Runge-Kutta final answer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align: center; font-family: montserrat\">Runge-Kutta Method</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>When step size, h=1</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]\n",
      "y_ Runge-Ketta: [0.0, 16.256, 28.438, 39.122, 49.254, 59.183, 69.036, 78.862, 88.678, 98.49, 108.301]\n",
      "y_ exact: [0.0, 16.251, 28.431, 39.113, 49.243, 59.171, 69.025, 78.851, 88.667, 98.479, 108.29]\n",
      "v_Runge-Ketta: [20.0, 13.631, 11.243, 10.347, 10.012, 9.886, 9.838, 9.821, 9.814, 9.811, 9.811]\n",
      "v_exact: [20.0, 13.559, 11.189, 10.317, 9.997, 9.879, 9.835, 9.819, 9.813, 9.811, 9.81]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiEAAANsCAYAAACNpniBAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAClQElEQVR4nOzdeZxO5f/H8ddl7FsUypalZJkVY6tkpCyRKIVUloSWb6RNlDZKiSSVKFtEKJFElLHvGSopKvsuys7MfH5/zMz9mzEzDMacWd7Px+N+zJz1+tzHmPs917nOOc7MEBEREUlr2bwuQERERLImhRARERHxhEKIiIiIeEIhRERERDyhECIiIiKeUAgRERERTyiEiEiacs4tcc5V9bqOpDjnrnXOHXXO+Xldy/k4575yzjX2ug6RS6EQInIRnHNbnHMnYj+w9jjnxjjn8ntd19mcc68458bHmy7pnNvonBvqnHPn2dacc9fHmw5zzu24xHruBI6Y2drzrFc2tv3sl9LehTKzbWaW38yi0rLdpDjnijvnZjjndsUei7JnrTIA6O9BaSKpRiFE5OLdaWb5gRCgKvCCt+Wcm3OuDLAQmGFmT5o3dyrsBnzmQbsZUTQwG7gnqYVmthIo6JwLTdOqRFKRQojIJTKzPcAcYsJIkj0GsT0nt8V+/4pzbrJzbpxz7ohz7tf4HyTOuWrOubWxy6Y4575wzvWLt7yZcy7COXfYObfUORd0vhqdc9cRE0A+N7Pn4s3v5Jz7zTl3yDk3Jzao4JxbGLvKutjenvbAd0CJ2OmjzrkSzrmazrllsbXsds4Nc87lTKaGnMCtwIJ482o651Y75/5zzu11zg2OXRTX/uHYtuqcq97YZeace9I595dz7oBzbqBzLsnfccm1G78HxjlXJ957PeqcO+mc2xK7XjbnXC/n3J/OuYOx/55Xnu/f4UKY2V4z+xBYdY7VwoGmqdmuSFpSCBG5RM65UkATYPMFbNYcmAQUAmYAw2L3lROYBowBrgQmAi3jtVUNGAV0Ba4CPgZmOOdynaOt8sR8qH9sZi/F21cLoDdwN1AUWBTbHmZ2S+xqwbGnJ8bGvsddsdP5zWwXEAU8BRQB6gANgMeSqaMCEG1m8QPae8B7ZlYQuA6YHDs/rv1CsW0tO1e98bQEQoFqwF1Ap2RqSa5dHzNbFvdegcLA8njtPQm0AOoBJYBDwAdJNRQ7zuTwOV73J1NjSvwGBF/C9iKeUggRuXhfO+eOANuBfcDLF7DtYjObFTv24DP+/4OkNpAdGGpmZ8zsK2BlvO0eISZMrDCzqNhwcCp2u+QEAPmAL86a3xV408x+M7NI4A0gJH7vwvmY2RozW25mkWa2hZhQVC+Z1QsBR86adwa43jlXxMyOmtnyczSXknrfMrN/zGwbMARom8y+LqRdgKHAMaBPvFr6mNkOMzsFvAK0SmoMS+w4k0LneH1+nrbP5Qgxx1UkQ1IIEbl4LcysABAGVCKmNyCl9sT7/jiQO/YDrASw86zxGtvjfV8GeDr+X9JAaWJOk7SLd+rgu3jbzCCm9+THsz6wywDvxdvPP4ADSqb0TTjnbnDOzXQxg3P/IyYYJHccDgEFzpr3MHADsNE5t8o51+wczaWk3vjHaisxxzMpKW7XOdeVmH/j+80sOl4t0+LV8hsxvUJXn6P+y6EAcDiN2xRJNQohIpfIzBYQc/rkndhZx4C8cctdzOWeRVO4u91ASecSXLlSOt7324H+Z/0lndfMJprZhHinSpqcVWNPYCYxQaRkvH11PWtfecxsaXJvNYl5HwEbgQqxpzZ6ExMMkrIJcPHax8w2mVlboBjwFjDVOZcvmbZSUm/8Y3UtsCvJN5J8uwk45+oCrwN3mdm/Z9XS5KxacpvZziT2ca1LOLbk7Fe7JI9WylQG1l3C9iKeUggRSR1DgNudcyHAH8T0bDR1zuUAXgTONWYjvmXE/EX9ROzgyLuAmvGWjwS6OedquRj5Yts5u4chKU8APwI/OOeuBoYDLzjn/AGcc1c45+6Nt/5eYsaTxJ++yjl3Rbx5BYD/gKPOuUrAo8k1bmZngHnEO13jnHvAOVc0tofhcOzsKGA/MVeHxG//fPUCPOucK+ycKw10J/EpqPO1G3+d0rHbP2Rmf5y1i+FAf/f/A3mLxv5bJfW+t8ULh0m9JiS1Xex+c/P/Pzu5Yqfjq0fMgGGRDEkhRCQVmNl+YBzwUuxfzI8BnwA7iekZSdH9NczsNDEDLx8m5sPxAWJ6ME7FLl9NzLiQYcSc3tgMdEjhvo2YsQwriQkDi4jpBZgUeyrlF2IGn8Z5BRgbe8rhPjPbSMzAzL9i55UAngHuJ2ZswkiS+dCP52PgwXjTjYFfnXNHiRks2sbMTprZcWLugbEktq3aZjbtPPUCTAfWABHAt8CnydSRZLtnrdMAuIaYXpK4XotfY5e9R8xpru9jxwUtB2qd571fjBPA0djvN8ZOA+CcqwEci71UVyRDct7cKkBEUso5twIYbmajva4lNTjnFgP/O98Nyy5iv0bMaaELuUopw3LOfQl8amazvK5F5GIphIikM865esDvwAGgHTFd/+XNbLenhaVzWS2EiGQGaXpLZBFJkYrE3LciP/An0EoBREQyI/WEiIiIiCc0MFVEREQ8kS5PxxQpUsTKli3rdRkiIiKSCtasWXPAzBLdLyldhpCyZcuyevVqr8sQERGRVOCc25rUfJ2OEREREU8ohIiIiIgnFEJERETEE+lyTEhSzpw5w44dOzh58uw7K4ukjty5c1OqVCly5MjhdSkiIllChgkhO3bsoECBApQtW5aEDxgVuXRmxsGDB9mxYwflypXzuhwRkSwhw5yOOXnyJFdddZUCiFwWzjmuuuoq9bSJiKShDBNCAAUQuaz08yUikrYyVAgRERGRzEMhxGNly5blwIEDF739kCFDGDduHAAdOnSgXLlyhISEEBISwo033phaZQLwxhtvJLts1KhRBAYGEhQUREBAANOnTz/nvjp06MDUqVPPuU54eDhLly71TQ8fPtz3Xi/Uzz//TIcOHS5qWxERuTwyzMBUSSwyMpJRo0bx008/+eYNHDiQVq1aXZb23njjDXr37p1o/o4dO+jfvz8//fQTV1xxBUePHmX//v2X3F54eDj58+f3halu3bpd9L4CAwPZsWMH27Zt49prr73k2kRE5NKpJySFXnrpJd577z3fdJ8+fRg6dGiCdT766COee+453/SYMWP43//+B0CLFi2oXr06/v7+jBgxItH+t2zZQkBAgG/6nXfe4ZVXXgHgzz//pHHjxlSvXp26deuyceNGAH788UeqVatG9uznzpJPPvkkr732GgBz5szhlltuITo6mm+++YZatWpRtWpVbrvtNvbu3QvA0aNH6dixo69n48svv6RXr16cOHGCkJAQ2rVrl2D/+/bto0CBAuTPnx+A/Pnz+64wiYiIoHbt2gQFBdGyZUsOHTqUqL74vUGrV68mLCyMLVu2MHz4cN59911CQkJYtGgRr7zyCu+888459xsWFsbzzz9PzZo1ueGGG1i0aJGvnTvvvJNJkyad81iJiGRFYWFhhIWFpXm7GbInpEePHkRERKTqPkNCQhgyZEiyyx9++GHuvvtuunfvTnR0NJMmTWLlypUJ1mnVqhV16tTh7bffBuCLL76gT58+QMzpiiuvvJITJ05Qo0YN7rnnHq666qoU1dalSxeGDx9OhQoVWLFiBY899hg//vgjS5YsoXr16gnWffbZZ+nXrx8A/v7+TJgwgQEDBlCjRg3q1q3Lk08+yaxZs8iWLRs333wzy5cvxznHJ598wttvv82gQYN4/fXXueKKK/j5558BOHToEPfccw/Dhg1L8rgHBwdz9dVXU65cORo0aMDdd9/NnXfeCcBDDz3E+++/T7169ejbty+vvvrqOY9znLJly9KtWzfy58/PM888A8APP/zgW36u/UZGRrJy5UpmzZrFq6++yrx58wAIDQ1lwIABCYKiiIh4J0OGEC+ULVuWq666irVr17J3716qVq2aKEQULVqU8uXLs3z5cipUqMDvv//OTTfdBMDQoUOZNm0aANu3b2fTpk0pCiFHjx5l6dKl3Hvvvb55p06dAmD37t1Urlw5wfpJnY7JmzcvI0eO5JZbbuHdd9/luuuuA2JOo7Ru3Zrdu3dz+vRpX+/FvHnzEvQYFC5c+Jw1+vn5MXv2bFatWsUPP/zAU089xZo1a3jqqac4fPgw9erVA6B9+/YJ3sfF+vfff8+537vvvhuA6tWrs2XLFt/8YsWKsWvXrktuX0REUkeGDCEp+Uv6cujcuTNjxoxhz549dOrUCYCOHTuydu1aSpQowaxZs2jdujWTJ0+mUqVKtGzZEucc4eHhzJs3j2XLlpE3b17CwsIS3Y8ie/bsREdH+6bjlkdHR1OoUKEkeyDy5MmT4vta/Pzzz1x11VUJPoT/97//0bNnT5o3b054eLjv9I+ZXfDlqs45atasSc2aNbn99tvp2LEjTz31VIq2jf/eU+M+Hbly5QJiwlFkZKRv/smTJ8mTJ88l719ERFKHxoRcgJYtW/r+4m/UqBEAo0ePJiIiglmzZgExf4V//fXXTJw4kdatWwMxf7kXLlyYvHnzsnHjRpYvX55o31dffTX79u3j4MGDnDp1ipkzZwJQsGBBypUrx5QpU4CYgLBu3ToAKleuzObNm89b99atWxk0aBBr167lu+++Y8WKFb66SpYsCcDYsWN96zds2JBhw4b5puPGW+TIkYMzZ84k2v+uXbsSDI6NiIigTJkyXHHFFRQuXNg3LuOzzz7z9V7EV7ZsWdasWQPAl19+6ZtfoEABjhw5kmj9lO73bH/88UeCcTciIllV3BiQuNeCBQtYsGBBovmXm0LIBciZMyf169fnvvvuw8/PL8l1ChcuTJUqVdi6dSs1a9YEoHHjxkRGRhIUFMRLL71E7dq1E22XI0cO+vbtS61atWjWrBmVKlXyLZswYQKffvopwcHB+Pv7+y5/bdKkCQsXLkywn2effdZ3iW5ISAinTp3i4Ycf5p133qFEiRJ8+umndO7cmZMnT/LKK69w7733UrduXYoUKeLbx4svvsihQ4cICAggODiY+fPnAzFjU4KCghINTD1z5gzPPPMMlSpVIiQkhC+++MI3iHfs2LE8++yzBAUFERERQd++fRO995dffpnu3btTt27dBMf1zjvvZNq0ab6BqfGlZL9nmz9/Pk2bNj3veiIiWcWZM2fYsGGDZ+07M/Os8eSEhoba6tWrE8z77bffEo1/SGvR0dFUq1aNKVOmUKFCBU9ridOyZUvefvvtdFNPenXq1Cnq1avH4sWLz3k1UXr4ORMRSQtfffUVjz76KIcOHaJkyZKULl060R+2qcU5t8bMQs+er56QFNqwYQPXX389DRo0SFcf+AMGDGD37t1el5Hubdu2jQEDBpz3cmYRkczu4MGDtG3blnvuuYeSJUuyevVqypQpQ7ZsaR8J9Bs5hapUqcJff/3ldRmJVKxYkYoVK3pdRrpXoUKFdBUeRUS8MG3aNLp168ahQ4d47bXX6NWrFzly5PCsHoUQERGRTO7gwYM8+eSTfP7554SEhDB37lyCgoK8LkshREREJDObPn06Xbt25eDBg7z66qu88MILiXo/wsPDPalNIURERCQT+ueff3jyySeZMGECISEhzJkzh+DgYK/LSkADU0VERDKZb775Bn9/f7744gtefvllVqxYke4CCCiEXFZxD3S7UH379vU972TIkCEcP378vNucOHGCevXqERUVxZYtW8iTJ0+C+4WMGzfuompJSnh4OEuXLk1y2d69e2nWrBnBwcFUqVKFO+6445z7OvvBfcl54403EkzHPVn3YrRp04ZNmzZd9PYiIunVoUOHeOihh2jevDnFihVj1apVvPLKK+TMmdPr0pKkEJIOvfbaa9x2221AykPIqFGjuPvuu303+7ruuuuIiIjwvR566KFUq+9cIaRv377cfvvtrFu3jg0bNjBgwIBUafPsEJJc+ynx6KOP+h4yKCKSWcycORN/f38+//xz+vbty6pVqwgJCfG6rHNSCEmh559/ng8//NA3/corrzBo0CAg5qFxNWrUICgoiJdffjnRtmbGs88+S0BAAIGBgXzxxRe+ZW+//TaBgYEEBwfTq1cvADp06MDUqVMZOnQou3bton79+tSvX59PP/00wfNYRo4cSc+ePYGYu6redddd53wPW7dupUKFChw4cIDo6Gjq1q3L999/D0CLFi2oXr06/v7+jBgxwrfN7NmzqVatGsHBwTRo0IAtW7YwfPhw3n333STvZLp7925KlSrlm44bfX2uYxBnzJgxPPHEE77pZs2aER4eTq9evThx4gQhISG+u7XG9TIlt9/w8HDCwsJo1aoVlSpVol27dsTdmK9u3brMmzcvwXNlREQyqkOHDtG+fXvuvPNOihQpwsqVK3n11VfTbe9HAmaW7l7Vq1e3s23YsCHBdL169RK9PvjgAzMzO3bsWJLLR48ebWZm+/fvT7TsfH766Se75ZZbfNOVK1e2rVu32pw5c+yRRx6x6Ohoi4qKsqZNm9qCBQvMzCxfvnxmZjZ16lS77bbbLDIy0vbs2WOlS5e2Xbt22axZs6xOnTp27NgxMzM7ePCgmZm1b9/epkyZYmZmZcqUsf3795uZ2dGjR618+fJ2+vRpMzOrU6eOrV+/3k6dOmVXX321r7a///7bcufObcHBwb7XwoULzcxs5MiRds8999jbb79tXbp08W0T1/bx48fN39/fDhw4YPv27bNSpUrZX3/9lWCdl19+2QYOHJjkcZo9e7ZdccUVFhYWZv369bOdO3ee8xj8/fff5u/vb2Zmo0ePtscff9y3r6ZNm9r8+fMTHMs45zu28+fPt4IFC9r27dstKirKateubYsWLfJtf9ttt9nq1asT1X/2z5mISHo2c+ZMK1GihPn5+dmLL75op06d8rqkJAGrLYnPe10dk0JVq1Zl37597Nq1i/3791O4cGGuvfZahg4dyvfff0/VqlUBOHr0KJs2beKWW27xbbt48WLatm2Ln58fV199NfXq1WPVqlUsWLCAjh07kjdvXgCuvPLKc9aQL18+br31VmbOnEnlypU5c+YMgYGB7Nq1i0KFCiVYN+50zNk6d+7MlClTGD58eILlQ4cOZdq0aQBs376dTZs2sX//fm655RbKlSuXovoAGjVqxF9//cXs2bP57rvvqFq1Kr/88kuyx+BSr1NPbr8FCxakZs2avl6ZkJAQtmzZws033wxAsWLF2LVrF9WrV7+k9kVEvHD48GGeeuopxowZQ0BAADNmzMiQv88ybAg51zXNefPmPefyIkWKXNQ10a1atWLq1Kns2bOHNm3aADE9SS+88AJdu3ZNdjtL5vk8ZoZz7oJq6Ny5M2+88QaVKlWiY8eOAOTJk4eTJ0+maPvjx4+zY8cOICYwFShQgPDwcObNm8eyZcvImzcvYWFhnDx58qLqg5iwcv/993P//ffTrFkzFi5cmOwxiC979uxER0f7plPyns6131y5cvm+9/PzS3D65eTJk+TJk+e8+xcRSW++++47HnnkEfbs2UOfPn146aWXEvy+y0g0JuQCtGnThkmTJjF16lRatWoFxPzlP2rUKI4ePQrAzp072bdvX4LtbrnlFr744guioqLYv38/CxcupGbNmjRs2JBRo0b5Bp7+888/ido8+3H2tWrVYvv27Xz++ee0bdsWiHlyb1RUVIo+tJ9//nnatWvHa6+9xiOPPALAv//+S+HChcmbNy8bN25k+fLlANSpU4cFCxbw999/J6jv7Jri+/HHH33v58iRI/z5559ce+21yR6D+MqWLUtERATR0dFs376dlStX+pblyJGDM2fOJGovJftNyh9//IG/v/951xMRSS8OHz5Mp06duOOOOyhUqBDLly+nX79+GTaAQAbuCfGCv78/R44coWTJkhQvXhyAhg0b8ttvv1GnTh0gZsDk+PHjKVasmG+7li1bsmzZMoKDg3HO8fbbb3PNNdfQuHFjIiIiCA0NJWfOnNxxxx2JrgLp0qULTZo0oXjx4syfPx+A++67j4iICAoXLuxbr2HDhixevNh3Vc2ff/6ZYFR0p06dCA4OZtWqVSxZsgQ/Pz++/PJLRo8ezf3338/w4cMJCgqiYsWK1K5dG4CiRYsyYsQI7r77bqKjoylWrBhz587lzjvvpFWrVkyfPp3333+funXr+tpZs2YNTzzxhK9Xo3PnztSoUYPQ0NAkj8GWLVt82950002UK1eOwMBAAgICqFatWoLjEBQURLVq1ZgwYcJ5j+3GjRuT/Xfcu3cvefLk8f0bioikd7Nnz6Zz587s3r2bF154gZdffjlDh484LiXd5GktNDTUVq9enWCeHrH+/5o1a8ZTTz1FgwYNfPPWrl3L4MGD+eyzzzysLGN49913KViwIA8//HCiZfo5E5H05N9//6Vnz56MGjWKKlWqMGbMGGrUqOF1WRfMObfGzELPnq/TMRnI4cOHueGGG8iTJ0+CAAIxA2fr169PVFSUR9VlHIUKFaJ9+/ZelyEick5z5swhICCAMWPG0KtXL9asWZMhA8i56HRMBlKoUCH++OOPZJd36tQpDavJuOIG9IqIpEf//fcfTz/9NJ988gmVKlVi6dKl1KpVy+uyLgv1hIiIiKQT33//PQEBAYwaNYrnnnuOtWvXZtoAAgohIiIinvvvv//o0qULjRo1Il++fCxZsoS33nqL3Llze13aZaUQIiIi4qG5c+cSGBjIp59+yrPPPstPP/3ku0oxs1MIERER8cCRI0fo2rUrDRs2JHfu3CxevJi33347S91I8YJDiHNulHNun3Pul3jzrnTOzXXObYr9Wjjeshecc5udc7875xqlVuEpERYWRlhYWFo2eUHKli3LgQMHLnr7IUOGMG7cOCDmoXflypUjJCSE4OBgfvjhh9Qq84LFfxBddHQ07du3p1OnTsne3TQiIoJZs2b5ps/1lN74Zs6cmeQDA0VE0rt58+YREBDAyJEjefrpp4mIiPDdbyoruZiekDFA47Pm9QJ+MLMKwA+x0zjnqgBtAP/YbT50zvlddLXiExkZyahRo7j//vt98wYOHEhERARDhgyhW7duHlYXw8zo1q0bZ86c4ZNPPkn2FvAXG0KaNm3KjBkzfHdoFRFJ744cOcKjjz7K7bff7uv9eOedd7JU70d8FxxCzGwhcPb9xe8CxsZ+PxZoEW/+JDM7ZWZ/A5uB899TOx166aWXeO+993zTffr0YejQob7pjz76iOeee843PWbMGP73v/8B0KJFC6pXr46/vz8jRoxItO8tW7YQEBDgm37nnXd45ZVXgJg7nzZu3Jjq1atTt25d351Af/zxR6pVq0b27Imvsq5Tpw47d+701RHXKwExNzqLe25O/vz56dOnD8HBwdSuXZu9e/f62qxduzY1atSgb9++5M+f37f9wIEDqVGjBkFBQefthejevTsHDx5k3LhxZMuWjWPHjtGpUydq1KhB1apVmT59OqdPn6Zv37588cUXhISE8NZbbzF8+HDeffddQkJCWLRoEd988w21atWiatWq3Hbbbb46nXOEhYUxc+bMc9YhIpIe/PjjjwQGBvLxxx/Ts2dPIiIiuPHGG70uy1OpNSbkajPbDRD7Ne6e5SWB7fHW2xE7LxHnXBfn3Grn3Or9+/enUlmp5+GHH2bs2JicFR0dzaRJk2jXrp1veatWrfjqq69801988QWtW7cGYNSoUaxZs4bVq1czdOhQDh48mOJ2u3Tpwvvvv8+aNWt45513eOyxxwBYsmRJsk9MnD17Ni1atDjvvo8dO0bt2rVZt24dt9xyCyNHjgRiwkP37t1ZtWoVJUqU8K3//fffs2nTJlauXElERARr1qxh4cKFSe77888/Z82aNUyaNMkXlPr378+tt97KqlWrmD9/Ps8++yxnzpzhtddeo3Xr1kRERPD888/TrVs3nnrqKSIiIqhbty4333wzy5cvZ+3atbRp04a3337b105oaCiLFi1K0bEUEbnckhoGcPToUR577DEaNGhAjhw5WLRoEYMGDcqyvR/xXe6blSXV/57kwAAzGwGMgJjbtl9MY2f/wy9YsCDJ+RfzBN2yZcty1VVXsXbtWvbu3UvVqlW56qqrfMuLFi1K+fLlWb58ORUqVOD333/npptuAmDo0KFMmzYNgO3bt7Np06YE2ybn6NGjLF26lHvvvdc379SpUwDs3r070e3Fn332WZ577jn27dvnewjdueTMmZNmzZoBUL16debOnQvAsmXL+PrrrwG4//77eeaZZ4CYEPL9999TtWpVX32bNm3illtuSbTvatWqsXHjRlauXOk7Dt9//z0zZszgnXfeAWKeZLtt27bz1rljxw5at27N7t27OX36NOXKlfMtK1asGLt27TrvPkREvDB//nw6derE1q1b6dGjB/379ydv3rxel5VupFYI2eucK25mu51zxYG4x8juAErHW68UkGE/MTp37syYMWPYs2cPnTp1omPHjqxdu5YSJUowa9YsWrduzeTJk6lUqRItW7bEOUd4eDjz5s1j2bJl5M2bl7CwsERPu03uEfbR0dEUKlSIiIiIRLXkyZMn0X4GDhzI3XffzdChQ2nfvj1r1qxJdt8Q82TauHEaZz/qPilmxgsvvEDXrl0TzP/ggw98vShxYzsqVarEa6+9xn333cecOXPw9/fHzPjyyy+pWLFigu1XrFhxznb/97//0bNnT5o3b054eLjvVFXc+9FfEyKS3hw9epTnn3+eDz/8kOuvv54FCxYkeNinxEit0zEzgLiHcbQHpseb38Y5l8s5Vw6oAKxMYvtUER4enuBVr1496tWrl2j+xWrZsiWzZ89m1apVNGrUiNGjRycYVHn33Xfz9ddfM3HiRN+pmH///ZfChQuTN29eNm7cmGQPxdVXX82+ffs4ePAgp06d8o1xKFiwIOXKlWPKlClATAhYt24dAJUrV2bz5s2J9pUtWza6d+9OdHQ0c+bMoWzZskRERBAdHc327dtZufL8h7927dp8+eWXAEyaNMk3v1GjRowaNYqjR48CsHPnTvbt28fjjz9OREQEERERCU7f3HjjjQwfPpymTZuybds2GjVqxPvvv++7Smbt2rUAFChQgCNHjvi2O3v633//pWTJmLN4cafE4vzxxx8JxtOIiHjt8OHDBAUF8dFHH9G9e3fWrVunAJKMC+4Jcc5NBMKAIs65HcDLwABgsnPuYWAbcC+Amf3qnJsMbAAigcfNLMM+YS1nzpzUr1+fQoUK4eeX+CKfwoULU6VKFTZs2EDNmjHjbxs3bszw4cMJCgqiYsWKSd6AJkeOHPTt25datWpRrlw5KlWq5Fs2YcIEHn30Ufr168eZM2do06YNwcHBNGnShAcffDDJOp1zvPjii7z99tvMmzePcuXKERgYSEBAANWqVTvv+xwyZAgPPPAAgwYNomnTplxxxRUANGzYkN9++813GVn+/PkZP348xYoVS3ZfzZo1Y//+/TRu3Ji5c+fy2muvERQUhJlRtmxZZs6cSf369RkwYAAhISG88MIL3HnnnbRq1Yrp06fz/vvv88orr3DvvfdSsmRJateuzd9//+3b//z583nzzTfP+55ERC6H+Kf7o6KiWLx4MQC5c+cmKCiIiIgI7rjjjkv6Azgzc8ndu8FLoaGhtnr16gTzLuYR63E/HKn1jx8dHU21atWYMmUKFSpUSJV9XoqWLVvy9ttvp3otx48fJ0+ePDjnmDRpEhMnTmT69Onn3zCN7d27l/vvvz9V74lyMT9nIpJ1xX3OHD58mN9//913yvvmm29O8MdqVg8hzrk1ZhZ69nw9RTeFNmzYQLNmzWjZsmW6CCAAAwYMYPfu3alez5o1a3jiiScwMwoVKsSoUaNSdf+pZdu2bQwaNMjrMkQkC/v222/p3bs3Q4cOpXz58hQoUIBChQpl+dCRUpm6J0TkQunnTERSatGiRXTs2JE///yTJ554ggEDBtC0aVNAPR9nS64nRM+OERERuQDHjx+nR48e1KtXj6ioKObPn8/7779Pvnz5vC4tw9HpGBERkRRavHgxHTt2ZPPmzTz22GO89dZbCe4qLRdGIUREROQ8jh8/Tp8+fXjvvfcoU6YMP/zwA7feemui9XQa5sIohIiIiJzD0qVL6dChA5s2beLRRx/lrbfeokCBAl6XlSlkqjEhW7dupX///sk+Mt7M6N+/P1u3br3stVxs91zfvn2ZN28eEHO/jpQ8IfbEiRO+c5NbtmwhT548hISEUKVKFR566CHOnDlzUbWkhrJly3LgwAEg5qqbcuXK+W5SlpSz3/Mbb7yRonZuu+02Dh06dGnFiojEc+LECZ5++mluvvlmTp8+zbx58/jwww8VQFKTmaW7V/Xq1e1sGzZsSDTvbP369TPAevToYdHR0QmWRUdHW48ePQywfv36nXdflypfvnyXvI8yZcrY/v37z7vesGHDbMiQIWZm9vfff5u/v7+ZmUVGRlr9+vVt/Pjxl1zLxYp7D+vWrbOyZcvaihUrUrR+nJQexzFjxqTKv2tKfs5EJPNbunSp3XDDDQZY165d7b///vO6pAwNWG1JfN5nqp6Q3r1706NHD4YMGULPnj19PSJmRs+ePRkyZAg9evSgd+/eF7zvuGcAxHnllVcYNGjQeR9tb2Y8++yzBAQEEBgYyBdffOFb9vbbbxMYGEhwcDC9evUCoEOHDkydOpWhQ4eya9cu6tevT/369fn000956qmnfNuOHDmSnj17AjF3Vb3rrrsSte3n50fNmjXZuXMnkLBXYvXq1b6b7Lzyyit06tSJsLAwypcvz9ChQ337eP3116lUqRK33347bdu29T187s8//6Rx48ZUr16dunXrsnHjxmSP3W+//UaLFi347LPPfHeS/f7776lTpw7VqlXj3nvv5ejRo4nec69evThx4gQhISG+Jxa3aNGC6tWr4+/vz4gRI3xtNG/enIkTJyZbg4hISpw4cYJnn32Wm2++mZMnTzJ37lyGDx+u3o/LJalk4vXrYntCzBL2eMT1iJw9fTF++uknu+WWW3zTlStXtrFjx9ojjzxi0dHRFhUVZU2bNrUFCxaY2f//BT916lS77bbbLDIy0vbs2WOlS5e2Xbt22axZs6xOnTp27NgxMzM7ePCgmZm1b9/epkyZYmYJewWOHj1q5cuXt9OnT5uZWZ06dWz9+vV26tQpu/rqq311xe8JOXHihIWFhdm6desS7W/VqlVWr149MzN7+eWXrU6dOnby5Enbv3+/XXnllXb69GlbtWqVBQcH2/Hjx+2///6z66+/3gYOHGhmZrfeeqv98ccfZma2fPlyq1+/fpLHrUyZMla4cGH79ttvffP2799vdevWtaNHj5qZ2YABA+zVV19NVGP84xgn7jgdP37c/P397cCBA75l119/fYLpi6GeEJGsa9myZVaxYkUDrEuXLvbvv/96XVKmQTI9IZluYKpzjsGDBwMx4wuGDBkCQI8ePRg8eLDvqbEXqmrVquzbt49du3axf/9+ChcuzPr168/7aPvFixfTtm1b/Pz8uPrqq6lXrx6rVq1iwYIFdOzY0fdI5yuvvPKc7efLl49bb72VmTNnUrlyZc6cOUNgYCC7du2iUKFCCdb9888/CQkJYdOmTbRq1YqgoKDzvr+mTZuSK1cucuXKRbFixdi7dy+LFy/mrrvu8j2l9s477/S9z6VLl3Lvvff6tj916lSy+77tttv45JNPaNSoEX5+fixfvpwNGzZw0003AXD69Gnf82jOZ+jQoUybNg2A7du3s2nTJq666ioAihUrxq5du3zTIiIpcfLkSfr27cugQYMoWbIkc+bMoWHDhl6XlSVkuhAC/x9E4gIIcEkBJE6rVq2YOnUqe/bsoU2bNmzZsiXJR9vHZ+cYJHuh9XTu3Jk33niDSpUq0bFjRwDy5Mnje1ZBnOuuu46IiAh2795NWFgYM2bMoHnz5mTPnp3o6GiARNvkypXL972fnx+RkZHJ1h4dHU2hQoWIiIhIMD8qKorq1asDMadHXnvtNQCGDRtGt27deOyxx/j4448xM26//fYLPn0SHh7OvHnzWLZsGXnz5iUsLCzB+zh58qQvMImIpMSKFSvo0KEDGzdupHPnzrzzzju+h3bK5ZepxoTEsdgxIPHFHyNysdq0acOkSZOYOnUqrVq1SvbR9vHdcsstfPHFF0RFRbF//34WLlxIzZo1adiwIaNGjfJdCfLPP/8kau/sR9rXqlWL7du38/nnn9O2bVsg5sm9UVFRiUIFQPHixRkwYIDvKbNly5ZlzZo1AHz55Zfnfb8333wz33zzDSdPnuTo0aN8++23ABQsWJBy5coxZcoUIOZ4r1u3Dj8/PyIiIoiIiPAFEIBs2bIxceJEfv/9d/r27Uvt2rVZsmQJmzdvBmKuv//jjz+SfM85cuTwXd3z77//UrhwYfLmzcvGjRtZvny5bz0zY8+ePZQtW/a870tE5OTJk/Tq1Ysbb7yRo0ePMnv2bEaOHKkAksYyXQiJCyBxg1Cjo6OTHKx6Mfz9/Tly5AglS5akePHiNGzYkPvvv586deoQGBhIq1atEnyAQsyTboOCgggODubWW2/l7bff5pprrqFx48Y0b96c0NBQQkJCfAM+4+vSpQtNmjShfv36vnn33XcfN910E4ULF/bNa9iwoe/x0Wdr0aIFx48fZ9GiRbz88st0796dunXrJni6Y3Jq1KhB8+bNCQ4O5u677yY0NNT3H3TChAl8+umnBAcH4+/vf96n7ObKlYvp06czY8YMJk+ezJgxY2jbti1BQUHUrl3bN7D17PfcpUsXgoKCaNeuHY0bNyYyMpKgoCBeeuklateu7dv/mjVrqF27NtmzZ8rOPRFJRatWraJ69eq89dZbdOzYkV9++YVGjRp5XVbWlNRAEa9fFzswNblBqKk1ODU9aNq0qc2bNy/BvJ9++skeeOCBy9LekSNHzMzs2LFjVr16dVuzZs1laedSPfnkk4mOy8XQwFSRzOvkyZPWq1cvy5Ytm5UsWdJmzZrldUlZBllhYOobb7zh6wGJPwbk7MGqRYoUoU+fPl6WesEOHz5MzZo1CQ4OpkGDBgmWVa1alfr16xMVFZWiHo4L0aVLFzZs2MDJkydp37491apVS9X9p5aAgIBEx0VEJM6qVavo0KEDGzZsoGPHjgwePDjRoH5Je5kqhDzwwANAzP1Czh70GRdEihQp4lsvIylUqJBv3ERSOnXqdFna/fzzzy/LflPbI4884nUJIpIOnTp1itdee4233nqLq6++mm+//ZY77rjD67IkVoYKIXaeK0rKlClzzh4O51yG6wGRtGOXOHBZRNKXNWvW0KFDB3755Rc6dOjAu+++q96PdCbDDEzNnTs3Bw8e1AeFXBZmxsGDB8mdO7fXpYjIJTp9+jQvvfQStWrV4uDBg8ycOZPRo0crgKRDGaYnpFSpUuzYsYP9+/d7XYpkUrlz56ZUqVJelyEil+Cnn36iQ4cO/Pzzzzz00EMMGTIkwdWEkr5kmBCSI0cOypUr53UZIiKSDp0+fZp+/frxxhtvUKxYMWbMmOG7y7OkXxkmhIiIiCRl7dq1dOjQgfXr1/Pggw8yZMiQ8z4KQ9KHDDMmREREJL7Tp0/z8ssvU7NmTfbt28f06dMZN26cAkgGop4QERHJcNatW0f79u1Zt24d7dq1Y+jQoQofGZB6QkREJF0KCwsjLCwswbwzZ87w6quvEhoayp49e/j6668ZP368AkgGpZ4QERHJENavX0+HDh1Yu3Yt999/P0OHDuWqq67yuiy5BOoJERGRdO3MmTO8/vrrhIaGsnPnTr766ismTJigAJIJqCdERETSraNHj1K7dm1++ukn2rRpw/vvv0+RIkW8LktSiUKIiIikC/HHf0RHR7No0SIg5j5RVapUYffu3bRq1Yrw8HBvCpRUpxAiIiLpyrFjx9i4caNvOjQ0lJw5c3pYkVwuCiEiIpIuzJs3j7fffptXX32VK664gmuvvZaiRYuq5yMT08BUERHx3K+//kqdOnXo06cPd911F7/++itFixb1uiy5zBRCRETEM5GRkbz55ptUq1aNLVu28MUXXzB58mQFkCxCp2NERMQTGzZsoEOHDqxatYp77rmHDz/8kGLFinldlqQhhRAREUlTkZGRDBo0iJdffpn8+fMzadIk7rvvPpxzCdbTWJDMTyFERETSzMaNG+nQoQMrVqygZcuWfPTRR1x99dVelyUe0ZgQERG57KKiohg4cCAhISFs2rSJzz//nC+//FIBJItTT4iIiFxWv//+Ox07dmTZsmXcddddDB8+nGuuucbrsiQdUE+IiIhcFlFRUQwaNIiQkBA2btzI+PHjmTZtmgKI+KgnREREUt0ff/xBx44dWbp0Kc2bN2f48OEUL17c67IknVFPiIiIpJqoqCjeffddgoOD+e233/jss8/4+uuvFUAkSeoJERGRVLFp0yY6duzIkiVLaNasGR9//DElSpTwuixJx9QTIiIilyQ6OpohQ4YQHBzMr7/+ytixY5kxY4YCiJyXekJEROSibd68mU6dOrFo0SKaNm3Kxx9/TMmSJb0uSzII9YSIiMgFi46OZujQoQQFBbF+/XpGjx7NN998owAiF0Q9ISIickH+/PNPOnXqxMKFC2nSpAkjRoygVKlSXpclGZB6QkREJEWio6N5//33CQoKIiIigk8//ZRvv/1WAUQumnpCRETkvP766y86derEggULaNSoESNHjqR06dJelyUZnHpCREQkWdHR0XzwwQcEBQXx008/MXLkSL777jsFEEkV6gkREZEk/f333zz88MPMnz+f22+/nU8++YRrr73W67IkE1FPiIiIJBAdHc1HH31EYGAgq1evZsSIEcyZM0cBRFKdekJERMRny5YtPPzww/z444/cdtttfPLJJ5QpU8brsiSTUk+IiIhgZnz88ccEBgaycuVKhg8fzvfff68AIpdVqoUQ59xTzrlfnXO/OOcmOudyO+eudM7Ndc5tiv1aOLXaExGR1LF161YaNmxIt27dqFWrFj///DNdu3bFOed1aZLJpUoIcc6VBJ4EQs0sAPAD2gC9gB/MrALwQ+y0iIikA2bGyJEjCQwMZNmyZXz00UfMnTuXsmXLel2aZBGpeTomO5DHOZcdyAvsAu4CxsYuHwu0SMX2REQkBcLCwggLC0swb9u2bTRu3JguXboQGhrKzz//TLdu3dT7IWkqVUKIme0E3gG2AbuBf83se+BqM9sdu85uoFhy+3DOdXHOrXbOrd6/f39qlCUiImcxMz755BMCAgJYsmQJH3zwAfPmzaNcuXJelyZZUGqdjilMTK9HOaAEkM8598CF7MPMRphZqJmFFi1aNDXKEhGReLZv306TJk145JFHqFatGuvXr+exxx4jWzZdoyDeSK1LdG8D/jaz/QDOua+AG4G9zrniZrbbOVcc2JdK7YmISAqZGXv27CEgIIDIyEjef/99hQ9JF1IrhGwDajvn8gIngAbAauAY0B4YEPt1eiq1JyIiyYg//uPUqVMsX74cgCuuuIKAgACmTp3K1KlTCQ8P96ZAkVipEkLMbIVzbirwExAJrAVGAPmByc65h4kJKvemRnsiInJuZsbevXvZvHmzb15wcLAGnkq64szM6xoSCQ0NtdWrV3tdhohIhrRr1y66dOnCt99+y80338zp06fJkyePej7EM865NWYWevZ8nRAUEckkzIxx48bh7+/Pjz/+yLvvvsuCBQvIkyeP16WJJEnPjhERyQR2795N165d+eabb7jxxhsZPXo0N9xwg9dliZyTekJERDIwM2PChAn4+/szd+5cBg0axMKFCxVAJENQT4iISAa1Z88eunXrxvTp06lduzZjxoyhYsWKidbTWBBJr9QTIiKSwZgZEydOxN/fn9mzZzNw4EAWL16cZAARSc8UQkREMpC9e/dyzz33cP/991OhQgXWrl3LM888g5+fn9eliVwwhRARkQzAzPjiiy/w9/fn22+/5a233mLx4sVUrlzZ69JELppCiIhIOrdv3z7uvfde2rRpQ/ny5Vm7di3PPfcc2bNrWJ9kbAohIiLp2JQpU/D39+ebb77hzTffZOnSpVSpUsXrskRShUKIiEg6tH//flq3bs19991HmTJlWLNmDb169VLvh2QqCiEiIunMl19+ib+/P9OmTaNfv34sW7aMgIAAr8sSSXWK1CIi6cTBgwd54oknmDRpEtWqVeOHH34gMDDQ67JELhv1hIiIpAPTpk2jSpUqfPnll7z22mssX75cAUQyPfWEiIh46ODBgzz55JN8/vnnhISEMHfuXIKCgrwuSyRNqCdERMQjM2bMICAggMmTJ/PKK6+wcuVKBRDJUtQTIiKSxv755x+6d+/O+PHjCQoK4rvvviMkJMTrskTSnHpCRETS0MyZMwkICGDixIn07duXVatWKYBIlqWeEBGRNHD48GF69OjB2LFjCQwMZObMmVSrVs3rskQ8pZ4QEZHLbNasWfj7+zN+/Hj69OnDqlWrFEBEUAgREblsDh8+TKdOnWjatCmFCxdm+fLl9OvXj1y5cnldmki6oBAiInIZzJ49m4CAAMaOHcsLL7zAmjVrCA0N9boskXRFIUREJBX9+++/dO7cmSZNmnDFFVewfPly3njjDfV+iCRBIUREJJV8//33BAQEMHr0aJ5//nnWrFlDjRo1vC5LJN3S1TEiIikUFhYGQHh4eIL5//33H8888wwjR46kUqVKLF26lFq1aqV9gSIZjHpCREQuwbx58wgMDOTTTz/l2WefZe3atQogIimkECIichGOHDlCt27duP3228mdOzeLFy/m7bffJnfu3F6XJpJhKISIiFygH3/8kcDAQEaMGMHTTz9NREQEderU8boskQxHY0JERJIRNwYkzoIFCwBo0KABefLkITg4mNWrV5MnTx4PqhPJ+BRCRERS4PDhw77vS5YsSbly5fDz8/OuIJFMQCFERCQZ4eHhHDt2jBdeeIH333+f3LlzU7FiRSIiIrwuTSRTUAgREUnG4sWL6dChA3/++SdPPvkkP/30k3o/RFKRBqaKiJzlxIkT9OzZk1tuuYXo6Gjmz5/Pe++9pwAiksrUEyIiEs+yZcvo0KEDf/zxB4899hhvvfUW+fPn97oskUxJIUREBDh58iR9+/Zl0KBBlCpVinnz5tGgQYME65x9p1QRuTQKISKS5a1cuZL27duzceNGunTpwsCBAylYsKDXZYlkehoTIiJZ1qlTp+jduzd16tTh6NGjzJkzh48//lgBRCSNqCdERLKkNWvW0L59e3799Vc6derE4MGDueKKK7wuSyRLUU+IiGQpp0+f5qWXXqJWrVocOnSIb7/9lk8//VQBRMQD6gkRkSxj7dq1dOjQgfXr19O+fXveffddChcu7HVZIlmWekJEJNM7c+YMr776KjVr1mTfvn3MmDGDMWPGKICIeEw9ISKSqa1fv54OHTqwdu1a2rVrx9ChQ7nyyiu9LktEUE+IiGRSkZGR9O/fn9DQUHbu3MlXX33F+PHjFUBE0hH1hIhIpvPrr7/SoUMHVq9eTZs2bXj//fcpUqSI12WJyFnUEyIimUZkZCRvvfUW1apVY8uWLUyZMoWJEycqgIikU+oJEZFMYePGjXTo0IEVK1Zwzz338OGHH1KsWDGvyxKRc1BPiIhkaFFRUQwaNIiQkBA2bdrExIkTmTJligKISAagnhARybD++OMPOnbsyNKlS7nrrrsYPnw411xzjddliUgKqSdERDKc6OhohgwZQnBwML/99hvjx49n2rRpCiAiGYx6QkQkQ9m8eTOdOnVi0aJFNGvWjI8//pgSJUp4XZaIXAT1hIhIhhAdHc2wYcMIDg5m/fr1jBkzhhkzZiiAiGRg6gkRkXTv77//plOnToSHh9O4cWNGjhxJqVKlvC5LRC6RekJEJN2Kjo7mo48+IjAwkDVr1vDpp58ya9YsBRCRTEI9ISKSLm3dupWHH36YH374gdtvv51PPvmEa6+91uuyRCQVpWpPiHOukHNuqnNuo3PuN+dcHefclc65uc65TbFf9dhKEUmWmTFy5EgCAwNZsWIFH3/8MXPmzFEAEcmEUvt0zHvAbDOrBAQDvwG9gB/MrALwQ+y0iGRxYWFhhIWFJZi3fft2mjRpQpcuXahRowY///wzXbp0wTnnTZEiclmlWghxzhUEbgE+BTCz02Z2GLgLGBu72ligRWq1KSKZg5kxevRoAgICWLRoER988AFz586lbNmyXpcmIpdRavaElAf2A6Odc2udc5845/IBV5vZboDYr7qXsoj47Ny5k2bNmtGpUydCQkL4+eefeeyxx8iWTePmRTK71ByYmh2oBvzPzFY4597jAk69OOe6AF0AnfsVyQLMjH379hEQEMCpU6d47733eOKJJxQ+RLIQZ2apsyPnrgGWm1nZ2Om6xISQ64EwM9vtnCsOhJtZxXPtKzQ01FavXp0qdYlI+hB//Mfp06dZtmwZAAULFqRixYrkzZsXgPDwcA+qE5HLyTm3xsxCz56fan9ymNkeYLtzLi5gNAA2ADOA9rHz2gPTU6tNEcl49u3bx6pVq3zTISEhvgAiIllLat8n5H/ABOdcTuAvoCMxQWeyc+5hYBtwbyq3KSIZwNSpU3nsscdYsGABNWvWxMzImzevej5EsrBUPflqZhFmFmpmQWbWwswOmdlBM2tgZhViv/6Tmm2KSPr39ddf4+/vz9dff80bb7zBkiVL1PshIrpjqohcPocOHeLJJ59k/PjxVK1alXnz5hEYGOh1WSKSTmgYuohcFrNnzyYgIICJEyfy8ssvs2LFCgUQEUlAPSEikqr+++8/nn76aT755BP8/f2ZMWMG1atXT7SexoKIiHpCRCTV/PjjjwQGBjJq1Cief/551qxZk2QAEREBhRARSQXHjh3jf//7Hw0aNCBXrlwsXryYAQMGkCtXLq9LE5F0TCFERC7JkiVLCAkJYdiwYXTv3p2IiAjq1KnjdVkikgEohIjIRTl58iTPPPMMdevWJSoqivDwcIYMGaJLb0UkxTQwVUQu2MqVK2nfvj0bN26ka9euDBw4kAIFCnhdlohkMOoJEZEUO336NC+++CI33ngjR48eZc6cOQwfPlwBREQuinpCRCRF1q1bx0MPPcT69evp0KED7777LoUKFfK6LBHJwNQTIiLndObMGV5//XVCQ0PZu3cvM2bMYPTo0QogInLJ1BMiIsnasGED7du3Z/Xq1bRp04Zhw4Zx1VVXeV2WiGQS6gkRkUSioqIYOHAg1apVY8uWLUyZMoWJEycqgIhIqlJPiIgksGnTJjp06MDSpUtp2bIlH330EVdffbXXZYlIJqSeEBEBIDo6mvfff5/g4GA2bNjA+PHj+fLLLxVAROSyUU+IiLBlyxY6derE/PnzadKkCSNHjqRkyZJelyUimZx6QkSyMDNjxIgRBAYGsnr1aj755BO+/fZbBRARSRPqCRHJonbs2EHnzp2ZM2cOt956K6NGjaJMmTJelyUiWYh6QkSyGDNj3LhxBAQEsGjRIoYNG8bcuXMVQEQkzaknRCQL2bNnD127dmXGjBncfPPNjB49muuvv97rskQki1JPiEgWMXnyZAICApgzZw6DBg0iPDxcAUREPKUQIpLJHThwgNatW9O6dWvKly/P2rVr6dmzJ35+fl6XJiJZnEKISCY2ffp0/P39mTZtGv3792fp0qVUrlzZ67JERACNCRHJ8MLCwgAIDw/3zTt8+DDdu3dn3LhxhISEMHfuXIKCgrwpUEQkGeoJEclkZs+eTUBAABMmTOCll15ixYoVCiAiki4phIhkEkeOHKFLly40adKEK664guXLl/Paa6+RM2dOr0sTEUmSTseIZAKHDh0iMDCQbdu28dxzz/Hqq6+SO3dur8sSETknhRCRDCZuDAhAVFQUixcvBiBPnjwEBwezYsUKGjdunGCMiIhIeqQQIpJB/ffff2zcuNE3Xb16dV12KyIZikKISAYzd+5c+vfvT79+/ShevDhXXnklhQsXVs+HiGQ4GpgqkoFs3LiRG2+8kVdffZW2bdvy888/U7hwYa/LEhG5KAohIhlAdHQ0Q4cOpWrVqvz1119MmTKFzz77jEKFCnldmojIRdPpGJF0bvv27XTs2JEffviBO+64g08++YTixYt7XZaIyCVTCBFJp8yMzz//nMcff5zIyEg+/vhjHnnkEZxzCdbTWBARyah0OkYkHTp48CD33XcfDzzwAP7+/qxbt44uXbokCiAiIhmZQohIOjNr1iwCAgKYPn06b775JgsXLuS6667zuiwRkVSnECKSThw9epSuXbvStGlTihQpwsqVK+nVq5fu/SEimZZCiEg6sHTpUkJCQhg5ciTPPvssq1evJiQkxOuyREQuK4UQEQ+dPn2a3r17U7duXaKioggPD+ftt98mV65cXpcmInLZ6eoYEY/88ssvPPDAA6xbt46HH36YwYMHU7BgQa/LEhFJM+oJEUljUVFRvPPOO1SvXp3du3czffp0PvnkEwUQEcly1BMikob+/vtvOnTowMKFC2nRogUjRoygaNGiXpclIuIJ9YSIpAEzY9SoUQQFBbF27VrGjBnDV199pQAiIlmaekJELrO9e/fSpUsXZsyYQVhYGGPGjKFMmTJelyUi4jn1hIhcRl9//TWBgYHMmTOHwYMH88MPPyiAiIjEUggRuQz+++8/OnbsSMuWLSlVqhRr1qzhqaeeIls2/ZcTEYmj34giqSw8PJygoCDGjRtHnz59WL58Of7+/l6XJSKS7iiEiKSSkydP8vTTT3PrrbeSI0cOlixZQr9+/ciZM6fXpYmIpEsamCqSCtauXcsDDzzAhg0bePTRRxk4cCD58uXzuiwRkXRNPSEilyAyMpL+/ftTs2ZNDh06xOzZs/nwww8VQEREUkA9ISIXafPmzTz44IMsX76c1q1b8+GHH3LllVd6XZaISIahnhCRC2RmDB8+nODgYDZu3MjEiROZNGmSAoiIyAVST4jIBdi1axcPP/wws2fPpmHDhowaNYqSJUt6XZaISIaknhCRFJo8eTKBgYEsWLCAYcOGMXv2bAUQEZFLkKohxDnn55xb65ybGTt9pXNurnNuU+zXwqnZnkhqCgsLIywsLNH8Q4cOcf/999O6dWuuv/56IiIiePzxx3HOpX2RIiKZSGr3hHQHfos33Qv4wcwqAD/ETotkGHPnziUwMJApU6bw2muvsWTJEm644QavyxIRyRRSLYQ450oBTYFP4s2+Cxgb+/1YoEVqtSdyOR0/fpwnnniChg0bUrBgQZYvX85LL71E9uwaRiUiklpSsydkCPAcEB1v3tVmthsg9mux5DZ2znVxzq12zq3ev39/KpYlcmFWrlxJ1apV+eCDD+jRowdr1qyhevXqXpclIpLppMqfdc65ZsA+M1vjnAu7mH2Y2QhgBEBoaKilRl0i53L2+I8FCxYAUKtWLXLlykVQUBBr164lT548HlQnIpL5pVbf8k1Ac+fcHUBuoKBzbjyw1zlX3Mx2O+eKA/tSqT2RVHXixAnf91dffTXXX3+9Tr2IiFxmqfJb1sxeAF4AiO0JecbMHnDODQTaAwNiv05PjfZEUkN4eDgAkyZNomvXrvj5+XHDDTewYcMGbwsTEckiLvefegOAyc65h4FtwL2XuT2RFDt27BhPPvkko0aNok6dOkRHR5M7d26vyxIRyTJS/WZlZhZuZs1ivz9oZg3MrELs139Suz2RixEREUH16tUZPXo0L774IgsXLlQAERFJY7pjqmQpZsbQoUOpVasWR44c4YcffuD111/X+A8REQ/oN69kGQcOHKBjx47MnDmTO++8k1GjRlGkSBHf8rgxIiIikjbUEyJZwo8//khQUBDff/89Q4cOZfr06QkCiIiIpD2FEMnUzpw5Q58+fbjtttsoWLAgK1eu5H//+5+e+yIikg7odIxkWlu2bOH+++9n2bJlPPzww7z33nvky5fP67JERCSWQohkSpMnT6ZLly6YGZMmTaJ169ZelyQiImfR6RjJVI4dO8YjjzxC69atqVy5MhEREQogIiLplEKIZBrr1q0jNDSUTz/9lN69e7Nw4ULKlSvndVkiIpIMhRDJ8MyMYcOGUatWLf7991/mzp1L//79yZEjh9eliYjIOWhMiGRoBw4coFOnTnzzzTc0bdqU0aNHU7RoUa/LEhGRFFBPiGRY4eHhBAcHM2fOHIYMGcI333yjACIikoEohEiGExkZyUsvvcStt95K/vz5Wb58Od27d9e9P0REMhidjpEMZevWrdx///0sXbqUTp068d5775E/f36vyxIRkYugECIZxtSpU+ncuTPR0dF8/vnntG3b1uuSRETkEuh0jKR7x48fp2vXrtx7771UrFiRiIgIBRARkUxAIUTStfXr1xMaGsrIkSPp1asXixcvpnz58l6XJSIiqUAhRNIlM+ODDz6gZs2aHDp0iO+//54333xT9/4QEclENCZE0p2DBw/y8MMPM336dJo0acKYMWMoVqyY12WJiEgqU0+IpCsLFiwgJCSEWbNm8e677zJz5kwFEBGRTEohRNKFyMhIXn75ZW699Vby5MnD8uXL6dGjB9my6UdURCSz0ukY8dy2bdto164dixcvpn379gwbNkz3/hARyQIUQsRTX375JZ07dyYqKorx48fTrl07r0sSEZE0or5u8cTx48fp1q0brVq1okKFCqxdu1YBREQki1EIkTT3yy+/ULNmTT7++GOee+45Fi9ezHXXXed1WSIiksYUQiTNmBkfffQRNWrU4MCBA8yZM4e33nqLnDlzel2aiIh4QCFELouwsDDCwsJ80//88w/33HMPjz32GPXq1WPdunU0bNjQuwJFRMRzCiFy2S1atIjg4GBmzpzJO++8w6xZs7j66qu9LktERDymECKXjZnx6quvEhYWRu7cuVm6dClPP/207v0hIiKALtGVy+TkyZNs3LiRhQsX8uCDD/LBBx9QoEABr8sSEZF0RCFEUkX88R+HDh1i/fr1AFSqVIlt27Zx5513AhAeHu5BdSIikh4phEiq2rVrF5s3b/ZNa+yHiIgkRyFEUsW8efPo0aMHCxYs4I477uDff/8le/bs6vkQEZFkaYSgXLJDhw7RpEkTPvjgA5555hlmzJhB9uzKtyIicm76pJBL8vvvv3PnnXeyZcsWRo8eTYcOHbwuSUREMgiFELlo33//Pffddx85c+Zk/vz53HTTTV6XJCIiGYhCiFwwM+P999/nqaeewt/fnxkzZlC2bNkE62gsiIiInI/GhMgFOXPmDN26daN79+7ceeedLF26NFEAERERSQmFEEmxgwcP0rBhQ0aMGMELL7zAV199Rf78+b0uS0REMiidjpEU2bBhA3feeSc7d+5k/PjxtGvXzuuSREQkg1MIkfOaNWsWbdq0IW/evISHh1O7dm2vSxIRkUxAp2MkWWbGoEGDaNasGddffz2rVq1SABERkVSjECJJOnXqFA8//DDPPPMMd999N4sWLaJ06dJelyUiIpmIQogksm/fPm677TZGjx5N3759mTx5Mvny5fO6LBERyWQ0JkQSWL9+Pc2bN2fv3r1MmjSJ1q1be12SiIhkUuoJEZ/p06dz4403cubMGRYtWqQAIiIil5VCiGBmDBgwgJYtW1KlShVWrVpFaGio12WJiEgmp9MxWdzJkyd55JFHGD9+PG3atGHUqFHkyZPH67JERCQLUE9IFrZnzx7q16/P+PHjef311/n8888VQEREJM2oJySLWrt2Lc2bN+eff/5h6tSp3HPPPV6XJCIiWYx6QrKgL7/8kptvvhnnHIsXL1YAERERTyiEZCFmxuuvv06rVq0ICgpi5cqVVK1a1euyREQki8q0IWTr1q30798fM0tyuZnRv39/tm7dmsaVeePEiRO0bduWvn378uCDDzJ//nyuueYar8sSEZEsLNOGkPHjx/Piiy/Ss2fPREHEzOjZsycvvvgi48eP96jCtLNz505uueUWJk+ezIABAxg7diy5c+f2uiwREcniUm1gqnOuNDAOuAaIBkaY2XvOuSuBL4CywBbgPjM7lFrtJqd3794cOHCAIUOGADB48GCcc74AMmTIEHr06EHv3r0vdymeWrVqFXfddRdHjhzh66+/pnnz5l6XJCIiAqTu1TGRwNNm9pNzrgCwxjk3F+gA/GBmA5xzvYBewPOp2G6SnHMMHjwYIEEQiR9A4oJJZvXFF1/QoUMHrrnmGubMmUNgYKDXJYmIiPikWggxs93A7tjvjzjnfgNKAncBYbGrjQXCSYMQAomDSFwYeeKJJzJ1AImOjuaVV17h9ddf5+abb+arr76iaNGiXpclIiKSgEtu4OYl7dS5ssBCIADYZmaF4i07ZGaFk9imC9AF4Nprr62emgNGzYxs2f5/+EuxYsV47LHHePTRRylWrFiqtZMeHDt2jPbt2/Pll1/SsWNHPvroI3LlyuV1WSIikoU559aYWaLngaT6wFTnXH7gS6CHmf2X0u3MbISZhZpZaGr+1R43BiS+fPny8corr1C6dGkGDBiQam15bfv27dx8881MmzaNQYMG8emnnyqAiIhIupWqIcQ5l4OYADLBzL6Knb3XOVc8dnlxYF9qtnkuZw9CjY6OpkePHvz999889NBDPPzww1x//fUA/PPPP8yYMYPo6Oi0Ki9VLV++nBo1avDXX3/xzTff0LNnz0x7uklERDKHVAshLuYT71PgNzMbHG/RDKB97Pftgemp1ea5nB1A4saADB48mB49ejBu3Dhy5crlu1vo2LFjueuuu6hYsSLvv/8+R48eTYsyU8Vnn31GWFgY+fLlY9myZdxxxx1elyQiInJ+ZpYqL+BmwID1QETs6w7gKuAHYFPs1yvPt6/q1avbperXr58B1qNHD4uOjk6wLDo62nr06GGA9evXz8zMTp8+bZMmTbLatWsbYFdccYU988wzFhUVdcm1XC5RUVH2/PPPG2BhYWF24MABr0sSERFJBFhtSXzep+bVMYuB5Pr/G6RWOyn1wAMPADH3Czn7tERcj0iRIkV86+XIkYPWrVvTunVrli9fzpAhQ/j99999A1p///13brjhhnRziuPIkSM88MADzJgxg65du/L++++TI0cOr8sSERFJsctydcylCg0NtdWrV3tdBlFRUfj5+bF161bKly9P9erV6dGjB/fee6+nH/hbtmyhefPm/PrrrwwZMoQnnngi3YQjERGRs6XZ1TGZiZ+fHwBFihRh2LBh/Pvvv7Rr146yZcvy5ptvcvjw4cteQ1hYGGFhYb7pxYsXU6NGDbZt28Z3333H//73PwUQERHJkBRCUiBfvnw8+uij/Pbbb3z77bf4+/vz8ssvc/z4cQBOnTqVJnWMHj2aW2+9lcKFC7NixQoaNmyYJu2KiIhcDgohFyBbtmzccccdfP/992zZsoUSJUoA0LRpUxo3bszs2bOTfWrvpTAznn76aTp16kS9evVYsWIFFStWTPV2RERE0pJCyEWKCyDR0dHUr1+fdevW0aRJE/z9/fn44499vSSXKjIykl9++YXBgwfzxBNP8N1331G4cKIbzoqIiGQ4GpiaSk6fPs3kyZN59913+emnn3j33Xfp0aPHBe8n/viPqKgoFi9eDECFChV8wQcgPDz8EisWERFJGxqYepnlzJmTBx54gNWrV7Nw4UI6duwIwPjx42nXrh2rVq26oP1FR0fz66+/+qbjBxAREZHMINXuEyIxnHPUrVvXN33w4EG++eYbPv/8c2688UaeeuopWrRoQfbsSR/68PBwoqOjeeihh1i0aBEVK1bkmmuuUc+HiIhkOuoJucy6d+/Ojh07GDJkCLt37+bee++lZcuW59zmueeeY8KECfTv359rrrkmjSoVERFJWwohaaBgwYJ0796dTZs2MW3aNJ544gkA/v33X3r06MGmTZt86/bp04dBgwbx+OOP88ILLyTal5nRv39/tm7dmmb1i4iIXA46HZOG/Pz8aNGihW966dKlfPjhhwwdOpRmzZrh7+/PgAEDfOuezeI9lA9iAouIiEhGpRDioSZNmrBt2zY+/PBD3nvvPb755hvy58/P/fffz9ChQ8mWLRvz58/HOZfoqcC9e/f2unwREZFLotMxHrvmmmu48847iYyMpHTp0tx3330MHz6cHj16MGTIELp27ZoogAwePFi3ahcRkQxP9wnx2B9//MFNN91EgQIFWLp0qW8g6sGDB7n66quJioryrduoUSM++ugjypUr51W5IiIiF0z3CUmHdu/eTaNGjXDOMWfOnARXwlx11VUJ7hMCMGfOHGbPng3A5s2bady4MT179mTkyJEsWbKEf/75J03rFxERuRQaE+KRf//9lyZNmrB//37Cw8OpUKFCguVmxvDhwxPMe+ihh7jnnnsAOHToEPv27WPhwoWcOHHCt86sWbNo0qQJv/32G/PmzaNKlSpUrlyZ4sWL6xSOiIikK+oJ8cDJkydp0aIFv/76K1999RWhoQl7qM4eAxIdHU2PHj0YN24cb775JmZGjRo1+Omnnzh69Ch//fUX3377LQMHDiQkJASAH3/8kSeffJLbbruNkiVLUrhwYWrXrs22bdsA2LFjB3/99RfR0dGp8p62bt1K//79k32Any4tFhGRRMws3b2qV69umVVkZKS1atXKABs/fnyi5dHR0dajRw8DrEePHhYdHX3O+cmJjo62Xbt22Q8//GDvv/++PfbYY1a/fn07evSomZk9++yzBlju3LktJCTE2rZta6+//rqdOXPGt/2F6NevX7K1xa+9X79+F7RfERHJ+IDVlsTnveeBI6lXZg0h0dHR9vjjjxtggwYNSnKdtPow//XXX+2TTz6xnj17WpMmTaxMmTJWpEgRX5sPPfSQVapUyVq2bGm9e/e28ePHW0RExDnfW2qEJxERyXwUQtKBuIDxzDPPJLvOli1brF+/fsl+WEdHR1u/fv1sy5YtqV7fyZMnfd9/8MEH1qJFC6tYsaL5+fkZYEFBQb7lzz33nD399NP2ySef2JIlS+yff/5JMnCk5wDi5bEWEclKFEI89sknnxhgDzzwgEVFRXldzgU5deqU/frrr7Z8+XLfvAYNGlju3LkN8L3uv//+BMEj7tWmTRv77bff7NChQ969iSRk1FNIGTU8ZdS6ReTSKYR4aPr06ZYtWzZr1KiRnT592utyUk1kZKT9+eef9s0339jbb79tkyZNMjOzY8eOJQghca8ePXr4lhctWtSuv/56Cw0NtQYNGtjdd99tX375pZmZHT161N59910bNWqUffnllzZv3jxbtWqVHThwIFXrz6inkDJqeMqIdWfU4KS6005GrNks7etWCPHI4sWLLXfu3FajRg07cuSI1+VcdtHR0da9e/cE4aN58+b22Wef2cqVK83M7L///rOuXbtamzZtrEmTJlanTh2rUqWKffTRR2Zmtnnz5iRDzNChQ83M7Oeff7Y8efLYNddcYxUrVrSaNWva7bffbvPmzTMzs61bt9prr71m7733no0dO9a+/vprmz9/vh08eNDMzM6cOZNgAG5GOoVklnHDU0asOyMGJzPVnZYyYs1maV+3QogHfvnlFytcuLBVqFDB9u3b53U5l11qfaBHRUXZP//8Y3///betXbvWwsPDbfr06bZ582YzM9u2bZs988wz9sgjj9h9991njRo1slq1atns2bPNzGzevHlJhpiZM2eaWUzPFGD58uWzEiVKWOXKle2aa65JsG6VKlWsS5cu9sQTT1jPnj3t+eeft127dpmZ2U8//WSDBw+2YcOG2YgRI2z06NE2YcIEX8j8888/be7cuRYeHm5Lly61VatW2bp163zB599//7U9e/bYP//8Y0eOHLFTp05d8AdvRgxPZhmv7owYnMxUd1rKiDWbpX3dyYUQ3azsMtm+fTuNGzcmV65czJkzh6JFi3pd0mVllvTzbQYPHgzge/JvSp57ky1bNgoXLkzhwoWTXF66dGkGDhyY7PYNGjTg9OnT/Pvvv77X4cOHCQoKAuCGG27g1Vdf9c2PW2fPnj2+ffz3339Mnz6d06dPc+bMGU6fPs1DDz1E8eLFWbhwIT179kzU7tatW8mfPz8TJ07kxRdfTLT84MGDXHnllbzxxhu89dZbiZafOnWKnDlz8txzzzF69Ghy5sxJjhw5yJkzJ/ny5WPt2rUAvPHGG8ybN48cOXJQrlw5hgwZ4ju+PXr04Nprr6VDhw5ky5bN9ypWrBj9+/cHYNiwYWzatMm3zM/PjxIlStCjRw8ARowYwa5duxJsX7p0aR588EEAxo4dy6FDh3zbZsuWjTJlynDHHXcAMHnyZE6cOJFg+zJlynDjjTfinKNBgwb8+eefCepu166d72cj7q7Azjnf69prr6VixYpERUWxYMGCRMvLlClD2bJlOX36NKtWrUqwHKBMmTKUKFGCkydP8vPPPydafu2111K0aFFOnDjBH3/8kWB5p06dOHnyJEOGDOHMmTM89thjvPXWW4wbN46HHnqILl26cPToUQoUKMDRo0fZuXOn7980bv+lSpUib968HDlyhL179yb6ty9VqhS5c+fmv//+48CBA0kuz5kzJ//991+COyPH7b9kyZJkz57d97Mc97Nw5MgRhgwZgpnx7rvv8vjjj/PRRx/x8MMP07NnT1+tJUuWxDnH4cOHOXbsWIK2nXOUKFECiLlJYvybI0LM/9e4uz3/888/nDp1KsFyPz8/ihUr5lt++vTpBMuzZ89OkSJFfMufe+45jh07xpAhQzh27Bhvvvkm/fr18z1L6/nnn2ffvn2+7XPmzOn7XbF///5E9z7KlSsXhQoVAmDfvn0xf33HkydPHgoWLOhbfrY8efJQoEABzIz9+/cnWp43b14GDx6MmTFkyBCOHz/Oa6+9Rt++fRkxYgSPP/44gwcPJioqKsm7WhcoUIA8efIQGRnJoUOHklyeO3du3++0sxUsWJBcuXIlu/yKK64gZ86cnDx5kiNHjiRY9sILLxAVFcWQIUOIjIxk6NChaf+csqSSidevjN4TcvDgQatSpYoVLFjwnJe1ZiYZtUvSLGF9ca9z/QVw6tQpO3TokO3du9d27Nhhf/31l/3+++++8T7bt2+3RYsW2Q8//GCzZ8+2GTNm2NSpU33Lly9fbh9++KG99957NnDgQHvjjTfslVde8Q1YnjRpkj366KPWuXNne+ihh6xNmzZ2//33+9rv37+/1a1b12rVqmXVqlVLUHd0dLR16dLFypYta9dee62VKlXKSpQoYbVr1/Ztf9ddd1mhQoWsYMGCli9fPsuTJ4/VqFHDt7xGjRqJepFuvvlm3/JKlSolWt6kSRPf8lKlSiVaft999/mWX3HFFYmWd+zY0bc8W7ZsiZZ3797dzJIfb/Tiiy+amdmePXuSXP7WW2+ZmdmmTZuSXP7hhx+amdnatWuTXD527NhEPyPxX9OmTTMzs2+//TbJ5XGnCr/44oskl69YscLM/n8A+9mvX3/91czM3n333SSXb9u2zczMXnvttWRrPNcrMjLSzMweffTRRMty587t+7d54IEHEi0vWrRogp+ts5eXL1/et/zWW29NtDw4ONi3vGbNmsnW2KNHD6tcuXKi+Y0bNz7nz9699957zp+9Tp06pehn7/jx4xf1s/fmm2+aWfKnmT/44INz/uyNGzfOzMwWLlx4zp+9WbNmXdTP3rJlyy7o99/FIpmeED3ALpUdP36chg0bsmrVKubMmUNYWJjXJaWJrVu3Mn78eHr37p1kcjYz3njjDR544AHKlCnjQYVJsyR6cDLKE4vj1x4ntWqO+wURHR1NdHQ0ZkauXLkAOHLkCFFRUURFRfmW58iRgyuvvBKIuRvvmTNnfMuio6PJnz8/JUuWBGD9+vW89dZbfP755772OnbsyKeffopzjuXLlyf6RVW8eHGuu+46oqKiWLJkSaLlZcqU4brrruPUqVMsXLjw/883x76XG264gfLly3Ps2DHCw8MTLQ8MDKRcuXIcPnyY+fPnJzxnDdSoUYNrr72WbNn+/ybTn3/+ue8433zzzZQqVYpdu3b5emri/2699dZbueaaa9i6dSuLFi1KdLwbN25MkSJF2LRpE8uWLUu0vHnz5hQqVIgNGzawcuXKRPu/9957yZ8/PxEREfz0008JlpsZjzzyiG/dESNGJPr56NSpE9myZWPx4sX89ttvCZb5+fnRqVMnAObPn8+mTZsSLM+dOzcPPfQQEPN8qy1btiRYXrBgQdq2bQvAN998k6CnCGKek3XvvfcC8NVXX/l6I8yMxx57zLdedHQ0X3zxRaLegtKlS9OsWTMAxo0bl6gn57rrrqNhw4YAfPrpp4l6YipVqkT9+vUB+OijjxL1lAQFBXHzzTcTGRnJiBEjOFv16tWpVasWx48fZ/To0TzxxBO+ZcOGDaNOnTpUq1aNf//9lwkTJiTavm7dugQGBrJ//34mT56caPltt91GxYoV2bVrF9OmTUu0vEmTJpQvX56tW7cyc+bMRMubN29O6dKl2bx5M3PmzEm0vFWrVhQrVizBz3Z0dHSq/95L7gF2nvd6JPXKqD0hZ86csTvvvNOcczZlyhSvy5HzyKjncs0y3tiKOJmhbi7jX4upTXWnnYxYs1na1Y0Gpl5e0dHR9vDDDxtgw4YN87ocSYGMegopo4anzFR3eq43jupOOxmxZrO0rVsh5DJ78cUXE5wflPQvo17fn1HDU0asOzMFp3PNTy8yYt0ZsWaz9HN1jOeBI6lXRgshH3zwgQHWuXPndPeDJplPRg1PGbHujBiczFR3WsqINZvpPiGZJoRMmTLFnHPWvHlz330gRCRzyIjByUx1p6WMWLNZ+rljqq6OuQTh4eE0atSI0NBQ5s6dS968eb0uSUREJN1J7uqYbEmtLOe3bt067rrrLq6//nq++eYbBRAREZELpBByEf7++28aN25MwYIFmT17tu/+CCIiIpJyum37Bdq/fz+NGjXi5MmTLF68mNKlS3tdkoiISIakEHIBjh49StOmTdm+fTvz5s3D39/f65JEREQyLIWQFDpz5gytWrVizZo1TJs2jZtuusnrkkRERDI0hZAUiI6OplOnTsyZM4eRI0fSvHlzr0sSERHJ8DQwNQWef/55xo8fz+uvv07nzp29LkdERCRTUAg5j8GDB/POO+/w+OOP06dPH6/LERERyTQUQs5hwoQJPP3007Rq1Yr33nsv3T7SXUREJCNSCEnG999/T4cOHQgLC+Ozzz7Dz8/P65JEREQyFYWQJKxevZq7774bf39/vv76a3Lnzu11SSIiIpmOQshZNm3axB133EHRokX57rvvuOKKK7wuSUREJFNSCIlnz549NGrUCDNjzpw5FC9e3OuSREREMi3dJyTWf//9R5MmTdi7dy/z58/nhhtu8LokERGRTE0hBDh16hQtW7bkl19+4ZtvvqFmzZpelyQiIpLpZfkQEh0dzUMPPcSPP/7IuHHjaNy4sdcliYiIZAlZekyImdGjRw8mT57MwIEDefDBB70uSUREJMvI0iFkwIABvP/++/Ts2ZNnnnnG63JERESylCwTQsLCwggLC/NNjxo1it69e9OuXTsGDhzoXWEiIiJZVJYJIfHNnDmTLl260LBhQ0aNGkW2bFnyMIiIiHgqTT59nXONnXO/O+c2O+d6pUWbyVm2bBn33XcfISEhTJ06lZw5c3pZjoiISJZ12UOIc84P+ABoAlQB2jrnqlzudpNy7NgxmjVrRsmSJZk1axYFChTwogwREREhbS7RrQlsNrO/AJxzk4C7gA2Xs9H44z8AFixYAECOHDm4/vrrue+++wAIDw+/nGWIiIhIMtLidExJYHu86R2x8xJwznVxzq12zq3ev3//ZSsmMDCQPHnyXLb9i4iISMqkRU+IS2KeJZphNgIYARAaGppo+YU6u4cjLCyMyMhIFi9efKm7FhERkVSQFj0hO4DS8aZLAbvSoN1EsmfP8jeIFRERSTfSIoSsAio458o553ICbYAZadCuiIiIpGOXvWvAzCKdc08AcwA/YJSZ/Xq52xUREZH0LU3OT5jZLGBWWrSVHF0FIyIikr7oVqEiIiLiCYUQERER8YRCiIiIiHhCIUREREQ8oRAiIiIinlAIEREREU8ohIiIiIgnFEJERETEEwohIiIi4gmFEBEREfGEQoiIiIh4wpmZ1zUk4pzbD2y9DLsuAhy4DPuVpOl4px0d67SjY522dLzTzuU81mXMrOjZM9NlCLlcnHOrzSzU6zqyCh3vtKNjnXZ0rNOWjnfa8eJY63SMiIiIeEIhRERERDyR1ULICK8LyGJ0vNOOjnXa0bFOWzreaSfNj3WWGhMiIiIi6UdW6wkRERGRdEIhRERERDyRZUKIc66xc+5359xm51wvr+vJrJxzpZ1z851zvznnfnXOdfe6pszOOefnnFvrnJvpdS2ZnXOukHNuqnNuY+zPeB2va8qsnHNPxf4O+cU5N9E5l9vrmjIT59wo59w+59wv8eZd6Zyb65zbFPu18OWuI0uEEOecH/AB0ASoArR1zlXxtqpMKxJ42swqA7WBx3WsL7vuwG9eF5FFvAfMNrNKQDA67peFc64k8CQQamYBgB/QxtuqMp0xQOOz5vUCfjCzCsAPsdOXVZYIIUBNYLOZ/WVmp4FJwF0e15QpmdluM/sp9vsjxPySLultVZmXc64U0BT4xOtaMjvnXEHgFuBTADM7bWaHPS0qc8sO5HHOZQfyArs8ridTMbOFwD9nzb4LGBv7/VigxeWuI6uEkJLA9njTO9AH42XnnCsLVAVWeFxKZjYEeA6I9riOrKA8sB8YHXv66xPnXD6vi8qMzGwn8A6wDdgN/Gtm33tbVZZwtZnthpg/KIFil7vBrBJCXBLzdG3yZeScyw98CfQws/+8riczcs41A/aZ2Rqva8kisgPVgI/MrCpwjDTors6KYsci3AWUA0oA+ZxzD3hblVwOWSWE7ABKx5suhbr2LhvnXA5iAsgEM/vK63oysZuA5s65LcScYrzVOTfe25IytR3ADjOL69mbSkwokdR3G/C3me03szPAV8CNHteUFex1zhUHiP2673I3mFVCyCqggnOunHMuJzEDnGZ4XFOm5JxzxJwz/83MBntdT2ZmZi+YWSkzK0vMz/SPZqa/Fi8TM9sDbHfOVYyd1QDY4GFJmdk2oLZzLm/s75QGaBBwWpgBtI/9vj0w/XI3mP1yN5AemFmkc+4JYA4xo6xHmdmvHpeVWd0EPAj87JyLiJ3X28xmeVeSSKr5HzAh9o+Zv4COHteTKZnZCufcVOAnYq64W4tu356qnHMTgTCgiHNuB/AyMACY7Jx7mJggeO9lr0O3bRcREREvZJXTMSIiIpLOKISIiIiIJxRCRERExBMKISIiIuIJhRARERHxhEKIiKS52KfRPuZ1HSLiLYUQEfFCIUAhRCSLUwgRES8MAK5zzkU45wZ6XYyIeEM3KxORNBf7hOWZZhbgdS0i4h31hIiIiIgnFEJERETEEwohIuKFI0ABr4sQEW8phIhImjOzg8AS59wvGpgqknVpYKqIiIh4Qj0hIiIi4gmFEBEREfGEQoiIiIh4QiFEREREPKEQIiIiIp5QCBERERFPKISIiIiIJxRCRERExBMKISIiIuIJhRARERHxhEKIiIiIeEIhRERERDyhECIiIiKeUAgRERERTyiEiIiIiCcUQkRERMQTCiEiIiLiCYUQERER8YRCiIiIiHhCIUREREQ8oRAiIiIinlAIEREREU8ohIiIiIgnFEJERETEEwohIiIi4gmFEBEREfGEQoiIiIh4QiFEREREPKEQIiKJOOe6OueGeF1Hcpxz3znn2ntdx/k455o75yZ5XYdIeqUQIpKOOOe2OOdOOOeOxnsNS+MacgIvAgNTsG64c67z5a8qITNrYmZj07rdpDjnXnfO/eyci3TOvRJ/mZnNAAKcc0HeVCeSvimEiKQ/d5pZ/nivJ5JayTmXPYl5fhfSUDLr3wVsNLOdF7KvLGwz8BzwbTLLJwJd0q4ckYxDIUQkg3DOdXDOLXHOveuc+wd4xTk3xjn3kXNulnPuGFDfOVc5tofisHPuV+dc83j7SLR+Ek01ARbE2ya3c268c+5g7D5XOeeuds71B+oCw+L32DjnKjnn5jrn/nHO/e6cu++s9ofHLj/inFvgnCuTzPtNst3YZb4eGOfcurN6jsw5Fxa7rLZzbmns9uvi5qcmMxtrZt8BR5JZJRxomtrtimQGCiEiGUst4C+gGNA/dt79sd8XAFYA3wDfx67zP2CCc65ivH3EX39xEm0EAr/Hm24PXAGUBq4CugEnzKwPsAh4Iq7HxjmXD5gLfB7bflvgQ+ecf7z9tQNeB4oAEcCEZN5rku2evZKZBcf1GgE9Y2v/yTlXkpjeiX7AlcAzwJfOuaJJNeacmxkbVpJ6zUymxpT4DSjrnCt4CfsQyZQUQkTSn6/P+gB8JN6yXWb2vplFmlncB/J0M1tiZtFACJAfGGBmp83sR2AmMWGAs9c3s5NJtF+IhH/VnyEmBFxvZlFmtsbM/kum9mbAFjMbHVvjT8CXQKt463xrZgvN7BTQB6jjnCudxL4upF2cczcTEziax673ADDLzGbFvte5wGrgjqS2N7NmZlYomVez5NpNgbhjWegS9iGSKSU6pywinmthZvOSWbb9PPNKANtjA0mcrUDJ8+wjvkPE9JLE+YyY3ohJzrlCwHigj5mdSWLbMkAt59zhePOyx+4jUftmdjT21FKJJOpKcbuxIWYy0N7M/ohXy73OuTvjrZoDmJ9E3ZdT3LE8nMbtiqR76gkRyVjsPPN2AaWdc/H/b18L7Exm/aSsB27wrWx2xsxeNbMqwI3E9HY8lMy+tgMLzupFyG9mj8Zbx9fr4ZzLT8ypkl2J3tS52/VxzuUBvgaGxI7NiF/LZ2fVks/MBiT1pmMv+z2azOu7pLZJocrE9A4l24sjklUphIhkLiuAY8BzzrkcsQMx7wQu5F4Vs4B6cRPOufrOucDYK2n+I+Y0SVTs4r1A+XjbzgRucM49GNt+DudcDedc5Xjr3OGcuzn2UuDXgRVmlqh35jztxjeKmKt53j5r/njgTudcI+ecX+xA1zDnXKmk3nTsZb/5k3k1Se5gxb7H3MT8Ps0e2078q47qAZcSYkQyLYUQkfTnm7P+Cp+W0g3N7DTQnJgrXA4AHwIPmdnGC2kfqOScKxE7fQ0wlZgg8BsxV86Mj132HtDKOXfIOTfUzI4ADYE2xPRu7AHeAnLF2//nwMvAP0B1YgaqJuVc7cbXBmh51jGrGxts7gJ6A/uJ6Rl5ltT/vTeSmAGzbYkZ43ICeDDe8rbAx6ncpkim4MzO1zMrIlmNc64LUMXMeqTyfscAO8zsxdTcb3oVOx7lQTO777wri2RBCiEikmayWggRkXPT6RgRERHxhHpCRERExBPqCRERERFPpMublRUpUsTKli3rdRkiIiKSCtasWXPAzBI9MiFdhpCyZcuyevVqr8sQERGRVOCc25rUfJ2OEREREU8ohIiIiIgnFEJERETEE+lyTIiIiMiZM2fYsWMHJ0+e9LoUSaHcuXNTqlQpcuTIkaL1FUJERCRd2rFjBwUKFKBs2bI457wuR87DzDh48CA7duygXLlyKdpGp2NERCRdOnnyJFdddZUCSAbhnOOqq666oJ4rhRAREUm3FEAylgv999LpGBERyfAOHTrEmDFjWLJkCWZGrVq16NSpE0WKFPG6NDkH9YSIiEiGNnnyZK677jrWrFnDvffeS+vWrfntt9+oUKECY8eOvaR9+/n5ERIS4nsNGDAglar+f61ateKvv/5K9f3GCQsLS9UbgO7fv5/GjRunyr7UEyIiIhnW/Pnz6d69O+Hh4QQFBfnm33ffffTq1YsGDRpw1VVX0axZs4vaf548eYiIiDjnOlFRUfj5+SU7fa7tNm7cSFRUFOXLl7+o+rxQtGhRihcvzpIlS7jpppsuaV/qCUlntm7dSv/+/Unu6cZmRv/+/dm6Nck74IqIZCmvv/46gwYNShBA4lSsWJGPPvqI1157LdXbLVu2LK+99ho333wzU6ZMSTQ9ceJEAgMDCQgI4Pnnn/dtlz9/fvr27UutWrVYtmwZEyZM4K677gLg008/5amnnvKtO3LkSHr27Jmg3e+++4777rvPNx0eHs6dd94JwKOPPkpoaCj+/v68/PLLSdadP39+3/dTp06lQ4cOQEzvxj333EONGjWoUaMGS5YsAWDBggW+XqCqVaty5MgRAFq0aMGECRMu9vD9PzNLd6/q1atbVtWvXz8DrEePHhYdHZ1gWXR0tPXo0cMA69evn0cVioikjQ0bNpxz+bZt26xIkSJ26tSpZNeJjIy0UqVKnXdfycmWLZsFBwf7XpMmTTIzszJlythbb73lWy/+9M6dO6106dK2b98+O3PmjNWvX9+mTZtmZmaAffHFF77tbrnlFlu/fr2ZmR09etTKly9vp0+fNjOzOnXq+JbFOXPmjJUuXdqOHj1qZmbdunWzzz77zMzMDh486HvP9erVs3Xr1pmZWb169WzVqlVmZpYvXz7fvqZMmWLt27c3M7O2bdvaokWLzMxs69atVqlSJTMza9asmS1evNjMzI4cOWJnzpwxM7MdO3ZYQEBAkscsqWMNrLYkPu91Oiad6d27NwcOHGDIkCEADB48GOccZkbPnj0ZMmQIPXr0oHfv3t4WKiLisT179nDttdeSM2fOZNfx8/OjfPny7Nmzh8qVK19wG+c6HdO6deskp1etWkVYWBhFi8Y8NLZdu3YsXLiQFi1a4Ofnxz333OPbZvfu3b718uXLx6233srMmTOpXLkyZ86cITAwMEEb2bNnp3HjxnzzzTe0atWKb7/9lrfffhuIGRszYsQIIiMj2b17Nxs2bEiyhygp8+bNY8OGDb7p//77jyNHjnDTTTfRs2dP2rVrx913302pUqUAKFasGLt27UrRvs9FISSdcc4xePBggARBJH4AiQsmIiJZWZEiRdi5cyeRkZFkz570x5mZsX379stylUy+fPmSnLZkTqdDzB1F448XyZMnT4L7anTu3Jk33niDSpUq0bFjRwD69OnDt99+C0BERAStW7fmgw8+4Morr6RGjRoUKFCAv//+m3feeYdVq1ZRuHBhOnTokOT9OuJ/dsRfHh0dzbJly8iTJ0+C9Xv16kXTpk2ZNWsWtWvXZt68eVSqVImTJ08mWvdiaExIOhQXRHr06MGQIUPIli2bAoiIyFnKlStHuXLlmDlzZrLr/PDDD+TLl4+AgIA0q6tWrVosWLCAAwcOEBUVxcSJE6lXr16S61auXJnNmzcn2Hb79u18/vnntG3bFoD+/fsTERHh65EJCwvjp59+YuTIkb7el//++498+fJxxRVXsHfvXr777rsk27v66qv57bffiI6OZtq0ab75DRs2ZNiwYb7puLb+/PNPAgMDef755wkNDWXjxo0A/PHHH6lyTBVC0qn4PSJxFEBERBLq06cPTz75ZJKXuG7fvp1u3brRp0+fi/7deeLEiQSX6Pbq1eu82xQvXpw333yT+vXrExwcTLVq1XyDT8/WtGlTwsPDE8y77777uOmmmyhcuHCS2/j5+dGsWTO+++4731U/wcHBVK1aFX9/fzp16pTsVSsDBgygWbNm3HrrrRQvXtw3f+jQoaxevZqgoCCqVKnC8OHDgZge+YCAAIKDg8mTJw9NmjQBYq5Katq06XmPxXklNVDE61dWHpgaJ/4g1LhXUoNVRUQyq5QOJh0+fLhdeeWV9uSTT9rcuXPthx9+sKefftquuuoqGzRo0GWu8tIcP37catWqZZGRkb55TZs2tXnz5nlY1fnVrVvX/vnnnySXXcjAVPWEpEN21iDU6Oho36mZnj17nvN8o4hIVtO1a1fWrl1LgQIF6NevH6+++ip+fn6sXLky0SWu6U2ePHl49dVX2blzJ4cPH+aGG24gT548NGjQwOvSkrV//3569uyZbE/NhdDA1HTm7AASdwomqcGqOjUjIhLj2muvpV+/fl6XcVEaNWrk+/6PP/7wsJKUKVq0KC1atEiVfSmEpDNvvPFGkoNQzw4iRYoUoU+fPl6WKiIickkUQtKZBx54AIi5X8jZPR1xQaRIkSK+9URERDKqFI0Jcc41ds797pzb7JxLNDTYxRgau3y9c65a7PyKzrmIeK//nHM9Uvk9ZCplypQ550hu5xx9+vShTJkyaVyZiIhI6jpvT4hzzg/4ALgd2AGscs7NMLMN8VZrAlSIfdUCPgJqmdnvQEi8/ewEpiEiIiJZXkp6QmoCm83sLzM7DUwCzr7g+S5gXOyVOMuBQs654met0wD408z05DUREUkVl/uhn35+fgnuEzJgwIBLKTdJrVq1SvI+JylRtmxZDhw4cMHbDR8+nHHjxgEwZsyYFN2C/bbbbuPQoUMX3Na5pGRMSElge7zpHcT0dpxvnZLA7njz2gATk2vEOdcF6AIxo5xFRETOZ/z48bz44oscOHAg0VWD8a82BC5qMP+5nh0TJyoqKsGt2M+ePtd2GzduJCoqivLly19wbZeiW7duvu/HjBlDQEAAJUqUOOc2Dz74IB9++GGqXhSRkp6QpAYnnB05z7mOcy4n0ByYklwjZjbCzELNLDTuYT4iIiLn0rt37yTvo3T27Q5S+6GfZcuW5bXXXuPmm29mypQpiaYnTpxIYGAgAQEBPP/8877t8ufPT9++falVqxbLli1jwoQJvrupfvTRRzz33HO+dceMGcP//vc/ICZs1axZk5CQELp27UpUVFSimgYPHkxAQAABAQG+4AUwbtw4goKCCA4O5sEHHwTglVde4Z133mHq1KmsXr2adu3aERISwrfffkvLli19286dO5e7774bgObNmzNxYrJ9CRcnqTuYxX8BdYA58aZfAF44a52Pgbbxpn8Hisebvgv4/nxtxb10x1QREUnpHVPj32E67s7SZ09frGzZsllwcLDvNWnSJDMzK1OmjL311lu+9eJP79y500qXLm379u2zM2fOWP369W3atGlmZgbYF1984dvulltusfXr15uZ2b59++y6667zLWvcuLEtWrTINmzYYM2aNbPTp0+bmdmjjz5qY8eO9bW7f/9+W716tQUEBNjRo0ftyJEjVqVKFfvpp5/sl19+sRtuuMH2799vZmYHDx40M7OXX37ZBg4caGZm9erVs1WrVvmOZcWKFW3fvn1mZta2bVubMWOGr6brr7/eDhw4cM5jdiF3TE3J6ZhVQAXnXDliBpa2Ae4/a50ZwBPOuUnEnKr518zin4ppyzlOxYiIiFyss++jFNcLkBoP/TzX6Zi4h8edPb1q1SrCwsKI69Vv164dCxcupEWLFvj5+XHPPff4ttm9e7dvvaJFi1K+fHmWL19OhQoV+P3337npppv44IMPWLNmDTVq1ABinmdTrFixBG0vXryYli1b+p7ke/fdd7No0SKcc7Rq1cr3FOErr7zynO/XOceDDz7I+PHj6dixI8uWLfONHQEoVqwYu3bt4qqrrjrnflLqvCHEzCKdc08AcwA/YJSZ/eqc6xa7fDgwC7gD2AwcBzrGe0N5ibmypmuqVCwiInKWuCAS/zTE5b6zdNwH/tnTdo5Ha+TOnTvBeJE8efJw8uRJ33Tr1q2ZPHkylSpVomXLljjnMDPat2/Pm2++mex+k2vTzC74GHTs2JE777yT3Llzc++995I9+/9HhZMnT5InT54L2t+5pOg+IWY2y8xuMLPrzKx/7LzhsQGE2N6Wx2OXB5rZ6njbHjezq8zs31SrWkREJB6LHQMSn1fP2qpVqxYLFizgwIEDREVFMXHiROrVq5fkupUrV2bz5s2+6bvvvpuvv/6aiRMn+npWGjRowNSpU9m3bx8A//zzT6KrfW655Ra+/vprjh8/zrFjx5g2bRp169alQYMGTJ48mYMHD/q2PVuBAgU4cuSIb7pEiRKUKFGCfv360aFDB998M2PPnj2ULVv2oo5LUvQAOxERydDiAsjleOjniRMnElyi26tXovt1JlK8eHHefPNN6tevT3BwMNWqVfMNPj1b06ZNCQ8P900XLlyYKlWqsHXrVmrWrAlAlSpV6NevHw0bNiQoKIjbb7+d3bt3J9hPtWrV6NChAzVr1qRWrVp07tyZqlWr4u/vT58+fahXrx7BwcFJPtCvQ4cOdOvWjZCQEE6cOAHEnEIqXbo0VapU8a23Zs0aateunaBn5JIlNVDE65cGpoqISEoGpiY3CDU1B6deTsePH7datWpZZGSk16Uk8Pjjj9snn3ySYN6TTz5p8+bNO++2qT0wVUREJF3K6A/9zJMnD6+++io7d+5MN/fIql69Ovny5WPQoEEJ5gcEBNCgQYNUbUshREREMqzM8NDPRo0aeV1CAmvWrEly