softmax_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Softmax Regression\n",
    "\n",
    "An extention of logistic regression for non-binary classifcation is called softmax/multinomial regression. This can also be seen as a one layer neural network in and of itself.\n",
    "\n",
    "**MNIST** can be classifed from this methodology. \n",
    "\n",
    "In softmax regression we obtain a vector of probabilities for each $k \\in \\mathcal{C}$. This probability is obtained by applying the softmax function to the linear regression models for each class. That is\n",
    "\n",
    "$$\n",
    "\\sigma_{\\text{softmax}}: \\mathbb{R}^{n\\times1} \\rightarrow [0,1]^{K\\times 1}.\n",
    "$$\n",
    "\n",
    "The basic set up of using softmax regression is as follows:\n",
    "1. Have a list of all features/covariates $\\mathbf{x}$.\n",
    "2. Apply the linear regression for each class, i.e., $\\mathbf{w_i}^{\\text{T}}\\mathbf{x}~~i\\in\\{1,\\ldots,K\\}$.\n",
    "3. Apply the softmax function to the output vector of the different linear regression scoring models.\n",
    "4. Return the class which has the largest probability of being true.\n",
    "\n",
    "Parameter optimization is done via MLE. The process is slightly more involved than for logistic regression. Suppose we have a training set $\\mathcal{D} = \\{(\\mathbf{x}_i, \\mathbf{t}_i)\\}_{i=1}^n$. \n",
    "\n",
    "Each r.v. that is observed has some probability of being in a class $k \\in \\mathcal{C}$. Similarly to logistic regression we can write the probability of being in class $k$ given the obseervation $(\\mathbf{x}, \\mathbf{t}) \\in \\mathcal{D}$ and the weighting matrix $\\mathbf{W}$ as \n",
    "\n",
    "$$\n",
    "\\mathbb{P}(Y = l| \\mathbf{x}, \\mathbf{W}) = p_1^{\\mathbb{1}_{\\{t_1 = l\\}}} \\cdot \\ldots \\cdot p_n^{\\mathbb{1}_{\\{t_n = l\\}}}\n",
    ".$$\n",
    "\n",
    "With an entire dataset $\\mathcal{D}$ we can derive a loss function using a likelihood based approach:\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\begin{split}\n",
    "        L(\\mathbf{W}) \\triangleq p(\\mathcal{D}|\\mathbf{W}) & = \\mathbb{P}(Y_1 = t_1, \\ldots, Y_n = t_n|\\mathbf{W}) \\\\\n",
    "        & = \\mathbb{P}(Y_1 = t_1 | \\mathbf{W})\\ldots \\mathbb{P}(Y_n = t_n | \\mathbf{W})\\\\\n",
    "        & = \\prod_{i=1}^n \\prod_{l=1}^K \\Big[\\frac{\\exp{\\mathbf{w}_l^{\\text{T}}\\mathbf{x_i}}}{\\sum_{j=1}^K \\exp{\\mathbf{w}_j^{\\text{T}}\\mathbf{x_i}}} \\Big]^{\\mathbb{1}_{\\{t_l^{(i)} = l\\}}}.\n",
    "    \\end{split}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To simplify the mathematics slightly we introduce two new notations following Bishop. \n",
    "\n",
    "For a target vector $\\mathbf{t}_j$ we introduce a new matrix $\\mathbf{T} = [t_{ij}] \\in \\mathbb{R}^{n\\times K}$ which keeps track of the values in a target vector, raning from $j=1,...,K$ for each sample $i=1,...,n$.\n",
    "\n",
    "Secondly, we define \n",
    "$$\n",
    "y_l(\\mathbf{x}_i|\\mathbf{W}) \\triangleq \\frac{\\exp{\\mathbf{w}_l^{\\text{T}}\\mathbf{x_i}}}{\\sum_{j=1}^K \\exp{\\mathbf{w}_j^{\\text{T}}\\mathbf{x_i}}}.\n",
    "$$\n",
    "The likelihood function thus simplifies to \n",
    "\\begin{equation*}\n",
    "    \\begin{split}\n",
    "        L(\\mathbf{W}) \\triangleq p(\\mathcal{D}|\\mathbf{W}) & = \\mathbb{P}(Y_1 = t_1, \\ldots, Y_n = t_n|\\mathbf{W}) \\\\\n",
    "        & = \\prod_{i=1}^n \\prod_{l=1}^K \\Big[y_l(\\mathbf{x}_i|\\mathbf{W}) \\Big]^{t_{il}}.\n",
    "    \\end{split}\n",
    "\\end{equation*}\n",
    "Next, we obtain the cost function by the negative log-likelihood as\n",
    "\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\begin{split}\n",
    "        \\mathcal{J}(\\mathbf{W}) \\triangleq - \\ln p(\\mathcal{D}|\\mathbf{W}) & = -\\sum_{i=1}^n \\sum_{l=1}^K t_{il} \\ln (y_l(\\mathbf{x}_i|\\mathbf{W})),\n",
    "    \\end{split}\n",
    "\\end{equation*}\n",
    "\n",
    "of which the gradients are calculated in the following manner\n",
    "\n",
    "$$\n",
    "\\nabla_{\\mathbf{w}_j}\\mathcal{J}(\\mathbf{W}) = \\sum_{i=1}^N(y_j(\\mathbf{x}_i) - t_{ij})\\mathbf{x}_i \\in \\mathbb{R}^{M\\times 1},\n",
    "$$\n",
    "where $M$ is the number of features. However, we can simplify this to a greater extent, to obtain the following expression instead:\n",
    "\n",
    "$$\n",
    "\\nabla_{\\mathbf{W}}\\mathcal{J}(\\mathbf{W}) = (\\mathbf{Y}-\\mathbf{T})^{\\text{T}}\\mathbf{X},\n",
    "$$\n",
    "where $\\mathbf{Y}$ is the predicted values, $\\mathbf{T}$ are the target values which are one-hot-encoded, and $\\mathbf{X}$ are the input feature vectors stacked into a matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To train the model we do this without any regularization of $\\mathbf{W}$, and we use standard gradient decent, meaning \n",
    "\n",
    "$$\n",
    "\\mathbf{W}_{n+1} = \\mathbf{W}_n + \\eta \\nabla_{\\mathbf{W}}\\mathcal{J}(\\mathbf{W}).\n",
    "$$\n",
    "\n",
    "For some learning rate $\\eta$, which will be set as a constant. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1. Importing Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Plotting configuration.\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.style.use(['science', 'notebook', 'grid'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing MNIST dataset. \n",
    "from mnist_utils.data_reader import (TESTING_DATA,\n",
    "                                     TESTING_LABELS,\n",
    "                                     TRAINING_DATA,\n",
    "                                     TRAINING_LABELS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 245,
       "width": 248
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(TRAINING_DATA[250])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Configuring Data and Encoding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_hot_encoding(array: np.array) -> np.array: \n",
    "    data_length = len(array)\n",
    "    feature_length = max(array) + 1\n",
    "    dim  = (data_length, feature_length)\n",
    "    one_hot_matrix = np.zeros(dim)\n",
    "\n",
    "    for i in range(data_length):\n",
    "        digit = array[i]\n",
    "        one_hot_matrix[i][digit] = 1\n",
    "\n",
    "    return one_hot_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vec(matrix: np.array) -> np.array:\n",
    "    vec_matrix = np.zeros(0)\n",
    "    \n",
    "    return np.append(vec_matrix, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(x: np.array, W: np.array) -> np.array:\n",
    "    score_vector = np.exp(W @ x.T - np.max(W @ x.T))\n",
    "    normalizing_constant = np.sum(score_vector)\n",
    "\n",
    "    return score_vector / normalizing_constant\n",
    "\n",
    "def _Y_matrix(X: np.array, W: np.array) -> np.array:\n",
    "    Y = []\n",
    "    for x_data in X:\n",
    "        Y.append(softmax(x_data, W))\n",
    "    Y = np.stack(Y)\n",
    "    \n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = one_hot_encoding(TRAINING_LABELS)\n",
    "\n",
    "x_values = []\n",
    "for digit in TRAINING_DATA:\n",
    "    x_values.append(vec(digit))\n",
    "ones = np.ones(60000)\n",
    "X = np.stack(x_values)/255\n",
    "X = np.insert(x_values, 0, ones, axis=1)\n",
    "\n",
    "# Initial weight matrix W.\n",
    "dim = (10, np.shape(X)[1])\n",
    "W = np.random.uniform(-0.000000001, 0.000000001, dim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Cost Function and Jacobian Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "EPSILON = 1e-32\n",
    "\n",
    "def cost(X: np.array, T: np.array, W: np.array) -> float:\n",
    "    cost = 0\n",
    "    dim = np.shape(T)\n",
    "    Y = _Y_matrix(X, W)\n",
    "\n",
    "    number_of_observations = dim[0]\n",
    "    number_of_categories = dim[1]\n",
    "\n",
    "    for i in range(number_of_observations):\n",
    "        for j in range(number_of_categories):\n",
    "            cost = cost - T[i][j] * np.log(Y[i][j]+ EPSILON)\n",
    "            \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(X: np.array, T: np.array, W: np.array) -> np.array:\n",
    "    Y = _Y_matrix(X, W)\n",
    "    return (Y-T).T @ X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 1/100\n",
      "----------------------------------------\n",
      "Loss:                             417559\n",
      "Max Weight:            82034.19989153714\n",
      "Min Weight:           -80429.19704184137\n",
      "\n",
      "Epoch: 2/100\n",
      "----------------------------------------\n",
      "Loss:                             414317\n",
      "Max Weight:            82050.33989153714\n",
      "Min Weight:           -80038.97704184137\n",
      "\n",
      "Epoch: 3/100\n",
      "----------------------------------------\n",
      "Loss:                             413286\n",
      "Max Weight:            82197.27989153714\n",
      "Min Weight:           -79710.61704184137\n",
      "\n",
      "Epoch: 4/100\n",
      "----------------------------------------\n",
      "Loss:                             411370\n",
      "Max Weight:            82184.69989153714\n",
      "Min Weight:           -79308.31704184136\n",
      "\n",
      "Epoch: 5/100\n",
      "----------------------------------------\n",
      "Loss:                             411223\n",
      "Max Weight:            82334.97989153714\n",
      "Min Weight:           -78998.75704184137\n",
      "\n",
      "Epoch: 6/100\n",
      "----------------------------------------\n",
      "Loss:                             411812\n",
      "Max Weight:            82279.17989153713\n",
      "Min Weight:           -78601.73704184136\n",
      "\n",
      "Epoch: 7/100\n",
      "----------------------------------------\n",
      "Loss:                             413286\n",
      "Max Weight:            82449.31989153713\n",
      "Min Weight:           -78275.13704184136\n",
      "\n",
      "Epoch: 8/100\n",
      "----------------------------------------\n",
      "Loss:                             417854\n",
      "Max Weight:            82337.95989153713\n",
      "Min Weight:           -77887.59704184136\n",
      "\n",
      "Epoch: 9/100\n",
      "----------------------------------------\n",
      "Loss:                             423307\n",
      "Max Weight:            82548.41989153714\n",
      "Min Weight:           -77549.49704184136\n",
      "\n",
      "Epoch: 10/100\n",
      "----------------------------------------\n",
      "Loss:                             443054\n",
      "Max Weight:            82309.17989153713\n",
      "Min Weight:           -77149.43704184136\n",
      "\n",
      "Epoch: 11/100\n",
      "----------------------------------------\n",
      "Loss:                             482327\n",
      "Max Weight:            82658.93989153713\n",
      "Min Weight:           -76863.23704184136\n",
      "\n",
      "Epoch: 12/100\n",
      "----------------------------------------\n",
      "Loss:                             583125\n",
      "Max Weight:            82033.04384671863\n",
      "Min Weight:           -76431.27704184136\n",
      "\n",
      "Epoch: 13/100\n",
      "----------------------------------------\n",
      "Loss:                            1075251\n",
      "Max Weight:            83785.63989153712\n",
      "Min Weight:           -76119.96777378976\n",
      "\n",
      "Epoch: 14/100\n",
      "----------------------------------------\n",
      "Loss:                             900550\n",
      "Max Weight:            81969.52384671864\n",
      "Min Weight:           -75841.88777378976\n",
      "\n",
      "Epoch: 15/100\n",
      "----------------------------------------\n",
      "Loss:                            1000685\n",
      "Max Weight:            84100.43989153711\n",
      "Min Weight:           -78568.71704184136\n",
      "\n",
      "Epoch: 16/100\n",
      "----------------------------------------\n",
      "Loss:                            1388035\n",
      "Max Weight:            84306.65989153711\n",
      "Min Weight:           -77576.33704184135\n",
      "\n",
      "Epoch: 17/100\n",
      "----------------------------------------\n",
      "Loss:                            1339330\n",
      "Max Weight:            85292.17989153712\n",
      "Min Weight:           -82625.21704184136\n",
      "\n",
      "Epoch: 18/100\n",
      "----------------------------------------\n",
      "Loss:                            1248480\n",
      "Max Weight:            85336.08384671864\n",
      "Min Weight:           -81803.03704184137\n",
      "\n",
      "Epoch: 19/100\n",
      "----------------------------------------\n",
      "Loss:                             864814\n",
      "Max Weight:            85715.98384671863\n",
      "Min Weight:           -81607.15704184136\n",
      "\n",
      "Epoch: 20/100\n",
      "----------------------------------------\n",
      "Loss:                             722238\n",
      "Max Weight:            86160.82384671863\n",
      "Min Weight:           -81335.97704184137\n",
      "\n",
      "Epoch: 21/100\n",
      "----------------------------------------\n",
      "Loss:                             633450\n",
      "Max Weight:            85723.72384671863\n",
      "Min Weight:           -81124.85704184137\n",
      "\n",
      "Epoch: 22/100\n",
      "----------------------------------------\n",
      "Loss:                             652755\n",
      "Max Weight:            86728.88384671863\n",
      "Min Weight:           -80819.87704184138\n",
      "\n",
      "Epoch: 23/100\n",
      "----------------------------------------\n",
      "Loss:                             724522\n",
      "Max Weight:            85631.02384671863\n",
      "Min Weight:           -80367.99704184137\n",
      "\n",
      "Epoch: 24/100\n",
      "----------------------------------------\n",
      "Loss:                             922655\n",
      "Max Weight:            87763.30384671863\n",
      "Min Weight:           -80129.99704184137\n",
      "\n",
      "Epoch: 25/100\n",
      "----------------------------------------\n",
      "Loss:                             848603\n",
      "Max Weight:            86445.76384671863\n",
      "Min Weight:           -79554.61704184137\n",
      "\n",
      "Epoch: 26/100\n",
      "----------------------------------------\n",
      "Loss:                             838214\n",
      "Max Weight:            88179.68384671863\n",
      "Min Weight:           -80163.47704184137\n",
      "\n",
      "Epoch: 27/100\n",
      "----------------------------------------\n",
      "Loss:                             734911\n",
      "Max Weight:            87899.98384671863\n",
      "Min Weight:           -79544.49704184137\n",
      "\n",
      "Epoch: 28/100\n",
      "----------------------------------------\n",
      "Loss:                             785605\n",
      "Max Weight:            89057.94384671864\n",
      "Min Weight:           -80845.87704184138\n",
      "\n",
      "Epoch: 29/100\n",
      "----------------------------------------\n",
      "Loss:                             763353\n",
      "Max Weight:            88799.18384671865\n",
      "Min Weight:           -80008.93704184137\n",
      "\n",
      "Epoch: 30/100\n",
      "----------------------------------------\n",
      "Loss:                             877487\n",
      "Max Weight:            89736.56384671865\n",
      "Min Weight:           -84996.25704184137\n",
      "\n",
      "Epoch: 31/100\n",
      "----------------------------------------\n",
      "Loss:                            1153281\n",
      "Max Weight:            89708.36384671865\n",
      "Min Weight:           -83965.57704184137\n",
      "\n",
      "Epoch: 32/100\n",
      "----------------------------------------\n",
      "Loss:                             926707\n",
      "Max Weight:            90569.46384671866\n",
      "Min Weight:           -89915.59704184138\n",
      "\n",
      "Epoch: 33/100\n",
      "----------------------------------------\n",
      "Loss:                             655113\n",
      "Max Weight:             91672.2970405055\n",
      "Min Weight:           -89584.15704184138\n",
      "\n",
      "Epoch: 34/100\n",
      "----------------------------------------\n",
      "Loss:                             466559\n",
      "Max Weight:            91021.68384671866\n",
      "Min Weight:           -88958.41704184137\n",
      "\n",
      "Epoch: 35/100\n",
      "----------------------------------------\n",
      "Loss:                             421244\n",
      "Max Weight:            91231.54384671866\n",
      "Min Weight:           -88680.33704184137\n",
      "\n",
      "Epoch: 36/100\n",
      "----------------------------------------\n",
      "Loss:                             419549\n",
      "Max Weight:            91542.78384671867\n",
      "Min Weight:           -88271.25704184137\n",
      "\n",
      "Epoch: 37/100\n",
      "----------------------------------------\n",
      "Loss:                             412549\n",
      "Max Weight:            91757.44384671867\n",
      "Min Weight:           -87950.17704184137\n",
      "\n",
      "Epoch: 38/100\n",
      "----------------------------------------\n",
      "Loss:                             411296\n",
      "Max Weight:            92030.60384671867\n",
      "Min Weight:           -87571.97704184137\n",
      "\n",
      "Epoch: 39/100\n",
      "----------------------------------------\n",
      "Loss:                             408644\n",
      "Max Weight:            92231.48384671868\n",
      "Min Weight:           -87241.59704184136\n",
      "\n",
      "Epoch: 40/100\n",
      "----------------------------------------\n",
      "Loss:                             405476\n",
      "Max Weight:            92484.90384671868\n",
      "Min Weight:           -86884.15704184136\n",
      "\n",
      "Epoch: 41/100\n",
      "----------------------------------------\n",
      "Loss:                             404518\n",
      "Max Weight:            92644.50384671868\n",
      "Min Weight:           -86556.49704184136\n",
      "\n",
      "Epoch: 42/100\n",
      "----------------------------------------\n",
      "Loss:                             402381\n",
      "Max Weight:            92865.20384671868\n",
      "Min Weight:           -86209.49704184136\n",
      "\n",
      "Epoch: 43/100\n",
      "----------------------------------------\n",
      "Loss:                             400244\n",
      "Max Weight:            93023.24384671867\n",
      "Min Weight:           -85872.47704184135\n",
      "\n",
      "Epoch: 44/100\n",
      "----------------------------------------\n",
      "Loss:                             399065\n",
      "Max Weight:            93245.60384671867\n",
      "Min Weight:           -85530.97704184135\n",
      "\n",
      "Epoch: 45/100\n",
      "----------------------------------------\n",
      "Loss:                             397370\n",
      "Max Weight:            93379.40384671868\n",
      "Min Weight:           -85203.71704184136\n",
      "\n",
      "Epoch: 46/100\n",
      "----------------------------------------\n",
      "Loss:                             395086\n",
      "Max Weight:            93591.82384671867\n",
      "Min Weight:           -84856.21704184136\n",
      "\n",
      "Epoch: 47/100\n",
      "----------------------------------------\n",
      "Loss:                             395528\n",
      "Max Weight:            93705.16384671867\n",
      "Min Weight:           -84511.97704184135\n",
      "\n",
      "Epoch: 48/100\n",
      "----------------------------------------\n",
      "Loss:                             395602\n",
      "Max Weight:            93912.54384671868\n",
      "Min Weight:           -84165.83704184135\n",
      "\n",
      "Epoch: 49/100\n",
      "----------------------------------------\n",
      "Loss:                             393023\n",
      "Max Weight:            93994.80384671867\n",
      "Min Weight:           -83824.47704184135\n",
      "\n",
      "Epoch: 50/100\n",
      "----------------------------------------\n",
      "Loss:                             394718\n",
      "Max Weight:            94215.72384671867\n",
      "Min Weight:           -83480.83704184135\n",
      "\n",
      "Epoch: 51/100\n",
      "----------------------------------------\n",
      "Loss:                             395749\n",
      "Max Weight:            94265.44384671867\n",
      "Min Weight:           -83154.97704184135\n",
      "\n",
      "Epoch: 52/100\n",
      "----------------------------------------\n",
      "Loss:                             394644\n",
      "Max Weight:            94496.66384671867\n",
      "Min Weight:           -82835.23704184135\n",
      "\n",
      "Epoch: 53/100\n",
      "----------------------------------------\n",
      "Loss:                             396265\n",
      "Max Weight:            94487.86384671867\n",
      "Min Weight:           -82496.97704184135\n",
      "\n",
      "Epoch: 54/100\n",
      "----------------------------------------\n",
      "Loss:                             400760\n",
      "Max Weight:            94746.86384671867\n",
      "Min Weight:           -82181.77704184136\n",
      "\n",
      "Epoch: 55/100\n",
      "----------------------------------------\n",
      "Loss:                             407318\n",
      "Max Weight:            94664.30384671867\n",
      "Min Weight:           -81843.71704184136\n",
      "\n",
      "Epoch: 56/100\n",
      "----------------------------------------\n",
      "Loss:                             430159\n",
      "Max Weight:            95026.28384671867\n",
      "Min Weight:           -81537.71704184136\n",
      "\n",
      "Epoch: 57/100\n",
      "----------------------------------------\n",
      "Loss:                             474148\n",
      "Max Weight:            94726.00384671867\n",
      "Min Weight:           -81154.73704184136\n",
      "\n",
      "Epoch: 58/100\n",
      "----------------------------------------\n",
      "Loss:                             623724\n",
      "Max Weight:            95501.62384671866\n",
      "Min Weight:           -80864.13704184136\n",
      "\n",
      "Epoch: 59/100\n",
      "----------------------------------------\n",
      "Loss:                             790394\n",
      "Max Weight:            93861.02384671866\n",
      "Min Weight:           -80300.69704184135\n",
      "\n",
      "Epoch: 60/100\n",
      "----------------------------------------\n",
      "Loss:                            1398571\n",
      "Max Weight:            96751.88384671866\n",
      "Min Weight:           -79997.05704184136\n",
      "\n",
      "Epoch: 61/100\n",
      "----------------------------------------\n",
      "Loss:                            1039884\n",
      "Max Weight:            96352.36384671865\n",
      "Min Weight:           -79081.95704184135\n",
      "\n",
      "Epoch: 62/100\n",
      "----------------------------------------\n",
      "Loss:                            1164481\n",
      "Max Weight:            96384.84384671865\n",
      "Min Weight:           -89992.87704184135\n",
      "\n",
      "Epoch: 63/100\n",
      "----------------------------------------\n",
      "Loss:                            1015421\n",
      "Max Weight:            96617.50384671865\n",
      "Min Weight:           -88956.69704184135\n",
      "\n",
      "Epoch: 64/100\n",
      "----------------------------------------\n",
      "Loss:                             874761\n",
      "Max Weight:            97046.26384671865\n",
      "Min Weight:           -92927.05704184136\n",
      "\n",
      "Epoch: 65/100\n",
      "----------------------------------------\n",
      "Loss:                             786120\n",
      "Max Weight:            97071.28384671865\n",
      "Min Weight:           -92148.07704184136\n",
      "\n",
      "Epoch: 66/100\n",
      "----------------------------------------\n",
      "Loss:                             788552\n",
      "Max Weight:            97553.40384671865\n",
      "Min Weight:           -92447.39704184137\n",
      "\n",
      "Epoch: 67/100\n",
      "----------------------------------------\n",
      "Loss:                             994643\n",
      "Max Weight:            97487.64384671865\n",
      "Min Weight:           -91651.95704184136\n",
      "\n",
      "Epoch: 68/100\n",
      "----------------------------------------\n",
      "Loss:                            1016379\n",
      "Max Weight:           103358.73704050551\n",
      "Min Weight:           -94482.99704184136\n",
      "\n",
      "Epoch: 69/100\n",
      "----------------------------------------\n",
      "Loss:                            1043863\n",
      "Max Weight:            97885.06384671865\n",
      "Min Weight:           -93650.71704184136\n",
      "\n",
      "Epoch: 70/100\n",
      "----------------------------------------\n",
      "Loss:                            1080115\n",
      "Max Weight:           111374.71704050551\n",
      "Min Weight:           -96619.69704184135\n",
      "\n",
      "Epoch: 71/100\n",
      "----------------------------------------\n",
      "Loss:                            1126756\n",
      "Max Weight:            98677.46384671865\n",
      "Min Weight:           -95708.27704184136\n",
      "\n",
      "Epoch: 72/100\n",
      "----------------------------------------\n",
      "Loss:                            1203680\n",
      "Max Weight:            115649.4770405055\n",
      "Min Weight:           -98967.61704184135\n",
      "\n",
      "Epoch: 73/100\n",
      "----------------------------------------\n",
      "Loss:                            1143334\n",
      "Max Weight:             99761.9370405055\n",
      "Min Weight:           -98055.29704184135\n",
      "\n",
      "Epoch: 74/100\n",
      "----------------------------------------\n",
      "Loss:                            1255406\n",
      "Max Weight:           116918.13704050549\n",
      "Min Weight:          -100144.35704184134\n",
      "\n",
      "Epoch: 75/100\n",
      "----------------------------------------\n",
      "Loss:                            1018958\n",
      "Max Weight:            104156.5970405055\n",
      "Min Weight:           -99296.79704184135\n",
      "\n",
      "Epoch: 76/100\n",
      "----------------------------------------\n",
      "Loss:                             774921\n",
      "Max Weight:            112070.7370405055\n",
      "Min Weight:          -101024.17704184135\n",
      "\n",
      "Epoch: 77/100\n",
      "----------------------------------------\n",
      "Loss:                             521894\n",
      "Max Weight:            106362.2170405055\n",
      "Min Weight:          -100406.77704184136\n",
      "\n",
      "Epoch: 78/100\n",
      "----------------------------------------\n",
      "Loss:                             454327\n",
      "Max Weight:           107473.41704050549\n",
      "Min Weight:          -100325.79704184136\n",
      "\n",
      "Epoch: 79/100\n",
      "----------------------------------------\n",
      "Loss:                             429128\n",
      "Max Weight:           105674.55704050549\n",
      "Min Weight:           -99966.19704184135\n",
      "\n",
      "Epoch: 80/100\n",
      "----------------------------------------\n",
      "Loss:                             420580\n",
      "Max Weight:           104972.17704050548\n",
      "Min Weight:           -99700.95704184135\n",
      "\n",
      "Epoch: 81/100\n",
      "----------------------------------------\n",
      "Loss:                             417338\n",
      "Max Weight:           103831.95704050548\n",
      "Min Weight:           -99403.05704184136\n",
      "\n",
      "Epoch: 82/100\n",
      "----------------------------------------\n",
      "Loss:                             410781\n",
      "Max Weight:           102860.93704050548\n",
      "Min Weight:           -99096.99704184136\n",
      "\n",
      "Epoch: 83/100\n",
      "----------------------------------------\n",
      "Loss:                             409675\n",
      "Max Weight:           102674.42384671867\n",
      "Min Weight:           -98792.37704184136\n",
      "\n",
      "Epoch: 84/100\n",
      "----------------------------------------\n",
      "Loss:                             404739\n",
      "Max Weight:           102893.02384671867\n",
      "Min Weight:           -98468.81704184136\n",
      "\n",
      "Epoch: 85/100\n",
      "----------------------------------------\n",
      "Loss:                             403044\n",
      "Max Weight:           103040.04384671868\n",
      "Min Weight:           -98158.39704184137\n",
      "\n",
      "Epoch: 86/100\n",
      "----------------------------------------\n",
      "Loss:                             400170\n",
      "Max Weight:           103246.50384671868\n",
      "Min Weight:           -97843.91704184137\n",
      "\n",
      "Epoch: 87/100\n",
      "----------------------------------------\n",
      "Loss:                             400023\n",
      "Max Weight:           103378.10384671869\n",
      "Min Weight:           -97523.15704184138\n",
      "\n",
      "Epoch: 88/100\n",
      "----------------------------------------\n",
      "Loss:                             396192\n",
      "Max Weight:           103574.94384671868\n",
      "Min Weight:           -97204.45704184138\n",
      "\n",
      "Epoch: 89/100\n",
      "----------------------------------------\n",
      "Loss:                             395234\n",
      "Max Weight:           103687.98384671868\n",
      "Min Weight:           -96849.25704184138\n",
      "\n",
      "Epoch: 90/100\n",
      "----------------------------------------\n",
      "Loss:                             393097\n",
      "Max Weight:           103868.26384671868\n",
      "Min Weight:           -96522.61704184138\n",
      "\n",
      "Epoch: 91/100\n",
      "----------------------------------------\n",
      "Loss:                             393244\n",
      "Max Weight:           103971.02384671867\n",
      "Min Weight:           -96171.63704184139\n",
      "\n",
      "Epoch: 92/100\n",
      "----------------------------------------\n",
      "Loss:                             391181\n",
      "Max Weight:           104151.90384671868\n",
      "Min Weight:           -95846.79704184139\n",
      "\n",
      "Epoch: 93/100\n",
      "----------------------------------------\n",
      "Loss:                             391255\n",
      "Max Weight:           104223.90384671868\n",
      "Min Weight:           -95486.01704184139\n",
      "\n",
      "Epoch: 94/100\n",
      "----------------------------------------\n",
      "Loss:                             389928\n",
      "Max Weight:           104407.04384671868\n",
      "Min Weight:            -95146.4570418414\n",
      "\n",
      "Epoch: 95/100\n",
      "----------------------------------------\n",
      "Loss:                             389265\n",
      "Max Weight:           104445.40384671868\n",
      "Min Weight:            -94796.1770418414\n",
      "\n",
      "Epoch: 96/100\n",
      "----------------------------------------\n",
      "Loss:                             389781\n",
      "Max Weight:           104651.10384671867\n",
      "Min Weight:           -94450.87704184139\n",
      "\n",
      "Epoch: 97/100\n",
      "----------------------------------------\n",
      "Loss:                             390960\n",
      "Max Weight:           104650.30384671867\n",
      "Min Weight:            -94109.1170418414\n",
      "\n",
      "Epoch: 98/100\n",
      "----------------------------------------\n",
      "Loss:                             390518\n",
      "Max Weight:           104859.44384671867\n",
      "Min Weight:            -93771.9970418414\n",
      "\n",
      "Epoch: 99/100\n",
      "----------------------------------------\n",
      "Loss:                             393392\n",
      "Max Weight:           104825.08384671867\n",
      "Min Weight:           -93420.95704184141\n",
      "\n",
      "Epoch: 100/100\n",
      "----------------------------------------\n",
      "Loss:                             395234\n",
      "Max Weight:           105071.38384671867\n",
      "Min Weight:           -93083.83704184141\n",
      "\n"
     ]
    }
   ],
   "source": [
    "NUMBER_OF_ITERATIONS = 100\n",
    "LEARNING_RATE = -0.02\n",
    "\n",
    "for i in range(NUMBER_OF_ITERATIONS):\n",
    "    # LOSS\n",
    "    current_cost = cost(X, T, W)\n",
    "    # Update weight\n",
    "    W = W + LEARNING_RATE * gradient(X, T, W)\n",
    "    print(f\"Epoch: {i+1}/{NUMBER_OF_ITERATIONS}\".ljust(1))\n",
    "    print(\"-\" * 40)\n",
    "    print(\"Loss: \" + str(int(current_cost)).rjust(34))\n",
    "    print(\"Max Weight: \" + str(np.max(W)).rjust(28))\n",
    "    print(\"Min Weight: \" + str(np.min(W)).rjust(28) + \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_training = 10000\n",
    "total_correct = 0\n",
    "confusion_matrix = np.zeros((10, 10))\n",
    "\n",
    "for i in range(total_training):\n",
    "    data = np.insert(TESTING_DATA[i], 0, 1)\n",
    "    prediction = int(np.argmax(softmax(data, W)))\n",
    "    answer = int(TESTING_LABELS[i])\n",
    "\n",
    "    if (prediction == answer):\n",
    "        total_correct = total_correct + 1\n",
    "\n",
    "    confusion_matrix[prediction][answer] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9103"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Total accuracy.\n",
    "total_correct / total_training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CECbf/8eJwqTUyB6rnLR3oFakh9s8Ppbw5IUy1PDdhOqGzgnH1gM1yEUaJupQxMVe5M7vCwzFr3vqgwi6YxPe/SHJwlo0QB4+ETyKHAzFePce3V+1K2HfHjQU3R85fBck/Y96kytpe+txs5O2B36LBDCRocBnaVwQjLbRgDwXkM3mTHSZh0rZERQoswEFdJ0apFFpUIsq7kIkgmGhE3KNvwj8mqZjgiOQ1yhMHASeTNrXEwV1Dcv51X0QwRon7ZDiuDv4eST3prQC1/pUQ7Re1rvOhq3AdhQ4M4F49TkLUMjM12hbi9e90hygFxp97Idk+CXUU3zU2W9kh9fQUx2FiWA2mEdj99xIVEmHveG2DJX6MTSOBggDJyObZhDvrYKa7NNo6iYNkmnAENTwKUZ113xk9yPAzaQej80OPk6RiA6xhPR0Go+EnoLaPfOpQxXAFW24UoOTFgLXo9YTyJ1wLfDfyFG7AXONZoMFKESqHLgyYFs+LnzHSQ+i8bWZKNjkWnJd+bUNV1yOC9QKb95CU1BOdLYuyCP3CvAEap5fEJh1jTkr6e8+qBFUDMxFXYbrcmqBD07Xlnp6LfUUg8W1vibFcS/rEz+P9fifuEd+s8fRTHDDdPoRF0CXYtRbAY0PGG3jHdS77gV8gbbPbTUa0wWVjOtRSNmMYM1plm2oYdmNcE2NAEUfvIxqnovQcFMxGpy5Ftk8l/AHHrldh4qcX8kHESx30l0pjrsPI9WYYbC4Y4Hu2GAy7q9KtL6U+I31kvb4vto2Wufe21QNCLeibut1os58NMbSGwlgmNxJHzd6oIaGO8k7jIQxIMZlpZN6jaUVo4C5GOoNhhnXHZ77usuHJzjUSdcRdxS61KAWVRF6OOHEzU5rPI65+4Ym7GtH3Pm43eN/4vuSe2+Z4kbcbifuGk3EDZQpbeN1oswc1LLuiwQw7GNVHwfc5mYYp3uENSDGxZ0XnGoahLs/TFOnvNjopG2tI1vGBxEsRRFJe5FLKZHZKFNNQq2UcOLOCnPn/rnsRVPV26Gp6om4nfnZNJ4BeQRNqRCT2mhZTzQwvw+NVSWyGkl0B+JuUSMz3kBjVP2AzxOupbzymV14D4/E0P2uBgYRTpfzB6gWGEX4AmJAQSag3mryWlirUKejPeGIEdiO9/zwPcBzzufJObfCp8CYi9BKBS+huSrusmkVyJGYPDiaKR/xtPPpoJNugn/u6wScl3D2HOITN6qcdDHKHqDskbiO6CA0vDwf+F80cuEum3YYRX/2SLJoHFqTYTHwOxTzFkPZUO3cCWTnAV+KXBsvIldIf5SJVqCW9JWEZ7z1I2eD9J5UkCxGTZgClCOSJ7qAnvoUvwxqgXy6t6uR2A1G97AjEr5KlHe7oHwdRsIcEAOqV0agaWf3opqoK3Ivr0S10HmEo0G3DI1PDkX5oAQNj61EcwdH48dUGZ9EsBQtODYb9U5WowdzAtlZQLuKJUl79jgbaD2VxOK/BhW3RDYS74BD08W0z0dxS++ilQ0LUP+guQW0L0MCuhBYgrJfL/RYX+QzZKcj3h1NtXgdCV8lykxj0L0Nk5u5CjJ6UkGy10ljeAsgqNU9xQ9j0iCf7u1wVNltQA24I8gTVIa8IycQzl7gdlS+whgQ41KIvBYL0ISsFcjb1hHZfCLh8QwNR90Rd37oUdRgd8vVFPxwiRfEYsnjdM6BggLnwJ05NyIb3MldQZuQEXdxd9AmZIAF1hj5SFHQBhih4AcAxGIxT0UNW2iTYRiGYfiGiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILD69VDf35Nf7+SB21g+CNiFtCmbdG7QJGXIgaAOMUNA7aAMyJJ/y7f6gDcga1hM0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBafFtB+FdgK7AIOOZftAYwBjgc6+WNGRqwF5gMbgcPIxj7AScju7BOLwYNb4MGt8GG1/h7XGW7qDzf3h8KC+LmLD8DTO+DVPbDuMOyqhV5F8Ike8N0hMK1r0+//0Tq4qyL19V+cDBeUtfVXVANLgQ/RM98HtAP6ASc4m1fbaz3wMlAJ1ALlwInAJ1Kc7we/APamONYF+J5/prTI+8DfWzinAPiJD7Zkgv/lzJuDwCJgGbAZPfd2wADgFOBkGufDPwJvt/CdY4Fbs22owxJ077Y4Ww0wDbjO49zdwE+b+a4pwOeybF8mBKsPPongfFQJDgc6A0dRRnsDFd4vAd39MSUtXgLmAN1QRu6EKvctqLLOTeG8fjn8dRv0LoLP9oZO7eDV3fDVlTBvHzwyPn7uV1bCgv1wbFe4qhd0aQeLD8Jj2+HJHfD4BLgqxSL6X+gLQzs03T+yYzZ+xSLgCXTvRgE90er4S4HHgBXAF1GF7LIMeAhlx6koj3wAzED3+4vZMKyVdEAVcjIlfhvSAv2AM1McqwTWAaP9Myctgiln3iwE/oLqoTFAKXpTwiLgEZQf/4V4vp0CpGoxzgd2AsfkzlxeQ/epBNm8PY3/6Z/Cpr5ZtKs1BKsPPongHSkuNRMVgjnAxf6Y0iLvInumApfT1O76nFx1xg4J4LAO8M50KC/W/qMN8Mll8KcquKI8LmzX9YE/j4eRSY2kv1RJTG9eCZeUQ7FHJ+qGfnBGz5z8DPT6mi8D42nccr4E+CVqwS5BlQjAESSOBcA3gcHO/ouA+4DFqCBMy5XBLdABODuga2dCP2fz4n4nne6TLekQTDlLTR/g68BEGufbK4GfoTz4PnCss3+qsyVzCHk02uPdeMoWlyNhKEc9wt+l8T/9gfNzaFNrCVYffPIzpdLaCU662x8zWqQOtbC6410wQS6S7DNjh9LbBscFECRiPxmuz/dtiu//5qCmAghwXV8Y1VHu0WUHc2JqC4xGrc3krNUNuZUA1iTsX4xcUdOICyBAEfGMPyfrVkaHKuRq7Ia/PavmCK6cpWYsMJmm+bY7cLrzeVUa3zMfufOnAh5jElljJNCLxh6VfCVYfQj4pbpupgrLyy/XIHfMyShzrQS2ods0kMaVdHapqlE63MMl6e57a596hl69u0SKnOPtU5SPOXvhvQNQH5Nb9OyejYU3d7gVW+IPcPPAOI/zRwDFyDVWRzDZtQ4J9V7Hlr7AUPInpuw9Jz2W8NgcXDlrHV75NhVvOelpObKlLexH45jVyO04BPUOw4o/+uBzrTIP+XuPoIHQDcgNcaq/ZqRks5O2B36LCmYiQ4HPogyUXVwRWn+46bF1zr66mD6Pbeby8/fB8moYUALHdPE+59/XN/67pBC+Oxh+PAwKctawrEcuMGgseO5YhldGb4fGZqrQGEsQYxcHgSeT9vUErgKG+W9ORtQiAS8k7sYLA8GVs8ypJx4A09IY31r02/qgnmXYWEXT3uwIdK9zNj6SAcHoQwAiWJ3w90jkDglDZoe4bXOQq+EmNM6yBw3irwEedfZnl4vL4NFt8KuNcE0fKC3S/toGuDNBtPbUpf6O3bXw+eX6/F+joF2SoE3uCg+N1Xhgv2LYXguv7IYfrIO7K9Qz/NmIrP6sBJ5FGXs8jUXwiJN6ROoA4HaNPVoHOWcaai33Qb3APcjd9R4KlriZ1ONwYWAZur9jULRdWAiunGXO31EAyjHE3XOpCGsvsAg4F/0GN5hnC/AKutf/i6JYgw72CkYffBbB7zjpQTROMRMN2l9LOCqTBictBK4n3jrqi2z8b6ACtVCy67K5po+CX17eDeMXwOXl0KEQXtsDW2tgcAlsqEntkKmuh8uXwurD8K+D4VMeHasrezX+e3A7Tb+Y1hVOfA9+sQFuHZQL1+gbwOtITK7P9pfnkLOS/u6DCmUxMBeYhXdIelhwXaHHBWpFU4IrZ5kxE4Xv90URis1xCN3vXAfEtIauwAVJ+0agRtx96D4vQNORgiQYfQhokKAL6g1cj1r4M4Ixowlur6MfTd0DxSjkH2AT2aZdATw7Ce4Zofl+D1dpG9UR5h0LXZ3mSm8Pgaquh4uXwJx9ErH/GJnZtad1heO7QW0M3t7f9t/SmDdRa7ov8A2aturcHuARvHF7gFmZv5EljnfSiiCNaIFtqHLrRvimRgRXztJnFvA4svE2Wu6NLECuvFwHxGSTdmjeLmgKTVjwVx8CDozpgdwhVaglFfSk+XInbck1V5uTqxcVwu1DtCVypB5WH4LyIhiWpAUH6iSAb+1TDzBTAXTp5bhfq7MamT4bZeB+KPzcq3LojVp924FBScfqUWRYIfFnEwbcCjE3+SA7hDEgxiXYctYyrwF/Q0Ejt6KGREu4rtCge1OZ4gYOHA3UCm964Ic+hKB0HHDSMIT6Dkd2bCfusknEHcAv9c0i0AT4ozH4bJ/G+/fVwXmLJYD/NqT1AljbAO87j8ErOrV1vIYEcADqAaZqHbu9lBUex9aiwjmMwNtrjdjopGEIJvAirAExLuEsZ+IlJICDUA8wHQFch3qtfQjPNJR0qXTSNi8VlSNyrw8+iOAuvF1dMeTzrUYZLgzurp4oE++j6ZJIq9Egcgfi7prsst8j6GXxAfjuGujZHr6X0EPcUwvnLIL5++GuYXB3CwEtB+pgZXXT/Ucb4JbVGm8c2wmmZ8WT8zIKhBmEeoApwlQBTZrvjCYib0jYXws873wOInp4O96t4z3Ac87nyf6ZkxEfIDfSKMIVEOMSbDlLzXPIdT8E9QDTLQxhDYhx2YR3Y2MVGq6A4BajCF4ffGher0Y/ZjAqkB3RD6tEFUoX4NLcm5E2l6IoxhfR/KX+yM4VqDVyJandOG3j3MXQsRCO6awxwBXV8Pwu7Xt2EvRPCN66apnm+o3oCA0xrQuazBW9YIpTjnfVwrgFErlxnRUduqMWXt8D64/I1frohMbrk7aOd4AXUPtqOPFClkgp8bGIDsA1aC3G/0GFsROqyLcjkfRamSPXLEPBL0NRvi1BrtmVaO7gaMIztSeZsAbEJBJcOfNmHvAPlG9HojormXI0tzGRwwQTELMMlRGI95YqUVQtqGF5mfP5H8AO4nkZFB3qLlpxAcFN9wleH3wQweGo8tiAMv0RNPhdBkxClWEYeoEu3YGvoWjGFehhlKCW6+loMm9uuLqXXJ9/3gaH6zXX7+b+cMcQGJhUH6x3Gk9rD6deFHtox7gIlhbBNwbCO/sVgbq7VpPuR3SE2wfDrYO9g24yZ5eTNqCoUC9GEhdBUD74JgrZXoJEphy4At3zIFzlw9HcRHe+0lFUKQ9BwjwlILtaYjvKs2EMiEkkuHLmzU4nbcBbAEH3M1kEF6DFq4/D34CYLcQbOy67iJe/nsRF8FgkmhuBj9BYe1fkyTgV5fWgCF4fCmKxmPeBggLnwJ05NSB7FAVtQEbEzvpB0CakTcGse4M2IUMOtHyKEQHCshJVuuRTvs16GHkOuQuAWCzm2WoNQWCMYRiGYQSDiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILD68VNcvaoM2ICMKZv0yaBPSJnblt4M2ISMKZuTLOzBBb/vOJyqCNiADdgdtQIYMCNqADMiv+rY5rCdoGIZhRBYTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZDERNAzDMCKLiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZk8ektEq8CW4FdwCHnsj2AMcDxQCd/zGg1S4EZzudLgWk+X38JsBbY4mw1jg3XNfM/DcA7wEJ072uBbsAg4EKgV5utisXgwQp4sBI+3A8xYFxXuGko3DwUCgvi5+49Cg9UwOJ9sGgfrDoI9TF49RQ4p3fqa9TH4Ndr4Y+VsPogdGwHJ5bCD8bAyWVt/gktsBy9NWEbUAUcBSYCV+X6ws3wN8emKuAgUAyUAVOBc4AuLfz/Q8Bbzud7gD45sbJlwlgnLAPWOXZtReVsCnBNM/9TCcwCNqAyVg5MB04m932Mx4D1KC8cQHmhHNUN5wJdE869H5jTwveNB+7IvplAZvd2J/ABsArlj4NAR1R3nQqMyKplPongfKAfMBzojCqTzcAbwPvAl4Du/piSMfuAF1AGOxqQDa8h8StB92l7C+fXoMpuDdAfFcr2wH6UEXeQDRG8/j346yboXQKfHQid2sOr2+Gri2HeLnhkevzcikPwrx/q88COUF4M22qa//5YDK55B57cAmO6wDeGw+5aeHwTfGI7PHU8XN6/zT+jGd5EAliMGhA7c3mxNHkFGAJMQDbVoAbSM6g8/QCJoheLkQB2AI7k2tAWCGOdMAtV0MXOtXe0cP6HwF9Q2ZqEhHsF8BwSx+YaqdngJfQqrmOI54U1qME+G7iTeF44ltRlfi6qUyblztSM7u0rqOPRGzWKOjnnr3C2S4FTsmaZTyJ4R4pLzUStkznAxf6YkhExVLl0AsYCbwdkx+Uo45SjCu93LZz/BCoMVwMneRyvb7NFM7ZIAId1gnfOgPIS7T/aAJ9cAH/aCFf0g6ucV6QN6QSvnQJTe0BpMdywEB7e0Pw1HtskATy5FGaeCh3aaf9XhsGpb8KXF8FZvaBrUZt/TgrOR5VLKarUHs7VhTLgd4DXD34KVb7PA5/3OL4f+CPqZe0DVubKwDQJY51wCSpnZaix+EAz5x4B/g4UADcDA5395zr/twx5cCbnyljg90hUknkC+AfwLHCDs2+6syVTjfJMe+AT2Tfxn2Ryb0cDp9P0/YrrgD+gTslEVDbbjk9jgqm0doKThvXllwuQu+FyvDObX4xErbiClk4ENgGLkKvBSwAB2rXZohlblN42Ki6AAMWF8JNx+nzfuvj+nsVwdm8JYLr8br3Su8fHBRDguJ7wmQGw46hEMncMQ4U2nfvuF6kU/zgn3ZbiuCvgn8uuOa0mjHXCCNTQTOd5L0MCMpm4AIKez3nO5/lZta4pqQrT8U5alcZ3zEW98Ok0dp9mm0zu7XS8XzA83NnqUaM0OwQcGLPKSZsZFAqMHahVegJyP+UL7zvpVOAwGhOciXqx2XPnVTmuzOEeQzfDOyt9a5d6hq3hSD3M2w2d2sFpHt69C52hrFkteawiw2InHeRxbA7KF1+g5THDoAlznZDIWicd7XFsGBLDSqDON4viLHLSwWmcO9tJz8yNKVmnMCltOz65Q13moVbHEeQf3oAG5k/114wWaUB+9e7A2QHbkikbnXQP8DMUdOBSgHqHV9LWTFTuNELXH2p6bF210rqYPo9tRQNzbbWCYoZ3hvYepo5y6vJVBzP/7o8HL6IxoMPIW7EaCeBFSeftBP6KnrvfAV3pkC91QjJug7Lc41g75ELfhnq0uRb051FeOITywiqUFy5p4f9Wo/qiLwqKCTt7UOOjCDU0skMAIlid8PdI5Grs7K8ZLfIGciV8kdTup7DiqsI/0ID5BSjqrhKNG81DvYHz23SVi/vCo5vgV2vgmoFxN2dtA9y5In7enlbGEu2rVdo9RQ7t7jyWvbWt+/785yU0zucyEQWTJI6TNAAPooCqXAdptJZ8qROScQOLOqQ47u4/7IMtL6JxXpdJaJyypTGz1530jBzYlG3qUDRsHYpuz170sM8i+B0nPYhaIDNR6O61KFIsDGxCEXQn4e1aCjsxJ+2Nxn/cbtRo5A77FRL5s2nL479mIPxpA7y8Hca/Bpf307jda9th6xEY3BE2HG48TcLIJvc66T4UBPUk8CPg2yhiEBRltxK4hfCKSj7UCWHnPifdh3p3j6Mo4duI54VkDqGYh1wHxGSDBvSbKpHAZ9fegMYEuwDjgOtRS2lG86f7RgPwNAqGyBcfeTIdnXQ8TR9vf+SmqaHlaRbN064Anj0J7pkAvUoU6fnwBrkp550OXR197V3S/Pekwu3p7UsxpOL2FHvkW0c963RH4e+3ISF50NlfhXr+p5LbCMVsEdY6IRVuTy/VVBN3f8cUx3NBdxRUcjvKC//bzLl+BcS0FVcAlyEB/AzZDlTzuSeYTA8U9ViFWiZBT5o/iiZnAvw0xTnPOtsJyNUYNnqhcZVUha8T+o1t9yMWFcLto7UlcqQeVldr3HBYKzsgIzpLaNdVQ11D03HB1Y7Xd3TY4zx8oxw1cjagidNbkOvInW7gxfec9JuEZ7ywB+GqE1JRjrxGO2kcHQqKXtyNGqGlPtsFsm0A6jkdwFvkZjvpWT7Z1BrqkQt0GYp2/zS56LcFLIKghwThCENvh6IqvdiKCuZg1FNMzvhhYTSKCPUKj64jPkm1Z84seGyTokI/24Zb1KGd5ge+tUvbmUnzfF90ZgKc1fY5/x8j9jppIaoIT0tx3lLkOjsO9Wi8gjuCJEx1QipGoIjcVaiCTmQ9amQOI7gqdo+TeonGGtRY6ot632GkDgV0LUcNtKvJlePShye0C41HJA8gx9AqAtVo7M1Pt0EqioDLUhybjYRlMuFpNXsxEUWLLUausMQw6VeRm2Yk2Zhour8WuiW5Ixfvhe9+AD2L4Hte0eMZ8NVhEsAfLG88Wf7dPfD4ZuhVDJ/M6YoxYaMKPbfk3pEbzbwfPdvOznZjiu+5B4ngJwlm2bR8qhNSMREFJy1BS6S5Lb5aNBYLcGIOr78VuT+98sJTKC+Mwnss2A2ICeuQTx3wJzSePR0tU5i7kTsfRHA1GuwejFwdHVEmr0StlS5oGRwjNcvQWnoQbyVXAo86nzsTF+8StB7fH9CA+URUWDagFmoX1KpqO+fO1Vqex3TTGOCKA/B8lfY9exL0T6rDvrMMdjrRonMcr/N/roY/O7M6rugHVySI2jUD4e9bNCF+6iy4tB/sOqpl0+pj8MDUpiKcXT5yNohH3W5C48agCug8/GMpCoAZhVyGnVFltxL18LsTXyEkzIS1TvjQ2SD+vDeg9VpB99tdxaYDqpz/glZuSVw2bQcqd7lchmyJY9dolBe6oLzwERrv746ihZM5jAJiikjtKcgFmdzbGShPd0a/Y6bH9w0nW2uI+iCCw5F/fANqvRwhvujvJDS2FuYWXxjYAryXtG8X8fHLnjTuwY5BEYGvogrnCBoXOAkt65SdNRmv7g+PbZaIHa6HAR20cPYdY7Q+aDJPboHKpHmFryTE5wzt1FgECwrg0ePg5HXwUCX8z1r1Bj9R7tcC2lWosklkD3FXU3f8FcHxqOJajcrTIdTo6YN6I+ksoB0GwlonbCG+2ITLbuKr1/Sg8VJuE9BUhNdRI7UO/YaL0dqWuXTnTkBLi61CjQc3L/RF84DPwzsvzEWBcSfib0BMJvfW3VeNtwC6ZEcEC2KxmPeBggLnwJ1ZuZCRTHbWvfOD2JW3BW1CRhTMyKc8OzRoAzKkImgDMiDfGtdeS4WFlc1BG5ABCgCLxWKerRJ7n6BhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmTx4aW6hje1QRuQNvn1fj6I3XBX0CakTcH/3RO0CRmSP+/B1FvU84l8ekdfPr37sHmsJ2gYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILD4uoL0feB1Ygxa27QKMBU4HOvpnRlqEzdZlwDpgq7PVAFOAazzOrQfeds7bAmx39l0FHO+DrS0R3L19fiPcuwKW74VdNdCvIxxbBrdOgJN6Nz73QC3cswyeqoCKg9CxPRxfDv96DJzdv/G5sRi8vBme3wRvbYPKajhcB0O6wIUD4I5J0CdrPy2TvOBSCcwCNqCF28uB6cDJ5LYdvARYi/LhFsfWacB1HufucWzc5Hw+BHQGylC+PRZol0NbW2IlMA/YgWzrCvQHTgEGB2BPPuUDgMeA9UAVcAAodq4/DTgX3c9kGoA3gTnARsfmHsBw4JNAv6xY5pMI7gYeAqqBMejHbwYWoMrwRqCTP6a0SBhtnYUyejHQHRXEVBwFnnM+d3G2fTm1Ln2Cu7e3vwc//wDKSuCKwVBeAmsOwDMb4alKeOQ0uH6Ezt1TA6e+KLGc0AO+MgYO1sEzG+CcV+DBk+FLo+PfXVMPF74GxYXwiT5wTn+oj8GsrRLdx9bDWxfBqKy8gCGTvADwIfAXVNQnofu7AuWRSrwFKVu8hsSvBNm6vZlzdwHvI0E5xrGzGvgIeBxYCNxMMEL4MvCWY9M4J93t2LYcVchTfLYpn/IBwEvAUPRsuyHRXgPMAGYDd6IGj8sR4L/Q/R0CnAYUoQbSSiSmeSWCL6AMfQFwQsL+l4H56IFe4o8pLRJGWy9BGb0Mtf4eaObcIuCLKIN0A14FZubawDQJ5t5WHYJffAh9OsDSy6F3Qq/s9a1w1svww0VxEfzRYgngVUPg8dOhvdNI/tk0mP4cfHMBnD8ABnbW/naFcPdU+NpY6FkS/+6GGHztbbh/Fdz6Djx7TjZ+TSZ54Qjwd6AACchAZ/+5zv8tQ721ydkwzIPLHVvLUY/wd82cOxT4CU17JPXA/ajCXIb/YnMA9US6AN9wUpd1qFE3MwC78ikfAPweCXYyTwD/AJ4FbkjY/xASwC8CZ3n8X13WLPNhTHA3KgA9aOqOOwNV2ktRDyZowmrrCFSRFKRxbnvUywrbe9+Cu7eV1RKkE3o1FkCAM/tB1yLYcSS+b8YGpT+eEhdA0P/eOh4O18NDq+P7iwrh3yY3FkCAwgL44RR9nl2VrV+TSV5Yhhodk4lXfKB7fZ7zeX62DPNgJNCL9POtV3XUDvUeAHZmya5M2AvE0P3rknRsOOrlVvtsE+RXPgBvAYR4XZBYQCrQkM4JeAsgZLP/5oMIVjjpcJo+sBLk/qhFYwFBU+Gk+WBrvlHhpP7f21Hd5Kp8ZyfsPNL42JtVGv87J2Gcr8p5F+twj2EKd9/Mreldu8gpYe19KGlNWeukoz2ODUOVYCXZbFVnnwbktoNsub8yowwJ8Saait165NYb4bdRGRLmfLDISRPHVec56Ulo/HUu6i3OArZl3QIf3KFu660sxfFS9JB2oQoySPLJ1nwjuHtbWgL/cSzc+i6Mf1pjgmUlsPYA/GMDnNsf7j8pfn55CWw9DOsPwvgejb9r3QGlK9McZnV7jBcE8iJu956Xexxrh+75NtRL7+1xThAcRJVeDInOKvQ7pgITArCnE3A+8CLwa5qOCY5Abt8wE6Z88DxqOBxCjYhVwCAaD4Osc9KdwG0oT7gUoN7h58lWH84HEaxx0g4pjrs+pCMpjvtJPtmabwR7b2+ZAEO7wI1z4YFV8f0ju8INIxu7SS8eCA+uhjsXwWOna8wP5DL9r+X6vCcNr+27O+GuxXK33j01az8lA9x7meqeu/sP+2BLulQDryT8XYDc5RcFYo04GbnxZwDvJewvQ9GNyW7SsBGmfPAijQP1JqFxysThG6elyV9RVPDVxBvJf0RjsN1QxHvb8XGKhGEEx8+Xwfffh2+Ng2+Mg74d4aN9cMdCuO5NWLwbfj5d5/54Kry8BZ6shCn/gLP7QXWdIkkHdIIN1Rrva45V++DS16C2QUI6ImxDtKGlD/BL5Abdh8azXka9hpsIJor8LRRgdqKzdUG9lFdQYMdWFOxltMx9TroPWI0if3+AenxDnWMNTtoPBSO5Pb4JwDeBf0diehnZkDAfRipaauG31EPwk3yyNd8I7t7O3gq3L4TLBsGvjte4Xqf2MK0MZpwlYfvlh3FXZ79O8O4l8PWxGi/87UrNAfzMUHjiDJ3TuxkzV+2DM1+G3UclgJcFMY0MiN/LVPfc3R+2ebqgqqkn8AnUE6hEYfZ+sw6J8FjUGy1FQR79gWtRj2QuciWGlTDmg+5ojuLtyN35vwnH3IbOVJpK1BAUbHUETa9qOz6IoOuH3pXiuJt5Uo0V+Uk+2ZpvBHdvn3Nibc70iKvo5EyCb4jBogTT+nSE+06Eik/B0c/Dls/A/5yoXiDAcV7DK8CKvXDGSwrAeeIM+OTQLP6QjHGN9IqqrEf3vBBV7GFmrJOubfas3LDSSYd5HCtG0ZYx1BsMK2HOB+XAACRorhvULaidU/yPu782Kxb4IIJDnXQdyiyJ1KDVC4poHLobFEOdNB9szTeGOqn/97amXumOFA1hd39xGvOwH1mj9FqP2J1leySAu2vg72fC5YH1AF3cqMVVHsfWo0pkCOEfFXHHkIIIsXUyT8ppEO7+IFezaYmw54M9Tuo+X3dKjFekeC3xCNEULdEM8SFXlaKHsBd4J+nYbPSjJpF6Homf5JOt+UZw9/a0Pkp/vxI2J9VlL26CuduhQzs4uZf2NcTgoEcj809r4ZG1cHJvRZgmsngXnPmS3KfPnA0XD8r6z2gFE1GreQmNK5Ra4sEnJ/ptVAo2ER8LSqQGeNr5PM43a+IMcdL30JJ/iaxCjbf2BLN0WroEnQ+2omjQZBrQmOp+YBTxHt505AqfT9Pe/9POd41DwUptxyfpvwitAPASanm4y2VVIPdXqgmRQRBGWz90NoiHC28A/uZ87gxcnHD+bOJLVLlumoXE5+oNJZh1RIO5t1cPhXNWwWtbYdzTcOVgBcas2AfPbVS/9J5jocwZOjlUB30eh3P7KaClEAnl2ztgXHe5ORMDY/bUwNmvqAd4dj94e7u2ZG4ZDz1Kmu7PjEzyQgcUQfcXtGJH4nJZO1DlOKmtBjXDMuAD57Pr6qoEHk2w9TLn8ysoHwxFlVsxajB9hKIWhwJn59DWVExAjbe1wL2o8u2K7t9KlHvOw/+AnXzKB0scu0aj8bwuSPg+QvVUd+BLCed3AL4M/Aq4m7gorkUNj25oicXsUBCLJbumnAMFBc6BO7N0qX2ocl5DfAHasC6g7YetmXxPS0uf9QC+l/D3/UhkUjEN+HQG189m6HTu723shrua7KttgN8463gu3yehKy3ReOC3xsF5Axqf+5W3Yc422OQ0YEd1hU8Pk5B1Smo6VhyAYU+1bNf6T8LQpAn4Bf93T4a/LtO8ABKX14lPiC5DFcspZO4MKsrg3JdpPN0hmZ4oMhC0RNYiVJEfRCsHdULjQ5NRoy1Tl2O28m09Wt92KRKNWpRXB6Ie1KgsXSeTPknQ+SCTia8b0UT3VWj88RAKlOuLlps7D+9pJpXAM0gsD6HfNBm4AuWddPkcALFYzDOm20cRNBoTNuFvjjDNI2sZLxEMK5mLYNBkIoJBk1/5Nvxjs4kEsvpDK2leBO19goZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBYTQcMwDCOymAgahmEYkSWNF1jly3vv8u3dYflk77igDciIgv/Ln3dgxuYnv/g03BSc+NugTciA/UEbkCH59I6+7UEbkDWsJ2gYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmRJ4y0S6bIMWAdsdbYaYApwjce5O4EPgFXALuAgelvFIOBUYET2zGoVr6LfsAs4hG5TD2AMcDzQKTDLGnMI+AhYDWwDDgDtgN7o3k8FCgKw6y/E88IBoBjoBUwHzge6Jp1/GHgGeAfY4Zw/ArgUmOiPySnZD7wOrEF2dgHGAqeTqzes/N9z8MW7mz+nsBDq5+nzDT+Gh19o/vyzpsPM+5ruf/h5+M1TsHw9tCuEqaPhO9fBJae2zvbGHASWoLK+BdiL8ucA4ETgJFpuh/8ZcH4oP0J522+WAxWojFUBR1G+vCoAWxL5G7KrCt3rYqAMlftzUF5tjoeAt5zP9wB9cmKlWAKsRflgC9KHacB1zfxPA6oTFqK6pBbohnTiQlSntJ0siuAsZGgx0B1VZql4BViKMvQYJCo7gBXOdilwSvZMy5j5QD9gONAZZfrNwBvA+8CX0G8MmuXA8yizD0MZpBrdw2dRxf0p/BfCFxx7Jjk21SChfhKYCfwEKHfOPYgqt03AQFR4jwDvAT8FbgbO8s/0RuxGFUU1yqflKB8sQPf2RnLRIJoyGu78kvext5bArPfgwpPi+644HYb28z7/Ty/Bus2Nz3f5zq/hl3+Fgb3hy5fD0Vp47FW49DvwP7fBNz7V1l/yPvAYKiujgZ6oUbQYNZSWAzeROn8uRQJYgvJQULyJBLAY5eedAdqSyCvAEGAC8XK2FjUo3wB+gETRi8VIADug8pZrXkPiV4LyQ0uvYqpBZW8N0B81oNujRuk6pBehE8FL0I8rQ0Y+0My5o1FLOvn9WeuAP6BKdCJ6sEFwB963ZiYwx9ku9tUib8pQT3s0jSuSs9H9dxsV432264+owkjmMeBpVEjdWv5JJIDHA99GPQXQ7/o+8H/AZFIX5lzyAhLAC4ATEva/jBpKs1C+zy5TRmvz4qSblN58eXzfFadrS2bvAfj5n6G4CG5Iyq7zlkoARwyEdx+Cnk5R++51cOwN8J3/gUtOgaH92/JL+gBfAY6hcY/vMuDnwCJUGU/1+N8DwF+BY1HFt7othrSR81FdVApUAg8HaEsivwOKPPY/BTyHGsif9zi+H5XR44F9wMpcGZjA5UgfypFQ/66F859AAng18hgkU581y7I4JjgC/cB0eh3T8X6B5HBnq0eZLShStQ0mOOluvwxpgWGoh5J8z7ugewxyl/iNlwBCPDNXJex710k/RVwAQQXmYtQLn51N49JkNyqsPVBlkcgZqPJZiuzzh2VrYP4HMKAXXJyGo+RPL8LhGrjqDCjv0fjY/85Q+m83xAUQJHpfvxpqjsIfn2+rxWOQNyC5mukOnOZ8XpXif//qpJ9pqxFZYBhqhAUxtNAcXgIIcJyTbktx3BXxz2XXnGYZiXpu6dzDTaiBNAVvAYTGdUXbCGFgTGFSGibcAhvEuESmhPE+LnTSwQn79jqp13iEe58/yJVBzVDhpMNpWnBL0G+oRQXWH37/tNIvXQbt0qgDHnhG6c1XND026z2lF5zY9JjrOnXPyQ3tktJE3kZjSJ+l5XEtoymLnXSQx7E5yE39BcJ7b9930qloHH4h8sK9TS5c0Vl0h2aDPaj1XYRaX0EzD7X0j6Dxzg2oss5K1EAOaUC9FFALLCieRffuEHJ1r0TikeDLoxt67tvRmGAi7rjBltya6Ylb2FK5YUtRXt2FhDK3HD4Cf35Z4nfTZS2f//YyWLYWRg+GM49tfKz6MGzeAV06Qb/ypv87yqk7V21ou93e1KNxVWjqqt+FXGHHIze40TIvojG0w8B65DoeBFyUdN5O1MM+CQWlhJWNTroH+BmqP1wKkP1Xkq0GfohEsA6NGdWhyJ8wRGDOQ2NCLiNRBd45GHPS5jUkIKMIVgSfQ2MOLpOBr9J4rHcqGlt7Ao0Juhl7PxqTg8bPwC/cQIwOKY6XOKkfQQXwt5ka47v4FBiURhCf22v88uVNj+07qLR7imzc3ekg7D2YsZlp8jRq2EygsQg2AI+ge/vpXF38Y8hLqLy4TERj7onlrAF4EN3b5iIyw4Cb8f6BxpMvQMMSlWi8cx7qxZ6flauFRAQbgMfRj5wEfCJYc/7Jd5z0IGqdzATuB65F0aNhZAFyG5Sj1lKQ3O+ke5Er+VEUdPSvxHv6n0KurwXA7SjT16Do0FLUeg3bWIz/uKL2L1e0fO6+gxJNr4CY4HkdlaM+wA1Jx2ahXszXCEcjOF+410n3oWCSJ1HE9beBoc6xV5An5hbC34iPOWlvNG7pNoxHIzfur1D069lkQ8JCMGDkCuAyJICfIXyVXhdgHHA9cjnMCNaclLyDWoW9UGbJzTy2zOmB3FvfR1F/v0k41hNNhTgP3dtX0KD4SajAQjDTUVrq6bXUU8weH66Decs0leGik1s+/88vwaEj3gExEO/p7UvRwXZ7ij2yPmQ0G/X4+9G0Mt6GWv4noYaQkTndUTTtbajh/qCzvwr1oE4lP1zMbr01nqYS1R81jmtoeZpFegTcE6xHLtBlKBLo04RCl1PSAwlMFfJTh6m1Oh+F7vdGYdFhbO31QuN+Fch947preqA5dzcmne8GxOR+zK0p7mDZrhTH3Qjh3E/d+GdAzKWZBcSk6jV27qgI0807YOvOpuOCq50hmdGDm/5v65mFeij9UQ8lecGErWgo5G1n8+JHTnozqi8Mb8rRfd6AGp1b0L11p3d58T0n/SbBjxf2QranasR3QuWyNitXC1AE69Ag7XJ0068m3ALocsBJw9RbnYNcTH2R+yBM4pzMHidN51m/6aRBBCINddJ1yD2T+LxrUCEtomkwT3Y5UqMJ7+3aKSq0JRZ8AEtWS8DOODb1eWdN1xSKl+bDF5OmOr74dvyc7PAKGgccCHwL76jEMiBVN/cD1GiahnreQcwZzTf2OmkhEsXTUpy3FLlRj0P31iNSyndGo4jQKo9jdcQXYumZlasFJIJ1wJ+Qj3o6Wn4oLAK4C/Wikt1cMdSarUaRV2FxNb6B3Ez9kAAGbdcW1LNLFuIGtMzTPpTJuyTsP0rT+/0mWtFiNPE5j35Siua+rkVu5sTJ8rNRK/RYUs+JzA5PzII9+zVxPa2AGHdahEdATCJfuVIi+NP/gys+EZ8rWLEFfvMklBTDF7MynvgCCpAajHoZqTwUg9Bwgxf/hUTwMvJjepIfVCFPilc5m4Hu10h0vzvT1Mvicg8qk58kt8umZcJENNF/MWoAJ7okXkVDFCPJ1mIqWRTBD50N4tE9G1DFB3oQbqmagQSwM/Jjz/T4vuEEs4boamTPYFSZd0TCV4l6MV3Qsm5hYDGqkAuQvQs8zumBv66jxSgAZixya3RFhWw58uH3QO4sl6PAv6CM3wf9lpXoOQxAY0dBNZAuQks3vYRCz91l0ypQbyT3y7m5rlCvuX7J7K+Gx1+TgH2hBQE7eRLc+ln41aMw6Xq4+iwtm/b4a7B7v5ZNa9