jupyter-notebooks/aula05-transformacoes-homogeneas-espaco-configuracoes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def Rz(theta):\n",
    "  \n",
    "    return np.array([[  np.cos(theta), -np.sin(theta), 0 ],\n",
    "                      [ np.sin(theta),  np.cos(theta), 0 ],\n",
    "                      [ 0            ,  0            , 1 ]])\n",
    "\n",
    "# Apenas para visualização de um referencial no plano\n",
    "def plot_frame(Porg, R, c=['r', 'g']):\n",
    "    \n",
    "    axis_size = 3.0    \n",
    "    axes = axis_size*R\n",
    "    \n",
    "    x_axis = np.array(axes[0:2,0])\n",
    "    y_axis = np.array(axes[0:2,1])\n",
    "        \n",
    "    # X\n",
    "    plt.quiver(*Porg[:2], *x_axis, color=c[0], angles='xy', scale_units='xy', scale=1)\n",
    "    \n",
    "    # Y\n",
    "    plt.quiver(*Porg[:2], *y_axis, color=c[1], angles='xy', scale_units='xy', scale=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transformações homogêneas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.8660254 -0.5        0.        10.       ]\n",
      " [ 0.5        0.8660254  0.         5.       ]\n",
      " [ 0.         0.         1.         0.       ]]\n",
      "[[ 0.8660254 -0.5        0.        10.       ]\n",
      " [ 0.5        0.8660254  0.         5.       ]\n",
      " [ 0.         0.         1.         0.       ]\n",
      " [ 0.         0.         0.         1.       ]]\n",
      "[ 9.09807621 12.56217783  0.          1.        ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 14.0, 0.0, 14.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pb = np.array([3, 7, 0, 1])\n",
    "\n",
    "pa_borg = np.array([10, 5, 0])\n",
    "\n",
    "theta = np.deg2rad(30)\n",
    "Rab = Rz(theta)\n",
    "\n",
    "# Concatena o vetor origem ao final (coluna)\n",
    "Tab = np.column_stack((Rab, pa_borg))\n",
    "print(Tab)\n",
    "\n",
    "# Concatena o vetor auxiliar embaixo (linha)\n",
    "aux = np.array([0, 0, 0, 1])\n",
    "Tab = np.row_stack((Tab, aux))\n",
    "print(Tab)\n",
    "\n",
    "pa = Tab @ pb\n",
    "print(pa)\n",
    "\n",
    "\n",
    "# Plotando os referenciais\n",
    "plt.figure()\n",
    "plot_frame(pa_borg, Rab, ['g', 'g'])\n",
    "\n",
    "# Vetor Pa_borg\n",
    "pa_org = np.array([0, 0])\n",
    "plt.quiver(*pa_org[:2], *pa_borg[:2], color='g', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "# Vetor Pb\n",
    "pb_aux = Rab @ pb[:3]\n",
    "plt.quiver(*pa_borg[:2], *pb_aux[:2], color='g', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "# Vetor Pa\n",
    "plt.quiver(*pa_org[:2], *pa[:2], color='b', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "plt.plot(pa[0], pa[1], 'o', color='b')\n",
    "\n",
    "plt.axis('scaled')\n",
    "plt.axis((0, 14, 0, 14))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformações compostas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11.24264069  7.75735931  0.          1.        ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 15.0, 0.0, 15.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cxwJTs3rbavo+1xeAY1sd+223cEKbE6iVBd/wDL1jAFDVeUDGRUSBdQsp2r0dZtwIC5+GgpYwaDwcMTDlp6ldqzadCzv7UGB65n05jz/0/wMDjhzAYU0PC7uc0GTUMaQqqh2DdQspWjMTJg6F7avgiMHQZwQURP/Ecj6IRMeQK6xbqKGyXfCfe9xScPUaQb9noMsQm2otB+V9MNi4hRraMA8mXuYWjW3Xy4VCk/xttXNd3geDdQvVqCiHDx+Bd+9106v1Gg7dr7ep1nJcXgeDdQvV+GoFTBoKa9+Flse7qdsLjw67KhOAvA4G6xaSUIX5I+Dtm6BsJ/S4G3rcA7XrhV2ZCUjeBoN1C0l8vQ6mXAkrJ7ohzf3GwCE9wq7KBCxvg8G6hSosfRHevBp2bYFu18APH4G6Cd+LM3kgL4PBuoVKdn0Fb/0SFo+FRofABZOgqG/YVZkQ5WUwWLcQ57M3YdJP4esvoNNFcOYf4YB8Pygm74LBuoWYvaXw79vho99Dg2Zw7vPQ+aKwqzIRkXfBYN0CbqWnNy6Dr5a6twxnj4LGbcKuykRIXgVD3ncL5Xvh/Ydg1oNQuz6c+SfodrUNaTYJ8ioY8rpb2LzEDWlePxta94D+Y9zHkcZUIW+CIW+7Ba1w5xH+fbtbXv6UB+HE2yDiMxGZcOXNb0dedgvbP4fJl8PqaXBQF+j/HLQ6PuyqTBbIi2DIu25BFRY/58Ym7N4OP/gVnPpQ0vkXjaksL4Ihr7qF0k1u9OLyce5r0YNecV+TNiYFOR8MedUtlEyAKT+D0vVw9E/hjCdSmn/RmH1yPhjyolvYs8Ot47Dgr3BACxj4MnQcHHZVJotlHAwiUhuYDXyhqgMyL8k7edEtrHkHJg2BbSuhw0A4e6SbnNWYDHgxDc/1RHQx25xeVapsN8y8Df5xOuzcBH2fducTLBSMBzLqGESkLXAu8BDwK08q8khOdwsb57vBShvnu4Vd+o2GA4vCrsrkkEw7ht8BtwJJFyAMa1HbnOwWKsrhg4fhuWLYsgR++L9w4XQLBeO5tDsGERkAbFDVOSLSK9l2qjoCGAFuXYl095eKnOwWtn4KE4fA2v9Ai+PgnGehsGvYVZkclclbiVOAgSJyDtAAaCIiz6nqpd6Ulr6c+iRC1X3aMONGN//iSXfCyffa/IvGV56sRBXrGG6u7lOJIFaiyqlVpb750o1L+PR1aNrBzb/YpmfYVZkIs5WoksiZbmHZOLeC9K7N7qvRpz/qVn8yJgCeBIOqzgBmePFcmciJcwu7tsL062DRs9CwNfzoDTi8f9hVmTyTUx1D1ncLn01z34bc8TkceSGc9Sc44KCwqzJ5KGeCIau7hb074Z07YO4TUL8pnDMWOl9sMyuZ0ORMMGRtt/DlbDdYacsSOKyPG8HYuG3YVZk8lxPBkJXdQvle+OA3MOsBqFUXev8Bjvu5LRZrIiEngiHruoUtS12X8OWHcPCJbv7F5p3CrsqYb2V9MGRVt6AVMO9PMPNWqNgLPf8HTrrD5l80kZP1v5FZ0y3sWAOTLofVb0Lzzm5J+YMzHodijC+yOhiyoltQhSV/h2m/gN3boPsNcOqvoe4BYVdmTFJZHQyR7xZ2boY3fw7LXoTG7WDgS3Bo77CrMqZaWRsMke8WVk6EyVe47zt0GeLmX2zQNOyqjKmRrA2GyHYLe76Gt2+G+X+BBgfBef+CIy8IuypjUpKVwRDZbuGLd938i1tLoP0AN/9iw4PDrsqYlGVlMESuWyjfA+/eBx8+DHUKoM9IOOZKG9JsslbWBUPkuoVNC+GNS2Hjx9DmVDf/YtP2YVdlTEayLhgi0y1UlMOcx+E/d7nbpz0MxTdBrdohFmWMN7IqGCLTLWxbCZN+CmtmQotj3WClFseGWJAx3sqqYAi9W1CFhX+D6dfD3m/ghNug5/1Qp34IxRjjn6wJhtC7hW/Ww9RhUPIqHNjenUtoe2oIhRjjv6wJhlC7heUvu/kXd26EY66CXo9BvcYBF2FMcLIiGELrFnZvc28bPhkNBa3g/AnQ/twACzAmHJksONMOGAMcjFuJaoSqPuFVYfFC6RZWT3cnGHesho4XwFl/hoLCgHZuTLgy6RjKgJtUda6INAbmiMhUVV3kUW1ACN3C3p3uI8g5j0P9A90nDkddYoOVTF5JOxhUdR2wLnZ9h4gsBtoAngZDoN3C+rluZqXNi9y3IPs+A03a+bxTY6LHk3MMIlIEHA+8X8Vjw4BhAIceemhKzxtYt1BRBh/8Ft67382mdMYTcPy1Nv+iyVsZB4OINALGATeo6vbKj2eyqG0g3cKWZe6LT+veh1Y/cG8dDjrKp50Zkx0yCgYRqYsLhbGq+pI3JTm+dwuq8PFT7ivS5XvcQrEn3QW16/qwM2OySyafSggwClisqsO9K8nxtVvY8YWbROWzKdDsSNcltD7R450Yk70y6RhOAS4DFojIvNh9d6rqG5kW5Wu3sOQFmHYN7PoKjv8lnPZbqFvg8U6MyW6ZfCrxDuDLZ3i+dAs7t7hAWPoPaNQGLvgHFPXx6MmNyS2RG/noS7ewclJs/sV1bkxC799Dg2YePbkxuSdyweBpt7D3G3j7FneSsUFzGPBP6PRjL8o0JqdFKhg87RbWznKDlbaugMP7w9mjoFFrT+o0JtdFKhg86RbK98B7/+MWjK3dwH3H4dhhNqTZmBREJhg86RY2feK6hA0fwSE93ZwJzY7wtE5j8kFkgiGjbkErYM7v4J073fVTfw0n3GrzLxqTpkgEQ0bdwvbPYOJQWPM2FHZ1g5VaHudHmcbkjUgEQ1rdgqqbQGX6dW71p+Kb4ZQHoE4DP0s1Ji+EHgxpdQulG9xUaytegSZFbmaltqf7WKUx+SX0YEi5W1jxKky9yoVD1yuh13Co38TvMo3JK6EGQ0rdwu7tMONGWPg0FLSEQePhiIGB1GlMvgk1GGrcLayZ6U4wbl8FRwyGPiOgoEUwRRqTh0ILhhp1C2W74J27Yc5wqNcI+j0DXYbYYCVjfBZaMFTbLWyY5wYrbVoI7Xq5UGhyWKA1GpOvQgmG/XYLFWXw4SNuWXmp5U4udr/e5l80JkChBEPSbuGrFTBxCKx7D1oe7wYrFR4dRonG5LXAg6HKbkEV5v8FZtwE5bugx93Q4x6oXS/o8owxhBAMCd3C1+tgypWwciI06wj9xsAhPYIuyxgTR1RTmtE9I8XFxVpePpuSEli1Cppv/Ce8+XPYtQW6XQM/fATqNgysHmNyjYjMUdXiTJ8n0I5h61YoKYEH7/mK5u9dC0v+Do0OgQsmQVHfIEsxxuxHRqf6RaSfiCwVkRUicnt1269dCwO7TeWO1se4UOh0EQxZYKFgTMRksq5EbeCPQB9gDfChiLy6v0VtC+uvZvxlZ0NFMzj3eeh8Ubq7N8b4KJO3EicCK1T1UwAReQEYxH4WtW3ZaCN72vSl3rmjoHGbDHZtjPFTJsHQBvg87vYa4KTKG8Uvagvsrn/x5IXQNoPdeqoQ2BR2EXGiVg9EryarZ/86efEkmQRDVV9YSPiII35RWxGZ7cUZU69YPdWLWk1Wz/6JyGwvnieTk49rgHZxt9sCazMrxxgTBZkEw4dARxE5XETqARcBr3pTljEmTJmsXVkmItcCk4HawNOq+kk1PzYi3f35xOqpXtRqsnr2z5N6Ah35aIzJDvZdZmNMAgsGY0wCX4KhuqHS4jwZe3y+iHT3o47YvtqJyHQRWSwin4jI9VVs00tEtonIvNif//arntj+VonIgti+Ej5eCvj4dIr7e88Tke0ickOlbXw/PiLytIhsEJGFcfc1F5GpIrI8dtksyc+mNDQ/g3oeFZElsdfkZRFpmuRn9/v6eljPfSLyRdzrck6Sn039+Kiqp39wJyJLgPZAPeBjoEulbc4BJuLGQvQA3ve6jrh9tQa6x643BpZVUU8vYIJfNVRR0yqgcD+PB3Z8qnjtvgQOC/r4AKcD3YGFcfc9Atweu3478HA6v28e1nM2UCd2/eGq6qnJ6+thPfcBN9fgNU35+PjRMXw7VFpV9wD7hkrHGwSMUWcW0FREfFmjXlXXqerc2PUdwGLcqM0oC+z4VHImUKKqnwWwr+9R1ZnAlkp3DwJGx66PBgZX8aM1+X3zpB5VnaKqZbGbswhwCG+S41MTaR0fP4KhqqHSlf8h1mQbz4lIEXA88H4VD58sIh+LyEQR8Xs+OQWmiMic2JDxykI5PrixKM8neSzI47NPK1VdBy7ggZZVbBPWsboC19VVpbrX10vXxt7aPJ3krVZax8ePYKjJUOkaDaf2kog0AsYBN6jq9koPz8W1z92A3wOv+FkLcIqqdgf6A78Qkcrr64VxfOoBA4EXq3g46OOTijCO1V1AGTA2ySbVvb5eeQroABwHrAMeq2KbtI6PH8FQk6HSgQ6nFpG6uFAYq6ovVX5cVber6tex628AdUWk0K96VHVt7HID8DKu3YsXxnDz/sBcVV1f+YGgj0+c9fveQsUuN1SxTdC/S0OBAcAlGnsTX1kNXl9PqOp6VS1X1QpgZJL9pHV8/AiGmgyVfhUYEjv73gPYtq9l9JqICDAKWKyqw5Nsc3BsO0TkRNxx2exTPQ1FpPG+67gTWgsrbRbY8YlzMUneRgR5fCp5FRgauz4UGF/FNoENzReRfsBtwEBVLU2yTU1eX6/qiT/vdH6S/aR3fLw8cxp3JvQc3Nn/EuCu2H1XA1fHrgtukpcSYAFQ7EcdsX2dimud5gPzYn/OqVTPtcAnuDO2s4CePtbTPrafj2P7DPX4xPZXgPuHfmDcfYEeH1worQP24v6XuxI4CJgGLI9dNo9tewjwxv5+33yqZwXu/fq+36M/V64n2evrUz3Pxn4/5uP+sbf26vjYkGhjTAIb+WiMSWDBYIxJYMFgjElgwWCMSWDBYIxJYMFgjElgwWCMSfB/FZh6oA7WcokAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Vetor auxiliar\n",
    "aux = np.array([0, 0, 0, 1])\n",
    "\n",
    "pc = np.array([2, 2, 0, 1])\n",
    "\n",
    "aorg = np.array([0, 0])\n",
    "\n",
    "\n",
    "# Definindo Tbc\n",
    "pb_corg = np.array([0, -6, 0])\n",
    "Rbc = Rz(np.deg2rad(-45))\n",
    "Tbc = np.column_stack((Rbc, pb_corg))\n",
    "Tbc = np.row_stack((Tbc, aux))\n",
    "\n",
    "# Definindo Tab\n",
    "pa_borg = np.array([5, 10, 0])\n",
    "Rab = Rz(np.deg2rad(45))\n",
    "Tab = np.column_stack((Rab, pa_borg))\n",
    "Tab = np.row_stack((Tab, aux))\n",
    "\n",
    "\n",
    "# Definindo Tac\n",
    "Tac = Tab @ Tbc\n",
    "\n",
    "\n",
    "# Plotando os referenciais\n",
    "plt.figure()\n",
    "\n",
    "# Frame C->B\n",
    "pa_corg = np.array(Tac[:,3])\n",
    "pb_corg_aux = Rab @ pb_corg\n",
    "Rac = Tac[:3,:3]\n",
    "plot_frame(pa_corg, Rac, ['g', 'g'])\n",
    "plt.quiver(*pa_borg[:2], *pb_corg_aux[:2], color='g', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "# Frame B->A\n",
    "plot_frame(pa_borg, Rab, ['b', 'b'])\n",
    "plt.quiver(*aorg, *pa_borg[:2], color='b', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "\n",
    "# Calculando pa\n",
    "pa = Tac @ pc\n",
    "print(pa)\n",
    "\n",
    "plt.plot(pa[0], pa[1], 'o', color='darkorange')\n",
    "plt.quiver(*aorg, *pa[:2], color='darkorange', angles='xy', scale_units='xy', scale=1)\n",
    "\n",
    "plt.axis('scaled')\n",
    "plt.axis((0, 15, 0, 15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inversão de transformações"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.8660254 -0.5        0.         4.       ]\n",
      " [ 0.5        0.8660254  0.         3.       ]\n",
      " [ 0.         0.         1.         0.       ]\n",
      " [ 0.         0.         0.         1.       ]]\n",
      "[[ 0.8660254   0.5         0.         -4.96410162]\n",
      " [-0.5         0.8660254   0.         -0.59807621]\n",
      " [ 0.          0.          1.          0.        ]\n",
      " [ 0.          0.          0.          1.        ]]\n",
      "[[ 0.8660254   0.5         0.         -4.96410162]\n",
      " [-0.5         0.8660254   0.         -0.59807621]\n",
      " [ 0.          0.          1.          0.        ]\n",
      " [ 0.          0.          0.          1.        ]]\n"
     ]
    }
   ],
   "source": [
    "pa_borg = np.array([4, 3, 0])\n",
    "\n",
    "theta = np.deg2rad(30)\n",
    "Rab = Rz(theta)\n",
    "\n",
    "aux = np.array([0, 0, 0, 1])\n",
    "Tab = np.column_stack((Rab, pa_borg))\n",
    "Tab = np.row_stack((Tab, aux))\n",
    "print(Tab)\n",
    "\n",
    "# Transformação inversa\n",
    "Rba = Rab.T\n",
    "pb_aorg = -Rba @ pa_borg\n",
    "\n",
    "Tba = np.column_stack((Rba, pb_aorg.T))\n",
    "Tba = np.row_stack((Tba, aux))\n",
    "print(Tba)\n",
    "\n",
    "# Calculando a inversa\n",
    "print(np.linalg.inv(Tab))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Espaço de configurações"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# conda install scikit-geometry -c conda-forge\n",
    "# https://scikit-geometry.github.io/scikit-geometry/\n",
    "import skgeom as sg\n",
    "import skgeom.draw as sgdraw\n",
    "\n",
    "# conda install --channel conda-forge shapely\n",
    "# pip install descartes\n",
    "\n",
    "# https://pypi.org/project/Shapely/\n",
    "# https://shapely.readthedocs.io/en/latest/manual.html\n",
    "from shapely.geometry import Polygon\n",
    "from shapely.geometry import Point\n",
    "\n",
    "from descartes.patch import PolygonPatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "WORLDX, WORLDY = 50, 32 \n",
    "\n",
    "# Criando obstáculos\n",
    "obs1 = Polygon([(10, 20), (5, 20), (5, 10), (15, 15)])\n",
    "obs2 = Polygon([(35, 15), (40, 25), (45, 15)])\n",
    "obs3 = Polygon([(20, 10), (15, 5), (30, 5), (35, 10)])\n",
    "obs4 = Point([24, 22]).buffer(5)\n",
    "\n",
    "obs_set = [obs1, obs2, obs3, obs4]\n",
    "\n",
    "# Método para plotar o mapa\n",
    "def plot_map(obs_set):\n",
    "\n",
    "    fig = plt.figure(figsize=(8,5), dpi=100)\n",
    "    ax = fig.add_subplot(111, aspect='equal') \n",
    "\n",
    "    for obs in obs_set:\n",
    "        ax.add_patch(PolygonPatch(obs, facecolor='gray'))\n",
    "        \n",
    "    ax.set_xlim(0, WORLDX)\n",
    "    ax.set_ylim(0, WORLDY)\n",
    "\n",
    "    \n",
    "plot_map(obs_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robô circular"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.patches.PathPatch at 0x1bf820248b0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9Z40qk1LcOWkSfzpyhFeffZbH/uZviIqK0ruskKNpGmvffJP6DRt4MC+PvL5BBEFJKcWywkJMlZVseuEFEhITmTFjht5liSGSUclChJjPPvuMTb//PQ+kpRluJGMg+DSNo01NbK6sZFNlJfvq66lpa2PgnS3aasWWkkJ0XBwWiwWLxYLVasVisRAZGYnH48HtduN2u3G5XLjdbpw9PbS2tNDZ03NhOxlxcUzLyGBpfj5LCwqYlZ1NZBisAGHv6eGPp04x9u67WX3PPUFzeDNYbNywgR3PPsu9NhsTU1P1LscvNE3j3RMnOJCaykP/439QIDMhBJRMVyOEuKyqqiqe+7d/Y3F3N8sKC/UuJ2DqOjtZd+wYn1ZWsrmqipaeHiJMJnJzcsjOySE1NRWbzYbNZiM2NnbYYcbhcGC32y9c6uvqqK6uxuV2ExMZyaK8PJYVFHDrxIlMTkvz819pHMeamljT0cFNP/whs2fP1ruckFFeXs5b/+f/cIPJxLwQm1vU6/Px8tGj1E+cyON///cDwUUEgARDIcQl9fT08NR//ifJBw/yzZKSkBts0uFysfbYMV4oK2Pz2bOYTCZycnLILyigoKCAnJwcLKNwuNfr9VJfX09lZSVVlZXUVFfjdLuZnpXFQ1Oncm9JCVnx8QGvY7S9f/Ik+1NTeexnPyMzM1PvcoJee3s7v/uXf2FiZSW3T5oUkp1YR28vvz96FNvXv85DjzwSkn+jEUgwFEJ8iaZpvPrSS5xbt47HJ04kwQCrI/iDpml8fOYMfzxwgL9UVOD2eCgoKGBqaSmTJ08mOjpa7xLp7e3l5MmTlJeXc/LECXw+H8sLC/nW9OmsnjIlZA43e3w+njl8GPf8+Xznhz/EGiLPMT1omsYLf/4zLe++yxPFxSF9HvCZ1lZeaGrihh/+kHnz5uldTkiSYCiE+JJdu3bx4X/9Fw/0D5QIdl6fj3XHj/Mv27ZxoL6ezPR0SkpLmTp1qqEPSTkcDo4ePUp5WRmVVVXkJiby0wULeGTGDKJDYMkwe08PT58+zeT77+f2O+/Uu5ygtW/fPt598km+mZZGYXKy3uUE3EenTrE3LY3v/9M/kRwGf+9ok2AohPiC5uZmnvrFL5jV1MQN48frXc6IuL1eXi4r45fbt3PSbmdsYSELFy1i7NixQXcYqqGhge3btnHkyBFSYmL4ydy5fG/2bBKDfGTvoYYG1rlc3PvTnzJp0iS9ywk6LpeL//rFL5hw4gS3hcm/n9vr5b8PHyb/vvu46+679S4n5EgwFEJc4PP5ePYPf6Dno494vKQkaA9baprGOxUV/O1HH1Hd1sbkSZNYuGgROSFwQr7dbmfHjh0cOniQGLOZ/9+yZTwxe3bQzi2paRqvHj1KXXEx3//pTw1xOD+YfLxxI7ufeoq/KSoKmVM+rsbBhgbe9np59J/+idzcXL3LCSn+DobB+c4khABg9+7dnNuyhVsLCoI2FJ5qaWHVK69w+5o1WFNT+d73vsc9994bEqEQwGazcfPNN/PDv/1bJpSU8LcffsiMP/yBbdXVepc2LEopbh4/Hk9ZGR++/77e5QSVjo4Odr3/Pgvi4sIqFAJMy8gg025n4/vvY7SGlPgiCYZCBKnOzk42rVvHbJMpKCfF7ent5X99+ilTfvc7djc1ce+993L/Aw+Qnp6ud2kBkZCQwM0338y3H3uMtogIrn32WR56+20au7r0Lm3I4q1WVqalceiDD6iqqtK7nKCxfds2IquqWBCGHTOlFMvHjKF61y7Onj2rdzniK0gwFCJIbfjwQyJPnWJZEE4eu7e2luLf/55/3bGD+QsX8sT3v8+kEJ2y42JjxozhkW9/m5tvvpm1J05Q9Jvf8ObRo3qXNWQzMjPJaWnh/XXr8Pl8epdjeB0dHezfsIH5iYlYQ3gU8leZkJJCdns7mzdulK6hgUkwDEE+nw+n00l7ezvt7e04HA68Xq/eZQk/qqyspPyjj7g+LS2oRrtqmsb/2bmTBX/+M57oaJ743vdYvnz5qMw/aCQmk4mZM2fy/b/5G3LHjWP1G2/wvffew+nx6F3aVVNKsaqwkPO7d7Nnzx69yzG87du2EVldzdwxY/QuRTdKKZZK19DwwvNrS4jo6emhqqqK+vp6mpvt1Nbaqa1tweFw4/XCQBaMiOi7REVFkpWVzJgxNtLSbGRmZlJQUEBcXJy+f4gYEq/Xy/vr1pHT0sL0qVP1Lueq2Xt6ePidd3j3xAnmz5/PddddhzlMOycDYmJiuGv1agr27eNPH37Itpoa3ly9mqIgmXIoOz6emUqxad06SkpK5L3kMga6hYvDuFs4YEJKCtm1tWzeuJHC73wnLI4SBJvwfoYGGU3TqK+vp7y8nCNHznDyZCNtbeB2xwOpWK05REeXYjZHYzZbL3RhvF43Xq+btjYHDQ2t7NxpR6nDmM3bSEqCsWNTKSkZS0lJCbm5ufJCNbh9+/bRtHs33yksDJp9tae2ljtef5223l7uu+8+Jk6cqHdJhqGUYvbs2eTm5vLWG28w4+mn+fMtt3BPSYnepV2V6woLOXrsGB9v2MBtd9yhdzmGdKFbOGWK3qXobqBr+MquXZxdsYKxY8fqXZK4iATDINDd3c3+/fvZvbuMY8eaaWuLxWIpIilpAfn5+URFJQ3rcd3uLtraKjl4sJJduypISNjDhAlJzJs3lVmzZhl6IuFw5XK52LJ+PTOUCppl194/eZI7X3+d9MxMvrN6tTyvLiMzM5Nvf+c7vLt+Pfe+9RZ1nZ38eP58vcu6oujISJbabHywcSPzFy4kIyND75IMRbqFXyZdQ2OTZ6mBtbe3s337Dj755HOqqsBsnkJ6+g3k5o5FqZGfHmqxxJGeXkJ6egmaptHeXs3hw2V8/vlexozZwfLlpSxatJDU1FQ//DXCH3bs2IH7+HGWTpigdylX5YVDh3jknXeYUFTEnXfdRWQQnQ+pB6vVyh133kliUhI/2bCB+q4u/u366w3/wTkzK4ud5eV8smED93/jG3qXYyjSLfwy6RoamwRDA3K5XGzatJn33ttNba2VhISFTJw4h8jImIBtUylFUlI+SUn5eDwrqa/fz/PP7+Sjjw6ycuV0Vq68ntjY2IBtX1xZd3c3O99/n7nR0UExB9q/b9/O33/8MdfMmMFNX/86EUE6z+JoU0px/fV9r7d//+gjGru7+dPNNxt6nsoIk4nlmZm8tXkzNUuXygTG/aRbeHnSNTQueaYaiKZplJeXs3btBsrLXSQkLKO4eC4REaM7YtNstpKbu4AxY+ZQX/85L764iT17jnHHHdcxc+ZMTEG6YkOw2717N5w9y0KDn5+naRr/8Mkn/Gr7dhYvXsyyZcvkTX8Y5s+fT2xsLC+//TbNPT2svftuQ4eLkvR0tpaXs3XTJu5/6CG9yzEE6RZennQNjUs+4Q3C4XDwyitr+Pd/X8uxY/lMmPAD8vOvHfVQOJjJZGbMmDlMmvQDKiun8OST7/HnP79AZ2enbjWFK5fLxZ6NG5kZFUWMwQ/H/tv27fxq+3a+9rWvsXz5cgmFI1BaWsp999/PhjNneOjtt/EZeO43pRQL09M5sXUrjY2NepejO5m38MpkXkNjkmBoADU1NTz55FO89VYViYn3MnnyaqKijHOCvsUSy8SJt5CR8TDvvWfnV7/6PadOndK7rLCyb98+ek+dYr7BD9E9e+AAP/vkE5YsWcL8IBg4EQzGjx/PHXfeyRtHjvC3H35o6A/QkvR0kpqb2fbZZ3qXojuZt/DKZF5DYxpSMFRK/UwptVcp1amUOq+UelspNfGi+zynlNIuuuzyb9mho6ysjF/96lk+/zyBoqLHSU2dpHdJl5WUVMDkyY9z/PgY/v3fX2Lnzp16lxQWPB4POzduZJrZbOhzC9dXVPDY+vXMnDmTpUuX6l1OSJkyZQqrbrqJ3+zZw79u26Z3OZcVYTKxIDWVw5s20dLSonc5upFu4dWTrqHxDLVjuAT4LTAPWEHfOYoblFIXj0r4EMgadFk1wjpD0s6dO/nv/15Lc/M0iosfNlSX8HIsllimTLkfh2MRTz/9ERs2yIs50A4ePEj38eMsNHC3cEdNDavffJOJkyZx0003yeHjAJg9ezZLly7lHz/9lD8fOKB3OZc1IzOTmPp6dmzfrncpupFu4dWTrqHxDCkYapp2g6Zpz2madkTTtEPAt4A8YOZFd3VpmtYw6BK+Xx0v45NPPuWppz7C5bqWoqJbMJmMO+LwYkopxo69HrP5Bp59djvvvLNewmGAaJrG7i1bmOTzYYsJ3Kj0kWjs6uK2NWvIys7m9jvukMFJAbRkyRJmzpzJd999lz21tXqXc0mRERHMTUri0KZNOBwOvcsZddItHDrpGhrLSN/BB1pcFwe/pf2Hmk8opf6olEq/3AMopaxKqYSBCxAcs/aOwK5du3jxxc+IiFjB2LHXBW13JSdnHomJt7Fmzed8/PEnepcTkqqqqmgqL2dOVpbepVyST9O4f906nMCdq1fLPIUBppTixhtvJDMri7vffJM2p1Pvki7pmqwsfOfOcejQIb1LGXXSLRw66Roay7CDoepLM08C2zRNOzzopg+AB4DlwP8AZgOfKqUud3LUz4D2QZdzw60pGJSXl/PnP3+Iz7eIvLyFepczYpmZ04mNvYGXX94m5xwGwN7du0ltb6cgKUnvUi7pX7dtY9OZM9x2xx3EB8lKLMHObDZz5113cd7h4Nvrjdmtj7NYmAzs/ewzQ9YXKEbvFv6/W7YQ+y//wv66Or1L+RLpGhrHSDqGvwFKgfsGX6lp2hpN097TNO2wpmnrgRuBIuCmyzzOL+nrPA5cckZQk6HV1dXxpz+9TUfHdAoLr9O7HL/JyZmHz7eI5577SEYr+1FPTw/Ht29nls1myK7y1qoq/temTVy7eDHjxo3Tu5ywkpyczM233spbR4/y1L59epdzSbOys7EfOUJ1dbXepYwaI3cL25xO/mPnTnp6e/n5li16l/Ml0jU0jmEFQ6XUfwO3AMs0TfvKDp+mafVAFXDJNbw0TXNpmtYxcAFCcpI8p9PJCy+8QU1NBkVFNxvyg34kCguvo6VlAi+8sE7mOfSTo0ePojU0UJJ+2TMxdNPmdHLv2rXk5eayZMkSvcsJS1OmTGH27Nn86KOPOHz+vN7lfEl+YiJJnZ2UhcnhZKN3C3+9axdOr5cVK1bw7okT0jUUlzXU6WqUUuo3wB3Ack3TrhjrlVI2IBeoH16JwU/TNP7yl3fZs6eHCRNWB9VAk6ullGLChNsoLzexZs1b+Hw+vUsKemX79zPW5yPOot8k55fzvzZtwu50cvudd8pSdzpauXIlScnJfPe99wz3QaqUYmpcHEd27sTj8ehdTsAZvVv4f3btYubs2cybN480m026huKyhtox/C3wIHA/0KmUyuy/RAMopeKUUv+hlJqvlCpQSi0F1gPNwDo/1h1UKioqeP/9w2Rm3kx0dLLe5QSMxRJLfv6dfPJJJfv379e7nKDW2tpK9eefU5qWpncpX3KwoYHf7d3LkqVLSUw0/hRLoSwyMpIbVq1iR3U1L5WV6V3Ol5RmZOCsrg75U0yCpVu4YMECIiIiWLR4sXQNxWUNNRg+Qd95gJvp6wAOXO7pv90LTAXeAU4Az/f/d76maWF5fLG3t5e33vqA7u4JpKUV611OwCUlFQDXsHbtJ3R3d+tdTtAqLy8nsrmZSampepfyBT5N43vvv09aaipz587VuxwBjB07luLiYv7Hxo20G2yUclpsLJkOB2UHD+pdSkAFS7dwYIBYSUmJdA3FZQ11HkN1mctz/bc7NE37mqZp6ZqmWTRNy9c07WFN02oCUn0Q+OyzrRw40MXYsTeG3HmFl1NYeB0VFbBhw8d6lxK0Du/dyySzGYvBDtO+eOgQO2tquGHVKjmEbCArV66kw+3mnzZv1ruULylNTubE7t24XC69SwmIYOoWDpCuofgqMhNtAHV3d/P++zuJiVlAdHSK3uWMGoslFpttORs2HKS5uVnvcoJOS0sL548fp9hgh5E7XS7+r48/pqSkhMLCQr3LEYMkJiZy7ZIl/HbPHsMNRJmSloanoSFkDycHW7dwgHQNxeVIMAyg3bt3U1WlyM1dcOU7h5isrGtobIxj27bwXRZruCoqKjC3tjI22Vjnoz61bx+tDgcrVqzQuxRxCfPmzSMhIYFfbN2qdylfkBQVRYbLxYmKCr1L8btg7BYOkK6huBwJhgHicrnYuHEPUVEziYyM1rucUWcymUlOns+nn5bR0dGhdzlBpeLwYQrBUIeRnR4P/7FrF6XTpsmAE4Mym83MX7iQ148c4XSLsVYhnRgfz4l9+0JutoJg7RYOkK6huBQJhgFy6NAhTp92k5s7X+9SdJOVNZPa2kj27t2rdylBw+12U3P4MBMM1i187uBBmrq6WLgw+FfrCWUzZswgNiaGf9turE79+JQUHHV11NeHzqxlwdwtHCBdQ3EpEgwDZN++MjRtPFZrgt6l6MZstmKxFLN7d7m8qK/SuXPn8La0GGoJPI/Px79u386UKVNINdgoafFFkZGRzJk3j+cOHaLOQBPNj4mPJ7Kzk8rKSr1L8Ztg7xYOkK6huJgEwwBoaWnh4MFzpKWV6l2K7jIypnLiRBs1NWE7MH1IKisrienpIS0mRu9SLnj9yBGq2tpYdO21epcirsLs2bMxm808aaC1yyNMJvKUovL0ab1L8YtQ6BYOkK6huJgEwwA4cuQILS0WbLaJepeiu8TEfDo6Ejl8+LDepQSFypMnKTCZDDW10e/372dsYSFZWVl6lyKuQlRUFDNmzuSZgwdxe716l3NBQXw81YcPh8R5hqHSLRwgXUMxmATDADhx4gxKFRIREal3KbpTSmG1jufIEXlBX4nb7ab26FEKDXQYuaqtjW1VVUybPl3vUsQQTJs2jTaHgw8NNEVMQVISrvPng/48w1DqFg6QrqEYTIKhn3k8Ho4cqSEhoUDvUgwjObmQ06eb6Orq0rsUQxs4vzDfQMHw1cOHsZjNTJo0Se9SxBBkZGSQlZHBS+XlepdyQXb/eYZVVVV6lzIiodYtHCBdQzFAgqGf1dbW0tzs6V8aTkDf4eS2NkLqxPNAqKurw+pwGOb8Qk3TeKGsjKJJk7BarXqXI4aoeOpU/lJRQYdBVhyJMJnIAupqa/UuZdhCsVs4QLqGYoAEQz+rr6+nu9tMXFyG3qUYhtUaT29vIg0NDXqXYmj1dXVkapphzi8sa2zkWFMTpaUyiCoYTZ06FbfHw9pjx/Qu5YLs6GjqDHR4e6hCtVs4QLqGAiQY+p3dbkepFJSSf9rBlEqludmudxmGVnfyJNnRxpkMfc2RI8TFxDBu3Di9SxHDkJiYSEFBAa8aaOBXVlwcLdXVOJ1OvUsZslDuFg6QrqEACYZ+19hoRymb3mUYjtVq49w5CYaX09vbS2ttLRlxcXqXcsHGs2cpHDeOCAOtwCKGZvyECWytrjbM6OSMuDjo7qapqUnvUoYs1LuFA6RrKCQY+ll9fStRUcZatcIIoqKSaWho1bsMw2ppaQGHA5tBOoYdLhcH6uooKCjQuxQxAgUFBTh6e9lnkO5PSnQ0OBzY7cH1JTEcuoUDpGsoJBj6WXe3C7PZGB/uRmI2R+Fw9IbEHGaBYLfboacHm0EGnmyvrsaraRIMg1xmZiZRFgubDTLwyxIRQaKmBV0wDJdu4QDpGoY3CYZ+5nS6iYiw6F2G4ZjNVrzevrn6xJfZ7XaivV5iIo0x9+WmykoS4+NJSUnRuxQxAhEREeTm57PJIMEQwAbYm5v1LuOqhVO3cIB0DcOb8Z7lQczn8+Fyeb4UDD0eDz09PfT09OBwOHC73Xi9XrweD16PB8Lgid3VVYXHW8FLL75IckoKFouF+Ph4bDbbhUs4T4lit9sx0pmpn1ZWkldQYJgR0mL4CgoK2LZ5M26vF4sBzhe1WSxUB9GUNRe6hVOm6F3KlwSiWzigpKSEbZ99xs+3bGH9fff59bFHaqBr+MquXZxdsYKxY8fqXVJIkWAYAF6vh6amJtra2mhraqK7pQV6e6G3FwtgBSI0jQjAYgqPpm2kqx58Naj16+m0WHADxzWN7ogIiIlBxcWRNXEiBRMnUlBQQGFhIZEG6Z6NBnt9PTYDfGgD9Hq9HGpoYKWsdhIScnNzcfT2crSpiemZmXqXgy0mhgPnzqEZaGqmyxnoFi4Oo27hgIGu4bp169hfV8fM7Gy/b2MkJqSkkF1by+aNGyn8zncM/1wKJsZ7pgcpr9fLyZMnqa46TV3lduKpItrrJSkigtyoKGJjYoiJjCQiTILgxc53d+HTEnmgtJSoQW+wTo8He08Pjd3dVG3bxuFNm9gRHY0lO5vJ8+dTOm0ahYWFmEL8363j/HkKo6L0LgOAyrY2PD4fqampepci/GBgP5602w0RDBOsVjz9R09iDHJO7eWEa7dwgHQNw5MEwxFyuVzs27ePnRs30nXyJJ5Tp8jwTqY0I+kLASjceX0eIiO0Lx3KijKbGZOQwJiEBK7JykLTNOwOB0fOn6fspZc49PbbJE2axMIVK5g+fXpIdhE1TaOzpYU4izHOTT3RPzDAZjPSwW0xXDExMcRFR1/Yr3qLt1igrY3Ozk5DB8Nw7hYOkK5heDLesz1IuN1uduzYwa6PPqL31Cmmmc3MHTOGqJxODp83Syi8iMfnIsGqMF3hhauUIjUmhiUFBSzWNGo7O9l16BDvl5WxZdIkFn7ta8yZMyek5tbr6enB53T2fWAawAm7HYvZHLAuhBh9KTYbJ1pa9C4DoO8LkNtNV1cXGRnGXSEq3LuFA6RrGH4kvQyRpmkcP36cD9eupfvgQWZbrcwfP56E/oET2XFm9tV16Fyl8Tg8nWQnDK3bp5QiJyGBuxISWO5wsK2igg3HjrF/9mxW3XFHyLwJ9PT0QG8vsQbpnpyw27HZbCF/+D6cJNtsHDdIxzDWYoHeXrq7u/Uu5bKkW/hX0jUMP/LOPwRdXV288sILrPnXfyXj4EG+N3YsXxsUCgHSYqNBM8Y3cyNxedoYEz/8w8Ap0dHcMnEij+fmErNjBy/84hesffNNXC6XH6vUh9vtBq8Xq0G6oMdbWkiWw8ghxWazUWGQKWIiTSaU12voqavCbd7CK5F5DcOLBMOrdObMGZ76j/+g/u23uS8+nvuLi/tm8b+ILSYGVCs+zRhLUBmFUs2k+qEjlhEXx7emTuW2yEgqXn2Vp3/9a+oMOM/WULhcLjDIVCIADV1dchg5xMTHx9PudNJrgKXxlFJYlDJsMAzHeQuvROY1DC8SDK9A0zQ+27KFF3/1K9IPH+bxyZOZ+BWjNbPj44mzOOhyS9dwgNPTRaSpjWw/hQ2lFNMzM3l8/Hiidu/mmX/9V/bv3++Xx9aD2+0Gj8cwwbDT7cZikPMdhX8MzBHaZZAwZgHDdvulW3hp0jUMHxIMv4LP5+O9d9/l0z/+kSVOJ98oLr7iyNGsuDjSYnppczaMUpXG1+ZsIDnaSX5iol8fNzk6mkdLSrimuZn1v/0tmzdtCspviwOHko0SDLslGIacgf1plGBoxZirIEm38PKkaxg+JBhehsfj4Y01a/j85Ze5NTaWpVe5CkSEyURJehQdLuO9cPTS5mygyGYmOgBTzUSYTKyaMIHrgc3PPMP7770XdOsxu1wuTJqG2SCDPbpdrrBehSYUDQTDToOEMQvGDIbSLfxq0jUMD8b4JDIYn8/H2jff5OTatdyTmsqMrKwh/f4EWxJQhcdnvDe+0aZpPtzeM0xJSwjYNpRSLMrL49bYWPa99BJ/efvtoAqHPp+PCDDEaDq310uvzycdwxBzIRga5PCtSdPwGuB8x8GkW3hl0jUMDxIML6JpGh9+8AHH3n6buzIyvvJ8wsspSU8nPbaD5p7qAFQYXFqd9SRFNTM1PT3g25qRlcUdyckcev31oAuHRjFwqFGCYWgZmBje6fHoXEmfK81nqgfpFl4d6RqGPgmGF9mxYwd7Xn2VmxMTmTTMJcESrFZmZllo7jnp5+qCT2PXKaakQWZc3Khsb2pGhoTDERg4z9Fo3RwxMgOvAyMGMiOQbuHVk65h6JNgOEhVVRUfv/wy15pMXDPEw8cXuyYrDbPpNI7e8J3sutfrxKudYM4Y26geJg3GcGiUN7CY/s6SEc//EsM3sD/jDXLuqDGe7X8l3cKhka5haJNg2K+np4e3XniBvMZGlhUWjvjxStLTKbI5qG4/7IfqglNt53HyE9uYOcKQPRzBFA4tFgsepfAZIByalCLWYpFgGGIG9qdR1uN2Y5zTFaRbOHTSNQxtEgz7vfuXv+A5cIA7i4r8crglMiKCleMy8PjKcHl6/FBhcPH43HS4DnJdYVLfElg6CJZwaLFYICICt0EO38ZaLIadY04Mz4WOoUHCmFspwwRD6RYOj3QNQ5cEQ+DUqVMc3bCBGzMyvrC83UjNys5mfEon1e1lfnvMYFHbcZwx8U0szMvVtY5gCIdGC4Zx0jEMOQNB3ygdQ5emGWJKJOkWDp90DUNX2AdDj8fDB2vXUtDRQYmfR85Gmc3cPDETj29/WK2E4vR00eHazU0TkkmMitK7HMOHQ6MFw0SrFYfDoXcZwo+cTicRSl04h1Rvbk0zRMdQuoUjI13D0BT2wXDv3r207t/PqsLCgAyQmDtmDHPGuDjTuiNsvrWcad1LaUY7ywoL9C7lAiOHQ6vVChERuAwylcj45GTaW1v1LkP4UWtrK/nJyYaYK9OnaXgMcChZuoUjJ13D0BTWwdDj8bBjwwamKUV6bGxAthFhMnHH5EJSok9Q11kRkG0YSXNPNdaIMu6YnGu4N1ujhsOoqCgwmw0zx1yRzUaL3a53GcKP7HY7k2w2vcsA+udSNJv7nvc6km6hf0jXMPSEdTA8dOgQXceOsTAvL6DbKUxO5raJcbQ6PwvpQ8pOTxd1nZ+waoLZ74fl/cWI4TAuLg4sFsOsY1tks9HW2SkDUEJIm93ORIMEw06XCyyWvue9TqRb6D/SNQw9YRsMNU1j+8cfM9nnIzUmJuDbu2HCeK7N6+Z0yyd4fb0B395o82leTto3MSu7hdsmFRnikNXlGC0cms1mohISDLOObVF/gGhpCd0vMeHE6/Vib229sF/11uV2g8WiaydMuoX+JV3D0BK2wbCmpoaWY8eYk509Ktszm0w8WDqRCSmVHG/ejE8zxkADf9A0jRP2HWTHH+cbpeOJNsgJ7l/FaOEw3mYzzDq2AwHCLoeTQ0JbWxten88wwbDT7QarVbeOoXQL/U+6hqElbINh2aFDJHZ0kJ+YOGrbtMXE8N1Z48iIO8QJe+gMRjnb9jnxlj08NjOP3FH89xwpI4XD5KwsWg0SDFOio0mLjaWhoUHvUoQfDOzHKWlpOlfSp8XhICEtDbNOoUy6hYEhXcPQEZbB0Ov1cmTnTqbGxY36Ic9xKSl8d2YuCdY9nG7dG/ThsLq9HMVWHpmRTmlGht7lDJlRwqEtLQ0j9eeWFhRQXVmpdxnCDyorKxlns43aeuVXYu/pwZarz/ym0i0MHOkaho6wDIbnzp3Dce6cbt+gp2Zk8Ng1mcREbqXCvi0oDytrmsbpln34tI/55rRE5uv0Ru8PRgiHNpuNVsBrgMEwAMvy86mtq5MBKCGgurKS5fn5epdxgV3TsOn0JVK6hYElXcPQEJbBsLKykqjubl2/Qc8eM4a/mZNDWuxujjYF14AUn+alwr6N6MgtPDErjeVjR762tN70Doc2mw1fVBRtTueobvdylhYU4PX5qKmp0bsUMQJdXV00NjWxrKBA71KAvi+Udk3DpsP5jtItDDzpGoaG8AyGp06RbzL5ZU3kkZiakcGP5o5lbNIhDp9/OyimsnH0dnD4/LtkxO7ih3NzmZuTo3dJfqNnOLTZbBATg90gK45MSk0lLTaWSjmcHNQG9t8SgwTDTrebXqtVl2Ao3cLRIV3D4Bd2wVDTNM4dO0aeQV5841JS+OmiYpYWnKOy7U1qO44b8puMpmmc7z7LqZY3mDvmFD9dNMmwcxWOhF7hMD4+HktiIk3d3aOyvStRSrGsoIAqefMMamfPnmW8zUa2Qd7vmrq7ITp61IOhdAtHj3QNg1/YBcOOjg5629sDttLJcNhiYvj+nGl8a7pC430On3/PUN1DR28HR5s20tP7DvcUu/jRvGmG+aAJBD3CoVKKzPHjqe/qCvi2rtbNRUXU1NbS1tamdyliGLxeLyeOH+fmCRP0LuWC+q4uLCkppKSkjOp2pVs4uqRrGNzCLhja7XZwOLCNwqTWQ2E2mbipaAL/97WFLMg9wbmOVzlp34XLo18Hqdfr5Ezrfs60vsKMrHL+YVEOq4snG/Ibt7/pEQ6z8vKo8xpnINJtkyYRHRlJeXm53qWIYThz5gyd3d08WFqqdykX1Hd2kjVhwqjOBiHdwtEnXcPgNqRgqJT6mVJqr1KqUyl1Xin1tlJq4kX3UUqpnyul6pRSDqXUZqVUsX/LHj673Y7J6SRJ53U6L6cwOZkfzZvOD+cmkJe4lVMtL1LRvANHb8eo1eDydHOqZQ8V9hdJi/2UJ2Zb+bsF05mUmmroFU38bbTDYXZ2Ni0REYZZMznOYuG2SZM4XFYmb55BqKysjImpqczIzNS7lAvqfD6yArwE6cWkW6gP6RoGr6F2DJcAvwXmASsAM7BBKTX4uOzfAz8BfgDMBhqAjUopQzzre3p6iAHdB558lQiTiQW5ufzz0hn87bwYimw7qGp/gfLGD6jvPInH5/+l07w+D+e7z3Lk/EZOt75AbsIWvjfbzP+zdBrLCwuJjIjw+zaDwWiGw9zcXEhMpLq9PWDbGKoHp06lsalJJrsOMi6Xi4rjx/nG1KmG+TLX4XLRGhnZ9zwfrW1Kt1A30jUMXkN6pWiadsPgn5VS3wLOAzOBz1TfO9CPgF9omra2/z7fBBqB+4Gn/VDziLhcLqx6F3GVosxmFuXlMXfMGA6fP8/n9SfZX3+E480JQD4J1mySojKJs6RgUkMLbprmo8vdSpuzgQ5XPRqVpES3sbwwkpnZqUzLmGDIN1I9TO2fc23t668DcMttt2Ey+f8sjOTkZBJyc6k8edIwy5etGDsWW0wMZWVlZGVl6V2OuEoVFRW4e3u5f+pUvUu5oKqtDZKSKBjFEdIXuoVTpozaNq9WKHcLB5SUlLDts8/4+ZYtrL/vPr3L+YKBruEru3ZxdsUKxo4dq3dJhjHST/6B9c8GRkoUApnAhoE7aJrmUkptARZwiWColLLCF7JaQF8hbrcbSyA3MESfnj1LfWfnVd03ygwzMhW1HbU0dJ2ipgNO2qNweWOBZMBGpCmeCJMFkzJjUn2716d58GkevJobj7cbDTvQiiWii3iLg5wEyIyLIichgTiL4qTdzskArJM7NSODqenphulgDMVohEOlFAXFxVQeOuTXxx2JyIgIHpg6lT8fOsSyZcuwWIz06hGXs3/vXhbl51OYnKx3KRdUtrWRNnMmsaM08G+gW7hYuoW6Gegarlu3jv11dczMzta7pC+YkJJCdm0tmzdupPA73wnKz6ZAGParpb87+CSwTdO0w/1XD5zM0njR3RuBy029/zPgn4dbx1D19vYSOVobu4KDDQ1c98ILfnxEBUTTt1sj+OuZAl7AB3gAB6Bf2/zxWbP43apVQfkCHI1wWFBYSLnJhNPjIcogH2Y/njeP3+7Zw+eff868efP0LkdcQVVVFVU1Nfz3vffqXcoXVLrdjBvFzp10C41BuobBZySfPL8BSoFFl7jt4uShLnHdgF/SFzAHxAPnRlBX0OjsX27s8ccfD8i8XgPnTRglhB08eJCn3nsPQMLhZRQUFKAlJVHd3m6Yw8kFSUncO3Uq7+3YwaxZszAbJLCKS9u2dStT0tO5qahI71Iu6HC5sEdGct0oHUaWbqFxSNcw+AzrFaOU+m/gFmCxpmmDQ9zAGeqZQP2g69P5chcR6DvUDFxYkDUcd4rZbCYy0ih9zMCZPXs2JpOJp9avByQcXkpycjKJeXmcqagwTDAE+NnChbxcVkZ5eTkzZszQuxxxGfX19Zw8dYqXbr/dUAPszra2QnIy+aO0ZrN0C41FuobBZajT1Sil1G+AO4DlmqZdPM77LH3hcMWg37HQN5p5xwhrFSFg5syZ3HzzzTy1bx/fe//9oB0NFqjRykopJkyfzomeHkP92xSnp3PzxIns2LZt1NeRFldv+7Zt5CclcU9Jid6lfEGF3c6YkpJROb9QRiIbj4xQDi5DbXP8FniQvhHGnUqpzP5LNIDW9y/6a+AflVK3K6VKgOeAHuAVv1UtgpqEw682cdIkWmJiaO7p8cvj+cs/LlpEk90uE14bVENDA0ePHuWnCxZgDsCo+eHy+Hyc8vmYOEojpGXeQmOSeQ2Dx1DfPZ6gbyTyZvoOFQ9c7hl0n1/RFw5/B+wDxgArNU27uqG3IixIOLy8wsJCIjMzOd7c7IcK/WdeTg53TZnCJxs34nQ69S5HDKJpGh+8/z4TbDYeveYavcv5gsq2NtxJSUycOPHKdx4h6RYal3QNg8eQgqGmaeoyl+cG3UfTNO3nmqZlaZoWpWnakkGjloW4QMLhpZnNZibOmcNhA010PeDJlSvpdbnYvHmz3qWIQcrKyqiqruZ3q1ZhMdhk9OWNjdgmTiQ9PT3g25JuobFJ1zA4GOd4gwhLEg4vrXT6dBpjYmjs6vJThf6Rm5jIPy9ezJ7du2lsvOR4MjHKnE4nH2/YwN3FxSwvLNS7nC9we70c83opnTs34APNpFtofNI1DA4SDIXuJBx+2bhx44gpKKDMgOHrx/PnMy4lhQ+CeF+Fkk2bNuF1u/nPlSv1LuVLKpqbcaekMHUUzi+UbmFwkK6h8UkwFIYg4fCLIiIiKJ43j/LubsP9W1giIvjtjTdSWVXFvn379C4nrFVVVbF3zx7+eckSchIS9C7nS8qbm8mdMYOUlJSAbke6hcFDuobGJ8FQGIaEwy8qnTaNjoQEKtva/FugH6wYN44nZs1iw4cf0tDQcOVfEH7X09PDurfeYl5uLj+ZP1/vcr6k2+3mlFJMnTkz4NuSbmFwka6hsUkwFIYi4fCvcnJySJk8mQMGDV5Pfu1rTEpN5a033sDlcl35F4TfaJrGO2+/jertZc2ddxpqepoBZY2NqKwsiouLA7od6RYGH+kaGpvx3k1E2JNw2Ecpxaxrr+WIz0e32x2gKocvymzmzdWr6e7o4P3339e7nLCya9cuKk6c4MXbbjPkIWRN09jb0sKURYsCPqm1dAuDk3QNjUuCoTAkCYd9pk+fjsrJMWzXsMhm4w9f/zqHDh3iwIEDepcTFs6dO8fHGzfyk/nzDbUe8mCnW1tpSUpizrx5Ad2OdAuDl3QNjUuCoTAsCYcQExNDyeLF7GltxWvQpegeKC3l29dcw7vr13P69Gm9ywlpdrudNa++yqzsbH553XV6l3NZu+vryZw+nZycnIBuR7qFwU26hsYkwVAYmoRDWLBwIR1paZSfPx/ACkfmd6tWsWLsWF5fs4Y6A377DwWdnZ288tJLZEZF8e599xluIusBDV1dnIyMZMGyZQGdu1C6hcFPuobGJMFQGF64h8P09HQmLl7MtsZGw/7tkRERvLl6NaVpabzy0kvY7Xa9SwopTqeTV19+mUiPh40PPkhqTIzeJV3WtupqkqdOpaSkJKDbkW5haJCuofFIMBRBIdzD4bVLl9KckmK49ZMHi7VY+OD++8mOieHlF1+ks1OWR/cHj8fD66+9RndbGxsffJD8pCS9S7qsFoeDIyYTC66/HlMAR0pLtzB0SNfQeCQYiqARzuEwJyeHgnnz2Fpfb+i/2xYTw8YHH8Tq9fLCc8/R2tqqd0lBzeVy8eorr1B77hzr772XklFYb3gktldXEztpEjNmzAjsdqRbGFKka2gsEgxFUAnncHjt8uXUJSRw2uBhKy8xka0PP0ycz8ezzzwjE2APU1dXFy889xzna2v56IEHuDY/X++SvlK708lBj4d511+POYBdPOkWhh7pGhqLBEMRdMI1HI4dO5a8+fP5+Nw5w//N41JS2PnII4yNj+f5Z5+lsrJS75KCSktLC88+8wy9nZ1sffhhlhQU6F3SFW2qrCRq8mRmz54d0O1ItzA0SdfQOCQYiqAUjuFQKcX1N95IQ3IyR5qaRrHK4cmIi2PLN7/JvOxsXn7xRY4ePap3SUGhrq6OZ595hiSl2PXII0zLzNS7pCs6393NIWDxTTdhtVoDth3pFoYu6RoahwRDEbTCMRzm5eVRtHQpn9TX4zHovIaDJVitfHD//dw+aRKvv/46GzZswOPx6F2WIWmaxr59+3j2mWeYkJjIzkceoTA5We+yrsrHlZUklpYyM8DrIku3MLRJ19AYJBiKoBaO4XDFDTfQPmYMO2pqRrHC4bOazbx2553858qV7Nm1i+effVYGpVzE6XTy5ptv8u677/LojBlse/hh0gK8lJy/nLDbOREdzYpbb5VzC6VbOCLSNTQGCYYi6IVbOExLS2P+LbewtbOTNqdzlKscHqUUP5k/n+2PPIKpu5s/PPWUHFruV1tbyx+ffprqU6d4/a67+P1NNxEdGal3WVfF4/PxwblzjF26lClTpgR0W9ItDA/SNdSfBEMREsItHC5esoSo0lI+PHNmlCscmTljxnDwu99l1bhxvP7666xbt46uri69y9JFb28vmzZt4s/PPENBdDQHv/tdVhcX613WkGyvrqYjN5dVt9wiq5xIt9AvpGuoPwmGImSEUzi0Wq187Y47OB4VxamWFh2qHL6kqCjeuOsu/njzzVSdOMHvfvMb9uzZM6RlAoOZpmkcP36c3//2t+zYto2fLlzIjkceYWyQnE84oNXhYGtXF/NvvpnU1NSAbku6heFFuob6kmAoQko4hcPi4mIKlyzh/Zoaer1eHaocPqUU377mGk7+4AfcP2UKH7z/Pn/6wx+orq7Wu7SAamlp4dVXXuG1115jls3GkSee4BfLlxt23ePL0TSND86cIWbaNBYvWRLQbUm3MPxI11BfEgxFyAmXcKiU4qZbb6WjoIBPgvSba2pMDH+8+WZ2ffvbZJpM/PnPf+b1NWuoM+CHwUi0trby3nvv8fvf/pae8+dZe/fdfPjAA0yw2fQubVjKGhs5ER/PTXffjcViCei2pFsYnqRrqB8JhiIkhUs4TE1NZfnq1ez2+ahqa9OnSD+YM2YMex59lGduuQVHQwN/+MMfeOnFFzl79mzQ7juA8+fPs3btWv77v/6LU4cP80+LF1Px/e9z++TJAT0nL5A6XS4+OH+e0lWrmDhxYkC3Jd3C8CVdQ/0Y75UmhJ8MzKn21Pr1APxu1aqg/DCempEBwNrXXwfglttuw2T663e6efPmcaysjLc/+ojvxsURZcAP0KsRYTLxyIwZfHPaNN48epRfbNvG888/T25ODvPmz6eoqIjIIBit6/P5qKysZM/u3RyvqCA7IYEnV67k29dcQ2yAu2uBpmkab588ibm0lBtvuing27vQLQzwiOfhkG5h4JWUlLDts8/4+ZYtrL/vPr3L+YKBruEru3ZxdsUKxo4dq3dJfhOcnyBCXKVwCIcmk4k77rmHp86eZf3Jk9w1aVJQ/o0DIkwm7ikp4e7iYj44dYp/2baNN954g2irlUlTplBaWkp+fv4XwrHeNE2joaGB8vJyjpSX097ZSVFqKn++5RYeKC0NunMIL2d7TQ2nU1L4xje+QXR0dEC3NdAtXCzdwrA10DVct24d++vqmJmdrXdJXzAhJYXs2lo2b9xI4Xe+E9Tvu4MZ79UmhJ+FQzhMTk7mloce4o3//E8K6+uZZbA30OFQSrFqwgRWTZhARXMzL5eX82J5Oc8fOEBSQgJTSkoYN24cubm5AT/P7VK8Xi91dXWcOXOGo4cP09jUREpMDA8WF/NgaSlzx4wJyufZ5VS3t/NpdzfXPvYY48aNC/j2pFsoQLqGepBgKMJCqIbDW2+//cLfUVxczNnbb+fD558nNyGBjLg43er0t4mpqfw/y5bxv5cuZde5c7xUXs4bhw6xY8cOIkwmcsaMIa+ggIKCAsaMGUNUVJTfa+jt7aWhoYHKykqqKiupqa7G1dtLrMXCzUVFfGPFClaMHUtkiHQHB+vp7eWtykpybriBZcuXB3x70i0UA6RrOPqM94oTIkBCLhy+8QbWqChuuPHGC3/H1264gZrTp3ljyxa+U1ISMocwByilmJ+by/zcXH5z440ca25mc2Ulmyor2bR/P1u3bgUgMS6OFJuNZJsNW/8lNjYWq9WKxWK5cDGbzXi9Xtxu94WLy+XC4XDQ0tKC3W6nxW6n1W6npa0NDYi1WLg2L4/HlixhaUEB12RlYTbQYW1/0zSNd06cwD1lCnfee++oHMKXbqEYTLqGo0uCoQgroRQOXV4v7776KnHx8Vx77bUAREZGsvrBB/lDXR3rKiq4O4hHv16JUoopaWlMSUvje7Nno2kaR5uaONDQ0Ld+r93O8bo6tpeX09Pbe8nHiDCZ8F5mYu3IiAjGpqRQbLNRNGUKRTYbU9PTuSYrKyS7gpfzWVUVFcnJ3PfQQyQmJgZ8e9ItFBeTruHoMt6rTogAC5VwOCs7m67KSj557jkSExMpLS0F+qawufPRR3ntySfZUlXF0oICfQsdJUopitPTKU5P/8L1mqZR39WFvaeHTrebLrebTpeLLreb7t5eos1m4iwW4iwW4q1W4iwWkqKiyE1IICKEO4FX41hTE5vcbpZ961sBn5pmgHQLxaVI13D0SDAUYSlUwuGS/HzaKipY//zzZP/sZxeWJps4cSLLH3yQT556itTz5ym5KCyFE6UU2fHxZMsH+ZA0dHWxrrGR4tWrWbx48ahsU7qF4nKkazh6wvvrsAhroTAJ9sDI3aQzZ3jjpZfoHXTIdNGiRZTefjvrmpo429qqY5Ui2LQ6HLx0+jSpS5d+YYBToMkqJ+KryGooo0OCoQhroRAOLRER3DVuHPZt2/jk448vXK+U4tbbb6fwppt47dw56js7daxSBIsut5sXT5zAumABD3zrW6M2FZCsciKuRFZDGR0SDEXYC4VwmBEXx7KEBHavX09jY+OF6yMiIrj7/vtJXb6cl8+epcXh0LFKYXQuj4eXjx+nd/p0vvHYY8TGxo7atqVbKK6GdA0DT4KhEIRGOJyXk4Otvp7333nnC/VbLBbuf/hhrPPn89KJE3S53TpWKYzK4/Ox5vhxWiZM4MHHHycpKWnUti3dQnG1pGsYeBIMhegX7OEwwmTixtxcqrZu5ejRo1+4LTY2lm889hiea67h+WPHJByKL/D4fKw5dozq3Fzue+IJMvrnyhwt0i0UQyFdw8CSYCjEIMEeDselpDDO4WDrxx9/qfakpCS++b3v4ZwxQ8KhuGAgFJ7NyeG+H/yAglGe3qi7u5v9GzdKt1BctWDpGm799FO9SxkWCYZCXCTYw+GiMWNo+PxzTp8+/aXbbDYbD3//+zhnzOC5Y8doczp1qFAYhdvr5dWjRy+EwtFYA/lie/fuRVVXM9tg04+AdAuNzOhdw4WZmZzdtYuGhga9yxkyCYZCXEIwh8OCpCTGdHayffPmS95us9n41g9+gHfuXJ6pqOB8d/foFigModvt5vkjRzg3bhwP/PCHuoRCj8fD3k8/ZbrVSnRk5Khv/0qkW2hcRu8aTk5LI9FuZ9eOHXqXMmQSDIW4jGANh0op5mZkcHbvXtra2i55n5SUFB79wQ+IXbqUP58+TXV7++gWKXTV6nDw52PHaC8t5eEf/YjCwkJd6jh69CjdJ04wNydHl+1/FekWGp+Ru4YmpZibkkL5li309PToXc6QSDAU4isEaziclJpKpN3O4cOHL3ufuLg4Hv7ud8lctYoXamqoaG4exQqFXhq6unjmxAm0efN49G//lqysLN1qOVJWRm5vL6kxMbrVcDnSLTQ+o3cNSzMy8DU0UFFRoXcpQyLBUIgrCMZwaImIYKLJRPnevV95v6ioKB58+GGK7rqL15qb2VlTExR/nxieE3Y7z549S/zy5Tzy/e+TnJysWy0ul4tTe/cyZRSnxbla0i0MHkbuGsZZLOR7vRwtK9O7lCGRYCjEVQjGcFiclkbj0aO0XmE5PLPZzF13382CRx7hI03jnYoKPD7fKFUpRoOmaWyrrubV5mYKbr+dh7/zHeLi4nSt6cSJE3gbG5mSlqZrHZci3cLgYfSu4ZTkZM7s348ziAb6STAU4ioFWzgsSEpCdXRQVVV1xfuaTCZWrFzJHT/6EYczM3n28GEZsRwiXB4Pbx4/zsdKce23v829DzyA1WrVuywqKytJ7+0lMSpK71K+QLqFwcfIXcPxKSl47XZqamr0LuWqSTAUYgiCKRxGR0aS7vFQVVl51b9TWlrKt/7u7+ieNYunTpzgWFNT4AoUAVfX2cnTR45wqqCA1T/5Ccuvuw6llN5lAVBz4gS5o7QO81BItzD4GLlrmBwVRazTKcFQiFAWTOEwPyqK6uPHh/Q7Y8aM4bs//jGFq1ezpr2d90+elEPLQUbTNHafO8cz1dVEXXcd3/3pTykuLta7rAucTidNZ86Qm5iodylfIN3C4GXUrqFSilyTiZogWgVFgqEQwxAs4TA9NpbWujq8Xu+Qfi86Opq7772XVT/8IftTU3nm8GGag2zKhXDV09vLmmPH+ACY/cgjPPL446SkpOhd1hecP38eraODbIOFL+kWBi8jdw2z4+JoOHVK7zKumgRDIYYpGMJhSnQ0vu5u2ocxT6FSijlz5vDtf/gH3PPn89SZM+yoqcFnwL9T9DnW1MRvjx6lasIE7vu7v+OGG2/EbMBl5tra2sDpJMlA5xdKtzD4GbVrmBwVhaOtDZfLpXcpV2XIwVAptVgptV4pVaeU0pRSt110+3P91w++7PJbxUIYiNHDYUp0NDgctLS0DPsxsrKyePxHP2LWo4+yMTKSZw8fpklWSzGULrebN48dY01XF7l33cX3f/YzJk6cqHdZl9XW1kaspmGJiNC7lAukWxj8jNo1TIqKAqfzsgsOGM1wvkrGAoeAZ4G3LnOfD4FvDfrZPYztCBEUZs6cCcBT69cD8LtVqwxzgn+C1QpuN52dnSN6nMjISG648UYmT5nCX15/nd/v28c8i4Ul+flYDdiRChc+TWNPbS2bWlqImDKFO+6+m6lTpxrm+Xc57e3tGOnsQukWho6SkhK2ffYZP9+yhfX33ad3OQB9I++dTtrb28nIyNC7nCsa8ju6pmkfAB8AX/Xm49I0LfhWjhZimIwaDk1KYQZ6e3v98nj5+fk88eMfs3PnTj57+23KjxxhZWYmJenphvh7w0lVWxvvV1dzPj2dmd/6Fsuvu44YA64gcilutxsjjUeWbmHoGOgarlu3jv11dczMzta7JKwREeD14nYHR48sUF/1lyqlzgNtwBbg/9Y07fyl7qiUsgKDJ9WSr2siKA0Oh2aTif++8UadK+rjz2AIfRNiX3vttUydOpWPPviAtzZuZP+RI3wtP58s6bYEXLvTySdnz1JmNjPmuut47PbbyTbAh99QeDwezAY57aLN6eR/b9lCdHQ0p0+f1rsc4Qc+n49Is9kwXcMIkwk0bciDAPUSiGD4AfAGUAUUAv8v8KlSaqamaZc68/JnwD8HoA4hRpXT6aSzsxOL2cxn1dV6l3NBJP4NhgOSkpK45777ODV7Nh++/TZP799Pic/H8oKCvnMbhV/19PaytaqKvS4X1smTueW225gxY0ZQdmq9Hg9GObswJjISAIfDwdtvv61vMcKvrP37Vm8RSoHPh8fj0buUq+L3YKhp2ppBPx5WSu2jLyTeBKy9xK/8Enhy0M/xwDl/1yVEoDidTnbt2sWeXbvwejw8MXMmP124UO+yLuil7xzBQBk/fjzf+8lPOHjwIJvfe4/flJczzWRiYV4eqUFyaNPIutxudp07x97ubrRx41i0ahXz5883xOolw2UymTBK78QSEUHv//pfhhs4JkYuwmSMiVd8mgZKYTJIPVcS8LPGNU2rV0pVARMuc7sLuNBJDMZvvyI8XRwIH+8PhEY6nKppGi5NIyrA04KYTCauueYapk6dyt69e9m5cSMHjx1jss/Hotxcw81XFwzanE62V1dzwO3GVFjIrOuvZ+GiRcTGxupd2ohFx8TQbKD3enOQfGCL4OT0eMBsJjpIjqQEPBgqpWxALlAf6G0JMRqCIRAOcHu9aGbzqHWXIiMjWbBgAXPmzOHQoUNs//hj/lBWxriqKhZkZzM2OVm+/F1BfWcnu2prKdc0oiZM4NoVK5gzZ07QfKhcjejoaBx6FyHEKHF4PBAZGTSv4SEHQ6VUHDB+0FWFSqnpQEv/5ef0TWNTDxQA/wI0A+tGVqoQ+gqmQDig0+2GyMhR7zKZzWZmzpzJjBkzOHr0KNs++YQXDx7EVlPDrJQUpmdmEm2Q83+MwOPzcbSpiT3nz3MuOprEkhJWXn8911xzDRYDric8UjExMXRpGpqmyRcFEfK6+9+Hg2XWgOF0DGcBmwb9PHB+4PPAE8BU4CEgib5wuAm4R9O0kU2kJoROgjEQDmju6YGYGFJTU3XZvslkoqSkhOLiYmpqati7ezcfb93KxxUVFJlMlKalMcFmC8tDeZqmUdXeTlljI0fdbpw2G2Nvuol75s9n4sSJQXM+0nDYbDackZF09/YSF4LBV4jBmnp6MMXFkZycrHcpV2U48xhuBr7qK97Xhl2NEAYSzIFwQFN3N1EZGcTFxelah1KKvLw88vLy+NqNN1JeXk7Z3r2sKS8n6sgRplgslGZkkJeYiCmEO0iaptHY3U15YyPlXV10JCaSXFrKnLlzmTZtGjabTe8SR0VaWhrExtLU3S3BUIS8pu5uUsaNM+TylJcSHFUKMYpCIRAOON/dTWpenqEO18XFxTF//nzmz59PU1NTX0jctYvPT5wgpqaGoshIJtpsjE1ODolVVTw+H9Xt7VQ0N1PhcNAWE0NMQQHF8+ZROm0aOTk5hto/oyElJYWI+HjOd3VRGCRdFCGG67zTSVpent5lXLXgf9cVwk9CKRBC/6FKr5eS8eOvfGedpKWlsXz5cpYtW0ZtbS0VFRVUHDzIwYoKVEUF2T4fBTExFCQlkZeYGBRB0ePzUdvRQWVbG5WdndQohSchgYSJE5l4zTVMnDSJwsJCIgy0TvBoM5lMjJk8maqPP2ZuTo7e5QgRMB6fj3PAUgmGQgSPUAuEA5p7euiIjmbs2LF6l3JFSilycnLIycnhuuuuo7W1lbNnz3L2zBnKDh9m+7lzqIYGsnw+xlitZMfHkxUfT1pMjK5zlfk0jVaHg/quLuo6O6lzODgHeOLjicrMJH/FCq4bO5bCwkIyMjLCrjP4VcZOnMiuDRvwaVpInz4gwltNezu9iYmMGzdO71KumgRDEbZCNRAOONPaSoTNRl4QfVMdkJycTHJyMtdccw3anXfS0tJCZWUlVZWVVJ45w76qKrTz51E9PSQDNsAWFYUtOpqU6GgSrFbirVasEREjDmNur5cut5sOl4sWhwN7Tw92hwM70KJpeKOjIS6OpIkTyRo3jusKCigoKCAjIyOkB5CM1Lhx49gcF0ddZyc5CQl6lyNEQJxpbSU2P5+MjAy9S7lqEgxF2An1QDjgaFsbBQsXBv10J0opbDYbNpvtwnrUbrebhoYGmpqasNvt2JuaOHXuHHvr6/F2dUFrK7jdmD0eYk0mLJqGBbBoGlalsERE9C1T1c+nabi9Xtz0zbbv7r84AJfJBBYLWCyo2FiS8vKw5eQwNj2d2f11ZWVlBc1UFEaRnZ1NTG4ux6qqJBiKkKRpGkc7OxkfZEtXSjAUYSNcAiFAi8NBVWQkd86apXcpAWGxWC6Mch7M5/PR3t5OR0cHXV1ddHZ20tPTg9vtvnBxORy0Oxz4Bi1or5TCEhODNSqKBKsVi8WCxWIhKiqK+Pj4C5ekpKSgGVlodBEREUxdsIBDR49ynRxOFiHoXEcH9oQEbpo+Xe9ShkTe4UTIC6dAOOBgQwPWvDwmTZqkdymjymQyXTgMLYxv+owZ7E5O5lRLC0VhMlWPCB8HGxpILC6msLBQ71KGRIKhCFnhGAihbxTcgc5OSu68k0hZXUQYWGZmJpmlpezZulWCoQgpPb29lPf2Mn/hwqA6jAwSDEUICtdAOGB/XR1dmZksWLhQ71KE+EpKKRZddx1v7tlDbUcHY+RcQxEidp07h1ZQwJw5c/QuZcgkGIqQEe6BEPq6hdvsdqY+8EDYrKIhgtuUKVNInTGDLbt3c39xsd7lCDFijt5ednd1Mfv++0d9nXp/kGAogp4Ewr/aU1tLV1YWi5cu1bsUIa6KyWRi8cqVrD1wgMq2NgqSkvQuSYgR2Vpdja+wMGiP2kgwFEFLAuEXtTmdbGprY86jj5Kamqp3OUJctalTp7L32mt576OPeDwhQddJy4UYiYauLnb19rL8ttt0X6N+uCQYiqAjgfDLNE3j/dOniZ4+neXXXad3OUIMiVKKr99+O0+Xl7OjpoZr8/P1LkmIIdM0jXfPnMG2aBHz58/Xu5xhk2AogoYEwss71NjIidhY7rnrLqxWq97lCDFkGRkZzL/1Vjb/8Y+M6+wkW17XIshsq66mNj2dh++8M6jXQpdgKAxPAuFXa+jq4t3mZmY88ACTJ0/Wuxwhhm3Z8uWcPXGCNz75hO8WFxMlk4mLIFHZ1sanDgfXPvgg+UHe8ZZXnTAsCYRX5vR4WHP6NGnLl7Pq61/XuxwhRsRsNrP6gQd4uraWdRUV3DNliqyIIgyvw+XizaoqCr7+dZYuW6Z3OSMmwVAYjgTCq+P2ennl6FGcU6bw0IMPBnQy687Ozr41ifsvXV1duF0u3A4HHpcLn88XsG2L8OONjOT1hgZ2nT1LSXo6gY6GSikskZFYzGasZjMJViu26GhsMTGkxsRI51JcVk9vLy8eP07ErFncec89mEJg4JQ824VhSCC8eh6fjzXHjtEwbhwPPfGE35eA6+7u5tSpU1SePUvlkSO0VldDdzcmp5MkIB6waBrRJhNmk0m6OsKv0oDsmBhqa2vxNTeTGeDRnRrg9vlwaxpdSnEG6ACIjERZLGTYbBSkplKQlMS45GQig/j8MeE/bq+XV44fp7ukhEe++92gHYV8MQmGQncSCIem1+vlzePHqcrN5YHvfY+cnBy/PK7b7eb48eOUff45Z/btw3f+PBkeD0XR0eQnJZGenU1yVJRMJSJGTU1ODqf37ydP0yhMShrVpcXcPh8tHg8NbjeV585xvKqKXWYzlvh4JufmUpqRQWFysnwpClOO3l5ePXaMpgkT+OYTT4TUFGESDIVuJBAOXZfbzavHj3O+sJB7Hn/cL4uzd3d3s3v3bvZs3Ijz7Fnyenu5MSWFKePHE2ux+KFqIYYnNzcXgNMHDuCy25los41aELOYTGRaLGRaLEzv7wTZe3s53N1NWVkZhyIjSU5PZ+HYsUzPzMQsX5jCRpvTyUsVFfQUF/ONxx8nOztb75L8SoKhGHUSCIfnfHc3r5w6hWfaNL71ne+M+M3I4XCwZfNm9n/8MaqqiplRUczJzyc5OtpPFQsxcrm5uVgsFo5//jmu8+eZkpqKRadDubbISJYkJbFY06hzu9lRX897DQ1sTk1l0fjxzM7Olo56iKtqa+PNqirMc+fy6GOPheTSoxIMxaiRQDg8mqaxu7aWj9vasC1Zwre+9S0SExNH9HgHDx5k49q1eI8eZWF8PHMmTiQmgINXhBiJjIwMrPPnc/TgQfY2NDA5MZEUHb/AKKUYY7WyOi0Ne28v25qb+ai5mc/HjGHV5MmyrF8I8mkan1VVscXpJO/GG1l9//0hc07hxSQYioCTQDh8bU4n60+d4nRyMvMefZTrrr9+RKOP29raWLtmDdWffUapx8OKoiLiZUJsEQSSkpKYtWABx48epez0acb09FCQlKT7QBBbZCS3pqYyx+Xi/epqnmtqYkZRETdOmKBbZ1P4V2NXF++dOUNNRgZLHn6YxYsXh8To48uRYCgCRgLh8Lk8HrZWV7PL4SC6tJRvPPAA48aNG9FjHjt2jHdeeIGo48d5OD9fuhoi6FgsFqZOm0Ztaipnjx3jfFMThbGxZMXFjerAlEvJslp5JD2dA11dfHjoEDUtLawuLSUjRLtK4cDR28umykr2ejzYFizg4dWrg37y6qshwVD4nQTC4fP4fHxeX8+W5mbchYUsvPlmFi5ciGUEg0B8Ph8bN2xg5xtvMKWzk1tkRQkRxJRS5OTkkJaWxpnTpzlx6hTnGhvJi4sjPTZW11HCSimuiY8nLyqKN2tq+GNHBzdPn860zEzdahJD1+12s7u2lj2dnfjGj2fFbbcxd+7coF7mbijk00H4jQTC4RsIhFubm+nKyqL0wQdZfv31IzqXEMDj8bDurbc4um4dN8bFMWfyZN07K0L4g9VqZfKUKYzJyaGqspLjVVWcbWxkTHQ06bGxun75SY2M5Nvp6bxnt7Nuzx66pk9nQW6uvPYMTNM0znV0cKixkYNuN6aCAmbedx8LFi4kPsw+wyQYihGTQDh8lwqEi5cu9ctIN5fLxZqXX6b6gw+4Oz2dyWlpfqhYCGNJSEhgamkp3ePGUVNdTWV1NWfa2kj0ekmLjiY5KoqYyMhRD2VmpbjFZiO+rY2N+/fT5XKxcvx4CYcG4vH5ONfRwemWFg53ddEaH0/8xIksXraM2bNnEx2mMzRIMBTDJoFw+AIZCKEvFL783HM0btjAg7m5cj6hCHmxsbFMmjyZ8RMmYLfbaayv53R9PVpXF5G9vSQqRWxkJNGRkUT3L30XoRQRAVy5RynF8uRkYjs6+KCsDLPJxHUjPFdYXD1N0/D4fLi8XlweD+0uF/aeHuwOB/UOB7VK4UlIIDonh8lz53LrtGnk5eWF9MCSqyHBUAyZBMLhC3QghEGh8KOPeKiggDEJCX57bCGMzmw2k5GRQUZGBt6pU+no6KCtrY321lbq29tx9/SA0wleL2ga+HygaQFfjzmtp4f//uwz1pw7R05KSoC3JqBvqUMtIgIGLlYrpthYkseNIz0/n+sLCykoKCA9PT3sw+BgEgzFVZNAOHyjEQhBQqEQg0VERJCcnNy3lnj/KkFerxeHw4Hb7cbr9eL1evH5fGiaFtBaxgPJ586xPSqKyffeS0FBQUC3J/o6tlarFYvFgsViITExkaSkJAmBVyDBUFyRBMLhG61ACBIKhbgaERERuk1MfF92NuZjxzj9+edcf/31fYFVCIORYCguSwLh8I1mIAQJhUIEA6UUtxQV8dSRI7z5yis88vjjYTMFiggeEgzFl0ggHL7RDoQgoVCIYBJlNrO6sJBntmzhsylTWLZsmd4lCfEFEgzFBRIIh0+PQAgSCoUIRmMSElgUHc22t99m2rRppMhgFGEgEgyFBMIR0CsQgoRCIYLZtXl5lB0+zAfr13P/Qw/J/IbCMCQYhjEJhMOnZyAECYVCBLvIiAhuGDOG1zZt4vTChYwfP17vkoQAJBiGJQmEw6d3IAQJhUKEiok2G2Pq6tj66acSDIVhSDAMIxIIh88IgRAkFAoRSpRSXJudzWu7dlF9ww3k5eXpXZIQEgzDgQTC4TNKIAQJhUKEook2G2m1tezYupW8Bx7QuxwhJBiGMgmEw2ekQAgSCoUIVUopZqem8uGuXXTfdhuxsbF6lyTCnATDECSBcPiMFghBQqEQoa44LY0PT53iyJEjzJkzR+9yRJiTYBhCJBAOnxEDIUgoFCIcxFosjNc0yvfvl2AodCfBMARIIBw+owZCkFAoRDiZnJLCX8rLcTgcREdH612OCGMSDIOYBMLhM3IgBAmFQoSbwuRktOpqqqqqmDRpkt7liDAmwTAISSAcPqMHQpBQKEQ4SoqKIsnlorKyUoKh0JUEwyAigXD4giEQgoRCIcJZvtlMzalTepchwpwEwyAggXD4giUQgoRCIcJdWmwsFefOoWmarJ0sdCPB0MAkEA5fMAVCkFAohABbdDTO1lZ6enpkPkOhmyEHQ6XUYuDvgJlAFnC7pmlvD7pdAf8MfAdIBnYD39c07Yg/Cg4HEgiHL9gCIUgoFEL0scXEQGMjdrtdgqHQzXA6hrHAIeBZ4K1L3P73wE+Ah4ETwP8ENiqlJmqa1jnMOsOCBMLhC8ZACBIKhRB/FRsZCW43PT09epciwtiQg6GmaR8AHwBfOgeiv1v4I+AXmqat7b/um0AjcD/w9MjKDU1Op5PNmzdLIByGYA2EIKFQCPFFlogI8Hpxu916lyLCmL/PMSwEMoENA1domuZSSm0BFnCJYKiUsgLWQVeFXRp67tlniVBKAuEQBHMghNAJhU6Ph311dVQ0N+tdihDDNjcnh5L0dL3LwGwyYfL5cLlcepciwpi/g2Fm/38bL7q+Eci/zO/8jL5zEkeFUgpttDZ2BRNsNpYWFjItPV0C4VUK9kAIoRMKe3p7ueW11/jkzBm9SxFiRG6cMIH3779f7zJQShEBeL1evUsRYSxQo5Ivzl7qEtcN+CXw5KCf44FzgSgKwGKxYJQmfWZcHJseekjvMoJCKARCCL1QuLWmhm9+85sUFBToXZIQQ+JyuXj15ZdpOX+ef1q8WO9yANA0jV76PqeE0Iu/g2FD/38zgfpB16fz5S4i0HeoGbjQNw/03E1GCobiykIlEEJohsL7H3hAQqEIOoND4YYHH2ReTo7eJQHg9nohIkKCodCVv4PhWfrC4QrgAIBSygIsAX7q520Ni9VqxakZ5WCyuJxQCoQgoVAIo3C5XLzy0kuGC4UALq8XzGasVuuV7yxEgAxnHsM4YPygqwqVUtOBFk3TqpVSvwb+USl1EjgJ/CPQA7wy8nJHLjExEYfJhMvjwWqW+b2NJtQCIUgoFMIojBwKAdqcTrBaSQjS9wgRGoaTjGYBmwb9PHB+4PP0zV34KyAa+B1/neB6pVHmMExJSYGYGFocDhnsYSChGAhBQqEQRmH0UAhg7+mBmJi+zykhdDKceQw30zeY5HK3a8DP+y+GY7PZIDoauwRDQwjVQAgSCoUwimAIhQB2h4PE8eOJjIzUuxQRxsLuWGp0dDTxmZnUnz5tiHmrwlUoB0KQUCiEUQRLKARo6OkhXV5jQmdhFwwB8ouLqSov17uMsBTqgRAkFAphFMEUCr0+H9XA4rFj9S5FhLmwDIYFhYW8LwNQRlU4BEKQUCiEUQRTKASo7+rCHRcnrzWhu7BMRYWFhfgSEznb1sak1FS9ywlp4RIIQUKhEEYRbKEQ4HRLC5b0dLKysvQuRYS5sAyGNpuNjJISDu/YIcEwQMIpEIKEQiGMIhhDoaZplHd0MOnrXyciIkLvckSYC8tgCDB11iy2bN+O2+vFIi9Evwm3QAgSCoUwimAMhdB3GLk5NpYbpk/XuxQhwjcYlpSU8LHNxpHz55khrfsRC8dACBIKhTCKYA2FAIcaGogdN46xMvBEGEDYBsOkpCSKFi5kx9q1TM/MDPgazaEqXAMhSCgUwiiCORQ6ens54HQyd8kSTCaT3uUIEb7BEGDRkiX8edMmTtjtTJRzDYcknAMhSCgUwiiCORQC7KmtxZeXx7x58/QuRQggzINhXl4eeXPn8tlHH1Fks0nX8CqEeyAECYVCGEWwh0KXx8Pujg6uWb2a2NhYvcsRAgjzYAiwbOVKnt+zh7LGRqZlZupdjmFJIOwjoVAIYwj2UAiwpaqK3sJCFi5apHcpQlwQ9sGwsLCQ4pUr2fjaa0xKTZUJry8igfCvJBQKYQyhEAqburvZ5XKx9NZbSUxM1LscIS6QFASsvOEGfrNnD5+cPcuqCRP0LscQJBB+kYRCIYwhFEKhpmm8d+YMSXPmsGDBAr3LEeILJBgCiYmJXH/33XzwX//FeLudojANPyCB8FIkFAphDKEQCgG219RQlZrKN1avxixHqYTByDOy35w5czh9ww28vW4dT8TFEW+16l3SqJJAeGkSCoUwhlAJhdXt7Xza3c2ixx6TeQuFIUkw7KeU4tY77uCps2dZc/Ag3ywuJjIMVkSRQHh5EgqFMIZQCYUdLhdvVlaSc8MNLFu+XO9yhLgkpWma3jV8gVIqAWhvb28nQYcP4rq6Op578kkKq6q4Z8oUTCE6hc2XAuF110kgHERCoRDGECqh0NHby7NHj+KaNYtH/+ZvdPl8E6Gpo6NjYABToqZpHSN9PAmGl3Dy5Ele/fWvmd7Sws1FRSE1v6EEwiuTUCiEMYRKKOz1ennxyBGaJk/m0R//mFRZUEH4kQTDUXLw4EHeeeoppra2cuvEiUQE+VJFEgivjoRCIYwhlELhq8eOUVNQwDd/9CNygvTvEMYlwXAUHTlyhLVPP824+npWT5oUlOccSiC8ehIKhTCGkAuF+fk88Dd/I69FERASDEfZqVOnWPPUU6ScPs3dEyZgi4nRu6SrIoFwaCQUCmEMEgqFGBoJhjpobGzk9RdeoGvXLm7JyKA4PV3vki5LAuHQSSgUwhgkFAoxdBIMdeJyuVj/zjscfvddpjid3DBuHAkGmutQAuHwSCgUwhgkFAoxPBIMdaRpGocPH+ajt97CXV7OsqQkZo8Zg1nHgSkSCIdPQqEQxiChUIjhk2BoAE6nk08+/ph9779PXH09i2w2rsnKGtXBKU6Ph8/r69nZ0iKBcBgkFAphDBIKhRgZCYYG0tzczNYtWyj/9FOi6+uZFhvL9MxM0mNjA7I9TdM4393N/vp6DrpceLOzmbp0KdcuWSKBcAgkFAphDBIKhRg5CYYG1NLSwu5duyjfsYOes2fJdjiYlJjI2ORksuPjR7R6itfno6Griwq7nSMdHdhjY4kpKGDW8uXMnj2b+Ph4P/4loc/tdvPSs89KKBRCZxIKhfAPCYYG5vF4OHnyJGUHD3Lm4EFcDQ1EdXUxBkiPjiYtNhZbdDQxkZFER0YSZe5bqtrj8+H1+XB4PLQ7nbQ5nbQ4HJzr6aFOKXpjY4keM4ZJc+YwpbiYwsJCzGZZ5nqovF4vr7zwAufefZeH8vMlFAqhEwmFQviPBMMg4fP5qK2t5cyZM9TX1nK+spLWujq0nh7o7QWPp++/SvVdTCYwmyEqChUdTWJ6OtkTJpCbn09ubi5ZWVlEBOEE20ahaRpr33yTo6+/zjfGjKEgKUnvkoZFQqEIdhIKhfAvfwdDaTsFiMlkIjc3l9zc3AvX9fb20tbWhsPhwOFw4HQ6ATCbzURERBAVFUVSUhLx8fESAv3sk48/5vDataxOT5dQKIROJBQKYXwSDEdRZGQkaWlpepcRdk6cOMG2119nZUwMU4L0319CoQh2EgqFCA76TcAnxCjo6Ojg7RdeoKitjflB+kEkoVAEOwmFQgQPCYYiZGmaxttvvon5yBFuKypCjWB0uF4kFIpgJ6FQiOAiwVCErKNHj3Jm82a+npNDTGSk3uUMmYRCEewkFAoRfCQYipDkdrv5aO1aJjmdFAXh5N8SCkWwk1AoRHCSYChC0o4dO+g5dIivFRbqXcqQSSgUwU5CoRDBS4KhCDkul4tdH33ErKgokqOj9S5nSCQUimAnoVCI4CbBUISc/fv303v6dNCNQpZQKIKdhEIhgp8EQxFSfD4fOzdupNRkIjEqSu9yrpqEQhHsJBQKERokGIqQcubMGTpPnWL2mDF6l3LVJBSKYCehUIjQIcFQhJSygwdJ7e4mKy5O71KuioRCEewkFAoRWiQYipDhdrs5vmsXpYmJQTGZtYRCEewkFAoReiQYipBRXV2Nu6EhKNZDllAogp2EQiFCkwRDETIqKyuJcziwGXyKGgmFIthJKBQidEkwFCGj8sQJCiIiDH0YWUKhCHYSCoUIbRIMRUjwer3UHT9OXmKi3qVcloRCEewkFAoR+iQYipDQ2tqKr7ub9NhYvUu5JAmFIthJKBQiPEgwFCHBbrdDT48hzy+UUCiCnYRCIcKH34OhUurnSintokuDv7cjxGB2ux1Lby9xFovepXyBhEIR7CQUChFezAF63CPA9YN+9gZoO0IA0NPTQ6xShhp4IqFQBDsJhUKEn0AFQ4+madIlFKPG7XZj0TS9y7hAQqEIdhIKhQhPgQqGE5RSdYAL2A38o6ZpZy51R6WUFbAOuio+QDWJEOZ2uzHKQWSfpnHLa6/xyZkzTJ06lebmZpqbm/UuS4ghKTt0iFYJhUKEnUAEw93AQ8AJIAP4n8AOpVSxpmn2S9z/Z8A/B6AOEUa8Xi8RehfRz6QUHW43JqU4cvgwRw4f1rskIYYs3mqVUChEGPJ7MNQ07YNBP5YrpXYCp4FvAk9e4ld+edH18cA5f9clQltkZCS9ehcxyJ5HH9W7BCHCloRCIYYvUIeSL9A0rVspVQ5MuMztLvoOOQMYavCACB5Wq/WvTyIhRNiSUCjEyAR8HsP+cwgnA/WB3pYIXxaLRYKhEGFOQqEQIxeIeQz/Qym1RClVqJSaC7wJJADP+3tbQgxITEykC/D4fHqXIoTQgYRCIfwjEB3DHOBVoAJYC7iBeZqmVQVgW0IAYLPZ0KKjaXU49C5FCDHKJBQK4T+BGHxyr78fU4grsdlsEBOD3eEgzaDrJQsh/E9CoRD+JWsli5AQGxtLTGoq9Z2depcihBglEgqF8D8JhiIkKKXILymhsqtL71KEEKNAQqEQgSHBUISMgrFjOacUvV5ZmluIUCahUIjAkWAoQkZhYSHexESq2tv1LkUIESASCoUILAmGImSkpaVhmziR8sZGvUsRQgSAhEIhAk+CoQgZSilK587lmNcrh5OFCDESCoUYHRIMRUiZOnUqbpuNY83NepcihPATCYVCjB4JhiKkpKSkMG7ePHY0NqJpmt7lCCFGSEKhEKNLgqEIOYuWLqUhIYFTLS16lyKEGAEJhUKMPgmGIuQUFBSQM2cOW2trpWsoRJCSUCiEPiQYipCjlGLpypVUJyZytKlJ73KEEEMkoVAI/UgwFCFp/PjxTLr+ej6qr8ctI5SFCBoSCoXQlwRDEbJuuOkmegoK2HT2rN6lCCGugoRCIfQnwVCErKSkJJavXs1Or1cGoghhcBIKhTAGCYYipM2fP5/xX/sa62pq6HS59C5HCHEJEgqFMA4JhiKkKaW4ffVqTNOn80ZFBR6fT++ShBCDSCgUwlgkGIqQFxsby92PPEJ9YSFvHT+OT6awEcIQJBQKYTwSDEVYyM3NZfV3v0tFWhrvnzwp8xsKoTMJhUIYkwRDETaKioq45bHH2BcXx19OnJDOoRA6cfT28uLRo9QUFEgoFMJgJBiKsDJ9+nTu+MEPOGSz8drRo/TKHIdCjKoOl4tnjx2jefJkvvmjH0koFMJgJBiKsFNaWsoDP/4xlfn5/PnIEVocDr1LEiIsVLa18cfjx3HPmsUjP/oROTk5epckhLiIMtq5VkqpBKC9vb2dhIQEvcsRIay+vp43XniB7j17uDkjg5L0dL1LEiIk+TSNrVVVbHY6yb/+eu685x7i4+P1LkuIkNDR0UFiYiJAoqZpHSN9PAmGIqy5XC7e/ctfKF+/nhKXi5Vjx5JgtepdlhAho6Gri/fOnuVcWhpL7rmHxUuWYDLJwSoh/EWCoRB+pmka5eXlfPTmm/QeOcLSpCTmjhlDhHx4CTFsjt5eNldWssfrJXX2bL5+113k5+frXZYQIUeCoRAB4nQ62fTpp+x5913i6+tZYLNxTVYWlogIvUsTImh0ud3sOneOvd3daGPHsvT225k7dy4R8joSIiAkGAoRYE1NTWz77DPKN20iqq6Oa+LiKM3IID02Vu/ShDAkTdOobm/nUGMjZb29mMaOZfb11zN/wQLi4uL0Lk+IkCbBUIhR0tbWxs4dOyjbtg1HVRWZDgfFiYkUJieTFRcnh5pFWHN7vdS0t3OmtZXDXV20JyaSVFTENYsWMXv2bKKjo/UuUYiwIMFQiFHm9Xo5deoUZQcPcnLfPtxNTVi6usgF0qOisMXEYIuOJs5iwWo2Y4mIINJkQimld+lCDJumabi9XlxeL26vl3anE7vDgb2nhwaXi1qTCV9CArHZ2UyeM4fSadPIzc2V570Qo0yCoRA68vl81NfXc/bsWaorK7GfO0drXR2+7m5wu8Hr/etFiGAXEQFmc99/rVbM8fHYcnJIzcmhoLCQgoICUlNTJQwKoSMJhkIYjNfrpa2tje7ublwuF263m97eXlmPWQQ1pRQWiwWr1YrFYiEhIYGEhAQJgUIYjL+DoXnkJQkR3iIiIrDZbNhsNr1LEUIIIUZEzp4XQgghhBCABEMhhBBCCNFPgqEQQgghhAAkGAohhBBCiH4SDIUQQgghBCDBUAghhBBC9JNgKIQQQgghAAmGQgghhBCinwRDIYQQQggBSDAUQgghhBD9JBgKIYQQQghAgqEQQgghhOgnwVAIIYQQQgASDIUQQgghRD8JhkIIIYQQApBgKIQQQggh+kkwFEIIIYQQQACDoVLqe0qps0opp1Jqv1Lq2kBtSwghhBBCjFxAgqFS6h7g18AvgBnAVuADpVReILYnhBBCCCFGLlAdw58Az2ia9idN045pmvYjoAZ4IkDbE0IIIYQQI2T29wMqpSzATOBfL7ppA7DgEve3AtZBV8UDdHR0+Ls0IYQQQoiQ4u+85PdgCKQCEUDjRdc3ApmXuP/PgH+++Mrc3Fz/VyaEEEIIEZpSgBGnxEAEwwHaRT+rS1wH8EvgyUE/xwPngBygMzClCR3Ifg1Nsl9Dk+zX0CT7NTQN7NcWfzxYIIJhM+Dly93BdL7cRUTTNBfgGvhZKTXwv52apsnx5BAh+zU0yX4NTbJfQ5Ps19A0aL/6hd8Hn2ia5gb2AysuumkFsMPf2xNCCCGEEP4RqEPJTwIvKqX2ATuB7wB5wFMB2p4QQgghhBihgARDTdPWKKVswD8BWcBhYJWmaVVX8esu4H8z6PCyCAmyX0OT7NfQJPs1NMl+DU1+3a9K0y41HkQIIYQQQoQbWStZCCGEEEIAEgyFEEIIIUQ/CYZCCCGEEAKQYCiEEEIIIfoZLhgqpb6nlDqrlHIqpfYrpa7VuyZx9ZRSi5VS65VSdUopTSl120W3K6XUz/tvdyilNiulinUqV1wlpdTPlFJ7lVKdSqnzSqm3lVITL7qP7Nsgo5R6QilVppTq6L/sVErdOOh22adBrv+1qymlfj3oOtmvQah/n2kXXRoG3e6X/WqoYKiUugf4NfALYAawFfhAKZWnZ11iSGKBQ8APLnP73wM/6b99NtAAbFRKxY9OeWKYlgC/BebRN1m9GdiglIoddB/Zt8HnHPAPwKz+y6fAO4M+TGSfBjGl1Gz65hEuu+gm2a/B6wh90wAOXKYOus0/+1XTNMNcgN3A7y+67hjwS71rk8uw9qcG3DboZwXUAz8ddJ0VaAO+q3e9chnSvk3r37+LZd+G1oW+9VYflX0a3BcgDjgBXA9sBn7df73s1yC9AD8HDl7mNr/tV8N0DJVSFmAmsOGimzYAC0a/IhEAhfStoX1hH2t9a2VvQfZxsEns/+/Aou2yb4OcUipCKXUvfV3/ncg+DXa/Bd7TNO3ji66X/RrcJvQfKj6rlHpNKTW2/3q/7ddALYk3HKlABNB40fWN9P2xIvgN7MdL7eP8Ua5FDJPqW7H9SWCbpmmH+6+WfRuklFJT6QuCUUAXcLumaUeVUgMfJrJPg0x/wJ9J3+kBF5PXavDaDTxEXyc4A/ifwI7+Uz/8tl+NFAwHXLwUi7rEdSK4yT4Obr8BSoFFl7hN9m3wqQCmA0nAncDzSqklg26XfRpElFK5wP8HrNQ0zfkVd5X9GmQ0Tftg0I/lSqmdwGngm8Cugbtd9GtD3q+GOZQMNANevtwdTOfLCVgEp4HRU7KPg5RS6r+BW4BlmqadG3ST7NsgpWmaW9O0U5qm7dM07Wf0DR77W2SfBquZ9O2j/Uopj1LKQ9/gsR/2///AvpP9GuQ0TesGyoEJ+PH1aphgqGmaG9hP34jHwVYAO0a/IhEAZ+l78l7Yx/3nli5B9rGh9U+D8BvgDmC5pmlnL7qL7NvQoeg7aV32aXD6hL6RqtMHXfYBL/f//xlkv4YEpZQVmEzfoBO/vV6Ndij5SeBFpdQ++s55+Q6QBzyla1Xiqiml4oDxg64qVEpNB1o0Tavun0vrH5VSJ4GTwD8CPcAro12rGJLfAvcDtwKdSqmBb6XtmqY5NE3TZN8GH6XUvwAfADVAPHAvsBS4QfZpcNI0rRM4PPg6pVQ3YB84J1j2a3BSSv0HsB6opq8T+D+BBOB5f75eDRUMNU1bo5SyAf9E3/w8h4FVmqZV6VuZGIJZwKZBPz/Z/9/ngYeBXwHRwO+AZPpOpl3Z/2YmjOuJ/v9uvuj6bwHP9f+/7NvgkwG8SN/7bTt9893doGnaxv7bZZ+GJtmvwSkHeJW+wbpN9J1XOG9QRvLLflX9c90IIYQQQogwZ5hzDIUQQgghhL4kGAohhBBCCECCoRBCCCGE6CfBUAghhBBCABIMhRBCCCFEPwmGQgghhBACkGAohBBCCCH6STAUQgghhBCABEMhhBBCCNFPgqEQQgghhAAkGAohhBBCiH4SDIUQQgghBAD/fzo2TfCCqmzYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = 3\n",
    "\n",
    "obs_set = [obs1, obs2, obs3, obs4]\n",
    "\n",
    "obs_set_dilated = []\n",
    "for obs in obs_set:\n",
    "    obs_set_dilated.append(obs.buffer(R))\n",
    "\n",
    "plot_map(obs_set)    \n",
    "    \n",
    "for obs in obs_set_dilated:\n",
    "    plt.gca().add_patch(PolygonPatch(obs, facecolor='red', alpha=.5, zorder=0))  \n",
    "    \n",
    "\n",
    "# Robô\n",
    "robot = Point([7, 23]).buffer(R)\n",
    "plt.gca().add_patch(PolygonPatch(robot, facecolor='blue', alpha=.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robô poligonal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 32.0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skgeom import minkowski\n",
    "\n",
    "obs1 = sg.Polygon([sg.Point2(10, 20), sg.Point2(5, 20), sg.Point2(5, 10), sg.Point2(15, 15)])\n",
    "obs2 = sg.Polygon([sg.Point2(45, 15), sg.Point2(40, 25), sg.Point2(35, 15)])\n",
    "obs3 = sg.Polygon([sg.Point2(15, 5), sg.Point2(30, 5), sg.Point2(35, 10), sg.Point2(20, 10),])\n",
    "obs4 = sg.Circle2(sg.Point2(24, 22), 5**2, sg.Sign.CLOCKWISE)\n",
    "\n",
    "obs_set = [obs1, obs2, obs3, obs4]\n",
    "\n",
    "fig = plt.figure(figsize=(8,5), dpi=100)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "\n",
    "for obs in obs_set:\n",
    "    if isinstance(obs, sg._skgeom.Circle2):\n",
    "        sgdraw.draw(obs, fill=True, color='gray', ec='k', linewidth=1)\n",
    "    elif isinstance(obs, sg._skgeom.Polygon):\n",
    "        sgdraw.draw(obs, facecolor='gray', line_width=1)\n",
    "\n",
    "ax.set_xlim(0, WORLDX)\n",
    "ax.set_ylim(0, WORLDY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1bf82702670>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "robot = sg.Polygon([sg.Point2(0, 0), sg.Point2(3, 0), sg.Point2(0, 4)])\n",
    "#robot = sg.Polygon([sg.Point2(-1, -1), sg.Point2(2, -1), sg.Point2(-1, 3)])\n",
    "#robot = sg.Polygon([sg.Point2(-1, -1), sg.Point2(1, -1), sg.Point2(1, 1), sg.Point2(0, 3), sg.Point2(-1, 1)])\n",
    "\n",
    "plt.figure()\n",
    "sgdraw.draw(robot, facecolor='red')\n",
    "plt.gca().plot(0, 0, 'b*', markersize=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 32.0)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,5), dpi=100)\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "\n",
    "# Calculando o Minkowski\n",
    "obs_set_dilated = []\n",
    "for obs in obs_set:\n",
    "    if isinstance(obs, sg._skgeom.Polygon):\n",
    "        result = minkowski.minkowski_sum(robot, obs)\n",
    "        obs_set_dilated.append(result)    \n",
    "        sgdraw.draw(result, facecolor='red', line_width=1, alpha=.5)\n",
    "\n",
    "# Plotando o Mapa\n",
    "for obs in obs_set:\n",
    "    if isinstance(obs, sg._skgeom.Circle2):\n",
    "        sgdraw.draw(obs, fill=True, color='gray', ec='k', linewidth=1)\n",
    "    elif isinstance(obs, sg._skgeom.Polygon):\n",
    "        sgdraw.draw(obs, facecolor='gray', line_width=1)\n",
    "\n",
    "ax.set_xlim(0, WORLDX)\n",
    "ax.set_ylim(0, WORLDY)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Para praticar\n",
    "\n",
    "- Faça o cálculo de $P \\oplus -Q \\Rightarrow P \\ominus Q$\n",
    "- Aproxime o círculo de um polígono regular e faça o cálculo\n",
    "- Faça testes com polígonos não-convexos\n",
    "- Faça o cálculo considerando também rotações (C-space tridimensional)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}