/iOPPJLqbSmEiIhIumXnuboj7qGfyYl76KekDbvA8TcamCoiIulS7ty5OXjwoCdXuMiFMzMOHjxI7ty5U7yNekJERCRdKlWqFDt27GD//v1elyIplDt3bkqVKpXi9RVCREQkXcqRIwflypXzugy5jHQ6RkRERDyhECIiIiKeUAgRERERTyiEiIiIiCcUQkRERMQTCiEiIiLiCYUQERER8YRCiIiIiHhCIUREREQ8oRAiIiIinlAIEREREU8ohIiIiIgnFEJERETEEwohIiIi4gmFEBEREfGEQoiIiIh4QiFEREREPKEQIiIiIp5QCBERERFPKISIiIiIJxRCRERExBMKISIiIuIJhRARERHxhEKIiIiIeEIhRERERDyhECIiIiKeUAgRERERTyiEiIiIiCcUQkRERMQTCiEiIiLiiRSFEOdcY+fc7865zc65Xkksd865obHL1zvnqsVbVsg5N9U5t9E595tzrk5qvgERERHJmM4bQpxzfsAHQBOgCtDWOVflrNWaABViX12Aj+Itew+YbWaVgGDgt1SoW0RERDK4lPSE1AQ2m9lfZnYamATcddY6dwHjLMZyoJBzrrhzriBwC/ApgJmdNrPDqVe+iIiIZFQpCSElge3xpnfEzkvJOuWB/cBo59xa59wnzrl8STXinOvinFvtnFu9f//+FL8BERERyZhSEkJcEvMshetkB6oBH5lZVeAYkGhMCYCZjTCzUDMLLVq0aArKEhERkYwsJSFkB1A63nQpYFcK19kB7DCzFbHzpxITSkRERCSLS0kIWQVUcM6Vc87lBNoAM85aZwbwUOxVMrWBf81st5ntAbY75yrGrtcA2JBaxYuIiEjGlf18K5hZpHPuCWAO4AeMMrNfnXPdYpcPB2YBdwCbgeNAx3i7+B8wITbA/HXWMhEREcminNnZwzu8FxoaaqtXr/a6DBEREUkFzrk1ZhZ69nzdMVVEREQ8oRAiIiIinlAIEREREU8ohIiIiIgnFEJERETEEwohIiIi4gmFEBEREfGEQoiIiIh4QiFEREREPKEQIiIiIp5QCBERERFPKISIiIiIJxRCRERExBMKISIiIuIJhRARERHxhEKIiIiIeEIhRERERDyhECKpYuvWrfTv3x8zS3K5mdG/f3+2bt2axpWJiEh6pRAiqWL8+PG8+OKL9OzZM1EQMTN69uzJiy++yPjx4z2qUERE0pvsXhcgmUPv3r05cOAAQ4YMAWDw4ME453wBZMiQIfTo0YPevXt7W6iIiKQbCiGSKpxzDB48GCBBEIkfQOKCiYiICCiESCo6O4jEhREFEBERSYpLbiChl0JDQ2316tVelyEXyczIlu3/hxtFR0crgIiIZGHOuTVmFnr2fA1MlVQVNwYkvqQGq4qIiCiESKo5exBqdHQ0PXr0YMiQIQoiIiKSiMaESKo4O4DEjQFJarCqTs2IiAgohEgqeeONN5K8CubsIFKkSBH69OnjZakiIpJOKIRIqnjggQeAmPuFnN3TERdEihQp4ltPREREV8eIiIjIZaWrY0RERCRdUQgRERERTyiEiIiIiCcUQkRERMQTCiEiIiLiCYUQERER8YRCiIiIiHhCIUREREQ8oRAiIiIinkhRCHHONXbO/e6c2+yc65XEcuecG/p/7d17eFX1ne/xzxcoUi/HywSTQEhAiygVLxABpdKpFUUFKa0KMoBSBLHaY4rjLaRV5yGcPlNlomNHuQzHgchQK4JIkcs4c7S1liFRqyA6BjQawZKIQrgImP09f2SHxrCTbCXZv72T9+t59gN7rd9mfbKM2Z+s9VtrR9e/YWb9661738zeNLPXzYzboAIAAElxfHaMmXWU9GtJwyRVSNpgZivc/a16w66Q1Dv6GCTpseifdb7n7lUtlhoAAKS8eI6EDJRU5u5b3f2gpCWSRjUYM0rSQq/1J0knmVlmC2cFAABtSDwlpLukD+s9r4gui3eMS1prZqVmNrWxjZjZVDMrMbOSysrKOGIBAIBUFk8JsRjLGn70blNjhrh7f9WesrnVzIbG2oi7z3X3XHfP7dq1axyxAABAKounhFRI6lHveZakbfGOcfe6P3dIWqba0zsAAKCdi6eEbJDU28x6mVlnSWMlrWgwZoWkidGrZAZL2uXu283sODM7QZLM7DhJl0na2IL5AQBAimr26hh3/8LMbpO0RlJHSQvcfZOZTYuuf1zSKklXSiqTtE/SpOjL0yUtM7O6bS1299Ut/lUAAICUY+4Np3eEl5ub6yUl3FIEAIC2wMxK3T234XLumAoAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCDiKiFmNtzM3jGzMjO7J8Z6M7NHouvfMLP+DdZ3NLPXzGxlSwUHAACprdkSYmYdJf1a0hWS+kq63sz6Nhh2haTe0cdUSY81WH+7pM1HnRYAALQZ8RwJGSipzN23uvtBSUskjWowZpSkhV7rT5JOMrNMSTKzLElXSZrfgrkBAECKi6eEdJf0Yb3nFdFl8Y4pknSXpEhTGzGzqWZWYmYllZWVccQCAACpLJ4SYjGWeTxjzGyEpB3uXtrcRtx9rrvnuntu165d44gFAABSWTwlpEJSj3rPsyRti3PMEElXm9n7qj2Nc4mZFX/ttAAAoM2Ip4RskNTbzHqZWWdJYyWtaDBmhaSJ0atkBkva5e7b3f1ed89y957R1/2nu49vyS8AAACkpk7NDXD3L8zsNklrJHWUtMDdN5nZtOj6xyWtknSlpDJJ+yRNar3IAACgLTD3htM7wsvNzfWSkpLQMQAAQAsws1J3z224nDumAgCAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEoN0qLy9XYWGh3D3mendXYWGhysvLE5wMANqHuEqImQ03s3fMrMzM7omx3szskej6N8ysf3R5FzP7bzP7s5ltMrMHWvoLAL6u4uJiFRQUaPr06UcUEXfX9OnTVVBQoOLi4kAJAaBt69TcADPrKOnXkoZJqpC0wcxWuPtb9YZdIal39DFI0mPRPw9IusTd95jZNyT9wcyed/c/tfDXAXxl+fn5qqqqUlFRkSRp9uzZMrPDBaSoqEh5eXnKz88PGxQA2qhmS4ikgZLK3H2rJJnZEkmjJNUvIaMkLfTaXyf/ZGYnmVmmu2+XtCc65hvRR+xj30CCmZlmz54tSV8qIvULSF0xAQC0vHhKSHdJH9Z7XqHaoxzNjekuaXv0SEqppG9J+rW7r//6cYGW1bCI1JURCggAtL545oTE+inc8GhGo2Pcvcbdz5OUJWmgmZ0dcyNmU82sxMxKKisr44gFtIz6RaQOBQQAWl88JaRCUo96z7MkbfuqY9z9M0n/T9LwWBtx97nunuvuuV27do0jFtAy6uaA1BdrsioAoGXFU0I2SOptZr3MrLOksZJWNBizQtLE6FUygyXtcvftZtbVzE6SJDP7pqRLJb3dcvGBo9NwEmokElFeXp6KioooIgDQypqdE+LuX5jZbZLWSOooaYG7bzKzadH1j0taJelKSWWS9kmaFH15pqR/i84L6SDpKXdf2fJfBvDVNSwgdadgYk1W5dQMALS8eCamyt1XqbZo1F/2eL2/u6RbY7zuDUnnH2VGoFXMmjUr5lUwDYtIWlqaZsyYETIqALRJcZUQoC0aP368pNr7hTQ80lFXRNLS0g6PAwC0LEvGc965ubleUlISOgYAAGgBZlbq7rkNl/PZMQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgKCEAACAISggAAAiCEgIAAIKghAAAgCDiKiFmNtzM3jGzMjO7J8Z6M7NHouvfMLP+0eU9zOy/zGyzmW0ys9tb+gsAAACpqdkSYmYdJf1a0hWS+kq63sz6Nhh2haTe0cdUSY9Fl38h6Q53P0vSYEm3xngtAABoh+I5EjJQUpm7b3X3g5KWSBrVYMwoSQu91p8knWRmme6+3d1flSR3r5a0WVL3FswPAABSVDwlpLukD+s9r9CRRaLZMWbWU9L5ktbH2oiZTTWzEjMrqaysjCMWAABIZfGUEIuxzL/KGDM7XtJSSXnuvjvWRtx9rrvnuntu165d44gFAABSWTwlpEJSj3rPsyRti3eMmX1DtQXkSXd/5utHBQAAbUk8JWSDpN5m1svMOksaK2lFgzErJE2MXiUzWNIud99uZibpXyVtdvfZLZocAACktE7NDXD3L8zsNklrJHWUtMDdN5nZtOj6xyWtknSlpDJJ+yRNir58iKQJkt40s9ejy/LdfVWLfhUAACDlmHvD6R3h5ebmeklJSegYAACgBZhZqbvnNlzOHVMBAEAQlBAAABAEJQQAAARBCQEAAEFQQgAAQBCUEAAAEAQlBAAABEEJAQAAQVBCAABAEJQQAAAQBCUEAAAEQQkBAABBUEIAAEAQlBAgxZSXl6uwsFCNfQK2u6uwsFDl5eUJTgYAXw0lBEgxxcXFKigo0PTp048oIu6u6dOnq6CgQMXFxYESAkB8OoUOAOCryc/PV1VVlYqKiiRJs2fPlpkdLiBFRUXKy8tTfn5+2KAA0AxKCJBizEyzZ8+WpC8VkfoFpK6YAEAyo4QAKahhEakrIxQQAKnEGpvcFlJubq6XlJSEjgEkPXdXhw5/ndoViUQoIACSjpmVuntuw+VMTAVSVN0ckPpiTVYFgGRFCQFSUMNJqJFIRHl5eSoqKqKIAEgZzAkBUkzDAlI3ByTWZFVOzQBIZpQQIMXMmjUr5lUwDYtIWlqaZsyYETIqADSJEgKkmPHjx0uqvV9IwyMddUUkLS3t8DgASFZcHQMAAFoVV8cAAICkwukYAAl16NAhPf/883rvvfd0wgknaMSIETr11FNDxwIQAEdCACTMwoULlZOTo1/96lcqKyvT2rVr1adPH02ZMkX79+8PHQ9AgnEkBEBCzJ8/X4WFhfrd736n888///DyTz/9VLfeeqtGjRqlVatWqVMnfiwB7QVHQgC0uj179ujuu+/W6tWrv1RAJOnkk0/WwoULVV1drWXLlgVKCCAESgiAVveb3/xGQ4cOVZ8+fWKu79Spk372s5/p8ccfT3AyACFx3BNIURUVFZo7d67++Mc/yt01aNAg3XzzzcrJyQkd7QibN2/WRRdd1OSYIUOGKC8vLzGBvqL9+/dryZIleuaZZ7R792716tVLkydP1ne+852kvitteXm55syZo/Xr18vMdNFFF2nq1KnKysoKHa1R7q4XX3xRCxYsUHl5uU488URdc801uu6669SlS5fQ8Rq1d+9eLV68WMuXL9fevXt12mmnacqUKRo8eHBSf49s3bpVc+bM0YYNG9ShQwcNHTpUU6ZMUWZmZkK2z5EQIAXNmzdP55xzjnbu3Kk777xTd999t/bv36/+/fvrkUceCR3vCMccc4yqq6ubHFNdXa1jjjkmQYni9+abb6pPnz5aunSpJkyYoPvvv1/nnXeebrrpJo0ePTppJ9T+8z//s/r37699+/bp7rvv1p133qlPP/1U55xzjubOnRs6Xkx79+7VlVdeqZ/85Ce64IILdP/992vcuHFavHixzjrrLG3evDl0xJhKS0t1xhlnaOXKlZo0aZLuu+8+9e3bVxMmTNCYMWN04MCB0BFjevDBBzVw4EDV1NTo3nvv1d///d9r+/bt+va3v62FCxcmJoS7J91jwIABDiC2lStXeo8ePfzdd989Yt3777/vPXv29N/+9rcBkjXu97//vffu3dtramoaHfOLX/zCb7311gSmal5lZaV369bNFy9efMS6AwcO+LXXXuvjx48PkKxpTz/9tPfs2dPfe++9I9a9++673qNHD3/uuecSH6wZ11xzjY8fP94PHTp0xLoFCxZ4dna2f/bZZwGSNW7btm2ekZHhS5cuPWLd/v37/eqrr/apU6cGSNa0RYsWee/evb2iouKIdZs3b/Zu3br5unXrWmx7kko8xvt98MIR60EJARp34YUX+rJlyxpdv2bNGj/33HM9EokkLlQzIpGIDxgwwB9++OGY699++23v2rWrb9q0KcHJmvbLX/7Sb7zxxkbX79271//mb/7Gt2zZksBUTYtEIn7uuef66tWrGx2zfPlyHzx4cAJTNe+tt97yjIwM//zzzxsdM2bMmEa/h0L5xS9+4bfcckuj63ft2uUnn3xyzDf7UCKRiJ9xxhn+4osvNjpm8eLFfskll7TYNikhQBuwdetWT09Pj/mbYp2amhrPycnxjRs3JjBZ87Zs2eI5OTk+depU37hxo0ciEd+5c6cXFRV5RkaGP/HEE6EjHqFfv37+8ssvNznmpz/9qRcWFiYoUfM2btzo2dnZTR51OnTokGdkZCRVeSooKPC77rqryTH/8R//4RdccEGCEsXn9NNP91dffbXJMTfddJPPnj07QYmat2HDBj/jjDOa/EXlwIEDfsopp/hHH33UIttsrIQwJwRIIZWVlerRo0eT99Lo0KGDsrOzVVlZmcBkzTvttNO0YcMGZWRk6LLLLlPnzp2VmZmp9evX69lnn9UNN9wQOuIRKisr1bNnzybH5OTkJNW+rqqqUk5Ojjp0aPzHe6dOnZSVlZVUuePZ1z179kyqzFLt/k7F75GePXs2OWG27v/PqqqqVs1CCQFSSHp6usrLy3Xo0KFGx9TU1Oi9995TRkZGApPFp2vXrnrggQf00Ucfae/evdq/f78WL16sgQMHho4WU0ZGhsrKypocs2XLFqWnpycoUfPS09P13nvvqaamptExhw4d0gcffJBUuePZ12VlZUn3fZ2enh7X90gy5U5PT9eWLVtqT4c04vPPP9e2bdta/SMV4iohZjbczN4xszIzuyfGejOzR6Lr3zCz/vXWLTCzHWa2sSWDA+1RTk6OzjrrrCZv6vX8888rMzNTZ555ZgKTfXWdO3dO6ksXJWnChAmaM2dOo+urq6u1ZMkSjRs3LoGpmnbmmWcqMzNTq1atanTM8uXLdeaZZzb7G3wi/d3f/Z0WLVrU5NVGc+bM0cSJExOYqnkTJ05s8nvk008/1fLlyzVmzJgEpmraeeedpy5duuiFF15odMxvfvMbDRw4sPXLU6xzNPUfkjpK2iLpNEmdJf1ZUt8GY66U9LwkkzRY0vp664ZK6i9pY3PbcuaEAM1at26dZ2Zmxpzz8c4773hWVpavWLEiQLK2Z+fOnZ6dne3z5s07Yt2+fft8xIgRPmXKlADJmvbcc895VlaWv/3220es27hxo2dmZvratWsDJGva+PHj/Yc//GHMyamPPPKIn3baab579+4AyRq3Y8cO7969uy9atOiIdXv27PFhw4b57bffnvhgzXjqqac8Jycn5ryg1157zdPT0/2ll15qse2pkTkh8dysbKCkMnffKklmtkTSKElv1RszStLC6Ib+ZGYnmVmmu29395fMrOfRVSWgde3evVurV6/Wrl27lJ2dre9///tJ+xkml156qR588EFdfPHFGjlypK6++mqZmVatWqWlS5fqoYce0siRI0PHbBNOPvlkrVu3TldddZUWLVqkG264QWlpaXrjjTc0d+5cDR06VI8++mjomEcYMWKEKisrNXjwYP3whz/UVVddJXfXc889p2effVaPPvqohg0bFjrmEebNm6eJEyeqT58+mjp1qvr166ePP/5YTzzxhHbu3Kl169bphBNOCB3zS7p27ao1a9ZoxIgRWrBggSZOnKhTTjlFr776qubNm6fhw4frwQcfDB3zCNdee62qqqo0YMAAXXfddRo+fLhqamq0fPlyrVq1SnPnztXFF1/c6jnMmzgnJElmdo2k4e5+U/T5BEmD3P22emNWSvqlu/8h+vwFSXe7e0n0eU9JK9397Ca2M1XSVEnKzs4eUF5efjRfFxCXQ4cOKT8/X/Pnz9eQIUOUnp6ujRs36uOPP9bMmTM1YcKE0BEb9cknn2jBggV6+eWX5e668MIL9eMf/7jVz+G2R4cOHdKzzz6rpUuXqrq6+vAdU88777zQ0Zq0Y8cOLViwQK+88orMTEOGDNGkSZOUlpYWOlqTSktLv3TH1GuvvVYjRoxI2l8MJOngwYN65plntHz5cu3Zs0enn366pkyZorPPbvRtLyl8/PHHmj9//pfumHrjjTfq5JNPbtHtmFmpu+cesTyOEnKtpMsblJCB7v7TemN+J+n/NCghd7l7afR5TzVTQurLzc31kpKSuL4w4OuKRCK6/vrrVV1drfnz56tbt26H123YsEFjxozR3XffrZtvvjlgSgBIfY2VkHhqZYWkHvWeZ0na9jXGAEll7dq12rRpk0pKSo74TIoLLrhAa9as0cCBAzV27FideOKJgVICQNsVz9UxGyT1NrNeZtZZ0lhJKxqMWSFpYvQqmcGSdrn79hbOCrSoOXPmKC8vr9EPxerdu7eGDRumJ598MsHJAKB9aLaEuPsXkm6TtEbSZklPufsmM5tmZtOiw1ZJ2iqpTNI8ST+pe72Z/bukVyT1MbMKM5vcwl8D8LVs3Lix2YlX3/3ud/Xmm28mKBEAtC9xzfJx91WqLRr1lz1e7+8u6dZGXnv90QQEWkvnzp21b9++Jsfs27dPnTt3TlAiAGhfuGMq2q3LLrtMTz31