{ "cells": [ { "cell_type": "markdown", "id": "54086665-879b-438f-af50-2ee8ccb39d49", "metadata": {}, "source": [ "## MT09 - TP5 - Automne 2024\n", "### Problèmes aux moindres carrés\n" ] }, { "cell_type": "markdown", "id": "e5dd0ce4-cb08-4aba-a9ac-bd51b794385e", "metadata": {}, "source": [ "#### Exercice 1 - Approximation affine par morceaux\n", "\n", "On considère le nuage de $m$ points $(x_i,y_i)_{i=1,...,m}$ suivants donnés par les tableaux $x$ et $y$ du script code python ci-dessous :" ] }, { "cell_type": "code", "execution_count": 5, "id": "1d688136-b21c-44fb-a51f-a99f4f62a3f6", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "m = 20\n", "# Data : \n", "xi = np.linspace(0.0, 5.0, m) + 0.05*np.random.randn(m)\n", "yi = 0.8 + 0.5*xi-xi**2/6 + 0.2*np.random.randn(m)\n", "plt.plot(xi, yi, 'o'); plt.grid()" ] }, { "cell_type": "markdown", "id": "54b3f1d5-16ba-4ade-8fb9-787fc1146231", "metadata": {}, "source": [ "On souhaite représenter ce nuage de points par une ligne brisée en minimisant les écarts aux carrés entre les points et la ligne brisée.\n", "Dans un premier temps, coder la fonction dite chapeau ```y = phi(x)``` définie par\n", "\n", "$$\n", "\\phi(x) = \\max(0, 1-|x|).\n", "$$\n", "\n", "Représenter graphiquement la fonction $\\phi$ sur l'intervalle $[-3,3]$." ] }, { "cell_type": "code", "execution_count": 6, "id": "1d356719-f874-4991-ab99-db793ff66ead", "metadata": {}, "outputs": [ { "data": { "image/png": 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AGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQpNETuvPPOWLx4cXR2dsYZZ5xR5KkAgCZUaIgcOXIkrrrqqrjhhhuKPA0A0KSmFLn4hg0bIiLigQceKPI0AECTKjREajU8PBzDw8PHbw8NDUVERKlUilKpVNdzVdar97qtyKyqZ1bVM6vqmVVtzKt6Rc2qlvXayuVyua5nP4kHHnggbrrppvjTn/405v3Wr19//CrK/7d58+bo7OwsaHcAQD0dPnw4rrnmmhgcHIzu7u4x71vzFZFTxcL/9+yzz8bChQtrXTpuueWWWLdu3fHbQ0ND0dvbG319faf9QmpVKpWiv78/li1bFu3t7XVdu9WYVfXMqnpmVT2zqo15Va+oWVVe0ahGzSGyZs2auPrqq8e8z3nnnVfrshER0dHRER0dHaOOt7e3F/ZgKnLtVmNW1TOr6plV9cyqNuZVvXrPqpa1ag6Rnp6e6OnpqfWPAQCMUuibVQcGBuL111+PgYGBOHbsWOzduzciIi644IKYMWNGkacGAJpAoSFy++23x4MPPnj89vz58yMiYvv27bFkyZIiTw0ANIFCf6HZAw88EOVyedSHCAEAIvxbMwBAIiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKSZkr2BsZTL5YiIGBoaqvvapVIpDh8+HENDQ9He3l739VuJWVXPrKpnVtUzq9qYV/WKmlXl53bl5/hYGjpEDh48GBERvb29yTsBAGp18ODBmDlz5pj3aStXkytJRkZGYv/+/dHV1RVtbW11XXtoaCh6e3tj37590d3dXde1W41ZVc+sqmdW1TOr2phX9YqaVblcjoMHD8acOXNi0qSx3wXS0FdEJk2aFHPnzi30HN3d3R6oVTKr6plV9cyqemZVG/OqXhGzOt2VkApvVgUA0ggRACDNhA2Rjo6OuOOOO6KjoyN7Kw3PrKpnVtUzq+qZVW3Mq3qNMKuGfrMqANDaJuwVEQAgnxABANIIEQAgjRABANIIkYj41Kc+Feecc05MmzYtzj777Lj22mtj//792dtqOL/+9a/jC1/4QsybNy+mT58e559/ftxxxx1x5MiR7K01pDvvvDMWL14cnZ2dccYZZ2Rvp+Hcc889MW/evJg2bVosWLAgnnrqqewtNZydO3fGlVdeGXPmzIm2trZ49NFHs7fUsDZu3BiXXnppdHV1xVlnnRUrV66MF198MXtbDenee++ND3zgA8d/idmiRYviRz/6Udp+hEhELF26NL7//e/Hiy++GD/4wQ/ipZdeis985jPZ22o4v/jFL2JkZCTuu+++eOGFF+Ib3/hGfPvb345bb701e2sN6ciRI3HVVVfFDTfckL2VhvPII4/ETTfdFLfddlvs2bMnLr/88li+fHkMDAxkb62hHDp0KC6++OK46667srfS8J588slYvXp17Nq1K/r7++Po0aPR19cXhw4dyt5aw5k7d2589atfjd27d8fu3bvjiiuuiBUrVsQLL7yQs6Eyo2zdurXc1tZWPnLkSPZWGt7Xvva18rx587K30dA2bdpUnjlzZvY2GsqHPvSh8qpVq0449r73va988803J+2o8UVEecuWLdnbaBqvvfZaOSLKTz75ZPZWmsKZZ55Z/s53vpNybldE/sLrr78e3/3ud2Px4sX++egqDA4OxqxZs7K3QRM5cuRIPPfcc9HX13fC8b6+vnj66aeTdkWrGRwcjIjw/HQax44di4cffjgOHToUixYtStmDEPk/X/7yl+Md73hHvPOd74yBgYHYunVr9pYa3ksvvRTf+ta3YtWqVdlboYkcOHAgjh07FrNnzz7h+OzZs+PVV19N2hWtpFwux7p16+Kyyy6Liy66KHs7DelnP/tZzJgxIzo6OmLVqlWxZcuWeP/735+yl5YNkfXr10dbW9uYH7t37z5+/y996UuxZ8+e2LZtW0yePDk+97nPRXmC/NLZWmcVEbF///74xCc+EVdddVV88YtfTNr5+Hsrs+Lk2traTrhdLpdHHYO3Ys2aNfH888/H9773veytNKz3vve9sXfv3ti1a1fccMMNcd1118XPf/7zlL1MSTnrOFizZk1cffXVY97nvPPOO/7fPT090dPTE+95z3viwgsvjN7e3ti1a1faparxVOus9u/fH0uXLo1FixbF/fffX/DuGkuts2K0np6emDx58qirH6+99tqoqyRQq7Vr18Zjjz0WO3fujLlz52Zvp2FNnTo1LrjggoiIWLhwYTz77LPxzW9+M+67775x30vLhkglLN6KypWQ4eHhem6pYdUyq9/85jexdOnSWLBgQWzatCkmTWrZi2on9XYeV7xp6tSpsWDBgujv749Pf/rTx4/39/fHihUrEndGMyuXy7F27drYsmVL7NixI+bNm5e9paZSLpfTfua1bIhU65lnnolnnnkmLrvssjjzzDPjV7/6Vdx+++1x/vnnT4irIbXYv39/LFmyJM4555z4+te/Hr///e+Pf+7d73534s4a08DAQLz++usxMDAQx44di71790ZExAUXXBAzZszI3VyydevWxbXXXhsLFy48fmVtYGDA+43+whtvvBG//OUvj99++eWXY+/evTFr1qw455xzEnfWeFavXh2bN2+OrVu3RldX1/ErbjNnzozp06cn766x3HrrrbF8+fLo7e2NgwcPxsMPPxw7duyIJ554ImdDKX9Xp4E8//zz5aVLl5ZnzZpV7ujoKJ933nnlVatWlV955ZXsrTWcTZs2lSPipB+Mdt111510Vtu3b8/eWkO4++67y+eee2556tSp5UsuucRfszyJ7du3n/QxdN1112VvreGc6rlp06ZN2VtrOJ///OePf++9613vKn/0ox8tb9u2LW0/beXyBHlHJgDQcCbWC/wAQEMRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAGiECAKQRIgBAmv8FrMrFo9Y25ekAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def phi(x):\n", " y = np.maximum(0.0*x, 1-np.abs(x))\n", " return y\n", " \n", "xd = np.linspace(-3.0, 3.0, 400)\n", "plt.plot(xd, phi(xd), '-r', linewidth=2)\n", "plt.grid(); plt.axis('equal');" ] }, { "cell_type": "markdown", "id": "95453e70-1bf1-48a9-8b93-8d9ce34e40d8", "metadata": {}, "source": [ "On cherche ensuite une approximation $f(x)$ de la forme\n", "\n", "$$\n", "f(x) = \\sum_{j=0}^5 \\, u_j\\, \\phi(x - j),\n", "$$\n", "où les $(u_j)_{j=0,...,5}$ sont les inconnues. Réécrire le problème aux moindres carrés\n", "\n", "$$\n", "\\min_{(u_0,...,u_5)} \\quad \\frac{1}{2}\\sum_{i=1}^m\\, [f(x_i)-y_i]^2\n", "$$\n", "\n", "sous la forme\n", "\n", "$$\n", "\\min_{u\\in\\mathbb{R}^6} \\quad \\frac{1}{2} \\|Au - y\\|^2\n", "$$\n", "en déterminant la matrice $A$. Coder en python la matrice $A$, résoudre les équations normales et tracez sur le même graphique le nuage de points et la fonction d'approximation $f(x)$ ainsi trouvée. Afficher le vecteur $\\mathbf{u}$. Comment interprétez-vous les valeurs $u_i$ de $\\mathbf{u}$ ?\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "2a4618a0-88c6-4cd5-be76-909561690c97", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A^T A=\n", " [[1.77034348 0.70511822 0. 0. 0. 0. ]\n", " [0.70511822 2.6528996 0.55611783 0. 0. 0. ]\n", " [0. 0.55611783 2.38570395 0.58692395 0. 0. ]\n", " [0. 0. 0.58692395 2.68029174 0.61010193 0. ]\n", " [0. 0. 0. 0.61010193 2.6973224 0.55307499]\n", " [0. 0. 0. 0. 0.55307499 1.63823271]] \n", "\n", "\n", "Det(A^T A) = 92.68130033881187 \n", "\n", "u= [ 0.67745209 1.16149808 1.24876429 0.66990868 -0.1666679 -0.94452839]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = np.zeros((m, 6))\n", "for i in range(0,m):\n", " for j in range(0,6):\n", " A[i,j] = phi(xi[i] - j)\n", "print(\"A^T A=\\n\", A.T@A, \"\\n\\n\")\n", "print(\"Det(A^T A) = \", la.det(A.T@A), '\\n')\n", "y = yi\n", "import numpy.linalg as la\n", "u = la.solve(A.T@A, A.T@y)\n", "\n", "def f(x, u):\n", " n = u.size\n", " y = 0.0*x\n", " for j in range(0,6):\n", " y += u[j] * phi(x-j)\n", " return y\n", "\n", "print(\"u= \", u)\n", "plt.plot(xi, yi, 'or')\n", "xd = np.linspace(0, 5, 200)\n", "yd = f(xd, u)\n", "plt.plot(xd, yd, '-b'); plt.grid()\n", "plt.plot(range(0,6), u, '+b'); plt.xlabel('x'); plt.ylabel('f(x)')\n", "plt.rcParams[\"figure.figsize\"] = 6,4 # taille de la figure\n", "plt.savefig(\"regression.png\")" ] }, { "cell_type": "markdown", "id": "833c28d6-c8ec-4589-af4a-12c87100048e", "metadata": {}, "source": [ "#### Exercice 2 - Recherche d'une ellipse passant par un nuage de points\n", "\n", "On considère le nuage de points $(x_i,y_i)$, $i=1,...,m$ générés par le script python ci-dessous :" ] }, { "cell_type": "code", "execution_count": 8, "id": "1d84359f-80e0-4bcc-9168-7ff9880dee37", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a = 2.5\n", "b = 1.1\n", "m = 50\n", "theta = np.linspace(0, 2*np.pi, m)\n", "sigma = 0.1\n", "xi = a * (np.cos(theta) + sigma*np.random.randn(m))\n", "yi = b * (np.sin(theta) + sigma*np.random.randn(m))\n", "plt.plot(xi, yi, 'or'); plt.axis(\"equal\"); plt.grid()\n", "plt.xlim([-3, 3]); plt.xlabel('x'); plt.ylabel('y');" ] }, { "cell_type": "markdown", "id": "bb8405e5-978b-4c48-b76e-06857d5e8b32", "metadata": {}, "source": [ "Par ces points, on va essayer de faire passer \"au mieux' une ellipse de paramètres d'axe\n", "$\\hat a$ et $\\hat b$, d'équation \n", "\n", "$$\n", "\\frac{x^2}{\\hat a^2} + \\frac{y^2}{\\hat b^2} = 1\n", "$$\n", "\n", "ou, de manière équivalente, d'équations paramétrées\n", "\n", "$$\n", "\\begin{array}{l}\n", "x(\\theta) = \\hat a \\cos(\\theta), \\\\\n", "y(\\theta) = \\hat b \\sin(\\theta), \\quad \\theta\\in[0, 2\\pi].\n", "\\end{array}\n", "$$\n", "\n", "On pourrait chercher $(\\hat a,\\hat b)$ qui réalisent le minimum de\n", "\n", "$$\n", "\\min_{(a,b)} \\quad \\frac{1}{2} \\sum_{i=1}^m \\left[ \\frac{x_i^2}{\\hat a^2} + \\frac{y_i^2}{\\hat b^2}-1\\right]^2\n", "$$\n", "\n", "mais ce problème ne peut pas être mis sous la forme $\\min_u \\frac{1}{2} \\|Au-b\\|^2$. On considère plutôt le problème aux moindres carrés\n", "\n", "$$\n", "\\min_{u=(u_1,u_2)} \\quad \\frac{1}{2} \\sum_{i=1}^m \\left[ x_i^2\\, u_1 + y_i^2\\, u_2 -1\\right]^2\n", "$$\n", "puis on affectera $\\hat a = \\frac{1}{\\sqrt{u_1}}$ et $\\hat b = \\frac{1}{\\sqrt{u_2}}$. Ecrire ce problème de minimisation sous la forme\n", "\n", "$$\n", "\\min_u \\quad \\frac{1}{2}\\, \\|Au-b\\|^2\n", "$$\n", "\n", "où l'on déterminera la matrice $A$ et le second membre $b$. Résoudre les équations normales, calculer\n", "$\\hat a$ et $\\hat b$. Sur le même graphique, tracer le nuage de points $(x_i,y_i)$ et l'ellipse de pramètres\n", "d'axe $\\hat a$ et $\\hat b$." ] }, { "cell_type": "code", "execution_count": 9, "id": "da6e3f75-6ced-432b-84af-f7dd03d90b9a", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2.5, 1.1]\n", "[np.float64(2.63386646505248), np.float64(1.1336802756977964)]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = np.zeros((m,2))\n", "A[:,0] = xi**2\n", "A[:,1] = yi**2\n", "y = np.ones(m)\n", "import numpy.linalg as la\n", "u = la.solve(A.T@A, A.T@y) # Equations normales\n", "# u1 = 1/a^2, u2 = 1/b^2\n", "ahat = 1.0 / np.sqrt(u[0])\n", "bhat = 1.0 / np.sqrt(u[1])\n", "theta = np.linspace(0, 2*np.pi, 200)\n", "x = ahat * np.cos(theta)\n", "y = bhat * np.sin(theta)\n", "plt.plot(xi, yi, 'or')\n", "plt.plot(x, y, '-b')\n", "plt.plot([0, ahat], [0,0], 'g-o')\n", "plt.plot([0,0], [0, bhat], 'g-o')\n", "plt.grid(); plt.axis('equal'); plt.xlim([-3, 3])\n", "print([a,b])\n", "print([ahat, bhat])" ] }, { "cell_type": "markdown", "id": "bdf77217-9360-404d-8649-25b1a7b1e007", "metadata": {}, "source": [ "#### Exercice 3. Moindres carrés avec régularisation de Tykhonov.\n", "\n", "Soit $L=3$. On considère le nuage de points $(x_i,y_i)$, $i=1,...,m$ avec $x_i\\in [0,L]\\ \\forall i$ tel que défini ci-dessous :" ] }, { "cell_type": "code", "execution_count": 13, "id": "528e7d74-76d4-4192-adc8-9805891a7647", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "m = 200\n", "# Data : \n", "L = 3.0\n", "xi = np.linspace(0.0, L, m) \n", "yi = 0.8 + 0.5*xi-np.sin(3*np.pi*np.cos(xi)) + 0.3*np.random.randn(m)\n", "plt.plot(xi, yi, 'o'); plt.grid()" ] }, { "cell_type": "markdown", "id": "d2de79e1-2d70-42c5-a0df-51879d797d5d", "metadata": {}, "source": [ "On réutilise la fonction $\\phi$ de l'Exercice 1. Soit $n\\leq m-1$ et $\\mu$ un scalaire positif ou nul. On considère la fonction de régression affine par morceau\n", "\n", "$$\n", "f(x) = \\sum_{j=0}^n u_j\\, \\phi(x - \\frac{j}{n}L)\n", "$$\n", "\n", "et le problème de minimisation régularisé\n", "\n", "$$\n", "\\min_{\\mathbf{u}}\\quad \\frac{1}{2} \\sum_{i=1}^m \\Big[ f(x_i)-y_i \\Big]^2\n", "+ \\frac{1}{2} \\mu \\sum_{i=1}^m u_i^2.\n", "$$\n", "\n", "Réécrire le problème de miminimisation sous la forme\n", "\n", "$$\n", "\\min_{\\mathbf{u}}\\quad \\frac{1}{2} \\| A\\mathbf{u} - \\mathbf{y}\\|_2^2\n", "+\\frac{1}{2}\\mu\\, \\|\\mathbf{u}\\|_2^2.\n", "$$\n", "\n", "Pour la mise en oeuvre, on considèrera $\\mu = 10^{-15}$ et $n=80$.\n", "Codez la matrice $A$ et résoudre les équations normales associées au problème de minimisation.\n", "Afficher la valeur de $\\|\\mathbf{u}\\|_2$." ] }, { "cell_type": "code", "execution_count": 14, "id": "e129c9fc-4425-4d0b-b790-4a4efc320cf3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "151.12057684626558\n" ] } ], "source": [ "n = 100\n", "# Parametre de regularisation\n", "mu = 1e-15\n", "\n", "\n", "A = np.zeros((m,n+1))\n", "Id = np.eye(n+1)\n", "\n", "for j in range(n+1):\n", " A[:,j] = phi(xi - j/n * L)\n", " \n", "u = np.linalg.solve(A.T@A + mu*Id, A.T@yi)\n", "print(np.linalg.norm(u))" ] }, { "cell_type": "markdown", "id": "d8783e39-f30d-40a9-9654-c12c3668f954", "metadata": {}, "source": [ "Codez une fonction\n", "\n", "```\n", "def f(x, u):\n", " # ...\n", "```\n", "\n", "qui implémente la fonction de régression $f$ avec le vecteur de coefficients $\\mathbf{u}$. " ] }, { "cell_type": "code", "execution_count": 15, "id": "4dbd14b5-9d6b-4c6a-be16-d724a67d018f", "metadata": {}, "outputs": [], "source": [ "def f(x, u):\n", " fx = 0.0*x\n", " n = u.size - 1\n", " for j in range(n+1):\n", " fx += u[j] * phi((x- j/n * L))\n", " return fx" ] }, { "cell_type": "markdown", "id": "6c11b67a-f0bd-4876-8a04-f40cbd3b23d3", "metadata": {}, "source": [ "Sur le même graphique, tracez le nuage de points ainsi que la fonction de régression.