diff --git a/week1/notebook.ipynb b/week1/notebook.ipynb deleted file mode 100644 index 5c1f615da1fb702467c49a43fb73285f532def59..0000000000000000000000000000000000000000 --- a/week1/notebook.ipynb +++ /dev/null @@ -1,450 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "alive-musical", - "metadata": {}, - "source": [ - "<h1 style=\"text-align: center; vertical-align: middle;\">Numerical Methods in Accelerator Physics</h1>\n", - "<h2 style=\"text-align: center; vertical-align: middle;\">Python examples -- Week 1</h2>" - ] - }, - { - "cell_type": "markdown", - "id": "failing-diamond", - "metadata": {}, - "source": [ - "<h2>Run this first!</h2>\n", - "\n", - "Imports and modules:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "expressed-airplane", - "metadata": {}, - "outputs": [], - "source": [ - "from config import *\n", - "%matplotlib inline" - ] - }, - { - "cell_type": "markdown", - "id": "seven-carol", - "metadata": {}, - "source": [ - "<h2>Phase space plots based on Lagragian (slide 21)</h2>" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "mineral-analysis", - "metadata": {}, - "outputs": [], - "source": [ - "m = 1 # point mass\n", - "g = 1 # magnitude of the gravitational field\n", - "l = 1 # length of the rod" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "forced-recommendation", - "metadata": {}, - "outputs": [], - "source": [ - "def plot_arrow(theta, p, dt=1):\n", - " # equations of motion:\n", - " dtheta = p / (m * L*L) * dt\n", - " dp = - m * g * L * np.sin(theta) * dt\n", - " \n", - " # plotting\n", - " plt.scatter([theta], [p], s=50, c='r', marker='*', zorder=10)\n", - " plt.annotate('', \n", - " xytext=(theta, p), \n", - " xy=(theta + dtheta, p + dp), \n", - " arrowprops=dict(facecolor='black', shrink=0.03))" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "artificial-picnic", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plot_arrow(1, 0)\n", - "plot_arrow(0, -1)\n", - "plot_arrow(-1, 0)\n", - "plot_arrow(0, 1)\n", - "#plot_arrow(1/1.41, 1/1.41)\n", - "\n", - "# increase momentum:\n", - "#for i in np.arange(0.4, 2.5, 0.2):\n", - "# plot_arrow(0, i)\n", - "\n", - "# increase angle:\n", - "#for i in np.arange(1, np.pi * 1.1, 0.2):\n", - "# plot_arrow(i, 0)\n", - "\n", - "set_axes()" - ] - }, - { - "cell_type": "markdown", - "id": "norman-mayor", - "metadata": {}, - "source": [ - "<h2>Hamiltonian of the pendulum (slide 25)</h2>" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "young-facing", - "metadata": {}, - "outputs": [], - "source": [ - "def hamiltonian(theta, p):\n", - " T = p * p / (2 * m * L*L)\n", - " U = m * g * L * (1 - np.cos(theta))\n", - " return T + U" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "extreme-leave", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "<Figure size 432x288 with 2 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "TH, PP = np.meshgrid(np.linspace(-np.pi * 1.1, np.pi * 1.1, 100), \n", - " np.linspace(-3, 3, 100))\n", - "\n", - "HH = hamiltonian(TH, PP)\n", - "\n", - "plt.contour(TH, PP, HH, levels=10)\n", - "plt.colorbar(label=r'$\\mathcal{H}(\\theta, p)$')\n", - "\n", - "set_axes()" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "comparable-duncan", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "<Figure size 432x288 with 2 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "TH, PP = np.meshgrid(np.linspace(-np.pi * 1.1, np.pi * 1.1, 100), \n", - " np.linspace(-3, 3, 100))\n", - "\n", - "HH = hamiltonian(TH, PP)\n", - "\n", - "plt.contourf(TH, PP, HH, cmap=plt.get_cmap('hot_r'))\n", - "plt.colorbar(label=r'$\\mathcal{H}(\\theta, p)$')\n", - "\n", - "plot_arrow(2, 0)\n", - "\n", - "set_axes()" - ] - }, - { - "cell_type": "markdown", - "id": "different-verification", - "metadata": {}, - "source": [ - "<h2>Explicit Euler Method (slide 28)</h2>" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "every-howard", - "metadata": {}, - "outputs": [], - "source": [ - "def solve_euler(theta, p, dt=0.1):\n", - " theta_next = theta + dt * p / (m * L*L)\n", - " p_next = p - dt * m * g * L * np.sin(theta)\n", - " return (theta_next, p_next)" - ] - }, - { - "cell_type": "markdown", - "id": "federal-competition", - "metadata": {}, - "source": [ - "<h3>First example</h3>" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "proved-officer", - "metadata": {}, - "outputs": [], - "source": [ - "theta_ini = -1.1\n", - "p_ini = 0\n", - "n_steps = 100" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "lovely-major", - "metadata": {}, - "outputs": [], - "source": [ - "results_euler = np.zeros((n_steps, 2), dtype=np.float32)\n", - "results_euler[0] = (theta_ini, p_ini)\n", - "\n", - "for k in range(1, n_steps):\n", - " results_euler[k] = solve_euler(*results_euler[k - 1])" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "renewable-convert", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.contour(TH, PP, HH, levels=10, linestyles='--', linewidths=1)\n", - "\n", - "plt.plot(results_euler[:, 0], results_euler[:, 1], c='b')\n", - "\n", - "set_axes()" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "gentle-macedonia", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAEtCAYAAABZOiSWAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAABAe0lEQVR4nO3dd3hU1dbA4d8kQAgtEQVEVMDCokqzIQpcQf1QKSpebFFBQRRRrljADiqoFAuKYAcEkWsBFQUvVUBFVERR3KgUFRARSCgCgeR8f+wzyUwySSaTSeYkWe/z8IzZp2TlOJmVfc7ea/scx0EppZTyqrhYB6CUUkrlRxOVUkopT9NEpZRSytM0USmllPI0TVRKKaU8TROVUkopT9NEVUJEJFVEUmMdR2mh16vw9JoVnl6zwovFNdNEpZRSytM0USmllPI0TVRKKaU8TROVUkopT9NEpZRSytM0USmllPI0TVRKKaU8rUKsAygtfD7fYWxi3x3J8XFxcUnueVKjGFaZpder8PSaFZ5es8KL4JrVADIdx4k43/h0Parw+Hy+TMCXlJQU61CUUqrUSEtLA3Acx4n4Dp72qMK3OykpKSk1NTXWcSilVKmRnJxMWlpaRHei/PQZlVJKKU/TRKWUUsrTNFEppZTyNE1USimlPE0TlVJKKU/TRKWUUsrTNFEppZTK0w8/wIAB8MADkJ4emxh0HlUx2b9/P7t37+bgwYPopGqlQvP5fCQkJFCjRg0SExNjHY4KcPAgjBoFI0fCoUO2rUMHOO+8ko9FE1Ux2LlzJ9u2bcv6JYyL046rUqFkZGSwa9cudu7cSZ06dahZs2asQ1LAypVw/fXw44/ZbdWrw8knxyYeTVRRtn//frZt20b16tWpW7cu8fHxsQ5JKU/LyMhg69atbNu2jcTERO1ZxdChQ/DYY/Doo5CRkd1+xhnw8svQoEFs4tI/9aNs9+7d+Hw+TVJKhSk+Pp66devi8/nYs2dPrMMpt37+Gc46C4YPz05SVavCs8/C8uXQvHnsYtMeVZQdPHiQhIQETVJKFUJ8fDwJCQkcOHAg1qGUS2+9BTfeCHv3Zredcw5MngwNG8YuLj/tUUWZ4zj6TEqpCMTFxenAoxJ24ADcfDNccUV2kqpUCZ54AhYt8kaSAu1RKaVUubR5M1xyiR044XfiiTBzJrRpE7u4QtE//ZVSqpz58ks47bTgJHX55fDNN95LUqCJSimlypU337TzobZutV/Hx9sBE2+9BTVqxDa2vGiiUsVi/PjxiEiB/1JSUiI6f0pKCiLCwYMHoxx5bitWrEBEGDNmTMTnWLJkCWvXro1iVMVv9erVfP7557EOQ0XR2LFw1VV2Mi/AEUfAvHkwaBD4fLGNLT/6jEoVq86dO9OkSZM8t9erV68Eo4lMvXr1uPXWW2nbtm1Ex0+fPp3hw4fz0ksv5XstvGTx4sUMGDCAhx56iHbt2sU6HFVEmZlw553w1FPZbU2awAcf2OdSXqeJShWrLl26cOmll8Y6jCI59thjGTRoUMTH79ixI4rRlIydO3fqCLwy4tAhW2Vi+vTstnPOgdmzbY+qNNBbf0opVUalp9uh54FJ6rLL4JNPSk+SAk1UykOGDh2KiPDrr78Gtf/666+ICEOHDi3wHO+//z6XX345rVq14tRTT6Vfv3589913Qfu8++67iAhz584lJSWF5s2b07lzZ3bu3BnynKGeUZ177rlcf/31GGO48cYbadOmDW3atOGWW25h/fr1WfulpKTw3HPPAdCvXz9EpNDxAqSnp/Pcc8/RpUsXTjnlFHr27Mn8+fO57777gs5Z0M/2008/MWTIEDp06EDz5s059dRTSUlJ4dNPP806x9ChQxk2bBgADz/8MCLCH3/8kbV99uzZXH755bRs2ZI2bdqQkpLCkiVLQl6zN998k0GDBtGiRQs6dOjAunXrQl5jFX0HDsCll8K772a3DRhgB01Urhy7uCKht/5UmTFu3DgmTZpE/fr16dWrF4cOHWLu3LlcddVVTJgwgQ4dOgTtP2LECI455hhSUlLYsWNHoQuibtmyhauuuoqTTz6Z3r1788svv7BgwQK+++47Fi5cSKVKlbjkkksA+PLLL+nWrRv169ePKN7bbruNRYsW0bx5c8477zyMMdx6660cc8wxIWML9bOtWrWK6667jsTERM4//3ySkpJYv349ixYt4quvvmLatGm0adOGLl26sHv3bhYsWECnTp1o3rw5NdzhYCNHjmTy5MkcffTR9OjRg0OHDrFw4UL69+/Pfffdx7XXXhsUx/jx46lRowYpKSls2LCBE0vDA5Ey4MAB6NnTDpTwu+MOGDPG24Mm8qKJShWr+fPns3nz5jy3X3HFFdSqVavI3+fbb79l0qRJnH322UyYMIGEhAQABgwYwGWXXca9996blTz8KleuzLRp07L2LaxNmzbRt29f7rnnnqy2u+++m9mzZzN//nwuvPBCLr30UjZv3syXX35J9+7ds5JPYeKdO3cuixYtolu3bjz55JNZlU/Gjh3Liy++GDK2UD/bM888Q2ZmJm+99RYNAqqLvvXWWzz44IN89NFHIRPVlVdeCdhkO3nyZFq3bs2kSZNISkoCshP2E088QadOnTj++OOzzr1//34+/PBDrYpegtLT7ZyowCR177220GxpTFKgt/5K3Nixtly+z+fdf9Wr2zijYcGCBTz33HN5/vv777+j8n3ede9v3HXXXUEfznXr1uWqq65i+/btLFu2LOiYTp06RZyk/Pr16xf0dceOHQH4/fffoxbvrFmziIuL48477wwqz3XzzTeTnJwc8vyhfrY+ffowZsyYoCQFcPrppwOQmpqab8zvvfceYG8N+pMUwDHHHMPAgQM5fPgws2bNynVuTVIl5/BhO/z8ww+z2x56yFZEL61JCrRHVeLGjg0u/OhFe/faOIcMKfq5Ro0aVSKj/n744QcAPv74Y/73v/8Fbfvll18AWLt2Leeee25W+3HHHVek71mjRo1cH8LVqlUD4JB/pbkoxLtmzRpq167N0UcfHbRflSpVEBFWrFiR6/yhfjZ/Et22bRvGGH7//Xd++eUXvvrqKwAyMzPzjdkYQ6VKlTjllFNybfMP3TfGFBiHKh6ZmdCnD7zzTnbb0KE2UZV2mqhK2JAh8PDD3k5W1apFJ0mVJP/yEBMnTixwH7/KRXyiHHgb0c/n/tla0NDuwsS7a9euXIMw/PK6bRrqZ9u8eTOPPPIIixcvxnEc4uPjOeGEE2jevDnr1q0rMOa9e/dSpUqVkEWXa9euDdhbfQXFoaLPcWDwYHjjjey2wYPt6ryluSflp4mqhA0ZUvqSQEnJ60M+nKUfqlSpQqVKlVi9enWpqF5fmHirVavGvn37Qm7Lqz0nx3EYMGAA69evZ+DAgXTu3JkTTzyRhIQE1q9fn3VbLz9Vq1blt99+y1rKJtDu3bsB8rwVqYrXY4/B+PHZX990E4wbVzaSFOgzKuUhFStWBHJ/+P72228FHisipKenhxz+/Omnn/LUU0/x008/RSfQQvKF+LQoTLxNmzbl999/zzV8PjMzkzVr1oQVgzGGdevWceGFFzJo0CCaNm2alWz8w+kD/0AIFXPjxo1xHIdvvvkm17aVbnXTk046Kax4VPRMmgQPPJD99b//Dc8/X3aSFGiiUh7S0F38ZvHixVltBw4cYPLkyQUe27NnTwAee+wx/vnnn6z2nTt38vDDDzNp0qSYLXFeoYK9cZGenp7VVph4L7nkEjIyMhg7dmzQc6SXX36Z7du3hxWD/zZlzioZ27dvZ9y4cQAcPnw4rJhHjx5NWlpaVvuWLVsYP348FStWpGvXrmHFo6LjvffselJ+XbrAlCm20GxZorf+VLEqaHg6QP/+/UlISOCiiy7i6aefZuLEiWzatIk6deqwYMECkpKSsnpbeWnXrh1XXXUV06dP5+KLL6Zjx474fD7mzZvH33//zW233RY0h6kk1alTB7BzilavXs2gQYMKFW+3bt2YNWsWb7/9Nj/99BOnnnoq69atY8WKFdSoUYO9YTzwbNCgAaeccgrLly8nJSWFli1bsmPHDubPnw/Y3mzgqD9/zFOmTGH79u1cd911nHHGGaSkpDB16lS6d+9Op06dSE9PZ+HChaSlpTFs2LCsPzZU8Vu+3I7w83eETz3VTu4t4kBWT9JEpYrVggULWLBgQb77XHfddSQkJFC7dm0mT57M2LFjWbBgAVWqVOG8887jzjvvpH379gV+r4ceeojmzZszY8YM3n33XSpVqsSJJ57I/fffH9O/9C+88EKWLFnC4sWLmT59OpdccgknnHBC2PH6fD6ef/55xo8fz5w5c5g2bRonn3wyEydOZPz48VmjBPMTFxfHhAkTGDNmDJ999hnfffcdRx99NF26dGHgwIEMHTqU1atXs2fPHqpXr85pp53G1VdfzezZs5k2bRrt27enVq1a3H///TRt2pRp06Yxa9asrFGAffv2Dev/kYqOtWuhWzc7sRfgpJPgo4/s1JKyyKeFJ8Pj8/lSk5KSkgqaa7Jp0yaAmP31rsqerVu3Ur169ayh74H+9a9/kZCQwNy5c2MQWXTp7054tm6Fdu3AvVzUrg2ffebdKujJycmkpaWlOY6THOk59BmVUh730ksv0bZt21w1AD/++GO2bNmSNWFXlX179sBFF2UnqapVYc4c7yapaNFbf0p53KWXXsrMmTPp06cPF1xwAUceeSQbNmxg0aJF1KpVq0hLkKjS49AhO6Jv1Sr7dXw8/Pe/9tlUWaeJSimPa968OW+++SYvvvgiy5YtY9euXRx11FH06tWLgQMHRqVWovI2x7Gj+wLv8E6cCOVlkKUmKqVKgRYtWjA+cEanKldGjIBXXsn++v774cYbYxdPSdNnVEop5WGvvGLLrvlde61NXOWJJiqllPKojz6y5ZD8zjsPXnqpbFWdCIcmKqWU8qAvv7TrSmVk2K9btbKV0UPUQi7zNFEppZTHrF0LF14I/upa9euX7Qm9BdFEpZRSHvL773DBBeAvy3jkkXa0X926sY0rljRRKaWUR+zYYZOUf4HoqlVtT6px49jGFWuaqJRSygNSU+H88+1tP4CKFW11dC08oolKKaVibu9e+0zKv9SXz2eX6zjvvNjG5RWaqJRSKob277eV0D//PLvtpZfgiitiF5PXaKJSxWb16tV87v72rVixAhFhzJgxMY5KKe/Ytw8uvhgC1grl2WfhhhtiFpInaaJSxWLx4sX07t2bjRs3xjoUpTxpzx5bq2/hwuy2xx8HrTGcm9b6U8Vi586d6FpnSoWWlmaTVODtvlGj4J57YheTl3k+UYlIPeBH4B5jzMQwj2kOjATOAioCy4Bhxpjv8j1QKaWK2datNkmtXp3dNnYs3HFH7GLyOk/f+hOR6sB7QI1CHNMMWA6cA8wA3gQ6AJ+5CUwVs6FDhzJs2DAAHn74YUSEzZs3Z22fOXMmF198MS1atOBf//oXzz77LIcOHcp1nqVLl5KSkkLr1q1p3bo111xzDUuXLg35PWfPns3ll19Oy5YtadOmDSkpKSxZsiRoH/9zsjfffJNBgwbRokULOnTowNSpUxERJkyYkOu827dvp2nTpgwZMqQol0QpAH75Bdq3D05Szz6rSaognk1UIlIf+BQ4rZCHPgNUBtobY241xgzAJqoKwLPRjVKF0qVLFzp37gxAp06duPXWW6lRw/6t8e677/Loo4/SpEkTrrzySnw+H88//zxPPPFE0DlmzJhBv3792LBhA926deOyyy7jt99+o1+/fvz3v/8N2nfkyJHcfffd/PXXX/To0YMLLriAdevW0b9/f6ZMmZIrvvHjx/Pzzz+TkpJCs2bN6NmzJ5UrV2bOnDm59p0zZw4ZGRl07949WpdHlVMrV8JZZ8GGDfbr+Hh49VV9JhUWx3E8969Ro0aDGzVqtLtRo0aHGzVqtKBRo0ZOo0aNBoRx3Mnuvm+E2DbZ3dYgkpiA1KSkJKcgGzdudDZu3FjgfmXdO++84zRq1MiZPn264ziO88UXXziNGjVymjZt6nz77bdZ++3YscNp3bq107ZtWycjI8NxHMfZsmWL06xZM6dbt25OWlpa1r5paWlO165dnRYtWjjbt293HMdxVqxY4TRq1Mjp3bu3k5qamrXv5s2bnY4dOzpNmzZ1Nm3aFBRDq1atnB07dgTF+5///Mdp1KiRs3bt2qD2yy67zGnXrp1z6NChKF4dFUpZ/t156y3HqVzZcewSiI6TmOg4H3wQ66hKRlJSkgOkOkXICV7tUQ0GNmF7QlMLcVwH93VRiG3+to6RhxUFY8faypI+n3f/Va9u4ywG7du3p2XLlllf16xZk5YtW7Jnzx5SU1MBeP/99zl06BC33XZbVk8MoEaNGvTv35+DBw/y8ccfA/Dee+8B9nZjUlJS1r7HHHMMAwcO5PDhw8yaNSsohtNPP52aNWsGtfXo0QMgqFe1adMmvv/+ey688EIqVPD841zlQY5j15Lq3RsOHLBtRxwB8+fbYekqPF797bsJmG+MyRCRRoU47kT39dcQ2za6r4U5X/SNHWunoXvZ3r02zmJ4LlO/fv1cbcnJyQDs378fgB9++AGA5cuXs9ZfT8b1119/AWS1G2OoVKkSp5xySq7ztm3bNmufQMcdd1yufdu3b8+RRx7JnDlzsp5HffDBBwB069YtvB9OqQBpadCnjy2D5NeoEXz4IZx8cuziKo08maiMMfMiPPRI9zU1xLY09zUpxDZEJNQxWeLi4kIeV2hDhtg/sbycrKpVK5YkBZCQkJDnNscdzr5nzx4Apk+fnue+/n327t1LlSpViIvLfXOgdu3aQHYC9KtcuXKufStUqMBFF13ElClTWLVqFa1bt+bDDz+kQYMGQT1ApcKxejX06