VKPr3V1LlizR8OHDE5gKANoPSgjarVtuuUXz58/X22+/HXP9k08+qerqal1++eUJTgYA7QMlBC3O3fX5558rEomEjtKkM844Qw899JAuueQSPfbYY6qurpYklZeX66677tKdd96ppUuXNvlBYACAr4+frmgxVVVVuu+++5SVlaUTTzxRXbp00Y9+9CP9/ve/Dx2tURMnTtTTTz+tF154QaeeeqpOPPFEnX/++Tp06JDWr1+vfv36hY7YZpSXl6uwsLDRD81ydxUWFoobFQLtByUELeKDDz7QoEGD9NFHH2nNmjU6cOCAPvnkEw0bNkzXX3+9HnvssdARG3XRRRfp6aef1q5du1ReXq7Kykr90z/9k7Kzs0NHa1OKi4tVUFCg6dOnH1FE3F3Tp09XQUGBiouLAyUEkGjJew9cpJRx48bp5ptv1l133XV42QknnKBp06bp8ssv10UXXaRBgwapf//+TfwrYXXu3JkrYVpRfn6+qqqqVFRUJEmaPXu2zOxwASkqKlJeXp7y8/PDBgWQMJQQHLXS0lJVVFTojjvuiLm+V69eysvL06OPPqoFCxYkOB2ShZlp9uzZkvSlIlK/gNQVEwDtAyUER+3555/Xddddp44dOzY6ZuzYsRo0aFACUyEZNSwidWWEAgK0T8wJwVE7cOCAjj/++CbHHH/88Tpw4ECCEiGZ1S8idSggQPtECcFR69u3r/7whz80Oebll1/WWWedlaBESGZ1c0DqizVZFUDbRwnBURs9erRef/11vf766zHX19TU6KGHHtK0adNirkf70XASaiQSUV5enoqKiigiQDvEnBActS5duqioqEgjR47Ub3/7Ww0ePPjwus8++0y33367OnTooLFjxwZMidAaFpC6UzCxJqtyagZoHyghSWr37t0qLi7WSy+9pEgkogsuuECTJk1SWlpa6GgxjRs3Tp06ddKYMWOUkZGhAQMGaOfOnVqzZo1Gjx6tlStXcvlrOzdr1qyYV8E0LCJpaWmaMWNGyKgAEoQSkoRWrlypG2+8Ud/73vc0atQodezYUWvXrlXv3r314IMPavLkyaEjxnTdddfpRz/6kdatW6eysjIdd9xxevjhh5Wenh46GpLA+PHjJdXeL6ThkY66IpKWlnZ4HIC2z5LxHGxubq6XlJSEjhHEK6+8olGjRmnlypUaOHDgl9b9z//8jy699FI9/PDDGj16dKCEAAB8NWZW6u65DZczMTXJzJw5U7NmzTqigEi1H7g2b9483X///UzgAwCkPEpIEtmxY4f++Mc/aty4cY2OGTZsmPbu3as///nPCUwGAEDLo4QkkR07digzM1PHHntso2M6dOigb33rW9q2bVsCkwEA0PIoIUnklFNO0V/+8hcdPHiw0THurg8//DBpr5IBACBelJAk0q1bN/Xr10/Lli1rdMwrr7yigwcPKjf3iPk9AACkFEpIkrn33nt1xx13qKys7Ih1H3/8sW666Sbde++96tCB/3QAgNTGfUKSzOWXX64HHnhAgwYN0oQJE/SDH/xAHTt21Jo1azRv3jzddttt+vGPfxw6JgAAR41fp5PQ5MmT9dprr+m4447Tz3/+c91zzz3as2ePXnzxRf385z8PHQ9oN8rLy1VYWNjoJfHursLCQpWXlyc4GdA2cCQkSWVnZ6uwsDB0DKBdKy4uVkFBgaqqqo74TJv6n4UjiVvNA18DJQQAGpGfn6+qqqojPlyv4Yfx5efnhw0KpChKCAA0orFP+Y31acAAvjpKCAA0oWERqSsjFBDg6DExFQCaUb+I1EnmAsKEWqQKSggANKNuDkh906dPT9oPkqybUBsrY93XUlBQoOLi4kAJgVqUEABoQsNJqJFIRHl5eSoqKkraIpKfnx8zIxNqkWyYEwIAjWj4pl13CibWZNVkOjXDhFqkDHdPuseAAQMcAEKbOXOmS/K8vDyPRCJfWheJRDwvL88l+cyZMwMlbFr9jHWPWF9Lsnj//fd95syZjeaLRCI+c+ZMf//99xOcrO1J9L6WVOIx3u+DF45YD0oIgGTQFt4UI5HIl0pIshYQ99Qvfakk0fuaEgIA7UyqHQmpn7d+zsaW4+tL9L6mhABAOxLrzSQV3shTNXcqSuS+btclpKamxtevX++rV6/2jRs3tui/DQDJJtWPKKTaEZxUlqh93VgJsdp1ySU3N9dLSkqO6t8oLy/XokWLlJaWpn/8x3/UN7/5TXXr1k3vvPOOMjIy9A//8A8qLS3V+PHjlZOT00LJASC8wsJCFRQUxLwKxv2vV/zMnDkzaT94z93VocNf7yIRiUSS8mqe8vJyFRcXKz8/P2Y+d9esWbOS+r0mEfvazErdPTfmxpPt0RJHQuom3aSlpfkrr7xyuNV98cUXvnz5cj/uuOOY4ASgTUr1CbWpdCQk1SfThj4SElcpkDRc0juSyiTdE2O9SXokuv4NSf3jfW2sR0uUkJKSksNFo7HDkcccc4zv2rXrqLcFAGgZqTYnJJVPfaXEnBBJHSVtkXSapM6S/iypb4MxV0p6PlpGBktaH+9rYz1aooRMnjzZZ86c2eQOHj16tP/Lv/zLUW8LAHD0UvUNPdWKk3sKXR0j6UJJa+o9v1fSvQ3GzJF0fb3n70jKjOe1sR4tUULOOeccLy0tbfJQ07x583zSpElHvS0AwNFL5VMbqXQKyT157hMSz23bu0v6sN7zCkmD4hjTPc7XSpLMbKqkqZKUnZ0dR6ymdejQQTU1NYdvX1x362Lpr7dYrqmp+dJkHABAOOPHj5ekmJM8636Wp6WlHR6XTJp6r0lGybKv43kHjrUHG15S09iYeF5bu9B9rrvnuntu165d44jVtIsvvlgrVqw4PBO8vroPdHr22Wf1ne9856i3BQA4ejk5OZoxY0ajb9xmphkzZiTlVSZNvdcko2TZ1/GUkApJPeo9z5K0Lc4x8by2Vdxyyy16/PHHNWXKlJiffjlmzBht2LBBY8aMSUQcAEAbVVdAUumTlpNGrHM0/uX5Hp0kbZXUS3+dXPrtBmOu0pcnpv53vK+N9WiJOSGRSMSHDh3qknzkyJF+8OBBd3evrq72Sy65xCX56NGjk/Z8HQAg+aXqZNpEUyNzQpo9EuLuX0i6TdIaSZslPeXum8xsmplNiw5bFS0bZZLmSfpJU6/9uoXpq5g1a5ZeeukljRw5Ujt27FD37t3Vr18/9ejRQ8cee6zGjh2rZcuWadasWYmIAwBog2bNmnX4CEj9OSB18yrqjojwXhNbPBNT5e6rVFs06i97vN7fXdKt8b42ERpOuvnggw/02WefKSMjQ6eeeqrcXWeffXZSTnACAKSGZJngmara7G3bAQBAcmjstu1cnwoAAIKghAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAACAICghAAAgCEoIAAAIghICAACCoIQAAIAgkvK27WZWKam8Ff7pNElVrfDvIjb2d+KwrxOHfZ1Y7O/Eac19nePuXRsuTMoS0lrMrCTWvevROtjficO+Thz2dWKxvxMnxL7mdAwAAAiCEgIAAIJobyVkbugA7Qz7O3HY14nDvk4s9nfiJHxft6s5IQAAIHm0tyMhAAAgSVBCAABAEO2mhJjZcDN7x8zKzOye0HnaKjPrYWb/ZWabzWyTmd0eOlNbZ2Ydzew1M1sZOktbZ2YnmdnTZvZ29Hv8wtCZ2ioz+1n0Z8hGM/t3M+sSOlNbYmYLzGyHmW2st+wUM1tnZu9G/zy5tXO0ixJiZh0l/VrSFZL6SrrezPqGTdVmfSHpDnc/S9JgSbeyr1vd7ZI2hw7RTjwsabW7nynpXLHfW4WZdZf0vyXluvvZkjpKGhs2VZvzhKThDZbdI+kFd+8t6YXo81bVLkqIpIGSytx9q7sflLRE0qjAmdokd9/u7q9G/16t2h/S3cOmarvMLEvSVZLmh87S1pnZ/5I0VNK/SpK7H3T3z4KGats6SfqmmXWSdKykbYHztCnu/pKknQ0Wj5L0b9G//5ukH7R2jvZSQrpL+rDe8wrxxtjqzKynpPMlrQ8cpS0rknSXpEjgHO3BaZIqJf3f6Omv+WZ2XOhQbZG7fyTpQUkfSNouaZe7rw2bql1Id/ftUu0vlJJObe0NtpcSYjGWcW1yKzKz4yUtlZTn7rtD52mLzGyEpB3uXho6SzvRSVJ/SY+5+/mS9ioBh6vbo+hchFGSeknqJuk4MxsfNhVaQ3spIRWSetR7niUO7bUaM/uGagvIk+7+TOg8bdgQSVeb2fuqPcV4iZkVh43UplVIqnD3uiN7T6u2lKDlXSrpPXevdPdDkp6RdFHgTO3BX8wsU5Kif+5o7Q22lxKyQVJvM+tlZp1VO8FpReBMbZKZmWrPmW9299mh87Rl7n6vu2e5e0/Vfk//p7vz22IrcfePJX1oZn2ii74v6a2AkdqyDyQNNrNjoz9Tvi8mASfCCkk3RP9+g6RnW3uDnVp7A8nA3b8ws9skrVHtLOsF7r4pcKy2aoikCZLeNLPXo8vy3X1VuEhAi/mppCejv8xslTQpcJ42yd3Xm9nTkl5V7RV3r4nbt7coM/t3SX8rKc3MKiTdJ+mXkp4ys8mqLYLXtnoObtsOAABCaC+nYwAAQJKhhAAAgCAoIQAAIAhKCAAACIISAgAAgqCEAEi46KfR/iR0DgBhUUIAhHCSJEoI0M5RQgCE8EtJp5vZ62b2q9BhAITBzcoAJFz0E5ZXuvvZobMACIcjIQAAIAhKCAAACIISAiCEakknhA4BICxKCICEc/dPJL1sZhuZmAq0X0xMBQAAQXAkBAAABEEJAQAAQVBCAABAEJQQAAAQBCUEAAAEQQkBAABBUEIAAEAQ/x84RNYJEW+jPwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = 9.81\n",
    "c = 1\n",
    "m = 1\n",
    "a = 0\n",
    "b = 10\n",
    "n = 10\n",
    "h1 = (b-a)/n\n",
    "r = 3\n",
    "\n",
    "t = [0]\n",
    "for i in range (0,n):\n",
    "    t.append(t[i] + h1)\n",
    "t = list(np.around(np.array(t),r))\n",
    "\n",
    "#velocity na hinihingi sa problem\n",
    "v = [20]\n",
    "for i in range(0,n):\n",
    "    h = h1\n",
    "    F1 = h*(g - (c/m)*(v[i]))\n",
    "    F2 = h*(g - (c/m)*(v[i] + F1/2))\n",
    "    F3 = h*(g - (c/m)*(v[i] + F2/2))\n",
    "    F4 = h*(g - (c/m)*(v[i] + F3))\n",
    "    v.append(v[i] + (F1 + 2*F2 + 2*F3 + F4)/6)\n",
    "v= list(np.around(np.array(v),r))\n",
    "\n",
    "#velocity na kelangan sa y-values\n",
    "v1 = [20]\n",
    "for i in range(0,2*n+2):\n",
    "    h = h1/2\n",
    "    F_1 = h*(g - (c/m)*(v1[i]))\n",
    "    F_2 = h*(g - (c/m)*(v1[i] + F_1/2))\n",
    "    F_3 = h*(g - (c/m)*(v1[i] + F_2/2))\n",
    "    F_4 = h*(g - (c/m)*(v1[i] + F_3))\n",
    "    v1.append(v1[i] + (F_1 + 2*F_2 + 2*F_3 + F_4)/6)\n",
    "v1= list(np.around(np.array(v1),r))\n",
    "\n",
    "# y-values na hinihingi sa problem\n",
    "y = [0]\n",
    "for i in range(0,n):\n",
    "    F = []\n",
    "    for j in range(0,2*n,2):\n",
    "        h = h1\n",
    "        f1 = h*(v1[j])\n",
    "        f2 = h*(v1[j+1])\n",
    "        f4 = h*(v1[j+2])\n",
    "        F.append((f1 + 4*f2 + f4)/6)\n",
    "    y.append(y[i] + F[i])\n",
    "y= list(np.around(np.array(y),r))\n",
    "\n",
    "#exact solution\n",
    "x=np.linspace(a,b,n+1)\n",
    "y0=(m*g/c)*x + (20-(m*g/c))*(1-np.exp(-x*c/m))*(m/c)\n",
    "y0= list(np.around(np.array(y0),r))\n",
    "v0=20*np.exp(-x*c/m) + (m*g/c)*(1-np.exp(-x*c/m))\n",
    "v0= list(np.around(np.array(v0),r))\n",
    "\n",
    "E_v = []\n",
    "for i in range(0,n+1):\n",
    "    E_v.append(v[i]-v0[i])\n",
    "    \n",
    "E_y = []\n",
    "for i in range(0,n+1):\n",
    "    E_y.append(y[i]-y0[i])\n",
    "\n",
    "print(\"t: {}\".format(t))\n",
    "print(\"y_ Runge-Ketta: {}\".format(y))\n",
    "print(\"y_ exact: {}\".format(y0))\n",
    "print(\"v_Runge-Ketta: {}\".format(v))\n",
    "print(\"v_exact: {}\".format(v0))\n",
    "\n",
    "fig, axs=plt.subplots(2,1)\n",
    "fig.set_size_inches(9,15)\n",
    "axs[0].scatter(t,y,marker = '+', edgecolors='none', s=100,facecolors = 'black', label = 'y-value(Runge-Ketta)')\n",
    "axs[0].scatter(t,v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'velocity(Runge-Ketta)')\n",
    "axs[0].plot(x,y0,c='black', label = 'y-value(Exact Solution)')\n",
    "axs[0].plot(x,v0,c='black', linestyle = 'dashed', label = 'velocity(Exact Solution)')\n",
    "axs[1].scatter(t,E_y,marker = 'o', edgecolors='black', s=90,facecolors = 'none', label = 'Error(y-values)')\n",
    "axs[1].scatter(t,E_v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'Error(velocity)')\n",
    "axs[0].set_title('Runge-Ketta (step size = 1)')\n",
    "axs[1].set_title('Error (step size = 1)')\n",
    "axs[0].set(xlabel='t')\n",
    "axs[1].set(xlabel='t')\n",
    "axs[0].legend()\n",
    "axs[1].legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>When step size, h=0.5</h3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0]\n",
      "y_ Runge-Ketta: [0.0, 8.915, 16.252, 22.632, 28.432, 33.879, 39.113, 44.218, 49.244, 54.223, 59.172, 64.104, 69.025, 73.94, 78.851, 83.76, 88.667, 93.573, 98.479, 103.385, 108.29]\n",
      "y_ exact: [0.0, 8.914, 16.251, 22.631, 28.431, 33.879, 39.113, 44.217, 49.243, 54.222, 59.171, 64.103, 69.025, 73.94, 78.851, 83.759, 88.667, 93.573, 98.479, 103.384, 108.29]\n",
      "v_Runge-Ketta: [20.0, 15.993, 13.562, 12.086, 11.191, 10.648, 10.319, 10.119, 9.997, 9.924, 9.879, 9.852, 9.835, 9.825, 9.819, 9.816, 9.813, 9.812, 9.811, 9.811, 9.81]\n",