tqMSAX/XPo+Y1EQTHJlJF6QnRY+MjZIF63bUK9W5AQneezTUuRe3kUKmedkfCtRD2l7jQNPAqSZcSHN1xvWiWqK0D2u66OErRi1B+A+1Dd0B3pyXpUB1+dNcuyKIJbiE9ydNlNfOykB3ERdPdV4y2ALkGI4HBk3wY0TnGE+MK0k1CPIOjelsteJ43hLYCgtQWn+GGMw0TUSl2JxKIaZep+yCVzIY3dYe1RJbgSFRSQW/czSIRKCI5S4MuoobEGCXNXlAdyt4C2y4r1MGdJ+gExf3lJcwCvOdc7ICaZX34bJo7QAtq/f1qLck8bo6XTsrOAtjvXsgF5UbwYRfhFsApFMCeyh7hrvzv+i+B4VJ5Wo7rqECorfZBbOZ0FtP1kC4r4TmQX8TH3nsRFELTa0C2o57ca1cNdUV45l2wGyxXEYjHvAwUFzoF7snax3HI4aAM+xowL2oAMWRG0AWkTm39X0CZkRMGJvw3ahAxItWxYWBkatAEZEJalI9PhNgBisZhnIEdYBuIMwzAMw3dMBA3DMIzIYiJoGIZhRBYTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZDERNAzDMCKLiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkSeOlunW5tyKShOXFvOmQP+/nE92CNiBtCk7Ml/d1ithNXwvahLQpePDOoE3IkHx6/+HH5/2t1hM0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRJY0FtDOJmuB+cBGtABrJ6APcBIwxl9TMmIpMMP5fCkwLUBbkokB7zrbNufv3sBxwPGEq51zCPgIWI1sPQC0Q/ZOAaYCBT7btATlyy3OVoOe73XN/E8D8A6wENgK1KJFuwcBFwK9cmjvMmCdc92tjr1TgGs8zt0JfACsAnYBB9HC7YOAU4ERWbPq+Q1w74ewfA/sqoF+neDYcrj1GDipT+Nza+rhwZXw8GpYtx+O1MOgznDuALhtIgzp2vT7tx+GXyyFFzZB5UEoLoShXeCaEfCVsdC1OGs/xYPlQAXKs1XAUWAicFUuL9oC4cwHrWM/8DqwBulCF2AscDp+vGjARxF8CZiDKouxSACrUcWznvCK4D7gBaAYZf6w8TiwGGWcyUARykxPA5XAZ4IyzIPlwPPI1mEoL1Sjt1Q8i+z+FP4K4WsoD5YA3YHtLZxfAzyEbO0PTEfFaD+qlHaQWxGchSq9YmTvjmbOfQU14Hqj8tXJOX+Fs10KnNJmi25/B36+FMpK4IohUN4B1uyHZyrhqfXwyOlw/SidW9cAZ78Ac7fB2O7w2RFQ0g7e3QH/sxweWQPzLoXxPePfX3EATngGth+BM/rBhQMlnK9shn99B/68BuZfBh1zVpu9iQSwGOXZnbm6UAaELx+0jt2oPFU7tpUDm4EFqIzdiOzNHT6J4LtIAKcCl3tctt4fMzImBjyDHsJY4O1gzWnCB0gAS4GvA52d/XXAn4FFwATgmCCM86AMtVRH01jozgYeIF4ox/to0+WoEilHPcLftXD+E6hwXo08GMnkOi9fguwtQ6L7QDPnjkat6QFJ+9cBf0CNu4m05dVTVYfgF8ugT0dYehX0Tmi4v74FznoBfvh+XARnVEgAz+4Pr1wIhQnZ4M6F8ONF+r6HPhHf/59LJYA/mgZ3Jjhh6hvgvJdg1hZ4Yj18flSrf0YLnI/uUSlqWD6cqwtlQLjyQet5AQngBcAJCftfRl7DWei35g4ffGV1qLXdHW8BBLnEwsgC1Eu9HLW4wsaHTnoacQEE3ePznM/zfLWoeYah1l5yT68L6lGB3E5+MhL13NLpfW5CDYspeAsg5D4vj0CCnY6902la8QEMd7Z6VKm3nsqD0BCDE3o1FkCAM/tD1yLYcSS+b90BpRcPaiyAAJcPUboj6VV17v9cNrjx/naF+h6v/8kuw5DY+O2qb45w5YPWsRs1PHugoZtEzkBeraXk2gPngwiuQUo/AT2wlci9MA/YkPvLt5odwEzUOhkSsC2pOOikpR7H3H0V5MeLkQuT0jDyvpNORWMXC1EeeZtwuMgyITv3e1Q3jc+9swN2Hml87M2tcKAWzukf3zfBcXO+uEnimchzTnVwTlJ97f7P8xsb72+IwYsbJaZn9cdoFUGWuwonHU5TMS8BBqPx9k05tcIHd+jmhEv9lqZvTx4KfJbGPZmgaUCBMN2Rqy6suL7y3R7H3H0NzufevljUOhpQiw/UMwsrbi28B/gZCvRxKUC9wysJt5CD7F+LWtrD2vRNpR3gP46HW+fD+Cc1JljWAdbuh39sULDL/afGz794EFw1FP5eAROfkuAVF8LCnTBnG3xzPHw9yRv+r5MkkP++EF7fCtPK4GgDvLIJqg7Dg6fB1PI2/YyIkr180DrchmNZiuOlyL5dSChzgw8iWO2kc5Db6SagH3oAL6Ge4qPO/rDwBooC+yLKIGFlLIpunIOCYlxRrAdeTTgvp76iLPAaCkgZRbhF0O15/wONs16AXDmVwFPIu9EFjSGFlTrgMSe9kGwEHdxyjCI1b3wLHlgZ3z+yG9wwqrGbtKAAnjwb7nof7l4My/fGj53dH64dCe2T2hC9Oyrw5cY3YUalxgBBzY4vj23c0zTSJfv5IHNqnLRDiuMlTnokxfHs4EOTtSHhUtejnl8J0Be4Fg3GVhAe1+gm4C3Uqh8UsC0tMRkNeu8CfgX8HVXQ96J72sM5L0xjGcksQO7EctSLCjOu/6438Dk0vacEPYMvoPv8BuF1PzegaOJKYBLwieZPT5OfL4GrZ0rw1n4aqm+AhVfA8K5w3Wz41wXxc4/UwWdmwS8/gN+cDFuvhX2fhxfO1/jiJ55TVGkiFQe0f9kenbfv8/q/350Cf1kDxz0D6w9k5adEhNzkg3zFBxF0m4H9gJ5Jx4pR6x9y7fdNjwY0taAMODNYU9KiEFW+FyB38vvOVg58lXhLqksg1rXMO8gb0Av9jtzPCWobrn3jaVp0+iP3TQ0tT7MIArfiW4Yqvs+QjcbR7C1w+7sKWvnViTC8G3RqD9PKYca5MKCTBG/dfp1/zxJFcv70WPiXcdC3E3QrhgsHqYdY2wDfTgrCvuENCeBTZ+u8bsX6v38ZBz+dDtsOq2dppENu8kHraKmn11JPMTv44A51nfWpfohbsdTm3pQWOYp6VQA/TXHOs852AhKfoGmHIqnOSNpfi3zunfEOnAma+SgMujfwecI1JpyKXshjkUqsO6H8E4a8nEg9cn0tQ5GtnyZb7d/nnGHSMz1ckp3aw/G95MJctEsC2dz5k8ugZ4l6hLuOaGzxwFF4owpKS2CSx9DRmf2ULsy3uKRAyF0+aB2uNuxKcdyNa0g1ZpgdfBBBN/JnO2qFJN90N1AmDBV1OxT558VWNE44GD2UgX4Z1UqWoEw/OWhDPJiDoir7IrdiEOMRrWE0igit8jhWR3zCcrLHI0jqgL+ihQqmofmN2av4apxpkTtSNObd/cWFLZ9fUy/RSzz/qDOasv8oHK2H4qQZKMnfb6Qit/mgdQx10nVoqCGxR1qDGpxF5Lqu9eEu9ERzw/bRdLL5ahQY04G4WzRIioDLUmzuijaTnb/DMgHdq/bZAryIeixn+GpNy7yBBLAf6gHmiwBCfELxYpqOYb+KnsVIgpl07EUd8CdU8U0nFxXfaX2V/v4j2Fzd+NiLGzUxvkM7OLlP4/N/tjguiC4/eh/qYnBcr/gyaGUdYFwP7f/JosbnH6lTcA0oqMZIRe7zQesoRfMd96KhkURmI4/KJHI9R9unFWMuRT2pF9E8wf4oOnQFUv8rybXf9+PLH9Bj7It87NvR+pxFaJwtLBUySDxmo2c+GAXFJNMDuWr8YhlaeQe0likoYOBR53Nn1OgB3d9r0D2/D4lidySI69HY69U5tvdD4oskuNGqG4C/Jdh7sfN5BipvnR07Z3p833Dasnbk1cMUnfnaFhj3JFw5FPp2hBV7Na0hBtxznMQM4N+mwLMbYOYWGPsEXDBQy53N3aa5hh3bwb0nNr7Gr0+Ci1+W4L26WYJ6uE5zDSsPKgr19pw6PD5yNojf800ofgDUkDsPfwlXPmg9F6Fl015CZchdNq0CedzOyrkFPolgd+BraJHUFaiSKUG9q9MJv2sxzByD5tgtQi2n7mj1hTOdz2Fir5PG8BZA0MIEU/wwxmEL8F7Svl3Exyl6EhdBUJ69BfX8VqPeX1cUTXwuub/nW4hP2nfZTXz8pAfxys/dV413xefS+sqvsABeuAB+sxweW6tl0Q7VaQzvokHwrQlwXkLxHtAZ3r8C/mOpFt3+42pNeu/XSdGlt0+GsT0aX+OcAfDu5fCfy+CNrXDfcmhXoOjTOyZrHmGPEnJIFRpeSGSPs4Geud8iGK580HpKgS+jxvEaVKa6opgLfxbQLojFYt4HCgqcA3fn3IjsELZghJYIeyRkImGfZ5hMmHq/LZFf+TZ20/eCNiFtCh68M2gTMsTqhNxwFwCxWMwzDDYMjmHDMAzDCAQTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZDERNAzDMCKLiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZ0nipbn6978zIBfn0njOA/UEbkAFFQRuQEfn0jr7YKXcFbUJGFMz9ZdAmZEA+vbOzeawnaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBYTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZEnjLRLZYDlQAWwDqoCjwETgKn8unxFhtHUZsA7Y6mw1wBTgGo9zdwIfAKuAXcBB9BaIQcCpwIjcm5uRvfXA2855W4Dtzr6rgON9sDUVh4CPgNUoLxwA2gG90W+ZChQEZVwKfgHsTXGsC/A9/0xpkeDKWSwGD27T9uEhiAHjOsJNfeDmvlCY8FiXVcO9W2BhNWyqgf310LsIxnSEr/WDK0uhoIVssLMWJi6Cqlo4pSvMmZSNX7EEWIvKzBZUxqYB13mc+yjwXgvfNxL4ajYM8+AgsvcDZOteVJYGACcCJ9G4P7YL+Pdmvu9Y4EtZs84nEXwTZfZi9AqOnf5ctlWE0dZZSCSKge7AjmbOfQVYiirrMUAn5/wVznYpcEoujSUze48Czzmfuzjbvpxalx7LgeeRPcNQXqhG9/BZYA3wKcInhB1QpZJMid+GtEBw5ez6VfDXnRKzz/aCToXw6l746jqYdwAeGR0/d+FBeHo3nNgVTu4K3dtD1VF4djd88iP4XK/G53vxL2vhYH22f8VrSFBKUBnb3sy5xwClKY4tRKIzNqvWNeZ94DFk52igJ2pULgb+gsraTTQtSwMBrxZD/6xa55MIno8yeilQCTzsz2VbRRhtvQRloDLUw3qgmXNHA6ejVlYi64A/AC+gFncu3weWib1FwBeBfo5NrwIzc2hbupShnutoGhfOs9HvcRsV4/03rVk6IBvDTjDlbMYuCeCwEnhnMpQ7r3M82iBR+9MOuKIMrirT/s/2ghv6NP2e/XVw4lKd/41+cHxX7+s9sh3+vgt+Oxy+ti6bv+RyVMbKUY/wd82cO9HZkjkMvI56Zcdl07gk+gBfQWKc2OO7DPg5sAgJ4tSk/xuI6pLc4tOY4DBUqYSt1exFGG0dgTJ7OjZNp6kAAgx3tnpU6eSSTOxtj3qsYXtJ5zBkV/Jv6ILuMcidZ7SOYMrZjF1KbxsQF0CA4kL4yWB9vm9rfH9JihqyW3s4v4c+rz7sfc6GGvjWOvhSb7iwZ5vM9mAk0Iu23b/30EvTJ6J8nSvGoB5d8s3sDpzmfF6Vw+s3j089QSMcFCalRusI832sQ63qvcjV2BcYSjht9Z+qWqXDOzQ95u57a796hsXN3LJD9TDL8dpP7Nz0eCwGN6yW+/RXw2B3Xdvszg0LnNTLfe4X7ZLSRPYCb6FhiM6o4TQw6xaYCEaGPchtUoQyk9E6GtCYK6g1HjYOAk8m7euJAk7suZc7Nd76I02PrXP21cX0eWyn+LE1h+HPO6A+Bttq4fk9sOUo3DEQJnmI4H9vgdn74JUJ6jWGTwQr0Lh9L4LLx/XEhdhrWOEjZ0tkFPAFUo9xZo6JYCSoQwPTdcCFKFjGaB2voSCEUYRPBKcBQ9AYTDFq+MxHbq9HgJvR2Gt0ubgnPLoTfrUFrimHUsclWtsAd26Mn7cnSbTWHIG7Eo4XF8B/DoXbPGI0lh+C72+Ar/SFc3pk+xdki/lOekKANjyNgnsm0FgEi1E9NRkNqwBsRoFqq4B7ge+TrWAvE8GPPQ3A42gccBLwiWDNyWsWoOkc5cCVAdvixVlJf/dBARTFwFwUtesVQh8drumlYJaX98L4RXB5KXQohNf2wtZaGFyisbzCpKG2C3pC7BSJ5YYa+MsO+H4lvLEPnhobd53WNsDnVkG/Ivj5UJ9/XNocRlMWch0Q0xyvowC4PsANSce6oij2REYB3wR+iXqxc2ma31uHDRR8rHEFcBkSwM8QroCffOId4CXkPvoCmnuZL7jzLSuCNCIUtCuAZ8fBPUOgVxE8vF3bqI4wbyJ0dYamehd5/39RIYzoCD8cDD8eDM/tgV8nBNL8v02wqBr+OAq6eA1zhYKFxOdl5jIgJhWzgSeQV+IWNN6XDu2IT+9akzVrrCf4saUeuUCXocndn8baPK1lPvAymnv5edIvtGHBtbc2UCvCQlEh3D5QWyJHGhTpWd4ehnkEziRzYU+4o1Jjf99xArLfr9bk+zM+8P6fuQegYC50bwd7T2zTz2gDQQbEzEJj1v2Bb6NeXya4on00axaZCH4sqQP+iiahTgOuxgSwtcxBbpu+wOfIz/FUdzAr63H6Hyse2wFHY5obmA6ba5S2T3CunNsjHnyTyMEGeHwn9CmCS3pCp8B6iZVoHC6IgJhX0DjgQOBbtK4Xut5Jy7Jkk4ngx5A64E/ASjSf7SpMAFvLG8h10w8JYJhdoNuBHmj8L5E9xFfkmeynQaFlf50iNhNZfBC+WwE928P3EqbZvncApnt0VnbUwvec6bYXJ7Qtvp4i7qjiiERwZAd4cFSbzG8jbkCM393QF1A+HIzG9przpmxAQplcb32EepKQzSUVfRLBxFDXg066CbUKQK3r8/wxpUXCaOuHzpZo0wbgb87nzsDFzucZSAA7o8moXquvDCe3a4hmYi9IaNxln9wBloXEx7CG4v86oouRXQWo4C7wOKcHcjWHgWUoWGAosqsE2I3yQh1a+ebUgGzzIrhydu6H0LEQjumkMcAVhzXloWOhxgv7JwQd3rQWdtVqRZjBxRpTrKiBF/bA4Qa4ohRu9FhRJvcsQ2txgpYgA/XyHnU+d0YrsiRyBOXr9sQXfPCD+UgAC1Hv83WPc8qIu2efQvXBcOLei80oL4OCZrJXf/kkglUoGimRPc4GqqzDIoJhtHULWn8vkd3OBqr0Lk7YD5pg2tzyY7kUwUzsBWXu9UnnV9J4ZRu/RXCvk8bwFkDQdIQpfhiTBsPR+ptbUYPjKFpCzbVxCuEKigqunF1dBo/t1Ly/ww0woBhu7qM5fwOTou6/019rh75/EF6ulbu0vD2c1V3rhn66vOUFtHPDFpouir3L2UDikSyC76N8MQV/A2LcdWEbiPfkkhlFXASPR3mjEg3p1KOxw2nAGWTbjVsQi8W8DxQUOAfuzOoFDZcwu9bynRTrWIWSFGGIoSV/gmtip9wVtAkZUTD3l0GbkAH5VH99DYBYLObZXLHBIsMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZDERNAzDMCKLiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCwmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyOLTS3X9IJ/ebwUwIGgDMmB7y6cYrSSQ15K3gYqgDUibgrn59S7U2H23BW1C2hR84+6gTcga1hM0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBafFtB+FdgK7AIOOZftAYwBjgc6+WNGI5YB6xy7tgI1wBTgGo9z64G3nfO2oAWl64GrkP1+8BiwHqgCDgDFQDkwDTgX6OrxPw3Am8AcYCNQi+77cOCTQL8c2boEWIvu1RZ0b6cB16X5/48D7zif70C/MwhiwLvOts35uzdwHHruQbQh/4YWsa4CDqJ8UAZMBc4BuiScuwt4HqgEdqKy1wXoBZwGnERwa+iHsU5IxXJ0z7eh+34UmIjKf+55/gO4dzYsr4Jd1dCvGxw7GG49E04aHj9v4x74f6/Awg1QuRv2HIayTjCiF9x4Ilx/PBS1a/zdm/bAwwtg8WZYtBHW7YJYDFbfCSN7+fLzHNYC81E9dRg9/z4oj47J6ZV9KgHzUYU7HOiMMtFm4A3gfeBLQHd/TPkns1AhLHauvaOZc48Czzmfuzjbvpxa15SXgKHAMUA3JCxrgBnAbOBOVBm6HAH+CxXgIajSKwL2ACtRYc6VCL6GxK8E3dtM3kLxIRLAEvQbg+RxYDF63pPR/VsDPI2E5TMB2PQKep4TiOeDtcAzqDz9gHg+2IHK3nDUCOmMhHMZ8BAwD/gOkFQz+kIY64RUvIkEsBjd852+Xfn2p+Hnr0FZZ7hiEpR3gTU74Jml8NRieORzEjeAtTvgL+/CCUN1bmlnieaLy+HGv8Cf3oVXvg7tEx73exvgB89BQQEMK4PuHWDvYd9+nsNLqKHeDRiLBLAa1SHr+ZiI4B0pLjUT/fg5wMX+mPJPLkGFrAz1CB9o5twi4Iuo0HZDrdiZuTYwid+jQpjME8A/gGeBGxL2P4QE8IvAWR7/V5dl+xK5HN3bclRB/y7N/zuIfs8U1Ntdmwvj0uQDJIClwNdRRQ26b38GFiEhOsZnu36H8mMyT6GG2vPA5519I4H7aNpjrQN+CXwELMQ/b0YiYawTUnE+KvelqPHzsC9XrdoPv5gJfbrC0u9D7wRnz+ur4Kxfww+fj4vgycNhz8+hMOlx19bDeffpf/6+BD49LX5s+mB48xaYPAC6dYQz/hveWJPrX5bIu+hZT0X1RnKeqM+5BT75c1Jp7QQn3e2PGY0YgSrpgjTObY9aI91yalHzeAkgxCuwqoR9Fch9ewLeAgi5bf+MRC63dO5tIk84qT9upub50ElPIy6AoPt2nvN5nq8WCS8BBLloQT0Wl/Z4F/H2qNJJPt9PwlgnpGIYaixnmp/bRuVuaIipZ9c7abTjzNHQtQPsOBjfV9y+qQCCXKBXTNLn1UlOmYE94bSREkD/qUNeo+54CyD44aUI+KW6q5y0d6BW5DeLnHRwwj63cj4JjbcsQmMvXVAlE8YXub6Del9fpLHoBIVbu5R6HHP3VaCCHIZ3Uy920kFpnNsALM3gfD+xOsFlVC8J2zuVsPOgXKEub66BA0fi4tYc9Q3wgtOmmxSqd3mvQW7Pk1EDYyVqlLUHBtK4TssdPpfeecj3fwSNx21AFfKp/pqR1zyPxoEOIX/5KlSRXZJwzjon3QncRrxCB2W2s5DLLCzBwbvRmNax+O9eTIUbmOHVI3H3NTifg6iwX0T54DDKB6tRPrjI49wDyM0Ycz5/iMZpT0Su5yCxOiEVpZ3hPy6HW/8O4++W4JV1hrU74R/L4NyxcP9nm/7fzoNw3xt62jsOwqsfaRzx2ulw6UTff0YzbHbS9sBvaeqVGAp8llw3igMQweqEv0eibnAYWv75wos0DsqZBNxMY1ftASf9KxKWq1HvZS3wR1QhdiMcbscGFPlaDFwRrCmNGIuiXOegoBhXFOvRmLCL71EEDi8B+xP+noiCSbxc9gdRI8OlALgARQgHjdUJzXHLmTC0VIEtDyR430f2ghtOaOomBYngXS/G/y4ogO+cDT+7LPf2Zob73Oeg4ZObUNzFHpS/1wCPOvtzh88i+B0nPYhCYWcC9wPXkrtIxY8b9znpPtT6fxxFBN6GWk4gYQHd028Q7/FNAL4J/DsS08sI3pX3JhLnmwhXWPxk5EZeBfwKGI/u1RrUyOgB7MXvcaI49zrpPmTTk8CPgG8Tzwcu/VDjpwFVMAtRhOtq4BYaT6vwG6sTmuPnr8L3n4VvnQ7fOB36doOPtsEdz8B1D2tqw8+vaPw/Y/tC7D65QTfvhRlLFEAzZy08/1X1MMOBW08VAtcDPZ2/+6Ln/99oyGEDuXSNBuQP6wKMQz/8MArzNzKjOzAduB1VIP+bcMwVk6k0fcRDUKvrCHF3RFDsQGJ8HMoPYaIQ+ALqMXVGYfvvo2Cqr6IpHBCsgIDywbHE3d4PNnNuIQrwOA/9trWEp+xZnZDM7FVw+zNw2UT41SdheDl0KoZpg2DGzTCgB/xyJqxLMWOjXSEMLoVvnwn3XwPzKySG4cGNxulHXABdioFRzudNObUi4G5AD1QhV6ExrjD1BPKFcmAACt0+gCbN90PjgqmafO7+2pxb1zxVKLDEnZDuxf9z0huQy89P2gFnOFsitWi8tTPegTNBUA70R61mNx80h3svV+bSqFbQA6sTxHMfKD1zVNNjnYrh+CHq5S3aKIFsjgudoNvZq7NrY9twje6Q4rgrkrmtp4L2hREfvwrKrfRxYI+Tur2+Y4C5eLegaokPQAe1EotLKannqK1AeWMy6nWFRWxAY4X1yLYwsddJ03HwJOeZMGF1AkCNM5U3cRpEIu7+4jRq8c17lbYP1eMejp7xduQaTTbOradyW/Z9uCW7kOstmRjy/1ejqLZAJqrkCVtRqziZBjS3bj9yHbg9vOnIvTCfphPOn3a+axxqdQfJALTqitfmRlxe5PwdRGy3V77dgly4HWnaQ8w1bu8omQY0WX4/Cixx80EF8XGXRI6goCkIRsitTkiH00Yq/f3cuIi5vPghzF0HHYrg5GHa9/5GjQMmc7AGvv2kPl88oenx4OiJ5l/vQ/OaE1mNxro7EHeL5gYfeoKrUcYejCrdjiiTV6LWaBfg0tyb0YQPiU+IdptaG9DajKCKJHHFitnEl//a6qQLUUUDCkbI1cobSxy7RiNXURdU4X3k2NQdRQa6dAC+jAI67iYuimtRoEc34MYc2Qpalsvx5fyzVV+JIr1A9zZ0oWoe/AEVkb6oN7od3fMiNKbm9+IJS1EAzCiUDzqjfLASja92p/GqQf9A5W8kGgssRlM6liExHUkwq7KEtU5IxUfOBvG6YhNqUIJctueRba6eAueMgddWwri74cpJCoxZUQXPfag1Pu+5DMqcYekfvyhhPHkYDO4pl+nGPVo2be9hrShzx/lNr3PDnxJ+qdP5uv1pTcYHuOlkOHVE1n+ew6WoPn0R5eP+KA+sQL3EK0ntLs0OPojgcFTwNqAfe4T4or+T0KomQbT4tqBAh0R2E58D1oPGFcRKNB8rkUpnc8mVCE4ATkcCVokqsBJUOV+JCmBygMZEFC34DBL7Q+g3nYWmIiQPRGeTLcB7Sft2ORvOtfNBBI9BwrMIuZG7o2d8JsGsazkerWCzGpUnNx/0QROOkxfQPt05vh7l36Oowh6KgpFOI5h1Q8NaJ6SiCjVEE9lD3KXcnVyIYGEhvPA1+M2b8NhCmLEUDh2F0k5w0Xj41hlwXkI82ZdPhi4l8E6Fxv4OHYWenbTY9qenwo0nNV431OXhBU33/T3h554xKpci2B34GvA6Er5KlGfHoPw7MFcX/icFsVjM+0BBgXPgzpwbkR3CVGjSIVRLN7RAJgtgh4GgA34yIYyr9zRHRdAGfGyJ3XdX0CakTcE37g7ahAz4AQCxWMxzkDlUw6SGYRiG4ScmgoZhGEZkMRE0DMMwIouJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBYTQcMwDCOyfIzeJ5hvFAVtQAb48O7lrDIpaAMyYGnQBmTI4aANyICRQRuQIZUtnxISYtf/IGgT0qbgz0rtfYKGYRiGkYSJoGEYhhFZTAQNwzCMyGIiaBiGYUQWE0HDMAwjspgIGoZhGJHFRNAwDMOILCaChmEYRmQxETQMwzAii4mgYRiGEVlMBA3DMIzIYiJoGIZhRBYTQcMwDCOy+Ph6gP3A68AatBJ9F2AscDrQ0T8z0iJfbH0f+HsL5xQAP/HBlnSIAe862zbn797AccDxBNcmuwHYnuJYT+AvCX/vAP4GrHY+HwC6Af2Ac4GzyG2xWgasA7Y6Ww0wBbjG49ydwAfAKmAXcBDl30HAqcCIHNqZDmErZ48B64Eq9FyLgXJgGnq2XRPOvR+Y08L3jQfuyL6ZLfILYG+KY12A7+X06s9vgntXwvJ9sKsG+nWEY0vh1nFwUq/G5x6ohXs+hKc2QMVB6Ngeji+Dfx0PZ/dr+t0/WgJ3LUt97RfPggv6Z2avTyK4G3gIqAbGoIy1GViACsCNQCd/TGmRfLK1H3BmimOVqLIc7Z85LfI4sBgVxMnodVJrgKeRvZ8JyjCgM3C5x/7kyngrqrjHIBHpiirM94D/BmYBPwXa5cjOWY4NxUB3JMSpeAW9qqm3Y28n5/wVznYpcEqO7GyJMJazl4ChwDGoYVPj2DIDmI1eK1fmnHss0KvJN4i5qFEV5Cu9OgAneewvyelVb38ffr4cykrgioFQ3gHWHIBnNknoHjkZrh+uc/fUwKmvSCwndIevjIaDtTr3nJnw4InwpRRvw/rCcBjauen+kV2b7msJn0TwBZTZLwBOSNj/MjAfFexL/DGlRfLJ1n7O5sX9TjrdJ1ta4gMkgKXA15HoANQBfwYWARNQBRQEnYHr0zhvHOoJJvda64AfINGZC3wiq9bFuQSJXxlq5DzQzLmjUa9qQNL+dcAfUF6fiCp8vwljOfs9alwk8wTwD+BZ5DUAlSuvslUNPI+q1lzlgXToAJzt6xWrDsMvVkCfDrD0EujdIX7s9So46zX44dK4CP5oqQTwqkHw+GnQ3ilSPzsC01+Ab74L5/eDgR5id8NwOKNvduz2wf+0G1gL9EAur0TOQL2BpcDR3JvSIvlka3NUARtR5TYmYFtcPnTS04gLIKiyOM/5PM9Xi1pHEd7Fpj1wovN5Sw6vPwL1mjzfD5rEdJoKIMBwZ6snmBe5hrWceQkgxG2sSuM75iK7p9PYffrxp7IaGmJwQnljAQQ4sy90LYIdR+L7ZmxU+uPJcQEE/e+t4+BwPTy0Nvd2+9ATrHDS4TQtuCXAYFQgNjnnBEmFk+aDrc3xnpMeS3hinw46aanHMXdfBepRBfEm+1rU+9iBnvUw1CtN161ZT/y+D8u6ddmnMCn1kwonzZdytshJB6dx7mwnTTVM4Rd1yPOyF4l7X+Tqzd3zHtUVigvhnZ2w84hcoS5vbtP43xWD4vuqHEEc3qXpd7n7ZlbBDz28ynN2wHu7oT4mt+jZfRtfLxN8qG12OmlZiuOlKMPvIvgMn0+2pqIWZf5CJIJhwR3f2e1xzN3X4Hzu7YtFjdmDAgoS6Qv8f8hlmMw+5B5zPy9CPcAzaOzeCyN7UD4uIhjBDns5ex6NBx5CgTKrUDBRS+7Z1cgD0xcFxQTJQeDJpH09gavI1TMvLYH/mAq3LoTxz0rwykpg7QH4xyY4tx/cn1A0yktg62FYfxDG92j8XeucNvPK/d7X+vcljf8uKYTvjlevsiAdJ0kCPohgjZOmkml3oPZIiuN+kk+2pmIZsm8McjeFhbHAEhRRN5m4KNYDryacd9hnu0CRfxOAISgQpgoJ3EvAD4Ff0rQy3g/8NeHvAuCTwBdybWwbqUNRkHXAhQQT5BX2cvYiati4TAJupuWx09ed9Iwc2JQJ01Be7oN6gXvQOOt7wCPot6SKJWgbt4yDoV3gxrfhgTXx/SO7ahwv0U168QB4cA3cuRQeOxXaOZ3UHUfgvz7S5z1JHvHJPeGhk+CMPoo63X4EXtkCP1gCd3+gnuHPpmZmcxB+JyOnuC654wK1oimTUW9pFfAr1FJuj6LvDiDB3kt6Y13Z5rqkv4cC30SC+Hc0ReLfk84ZhII76lGPZR4K8PkQuItwjgc1oAjdSlSxBxm4EWbuc9J9qHf3OAp6ug3lDS8OocjWoANiQNN0EumDIp+L0ZjlLJrm+ezw8w/h+4vhW2PgG2Ogb0f4aB/csRiumwuL98DPp+ncH0+Cl7fAkxtgygtyaVbXwTMbYUAn2FANhUnVwZVJHunBneGmUTCtFE58WYE5t47LzDXqw4BAS626llqFfpJPtnqxDdiAWqxhmhoBympfQNGAndEcx/dRkMdXid97jwGCwLjIST9o5px2yH17BRLOj4A/5dasVuEK4DIkgJ8hmAYH5E85644CXG5H7sX/bebcfAiIcQN8KnLy7bOr4PZFcNlA+NV0GN4VOrWHaWUw43QJ2y9XwLoDOr9fJ3j3Qvj6aI0X/nYVPL8ZPjMUnnDaEckBNqmYVqb5hbUN8PbOls9PxIeeYLmT7kpx3B0PSjU+4Cf5ZKsXYQyISaQdchWdkbS/Fo0TdcY7cCYoujtpum45N2S+mdm8gVCPXKDL0MT6TxNs/si3claOomwrkdfCS+RmO2lyLyxMuFHZtTn59uc2Kz2zT9NjnZxJ8DM2wqI9EkiAPh3hvuPjfW+XWU4g7nEZZIFejmBW12Vkth8iONRJ16EVQhJbnzWo51IEDMy9KS0y1EnzwdZkwhoQkw5LUEU9OWhDknAGJkh3QpJbqedqonxrqENjl8vRWNHVBN9AGuqk+VTO9jip171bg2zui+aRhhVnTgI9c/LtNQ1Kd9R4H3enRxSnkf0eWaf02qHpXbu2Ad532k5e0abN4UNpKEVzm/YC7yQdm40q70mknqPjJ/lkazIfoKCSUYQrICYRrx7VFhSI0JFgAgo24G3XNuB3zufE1v0aJNjJHCbuLgvLeGwdcs0uR73UMAgghLOcbUXjesk0oMny+1HZ8pi5/c+AmKCnRYBWqvGaX7kHeM75nJvG5mlOUPfvV8PmpFv54maYuwM6tIOTnYV2GmJaISaZP62TCJ7cq/GUigO1sHJf0/OP1sMt72kMcWw3mJ6hA8GnwJiL0BJJL6GQY3eJpArk8giTCyGfbE0krAExifwBZbm+aFxoO+ptFaHxwiBWLnkTLYt1DBrb64gqxHdRZXIcCit3cXtV49GyWSVobuFCNG40Drkbc8WHxBcecOdebkCr2IAq6YudzzOAlc6+7sBMj+8bTjBriIatnC1B93A0eq5dkPB9hPJpd+BLHv93GAXEFKGFIIJmGRqfHIoawyXIvbwSNYpGo3Vjs8/Vg+GcvvBaFYx7Fq4cBH07wIp9cpXGgHumatoEwKE66POkpk6M6Krm2dwdGtMb1x2eOK1xYMyuGn3v9DId79dRvcvXt2maRXkJPHpq02CalvBJBEuBL6NW3hoUcdUVzacK26LU+WSry3Y0XhHGgJhEjkErgSxCrf3uaLD+TOLjb34zGVW+a5G4HUGiMR4tO3UWjd11F6A8sBL9lhpUYY5EleB55NYdugUFFCWym/g4Wg/iIujuq8ZbAF2CEMGwlbMJznVXobJ0CAlIX+BK9Fy9/GxzUR44kXAExAxH4+tbUePoKAowGoLGg6eQq4CowgJ44Sz4zUp4rFLjf4fqoLQYLhqgiNHzEha3LmkH1wyFOdvh1a3aN6ob/HQK3DJW44iJlBYr4vSdXYoq3X1UrtURXeD2CYoKTTeQJpGCWCzmfaCgwDlwZ+bfaqRBUdAGZEC+zaQJcuHiTFkatAEZEsQ8ztaSYvXl0BLEEnatI3b9D4I2IW0K/qw0Fot5qn8YBggMwzAMIxBMBA3DMIzIYiJoGIZhRBYTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZDERNAzDMCKLiaBhGIYRWUwEDcMwjMhiImgYhmFEFhNBwzAMI7KYCBqGYRiRxUTQMAzDiCxpvErJMAzDMPIbe5WSYRiGYSSRsidoGIZhGB93rCdoGIZhRBYTQcMwDCOymAgahmEYkcVE0DAMw4gsJoKGYRhGZPn/AXw+KQGDiN5WAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 224,
       "width": 224
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Confusion matrix.\n",
    "fig, ax = plt.subplots()\n",
    "ax.matshow(confusion_matrix, cmap=plt.cm.jet)\n",
    "\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        c = confusion_matrix[j,i]\n",
    "        ax.text(i, j, int(c), va='center', ha='center', color='black')\n",
    "ax.axes.get_xaxis().set_visible(False)\n",
    "ax.axes.get_yaxis().set_visible(False)"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "dff8b73526701c08e8c4b8ff311f76facea885c22db9ac0534f1f6f35e78fb53"
  },
  "kernelspec": {
   "display_name": "Python 3.9.13 ('venv': venv)",
   "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": "3.9.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}