commit 927824a70697a0cb4c249e52069dd428d256f195 Author: AINDUSTRIES Date: Mon Aug 18 12:04:55 2025 +0200 Initial commit diff --git a/Chapitre1-Bissection.ipynb b/Chapitre1-Bissection.ipynb new file mode 100644 index 0000000..580d5a1 --- /dev/null +++ b/Chapitre1-Bissection.ipynb @@ -0,0 +1,110 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "436e1fcf-057d-40fa-9f18-1ca88873d212", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d096b9af-5b85-4d69-b431-8d86669a5834", + "metadata": {}, + "outputs": [], + "source": [ + "def f(x):\n", + " return 4*x**3 - 24*x**2 + 48*x - 32" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1a47d15f-3f4c-4e9e-9522-e5fe7d3f5cc4", + "metadata": {}, + "outputs": [], + "source": [ + "def bissection(interval, f, tolerance=1e-5):\n", + " x = (interval[1]+interval[0])/2\n", + " fx = f(x)\n", + " while abs(fx) > tolerance:\n", + " if f(interval[0]) > 0 and fx > 0:\n", + " interval = [x,interval[1]]\n", + " else:\n", + " interval = [interval[0],x]\n", + " x = (interval[1]+interval[0])/2\n", + " fx = f(x)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "f9f8fd12-9959-448a-994c-53607406ef71", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xs = np.arange(0,4,0.1)\n", + "ys = np.array(f(xs))\n", + "root=bissection([1,3],f)\n", + "plt.plot(xs,ys,'r')\n", + "plt.plot(root,0,'.b')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2654770b-66c2-4920-9c56-5e95a906ead5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Chapitre1-Newton.ipynb b/Chapitre1-Newton.ipynb new file mode 100644 index 0000000..09cd03b --- /dev/null +++ b/Chapitre1-Newton.ipynb @@ -0,0 +1,109 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "d7941891-67e3-40c8-b0db-79d9b329560d", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9c9755d9-ae58-4c90-bc01-4b68118236d8", + "metadata": {}, + "outputs": [], + "source": [ + "def f(x):\n", + " return x * np.e**x - 1\n", + "\n", + "def fp(x):\n", + " return np.e**x + x * np.e**x" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8e1768fd-71dd-479c-892a-afc653f48c56", + "metadata": {}, + "outputs": [], + "source": [ + "def newton(x,f,fp,tol=1e-5):\n", + " fx = f(x)\n", + " while abs(fx) > tol:\n", + " fx = f(x)\n", + " fxp = fp(x)\n", + " x = x - (fx/fxp)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f9762b65-df91-41db-aea0-2d432665841f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xfs = np.arange(0,1.2,0.01)\n", + "yfs = np.array(f(xfs))\n", + "x = newton(1,f,fp,1e-10)\n", + "plt.plot(xfs,yfs,'r')\n", + "plt.plot(x,0,'.b')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2f657470-4854-4b0f-bc48-7fb996612881", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/Chapitre1-PointFixe.ipynb b/Chapitre1-PointFixe.ipynb new file mode 100644 index 0000000..c98d364 --- /dev/null +++ b/Chapitre1-PointFixe.ipynb @@ -0,0 +1,105 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "49d00265-ce59-4299-ba97-579e229276d0", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f8444097-9306-4925-9812-acf7170c8b8e", + "metadata": {}, + "outputs": [], + "source": [ + "def f(x):\n", + " return (x**2 * np.e**x + 1)/(x * np.e**x + np.e**x)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "0deda420-a608-488f-98d3-0fe691eeab47", + "metadata": {}, + "outputs": [], + "source": [ + "def pointfixe(x,f,k=50):\n", + " for _ in range(0,k):\n", + " x = f(x)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "34abdcc0-8f88-4b99-a04d-5c8b074231ba", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABYdklEQVR4nO3dd1xV9ePH8ddlu8CNiqipmTNxkivTHKlprsCN5vxqltpylGZW2LbSXDkyByCOSk0rR5pa5qAsR67c4EpAVNY9vz/OT81S8yJwuPB+Ph7noRzv9b6PIPfNOZ/z+dgMwzAQERERsYiL1QFEREQkZ1MZEREREUupjIiIiIilVEZERETEUiojIiIiYimVEREREbGUyoiIiIhYSmVERERELOVmdYC7YbfbOXXqFPny5cNms1kdR0RERO6CYRjEx8dTokQJXFxuf/7DKcrIqVOn8Pf3tzqGiIiIpMHx48cpWbLkbf/cKcpIvnz5APNgvL29LU4jIiIidyMuLg5/f//r7+O34xRl5NqlGW9vb5URERERJ/NfQyw0gFVEREQspTIiIiIillIZEREREUupjIiIiIilVEZERETEUiojIiIiYimVEREREbGUyoiIiIhYSmVERERELKUyIiIiIpZSGRERERFLqYyIiIiIpVRGREREcrCle5fSKaITqfZUyzKojIiIiORAV1OuMnTVUDpFdGLp3qXMiZpjWRY3y15ZRERELHHwwkGCFgexK3oXAC/Wf5GQ6iGW5VEZERERyUHCfwun/1f9iU+Kp3DuwsxrP49W97eyNJPKiIiISA5wJfkKw1YPY8bOGQA0KtWIRZ0W4eftZ3EylREREZFsb/+5/QRFBvFrzK/YsDGm0RjGPTION5esUQOyRgoRERHJEPN/nc+gFYNISE6gaJ6izO8wn+blmlsd6yYqIyIiItnQ5eTLPL3q6et3yTQp04QFHRdQPF9xi5P9m8qIiIhINvP7md8Jigxiz9k92LAxrvE4Xn74ZVxdXK2OdksqIyIiItmEYRjMjZrLkFVDuJJyhWJ5i7Gw40Ka3NfE6mh3pDIiIiKSDVxKusTglYP5/NfPAWhetjnzO86naJ6iFif7byojIiIiTu7XmF8JWhzE/vP7cbG5MKHJBEY2HImLzTkmWlcZERERcVKGYTBz50yeXf0sV1Ou4pfPj0WdFtGodCOrozlEZURERMQJxSXGMXDFQMJ+CwOg9f2t+az9ZxTOXdjiZI5TGREREXEyu07vIigyiIMXDuLm4sabTd/kufrPOc1lmX9SGREREXEShmHwyc+fMOKbESSlJlHKpxRhncKo51/P6mj3RGVERETECVy8epF+X/Zjyd4lALR7oB1znphDwVwFLU5271RGREREsrifT/5McGQwRy4ewd3Fnbebv82zgc9is9msjpYuHL64tHHjRtq2bUuJEiWw2WwsX778rp+7efNm3NzcCAgIcPRlRUREchzDMJj04yQazG7AkYtHuC//fWx+ajPDHhqWbYoIpKGMJCQkUL16daZMmeLQ8y5evEivXr149NFHHX1JERGRHOfClQu0D2/P8DXDSbYn06lSJ3YO3EkdvzpWR0t3Dl+madWqFa1atXL4hQYNGkS3bt1wdXV16GyKiIhITrP1+Fa6LOnCsdhjeLh68H6L9xlcZ3C2Ohvyd5lyD9CcOXM4fPgw48aNu6vHJyYmEhcXd9MmIiKS3dkNO+9sfoeH5z7MsdhjlC9Ynh/7/siQukOybRGBTBjAeuDAAUaOHMmmTZtwc7u7lwsNDWX8+PEZnExERCTrOHf5HCHLQ1h1YBUAXap2Yfrj0/H29LY4WcbL0DMjqampdOvWjfHjx1OhQoW7ft6oUaOIjY29vh0/fjwDU4qIiFhr09FNBEwLYNWBVXi5eTH98eks7LgwRxQRyOAzI/Hx8Wzfvp1du3bx9NNPA2C32zEMAzc3N7755huaNm36r+d5enri6emZkdFEREQsZzfsTPxhImPXjyXVSOWBQg8Q8WQED/o+aHW0TJWhZcTb25vdu3fftO+TTz5h3bp1REZGct9992Xky4uIiGRZZxLO0GNpD749/C0APR/sySdtPiGvR16Lk2U+h8vIpUuXOHjw4PWPjxw5QlRUFAULFqRUqVKMGjWKkydPMm/ePFxcXKhatepNzy9atCheXl7/2i8iIpJTrD+ynm5LuxF9KZpcbrmY0noKvQN6Z+tBqnficBnZvn07TZo0uf7xiBEjAAgJCWHu3LmcPn2aY8eOpV9CERGRbCLVnsrrG1/ntY2vYTfsVC5SmYjOEVQpWsXqaJayGYZhWB3iv8TFxeHj40NsbCze3jljMI+IiGQvp+NP02NZD9YdWQfAUwFP8XHrj8ntntviZBnnbt+/tTaNiIhIBvv20Lf0WNaDMwlnyOOeh6ltptKzek+rY2UZKiMiIiIZJMWewqsbXuXNTW9iYPCg74OEdw6nYuGKVkfLUlRGREREMsDJuJN0XdKVTcc2ATCw1kA+aPkBudxzWZws61EZERERSWdfH/iaXst7ce7yOfJ55GNG2xl0qdrF6lhZlsqIiIhIOklOTebldS/z9pa3AahRrAYRT0ZQvmB5i5NlbSojIiIi6eBY7DG6RHZh64mtADxd52neafEOXm5eFifL+lRGRERE7tGX+7+k9/Le/HX1L3w8fZjVbhadKneyOpbTUBkRERFJo6TUJEZ+N5IPfvwAgDol6hDWOYyyBcpanMy5qIyIiIikwZG/jtBlSRe2ndwGwLDAYbzV/C08XD0sTuZ8VEZEREQctHTvUp764iliE2Mp4FWAue3n0u6BdlbHcloqIyIiIncpMSWR5795nsk/TwbgoZIPEdYpjNL5S1uczLmpjIiIiNyFgxcOEhwZzM7TOwF4sf6LvN70ddxd3S1O5vxURkRERP5DxO8R9PuyH/FJ8RTKVYh5HebR+v7WVsfKNlRGREREbuNK8hWGrxnO9B3TAWhYqiGLOi2ipHdJi5NlLyojIiIit7D/3H6CIoP4NeZXbNgY3Wg0rz7yKm4ueutMb/oXFRER+Yf5v85n0IpBJCQnUCR3ERZ0XEDzcs2tjpVtqYyIiIj8v8vJlxm6aiizo2YD0KRMExZ0XEDxfMUtTpa9qYyIiIgAe87uIWhxEL+f/R0bNsY2HssrD7+Cq4ur1dGyPZURERHJ8eZGzWXwysFcSblCsbzFWNBxAU3va2p1rBxDZURERHKsS0mXGLJqCPN+mQdA87LN+bzD5/jm9bU4Wc6iMiIiIjnS7pjdBEUGse/cPlxsLrz2yGuMajQKF5uL1dFyHJURERHJUQzD4NOdn/LM6me4mnIVv3x+LOq0iEalG1kdLcdSGRERkRwjLjGOgSsGEvZbGACtyrdiXod5FM5d2OJkOZvKiIiI5Ai7Tu8iKDKIgxcO4mpzJfTRUJ6r/5wuy2QBKiMiIpKtGYbB1O1TGb5mOEmpSfh7+xPeOZx6/vWsjib/T2VERESyrdirsfT7qh+ReyIBaPdAO+Y8MYeCuQpanEz+TmVERESypZ9P/kxwZDBHLh7B3cWdt5q9xbCHhmGz2ayOJv+gMiIiItmKYRh89NNHvPDtCyTbkymTvwzhncOp61fX6mhyGyojIiKSbVy4coGnvniKL/Z/AUDHSh2Z1W4W+b3yWxtM7khlREREsoUfT/xIcGQwx2KP4eHqwXst3mNInSG6LOMEVEZERMSp2Q077299n1FrR5FiT6FcgXJEPBlBzeI1rY4md0llREREnNa5y+fovbw3Kw+sBCC4SjAz2s7A29Pb4mTiCJURERFxSj8c+4GuS7pyIu4Enq6efNTqI/rX7K/LMk5IZURERJyK3bDz1g9v8cr6V0g1UqlQqAKLn1zMg74PWh1N0sjhOXA3btxI27ZtKVGiBDabjeXLl9/x8UuXLqV58+YUKVIEb29v6tWrx5o1a9KaV0REcrAzCWdotaAVo9eNJtVIpceDPdgxYIeKiJNzuIwkJCRQvXp1pkyZcleP37hxI82bN2fVqlXs2LGDJk2a0LZtW3bt2uVwWBERybk2/LmBgGkBfHPoG3K55WJWu1nMaz+PvB55rY4m98hmGIaR5ifbbCxbtoz27ds79LwqVaoQHBzM2LFj7+rxcXFx+Pj4EBsbi7e3BiWJiOQkqfZU3tj0BuO/H4/dsFO5SGUiOkdQpWgVq6PJf7jb9+9MHzNit9uJj4+nYMHbrwuQmJhIYmLi9Y/j4uIyI5qIiGQx0Zei6b60O+uOrAOgT0AfPm71MXk88licTNJTpq+b/O6773Lp0iWCgoJu+5jQ0FB8fHyub/7+/pmYUEREsoLvDn9H9WnVWXdkHXnc8zCv/TxmPzFbRSQbytQysnDhQsaPH09ERARFixa97eNGjRpFbGzs9e348eOZmFJERKyUYk/hlXWv0OLzFpxJOEO1otXYPmA7Pav3tDqaZJBMu0wTFhZGv379WLx4Mc2aNbvjYz09PfH09MykZCIiklWcjDtJt6Xd2Hh0IwADag5g0mOTyOWey+JkkpEypYwsWrSIp556irCwMNq0aZMZLykiIk5m9cHV9FzWk3OXz5HXIy8z286kS9UuVseSTOBwGbl06RIHDx68/vGRI0eIioqiYMGClCpVilGjRnHy5EnmzZsHmJdmQkJC+PDDDwkMDCQ6OhqAXLly4ePjk06HISIizio5NZlX1r/CW5vfAqBGsRqEdw7n/kL3W5xMMovDY0a2b99OjRo1qFGjBgAjRoygRo0a12/TPX36NMeOHbv++BkzZpCSksKQIUMoXrz49e3ZZ59Np0MQERFndTz2OI989sj1IjKkzhC29N2iIpLD3NM8I5lF84yIiGQ/X+3/it5f9ObClQt4e3ozq90sOlfubHUsSUdZdp4RERHJ2ZJSkxj13Sje//F9AGqXqE1453DKFihrcTKxisqIiIhkmiN/HaHLki5sO7kNgGGBw3ir+Vt4uHpYnEyspDIiIiKZYtneZfT5og+xibHk98rP3Cfm8kTFJ6yOJVmAyoiIiGSoxJREXvj2BT7e9jEAD5V8iLBOYZTOX9riZJJVqIyIiEiGOXThEMGRwew4vQOAF+q/wBtN38Dd1d3iZJKVqIyIiEiGiPg9gn5f9iM+KZ5CuQrxWfvPaFNBE1/Kv6mMiIhIurqacpXhq4czbcc0ABqWasiiToso6V3S4mSSVamMiIhIuvnj/B8ELQ7il5hfsGFjVMNRjG8yHjcXvd3I7emrQ0RE0sWCXxcwcMVAEpITKJK7CPM7zqdFuRZWxxInoDIiIiL35HLyZZ75+hlm7ZoFwCNlHmFBxwWUyFfC4mTiLFRGREQkzfac3UPQ4iB+P/s7NmyMbTyWVx5+BVcXV6ujiRNRGRERkTSZGzWXIauGcDn5MsXyFmNBxwU0va+p1bHECamMiIiIQy4lXWLIqiHM+2UeAM3KNmN+h/n45vW1OJk4K5URERG5a7tjdhMUGcS+c/twsbnw2iOvMbLhSF2WkXuiMiIiIv/JMAxm7ZrF0K+HcjXlKiXylWBRp0U8XPphq6NJNqAyIiIidxSfGM/AFQNZ9NsiAB4r/xjz2s+jSJ4iFieT7EJlREREbisqOoqgxUEcuHAAV5srbz76Js/Xfx4Xm4vV0SQbURkREZF/MQyDadunMXzNcBJTE/H39iescxj1/etbHU2yIZURERG5SezVWPp/1Z/FexYD0LZCW+Y8MYdCuQtZnEyyK5URERG5bvup7QRHBnP4r8O4ubjxdrO3GfbQMGw2m9XRJBtTGREREQzD4KOfPuKFb18g2Z5MmfxlCO8cTl2/ulZHkxxAZUREJIf768pfPPXlUyzftxyADhU7MPuJ2eT3ym9pLsk5VEZERHKwn078RHBkMEdjj+Lh6sF7Ld5jSJ0huiwjmUplREQkB7Ibdj7Y+gEj144kxZ5CuQLlCO8cTq0StayOJjmQyoiISA5z/vJ5QpaHsPLASgCCqgQx4/EZ+Hj5WJxMciqVERGRHGTzsc10WdKFE3En8HT15MPHPmRArQG6LCOWUhkREckB7Iadtze/zcvrXibVSKVCoQpEdI6gerHqVkcTURkREcnuziScodeyXqw5tAaA7tW6M7XNVPJ55rM4mYhJZUREJBv7/s/v6bqkK6cvnSaXWy4mt55Mn4A+uiwjWYrKiIhINpRqT+XNTW/y6vevYjfsVCpciYgnI6hatKrV0UT+RWVERCSbib4UTY+lPVh7ZC0AvQN6M7nVZPJ45LE4mcitqYyIiGQjaw+vpfvS7sQkxJDbPTdT20ylV/VeVscSuSOVERGRbCDFnsJr37/G6xtfx8CgatGqLH5yMRULV7Q6msh/UhkREXFyp+JP0XVJVzYe3QhA/5r9+fCxD8nlnsviZCJ3x8XRJ2zcuJG2bdtSokQJbDYby5cv/8/nbNiwgZo1a+Lp6Un58uWZO3duGqKKiMg/rT64murTqrPx6EbyeuRlYceFzGg7Q0VEnIrDZSQhIYHq1aszZcqUu3r8kSNHaNOmDU2aNCEqKophw4bRr18/1qxZ43BYERExpdhTGPXdKFotaMW5y+cIKBbAzgE76Vqtq9XRRBzm8GWaVq1a0apVq7t+/LRp07jvvvt47733AKhUqRI//PADH3zwAS1btnT05dNXaips3QoNG1qbQ0TEAcdjj9N1SVc2H98MwODag3mv5Xt4uXlZnEwkbRw+M+KorVu30qxZs5v2tWzZkq1bt972OYmJicTFxd20pbvLl6FpU2jcGH78Mf3/fhGRDLDijxUETA9g8/HNeHt6s/jJxUxpM0VFRJxahpeR6OhofH19b9rn6+tLXFwcV65cueVzQkND8fHxub75+/unf7DcucHfH+x26NkTLl1K/9cQEUknSalJPP/N87Rd1JYLVy5Qu0Rtdg3cRefKna2OJnLPMryMpMWoUaOIjY29vh0/fjxjXmjyZChZEg4ehOefz5jXEBG5R39e/JOH5zzMe1vNy93PBj7LD31+oGyBshYnE0kfGV5GihUrRkxMzE37YmJi8Pb2JleuW4/29vT0xNvb+6YtQ+TPD599Zv5++nRYuTJjXkdEJI2W71tOjek1+OnkT+T3ys+y4GVMemwSnm6eVkeT7MJuh127LI2Q4WWkXr16rF279qZ93377LfXq1cvol747TZvC8OHm7/v2hbNnrc0jIgIkpiTy7NfP0iG8AxevXiTQL5CogVG0r9je6miSXRgGrFoFNWvCQw/BsWOWRXG4jFy6dImoqCiioqIA89bdqKgojv3/QYwaNYpevW5MPTxo0CAOHz7Miy++yL59+/jkk0+IiIhg+LUCkBW8+SZUrgwxMTBwoPkJEhGxyKELh2gwuwEfbfsIgOfrPc+mPpsonb+0xckk29i82byBo00b+OUX8PIyf7WK4aD169cbwL+2kJAQwzAMIyQkxGjcuPG/nhMQEGB4eHgYZcuWNebMmePQa8bGxhqAERsb62jcu7dzp2G4uxsGGMbcuRn3OiIidxDxW4ThHept8CpGwbcKGiv2r7A6kmQnO3caRuvW5nsdGIaXl2E8/7xhnDuXIS93t+/fNsPI+qcB4uLi8PHxITY2NuPGjwBMnAijRkG+fPDrr1CmTMa9lojI31xNucqINSOYun0qAA38G7Co0yL8fTLgbkLJefbuhbFjITLS/NjVFZ56ytxXsmSGvezdvn9nybtpLPPCC9CgAcTHQ69e5qRoIiIZ7I/zf/DQpw9dLyKjGo5iQ+8NKiJy744cgZAQqFrVLCI2G3TvDvv2wYwZGVpEHKEy8neurjBvHuTNC5s2mWdKREQy0MLdC6k1oxa/xPxCkdxFWN19NW8++iZuLlrHVO7BqVMweDA88ID5vma3Q4cO5ln/+fOhfHmrE95EZeSfypY15x8B8/TVpk3W5hGRbOly8mX6f9mf7ku7cynpEo+UeYSoQVG0LG/xMhni3M6dM+fNKlcOpk6F5GRo0QK2bYOlS80zJFmQysithISYl2nsduja1fzkioikk71n9xL4aSCf7voUGzbGPjyW73p+R4l8JayOJs4qNhbGjYP77oP33oOrV811177/HtasgTp1rE54RzoPeDtTpphNct8+s5isWAEu6m4icm8+i/qMwasGczn5Mr55fFnQcQGPln3U6ljirBISzLP5b70Ff/1l7qtZE954A1q2NMeIOAG9u95O3rwQEWHee/311/Duu1YnEhEnlpCUQO/lven9RW8uJ1/m0fseJWpQlIqIpE1iInz8sXk5ZuRIs4hUqmQOUt2+HR57zGmKCKiM3Fm1avCROekQo0fDli3W5hERp/Tbmd+oPbM2n/3yGS42FyY0mcCaHmsolreY1dHE2aSkwOzZUKECPPOMOVnnffeZS5vs3g2dOjlVCblGZeS/9OtnjhtJTYUuXeD8easTiYiTMAyDT3d+Sp2Zddh3bh8l8pVgXa91vPzwy7i6uFodT5xJaiosWGDOFt63rzl1e4kS5iDVa8MJXJ33a0pl5L/YbOYievffD8ePQ58+mi5eRP5TfGI8PZb1oP9X/bmacpXHyj9G1MAoGpdpbHU0cSapqRAWZt4F06MHHDgAhQubg1QPHoRBg8DDw+qU90xl5G7ky2eOH/H0hK++grfftjqRiGRhUdFR1J5Zm4W7F+Jqc2XioxNZ2W0lRfIUsTqaOAu7HRYvhgcfNM/O79sHBQqYa6kdPgwjRsBtVr53RiojdysgAD780Pz9qFHmrVIiIn9jGAZTf57KQ58+xB/n/6Ckd0m+7/09LzV8CRebvt3KXbDbzflAAgIgKAj27IH8+WHCBPjzzxtLlmQzurXXEQMGwM8/w6xZ5viR7dvNkcwikuPFXo1lwIoBRPweAcDjFR5n7hNzKZS7kMXJxCkYBnz5pTlXyLXVc729zTMgzz5rFpJsTGXEETabOf/Ib7/BTz9B+/awdat5G7CI5Fg7Tu0gKDKIw38dxs3FjbeavcXwh4Zjc8K7GiSTGQasXGmWkJ07zX358sGwYTB8uHlpJgfQeUNHeXrCkiVQrJhZSjSgVSTHMgyDj3/6mPqz63P4r8OU9inND31+YES9ESoicmeGYc5hFRgIbduaRSRPHvMyzJEj8NprOaaIgMpI2vj5mRPLuLubv771ltWJRCST/XXlLzpFdOKZ1c+QlJpE+4rt2TVwF4ElA62OJlmZYcA330D9+tC6tXnpP3duePFFs4S8+SYUynmX9lRG0qpBA3P2OzAnRFu92to8IpJpfjrxEzWm12DZvmV4uHrw0WMfsTRoKQVy5ZyfZMVBhgGrVkG9euY07T/+aN4N89xzZgl56y0oknPvtlIZuRcDB0L//uYXWdeu5v3fIpJtGYbBe1veo+GchhyNPUrZAmXZ8tQWhgYO1WUZubVrA1Pr1IE2bczxhl5e5qDUw4fNpUaKFrU6peU0gPVeffyxOXZk61bzC23r1hx5ik0kuzt/+Ty9v+jNij9WAPBk5SeZ2XYmPl4+FieTLMluh2XLzFtyr90dkzs3DB5sng0ppqUA/k5l5F55epr3hAcGmmdGOnY0rwd6elqdTETSyeZjm+m6pCvH447j6erJpMcmMbDWQJ0NkX9LTTXHEk6YAL//bu7Lmxeeftq8TTcHX4q5E12mSQ/Fipm3Znl7w8aN5no2usNGxOnZDTsTf5hI47mNOR53nPsL3s+P/X5kUO1BKiJys5QUc+2YqlXNeah+/918T3jlFXOystBQFZE70JmR9FK1qtmGW7WC+fOhfHnzvnERcUpnE87Sa3kvVh80B6d3q9aNaW2mkc8z+81+KfcgORkWLoQ33rgxbjB/fnOOkGeeyfaTlaUXnRlJT82bmysoArz6Knz+uaVxRCRtNh7dSMD0AFYfXI2Xmxeftv2U+R3mq4jIDUlJ8Omn8MAD0Lu3WUQKFTJvzT16FMaOVRFxgM6MpLf+/eHQIfM2rb59oVQpaKxVOkWcQao9ldAfQhm3YRx2w06lwpWIeDKCqkWrWh1NsoorV2D2bHPB1GPHzH1FisALL8D//qcZudNIZSQjXFtVcfFi6NABtmyBihWtTiUidxBzKYbuS7uz9shaAEKqhzCl9RTyeOSxOJlkCbGx5pnvDz6AM2fMfcWKmZOVDRxo3ikjaaYykhFcXOCzz+D4cXNimxYtYPNm8Pe3OpmI3MLaw2vpvrQ7MQkx5HbPzSetPyEkIMTqWJIVnD1rrtg+ebJZSABKlzZLSJ8+5sRlcs9URjJKrlzmRDeNGsH+/WYh2bQJChe2OpmI/L9Ueyqvff8aEzZOwMCgatGqRHSOoFKRSlZHE6sdPw7vvQczZpiXZgAqVTLXjunSxVwORNKNykhGKlLEnHOkQQPYt8+802bdOnNFRhGx1Kn4U3Rb0o3vj34PQL8a/fiw1Yfkdtfp9hztwAFzzN+8eeadMgC1a5vLfjzxhHnmW9Kd/lUzWqlS8O235hmR7dvNL+arV61OJZKjrTm4hoBpAXx/9HvyeuRlQccFzGw3U0UkJ4uKguBgc3zfrFlmEWnSxPyBcts2c/yfikiG0b9sZqhY0VwqOm9eWL/eXMcmJcXqVCI5Too9hVHfjeKxBY9x9vJZqvtWZ8eAHXSr1s3qaGKVzZvNpTxq1ICICHMa97ZtzRsP1q0zp2zQBHcZTmUks9SubY4h8fSE5cthwADN0iqSiY7HHueRuY8wcfNEAAbXHsyP/X6kQqEKFieTTHdtBd3GjaFhQ/P3Li7mD4q//GJ+r65Xz+qUOYrGjGSmJk0gLAw6dYI5c8wzJR9+qNYtksFW/rGSXst7ceHKBbw9vfm07ac8WeVJq2NJZktKgkWL4J13bqwb4+FhTlr2wgvmzNliCZWRzNa+vTlhTu/e5oq/NhtMmqRCIpIBklOTGb12NO9ufReAWsVrEd45nHIFy1mcTDJVXJx5V8ykSXDypLkvXz5zfpBhw8DPz8p0gsqINUJCzMFR/fvDRx+ZReSDD1RIRNLR0YtHCY4M5qeTPwHwTN1neLv523i6aUXtHOPUKfPs87RpZiEBKF7cLCADB4KPj6Xx5AaVEav062f+2r//jUs177+vQiKSDpbvW06fL/pw8epF8nvlZ84Tc2hfsb3VsSSz7NkD775rLlp67fbcypXh+eehWzdz7J5kKWkawDplyhTKlCmDl5cXgYGBbNu27Y6PnzRpEg888AC5cuXC39+f4cOHc1W3t5qFZMYM8/eTJsFzz2lQq8g9SExJZNjqYXQI78DFqxcJ9Atk18BdKiI5gWHAxo3mnTBVqpjj8pKTzYknv/oKdu82Z0xVEcmaDAeFhYUZHh4exuzZs43ff//d6N+/v5E/f34jJibmlo9fsGCB4enpaSxYsMA4cuSIsWbNGqN48eLG8OHD7/o1Y2NjDcCIjY11NK5zmD7dMMz/SoYxfLhh2O1WJxJxOocuHDJqTa9l8CoGr2I8t+Y5IzEl0epYktFSUgxjyRLDCAy88X3UZjOMjh0NY+tWq9PleHf7/m0zDMd+FA8MDKROnTpMnjwZALvdjr+/P0OHDmXkyJH/evzTTz/N3r17Wbt27fV9zz33HD/99BM//PDDXb1mXFwcPj4+xMbG4u3t7Uhc5zFjhnkNE2DoUPNMiSbYEbkrkXsi6ftlX+IS4yiYqyCftf+Mxys8bnUsyUgJCeYaYJMmmbOmgnnWo3dv8yzz/fdbmU7+392+fzv0bpeUlMSOHTto1qzZjb/AxYVmzZqxdevWWz6nfv367Nix4/qlnMOHD7Nq1Spat25929dJTEwkLi7upi3bGzDAHGQF5l02ffpoYjSR/3A15SpDVg7hycVPEpcYRwP/BkQNjFIRyc6OH4eXXoKSJWHIELOIFCgAL78MR4+a30dVRJyOQwNYz507R2pqKr6+vjft9/X1Zd++fbd8Trdu3Th37hwNGzbEMAxSUlIYNGgQo0ePvu3rhIaGMn78eEeiZQ8DB0KePGaznzcPLl6E8HDw8rI6mUiWc+D8AYIig4iKjgJgVMNRjH9kPO6uWsAsW9q2zbzrcPFiSE0195UvD888Y/7wljevtfnknmT4dYANGzbw5ptv8sknn7Bz506WLl3KypUrmTBhwm2fM2rUKGJjY69vx48fz+iYWUePHrBsmVlAvvwSWre+cUuaiACwaPcias6oSVR0FIVzF2Z199W8+eibKiLZTUoKREaai40GBpqTRqamwiOPwBdfmAuQDh2qIpINOHRmpHDhwri6uhITE3PT/piYGIoVK3bL57zyyiv07NmTfv9/K2u1atVISEhgwIABjBkzBpdbjIvw9PTEMyePeG7bFlavNn9dvx4efdRc26ZwYauTiVjqSvIVnl39LDN3zgSgcenGLOy0kBL5SlicTNJVbKy5WN1HH5mXXgDc3c3bcocNg4AAK9NJBnDozIiHhwe1atW6aTCq3W5n7dq11LvNPP6XL1/+V+FwdXUFwMGxszlL48ZmEbm22m+jRnDihNWpRCyz79w+6n5al5k7Z2LDxisPv8J3vb5TEclODh2CZ581x4M895xZRAoXhldegWPHYO5cFZFsyuFJz0aMGEFISAi1a9embt26TJo0iYSEBPr06QNAr1698PPzIzQ0FIC2bdvy/vvvU6NGDQIDAzl48CCvvPIKbdu2vV5K5DZq1YJNm8xVI/ftg4ceghUr9J9Rcpx5v8zjfyv/x+Xky/jm8WV+x/k0K9vsv58oWZ9hmN/nPvjAvPRy7YfUKlXMsyDdu0OuXJZGlIzncBkJDg7m7NmzjB07lujoaAICAli9evX1Qa3Hjh276UzIyy+/jM1m4+WXX+bkyZMUKVKEtm3b8sYbb6TfUWRnFSuaS1y3amXOKtiwobnM9R3uRhLJLhKSEnj666eZGzUXgEfve5T5HedTLO+tLwuLE7lyxVy0bvJk2LXrxv5WrcwS0ry5ZqTOQRyeZ8QKOWKekf9y8SJ07gxr15rzj3z8MQwebHUqkQzz+5nfCYoMYs/ZPbjYXHi18auMbjQaVxedUXVqR47A1KnmmJALF8x9uXJBr17mJZpKlazNJ+nqbt+/tTaNs8ifH1atgkGDzGmOhwwxr6++/TbocpdkI4ZhMHvXbIZ+PZQrKVconrc4izotonGZxlZHk7QyDPjuO/OHqBUrblyKKVPG/F721FNQsKClEcVaKiPOxMPD/GmifHkYM8ZcWO/wYXMxqDx5rE4ncs/iE+P538r/sWD3AgBalmvJvA7zKJqnqMXJJE3i4sxZUqdMgf37b+xv0QKeftq83KwfpgSVEedjs8Ho0VC2rDk52vLl5p02S5eaP2WIOKlfon8hKDKIP87/gavNldebvs6LDV7ExaZlEZzO3r1mAfnsM7h0ydyXL5/5PWvIEHjgAUvjSdajMuKsunQBf3/o0MEc/FW7tjlb66OPWp1MxCGGYTB9x3SGrR5GYmoiJb1LsqjTIhqWamh1NHFEUpJ5N8y0abBu3Y39lSqZZ0F69jQLicgtqIw4swYNzDlIOnaEHTvMU59vvw0jRmgUujiFuMQ4+n/Vn4jfIwB4vMLjzH1iLoVyF7I4mdy1P/+EmTPNS8jXJsR0cTEnbRw6FJo21fcj+U8qI86uVCnzHv3Bg80JgZ5/3iwon36qcSSSpe04tYPgyGAO/XUINxc3Jj46kRH1RmDTG1fWl5pqDqifNs2cHfragNRixaBfP3MrXdrajOJUVEayg1y5YPZsqFPHvDUuLAx+/91c46ZcOavTidzEMAwmb5vM898+T1JqEqV9ShPWOYyHSj5kdTT5L6dOmWdAZs40V8+9plkz806/du3MadtFHKQykl3YbObZkQcfNOcj2b0bataEGTMgONjqdCIAXLx6kb5f9mXp3qUAtK/YntntZlMgVwGLk8lt2e3m/EbTppljQq6tmFuokLla7oABcP/91mYUp6cykt00bGiOHwkONmdu7dLF/EYyaRLkzm11OsnBtp3cRnBkMH9e/BN3F3febfEuQ+sO1WWZrOrkSfPS7+zZ5hQC1zRsaJ4F6dTJXF1cJB1oBtbsKiUFxo+HN94wr+dWrmzebVO1qtXJJIcxDIMPfvyAl757iRR7CmULlCW8czi1S9S2Opr8U3KyOSnZrFnmWBC73dzv7W3OkDpwoL6HiEPu9v1bZSS7W7fOXGgqOtr8KWbSJPO0qn4alUxw4coFei/vzVd/fAVA58qd+bTtp/h4+VicTG6yf79ZQD77DM6cubH/4Yehb1/z0q/OrEoaqIzIDWfOmJMNff21+XGHDub136Ka1VIyzpbjW+gS2YXjccfxdPXkg5YfMKj2IF2WySoSEmDxYrOE/PDDjf3FikFIiDlFe4UK1uWTbEFlRG5mt5tLdI8caV7CKVLEXKyqUyerk0k2YzfsvLP5HcasG0Oqkcr9Be8n4skIAooFWB1NDAO2bTPHgSxaBPHx5n4XF2jTxjwL0rq17oiRdKMyIre2a5f5U8/u3ebHXbuaS3hrkSpJB2cTzhKyPISvD5pn4bpV68a0NtPI56mZNy117Ji5htW8eTevEVOunFlAQkKgRAnr8km2pTIit5eYCK+9BhMnmmdMihUz5w14/HGrk4kT23h0I12XdOVU/Cm83Lz4uNXH9K3RV5dlrHLpEixZYhaQ9etvTEyWO7c5a3O/fuaYEH1+JAOpjMh/27bN/Ilo3z7z45494b33zEs4Incp1Z5K6A+hjNswDrthp2LhikR0jqCabzWro+U8qalm8Zg3zywily/f+LNHHjH/v3fqpDViJNOojMjduXIFXnkF3n/f/MmpYEFzfZs+fczryCJ3EHMphh7LevDd4e8ACKkewpTWU8jjoaUIMtXevWYBmT8fTpy4sf/++81bcnv21PTsYgmVEXHMjz+aExn98ov5ccOG5h03VapYm0uyrHVH1tF9aXeiL0WT2z03n7T+hJCAEKtj5RwnT5pzBy1aZK5HdU3+/OZkh716wUMP6TKMWEplRByXkgIffgjjxpm3/bm5mQvvvfKK5hiQ61Ltqbz2/WtM2DgBA4MqRaoQ8WQElYtUtjpa9nf+PERGmgVk48Yb40BcXc27YHr1Msd+aWZUySJURiTtjh2DZ54x16EAc2Xgt94yp5jXT1k52qn4U3Rf2p0Nf24AoF+NfnzY6kNyu6usZphLl8z/i4sWwZo15g8N1zRoYN4R9+STmjdIsiSVEbl3X3wBQ4feWJ2zfn1zrpK6da3NJZb45tA39Fjag7OXz5LXIy/TH59Ot2rdrI6VPSUmmpMULloEX31lju26JiDALCDBwRoHIlmeyoikj8uXzTtsJk68MTK/Rw8IDYWSJa3NJpkixZ7C2PVjCf0hFIDqvtWJeDKCCoU0O2e6Skw0F7WMjISlSyE29saf3X+/WUC6dIFKlazLKOIglRFJX6dOwejR5toVALlywXPPmWNKfLTOSHZ1Iu4EXZd05Ydj5nTh/6v9P95v+T5ebhqTkC6uXDEvvURGmmdA4uJu/Jmfn1k+unaFmjV1iVScksqIZIzt22H48BtrWRQoAC++aF7OyaPbObOTVQdW0WtZL85fOU8+j3x82u5TgqoEWR3L+V26BKtWmQVk1SpzsPg1xYubE5IFBZl3tOn2enFyKiOScQwDli0z77LZs8fcV7SoeeZk4ECN5HdyyanJjFk3hne2vANAreK1CO8cTrmC5SxO5sRiY80zH5GR5pmQq1dv/FmpUuaquJ06mbfiqoBINqIyIhkvNdUcYPfqq3DokLnPzw/GjDEnTVMpcTpHLx6ly5Iu/HjiRwCG1h3KO83fwdPN0+JkTujECVixAr78Er77DpKTb/xZ+fJm+ejcGWrV0iUYybZURiTzJCfD3LnmejfXZn/09TUv5/zvf6DPmVP4Yt8X9PmiD39d/Yv8XvmZ3W42HSp1sDqW8zAM2LnTPAPy5ZfmopR/V7nyjQJSrZoKiOQIKiOS+a5eNRfce+edG7cD+/jA4MHw7LNmQZEsJyk1iRe/fZEPf/oQgLp+dQnvHE6Z/GWsDeYMrlyBdevM8rFihTnQ+xqbzbzs0rYttG+vu2AkR1IZEeskJ8PCheZEaXv3mvu8vKB3b3Oga2XN1JlVHP7rMMGRwWw/ZU4n/ly953jz0TfxcPWwOFkWFh1tFo+vvoJvv715DpA8eaBFC2jXzpwRVRORSQ6nMiLWs9vNnxhDQ80Vgq959FGzlDz+uDmNtVgick8kfb/sS1xiHAVzFWTuE3Np+0Bbq2NlPUlJsHWrOfB09ep/X37x9zfPfrRta66Mq7FSItepjEjWYRjw/ffmujdffmmWFDBnjxw8GPr2hUKFrM2Yg1xNucpza57jk+2fAFDfvz6LOi2ilE8pi5NlIYcPm+VjzRpzIrJLl27+8zp1bhSQ6tU1/kPkNlRGJGs6ehSmTjXHlly4YO7z9IQOHcw7cB59VGdLMtCB8wcIjgxmV7T50/1LDV5iQpMJuLu6W5zMYhcvmoX5u+/MAnLgwM1/XqSIefnlscegeXONfxK5SyojkrVduQJhYfDxxzef9vb3N8eW9O4NZctalS5bCvstjP5f9edS0iUK5y7M5x0+57Hyj1kdyxoJCbB5szn4dN062LHjxhk7MFesrl8fWrY0txo1NP+HSBqojIhzMAyzjMyeDQsWmD+hXtO4sTkddqdO5k+mkiZXkq8wbPUwZuycAcDDpR9mYceF+Hn7WZwsEyUmmuOWrpWPrVtvnvcD4IEHoEkTs3w0bapb0kXSQYaWkSlTpvDOO+8QHR1N9erV+fjjj6l7h5VcL168yJgxY1i6dCkXLlygdOnSTJo0idatW6frwYiTu3rVXCl49mzzLoVrX5qurublm+Bg83JOgQLW5nQi+87tI2hxELvP7MaGjTGNxjDukXG4ubhZHS1jxcbCli3msgWbNplFJDHx5sf4+5tfV02bmiVECz+KpLsMKyPh4eH06tWLadOmERgYyKRJk1i8eDH79++n6C1uY0tKSqJBgwYULVqU0aNH4+fnx9GjR8mfPz/Vq1dP14ORbOTYMfMyTni4OZHUNe7u5jX7J54w78YpUcK6jFnc5798zv9W/o+E5AR88/gyv+N8mpVtZnWsjHH6tFk6Nm0yC8ivv9582QXM22ybNDHLR9OmUK6cBp6KZLAMKyOBgYHUqVOHyZMnA2C32/H392fo0KGMHDnyX4+fNm0a77zzDvv27cPdPW2D5FRGcrgDByAiwiwnv/1285/Vrn3jroaAAL25AAlJCQz9eihzouYA0PS+pizouIBieYtZnCydXL5sFtSffjLPePz0kzkw+p/KlTMXm2vUyNzuv19fHyKZLEPKSFJSErlz5yYyMpL27dtf3x8SEsLFixf54osv/vWc1q1bU7BgQXLnzs0XX3xBkSJF6NatGy+99BKut7lrIjExkcS/nVKNi4vD399fZUTMhfmWLTMnnPrpp5v/zM/PPGvSrJl5+r1YNnnzdcDvZ34nKDKIPWf34GJzYVzjcYxpNAZXFye9Qyk1Ffbvv7l4/Pqruf/vbDbzFttGjcwC0rChzpqJZAF3W0YcunB87tw5UlNT8f3HbW2+vr7s27fvls85fPgw69ato3v37qxatYqDBw8yePBgkpOTGTdu3C2fExoayvjx4x2JJjlF5crmNmaMORPmypVmMfnmGzh50lwjZ+5c87FVqtwoJg0aQMGCVibPUIZhMCdqDk+veporKVconrc4Czst5JEyj1gd7e5dvWqe+dq1C6KizF9//dW88+WfihWDwMAbW+3aGnAq4sQcOjNy6tQp/Pz82LJlC/Xq1bu+/8UXX+T777/np3/+pApUqFCBq1evcuTIketnQt5//33eeecdTp8+fcvX0ZkRcdiVK+Z4ge++Myep2rXrxgDYaypVMm/XbNDA3LLJaftLSZcYtGIQC3YvAKBFuRZ83uFziubJolORG4Y5xmPPHrNsXCsee/f++4wHQO7c5sq2fy8fJUtmi8+dSHaXIWdGChcujKurKzExMTftj4mJodhtTokXL14cd3f3my7JVKpUiejoaJKSkvDw+PcaGJ6ennh6aslycUCuXOakVC1amB+fOwfr15vFZP16+OMP881u716YNct8TKFC5ptczZo3trJlnepN7pfoXwiKDOKP83/ganNlQpMJvNTwJVxsWWBODMMwF0zcs+ffW2zsrZ9TqJA5p8e1LSAAKlTQRHgi2ZxDZcTDw4NatWqxdu3a62NG7HY7a9eu5emnn77lcxo0aMDChQux2+24/P+kQX/88QfFixe/ZRERSReFC8OTT5obmOVkyxZz27wZfv4Zzp83L+98882N5/n4mG+AVaveuCRUubI5z0kWKimGYTBjxwyeXf0siamJ+OXzI6xzGA1LNczcIKmp5uWxQ4f+vf3xx7+nUb/G1RXKlzcvpQUE3Cgefn5Z6t9ZRDJHmm7tDQkJYfr06dStW5dJkyYRERHBvn378PX1pVevXvj5+REaGgrA8ePHqVKlCiEhIQwdOpQDBw7w1FNP8cwzzzBmzJi7ek3dTSPpLjERfvnFvDywc6e5/fqruSjarRQsaF7mKV/ePHty333mr2XLmuMXMvENNC4xjgFfDSD893AA2tzfhrnt51I4d+H0f7GEBLNsnDhhbtd+/+efZuE4cuT2/2Zg3opdocLNxa5yZfMSmc5+imR7GXKZBiA4OJizZ88yduxYoqOjCQgIYPXq1dcHtR47duz6GRAAf39/1qxZw/Dhw3nwwQfx8/Pj2Wef5aWXXkrDYYmkE09PqFvX3K5JTjYvIURFmZdzrl1SOHzYXEdn82Zz+ycvL/Mn+hIlbmx+flC8uHlGpVChG1uePGkuLidOwMof/yB0z1McNTbj5uJG6KOhjKg34u4vy6SkwF9/mWeKrm3nz9/8+9OnbxSPv8+Iezvu7lCmjHkr7bWtfPkbWxpv6ReRnEPTwYv8lytXbow5OXLELCfXtmPH/j251p14eJilxNsb8uY1t3z5zF/z5DGLjbu7uXl4XP/1023VGPBFawzDBWypFHx8GCurxfFQanHzUondbuZMSDAvjSQk3Pz7a7/GxTl+/HnzmrOV+vmZA0dLljQ/vlY8/P01pkNEbklr04hkhuRkc5DmqVPmmYRTp27+/fnzN7Y7Xc64g989/aiaeBS48YbvSgp/UoaSnExb7gIFzFJUuPCN7drHvr43Soefn26ZFZE0y7DLNCLyN+7uN8aO3IlhmGcmzp83L/nEx5tnK65t1z5OSjK35GRISmIbJ2j311WYf/OZh1TcONhpJCVLHzFXk3VxMe8oypPnxnbtbMvff58/vzn+xU3/9UUk69B3JJHMYLPduCxTuvR/PtwwDCb9OImXvptGsltRsKWC8bczI65QftLToLXdRCQbyAKTEYjI3124coH24e0Z8c0Iku3JdK5Xj48+Sbw+LMPVFaZP1yKzIpJ96MyISBay5fgWukR24XjccTxcPfig5Qf8r/b/sNlsdHgcDh40b1BRERGR7ERlRCQLsBt23t3yLqPXjibVSKV8wfJEdI6gRvEa1x9zbUypiEh2ozIiYrGzCWcJWR7C1we/BqBr1a5Mf3w6+TzzWZxMRCRzqIyIWGjT0U10WdKFU/Gn8HLz4qPHPqJfzX7YNCW6iOQgKiMiFrAbdkI3hTJ2w1jshp2KhSsS0TmCar7VrI4mIpLpVEZEMlnMpRh6LuvJt4e/BaBX9V5MaT2FvB55LU4mImINlRGRTLTuyDq6L+1O9KVocrvnZkrrKfQO6G11LBERS6mMiGSCVHsqEzZO4LXvX8PAoEqRKkQ8GUHlIpWtjiYiYjmVEZEMdjr+NN2Xdmf9n+sB6FujLx+1+ojc7rktTiYikjWojIhkoG8OfUOPpT04e/ksedzzMP3x6XR/sLvVsUREshSVEZEMkGJPYdz6cYT+EIqBwYO+DxLROYIHCj9gdTQRkSxHZUQknZ2IO0G3Jd3YdGwTAINqDeL9lu+Tyz2XxclERLImlRGRdLTqwCp6LevF+SvnyeeRj5ltZxJcNdjqWCIiWZrKiEg6SE5NZsy6Mbyz5R0AahavSXjncMoXLG9xMhGRrE9lROQeHYs9RpfILmw9sRWAoXWH8k7zd/B087Q4mYiIc1AZEbkHX+7/kt7Le/PX1b/w8fRh9hOz6Vipo9WxREScisqISBokpSbx0rcvMemnSQDUKVGH8M7h3FfgPmuDiYg4IZUREQcd+esIwZHB/HzqZwBGPDSC0GaheLh6WJxMRMQ5qYyIOGDp3qU89cVTxCbGUsCrAJ+1/4y2D7S1OpaIiFNTGRG5C1dTrvLCNy8w+efJANQrWY+wzmGU8illcTIREeenMiLyHw5eOEjQ4iB2Re8C4MX6L/J609dxd3W3OJmISPagMiJyB2G/hTHgqwHEJ8VTOHdh5rWfR6v7W1kdS0QkW1EZEbmFK8lXGLZ6GDN2zgCgUalGLOq0CD9vP4uTiYhkPyojIv+w/9x+giKD+DXmV2zYGNNoDOMeGYebi/67iIhkBH13Ffmb+b/OZ9CKQSQkJ1A0T1Hmd5hP83LNrY4lIpKtqYyIAJeTL/P0qqeZEzUHgCZlmrCg4wKK5ytucTIRkexPZURyvN/P/E5QZBB7zu7BxebCuMbjGNNoDK4urlZHExHJEVRGJMcyDIO5UXMZsmoIV1KuUCxvMRZ1WsQjZR6xOpqISI6iMiI50qWkSwxeOZjPf/0cgBblWvB5h88pmqeoxclERHIelRHJcX6N+ZWgxUHsP78fF5sLE5pMYGTDkbjYXKyOJiKSI6Xpu++UKVMoU6YMXl5eBAYGsm3btrt6XlhYGDabjfbt26flZUXuiWEYzNgxg7oz67L//H788vmxIWQDoxuNVhEREbGQw9+Bw8PDGTFiBOPGjWPnzp1Ur16dli1bcubMmTs+788//+T555+nUaNGaQ4rklZxiXF0W9qNgSsGkpiaSOv7WxM1KIpGpfX1KCJiNYfLyPvvv0///v3p06cPlStXZtq0aeTOnZvZs2ff9jmpqal0796d8ePHU7Zs2XsKLOKoXad3UWtGLcJ+C8PNxY23m73NV12/onDuwlZHExERHCwjSUlJ7Nixg2bNmt34C1xcaNasGVu3br3t81577TWKFi1K37597+p1EhMTiYuLu2kTcZRhGEzZNoWHZj3EwQsHKeVTio29N/JCgxd0WUZEJAtxaADruXPnSE1NxdfX96b9vr6+7Nu375bP+eGHH5g1axZRUVF3/TqhoaGMHz/ekWgiN7l49SL9vuzHkr1LAGj3QDvmPDGHgrkKWpxMRET+KUN/PIyPj6dnz57MnDmTwoXv/pT4qFGjiI2Nvb4dP348A1NKdvPzyZ+pOb0mS/Yuwd3FnUktJ7E8eLmKiIhIFuXQmZHChQvj6upKTEzMTftjYmIoVqzYvx5/6NAh/vzzT9q2bXt9n91uN1/YzY39+/dTrly5fz3P09MTT09PR6KJYBgGH/70IS9++yLJ9mTuy38f4Z3DqeNXx+poIiJyBw6dGfHw8KBWrVqsXbv2+j673c7atWupV6/evx5fsWJFdu/eTVRU1PWtXbt2NGnShKioKPz9/e/9CESAC1cu0D68PcPXDCfZnkynSp3YOXCnioiIiBNweNKzESNGEBISQu3atalbty6TJk0iISGBPn36ANCrVy/8/PwIDQ3Fy8uLqlWr3vT8/PnzA/xrv0habT2+lS5LunAs9hgerh683+J9BtcZjM1mszqaiIjcBYfLSHBwMGfPnmXs2LFER0cTEBDA6tWrrw9qPXbsGC4uulNBMp7dsPPelvcYvW40KfYUyhcsT0TnCGoUr2F1NBERcYDNMAzD6hD/JS4uDh8fH2JjY/H29rY6jmQB5y6fI2R5CKsOrAKgS9UuTH98Ot6e+voQEckq7vb9W2vTiNPZdHQTXZd05WT8SbzcvPjwsQ/pX7O/LsuIiDgplRFxGnbDzsQfJjJ2/VhSjVQeKPQAEU9G8KDvg1ZHExGRe6AyIk7hTMIZeiztwbeHvwWg54M9+aTNJ+T1yGtxMhERuVcqI5LlrT+ynm5LuxF9KZpcbrmY0noKvQN667KMiEg2oTIiWVaqPZXXN77Oaxtfw27YqVykMoufXEzlIpWtjiYiIulIZUSypNPxp+mxrAfrjqwD4KmAp/i49cfkds9tcTIREUlvKiOS5Xx76Ft6LOvBmYQz5HHPw7THp9HjwR5WxxIRkQyiMiJZRoo9hVc3vMqbm97EwOBB3wcJ7xxOxcIVrY4mIiIZSGVEsoQTcSfotqQbm45tAmBgrYF80PIDcrnnsjiZiIhkNJURsdzXB76m57KenL9ynnwe+ZjRdgZdqnaxOpaIiGQSlRGxTHJqMi+ve5m3t7wNQM3iNQnvHE75guUtTiYiIplJZUQscSz2GF0iu7D1xFYAnq7zNO+2eBdPN0+Lk4mISGZTGZFM9+X+L+m9vDd/Xf0LH08fZrWbRafKnayOJSIiFlEZkUyTlJrEyO9G8sGPHwBQp0QdwjuHc1+B+yxOJiIiVlIZkUxx5K8jdFnShW0ntwEw/KHhTGw2EQ9XD4uTiYiI1VRGJMMt3buUp754itjEWAp4FWBu+7m0e6Cd1bFERCSLUBmRDJOYksjz3zzP5J8nA1CvZD0WdVpE6fylLU4mIiJZicqIZIiDFw4SHBnMztM7AXix/ou83vR13F3dLU4mIiJZjcqIpLuI3yPo92U/4pPiKZSrEPM6zKP1/a2tjiUiIlmUyoikmyvJVxi+ZjjTd0wHoGGphizqtIiS3iUtTiYiIlmZyoiki/3n9hMUGcSvMb9iw8boRqN59ZFXcXPRl5iIiNyZ3inkns3/dT6DVgwiITmBonmKMr/DfJqXa251LBERcRIqI5Jml5MvM3TVUGZHzQagSZkmLOi4gOL5ilucTEREnInKiKTJnrN7CFocxO9nf8eGjXGNx/Hywy/j6uJqdTQREXEyKiPisLlRcxm8cjBXUq5QLG8xFnZcSJP7mlgdS0REnJTKiNy1S0mXGLJqCPN+mQdA87LN+bzD5/jm9bU4mYiIODOVEbkru2N2ExQZxL5z+3CxuTChyQRGNhyJi83F6mgiIuLkVEbkjgzD4NOdn/LM6me4mnIVv3x+LOq0iEalG1kdTUREsgmVEbmtuMQ4Bq4YSNhvYQC0Kt+KeR3mUTh3YYuTiYhIdqIyIre06/QugiKDOHjhIK42V0IfDeW5+s/psoyIiKQ7lRG5iWEYTN0+leFrhpOUmkQpn1KEdQqjnn89q6OJiEg2pTIi18VejaXfV/2I3BMJQLsH2jHniTkUzFXQ4mQiIpKdqYwIAD+f/JngyGCOXDyCu4s7bzd/m2cDn8Vms1kdTUREsjmVkRzOMAw++ukjXvj2BZLtyZTJX4aIzhHU8atjdTQREckh0jQaccqUKZQpUwYvLy8CAwPZtm3bbR87c+ZMGjVqRIECBShQoADNmjW74+Ml81y4coEO4R0YtmYYyfZkOlbqyK6Bu1REREQkUzlcRsLDwxkxYgTjxo1j586dVK9enZYtW3LmzJlbPn7Dhg107dqV9evXs3XrVvz9/WnRogUnT5685/CSdj+e+JEa02vwxf4v8HD1YHKryUQ+GUl+r/xWRxMRkRzGZhiG4cgTAgMDqVOnDpMnTwbAbrfj7+/P0KFDGTly5H8+PzU1lQIFCjB58mR69ep1V68ZFxeHj48PsbGxeHt7OxJX/sFu2Hl/6/uMWjuKFHsK5QqUI+LJCGoWr2l1NBERyWbu9v3boTEjSUlJ7Nixg1GjRl3f5+LiQrNmzdi6detd/R2XL18mOTmZggVvf4dGYmIiiYmJ1z+Oi4tzJKbcxrnL5+i9vDcrD6wEILhKMDPazsDbUwVPRESs49BlmnPnzpGamoqv780Lo/n6+hIdHX1Xf8dLL71EiRIlaNas2W0fExoaio+Pz/XN39/fkZhyCz8c+4Ea02uw8sBKPF09mf74dBZ1WqQiIiIilsvU6TQnTpxIWFgYy5Ytw8vL67aPGzVqFLGxsde348ePZ2LK7MVu2AndFMojcx/hRNwJHij0ANv6b2NArQG6bVdERLIEhy7TFC5cGFdXV2JiYm7aHxMTQ7Fixe743HfffZeJEyfy3Xff8eCDD97xsZ6ennh6ejoSTW7hTMIZei7ryTeHvgGgx4M9mNpmKnk98lqcTERE5AaHzox4eHhQq1Yt1q5de32f3W5n7dq11Kt3++nC3377bSZMmMDq1aupXbt22tPKXdvw5wYCpgXwzaFvyOWWi9ntZjOv/TwVERERyXIcnvRsxIgRhISEULt2berWrcukSZNISEigT58+APTq1Qs/Pz9CQ0MBeOuttxg7diwLFy6kTJky18eW5M2bl7x59caY3lLtqbyx6Q3Gfz8eu2GncpHKRHSOoErRKlZHExERuSWHy0hwcDBnz55l7NixREdHExAQwOrVq68Paj127BguLjdOuEydOpWkpCQ6d+58098zbtw4Xn311XtLLzeJvhRN96XdWXdkHQB9AvrwcauPyeORx+JkIiIit+fwPCNW0Dwj/+27w9/RfWl3ziScIY97Hqa2mUrP6j2tjiUiIjlYhswzIllPij2F8RvG88amNzAwqFa0GhFPRlCxcEWro4mIiNwVlREndjLuJN2WdmPj0Y0ADKg5gEmPTSKXey6Lk4mIiNw9lREntfrganou68m5y+fI65GXmW1n0qVqF6tjiYiIOExlxMkkpybzyvpXeGvzWwDUKFaD8M7h3F/ofouTiYiIpI3KiBM5FnuMrku6suX4FgCG1BnCuy3excvt9rPZioiIZHUqI07iq/1f0fuL3ly4cgEfTx9mtZtFp8qdrI4lIiJyz1RGsrik1CRGfTeK9398H4A6JeoQ1jmMsgXKWpxMREQkfaiMZGFH/jpClyVd2HZyGwDDAofxVvO38HD1sDiZiIhI+lEZyaKW7V1Gny/6EJsYS36v/Mx9Yi5PVHzC6lgiIiLpTmUki0lMSeSFb1/g420fA/BQyYcI6xRG6fylLU4mIiKSMVRGspBDFw4RHBnMjtM7AHih/gu80fQN3F3dLU4mIiKScVRGsoiI3yPo92U/4pPiKZSrEJ+1/4w2FdpYHUtERCTDqYxY7GrKVYavHs60HdMAaFiqIYs6LaKkd0mLk4mIiGQOlREL/XH+D4IWB/FLzC/YsDGq4SjGNxmPm4s+LSIiknPoXc8iC35dwMAVA0lITqBI7iLM7zifFuVaWB1LREQk06mMZLLLyZd55utnmLVrFgCPlHmEhR0XUjxfcYuTiYiIWENlJBPtObuHoMVB/H72d2zYGNt4LK88/AquLq5WRxMREbGMykgmmRs1lyGrhnA5+TLF8hZjQccFNL2vqdWxRERELKcyksEuJV1iyKohzPtlHgDNyjZjfof5+Ob1tTiZiIhI1qAykoF2x+wmKDKIfef24WJz4bVHXmNUo1G42FysjiYiIpJlqIxkAMMwmLVrFkO/HsrVlKuUyFeCRZ0W8XDph62OJiIikuWojKSz+MR4Bq4YyKLfFgHwWPnHmNd+HkXyFLE4mYiISNakMpKOoqKjCFocxIELB3C1ufLmo2/yfP3ndVlGRETkDlRG0oFhGEzdPpURa0aQmJqIv7c/YZ3DqO9f3+poIiIiWZ7KyD2KvRpLv6/6EbknEoC2Fdoy54k5FMpdyOJkIiIizkFl5B5sP7Wd4MhgDv91GHcXd95q9hbDHhqGzWazOpqIiIjTUBlJA8Mw+Oinj3jh2xdItidTJn8ZwjuHU9evrtXRREREnI7KiIP+uvIXT335FMv3LQegY6WOzGo3i/xe+S3NJSIi4qxURhzw04mfCI4M5mjsUTxcPXivxXsMqTNEl2VERETugcrIXbAbdj7Y+gEj144kxZ5CuQLlCO8cTq0StayOJiIi4vRURv7D+cvnCVkewsoDKwEIqhLEzLYz8fb0tjiZiIhI9qAycgebj22my5IunIg7gaerJx8+9iEDag3QZRkREZF0pDJyC3bDztub3+bldS+TaqRSoVAFIjpHUL1YdaujiYiIZDsqI/9wJuEMvZb1Ys2hNQB0r9adqW2mks8zn8XJREREsqc0LZoyZcoUypQpg5eXF4GBgWzbtu2Oj1+8eDEVK1bEy8uLatWqsWrVqjSFzWjf//k9AdMCWHNoDbnccjGr3Sw+7/C5ioiIiEgGcriMhIeHM2LECMaNG8fOnTupXr06LVu25MyZM7d8/JYtW+jatSt9+/Zl165dtG/fnvbt2/Pbb7/dc/j0kmpP5bXvX6PpvKacvnSaSoUr8XP/n3mqxlMaHyIiIpLBbIZhGI48ITAwkDp16jB58mQA7HY7/v7+DB06lJEjR/7r8cHBwSQkJLBixYrr+x566CECAgKYNm3aXb1mXFwcPj4+xMbG4u2dvnexRF+KpsfSHqw9shaAPgF9+LjVx+TxyJOuryMiIpLT3O37t0NnRpKSktixYwfNmjW78Re4uNCsWTO2bt16y+ds3br1pscDtGzZ8raPB0hMTCQuLu6mLSOsPbyWgGkBrD2yltzuuZnXfh6zn5itIiIiIpKJHCoj586dIzU1FV9f35v2+/r6Eh0dfcvnREdHO/R4gNDQUHx8fK5v/v7+jsS8K5eTL9N9aXdiEmKoVrQaOwbsoGf1nun+OiIiInJnaRrAmtFGjRpFbGzs9e348ePp/hq53XPzWfvPGFBzAD/1+4mKhSum+2uIiIjIf3Po1t7ChQvj6upKTEzMTftjYmIoVqzYLZ9TrFgxhx4P4OnpiaenpyPR0qRl+Za0LN8yw19HREREbs+hMyMeHh7UqlWLtWvXXt9nt9tZu3Yt9erVu+Vz6tWrd9PjAb799tvbPl5ERERyFocnPRsxYgQhISHUrl2bunXrMmnSJBISEujTpw8AvXr1ws/Pj9DQUACeffZZGjduzHvvvUebNm0ICwtj+/btzJgxI32PRERERJySw2UkODiYs2fPMnbsWKKjowkICGD16tXXB6keO3YMF5cbJ1zq16/PwoULefnllxk9ejT3338/y5cvp2rVqul3FCIiIuK0HJ5nxAoZOc+IiIiIZIwMmWdEREREJL2pjIiIiIilVEZERETEUiojIiIiYimVEREREbGUyoiIiIhYSmVERERELKUyIiIiIpZSGRERERFLOTwdvBWuTRIbFxdncRIRERG5W9fet/9rsnenKCPx8fEA+Pv7W5xEREREHBUfH4+Pj89t/9wp1qax2+2cOnWKfPnyYbPZ0u3vjYuLw9/fn+PHj+eYNW9y2jHntOOFnHfMOe14Iecdc047Xsg+x2wYBvHx8ZQoUeKmRXT/ySnOjLi4uFCyZMkM+/u9vb2d+pOdFjntmHPa8ULOO+acdryQ8445px0vZI9jvtMZkWs0gFVEREQspTIiIiIilsrRZcTT05Nx48bh6elpdZRMk9OOOacdL+S8Y85pxws575hz2vFCzjtmpxjAKiIiItlXjj4zIiIiItZTGRERERFLqYyIiIiIpVRGRERExFLZvoxMmTKFMmXK4OXlRWBgINu2bbvj4xcvXkzFihXx8vKiWrVqrFq1KpOSph9HjnnmzJk0atSIAgUKUKBAAZo1a/af/0ZZjaOf42vCwsKw2Wy0b98+YwNmAEeP+eLFiwwZMoTixYvj6elJhQoVnOpr29HjnTRpEg888AC5cuXC39+f4cOHc/Xq1UxKe282btxI27ZtKVGiBDabjeXLl//nczZs2EDNmjXx9PSkfPnyzJ07N8NzpidHj3np0qU0b96cIkWK4O3tTb169VizZk3mhE0nafk8X7N582bc3NwICAjIsHyZLVuXkfDwcEaMGMG4cePYuXMn1atXp2XLlpw5c+aWj9+yZQtdu3alb9++7Nq1i/bt29O+fXt+++23TE6edo4e84YNG+jatSvr169n69at+Pv706JFC06ePJnJydPG0eO95s8//+T555+nUaNGmZQ0/Th6zElJSTRv3pw///yTyMhI9u/fz8yZM/Hz88vk5Gnj6PEuXLiQkSNHMm7cOPbu3cusWbMIDw9n9OjRmZw8bRISEqhevTpTpky5q8cfOXKENm3a0KRJE6Kiohg2bBj9+vVzqjdnR49548aNNG/enFWrVrFjxw6aNGlC27Zt2bVrVwYnTT+OHvM1Fy9epFevXjz66KMZlMwiRjZWt25dY8iQIdc/Tk1NNUqUKGGEhobe8vFBQUFGmzZtbtoXGBhoDBw4MENzpidHj/mfUlJSjHz58hmfffZZRkVMV2k53pSUFKN+/frGp59+aoSEhBhPPPFEJiRNP44e89SpU42yZcsaSUlJmRUxXTl6vEOGDDGaNm16074RI0YYDRo0yNCcGQEwli1bdsfHvPjii0aVKlVu2hccHGy0bNkyA5NlnLs55lupXLmyMX78+PQPlAkcOebg4GDj5ZdfNsaNG2dUr149Q3Nlpmx7ZiQpKYkdO3bQrFmz6/tcXFxo1qwZW7duveVztm7detPjAVq2bHnbx2c1aTnmf7p8+TLJyckULFgwo2Kmm7Qe72uvvUbRokXp27dvZsRMV2k55i+//JJ69eoxZMgQfH19qVq1Km+++SapqamZFTvN0nK89evXZ8eOHdcv5Rw+fJhVq1bRunXrTMmc2Zz9+1Z6sNvtxMfHO8X3rXsxZ84cDh8+zLhx46yOku6cYqG8tDh37hypqan4+vretN/X15d9+/bd8jnR0dG3fHx0dHSG5UxPaTnmf3rppZcoUaLEv765ZUVpOd4ffviBWbNmERUVlQkJ019ajvnw4cOsW7eO7t27s2rVKg4ePMjgwYNJTk7O8t/U0nK83bp149y5czRs2BDDMEhJSWHQoEFOc5nGUbf7vhUXF8eVK1fIlSuXRckyz7vvvsulS5cICgqyOkqGOXDgACNHjmTTpk24uWW/t+5se2ZEHDdx4kTCwsJYtmwZXl5eVsdJd/Hx8fTs2ZOZM2dSuHBhq+NkGrvdTtGiRZkxYwa1atUiODiYMWPGMG3aNKujZYgNGzbw5ptv8sknn7Bz506WLl3KypUrmTBhgtXRJAMsXLiQ8ePHExERQdGiRa2OkyFSU1Pp1q0b48ePp0KFClbHyRDZr179v8KFC+Pq6kpMTMxN+2NiYihWrNgtn1OsWDGHHp/VpOWYr3n33XeZOHEi3333HQ8++GBGxkw3jh7voUOH+PPPP2nbtu31fXa7HQA3Nzf2799PuXLlMjb0PUrL57h48eK4u7vj6up6fV+lSpWIjo4mKSkJDw+PDM18L9JyvK+88go9e/akX79+AFSrVo2EhAQGDBjAmDFjcHHJXj+D3e77lre3d7Y/KxIWFka/fv1YvHixU5zNTav4+Hi2b9/Orl27ePrppwHze5dhGLi5ufHNN9/QtGlTi1Pem+z1v/JvPDw8qFWrFmvXrr2+z263s3btWurVq3fL59SrV++mxwN8++23t318VpOWYwZ4++23mTBhAqtXr6Z27dqZETVdOHq8FStWZPfu3URFRV3f2rVrd/0uBH9//8yMnyZp+Rw3aNCAgwcPXi9eAH/88QfFixfP0kUE0na8ly9f/lfhuFbEjGy4FJezf99Kq0WLFtGnTx8WLVpEmzZtrI6Toby9vf/1vWvQoEE88MADREVFERgYaHXEe2fxANoMFRYWZnh6ehpz58419uzZYwwYMMDInz+/ER0dbRiGYfTs2dMYOXLk9cdv3rzZcHNzM959911j7969xrhx4wx3d3dj9+7dVh2Cwxw95okTJxoeHh5GZGSkcfr06etbfHy8VYfgEEeP95+c8W4aR4/52LFjRr58+Yynn37a2L9/v7FixQqjaNGixuuvv27VITjE0eMdN26ckS9fPmPRokXG4cOHjW+++cYoV66cERQUZNUhOCQ+Pt7YtWuXsWvXLgMw3n//fWPXrl3G0aNHDcMwjJEjRxo9e/a8/vjDhw8buXPnNl544QVj7969xpQpUwxXV1dj9erVVh2Cwxw95gULFhhubm7GlClTbvq+dfHiRasOwWGOHvM/Zbe7abJ1GTEMw/j444+NUqVKGR4eHkbdunWNH3/88fqfNW7c2AgJCbnp8REREUaFChUMDw8Po0qVKsbKlSszOfG9c+SYS5cubQD/2saNG5f5wdPI0c/x3zljGTEMx495y5YtRmBgoOHp6WmULVvWeOONN4yUlJRMTp12jhxvcnKy8eqrrxrlypUzvLy8DH9/f2Pw4MHGX3/9lfnB02D9+vW3/D957RhDQkKMxo0b/+s5AQEBhoeHh1G2bFljzpw5mZ77Xjh6zI0bN77j451BWj7Pf5fdyojNMLLheUsRERFxGtl2zIiIiIg4B5URERERsZTKiIiIiFhKZUREREQspTIiIiIillIZEREREUupjIiIiIilVEZERETEUiojIiIiYimVEREREbGUyoiIiIhYSmVERERELPV/xYKu6wUCE74AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "xfs = np.arange(0,1.5,0.01)\n", + "yfs = np.array(f(xfs))\n", + "xs = np.arange(0,1.5,0.01)\n", + "x = pointfixe(1,f,1000)\n", + "plt.plot(xfs,yfs,'r')\n", + "plt.plot(xs,xs,'g')\n", + "plt.plot(x,x,'.b')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "36581611-449c-487d-8e9d-73e78b900c35", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}