01_Student_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Rhyme](https://rhyme.com/assets/img/logo-dark.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 1: Introduction\n",
    "\n",
    "Welcome to Basic Image Classification with TensorFlow.\n",
    "\n",
    "This graph describes the problem that we are trying to solve visually. We want to create and train a model that takes an image of a hand written digit as input and predicts the class of that digit, that is, it predicts the digit or it predicts the class of the input image.\n",
    "\n",
    "![Hand Written Digits Classification](images/1_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import TensorFlow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using TensorFlow version 2.16.1\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "# tf.logging.set_verbosity(tf.logging.ERROR)\n",
    "print('Using TensorFlow version', tf.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2: The Dataset\n",
    "### Import MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
      "\u001b[1m11490434/11490434\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m10s\u001b[0m 1us/step\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shapes of Imported Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28)\n",
      "y_train shape: (60000,)\n",
      "x_test shape: (10000, 28, 28)\n",
      "y_test shape: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print('x_train shape:', x_train.shape)\n",
    "print('y_train shape:', y_train.shape)\n",
    "print('x_test shape:', x_test.shape)\n",
    "print('y_test shape:', y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot an Image Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.imshow(x_train[0], cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\n"
     ]
    }
   ],
   "source": [
    "print(set(y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 3: One Hot Encoding\n",
    "After this encoding, every label will be converted to a list with 10 elements and the element at index to the corresponding class will be set to 1, rest will be set to 0:\n",
    "\n",
    "| original label | one-hot encoded label |\n",
    "|------|------|\n",
    "| 5 | [0, 0, 0, 0, 0, 1, 0, 0, 0, 0] |\n",
    "| 7 | [0, 0, 0, 0, 0, 0, 0, 1, 0, 0] |\n",
    "| 1 | [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] |\n",
    "\n",
    "### Encoding Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.utils import to_categorical\n",
    "\n",
    "y_train_encoded = to_categorical(y_train)\n",
    "y_test_encoded = to_categorical(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validated Shapes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_train shape: (60000, 10)\n",
      "y_test shape: (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "print('y_train shape:', y_train_encoded.shape)\n",
    "print('y_test shape:', y_test_encoded.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Encoded Labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 1., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_encoded[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 4: Neural Networks\n",
    "\n",
    "### Linear Equations\n",
    "\n",
    "![Single Neuron](images/1_2.png)\n",
    "\n",
    "The above graph simply represents the equation:\n",
    "\n",
    "\\begin{equation}\n",
    "y = w1 * x1 + w2 * x2 + w3 * x3 + b\n",
    "\\end{equation}\n",
    "\n",
    "Where the `w1, w2, w3` are called the weights and `b` is an intercept term called bias. The equation can also be *vectorised* like this:\n",
    "\n",
    "\\begin{equation}\n",
    "y = W . X + b\n",
    "\\end{equation}\n",
    "\n",
    "Where `X = [x1, x2, x3]` and `W = [w1, w2, w3].T`. The .T means *transpose*. This is because we want the dot product to give us the result we want i.e. `w1 * x1 + w2 * x2 + w3 * x3`. This gives us the vectorised version of our linear equation.\n",
    "\n",
    "A simple, linear approach to solving hand-written image classification problem - could it work?\n",
    "\n",
    "![Single Neuron with 784 features](images/1_3.png)\n",
    "\n",
    "### Neural Networks\n",
    "\n",
    "![Neural Network with 2 hidden layers](images/1_4.png)\n",
    "\n",
    "This model is much more likely to solve the problem as it can learn more complex function mapping for the inputs and outputs in our dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 5: Preprocessing the Examples\n",
    "\n",
    "### Unrolling N-dimensional Arrays to Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train_reshaped shape: (60000, 784)\n",
      "x_test_reshaped shape: (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "x_train_reshaped = np.reshape(x_train, (60000, 784))\n",
    "x_test_reshaped = np.reshape(x_test, (10000, 784))\n",
    "\n",
    "print('x_train_reshaped shape:', x_train_reshaped.shape)\n",
    "print('x_test_reshaped shape:', x_test_reshaped.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Pixel Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 9, 11, 14, 16, 18, 23, 24, 25, 26, 27, 30, 35, 36, 39, 43, 45, 46, 49, 55, 56, 64, 66, 70, 78, 80, 81, 82, 90, 93, 94, 107, 108, 114, 119, 126, 127, 130, 132, 133, 135, 136, 139, 148, 150, 154, 156, 160, 166, 170, 171, 172, 175, 182, 183, 186, 187, 190, 195, 198, 201, 205, 207, 212, 213, 219, 221, 225, 226, 229, 238, 240, 241, 242, 244, 247, 249, 250, 251, 252, 253, 255}\n"
     ]
    }
   ],
   "source": [
    "print(set(x_train_reshaped[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_mean = np.mean(x_train_reshaped)\n",
    "x_std = np.std(x_train_reshaped)\n",
    "\n",
    "epsilon = 1e-10\n",
    "\n",
    "s_train_norm = (x_train_reshaped - x_mean) / (x_std + epsilon)\n",
    "s_test_norm = (x_test_reshaped - x_mean) / (x_std + epsilon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Normalized Pixel Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{-0.38589016215482896, 1.306921966983251, 1.17964285952926, 1.803310486053816, 1.6887592893452241, 2.8215433456857437, 2.719720059722551, 1.1923707702746593, 1.7396709323268205, 2.057868700961798, 2.3633385588513764, 2.096052433197995, 1.7651267538176187, 2.7960875241949457, 2.7451758812133495, 2.45243393406917, 0.02140298169794222, -0.22042732246464067, 1.2305545025108566, 0.2759611966059242, 2.210603629906587, 2.6560805059955555, 2.6051688630139593, -0.4240738943910262, 0.4668798577869107, 0.1486820891519332, 0.3905123933145161, 1.0905474843114664, -0.09314821501064967, 1.4851127174188385, 2.7579037919587486, 1.5360243604004349, 0.07231462467953861, -0.13133194724684696, 1.294194056237852, 0.03413089244334132, 1.3451056992194483, 2.274243183633583, -0.24588314395543887, 0.772349715676489, 0.75962180493109, 0.7214380726948927, 0.1995937321335296, -0.41134598364562713, 0.5687031437501034, 0.5941589652409017, 0.9378125553666773, 0.9505404661120763, 0.6068868759863008, 0.4159682148053143, -0.042236572029053274, 2.7706317027041476, 2.1342361654341926, 0.12322626766113501, -0.08042030426525057, 0.16140999989733232, 1.8924058612716097, 1.2560103240016547, 2.185147808415789, 0.6196147867316999, 1.943317504253206, -0.11860403650144787, -0.30952269768243434, 1.9942291472348024, -0.2840668761916362, 2.6306246845047574, 2.286971094378982, -0.19497150097384247, -0.39861807290022805, 0.2886891073513233, 1.7523988430722195, 2.3887943803421745, 2.681536327486354, 1.4596568959280403, 2.439706023323771, 2.7833596134495466, 2.490617666305367, -0.10587612575604877, 1.5614801818912332, 1.9051337720170087, 1.6123918248728295, 1.268738234747054, 1.9560454149986053, 2.6433525952501564, 1.026907930584471}\n"
     ]
    }
   ],
   "source": [
    "print(set(s_train_norm[0]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 6: Creating a Model\n",
    "### Creating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Rasika Srimal\\AppData\\Local\\Programs\\Python\\Python312\\Lib\\site-packages\\keras\\src\\layers\\core\\dense.py:87: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead.\n",
      "  super().__init__(activity_regularizer=activity_regularizer, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense\n",
    "\n",
    "model = Sequential([\n",
    "    Dense(128, activation='relu', input_shape=(784,)),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense(10, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Activation Functions\n",
    "\n",
    "The first step in the node is the linear sum of the inputs:\n",
    "\\begin{equation}\n",
    "Z = W . X + b\n",
    "\\end{equation}\n",
    "\n",
    "The second step in the node is the activation function output:\n",
    "\n",
    "\\begin{equation}\n",
    "A = f(Z)\n",
    "\\end{equation}\n",
    "\n",
    "Graphical representation of a node where the two operations are performed:\n",
    "\n",
    "![ReLU](images/1_5.png)\n",
    "\n",
    "### Compiling the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\">Model: \"sequential\"</span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1mModel: \"sequential\"\u001b[0m\n"
      ]
     },
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      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Layer (type)                    </span>┃<span style=\"font-weight: bold\"> Output Shape           </span>┃<span style=\"font-weight: bold\">       Param # </span>┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ dense (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                   │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">128</span>)            │       <span style=\"color: #00af00; text-decoration-color: #00af00\">100,480</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_1 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                 │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">128</span>)            │        <span style=\"color: #00af00; text-decoration-color: #00af00\">16,512</span> │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_2 (<span style=\"color: #0087ff; text-decoration-color: #0087ff\">Dense</span>)                 │ (<span style=\"color: #00d7ff; text-decoration-color: #00d7ff\">None</span>, <span style=\"color: #00af00; text-decoration-color: #00af00\">10</span>)             │         <span style=\"color: #00af00; text-decoration-color: #00af00\">1,290</span> │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mLayer (type)                   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mOutput Shape          \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1m      Param #\u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩\n",
       "│ dense (\u001b[38;5;33mDense\u001b[0m)                   │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m128\u001b[0m)            │       \u001b[38;5;34m100,480\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_1 (\u001b[38;5;33mDense\u001b[0m)                 │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m128\u001b[0m)            │        \u001b[38;5;34m16,512\u001b[0m │\n",
       "├─────────────────────────────────┼────────────────────────┼───────────────┤\n",
       "│ dense_2 (\u001b[38;5;33mDense\u001b[0m)                 │ (\u001b[38;5;45mNone\u001b[0m, \u001b[38;5;34m10\u001b[0m)             │         \u001b[38;5;34m1,290\u001b[0m │\n",
       "└─────────────────────────────────┴────────────────────────┴───────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Total params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">118,282</span> (462.04 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Total params: \u001b[0m\u001b[38;5;34m118,282\u001b[0m (462.04 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">118,282</span> (462.04 KB)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Trainable params: \u001b[0m\u001b[38;5;34m118,282\u001b[0m (462.04 KB)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"font-weight: bold\"> Non-trainable params: </span><span style=\"color: #00af00; text-decoration-color: #00af00\">0</span> (0.00 B)\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1m Non-trainable params: \u001b[0m\u001b[38;5;34m0\u001b[0m (0.00 B)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.compile(\n",
    "    optimizer='sgd',\n",
    "    loss='categorical_crossentropy',\n",
    "    metrics=['accuracy']\n",
    ")\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 7: Training the Model\n",
    "\n",
    "### Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/3\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m11s\u001b[0m 4ms/step - accuracy: 0.8186 - loss: 0.6114\n",
      "Epoch 2/3\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m6s\u001b[0m 3ms/step - accuracy: 0.9432 - loss: 0.1987\n",
      "Epoch 3/3\n",
      "\u001b[1m1875/1875\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m8s\u001b[0m 4ms/step - accuracy: 0.9586 - loss: 0.1444\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.src.callbacks.history.History at 0x2c63ffa40b0>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(s_train_norm, y_train_encoded, epochs=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 3ms/step - accuracy: 0.9539 - loss: 0.1523\n",
      "Test set accuracy: 96.05000019073486\n"
     ]
    }
   ],
   "source": [
    "loss, accuracy = model.evaluate(s_test_norm, y_test_encoded)\n",
    "print('Test set accuracy:', accuracy * 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 8: Predictions\n",
    "\n",
    "### Predictions on Test Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1m313/313\u001b[0m \u001b[32m━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[37m\u001b[0m \u001b[1m1s\u001b[0m 2ms/step\n",
      "Shape of preds: (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "preds = model.predict(s_test_norm)\n",
    "print('Shape of preds:', preds.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rb5yAb6lcubJHeVq79dZbvTLPjh07bFn58uW9MndGwxVaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR2JTqBQwbbbQtGlT49j9+/cb8xIlStiyIUOGpKwwwIsqVKiQpsd7+OGHjXmhQoWM+bFjx4z5jBkzvFZTaihQoIAt69evXzpUgptZtWqVMXe19oC09swzzxjzPn36uD1H8+bNjbmrje1SOlYyv4/ydA5XunXr5pV5gLTmapM3V7krmXUDKBOu0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSDS0AAAAAwJHY5TgF9u7da8s2btzo0RyjR4+2ZcWLF092TcC/NWvWzJbNmTMn7QvxwFdffZVqcwcFBRlzf3/3f7fXsmVLY37HHXd4VEvt2rU9Go/0M3v2bGN+7do1W1a5cmXj2Hr16nm1JuDf2rRpY8yHDx9uy06ePJna5aRI3rx5jXmZMmWM+ccff2zMXe2MD2R0fn5+HuXgCi0AAAAAwKFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj0dACAAAAAByJXY7dcPDgQWPeuHFjt+cYOXKkMW/RokWyagLcMWvWLFtm2vVSkq5cuZLi4+3cudOYz5gxI8Vzd+rUyZhHRUW5PccDDzxgzF3tngnf8vfffxvzRYsWuT3HQw89ZMwDAgKSVRPgDlfPg19++aUtc7XT/TvvvOPFipLvtddeM+Y9evRI40qA9HHp0iWPxoeEhKRSJc7BFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHYlMoN4wfP96Yu9osyqRevXrG3M/PL1k1AcnVp0+fND/m9OnT0/yYgKeCgoKMea5cuYx5q1atbFnPnj29WRKQInXr1nUrk1xvdDlhwgRjPm/ePFt23333Gcd27drVmFuWZcvKli1rHAv4ismTJxtzV69F/fv3T8VqnIErtAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCR2Of6XVatWGfMPPvggjSsBAKQ1V7scr1mzJo0rAdJe06ZNPcoBpI5q1aoZ8xdeeMGYN2jQIDXLcQSu0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSDS0AAAAAwJHY5fhffvrpJ2MeExPj9hwlSpQw5jly5EhWTQAAAAB8w7x589K7BMfhCi0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj0dACAAAAAByJXY5ToFKlSrZs6dKlxrHh4eGpXA0AAAAA+Bau0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSm0L9y6uvvupRDgAAAABIP1yhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCS3NoWyLEuSdP78+VQtBviv62vu+hpMD6x/pCfOAfgy1j98HecAfJm769+thjYmJkaSFBkZmcKygOSJiYlRWFhYuh1bYv0jfXEOwJex/uHrOAfgy262/v0sN37lEx8fr+joaIWGhsrPz8+rBQI3YlmWYmJiFBERIX//9LlDnvWP9MQ5AF/G+oev4xyAL3N3/bvV0AIAAAAAkNGwKRQAAAAAwJFoaAEAAAAAjkRDCwAAAABwpDRraOt/Wl+9vuuVVofLEIq9U0zvrH0nvctABuGL54AvPmaY+eJa4DUA/8Y5AF/G+kdqSrOGdlbbWRpy95Bk//yhc4fUfHpzZXsjm/KPyK+Xv39Z1+KvebHCjGXgioHyG+Rn+y/7sOxeP5bfID/N+X1Oiucw/Tfi5xHeKTITSOk58Pyi51V1QlVlHZpVlcZV8l5hGdS2o9v06DePKnJMpELeCFGZD8vo3bXvpsqxvPGi8+aqN1Xt42oKfTNU+UfkV+sZrbXr5C7vFJgJpGT9p+VayCguXbukJ+c8qfJjyytwcKBaz2idasfyxvr/8eCPuu+L+xQxKsIrrymZUUrOgVN/n1LTqU0VMSpCWYdmVeSYSPVY2EPnL2fu7wXdfmy76kyuo+ChwYocE6nhPw9PleN4Y81alqX+y/ur0KhCCnkjRI0+a6Q/Tv3hnQIzgZS+B7ru1N+nVGR0EfkN8tPZS2dTXpgD7Dm9R6FvhirXW7lSZX5vP2d3m99NfoP80rSZd+t7aL0hPCQ82T8bFx+n5tObq2COglrdabWOxBxR+zntFRQQpGENh3mxSrsrcVeUJSBLqh7D5KWaL6nbHd2SZA0/a6hqEdXSvBZ3HHnxSJI/L/pjkTrN7aQHyj6QThVlPCk5B67rWKmj1v21TtuPbfdCRe5Jr3Ng05FNyp8tv6beP1WRYZFafXi1uszrogD/APW4s0ea13MzKw+uVPdq3VUtopquxV9T32V91XhqY+18dqeyZ/H+L6KcJiXrPz3XQnqt/7j4OIUEhuj5O5/XN799k+bH99SFKxdUsUBFdazUUW2+apPe5WRIKTkH/P381apUKw1tMFT5suXTntN71H1hd52+eFrTH5juxSrt0uscOH/5vBp/3liNbm2kcc3HacfxHer4bUflCs6lLlW7pHk9NzP85+F6b917mtJ6im7JfYteX/66mkxtop3ddyo4MDi9y0t33ngPJEmd5nZShQIV9FfMX16Z72bSa/1fdzXuqh795lHVKVpHqw+vTrc63DX7t9la++daRYRGpO2BrTRSb3I9q+einsn62YW7F1r+g/ytozFHE7OxG8ZaOd/MaV2+dtmjGrov6G51X9DdyvlmTivP23msfkv7WfHx8YljosZEWYNXDLbazWpnhQ4LtTrM7mBZlmWtOrjKqj2pthU8NNgqMrqI9dzC56zYy7GJP3cs9pjVYnoLK3hosFXsnWLW1G1TragxUdaYNWOS9Zj/a+uRrZYGyvrxwI8e/Vz0+Wir2bRmiXVN2z4tSV1RY6IsDVTif1FjorxSb6svWlkNpjTwylyZRUrOgX8bsHyAVXFsxWT9bIfZHaxWX7SyBi4faOUdntcKHRZqdZ3XNcl5dP086bmop5Xn7TxW/U/rW5ZlWTuO7bCaTm1qZX8ju5V/RH7riVlPWCcunEj8udjLsVa7We2s7G9ktwqOLGiN/Hmk1x7zdc/Of9a6+9O7PfqZ85fOW49985iV7Y1sVsGRBa3Rq0cnqave5HpJzgEN9M7T4vHY45YGylp5YKVX5nO6jLAWnPoacP28TY70WP8aKGv2b7NTPE9m4+1z4N2171pFRhfxuAannAMfrf/Iyv1W7iSvT68secUq9X4pj+ZJi/dB8fHxVsGRBa0RP49IzM5ePGtlHZLV+mLHFx7Plxl5Y/1/tP4jq97ketbSfUstDZR15uIZj2twyvq/rs/3fawnZj1hTd4y2Qp7M8zjn0/LPuDPc39ahUcVtn459otXeyB3pNkV2v/qNr+bpm6fesMxsX1jJUlr/lyj8vnLq0COAol/16R4Ez2z4Bn9evxXVS5U2e3jTtk2RZ0qd9L6zuu1MXqjuszvoqJhRfV01acTx4xcM1L96/bXgHoDJEl7T+9V06lNNbTBUE1qOUkn/j6hHgt7qMeiHprcarIk6ck5Tyo6JlrLOyxXkH+Qnv/ueR2/cDzJse+ddq9WHVzlsraoXFH69dlfjX83cfNE3ZbnNtWJquP2Y5Wk9nPa6+TfJ7WiwwoFBQSp9+LeSera8PQG5R+ZX5NbTVbTEk0V4BcgSVp1cJXunXbvDece32K8Hq/wuC0/FntMC/5YoCmtp3hUq6/x5BzwpqX7lyo4MFgrOqzQgbMH9NS3TylPSB690fCNxDFTtk3RM3c8o587/ixJOnvprBpMaaDOVTprTJMxunj1ol754RU9/PXDWtZhmSTp5SUva+XBlfr2kW+VP3t+9V3WV5uPbFalgpW89pjPXT7n8W95ey/urZ8P/ay5j8xVgRwF1H95/yR1zWo7SxXHVVSXKl2SPA8cOndIZT8se8O5+9bpq751+rqsVfLeb6Uzm/RYC5JzXwOSK73WP24uJedAdEy0Zv02S/Wi6nl8XKecA2v+XKO6UXWTXB1rUryJ3v75bZ25eEa5Q3K79XjT4n3Q/rP7dTT2qBrd2ijx78KCw1S9SHWtObxGj5R7xK1afYmn63/niZ0a/ONgreu8TvvO7Ev2cZ2y/iVp2f5l+nrn19rabatm/TYrWY83rfqAeCte7Wa308s1X9bt+W9PVq0pkW4N7eC7B+ulmi+5NfZo7NEkzaykxD8fjT3q0XEjc0ZqTJMx8vPzU6m8pbTj+A6NWTsmyUJucEsDvVjzxcQ/d57bWY+Xf1y97uolSSqZp6Teu/c91fu0nsY2H6tD5w5p0Z5FWt95vaoVTrgl+JOWn6jMh2WSHHvifRN18dpFl7UF+QcZ80vXLmnajmn6X+3/efRYfz/5u37Y94M2PL1Bd0TckVBDy4kq+X7JxDH5sueTJOUKzqWCOQom5ndE3KGt3bbecP4C2QsY8ynbpig0S6jalOG2sxvx5BzwpiwBWTSp1SRlC8qm2/PfrsF3D9bLS17WkAZD5O+X8LH6kuElNfyefz6rNPTHoapcqHKSW/wntZqkyDGR2n1qtyJCI/TJlk809f6panhrQ0nSlNZTVGR0kSTHTsljXn14tb789UsteGyB2z8TczlGU7ZN0fQHpifWNbnVZEWM/udWmPCQcAX4BSg0a2iScyAiNOKm54Crhireilev73qpVmQtlctfzu16fUlar4XrnPgakFzptf7hnuScA49+86i+/f1bXbx2Uffddp8mtpzo8XGdcg4cjT2qW3LdkuTv//3ez52GNq3eB11/L/rf90UFshfQ0QuevU/1FZ6s/8vXLuvRbx7ViHtGqGhY0RQ1tE5Z/6f+PqUn5zypqW2mKmfWnMl6rGnZB7z909sK9A/U89WfT1atKZVuDW3+7PmVP3v+ND/uXUXukp+fX+KfaxSpoVFrRikuPk4B/gm/lbij0B1JfmbbsW3afmy7pu2YlphZshRvxWv/mf3afWq3Av0DVTWiauLfl85bWrmCcyWZp3DOwsmqefZvsxVzJUYdKnbw6Od2ndylQP9AVSlUJTErEV5CuYNv/iIQEhSiEuElPK5VkiZtmaTHyz/OZ0ZuIr3OgYoFKipbULbEP9coUkOxV2J1+NxhReWKkiRVLVQ1yc9sO7ZNy/cvV45hOWzz7T29VxevXtSVuCuqXqR6Yh4eEq5SeUslGZvcx/zL8V/UakYrDag3QI2LN3b75/ad2aer8Vd1Z+E7E7Ow4DCVylPqBj+VINA/MNnnQPcF3fXL8V/0U8efkvXzviCt18J1TnwNSK70Wv9wT3LOgTFNxmhAvQHafWq3Xl36qnov7q2Pmn/k0Ry+dA6k1/sg3Jwn6//Vpa+qTN4yeqLCEyk+rlPW/9PzntZj5R9T3ai6njy8JNJq/W+K3qR3172rzV03J/m3TUuOuOW4YI6CWv/X+iR/dyz2WOLfedt/N3CJvRKrrlW7Gn/rUDSsqHaf2u3WvMm93WzilolqcVsL21Xq1JTcW45XHVylXad26csHv0zN8jKF9Lrl2B2mc+C+Uvfp7UZv28YWylFIe07vcWve5DzmnSd2quFnDdWlShf1q9vPreN4Q3JvueyxsIfm/zFfPz75o4rkLOLiJ5GR10JGew1ID9xynPqScw4UzFFQBXMUVOm8pRUeEq46k+vo9bqvq1BoIa/WlhHOgYI5CurYhWNJ/j413/v9lyfvg67Xc+zCsST/Wxy7cEyVClRKzTIdy5P1v2z/Mu04vkMzB8+UlNBMSlLe4Xn1Wp3XNOjuQV6tLSOs/2X7l2nurrkauXqkpH8a6MDBgZpw3wR1rNzR3YeTLJ6s/1WHVun4heMqOqZo4t/FWXF68fsX9c7ad3Sg14FUrVVyyC3HNYrU0Bur3tDxC8cTf5uzZN8S5cyaU2Xz3fgF97/W/bUuyZ/X/rlWJcNLJv5WxqRKoSraeWKny99UlM5bWtfir2lT9KbEWw12ndxl2048Obeb7T+zX8v3L9fcR+e6/DlXSuUtpWvx17TlyJbE3xrtOb1HZy6dsR03Lj4uSZbcW44/2fKJqhaqqooFK3pcr69Jr1uOtx3bpotXLyokKERSwjmQI0sORYZFuvyZKgWr6JvfvlGxXMUU6G9/2igeXlxB/kFa9+c6FQ1LeEI7c/GMdp/aneQzXp4+5l+P/6oGnzVQh4odknzG11235r5VQf5B2vDXhsS6zl06p92ndif5rWeWgCy2c8DTWy4ty9Jzi57T7N9na0WHFbol9y03+Emk9Vq4zmmvASmRlusfnkvpa0C8FS9Juhx32aOfc8o5UKNIDb227DVdjbuqoICEfMm+JSqVp5Tbn59Nq/dBt+S6RQVzFNTSfUsTP59+/vJ5rftznZ654xm3avU1nqz/bx7+Jsm62fDXBnWc21Grnlql4uHFPTquU9b/mk5rFGf9sya//f1bvf3z21rdabUKh7p3pTet1n+7Cu2SfH5ckppMbaJ2FdrpqUpPuVVrSjniluPGxRurbL6yaje7nYY3Gq6jsUfVb1k/da/WXVkDs3p03EPnDqn34t7qWrWrNh/ZrPfXv69RjUfd8GdeqfWK7pp4l3os7KHOVTore1B27TyxU0v2LdEHzT5Qqbyl1LREU3Wd31Vjm49VoH+gei3upZDAkCTzJOdWm0lbJqlQaCHdW+LGvyUxKZ23tBrd2khd5nfR2OZjFeQfpBe/f1EhgSHy0z+3BBTLVUxL9y9VraK1lDUgq3KH5E7WrTbnL5/X1zu/vum/JxJ4ervZntN7FHslVkdjj+ritYvaenSrJKlsvrIebSl/Je6KOs3tpH51++nA2QMasGKAelTrkfj5WZPud3bXx5s/1qPfPKo+NfsoPCRce07v0YxfZ2jifROVI0sOdarcSS8veVl5suVR/uz59dqy12xzevKYfzn+ixpMaaAmJZqod43eiZ9RCvALSPzMx82EZg1Vh4od9PKSlxUeEq782fNrwIoB8vfzt50DPx76UY+Ue0RZA7Mqb7a8Ht9y2X1hd03fMV3fPvKtQrOGJtYbljUs8ZcH+Edar4XrnPQasPPETl2Ju6LTF08r5kpM4jn/743WbiQt13/sldgkd2rsP7NfW49uVXhIeGIzjaQ8OQcW/rFQx2KPqVrhasqRJYd+Pf6rXl7ysmpF1lKxXMU8Oq5TzoHHyj+mQSsHqdPcTnql1iv65fgvenfduxrTZIzbc6TV+yA/Pz/1qt5LQ1cNVck8JXVLroSv7YkIjVDr0q3drteXeLL+/9u0nvz7pCSpTL4yttt6b8Yp679MvqSfv90YvVH+fv4e7cuRVus/T7Y8ypMtT5IsyD9IBXMUtH30LLW4fgebgQT4B2j+o/MV4BegGp/U0BOzn1D7iu01+O7BiWMOnD0gv0F+WnFgxQ3nal+hvS5evag7J96p7gu7q2f1njf9PrMKBSpo5ZMrtfvUbtWZXEeVx1dW/xX9k3zH0uRWkxURGqF6n9ZTm6/aqEuVLin+fGS8Fa9Pt32qJys+afzN0YoDK+Q3yE8Hzh5wOcdnrT9TgewFVHdyXd3/5f16usrTCs0amuTzraMaj9KSfUsUOSZSlce7v2P0f834ZYYsy9Kj5R5N9hxwrfPczqo8vrLGbxqv3ad2q/L4yqo8vrKiY6ITx/gN8tOnWz+94TwNb2mokuElVXdyXbWd2VYtS7XUwPoDb/gzEaER+rnjz4qLj1PjqY1Vfmx59VrcS7my5kpsWkc0HqE6UXV03xf3qdFnjVQ7srbts7iemLlzpk78fUJTt09VoVGFEv+r9vE/38Xsznk/uslo1YisoRZftFCjzxupVmQtlclXJsk5MPjuwTpw9oCKv1dc+UZ41iBdN3bjWJ27fE71p9RPUu+Xv3L7fUp5ay1IznoNaDatmSqPr6x5u+dpxYEViee8J485rdb/xuiNSerr/X3vhH+n5f2TNR+SCgkM0cebP1btSbVV5sMyemHxC2pZqqXmPzY/cUxmOwfCgsP0fbvvtf/sflWdUFUvfv+i+tftn6TWjPQ+qE+tPnruzufUZV4XVfu4mmKvxOq7J75jP5E0ktnWvzsy0vpPd2n2BUGpbNm+ZVaut3JZp/8+7XKMt78DLr1N2jzJKvFeCevKtStu/8zhc4ctDZT1w94fUrEypId9p/dZgYMDrd0nd7sck5Lvs8yI3Dnv/yv2cqwV9maYNXHTxFSsDGnNF18DWP/4N188B3gfhOtY/+7JrOs/3W459raFfyxU39p93f5cRWawcM9CDWswLPGzJSbL9i9T7JVYlc9fXkdij6jPkj4qlqtYinZNQ8a08I+F6lKli0rmKXnzwZmEO+f9liNb9PvJ33Vn4Tt17vI5DV6ZcGdHq9Kt0qpMpAGffA1g/eNffPIc4H0Q/h/r38xX1n+maWhHNB6R3iWkua8f+vqmY67GXVXfpX2178w+hWYNVc3ImprWZtoNFz+cqfud3dO7hDTn7nk/cs1I7Tq5S1kCsqhqRFWtemqV8mbLm8rVIS354msA6x//5ovnAO+DcB3r38xX1r+fZVlWehcBAAAAAICnHLEpFAAAAAAA/0VDCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcKRAdwbFx8crOjpaoaGh8vPzS+2agESWZSkmJkYRERHy90+f37+w/pGeOAfgy1j/8HWcA/Bl7q5/txra6OhoRUZGeq04wFOHDx9WkSJF0uXYrH9kBJwD8GWsf/g6zgH4sputf7ca2tDQ0MTJcubM6Z3KADecP39ekZGRiWswPbD+kZ44B+DLWP/wdZwD8GXurn+3GtrrtxfkzJmThYx0kZ63uLD+kRFwDsCXsf7h6zgH4Mtutv7ZFAoAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADhSYHoXAAAAANzImTNnjPmhQ4dSPHdUVJQxHzNmjC0rV66ccextt91mzCtWrJj8wgC4hSu0AAAAAABHoqEFAAAAADgSDS0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJHY5zoDmzZtnzFu2bGnM33//fWP+zDPP2LKAgIDkF4ZM4fjx48b84YcfNuY1a9Y05l26dLFlxYoVS3Zd6encuXPG/Mcff7RlTZs2NY4NCgryak0AkNnNnz/flrl6D7RixQpj/scff6S4jlKlShnzAwcO2LLLly97NHd8fHxySgLgAa7QAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBKbQqWzU6dO2TLTZk438txzzxnzTp062bKQkBCP5oaznTlzxpbdfvvtxrGuNkYqUKCAMXfiBlCuHmOVKlWM+cmTJ23Zxo0bjWNLliyZ/MKQoZ0/f96Y/+9//7Nlv/76q3HsDz/8YMzZTAxOtXfvXlv24YcfGsdOmDDBmF+8eNGWWZaVssKSYdeuXWl+TADewxVaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Erscp7Mff/zRlv31118ezfHoo48a8+Dg4GTVBOcx7cYrSQ8//LAtM+2sLUndu3c35u+//37yC8tghg4dasz3799vzE07c7KbceY1depUY96vXz9jfujQIbfndrVTcp48edyeA8hI/vzzT1v2zjvvpH0hHihdurQxL1euXBpXgsxqz549xtzV+7TZs2fbshUrVhjH+vubr0N269bNmNesWdOWZdb3MFyhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI7HLcRq5fPmyMXe166on2rVrZ8z9/PxSPDecYfPmzcbc1U55Jv379/dSNRnDL7/8YstGjhxpHHv//fcb87Zt23q1JmQMpt1ZJemFF14w5q52p/TkOfa5554z5h988IEtCw8Pd3te4EZMa9fVTsS1a9c25k2bNjXmWbJksWVhYWHGsTly5DDmsbGxtqxJkybGsa52Iq5evboxr1y5si0LCQkxjs2ePbsxByRpx44dxvzDDz+0ZbNmzTKOPXHihFdr+re1a9ca86CgIFtWqlQp41hX5/+7775ry0znfnrjCi0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAjsSlUGtm+fbsxd7WZj0lgoPl/rnvvvTdZNcF5jh8/bsy/+eYbt+eYNGmSMc+XL1+yakpvps2fJOmee+5xe442bdoY89DQ0GTVhIzN1eZgp06dSrVjzpgxw5gvWrTIlvXr18841tXGUhlxgw6krQsXLhhz0/Pgtm3bjGPnzJnj0TFr1Khhy7Zs2WIcW6xYMWN+6NAhW1akSBHjWH9/rsHAO1y9Jzdt8iRJX375pTE/d+6c28d0ta7r1Kljy1ydLyNGjDDmVatWNebr1q2zZa5e5xYuXGjMK1asaMu6detmHJueeHYAAAAAADgSDS0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAjsctxGpk1a1aK5/Bk11ZkTi+++KIxnzp1qjGvUqWKLXvooYe8WlN6++mnn4z50aNHbdlTTz1lHPvEE094tSZkHAcPHrRlkydP9mgO0y6PklSgQAFbtmTJEo/mNu2S6WoX5scff9yYFyxY0KNjwrmuXLlizB977DFjbtrRuG/fvsaxjRo1Sn5h/8/V7qyuFC1aNMXHBG6ka9eutmz27NnGsSdOnPBobtM5U758eePYYcOGGfPg4GC3j7dmzRpjPnbsWGNues+zdetW41hXryPPPvusLXvggQeMY9Pz2zK4QgsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEdil+M0snLlSrfHZsmSxZi72iENvsPPz8+jvHDhwrbM1frKKC5evGjMXa3/Dz/80Jib/k0mTZqU/MLgSKYdHc+fP28cW7duXWPu6vn70qVLtmz69OnGsW+++aYx37Nnjy0z7dAtSa1atTLmixYtMubh4eHGHM4QGxtry1w9D86bN8+Ym3Ydffnll41js2XL5kF1QPowPe9K0vDhw435xx9/bMssyzKOzZ8/vzF/5plnjLnpXMqePbtxrDecOnXKmF+7ds2YDxo0yJY1adLEOPbAgQPJrisj4AotAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciV2OvWz16tXGfM2aNW7P4WqnwUqVKiWnJPiw+fPn27LGjRsbx+bKlcuYu9rdzxtWrFjhViZJa9eu9Wjuhx56KBkVIbO5fPmyLXO1K/gLL7zg0dzBwcG2rGPHjsaxM2fONOZ79+61Za524HT12pDRdy5H8syZM8eWvfXWW8axUVFRxnzVqlW2LCwsLEV1AenJ1XuEESNGGHPT86npGyAkadasWcb8zjvvdK+4ZIiLi7Nlhw8fNo5t3769MW/evLkxP3PmTPIL+3/t2rWzZa7eL6YnrtACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4EptCedmGDRtSPEdqbsIDZ+vZs6cxX7ZsmTGPjo62ZStXrjSOdbURzbfffutmdZ4zHdPVhj2uFC9e3JgPGzYsWTUhc/niiy/cHrtgwQJj3rp16xTXsXHjxhTPcddddxnzHDlypHhuZDyuNpk0qVy5sjEvUqSIt8oBMoRr164Z84CAALfnCAoKMubr1q0z5q429fv999/dPmZISIgx/+2339zKJClv3rzG/OjRo27X4UqBAgWMeb9+/WyZq3+/9MQVWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBK7HHuZp7sc58qVy5Y9++yzXqoGmU3VqlWN+Y4dO4z51q1bbdl3331nHDt8+HBjnj9/fmPeoUMHY+6Jdu3a2bIKFSp4NEfNmjWNuavdj+FbHn30UVvmauduV8/frnayNJ13s2fPNo49c+aMMTe9BrgaO2HCBGNuOo8kqWzZssYczuBqZ1WTRYsWGfNBgwbZspYtWxrHutopGchIGjZsaMzvvvtuY75kyRJbdvDgQePY559/PvmF/b/AQHNr5Wp3Zk94upuxv7/9umWbNm2MY9977z1jXqhQIY+OmV64QgsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEfysyzLutmg8+fPKywsTOfOnVPOnDnToi5H+Omnn2xZ3bp1jWNd/TNHRUXZsgMHDqSorswkI6y9jFBDZrVv3z5b5mp34kqVKhnz77//3pjny5cv2XVlJBlh/WWEGpLr9OnTtszVGjt37pwxd/X87efn53Yd99xzjzH/8MMPbVmLFi2MY3fv3m3Mu3TpYszHjRvnZnUZV0ZYe+lVg2l9ebLmXAkICDDm3bp1M+bVq1c35ocPH7ZlJUqUMI69/fbb3axO+vXXX415jRo1jHmRIkXcntuJfPkc8IazZ8/asrfeess49ueffzbmefLkMeZFixa1ZZcvXzaO3bZtmzFft26dMfeGZ555xpYNGzbMONa0435G4O7a4wotAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAIwWmdwFOdurUKVvmxh5bSbjaKATwBYMHD7ZlrjY9GT58uDHPLJs/IXWEh4fbsq+//to49sEHHzTmnmwW9fzzzxvHvv3228Y8ODjYlrVp08Y49s033zTmixcvNuZ79+61Za42xELG89JLL9myUaNGpXjeuLg4Y27aoOxGeVrLnz+/Ma9fv74xnzFjRipWA6cwbXbkalOo1NS+fXtj7smmUK42RRo9erQxf/LJJ22Zq03hnI4rtAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCR2OU4BVztlmph2WZOkLl26eKkaIONyda5MmTLFlrnaxS9PnjxerQm+q1GjRsZ85syZxnz69OnG3PS8btq5WzLvZuzK66+/bsx/++03Y/7tt98ac1MtpnMOGZNpJ9aHH37YOPbxxx835levXrVlf/75p3Gsq92PM4rjx48bc1evL+XKlbNl/fr182pNwH+5+kYGb+y6PXbsWGP+2GOPpXhup+MKLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHIldjt3gakdAVztfmhQpUsSYV6tWLVk1AU6yaNEit8c2b97cmFepUsVb5QBGrnY/dpWnlpCQEGPetm1bY+5ql+Ply5fbstOnTxvHhoeHu1kd0kpAQIAtc/WeYffu3W7Pu3TpUmNu2hFZkgYOHGjM169f7/YxU5NlWcZ806ZNaVwJfM3EiRNt2dChQ41jXZ1fJqYduiXpgQcecHsOX8MVWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBK7HLth9erVxtzVznomrVq18lY5gOO42uU4e/bstuyll15K7XIAR3r44YeN+dy5c435jBkzbNkHH3xgHNu/f//kFwZHadiwoUfjt27dasxNuxwHBQUZxz711FPG/Omnn7ZlY8aMMY715JslAG9ytaP3iy++aMtiYmI8mjs0NNSWjR071jg2a9asHs3tS7hCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4EhsCuWGU6dOuT02b968xrxXr15eqgbIuMaNG2fMjx49aswLFChgy6pUqeLVmoDMwt/f/DvoPn36GPM5c+bYsoEDBxrHPvLII8b8tttuc6s2ZF6NGzc25n379rVlV69eNY6dMGGCMf/jjz9s2YoVK9wv7gYKFy7slXmAefPmGfPz58+7PYdpE0zJvKlf7dq13Z4XCbhCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR2KXYzcsXrzY7bGRkZHGPCwszFvlABmWq12O/fz8jHmzZs3cnjsmJsaYnzlzxpgXLVrU7bkBJ6tUqZIxHzJkiC176aWXjGNfffVVYz516lRbFhIS4n5xcLwyZcoY87Zt29qyL7/80qO5ly9f7vbYwEDzW9bmzZsb87ffftujWgBX7zOGDx+e4rmfeOIJY16/fv0Uzw2u0AIAAAAAHIqGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSDS0AAAAAwJHY5fhfrl69asz37Nnj9hzBwcHGPCgoKFk1AZmZaddK066qkjRmzBhjXq5cOWM+ZcqU5BcGZALt27e3ZePHjzeOnTVrljH/448/bFmFChVSVhgcxdWu1u+8844tc7VL7KZNm4z5sWPHbFmxYsWMY03rWZIGDhxozAFXYmNjjbmrHb2vXLni9twVK1Y05qbzBd7DFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHYlOof/H3N/f31apVM+a//vqrLStZsqRXawIys48//tiWTZw40Ti2c+fOxvz111/3ak1AZpEvXz5b9sMPPxjHRkVFGfO33nrLlk2fPj1lhSFTKFCggC2bP3++ceznn39uzNesWWPLXG3ylD9/fveLA25g2bJlxvyvv/5K8dyjR4825q42jYV3cIUWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkWhoAQAAAACOxC7H/xIQEGDM33jjDWPu5+dny6pUqeLVmgAnef/99435gAEDjHndunVt2TPPPGMcmzt3bmOeJUsWN6sDULRoUWN+zz33GPO5c+fasp07dxrHli1bNvmFIVNr166dRzmQmrz17Qh9+vSxZQ0aNPDK3PAMV2gBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBI7HLshoiICGM+adKkNK4EyNjq1KljzJctW5bGlQDwxMyZM415xYoVbdmePXuMY9nlGIATnD592qPx+fPnN+a9evXyQjXwBq7QAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkdjlGAAAH5czZ05jvn///jSuBABSV+/evT3KX3/9dWNeqFAhr9WElOEKLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCOxKRQAAAAAn/DCCy94lCPj4wotAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI7m1KZRlWZKk8+fPp2oxwH9dX3PX12B6YP0jPXEOwJex/uHrOAfgy9xd/241tDExMZKkyMjIFJYFJE9MTIzCwsLS7dgS6x/pi3MAvoz1D1/HOQBfdrP172e58Suf+Ph4RUdHKzQ0VH5+fl4tELgRy7IUExOjiIgI+funzx3yrH+kJ84B+DLWP3wd5wB8mbvr362GFgAAAACAjIZNoQAAAAAAjkRDCwAAAABwJBpaAAAAAIAjpVlDW//T+ur1Xa+0OlyGUOydYnpn7TvpXQYyCF88B3zxMcPMF9cCrwFIVL++1KtXeleRtnzxMcMlX3wN8MXHnF7SrKGd1XaWhtw9JNk/7zfIz/bfjF9meLHCjOXStUt6cs6TKj+2vAIHB6r1jNapdixvvOn68eCPuu+L+xQxKkJ+g/w05/c5XqktM0npOSBJn279VBXGVlDw0GDlH5Ff3Rd091J1Gdupv0+pyOgi8hvkp7OXznp9fm83Hm/99Jb8BvnxQvYvKVn/n2791Pga4DfIT8cvHPdypRnHV79+pUrjKinbG9kU9U6URvw8IlWO4431H3M5Rr2+66Wod6IU8kaIan5SUxv+2uCdAjODWbOkISl4/t+wQWrYUMqVS8qdW2rSRNq2zWvlZViffipVqCAFB0v580vdU+E1zxuN96efSn5+Sf8LDvZCcZlHSt8DLd23VDU/qanQN0NVcGRBvbLkFV2Lv+bFCjOetHrM3mi8r8Zd1eCVg1X8veIKHhqsiuMq6rs933mnQDe49T203hAeEp7iOSa3mqymJZom/jlXcK4Uz3kzV+KuKEtAllQ/zn/FxccpJDBEz9/5vL757Zs0P76nLly5oIoFKqpjpY5q81Wb9C4nQ0rpOTB6zWiNWjNKI+4ZoeqFq+vC1Qs6cPaAd4q7gfQ6B/6t09xOqlCggv6K+Std63DHhr82aPym8apQoEJ6l5KhpGT9t729bZLnfkl6cs6TunTtkvJnz5/S0m4ovdb/oj8W6fFZj+v9e99X4+KN9duJ3/T0vKcVEhSiHnf2SPN6bqbzvM765fgv+vz+zxURGqGp26eq0eeNtPPZnSqcs3B6l5f+wlPw/B8bKzVtKrVsKX30kXTtmjRgQEJTe/iwFBTkvTr/68oVKUs6Pf+PHi2NGiWNGCFVry5duCAdOJA+tbgjZ05p165//szX2ySRkteAbUe3qdn0Znqtzmv67P7P9Nf5v9RtQTfFWXEa2XikF6u0S6/XgPR8zMnRb1k/Td0xVR/f97FK5y2txXsW6/4v79fqjqtVuVDl1C/ASiP1Jtezei7qmeyf10BZs3+bneIaui/obnVf0N3K+WZOK8/beax+S/tZ8fHxiWOixkRZg1cMttrNameFDgu1OszuYFmWZa06uMqqPam2FTw02Coyuoj13MLnrNjLsYk/dyz2mNViegsreGiwVeydYtbUbVOtqDFR1pg1Y1JUs2VZVofZHaxWX7RK1s+ev3Teeuybx6xsb2SzCo4saI1ePTrJ/xb1JtezNFBJ/kspb/xvlRml5Bw4/fdpK2RoiPXD3h9SVMP1tTRw+UAr7/C8VuiwUKvrvK7W5WuXk9TZfUF3q+einlaet/NY9T+tb1mWZe04tsNqOrWplf2N7Fb+EfmtJ2Y9YZ24cCLx52Ivx1rtZrWzsr+R3So4sqA18ueRKT7vLcuyPlr/kVVvcj1r6b6llgbKOnPxjEc/n5bnQMzlGKvkeyWtJXuXeOWxZybe/Pc4HnvcChocZH229TOPa3DKa8CjMx+1HvzqwSTZe2vfs4qMLpKk3ptJi/X/95W/rYBBAdb8XfOT5FXGV7FeW/qax/NlSvXqWVbPnsn72Q0bLEuyrEOH/sm2b0/I/vjD/Xk6dLCsVq0sa+BAy8qb17JCQy2ra1fLuvzP879Vr55lde+eUGuePJZVP+H539qxw7KaNrWs7NktK39+y3riCcs68c/zvxUba1nt2iX8fcGCljVyZMoe8+nTlhUSYlk/pOw1z7p61bKee86ywsIsKzzcsvr0saz27RP+HSwr4d9ESvrf/v2eH2fy5IRjwKWUvAa8+sOr1h0T7kiSzf19rhU8NNg6f+m82/M46T2Qtx7z1bir1nMLn7PC3gyzwt8Ot/p838dqP7t9Yl/RYXYH22vA/jP7Pa630MhC1gfrPkiStfmyjfX4N497PFdypNkV2v/qNr+bpm6fesMxsX1jk/y5+8Lu6jy3s27Nfau63dFNT1V6yuMveJ6ybYo6Ve6k9Z3Xa2P0RnWZ30VFw4rq6apPJ44ZuWak+tftrwH1BkiS9p7eq6ZTm2pog6Ga1HKSTvx9Qj0W9lCPRT00udVkSQlXC6JjorW8w3IF+Qfp+e+et90Kd++0e7Xq4CqXtUXlitKvz/7q0eO5md6Le+vnQz9r7iNzVSBHAfVf3l+bj2xWpYKVJCXcAlJxXEV1qdIlyb/BoXOHVPbDsjecu2+dvupbp69X6/UlnpwDS/YtUbwVr79i/lKZD8so5nKMakbW1KjGoxQZFunRcZfuX6rgwGCt6LBCB84e0FPfPqU8IXn0RsM3EsdM2TZFz9zxjH7u+LMk6eyls2owpYE6V+msMU3G6OLVi3rlh1f08NcPa1mHZZKkl5e8rJUHV+rbR75V/uz51XdZ3yRrzdPHLEk7T+zU4B8Ha13nddp3Zp9Hj/O6tDwHui/sruYlm6vRrY009MehyarXVyTnNeC6z7Z9pmxB2fRg2Qc9Pq5TXgMux11WtqBsSf4+JChEf57/UwfPHVSxXMXcerxpsf6vxV9TnBWn4MCkt1iGBIbop0M/uVWnz+nWTZp64/Wv2P9f/6VKSXnySJ98IvXtK8XFJfz/ZcpIxYp5dtylSxNuhV2xIuFq51NPJcz9xj/P/5oyRXrmGennhOd/nT0rNWggde4sjRkjXbwovfKK9PDD0rKE53+9/LK0cqX07bcJtwb37Stt3ixVqpS8x7xkiRQfL/31V8LjjImRatZMuGIb6cFr3ttvS9OmSZMnJ8zz7rvSnDnS3Xcn/P2770q7d0vlykmDBydk+fIl/N8cOW489xNPSOPGJa09Kiqh7ipVpGHDpNtvd79WH+PJa8Dla5ftzy9BIbp07ZI2Hdmk+sXqu31cp7wH8tZjfvuntzVtxzRNbjVZZfKV0btr39Wc3+fo7mIJ58C7Td/V7lO7VS5/OQ2+O+EcyJct4RzIMezG58ATFZ7QuBYJ58DlOEO9afgakG4N7eC7B+ulmi+5P77+YDW4pYGyBWXT93u/17MLnlXslVg9X/15j44bmTNSY5qMkZ+fn0rlLaUdx3dozNoxSV7IG9zSQC/WfDHxz53ndtbj5R9Xr7t6SZJK5imp9+59T/U+raexzcfq0LlDWrRnkdZ3Xq9qhatJkj5p+YnKfFgmybEn3jdRF69ddFlbkL93bxuKuRyjKdumaPoD09Xw1oaSEm7bjhgdkTgmPCRcAX4BCs0aqoI5CibmEaER2tpt6w3n98Zt5L7Mk3Ng35l9irfiNWzVML3b9F2FBYep37J+uufze7T9me0e3Q6TJSCLJrWapGxB2XR7/ts1+O7BennJyxrSYIj8/RI+Vl8yvKSG3zM88WeG/jhUlQtV1rCGwxKzSa0mKXJMpHaf2q2I0Ah9suUTTb1/auJam9J6ioqMLpLsx3z52mU9+s2jGnHPCBUNK5qshjYtz4EZv8zQ5iObteFpPjfoDk9fA/7tky2f6LHyjykkKMTjn3XKa0CT4k30wuIX9GTFJ3X3LXdrz+k9GrVmlCTpSMwRtxratFr/oVlDVaNIDQ35cYjK5CujAtkL6ItfvtCaP9eoRHiJm9bpkwYPll5yc/2HhiY0oK1b//M53JIlpcWLpUAP38ZlySJNmiRly5bQbA0enNCMDhki+fv/M/fwf57/NXSoVLlyQoN23aRJCY3l7t1SRERCgz11asLnfKWEprhI0ud/jx7zvn0JjeGwYQlNZ1iY1K+fdM890vbt7t8G/f770quvSvffn/DnDz6QFi785+/DwhLmypZNKlgw6c9u3XrjuXPm/Of/L1Uq4d+kQgXp3Dlp5MiEBvzXX+3/DpDk2WtAkxJN9M66d/TFji/08O0P62jsUQ1emdB8HYk54tFxnfIeyFuP+f317+vV2q/q/jIJ58AHzT7Qwj3/nANhwWHKEpBF2YKyJXkNkHTT14CcWf85B5oUb6LRa0erblRdFQ8vrqX7lmrWb7MUZ8W5XWtKpFtDmz97fo8++/R6vdcT///KhSrrwtULGrF6hMcN7V1F7kpyVbdGkRoatWaU4uLjFOAfIEm6o9AdSX5m27Ft2n5su6btmJaYWbIUb8Vr/5n92n1qtwL9A1U1omri35fOW9r2Gd+0/hzRvjP7dDX+qu4sfGdiFhYcplJ5St30ZwP9A3kjkso8OQfirXhdjb+q9+59T42LN5YkffHAFyo4qqCW71+uJiWauH3cigUqJrnyU6NIDcVeidXhc4cVlStKklS1UNUkP7Pt2DYt37/c+Nu6vaf36uLVi7oSd0XVi1RPzMNDwlUqb9K15sljfnXpqyqTt4yeqPCE24/tv9LqHDh87rB6ftdTS9otsf2GEmaevgZct+bwGv128jd9fv/nyTquU14Dnq7ytPae3qsWX7TQ1birypk1p3pW76mBKwcmvum6mbR8Dfj8/s/VcW5HFR5dWAF+AapSqIoeLfeoNh3Z5PYcPiV//oT/3HHxotSpk1SrlvTFFwlXaEeOlJo3T9gsKsSDX+xUrJjQvF1Xo0bClcXDhxOuLkpS1aTP/9q2TVq+3HzFcu/ehPquXEn4nOt14eEJTd6/efKY4+Olq1el996TGie85umLLxKazuXLEz4/fDPnzknHjkl3/rP+FRCQ8Pji42/+8yU8eA9Uo0bCf9fVrJlwRXj8+JRtBpaJefIa0Lh4Y424Z4S6LeimdrPbKWtgVr1e93WtOrTK7efD65zyHsgbj/ncpXM6duFYkteAAP8AVS1UVfHWzc8BT14D3m36rp6e97RKf1hafvJT8fDieqrSU5q0dZLbc6SEo245/rfqhatryI9DdPnaZWUNzOrV2rJnyZ60jiux6lq1q7F5LhpWVLtP7XZr3vS45Ti5uOU49XlyDhTKUUiSVDbfP/+b5MueT3mz5dWhc4e8XpvpHLiv1H16u9HbtrGFchTSntN73JrXk8e8bP8y7Ti+QzMHz5SU0EBIUt7hefVandc06O5Bbh0zuTw5BzYd2aTjF46ryvgqiX8XZ8Xpx4M/6oP1H+hyv8uJzRISJPc1YOLmiapUsFKS5tHbMsJrgJ+fn96+520NazhMR2OPKl/2fFq6b6kk6dbct7r7UJLN09eA4uHFtfLJlbpw5YLOXz6vQqGF1HZm2zSp1ZE8uf12+vSE24PXrPnnKur06Qm7HX/7rfTII96tLXvS9a/YWOm++xJu3/2vQoWkPe49/3v0mAslvOap7L/WYL58Ut680iHvv+YZeXrL8b8FBSVc1Xb338YHefoa0LtGb71w1ws6EntEuYNz68DZA3p16aup8hyTEd4DSWn7mE08ueU4X/Z8mvPIHF26dkmn/j6liNAI/e+H/6VZrY655fi/th7dqtzBuT1uZtf9tS7Jn9f+uVYlw0ve8M1mlUJVtPPETpe/qSidt7SuxV/TpuhNibeb7Tq5y/b1Iml9y/GtuW9VkH+QNvy1QUXDikpK+G3N7lO7VTeqbuK4LAFZFBef9JYAbjlOfZ6cA7WK1pKUsK6K5Ey4heX0xdM6+ffJxN8oumvbsW26ePVi4u2aa/9cqxxZctzws7hVClbRN799o2K5iinQ3/60UTy8uIL8g7Tuz3WJa+3MxTPafWq36kXVSxznyWP+5uFvkpwvG/7aoI5zO2rVU6tUPLy4W3Ok1TnQ8JaG2vHMjiR/99S3T6l03tJ6pdYrNLMGyXkNiL0Sq692fqU3G76Z7OM67TUgwD8g8cruF798oRpFaihf9nwu5/i39HgNyJ4lu7Jnya4zF89o8Z7FSW7bw794cvvt338nNLL/3jPk+p/dudL4b9u2JVxRvX5Vd+3ahMbtRp9LrVJF+uabhM/rmm5xLl48oYFbt04qmrDOdOZMwu3I9f55/vfoMddKeM3Trl3/3LJ7+rR08uQ/V5JvJixMKlAg4Sp23f9f73Fx9s/2ZsmSkP+XJ7cc/1dcnLRjh9SsmXu1+qDkvAb4+fkpIjThIxNf/PKFInNGqkqhKjf5qaSc8h7oupQ85rDgMBXIXkAb/tqQ+JwfFx9n+2yv6TVA8uyW4+uCA4NVOGdhXY27qm9++0YP3/6wW7WmlCNuOZ63a56OXTimu4rcpeDAYC3Zu0TDfhqml2p43hAfOndIvRf3VteqXbX5yGa9v/59jWo86oY/80qtV3TXxLvUY2EPda7SWdmDsmvniZ1asm+JPmj2gUrlLaWmJZqq6/yuGtt8rAL9A9VrcS+FBCa9DcjTW453ntipK3FXdPriacVcidHWo1slKckivJHQrKHqULGDXl7yssJDwpU/e34NWDFA/n7+8tM/L4zFchXTj4d+1CPlHlHWwKzKmy2vx7ebxV6JTfIbqv1n9mvr0a0KDwlPPLmRlCfnwG15blOrUq3U87uemnDfBOXMmlOvLn1VpfOWTvxgv7uuxF1Rp7md1K9uPx04e0ADVgxQj2o9bngLS/c7u+vjzR/r0W8eVZ+afRQeEq49p/doxq8zNPG+icqRJYc6Ve6kl5e8rDzZ8ih/9vx6bdlrtjk9ecz/bVpP/n1SklQmXxm3v7Irrc6B0KyhKpe/XJIse1B25QnJY8uRIDm3HH/5y5e6Fn8tRbehO+U14OTfJzVz50zVL1Zfl65d0uQtk/X1zq+18smVbs+Rlq8Bi/csliVLpfKU0p7Te/TykpdVOm9pPVXpKbfn8Cme3H57zz0Jn3Pt3l167rmEJvattxKay7s9e/7XlSsJty/365dw1XfAAKlHj3+u/Jp07y59/LH06KNSnz4JtxPv2SPNmCFNnJjQEHfqlFBjnjwJj+u11+xzevKYb7tNatVK6tlTmjAhoXl89VWpdGnPHvNzz0lvvplw+3Dp0gmfqT1zJukvB4oVS2jGDxxIeCzh4Qm1e3LL8eDB0l13JfzM2bMJXzV08GDCRlow8vQ1YMTPI9S0RFP5+/lr1m+z9NZPb+mrh77y+BfGTnkP5K3H/Nydz+nNn95UifASKp23tN5f/77OXDqT5KM3xXIV07q/1unA2QPKkSWHwkPC5e/n79FrwLo/1+mvmL9UqWAl/XX+Lw1cOVDxVrz61Orj9hwp4dmN5+kkKCBIH274UDU+qaFK4ypp/KbxGt14tAbUH5A45sDZA/Ib5KcVB1bccK72Fdrr4tWLunPineq+sLt6Vu+pLlW73PBnKhSooJVPrtTuU7tVZ3IdVR5fWf1X9E/8jYn0/xtthEao3qf11OarNupSpUuKvx+x2bRmqjy+subtnqcVB1ao8vjKqjz+n+9ycucxj24yWjUia6jFFy3U6PNGqhVZS2XylUnyOb/Bdw/WgbMHVPy94so3wr3f/P/XxuiNSerr/X3vhH+n5f2TNR/sPrv/M1UvXF3NpzdXvU/rKcg/SN89/p2CAv65quM3yE+fbv30hvM0vKWhSoaXVN3JddV2Zlu1LNVSA+sPvOHPRIRG6OeOPysuPk6NpzZW+bHl1WtxL+XKmivxCXtE4xGqE1VH931xnxp91ki1I2vbPofibRnpHEDq+2TLJ2pTpo3xFxqZ8TVgyrYpumPCHao1qZZ+PfGrVnRYkeSzUBlp/Z+7fE7dF3ZX6Q9Lq/2c9qpdtLYWP7E4yfMTkql0aWnevITNkGrUkOrUkaKjpe++++fWXCmhSfv00xvP1bBhwqZPdetKbdsmfLftwIE3/pmIiIQdj+PiEj7PWr681KuXlCvXP03riBEJdd13n9SokVS7tv2zuJ767LOEz+U2b55wpTcoKOEx//t7d2/2mF95JaERb98+4d8uR46Ez98G/2uvg5deSvhsbdmyCbc1J+eW5jNnpKefTvjcbLNm0vnz0urVSW+ZRoos2rNIdSbX0R0f36EFfyzQt498q9alWycZk9neA3njMb9S+xU9Wu5RtZ/TXjU+qaEcWXKoSfEmSV4DXqr5kgL8A1T2w7LKNyJfsj7KdunaJfVb1k9lPyyr+7+8X4VDC+unjj+5fQEixdLky4HSwLJ9y6xcb+WyTv992uWYzPa9kO485v+KvRxrhb0ZZk3cNDEVK0N62Hd6nxU4ONDafXK3yzEp+U7jjIhzANfxGuAe1n8mtW+fZQUGWtZu18//id9Dm1m485j/Ky7Osm67zbL69Uu9upAufPE9kDuP+b/i4uOs296/zeq3NHOdA+l2y7G3LfxjofrW7qvcIbnTu5Q0485j3nJki34/+bvuLHynzl0+l7jld6vSrdKqTKSRhX8sVJcqXVQyT8n0LiXNcA7gOl4DzFj/PmLhQqlLl4Srr77Cncd88KD0/fcJV3gvX0742p79+6XHHku7OpEmfPU90M0e88GzB/X93u9Vr1g9Xb52WR+s/0D7z+zXY+Uz1zmQaRraEY1HpHcJac7dxzxyzUjtOrlLWQKyqGpEVa16apXyZsubytUhrXW/s3t6l5DmOAdwHa8BrrH+fUB333v+d+sx+/sn3JL80kuSZUnlykk//JBwazAyFV98D+TOY/b389en2z7VS0tekmVZKpe/nH5o/4PK5Mtc54CfZVlWehcBAAAAAICnHLEpFAAAAAAA/0VDCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcKRAdwbFx8crOjpaoaGh8vPzS+2agESWZSkmJkYRERHy90+f37+w/pGeOAfgy1j/8HWcA/Bl7q5/txra6OhoRUZGeq04wFOHDx9WkSJF0uXYrH9kBJwD8GWsf/g6zgH4sputf7ca2tDQ0MTJcubM6Z3KADecP39ekZGRiWswPbD+kZ44B+DLWP/wdZwD8GXurn+3GtrrtxfkzJmThYx0kZ63uLD+kRFwDsCXsf7h6zgH4Mtutv7ZFAoAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkWhoAQAAAACOFJjeBQDIGC5fvmzMa9asacy3bNliy1q2bGkcO2fOnGTXBQAAALjCFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSuxy7YdWqVcbctPvrrl27jGPnz59vzBcsWGDLmjdv7kF1Uo0aNYx5nTp1PJoHvsHVbsYvvPCCMd+6dasx9/Pzs2VVq1ZNdl0AAABONnDgQGM+aNAgY16/fn1btnz5ci9W5Bu4QgsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEfyyV2Oz58/b8wff/xxY7506VJjHhISYsuuXr1qHBsTE+NmddKPP/7o9lhXdUhS9uzZbdnYsWONYx988EGPjgnneu+994z5+PHjjXnDhg2N+eDBg23ZXXfdlfzCAACOcebMGVu2ZcsW49jvvvvOmI8YMcKWmXbQl6SHHnrImEdFRRnzF1980ZYVKFDAOBbwlpUrV3o0fsWKFW5lknlHZCTgCi0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj+eSmUK+88ooxnz9/vkfzXLx40ZaVKVPGODZ//vzGPGfOnG4fLz4+3pgvWLDAmJvq69Spk3HsbbfdZswrVKjgZnVwiiNHjng0vlGjRsacDaAAIPNwtanlqFGjjPkHH3xgyzx9fTFtAOVqU6iZM2d6NPfJkydt2aRJkzyaA/CUqw2dvDEHm0K5xhVaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Uqbf5fiXX36xZZ7ulBcZGWnMP/vsM1tWokQJ49hcuXIZ8xw5crhdh6tdjgcPHmzMhwwZYsvOnz9vHDtw4EBj/sknn9iy3Llzu6gQThAbG2vMs2TJYsxd7XIM+LotW7bYstdff904duHChcbcsixb5mqX14ceesiYv/HGG8a8UKFCtmz58uXGsQ0bNjTmISEhxhyZz/jx4435a6+9lmrHNO3aunLlSq/MPWXKFFvGLsdwAlfvyeEaV2gBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBImX6XY9OOridPnjSOdbWzZJ8+fYy5aXe+1OTvb/79g6vd0K5cuWLLRo4caRw7e/ZsY96xY0db1qJFCxcVIqOJjo62ZRMnTjSOrVmzpjGvUqWKV2sCMqqrV68ac1e7rj755JO27MiRI8axrl5fPBnraod+VzsRHzp0yJatWLHCONa0a78kPfHEE8YczmX69gfJ/M0I3vL2228b8549e9qy/v37G8cOHz7cqzUByDy4QgsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBImX5TqMuXL7s91rTBhyT16NHDS9WkrWHDhtmyGTNmGMfu37/fmM+aNcuWsSmUcwwdOjS9S0h1a9asMeZ//vmn23NUrFjRmN92223JqgnOtHnzZmPepEkTt+eIiIgw5h988IExz5Ytm9tzHzx40KM5nnvuOVuWNWtW49hChQq5XQecw7QBVN++fY1jT5w4YcxdbVIWFRVly+bOnWscW7ZsWWNu2uxy8ODBxrH333+/MW/ZsqUxNz2eChUqGMdu377dmAOeGjBggDEfNGiQ23O42uzVVQ6u0AIAAAAAHIqGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSDS0AAAAAwJEy/S7Hr7/+uttjq1evnoqVZAxNmzY15mPHjjXma9euTc1ykMoWLFjg9tjOnTunYiXue+aZZ4y5q8dy5swZY/7333+7fcycOXMa8969e9syT55TkDGZdn6VXO+W6kqjRo1s2ZtvvmkcW6VKFY/mNomOjjbmrVq1MuZnz561ZX369DGObdiwYbLrQsa1ZcsWWzZ//nzjWMuyjHlQUJAx7969uy0rV66cB9WZuTrenXfeacxdfUPFqFGjbNmOHTuMY7t06WLMJ0yYYMwBVzzZzRjewxVaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4UqbZ5Xjfvn3G/K+//rJluXLlMo4tX768N0vKkBo0aGDMXe1yDGdwtaPv1atXbVmRIkWMY13tFOmJa9euGfPNmzcb89atW9uyo0ePGse62oEzX758xty0A62rOg4dOmTMx48fb8vat29vHBsVFWXMkfEMHTrUmJ84ccKYt2jRwpibdlEtWbJk8gu7CVe7M7ta1yaudrpH5rRo0SJb5ufn59Ec9evXN+YvvvhickryurfeesuYmx67q12ON2zY4NWaAKQtrtACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRMs0ux1OnTjXmpt2PH3zwQePYmjVrerUmIK1MnDjRmB87dsyWde3a1SvHjI6OtmUTJkwwjh0yZIjb8xYuXNiYt2vXzpg/++yzxtzVbs4mLVu2NOYLFiywZUeOHDGOZZfjjOnpp5+2ZV999ZVxbI4cOYy5q11UU2tHY9Pu5JL05ptvGnNXO4CbdqetV69esutCxnXq1Cljvm7duhTP7eq5N6Mz1d2nT590qARAauMKLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCNlmk2hvvjiC2OeK1cuW9azZ89UrgZIW1u2bHF7rLc2shk6dKgtGzdunHGsn5+fMW/YsKEtGz16tHFsuXLlPKjOMyVKlEi1uZG+Nm7caMtcrcfs2bMb87Jly3q1pn8zbQD1+uuvG8f++OOPxtzV4+nfv3/yC4OjbNq0yZgfOHDA7Tnq1q1rzJs3b56ckhzl7Nmzxty0CWChQoVSuRoAnuIKLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHCnT7HLsSunSpW1Z7dq106ESIPVER0en2ty7d+825jNmzHB7ji5duhjzd99915ZlyZLF7XlTW9WqVW1ZlSpV0qESOJ2r3WY/+ugjWzZq1CiP5o6IiDDmlSpV8mgeOJdpN29PDRo0yJjnzp07xXNndIcOHTLmv/zyiy1jl2OktoEDB6Z3CY7DFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADiS43Y5vnDhgjG/du1aGlcCZBznz5835pZluZXdyPvvv2/Mz549a8sef/xx49ixY8d6dMy0Fhsba8wDA+1PkRlpF2bcXJkyZWzZ9u3bjWNPnz5tzCtXrpziOk6cOGHMTTuU+/n5eTR3w4YNjXmuXLk8mgfO9ffffxtzT57v69Wr561yMixPX/8AOANXaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj0dACAAAAABzJcZtCffnll8Z8z549xjxv3rypWY7jzJ0716PxQUFBqVQJvMnVJjKm3NMNZ0yb1riax9XYjMJVfRMnTjTmDzzwQGqWgzTwySef2LKYmBjj2AULFhhzV5tIeYPpOfnzzz83jp05c6Yx79atm1drgvNs3LjRmHv6fJ/ZefJaCcA5uEILAAAAAHAkGloAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHctwux3Dfpk2bbNm8efM8muONN97wVjlwqAkTJhjz1atXu5VJ0rBhw4x5165dbVmePHk8qM4zbdq0MebZsmUz5i+++GKq1YK0ERISYstcPQ+uWLHCmLvaQdakbNmyxrxZs2bG/Nlnn7VlX3/9tXFsqVKljHnx4sXdrA6ASWhoqDFPzdcjAN7DFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADgSuxxnAqbdjCVp1KhRtuzs2bPGsbVr1zbmTZs2TXZd8L7o6GhjfuTIkVQ7pqtdHjdv3mzLWrZsaRz7+uuvG/PFixfbsvnz5xvHutqF0tX4oUOH2rItW7YYx/br18+Y33XXXcYcmVP9+vU9yr1h3LhxtszPz884tlq1asY8X758Xq0JyAw+++wzt8cOHDjQmFepUsVL1cBXuHq9cLWLvomr9egqB1doAQAAAAAORUMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHImGFgAAAADgSI7b5bhYsWLGPGfOnGlbSDqIi4sz5iNHjjTmM2bMsGVFihTxaI7AQMctkUwtIiLCmN92223G/ODBg7Zs2bJlxrFdu3Y15tmyZTPmhQoVsmUbNmwwjnW1E3GZMmVsmauduF988UVjPnHiRGNuqtvVbsaudmEGvOXAgQNuj3W1o3evXr28UwwynbfeesuYb9261ZadOHHCOLZjx47GfNKkScmuKz2ZHmf+/PmNY7t165ba5QBIRVyhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCTH7fjToEEDY+5qs5xz587ZspMnTxrH5s2bN/mFJdP27dtt2UcffWQcu3nzZmPuaiMek6lTpxrz6tWruz0HMp5PPvnEmDdv3tyWLViwwDi2cePGxrx3797G3LQplCvr1q0z5sOGDXN7rGVZxrxUqVJuz33//fe7KhFIVYMHD3Z7bIsWLYx5lSpVvFUOMplKlSoZ8xEjRtiyDh06GMd+9dVXxrxHjx7GPKOsx6efftqYHzt2zJY9/PDDxrHBwcFerQm+YcWKFW5lSH1coQUAAAAAOBINLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCM5bpdjT/3222+2rEmTJsaxnuza6i2mHV1d7cLsSr58+Yz5fffdZ8uqVavm0dxwhiJFihjz7777zpbdfffdxrFr1qwx5g899JDbdbjaidjPz8/tOVx56qmnjPnw4cONeZ48eVJ8TMBTv/zyizGfNWuW23M0bdrUW+XAx9WqVcuWPfbYY8ax06dPN+YrV6405mm9y/GyZcuMuatzq0CBArasf//+Xq0Jvm3QoEHpXQL+H1doAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHImGFgAAAADgSJlml+Nhw4YZ8yFDhtiyzZs3p3Y5KeLvb/49g6tdW3v37m3M//e//3mtJjiTaefutWvXGsd++eWXxnzPnj3G/OOPP7ZlnTp1Mo51taZNXM1RunRpt+cA0suWLVuM+fnz5425aQfw4OBgr9YE33XrrbfasqFDhxrH/vzzz8bc1U6uJ06csGWu3ou5snv3blu2fv1641hX73XOnj1rzF966SVbVrZsWfeLA/7fihUrPMo9sXz5cltWv379FM/ra7hCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4EiZZlOo+++/35hXr17dljVt2tQ4dseOHV6tyR1dunSxZZUrVzaO7datW2qXAx+QK1cuY961a1eP5hkxYoQXqgEyF9NGOZJ58ydJKleunC178MEHvVoT8G/FihUz5qtXrzbmrt57fPTRR7Zs0aJFHs3Rv39/W3by5EnjWFfuu+8+Y256fwWktgEDBhjzgQMHpm0hPoYrtAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcKRMs8uxKxEREbZs+/bt6VAJACCz+/zzzz0a365du1SqBPBMoUKFjPlnn31mzHft2mXLhgwZYhz77LPPGvOXXnrJzeqkBx54wJhXqVLFmAcGZvq3uEgj9evXN+aWZaVtIXCJK7QAAAAAAEeioQUAAAAAOBINLQAAAADAkWhoAQAAAACOREMLAAAAAHAktoADAMBLypQpY8zZXR9OFRYWZszvvPNOWzZv3rzULgcAbLhCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR2KXYwAAvOTee+815vv27TPm1apVS81yAADI9LhCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4EhsCgUAgJe0a9fOoxwAAKQMV2gBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAcya1NoSzLkiSdP38+VYsB/uv6mru+BtMD6x/piXMAvoz1D1/HOQBf5u76d6uhjYmJkSRFRkamsCwgeWJiYhQWFpZux5ZY/0hfnAPwZax/+DrOAfiym61/P8uNX/nEx8crOjpaoaGh8vPz82qBwI1YlqWYmBhFRETI3z997pBn/SM9cQ7Al7H+4es4B+DL3F3/bjW0AAAAAABkNGwKBQAAAABwJBpaAAAAAIAj0dACAAAAABwp1Rra+p/WV6/veqXW9I7lN8hPc36fk95lIJWx/s2KvVNM76x9J73LQBrgHDDjNcA3sP7NWP++gfVvxvpPPanW0M5qO0tD7h6S7J9/ftHzqjqhqrIOzapK4yoZx2w/tl11JtdR8NBgRY6J1PCfhyf7eE6x4sAKVRlfRVmHZlWJ90ro062fev0YB84ekN8gP209ujVF81y6dkndF3RXnuF5lGNYDj3w1QM6FnvMO0VmcKm9/i9du6Qn5zyp8mPLK3BwoFrPaJ38Yh3EsiyNXD1St71/m7IOzarCowvrjR/f8PpxvNV4/3X+Lz0x6wnlGZ5HIW+EqPzY8toYvTHlBTpAap8DKw6sUKsZrVRoVCFlH5ZdlcZV0rTt01JQsTN8uP5DlfmwjELeCFGpD0rps22fpcpxvPHG61jsMT0550lFjIpQtjeyqenUpvrj1B/eKTCDS+31v+vkLt095W4VGFlAwUODdeu7t6rfsn66Gnc1BVVnfLwHcoa06AGu23N6j0LfDFWut3Il+3hOcCTmiB775jHd9v5t8h/kn6q/MPDG8/+s32ap8eeNlWd4Hq+cTzeTag1teEi4QrOGpmiOjpU6qu3tbY1/d/7yeTX+vLGiwqK0qcsmjbhnhAauGKgJmyak6JjuSK8XjP1n9qv59Oa6u9jd2tp1q3rd1Uud53bW4j2L06Wem3nhuxc0b/c8ff3Q11r55EpFx0SrzVdt0rusNJHa6z8uPk4hgSF6/s7n1ejWRik6jqeuxF1J0+P9W8/vemri5oka2Xikfu/+u+Y+Mld3Fr4z3eq5kTMXz6jWpFoKCgjSoscXaeezOzWq8SjlDs6d3qWlidQ+B1YfXq0K+Svom4e/0fZu2/VUpafUfk57zd89P0XHdEd6vQaM3TBWry59VQPrDdSvz/6qQfUHqfvC7pq3a1661HMjlmWp9Zette/MPn37yLfa0nWLosKi1OjzRrpw5UJ6l5fqUnv9BwUEqX2F9vr+ie+1q8cuvdP0HX28+WMNWDEgRcd0B++B3MN7oNRb/9ddjbuqR795VHWK1knRsTyRXuv/ctxl5cuWT/3q9lPFghXTpQZPXLhyQbWL1tbbjd5OmwNaqaTe5HpWz0U9UzzPgOUDrIpjK9ryj9Z/ZOV+K7d1+drlxOyVJa9Ypd4v5dH8UWOirMErBluPzHzEyvZGNitiVIT1wboPkozRQFkfrf/Ium/6fVa2N7JZA5YPsCzLsub8NseqPK6ylXVIVuuWd26xBi4faF2Nu5r4c7tP7rbqTKpjZR2S1SrzQRnr+z3fWxooa/Zvsz2q8bo+3/exbv/w9iRZ26/bWk0+b+LRPL+d+M2q9UmtxLqW7F2SpC4NVJL/6k2u53GtZy+etYIGB1lf//p1kuNqoKw1h9d4PJ/TpPb6/7cOsztYrb5olaz5602uZ3Vf0N3qvqC7lfPNnFaet/NY/Zb2s+Lj4xPHXD9H2s1qZ4UOC7U6zO5gWZZlrTq4yqo9qbYVPDTYKjK6iPXcwues2MuxiT93LPaY1WJ6Cyt4aLBV7J1i1tRtU62oMVHWmDVjklXrzuM7rcDBgdbvJ35P1s9fd/7Seeuxbx6zsr2RzSo4sqA1evXoJP971Ztcz3YOJMcrS16xak+qnaJanSwtz4Hrmk1rZj015ymP5nfSa0CNiTWslxa/lCTr/V1vq9YntTyaJ/p8tNVsWrPEc3Pa9mlJzs2oMVFJ1n/UmCiPa911cpelgbJ+OfZLYhYXH2flG57P+njTxx7P5zTpsf5f+O4Fj59znLT+eQ/kHGm1/vt838d6YtYT1uQtk62wN8M8nt9J6//fUvLvmxbP//+2/8x+SwNlbTmyJUXz3Exg2rTNUrf53TR1+9QbjontG+v2fGv+XKO6UXWVJSBLYtakeBO9/fPbOnPxjHKHuH8VZMTqEepbp68G1R+kxXsWq+d3PXVbntt0T/F7EscMXDlQbzV8S+80fUeB/oFadXCV2s9pr/eavqc6UXW09/RedZnfRZI0oP4AxVvxavNVGxXIXkDrOq/TucvnjLcH3P7R7Tp49qDL2upE1dGixxclPub/Xo1rUryJei22z+tKXHycWs9oraJhRbWu8zrFXInRi9+/mGTM+s7rdefEO/VDux90e/7bE/+Np22fpq7zu95w/kWPL1KdqDradGSTrsZfTVJv6bylVTSsqNYcXqO7itzlds2ZgbfXvzdN2TZFnSp30vrO67UxeqO6zO+iomFF9XTVpxPHjFwzUv3r9teAegm//d97eq+aTm2qoQ2GalLLSTrx9wn1WNhDPRb10ORWkyVJT855UtEx0VreYbmC/IP0/HfP6/iF40mOfe+0e7Xq4CqXtUXlitKvz/4qSZq3e55uzX2r5u+er6bTmsqyLDW6tZGG3zNc4SHhbj/e3ot76+dDP2vuI3NVIEcB9V/eX5uPbFalgpUkJdwqVXFcRXWp0iXJv8Ghc4dU9sOyN5y7b52+6lunryRp7q65alK8iR76+iGtPLBShXMW1rN3PJtkTl+SFufAuUvnVCZvGY9/zimvAZfjLis4MDjJ34cEhWj9X+t1Ne6qggKC3Hq87ee018m/T2pFhxUKCghS78W9k5ybG57eoPwj82tyq8lqWqKpAvwCJEmrDq7SvdPuveHc41uM1+MVHtfla5clKUm9/n7+yhqYVT8d+kmdq3R2q9bMIrXX/57Te/Tdnu/UpoznVwCdsv55D+RcqbH+l+1fpq93fq2t3bZq1m+zkl2bU9a/t6TF8396SLOGdvDdg/VSzZe8Nt/R2KO6JdctSbICOQok/p0nDW2torX0v9r/kyTdluc2/Xz4Z41ZOybJYn6s3GN6qvJTiX/u+G1H/a/W/9ShUgdJ0q25b9WQu4eoz5I+GlB/gH7Y94N+P/m7Fj+xWBGhEZKkYQ2H2RbDwscW6mq869sXQgJDkjzmAtkL2B7z+cvndfHqRYUEhfz3x22W7FuivWf2asWTK1QwR0FJ0hsN3tA9n//zWPNlzydJypMtT+IYSWpZqqWqF6l+w/kLhxZOrDVLQBblCs6VtN7sBXQ09uhN68xsvL3+vSkyZ6TGNBkjPz8/lcpbSjuO79CYtWOSNF4NbmmgF2v+86LfeW5nPV7+cfW6q5ckqWSeknrv3vdU79N6Gtt8rA6dO6RFexZpfef1qla4miTpk5afqMyHSZuNifdN1MVrF13WFuT/zxv0fWf26eDZg/p659f6rPVnirPi9MLiF/TgVw9qWYdlbj3WmMsxmrJtiqY/MF0Nb20oSZrcarIiRkckjgkPCVeAX4BCs4YmWf8RoRHa2m3rDef/d2O978w+jd04Vr1r9Fbf2n21IXqDnv/ueWUJyJL4vOFLUvsc+OrXr7QheoPGtxjv8c865TWgSfEmmrhlolqXbq0qhapo05FNmrh5oq7GX9XJv0+qUGihmz7W30/+rh/2/aANT2/QHRF3SJImtpyoku+XTBxz/TUgV3CuJOfAHRF33PQcuP4adf3N+6tLX9X4FuOVPUt2jVkzRn+e/1NHYo/ctM7MJrXWf81Pamrzkc26HHdZXap00eC7B3s8h1PWP++BnMvb6//U36f05JwnNbXNVOXMmjNFczll/XtDWj3/p4c0a2jzZ8+v/Nnzp9XhPFKjSA3bn99Z906S7Pr/8NdtO7ZNPx/+WW+s+mdDmjgrTpeuXdLfV//Wbyd+U2TOyMSFbDqOlHAFKi3tOrlLkTkjkyxSdz+DGJo1NMWfifBVGXn931XkLvn5+SX+uUaRGhq1ZpTi4uMU4J/wm7k7CtnX//Zj2zVtxz+b8FiyFG/Fa/+Z/dp9arcC/QNVNaJq4t+Xzlva9uJeOGdht+uMt+J1Oe6yPrv/M92W5zZJCU1y1QlVtevkLpXKW+qmc+w7s09X468mWfNhwWEqlefmPxvoH6gS4SU8qveOiDs0rOEwSVLlQpX1y/FfNG7TOJ9saFPzHFi+f7me+vYpfXzfx7o9/+0e/7xTXgNer/u6jsYe1V2f3CXLslQgRwF1qNhBw1cPl7+fe1ti7Dq5S4H+gapSqEpiViK8hFuf7Q4JCnH7HAgKCNKsh2ep09xOCh+e8EuiRrc20r0l7pUly605MpPUWv9fPvilYq7EaNvRbXp5ycsauXqk+tTq49EcTln/3sB7oPTh7fX/9Lyn9Vj5x1Q3qm6K5/K19Z8Wz//pwbG3HBfMUVDHLiTdLe767nH/fqLyluxZsif5c+yVWA2qP8h4e89/bwm7EU9uN3D1mHNmzenWbyZTypPbbQrmKKgrcVd09tLZJE3MsQvHUuV/n4wuI99y7A7T+u9atauer/68bWzRsKLafWq3W/N6cstxoRyFFOgfmNjMSkq8vfTQuUNuNbQp4ektx4VCC6lsvqTjy+Qto29++ybVaszIUuscWHlgpe774j6NaTJG7Su2T255N5URXgNCgkI0qdUkjW8xXscuHFOhHIU0YdMEhWYJTfytemry9JazqhFVtbXbVp27dE5X4q4oX/Z8qj6xuu0XZL4gtdZ/ZFikJKlsvrKKs+LUZV4XvVjjxcRfRnpLRlj/vAdyLm+v/2X7l2nurrkauXqkpH9+oR44OFAT7pugjpU7pqje/8oI6z+9ccvx//P27QY1itTQa8teS/K5oSX7lqhUnlIe3W4sSWv/XJv0z3+tvennsKoUqqJdJ3e5/G1FmXxldPj8YR2JOZJ4G9h/jyN5drtBjSI1tHDPwiR/v2TfEuNvfVwplbeUDp8/rGOxxxJv0d7w14YkY65/XiQuPi5J7sntNlULVVWQf5CW7luqB8o+ICnhN0OHzh1SjUj3680sMvItx+v+Wpfkz2v/XKuS4SVv+IaoSqEq2nlip8v1XzpvaV2Lv6ZN0ZsSbznedXKXzl46m2ScJ7cc1ypaS9fir2nv6b0qHl5ckhIbZ3d/y3lr7lsV5B+kDX9tUNGwopISPne5+9TuJL/pzRKQxbb+Pb3luFZkLe06tSvJ3+8+tVtRYWn7G9mMIjXOgRUHVqjF9BZ6u9Hb6lK1S7LnccprwHVBAUEqkrOIJGnGrzPU4rYWbl+hLZW3lK7FX9OWI1sS76DYc3qPzlw6k/QY/kG2cyC5t5yFBYdJkv449Yc2Rm9M0dd5OFVavAbEW/G6Gn9V8Va8AuR+Q+uU9c97IOfy9vpf02mN4qx//vf59vdv9fbPb2t1p9WJ/xu4yynr3xvS4/k/rWTYW473nN6j2CuxOhp7VBevXUz8/qKy+coqS0AWPVb+MQ1aOUid5nbSK7Ve0S/Hf9G7697VmCZjPK7t58M/a/jPw9W6dGst2btEX//6tRY8tuCGP9O/bn+1+KKFioYV1YNlH5S/n7+2HdumX47/oqENhqrRrY10W57b1GFOB424Z4TOXz6v15a9ZpvHk9sNut3RTR9s+EB9lvRRx8odtWz/Mn3161c3rfXf7rn1HhXPXVwd5nTQ8HuGK+ZyjPot7ydJ8lPCbaf5s+dXSGCIvtvznYrkLKLgwGCFBYd5dLtNWHCYOlXupN7f91Z4SLhyZs2p5xY9pxpFavjcZgiS99e/JO08sVNX4q7o9MXTirkSkzjm+uZG7jp07pB6L+6trlW7avORzXp//fsa1XjUDX/mlVqv6K6Jd6nHwh7qXKWzsgdl184TO7Vk3xJ90OwDlcpbSk1LNFXX+V01tvlYBfoHqtfiXrYnZ09uOW50ayNVKVRFHed21DtN3lG8Fa/uC7vrnlvvSXLV9kZCs4aqQ8UOennJywoPCVf+7Pk1YMUA+fv5J65/SSqWq5h+PPSjHin3iLIGZlXebHk9vuX4hbteUM1JNTVs1TA9fPvDWv/Xek3YPEETWqT+V4tlRN4+B5bvX64WX7RQz+o99UDZBxI/l5YlIItHm4RJznkN2H1qt9b/tV7VC1fXmUtnNHrNaP1y/BdNaT3F7TlK5y2tRrc2Upf5XTS2+VgF+Qfpxe9fVEhgiO0cWLp/qWoVraWsAVmVOyS3x7ecff3r18qXPZ+KhhXVjmM71PO7nmpdurUaF2/s9hyZhbfX/7Tt0xQUEKTy+csra2BWbYzeqFeXvqq2t7d1e3Ow65yy/nkP5FzeXv9l8iVtODdGb5S/n7/K5S/ncW1OWf+SEv8dYq/E6sTfJ7T16FZlCchiuxvMlbR8/j998bQOnTuk6JhoSQm/0JES7rRIjbsUUu17aFOq89zOqjy+ssZvGq/dp3ar8vjKqjy+cuI/TFhwmL5v9732n92vqhOq6sXvX1T/uv2T/JZ+xYEV8hvkpwNnD9zwWC/WeFEbozeq8vjKGrpqqEY3Ga0mJZrc8GealGii+Y/O1/f7vle1j6vprk/u0pi1YxKvvvj7+Wt229m6eO2i7px4pzrP66w3Grxxwzlv5pbct2jBYwu0ZN8SVRxXUaPWjNLElhOT1Prp1k/lN8jP5RwB/gGa88gcxV6JVbWPq6nzvM56rU7CSXb9NolA/0C9d+97Gr9pvCJGR6jVjFbJqndM0zFqUbKFHvjqAdX9tK4K5iioWW2TvxOdL7nZ+pekZtOaqfL4ypq3e55WHFiROOa6618Ov+LAihseq32F9rp4NWGddl/YXT2r97zp1a4KBSpo5ZMrtfvUbtWZXEeVx1dW/xX9k3xeZHKryYoIjVC9T+upzVdt1KVKlxR9hsbfz1/zHp2nvNnyqu6nddV8enOVyVdGMx6c4dFjHt1ktGpE1lCLL1qo0eeNVCuylsrkK5PkNqHBdw/WgbMHVPy94so3Inm3clYrXE2z287WF798oXIfldOQH4fonSbvpNvtOE5zs3NgyrYp+vvq33rzpzdVaFShxP/afPnPLWCZ7TUgLj5Oo9aMUsVxFXXP5/fo0rVLWt1xtYrlKubRY/6s9WcqkL2A6k6uq/u/vF9PV3laoVlDk5wDoxqP0pJ9SxQ5JjLJ84onjsQeUbvZ7VT6g9J6/rvn1a5CO33xwBfJmsvX3Gz9B/oH6u2f39adE+9UhbEVNGjlIPWo1kMTW05MnCOzrX/eA/kOd94D3UxmW/+SEv8dNh3ZpOk7pqvy+MpqNq2ZR485rZ7/5+6aq8rjK6v59OaSpEe+eUSVx1fWuI3jkjXfTaXqlwKls0mbJ1kl3ithXbl2xeWYlHwvZkbUf1l/j78z7aeDP1kaKGvPqT2pUxTSxbJ9y6xcb+WyTv992uUYb31XXEbhzmP+r9jLsVbYm2HWxE0TU7EypAdffA1w5zH/1+Fzhy0NlPXD3h9SsTKkNV9c/7wHwnW+uP59+fk/zW45Tg8L9yzUsAbDPL79xskW7VmkD5p9cMMxs3+brRxZcqhknpLac3qPen7XU7UiayV+LhGZw8I/Fqpv7b4ef6bcydx5zFuObNHvJ3/XnYXv1LnL5zR4ZcLXXLQqnbzfwiPj8sXXAHce87L9yxR7JVbl85fXkdgj6rOkj4rlKuaVHUORcfji+uc9EK7zxfXvy8//mbqh/fqhr9O7hDS3/un1Nx0TcyVGr/zwig6dO6S82fKq0a2NbvqZSTjPiMYj0ruENOfuYx65ZqR2ndylLAFZVDWiqlY9tUp5s+VN5eqQ1nzxNcCdx3w17qr6Lu2rfWf2KTRrqGpG1tS0NtN86o2fL/DF9c97IFzni+vfl5///SzL8r0vhAMAAAAAOF6G3RQKAAAAAIAboaEFAAAAADgSDS0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4UqA7g+Lj4xUdHa3Q0FD5+fmldk1AIsuyFBMTo4iICPn7p8/vX1j/SE+cA/BlrH/4Os4B+DJ3179bDW10dLQiIyO9VhzgqcOHD6tIkSLpcmzWPzICzgH4MtY/fB3nAHzZzda/Ww1taGho4mQ5c+b0TmWAG86fP6/IyMjENZgeWP9IT5wD8GWsf/g6zgH4MnfXv1sN7fXbC3LmzMlCRrpIz1tcWP/ICDgH4MtY//B1nAPwZTdb/2wKBQAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHCkwvQtwsk2bNtmy2bNnG8d+8803xnzXrl22zLIs41g/Pz9jXrVqVWNepkwZW/bqq6+6PRYAAGQcsbGxxvzw4cPGfOzYsW7P3bFjR2NeqVIlt+cAgPTAFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHoqEFAAAAADhSpt/leMKECbbs999/N45dtWqVR3Obdjl2tROxJzsXd+3a1Tj2/vvvN+aNGzd2VSIAAHAg047GI0aMMI4dMmRIio83btw4Y962bVtj/u6779qy8PDwFNcBwDOPPPKIMW/RooUte+KJJ1K7nHTBFVoAAAAAgCPR0AIAAAAAHImGFgAAAADgSDS0AAAAAABHyvSbQpk2WHK1cVO2bNmMeZkyZYx5r169bFnp0qWNY/PmzWvM27RpY8yBjGLFihXGfNasWbZs5syZxrFHjhwx5pUrV7ZlDz/8sHHs//73PxcVAkDmM2zYMFv21ltvpdrxrl27ZsynTZtmzJcuXWrLPv30U+NYNq8EUi4+Pt6YL1u2zJiXLVs2NcvJULhCCwAAAABwJBpaAAAAAIAj0dACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR8r0uxybdhGeM2eOcayr3Yw3bNjgzZKAdHX06FFjfv/99xvz9evXG3PLsmxZZGSkcWypUqWM+eHDh23Za6+9ZhwbFRVlzB999FFjDudYuHChMTetyStXrqT4eCEhIca8VatWHs1jWpM9e/Y0jl23bp0xN+2AX7t2bY/qQOZ0yy23uD3W1bc39OjRw5bdfvvtxrGuzq3+/fsbc9Nriatz6JVXXjHmffr0sWWuvnEC8HVbtmwx5idOnEjjSjIertACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4Eg0tAAAAAMCRMv0ux+PGjbNlmzdvNo49ePCgMT906JAxL1q0aPILA9LAyZMnbVmzZs2MY7du3WrMXe0uPH78eFtWvXp149iwsDBjbtrluGXLlsaxX3/9tTFv27at2+MrV65sHFuyZElj7mrnUHiXq+dYb+xobHLx4kVjPmPGjBTPPWbMGGPu6rH4+9t/r+zqPHrooYeMedmyZY15sWLFbJmrHceR8cyePdvtsQ8//LAxf/fdd1NcR8WKFY256VskTp06ZRw7ePBgY753715bNmnSJOPYoKAgVyUCHtm9e7cxf+mll4z5+++/b8xdvT/KKMqXL5/eJaQZrtACAAAAAByJhhYAAAAA4Eg0tAAAAAAAR6KhBQAAAAA4UqbfFCpfvny27OmnnzaO7devnzE3bawjsSkUMr4RI0bYMlebPxUuXNiY79q1y5hnyZIl2XVdFxkZactmzpxpHJs1a1ZjvnDhQmP+6KOPul3HhQsXjHlISIjbcyD5OnXqZMxNm8Ds2bPHONaT52NXm0LNnTvX7Tlc+e2334z58ePHjXl8fLwtW7NmjXGsq9yV4OBgW9anTx/j2EGDBnk0N1LfokWLbJmrjepee+21VKujTp06xvzbb7+1Za+++qpx7KpVq4z5tGnTbJllWcaxn376qTEPDMz0b2XhZWvXrjXm8+bNM+YdOnQw5mm9KZSr1z9XXL2vy4y4QgsAAAAAcCQaWgAAAACAI9HQAgAAAAAciYYWAAAAAOBINLQAAAAAAEfyya3hTLtKSq531tu5c6dH4z1RpkwZW5YtW7YUzwvfMmPGDGM+evRoW5YnTx7jWFe7s3pjN2NPFC9e3Ji7Og/btWvn9tytW7c25qbdYJF2TLsZS653P04tvXv3TvEcO3bsMOZLlixxe44vvvjCmG/cuNGjWi5dumTL3n33XeNYV489LCzMo2PCexo1amTLli5dahybI0eO1C7HpmbNmrZs+PDhxrHNmjUz5mfOnLFl06dPN45t2bKlMX/44YddlQgYLVu2zKPxGWW34PHjxxvzXLlyGfMqVaqkYjUZC1doAQAAAACOREMLAAAAAHAkGloAAAAAgCPR0AIAAAAAHImGFgAAAADgSJl+l+MTJ07Ysk8++cQ41s/Pz5h36NDBmJt2OXY1h6sdke+//35b9vjjjxvHtmnTxpgD27dvN+ZxcXG27PbbbzeOTY9dMj1RpEiRFM8RGhpqzF2dt4Cnypcv71Fu8uyzzxrzv/76y5i/9dZbxnzixIm27Ny5c8axo0aNMuaDBw825kh9pm9BcLXLsSdM60Jyvbtw165dU3zMxx57zJh/+OGHbs+xe/fuFNcB3xMTE2PLXJ1Hbdu2NeZ33nmnV2tKrmvXrhlzf3/z9cnAwEzf5iXiCi0AAAAAwJFoaAEAAAAAjkRDCwAAAABwJBpaAAAAAIAj0dACAAAAABwp02x/ZdrNWJLq1q1ryw4ePGgcW7VqVWNu2mlQkmrXru1mddLHH39szDdv3mzLZs2aZRzraifWDRs2GHNT3dmyZXNVIhxs7969bo/t06dPKlaSehYvXmzML1265PYcDz30kLfKAVJNcHCwMS9evLgxf+WVV4y5aTfbnDlzGsc++eST7hWHNHPHHXe4PdbVTvem58cePXoYx165csWYr1ixwu06UpOrb6goXbq0Mb/nnntsWVhYmFdrQsa3c+dOW/bnn38ax7razdjVLsKp5ezZs8b8t99+M+aNGzdOxWqcgSu0AAAAAABHoqEFAAAAADgSDS0AAAAAwJFoaAEAAAAAjpRpNoX6/fffjfmuXbts2QMPPGAc+/XXX3u1pn/r0qWLMT958qQtmzp1qnHsnDlzjHm1atWMedmyZW2Zq8foauMrZCx///23MZ89e7bbcxQuXNhb5aQKVxuT9O3b15hfvnzZmIeGhtqy8uXLJ78wIIP69ttv3R57/vx5Yz5z5kxj7tRN5DKD1q1b27LPPvvMOLZBgwbG/NixY7bM1aZjrp57MwpXG3o+/PDDxty0CaarDTpbtWrl9hxwlp9++sntsfXr10+9Qjzw5ZdfGnNTzyCZN8D1NVyhBQAAAAA4Eg0tAAAAAMCRaGgBAAAAAI5EQwsAAAAAcCQaWgAAAACAI2WaXY7r1KljzOPj49O4Es/kzZvXlvXq1cs41lU+YcIEY27aza9evXrGsYsWLTLmVatWNebIWK5du5beJSTL1atXbdmyZcuMY/fu3evR3B07drRlUVFRHs0BZCT79u0z5gMHDnR7jrCwMGP+9NNPJ6ckpKKcOXPasieeeMKjOXLkyGHLXH2TgqtvQTh9+rQxX7BggUe1pDXTtwI8/vjjxrGudsCfNm2aLStXrlzKCkOqcPWNBx9++KEtCw8PN46Njo52ew7JvIu4q2+jWLlypTE3sSzL7bGSdPHiRY/GZ0ZcoQUAAAAAOBINLQAAAADAkWhoAQAAAACOREMLAAAAAHAkGloAAAAAgCNlml2OfVmXLl2MeZs2bWxZ3bp1jWObN29uzD/66CO35kXaCAw0n7LFihUz5gcOHLBl33//vXFsxYoVk1vWTR05csSYf/7557bsf//7n1eO+eSTT3plHiCjmDdvnjGPjY11ew5Xuxnnzp07WTXBeVq0aOFRHhcXZ8xjYmLcPqZpN1hJ8vPzs2X58+d3e15JGjBggDGfNGmSLbtw4YJx7I4dO4z5iy++aMvefvtt49hKlSq5qBBp4dKlS8Z8//79bs9x3333GXN/f/P1v7Jly9oyV+/HmjVr5nYdP/zwgzF39Rhfe+01Y276JpX27du7XYeTcIUWAAAAAOBINLQAAAAAAEeioQUAAAAAOBINLQAAAADAkdgUKhMzfRh83LhxxrGmjQ8kqVu3brbs0KFDxrG9evVyvzgkS5YsWYz5jz/+aMxNGxb06dPHONbVZlEPPPCAMd+5c6ctc7VJiKv6TBuFhIWFGceePXvWmEdFRRnzyMhIYw5kdH/88Ycx79evn0fzZM/+f+3dd3hT5f/G8TsdtKWUsqGFsmWIjAIiQ6YgqGwVFBQUARdfEXCAgw1OloqKMgRZCggKMmQIskE2six779EKFGjz+4NfKzVPIClJ29O+X9flddm7T04+Kc/JySfn5EmwQ/bCCy8kqyakH2fOnDHme/bsMebVq1c35tmyZXP5Pt0Z664RI0YY89atWztkL7/8snGss0WhFi5c6JA5WyBo3rx5zkpECggICDDmJUqUcMhOnTplHPvOO+8Y8/bt2xtzdxcwc1XBggWN+eHDh425v7+/MTe95mdRKAAAAAAA0hAaWgAAAACAJdHQAgAAAAAsiYYWAAAAAGBJNLQAAAAAAEtileMMplatWsbc2ep8pvHOVkRmlePUU6BAAWM+ceJEh2zQoEHGsYsXL3YrN624XKRIEePYOnXqGPM2bdo4ZI0bNzaOtdlsxrxevXrGPEeOHMYcSEtMK86++eabxrExMTFubXvAgAEOWalSpdzaBqxt9uzZDlnXrl2NY48fP27Mp06dasybNWuW/MJSgGl15hUrVhjHVqxY0Zjv3bvXIVu9erVx7Pz58415o0aNnJUIDwoMDDTm69evd8hu3LhhHJsarxuOHj3qkJ0/f944tkKFCsZ8/PjxxjwoKCjZdVkNZ2gBAAAAAJZEQwsAAAAAsCQaWgAAAACAJdHQAgAAAAAsiYYWAAAAAGBJrHIMSVKuXLmMec2aNR2yXbt2ebsceEjTpk0dskceecQ4dsOGDW5t27TKsbOVIp3Zs2ePQxYbG+vWNp544gm3xgNpyQcffOCQ/fzzz25to2jRosbc2Wq2yDiio6MdMmerGTt77m3ZsqUxN60YXK1aNTeqS3khISHGfPLkycbctFLypUuXjGM/+ugjY84qx6kra9asqV3CbZlWx3a2ov1jjz1mzMuVK+fRmqyIM7QAAAAAAEuioQUAAAAAWBINLQAAAADAkmhoAQAAAACWREMLAAAAALAkVjmGJGnnzp3GfNasWQ7Zvffe6+Vq4E3+/v7GvGrVqilciXTkyJG73kZq1A24a+rUqcZ82LBhLm8jS5Ysxtz0PC1JPj68Z53RtWnTxiE7duyYcexbb71lzO12uzGPi4tLfmFpzNatW415fHy8y9tgpVkkx/nz510eW7duXS9WYm0c7QAAAAAAlkRDCwAAAACwJBpaAAAAAIAl0dACAAAAACwp3S8KZVpwI3fu3MaxzzzzjLfLSXUHDx405u+++64x/+effxyyZcuWebQmZFzTp09P7RIAj3L2/Pjiiy8ac2cL7ph89913xrxs2bIubwPo3LmzMZ83b54x//333415u3btHLI6deoYx/bs2dOYlyhRwph7wogRIxyy0aNHG8dGRUUZc3f2T8DbMmXKlNolpFmcoQUAAAAAWBINLQAAAADAkmhoAQAAAACWREMLAAAAALAkGloAAAAAgCWlm1WOf/rpJ2Peo0cPh8zZapNpZZXj06dPG/OZM2e6tR3T+I0bNxrHOlv5+fvvv3fISpUq5VYdwKFDh4z5lClTXN5G7dq1jXnWrFmTVRNwty5cuOCQNW7c2Dg2JibG5e126dLFmDdt2tTlbQDOOHvO/Pnnn415uXLljPnx48cdMmcrcZteS0iSj4/3zqtcv37dK9utUqWKMe/du7dX7g/AnXGGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSDS0AAAAAwJJoaAEAAAAAlpRuVjl2xm63O2SjRo0yjp0xY4Yxb9mypcvb3rVrl3Fszpw5jfmsWbNc2q4k2Ww2l+uQpNKlSztkbdu2NY595513jHmuXLmMOeCOqKgoY37x4kWXt9GsWTNj7ueX7p/GkMri4+ON+fjx4x0yd1YzlqTKlSs7ZEOHDjWO9ff3d2vbgDuyZMlizPft22fMTfN/6tSpxrHbtm0z5seOHXOxOu+qUaOGMW/YsKFD1qlTJ+NYZ6/zgNtZtWqVy2N3795tzGvWrOmpciyLM7QAAAAAAEuioQUAAAAAWBINLQAAAADAkmhoAQAAAACWlG5WU3G2cNP8+fMdMtNCTLczc+ZMY37q1CmH7N577zWOdbag04svvuiQOVuIqUWLFs5KNCpVqpRDljlzZre2AXjC6dOnXR7rbI7+73//81Q5gFvWrFljzF9//fW73vbbb7/tkLH4E6ygffv2LmWSdOLECWMeHR3tkH377bfGsXXq1DHmf/75pzEvUaKEQ1apUiXj2IIFCxrzgIAAYw54imkfcCZ79uxerMTaOEMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABLSjerHDvTsGFDl7Lb+eqrrzxVDpAhzZgxw+WxZcuWNea+vr6eKgcwunTpkjFv3LjxXW+7Zs2axrx58+Z3vW0grcuXL5/L+ccff+zWth999NFk1QSkBY0aNXLIgoODjWMfeeQRb5djWZyhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJZEQwsAAAAAsCQaWgAAAACAJaX7VY4BpL5p06YZc5vN5pBFRkZ6uxzAaNGiRcb8/PnzLm/D2WrGU6ZMMeZ+fhyGASCj6tGjh0sZbo8ztAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJZEQwsAAAAAsCSWVwTgdXa7PbVLAO6oTJkyxjxfvnzGvESJEg7ZpEmTjGPz58+f/MIAAIBTnKEFAAAAAFgSDS0AAAAAwJJoaAEAAAAAlkRDCwAAAACwJBaFAgBAUsmSJY358ePHU7gSAADgKs7QAgAAAAAsiYYWAAAAAGBJNLQAAAAAAEuioQUAAAAAWJJLi0LZ7XZJ0qVLl7xaDPBfCXMuYQ6mBuY/UhP7ADIy5j8yOvYBZGSuzn+XGtro6GhJUkRExF2WBSRPdHS0QkNDU+2+JeY/Uhf7ADIy5j8yOvYBZGR3mv82uwtv+cTHx+vYsWMKCQmRzWbzaIHA7djtdkVHRys8PFw+PqlzhTzzH6mJfQAZGfMfGR37ADIyV+e/Sw0tAAAAAABpDYtCAQAAAAAsiYYWAAAAAGBJNLQAAAAAAEvyWkNb57s6en3+697avGXZ+tk0a9es1C4DXsb8Nys8vLCGrxme2mUgBbAPmHEMyBiY/2YcAzIG5r8Z8997XPranuT4qfVP8vfxT/btX5v3mlYeXqntp7ardK7S2vzS5iS/P3DhgIqMKOJwu9UvrFbVAlWTfb9p2dIDS1V3fF2H/HiP48qXJZ/H7ifhb7vpxU2qkK9CsrdT57s6WnZwWZLsxUov6uvGX99lhWmft+e/dHPltyGrh+ibDd/o4MWDypU5l16p/IrerfXuXVSetv34148avHyw9pzdo9zBudXl/i56s8abHr+fwsML6/Wqr+v1qq8nexvRsdF6//f3NXPXTJ3655Qi80VqRKMRuj///Z4rNA3z9j7Qd2lf9VvWz+F2mf0z6593/kn2/aZlz816TuO3jHfI7819r/565S+P3Y8njgHOjtGS9OMTP+rJMk/eRYVpX0ocAxZELVCfpX301+m/FOgXqFqFamnIw0NUOFvh5Beehu0+s1sv/fqSdpzeoYtXLyo8JFxtyrZRn9p95O+b/L+1ia2fTTNbz1TzUs2TvY2+S/tq6vapOnzpsDL5ZlKlsEoaVG+QHijwgOcKTaNSYv6n1OuBtCjqXJQiR0XK1+arCz0veHz7npj/t3ppzksatWGUhjUcdlevq27Haw1tjqAcd72NDhU6aO3Rtdp6cqvTMYueXaQyecok/pwzKOdd3++dXI+77vEnT3fs7rJbWQOyJv6cJzhPqtVyJ50qdlL/uv0Tf87snzkVq0k5KTH/u87vqt/2/qZPH/5UZfOU1bkr53Tuyrm7vt87uRZ3TZl8M3n9fv5r3t/z1Pantvr8kc/1cLGHtfP0TnWa3UlB/kHqUqVLitdzJx1nd9T2U9v1fYvvFR4SrolbJ6r+9/W145Udyp81f2qX53Xe3gfeqP6GXqr8UpLsoQkP6f5w779hkFrHgBGNRujD+h8m/nwj/obKf11eT96b9prDiKwROt7jeJLsmw3f6JNVn+iRex5JpapSjrfn//7z+9VsajN1r9Zdk1pO0sXYi+q2oJta/tBSG1/ceNf3fTupdQzw9/VXu3LtVDGsorIFZtOWk1vUaXYnxdvjNfihwSlez52UyFlCXzz6hYpmL6or169o2Jphenjiw4r6X5RyB+dO7fK8ytvzPzVfD6TW/E9wPe66np7xtGoWrKlVh1elWh2umrlzptYcWaPwkHCv3k+aveT4s0c+06tVXlXR7EVvOy5n5pzKlyVf4n/uvsgoPLywBiwboKdnPK3gwcHKPzS/Rq4bmWSMrZ9NX63/Sk2nNFXw4GANWj5IkvTzrp9VcVRFBQ4MVNERRdVvaT/diL+ReLu/z/6tWuNqKXBgoO4dea8W7l3oVm3O5AnOk+Qx+9jc+2fcdWaXHhz7YGJdi/YtSnIZXMK76pGjImXrZ1Od7+oku9bM/pmT1HprI56eeXv+7zy9U1/9+ZV+fupnNS3ZVEWyF1Gl8EpqUKyB23V2mdtFXeZ2UeiHocr1cS69v+R93fptXgn7SLuZ7ZT1g6zqPLuzJGnFoRWqOa6mggYFKWJYhF6b95r+ufbvmbFT/5xSkylNFDQoSEVGFNGkrZOS8Zf41/dbv1fzUs31UuWXVDR7UT1W4jH1erCXPlr5kdz59rHo2Gi1/amtggcHK2xImIatHpbk36vOd3V08OJBdVvQTbZ+Ntn6uf+de1euX9GMHTP0cf2PVatQLRXPUVx96/RV8RzF9dWfX7m9PSvy9j6QJVOWJM8tJ2NOasfpHXoh8gW37sdKx4DQwNAkj/nPY3/q/JXzer7C825tJyWOAb4+vklqzZcln2bumqlW97ZSlkxZ3N6e1Xh7/m84vkFx9jgNrDdQxXIUU8Wwinqj2hvafGKzrsddd6tOqxwDimYvqucjn1f5fOVVKFshNS3ZVG3LttXyQ8vd2s7x6ON6bPJjiXVN3jY5yaWghYcXliS1+KGFbP1siT+7q03ZNqpftL6KZi+qMnnKaGjDoboUe+m2J2nSC2/Pf0+9HrDS/E/w3pL3VCpXKbUq0ypZt0+p+S9JRy8d1f/m/U+TWk66qzP2rvDaGdr/emnOS5q4deJtx8S8E+P2dptOaaqrN66qRM4SeqvGW2pasqnb2/hk1Sd6p+Y76lennxZELVDX+V1VImeJJM1B32V99eFDH2p4o+Hy8/HT8oPL1W5WO33W6DPVLFRTe8/tVec5Nyd5nzp9FG+PV8sfWypvcF6t7bhWF2MvGnfuMl+W0cELB53WVrNQTc1rOy9JVuHrCoqNi9V9ee5T39p9VaNgDZcfa1x8nJpPba6CoQW1tuNaRV+LVo/feiQZs67jOlUZXSXx7HfCO1GTtk7Si3NevO3257Wdp5qFaib+PGnbJE3cOlH5suRTkxJN9H7t9zPMWdpbeXr+z94zW0WzF9WcPXPUaFIj2e121S9aXx83+Njtd0bHbxmvFyJf0LqO6/TnsT/VeU5nFQwtqE6VOiWO+XT1p+pdq7f61O4jSdp7bq8aTWykgfUGamzTsTp9+fTNg8K8LhrXbJykm5dHHos+pt/b/y5/H3+9Nv81nfrnVJL7fmTSI1p+0PmLkULZCiVeShkbF+swd4L8g3Tk0hEdvHjQ5cvsui/orpWHVuqXp35R3ix51fv33tp4fGPipZU/tf5J5b8ur84VOyf5Gxy6eEj3jrz3ttt+p+Y7eqfmO7oRf0Nx9jgF+gUmrdcvSCsOrXCpzvTGW8eABKM3jlaJnCWSPP+4ymrHgARjNo1R/aL1VShbIZcfa0ofAxJsOLZBm09s1shHRxpulf55ev5XCqskH5uPxm0ap+cqPKeYazH6fuv3ql+0vttv7FvlGPBfUeeiND9qvlqWbunW4203q53OXD6jpe2Xyt/XX90XdE9S1/pO65Xn0zwa12ycGhVvJF+bryRp+cHlemTS7a8uGNV4lNqWa+uQX4u7pm82fKPQgFCVz1ferXrTA0/Pf0+9HpCsNf+X7F+iaTumafNLm/XTzp9cfoy3Sqn5H2+P17Mzn9Wb1d9MciWtt6RYQ9u/bn+9Uf0Nj20vS6YsGvLwENWIqCEfm49m7Jyh5lOba9ZTs9xuamsUrKGeD/aUdPMSkZWHV2rYmmFJXsy0ua+Nno/8913wDj93UM8aPdW+QntJN985HFB3gN5a+Jb61OmjRfsWadeZXVrwzILE0+yDHxrsMBnmtpmr6/HO300N8gtK/P+wLGH6+rGvVTm8smLjYjV642jVGV9HazuuVcWwii491oX7Fmrv+b1a+tzSxM/dDqo3SA2+//exJlwKk3D2O0HTkk3v+NmP/CH/XkrZpmwbFQotpPCQcG09uVVvL3pbu8/u1k+tk7cTWpmn5/++8/t08MJBTdsxTROaT1CcPU7dFnTTEz8+oSXtl7i1rYisERrWcJhsNptK5iqpbae2adiaYUmezOsVqace1f990dvxl45qW7Zt4mch7sl5jz575DPV/q62vnrsKx26eEjzouZpXcd1iZ8ZHdN0jEqPLJ3kvkc3Ga0rN644re3Wd/QaFmuobgu66bnyz6lukbqKOhelIauHSLr5jqMrB7Do2GiN3zJekx+frIeKPiRJGtdsnMKH/nspTI6gHPK1+SokICTJ/A8PCTd+judWCW8mhASEqFqBahrwxwCVzl1aeYPzasr2KVp9ZLWK5yh+xzrTI0/vA7e6euOqJm2blPg87i6rHANudSz6mOb9PU+TH5/s1mNNyWPArcZsGqPSuUqrekR1t+pNLzw9/4tkL6LfnvlNraa30otzXlScPU7VClTT3LZz3d6WVY4BCaqPqa6NxzcqNi5WnSt2TvKxpjvZdWaXFu1bpPWd1qtyeOWbNTQdrXs+vydxTML8zxaYLcn8rxxe+Y7HgLzBeZP8PGfPHD01/Sldvn5ZYSFhWvjsQuXKnMvletMLT89/T7weSGCV+X/28lk9N+s5TWw5MdlXO6bk/P9oxUfy8/HTaw+8lqxa3ZViDW2e4Dwe/axnrsy51L1a98Sf789/v45FH9Mnqz5xu6GtVqCaw8/D1w5PkiX8wyfYcnKLVh5emXjpmSTF2eN09cZVXb5+WTtP71RE1ogk14z/934kufXOeslcJVUyV8nEn6tHVNfe83s1bM0wfd/ie5e2sfvMbkVkjUgySavkr+LSbUMCQhQSEOJyvZ0rdU78/7J5yyosJEwPTXhIe8/tVbEcxVzeTnrg6fkfb49XbFysJrSYoBI5S0i6+WRZ6ZtK2n1md5J5cidVC1SVzfbvZbXVClTTkNVDFBcfJ1+fm+/MVQ5znP9bT27VpG3/XkJjl13x9njtP79fe87ukZ+PnyqFV0r8falcpZQtMFuS7bjzWdJOFTtp77m9ajylsa7HXVfWgKzq+kBX9V3W1+XL7ved36fr8deTzPnQwFCVzHnnv5efj59bzej3Lb5Xh186KP/Q/PK1+apiWEU9fd/T2nB8g8vbSE88vQ/caubOmYq+Fq325dsn6/ZWOQbcavzm8coWmM3tRTtS8hiQ4Mr1K5q8bbLer/W+27dNLzw9/0/EnFCn2Z3Uvnx7PX3f04q+Fq3ev/fWEz8+oYXPLkzynH4nVjkGJPjhiR8UfS1aW05s0ZsL39Snqz7VWzXecum2u8/slp+PX5KTAMVzFFf2wOx3vG2Qf5Dbb0jWLVxXm1/arDOXz+jbDd+q1fRWWttxbZpe+8QbPD3/PfF6IIFV5n+n2Z3Upmwb1SpUy52Hl0RKzf8NxzZoxNoR2vjiRreei+6G5S85vtUD+R/Qwn2e+ZzqfwVnCk7yc8y1GPWr0894qct/LzO8nbu53EySqoRX0YrDKXMJ491cbibd/PeRbl4mlNEaWk/P/7AsYfLz8UtsZiWpdK6b7/wdunjIrYbWFab5/2KlF43vvBUMLag9Z/e4tF13Lrex2Wz6qMFHGvzQYJ2IOaHcwbm1eN9iSbrjZ+09wZ1LjiWpWI5iWvbcMv1z7R9dir2ksJAwtZ7eOkVqTYu8eQwYvWm0GpdorLxZ8t55cDKlpWOA3W7X2M1j9Wy5Z1N0cZLkHgOm75iuy9cvq135dt4sL03z9PwfuW6kQgND9XGDjxOziS0nKmJYhNYeXevxb3tIC8eABBGhEZJuru4dZ49T59md1aNaj8Tmw1uSc8lxcKZgFc9RXMVzFFfVAlV1z+f3aMzGMepVs5dXa01rPD3/U/r1QFqY/0v2L9Evu3/Rp6s+lfRvA+3X30/fNPlGHSI7uPpwksWd+b/80HKd+ueUCg4rmPi7OHucevzWQ8PXDNeB1w94vD7LXnJssvnEZoVlCXP7dmuOrEn689E1ic2BMxXDKmr3md1O360onbu0Dl86rOPRxxUWEma8Hyn5l5sl2HzSvcdcMldJHb50WCdjTia++Ft/dH2SMQkvkOLi45Lkd3O5mXTz30dS4t8jI/H0/K9RsIZuxN9IcrY74QnU3TM+a4+uTfLzmiNrdE+Oe2774qBiWEXtOL3D6fwvlauUbsTf0IZjGxIvt9l9ZrcuXL2QZFxyLjfz9fFNfFdzyvYpqlagmssrRhbNXlT+Pv5af3S9CobefKK9ePWi9pzdk+Rdz0y+mRzmvzuXHN8qOFOwgjMF6/yV81oQtSDJC9CMxFvHgP3n9+v3/b/rl6d/SfY2rHYMWHZwmaLORemFiu4tgCWlzjFgzKYxalqyabpf2fV2PD3/L1+/7HAmKuGzbvH2eLe2ZbVjwK3i7fG6Hn9d8fZ4+erODW3JXCV1I/6GNh3flHj2LOpclM5fPe9wv/+d/8m55NhUb2xc7B3rTG+89fx/N68HElhl/q9+YbXi7P/OyZ93/ayPVn6kVS+suu1r71ul1Px/ttyzql+0fpLfNZzYUM+We9btRQxdlWYvOY46F6WYazE6EXNCV25cSWyG7s19rzL5ZtL4zeOVyTeTIsMiJUk/7fxJYzeP1egmo92ubeXhlfp45cdqXqq5Fu5dqGl/TdOvbX697W161+qtxlMaq2BoQT1x7xPysfloy8kt2n5quwbWG6j6ReurRM4Saj+rvT5p8IkuxV7Su0scvx/UneZj+JrhKpKtiMrkKaOrN65q9MbRWrJ/iX575jeXt9GgaAMVy15M7We118cNPlZ0bLTe+/09SZJNNy8LyBOcR0F+QZofNV8FshZQoF+gQgND3brcbO+5vZq8bbIevedR5cycU1tPblW3Bd1Uq1AtlctbzuV60wtPz//6ReurYlhFdfilg4Y3HK54e7xenfuqGhRtkOSsrSsOXTyk7gu668VKL2rj8Y36fN3nGvLwkNve5u0ab6vq6KrqMreLOlbsqGD/YO04vUML9y3UF49+oZK5SqpR8UZ6cc6L+uqxr+Tn46fXF7zu8OLcncttzlw+o+k7pqtO4Tq6euOqxm0ap2k7pmnZc8vufOP/FxIQovbl2+vNhW8qR1AO5QnOoz5L+8jH5pM4/yWpcLbC+uPQH3rqvqcU4BegXJlzuX3J8YKoBbLLrpI5SyrqXJTeXPimSuUq5bUn87TO0/tAgrGbxiosJEyPFE/+V8FY5RiQYMymMXog/wO6L899bt82pY4BCaLORemPg38k67Od6Ymn5/9jJR7TsDXD1H9Z/8RLjt9Z/I4KhRZSZL5It2qzyjFg0tZJ8vf1V9k8ZRXgF6A/j/2pXot7qXWZ1i4vhFUqVynVL1pfned01lePfSV/H3/1+K2HgvyCHI4Bi/cvVo2CNRTgG6DsQdnduuTyn2v/aNDyQWpasqnCsoTpzOUzGrl+pI5eOpomv2bL2zw9/z3xeiCBVeZ/6dxJ32T989if8rH5uHUcSKn5nzNzTuXMnPRrVP19/JUvSz6PX0GYwGtf23O3Ov7SUZGjIjVqwyjtObtHkaMiFTkqUseijyWOGfDHAFX6ppIeGP2Aft79s3544ocki3YsPbBUtn42Hbhw4Lb31aNaD/157E9FjorUwOUDNbThUDUs3vC2t2lYvKHmPD1Hv+37Tfd/e7+qjqmqYWuGqVDozRcnPjYfzWw9U1duXFGV0VXUcXZHDao36LbbvJNrcdfU47ceKvtVWdX+rra2nNyiRc8uSlzcRpK+2/zdbb9mxNfHV7OemqWYazG6/9v71XF2R71b8+aLrITL5Px8/PTZI59p1IZRCh8armZTm7ldaybfTFq0f5EenviwSn1RSj1+66HHSz+u2U/PdntbGdGd5r+PzUezn56tXJlzqdZ3tfTY5MdUOndpTX1iauI2Dlw4IFs/m5YeWHrb+2pXrp2uXL85T1+d+6q6PtA1yeefTcrlLadlzy3TnrN7VHNcTUWOilTvpb2TfF5wXLNxCg8JV+3vaqvljy3VuWLnu/4Mzfgt41X5m8qqMbaG/jr9l5a2X5rk83+uPOahDYeqWkQ1NZ7SWPW/r68aETVUOnfpJJeJ9q/bXwcuHFCxz4op9yfJO6t0MfaiXp37qkqNLKV2s9rpwYIPasEzC1L1O6ytxJVjQLw9Xt9t+U7PlX/O+G56ejsGSDevKJixY4bTrydKK8eABGM3jVWBrAX0cLGHk72NjOhO879ekXqa/Phkzdo1S5GjItVoYiMF+AVo/jPzFeR/80VzejsG+Pn46aOVH6nK6Coq91U59VvWT13u76LRTf89keHKPj+h+QTlDc6rWuNqqcUPLdSpYieFBIQkOQYMeXiIFu5bqIhhEYoc5d4bBNLN/WzXmV16/MfHVeKLEmoypYnOXjmr5c8vT5EVX63Oled/T7wekKwz/12RVuZ/qrCnY2M3jrUX/6y4/dqNa07HFBpWyD5s9bCUK8rLei/pba89rrZbt1lxcIVdfWWPOhvlnaKQKpbsW2LP9mE2+7nL55yOqT2utr3rvK4pV5SXufKY/ysmNsYe+kGoffSG0V6sDKmBY4BrOAakTxnxGODKPv9fhy8etquv7Iv2LvJiZUhpzH/XpJf5n2KXHKeGuVFzNbje4Ax1RmRe1Dx98egXtx0zc+dMZcmURffkvEdR56LUdX5X1YiokeEWakrv5v49V+88+I6yB9159br0wpXHvOn4Ju06s0tV8lfRxdiL6r/s5lc+NCuV/LNQSJs4BphxDMgYMuQxwIV9fsn+JYq5FqOyecrqeMxxvbXwLRXOVviuVo9F2sP8N0uv8z9dN7TTnpyW2iWkuHWd1t1xTPS1aL296G0dunhIuTLnUv2i9e/4eQFYzycPf5LaJaQ4Vx/zp6s/1e4zu5XJN5MqhVfS8ueXZ8jvBkzvOAaYcQzIGDLiMcCVff563HW9s/gd7Tu/TyEBIaoeUV2TWk7KUG98ZQTMf7P0Ov9tdrvdntpFAAAAAADgrjS7KBQAAAAAALdDQwsAAAAAsCQaWgAAAACAJdHQAgAAAAAsiYYWAAAAAGBJNLQAAAAAAEuioQUAAAAAWBINLQAAAADAkmhoAQAAAACWREMLAAAAALAkP1cGxcfH69ixYwoJCZHNZvN2TUAiu92u6OhohYeHy8cndd5/Yf4jNbEPICNj/iOjYx9ARubq/HepoT127JgiIiI8VhzgrsOHD6tAgQKpct/Mf6QF7APIyJj/yOjYB5CR3Wn+u9TQhoSEJG4sa9asnqkMcMGlS5cUERGROAdTA/MfqYl9ABkZ8x8ZHfsAMjJX579LDW3C5QVZs2ZlIiNVpOYlLsx/pAXsA8jImP/I6NgHkJHdaf6zKBQAAAAAwJJoaAEAAAAAlkRDCwAAAACwJBpaAAAAAIAl0dACAAAAACyJhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJZEQwsAAAAAsCQaWgAAAACAJdHQAgAAAAAsyS+1CwBgTZs2bXLI3n//fePYuXPnGvPMmTM7ZH/88YdxbMWKFd2oDnBu6NChxrxHjx7GfNWqVca8WrVqHqsJAAAkD2doAQAAAACWREMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSaxyDCBZevXq5ZAtXLjQONZmsxnzLFmyOGTOVqCdOHGiG9UBzg0fPjy1SwAAAB7CGVoAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSqxwDuK0lS5YY840bN7q8jTfffNOYd+jQwSE7d+6cy9sF7uTw4cMuZZI0ZMgQY16tWjWP1gTAOWer5c+YMcOY//jjj8b8/PnzHqvpVj4+5nNBa9euNeaVK1f2Sh1IOc6OAZ988olD9uCDD3q7HBhwhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSWBQqlR08eNAh++yzz4xj//zzT2M+cuRIY37fffclvzBkOGfPnjXmTz75pDG/cOGCQ9akSRPj2IEDBxpzPz+eguBd06ZNc3lsgQIFvFgJkP798MMPxnz27NnGfO7cuQ6Z6dgiSXa73Zjfc889xrxjx44O2QMPPGAc6+z1kmmhuG+//dY41tmiVSwKZR3OFrvctm2bMc+RI4c3y4EbOEMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABLYolRD9uzZ48x/+KLL4z5hAkTHLKLFy+6dZ+NGjUy5nPmzHHIDh8+bBxbqFAhY16uXDm3aoF1rV692pg7W3HSpGfPnsac1YyRWtxZ5bhatWperASwprfeesuYf/755w5ZbGyscayzFYpLlizpkDVs2NA4tlu3bsY8MjLSmPv7+xtzd1SpUsUh+/vvv41jna3mj7QnPj7emL/99tvGPFOmTMY8d+7cHqvpVr169TLmzlbMfvzxx71Sh5VwhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJbE0qMucLYa2o4dOxyyBg0aGMeeOHHCozXd6ujRo8a8du3aDtmlS5eMY52t7rlixQqHzMeH90HSo2XLlhlzZ6tTNm/e3CGrWrWqJ0sCXOZsBfc1a9Y4ZBEREcaxznIgIxs/frwxv3r1qkPWqlUr49g33njDmJcvX94hc7aibGqoW7euQ/bMM88Yx/r6+nq7HHjIjz/+aMyPHDlizLdv327MvbXKsbMVuqdOnWrMWeWYM7QAAAAAAIuioQUAAAAAWBINLQAAAADAkmhoAQAAAACWxKJQtzh9+rQx//zzz435gAED7vo+s2XL5pA5W7jJ2eJUzjjbjsmuXbtcvk8WhbK2U6dOGfN58+YZc5vNZsxffvllj9UE3K1hw4a5PPaJJ57wYiV3b/Xq1cbc2cJXzpgWxHryySeNY50tDAjUqFHDmM+cOdMhe+yxx4xj77//fo/WlFKKFSuW2iXAC3bu3GnM27dvb8zDw8O9WY6DEiVKGPNZs2alaB1WQmcCAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABLYpXjW7z77rvG/Ntvv3V5G5kyZTLmI0aMMOZFihRxyPr27Wsca1qx0l25c+c25j///LMx9/NjiqQ3EyZMMOY7duww5lmzZjXmOXPm9FhNwN06cuSIy2OrVq3qxUrcY1rRuHXr1sax7q5ybOJsNehVq1YZc1Y/zjj27NljzOfPn2/MTa9fWrRo4dGagLt14MABh+zLL780jnXWB6QV+/fvN+aHDh0y5gULFvRmOWkKZ2gBAAAAAJZEQwsAAAAAsCQaWgAAAACAJdHQAgAAAAAsiYYWAAAAAGBJ6X4J2/j4eIfsiSeeMI51ttKvj4+57y9XrpxDNnr0aOPYhQsXGvPXX3/dIdu1a5dxrCdUrFjRmLOSZcbhbDVjZ0wrWUrO5xIA15lWHXZ3NeMhQ4YYc9PzurMVlLt3727MTaswI336+uuvjfmVK1eMeaNGjRyykJAQj9YE3K3p06c7ZFmyZDGObdu2rbfLcYmzfiQuLs6YO1vln1WOAQAAAABI42hoAQAAAACWREMLAAAAALAkGloAAAAAgCXR0AIAAAAALCndr3L82WefOWQzZ850axulSpUy5j179nTIHnzwQePYq1evunWfnlCiRAmHbNSoUSleB9KWefPmuTX+5Zdf9lIlQMbhbLXgadOmubyNH374wZi3atXK5W1UrVr1rutA+uRsNWNnTK8xgNRy6NAhYz5gwACH7M033zSOzZ07t0drcoXpm02crXLctWtXY169enWP1mRFnKEFAAAAAFgSDS0AAAAAwJJoaAEAAAAAlkRDCwAAAACwpHSzKNT169eN+UcffXTX2zZ9YFuSnnrqKZe3kSNHDmP+v//9zyFbtGiRcezKlStdvj9J6tChg0NWqFAht7aBjMNutxvzX375xZhHRUU5ZDt27DCOnTt3rsv3abPZjGOdzd3evXsb83bt2jlkvr6+xrGAtw0bNszlsZ5Y/MlTfvzxxzRRB7zv119/NeYhISHGvHnz5l6sBjCLi4sz5mPHjjXmptcZr7zyikdruhthYWEOWc6cOY1j/fzSTdvmcZyhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJZEQwsAAAAAsCQaWgAAAACAJaWb5bJ8fMy9eZEiRRyyEydOuLXtoKAgYx4QEOCQdenSxTi2e/fuxvzw4cMOmbsrM1etWtWYv/zyy25tBxmbs9WF582b51buzrbLlCnjkDlbKfnQoUPGvGPHjsb8zJkzDtmbb77prERYXIECBVwee+TIEa/VYXpOl6Rp06YZc9PzN6sIw5tiYmKM+aVLl4x5yZIlXd7O9u3bk1/Y/ytevLgxDwwMvOttw/qio6ONeb9+/Yz5Y4895pA5++aR1BAaGuqQ1a1bNxUqsTbO0AIAAAAALImGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSDS0AAAAAwJLSzSrHvr6+xnzu3LkO2Zw5c4xj/fzMf44KFSoY81KlSrlWnJyvKti3b1+H7OrVq8axISEhxnz8+PHGPGvWrK4VB9yGs3lXrVo1h6xdu3bGsbly5TLmtWrVcsj++OMP49hvvvnGmP/000/GvGfPng5Z4cKFjWOffPJJYw7r6NatmzEfNmyYQ9ajRw/jWGer0bvD2badSem552wV5oiICGPOisvpz6pVq4z5xYsXjfmff/5pzMuWLeuxmm4VGRlpzHv16mXMmzRpYsxZFTl9Mn3DiCTVrl3bmK9bt84he/vtt41jna2w3aJFC2Pu7LXN3br//vuN+ahRo4z5Sy+9dNf36ewY4OxbZNIaa1QJAAAAAMB/0NACAAAAACyJhhYAAAAAYEk0tAAAAAAAS0o3i0I5ky1bNofsmWeeSfE6ZsyYYcxnzpzp8jZat25tzEuUKJGsmpAxPffcc8b8o48+MubO5p2zxQnuVoMGDYx51apVjfn27duN+Z49exyygwcPJr8wpGnOFrQwzZs1a9YYxw4dOtSYe2KxKGcKFCjgtW3/+OOPDpmzxz5kyBCv1YG0pUiRIsa8YcOGxjw0NNSYFytWzOX7PHLkiDHfuHGjQ7Zp0ybjWGcLlD399NPGfOzYsQ4ZC0VZX1BQkDGfP3++MTe9zt61a5dx7IQJE4z5xx9/bMzdmU92u92Y22w2h+zChQvGsc72I2cLXpoWWHO2HzlbWNHZIlxpDWdoAQAAAACWREMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSel+leOUdu7cOWPuzgqSBQsWNOYjR45MVk3ArXLmzOnW+HXr1nmpEveEhIQY8wcffNCYm1Y5RsZjWrnR2crdPXr0MObOVgY2bXvatGluVCdVq1bNrfEmptWMJemNN95wyJytBv3kk0/edR2whnvuuceYO1sl1puuXLnikO3YscM4tn///sZ8ypQpxrx06dIO2fvvv+9GdbASZysOO1sF26Rfv37G/PLly8b8+vXrDtmpU6eMY9evX+9yHV988YUxv3jxojHfvHmzMTc93/v7+7tch5VwhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSaGgBAAAAAJbEKsce1rhxY2O+bds2l7fRu3dvY54pU6Zk1QTcKnPmzMbcbrcb8xs3bhjz2NhYhywgICD5hd3Bpk2bjPkvv/xizJ09HmQsrVq1csiOHDliHDt8+HBj7mzlYndXNDZZvXq1S5kkTZ8+/a7rWLVqlTF3tvox4E1BQUEOWb58+YxjDxw44Na2c+fOnZySAAfOXjeZhIaGGnNnq4ubzJkzx5hHRUUZ8xw5chjz9LqisQlnaAEAAAAAlkRDCwAAAACwJBpaAAAAAIAl0dACAAAAACyJhhYAAAAAYEmscnwX9u3b55Bt377drW2YVkV+7rnnklsScEevvPKKMV+/fr0xnzBhgjH/3//+55CNGDHCONa0kqUzhw4dMuavvvqqMT9z5owxt9lsDhmrXkKSunfvbsyffPJJYz5s2DC3cne0bt36rrdRtWpVY/7jjz86ZKxmjLRk2bJlDtlrr71mHLt161ZjXrNmTWPetm3b5BcGpEFt2rQx5tmyZUvZQtIgztACAAAAACyJhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEotCueDo0aPG/KGHHnLIoqOjjWMLFixozEeOHOmQ+fr6ulEd4BlDhw415osWLTLmY8aMcXnbTzzxhDH/559/HDLTYlOSdPz4cWMeHh5uzJ9//nmHrH379s5KBJwumORs3zDlzp7rDx8+7HId3bp1M+bOFn9q1aqVy9sG3HXt2jVjnilTJofs8uXLxrH9+vUz5qbXQKbjguR8/jvbP0NCQow5kNY9+uijxnzs2LEpXIl1cIYWAAAAAGBJNLQAAAAAAEuioQUAAAAAWBINLQAAAADAkmhoAQAAAACWxCrHLti4caMxP3DggMvb6NChgzF3tiImkNKyZ89uzH/++Wdj3qxZM4fM2crHznK73e6Q2Ww249j69esb8w8++MCYV6xY0ZgD3uRsRe9hw4a5vI0jR44Y8+nTpxtzZ6szV6tWzeX7RMbh7NsY5s6da8z37t1rzE0rz8+ZM8c41tnrpcDAQIesb9++xrHdu3c35qxmjIxi+/btxnzfvn3GvGjRot4sJ03hDC0AAAAAwJJoaAEAAAAAlkRDCwAAAACwJBpaAAAAAIAl0dACAAAAACyJVY5vsW7dOmPerl07l7cREBBgzB999NFk1QSkNmerBc+ePdshe//9941jna2eWadOHYfskUceMY7t2rWrMc+UKZMxB1LD0KFD3RrvbOVik6pVqxrzAgUKuHWfSH/i4uKM+ZAhQxyy9957zzi2VKlSxnzPnj3GPDY21iHz8TGfJ3E2d7/88kuHLDIy0jgWyCgaNWpkzJ999lljfvToUWPOKscAAAAAAKRxNLQAAAAAAEuioQUAAAAAWBINLQAAAADAkjLkolD//POPMe/Tp48xv3Dhgsvbzp49uzHPkiWLy9sArKBChQoOmWmhKADOF4tydxEpwKRXr17G/JNPPnF5G9u2bTPm/v7+xrxKlSoOWb9+/YxjnS1yA8BRtmzZjHnZsmWN+XPPPWfM9+7d66GK0j7O0AIAAAAALImGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSDS0AAAAAwJIy5CrH33zzjTGfP3++W9vJly+fQzZv3jzj2NKlS7u1bQAAAFfUqFHDmB8+fNghO3jwoHFs165djXnz5s2NeUBAgGvFAXCLn5+5PevcubMxX7lypTfLsQTO0AIAAAAALImGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSDS0AAAAAwJIy5CrHvr6+xjxbtmzGvFu3bsa8U6dODllYWFiy6wIAAHBXs2bN3MoBWE+XLl3cyjMSztACAAAAACyJhhYAAAAAYEk0tAAAAAAAS6KhBQAAAABYEg0tAAAAAMCSMuQqx6+99ppbOQAAAAAg7eEMLQAAAADAkmhoAQAAAACWREMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABLoqEFAAAAAFgSDS0AAAAAwJL8XBlkt9slSZcuXfJqMcB/Jcy5hDmYGpj/SE3sA8jImP/I6NgHkJG5Ov9damijo6MlSREREXdZFpA80dHRCg0NTbX7lpj/SF3sA8jImP/I6NgHkJHdaf7b7C685RMfH69jx44pJCRENpvNowUCt2O32xUdHa3w8HD5+KTOFfLMf6Qm9gFkZMx/ZHTsA8jIXJ3/LjW0AAAAAACkNSwKBQAAAACwJBpaAAAAAIAl0dACAAAAACyJhhYAAAAAYElea2jrfFdHr89/3Vubt6QDFw7I1s+mzSc2p3Yp8DLmv5mtn02zds1K7TKQAtgHHHEMyDiY/46Y/xkL+4Aj9gHv8VpD+1PrnzSg7oBk3XbLiS16esbTihgWoaBBQSo9srRGrBnhMG7pgaWqOKqiAgYGqPhnxfXd5u/usuq07XrcdfVf1l/FPiumwIGBKv91ec2Pmu/x+/HUDrf33F61+KGFcn+SW1k/yKpW01rpZMxJzxSZxnl7/h+PPq42M9qoxOcl5NPPJ8McNGJvxOrdxe+q0PBCChgYoMLDC2vsprEevx9PNd47T+9U0ylNFfphqIIHB+v+b+/XoYuH7r5AC/D2PvDTzp/U4PsGic8v1cZU04KoBZ4oPU27cPWCXv31VYUNCVPAwACV+LyE5v4916P34ckXXasPr1a98fUUPDhYWT/IqlrjaunK9St3X2Qa5+35v+LQCtUYW0M5P86poEFBKvVFKQ1bPcwTpadZ323+TrZ+tiT/BQ4M9Pj9LD2wVLZ+Nl24euGutlN4eGGHej9c8aFnirSAlOgDEqw8tFJ+/f1U4esKyazWeqZunypbP5uaT23u8W17ah9IEHsjVhW+ruDVZt7PK1uVlCMoR7Jvu+H4BuXJnEcTW0xURGiEVh1epc6zO8vXx1ddqnSRJO0/v1+PTX5ML1V6SZNaTtLi/YvV8ZeOCssSpobFG3rqYRhdj7suf19/r96HyXtL3tPEbRP1bZNvVSpXKS2IWqAWP7TQqg6rFBkWmeL13M4/1/7RwxMfVvm85bWk3RJJ0vu/v68mU5poTcc18rGl76vdvT3/Y+NilTtzbr1X6z0NW5OyL2JSa/5LUqvpN98UGdN0jIrnKK7j0ccVb49PlVruZO+5vXpw3IN6IfIF9avTT1kDsuqv038p0M/zL8DSIm/vA38c/EMNijbQ4HqDlS0wm8ZtHqcmU5pobce1Xn8+TK194FrcNTX4voHyBOfR9CenK3/W/Dp44aCyBWZL8VpcsfrwajWa1Ei9Huylzx/5XH4+ftpycku6f/6XvD//g/2D1eX+LiqXt5yCMwVrxaEVenHOiwrOFKzOlTp76mEYpeYxIGtAVu3usjvxZ5vS9nei9q/TX50qdUr8OSRTSCpWk7K8vQ8kuHD1gtrNaqeHij6UYidNUnMfkG6+6fjGb2+oZsGaqVaDO95a+JbCQ8K15eQW792J3Utqj6tt7zqvq8e298qcV+x1v6ub+PNbv71lLzOyTJIxrae1tjf8vqFb21Vf2b9c96W90cRG9sCBgfYiw4vYp/01LfH3+8/vt6uv7FO3TbXXGlfLHjAgwD5u0zi73W63f7vhW3upL0rZAwYE2Et+XtI+ct3IJNtee2StvcLXFewBAwLslUZVsv+04ye7+sq+6fgm9x78/wv7NMz+xdovkmQtf2hpbzujrVvb2Xl6p73GmBr2gAEB9tJflLYv3LvQrr6yz9w502633/yb3Ppf7XG13a51QdQCu08/H/vFqxcTswtXLthtfW32hXsXur09q/H2/PfUfRUaVsjef2l/+1PTn7JnHpTZHj4k3GGOJewjTSY3sWcelNne5/c+drvdbp+1c5Y98utIe8CAAHuR4UXsfX/va78edz3xdnvO7LHXHFszcZ79FvVbknnmrnl/z7OHfhBqP3v5bLJun+DYpWP2Ryc9ag8cGGgvPLywfdLWSfZCwwrZh60eZrfbb/5Nbp3/hYYVStb9tJ7W2v7MT8/cVa1WlpL7QIJ7R95r77e0n1vbtdIx4Kv1X9mLjihqv3bjWrJunyAljgF2u93+wLcP2N9b/N5d1WpVqTH/W0xt4fZzjpXm/7hN4+yhH4Qm67a3Wnlopb38V+UT65q5c2ZiXQmP99b/2s9sn6z7ufW4khGl1D7Qelpr+3uL37P3+b2PvfxX5d3erpX2Abvdbr8Rd8NefUx1++gNo+3tZ7a3N5vSzO1tpNQ+YLfb7XP3zLWX+qKU/a9Tf931Y78dr52h/a+X5rykiVsn3nZMzDsxTn93MfZiknd7Vh9ZrfpF6ycZ07BYQ72+4HW3a3v/9/f1Yf0PNaLRCH2/5Xs9Nf0pbXt5m0rnLp04pufinhry8BBFNotUoF+gJm2dpN6/99YXj36hyHyR2nRikzrN7qRg/2C1r9BeMddi1HhyYzUo1kATW0zU/gv71XV+V4f7zjI4y21re6bcM/q68deSbp6V++/ZnSC/IK04tMLlxxoXH6fmU5urYGhBre24VtHXotXjtx5JxqzruE5VRlfRomcXqUyeMsrkm0mSNGnrJL0458Xbbn9e23mqWaimYm/EyiabAnwDEn8X6BcoH5uPVhxa4fBvl955ev570ierPtE7Nd9Rvzr9tCBqgbrO76oSOUuoQbEGiWP6LuurDx/6UMMbDZefj5+WH1yudrPa6bNGn6lmoZrae26vOs+5eVagT50+irfHq+WPLZU3OK/Wdlyri7EXjZdFl/myjA5eOOi0tpqFampe23mSpF92/6LK4ZX18cqP9f3W7xXsH6ymJZtqQN0BCvIPcvnxtpvVTmcun9HS9kvl7+uv7gu669Q/pxJ/v77TeuX5NI/GNRunRsUbydfmK0lafnC5Hpn0yG23ParxKLUt11bx9nj9+veveqv6W2o4saE2Hd+kItmLqNeDvdS8VHOXa01PvL0PxNvjFR0bnaz9xCrHgF92/6JqBarp1bmv6ufdPyt35txqU7aN3q7xtnx9fF16rCl1DDj1zymtPbpWbcu2VfUx1bX3/F6VylVKg+oN0oMFH3Sp1vTE2/N/0/FNWnV4lQbWG+h2bVaZ/5IUcy1GhYYXUrw9XhXDKmpwvcEqk6eMy4/1UuwlNZnSRI/e86gmPz5ZBy8cTPK6MSJrhGa0mqHHf3xcu7vsVtaArAryu3l8Gbx8sAYvH3zb7e94dYcKhhZM/PnDFR9qwB8DVDC0oNrc10bdqnWTn0+KvfROU7yxD4zbNE77zu/TxJYTNfAP9+d+AivtA/2X9Vee4Dx6oeILWn5ouduPNSX3gZMxJ9VpdifNemqWMvtndrtWd6TYXtW/bn+9Uf2NZN121eFV+uGvH/Rrm18TsxMxJ5Q3OG+ScXmz5NWl2Eu6cv2KWy9wn7z3SXWs2FGSNKDeAC3ct1Cfr/tcXz72ZeKY1x94XS1Lt0z8uc/SPhry8JDErEj2ItpxeodGbRil9hXaa/K2yYq3x2tM0zEK9AtUmTxldOTSEb3868tJ7nvzS5tvW1vWgKyJ/9+wWEMNXTNUtQrVUrEcxbR432L9tPMnxdnjXH6sC/ct1N7ze7X0uaXKlyWfJGlQvUFq8P2/zUvu4NySpJyZcyaOkaSmJZvqgQIP3Hb7+UPyS5KqFqiq4EzBenvR2xr80GDZ7Xb1XNRTcfY4HY8+7nK96YWn578n1ShYQz0f7ClJKpGzhFYeXqlha4YlaWjb3NdGz0c+n/hzh587qGeNnmpfob0kqWj2ohpQd4DeWviW+tTpo0X7FmnXmV1a8MwChYeES5IGPzTYoSGc22aursdfd1pbwpOoJO07v08rDq1QoF+gZraeqTOXz+iVX1/R2StnNa7ZOJce664zu7Ro3yKt77RelcMrS5JGNx2tez6/J3FMwvzPFpgtyfyvHF75jvtrwnPSqX9OKeZajD5c+aEG1h2oj+p/pPlR89Xyh5b6vf3vql24tkv1pife3gc+XfWpYq7FqFWZVm5v3yrHgH3n92nJ/iVqW7at5raZq6hzUXpl7iu6Hnddfer0cemxptQxYN/5fZJuvhn2aYNPVSFfBU3YMkEPTXhI21/ernty3nO7zaQ73pr/BYYW0OnLp3Uj/ob61u6bOI/dYZX5XzJnSY1tNlbl8pbTxasX9enqT1V9bHX99cpfKpC1gEuPdfK2ybLJpm+bfKtAv0Ddm/teHY0+qk6zb14W7Ovjm9g05QnOk+Ry/pcqv3TH55eE450kvfbAa6oYVlE5gnJo1eFV6rW4l47HHNfQhkNdqjW98fQ+8PfZv9VzcU8tf375Xb9JYJV9YMWhFRqzacwdb3M7KbUP2O12Pffzc3qp8kuqHF5ZBy4cSHbNrkixhjZPcB7lCc7j9u22n9quZlObqU/tPnq42MNeqEyqFlEt6c8Fqmnzyc1JsoQXv9LNz4fuPb9XL/zyQuIEkKQb8TcUGhgq6eZiMOXylktyRrVagaT3I0nFcxR3uc4RjUao0+xOKjWylGyyqViOYnq+wvMau9n1RXF2n9mtiKwRSV6kVMlfxaXbhgSEKCTAtc9/5A7OrWlPTtPLv76sz9Z+Jh+bj54u+7QqhlXMEJ+f+q80Pf8LOM7/4WuHJ8lunf+StOXkFq08vFKDlg9KzOLscbp646ouX7+snad3KiJrRJKDu2n+F8pWyOU64+3xstlsmtRyUuJ+NrThUD3x4xP68tEvXXoTa/eZ3fLz8VPFsIqJWfEcxZU9MPsdbxvkH+Ty/prwud5mJZupW7VukqQK+Spo1eFV+nrD1xmyofXmPjB522T1W9ZPPz/1c7LuwyrHgHh7vPIE59E3Tb6Rr4+vKoVX0tHoo/pk1ScuN7QpdQxI2AderPRi4pthkWGRWrx/scZuGqsP6n/g0nbSC2/N/+XPL1fMtRitObJGPRf3VPEcxfV02afdug+rzP9qEdWS1Fo9orpKjyytUX+O0oB6ri0+tPvMboe6XJ3/OYJyuHUFSPdq3RP/v1zecsrkm0kvznlRHzz0gQL8Am5zy/TJk/tAXHyc2vzURv3q9FOJnCXuujYr7APRsdF6duaz+rbJt8qVOZdLtzFJqX3g83WfKzo2Wr0e7JWsOt2Vpi853nF6hx6a8JA6V+ys92q9l+R3+bLk08l/kn74+2TMyZunxt04O+uq4EzB/9Z57Wad3zb51uHd6oTLE13lzqUGuYNza9ZTs3T1xlWdvXxW4SHh6rmop4pmL+rWfSaXO5ebSdLDxR7W3tf26szlM/Lz8bt5xuvTfCpaJmXqTUs8Pf9T2q3zX7q5D/Sr0y/Ju5UJ3Fn0yJ1LjsNCwpQ/JH/iwUKSSucqLbvsOnLpiNfP+LhzyXGuzLnk5+One3Pfm+T3pXOV1orDrn9EID3x1j4wdftUdfylo6Y9Oc2rH2VIC8eAsJAw+fv4J7m8uHSu0joRc0LX4q4lXhrsLe4cA8KyhEmS4z6Qu7QOXcoYK33fylvzv0j2IpKksnnL6uQ/J9V3WV+3G1pXpIX5/1/+vv6KDItU1Pkot+4zuZJzyfGtHsj/gG7E39CBCwdUMldJb5SYpnlyH4i+Fq0/j/2pTcc3qcvcm4tExdvjZZddfv399Nuzv6lekXoerT+194G95/fqwIUDajKlSeLvEt449Ovvp91ddqtYjmJu3be73NkHluxfotVHVitgYNI3byp/U1lty7XV+ObjPVpbmr3k+K9Tf6nehHpqX769Bj00yOH31QpU09yopF9VsHDfQuO7H3ey5sgatSvf7t+fj65RZD7nq2TmzZJX4SHh2nd+n9qWa2scUzp3aX2/9XtdvXE18QX+miNrHMa5c6lBgkC/QOXPml/X465rxs4Zbl1iVzJXSR2+dFgnY04qb5abl0euP7o+yZiEF0Vx8UkvZXbncrNbJbyTtGT/Ep3655Salmzqcr3phafnvyf9d16uObpGpXOVdjL6pophFbX7zG6n7yyWzl1ahy8d1vHo4woLCTPej+TeJcc1Impo2l/TFHMtRlky3TwA7Dm7Rz42H5cvNyuZq6RuxN/QpuObVCm8kiQp6lyUzl89n2Scv4+/w/x355LjTL6ZdH/4/dp9dneS3+85t0eFQl0/K52eeGMfmLJtijr80kFTH5+qx0o8luzarHIMqBFRI/EytoQrXfac3aOwLGEuN7MpdQwonK2wwkPCtfvMf/aBs3v0SPHbvzGUHqXEMSDeHq/YG7Fu12aV+f9fcfFx2nZymx6959HbbuNWJXOV1MRtExV7IzbxLKmr89/dS47/a/OJzfKx+STrLGV64Ml9IGtAVm17eVuS7Mv1X2rJ/iWa3mq6imQr4lZtVtgHSuUq5fCY31vynqKvRWtEoxGKCI247XYSpNQ+8NkjnyX5TP+x6GNqOLGhfnjihzseR5IjTV5yvP3UdtUbX08NizdU92rddSLmhKSb73okfLbnpcov6Yv1X+ithW+pQ2QHLdm/RD/+9WOyPmc4bcc0VQ6vrAcLPqhJWydp3dF1GtN0zG1v069OP7027zWFBoaqUfFGir0Rqz+P/anzV8+re7XualO2jd5d8q46ze6kXg/20oELB/Tp6k8dtuPO5TZrj6zV0eijqpCvgo5eOqq+y/oq3h6vt2q85fI2GhRtoGLZi6n9rPb6uMHHio6N1nu/33zXK2H5+zzBeRTkF6T5UfNVIGsBBfoFKjQw1K3LzaSbH9Yvnbu0cmfOrdVHVqvr/K7qVrVbhnxn0tPzX1Lid3nFXIvR6cuntfnEZmXyzeRwRuROVh5eqY9XfqzmpZpr4d6FmvbXtDvuR71r9VbjKY1VMLSgnrj3CfnYfLTl5BZtP7VdA+sNVP2i9VUiZwm1n9VenzT4RJdiL+ndJe86bMedS47blG2jAX8M0PM/P69+dfrpzOUzenPhm+pQoYPLV2WUylVK9YvWV+c5nfXVY1/J38dfPX7roSC/oCRf/1A4W2Et3r9YNQrWUIBvgLIHZXfrkmNJerP6m2o9vbVqFaylukXqan7UfM3ePVtLn1vq8jbSE0/vA5O3TVb7We01otEIPVDggcQxQX5BSc7iu8Iqx4CXK7+sL9Z9oa7zuup/D/xPf5/9W4NXDNZrVV5zeRspdQyw2Wx6s/qb6rO0j8rnK68K+Spo/Obx2nVml6Y/Od3letMLT8//ketGqmBoQZXKVUrSza+x+nTVp3rtAdfnQgKrzP/+y/qraoGqKp6juC5cvaBPVn2igxcPuvW54YS6Os/prJ41eurQxUOJdSXM/0KhhWSTTXP2zNGj9zyqIP8gZcmUxa3LLVcfXq21R9eqbuG6CgkI0erDq9VtQTc9U+4ZZQ+680dc0iNP7gM+Nh/dl+c+h+0H+gU65K6wwj5gemwJn2915zGn1D7w3ysVEk5EFMtRzOWTEO5Ikx9mnL5juk5fPq2JWycqbEhY4n/3f3t/4pgi2Yvo1za/auG+hSr/dXkNWT1Eo5uOTvIdtAlfwn0n/er009TtU1Xuq3KasHWCpjw+5Y5NQceKHTW66WiN2zxOZb8qq9rf1dZ3W75LfFcoS6Ysmv30bG07uU2RoyL17pJ39VH9j5L5F7np6o2rem/Je7p35L1q8UML5Q/JrxUdViT5wPadHrOvj69mPTVLMddidP+396vj7I56t+bNRiPhHSQ/Hz999shnGrVhlMKHhqvZ1GbJqnf32d1qPrW5So8srf7L+uvdmu/q04cdd2Yk5cr8l6TIUZGKHBWpDcc3aPK2yYocFalHJ/37TnXCF2Pf6YP4Par10J/H/lTkqEgNXD5QQxsOveN3OTcs3lBznp6j3/b9pvu/vV9Vx1TVsDXDEs8++th8NLP1TF25cUVVRldRx9kdNaje3Z1pzpIpixY+u1AXrl64ecnKT23VpEQTffbIZ2495gnNJyhvcF7VGldLLX5ooU4VOykkICTJpdJDHh6ihfsWKmJYhCJHJe87TVuUbqGvG3+tj1d9rLJfldXojaM1o9WMDLnCq7tc2Qe+2fCNbsTf0KtzX00y5tZVJNPbMSAiNEILnlmg9cfWq9xX5fTa/NfU9YGuiYu6ufKYU/IY8HrV19XrwV7qtqCbyn9dXov3L9bCZxd6/bI4q3Nl/sfb49VrcS9VGFVBlb+trJHrR+qj+h+pf93+iWPS2/w/f+W8Os3upNIjS+vRSY/qUuwlreqwKkmtfZf2VeHhhZ1uI2tAVs1+erY2n9isCqMq6N0l76p3rd6S/p3/+bPmV786/dRzcU/l/TRv4iWt7gjwC9DU7VNV+7vaKvNlGQ1aPkjdqnbTN42/cXtbGZGrr4PuJL3tA65IK/tAivPKlwGlEb2X9L7j9+fdzfdipkWuPOb/WnFwhV19ZY86G+WdopAqxm4cay/+WfHbfmdlevuePFce838dvnjYrr6yL9q7yIuVITVwDHANx4D0KSPO/3Yz27n9nZkTt0y0+/f3t1++dtk7RSHVsA+4Jj3sA+n6y7DmRc3TF49+kdplpChXHvPMnTOVJVMW3ZPzHkWdi1LX+V1VI6IG75qnM3Oj5mpwvcHy9/VP7VJSjCuPecn+JYq5FqOyecrqeMxxvbXwLRXOVli1CtVKwUqREjgGmHEMyBgy2vy32+1aemCpVjx/+4X3JmyZoKLZiyp/SH5tOblFby96W63KtPLKgqJIXewDZulxH0jXDe26TutSu4QU58pjjr4WrbcXva1DFw8pV+Zcql+0voY8PCQFqkNKmvbktNQuIcW58pivx13XO4vf0b7z+xQSEKLqEdU1qeWkDNX4ZxQcA8w4BmQMGW3+22w2HXzd+ar5CU7EnFDv33vrRMwJhYWE6cl7n/T64otIHewDZulxH7DZ7XZ7ahcBAAAAAIC70uSiUAAAAAAA3AkNLQAAAADAkmhoAQAAAACWREMLAAAAALAkGloAAAAAgCXR0AIAAAAALImGFgAAAABgSTS0AAAAAABL+j+d9cyZTvrnZwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1200x1200 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 12))\n",
    "\n",
    "start_index = 0\n",
    "\n",
    "for i in range(25):\n",
    "    plt.subplot(5, 5, i + 1)\n",
    "    plt.grid(False)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "\n",
    "    pred = np.argmax(preds[start_index + i])\n",
    "    gt = y_test[start_index + i]\n",
    "\n",
    "    col = 'g'\n",
    "    if pred != gt:\n",
    "        col = 'r'\n",
    "\n",
    "    plt.xlabel('i={}, pred={}, gt={}'.format(start_index + i, pred, gt), color=col)\n",
    "    plt.imshow(x_test[start_index + i], cmap='binary')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(preds[8])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}