\n", "Affichez aussi la valeur du conditionnement en norme 2 de la matrice $A^T A + \\mu I$." ] }, { "cell_type": "code", "execution_count": 16, "id": "b9aec732-27f6-42b8-a016-1527fb24416c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27704280.467446554\n", "151.12057684626558\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xd = np.linspace(0, 3, 400)\n", "plt.figure(figsize=(12,6))\n", "plt.plot(xi, yi, 'om'); plt.grid()\n", "plt.plot(xd, f(xd, u), '-b')\n", "print(np.linalg.cond(A.T@A+mu*Id))\n", "print(np.linalg.norm(u))" ] }, { "cell_type": "code", "execution_count": 17, "id": "db9a7765-8143-4524-888a-e93cbccd24e9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27704280.467446554\n" ] } ], "source": [ "print(np.linalg.cond(A.T@A+mu*Id))" ] }, { "cell_type": "markdown", "id": "5fbcf543-73f1-41ae-b301-15f7c2197e8f", "metadata": {}, "source": [ "Recommencez en testant différentes valeurs de coefficient de régularisation $\\mu$ :\n", "$\\mu = 10^{-4}$, $10^{-3}$, $10^{-2}$, $5.10^{-2}$, $10^{-1}$, $1$ et 10. Affichez à nouveau le nuage de points et la fonction de régression résultante. Observez l'influence du coefficient de régularisation sur la régression." ] }, { "cell_type": "code", "execution_count": 21, "id": "47624213-36c1-427a-9bab-32feff2fcd34", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "149.6899947398334\n", "27311942.822800986\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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f/8knV4XVPOH+0qltNh0OHRoNAJg8GUhK8u/5lSBcloGqqkE11YV2JNxoLHNJox+KIFyvzwjocaRiEE5ERERERD7RBrZnzkx3uO/TT2+GzRbl1zzhYC591V869Zkz+TCbYwH4Nx9cEcx54UoQHh1tQXPzlTh27E4cPLgUZWU5MJlKhmROeELCYhgMWQAkD0dIMBiykZCwODgNGMYYhBMRERERkU+0gW1VVaHDfa2taSgvX2ifJ9wfJaX94MGlLkGmJ0eOACUlvgWe/aVJHz+uRt6hCsLddULIMnDqVA8AICOjCjpdr/14JY3ebH7Xvi9YI+GSpENu7jPKLed7AQC5uWshSeFXByDcBTUIf/bZZzFr1izEx8cjPj4eCxcuxIcffuj1MVu3bsW8efMwatQoTJ48Gc8991wwm0hERERERD7SBrbV1TNc7t++/VaX49xpaXnb76WvSkuBuXOB224D0tOBb3wDOH/e8+/oL006kEG4Nn3cV546IY4c+Se6ukT97MxM5ycWqfUNDQ9CpxPbwVyizGhchcLCt2AwjHfYbzBkobDwLa4TPkBBDcKzsrLwq1/9Cnv27MGePXtwzTXXYOXKlSgvL3d7fFVVFVasWIHFixdj//79+NGPfoTvfe97WL9+fTCbSUREREREPtAGttXV6kh4VJRII9++fRVk2XsAXFaWhnvvBU6fLnRzr/ulr06fFsG3snb2pUvASy+JfbK7Kd/oP51aG4TPneuxuR5NVKfD4+xZ/x7rrWDcli2/sd/OzDzl/FAAMiyWGowdK0bLgxmEAyIQLy6uRlHRFhQUvIaioi0oLq5iAD4IQQ3Cb7rpJqxYsQJTp07F1KlT8ctf/hJxcXEoKytze/xzzz2HCRMmYO3atSgoKMB9992He++9F0899VQwm0lERERERP0QqdI2REeLCmZKEB4f34y5cz8CADQ15aC2djEsljq3c7zPnwd++9v5+PDDL+Ohh7bh5MnZ7n6TQ0p7Zydw003qqPf06eoSXaWlwFtvuW+vt3Tqnp4YnDpVBECMaGvnWPsqNRXQ68V2TY2bV+Fhvnt/BePq69U1ycaP9zzEPnasqEwfrDnhWpKkQ2LiEqSl3YHExCVMQR+kIVsn3Gaz4c0330RnZycWLlzo9phdu3Zh+fLlDvuuv/56rFu3DlarFTExMS6PMZvNMJvN9tsdfWeh1WqFVekqC1NK+8K9nRQ+eM6Qv3jOkD94vpC/eM6MHC0tb+P06TWwWOoAABcuJKC5WaQo5+SU4/LLP8SePdcDAD77bDays78KANDrx2Py5N8hOVmkqb/7bi+sVgMA4OLFRDz66Ed4+uklmDz5iMvvvHSpBnFxVvzhD1E4elQEfdOmydi6tQfbt0tYtUqEMo88ImP58h6MHu3a7oSEm5Cf/4ZD2wHgzJnlsFpHAQDmzu2F1TqwgnBZWdE4fVpCTY0Mq7XH499L+7eIjk7yWjCurk5dk8xbEB4fr6SjO/7u4SZSPmf8aV/Qg/DDhw9j4cKF6O7uRlxcHN5++21Mnz7d7bGNjY1IS0tz2JeWloaenh40NzcjI8M1reXJJ5/EE0884bJ/06ZNGO3unRiGNm/eHOomUIThOUP+4jlD/uD5Qv7iOTO8RUfvwujRvwYg1scGHFPRc3LKMWfOJ/bb+/Zdi9tu+wMAkV597NhX0NX1Q/T0LMS6dZcBUK/pOzqS8cgjH+Ppp5cgJ+eYw+/dt+8MLl3aiF//ehkAHSRJxgMPbMHOnRcgScDcucXYty8NNTUSvv3tU7jjjuMeXoEBwO+h0x1FVFQrensTsX37Svu9iYmHsWFD9YD+NrGxVwJIQVubhPXrNyE2tsft30v7tzCbb8KoUZ6fUxuEu0tHl2VAllMgy2YAY2GxSHjnnY3Q63tdjh1Owv1zpqury+djgx6ET5s2DQcOHEBbWxvWr1+Pe+65B1u3bvUYiEuSY6qI3DfJw3m/4vHHH8eaNWvstzs6OpCdnY3ly5cjXslTCVNWqxWbN2/GsmXL3I7yEznjOUP+4jlD/uD5Qv7iOTP8ybINe/Y8AIvFcX9VlVqUbfLk08jLa0RCwjm0taXi4MElsNl00OlsfUGohMTE/0NBwU9x++1iFDwp6RzS0k7j2LFitLWl4pFHPsbatVcjO/skAAl6/XgsX/4oXnghBm1tYhT81ltl3H+/uhxWbi4wZ46Mnh4J77wzDT/72RRMmuTt1dxk3/rTn9R06u98Zzry893HJv35xz90UMpdFRQsR0GB+78XAPvfIi5uF3q8DFwr6ehRUTakp59xfhZIElBQ8Cfk5CTh6FGxd+HCL8BpLHPYiJTPmQ4/5gUEPQjX6/XIzRW9OfPnz8fnn3+OZ555Bs8//7zLsenp6WhsbHTYd+7cOURHRyM5Odnt8xsMBhgMBpf9MTExYf2fpBVJbaXwwHOG/MVzhvzB84X8xXNm+Gpt3emQUq3QjoRPnPg5entNmD17C0pLv4LOznE4cWIuCgo+7ztChsVSizff3IzubhEI33jjBXz5yzdgzZqPcPLkPJw/n4Gf/ORd/PWvM6HT9SIv7xlERY3Cb3+r/s4f/zgKMTFqSasZM4CHHwaeegowmyX8x3/EoMTz6mZ2PT3Ajh1iOy0NmDEjBh7G+/qVk6NuNzbGYMIE938vlYyenmbExBhhtTbDeV64LKsj4ePHd2PsWKND6rrBkIXc3LUwGlchMVF93KVLMRjub8Fw/5zxp21Dvk64LMsOc7i1Fi5c6JJmsGnTJsyfPz+s/+BERERERMORp6XGtEH4pEliKHju3I/t+/bvv8blMW++qZbx/spXJuLyy9fhD3/4OiZNOgwAOHu2APv23W1f+uqNN4DqanH8F77gvoL5f/4n7CPAb78N+JKxvG8fcPGi2F6yBAMOwAEgO1vdrqnpf2k2RWrqXX1bjr+8tTUdFy+K6Do/f4zXquTaYnLBrpBOgRXUIPxHP/oRtm/fjurqahw+fBg//vGPUVpairvuEifd448/jrvvvtt+/P33348zZ85gzZo1OHbsGP76179i3bp1ePTRR4PZTCIiIiIicsPTUmNKOnpiYiPGjWsBAMyd6zgvXKunJxq7dn0RADBmTBtmznwHRuMqLF9+AP/93+pxH320DkbjKvT2Ak8+qe5//HH37YuPB379a/X2o496XrJMUVqqbi9d6v3Y/jgH4f2tTa5ISVnpdv3t2lq1QTNmeK9Krp15yyA8sgQ1CG9qasLXvvY1TJs2Dddeey12796NjRs3YtmyZQCAhoYGnNUsqjdp0iRs2LABpaWlmD17Nn7+85/j97//PW677bZgNpOIiIiIiNxwt9Z2a6sRbW2pAERRNr0+C3p9FjIzTyMtTcxhPnx4ESwWvf0xlZWz0dmZAAC47LIPUVv7fciyDZKkw5e+NBOTJ4vjNm2ScPw48M9/wj7f+corgcXqVHAXX/saML9vye9Dh4CdO72/Jm0QvmRJP3+AfmiD8LNn+1+bHJBgMGQjIWGx2/W3bbaX7UdOmlThssSbFkfCI1dQg/B169ahuroaZrMZ586dw0cffWQPwAHgpZdeQqn2XQDg6quvxr59+2A2m1FVVYX7778/mE0kIiKiEczTOr5EJLhba9s5FT0v7xnk5T0DSYK9SrrFEuuQkn769Ez7dkHBZ7BYau3rgOt0wHe+o/7O3/wGDqPjP/qR95TxqCjgoYfU225KT9n19ADbxa9FejowdarnY30xYYK6XVPjfW1y5XZu7lr7iLZ2pLun5zy2bHnTfnR09N0oK8uByeR+ors2CG9r86/d/OwLrSGfE05EREQUDkymEpSV5eDgwaU4duxOHDy41OsFL9FIZTSuckid1gbhV1yxCEbjKvsxV1+tDkNv2PBN+3ZVlRqET54s5oBr50/fey/s63z/9a/AZ5+J7aIi4IYb+m/j6tVAUpLYfvNNoKXF/XG7dgVuPjggAuG4OLFdUyN+Ov+9FAZDln2+uzOTqQTl5atRWamWd8/JOQqzuQ7l5avdfi4prxcAzp/3vc387As9BuFEREQ04igXvNqqwwC8XvASjWTa1Om2NnXYubh4rsMxa9Y8D6OxEwCwc+dKnD8vqqZpR8KVQmza+dOJicB997n+3scf9y1QHjUKuOcesW02Ay+/7P64v/5V3fYluO+PJKkp6TU16nx0d6nm2qJqWrJsQ2XlQ+jtVTs4MjJOIza2E0r19MrKh11Gq7WLR3nqdHDGz77wwCCciIiIRhTlgtd5aaC+ewG4v+AlGumU1OnTp/Ps+woLHY/R63W4775YAIDNFoONG78OQB0JT0g4h8TEc9Drs5CQ4DjR+ze/Af72N+Bb3wKuuAL4/veBL33J9/Z961vq9p//DHR3O97f1gb8/e9ie9w4MXoeCEoQfumSYzDsraiaY7u2w2yuxblzE3Dp0lgAwKRJRzRHyDCba+zp+wp/g3B+9oUPBuFEREQ0oigXvJ65v+AlIjHSWy5WJMP48UBCgusx992nhhgffPBvOH8+Da2tYkR88uRDfT9/6xKUGgzA3XeLOd07dwK/+52Y7+2r/Hy12nllpZhnrq2U/n//JwJlQBRzU9LfB8t5Xri/lLR8peI8AOTkHPF4nMLfINzfz776euCjjwAbY/KAYxBOREREI4qv6/j6ehzRSNLQALS2iu0ZM9wfM3kyoNRirq+fgvXr1fT13NxqdHX9EMnJtwalfWvXArFiIB4vvgg88gjwyivAe+8Bzz6rHqcdNR8s52XK/KWk5WuDcMeRcMfjFP4G4f589nV1AcXF4v/x5z/36WHkBwbhRERENKL4uo6vr8cRjSTKKDjgmoqupQ1y33rrh/bta6+9Bz09C4PQMmHWLGDdOvX200+L0fWVK9W2FxcDM2e6f/xADDYIV5Y18xyEq8uaaY0eLebCA74F4f589n34ofpaPv7Yp4eRHxiEExER0Yjizzq+ROToiCY29BaE33wzkCqWEofFooYcM2cOshy5D26/3YYHHzzr8X7tcmiB4LxWuL+UZc2UIDwqqgfZ2ceVewE4LmumPk4dDfclCPfns++tt9S9p075/lrIN9GhbgARERHRUFIueMvLV0NcjGqLFHm+4CUix5FwT+noAKDXA1//uii2ppAkYPp0GefOBa15MJlKUFn5EG69tRaTJ1+Nc+eyYTZPhMFwB3p6CpGXB3z1q4H9nYOdEw4AiYmrUFMjJl9nZ5+AXm8BIJY1y81d67aqOiCC8Lo6EYTLsvdK8r5+9nV36/D+++o9DQ1AV1fg5tATg3AiIiIagZR1fCsrH3IoVNTfBS/RSKcNwqdP937sffc5BuFTpgQ3kFOW3wJkSBIwe/bWvnskAP/tcY3uwcrKUrcHGoRXVgIWi+j4mz07BQUFr0Gvz0BCwmKvHYLKSLjFAnR2qmuWe+LLZ9+776prqSuqqrxnPpB/GIQTERHRiGQ0rkJKykq0tW2HxdLg0wUv0UimrYyek9N/wJeXB1xzDfDJJ+J2IOdhu7atv+W3JFRWPoyUlJUBf4+PHi2C4ZaWgQfh2jT/efNSkZZ2h0+Pcy7O1t//CdD/Z582FV1x6hSD8EBiEE5EREQjlrKOLxH1r6YGuHBBbPsakH3rW2oQPm9ecNoF+Lf8VjDe89nZIgiurRVLeun8jPO1Qbi3NH9nzkH4xIm+Pc7TZ5/ZDPzzn67Hnz7te5uofwzCiYiIiIioX74WZdP60peAAwdEcPrv/x6UZgEI/dKDEyaI12mzAY2NYg11fwQqCB+sjz8G2tvFdm6uSJMHWJwt0FgdnYiIiIiI+uVrUTatqCjgySfFWt1JScFpFxD6pQcHu0yZEoSPGiXWWfdVoINwbSr6o4+q2wzCA4tBOBERERHRCCPLNrS2lqKp6XW0tpZClkVl7n37gJMn3T9mICPhQ0GWbZBlG6KjvUX5wV16cDBBeHe3+jefPt2/VPbBBOE9PYDVqt62WoF33hHbcXFifXWlkB7T0QOL6ehERERERCOIsoyXdg612VyI55//EG+/nQ29Hjh8GJg61fFxyki4JAEFBUPYYC/cvRZXwV96cDBrhVdUAL29YtufVHTAMQhvbvb9cTt2iKJ5M2YApaVAfDywZQvQ2iru/+IXgdhYMSp/5Iiojj6Que7kHkfCiYiIiIiGGVkWRdHmzQOOHVP3K8t4aYPWxsaJ+OpXN+Ltt0UkabEAb77p+Hy9vcDRo2J7yhQRoIWau9fijsGQFbTlyRSDWSt8oPPBgYGPhP/mN2Lke/9+4IUXxL7169X7b7tN/JwyRfy0WMR65BQYDMKJiIiIiIaZI0eAv/xFpJdfd53Y52kZr7/97b/Q3JzlsG/zZsfnq6oCLl0S20Odiu4udd77kmRCdHQSioo+QnFxVVADcGBw6ehDHYSbzWrFegB45hmREv/22+J2bCxwww1iWzs/nSnpgcN0dCIiIiKiYaZWMzhcXw90dgIWi+syXrIM7N9/LQBAr7+ExMRzaGqaiE8/BS5eVNedHkhRtkBwl25uMGQhI+Pf+h0B7+k5D0AXtBR0WbbZ19qOjc2EJF0FWZbCPgjfvl2cD4raWuCLX5RhMom0/euuM2H06CQAOvtIOCCKsy1Z4l/7yD2OhBMRUb88FfAhIqLwdP684+2NG90vz1VfPxlNTWJx6RkzduLyyz8AIFKVt25VP/s//1wdBh2qkXBP6eZmcx2qq/+fT88RrCXJTKYSlJXl4ODBpTh27E4cPboEyclNAPyfE64E4fHxQFaW92OdJSSIOfqA70H4xo2u+z7+WLJvL1z4dZSV5cBkKnEYCWeF9MDhSDgREXnlaRQiN/eZoKf3EQWaduRKr89AQsLioI2SEYWSyeR4e/164JprXJfnOnBgqX17zpwtmDjxKN577zsAgFdeeRFjxvwbAGDXrlcBiIhsKEbCvaebe05BdxaMJcmUzgHndqSmVqG5OR1NTSLl22Do/7k6OoAzZ8T2jBlqQO0rnQ5ITBSdLr4G4R9+KH5GRQF5eR04fjzeft+3v/0DLFy4AWazhPLy1UhM3AhgOQCmowcSR8KJiMgjb6MQ5eWrYTKVhKhlRP5zHrk6eHCpfbSHaLhxDsLffx+IjV0MgyELSrVwANi/Xw3CZ88uxeWXn0RUlAgud+8utt9XXS2Gv6OiepCY+E7Q2q1oa3NNnfdPcJYk89Y5YDSqeei1tb5ljGnT/AeaYaCkpPsShJ89qxbYu/xyGffd9yAAQJJ68cgj/4bbb3+q70jx+iyWf4ckiW0G4YHDIJyIiNzyZRSisvJhpqZTRNB2KMkycOTIQjQ3Z7BDiYYt5yD8wgXg4491yM19pm+PBFlWR8JHjbqI/PzPMXv2/0NBwT4AQHX1DJhMmbDZdDh7VqxJlpV1EjU13wv6Z79/aeTOw8fBW5LMW+dAaqoahB89etin59u7V92ePXtgbVKC8I4Ox3W/3dGmol99dTXmz38Zf/nLbLz0UgG++MX/dTpaRm/vaaSnWwD4X3COPGMQTkREbvU/CiHDbK5BW9v2IWsT0UA4dyi9+uqP8eCDn+Lf//0zXLgwDgA7lGj4cQ7CAZGSbjSuQmHhWzAYxqOmZhpaWjIBALNnf46iojcQE2PE3Lkf2B+zd+91qKqaAatV5FZPmnRkSD77fU0jnzjxCRgM4x32BXNJMm+dA9og/MyZSz49nzYInz9/YG3SFmdzrgXgzDEIPwEAyM09iAkTTnh8THr6BQBAU5NYqowGj0E4ERG55esoRLCK3hAFirZDqb09Ga+99h8AgObmLHz44b1ghxINR9ogPLqvCtT77wM2mwjEi4urYTK9Zz/mlluuhtG4ChZLA+bPV9cn27t3mUPK+syZ4n0S7M/+hATX1HlHIt08J+fHKC6uRlHRFhQUvIaioi1BXZLMW+dAaqpaka2pKc2n59uzR/yMjgZmzRpYm1JS1G1vKekWC/DRR+pjFizwYdI6gKws0YEpy0ADv/IDgkE4ERG55esoRDCK3hAFkjZYWL/+IXR3x9lvv/32d2GzRbkcRxRpnFexaG4WgdPYscDNN4tjTCZg926x3d2tw6uvTrU//pprxPtAr8/A9OlliI0Vo597917nUrxNOS6YJMkxdd7pXgBqurkk6ZCYuARpaXcgMXFJUIsteusc0I6Em0w5/T5XV5c6P7uwEBg1amBt8nWZsk8/FdMSAOD664GkpP46OsRa65mZ6qg+U9IDg0E4ERG55esoRKCL3hAFmhIsXLw4DiUl33O4r7FxEnbt+qLDcUSRxl3RwYaGNgCA0QjcdJN67D//KUY0v/lN4MABsW/qVGDuXLGdkLAYY8akY/bsUgBAa2s6yspWAADi45uRk3N0yD77tanzWsFMN++Pt86B1FR1CldNTf9h1sGDQG+v2B5oKjrgexCuTUX/whf66+gQenrOQ5J+b79dO5haeWTHIJyIiNzyZxSCKJwpHUrvvPMAOjvFHPBJk9SiSSUl37MHFc6jiZwnTuHO3SoWNpsOHR2JAICxY6txxRU77RWu33sP+M1vgNdfF8eOGQO89ZZY6gpQP/vnzfvI/ny9vSKfffbsUkRFyUP62a+kzg9VurmvbXLXOZCWpodeLz4zfFlTW0lFB4B58wbeHl+DcGVpMkkSI+GA59eiZTSq51ZFhW8F58g7BuFERORROI5CEPlLCSo++eR2AEBUlA0/+9kqZGWJQkT7918L4H/R3PwulzCjiOJpFYv2djUqGz36MOrrF2HGDBHxHT0KPP64euyrrwIzZzo+r9G4Crff/kWX37dgwYGQfPYPZbq5r9x1DlxxxWkUFYm2HT8ONDd7fw5tUbZgB+H19cChQ+rvMhrV+5TXMmvWR4iOTnJ5rHbptWPHPmPnZABEh7oBREQU3ozGVUhJWYm2tu2wWBqg12cgIWFxWFwEEfkqJmYVqqtFoJKbux9ZWZW48ca/4Pnn/wcAsGVLGszmL8A5mFGWMGOnE4UjT6tYtLerEda4caJCW3FxCQ4fXgBApKMDwM9+Btxyi/o4WbbZP+sLCjIwfryMujo1E+ob33gCRuPw+OzXvtaBfq8pnQNaV10FfP652N6xw/Hv60wJwgdTlA0AUlPV7aYm98doU9FvuMH1fmVufU+Pa3l17Uh4Y+M4tLVtd3nd5B+OhBMRUb/CcRSCyB9lZYAsi2BiyZJ0FBS8hrvu+rL9/n/9qwHOAbgg9nEJMwpHnooJtrVpg3AxHHvFFe86HPOlLwE/+Yl623le+aFDS1FU9Kb9/tRUYPr04fHZ724OfaCyXq66St3ets3zcZ2dalG2GTMGXpQNADIz1e36evfH9BeEA57Pp+TkBkiSmLx+7lw2i1gGAINwIiIiGvZ27lS3r7kmC2lpd+DKKxfY0zj37bvcXiXdFZcwo/DkqZigNghPSBAj4RMnHkN+viiNPnPmBbz4opgbDLifVw4Ac+aogfuSJerxkczTa1WyXgYbiC9apG57C8IDVZQNADI0p4GnIFwZdY+LAxYscH+Mp/MpJsaKxEQxxN7cnMUilgHAIJyIiIiGvU8/VbevuEL8jIoSgQUAXLyYiFOnirw+RzBHf1gQjgbC0yoW7oJwSQKefPKLeOKJVXj33Q8xZoy439O8cgC44or3kJV1AjExZtx/f+Sfk95ea6CyXpKS1Dn2+/cDHR3ujystVbcHG4SPHm1DfHwPAKC2tsul/RYLUF0ttvPy1HXjnfmy/FpLSwbGjOGqKIPFIJyIiIiGtZ4edW3k7GzxT7FUXf4Y+/dfA5stChaL3u3zBGv0J5ipsTS8eVrFwt2ccABISGjGVVe9jYQEdRKxp3nlADB69EW89FIB3nknBbNnByYTRJZt0OkOw2R6Y8g7nLy91r7WDSrrRelMmz9fFH3s7XXsANRSKpUDwPLlA/p1ANTPj8RE8Tvr62Xs2uX4+XHmjDrqnpvr+bm8rYqizAuX5Sg0NQ1sWkJ/nY2HDwMNIyTTnUE4ERERDWuHDon5l4A6Cq645hp1e9Omr+GrX63EqlXn8MEH92qOkoK2LnKwU2Np+HO3ioW7kXDB9VzuL8NDp+vF6NEXA5IJYjKVYM+eXMTF/SdOnLh7yDucfH0NA3mt2s607Gx1sv3Gjcddjm1tVYPz/Hxg0iS/f539dyqfH8nJIg+9u3sMzp+/4PD5oV0uzVsQDnhbfq3dvl1T4/wo39rqrbPxrbdEcbpp04B9+/x//kjDIJyIiIiGNe188CuvdLwvPx9ITxfbp08XobFxEjo7x+Gpp9bh6af/jJ6eGAAIyrrIQ5EaSyODdrms8eMf9hCEi5FN53PZ1wyPwWaCKAGjxVLnsH8oO5yC9VqdO9NmzVJH0j/6qMXltW3erI5MeyqS1h/nzw8lCAdEyjigfn5UVqqP6y8IB9wvvzZ//j32+2u9JRO44Utn41//KvZduADcdhtw3rVI+7DCIJyIiFz09o6clDAa/tzNB1dIkmNKutZ77/071q//edCWJwt2aiyNLMoqFnl5T6OnRz2plSDcYMhyey57mwfc98yDzgQJlw6nYLxWd68tObkR2dliBLy8/Aq89tp6h9e2YYP6+BUr/HgBGs6fHykpahDe3JwJ7eeHNgifMsW353deFWXCBDVs9CcI9+X//tixH2DrVvX+6mrgrrvUjorhiEE4ERG5zNO6+WYZmZnA174mCroQRbLPPhM/R48GitzUXtNeBH/hCzJ+97vjkCRxQbht22NBWx88mKmxNLIpI+GjRtkwZ85fUFS0BZdfXono6CSX+bje5gF7Gj33vz3h0eEUjNfq6bV9+ctP2bd/9atfoK5OpOT09qrLhY0ZAyweYN+G8+eC40h4psNx/o6Eu5OVpW77E4T78n+/f/94dHU5/n9s3Ah88IG4Pmlv34qYmG1ob986bDKDPNTGIyKikcJkKkFl5UP2L8mzZ6figw9ED/6rr4qUsDffFAEMUaTp7VXnL+bmuq8KfOed4qIyKgp4+GEJev00rF8v0tiPHpVQWTnwC1dvhioNmEYeU18GutGoQ3r6HTCZSrB79xSHYMhgyEJu7jMwGlfZ5wFrvwvUY9YOuiMqnDqcAv1aPbV5xYp1+Oiju3Dw4BI0Nk7CihXjkJUFXLoENInVvnDNNYDBMLDX4fy5oB0J1wbhen2GfU54bKzjcmb+0Abh/swJ9+X/dO/eZfbtm28G3ntPbL/zzimkpCyB2VyL0aOBI0d+53DeRjIG4UREI5gyT0ubJvbppzc7HLNhA3D//cDLLw9x44gCoLkZsFrF9vjx7o+JigL+4z8c9918szqX/J//BL7//cC3TUmNNZvr4D5VU4LBkBWUgnA0fPX2Ai0tYttodP85D6jzcZUUdaNxFVJSVqKtbTsslgbo9RlISFgckFoI4dbhFMjX6qnNUVEyHn303/DNbx6CxRKLw4eTcPiw4zEDTUUHXD8/tCPhIh1dfH6MHbsYp0+L/VOmiM+7gchU43q/RsJ9+T/du/c6+/avf23DBx/oYLMBH39sxte+5n4eebCmCQ0VpqMTEY1QnuZpaYNwg+ESAOAf/xDLPBFFmjpNDShPQbg7N2v6ot59N3Dt0RqKNGAaeVpbAVtfxq7RKPs1F9t5HnCgzr2hmHfur0C9Vm+vLSurEt/97sOIinJNoZ41C7jjjgH9SgCunx/uRsJzc9eirk5nn1bm63xwdwwGILVvZTt/RsL7+7+/eDEeFRWXAQAmTixHa2sOZs8WvUhnzkxHS0u60yOGR9FKBuFERCOUu3labW0pKC8XlasmTjyKhQtFTpjZDJw4MeRNJBq0gQbh06YBeXlie8cOdWQx0DwtB+SpiBZRf0yaFcnGjWsatnOxw0V/r+2mm/6CU6fex7lz4nOkrU1UAD9wABg3bnC/W/v5kZSkpn2fPz/J/vnhz/Jk/VFS0hsb1Y6e/nj/+wAHDixBb6/4f5837yOYzXUoKHjWfv/+/e4qZ0Z+0cqgBuFPPvkkFixYgLFjxyI1NRW33HILjh93XStPq7S0FJIkufyrqKgIZlOJiEYcd/O0yspW2L8Mr7jiPUyZcsh+38GDQ9Y0ooAZaBAuSepouM0GfPhhYNul5W45oOLiKgbgNCDaIDwxsc2nxwzlXGy9PtNh/3DocOqvMy0nZyWMRiApSQTecXHiMyZQv7u4uBoLFvwLSUlmAMCFC/Psf89AFGVTKCnpNpvjeeZLG939fQDgs8/UNdrmz98MQMacOZ/Y9+3ff43H543kopVBnRO+detWPPDAA1iwYAF6enrw4x//GMuXL8fRo0cxZswYr489fvw44uPj7beNRqOXo4mIyF/u5mlpU9GvuOI9XLiQZL998ODgUueIQmGgQTgggvDf/lZsv/8+8NWvBq5dzpTUWKLBam5Wt1NT9T49ZijnYo8btwKbNj2FuXMnIjY2O2DzzkMtmHPq+6N8fowfL4qp1tdLkGUR6A9keTJPtPPC6+uBdOdMcS+0f5/W1o9x9uwv0N6ehM2bvwYAGDWqE0VFWwEAhYW7EBPTDat1lNcgPJKLVgY1CN+o1N/v8+KLLyI1NRV79+7FVVdd5fWxqampSEhICGLriIhGNueiLhaLHp9/fn3ffedQUPAZLlyYZz/+0CEPT0Q0RGTZ5vcF7mCC8CuuEKsCdHWpy5wRhTvtCGV2dk7YFf+TJB1stpkwGlcgJiZmyH7vUAh1Z1pmJnD4sFha9Px5IDk5OCPhgAjC58717/HK30cZwX7vvX9Hd7cYmL3hhnUYPfoiAMBg6MaMGZ9i//5r0NAwGQ0NOcjIqNY+U8QXrRzS6ujt7e0AgKSkpH6OBObMmYPu7m5Mnz4dP/nJT7B0qbv5AIDZbIbZbLbf7ujoAABYrVZYlXKoYUppX7i3k8IHzxnyV3/nzKRJv0VFxe0AJJw6VYTu7jgAwIIFG6HT9eLyyx9BQoKMtjYJBw/KsFpZnW04C+fPmJaWt3H69BpYLGpUrdePx+TJv0Ny8q0eH1dbq4My+y411Qp/X1pRkQ67dkWhqgo4d86KxMSBtH74CudzZqRqbIwCIDqnkpJ6HT7nHQNxkQ89adJT6OnpBdA7JO3jORM86enq592ZM1bExwOVldEAJMTEyEhP7/H7M1ArLU2CEj7W1PTAanXXsdM/nc4Is3kU3n77QQBAVJQNX/rS0w7HzJnziX0UfP/+pcjIeLHvntCct77w55wesiBclmWsWbMGixYtwowZMzwel5GRgRdeeAHz5s2D2WzGK6+8gmuvvRalpaVuR8+ffPJJPPHEEy77N23ahNERsqjt5s2bQ90EijA8Z8hfrueMDTrdUURFtUKSvgKDYTNOnlS7tPPzj6Kz8zF89pkB48e3oK0tBfX1Et544yPEx1uGtvE05MLtMyY6ehdGj/41AMd5lGZzHY4d+wq6un6Inp6Fbh9bUbEUQDxiYmzYvXuD3/Mwk5JmApgMAHjuuc9QVNTs/QEjVLidMyPZ55/PACDyjk+e3IXoaAOiox9DbOz/IipKrTDY25uMS5e+id27DQA2DHk7ec4EXldXPoBpAID33vscNTUmnDq1AkAMUlJasWXLL9HbmwibbTqUjhp/1NWlASgGAGzdWonMTO+1vjyzobT0O2htTQMAXH31mw4j3bIMzJ69z357//5rsGKFCMJDfd5609XV5fOxkizLA+vC8NMDDzyADz74ADt27ECWdrV3H9x0002QJAnvKSu3a7gbCc/OzkZzc7PDnPJwZLVasXnzZixbtmzYpeNQcPCcIX+5O2fcjSjGxGTiD394F3//+3wAQGmpGVdcIXrTv//9KPzpT+LL+l//6sHSpUPytUEhEI6fMbJsw549uQ7nqyMJev14zJ9/0m1qelpaNFpbJUyaJOP4cf8zOV5+WcJ994kxiyeftOGRR8Jn1CUchOM5M9LdfbcOb7whPr+PHLFi6lSxX5Zt6OjYYZ/OER+/KCRzsXnOBM9zz0Xhe98T/6d/+UsPvvIVGfHx4m88c+Z2/P73YkDTlywidw4cAC67TDzfN7/Zi2efHdgSYTYbMH16N6qqxva1ex6mTVOCbtFTOmXK31FQsBqdnRLS0rqxbt2PMW/eMiQlBW7pvEDr6OhASkoK2tvb+41Dh2Qk/MEHH8R7772Hbdu2+R2AA0BxcTFeffVVt/cZDAYYDAaX/TExMRHzxo6ktlJ44DlD/lLOGZOppC8t0TGQtlobsH+/2JYkYP58A5RTbM4c9bjy8mgsXz40babQCafPmNbWnV4CcEDUM6hFZ2eZy1zMS5fEmskAMH68NKDXdNll6vaBAzrExITnxV+ohdM5M9Jpl9PLzIyB+t8Sg5SU60LRJLd4zgRedra63dQUjcrKDwGI6uOJiU32+yyWelRU3O53VfqJE9XtxsYoxMQMbKGtf/4TqKoS//fz5u3QBOCionxu7loYjatw1VViZYqmplGorl6B5cuvCutzxp+2BXWJMlmW8d3vfhclJSX45JNPMGnSpAE9z/79+5GREbnV74iIwoEs21BZ+RDcFeexWqNRVTUTAJCfL0O7gEVRkbrN4mw01HxdgsbdcYMpyqYoKABGjRLvmc8/70BraylkeWCjP0RDQSnMFh0NsMbxyOJYOK0X+/f/0X47IeGc5kjxmVZZ+bBfn2cpKeK8Ahw/X/0hy8BvfqPe/sUvFnpcnvEaTWH0Q4dSBvYLw1RQR8IfeOABvPbaa3j33XcxduxYNDY2AgDGjRuH2NhYAMDjjz+Ouro6vPzyywCAtWvXIicnB4WFhbBYLHj11Vexfv16rF+/PphNJSIa9tratsNsrnV735kz02G1iqyiGTPOAUiz31dYCERFAb29XCuchp6vS9C4Oy4QQXhrawmmTMlBeflcnD4dj507VyI5OR65uc9E9LrGNHwpQXhKSuDWoqbIoA3Cz55tQXa22umemHjO6WgZZnMN2tq2+1zRPSoKyMgAampEdfSB2LED2L1bbM+aBVx/vQ6S5P73a4Pww4eH13LVQR0Jf/bZZ9He3o4lS5YgIyPD/u/vf/+7/ZiGhgacPXvWfttiseDRRx/FrFmzsHjxYuzYsQMffPABVq3iFx0R0WB4G1E8cUItylZY6Ni9HRsL+5zC8nKghwXSaQgpS+kp8wRdSTAYst0uVTPYINxkKkF5+WpMmVJm31dZORtmcx3Ky1fDZCrx/0mJgkiW1SDcOLxiFvJBWpra8VJfL6GtLdV+n+NIuMrXbCOFEuifO4cBVVrXjoL/4AfeO4qKimBfkeLIkRT0DqOSHEFPR3f37+tf/7r9mJdeegmlpaX224899hgqKytx6dIlnD9/Htu3b8eKFSuC2UwiohHB24jiiRPqeuBz57p+NeTni58Wy8B7v4kGQpJ0yM19RrnlfC8AIDd3rdtCPYMJwrXTN6ZO3WvfL94rA0vlJAq2CxfE5zTAIHwkiokBUvvi7sZGvb36OOA4J1zL12wjhXa0vS/J2WcHDgDvvy+2s7OBr3zF+/E6HbBkidi+cEE/rKbEBTUIJyKioSfLNrS2lqKp6XW0t28FIIIEbyOK2uXJFi2a6XK/tqRHVVWgW0zkndG4CoWFb8FgcIykDYYsr4WFBhOEa6dvTJ2qFg1S3ytqKidRuFBGwQEG4SNVamobAKCpKRbnz6fb97umo3vOIvLGcd65f237xS/U7R/8APCljpk2Jb20dPiErkO2TjgREQWfyVSCysqHHOZ+jx2bjJaWPyM9/cvIzX0G5eWrIQJxMZpns+lw6pSovpaTcxGJiXEuz5uTo25XVwNXXx2810DkjtG4CikpK9HWtt2+xFJCwmKvS9UMJgjXpmjm5JQjJsYMq9XgkDXifJwzm02kB0fzaouGCIPwkc1kKsGYMXoAX4TNFoPq6un2+xzT0b1nEXmj/Sz1Jwg/cgRQSnylpQH33efb4xyDcAk/+IHvvzOcDZ/uBCKiEU6Zv+pcfE2SWlBRcTtMphK3I4pnz+bDbB4NAFiwwDUAB1yDcKJQkCQdEhOXIC3tDiQm9r9WrDYI147e+EKbohkTY8WkSYcBADU103Dp0hi3x2mZzcDcuUB8PPDRR/79bqKBYhA+cilTaJKT1ci4slJdY1Q7Et5fFpE3Ax0J/+Uv1e3HHhP1ZnxRUAAsWtSLG26owr/92/CZFM6+WSKiYcDb8mNK0ZPKyoeRkrLSZUTxwAE1FX3BAvfPrw3CmY5OkUIJwlNSAIPBv8cq0zfM5joo88JPnJgPWY5CZeVszJz5KQyGLI+pnLt2qUv6LVsGXLxog8Xi+yg+0UAwCB+5lCk0KSn1mn1ignh0tAVxcW0AgClTnkZW1oMD/vwZSBB+/Dig1OVOSQG+/W3ff58kAZ98YsOGDYewYkWW7w8McxwJJyIaBrwtPyY4zl/VjigeODDNftSVV7p/NEfCKRxp6x84r99ts6kXiAOpjO5cEC4vT50XrqSke0vldH6fPPDAn3Dw4FIcO3YnDh5cirKyHFZXp4BjED5yKVNjtCPhioSEc/YOeb0+bVAdgNog3Ne1wv/7v8XUHAB45BFgzBjvx48EDMKJiIYBX5cYcXfcjh3ip8EAzJvncjcAkVKblCS2GYTTUKqoAJ5+GqisdNxvMpWgrCzHY2BbV6cup6ftRPKHdvrGtGlqhfRTpxb3m8p55ozj7dde+zZqavLst7nMGQUDg/CRS5kaox0JV2hT0f2thu7M35Hw06eB//s/pR3AAw94P95b5+pwwiCciGgY8PVL1fm4xkbg1CmxvWCB95RdJZCprR26tcJHypcxuWpsBO65BygsBNasAVasUEdSPNU/0Aa2ynkNAFOmDLwdRuMqFBdX4+abf4foaDEfsabmtn7nUp4963jbajXg9dd/qNnDZc4o8BiEj1zKFJrkZNfOdlGUbWDV0F2fCxg1Smw7B+HuvrOffFJkJgHAww8DY8d6fm5PnastLW8Pqs3hiHPCiYiGAef5q64kt/NXd+5Utxct8v47Jk0C9u0TX6Y1NY7LlgWDu0rvBkMWcnOfGVAxGYocsgzcfDPw+efqvpMngb17gXnzPNc/EPskVFY+jFOnboEy1jB58uDaI0k6ZGRchRkzxDq3R49K6OoCRo/2/BjnkXAAOH58vkt7lWkiiYlLBtdIIjAIjwSybPNrlQdfKVNoGhpch5qVyugDqYbu+nvEaPjp045BuLvv7EuXZuJvfzsAIArx8cD3vuf5eZXOVefPdrO5DhUVtyM6+jEAKwbV9nDCkXAiomHAef6qljJ66O7LV0lFBzzPB1cM5bxwX0Y6afgqL1cDcJ3mlH3nHd/rHxw9WmPfM5iRcK25fTUMe3vVomueKEH46NEdmDjxKACgpiYfNpvrBbCv00mI+tPcLH5KkjqFiMJHf9NoBstoXIUrrvgTdLoep/1dA66G7o6Skt7aCly65Pk7u6ysAFarCDe/+U0xiu6Ot+Kyyr7Y2HXDKmuIQTgR0TDhbvkxAJDlFOTnv+H2y1c7En7FFdrHuKaUDVUQ7suXMVN4h7f331e3f/hDtcL/O+/4HrBq09EHOxKu0NZM2LvX83G9vSJbBADS0s4gJ6ccgEhJr6tz7REY7BxNIoUyEp6U5NiBRaE3VJ3L6emrkJ7u+J9fVPStgGaQOa4V7vk7e//+pfbtK6/c7/F725fO1aioZnR07PByTGRhEE5ENIwo81eLiragoOA1zJixGRcuPI/k5Ftdju3sFOnlADB9ujpq4qmnPinpU/tjg7lMmb+V3mn40Qbh994LLFwotsvLgZoa3yLqmppEAEBU1MALszmbq67mZ3/vuHPunFgnHADS088hJ+eo/b7q6kLNkYGZo0mkUIJwpqKHl6HuXM7MdMyIS0sLbMinLc524sQhj9/Z+/dfA0AskTZ69CKPo/6DKS4bqRiEExENM9rlx8aNuxqA++GQd95Ri6Uo88G99dSbzd+y3w7mSPhI/DImVUuLWGMbAAoKRCr5rZo+pC1bFsBgyILztAuVCGyrq0X1n+xsQK8PTNuKitTRRW8j4dXV6oX05Mnx9pFwcZ8ShIv2B2KOJhEg0oI7O8U2g/DwMtSdy9ogGQBSUwPytG6fv6am0+0x585lobZ2KgBg+vQyxMZ2eRz1H2hx2UjGIJyIaATaswf4lhpT4wtf6L+nPj1drTQVzCB8JH4Zk2rjRpHODQA33ih+rlyp3r9+fRQmT3Zf/0C5nZLyJ7S2iu1ApaIDQGys6BgAxKi8xeJ6jMlUgo8/VgsjjRnzFqZMUS++z5yZDkAUGQzkHE0iFmULX0PduTyUQbjJlO72GG0q+pw5n/RtuR/1V4rLeutc7e1NQXx8PxVkIwiDcCKiEaapCbjpJqCrS9y+807gllv676mPjb1or7AazHR0X76MmcI7fGlT0b/4RfEzL08sVQYAu3cD3/rWKmRlvetS/0AJbDs6brLvC1RRNsXMmeJnTw9w4oTjfUomSW1tnH1faupZZGTsQXS0iNgbGm5AUdEWFBdXMQCngGIQHr6GunPZOQhPSwvI07p9/tbWyW6/s5VUdEAbhAPuRv29FZdVbl+69M1hlTXEIJyIaIRZt06swQyINPR160ThK1964NPTqwEAdXXuRwEDwZcvY6bwDk89PWIkHBBVdLXFAv/rv9QCbe+9B9xyy02YNUutf6ANbINRlE0xY4a6vXPnTnvhQm0mSVPTRPsxaWlnEB1tRVaWiNhPnRqHDz9cgvnzdXjllcC2jUY2BuHha6g7l52D8ECfD9rnb2iIcvnOlmU1CDcYulBQsNvlOZyvOTwVlzUYspCf/wZ6ehYG7gWEAQbhREQjzJ496vbzzwOjRoltX3rg09KqAYgv2Joa78cOhrcvY6bwDl8nTwJtbWL7mmuAmBj1vi9/GdiwAUgU9dZQXg689JJa/yAxcYm9Y+b0afVxgR4Jz87eZd/eufMTe+HCM2d+ac8kaWqaYD8mLU1M41DmhVssEu66SxR2e+yxwLaNRjYG4eFrqDuXtUHyuHGAwRCQp7XL0Fwu1Ne7fmfX1eXi3DnxOThz5g7o9a699u6uOZyLyyqdq+6Ky0a66FA3gIiIhtaBA+LnmDHAtGnqfqWn3myug/t54RIyM1vtt2prAx/gaBmNq5CSshJtbdthsTRAr89AQsJijoAPY4cPq9uzZ4s6Bdr//+uvX4xNm3RYsEAc89RTwLe/DUQ7Xc0EayTcZCqBTvcDAOIXVFWJYXGzuQ7V1f8PVVXTYTBcso+E63RWJCWJtBNtcTZFY6OYFjJ6dODaSCPXuXPqNoPw8KMEqpWVDzlM/TIYspCbuzagncvaIDzQ88EBYOxY8e/CBRGEA+p3dmtrKT744AP7sY6p6IAY9c/yOOqvFJd11BuopocNBuFERCNIW5s6n3vWLMd1ZJWe+vLy1RA989pAXPTUT59ebN8TzJFwbZtcv4xpuDpyRN3Ozi5DWdmX3FysPoPly1dh0yZRIPDNN4E77nB8nmCMhCvp5unpdRg1qhPd3WPsQTggY+/ea/GDH2xCdLQFVqtIL0lNrYFOJy4e3QXhgOjMmjpVvd3VJUatuMYz+aupSd0O9BxgCoyh6lzWBuHBOhfGjwcqKtQgHBDf2UlJ1+LkSbWH3zEI55QyBdPRiYhGkIMH1e05c1zv7y8NPD+/yL6v1ttqK0QDoA3CY2K+5napvPLy1fj2t9WCPr/5jZgeoaWMhCcmqunrg6UULoyKku0BdX39FHR3xwIA3n77u5DlKHsADqip6AAwadJRuKPtzNq7V4xaTZ0KdHQEpt00cjAIjwzaZUS102gCKSUFWLFC1NG4666APz0ANdC/eFGMiCt6e4FPP80CAIwZ04GpU/fZ7+OUMhVHwomIwphzOu5ge8z371e3Z892f4y3nvrsbPU4BuEUaEo6usFwCenpp90cIQOQkJ5+F+bPP4M9eyQcOACUlgJL+1bDsVjUwHby5MC9h7RFhHJyjqCi4jLIchTOnCnA+PGV+OyzG1wek5p6tm9LwvjxlRgzxorOzhiHY7RB+F//KtZ5Pn0a+OAD1xF+Im+0QXi6+1WjaAR5/33g/HkgOTk4z68dba+vV6e3lZer9QmuuWYs5s79iFPK3GAQTkQUpkymEg9zx54ZcC+yNgh3NxKu8JQGnpWlbg9FOjqNHF1d6gj2xInl9jRuVzIslhp8+9vHsGePWHP7lVfUIHznTnWd8QkTalBWdkVA3kPaIkKTJqlD9lVVM1BVNQNWq2vlo+TkBs3vXIv//d8YvPSSmAryP/8jjtG+j7Tvzz17GISTf5QgPDo6cBkgFLkkKXgBOOAYhNfVqUH4J5rs82uukTilzAOmoxMRhSFlvWFP6bgmU8mAnlcpyqbTOS615Kv0dHWuKkfCKZCOHVPTyidPPuz9YADXXXcE8fFi+6231HXvX3hBPWbGjB8E7D2kXWJIO7+7unoGSku/Yr99551PIiqqBwCwcuVoh6XTbr9dLMF2++3q8ypBuM3mOF1k716/mkdkD8JTU4EoXuFTkDmPhCscg/Cha0+k4VuUiCjMaNcbdnMvAKCy8uG+tYnFMkfXXacWXPPEbAaO9k1LLShQlybzh06nfvEyCKdA0lZG1440ezJuXCpWrxbbFy4A//ynSIFcv17sS0howaJFb7t5pON7yFfaJYYmTVKD8IMHr8aePcsAAEZjDb75zR9j3bpZeOGFuZgw4Sm36ZfaaR1KEH7ypNqRAIglzHqHX0FgCpLeXrU6OueD01BwF4T39IjpQYCYlz6Qzv6RgkE4EVGYUQpAeSbDbK5BW9t2fPSRSGv9+GPgu9/1/rzl5eILEvCeit4fJSX93DkR2BMFgrYoW15eE1zX0lVIMBiykZCwGF/9qrr3lVeAv/0NsFrF7euvX+d2bVpBfQ/5QylcOH68hLg4sVxfRcVlsNnEPO8lS/7RV7jtGPLy9nv8HSkp6rq9ShCuTUUHRMfCyZN+NY9GsPPnRTYFwCCchoa7IHz/frWo5NKlzMjwhn8aIqIwoy0A1d9xL72k3v7wQ6Cy0vPxvhRl84V2FK+ubuDPQ6SlDcKvu+7Ovi3nQNxxeZurr1bPx40bxbrhihtv/N9+f6ev7zUto3EVFi6sRn5+u8t91177uk+/Q5LUzixPQTgg5oUT+YKV0WmojdcsoqIE4f/4h7rv2muHtj2RhkE4EVGY0RaA8qa7Owtva7JtZRn48589H+9rUbb+sDgbBYOSjp6YCMyYscLrUnlKUbWoKHX5HZtNDUQWL25Fdnb/w8i+vtecSZIO99/fiaioHsTEmDF9+i489NB3MG2a60RuT79D6Tzo6BD/9u1zPYbzwkcuWbahtbUUTU2vo7W1tN+pEwzCaahlaD7a6utFZpwyMKDXA7fdFpJmRQxWRyciCjNKASizuQ7u54VLMBiysGnTlbh0yfGev/4V+NnPgLg410cpRdmAwY2Ea4NwzgunQDh/Xh1JmTFDjBR7WypP64EHRBp6Q9+As14P/Oxn8T69hxISFg+4zffem48pU6bBYqmFXu9uXob33+E8L1zpJBs7Vl1zlyPhI9NAVsZgEE5DzWAQ1ddbWsTn97vvAs3N4r5Vq8S0G/KMI+FERGFGWwDKWzruyy+rH+Hz54uf7e3Aq6+6Pmdvr1p5eeLEwS1fw7XCKdAqKtRtbSEfZam8tLQ7kJi4xO36sllZwJkzwNmzojhhczOwZIlv76HBrFcrSToUFv6mb965/79D+z769FPREQEAV14p3qOACMxtvteOo2FgoCtjMAinUFDmhdfXA3/5i7r/3/4tNO2JJAzCiYjCkFIAylM6bnv7KuzYIfZNnw48/7x6jLsg/NQp4OJFsT2YVHSA6egUeNoCZBkZ+3xKv9WKiRFB7cSJNvT0iBTe6OgkTJ/+j35T2gejv/ept9+hDcLfe0/dnjNH7VS7eBE4cWLQzaQI4c/KGM4YhFMoKEG42Qx89JHYnjwZWLIkZE2KGExHJyIKU97Scf/wB/W4e+4B5s4Fpk0Djh8HysrEiPi4ceoxBw6oI3WDSUUHmI5OgXfoUAWAfABAdPR/4eDBD/pNv3XmKYV3ypTfISbG6DWlfTB8TZt3pg3C339f3Z4zR6SkK0utffSRWFKQhj9/VsZITFzicA+DcAqFKVNc9913H6ui+4J/IiKiMOYuHbe3F3j5ZXF/VBTsyzRdf734abOJJcu0tEH4YEfCMzLEeuGAYxDubyEhIkAEzwcOqFUDx48XJf77S791fg5PKbxHj34FPT3nvaa0D5YvafPOtEG41oIFwIoV6u3f/U5dds1ffE9GFn9WxnDGIJxC4dFHxeeV0Shu5+YC3/pWaNsUKRiEExFFmK1bbThzRmwvXdqCjAxxYf2FL6jHbNzo+JhDhwI3Eq7TqVVRlXR0k6kEZWU5OHhwKY4duxMHDy5FWVmOTwEUjVxK+m1dXS4AICrKhvT0KuVeAJ7Tb52fYyApvKHkLgi/+WYgJwcoKlLfz9XVwOuuK5/1i+/JyONrtX53xylBeFSUKJZFNBQmTQI++AA4d06s8nDiBM8/XzEIJyKKICZTCZ56Sr2IvuKKB+wX1ldfLaqVAsC//iWWLFMoI+FJSZ5H4PyhpKSfOwfU1r4zoEJCNLLJsg21tX9Ad3ctamvzAACpqWf7Cp3Zj7Kn33riTwpvOElIcLwtScB//7d6+8c/VreffFIUV/SVyC64A08//TD++tefwWqNAcD3ZLhTVsZwLfSnkGAwZLutuK8E4ampaqYS0VAaO1Z8jpFvGIQTEUUIk6kEe/bcg08+uQEAMGZMG6688l37hXVnZwmuukoce/asmB8OAK2tBjQ1iW/GOXMC8yWpDeR37/4NIm0UkkJLGaU9der76OhIRmdnAgA1Fd2ZtzTdwaTwhpLz+/Duu4HCQvX2okXA4r5Yq6LCsXibN0pmwDvvfAdvvvkIXnnlP/Hqq0pEz/dkOOtvZQyLxYDU1D+6THeQZdEhCjAVnShSMAgnIooAyoX1xx/fju5usQj40qV/h8HQDe2F9fLl6nCZkpJ++rRaoW2wqegKx+Js3mp8hucoJIWO8/xtJRUd8ByEe0vTHUwKb6itXi1+ShLwxBOu9z/yiLq93ce3kJIZsH27WtDutdceR1XV9L5bfE+GM3cV91977Ye49VYTrr/+EnJzb8aPfuT4mLY2wNKXQMIgnCgyMAgnIooAbW3b0dnZiNdee9y+b8WKdZojxIX1FVfsse959lng9GmgsjLBvm+wRdkU2iDcZMryfGCfcBuFpNBwN3/bMQg/6fQIz+m3isGk8Iba//wP8P3vA5s2qWuDa82cqW77uhygxdKAtrYUlJdfYd/X06PHb3/7F/T2Sg7HUXgyGlehuLgaRUVbkJJSgv/93yfR1qZOtH3mGaCnRz2eRdmIIg+DcCKiCGCxNGDz5q+ioWEyAGD+/E0oKPjc5bjJk09het+A14kTwOzZ0Xj9dXV9o0CNhGvT0X0Jwgc6CvmrXwHXXAPs39//sRT+3M3f9jwSLgLG3Ny1XquN95fC68tzhEpOjqh+ft117u8fr1l+3NcgXK/PQFnZjejtdXy95eVXYOvW1Q7HUfhSKu7v2XMrZNnxvO7qAo4cUW8zCCeKPAzCiYgiQFRUpmZeJ3D33W5yVwEYDBlYvx6YOlXc7u5WL94KCoD8/MC0RzsSfv58AYIxCrlnD/D448CWLY4FqyhyuRt9VYqyAY5BuMGQhcLCt3xaJ9xdCq+/zxGODAY1qPI1CE9IWIxdu263377jjl/Zt48eXYhwzgwYabq7HQtouvPBB+r2arUPBWVl6jaDcKLIwyCciCgCvPfeYtTXixHDuXM/wsyZnzodoV5Y5+cDn38O3N53HZ6ZeRG/+Y0Nn34auKq52iC8s/N6exuc2wQMfBRy7Vp1+8QJvx9OYcjd6KsyEi5JvcjMPA0AmDLlaRQXV/kVPGtTeAsKXkNR0Ra/nyMcKVknDQ2OKciedHfrsGePGFpPTGzCrbf+0X5fTc00AOGbGTBSyLIN69cfRFJSDy67rB1ms/sieRaLWOkCECtbPPywet+uXeo2g3CiyMMgnIgozJ0/D/zHf6gf1/fc8zOnI1yD3fh4sbawyWTFn/70MR5+uNdlSaTByMgQ69ECgMmU6dMo5IEDNtx5ZwP+/vctaG0t9Vqdub4e+Pvf1dvV1f2PGFH4czd/W+lcSk2tgV5vgcGQjaysBwcUJCopvGlpdyAxccmwCDSVILy3V7wv+vPxx0BXlyiWuGjRJ0hJqcPo0R0AgJqaGRGdGTAcKCsD/O53Z3DpUjT27BmHP/3p6zh37k20tpaiqel1++fjjh3AhQvicTfcAMyfD+j14rZ2JLyxUd1mEE4UGbyVtCUiojDw+ONAc7PYvvnmWixYUAWzWb3fYMhCbu5atxfW48YFZ93O6GgRiNfViTRZo3EVUlJWoq1tOyyWBuj1GUhIWGwPgg4e/BDFxUtgNmfgww91WL8+HbGx45Gb+4zbdv/5z46jfh0dogJwYmLgXwsNHWX+dnn5agASOjoS0NEhCk5lZopUdI7SOtLWX6ipASZM8HysLNvwwQf1AMSD7r13NWbPzkBenhUHDwINDdkYO9bLE1BQKSsDyLKMI0fUwnk7dlyGuXO/7HCswZCFN9/8BICYrnHjjWJ6wty5IgA/cQJoaQGSk0UBToW7An9EFH6COhL+5JNPYsGCBRg7dixSU1Nxyy234LiycK0XW7duxbx58zBq1ChMnjwZzz33XDCbSUQUtnbtAl54QWzHxQF//nNW2KTcKsFBU5NIm/Q0CtnQ8DbuvnsMzOZYAEBbWypaWjLs65ubTCUOz3vpEuDuY7+6OnivhYaOdv726dNq+e8JExo5SuuGcxDuiTLCundvuX1fdPTl6Ok5j5kzRUeHLEuodL8KHAWZdmWAmpqp6OhIsd+3e/cNLsebzXX44AOx5KROB1zfN+unuBiax4mfJ/sWFYiKAiZNCkbriSjQghqEb926FQ888ADKysqwefNm9PT0YPny5ejs7PT4mKqqKqxYsQKLFy/G/v378aMf/Qjf+973sH79+mA2lYgo7HR3A9/8pnr7F78Q1ZLDJeVWOy/cU5qsLNvwk59U4dChqxz2i3nA6vrm2tT0vXvFCA+gprwDQFVVIFpN4cBoXIWsrGr87nf/su+77ro7GIC74UsQrl17XZn3PWZMO8aMOYDy8tXIylID84qKYLaWPNGuDKBdPg4QUzJqa3Md9p04Mdv+f3nFFTKSksR+bRBeViam6ShB+MSJaro6EYW3oKajb9y40eH2iy++iNTUVOzduxdXXXWV28c899xzmDBhAtb2VeQpKCjAnj178NRTT+G2225zOd5sNsOsycvs6BDznqxWK6xWa4BeSXAo7Qv3dlL44Dkzsvz4x1E4dkwE2HPn9uJb37LB3//6YJ4zmZlRAET7qqp6MH6866TttratePPNr7vsr6vLw+zZ26Csb97SsgXjxl0NADh+XILy9TRvXi8+/1xE4qdO2WC19gb8dZBqqD5j2tqA5cujUVMzCgAwc6aMO++0wWr1XCdgpEpPV98PZ864vgdk2YaTJ78H8V4ahaYmkY+cnX0ckiQDkBAX93sAzwMAjh4N7PuI30u+uXRJ7UFxDsIBoKxsBVav/r399t///qh9++abK2C1iiB9/nwAiAEA7NrVi/p6Gzo6xO3c3N6IeA/xnCF/Rco540/7hnROeHt7OwAgSenOc2PXrl1Yvny5w77rr78e69atg9VqRUxMjMN9Tz75JJ54wnWpnk2bNmH06NEBaHXwbd68OdRNoAjDc2b4O3o0CU8/vQgAEB1tw9e/vhWbNl0Y8PMF45y5cGEKgBkAgPffP4COjjo3x+zHhQuuiyBr14YGgM8++xBWq8iS+te/8gGIEaAJEyrx+edivbWtW89g6tTDAXwF5EmwP2NefLEQFRXiHEhPv4g1a3Zg+3ZzP48amUymWADiumjPnnPYsOEzh/t1usOIixPvvbq6XMiy6LTKzlam/8nIyFBXU/jkk3oUFe0LeDv5veSdTncGcXFi+8iRK13u/+yzG+xBeGPjRJSWijniCQnnMGXKS9iwQQTusgwkJl6P1tZR+PRTG15+uQyAWG4uJqYaGzZEzmckzxnyV7ifM11dXT4fO2RBuCzLWLNmDRYtWoQZM2Z4PK6xsRFpTqUd09LS0NPTg+bmZmRkOC5v8vjjj2PNmjX22x0dHcjOzsby5csRHx8f2BcRYFarFZs3b8ayZctcOheI3OE5MzJ0dgKPPBINWRYV1X72M+D++we2pm8wz5nOTgkvvii2U1LmYMWKIpdjPvhAzVm/4op38emnKwG4BuGXXXaDfST8jTfU9Pr77psMdTZSDlasyAYFz1B8xjQ2AnfcIS4/Ro2SUVpqwOTJ1wbldw0HPT3At78to7dXQk9PGlasWOFwv8nUYV/CT0lfBrRBOJCVdRKSJEOWJXR2jseKFekBax+/l3wjy9djz57n0Nx8CWfOTAcA5Od/hpaWDJhM2ThwYAm6u2MxatQlvPnm99HbK94jt976ByxevMz++QgAV12lw7vvAl1dMWhuVkfVr7lmYkR8RvKcIX9FyjmjZGT7YsiC8O9+97s4dOgQduzY0e+xklMpX7lvXRrn/QBgMBhgMBhc9sfExIT1f5JWJLWVwgPPmeHtP/8TOHVKbC9cCDz2mA46Lwt8y7LNY1VyRTDOmZwcdbuhQYeYGNc2NjTMsW/Pn78Ju3evgM0WownCJRgMWUhOXmpvs3bu91VXRUOvF4Xfzp6NQkwMV9YcCsH8jHn6aVF8DwDuv1/CtGn8LHNH+75OS1uFhgYDamtd3wOxsWrQ5SkI1+vNmDChG2fOxOL48ShER0cFfNUEfi/1JwZ5eb/Htm3r7HtmzNiJ7u7ReP/9b8NqHYXdu1dg9uwt2LDhPgDAqFGd+PKX30Vy8k8dPtOvvBJ4912xre20zM93/zkcrnjOkL/C/Zzxp21DEoQ/+OCDeO+997Bt2zZkaSv5uJGeno5G7YKHAM6dO4fo6GgkJycHs5lERCH3ySfAH/8otmNjgZdeEpVxPTGZSlBZ+ZC94A+gLFnmfumvQNIWjKqtdX/M8eNqwDBpUjkyMqpQWzu1L21WgiS5LkmlLLczfjwwerQoNnTypLpWeDCWXKOh0dAAPPus2I6NBX74w9C2J5S8dZ45v68TEz9FQ8NCNDUBZrNYqkqhrL1uNtfh7Fl3Qbjo6CooGIUzZ8S6042NYolBGlpG4yo0NU233y4s/BRxcW14//1vAwDef/9bOHs2H93dYwAAN9zwIubN+6lLp6q2OJu2KGZeXvDaTkSBFdQhBVmW8d3vfhclJSX45JNPMMmHdRMWLlzoku+/adMmzJ8/P6x7PoiIAuFRtRYPfvUrYOpUz8dqKyJreVr6K9DS09Xq5Z6qNmsrMefltWP8eFHGt7s7DhcvznVZkurCBcBkEttTpoifyoj7hQvA+fMBfAE05F54QVT9B4DvfEecQyORspzYwYNLcezYnTh4cCnKynJgMpW4fV8bjeob7NAhx6K3ytrrgDoSLkm9yMo6CUD0WOXmrkV+vtp75cNqsRQkBw7k27dvueUufOMbP8bEiRcBAHv2LMc//vEIACAqyoYf/SjXbWfqvHmunbM6HZcnI4okQQ3CH3jgAbz66qt47bXXMHbsWDQ2NqKxsRGXlDw0iDndd999t/32/fffjzNnzmDNmjU4duwY/vrXv2LdunV4VHtlSkQUhmTZhtbWUjQ1vY7W1lKHZbd8cfEicOCA2C4sBL77Xe+/S1lz1s29AFyX/gq0mBg1iPI0Eq4E4QkJwA037EFRkTpvfNy43S4XmEoaPgBMnix+atPeuVZ4ZNu+Xd1+8MHQtSOUvHee3Ybjx78F5/d1aqoahH/++TqX97XRuArTp7+F2tr8vuPPwmDohsGQZe/omqYOknOZshCxWoHP+urqTZwIzJ59C5KTl+A734mzH3PxYiIA4EtfkjB//hfcPs/o0UCRUwmOnBzxmUxEkSGoQfizzz6L9vZ2LFmyBBkZGfZ/f//73+3HNDQ04OzZs/bbkyZNwoYNG1BaWorZs2fj5z//OX7/+9+7XZ6MiChcKCNb+/df4zKy5avDh0W6NSDmgkd5+YTWrjnrnlj6q6Oj/zocg6GkpDc1iXnbWl1dwJkzYjs/H4iK0mHGDHVKUmWla569kooOuI6EAwzCI5nNpgYgmZkiCBlpfOk86+lpcblHG4TX1RnQ1rbd5RhZXoWLF8cBAAoKDCgq2oLi4ip7R1e+OgDLkfAQOXhQfC4CwBWaVcq+/nXXAPoHP/B+ib5woePt3Fz3xxFReAp6Orq7f1//+tftx7z00ksoLS11eNzVV1+Nffv2wWw2o6qqCvfff38wm0lENCjKyNZrr92KG2+8gL/+9WcA/E8LP3hQ3XYe5XBmsTT49Jy+HjdQSpkPWXacmwgAx4+ro3WTJjVAlm0OF4qVla7Ppx0JZxA+vFRUiCkFgOOc1pGk/84z97Tp6OfOZbt9X2sD65kzM5CYuMRhLrGSWQI4vo8Gm8FDvvtUXSkOV2pWKUtNBbRjTddcI1LOvXF+D3E+OFFkYZlZIqJB0I5slZR8D93dY/D66z9Ed3cs/E0L1wbh2dkfeb0g1ut9q6rk63EDpa21qU1JN5lK8M9/fs9+Oy7uGZSV5SAp6V/2fe6CcO1IuBI0aOc5VlX1MmCIULt3q9uXXx66doTSQDvFjEb1zXXuXLbb97U2xVybeq7IzFTnESsZKt7mplPgaYNw7Ug4IOqBxMYCej3wxBP9PxeDcKLIxiCciGgQtCNbra1pAICeHj3Ky5VcQZEW7i591NmePWoaqk53m9cLYqUislJ4yZUEgyEb8fGL/Hk5ftNWSFdG15TMgNOnjfb7JkyogNlchwsXboJO1wtgYCPh+/d/woAhQu3a1WvfLizcPyI7UAbaKaZNRz9/PhcJCYsBOI5iHzyoHuMuCI+OVjvNzpwJfWHHkWjnTvFzzBhg5kzH++bNA44eBY4dAxb58LE9ZQqQkqLeZhBOFFkYhBMRDYIysmWxGHDp0lj7/oMHr3Z7nCdNTSU4ckSsO5SeXoW4uA4Ani+ItRWRXQNxtSKy89I2gTZdXW0Hu3c7ZgacPatOQp0woQKAjOjoHqSnizogJ0+qc+AVShA+diygrEqZlgYYDCJga2hIczieAUNkMJlKUFoqhmqjonoQFbVoRHag+NJ5Fh2d3He/ekxi4jlERYn3wMWLCyBJOpdR7H371FQad0E4oM7DP38eOHTocYSysONIU1OjZgsVF4tOEWc5OY7TBryRJMd54do5/0QU/hiEExENgjKy1d6e4rDfOQj3NgImyzZs3fo0urtFhdzc3APaewG4vyA2GlehsPAtGAzjHfZrKyIH25VXqgXktm51zAxQgnCdzorMTGWIW8b48ccAiGrwjY3qc/X0qGmyU6ao64FLkg3JyeI5TSZN/nvf8wEMGMKZyVSCPXvuwenTIjKcPPkwYmO7RmQHii+dZ9OmveDyvtbpbEhKagYANDUluh3FVpYnGzWqE3q9+7/phAnQHO+tg873DB7yjbdU9IH6r/8S9UMeeYTLkxFFGjf9cERE5CtlZMs5CD927HJYLAbo9RYYDFn29FFnsmxDbe0fcOyYOsI7ZcpB56PsF8SJiUsc7jEaVyElZSXa2rbDYmmAXp+BhITFQR8BV8THA3PmAHv3iurujY0ipd5mi0JtrVjkPDPzFKKje+yPmTChAp99dgMAMY81o69/4uxZUUEbUFPRARHYp6RIqK+fiIsXE3Hp0hjExnZqWuH570OhpWRGHD8+D7294pwsKFAmh8sAJFRWPoyUlJVDds6GmtJ5Vln5kEMQbTBkITd3rb3zzPl9nZOTiuZmoKlJRkXFGmhHsa3WGDQ0iCgsK+sETp9+GKmprn9TbUX6pqaJyMk55rWtwS7sOJIoqeiAY1G2wZg/X13WkogiC4NwIqJBUEa2Pv30WYf9VusoHD1ajNmzt3lMCzeZSuwX4qdO/cy+3zUIFzxdEEuSLqTB59VXiyAcAPbunYasLODw4cUwm0cDcH09EyaoF/5HjwJLl4ptd2uEA+J1G43qfGKTaTwmTDjh0g4GDOFHyYw4duxO+77p08s0R4zMDhRfOs+c39eZmeJnb6+ExkYrjGrJBdTXT0Fvr7iky84+7vFv6hyE9yfYhR1Hkl27xE9JGlhhQlm2hayzlYgCj0E4EdEgGY2rEBfnnCYNHDlyM+6663tu08KVdFJlNOvUKXVNMk9BeLheEF99NfC734ntPXumY8qULGzbttp+/5VXvqs5WkJenlqA7uhR9Z4yTWymnWuu12fAaFRLazc3uw/Cw/XvM5IpHSNqoULtSLjrcSOJv51n4zWzTlpaMmE0qmsCKqnogFJ/wf3fVBuENzfPgEiBdzcvXPKawUP+6e0FysvFdm4ukJDg3+O1HbYKkTnxzJBMOyLyhJ1DA8c54UREAWCxXOay7/Tp77u9QNIWL1MoQfjo0R1IT692eoSodB6uF8SLF6vzt7dti8Lkyc9g+/ZbAQAxMWYsXPh+35HioKVLv2F/7NGjsr2686ZNrfb9yug4IFL+MzIu2m+7zgsP77/PSKbXZ0CWgcOHRbnn+PgWZGcfd3sceaeMhANAc3Omw33aIFz5+7r7m2qD8M7OlX1boSvsOFKcOQNcuiS2tR2MvmAVewpXXOJwcBiEExEFQHOz675duySYza77tcXLAODixXh7aujkyYcQFaUdmQr/C+LERGDWLLF94ACwb98qNDeLYbv58zdhzJgLANSCcdOmfRGpqeL4Q4dMOHhwKQ4cuBe7d4v09YkTLzoEC5Kkw6xZN9pvOwbh4f/3GckSEhajsXEJOjpEzYQZM3a6nN/sQPGNNghva1NGsYWzZ7VB+AmPf1NtYbbGxuyQF3YcKY5ppt4XFPj+OHcdtpp7AbAoJYUGO4cGj+noREQBYDKp29OnizTr7m7g889d13x1ThOtri60b0+efNjhPudiTeHq6quBgwfFkmNr1qj777orDwUFr7mkqeXlmXDunBHnz6eivT0JlZVzYLWKJdpmzHgDJlOSw2suLCy2b2uD8Ej5+4xUkqRDQ8Nv7bdnztRW22YHij+06ei9vV8D8CSUdHLHkfATyM39m9u/aWwskJoKnDsnRmdDXdhxpNAG4f6MhDt32LoamTUVKLT67xwaeQU3B4Ij4UREAaAdCV+tTofG1q2uxzqniVZVzbBv5+QcsW9PmfI0iourIiLAXLJE3a4QU1IRHQ3ccUc+0tLuQGLiEvuXsSzbkJa2wX782bMF2LfvGvvtOXM+cRndydIMflssX0ZBwWsoKtoSMX+fkezAgbn27Zkzd9i3OeLqH+1IeGtrvsMothKEG40NmD//b17/pkqWSX09YLGoc9Od36cUONraF/6MhPtaK2Ek1lSg0PGnc4g8YxBORBQA2pHw225Tt0tLXY9VljVTRgK1QfikSeVQUnSzsh6MmAviFSvEP61rrgGSklyPbWvbjqysz+y3z5wpwP792iD8Y5cv8NRUEdQDQFNTCgOGCLKjL+4eNUrG6tW/YgfKAGmD8Pp6MYpdXFyN7Ozt9nT/mTPT+/2bKinpsgzUeruOpoDRjoTn5/v+OF9rJVgsTUxJpyHDzqHAYBBORBQAykj4qFHAzJlq6uinnwJWq+OxyrJmfbdQXa0dCRdDJpGQoivLNntRta6uUrz/vg2bN4s1cDMzgf/8T/ePs1gaMHGielVaXr4Qx48vACAyAZKSztmPU+h0ahDCwCFy1NUBVVVi+/LLJaSlXc0OlAFKSgIMYsYG6vsKo0uSDk1N6nyXadOci6y50tZbOHMmkC0kd2RZDcKzs4G4ON8f69xh68mpU99nQSwaMr52DrHgpncMwomIAkAJwlNSRKVwJT27qwvYs8f1eKNxlT2dVBkJT0xsRFraqCCk6NrQ3r4VTU2vo7W1NCAjJp6qohYVlWDHDhF8Oc+FV+j1GfbOBgDYuPFe9PaKgGzOnE8cjtNSUtJNJjHfnsLfdk024mLWXhsUSVI7ourq1P3HNcXmp01DvxiED62mJqCtTWz7WxnducPWGxbEoqHSf+cQC276gkE4EdEgybIahBuN4ufVV6v3u5sXLo5dhcmTq9HWJkqFz5plCHiKbkvL2xg79ls4cmRZwJYQGWxV1ISExUhPj8HYsedd7luw4F/w9AWunRdeXw+KADvUKeAeO2XId0qGTWuruuSVv0H4hAlqJ1xFRRXTmINsoPPBFdoOW+9YLZ2GhvfOIRbc9BWDcCKiQWpvB3p6xHaKmJrpUxAOAEePql9SRUWJAf3SMplKUFFxOySpxWH/YEZMArFkjiTpkJf3DNLTqxz2L1r0Ni6/fCMA91/g2iCcKemR4bO+qf+SBCxcGNq2DAfO88IB/4Jwk6kE7e1q8YZDhz5hGnOQaeeDjx//2YCykZT5/1OmPN3PkSyIRUPDU+cQC276jkE4EdEgaYuyKUF4Xh6Qni62d+xQg3RnR9Ri6Jgxw/0xA6ENliWXjLGBj5gEqiqquKhUq7ZNnnwQP/nJnYiNHe/xC5xBeOSprBQ/J0wA4uND25bhwDkIl2Vg715xOzbWcR1wZ0oGS3Lybvu+urpcpjEH2b59p+zbev0jA85GkiQd9Po0n45lQSwaCkrnUFHRFhbcHAAG4UREg6RdnkxJR5ckdTT84kXg8GHXxwHBC8KDtYRIIKuiPvbYJOTkyLj22hZs2HASl132odcvcAbhkaW1VfwDgMmTQ9uW4UK7Vnh9vejkqKkRt6+8UhQwdEfbKRcX147ExEYAQE1NPpjGHDwmUwn271cn3k+cKHLTB9rxwYJYFG64xOHAMQgnIhokbRCujIQDwIIFvfbtnTsr3F7gaoPwwsLAtSlYS4gE8iJwxgygqkrCRx8lY9q01f1+gTMIjyxVmtkGU6aErh3DiXYkvK4O+Phj9fa113p+nHOn3IQJFQCA1tY0dHQkgmnMgad0fJw5IyaCJyScw7hxSh2MgXV8sCAW0fDBIJyIaJC06ejKSLjJVAK9/g77/k8+2eSSgijLahCenR3YdN1gjZiE8iKQQXhkOaVm4XIkPECcR8I/URcT8BqEO3e2aZcIPHs23+NxNHBtbdtx/nw7zp8Xn7FKx4fK/44PFsQiGj4YhBMRDZLzSLgy93LixM32/adOzXZJQayuBjo6xP2BTEUHghcsh/IiMD0diOr71mIQHv5On1a3ORIeGNqR8NpaNQhPSADmzvX8OOfOtuxsNSDUBuFMYw4ci6UBtbV59ttZWSc8HucPFsQiGh4YhBMRDZI2CE9OVudexse3Ii1NzAesrJyN3r7sdCUFcdMm9XHFxYFtkzZYll0KmQ8uWA7VRWBMjFrs7tQpwMbpq2GtslKdjpGSspfzjQMgM9OGqCjxhn777V609C18sGSJ5/nggGunnONIeAGYxhx4en0Gamun2m9nZZ30eJy/WBCLKPIxCCciGiRtOrrBsNdh7uWUKQcAAF1d8WhomARtCuKGDerjbrwx8O0yGlchP/8NyHKyw/5ABMuhugi87DLx8/x5YMuWoP4qGgSTqQQHDuy03754cRmXwhokk6kEhw7lYNmyvwEALBb1Es5bKjrgmsGiTY1WRsKZxhxYCQmL0dg4z37bdSR8cB0fLIhFFNkYhBMRDZJ2JDw+vs7hvtzcA/btysrZ9u0LF5rw0UdiOy0NmDMnOG1LTr4VFy68gBkzNgc8WA7FReBdd6nbr7wS9F9HA6BMx6itFZP44+JaER/fyqWwBkH5m5rNtfjudx9CRsZph/tnz97s4ZEqbQaL0ViLUaMuAgDOnp3JNOYAk2Ub2tq249y5JfZ9jiPhnL9NNNIxCCciGiTtSHhqapLDfXl5++3bp07Ntm/v2ZOPri6x/YUvqHOdg0OHceOuHhYjJl/8IjBunNhevx7o7Axte8iRUhG6p0eHc+fEotVqwMilsAZCu7wYAMTFdeDHP74LUVE9AICUlFpERX3Tp7+pksEyZ84nmDrVAgBoaJiIsWMZgAeKyVSCsrIcHDy4FCdOiP8TSepFZqZaqZDzt4mIQTgR0SApI+GJiYDRuMhh7qXrSLhIQdy2baZ9/4oVQ9bUiDdqFPClL4ntzk7g3XdD2x5ypCyF1dQ0Eb29orNHG3xwKSz/OS8vBgCFhWX4yU/uRFFRKR555FuwWHz/myoZLDNnig7D3l4JJ91PVyY/aTMWZBn2OeGpqTUwGLqRlfUw528TEQAG4UREg6YE4SkprnMv09LOIC6uFQBw8qTIOc/NXYuNG8XHr04HLFs21C2ObF/7mrrNlPTwIMs2tLaWwmRaDwCor1fXJMvMPO1yPJfC8p2nv9XSpW9i7dqlKC7+0OtxnuSrRdFx7Jjn48g3zhkLHR3JuHgxEYAyH1yCybQeCQmLIzobiYgCg0E4EdEg2GxAe7vYTurLRNfOvZQkdTS8uTkLqalvo6YmE8ePi2OvuEJGYuLQtzuSLVoETJwotjdvBi5cCG17Rjpt+m19/R8BAA0NahDuPH8Z4FJY/vD1b+Xv37SgQN2ucF7CmvzmnLFQU6NWRh8//iSYBUJEWgzCiYgGQRsAKnOVAcfq4Zddpl4cb9hQgr/97VX77cLCX7FQlZ+iotQUfpsN2LMntO0ZybTpt1r19erC4I7p6FwKy1/Oy4u5GtjflCPhgeWciaBdIzw7+4TH44hoZGIQTkQ0CMooOADExzvep8y9vOEG9Wp369YrsHu3Ogl8/vw3WDF6AJSlygBg9+7QtWOkkmUbzp//GMeP/xuU9Fst9+norAg9EM5TXJzuBTCwv2lenrq2+NGjg2sjuWYiaNcIFyPh7o8jopGJQTgR0SBog3DtSLjWsmU2GAyXAAA7dtyK/fuXAhBVjSdPPgSAFaP9dfnl6jaD8KGlpJ8fOnQdenrOuz1GGQnX6axITa0BwIrQg6Gd4qI1mL+pXg9M7YsTjx0DrNZAtHTkcs5Y0I6Ei+XJmAVCRKroUDeAiCiS+RKEWyzbMX9+G3buvAVtban2/ZdfvgGSBGjnCiYmLglia4ePadNE5kFHB/DZZ6FuzcihpJ+7G/1W2GxRqKsTAUh6ejWys/8dRuNtLEg1SEbjKqSkrERb23ZYLA3Q6zMG/TctKlID8OPHgRkzAtjgEUbJWBDvD8k+Eh4V1YOMjGoAzAIhIhVHwomIBsG3ILwBixa97bL/8ss/dDmOfBMVBSxYILbr64HaWu/H0+A5V3/2pKFhMrq7xwAAJk8+DKPxtohfnz5cKFNc0tLuCMjfdNYsdfvgwUE9FUHNWNDrx9s7ojIyqjBmTDqzQIjIAYNwIqJB6OhQtz0F4Xp9BhYufB9RUT32fdHRFsyd+7HLceQ7pqQPLXfrVbtz6pQa2eXlnWH6bRgrKlK3Dx0KXTuGE6NxFTIyqu0dUdOnJ3FdcCJywSCciGgQfBkJT0hYjNTU0Sgq2mbfN3PmdowZo5RW51zBgWAQPrR8zdQ4fVoNwhctWsgR8DDGkfDg2LNHPeeLi5P5HiAiFwzCiYgGwZcgXJkruGjRO/Z9xcUfKPcC4FzBgWCF9KHla6aGNghfvLg4WM2hABg/HkhMFNscCQ8cbZ0K7ecUEZGChdmIiAbBlyAcECmKjz4ahaNH34PFYsVNN70AQFQ3zs1dy1TFAUhPByZMAM6eFWuF9/QA0fxWCxql+rPZXAdP88Kjo5NQW3s9AGDMGGDyZLeHUZiQJJGSXloKNDQAJhNgNIa6VZFPG4QrtSuIiLR4uUJENAi+BuEAMGHCLdi82dZX3fgvAaluPNJddpkIwru6gMpKID+//8fQwDhXf3YMxEVGR2bmi6iuHg0AmDlTFNCj8DZrlgjCATEafu21IW1OyMmybVAV6Ht6RKcgAEycCKSlBamhRBTRGIQTEQ2CNgiPj+//eKW6MQXGpEnqdkMDg/BgU6o/V1Y+5FCkTcnoOHnyZvs+7XxjCl/OxdkGFoTb0N6+FTabKaI7F02mEg/n9jM+ZysdOyY6BQGmohORZwzCiYgGwZ+RcAq89HR1u6kpdO0YSbytV71+vXocg/DIMNjibC0tb2Ps2O/gyJEW+z5/A9dwYDKV9GV5OE61MJvrUF6+2uclxjgfnIh8EdREsW3btuGmm25CZmYmJEnCO++84/X40tJSSJLk8q+ioiKYzSQiGjBfligj38myDa2tpWhqeh2traWQZZvX47VBeGNjkBtHdp7Wq9YW92IQHhkKC9VpA/4WZzOZSlBRcTskqcVhvxK4mkwlAWplcMmyDZWVD8F9rQOxr7Ly4X4/jwAG4UTkm6COhHd2dqKoqAjf+MY3cNttt/n8uOPHjyNek9dpZJUQIgpTyki4wSD+0cANJBVUO9+SQXjoaYO4mTND1w7yXWwsMHUqUFEBlJcDVisQE9P/47SBqyS53AtAQmXlw0hJWRn2qeltbdsdPndcyTCba9DWtr3f6URKEB4VBcydG6gWEtFwE9Qg/IYbbsANN9zg9+NSU1ORkJAQ+AYREQWYEoRzFHxwBpoKypHw8NHTowbhEycC/BqPHEVFIgi3WIATJ8ToeH8CGbiGmsXSEJDjurqAw4fFdmEhEBc32JYR0XAVlnPC58yZg+7ubkyfPh0/+clPsHTpUo/Hms1mmM1m++2OvtxQq9UKq9Ua9LYOhtK+cG8nhQ+eM+GnvT0agIT4eBlWa0+om+MiEs4ZWbbh5MnvwXMqqISTJx/CuHErXEbUkpMBQAzbNTb2wmrtP12UPBvM+bJhg4QLF8Rlxbx5/L+IJIWFUQDEe2vv3h5Mnep+CTqtS5dqHG7v3v0FlJR8D6tW/R6XX77R4bi4uPD9/AEAnc63jEudzuj1vfHZZxJsNvEemD+f7wFPIuF7icJLpJwz/rQvrILwjIwMvPDCC5g3bx7MZjNeeeUVXHvttSgtLcVVV13l9jFPPvkknnjiCZf9mzZtwujRo4Pd5IDYvHlzqJtAEYbnTHiQZaCjQ6kG3YYNG7aFtD3ehPM5o9MdRlxcnZcjZFgstdi06SnYbI45zr29QHT0TejpicKJEx3YsGFrcBs7QgzkfPnVrxYAyAQA5Od/jg0bmJoQKSyWNADFAIB3363CuHFH+32MTnfGYaT3mWf+hIaGyTh+fD7eeisT0dGiU3LfvjOw2TYEo9kBZMPYscmQpBZIEmCz6dDYmIPMzFOQJPFZL8sp2LmzA4Dn1/Luu1MAzAAAjBp1CBs2nBma5keocP5eovAU7udMl7I0gg8kWZb77+4MAEmS8Pbbb+OWW27x63E33XQTJEnCe++95/Z+dyPh2dnZaG5udphXHo6sVis2b96MZcuWIcaXCVg04vGcCS8XLgDJyeL/4ZprerFxY/iNekTCOWMyvYETJ+7u97ipU1+G0Xi7y/5Jk6JRVychPV3G2bPhl40QSQZ6vpw7B+TkRKOnR/w/nD7dg+iw6uYnb2pqgClTxP/3F77Qi/fe6/+zTJZt2LMnFxZLPS5dGo0VKy7a73vyyRUoLt4IvX485s8/GfZzwgFR5b2i4nbIMvDQQ1tx+PBi3Hff47jrrl8DAPLz30By8q1en+Ouu3R4801R5e7zz60Oy7+RKhK+lyi8RMo509HRgZSUFLS3t/cbh4b9V2RxcTFeffVVj/cbDAYY3FRDiomJCev/JK1IaiuFB54z4eHSJXV73LgoxMQEdcGJQQnncyY2Ntvn49y9hvR0oK4OMJkkREXFQBf+1/thz9/z5e9/F3PCAeCeeyTExobnuUbuTZoEJCYCra3AoUO+fpbFIC/v9ygvX42amjyHez7++E4UF29EXt4z0OtHBafRAZae/mXodNEoK/slDh9eDEC8jnvv/T/k5q71aXmyPXvEz9hYYPbsGHZE9SOcv5coPIX7OeNP28L3irHP/v37kZGREepmEBG54BrhgZGQsBgGQxYAlxLLfSQYDNlISFjs9l6lOJvNBrS0uD2EgkiWgXXr1Nvf+Ebo2kIDI0nqknL19UBzs2+PMxpXIT//DdTUzHPYv3PnrZg06e2IWiccEK8nPl5dY6ymphBz51b59DpMJqCqSmzPmwcG4ETkVVCD8IsXL+LAgQM4cOAAAKCqqgoHDhzA2bNnAQCPP/447r5bTUFcu3Yt3nnnHZw8eRLl5eV4/PHHsX79enz3u98NZjOJiAaEQXhgSJIOubnPKLec7wUA5Oau9ZjSymXKQqu0FDjaN4V40SJg2rSQNocGSJs67c964cnJt+LUqTUO+y5dGoOyspUBatnQOnVK/ZwRtSZ8S635/HN1m+uDE1F/ghqE79mzB3PmzMGcOXMAAGvWrMGcOXPwX//1XwCAhoYGe0AOABaLBY8++ihmzZqFxYsXY8eOHfjggw+walVk9aQS0cjAIDxwjMZVKCx8CwbDeIf9BkOWx+XJFFymLLR+/Wt1+zvfCV07aHCUkXDAvyAcAOrrx7rse+21QTYoRCorHW8fOdL/Y2TZhq1bq+23FyzoDWyjiGjYCWqyzJIlS+Ct7ttLL73kcPuxxx7DY489FswmEREFDIPwwDIaVyElZSXa2rbDYmmAXp+BhITF/RZ10gbhTU1BbiQ5OHAA+Ne/xPakScCXvhTS5tAgaEfCDx7077H19aJMuiQBqanifbhxo1h3XK8PYCOHwMmTjrcPHwbuuMPz8SZTCSorH8LWrc8DyAEAxMQsgsn0aMSl4xPR0An7OeFEROGKQXjgSZIOiYlLkJZ2BxITl/hUVZnp6KHzP/+jbj/yCOfBRrLCQiCq76rQn5FwWQbq6kQQPmECsGSJ2G+xAKdPB7aNQ8F5JPzwYc/HmkwlKC9fje7uWhw7JnLQx40zISmpDOXlq2EylQSxpUQUyRiEExENEIPw8MB09KFnswFPPy2qogNASgoLskW62Fhg6lSxXV6uVrvvj8kEdHWJisDTpgH5+ep9FRUBbmSQybLv6eiybENl5UMAZDQ0TEJHRwoAID//M0iSyAKtrHwYshx+S1cSUegxCCciGqCODnWbQXjoMB19aFmtwPLlwJo1IhgHgO9/Hxg9OrTtosGbOVP8NJtdg1FPTpxQiylOnepYmO/48QA2bgg0NQEXLzruq64GLlxwPbatbTvM5loAQGXlbPv+/HylQpsMs7kGbW3bg9JWIopsDMKJiAZIOxIeHx+6dox0TEcfWq++CnzyidiWJOChhwCWcxkeCgvV7fJy3x6jnUM9dWpkj4R76nhwNxpusTTYt1ta1KV009OrPR5HRKRgEE5ENEDt7doKuJ8x7TBE4uOBUaPENoPw4Nu1S91+/XVg7VrOBR8utEG4suxcf5xHwpWUdiDyRsK1QfiUKeq2u3nher0aeLe2quk4SUmNHo8jIlIwCB9BZNmG1tZSNDW9jtbWUgYMRINgMpWgqmqz/XZt7UqUleWwEE8ISJKaks4gPPj27hU/JQm48cbQtoUCa2Aj4WoQPm0aMGYMkJ0tbldUiHnWkUI7qq9dHdfdSHhCwmIYDFkAJJw/rwbhiYnKnBgJBkM2EhIWB6WtRBTZGISPECZTCcrKcnDw4FIcO3YnDh5cyoCBaICUirgXLqhr74wZ0w6zuY4VcUNESUlvaRFzlik4zGZ1VLCgAIiLC217KLByc4EYUWPN7yDcYJDtwbeSkt7aCjQ3B7iRQaQdCb/1VnXb3Ui4JOmQm/sMAKC1VZ0TI0bCxd8kN3etTys8ENHIwyB8BFACBqWAiIIBA5H/tBVxOztFNTadzgqD4RIAVsQNFW1xtnPnQteO4e7wYbWTY9680LaFAi8mRi2sdvx4/x1aNhtw6pTYnjIF0PXFm9ribJE0L1wJwnU6cX6nporbntLqjcZVKCx8C62tEwAAktSLhAQTDIYsFBa+xXXCicgjBuHDnDZgcHMvAAYMRP7QVsTt7BTV2MaMaYdkz8hkRdxQ4DJlQ2PPHnV7/vzQtYOCZ/p08dNq7b9C+unTgMUiPvymTlWvM7TF2SJlXrgsq+noEycCej2QkyNuNzSILBB3jMZV6OwsAgAkJVkwd+5HKC6uYgBORF4xCA9TgZq/rQ0YPPwmBgxEbnh6D2or3Soj4XFx7S6PZ0XcoaUNwuvqQteO4U6ZDw5wJHy48mdeuLZ42/Tp7oPwSBkJN5nUpcjy8sTPiRPV+/fv/6fb6zFZBhobRUdERsYoJCYuYQo6EfWL9UzDkMlUgsrKhxyCZ4MhC7m5z/jds+prIMCAgQhoawMSEry/B5VKt7KsBuFjxrgG4ayIO7S0lYy1xZUosJSR8KgoYPbskDaFgsQ5CF+92vOx2iC8oEANwiMxHV076p+bK34ajScAiHLvn376NLq7t7hcj7W3AxaLOF7bGUhE5A1HwsNMoOdv+xoIMGCgke5//gdITARWrz7r9T1otYr5fhZLLHp6RGG20aM7NEeyIm4oKCNXAIPwYOnuVqtET58uqmDT8DPQkXBtEJ6ZacOYMWLE+NixroiY8qb93MjNFddj0dF/sO9rahLD4s7XY9rpLwzCichXDMLDSDDmb2uX0HCPAQMRALz0kvi5fv0EXLwY7+YI8R48deoRTJnytH0UHNCOhLMibqgwCA++Q4eAnh6xzVT04Ss3V8yHBnwPwqOiZPv64CZTCXbvzkFm5gEAQHW1Adu2TQ37IrCOI+Hieiwtrdq+TwnCna/HmprUx6WpRdKJiLxiEB5GgjF/W7uEhmsgzoCBSNGgmZFRWTnbw1HiPRgTkwKj8WX73vj4FgBgRdwQSk4WmQwAg/Bg0c4HZ1G24Ss6Wk0nP3FCTbV21tsLHDsmttPTOzFqlGM238SJx/qO06GiIjHsV2PRBuGpqXtgNtciNfWsfZ8ahAPa6zGOhBPRQDAIDxFZtqG9fStiYrahvX0rZNkWtPnbyhIaBsN4h/0MGIiE7m6xnq3ixIm5Xo8X78Fl9ts5OQtRVLSFFXFDTBkNr6kBLl0KbVuGI22QMnNm6NpBwaekpPf0eO7UOnNGfZ9lZV1wyeYrKNhtP7a8fCGA8F6NRXmdUVFAeno1ACA9/Yz9fscgXLBYGjgSTkQDwsJsIaAt+jR6NHDkyO9gMGQhI+PffHr8QOZvG42rkJKyEm1t22GxNECvz0BCwmKOgBMBDhdRAHDypPcgXK/PQEuLenvChAIkJhYEoWXkj7w84LPPxPapU8CMGaFtz3CjrTqflRW6dlDwFWg+zioqHOeJK7TzwbOzL6Cjo9whm2/GjJ327SNHrsSqVX+0jx4nJi4JfKMHQZbVTqYJE4CxY0U0HRfXjjFj2tHZOQ5NTRNcHqfXZ3AknIgGhCPhQ8xb4bXq6v+H6OhkBGv+tiTpkJi4BGlpd3AJDSKNBqfkEs9BuPoe1AbhyclBaxr5gfPCg0eWbTh7ts1+OyMjPEczKTC0QbiScu5MG4RnZV1wydKbMuUQRo26CEAE4YpwXI2lpUVUOQfE54i2nk5amhgNN5my0durXJ+p3wUcCSeigWAQPoT6L7ymDb45f5toqGhHMgCgpmYaLl1yLv3s+B48f169JykpuO0j3zAI940s29DaWoqmptfdrnvszGQqQVlZDs6cET1PY8eex8GDOWE9v5cGx3kk3B1tcJ6dfcElS0+ns2H69DIAIoA9d06kT4TjaizOldG19XSUINxqNeD8+XQ4fxdwJJyIBoJB+BDypfBaT08LJk78KedvEw0h55Hw3l4damquddjn/B7kSHj4UaozA6KgFLlSAuqDB5fi2LE7cfDgUpSVeQ6oleyt7u5amEzieyk5uX7Ay2ZSZMjLE3OjAV9Hwi8iPn6Ry2oshYWf2rePHFkUtquxuF8jXNTTycxUP+ybmia6fBcoI+FRUfwuICLfcU74EPI1BWv06DwUF1dz/jbREHEeCQcAi+VtFBVt8/ge5Eh4+JBlG9ratmPcuGYAqwFwJNwdJaB2zsZSAurCwreQkHCTfb82e+vChURYraMAACkpdVCytyorH0ZKykp+Pw0zBgMwebIITisqRCX0KM2wjSyrQXhOjoxRo2z20WNxjkkAZJd54Q8++KWwPFe0Qbg2o8ZoXIUFC3qxfr24bTCsQ3HxNIfXoHx/pKYCuvB7aUQUpjgSPoR8TcHS6zM4f5toCDmPhAPA/v1RXt+DHAkPD9qR3bq6LyEh4RwA4PhxlkfX6n86lGvlam32VnOzmp2VklJvf5y/y2ZS5FBS0ru6gFqnJL76euDCBbGdn6+eU86rsUyfXgZJ6gUAVFZ+NSyz+WTZhvJydWL3lCmO0zNyctRL5fPnpzt8F/T2AufERw5T0YnILwzCh5C20Id7gyu8RkQD4y4I37fP+2MYhIeeu0KX48eLIfCmplhUVb0bqqaFHV+mQ5nNNejo2GHfo83eam7OtG+LkXC4PY6Gj/x8dds5Jf3UKXV76lTHjh2jcRWKi6tRVLQFCxY8h+nTuwAA5eUJ9sA9XCideOXlYt63JPXi3LlpDtMsJmpWJjtzxvHxra2A1Sq2WZSNiPzBIHwIaQt9sPAaUfhQ0gmjotQLzyNHALPZ82OUdPRRo4DY2OC2j1x5GtnNylLz0LdtezZs1yQear4GytrjtNlb2pHw5OR6h8eEY6EtGjxvFdK1QfikSa6P1WbzLV4cB0CMGv/rX5/4VAxwKGg78erqxETw1NSzAE471DvwFoSzKBsRDRSD8CHmnKqlYOE1otBRRsJTU4EFC8R2T48IxD1RRsI5Ch4ankZ2tUF4VdVY1Nb+ISwu+EPNn+lQCm32VkuLu5FwZm8NZ94qpJ8+rW5PmuRuioNq5szP7dsffFDabzHAoaDtxGtvT8KFC6Kwx/jxlXCenpGWBuj14nHOQTiXJyOigWIQHgJKqtaMGZvR1bUGM2ZsRnFxFQNwohDo7VUvpNLTgbmaJcK9paQrI+EsyhYankZ209Kq7dvNzZk4der7Ib/gDwe+ToeKj1+k7tFkbzU3Z9n3iznhzN4a7rylo/sahJtMJUhM/Ir9trJeeKir62s78aqqZtj3iyAc0NY7iIoCsrPF3upqUZROwZFwIhooBuEh8sknOvy//7cUP/vZoxg37mpexBCFSEuLGPUGgIwM34Lwri6gu1tscyQ8NDyN7MbHq2XrldGtUF/wh4OBTodSsrfOn59i35eSUsfsrREgIUENLL2NhOfkuH+8Mtqcnl6FpCTRaXb06ELYbFHwVAxwqGg78davf9i+PW3aHrfHTZsmbl+86DgazpFwIhooBuEh8oMfAH/+sw67d2e4VB0loqHjPJIxe7Z621MQri3KxpHw0PA0sjt2rDYIT+zbCu0Ff7gY6HQoo3EVLl26DgAQFdWLq69+ndlbw5gs29DaWoqmpteRl9cKQFQA1y7LqAThmZmea2Ioo82SBPtSZV1d8aiuLlR+U8iq6yudeMePz8WOHbcCEJ1Ly5a96vY4T52z9ZryCJnqjA0ion4xCA+RlSvV7fff538DUahoK6MnJp7BpUuvY8oUUc334EG18q2W9mKUI+Gh4Wlk191IuMDltADHytUFBa+hqGiLTwF1XZ34G6enR8FoZPbWcKVd8u/YsTuRmPi6/T4lJf3iRXVZrsmTPT+XdrTZeb1wT8cNFaUT729/+6l93113/RJ6vVKN07Hewbx56mMZhBNRIDD6C5FbblG3//lPT3P0iCjYtCPhVutTOHbsTkyY8B4AUR3dOQ0T4PJk4cLdyO7Ysa32bccgXOByWo6VqxMTl/QbUPf0qGm3DDSGL3dL/k2YoH4A7tsnUrWrqtTHeAvCtVNGvAXhoaiuL0k6NDe/il27bgIgqqKvWLFOuReA4/QM7Uj43r3qtjYIz+AiAUTkBwbhITJrFpCTI1Ikt2yR0NYW2vYQjVQnT6ol0JOTRYCWl6cOdZSW7nF5jHYknOnooaWM7E6Z8jQAIC6uzX5fR4frfw6X0/JfY6NajGr8eO/HUmTytOSfWqgM2Lv3U8iyzWE+uLcgXDtlJDf3APT6SwC0QXjoqut3dgJr1lxtv/3Vr/4Cer0FgPvpGdnZaofr3r3q+0EJwseOFf+IiHzFIDxEJAm46aZeAEBPj4QPPwxxg4hGIFm24cSJMvvtpCQxLJ6Xt9++b8eOgy7ziDkSHl4kSYesrAdhMGRBp+vFmDFtAJxHwrmc1kAx5Xb487TknzYIP3s2FW1t2x2C8ClTXB5ip50yEhPTg/z8zwAAjY2T0NwsTqRQVdd//HGgsu+lFRfLePzxO71Oz5AkdTTcZFLfE8pPvi+IyF8MwkPo5pvVHud33gldO4hGqra27TCZ4uy3lQq+2iC8oiLPZR4xC7OFH+0FvzIvXC3MxuW0BqOuTt3mSPjw5GmaRnp6NaKiRCdkbW0eLJYGn0fCAccpI9qU9BMnvuh3dX1twbjW1tIBF1nctQv4wx/Edmws8Le/SUhJ6X96hnNxtgsXxPx4gEE4EfmPQXgIXXmljLFjRfrThg1i/ikRDR2LpQEtLWp6sjISPm5cC9LSxDo0J0/OQXe34wUqC7OFJ+WCf9w4cWV84UISenslLqc1SBwJH/48TdOIibHaPwvr63NhNjfh9Gl1AKG/IBxQp4xcf/3N9n1m87N+vR+dC8YdPLgUZWU5A1p2sETzkF/+Epg61bfHORdn4/uCiAaDQXgIRUcD8+eLi/6LF4EtW0LcIApYTztFBr0+A62tYiHc0aM7EBvbZb9PmRd+6dJY1NY6XmkyHT18GY2rkJU1EwDQ26vDlClbuZzWIHEkfPjztOQfAIwffxIA0Nk5Dvv2/RLl5SKPOzbW97WxJUmHyy+fYb999Kjvl5/uCsYBgNlch/Ly1X4H4mfPqts33+z5OGfOI+HalTUYhBORvxiEh9jll6ulmZmSHlqB7GmnyJCQsNgehCcmNjncN2HCMft2a+t8h/tYmC28JSWpgURv72KmoA+SNghnsDE8eVryD3CcF15TMxX19dkAgIkT2yH5sbjLlCmAXi+2y8t9e4yngnF99wIAKisf9qvDXBuEZ2X5/DBMngyMGye29+5lZXQiGhwG4SE2e/Y5jBolvkjefRfo7Q1te0bqSHCge9opMlitOly8KK6qEhLOOdyXlKQG5U1NjkEc54SHN+3/ibbDhAamVvOx6E/QQpHF3ZJ/gGMQfvjwYlitowAAKSmf+XWNEB0NTJsmtk+eBCyW/h/jqWCcSobZXONSt8MbJQhPTwcMBp8fBkkC5swR23V1wH61dAg7p4jIbwzCQ2zUKBuuvVYE4Y2NwGefBfb5W1qAo0fV5TS8GakjwcHoaafIoA2mExM7He5LTe2xbzc5DpLbHxcXp47sUPjQBuGtrZ6PI9/U1IifcXHqSCANT85L/gGOQfj27eq0jrS0clRV/RTt7VsB+Pb9WFgofvb0iEC8P54Kxg38ODWNfMIEnx7iQDsv/IMP1G0G4UTkLwbhYWDlSnX4+913A/e8ra2i4EhhIfDmm96PHckjwcHoaafI0NysbuflXYeioi32ZWoWL/69/b7GRsfHKaOrnA8enjgSHjiyrI6EZ2XBr/RjikySpINer0721gbhFRWX2bdnztyOs2d/gSNHlmHs2G+hpeXtfp9bCcIB31LSPRWMG+hxdXXqoMRAgnDtvPBj6owlBuFE5DcG4WHgxhtlRPX9TwRyXvj27eoF6Msvez5upI8EB7qnnSKHyaRuG41RSExUl6nJyFBT0LVBuCwzCA93iYnq9nAPwoM9hej8eeDSJbGdnR3Qp6Ywpg1qMzKqIEmOc+VGjerE5Zd/aL8tSS2oqLi93w57f4NwbwXj+n4zDIZsJCQs7v/J4DgffLBBuBbnhBORvxiEhwGjEbjySrFdUSH+DYTzxVh5ufqluW2bSP9yZ6SPBAe6p50ih3Yk3Gh0vE9b9Vebjn7hgvpe4nzw8DRSRsKHYgoR54OPTNrgV683IzW1xuH+4uL3MWrUJfttJUOivw57f4NwbwXjlNu5uWt9Lr442CA8Lw8YM8ZxX0ICMHq0/89FRCMbg/Awccst6vbzz/v/eHcXY1u3qqlhFy6IJTXcGekjwYHuaafIoQ3CU1Ic7xs3Ti3aox0J5/Jk4W8kBOFDNYWoRhN7cSR85HAOfpVlyhRLlvzDzaP677CfPFn9XPW1QrqngnEGQxYKC9/ya/nBM2fUwYmkpCN+Z47odMDs2Y77mIpORAMR1CB827ZtuOmmm5CZmQlJkvCOD7nWW7duxbx58zBq1ChMnjwZzz33XDCbGDa+9jWx5iYAvPCC44V+fzxdjJ0+neNwu7TU/eNH+khwoHvaKTLIsg1nz1bZbycnO16MSZKongt4DsI5Eh6eAlGYLZxXihjKKUQcCR+5tMGvdl64cyq6M28d9gOpkK60pbi42qFuR3FxlV8BuMlUgj17XrPf7uq6Z0CZI9ribACDcCIamKAG4Z2dnSgqKsIf//hHn46vqqrCihUrsHjxYuzfvx8/+tGP8L3vfQ/r168PZjPDgtEIfPObYrurC/DxT+bxYqy3V8LZswUO+7Zscf8cHAkObE87hT8lc+TEifft+5qabnG5GFNS0ltaAKtVbGtHVjkSHp4GOxIe7itFDOUUIm0QzpHwkUcJfufPX2bf55yK7qy/DnslJd1mA06c8L0tkqRzqNvhT8e4MljR0KB+aKelnR1Q5ojzvHAG4UQ0EEENwm+44Qb84he/wKpVvgUwzz33HCZMmIC1a9eioKAA9913H+6991489dRTwWxm2HjkEZHqBAC//z3w4otAWZn35cU8XYw1NU2E2ew4SWnHDjWQ0OJIsBCInnYKf9rMkfZ2NQc9NvaYy8WYMhIuy2oRN46Eh7/BFGaLhJUihnIKEdPRSZJ0uPHGKfbbX/zi/3o60qcOe3/nhQ+WdrCiqUlMBNfrL2HcuGYMJHOEQTgRBUJ0qBugtWvXLixfvtxh3/XXX49169bBarUiJibG5TFmsxlms9l+u6OjAwBgtVphdRdxhhGlfcrP8eOB22/X4f/+LwrnzwP33iuO+/Ofe3Dffe4j8UuXatzur64udNl38SKwe3cPLr/c9bkSEm5Cfv4bOH16DSyWOvt+vX48Jk/+LRISbgr7v2egxMVdad/u6ekF0Ov54CHmfM6Qf2TZhpMnvwflwqutTa3GNm6ciLJPnnwI48atgCTpkJoaBUB0PtXWWmE0AiaTum/cuB5YrV56ycLASDxnoqOBUaOi0d0toaVFhtXqoSqlE+fzw+leAJLD+REqOp2x/4P6jvP3/935fKmp0UHpr09Ls7rtyKXhb9YsYMcOCefPb8XYsR9DdNCr7xNZFlN4Jk16qt/vzWnTJCiXnwcP2rBqlX/fsb294nf5ulxee/tWmM21kGXg3DkRhKelndU8XmSOtLRswbhxV/f7fLm56ueLeC4brNbwuU6IBCPxe4kGJ1LOGX/aF1ZBeGNjI9K0JYkBpKWloaenB83NzchwswbEk08+iSeeeMJl/6ZNmzA6QspVbt682b69cGEc3nzzalgs6n/Niy+akJn5mdvH6nRnEBfnur+6erp9e9asrTh0SHyxPP/8CbS0nHR9AADAAOD30OmOIiqqFb29ibDZpsNk0gHY4O/LoiDSnjPkO53uMOLi1E4mZSQ8OtqCMWNEB57FUotNm56CzTYTHR35AMQExvff34OGhnMoK5sKQEz1qKragw0bmhAJRto5M3r0cnR3x6KhoRsbNmzy6THO54eiqysOv/rVS6iuLsRPf/olnD8vzo/QsWHs2GRIUovbQESWAVlOwc6dHRjoZ7dyvhw/fi2AOMTGWrFzJ78HCOjsfAyxsf+LqCg1LUiWU9DV9U3s3m1Af+dcc/NoACK9/eOPz+Hyy91f37jT0DAGP/7xlYiLs+K//3s74uL672CLidmG0aOBixcTcOnSWABAaupZl+M+++xDWK2dPrUjO/sqnDyZ2NemvdiwYXgWrg22kfa9RIMX7udMV1eXz8eGVRAOAJLTFYXcl4vtvF/x+OOPY82aNfbbHR0dyM7OxvLlyxEfHx+8hgaA1WrF5s2bsWzZModR/uXLZXz+eQ/uu0+HS5cktLamY8WKFW6fQ5avx549z8FiqYe2V/rMGTUIX736DXsQ3tSUjxUr8vpp2U0Dfk0UXJ7OGfKNydThMAdRCcLHjWt2CGbmzp0Io3EFzp6Nwj/6igBPmLAAK1bI+OgjdRbP8uXzUVwc/iPhI/GcyciI7lvjepTHz09nzucHAFgsBnz/+1tw4sR8AEBJyYN44YVYGI2+PWewtLT8GRUVt/fd0p6DEiQJKCj4E5KT/f8s154v0dExaG0VlwkTJ0b7/Hek4W4FZPmn6OjYAYulAVFRRuze3YVly77g02dMby/w6KMyOjslNDd7vr5xZ82aKJw/r8P587E4f/4L+PKX+x+Bbm8fgyNHfmdPRQfcB+GXXXaDTyPhAPCvf0XhZN94xq23zsW8eeH9PRBuRur3Eg1cpJwzSka2L8IqCE9PT0ejtgwxgHPnziE6OhrJHiogGQwGGJT1LjRiYmLC+j9Jy7mteXni31NPAfv3A1VVEnp7Y+DmZQKIQV7e71Fevhra9DAlHV2SenH33V/A888DdXXAzp1RkOUo6PVBf1kURJF0foeT2Fh1UqssA+3tIq1XzA10PC4mJgbjNXX6mpujERMDtLWp+9LSxL5IMNLOGeUr49IlCT09MfbVJ7zRnh+AOEf++79fsQfgAFBdPQOxsZaQ/y3T078MnS4alZUPOcxfNxiykJu7dtC1LGJiYtDREYNLffW3JkyQQv6aKZzEICXlOgBK+uUGvz5jZswAdu8GTp+WcPbsO0hKMiIhYXG/0zw2aZJaNm/W4cEH+58Wkpy8FAZDFs6dm2jfl5amDcIlGAxZSE5e6vM0kx/8ADh0CJg+Hbj88mifU+PJ0Uj7XqLBC/dzxp+2hdU64QsXLnRJM9i0aRPmz58f1n/wYMnPFz9tNqCy0vNxzpW9e3slnDkj0mUnTOjCxIkrsWSJOLarC9izJ4iNJgpj2pUALl2Kg9UqeraU+eDOhYW0s2OU/kEWZosM2uJsvi5T5rxSxMGDV2Hr1i85HNPaOt7nlSKCvcxZsItJcnky+v/t3Xl8VNXdP/DPZJkJkJXsISELgRACBEiABI2AaFDqij5uLdVWrda6UGqtaG21Plb9uYEPVWvdqtTKUwGXB1xQCaCAEPYdAgkhITtZWJNJcn9/nNy5d2burJlJJsnn/Xrxyp07587chJOb+d7zPd/jLSNHKstDfvXVS06tQHDsmHk19e++A1QlgWySi89qj4S7V3w2NVUUu33zTefnphMRqXk1CD9z5gx27tyJnTt3AhBLkO3cuRPl5eLit3DhQvz85z83tb/33ntx/PhxLFiwAAcOHMA777yDt99+Gw8//LA3T9NnyUE4ABw8aL+t+sNYaOhKXLggJoqPHy++zpyptLW1VBlRf6deCUAeBQfkkXDrD2NydXQAqOma+i1X29bpzAM98i3uLFNmuVJESclEqza1tUno7HT8YV1rmbNNm5JRVvYXjwbl3Vm2yRFWRidvqKtbgYiIV0yPjx4dD8DxCgRffmn++OxZEQg7Izp6Ljo7HzA9loNwLkNKRL3Fq0F4cXExJk6ciIkTxQeZBQsWYOLEifjTn/4EAKiqqjIF5ACQmpqK1atXo6ioCBMmTMDTTz+NV199FTfccIM3T9NnZaqW+XYUhAPKh7G6umtN+8Z0TQ2XR8IBBuE0sMmZI+fOKSsIhIXVa34YszcSHh6uLClIvsfdtcLVmUUVFUr9jKFDawEA7e1+qLSu3WbG1jJnbW2VKCv7s0+uPa6FI+HkafJyYWlpu037SkvlIof2lwv74gvr17MMzO2pr88wbU+bNt/tzBFvZ7gQ0cDg1TnhM2bMMBVW0/Lee+9Z7Zs+fTq2b9/uxbPqO9Qj4QcOOH+cet1NOQhPSxMjGSdOABs3ihQu7TnmRP1fdPRcxMUpN6syMn6CvLx7rUYRg4OBIUPEiItlEM5UdN+m/v9xNh1dFh09F1FR16Kpqdm0b86cKCxdKrbLyoDhw7WPlYOM8+cH4+WX30BoaAPuuecR6PVtVm3lkT9fHYnjSDh5WlPTBrS2ViA1VakgLI+EC2K5sKamDYiImGHa29oq0s8B8bvd1CQKvH35JfDCC869t2rMBxMmXO1UnQhLdXUrbNRhWOyTv8NE5Lt8ak44mRs5EvDr+h9yZiRctn+/si0H4TqdkpJ+/jywxfkVQYj6HGdGKhoalIA7KSnFZhqvnJJeUyPqM8iF2WzUiiQfoZ4q4MpIuEyn80dZmYjkw8OB3Fzlz2VpqY2DoAQZy5c/hG+++RlWrHgI//znkzZa2x/5620cCSdPa2sTS3mFhZ1CVJRIKSktHQfL8Rq5nWzDBlHTBgCuvhqYMkVs791r3k/tkYPwmBi4HYBrZbg4SqMnItLCINyHBQWJ4h+ACMLtJBWYUQfh6pR2dUp6UVF3z47IN2nNxdVK+62rU7ajomy/nhyENzaKQFz+PeRIuG9zNx1dduGC8qF95EggJUUJkg8cKLUZNMvBw44dSiGOjz76PQ4dyrHxTsrIn69hEE6eptfHm7bllPTTp4eivn6YzXaAedr5FVeIf7JvvnH8vkYjcPKk2LaVxWKPnOFivhyg6VkAvnszjYh8E4NwHyenpJ8969zdXklSgvCUFJFKK1MXZ+vNIJzzqchbXBmpqFetSmYvCFfPC1dPC+FIuG9TB+HqGy7OOnZMueGSlFSO06eVT/07d66zOZ9br49He3sA9u/PM+3r7AzA88+/i7Y222tDWo78+YKqrlMaPBgIDe3dc6H+Qb0CQWrqHtP+Y8fkeeHmK1TI5CDczw+4/HIgP195zplMwZMnRfo64F4QLme42Oa7N9OIyDcxCPdxrlRIB0Sgfvq02JZT0WUpKTCte1xcrPxB6knOjlISucrVkQp1EB4drXFIF3WFdHWWCUfCfZt65NbZdFU19VJIISHvYujQzabH1dUpNlNQw8MLcPz4bNMKFbLS0nEoKrrJ5vtZjvz5AjkIj4/nMkzkGeoVCEaMUAfh42FrubATJ5RaN1OmiBugaWnKa9qbHiJTzwd3Jwh39iaZL95MIyLfxCDcx7laIV0dJGRlWT+f05UR2dJif+1xb+B8KvImV0cqnE1HV4+Eq4seciTct6kLiak/gDvryBFlOzHxEAYPPoPQUHHnpro6BbZSUHU6f5w8+VfT44IC5bq2b980jXfSHvnrbefPK/UP4n3v/gD1YfIKBKNHV5v27d+fZ3O5MHUq+pVXiq/Dhys1c44dc/ye6muAO0UGnb1J5os304jINzEI93GuVkjXKsqmlqOalrhtm/vn5SrOpyJvc3Wkwtl0dPWoydatyjaDcN8WHKxkK3Q/CBcP4uLKAAB1dUlobw+ArRTUHTuUas833fQidDqRdnToUK7Fu2iP/PmCaiU+YhBOHhcdPRe33fYlIiPFqgE7d16NnBzt5cLUS5PJc8H1eiXbpSdGwtVp9Np882YaEfkuBuE+wtY8aVfT0bWWJ1PLVX0GtBeEnzkD3H03cNddYkSkuzifirzN1ZEKOQgPCbG/XF+GsrQsdu1StpmO7vuSk8XXigpR2d4VWkF4fLz4tN/Z6Y+6OiXfXX0DSJKA778X2+HhEm699a9ITxdzhI4dGw+jMdDU1tbIny+orlaCDQbh5A3+/v6YPVvUSThzJgCbN1vfiDIalcJrUVHmn2HklPSGBqC52epQM90NwtVp9NaBuO/eTCMi38Ug3Ac0NKy0OU86MlKZr+pqOro6lV3m7Ej4H/4AvPUW8PbbwIsvOvd92MP5VORtro5UyEG4vVFwwDwIVwdyHAn3ffKH7Y4OZX6zs+Q54WFhdQgOFp/w5ZFwAKiqSjVtq28AHT6sTHW46CIdIiNnYOrUMACA0WhAYOBGZGZ+iOzstcjL0x758wXqn5e6LgKRJ82erWx/8UWn1WDExo1KnZvCQiUFHVBWjwEcj4Z3NwgHlDR6g8G8krsv30wjIt/FILyXBQRswsGDt9idJy2PhldV2b/bq66MPny4GOGzFBurFGfbvl27ONumTcDrryuP//Y3oLXVhW9KQ3+ZT8XK7r7LlZGKjg5l2SpHQfjQodptOBLu+9Qftl1JST97Vr2cURnk/hMbW2ZqI+aFW6egyqPgAHDxxeKr+ubnkSO5iI29FRERM3x61KymhiPh5H2Fhcr2ypV7rQYjVqw4ZHpeng8uc6U4m/z7r9eLdcLdFR09F3l5ZcjOXtsnbqYRke9iEN6LJKkDgwa9BUfzpDMylEjZ3mi4OkjXSkWX2SvOZjQC99xjviZ5TQ3w4Ye2X88Z/WE+FSu7+z5nRyoqKpQ+7kyAoR4Nl3Ek3Pepg/Djx5VtRzfT1NfFMWPkT+w6Uzo6AFRXiwjAMgW1uFg59qKLxFd1EK5+3pepR8IZhJO3xMUB48Y1AQAOHRqPU6eUCLm1tRKrVinz4dQBO2AehDsqziYH4UlJ5qPp7tDp/BERMaNP3EwjIt8V0NsnMJC1tHwPP78GOy3EPOmUlGMA0gGIIHzqVO3WlvPBJakDTU0b0NZWBb0+HuHhBdDp/JGTA3z2mWi3bRswapRy3HvvAXu6Vg1JShJLgwDAyy8Dd9zh/jI19fX+KC1dhn37XsOZMxE4cyYMQUFnceWV7yI4uAWAb8+nkiu7W94wkTMWmIrmO6Kj5yIq6lrNvi87elRpn57u+DUzMoAffjDfxyDc92mNhNfVrUBJyUNm2UcGQyLS0xebfofV88HHjUtGVtbHKCl5yCwdvaZmjObvvXo5tJEjxdeJE8W1U5J6tiBmd3BOOPUESerAhAlLsWfP/QCA4uJCFBYuBQDU18fh6NEJAIDcXAkxMeYfQJxNR29uFoMOgPup6EREnsYgvBc5O/85NbUC6iDcFvV88OHDt2Hz5us0P2jm5CgfGrdtA269VTnu88+V7Q8/BB55RKSn790LfPstcNllTp2ymRMnOjB6NHDu3DQA5kv0lJePxmOPPYP09EUeD2Jt3YRw53XsV3bXoaRkPqKirvXZmwgDjTxSYYs6CB8xwvHrWY6E+/sDoaFunRr1ILkwGwAcOVKJI0deRGXlIqt2ljfTvvtOeW7MGOXGTnLyD/Dz60Rnpx/q6q5HdLT1XUl5BNnPT6nnERwsimweOADs3i2m99grBugLWB2dekJT0wZMmvQffPCBCMK3bp1tCsK3blUmjE+ffhxAitmxzo6Ee2I+OBGRpzEdvRc5O/95zJgg07a9ZcrUQXhg4P0255knJ68y7VOPyrS3A0VFYjs6Gpg2DXjoIeX5r75y6nTN1NWtwBtvPIJz57SD023b7sDUqZ6fT+XJ1HFWdu9/1OnGzo6Eq4WHX0BTE2sC+Dr1B+79+7fj6acjcOutx/D999datFSm/xiNHfj4Y7F30CDg8svFtk7nj4SES5CZKf5s7t2r06yVIc8lj4sTN2tkclVno1Hc1PQFFRW2b+xWVYkbDAEBzPog72lrq0JW1iYMHiyGqrdunY3OTtH3tmy5wtRuxowjVsfGxACDB4ttBuFE1NcwCO9FoaEXo7MzEo7mSY8bNxlBXXG4vZFwdTr68OH7NVqID5qnT/8aCQlie+dOZW7s1q1KFdJZs8RIzpQpytHOrMWpJqdwV1QoQ4bXXbcECxf+HKNHbwEAVFUZcPy4Z0eP5fe1V+zOFazs3v90dyR88OAy1gToA/z8ViAgQKxDfPDgZHzwwZ9QXZ2K5557D01NltX2xM20zz/fa6pu/pOfiFFstUmTxFetYLqjQ9TQAKxHj31pXvgnnwCXXiqmHGVmiulGluSR8NjY7s+hJbJFr49HYKAREyeK9JPm5mgcOTIJHR3+KC4Wk8CDgxsxdare6lidTklJLyvTLjQLMAgnIt/EP629SKfzx/nzd8mPLJ8FIOZJ+/v7m4KAo0fFhz9L6sro0dEnTPOsNVqitfUEMjIaAQBNTcqHRnktTkBJO09KUkZzXAnC1Snc6qV8rrnmDRQWfoD8/P8z7dvgwQFkx6njYrTLlRHM/lLZnRRyEO7v79yHspCQlfDzazc9Dg0VtRzcvbFD3idJHTh27CHExIjCFo2NyjpbZ8+G4513ntY8bvlyJeq++Wbr5+0t81hbqwQCCQnmz8nBOyBS0nvL998D118PrF2r7Hv4YfNMp44OZZk1pqKTN8lFW6dMUTrgli1X4MCBKThzJgIAMGVKEQIC2jX/bqemir/rra3AgQMbNdswCCciX8QgvJe1t+dj9OiPHFZzlpcpa2+3rmgOiEC6UcTVSE7WGgU3N2JEnWlbHl3XCsIDAkQgDrgWhKtTuGtqUkz75cJG48evN+3zZBDujdTx/lDZvb/pzlJxkqT8DqWkAIGBjt+rvPxBJCQo+Y5hYXJBRfdu7JD3ydeC2Njjms+vWnU3jh4dZ7bPaAzEqlXiU3pwMDBnjvVx6mB6+3bz5+xVFFevWHGoa9Wl3ljy8D//UbblOeuSBNxyi3JzqrnZYEoJZhBO3iQvLTl5shKEb9062ywVPTf3M+zadZlV5lFd3QoMGvSO6fF33z2imZ3EIJyIfBGDcB8QGXm9w3UnMzOV9lop6er54CkpjoPw0aOVgPLgQbEu7qZN4nF6unlBIzndq7HR/jrlaurUbHkkPCysDoMGne16/y2mNFFPBuHdTR2vqADeeUcZBQJcW3+avK+78/3r6oAzZ8S2M6nocjCXlKSsVxsSckrVgjUBfJH8Ox4To71AeGenP/7+9/+n2qPDrl23oblZ3JW55hplvqnahAnKKhGWI+HyfHDAeiQ8MlKZW33woHY//uSTaViypNilNc1dIUlK8c2AAODwYeDarunxTU3A013JAY2NSh0SBuHkbdHRc3HZZS9i+HBxd3Tfvnx88cWdpuenTPkSgHnmkTztLCZmj6ndyZNpmtlJ6hUL5EEFIqLexiDcRzhad1IeCQe0g3D1fPARI6rgaNR20iQl+jhwQATCcpr7rFnmRzi7DIianJptNAaivl6M8quX9wkKOo9Ro8Qn2EOHRBqnJ3Q3dfy664A77xTLsak5u/40eZcn5vu7WpRNDubUQbicjq7VjnyD/DtuGYQXFv4TcXHiQrZ16xWoqUmCfL0sLn7K1E4rFR0AQkKUZR137wba2pTnHK2tLU8rqqwEiotvN/XjI0cm4He/W4MbbtiEBx7IRUHBWZvzW7vjwAHlGj59OhAeDrz/vlKpffNm8ZVBOPW06Oi5uPZaUe68szPA9LkhN/crREbKpfpF5tGRIw/hyBEx7Sw+XslQqqpKg1Z2kvz5YsgQ8Y+IyBcwCO8j1EG4VoV09Uh4QYGcQ2l71DYzUwnyDx7UTkWXuROEyynctbXDIUmim8kffOVzmThxl+nR998797rOvq87qeOnTikjW998A6vKx9HRcx1mLJB3SFIHTp36FocO3Y3uzvd3tSibHMyZB+GnbLYj3yBfC2JjT5jtnz79Y1x5pTqF9VYYDIkYNWo5vv5apACFhACzZ8MmeV54W5v5tdfeSDhgXuDvxImRpu3nnnsP27dfZrpWlpcPQU2N51PT/08pxYGrrhJfQ0OBsWPF9uHDIiuqsVFZP41BOPWUK680/0gaEVGNP/zhFxatJLS1VaCtTdzAUk83qa1NMrVRZyfJmW3y9AsiIl/AILyPGDVKSYF0FIRPmzbD4ahtbCwQFib2q4NwnQ6YOdP8td0JwuUU7upq5WBlJFx8I1dcMd70nKeC8O6kju9S7gmgrQ3YsUP79e1lLJDnyWm7u3dfhvZ26+BX4VxauDoId2YkXA7m8vNXYciQJgQGtiIvb5WqBWsC+CL5WqAeCdfrz2PSpG9x2WX/Mu1bv/5PmDq1FPv2XW+qq3HVVfbX8bZVnM3ZkXAAOHFCPGhtDUJp6Tirtnv37rR9Ai6S556vXKmkHMlBOCBS7EU7sfTaqVPKSHhQ0Poem69OA9v06UBQkCiA6efXgT/96RZERdnPMIqOVrKi5NFzWVtbFTo6xA12QCxpRkTkKwJ6+wTIOYMGAWlpIoDYt09Ur1WvQSsH4fHxQEQEAMxFVNS1aGragLa2Kuj18QgPLzAFjTqdmGe+ebMoWiLPQZw0yXpNWHUQbm8tTkvR0XPh55diehwfLyJ4gyER6emLMG7cNNNzGzc6/7rOvG9W1scoKXnILG1Zfl9bI9fqIBwQc+Tz8jx3XuQ6Of1ce/Rbm6O0cHU6ujMj4XIw19p6I/7znyS0tRlUhdlYE8CXRUfPxfTpSv7pxInfISjoPFJT2zF5cgO2bo3EwYNDsGcPsEI1k2Gug+QWy+Jsd3ZNX3VtJDzD9FUeAVcrLT1v/yScVFe3AiUlD6G29hy2bBFBeHLyEYSF7QEgvlE5CAeAXbt0aG5uMj0+d+5h7Nq1tev6uZiZP+Q1gwcDzzxzDK++asRttz2HCRPWOTwmNPQUAgMvwGgMsgrC9fp4NDQoy7ByJJyIfAmD8D5k4kQRhJ8/L+ZRy9V2a2uB+nqxnZWltJdHbW0ZPVqZAyizTEUH3BsJl9XXK59WJ0++GdnZN5vdDEhIEB9cy8pce11HoqPt34TQYhmEW/5sqGfZX27ONkdp4eqR8LQ0517T3Rs71PumTJmNBx/sxHffncN//7c/srPXIjy8AL/4hT+2bhVt3n8fWLlSbAcFAVdcYfv1AHEtlmmNhPv5aY+6qYPw8nIxx6isTCmbnp6+AyUlE7teq/t54OqbWFu33orOTnH9y8v7FPv2PWLKjFIH4T/+WIaWFuVGVmSk2JbrLrAGBnnTb387Avn5KWhtrbTRQge9XgTbbW2V0OkkREdX4uTJEairSzS1MRgSER5eYFYvh0E4EfkSpqP3IeoPfupUaXUqunoZHEfU88xllkXZACAuTnwwBVwPwtXB9aRJM6xSuBO7/mbW1mqvf94drqaOMwj3LY6Xm7PkXFq4PBI+bJjIMHEWawL0XYsX+2HPnmBcdtkVpmvBTTeJCuEA8MorYplHQMwFDw62+VIAxFQe+QbO3r3K2uDySHhsrHmmkmzECMDfX9xUkkfCy8qUO6dTpnxh2q6rS0V3WN7E2rdPyTyaPFlUm5ZrKIxXZgZh27ZmnDql3ACIiKiRX9HsGCJvcGZK2ciRizFypNImKkoE7GfORODCBbGkgZydpF7phEE4EfkSBuF9iKeDcPWyZ4CYA3nxxdbtdDqxnjIggmrJhYFJddCuXvZMNqwre0ySzOdT9jSj0bzCPCBS9NXppdSzXKs27lxaeEuLkjXiTCq61buwJkC/ERkJ/OxnYlt9TbvhBueOH9c1jfvsWXGd6+gAamrEC0VHn9KcR63XA2lpoq9WVIxCZ6cfjh9XLtpTp35p2i4v796fZ8ubWIcO5Zq2MzKKoa6hEBqq/D6UlGTi6NFsAMDQoVUIDFTfHeVyfOR9zqxGom4TFaX08+bmSUhJeRKdna1obCxCbW2n6nV77FsgInKIQXgfYisIVweP3RkJv+gi2yODckr6+fPKiJEz5JHwuDjt1x6m+htbqco+kwsJ1dT8u0eKAh08aL7UkIyj4b3HlWrjzi4V52pRNurfXn8d+NOfRIVwQIxwqwuW2TN2rPLhftOmvThw4HN0dIgAe8iQH2yuXy+npF+4MAQtLTmmINxgOIeJE08gMFC87vHj6Bb1Taz29gCUlEwAACQmHkZwcLNVOzklva1tEFpbxWjizJnLHL42kTc4k3kktxkzRhk9qK2NR1nZn3HgwG3YtWsmtm79k+k5FmYjIl/CILwPiYsT/wARhHd2ikB1504lKnYlCE9LAwIDlcda88Fl7swLP39eGd2WR9ItaQXhcjXsXbtmmv6Qan2Y9SR1Knp+vrLNILz3OF5uDggIGIrs7G+cTgt3tSgb9W9BQcBTT4lr2rvvilUaRGFL++rqVmDQoPtMj7/7bhk2bVI+7A8daj6PWn3tUs8LDwjYhMpKsej46NEduPjiEiQliT/L3Q3C1TexysqyYDSKOUWjRhVrtlPPCwcAP7923HjjIoevTeQtzmQe6XT+GDFiuOlxdbXe7Pn6euVDDkfCiciXMAjvY+QPSo2NwKefTusKVMW+oUNr0dnpfKAaEACMVJaq9XgQLldctzxezTIIlwsJWc4F1vow60nqIPyee5RtBuG9Rz038N///gNefPFNNDfLpft1AHTIyPgHIiJmOZ0WzpFw0jJ0KHDHHcp62fbI16ikpCLTvmPHxqG+XimHHhUlz2OxnketDsI//9wfnZ3iJtO4cSHQ6fxN03aam8U/d6lvYlmnogOWNRQsg/AZM/6DuDjLOwFcjo98T0KCkilnWSG9qSnKtB0VxVoGROQ7GIT3MeqU9H374tDcHInGxlgAQHLyXpcD1SuvFF9HjzZfdseSO0G4up0zI+EVFZ12qmF7tyiQOgi//HKl6FJxsecLxpHzxOj213jzzeewatXdeOGFtwA4n35uiSPh1B3qYmfDhpUgMPACAKC0dJxZMTN5JLzrKLN51Oog/JNPlG05i0ldO6M7o+Hqm1iHDk027R81ahu0aihYBuE33fSS5StaHUPkC8LClD/gdXWWQbiSg24wbO2xcyIicoRBeB8zYYISgJaUTDRb3iYlZV/XfucD1WefBb75BtiwQbuar8ydIFy9prgzI+FlZXUOqmF7ryiQHIRHRYm11uX1wc+fB3bv9vjbkQuqq5UUjR9+uA41NbvcrkquHglnEE6uUhc78/fvQEqKqIpZUTEKJ08q690pI+EKeR71uHFKVfbaWuV5eXlJTwXhgFLg6sgRcUHT6ToxcuQOzZtYw4YpdUJycg5h3Lhqs9dy98YXkbdFRZ0wbdfXJ5o919Sk5KCHhJSDiMhXcJ3wPmbEiGIAUwEAR45MxNChygel5OT9UAeq9tYIlwUGai9LZsmdIFwdvKpHf9RsFWazx9NFgaqrlQ/D2dmiGnxeHvDhh2Lf5s1ATo5H35JcYBmILFw4Htdc49ryYjI5CI+MBMLDu31q1I9IUgeamjagra0Ken08wsMLrEZ8La89qal7cOTIJHR2+mP7duVCKq+trSbPo46IAObPB1580fx5T4+Ey0JD5+LoUZFJlJ5+GtOmfab5vel0wFdfAV9/3Y5Bg44iN7cEZ89utvvzIPIFSUnh0Ok6IUl+GiPhIgg3GM4hIoKV2YjId3AkvI9JSDiGwYNbAACHD+eYrTErgnDB04FqRISoHAw4H4Tv3KlsW6Y6yoKDlcrENTUhTr2up4sCqVPRs8XKPGbF2TZtMm/f0gKcPu3RUyA71GvNA6L/Pfec/WPq6oCFC4G//13Zd+ECUNGVaMFRcFJzthik5bUnLW2PaVud8m2ejm49j/rJJ4HhSi0pGAzKjU51EF7uwsBdZSXw9tvAnj3mS67t3QsYjSKVfOrUMLtL6w0fDtx+u4TgYCOX46M+Izr6YkREiLUnLeeENzeLIDwiooG1DIjIpzAI72OCguIxevQWACLtasOG603PpaYqa5V5o3qt/CGxvBxob7fftqNDGQkfMUIJtLXIo+FVVYOg19urhu2dokBaQfj48aJyMmBenG37dlGhPiPD+ZsR1D3qINyv64r1/PPm87vV1qwR/3/PPQfce68Y3QPE/5ccnLAoG8lcKQZpWbE/LU1J95Ek0TlTU/eo0tG151EPGQL87W/Ke40Zo0wHcmck/PPPRVG5u+4SfT8jA3j0UaCoCPif/1Ha5ebafAmiPkun80dSkqiCfupUHDo6xC9TZ6cOLS2imGdcXDBvJBGRT2EQ3seEhxdg5sy1psfy/Kfw8FqEhTXAm9Vr5SC8o0MZUbTl0CExnxowLyanRQ7Cz5/XITr6ta69loG494oCaQXher2Sgn70qBhZBYBXXlGWXnv2WY+eBtkgB+GDBwMPPyy2W1uBBx4wH/FrawN+/3ugsFBMMZAtFrWpWJSNrKgLrWk8C8C8xoa62BmgMxsJB8SyXr///Z3QdV2+7M2jvuoqMSKeni6WSZMlJsJ0vDNB+MsvA9dcAzQ1KfuOHBE3qmbOBP75T2X/5MlWhxP1C8nJYm3Bzs4AnDolitWePj0UnZ3i80J8vBNrDxIR9SAG4X2MTuePO+6YBj8/88JrIhXd84GqJIm1yGtq/o34eKX4iXoUWN2msbEIktThVCq6TD0vvLX1amRlfQyDwTylzJtFgeQgPDAQyMxU9qtT0n/8UQR+n32m7PvnP5V10Mk7JEkJwpOTgSeeEEEKAHz5JbBkibgp9MMP4v9LPc9WHjX/4gvg8GEuT0bW1IXWtFkXg5SLnRkMwzB0aDVCQ+tNz82ffxi33PL/kJn5IbKz1zosIPjnP4uA+eqrlX0Gg8i2ARwH4adOAX/4g/L4iiuAGTOUvi/T6YCf/1wpOEnU36g/R0REfIbMzA8RE7PatI9rhBORr2Fhtj5o7NifID+/Dj/8oPxVSU7eD4MhEenpizwWqNbVrUBJyUOmD6kBAb8BsASACMJnzrRuA4iA+YcfvgUwCoDzI+GAmNc4duxcREVd67BIkidcuAAcPCi2x4wRI+Ay9QfWTZvEB9uWFmVfWxuwaJEYcSLvqK0V/0eAWOYuOFhkI/zXf4l9Dz4oApnGRuUYvV78n7S1KQHKkiXmo+YcCSfA+doZlu2io5Vr1E03NeCtt6JQUCDh2WfHQK8fY+NVnJecLG7wVVeL/i9PjbG0ZYsyNeinPwU++EAE3LW1wKefiptTaWliDXT1HHSi/kb9OeL06RzExuaY/rYDDMKJyPdwJLyP+ulPzf+iXHzxZW4v26RFa55kXJwy/L1v30G7cyl//FEZwnE1CAfgdlGg8+fFyKiz9u9X2sup6DJ1EL55M/Dxx9bHv/EG0Nzs/PuRa9QjgfJa8zfcANx+u7JfHYCPHi3+r+bPB+6+W6SwA8C774r5/DIG4QQ4XztDq518jXrjjQzs3Qt8953O7CZed8h9HbBfe+LHH5Xtn/xESWOPiRH9/733gD/9iQE49X+JqpXJ5M8R8jQyQPxOEBH5EgbhfdTcueYph7m5ozyagq41TzI+Xvk0uGfPbhw+fI9VG3G8hCNHROQdEyOZUittUQfh8lzzI0fEh8hnnwXOnnXuvJ9+GggJEaNGqanAJZcAP/sZsHq17WPUafOWQfiwYcof9k2bgBVd9ZmCg4F588R2S4sIxMk71EXZ5MBEpxNB9TffAAVdpQ8mTRLTA3buVG76REQo/09nzgAbN4rtIUOA2NgeOHnyeZaF1qw5rrHh7y/W+A7wYF6ZelrM3r2226mLRjLVnAYyrc8R6iCcI+FE5GsYhPdRsbFi7h8ggvGxYz332rbmScbFlZm2T54cBqOx3qoNANTVJaKlJQoAMHZso2l0xhbLkfClS0VQ9dZbwGOPiUq/K1bYPh4QqcYvvihGtdvbRfC2YQPwr38B119ve+62VlE2tdmzxdfz55UR76uuAv74R2XUadEiJWWaPEsrCAfEz37WLGD9enEjZNs2MefVYDA//ne/s07lHTECDvskDQyWhdYsngXgnWKQjowbp2zv2aPdRpKUkfDoaPPfD6KBRiujjkE4EfkyBuF92OLFohDP4sWe/QNja55kUNB5RESIstPV1ak2jy8pmWDazsqqttlOpk4jW7pUjF6eOaPsq6wEbrzRer1utePHlfnaISHA0KHKc21tYtRUi6Mg/LnnlJsdshtvBEaNEtkIgJi3+cEHts+N3GcrCFcLsbO8/MiRwAsvmO/jKDipqQutqXmzGKQjzgThR44oUzHy8nhjiQY2BuFE1NcwCO/Dxo4VlZ/vv9+zr2tvnmRCwjEAQENDAlpbtasFHT6cY9rOztZa+sdcTIySynnunLL/Zz8DrrxSbEuSWIrHFnlNcgC48869KCkpwpo1yuRwrSBckpQgPCEBiIqybhMVBXz7LfDSS0BYGHDxxWIkHDCvSvzCC67NRSfnqINw9frJrvjNb8xvsDiqUUADT3T0XOTllSE7e63Tlc29KS1NqWdgKwhnKjqRIjRUuSErB+G1tcrzDMKJyNcwCCcr9uZJqouz1dRoR0WbNl1l2p41a7TD9/PzA+LjlWB9yJAO/POfnfjgA+CTT5SRy5Urba9PvnHjftN2WNhT2LVrJgIDR2HwYFE6+JtvzKtjA8CJE8raulqj4OrzW7AAaGgQKe5yyvPkyaJCPCBGpT791OG3Si6SC7MFBblfWEenE8uZ5eYC8fGi1gCRJXeLQXqDn5+YZw4Ax45JqKhYb7YEJGBelG3q1F44SSIfI4+GV1SIv/ccCSciX+b1IPy1115DamoqgoKCkJOTgw0bNthsW1RUBJ1OZ/XvoHqdCfI6e/Mk1cXZqqqsU9Krq4fj8OFcAMD48Y1ISXH8QbaubgUuuURUNxs5cjtefz0TI0cmo65uBfR64Fe/Eu06OoCXXtpr9kFUPn7z5n2mx2lpYlhckkoxduwaAMDJk4BlN9qyRdmeNMnhacJf41t5+GFl214BOHKdeo3wlJTupdvGxYmgpbKSa4RT3zB+vPgqSTp8/vnDOHDgNuzaNRObN6d0XfPE8zqduCFINNDJQfi5c6KGixyEBwWJgqpERL7Eq0H4smXLMH/+fDz++OPYsWMHCgoKcOWVV6K8vNzucYcOHUJVVZXp38iRI715mqTB1jxJ9Ui4VhD+/ffXm7ZvuinC4fvIy5zdddd9WLYsCX//ew6Sko6gtbUS+/bdiLq6Ffiv/1oNf38jAOC992KwdesVpg+iciX3Y8fEJ1a9/jyGDSvpenUJOTnfmt7LMiXdEyNJBaqiyfv3225HrquvV6YneKLolJ8f581S35GaqhSsOHZMmSTe2lqJbdvmYdeuTgBixDw0tMdPj8jnWM4LlzPn4uJ47Sci3+PVIPzll1/GnXfeibvuuguZmZlYtGgRkpKS8Prrr9s9LiYmBnFxcaZ//lpDkOR18jzJ8eO/QUCAqHSmHglXF2cLDIxGZuZSbN/+pGnfXAfTKS2XQouJqVD9oRT7Dh36FRoarsIllywHADQ1xeCbb24zBenHjz+D5uYGVFSIGzWpqXvh799peo9Jk9aYtr0RhIeEKGvw7t9vnfJO7nOmKBtRfyRJHQgN/avpcWnpOPWzKC8fjY4O8eebo+BEgrrI6969ynSztLReOR0iIrs8uLKpuba2Nmzbtg2PPvqo2f7CwkJslBfstWHixIm4cOECxowZgz/+8Y+YKU+81dDa2orW1lbT45auEtlGoxFGo7Eb34H3yefn6+cZEnIJ0tNfx8GDtyA+vsy0/+TJNMjp6iNGLEFb2/XYvFl0qZEjzyIsbAXq6+MRGnqx5vzK5uZ1mkuhKSS0tzcAAG64YTHWrr0FALB06R9RWPgBAgI6cOLEYpSVZUGSxAdSORVdlpa2B+HhtWhqisHatRLOn29HQABgNALFxQEAdEhNlRAR0Q53/xsyM/1RXu6H5magvNyIhAT3XscZfaXPeMLRozrIl6jExA4YjZ32DyBNA6nP9BfNzeuQlPSd6bF6JBwAamuTTNvJyZ793WB/IVf5Sp+Ji/MDID5rFBV1mLZTUzthNLJyqi/xlT5DfUdf6TOunJ/XgvD6+np0dHQg1mI9oNjYWFRXay9bFR8fjzfffBM5OTlobW3FBx98gFmzZqGoqAiXXHKJ5jHPPvssnnrqKav9X3/9NQbL5WV93Jo1axw36nUGBAQ8gqiodxEYeAFGYxCOHRuPzs5InD9/J3780YCvvtoHSZoAAJg69RUcPvwEAHS1uQvt7flmrxgYuB7O/hdlZW1Gbu7XKC4uRFVVGr766uf4yU/eQUfHKRw9ep2pnWUQ7ucnYdKkb/Hdd7fi9GkdlizZiFGjmnDsWBjOn58BAEhMrMTq1dvc+qkAgMGQBUBMNH7vva2YMKHO/gEe0Df6TPesWZMGQAQfDQ07sXq1vRs25MhA6DP9RWDgeoSH1yMiohqNjXEWI+FATc1w03Zj4y6sXn3C4+fA/kKu6u0+