mUHT/h16QIzZ9oeVXkTFxeXVNBnrDEmOa9tnkxURVDRfT0YYpu/LfenVEkaMqTYkkBZUaVKFQA+/fRT6tSpk+++VatW5bfffuPgwYO5kuDu3buB7B5bQXr27MmUKVOYN28eiYmJbNiwgUH6pFsVguPYpeMHDcq+1Qf267FjbaFZVXhlLVH5/3QOtQam/1NsX6gD88vmAD6fL5U8emMqN18R1soWEebPn8+aNWtyJarvvvuOefPm0alTJ0477TQaN27Mjz/+yDfffEO7du2C9l25ciUAJ510Uljft1mzZpx00kksWrQoK7npbT8Vrh07oF+/4Ft9VavCyy9r3b7MzMy0gj5j8+PVwRSR2uW+hkoo/ra0ENtUlPkHH6Snpxf62G7duhEfH8+4cePYuXNnVvuBAwcYMWIEL7/8MocPHwZsLwhg9OjRpKVl/6/dsmUL48ePp2LFinTt2jXs792jRw82btzIzJkzadmyZchnakrl9MkncMopwUmqaVM7JL28J6loKGs9qnXua0PsHKxADd1Xgyp2/p7QlClT2L59O02aNAn72IYNG3LHHXcwevRoLr74Ys4991yqVKnCwoUL+f333+nVq1dW7+mMM84gJSWFqVOn0r17dzp16kR6ejoLFy4kLS2NYcOG0bBhwwK+Y7Zu3boxbtw4Nm/eTN++fQv3Q6tyJy3N3sl/5ZXg9ltugdGjwb2LrYqorCWqZe5rR2Byjm2d3NfPUcXutNNO4+qrr2b27NlMmzYtZNWH/Nx44400bNiQ119/nTlz5uDz+WjQoAEjRoygV69eQfvef//9NG3alGnTpjFr1qysUYB9+/alffv2hfq+devWpVWrVlnD0pXKy4cfwoABEFB0hVq17CReHXoeXT7/SCuvEpHrgdeAm8Op9Sciy4C2wJnGmNVuW2tsglpmjOkSSRw+ny81KSkpyT/XJy+bNm0CQg/DVt6Xnp7O2WefTdu2bXnhhRdiHU65Ulp+d/74A26/Hd59N7i9Vy947jkoYPxPuZOcnEyanbmfHOk5Sm2PSkQaANcDG40xrwdsuh1722+piExz264B0rETiZXK0/Tp00lLS+Pf//53rENRHnPoEDz/PDzwQPDsklq1YMIEm6hU8Si1iQpoADwELAFe9zcaY74WkQ7AKLIT1KfY6ulrSj5MVRoMGjSIn3/+mQ0bNtCsWTM6deoU65CUhyxcCLfdBu5c9Cx9+sCTT8JRR8UmrvLC84nK7S29HqJ9MRByDLQx5mvg/OKMS5UtNWvWZOvWrbRt25Ynn3yySMPrVdmxYQPcfTe8/XZwe5MmMHEidOgQ+jgVXZ5/RuUV+oxKqeLlpd+dPXtg5Eh46ik4GFA+oGpVePBBGDwYKoWaralyKdfPqJRSKtoOH7aj9h58ELZtC9521VX2Nl+9erGJrTzTRKWUKvccBz7+GO66C378MXjbaafB00/btaRUbJS1yhRKKVUoX30FnTvDRRcFJ6l69WDKFPjiC01SsaY9qijz+XxkZGTEOgylSp3MzEzi4+NL7PutXw/33w9vvhncXq0aDBtmn0NpZQlv0B5VlCUkJHDw4EFNVkoVQkZGBgcOHAi5BEu0bd9uJ+w2bhycpOLj4eab7dIc996rScpLNFFFWY0aNXAch61bt2qyUioMGRkZbN26FYDq1asX2/fZtw8eewxOPBGefdZO4PW75BI7R2rCBK0s4UV66y/KEhMTqVOnDtu2bWPv3r0kJCSEXNRPKWVv9x08eBDHcahTpw6JiYlR/x6HDtmiscOHw59/Bm9r3x6eeMK+Ku+KOFGJyClAK6A2kIxdVfcvYJUx5vsoxFZq1axZk8TERPbs2cOBAwfQuWpKhRYfH0/NmjWpXr161JOU49iJuvfdBz//HLytSRN4/HHo1g10brf3FSpRicgZwM3AxUDggso+wAnYbyfwIfCCMebLKMRZ6iQmJhbLX4dKqYItWgT33GPXgwpUrx6MGAHXXgsV9H5SqRFWZQoR6QiMxlYl9wGHge+BtcAOYDd2YcKaQFOgBRCPTV5fAXcZY3KuD1WqhFuZQikVO99+C0OHwrx5we3JybZ90CAdJFHSSqQyhYi8C/TALvP+JjAFWGqM2Z/PMYnYNaGuBboDi0RkljHmskgDVUqpvKxfb6uaT58e3J6QYIvJDh0KNWvGJjZVdOF0fjsDjwFjjTFhLePuJrG5wFwRSQLuBG6LOEqllArhr7/g0UdtgdjAUXxxcXD99fDww3DccbGKTkVLOImqoTFmZ6TfwE1uD4jIU5GeQymlAu3ZA+PGwZgxwWtDAXTvbgvKNmsWm9hU9Gn19DDpMyqlYi89HV58ER55xPamAulQc2/S6ulKqXIhMxNmzLDPodavD97WrJntQelQ87IrokQlIpWAG4A2QB3gb+BbYLYxZlPUolNKlWuOA598YgdDfPtt8LbjjrM9q2uuseWPVNlV6EQlIicAC4DjCV5h1wHGish04G5jzLZQxyulVDhWrrRzoRYtCm6vWdNO4r3lFiiB0oDKAyKp7TMGqA/8gR3N1x24EngWW5kiBfhKRFpHK0ilVPnx88/w73/D6acHJ6nERFssdv16uOMOTVLlSaEHU4hIKpABNDPG/JljWwXgP9jh7DuAlsaYv3KdpBTSwRRKFa9t22w9vpdesivt+sXHQ79+dtXdunVjF5+KTDQGU0TSo6qEnfD7Z84NxpjDxpjR2OdXdYChkQamlCof9u61851OPBFeeCE4SfXqZauav/CCJqnyLJJEtYkCnm0ZY6Ziyyv1jOD8Sqly4PBhO1H3pJNsT2rfvuxtnTrBihXw3/+CSMxCVB4RSaL6GDhXRI4uYL/vAP0bSCkVxHHg/feheXO7UOG2gGFXLVrARx/BwoX2GZVSEFmiehLYDrwlItXy2a8+sDWiqJRSZdK330LnztCjBxiT3X7ssfD667BqFXTtqvOhVLBIEpXBVk8/G/heRK4TkaB6xCLSDzgTeL3IESqlSr0//4QbboA2bYJH8tWoAaNGwbp1cN11Oh9KhRbJhN8EoKH73/WBV4EXReRHIM3ddizwHPBINIJUSpVO6el22fcRI2x9Pr/4eHvb78EHoVat2MWnSodIElU1oBl2baq22OoULd1/gfoCbUTka+Br7LpUa40xWlxQqXLgf/+DW2+1vaVAF11ki8k2bhybuFTpE5WitCISj10w0Z+42mITl/+WoP+b/GOMqV7kbxgDOo9KqfBs3mwn5M6cGdzeuDE8/TRccEFMwlIx4pmitMaYDOyKv9/jPpcSkTigCdmJ61Ry97qUUmVERoad7zRsWPDSGzVq2OHnAwdCxYqxi0+VXsVWPd0Ykwn84P6bCiAiOpZHqTLohx9s9YjPPw9uv+YaGD0aji5oMotS+Yhk1F/E9PmUUmXL4cPw2GPQunVwkmrc2I7umzpVk5QqOl2PSikVkbVr7ZDylSuz2ypWtIVjhw2DhITYxabKFk1USqlCcRx4/nm48044eDC7/fTT4dVXdQl4FX0leutPKVW6bd9uV9IdNCg7SVWqZCftLl+uSUoVD+1RKaXCsnAhXH21rTLh16qVfQ7VvHnMwlLlQLH0qERkoYjME5HLi+P8SqmSk5kJjz4K550XnKSGDIEvvtAkpYpfcfWoOrmvXUTkTmCoMWZRPvsrpTxoxw47xHzu3Oy22rVhyhSduKtKTnElquHY3lproCMwH9Byk0qVIqtXQ8+esHFjdluHDjBjhi5iqEpWsSQqY8xw/3+75ZV0ZRmlSpGZM6FPH/jnn+y2oUPhkUeggj7ZViWs2N9ybnmlzwvcUSkVc5mZtqL5Y49lt1WrZgdM9OwZs7BUORd2onLLH50KNHCbdgLrjDG/F0NcSqkS9s8/dgLv229nt518MsyaBU2bxiwspcJLVCJyAzASOCrEtr+ARcBbwIduD0opVYps3Qrdu8NXX2W3XXCBfR6VnByzsJQCwhieLiJXAy8BtYDVwCfAUiAV8AF1gCuAd4FfROSa4gpWKRV9338PZ5wRnKRuuw0+/FCTlPKGcHpUQ4B04EJjzEJ/o4i8BlwLXAR0AS7Bru47WUS6A9cYY9KjH7JSKlrmz4fLLoPdu+3X8fEwfrxdfVcprwgnUQkwPzBJBTLGzAXmAneKSFfgcaAXUBGbvJRSHvTaa9C/v62ADlC9un0+df75sY1LqZzCqUyxF9gfzsmMMR9jB1z8F+guIlcWITalVDFwHLuQYd++2Unq2GNh2TJNUsqbwklUy4FOIlI1nBMaYw5hbwluA24qQmxKqSg7dAhuvBEefji7rWVLWwrplFNiFpZS+QonUY0DagIvucvLF8gYcxA74KJV5KEppaJp7147su/VV7Pbzj8fli6FevViF5dSBSkw8RhjlgGPYkf2LRWRM8M894lFCUwpFT1//gkdOwbX7LvuOjuyr3r12MWlVDjC7SE9BNyFff60XES+Ak4DEJEagfuKSD0RmYit87cy57mUUiXrp5+gXTv45pvstvvvt4MpKlaMXVxKhcvnOE7YO4tIY+ARoCfZRWYd7GCLvUAlIAk7v+og0NEY82UkgYlIBeB2oB9QH9gMvAyMDmdSsYicgy2Oezo2IX8NjDDG/C+SeHw+X2pSUlJSampqJIcrFRNLl0KPHrBrl/06Ph5eeAH69YttXKr8SE5OJi0tLc1xnORIz1Go9aiMMT8ZYy4HjgMGAbOwCSQRqA0kAwfc9tMjTVKuicAY4E/gGeAvYBTwan4HAYhIZ2AhcAbwJvAa0ByYJyI6ZF6VCzNmQJcu2UmqShWYPVuTlCp9CtWjyouIJGKTVKYxZlsUznc2djDGG8aYFLfNh006vbE9tU/zOf4roCVwpjHma7etEbAK2G6MaVDYmLRHpUoLx4HHH4d7781uq1MHPvgATjstdnGp8qnEe1R5McbsN8ZsjUaScvnnxWctF2KMcYBh7pd98zrQHZnYBvjOn6Tc49dhk199EakTpTiV8pSDB+3yHIFJqkkTO/xck5QqrYplKfoo6AD8YYz5JbDRGLMB2IRdjDEkY0wmtg7hMe5zrkB1gcNAWlSjVcoD/v7b3uqbPDm7rVMnWL4cGjSIVVRKFV04RWmHiEhCUb6JiCSIyJBw9wWOBX7NY5eN2F5RfjG9BBwNvCgidUXkSBF5EjgFmGSMORB+9Ep53/ffw+mn2+oSfn37wrx5cMQRsYtLqWgIp9bfaGCwiIzBPjPaEe7JReQobJWKIdjEMTaMw2q6r6l5bE/Djiqsjh1ZGMow7EjEB4E+Ae1PYYfZh4o1r+8HQFxcXFJ+25WKlbfftnOi/Kvx+nzwxBNw5532v5WKtbi4uKSCPmONMcl5bQsnUZ2P/YB/CnhCROZi15/6AlhrjNnt39GdU9UUOBM4F7gAW5x2DXBdGN8Ld3/IOwn52yvnc46LgYHYEYOzsUPpewADsEuVTM77UKVKh4wMuxrvyJHZbdWqwRtv2CHpSpUVYY36cwcoXIcdkt4KO3fKLwM7h6oa2XOrwPZ6VgHjgSnus6Nwvlct7FD0WcaYXEPJRWQ20B2oaYzZFWJ7Q8Bgbx2e7e8BuuddCpwENDfG/BROPFk/jI76Ux6ybRtcfTUsWJDddtJJdjXeZs1iFpZSuURj1F9YK/y6SeY14DUROQ3bO+mETVpVsEPTAfYB3wKLgfeNMZFUpkgDMrETh0Pxt+/OY/vV2F7Z8MDblMaY7SLyADATuAa4P4LYlIq5pUuhd2+7Kq/f//0fTJ+uz6NU2RTuUvQVgIruMPSVBJRGEhF/oko1xvxT1ICMMekisgm7CGMoDYFf8qlOcZz7GqrH9KP7emwRQlQqJjIy7G2+4cPtf4N9BvXAA/YWYHx8/scrVVqFlaiAI4B7gDtzbnCTU5ETVA7LgBQRqW+M2eRvFJETgOOBqfkc65/L1Qjbuwt0kvv6Z5TiVKpEbNoE11wTPKrvqKNg2jRdQ0qVfeHOo9oF3C4iK0VkqIg0L+gAEWkvIrUjjGuK+zrSrUjhr0zhf2z8Yj7HvoN9hvaAiGTdCBGRJLInEP83wriUKlGOA1Om2DWjApPUOefYIrOapFR5EHYJJRH5H9CZ7IEUvwNz3H8Lc85NEpHjgIeMMTdGEpiIzMCWS/oMOwiiA9AOeM0Y09fdJxkYjL3t+HTAsSOAB4Ct2MQVhx2AcSwwyhgTMG8/PDqYQpW0rVvhppts6SO/+Hi76OGwYXqrT5UOJV1CqScwlOznU8djh3t/AOwQkQ9EZICboMDOYypKAdhrgYex1SQGA0e63z9w1eBk4CF3exZjzIPY9bM2Ycst9QG2AFdHkqSUKkmOY5fgaNYsOEmdcIIdSHH//ZqkVPkSUVFad6h3V+x8pV4Bm/wn24wdnl4XqBTu0HQv0x6VKgnr1sGAAbBoUXD7wIF2Em/VqrGJS6lIRaNHVeTq6SKyGtuj6YFNXCcEbP7KGHN6kb6BR2iiUsVp/36biB5/3BaW9WvQAF55Bc49N2ahKVUkJTaPqgBHGGMWYatVDBaRpsBFwDHA81E4v1JlluPA++/D4MGwcWN2e1wc3HGHfR6lvShV3kUjUQUxxvxI9nwlpVQe1qyxyeh/OdacPvVUmDQJ2rSJTVxKeY1Xl/lQqszats0+h2rZMjhJ1axpE9QXX2iSUipQ2D0qt+CsABuMMX8HbNL6zEqFYe9eGDcORo+2/+0XFwf9+8Ojj8KRR8YuPqW8KtwSSgnAWuxSHYjIj9j5Ux9hC8gqpfJw6BC8/DKMGAF/5qiJcv75MHYsNC9wCr1S5Ve4Pao62KHmfs2wy3ncBRwSkcnY+VRzjTF7QxyvVLmTmQkzZthafOvXB29r1gyefBK6dtU1o5QqSLiJarv72gNIxFaJ6IotEFsJW438GmzSWgLMAl43xuyParRKlQKOA7Nn2wS1Zk3wtnr14JFH4NprddKuUuEqTAmln4C2xph9AW2NgQvdf+eQveihA2xw90+LasQxovOoVEEcxy79/sAD8NVXwduOOMKWPbr1VkhMjE18SsVCSc+jmgm0Bz7xN7iLD/4EjBORasB52DlUF2En/vYCXok0OKVKA8exCxg++CB8/nnwtqpV4fbb4a67IDk5JuEpVeoVJlE9ha1a/kmoje6zqfeA90QkHhgCnFjkCJXysEWL4KGHbA2+QAkJtuzRPfdA7UjXEFBKAYWYR+Uu+z5FRK4KY98MY8yTwDdFCU4pr1qyBDp1sqWNApNUpUo2Qf36qx3Np0lKqaIrdK0/EfEZY4pWILAU0mdUCmyCGj48d9HYChWgb1+47z44/vjYxKaUF8Wk1l95TFJKLVli6+4tXhzcXqECXH+9TVANGpR8XEqVB1Gv9adUWZJXgoqPtwnq3nvtOlFKqeKjiUqpHBzHJqbhw22iCqQJSqmSp4lKKZfj2GdPw4fDp58Gb6tQAa67ThOUUrGgiUqVe/55UMOHw7Jlwds0QSkVe5qoVLnlOPDJJ7ZY7GefBW+rUAH69LEJSgdJKBVbmqhUueM48PHHNkGtWBG8rWJFO8x82DCoXz828SmlgmmiUuWG48CHH9oElbMWX8WKcMMNNkHpPCilvEUTlSrzMjNtNfNHHoFVq4K3VaoE/frZUkfHHReb+JRS+dNEpcqszEx4912boL77Lnhb5cp2Vd2777ZLbyilvEsTlSpzMjLg7bdtgvrhh+BtiYkwYICtZl63bujjlVLeoolKlRkZGfDWW/Doo7B2bfC2KlVssdg779RCsUqVNpqoVKnnT1AjRoAxwduqVYNBg+A//4FatWITn1KqaDRRqVIrvwRVvTrcdptNUEceGZv4lFLRoYlKlTqZmfYZ1MMP577FV6MGDB5s/x1xRAyCU0pFnSYqVWo4Drz/vl3yPecovho1bO/p9ts1QSlV1miiUqXCggW2nNGXXwa3V69ue0//+Y8mKKXKKk1UytO++cZOxp0/P7i9alX7DGrIEH0GpVRZp4lKedKGDXbV3DffDG5PSIBbboGhQ3WYuVLlhSYq5SmpqfDYY/Dss5Cent0eF2ermT/0kJY6Uqq80USlPOHwYXjxRTtQYseO4G09e8KoUdC4cUxCU0rFmCYqFXNLltjnTTlH8p15JowZA+3bxyYupZQ3xMU6AFV+bdkCV14JnToFJ6kGDWDGDLuYoSYppZQmKlXiDh+Gp5+2t/JmzMhur1LFPp9auxZ69wafL2YhKqU8RG/9qRK1cqVdXuPbb4Pbr7gCRo+GY4+NSVhKKQ/THpUqEXv32km5Z54ZnKSaNIFFi+wwdE1SSqlQtEelit0nn9hVdH/7LbstMdGO8LvjDrvKrlJK5UUTlSo2u3bZyhGvvRbcft55MHEinHBCbOJSSpUumqhUsfjgA7jpJti6NbvtyCPtIIqrr9aBEkqp8OkzKhVVu3bBtddC9+7BSap3b/jxR7jmGk1SSqnC0R6VipqPPoIbbwxOUHXqwAsvwCWXxC4upVTppj0qVWS7d9sEddFFwUnq6qttL0qTlFKqKLRHpYpk4UJbLDZwRF/t2jBpkq3Rp5RSRaU9KhWRffvg1luhc+fgJPXvf8MPP2iSUkpFj/aoVKEtXWp7Ub/+mt1WsyZMmGAHTSilVDRpj0qFbd8+uP126NgxOEl17257UZqklFLFQXtUKiyffgp9+wYnqKQkeOYZOxxdh5wrpYqLZxOViFQAbgf6AfWBzcDLwGhjTEYYxx8BPARcCtQCNgKTgXHGmPR8DlUBdu+Ge+6xlSQCde1qFzrU+nxKqeLm5Vt/E4ExwJ/AM8BfwCjg1YIOdJPUcuA24BvgeeCAe/zLxRRvmTNnDjRvHpykkpLg1VftNk1SSqmS4MlEJSJnAzcAbxhjOhljhgLtgbeAa0WkQwGneAxoAvQzxvQ0xtwJnArMA1JEpFXxRV/6bd0Kl18OF18Mv/+e3d6tm30W1aeP3upTSpUcTyYq4Gb3dbi/wRjjAMPcL/vmdaCIVAOuBxYaY14JOD4DGIHtkVWJcrxlQkYGPP+8XdDw7bez22vVsgsczp4N9erFLj6lVPnk1WdUHYA/jDG/BDYaYzaIyCagYz7HdgQSgbdzbjDGfAZ8Fs1Ay4rPP4eBA2HVquD266+3CxoedVRMwlJKKe8lKhFJAI4FluSxy0agg4gkGGMOhtje3H39QUT6YgdkCHYwxiRgjDEmM7pRl15bt8K998Lrrwe3n3yyrS7xr3/FJCyllMrixVt/Nd3X1Dy2pwE+oHoe2+u6r3dhE9NP7qsDPAG8GJUoS7kDB2DUKGjUKDhJVa4MjzwC332nSUop5Q2e61EBFd3XUL2lwPbKeWyv6r5eCJxvjFkAICL3AQuAG0TkDWPM4sCDRCQ1v6Di4uKS8g+7dMjMhOnT4b77gksfAfToYdeLatAgFpEppcqquLi4pII+Y40xyXkeH+2AomC/+5rXAuUJ7uu+PLb7b+u9609SAMaYvcCD7peXFynCUshxYN48aNsWUlKCk1SzZna5+FmzNEkppbzHiz2qNGyyyasH42/fnc/xAF+H2Pat+3pizg35ZXMAn8+Xmk9MnrZsme1BffppcPtRR8Hw4dC/P1Tw4jtBKVUmZGZmphX0GZsfz/Wo3KoRm4CGeezSEPgln+oUP7uvoXpk/tuK/0QeYenxxRfwf/8H55wTnKQSE+H++205pFtu0SSllPI2zyUq1zKggYjUD2wUkROA44HP8zl2qft6bohtp7qv3xc5Qg/7/HOboNq1s7f7/CpUgAED4Jdf7ICJGjViF6NSSoXLq4lqivs6UkR8AO7rSLc9z5F7xpifsMmqo4hkPYsSkRrAw8BhYFoxxBxTjgPz59uRemedFZygfD77XMoYuyz8McfELk6llCosn+M4sY4hJBGZAfTGTtBdip0E3A54zRjT190nGRgMpBpjng44VtxjagKzgD+AbsAJwAPGmEcLG4/P50tNSkpKSk1NjfRHKhYZGXYQxBNPwMqVwdvi4uCqq+xtPpGYhKeUKueSk5NJS0tLcxwnOdJzeLVHBXAttgdUF5uMjgSGAjcF7JOMrZA+OPBAY4zB3uabBpzjHpMKXBNJkvKi/ftt9fImTaBXr+AkFR9vl95YuxamTtUkpZQq3Tzbo/Iar/So/v7brqT73HOwfXvwtoQEuOEGuOsuHWaulPKGaPSodLxXKfHTT3Yy7uTJtqpEoORkO3pv0CA4+uhYRKeUUsVHE5WHOQ4sWABPPQUffZR7+3HH2aXh+/eH6nkVlFJKqVJOE5UH7d9vyxw9/TSsWZN7e5s2MGSIXTOqYsXc25VSqizRROUhW7bY50+TJtlnUYF8Prtw4R13QIcOunChUqr80ETlAV9+Cc88AzNnwuHDwduqVrUr6t52m116QymlyhtNVDGSng7vvGMT1IoVubcffzzceivceCMccUTJx6eUUl6hiaqE/fWXvbX3wgt20cKczj4bBg+2S25oDT6llNJEVWK+/hqefRZmzLC9qUCVKsGVV9rbe23axCY+pZTyKp3wGyafz5eaBEmpsQ5EKaVKkWQgDcpsCSWllFJKE5VSSilv02dUhZGUBB6rnq6UUp6WnAxpaQXulh/tUSmllPI0TVRKKaU8TROVUkopT9NEpZRSytM0USmllPI0TVRKKaU8TStThMnn82UCvqSkpFiHopRSpUaaHZruOI4TccdIE1WYfD7fYWwPdHckx8fFxSUBZGZmFm1CQTmh16vw9JoVnl6zwovgmtUAMh3HiXjeriaqEiIiqQDGmOTYRlI66PUqPL1mhafXrPBicc30GZVSSilP00SllFLK0zRRKaWU8jRNVEoppTxNE5VSSilP00SllFLK0zRRKaWU8jSdR6WUUsrTtEellFLK0zRRKaWU8jRNVEoppTwt4iKBKjwiUgG4HegH1Ac2Ay8Do40xGbGMLdZE5DhgOPB/wFHAX8AHwIPGmO0B+40Hbs3jNI8ZY+4v7li9Itxroe87EJEGwIaC9jPG+Nz9PwAuzmO3fsaYl6MXnbeISD3gR+AeY8zEHNsK9V4SkT7AYOBkYAfwJvCQMWZ/pPFpoip+E4EbgCXALKADMApoAlwXu7BiS0RqAl8AdYEPAQO0BgYA54nI6caYne7uLYBdwLMhTvVpCYTrJeFeC33fQSr2D6FQTgUuIviatcAmtikh9v8mqpF5iIhUB97DVjkPJez3kojcDzwCrMK+R1sBdwGnish5kf6RpKP+ipGInA0sBd4wxqS4bT7sXxi9gY7GmPL2QQuAiEwC+gPXGWOmBLTfBzwKjDHG3OW27QBWGWO6xCRYDwnnWuj7Ln/uB/N3QDWghTHmTxGpAaQBrxhjboxpgCVIROpjk08rt+nmwB5VYd5L7rl+BZYBnf1JSUSexCaroN/1wtBnVMXrZvc16686Y4wDDHO/7FviEXnHhcAvId64TwAHgK4AInIMUBNYU7LheU8hroW+7/I3CmgA3G6M+dNta+6+lpv3mYgMBr7H9iQX5rFbYd5L/YF44NEcPafhwD8U4X2niap4dQD+MMb8EthojNkAbAI6xiSqGBORisBY7AdGThnAYexfu2B/iaAcfYDkI9xroe+7PIhII+AmYJkxZnrApvL4PhuMfT90AKbmsU9h3ksdsL+/S3Psuw9YCZzlPu8qNH1GVUxEJAE4FntfN5SNQAcRSTDGHCyxwDzAGHMIeDqPzZ2xScr/Zvd/gBwvIkuwz7EOAnOAe40xW4oxVK8p8Fro+65Aj2I/94bmaPdf21YiMhJohn3G9TZ2cE9ZXAH4JmC+MSbDTeBBIngvnYhNaqHeVxuxSa0h8HNhA9UeVfGp6b6m5rE9DfAB1UskmlJARBKBce6X/hFW/g+Qe4AtwIvAWuxD3BUiUrdEg4ytcK6Fvu/yICLHA5cCnxljlufY7L+2DwE/YK/tNuA2YImIVC2xQEuIMWZeAYMbCvteOrKAfQGSChFiFu1RFZ+K7mtef7X62yuXQCye594OnIH9wJhljHnX3XQIOxKrtzFmZcD+/kEXTwFXlHC4sRLOtbjbbdb3XW4DsM9QxoTY9g92eHY3Y8x6ABGJAyZgex4PkLsXVtYV9jOsYiH2LRRNVMXHP2egUh7bE9zXfSUQi6eJSGXgLaA78DVwrX9bPiOwRmGHzPYsL7exwrkW2PkuoO+7UK7BztWbnXODMaZriLZMEbkTSMGOcCtviaqwn2H7C7Fvoeitv+KTBmSSd1fX3767ZMLxJhFJBv6HTVJfAecbY/YUdJwxJhNYjf0FKE+3/3LJcS2S0PddLiLSEjgOeM+9XmExxuwF1gH13R5WeVLYz7BdYewb0bO+8nbhS4wxJh07KqZhHrs0xA7PLhdVAkIRkTrYCZdnA4uBcwMm+SIilUTkdBFpm8cpEt3XA8UaqAcU4lrsRt93ofh7TO/k3CAiVUWknYg0y+PYRCC9MAmuLIjgM2wdcKx7Gz/UvvuB3yKJRRNV8VoGNHAnwmURkROA44HPYxKVB4hINWAu9pnUbOD/QvSkErDXKNetGhGpArQBNgfMhSnLCnMt9H2X2xnY3kGon70+8Bl2AEUQd4DKCdhb0uVRYd5Ly7DPqdrl2LcqcBrwlTHmcCRBaKIqXv7JrCPd2dz+Wd0j3fZcvxjlyBjsbPi5QK9Qz5jcxDUPqCciWfXt3Gv4OFALeKFEoo2xQl4Lfd/l1hr42b2VF8QY8yN2IMVZItLN3y4ilYDnsB++E0oqUI8pzHtpOnYe1Qj32vk9hO2VRvy+0xJKxUxEZmAfxH6GnRvUAfsXx2vGmHJZIcAdJrweOwJrArA9xG57jTFj3Pkdn2GHvn6Ivb1wNnA69nbhBe4tijKvMNdC33fZ3Emm6cBiY8y5eezTHpiPTUpvA38C5wFNgenGmKtLKNyYEJHrgdfIUULJ3Rb2e0lEHsdOn1iDnd/XCrgA+xy6a6S3nHXUX/G7luy5LoOx93yHkj1fqDw6C5ukAG7JY59t2Hp/60TkVGyhywuA87HX8CHgyfKSpAAKeS30fZetJna+T54P8o0xy0XkTGy5nwuwPYB12HlUz5dEkB5WmPfSMGx19Vvcfbdgy6LlLKtUKNqjUkop5Wn6jEoppZSnaaJSSinlaZqolFJKeZomKqWUUp6miUoppZSnaaJSSinlaZqolFJKeZomKqWUUp6miUoppZSnaaJSKgb8BT6VUgXTWn9KFYGINMTWNDsfuzCfg61vthB4zhjzQ4hjrgE6AXmt2OtpInIytg7eN8aYvNbHUipqtEelVIREpDt2eYjbsGsdLcRWMfcBA4DVItI/xzEdgKnA0SUabHT5k9PKmEahyg3tUSkVARGpCUzDJqguxpgFObZfBswAXhCR5QE9q7Lwx6E/UX0V0yhUuVEWfmmUioUeQDXg5ZxJCsAY8w7wDPZ37IYSjq24aY9KlSjtUSkVmVph7PMmUAd7exAReR27pg/ARSLiAJONMde7231AH+AmoBm2t7YKGGeMCVqCPuBcTYFuwM3u91oPvIR9PpaR45juwO3uuZOA37ELMI4yxoRavDIXN8Y2wH7ghxzbTgL+i10s71ngTmPMoXDOq1R+NFEpFZnV7mt/EfkaeDPnh7Ix5msgJaDpM6Ae0AW7uNxit82fAKYCVwO7geXYRNUJmCUiDxpjHgkRx2jgImAF8C1wLvA00B74t38nEbkOeB04gF2ldQ9wKvAfoJuItDTG/BPGz30iNsl9bow5HHD+XsAr2B7kFcaYt8I4l1Jh0Vt/SkXmE+zgicrAZGC7iLwjIoNEpHmoA4wxLwKPuV9+a4y5xm0D6I9NUp8BJxtjLjDGdMX2mDYAw0Xk7BCnvQjoY4w50xhzCdAYMMDlInJ5wH4PAoeBVsaY840xlwEnuT/HScAVYf7cQbf9RKSSiDyL7UltBk7XJKWiTROVUhEwxjhAd+AFbAJIAi7F3vL6XkR+F5FHRaRamKccgh3anmKM+Svg+2wA7sCOJLw9xHEzjTGvB+y/FbjV/fKmgP2OAQ4B2wL2PeR+3/64PbswZA2kEJH62N7ZIOAtbJJaG+Z5lAqbJiqlImSM2WeMuQU7f+pm4B3gb3fzscB9wBoROT6/84jIMcDJwG/GmPUhdpmPvQ3YMcS2mSHaFgL7gHNExP87vhRIBFaKyH0i0sr9GdYYY14yxvyUX4wB/InqaOzzs9bAYGPMFcaYvWGeQ6lC0WdUShWRMeZPYCIw0X3WdApwOXZ+VX3srcF/5XOKY93X+u4Ai7zUEpGKOZ6F/RoinkwR2YJNfkcC27G9ptlubI8Cj7r7zAKeN8b8WOAParVxX58E/gE6GWPC7Y0pFRFNVEoVkttLOQWoYYz5NHCbe0twNXay79vYZzmdRKSOMWZb7rMBEO++/gnkGuqeQ0XsLTy/w3ns5+9JZbhxbRSR1kBn7ND684BGwC3YASFXuEPq8yQiJwLJwNfYz46WwJmEf9tQqYhoolIqMl8AFUQkOa9bXsaYb0XkW+zoupoEPB/KYav7usMYc00h46gHrAlsEJF4t32fMWZnQDyZwP/cf4hIA2Ao9lnWSOyty/z4b/stA8ZgRxqOFpGNxph3Cxm3UmHTZ1RKFZL7gb8C2xMakNd+IpIAHI+9RbbBbc51a88YsxH4A2gkIieEOE8bEflZRKaG+Db/F6LtAuxoRH9Cqi8iq0VkTojvOwj7/Ou4vH6OAP5EtcoY8wdwMfZne0NEzgjjeKUioolKqciMxCadUSLyHxGpFLjRLbE0BagNTDLGHHA3+V+TcpxvPPa23lQRqRtwniOBl7FDyDeQ280i0ilg/+Pcc4EdgQjwG7ZH938i0i3H8b2xnwPhVJnISlQAxphV2GHtlYD33QK9SkWdz3Hye3arlMqLiNwCPIX9oN6N7WXtwlaIOAPbq/kQuMwYk+4eUxtbXT0emAssNcaMdG/XzcbOi9oDfIlNaucANYAlwP/5E15AZYo/sEPPFwN7sc+gqgJPGGOGBsR6IfABNil9iU1exwOnY3tFHY0x+dbuE5GdQBWgWo7JvgOB54CfgLOMMbvCv4pKFUx7VEpFyBgzAWiBTVYbsD2OSwDBDorobYzp5k9S7jF/YZ8J/YatItHFbc/ADnK4BViLHaRwDnZU3x0EJKkc7saO4hNskvre/b5DA3cyxnyEvSU4D9s764kdbfgG0CaMJHUCcASwJjBJued+3r0GjbFVNBLyO5dShaU9KqVKoYAe1eXGmLdjHI5SxUp7VEoppTxNE5VSSilP00SllFLK0/QZlVJKKU/THpVSSilP00SllFLK0zRRKaWU8jRNVEoppTxNE5VSSilP00SllFLK0zRRKaWU8jRNVEoppTzt/wHvYFmvNVdopwAAAABJRU5ErkJggg==\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(\n", - " hamiltonian(results_euler[:, 0], results_euler[:, 1]), \n", - " c='b', label='Euler integrator')\n", - "plt.axhline(hamiltonian(theta_ini, p_ini), c='r', label='theory')\n", - "\n", - "plt.xlabel('Steps $k$')\n", - "plt.ylabel(r'$\\mathcal{H}(\\theta, p)$')\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "id": "abroad-flour", - "metadata": {}, - "source": [ - "<h3>Second example: even worse!</h3>" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "brief-emerald", - "metadata": {}, - "outputs": [], - "source": [ - "theta_ini2 = -3.\n", - "p_ini2 = 0\n", - "n_steps = 100" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "graphic-laundry", - "metadata": {}, - "outputs": [], - "source": [ - "results_euler2 = np.zeros((n_steps, 2), dtype=np.float32)\n", - "results_euler2[0] = (theta_ini2, p_ini2)\n", - "\n", - "for k in range(1, n_steps):\n", - " results_euler2[k] = solve_euler(*results_euler2[k - 1])" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "allied-poverty", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaEAAAEpCAYAAAA6S513AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAADBkklEQVR4nOydd3gU1feH3+3pvUMCoS29d+lFQAR776jYsf/sfu29YUNFBQsiggoiRXrvLYS2lISE9F62787c3x8DighKyc4G2Pd59iFsdufc3czM595zzj1HI4QgQIAAAQIE8Adafw8gQIAAAQKcvwREKECAAAEC+I2ACAUIECBAAL8REKEAAQIECOA3AiIUIECAAAH8RkCEAgQIECCA3wiI0BliNpurzGZzlb/HcTYR+M5OjcD3dWoEvq9Tw9/fV0CEAgQIECCA3wiIUIAAAQIE8BsBEQoQIECAAH4jIEIBAgQIEMBvBEQoQIAAAQL4jYAIBQgQIEAAvxEQoQABAgQI4Df0/h5AfUCj0XhRBLnmVN+r1WojDx+jqo6Hdc4S+M5OjcD3dWoEvq9T4wy/rwhAFkKctpZoAv2EQKPRyIAmMjLS30NRByGAw393jRZk6fDPGuX/vrYtZOVnrQ4kD6BRftZofGxbBllWbAG4HYdta0Gn/+v5ACeP5FW+UyEDGjCalOdAOZe0KjhbJK9iX4i//o5CqHM+CfGXrSN2wfe26wnV1dUAQghx2n/owEpIoSYyMjKyqqrK3+OoM4QQCLcdYa9C2KvQmELRxTXGtWsJaLRoQ6LQhsehi2nowzHIiKoS0BnQhEXh/PUdNAYT2sR0dGlt0CU385FdgagqRT60D12bnkj7tuKa8RGayHh0DZpg6DMKTVwD8LjRmIJ8MobzESEEGo0G7+5NSPu3IednIVeXEfL4Z8i5FuTyQnSpzdHENUDjA3ESbqciDFodrkVfI2rK0Malom/WFV2jtn+OzxcIyYtGp8dbtA+5ugjZVonGYMLUbhhyTSnC40ATEoUmKAyNryd6KhIVFUV1dfUpe5COJrASQlmGns0iJCQPsrUC4ahBOGrQxqaiDY3BlTkfbXAkmpAodJFJaCPifTuOI6sclwPPpt+Rig+iMZjQtx+EPr0DwmlDExRa93YlL6KiGG18AzwbF+FZ9jMIgTa1OabRd4LeCAg0puA6tx3g3xGShEanQ8ragWfrMuRD+xD2WoLveQN0ekRZAdqGzdAY634yINwO5JKDYAhCm9AY1+8fogmNViZByc3QxiTXuc0/bQsBXjcagwmpMh+pLAdhr0Z4HJjaj0B43cjVhWiCItAER6AxhfpMIH3JYRGqFkJEne4xAiJE/Reho09o2VqOVFWEcNYinFYMzXuBx4nnUCbaYOWE1kYmoQ0KU2dsThvSoV3IxdlIxdkYulyELrUVUk4m2sR0tKFRdW9TltFotXg2LcKbuRY5/wDa+AYEjX0FUVkCGg2aqHi/XtRHZt1yRRnSoYPI1ZUIay3Gnv0RsoRj6lcIux3hsGO8YCBBQy+m5plxyKVFCK8HXYM0Il4ej+3rj3Evnnv4qBoiP5yMlH8I24evgdGIxhRE8FU3Y+jVH+vb/0NjMqEJDkXfzIxp0Ag8OzMQLifayGi0UdFoYuL8frMT1moICUfO24/7j++Qi3LRJjTEeNGtaBs0BacdTUjdn7/CZf/zPNXoDBg6D8OzYxnoDOgSGqOJTvbJCu1vY5C8oNUhnLVIpdkIRw2yoxpDWke0kYl4sjYqqyVTGNqwWLQhkT5dwZ0pARGqI/wpQuJwfEbYKhEel7JsNwSji07Bc3ALck0xwmVHYwrF1H44UmUBsq0CbVAYmqBwZYmvUixDCIGoLUcuzkYuzkbffjBIHry7V6FNbII2oTGasGifXDBS1k6krB1IB3eBVkvwmP/h3bMJtDp0qS3QBNf9CuvfEG4XcnEhUlEBGlMQhvadsU/5Em/mFuTyUoTLRfS3v+FaMh/X0vmKAIRFEHTJNWhCw/CsX4kmJBSCQ9ClpKJLTEYqzAedFo3eAAYj2vAIhMuF8HoOGxXKe7we5KpK8LgRbhfa6Dg0kVF41q1EOOwIuxVNdAymCwbh+HkKnh1bEVWVCGsNkV/8hHvZHzjn/II2Nh5tfCJBIy9HGxuPlJeDLqmBYkPN79LjViYScckIpx3H58+gjYpHm94afcf+6FLSfWZbyrMgFe5DLs4CrY6gi+5DLstTJjIqiNLRCMmLXFWIcFkRTiuasBj0CU1xZf6hxL1MoWhDozGkdUC2liPcDjSGIDCYDq+k1HfzBUSojtBoNFWR4aGRRUu+A70RbVA4xpb9kMpzkaoK0WiVYKc+2QyAVHZQCbpqtMpsJSwGb0kWyF7lRmEwoYtrjFR+CNlaBrKEkLwY0rsi2yrw5mxDeN0guTE07ow2JhX37qVo9EFojEFoIxLQxaYh2ypBq0NjDEGjUz98J2QZUV2CXJqLrllXpKwteDOXoU1srLg0GrZCYwqpe7teL3LePqTsnWhCwjD0GI5r1hdoQsLRpbdBm9bCJ+6b447FbsNj2Ymcl4uUn4Ohex8MHbpQeePFaGPi0CUmY+jcg6CLr8SzOxMAbWycIgwGgypjPFVkWy1yfh5yeSlyaRGGXv1BkrC+8YwiqkHBBF99M0EXXY5zwW9oI6PRpaajTUxGo/P9hEdIXuSCbKTsXegaNkWb2gLnpJfQppnRpbdB17iVT1yrwutGozfitazHu289wl6LNj4VY7/rFRHQ6f13HbrtCLcdZAldVDJSWQ5SZR7C4wKPE2Orgcj2KjzZG9HoTaAzoE9phTYyCe/BzaDRgU6HNjgKXVwaUkWecjw0oNGgT2yGbK9Cri7+M3lIG5umfB95mQhJAtmDNiIRfWIz3JYVyNYKkgbcQLXVHhChM+XISqiyvPSwOHjRhkQi26uVwL7sVf74sY1AlvCW7P/rDxWZjC4qCc+hTEWENFo0plD0ic2QqgoRzlpFSLQGtDENFEFy2dHojUqsQqurN0ttIXkRteVooxLx7lmDJ3MpGlMo2oRGGDqPAL3RNwFlWUYuOYRGp0cTk4T9nXvRRsYqN5yWXdE1Mte5zeMhFebj2b4ZKXsfUk4Wofc+jvB6sU/6BF3DRugapGLo2A1dg7Q/Yx3nGkIIRGUFaDVoo2Kwf/cFUs4BpEMH0SY3JOKFd3EtmoNw2NE1boouvTnasHDfjkmWlUlJ1g5FmFLSMQ67Ec+mRWjjGqBt2ByNvu7FQThtyOX56Bq0wGtZj2fbArQxKWgTGqE39/JJfPNMELIMXtfhe5gHjSkUDEFIpdlKBqwsKQlKsal4S7IQjprDmX1gaNQJubYMqSLvcEajBl1cYzTGYGXSrdWj0RnQBIUpLkK3A7Q6ouMSAiuhuqC+x4R8hfB60OgNePesRcrdgVxZhDYmBeOQMQhblXLSBfsmtiSEAIcV15xJSFk70JhCMA68An2Hvgi30+crHW/2frw7tuHNsiDl5RDxxgQ8G1bh3rQWfXozdI2bom/eKpA9dxRHMsDc61bgydiMdPAAUkkhUROn48nYhJS1F32zluiamdGG+liYhMCzeBrSvgzkiiL0XQZhGn4TwlYDIeE+mdgJjxO59BByyUH0rfoglx3Ck7EQbVwa2rhUdCnN0KgUi60vBNxxdcT5IEJ/ps/uWYtcmoNclocmKgHTwJuR8i2g1aONa4jGYPKNfbcLKXsH0v5MpAPbMfQZhb5DP7wZKxQXW3SCT+wCSCWFePfswLtnJ0heQu95DMeM75BLS9A1M6Nv2gJd42aq+v/PFf48ryw7ca9Zhnf/HrxZ+4h890vQaPBkbkbfsh26ho189v0KWw3CWoU2MQ3nt68jF+eia9oOXYvO6Nv29IlNOOw5qCxUhKksF525F9rwGNzrZqKNa4g2LhVtTINzOiszIEJ1xLkoQsLjQsrailxRoLgUUloczgZajiY0Em1sKprwGN/tm5Bl5MJspP3blRuBJOGaMwlds/bomrZHm+Sbm5KQJKTcbLy7t6MJDcfUfyg1Lz6GJigYfcu2GFq1Q9+idZ3bDfAXRzLApNxsnDN/xGvZgaipJuyxF9C36Yh33270zVuiMRjr3rYQiIpipAPbEbVVGAdfjXvFTHDa0TVrjzbNrCR++AjhdSMX7kcuO4RclocutRX6lr1xr5+FJixacedFJ9c7V97pEhChOuJsFSEhS6DRIKxVSNlbkSuLEVVF6DsMQdewJZ7N89HGJKONbYAmMsHnQVW5uhxNWBTywV04p3+IJjQSXbN2GHoMQxuT5BObQpaRDu5HYwpGm5hM1R1XogkNw9C6PYae/TB28d1MuC4RkoRwupFdLvBK6BNikWqsSOVVf75GnxiHxmjAW1aBxmBAG2RUUrL19T82JVdVoDGakG1WrG88i1RwCH0zM0GXXIuxay+fxtik/ANIezYjHchE1JQT/MjHiLJ8QIMmvoHPY7JCyEjZ25ErCxGVhWhCozD2uhzP9iXg9aCJTkQbmejTfUu+IiBCdUR9FiEhBDiVlE1tdDLSoV14szMQNWUIawWmi8eB5EHK3o4mKhFtdJKywlEpbVsqysG7ZalygdtqCL7jRTRhUQiXA21kbJ3bE0KALCNqqrBNHI93xzY04REEXzcGU59ByLU1aMMj6tzuKY3RK4FWg1RVg2PzTqTSCrzlVYT260ZQ2+bk3fEMcnUtstVOcJc2JL3+GPl3PYd943Y0JhPaICNNln5PzewllH8y5c/jJr70IIZGKeRe/SB4vMguN5GXDSXh2Xs5dNPjeApL0IWHYkhLIWX8s1iXrse5bRe62Gj08TGE9O2C1mRCyDJaU92vQk4F2WbFu2cH2phYdA0bUXX7leiatsDQvjOGLr3Qp/kmLVt43GgMRjybl+BZ9gsIGV3T9hgvugWMQaomCUlFWchlhxCVRQiXHdOQ2/DuXY+UvxdNRBza8Fh0jdrB4RWjWtf0qRAQoTriz+y4ygpVc+2FLP1Zd0ouPKBsQLXXKPsD0jvgWjEVuWCfsmckOhnToFuQSnMRtmq0EXFoIuJ86lr4x3glCbkgC+nAdqTsXQTd8H/I+fuRDu1D17Qd2uR037jY7DbcW9bjzdiEJ2MTwTeNxdizH+5VSzC064w2znfxpBMhVVbjzs5Dqq4lbGBPqmfMp/rnP/AWluKtqCJ93pdIFdWUfzYVfXwMurhowgb3JqhVU2xrtqCLCEMbFoouKgJdVPgZb0iUqmuRaqzItTaEVyK4vRnH5h3YN2xHKq/CW1pB/NN34zlURP6Yp9BGhKJPiif27usIG9Kb6p//wJCSgCG9obLiUjljU7bW4t25Dc/2zWgTkgm+5Brs336ONilFyUhMqPuVtBACUV6IlL0LfdfBeDf8gXfzMiWe1LQd2satVL2+AGRbNaKiALm2HFFThqHDEOTqEtxLv0UTEoEmNAp9675ok5shHdiMJigUTXA4mtAo1ZMihBBER0cHRKgu0Gg0VZGhwZGFXzwOxiC0kQmYht6ONzsDOX8P6E2gN2Bo3RcAb9bWw2nXOrTxqWhjG+Ldvwm8bmU3f1Ao+iad8B7cjlyaC5IH4XFh7HmZklGz8XeEywYeN4beV6JLbYV72ffKSRYcjja+EboGLZBtVWiMwT5LFvgvhBCIsgLkohz07XrjXjAF795th+M67dClt/VNaqwk4d23G8/WDZgGjUDYrTh++ApDx24YOnRF2yBNtZukt6IKtyUb174c9HHRhF/Un0M3PY5rbzbGxg0xtW1O4nP34dp7EKnGiiE5Hn1CLBpD/S3LKGQZqawST2Ep+vgY9AmxFL/wIZ6cAtwH8wjp1p7k956icvLPCI8XY7PGmMzpGFLUFXvXsj/wbN2AZ9tGDB27Efbwc0j5uWjjEtGY6v6aEJIXOf8A0oFMpP3bMV1xH3jdePdsQde0rc8mWSc7NmGrQtiqFU9HSASeDbMRDqVyijamAcYeo3Et/wFRVQTGYDSmEGXiWngA6dAuRVD1BnRNOqMxBiEd2Hq4aLEGTXQSuoTGeA9sRjhtSjq3wYS+ZW+8BzOR8/cotfk8TgwXXI2wVuJeMpnkO96k2u4MiNCZ8udKqKIc3A6Ex402PAa5ugS5sgi8bvB60DVuj/B6kPZtUPb7CBldSgt0Kc3xbF2AkDxotDo0odHozT2QCvYhastBp+yA1zVsCZJX2Q1tCj28/K8/GVmK68+OJjgU97Jf8G5cqFQkaNoO4+g7AXx2EcpVFWgiovBs24jt/VfQxsVj6NgN00WXo4tP9InNoxFC4C0sxbljL65d+wnp3Ymg9i3JGngTpmaNMDZvRGjfroQN7Ilss6MJCa43+7vqGuHxojHoqV2wCufWXbj25yBV1dBo+kfU/LYY5459BLVtjqlNc4zpDX1f6uaw+1UbFYN1/Ku416/C0Kodhh59CLpwtE9ty2UFeDYsQMraiaipIOj6x9A2aIpcXog2IbXeZVQKj0sREbcD4XWjS0xHrixCLslBSB7wutGld0RjMOHZsfzPiva6w0WFPTtXKNXlNTo0wWHozT2Ry/KQa8uV6gxGk7LfUasFIYiOjQushOqC+hwTUgPv9tVI+zOQsnehiY4neMz/kPIPoAkORROd6LObrZR/CNfKRXg2r0UuzCfinYlowsLB5UQb69tiq7LNgXPHXpwZuwkfPRhvYSkF414mqI1ycw0f1hdTi8b1um6XP3DuPoB91Wacu/bh2rGP1B/ew1tchnXRGoI6tCS4Yyt00b5tiSLbavFmbEYuKyFo9NXYf/gK4XRg7NoLfav2PqtUIaxVYAhC1FbgnPIWwmFD17gVhp4j0DVudV6eK4GYUB1xvoiQkGXk4lzk3D1IORa0UXEYL7wB97Jf0ISEoUtvgyYuxXdp23YbnoxNeLZuIOTOB/Fs24R35zYMXXoqNw8fuPaO4C2rxLFlJ2FDL6B29hKKX/wIk7kJwR1aEnXjJegPu5rOt5tIXeDOzqPm96U4t+3GuX0PyeOfJaidGevC1QR3bYshNdmn36v34AFlo/HmdYjqSiInTEUuyEMTEoI2uu6TY44g11QgZ+9Ek9AQbUwS9vfHoWvYXCkv1KIjuqRGPrNdXwiIUB1xroqQsNUg5R9APrQXbYNm6Fp0wjnxObRJjdCmtUDXuLVPN4kCyJXlaKNjcc6ejv2HrxQ3SpeemAZfhCbId5v4ZLsTbUgQ1T//QeWkn/GWVhDcuQ1Jb/2f4kLR6/yeIXYuIiQJBHhLyil79yvsGzPR6LTEPzGW8OH98JaUo0/wnTAIpwNNUDCOmT/inPEd2uSGGLv1Juiy631ey0+urVImeLkWtHENMHQbomxVCItCl9oCbWpzn2SM+pOACNUR54IICYcVufAgckE2upZdQKvFMeEptClN0KW2QNemO7pk31UjPhrvgb24Vy/Fs2kNwm4jcsJUhLUGTVAwmuC6L3h6BMfmHViXrMW+dhtSVS3pi7/BvTcb4ZUwtWxyTtZ6q+8IIfDkFKAJMqILDyV72Bi0ocGE9OxI+MWDCOnWzne2vV68u7bj2bmN4Gtvw714Lt79ezB07Y2hXWefJDcci5S9C+nQXuTcvWAKIuiqcXjWzEW4HWiTGyvJDuG+qTyvBgERqiPOJhESkoSoLEYuPoRcnIuh7yVI+7bh+uVTZYWTnI6h+1A0cSlKRW8VAqeyzYpn2wakg1mE3HAHznm/IleUY+zWG12zlr5J2xYCz8E8bMs3IlVWE/fwbVR8OR3hchHSuzNBbVvUuww1yeHGVVSBu6waT5WNiA5N0JoMHPp6AZLdiWR3EdmlOcmXX8Del6dgP1gMssAQE06bd8dS+MtqSudvQmPUozXoafrYFaDRkP/jMvShweijQons1IywFg2wHyzCEBmGPjKkXgXPhRC49x3EvmYr+qQ4wob1pXDcy5haNiGkr7KPylfjlYoKcK9djmfzOqTsfUROmHq4NThoY9RboUj7tyNl7VAmjZUlBD/4PtKeTci5FjSJaWgT09DGN/Spe7quCIhQHVFfRUjKP4BcfAhRXojwejCNuBnX/O+Q9mxCG98QbVIaht4Xg8EEWq2qN5sjm0JtX3+Ma9Ecxc3WrTemYZf4bFYnu9x4i8swpqWQd+czuPflENK3K2GDehI20L+VESSnG0dOCbLbQ0S7dPK+W0zFyh04iypwFVfRZ837FP68igPvzMAYG4EhJpymj19JSJNkDn44C11oELoQExEd0onu2YrSxVuRbC40Oi3aIAPxgztRuysXqyUP4fEiuzwkXtwDr81J3neLkWodeGpsJFzUjcSLurN26FM4ckqQbE7ih3am4+RHyf1qPvasIoJT4wlKiyd+aGc0ev9WcRdC4Fi3DdvKTdhWbMTUqinJbz+BY9tujE1S0UX4qICu3YYmJBTXysXYv3gfbWIKxm69MY24DG2EbxMrjodUeBBp3zbkohzkkjyCrnsU4bLjWTIDTWwS2tgkpexQTFK9quAeEKE6QuknFBZZtn4JmtAINOHRPouVCLcLUVOOsFYrm05TmqAJicA952vk6nJETTm6Jm0xjboD16wvEF432thktPEN0bfp4dcMHM/ODNzrV+LZtAZtRBQRb3yKVJiPNjrGp/Gd6l8XYF20Bsf67YSP7E/iiw/iLa9CFxOp+nfhqbJi3XMIqyWP0BYNienVitX9HsNxsJighnHEDe5Iy5dvoXTxVrxVNkzJMQQlxxDcKMEvKxLZ7cVrdWCMCadi7W5qMrJwHirFkVdGx68fIX/KEva/PYOQ9ERCmzWg8b0XE9woAU9FLcaEKPU3rbrcaE1GCp94G9vitZhaNSV81CCirh7hM5vC68W7JxPPxjUEXX0zUtY+XMsXYuzSC0PHrj51If/ruOxWpIO7kMuLEBVF6Nv0RNu4FfbXxqAJi0QTGYfe3AVDn1F4d28Cj+vw/SsKbULqnx2I63RMXg+ithJhr0VYq4jrPojqmpqACJ0pymbVkMiiL15AWGuUzp13vIh78TQ86+YrVXCNQQRd/xjIEq653yh12HQ69B36om/TE+fPH4PTAZIXTWwyppG34l40De/OdeB2Ilx2Qh79BCnHgvuP79CERqIJjcDQ+2K0DZvh3b4SbXgMmshYpTW1D4o7nipyWQnurRvA5STo4iuxf/sZmqBgDF16oWvS3Gc3KHd2HtbFa9EGm4i6YTRl47/B2CSV0D5d0UWrV5LHVVxJ9dYD1GzPJvnyCwBYd+HThJkbEmZuSNLlFxDbrx3OgnKMCVFoz4IabsciZBlXUSX2rCJs+/OJH9oZyelmw8X/A42G8DaNSBszjIQRXXHml2FKiVVNmGSHE/u6DKSqaiIvu5CSVz9FGxJM6ODePnXbyRVluNcsw715Hd49O4h46X10DdKQy0vRNmzk9/iNkLyImgpEVSkYTOgaNsOzajZSQZbSOl3yEHzny7hXzMSz7GelWKoxCNM1D6ExBeGaNVEpAaTTo2/XG32HPsqE11YDkoQmMhbT6Dtwr5iFN2Olcv9yOwm+901EWQGumZ8rYhcaQdJ9r1FdWxsQoTPlRO44IcvgsiNcTmWWERWvtFbOP6CU3JG8aOMboI1LwWvZArIMOp3SAbRhM+SqMvC4wGhSOpCa6vcGR+HxIGpr0MbEUvP8w0jZ+zF07Iqx9wCMvfr7zq4QCLsDTXAQuVeNw1taQdjg3kRcPIDgLm19ZvdoJIebmowDVG3cS6O7RlI8ZwN7np5ERIcmRLRPp8H1AwlulKBanM3fCCFwFVVSuzOHoOQYwlqlsrr3I7graons2ITEUT1peNNgZLcXrVGd2IUz04J10Rqsi9eiiwon9ft3laoPcdE+i/8Jhx0MRqTsfVjfeh40WgyduhN08RXoUhv7xGZdIYQAjwvhtCv3r4hYkCXkvP1/3b9iEtEmpOLdtw08bqV7bHAoujSzcv9yOZT7lzEIgsP+ce4H3HF1RH2NCamBkCRcf8zCs20j3p0ZmIZeTMit9yIV5qFN8F07ZyHLOLftpnbBKqwLVxN+YR/inxiLOzsPQ6MUn9/ovbV2rHsOEdXNTPYnsznw9gzCWjYkqmsLmj52BbqwYDQ6bb2eNPgDV2k1NVv3g0ZD/NDObBj9P7y1DqJ7tiSmb1sSL+quyjikqlp0UeEUPfcB1kVrCBvYg7AL+xA2oIfPbAohkA4dxLN1A4ZO3dEEBWH78A0MHbti6NAVXZMW9SZWoxYBEaojzicRkstK8GRuwZO5FX2L1gQNvwT75E+VCsYduvk0KCu8Eo5NmWhMRoLamcm77UlCenYgbOgFGJs39ukN/0gs7dDkBRRMW6EIUI+WdJ76JO6yGnQhJvShgS6qp4rs8VKbeZDKdbtxl9fQ4rkbyBo/E1dRBTF92xLTpy2GCN/GVDyFpVgXrsadlUviC+Oonbsc9DpC+3ZFG+y7v6lwu/Bs34InYxPejE2Yho3GdNHluBbOxtC6g6o1Dv1FQITqiHNZhOSKMjw7t6Fr1BRtZDTV425G36YjhnadMHTuiS7R9z1MZKeL0je+wLpoNfrEOGLGXkP4sL4+t2s7UEDZom2ULctAsrvoPusFypZsQ2s0ENm1Obog/8fdzkVqd+VStjSDihWZ1O7Kpd/WT7BZ8pDdXiI6+L4IaO28FVT/NBfnzn2EDuxJ0huPqSIGSu1FB7YvP8SbuQUhSQRfcSNBF12GXFGGJlq9eJpaBESojjhXREhIElJeDrqEJKSiAqxvPoewWdG3aU/QpddhaNnWJxkz/xiHV8KxcTu1f6zE1KopkVdfRPUPswnp2xVjWorP7MouDxVrduG1Okga1ZOMOz9AHxZM7KAOxPZtiyFK3VL3AUD2Smj1Ogp/XkXWB7/iqbASN7gD5pdvwRDp2+6i3ooqnNsthA3oQcnrn+MtKSd8eF9C+3ZDG+LbVa8QArkoHyQJbYM0ah66DbmmGn3Lthi7X4Bp4PBzotZcQITqiLNRhJQ2xmVoY+PxZG7BMeN7pP170ERGEfb4i+iSGyKXFisuARUC6UpnUBdCCA4Ovx19cjzhw/oRPqIfhga+q4J95ELe8eAESuZuJMzckJRr+tPwpsE+s1mXSB4vQpLRBxkpt+ThsTmRXB4MoUEktE+nJDMbW1Gl8mKNhrT+7XBV26g+WIw+xIQxNJiQhEgMwf5p93Gq2HNKqFi+nQY3DiJ/ylKKZ68jfnhXEkZ0Iyg5xmd2vRVVWBetxfrHStzZeaQvmoy3pBxdVATaIN9/d0II5NJivHsyQZYxDRhG7StPItdWoze3Qd+8Faa+Z8c5ezTnrQiZzeZU4EVgOBAHlACzgectFkvpqR6vvouQcLuQqyrRJSThWvYH7hWL8GbtAyDq0ynIlRVIhXnoW7RWdaOdkCQcGzOpnb8S66LVxNxxFdG3XuHz+mCukipK5m+iZO5GgpJjaPP+XZQv305Y60aY4tXfaHg8JJcHnclA+Z5DFG7aS21BBfbSKno8cgW2kirm3f0hziorXoebvs/fQIcxw/hp1P8A0Bn1JLRLp+8LN7Lls9/JX28BlGSOEZ+No3DjXta9MwOvw43H7qTPczeQekFrvuryAEFRoZiiwmh+cQ+6jbuEHT8sRXJ5CE+JJTw1jvjW9aeoptfmpHxpBiXzN1G2aCs9F76O1mTAa3UQ2sR3bmLZ6UIbZKLso++o+m4moX26Eja8L2GDe6maWCCcDrz7LXgtO5Erywm9YxyO6d/i2bYRXeOm6Bo1VYQpqP5m1Z6XImQ2m2OATCAZ+B2wAJ2AwcABoLvFYqk4lWPWBxESkhe5vBS5uBBNcAj6Zi2xTXgXT+YW5PIS9K3aE/HCu3h2ZiDsNnTpzdDGxqt+ch4RHl10BPqURPLveIawIb0IG9bXp642V0kVnioboc2SWd3nUSLapZMwsjtxgzv6LaFACIG1oByv00100xTWv/8Leat2Un2wGI1ex23rx7P3t3UcWrWDsOQYQhOiaHZRd3RBBuyl1QRFhWEMC6qTlaoQAq/DhbPKhrOiFp3JQEzzBuycupTSzIPUFlYguTxc+sOTbPlsDvvnbCAqPZHoZg1oe+MgjOHBaLRatDr/pJ/LHi9ag57ShVvY+cgXGOMiSBrdi4a3DMEYE+4zu8oKaQ2ODdtJevsJ7Cs3ITtdPk9qOBFyTTVS9j68Bw8g5WQReueDeLZuwP71x2hTG6NrkIpp6MXoUtORC/PRxiegMfpvFXy+itDnwFjgFovF8u1Rzz8DvAK8Y7FYHj+VY2o0mqrI4KDIvJefRBMdiy6pAUEXXYZUkIdcXYkmNAxNUDDamDg4PFP6t5v/EReRbLMirLUIhx1hrUXfqh1yUT7udSuQK8sRlRWYRl6OLjWdqjGXoY2MRpuYjLHfUIKGjcazKwNteCTaZP/XkZKqain7YBLWRWvQJ8YRO+5mwvr7Nh1XSDL5U5dRNHMNNRlZpD94Ken3j1YlrnUssiRTdaAQQ6iJ0MRoZl7/BmW7ctCZDLS6qh+9n7yG3OWZaA06IhslEJYcU2/3EzmrbFTuz6cqq4iK/QV0vmckZTtz+H3M+8SaGxLXOo22NwwioX06ktuLTqV9QEcQkkzlBgvFv62lySNX4Coop3zVTpJG9yQ41bd9pqxL11H17UycO/cRckEXkt98HI1R3RbfxyJkGbm0GOnQQeSCQ0p6eEQUNU/cg1xeiiYsnKCLLiP4qptx/PIDeNxoIqPRxsZh7HaBcq9xOtAEhyiVTUxB/3n/wutVNt4HBSOVlSDKS5GttYjaaox9hyDt34Nz/kwaPvky1U7XeSdChwCnxWJpfszzeqAWOGCxWE5ph6NStic8snj2z8iV5SB5Cb7iRlyL5uBaNAdhtyEcdsL/9w5ybQ21T98Pej3oDQRfexvBl1xD1dirkWuqweNB36IVEa9/gu3z9/FsXocmOBhNaBjhz72FVJCHe/UStNGxaKJjMbRqhyYmTtmpXI8KFspuN/Y1W7EuXE1ov26EDepF5fezCBvcy6crHsnuouSPzWiNehIu6saepycTc0Fr4gZ3QhesXjabq9qGzmjAVlLF4scnUpKZTUhsBD0fv4oWl/Qif90eopslExJ3Zu4/jwfKy6GyEqqqlMeJfna7lYaWOt1f/x7985F/Q0MhIUF5xMf/9XNCgvK7E91/3LV2yvbkUbYzh5QeLQlNjGJyjweJMTckuUszmo3sQUp38xl93tPBujef3C/mUjxnA6FNk2n78b2ENE7yqU1veRWODdsJH9GP8s9/xJm5l/BhfQgd0ANduG8TKk4FIUmIqgoQAm1cAq5lfyDlH0LUVIFeT+idD+GYNQ3XvJnKZNhpJ/LdL5Frqqh98XHlpNFoCLnudoJGXUnlzaMRtdWg1WHo0IXw59/G/s0EPDu2oQ2PQBMeSei9jyGXleDds4PES6+h2mo9f0TIbDYbgPuAGovF8vUxv9MANUC5xWJpfCrHPVV33J8zBa8H9Ho0BiPCblOuboNRqZpQT324/4ZscwACqaqWnCvuw9SsEWFD+xA2vC+GxDif2haSzM5HPqdk3iYiOzcj7Y7hxA/p5FObx1Kxv4Cd3y8hb91uqg8WM2rSoyR0SKdgvYXEjk0Jij697DqbDQ4cOP4jJwckqY4/yL8QFPSXIDVsCC1bKo9WrcBshshjNNVjd1K6I4fCzfuIbJRA0xHd+OXKV4hqkkTD3q1p0LMVYT5MKDga2e2lfPl2Yvq0pXzZdvKmLCHlyj7ED+vq0wmKVFWLddk6rAtW4diyiyZLvkOqqUVjMKCPjfKZXV8iZFmpkHDk5DMYlPvYkaoJJ7mKPy/dcSfCbDYPARYC8ywWy0Wn8t76EBPyF1Ktjdp5K7AtXYdjYyaJrz5M2IV9kEorfJpcAMp+koLpKzBGh5M+7hIKf11DzAWtMSVE+dQuKKnDhZv3cWhFJrkrdjDiswdw1djJXrSVhr1bk9A+Hd0ploKRJNi1CzZuVB6ZmbB/PxQX++hD+IDk5L+E6cijQwdIPJzgKISgwpJH3rrd5K/ZjSkyhMFv38muacsJjougYe/WqmTqea0OSuZupHDGSqq3ZdFj7stKkVidb6vJH0lqqJ4+j9K3v8TUIp3QQT2JumYk2lDfFfGtrwRE6DBmszkYWA+0A66wWCy/HPP7qn97//79+yPDw8M5H0RI6eeSg235BkIH9kAbbKLs3UmEDupJaL9uPiudf7R9hGDjJS/iOFRKypV9SbmmH6HNG/jULoCjspa81btoNrI7GV/9wZ6fV5LWvz2pfduS0s18SrEPISArSxGbDRuUf7dsAbv91McVFwfR0cojKuqvf4/+OToaTCZF6GRZ+ffon49+rqYGSkuhpER5HP2z03nq4wNo0gR69YLevZVH27aKR/oI2ycvZP+c9ZRkHqTZRd0Y8t5deJ1u9CpsCHYWVWBKiKLwl9Xsf+MnUq7pR8pV/Qhp7LutAXDYZb12G7blG4h/YiyODduxb9xO2IAeBHVoeV6U8ImKiqK2tpZmzZpV/9vrLBZL1Il+d9aL0GEX3QxgNDDTYrFcdpzXVP3bMc51EZJtDjRGA649Byh48FXQagjt353oG0djTE/1vX2Pl7LF2yiYtvzPBm21O3MIa5mKRoVsrOxFW9n6xVxKdxykQa/WXPjBXRjCTi3tVQjYsQMWLlQeGzZAxUnmYOr10LgxNG2qPJo1++vn9HQIUalTgBCKa7CkRFmdZWXBnj1/PfbuVeJOJ0NoKPTooQhSr17QsyfExICrxk5VdhGJHZow7+4PqTpYTJMLO9NkeFfiWvm2jI0QgtrMg0oyy6w19Jj3KoaoUDR6nSoZlO6sQ9T8thjb8g14ispI+2k8uqgIhNtz1rrt/ovzXoTMZnMQMA1FgDYDAy0WS+2pHudcdMd58osVN9vqzTi3W0j95k0MjRvgLSrD2FSdmlaSw402yMDagU+gDwsi5doBJI7u6fNaYtW5Jeyfs4HcFZmM/vZxircewFVtI7VPW/SnEDsoKYFFi2DBAuVRWPjf70lJgW7dlEeXLkqcJTX176uG+ookwcGDfxemXbuUFd7JrKC6dIGLLlIe3bqBBpnCTXvJ+mMzFfvyGf3t4+Sv240pPIS4Nr5tiXAk5btwxip2Pz2JxIu6kXL9QKK6tVDl3PcUlqJPjMW+ajOFj72BoVEKoRd0IfKakRiSfZvhpybntTvObDZHoWxQ7QNsAoad6v6gI5ztIiSEwH0g97A7IJPEF8fh2pOFdcEqQnp3IqRHR9X81V6rg6KZayn4cRmm5Bg6THwId0WtT/d6gDIDN0WEsP79X9g+eSFNR3Sl2cgeNOzd+qT3vni9sGLFX6Kzdeu/vz46+i/BOfJI8V3ioN9wu2HbNli7FtasUR55ef/+nthYGD5cEaRhw5T/g+K22zpxLlqdjhaX9qL7w5f7XBRcJVUUTF9J4U8r6DL9GYTHi0avw5QY7VO7RxBuD45tu7Cv3kLEFcMQDiel704ipFs7gru3J6h1s3rXiv5kOW9FyGw2J6IkIbQDlgGjT2cFdISzTYSE24PLkoXLkk3klcMpn/ADNb8sILh7e4K7tSN8aB9Vg6RCCNxlNZjiI1k3/BmCkmJIuW4AcYM6oPXhxeWxOzkwfxN7Zqyi3HKIW9eOx21zYAwLPumkAq8Xli2Dn36CX35R0qVPRHQ0DBkCF14IAwYo7rRTvX8KIbBV1qI3GjAEGcn4YwO2KiuOWjsxDeLpOqo3S76aw6Gd2XjdXjQaGPPRQ+xcto2105eiN+rRGw0Mun0k0UmxLP/uD4IjQgiJCKVBq0aktEjFWllLSESoTzeeHjr0d1HasuXEWX5areK6GzkSRo2Ctm0FJRlZFG/dT4cxw8iYtAAhy5gv7U1wrO+bFhbMWMmepycT3aMlDW4YSNyQTqo2JJRtdmyrt+DYlIl9w3Zibr2C8Iv6U/HVdII7tyGondnnte3qivNShMxmcxiwEugIzAKusVgsrjM5Zn0WIeHx4s7OQ6quJaRbO0re+Jzqn+ZiSE0muHNbEp69B2Thl5nUkRlmwdSlhDZrQMfJj/7pBvEVQpYp25VLfNvGrH3zJ0p35dDyir40Gdr5pF1tR1Y8P/0EP/8MZWXHf51er8Q7LrxQeXTp8ude5X/FZXdSfKCA4qwCyg6VMOCW4eTvzuG7xz+lqqgCQ5CRa166nS6jevPV/R8QEhlKcHgIqW3S6XZJH3Yu3UpNWTV6ox6dQU/ni3pSkl1IbmYWXrcHr9tL6wEdMQabWPT5bzisDuxVVsy929Ln+iG8ffmz5GYeICI+isYdm3Pnp4+wZ3UmlQXlJKQnkdSsIaF1XMy1ulqJlc2dC/PmQVHRiV/bqhVcdx1cey00bw4FGyzs+GEp2Qu3kNavLcM/fcDnqyOvzUnxrLUUzVxDh0mP4jxUisagI7Sp+ktZIQRyrY2Kz3/EsXkHrr3ZxNx5DbH3XE/tglUYkuMxNm+sSo27U+V8FaHPgLuA+cAoi8XiPdNj1gcREl4JT2EJ7qxD6KIiCO7Qkryxz+LYlIk+KZ6w/t2Jf2IsnvxidFHhaEP90/de9ko4cooJbZrClhvexBgXSYMbfO9rtxVXsuunFez6cTmGEBNX//YiuiDDSduUZVi5EqZNU4SnpOT4r2vQAC65RHEhDRgAEf8xMS/PKyV3RxZ5O7OpLavh+tfH8vt7P5GxYCOJTZOJS0tiyNhR6PQ6akqriEqKwaTCLNfr9lJdXIHD6qBhq0ZsnbeOjAUbKckqpOhAPi8u+5DyvFI2/76Ghm0ak9omnaSmDepk9STLivtu7lzlsW6dkhRxPLp0UQTp6qshMcZJyfYsGvZqzYoXvkOj0dDm+oHEqJA5WfDTCva+NIWQJkk0uGEQyZdf4NPJ1L8h3B5khxNdZDjFL3yIc7sFd3YeYYN7kfzOk1iXrkd4PBibpmFomITW5L+WJOedCJnN5jQgC9ABnwLHK1ZqtVgs75zKcTUaTVVEUHDk3qfewpAcjyEthfBhfZEqqxFeCV1k+GmX7hBCIFxupKoa9IlxeAtKsG/IwFtYireojMirhqNPiid78C3o4qIxNm5AxGVDiRg1CNf+HAzJCfVi/4Etq5CCqcso+GkFkZ2a0XHyoz4vRS9LMgXr99CgVysyv11E2a5cWl87gMSOTU7abmEhTJ4MX32lbA49HikpcNVVyqNXL8V9dDzcDhfZW/eRtWUvpmATg24fydfjxuO0Okhtm05a2yZ0uLDb6X1YFTlyzZflFrNlzjoO7czm0M5srvrfraR3asGiL34jvXMLmnZtWScrprIyJcY2ezb89tuJ09j79lUE6corwWgrZuePy9g9fQWJHZtx8VcPn/E4/gvZ46Vs4VZK5m+kzft3U7XRgsagJ7JzM79vPhduj3IPSYil6qe52Jatx52Vh1RRRdN107Et34B1wSr0yQnKpHVwL7ThIUilFeiiItGE/Hupnn+17ZWQamrRmoxogkxYF6zGW1yKp7CM5q88Qo3dfl6J0LXA1P94WbHFYjmlmh4ajaYqMiwsMnvC93gLSxFeiYSn7qLi6xlUfjUdqcaKRqej0S+fINsdFD39HhqjAY3RQNT1o4i4eCB5Y59FrrUh3B5MLRqT9PpjFD8/nuqZC9GgQRsVTvq8r3Du3Ef1z39gSI5HnxRPaN+u6FMSEG6PX2c0x8Nrc1K74yDRPVqy6/++RBdsIuXaAYS38m1at6O8hp1Tl7FjyhKCY8IZ/f3/ERx98okNXq/iEvryS5gz5/ixiuRk5WZ39dVKmvHxhMfj8pC12YIx2ETjjs14pve9RCfH0rSrmVZ9O9Cqb/sz+JT1k9ryGlZ89wcHNls4uHUfox67loG3jmDXigzSOzYn+AwzG202+P13mDpV+RsdLyXcYIBLL4WxY6F/Xy812YXEtkxl/n0fExofRbtbhhCV7tuyPaDEjrLe+RmNUU+D6wbQaOxFqmwpOBWEJKHR6XBnH8KxeSeeolK8haXE3HEVAHm3P6NMpj0eYu+5gdj7buDQbU8iV9eiMRowNkkl6bVHqZz8M7ULVyPcHoTbQ8MvX8O19yAFD7yIcHnQhoeQ8My9hF88kMJHXkcfH4M+OZ4m4249v8r2+Ir/cscJIRBOFxqjAeHy4MkrRLjcSv5/SiKG5HgcW3YqxzIZ0YaHYkxLQbbZQa+vd+LyX1Rv2U/ed4spnrOBuIEdaPeZ7330AMXbDhDftjEH5m0kd3km7W4eQkL79JN+/4ED8PXXMGnS8dOpo6L+ikVccMHx4zuyJOOyOfl63HgObNpDUrOGDL5jJF0u7o3k8Z5yFYWzGcnjxePyoNPrmHDnW2Rv2UvDVo3od9Mwul3S54yPX1UFv/6qCNLixYob71iaNIE77oDbboNgdwk7pixh97QVNB3RlYGvjznjMfwXQggq1+2hYvl2mj15DUWz16E16Ikb3NFv7rrTQXi8CFlGazLizj6EbHci3B40RgNBbZrjPpiPt6wSjdGA1mT4c/+g8HjQhJx4T915547zFfUhJuRvHIdKqVpvIfnKPmSNn4lGoyH56r4EJfm2Lpjk9rJv9joyJi3AWVnLJd8/cUqzXCGUG9j77yvxh+MxYIByI7v8cgg+xrMphCAn4wBb560jc/Fm+lw/lIG3jSBjwUaa92hd5wH8sxm3083+9bvQGfS06NWGdy5/lgYtG9FxeHfMvduekUAXF8OMGfD990oM6Vj0eiWz7s47YVA/N7b8UqKbpzDn9vdJ6dGSNtf2x+TjTq0Axb+vJ+ezOdizi0m+sg8tXrjR7646fxIQoTrifBahknmbyP1yHrU7c0i+vA/mV29R5aJyVNSiDzJQtGU/mz6ZTcfbh9NoYIeTDow7nfDDD/DBB0qNtmNJTIRbb4Xbb1cysI5GCMHBrfsIj49Cq9Py0U2v0nF4dzoM7UZa+yZo62kLhvqEEIKSrEK2L9rEtvnriWuUyG0fjCN/Ty5JTVPOSJB27ICJE+G775Qq4seSlgb33KO469w5B8j4+g9ylmbQ/eHL6Hj78DP4VCePPbuIyg0WGlzTn4OfzgatluTLL1Cl7mF9IiBCdcT5JEKy20vZkm1UbdxLi+eup2jmGjR6HXFDOqFToc5Xxd58tn45jwNzNzB8wjjS+p5S1w1KSmDCBPj0039muGk0MGKEMlseOVKJLRyNtaKGxV/+zqbZa9AZdFzz4u3nZFzHH0geL1q9jk9ueY3cHVl0GtGTHpf3p0mXFqd9TIdDyWScOFFJqT+W4GC45RYYNw5SoypwVNQS06IBS5/4ilZX9SOlZ0tVJlSVGyzkT1lKybyNxPRtQ4cvlSSK82GFFBChOuJ8EaGcL+aS9cGvhDZLIfnyC2h48xBVGq8JIZC9EtbCCmZc+iJtbxpMu5sGn1IvHosF3noLpkwB1zG7wkJDlZjBuHH/XPXYq21smr2a1NaNSWrWkHmf/ELXUb1JbZN+Xtwk/EHZoRI2/bYagOH3Xcam31bTpKuZmJTTbweyZ4+SaDJ58vE3FA8fDg89BIMHeNn903K2fTkPY1gwfZ67gQY9W5623VNBsruo3ZlDVLcW7HhwArLDTdKlvYkd1EGVCZ4/CIhQHXEuipCQZKo2WiievZ6qzfvoMfdlajMPYogOIzgtQZUxyF6JA/M3seWzOTQb2Z0u91x8yp06d+yAV19V9vcce6o2bAgPPKCsfKKPqcBirahhxsvfkLloM636tefCey4lrW2TOvhUAU4FIQQ/vTCJTbNW0ahDMwbdPpLW/Tqc9vFcLuVceP99ZS/SsbRuDQ8+CDdcL1O8eiuhSdFEN0liz8+raXV1XwwqVSJwV9RSPHsdRTPX4qmopdeyt3DmlWGMjzynBCkgQnXEuSJCsseLbX8h4a1S2fHgBGozD5IwsjtJo3uq0irhaCS3lx8ufIrg6DA63TWSJhd2PqVV15Yt8MorSvbUsXTrBo88Aldc8XeXm9PqYP0vy4lNTaBVn/asmLKQbqMvICzG96VgAvw7boeLLXOVXas9rxzAqh8W0W5IFyITTq9+mxCKi+6DD2DWrH9OUOLjlZXRvfeCzl7Oyhe+p2CDhfa3DqX9rRcSFKVed1TJ7kIXYsLyv+/I/2EpcYM7knhxDxJGdj/rV+MBEaojznYRKvljM0W/rKZsaQaRHZvQ5adnkJxu1Wdcrho7O75fjLvWQa8nrqYyq5DoJsmndIx16xTxmTPnn78bPhyeeUZJrz762vU43cx88wc2/LqC5j1bM+zey2jUvukZfhr/IssyHpcHjUaDMciIy+FCIDAYDejO8j41XreXn174ms2/r6XNgI4MHTua1LYnn4p/LAcOwEcfKRuSrda//y4iQkliePhhMFoL2DJhDh3vHEFIXARel4fwFN82bjwWV0kVJfM3UZORRZt3x1L48yq8tXbiBnciOPXsq64dEKE64mwSIdkrUZORRfmy7XgqrbR85RZyv5qP1mgg/sLOqlUGPpaNH81i28R5NBrQns73XExcq7RTev+WLfD00/DHH//83SWXwLPPQteuf3/+wKY92GvstB3YicVf/k6nET2JbVh/L2RbrY3CnEIKc4voOaQH2XsO8suXv1BZVoW1ysqND99Axws6cmX7q/C6veiNevqP6s//vf8Yz9z8HBlrMvC4PYRGhPLLjhnM//EPZk6aRXhUOFExkdz06E3EJsSwYckGktKSSG6UTGRMZL2dbdurraydvozo5Fg6jujBruXbaN2v42mXDqquVoTogw+UAqtHYzIpmZKPP670dspetJWFD31Gk2Fd6HLfqFOeLNUV5cszKfhpOWVLt2OKj6Tnwtfx1trRBZvQhdS/WnHHEhChOqI+i5Ds8VK7IwfZ7SG6R0vWX/QcksNFbL92xA/rQkzv1n4bm7WwnJxl22lz3UD2z9tIfOtGRDY6tXjTnj3w3HPKHpGj0WiUMjrPPAPtj0lg275oEwsmzKKmtIpRj15TJxsn6xKHzcH+HQfI3p2F0+Hi6nuuYsILnzH3h3mkNEomKS2Zx959BGuNjZ0bdxAVG0VEdAQpjVMIjQjF4/KgN+qPmyouhMDj9mA0GamprKUkv5jaqlqqyqro2KcTHreHiS9PpDC3kMKcQi674zJufOgGvnh5ItHx0aS3bEzz9s2JjDn5pBA1qC6p4vM738JeY2PInaPocUV/DKbTK5Xldivp+2++qZxfR6PTKRuWn3kGGidayZi8gJ0/LOWGRW9gCA1StZr20QhZxra/kLAWDcj5fC773/yJiA5NiOnbhrQ7Rvi8B9fpEhChOqK+iJAQAldhBWg0mBKj2HLt61Rt2kdwWgIp1/an8d0jkRxudKfQmM0XVB8sZtPHv3Fg/iZaX9ufC56+9pSz7HJz4cUXlWyno3fKa7Vw/fXKqqhVq7+elyWZov15pJjTmPHSZNI7t6DTiJ4+bVdwMgghyM/OJ3PDDoKCgxh4yQAeuvRhJEmmaZsmmDu0YMR1I3A5XBiDjKqvSiSvhFanZf6P88nec5Ds3dlExUbxzISn+fWrmQC069GW9FbpfnfzCSHYv2E3CybMou+NQ2ndryOS13vaBV9lGWbOhNdfh02b/v47jUapnPHcc9CimVIJY/lz31CdU0K3By8luUvz4x5TLbxWh1KpYdUOmv3f1ZQu3srBj2cT1bU5EZ2aEjewA0YV2l78FwERqiM0Gk1VRGh4ZM7STYSkJ2GIDfdtG2JZxlVchT27iDBzQySHm50PTqB2t+JDaP70tTS8cRAVa3cT3joNgwo7wU+G6oPFRDRKIPPbRTjKa+hw2zCCok+tokBpKbz2mrLP59i6YZdfrsSDjhYfySuxafZq5n30Mwnpydz71ZN18EnOjPKiciRJIiYhhlv63IYQgvY929FvZD96D+vl88KudcXahevYsGQDmet34PV4mbTiKw7uOYjeqKdhk4Z+/wy7lm/j20c/YfCdo+h304WnLUZHqmq8/josWfL332k0cM01h8WoiZvd01ey+dPZJLRP56LPH6yDT1E3SA431dsOULN1P9VbD5D+wCXoI4LJvO8TwlulEdYylZg+bQhrmYqQZVW2XtgPFpPcthk1tkDtuDNGo9FUhZtCIhf0fwh7dhFByTH0Xv42+dOWU7V2N8b4SAwx4TS4bgBCVvrYa4ON6IKNBKXEYoyNoHZXLsLjVRICQkxEtEunbGkGtTtz8FTW4i6tps0Hd1P06xp2PvoF+tBgQpokYX75ZsJaNKRy3W7CWqVhSor2+8V/LKU7DrJh/EwKN+3l2rmvEJZ86qV8nE4lePzKK1BT8/ffDR2qpGF3O04B6p9f+ZaDGfu5+OGradGrjd++G1uNjZ8+m866hesoKyrn9qfGcNH1IygvLicmIabe/c1OFYfNQXBoML9N/o0fP/0JnU5Lj8E9uPOZOzAF+y82UWDJZe6HP7N//S6emvs2kWdYkWD9enjppX+WeDpajMzNvZTvOURCu3RWv/4jDXq0pNHADvXubyw53FRv3Y91dy7WPXnE9GtL0qieLGtzF7oQE6aUGGJ6t6bZE1dT8sdmXMWVGKLD0IcGEdu/Pd4aO86CvzZdBTWMQxdsonL9HmSHC0+NnaCkGGL6tCHrvV+o2rJf8dQAvRa/Qd63i2h15yisbmdAhM6Uo91xQggkmxN9WDC1O3Oo3rwPd1kNnior6Q9eirOgnL0vTkFyuJAdbhrdezEpV/Zl3bCnEV4ZXbCRyK7NMb9wE3nfLsKWXYQhKgxTYhTJV/RBdntBltGH108f79EIIchdnsnixybS+Z6RtLl+IIZTvCEJoTSPe/JJOHjw77/r0UOZnQ4c+HebmYs3M/+jX7hr4uMER4RiMJ1836C6QgjBvu37WPbbctr1aEvXAV35/v0pdB/cnZadzH53XfkSIQQ5e3PIWLud0beMYva3v7Nv+z76j+5Ppws6ovND3KQst5i4tERWfL8AjUZD76sHnlFpoA0bFDE6NgvziJvuhRegRQvYN3sdG8fPRGc00PP/rqLRgPpfYUNyunEWlCuCodUS06uVMqFeb8FTWYtkd9Hp+/+jbPE29r/x05/vM794I5Gdm7H1lnfRBRvRR4QQ278dDa4dQMncjUqYIDmaoJTYP8sTBdxxdUR9iQnVB4QQ5K/dzcaPZtH+lqE0HtwRIcnoTyPde906ZT/P2rV/f75FCyVofMklf0+1Ltyfx5QnPsdptTP6setoN6SLX8SnoriCR696HIABo/tz4VVDSWmsfsfN+kJZYRnLf1/BslnLKCkoZdKKrzAYDRhOs8fWmZCbmcXMt36g/FAJox69lq6jep/R8TZuVGKTx4qRTqeUBHruOWiUJpP1x2Zkr0Szi3twcMk2Gg04+TqH5zJ1IUJKm4Lz/AFURUZGivMde1m1mH7pC+Lbfo+KnT8uE16357SOc+iQENdeK4SyDvrrERsrxEcfCeF2//31RQfyRVlusagqrhBrZywTkleqg09z8rhdbrF01jLxf9c9KX79eqaQZVnsy9wnZFlWdRxnA6UFpUIIIb5591tx97B7xaxJs4S12qr6OPaszhS/v/+TEEKIioKyMz7ehg1CjBz5z3PWYBDi3nuFyM9XXueotIrpl70ovu17ZtfIuUJkZKQAqsSZ3H/P5M3nyuN8FiHJK4l9v68X++duELIsiwN/bDptEXA6hXjtNSFCQv55IT/2mBCVlX9/vbWyVvz0wiTxWMcxYuu89Wf+YU4RWZaFtdoqrul8nXjs6v8TS2YuFS6HS/VxnI1IkiQ2r9gsXr77FXFtl+uFy+kSbpf7v99Yx3g9XvHCwAfF53e9LYqzC8/4eOvWCTF06D/FKChIiEceEaKkRDlvDq3ZKX659jWx97e1QvJ4hdvurINPc/YREKGACJ02siyL3TNWim/7PyamjXpe5CzffkbHmzNHiGbN/nnxXnmlEPv3//P1klcSLwx8UPzwzERRU1p1RrZPlQO7Dog3xr0pJr/9jRBCiKJDRaraP9ew1dqEEEJ88OR48X/XPSk2r9is6irS5XCJeR//Ih7rOEZsmbu2To65bJkQffr883wOCxPi+eeFqK5WXndEkL7sdK/Y9Ols4aq114n9s4WACAVE6JRx252icIuiCitfniJyV2ae0Q1j/34hRo3658Xarp1yIR/L3nU7xbT/fSVkWRb2Gttp2z0dZFkWz495QVzT+Trx4yfT/OJGOpdxu9zij2l/iNsH3imeuuFp1e1XFVeImrJqUZxVINb9svyMhVCWhZg/X4iuXf95fsfECPH220LYD2tO6a5cMe+ej8QX7e8WVTnFdfBpzg4CIhQQoZPGUWkVG8bPFBM73iMWPfbFGR/P6RTipZeEMJn+fnFGRQnx4YdCeI5xlVeXVIqvHxwvnu51t9g0e7WqM+Xt6zLF9M9nCCGEyFi7XbicAZebL5EkSeRl5QkhhHj/iQ/E0lnLhCSpF+c7tOugeG3k/4l3r3pe5Ftyz/h4sizEr78K0abNP8UoJUWIzz77K85ZnVsiZFkW279dJJY9O1lU55acsf36TECEAiL0n7gOrzYWPfaFWPDQBFFuyTvjYy5eLESLFn+/GDUaIW6/XYjiYyaBklcSsiyLNT8tFb+89p1w2hxnbP9ksWTsFU9e/5S4sdfNYsH0harZDaAgy7LYuHSjuH/kA2LskLvEpuWbVbMteSWx7Nv54oWBDwq3s25iVV6vEN9+K0R6+j/FqGlTIaZMEeKI1lqLK8WqV6eKL9reJebf/8k5m8AQEKGACJ2Qoq37xbx7PxJfdb1feJ3uOll5FBUJceON/7wAu3QRYv1x8grydueIN0c/JXYs2XLGtk+FqvIqIYQQ0z+fIX77ZrZfAuYB/kKWZbHmjzVi1TxlBXxg1wHVbHs9XiHLsvj28U/r7Dx0uYT45BMhkpL+eS20by/E7NnK6kkIIZzVNmGZpcSpdv64TGQt3CJkFVeFviYgQgER+htHTu6tE+eJST3GiS1fzBXO6jOPu8iyEBMnKq62oy+4iAghPv5YmSEejdftEb+9+6N4vNMYsfKHhaq5YuxWu/jq9a/FFe2uEuXF5arYDHBqFOYWimu7XC/eGPemKCs889Tqk2XXigzxbJ/7xKSHPhS15dV1ckybTYg33hAiOvqfYtS79z9jovvnbhBThz8tvhvwuNg1bXmdjMHfBEQoIEJCCCHsFTVi48ezxOReD4ma/DLhqrEJyeP97zeeBHv3CjFgwD8vsmuu+WvvxNE4au1CkiTx2ztTRWWRekJwYNcBcV3XG8Qb4978cy9LgPqJ3WoXX78xSVzR7iqRs+/MYzYni9PmENNfmizWzlgmZFmus7hkZaUQzzzzz60JIMSFFyp7kI4gy7LIXbVDbPlirhBCCMuvq0XVwbM3kaEuRChQMYGzs2LCkb9bztIMFoz7lPShXegw5kIS2p1+c7Cj8Xjg3XeV8iUu11/PN2miFB8dNuyY1zvdzH5vGntWbufJOW8etw2BLyg4WICt1kaj5o04sDuLVp1aqmK3rnC53FRXVpOQFM+2zZlkbtuFtdaGzWbnrnG3UnCokB8mK30uNFotoy4fTpfuHfhm4o9Ex0QRnxBLaqMGNEw7+yo6lOSXEJ8Sz9oF64iMiaBNtzaq2d46bx2bflvNtS/fQXhc3bS1KC5WivN+9tk/i/Necgm8/DK0a/f359e9+zOZ3ywksVNTOo4ZTlr/Y15Qz6mLigmBuhNnGY6KWjK+/oOpw56heFsWyV1bcNPydxj6/l11JkCbNyvFRJ966i8B0ungiSdgx45/CtChHdm8NvIJyvNKeeD751QRIMkr8dOE6Ywb/RDZew5iDDLWawFyuz3syNjNnp17AXj4rmfo12kkHdP78th9zwOw35LF3t0HqK2xEhSkVIwODQulmbkJzcxNaNwkjdDQYGRZJvtADgvnLuXDtz7nqwnfA/DoPc9y7cW389SDL/Htlz8evdKvlyQ0SECj0aDRwCv3vMaHT3+Mrdamiu22AzsTl5bIq8MfY8uctf/9hpMgMRHGj4e9e+HWW5W2JEeYNQs6dFB6Ge3d+9fzPR+9glvXj6f5yB5UZRcBsOvH5VQfLK6TMZ0NBFZC1P+VkOT2otFqKNy4l9/veJ/0IZ1odVVfGvZuXacl251OpajjW2+BJP31fOfO8OWX0KnTMePySkgeL+X5pRRaDtF5ZK86G8t/8dp9r1NdUc1DbzxIciP/dMX8N5wOJx6vF4Cx1z9EZsYuGqY14KYxV3PDmKvYtjmT6JgoUhomYTDUTQ224sJSsvYfJHt/DgUFRTz2zP2Mf/MzFs9fQY8LutC9dxf6DeqFKaj+deysrarly9e+wu1y88T4/1PNbvbWfayZtpjrXht7WBDrrlbhnj3wv/8pBXyPRquFG25Q6tI1P6ZtkRCCVS9NYc8vq4k1N6TT2ItIH3LMhVePCNSOO4djQl63R+Qs3y4WPfaF+KLdXSJv7W7hcbjqJNHgeKxdK0SrVn/3ZwcHKxvyjt3zI4RS7+3NS54WCz6f5ZPxHA9JksSC6QuFy+kSZUVl9a62W011jZgyabq447pxon2jPmLG1N+ELMti1bJ1orbGPxtjXS632LR+m/jkvS/FLVfeI6qrasTmDdvEZ+MniX0W9bLUThaX0yUqSivF129MEk4VS+E4rA7x5uinhGXNjjo/9rZtx9/QrdUKcfPNQuzb98/3eJ1usW/OerF39johhBDLnvtG7P1trXBZ1dvicDIEEhPOMRFy1drFvjnrhaPSKnJXZoppFz8vNn82R9Tk+S7QbrcL8eijygVx9AXSv//xy+0IIcTaGcvE453GiKWT56mW+VZZVimevulZ8cCoB0VZkXpZVf9FTU2t+On7X8XuHRZRXFgiHhr7tJg1Y56orKjy99BOyJ6de8Xzj78mercbLi7qd7XIPXjme8fqkuqKGvHK3a+KOwffJQ5aDqpmN3PJZvFk97Fi5ls/CG8dJfYczdq1SqLCsWKk0wlx001C7Np1/PfJkiR2Tl0mZl7/hpjQ8nax9h1l43V9qFcXEKG6FKGICOF1qbuhzG13ClmWRd7a3WL6ZS+KCS3GiF+ve11U7D9O2pkPWLdOCLP57xdEaKiyB+J42uI5/P2s/GGhyNudo8oYhRCitqpWXNftBvHla18JTz3Z9FdSVCoeuedZ0b5xX3HXTY+IzG0nuIPUYyRJEmtXbhRut1vMmjFP3HbN/WLh3GXCc7ylr8rIsizmTZ0vbuhxk7Bb1avHVl1SKT4b+7YozirwmY3Vq49fJFWjEeLyy4XYtOnE73VWWUVlVqGQZVl8N+BxMWXoU2LFi9+LQ6t3+my8J0KWJBERHhEQobp4AFWhhiDxafMxYvplL4oN42cKIZTWBp46qqrsPbxrO2/NLrH0mcli6vCnxafNxwhrUYWoyikWOcu2qzazcTqFeOqpf65+hg4VIjv7+O/JyTwgnu//gCjYd0iVMQqh3Ij2bt8rhBAid796qbwnwuPxiF+mzRYb1mwWdptdfPXpd6K8rMLfw6oTHHaH+PnH2eKKYTeLPh1GiOLC+lFu5ogALZyxUPUK59NfmuzT6u6rVgkxePA/xQiEGDZMiEWL/tr0ejwkj1cUbt4nNnzwq1j//i9CCCGWPTtZLHz4M5ExaYHIW1N3EyPJ4xUV+/NF1gKl6sWu6SvEZ63vFCE6UyBFuy44kphQkldI8bYD2EqqaHl5H1a/OpWMSQsITYgiLDmGUZMfpSavnOxFWzCFh2AMD6ZBz5aExEdxYN5GJLcHd62DiLQE0od0YvXrP1Kwbg+1BeVodVpuXTee7MVbqdxXQHLX5iS0S0dnUrcx2LZtcPPNkJn513NhYUo69p13/r3JHBwOlP6wiNnv/sjVL95+xk3EThanw8l7j71PcV4x7/3yrl87mXq9Xmb88BufjZ9ESsNkHn/ufjp1rf8dNk8Xy659tGjVjB+//YWyknJuvvNaIqMi/DYer8fL6w+8QUl+Kf/74jnikuNUsXtw236+vO99Oo3owaVPXH9GnVz/jbVrlQ7Ds2f/83cdOiiNIa+9Fown0VeyYm8++et2U7orB0dZDSO/fJitX8xl78y1hKXEEJYSS9f7RqHRajm4eBv6IANoNMS1TiOmeQN2Tl2Ks9KKq8ZOcGwEne4cwbJnJrP7pxWEJEQRa27IiM/G4aqxodFoSG6aFuisWhf8W3ac5PZSm1+GtbCCBj1bUm7JY++stbhr7LhqHbS/ZQhxbRqx+NGJaA06jOEhpHRrQYtLepG/djcanZawlFjCkmP82onR61Wy3l54QdkDdISBA+Hrr6Fx4+O/z+Py8O2jn3Dxw1eT2FSdvSjlxeU8d+vzNDY35sHXx2E6xZbidYUsyxQVFJOYnMCzj7zKFdeNomvP+pupVNdk789hwvivWTx/BbfdfQP3PXK76p1ujyCE4MePp/HbN7N5d8bbqnW6tVbW8s0jH9NhaDf6XD/Ep7a2b1fE6KefQJb//rvkZLj7brjjDkg5xY/urLRSdbAYa0E51sIKzJdfgKvaxqaPZuF1KjeDFpf0osmwLqx8aQpanRZjWDDRLRrQbEQ37GXVGEJMGEKC/nHsQHZcHbrj6kNigq/Yt0+IXr3+vtwPDla6nJ4or6A0p0hMvPdd4VI5+CnLsqitqhWzv/vdr9lv61ZtEqMGXCcevkv9lgT1jZzsQ+KrT78TQghh2b1f1YrYx7Jjww7h9Xj/7GGkBpIkCckrCcuaHWLfet/H/vbtE+K++45fgUGnE+Kyy5QWE/WhBF0gMSEgQv+KLAvxxRf/PJl79FDK8ZyIXSsyxP91uUMsmTRXVSHYvGKzePL6p/yeev3Oqx+LPh1GiN9+nu/3sdQnZFkW142+U1wx/BaxZ9dx8opVQpIkcc9wpbW4mhy5LpZ9M08Ve+XlQrz+utIu4nhxo7Q0IZ58UogddZ9VftIERCggQiekpESI0aP/ftLq9UK88srx9/0cobKoXDzV825hWatuts2qeavFlR2uFhlrz6zD6+kiy7KYO2uhsNvsIvdgnrDbzq8OmSeLJEliyqTpomuLgWL+7EV+G0dBTqG45YJbxQ8fTlV1olBysFC8NORhMffDGarZdLmEmDr1+DUcjzw6dFCu7YyMf09mqGsCIhQQoeMyZ44QiYl/P0lbtRJi87+0c/G4PCJj4UYhhFDdBVecXyKu7XK9sGT8y/LMh5SVVoixNz4shve5SuRkq5f9dzaTn1coSkvKRf6hAr9tei0rKhMPXfaw6gVr7TU2UZpbLJw2h6itqFHV9u7dQjz0kNLZ9USClJYmxL33CjF9utJ+xRdkZwvx5ZdCGAwBEQqI0FHY7ULcf/8/T8oHHvirDfFx31dtE+NvfFlMuP1N1f39BTmFQgihqo//aKy1NtG340Xi9f+9L5yBjqunzOL5y0XXFgPFrOlz/WJflmUhSZJYOXeV6q7TDTNXiv8NHCdKc3x0p/8XXC4hZs0S4qqrhAgKOrEggdKA8qabhHjzTWWCmpWlvP9ksNmUTbSzZwvx8stKPCot7ejjB0QoIEKH2b5diLZt/37yJSUJMe8/3NeVReXipaGPiB+emeiTXeL/xvLfV4hrOl8nrNXql7SRZVls3aS4/rL2q7fx9lxkV6ZFDOp2iXjt+ff8Yt9aYxV3Db1bTHprsuq2l307XzzR9U6xf9Me1W0fobpaiO+/V9qrREb+uyAd/YiNVe4ZvXopFVKGDhVi0CAhunVTNrHHx5/McQIidN6LkCwrWW4m099PjtGjhSj9Dy+FLMvC5XCJDTNXqj6L3LR8s7iq4zVi/071XTlut1s8Me4FccngG4TbHei6WhfU1NSKjWu3CFmWhU3FCgdHqCitFGMG3CFmfPGz6rZ3LN0qFk2crbrd4+F2C7F4sbIZvU8fIYzGkxelU3kEBysliIKCAiJ0XotQaek/CyMGBwsxYcJ/ByezNlvEO1c8K7x+KIMjy7J49tbnxfZ1marbttbaxK1X3yduu+Z+YfWTC/BcZs2KDeLCXpeLvFx1Sk8dTXFesfjilYl+y2jcsWSLWPdz/eqY6nAIsXKlUorrnnuE6NtX8ZAcWy3lRA+9XogmTYQYOFBx9X/9tVKQ9cjcLdDUro6o760cjseyZUo5+IKCv57r0AGmToVWrf79vbtXbmfSg+O56Z37aDeos0/HeSzlxeUYjAbCo8L9svHRWmvjm4lTuWvcrej1vtkBf74z6bMpfPnp93z786c0bV43Pa5OhQM7D+B2uWnV+T8uhDqmcF8en9z6GoPvuJiBt12kqu1TRZKgpASKisDhUJrwud1Km4nwcKWKSmSkskn234qVBDarnocrIY9HiOefV4odHj1jefBBZdbzX9iqasVTPe9WZdPdsbgcLnH/yAfEr1/PVN12dVWNeOSeZ0VNTa3qts9HZkz9TTw57kW/2F6/eL24pvN1oqRA/fp3ZYdKxHN97xcrf1ioum1/EFgJ1RFny0ooPx+uvx5WrPjrubg4mDwZRo787/eXHyohNjUBp9VBUFiwz8Z5It57/H3sVjvPfPq0qqsgu83BzVfcTYcubXn2lcf8VnrmfEMIQf6hQjQaaJCqbvvxqR//yJo/1vLez+9gMKpbn7GysBwhBFGJ/i3VpQaB9t7nEfPmQceOfxeggQMhI+PkBGjP6kzevPRpKgvL/SJA+dn5WLZZePSdR1QVASEEj977LI2bNgoIkMpoNBpWLF7DmGseoLqqRlXb1953Dc3aNqUkv0RVuwDRybHEpMQx5cnPWDp5nur2zzrOZBl1rjyox+44j0cpzXG0602rFeKll4TwnmRG9b71u8TjnW/3iwtOCCHcLiWKqXYK+BHWrtwoXK5AFpy/eOWZd8S1F9/ul7+Bx+3xWxuQskMl4tkL7hUrvl/gF/tqUBfuuMBKqB6Tn6+sdt5446/nUlJg6VKlP/3JdjdYNXURt30wjmbd1Q3UgjLJefaW59iwdCM6vbrtGGb/8gfTvvuVnn26YlTZJRPgL5566WGSGySy35Kluu09W/fw1A3PYKu1qW47tmE846Y8x9zxMyg+UPDfbzhPCcSEqJ8xoUWLlPhPaelfzw0fDt9+C/HxJ3eM6pIqJK+X6ORYv7mh5v04nznfzWH8rA9UFaHs/TlcPfI2vpkxgdbtzKrZDXBihBAcysknrXFDVe2++9h7GIxGxr12v6p2j2CtqCEsJgKP040h6CSaAp1FBGJC5yCyDC+/DBde+JcAabXw2mswZ87JC5DH6eaLu95m8+w1fhOg2qpaJr05mYffekhVAZIkicfvf54HHh8bEKB6xN49B7j6ojFUVlSpaveu58ay5o/VFBz0z2okLCaCysJyXhr6CFXFFX4ZQ30mIEL1iIoKGDUKnn9eif4AJCXBkiXw1FOKGJ0MQgimPvslUUkxDL7zYt8N+D8wBZl4/L3HaNqmqap2XU43g4f358YxV6tqN8C/Y27VjJGXDeWVZ99V1W5YZBifLZigWiO84xGdHEvvawbx+di3cTvdfhtHfSQgQvWEbduga1eYO/ev5wYMgK1boX//UztWWW4xxVkF3PTOfWhPVrnqmJKCUnZu2km3gV1VtVtaXEZRQTH3PDTGb589wIl59On72bRuKxlbdqhqNyo2inlT57F5xRZV7R7N8PsuI6ZBPPM++tlvY6iPBK7SesAPP0Dv3pCd/ddzTzwBCxcqK6FTwWl1EJeWyGM/v0xQ6D/b8arFtE+m+eWC/+DNz5j2/a+q2w1wcoSEBvPj71/RvlMb1W0Hh4bw7bvf4q84uEaj4YbX72Lo2FF+sV9fCYiQH5EkePxxpfyOw6E8Fx4Ov/yiZMSdalUZWZb5dMwbbF+4ya/7YSrLqlg6axlXjL1CVbu5B/P44/cl3PPQGFXtBjg1klMSWThvGSuXrlXVbt+RfaittrJ93XZV7R5NSGQoxuAgPr/rHezV6mfs1UcCIuQnqquV+M877/z1nNkMGzbAZZed3jHXTFuC1+2l3eAudTPI02TpzKVcMLw30XFRqtr97stpXHPTZURFR6pqN8Cp4/V4+eidiara1Ol0XH7HZRzYqX6q+NHojXoi4iKZ9dYPfh1HveFMNhmdKw9U3qyalaV0Oj16A+qoUUJUVZ3+MWsrasTjnW8Xh3YdrLuBniZer1fUVqlfo626qkZUVVarbjfAqePxeES/TiPFts3qV1KvD9iqrOLJ7mNF9tZ9/h7KGRHYrHoWsnEj9OwJu3f/9dzTT8PMmUrV2tMlODyEu754nIatGp3xGM+EnL05rPljLWGRYaraXb96MznZh4iMilDVboDTQ6/Xc9UNl7Jhjfpxw9nf/s7CGYtUt3s0IZGhXPX8rTitdr+Ooz4QECEVWbhQqYBQcricldEI338Pr7568unXx8NWZWX7wo007eL/PTELpi9k/479qtv98O3PKcgrVN1ugNPnvkdu5877b1bdbnR8NIt+9q8IAXQe2YsWvdqe97Ghs1KEzGaz3mw2P2o2m/eYzWaH2WzebzabnzSbzerWhTkFZs+Giy8G2+HzLSYGFi9WkhLOlA2/rmDb/A1nfqA6YMvKrXQf1F1Vm7W1VjK37qL/4AtUtRvgzNBoNEz6bAo7Mnb/94vrkC79OrN7yx5cDpeqdo/Hyh8WMuOlyf4ehl85K0UI+Ax4BygCxgMlwOvA1/4c1IlYsACuvFJpGgWQmgqrV0OfPnVz/LXTl9HrqgF1c7AzwFptpeBgAS3aN1fV7rqVm+jYtR1Bwf5LSQ9wepQUl7Fo3jJVbQaHBtO5b2eKDhWpavd4dB7Rk4yFm3BaHf4eit84qSRgs9lsBG4HOgOJQBmwDZhlsVhyfDa644+lz+GxfG+xWG46/JwGmArcbDabv7JYLCv+7RhqkpkJV1zxlwA1bapUQEhLq5vjlx0qoaakkha929bNAc+AkPAQvl72per9W/oO7EmHzurvOwlw5nTv1ZlvJk5V3e4LXz6vus3jER4XSXqn5uxakUHni3r6ezh+4T9XQmazuQlgAT5GuflfDNwKvA/sN5vN35jN5kRfDvIY7jn874tHnrBYLAJ46vB/680mEYcDrroKrFbl/6mpdStAADEN4nh85mv1ojpAjiUHu039QOu2zTsIDgmsgs5GzG2as8+S/d8vrGP2bt/Hb5N/U93u8Rh0+0iik2P9PQy/cTJ3rneARkAe8BgwGrgO+BDFDXYTsMlsNnfy1SCPoR+QZ7FY/hb9tlgs2UAOcIpFbnzH+++DxaL8HBqqlOSpSwECOLBxD/p60qZg/rQ/WL9Y/djUUw+/RGlxuep2A5w5ySmJLN2kvhg4bHaW/rZMdbvHo3W/DjTqoG59xfrEyYjQIKAS6GGxWN6zWCy/WyyWaRaL5WEUcXoCxUU312w2J/hwrJjNZhPQEDhwgpccBBodfp1fkWX46KO//v/229DWBx6zmW9MoTTH/75tgKqyKqJU3qAKUFFaSXzi+TuTPJvRaDQsnLtU9cra0XHRVJdXq2rzRHicbh7rcBuyLPt7KH7hZETICKy0WCz/uNNZLBavxWJ5G8VNlwg8WcfjO5aYw/9WneD31YAGCPfxOP6TvXuh6PA3FhcHd9zhGzsVBWXENIjzzcFPkdpqKxFR6n71Ho8Hh8NJWLi6+5IC1B1ffvIdB7NyVbUZHh1BbZVVVZsnwhBkRG80UFumbgv0+sLJJCbk/NfrLBbLd2az+UngUuCROhjXiTjidzpRbuWR5/8WIDCbzVX/dlCtVlvndV6czr9+btcODD7ymAlJRneqReZ8xJVjL6dRc3U3y2q1Wl774Dm/1soLcGbo9DpkWd2iopExEXy1TN2yQf+GTq9DnKUrIa1WG/lf91iLxRJ1wvefhI15wCCz2fxf9Zy3A8kncbwz4Uge44naEx5xw/l991eHDjBiBEREwH33+c7ONS/fTnBEiO8MnALte7YnIkbdigU6nY7RV4xQ1WaAukXIMmrPIbxuL7s2q7s/6d8wX9AOnaF+TCbV5mQ+9VvAFcA0s9k80mKxnGgN2wjw9Zb1akAGTrRyOfL839a1/6bCoLT3/pdjnhYajZKI4PWeejXsU6HtwM6+O/gp8ua4t+g9vDcDLxmgqt3OzfqzYfdiQkKDVbUboG546qVHaNaiiao2SwpK+OyFz+g5pIeqdk/Ere/5p/V4XSDLcvV/3WP/jZNZCVkAL9AHyDSbzbeYzea/Tb3NZvOdQE9g8ukO5GSwWCxuFPdg+glekg7st1gski/HcSr42lP2zaOfsHX+et8aOUkiYyOpKq9S3W5MbDSlJWWq2w1QNySnJBAeoW5Mr7q8msjY+lFtvSy3mKnPfunvYfiNkxEhE8rNXYOy2vkaqDSbzVvNZvMys9mcg1LB4GPgZZ+N9C9WAY3NZvPfgg+H9zOlAeo2KfEzjTo05cAmi7+HAUBSahJFuepn6qU1bqh6YDtA3VBWWsHFA65T3W5BTiFJqafYMdJHWNbswFHj9wiC3ziZeXoY0AbocvjRGehw+HE0Y4DOZrN5M7AZ2ATsPryRtC75FmVv0mtms/lGi8UiDldMeO3w77+oY3v1mtb9OvL52LcRQvg9ON+mexss29QXxIsuGYrBV5kfAXyKZfc+WrZurvq526pzS1Kbpqpq80TsWpFBu0H1x62uNv8pQhaLxQtkHH58DXC4UGhr/hKlLiii1Pvw44jw2KnjdGmLxbLIbDZPA65HWRGtRNnA2guYZLFYVtWlvfpOijmVLhf3wuPyYAw6Ub6GOrTq1JJWnVqqbvf6W69U3WaAumHL+gza+aHVd2h4KA3SG6hu91hkWaY4q4BrX7rd30PxGxpRR/3WzWazFmjFX6LUFehgsVjqfOPI4Vp2TwG3ACkocaKvgfcsFovnVI+n0WiqIiMjI6uqqup0nGridrgwBvt9jy6v3fc6195/DU1aqRdodjldXDf6Tn6a+zX6epKuHuDk+OP3xaQ0TKZdx9aq2XS73FzV4Rp+2Pg9oeGhqtk9EfXBi3G6REVFUV1dXS2EiDrdY9TZFWuxWGRg5+HHd/BnYdE653CCwoscVT/ufMZaWcvLQx/huYXvERbt3326YZHhbFy6SVURMgWZkGWZ9as3c0H/+pHtFOC/cbncDBkxAJ1O3Q4sOzbsIK15mt8FSJZlvnn4Y6549mYi4qP8OhZ/4tOqlz6IBwU4DmHR4bQf2pUlX83x91Doe9EFrJqrvkd09BXDmTl9rup2A5w+U7/5mZeeekt1uyvnrqLvRXXUR+UMyFiwkeKsAsLj6keWnr/wf+nlAHXC8PsuZ+WUhVQU+DdVuX3P9oRFhqneMGzU5cNxOpzUlXs5gG8RQjDjh1kMGTFAddutu7Sm/6h+qts9Go/Lw29v/8jIh68+a11xdUWdxYTOZs6FmBDAzqVbadLVTHB4/aig4A/OZv/6+cTqFet56cm3mLdquqptSCrLqoiMifB765Oy3GKWTprHlc/fclafr3UREwqshM4h2gzsRGVBGbtWZPh1HE6HkwcuHofDpm63yLLSCkb2vwaX0/9tmwP8O+Hh4Tz98iOqioEQghduf4ENSzaqZvN4VBSUEZkYw1X/u/WsFqC6IiBC5xhup5tvHvmYqqIKv40hKDiIpNQkZn/3u6p24+JjSGucyjcTf1TVboBTIyf7EM1apNN/8AWq2t22ehu1VbV0G9hVVbtH43F5mDDmTTIW+FcI6xMBETrHaNyhGf1vHsY3j3yMLPmvKu/1467j5y9+wWF3/veL65DHn7ufiR9/Q3lZpap2A5wcXq+X+8f8H8sXr1bVrhCC7z/4geseuE71bLyj+e3tqcSlJdDl4l5+G0N9IyBC5yDD7r2M8NgIynKL/TaG9FbpXHrbJdRUqNs4rGnzdJ544SG8Hq+qdgOcHF9PmEJkVATDRw1W3fbV91zJoEsHqm73CPl7ctn2xwZueOOugBvuKAKJCZw7iQnHIksyuTuyaNyhmd/GYKu14XZ5iFa542pJUSmHcgvo0v3Y6lIB/EVlRRXDLriSn+d/Q2oj9aoVuF1ulv22nKFXDvHbzd9ld2IKCcJpdRAUdu5Uew8kJgT4VyryS5lw+5tY1uzw2xjmfD+X9x57T/XU6dycfO699TEK8utH6/PzHSEE0TFRzF81XVUBApj60Y+snr/GbwJUfqiEl4c+QlVRxTklQHVFQITOYeLSEhnz4YN8PW48BXsP+WUMl91+KSX5JSyZuVRVu117dOS2u67nobFP4/GcciWnAHXMi0++ydxZC4mJjVbVbtbuLH7/fg7jXvVPvx57tZVPbnudwXeOIiopxi9jqO8EROgcx9y7LVc+dwubflM3EHwEg9HAo+88wlevfY3ToW6SwtgHbiEhMY6d2/eoajfA3/nuq2msWraevgN7qm570c+LueOp24lNilXdNsCMl76hzcBODLw10P33RARiQpy7MaFjydl+gNDocOJSE1S3XVlWRXRclOqbSY/Y275lJ+07q1+t+XxnzYoNPHrPs0yb8zVpjRuqaru2qpawSKVZntquOKfNiZCV7NSgsOBzNhEhEBMKcErkZmbx4Q0vU36oRHXb0XFRzJs6j69e/1pVuxqNBpvVzrg7n+T7r39S1fb5jizLdOraju9+/Ux1AVo6axlPXP8U4B8BmnD7myz/dj7B4SHnrADVFQEROo/oe8NQBt0+kvevfZHSHPUD9r2H9WbFnJUs+VXd+FBoWAjf/jyBzz+czA+TZ6hq+3xl/erNXD1yDEaTkWYt1KuoDrB/x34+fX4Cj77ziOoC4Ki188ktrxLfKJEL775UVdtnKwEROs8YcMtwRj54JW6HW3XbkTGRvPDl80x44TOydmepajutcUO+//Vztm3ORJb9t4n3fGDpgpXcP+ZxHnnqXtU3hgoheO/x93ng1fto2lpd8QPYs2o7DVs35vrXx6LVBW6vJ0MgJsT5ExM6lukvTqbzyJ407apuN9S9GXtJb5WOweifltxFhSVM+/YX7n/sTr/unj8XKSsp57ILb+LDL9+gU9f2qtp22J2YgoxYq21EqNxXqyK/jJzMA3Qafn71swrEhAKcEa37d+TzsW+TuWSLqnZbdGiB2+nmsasep7yoXFXbACEhwaxfs4X7x/wftbVW1e2fi0iSxNIFK4lLiGXRul9VFyC3083/xrzAgp8Wqi5ABXsP8d7Vz1NZoP65fC4QEKHzmDYDOnLPl08w5YnPyNq8V1XboRGhdB3QlcevfYLKUnXrvEVEhjPpp4+JiY3mhtFjkSRJVfvnGmUl5dxy5b18/dkU3G4PpiB128y7XW5eHPsykTGRDL1qiKq2szbv5YPrXmT049cxaMxFqto+Vwi44zh/3XFHqC6pJDwuktKDRcQ3SlLVl/3d+9+zYclGPvztA79kEeXlFtAgNZkNa7bQvXfnQCbTKZJ9IJcbLx3Llddfwrj/G+sX9+bv381h84rNPPPp0+gNetXsepxuXA4XxVkFNO1iVs1ufaIu3HEBESIgQkf4fOzbSJLEbR+MU60xnhCC4rxiEhsmUltlVd2VAlBdVcO1o+4grVEDXn7naRKS4lUfw9mG3eagsKCI1EYN2bpxOz0u6KL6GJwOJ4UHC2lkboQsyaoJkCzJ/Pr691QXVzDmo4dUsVlfCcSEAtQpd3zyMNFJsbxz+bOqVeDWaDQkpSaxc+NO7ht5P/nZBarYPZrIqAhmLvoec5vmjBxwLXv3HFB9DGcT61ZtYuSAa/jlx98xGg1+ESBbjY2nb3yWuT/MQ6vVqiZAjho7E25/k7zdOVzz8h2q2DznEUKc9w+gKjIyUgRQWPH9AlGcXShkWVbV7u/fzxHXdL5W7NqyW1W7R2PZvV94vV6xZsUGkbltl9/GUV/54I0Jone74WLRvGV+G0NxfokYO+Qu8dEzHwtJklS1nbFwo/jx+a+E1+1R1W59JTIyUgBV4gzuvwF3HAF33ImY+sxEolNiGXbvZarFStYtWs+GxRsY9/oDqtg7EXNmLuDlp9+h3+BePPr0/SQmn78uOpvVzvdf/8StY6+jIK+IhKR4QsPUcdcej5y9OWxesYXLbr9UtfNy67x12Cqt9Lle3cSH+k4gJlRH/JcIicP1x6qyiyi35OGuteOuddDqqr44Kqzs+WUVAFq9jkYD2pPQLp2cpRmExEcSlhJLUHTYWRnwriqqYOI97xIWG8HN79xHaFSYarbzsvJYs2AtV911pd++u9paKxPe/5rdO/cyadrHuN0ejH7a2+QPrLU2pkyaztefTaFXn278743/Izomym/jWTVvFRlrtnPfy/eqZlPyeJn55g9snbeeOyc8QqP2TVWzXZe4a+3YSqqIbppCuSWPgvV7cFsdeF0eWl7RB1N4CNu/WYghNAhTeAjxbRsR37Yx9tJqTFGh6E7g7qwLEVIvleQswet0ow8ysu3L+RRstFBuyUOr03LD4jfJWb6dQ8szMUaGYgoPRnJ7QQiErAi5x+bEY3cBkPntImryy7EWlJPSrQUXT3qUjEkLcFsdxLVOI6lzM4L9EIQ/FaKSYnh42ovMfHMKm2avpv9Nw1SzHRQcxMo5q7Bss/DYu48SHKp+H5bw8DD+7/lxyLKMEILRg66nW89O3HHfTTRKT1V9PGpRUV6JwaBn/95sdu/Yy7czPsXcurnfxiNJEt+++x2Lfl7M/yY+r6rt2e/9RHF2AU/NeVPVSdjp4rE7Kc7IQnJ6aDSwA8uemYxl5hpkj0RkWjzXLXwdW1ElZbtzMYYFozMZQIBAIHu81OaXUV5jR2vQEd+2MXPueJ+SzGxCE6JI7deOwW/dQemuHPQmA1FNkutkzIGVEMpKKNQUHPlxxztp2Ls1Q967i13TlqMPMhJrbkhko0T0wcbTPr7k8aIz6MlasJmCDRZKd+ZQk1vKzaveJXd5JrbiSlL7tCG8QVwdfqq6J3PxZkoPFjHgthFotb7PaXE73Xz07McUHCzknelv+X01WV5WyaTPvmfad79y+703cfeDt6leFdxXCCHYvnUnUyZNZ+HcZbz76csMGtbP38MCYPGvS5g7ZR7PfvaMah16MxdvJqVFKmGxERiCjKqc76eDo7IWj81FRMM4frnqFYozsolrlUrTEV3pfPfFVOeUYIwIJijq9L0xksdLbV4ZzkorSZ2bseXzuWyfvACPzcnDe77B5nEG3HFnikajqYoIC488mGEhKj1JlZvKkZtX7sod7Jq6jEOrdxIUGcqVM/+HPsiAzmhAq69fJWVKc4qY9OBHhEaHcfM79xEeG+Fzm0IIyorKiE2MZfPyLXQd0MXvN32H3UF1dS3h4WFcfuFNDBkxgEuvHklzs/q1ys6UosIStBoNXknihkvHcu1Nl3Pl9ZcQG6du87njkbl+Bx63m44XdFQtBdvj8vDr69+zfeFGxn72GGnt6t/f1ONwsfmT2Rxcso2q7CK6P3gZne8eSfmeQ0Q2TkQfdPoT5lPBWlhBSvNG1NqsARE6U+pDYoKQZSr25hPbMpUdPyxl7evTaDykI80u7kFa33bojPXDcyp5vMx+dxqF+/O458snVLNbWVrJ49c8QbO2Tbn/5fv+7BPjbyy79vHrT3P4bcY8bhl7HXeNu5UD+7Jp0qyx38XyRNTWWvnlx99ZNG8ZOzJ28+p7z3LRJUPrzarO6/Hyw0dTmTtlLo+9+yhdB3RVxa4QgvHXv0RIZCg3vnk3IfXkHBOyTNGW/ez7fT1JHZvSfHRP1r/3C6l92pLUuZlf7w2BxIQ6oj6I0LHUFpST9cdm9s1ex4gJD+C2OrCVVNGgZ6t6caPwuDx43R4WTZzNsHsvw6jC7MvpcDLxlS9Zv3gD42e9T2yif7plHg9JknDYnRgMekb2vxaH3UGfgT25+LJh9B3Yy69jqyivZOPaLaxfs4URowZjbt2cV597l0EX9qX/4AsICg7y6/iO5d1H36O8pIJH335YlY6osiyTuWgz7Yd2pTSnmPhGifXiGpMlGVeNjR+HP4sh1ESL0b1ocUkvotKT/D20PwmIUB1RH0XoWA6t3smK579DcrlpdXV/2t86FFOE/9JkQdm498PTX1BgyeWW9+8nra06rou9GXtp3r45uzbvJr1lY0L8mC58IrL357B6xXpi42IYMXoIN152F5FREbTt0IpOXdvTrmNrgoJNdVrmRghBaXEZWftz2L1zL6MuH05O9iHGXPMAXXp0oEfvLowYPUT1BnMng+SVmDNlLkOuGIzH7SEiOkIVIagqquC7xyfgtNq5/5tnCPbzNeWssrFv9jp2TVtOs4u60eXeUVQeKCCqSXK9EMZjCYhQHXE2iBAcLnGzLYs9P6/igqevodySh6OshkaDOvqtd4kQgg0zVzLzjSk8PectwuMiVbM94YXPWD1/Dfe/ch89h9TvEvrZ+3PI3LaLHdv3oNfrEELwzcQfaZiaTIO0FN799GVqqmtZtmg1YeGhhIaG0KFzG5JSElm3ahOgrLYioyJp36k1C+YuZdf2PZSWlFNbY+XDL99g4sff8sXH39C4SRqt2rTg7gdv/bMEkV5fP9y5x2P/jv28/3/jCQkP4cnx/6fK6geg+EAB7179PANuHs6w+y5D56cYrBACyelBliS+ueARGvZuRaur+pHWv32970kUEKE64mwRoWPJXbmDdW9Px1ZcRftbhtBhzDDVgpLH4na6MQYZWfzl77To1ZbUNo1Vsbt19TbGP/khI64bzjX3Xq2KzbrCYXeQm5NPfm4BfQb2Inv/QaZ+8zNWqx27zc71t15Jzz5dueVKZV+MTqejZ5+u3Pvw7Xz31TTKSyuIT4gjPimOoSMGIISot1lcJ6KipIJ7R9zPbf93KxdePVSd1U9xBSXZRTTr3pLSg0UkNknxuc3j4XW62TtrLRlf/0GjgR3o/eQ1uG1OjKH1yz36bwREqI44W0XoCCWZ2ez5eRV9nruBwk17MYYFE9+mkV/Gsm7GMn55/XsuuGYQF427EoMKouhyuLDbHAhZZsH0hVx+uzoxqgCnhyzLLPl1CcV5Jdzw4PW4HC5Mwb5v/yDLMmt+XMJv70zlwnsuZcido3xu83gIWUYI+L7/Y0SmJ9FxzDDS+rdDc5ZNICAgQnXG2S5CR7Pnl1WseX0a0U2T6XTXSBoNaK+6L7m6pIqfXvia1DbpDL/vMtXslhWW8cnzn7J/5wHueOp2+l3ct1760c9ndm7axecvfYEsSdz38r206txKNds/v/ItBzbu4YY376ZByzTV7B6hZHs2W7+Yi0ar4cIP78VZZSMoKlT1cdQlARGqI84lEQKQ3F72zV7HoVU7GfLeWCoseUSlJym7o1VElmRyd2Sx6odFXPrE9YTF+H5fEcC2NRlMfmsyz332LOHR4RhNgVWRv6koqSAmIYapH/9IfHIcgy4bpIrr0OPysPTrOVxw3RCELBMSGeaXOMv8+z6mcNM+OowZRpvrBvg9qaiuCIhQHXGuidCxLH5sIjlLM2g/5kLa3TRE1QvAUWvn9/d+YvPs1VzyxA30vLK/qquTCS98xsG9Odzy6E207tJaNbsBFPKzC5gyfgqbV2zhq6UTVd3fZVmzg6nPTiSpaQOue3UskQlRqtmW3F72zlxD3tpdDHnvLioPFBLVOLHebUA/UwIiVEec6yIEULY7ly2fzUH2Sgz/5P4/a+SpRe6OLOZ//Au3vv8AWp0OvUob7LweLwumL2TK+B9o3aU1z3z6lCp2A8Dahet499H3uOS20Vx++2WERqjneqouqeS9q//HFc/cTPuh6mx2PcLemWtY88Y0opok0/mei0nt0+acdQsHRKiOOB9E6AiyJCNkme/7P05a/3Z0uXcUEanqtin4+OZXiWkYz+jHrlXNRed2uTm45yAtOrRg4qtf0rpLa3pd2POsyyar7+zesptpn07nqruuoEnrJng9XsKj1CnU63G6WfzV79gqrVzx7M3Ikqya681ZZWP39BV0GDOMgvV70AebSOp0dlbcPhUCnVUDnDJanRadQc/Vs18kKCqMaRc9x64fl6s6hjEfPYjeqOeloY+wcdYqVWwaTUZadGgBgLmjmR8+nModg8aydOZSVeyf6xTnFfPIFY/x2v1v0KlPR5q0aUpwaLBqArR90SZeGfYoORkH6H+zUu1dDQGylVSx5o1pfNf3Ucr3HMJjc9Kwd+vzQoDqisBKiPNrJXQsziobksuNkGVWvvQDXe8bRXzbxqrYLrDk4qi107hDM/asyqT1gI6quS2EEGSuy8RmtdNzSA+mjP+BXhf2omnr+lewsr5Skl/C/B//oGXnlnTs1YF1i9dzwbDeqm76LMstJi4tkRXfLSC+cRKt+rZXxW5tfhnBMREUbLCQtXALne+6SHWPQn0g4I6rI85nETqCx+Fi55SlbPlsDvHtGtPvfzcS2ThRFdvleaV8OuYNwqLDueypG2ncsZkqdo/gcXv48ZNp/DFtAZExkdz48A30GtpT1TGcTdRU1vLGA29gydjLwEsGcNntl9IgvYGqYyg/VMJv7/7I3rU7eW7Bu6oVG60+WMymT2eTNW8TF096hOSuLVSxW18JiFAdERChv/A63eyatpymw7vitjmxFVXSoJfvi6ZKXom105cyd/wM7p30FA1bqb/ZVpIktq7cisFkoG23trz18Dv0GNSdXhf29EtTvfqC1+Nly6qtLPttOe17tOPCq4eyau4qegzuocom02PZs2o7X93/Af1vHs6Qu0YTpEKFASEENYdK+WnU/2h302A63D6s3jelVIOACNURxxMhyenGVVSJu7SKqG5manYcpGzxNrzVNiSHi9TbhmGIDmPP05P+fE/coI40uG4A2R/OwlNtwxAdRlBKLMmXX4CruBLhlTAmRKFVoS9KXZC/djdLnvyK4Jhwuj90Oan92vpcjDwuDwaTgSVfzSFvdw4jH7yS2NQEn9o87jjcHpb/voJls5axY+NObnr4Rq6483IcNsd5IUgOuxOv24Msy9w+4E4aNmlA/9H96X9xP2ISYlQfj73axqKJs2l5QTsad2qOy+pQpU5h6a4cNo6fSUK7dLrePxqPw4XBD8J7utTuzMGZX4a7ohaABtcOoGTuRkoXbUV2upE9Xswv3oRkc3Lg7Rlogwxog00kXtSd2P7tyJ+6DF2wEUNsBMFpCYQ0+vu1GGjvXYcIt5fcL+eTdsdwMu78gJJ5GzElRROUEku3WS8gWR14a+yKsDSIRRdiQhdiInFk9z+PEXK43a0pKRohBO7yGrw1dgAKf15FzudzcZfVYIyPpPvsF5E9XkrmbCC0RUPCW6USlBpfr1I5G/RqxQ1L3mL/7HVsGP8rSV2aIXm8BEWG+qzEiOHwhtpeVw1k0cTfeGPUk3Qa0ZNrX7lD1U2GBqOBIZcPZsjlg6mtqsVhcyB5JW7rN4aEBol06deZXhf2okV7/7W9rmtqKmuZP20+W1ZsZc/WPdz74t1cePWFfL5ggmpFRY/F7XSz4NOZLP/uD9oP6UJcWiLGIKPPyzLJkszcseMp2XaAjmMvot1NgwDqnQC5SqrQHv4u9r/2I/bsIuxZRcQP7UzL124l+6NZyn0rJpzgwwJijI8gsmMTtCEmtHodurBgtEYD8cO7Irs8SE43+khlL2HtjoO4Sqpwl1UTnJZA2/H3sPPhz6nJzCYkPQnZ5TnjzxBYCXG4s2pIaOS+n5eRMLwrXqsDXYjJJzda2SvhKqzAlByDI6eYvG8XY7XkYd2dS/NnriPp0t7se20qkR2bEtm5Wb0TpuXPf0v+ml10feASml3cw+fCYK2sZdfybXS/tC9b5q4jtU1j4hv5r5+K2+Vm1+bdbF6xmciYSK4cewWf/m8CEdERtO/RjuYdWhAcUv8LUHo9XrJ2Z7Njww4y12dy2ZhLSWuRxnfvfU+Xfl3o0Ku9qvt6jsVaWUtVYTnJLVKZ9fZU+l4/xOd/dyEEBev2UG7Jo/2tQ8ldkUlKd7PfigIfi6u0GkN0GNZduex7/UdqMrIRkkS7j+4ldkAHDn2zkJD0JELSEwlqEIfOR+P2VFmxZxVhzy7CfOMwap32gDvuTKkvMSEhBJLNSe5Xf1Cz9QBVm/eRcnVfWjx3A4W/rCa0RQPCW6f5tdChEILcZdvZMH4m+mAjl01Vb/PnH5/OZNHE2bTu14Ghd1/il7jR8diwZAPb1mSQuX4HpiAj70x/m4UzFlFTWUOjFo1o3KIRsUmxfptMWKutZO85SM7eHLJ2ZXHL4zdjydjLxFe+pG33NrTr3o4u/TsTGaNeG44TUVlYzpKv5rB2+lIG3zmKEfdfrordnKUZbPxwJvayGro/fBktL++jit3/onL9HvJ/WErVBgvushp6LnwNbZCRmm1ZRLRPx5Qc49dJaiAmVEfUFxE6FiEEssuD1mRgz9OTKV+WgafaRsMbB9P86WuR7C50If5xDwghcJTVEBwXwZwx79Hwgja0uX4A/9/eeYdHcZ19+57Zql1Jq94BCQkG0SS6wRTjgnE37r0ljtPj9LjkjWOnOHGLneaW2I4d94oLNjam917FgJCEeq/bd2fO98cKXl4+bAPWrgTMfV1cw86u5jy7c+b8TnnO81iiPArwdXtZ/vKn+Hq8XPLza2nYW0tWUe6AGS0eSJG9euFqNi3fTNWe/dRV1vHiqhdY/ekalsxfQvaQbNKz0zl97jQSkxPpaOkgISkBu8N+zN8j4AvQ09mDJEmkZqWy/KMVVJZV0lDdgNft47f/+g1vPPkmKxasYMjwIRSMKODsy8+K2f6do8XX4yUuwcETN/6OnOGDOOubF5KcHd0pQF2LpM3OmTScLc9+jCMjiaILJvdbDp9Ql4e2JdtoW7KNzg17mPrZg3RuKsej1pA0eQTxSh7SAMsvZIhQHzFQRehI+OtaCbZ2k1gylPXzfkuow0PamSWkz51I8mSlX2xq2lrBhr/Np2HDHk6/6xqKr5oZk3LDwTAPXvwrTCYTs289jwkXTotJ6ojjpam2iV0bdlG/v4G2xjbmffNSJEniF9f8CneXm3AojDPBiS3OhtVuxWa38cibD1G2aTfP/ek5dF0nGAhx2y9vZdyMcVwx9koQkJCUwOxLzuCO//kWbz71Fp4eD9mDs8jJz2H05NH9/bW/EF3XKVu6lcXPL8Db6eYX7/3hoIhHEy0QouytFWx+8kPi0hKZ9+rdmGIURupQhBC4y2ro3lZB7jVnsOf+/+JWa0mbXULKjNE4hw+cztUXYYhQH3EiidChCE2na/M+WhdtJtjazciHvkn9G8swO+NInV2CKS62DXL73jqCPT7Sx+Sz4W/zGXXNGcRnR9eTStd1di3dwpLnFlA4aQTn/eByelq7Yprhta8IBoJ4uj0E/AGC/iABf4ChxUPx9Hho2N+AJMvY7FbSstNwxDsI+APY7LYB31AdjhYKY7KY+e9dT1G9vYIzbj6PiRdFvwMR8vqxOOxseuojalfuZMJ3LiTntBH98vtVPfkh1c9+DEDmBZMZft8NJ9x9BEOE+owTVYSORMObK6h9eTE92yvJvHAKox67I+Y2BN0+1j78FmVvLqdw7kQmfO8ikgqi70wghKCntYsHzvkJRZOLmX7t2RTPLBnwKZJPBYQQ7N+2j5WvfEbZ8u38dsnjhAIhbM5jn4I8VjzNnWz99yfsfHkxV753H678zJg2+HpYo2PlLpo+XIu3somJb9xD+6pdWJITiB+Rd0KKzwEMEeojTiYROkCgpYuenVWknVHCzp8+jdbjI/OSqaSdVRo1r5nD8bX3sP0/n5F7WjHpY/Jp2V5FzhQl6g+d3+Nnw/wVrHx1EdOvPZupV82mva6VtH7Yb3Sq4/f4sTvtfPDY66x7ZznTrj6TqVfOjllahbo1u/nwm48y/JJpjLv9vJhFARG6jq+6BUd+JptvfphAYweZF00h84LJOGLQIYsVhgj1ESejCB1KsLWbpo/W0fjOKoJt3Uxb+hDBli6sqYkxW+hsLathwR2PY010MP6O8yk8b1JMcqvouk5bTTMPXXYv2UV5TLl8JqXnTsHhOrEzWg5kQv4gO5dsYd27yyhfV8b9y/+O0HVsTnvUo5YLIahbU8bmpxcw+rrZDJoxmpA3QFxKbBwxenbup+HtFTS8vZL4EYOY8MpdaL5gzKfGY4UhQn3EyS5ChxL2+DE77ez6+bO0fLqJ7MtPJ/uKmSQUD4p62bqmU7lwI5ufWcAZv7+F+OxUJAlsMRCEcDDM9kUbWP/eCqZcNovimSVsW7ie0WeOxx5/8kdAiDZaKEzl5r0UTS5mwV/fYvfKHUy6+HQmXDiNuBglUXQ3dvD+LQ8T9gcp/cZciq+YgTkGjb+/oZ2e7ZWkz5nA7l+/gGy1kH35dBJGxj6FeKwxRKiPOJVE6FDcu2uof2M5PdsrGf/a3fTsqMKem4Y1Rr3Gve+vYfFdz6HMm0bJbefGZN3oAO11rbx899NUbFQZPnUUc793WcwDp54MVGzcw4pXPmP7ZxvIKMjmBy/9Gpsjds4S3tYudv53Ma78TIZdNIWaFTsjSeRisJeuecEGqv/9Cd3bKsi5ciYjfndz1MscaBgi1EecqiJ0OHv/8Co1//6ElOmjybn2DDLOnRD1Mt0N7Wz/z2eUvbGcaz/9AyazCbPDHjNnAm+Xm22fbiBvZD6uzBSe+c4jjJ49jlGzx5OjDDqhF42jQVttCzuXbKZi0x5ufuR7bPlkHR31bZTOnUxKTlrM7NACIRb98l9UfbaJwvMmMe5b55MyLLqRvIUQdK7fQ9emcvK/fQE1L3yKOdFJxtyJJ+1021dhiFAfcawiJEJhRDCICIZAljG5EtA9XkQwjGS1INmsSCdoLvlwj5fG+Wtwl9Uw4nc307JwI3H5WcQPj+4DfiAL5vrH32XX60sZc+NZFF89K6aRikOBEOqq7WxftIldSzYz44Y5zPn2JWz5eB3544pIyox94M7+xtvlobmqgfySIl6/7zk2zF9B8YwSRp85nvEXTI1p7qCwL8je99cAUHzVTMreXE7BWeOwJ0c/jUPdy4up/Nt8JFki9/ozGfLtC07YDorQNEQwFPmnaZhcCaDpaG5PpP2yWpAslqP6foYI9RGSJHW6EhNddR8tJtzYQrixFdeVc9E9Xpr+5wm0rh50t4ekGy8l5dbL2TfzOnSPF8liwT56GHnP/oHmP/yT7vmLIjc2EGLospfx79hD8wN/R453YEpKJOVbV+OYUkL7s29gyUrDnJWOZUgOlqyBmwyr8m/z2f/UR8QNTmfQzeeQE4ONqI2b97HthU+pX1PGjcsfIewLYk2Ii+lDL4RAD2toms5zP3yc8nVlOFxOzrj1fGbfch4dDW24MpNPqvTgQggCHj/2+Dg+/vs7bPpwNS37GymeMZZvPfkzvF1u7AmOmH9nIQQrf/8KZW8sJ2NsAePvOJ9B06O7CVcPhmn5bBMdK3cx4ve30PLZZiwuJ66Jwwak+OjBIIEdewk1tBBuasVaOJj4WZNp/NXDBPZUoru9mNKSGfzyozQ/+BRdr34Y6SybTAx67S+Em9qo/8H9EAqjB4Ok/+Q2km+5jMpzb0OymJET43FMHkvanbfQ88lytI5uzFlp5F18Dl09PaeWCCmKchPwfWA0IICtwEOqqr5zvNc8EMB0x1Xfj4hDZhquay9EdsYR2FmOyZWAnODAlJyEfJRhaYQQiECQcEs7eo8HrbMba8EgTKku2v76UkTsGlqwlyik//x2Gn72YO9n8rCNKMR1+bkITUMy9f+ISg9rtH2+BW9lE0PuOJ/aFxfhVPJImjQ8qg+kFghhsllYcs/z1K7axahrz2DEFTNi5ul0KLqu07i3Fi2kMWh0AY9e9Rtqy6oYMqaQ4hljmfOdS/F0urHHx8V0dHC8CCEIB0KYbRY+/MsbVO+ooHrrPgonF3P7P37C9s83EZ8Uz6DRQzH3QzSBkC/Avo/W4+9wU/rNuex+awXZk4bjGhx9N/ua5xey76G3cA7LIeeaWeRcNbNf4zUeQPf5kePsBPZU0v3eIoKVNYSqG0i/69vYhudT//37MeekY8lKxzF9As7TJ+DbvAvJbEJOiEdOdGJOSTqqsg5Ergg1tkTary43ktlEXGkx3e9/jm/9dkKNLYx87iF6wsFTR4QURfkV8EegGviASCqKy4A04Eeqqj5xPNcdCGtCwep6ghU1hKpq0Tp7SLvzFloe/hc9C5ZiKy7Epgwl+eZ5yAnOfu+JVf/rY6r/vRCAId86j0E3nxPV8oQQ1K9T2fnKElp3VHHtp3/E09iBI90VEzfvL8Ld3s3+rfsIeP2Mv2AqL9/1NGvfXkp6QTZZhblkFGSTPiSL9CGZZBXlEp+SGFP7hBC423toq2kmoyCboD/A/D+/QkN5LY3ldZz73UuZ+73L+OyZ90nNS2fwmEJSctP6vX6t/P0r7Hp1KZnjCxlz09kUnDUuquWF3T4a31tN62ebKXn2x3RvrcDscuAszIlquV+GHgwiW630fLoS98fLCOyuIFTfzNCl/yVU04BnxUasBXlY83OxDMlFtvXPmtQpNR2nKEo+oAK7gemqqvb0ns8ENgIpwGBVVVuP9doDQYSOhNB1QtUNBNQKAmX7SLnjGtyfr6H1kX9jL1GIGz+KhHNnYM6Ifa6XA4u0gfo2si6dxr6H3yRhdD5pZ4+LqjDoYQ3ZbGLxXf+mYuFGhl8yjeIrZ5BWPDDcYYO+AI376mgsr6O5ooHWmiZa9jcx+szxnPf9y3js6vsIh8IkprnIUQZx0U+vYe/aXTRXNRKX4MDutFM0ZSRaMExrddPB39KVmUx8cgJVW8oJBYKEg2HsTjsF44ez5ZN11O6qwt3ejbfTza1P/Ig1by7l1XufwWK3kjoog+v+8C0y8rPZtGANWUW5ZBflxiwl9lfRU9/G7rdW4G/vYcZvbqBy0WbSRw4mPsoBTAGqn1tI+R9fI/m0EeReO5v0OeP7LUhoz4JleFZswL91NwD5HzyNZ8UGtLZObMWFWAsGIQ2whJinmgh9E3gGuFFV1ZcOe+9e4AHgSlVV3zzWaw9UEToSQghC++vxbynDt3knSddehOSMo+V3/yBu0ljiJo3BPmpYzB0j6l5dQu2Li/DXtlLwg0sY/M25US+zY189u99aSdvuGi7890+oX6cSn51C4qCBu8bWVttCR30rPW1dIEmMmzuFDe+vomzZFvxuHz63j1sf+wHNVQ289ut/oes6AHO/dxkTLz6dP196DyaLCbPVQuFEhQt/fBUrX/ucjrpW4lMTiU9JZPwFpxHyB5EkCesAS8J2gAOOKAt/9E/2f76VogunUHzlDLLGR9dNPtDcScNbK2iav4YJb95LoKkDs9OOLTM5quUeihCC4L5qfOu34123DZMrnsz7fkjH828h2WzYS4uxDcs/IZybTjURmgqcDbyoqmrVYe/9DHgIuFVV1eeP9donkggdCd3jw7NyI7712/Cu20bSVefjuvZCut5YgGNyCZb82EXjde+uIdDSRcr0Uey88ymSTxtB5sWnYXZGP9Hb+sffZcu/PyEpP5Phl06j5NY5US/T4Ojxd3qoXLiRvR+sRWg6l/z3l7SptSTlZ2LqzagbDYSuI8kyNc8vZO/vXyXj/EnkXHMGyTEMXhpubsO7ajOmFBeOGROpuf6nWPNziZs0JvKM5sYmnFBfc0qJ0JehKMpyYDowRVXVdcf69ye6CB2OEALd46Xlj0/hXbkJyWoh5TvX4po3BxEKx2RIL4Sg5eON1L2ymI41uyn40aUUfO+iqJerhcLUrthJ2546xt9xPpufWYDQdIaeOyGmm2ENInhbuuipayWztJC3r/o9NpeTYRdMJv/scVijHKnCvaeO+teW0PD2SqZ+9iBC0zE5bJhjECHjwDYOkKi58WeE6ptwTCkl8bI5xM+aHPXyY4UhQoCiKNcDLwHbgFJVVf+/L6QoSueXXaO8vNyVkJDAySJChyKEILi3CgBr4WAqzrwJm1KAc9Zk4s+YEpMeWKCpg2BrN04ljw2XP0DqrDHkXDmTuBhMm9WtLmPP/NVULNxIYl46V7z7G/wdbmyJjn51ajjZ2fz0R5R/tJ6O8jpGXXcmp999zcERSTQJdXuxJDqoeeFTKh55m+wrppNzzRlR3+cGoHv9uD9dgWfpejyrNpL2g5tIuv5ifNtU7COLTojptWMlKSmJnp4eioqKur7sc6qqJn3Re/0uQoqiVAFflaf556qqPnyEv50FLCDiJXe6qqrrv6CMzi+7+MksQoej9XjwrtqEZ8lazBmppP34VrreWYhNGYqtuDCq0xNCCLq3VFD/2lIa31vN4G+cS+HPrkAPhZGjPDoTuk7X/maSCrJY8buXKXttGYNnjWHwrDEo8043BOlrEOjyULu6jOql24lLTeC0n13B1ucWklSQRd7U4qhOtQHooTBti7dS//oy2pZsY9ryRzAnOpBtlqjf12BNA55Fq4mbMApLXjZN//MXnLMm45w5qV8chmLNySJCjwFf1SV+WVXVjw77u3OAd4E44KbDnRWOhZNtOu5YEELQ+thzuD9ZgQiFSbr+IlK+cWXUy9UDIUKdbizJCSyf/ENSpo0k+4rppMwcExNBcDe0UbV4G40b93LWw7ez593VNG4uJ29qMTmnjYhppIYTjZAvQMP6PdgSHWSMLeC5KT8iZVgug2eNpeDsUpJj4NoshKB7awWJYwuo++9i6l5ZQs41s8i6+DQsSdHz+hNCgK4Tqmmk/kcPoLV14pw1meQbL8U2YmjUyh2onLLTcYqiXAc8D5iAbxyPM8KhnMoidAAhBMHy/WjtXTimlFB7+z2Ys9JJmDMdx5QSJGv0erPB1m4a31tF/RvLSZk2kuH/cz2e8nochdkxWzhuL6+ncuFGaleX0bBhDzcsfoiQ10/z1kqyJw0nITe13/fP9Be+9h5kk4yu6Xxw26O0lVWTNmoIJbedy7ALpxz0dIuJLbWt1L+2lIa3VoAumPDmvdijfG+EruPfvgf3whW4F64g7Re345w5icDOvdhLRgyIDeX9xSkpQoqifA/4KxACrlNV9a2ve80DYXtaN65FcsRjysnD//G76I0N6D1dSA4nzm/8AP/81wl8vgARDkM4RMJvH0Nva8H9yG8PXIe4a27FdvYFdP/quyDJSHFxmIYV47j2NgIrP0dvbkJ2JSElpWApmRCJ+WAyDbgGLlTXSM/Clbg/WY6cmEDe0w8QKN+PZVB2VDfG6WENNJ1VZ/4SdJ2sS6aSfcUMnEWx2ziohcLIZhNNWyrY9M8PaNiwByEE5z99J+mjBlO7qoy0kYOJz04ZcPft6+Jr78GaEEdXVRNrH32b5m0V+DvcnP3Itxh67gTq1uwms3QolqOMHNIX+OvbaJq/hrybzqZ99S5aP9tC9hXTcY0vitrvLzQN3+YyrEPzCNU00nT3I8TPmU7CuTOwKgUD7r6LcBi9oRa9ow29vQ05KwfLiNF4X3oavakB4fMiuZKI/8Fd+N54kcDnCyAcQug6iQ/+A725Efej9yOZzWC2EHflTdjOmEPPA78AiwUpzol5WDH28+cR2rYR4fUgJ6eSNnkaXd3dp44IKYpyA/AfwAtcqqrqZ31xXUmSOl12m2v/d67HdvYF2M+/DP/81xFaGDnBhZScinXCaWgtTQh3N5LZAmYLcnomCB3RHZkOFbqO5HAiO+MJV+5F+LwInw8pLg7LyBICKz9H21OG3t2J3tlBwr1/Irh0IZ6nHkVOzUDOyMRxw7cwDSogtGUdcnYepuw8JEt059S/ChEMIVktNPziT3iWrMM5azIJF86OqpfPgfWjxvdWETc4g8G3nUv1cwtJnTk65jvZhRC4G9qxuZz42rpZcvdztOzcjwjrTLv7akZdO5vdb60gISeVpKFZODKSBlwjdTj+Djc99W2kjxpC5Web2f6fz2jbXUPQ7ePKd+/DmuigdtVOMkuGklSQ1S9ha9pXl1H+4Gt41Foy5k6k6O5rsEU5I2uorpH2f7+Fe+EKTKlJZD1wJ7bR0Q1PdTQITUNvbcaUmU14bxmBpQvRG+vRm5twfPvHyGkZ9Nz/C+TkFOTkVKxTZ2GdOovA8kgTKdkdyK4kzMNHone0IXw+MJuRTCakpGTQNER3F0LTIBxCSnAhJ7oIbVmP8PsQXg+SMwHrlOn4P3iT0LZN6B1tDH7iObqDoVNDhBRFGQpsB6zAOaqqLumra/f3dJzw+9BbmtBamjAPHQ66huefD6PV16K3NhF31c3EXX4D/o/eRk5OxTSkEDkrp18ahnBLO+5PVxJu7SDthzfR+dqHmNNScEyfEN0RUjDMnvteoumDtVhSEsj//kXkXDEjauUdDZ7mTgAc6S6W3P0cbbtr6KxsImtcIRc+91M2PfkB7oZ24nPSiM9OYdhFUwh5AyAEFqc9er343me6cVM53uZO3I0d2FwORlw2nSX3PM+e91ajaxopw3K58t3f0KbW0l3TQqoyiMTB6f3W4PpqW2lesJ7mj9Yz9ukfEWrrxru/mbTZJchRil8nNA3fpl30fLyMpOsuQrJa6PlwSWTEU5AXlTK/1B4hEO2t6F0dmIcOx/fuqwSXfYpWX4uc6ML1txfRaqoI79yKnJWLnJ6JKWcQkq1/NiWfUtNxiqI8A3wT2AW88QUf+0BV1Q3Heu3+FqEvQ4SCiGAQ2RmP77XnCe9T0aoqkHPySLzvEQIrPwdNwzxsZESYYtyAdL37Kd3vfEpgdwWJF59Jxj3fjWp5QtPp3LAHhCBpssL6efeTNGEYGedNxDV+WL+FXDkULRjGZDVTu2oXLTv3465rw9vWzbl//S47Xl7M8vteQtc07ElOzn/6ThJyUlj082exOO1YHDbyzxrHsAunsPEf7+PvcAMQl5rA+G9fSPlH66hZvgMtECLkCzDzvhtxN7Sz6Bf/ItDpxt/pYeovr6TktnN5+8rfY0t0EJ+dQvbEYSjzTqdrfzMWp4241MT+790LgbeiAWdhDjUvfEr5g6+Tfs44Mi6YQtoZY5Gj5FUneqNQ+LeUUf+j32FOSyb+3Bm4Lj8Xc3ps03XoHW2IQABTVg7ux35HaMs6QMIyaRrx3/8l4X17QNcw5Q1BiotNhtpj4VQTod2A8hUf+46qqk8e67UHsgh9ESIUQrJYCHz+McH1Kwnv2YVkseD65ytoVfsQXg/mohEx6yGFWzsIVlTjmFxCw88eBJOJhHOn4zg9eiMkIQQ926to/mgdzR9vxFU6lFF/+TadG/cSr+TFZFPi8RL2BfF3ebC7nAihU79WJeQNEPL4SR6WQ9a4Ina+shh/pweIpEAffd1s6teptKm1mCxmzA4b+WeWIHRBd3Uz9uR47MnxmONil9n0eOjeXknDG8tpWbgJPRhi6qI/IVnNUXWpFrqOb9Mu3J8so2fhSnL+cg/WoiForR0xG/EILQzhMAiB5+9/JrxnF8LrwX7pNcRdfgOh3TswpWcipfR/ENmj5ZQSoWhyIorQkdC7OpFdSQRWfI5//uto1ZWYhgwl4a7fI9kiC8mx6E2Fm9si0X8/WY7u8zPkjb8SrK7HnJkW3Sm7QAjZZmHLNx6lbfE2XOMKyb58OrnXzY5amQZfja+2lbbFW+lYpzL68W/T9OE6PHvqSJ8znoTR+dF1Lti0C/uoYXjXbKb18RdIOHcGCXNnYh06KCplHo7e2U7g0w8J7dxCeM8uHLd8F9s5FxJc9hnmwuHIOYMGRJqI48UQoT7iZBGhwxEBP2F1F+ZRJYTWrcT9xB8wDxmKeewE7HMuQk6Lfm4WPRBEtllpuv9v9Hy4BOfMSSTMnUn8WVOjWm7Y46d9+Q7Cbh85V8xg+3f/hmQxkTpjDMnTR2LPOvWypMaKULcXz946kiYMQ/2f/1D/5nJSZ44h7axSsi6dFvWNycHKGjpemo974QrMaclkP3IXloK8qI8uhKahVe4ltH0ToW2biLv6FkwZWfjfew3zqFLMI0YjJ7qiakOsMUSojzhZRehwRCBAWN1BaNtGbOdchPC68b7wJJaSiVhKJ2LKj57LK/yvU0OwooaMe79L9/ufI5lMOGdNQnZGd4TmqWigbfFW2lfsJNThZtK7v6H5o/VogRDJp43Anm2I0vFyIL3G/ic/pOGdVXj21pE6awylz/2UUKcbc6Ijqr19EQrjXbsF98KVpP7gRsLNbXiWb4iJc4HWWE9oy3pss84htHUDvpf/jXnsOCxjxmMZO2FAruP0JYYI9RGniggdjvB5CW3bSGjrRkJb1hN3zS1Yp55BcM0yLCUTkBOTolp+z8IVdL35Cf5NO3FMH0/2Y/cAxGw+vPG91TS+s4qOtbuxJMczbdnD+Gtb0DwBnEqeEcrnS2h4awUd61Q616nYs1MY//KvaP54A2aXk6TxRVFzKjiA7g8g2224F62m8Z5HsObnET9nOq7LzsWUFL1oFyIYQLLaCK5djveFJxE+L5bSiThuvAMp+dTb0GyIUB9xNCIkdB20MJLFivD2IPxe0DUQAiklC8JBRE8HmMwgm5Di4sFiPXD9GH2Tr4fQdURnB54nH464gOYOJu7Km7BOmnYw3W800LrdBHbuxTF1HE2//RvByhriz5pK/JlTYxJgVeg6vv3NOAqyaHh7JfseeYtAfRsJo/MZ8/fvYXY58de34yzKjvpU0kBD8wVpXbSZ7q0VdG+rJPm0Yob+eB67f/0CcblpuCYNJ3FsQUx+F62zB/eSNbg/W41vzRaGzH8SyW5FBENYsqIXDFdrrCe0bgXBTWvR9pbhevp1RE83wufBNKTwhFjTEUKApiGZzQifB+H3RNovXUdKyYRwGNHdBiYTyGakuHgkm/0rg84aItRHHIiY0PzGPxCeboS7G9OYqVhKZ+J94ieIrlYIh5CHjCDutt8QWPAftLL1kRsmycTdfj9a3T6CHz4HmgZaGOvcGzEVT8L7wE1gsSLZHJhGTsF2wS0EF7+J6GpDinchxSdhnnIueHsQ4SBSfPKACAMiQkHCZduRXEmYMrLp+sFNmMdOwDrhNMylk5Cd0YnPpfv8eFdvxr1oNb5NO8l//2kCagUAtpHRnS48lFC3l+6tFSRNHE7Pjip2/Oif+OvbcA7LZfi915EyYxStn28lfngu9ty0AeEafrwcaAMC9W00L9iAe08t7t015H/3IlJmjGbbHU+QWFKAq2QoieOKsKXHbl0jWF2PZ9l6kq69kO73FuFZvIb4s6bhnDUZU3J00qWLUJDwzq2E1Z3EXX0L/o/eQavci2X8aVhKJiA5nFEp95hs1PVIW9XTjpySBVqY0NpPEJ4uhLsL0/BxWCacie/pX6O31ELQj5w1hLjvPEjws9cIb13e22GWsd9yL6KjmcC7T0WESQtjOfNKLONn4/ntDSBJYLVjHj4O22XfJbjkbfTWeqR4F5lXfpsut9cQoa9LZCSU6Gqe/x+k+EQkZyJyxiDk5AyEuwusNjBbj6vHI3QdQoHIyEmSkBNT0Cp3orc1INzdEPRhnXM9oU2LCS16HeHtQUpIwnbtz5DikwhvWoycmo2UmhU5WvtnU5rW1EBo4xpCG1b9bxiizz/GrIzElBud1NoHRl/d735G25OvoHt9OGdNJuOubyPHMGzMAcIeP+5d1djz0jA5bGy7/S+499YRau9hyO3nM+zea9n/dCTObtygDOIGp5Mw6qsCxEcfIQThTg/+hnY0j4+kSQpNH6yl8b3VeCsb8VY0Mm3Jnwl1eqh9cRHxSh5OJQ9X6VDMCbFd0zjQ8+7+YDFt//gveo8H5xlTSP/F7ZgSotf4C58XKc6B7/UX8L/3GqZB+VgmTsU+71okU/+NfvX2JvTmGkRbI3pnK9bzbya8eSnBD/4FtjjkhBSsl9yOnJxBaM3HkY6tMxE5czByWg56TweS2QpW+3F1boUQEA5BwIcQOnJCMlptOXprPbi7SJ97DV0eQ4S+NgNpTUj0Doul+CSE30N4zQL0tkb0tgYs48/EMu18/K8/jpyUhpw5BDl3KHJabMPYQMQTyPv0XwhuXI1ktWG/6Ars582L6rRdsKoO75otuK4+n87/zsezaDXOWZNwzJiEdeigfpv21LwBNF8Aa2oitS8uomdXNb6aFmSzidLnf8qeB16m8Z2VWNNdWNNcjHr0W2jeAA3vrMSS6MSc6MA1oQhnYQ4d61Qkk4xsMWN2OXEMycBf10rYEwBdRw+FSRidT7C5k56y6kjZ3gApU4sxJzqoeOwdQh1ugm3dJE8tJv87F7Lm3Hvw7qvHlp1CwsghjH3qh3SsU/HXtuIoyMIxNAuLq/9696GmVrzL1uNZvgHf1t0M/fR5gpU1iFA4MvqN0nRXuGofobXLCa5fhQj4Sfrrf9DqqpESEqO+HnpEe8rWozdUobfUItmd2C75FoGPX0S01PV2QrMwT5oDoSBIUr91SA/FmI7rIwaSCH0VQtfR1E3oTdXoTdVIrlRsc28k8NELEAogZ+cj5wzFlFcUG3uEQKvciwgEsBSPoevn38KUlYtl4jQs4yZHzSVV93jxrt6CZ3mk8Rr030cR/gCBsn04ppZiSh44rrCaP0igqZNQWzfB1i5Spo8m0NRB3atLCXd5CPd4yb5iBqlnjGXDvPvR/EFESMM1voiRD32Tsrueo3359shI2mJmysI/0LZ4K/ufXoDJYcPksDHkjvOJH55H9b8+xuJyYk1z4RyWg3NY7sH9UwMF3evHt2E7wao6km+6lNa/PE+opgHnjEk4pk/AnJYclXJFwB+JedbWgn3uJXhf+CfoOpZJ0zCPGBMJ3hkDRMBPeNeaiODUV2IaVop11jwC7z2N5HQhZ+RFnuP06Cfi+7oYItRHnEgi9EVo9RXoteXo9ZUIdyf2G35JaOPnkUo+eDjyoGFIyZlRHy3o7a0EN64htH4Vks1G/E9/Q3DDakyZ2ch5Q6JS/oHRl2/rbtqffAXfhu1YBmWT9cefYi0YhB4MYorv/3n8UxU9GERraceSm0XTfU/Q/f7n2EcOwzlzEim3XxXVskUoiGSx4vnHQwRWfI556HCs02djn3tpVMs9WL7PE5l+r9mLVluOZcbFmAYrBN5/FlN2QW+nsSDiyHQCYohQH3EyiNCR0Jtr0PZuQ6vdg16zl7jvPIje2YJeVYY8WEHOLohJ78/70jMEly4EswXrrHNwXHNrVMsToTD+HXuwFg0hWFFD7W2/wlo4GMfEMSReNgdbUf+v05zMHOgUtD/zGp6Vm/Bv30P8WaeR/edfEqyqw5yRGtU1vfDeMoIbVhPasBo5NY2Eu/9IuHx3JOBnfBTdt3Ud0VKHVq2iVe/Ges51iI4WQsveQR40DFPeMOS8IiT7ybN3yBChPuJkFaEjoTXuJ7xhEXq1it7ehP3me5DTc9EbKpHzhiFZohfnTavah97ciHXKdNyPPYAI+LFMmIp1wmnIKWlRKRciURv8W3fjW78dx/QJWIfkUnPDT7GXFhNXMoK4KSVYB8d+Xe1kQQ8GcX+6MvIbb9qFvWQEmb/+Hp3/nY85N5O4CaOj6lSge9yEt6wH2YR16kx6/vRrTFk5WCZMxVw8OmqOBULX0Rur0Gv2Yp48h/CqjwitX4hpsII8WME86jSkuJN7BG6IUB9xKonQoQifByxWRHsjgXefQm+uRc4txDr7Ckz5xQgtHLUHWO/uJLRpHaGNq9Ea63A99DShnVvBZMI8bERUPZKEphHcux/fpp34t6nYxwwn6fqLafj5nzCnp2AbVYR9jGII0xHQ3B58a7fh37mXwM69JFx8FgnnzqDxF3/GNqqIuHEjsY0aFtUYgUIICAbAbKHngZ8TVndhKR6D7azzsZ4evTiBQtcR3W3ISekEl71HaMV8pIRkTAUjsZ57A5jMJ8Seob7EEKE+4kgiJAJeRCgAQT/IMnJSJnprDXpPe+8mVR3T0HEIdwd6474DV0LOLkRyJqFV74w0pGYrksOF7EqPbBCTTZF9Q9LAq6zC70WrVpFTs5BscXgf/zGmQcORC0ZhLp4YNS+8A9M3/oXvE1jwDnprM5bSSTjvvCeSnTZGD7Zn5Ub8O/YS2LEH2ZVA1u9+TOvjL6C1d2Idlo+taAhxU0pOmM3HX5dgTQPe1VsIlu8nsKeSjLu/DZJEy5+fwT5qGLZRw4ibMApzSlLUbRGhIKENqwltWktw8zpss+fiuP6bhHZtw1w4/GCA3mgQ3raCcNl6tMpdyKnZxN1+P3pbI5LNjhSfFLVyjxchBAgdSTahd7cgAj7QQiCZMGXmR9qxzuZIO4bAVFCKCPrQ61SQZJBNyGmDkF3paPV7I+JqtoI9HtnpQgj9YPvVFyJ0am3//jK0EP75f8E8Yirm4VMIfPT3yA2x2JAz8rFOuhC9pQa9rTYiJLIJU0EJBP2RGwogBHJqDsQloNeW9YZuDyFnDEEeM5vg2nfRGytBCyE5k7Bf8mPCVdvQa3ZBXAJSXALmoePAYkf4epAciTHdoyDZHZiHjzv42vGTv6JVlaFV7ECr2YuUmk1w/jPIuYWYCscgJ/dNANQDjbp9zkXY51yE3t5KWN2FZDLjfflfhNatwFI6GUvpRMyjSqOWadZ5+gScp0/4P+fiz5qKb+tugnv3412xkbgpJXS+/D7d8xdhLcjDkp+H67I5yK54dLcXU7LrhBEprceD3uPBkpNBz8fL8K7eTLCyllBtEwULnyO4pwr/ll1Yi4bgnDUJS24WsjOOvGd+H3XbhBZG27eH0Jb1mJVRmIvHEPh8AZaxE0m89BrknEgUbMvIsX1brqc7Ut/3RbwRbZd8CxH0Y1ImYJ17E7IrFQA5NatPyz0q23obf93did5ag/B1g68H07BJgERw2cuIgBcCXszF07GUnk1o/YeIUADJbEVKTIuIUHcreks1yDJIMiZdg1AAvbMJdD0iYI5EcKUTVldH0oCHAsgpOVhPu5TgslfRmyqQbA4IB7/29zJGQvxvxIT2mnKkuEQkS3T974WuQdCPZHei97RHhM3nRvh6MI84DRHwEVz634gQ2Z2Yx56JuXAC4d2rkeISkBJTkRJSI72TGCI0jfC25Wjl29AqdmIeOQnbRd9Eq9mLnJYTlflvoWlo5bsJbl5HePsmEu55kHB1JeGdW7GMHY9p6PCYR5jQunoIlu8nWFl70M043NJO7TfuQgRCmLPSSP3u9SRedCZtf38JOd6JKS0Z6+Bs7GMUtG53JK2yo2+zqwohEIEgercbU1JiJPrE2q1oLe2EW9qJmzQG5+kTqL76ToIV1QhdJ/6sqWT/+Zd0f7gEvbMbS0Ee1oJBmLNim9NGCIFeV43kSka4u+n++R3IaRmYx07AduZ5mPMLo1NuKIherQJgKhyD78m7keKTMBWNwVRUEvM9eELXEO52CIeRU7IJla1Er9+LcHcg/G7sV92DXrubcNW2SFsVl4ApfyyS3YHobkWyOcHmiO50thCRDfgBLyl5BXR1dxvTcV+XgbomJHQN4e2OVCh7POEtn6L3tEY2syakYpt1HaGdyyDoQ0rKRE7KQkqKvhs29FbEgA/J7sD/xhNo6ibkzEGYx0zDctp5US07XLWPwGcfEt62Cb29hYTfP4GcloHe3IRpyNB+nZfXPT5CjS2YEpyY0lPoePZ1ws1thFs7sA7OIe3Ht9J49yP0fLwMEQwhxzsoXP4q7sVraH/qVSS7FcliIe2HN2EtGkLjXQ8fvLZj2niSr784El9vbxV6IIBstzPoxYdof/YNWp94AUmSkBOc5P3rD0h2O60PP4spNRlzegqO08cTV1pMsKIGU2oScmJ8v43aDrQ7eu1+fG+9RGj75khE9R/ehbl4LKK7Ezk5NTrlhkMgmwi8/BDa/t2RejvxLCzjzojqZuv/Y4euR4SlsxHJmYSUkkPg4ycRXc0RYckrxjLhPLTGCtC1SDgvZ1K/Rm84EsaaUB8xUEXoyzjwsGiNFeit1YjOJoSnC+uc29Eqt6A3ViCnZCMl5yCn5UW98h7oUQpvD+Yx0/C//ngkLXHhGEyFY5FTohOIVO9oQ4pPRKssx/2XBxA9PZiLxxB35Y2YikYcDNo4EBGhcO8UXiJaRzehukZ0fxBCIazDC5ATHHiXbzz4eXN2OvaRRfi3q+i+AJLdhuywYysagu4PgCwhW2M7Oj4WtJYmQhvXEC7bTnjnFuLv/ROSw0Fo83osY8cjZ+VGZx9ZKIhWth5t3za08m2YJ52N9YzL0cq3IecWRt2DTWhhRGcTens9cnYR6DqBBf9AsjmQkjIxF03ElDcCvbulV2gGzsbir8IQoT7iRBShL0PvaUNvqkRvb0DvaMB6+lUQcBNW1yCn5iGnDYqMmKIoTHpPJ3rFdrTybehdrcTd9hvCezaDpmEqGBm1vRJ6eyuhnVsxF40As5muH96MuVDBPGI01qmzMBcOj0q5Bv8X4fcRLlcJ795OuHw38T/7LaH1qwiuX4ll5FjMxWORc6KTaE6EQ+jVKlr5tsiUWm4hgbf/3tshGoOUkhW9bK5CR3S3orfWYiooQa/dTXDVW0gJKcgpOZhHTkdKSINwEMka+/iHfY0hQn3EySZCR0L4etDqVPS2OvTWGixjz0TOKiS87fOIJ0z64MhiZBQJb19FaNNi9Jq9yNn52G+5NxIHy2KNniu4p4ewuovw7h2YC4djmTyd7l/cgSlnEOaiYswjxxrC9DURoRBadSXhfSqip4u4y2/A8+wThPeWYRkxGvOI0VgmTouaQ4kQAtEbwkp0d+B79n+Q03MxFY7FXDI9qus6IuBD727BlD6YcNkqQtsXI9nikFPzsEy6MBKpGmK+fhsrDBHqI04FEToSIuAjvHddxGWztQbziKlYRp9BuHIrcnIWkis9Kq7kIhREb6jCNHg4oRXvE1z6Nqb8kZgKR2MedwaSLa7PyzxYthDotfsJ7y0jvLcMyZWM45pb8fzzYYTPi6mgCHPBMCylk6Jmw4mM7ulB21+BVrUPKT4B28xz6L7rewivB1PviNM+56LY2NJUTXD5e2j7diDZ7Ngu/z5yztDIGmkUwuBE1pMCSBY7oR1L0aq2ITydEe/ZM24AX3ckF4/95N6geiiGCPURR9wnpIURwYh/vdDDyHEuMJnR22sP+uHL9gTkxHS09lpEyA9ISCYzprQh6N4uhL8nUillE5IzCSQTaEEwWZDk/s8ZdCiRpFdhMJkIrX0PvakKEfRhHj4ZS8nZ6O6OiMt4FOw+6BZbsQPreTehVZUR3r4SU8FoTENHISdFL2HZAcLVlWjlKuGqckR3J/F33ovvrf8S2rIO06ACTHmDsc6ag2S3x3TvUn8h/D7CFXvQaqvR62uwlE7CPHocnbdcgpwzCHNBEZbxU7BOmYHQtKh7KApvD1rlTrSKnWgVO7Bf9zOQTWiVO/t0u8CRCJdvRG/ch95SjZSUgW32TWiNFUgWG1Jy1sB7lnUdEJF9Qt6ug20YkowpMQPd3Ybu6wahgxCY0oZAOIjW2RDZliJJyPGpyHGJkXOyKfIdLXZkmzPi3SvJSJJk7BPqU3QN/+b3IRzENmEeemcD4dodkeG0yYwlbwySw3XwRkmyjJBlIB3hdyOCXhACIZswpQ1B+HvQ2vaDpiF0DUvBBBCC4O6lESGSZMy5ozBnKwTL10RCs1vsyA4XprR89IAHAMkSF5MGT5IkMEemS6ynzQNAeLsjQgyENn6E3liJnD4IU85wzCOm9l3ZzkTMY6ZhHjMNADlrCKbudrTyrQQ/fQX7dT9DSkpH27cNU8FIZFffh/gxDy7APLiAQ53zbWdfgLlwOFpNFVp1JSAIbVqH++H7IgFZs3Kxz7sWszKK0PpVyBmZyKkZSAmJA36vkPB60Ls6MWXnEtq9g9C6lehN9WiNdcTfeS8iFMT3n6eQcwdhyhkcSV1tNpP04gf/33eLhgAJrxttfxl69R4s51xLWN2ItmMtpqGjME88Eyk1G0mW+3S/jhA6orMZvbkKrakSOSkDy9izEN4u5KxCzGPPQkpIAcCUNbTPyj062/53FKZ7u9C7myMd35AfU/YIAELqMkQ4CLqGObcYc+4owjXbEFoo0hG2J2JKzED4ehA9rQcFByEinW5fV+T/QkeyOhD2BLSmctC1SEfcmYycP4HQvnXonXVgsoIe/trfzRgJ8b8joY7mht7kdVHu1QnRu1sZJJMZrasJgj5E2A+yBXNmIaHaHWitVRAKgMWGbcxchK8bvasRyeZEsidE9gnE0GVTBLzozfsRfjfmYZMIrn0P4e5AziyI/EvL6/Ppu8ioUyDaGggueg2tqgzJFof1om9gKhyL6GhGSs6I7Z4WnxetqQG9oQ5TQRGyKwn3o/ejNzeit7VgOW0m8d//JZ6nHkPv6kB2JSNnZBI377qIoDU3IjnjkeIcmLJzIx2dcCiyNnYMHY6Dz244hOjqRPi8CJ8XOSMLKT6RwKfvI9w9EbHJHYT9vHm4H3uA4PpVkR5wTh6uR54ltG0T4T07kTOzMWXmYsofGvNcNcLdid7agCm/mOBnrxFa+3Ek4GfBSCxTz49KTMNDRUdKykJOyyWw4MnIGmlmAabMgqivk/4fe7QwIuBG+N2RzfBJ2YSqt6J31Ec6uRYbtpIL0Lua0DvrkaxxYLZhSs4BkwUR9EXWnkyWqD8PQtchHCQ5I8uYjusLBvKakNB1RMiHbHOiezvR2moOVlTz4BJkewLBfWuQ7YlIcYnIiRnIjtjk0hEBX6TX2FyJ6GjEetYt6HUqeldL5AFOyelzQT8QqRhHJBqy/8m7AJCHKJjHzcY8rCRmez2+0Mbe6anw3jK05gZEZwciHCbukqsJLP+MwOcfI7we8HmJ//lvEQE/3Xf/oFeILMRdcytx866j64e3oLu7ATAPHUbCvX/C8+zjBBd/ggiHIRQk6d/vEC7fjecfDyE5nEhxDuKuvgXLuMl4n/4LUkICcmISpoIiLGPGo7c2Q5wj8tn+3CPk8yA54gl+/gbh7asQnm5MRWOwX3UnwtsDtrg+72AJIRDdLUj2eETQT+CTpyKzD5kFmArHY0qPTobg/88OXUN4OtB93Qhfd+SZTcomsHk+ksWOZItHTszAnDUsMp0myRF37gE27QfGmlCfMZBF6KsQuobubkMcqNDxqZjShhDYsRDJbEOKcyEnpmNKzo1J46y31kRCETVVIjyd2C/6UWQk43cjJWX1+dSiEALR0YRWvQfZlYo8pBjfYz9ASs7ENGgYpqKxmApG9WmZ0SKSCj4IsoxksaJ3tkfCqACYzMiupMhoR9ciDbTFGvNoEcfDgXoXXP4e+v7daLXlmPKLsV/zE7TKnRAXj5wxKCp1A0B0NRPesRStqRLJZMYy9TLk9MEInxvZGd0Omwj50Xta0b2dCG8n5rzRIMmEKtYjx/V2HF1ZyA5Xv3eejgdDhPqIE1mEvggR9EacI7xdIEm9a0+rEX4PsjMZyZmMKb0gqpVe+D1gc6A37iO04UOE342ckY+ldA5SQipIRMf7zudGqy1Hr9mLZLVjmX4R/jf/BuFgJOtsb+w7g+ggAj7Cmxaj11ei1e3DPGIC1jnXE1rxPlJyBvKgYciJKdEp29uNVr8HvakSrakS2+ybwGJHb9qHnDkUOT46WVsB9IAH0dOK7ulAeDuxKDPQOxvQWvdHghg7kpATM04qd21DhPoISZJ0QHK5Bk5K6OgRWWNBiEggVhEJWBhRhN6Fymii65HAiUJEgh9KcuS1LEdsiBa9Ho2RAI0CLNaIN2Cvp0/EhoE/qhhwCBFZnNZ7f1+zJfI7Hnpvox0xvjeqPSZL7/095J5Gu05x+LMkep8hKfrP0gCgq6sLQAghjvsmGyIESJIUBmSg+1j/VpZlF4Cu6119bdfJivGbHRvG73VsGL/XsfE1f69EQBdCHPcCniFCXxNFUToBVFVN6l9LThyM3+zYMH6vY8P4vY6N/v69Tu4ddwYGBgYGAxpDhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1jn5CBgYGBQb9hjIQMDAwMDPoNQ4QMDAwMDPoNQ4QMDAwMDPoNI723gcEARVEUM/Aj4HZgCFAHPAs8pKqq1p+2GRj0FcZIyMBg4PIk8DDQCDwONAN/BP7dn0YZGPQlhnecwYBFUZQiYC9wH/A3YB5wATAGyAWCwHbgOeA5VVX1/rG071EUZTqwHHhJVdUbe89JwCvA1cAsVVWX9aOJA5pTue6caBgjIYOBzLze47vAlcAzwBRgLfAX4C1gNJEpqtd7G+mThe/0Hn974ISqqgK4q/flbTG36MTiVK47JxTGmlAfoyjKPODto/ioBiSrqtoTZZNOZC4FKlVV3aooSipwMfDhob1WRVHuBtYBlwOXEWlcTgZmArWqqpYfelJV1UpFUfYDs/rHrBOGSzl1686XMtDaKEOE+p42Ir2u24HNwPxD3psMnAe8Dyw6FQToeCu8oiiZwGnAEwCqqn5+pD9SVbVRUZQngd8DZ3ASNCSKotiAPGDpF3ykCpipKIpNVdVAzAzrB46n/pzKdecoGVBtlCFCfYyqqssURckhcoNfV1X1wQPvKYryOJEb/Kiqqkv6ycRYc7wV/mIi08XvHEUZod5j+GtbOzBI6T12fsH7XYAEJAAntQhxfPXnVK47X8lAa6MMEYoOJb3HLYedH9d73Bo7U/qXr1Hh5wGtwMovu36vG/NNvS8/7iu7+xlL7/GLBObAeXsMbOlXjrP+nMp152gZMG2UIUJHQFGUKiL7Mo6WX6uq+rtDXpf2Hg/eyN6FzxKgRlXVjq9r4wnGMVV4RVESgDOBl49iP8yDRBaYF6iq+snXtHOg4Os9Wr/gfVvv0RMDWwYCR11/jLpz1JT2Hvu9jTJE6MjsA/zH8PnWw16XAs2qqjYccq4ISAROOLfafhDl84g0tO9+hV0/BH4KqPxvj/ZkoAvQAdcXvH/gfHdszOl3SnuPR1N/TvW6c7SUMkDaKEOEjoCqqmcd798qipIBZAELD3vrRJ6Ki7UoX0qkl3/4b3gQRVG+T2QDZxlwpqqqh5d5wqKqarDXA67gCz5SAJSfQlETSjn6+nMpp3DdORoGWhtliFDfU9p7PPxGnrAiFEtRVhTFApwPfKKq6hGFT1GUO4HHgB3AWaqqNh+vfQOYFcCNiqIMUVV1/4GTiqIMBQYDL/abZTHkWOqPUXeOmtLe44Boo4zNqn3PF81fj+497oidKQOC0t7j0Vb4M4lMN717pIspivJLIo3IFmD2SdyI/Kf3+IcDGyl7j3/oPf90v1gVe0p7j0dTf4y6c3QMqDbKEKG+p7T3ePhDc8DttrR3H8OpwrFW+EuJuMt+cPiFFEX5NZHF5I1EerEn7TSKqqqfAa8B1wErFEV5kIi319VEwsys6E/7Ysix1J9LMerO0VDaexwQbZQxHdf3lBBZP9l92PlXgFHAU0RCrrwZY7v6i9Le45dV+HZVVZt6e/oXA0sPd1ZQFOVm4H4imxKXAz9UFOXwsraoqvpuH9re39xEZN3iZuBOYD/wK+DRfrQp1pT2Hr+0/hAJ7mrUnaNjQLVRhgj1Maqqjv6C838jEkjxVONYKvwUIIdIpOjDObBIbyLSIB+JF/gKr6gTCVVVg0Rix/32qz57EnO09acWo+4cFQOtjTKiaBsMGHqnnH4JDFJVtba/7TE4cTDqzomLsSZkMJC4FNhoNCIGx8GlGHXnhMQYCRkYGBgY9BvGSMjAwMDAoN8wRMjAwMDAoN8wRMjAwMDAoN8wRMjAwMDAoN8wRMjAwMDAoN8wNqsaGAxgFEWZDvwEmA7EE0k98Iiqqi/1q2EGBn2EMRIyMBigKIryWyKpCmYRCTezhEiUgBcVRbm9H00zMOgzjH1CBgYDEEVRfgo8DLwOfFNV1Z7e82cDnxLJ2ZR1CuUUMjhJMUZCBgYDDEVRionEQFsLXH9AgOBgdO0tQBowsV8MNDDoQwwRMjAYeNwPWICfqqoaPsL7Tb3H/JhZZGAQJQwRMjAYQCiKkg3MAzarqrryCz4WF0OTDAyiiuEdZ2AwsLicSMoBu6Ioz3/BZ8b0HttjYpGBQRQxRMjAYGBxVu+xuPffl7EnyrYYGEQdQ4QMDAYWB5wNUg7PEAqgKMp5wEdEMolWx9IwA4NoYKwJGRgMEBRFcQC5gO9IAtTLgZHSYlVVjf0VBic8hggZGAwckgAJcB/pTUVRJOCy3pevxcgmA4OoYoiQgcHAQe89Wr/g/blAAVADfBATiwwMoowhQgYGA4cmwAe4FEUZdOgbiqJYgQd7X/5aVdVQrI0zMIgGhggZGAwQetd4Pul9+esD5xVFsQMvAmOBt1VVfaEfzDMwiApG7DgDgwGEoihjgXWADdgE7ANmAFnA+8BVqqr6+89CA4O+xRAhA4MBhqIopwG/Byb1ntoCPG2kbzA4GTFEyMDAwMCg3zDWhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+g1DhAwMDAwM+o3/B8cW7P3OIWHBAAAAAElFTkSuQmCC\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.contour(TH, PP, HH, levels=10, linestyles='--', linewidths=1)\n", - "plt.plot(results_euler2[:, 0], results_euler2[:, 1], c='b')\n", - "set_axes()" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "deadly-privacy", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "2.0" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "h_sep = hamiltonian(-np.pi, 0) # Value of Hamiltonian at separatrix\n", - "h_sep" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "prompt-success", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(\n", - " hamiltonian(results_euler2[:, 0], results_euler2[:, 1]), \n", - " c='b', label='Euler integrator')\n", - "plt.axhline(hamiltonian(theta_ini2, p_ini2), c='r', label='theory')\n", - "plt.axhline(h_sep, c='k', label='$\\mathcal{H}_{sep}$')\n", - "\n", - "plt.xlabel('Steps $k$')\n", - "plt.ylabel(r'$\\mathcal{H}(\\theta, p)$')\n", - "plt.legend(bbox_to_anchor=(1.05, 1))\n", - "plt.ylim(top=2.1);" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "configured-print", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "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": "3.9.18" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -}