{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ecological-touch",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "under-employer",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "IOPub data rate exceeded.\n",
      "The notebook server will temporarily stop sending output\n",
      "to the client in order to avoid crashing it.\n",
      "To change this limit, set the config variable\n",
      "`--NotebookApp.iopub_data_rate_limit`.\n",
      "\n",
      "Current values:\n",
      "NotebookApp.iopub_data_rate_limit=1000000.0 (bytes/sec)\n",
      "NotebookApp.rate_limit_window=3.0 (secs)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "decent-humidity",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = [1, 2, 3, 4, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "secondary-embassy",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "opposed-intake",
   "metadata": {},
   "outputs": [],
   "source": [
    "L_np = np.array(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "narrow-brook",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "canadian-station",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5]\n"
     ]
    }
   ],
   "source": [
    "print(L_np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "classified-death",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[1 2 3 4 5]'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "str(L_np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "knowing-appeal",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'array([1, 2, 3, 4, 5])'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "repr(L_np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "surprising-stability",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_np.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "casual-stamp",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['1', '2', '3', '4.0', '5'], dtype='<U32')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2,3,4., '5'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "other-photograph",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 7, 14, 21, 28, 35])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_np * 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "plain-strategy",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 16, 25])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_np * L_np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "static-prevention",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x * x for x in L]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "metric-interaction",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addition af to lister: 1.552001714706421\n",
      "Addition af to lister: 2.0229992866516113\n",
      "Addition af to lister: 1.872999906539917\n",
      "Addition af to lister: 1.7669994831085205\n",
      "Addition af to lister: 1.378997802734375\n"
     ]
    }
   ],
   "source": [
    "L = range(10_000_000)\n",
    "\n",
    "from time import time\n",
    "\n",
    "for _ in range(5):\n",
    "    start = time()\n",
    "    S = [x + x for x in L]\n",
    "    end = time()\n",
    "\n",
    "    print('Addition af to lister:', end - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "fixed-kenya",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Addition af to Numpy lister: 0.24399447441101074\n",
      "Addition af to Numpy lister: 0.02099919319152832\n",
      "Addition af to Numpy lister: 0.02700066566467285\n",
      "Addition af to Numpy lister: 0.026999950408935547\n",
      "Addition af to Numpy lister: 0.029006242752075195\n"
     ]
    }
   ],
   "source": [
    "L = range(10_000_000)\n",
    "\n",
    "L_np = np.array(L)\n",
    "\n",
    "for _ in range(5):\n",
    "    start = time()\n",
    "    S = L_np + L_np\n",
    "    end = time()\n",
    "\n",
    "    print('Addition af to Numpy lister:', end - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "hybrid-place",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = np.array(range(20), dtype='uint16')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "worldwide-fountain",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([    0,     1,    16,    81,   256,   625,  1296,  2401,  4096,\n",
       "        6561, 10000, 14641, 20736, 28561, 38416, 50625,     0, 17985,\n",
       "       39440, 64785], dtype=uint16)"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L * L * L * L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "polar-champion",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint16')"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "pleased-macintosh",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = range(10)\n",
    "Y = [x * x for x in X]\n",
    "\n",
    "plt.plot(X, Y, '.-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "cellular-gallery",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18080e4e220>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array(range(10))\n",
    "Y = X * X\n",
    "plt.plot(X, Y, '.-r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "technical-identifier",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x18080f49e20>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, X ** 2, '.-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "tracked-vaccine",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "remarkable-diagnosis",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.arange(10)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "grave-albania",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x180810ae940>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 5, 11)\n",
    "plt.plot(X, X**2, '.-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "indie-greensboro",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Enabling eager execution\n",
      "INFO:tensorflow:Enabling v2 tensorshape\n",
      "INFO:tensorflow:Enabling resource variables\n",
      "INFO:tensorflow:Enabling tensor equality\n",
      "INFO:tensorflow:Enabling control flow v2\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf  # a Machine Learning library\n",
    "\n",
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "published-connectivity",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "defined-essex",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "decimal-beach",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train[6721][11][7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "romantic-armstrong",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train[6721, 11, 7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "loved-facility",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "blessed-cleaners",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "sixth-external",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x18097ffe8e0>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x_train[0])\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "gothic-interpretation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000,)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "palestinian-casting",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('uint8')"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "explicit-domestic",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4], dtype=uint8)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "bacterial-there",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+Q9JTkjZoKFizO9TbQg0dom+QtL72d36n37tCX21537hcFkiCE3RAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kMT/A65XcTMQuIbWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4EzObkJ04kZlNkHSpWm8q6vWSlmX3l0m6r8ReXqdVpvHOm2ZcJb93pU9/7u5N/5N0mQbPyP9W0t+V0UNOX2dL+nX293jZvUlap8GPdX0aPLdxtaS3SOqWtEfSg5KmtFBvP5C0Q9JjGgzW9JJ6u0iDH9Efk7Q9+7us7Pcu0VdT3je+LgsEwQk6IAjCDgRB2IEgCDsQBGEHgiDsQBCEHQji/wEehlE7rasv6gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ctitruodY4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iZh8ws4skfVrSyjr08Q5mNjw7cCIzGy7pY2q8qahXSlqY3V8o6ek69vJbGmUa77xpxlXn967u05+7e83/JN2gviPyv5J0dz16yOlrkqQXsr+t9e5N0gr1fazrVt+xjdskjZa0WtJOSf8taVQD9faopM2SNqkvWG116m2O+j6ib5K0Mfu7od7vXaKvmrxv/FwWCIIDdEAQhB0IgrADQRB2IAjCDgRB2IEgCDsQxP8DAiFkQgkcky4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EYQeSIOxAEoQdSOL/AGYjLzDJHflvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAORklEQVR4nO3df4wc9XnH8c/jy/kHBgcbO9fDMQFiaGVF7UGvJgk0JaJBxKpiHCSKJVKHoh5pcASRqUKhUkjTRE5VQCRKrRyxGyelIKRAsSIrwXHTGhJwfEY2/tVgQm3Z17MPcCMbSuw7++kfN9AL7Hz3vDu7s3fP+yWtdneenZ3HK39uZve7O19zdwGY+CaV3QCA5iDsQBCEHQiCsANBEHYgiHc1c2OTbYpP1fRmbhII5dd6XSf8uFWq1RV2M7tG0gOS2iR9291Xph4/VdN1mV1VzyYBJGz2jbm1mg/jzaxN0jclfVzSAklLzWxBrc8HoLHqec++UNKL7v6Su5+Q9IikxcW0BaBo9YR9rqQDo+4fzJb9BjPrMbM+M+sb0vE6NgegHg3/NN7de92929272zWl0ZsDkKOesPdLmjfq/nuzZQBaUD1h3yLpIjO7wMwmS7pB0rpi2gJQtJqH3tx92MyWS/qRRobe1rj7rsI6A1CousbZ3X29pPUF9QKggfi6LBAEYQeCIOxAEIQdCIKwA0EQdiAIwg4EQdiBIAg7EARhB4Ig7EAQhB0IgrADQRB2IAjCDgRB2IEgCDsQBGEHgiDsQBCEHQiCsANBNHXKZmC8OOenM5P1SebJ+ssf/lWB3RSDPTsQBGEHgiDsQBCEHQiCsANBEHYgCMIOBME4O0J6YXV3sr7lvAeS9Q89dWuyfqG2nW5LDVdX2M1sn6Rjkk5KGnb39CsIoDRF7Nk/6u6vFPA8ABqI9+xAEPWG3SU9aWZbzayn0gPMrMfM+sysb0jH69wcgFrVexh/hbv3m9l7JG0ws/90902jH+DuvZJ6JWmGzUr/egBAw9S1Z3f3/ux6UNLjkhYW0RSA4tUcdjObbmZnvXlb0tWSdhbVGIBi1XMY3yHpcTN783n+xd1/WEhXQAFeWJV/oLnl6vuT6x47lX7HOeM/ptXUU5lqDru7vyTp9wrsBUADMfQGBEHYgSAIOxAEYQeCIOxAEPzEFRPWlZfsya2dNWlyct3P7r8mWZ/9rWdq6qlM7NmBIAg7EARhB4Ig7EAQhB0IgrADQRB2IAjG2Se4Nxanzycye8V/JevH/7QtWR8eOHTaPRVl8LMfTta/1pH/M9Z/Pvq+5Lr/89fnJeuT9Gqy3orYswNBEHYgCMIOBEHYgSAIOxAEYQeCIOxAEIyzT3A3rvxBsn7TjAPJ+h///l8m61N/UN44+7Jb1yfrXVOm5Nb+4stLkuvOemr8/V69GvbsQBCEHQiCsANBEHYgCMIOBEHYgSAIOxAE4+wT3MCJs5P1U9qfrA9PswK7OT2n/uiSZH3xmd9I1oc8f1rl4anl/bvKUnXPbmZrzGzQzHaOWjbLzDaY2d7semZj2wRQr7Ecxn9H0tunx7hT0kZ3v0jSxuw+gBZWNezuvknSkbctXixpbXZ7raRri20LQNFqfc/e4e4D2e1DkjryHmhmPZJ6JGmqzqhxcwDqVfen8e7ukjxR73X3bnfvblf+DxMANFatYT9sZp2SlF0PFtcSgEaoNezrJC3Lbi+T9EQx7QBolKrv2c3sYUlXSpptZgclfVHSSkmPmtnNkvZLur6RTSJt79cvy609fk56LHrVry5O1s9+tj9ZH05W09rOfney/sodryfr574r/bbw8/+df175jtVbk+vmvi8dx6qG3d2X5pSuKrgXAA3E12WBIAg7EARhB4Ig7EAQhB0Igp+4jgNtvz0/Wf/en6zKrf2vDyXXfezuq5P1aQd+nqzXY+8/XpCs77z0wWT9x2+clX7+Pzh+2j1NZOzZgSAIOxAEYQeCIOxAEIQdCIKwA0EQdiAIxtlbgF/elazfsDo97XL3lJO5td/54W3JdS/+18aNo0vSvr/7UG6t7yP3VVk7/d/zC9/+82R9rn5W5fljYc8OBEHYgSAIOxAEYQeCIOxAEIQdCIKwA0Ewzl4Aa5+crA8s707W++5In+653dqS9SHP/5v9ya7nkuuu+1r+OLgkzf/S9mR90m+9J1n/xKJnc2ttSk+b3PWz9Dj6eSsZRz8d7NmBIAg7EARhB4Ig7EAQhB0IgrADQRB2IAhzb97ktDNsll9mE2/y18Ofy58aWJI23/lAXc8/qcrf5O8enZtbu3HGgbq2fdeh/OmgJelj796VrH902mu5tc3H25PrfuXCrmQd77TZN+qoH6n4BYaqe3YzW2Nmg2a2c9Sye8ys38y2ZZdFRTYMoHhjOYz/jqRrKiy/3927ssv6YtsCULSqYXf3TZKONKEXAA1Uzwd0y83s+ewwf2beg8ysx8z6zKxvSMy9BZSl1rCvkvR+SV2SBiTdm/dAd+919253727XlBo3B6BeNYXd3Q+7+0l3PyXpQUkLi20LQNFqCruZdY66u0TSzrzHAmgNVcfZzexhSVdKmi3psKQvZve7JLmkfZJucfeBahsbz+PsL38m/3ffT/9Nehy92hzpu4emJ+t333FLsj711RO5tTlf3Zdc95/OfzJZr6badwBO6VRu7WSV/3ubfp2ef/2B6z6Z3vb2Pcn6RJQaZ6968gp3X1ph8eq6uwLQVHxdFgiCsANBEHYgCMIOBEHYgSA4lfQYLfiz/GGcda93JNf9am+lAY3/13lv+pTIZ2hzsp7y6orfTdY//40/TNbvP/epmrddTZulTyX9VzuuS9bP3b67yHYmPPbsQBCEHQiCsANBEHYgCMIOBEHYgSAIOxAE4+xjtPVHC3JrRx6ZnVy38xflTS38RsfUZP1zc/6tyjOkT/f8wb9dnqzP3v56lefPN+/F/mT9ZM3PHBN7diAIwg4EQdiBIAg7EARhB4Ig7EAQhB0IgnH2MTrvS/lj5WWP97bNmZNbO3jdcHLd+e3pWXoeOtaZrM/+1jPJej3Kfl0nGvbsQBCEHQiCsANBEHYgCMIOBEHYgSAIOxAE4+wTwN4V83Nre676enLdZ46nf6/+6CfS55WXflmljlZRdc9uZvPM7CdmttvMdpnZbdnyWWa2wcz2ZtczG98ugFqN5TB+WNIKd18g6YOSbjWzBZLulLTR3S+StDG7D6BFVQ27uw+4+3PZ7WOS9kiaK2mxpLXZw9ZKurZBPQIowGm9Zzez8yVdImmzpA53H8hKhyRVnPDMzHok9UjSVJ1Rc6MA6jPmT+PN7ExJ35d0u7sfHV1zd5fkldZz915373b37nalf3QBoHHGFHYza9dI0B9y98eyxYfNrDOrd0oabEyLAIpQ9TDezEzSakl73P2+UaV1kpZJWpldP9GQDqG2BRcn619e8khu7aRXPOB6y03rPpOsz3/h2WQd48dY3rNfLulTknaY2bZs2V0aCfmjZnazpP2Srm9IhwAKUTXs7v60JMspX1VsOwAaha/LAkEQdiAIwg4EQdiBIAg7EAQ/cR0Hrn/s35P1JWfmf5/p0mdvSq47/3bG0aNgzw4EQdiBIAg7EARhB4Ig7EAQhB0IgrADQTDOPg585YnrkvWlN+afLnra+hlFt4Nxij07EARhB4Ig7EAQhB0IgrADQRB2IAjCDgRhXuW84kWaYbP8MuOEtECjbPaNOupHKp4Nmj07EARhB4Ig7EAQhB0IgrADQRB2IAjCDgRRNexmNs/MfmJmu81sl5ndli2/x8z6zWxbdlnU+HYB1GosJ68YlrTC3Z8zs7MkbTWzDVntfnf/h8a1B6AoY5mffUDSQHb7mJntkTS30Y0BKNZpvWc3s/MlXSJpc7ZouZk9b2ZrzGxmzjo9ZtZnZn1DOl5ftwBqNuawm9mZkr4v6XZ3PypplaT3S+rSyJ7/3krruXuvu3e7e3e7ptTfMYCajCnsZtaukaA/5O6PSZK7H3b3k+5+StKDkhY2rk0A9RrLp/EmabWkPe5+36jlnaMetkTSzuLbA1CUsXwaf7mkT0naYWbbsmV3SVpqZl2SXNI+Sbc0oD8ABRnLp/FPS6r0+9j1xbcDoFH4Bh0QBGEHgiDsQBCEHQiCsANBEHYgCMIOBEHYgSAIOxAEYQeCIOxAEIQdCIKwA0EQdiCIpk7ZbGYvS9o/atFsSa80rYHT06q9tWpfEr3Vqsje3ufucyoVmhr2d2zcrM/du0trIKFVe2vVviR6q1WzeuMwHgiCsANBlB323pK3n9KqvbVqXxK91aopvZX6nh1A85S9ZwfQJIQdCKKUsJvZNWb2CzN70czuLKOHPGa2z8x2ZNNQ95XcyxozGzSznaOWzTKzDWa2N7uuOMdeSb21xDTeiWnGS33typ7+vOnv2c2sTdILkj4m6aCkLZKWuvvupjaSw8z2Sep299K/gGFmH5H0mqTvuvsHsmV/L+mIu6/M/lDOdPcvtEhv90h6rexpvLPZijpHTzMu6VpJn1aJr12ir+vVhNetjD37QkkvuvtL7n5C0iOSFpfQR8tz902Sjrxt8WJJa7PbazXyn6XpcnprCe4+4O7PZbePSXpzmvFSX7tEX01RRtjnSjow6v5BtdZ87y7pSTPbamY9ZTdTQYe7D2S3D0nqKLOZCqpO491Mb5tmvGVeu1qmP68XH9C90xXufqmkj0u6NTtcbUk+8h6slcZOxzSNd7NUmGb8LWW+drVOf16vMsLeL2neqPvvzZa1BHfvz64HJT2u1puK+vCbM+hm14Ml9/OWVprGu9I042qB167M6c/LCPsWSReZ2QVmNlnSDZLWldDHO5jZ9OyDE5nZdElXq/Wmol4naVl2e5mkJ0rs5Te0yjTeedOMq+TXrvTpz9296RdJizTyifwvJd1dRg85fV0oaXt22VV2b5Ie1shh3ZBGPtu4WdI5kjZK2ivpx5JmtVBv35O0Q9LzGglWZ0m9XaGRQ/TnJW3LLovKfu0SfTXldePrskAQfEAHBEHYgSAIOxAEYQeCIOxAEIQdCIKwA0H8HyUxMIiK7eBPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for image in x_train[:10]:\n",
    "    plt.imshow(image)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "swiss-slave",
   "metadata": {},
   "outputs": [],
   "source": [
    "image = x_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "occasional-rabbit",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,  30,  36],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,  49, 238, 253],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,  18, 219, 253],\n",