      "v_exact: [20.0, 15.991, 13.559, 12.084, 11.189, 10.646, 10.317, 10.118, 9.997, 9.923, 9.879, 9.852, 9.835, 9.825, 9.819, 9.816, 9.813, 9.812, 9.811, 9.811, 9.81]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = 9.81\n",
    "c = 1\n",
    "m = 1\n",
    "a = 0\n",
    "b = 10\n",
    "n = 20\n",
    "h1 = (b-a)/n\n",
    "r = 3\n",
    "\n",
    "t = [0]\n",
    "for i in range (0,n):\n",
    "    t.append(t[i] + h1)\n",
    "t = list(np.around(np.array(t),r))\n",
    "\n",
    "#velocity na hinihingi ni sir\n",
    "v = [20]\n",
    "for i in range(0,n):\n",
    "    h = h1\n",
    "    F1 = h*(g - (c/m)*(v[i]))\n",
    "    F2 = h*(g - (c/m)*(v[i] + F1/2))\n",
    "    F3 = h*(g - (c/m)*(v[i] + F2/2))\n",
    "    F4 = h*(g - (c/m)*(v[i] + F3))\n",
    "    v.append(v[i] + (F1 + 2*F2 + 2*F3 + F4)/6)\n",
    "v= list(np.around(np.array(v),r))\n",
    "\n",
    "#velocity na kelangan sa y-values\n",
    "v1 = [20]\n",
    "for i in range(0,2*n+2):\n",
    "    h = h1/2\n",
    "    F_1 = h*(g - (c/m)*(v1[i]))\n",
    "    F_2 = h*(g - (c/m)*(v1[i] + F_1/2))\n",
    "    F_3 = h*(g - (c/m)*(v1[i] + F_2/2))\n",
    "    F_4 = h*(g - (c/m)*(v1[i] + F_3))\n",
    "    v1.append(v1[i] + (F_1 + 2*F_2 + 2*F_3 + F_4)/6)\n",
    "v1= list(np.around(np.array(v1),r))\n",
    "\n",
    "# y-values na hinihingi ni sir\n",
    "y = [0]\n",
    "for i in range(0,n):\n",
    "    F = []\n",
    "    for j in range(0,2*n,2):\n",
    "        h = h1\n",
    "        f1 = h*(v1[j])\n",
    "        f2 = h*(v1[j+1])\n",
    "        f4 = h*(v1[j+2])\n",
    "        F.append((f1 + 4*f2 + f4)/6)\n",
    "    y.append(y[i] + F[i])\n",
    "y= list(np.around(np.array(y),r))\n",
    "\n",
    "#exact solution\n",
    "x=np.linspace(a,b,n+1)\n",
    "y0=(m*g/c)*x + (20-(m*g/c))*(1-np.exp(-x*c/m))*(m/c)\n",
    "y0= list(np.around(np.array(y0),r))\n",
    "v0=20*np.exp(-x*c/m) + (m*g/c)*(1-np.exp(-x*c/m))\n",
    "v0= list(np.around(np.array(v0),r))\n",
    "\n",
    "E_v = []\n",
    "for i in range(0,n+1):\n",
    "    E_v.append(v[i]-v0[i])\n",
    "    \n",
    "E_y = []\n",
    "for i in range(0,n+1):\n",
    "    E_y.append(y[i]-y0[i])\n",
    "\n",
    "print(\"t: {}\".format(t))\n",
    "print(\"y_ Runge-Ketta: {}\".format(y))\n",
    "print(\"y_ exact: {}\".format(y0))\n",
    "print(\"v_Runge-Ketta: {}\".format(v))\n",
    "print(\"v_exact: {}\".format(v0))\n",
    "\n",
    "fig, axs=plt.subplots(2,1)\n",
    "fig.set_size_inches(9,15)\n",
    "axs[0].scatter(t,y,marker = '+', edgecolors='none', s=100,facecolors = 'black', label = 'y-value(Runge-Ketta)')\n",
    "axs[0].scatter(t,v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'velocity(Runge-Ketta)')\n",
    "axs[0].plot(x,y0,c='black', label = 'y-value(Exact Solution)')\n",
    "axs[0].plot(x,v0,c='black', linestyle = 'dashed', label = 'velocity(Exact Solution)')\n",
    "axs[1].scatter(t,E_y,marker = 'o', edgecolors='black', s=90,facecolors = 'none', label = 'Error(y-values)')\n",
    "axs[1].scatter(t,E_v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'Error(velocity)')\n",
    "axs[0].set_title('Runge-Ketta (stepsize = 0.5)')\n",
    "axs[1].set_title('Error (step size = 0.5)')\n",
    "axs[0].set(xlabel='t')\n",
    "axs[1].set(xlabel='t')\n",
    "axs[0].legend()\n",
    "axs[1].legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>When step size, h=0.2</h3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: [0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.2, 6.4, 6.6, 6.8, 7.0, 7.2, 7.4, 7.6, 7.8, 8.0, 8.2, 8.4, 8.6, 8.8, 9.0, 9.2, 9.4, 9.6, 9.8, 10.0]\n",
      "y_ Runge-Ketta: [0.0, 3.809, 7.283, 10.484, 13.459, 16.251, 18.893, 21.411, 23.829, 26.164, 28.431, 30.643, 32.81, 34.939, 37.038, 39.113, 41.167, 43.204, 45.228, 47.24, 49.244, 51.239, 53.229, 55.214, 57.194, 59.172, 61.146, 63.118, 65.089, 67.057, 69.025, 70.992, 72.957, 74.922, 76.887, 78.851, 80.815, 82.778, 84.741, 86.704, 88.667, 90.63, 92.592, 94.554, 96.517, 98.479, 100.441, 102.404, 104.366, 106.328, 108.29]\n",
      "y_ exact: [0.0, 3.809, 7.283, 10.484, 13.459, 16.251, 18.893, 21.411, 23.829, 26.164, 28.431, 30.643, 32.81, 34.939, 37.038, 39.113, 41.167, 43.204, 45.228, 47.24, 49.243, 51.239, 53.229, 55.214, 57.194, 59.171, 61.146, 63.118, 65.088, 67.057, 69.025, 70.991, 72.957, 74.922, 76.887, 78.851, 80.814, 82.778, 84.741, 86.704, 88.667, 90.629, 92.592, 94.554, 96.516, 98.479, 100.441, 102.403, 104.365, 106.327, 108.29]\n",
      "v_Runge-Ketta: [20.0, 18.153, 16.641, 15.402, 14.389, 13.559, 12.879, 12.323, 11.867, 11.494, 11.189, 10.939, 10.734, 10.567, 10.43, 10.317, 10.225, 10.15, 10.088, 10.038, 9.997, 9.963, 9.935, 9.912, 9.894, 9.879, 9.866, 9.856, 9.848, 9.841, 9.835, 9.831, 9.827, 9.824, 9.821, 9.819, 9.818, 9.816, 9.815, 9.814, 9.813, 9.813, 9.812, 9.812, 9.812, 9.811, 9.811, 9.811, 9.811, 9.811, 9.81]\n",
      "v_exact: [20.0, 18.153, 16.641, 15.402, 14.389, 13.559, 12.879, 12.323, 11.867, 11.494, 11.189, 10.939, 10.734, 10.567, 10.43, 10.317, 10.225, 10.15, 10.088, 10.038, 9.997, 9.963, 9.935, 9.912, 9.894, 9.879, 9.866, 9.856, 9.848, 9.841, 9.835, 9.831, 9.827, 9.824, 9.821, 9.819, 9.818, 9.816, 9.815, 9.814, 9.813, 9.813, 9.812, 9.812, 9.812, 9.811, 9.811, 9.811, 9.811, 9.811, 9.81]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x1080 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g = 9.81\n",
    "c = 1\n",
    "m = 1\n",
    "a = 0\n",
    "b = 10\n",
    "n = 50\n",
    "h1 = (b-a)/n\n",
    "r = 3\n",
    "\n",
    "t = [0]\n",
    "for i in range (0,n):\n",
    "    t.append(t[i] + h1)\n",
    "t = list(np.around(np.array(t),r))\n",
    "\n",
    "#velocity na hinihingi ni sir\n",
    "v = [20]\n",
    "for i in range(0,n):\n",
    "    h = h1\n",
    "    F1 = h*(g - (c/m)*(v[i]))\n",
    "    F2 = h*(g - (c/m)*(v[i] + F1/2))\n",
    "    F3 = h*(g - (c/m)*(v[i] + F2/2))\n",
    "    F4 = h*(g - (c/m)*(v[i] + F3))\n",
    "    v.append(v[i] + (F1 + 2*F2 + 2*F3 + F4)/6)\n",
    "v= list(np.around(np.array(v),r))\n",
    "\n",
    "#velocity na kelangan sa y-values\n",
    "v1 = [20]\n",
    "for i in range(0,2*n+2):\n",
    "    h = h1/2\n",
    "    F_1 = h*(g - (c/m)*(v1[i]))\n",
    "    F_2 = h*(g - (c/m)*(v1[i] + F_1/2))\n",
    "    F_3 = h*(g - (c/m)*(v1[i] + F_2/2))\n",
    "    F_4 = h*(g - (c/m)*(v1[i] + F_3))\n",
    "    v1.append(v1[i] + (F_1 + 2*F_2 + 2*F_3 + F_4)/6)\n",
    "v1= list(np.around(np.array(v1),r))\n",
    "\n",
    "# y-values na hinihingi ni sir\n",
    "y = [0]\n",
    "for i in range(0,n):\n",
    "    F = []\n",
    "    for j in range(0,2*n,2):\n",
    "        h = h1\n",
    "        f1 = h*(v1[j])\n",
    "        f2 = h*(v1[j+1])\n",
    "        f4 = h*(v1[j+2])\n",
    "        F.append((f1 + 4*f2 + f4)/6)\n",
    "    y.append(y[i] + F[i])\n",
    "y= list(np.around(np.array(y),r))\n",
    "\n",
    "#exact solution\n",
    "x=np.linspace(a,b,n+1)\n",
    "y0=(m*g/c)*x + (20-(m*g/c))*(1-np.exp(-x*c/m))*(m/c)\n",
    "y0= list(np.around(np.array(y0),r))\n",
    "v0=20*np.exp(-x*c/m) + (m*g/c)*(1-np.exp(-x*c/m))\n",
    "v0= list(np.around(np.array(v0),r))\n",
    "\n",
    "E_v = []\n",
    "for i in range(0,n+1):\n",
    "    E_v.append(v[i]-v0[i])\n",
    "    \n",
    "E_y = []\n",
    "for i in range(0,n+1):\n",
    "    E_y.append(y[i]-y0[i])\n",
    "\n",
    "print(\"t: {}\".format(t))\n",
    "print(\"y_ Runge-Ketta: {}\".format(y))\n",
    "print(\"y_ exact: {}\".format(y0))\n",
    "print(\"v_Runge-Ketta: {}\".format(v))\n",
    "print(\"v_exact: {}\".format(v0))\n",
    "\n",
    "fig, axs=plt.subplots(2,1)\n",
    "fig.set_size_inches(9,15)\n",
    "axs[0].scatter(t,y,marker = '+', edgecolors='none', s=100,facecolors = 'black', label = 'y-value(Runge-Ketta)')\n",
    "axs[0].scatter(t,v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'velocity(Runge-Ketta)')\n",
    "axs[0].plot(x,y0,c='black', label = 'y-value(Exact Solution)')\n",
    "axs[0].plot(x,v0,c='black', linestyle = 'dashed', label = 'velocity(Exact Solution)')\n",
    "axs[1].scatter(t,E_y,marker = 'o', edgecolors='black', s=90,facecolors = 'none', label = 'Error(y-values)')\n",
    "axs[1].scatter(t,E_v,marker = 'x', edgecolors='none', s=90,facecolors = 'black', label = 'Error(velocity)')\n",
    "axs[0].set_title('Runge-Ketta(stepsize = 0.2)')\n",
    "axs[1].set_title('Error (step size = 0.2)')\n",
    "axs[0].set(xlabel='t')\n",
    "axs[1].set(xlabel='t')\n",
    "axs[0].legend()\n",
    "axs[1].legend()\n",
    "plt.show()\n"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}