U1UVB0Ckta1efRaAmKfR3r4Wa9asRmdnBDo6xkAOzqn39Xafob7H1/vMOfUyTw54LQiX6Swm4kiSZLVPlpGRgYyMDNPj/Px8nDhxAi+++KLNIHzhwoVYsGCB6XFLSwuSkpJQWFiIUB+fKGc0GrFmzRpcfvnlCAwM7O3TccIcSNKTmDDhArZuDUJl5UhkZJxATIz4g/bKKw2mlgUFK0zbfn6nMGTI/8Po0R8hMlKZM97cPAR799pZd8zCHXf8GcXFhQCADz54AoWFHyAw0IjSUiWXfMSI3RZH6ZCVdRjfdQ0qRUZehDlzJLz5pjIT49pr4zFnzhynz8NSba0On30mtkNCpmLOHO+N2Pa9PuO+9euV/6M5c7Ixffr4Xjybvmsg9Zn+Qr42pqXtwbZtcWhqisGpUzEYOlSsuVRbqwThV101HtOnj7P1Ui5jfyFX+UqfiYsDnn1WbJeXK5//UlLewODBHwMA9PphSEt72eyzCPU8X+kz1Hf0lT4jZ2Q7w2tBeFRUFPz9/a1GvWtra61Gx+3Jy8vD0qVLbT5vMBhgkNeMUgkMDPTp/yS1vnSuQCAKCoKwdat4tGNHEK66Cjh1qgPffx8JAIiNLcPIkTtUx0gAdCgtfRixsTeYUtMjI2fCYEhEa2sl5Dng9mRlbcbkyV9i69YrUFOTgi+/vANXX/0PVFQUmtqkpakX1RU3e6ZMudy0p6wsAIGBMJ0/AGRmfoszZ/QIDy9wa1micarPv4cO+SMw0Pt32ftWn3FPVZWyPXy4+H8j9w2EPtNfyNfG1NS92LZNXL9KS8di6FBxN1Gdjp6W5p3fDfYXclVv95lk7VVTkZBw1LTd1nYSBw/egqysjxEd7aBwDXldb/cZ6nt8vc+4cm5eK8ym1+uRk5NjlTawZs0aTJs2zenX2bFjB+Lj4z19etQN+aqs8k2bxNf//d/D6OgQHa+gYIVGJVIJra0n0NSkLFFnbyk0+XFAQKTZc3fc8WfT9r/+9ThaW8fi4EHxlzcqqhphYcpovMGQiKysj5Gbq/S3I0fE140bW7pevw0BAdeYLf3jqsxMZXvfPtvtyDmS1IHGxiKUldWY9qmr3hL1Z5LUgaamDYiKuhFJScq6ipWV8tp6OrORcK3fDfl3yHJtcaL+LCYGCNAYWkpIOKZ6JG74l5TM5+8FEfUqr6ajL1iwAPPmzUNubi7y8/Px5ptvory8HPfeey8AkUpeWVmJ999/HwCwaNEipKSkICsrC21tbVi6dCmWL1+O5cuXe/M0yUVaQfhnnymLcF5yie1Atq2tyuyxvBRaSclDZkXaDIZEpKcvAgDs23cjRCAuYcyYLZg6dRV+/PEnqKlJxv33b0RzswjSL700BtnZa9HWVgW9Pt40sh0aKpan6uwUQfiRI5/jyJGrAQDp6Tuh14vCfnLFdVfvkIeFiaqsFRVKhXQuh+KeuroVpr5QXn4YQCyCg5tx7ty3GDKEoxbUv6n7PwAMG3ap6bmTJ0UQbjAk4tSpCQBE+q1lIpjla8jHpKcv5sgf9Wt+fkB8PHBCVSIhNLQBwcHNFi2VQYGIiBk9eIZERAqvBuE333wzGhoa8Je//AVVVVUYO3YsVq9ejeSunKGqqiqzNcPb2trw8MMPo7KyEoMGDUJWVhZWrVrVrfm65HnDhgFJSeIP3ZYtQHMzsHatKAkeEVGNMWM22TxWr7fOaoiOnouoqGvR1LTBKoAGYBWk33HHk/jxx58AAEpKQgAAgwYBzzzjp/kH1WAQy4iVlQElJRJWrfoIgAjCMzNV65R1pc2XlMxHVNS1LqWmjxkjgvDGRqCmRnw4JtfIa8YDEiQJqK8XQ3yRkRVu3Rwh6kvU/V82bFiJabuh4QpkZ0/G4MEFqKkR16bhwx2/BuD+DUaiviYx0TwIj48/ZrOt5aAAEVFP8nphtvvuuw/33Xef5nPvvfee2eNHHnkEjzzyiLdPqU+SUxS1gtTekJcn/tCdPQu8+CJw4YI4l4sv/tRsnW6FDgZDIsLDCzRfT6fzt3lH2jJIz86Ox6pVEv7v/5Th5v/+byA9XfNwAMDIkSIIb27WYf16pZBbZuZmi5bu3SEfMwb4+muxvX8/g3BXWa4Zf+ZMOFpbRen8qKiTAODWzRGivsCy/8tiYk6YVqM4elTUrSgr84fU1UwdhNt6ja5n4e4NRqK+xHJ6hno+uCWtQQEiop7itTnh5Dl1dSuweXMKdu2aiQMHbuvW/GVPUaekv/SSsi2qomvP705PX+T2hz85SI+NvRURETPw1FPKe0ydCjz0kP3jR45UtuX1xgFgzJgfNVq7foc8K0vZ5rxw1zU1bTBLn5VHwQEgKkoU7rOsKUDUX1j2f5mfn2Saz1pZORynTm0wG+VLUuqz2XwNBX+HqP+zDMK1R8J1MBiSbA4KEBH1BAbhPk5OL7T8cCWnF/ZWIK4Ows+fF1/j4oDbbrsXBoP5X0G5QJon0yAnTQI++gh44AHgk08AfwexvXqUvKkpBgAQGlpv8y65q3fIx4xRthmEm3OmSJTlTY/6+gTTtgjCtdu58h5EvsreTT85Jb2tbRCOH2+GagaX2Ui4szcOmYJL/Zn1SLhlEN79QQEiIk/wejo6ua8n0gvdTXOfOBHQ64G2NvF42DDg44+BYcOuR0LCNV5PnZekDhQWbsCMGeI9JMn+e6hHwmWZmT9qFFCznzZvi2p5e5SWunSoz9DqCw0N/jh2DJg82b1ic84WibK86WE9Eq7dzpX3IPJV9m76DRt2xLRdUZFsMwh39sYhU3CpP0tMNH+cnGy+Zq9c9JV/G4iotzEI92GupBe6U+GzO8GLwSBGoV9+GbjuOuAf/wAixTLhdud3e4I75601Xzwzc4vFHvfvkA8dKorDnT8PVFRIaGxc5zPz952h9TOVpHTMm7cLlZWDsWiR45R/rdd0tkhUeHiB2Zrx5kH4Sdi6OeLKe/haXQUimWX/V1MXZ6uqGm8zCLf3GoJ7NxiJ+hLLkfCrr/43QkPv43WfiHwO09F9mDfTCz2R5v7ii8CZM8CKFUoA7m3unndamli+RG38ePNU9O6kzet0yh//48dP+9T8fUds/Uy3b09BZaUojvbll669puMsDvN1Wi3XjLcOwq1vjrjyHr5YV4FIZtn/1YYNU65TR4/6mQXh6jnh9l6DKbg0UKiD8MBAIDHRvJ4M+z8R+QoG4T7MW+mFrgZI9gwe7NJbd0t3zluvB7pWxjO5/fZ/Ijt7LTIzP0R29lrk5ZV2K0UtNrYOAHD2bCjOng0x7e/t+fv22PuZ7t07zbR97JjWz9w2d4pEyWvGGwzDzOaEJyRImjdHnH2PsrJnfLKuApGauv+rpaWdMW0fOaIsv2QwANHRzr2GN+pyEPkidRCemuq4XgwRUW9hOroP81Z6obfT3L2lu+ednq7M187IAIYO9Qdg3c4dktSB4OD1AG4AIOY0Dxly0HRevro8kL2f6d69F5m2y8okdHbqrLIJbHE3i0Neju7cuXMAAH9/CXPmbEZAgPXPzNn3qKxcDC7bRH2B5XKMen08QkIKEBgIGI1ASQlMI+FJSdbZPbZegym4NFAEBQHXXgt8+ilw2229fTZERLZxJNyHeSu9sK9W0e3ueauLs02dqtnEbU1NGxAZedj0uK7OojqMjy4PZOtn1dHhh/3781Tt/HDypPOv250sDp3OH9XVIpMgLk6nGYC78h7t7afsPOub/y80cFkuxxgQ4I+0NPHc3r1AS1edKfV8cEevwQCcBpIVK0TGyJ//3NtnQkRkG4NwH+eN9MK+WkW3u+c9erSynZen2cRtbW1ViIpSRpStg3ClnS+x9bMqLR2Lc+dCzfYd01pu1QY5i8P65pHM9jqtRiNQUyO2ExKsnnbpPQIChjp1vr72/0KkprW6g70gnGgg8/OzrpJORORrGIT3AdHRc5GXV+ax+cvdCZB6U3fP+6c/FcH39OnAvHmePTe9Ph7R0Y6DcK2gtzfXuLb1M1WnostcCcK7k8VRXQ1IXdnjlpVuXX2PxETnSrr72g0nIjWt1R1SUnr8NIiIiMhDGIT3EZ5ML+yrVXS7e95DhwKbNgFFRUBwsGfPLTy8AMOGGU2P1dW95fPTukHgbtVuTwXutn6m+/ZNs2rr6vrn7mZxqNPe7QXhzrxHcvLjffKGE5HamDHmj9PTgZ//vHfOhYiIiLqPhdkGKDl40V5ve5HPVtH1tfNWrz2dlTXLtN98JFz7BoEra1yrBQRsQnHxb9DWVmna5+z67lq0fqbdHQlXv7arRaIqlW/LYRDuzHukpy/u+jnrYP6z9t0bTkRqN98MrF4NtLUBd94JXHMNEMC/3kRERH0W/4wPYH21iq67560OmD3xvdbVrTALXDs7dQgIeADt7XqzIFzrBoHj5da0q3Y3NKzE4MHPo63N/AhHgbsj6p9peXkTqqtTAQCTJwNbt4o27gThgJLF4Sx1EG5vTriz7+FrN26IXBUaCqxc2dtnQURERJ7CIHyAczVA8hWunrdlwAw4N3psK3DXGsX285MQFVWJ6upUnDo1CpmZH9oM9t1Zbk2SOnDs2AKb7bu73Jb8M/3hB2XfpZeKKrPV1a6no7urrEzZTkryzGv21RtORERERNT/MAinfs/dtG9bgfuIES/j6NEFVq8HANHRFaiuTkVj42CEhNyEwYO1gzx3llsTAWQldLamN3tofff9+5XtsWM7MXz4aVRXh6GqCjh7tgNDhng3cFWPuI8Y4bnX7as3nIiIiIiof2FhNurXHKd9AyUl860Km8mBu+VodWtrJfbvv8nmKLa6QvqBA8U2z8ud5dZ6an13dRDe3j4HoaGfmx5/+unlDovGdZcchAcGcpkZIiIiIup/GIRTv+ZK2rdpjxOBuy3qIPz48TM227mz3FpPre9+4EDXGeg6ERe3HvHxytD08eODsW/fjV4LxCVJCcJTUgB/ZosTERERUT/DIJz6NXfTvu0H7rZFRanXCrddVcyd5dbCwwug1w8zraGt8ardXm5LkoADB8QbxMWVISjoPBISlCC8qkoUbNPKHvCE+nrgTNe9i7Q0j788EREREVGvYxBO/Zo30761REcrpb1PncoAYHtNb3trXI8ZswwBAUPNjtHp/JGW9nJXK++s715ZCZw+LV4rOVnkpcfFKRXZqqrSoJU94ClHjyrbDMKJiIiIqD9iYTbq1+S079bWSminkutgMCS6lfYtH69+XXUQXlnp57Aqu1bVbqOxHkeP/lbzmMjI63Hu3B8QEbFUY51w+8ttObNEm3o+eHKyyEtXj4SfPKlExt2de65FXZSNQTgRERER9UcMwqlfk9O+RXV084DZXtq3M4G7qJJuHiwPG6akaB89etKpquzqqt11dSuwf/9NNo8ZPfojtLfnIzf3SZw9u9np5bacXaJNng8OKCPhkZEnERjYCqPRYFo/HOj+3HMt3qqMTkRERETkK5iOTv2evbRvreXJnJ2vHRNzI/LyypCdvRaZmR8iO3st5szZBL1etPz220js3ZuncUbaVdmdKQh37NjvAHSYAvfY2FsRETHDYQBuq9K7ZZE1rZFwf/9OxMYeByBGwiWp+3PPbeFIOBERERH1dwzCaUCIjp5rFTDn5ZXaTN92NnC3DIYDA/3x61+LtkajAU888QmqqlI03sF6XrUzldzb2irg77/fThuLI1xcok0dhA8ffhDyTQe5QvqFC8Foaop2eu55Rwdw000ioN640fH5qoPw1FTb7YjIc9R1K5qb1wHwfNFFIiIiUjAdnQYMddq3M7TmaztK+waAF14Atm2rxvffx6GpKQYLF/4fliyZhuDgFqu26nnVzs6x9vNrdPp7cGWJtvDwGaYgfNgwYOrUd0wp7OplygYN+gjR0TOdev9164D//Eds/+xnIsgPCrLdXi7MFhUFhIY69RZEA4oztR1coTVVJSQkEg0NryEu7iZPnDIRERFZ4Eg4kR2upH3LAgOB998vQVLSQQDA8eNZeOqp/0VHh/Wx6nnVzs6x7uyMcKod4NoSbXV1wKlT4nFmpnn2QHZ2vqltY6NzATgAfPutsl1aKm5Q2HLhgqjODjAVnUhLXd0KbN6cgl27ZuLAgduwa9dMbN6cYjalxNXX05qqotM14ODBW9x+XSIiIrKPQTiRF6Sk5OOll+5GaGgDAKC4eDZeffV/VGt8W8+rlgvCWc9DV47R6xPR0THG6fNwZYk2dVG2MV1vId+EyM6eaHpOnTLuiDoIB4C//hUoK9Nue/w4TD8fFmUjMudKbQdn2Juqouu6BFnWrSAiIiLPYBBO5AU6nT9mzPgt/vKXuQgIaAMAfPbZr/HBB3+ErarszhSES0t7CYDzqafOBPbyzYBdu5S9YyzifPXIdGkpbFLPLT1+fAO2bjX/gH/hArBggfaxLMpGpM3V2g7OcGWqChEREXkWg3AiL4mOnovbbnsIjz32sGnfu+8+jdWrH9Wsyi4fY68gXGTk9S6dg7OV3nU6f2zdqjyTk2PeUl0kzdZIuGWq7NKlL6CzU7zH7bcDsbGi3cqVwFdfWR/PIJxImzcCZlemqhAREZFnMQgn8qLo6Ll48slX8Je/lJj2vfTSM9i9W7squ3yMZSX35uZSXHXVXDzwgB+qqoa4fA7OVHqXg3C9Hhg/3vw1wsOBiK6p6FpBuFaq7Pbts0zbl166yWw++IMPAq2t5q8hF2UDGIQTqXkjYHZlqgoRERF5FqujE3mZTuePJ55Ix+nTojBZZ6cON98MbNsGJCfbPkZdyf13vxOVxbds8YdONwv793fi1VedPwdHld6bmoBDh0TbCRNgWutcLS1NnPOJE4DRKArQAbZTZeUg3M+vA3Fxd+Oyy3bh73/3xw8/AIcPA4sWAX/4g9KeI+FE2rwRMMtTVVpbK6Gd5q6DwZBoVreCiIiIPIMj4UQ95LnngDlzxHZDAzB3LtDW5vi4igrz9bslSYf/+R9/lJSo9ylzsRsbizTnhtqr9L5tm9Ju8mTt85AD485OoLxc2a+VKnvqVCzKysYCAEaNKoZevw/NzRuwZAng13XVee01qArVKUG4Xi+WSCMiwZXaDs6yN1VF/r20rFtBREREnsEgnKiH+PkBS5cqlb+3bweWL3d83DffKNtDhypR6/r14qsnli1Szwe3FYTbmheulQK7e7cSDEya9J2p3YQJwMyuFc7Ky5Uib5KkvGZKCuDPz/1EJq7UdnCFrakqkhSF0aM/0qxbQURERN3HIJyoB0VEAH//u/J46VLHx6xZo2wvWNBp2l63znPLFqmD8ClTtNvYqpCulQJ74MBU0/bYsT+YtZsxQ2lXVCS+1tUBZ89avw8RCc7WdnDnddU1KMaOXYPTp//uchFIIiIich6DcKIeNnMmkJQktr/6Cqipsd1WkpSR8OBg4L77OqHXi1Tz9esljy1btGWL+BoSAmRkaLdRB8d79uw3pb1rpcqqg/DMzC1mqbLySDigBOEsykbkmFbRxry80m6PWKunqoSFTYcryyASERGR6xiEE/UwPz/gpz8V2x0dwEcf2W67Zw9QWyu2Z8wQgfioUacAAGVlOpSX25ojCsjLFpWWPmlznjgAVFeLeeeAWJrMz8ZVITRUWVdsz569prT3+vpPzVJl29sDcPiwWOMsPv4YwsPrzVJlJ08GBg8WrdeuNU9FBxiEE9ljr7YDERER9Q0Mwol6wbx5yvYHH9hup05Fv+wy8TUrq8G0b/fuSxy+V3n5f9udJ+7MfPC6uhVoabkGfn4ikK+uFhPE5bR3cV4iVbasLAutrYO79u2xSpXV64GLLhLbFRUiAFcH4fKceSIiIiKi/ohBOFEvGDMGmDRJbG/bBhw4oN1OXZTt8svFV3UQvmuX7SC8qioF69bdgPp6MRfb1jxxORUd0J4PLi9BFhjYhujoEwCAioqRXRWUlbT3qKhrkZdXhtOnl5mOvfLKqzVTZdXzwteu5Ug4EREREQ0cDMKJeol6NFyrQFtrqyi+BgAJCUBmptjOyGhEYKAIfvfsuRRayxadPRuCBx74AU8++TFuvvkEfv/7r/DVVz/D+fNDrOaJOxoJVy9BlpR0qOv1w9HYGNPVQqS9NzVtgE7njz17lEnleXnalxjLeeHqIFxdhZ2IiIiIqL9hEE7US269VVmKa+lSsf622saNwPnzYvuyywBdV6xtMHQgN1cE4eXl6aiuHg7LQLyo6CY0NCQAADo7/VFcXIjnnnsfc+dWY/ny2Whq2gBAzMeWg/DoaGD4cOvzVC9BJgfh4r1Ha7b78UfxOCAAmDhR+3vPzQWGDBHb334r4ciRVgBAVFQbgoMdF5IjIiIiIuqrGIQT9ZLYWCXFvLwc2LDB/HmtVHTZpZcqFdHfemsz9HrzZYtWr77TtC2nkAPAhQtD8Morr2PfvjMAxFJjp0SdN0yerAT6auolyIYPP2jaPnEiw6pdS4uSWp+dDQwaZP16ABAYCFx6qdiurtahqsrQda7bXV7jnIiIiIioL/F6EP7aa68hNTUVQUFByMnJwQbLSMPCunXrkJOTg6CgIKSlpeGNN97w9ikS9Rp7Bdq0irLJHnigE3FxYvvbb+Owd+9xZGevxfDhf0RZWSb2788HAKSl7cKyZcPx6qsXoaBABLadnQF45pk8AI7ngwMwW4JMPRKuBOE60xJkxcXomitu+/Vk11zzo9W+hISjLq9xTkRERETUl3g1CF+2bBnmz5+Pxx9/HDt27EBBQQGuvPJKlJeXa7YvLS3FnDlzUFBQgB07duCxxx7Dgw8+iOXLl3vzNIl6zXXXiWXHAOA//1HSz0+dAoqLxfbYsTAF3LKhQ4G331Ye/+53fmhqmoHU1Cfx9dcPmfbPmfM2dDpg3LiNeOyxnyEqSszt/vLLKKxd61xldJ3O37QE2fDhlunoYuhcXoLs+++V46ZOhU2S1IH09J9hyJAms/0JCcfg6hrnRERERER9iVeD8Jdffhl33nkn7rrrLmRmZmLRokVISkrC66+/rtn+jTfewPDhw7Fo0SJkZmbirrvuwi9/+Uu8+OKL3jxNoh4lSR1obCxCTc2/0dpahBtuEJPBW1qAjz8WbeT1swHrVHTZnDnAXXeJ7TNngF/8Amhs9MeaNbcDAAIDW3HZZf8ytQ8KuoA77/yj6fHvfgds3qy8nq0gHACio+ciK+tjDBumw6BBpwGIkXCDIdFsCbJvv1WOUVdAtyTmpJdgxoz/NdsfHy9XaFOKvRERERER9ScB3nrhtrY2bNu2DY8++qjZ/sLCQmzcuFHzmE2bNqGwsNBs3+zZs/H222/DaDQiMDDQ6pjW1la0traaHre0tAAAjEYjjEZjd78Nr5LPz9fPkzynoWEljh1bgLa2StO+nJz/wj//KYLRhx+WcNll7fjqKz8AomrbzJntMBpFRG7ZZ557DlizJgDHj+uwbh2QkSGhvj4IAFBQ8BXCwk6Z3kevH4YHH5yDL7+UsGuXDjt2KOeVnCwhPLwd9rpiePjVyM2dg5Ej27B7N1BdPQJjxx5GUJA/jEYjzp4FNm0KAKDDiBESEhJsv97582Ke+uzZ72PVql+Z9itBuNIuOJi/H93B6wy5gv2FXMU+Q65inyFX9ZU+48r5eS0Ir6+vR0dHB2JjY832x8bGorq6WvOY6upqzfbt7e2or69HfHy81THPPvssnnrqKav9X3/9NQYPHtyN76DnrFFP/qV+KyBgEwYPfh6AeQG0rKz/ID//M2zadA1qa3WYPbsJ5eWhAPwRENCJc+e+xOrV5mnZ6j5z111ReOKJiwAA9fXihcPCWnHDDUE4c+Zp+Pk1orMzAh0dY1BX549bbvkeu3YVmL3esGEnsXp1sVPfR3j4JACh6OzU4b33NmL4cDEyvmNHNIzGaQCAESOOY/XqXTZfw9//OIKDgbFjf0B8/DFUVYnFwUU6umL79uPo6Fjt1HmRfbzOkCvYX8hV7DPkKvYZcpWv95lz58453dZrQbhMZ1FuWZIkq32O2mvtly1cuBALFiwwPW5paUFSUhIKCwsRGhrq7mn3CKPRiDVr1uDyyy/XHOWn/kOSOlBc/Bu0tVk/5+cHPPzwPfjFLwrQ0hKBPXuiTc8VFABz5842PdbqM3PmADU1HViyRIycJyVJWL3aDxkZMwHMhKU5c4DDhzvx7rvKbJSrr47DnDlznPpetm/3w/r1Yjsm5hLMmSN+RzdsUF7v9tsTMWfOMK3DAQCSNBvFxW+gre0k7rzzcTz//HvIz/8cMTEVXS100OuHobDwYeh0/k6dF2njdYZcwf5CrmKfIVexz5Cr+kqfkTOyneG1IDwqKgr+/v5Wo961tbVWo92yuLg4zfYBAQGIjIzUPMZgMMBgMFjtDwwM9On/JLW+dK7knsbGH8xS0C0NHVqNhx66F08/vcy0b9IkYPFiPwQGWpdusOwzzz8PnDsHNDYCixbpMHy4/f70wgvA558D9fXicV6ePwIDnQt2s7KU7aNHAyCfRlGRsv/yy5X92gIxcuSr2LfvRsyatQzTp3+MgID2rufEDbeRIxdDrw9y6pzIMV5nyBXsL+Qq9hlyFfsMucrX+4wr5+a1wmx6vR45OTlWaQNr1qzBtGnTNI/Jz8+3av/1118jNzfXp3/gRI60tVU5bHPppf+LZ5/dip//HPjiC1Edfdw4515/8GBRLX3FCmD4cMftIyOBd94BhgwBLr4YuOgi594HADJUy4Mf7Fo2/NQpYPt2sT1+PBAdbX2cJbnYm8EwTBWAw6rYGxERERFRf+LVdPQFCxZg3rx5yM3NRX5+Pt58802Ul5fj3nvvBSBSySsrK/H+++8DAO69914sWbIECxYswN13341Nmzbh7bffxr///W9vniaR1+n11vUMtNxzz1lERHj5ZLpcfbUInvV6144bOVLMaZck4FDXimVFRUo191mznH+t6Oi5iIq6Fk1NG9DWVgW9Ph7h4QVMQSciIiKifsurQfjNN9+MhoYG/OUvf0FVVRXGjh2L1atXIzk5GQBQVVVltmZ4amoqVq9ejd/+9rf429/+hoSEBLz66qu44YYbvHmaRF4XHl4AgyERra2VkNfBNqeDwZCI8PACjee8x9UAHBCj7sOHA8ePi5Hwzk7zpclcCcIBsQ55RMQM10+EiIiIiKgP8nphtvvuuw/33Xef5nPvvfee1b7p06dju5zXStRP6HT+SE9fjH37boSY86wOxMUc6PT0RX1mBDg7WwThLS3A7t3Ad9+J/QEBwCWX9O65ERERERH5Mq/NCScic+o50Gp9cQ705Zcr2++8o8wNnzIFCAnpnXMiIiIiIuoLvD4STkSK/jIH+oorlO033lC2XU1FJyIiIiIaaBiEE/Ww/jAHOj0dSEsDjh0DjEZl/6WX9t45ERERERH1BUxHJyK3qEfDAWDQICA/v3fOhYiIiIior2AQTkRumT3b/PHFFwMGQ++cCxERERFRX8EgnIjcMnMmEBioPOZ8cCIiIiIixxiEEw1QktSBxsYi1NT8G42NRZCkDpeODwkBLrpIecwgnIiIiIjIMRZmIxqA6upWoKTkIbS2Vpj2GQyJSE9f7NJSaY8/DuzdKwqy5eR440yJiIiIiPoXBuFEA0xd3Qrs23cjAMlsf2trJfbtu9GlNctnzerAoUMbYDRWoanJueXWJKmjzy/RRkRERETkLgbhRAOIJHWgpOQhWAbgXc8C0KGkZD6ioq51GBi7M5ruqRF4IiIiIqK+inPCiQaQpqYNZgGwNQmtrSfQ1LTB7uvIo+mWryWPptfVrfDIMURERERE/Q2DcKIBpK2tqtvtHI+mAyUl880KvblzDBERERFRf8QgnGgA0evju93OndF0T43AExERERH1dQzCiQaQ8PACGAyJAHQ2WuhgMCQhPLzA5mu4M5ruiRF4IiIiIqL+gEE40QCi0/kjPX2x/MjyWQBAevoiu0XZ3BlN98QIPBERERFRf8AgnGiAiY6ei6ysj2EwDDPbbzAkOrU8mTuj6Z4YgSciIiIi6g+4RBnRABQdPRdRUde6tV63PJou1hrXwbzYmvZoujvHEBERERH1RxwJJxqgdDp/RETMQGzsrYiImOFSAOzOaHp3R+CJiIiIiPoDjoQTkVvcGU3vzgg8EREREVF/wCCciNwmj6Z7+xgiIiIiov6C6ehEREREREREPYRBOBEREREREVEPYRBORERERERE1EMYhBMRERERERH1EAbhRERERERERD2EQTgRERERERFRD2EQTkRERERERNRDGIQTERERERER9RAG4UREREREREQ9hEE4ERERERERUQ9hEE5ERERERETUQxiEExEREREREfUQBuFEREREREREPYRBOBEREREREVEPYRBORERERERE1EMYhBMRERERERH1EAbhRERERERERD2EQTgRERERERFRD2EQTkRERERERNRDGIQTERERERER9RAG4UREREREREQ9xGtBeGNjI+bNm4ewsDCEhYVh3rx5aGpqsnvMHXfcAZ1OZ/YvLy/PW6dIRERERERE1KMCvPXCt912GyoqKvDll18CAH71q19h3rx5+Pzzz+0ed8UVV+Ddd981Pdbr9d46RSIiIiIiIqIe5ZUg/MCBA/jyyy+xefNmTJ06FQDwj3/8A/n5+Th06BAyMjJsHmswGBAXF+eN0yIiIiIiIiLqVV4Jwjdt2oSwsDBTAA4AeXl5CAsLw8aNG+0G4UVFRYiJiUF4eDimT5+OZ555BjExMTbbt7a2orW11fS4paUFAGA0GmE0Gj3w3XiPfH6+fp7kO9hnyFXsM+QK9hdyFfsMuYp9hlzVV/qMK+enkyRJ8vQJ/PWvf8V7772Hw4cPm+0fNWoUfvGLX2DhwoWaxy1btgzBwcFITk5GaWkpnnjiCbS3t2Pbtm0wGAyaxzz55JN46qmnrPZ/+OGHGDx4cPe/GSIiIiIiIiI7zp07h9tuuw3Nzc0IDQ2129alkXBbAa/a1q1bAQA6nc7qOUmSNPfLbr75ZtP22LFjkZubi+TkZKxatQpz587VPGbhwoVYsGCB6XFLSwuSkpJQWFjo8JvvbUajEWvWrMHll1+OwMDA3j4d6gPYZ8hV7DPkCvYXchX7DLmKfYZc1Vf6jJyR7QyXgvD7778ft9xyi902KSkp2L17N2pqaqyeq6urQ2xsrNPvFx8fj+TkZBw5csRmG4PBoDlKHhgY6NP/SWp96VzJN7DPkKvYZ8gV7C/kKvYZchX7DLnK1/uMK+fmUhAeFRWFqKgoh+3y8/PR3NyMLVu2YMqUKQCAH3/8Ec3NzZg2bZrT79fQ0IATJ04gPj7eldMkIiIiIiIi8kleWSc8MzMTV1xxBe6++25s3rwZmzdvxt13342rrrrKrCjb6NGjsXLlSgDAmTNn8PDDD2PTpk0oKytDUVERrr76akRFReH666/3xmkS9RmS1IHGxiLU1X0Ef/89kKSO3j4lIiIiIiJyg9fWCf/Xv/6FBx98EIWFhQCAa665BkuWLDFrc+jQITQ3NwMA/P39sWfPHrz//vtoampCfHw8Zs6ciWXLliEkJMRbp0nk8+rqVqCk5CG0tlYAAIKDgeLiNzBy5KuIjtaulUBERERERL7Ja0H40KFDsXTpUrtt1IXZBw0ahK+++spbp0PUJ9XVrcC+fTcCMF/EoK3tJPbtuxFZWR8zECciIiIi6kO8ko5ORN0nSR0oKXkIlgF417MAgJKS+UxNJyIiIiLqQxiEE/mopqYNphR0bRJaW0+gqWlDj50TERERERF1D4NwIh/V1lbl0XZERERERNT7GIQT+Si93rml+ZxtR0REREREvY9BOJGPCg8vgMGQCEBno4UOBkMSwsMLevK0iIiIiIioGxiEE/konc4f6emL5UeWzwIA0tMXQafz79HzIiIiIiIi9zEIJ/Jh0dFzkZX1MQyGYWb79fphXJ6MiIiIiKgP8to64UTkGdHRcxEVdS2amjbg/PkT2L79OAoLH4ZeH9Tbp0ZERERERC5iEE7UB+h0/oiImIHgYCM6OlYzBZ2IiIiIqI9iOjoRERERERFRD2EQTkRERERERNRDGIQTERERERER9RAG4UREREREREQ9hEE4ERERERERUQ9hEE5ERERERETUQxiEExEREREREfUQBuFEREREREREPYRBOBEREREREVEPYRBORERERERE1EMYhBMRERERERH1EAbhRERERERERD2EQTgRERERERFRDwno7RPwNEmSAAAtLS29fCaOGY1GnDt3Di0tLQgMDOzt06E+gH2GXMU+Q65gfyFXsc+Qq9hnyFV9pc/I8accj9rT74Lw06dPAwCSkpJ6+UyIiIiIiIhoIDl9+jTCwsLsttFJzoTqfUhnZydOnjyJkJAQ6HS63j4du1paWpCUlIQTJ04gNDS0t0+H+gD2GXIV+wy5gv2FXMU+Q65inyFX9ZU+I0kSTp8+jYSEBPj52Z/13e9Gwv38/JCYmNjbp+GS0NBQn+5Q5HvYZ8hV7DPkCvYXchX7DLmKfYZc1Rf6jKMRcBkLsxERERERERH1EAbhRERERERERD2EQXgvMhgM+POf/wyDwdDbp0J9BPsMuYp9hlzB/kKuYp8hV7HPkKv6Y5/pd4XZiIiIiIiIiHwVR8KJiIiIiIiIegiDcCIiIiIiIqIewiCciIiIiIiIqIcwCCciIiIiIiLqIQzCiYiIiIiIiHoIg3Ave+2115CamoqgoCDk5ORgw4YNdtuvW7cOOTk5CAoKQlpaGt54440eOlPyBa70l6KiIuh0Oqt/Bw8e7MEzpt60fv16XH311UhISIBOp8Mnn3zi8BheYwY2V/sMrzMD27PPPovJkycjJCQEMTExuO6663Do0CGHx/E6M3C502d4nRnYXn/9dYwfPx6hoaEIDQ1Ffn4+vvjiC7vH9IdrDINwL1q2bBnmz5+Pxx9/HDt27EBBQQGuvPJKlJeXa7YvLS3FnDlzUFBQgB07duCxxx7Dgw8+iOXLl/fwmVNvcLW/yA4dOoSqqirTv5EjR/bQGVNvO3v2LLKzs7FkyRKn2vMaQ672GRmvMwPTunXr8Jvf/AabN2/GmjVr0N7ejsLCQpw9e9bmMbzODGzu9BkZrzMDU2JiIp577jkUFxejuLgYl156Ka699lrs27dPs32/ucZI5DVTpkyR7r33XrN9o0ePlh599FHN9o888og0evRos3333HOPlJeX57VzJN/han9Zu3atBEBqbGzsgbMjXwdAWrlypd02vMaQmjN9htcZUqutrZUASOvWrbPZhtcZUnOmz/A6Q5YiIiKkt956S/O5/nKN4Ui4l7S1tWHbtm0oLCw0219YWIiNGzdqHrNp0yar9rNnz0ZxcTGMRqPXzpV6nzv9RTZx4kTEx8dj1qxZWLt2rTdPk/o4XmPIXbzOEAA0NzcDAIYOHWqzDa8zpOZMn5HxOkMdHR346KOPcPbsWeTn52u26S/XGAbhXlJfX4+Ojg7Exsaa7Y+NjUV1dbXmMdXV1Zrt29vbUV9f77Vzpd7nTn+Jj4/Hm2++ieXLl2PFihXIyMjArFmzsH79+p44ZeqDeI0hV/E6QzJJkrBgwQJcfPHFGDt2rM12vM6QzNk+w+sM7dmzB8HBwTAYDLj33nuxcuVKjBkzRrNtf7nGBPT2CfR3Op3O7LEkSVb7HLXX2k/9kyv9JSMjAxkZGabH+fn5OHHiBF588UVccsklXj1P6rt4jSFX8DpDsvvvvx+7d+/G999/77AtrzMEON9neJ2hjIwM7Ny5E01NTVi+fDluv/12rFu3zmYg3h+uMRwJ95KoqCj4+/tbjWLW1tZa3b2RxcXFabYPCAhAZGSk186Vep87/UVLXl4ejhw54unTo36C1xjyBF5nBp4HHngAn332GdauXYvExES7bXmdIcC1PqOF15mBRa/XIz09Hbm5uXj22WeRnZ2NxYsXa7btL9cYBuFeotfrkZOTgzVr1pjtX7NmDaZNm6Z5TH5+vlX7r7/+Grm5uQgMDPTauVLvc6e/aNmxYwfi4+M9fXrUT/AaQ57A68zAIUkS7r//fqxYsQLfffcdUlNTHR7D68zA5k6f0cLrzMAmSRJaW1s1n+s315heKgg3IHz00UdSYGCg9Pbbb0v79++X5s+fLw0ZMkQqKyuTJEmSHn30UWnevHmm9seOHZMGDx4s/fa3v5X2798vvf3221JgYKD08ccf99a3QD3I1f7yyiuvSCtXrpQOHz4s7d27V3r00UclANLy5ct761ugHnb69Glpx44d0o4dOyQA0ssvvyzt2LFDOn78uCRJvMaQNVf7DK8zA9uvf/1rKSwsTCoqKpKqqqpM/86dO2dqw+sMqbnTZ3idGdgWLlworV+/XiotLZV2794tPfbYY5Kfn5/09ddfS5LUf68xDMK97G9/+5uUnJws6fV6adKkSWZLNNx+++3S9OnTzdoXFRVJEydOlPR6vZSSkiK9/vrrPXzG1Jtc6S/PP/+8NGLECCkoKEiKiIiQLr74YmnVqlW9cNbUW+RlXSz/3X777ZIk8RpD1lztM7zODGxafQWA9O6775ra8DpDau70GV5nBrZf/vKXps++0dHR0qxZs0wBuCT132uMTpK6ZrITERERERERkVdxTjgRERERERFRD2EQTkRERERERNRDGIQTERERERER9RAG4UREREREREQ9hEE4ERERERERUQ9hEE5ERERERETUQxiEExEREREREfUQBuFEREREREREPYRBOBEREREREVEPYRBORERERERE1EMYhBMRERERERH1kP8PWvGzfbSgfw0AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu = 1e-6\n", "#u0 = np.zeros(n+1)\n", "#u0[0] = np.mean(yi)\n", "u = np.linalg.solve(A.T@A + mu*Id, A.T@yi)\n", "print(np.linalg.norm(u))\n", "print(np.linalg.cond(A.T@A+mu*Id))\n", "\n", "xd = np.linspace(0, 3, 400)\n", "plt.figure(figsize=(12,6))\n", "plt.plot(xi, yi, 'oy'); plt.grid()\n", "plt.plot(xd, f(xd, u), '-b', linewidth=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "dd3e5800-d44d-41fa-94a3-09a11fa6946b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 19, "id": "d9b440a3-22b5-422d-b773-fa920821e940", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.205510584025289\n", "96095.92498596171\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu = 2e-2\n", "u = np.linalg.solve(A.T@A + mu*Id, A.T@yi)\n", "print(np.linalg.norm(u))\n", "print(np.linalg.cond(A.T@A+mu*Id))\n", "\n", "xd = np.linspace(0, 3, 400)\n", "plt.figure(figsize=(12,6))\n", "plt.plot(xi, yi, 'oy'); plt.grid()\n", "plt.plot(xd, f(xd, u), '-b', linewidth=3)" ] }, { "cell_type": "code", "execution_count": 20, "id": "35d95ee5-76f3-4c96-ad28-ffb08acd4d86", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.729331376697857\n", "19273.46369403537\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu = 1e-1\n", "u = np.linalg.solve(A.T@A + mu*Id, A.T@yi)\n", "print(np.linalg.norm(u))\n", "print(np.linalg.cond(A.T@A+mu*Id))\n", "\n", "xd = np.linspace(0, 3, 400)\n", "plt.figure(figsize=(12,6))\n", "plt.plot(xi, yi, 'oy'); plt.grid()\n", "plt.plot(xd, f(xd, u), '-b', linewidth=3)" ] }, { "cell_type": "markdown", "id": "a7070eff-ee1f-4504-8274-9718413617f7", "metadata": {}, "source": [ "#### Exercice 4 (optionnel) - Identification de paramètres d'un système masse-ressort\n", "\n", "On considère ici un système masse-ressort linéaire avec amortissement, $m_0$ est la masse, $k$ est le coefficient de raideur du ressort et $a$ est le coefficient d'amortissement. Le mouvement du point matériel est gouverné par l'équation différentielle du second ordre:\n", "\n", "$$\n", "m_0\\, \\ddot{x}(t) + a\\, \\dot x(t) + k\\, x(t) = 0\n", "$$\n", "\n", "où $x(t)$ représente la position de la masse au temps $t$.\n", "L'équation caractéristique correspondante est:\n", "\n", "$$\n", "r^2 + \\frac{a}{m} r + \\frac{k}{m} = 0\n", "$$\n", "\n", "avec le discriminant $\\Delta$ fonction de $m_0$, $k$ et $a$ :\n", "\n", "$$\n", "\\Delta = \\left(\\frac{a}{m_0}\\right)^2 - 4 \\frac{k}{m_0}.\n", "$$\n", "\n", "On suppose $\\Delta<0$, si bien que la masse à un mouvement oscillatoire amorti. Sans conditions initiales, la solution générale est de la forme\n", "\n", "$$\n", "x(t) = A\\, \\exp(-\\frac{a}{2m}t)\\, \\cos(\\frac{\\sqrt{-\\Delta}}{2} t) \n", "+ B\\, \\exp(-\\frac{a}{2m}t)\\, \\sin(\\frac{\\sqrt{-\\Delta}}{2} t) \n", "$$\n", "\n", "avec deux constantes réelles arbitraires $A$ et $B$. \n", "\n", "Dans la suite, on considère $m=1$, $a=0.4$ et $k=11$ et on suppose $A=1$ et $B=0$ correspondant à $x(0)=1$ et $\\dot x(0) = -0.2$. La solution est donc\n", "\n", "$$\n", "x(t) = \\exp(-\\frac{a}{2m}t)\\, \\cos(\\frac{\\sqrt{-\\Delta}}{2} t).\n", "$$\n", "\n", "Sur brouillon, calculez $\\dot x(t)$ et $\\ddot x(t)$. Ecrire une fonction \n", "\n", "```\n", "x, xdot, xdotdot = xressort(t)\n", "``` \n", "\n", "qui retourne les valeurs $x(t)$, $\\dot x(t)$ et $\\ddot x(t)$ au temps $t$. Afficher le résultat de\n", "```xressort(0)```." ] }, { "cell_type": "code", "execution_count": null, "id": "eb6d8244-4b12-4736-ad05-a26597942ac4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 435, "id": "23051076-08f4-4714-a60c-6af738f1633a", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(np.float64(1.0), np.float64(-0.2), np.float64(-10.920000000000002))\n", "(np.float64(-0.8070671630222583), np.float64(0.6172977807224753), np.float64(8.630819680955852))\n" ] } ], "source": [ "m0 = 1\n", "a = 0.4\n", "k = 11\n", "\n", "def xressort(t):\n", " Delta = (a/m0)**2 - 4.0*(k/m0)\n", " x = np.exp(-0.5*a/m0*t) * np.cos(np.sqrt(-Delta)*t/2)\n", " xdot = -0.5*a/m0 *x \\\n", " - 0.5*np.sqrt(-Delta)*np.exp(-0.5*a/m0*t)*np.sin(np.sqrt(-Delta)*t/2)\n", " xdotdot = -0.5*a/m0*xdot \\\n", " + 0.25*a/m0*np.sqrt(-Delta)*np.exp(-0.5*a/m0*t)*np.sin(np.sqrt(-Delta)*t/2)\\\n", " + 0.25*Delta*np.exp(-0.5*a/m0*t)*np.cos(np.sqrt(-Delta)*t/2)\n", " return x, xdot, xdotdot\n", "\n", "print(xressort(0.0))\n", "print(xressort(1.0))" ] }, { "cell_type": "code", "execution_count": null, "id": "54492e61-049f-442c-b8b8-4a8fdec24246", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "83dcf94b-8685-4779-a328-2223f0afe4fa", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "ff41dcdc-59ba-4892-9a14-4e0fd7962852", "metadata": {}, "source": [ "L'exercice consiste à étudier si, à partir de la connaissance de la position $x(t^n)$, la vitesse $\\dot x(t^n)$ et l'accélération $\\ddot x(t^n)$ à différents instants $t^n$, **connaissant la masse $m$**, on est en mesure d'identifier les caractéristiques mécaniques du ressort, c'est-à-dire la **raideur $k$** et l'**amortissement $a$**. Pour chaque instant $t^n$, on a donc\n", "\n", "$$\n", "\\ddot x(t^n) = - \\frac{a}{m}\\, \\dot x(t^n) - \\frac{k}{m}\\, x(t^n)\n", "$$\n", "\n", "Les mesures de $x(t)$, $\\dot x(t)$ et $\\ddot x(t)$ ont sujettes à des incertitudes de mesures représentées par un bruit gaussien. Considérez le code python ci-dessous pour la génération de données. Dans ce cas,\n", "\n", "$$\n", "\\ddot x(t^n) \\approx - \\frac{a}{m}\\, \\dot x(t^n) - \\frac{k}{m}\\, x(t^n).\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "id": "b1749152-3a5a-443b-8f95-785f6f147095", "metadata": { "tags": [] }, "outputs": [ { "ename": "NameError", "evalue": "name 'np' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[3], line 2\u001b[0m\n\u001b[0;32m 1\u001b[0m N \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m200\u001b[39m\n\u001b[1;32m----> 2\u001b[0m t \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m10\u001b[39m, N)\n\u001b[0;32m 3\u001b[0m x, xdot, xdotdot \u001b[38;5;241m=\u001b[39m xressort(t)\n\u001b[0;32m 4\u001b[0m x \u001b[38;5;241m=\u001b[39m x\u001b[38;5;241m*\u001b[39m(\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m0.02\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrandn(N))\n", "\u001b[1;31mNameError\u001b[0m: name 'np' is not defined" ] } ], "source": [ "N = 200\n", "t = np.linspace(0, 10, N)\n", "x, xdot, xdotdot = xressort(t)\n", "x = x*(1 + 0.02*np.random.randn(N))\n", "xdot = xdot*(1 + 0.02*np.random.randn(N))\n", "xdotdot = xdotdot*(1 + 0.02*np.random.randn(N))" ] }, { "cell_type": "code", "execution_count": 2, "id": "9e056459-d8cb-4705-b17f-85e490dcccab", "metadata": {}, "outputs": [], "source": [ "import numpy.linalg as la" ] }, { "cell_type": "code", "execution_count": 438, "id": "4d74949b-3850-4d1a-9848-4e66ae4aaf22", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[267.69233772 -9.75714967]\n", " [ -9.75714967 24.96890598]] \n", " [ 0.39479381 11.03294729]\n", "k_estim = 11.032947291381301 , a_estim = 0.3947938119859051\n" ] } ], "source": [] }, { "cell_type": "markdown", "id": "77e697c7-ec3c-4bd1-a9f7-7e1af8cbfd12", "metadata": {}, "source": [ "On considère le problème aux moindres carrés\n", "\n", "$$\n", "\\min_{u=(k,a)}\\quad \\frac{1}{2} \\sum_{n=1}^N \\left[ \\ddot x(t^n) + \\frac{a}{m} \\dot x(t^n)\n", "+ \\frac{k}{m} x(t^n)\\right]^2.\n", "$$\n", "\n", "Ecrire le problème sous la forme matricielle\n", "\n", "$$\n", "\\min_{u=(k,a)} \\quad \\frac{1}{2} \\|A u - b\\|^2\n", "$$\n", "\n", "en déterminant la matrice $A$ et le second membre $b$. Résoudre les équations normales et affichez les valeurs\n", "estimées $(\\hat k, \\hat a)$ et $k$ et $a$." ] }, { "cell_type": "code", "execution_count": 1, "id": "46704a0e-50c5-40dc-a4db-91ffb1951cbe", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'np' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[1], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m A \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((N, \u001b[38;5;241m2\u001b[39m))\n\u001b[0;32m 2\u001b[0m b \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m-\u001b[39m xdotdot\n\u001b[0;32m 3\u001b[0m A[:,\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m=\u001b[39m xdot\n", "\u001b[1;31mNameError\u001b[0m: name 'np' is not defined" ] } ], "source": [ "A = np.zeros((N, 2))\n", "b = - xdotdot\n", "A[:,0] = xdot\n", "A[:,1] = x\n", "u = la.solve(A.T@A, A.T@b) # Resolution des équations normales\n", "print(A.T@A, \"\\n\", u)\n", "ahat, khat = u\n", "print('k_estim = ', khat, ', a_estim = ', ahat);" ] }, { "cell_type": "markdown", "id": "26e72adf-65a2-4d61-b3fa-e239c3af5b99", "metadata": {}, "source": [ "Sur le même graphique, tracer la solution exacte $x(t)$ et $\\hat x(t)$ correspondant à la solution de paramètres mécaniques estimés $\\hat k$ et $\\hat a$." ] }, { "cell_type": "code", "execution_count": 439, "id": "7d0ddf4b-9ca2-4e96-9ecb-7c92bd24db97", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Deltahat = (ahat/m0)**2 - 4.0*(khat/m0)\n", "xhat = np.exp(-0.5*ahat/m0*t) * np.cos(np.sqrt(-Deltahat)*t/2)\n", "plt.plot(t, x, '-b', alpha = 0.5)\n", "plt.plot(t, xhat, '.r', alpha = 0.5)\n", "plt.grid()\n", "plt.rcParams[\"figure.figsize\"] = 8,5 # taille de la figure" ] }, { "cell_type": "code", "execution_count": null, "id": "bbbebb41-a357-4531-9f74-96aaeb955c4a", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }