliuxAZr9OOzZRjVsbrrOOy5HgFGbPTjEvG6+xjDNsxOy8Tc6WUHbgPuBFYA9ymlFpjYEi/Am4Y9717gJ1a6wJgp/frUBsFvqq1Xg0UAV/wvk5miG0IuEZrvQG4GLhBKVVkktgA/h7PAmUfs8QFsF1rfbFfb1UzxXYeGa8zYtYxK+N19iw1XkHG7AzIeJ298B2zWut594Gn88sLfl9/Hfi6wTHlAif8vj4DZHo/zwTOmOB1exJPxxtTxQbEAYfw7AJreGx4+uvvBK4Bdpjp9wlUA2njvmeK2C4Qs4zX2cdpujEr43VGsVluvHrjkjE7uxhlvE4vprAes/NyxhxYAtT6fV3n/Z6ZLNRaNwJ4/80wMhilVC6wEdiHSWLzXso6gmczqZe01maJ7X+ArwFuv++ZIS7w7JT7olKqRHm2zjZTbJOR8ToLZhuzMl5nxYrjFWTMzpiM1xn5H8J4zIZ0508TURN8T/pGTkIplQD8GfgHrXW3UhO9fKGntXYBFyulkoG/KKXWGRwSSql3Ay1a6xKl1DaDw5nI5VrrBqVUBvCSUuq00QFNg4zXGTLjmJXxOitWHK8gY3ZGZLxO33wYs/N1xrwOyPb7OgtoMCiWyTQrpTIBvP+2GBGEUioSzwHjEa31E2aKzUdr3QnsxlNDaHRslwPvVUpVA78HrlFK/c4EcQGgtW7w/tsC/AXYYpbYLkDG6wyYfczKeJ0+i45XkDE7bTJeZyzsx+x8TcwPAAVKqTylVBRwK/CUwTGN9xTwCe/nn8BTexZSynPa/hBwSmv9I5PFlu49k0cpFQtcC5w2Ojat9de11lla61w8f1evaK0/ZnRcAEqpeKVUou9z4HrghBlim4KM12ky65iV8TpzFh6vIGN2WmS8zty8GLNGFMeb4QO4CTgLVADfMDiWx4BGYATPTMOngFQ8ixvKvP+mGBDXFXguPx4Djng/bjJJbOuBw97YTgDf8n7f8Nj8YtzGWwtTDI8LyAeOej9KfX/3ZohtGrHLeJ1ebKYcszJeZxWPZcerN04Zs1PHJeN1bnGG5ZhV3gcJIYQQQgghDDRfS1mEEEIIIYQwFUnMhRBCCCGEMAFJzIUQQgghhDABScyFEEIIIYQwAUnMhRBCCCGEMAFJzIUQQgghhDABScyF4ZRSC5RS9yqlVhsdixDiwmS8CmEdMl6tRxJzYQabgW8DkUYHIoSYkoxXIaxDxqvFSGIuzGAjMAScNDoQIcSUZLwKYR0yXi1Gdv4UhlJKnQJWjfv2n7XWHzQiHiHE5GS8CmEdMl6tSRJzYSil1CXA74FS4N+8327UWtcYF5UQYiIyXoWwDhmv1hRhdABi3jsKZAE/0VoXGx2MEOKCZLwKYR0yXi1IasyF0dYCUcAhowMRQkxJxqsQ1iHj1YIkMRdG2wRo4IjBcQghpibjVQjrkPFqQZKYC6NtBCq01t1GByKEmJKMVyGsQ8arBUliLoy2BmnjJIRVyHgVwjpkvFqQLP4URusENiml3gl0AWVa63ZjQxJCTKITGa9CWEUnMl4tR9olCkMppdYBDwHrgRjgSq31G8ZGJYSYiIxXIaxDxqs1SWIuhBBCCCGECUiNuRBCCCGEECYgibkQQgghhBAmIIm5EEIIIYQQJiCJuRBCCCGEECYgibkQQgghhBAmIIm5EEIIIYQQJiCJuRBCCCGEECYgibkQQgghhBAm8P8BGnsloLJl7KUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=1, ncols=3, sharey=True, figsize=(12, 4))\n",
    "for col in range(3):\n",
    "    plt.sca(axes[col])\n",
    "    plot_series(X_valid[col, :, 0], y_valid[col, 0],\n",
    "                y_label=(\"$x(t)$\" if col==0 else None))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E' utile, come fatto per il perceptron, definire alcuni modelli baseline per confrontare le performance ottenute.\n",
    "\n",
    "Il primo modello restituisce il valore della serie al tempo $t-1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.020709343"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = X_valid[:, -1]\n",
    "np.mean(keras.losses.mean_squared_error(y_valid, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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C1o24JeMyk+gSHcEf5m8lqWt02H/RtKTSDjnpicy8P5dFRRUsKtrP84tK6dU9lm9eNDDQoRmvlaUHuHFGwZcmAe0aHUHP+BgEz1UmqqzafpAJA3ue8rFys5KJjnRRV+/2rkn+5eNz0hPJSU8kqWs0j39YyNwNe7h8RG/fvyjDyrIqHnztcwDeX7ubW8enO+bDe+2OQ5yoa2DdzkNMe7Yg7KvFrfdXO+WkJ/KdSwbzt/tyuWpkH/73g838cf7WQIdlvF5YXHoyoQhwx4R01vzsMp66aTQxUS4iBG+COP1stjnpicy8L5fvX5Z9yg+K+y/IYlif7jzy7noOn7Au551h8baKk3/X+ga3X6a4b6uC4koaZ2qprXdWbIHguCsVEZkC/B6IAJ5V1cea7Z8G/Nh7txr4N1Vd491XChwBGoB6VR3TWXFGRbj43U2jiY5w8eS8LWw/cJSMnl3JzbJeYYFyoq6BguJKBE91VVSki6mj+xEZ4TqZIAqKK8nNSm7z36jxauRUoiJcPPaNs7n2T4t4/MPN/M/Xz/bBqzFNxUd7Pqpc7fhS4C+NV7Q19W5ctlqss5KKiEQATwOXAjuA5SLynqpubHJYCXCRqlaJyNeAGcD4JvsnqWqFP+KNjHDxxA2jOHS8jr+v3IkAMVHWKyxQnvushIrqWn5xzQiqa+q/kjzakiA6atSABO46L5PnF5Xw9dH9GJOR1CnPE6627KsmJtLFt/IGcv7gFEf9fzWuFnv3C8sY0be7o2ILBKdVf40DilS1WFVrgVnA1KYHqOpiVW0cbVYA9PdzjF8S4RLOSUsAPPX1dvkbGPuOnOBPC4q4bHgv7jwvg29PGuT3f+7/uGwI/RLi+PGba0/2FDRnrr7BzdwNe7h0eC8emjzEkR/aOemJTB7Wi637qsN+1mJHXakA/YDyJvd38OWrkObuBT5ocl+Bj0REgb+o6oyWThKR6cB0gJSUFPLz888kZmIPNRDpgnq3px4/5mAZ+fnBswxxdXX1GZdBoD2/voYTdQ1cnHy4w6/FF+Vw00A3T608zn1/nkevLi6GJkUwKNE5PZXawmnvh42VDRw4Wku664Df4upIGfSoraOiupZZ/1xAn3infV/vmI6Ug9OSSkujmVpM+yIyCU9SOb/J5omquktEUoF5IrJZVRd+5QE9yWYGQHZ2tubl5Z1R0HnAyNGV3PbsMvKyU7jv2k5ryukU+fn5nGkZBNLGXYf5dO6n3DMxk5uvHN7hx/FFOeQByw8v5dOtFbikgejIhqCrDnXa+2He2+uIi9rJg9+Y5LfBhR0pg/SKo7ywIR9SB5EXIqPrO1IOTkunO4ABTe73B3Y1P0hERgLPAlNV9WRdk6ru8v7eB7yNpzrNL8ZlJpM7MJnSyqP+ekqDZ9qOR+dspEdcFN+5ePDpT/CDkf17AJ7xLZ5Bsn5p4gtJDW5l7oY9XDws1fGj1TOSu5DSLYalYV797bSkshwYLCKZIhIN3Ay81/QAEUkD3gJuV9UtTbZ3FZFujbeBy4D1foscGJeRyJa91VQdrfXn04a1f23ex6KiSh66ZDA9ukQFOhzAs85GTKTnX0uBJdsOcKy2PrBBBamlJZVUVNdy5dl9Ah3KaYkI4zKTWFpyIKzbVRyVVFS1HngQmAtsAmar6gYReUBEHvAe9giQDPxJRFaLyArv9l7AZyKyBlgG/FNVP/Rn/GO9PX5W2Ky1flHX4ObROZvI6tk1oOtqNNfYG+gHlw3h1vFpLNpWwbVPL6akwq5i22vOut3ERrnIy04JdChtMj4zid2HTrCj6nigQwkYp7WpoKpzgDnNtj3T5PZ9wH0tnFcMjOr0AE9h1IAEoiNcLCuptDmA/GBmQRnF+4/y7B1jiIpw1PejL3VfnjKiNw/N+pxr/vgZ35o0ELfSrrEy4arBrXy4fi8XD02lS7TjPqpaND7TM0ZlWckBBiS1Pg1QKHPWf2KQi42KYNSAHiwrtSuVzrawcD+PfbiZs/t155JhqYEO55QuHJLCP/79fFK7x/DrDwv5zdxCpj1bYOuwnMby0gNUVNdwRRBUfTUanBpPQpcolpaEb7uKJRUfG5uRxIadh6wOvRPN3bCHu15cxok6N4V7q1m1/WCgQzqt/olduMY7s66NZ2qbxqqvi4c6+0tDUy6XMDYjiWUlBwIdSsBYUvGxcZlJ1LuVz4Pggy7YqCpvrdrBv7/2OY3zRTY4bB6oUzl/cMrJBnyx6TxOqcGtfLB+D5Oyg6fqq9H4zCRKK4+xN0yXGLak4mM56Ym4BJaG8TeVzlBZXcMDf1vJ92evIatnV2Ii2zc5pBM0NuCf3a87EQKZPbsGOiTHWlF6gP1Hgqvqq9G4TE+HnXC9WgmurwBBoFtsFMP6dGd5mL6hfG1lWRWvLCnlX5v3caLOzX9+bSj3XZDF6vKD7Z4c0gly0hN56sbRXPrbhbyypIyHJjtjbI3TzFm3m5jI4Kr6ajS8T3fiYyJZVnLAUYuJ+YsllU4wNiOJWcu3U1vvJjrSLgY7allJJbfMWEqDKgI8deNorj23H9C5k0N2tsG9unHx0FReXlLKNy/KctSCU07g9lZ95WWn0DUm+D6iGmfFDtfGep9/4onIH0XkHy1s7y4iPxeRYU22fU9E1opISH3yjs9M4kSdm/W7DgU6lKD2h/lFNHgHkbkEdh0Knb7/91+QReXRWt5atTPQoTjOirIq9gVp1VejcZlJbNlbzYEwHAjt0w9zERkIfBP4RQu7xwA/A5oOe34GSAXu9GUcgdY47Xm41qn6wvqdh1iyrQKXEHRtJ22Rm5XE2f168Oynxbjd4Tv6uiVz1u0mOtLFJcOCd6zXeG+7yvLS8PsM8PUVwneBNaq6ooV95wA1wMm1UVT1OPAy8AMfxxFQKd1iyOrZ1dpVOuhEXQPfe301PbvF8OJd40678mIwEhHuvzCL4oqjzN+8L9DhOMaK0gO8sbKc0f17EB+EVV+NRvZPICbSFZZfLNuUVERkkIjUicgvmm3/s4gcEZExIhID3Aa82sL5m4DfADFAnYioiLzh3T0LGC4i553RK3GYsRlJrCirsm+hHfDkR4Vs3VfN49eP4sLslICsjeIPV5zVm34JccxYuC3QoTjCyrIqbv3rUqprGvi8/GBQDw6NjnRxblp4tqu0KamoahGeWYG/JyI9AUTkEeAe4FrvlUkukAB82sJD3AEUA/8AJnh//sO7bzVwGJjS0RfhROMykzh0vI4t+44EOpSgUlBcybOflXBbbhoXDQmO+Z46KjLCxb3nZ7K8tIpV24P3A9RXCoorqWtwA57G+mAZf9SacZlJbNx1mMMn6gIdil+1p/rrF3jWjf+xiNyLp33kdlX92Ls/F89g4bUtnLsGzzT2/1LVAu9PGYCqur3n5HbwNThSuPdV74gjJ+r4wd/XkJbUhZ9cMez0J4SAG8cOoHtsJM9+WhzoUAIuNyv55IpKodCGNj4zCbcS1FdcHdHmpKKqe4DfAf8O/AX4jqrObnJIX+Cwdxng5kYA0cCqVh5+v/f8kNE/MY7e3WMtqbTD/7y/iV0Hj/PUjaOCbhR1R8XHRDItN50P1++hLMzX4slI7oIqnD+oZ0i0oZ2TlkhUhITdZ0B7G+q34mkXWaKqTzfbF4unIb4l5+K5ilndyv7jQFw7Y3E0EWFsZhLLS8N7bYW2+njjXl5fUc4DFw0kJz0p0OH41V3nZRDhEp7/rCTQoQTUZ0Wexcx+cHl20CcUgLjoCEb2T7Ck0hoRuRjPFcoSYKKINJ9mvhJo7Z1wDrBNVQ+3sj8JCLnl8cZlJrH3cA3lB0JnfEVnWLB5L9+Z9TnpyV347uQhgQ7H73p1j2Xq6H68tqyc38wtDLvqkkafbq2gR1wUZ/frEehQfGZcZhJrdxzkeG1DoEPxm7b2/joXeAdPY30esB34VbPDNgNRItK/hYcYTpOuxC3IBArbEkswGecdrxKOPUDaakXpAe59aQXHahvYc+gE63aG54DRiQN7Utvg5ukFRWE5Lb6q8unW/Zw/qCcRLgl0OD4zLjOJugbl5++tD5u/6WmTiogMAj4APgL+3dtm8gvgChG5sMmhC72/W1oX/iAwSkQuF5FcETnZAiciCcCQJueHjMGp8fSIiwrLAVBt9buPt56ccbg+iGYc9rXG2QIUqAvDafG37qtm7+EaLhzSM9Ch+FSkN0HOXrEjbL4snDKpiEhvPMlkEzDN21MLPAMWNwOPNR6rqqV4lvG9uoWHegTYi+dqZwnQtGvPlUAt8HZHXoCTedZWSGS5LdrVogWF+/isKHRHzbdHblYyURGeDyCXK/ymxV+4ZT/gWR4glKzd4bnyDqcvC6dMKqq6R1WzVDVPVWuabG9Q1WGq2nzA4p+Bb4hIl2aPs15Vx6tqnKqKqn7WZPdtwN9VtRJARKaISKGIFInIw81jEo8/ePev9VbN0ZZzA2FcZhIlFUfZdyQ811ZoTVnlUR567XOG9enO3+4dH5Kj5tsjJz2RmfeNp3tsJEN7dwu7cvh0awUDU7rSLyGk+uuQm5V88molMiI8vjT5epqWV4CdwLfacrCIjAYm4Z0rTEQigKeBr+Fph7lFRIY3O+1rwGDvz3Q8iayt5/rdWG+7yv+8vyksLn3b4lhtPd98ZSUiwl9uy+G8QT1DdtR8e4zLTOaBvIGs23mYrXvDZ9DsiboGlpZUckGIXaWA58vCL6eOAODBMHmP+zSpqGoDnlH2x9p4Sm/gbu+IffC0xxSparG37WYWMLXZOVOBl9WjAEgQkT5tPNfvGkcIv7dmV9jUqZ6KqvKfb62jcO8Rfn/zaNKSu5z+pDBy05gBREe4eKWgLNCh+M3KsipO1LlDrj2l0Y1jBtAjLortB9r6sRjcxEljKETkemCKqt7nvX87MF5VH2xyzPvAY41VaCIyH/gxkHG6c5s8xnQ8Vzl0Sx2Qk3T3nzv1dRljTCgp+/VVK1V1TEv7nDZsuaW+hM2zXmvHtOVcz0bVGcAMgOzsbC187Mr2xNguK8uqmPZsASfqPFcsD39tKA9cNLDTnq8j8vPzycvL6/TneXlJKT97bwNj0xOZNX0CLod1HfVXOZzOmvKDTH16Eb+4ZgR3npfh9+f3dzl87fef0iMuklnTJ/jtOU/H12Uwe0U5P3pjLXO+cwHD+3b32eN2ttbKQX7d+jlOWxxrBzCgyf3+wK42HtOWc/3O0wCby/cmD2ZgSlf+MH8rm3a3NgY0dM3ftJdH3t2AqqdHzOflBwMdkmONGpDAqP49eHlJacjPxrDvyAk27T4cku0pTeV5J0f9xNvLLZQ5LaksBwaLSKaIRAM3A+81O+Y94A5vL7Bc4JCq7m7juQGRk57IQ5OH8Or9uXSLjeS+l1aw/0hrM9qEpj/lF528XRfG41Ha6o4JGWzbf5TF20K7nBZ5p2a5MMSTSmr3WIb16c4nW0J/7RxHJRVVrQceBObiGRszW1U3iMgDIvKA97A5eKbRLwL+irenWWvn+vklnFKv7rH89Y4xVB6t4YG/reREXXhM3bD38AnW7DhEhEjYj0dpqytH9iGpazQvLS4NdCid6tMtFSR2iWJEEFUJdVRedgorSqs4EuJT4TsqqQCo6hxVHaKqA1X1Ue+2Z1T1Ge9tVdVve/ef3XSVyZbOdZqR/RN48obRrCyr4idvrQv56g2AP+dvA4U/3nJO2I9HaavYqAhuGjuAjzftZefB0Jw7TlVZuLWC8wenOK59rTNcNCSFereG/NWn45JKOLhyZB++O3kwb32+kzufXx7S3Yx3HzrOq8u2c31Of64Y2cfGo7TDtPFpAMwM0e7Fm/ccoaK6hgsGh2ZX4uZy0hOJj4kkvzC021UsqQTIBYN64hJYuHU/t/41dMev/GnBNtxu5duTBgU6lKDTP7ELk4f1Ytby8pCsKv10q+fDNdTbUxpFRbiYOCiZhVv2h3QNhSWVAClossZCbYjOCbTr4HFeX17ODWMGMCDJBjl2xJ3nZXDgaC3fn7065L54fLq1giG94undIzbQofjNRUNS2XnwOEX7qgMdSqexpBIguVnJREd6il+BsRmhVyX09IIiFOXBi+0qpaNiI10IMGfdnpCakcEzNcuBkO9K3NxF2aHftdiSSoA0jl/5+mjPKspHa0KremNH1TFmryjnprEDQm6SQH8K1SvaZSUHqK13h017SqN+CXEMTo0P6XYVSyoBlJOeyOPXjyKxSxRvrNoR6HB86ukFRQhibSlnKDcrmZioL65oczNDY6nlN1aWEyFCdET4fQTlZaewrOQAx2rrAx1Kpwi/v6jDREe6uGZUX+Zt3MuhY6HRf738wDH+vmIHN48bQJ8edpVyJhqvaC8f0QtVOHg8+N8jK8uq+Mea3TSocs9Lod37sSUXDUmlNoQHAFtScYDrcvpTW+/m/XUBn1XGJ/7vX0W4XMK38uwqxRdy0hP5v1vPJT25C09+tAW3O7h7Dr39+c6Tk/KFy8JVTY3NTCQuKiJkq8AsqTjA2f16MDg1njdXBn8V2Jy1u5m9spzJw1LDqldPZ4uKcPHdyYPZuPswH6zfE+hwzkhpxVEgfFf7jImM4LyBySHbWG9JxQFEhOtz+rNq+0GK9wdnV0NV5dWl23nwtVWowvxN+8KuWqOzXTOqH4NT43lqXiENQXq1svvQcQqKK7l6ZJ+wnl3houwUyiqPUeJNsKHEkopDXHtOP1wCb63aGehQTmtlWRVPLyhiZVkVxfureWreFvJ+k89P3l5H42ddfQjXGQdKhEv4/qVD2Lb/KO+udv77pCUvLS7DrcqPpgwN69kV8oakAvBJYehNMOm09VTCVmr3WC4YnMLbn+/k+5cOcexcSI3rw9TUuUFAFURg4sCeXDWyD899WkJdgzssqzX84fIRvRnRtzu/+3grV4/qS1QQ9Z46VlvPa8u2c/mI3mE/GDYtuQt9esTy0pIyzu6fEFLJNXjekWHgupz+7Dx43NHf8AuKK6mpc6N4EkrekBSWPHwJf7tvPD+8fCgz788N62qNzuZyCT+4LJvt3h52weTNVTs5dLyOe8/PDHQoAbeyrIp9R2ooqTjKtBCbpsmSioNcNrwX3WIjHT1mZXyTcRKxUS7+/ZLBX2qQz0lPDOtqDX/Iy07h3LQE/vivrUEzJ5jbrbzwWQmj+vew9waeL2eNvfhCrXuxJRUHiY2K4KqRffhw/R6O1jhzYFRtvecq5cqze9vVSICIeK5Wdh86watLtwc6nDbJ37KP4oqj3HN+JiLOrNr1p9ysZGK80zS5REKqqtiSisNcd25/jtU2MGfd7kCH0qJZy8vpHhvJkzeOtoQSQOcN6sl5A5P5/fwt/O7jLY6vPnnusxJ6d4/lirP7BDoUR8hJT2Tm/bn06RHLwNT4kPpfsqTiMDnpiWQkd+FNB1aBVR2t5cP1e7j2nH7ERkUEOpywd9XIPhw6Xs/vP97q6MkmN+85zKKiSu44Lz2oOhZ0tpz0RL5+Tj+27at2bM1ER9hf2GFEhG+c25+C4gP8as4mR31QvPX5Tmob3Nw8Li3QoRigyjutj+LskenPf1ZCXFQEt9r75ismZCVT71ZWOOj//Ew5JqmISJKIzBORrd7fX7keFJEBIrJARDaJyAYReajJvp+LyE4RWe39ucK/r8B3BqfGA/DXhcWO+Qaqqry+fDujBiQwrE/oryceDHKzkomK8LRPuFzOrJevqK7hndW7uC6nHwldogMdjuPkpCcS6RLHfiHoCMckFeBhYL6qDgbme+83Vw/8h6oOA3KBb4vI8Cb7f6uqo70/czo/5M5R7B1lqzhnuvNV2w+yZW81t4wdEOhQjJdnssnxdI2OYKRDxzr8raCM2no3d0+0bsQt6RoTyagBCSwJoXXrnZRUpgIveW+/BHy9+QGqultVV3lvHwE2Af38FaC/NO0Z4tYvrlwCaday7XSJjuCqUX0DHYppYlxmMveen8mq7VWUHzgW6HC+pKC4ghkLizk3LYGBKYF/DzvVhKxk1u08RHWItKuIU9ZKFpGDqprQ5H6Vqrb61UtEMoCFwFmqelhEfg7cBRwGVuC5ommx3khEpgPTAVJSUnJmz57to1fhO0VVDRTsqWdheT29urr4yfhY4iI7pytmdXU18fGt/9Mfr1ceWnCM3D6R3HNWTKfE4ASnKwenqjzu5gefHOfKrCiuH3LmVUy+KIeiqgb+d9kJGhQiBR4eF8ugxODp3OHP98LGygYeX36C7+XEMCrFWZOctFYOkyZNWqmqY1o6x6+vQEQ+Bnq3sOun7XyceOBN4Luqeti7+c/Af+OpNfpv4EngnpbOV9UZwAyA7OxszcvLa8/T+0UecB+wcMt+7n5xOa9t78pzd47plN4z+fn5nKoMZi4to7ZhPd+fOp7RAxJ8/vxOcbpycLIP9q2goLyKp+658OQy1R3li3LYsKCIBi0EPP+QNQnp5AXRUgj+fC+Mr23gt6vmcqxrP/LyhvnlOduqI+Xg1+ovVZ2sqme18PMusFdE+gB4f7c405qIROFJKDNV9a0mj71XVRtU1Q38FRjX+a+o8104JIVHv34WC7fs55F3NxCIK8tZy8oZ2rsbo/r38Ptzm7aZlptGRXUtczc4Y1r84X09nTmE8Jzevj3ioiM4Z0AiSxzQduoLTmpTeQ+403v7TuDd5geIZyjuc8AmVX2q2b6mo6quBdZ3Upx+d/O4NP4tbyCvLdvOXxYW+/W51+88xLqdh7h57AAbCe1gFw1OoX9iHDOXlgU6FAD2HDoBwB0T0m3mhTbIHZjM+p2HOHwi+Ff2dFJSeQy4VES2Apd67yMifUWksSfXROB24OIWug4/LiLrRGQtMAn4np/j71Q/vCybq0b24bEPNvOH+VtPTj3f2WYt305MpItrz+nf6c9lOs7lEm4dn0ZB8QGK9h0JdDjMWbebjOQu/PyaEZZQ2iA3Kwm3wrLiA4EO5Yw5plVIVSuBS1rYvgu4wnv7MzxX1C2df3unBhhgLpfwmxtGUbTPs36JSzzr23fmt8DjtQ28+/kurji7Dz26RHXKcxjfuXHMAH47bwszl27nZ1ePCFgcB47WsnhbJQ9clGVXt210bloi0ZEuCoormTy8V6DDOSNOulIxpxEbFcHkYZ43nFs7fxT10/lFHKmp59y0hE57DuM7PeNjmHJWH95cuYPjtYGbvXjuhj00uNXm+WqH2KgIzk1LCIl2FUsqQWbS0NSTo6ilk2Y3dbuVvxWU8fS/igB41GHTxZjW3TY+jcMn6vnHml0Bi6Gx6mu4zbzQLhOyerJx92EOHqsNdChnxJJKkMlJT2TW9AkM7d0NRekWe2Y1mCvLqnh/W+3JpYGf/KiQC59YwH+9s57GfmZOnlfKfNm4zCQGp8YHrMG+serrirP7WNVXO+VmJaEKy0qCu13FkkoQapyeo0dcND98Yy0N7o51M15ZVsWtfy3gja11XP/MYi5+8hOeXlBEZs+ufOfiQcRGuogQ6xIaTESEaePTWLPjEOt2HPL7839kVV8dNjotgZhIV9BXgVlSCVLJ8TH87OrhrCk/yPOflbT7/ANHa3li7mZq6t1Ak6WB//MSXrl3vGdJYFsaOChde25/oiNc/PTtdX6vtvznut2kJ3dhRF+r+mqvmMgIxmQkBv08YJZUgtg1o/oyeVgvfvNRISXeSShPZ9+REzz6z41MfOxfFBQfwCWe7nSNSwP36m5LAwe7on3VNLiVtTsPcasf1z+v8lZ9XWlVXx2Wm5nM5j1HOHA0eNtVLKkEMRHh0WvPIjrSxY/fXHtyzeuWzN2wh2/8aRETH/sXz31WwpSzejPvexfy9wfO47rBUXY1EkIKiitRb4tYTb2bf671T6P9Rxut6utMTRjoqWZeVhK8VyuOGadiOqZX91j+35XD+dGba5m5bDu356af3Hf4RB1z1+/hbwVlrPHWr0eI8MdbzuHKkV/MNnxkYLQllBCSm5VMdKSL2no3boXZK8q5elRfzknr3L/x+2ut6utMjeyfQFxUBEu2VTLlrOBMzpZUQsANY/rzj7W7ePT9jZRWHCUhLor1uw6xoHA/tfVuesRFIuD97qqUVjprinTjW56OHLkUFFeSmdyVxz7czLRnl/KX23O4YHBKpzxnY9XX9AttwOOZiI50edpVgrix3pJKCBARbh2XxqdbK3jO22if0CWKW8elcc3ovqhbmfbcUurq3daTK0zkpCeevPock5HIHc8v454Xl/O7m87hypG+/wbcWPV1pVV9nbHcrGSemFtIRXUNPeODb6kJSyohorji6MmrEZfAfedn8uDFg0/ub/zmmpuVbFVdYSa1eyyvf3MC9764nAdfW8WaHVn0iIvy6Xvhn+v2kJZkVV++0Niu8st/bOTO8zKC7v/VkkqIyM1KJibKdfJqZMLAnl/a3/Sbqwk/PeKieOXe8Ux7toAZC4sRICbKN3PHHTxWy+KiCu67wKq+fKG+wdPN/701u/ho456g60Rjvb9CRGM9uo0rMa2Ji45g0tBUwHNFW+ujmRI+2rCXerdyVSdUq4Wj5aVfdAEPxtks7EolhNjViDmd8wb25P8ii04OevVF+9qry7bTIy6KmrrATWIZSnKzkomOcFHb4Mbl6pz5/TqTXakYE0Zy0hN59f5cJnjX7zjT2qoP1u1mdflBDh+vY9pzS23iUR/ISU/ktfvHk9w1mn4JcUE3S7glFWPCTE56Is/eOZaUbjH8z/sbO7xEtary67lfrEMfjFU1TpWTkcQPLs+mtPIYBUG2cJclFWPCUNeYSH54WTarth/k/bW7O/QY76zeSWnFUSJdYhOPdoJrz+lHUtfok8MEOtvjj8OCBac+ZsECz3GnYknFmDB1XU5/hvfpzmMfbOZEO9tDKqtr+OU/NnJuWgKzplsHkc4QGxXBbePTmL95L6VtnNvvTIwdCzfe2HpiWbDAs3/s2FM/jmOSiogkicg8Ednq/d3iu1NESr1r0a8WkRXtPd8Y4xHhEv7rymHsPHic5xe179vwf7+/keqaen593UjGZCTZxKOd5LYJ6US5XLzQzr9PR0yaBLNnt5xYGhPK7Nme407FMUkFeBiYr6qDgfne+62ZpKqjVXVMB883xgDnDerJ5GG9+NOCbew/UtOmcxYU7uOd1bv4Vt4gBvfq1skRhrfUbrFcPaovf1+5g0PH6zr9+VpKLO1JKOCspDIVeMl7+yXg634+35iw9JMrhnKiroGn5m057bFHa+r5r7fXMyg1nm9NGuiH6My952dyrLaBWcu2++X5miaW55/PaFdCAZCO9vzwNRE5qKoJTe5XqepXrqdFpASowtPh5C+qOqM953v3TQemA6SkpOTMnj3bly8l6FRXVxMfHx/oMAIunMth5qYaPi6r55cT40iUY62WQ+NxPxkfy+DECD9H6T9Oey/8etlx9h5TnrgwjgiXf2YteP75DF55JYPbby/lnntKv7Rv0qRJK5vVFJ3k18GPIvIx0LuFXT9tx8NMVNVdIpIKzBORzaq6sD1xeBPRDIDs7GzNy8trz+khJz8/n3AvAwjvchg9rpaLnsjn76XRDO5Sz61nj/pKG8nn26v4eO5ibp+Qzv1TzwpQpP7htPdCfepe7nt5BceSs7l6VN/Tn3CGFiyADz6A228v5YMPMrj77ow2X6n4Namo6uTW9onIXhHpo6q7RaQPsK+Vx9jl/b1PRN4GxgELgTadb4z5qoQu0Xzj3H68sKiUtcDbRYu5IWcAl43oxVn9elBacZRvv7qKpC7R/PDy7ECHG3YuHppKZs+uPPdZSacnlaZtKCKl3H13+6rAnNSm8h5wp/f2ncC7zQ8Qka4i0q3xNnAZsL6t5xtjWpfUNZrGihW3wusryrn3pRWM/9V8bppRQEV1LYdP1LFlb3VA4wxHLpdw98QMVpcf7NRZC1pqlD9Vr7AWY+206NrvMeBSEdkKXOq9j4j0FZE53mN6AZ+JyBpgGfBPVf3wVOcbY9rmvIE9iYly4QJio1zMvG88bzwwgUu8k1ACuN1qo+YD5Lpz+9M9NpIn5xby9IIinyeXU/Xyak9iccyEkqpaCVzSwvZdwBXe28XAqPacb4xpm8aZrl/7eDm3TB57sk3lW5OERdsqbJG3AOsaE8mkoam8u3oXBSWVREf6ZumCRsuXn7qKqzGxLF9+6sdxTFIxxgReTnoiRwZGf+mDqunyxLbIW2D16RELeKonG+da89Xf40c/Ov0xkyZ5fn7849aPsaRijDktW1bBGS4d3psZC4txK0RFOPOq0UltKsYYY04hJz2Rn109AoB7L8h0ZKK3pGKMMUHkjgnpDOkVT37h/g4vW9CZLKkYY0wQERHumJDBhl2HWbX9YKDD+QpLKsYYE2SuPacf3WIieXlJaaBD+QpLKsYYE2S6xkRy/Zj+zFm3m31HTgQ6nC+xpGKMMUHo9tx06hqUWcvKff/gM2dCRgYXXXwxZGR47reRJRVjjAlCWSnxXDgkhZlLy6hrcHfoMVaWVfH4h5u/PDp/5kyYPh3KyhBVKCvz3G9jYrGkYowxQerOCensPVzDRxv2tvvcvy8v54ZnFvOn/G3c+teCLxLLT38Kx459+eBjxzzb28CSijHGBKm87FQGJMXxUjsa7Av3HOGbr6zgh2+uxe3tkVzf4P5iTrftrSwG1tr2ZmxEvTHGBKkIl3B7bjq/mrOZTbsPM6xP9xaPW1lWxQfrdrN5zxEWbasgPjqSG8f0573Vu6hraDanW1qap8qrubS0NsVkScUYY4LYjWMG8ORHW3h5SRn/+42zv7RPVXl9RTk/fWs9Dd6Bktee049HrhpOYtdobhqb9tU53R591NOG0rQKrEsXz/Y2sKRijDFBLKFLNF8f3Y93Pt/Jw1OG0qNLFIeO1/HO5zt5bdl2Nu85cvLYCIFBqfEkdo0GWpnTbdo0z++f/hTdvh1JS/MklMbtp2FJxRhjgtztE9J5fUU5d76wlB5xUSwtOcCJOjdn9evO9AuzeHlx6VeruU5l2jSYNo1POrCssiUVY4wJcjX1bkRgdfkhAC4b3ovvXDKYs/r1AODyEb39tnSBJRVjjAlyBcWVCKB4qrhGDUg4mVDAv0sXWJdiY4wJcrlZyURHuogQAr46p2OuVEQkCXgdyABKgRtVtarZMdneYxplAY+o6u9E5OfA/cB+776fqOocjDEmxDlpdU7HJBXgYWC+qj4mIg97739p0UpVLQRGA4hIBLATeLvJIb9V1d/4J1xjjHEOp6zO6aTqr6nAS97bLwFfP83xlwDbVLWFUTrGGGMCwUlJpZeq7gbw/k49zfE3A6812/agiKwVkedFJPAp2xhjwoz4czlKEfkY6N3Crp8CL6lqQpNjq1S1xcQgItHALmCEqu71busFVODpAPHfQB9VvaeV86cD0wFSUlJyZs+e3eHXFAqqq6uJj48PdBgBZ+XgYeVgZdCotXKYNGnSSlUd09I5fk0qpyIihUCequ4WkT5Avqpmt3LsVODbqnpZK/szgPdV9azTPW92drYWFhaeQeTBL78DA5xCkZWDh5WDlUGj1spBRFpNKk6q/noPuNN7+07g3VMcewvNqr68iajRtcB6n0ZnjDHmtJyUVB4DLhWRrcCl3vuISF8ROdk1WES6ePe/1ez8x0VknYisBSYB3/NP2MYYYxo5pkuxqlbi6dHVfPsu4Iom948BXxnZo6q3d2qAxhhjTstJVyrGGGOCnCUVY4wxPmNJxRhjjM9YUjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM9YUjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM9YUjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM9YUjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM84JqmIyA0iskFE3CIy5hTHTRGRQhEpEpGHm2xPEpF5IrLV+zvRP5EbY4xp5JikAqwHvgEsbO0AEYkAnga+BgwHbhGR4d7dDwPzVXUwMN973xhjjB85Jqmo6iZVLTzNYeOAIlUtVtVaYBYw1btvKvCS9/ZLwNc7JVBjjDGtigx0AO3UDyhvcn8HMN57u5eq7gZQ1d0iktrag4jIdGC6926NiKzvjGCDSE+gItBBOICVg4eVg5VBo9bKIb21E/yaVETkY6B3C7t+qqrvtuUhWtim7Y1DVWcAM7wxrVDVVttwwoGVgYeVg4eVg5VBo46Ug1+TiqpOPsOH2AEMaHK/P7DLe3uviPTxXqX0Afad4XMZY4xpJ8e0qbTRcmCwiGSKSDRwM/Ced997wJ3e23cCbbnyMcYY40OOSSoicq2I7AAmAP8Ukbne7X1FZA6AqtYDDwJzgU3AbFXd4H2Ix4BLRWQrcKn3flvM8OHLCFZWBh5WDh5WDlYGjdpdDqLa7iYJY4wxpkWOuVIxxhgT/CypGGOM8ZmwTSqtTfcS6kTkeRHZ13RsTrhNcSMiA0RkgYhs8k4N9JB3e7iVQ6yILBORNd5y+IV3e1iVA3hm6xCRz0Xkfe/9cCyDUhFZJyKrRWSFd1u7yyEsk8pppnsJdS8CU5ptC7cpbuqB/1DVYUAu8G3v3z/cyqEGuFhVRwGjgSkikkv4lQPAQ3g6/zQKxzIAmKSqo5uMTWl3OYRlUuHU072ENFVdCBxotjmsprhR1d2qusp7+wieD5N+hF85qKpWe+9GeX+UMCsHEekPXAk822RzWJXBKbS7HMI1qbQ03Uu/AMXiBF+a4gZodYqbUCMiGcA5wFLCsBy81T6r8QwWnqeq4VgOvwN+BLibbAu3MgDPF4qPRGSldyor6EA5BNvcX77ik+leTHATkXjgTeC7qnpYpKW3RWhT1QZgtIgkAG+LyFkBDsmvROQqYJ+qrhSRvACHE2gTVXWXd97EeSKyuSMPEq5XKqea7iUc7fVObUO4THEjIlF4EspMVX3LuznsyqGRqh4E8vG0t4VTOUwErhGRUjzV4BeLyN8IrzIAQFV3eX/vA97G00zQ7nII16RyqulewlFYTXEjnkuS54BNqvpUk13hVg4p3isURCQOmAxsJozKQVX/U1X7q2oGns+Bf6nqbYRRGQCISFcR6dZ4G7gMzxpX7S6HsB1RLyJX4KlLjQCeV9VHAxuRf4jIa0Aenimt9wI/A94BZgNpwHbgBlVt3pgfMkTkfOBTYB1f1KP/BE+7SjiVw0g8ja8ReL5gzlbVX4pIMmFUDo281V8/UNWrwq0MRCQLz9UJeJpFXlXVRztSDmGbVIwxxvheuFZ/GWOM6QSWVIwxxviMJRVjjDE+Y0nFGGOMz1hSMcYY4zOWVIwxxviMJRVjHEhEuovIz0VkWKBjMaY9LKkY40xj8AxMjQp0IMa0hyUVY5zpHDzrnWwMdCDGtIeNqDfGYURkEzC02eY3VfX6QMRjTHtYUjHGYURkLJ4ZczcAv/Ju3q2qZYGLypi2Cdf1VIxxsjV4lmP4o6oWBDoYY9rD2lSMcZ4RQDSwKtCBGNNellSMcZ5z8axEujrAcRjTbpZUjHGec4Btqno40IEY016WVIxxnuFYV2ITpKyh3hjnOQicKyKXA4eArapaGdiQjGkbu1IxxnkewbPU8zvAEsCmajFBw8apGGOM8Rm7UjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM9YUjHGGOMzllSMMcb4jCUVY4wxPmNJxRhjjM/8f1N1tZrWpjgfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_series(X_valid[0, :, 0], y_valid[0, 0], y_pred[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il secondo modello e' una rete fully connected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "219/219 [==============================] - 0s 1ms/step - loss: 0.0823 - val_loss: 0.0449\n",
      "Epoch 2/20\n",
      "219/219 [==============================] - 0s 602us/step - loss: 0.0353 - val_loss: 0.0273\n",
      "Epoch 3/20\n",
      "219/219 [==============================] - 0s 632us/step - loss: 0.0227 - val_loss: 0.0189\n",
      "Epoch 4/20\n",
      "219/219 [==============================] - 0s 578us/step - loss: 0.0161 - val_loss: 0.0141\n",
      "Epoch 5/20\n",
      "219/219 [==============================] - 0s 642us/step - loss: 0.0123 - val_loss: 0.0113\n",
      "Epoch 6/20\n",
      "219/219 [==============================] - 0s 576us/step - loss: 0.0100 - val_loss: 0.0095\n",
      "Epoch 7/20\n",
      "219/219 [==============================] - 0s 600us/step - loss: 0.0086 - val_loss: 0.0084\n",
      "Epoch 8/20\n",
      "219/219 [==============================] - 0s 650us/step - loss: 0.0077 - val_loss: 0.0077\n",
      "Epoch 9/20\n",
      "219/219 [==============================] - 0s 572us/step - loss: 0.0071 - val_loss: 0.0072\n",
      "Epoch 10/20\n",
      "219/219 [==============================] - 0s 646us/step - loss: 0.0066 - val_loss: 0.0068\n",
      "Epoch 11/20\n",
      "219/219 [==============================] - 0s 622us/step - loss: 0.0063 - val_loss: 0.0066\n",
      "Epoch 12/20\n",
      "219/219 [==============================] - 0s 544us/step - loss: 0.0061 - val_loss: 0.0064\n",
      "Epoch 13/20\n",
      "219/219 [==============================] - 0s 629us/step - loss: 0.0059 - val_loss: 0.0062\n",
      "Epoch 14/20\n",
      "219/219 [==============================] - 0s 574us/step - loss: 0.0058 - val_loss: 0.0061\n",
      "Epoch 15/20\n",
      "219/219 [==============================] - 0s 630us/step - loss: 0.0057 - val_loss: 0.0060\n",
      "Epoch 16/20\n",
      "219/219 [==============================] - 0s 578us/step - loss: 0.0055 - val_loss: 0.0058\n",
      "Epoch 17/20\n",
      "219/219 [==============================] - 0s 661us/step - loss: 0.0054 - val_loss: 0.0057\n",
      "Epoch 18/20\n",
      "219/219 [==============================] - 0s 621us/step - loss: 0.0053 - val_loss: 0.0056\n",
      "Epoch 19/20\n",
      "219/219 [==============================] - 0s 639us/step - loss: 0.0053 - val_loss: 0.0056\n",
      "Epoch 20/20\n",
      "219/219 [==============================] - 0s 648us/step - loss: 0.0052 - val_loss: 0.0055\n"
     ]
    }
   ],
   "source": [
    "tf.random.set_seed(42)\n",
    "\n",
    "model = keras.models.Sequential([\n",
    "    keras.layers.Flatten(input_shape=[50, 1]),\n",
    "    keras.layers.Dense(1)\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\")\n",
    "history = model.fit(X_train, y_train, epochs=20,\n",
    "                    validation_data=(X_valid, y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_valid)\n",
    "plot_series(X_valid[0, :, 0], y_valid[0, 0], y_pred[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infine definiamo un RNN con una sola unita' ricorrente e funzione di attivazione $tanh$ - default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "219/219 [==============================] - 1s 6ms/step - loss: 0.0842 - val_loss: 0.0462\n",
      "Epoch 2/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0412 - val_loss: 0.0374\n",
      "Epoch 3/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0347 - val_loss: 0.0324\n",
      "Epoch 4/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0306 - val_loss: 0.0290\n",
      "Epoch 5/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0277 - val_loss: 0.0265\n",
      "Epoch 6/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0255 - val_loss: 0.0245\n",
      "Epoch 7/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0238 - val_loss: 0.0230\n",
      "Epoch 8/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0224 - val_loss: 0.0217\n",
      "Epoch 9/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0212 - val_loss: 0.0206\n",
      "Epoch 10/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0203 - val_loss: 0.0197\n",
      "Epoch 11/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0194 - val_loss: 0.0189\n",
      "Epoch 12/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0187 - val_loss: 0.0183\n",
      "Epoch 13/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0181 - val_loss: 0.0177\n",
      "Epoch 14/20\n",
      "219/219 [==============================] - 1s 6ms/step - loss: 0.0175 - val_loss: 0.0171\n",
      "Epoch 15/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0170 - val_loss: 0.0167\n",
      "Epoch 16/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0166 - val_loss: 0.0162\n",
      "Epoch 17/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0162 - val_loss: 0.0158\n",
      "Epoch 18/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0158 - val_loss: 0.0155\n",
      "Epoch 19/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0155 - val_loss: 0.0152\n",
      "Epoch 20/20\n",
      "219/219 [==============================] - 1s 5ms/step - loss: 0.0152 - val_loss: 0.0149\n"
     ]
    }
   ],
   "source": [
    "tf.random.set_seed(42)\n",
    "\n",
    "model = keras.models.Sequential([\n",
    "    keras.layers.SimpleRNN(1, input_shape=[None, 1])\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer='sgd')\n",
    "history = model.fit(X_train, y_train, epochs=20,\n",
    "                    validation_data=(X_valid, y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_valid)\n",
    "plot_series(X_valid[0, :, 0], y_valid[0, 0], y_pred[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infine inseriamo piu' hidden layer costituiti da piu' unita' ricorrenti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "219/219 [==============================] - 4s 18ms/step - loss: 0.0481 - val_loss: 0.0129\n",
      "Epoch 2/20\n",
      "219/219 [==============================] - 4s 17ms/step - loss: 0.0120 - val_loss: 0.0103\n",
      "Epoch 3/20\n",
      "219/219 [==============================] - 4s 17ms/step - loss: 0.0083 - val_loss: 0.0074\n",
      "Epoch 4/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0071 - val_loss: 0.0070\n",
      "Epoch 5/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0061 - val_loss: 0.0062\n",
      "Epoch 6/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0056 - val_loss: 0.0053\n",
      "Epoch 7/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0053 - val_loss: 0.0049\n",
      "Epoch 8/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0050 - val_loss: 0.0051\n",
      "Epoch 9/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0047 - val_loss: 0.0068\n",
      "Epoch 10/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0046 - val_loss: 0.0045\n",
      "Epoch 11/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0044 - val_loss: 0.0045\n",
      "Epoch 12/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0043 - val_loss: 0.0044\n",
      "Epoch 13/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0042 - val_loss: 0.0043\n",
      "Epoch 14/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0041 - val_loss: 0.0042\n",
      "Epoch 15/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0040 - val_loss: 0.0049\n",
      "Epoch 16/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0040 - val_loss: 0.0040\n",
      "Epoch 17/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0039 - val_loss: 0.0043\n",
      "Epoch 18/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0039 - val_loss: 0.0039\n",
      "Epoch 19/20\n",
      "219/219 [==============================] - 4s 16ms/step - loss: 0.0038 - val_loss: 0.0039\n",
      "Epoch 20/20\n",
      "219/219 [==============================] - 4s 17ms/step - loss: 0.0038 - val_loss: 0.0041\n"
     ]
    }
   ],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True),\n",
    "    keras.layers.SimpleRNN(1)\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\")\n",
    "history = model.fit(X_train, y_train, epochs=20,\n",
    "                    validation_data=(X_valid, y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = model.predict(X_valid)\n",
    "plot_series(X_valid[0, :, 0], y_valid[0, 0], y_pred[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dal momento che per l'ultimo layer non ci interessa l'ouput $h_{out}$, possiamo utilizzare un livello denso con una singola unita' di output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/20\n",
      "219/219 [==============================] - 3s 14ms/step - loss: 0.0375 - val_loss: 0.0147\n",
      "Epoch 2/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0114 - val_loss: 0.0091\n",
      "Epoch 3/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0077 - val_loss: 0.0070\n",
      "Epoch 4/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0061 - val_loss: 0.0059\n",
      "Epoch 5/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0052 - val_loss: 0.0054\n",
      "Epoch 6/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0047 - val_loss: 0.0048\n",
      "Epoch 7/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0044 - val_loss: 0.0045\n",
      "Epoch 8/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0041 - val_loss: 0.0043\n",
      "Epoch 9/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0039 - val_loss: 0.0041\n",
      "Epoch 10/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0038 - val_loss: 0.0039\n",
      "Epoch 11/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0037 - val_loss: 0.0039\n",
      "Epoch 12/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0036 - val_loss: 0.0037\n",
      "Epoch 13/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0035 - val_loss: 0.0037\n",
      "Epoch 14/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0034 - val_loss: 0.0035\n",
      "Epoch 15/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0033 - val_loss: 0.0034\n",
      "Epoch 16/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0032 - val_loss: 0.0035\n",
      "Epoch 17/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0032 - val_loss: 0.0033\n",
      "Epoch 18/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0031 - val_loss: 0.0033\n",
      "Epoch 19/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0031 - val_loss: 0.0033\n",
      "Epoch 20/20\n",
      "219/219 [==============================] - 3s 12ms/step - loss: 0.0031 - val_loss: 0.0032\n"
     ]
    }
   ],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.SimpleRNN(20),\n",
    "    keras.layers.Dense(1)\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\")\n",
    "history = model.fit(X_train, y_train, epochs=20,\n",
    "                    validation_data=(X_valid, y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(X_valid)\n",
    "plot_series(X_valid[0, :, 0], y_valid[0, 0], y_pred[0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per predirre i prossimi $k$ valori futuri come primo approccio posso utilizzare le predizioni eseguite fino al passo $t+1$ come input del mio modello. In sostanza, predico sulle predizioni. \n",
    "\n",
    "Ho un problema di accumulazione dell'errore di predizione."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_steps = 50\n",
    "series = generate_time_series(10000, n_steps + 10)\n",
    "X_train, Y_train = series[:7000, :n_steps], series[:7000, -10:, 0]\n",
    "X_valid, Y_valid = series[7000:9000, :n_steps], series[7000:9000, -10:, 0]\n",
    "X_test, Y_test = series[9000:, :n_steps], series[9000:, -10:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X_valid\n",
    "for step_ahead in range(10):\n",
    "    y_pred_one = model.predict(X)[:, np.newaxis, :]\n",
    "    X = np.concatenate([X, y_pred_one], axis=1)\n",
    "\n",
    "Y_pred = X[:, n_steps:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.mean(keras.metrics.mean_squared_error(Y_valid, Y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_naive_pred = Y_valid[:, -1:]\n",
    "np.mean(keras.metrics.mean_squared_error(Y_valid, Y_naive_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.Flatten(input_shape=[50, 1]),\n",
    "    keras.layers.Dense(10)\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\")\n",
    "history = model.fit(X_train, Y_train, epochs=20,\n",
    "                    validation_data=(X_valid, Y_valid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definiamo un RNN che restituisce un vettore di 10 elementi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.SimpleRNN(20),\n",
    "    keras.layers.Dense(10)\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\")\n",
    "history = model.fit(X_train, Y_train, epochs=20,\n",
    "                    validation_data=(X_valid, Y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new, Y_new = series[:, :50, :], series[:, -10:, :]\n",
    "Y_pred = model.predict(X_new)[..., np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_multiple_forecasts(X_new, Y_new, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Possiamo addestrare il modello in modo che predica i prossimi $k$ valori ad ogni time step, anziche' all'ultimo step $t=50$. Sfrutto gli aggiornamenti del gradiente provenienti da tutti gli output $y_{t}$. Il modello risultante e' nella categoria many-to-many.\n",
    "\n",
    "Dobbiamo modificare il vettore delle etichette = sequenza di vettori"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_steps = 50\n",
    "series = generate_time_series(10000, n_steps + 10)\n",
    "X_train = series[:7000, :n_steps]\n",
    "X_valid = series[7000:9000, :n_steps]\n",
    "X_test = series[9000:, :n_steps]\n",
    "\n",
    "Y = np.empty((10000, n_steps, 10))\n",
    "for step_ahead in range(1, 10 + 1):\n",
    "    Y[..., step_ahead - 1] = series[..., step_ahead:step_ahead + n_steps, 0]\n",
    "Y_train = Y[:7000]\n",
    "Y_valid = Y[7000:9000]\n",
    "Y_test = Y[9000:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 10)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y[1].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ogni layer deve restituire sempre una sequenza => **return_sequence=True**. Inoltre, possiamo utilizzare il layer **TimeDistributed** per applicare il layer ad ongi time step della sequenza di input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.SimpleRNN(20, return_sequences=True),\n",
    "    keras.layers.TimeDistributed(keras.layers.Dense(10))\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La loss function si calcola sull'ouput dell'ultimo time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.autograph.experimental.do_not_convert\n",
    "def last_time_step_mse(Y_true, Y_pred):\n",
    "    return keras.metrics.mean_squared_error(Y_true[:, -1], Y_pred[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(loss=\"mse\", optimizer='sgd', metrics=[last_time_step_mse])\n",
    "history = model.fit(X_train, Y_train, epochs=20,\n",
    "                    validation_data=(X_valid, Y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(43)\n",
    "\n",
    "series = generate_time_series(1, 50 + 10)\n",
    "X_new, Y_new = series[:, :50, :], series[:, 50:, :]\n",
    "Y_pred = model.predict(X_new)[:, -1][..., np.newaxis]\n",
    "plot_multiple_forecasts(X_new, Y_new, Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Long memory cells\n",
    "Usando la cella di memoria base lo stato dei primi elementi della sequenza puo' non influire sulla predizione al tempo $t$. Per alleviare questo fenomeno sono state proposte diversi cell con memoria a lungo termine - long-term memory.\n",
    "\n",
    "### Long short-term memory - LSTM\n",
    "\n",
    "![](lstm_cell.png)\n",
    "\n",
    "dove informalmente $\\mathbf{h}_t$ rappresenta la memoria a breve termine, mentre $\\mathbf{c}_t$ rappresenta la memoria a lungo termine.\n",
    "\n",
    "![](lstm_equation.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gated Recurrent Unit - GRU\n",
    "\n",
    "![](gru.png)\n",
    "\n",
    "I vettori $h$ e $c$ vengono uniti. C'e' un solo gate controller $z$ che controlla forget e input gate. C'e' un nuovo gae controller che agisce sull'input del main gate $g$ e sceglie quale parte dello stato precedente utilizzare. \n",
    "\n",
    "![](gru_equation.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Keras vengono rsi disponibili i due layers: **LSTM** e **GRU**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.LSTM(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.LSTM(20, return_sequences=True),\n",
    "    keras.layers.TimeDistributed(keras.layers.Dense(10))\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"sgd\", metrics=[last_time_step_mse])\n",
    "history = model.fit(X_train, Y_train, epochs=20,\n",
    "                    validation_data=(X_valid, Y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(43)\n",
    "\n",
    "series = generate_time_series(1, 50 + 10)\n",
    "X_new, Y_new = series[:, :50, :], series[:, 50:, :]\n",
    "Y_pred = model.predict(X_new)[:, -1][..., np.newaxis]\n",
    "plot_multiple_forecasts(X_new, Y_new, Y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "tf.random.set_seed(42)\n",
    "\n",
    "model = keras.models.Sequential([\n",
    "    keras.layers.GRU(20, return_sequences=True, input_shape=[None, 1]),\n",
    "    keras.layers.GRU(20, return_sequences=True),\n",
    "    keras.layers.TimeDistributed(keras.layers.Dense(10))\n",
    "])\n",
    "\n",
    "model.compile(loss=\"mse\", optimizer=\"adam\", metrics=[last_time_step_mse])\n",
    "history = model.fit(X_train, Y_train, epochs=20,\n",
    "                    validation_data=(X_valid, Y_valid))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(43)\n",
    "\n",
    "series = generate_time_series(1, 50 + 10)\n",
    "X_new, Y_new = series[:, :50, :], series[:, 50:, :]\n",
    "Y_pred = model.predict(X_new)[:, -1][..., np.newaxis]\n",
    "plot_multiple_forecasts(X_new, Y_new, Y_pred)\n"
   ]
  }
 ],
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