       "       [  0,   0,   0,   0,   0,   0,   0,   0,  80, 156]], dtype=uint8)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image[:10, :10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "quarterly-marks",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False],\n",
       "       [False, False, False, False, False, False, False, False, False,\n",
       "        False]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image[:10, :10] > 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "answering-proxy",
   "metadata": {},
   "outputs": [],
   "source": [
    "image = x_train[0].copy()\n",
    "image[image > 100] = 255\n",
    "image[image <= 100] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "latter-stand",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1809810cb20>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "continuous-malaysia",
   "metadata": {},
   "outputs": [],
   "source": [
    "image = x_train[0].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "alien-costa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x180982e9ac0>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(image, cmap='Greys')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "greek-frame",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, ..., False,  True, False])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train == 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "minimal-desperate",
   "metadata": {},
   "outputs": [],
   "source": [
    "sixes = x_train[y_train == 6, :, :]  # udvælg alle rækker svarende til y_train indeholder 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "agricultural-registration",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5918"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sixes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "frank-arrival",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pjmb0kNPXmZL+J7tsbnZvkh7V0Nu6fg0d27he0scl9Ujqk/RjSZNbqLfvSXpR0kYNBWtqk3q7TENv0TdK2pBd5jX7tUv01ZDXja/LAkFwgA4IgrADQRB2IAjCDgRB2IEgCDsQBGEHgvh/ExM5vQoWBRcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAANs0lEQVR4nO3df6zV9X3H8dcLiqC0LKCVUWTaGbSlP8T1Fu1qHMa0oWQNsm6mJLNsdb1mK50a02jaZHVLnGb1x5aswcBkpa6laaJWsrhVxupM045xZVRAqyjChPBDZRs65dflvT/u1+YK93zO5fyG9/ORnJxzvu/zvd+3J774fs/3c77n44gQgNPfmG43AKAzCDuQBGEHkiDsQBKEHUjiXZ3c2BkeHxM0sZObBFI5qP/T4TjkkWpNhd32PEl/I2mspL+LiLtKr5+gibrMVzezSQAF62JtzVrDh/G2x0r6lqTPSJolaZHtWY3+PQDt1cxn9jmSXoiIbRFxWNL3JS1oTVsAWq2ZsE+X9PKw5zurZe9gu9/2gO2BIzrUxOYANKPtZ+MjYllE9EVE3ziNb/fmANTQTNh3SZox7Pl51TIAPaiZsK+XNNP2+22fIenzkla3pi0Ardbw0FtEHLW9RNKPNDT0tiIitrSsMwAt1dQ4e0Q8JumxFvUCoI34uiyQBGEHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0l09Kekkc+Yj36gZu21OweL6/7rJQ8W67+78EvFeqzfVKxnw54dSIKwA0kQdiAJwg4kQdiBJAg7kARhB5JgnB1NOTT/48X63y+9r2Zt3cEZNWuS9JEfLSnWZ738crF+tFjNhz07kARhB5Ig7EAShB1IgrADSRB2IAnCDiTBODuK/vf3Ly/W//HOe4r1jz9+U83aB29+vrjuRQcGinXG0U9OU2G3vV3S65IGJR2NiL5WNAWg9VqxZ78qIl5twd8B0EZ8ZgeSaDbsIelx20/Z7h/pBbb7bQ/YHjiiQ01uDkCjmj2MvyIidtk+V9Ia27+IiCeHvyAilklaJkmTPCWa3B6ABjW1Z4+IXdX9PkmPSJrTiqYAtF7DYbc90fZ73n4s6dOSNreqMQCt1cxh/FRJj9h+++98LyL+uSVdoWN86YeK9Uf+8u5i/Y+2fa5Yv+hL/1mzNnis/LvxaK2Gwx4R2yRd0sJeALQRQ29AEoQdSIKwA0kQdiAJwg4kwSWup7kxEycW67+69L+K9btfubJYP/y5OheaMrzWM9izA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EASjLOf5n5x76xi/cHpf12sf+HqLxTrg6++eLItoUvYswNJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoyznwbGnHVWzdrKTy0vrvvFOj8FPfg84+inC/bsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5AE4+ynga1/8dGatQve9Xhx3Tdvf1+xPlZ7GuoJvafunt32Ctv7bG8etmyK7TW2t1b3k9vbJoBmjeYw/tuS5h237DZJayNipqS11XMAPaxu2CPiSUn7j1u8QNLK6vFKSde0ti0ArdboZ/apEbG7erxH0tRaL7TdL6lfkiao9ne4AbRX02fjIyIkRaG+LCL6IqJvnMY3uzkADWo07HttT5Ok6n5f61oC0A6Nhn21pMXV48WSHm1NOwDaxUNH4YUX2KskzZV0jqS9kr4h6YeSfiDp1yTtkHRtRBx/Eu8EkzwlLvPVzXWME1zwH2fWrO19a1Jx3bd+a2+r20EXrYu1OhD7PVKt7gm6iFhUo0RqgVMIX5cFkiDsQBKEHUiCsANJEHYgCS5xPQUc/OycYv2+9/1tzdrC37m+zl9v79Dbmwsvq1k7c8/B4rr+2c9b3U5q7NmBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnG2U8BuxYdLta/9T8frFkbs7k85fKxOtvec/NvFusP3nhvsf6hcRtq1v772FvFda+8/6vF+ow7flqs453YswNJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoyznwI2Xnl/sT73z2+uWTv7zZ8V1x0zYUKx/md//A/F+hfvqL1tSTr34edq1vb83sXFdZ/4+jeL9QXbbinWJ63692I9G/bsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5AE4+w9ID5xSbF+pmtfEy5JPtr4tg/O/Uixfuv62tfKS9KFy8vj+IOF2nvvL697+Se+UqxfdePmYn3nqmI5nbp7dtsrbO+zvXnYsttt77K9sbrNb2+bAJo1msP4b0uaN8Ly+yJidnV7rLVtAWi1umGPiCcl7e9ALwDaqJkTdEtsP10d5k+u9SLb/bYHbA8c0aEmNgegGY2GfamkCyXNlrRb0j21XhgRyyKiLyL6xml8g5sD0KyGwh4ReyNiMCKOSVouqTzNKICuayjstqcNe7pQUnkMBEDX1R1nt71K0lxJ59jeKekbkubani0pJG2XdEP7Wjz9vTm9fE15PVO2vNHwumeuL/+u/MWbyr01McRf18yl5b9+/0P/Vqz/tj7WynZOeXXDHhGLRlj8QBt6AdBGfF0WSIKwA0kQdiAJwg4kQdiBJLjE9TQw9sVdNWulS0wlafC13r3sYewLtf+7cPLYswNJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoyz94BwuT7WOf9Nfm3+RcX6S0dXd6iT00PO/4uAhAg7kARhB5Ig7EAShB1IgrADSRB2IAnG2XuAo1wfjGOdaaTDPL48Q9DZf7ijWJ/3RHlK55kqT3WdDXt2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCcfYe8Csb9hbrTxwcV6zv6P9Azdp5d/60oZ5apTSW/tJ3Li6uu+Tc8pTMvq78QwDtnE76VFR3z257hu0f237G9hbbN1bLp9heY3trdT+5/e0CaNRoDuOPSrolImZJulzSl23PknSbpLURMVPS2uo5gB5VN+wRsTsiNlSPX5f0rKTpkhZIWlm9bKWka9rUI4AWOKnP7LYvkHSppHWSpkbE7qq0R9LUGuv0S+qXpAk6q+FGATRn1Gfjbb9b0kOSboqIA8NrERGSRrycIyKWRURfRPSNU/nCBwDtM6qw2x6noaB/NyIerhbvtT2tqk+TtK89LQJohbqH8bYt6QFJz0bEvcNKqyUtlnRXdf9oWzpM4Oi27cX6V1bcUKw/8SffrFm7Sl8trnv+8ueK9cMfPr9Yf2X2hGL9T294uGbt1aPl6aL/6ZqPFeuDO7cV63in0Xxm/6Sk6yRtsr2xWvY1DYX8B7avl7RD0rVt6RBAS9QNe0T8RFKtby9c3dp2ALQLX5cFkiDsQBKEHUiCsANJEHYgCS5xPQXMuKN8mercwlh6aQxekiYvKY+T1/PS0YPF+rwf3lKzdvGtG4vrHjvIOHorsWcHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQ89CMznTHJU+Iyc6Ec0C7rYq0OxP4Rr1Jlzw4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJ1A277Rm2f2z7GdtbbN9YLb/d9i7bG6vb/Pa3C6BRo5kk4qikWyJig+33SHrK9pqqdl9E3N2+9gC0ymjmZ98taXf1+HXbz0qa3u7GALTWSX1mt32BpEslrasWLbH9tO0VtifXWKff9oDtgSM61Fy3ABo26rDbfrekhyTdFBEHJC2VdKGk2Rra898z0noRsSwi+iKib5zGN98xgIaMKuy2x2ko6N+NiIclKSL2RsRgRByTtFzSnPa1CaBZozkbb0kPSHo2Iu4dtnzasJctlLS59e0BaJXRnI3/pKTrJG2yvbFa9jVJi2zPlhSStku6oQ39AWiR0ZyN/4mkkX6H+rHWtwOgXfgGHZAEYQeSIOxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAlHROc2Zr8iacewRedIerVjDZycXu2tV/uS6K1Rrezt/Ih470iFjob9hI3bAxHR17UGCnq1t17tS6K3RnWqNw7jgSQIO5BEt8O+rMvbL+nV3nq1L4neGtWR3rr6mR1A53R7zw6gQwg7kERXwm57nu3nbL9g+7Zu9FCL7e22N1XTUA90uZcVtvfZ3jxs2RTba2xvre5HnGOvS731xDTehWnGu/redXv6845/Zrc9VtLzkj4laaek9ZIWRcQzHW2kBtvbJfVFRNe/gGH7SklvSPpORHy4WvZXkvZHxF3VP5STI+LWHuntdklvdHsa72q2omnDpxmXdI2kP1AX37tCX9eqA+9bN/bscyS9EBHbIuKwpO9LWtCFPnpeRDwpaf9xixdIWlk9Xqmh/1k6rkZvPSEidkfEhurx65Lenma8q+9doa+O6EbYp0t6edjzneqt+d5D0uO2n7Ld3+1mRjA1InZXj/dImtrNZkZQdxrvTjpumvGeee8amf68WZygO9EVEfEbkj4j6cvV4WpPiqHPYL00djqqabw7ZYRpxn+pm+9do9OfN6sbYd8lacaw5+dVy3pCROyq7vdJekS9NxX13rdn0K3u93W5n1/qpWm8R5pmXD3w3nVz+vNuhH29pJm232/7DEmfl7S6C32cwPbE6sSJbE+U9Gn13lTUqyUtrh4vlvRoF3t5h16ZxrvWNOPq8nvX9enPI6LjN0nzNXRG/kVJX+9GDzX6+nVJP69uW7rdm6RVGjqsO6KhcxvXSzpb0lpJWyX9i6QpPdTbg5I2SXpaQ8Ga1qXertDQIfrTkjZWt/ndfu8KfXXkfePrskASnKADkiDsQBKEHUiCsANJEHYgCcIOJEHYgST+H+vSFbz8LeCfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for image in sixes[:5]:\n",
    "    plt.imshow(image)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "defined-mention",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5918, 28, 28)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sixes.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "chubby-speaker",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x180861eb6a0>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#S = np.sum(sixes, axis=0) / sixes.shape[0]\n",
    "S = np.average(sixes, axis=0) \n",
    "plt.imshow(S)\n",
    "plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "rubber-color",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7SPqZ7Rds7x90MSvYHREnq8unJO0eZDEraFzGu58+tsz40Dx37Sx/3ik+oPukmyPiDyV9QdJXq5erQymW3oMNU+90Vct498sKy4z/xiCfu3aXP+/UIMI+JenqZT9fVW0bChExVX0/I+lxDd9S1Kc/XEG3+n5mwPX8xjAt473SMuMagudukMufDyLsz0vaZ/uztsclfUnSkwOo4xNsb6o+OJHtTZI+r+FbivpJSfdUl++R9MQAa/mIYVnGu26ZcQ34uRv48ucR0fcvSbdr6RP5/5X0d4OooaauayX9Z/X18qBrk/Soll7WzWvps417Je2UdEjSa5L+Q9KOIartnyW9JOmoloK1Z0C13ayll+hHJR2pvm4f9HNXqKsvzxuHywJJ8AEdkARhB5Ig7EAShB1IgrADSRB2IAnCDiTx/4wavYqvDce/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAARuklEQVR4nO3dbWyd5XkH8P//+By/YDtvJDFJGl6bdguwhsrQSUUbFVoF7EOoVKEirWISmvuhSK3WD0PsQ/mIprVVP0yV0oGaTh1VpRaRD2wli6qxSivCQBoS2IBmCcQkNnn1S/xyjs+1D36CDPi5bnPek+v/kyzb5/Ljc/ux/37OOddzPzfNDCJy5Su0ewAi0hoKu0gQCrtIEAq7SBAKu0gQxVbeWTd7rBf9rbxLkVDmMIMFm+dKtbrCTvIeAD8E0AXgn83sCe/re9GPL/Dueu5SRBwv2oHcWs0P40l2AfgnAPcC2AngQZI7a/1+ItJc9TxnvwPA22Z21MwWAPwcwO7GDEtEGq2esG8D8O6yz09kt30IyRGSoyRHy5iv4+5EpB5NfzXezPaY2bCZDZfQ0+y7E5Ec9YR9DMD2ZZ9/KrtNRDpQPWF/CcAOkjeQ7AbwNQD7GjMsEWm0mltvZlYh+QiAX2Op9faUmR1p2MhEpKHq6rOb2XMAnmvQWESkiXS6rEgQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEHWt4iotUuhyy+zKr7O75G9bSvwJON97VRYXc0u2WPW3LZfdslUqfr1q+cVq/riuVHWFneQxAFMAFgFUzGy4EYMSkcZrxJH9S2Z2ugHfR0SaSM/ZRYKoN+wG4HmSL5McWekLSI6QHCU5WsZ8nXcnIrWq92H8nWY2RnIzgP0k/8fMXlj+BWa2B8AeAFjDDc4rJiLSTHUd2c1sLHs/AeAZAHc0YlAi0ng1h51kP8nBSx8D+DKAw40amIg0Vj0P44cAPEPy0vf5VzP794aM6nKztA/yy4leNfv63HphzaBbX9y8Prc2c12/u+2F6/w/gdkt/jOvyoDfK2c5f9/0TvjHmsF3/e+95uisWy+Nnc2tVc+ed7etzlx065djn77msJvZUQCfa+BYRKSJ1HoTCUJhFwlCYRcJQmEXCUJhFwlCU1xXy2mvsbvb3bSwbq1bt6ENbv3CDn/7M7fmt/ZKu8652z5w46tu/d7BQ259U9eCWz9aXpNbe/rMF9xt97++063Pvuq3FTf25f959x5NHOeqftuvOjuX2L7zWnM6sosEobCLBKGwiwShsIsEobCLBKGwiwShsIsEoT77JYlpqoWenvxaoo++uH2zWz+7c8Ctn77d7/l+/nNv5ta+uvlld9tNxUm3fmR+q1sfr/g/+3w1/1LWXfSnz27c5I/t3NaNbn3mdP59l877+7wwNe3WuZC4zLUlLpNtrb9ok47sIkEo7CJBKOwiQSjsIkEo7CJBKOwiQSjsIkHE6bOnLvdcTCxtPJh/OefqNVe7257/jD/v+sxtfs/1T2495tZvX3c8t7b/3M3utv/1fze5dXvnKrde8NvNWNiYP6973Ra/j17s8nvVlTX+nPGFwfx5/tUe/0+/q3jlRUNHdpEgFHaRIBR2kSAUdpEgFHaRIBR2kSAUdpEgrrxmYh76/9cKfb3+9mvz5z/Pbk0si7zDv+8Nnz7t1q8fOOPWnx//49zaO6Pb3G03ver3+K8an3fr8+v98xNO35r/J1YZ8vfL0OCUWz+31j8HYLEvv25dieNc4ryMy1HyyE7yKZITJA8vu20Dyf0k38re5y8QLiIdYTUP438C4J6P3PYogANmtgPAgexzEelgybCb2QsAzn7k5t0A9mYf7wVwf2OHJSKNVutz9iEzO5l9fArAUN4XkhwBMAIAvfCfY4lI89T9aryZGYDcV3nMbI+ZDZvZcAn5F20UkeaqNezjJLcAQPZ+onFDEpFmqDXs+wA8lH38EIBnGzMcEWmW5HN2kk8DuAvARpInAHwXwBMAfkHyYQDHATzQzEE2Arvy5zYDABJ99qrT053e4u/GuW3+pO+b13709c8Pe3PSv+788YP513bf+jt/zvfAm+fduhX948HFoXVufd6Zz377NSfcba/t89eWf28yf+13ADDm/85Y8efKW6XO9dXbcF34lGTYzezBnNLdDR6LiDSRTpcVCUJhFwlCYRcJQmEXCUJhFwniypnimrpUdGJKI0v+VM3Fge7c2sJa/7671/jTRFP+MOEvTTxwPP9n6znn3/fiGr/leHFrn1s/e7P/s3/mlndza3+16b/dbU8lloNeWNjl1gcm89tfXTOJ30l5wa+nlmTuQDqyiwShsIsEobCLBKGwiwShsIsEobCLBKGwiwRx5fTZUwqJ/2uJPnzVmepZzW/BL33rxNLD02X/Cj7lef/XVHKu9nVuh99HL/f7ffKZa/2xb73llFv/22ufz619qW/O3fbJC/7U3vnT/jkAm9/Pn6ZamJp1t60u+NOSrdp5U1hTdGQXCUJhFwlCYRcJQmEXCUJhFwlCYRcJQmEXCSJOnz0l0TelUy8kpj7Pzvlz5ecqfn1gjd8Tnvps/v/smcS069KAP/gbNvmXc/7La15z63/edzH/vun/3C9O3ujW+9/x/3x7J2ZyazadPy4AsMXEpaQ1n11EOpXCLhKEwi4ShMIuEoTCLhKEwi4ShMIuEkSYPnuyb1r25y8Xp/PrPef8+egz7/v1M/3OhHQAA73+Nc6vusYfu6dY8PvFpYK/30r064vO0sVHyv75A79793q3vvaEP/bieaeXnrou/GU4Xz0leWQn+RTJCZKHl932OMkxkgezt/uaO0wRqddqHsb/BMA9K9z+AzPblb0919hhiUijJcNuZi8AONuCsYhIE9XzAt0jJA9lD/PX530RyRGSoyRHy6hvzTMRqV2tYf8RgJsA7AJwEsD38r7QzPaY2bCZDZfgv1AlIs1TU9jNbNzMFs2sCuDHAO5o7LBEpNFqCjvJLcs+/QqAw3lfKyKdIdlnJ/k0gLsAbCR5AsB3AdxFchcAA3AMwDeaN8RVcvq5AIBEn93m/GuYF87nz40eHPOfnlT6/QvLT5f9dcinN/h9dJby+81WSfw/r/jXjZ9Y67/OMrYu9+UaAMDblfyx7Zu8zd22fLzfrfed9n+nnM0fe7VccbdNzldP/b11oGTYzezBFW5+sgljEZEm0umyIkEo7CJBKOwiQSjsIkEo7CJBaIrrpfqc32LiuQu5td7EctBXl9e49b7Tfmtufo1/yeVq0W+feRb9VY8x9Wn/e4/P+z/bf858Nrf2b+/tdLftO+Xv19KU3y6F115LtM4uxyWZU3RkFwlCYRcJQmEXCUJhFwlCYRcJQmEXCUJhFwkiTJ891VetLvjTSAvT+VNcuehPh+y56PeDu8f9S0lX+xJ99p78X+Nin/8rnrzO7/FPJdrNJ2f9PvuZ+T/Krb33ztXutlef8++8sJC4PHi19mWVWfDPLzBLnNvQgVNgdWQXCUJhFwlCYRcJQmEXCUJhFwlCYRcJQmEXCSJOnz0lcelgrw+f6rNzPjFXfmrKrRd6/EtVdzlLPtvWde62i36bPXk4ODnp99lnLuaPvXvc//Prnk70qp3LVAPoyF53O+nILhKEwi4ShMIuEoTCLhKEwi4ShMIuEoTCLhKE+uyXJHuyzrLIiWnVyeV/E/Ou2dXlf/tifr281p8Lv7Cu9mvOA8CFc/6yyjyff//95/37Ls4nlmRWH/0TSR7ZSW4n+RuSr5M8QvJb2e0bSO4n+Vb23l+oW0TaajUP4ysAvmNmOwH8KYBvktwJ4FEAB8xsB4AD2eci0qGSYTezk2b2SvbxFIA3AGwDsBvA3uzL9gK4v0ljFJEG+ETP2UleD+A2AC8CGDKzk1npFIChnG1GAIwAQC/8a62JSPOs+tV4kgMAfgng22Y2ubxmZgZgxVdLzGyPmQ2b2XAJ/oQOEWmeVYWdZAlLQf+Zmf0qu3mc5JasvgXARHOGKCKNkHwYT5IAngTwhpl9f1lpH4CHADyRvX+2KSO8EtD/n8puf54pB/z2VnnjQG7t4kb/V1y5ym9fccFvj/Gi39rrvpD/sxdnUpeKTrTWUpeKpjN2r3aFWs1z9i8C+DqA10gezG57DEsh/wXJhwEcB/BAU0YoIg2RDLuZ/RZA3r/Buxs7HBFpFp0uKxKEwi4ShMIuEoTCLhKEwi4ShKa4NkBqeV92+71oOpeCBoDq+kG3Prc5/8zE+cQUViv4veziRf940DXrf//StLOtf4VtcDHVZ/fLKDhj92pA8twIMDG25Lzn1tORXSQIhV0kCIVdJAiFXSQIhV0kCIVdJAiFXSQI9dlXy+u7Ji71zL5et24Dfp+9vM7ffn4w//6rfosfhdR89Vl/+2Kynt+P7krMV0/22VOHKmfOOhPz2S1x7gQ6r42epCO7SBAKu0gQCrtIEAq7SBAKu0gQCrtIEAq7SBDqs1+S6Lt6c9ZZ9Hdjql7t8a8bv9hT+//k1JzxQqJfXFhIfP85vxfe5WxfTGxbqNQ5n70e1StvOWgd2UWCUNhFglDYRYJQ2EWCUNhFglDYRYJQ2EWCWM367NsB/BTAEAADsMfMfkjycQB/A+D97EsfM7PnmjXQjmZ+T9YW/YYwF8puvTRdcet9xfxzAIpzqeuf++cXdC34Yy/MJ3rlzpz0rlm/yV+c8k8SKMz4k+ltbi6/VvH3KSzRxE/VO9BqTqqpAPiOmb1CchDAyyT3Z7UfmNk/Nm94ItIoq1mf/SSAk9nHUyTfALCt2QMTkcb6RM/ZSV4P4DYAL2Y3PULyEMmnSK7P2WaE5CjJ0TIS526KSNOsOuwkBwD8EsC3zWwSwI8A3ARgF5aO/N9baTsz22Nmw2Y2XEL+mmQi0lyrCjvJEpaC/jMz+xUAmNm4mS2aWRXAjwHc0bxhiki9kmHn0mU4nwTwhpl9f9ntW5Z92VcAHG788ESkUVbzavwXAXwdwGskD2a3PQbgQZK7sNSOOwbgG00YX+sk22f5bSKb9VtALPttHs7MuPXixGm/3pP/9Cg1vTap6reYrFLHNZWriW0T+62aaJ+Zs71V/HZn6u/hcrSaV+N/C2ClZmzMnrrIZUpn0IkEobCLBKGwiwShsIsEobCLBKGwiwShS0mvVh19Vyv712NO1XGx5rsW+YCO7CJBKOwiQSjsIkEo7CJBKOwiQSjsIkEo7CJB0Fo4b5fk+wCOL7tpIwB/snb7dOrYOnVcgMZWq0aO7Toz27RSoaVh/9idk6NmNty2ATg6dWydOi5AY6tVq8amh/EiQSjsIkG0O+x72nz/nk4dW6eOC9DYatWSsbX1ObuItE67j+wi0iIKu0gQbQk7yXtI/i/Jt0k+2o4x5CF5jORrJA+SHG3zWJ4iOUHy8LLbNpDcT/Kt7P2Ka+y1aWyPkxzL9t1Bkve1aWzbSf6G5Oskj5D8VnZ7W/edM66W7LeWP2cn2QXgTQB/AeAEgJcAPGhmr7d0IDlIHgMwbGZtPwGD5J8BmAbwUzO7JbvtHwCcNbMnsn+U683s7zpkbI8DmG73Mt7ZakVbli8zDuB+AH+NNu47Z1wPoAX7rR1H9jsAvG1mR81sAcDPAexuwzg6npm9AODsR27eDWBv9vFeLP2xtFzO2DqCmZ00s1eyj6cAXFpmvK37zhlXS7Qj7NsAvLvs8xPorPXeDcDzJF8mOdLuwaxgyMxOZh+fAjDUzsGsILmMdyt9ZJnxjtl3tSx/Xi+9QPdxd5rZ5wHcC+Cb2cPVjmRLz8E6qXe6qmW8W2WFZcY/0M59V+vy5/VqR9jHAGxf9vmnsts6gpmNZe8nADyDzluKevzSCrrZ+4k2j+cDnbSM90rLjKMD9l07lz9vR9hfArCD5A0kuwF8DcC+NozjY0j2Zy+cgGQ/gC+j85ai3gfgoezjhwA828axfEinLOOdt8w42rzv2r78uZm1/A3AfVh6Rf4PAP6+HWPIGdeNAH6fvR1p99gAPI2lh3VlLL228TCAqwEcAPAWgP8AsKGDxvYvAF4DcAhLwdrSprHdiaWH6IcAHMze7mv3vnPG1ZL9ptNlRYLQC3QiQSjsIkEo7CJBKOwiQSjsIkEo7CJBKOwiQfw/IZJtzZ7TDp4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for digit in range(10):\n",
    "    plt.imshow(np.average(x_train[y_train == digit], axis=0))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "capital-impression",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,\n",
       "       0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(0, 1, .05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "peaceful-coalition",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "considered-bennett",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([[1,2,3],[4,5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "sapphire-killer",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = np.array([1,2,3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "collected-circle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "orange-domestic",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6,)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "continuous-programming",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.reshape(3, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "earlier-tumor",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5918, 28, 28)"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sixes.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "upset-certificate",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "28 * 28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "amended-variety",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x18087653a00>"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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shdsa09UwWghOp6lcArOnya66g4dZZjIUb4Dd0BRvMniPMCSFGwJvOkTbGmR8W4VlkluWyIsNxj6xTu/EWP94g9wdgT7epbsY4pXNgauWvSuwcj5mV1C63kMWciAEVkuzUStgXc1QXHYHD7XpacZzHTZenyaz7Q92brsZMT3W4Nr1OUSk47gSsHa74EvSt230KIqkv5DsnXcQhWGBWLU7pKqKneen4vhq9Ppl0qAiwo1k/e+9kPvCkP44MRfnUR945JA+ylqsfdBKQG+U5yEiaJ0O0Z2h8UXVOoYPvWM+jNSXot09ehOSxrkQeUBfPWvSOhq7JAP9zi6bzwi8UtKQVL3B+kfVAGC6L7rnUvveDkKDyA8fHqKI3U+4WO0IbQiEFT+cOgxpfbRDZjtCWcB07IqKlEP7Q12cTRORDqk9G8dUslCg+1yb7k6WU8Ud6ifj3VPm8zSecAnqDn/xma/QOG6gej2MSonGRZ8olHzfD3yN3YcyRLUGMpOh9nBEGBgsfugOrQWHqFpHOA47j8Hd7TLps3W8sjVY1LYes3hmconZo7vIUA93vOks3/34Wyx+bIUoP5Ks8QOKT20TfrCBHqkZas8jf6NBfi0g2thM3uOtZIz6Xsp9b0h4Pu1559D2bq3VCQoKeaAanr3dIDfVBmukwKoVxVs97LyPHtndtNIUl0OQmmhkR9JRRHZ9P20bJvWrEr+UPEXleTjbBr0JmThP1XMJailCR4BtIbPZgR5Am4Lm8TRiYTb+2/VQSiIizd7jEd2TlcHxQmqmXo548uQyrSPxbdXdLrYdMfVlyZTTpDOvQYgYmpQKKb9l8E5rhiAX7xja8zEyIc7VNFea07iTxAagNSIVoZoWR/N7MXZOxch05SgmKi0+sXAtzgr2dwa/rPje4pv8/PHPYe8NIUK9SYsfH3uJ8VQH8+oQMSIcm1org/nlIup2Ekkiej7pGzv3BKbum8n9bUhCoIOA4o32ME0sRJzNK2WZ/SKIUjFWOw5GsUBYTGF+tgR9F0Sm4gybloLMl3ODmyUsG6NSwmpFVF4zBzuPcByM8XHSuyGlawwr8KaJMTlBbl0x/nYYx05CgDQwJifIL0Pliodx4ijGRLyTGOUixSsm+ZX4QdtHb8hCDudqmtRml7GXtmE3TlzIUhHn7Qx23ef4r0Zkr8QrssznMN/MYXYi3vnNs8x9thFfh3QK9XoRoeDXbzzM9EtRnNK3LazXcnhlwa3aGBNvKNAKIQTZlzMERc219SlK1+P4SgchhdcchBZ8/vYpsht9fRRRvGqyU83zm+88TGQPF4mFP4r4TPNB6lEWb2KYtq58fpmf+czPcqsxhl6YGujDrW0m/n0ad0JjzA71ANGtFbhHYqFvJve3IUH8oG5UUfvFOq0RhqR1LEtvTKL2+tkiz0N1emw9lcUdZ1AlV66Lara5+4kUboVBnUMHPqrR4s4nbfyiGPj+2vNQ9QZ3P26gZYx/g37gW62z8aH4IRtAmlSE2quy+3iEsiTRzSWinR0AolqDxvkAbUnCpZVBpi+qNegthEQ5GxFGRLUYrBnt7tI9EtI4laE7aaH7SZZor0p3MWT9eYf2iRCj2oyR0bt7+CXF9hNwZKxKZr0HKopjSAeih1t8ePZm7HppTdRsogyYubjJVGVYINaBj9XSPHD+DlJqvOJ+QUqTW4947sQtDFPhVkawee2ALa/Aq60jVM9aQxS+lCwc2+H5qdtsP10e6IVpsfmMoPzIDs1HZ5NG8+R5Nn7oWIxZPHj783mM/mL5Xsr9bUhag1bobDqx7SvXJb0bkFuPUCOxkA58zI7GbpBIUOgwIL0p0AaDloX4BUVqT6AMDmH9Mhsyjm3KyZuYXTFjmEuxMIT2CElu2SRyROIBEZZJZtkicoxEu4ewTDIrJn7eQmVSg/hCmBa5myZaEq/+QX/3NAwKV01MF1Kb5vA7hCB/S2J4guuX52Nc4v55rmt81+Kr28dI7Q4zieldjRuaWEZEdn2ot7oaLzIp5XqUrw/1Zk9xuzFOudhh6utD4xNKs9Yt8tmvXWTus3sDvKBOO1hGxGf+5TNMvlQbxH/CjpsAg9+aIH9tiHgXpons+uTvRuhistwA/etcLh3S/1nLe9bY9ycVo1CIV/0DGToqpUNpUQBlCBAgU07iPXZbI8N4JxlAToQkVVekaiDT6cHxwjTJrimchiJqjqRqs2kKyzHWLry9PNQX85SvRdg1n3B12IJlTE1QvhaS2vES2SVjZorKtQizEw6MBcCYnGD8Uohd9xF3RhrcZqeoXAsJ05IgLQZxnjE3g93U+EVBVNHodGz0xvg4hq8x24JgOiQsOsj+tUSA2LWppzPYZZsU/QK3BfUrY+ymNYtphSGNeBdzBLffmkOlFUctFRu+itBCsLYWx2rpaUnastGBjwwUNzcnEBF0jhdJX7fQgY8II1a2K1gl6M3lye6NEa6tg5RYDYmWyYyMDkNkz4+vReNw5jZc30xcu/dK7psdSfXcQXFwX4xCAbZ3URl7EKhD3IaQvr2HskScIu2LzGbJbAUx6HKkT8nIZUFD/VTycohiAS0FrXkj2fBn2ShL0Fqwk42DhoFXlIN2hVHpjRn0pg7oI0VzwaA7cwCapBR75032LqQT56+7LjsPmeydl1g9PWgb1+0OjdPQOqpIna0j+m3a2nVpHgflaL77wXcw63ESQ3ke7QUwXMF8pY7diHdhHUV0JwUiFJQXa8homG3rjQu0oZk92i9+9/VBVmJlfRbm97A6YdzJC0Qpk9mxBoUTdZw9b6BXhQxPHlnBuNjArvuxERGnst2FgN6kQB2AfOnNHcKchS4fpiMwF2YPNW++F3LfGJIOfIxKKakLw7i+o0jUYXQQoo3+qj0qUYTV9OM09Ggh1ffJbvoIRbK9otsjsxPilUXsegz0Xeymojc5TE1D/EDbLUVnViZurm62sLqaztSBrF29QWZb4ZYP6JstUjt99EE0NHjd6ZDZ0qS3IH+jNeAvUM02mXUBpib6ehnd6xtSr4dTFZz84DJ/8NJFZKs3+L3pbcFPf9/nubNbxmz0s2oqIr2jyT9QpbpTwK4O8Y2parxTrC+NY3jDc5KRJqinWNsuoUd/gyWJtCCIDJSd7Dq+Vp1gsVxDm8PHTzeaTH3BwD3qo1JJR0n7Ps1FE+ElwcDxtW0nFsX3Su4bQwJQB7Z21e3GUBhLJkCtqtNB5dIYvk5AdZTrEhRsDI9hcqKvV5bEqZIovKpWizAjsVvJmEp1OiDAqSbbMVSng7IEdl0n3I2o2cTPCqwOSXR5q0VkC2RAok6lWi1kGEN4gjNzA6NU3S5mT9ObgvWPFgdxmw580jsKc6xHby5CpONdTIchuTWFKRTa0uhUf/HoJwkaYRq/bSdAv+k9xXS+hVE1hw+6ENgthRz3MJvJ1d/sKkQ6RCuBPlCIbrkOE/l2AiUf5h0arQxSaOw7I9Cu00epXhBMTDUwb6wmPseYnMDqaKI7ST3EafP9Yu97Ke/9GfwJxJieTDbYQey/Z6xD4EVxbQmvKBFm0k1wVqr0JmPY0aiY7QB3ksTOA2A1Q7x3SQqJSOOOJ5MHAMqAIHc4TStDYijOAQnTINRhdLtfiD/D2m4ljNIrxx+S2tODnQegNyEJ2japDQM1sni4FUndSyM8mWjVbk8brPVKEMhE/49XkNzYmMRuSKTbT+BoTWQL9FYKqy3ixru+RCmJseVA3cboDvXumEkYGiyvjg8XDyHoTTmcnd3i2voUOjdMi4u7WxRuwu5yBVE4kFQIAsKMiDuKD0o6Fbvm77HcV4akdnbRKhmMmvNz2K/dTLhACIF+4DhWVx/KtgVzpTjbNhJ7IATemIP0SLhqwrKpnXEGxddR/e4Fi/L1KJk8KBSonRNMvJk0CmN8jMZpGHszyTlgTEzQmxKMvbSNOTM9wPkZExNEaZj5w3Uw5OABMsYqBFk4/m+2MHsaY25m8PlhBs78Ly5OA8TR+cH5hGnwf3EagO7DiyAEMpslSsFb/yHu2N1+PsYkykyGMCswbqZxpyLWP1KKd0Np4I5JDFcQ5DVrHx6iMLxC3GoiQ9h+PDNYWFJ7Ib16CiE11Qv92EZriq/HRgQQlob3QLVa1B7UoEmgTgD8k3EyJdzY4qCESyuJXq73Su4vQ3LdQxka7fkgxSCYjZWaMGfj1CNUO8noE+RMMus62W2pNWFKMPFWkHDtdBggA01xOZlt01GEU9Nk1pI3XHke6W1xqOFPtzukN5M4O4hjLacGGBLVbA2TB60WdqOffdveG7AF6U4Xu6HxZ4sUr9TjFpL+5zs1zd5D+ZjwZTWG0qieS25dUT0vSM21Sd+MG+a051G6FRLZkF41mXxxD7RGuR7l6z5aQv6mwcxX+ruhiijdDIgcTeEmTL08dGcrbzcJxgMy65KJN9zBb3TevoNMRVC3KS4NF5bozip6PcXceD3RsaujiMpbgtMPrCYXOcDaaccZ2APewr0k95UhvZto1z3sIwvBzsNDJp2BSIOV7xdEKZFwpYTjsPMjLjsPWYl6lHQc1PfWWH826TYaE2Nk/9wmm88kXRBjcoLy96+x/fiB9opjC0z/8Ap7D5eS53lykakfvMPad00gjswNM1sPn2buJ5e4+tfKbP3omcFuGzz9ANM/tsKtn5bc/rEy4ki880SPnWXuJ5fY/YBPZzGk/ZGz8fkfmSP1X24QnnDpbWfY/sh0vPMUC7T+qyZcaNE76nP3e8ZjQhTLZOWnIxafWSX6YIOlH+ijuYXg7sdMfuwjXyX9I1vc/nPGYPfce6jAP/nwv+ITP/kSy99vD1zs6MQM/68nf4N/+D2/xNIPOAOUvCwWePKZa/zimX/N9Z/JJNDzrSOCn5z9OuvfM5dsjExZbHwkQl84xb0q970hiUya7tMnkylQrcmvRtROWcmYSkWMvWLQPBUls2qeR/bFLN0jYUKvPA/vGxWCok7c2Ghrm+2XZuJWhBEJV9e48/YMXiUZI0VXb3Lt+twhMKt+5wa3tsZxanpA6AggXrnMzZ1xxl6RTPziywMDM7/2DndqZfLv2Ey8ptCrcSOifOUK17cmkPW4qJl/O4YOqZU11nZLHJve5UeeeoXcatzyrZptGo0MP/fAl/gXH/nnpKoxb58OQlTb4odm3uC5+dtYnRiXt78YLTp7tFwHu2oM2kH8ksASIRtusV/Qjhei/VT/FXcOoysGKHmRy6IQvOQeYew1OfhtwrQwe/C/Ln+Q8UtJlidu3uHULwUYu++9C/fN5L42JJlKIdIpMsv1xLZvjI8R2YLspkq0J5sL88gAcstGAsxqHl0kvatIbZqD9m0A88gClasRZlck6kjm0UXyyxqzmzQMc36O8mWBkSx3Yc7Nkr8eM5SOijE9hX05Q3ig890YH4M3C4eOl/kc/rUCWkJuZaStI52CqzmMniC7YqJyfdoty0TfydALLJY6Y5huFC8IWiF3bK50Z/jdxkXyd/w+9bPC3jP4/N4ZrtSmmXgjGNTnsuuCX11/DM83qbyjB1nG3Jri16tPEGpJ+Z1hh2x6y2UnLDBlNUjtieH1jhRNP0VHxe8fLHQ6RscXHZcgm0woidkp6ifT73mrxB8n97UhKc9DmwbC9ROumu652C2F6apEIKq73bjS39FJiFC7g4g0IiJJ7RWEBFlJmNbJnS0I0RL8oj6ULQzTgiB7oAU6itAmhBkQj5xPfpaIs3zRhx8dYsaEIEppgrwgfP6hAcgV4gxflILtJ/LI/Z4qw8AvK8KiIsxoVCpeVIRpohzN5l6RK390CrHfz2MYaAO+tn6U3/jSU3G9yvdjF1nDnWaZei9Fb8wYINFRsLpX4uzUNkFWDNDwZlfx0sYRJp02kSWGHbK9gF9be5SdMB93+e4j2ns9lBZ8T/Y6yhzuYFppwqzmh6bfOHyjLTPOkL5bc+c9IvcNROiQSANzcY7uyXGc3R5yKxMbRz9j154xSFfjHWlfH55dJLIFqboeQoGEIDyzQGQLirdUIkYKjkwglGbmayrRih0ujGP4MPelMKGPpsuYXc34217CsKPpMeyGpnzdg1FWoFIeqw1T3+hivHWLqJ8Y0dk0VlMw8+UmstGFff66bAazI5j5motfTGLqrKZk7C3N3kMgAoUWfXdKQfFLKWoPRQQZE0caoDTSFfCHFcQxTWfGoigkaIXhCpqvTKBNjRwTlAwDrSLMnibYzPC2P0t6PN6htYoQkaZey3IjO0FvOjZSwhARRGQtn02vSG9Cx7ujFw1AwQ1lEKXEAGqEinBqgrfaC4RpyWiuNbp8nZmrtwjvASjQN5P7d0fSinCySOb6DrIXJHaYzkKG4nJAesdP6LszDpntkMzmAf20g+lp8ku9oSEJQW8qheFpsrebiWxhbyqFDDWZW7WE3i/amJ7G3koWjqNCHFDbW+0kuDYX683dNgRDKjCdcjB7IBtdVCE97MI1DISC9pzN7oPmoBMWrZGeoHFcEix4RLlh4dVuSFrHwJns4heNGOQbRVgdQeuEIqoEg9oUWmN2wVv0COZ81Mgya7owfnKPyfHmgI0o1kc8fmKFo/m9pIvqB5wvbvBAZh2zN/IGrbi+OsWr7kLsAeyjEoSgdDPkhZVTOPXDfUejDZT3otzHhqQxN2rQc+NC436SQGsKr2+iBRhNf5gV0pria1v0JkyilHFAv4mXl/gVe8Rn1xReWUNZgt58PpGEyL+2jpbgzRUTSYj0pVUiS+DNFBJ669IKhgf+VC4B+TdurGL0NO6REqJYGHy3uLOOUNA9PYbsBcMdbH0Tqw1hSnDk08P0t2o0cWrglzTzv25iXVoepLMzm5qgGJH/dI7yi6sDxHzujkZEgtw1m+kvVAcLQmElwti1oWFRvh4O0PC5VZ+dlTJ7b0yS3dCDJIG11+WVN0/y+c89TPEmgySE6Hn86tuP8k+Xnie7Nhy7o/0AGhb/au0Z7NawBR1i3J6UmjBtJK6fUSjgfuKRAZvSvSj3ryERZ8nURIlwYSKBt1IbW7gVk8a5fIJTQe9W8XOCMC0T7RK63sQdi1k+E8e3OwQZEWPLRnYe7XrDJrbR+lIYYrq6T7k7cmmjCKujUJaE2amhUUYRdlujTIFamBxCe7TGamsiW6ItA7nfhi7j7liro5GNzrDY3OfZK1+B3Iu3hlTGUhCmBOPfMBj/2nZMstk/PkpBZkNgtkHsDJEQkSMQGoyeILU9zJ5pCSIXEpQi7PZIHKkgPd0mmPZjQsn9412XsUob24jdwoE+CNGGpmj3yG4GifumJbiuRXqtk7iuIp8j+8bd95lWv2OiNSjiwt7Ig6v8AGUJZEgi26a6XZAkKHohDoBlGNNcHdQHOUGQT6bPdLeLsiFKH/icbg+/IIjSZsLwVM+lO2Fg9KI4zd1/TfVculOS9HoH/cqlQaCuXY/OjCB/rYa+enswN0m5Hl5JkFv3UMUsar9QGwb4Bcjf9eO2kv5qrsOQIA9CQ+2xiTh+AVARQU7QndaEn6ijp4ZEMG5ZomZdjONt2keH0BuvYqE9g/wNk95IA19YTtNby5G54dCbHHG/xspU61l2W1m608PjZS4LhuYHJt6gPWsN+44Mg9ARPLp4l7B4gHjT89DZ9Lu2y9wrcu+e2Z9A5E498eBK26J0tY0WJBAPMpNh/O0e0cHBFpbF5Ou9mM1nRIRtU74WJMje4w+S5NaiBNoZAMMgVdNEqQPtGIaB01D4RSuBFxNC4FQ13flc7Lbsd4saklRV0z1SRAgxyAAKGafWG8dSaCGQIwxJVhu2nnDoHa8Ms3lCYLWgPSdiZqMR5iSzq8kvgfxSKQat9n+L01DkXkkj38xj+Gqgtxsh2ZsWhgdOQw/OVQYRZkfiVDV2c6TephTKM+g1UgnSfUwTqxYvWKn6CHOSbROlQGmBszwCZhWC4OwCvZPjRNU696rc34YkBOIAaSAQ9wWNp7C6B+D1UtCZdshuJTFyQgj2zqXI3zjALy4F1Qcsipeqh46vnjPJvZPEfgkhqJ+QZC8l2W4Qgto5QfZGdZC1ij9f0p0RZO4e5jX3i4L03VYSXCskkQOlGz2irDXI5u3rvYrmzicNtDPSImKC+USN3U+5hGPDHSayBfXziiAD3blhlkBEMZH+9Nc9/Ozw8TB8hVfWVK7Gu+J+8C+7PkE5ZjvyysN6m+j0MNIh6aIb93/tT6moNwgmA07Y2wQjO7rqxZyAGdOP+QoHP0Bj39rE2e3dE+0S30zub0PSGtFsDzpC90V1u0hfUT9uJoL7qNlGS1j/gJGozahul1Rdc/On8ol+JNXpkd1QLP/IRBLx0O2S2tPc+dEklEV1u6SqmvXvGx1YGAfYqT3B9gcmBnwNsd7H7EH9fDHuqO3vqvvJhea5YkzxOwpnUlA/lcboBUR9127/oXb2BBOvgr4Td+cKI+aVaK8W0DUba6lv+ELEtaNcyMlP3iZzdxiTKFPA6Q7bP+fGsVBf71YsUmcaLP2AlSg4h4UUU4tV3DEwegxdbMfmwbkN3K1snJ0bcb2nZ2q81juW5P/TGr8geKKwQrCYJNjUuQwbHygkOArvNblvDEk4zpA/ui8ylQLLIhrLJfTG+DhmJ6R8ffiwQYyedhoRc1880No9PoYMNHNfUBgTQ3ZWYypulR67EiU6MY2pSbSA8vUQc26o33e1chtRTKM7+N5yX98/fv/8y2UiG3J3vcRvk8UCyoDsmhuzHe1/fjFPmIFULUYojBJHRmlI7WqcpkL02wqEbeMXNWZbIso+Ot/XGwZhFugZeKGJsvuxoRC4FYHfcPBuFBIjLnvjks5anuINidUZ1tu8MZvtm2PIANK7auBK62yaa9uT6ExIYWWYrBGGpNVL0YjSZHaStMTZTcX/dOlDSC+Z/hZ+QHEpHMZ4I++JaYvf75D9lkRmMgjDODzWwzDANDB2W0mQY7eL0fJI7SYBrbrTwWoGGD2FsIaQItVsYXUUIhppfiMmfDR8HcdaKWew8ke7ezHCwJHolD3Qq70qWsbZp1FiymivhghBhDrRK6TqjXh2kNYJJlnVaKIN8Mt27NrtJyfqDQwXWnMmjdO5QYYxancwu9A6Bs1Fc0DvrNwYjR7OelReSCH6ZCkD9PpUh7XPLmK0+luM1mR2FDITkl8m0SFbuuGjHYXR03EWri+5G3XQcXtFYofZreHupSmPtVGjMMhIEVwp8Hhm6RAEyuwpgp6F8JOGpF0PuxEm3eLBm8x7osZ0XxiS6nYPk5709f5cGX++nIgltOex81SZ9mImybWgFJvPZojSknCUpVMItp6wMHxFdHNpmEmybbYfkzj1kOjakNhdCEH9LGQ2PKKbS0O9bdM8ocndasddtPsfb1t0FjTp1VbSTUs5eBWNtddJFGqFbRNmNM6Oi6o3kvqsJrcZ4TSGcZ6wTIIsfZ69eNWHeOcJslB4JcXu8wH+XH/XExK/KOjuZZj/5ArdY4VBXc2tSAxDUX/GIygNUdt+0WR8pkH9nMYryYELHJYznHpwFWVr2vMjiREhmD6yRxAZ8cCy/YVOK/zJEInCzyWBxkFO8uzpW8jmgfaUah17rZHoat5/T7RzbxBH3heG9M1E2Db2zQ3sN24lWr5lsUBuPcRuRYl6kRyrULoZEdky0drNsQUKtxWdGSsBchUzk+SXYiTBKHZOjlXI3RG0Fp0Ebk5WymTvStoncokdUhby8UzWhSR5h7At0puC9unyAfydwKkLmiezhBdPDNPZQYjZEdRPGjSODonsdRAifdh9TOPnGdBT6TDA8CHIwdjXrLivB0BFmB0oXLbY+1eLpFc7A5csVVU4r2dJX01hNf1h4bUVsrcSf19+2R1cb7PWpR3YRPmIscvhYKHQnk/Hs0lZIWOXD0w21PDvdp/CbiYhP0Fa4iuDcLqU0MtCjrXvnord7ntU/qOGJIRYEEJ8XghxWQjxjhDi5/v6ihDis0KIG/3/l/t6IYT4x0KIm0KIt4QQj36nTl4HIVGtTjSyagNgmmRu7tGasw6w/5hkV9rUTyZ9CtnpUbjdw8+LBGhVeD7la33CkNFVTykqVzy0FMkCbhBQuhUSpg60S/g+hZUwxpYl9AG5dRUH/qOfH0VkNjVWR2FdGu6QaEV6R+PUNONvdodNiFqR2YqPGbsSomv1vl6TW1P05qIYRbA3XNHzayHuhMbqaYyd+kCfu+vRPh5itcFcG7qhzk4XZ7KLlmA2R3bVWpON7RJm3UT6I8Vp36e1mad+aSzBwKqVxmgafPH2yXgA2ciC054X+JFJ60gmofcePkbrdISuvPdEkN9MvpUdKQT+D1rrB4Cngb8mhHgA+NvA57TWp4DP9f8G+G7gVP+/nwX+ybf9rPdFRYhzJxJUXAB4HnvPTFG+3ks+oK7HxvNF8neTIFR6LusfzCIOZlc9n7UPZwiyJIc6K8XWEw7KShZ8hRDsXDRBk0Q2CMHeeTNOJ48SRNoWtdMSP3dQb9OeE0S2iGfn7utNk96EwOzqOLbap1E2DLpTgvxtGde29r9bCJpHJSIQdCdl4je05k0qj26z98PduNjZF79oMXd0l9L3rRNNDxMgQSXNp45f4blnLtM6PYRGqYkSnzh7hT//yRepnxoyqop0iicevMX/8CO/nJiCLqTAXOzwH579n2kcl4mdyqlrvmviEkaQnDqRemeVyhtJzol7Tf6jhqS13tBav9b/dwu4AswBPwj8y/5h/xL4of6/fxD4JR3LS0BJCDHz7T5xIEZ6GyJBxQUQNZr4eYFZ7yX04dY2URqsThLyE25tE6VAhEkSkliv0UIkUd47e3jlPr/AiKFGu3u4k/EOk2ARqtbpTUdxwXeURajRxJ2KML0D+m6X3kxcm2Gkb0qHId6YonFSsvl0ZvC7tdIEeU3riR5rPxwMeM0Bwozm4qO36DzdJVoYFoP9PDw1uQJA88JwiFtn2uC5qdusLE+w+/AwG+oXTJbbY7z4tQdoHjGG5yslt1vj/MrbjxNmGAGhSpbqY/zWzqOJIc0Iiddy8LSBlWQBwOpAS73LBD4zZqnVpcNMq/eK/IliJCHEUeAR4OvAlNZ6f1bkJrCf750D7o68bbWvO/hZPyuEeEUI8UqAd/Dl5EmmUu/K7yzT6TjTdqCYKWw7pivO2MPBYYAwLVI7mvZsso60P0O2OysSaWhhGNhNQWdBJ5hqhGFg9gStoyLRKi1ME7suaR5N8toJKZCejB/AA7NljY6kO3EAaqQ0hivximIATIU422Z4AjSMv+0PiWC0QmhQPZPp37OHD3MfFX6rOs7Y76aQzeHCYrVhuT2GvJIjtzIM7q2O5pizQ2asS2FluHiYnYifm3uBx568QXpniGwQQcR/u/g5njyxjF3Xwx06DHlu5jZnclvYDUZgSwEIeNU9EiMkRsRpRPzSjacweknXQHe6MRdFeKCNQgiMU8cPF+TfA/mWDUkIkQN+HfjvtNaJnl8dP8l/ovZFrfUvaK0f11o/buH8sccq1z0cB9HntTMOX0Rh2xiuwp1MTtqT6RRCxY10an64OhvFAsoWGC6I7DDZIPN5/IImsy6SXA6FHH5RMXYpSsRIIp/HL0fMfambqMLLcpkoF8Wza0eM3pwcJyxETL2whXCcgYtqTk0QFiKm/3ANDGNg3Mb4OEFBceyXNwiyBubM1OD8g1LEyV8KaM1L9Gy8SMhsFncmIvtvizROyRitTmzw7aOKG39wguBUj/aR/m/uIzD+/lsfw+3atGeG0KGdRxz+2eYHufQHZwhGPOn2ySJfbp3h5j8/Q29KDI17okKoDP63F5+ncXaIhRSmRXm8xevtI+w8pRILTmvB5P947jNsPGsmjEM4NpEDnTMHkg1aE924fQgV8l7It2RIQgiL2Ij+jdb6N/rqrX2Xrf///XzyGjBa2p/v674jYqztHqovyD4vmtUOExzc+vg8kROPtNdvXB7o/YePEWTjAmu4PoT3BA8eJUprpr7eSqTf/YeOotIqhg6NunAnZtC2xlrZSbpqi5MIJZLjLQE1