Introduction to Machine Learning - 3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 10, 10, 10, 10])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full(5, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty(7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 4, 1, 3, 2, 4, 1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([0, 3, 4, 1, 3, 2, 4, 1])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 2, 3, 1, 4, 3, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 4])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 2, 4, 1])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[3:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2D arrays "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some Vocabulary\n",
    " - In NumPy, each dimension is called an axis.\n",
    " - The number of axes is called the rank.\n",
    "     - For example, the above 3x4 matrix is an array of rank 2 (it is 2-dimensional).\n",
    "     - The first axis has length 3, the second has length 4.\n",
    " - An array's list of axis lengths is called the shape of the array.\n",
    "     - For example, the above matrix's shape is (3, 4).\n",
    "     - The rank is equal to the shape's length.\n",
    " - The size of an array is the total number of elements, which is the product of all axis lengths (eg. 3*4=12)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 5)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.zeros((3, 5))\n",
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.arange([start, ] stop, [step,])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,\n",
       "       34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66,\n",
       "       68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(0, 100, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.linspace(start, stop, num=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
       "        -9.19191919,  -8.98989899,  -8.78787879,  -8.58585859,\n",
       "        -8.38383838,  -8.18181818,  -7.97979798,  -7.77777778,\n",
       "        -7.57575758,  -7.37373737,  -7.17171717,  -6.96969697,\n",
       "        -6.76767677,  -6.56565657,  -6.36363636,  -6.16161616,\n",
       "        -5.95959596,  -5.75757576,  -5.55555556,  -5.35353535,\n",
       "        -5.15151515,  -4.94949495,  -4.74747475,  -4.54545455,\n",
       "        -4.34343434,  -4.14141414,  -3.93939394,  -3.73737374,\n",
       "        -3.53535354,  -3.33333333,  -3.13131313,  -2.92929293,\n",
       "        -2.72727273,  -2.52525253,  -2.32323232,  -2.12121212,\n",
       "        -1.91919192,  -1.71717172,  -1.51515152,  -1.31313131,\n",
       "        -1.11111111,  -0.90909091,  -0.70707071,  -0.50505051,\n",
       "        -0.3030303 ,  -0.1010101 ,   0.1010101 ,   0.3030303 ,\n",
       "         0.50505051,   0.70707071,   0.90909091,   1.11111111,\n",
       "         1.31313131,   1.51515152,   1.71717172,   1.91919192,\n",
       "         2.12121212,   2.32323232,   2.52525253,   2.72727273,\n",
       "         2.92929293,   3.13131313,   3.33333333,   3.53535354,\n",
       "         3.73737374,   3.93939394,   4.14141414,   4.34343434,\n",
       "         4.54545455,   4.74747475,   4.94949495,   5.15151515,\n",
       "         5.35353535,   5.55555556,   5.75757576,   5.95959596,\n",
       "         6.16161616,   6.36363636,   6.56565657,   6.76767677,\n",
       "         6.96969697,   7.17171717,   7.37373737,   7.57575758,\n",
       "         7.77777778,   7.97979798,   8.18181818,   8.38383838,\n",
       "         8.58585859,   8.78787879,   8.98989899,   9.19191919,\n",
       "         9.39393939,   9.5959596 ,   9.7979798 ,  10.        ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-10, 10, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.random.rand and random.rand.randn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.68076381, 0.66950138, 0.70204864, 0.77090318, 0.50351903,\n",
       "        0.32740176, 0.20130553, 0.64916704, 0.24720799, 0.90666457],\n",
       "       [0.28122374, 0.85710961, 0.81241079, 0.49374773, 0.46257895,\n",
       "        0.66024162, 0.0680719 , 0.59394141, 0.50147748, 0.10631749],\n",
       "       [0.94033594, 0.32513595, 0.24641649, 0.50776457, 0.58386121,\n",
       "        0.8903366 , 0.08590668, 0.31122996, 0.71874702, 0.11281779],\n",
       "       [0.98787115, 0.37721684, 0.2442322 , 0.72114373, 0.62763739,\n",
       "        0.09427322, 0.34548982, 0.89914035, 0.23224066, 0.24225256],\n",
       "       [0.95896589, 0.50339153, 0.78766319, 0.25367457, 0.95498622,\n",
       "        0.67386832, 0.13962875, 0.03295382, 0.63223609, 0.03707133],\n",
       "       [0.64755503, 0.92789615, 0.15892016, 0.8222263 , 0.30404551,\n",
       "        0.52555307, 0.87886925, 0.94192646, 0.34356823, 0.28705004],\n",
       "       [0.08818526, 0.02490175, 0.71200947, 0.05333841, 0.05112491,\n",
       "        0.18633797, 0.74262129, 0.85691335, 0.22179628, 0.06167606],\n",
       "       [0.03247855, 0.8111966 , 0.65750908, 0.27330152, 0.31863484,\n",
       "        0.68881952, 0.13918096, 0.14446222, 0.69881037, 0.74470818],\n",
       "       [0.45983252, 0.94237078, 0.54967626, 0.16103033, 0.46008198,\n",
       "        0.29867309, 0.30542919, 0.22263516, 0.68152128, 0.04296581],\n",
       "       [0.69208444, 0.34391257, 0.65353671, 0.3100245 , 0.3983442 ,\n",
       "        0.7746843 , 0.21286336, 0.02414985, 0.52329906, 0.99284211]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(10, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": [
    "plt.hist(np.random.rand(100000), bins=30);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.40854997,  1.36831626, -0.37289642, -0.91405467, -1.53116674,\n",
       "       -0.74402301,  0.6067642 , -0.06674025,  0.73953331, -2.04039227])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": [
    "plt.hist(np.random.randn(100000), bins=30);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.ones((10, 10))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_reshaped = x.reshape((25, 4)).copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "x.shape = (25, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "x[0, 0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_reshaped"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ravel(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditionals "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.07632474, 0.04238208, 0.42445023, 0.23697301, 0.03498591],\n",
       "       [0.72851187, 0.17066726, 0.00478761, 0.55844777, 0.13440974],\n",
       "       [0.65771989, 0.99342262, 0.73306164, 0.33822265, 0.8608125 ],\n",
       "       [0.95471199, 0.51477053, 0.16172291, 0.12982576, 0.28919485],\n",
       "       [0.39684468, 0.76405821, 0.70248555, 0.85501762, 0.66054196],\n",
       "       [0.76886514, 0.47567771, 0.36694464, 0.26902088, 0.45817964],\n",
       "       [0.12803781, 0.84063102, 0.91112911, 0.15619146, 0.87356605],\n",
       "       [0.88650494, 0.25778059, 0.85973981, 0.46415125, 0.73844464],\n",
       "       [0.63317545, 0.52990894, 0.22001314, 0.67173202, 0.18528726],\n",
       "       [0.93050189, 0.98286719, 0.30626011, 0.45688792, 0.17722499]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.rand(10, 5)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True, False],\n",
       "       [False, False,  True,  True,  True],\n",
       "       [False, False, False, False,  True],\n",
       "       [False,  True, False,  True, False],\n",
       "       [False,  True,  True,  True,  True]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.03070928, 0.18163146, 0.12862278, 0.39536657, 0.10646301,\n",
       "       0.38371109, 0.0799962 , 0.11329527, 0.13195772, 0.01021905,\n",
       "       0.29373289, 0.09286512, 0.33337417, 0.25631849])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x < 0.5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## np.mean(), np.sum(), np.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.16302319, 0.31936485, 0.71664786, 0.41004521, 0.6757896 ,\n",
       "       0.4677376 , 0.58191109, 0.64132425, 0.44802336, 0.57074842])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.81511597, 1.59682425, 3.58323929, 2.05022604, 3.37894802,\n",
       "       2.338688  , 2.90955545, 3.20662123, 2.24011681, 2.8537421 ])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.95471199, 0.99342262, 0.91112911, 0.85501762, 0.87356605])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.max(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
       "       34, 35])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(36)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9, 10, 11],\n",
       "       [12, 13, 14, 15, 16, 17],\n",
       "       [18, 19, 20, 21, 22, 23],\n",
       "       [24, 25, 26, 27, 28, 29],\n",
       "       [30, 31, 32, 33, 34, 35]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(36).reshape(6, 6)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  4,  3,  2,  1,  0],\n",
       "       [11, 10,  9,  8,  7,  6],\n",
       "       [17, 16, 15, 14, 13, 12],\n",
       "       [23, 22, 21, 20, 19, 18],\n",
       "       [29, 28, 27, 26, 25, 24],\n",
       "       [35, 34, 33, 32, 31, 30]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:, ::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "a[3, :] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Broadcasting\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],\n",
       "       [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],\n",
       "       [40, 41, 42, 43, 44, 45, 46, 47, 48, 49],\n",
       "       [50, 51, 52, 53, 54, 55, 56, 57, 58, 59],\n",
       "       [60, 61, 62, 63, 64, 65, 66, 67, 68, 69],\n",
       "       [70, 71, 72, 73, 74, 75, 76, 77, 78, 79],\n",
       "       [80, 81, 82, 83, 84, 85, 86, 87, 88, 89],\n",
       "       [90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(100).reshape(10, 10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3, 47])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0, 4], [3, 7]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [2., 2., 2.],\n",
       "       [2., 2., 2.],\n",
       "       [2., 2., 2.],\n",
       "       [3., 3., 3.],\n",
       "       [3., 3., 3.],\n",
       "       [3., 3., 3.]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q1 = np.ones((3, 3))\n",
    "q2 = 2 * np.ones((3, 3))\n",
    "q3 = 3 * np.ones((3, 3))\n",
    "\n",
    "np.vstack((q1, q2, q3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 2., 2., 2., 3., 3., 3.],\n",
       "       [1., 1., 1., 2., 2., 2., 3., 3., 3.],\n",
       "       [1., 1., 1., 2., 2., 2., 3., 3., 3.]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((q1, q2, q3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3, 3)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.stack((q1, q2, q3)).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [2., 2., 2.],\n",
       "       [2., 2., 2.],\n",
       "       [2., 2., 2.],\n",
       "       [3., 3., 3.],\n",
       "       [3., 3., 3.],\n",
       "       [3., 3., 3.]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate((q1, q2, q3), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [5, 6, 7, 8, 9]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1 = np.arange(10).reshape(2, 5)\n",
    "m1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 5],\n",
       "       [1, 6],\n",
       "       [2, 7],\n",
       "       [3, 8],\n",
       "       [4, 9]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dot Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix = np.arange(9).reshape(3, 3)\n",
    "identity = np.eye(3)\n",
    "identity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 4., 0.],\n",
       "       [0., 0., 8.]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix * identity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 2.],\n",
       "       [3., 4., 5.],\n",
       "       [6., 7., 8.]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.dot(identity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "identity.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 2.],\n",
       "       [3., 4., 5.],\n",
       "       [6., 7., 8.]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix @ identity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 5,  7, 11],\n",
       "       [21, 29, 31]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix = np.array([[1,2,3],[5,7,11],[21,29,31]])\n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.31818182,  0.56818182,  0.02272727],\n",
       "       [ 1.72727273, -0.72727273,  0.09090909],\n",
       "       [-0.04545455,  0.29545455, -0.06818182]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linalg.inv(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00, -1.11022302e-16,  3.33066907e-16],\n",
       "       [-2.22044605e-16,  1.00000000e+00, -8.88178420e-16],\n",
       "       [-2.22044605e-16, -2.22044605e-16,  1.00000000e+00]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linalg.inv(matrix) @ matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43.99999999999997"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linalg.det(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvalues, eigenvectors = linalg.eig(matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalues and Eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([42.26600592, -0.35798416, -2.90802176])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.08381182, -0.76283526, -0.18913107],\n",
       "       [-0.3075286 ,  0.64133975, -0.6853186 ],\n",
       "       [-0.94784057, -0.08225377,  0.70325518]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Mv - \\lambda * v = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.66133815e-15,  1.66533454e-15, -3.21964677e-15],\n",
       "       [ 7.10542736e-15,  5.52335955e-15, -4.88498131e-15],\n",
       "       [ 3.55271368e-14,  5.08620923e-15, -1.02140518e-14]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix @ eigenvectors - eigenvalues * eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular Value Decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0, 2],\n",
       "       [0, 0, 3, 0, 0],\n",
       "       [0, 0, 0, 0, 0],\n",
       "       [0, 2, 0, 0, 0]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4 = np.array([[1,0,0,0,2], [0,0,3,0,0], [0,0,0,0,0], [0,2,0,0,0]])\n",
    "m4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  0.,  0.],\n",
       "       [ 1.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., -1.],\n",
       "       [ 0.,  0.,  1.,  0.]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U, S_diag, V = linalg.svd(m4)\n",
    "U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.        , 2.23606798, 2.        , 0.        ])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S_diag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.        ,  0.        ,  1.        ,  0.        ,  0.        ],\n",
       "       [ 0.4472136 ,  0.        ,  0.        ,  0.        ,  0.89442719],\n",
       "       [-0.        ,  1.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  1.        ,  0.        ],\n",
       "       [-0.89442719,  0.        ,  0.        ,  0.        ,  0.4472136 ]])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$M = USV$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4, 4), (5, 5))"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U.shape, V.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 1, 2, 3]), array([0, 1, 2, 3]))"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag_indices(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = np.zeros((4, 5))\n",
    "S[np.diag_indices(4)] = S_diag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.        , 0.        , 0.        , 0.        , 0.        ],\n",
       "       [0.        , 2.23606798, 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.        , 2.        , 0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.        , 0.        ]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 2.],\n",
       "       [0., 0., 3., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 2., 0., 0., 0.]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U @ S @ V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_coords = np.linspace(-5, 5, 100)\n",
    "y_coords = np.linspace(-5, 5, 100)\n",
    "\n",
    "X, Y = np.meshgrid(x_coords, y_coords)\n",
    "Z = np.sin(X) ** 10 + np.cos(10 + Y * X) * np.cos(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x22233e51ef0>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8))\n",
    "plt.imshow(Z, cmap='Reds')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Augmentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Read Images\n",
    "\n",
    "<html>\n",
    "    \n",
    "   <img src='images/cat.png' style='width: 400px;'>\n",
    "   \n",
    "file: data/cat.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "img = plt.imread('images/cat.png')[:, :, :3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8       , 0.74509805, 0.69411767],\n",
       "        ...,\n",
       "        [0.54901963, 0.44705883, 0.34117648],\n",
       "        [0.5764706 , 0.47058824, 0.3647059 ],\n",
       "        [0.59607846, 0.49019608, 0.38431373]],\n",
       "\n",
       "       [[0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8       , 0.74509805, 0.69411767],\n",
       "        ...,\n",
       "        [0.54901963, 0.44705883, 0.34117648],\n",
       "        [0.5764706 , 0.47058824, 0.3647059 ],\n",
       "        [0.59607846, 0.49019608, 0.38431373]],\n",
       "\n",
       "       [[0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8039216 , 0.7490196 , 0.69803923],\n",
       "        [0.8       , 0.74509805, 0.69411767],\n",
       "        ...,\n",
       "        [0.54901963, 0.44705883, 0.34117648],\n",
       "        [0.5764706 , 0.47058824, 0.3647059 ],\n",
       "        [0.59607846, 0.49019608, 0.38431373]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[0.19215687, 0.14901961, 0.0627451 ],\n",
       "        [0.19215687, 0.14901961, 0.0627451 ],\n",
       "        [0.1882353 , 0.14509805, 0.06666667],\n",
       "        ...,\n",
       "        [0.8862745 , 0.7764706 , 0.7294118 ],\n",
       "        [0.8862745 , 0.7764706 , 0.73333335],\n",
       "        [0.8862745 , 0.7764706 , 0.7294118 ]],\n",
       "\n",
       "       [[0.18039216, 0.14901961, 0.05882353],\n",
       "        [0.1764706 , 0.14509805, 0.05490196],\n",
       "        [0.17254902, 0.14117648, 0.05882353],\n",
       "        ...,\n",
       "        [0.8784314 , 0.76862746, 0.72156864],\n",
       "        [0.88235295, 0.77254903, 0.7254902 ],\n",
       "        [0.88235295, 0.77254903, 0.7254902 ]],\n",
       "\n",
       "       [[0.16862746, 0.14509805, 0.05098039],\n",
       "        [0.16470589, 0.14117648, 0.04705882],\n",
       "        [0.16862746, 0.13725491, 0.05490196],\n",
       "        ...,\n",
       "        [0.8745098 , 0.7647059 , 0.7176471 ],\n",
       "        [0.8784314 , 0.76862746, 0.72156864],\n",
       "        [0.8784314 , 0.76862746, 0.72156864]]], dtype=float32)"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(563, 750, 3)"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "invert_cat=np.zeros((b,a,c))\n",
    "img.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 563)"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a,b,c=img.shape\n",
    "range(a)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(a-1):\n",
    "    for j in range(b-1):\n",
    "        for k in range(c-1):\n",
    "            invert_cat[j,i,k]=img[i,j,k]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 3, 2, 1]"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1, 2, 3, 4]\n",
    "x[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x22233891a20>"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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veRWv8YlP8L0v9YHCAss9oN+h8C73gaUhIeLqAOj1eJ/+Evvt7DxB9XTtwAjO1Vo7yQNBaRYmPyAv1QUaJxAE9TMsOjMBfqdZi/zA/4Qmj/alFbxQoGQFXBTMK2kZYF6A9Jza0SAvaz+5dfWvRQj0OCd2nFEtZP2zNw0n75zgOM8Qtjk3hY8WKGYewrU/pf9Mr1uDMMpKP6wFrrsO2N1lzFerka2HPyZ4zidO+fcQR97YL+RZ05h2iDXUIBqAWjcSJeAoYEkMvO0Hgfe/jykCjbysNCYsizp+DJZ61Db9PoUvTYFDR4DuABiuUGuFZM/TtYMlOOFkXVzxm8snZCNQKIKnfxsAsB6y6e+Gl0AFD2VCO6T9APLSxetsxHkIeLijOFw1ypwQ1V7I1F6Ze8RFTWf8c7WUsARTTtSZVwijJDZFIxpUhUjju0on/Y38M0byewv5pA+u8losz0VwKtoE45loGOdp71JIBx1MB37uJAr5uiPA7haQV4RGtqDARREXkzQlFPv+NwHv/wAJnKiZj/zQ/tYlCZ31ZWB7k/2IxG9UJoARSPdDPw588EPA//N7vH6WEo7ZhD4Z54DdGdBNAMSEZ8tLtGv6S8A3fAPhaVUBF84S1u23HQzBUVgWwLNFgzaEPKF/RQ35GvNEQOuICzVGE3ymQhoc3/6+oGX2QIlt07QR7Z9ZuKZOVIVkiwlk7TMZEeyGE7iQDMqiIPM1GlEbVPBQTYUt1DBWwkmUIbQxxyVWaKV2i5sXHIVuM2HRVNNUIjyFkzEWFk+JicQCN17vz3WWz9jNgErSoCMDdBzw+jcBH/4wWpdCWZP50pix0E7qdimApyc07mPHZ6sq4Pgq8CM/CvzarwHra+K7aYB+j3ZLA2ClSwp6OCUkSyxJhuEAePHX03Y6f47njEdCe4dR1ldpB0NwcLltYIDAYpYcE5nNOhkj+d0ArQc+DHPZy7eweK9F2BZCpis5Jvf6u7128PkiyRFee9EuW/SptNBJQvt3dvh7WQssq+EpYbXjZEzSTIQ58RM8hYyN+mwwTw60uThiX9XV5QJe1xzjVmvVwNIKvzt3XoQWFIY6lpRnEYpvfhnwlXs4Qa1Fm1pQFPSr1MbT6wCwukZ2r6z5HGXJ3KBbbwcOD4F/+6s06tV3k0q2aL/LeLWlAdBzwMoaNfahdeDEMeCmm4HHHqfwLw+B7R3CvRg+jGc/7cAIzjNqgtUV1zYugGELGiTUNggm+WX2S6gxIJMy+BuYn/yXxaPtpRkXmgv6oOc0Tn7gtU5ZApMpWa6tLWAypi/DNeIcbbig1IbMoXGEP6k4BLPELwCzlGOTGEKhMuhLG3KjNk3hhcnUvJet+VMEUProIeDYOnDfw7x/L6KhbgFUonnyGjhyCHj4CeDiRYGTETVgaT2J4yrf1zTl/xsbtE/yAuhY4H94O/B/vof5+MlArpNxEmcJBWAgBn+WASYheXDTzXyOugTuf4BEwO4E2NikoKUxBViDRvfTDozg1AurvJOHUO0Twh40nLANMLeKA5gLjIyC6zQghHHB8cqgOMPJ14bJwNtEodQ4cbZdSeMsarb2e4U2hnDHyA1aal2ub+TYWAQgAl94UwnxUHuveS6h9hqOUjlOHmcAV/Lhq8YHVGr4SuECzRKMa6j12gVBopu19oMzaFm/NAGOHAPuf5AawUrcWWNpeHdj+mv6A+Du1wHv+W0fgBpGPbSZsY42Rl0BRw4DZy/wPuMRDfgTNwL/8d0UhlTIhAjAMOX/SYI2sbHXY5+OX8fPx9uEfZvbwOHjwGQLmI1lHBLASEUdeQ37agcicgDwE08F5bLI4KC1Xvnwb5msOhmAgOZdgExhzNki7f10bU82Llixw5/FPJdFf0zbNzM/mVSg41jKGHWJzQcD/iz36eVeHQK9DlfMLAF6qQ+vr7X+WeM1WV3QZspntEXy0vtvnGhuzXkxEW0ppbuNoTBEEZCBkcTf/i3APfcBM3lfUUOhgvOCGjngrW8Ffu+9nNSNoyaoJVXAwBMXymgNh5zko20ACfDOd7IM1Ze+TKFJUvazmAKH1xk20w2cmHEGXH8TS45tXgD6GVBOgO2LwMoycOokWboyJ6TUeVKVhLhP56QO24HROGFrw1iCCa2MEILPF2npKPIBncC8dgiFyzm0jlEAvpDHPgUobIv2yl6a5+nsHu27WzhXnyeKKECdDsdgKgKnGqJKfF59JXCnqXndSp7LNjSea2EZ4XykcCy0bBxTU00m1FQm5qpdVWhTGYzjRH3Fy4FPfkrgoSWEizPCqghAAobCvPBFwO+8l4uZMpFqS4XjEIumSFLghuuBxx8D0g7wj94B/IdfFXgqwaFo2O9sSAatLjxTdvgwcNc3MfZt0AVuvRV46gmO3doK8MRpRkZ0loQxrIBEhF3j4Z41csAY824A3wvgvHPuJfLZGoDfB3AzgMcB/JBzbtMYYwD8OwBvAjAB8BPOuc/vryteG+hKrE3hjIGHXgAu49zLki9TGS7nggkZCoqs7E55aiwIjQpuCB3DPl7tGa7wuVM8r5o10DaLWkr7qYITx5wcSXC+pjAnAqUaif7Vsk3G+gjmNJXVOubqniZeYBSyzmaA2aY2mk4ppCYGIIlmnRh45auAT/0NWrgMUMCiSOwKR+10y3XMdamBNsNTtU23SwG1kjBnYmHeUmD7Eu2du14B/Np/gA/gMCQKBhG17vIQKMYkJ9bWgW/9FuCBB4DHnwCWlqldH3oIuP56YDoBHnuSz22tQNaK9HUt1D8i9nu/i+d+oNpvAvjuhc9+EcBfOOdeAOAv5G8AeCOAF8jP2wH8H/vrxnxbXKGN2B/hZ/Ve5wWqd/H8vbSCxkdpgKEGby4aiPuBc60w7nFcCNdCx6KWW1IBqAKIpenfaqOkKSdc2uNP0uVPmnJFTVNOzKwDDJc5oVbXgEOHgWPHgaPHgGPHiPuPHQOOHmEy1+FDwPo6sLoK9JeBnkCeTENapO9JDBw9DHz2C2hTClIhA4wIo4n4exwDd9wBnHzKF/HIMsaQxZIXE74jC35/660UwP/mrcBff9xT1A2ocSLDfhw6BAx7fFcvfjGwvgp85lM8d32d6Q+znON0cRM4dZ5BolbOj2WBCcOmNFphv+2qGsc591fGmJsXPn4zgO+Q398D4OMA3imf/5bjFgifNsasGGOOO+fOXO0+mqClEcVW8Ln6LDQdWSGcDSfzFSZ6GKcWGvBa/dI5+BRciZxVGyn0lYRC0d4qgGHt9RvM1UNbtHHqxvc5LDIR9rupvG3iRJCNkbx4oA0NqmvaNrXichGyRCCTMTS2FY7p/6rBEPnJorSwBWAqrvrQa8jEXVlj+H6T8/+6ps1hQB9JEpHyLkrgB/5b4Lfe4x2mnZj9uvEGaoTRlIUN05iwsp8Cd9wGHDsEPPpV4Dd/k8lreUXK2ZRAVFOQllfIsNUl8MY3Ap/7DHDTrezfC+8A7r2Xz3XLTcAjD4tPq6A/S6MvytI7VLs99k1tuP22Z2rjHFVhcM6dMcYckc/3Krh+AsBlghPWjj56ZP67r8VYv8w/El4jhFpPA6FU87TXdXsfc3kHMGeHLbbQJ6PCEGZgtjZa468fhrvUFSeW2jTAfBzX4jMnmeD/xEOyJCGUSiNPOliLNjhS7wkAZcYVuSMh+M4I0dAAN98CfPGLUvxCxr6Nvm64kCUpcOfLgL/7O7RRHVkXFJ4OaemdHWBzUzSp4cIVxcDLXg785V8CTUShcYbaM4056SH21a23Atevc/Lfcw+wuk4C4MUvBr58L/tz4y3AQ1+htht0uShojYYs88+dZj7xLRVW7u/LAbrXbfecWs65dwF4FwC86IXGGfhJoifphHaB5tHYsdAOABYEKLiPTsorOTMBtJmiBvAF/0L7xwR90GtcYYB1QqlwtDFmta+rrJAt7GOYj6PPaW0AJSN/PdUSSu9Gkk0Zx9QGXbFdolTShC3anP7F59fr1DVXYSsTVQ35JAG+7kXAF74oOVJioIeTrHWWOuD2W4EPfYSQ0waT8cQhGvPGcfJqHYPYAj/wZuAjHwUeeQw4fBSYbdCG6QiDNpBcmW+6k6E9WxeBzQ3g+FEK5AtuA776IPt36wuBJ58Etrd4Ti+jXyqKpObAKm24NOWYbGxSW2mZ3eeaVTunEMwYcxzAefl8XwXXr9TCF9vCmn0Y44twZ89Ytyscr00hlsFV7rlAXMzdN/hdMypVe5QlV8Ci8EGboYAohFImTQWwnZRGSA+BE3qMA4UlTalxskz8HDGFJkq8rTTXT1mBDUR4jAiNMJFRzHNvO0HIo9mUUUTIpKE+TlI7yxL4kbcBf/wB4NAKox2s2F+TKZ2l3ZSVZNbXSDGbGnjL93PSX7xA26yqJLU5AboyJnUOvOqbmfT2lS9TGI4dBo4fI3R7/BR3HLjtduCRB+YhrfqHTAOkXc886vxqwDFragr7ftsz9eN8AMCPy+8/DuCPg89/zLC9CsD2fuwbYF5zPJ0z8UptHzL29NfaB6wLr7MXYRDaNG0uS+XTkGdT+lFy2QFAiQEXCI/aIjrRwzSEUkPrAxauFTq1XeAnv/YvTJdo+7jQ35atNPPQsddHm8sfCl8WE0alKe2El7wY+KM/ovMxS0lAHFrjd/0OJ3hs6Xe68XraRd/zJgAOOH+eC8Tqsi+fu9SnbZRa4Phh+mwefQi46QTjzdZXOFabm4wsuO0FwMMPS1hS6Z+5FM1eylhpNHiS8J3EYvsYK3T9Pufbfujo94JEwCFjzEkA/yuAXwHwB8aYnwLwJIC3yuF/ClLRD4N09E/upxMO0ungZbe+DTW6rzCp2yr1crx1PiZLI6NbIqHhjwNah5wBLqsyY8x8+D7gYVxLjWt/wr4oASDOwDY1uWKAZjmjUVw1XOGiiKthKpX7k4wrMoScmIIvNYYwbwVTp6PYe/YbJ157S8PeRFLZxXmCoVZ4Cy8sFcSnohHZBTDNqQmmEvT5mtcAf/anXslaGe/IENZlEhoTJcDLXgJ88IMMcVk5BnR2uZJfugTcdB2wtE77af0wx/H7Xg+cfoKpCKYhQXDdGheW9VVgmADjDeAnfwp45FHgycfl2Bi442aG7+Q57aosBR64X2pNC9wsKjo4G9Ceq+R9mIwCub3LZzh6jMencs6zZuM45374Cl/dvcexDsA79nfr/TUVIHWKztUTE+FQujq0S1rjGfJZMCCa3DZ3jwWf0FxTI15mj9NrtheQe0lkshHhdCWPr5yE7Bf80S0wEvGtWPGIJwknhpI7SYO5OnONkTB4gUmxjEskpZbKgkJUyue6GIWaoqXEG786l0FxjtEufSyNAT7zGe94VpYutVwIsg4Zr6gBfuLHgHf/XzTel5boRxl2PSFy5CidlFEM3HAjw2jOngVeeifw1FPUajsjYGUFWBtxHLoJcPe3MCBztEt7ZnUFWFllVLM6LFdWgSefoK/GpR56KtTV57URg0a7fUlxaAgJlRrXtPXnXeRA2OlFewEIHIcA2jwZoK2OE8uEbnD5AKhAmQD2hNTjnJYLfm/jqeQ41TQaUKm/h/dxAtHaGnGNt3cmE0nUqrgaWwvA0haIY8lsFG1nndgcck0F1cWMRIFOjFjOKWofGVAIS2YtEIthvBgJXWrmp6QsVAWwMwbGO8B0zHD7rS1h0QQHJwmjAqKYkQJ9KXLxnt+g4PeX6DNaP0Tj3Rhg7TAFopfwOjcOgPvuBW6+GZhsUwCvv57hPZnAuiOHgW/7VuD+eykYwwG18q23AQ88CGR9aubpFNi4yP+t5aI1y5mo1un4TNEk5n12t1lAvt9jaE+/x8VjOfYZpvttB0ZwFpsLJuxerWlwWSR0GHHQ2iDhZw18BZqrrC5h7FgrRMYb2nsxdW2VG0j2YQKYglqyqv3uZFUDJFUghAZzmaPtDnK6aDT+xc5mpGwbR7gXC3MVK5lixX8CTyBYizbyWQmL2nkts7XJCbS7Szh41zcCH/kw6OtpPGFS14yPU2fnYAC8+U3Ar/1HoLtEh+zqCoUp73mn7NISBS7N6GDdvMS+bVygLTSa0gbJMuDYCeCN30VC4tbbgXNnKAh33AE8+CD70elQoMcXyb45x3PjCIgkGU+riMYx7a5CKvcow9jt+rJSJiD8hDOfAAAgAElEQVQ+npf5OM55ulWFoBWARYEAWm1grGQjgpqghg/ga1OmwQFrgsluI7E17LxwqH/BLgpOcFy4I4JeD+D1GgM04mSLI6AjmqtqvG+mjmWFa8DksgqoxPeiqdORQEgD7jo2Lfj39hYnWtPw+tsb7O/aEaArBu9sBnT6XlCMk2Qz3Xmg8RAtn1CAjAHGu8CHP8R7RjFtJSN2W7dLv0xsGPX8mlcDX7kfWFrls19/HQMuOylw/XFJgZZdAPoDXn9nG7jpJuArXwFuuIF5Mtsj4LpjwOYW8PJvBk6eB07cAGxtAGsnmEdz7iLHpd8n3K0mhLUVgCijEBcT2jtVCdiud5pOpl77uILERl5RSzbiZO73vP26n3YwBEdXWlw+IdtDAgwaCk54DciKayAxUoLdNBKg3c7QemM/Uj9H4JfQvxc1C4K+XfZd8AyoPHWscC8S9qsQ/4XWNu7Cs3D6nIrNlTYtJXZsc1OihiW0PzKc+KlUpiwKwhKI4G1v0tBPEiEnZAcC1XR1zX5mYmCXJfBN3wh8+m/QRkznCoOUQesSFq+vE2JZA6w/RdLj2DFqlOGyf1caY6eFCAcD2izWMpKgqzsHALjj6+jLGfT9+77pJuDJxxiZ0OlQ4517jFqsK4GpqaHQGEPKuShYnuqJJ8jspSnHXbf3AHx0xWDgQ5qA55vgBG3Rq962et7uAJ5GwOCNacCzQImEnpjIT/wo8qtrS0lbXKZV5jQPFihf0Yhz0QDw/Zy7lwhQW2pWNFQbUVB7WFZIWvN4BOzuABvbQDnmqruUceXPQVuo35NJnfD3uktGyzjCr07GMVGYo9sVKqU8HXMlP3WS8WuR5e7SaHhMVdPuGnRpzB85AjzwECf58evZ38NHac/0+2hrrxlLwdFnVsp8bU2CViWX55Zbga9+lRO+1wd2N/k8p55kn6uCMWpPPcVjxiNCvyqnz2c8pt1lDDBco33WE7Ji4xLHUctEjceMrh4MfOqGprQ/v8iBBVJgL6pXYZT6PHQLidAOaIt0gJg1sZ650ghjjRZu8b/xuDesPdYSAcFPg8v7p2SFEhDhvjuAZGiKYBntj3j4wxpeyvQ4eB9Qm99iOEHjiJomS3yWZCxsnKYd9PtksPKcBcWLyvuA1LkaRlcYI1VsVqktzp2hEOUz3i81nFiXzgPLy7zX2irwylfTaRknwHCJz60JZLEIRJIGUQly71J8KOvrhHRRBFx/guH/WUyBakDBfPIJ5tkAwE4OnD1POnvnEu8XRcDGmM/Q6XiYPx5LblHmx3B56ANOZzNg/bjEqnV5TqezgCCu0g6G4AQwbK7GmH7tAj+O/KNbeGtTIWjAFTyNJHQkIWsVJd4bngBt9ZUIXn1r6SilX9sbivHYCkxwX+1PaHs1hlBRSzE1gVB1ZcXvSomipMPJ55z366hnvirEwE74gvOcLJtNaGtowb9EoEZdcXL3ukDdB7pjhpdoXWaAmsQ53ltJg9mMNtnOhJO/LfsLRiGnEeAq1iRbWga+4SUUmuUVjmenI+9I+tntAhDioi2Ubv077nREsOT3x5/wMXJpJqFJpUR7J8BgSA3jGlkEu4AtGC2Q9aX/EpqzcZ73STK0RUyUbdNSVfrc6ijVRTT+GqThYAhOAKs0+DD0dGu+hu7wNeftFqMXTpyBJnDQSR56mnh8q5sKtXYNPMFgVTgE7mktA9Uq4R44IWunn9c10FaRqfhiZwH06mWETEnCWl5JjPZlQih160R4pABFVbFaTNoB+g1tnU5KYYFBW1Wm1+Fz97reN+EcbSjdm7MUZi3OeJ8sE+IgErh2lv+XArOWl9jn2VgKDW6RXj5xgrFm3S7HzWVkrTo99i2LJRVdIrpji5a2V+2TZXy+6VjGzAD9VY5nElMQVtZom+3skhhZO0pbyjiSA4DYJgkXwO1tar9Tp4CB5XsfjRhZMBOSpCfhPMWMdHokdm5RS0Dq80njhPZMmBOhmiCKODAtZGq88FQVgCjg4UU4ssxHvy6G1IdC07ZQo4nGWMw01XvrZ6Ehr4yg+myU/tRKNZH4a7pdSfiSyRr6gfTaDbyNFZaT0qLgSmw4FTI5ToM7EzGGlR1MEikrZSR6OvMaPI68XZWJhlgesqpnZAnLZj36d5IMeMELgd0pNWeWArDCFDqfTTpH2QsyCOunZRk/z4XhsxGZuUaS3HY2OfSrK8Bjj3BCH5KIaANqmLykLfbUGWZ3bm+z/3lO4ZhOgNxSkMdj0e4pMJ5wnNYEJmqfongPu/pp2oEQHGv4MDrYYZzW4mdt8GPNyW0lCSxuvAe4IxMoTfxkC38Uhsw5XRecX+EYttotsEEWhUVhme5iVubc4ryYeodrIgxTrydwUiYeIHS02CHq27GB8Og1JmPSw1FM28QI5ZqKIMZWQk8SXleDGq3jGBuBdYnEaMERMm1uUhuWObVbKkTG2jpX5TNn6YzMulKnLKVT0cQBo5WKX8kQ2un42mBxgOGCVohjNncC+WJS1vmE9x32WOUmjqkZOh2OUV0DF56SLNIphfzMKbGfchr8G9ucA2VBenw85vGV8xVtdndJNugCqMU+nlcax1o+oDJPiolDwQnDUXXCVg1XxapBW2+5gRjMYsOohgkNP3VUzmWKYv76+r/eK9QuykiFjkn9fTbzRQTzKW2HxnF11kBMxdT67CHkVJyt5IdqXRWgThKUMgIAgV5pLDn/qpUMJ89Mn8MQ4qhBnliOqWtI6Q4yAAYYV3wX3YRjuryMNs6tqqnJllckTi32NLVqM12VokjIlJZR4TU00gHBomBAW08DXvtdjh8a8cklgK3Z/8mYU2FlHdgdA9MNQsPJBEDEe3R7FNzhkIG1VQlMHNAZ8h1UUie73R0igP37lJuDIThqMOpkioThigJGSwf+Mn+O2AWlEfwMPzGVAAgpZR2cxco02kLopf+3BSYQRD1rnk01D9GmOV96rfvOCBRRDaiTrKpk/ggRYAzhRdOIYSte7LL0Ph0dG63ZrFVtipwUbgiRbDBRG1lgIH9noo3aslEzoNOllmoqb7ibPlm6oqAAZR06XzsCtVqbU+BgFHvNHTqxOfi+/1oaV3eHThPaMcNlarStTckOlWsVQpJAxjKTuVIVIjAVoVvUUJNa0IaMLHfNns7I1hkjfqzUO4KbBu3GWWHh96u1AyE41hIezMExCCvi/CRQOrrVFI6DpNG/tUwEzeprryWCV0OwfT1vo7SQC2jz/UMNE2qW8P+65kSr5Fp5UOu5zhkNjQaw4tCzqZAfEQCpHlMW8ig1z8nF1igBv8tyIatjJcICaoM8Z9ClA4Wn3xdanbclzSqCqQuIpk3rjgaNo+c9AhDnQLRECnvYF8o8Zl5MBE621VVh8jIRkoaMnY34uyIG8Q60qrwBNWIt/iAtEt/p0lEbWyCLGOyZCMyKE2Z3uprQcVZyTOOEE7cWO2zpMLCxA9x1F3DqKcak5eIItjHtzaYBBokIvSKHipU8u1K/QB3j+2kHQnBgLp/sc85GAHASDRB8b4NkMKWEAb5QNfZCAQHQbuEdCsWikNS1CGQ9/5kKjGqhMBmtqdFucQ5NeZa+aOanevZdIxO+Jkum/o26oBCOYq68U0sBSVR4OhQA60RAc2DsKDBO+qfRE6HPJrbsj7XCIhkfZuQcoVkp5/ciUr1pJvSwUOXWkMa3CsMaTzC0r9H4sdBaD+1iKO/RwVP7NvLvo9enhnYyoZuKWqcU7awafjIRjSgaq9uhtrnjRcD5i0w3qGvOjTRlpMVwSNtyuEQNVEg6wmxGOlvtQC2FtZ92IATHYB7364ftixBI0u5tqYIDoaBFYyTWaw3dtl1zUgBAS+PsJTC1ruqBTbOolUIyQAWnvZ5EPbuSdo1r+L8BEItmKifApOZkbKQC53gk2mpG2lcjl+MMDNlxwFRCbMpU/D9WaFzxD5U5tV2Zo41MiCOvqU0w2dtabZYrfpqAmz4VgNPYrciH7bfGfSMGNALoLGOiAmCsH2s9RkkYNN7O0njAuqFA9Hp+nOOYYxNL9HNe8LM890I3nQK7BQV7WgFf/xJqrV7GbNJjx4BTp2n8b29TSw4GfN6NHWA24tjiNHDsepIHK6tf25w9EIIDoHUAtk0YrHZPToBaxfjjF7WJet5V85SlhyjGzB8f1gJoX2wgJGZBYFohE02ix6sgaZJcU8l3kgNSC/Y2ooV2p4QLdcmJNpkAMGSTCtnIyVggGcCnA9Syws44iSpHIZEhQV17z7mruD6kqaesjWiYChIzJ2MSAXPRElrcI2rQ7imjtlGtBr0KY/AOAK/dQi2jERV1IxBI2Ef9uiWAQgTg5Hh5RiV3CiFZ4sQHrh49BnQkeHQwZAzcYOD7srbGkJxOh/4cTcXWbRBrULA6Uuet032eaRyAg6R+B3WC1sL/q81hnTBoMomrGm3krm5bEVs6s5wVskCExzkfUQzM2zZ1zclSK9SrAQi8CanVSvrUlpU1tEVaWFej3ZtTq2j2urQTHCgY+QwoI0IjF3P17MZ8wbu7/FxLFTlJW24LrNeAG9BhFzcsxq74ZzqlU89EQNcBJuNzxyYw4OWnJQWULoNASCcTS/IS2gVD3pGW0HLG25axTHoTo91TSANtrYxz5Dwzp3Xrake42vrFVHsXfF5NG1FipcgZuX3uLOPhKgd0pRhhWQEnTxHe3nA7cO4cA0iThDZjNQIOr/FdzHZZQ3p9nf4iUwOTHrDTpzbf75bkB0ZwqhqIhBVTvO4cMa5qgEpXeHgjvhFmRndhbqvhNDQkXcOJ1gpKAM8g19EU5CY4t669oehqv0IpJtc+qVCHq29dot3iIpIYOVfy79mEq+Zs6p/DJkA55XnFDBgZQq1ugrY8b1Hy+YoZkC7zWnnuq3FOdoHpMp+1gmfqNOnOIXAiOz6Tif1YzAW1iobSeLm21h0EHTZo9+mpRMMoNFZN1DqLW4nhWNmI9pqD1zQaz6ZVNlt0ALQb2nY6DPA8dEjed0GNUkpN7G4EXLoIrA1pE66vAfd+hXbN+jJtnTNnJOTG0a/T5AwCLXLaPvXzzcZxjpNmKjjaAYALNIABdF+XRUO+KfgCchGoUoTAdjigisGr0sMaa6lFALQZmq4JBEdXWZ1UjRecRVLBygt2kCiG2k9CK/ZHmYsAiGE+3qYgqLBNBQLWQjDsbMm9c1kFpWBeXdIpmGW+BsGslJfYMH/FWKB3iLFZCSTODH71Vu3sgLY4eyT0dGi3NI0Ipp4vfp9K+p3GHK+q9CEyAJid6ry9qkUVm9q/ax0LTSwrCj5fIQIVJ8DuSOCkkEZVSSGoa0Z/G8M+1PJ+bMPP19eYQXrmDANFowi478usitPUFPivu4PjZWLg9Gk6UdcPMSJ7v+1gCI6s8HlOdaorYCMGZbiC6cTW7S1iI9VfRHBUI1SSTx/F834W3dVL7SHl8ENBRTMvOFrsow4ERs83cq4KDMTojSPCBNOIISz7azbC9kzF618Usq0fRMNWkmSluTUJYEp5NueT1Cqho+EYEQCI/0giEKwl/FRfSmjHQTQlrF8Y4pgwWNklWIG9Ei5kpMRSVdGJqslxkH7HAr9Q81jN53HwAqDjHkW++owxFEB9fmO8Fo8iplPXlWdJo0jCZ8RvZHJq36JkAGp/iX1fGvPeDz1Ep2l6QmLZhrI4yzs1oDN3tIvLSh8/Xbuq4BhjbgDwWwCOcejxLufcv3s2C69rhctaPLwa46QBgUUJROIAc46YWeEVYoETjV/FopTQDxChLLy9UleBAGJeezT68lSI9PPaf98ej3mhan1LjY/ctmCOS1PI3/qMOdrs06rhnpudzOfnRBG1wtYYaITZqsX2mU4YmuJKXgvGb3ibdqndZjP6RLSv1sp4AVDaXhceTTfQSavp1TYRZ2HDqGg17JsKQMrjNWymkrEsKqkCKouMdWKCqRav0S56gB+3KPLCruykRlw7gVUXL3oneSp15KrSExHHjzOgttNnREGR+1jBtTXOg+VljlfWYcGPyS5w3XGyakXlNfJ+2n40TgXgnznnPm+MGQL4nDHmwwB+Aiy8/ivGmF8EC6+/E/OF118JFl5/5dPdoGmIMW1EIzdJZNUzFIKyZsUX1TpNOOkTsT0kSapWr7TAr6r0CVSqMcoCbf1opbnF/uZ1xY8TbknRQpja2w/OCTkgk84GgmxqxqrVOckKjUK2lmnLtpZSTAX7OJoxZ18jk+spC4XHltCl9TXUwMZpwpDdCdpktLoEBgUhzvKQ/UotUEcUvsgKrRwIumriWpyFlaOwAISAtYxdloEpxxIc2tRoCyWOxz57VB2IKiBt2S2ZRUa0koMIqkVb8SdMfIMlHT+bSY2DhhB3uAKUTpyi8hybFzmuhRO/UwxcOstxG/SBW2+hn+fhh7mYuIq1sbMUePg0q4uuLJHVVDfCftpVBUcKCmqd6F1jzP1gPehnrfD6bMIgwyxDS0c60SiZaJ+8QFuZEZCVTI7TFRnyQjQ1WT2muqIW4qXXYyFGrRa+aHTlrdHm/WuFF72Hrsya7KY2UkixasXOyYg09FQZo4BeLSVRzImAa5jN8pJM3kayQxu/m4EW14gdV8+JhNaX4gsZzej9n81YmFzhpZBhqKR8lGrVdpsQ8d8UAdQD6FHf3pa0jAxIA/tSQ1Z2dthnDZIsCk8yWGHg5ornB9q+KsUOlPCjSARJF77hUN4vOLl3d4FswHPilMLQ6zHqxDn2Y7zLaOknHxf7USj+fpfv1Uas3wBD5tF2AdPh9iEm8kjlau1rsnFk14KXAfgM/isLr4dF15cHwANfEsYkoZG7ssR5f/goMFgWFkcMbiuhKEbZLxcIgPNCFxmJoF1mvJJOxLoEoAlN8rdVOhUiDLVfkdtATGWOZBl1NdpNV9V/0Yi2aTTIMwdmRvL+JSpX0yQmY6/VmobwS5QWN5OtOXG10EVVMR16OgWOHie829wAnjrFZzx0mFBu8xLQLyUuTsKZUFHLpgJXq1pKTTkf3q/bttc1Iwe2NmUl7lNzFQXDgSa7HNtzZ+V88RnFER2zHU1FFhqu1eABW6qQUGsRpOn8GFrLhbSQyIqdbfpqopiCdOkS30Wnw/kRhkmVJT8fjwnhTp/m+D/6KHDzLcwb+sTfAieOc7DVCZuknkm9Wtu34BhjBgD+XwD/xDm3Y66cY7rXF+6yD4Ki6ycOGZc6oJ4Ag1Xg9C5w6Rwn86ULTJftCtU6lBTiRKJsKylaoRpFnW3KkJW5r9fcBmYWVOW5FHpQgaltYEM1woYZrrYA4GKPxTkmFFq1aZoCQMn/lVLPa9o5pisEgUwEndQayj7LJfxD6qYhoq9ha4uTpj/gROokXASmU4babG7QP7U1Jr5PIi4WxgKjHqFuFJFBghj3jficdCe3RoIkq8IXteh3OdH02SKgTYhDA1zaZMBnKtmoqmmNoeBofk9REhblUqTEGW8zxgJvEysa21DYyoIhOOp/mhUUDmsJ/2pxgK6uyoKSy5xI+QydjPNouEp7Z7jCoM/VVfbl0UcJAbOU7/jiDuHgobUrzN492r4ExxiTgELzu86598nHz1rh9SgWSCar4eEh8Mgl5mScepSbna4fAx5/nOp0ZZ2xSVFEB5iRiVZOeL6VhKXMUoPlYkRrYe3GkamqKgY4OtBIjwUKJhKGohmdaeIZl7Zav0Eb2aBxc2MpW1TO6KlWvF5X1D6jMSd244CoC9iKuDqLWYgvS0mjOyeTMGLE8O4uq+qvLpNlGm0AjzwB3HCck6qfAPWMQjcysrOZOEd1S/O+5O5DUh9mpY+hM4bjNdrhyp12uUiUksGa7UqBPwdc2CRUnI35M7XAYIl9O3VWyjQVQG/Ia/ZTv1GtagUIdNPtOzSduRD3QZp5LZ8kYutlPpENYH+ULIglyHS0IyW0DFMIti8Sicxy4BOfBA4vcTG6tEWNvbsDLPdoC8FSi7nLlvi9235YNQPg/wZwv3Pu3wRfaeH1X8Hlhdd/1hjzeyApcNXC63FMPF06apV+n0bboEdHYZaIoV0wkO+Jx8jVV2KkDgZcgdVzXdcS86ROTDcPEdKYeNop9JOCF4mMhgUN+kKCDtMULS1uIc5IEbxS2DxXE18bYfiKQvLc4SGhQroo8itwFNEJ19S+VNFkwj67hsI0NhS46ZSQYpYDWpVEnZgKeTT8ZnMHOC/aOusIAwb2bzxmv0uBibsjXns8Zn9WDtFGiFPG0q2uCPVtqPXOnyLM29jgSu4APPhQUKAjotZst0GHh72QxbH110lrXQROMkSNJzDU9zYYsB/nzlP419ZE6FJ/ngW17JmTRCJbl4BHHgJe+mLS9vfey+usHQImm+zPygqLI453fbT61dp+NM5rAPxDAPcYY74on/1PeBYLr2sAYqoriAWOHuVEznNCkDgDjiwTzm3u0tPuaqCZEKZUFfecnImG6PR5fgT6hqIYKC1V+Wwk1K2oddf4+gSNMDhNLZRvAaCmvZXPeM/JhPbJbCaTYwayUgUFdTKh0VwI5ZsKIZCkYuxaSTt2koSWAKkW70g8EaH/ry8DM4FcozFXyGLKsrKdiM9nLSdGlnLlPLzOLc/HI0YQl5WEyRSEejOBaYlolkqgmokJWR75KtDTFb/gtoiPPcZzNi7SSVvVQhJU9IOkHcK0wRFq3KTL62q0ufpNNBI+smh3J3CQhLWGi4TumhZngG4xmU9p8zURcP0tXqgaQyImEfunrsigjXZ4rTtuY0hO5yjw7XcD508DJ58AbrqRtnQ54zjddKNn+a7W9sOqfQJXRn5373G8wzMovJ5ltAd6HQpAU8sqD1GfwtQcko1RE7E3MjHubMQ8jDTjrsU33SordZeD3hNHWllSi21u8FgHtMGbvY4wOpBIhl3RMBNi+/EO4Ucx5cRoE6xEO9SyWu3sSOUV0XRIidljw+fIJEN1KDg+sgDEXzUQIiCfUXOU4ugcjymAh9eAcQ6UHS4K66sCoyw950nEe4x2CHWbipphecjPNzY985XE9F8UUqiwzDkG99/DldosA40F6iFw/1f4HiYj4MJ5HhulwLHrgMcfkcUtZlGPjQvcL3RnJ8jPcd5fo7uiOecdo2oyawasauU2ls2hLW5oxV5Tu2g24+ejHcJUEwHbNdAfStpBzhJU936V9iIc+znoCTMoRR7zWeCPu0o7EJEDgGgd8XUAQimXnAj5DOiuciBszUmYZBK6IobkaOShSGqAs08BMwdMCm5/N+ihdRZOtumEzHPWEuv1gPNnWZgiy2RPmJKF7FxDG6M7pKNye4sr1GSENr050YIZAucUhnV73tHoQMjkxAuept6DnWoKgeW94tizbSqcSYK2fFUnBVaHPG55mTRs05DW19JRO7t0HO7uMJwEkMk18ikR3Y4f69FIYuMAPPkU2n1k0j7tgl6PuzqfP03NVFW0FU7cTAGJY2DlBLVCmRNOd3qB0zL2GkKFSeFfm4IgUFALnJSlwOokoOJj0s3KymlpX/UHJBIFsLTix3RWEpotnWVp3o9+hGE3Vc53dukS8NKXAE+d3P98PRCC4xqq+NqxUmUDTsTtXWLoOAF2Nxg3VYFQpeuAosvJlAusqUQTra5zld3dJKQ6WQO33EzNNBJH16WLvM/5C6J5HHBOquF0h3wBW1veX7G0RJ9M4aitnKySLgM6FfuWWPpSCokfc2JvdDu0lzqxT53YkEr9WSapBikXjqYmZp9MebxtuBgsdbnSGgvk20AloSf9Ic/Tyj5VDfRA+FZWQGV8UcI4psDnhdDvjV+wphNgxwB3fRvwhfuERauAlYjM5mcfpTPx4kWvSX/gzcDHPyYR3wVw18uBhx6ldkst2uBSGPqajOFC1RhhP4UAgPEIQms2aA2DuqbGt5FkuAYRJSqIA9l1oAbHb2nNs4BRRJfA9ja1YKcD3HQzF87zZ0ggxQ1w4QLHtHq+aRxYTqRcKVJwEFdWvfcb8Px+KRECSUQbYTaS1U0oXq1LNjxMY3prkyWGqhQoxOmWi4Ff5MT8m8KqRR1gWQrd6Yua5bxPXnOilzPiY+SMOxuLnVTVAr0Cn9BsJg5IIRfqSrb8KPm/kgcaNVyOaZhPBEINBlz51UiOBZ5qrlEhUdUagRynFJbdXXGM7nBlTSWY0wilWzu0GzBNdwGTAF/8rNSnttSY3/MtvPYDD5DGnY08E/k7v0viYDYB3vwWHnPHi+mYXFEWT/xdUVBHIUwG1AIfs5kIikC57S0hG5LAYQ0P6dpoauOjFqz1pcCSSFCI2FODAbXzhQt831FEzWS6DKTt9QFIJPZ+2oERnDBNuaz48gE+4HgiBrwU6Fb4MplwwOMYbU6MFlFvKtKzy31O6M2LhCINmC04EbuhzllmtZDQmKIGNk5yYFZX0O7yrNmQs4rnJZardjfxacdNj0UulsSeMobQCSWN3NHEO+gSyTEBKORjYQ/rkgITpZyQvR5w+iydw1rzbDBkuM1EtkWMwEXACXScnKfX3YIlbVfFDtra4rPs7HB8el2OS69Hp+l/9+PAe95DYaoMtdnDjzC6+Ou+jhvojjbZv7f/LPCH7yMCeNvbuDDd8ULgvi+JYApMnU3EZ+V4Tc1Q1THVyGithzAZA0Zj+yzhmXOcD+E+qUXh2cvISvCp2DPDofdHAUQPR44CX/yCQMwN7rkTJcCDX6X905zhIm2xv3ZgBKdsvJFYyqqt6bt1zVVR6eKmgd+2ofaYWOlYJ17w3R068o4c96EkNvZ+FVcCK10WcWga4OLMC2YJoNnmSqVxVInhRClL2mIzSRcwAj1mM9peucbblYRdWcLVH0YWhFoK74nxrFmZpWQrzsQRubTsvemqYfNCIgvUJ2Xpu2gqoc0rkh+dDtmzNGXi1tohhtorFVw0vE9eAeU2x/zkWeD8JuFOpwe84Q3A5z/Hfn7pS5K+HAHf+wPAu98tZXkdF7Z77/W2Va/H+6mxrZHrCk01ikKfKY557PY2iZOtLc+0Vm/x8gkAACAASURBVJW38TRdI0wtieV9akT9cIh286zBgOO+LL6wWQ587nP+3EsbwPI62toQs4nXaFdr+xWw57Rp8KRW8E9TvvRO1wuNkQHuZFJcrvKDOZsJ9CikTFAE6FYY0wnD67OEK/N4QliSGiAFv0sqYMkCy10ADliRHb0aB1y8RD/HZEpNOJ36e09nZLhmEnMVA3NFBHUbwkphiUya4ZDXX1nxlfy7XULLTLz2K31/naUlvw3FZErIl+eEYN0ucO4CPeRbu8C5SxTc0yc5GS5s0ssfWcYDArQVGrDCy6wEtidMQf7136AvbVLwns4BX/gC+3FRKOhsAHz4L9iv3W3g+78X+OCH+FxlIfFwoGCcPcfxV39bU5G101pnau/p1iOuISFTK3VectIPBpIKbn3okRbRVydpvy/QXaCaazyE29qm4f+xv+ZzLq1wv51EIsA7HWrX1RXWd9tPOxiCA6mAKQ9a5RQWrTfgLLC8KkZ3Rm/6JEebHh3H1CRFTWN6NOJK2kTAKCcbNpsRKk1Lhq1ENX8K+d6Ir6Bp+HIHPWGPChHQhFADhpPVgYJRlfQZxEbSGRzQxLyPM8CFi8Dpi9Q8A6GkywnamnFJIhhbNm0qG06WoZR6UgHLc2/Iq/26dZGCNy0YtTDOWbyiERtuZ+S37zt8lL/PZuz7dOI12e4Y+NbXAsVICp444B//PPC3n2a0wDe+lM7ByRj46beD1HkFvP5N3C7jtd/GLTpGW4xgMA19PRfO8P2MJzLBU67yhRTgmEy8o7OsvD1pDN9np0fSQ7WPZsO2MYYaR9jwuDSReLkJ+12VwMUN4OImcP9XGT0xGXN+mYpz5babWdb3yHXATXc8i5ED/3809egD4kF2HLSZQKI8F85fPMTqMygLr84BDvj5M8BgRYRMdgLQ2loVyIrp4Ffg5JyKgR03wDACyowhMGVBuFcVZMY6GTAqCYesGtrgy84SToRujyEitpJSuKVE7woEzWfCjJWCzwXGVSlXYhtJGE4GVGMgH1EwTU2bTR2JztDg1vEbj+lJt5a+rbIWlipHW3kUkHJUMfs/m1L4x1PucaP5TMeOcYW/98scu//y5+y3NcC/+VVeZ2uLZXF3R8A9n6cWzXMihzhif/Q4XfTUJzUckJkcLnGSx+IYvnQJc3v4hLZQW//BeagGiHap/d+52I01uCCMRsDZM6xB3ZVih8sngOtvIMu2uuIjV3ae5ciB57xpqP50CiCTivxrHFBjSBfX4IRaWpWgTQ1J6VHQpoXfPOjUaeL62lHt746BjS2ukiVI8zYxqeQdCc1PDGOwsi5Qx8CFS5y8tdTdsjXaWl+arFZJ2Eu/D6AmPtcNlFBzb0tEhByR+I2MRBgUFfuYSljLcChlchuu+ofXPas3nfo4rbICI3or2dKvApbEj2Wd2DeyX83OSLZeB/DJT3qHYl6QYJjlfIZXvRp417tovyQZ8PM/D/zcz/EZv+MNwG//DkmJX/6fgX/9rymIP/MzhG4f/BCpZ42kHvSBM6fJAs5y4M5vAh56kPbbypKkdyulDz7/bCKRBglp+bYGtfXBo42ENlUlx1SdqgY8rnbCxAoTWQn58/GPkRw5cYxj9cLbgMNHSAg1FZ3GFy6wwMfyyv4h2IGAasC8iowiiaUqOIDt/iti52Qd7wCLLAdoOmWYTm08F28a2gTTnJOoMYQNmxPCtsrSjkpSoEmBcQTUCdr8/LHAwUagg4WE8VjaSNZysJUcUGwdC0U6ziUEqEM7Y5qTCev2qXHqhjBqWhFqTWvW/Tq/AVzc5vlxhz9RRwzxmQimY9gRnK8b3e9yMkSpOIjF/+Ect/Wra2qI8Zh+oSxiJPebXg9cOC1UvmpAsdve/z4SEK9/A/Dv/z1j4NIU+Ku/4mTLJ/791ULq1BVtla9/CfDRjxIO7+4AX/g8F70nnqDWaypqi6okVO12PAGgYTmhsa5GfZjuoXaO3r8WTXv6DPCpT9M5HIttdOI6xjgeOcRFeSCU+fq6/L5PmAYcEI0DR/hT5kLTlrKNnghQ5QA3lZTZjFTsyhq92Jc2CKF2wUmYyj6R21tcdXsdhoDEMdpCf7OSt40av3JDPfnCUEW1Tz1YWyPxMKkYiZx2uDqrRsxiHtvtiuYrqW0mFbXJWMoRaWLZpKCgzyRHaJozpWEk9+53mJ242qctF0uM3YoUQDeOdlot+Sqra3weG1MzdxJCm50xV3lNDShLatRZScM9S6gh/uB9gO0CqykF5BfeyX689i7gqU8ywHZnBDx+irbB6/8h8J3fCfyznycsM1PaF0UDnNnkve6+G/jYR4E3vhH49KeA224DHn2Iu6xdfwMXjzTis0SpZ8giDauB0M0V54fmEMFQw6nWKSWDVpPyZhKZ/tRJPlu/z/+zjFHcScKFtWlonxUzkinXXSdujucTOaDp0M4RE6vNYxpOjMSK8Aj1WhRCHVoO1KVLFIqtHQ7ATGjQIhjIQ0dktZ1RoKqGPpna0M5w4v3XPWKSFG1lmVxqBCSaogD2b3kFWF8RmJWg3eR2Y4sTfjLhS1V7Zlfi2/KcTI/G4cUpNeDuLifoeMLvxyOyWbu7dLiePcPFo9ejQCyvcAy2t33MmxbTAIRVgt/jUn1RanvB0J558EGOSbcHvOY1wPIaF5gbbqAA/oO7gU/9DbXRL/wC8Pq7gX/0MzS8p3ItzbGpSuD73kyN9LrXAe9/P/ANdwKf/gxw9iypbQ32VGFp9yuyPgwprAWheVTAvAZS2jmXINuy5Hh96Uv8/chRUvpLSxSgPPf37/X4+XCZ/puwDsJ+2oHQOBrUWGg6cQEg5sSymY+ATTtcHfoZMN2W8kUJM/z6K5xURUmNNM0BpAKhLCnI/hJw/hInwEyyD+NEQukTwraNDQBWQvtjDmqVe79RKlEFumHS7ibgujSwG/gXXJRS20ACO7dGABzLtLZCWNPeAMQeK8WeEygyngJmxr4cXucKXBVAAa6WK2ucENk2te7SCnOWlqTqfz+TgNiMWjHLPHM5nnHivPWHgHt+ifbKd90N/OOfI+nwsjuB//yfGK5y7DrgL/+aRI2rgf/xp0llJ5JSPZ3QvtrZAd7w3cAf/SFZuD/5Ey5cH/gAn81I5ISV+LBoXWC4CJAB3z+Atj6E1s3TPXaUDNJqnko/T2Tbjq0t4NbbfOT60pJA2AZY63ohNZYLU1kyeLc/8DBvP+1AaJyqYhhLq35LaovRlC94KuH6jfgCVCN0ZcPYbpc5Gk3DvJBSnXyFRANU9MdcuIB2k1oDiV2bcoWfFD5/XR2lGmTZlSSubkZiITWMGOilEpTYUECKhgIwK+Wli23UVh91JCcuXeI9dkZk4HSC1LVAHskDmknw4kxCgtIOtW+3Sy2adkS7CN7vd4XKln1hrj/GCXfbbeI4TTwzpYXnH3iAwry+ArzuO7hIjLYZz1XkwG/8BvDnf87+/dOfB+59iItPY5masbPLd3fyNPC930fq98xZBlGePi0Tc+STxA4dooClotE17j5J2D8HjoMWGnQ1n68qGWenzm2lrSsJLUokEHS4hDY79NBhkiCpBO6qPaiVWaqCfw+GkiYyxWWF5K/UDoTgzHIGcyImy1WDECqvGTQ5LRkj5Ur6PyDBlIAP1ZjNgMce5cC/+tWcpPlMJjMYyXv9DUJxNsxd6aSEN40BcnAln+U0FHs9tBs5JeKn6aXcoDVLPQVaQtgtADviK6pKH8lbNxQcE3PFnkz4+yTn/zaiFtXcm40NweqSMbq1w/e8M5I0aVlpUymt2zSyGAj+73e4esaGRnCvQ6hU1z7GL5OdCF7xauBDH6TQvfH1wL/4FxyPb38t8F/+M3DLLcDP/RMuLLe/EPj6FwJ/+CfAbsXI8+0RNYnNgP/lXwJPngM++lfAj/4k8KUvSypHzZgw3YP1/Hk+82jMsdgWyKo2mEZBq3C44DOtiadFUzT6oCNaL4poj956G/cpXVvz28cPBsJ+Am1kdlmQxChEq29tech2tXYgBKcB8Ld/x9VyR1b/pqCN04jh1zhvQ5Q5V4q88F7nXgeABc5cpPapIOm7JbCb8yVfdyMN5pnjal6UvIduWNSUQkZI8tp6l2WpopTMljE8Pot5r3FOCju1HPzphILXiF8oAsuxZikndFGTySvAY6oabYFC3WJCa09rduas8B7wuAfsNgxS7fS4Qu9sSX8NnazpEscld0A6AK47wRyeQQdtLedMVvsbT1CrpCnQXwYeeZLXXRsySPMd7+DCszsD/rd3Ar/yv7M6aBKjZaCqmvDu3Dng438BvO0Hgff9Ptra2dVMSAjZ1Lcrtd86kWhyCezU0sRq5LcFPWqOrc4F9f5qxECW0dltRWMNBpwbqbCxFmJHOQpWmvl4ubXDXHxmU5Iel85wodtPOxiC4ygwH/8EtcVsSizeOHFcVlTvm1s+AHQ0kWDEyjsA1fj94j3AK19F/41uEVFUhBXGij9EUhB0a3StxewiTjorITqDoTestfp/U5OcGAvFjViCNFOev7ElTjwJ9R8mdIiu9oFeLHAvAiD9r8QALsGfSU7Bn+ScVF2ppl/mQL7LwNRuxgiE85doyPf7nNTrfR8n1+sSGunOBsZ4Q7ksgZMnARjgRS8C7ryTGrjbJRFw+wuA3/1tLgxJBGxNgPseYLleRD57drAEfPZzwK+/C/j+twD/6Y/Z17qWLFPLcJaiErujIzFsJWPnNi+izSUKd4yY5eJnqjx8V9tPaxTogrO05CFqr+fDk8K61NMp2j2KVPvu7jLgd2sbePxJ2sBZur85eyAEByB1uzWmIfnSO+nvmEgcmDrC8pyDfe4cB6BpSALMCq6URUGbqDcEvnCPrFgzTqzNXeDTn5ZJX3CFg+V5vR5DXDY2ZIWXPmWZz++3DQAJ19EsztUlYc4qEhDLPWA5Am49BNxxDLj9KHD7EWA5A9wMMCVw/AjrGGcJtZCpCCW1qgsiYFTR9qkcIWztWHlydUjo0k25kndSOoC7A46Tq4Fjhwj9jh5mdmivCzzxpITmTH1m5coK8LGP8e8XvJCOzRjAj76N22d85z9g5PBkF/ij9wI//bMAYkLasey6cJ2wVu/7Y+D1rwd+572E1+Ocmn47J3y9sMnxbwxtie1tSVEQm6IufBFKNf5Vo6iQaHiS+sq0zkMSyfuBxCMatFrJGAm/yqUWgvXXP3cOuHBOIKEDbrxFkMU+6bIDwaqlMRmXGhzsP/sQ8N1vAD75Cb4YLd9kpZbAjmzGlGTeligKaqFS4M1oyhpajz1KIYzkHnfdBXzhXh+pUBRcZVeWqHVKgViTCdCzjFlzhkazs3RULgnESAzhwWhCKJQ6ZhjeeiOdi6UDLmwBO1M6Di9tA2fO0dbpZcBAnHylMH+dwMYrJHSlKIE89ltbRCkN4KLg90eOAI88Atx+uwRCRiQyDh/20dSABG3WAMSmuuUW5t40DVMGdn4HOH4UeOxx4C1vAX7lX/HZfvAtwIP3AlXE+w0NWcvU8pqf/wLwpu9hWI6NSbnrHj61YSBsTzTZrGDsXnaMMLLb9anideGJGw18jSK0NcA1Ul6bVjU18BS1FgZRJ6oSRwCfXePzOh32XXel0EBPZVn30w6E4KwsAycOA2e3+KJ3DPBnHyY9+sD99E4bIQDUsItiKc4x8akIaYd+n8rx+6EwKpUEi052gFOnhLWCfyGXLknKQA4Mu/TpNFYMe8kAXemBGqrDFUrrIsBJ0GAE3HAjV71LG7zHYyeB7TFhzu42r2n7FAyUrMm8skTYUgm1nmWkgAHeT9Mkhn3xawkxsDsByhG1azeTANWI5/Q7hC5VxRoDdU1a3dWc3L2CC8jJx4Bv/VbgIx/hpHzbDwMf+nPgicd5L2vpwHzHOyQObxVopsAr7gR+8seAf/5LwPe/GfiD93OljyIg6VEjWfGH2ZgLjibl9YT90g2qNrfoHAbQ7lSt2yVqRaClJa8pNfLdyffWir1b+uMbYc0Awn2NWFeNpakJmdD1WSZEDohu9tOuepgxpmOM+VtjzJeMMfcZY35ZPr/FGPMZY8xXjTG/b4xJ5fNM/n5Yvr/5avfIMuB1rwVuOsZJuTUBNkbAB/4cuOUFgO7NMt4VFkdWI82k3NxhSP3WLo3ZUl7SZ/6Oq6G2uAM8eRL47ruJ+0tHIUtTkgXdgfdWZxKOE6cUwLgHwDHY0gj9XAn2j2Lm9e9MgY0J8NUzwJceIhExHNApe/stwLEVYLwJ7GzQwL84JhNljVSSTHiPSNg2U/F+R9b4fdxhFO9oh7FzUSSZjas0kFdWqZG1yEenw/MOHyYUOXET82RuuVUiEdZY1MSmwMteCjz2MPDWtwL3fJGG+y//EvDL/5IxfYeXGRP3spcAP/3fA//8F4Ef+wngvX8kNoP4Y7Z2+dyNLHAzCT3aGjN9YVrRT9Qb0J9mYjJstVDORmwqK34tDY6d5iKERnxZU5I0NuKEV99YHFPLGEdhzgR+RQkFsNPhImes1F+ovTvAFV7grtb2o3FyAK9zzo2kMOEnjDF/BuCfAvi3zrnfM8b8OoCfAgus/xSATefc/0fdmwdZlldnYt/v7vftL/el9urq6q7eF6BBCMQ+iFUaZhBgeRzYRh4pHJblCXs0VjhkaZiBcGi0hDwaoWFsASMkN55BApqloaHF0phegF6ru5auJbNyX95+95//+M7v3ewGN9kxLUfxIjKyKvPlfXc563e+c841SqlfAvBRAO99oQ+wLOBlt8lK7a8Cz16ipc4A3Hc/8Oo7yDlbXaNieILqVFxgaBE46OXkhSWy3sG2mdv8zeeI6ZvuR9sDnjzNqrvZJ6lBBTw8T46TBh/o7i7DIsdhIlkVwTb7LuMRz98PgeU14PJFhmqvehVw6+2AV6fFj7rA+mWgiFhsW1kDHjwHrHY50A8pcGCGOUvNA3ZHfKCDjNfo+0SlpqapzBUPaB6kZ0szKqcjZNMwL7l9vg/ceQfGg0MiCVl7MrDj1A0UpjAArj8FXL7ERq+Dh3gNZlHXVAuwdoETR4BffDsJnr/zu8D//GFgmDJ0HZhcT2pFZiepeRUF8PrX0mO1J6Qv6iLff+gAoCr8m1CoUUqVoZkBfUxR30y6MR7GlCRMT48lRs+Qhw2/bTwCOSuPa0K6ONt/fgPsw+NovvryX1e+NIDXA/iM/PzPAbxb/v0u+T/k929QLzAvF8B4usnhQ8CrXgEcO8x50kkCXFkDPnsPsLLBBK83YJi0tkarOjnJBN8kkY5XNpyZvv43v1Gm10hx8/Jl4IbrGNJoiXErAb2GGV+kbKm9KAqoIT0Oh8T+h6MSmdvZpdAdOcR8QdnAD54Avvd94OwSsLQDFHXAmQCmDgLXnARedwdw4xHmI50c2JaZ0hWf1s8QHHMw7PFlEn86Ivpz5QqVxUy4qdVlLG6NPLCwQsAhCOmJwpD3qtlgq3CtTkZAFBMMmJ4F3vhGFooXFoB3vBv4/N8A0zL5Z26GjX//y28DH/kI8Ed/IqCNUGQy+TKDGLd3qXieB3zwg8CJE2yK29oCzjxDomeWkBFh0LE8pzEzY4YzqeQnCXOl2DDMVcnQMC0nlNWSYWBInwZoMLMJ9hJBTdfo3qa4/cJl+3qbUsqWYYTrAO4FcA7ArtZmr9l4sDqwZ+i6/L4DYPLHHPNDSqmHlFIPbe1QSKshcP21ZOu+6nZgri3DOjwK4vIa8KpXU2kGfYZzacGblYwI06Ypu/iUQx5SnAJ33w28590CZYbMCza3KHgTLWBmknmGqQkNY8bpjsOE1nHowTMJSfhkyPiNEmBlGViYAm44QSUeZEBUAJu7wLMXgUvbwGof2EiB9QxIa8CBw8Cb7wLedAfgpMDGgL0+tvdcNniSco6Z61DQzEDygwfpYbodzgtAQQ8Yj6gkhotluG1uQKPiCHO6XiOlfmoSOHGc9+3z9wA33gz8yq8Aj3yPA9SPHQWQkah6eBH4rd8FPvKviIi5NpkMsBhCaZshleOSKFpv8R588lPA8hIpQNubLLI2JWzKCobMTsB7ayD8NMV48S72eBRLQIE0fS7cPN6vI7zHvQM+DIxd8YV5IcVvZdHI5nvqR/t97UtxtNa51vpWcA70ywFc/+PeZnTiBX6395gf01rfqbW+c0KGJFgOId25KdJErj8FHDzAi9XgSKXPfgF4/d8jZLzRIWqVZhzp5EgHoImTu7u8icMR8H9+Arj9NhYkhwmwdgV482sZpmQFj7+xhvFW4gwSnw95Ra7D+k5UsJiayffegLH2yaNApIAVYTp0e+SnrW8yZ7h8CVjdBHYTYLUDpDa9wbXHgFuOAnbClgLXA6oO2dlmIPnEhBSAC9ZOsohkxpUVhpOrq7Tym2ucUGmWMxk/X0AKvILeWQqwJGcqbA57P3AAOHVKvK0FLF9mmPjkY8AH3gv8s39KL/dv/pCQvBMCcEviaxqzaP1f/ZfArbcQlbuwTEMySpmvDCJ+nhfQ8EWJoJVSVhhJ3SpJhFXhUMgrPpFOwT6Y8Lv8gWVLN23Bc0giAkZ7R+eaL20xfM/BqCAMyrpPtU4vvU/GzYtD1bTWu0qpbwC4C0BLKeWIVzmAcrD6Ejh0fUkp5QBoAth+4QOX/CnXIwR85BBw4SK9yC03U8ge+B5zmLs/C/ziO0g87PaZ4yiPCWAWlXwnzyu9CMAQy5eQLh0SDWq0gIkmG6x6PRYDH36s5MFVzPYzTaRsd0QL2d+hle31gZuOEk1a7wDVKWBxFjh+Evj9j3FUUhKTfFmrspI/Pw/YGbDQpCe49ijw7BWMd8NYoHBaigZgNADyFu/R4iIt7soKcPwYcPoZCvvGBv/u0kVg7gAT30NH2OGIiPC2KoAsoOBaBZNzO6e3VQo4dIiCuHSF4d70HPCq1wDPnAEe+H+Aa6+nBy2kbcGs8Ag9erfbb2dDnCceoyFbs5VNwEWlNG5X1oDJOhAIFccV6+/JoA3LLguRYxTVLuHqVBgXwyE/y1H0Yq5XTrYxaxnNl8lzzEY3rXn+e99jiWzs5/UTFUcpNQ0gFaUJAbwRTPi/DuA9AP4SPzp0/R8BeEB+f5+Mxf2JL0M3933G1recApADTz0FZE4Jp7761cA9XyFs/PKXsXK9tiUz2SyQYi5VaL8iuUEKPHMWeO8vAV/7MqCa9C7XnwQuPytDCSUZblYITphuTldqGCoHIABDf4d8uWYIVNvA2Q3+vA2GnJ/+NAf7xSMKy0yLnu700xzad+ok0G0Bi22GSy+7BXjg+4Teg5At3vGI603m5/iQn3mGYeWTT/Dcd3b4oCOZqTzo8TzPnWV3qe/TACwvkSCZpsD8QU7fzHvsgtSGsi8M8izn3zYmmMSvb/Bnhw5xkk29yg3P3SWg7gNT8+zh+bN/C3z5y8DCQVrvQZ/e0IApjit8MwvwQVDB8+jZLYsGMveAsEEDaHKOvaO5KI+AFkUyjIow5LFMSKbxo1Nx9rZcG2UMvNIbvdjXfv5kHsDXlVKPAngQwL1a68+D29d+Qyl1FsxhPi7v/ziASfn5b4ArDn/iy1yU2bxcFFz8c/IaMnddzVnIlga++U0+mLlDwLkLwC//MuNnaHqDRKgVw4jEyDhhTB8EwGf+L05mCYS/9OD3qIi+R+9y6RKAhL834V6SsFJuu8J+lv4cW1i3SQpc3AAuXKHn+dJXgO98V+Jt0IqOYr5PS2L7+GlgeYdfcIjGmXDDVnjOvhffBabaDFV2thmaNZtUnNnZ0sqOhty6DNDab24wP3rkESbkO5vA8kW2QhQZMOoCAxFupQhUuBbv9+QEaUzXnyLCtr7Gqn9YYShUC4F/8E7mdd+6H7jhFAV4eRm4cF56pBIqz7DPa7ruWuDVdwkqZgGrV5ibmgVTblDyzwCM5w4YpTEJvyGM2na5DNeQM12X4exehMz8vZmCY9a/m9xo78yKl6wfR2v9KLiF7fk/Pw/mO8//eYRyc8G+X4XGeAqnGcZtO4RGb7yRVlaB4ct2hxf/5HmgvwGcOQ28/33A1BzwL36fAlqV7V1pRIEY9ojUuS5w92eAf/Q+4O6/Yo3j/m8Dd70MePiHtMBveB1w/wMEEOpVthCYwedKEX7eGJBC4rvA6jpwYZX5w+e/yrg9C4CkB/iKymyBioCcyWgcAz94FMANwEwbCBXQrklbtgs0HSJJoUelX98gIAAwqa9UeBwza/nkItDdocBcepZ99Ztr9BZnzgJ33gKcP8O6z4F57h9qhFSQIGOeo8WMVgIgqQDXnuA1nnsSWLrMuQODGJibBd73fuCezwFnnwLWIxqINAZaMsugL2FvvcotB3nM1RsXzzOaKIRy1KhyjkRjgmjhuBVaEv8CGCu2QcG0JPFmJt3453s8iylJGIO816uMoe6i9FI/rlHuhV5XB1dNCzM5Li1AntM6Ox7QnCZFQysAOZcYWQoIIBZfAf/Hp4F//1fA//rPgKOLfFCDAWP1hqBzBnGpByQj/mcfFCVV7K48MAfUfODM08ChaT6UOGfY5ojlSwom/RbYet1LgXXp7owjfu8K28AqyFpwfYE9AUAJMVQRfNjtUfE2+4CqsUCYC2LUFKazLyhha4o1Lq05z3miBjx9moqztiqsbfB6LIvHeuxx8tXygrMMtvvkka2ukt6zvsmE2ozfNfMT/CoRyOGQedrsPM/j1A3AW14PfO5uYO0i71HdAXJpjdAKeM8/AI4vAjtrwCM/4P1IwM91fIaiE5Pc3WOWSxWq5B8qkMmBjEpSZFQkw0mzLeY4e9cXKsV7BCmImp4b01kMlH1RprnQc2n4IO+3FH4MjPXjX1eF4hQFw6qR9KAMIxlKkQkcbJOrZWjpWhNpMgP8bKkEX14Cfvt3Gbv/4b8Efu4WINoFdjYI2douwwHL4nHu+Tzwjrfxhl1aYo5w8jrhtgUUeDMIzzJCCd60VNq34xFzLTMAz8CkZkuBQYmGw7IGAc2YPy+E65YQDKjL2FjH5WeEPik5/BUD4QAAIABJREFUKysENp45zZ+FIY/5qHjhZp2Gxw0YEvaGgvh1CCPXQzKA0wx49DHgiceAhx4EHn6IPLeuDOfYy0A2tbU4wnj87OveQLTta/fx+E4d8JtEzt7z94HjB4H5CeA799Mz9YekFVkFFSD0iU52OywMb+zQOyUJC8OxdHHmRTmdNU1LuNjUeMzIq0JjvD4RKEM5gA8pR+ltDA3HdKEab2OWe5li635DtatDceQGxDnzk1jgS11QoCoVCkfoy3CFIbcNeMKUrZsRTg6Qu8CZZeC//03gjruAP/1TWhZLlTc8EkJotcJGrne8rWRCn38WgEVL/MpXMM8JAxqwPJEtzB5DDAVaPl+a3cyGakA8Z1qGDgbRMcIQDek5tWZoNDUBIONn+B77YdKUBsP0AA268ndtNrh5Hms5zaYk4qD3Wtsg/B3H5blFQ17XxjYLusMB2d29Dj/ThDqGPAk5V8sGXvMa4K1vo7I5Dj/ftknAvfOVDI3v/zppQAGInlWEHBtFZROamXedazYWbmwAZ84RQh/1ONAwisrGtdGIzzsVj1ikGPfXmBwm31PTec7mcfFchFiZu5lwbzynzyqZ13sLpft5XRUkzzzjAwUw3rVpFuR6Pq3WiZO0xIUGBpdEaTKGJf0+H16eAPCIXgUe8PFPAfW/Bv757/JBf+SjMlvMJnt6FAOzM8C997Lw98iDDLVuuxV48klOypxpE55ttykY0yHbg5O05Ekhp9XtdssahOMAocX/a4FAPY+FVa0JqS4skhPXqpFqMuyyf6Y9yTAHFpvQ0ojCfuIaKmMUMSm2JdFNY5mZDH6fm2ZNaCj0o6Vl5jxRxqElUcpQzwzZ6PWA+kDypRQwGwW0Zk60vMxQttPDeMHuW94MfOGLwA8fJDM8CHhtWwNSdFZ3eS3nLhMuTsRbmB0/jgIqMZ9xv8+IYH6e51Kr0xh2OqIwuiRiFgXRS1P4NLtD85xwsvEwls2czbWB8cYEiEJpjIm8wHO9zD4dztWhOGnORBxWeeKORXTEdRk2dbeY5A4GDMUGUjy7/nrg1jtY43n6aWCwTS8VJ8DGkJXqf/yrfCi//H7CuZ/9Ivvqd3dJ/QhDKtstdwKP/4Btv54LPPUEH/7itLRhp/SGFamFuK4MHSyA2SnJc1IKhfE0jkUBt21emyE+3nwrQ5j5aeDgFHttBgNgchawUnLknr0ErFWYo7Ra5OqdOM5CZK1GgWs36TVaLSpOnMg6dZs5zNmzwA0nhcKSMfyMY2BGBvQdOSwVfAkpXRE+M9GyIm3Hy0u8J1MTXBr15S8C1xxhGLe1Rp7gcMhc0nOJcl7epHdvNam0ls37nCQMH+OUXj5NiLxtbhKOjiKef7VOxe52hdwLshMA8RaSyxUOja+WkMyW8kEuSJspmuYCGhRFCSpYVol0vpjX1aE4KSdnmv0uts3YXplKdy4JL8TdivtNweT34YcZTvkWcPtr2Jj1rW/TM8y22SUZZcBn/m/g1S8DXnEdh1H8+V8A7gyZBVHM/p/Dh2VgXgpMLLBL8sbr+GC9gA/bc1klb9WpfD0FtKaJNm1tSo5k8/xdi6GXssgQTgGcupnKOlMFDk0CB6Z5PV6FUHBVAZl42tGAvLrvPyHIl6LlN9NwLl8m+dOSYmZ3h555t09QxJX8xA+p8I4DXFwG2hX5WY3oY1jBeAOD4/B8bJsQty6AV7ySXLNhn8pUb1CIvYDeNpatAGlOA1CrA14POLAgVKCC7RJKiaLmQnfJJMoQT9TpAjUtFX5J/IOAXtWAM7mASL7UbjRYGrCUzGrbE3rlRRmmAVQobYmsiTJBlwjcfl9XheLECXD6fOl+azU++CmZR9xs8wbXwnJ5U5oCWZ9eyUz8HI6A7z4MfF/maoU+qSQ33MipjpYiYvZUASwuAbfeBrzyLs7h+twXaB3PnpUpmAnQXQVSBaztsmU4B60gijIhX5wBLm0AWQc4PM21Id0hvyJhGSDjzpzFGbIiJiaAo1PAkUlgJgQOTQD/7tNkH89Nss8m6fIzdrfJ2J6ZIav67HkaiY114NDB8mHbNhP9ZoOC7mqgvwUcWWRbgrKA6SleX0Wmuqyvk31gwAzH4bGj0Z6Wcvn56irbEB67RM+yKXB2YKb8gPDyoE9D1+0zL4uScm5CLF2rI0tY1CAxdHNXEDGPxiH1qaCmzXvUL3OZPOM9tMDwy3Go8IUuh54UmsdzrbIQaoqhAMaLuZ4zCsr6KVScJAOWNvhv12XfxiASgEDTuqJ4LlRtWRSsrGD+oRVQ92jtKxXGsHFMb+S6rIK/+Q3sp19aA7rPMCcajvgw3/52rn547HEKhRfSSuY58NQzHHe0fIlK7VgYK0+WUTBXN4BwjihTtQrM2xSOcQuw9NdMtzmKdTYETh5gfvPEw2RY3/ZyQq+RxYce52wjX1rigw49hj3PngOOHCxZxdUqw5mjRyQZH1JIp2eoeNvbQC3jdU5LDnXhLBVhakoIlXtqIEApqBoCbSek88Cmh3IgLRkFB330elTALJffO4TL186Rsl8UINIl+Z1l0ThVQj6z3oDX02oCYVpW+M1+HZh6jLuH0GlIneJhXFfqPwLGZBK9QJWo2d56kKHemEGKhrmyn9dVoThpxrbiPKdFMcW9qs+iZZoyQU5jeh0DV0Jh3HdkdsbojGiNFlzfKYD5NmHuL3+VN6ZeA37u54CnTgP3f6uEt6enyQBu1Xg+sdQ2whq5ZgcPUEB9X9q9FT1BOwIaDq35bTcCLQC5Re9YqfD8ZprARBWY8KnEczOAFQGPPAB85bvAnT8LdNYJBgw9In4DQcDiRJq7LGB5hbT/MJRmriqvt1KRgRQZ6zWtFrlxheQuy0u8vtkpQsHHjlFpDDKnFBP1NAEZGLHkReIthtJsNj1DxK5QQKXJZ7a6KaxmYXbbDj3p6XMisDYFW1n0TgdngWgAXN7gdVx7DDi8wHNcW6HyWZLYm9nXRSHlhwpD8jQV9E+a1Exem6Ul+GAMlxb5cPUedsAeD2RmXr8YhvRVoThFwS5Ox2GMavbU+65wnCKgGDFsyFLmO65P2NO2aQ19m9Mt/QDj7W4FKAidjuyqjGW3Th/4D/+Rf/szr2I8/sC3gJXLDFU8H0iGXA2/u8s8IQYb0hYneb7dHaA1V9JqGjVgsmDYd/ttLOAtttjkVamQ0xZahIDbNeDCE8DXHwbOLgMHjvBzZmZIQ3ErhNYPHWE4BVXuzqlUGYq4HoEOV1q1mw1C7PU6tzUMh/SOgUPmBOocd+vYFMAkpbWv1jFuCEsll0wSetUoYjg06EqToQLOPcvi5dYmi7etOo1VtUIh9xx6lQun6REGwnhGQi9+/DgRtKVlAhtxQuUcRCyMeh6QyVy1rAB0IowNS5DTIWCFvD9K8TMtqeONiaFgDponpSeyXLIVFGhULcltjFKa8Vw/VaiabQHzk/QmtaqMgJJEvN8HapOc5O/6QB1A0qG1tcDKvGXLAtsOEStD7JucoCAsLFKwzTo7x+L/o4j99ZUqcPwQxqs0FhbZX7OzA8w3AVi05r4QFbd7wKHDROwqniBsPtCYBKIZ4MwTFEprBMQt6eoEhfbyMnB5BVhNedyJGq2zFbNJ7dAhWvCgCnS2gMkmrXKes3DYavKaZqd5vldWaHHP/5Ae4aabgIV53rtaA3jqcZnwOSmTdEChP3iQiup5ZcXelrAHRblCJJbGtMtLbLEYDMiX810amTzn9rjQA5ZWgMkZ4OIVYKCJOIYuvw6fIANjaxO4JOecaHr2M88yH1pcoEEY9ZlnDQeMGHZ3CRb4GeDG5TRTBYznr9kWPaYBYjLzc1PYzAjMmD2xZsyXAQ3MzGrTCPeTXleF4gBcg9Hp0OpUq4zvPUXBUpo3wqwtNMzYOKZiDWJpi0VZbCwKEg0X54hMIWeIVa2VxTNTza/6ADKGcK5Di1gkhFttmzO3cmEBZBlDpe1toaaErGv0++wgnZ4AGrex4PjsWeB8AQwUrXBWcIpPtUYP2aqylz8eEAAJQ153lJGMeXgBgCJMW6vw2K7N+7O6TmRQW7IEt0PB63QpdO1pAgnKJYfPtliPmWyVo5hmZp5LWTFhimEYFzkT7n6f4EB/QOWZmRI4OaEXMEJ33Q3A42c4e2GUcjzVxhZwcJHv3dnmjlFL6BepJjLX6dNL2gq49qSE5akMSU/5GYUuz204pNJUKmXolUo04vkYT74xntT8HaQ2VUBQWqfMeWzxsC/lzIG/85eyaX36Q0APgdqQCXdeL62elguMZKyt0rSWzSZQU8w9zJxl2ybaY9vchzKSxbWphG/9bjnhZn5O+j1EcAZCo6lX2XuSJDzuwiKLiv0R43OrIISbZ0R/pqaA3i5DgLlJIK4wlNrZJdMhLwSh6/GapnyGbJ4CDh6n0lxcAtwqjYTlsOP16BHAk00GjRrbny2HArm6Ahw+SoNzzQkK+tom74ESZK9ZpdC3W7y+i10WUs14WoOmpSnDS0NNSYUKs7FBqg8AwJalvEPAyWmsvJDhcbcLbF3g9yAAplzWl974GgIn330E2OnTKDgOcxDkMizSI9uh32drQ8UXoqwwGrKYXqTIMR77a9Yj+oGM8NKUjUGfz9W1aCifzwhwHMqSbZU1nb1eZ7+x2lWhOK4FTFWBTsGLbrdlZKskk1ZACwcpzG1KqJCJtXRshmWeS+UwPLFmk5Zqcqq8uUPpQlSKudPyRYnfPYYRfkAvsrTJJLfWYOPVzrO0lJ0ee2um24S3ex3AafI85ucopBWHvSq2TW/mhAByeoKJLr2LnQNtYT9AA48+DaxusYh57CCgU47q3drluVaqTIy1S7DimmtpAK5c4XldXuYmtChmQ9jZy8Cpa4Gqx3u5vc2QcmKCYdhMreRoaY3xoD/jsQ0taGuDirK0wUKjC9nSLfUs2wYyix5mOGTINhyS5BkeBS6vAo+dlsk3Cshsjr91DKXfk72sNsOyLAOCpiT0iYx9slhXi02/jZJO2BzQERXKtFab8VDpniR/zIa2y7xo3DyJ53mnfZLQrgrFsR2yn72CiWyeUWFGKfv/e0MmoYHPGD/OgVWh0NeE9JkJxypP+PDSQoRa2m57HcbYvRFDG0PlaTcAaApca4LWu0iZs+QpcGWZxb4o4meFC1TYAUgtqU2QY1VkzMMaIY/bH0qPu8MEXTtsWJuUxqvNTc6BDmRs65GDEqoVhJJdC2jO0pNlI4Y77SbDoNwGYgWcWaISmlWIo5wKePRGruyrhryW3ohJ+ZUrks/0GI6a+kaWSVVd+IGp/D8StPPiioTDCXOr/gjIK8CisCWSWBgTAbC9zvwp8IAzF7hZzrbIaxuOKOjQ0sDm0xPbVgnbGzaEF8ior5SNb9CA9mhosgwoPMqJAsNRXWC8ic91AUtoORo0BFEKBIKwQVEZlQlRIXWhDPvGo68KxXFsGUGkSBcZRox/m1WGDx5ojfwK0LF40paEXcOcN8aryPxkh14jElZvIZ6l3yMxMinosYIQqOxQUadaGG8vNjmUlmTTdYELS1TuMd1DUZlzQbF6HaJKjg/kUTk1p98Vqy7eLnFovQOfSXCRyXTJYg+h06YipSNa42fPA7feSmv/5BnOOrYdvufYMeD7PwDuuovk2NcdBdpHgCd/AFzIgFUFXHechmK7A1y4DNx0A73X1AwF0LSXFwXvq6mbjAYcd9XtsM7WGRBhmy7KQqmlqDSFpscAgJffzlzq4gqvs15na0fnohA8C7CMkANuKkYgI//MSfg9TgUhU1LXkoKmB+kgFW9eqUg9R5f5py3epMilv2sP7y6TQqlv8XiWyekU/8ayfsrqOJbiSNXRELh8hQrQkJsbjfgQHSlO5WIlApe8p3qDN9q2KIB5zukztsPhG1EqVJmYQtmq0HvVmjLATqxQnjEpVYrHdT0ex/OYH2zLCFtk5JclGYd3DGXaS18KeHkMQPH/9Row0Sbc3e1SKKvShz8cYbxqPbbZUrC+yfDSslhU9Cv8rFFSIkuw6GXSDGhPcfHt5hbPuZcR2RrGDKOOXkvvsLoGwAauOyV5WQIcOSJCl4Et4TkNQy55x3BApVhfl9FMEdE6y6JHzTI2qGUZYW6l6DGvLDGcroXctZol3B5h5SwY9wfyvJQUhbVwxQp6jl6Xz8cMTteCkDmClllSXPXcsmBZSH5jXqIHhJxR5jiJaSHIKCsmXMs05cfG/tkDV4fiWBSKQtF9Z+DNT3PQzPgsttXrQKXBsUNpCsTb9CK2y5DLUsxl+lI5r1WBmsXZAI7LcGFrjUrVyWnpXPE0gc+H2+8DXfFmVZ/vqdcEeVMM55KInam2R8h4NKKXGwhreWmVD7/oMpSZmuFnGPq/HzB3ivv8mbZ5rIVZIkieL0rapYBlGXMN12NuEyfkxa2v8j49c4ZV+M0dJt3rO4TM602gblEpJ6d4n48eLVcdAgJ+5GQ1QEvtI2LYMhwC51bY51MJGA3UhWc2HMogRIf3qiZD46dnqWy9LZ574HGloCUt4qsasIalgGYZBXzUAxKXwt3vAbOyel4LMTUTBoltWPOebIcQRM33RPmEtOmJtxmTVg06FwNaBiVairKjnD0tCPt8XRWKs3cSiRl5GqWkYex22VdvFkTVZFFQngNOhUlnUjCncSUxrFXK+kSaEo1a3yIyBasEBuKMSJdSLIq2ahTydAfox8yxGhVW2qs15hJKlOf0Gam6+3x4vSG5cXlG69gfAYFQgbqCpJkxVFZORV+XnycZvVo6ogdYvsKcwneIyB2YB3SN15gM2QrhBmy8O3eJwrS7Uxb8+hGRqJVNoAsCFZYF/OyrOQCw0ZD75/AYWcQYPxmW0PLyEpkQlsPrSYesWe3s0LpPtKj8vk+Er25TCLc7NGzQfF5XtqlUccrWEdcBIHlNljHEywUc8EGDNxpJ7uPyeZlz2LvScO98gCAoG98M3SeHfM9RzoxOMG7L9qRFxXGoODaodD9VOQ6A8bA55PQ84yFyHgtzWpfctW6HoU8qha94AKQO0M85CyxJSgpJ2GAIOFFjsus6MmHFoqUrNCvseVYqQKH5uyQFhjYTZUdCic0Oc6SKwKCORcsahhjPPG7X6N16AynMWWQ1KJtC6odEwFyXudZ8i4M1wobUkMTy1+oEG/pdjmpyxMP1ekC6W/Kxtnd5nN6Q1fpWg4TQC1eAEweAVOB03+FXJu0DVkFWQCiDTjxQ4XodehSzZHjUYd0pjngP2w2gs01IuNVm4bnqk2l95CDbuIOA57nQBs5d5BqXHDR0qRbmuA3kjnDWGvTEowHQdbgWZNIHMrcszo55ZRFn2GWmlUD6ccwOI6UAM4jNMblSwX8b5bLsPewDVSrNfnOcfYJvMNM8v6+U+rz8/yUbug6hQFjgBbi2rM2wRKBTKlQ2Aoa7HFw+7PDmm8HZOUr0JEqZLO/2ZN50RmttEkfHE1r/DPtgHLBuY1Y8mHGrJuGs10o+l21ToKt13nCtADgU3n7EwqTtMxHPc1rOnZ5QgTK2QG9vE/EyOy63t4jqXbxMqPiZM7wPuzvkl9VkWN5wwJA2rOzJ/2IyyTc6nPnWH7Jnpl5hwfHCCnBxlbnHd77DY3qgMg76vIdaQhizfKnXI+xeq/MeWBIFKF+6VnMZZl5wSs7sNA2SpflsQuHa1aVnqF7nde10pLtX0TgkhsCpGOb2Yxn42CPIokdCq9Iylaig0iSSh41k+GA0RLmYFzyP54+DsiyGsYErrQUQ8McpGdT2i/A4+1YcAP8dgKf2/P+j4ND1EwB2wGHrwJ6h6wB+X973wi9d0mQcqYTXqnxwhr9kK94c25yxEiIihOu2Q+THVLeHMrg8SmmJzYryKGICn8ZibUMm4f0hPcRgxM8LBa52bEHktmmpOx2yHKJYGsdS4MqqIHyRJLhynKVljLcGLK+wyOfLTOckYX6zscVjFBbfD1DQqgKZr6wwrHCFj6VBwqltE6pWSgqQQ3qHJKHHOLgILMwxwZ8/CFzZAL70NeCvvwg8fV4YBgMm4zDQvYRPnR6v8cIFCWG0kFVd3s9MoONajcCAWavY78tgRGkPgSoXhIXCCAlD8Xa2wNAWqTDaoeGJUqlZ+eWMBgNX+x7Pww94bMMCN/Ofx8PZjWfKyga9NCu9kuvyno7HQwkC95KjakqpAwDeBuDD4Cw1BQ5df7+85c8B/Da4reBd8m+AQ9f/WCmlftJQQuNdASHdga40L/igkkwQIcHzMxvjnaC5YhjU6ZAjVZN8IIqYSDt2icaFIZWw4pN3tbzBOofnEPq2lSyFkgawOBI6j4Rv8/O82cOElt615UE6/Mw0oTI0alT+MKRH6fQ53LzR4OAM12XY1Z6ihV9Zoxfr9GhRNzY57bIq2wQuXKBiDCUfCVxgc52k2H5fWM0CKWc527BbFbZ+xwNgRwFFCNz/CPDth4B3vwm44yaGnFtrLCj3OryX/T69WxwTDMgh7I2Qlf2hbDmbaDD0CioMfw7MAtqwPXIqQ6S4zmQ05PMNPRFilM2JDuj5UGA8+VOLQChN4MT1RKFCFpTTSEL7QsI1UTDX5/M2GhDFAhBo8ZzCXNAoZSLXfL9hUu/ntd8c5w8A/I8gxxLgAMJ9DV1XSpmh65t7D6iU+hCADwEcQassWpNqnyc/GAGdXRIk4wRIfHqFXCzicMSb67i8uaogGTQST9No0dLH0u6sBH7sDvl7M+VyKJ9nOGK2ReHJJEQJpI3BDBV/9iIffnNCWLk2FbC7y+OFPutPNemu/OFTQGAB11/Hh/rkWTIjnJjvv3yZhmFji0l14DF0asxQUTZ3+J556aSsVniNOx0+bNel8NouQ9mooBDnkCn/I4npxWobGPiz95G5PVMDIO0P3W2GfqsrbC7zfCp8e5pUqCgCtleA40d4nYXizG6roEHoySTRnV0age0ua1NOhYqTpwyvuiOCH5A6kuncrNUZbbSbVIZRJr1YVhlZwKJhc3yCKZAoxNKlHECRDZ1ryodZNZnZ/L0tSmQKpAV4DS/pQEKl1NsBrGutH1ZK/Zz58Y95q97H78ofaP0xAB8DgMOLSmvNOLfblxvpkKtWFIQklYQH1QqtoydDKra2mMSnqRTSFJXKzAjY7QLwmHcoBUmk6DG2OxSsMKRFU5AirJAMXZcK7Qd8X0UGAaaRhFA+UapuzBwplXqIX2OuM1EAR49xiPraBme22QWArIRSlQ089TT7cybbbNsOZDjgzhZw+CCFqtun1exsc17A+prUhVpU0P42haPIWZcxzWd5TnqPsnlvTF+LBeBv7wfuuLasjXRizmKIcmB2kqFvrYbxHO7ugAapsHivA8n7NrZZS5psUlmrVRq+JOLXoEcAII75XAYJ8xsUDOPqvhQ1NfMzT0CWXGgwptaTZeKtYj7jJKXB8JznNqUVBf/esaXb0yKSaXZ8jmtAe0K6NC0Joft57cfj/AyAdyqlfh6c/tMAPdBLOnRdQWL4gpbM9cpQx3FKZdKaNRcz59kkqubCW9KXb0YxeS4fVG/Emw5RQEBymVDCPelBiSXk8Rz2uDiOuHtLagFSXJxqM6TZ2pbcKWbOMZTO1UqVwrqzBTy9Qa5dfZ6hkx/QYg5H9IDbPSbYS0vSzWrRMh84IJNiTlM56jXWhzY3ed5ZRga2ZfG6MglzbKuM9y2LPysgVXvNRH03Y154epkDO4oUmAr4GZ4rPU2Sz+iYkqLk+MurVIiiIHgxPyd5g8P3d7tSe4n5vtDjdSYplTLOeX0KksO6BDMaVT4DU+1XigKfy713Ax5vJHUkM2jftD2b8baGtDleWegRaILUr5Qt8pbxuRWasqGyl9DjaK1/E8BvAoB4nH+itf6AUupuvFRD1w2ioSk0QUiu0SBmDWV+qlQgx+JNCzwSMdOC1f96nShar0eBjyLCwnkuLQFS0a+EVCQlYZ5tc/xsq0okb3eX6E6WEnWqVgnv7uyK51MMGTOpCVTrrGkEPpEfVacVLTQ7MT3FLk3HA7Z6rNckKeHnWg3oRHyg/Zg9RoOYjO6dDT7nQY/K1B+RQLo4SzQwSdiJeeoG4GsP02IPeqTmGAEwG8dMk5pn2MI5MGUDr70FuPNmFjZDB+hkHJvbkXkJfsBz7fekWa9BxajUab2zIRngts3PTh0BcRSRLsslKtaPhXyrONGzECEvcpJGqxU+P1+Uz3EYTQQ+vaXjSz+Oz2ewvctnWQ8oM4GL8Xy0vBCEzy49kJJ7YAaCmL07vR2ZHSchm/ndS6I4L/D6nwD8pVLqnwP4Pp47dP2TMnR9G8Av/aQDKZSQYQFao7wgnh+6kn/EpGxoUMC2tkSAxetsd4Ul3WbBsV4F1q8QgvQcKpJlS9uty7zEWDVVAN2ExMUsk85TxQdlWpIrPq3bMCE7OZD8Isr5gFXO5DdJmFttdcoiXqVCcmoeAZtdom69IVAf8Qn0e4C1yDCuWaVAePWS8l6pMDRyLHrJNKO3OnJUGOJpOc4pTSU5hoRlUvw0DARLcoDAY97VatGzdbeAI1PA6iTw+DOE0HsxrXqzKc8koycNK8BKn8jfzjrJnVNTAFKeo19haLy+BSyt0zhYOUfgjnJ6PBRATeouBrZXFr11EpPV7QhYY4tCDAa8Vjugl3Ic5lrGOAClt4HUZsxCrjjm/bctjLfG2bZM95F7YxRrP68XpTha628A+Ib8+zxewqHrSpWoWqYBSzokA8k/XLFqZoVgvQZAk3bfFyXIUw4AHw4JSS8cZg/7bdeyRtLpUXmmbcLDjkfB8n2pXQxIkQkrLLwWCtjsCaXGB9yMv7dtYGoBQEbIenNT0LKUsXWgSZ/p9ymYWzu8vp0+z1UBaFeZMCuHswwslIl7v8+i3uIBYHsDmG2RnnP0WNlmMDvHzzq3wvnVgxHvX5qSamM5FEArkaQ9pBDVCuDYHPAL7wJuuYGeuL8LHDpGgT64SKg6d4Fijfw5LZD3lTVgwaVhWRBmtJbwDgL7jgQFazjPy8mHAAAgAElEQVQsOh+c5Zbr3g6ABChGNFRpSq5fHAPWgILoFgQs0oLETkjhs0gITsDlM3Ol7mc2FATCBnBcnmsOKa4Kuphl5SwF00rhORgP9jfbD/Yq4E96XTXMAQimD/DGOh49SSKWIgnpksOQ1eXBgJBpv89QzLKEN5XTCmnNIp/jsAYTeIzra0I0rEgh0XEojG4ALDZYk1GKymv69Ss+z8O1SXTMMpDhoMkhiyOgp0tvYHpazFjawGObNQrG8WEo46uq9D5Vibkr0gs06PA6CgUcPEJS58IiH2qel1XvXPIVQytBzmPDYti6tiE7RTUwYQNzIXDjNcDrX8cZ2ZUKkNoAMgnBKry3tst7trbGNodKnR60LrtrtqSAOzNHdC8M+Mx6PaKNJlHPc35+Z8Dw2U5Avtpa6U2VoJipJsXJUGYceaYAowyty9x1by7znCRgT24Tj0qmt5mSA5R5n6HvKPkALZ74Ja3j/P/xsqTsa1pcbfCBuIpWx5WLLURI0gzjJbOG++R7dOW1gAo16gJwWBNJMlrlQvHhTLSFgSs3fyiJ7GSD4Ybjs97SqgBBjTWOSpWWe3OL0HQWswC4KU1vZkAGQIWYWxAllIETU1PS5digUilNKP7sBXZ6Bp6sExlJR2mf19Xr86tao6AVBRPw7oghap4JkgQJbSzSgiyX11sNgEMzwB1HgZffDJw4JkbDozEqEoIXG+tkks/PA4s7wNo2GdfrG0TB6jZzHxMmLV1mor2tgIUZhqOBz+P2OsJa7gETFWClx4jAlrJDJCxpaGGYC0y8tsHn4C2Uea3nSXTg8bkYUGe8EkTLIA9N5Yy0DBopSsaA59G7j4uzEPaAh/HM70Lu435eV43iFJAiFUAFEparI0jI2I1KEbNWE1Qk43sdUazuiAhaIGzmzKKSxdKz0xvRqm91ZSC55D/I+UDDivy7SuUtLKJPAG/+KGKinRYMSXoyA25+ntZ2d5M5jhLCab3OEK7ZFupPzmLnZBvjXZVTU8zJdrf5nsJigr7UBY4eliYxC+hc4lwBK+PqEzsE7HUiWHGPREnbLoeKhx5wzTywOAG85k7g8AESRoMaxgMBTaE4cAl0jCK2Q1dDjuYa9oQZkJHwOhgCtpA2s4LCO+oDHZ+Aih/SUFQqYow0IW7XEZSuEITUE+RTky3gaAlTR7yOeAhEMmfBD3nOYSAhs8VjGLhZS10miakMtsNzNl7GFYTRhGlK5MnxMEbkNDCetbCf11WjOMZH5hqAUGWyAuM9OVEKoC8WohD4MwBqkHnJUqDTloQtFqBchgVmtlmU8MFvSZ9NT9YV+jbJiXnGh97vsfi22SEiNDFFYVxdB+DQMm3v0mq2WlzfZ6ZdVqQRy9SAVtdki5kUPJsttmhnVULX1RrzuG6HnmgYsTV5t8u/6w4YduQFz2N5FZhuAcU2sDtkuNpqMIa3ICFuSmHRKTA3AVyzCBxaIPO72qbyujnGw+FNS0TgUuA02GLdqHH+dhzTkEQRrynLntuaUJVtEb5PNKxSleEcHYIEFZtDIPtD3j8lIJCZOJPnfG5xXnZx+gGNjiVVfl88jeei3PWZl2halvHcLUHRzHAXw5i3rRKmH+c07nNF8MWsNbw6FEeSvXE4ZoAC4RclKCHFPCe1ptOhdUxkMoltU5EAAB6RtSQFvCoVIs8o1FHAB5krhkT9PhBOkj5j6kJVmfcVhABcUmAyTTRtosE8IM6AxgFuLYtzjmnyfQqvH/B8HHnISKk0Scqw88g8vUo7IGAxLSN+RyM+3O1t0lUS6YTd3KTQXL7C9uuGTLsJHHoGP5DWAE9AApsKHbo837lZFi6rFV6j8bRxJiFxVXJJSA7lcOLniePA+TVgfpYjqyoe/zaoME+cnSHXLRDFGY4InY9G9LjtNnBpnblEvclr6UfSCiJMdyW1tsLkGBaPt7DA+W2Q3NGTHNYV+s3e+QK5ABKOhLF5TrbGeNi9uJHxPlALgM3vBhQwzW4/VWs+ACnoFxRc2yUsOz3BpNJVgqBInNuQTWWjiA/IcoFiCDICYsbs1SowWuUsAq0ZPmlgvCSpEO6b7wo6lNEShVKYTKTS7AloYRcAUrKLbYeeoj8Cvvkthjiuy9xqIBMvLYu5QVhjraLiEE6PBzxeltPyO4rXoVOec7/P4mqSAwPhXimXBdrRgChfcwcYuMxd2m2yCOYmZOFvhZX8PKMiFQWF1qtgHJYAZSxvkvNE8khDwbcEGkZGoKEoKNBRn0qyOM+SQKtJTx76UtvRVJRV2T7hOKxnweK5ZjuAF5cESw0AwkyoeFT0VkM4hbbUWRQACbPygtC2JeeayYQix2HQYvvidYqylmXCMyX0G63pbQ24UBT7z23M6+pQHEnOjMbrnGFUtyv9NTFgN/nWOC6/24oFv6H0+ccy3ANSAAuqrAcsLVM5lGJMjxxwQx5nug3UD5JbZm7q1iYfyHDIG9pq0JIrxRpFLFa5bjMBNWv34lymca7wfdUqK+KwONdgILWdOBVoXJeXH9hUtGqDAjjhkegKS+Deguhda5L8NRv0Mlsd6fCcpCfIbeDMRQry5AQZB9td8t2uu07uQUrBCwKeT1IAboUGpxAaUBjy72+6Dji3yn03cUqv1e1RaQ4folfsdSicQSAIpUvvtb7OPCwvqHxmO0C9yjBsa53nU/UJQzdCKm8oIVmayuBBCe80yiJ4lkttzhIDIdGK65ToapKQe+d5UjzVZShmGvkMyrZ3OPt+XleH4kAuQL5nOZDYLMJVZEjfaETh80N6izhhSHNpRegSIPQZhCwyjkmQubQqOxT2OKE1HoykT2RAbzLqYLxIKfB5zMkWlacRAnmPYUYCwrPdDsZjdrNCQqcacP4cBS5NyiEghc2azeKirBiUvhfLooexM6CosDa00yUamAf0MnFCZYEST5SUtCDbJrHVk/vmBsA3vi2DF6tlHvLoYxytOz0FVBdFAFXJxwsCHnO84Vlo9u0Wcz5oHrMje3dOnqTn3dykUZmbZaharUoeKbPvwjrJomZg+ihhKBonvGf1GlkX6YhF38CmUjVrvLeeTUUzBEwA4yHrZlC8LYpj2gosUD4AjHeF5lJAt+Xvn7/N+vnf9/O6OhRHgWGEKpEs436B8iZFQqmfmCRYoHLZJ9kBBoVg/4Lzq0IYB8NSgHRGtnXus3vTBkOoapV1FhtAMeC+mrhOK9xsAY8/yYdjFQy31rclaRUL1pqQVoSURctoWMbhecZcJMs5/aXZBDwNHJihNZyaYq9Mp0uFMjWevox0Wl1mk5mBqJOC1zwjTHDTWjExCXzzQdl3YxM9W77IvZy5zXzksccY/noehdjzykYvM7jCIE62S8/XrvNcdnZYZ1I5sHqJg9LXN+hFZw4TcZua5Hy3JCNwYYCHUSwTTzNpL3CkvlSQBXJgkkNJFHiMiummlXBRaUYdmbCle7mUDBx6yCx97nmbrdTaEsBEIGmDdOoCgIR9ti1UKsmtf+pQNTNB3lDgTXybiTcxMKNtM0xYWSH0qxUf8KhDoRpEPI7vU6gmWoL/K4Y6ExLvXzwP3HITlcWgNaZwdnmV4V+jSYFpTzDnSBPSRqp1PtChDJ3obJJBUJEkvVlj/jE5Res3HAKJ1A+MIo9EGJOUkHpVhhr2B5xnfegQeXor68CxQ6yxdCTcTEb8nCxj3tBuU4jnZ3i8yRZzrWaNLdpTE2RdTzbIkWs0CYfvHUhoqvC2DdbRPIazh4+TZnRlE1ChLJYKaQSmZ9gOsbPLe9vtULm3OsClNYZYZhPbQGhUZiNcVkiDogvApmKY6aKDPrBlE0UMQl7zQKYIOS7rda6h2GihO0mxOpE6UyHeo1IRcm7G97nCPrAkd3VsQuE8GPatOVeN4vi+MIqFu+V5TLZNbaXQDItSk1BaABxSaoYj3hjLBmDLsqOISFaWMeQJA9IsdneAaJVoVFcWx0YxPUgBYGIO8JqsI4xGFFzLZQiSKCbxVk4v4CgK7cx0CcUGPpXPsslcMEPAPZ9IoFLMJfpCBK02AFvQvSQh6DA/S494/jyFv7NDXtrSEnOZvkVBqtd4H/JciqcjKkVdll6FkwAKLrRKEyrL+jqPkUlDV5II+1zCGlNQNHG/7QATM8DhhAMGq4LA1aqEzBsNOe86jdhgxHtVq9GDavEWsCQsFk9iZp6NYt4XWxL0XQXU5jgtp1IT6pB4x1oN5RinQuRF8TlAC7HUEgaCNCxmWloLshIEGLPGRfZMu4lhJuznddUoTpbJcLuC4UqrRasdS5LelJ77EagoOzuss8RSBIXcpFzzYeQFhd/RFLC4W1JDXKf0aPGI8OjkpIwm6jPcmJ2mNe10gcXDRKySkdQUpHh45220mDs7ZXV/1CU1xfGla7KQxbqSQ3VlbrUbCnlzxOMGsh6wFjIP2drgWsVRjwq/vkrBqQTMA6KIf2/i+mGf4aJrlBsUpEOLwPmzPIeTxwleDEclEbRS4bVkGT8Hmta6ECveatPK55ph16UlwKnSAzsuhXSiDuxu0YJ3+vQUOz3gZ14J3HufCL8QLLOcXsKQNysew9+JJhG1k8f5LGyPCuVIC4lts9AaSq3GES6eH/L3WYpx+7NtUwksp/RMjl32be1VDp2RBfIinA2P958q8C/Vy5IzzxMZtLELNGYFYpQqcbVKyzncIjUjMi7YoqJEIwqLtmnNnQo9ASzWKsy+HVvz4cUpkatKlR2WaUqLXPXY7uy65LZducLEu+EyhJqdBR77IXdi5op5S5LIbGcHUB4r4ts9KvtwT++KU6GF3NzmUPW2rO0IG/RwtQonaDZr5IQdO8hcpd2WWokQVR2fgt3ZoVFJpbgYJQz7vBjwWmV+MdGmMpllWYHQVsxEIEfif88ViFfCuFAGKKYJFdKEdYUtw0RaDAcnJsqlW2urvJYnn+SA9/Pn+Qxy4a8ZwbYLAAXznUrAULPdBKBoMBtNnr/tll5R5wAEATOtA5ZFhrYGxkMLc1H+TOQHqpx1rSGompIakCm+q+dx317gddUoDpQIvEWvkKesWdiuDLPI+cAGQ4ZUZmpmknDckwapIpZQO7TmQ3UsPlAHtIheyBAjTaQIGFNJB1IVr9WAU7dSWDe2gfkDfEirq8CuxWGDz5yl5fZ9Iko5OAstk0Ln6gaVIhNmLzL+21hQX5r0qrMihAUhY0+xVlMLaRRuuw64dImQuc4Z+rRnWKzVCXlZk+KpsowhZZIRUHAcKkejCZw9w9A0y3hfnQoFMhBqTJ6IhRaP4IYA5LwqHlBUGUKateiuRUStPcl7WQs4y7vdolELPIas2zsAXM7H3tzgMt/1dYxRO23LfQikzmaz7aAu/LHtHn8eSE3H83lss64dSorWLsZjoUz13ww3yXPKizIyJkVuQyg2SqxV+Z79vK4axbFtUj5MUcpxaQk8p2x0CnxOpunscKVGkWM85CFOmIhXqryJtk22bp4xxMg1H3JPVnS4Ptm/vSET4PkjMuDvDAuSu13Sbh4/R2UzO0UXFshQsF2GV8vrYrVtns96hyNfGx5wYpLewBIrZ/qKllaAjQjwGnyITennaU9TEDp9KuDyEi359hY7P48eY6jkKoIBhre1tVUKSBhivER2elLanh1pl7ao4CfqzNPMwD4jcHv3gI5rauDvJiaA089QqbKMOU2S815ozfBpJDlMt8eGPNvn0qiFBbLCh30+Y1O9dy3mgcMqr2845LE3N4GJadkc4cjztMpcxJb8y2yrfv7WAa0xHqRulkgZhYFVomrj8bfgz/KcsrSf11WhOAoYT/IM/LIxLLQBJ+cFG7fs2nTtqS5RGhcy9imjsnhuuXxIg6FKXrAekkZMUo8eBV7/ZuBr9xFFW9nkg59oAb0EOLdML2Q5pJWkEfDKOxl2KAeI1jEeVWWEbLcLuEPg5UeY2Do23+sLZacCwM6BA00K3dlV4EqPMwtUi8iUzmWGWsTvl5c5AHBziyjd5ASQLLNvZn2TCnbkIC25ZRGgWJimoej1ytXp7QaBiJ1tgi+TUxgPXTfLaI0AmvBHKaE/adauFhaAdJPe1/JkTHECWD7GXZuFIoNcJzJqywcuXmI7hu/QI0YR4fqpFhdrLUzIUt82PVt9WhrwXCpklsp5SsmhyDlSyhJjkAlL3tRntBbmvFuyIKApM6YjVGuJbkDvpi0+q7+LuWp/py+lZUSTFMh8n3PBjh6WcU8gVLu5zZ6ZpODPIqGuuB6VSykqjecRGg1dmRcQUwDe917g9ruAM+eBT32CXaI3n2Sj1TvfSQV77CkZvCF8M88BXvNqjoQdJTwPWOWknTyjckUj4NBRoD7BQulOAWzkwGbBbtbEB1RAwQp94NRB4NZjUrfpCXHVY3Jt2hoaDQpRrQ6cvwCsrALXXUsFvOEk781wSKscePSam9vMyaKEUzQrNeZOuQAwjlMOHtlLbDTVc8sqBc5sdE4SCioAQNNT1EN6VFcoQYWUDjxPYGKx8vUqyalxCqAAVAb4mrWfakDlDwKGk8YLOo4UMAs+A9gM5TKN8XY2wzgZ99fsAQccC0Auyb+0i1s5PUUe0RAWqdRwcjAZyn4KcxxDd4klMVUi7EVeDr7IpNjnSu95UciwBQvPWSg1N8v3djp8aB/8IPDQw8CjPwD+9E8p/KoAPvA+oj9HT5Cm8rm/ASBkUUvQKc9h0vrMaeDYcXqAXMvcg0DIkRKCHZgDrBawEsmEUQkZPGm8snJgKqQyWy7gF+TkTdaBXkSFbFSJwI1i4MgC6zcjl0pRq7NA+NTTkm9s0si4DkO0QkKsKCV/LQiYi/Wl/rOxSi9UrZT7O/fuyBlvCNjjeXxPmM479F69DnDsKBHL7W3ei0EPqMoMgSgBoAT0cIGVLZlukwLJDq+v1WDI1qhSWVpNekTblqKphFfDIS27L17FBu9hJkpt5kjvPV/DPTNDPwoNhl/Gi+oSek9F1gqnNB4/dYpjQrWZGVq20ANm5mktlQKQ8SZW6xxjlHeFZhPS2ocVQEWyNiMBfvkDwL/9OKv8//JfURFDH3jVXcB7fhH49Cc5+OLuzwKDeyj4OfhAXRvjXZtpQnp9f1tCFEv6VzwZvSo1lTCkQK6vAp0Rq+2jES1dYTG8bNWAgYRwszWgHRIZOzIHPLPE2s7CLL3f7ARznFaTeV1FBscnMTB7kEbh0iXgxFEBOKT2Ffjs6swTLnmanS63CnQ6zBWHQ55zYDYCmMq6WOsiL59JklEI6xXgztuBJ54GHn2UhqlSpeLUKrxPjkP6kOOTObC5w8jAbM6zbRmuIsrhK0LZgVcaIhf8/K7w3yA1GICKAwVoX9oPMv7eNQibRAlawjJIzpJLWcCS4qthFrjyXluVed1+X1dNqOYoxrPb0rLb67G63+3QuoYhuVJrG7R+RcGBGU7GeV79HTKp//Gv8ff/+58AOwMKRrXC+WR/+HvA5XPA/fcCT18CfuujEppowrXtOik4FYeUklCRnj7bZrjnSu9IEOzhmg2I+kxPc4rNzg5ZDVo4UmlOz6U060JLV+hdNiJgMwb6KZV/slUuqW3WOYzR8RmKZbkIjaYQrV4h/DzZZALd6TKcm52jAVjfoPHwqlz8W5eu1CgihSislO3HJiSzrHK8VKEoc1qKi6rg+X/ja8DLX0E6T6NW5pyG8+b4JdRr1qTnwg00LSFRhHGDotnFk2U0IGaGXiHhVRbz2CYaMS0DEEBIF1SyQv8ow9m0bkcR70mnA/S2RYkgqJopgbyIzk/z2pfiKKUuKKUeU0r9QCn1kPxsQil1rwxdv1cp1ZafK6XUH8nQ9UeVUrfv92Rct4xRzRSabkfiXl32eqQpka/1HeAtbwOOnySOv7JK5VBy4+ZngI/+C+DUccBKgEcfBKIu8KWv8BhzB4icHT8OIOeIpHoAvOm1HC/r28C7fp51Ccctz8kokNbMEwLJJ5bW2LdyYIEe07YogKbJa1JqMRcvkMy51gP6oHWsVmWAuEC+ji353hCYm+I0mZtOAnfeKezgGLj1JtaJahUZ4JgCJ08w6U4LtjTUKsD6igyOrwDXXiO1EpRW1nHKOolhEjgiyMrhsJEwpIF/6Ht8JrNzLGqaXTnbsr0gznkPzPAVCwIHF0LIVAQ6BjJXzRSjbVHewiIaNznLvqNmnddgogDX4bMyaOqYl6bxnG1shiFgaFphhe9NExackxHRx9TkXaAi7tfpvBiP8zqt9a1a6zvl//8UwNdk6PrX5P8A8FYAJ+TrQ+A86Rd8KdDKDeOyUW13l9Mrd7sU3ETmotVbwMvvAg4sAv0E+Pd3A997mH03gXRTHj4I/G8fBl52Cvgnvw5cewo4dxn4d38JbKZAHlLxBluskYxG0txlA7fdylxoZhK4/nrguw9QaYMaE/XxkDu/DNF8n+yD3QF3xiQxE84ik5lfEhAXOTBVB2YarBPlBVukzY4ezxAfEwp3njAfqgdcO5/FwP3381yrNcbox49ScYuCnno0koKqz2OcPEE0y7YZptVlnUathvGAk70QtGlPN1sdRgnrNY+dBq65ntY6y4CLz/K6b72Z+aXvMy+LEqKY3Y6APXt7+gsJC30ZirjDZ20oNdUqazS2S88XVpmLma5N16WCGcU2JGBjxMwCqUwaIE1UsLeYGwrE7QKA3Oso4n2L4/17nv+UUO1d4LB1yPd37/n5JzRf3wUnfs6/0IFM8S0UeoXvEi4NKkC9DZy4sdxc4DrAd78DPHuBMXlmk0PmF8CvvBf4sz9gyPPh3wMeeIJD9v7Nx2nJcsURTRur9AqtZtlPMj0BvPMNwNoFwKvRMs0vcALlSAiM/YijagOLDz7OaXG1I54RtHBxzn0wSpGM6TpCNMyZM+SaOc+l87TS2xmV2SzPVR7rVA5YE2lOUYnzIaBlUGB7kgwBO+N1DHOg0pZlWTmVd2uNI3PbExTW4ycJrJgqugEGLId5iJY6SS4FyiSmcl5ZBd7yVuCZp+lBb3s58Iu/RAF9/FF6lNtfwetOJHl3q8BGn+ieI0wOKIw3WucFEDSJjBaFbGQTMEBJqSFNeW62Q6OiBBAwQ9aVtM8bpYxT5l5pwobBJJLPtRmRuBUWY2stflk+z69QZX6z3zxnv4qjAXxFKfWwDEsHgFmt9QoAyPcZ+fkiZOi6vJZQDmQfv5RSH1JKPaSUeqg3YJ4RDYGX3QG84+3MMWo+E79Rt8wrRiOMp9Q7CmjawI2HgQ//DvCN7wD/7a9zMMa5cyRF5mDI4rikwE/UgRtO8Xdxwmp2GFJxvvEdticozbrD395Pq9btUmnjAR/uREv2korFyzJaZm0q1XmZO5ge/V6vjMOLgtdQ5OWmgTSm1VYF70OW0QJbrmySA4GREyfp1To94LEneF+QMwSbmuBxppv8chSLvXlGIurcbDkkY1xMFOuuVdl1aWg1icxy2N4FPvVJ4B/+feZWDz8A7KwBP//zFLrOEPgP9xCGv+k6AEnZZGZa0G3Jl3zxFGkinaEiXDnIOUwiyXsk9zHAgGEtPL9gmwm513gbM57LjNFNBBgYbyJQgmj6bAep13gP01SM4EuMqv2M1vqKUmoGwL1KqdMv8N4fp7M/cjp7h64fO6i0ZZHz9ciT0iui2ZvfarBNt9mSiSseb0QtZGPYm38W+Ku/AO67D7i4BAwL4PGnGVpBCclP6gkTLf5tp8cTak0C555lg9ijj1MADh+hh3noB+RPmSmWUcwRSMgZH7ebFBrLllxVwpAkLavaWS5FWk8YEFWhexQyrxpEBCekIGr6iMwWBMvlewcRPyuoAf2Mi38HAyJovk9Ie1d2/QwATDX5714POHSQOzinpsoVhlqXYaElkK3rlElymrIY2++zZeDsGdZt/uovgf/hN4BPfooho+0DJ68HFqeBB58Cvn8aeMpj+HvXrcBX7+Mzq9YJaycpw9cEZGPEGalJdkE00WyIqNeB3EG5BbugcO9tPisELTONapaF8UYJkzOZEE/nz5VA001qidcKJb9K0n1qA/bpcbTWV+T7OoD/CE7wXDMhmHxfl7cvgUPXzesAyoHs/x/Hl/pDwqLicMQzK6QAaaxgVsjvAPz+71HI7v0GcOgUcN83Ob0mLjDe5xLF9Bar68D0vAxfjwiVbnWAc2epAKduJOPX85hsLyyWniiJgGuvlfAi48/GS6gG0q5gEle5m2YAXiDjjCyr3FtqhvAZyz/OMSChiVtaTdfhZJpOD/jhY0BrmoubQo/Fu5uu4/lVQs7JnmyxljQzy+W+p24AjhwDDh0WZjh4TEvgV7P41ljwJKFAGgVbWQO+9R2yLD7wAeYj//pjwKtfC8wv8ny//S1a7ne+lfDycETl/uKXeb/e9CapqWiGbJbN0EtZ4unk2ccjnl8alQn72KNYzwUy9s4JsG3eY8cpwSVjuU1tZlyjUWXZA2DIbI7re7xH+339RMVRSlWVUnXzbwBvBvA4yuHqwI8OXf/PBV27C0DHhHQv9CoyjNcuAEwSHZ+WyTEV5ZS0j7e+Bfid3wHuuAVY6wBffwjYGEiHoYzIVWCFuhoCJ04Aj3yf5MjugKNcteINf83PAg8/DGiPdZZ6ADzxBL2RobCsrQgtXfIHyxYOlEUSZ71GeFYB43gbEItul/3uZq+pifGVYrKuFEOZoSxfMqig6dFRAC4tM6Gfldltmyuk4dsWAYLbbgJmp1icPHEti7WHj3B3aKVS0lGMkkTCOgbG6O44Sd/elrB4QOv/lS8DH/sY8Gv/DcsBn/gL4OY7SKk5cQz4678FvvAF4IP/EJiuAlmfLAoA+NpXCa3fcIpcOz8oC5MKFFbTBGh6ctKI54KiFPq9L9vCePO06/DZBKI8Y7Kn2sMikGsHSmUZsw8M48Apkb39vPbztlkA31JK/RDA9wB8QWv9JQAfAfAmpdQZAG+S/wPAPQDOAzgL4M8A/OpP+gATb5t9MwfmSPqreES3fJluszhDaHUU0zJ/5kusjVgS/mixSH5IoU/5Zb0AACAASURBVLB8Cs2q9LIUBYW/UmF4VA2Be+4hu6AYMaGPwWS6Knw4BPR6VV+2EWj24fsKQApkQ+CaNgXad0sWdyyWU2c8PyO0WSIggk1+lqM4JqolBcpmlQRReISCN9YII+cAnr3Eh94dkkzq+MChIxIWghDuxDTzmWadXxVPUEurRM+MlTVonBbN6e5wV6jrs/h6ZZnMivmjAELgTz4B/NEfEkr/vT9mLrm2SuPRyYDP/S294q238J4aL+IHwJNPlxsY5iaAu+5giDyMZMucy+s188+UZqJfpGXOmBU0XJkCcgP1K0C7YCHUYa6Mgl5t78vMi1a69DpFVtbbzPyIl4wdLcPVb/kxP98C8IYf83MN4Nf29/Hmj/gwo5TU+ThhUlsXHtPiHOsq/T4ABTz4EGnsaVp+aWlms+yyqNZslgthk4Q/DwIqV68PvP+9wBc+x3Cu0AzDpqaAxx8nONDpsKiqNTlVsMpjDOVzE4/Q84EpYDeSaZwR72wuSNVImMJ5Qb5coYDJaaCIZJa0xbpLRcKFQV/QORnL26jzwa+uMzk/eJQepbB4Hbvb5LdNTlOoDWhh9mwWQmXS1h4IV/r/Ad6rOGIIurxMdOoXfgG45TbgD/6YOU5QI0jw679F5PK/+K+BJy8BXiIhVU6iaTQii7oSAr/6a8Bn7pYk38DEwpd77FHuCmqa4SgJt4YHPsYEZbO2Y7wMF6U3f04NSsCBPAOZA6kQSV2MB32Y+WuAsA4UlcbZQ9PZdxEHVwtzQJUFt16HhMdWE3jrmzhTeWudinP2rDSbbfDiRymFMkmfOwIoCNhFOBiUI57Myo7paQrmzbcAn/4LWlRI6BUlBAsqNYYXzTpDFbMeT0mlfDSUcMEDwiZBidkacGwWOHwMWDhENjH+3/bePNrSrKoT/J3zTXd6U7zIyMgJMtMEUhRFoRgEEUlFCynAbrRVFLsKpasbq0RplSqlWq3qtbBWW6CrBAW0OkspJ9RCEUlFBQGZZxvIJJOEJMkhpjfdd+/9pnP6j9/e3zn3xouMl2lAvKj1zlqZL+70Dec7e/rt395HUDVFdUYjxh6PvIGa94pV4LiwFe45wSC7mpCuszQUGpAjtaVp6SZ94S7e69IqcNsdbFSyM+U1n94ka2Fnl0pI2zEpeAEEZMo5zs2RNS6yjQ228f3MrXSp3vc+diHNM87bvSd4XTtngJ/4D8AzvgPozZgXqxzw8/8O3Q4B3tOK/PpvMGa89ioWAD726+hKppZ1OBkYHzpHr2JtjfeR50HpaNfNJJEEpeXzcLUwpwUyd5K7AYRVbcN9KkoYu8pKK3KOc7wX++CBxoHgqnlQC3vPevunfTPw8Q9w8d7lgeuvZWzypS/R7cp6DPQnNSc3zzkZqQ0Iy+nTwT1Sq7S8zCShsYSjkTI2KUs+oIdfB9x6K4V4PKaW3NlksjExQvXv0bf3NQu4jAHulUrIYyN+d6cArrsS3d490xJAwnhmJvmFywasKLUANkrg5CZb1RYZY7DhEIA0i68dlcN0yv03MwD3300WxDO+hfO3sUnXBQkpOEdWAUhC0xouxLYJMC0sX588ybmoK5ZMXHEN8Fdv5/YY//ZngW/4BuBDn6AlGJesSk0nwH13A799M/Dc7+EuED/5MuCXfwl4xc/zGmYC7+7OgDvuouZffTSV0fgMmdHXXy1FbCnnZkkaOybaPEVABCvum5e/uiVjLQnLeBe2xgc0LUloPb0co60jNrgLIImVUGG/UDRwUCwOuOgfcyMz7Y/5OloaA2qm++4jxwspNfxuKf3IHIPpNKW/PylJ3CzrEPh6xwewtCIuEIBHPJyxg2tplbKUrt6nPoWuj/Gp03SdMqlAnUhzxJlQXBSF2dhgReUnb2f90PEh8MgrgRuOAi/+PuCnfgy48TpgsAIkA+4r88hjwFV9IJeE4Qduo6aFkRqgArhfOmG2nn59r8fr3N5iqcDKkGTSD32I3/vcF0n6LCek8J/eYFnC6Q32mBtvMfl7eoOCduoU8M5306364he4oD//BSDp0/Le9J3AT/4E8E1PBX75/2E1py0A2yccvzMB/tkPAN/8rYxHbQa87Oe4CL/72UGpDEd0KRtDguidd/JempJ9FSZS/NYbMKbMh+jyS1kK6O62zouWb/ieMZwXZaaPd2Xf0ZIC0rScz0FflAaC9WkFFgfQbfWoTARzAcGBL/vwnsjQXXcBT34yA9DdKXD8CgaWd99NS7G1G+groyEX9qAX3I/rHkY/20THTdJQswLDRf9PHke3oNcLNR9K08iFfKgNuUdLADzLgsuIllHkDIqLnC5DbwB86jNAOwWWMvYt+MQHgb/+Myb91gvg8gxYcUA+I2x7coe5D+dpIYpC+rEJAVFdjMSKqzmim3jHF5gETfuMw+68kzHcSdki40t38ftnTglhdpMW+PRpWu085/bvsykrOx//BNlAuAd8/jYustf/FpAsUaj+8LfZCvjEfTLXEpi3DfCeDwC/8it8XWT0BP7gTcD/+kJ0dS625edpis59LQp0HW+WloRJ0EfXFy/uuqmIpA5t4NI0FJCuH4HEclUdqDRlKbQdG6ytumTCBOoAE55sf2v2QAhOkgB3fRH4xscBt34aePpTge/4NvrW959k+9YkJWiwuSFcI8ugME34UK+U1rNLsuFtJghKapkI9J6L8oorgf/+Z4yTpjVN+/0ngWseToFrG1qVlRXpUT1lHmXaMLmm7YqyjOfydWjUcXoH+NBHGYdsyX4wD78SeMTDgMsskGyw287GFpuZ/8NdwEbFHMzagH775mboQzCS9kebm3Sltra4507TEPm6+25aqDMbdCvLCZHC8Q63j6+mdOnu+CyrRce7ZEtPJvzv9Abwlj8npeYv/pLdOKebwEv/FWB6wNc/CfiNNwA3PQ34T/83q3FrR2qNT6jJmynwQy8Efvs3xSJ4AAPgjf8NePGP0CtY7ZGxMeiRauQlMazwcZoE9yrPQlMN54NwGTPPpNbFnkriVo+jbttkSjqTxjbWiGfhIlqNSI4RFseDwAYORoyTWGqHk3cANzwcuPGruAA+8mEu8J1tZsaXRtLuVVyYifjzV19JH399lawDDRSXl7lYRtKUbmnI3QVOnOJ5S/F5l1YoPEVBIdBe0cdvAD78UTYwPL0tnSylSYixFMqVEfNDlQGu+Cqe57b7gOaLICdsxG23y4aN/U7t8hyJIc+ulwPHVrile2IB2EBmHO9y8WxvU2CPHCVHbXqHdDOtgK9/LAP6rU3e70Dg87vvEatopQdCw0Yjp+4FPvpxHtOAcP5f/BXwvOcC7/97bsj7iv8L+MEfBH7tNYzP7tsGvvkxwO/8FvC8F9CV1e1UbMtWty/6F8DrXw/8y5cwnnEO+KM3kRHw3OcAf/RHFP7VI4Tge9JcMCbNJpHLpJag2wSqDXUzVR2oTAbhd96F3+kO5VqObgx5bam6fwjIXNvSgii9Zz/jQFictiWfrN8js7lI+ABvu41CA0uUzLZEYVaHLAGwYEUkRFsoggbQbahm/P5sKhp5Brzjnfx8MpN2UiU19unTsienCXX4ZwRaVv9bcx/9Prr9b5CgC8g3Nnkdy6tk4m5NuDXHP3wJ+OwJbjibJYSgbUZqzDVHGSDXZQAxioEkQyWxpzX11tKvr1uCJc5TKHZ2JHkHWtU0p+Cf2iR4MqtC51Bv6L4hYSzUtMDTnwFc/XDgu74L+JwU4k03ga0TwPe9AHj1bwD/+qXAO98GHBkCSSvdMgWxazxQW+Bf/u/AL/ws2wwrMDNrgN+8GfjhFwDH1wDUTNxmCKRNBXSsZH+ThGthOAxxRxLFH8riziXpqYs/TQN51buoPEIQM2VuqFumrIS4Uckl1cnTexZlPewqYLIBfPgDwGfuYs5idUjfd3ZamMlDNqZDDRwdEVmbttI/zVBLD3NSb2bgBA6lJHjtCBeyrzjxjQNMzd/OamCpACA8slEK3HEPcN2NhMjrmsdvSn7HVxTwM01oWr67G2r61XdftgAiOFQTvcMBF2DWUBOuDYB7tolcXX+MyFpbSy5KOmFuj3kfg4Q7z+UF8Ok7gMd8DbC7QUClroCkpgu5MyZ7YmdMYdw8TUbyfWeAf3oTcNvnGLS/973AW/6UgvJ1XwO895PAa/5f4Pf/GPjWZwMv+BfAcALc8jfA11wHvPcTdNvGfeCKCtjw4hb3gF96FXeNO/UlMpHXVoEjfeCWt7IU5GsfA9z5WWk6Uguq1hc3ueZcqWsGz7jLg1YDJhBnrVh8AF23o0ZZHQWQ+VAAZxU5c5irbrVWnqukDJom5HrONw6E4MAQnmwa4JZ30pVqGu7M3Mu4oC+7hu2FMOFEDodsVVRvAW3CHENdS418yzr1SrhfkCDyyU8G7v7joF1iMKAntPVBnwI13mVmvKmFPuIFhZtI9aP40bnh972h/z+ZcvKtDb2OrZvnUrUttfRoyJ0QhgWnQRnFzsv2ip4FWOOZfC6dSZeXGe+4Btj1zBnd+Vlg8zjRqKYBbB1oJv0+AEHmpiVzRY9+NDD5XSJln/4sF+5P/DiTqH/+dwAS4Ef+Dz6Xt74ZWG6BX/11xpe3fwR4+a8CR1pg2/KalKKTDGjRnvdc4B1v58bA+QoXWjUlcHHjo1gif++9oUlHUYQYxUVxiIeABWptPLqmLPqfpiHUklRTHlfdKe8FVJJjakJUraIHQguqfS7ZA+GqJZJ3+bM3s3rQWcYzV6wzbikS1mtcdSWp8asrXHQwjBcGGXD5Orla/R4fkmmpzTLDBZYl1KrVDB15MJfGdqMlCtlItpfYlYYgO7t0hfKU/vVMEDVvArQJzwfvPAPe1jIhWLaEzTd3aI2UeVtLfNQfSFVmn8eFlaAbtCzOABCGtDIfaslJlA03rh0NeA1nNpj78JaLsWzR9XHu9bigtUxBm4t8/oukJs1qWq/nPB94/0eBn/4pPo/Sc/PcP/8LYNAC3/+jwP/yA4x9rngk8J9/XoRTmgQWKSHtIudzecff0Vs4ukQmey8jxUa3ah9vE+g4doxz3e/T8vR68y2rAFFwEvflQiHShZ4k/L2WRlhIL4E2BP02Q1cKblN+Vyk5Wh8Uo3j7GQdCcFwLvOf9wBdPACt9oOfYobJIudBnJV0WawPlpaqooUY90dgVzXMSZZvhpO2tQNLaL6A7r8RDWRYl1aQ+vnaB+Hj8yqDNnLpdosXSlLmY4bK4CIIKwZGX1tZSvCaQeZLQdVjqS4kEZEc2SHY8lba+oiGrOvjwlfQqm8ykb5ynEjl1ksTI8RZzVbA8htb5ty0Xaq9Hy9yCxM0sk65CGfAnf8z2Uy/5MeD5/zOv0STAP/8BKp/Xv4H1Nn/2J8B3vwB43Next1u/pbBonilPqOgM2E/h1Dbds6Or0ptas/6i3auGqYHRMudXaTT9Pub6IZRlEARlEgDoGgnmeXgPYF5O2eqt1Ox0LGsE0EHjJVWEF7qQ7cs6xrt0F7wBegBuvIodYDKxPEkWutWvrnAiRiPgqGxzaB2tzVKfWeg8m3fHjGEPY20wDhNiwDQV0mYednXLpYtKJYH4Pfegq2nv9dB1gykK4cZVDMBrJ3HJiO6DNhZvPBO01soW9JabKFkjhNScQqc8si3ZtMpbxk3eh4XRVCEGyAyFp5qSHKt9n5dX6e5OS6Juuo/mZELu3awmCtdWtATTMROit98JvOddQK8FjCzUE2eAf/eLwGSL9/RtzwZ+8WeAx38H8APPIc3Ielbvpp7CMxjIAs/ZbPFv3gHc9ExhhlxBGF9zNUuj4AH0h1I+HbmYyvzQ0pKOV4ZwjFaEXBWFKjkFHWADxB+XiHfbuSfBfdvvOBCCM5lx4V4pbtlgKJpLzPPl69KLTIh8wwG67o51Q1M87LM3V2YJdHkveR5DTXf8GPMcuiW89wASaWtkpUVRRStST3ns5SHLGjbGobvorOQeOWVNBKsW6HXQY8WqbgSrNfKpaOG2ZsI2BQVrVwCO2Q4FaLzL685BYeylzE+Nd6TxRyJ1+RmvNUsiTWlkw1/H8uCNbVqqokfSat0wTqprHt85YLcFHnkdUO9y0TkA117LGpw/fQvwzGfyGJMW+ImfZh7m5Abrcv77m+km/sEtwDOeyOeiO9cVEpwPe8DRIYGMfh94/c3AU76FlqNIqFAMpOpSFIFvaIGsMNwhaFqWiqvlea9NE8CWouD8GifPO5M8jyRpux2yHY8PscBasmAQrFBi9w2qHQzBgWfVYOqBay7jw9XdheEZkPeGXFCDIbqqysRQ4DQRtrXFhV27kH3XPV+aVkiZBQVS4xstjJpF7pJqo+mUEHUjC0OtQ1VRAKey61gt9Pe2kQSbXE8m7mKaUnjrJrg1y0ti1ZpAuGyl6YVut2ctui0Hde/TyYyLrN8Xv1zY4NNStG/DY22P+XpahWC6GDAxq7+96dtkIQsi+ZjHMi77L78FfM9z6TI7Q8X0e7/Pdllv/Svy1X7rdeS2tUvAT/4o2RI+Y04n98ByQWbFZWuch34BvO1t3OnBSn2MWpREE9kZn7cSMQFeWyGQvFoMtUjK9lCGBRDcdCM8tawIFCzdqCxuNRXvmWPMpQYOGOD4qtDMl2kBdLKXlgWbF3djaYmLamk5dGoZCVVjaYl/80TaqRq6RoMeG7XnWWBha4tWpzXq4v/WjbhvMrnOE1VzRorkBBGbzehW6K7HrRMkxzJmSRMKYtGjJRn0WCg3GlBDVw1zQ7vSvUdbv1pP66ZWUwEIzT+sX8bz1a2ww6dUCOPdsDAmM+Z2JjPg3e8i3F02vLf1debGdsek38Dw/SwD3vg7wGfvAn7qp4Gf+yngCV8vra8A/NAPA8//bnYWdQlZAf0ceO3NrL95zS+zTLqeMk+zPKKV8hV3glsakF93552EmI9cjlB12obFq6RUILhwQGAXJMLeSDLQBWtD5armwZomCJc2X1ShU8FRRkJZ8lmqFdsv0fNACE6a0F/Pc+YVGkOEJs+5gIwG/DYs/H6flqMuQ/Cfpei2SnetdM2RiZhM0FEsCuGhKZDQVLQehfQzqCq6cLuSONUCuVp85kbyDeNdEIAQes+g4IJRSzMUAEA3bBr0+dd4iUccNWNd85gDIUZmVoTcED3MU96LsQGwyGThaAxXSFOP3XGgpZQl8P73kxC7uRN8/izjNb7tbayo1SA8LYAnPoUN6F/z68CLfxQox8LSmBFGHhTATglcfyPw2lcz//SSn2HSc2CkgE82kVpd5blGI+bpegWVovNMFh89Km13Jb5oJGC3lsJjgDnfqaoCB017Wed5eMZdExJQMcGG4rex1B51PRXK4Kk4F+g8lxZXTagrWcoHvrrOBVWVfJhZwebqrSQereOFm4TuR2r5/iAnsqZVfuWEDzqxRJUMuBgBnqvIJcdiqQXrisdVCoZJAJeK1TCEmb1jUD2VB5NlRMISQeuMCOYgpzJIRViPrkjcUgBtKtYRfHhZBnbWBwDNZYDn9Y5CozvWTaXQT1stVY7VrNsn+b2qoZ+fFazPsSlLqPsDxjWnBB4vK+D+DeBl/yfjrt2a9zUa8dpe/BLgP7ySVrItabF+/pXAtz+Fyuyz9wN//V7gF36Suzu86KXA//Rs4Btv5MKcTKhwrria83r0Mrq6V11L7l0jJQ2DHuOhNAtWPmZKqABplXAt3kIl1KrZTFwz8R60eX+eUKH5hs/XQpLU0pp4exx27tNYsaousRjHymLpD6il0UqG14jL1hNr0FIQ1KSXZUCivGfckNkgHLkwjbWZeJ6Eh6FZY41xcikhSFJ0OxAAQteQJGfjwjm95+Iu62D+ZwKzri7TIuaJCGXOHEVbU3PXDSk63gT42wOCkwZXIpE4r5T56Hxy0ayN9FRoKl5TbwCYnNehSFKSADc9XaxoE5LCk5Js6898RraVl/u+5Ra6drUDXvVq4NufJqBGQVrUN30TX5djEkRv+VvWFZmCFaLHBd0c9FgykEt+p9djfANIfVMarMdsxqRuzFju9ucRd1W3VPEiNKncXwwfK2zf9ZpW5NOEudPdLOL2uyqoMR3nvGv2wS7yL8ewlg91eShZ3wRAzdLpxFNTWyeM55QLNk+lTNgyBklTatm2lXoMoZNbiNUx4WFlnrt+6TaHTr8DaigvwpIJKpdYaqvJjGzkvEeBmc4CUdQ5ETpIGyQvjSksF1qSiGAJ52q3kkQqpCunPDzthqPuw86UsPhMEoJ5Sk0KLwoFRPtaD9x1Ly1zvy/z4AOiph1SteMOQE7bH/whdxtwLYUuL0LM973PB9ZyPo+0IKL3H18N/O7vAFeNiKJ97PPAv385sNIDbvsiG8N/9XWh7CNxFCRd0MvLdFk13kzEVT11ah706MAAF2IWZWOo0mwd57r1fI6aBHUIQf9AtrNUInFX+j6hCzudhVKRS7KQ7cgRcdmGNLdKpKwraZQHCf5aulVNw/5iKysUkpk0fMgzTnbqSQTt5ei2v/CO2i/LhNIidPPcEgFSiLLTchJvOAnEAQA+BLRVC7Si+ZsyVFgqOqNtbfMktH5ymgU3IsTy2aAncU8dYoEUCBvBOnTNz/u5xD6CHNYthaBpeBzfSOfLhHP19reHfm+VlCcgJTMCLbuEJkaK+ix7sWke6ZnPBJ7xJGE+WNKbXvyjskcPgGYGvP3viKIVBROsV17NVsLHr+BWivostY2T0mtUw3fJTM9r074QalE0ox/Pa1EIYioC0ko+x1s+l8VcjpJz05TPXpsvaichjXf2O/YlOMaYVWPMm4wxnzHGfNoY8+QL2XRdNYkxhJMNAgt4PBELUBFxKmVRKAtgecTF5CUpqaBCT8iB1YyLs4qQLuRAIWzsgWjwtg6wZ+dfg7/d2uoKD9H6sIjqhtrNa0xk+SBn08C0Xl4OXLTJNGS/hwktqjan0AWkgX+aotvBIbGMX3oW0EbjRiDr9SO8llnJZKaTRuizGTrmwfaOUImk+2h/EFC8PAde+IOcH+tZxfqwK5krS3vAK34R+P7nSozgaW1bz7KG0RJ7Jnz4NuCffSeAGhgsA+/8e+Dqa2iljlxGiHp1lZYu5pj1xI3q6DPyDHd3aQXUfVb0TcmyWRpgY4WWdfHrPKqAqaUCguAaExLLegy1iBeaOfArAN7mvb8R7HjzaVzApuvKXLWQ7K3EEKMeA9amYYKvKgHb0HUbT7nNR5LQrdJ2r4MBSaFFxmDYgxT2IqGG7lnWvqzkZE2nWh5g+J+FgAuSWPTiHxeQwq2W7lmpVJoGmDlapLaRRJ1Apq3ERg48tkkkIG2YJGwt3cva8+EmnjksZQeURvJZnnNUAWgsUBvGIPBCwanYMmq7BO4b052svTAfQO7fU5/E/EpZAmjodlnPOqL/+J8BIzUuaQ/44N8T2Cj6PP5mw/ZVaUor0y/Ym+FR1wNogawF/uQvySV0u1QUv/uHwFOeKgWBRwCXEWhRzpjzIeMPI8/A8p507WoMpI1O1IWtDGuZaJIFYEkIDiTgs2skBlXOn0lDUlwtXC3ubOMIskwELd3POK/gGGOWATwNwG8CgPe+8t5v4gI2XdfhxU3q5eh2W7NiTpOMi6GsOQk2DX6pmtleAZiKycjlAWClCUclpMcsDVBsv6Cw6dYOysotxDoom3lzJyA66ndr7YcymRX+jmHRuLNKkfIZZ4m4bZLENJ6afjoJvnoicVcTgQAOAk40AvWaqLIxJdDgwIWjfcisp2WCo2V81rMk7yXQb+1FwFp2EHrpS3iM1jC31BvK/RbAa34VeNKTgLVCKENCen3aU4FjRwlJL/eAb/tWgaAlTvqrW9BtFW+8VIAOJK2QBMuuWj6NrEPMH2saroHhkPeQeEFDIYIiayCmzSzGLHFTQmV1NC29F+2RrW2m9jP2Y3GuB3ASwH8xxnzUGPMG6eh54ZquT/gg0lQoGODD3y2pCVxLZAkZH+yJE7zx3aj1U2KJXLk+UCbA1FPbVhK8D2Wng1GP/zlpK+QFgYknPk2p0RX7z4ooEZeGRNt0Gn6n5r4Sa6FuwWwW2AHDAQPl1RHga7DcoaQFdeB/Vv5diYDOFPYuqEUN0G1H34IcOV1sSvVphWbST0nZqWrgVb8SoF3X8relY2Wta+leqpXtLwHf9WwK/HDAeqebnkZFtLbEuVweAO97F/CKl7MY79ga8BdvBb7ne4HLj5EJvTtmU8NenwIzHKKLI9UdVRJnh2hZyfIL9SZusr6zI9sytrRqfaEeWYMOjvNiiYEQ36hrqGUEaSJNHuV5FQUt8e4usF/qwH4EJwXwjQBe673/BrCv98sf4Pt7nfosA+i9f533/vHe+8cvySauaYSaAQLdiv86ka3txjvUpE0V/FvdRmNnAvSXaca3S3HTBBnT3Mqa5FPgWUptxXSrL51JclQTY160u8M8cNDv83txYOldyD7HGWwPXlvdBHg8L4Lm0+u0VjRfGpKS6oIUhaCLYNwEiIZupRmFWMUkDw92JP2wy4r9BZ73HAqDxgy6OxoS4LVvoCtbS27k87fLjm8pgYeb/yvwin/Lc/VzQtg729zFoKw5H0eOEM7u9zmvK6uch/tP8h60RZe185Azornt4ksbnkPMZAaoQKZVKPBT5CwWwsVj6Dk0xlHCrr7fAUb7HPsRnLsB3O29f7+8fhMoSBes6TpAzd9IXsUJPaR21LTOA/edJOIz6gHNhNoUkP04+4QzqwkZ035Gvzupia4ljoH42jI15UiqSrXWXYNQFRTN5puE2jgVCDQxhIOXRwE40LoOdQtGIlDayyvLaD1MQuhzZ5f35VupXxFCZJbSlelJ8m5YCEEy4z2nLrAQ1pYjNKphDJdljLOqlsG/hRA9C3Rb1t9/P+dZK1UzgeKrFiiGjFms5/3efw+Bk7UR7ymxpC09/GohTXppJuKBH3kxywLWVqg1LzsKXHGc5249a62OrFHZzWSblCRa3Frc1/UDEEBEGznGwmUM3cxaLO60pIJV66IuYVJs+AAAIABJREFUtnLWdAcGPY/m9IwhDSiXwr+iYLwbd9N5oHFewfHe3wfgi8aYR8lbNwH4FC5g03UDcNOkhnkcJ1WUbUO0azxmx82tHZrxfMDMvSJxtePklTWp6amlD5wkwhAo+P76UYmDQMGYNXQBtVhMkZXG8TyKyPRygVTTUFCVivvXL3jMXj80LjSGD7VFSMrBEJkDuGg9mNdRDZiBAfloRM2/2qcSWB1y8S71WauUifDqztza1SVPKVzWU0BrT63fiMtX1cB73wf05f1xRdBgskMi5qgHvOLnANQEIaY1t3RcGrDPwCDl1h7f+1zuJQTDOqWlJeDtbwW+9pFMUq8uAxunRLlYuoBLAyq49aNUNDtjlhN0nTdFAcWVnwC6kgAHKk9v+F3dBl7ROE1Gt16S1X4+qalCmNgA+DjDB9TPAiJaFPv21PZdOv2vALzRGJODDdX/OW8Jf2CMeRGAuwB8j3z3rQCeBTZdn8h3H3Bo6x87ClBhNeHC0y70Z04xSakcIyMI2qkzJIZWrRS85bRcrqHmLVLyp9KU3z99Jmi4XBArzSJnkgMoBJxIklAvYhPA5cFVMxDBlIeTKXTaJ9XHW547AeOyfgHkYh08aIVyz4fsJTdjDRe9Bs91I4CCsJeriq7YbMZrtR7QXsmtI3NgMuN7zYyxRj0NzONpDfzQDwK/fjPdt0GPQmIlvvyFfy+WLmf8duIMi8yyjJQlb4A7b+duEe9+Ny3IaInzOZ4Ba0f579OnCBJMJiSVzmaso5pNqXyAsEWKxobe8x5juLojflp0e/nUImy6F2u8hmJwJknQbeDbgTomgAQWPF9d8zqmdVBC+xn7Ehzv/ccAPH6Pj27a47seD7LpugcA4VeVG4CX6sZSchr1jL58XXGBKhjgDPusXXllSBQ6gVFdwkW5MeGiTXJ+nlh0HLfGh6RaOUPXjDtL+J0kp7CpsCJK2qnb0ECy7YK62STsrqAPwQCAIxoEcRdagbI1Tusa56X8blkS3LBWqjklftFd6dSP1wKvVtAFL0LnVcCkcK4SytAX7mIZemfpJN5ZGgFbY+A5zwLe8R7C0p+5lWyOa66hFZzNKAgf+hDwLU8DPv5x2eM04/zdcANw7z18HuMx8LjHAV/4QiCkOrEUq6u0OprFB/bO3C8KggIFXYEaIpSwDq5e10fAzrtwTRuESJuBaGyllJ4LKjhf7uFaCfhlIU0mfNDDJWpg11BD7GyxfLcwQDsTmDplNaO2vE0zaQ4oCa66BWwPqDzQ7AgR0Ii2deha6GYiiDrRZcXj9QSBKUt0xWTW8rxtC+yKsHoAsBT4US7uSSOClVPwjWeOR/uR2RRATctqETSvNi+f1ZKdF7pNC/ZgOHWSlthLvqJpuSgbQQT7OZGwaRky5FXJufjkPwDf8hTgL9/FZOVErO3qCt25Jz4BePd7wlysjgBf8u/UAB98H63MvfeyRKJXCLetYYJ3MODCXF1l62LdSgQIwr65yY5D29HGuZr8XQQCFkeMIJazUNMDBOulrxNRZkbyQ60HFRik7VcvfF/R0n2mcQ6G4MAzoZk3hKC1rVPi2R0/HwDI+OATsIlEUQAoWZfz2du5C8DODomInb8LxiKDHqHR3Z2guYqc/KparNrRI1xw4zE1vPrIA4lhtFBqZUUCfoGjT+W8LgcAjvBwZgEY1qHUdcjR9Ebo9pm0Obq6/kqSc6UEyBNhOSQaCDu6nzYBzmwz2dnI4shVm4p72pNCOwNa2tGI8eGJTb6+7wR71/VyEFiQilI7psC/9teERFkI2OAoGFkCFKtchI9/AvtsP/YbgfvuoXXPhTe2tk7W83BA7+CK4+zE6tpgrZOMFmd1lb3eSmGLDAZcB6lSlEQRaTtgI681h1e3PK8BP6vFfWsF5XReXktey8jrciL9q1WoQEFI8wsf43xZh7o+pQAEJhH/XbT55piB+HQWkliDASHeaQXYgv71zjbh7GPHuIA9gEffABw7wuIq5ykU22M+1NGIrp66b6alNvdJgJn7PTYVVw7V+rq4bxUfetGXuMIE90sfGCA5EimUSsWNqypRAuIWznYRttWLfHftCFO3FIxmCvgBXc5K4po6AVYKSXwKeuQEoUwkVpvKvkLW0s//4EeAH34h8HtvZO8z56lwbMP7WlkRYKMFrvsq4P67gKXjXFiDIfCxT/C6Pv4J4Mn/BPjc3ehqpnZ2uAPeffdR8Z06SZh6a5vXkufoIKmtLZ5ra4uLezxm05OZxKSNlAnoM1eLpYpC6U+DXqjl0Txc159A/noEq6ItcZ0P8VMcU+1nHAzBgYACUoRlDZANga0ZczK7skW5zakFd8fADdcD95yipj9yjMTC2YT0jssv545fp+8Hrn8ENe1A3IlZyf5sa2ucyFPSDjfNuMAGOYCU/n5RMO+wIk3bi4IPWjdzPXMaWDtNq9DUPM9MSq3Lim5a1QBpS3bApBTIHUKZafndQcEFrYtfoebcynYjkg9Sd0b99CRhfFEJDQgZ46JyJpozpZXNE1KG4EhDWhkC7/l7ADVRu9NjYKsk0JHlwMv+NfBLv8z7nU5C3ifvSZVrCtz4aOCOW9lq99hlbKmrEPOp+zkXU8mxJYlsHOyD1TGG7u72NpG58ZgLYbxDhVaWfK1KtW3RtYWynp5E44OiMhD0sOXvNE3QkUR9AAwgiKTzYl2VVWAuNVfNkGbvWlYGFj2a4JNbXFCt4YQsrQncXFAALr+cO5NdcxWD1FKC4fGYE7t6Ha2HSUX7WrpjfQUYEinVToVUuMKJHC7T588y+vNZRgpKZmUBOD6Y9SOiPBMKcL8gfO7B+ELbSDUzWsvplGwEzVIbxzgmA8mrU2UxiG/uJCjuZ4xRgHnSoveCGCZUDNMy5Jq8IXy/vhqSsknGuen32eT+qU8G/uFTPNbuDLj+SvZg+8D7gcvX6DreczeVSU+qU42VXtv3E37PMy7mfg+MI1pBI4dhUdYt503p+4qeOXG/piWPtbkZUNXRiPPlxIrH7W9jWo4H50DnRdkApg4dVgshBfuaFkZIG93xtHdBlu9/yR4IwalqauPRCDi1BRQlYBpgZgnv6h6PvQGF4NFfw+D7+lVqwSIDanF3ihyoC8nfDIAz4iq4hhq1BQDp3ew9XZU0pVD1Uj6IfEAYdyh8raJHxC9L0G0XoVn9LBM6kJGSBjH1q+Ii5cKEqCU5ubFFkKMpKWSb28D2jIJjIWxwA8DSerUtF46iYLMZr0c1dF/qZcqGD1MZFTahu5rn0i1ISpR1o9ptIZuO+kQtWxHStWXgjtuAr34UdzFAwt4BM+mhXc14P8WArpwifMvLVA7au/nMaTaJ1+49dR0WsIssD0Dr2074nDY3+d7ubnD/qkosrsQ2acLfqJuloErMMtAOrYqIFpJYt2nIbzkRsryg22sivuH5xoEQHA/AFEBTADuSES4KADWw3meA+VXXUqv1erQCHpxIJfjZgjkIY4NmNI7IDywtj25HmCYAXMgXoOXisgmrIrVBoTaEyHIKcia+sxF6TZKRoZ07YTxbwKfBzzaScXeev13J+ACXehQckwBrO9wx4J77qCR6Fjgzoc+eeLKhdTfmShJ4ihBp0DupqWFLRwBitsOONGlLBWBBpdCKhtfE34c+yX1Qb/lLLsx6wo27PIAnPBl485tZdHb1w8gaKAq6y0lKFPToMWkPnBLUWVlmnKn7+Ux2A+/Pi9VotT5DYliNyZyjsPR6gfpS10DSo6IoS3QNTLrfJrTKJiJmapxSK2oJKdWwPL8SX1P5TmK5lYsxfF8bhZxvHAjBMUb2mgHwrd8kLYF6RKWyTMqpEThlWUYNkaSBZauaqalCcK3bbyuRT/3lvfID+pt4wyPtB6C5ki4TLZbLGgqRcUFg1b1KDEEESP5Ef3tkTXYJa+mSrayzZKI35Ca4u7sCY89Em4LC0TpalQyAlkDoPjG7u1IAWMlmwZbweyaJU5tTsLIEQEXEa1cWyjv+jrma2ZTnaBp+/ta3UriHa8Jrq7jPTWqD21bX3PVtdQXIDatVl9cENElEYSToSkUqPfeuxBIKiEDOLTHe0pLETInEaybk0+JyaqVnxUVrmkxPJabRTqg7k1BdqnvqZD0qGf2t5tT2Mw6E4OjO0uvr0hMa5DdddoT/TmwgfmqQrAs9Jgdm4moNUmG6IiQi45ryePKBAGEufk8DcD2vF7hYC9e8JmAQrkXbTHn9rQnf0eP2ehSONKFlUKRofYVdQ8sWMGfkZ7K/S5KIm9nyHnt9qUSV6y/FnZs5/l75atbSmk5KoZakFNzUECTZ3AC+97uB976LwfZswsXtG+CpTwVuvy3kqNo28NQyqVa96iqCLjpf22O2sNJ4pSwJO29u8h60viZNxV2StIFJJYnbEojR8maACqpq6JY3DTpeYybxFUT56aJPU7rBu8IO2dqiMJZlKCs3hla96EuMUwVqz37GgRCcPCNyNepTiJwLHew7VMUHEqhaBBstau0pnCL8Rhe+9+Kj9+bhRhWejkYTCc5cACqfnQXyS9LUS97Gmc4YBDdQXKtYwA24ADXgXRlS6M2alASDv2tPMI+SeqJm2kPAWvrlrhGSpsQqXlyRIhdGdV9cWSesaI9uI93UiAbOmBS9/gYCBmlKdK8YcqfoEyc4dytLQdEoVK+1SyZCteBk14IkIISbm0HQvKfg7kosF+/0HMPHuou45s8U4MjzUAYej7i0I2ale0+XbTylQtWNlnuSw9Nz63q5pGKcNBHWcp+IWdtyO/JcTKs3dAVm08AniidGA0bvBfe3gWSo2l47dQJnr39g3n2L6e76mVqTxdet2/v76oYoBUShUGsY2zgvhFDP+KuX0vW64nLeT39AdkGyyXvb2gGsA2Ze3KmCr0tPtAhA19aqnjHf0s+YvC2nLDbT+/OWSNkVK1zAJ07xvDZhPDcYcWG9730ET3qWgqb9ApIk3NfODhdRrxfig91dup+NttuKCJfqWmr3ntaHWiddvBYh3tFmHt4wzpzUROzKSoRqUenJ+aqKc9jttN3QyhsjZdjg2lDofzoVIbqUBAeGMHNeBC3dy4O2hyAo+lcnSPMGQOSCGQASvDetMKWtLFyxWN5G82PQ1doA/J2CCN35Ez7gRNwVK0LrJInZCQkiK2NCzKPbgqsWVvet8eG8qVjXwZBbmWQJmeJ1zfspBoSMt7cEdk+Y4/ItWQStExrRFGiEs9VIok/3/cmtlFMLkLE0JIR+qiU48fWPBT7zaV6Psi+M5zYqSUaB72pdEjm2EfjboSszTzPmjxRStpZC1Oszdslzzl1dhmfnGjIQnGPfA+OoKHv9UAjYWJ5ndxJccC+uq5YNOMvzl+MAh1sPoKWrW9V8DidPMjRwPiiEre1LzFXzCBWBumGqNm9wgo6oX6wP7lwZ3hjP18XcsWTrEH/EIMHciI/rAFhOvMN8fNRd+8Ix9vos/ttlqJUqot9XoZRckQpkKy5a2dJXX04JYc8qWuTxDDBihQspB2+MgCagwMExWB/2gbQPnNqg69U2ZFArpDzZAh5xLePLDDzWjTcCn7uVm3xZAUpiq2wMQYjZjM8uj1AxTW5OBCXUPYjG48AimEktDXxAx0rJqXjP+iXt1tkK5aoVNka3W0GLbqc1VZJ1C7hpcO11zx1tWAIfqE0zET4FmvYz7Pm/8hUYfr6CTwEApZAoaqZCsRjEA/P/jol+QIAo4wUc+9WLrhai1zpB9gGEJR7xceLjLgoPEKyNjvjesozw7rFjRJRWloHLL2NdzlBaSfUyLm7dcVlrhYqe9JSz/E4mCcy6lmYmsvdQkfF3R4+QHT2dsGqz6IXf7GwH5FGfS3xvCgDoUC3vBKIvZyEWUshZcyxqjebmyAnULh6DA5XEYICuR7f+p/sK2SRYyNYFF17zOKok2xbdNojb24xxtD1UXP27n3EgLI6xIXmVCEcpMVwUSv+OWbTxol9cfDqsRceY1geTLbzuuF0LHCWFSLu3XOTanUNoYsHQxfCA0KbhoTRuinu/WcN7HY6AY5cDq2tcRBsb7MyT94GecL+KnjDIHdEwawFMaclWBoxP7ID5nV7KRoy1LNz1ozznsWNiBRrWNz3sWlKRWscNhI8dI/NZBafbDsPzPqqaVKSZJFUVwGgbCkfuiJpVFXM6ugPCzlbYBS+NgnMXrUrf8r/N07ReztB1A9DtpqabWjVNABySTFj20vhxNAoKoKp53QpaaKHhfoEB4IAIDgz9/USSdLDzFiKxhCBNGhATHXPuTxQgdkk2CG9J4oo2SnLFmv8sqyTXpa+VFGgk/tFj++hYi65ZfI3drS5YSr8gtCY6XppR02qskCbAhrhgvqabtpwzBtna4XX1U7pjRtArZwQRa2hF8oyvxxInqDLKcy7kTITqqquY/e8LWDArGSMpGVWtslZWNhXPkRtC4vq5brw1zLjYnJey7YIQ8M4OE9ozydc4z8RvIkqnAZVqVRHqHg7p0nmPrtXUrrhtVhOcoNJ1tSSIdwC03Cu1EqVsDNG/Ngd8j3PagQb7GAdCcAzmLUfn4kg80vrgWwPzQgIEC+G9xER6LHXjHAEBI0iWBoAqMHuNvRb/XgppEY3T987FtI1rU+aOscd3bRI0cp4Hf72Qwrn2BD8biXXSBKJunVjkjGtGIwIH1kvVa1R335OWTVVFF+7MmVAmfvw4XZ3NjaCcdNv0VmM0sZzapxqOpFInsWgj5MzJlPGWbykw5Ri47DiwcSaCh+uAsKlyUWDF2uC2DQuy4oFAnXFeeHPyPDSmmUqcM5uJpe5RQcBQ4Le2gbzkzgnj3XD+840DITg64oXX+sh/jRb3njFJ9H6MssUr3caLWX6rsVDsVp0rODzX4l60JvEx9/ruWed7gGMDIa5zjtq29sDAc+GsSbLQezIvdneFyiOgyoo09dA6lJ501ClyAi79PrpWVuqGlY3UtRRcZPqZzq33865abCHjKs34fWMAn3IRx4Vtmxt0A0+c4nm0i6nSchY9CV0XO7t0UeNtQXSXg8wGxki/z4Ty+nroy7a0xM9PnyGiWNc8jpaN6DHPNw6M4Oy16OaCf3lY+l6s0fcKwrv3EeTnXMK2eIzFcT7XazHw1/cWjxd/N7aKRoLevZA+1epWXLSR9GBoHZXBQIrv1lfpVukeMrqHUNOQjbGyIu2AU55ndRkwieyLaiQZ6oC1VR7PGv52bZm0mssvZ6Wtds7UQN4KRb+j7Yt1sGKJNNZxllahrJh62N3hze2MCVKUU2B9TV7n4ZklCAG/k/nKLOOUXo/8Oi9wtTOhmC1JeE/DIeO1PCdaqLU6ac7ylCShIG6cAa677hKj3OiIF38cOwDzscDiwpyDgOWvFa2byEONYx6jiTY7//u5RbuHX3YugGAv4dkr0IwZDbF17K7X0Tff63qMEdBAmM7WsZVvXTGgL/rAylG6JNunOF9aA6OLKBcApteTuKkMKKYxtEKJF46bXFvbsnZJYdwWYXF17rNop7IMbl+jGXkDrn49nuM1D4eMTSppGpJaYZPn6NpCaaGZ9+jaHEPmoW3pto1G/F1di7Br91SxmMvL/PeJE3QTP3c7cPwaqcWS3y0t8zenzgjtZx/jvHC0MeZRxpiPRf9tG2NeeiGbrnuIa2YkX6IBuJNgTxa9TqbGKApBKt9Jf9ctXKHEaIuhbjj+p+fo/tNjqoD6hf+EUqJ+fedheZlIt/AX84vfRRZI80Jd/qIN7mRMPVmcpyQLRMveCGSFy+LoJ8D6EhdLX5r0jUb8d7/PHg6JoYbPpXt/koXAOk2lBVYqhFCgazZvBeZWRZTGQg8BM5JoKoW1YTRZihDL6i4Pw4z5IieLPhNrGltjbQNsPalHqSNwkBvANICTPUy1saOeV+lWa+u87/VjwsZIZJMxw90uTEqgZDKj4PgLZXG897cCeCwAGGMSAF8C8CcITddfaYx5ubz+Gcw3XX8i2HT9iec/z4LWXtDcsdej2f3FRKbXBayv9VjyOxO9vxcMDfD3cbmtDnWZzpVZPhcYEL+XRN8zCPSScxxybuj8xJanK3MQV6uWupXjV0i9Dig4XhRLAiA/Eqzt0lIoR9e9aHTXbHgppxDtXkg+qI6C972uUXMiqog6Y7+AlLYtmSKpDXSYrt4mjVx3OZdx8xNlJYfVOiqD0ZA5o9aE63cIW3sU4opOdklk3T5DQVpaIiy9cWZvL+Fc48G6ajcBuMN7/wVjzHMBPF3evxnAO0DB6ZquA3ifbBFyxQM2JRTNv/gwVPsaI2iZJkDlM91WYw4wMNEi02x8FNieBQd3vh26HaMNMFdsZeNgWAV1j1hm8d8e8jrSYmqh9IW6pHu5f/E8mIV7iMseGmFGp2IlrBXt74Xe4ihkmnCMNXqW8Zq0PZL2L4s1lTGhA5GHLHBhZmh7Jh3qJs1m6OK3+DjG0HIbhMaPOgdVw8aIOk/eBRddSwi6edPnLzw2J+etPIW0buT3kGSunCNJmPytCsLbPbGiq6vS6RT7Gw9WcL4PwO/Kv+earhtjztd0fU5wjDEvBrcBweXrZ2f7+R3+Vc2jGwkBwffl+Rf+6oKO3SQXXseMhPhzXU/Gc3HUwrtSSoimj6zAsbE1O2vEQMAesZiep+PKRe/H1kWFJFYi8Xe8F1clDZ85cceqikGw9VK9KqiZok+KhC0CGh16Jp/pAmw9Ye/JZD5GjK9Jd0tLxZS6CLbWoUIKaczST6Uvmg3Uf0XUunIPi667jYO8Bu/Pt0KxArl+0wnJrVPpnuMNW4olhsjiTNzd/pgw+fo6cOIkE8LzPv25x74FR7p4PgfAvznfV/d47yxB9t6/DsDrAODGa42vqoXJTcJC04en2lLzNT5aWPHD9wjWSN0rdeO6+GRBG3ZWRM6prYNiXF9jkjnLtTDRepw5wGIfamzPvJEPC+hcqJ8BLbEuWgDd1iOpsJi17WuWSdIwdokjgETPoa5bkgShUQvbJaD1GJGnEOfFdJ73Qgr1vRQABA3rtqs3gSWiBYtzOR0TLTALoKXweaDbU1V7DaSpNO8Auu6d2hy/BROvXSMRMBl7LmR1cTwYi/NPAXzEe3+/vL5fXbB/bNN159gaanFbBi1QUn6Rumx7cdaMATRodQIKKJijn7cIggYE/lWMrnmIuxbB391YEAa1aovoF9QSqRZ3YfGqNdTsNeQa3eICMyGZp3CvFzcEeo0IrpguPF34XqymzlMr168ggLKbnZOF58+GYq3FfFmyB9yMTG5IFSUsXS+tR+q8UGGj672k8dwhzK2T4yZSlNbKzhC19AIwGQi2eIkv1V3VOdA8nwBATulaGefUzKLP1aJmtFKp5LPamlWsox7f2894MILz/QhuGhCarr8SZzdd/zFjzO+BoMB5m67XDZNgsdZMEBAVIxnprps90NXaxFqyEwDRiAmC2xWTR7WCVLW5Lp54LIIDALqA1SpEhLMt1+IxTBTHqFBpNnzutxpbIAiQiwVHryFe3JGQqOsU54n2slSd++WDVdHRFQFCrlkEI9wQryUB5oGZPe5fGwrGvMKz5kesh7GAF0tm0lBqXs4Y1EN7oUFADhOhlvKmEaFSWlYh9U2tuNwwhPATMOapKnFpe4ArgPWCaFu+T6LnvgTHGDMA8O0A/rfo7VfiAjVdb1vuIO09/V/j0VV3+ujBJyYE+rr9oFqQrpE2KDgm4XG0AEsFq+gRzjSRoHXuny46CHQcuYpAWIixUMXNHRbBgg6E0O/4gPqpGxMzCLrz4ex4ZvFa9P3FvJFzwXWLR+xSmu5/88Kl35kDUGQeOrfZSdcZGwkr9h6L87H4mQO6knRAELIkKDSATIgio1WAiSy1XqtY71ifWMk3WcPf6jxpXwplQ7QtLV2eBsZCEiuKBxj7Ehzv/QTA+sJ7p3GBmq6XFbtBWnFJrKHLZQyv0Ht0Zb8qJIgWp+7raCEmXSY/MSHnoT5zX2gdzoXS7ESy8ueatPjha/wQf6bXEb8GQizlRUMaH8VXeyzuGMzQ2GRxGHm/ywlFQbpfuLZz3Usc2+hQlBKYt6o2ElqArrJxQNILFZgqqF08hPnjKLizOJwcv0sjIFjBNkLUtM9z05BypHm17rpFQbbxdVq+zlMqylo6u2YS4+i2iVbeS/qhL/h+xoFgDpQN8Ln7hWMkwpFFi8NEmkbdMoAToEVOacrvZJBCLmHjJiAS1OuRm7QKoHA06VaOa5N57egwv4hV87rodSco+hfoEJzOz5drN+5swXISuylqpOTTzsWy0WIC5oJ4/auxkn5PaTuIFlW3r6Uc0/koVxVdOxBiKrXsccwTI3bGcsNeY6nZEylJVtaD7vrgQMWl78tlaI6SQhO5ch0QovMAxk/OECFLU3BbFgnuuySY7f7Mub7qNCjNphRPQ/uKa6cg54js6b5D+xkHQnBmFXDnfaJtVEAWXB5d3EC4uSzy6bUaMEvQ7R2p8OOKtLFd6pPjtCT78FhPbdOV2NqzF7ieb6/iuLkcD9AF7IAIUERCXHRZ9J/qZugi1bKH+Pxu8beL16ErRFzY2ArqdcbuXnecSAgXXTXdVPgsV1AOY4x01ymDwHaAisSkeu9d5a0InVqmTtn4KO5D8AJUCagy0wpQkwK+jqzYopKLRqPKJAVsPf9Z7KoDEvdeShandcC9Z4KrZKJJX+R1xcFufOPOSa7CAK2gcBkAWGB9ChyZAMeWie9nCVAOpFl3EzQScLbrBQShmUPP9DuxsMQ3Fbt3bv54c1/zYgUiaxMncYHwME38fqRUOgVj588VX/Nc3IKzF5iTwDn+fJHLFx9zDiZX6+CCl2BFCMpSEo4VsJe/1h07kqT43pV2A9BS6LouilDQFn9/L1dLr1eBlNQFzl2SzCvNS6ohofPSZ1kRkshN6CYkYuXq59acvSAThC0wUtHCO2Ngd4WarzdkvcioBKbSgqiqZb+ZhQUSjzn3TBb3YqCultIt/H5P0EDp6+JuqaaNj9VISgmLAAAGsElEQVT9jc6BhX/PgRjqr0SWY/Ee9O/cAlm47z3jNR991QQ0MssYP3SFfpGgqmXqKm0RXDEszJ1+d1EoVVKUh9hC5t8F9zae73hejOF54vkzRgAodYcXFPK5FNziOBCCY8CYZs5sm/Chc1xocR1IuoDmqCBptxVjJOcjmL2W2dYO3T6fzoVcDnC2OxWPWGjnNLn+je9HrFDstsXHmLt3OV67xyLt/r2XADyA9t7rFs6Cg89xjL1+80DzUtdkVMf3q7kZB4S2XfI8FuHtvYRz7l5MiEeUg9aaIDSZZYy8CKTMpQ6iWwYklo4smVrXGHQ63zgQgpNY0ixc5JNrmW2nrURDG1AQ1E0CRANZwf9VQyF6LyWHqfaAqyS4FK5Vx01DcFUswAbcKiSRpQD2sAiyCOM4Ye4zH2KPjgMnGrTTzEDX+UZ/00prI0XkHCSp59EBDmct6mhB6HV0sQLCgvSyeHQanQn3DmEvwwSaUed2Akj0WSRM9WiXm3hYI9ftgjVRUGAORpfvx/Vjc0LesmRbuXJIxJPwgfZUCC2qVncPzNkYhNdOBNA6MM8nqKGit7ru9jsOhOD0C+BrbxAtgXATruXCb5SwF2moxoX9Ucqa/9U169kbIGgzj66DvboXepzu3wJ9+kjoomcw50YBIZCdcy320PbqblqLs1jVZ1me+N9xnODDtXSKZMG1WjxW/LJbpJgXMqUhdXFT/N3IfJwVE0UXqsCElk3HW50v9nDoGAwRNL3oyunn8X0ZiOVIo8Xt579TllJaboKAdWyNyDNI9N9tcB3ja3sw40AITpEDNzyM/9at/rwPlkG73mhG2ZkQbO5MyDzYGbOSb5oCu7XsJykBryJoqUxOuyA8wB6umIvQLDsvJOoC+HY+9vJe4pX4ONHij48dW1EgaOZuRIv9fBYvfg8I5QtAcJX8wu+7IDw6pcG8IHXf1c+j+5FLhJdnpnmWrmOpnf+d0oIAzG1ruNdx9bUVBG4R1PCRQrJigesK8JLIrGuZY0hFqglxkB6nbQEbsQQ6RgX2Nw6O4FwV/Nm2RdelXzs1erEWDmJp5PWkZIeXrR02XtjaBU5uAjvSpihmF8RNCmMLEFuerjo0ur4HMuGLiNm5FnW8UFWTxmMvYCIW6tj92svKLF5DLOSLn8XH8EC4mMj9Xbyfjg29RyxhbdhceK6vw8KxFhnee414zmLrEl93bA2dE/dLXuverbq9im6JaUHQaNGLsNFx0nTfIQ6MfzCO3ZdpGGN2ANx6sa/jKzCOAjh1sS/iKzAu5ft8uPf+svN96UBYHAC3eu8ff7Ev4ss9jDEfOrzP/zHGPvOkh+NwHI54HArO4TgcD2EcFMF53cW+gK/QOLzP/0HGgQAHDsfhuNTGQbE4h+NwXFLjoguOMeY7jTG3SgPDl1/s6/nHDGPMNcaYvzXGfNoY8/8ZY35c3r9gzRsPyjDGJMaYjxpj3iKvrzPGvF/u8feluQuMMYW8vl0+v/ZiXveFGhdVcKTB4a+BjUAeDeD7jTGPvpjX9I8cDYCXee+/GsCTALxE7kebNz4CwF/La2C+eeOLweaNl8r4cQCfjl7/EoBXyT1uAHiRvP8iABve+xsAvEq+d8mPi21xngDgdu/957z3FYDfAxsaXpLDe3+v9/4j8u8dcGFdBd7TzfK1mwE8T/7dNW/03r8PwKp0DDrQwxhzNYDvAvAGeW0APAPAm+Qri/eo9/4mADfJ9y/pcbEF51zNCy/5IS7JNwB4PxaaNwI4X/PGgz5eDeCnEXiS6wA2vffahS6+j+4e5fMtLPSvuBTHxRacvTTPJQ/zGWNGAP4IwEu999sP9NU93jvQ92+MeTaAE977D8dv7/HVPfjUZ312yY6LTbl50M0LD/owxmSg0LzRe//H8vYFa954AMZTADzHGPMsAD0Ay6AFWjXGpGJV4vvQe7zbGJMCWAFw5it/2Rd2XGyL80EAjxBEJgd7U//pRb6mhzzEd/9NAJ/23v+n6CNt3gic3bzxhYKuPQn7aN54sYf3/t9476/23l8LPq+/8d6/AMDfAni+fG3xHvXeny/fv+QtDrz3F/U/sHnhbQDuAPCzF/t6/pH38lTQDfkEgI/Jf88Cffq/BvBZ+XtEvm9AVPEOAJ8E8PiLfQ8P8n6fDuAt8u/rAXwAbET5hwAKeb8nr2+Xz6+/2Nd9If47ZA4cjsPxEMbFdtUOx+G4JMeh4ByOw/EQxqHgHI7D8RDGoeAcjsPxEMah4ByOw/EQxqHgHI7D8RDGoeAcjsPxEMah4ByOw/EQxv8PEIFg4uhFKcUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(invert_cat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flipped Image\n",
    "\n",
    "<html>\n",
    "    <table>\n",
    "    <tr>\n",
    "    <td> <img src='images/cat.png' style='width: 300px'/> </td>\n",
    "        <td><p style='font-size:30px'>&rarr;</td>\n",
    "    <td> <img src='images/cat-flipped.png' style='width: 300px'/>  </td>\n",
    "    </tr>\n",
    "    </table>\n",
    "    \n",
    "    \n",
    "      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 90° Rotation\n",
    "\n",
    "<html>\n",
    "    <table>\n",
    "    <tr>\n",
    "    <td> <img src='images/cat-rotated-r.png' style='height: 300px;'/> </td>\n",
    "        <td><div style='width: 100px;'/> </td>\n",
    "    <td> <img src='images/cat-rotated-l.png' style='height: 300px;'/>  </td>\n",
    "    </tr>\n",
    "    </table>\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Translation\n",
    "<html>\n",
    "    <img src='images/cat-translated.png'>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}