XsauGrCzh7DtQSFVl/IYLQNdbyAL+QFRv8hlMDsS0fOwm+EwtnEczJaB0QvIbOvBJDxhmUgvHnwWZPUAZCtME8MV9M545HM9aqeGD3Nqtw/9WU+x++iwzSF/R/HypRM4Naif1YPW/tSuz6dvPUjjNEQpjewvRKLn8freHIXZFs6ugdFf0IQhqa0VmXYaWDU5OB7iSYR/79J34dRFIquqg4CxdyJkoA7zGhLTlyVGmb4H8q1k7QTwi8AVrfXfH3npd4Cf6f/7Z4DfHtH/dD979zTQGHEBv+0SzY0jjyUhOdHWNs0jJu3Z5E4n7m7SPAFBdiQgB5yr6/hlTXfCSBT37JsbGD2BcpI3z7myFhOAHKi0myvbyWkQfZGrO5itw5dabGwTOYBhxKyr+7Wtta04meA4hBtbA6J+tVslcjTB0UkiR6JuxzGObjSJHM3exQLbz0bI1T75Sc9F+oL2Ipx9YpnUerwY6DBEBgKERkoV8/PtXzsHQs/E7Aiyd+UIx7cAW5GqKey6RPXT32HWJO34TLyu49bx/b4jx+KB8hbtdoowPexHQkpENmTeriL95HVK1SJOT+zg1JILY1RrYDcj7IZ/iNcQiGtJo3Rs74F8KzvSc8BfAD4qhHij/9/3AH8P+IQQ4gbw8f7fAL8H3AZuAv8U+Llvx4kOBncdEJWyEAd6+XUYkq7GXHWjK1i0VyV3R8Ro5ESyYQezLSjd8pLJg53deAbSAZ66/eHPspGMllW7g5ZJBlQA/ACjJ9DdA/ogxOxxKFmiwxCrIRBSJllEgyDeYSo2YUYOFgMdxQmO5jEwOnKQzSOKQEN0rMflS4uI/eREFCF9MJ2QzmvjpPfHuuh4UofcsXHqMHZ5CAi2uv2WlRAmXxv2W9lVl9peDmX2C8L7v6Xe5I2dOYy7KXKrYlB3Uq4HdYvP7J0nu6ETY3esdohCUL7WSxaupUD6CmPp3pg88W7yH+Vs0Fp/Bfhm0dzH3uV4Dfy1P+V5HRJZyKGa7cTKIxwH4QYDAsVRfZAWMdOqbQ+MQ6ZSKAv8vMAYqwx4wWXKwfCgNe8wPj1FuBmDO4VtY7UFjXN5ynfHBn1BCIHRE7QfniXb7iSgS0IJ1MI0otEa4s76q7HMZQ8NlY4cElk2AJQiSmvURAnp2NAncNGRwmoJnD0vjkgHSQWFU5VUrkS0Z43hUDSlMXsC5ysZ6g+GhIVUvHJqHdMnL2fJPLJH+2qZgogJLM2uJipGdJ/tIoMsk4YRDyswwc777F60yN0xyPQ5GPxKCsMJ6Uw7WB2NcJz4ek+Ns7uVJ9MUyGCoN4oFdFrxyp1F8oLh2B0h2LmYors2zQk3SATc6onz7F5IMftaksH2XpL7BtkQ7VUPbd86COkuZBMDlPf1raOC8ldXk+T3fkBvUjP9e3cS5Pra93HHNWN/cHNgRPt6v6gp//61oRERQ5D8kiL7lRsJI9KuR5BTyOX1xLnqMCTMHN6pVM9FG/pQsJyYS9sbPjy6z0bUmU/TPJEeuDk6ipABrH8Ipn9oZYjyUFGcYv5UlY8+ehmrOrwWThXGLm5Tr+ZI7wz5IuyWJlPpMvlraXIb0eBc8ssuKSdg5qvxLrr/HekbOzy8sIqyQPoMoFH61gqzc1V++ic/i9PQA31Uq5FZsvivL3yFsbdHoF86Jo1x3sogV4eZSgD52lXmfnf9nqAm/mZy3xjSu4qKyKx0EOlUMstjmdhNiCaLiayQUciRX4b6swvxbKW+yFKRidc0tY+fSKK2J8YpXoedHz6bSIsbU5MUbgl2f/BsAjpkTE2Q3pbUP3Um4VIa42PYdUH7Q2cSp2+MVzB6gu6TJ5L6qUkQUHuoFHev7qPOKyWilGb3omDroyHisQdifamEV9aIkk+gDNxHj8UJhUKB7pSm0cjwwhsP4M7mkZkMMpXCHYeddybIv+EQ5mLmVGGatOck0TuFGJ2h41lTCEH1gTT+a2XckhG304/HtafGY9O8/vJJorQGwUAfPnGOrWqBX771OMpg0NBoHl3Ee7DLq40jRBlzcB9kJsPGsw75D20RHZtOXr/ZaXY+OJO4N9BPmpw+8T76+9shRq1F59wUMj0ykMv3mflKi5XvKyZmKkXNNhNvdNj4oIYRQsmoWiezFbD1nE6ARKOdXdJVRfWCTnCCR1vbZHYU9dMkC7WbW+RXFI3jMpEWj7a2Se9o6ieTLly0s0t6R9A4keS0jra2Se0K3LJEbCXR4k5VkF+Cwls2xnY91rdamD1B8cUUt1cmMdsxYUrU7mC6AnvZwSj4KEeiej2UH6BNjZ720B+uoQyB6nTRUYRf1HC2jfipHYKMjCcVCklvQuDOhmx/0idIi8F1as8aGDM9xp/cwurqQRdra9Hh5x76EhcmN0jvRQPUezBT5uce+hKhklhVd8CPJ/I5nCeq7NVzmMtbyVh1dYPy5TbRXjLrqcOQ6PqteyJuuq8NSTgOBCHptVZimp+wbbQhsBskAnwhBUHOwqrJQasBAFrhjluYTTmcaiGN+MHKS7KrScPQYYiXlxRvJs9HhyFuWVBYVof0flFQuhUe0gdZyK0fTjYEGSgu91sHRhr+olQc8EcO8ZCtvl560DypObKwi1nru0sqwnBh/MktxkttrHYfPKoinKrg4uIqrb1s3HekYjR5ZlMwV2mwuV6OoTp9zrlUVVOZq2PaUTwtsP+g2w3NdKVJrZMmt+YNzjVVi3ijNc+um8XZHUK1zHqXr1RP0PDTSC9ItIioFyoY17KH+o6M2SmMla33PDP3x8n9Y0jvsn3LdAqdTSO6XrIAmssiIs3kK13USFxiTIwjI01+mcHkBwBzdgarFZFdFRj7vAYqwpyaxHQ1heVoUPyEoZtSvO0lVsN9lyy/4ibiHqNURPqQ2kqOuJeZTJzmBoxzQ4J4YdlEaU1n2mDzR08O3CWkgTKhOx1zN0Rnhml/bUL+VJ31V2fonBi6oZENXd9i79IE7tiw1qIseOPt4xTetvFKQ2yeCDVrL84z9jWL9uzwmjsNTevSGLkvZmgujpQOWoq7K+Oot4vUTo4g5EPNG1tzrOxVqD44RJdow+DS+gyGUNQfGna8ykyG7qzGLyj8YwfmIBkG7oWF4XUYvMlIcF28l3LfGJJxYHo4xEkFnbbRKScZsEcRUcqkM59KtEXE2SqBEYAcAWoSRShHkK6qRLJh/z3KFINZp/vHG4HGLx3ItvV3rSB/ePxIkIegYCXBrMRYOLMTDea+Dj7Kgdx6yPhbvaS76WgMD6y2xrwbk4QI08SrKPyXKkQpHZOW7OvHI/wXx4iyasjBIA28MU3+hoGIiMldBucpSG+BeaCBzy3JPhiXuCFvH/IjIDvexZ0KE4PXrLrHT514hX/x2P+WAAPLWhN0PHUid2fkN2vF+Jua/JLEXh4mG4Rlo7Z2sP7o1UTCBwAVEd5dfd+1+5PIaJZtX1SngwgigvFMUt/u0Juy8XMikbWL9mrsPOygJYkW9GivxsYzBiJKZtCiWp2ND3CIREW3O2x9LDiMCWt3qD/jxVPKR/VBiPdgF2e7l7zpQqBO9fVBMGiWE7aFmvKwqz5+wUIejXceI5dFzbuMvePTXhB0HoohjDKXRUx65O8qUost9h6IiS5lJoOoxO5QebFG85iIoUjpFMFkQOtERON8SO2B2OhkOk37REj9cZ/tZzS187o/7sWmcS4iGA/pfbQdA3b757/1lOTsxBaPnF+KuRz612/7iTzzdpVfrT2BOXKdwrkxPn7yGv9+8wlkbyQ76XpUzwsaFwIYzVoGPqrnIh47f4hn/V6S+8aQvqkEIfbOAeJAIbHaisqV5HgQYZlkthSVt5tJfcohd0eQX0p+jkynKNw0SG8kOzZFLkvhDSc2gNHjS0WKL6UOFXBlpUz2GxnEgTS3nBjDeTWLCKK4fX2fg6FSJv96CunG8Z/uE0GKSonMG2n8gkFhSZO9GiMYRLFA5tU0uw9Dt5Fm9gt1dBjGxIqvp3EnFD3PZvYrHtrzEOlUnKzoSWRXMvlKP+YRgsIVE6Nm4uwYjL82xBiWLkvSdy14J8/YpX2wrGbq64rXlha59JWT5FejwY40++m7/LM7z/Ppmw+iRujMxGtX+PynH2WrnY+plffbMVyXI7/bJbNkgXMA7qMijPW9w5wN95Dc/4ZUa+DOJeH1Mpsmtdlh45lkg5jIpMlsh6x+opjAZslclsJKyOYzhSRmy3FI7yqaJ5LkKkQKq61xZ5M7oXZdhNIE5eTKuc9wGqUPjL3vD5fWTr/o2d891V6VMAVIkG0Xdelq/P6NLZQFXl7ilYfI8PDuOl4lTj9XJpqDVu1wfYPujAIt8D0LZce3O9rdi9HUCgxPDLgT9odMR+WQ/EoM+UEa8UR5F/xzXcbfjAhTQyyc1Y7IFXpk1wVBWg5caVXOs5Cr4bdsZKCRufgaymKByjOb5BwPbQiMfXS+EKx/IEvvjEf7wkxyHM/8HJ1HFogunkxi7e6B2Ghf7n9DKhVwNpNQnajeYO9ikYm3/KSrVq2zd87GapFIToRbO1QfMOMu0hGsXbSzR2tRYjejxI1VrRa9KYFdDxKGp3oxh5vVSFbgdRDil8DoeBwccBaliEfKHABdCg3uVAZ9gF1UhuCOCQxXD1ZoYZkx2HTao1bNDbp8hWGQX5KcfOwOQmisVj9VLw0yG5qph+N4cECMKQTZDYXhRASZfaLH2BXN7EZEdRvDU/HEw35B1q55tLZyGG48nHq/8Cp36ry9PcvcfJXupDFAdKh2h43NMj9/9HN0Zu1hkVVrshuasfFWDBUaHbvT62H2Iszd5BACmU5hzs0mKNTeK7mvDUk4DqqYgevLCb3MZAhygvQ76wm9UcgRpYknwo24CcZYBWVCYdlLDhSbnUZEIKPkfCRjYQ6z7wWKkQddLs5hN0GEKrkTHpnDqca4wNHsn5idwmqBNiXizPHh50xNIPvPvHusMjAyY3IizsLNqZiksT9r1SiX6E1qbCdgfLw14DyQxQKtY/H0ByEVnbl4p5TpFNWLivVbE6S3xDA7JyQ7jwjYcBBK446JgeFXz5qIXEiYljGKof/w+pUUF87eJcjH3OmDbmUhmMy1Wd8qxZx3IwVwmia/X7tAa0Em9IaneWZ6ieo5J5kkMk02n0oRVZKd0KrbBcd+V0T4n7Xc14ZEFBEWHOQBUgzdp51qPnWYqDFMQ+NoKkGWol0Xd0LRmbWTK6Hr0j4eEjkyCU8JQpoPe8hukARX+gH1R31EJ5n+JghpHVOYd3eS2T8hcMc1cml94L4BaNsiyEPmZhX7hTeGmL1cOk6v35bMfrlLtN0fxlzME2U0Zye3SJkh5nIfK5jLEmUUP/nQy/z0A98Yfq1lojMRTz98neD5Jl4ZkDHyPRwPELMupgtBXmMUYiIXd0wzOd4kveWhJcg+wYpXMvjw2PUBYlvM9hcK0+ADEzfJFlyUrWGyn7pWGp2L+FjpMvrJBswNF5bspseX105QuxAh8iPudBRx5N+vI7woaTRaE95eTjA2vVdyfxuSkFTPOOh8MlaRlRL1iwFONUjqJ8YwHmxQXE66XmJqHFUMKb+8ndBTKYGlyL28klDrtAO+RN5Jdodoy4RAord2Sb6gUWk1IL0ffG8QEpQVqt2JXZT+ziPa3bj14M4a+vEHBuNMRLODN66Y/f0N6qfSyAt9yNHGNlpq1n/hBHfXxmg9fQSIaayQ8Kuffp5XakfojfVT1q4HAr7+jTMUMi5BXseurmEgXIPQNdl5OsKbDdBuvEsbnqDouKx9KEPrTIDuxEDTyBKseSV2ngtpPOwPeq78hTEy0ucnTrxKMO8ProkxVmZutspjzhq9jRx6KW6mFpZN9WyKmUKT6S/LYUtJ/z7j+eg3Lt8T1FvvJve1IenAZ/rzO4jWSFZNGgjbZu4zksgZcbvyebRjY36liFceDmmW+TwYBuklm+bFiYFrIjMZdNomvWJT/+CxgQsiHAedtsksW+z8wJnB8cI0UaUs2SWT2g+cH8ZCQqBKWewdg95HkmMvo7F8jLK4eLo/DLlP7DhWiAGgD53CaLqoavxw6lIelVJsfHIGI9DI7VgvxsrobET9lKQy0SS1M0SbYyuCeZ8xp4MM4/MRto2VjY+pt9PIgIFLq9MR5raF0ZYYdROtNVpptKm5uTFBbyFEdoyBWxnZ8OLWcYxsQGrZHnQYR2mD3986z3aQp/R1e9BsqcsF9lpZ/kXtGcpvSeR0XHyVhRzteaj2MhiBHjLSCgHFHGq8eE+nwO9rQwJgt5pgu9kv0uWvN3DHzOGDGwREN24z8YZL9Yw5DFCVQt2+w9yXejFN1/4UPKXg2hLTX/Pw8iOt5krDrbuUr0f92avxrqeVRlxbobCsMHydRFosrVO4HfNqj0KN5J1tcnehO5dJ1E7Exh7pbUFvNo3ojfRIbe1SuGoS5KFwq4fe55BrtcldsQlzCvmbY1jL/ca+Zovi6zbOssNXPnuBiZfjwq7yPFIv59C2xms6LHzWi40lCCm8ZaPmXDInG1QuibgFREUUb0A25zJ3dJfCLRkXibWmcDeIZyCZEblVTbQT7zzOVoetVo4XN45TuBMOXFpRb+G2HD6zdpbJr9YIl+/E59Tu4NQEplQUX1odusBaIzo9dh8tIS7dTLjS95Lc94akey7COzyRQqzv4BXFYHiXcuO4xbmyRlDQyEpsfKrbRQc+9p0qnWNBvIr3j1euS2q9RfWRkWFYgY/qdMhsuOw9ooeGoSJUq4VTD9l5dOSyak20V8V0dZ+qaySLuLMTk9zPGomC877ez0rCpWFbRNSnRE7taoyWNygqR3tVwn5IsfeIGiAsVKeDXwBvIuKxj16N0+86Nhi/qNGG5sKp1XjnVhFoRZAH5Ru0NvM4jSGJfpAVtNbz7LwyRXpXDR5ot2Jyd2Ucr5bCaajBubozOTJ2wEKhhl0d1tXUVIXji9s8Pnk3niTSF5lO0Z1V1LvpxKICEB6ZxAj0EAd5D8p9b0iyXIKltWRwLwTdJ4+TvxslGumEabLxQ8fJ32bI5aDjprM7PzrH1JeNBERImCYrPzjOkU+rJGWyENz9eJZjv+UfQirsPGxz4t/UDp1P64jk2K8cGANjmnTmYPZ3Vw/p20cVTkMl5ykZBq3TIY3TsPHRSoLXQJma9KZEpyPou11IA6Ehu2zw9vZMPAAN4kbAmqDymsGtPzweD/zqXwunDuNfsVj4A2J2o76LarU14y8bTL4Wd+Pux3Opakhq1WLsZZPIFgNXN71Uo9rM8OarJ9h7KDNsQ7l6m9W9EpeqM9Qenxh4BlG9QfkdwaeOXKHzyGJiYTSurhCmBXIEyX+vyX1vSDg2YnoioTLGx0GDsofpW4iRB05Dk2qoBOZN5nOkdzR2K7niyWIhnpd64CoZ4+OktzVh5gBKuVLGakE4lj6sb0N4YGqGzOdJ7Qmi8ULyPPN5squSzN1WHHP0HyqZy5K7ZTL/QhA/zH3Eg8xksBuCworC3LVQmT7/tmUOBie3t7PDAWhCEqbALwi6x/04dgIQgiAXA2B3HzQTw5KDvEBG0Dxi4BWGLmpn2iK9rfHKgjA9bCnvHSvDUhZd8RGKwUIk5meQUlNJdZGBHuyeMpul+pDmRnsSu5lMEqE02c0owfB0r8l9b0i62SIcTyIbdLeL4fVBmqMzSnsuVk/FFLqjM2F77tCIRmfCul48peKAR6G7XeyWRoYHOls7XayOhiipV+3OYETKKM+e6nYxXI1yTPTTDw6MSbU7GC5EOSdOLJRKA70MQNmSMAOiz/Wnei6GFwNIU3sCzD6XQxDiNAABqXULp7o/dULh1DTaBEJJfnVYCkjtaLxiPF0itz7k7M5sRTSPC5QVT/Xbv37ZzYDWUTA7YLeG416sho9adLHuOjiNEfITQErFzb3xRMwoLBOzLbi1O0bkGIn7ICqluNGwd2/GR/CfgyF1e5g3k4VX1emQWt7DKyXjJtXtkrtWY/eiSA4U63bJX2uw+5CZyAqpTof87TbVs0loj+p0yK351A805CnXJV2NqJ1N7kja85AB9KZTCVdT+z7KFihLIl66NOw7iqIY8RBETL3USLSoRw44u148OLrfnCgsk8iGwq027RMhvbnhHKTIhumv9XBnA7qz8XlJx0FZgslXPMymQZjqIyRMC21C+UZMyj9g6pAGXkGSW9F0jkRY+8OYhaA1byEjqF8MyK4OH3S/bDM/UcOfDCm+MaQnE16A71n0OjaVLywP9FGzjQzjCRnOO6P8ohBNFGktGHHK/R6V+96QxNF5KCenPMh8nmCmRPlGQLIvqIQ7V6DyzrBoCzHBYm8xT+mGSkJQ8nkap/MUVpIwfZlK0VpwDjXkCcvGLRuk95JbmDBNgoxIoKDjF+LWhDBjIEeoiVExy0/7aBZtyuGEhzAkVdXUz2Sw2hq9FnPwac8jVdVsPVXAbBpkrsWZMx34ZDcVW0/GhdzsSgylUq5LbiNi8ymHMB8NoEM68CksB+xcNAlKariDqYjKlS7NE6CNEaiR1kx8eQu/EmEVfGQwvB7Z1+9iGRGpspsYohxtbhMFksnxZhKcqiIqlyOEEyXHfQLi8m0m72HiE/jPwZA6PcQBKlvVamF0fCInuSNFtRpmL4rjhhGXL6o3sDohWsRxyAB42WrF7ooBxpmTyIvnYr3rkt4LccsG6vmHkQ+eBeIHMVWNu2p58sJg19NhSOFOSHvGxDx+dOREI4rLsX6/zrIv+bWIzpREXFlK6FNVRXdKMP2Ha4mKvuFp2kc0hVskCsJaQvuii9E0MLbqw682Bb2THiITDse9EBu1d9xDpxRyBMUeFGzCI/HDPDqNIpzIc/L0BkJqZG8Y2+hygYlUmzAwElTDMpdFGJqt6xOJWbHCsmkeNXBupdDdZF3Qf+osypaHqKmN0yfelcr6vZD725CkgdraIVxOugLCNInSFm45ybUtTJPujBNzdo9OkXAcWvMOjRMS1ekNAmOZydCdMGjNGahby6i3YhiPzGbpTMfulPHSJdQ71wb61oIRI7dfuTwIvGUmQ2vBQCgIl4YoCZnJ0J4xsLo6kS2UqRTt6XhnSwwscxy6k/HEc91zBzGVME28kkQbcROi2OejkAZBVmDaIcrRqMoQae0VBdmii7QU7pHS4Dv8nCSV85Adg8aDpcH1C7KSVMbHbBpUHy4PURh9JqOgZ7Hx4bGhvtNDIbi4sMrmx6cG9TzV7WIYik888ya1Z4fdrfsI8+BsF3V8hCpeRRi9kPashThQ4oiu33pXKuv3Qu5rQxKWOSygjuodB2urgRYcMpjClTrK0omgX6ZTVN6o4ZcVsjDMrIlslvGXa7RORzGHuN5PGOQYf6VG/WzMm5fQv9GlcSr5vbKQZ+ySS+M0yWxhIU/plk/1/IEaWC5LcSmg+oBILAQynSK/GsWfn3Li39//Xbn1iCijKN0KBmM9hWVitTVBy6F4xUC2+zuJkNhNTWcri/N2hvS1rcEDLUNNbzeDdAXFy3WEaQ303VqaKKUo3uoNMoYiVIQq/k1j77gDPZGiYnc5ndsmfzdKxKSmFXE8vUt2cwQkLARWR+M4ASKIEr8bESMoovZ7j6n7ZnJfG5L2PFS3i3kk2bevOh2iu+sxa+gIib7qdODuBv5YRHhucaCP6g1EvYVztIX38LGhfmcHTIlZcdHzQ3BluLmFP5FFpRVyaiKh78ynsDoCY2E4dDnc2qZ2OkV6S2DODSfchNu7NI7bFG6DuTg//F3dHrXTFuUrOjlZUGnaMwbldyC8szrY8YRt0xuXlC6ZpG/tDVqyZalIkBUIV+JVQPdbRIxCrl+sjujNRARzFdAKo1AgcgQy14+ZHAukiF1dAYXxDlaj/8gEQZ9bwmKrkce57fQLuzHyPVgY5/dffYhf/cxzcedxX8TZ47hrOX79zsNEjjFAz5uL89TOa5SShLmRXrFUir0LGcK0wDh5NHH/zblZjDMn30d/f1tECFQ2fWggrzE/Q5gmiSIG9LG5mNb3oJswO0ZvM4fVSI6YCXM24W4KOUKLBRClJEZXJsauAFhthfSTLhxak92KMDwdcwzsi4qwmxptQLgydE9Vt0uqqmmckol2j6jZxPDBK4vEdPSoVkMLsJsaTGOQMIm2tuPWBl/Ew6NvLcf6egOrA7lSFznmY7wdT3SImk1MV/PciVuEhQhZaw8WKy0EC6U6MhRILx5xqQMfbQiiSKJNjV3z4sVKa8x6F5kLCCcCMneaAxdVrG2Tnm8xnumQfnt1kEiJ1reISiG2FWK+eWuwyyvXJb8axud/czl5bza2YK92TwBZ/zMwJIm4s37oYoZTRaZerKIOcKF1juaZeVFjVpNuwtYTeexdg970yAxZy2bryQypTYPOo8Nqu1EosPW4RWpb4j9zbtgvNDHB1lMWhSWF8cDpQdLCnJ9j+3GTsUs9jKnJQYrdOHmMxnHJ+OvJqezGA6fpzAoWPtNJICqMMyfxioKpb3QGmDaIGYiULQiy0DkxnEdrHjtClBZE+SgeWTkb74bmzDTKhNZmHnk3hTp/bHCeWsJXXjuHXTPonh6PuRyyWcKU4MrrR2KO8RM5ZCqFcBzcMQu1lEX6gvrZXIxsEAJ3roDqmhhVk73HKkPXbnKM7l6GbmCz+4ljQ5eykMPcsXhuboneB8+O3N+Y8rh1TGEeTbbFCMNITKd/L+W+NiSZz2MuzhEd4NM2jx3BaLp0jxQQi8OV2zh9gsxal/pJg2Cyv1MJgXnsCKXbAdrQw5SvNDBmp8ivqjh1fLVfC5EGTI6RXdcYPjhvLMWobSGgXMCug+lp1PWlAae1quSxmiC9kGhrO16FhSAaz2O6EKXMwUMOEFQymF1wJxz8Tz42eAiDyTzIWN/53oeRD8dMqyqXIshBqq5pLpr4H30YYZpo28IvwNSXDPJ3NMHiBDKVQisVUzq/aWA1BVHaRObzRFs71M5InB0Dsy0IshJZLKC6XdpzElUICbOa3rgEy0J7HmFacPG5G7inXXYf1nGMpDXObo+PX7yMUIL6mdjNBGB7D+FErCxPxFPQ+4kR3ekiFLy+O0fjyHCEJkLiFwyyaxK9m/QKdOATbmxyL8h9bUiq3SaYqwz4APYlWt1g+7kx0usdon5GDYCdKtf+Uoapl13kF1+PdVpDELL60wGLf+givvpm/8MjdC7D+scjFn+3MRitgooIJwo0T8D8b68PwaZa035gDOlD4RurQzJDramfL5Gq6kT6Ga3pzKcp3Qixl7bBMgcPjzduU77uk7nTYesJG7kYZ7G8ikX5ekDtjMlj/9dXWf14KTZIx2D8rYCNDylO/eQ1lv58DNbVaZvytYidT3nUz8Dqx7LxA13M49Sg9kRA8baiNe/EvVpjZcKcwp0KmXgjiNHw0xNxdvF0wIWTq0hP0HjKRY7F2LnOrOSvzn6ev3Dx60w/MOwh8itpPlC8xi/+6D8hsvu9Uf3frQPJ9EKV8beHU9CV6zL3xQDvtyeZ+ffXhsgTFVH48hIL/27l0IJ5L8l9bUjCtGJ/vd0e0Zkx74ImHkw8IrrXw+hK2nPJgp9qNAmbNrWzSQ5xvbwKpqZ+Pp9IZphX7xBO+/hz5USgm/vKLeoPxQPARjkYKl9ZZef5AJQauD4Axde2uPtdAu266FZ7kMHKv7nF3Y9bGBu7TLwRDo7Pv73N+nMm01/t8jvvPETlagzhsVerrH/ARISCZ8u3KL5toX0fsbHLzsOSk7M7zD+1Rnpbo1pt2NzBK8Njp5bZeVTg52MilahWJ70hmT22i1+M0/WsbaJ6LrnrFlfWppn+RoC97KC2Y9cyvaX5v9/4QX79lz/E9htTqD77q/Qjfm/vIf7bt34Cbel45CWAaVKebPGR6RvsPZBMEuw9aON/skn7+SQXushmuPPjRxK79r0m97UhIUWc4RlJKesoQjoOYUYgriWLmSKdxq5LKn9wPam3LVKbJlO/fyeJ8UqnMKomY19ZT6K8bQtaJtb1tURsJhwH6UrYOjD4KgwxalbMMpTLDs+358YDyISAsfKg/qO7Pay2iBMNAjCNwfGpXYHZ8jDWHYJc/3Ncj8yGYOZL8I++9vH+MGiNkJLUruDG5Tnu7pYwXeLfZ1tk1zV7bjZmEuqDR6XjkN7R7NRzmK7C8PrDytIpnLpGKYGfNxBhv0+pb+BzuQbupCK7PsTOWVtNVpplmpt5SpdHFqd2h+DLY3x27Sxjl5Nx7cTrHt6NAvk3kyh5Xa2x+G+Xk23695jc14akfR8RqkTNBq1j8viOHhYm+7IPBj0YoGo/iHewg01jQiIiMVh9h+o4jlAHSCt1JkX+dp94fkSCY1MUb8Q7X7SzN0BVuOfmqLzTx5pVsoMeqeDULKUbimh2jPUPGHSOlwDwT85QuhXSOFtEaGKDEYJwcZLCSohXklS+YZFbjxCGRI2VKN0OyS0ZZL+ci+s/6RSMlbGbmtXXZslsClI1hSwVEcUC7UWBuJlFhHEWUGbi6en1c5pM1qN5RBKlddy3pTWGrzGFIn+yjl9kUNui2WavnsMqufEwtf7ioTodshuK3dUSzkifEkDqyhrFm6DbSUyd6sRYw3cbb7k/LeO9lvvakNCaMGcd7lPRit6kgImxQ29pn/WJ5pNtF8KQ8GALJirJg6VAz7uHUug4Nt5k9K40UO0jahBA74vRDWieIN5h9LBZzmz71E/HUwXF69cGqXGjE1A9L/DLDrNfjsh8/p1Y3/bZfdBEG/G81n0wqNFyaR4x8YoCvn8PPxuPphRRROOoSZAD98Mtdh7JxFM1lKJ5NEZCRA50Jg10EKD76HKhQFkx0lsU82itcfYkndU8lWthzIPXJznxioKql6G+XiA830Yej+tz7oUFnj66xHNHl9h+LhpMHjSPLsJP7vK3Pvi7bD05bBERpsnSXz5O+xNtmBjpeCYuPocL48Ni7+hr6TQHaaDfC3nvz+BPKdGB8ZYQp0WVQxzAHxBry0I2kwyp2vVQ13OH+Ld1q42xnDo0mlLt1bDq/cHGo6vkzh5GV4BlYZw5OYTwrGxgdkVM+v/0QwNUhbG0ifQFOgjgwZPDWUF3NjBcQfryBk7VH6zy8s4GRgDlN2tMfgPYJ5i8s46WMHYloH6rwtg3YgPTK2sIBYVljdt0GH+ji/Y89N110rua3IokfKxFcSkg2quiWi0ym5rUrmDjeUFmRxGu3EX7PsVbitS2wdYTBmNvaqKrtwAo3fS5/s48Rlcy+Wtpomu34+vcDnjxpQe4Wptk9gU5TBRoTe31CaTQlK8OQcXCcXBqUMi6RIUDBJtnjyK7fmLwwb6EG/fGOMxv2ZCEEIYQ4nUhxKf7fx8TQnxdCHFTCPHvhBB2X+/0/77Zf/3od+jcQRrY9RBdSPKdYRiYbWidPbCyGRIkbHw8ObAKyyIoKLY+maxTYBhEKU37uQPBrxAoG4InziRjIaVRDkQXjhNdu5kYx+IXFfroHOJrbw5aKXS3izeuUMfn0K9dHlB+qXYHr6JiEpRXrgzwZKrRpDut2Hmqgl8QsZtIHMf0JjV3vkdy8sIqou8aqV6P3iTkfnqN/+lD/xqMIT1wd0rwg3/5izw8t4Y7ZgzOM0zDx37mJaQnYuJ8iHe9QPOB738doyvifq6+2A2fH3j2VbSI+6H2f7O5VuXjz73JqdIOjePDebfR5jbRsR5Z6dE8Ohxcrbpd7IbGNqIEEgLA2K4j1t/7gct/nPxJdqSfB66M/P3/Bv6B1vokUAP+Ul//l4BaX/8P+sd9Z0RF2DsdRDNZXDXKJco3w0M3RJZLTLyqYkbVUf3EGOOvSHKbyeBXloqUrgis1oF2iUqJ3PJhv1zkc6Q3xQCKM9CnUvGMJTN5uYVlUrgp0YLENDphmuRvS/yxDOGz54fk+qZJZlOSrkZxcbfv0grLJL0lcLYMOv/zXIJp1amDY4T8/G/+l1ib/V1BCKwWfGb9LK8sH6F0bXj9ZAj/4caDOHURN/bt6wPNCzfPUL4e4Yx2EivF5+6cpvK2IEwNW9MJAq7UpvnKK+fIbI6QwUQR2YzHa+0j8X3YT+7ouMv2f3/8j5Jt+sQew8aPn7knGFW/mXxLhiSEmAe+F/hn/b8F8FHg1/qH/Evgh/r//sH+3/Rf/5g4CNv9Nkp05WYMFRmRcHMLqxmxe8FMMHbqXo/mEYPdRzXG2Eg8pDW7jyn8nJFw1XQuzd6TIWbbT6S/o4ki9Ud97K0Dg5VnKrRPRFibSUSyWpykN6UxNpLJCXVsnu6UxqjHjKGDoPnkIu54DEPySkPqME4exSvHeLvbP5watF7Lk0dpngkJz3bZ/bEu3Ydi3J4xP0vzvM9UuoWa8lj/VMz/YOTztJ/osdfIkn4jzd2P5xGWjXAc9h6LUHezTL7isf2INeDm3nzaINpzyGx4bD4lB2N2qg8WUEqQaii2PxIMjFtNVRhPt5G+YO/jLkZxOOLSNiMWUlW2nlfD3yYNtIBAG6x9pJBMIOSzNE8o1OPnuFflW92R/iHwfwL2l6IxoK613l+yVoF97PsccBeg/3qjf3xChBA/K4R4RQjxSsBh3/dbFfnAKYyzJw7phdbMfM0bZMIgxpgVlyJmXtQwNWRnDZdWmHhFYgQaY3Koj67epPSGRet4NtF4p1+9TOGSTetsJRmfvXGVzF2D9vmJ5IPw1g2cmqB37kAd5NIN7JbAny2iq/XBSqyvxnGGiDSF1zcG4FR97TaGK7BbmvkXokGRU127hV01kEtpSr+dJf1GTHEV3lnDWbN58QsPghLMfCk+Pmp3MJdSqNUM7RMh42/HnHra98ncMTF70DxqU1hWA3fTqQqMnqQ74zD+hibqc+2l9yK6jTT1Ewbll61BgVr0fN544zhMe0z8gTNwT0Uhj/ulcdpRitkX5KB8YIxVMHua//7VH2Ts8jB2kqkU4WSB0/+ijvz6pXd7BO4J+Y8akhDi+4BtrfWr384v1lr/gtb6ca314xb/iVu2EITlNFHu8PvDdLzCDdiC9o9PxZ2q0eVhLckoFdl7SBNkkgPFzCMLeBUo3Ookm+hOHkVLyN5Jkrobi/OYHchd2Uu4J/LkEQwX0reSaXR5fBHDBWdpJ0GJLBfnsBuQXq6jG63hwzY7hVOD4s0u6dXWoBAtiwVSe4LKJY0RgO7TdAnLxGqBXRfk3nJQdn9X1Qq7JYgqIdllE232kyY6HmI2+dQmZk+T3gsHjXNmV3P8sbsEGQmCAWhWKM25Y+txzckSmPP99VQppk7tUim12bsgBmyxqlojsuCZ7A3WP6IGCZZoZ4fpz6yhlEgQeyo3Rpuot67eE+DUbybfyo70HPADQohl4FeIXbp/BJSEEPvL8Tyw/8SuAQsA/deLwIFRa98+sddqaOvweI/IkXSnrYRLJkwLryypnbQSO4l2PfLLkjCd7P+JVtdx6rD7UC6hV7dX0AZ0jhyAJt1ZjVPNi6Wk/tptvHLMrJrQ31iiM6djFqFR/a0VOouKsJJNDI0O767TmY+nDiJHAvhqjd6kJrMVxO3s/TrZ/rQLu6GZfM3FuDWkIDNcMHcs7IYm/+r6IJBP72gcM6T5oy2krwY7SeFOyGKuRu1TPbySHCxQqa0uSgvaRxRBdrhwCddHCk2tkUVEEK716Z2VorcQ8ra7QGrDTMB+When+b889vvDSRij1+TDjyYQ7/ea/EcNSWv9f9Zaz2utjwI/Drygtf4p4PPAj/YP+xngt/v//p3+3/Rff0Ef7BH+donW6GYL69bGoZeyy2383AGIUOBTXArozOtE7UG5btzoNpfsnNVRP4MkSLILRRGGB+GBVnYdRVjtGBOXfEGR2gV3Kn1In9kUuCOI83199q7EG3OSHNgqIntX4E46qDevDNO+WlO4Dd1pi8znLiUIVvJ3NPUHFH7RJKoNY7fspsI+2aS9wGB+E0B6N8QxQnodB3t7WFi2az57XgYVCcbfGBZMZctFa4Ex32X6697QPfV8qq0sHzx+k8XPJmftIjS3exMsfqY9vK5CUDtl8q9Xn6L8Vj1xOcRj52ke/eZey/3ej/S3gL8phLhJHAP9Yl//i8BYX/83gb/9pzvFP16i47OHJ7lJA3cmQ+FOmLiBMpulPWNSukYilWqUywRZyKzrBKWwcfIY2hDk1sIk79xDZzE8Tf7OATL+hx/Abmryt5PIBp66gNXWpNYPTP577DxWU5NeTR4vHzqLXdekN7vxKrzfavDQWUxX4+wFyIvnBiu0cSoeCeOWJZ1PPhjzQgiBOTNNZAH5kNUfCTFOHUOYJsbUJG5ZYBqK7Pka3edOIxwHo1CgecTkyuo0uTdTVB+t9Jv6BFtPZnnz1RMc+ZeS7cczAyLI7qkKNTdN5ss5Np92Bi0iIpchZQd8+QsXqJ1yBkkcrTUikPzu1Qepnc0Or6vWlG5FrO0VaZ9IohWMtV1yq35MTX0wbyUNZLnMey1/IkPSWn9Ba/19/X/f1lo/qbU+qbX+81prr693+3+f7L9++ztx4vtitNxDUB2Zcti9YOHnkwYmJ8dpLwiMA+UIvTCFOy7IbUSJnSccz6MlWO2kQUYZO3YDD6ZpHQOvLOL5SKPf2wtQNkgvSXwo3JAg/y5pdD+kMy+ons+jWyOA3J5P6whUz6UgVOj9ZrkgpHkcOnMaL2+gm/06VRjRnRWkbjoYGw4q48Qc3+0O3SkBXyzjv1TBz/X59LpdwoyAXYfiUkSQFcixCmhNbl3hLLRpLdh4ZWL2JiC92mYy28YrgV/SiBPxJAzdbDFXbFB5aIfaQwpx/mSsD0JEKPg7T/wOO8/Gxr0vfk4S+ia100YC0a8myyhHIlvuoWuOiuJO5vdY7ntkA2EU3+wRUd0u45cCxEGHMgix2nH//6gIL8QvxGnl0RXP3GvTOqaonUmiws1qh/ZRReNEJrFTGf3j3elsMjYLIhqnNOrA6EuhFO0j6vAqqzR+WZHbCNCLs/GMov2fUIqNdPvZMuH5fmNcpAgqcSDeOiJofuhkzCUhBb2ZkN4JD6slcGcyyHQKYdv4ZUXvyQ75uwqnHsbsPqZJb0KTPdqgOy5jLJ+MkSP1ExKvZ+GOCyJHD5iBGmeLXN+YpDcbombcQTE4OjVPxvT5gfm3McdcuBV3AJszU4yd2uPZ1AqpdYvoRgwsNkpF2vOC50/dZOplb+CeykyG7pECYVqiNw6M3bmH5L42JGGaUGscQjbIVAqjpzD85M6gqjVyqzGqeVT06gb5JUFmVyVjodUNMhuS3EZ4SG81JMVb3aTvv7UbQ3vuNIbgTUDf3UD6Atly4/rVvpGtb2G4AtH1MCYmEgw80hM4622aD5QQ/dVZ+AFGWzL2To/2IiirT36vFPnrFuNvanpHffycjIcu2zalSyallx14pEl30ownhDs25cuC9EtZdj7l0Z2yUM02IpuJ3d4Xy9Q/0G8BX9uIx97saJxraXIf3SK9LWIDEILemCRwTb7/ydcZ/2xq0DLfmU8zm25wtTPFsX+ghnGbaTCZbfMDr/0sx//ZyuD6RY0m6R3Nl985jfPazeE963bJfC5Oe4+ytd5rcv8akhDxKlrIJzFy0kCWith7XZxdP6kfq1B6p47VU8OHWRoxsuGdHm5JDplW+8dPfcPFKxrDgFYI5HiF6W8E9KZHdiohEGNlJl7TdI8WMfoT7SBmC6q8o2mfG0MdnRmAWkUuR24FOqfHiI5NI4v9rJ5l4lQF3myO/O12PNis/x2ZjbiRr3gDzH1+CaVAx+0Q49PNwbHa91EWWB1NJddF7XPlB0FMchKAYao4jiJGwe+PsHTSwWD8JoA7LjB74BgR6Z3houIXgUCy2i2R3h32TkW2oBM63GlVkN3hB6lilp+e/SrtWiYxeE06DvWzmomvWEmKLSHQ509QfHUzMWVx/7V7ZSDz/WtIWsdjTTw/WStSEeH2LsINkKOxioqINrdBQXNxhNlURUSr64hQ05kVyP0Zr/3jlSnwCmJI36V1vEprYgJHYxgsR6sbWB1Fe8YkHMm2RVvbWD1NkJXo1y4PukLD9U0yu/FwY165PGD/CZfvUFhWVM/YyJUtohu3B/r8asTqx2yKt130mzHPXrixSW5NsfmjHt7nxxn/9LX4fLa2KdyJ2P2YR/0L00x9di3+XXtV8ndD6hcDCn+UYeLlWjyuptWictnDHdek/ihP5Z24TqY9j5kXe4QZaP7GDKVr7f4YGM3i79VI37G4/nunMLvDGLPy1XVe+NoF7lybIiwNi9ni7hZ/6yt/nosn7qLPHBm5nRqjJ8j+1HoyzS0knYUMKz82d2jImEynkwiV91DuX0MiHk5cf24R48TRhN6cmWL9k5MI7wDV8JE57n5fhbkX6okCqzx9nLUPZTj6q9sJ9h9x5jjrH7SZ+f1VotqQREWcP8XWkxbTv3YzUSSMnj3P9mMmk79xNeEKRs9dYOeiQem3306cj3jsAfbOG+R/723EI2eHrt1j56mdk8z9h1U2/9zJGElOTHKy+5DB8V9tcPMnLPxPPhrrT5+gflpy5J9Kuo/22PzzZ9jnoth7wGDisw69B3vc/MtzCMvGGKuw9YRBdsmidl5z42dKyGzMMLv6UTtm7EkJbvxEFmN8DIRg/fk0vSM+QUFw/b9ODQq1W8+WqDy/Sed4wO2/OFxwvKPj/PRHvsT/85O/xs2ftIcLkRScP77G3174PdY/VBjs9DoIyS/Dna0K4cLITGAVkfmNrzP///3GoSFjqtu9JxINcJ8bkqrWcaoB0e07Cb1utXHHwagmZ7bSaONe6MGBrJpoddGPNg9lhGTXRZ3uHEoGCDcgON091B9j7XYxLjYO63c6hKe6MS3xKOKh7eKdcJGVMsZWfZCSl/UO4ekuOpumfN1H3+1Pu2v3CE70CHM2dtUgfbufraw18c91ac07zI7XyW1GCMNA79XoHfepXoCfvvB1StcBHc+s9acD9BMNfuKjL5LajqE6qtcjzCvOfGCJC//FZay2iBldtSZKwX/z1BexP7CL8OWgpUFE8MsP/BJ/87nPoAM5aDkxGx4fyV/mqLWDUGKg135AxengagttgFb7oFWFVxH82PlX8caS1888ukjn+x+7J+pF30zu3TP7FkQHPs5uDzFWSaxMUavF2DuKYH4MMcoXV6tReuEktYsOxRHYltrZRby6yPYH8ozduD142NX6JuY7s7QupkgvD41Vr25gX75INFmEEZ46vXQX9frD6LwLIzVivbyKdfVhdC5ZeNUra6RuPAymMRgBuf/51uUZRLeG+fnr0E82RNs7ZN5cxGzXOfH/uQ2OA0Kg6g3Sr5/CdCOMvz9G5voWodJErRa5qzZOVfOrex9m8aUtojCEMGT8RYvutM2vuI9z8oXWIP6Y/5zm7dQCF07fpXJZD3buxc90+V+mPoLRkVQui8HuMPWFbT78/N/A2HCYuBy3bgDI1W1+5g9+FpkPKL8lB3qiiK998SK3Hh4nszGCChcSq635t689yclGskygigfaZPoiHAdZKiaL1u+R3Nc7knlkAeGHCCeZzzaPLg5Bj9nhTRBnTxI5AtPVyYa8M8eQEYcGkHH2OFYb7MYBjNexBcwuh1xHcWwhbmUPD+tNl8SoRwCOL8bjWQ7M/RFH5uMhX0DwiccGq79cmCWyISw6LP+NB+NOUq0x5qbjblYNqx+x6J2aABVhTk/FDD42eBVN86HYZTIKBXpT8S5r3kxTOxtDoITjsHfOxKib3Pj8cbqTcrALbD+awWgZoKE7IwbXr/lQPNTNPN6Ou4D3W8qPTHHx/Ao/ceEVOvNDvcikGb+4zX915KtEqaEeHceKc3PVPppkxAu4tkT+0mEXTnveoCfrvZb72pDClbsI1z/keoXLd0AI/IKFGnlI1eUbMUZu2kggGLixQndWUTtlJPkfbt2lecFn96FUwvDE5g7dx3p0jyYn7bFbo/2AhzaSl1V0enQv9BJTGQBkp0f3hA9KHz7+SBiToHz21SEKo9WhNx9i7XaZ/1wnZjkidmW7RwK8gkTZmtRS7PKpZgt3JqL2aMi5p5cGxql6Lt35iPKHNnnmU28P5khp3ydKwfzFDYKcwh+BAGoJCw+v4+xJvIoa7CRCwSfOXcG2QvzSyHQJP2QxW+XlvSNxx9/I9I+MFfCv7j6NMhikv4VpETmw9dYUYXZk1q4QRI+cofrkJOKBk8nrZNnopx+MF873WO5rQzImJuieGh8CIvf1lTK10xKnlsR4mTNTtI4rsltRQi8WZlGFkPKNaEgbBXBsDhRULnsJSJE6NkvUM0hvJutIwalZRNM6ZNj+fAVdt4dsQCN6o24O+K/3JZytYNViFlGZTg96qvREJY5PhMAbc9Bn+qiAchEigdXVcQfwJ6bj9H0+hzY1zoaJ0oKNZyUyk0EWcmhHsb5ZZtxu0zwdIXM5pOPgzQTc3SozcX4H95Qbw2+EoDOvkUJz5JPL5I43BsmD1rzBY/kV/vKpr2JPdwep/bCQYiFV5S8tfBlvwR/OPNIxWcrfOflbeJUhSFiHAWYHvvdjL2MEIzGs1lh3d0nvhugrSZCMDnzky1cI76zxXst9YUijzXlDpQFSoGyZ4P02piYRtk16J578vS/mzDRqvEhuRVK4PMzAGYUCwWSe4hs2hbd2EyuhdizSyzbpm0m3wthrkV62MTaTdMj20jbOnkR0ktwP1rU1rKZMzAMCsC6vIL2Y42HUBZXv3EYo0PkM4tjCsBB5+w5mT7DzdJn1DxoYjTh+UXfXcXZMtp4CY6o3WCii3T3Sayb6TIerrxwhvyxQvR5RrUH+isXYeIsv/I9Pk71rxDUnz2P8aybprI/zjyvk3krFzEpaM/M1xcrWGOu/eRS+WB4kD8YuefzzpWf5x29+BOP1/CDRYm02+K3VixhozG1rMAxAd7rcuDLH7zYejmtf/bGeaM3YZY/P/+snsdbqiZ1euy52zXvXVnMdHBiI/R7JfWFIIp06tMqjFXqiQuazbyVS0LrVRleKcaxSHRb2VLOFCBVemUTLt+q5WNUu3Wk9GCUZf5BGNnt4Y4pDo2OCMHZvDogOw/j4dxF/LDpEooIQBJUILBNxdH4QjwjDwK/Eo012H6/EKWhiJEcwHmD4oGyNP1sC4mKmf8ylcqrKh47fxCv24xHbpnfMp5B1MRc7eBX6fNkmrbMBu6sl/ILAHdexSysktQc1vZU8XtmgfTQa7JbVMwZRI267aB0b/o7GcZtGJ41xM407pdD9xcI9PsaRfI2//cqPxIvC/tDlconsXIvfvPZQfM32Fwlp0Dxi015UVJ+aSriCTI6x+rE86kOPHLquMvUuz8Z7IPe8IYl+ZupQatpx6C3kUQeq3ToI2Xu0wsQfraCaw/YA1elQfbjMkd9tIWvtkeN92ieLzL/gH0oGdI+XmXiFwZTwfYkmixSvC9RYso+IUoHCLYk6MIpT5DLkbpl0H5pPFBVFKoVVNVj9/llaZ0oxtRRxQG62DJZ/eJzqgxAcn47f4DhYOxadGYGzJ2kv9j/LtrBWHKo3K3zj316MyTH7reOpFZvd7QLZz+XIL8dzoYRpklmyEKHAamsmX1bIShlhmWTvypgZVcDkSwJRKYM0cGoaq2kQOVC8Zgw6jE1X4+6lEUpgtgRiIe4CFqFmo1sg9AxkIBCzQ04Ky4j40TNvoA2Q+1RnKqJ0w0UVQyqv7Cbut15ZY/I1H/Pro5Qh/edgenIww+m9lHvekGQuizo6c5gc0DBQthhwAQzfIBBaE82OIUfaxhECw9d0FjKEM0k4voiges4hmEomDwxPsfsI6NThKkHt4QhZPcBFbUgaD4TIvXpCrS2T9omQzOUDhO+2RTAVMPf7W2SX2sOhy+kUYSVg9kWX7JrAWo9dSJHPEkwGZDY1vfmA9HZs+CKbwZ8KyaxK+HANq0/uIjJp3JmQ1B2b+gfcOKkQxTNaezMRRltSvahoHjVivWHQndGYbcnOE9A4IdFG7Dq3jsbXqf4Bl+ZJhU7H96O1IMlNtfnr/8V/wLkw/N1exeT/dvzTfPFj/wh1uoMYmdn7/Oxtfm7sqwQFjfaS7trYixZ6ZTWhk4U8hqcOFWQhTizdC+xC97whRXtV9CuXDl0s1XPJvbODyGYHUxkgTokWllzCnEXn3OTwDVqTW+miTIFfSe4wqe0eZk/3s0VDl8Le68bcb7kDRqwgf91E5w/UhUxJZsVMdLUCYBrkr5sQBImHQTsWqRUbqnXE9eWBi6oNSWrVxt7pULkaEO2Tu/gBzppFbiMgd9MidaceH991kW2D7KaiuZ2jcCeOJ1S9gexKwowmnfHJr0ZE7Q6q3UEoQZRVpOfaWG1NtFtF9XrIEMKMAhVn5PTaJjoMyd0V+JUI1Yp3Mm7Gda/CssJzLf7x2x+h00qh+8Xx3FKbX9l9mv/H+ncR1JzBb9Cuxzv1GVbDNHZdxDAvACHYfizNj/z8C+jzSQ4O1WwdIqC51+SeN6RvKioiurlEuL6BvnIr8dI+SYbZPVDPefM6fl6w9kETY4QURb5zG2XBnZ8KMR44PTx+aQ2hYf35VMJY5a27aBM2Pjw+iF8AxPI6MoLdD84n2YtW1mJG00cXk0H00l2UownOLyYgS2plDS01vfk8qS+8PSiWRptbaAF7D9hUroZE1+PfHe3uYjclO4+C7BiYX42ZWVW3i+EKph7a4vT4NoWXV+MpG4GP2RKcPr+KbUaMv9WLFyqtcaqCI+c2QcDEm+FgPpPd1NgVF7tqMPmKHuhT1RClJMFWmvHPpAYLhewF3GmXeXlzgamvyuF0wZTDVLrFC+0HmHplmCgwSiVaD3sE2kB2h4umzGQIHz/N6scLyOzIwiUExukTsQt7DyAe7l9D6ssh14446DfrHn7JTD64nkdmNyLMq0QRVHU6aCEwTIVoDOOnqNnEz0OQ14iOe0CvY9KQkZsYtVq4Y/EEPjXCCqr9gN581B8NOWLcUhKUFGHqQANiOoU3Hicb9uMmiHn2wqxm/G2P9PoQuiRzOSJbM/UNqLwtBouEzGSQgaD52WneePM40UwM8BSWjYwE167NMZ7r4I73MX5mTIe8Xi1y8bFbw2HWQhA5sDhe49izd+hNDCceakPwUw9+g+965k384kg62zY5mt/jL578eoJQEilZbZd4PncNZYzwYLRamBs2X9g+lbgW+9MC01s62UahNdH1WwjLfN+Qvh0SNdsJqqz9G9k+nsPPSszFucRrrbl4/Il6aFjcE44Tk5NspfGPDd1BmcmgbMhsioSPL1MplAXpXTVAbEOcAIkyCqujEi6isC2IwHAPZPT22x+8ZHOf6rmISGC1gqHrA6g+RbFfNJGrO0N+hF4PJHQnJE5DoWr14edo8AugDY3s9Gm9ogizDUbbQKLRIw+02Qa/bXN1ewplEn+HkMgQ7uyWWdoZG7RjAIhI86Xtk3xh5SThqKfbJ6lsRam467Yv2g84UdwlJQK8cpIfI8wp/uqRL6CySaydNgTVh/S7Gozqdt81dvqzlvvekFBRjDnblz7kxOooutOSaLVPr7W/eocawxXIN0ZGu0QRTgOshsT4xuWRz1ak9kAZEK0NEwUil0UG4JZkAiEhcvEISLcsE1knkXLQlmbv/8/efwdblmXnfeBv7+OuN8+7fPnSm6rMqizXZRpdbdDN7gZBEIQhIIgCh1QwNOSIbkYUKcWEImYiFFIMRzQaBTUQIRAgQRAkhIFtA7T3XTbLpHcv83l3vT1m7/lj33fuPS8LQoNEd2YqakVk5Hvrnnfvuefedfbaa33r+x5LNmtFPo/ORGy8kEqMA8ixEhQDVj+SIfjhYclXplOojEFg3P0rx+Pek7BtwpzCL0Ht51qII4Z6WTg2fkkRHOsyvVShu2gQ28Ky6E1pCqcqrNaKdMdlfO16k5Afb6Mu5+lOmhVGSEF3SpBJ+dgXc2YGSZhVqTPtcDS/h+/bhCliZIg/kWXcadNXNpE3XLlFLoMtFBd7hwcTuENlPp2J+Hzl3H2MtGHGIrUtjSTOQ2qPfCDZhw+hRtUlBqmTDIwocvxF14YeVwwWhUTvKQwJU5jJ2ZHA0GFId8pwvcmRD1E1WwRFheVrM8Kxn850ukRphdsyZeb9L4n2A3AVE++YDn88LuE6pPJ9Ji8G6E53SE2c8sjk+pRuKKxOGO+3RLGAyIRMvG2G7sSsWT1FLgu5kOyaZrrQpD9n0l1hWahCiLWa4nhpl9qx4VISZRXVzQKdapr23FCIIMgrOh2P4g3ozqi4kdovaTo9l/KNiN5UiBxIXHamBPfaZZxrGXpzYfwe+mWb53K3udcdM32qAbJBp1xeKt7gudQdIncofSlHEPPKljHfHUB6o8PEuyEic4CF6SGyRzqQrMlJkDKxOQUTXN1Jx7AIjawM9uwMkSeYuKiTxI6TkwgFc1/rJPyyVMRuC2a+VU/MI8lcFrdqMfWtPaKbd+LXEOkUVtui/PquGa3ex5EJgb3nkLm+Y9QgBhVI3W7T38qQvbyJDsJ4Q64qNTrrOQrXmwg93G+pShUaDq0Fm/64jhEUqtmCls3eBUXbd2F/MiGKoCfhcIfvLC+RquzfRRSyK0iVe+Qvu2b/oQwS2+oKMpk+dk/h7Up0pNBRRHrL3CxCT+DuWehBquvVNEFk0R9TuDuWuWkAlq/5Uv0M37pxlMyGGO4ZI8XXayf5mVf/U9zmsKStfZ/0HZertSmwRIIwk3duEKZETOryMNojHUjR7i74Ado7ICi2s0dqN0D6SRSxqjdAY/R9Ro9vNOhOa3bPHyhn933aSyG7F5IFDe0H9OcCegsH/N0eUTEkKibvnFprwrFgODIev7BGln1UPpsE0SqFzoZEBRd7txXvt3QYojMRIoKgFA0330qjpcbbsTg3voFfHOwlogihBeFuipeP3qQ9m/y4+22X5smQ/phJ37TSWL6guZmnftS679sR7KSpH5MoZ7jSawvu3psgvdBERiK+SYQpwWqnxPRUHaelh9wMY1kCLXlhcRkZjsxm5bJ0FwPybv8+yVIhhGF4PaiDhREfGF29HpQ90oEUj0rUk2oUqtPB7kbsPuEkytCq0yG3EdH6qcaQWhdTzZt4S9P+UAtrelhsUM0mpUs2e09FwwnPgT9/xWHzuWTpVXW7pO85rL+c1JxV7Q7upsPmy+PJwO50cG6k2X6xnKjm6X4fd9Vl+8m0aU7uFxWCkMxNl9Yhwclf6g4JH7Uit2zTmwt55deeoPCduwO3pnDNYurYHt9dP8zsN5qxP78sefLoPeaXdpl8MzArsVakdjTnztyjfSxg+tVgWBavaRZObNObDZl+TcXn69U0p45uIKVm4u3he3DaiqdKK/zI/CWKt4cVTBFEHMvsMuU1yd6qjXxomom5OgW3h3cj2bgWi/NoCbzHyIRqth4KKuNHO5CEQPf7BLOlhNuemUb6EeVrUdzvADOS7eck7meLCY5v6/gR/Lyg9Nks0fZOwh+mYOEPRYK91D5ymKAAC19OpoL24gJRSjP/hXoSdT43Q5TWzHxpJ5FqWjPT+AXF9Jc2sReGnATWxDhRRrPwu+t0Pn4e67FTxj8+Rm9Ccfj3G2w/l0e/cA4w1cXulGLiFYvGqRD/pIHpyJRHe0GzfWOCYqZLe9GQPQrLonFM8e7aHGt3JqieNBTOwrJoHoWbOxNMf9Vi95wTQ7Tac4LdZpa5L0sqZ6x4L9SdkOx1sviXi2w9K+P9X5SS3OlM8OXtk6y/lBqSXHZ8qmGGi5UFqk8MCyyq36cfWlxcWSCaShI+qnyKdCVCZO8vNoh06qGQe3mkA8kaH8M/dxjn9sgdTAh0PsvWB/Lkbo+MjwsBjk3jqGDsygGiQSmpH4fylVbSb1l0pzWFg+LAmRR+QeEsJyczVT5L5Jnp0NEPV2fTiEggOj30i08MWUcHGD6hNP0T04j9nlg6ZcawbTNIt5/qCNuK01K7oxH7aHLLQtuQqiq88S5Bzo77P2E+Ir0pybt9+oUhWYtKK8KdFBOHamYo0LbRUYSyNX7fYfeCQTZIzxuUwCGb8tl6DrzKsPji1RWT2Rb6aAevImImpPRmjxv1ScpeByTDZmqlzmdvnmUuW6c3NqKnFEX0LpfIZvr3fSvl7XVy37j5nmLM0e5eYv/6oOyRDqRodw/vbiWJ19Ka6MZtJl9vs/dkKem/dI35r/a482NeAjwa3bjN7LcUN/5SJpHCRddvMf4OXP/PZpPHX75OZkNy/W8eTqZ2l67h1gV3/saJRPMwun4LoeDezy4ivv12vI+IbtxG25rVH53D+vIb8ch0uHwPFOy+OEX21WXUu0O2IIRm90LepEuvGARDVK2iBTQOW+gbObJvrIA2Y+IiEAQFTc7pU7reNfuswMeuWVAMeHb6HqXbkdn0a01qR3JoqsInX36T/L0o3vS7dThR3uHv/cjvkF8LY/kWu6t5cfw2//TZf8PUG/24ryYDxV85/E0+MXGZxc82Eiv6z5x+nbQVMPfZEbV4IdFLXYLIum88pfPCcTb+4un3JNG3Jsbf3yP9qdlBbBtgNfvI6P4mnrvdxmnJBGIArcndaSL7Illi1ZrylRZRViFGAgytmXq9TzgZ3Pc8U28E9GbC+xDJM9+J6MwdaMgKydQrgu7sgdFqISldFbRnRXJ6VloUbli0FoRBbYz488uS5rEIpylivjhh22RXLYLpgDduL+Le2Y6PT+0JcsUu1+pTuLUw9tsdaPU9vrWxNEQkCIEMNZd2ZvhH737MbPwHFmQk/+KdF/ibr/4MwQhFtF90+bW15/inVz5CUBhJvYp5Ii35/NUz6BESTZHykJaif6OQ3PMIgVBQum1aBAdN9/2HgjjykQ8ktbXznnP7YSlFZjtMrDAIQftoEbcOzAyR4cJxqT5eQMz16Dw15FoTnsfWc3nIhlQ/fixOyWQmw/ZTHu6GQ/8DJ7EGJO4ym2X1oxbltyxkMR/j8KxSidWPC2a/PiiTD4LbGh9j60XF4d/rJsv0czNUnglZ/GwNRvdg87O0nu+y8JUe6c1e4nj7o7tYXWn6S4Pnl0cPEz3XQLoRjy+toyZL5vjDC7TP9Whu58g6PrXjbvw8zWMR7e9O0HlznOpZEZ9/7bRGfKnM4v9bsHPB9J1kKkXjqKDw9RTzv+yy9mFDsCkcl50nPdY/u0hwucDKx914Ra8+PclnV87wqdOX2fj41JCO69RhPn70Gv/xJ79K79xQy9fK51n9qM3qR2zEQCUwfqxcRhYLfL/ETv4k9mgHkjR9C3s+qYQnbBuhNFtPu0k+OtelPWPRe74Vq2+DuRt2piTlYpvUF94aPr3nEabB3nQp/rs34pRMeB6WD4Vb4Hzxjfg1hGPjNCTZLQMdGoUPWS05gA6N9LC0QvYkYS5ZXdStFsKXtJdy6PnhHI+q1VG7Hs0Fj+50Kt7vRDu71G6NISLozGhYMPNLenWD/r0cjhuy0SxQOWdUHqLVDaia4LmxPUl30swvRZtb2B3DyZDZ0NgtgcxmiWo13JqkM6vpzBnUtkinUX6A04TulMDPS9O/khId+GQ3FK2TAcGCT5gZvufyxT0ms23O51ZQ9rAxLt69yWeuPMal5ixOazgXFjUaLHwpNNRgI3ApMCltuLp2PwPrA7BHOpBkNoNwbKKNZLFB5vM4GzVKN6M4ZRK2jTU1SaqqcF/PxdzcwraRYyXcumb31lg8ESpsG5HP4VU1QSkyeDkAacWsRe15EWus7gNMZQDdcZlEhXsubk3QmrUTI+VYFpZvvoSyXBqmobaN1ZFoKZD1VrwHEK6D9hQy0uRfWzVQIswNQktNZl1w/F834slgHYSISCDfyVO5PsbYm4ObilZYfYFsWbx46A6lWwYbqJWBTzHR5/m/+ibKG3zRtcatQfZsldVPR/THlUmnVER2Q+E+VWXvcQtt67hRm1/tgwBRc7C6Yii9E4Tc2pzkl+8+j93Vw+thWVB1eePeIfplL5FJdMeNurw6On9fhc4+tGAQ+w94xOKRDiTVbCKy2fv6CKrVhiAkuzpMf/b3Mrm7HXKrKv7ArYlxtOtQvtlj6hURP5ccH0NnUuQ2Qua+KOIyulXIQSZNfjVi8s3hmIGVz6PLBbLrmuJtf9jjymTQ5QJeVVO+2hnCehwXxktk1gX55Q6dc/MDBQkLpsbJrggyqx3a52YR+1OkM5PkbtnIEHY/ehgmTEopFmZIb1hkdhTNE3nUoHxsTU+S2RR4e2B3BTrtGADq+BipbUFqV/Kli2dxWmbvZuWyyD6kLqf57BvncKumGSps24Bi3ymTveni7Q2/NpavaTbSKE/jViUya66z1fJBaEQgcNpiSH5Sa2DdTLNdKeC09VAft9/n0B8qoo6N0wqHQ47A2Ks7ZNYE1l7zvv2Q2qvA+tYD5214pAMJIDi9gPrgk0OH1ujAp/P4HNXTI83YdodwZZXeZIrWgozRAqrRJLp1l+6kS3diKA6smy3U8irdCduAOvdJI7s9opV1mvMWYWZ4vOr30bfv0ZkRdCccE8wY6Iu+s4JfEnRnU1Az6YmOIvTdNbpTJl3KXLxnSBS1Qq9s0J3SRFmHzHJ9qNq+soFf0LiNiNyaeV4ANneJUpDZ8rF8hVgZDNE1mnRmFd0ZTbTUM+hvFaFbbbrTmuBcm089/TZ6kGJp3yfIa8InW+Sm2igHVK+HVpowDcFiHy3A8odcC72yRAjNvkz3PgefP57mpbM30TM9RDj0i0Ke8x+9zsdPXMWrqSFCQmnasxZogbPXTlJB37jN7B9uoivV+ygHVKeTJN1/QPbIB5Ld7ONcO0DHJAStOdsQPu5feBWBtKicdnAaww9DdToIKaieHKpT7Pt1GNCaF0azdWC63wet6E5r+sWkX/X7ZmwhL4Z32jBE9XpYfegX5HDfpCJUu41bE/SLFuHmVgysVc0mqV1Bc8GDneoQXtNskqoIKqccZKTi1TCq1fCqsPrhFDtP2HEQR80mbk3Snw6ZHGuY5xq8N7cmCPs2b+wskL1jStOq18OrCvyGR2sny8S7QXyuqV2NkJrOYkhmU8fX1W1qSqU24ZxP6ZqOOTTsVsBsqo7tRuRXRqqVfoDSguPpbboT1nClAppL8HPPfofa+bEEtYA1McH2h6YJzy4lU7iHaGL2kQ4ke3YGubmXoCsWto1+/jzlqx1yn3kr4VcvniO/EjHzhU2s40div//RJ5l8K2DqtQ7y3Emz37FtopcvMPWG0Z2Nc3lpoZ57jNlvhmQ3o5ExAIH60JOMvxMYOqxRKNAPXWDssm9GOI4PFerEM48zdi3E8jXRh58aIhseO0VuQ9FcFNQ+eiyGLcknzpDa1XTmNHtnUsjHT5vjjy2R3lX4JVMkUM+ZaV57eorCssLdtpG/NEnvCTOha01MkKpo8hc9Uv9jmd5szgz7pUwjOH3PYerrhqRx/5yilEC1HMpvWwil4+KI24pIOyEITfW0iP32botbrQlOzWxTPSOGK0+3y5uvHmcrKBiW2UHgWbks5cuaX339AxRutYeFHdumf26RVF1hXbyRSOGsM8cfClQDPCKBZE1PJfssA1PjJUO9NbKxj6tASiMP+JVnkd4JEGEUS6XoMCRyJU49wF2vGZHjQWVNW2a4LnttZzgKvj8a3Vdkr+0NP1itEYERN8u9u5WEArV8RKQZ+84WamXYnZftPmgovVPF3WjEd3PR7mJ3FdOv+Qb1PKhWyd06VqApXYP2AsjOYA+4V0MLQWpHUjujCfKmMKJqdSJXYPUFtWOSKG2ZlXBQZWwvKLqTpsKpowjV7+NVNL2ZCCvQKHeYuuZX90GqAsQwtUttdZFCI3ddwxW+D8na3qUTulxdn2b2G0Pp0KhSBQHf3j5C+WpyGrmw3MPec7B2hqmaDkPsL71O8RvLSWAvEF269lBU7OB7DCQhREkI8RtCiKtCiCtCiBeEEGNCiD8UQtwY/F8eHCuEEP9UCHFTCPG2EOKp/9CTjLa2kblcImDAIAm0Lek+fSThF99+iyhlU/mhQwm//aU3ANj58HzCn/r9V/HLLlsfm02kC/aX3qA7k2L75dlEY1d86y26Uw57H5hKPI/41lvUl1yqzyXL8frNS1RPejSenEp88NGVG9SP2LSPFM1IxCD4wrsrVE/ahBmLzHaIGowmhGvrtObNR5baEagtsxJH9YbRdgrBq0jS3zWKd1prehMCv6Twy5rcqwPJGiFRtiDKKWonIH19G1Q04LYDLTWVM5LszSo6DBG2TWdCgoLmkqJ0dQAUFYK9c3m26zn0dJ/ijSHEqv3BU/RCh9NzW6RXhqgG6+Qx7LkOZ8qbWBtJ7d/WQoqwFKK2d7nPbPuhCZr3su91RfonwOe01qeBJ4ArGLXyL2qtTwBfZKhe/ingxODfXwP+2Z/GiapWK4al7JuwLIKxDOlbyYaszGbpzLikd5I8dTKXo7nokaom72xWsUBzwTLzOqOpQ7FA47BFuhol55TyeTpTkuxGsoIk83n8ksBtRomAtEpFgjw4zSiBLrdKRcIsOO0QXcwNgZ2ZDJEHqZ0+QU7Go/TS8whyUL7SIUobssX4OuQ0U6/16S4E6EOD3lMUEeQ0+dsScaiDf8JAbHQU0ZsAu25RfnqHxoXZ2N+eB6dmoU61qD1hblw6DOmNC6Qv0TN9Ko8PRdeUA+V8h6nxBs0jw9K+0wp5efoGKSswHOn7VqmzNFHhzZ0Fo1I+Yu1ZSarcQxxKQoFkKoV/bOq+G+nDZH9sIAkhisCHgF8E0Fr7Wusa8GPALw8O+2Xgzw9+/jHgV7Sx7wAlIUTyFv3vY1pzsGIjS0XsZn/Yo9j3F/J4tchw3I1sWmWpiNtSIEjgs8RYGasPyhaJkW8xVkb2QYQkn2dizMD6ZTLdlONl0PdzM4hSES0H3AzFYX9EZLMoC4KcTetEMaZeFikP5UBrMUX11Iioc8ojTGsqZzN0H+/GdGDCdQgKmvoxl/Jsg+6CeQ1h2/QnIsIMCKlpHRpM4EpBfzLE7gi2b40TZAakJULiFzWRp1GrGZQ1fN9+WcNEH3Y9RMSQj1zCoXyNWitjJl4He0llCzLSJ2v7dKas4Vh8PsuTY6v8N6d+l90nh+MmVrlMb0JTzHbpHE0GGI6D89btRIP7YbPvZUU6AuwAvySEeFMI8c+FEFlgWmu9z16/Cey34OeBlZG/Xx34EiaE+GtCiNeEEK8F/Pst2dFeBXl3E3aTK1W4uYW31WH3cRdZGsJKwtU17HbEyqc1enF41wvv3MXqa1o/Wyc6sRDvx8LlFeyeZucvd7BG7pLRyhp+Ce78lEisMNHGFp1Zzb1PuAl2I7W5TedwSP2oF1NoAahqje6hkH5Rkv6tV4arXhTRW/SxfM3hf/jGyP5ME04F5DZCTv2dVdRAERwp0bkQGUD05XGyb63FfhxN+1wPzwtI7Q32j7YNnsJ+ssbLz14myA4C2LIQEcw/tsWTH7hJ44g0NwshkD7MT9aYOb1N5fEhDCnMCm5WJijlOuw8PXhNoHHE5bMbj7HXz9I6NBQaa56fYsJp0lYHigQTZS585Bo/fugtUjvDHpLwPO7+rXNs/fTZh6pKd9C+l0CygaeAf6a1vgC0GaZxAGgDdvoTAZ601r+gtX5Ga/2Mw79/5aXz3FHEAW1RYTvsPFugfCM0U7QDk57H1nMus1+yUJdvxH5rfIzKOUHu14oGUT1Y+ezpSapnNVO/lCa8vTw8fmGO/njE8V8JEyJXcnEebWuO/UYzCU1anMdqSya/kRy7EEsLiFCQ3k2mfMzPQN8gG9STJ4eFlukJZN1GKNj5s8eRg9VTjpUQbQuvrog8YkydLOQhEKSupxjLdOlODtAcrgt90/8JlEVnxswo7a+wnh3y5uvH6Y+pGIZktwWVdobmH8wQ5VScBbgNTavjsXdxCpUdIkDyKyGeFXJ1Y4reQoAYjFHk39ril66+QCXM0TxMjDDRK+vc+JVTdJRL82huyIPR77P0P19j/J1OQizhYbPvJZBWgVWt9XcHv/8GJrC29lO2wf/735I1YHSXvzDw/alb3IMYZfIZqLhVH1dk7o7MI0kLOTdD+aVNg3gYnUhdmObxF2+S3UzKwARHpjn0xAZuNbkX6pyaYvHUFu5qciXsnBhn/OQeciUZMP1DJdzDLdhMqlp0lorkFhpk3l1PDBR2FgvMHd3Fq4XIzlASxV8oMXlqlzAj2bug0DNmzxAsjLNwaput5yQv/Phb7DxjVmE1M85LT17n9J+5wd8+8oXBimF4ux87u8J0voXSAv14E+G6WDNTzD+2hSUUuhRw7uk7yPExrGKB1Iu7/L2zn8f5yC6ffu4izEwYYbKnIn7puX/BT37ym3ziwrswYYJbW/D3lj7L/+2JL/DYiVXEIBVUg+zhqLuNPxXG6HbV61G8E/Ar33mRzFY/kcZHexWcrToJEbj4A384guuPDSSt9SawIoQ4NXB9DLgM/A7w8wPfzwO/Pfj5d4D/ZFC9ex6oj6SAf6qm+33TLB3ZI+l+H1Wtkr9loUf3TioiWlmn+s0ZtHPgbV+9zVt3F2jPHMBxXV7Gjywqj2USH1j69Tt4Vsj2h+cSYNPsW2sUUz1aLywl9mCpqxtMFVqoE4cSe63spU3GMl10IRuz9QBk31lHaYG31UbuNRCD1/Zu7xBEEquvmHxVIjomJXZW9+iFNnKpzUq7ZHSSALlT42ZtgrOFTSQK7WhzV6/WubUzwXiqzVY3j991DI6v1WZ1s8zNzUlK33F5e3keLKMXW10u89++/Sm8fzXGH9w8jegH6CAktWnzL3Z+iF//you8vTeHaJiSdpCRvNM7xG9tPsmtnQlD3ALIyXGmi03+1c4LpNacoR6VtGgccpBtC6IDe+FMhmg8jzyxdN93QDz9GOLCY/f5rcnJH2hx4nut2v3nwK8KId4GngT+W+C/Az4uhLgB/PDgd4DPALeBm8D/Avz1P80TTpgQuM0goToB5sL3pjTRAc5umcvSnQ/pTiRnhUQ+jwosLP+Acl42y14jS+FukLhDimyG5d0xJt6oJUbZEYK1apHszUaCBUenPbYbBi8njw7V5bTnslEtEJYzdD96btj0dR2qzQztpTz15w/FKZxOefQDh83nHGqnzd8DYFm4VkQu02O9UUDvx7zrYEtFJcjyC2svk122TDnbcRjPt3muuIwUGnvdI2q0IAhJZX2mxxrUzimoO6jtXcMklI5QkWT7GUHQswdwHYVyNc3Q48QTK2xulGNURXdC4oiIv3noi/gr2ThrCCfy/NjcW/zZ8bdI74yQn6RTND7e5tkPXMddryU/t7Eye+dyqOtJoTHA8MK/eek+f7Sz8wMtTnxPXK9a64vAM+/x0Mfe41gN/I3/sNP6Hk1rnI0GHFC8ixoNCrcMfGi0fhbVaqQ2bbrjmty+UwhTVu8foXnIImvb8aY/2t6l35qjM2lT8rwhXdbOHn5rGn/cwc1m42KAqtboVuZQmR4ynx9OhW7v0a1MgOjC1kh6t1PBr44j/S5eZQhnUjt79CtTIEz1Kx5o263Q3jzO+KqmPSuQtSYK0PUGa3ePkVl26BwJKA1AqGq3wvr1s6y5E2BpxpoGqaCqNTbfOcK/6H2A1lqB4prAymVR3R7BzTzWhTba0hRu2sixMuH6JtmbLud/9BbvpmcQXy4jyiWo1Slf0Uz9mSYzqQb3bh9GFsz7Lt0KuNGdZsMvkdkYkDv2etjbdb5TO0ovdAazUw468E0DfDlLa8aje3QcZ2RPqjMpIncwXzVSrAHTQkDIBz5u/kggG/73LLpx+z1Bi35RIFoHJiq1oa3Kbh2kDo6wOhKnOTIrJAQ6DBBtCy1FAnWsfR/ZsAkKVkKj1nCO2wQFF9UerlSq28Oq2wSFwZ1/399sYtct+uMp7I1qvLrpXh+7PnhdixgJrVptZF+iJQQFhQ5MWqTqDbA03dmIpSPb5G6a66HaHey2JDPZ5tzJFcrX+qheD9XvY3ehuZfl8MlNcutmpFwHPultwdp2ifxMk8ymIlxdM1i7Hc2dxhhKSby6JrxjmrupSsR2P893tw+T2dSE6yaL97Y7dCOHz6+eIb2t4x6gbrXphC69yMZt6aHKSBQR5RVSaNMmGLH+fJH6qfeuZUWNVmKM/UHZIx9I9uJCovcDpvehJURjucTeRngeQUGbPs++X2uE5xEVInIbI+MYWpu7ZTYit+4nUzvbhom+mVId1aK1bdRcD28nqS0r0ymcpRbeRiPBUy5zWeyjLZy6TzRZHM5OpTzsoy3sdoTdS3K/ZZYayACY6xEeHWnPSUhvWHx69l0ap0uD96AI84r+7QLTqSb1o178Gn5RY6VDWn2P2lErLi13ZjWLMxWalSzNw0Nyku604ERph27HpTMzJMtvHLZxZch0pmVI9AfWWcjx42Nv8JePftukzPvXr1zkL0y/wQfGlylcGwaAzGSwx3q8c2kR58q9xOcZeZK5r2n06ntstVV03xjNg7BHPpCIVMxRsG/CkuTWFEIlm7hCCJy6NHix0eau0jg7NkFWJgJPRxH2rkO/bCdBqP0+YjNFZzZJBKk6HcSWR+tokowjajbpb2RoHysPFeqAqFbHX8uydz5D+1A25nlQrRb99SzbT7nUjg0R0tFehc6dApVzGuVbOCumtK/DEHvHgWfq/K9XXiR/Y5/vTuNWJC//0Dvca5UpX+vGje30puRnzr5OP7QYuzrEwqW3BH9h7iK5cofytaFodWZD84HiHY7O7pqBycH1y69EPFW4x2K2wtjV4V4yvdbmjc4Su0Ge3MoIyX2jxW9uPcV395ZiDdz9axdtpMHS93EzuHUfuxOZMZMRs8bHEqQ0D9Ie6UCSmQyqlL//AcchtRsQFL3kaiUluXua7oSFdWYoHyIsSf6uqTTZi8OGrLAs0ptmjGK0qiZcM/Eq1P3VJTPIloQgyVwO6Qvcmm/GJUaOR0H5ep/8tepQZzWdxmkJpl/3mXq9Pxw2TKWQvmDqFZj+vBOnfMLzTBfv9SL6Sg7RHSKntQXfuHuU9UZhePMQAuXAG9VDdDrekHlWCISG3996nM5ygTA9vHnIEH7t3rPceneeXnF4w7G7Eb+x8hR/+HvP0lgc3nBku8c39o7xL77zErtPjFQ9uz3uVss8VV6h8vxM/PyGFlly8vgG+uzRxPWz2j5hJjlyAebG8jAoUcAjHkiq04Hb9wxv9YgJS2K3Q2SoEs1akc+RqhvZldH9k8hmSFWU2Y90kpx3+VWFnxPgOCPPb5HZ1vTK1n0w/vS2oDXrJNmLlMLbk9SPpZPdeaVI7Upa8y5s7MTNSZRC+oLuhE1qec+IUWNAqDKAICfIbAUwCqRVBq7jF0f47gARCqJI4lgHhaDBlRHTY42EflHkQqAGY+Mj344oBetbJZxmsm/jF2zWNsqEqYFAgTaMSNFYlq1WDjsfIKJhZiCyGXKpPvNeNVEllZ6HUPDs+N1k+VtaoDW1ExbyIaDd+qPskQ4kMMBNq1xM9HOiWh2r3Uf4KiZhBIi2d3Cag3GA3DAtiypVlC2MjMnUcAXTUUS/IAhyIh4RB0Nqr2wjRGxNDZUwjK4R2H2NNTmR8MsQM49UGKZ2yg8MBs83BYW4KtjvI32zCqidvZiaWPs+Vk8QuQK7M6Sn0r6PtiDIabKrMh670FFElNIIoJzpYjVGxM8szZXNaXKOHweSGBBN7rSyaFvHSHPhuAQ5wfh4i+JN6MyJ2B+5AiGgdB3a8xg4kecR5ByUkqitFN2pIW+Gf3wWRyreaBymOzby9Tu+RJSCt+vzBCPSpFaxQJTzyN9T6On7+0L20SXspcX7/D9oe6QDSdg27ScNjG+0qiZTKfaeKiP9kOjW3aE/l6Nx2MGrR0RXb8Z+q1igV5ZMvBMQXbo29JeL+EXB9CutRNnVKhfxC4LSO1XCldXE84QZKL1dMWSO+/6xEsqGsVe2ExVGq2iG24pvbqNHVhGZyyE05G806X/gZMxSKnM5ZAjF2wF3P5WLlcJlOk16W1C6DvqFOsFZQykmPY/smiDaSXFve4z28X0SFZfsKhSyPW6sDFmKEJLMhmY230T2pJG5GVQvM1uKMJL0xgROg3ikP70bkCt1qB83+yu0RvV6uHs9Mp7P0fNrFG8NRQCcq6sIoSk5HcbfHalsXr6BCOHSyiypy0MgTFStYr1z2wz77WMLRyxcXiG8u3Kf/wdtj3Qg6TAk+/o9Kp88majcqF6PiW9tc+fHk6mAajaZeLvNysecBNwkqtWZeKfL2svJokK0V2H8XZ+Vj+cSzxPtVRi/HHLvzybvkFG1SulmxOonJ5L+3T0ym5rNj03fd3x6W7P3/HRCbFo1m7g1ze7TBVKv3IjLu6rZxO7AzpMOC1/uoW4tG3+ng/Rh97mIbseNq16qZ1bIuVPb/EePvUpuUIQwiBDDnDo7UyW7Ycro++fQDR3ytyXF5TAuTshA02imya0p8msjoybdkH7fwe4K0rvDm4FVbXK2vMWT5VXSe8PjVa1O0e1RdjpGaSN+IDKofDuKm7r7pnt9rO3aexNBqiiRij8oe6QDCaDzxCFKVw/0EaTF+ienmfluREKC0vNY/tEs068k+xQym2X1Y2kWP5/EeFmFAmsvOyx8MfnBWpOTbD9lc+jztfv8u+cl81864C8VqZ+Cma/dPzfVOAbjrx/wZzK0FmH83TZMDRUshOfROqxIVTSV0x7WjAlM4bj0x81+yPVCgjOL8XVoHdaknYB73bHhXJAQNI7BncYYmztFupPOsPw9bfpIVl/TWLSHPOVSoALzddk9ZyX8th3Rm4yonZTDvaHW3GxMsNItUz05olQoBVc2p3FERON88oaT2tWEfRsOJ4cFRMpDZx9ekTH4P0AgedtdGsfvr9w5TU39iH1fmTuzJgx5+yh9UxSRWde0FpJVIe375FbALx/wt9u4dQhKqfv8XlUQZZPHq27PTLQe1Eb1A+yOQGXcRBFC9fpYfYEIInDsGIGtfR+3JsnfC8luqVh4a38lmfyuJLqRw9ke3FiU0VK6eX2Wup/C6u5T/WicpsASmqmJhtGKHVwPuwfZfI/upEAGw4ZpkBGgzf4sd2/o74+7ZFM+uWUrTuEAoqkSH5u+Rid0Kd4ZUjjLfI5nD93DERHZ1e4QeygErcMgLI1QKoFJ1N0ubO0a7u+HdJTi0Q4kIZCdPuWvJnNnmU4hwyHPQOzPZZGhJnIODOSVilg+iXIvgJw2hYQwnbxMYmGWVEUb1YdRO75IelcTpg8MGh47jFvTRN4B/5FDZDY1yrMTK6d9eIHs2qDKVW0MCUXm58hsaGSgsLsKDpmGrDUxTnpT05kRhAt9/NkCCIFVKJBdE1gdSbhf45YWMpUivaPZuDzF1naR7MaA3EVauDVN92oJK4DC3TBuH9g9jbPpELmQ3Y5iv7fns7NZxOoZNb/9Iou12+ALm6e5tjlFa86K1StUs8WbG/NkZJ/WoXRMyIk2BJdnFjZpnioP/Qwa6WcW7xdqe4jsweuq//uaENgz09BowSjxvbQQ8zMUb3YQ+kAZdbxEcTlA+irh17kM2c0Qe4QqF2mBlBTvhLi1kcFDIRB9n/ReiFvxk/6uT3onxK37ieEs0e2T2Y2w2kHS7wfG3+whxscMjGawJ/EaGqQkXJrGujbYTEcRXkPhtAKUZ8XSlwhJqqZJVTVRKoVTq6G0BilwWqaS905xgWPajNJrbSMDyK5J+l2PyAsN1Emb6eH0jjAMP3KEkF8Zv91ThCkRVxJlqLB3HLLbEb2iJNoZzH8FIet7E9iXslg9TVSrGb/S9HsuGdk3/ayRPlB2K6LRT5G700z4db+P1QtR99YeOBHkH2WP7oo0+MK1nl5Ej+DazKZV0JvyEKFK+FUpS79kY/XCYc6uInQ2RZiRpu+03xdSEdFYjiArEaEadtC1JpoqmSZtbyiUjNaoYgZtC0Q3SKZq2TQy0Mh2snmoMyn0IABVrT4yOyVRFvTHPPplbzhvpTVhWtJazFBfSsG+nE2/T5gSWL6meEvFCoa6Z4oKhbsRuatufKPYZ5lN72hTru9F8abd7mmzuqRBBiou4ni1kH4JOjP7K8iAnXWvRTTjs3texkLXALrRJJft0T/VBcEwPQ0D9JbHZ/bO08+LxHXSUrC+V6SzkCzuyHIZa203MXf2sNmjG0iYkfLs164a2toRi67dJP/KPbqzGeQTZ2K/fu1dSq9tsv6hHOLJs7FfvXWF/NUqyz+STYym69cvkbvbZvVjB7RiX30Hpxmy8XIxCWZ97V2kr9h+qZxI1dS7V0FA7cJk4nmiy9fR0gwEjlYdw9vLyAiCnIX3udfikYxwcwsZavysYPJLK4T7LEKNBl5DEWRNMO0Pz6leD7elaU8b3VdxdXlwQhHZzYjaCQizGu/qkCIsuxHQOKaQAaQ2hlU1pxHQnzVl8OzasGmt0y5am0Z0eaC/BCAyaaqbBdjzKF0fKhtKz0NoePX2YSZfHZJfIi1a85Koa5N7J4mpi47MsPHnj9zX/Bb2AS71B2iPdCAB4HnveYFrHzxMerNreOr2/Z7Hxidmya0o9FtXh37HZeMjE6YPM6ItJGybtY8UGLsaxqmG8DyEbbP+wRRjV/wkYFJabL7gUr6WrP4hBBvP2+TuHUCjC8HuExJvt3e//7wgs96773kqZwSl2z2ChXHs2enYv/OkUYPojkk4Mh/760ckflGgXOh+6HT8VI3DNpxsoxzN7sePxCt0e8ZB5SPahxR7T5XjFSMomKG7yuOC6qkh5Ef0Q/AltcdC9h5LD0fEw5Cx2TrWTIfGkWHqrfp99FSfQqFLd36kSKQi7I4mU+oSLCS1du1720a18MihJBYyDBGWldADflD2yAdStDNC3jgwrTROR5mq16g/MAQhB6t2OgzwC0ZdYp9DTofhQAoSqqeGW0nd7xvebotYV2jkhdFSUzt+/6ZYRoLaqcx9frRg5+lc8s6qNXZbsP1M1mzqR5DqXk2w8Xwa+8bqkBNcazLrsPWSIlVV6Gt3Yn9uTaGfrRPkFZlXluOXKN4JWBivkV9sUL7cHIJQV/uUpposnN4y/aXBdUpttCgdrzBzYZPc+hCcKnp95g/vceb0alJS1A9wLMVLS3cS7QnpeVhOxFSuRfbqcCRf2DbNgTSVs7qXuIFUP3yEzrxG7ia5v63xMbTvx9O3D9Ie+UCyjh+5X/pQRfh5i9aR/H3+MCtMuXfUtEa5kNrTyc2s1mgbg3Y+YFFKU7yd5M3b53kr3vHv91ua4p2DK48RBstuqURKGQNCOxq9MD1sHgsBGty6Rh2aQaaGARulBU7DIrveT4xqdMclna0s6U05lKYB+iWL27enGcuO7C+BMG3TuFWi0s6gRkbyw0KK6t0yq1enCXIj+79SjrXlCa6+c4j+2AgecWKMrXtjfOXiGXrTwxuIyOcJ6h63tyboL41K33h4NcFMsUk4XUpci9y9Lm5NoHPJG1FUqZr5qk7yPTwIe6QDSWazBDPFmOp33+yZaepHpBFjHvUvLdKe0xTvhsnU4Yi5FaaqKuG3zpwwQFZB0n/6OJl1g5QeNevEUbKrAmUny+jWyWNktgRhOhnB1vElMlsaq6sSQsP24UOk9jTZrcikpvs9nukpLB+y2wp98fJQUqZcRkQGoqMcGcON9lNeb6JL+1wvZhdCWvSLgumFKscLu3RnMnEK1ytbHH9ilZ869ia98pCPLsg7nH5shY+/8Ba9koxVCoUfcuHsHT7+/NtUT9nYswORs3qDl85f5y88+xqVM07Mn6CqVdLjXX7k1LtUTwx1kFS7jbenqXVTRFkn0dh1NmpMv9YjunkAIvQQIBr27ZEOJJHJ4Gw3EyMO5gHB9Kt9ooybZJnRmpnvKtOYHGWk8QMm3omw20m/6Afk72jTsxn1N9oGLX4gwKg1yWzviwuP+KsN3Lo2VcRR/07FkC1GOqnYV6mhbEG/JFE/dCH+UqlGEzTsPGGx+bdfiMWJDURI03jM594nvBhgq32fVFXTb3o49zzC/GCwT0W4Tc1OJc9rv/wEItIx1ZUMNTdWp/i9f/wyXjOKK2VCw1q9yOu/8CReUw/1i6SkGaT48heeJL2tUdWa8UcRN2sTfGn1pCHfHMEYdvfSNIMUmR2Fag0LGjKC+tVx3HfuJveevT7e3WRB6WGzRzuQXAfR6SUFlAHSKdy9Hr1pL3HXUqUcMtR0ppLkJ71Ts7RmLFMGHqm29ZbG6Y0L3HqQSPm6Z2bpTkhDZDjy/N2nl+gXJN5eskjQ/OBRnI7C22wn/R8+idvSpJarZmhtEGS950+S2VWMvVnF2W0hTxhu8/DZU1g9zey3A9y6pn1+3vTNzhxDhjDzRRu7K2icm0CmUtiLC3QnBWPfdQjKCr/oGA718TF2ngYdCXofaVI96WBNTiBsm63nBbPTNWpnYPspC/3YMQB2zzlM5NqICDafB/34cQD60zl+ZOYdgrGInRdCxOJg4++4vDx7k//y9Odpzw1FsXUYYjVsPCskyIq4LA5QvNPDaQsoHRiMrFRjnvOH1R7pQArX1gkXxlETSYrbcHkFfzyFGN3aCIG+fAvpG+nI0bKr+50rFFZCGoeTged8811y64ra8WSget+6Qn41MkSGI5b62iW8hqIzn8zlc59/hzAl6B5K7tlyf/AuYUrQWyqbL9Tgtb1vXqFfEHQX8oh+EOvd2q9eQ9ugHEG/LMi+PWhQXr2NluaO3jveI7vWRfV6RJvbuDUzJ5RbaKAcgWo2UfUG5XcF6WspokiQ2VaEm1topSldFmxdmkKEMPV6BG8ZNHxmS3P79jTtecGhL0TwjiHY9Is2/+SVj+FULRY+J9FrBvUenF3gc3fP8F9958eZfFPF6aZ16jipYw2+tnKM3Oqw6mlNjHPrJ1z8411wDqTAE+OGPOUhtkc6kGQmQ+NoBnFvPeG3igXWPuyS/caNpH96kuWfEIx9aSTX1go5Pcm9T8Pk55J0T9b8LNvPwMRvX074xfwMmy8ICp9N0kCJuWl2z0uyX7h03/F75wSZb15L+menqDwG6WtbidROjpVpHoEoJekeHY/v2rJcojMr8HOSyAXsgb9UpDslaCxKpiaH+0KZy9KdFlQf1xwf2yXyhuDX3qSgN6EIGkaIGkzT1C8JRCjQEmrHbDO1KwS9sgCp6U8odp50EgWNXKmLd7rO2kdADggine0W+VSf80trrH9MI/c5zze2aW9n+dChW6y/lIrfd1SpMfc1KBXb1M+NJ1oa4do6IpuJ918Poz3SgaR6fca+tQ7zB8YTajXmvhHS+tAJAyMCgwpYW2f2ixbN5w8PR9C1Jry7yvQ3JMHRmUQZOlpZp3RVEJ1cTHADqDv3GHtHoE8uJiZh1co6xZugTy8lO/YDvzqW7IOou2sUbhuA5ygbUbSxSWZNIH2N0MQkitHWNqlds48p3FXoAUwn3NrGbYBX1ahfn8TerJnj9yp4FY23I7n2uRMU3zV+1W6T2tVoWyP6ktKtMJ4vKt6JCMshmQ1BdlPFCJLJt3qk7rkc+oOI9JaO2ZDy12uoV0qUfzlH6bIkWjPNVNHpsf3mNPd+7Shjb1io5mAvZFk4NYs/uH6GwvJwzygcm93zEinAqwQxKSZA8y8+z/aHZ+8br4jtIWBbfaQDCRURrW2iVzeTfq1Jfe0SMtT3KVVk13pUj9uI0dFxKcjf7bH1XBaRShYuJi422Xsilxw1d11K1zvUzuQTY+5CCIq3Bmj0kb2WjhSFZZ/2kVyy0qQV+ZWQxrFsYh5JK016T7H1rIN38c4QRRBF2G3N1nMSt6mI9mmotMZtaJpHIcgKorXh9UhVNWFWY3eAfc1ZIF1RyL7ErVjkLg4H6aSvcbdsohSULw43+DIwaIcwI5m42IhTY9E16uXKEky+0RoWCfo+CJABjL/TGWobRRFhXmHdTlG43Y17gPuwpXorhd2Nkhi89T71kxCdS3I5gKnc2ocP3ef/QdujHUgYfoZED2bfLIvG4gFxKq1xrtwz/AaJidQs7t1dw2s3gtvTgY8IIrQgobKtOh2QAmWJJBSo10M70gTwSMDowAcp7pN70WGIloJU5QCdlIqwfM3sd/z7xgZSNUXxBrRnrHg0AcBrKPxyRPODHayFAU2XEMhIE873aR5RcHw4kh25AnmoTW5FE430bZQjCMqKwrIiLA73hr1JF6EhtRuwrzgB0D06jlcxlc1RMpjo0BSpbYFQYHWH/TZRyONOdnDawvB57/ulwDlXJ9zKYL2dJIEMMxaTb2jEt97ioKl2m3D53n3+H7Q98oEkx8fuw9oBBM+cYOYru+jRdEBabP3kKWa+20GPkArqXp/lv7TI2JVOjGwAc7e78xfKjF/qJmQXheex/XSG0o1OImCE51E57Rloz4gJx6Wx6JjqX+LkLTpTFlY/us/fKw3UKA6QX/aLktpZTfF2sunr5ySl+QaZ1zPo/TRKm5ERHUqsbpKCTAaaoOPSPALKHaanbj0EAe05idUZvkZmtUO/pPFLtgHlDiy1XKG5BN0JQ4AZswgtbxJ5oG2oPlaI/apSRVzKk/vQNps/PFRI1FGE/FqJlz9wieYnzibStfS9Oq1ZifXYKRImBNbZk4nZpQdlj3wgEUX3KbwB2E2f5umxREomXYcwJWjPJdM3WS4R5DTNw+nkRO3CLGFO4RecZEp29jj+e7CAce4EMgS7dqDTfv4EQoFdaSdWGOuUSVXclSTExV46hHLA6kUJ4nh7bpZ+SaBSis0PeOzLsFgT47TnBCfGd2id78USKjKfp7EkIRSolCYaDBYKz6N6ysLdcJC+wB8bfBGlxcaLHnbD4PZ2ninF57v+cgHlajoTFhsfGaqO15+aRtua7qRg9wkvXiWjY7N05yJ644LmYTkc7CvkKT2/xVOTq8nGtZB0p801zt1NtglEp4eMgN0DUKABY5FwHvw00CMfSFG1hl7fus/fH08hlE7Q2ap+H7ehqR+z4qE9gGhnF7chaCxJrJPHhnfP2/eQvqAzbWOdOj68S757A7+k6c6kEooH4t2bVM9omqfHkpqzV5epnNN0lkrJvdO9dfYuKLpHD2jjrm9SeTIyYsjLQ3KVaHePxumQ/HWb2W/34mapqjdpHw149doR3OUUDNJW3evTWQrwyj2s6a4hxsTsRzqHQoKFPvaTNXqlQXCrCL+oCcoRYdrQPu+fb+QajaTMTkQ4Uon2swK3bgoWfoF4IC/MOIhAMHYlpD+mhlW+TBopNOudIs0jOoY5SdfBOdHgb01/gZVPFBJVu9oH5nE+tUPnmcNJhMnkJGxX3ocI/YeaVS7T/fgTMZvOvtnzc3SmHDL3klUee2EeGcHC5+voEQ5uuXSI3Iri0OfqUBtqKlmH5ihfhvGLdUR9BHh55BDjb0PuVgM9Um0ThxeYuCjIrrSTRYiFWcYvCtIbbWRu2HsSc9OMvS2xehHi2XOGEB6QM1OU37HYetpl8688iX10afB+SxQv2YQvNrj9FxzUc4+ZfVA2Te6GA6EgONald2rGoNcdm9S6g3UxT+ZbWbQtDXrdsnB3LdLXUuR/vYBXV6ZaKQReVTD+qkV+RZHdUFgDCI/dhak3FdoSeBWNHNCKuW1Nelvj7fpYPeL9k9UL0bY2gF/B8MvuB2ScgP984Qukt0XMnqojRfRukc80z3P4t3YTe9vS1+4w+Z828X7/1eTes9dDPyQEkQ9+TfwPMFHMk95oc1DLVWdSlG60EUoZ+P2+ysNYntJAkn5UvUBnUxSWe2CJhAKfTnvk1nxUykaNMKRiSXLrPtq10aPIc6VI7w6Yd0Y5wf2AVM0Mzo2S64tOD6elsRs9uLNGNHhMt9rYHVPtcq7cIxrs83Sni1DQ3ckw8YZEvn4VrTW610co+OgTV5BCs7pzCBWGBtakobMUgK1xWh5jX/VBSJy2wKtqMps+O0+mSP+hOW+3Bpm9iOzNBmufGKM0qMKlKhqnFZFarlL/0en4BuLWQyLHxm70UE4m3ktajT5OM4O3p+lOE99YdBAQqjRfbp4FwbAiGQY4g0vZm8vjjLTuRtlpR+1hIM/ft0d6RdKVGrLVJ5jKJTmgd/ZQnkXtsSJWqRS75V6D7lyarReKMVgSaSG6PtWTabaeK8QpmfA8VMqmctpj77Fssi/kWNSOu9ROHvBnUzQO23QOJbvwOu1RO27Tm8kmAkyVC9ROSROQvj9M+8bL1E6D3fIRxULMdyDGSjSOKY7/m4DSzR7WnGlQynKJ1pGI5f/qFF94/THqZ8x7loUc/WM9pr9m8dMXXqNhUD1YhRy9c12j2PF/36F5LEIIgfA8ak/71I7ZXP3bOTqz2iDGhWD3Sc3W0y43/soUrSNDicudCy5bPxxw9a8X6J3sxbTCtfMlPvXJV/mRv/k1mO3F+xg1N8lzE3f5udJ36Zf0sDiRTqMsUAh2zx/Yw2YyRkzsISU+gUc8kKJGA2oN/IITb7DB8NQ5O23qRySiPCyNh2vrpNe71J7xjb4qmBH0OyvkNkJqz/bjUrru9xFX7uA1FPVTxCSNANxaIcwIupMy6b9xl964MHuO0Q99fYvWUoRXSaLUxcY2vfkA2fFNKrOftuxWCCZCZLVJtLI+ZFqt1VFphXN5FXdtiD9TjSZaalJ3dildtil/1yA9dLeH7ti4LcW//c5zHPnNxmBV7BI1HXpjGs8KWfyMMqX7IMSqODRPhJSnmky/qg2hpdY4TYlyweoLiletmOhSWSA6NnbdInMpFa8SkStYbo3zu3cfJ/tKJu4TyXaPaafB77XOkbtHDAbWvk93PuJud5yxK8nqpnAdwpKXQFPsW2Je6wHaIx1IYLr92Wt7Sd4GIBjLMPlWmPAL26E7lyZ3xUWPkO8Lx8YvWKRveoQnFoZPYlnIEAq3GE6dDo73KhqnpWNIDJhGbXrbYNuskQDGtilct6idzCZXTtsmd82hcbZ835fB3bLZ/dAC1szUcBVTGtmTVP7MMTonJ+MvJ4AIBes/Mk/tiQB6g4BVChEJKqdt0pOdYZlbClAQZRSXbiwQpfepiW2QGpkL8L85jhrcC4TnIUPoLQSkt8w8FEIgbJvMtkaW+2hbk10fkvSnahHrrQLNVppUZZjq9hZLrPVL/Otbz5KqDv3W4gLaU1yuThssZPzGBHgelVNe4lrvPybSDwff3SMdSMK2sU4cpXFuIgFqlNksUcamPWvByKZfZtOG7KNDohomPA8ZaJwOWG9eSzy/0zKsOfrKCA7PsvAaijAjCO8OnwcpSNU0kWcQy6PmtLTpCx3YHFt9o8p3cLbGqwwYe9ZG+AssC68iSe1FpL97M4GGsFuS7EZE4ZITl/x1pHBqktSOppzrEBQHpI5BiNOw8CoWHz13hdaMIXzc5xZXHZvu412ahyUym0UPuMgB6qcjGkeEmU4d7J/KhQ7FkxU6s2KgjKGRvuYnFi/y/3z6tw1Z/mCFTt/eY96r8VNH3iSzPTz/aGUdAsHmbpH05ZH3rDWqUmP6V9+9n5pYayOE9hDMJX1PgSSE+DtCiEtCiHeFEL8mhEgJIY4IIb4rhLgphPh1IYQ7ONYb/H5z8PjS9+3k83nCiTz5W81YEQ5MNWzlYw7ZjYhod3f4B7NTrP50QG49SoynR6cOsflTfaa/20580dXxBVZ+MmL+c9uJL21w9jCrn1LM/956Ys8TPH6Y9U+ETH/2XuLDDU8dYvcDERNfGvKQAwQn52mciih/JTmwpo7O05vSlL5xFyuXHa5Wc1P0xxTp9Rb9C0djvKCcmiAoR6b/IqB3YsAJPlYiKClKt/vsNbLsnjMDc1YuS5hXpDfNOTY/2DE3Gcsi8jRW3ebE/Dbui3vIKcNTp2ywMiGi7DP24iZMG7/d1bR7LkFkkf3wdrxvS213+eruCd7tLrD953oxv4Ta2eN/vf4CZ9NrrH7EiyuVOgzI37SxnYj2uSQRpFxaQJ9eiocJH0b7YwNJCDEP/E3gGa3144AF/Azw3wP/SGt9HKgCf3XwJ38VqA78/2hw3PfHoghndQ918XKyLLq5Q3pLkF5LNvbY2Ma9mTYQntF+xK0NWEnTnk8luuTWyjai5tA7XEr43eUdhC8JZoqJD9y9vgG+JNqfRB2Yc2sDbIWaSEKZ3BuDvUw5OX9jre4QTASo6TEz/bv/HrYraFfTOlYgzFhx2qr3qohAUD2TRzngbQzUKOoNhC/YeyxFfy/N2NUQHYZErbZpugr45r0jFL6WJqrV0WGIV5FYPtzZGaf7+jjRisHhpXc1kS/x0gE7F6dR103wpyoRth2RckJqr07Fx4teyEqtxBvVQ7hXMrEkpvBcpgtNbvSnKV3TQ1EBIWkvKubG6qTXW4kblD9fYveJ3Htyf8tM5pHaI9lAWghhAxlgA/go8BuDx38Z+PODn39s8DuDxz8mxPfnneooon9sKsHZIBwXWcjj1TRyVAPJ82B60lANZ2VcXZKZDGpxitSuoDsxxO3JVIpoYZLUliRyJdYgPxe2TTg/RmbVQlsy3gAL28Y/OUtmxUal7URD0T8xR2rFpXGyYCZeB0EZHJvFbkl2PzBB8IlnTIMRiGbGER2LzRdL9D9yHuvEAKw5UUJ7Ea1ZC8tXiGNmRF7kc1AKCHKw8LkKKjfYhzkOqhASZOH4r/o4rcGeShstqNppTfqredJ7QxS2DMA61STYzCTmudyG5omjq/h9h8jVceM1tdXhp4++yemxLfylYdVO7tV4ZnaFPz9zEX2+GY9LqFqde9tjfCBzi62PhAkewfGLgv/m6O+y8snkntG9smoAsCNN9PhznZ9JYA4flP2xgaS1XgP+IXAPE0B14HWgprXe3+2uAvu78XlgZfC34eD4+4RthBB/TQjxmhDitYD+wYe/JxPzM4hQxbxvYACiarJE87CI53XAVOF0yqFxOiS72htqEXU6iCCidSykdMOPU0HV6yG7AZ3FEKF1zCGnwxCr2qGzEKEtMRRQDkOc3Q6dowHSjxINRWevTf9oj+Jbu8ivvxmniXa1QzjjM/HZWzh/8BrRjnkN2eljTfSZ/coumYv3iG6Y/ZnoB2TKXQr3QpQjYB/lLQSpjE96T7Px8hhBfvBlzmaw0hGpiubup9NmDN1xkbkcYSEif9vQaK1/OsQaKxsy/jGN9+UCTlPQO9kzRP1C0FqQXP3qUeRKCmu2ixykldXHCvzb2xf4xutnGB9vxX7/5Czr7SKtKEUm1R8G2MmjRKHEIgngtQoF0HDdPzBzJAR6egy7qyE4AO7FiHGPpt0Pyr6X1K6MWWWOAHNAFvjkf+gLa61/QWv9jNb6GYd/T05nS9Kd8RJDcQDaEjgt7lM1V56NXbNwKskKn0o5WG2JW02OiEdZF3fXInOnnuz/FNKgwF2vJ45XGRfZtLB2kkBTLSXWhofwD4BWgxC5Z+6miVW13kRtphDNDtGhqaHyQ6VKdy2HsgW75xwYIDp0o0mvZTb5o9IqqtEk6lloYeA9Exc1OgxQ7Q7urkV/DIQWFC56qEbL6B1tClqHNf5cgHcrZaiuBrReyoVgMiDcThPtGgWN3KpPGFrYDUm1nkUNKIvdexUUgl+89gKV7cJQmubGMlRdSrKPaNtx5TFqNCjc67Pml82c0v511Rr1zjXGv7JyX+P9YbLvJbX7YeCO1npHax0Avwm8BJQGqR7AArA/1LIGHAIYPF4Ekrolf1q2UyG72kX1kiuabPYoLEd0z8wkUgTZCxh/R9M8XU5i4QJF4YagN5XMt4WG3Cr4U8mRcpSieM0iHD9ArdvxyS/L+2ijsCXpHYG2DzQUbYvs6kAKZSQV1LkM2TWJ9kyQ7TczRTZLdtUiu9yieHuESMWySF/zcDqK1oKMy9kA2etGbS98vI2fFwjbQUhBalfgH+7jTnawfB2nqG5TUzq7h2hZuHXixqtXjUidruFuOniVYWq8vx+zegLrdiqe59KNJvd2y3T2MqRvuwnyGO0pfqX6AuNvjYyhCEF71uVXLz1L8WryRmSNlemenUVVajys9r0E0j3geSFEZrDX+RhwGfgy8JODY34e+O3Bz78z+J3B41/S+vtTn1S1OvbyVlJwGWB7F7urCbJWYsWQlaZBf0/JBEuNtVMjyAvDPjpKQLhdo18SNBeTK6a1vkdvHLozyQahqDXpTmr8qSSyQWzs0pvQ6JSXCFQqdTrTmuDwJIwVh6iKbp/WkYj2mUn8ojskDvEDWscD6mfyphHaNTcQHYZ05yM6kzYyhNTWYCVWis58hNWDoOtQutmPp23b8xrvtofnhmS2lUlRhaA9L9hbLqNzhvlUDYj6Wws27VYKqyew28RQp/bxMmO5DjLASNrsK8yPl/nY0eucPLZBZnsoAyMcm8JMk1m3ZhiXRlYePycYK7YR7fvxc91x+9Hm/tZafxdTNHgDeGfwN78A/JfA3xVC3MTsgX5x8Ce/CIwP/H8X+Pvfh/M2JqTpmUyUEm7V7uLW/JijYN+irR3SVQO8HP1Ch+ubpLeHzcT4+LUNZACRd8C/s4tQGK6DUf/WNk5bEGSTEEa1V8FpCLSXDOxoZw+vJrDaPtG1m3FwhxtbZO9ZpNfbeN+4FO8Bo91dsrccMpsBhVttwjumnK6aTUqXJJntkMLdITGJ6vWYeF3itjT2joN7acWMlIehGZTTkHYDCldr5rW1ZvLNEJ2OyI+1zWTrIAAmLrZIZ3z6J7vMfLcbp7q5i+tIoeGZOtOvDlNpvbbJW3tz5N0eY5eHDEmq26WxnWPDL5FZTvIOWj50fQfRSqbeutsjvRMkGtAPm31PVTut9X+jtT6ttX5ca/2XtNZ9rfVtrfVzWuvjWuuf0lr3B8f2Br8fHzx++497/n/vky/kjNhyJZkKyFIR5VpkNpObUGtqgsgR93FzW5PjCGX0gBLHT07gtDT5e8m9jTUxjtOCsUtJOi5rZhqhILPSvO/4KAWylUxBrbGS8e81htg/DHmLX9CgoPPx8/FjVqmEX9b0Jhxu/McZM/KB2V81l6CxaLP250K6H3/CXIdUitppCLJmj1T/yLHB/I5L9bQkv6zxf2eSyoXyAC3usnPBZunfQubfFWkcS5uqmrTYejZP+V/lGP9CisaRVMxtUX1pgebvzOJ+ucj2U+khmcmTJ1i/PcEbtw6z8VIGOUAg2IcPMTZb53xmhfUfHktgG5uLgmNje/TOjqBLMOj51HozXk0fRnukkQ2qbrB20XaS80x3OvTLdlIfCdDtNsqBMGslU6wwNP5M8nLoIEBoUK5M9qkiZVLHYrLsqvs+bk3jTxwofoQhmU1N73DpvvfgVaB3ciYGh8b+qqC7kMXb7Q+phqMIb08QpgTHf72P6PTi5/cqgjAjmP68Q+bevqq5wqsK+iVBmNPx5K6OIpwWdCcFtccU+ZX9FDHAbsP2Uy7bL2rSu5FBhqgIu6vZviDZfVoZpMIgzUpVQhrHFPUTCqc9HLG3t+pML1VwMz5eRYMyeyG1s0e9meGze+fIbA+JN7Xvk1vV+MoyFcnRvWq3z9onJpDnhyIAD5s9soEkbNvgrJS+zy8nxrC7Cmd9ZKWSFkxPoqXA2/PjzTJCwPQEWkB620+ytk5PIELwKn6iIasWphDRYC8yqo4wP0nkCdzdTtI/Y143tZJcORkvE3ngrdYQqdTwnCaMP73ZpX48gzpqOgtioI7u1SPufjJN+5zhZpDlEjIEr6bZfhY6hweKfRNjiAicFoRjAX7ZRdgOVrmI3QanrdGOpjXvIVwXmckMRis06VWLftFCODYylcJtawq3oXRF0i8KhOvGPaDUjiS7IgkzAiwLYdtEE3m274yjlEBbmDmlgaKE2vPY6Q4KNYNKnD09RWdaYEuFHq3OSYtopkzhboSsjYg3P2T2yAaSDkOE66AajSHl1sBP3ye13aV+YWqIPFARot4kt+aze35kxdAa9mp4Tc36Dx0AQG6ZvdDah5IrjFzfIUoJ1j9USDQDxdoO2oK9C6VhUAByt4pfhOaZZFFE1Jv4BU3n2BjY1pCCqtEizGrCrIPTUXE5Xbfa+CUjNhYd7WF3zKqg+306s+aOf+7pO3THrMFeKKJ1NCJVUWTHutSO2mbPIwSNk4rsZoRb7tErywGhi6R+ArKbITxTx8+bPpnWmvoRSaquyP35TezuAHkfRVSPu8gQsh/dpnQzQDWb6CiidiLLxFKFkzM7jL/bNc+vNWE5zc9/6Os8O36XzFYQ99u01gRPtLi5M0F6baiOgVbIVg+7q1A79xd/rXL5Pccr9lPSH5Q9soEEoFpt5KE5OACvV40mQdEzjDejLD/NFkHeIr8WJhqmutnCzwlyKzopudgxMzvpXZ2ky+p06Y1BdkMlSFHo9+nM6oEcykgqGIb0xxXZuwfuqJZFmNcmFev7sRiAcIxWqwgVQoHaMwBYkc8hNDgtRf6badwtsxcTuSxyQOp457eOUby9r+Vk+mDNRUnvTp7sljLzV7ZNaluy+byFVkbhIvbvCjZetAlDi964iL+MmS3N7jmLzWqe9pzZZ+koIl1RtM6Ya1M96ZiVW2vyK32en16m4PSonkzHz+PeWOeLm6cItBWPvoMp1Iz9Xob+vRyyMrLH1Bp14w6ZK5vvPVL+R/SWvk9gmj/SHulAssol2KvFRIn7JuamqR9xSV3bSOxtxPwM1ZM2uSvJO5tYWqA9Jxh/bTfh5/gi/RJMfvcA6cbRBaK0pvROLamzdHQB5WjSd6qJwFOHZ4jSCquaJD9R4wW0pcEPIDWkS9ZpD+VqgoKD5ath2VeYYGks2gQFM2AYv7aAzqygcSqkfjRl0qgoIkppelMKa6FDa95AmnQQ4Bc06nAXxw1BmsKH9n2CPHCyzWy5gQzAnpqAKKI7KbCfrFHKm8qcTKdMyTovOHNknXbfxS+NcDakLZZSezxXumO4H/bPc6xIKdXl58rfwS+MEMEUClTPCC48ezMpuiwE4Q+dp/nk7HuuMFGl+p66sqrX+4HqzT7SgaRqdUOgr5NwE2oNk68fbIBWG3RmFVsfnopxbQDsVOke67P+8ckE5ZNY3yE602bzg2OoDz4Zf5Bic4/UmRobHxkj+vBT8f5JblUoHKux+bEp9ItPxLNH1m6DmSN7NJ6YxiqOTOF2+owfqVJ7amrwggPW0TAid7hOc8EmTMkhHk1rnKNN+mXIrunhnVtrvBMNurMhpbdtxt4d8E5YFuJwm+KxKn7bJbWnh5CmxS7ZTJ/gRoHOjEYNQKu9uYA/e/xd1t6cpTelzdCg0vTGNf/FmT+g03fpzij0gMGnXxL89OxrPDO7Qm9xZO8p4bi3STXM4r/UNCj2gb00dosvtM6y+eN+gtlWnmzxd+b/gGv/56nYLyyL1rzLyqeg/8mnYrQ4gHz8NMHHnyb86NP3oVt+0PZIB5JwXaKpctw0HD4wqARlD+x5pICJPkFOJMcuLMnSwi5hBlgfUZHzPB6fXye/FuLe2R6yi2bSzBUazH6tind3b7j6pDwcO2LmK7s4G7VhmmhZNDopChc3YaI81FmNFK2uR/nVTTOMt796BiG+bzP95S2K31mJqXp1p0sYSibeDbGCobSKrjfwfYv8TZvOnI5XKrW7h1aS6nqRv/7cl/HzZu4pqtaJ2kZd4h/+xC/jjw32Wr6P6Fls9QuEUz5BKTKpq4qwfKhHWXiliMqFJnUaQIeaUZpvfvlxnHQQM9umtnsoJP/yrQ8Mrz3A9h4d5TLt1JFyCAVSnQ69ukde+rh1mcAwjn9rk/SKTXq9PUSLA/rqTexmgPvq9QfOJPRIBJJw3ERBYd/00QXqZ/L3gRaDU/N0ZjXqVnL+Jzw6C3se8//LO4llP5qf4N67sxz6H99KkqIUsrx56Qi5L19NCIFpS3Ltxhzi3mbcFDUnKtir5GB7D7UvSwnQ9+n3XHSzhWh1hhVAP0ApYeh9bTvuF+lulzC00J5L68JCzNijO12i0EJEsPHDIXrerGSq2yPoOsgQXvzhd6mdMDNMOlKEDRerJbnZmSJKE696VsNip5XlVzZfxOrK+OaT2pFxRU1EQ9mV9LbgjeYivfMdhDNUO7d7mlW/zA995B20FnFwCz/krc4i//OL/5LeTjpxs/vW7lFeTN0l+43skEUoDJn7vMVPfOs/4+gv3k3Oc925y+F//JYZlxn9/MMQ8e23HgoSlEeCRUiHAdFe9T6/3KqQy93Psune3aVw+34+aNkLSW0ZnoXRiy+CiMINM0IRD/wJgcqlGH/DQhTysI8wF4JwqsDYG7aZyh0JvHCqQOkbqeH482BFCg5PUvpyCspF6k9MUvhCl6jmEyxOkvlqFjUR0D6SJ3c5Bc0manGWwtfT6HSEn5ekjs3DXgWOzFP8ZopeGWRD0p/J4bwjkIvzFN/w6JfhKxfPMK00CIk1M0X+uk1/TPOFbz3B1IpC2A6yVMTblQTNMpd0mfE7GuHYcb/q3lcXybeMFKhwHegK/Dx8/ZuP4VYkXp04Pe0VJf+/a+eJNjKktqXB2vV6aCm50Z7iazvHQYJIeejAR3e6bDam2VEenVlznuiBImFPM15qocYLsDrCR+55cOIw4t3rSQGyh8geiRVpXynhoKlGE2e7aUqgoyoPlSqNI0aWJQFavbVCZylAjyUH8sTGHrWnfZMK7vu1xtqoUHlCEc2UE35nvUrlQkQ4m3xda69F9XGFLmQTo+b2TpPaR7tE5SzZ3/hunJ7YlTb2p3epnymSXW7Bjkk3ZatL9GdqVB7LGerg9gCn1vWpPa6we4pzT99BRKYBKno+jVMRuVXNh5+8YvowKkL7Ps3TAWhw59v0xuXgy9yhsxjSmwnxi4rmoUGZ2w/oTUdEZ9p0pzXNI8KoTghJmNUce3IVv6zw88RDdkFO8MPHrqNKAe4I4qc/leZ0bpNm32PuiwKxz1VxfJGJXJtf2f0gM9+NsCbNhI09P8fay5KlYoX2kXy8FxK2jTi8wM7TRXji1ENBT/xe9mgE0h9hqt1G3VlBH55NEC+qbo+l3+2w9dHZBKBVdXtMf93i1s+NY8/Pxn7d6VB+1eHuT0wnj683KL8jWX+5gFUcjjnoepPCVZudp3MxgSIAO3vkb1lsfXA80Udia5f0mxmqZ3IJ1Lle36L31QnClEC9dSVOK/XaJuqbZZyOZu7/8zrRJcMjoZZXSa1bhGmJ/9dLOF81pPLh2gbejkW/JNj4vxxm7DffBkxJOb3iIE618L6eZ/ZX3o2vW+62zbOP30LM9Djya4NJ3cBn7KLkR0++w/yFDQ7/ftOkwCpi8k3F+fIaJ5++x9SbQbz/K98wsJ1CuUNmO4pvEk4z4LfvnWf3zhjKEYmR/7uXZ3lle5H2jBXztuu0h90RPFdcpjlnD/eFYYi6tYxyoDeTSbYbHiJ7pAMJzIevr9xKaJGizAi62xyUlvePDQOyGwFhWsNIiqA6HXIbEd0ZhRgpUKh2B+lD83iYkHuJ6g2kD/2yYBTYrloGghTkRaKPZJDVDLSOhq+ru12DtQsOqFdEEX5JY/kqgbQQliQoaLSA3mwuTiGFY+OXFa0jEesvFxBLA6yatAhymkzKp1+G3nMnYr9f1FT7GaKGS/P8sGrYLwu+s7PE3ZtTdObTsb9Xlry2t8i1txYJskOwbpCVbHbzdK6XDInL/gqt4UOzN5H9QZ9q8P5ko8Oxx9eot9JktqP4euiNbSIP/qc3X2bi7c7wOglB7S8+g7YF2Xc3E3tb+9DCQ8Pj8GgHkhBYZ04gD80lRymEIJwtG5aaA0LN3maLqdcOPI1lmoOZDYkqjEjZS0FmNyK9aid5FbQivxbiVTVyrDR0RxHpHY0MhnM85nCN7IN+j6stA+Bg7zCKcGuCyBGJ6V/lB6T2BF5T4X3jUrzP075PaktSuG6x8NsbRFduDv4gIr0tqN8sGyGyb1+N/fm7sNXM4Y11yb85YO3RmsLdiAvja5QX6ibdHPiLd3w+PHWD2dPbZDaGA5DZlQ5PFNdYenqVwq0hR4a92yTQFiefukf57ZECTrPFdjNH0HXIvzKUY9H9PmOXIPtmGufqCFuQ1ox/aZny1T66PpI7AuHKKkyNP/DSNzzKgSQE1vEjiEYbEYRDOi4hEE+dRXYC/KI9XEmkhXj6MaK8R68s0Wo4UCYeP0l6q09qT8P15djPE6ewOxHZdU10dajZI8+dwm6bEe5Riijr9HEyWyGFeyF6ZCW0jh2mfCMg8iD44afjHol1aJ7cqqIzLQl++GmssyeNf3oKr6rplSVWoWBYRoWhwJJ9CD0BjoM1PWVYgfJ53AZmfqiUxSoWkJkMMpVCS8hsSNLbCmFZ5rWlReQI2s0UXM2hO734RtQrS263xqmuFxFdP66WNhdcfufe4+y+Yn7f9/em0vzhxmlu3pilN5UeigrYFpdqs3QCl72nxoZsQe0OY9kOf/8Dn2Xvo0vx3lOHIX5ekP34FoxyAmJS7NRrNxOl732Lrt184KVveEQCSebz93e1hUQEIXgu4cp6QmxK1jtEBY/scsvctTCri2x0UY7FxNvdIWJcSETH9HDK13tJfaR6BxFpCndHCh1CIHoBSEF65wCsP4yQgcKrBvdB/kWkcZua9Lurw8qg1jgdTWpPE+Rt1PXBxIlj49UVXl1T/+RZ5MqmKSp4LtkthdNVdF4+YyphYQieh1dTCI3RKJooGy4K1yW9o2kvKPy8QC/OodpthBR4dYXY8khvC6Jjs6avJgSZXcXyF5cYe8Oie6RMuG32NpntkM7rE2TXoDudGvrvNVjfKuFULPyCHPbnNne5uz1Gyg5wOmrIzNrvs/bqHNc6MxRvdRKpWmZHsXV9Eg5MwsrpSdSJRR5meyQCSbWTF9w4I6LVdUNJNYps0Bq1vILVCehNZ+I7pw5D1G3T8+nMethLi/HzqDsraEdSO5oi+tATJmi1Rt1dM/wI5z3UD52PyQ/V3VXCjGTzeQ/7yFBqRK9t0ht32HkinSg26JV1OlMOfk7EX0CAaGOLXlHi5wX5b92J9wXRxha9MUmvLCi+tUs0+GJFWzv0SoJe0SJ7p040kLOJ9ir0S5IwJXCqvVhZPGo2CTKC3F1JcTlEtoc9GxkBAvy8aQvsXzu7o+id7MGP7iEDFV/31GaHxR+6R+En1814yn5zutPn42eu8MzLV03qur/Xs20en9/gL81/J5HSWqUSeqnLN7eOouzhA9b4GLVjkrF3kiMUMpuld3QC5Vr3VeyE42I9dirB2LRv9pHDCdTE99seiUD6ozBTOooITs7fR8eklWb3qSKpzXai/yTSabaeS1O43kg0UmWpyL2Pp0CAu1qNA9OanmTlEy6pikYEKp7QtCYn2HzOYu5rHcLpYtzMlONj1E5K5j6/jTw6FGqWkxM0lwQzn7lnuML3m6JjZVqHBfO/uZxQwZCFAq0FmP3cGnplSEIpc1lai4PVYbEwVH4o5GgtalJVxcqnirHwmvQ8GscVbkOzfcGhd3RicCEEu+cFVk8QpTWdQ7n4nHYfd9Btm9qNMXrjTpwJVB8vcP3mLGuvz9GcH9KNhVMFvnLnBFd+9QztOTkiTiCwZcQ/vvExKmetmNxFNZvYTsRfOfItVj+Wif3RXoX0juboX75O9RMn4iBQ7TbuXpcwayOPHEpybaQ8UOr+yVlpoR07kV5/v+3RCKQ/yoTE2btf1kVYFm5LE+W8RP9JjpdRDjSPH5DbK+bQ0jQEo9tDllSdzyADyK77yNevxl9onfZI7QqEBnnx+tCfS+PWQOVTqNv3hhWptIfTwvSjohGegpSH0zANW3t2SNQiPBe3Lghmy+hTR+IvrUh5eBWB8gSVsw72vlKh4+JVBZ0pSZjRqNzgeNdFKNj7QIjywKn1BihvB+VpFj6wRn8qwm5HBsEgLcIc2EUfu2sAsmJwbfslgVPwSW0P5osGVcnuTIooMrq5WgDBQIH98DRrrSLVRga3NrzUMp9Ha/ha9eSQK3xg/bKg6PQQB6CTotNn/SUXf/7A3qndMULc75Wt3Fz+gdJ0PbKBJDwPawCdGYXMy1QKa2EWoTT29rDKI2wb/9A4ThOyqyPYPGkRzBRJ7wiy6/7wQxGCYCKHWxO4tX5i7MKfL2H5YLX9xNhFf87cXWW9k0jteoslAKxKC33qSFyyDebK5suqNNUPLWEvmrK1Gi8QpcEvuew8V4DzpgihJs1oenvKIvLAPzRugq+YI8xowgzIUBAUU6aRmc1g9QSiJ4k8jV9OIV0HmU4hAkEncEht2rQWXEQ6jXBsgqzmxOx2TJgp0mkQAr8InzxxGW1jlPkGRZwgLfixU29TeTIiyOthO0AKHh/b5PjMDlGaeEQEIO0FLGX2UBax9hOAULDcGiO70U9QSqMU2XWNd2UtiWzQKp68vc9+gMhveEQCSTjuffmx7vcR+TxhMZ3o8aheD51y7yOm12GIU+kgA40IRy6+irBbPrIPdjOpgG5Xu9htQ+81mrc7lQ5aYNhuRhlBd8yHL1qdRF/L226b8ne7A+9cI6rVAEMQKRRYdzYp/NabhCumMSq6Rv0uc2OX6a/vwUXTkJXVFlYfSjd9SjcV9mtXzXscjJFYPvQO+XiXVgw1caVKlNaIkk/p/C5+yUb1ekTNJkLDXi1H5Go60wICM2TnVQRX785SWDZq7sI2zEq5Vc0X755k8qKP0yLWbMrf7fGdnSVwNEFeYw04vu3NGl+6cZLVWgm/oM3IC6Z31rhVohJk6ZdFvOIBpHY1d3fK2NUkCFm0Okx/fY9wJP3d/4wSAXfQfoAzSY9EIOnAf89lOlxZxd5roQ/w2qkbd2jNS3TmwCZ0fZvOrEC5yQqgWF6jcUKhUsm9ltip0JnTZhxjlNar2iLIgej5SX+rZ5qrkPQ3u9g9jXDdmK0HQHSNpq3IZsyKt7+BD0IjnWJZRJevD9+7UmQ2NTJQFL90Y7gaCsHYZY3VhYlvOLESuvQ8pl6F3OtpKpcnyN8wK7RMp5l6XZF6NUswGVK4a/SRhOMydi3Cu+Ox/bREBtoEvRBkdkL6y3l2zpt0MRoQQVr9iI1rU1g1m/wdidocfNmlxFpJIYSmeNPAucwfWNgdQc1PU76eXDWcjkIpmZizAtB9n8aZMtbEBN+zSStJG/B9tkcikP4ok9ksVGr3SaXITIapN3r0ZnPJu5IlKd5SVM5mEiuc7vUpXxY0llJJzF6tTnpL0J9JEkFGm9vYHQzWbtS/tkF/TBDNJz/waGWN7qQgOkCiH62s4RcEKp++zx95gqicSczfRFvb+EVBkLMJTx2KCwFRpUa/YM47sxvFG/Ko2ST0BEEesusinl9S3S5ojCJfxyJ/ZwDHCXxEpOlNh2gJ+bXBfk5rwxuuDTojsz2cDLb2zOqW3hJkN1XcPtCVKkE5orWTxW2qGJunOh2UA40gZfZCI8SRTkdxfGaHMH8gAFwHu6vuo1373zUV3fe9+H7aIx1IIpOh9rETCWVxMNW8vTMp3OrIjM9AGKs9Jxl/u5UomcuJcWqnNKVrrcTxVrlE43SEdy+JPJdjJdqLCnu9kvBbY2W6cxHWapLVyJqZpjepTD9o1D8/S3dGI1aTGqnW7AztBY29WaP33Il4T2VNTtAvg9VXLP9oGv384wP/ON0pQXYrYuWnQvZ+8jwIgT0zTWtRkN7S9Euw+elDpmQ8Vqa5aOHWDJpj7cN5ZMpQbDUWbaQv0Tasv2QZ7ahUit3H0yhPE2Rh84e0udtLi70XZmCij+XD9tPDsYvecyc4enyT1LrDzoXhmIa9uEDpsT2WshV2nxhZeaRF7ZjDVLppqoUjFm3vkL20Cdv3czYkhNseoD26gSQtdLtN6c0d1KjieCqFHDOAT+vWCBQ/k0FNlFEW2Pe2402rzGSIJku4dYm1WU0cHx2aIr1qwagCeiqFnp0gvZG8dMJxiWbGyd9IUn0J2yaaLJFdk8l+hxCofJbcXZEQSQMzB5VdE0STRVMdG+wj1HgJbw+aiy4aU6QAoFTAbUDlrMX0ZB23PbhJ2DYigvpJDWeaBnuozeh6mIbuoZB+SZNfUWBZ6H4f5YAqhDh1QX7ZjJSrXg+3oRk/UkXbmtxtyxRTVET5UoMLh1eoXzCC0Pv71dSrt2j2PX76x7+aULUIV9ZpXBznfG6F7NoIql9FFO6GfOfuErnlJLeFVSwQTpcSw5jxZXQfDjT4oxtIKkJ1u/QWSwlEsOr1UHsVgtyQuANMP0Ksbhi1vgOAVXlnFRGBHikQqHYbeXPVHN/pJp6fWys4bW0I5gemAx95a8Xw4DWGga3DEHF9GbTBmQ0f0HBnxXxxi1ms6anha9xcJkpBbyqFDDVqEMj66k1kpCne7DL1usK6aW4U0fVbuA3N1BsBldenKH7bMKqGK6vkVjUTF6FfSVN6t2aKELU6+buKwlUbpylIbweodttMo17y8VZcrADyq0M0d/lyg+qVcaQvKF8PYwyg3Gvw1soC1q7L9KtqiP/rdukHNv/60rMsfNlPBIy24JfvPs/kK7XER+q0IoJaCms9ufKodpf+ROo9RyhGsYgP0h7dQALDVbDTwTqahI8YCUdNcICxU/f6phR7eObA8YHpgUweSBF9H79IrJkUm1L0y2Io6Lxv0gzAHVxhhGURpgH3QDHDsQmyBj40ShAvbJvIA7sd4d3YjOFGwrbpjQnsWo9UJUQPSsfCdemXBan1DsWbxI1I4bj0xoxoNJh+zL6/X5S05zW9Uz2sfhSnvn7BwupDv6Sxu5G5GUmLMO/htIQB5Eba7MOEQBeyiOU02VUxrPJhmtCN3Sxh3aWx5MY3NatUJJgKuDC+RmcxP1y9hcAv2hw/sXGf8BpaGfS89fB+XR/eM/serT+Zob84llh9dBgiImge8hLplPIDrB40j+UT6Zf2TUm3e+xgIAXYHegfn0r6wxAZgn98NunvmfQmPHrAr7VZeQ4EMGD6MpPZRFPZoNEh8mSigStSHgjoLCW/aNLzCDKwd6FAb0zE6ZVIeYRpsHqa4iUbnU3FfuWB0xQ4dz20bfY2wvMIspLOUZ/c4xXCtCGIFI5N47CHe6GKfKFKv2SOFZZF/bEyU09t0TgVDolahKB9fhYnGyAiwwwrBzcRdfwQ+fE2t1vjdCatGJVi5fNsPSO5uz1GlDtQbLAssld2fqDFgz+pPfKBpDxJ6vqB7rYQdKcF/ZJE5ocVN2FZtA8pmgsSeySVEp5H81iEX7ASgSccmzAHYeZAudx18YuaMHdAKU5K/JKh0UqepKI/rogyB3phfkBvJkQGKiHrqPp9+kt9rL6KdYjADCb2znZx6wHON96Nv1iq36d7KKR4u8/Cv7xhBIoxgd2djyhf87H6mu5cLva3FxSFZU356R3u/KgXn0/9GNgVhxdnl1n72QCZy6J9n86soO/b9PsOW5/0EemUUcEYE6SdwPSRfqpi9ixaE2QkP33mDV5+5jKtD3bQ0YCy2LH4u6e/yH99+PfojYshuDedYv7ZdSbLTWRnBNojBP0PnyMaO1CBfcjskQ4kYdtkL22hqrUDfoeFLzQQoU7sb4QlWfpdn35Zo0fvblqz+FlF7bi8jwK5dE3RmjtAbRFFlC/rBC/bvhVvkNAn2n/+0hVBb8JNkOUDlN6x6cx6RjFvn6bLssi/6eGXbGS5HFemhBAUv5miP+bA+ZNxNU8IQfkti9aCS/fppSFRjBSULknu/LiNcgSZm4Og1EYPSv7sNltrZQ5/JkBHEToMKNyBU88t87mvXWD6t1zDr641uVWF54Y4b+Qof8OLCzyFuyHLW+PMf04SfG083iNl13p85t5ZvvOZc7jvZuKAcdYr/ObWU3yjfQq3MRxo1M0Wa6/NMZttEIxyp2uNt92lM5/BKpXuu94Piz3SgWTNzqA9F9U9sOSfP0HzaI7CSogYQQD3P/Q49SMemU2BGHTaAVqfPEdjySa1p7FGdEobP3KO3rgkvacSYMnmp87RL0tSe0lQZPflxwgzAu+g/yOPEXnC6L7ODlfC4LnT+CUzIRueOhRPvIbPnqI3pYlcSeXPHEMsmFRRPXmS1mHwc5Ld8zmC80vmiY4vUTtjRiV2zznUXzoM0sKanaZ6PiK1beEXYO/5aWQqhfA8aucUm3fHEV1J/ahrRumFpHoGGv0UUSmktWBhTZqeWGNJ8tL8HYSC3oTAGjdB3Jmy+ejxa+w9ZtFeioZMSJbk6elVJl/aoHe2O6yuWRaX12b4YPYatTN6uMpYFqldQcb2aSwlUzuhNZEriE4demhXpUc6kMKVVdTte1gjU6oAstHFaUd4e/1YlxXMJrk3LsitR8P5JSFQtvmXqmqirZ2h3xFYXY30NXp/pZIWQUbi1s0XPbFZLlhkNyKUc0DVQprXtNsR0fVbCX/hjsKth9i3NobpnYL87UEVKyNQpQFZYj+icAuUI+iPCTrTZj8itKZ43SLICZRtmH2EZaFdh8J1G7+ksHywewocB5HJkLtlgYLxi5LyjR4IiUyZm8zK2jjl1xwm3+wZei0hyGxoPnfpMcI0TL4VxCt9ei/iC9dOY/Xh0Od0LDTmVDpcq01R66YofyU1bMhubqN8i7WwTO7O8DqpZpPUrubl0nW6EyKJ8t7YpTsh6U4/HD2j97JHK5Bkcg9jFQoIywyTJXo01TrZy9tYV5O8dk6lx/ilgPzXbgwbr1qTXe2S2VYU//BaAoqU2QwMQfw3bwz3YHoog5J55VbyeTb7IATeW3eQmSF6wq36CAXuO8vI86exjy6Z82n6WL7GvbSCnh7DmjGrlV3vkqorsle2mXyjaRq8QiCbHZy24RYfvxxQemXdFAnqLZymRlugXJj66iZIgWh3B5Iqgta5PvnbLQPyDHwyWwqrK2nP768IEh1FlK+HZG64ZDcVQc6GAdaueMcnc9Vj4UsdghH5m8xqC+dOivmvtvALMm7IsrXLyto4vSsl+mURN2RVp0P+okegbUPIOQKlmvzKKv+vdz5O6XaUbGnsVZh6pUH+9bXE8Q+TPVqBdMBUtwfy/regO11aj08jxsoJYkl5a4Xmok10YsGMLQzMvrVB44ik/9TRIZmG1qRubVM/Dr2njw57GFrjrlbZOw/dZ48lqoXu8i47Twq6zxw19FaDoHRvbrDzpCQ4exj19lXC28vmfG6vsfOUJDo2a/z7Y+t31tg9ZxFOF5E3Vwg3twxAc2WdvccFdi8y6eBdA04N19apnYLCHUV6W6M3ttH9PuHaOu15QekqpK97WHtNVNuwlfZLEqsrsJ+uoqUg2t0zf5OWWB+ocvrvv0tr3oqboNKPOPqp2+z+Fz2qp60YtS1rLWae3+DWT2TpleQQMRKGWKkQ91TDlK4HVUnhuHSnNHf6k1g+iVSt9oF5Do9Xidwk4FguHWL140XUAYjVw2SPViCpKDHOgFaIgRJFwn/iMCs/EYFSCcRw54OnyP/EBvZW3Xw5B1b96FG8l3bx3l2JkdkAlRfn0SfaeN+6klipKs9PE40HeF9+O1EtbF6YJRgP8b54MXHanScO4c+EWN9+J+EPTy8SHu4hXr+a8ItDswTHuojXr8a0VGBEA8L5Pu7NLXaedGMKMiufRy918eoRF37+HcJnzNiF8Dz6j3VRLvzl/+jzLP/soK8mBPVTEcqGnzn6Brf/T8Q3ita8RCnJN+4dpXZKY42ZG0tv0iNn92neKGH1ienMtGNztryJck2J3xqMguhIcWR6j1KmS3daIZcMYacOAxDwkdxlmmf9BBA1f7vF02P3KPy1lQQ3e3T7HpkNza2fKT40kKCD9mgF0gHTYYhemI5lFWP/pRvkL3rUnptLTM+mv36VjVdnWfnx+QRPXfn3L1O9PcbazxxPlMXLn7tGuJum/YnHE2PLY394G9G20BeGhPsA+e/cRQQy/tLEr/vKLay6FX/J9s2+fBe952FNJUGuemUDseVhzUwN92YYWRq566KLOQ79/l48qqF9H7WZYvuCw7c+cx73+oAVSGnkvRStD3V4s77I+OV9iitJatviox+9yIK7R/pqKk6lRATHx3dRV3N4VYkeFHK0BW9tzlG+NBirH+yFVCHN5y6fpXxJEBSINYxkLkulk2bn9WmkL9CDsXiEJJgK+HfV55ANOwH7aRzPMe9V2fjtwwkePJny6E4Kjv5vrYe2l/RIBJJwXOzZmcQGFMycv+gFicocmGpeZktRfGMrOSE7OU5qRzD/B5UkI83UOKkdydwXK4mVSpSLOFVJ7kolMfciMmnstsTaO6B35LnIvkD0D4w42zbK1Ybje8S076Ndhc6kEmVx7ftE+QidSyPPnRzxB8bvWKx8ahx7YX74mKeZ+1aX/kRE95wJWOE6RJ6m+AcZ3tqco1c2aaiRZIGvfeYC/4/XfxS7C2hl8Ig2vHXlMGFWE6U0OgiRqRSdSUm/51I/BX5Rm7RaCKqPFTi/tEbzIx2sHjH3d//0HHnPZ/qZTTLrIg5Umc0gOhav7iySW5YIZ/iZlt7c5X/4gx9Bhgz3WoDq9Rm7FiY4Hh42e3jPbMR04Bsl8QPzJVGlClGEnkve0cPVNUpXGuy+lAy+cHmFmW81Wf30WIILLbq1zOy3+2x8ZCzxGuGdu0y9odh7bjL5/Mv3KF7DKAKO+u+tkr8taZ9PIhuinR1yyxa9U0m/ardJr9qEk/nEIKD2fVLrDlE+BbdXh/4owtu06c7lmP9qM4YI6TDE27LYeiZN4YZF6k4l9qe3Ja1Dgv6dPOMX67HfbYLVBb3lMXlxsOoEIW5Tk7ln47QE4+9odBSh/MD0fDY8MuuC7Ko5F7QmvRPy9p0F7EtZZEgcMO5Wi0bPY7ueM2Po+6l3EKAzET8yd4nspkqk5O0TYzDRZ/ZLOwk8pL04T2qri/j2Wzys9kgEEpgP/+A0pD09hV7fQtzbTGxaralJ5G6d4u1eIjWy52exd5sUb0UJwgx7Zhpvs0X5uj8U9Ro8f3a1Q/F2cmLTXpgnv+InR9YHx+fWI7ydZPphz86Q3tE4jX4iUM3zaKQfEb18YTguMTVJ6ZpCKM3OTz8Oz58fPM805asGA7f7ZI7+U0fN8YfmGb8cUViOGLvSJ5w0EChrbobSzQi7A+XLgihr9kHWxDj5VQMelYEwyA2tkbksqYoiSmmkL8y8kIoQjo3d11g9gQy0UX8f7A174xZaQ3pbU7wzHFrU0sjJhHdzZDdHJpIdB3vX4Z+/+RLZteR16o1ZqLaN6CYHNQkjg3Z4SHtIAEI/BOVEIUQTuPagz+NPYBPA7h971MNhj9K5wsN/voe11pMHnQ+LrMs1rfUzD/okvlcTQrz2qJzvo3Su8Oid7749Mqnd+/a+Pcz2fiC9b+/bn4I9LIH0Cw/6BP6E9iid76N0rvDonS/wkBQb3rf37VG3h2VFet/et0fa3g+k9+19+1OwBx5IQohPCiGuCSFuCiH+/kNwPoeEEF8WQlwWQlwSQvytgX9MCPGHQogbg//LA78QQvzTwfm/LYR46gGcsyWEeFMI8XuD348IIb47OKdfF0K4A783+P3m4PGlB3CuJSHEbwghrgohrgghXniYr+33ag80kIQQFvA/AZ8CzgI/K4Q4+yDPCQiB/6vW+izwPPA3Buf094Evaq1PAF8c/A7m3E8M/v014J/94E+ZvwVcGfn9vwf+kdb6OFAF/urA/1eB6sD/jwbH/aDtnwCf01qfBp7AnPfDfG2/N9NaP7B/wAvA50d+/wfAP3iQ5/Qe5/jbwMcxyIvZgW8W00QG+P8CPztyfHzcD+j8FjBfvo8CvwcIDDLAPniNgc8DLwx+tgfHiR/guRaBOwdf82G9tn+Sfw86tZsHRpR3WR34HgobpD4XgO8C01rrwXwCm8D+xOCDfg//GPh7wD6gbRyoaa33wYSj5xOf6+Dx+uD4H5QdAXaAXxqkov9cCJHl4b2237M96EB6aE0IkQP+N+Bva60TdJ7a3B4feN9ACPFngW2t9esP+ly+R7OBp4B/prW+ALQZpnHAw3Nt/6T2oANpDRidglsY+B6oCSEcTBD9qtb6NwfuLSHE7ODxWWB/9PZBvoeXgD8nhFgG/g0mvfsnQEkIsY+jHD2f+FwHjxeB+5npv3+2Cqxqrb87+P03MIH1MF7bP5E96EB6FTgxqDK5wM8Av/MgT0gY+b9fBK5orf+HkYd+B/j5wc8/j9k77fv/k0GF6XmgPpKmfF9Na/0PtNYLWuslzLX7ktb654AvAz/5R5zr/nv4ycHxP7C7v9Z6E1gRQuyPFn8MuMxDeG3/xPagN2nAp4HrwC3gv34IzueDmNTibeDi4N+nMXuJLwI3gC8AY4PjBabyeAt4B3jmAZ33h4HfG/x8FHgFuAn8O8Ab+FOD328OHj/6AM7zSeC1wfX9LaD8sF/b7+Xf+xCh9+19+1OwB53avW/v2/8h7P1Aet/etz8Fez+Q3rf37U/B3g+k9+3/3z4dCwAAAAAM8reexM5yiIFIMBAJBiLBIFg2aHO0il+1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = sixes.reshape(5918, 784)\n",
    "plt.imshow(image[:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "terminal-arena",
   "metadata": {},
   "outputs": [],
   "source": [
    "#    0 --> 1 --> 5\n",
    "#    |     ^     |\n",
    "#    |     |     |\n",
    "#    v     |     v\n",
    "#    2 <-> 3 <-- 4\n",
    "\n",
    "graph = [\n",
    "#0  1  2  3  4  5\n",
    "[0, 1, 1, 0, 0, 0], # 0 \n",
    "[0, 0, 0, 0, 0, 1], # 1\n",
    "[0, 0, 0, 1, 0, 0], # 2\n",
    "[0, 1, 1, 0, 0, 0], # 3\n",
    "[0, 0, 0, 1, 0, 0], # 4\n",
    "[0, 0, 0, 0, 1, 0]  # 5\n",
    "]\n",
    "\n",
    "G = np.array(graph, dtype='int8')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "adaptive-finance",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 1],\n",
       "       [0, 0, 0, 1, 0, 0],\n",
       "       [0, 1, 1, 0, 0, 0],\n",
       "       [0, 0, 0, 1, 0, 0],\n",
       "       [0, 0, 0, 0, 1, 0]], dtype=int8)"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "romance-sally",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [1],\n",
       "       [1],\n",
       "       [2],\n",
       "       [1],\n",
       "       [1]])"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "udgrad = np.sum(G, axis=1, keepdims=True)\n",
    "udgrad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "packed-riverside",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 2, 2, 1, 1])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indgrad = np.sum(G, axis=0)\n",
    "indgrad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "divided-optimum",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "pending-mediterranean",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.arange(1, 6).reshape(1, 5)\n",
    "Y = np.arange(1, 5).reshape(4, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "special-object",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4, 5]])"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "parental-terminology",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4]])"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "beautiful-alpha",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 5)"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "verified-renewal",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1)"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "hairy-contest",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20]])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X * Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "occupational-committee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4, 5]])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "polar-inquiry",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5]])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "incorrect-shape",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20],\n",
       "       [ 5, 10, 15, 20, 25]])"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X * X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "reserved-battle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4, 5, 6],\n",
       "       [3, 4, 5, 6, 7],\n",
       "       [4, 5, 6, 7, 8],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#assert X.shape == Y.shape  # if relevant\n",
    "X + Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "professional-charity",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 2,  4,  6,  8, 10],\n",
       "       [ 3,  6,  9, 12, 15],\n",
       "       [ 4,  8, 12, 16, 20],\n",
       "       [ 5, 10, 15, 20, 25]])"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T * X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "large-frequency",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True,  True, False, False, False],\n",
       "       [False, False, False, False, False,  True],\n",
       "       [False, False, False,  True, False, False],\n",
       "       [False,  True,  True, False, False, False],\n",
       "       [False, False, False,  True, False, False],\n",
       "       [False, False, False, False,  True, False]])"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "referenced-vacation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 8, 8, 8, 0, 0],\n",
       "       [7, 8, 8, 8, 7, 7],\n",
       "       [7, 8, 8, 8, 7, 7],\n",
       "       [7, 8, 8, 8, 7, 7],\n",
       "       [0, 8, 8, 8, 0, 0],\n",
       "       [0, 8, 8, 8, 1, 0]], dtype=int8)"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G_ = G.copy()\n",
    "\n",
    "G_[indgrad == 2] = 7\n",
    "G_[:, indgrad == 2] = 8\n",
    "G_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "id": "canadian-mitchell",
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = (indgrad == 2).reshape(6, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "id": "portuguese-facility",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [False],\n",
       "       [False]])"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask"
   ]
  }
 ],
 "metadata": {
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   "nbconvert_exporter": "python",
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