{"cells": [{"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["***\n", "# **EDO -- L3 MEU 2022/2023 -- Universit\u00e9 Paris-Saclay**\n", "***\n", "\n", "\n", "\n", "\n", "\n", "\n", "# TP 1 : Repr\u00e9sentation des solutions d'une EDO, r\u00e9solution approch\u00e9e par le sch\u00e9ma d'Euler explicite"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["Soit $f:\\mathbb{R}\\times\\mathbb{R}\\longrightarrow\\mathbb{R}$ une fonction de classe $C^1$ et consid\u00e9rons l'\u00e9quation diff\u00e9rentielle\n", "$$\n", "(E)\\ \\ \\ \\ \\ \\ \\ y'(t)=f(t,y(t)).\n", "$$\n", "On remarque que le signe de la fonction $f$ dans le plan $(t,y)$ donne le sens de variation des solutions de l'\u00e9quation $(E).$ \n", "\n", "On appelle **champ de vecteurs** associ\u00e9 \u00e0 $(E)$ l'application \n", "$$\n", "V:\\mathbb{R}\\times\\mathbb{R}\\longrightarrow\\mathbb{R}\\times\\mathbb{R},\\ \\ \\ (t,y)\\mapsto\\big(1,f(t,y)\\big).\n", "$$\n", "\n", "On repr\u00e9sente le champ de vecteurs en un point $P=(\\bar{t},\\bar{y})$ du plan par une fl\u00e8che correspondant au segment $[P,P+\\varepsilon V(P)],$ avec $\\varepsilon$ petit, partant de $P$ et pointant vers $P+\\varepsilon V(P)$.\n", "\n", "On remarque alors que si $y(t)$ est une solution de $(E)$ qui passe par le point $P$, le vecteur $V(P)$ est tangent au graphe de $y$ au point $P.$\n", "\n", "Dans la premi\u00e8re partie de ce TP nous allons observer ces propri\u00e9t\u00e9s.\n", "\n", "## 1. Repr\u00e9sentation des solutions d'une EDO\n", "\n", "Nous nous int\u00e9ressons aux trois \u00e9quations suivantes :\n", "\n", "\\begin{equation}\n", "(1)\\ \\ \\ \\ \\ \\ \\ y'=-2ty,\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "(2)\\ \\ \\ \\ \\ \\ \\ y'=y-t^2,\n", "\\end{equation}\n", "\n", "\\begin{equation}\n", "(3)\\ \\ \\ \\ \\ \\ \\ y'=ty^2.\n", "\\end{equation}\n", "\n", "**Q1)** D\u00e9terminer les solutions de chacune des \u00e9quations 1, 2 et 3.\n", "\n", "> **R\u00e9ponse:** \n", "\n", "Solution g\u00e9n\u00e9rale de (1) :\n", "$$\n", "y:\\mathbb{R}\\longrightarrow\\mathbb{R},\\ \\ \\ y(t)=Ce^{-t^2},\\ \\ \\ C\\in\\mathbb{R}.\n", "$$\n", "\n", "Solution g\u00e9n\u00e9rale de (2) :\n", "$$\n", "y:\\mathbb{R}\\longrightarrow\\mathbb{R},\\ \\ \\ y(t)=Ce^{t}+t^2+2t+2,\\ \\ \\ C\\in\\mathbb{R}.\n", "$$\n", "\n", "Solution g\u00e9n\u00e9rale de (3) :\n", "$$\n", "y:\\Big\\{t\\,|\\,C+\\frac{t^2}{2}\\neq0\\Big\\}\\longrightarrow\\mathbb{R},\\ \\ \\ y(t)=\\frac{-1}{C+\\frac{t^2}{2}},\\ \\ \\ C\\in\\mathbb{R}.\n", "$$"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q2)** Consid\u00e9rons l'\u00e9quation 1. Tracer sur le m\u00eame graphique, dans l'intrevalle $[-3,3],$ la solution de 1 qui v\u00e9rifie $y(0)=1$ et la solution de 1 qui v\u00e9rifie la condition initiale $y(0)=2.$ \n"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0, 0.5, 'y')"]}, "execution_count": 1, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "# Fonction f d\u00e9finissant l'EDO\n", "\n", "def f1(t,y):\n", " return -2*t*y\n", "\n", "# Solution de l'EDO\n", "\n", "def y1(t,y0):\n", " return y0*np.exp(-t**2)\n", "\n", "plt.figure(1)\n", "tt=np.linspace(-3,3,100)\n", "Y1=y1(tt,1)\n", "Y2=y1(tt,2)\n", "plt.plot(tt,Y1,label='y(0)=1')\n", "plt.plot(tt,Y2,label='y(0)=2')\n", "plt.title('Solutions de y\\'=-2ty')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["### Trac\u00e9 du champ de vecteurs.\n", "\n", "**Q3)** Dans la figure de l'exercice 1, tracer dans le plan $(t,y)$ le champ de vecteurs associ\u00e9 \u00e0 l'\u00e9quation 1, en utilisant les commandes :\n", "`t=np.linspace(-3,3,31)\n", "y=np.linspace(0,2.2,23)\n", "T,Y=np.meshgrid(t,y)\n", "U=np.ones(T.shape)/np.sqrt(1+f1(T,Y)**2)\n", "V=f1(T,Y)/np.sqrt(1+f1(T,Y)**2)\n", "plt.quiver(T,Y,U,V,angles='xy',scale=20,color='blue')`\n", "\n", "Ci-dessus, `f` d\u00e9signe la fonction d\u00e9finissant le second membre de 1.\n", "Limiter le graphique \u00e0 la fen\u00eatre $[-3,3]\\times[0,2.2]$ \u00e0 l'aide de la commande `plt.axis`\n", "Rajouter des l\u00e9gendes, des labels pour les axes et un titre \u00e0 votre graphique."]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0, 0.5, 'y')"]}, "execution_count": 2, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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5uFlZssw7gM90WZkse6q0lMfu1MlMW1NDJTc21kwL8F707On+f428vDykpqaik+QHveCkckM1by7z1XfvTk3X9MAA9Ju2bQtcfrmZtqyMguqqq8z+Uyu17eabZdpNs2bA+PGy1MDgYKBHD2qcJuTlURu67DLzmtPTGSi+9FKzuZ+TQ2YXF8dArQnZ2dSiL7/cbJpblkX37sDw4fa069fz/Kqq6LqySxLQGvjhBwrY0lK6/ezSPCsryczffbfuvktLA04/3X5tElx7La3gTZt80/TsSeEtid/UJ8jdrRsZlASRkfL4Qn1ppUHuVq1c1m95eTlatmzpVVAAFITVwt61lnD7J2n9/OQuNm9QSqFly5Y+LS3RGv7+z//3IThYln3jcJBpSKR0UBA3lkSwBARwA5x6qlnDqqykdtyvnyxzyd8f6NCBQsCEsjKue/BgM63FYM4/37zmrCxqbUOGmLWh1FQGrJs0MQuL6mqut6ICmDXLrEXu2QOcdhqVg5kz7Wmt4HazZvzOTTf5pt2xgwwyNJSuvtatgYULfQuLf/2L2Ui9e9d+f9UqZkTV1Px9q8KCnx/w9ttUKqrq9OF1YcIE4KefzMf7bwhy1zcjSipYLMvCgi9BAdSPUQcEnDhhIRUAEovNE57Kn931kOCkckNJs5YKC2XmJ1C/bKgjR7hRJCZzUREZgaTIRmsyVElxEkA3kTQ1OCeHlo0kHTYzk2uRmNhWJpREeCcnUxAmJgJdu9rTak2t//BhWfHjunXA3XcDX38NjBpl/9C5u6CKisj8fAnRrVuBX38Ffv+97melpWQC1rG0BvbtM6/VHbm5wNNP08qZOJGvF1/0nVwwZQo/v/BC++P27w9s2yZbw98RFlbWmR3qkxH1dy0LEwICqJxI4O9/YqwQPz85bX3h5yd3C0rxPyksLr9cnm44fTrw5Zcy2lNOoRYqERZt21L7lNROaA1cfbU8Hfbpp+WZUw8+SO3cFDQHgBkzgKeekgmLESPINDdvNtO2bk0tffp0s5XlcAAff0yGJ6mdeOklapyrVwMPP2xPO326K961cCEZsK+HLSqK8YwAjyfo6FH+zurVrgramhrgySfNawVoPaxbx720bBnPc8cO4NZbuQdGjqSV27w5GdjVV3MdAwbQPWcX/7rySuDDD7lmU63RnXdS8Eiek7lzeZ0klsXChRSEEmGxeTMzsiSKT3Y2M8dMbkkLubmyPQ+4YhbS49pZgBkZGbjmmmvw/fffIz8fePvtZ/DDDx/A398fr732GsaNG4fKykqcddZZWLFiBQKcG6y42F5g/fvf/8arr76KAwcOIDU1B1VVEaipMdee1UdYnVTCQlqU16qVvMCtdWu5FdKqFdcgSZ8MDeUDJrEs/Py4hkaNZOto00YWjAPoQpFet5gYWi0SYdG6NRmXxA3TpAk106Agsybk70/G+Nln5uA9QFec1rIiPnd30rx5TIX1BV/X4O67geuvr+3iDAhgsFyKRx/lddiwARg0yKUlnncecOaZVF4uvJDHzc11WWRnngn89pvv61JUxBjE4MFkxHbuwfJy3j9JzKK83JVcYkJ1tSvxwQR/f1oVEjdUaCiTNbrYzhl0QRK4t1BVJa/hqK62Z+ovv/wyrrmGk253796Nn3/+CvHx8UhPT8dZZ52F/fv3IygoCGeeeSa+/vprzHT6WR0OrsGXtTBy5Eicd955GOO8qQ6HzMVVnxqykypmIT3x4mK5m+bIEbmwqC8KC+VCKz9f7obKzZULC0kqrjvS0ymMJDh8mO4lCQ4dkmWFWNi5U16VffgwhZZUKGZmMu5T36SRpUuZ/TR7dv2+54mHHwZ+/pkM0FqzUkzHjoioXRMzbRrdZwCZ/8sve3eNAbRW1q1jkHvVKnsmHBfH7D6Luduhc2fuo0OHzHUR7duTNi3NrNW2aUNLLTPTzPhCQ7nW3Nz6MXYJrRUMl9JqDTzyyKN49dVXj73/0EMPYe7cufjuu+8wfvx4AMDy5YsxfvwlCA4ORqdOndC1a1dsdAaUJk2ahC/cNAxrH/i6DgMGDECMs9mdifbv4qSyLKR+xeJiea631fhM6v9zOFxFYyYUFHBzSxqa5efLK05zc13ZEyYGmZVFK0DKrK10UEkTxuRkarsSQWdpx5LaF2vdkZGyNih//sl4BUAt0eTO+/pr4JJLzGvwXM/DDzOO8Z/6iYOCaNVccw2ZuuXqGjSI1sa117r24wUXAGefTXfixo20LHzVy4wYQZdVbi5rZeyy6+Li6F5KS6Or69tvvdMB1OZffplusDfeAO64wzdtdDTw11+0cubPZw2DL7RqRWvh0CHWkZhS1/Py6IpavLh2IsjjS+OxO722xLNqskJC6roSPWHFoIJ/c+2dXm2bYc7EukGzigrusfPPvwrXXTcFt99+OxwOB7766it88803+PTTTxHs9BOmpqaha9fhxxoVRkdHI83pn+vduzc2OVPgiouLMWLEaFRVUSF2t4jmzZuHXh4mc0UFeWFamjkGmJ5u/7k7TirLQlrBXVxM7UyiKRw5ws0qqUKuquKxV6yQraOwkD2AJMjPB958U0abm8sHUtLpNDub1+Grr8y0DgcZ1O23y9aRnMxqdklANTGRGuo995hprf5USUn2riILlrA4epTMzIRvvgEuuoh/a20O8loxpeeek3f6NKF/f2DcOB7THR06cH2W4tC8ORn+vn10X/Xv71tpGjSIgfnrr+ea7azPuDjuTysrzA6dO1OJKC42Kxxt2tCiyM2tXQfgDRZjzMysm3HmDY0bU5GR0FoKoMTarA9tUBCfk65dY9CyZUv89ddfWL58OQYMGICKigq0ctsgVjaUN2Hl7++PoKAgFBcXo2nTpti4cRu++GIbfvllG7Ztc708BQXg8hRIPC3SbrrASWZZlJbKin327XO9TOmzubkUFKtXm/2hRUV8wP78U1aXkZ8vbw1y4ADTQDMyzG6gzEzSbthgPr+sLApDycay2iMsXUpmZYqh5Oay0rtxY+CMM+xpExPJ9L7/3mzFWS6oJ5+UrXvTJmrJTz1l9n8nJDBBwWKQb7/NtdgxtrfeIpN0eheOGx54gGnYEyfWTt32dItOm0bN/+GHgU8/9S2cQ0LIzIYPpzViJ9hateL+vO8+c+uI5s353J12mjku5O/PJJCYGFnqekQEmbTE6u3WjYKySxdg717X+94sgKQkPqv9+pktwfR07pt+/cwCo3FjMv8mTYDZs2fj448/RmZmJq666io0atSoVp1D+/btkJubciw1OzU1Fe3c3AwVFRUICQlBcXExRo0ajfJyJi+4r8GbZeHn57rOxxMnlWXhcDBzxASrKOmPP8y0v/9OrUlSlb1vH90iEgGgNR/GvXtlPWoOHOC/69ebaa0Kbkk+/aFD1JwlWUvp6UxNdDjYFsMOVgV3YqKZFiDd/Pl8gE3XY+dOMvNPPjEHSvPy+OCmpgLPP28u+PvyS2Z9ASyGu/12+ySEPXuAjz7isb1BWiPgDYGBzGq79lr7DJvzz3d1nu3Tx2UVecOwYdwXL79sZiYtWvDYI0ea1xoczOC+pHNwkya0mCQB5jZt2FRR4tpr1w647TYZbUAABZGUNjxcZllYgiIwEJg8eTJ+/vlnbNq0CePGjUP37t2RlJR0jHbixPOxfPlXUKoChw4dQkJCAoYOHQoAyMvLQ0REBAIDA9G0aVP89dc2zJ+/DX/9ZbYsgP/PhIVSqr1SaqVSardSKl4pdZsXGqWUek0plaiU2qGUGuj22RVKqQTn6wrJb4aHy/z//fpRC5H0b4qJoZ/1kUfMtDU19JU++qjZxVVaShPw4YflfW/Gj6crwYTQUGptd95pps3PB8aO5fmZAo7p6QySXnaZ2TWRm0uXSf/+dHuYkJHBgrxbbrFnjACFxYABLA60GLsvrF1LZmcVyNkVKmpNX/4FF/DvTz6hpuorJlJZyWr9996ra2U5HGSI8+bZr8+EPn3IsP/1L980YWHcS5a7zK51yymn8JrExZn3XVwclRRJOmpMTO2BT3Zo315W5ApQWAwYIKNt1Yr7TYKAAHl2YUCAuR2PBX9/V1wjKCgIp59+OqZNmwZ/f3+EhoaiS5cuSExMBAD06ROHc86Zhri4Xhg/fjzeeOMN+DtN5ZUrV+JcNwZlWQu+LOnXXnsN0dHRSE1NRd++ffHYY7PFa5biRFoW1QDu0lr3AjAcwE1KKU8xOAFAN+frWgBvAYBSqgWAOQCGARgKYI5Sypg3FBgoKy6zcswlgqW6mg+VJAXU8hX37m1+EI8e5UPdoYMsy0lrPgyS7KKiIm4qSRphQQGZ8ymnmF066ekURD16mK9HcrJLyzQ97JWVvHc5ORSIJjdbfDwbCJaWsvWIHax4RYsWPK5d2++tW9lCpGlT3r/wcLqhfDUIfPRR1mJ4MqicHCoiDzxgr+XbwV1w33svsHw541C+YLmiTBgxwtUbzQSrj5QEXbq4rF8T2rc/MTMtWreuX1HeiW734XA4sH79elx99dXHPr/55pvx8ccfH6O99tqHcODAAezbtw8TJkw4Rjdv3jxcd911sh8FcOuttyI1NRXV1dVIT0/Hk0++X6+W7RKcsJiF1joDQIbz72Kl1B4A7QC4Nz6+AMCnzmlN65VSzZVSbQCMAfCL1jofAJRSvwAYD8C2PK4+FdzSgT9HjshTLouKqFFKaicKClzmrQkOBzegdKBRYaE8hzw7m64ZSc+pjAwKLYmQTU7meiXHPXyYPun9+6mp26GmhplsOTkyAb52LXD//exma2rAOG+eq32Iw0ErY+1a7x1f//yTbipvre7Ly8lkZ58fj+iUVXAka2eygR/ymp+Bo43te7bU1HAvPfkkhc7EiYyLXHMNY2fu99aK70ycyLjQo4/an2N0NLNkJJlycXGutFwTOneWJYFYa0hJkdG2afPPV3D/nXYfu3fvxnnnnYfJkyejm1vL5cmTJyPP6Wf11e+psrISkyZNQndT10vBOiSWnhT/JwFupVQMgAEAPFuYtQPgvm1Sne/5et/bsa8FrRKEh8uS+u+4Q55ZdOONTKWU4Oyz6buWCItOnajxSoSFUswSys6WreOjj6iNSjB3LrV5yTpuvhmYM0cmLM4+m9abpLd/TAyzlCZMMKfk+vkxk23TJpnL4auveG6rVplTL++913UdVq+my89Xa/D+/dnFtg7DranG4md+xIYb3kWbitXAMprv7rHcBMfpWFtzPfY5zobnsMqqKq556lTGsxo35nWcMYOFeHffzeK8s88mMxg3jumiVmsVq8miN0yYwOSEnj15bLtg9BVXUMhKLIsnnqBiILEsPv+cwWWJ4rN2LYWyJLspM5PC3tSC3kJGhry+KDVVznQzM3kPe/XqhYM+pOdsZyFOTo53IRQUFITLPTJkiopctR4mr0V5Oa11SZ1FfWoxTriwUEo1AfAdgNu11vUcfGiG1vpdAO8CQMeOg0WGV2CgjKED9GtKfZuhodRWJJswKIg3VeKCslL3pJZFQIA8hdPS/CXWU/Pmrm6yJoSG0nqS1GMEBjLY6CuN0B1K0T+/bZtsfoS11rVrgWeesad1t4I++YQM0xeaNPFS2Jl/CAVvzcDNrXdDh3QATn0C6DMNCHJuiIoSYPs8dNv0IboVXwy06Q9cMg8Iq31BY2OZJJGaWtslFxdHBp6dTWHh70/Xy+bNZJKWK6pXL+8MJSKC8R7LFWUnLFq2pAUiGarUrBn3ssSysKYbSobzNGvG35dYFs2buxIwJKipkbuhtDbH0dxppVaIVZEthdZ8RkweFGsIlGQdUq8JcIKzoZRSgaCg+EJr7a3LTBoA91Zz0c73fL1vi/o0/JNWZde3grs+zbtO1Fzt7Gy5sJAUqbkjLU1WcAhQg5QIC6B+87oBzpGQBjPz8xkfkmqSR4/SxSQZrHQMh9eh+p0z4Xc0HWXnfQx12zZg5G1AszZASBhfYe2AU+8Bbt8BTH4HyDsAvH8mkF47GHH11dQkPduSjx/POMhPP7kqpWfMcAXRO3Vi6uy//+19iaNGUVMfNozWiJ3V0KcPMwsjIsx1Ml278hqnpponynXsSLdnSoq5pXrbtnz+MjLMRbQhIXz2srNl0/WUorCQaNaBgWS80gpuQEbr7y8XGP7+XLNEAFh80GoRcrxwIrOhFIAPAOzRWr/sg2wJgMudWVHDARQ5Yx3LAJytlAp3BrbPdr5nC6n0P3JEPvu2qKh+moXDIQ8KFhTIp5Hl5cmLDnNyuGkl55idTY1aknIM8JhSf3NSEh94ica5fz+Dy9I21wcPkjlKUlNXr3bFKySV+wsXsvW4WOva/hX0p+cjPb850s/5DY0GTwb8bDQX/0Cg3yXA1csAvwDgwwnA7iXHPlaKKbOPPFJbq/bzY63IO++40r/HjWPVuKUpHz7s+/5YwuLzz+latRub2qcPXXdbt3Jmhx26dmXsZu9eTmizQ4cOTN39/Xf297JDeDhdW8uXM63ahJwcFsRK3MYOB4WVJG29spIeA4kbuKyMvEIyObCsjPdM8jxZx5XQWhXcyclmxVVqiQEn1rIYCeAyAGcopbY5X+copa5XSlnJlD8COAggEcB7AG4EAGdg+0kAm5yvJ6xgtx2kM3WLi9l7RxLgOnKE2rRdJoqF6mpmWv38s2wdeXnAK6/Iad9+W6ZZ5ORQYG3ZYqbNzKQmIpkFbmkpN94o01gOH6YQ8jZFzhP79zP18uabzbRFRcxYOnJENrP7999ZMKY1ma0Jn35au6jSVvjv+BZYeB32lw7Db51+Rc9Rhv4K7oiMA65ZwX+/uRzY+8OxjyIiGP+6+uq61/qSS5i9BlDrHTWK5zhqFC0PX21hrLnaDz5IK8vOBdqrFwXxkCFmi69TJ+7Lmhrz+NwWLajIlJebe3sp5Zo9LbEiW7bksy1JL7cqrSXWZkgIaSXu6NBQ0komTzZp4mo5YoJVMyGhtc5JQlufjgMnTFhorf/UWiutdV+tdX/n60et9dta67edNFprfZPWuovWuo/WerPb9z/UWnd1vj6S/GZZmcwXum8ftV4JM83JoRYrKco7coSMbO1aMy3gquCWMN4DB+h6kVgtVgW33XQ1d9rDh2XXIj+f2u0ff8gsoowMtsS202At7N9PpvDjj2ZXhjVT+4UXZNdjzRoy108/9Z695I6UFGpwVtrx5s3As8/6IE7fBiy5GdmNR+KxAwsw6wZhp0d3NGkNzPoeaNsfWHAdkOMafDFuHLV2b8kY7i7XGTNcXW3nzPHNhK1K6MpKBvPthEXjxlSmHnrI7EoMDuYevuwycwsPpXjsIUNkjSCjohjDkVR7x8byvkkGhDVqRIEhEQAWrd0cdAtWlbyvRqUZGRk477zzAJDus8+ewYgRXdGjRw8sc27OyspKnHrqqah2C6oEBLgK/rxh5syZ6NGjB3r37o2rr74KWlf9/1OU909AKVmF86ZNvPCSSutVq6gpSBjvvn0UGJs3mwWA1mSKRUWsXjbh4EEyCMlIzC1bKDglPZkOHaIg2rXLbLWkpXG9SlFw2UFranl79sgG6Ozfz1YfgDmrZvt2pmq+9prZ3C8ooPZdWcmMMlMzxs8/d9Vu5OYyK8nrQ3c0F/j6UlQFReCS7z7B2+8FeTX5KysFLszARsDFnwOBIcBXM4ByVwrZs89yfoedwB05knuuvJznatf1dtQouuXuvtssBLp0IbOWtK6JiGDas4RRR0ZSCElige3asXBVko0UFcUKbkns0qrgllZlh4XJjuvvT6HiK3XdvUX5/v27sWwZW5T//PPPuPHGG1FTU1OrRbn7cf397YXF3r17sXPnTpSVlWHx4vfFnbWlOKmERfPmstS5AQMYaJNUFnfrxoDuy76iLm7w96d2M3eumfFWVNCff999slqEli0ZcJ061UxrFc699JKZtrCQgdN//9vM1NLS2Ab74os5ntMOubm8xgMH1m2G5w3p6azevukms2m8bRsrsc85x9zU8M8/ed1qapiCaZc+qzWziaxCul9/pTCqs56aKuDbWdBHc3Dtb5/j+Tdaea3b2bOHDFSUdhkWDUz7FChIAhZceyzy2qgR+2tddZVvt6mfH6+F1brcjgFacYvQUHNyRZ8+zJ6SVFt37Sqfz9Khg7yBXdu28sSHyEh5S/yAAHliR31oLab+6KPmFuU//LAY5557CUJCzC3KlXJVcXvDOeecA6UUlFIYOnQosrNTj3sF90nVSFDaD6WoiA+hhLakhIxG0ja7pIQMJzrazCCKimiytmol07Cqq6kJSVJtc3K4DsnciexsMqEePcw+zrQ00rRsaT62VWi3aZN5/KlVwZ2URCFkeuB37aJSsH+/eajQqlVsk96ihWtUqS9s2EA3inU/QkIYQ6lTKLjiKSBpNT4/+g76nzOgTgsRrVlEd9dd/D1xy/KOpwDjnwV+vBuVK1+COvUeBAYyRfiii1hw50vwzpjBeocpU+x/YtAgWVwIcGVESRSUbt1oIUtag3TowOCrRLFr00beRrt1ax8JDz/dD2TurPVWuJUJJShebVIDhFQDcGe+UX2ACXX9k1Zl+FVXXYUpU+xblGdkpKFDB9cFs2tRPno0Gwl6PqOejQSrqqrw2Wef4c4754rSbOuDk0pYSAtn8vPrX8EteeALC7kBJemwVgW3hPlbU6+kA43qMzfcquCWCBbroZVoeocP04UgiSkcOuTqFGoaHGRl/dTUUOCb7vn69WSyW7fSorS7j199Vbu24r33GBepVSmeuRNY+zrSoy7Ddz9fgoVeGgiWlzN7x9+ffvyaGhZKiqBn49SgNei8+gUMnz0FXYd1wcSJXNf06a5AtnXe1hjVPn0obIuKfO/t6mrSNmtmHpBlWWKSCX9a0y0one3dvj2FhQRRUXJh0aqVfNa5Vbt0vGmtymn3FuVZWVleW5Tb7UXPFuXbtm0TTXu88cYbceqpp2Lo0NENwsIO0gvzr3+Z5zFbePBBWdoeAEyeTHeORFjExjKAKREWfn7MjJHETQC6TyZNktHOm8e8e4nl9MgjDKBK6iymTKFrQjJTo0cPplGeeabZ5+3vz+D9xo2yDJnffiOD/O03Ht8Ozz3nYsIpKRSitR5OhwP4/g6gUXO0nvkEPpvp/YFfupQMed06MrCaGlnuPwBUVipM//hZrJn+G54fcxfeOLIQVVUKDgcFzrnnAqefDrz6Ko87YgT3hb8/LYAFC3wPPxo9msJm5EheQzuX3NSp/A1J2vO99/I6SWJv775Lhi6pb/j9d+CHH2S1OunpzCz0mgnlxQLYu4uuOEnr8327afmaMr0AV4IEYG5R3qxZO6Snu3Jh7VqUn3IKhx/ZWRaPP/44cnJy8Oqr7+DAAe4Pk/vsv6qC+/8S9RmrKq3gro90VoqWiNRqKSyUF9oVFMgti7w8WUNFgIKoulrWS0opPpQXXCCjTUmRtawGuKml1y4oiJbCwIFmWstv+9tvDBRLaAHS1mG6Wz8BUjcBk95GQNMW8ObF3L2bQemVK13n4u/PdGMp4uKi8O4nj+LWrnfjjKnfAX0uBEDL4cgRplA/+STdqMOHUzkYN44ptdddx5iSt5TQfv0oWEaNYj2CnbCIi2O8IiTEPHq3c2fWLEjafURH0wKR1MdERdG1K7EsWrXicy1tiWMV5UkQECCvs7IK7QD2gXr00UdRVVWFefPmoby8vFaL8vHjz8c118xARcWdSE9P99miPDAwEGvWbENSEoWyN2v6/fffx7Jly/Dbb7/B359BK4kg+K+p4P6/hvTET2QFd32ES33maufkyIWFNUlOAmv6nRQpKfKAY33maufmygUnwIwvST49QLdQXp6sTQnAazJ/PttnHENJDvDrHCBmNAvqvODIEbqdPv1UrjB4w9ixQHbHq5COAcCyB4GyQgDUsFevpjtt6VLSXnEFW5MAdEHt2cMkAW8YM4baerduFJ52acT9+vEa9+pFV5SdG6Z7d1og5eXmosqYGN6L1FRzJlu7dnxG0tO5P+xgadBZWbIWJZaSJBEYAQHy9hnWs19TY25RHhcXh7PPnoZevWQtygHfQuv6669HVlYWRowYgSFD+uPtt59AVZXZfSZtTQKcZMJCauofOWLefBasCm5p9bTDIavJAHhMabV3bi4DzBJkZdGfL3EL5OZSK5NO7MvJkbeiPniQzEFSw2FNLYyPl/mHd+2i9iup91i3ju4awNxiAqCmPmKER1798oeAylLg3Je9SletOY/j3ntlje9MeOxxfzy+5RXokhxgxZPH3o+OZtDecnUOHcpYT1ER4z4hIbRAvOG00/jdFStYZGoXY+jfn+m4CxYwcG6nUHTvTiG0Z49NTYoTHTsyjrR1q7mCu2lTnsvq1fIK7jVrZBXc1dW0mOpTwS2xhqwmfunp5hblZWXArFkP4ddfzS3Krdneviq4q6urceDAAWzbtg0bNmzDVVc9ipQU2agEKU4qYSGt4C4q4gMjoS8s5CaRzABwOCiIrHoBE7KzfU9Y80RuLjVIidaUnU3mK5mUZ3XflKTZAmSK990nW8ehQwxkLlpkpt27l8LiwQfNgrm01NUrRzIP3D1eIYlVvf8+24FbOLz+L2DH18DIW4FW3ttGP/88BePFF5uPL0FAAPDIWwPw5YFroDd/COS4gj9BQewgC/AaWA0EmzZlkN6X0tSmDffRZZfRcrCzfrp0ofY/e7Y5O61dO+79yEgKDjuEhvKltawoLzyc2q9kAFKHDhQCdgOuLDRqxDVICu0aN5bTNm1K2pSU3ejatSvOPPPMOi3KY5xBGMtj4eni89ai3MrclFac+/nJ1lsfr8lJJSyk0n/fPj4Ikkrr3FwyPYnmXVRUvwruvDxXMZUJBw7QHy4Zf5qZSeEmoc3IoLaydauZ1hqqtHq1bFRqSgp9/5IMlT176EpYssTsyti5k8zugw+4FhN+/50umHXrWMhnZ7nk5FDAWfGQoiIg+ZNngJDmbAzoBZZLR1JPUh9ERwOtpt6D8upG0L/7VtkvvZTFhABdc3YCccgQWhVz59rH7fz9yZhuuMFcle3nR+F2662yorymTZkAIREW7dszxiKp9ejenRaRhDYkRN5c0qKVMN+gINIOGsQW5S950cKsFuWBgd6rvb21KPf35zWWVmXbFfD9XZxUwsLPT1bBvWMHb6ipChkg4/fzk1UhJyaS8R84YHaJac3gXWiorO9UUhI3tmTN27ZRw5JkIiUluXzCJmshJYXnFRQkm8FdWkq3ksRttXcvBbJSZmGxdStdUC+8QIFr53c+coSfN23KWdYOhz291RfK6vD5+DWbMDpyGa2KkLqqeHIy6ynmzfOdeVKfjBNPjJ3UCmtrrgXiFwBZ3su4o6MZnLeus5s3ow5OO83VK8uODqBAzsiQjRTu1InWm9QCmDVLFkNq1451IZK2HFFRDPBbyRraRiuw0tYlcU5/f2rgktR8a1yrpCDOGsEqEVhWQZ5EYFnr8LQa7K6HBCeVsGjaVDZXu2dPbsL77jPTduzIh/GNN8y0fn7Ubv79b/MmrKqiW2D2bFlWT1gY1y0pqAoMJO0775hp8/M5G+G118xFeampZDJnnGGefW0FlE85RdakMDWVLqXLLnPFF3xh61b66i+6iJX1doL5jz+45upqWhezZvkWFlozmGud286dwAXNnkZhVQQwtG7r1fJy1j68+ab31GOHg+mnEgvPDqPvvRWl1U2Qt8D3QI7LL6egM8GKWwDmIHy/flROJBMJu3en0iERAB07kqFLEiuio+UaclSUe0FlCPLy8nwyyIAAeSJKQIA8ecZyj0ppARm9VcEtrSVTynOiokZeXh5CJN0FfeCkSp21mm2ZcOSIvIS/qIjMSNKd0WqAFxFhXoc1Y6FlS5kWUl3N1geSe52dTa1e0lIhI4Puu/btzdpbSoprbriJ0Rw8yJTKzZvNQ4rKy3kNdu9mcNhUx7F9OzXYRx4BvvzSXjP77Tdq0I0aMYbzyy++z3PNGv6+5Z5pU7UW/aNXomDIU0BwXY51660ULFYHWHckJLDyu7CQ/Yrqi6Ii3pfWrYGg5i1QOuhGtNz+HI7s34Fm3ev6WSZPppCdM8eesUVH01UrmWPSvz8bQUrQvTstWYmyFhMjb83frp08scN9Xnd0dDRSU1OR46MHd1kZr68kcaWykmm5xcVm2poaKkrSka3WqGIJMjPlgig7m8d13wshISGIlg6j8YKTTlhIoHX9Uhv9/GSCpbKStJJ02JISakGSdFiHg+uVthMODuamkmwsKytEohEePcprLNE0c3Np3VgFY3ZISyPz373bPHCopobMPDiYv2FKEd6/ny03srMpJOwCet9/XzuwfXTpv1AWGInwsVfXoV2xggzHV/3EvHnMirPayj/xhP063VFQQHfDSy8xxjBxInDJpBvReNfb2PvWv9D2rq+OCdTMTDLJxo0Z2P3jD1pQ3pCVxSD0oEHMULNrzZGT46q1MKGoyJXlZMLRo7xnkuNWVHDfS2JeNTVUZCxhERgYiE42edvLlgHffcciQRM2b+a9WLjQTJueTm+B5FoUF9MylVS+l5WRdutWmdfirrvYcsb0rNbHM3VSuaGkZuVDD8naWwDUHqWCZcIEPoySCu6uXYGzzpLVFvj5kdlIhcX338uK7ABuqKIimRVy++1cr6RZ2znn0E0kEUJdupCp2s2PtuDvz2E4CQnmzBuAFcCNG9OiGDvWnvaZZxhMBYCqhNXo7LcaAWfc5RqL6obTT6fW7U0gp6Yy5fSbb4CZM3n/hg6Vvfr14zyUsDDGAYYN4yu6a3P4j7oFQ8N+wpXjtiAvjwzy7LNdnXTday684fzzqaS4u6J84frrKVzKy825+E8/TcEtiZHNm0fm6Cu91x3r17OeJDXVTJuTwwpuSYILANxxh3zwzw03yGkffFA2dx6gu1pK+/PPpC0pMdNayTASS6g+wuKksiykwqKwUC4A6hsTOlGjUnNy5MLCmn4nhV0/IU8kJ5s7zlpITHTNhZAeW1rwt2mTrBGdhWXLKPjt4M74cxa9hqa6FZoOvcInrTdrs7SUqaxvvOESPADgHGEgQs+ezHDauLF2xlLNsOtRvup1XN3z3/jmm49www1s67JgAYXSqFHs3Ltnj/cMplNPdcVwrr/ePmY3cCC12G7dKJjt5knExtI6lKSid+rEBBOJsGjfnntTkqZtVXBL5nUDtJClAqB1a3kvqxYt5IVu4eGuYj8T72renEpHUZE53bVZM/ItyaTM/4oKbqXUh0qpbKWU17wZpdQ9bhP0dimlapRSLZyfJSmldjo/E4cHpScuueAWjh515YVL4K0zpC/k5tavglsqLDIz5cLCOi+pLzQ5WeaGAqjhdBUOjistdeWHS1AfYeFwMONMkkgAAMjZh7ZHl6N6wDWcMSGEVZg3e3ZtQVFf9OoF3H8/2424Z1L5N26KkBGXYVrvxdi2itVZV13liitkZpLx+OqBdeaZjOFUVFAA2CVtDBzILrwxMQzg2zGe2FjGkRo1onvODp07U1AUF5tdUe3a8Zyys81Wi8Vsc3Nl/ayaNOEaJLGT5s3l409DQ0kribOEhFDh2LvXTBsYyGdU4pILCOA+OHjQXKEuja0AJ9YN9TGA8b4+1Fq/YE3QA/AAgFUeo1NPd34uKLEhJPUKAIVFerpMABQWkoElJMiOrbWrFYMJeXmywjmAD8yhQ7I0zMxMWgrS6X5hYXTXSJCWRiFgGiIEuCyL338301oV3Ckpsl5AmzfT9y5xfezYwZx+Pz+ZxpX341uodAR7jVXY4YknqA3XaWn+NzBtGhlrndqNYdfBTwEvX/IOqqvJzAMCuD/btqUr1GpR74nRo1mXUllJhm1XWzNwIN1FS5ZQWNilbFrCYv16ulbs0L49hcSOHUxOsENwMPfyX39xHSbk55NWUgRaXMz0b9MaALq29u+nq9SEtDQKIMn43sxMPtOPPmqmPXqUzF9CC/AZeughs8VSn1Y/J0xYaK3/ACBskoHpAAS3zR55eTJmWlREzVQiAAoL+fBJCu0sRiQJhAHchM/4zoashZwcCiGJZpGVxY0lWXNaGjUnaQC2uprpoBJt6MABWgySFF4rXvHMM+a6jKoqCqtmzeh2MWlHy5bRtw8wvdS2xcrRPDQ9+CWyoi4BQpl9UF1t3ivffkvBL63Il+C559h65Jdf3N5s3gHodQFC93yKgBo6pWfPZoEiwI7KQ4d6b+MQGkrtPzKS/aPsUlIjI6mlz5lDIWTHdCzXyxlnmDuzBgbyvrVsKWuLEhlJoSHpMNyzJxUCSQX3wIFklBKX6siRPH/JrI7TT2e80FuGnCdOO433Y+RIM+3gwbxfEtrWrVlGMHq0WRhIY5vAf0GAWynVGLRAvnN7WwNYrpTaopS61vD9a5VSm5VSm6urc0TMdN8+arCSquycHGphEsZbXExhIWkNYh07MdHcUA0g89++XdamPCPD1X/HhPR0ajjbt5tN1pISPozffy/raZWUxLoFifYfH8/MsPffN/uHd+0io/n5Zwa7Tb7y5cspLDIzGdi0UyjK136IIFWOdlOZ5qQ1U1/t3BVbtlBIzJt3nOcHBPCY99zj8fsjbgIqioC/OGzi/PNpGVrpsF995ftenn46O+I+/rg5ntSxIxmkqXgPoHV6882yNt4REXTXmZIZAFpO551nTr8GGA857TRZYWBMDAWFRLC0b8/fHzbMTBsVxSp2ibCIiHBVqJsQFkalzpQtaCE8nDGq44l/XFgAmAhgjYcLapTWeiCACQBuUkr5PG2t9bta68Fa68H+/q1EKXn79lHySvyKf/1FzUbS+vjwYVeFsCR/u7ycWVmSquzDh7kBJIG23bupUUgyQ5KTaWk1b262WpKTXS0HTAFKrand7t7NdZhcfrt30yT38zP7hjdt4kP+yiv8v52wOHqUArxtWzKzggKbtVRXoGbtezjkfxb8IhnRfe01umF8zVTIyKDb6auv/rNOs74QGcmMtRkz3Nys0YOB9sOADW8BjhoEB1MYWj3J2rf33crDils0b24eK2y5oiTWb2wsGeU555hpO3eWzS4BWBdy4YWyeF2bNszAk7TEiIzkWiWxy4gI1rBIOjm3aME4naQ1f3g46SXCzZoDLrEsAN5fU/ZfffHfICwugYcLSmud5vw3G8BCAKL8m9BQ1/xkO8TE8MY/9JCZNiKCG3buXDNtVRU3yhNPmDOiKiu5Yc8/3+UisUNoKFNWH3zQTFtdTc37/ffNtFlZdB/cf7/54U1OprYSG0tt1w55eXx4Tz2VfmGTe/DwYaYojh5du9bBGzZtopY3dSrnOtg9xFZfKK1ZMDZjhu+kAr3zO4TqLLQ8j1ZFURG7nQYFec/SKitjbGHuXN9aemamrLLaDiNGMNupVvX+8Bs5r3sfB2/Pni2738OGMXANmF0QAwfSapIkYcTGUtmQpGB36kQrXJII0r69vF1KmzZyH3zr1nJa6WgAgNdK2vY/LMw1UliCwEB59mSTJvIxBVL8o8JCKRUG4DQAi93eC1VKNbX+BnA2AEHbOnmpvdUQTzoqtbJSPioV4A01HTsvzzWDW5IB5HBQY5LQWj39JTUOaWkUcpK54cnJ3IQdO5qrzq3g9v79DC7buWfKyngtdu1iEzjTA7FtG90C69dz6I9d5teyZaRRiv7/u+7yPZqy5Le3kVrZE836nwHAlTGzYUPd89WaDPqyy7wXwTkctAhiY2V1KZ7Iz+d5WlbQDTfwPh1rnRJ7HuMXGxgQ6tmTbkKTVRYURKYqyQKy0mcliI2VxbEAat2SjCWAwkKShQTwvCQuXYCMVDooKSJCPtKgRQv5OIPAwPrNkwDkWZnNmslSZ+uDE1ZnoZT6EsAYABFKqVQAcwAEAoDW2sormAxgudbaPRwXCWChIrcNADBPa/2z5DelFdytWsmadwG86Bajlvx+o0Yy6V9ZSQYt0Vq0rl+9QseOdG1JNLewMAoBSReAgAAyUMmYy7IylxZrmkqYnU2TeedOcyfSmhoy+5AQl9CwQ3ExfcLV1Ty+T5M//S80LdmOvAEvHpP0P/zA73oLrv7xB+/dtT4iahs3MtbRvz9dB7Nm2a/TgtaMZbVsyXhPu3b02d9+O7NxTj+d7qhp0wLQauCV8FvxOJCbCER0xZVXcvSqr4yZbdu4HssVZZe1tWsXLc3UVK7JTvk5dIjrlAgLK1PP1CwScCl1EmFRUcGXVFgUFMiFRVaWvCYjK8vV9seE1FT5tL68PF6L8nJzW57SUldNhqn4uF5NLrXWJ80rKmqQliAzU+vx40WkWmutBwyQ006ZovWBAzLa55/X+osvZLRr12p9ww0yWodD6/79ZbRaa33eeVqnpspo33lH6zfekNEeOaL1yJHydcyapfXmzTLa/HytR42SH3v1aq1nz7YhWHKr1k9Gal1WeOytM87Qev9+319xOHy/P3Om1o89pvXSpVrX1Gi9fbvstWmT1oMHa/3cc1qfeabWL7+sdUKC69j/+pfWAPeO40imrnqkhS5d/JDWWuuSEq379NG6utr7ukaP1jo7W+utW7WeMcPmWmitp0/XescOrceN0zotzZ72oYe0XrhQtuc++kjrJ57QeuxYM+2aNVpfeqnWF1xgps3J4V6bONFMq7XWvXvz/kowYoT8ebrySq179JDRPv+81jEx3B8mLF6sddeuWqenm2n37dO6c2etN2ww0zocWgPYrAX89X+2gltaZV1f1KcqOzdXluUB1K8quz7jWgFqY966pnpDUpK84CwhQZYdY2H3bt8uIk9s2CDLTrHwww82Te4qioGd84HeU4+1Id+2jXEiu/X70rYfeojXc84c13uSGQvuaz37bE5884wjXXMNrZb33wfuvjsSSSHnoO1f84BzHkFoaDBGjmQfo2uvrWvRnXUWXXEXX8w6B7vK4SFDGBuy+kjZxSLi4mhV+PubGxR26cLjSrT6Dh24lyW0LVvSipROy/T3l1WGA3RZSeusIiLk1kJ4OK11q0+cHdwruE3WQliYaxCbCf8VdRb/BKTCoqBAnrlSUUE/r9RcO3JE3lLZcjdIkJUlD7RlZHBDSf2bNTXyyumkJAYoJceW9m+y1lBZKZtbADBeYWpl7o5ffyWz9Ipd3wGVJcCgWcfeeuUVptnWF2+9RX/8f1Jv0bo1g+LTp9f1f0dEsL3HvfcyU6/NebPQWOfBsed7VFbSvXPffd7dMePGMYZz4ACflcsu872GIUMokP38mA1mlynXqxeLJCMiXBlqvtC1K9OkHQ6mNNvBiq2Ul5vT3JUiky4vlxW6hoby2ZaM/G3cmEJQMnfGEpSSRoJW2/E//jDTAjy/P/+UPXsVFYw3mQqVpYXMwEkmLEpLZXSFhfQXSqqQCwooLKRztQH7Zm7uyM1lzrsEWVmMLUiCZxkZfHC/+85MW1ZGBi2pZAUoLEpKaAWYsH8/hYWk+tZqDVJaKnvQ1q1jDUBhoTlYm5xMS8sS4nV8yls+BlrHMSUVvH579/ru3uoLS5awOO/jj+vXc8cb+valZXLJJWRU7lAKuPpqxl9Ce5+O3OoOKPj1YwQFMc01JMS7j33wYDLHdu14D+2CzAMGMO6VkMB6FrsYX48evH9//AEsXuybDqDFlZrK+JGpeNXfn+vctYtrMKGqisc1CSGADHf3btnerKzkdbCmEZpoDxyQdbP18+MzIilaDQ2lIvDOO2ZroFkz8ou5c82JKJLxCMfWKyf970d+vkwAFBZyU0m0ioICMvX6VHB/842ZFmCw79ln6zIDb8jOZhqoJDslI4NZThJBlJZGTfbee2UaS1kZtWepsGjUiOmtJljB7X//23xfHA6eY7t2TFM2CQt3F9SePR7DmNK3Ael/0apwPoVvvsnW4+4PpamqfONGnuf8+fLeYCZccAHTmn1ZOEoB8PNDVd8r0LLoDyDvAAYMIEPxJiz8/WkFJCYCr79ub8WFhtLae+QRast2LlDrfK+5xpyIoRSZ2aBBMpdj+/a0MCTu2j596DGQ9AAbPJhJK5L+YiNGcM2SCu7hw+kykli9AwfSsyCpnejeXV6U16iRi9YkWP5n3VAOh6zCef9+MhiJAMjJkdOWllIQbdwoc1tlZDDGIZlnffAgjysRcOnppJX0yU9NpTBMSzP3ZCorI8P5/HP5mNkFC6ilmwTRzp1kNM89Zy6W3LvXldf/+uvm7BNLWFRXs413Lb/21k+AgBCg7zQAPMdFi6jRW/jjD07k84XERMYI5s+vX6xIgvvuo5/6rbd807SZcCmqHf4oWkmT9vLLfVfvWq6oCRNIZ4d+/VjUeO+95pqMmBjWnEgEQMeOdIGZZnsDdHlOnSoTFh06MNYjERbt2jH2JhEWUVG0tCQxstataWlJhEWLFhSEEmHRpAkFoTReGB4ur/aW4qQSFgEBshbFhw7xYkqkanw8tQp/fzPDS093DQeSVFrX1HCDS2hTUrgRJcGzhASX1mgSWsnJPK+YGHMQLzmZ7ojwcLPLz5oxfvAgN7op9XDnTtJLGv1Z8YqPP+b52c0EKC3lfenShT2tag1jqjwK7PgWiJsCNGoOgOmq06a5zPOdO1k46atWIieH9B99JO/GWx8oRUto3jybjq5No5DRbAL8d34BVFMS+qp4PvtsCgvAnM47ZAiVDknxaq9etMJvuMFM27UrGaqk1UaHDrzXktTxdu3Y7kOSrBEVReYvSRpp1YrnJ2mf37IlBYBEaIaH04KTXAfLIpO28AgPl00trA9OKmEREsIH14TISEp1UxUyQEbXti27SJqES0kJC45uuMFci1BVxbjCyJF0N5gQEMBNKHlwS0pYwf3aa+Y1p6VRW5k5kw+aHZKS2POmbVs2rLNDXh6F2+jR1IpNGveBA8z779jRS6dVD1jxivHjgeuuo6vGF1audH1+7rn8+5iGuHsJUFkMDGSkV2vWMlhtMLRmG4+SEu+B+tJSYMoUuhLtWjZs2SIfcuMNISGMhdxxh2+BHjXhcjRRuajaY++wj44mUy8tNe8NKyNKknQQF0fFSpI40qULFTZT/Q1AYWF1fjahbVvvDRS9ITJS5rIGuI/LymTKZcuWrjoHE6wguzSpw99fnuQSFiZPtJHipBIW0qK8wsL6ZU5VVcmylvLyuEkkNzQ3l1p6fUrypWvOyOA5tmtn3uCpqS4Lx0R76BDXGx5ufhistNm9e+lusLs3R4+SIR44QKZs1w4bcM2m+PNPalp2leru8YolSzhU6PTTnR9u/xJo3hHoQJ/BL7+waM3SypXiPf3ii7puhZoatg65+mrf7VoyMykA58ypf9+o3Fyu12J+UVG0pKZP5731jHMFxp6JYt0amcvMmQqSSXkAYwCSXmsANWlJHAugZWGKAVmQWukA94GkvT3A6ymdqteqlbworz4V3PWJFwCu1GQJwsL+MwXFG06qOgupsOjVS9ZxFqDpWVMjq8to1ow3STpXu2dPmbDQmtq/pKMuQO1/+XLZsa0HV9KSomVLakGSJmlKsSr7mWfM9IWFjBFYFcZ2sFphBwdTWFxxhT1906YuP+/SpW4ZOEWpwKE/gNPuO/bUJiayUtpCRgYTCt56q+6DvWEDNW9frpwjR1h5vWUL1+lrIJEnHA4yptatmdAQHMz4wjPP0Hp54AEe95xzGM/4+WenMPQPgO49DVE73wFK84HGdU25n37iscaNc/3tCytW8LqFhLB+wa6Dwdat3POSCu7ERD6nEmGRlUVhKWlNcvQoBYWkOSjAmJt0qt7WrfJ2H1u2yAcK7d5N5m+qkAfohg4IoAAw8ZeiIq5BIiz+Zyu4IyNlFdwFBVqPGSMi1VrXrxp65kyt4+NltG+8ofV778lot2/X+vLL5euoz5qnT5ev+euvWUUsQXV1/arf771X6x9/lB+7b1/5sdPTPe75Hy9qPaeZ1nkHbdcjrbD3xK+/aj10qNZ3380q2YIC2SsvT+vJk1n9feWVWs+fz0p4C5s3a92smdZt22pdWcmq5aQk54cZO7Se00ynLHjX65rGjSNtaan5vlx1FSuAb7lF65Ur7WmfeELrb77Rul8/czXyvHlaP/201gMH2tNprfXGjazqP+UUM21hIa+FhFZrrnWQjF3o0aNZGS/BNddo3b27jPbFF7Xu1k3ro0fNtEuXat2zZ+1qfl9ITORxV6ww09angvukckPVx7V0oiq4c3PlfsXsbLkbKjPTXLlpwWrMJ0VysrzZ3cGDMssCoEYo6SNlQWJZWNi5s35V0YsXu8WGtAa2f0X3U4tOXukLCxkIlsTAPLFuHTOIlixh/EUp+uclrxYtGMxetYrrnTq1tlY/aBDjCJ060Uq65RZmhAEAovqguHFvlKz5Er/+Wndd555Lt1yjRnSt7NnjO2lj+HAmElhxC7vkDstdJXEZdevGPeRwmBNGYmJoKUjqp5o1Y2xJWmvl7y9v4hcZKa/Ktp59SSV5y5bMMpO4rVq04D6SVJ1bY2AllsX/bOpsfYSFJLgGuKqbpW0E8vJkTQcBCgtpqqU1V1uyadPTGeyTbvCjR+VBtgMHKCwk5quV4iqp39DaVXkuwZ9/1m/O9aJFwKRJzv+kbwVy9wP9LvFJ/+abTIeVujYtbN/OBIeFC3m//k5xXkgICyqfesrVTtwd3btTmERHU5gsX05XEQCsKZmO2CZbkLGz7sQpS1jk5/Oe26VWjhhBoZeTw0wvK4PKG/r0YQW3vz+TRuz2RrduvEaBgcxOs0NEBN0v5eUM8NtBKdKVl8vGGjduzGvw449m2qAgPv+SAj6leP6SWiuHg+4iSfFsdTXXu2SJTMiVlNCVaMoslMZAgJNMWJSUyOgKCugPTU010xYWkpEuWCA7dk2NeQ6xhexs+ezrzEyue8cOM216OpmupIq0upoPuaSKFHClwlqDduxgCYsvvjDTZmZSwGkteygtYaG1ubamqIjXzrJyyjd8CfgHA3GTvdKXlTEL6sorzetwR0ICaxe++ebvtSV3R3g46zauu45+fk/4+zM2FRDAmoWPP+b7Y++6CDXaH+1y6wa6O3fmdQ4JYfZScbFvzbJnT/rU/f1pgdgpE5060QLYvZtCw05AhoVR+9+2TdbCQ2vuI0lLjCZNSLt6tZm2aVPeL5/pyB7HPXBAVkUeFsb79dNPZtpWrXhcicCKjia/WrrUrBSHh5Nvff21WXGVztIATjJhUVQkC3Dl53NTScaf5ueT0UiK8gAKLOmwm8xMpmpK2ipnZvIhkPSnSUvjmiWCKD2dmSGPPiozh/PyeH6S6X5793KT33WXWRuyXFBLlpjbQFitGnr2pMvGTusF+OBaE9wqSitR/dd8IPbcY00DPfHhh8w6cmeQxcX2Zn1yMgdvffaZvB+WCR07UghMm2afjXPNNVxzTQ3gHxYJR+czMTjwa68q/hlnkEE++6y9QPP3p4t00iQKAzt3qZ8fM9juuou0JrRowWsVG2um7dqV409NresB0nTtKps8N2AAk1cGDZLRRkfL5nX37UtaSbV3t25U6iQjWKOjKQQkBXx+fqQdNar+GVe2xz1+h/rn4XDIBEBCAjVkCW1ODhmBpF9RWRkleny8yy1gh5QU0kuqsg8dorCQtPtIS+MxJQw9OZnmbV6eea52ZSU34ltvyeZq79lDxpSdbU5p3LaND9qDD5pTGpOSyEhLSoC77zbn1i9c6HJBzXt8OZr4FwD9pnulraqiRXbjja73ysro7vEVB8rKAiZPpuCvTxxFgv79ydinTPHtj2/enIzBsvYCB12CZkgDkuqq45YrKjycrjY7DB9O5eTpp83Fa3FxfPls1uiG7t1Z6CgRFtYMbomwaN+evy+Je7VtSyYtKYiLjOR9lVRwR0TQgpMIi5YtSS8RFkFBrvssgbSNSH1wwoSFUupDpVS2UsprMwul1BilVJFSapvz9ajbZ+OVUvuUUolKqfulvxkQIPMRp6VRoksmySUm0lzs0MEcA8jJoYY1YoQsN9zPj8eVpNqlpPDBkVScHjxI7a1zZ7PPMjmZpnPnzmbL4vBhHjcqShaXOXKEAf/Onc0DbLZtox+5stIc4/jzT/rbly2jwLArrqqooIXTty+tw+bJX6OgshXQxXsl3zffMKXUqouorOQM6LQ0703XCgoYiH7uORmD+Ds4+2zWc8yY4dtCu+02t9G/Pc4BgpuxOt0DI0fS/aO1eUbziBFUki6+2JwQ0qcPrb277jKfT7du/P3J3r2AtRATw2dE0u4jOprHllh2bdqwOFBSGR4ZSXrJzPBWrfhsSNZrtSiXdk8ODWUhqgQREVRwjidOpGXxMQDTqa3WWvd3vp4AAKWUP4A3AEwA0AvAdKWUaMpBUBA1MBOaNuWFl7Sg9vPjRrn7bnOwMz+fGu8FF1DLskNVFTWFuDjZTbWm9T3yiJk2L4+1JA8/bO6Tn5xM8/rMM82V5AcP0mxv3NgtA8cHrKywQYNYu2BipPv3AxMn8hxNwUwrXjFmDIvz7OaSr1jBc1MKGNrvCM7pugyF7SYD/nVvpsPBoKt7rcWGDQwme7MYSkp4zR54wKxRS6ey+cKsWbyWt9ziXZh27cpr99dfAAIbcezqnqVAVe0e1IGBdN9Jiu2GDaOw8PMzuzOsjChJF9Pu3Xm/TcWXAN1aKSmyyZbR0dx3kkSXNm0o6CXKZevWdEFKaCMi6C0w9dICyE+0llda+/nJizubN5cn/EhxwoSF1voPAMJaxloYCiBRa31Qa10J4CsAgoYY9cuG8vOT3fy8PHkFt7VRJemwubncJNKhQwAfWIkPMi2Nm1vSyyY5mUxSkuJ64IDLJ2261vv20c0QH0+BaHeti4sZHygr40Nmeng2bybjXLWKAsPuertnQe1b/D2C/SvQ6fyLvNL++CPdEu73pLiYmrVnm5Xycgr5a6+1F7Jbt7IITjo8x0JODhMl3AvSHn6Ye/H5570XwN1xh9s8iT4XAhVFQOIvdegsV5QJLVtyH0my6upT7d2tm8yNCXBfJiXJaK0gsAT1mdcdGSmv9g4NlafvAvKZMwAVP4l7G6CwkI53leKfjlmMUEptV0r9pJSydPF2ANydFqnO94yQRvZPO00m+QH2WAJktRNRUdxYvpq4ucPfn+anxK2kNQOu0t7zU6Zwc0vmag8fTgYkCUx27Uo6iRBq2pRuBktY2KG0lDGCbdvMHUMdDvaxCg5mhfOx1h0+0L27m094x3yUhXQAor23Gj1yhBakBa3pr3/4Ydc+sLBrF6/zpZf6/u0XX6RQCw4Gbr2Vf5teAwbQPTpuHF1LMTH8e98+KgqvvcbZI2edRcvGPYvttNPIhDMyAHQ6DQhtxQmATnzwAc9pwgRzts7XX/O+9O1rzsD77TcK+txcM/Pbto3H9Zbh5YnDh2lVSOZ1Fxfz2FJh8csv8gruBQvkTPqHH+Qp6+vXu4Z+mbB/P6+tpM4iN5eCQiIs6lPB/U8Ki60AOmqt+wF4HcCiv3MQpdS1SqnNSqnNlZWyBi5Tp8pMYIAujJoamfnXuze1Yoll0bo1XUUSy0Ip+s3tRlu64447yEgkcYXLL6cWK7Eszj6bFoJkVGrfvmRoksLDyEgyXctisIOfH3Dnnfzbaihoh7vuorlfXZSDHkG/I3jgVJ/m2YwZtX3YP/zAe+RNkA4ezLRWXygrIxPt35/xjC1bZK+//qLLqX9/WjMbNpCxW/5yrem3zsrikK2lS10ZckpR6L75JlDlCAB6TQL2/8yxseBxdu2iMuNw0Gr2hdWr+dtW3MIOW7fSymvTxqyBHzjAupCyMrNgKShgcoLdOi34+THBQNqX6c035W05Pv1UXsBnCQuJwLBqaCRrPnCA10MiLIqLKVwktPWpA/rHhIXW+ojWusT5948AApVSEQDSALjrrtHO93wd512t9WCt9eCmTQUqPXhzpONM+Rvyi5qTI7MsAD5Y0rnaVqGdBA5H/VLmkpLkldb1mattFT9K17J5syw7BeC1a9ZMXqmesHgRAvxq4Nf3QhG91uysK+ny64nSUrq+LrqITFcyt8EdTz1FH311NeNJ7nuvcWNmR23dSiZ+9938v4WRI1nX8sgjoCuquhzYS5/T5Ml0ywEUON9957vn0ejRjA1Zldx2xVv9+1Ort1xRdkIgNpZZcq1amfstde7MOJmk2jo01JXoIHHtBAWRTkJrKXQS4dKqFS1JiQCIiKA3RCIMW7bkcyQ5bng4985J44ZSSkUpRTailBrqXEsegE0AuimlOimlggBcAkBQpiVn6Hl5ZGKSm29tJmnr4+xsudWSlSWvJLeEhaStsqXNS+frZmbK258kJNAdJan8tFxQktYOALNpevWS0VrxCikC9szH0dCeQKTBJ+bE0qVkfvVpVwK4BMUll7Dj7N9pE225m1JTfbdr79OHlsUpp3AfWTERa77Hpk0AoocCYR2OuaLOOYeab02Nq9LcV5bayJEUFnv28Dt2hab9+lHQJyezzYldmnTXrrRuKitrJxJ4Q7Nm3MsOB/D44/a0AI9ZWWmeAw5Q6JaW8jqbEBBAXiGh1Zq84o03zLQWQ3/nHdmez89nHY+Jb/n787hLl5oTK/4r3FBKqS8BrAPQQymVqpS6Wil1vVLKOS0AFwLYpZTaDuA1AJc4e1tVA7gZwDIAewB8o7U2VAAQJSUyJpafT/+0pGahpISawttvS1bADWhqY2AhM5NVoZKAWHo6H3JJ5XRKCuMVzz9vprW0q48+kmktiYmMWUiuhyUsvvnGbBIXF9NKCAykv9yElStd8QrTfPSq3GR0C16PRkPogqqpsU8p/rtWxdGjDHbPnFn/6m9P+Pmx0G7DBt9T8vz8qCHfcw/jIwCtvoULnQzbzw/oPQU4sAI4movwcDLg1FRg9mx7CzQ6mrGPbt147+wquFu35t7x96dlYedateJuhw7JAtdNmzKYL0kQaNeOsR3JFMf27XlMU22RRZuYKAvgd+rEc5N0Wujalfdi+3az9d2lC70WGzeaY5dNm5Kn/PqrOdb6X+GG0lpP11q30VoHaq2jtdYfaK3f1lq/7fz831rrOK11P631cK31Wrfv/qi17q617qK1flr6m8XFskK0vDz69Lz13fFEbi4FhokhWSgro1YhkdiZmWSkko2VkUF3gGRUakoKBYtkwLxlhbz8sqzFdGoqN6HkesTH0+3w2GPmOgtrRsW+fXTDmLBhA1M79+3jHG47HFrC5jt+fZmj/OST9hXRixcz0OxZ4Wwn8CxBcfnl5rbpUgQEMJi9aJH9vTznHF4/S6M/9VRe85oa0BWla4DdiwDQ6lm8mEHzK66wZ1L9+lEAXH652W3boQMryTt0MGfKxcTQ6pLUQ3TvzpRqU5IEwL02apSsxqFnT95jSQV3jx60eCUjWDt35ktSwBcdTW+BpD4nPJxeCEkBH8B6qFNO+Xu9yXzhn86GOq6QVnAfPEitQlKVnZtLRrdxo5m2spIMpahI1q//8GHXzAQTkpIYMJXO1f7rL2pDJreVpd0lJpqFRXU1mcsLL8jOLz6ezHzfPnOWihXcvv9+c5ZKRgYfhqAgBnRNhYchid/hSLPBQIvOWLGCwsVX/YnDwdkRnrUb33/vm2GXlJChzZrFPk3HE8HBzMZ57z0yeW9Qii4dd4v24oudTDuyN9AqFthJgXn++a7jvPyyveY5ejRjLk89Zc6A69+fAvO++8znFBtLxUDCJLt0obvRMxvNGzp2pPtMIizatuUaJPO6o6IoMCTConVrWjjSau+wMFlRnp+fSwBIEBFhnnxZX5xUwiIoSNY+OzOTJqDk5icl8UE5/XRz+lxODjWw0aNlqXYBAXwYJJ1Wk5P5EEgehMOH+eCMHWvOJT90iOfXsaM51pKczABep06y65ybS7dS585mobV5M+9JURE1KLuAphWviI/n+u2KJSszEtAhaCeaDJ+CoiKmsGrtW1gsWsQguztzXLqUabLeCvOKiykoZs+2T6P9TxAaSgb/zDNUGLxh2jRmGdWxfpQCek8FktcBR9IRHc17kZdH5mPXxWDUKFqQ0dFm5te/PxWUa64xn09sLJ+rq68203buTNey1dvLDh068FpJeji1ayevtI6KootU0nOqdWsydokgbNyYt8fXpEVPBAdTCZAgMpIZlMcTJ5Ww8POTDSn39+eFv/ZaM21FBTfAzJnmVNScHG7CkSPNGktVFRlWRISs7UF5Odcs0dzS0qgJXXqpmaknJXGtvXubN2JCAh+uwEBzBbfFjLp0oTZrqlLfs4caVng4tXg798jKlRQWcXG8J3YdgZN+WAQA8IubhLAwfuepp7z7fR0OZhY98IDrvaIi0tfU1HVZWILiuuuYdmtCfQqwPNG8OZss3nsvrWfPYwUEcB1e+z31mgRAc+Y4uGZJ7MvKXJJMcrMyoiRuj9hYWrGS9u+dO9OKldRFdehAL4CkHqldOypSkuNGRdFdKzlueLg5xmPBKrKVVKcDFFhSt1J4uHysghQnlbCQVnDn55NZSzJVcnPpfpHUTmRnk5FK0mGzsykspPMbADIuU/sOgA/MkSO0FkxISuKGlVgKVtpsVpb5eljB7R07qJHbMZuiImqEAQH8jR497B+KjRupPSYkcN12a2l0cCGONB8OhLVDURHdbb7agyxYQA3avZgxIICa+Pff194v1tjUG25g5pMdVq+me60+mSc5OfzO6tWunP3WrRm8vuEGpsx6dsG98kpXMV0ttOpOd1Q82/lOmuRKobWDn58rYGuCleYqQY8esvgYQGVDetwOHeTzutu2lc/rbtlSlt4K8JrVRynw85PXcLRsKa8jsYTW8cRJJSykg2qmTqVGIcn/HzmSx5XUTnTpwodGUmjXuDGZjURYaM2MF0C25ptv5oMgERbnn8/NKmmoNmQItf9GjczraNuWgdHt282mfk0NM49SU6nx2R3b4eC1CApiFa5tM7ycfWgfFI8mw9kwbP58mua+jh8aSgbtjldfZTDWc151SgpdWnbW2I4d9BufeiqZ/JAhLj+5r1f//rQ2x45lNtupp9ISsOavt2/Pz15+mamcjz7qYk4hIbRwPvzQy2LiJgEp6+EoTENsLF2Vdll4b77J9Eur3sIOCxZQCDdrZs7tX7OGKdISppeQQCtKwtQLC3mNpVXZb71ljnVZeOkluQD49FMqohLFYPly8hZJPcSOHfQuSK5bZiafJYmw+K9Inf0nIBUWY8fKaYcM4UMlFRZBQTLLIjyczFwiLCy/pnRc6/TpdEVJuuqecw43l0RYDBtGLVfSfdOaQxAfz0wSO7RoQWa8fr3Z1+vn53L5LF9u8PfGLwSg4NfrfAAsVrNzF02YUPua5eSwqeENN9SllTSAzMri+V9+OZn91q3m17ZtZE5hYXT1paXVruBWCpgzh9bRW29R63af53HDDQyG19Gw4ygwD/2w6Nh++qVu26hjSE52NWw0CYuMDLZe6dfPnI1YUMDzCQszM8nqahYOam1mao0ase5EWtNjpWdLaH/9lXSStPxNm+iukjDqhASu1y4zz0J2Nq+XxMKpquK+kAiW/4rU2X8CUgFgBVGlKC+Xjx2tT1V2Roa8Kjs1VdbryUJNjfx6HDggExYA3QcSYQG42h5Iq6ytdFgJqqqoHduuO34h0PEUoFmbY8xTYm1ZeOopxgikPbncMX8+tf5163wX1vnCFVcwYL5ggfc2M02asGfVn3/SUnrqKRfTq6zkXh02zIMRtuyCI6F94bfb5Yr64gsmFnjD6aczNjRoEGnsGI9FY8Ut7JhqXJwrpXrvXntm3bkzXWASl1FwMM89PFw2e7pJE1pCEqbeti1jYxKmbgXDJV2GW7Wi69xUyQ5QUXQ45PO6rczM44mTSljUp4I7IkLu/wPktFlZcuaSnk6hJdFYLGEheRCKi/kwSJufHTpEJiopDrRGpUqqw634AyA7xw0baI1I2jBYgsWnyyp7D5Cz99jo1HnzmKQgxcGDjI2Y4hHe8M471Pp//pkxnvp0FrZw2WWMQUyc6HtccOfOZPqxsa7RnK1a0RrIzKzbpyl06GR0CtyEmrxk/PorrSZfEyCtuRe//ca4lnuDRU/060chsX49EwTsUtI7dqRysn8/3Xt2QdjgYO7h7Gzg+ut907kjP99cGQ7w+cjOrut29IbAQF5PyXgApagEPvGEeQ8rRR7w3HPm5yMwkLRvvWW2yAICyOO+/dZc+Fiv+Iqc9L8fpaWytsO5ucxyWr7cTFtRwYv/r3/J1pCf76qmNcGqsbD80XZITeUGN003A1yps489JltHebmrcZwJ+/axUEpyPbZvZ3A7Pt58rauqyBhatGChoklwuccrtm71IhjjFwLKD+h5PrR2xSssmPzVDz3E4r36mOlW5fdPP7FFhnT2gC9ceiktjIkT7QX/ww/T0rAe/Oefp7vNsw24f59JAICkHxfj9tspbHwFV5s04b7v14/nYacANWrE346Lc81S9wU/Px47KMjVHcEO7dpRo5coMrGxruQOE3r2lPv1Y2PJqCUuoF69KKRzc81xvZ49+fuZmeaO2Z07s44lIcHsFQkO5n3dutXsjahPD7mTSliUlMirsg8ccPbPMSAnh9qPZLA7QOHyzjuyjZWRQVeDpNAuLY10khGshw8zWPvaa+Y+MoWFZAbPPiubMZCYSG3lyy/NtFYm1COPmIvydu4kbWkpXT8m7em33zhPuqqKGmqtLp9aO11QI4GmkfjrLz5sFvPet8++d8/mzXyIPQcaORy+NUCHgx1uExIomKSuNxNmzGBK7MSJvplgTAxTn610WD8/tm+pkyXWojOONOkP/70L0aQJ53vbaZannspr8eKLZsHXty+two4dzbGy2FgmBkhcn927s8ZFMoK1SxcqEJIRrJ06MVlDUjsRE0OhKan2bteO1qSk1iMyki+J67VRIwoJ6VS9Fi14XKkrWoKTSljU1MiqspOS6E6RVGXn5JBR79xpdr1UV9Oy0FpWlX3wINchaVFy+DADmZL+NIcPM+OkutosAA4epD/299/N/XcsZvnMM/wNU9Bxxw7SHOtVZAMruP3iiwyu2rnbCgt5jVu0oAm/fbsH08veDeTuP+aC+vxzV2V1SQmZj6/8eq1ZZ+HeyRXged9yi3dNrKqKLiN/f2YiHc8HFKAr7IYbmD3nS2A89BCtGus6BAV5Z7ChQycjJnALanKTMHq0fcDfiltMmcKsOTsMHsz7PXeuWVDGxXF9kqK8rl3pypTMnu7UiYJCUpXdvr2rktyEtm2Zlisp4o2KcjFqE1q0oBCQzspu0YIjEySIjmZLl+OJk0pYBAXJZtRmZVGjmDjRTJuaSu3m8svN2q5VlHfKKbIAur8/TdEzzjDTHj5MugkTzHnZSUkMNo4da6a1pt91725uD56ayuytnj25DpMJn5Liml9uyvrasIEPY2EhH2I7t8uKFWRkpaUM8jZp4iG44hcdc0FVV9NlZe2LOXMoSH1lty1bxge+f3/Xe2VlZJgHD9YVBGVldG/FxbENSn3M+vrg4osprM4917sg7diR2u+SJfbHsVxRh34koV085ZRTGNNQytxmwgpym0bzAq4gtySG1K0blQdJ7CgmhvvnvPPMtO3bc/+Y5pADFBalpebRuQCtuZISWcW5vz9f0krroCB53C0iwjUh8njhpBIWfn6yttXV1fQRSkrni4oo0c84wxyozMoijaTpmFUUGBxcN4ffG44cIaO6/npz8WFKCpnHmWfWZnrecOAAtaCmTc0P5N69dHcEBLCS3K65XH4+M1Pat+f1MAUod+wgswsPZztqu+v3yy9M/WzcmPdm2TK3YkWt2TSv40igSSv8+itrHSyf8MCBtAK89RqqqaEwefLJ2u+/9RZdPKeeWvv9oiIy74kT6To70bjoIgZvzzuPe80z6eLBB2n12QYtw2Poitq3yPh7oaHy2QySiXoWevemsJAI1m7daPFKYkcxMUzWkBTnRkfzOZHQRkXRZSyxGK2srPpYl1LaFi18Jzt4omVLeR2JFCeVsJBqdVYnWUntRE4OmYgkHdbKhJLUTmRlUfrXZ95BSkrdTqjekJzM85OMSj1wgKawZG6DlQklqZ2wYhBbt5pN/fx8CqvAQFoKI0faMwdrQl51NWcjjBjh5lbK2et0QU0CUNsFBXC06COPeF/TF1/Q3eF5LXJzKRzdrdbMTJr5N9/MILQdtKY19McfvO+Sl6V5f/FFbWY9dSonBQ4ZQsHgjg4deF6m6uzQoZPQKXALqnPN5c6nnsp1m2C5niTzVtq3N3chtiCtILeOK63gbtVKlgoLcG/Vt3WGNMsoLEzO1Fu2lKXZAhQs9cn2lOA4e1f/WUgl9HXX0e0h6cly7rlkYBJh0bcvXxLasDAGZufPN9NqzYrdO+6Qrfmpp5gqKumTdc01LlebCWefTab+2mtmN1u3buwI+/XXZmERGMhYRXU1mbBdgNTh4HCboCDXJLdaSkL8IgAKiKWPcdYsV7AxIYG/5UuI9uhR95olJjKYvnZtbS20ooJxDTtLtqaGWVEvv0yhecopZoXG4WBDvl69yKQXL+aannjClYbcvj3P//XXyRy/+MK19x98kALlggvqCtzbbqOrLKj3BcCKx3DwhyXofsXNXtfx5JPsnXb66XRt2bk0Pv7Y1eRyxw57f/3y5WS8jRszu8eueWV8PK97VZW5P1V+Pq+HdP71XXfJGfo99/C3a2rMlsjcuVQYjxwxJwV89x3vUXa2mXbDBp6jRFikpvLaSeIxDRXcBgweLO8j1b07/ecSAdCmDTegxLJo2pQuF0mhnVKutiMSnH46/euSfk9Dh1LLk4xKjY3l5pbUDbRtS3qJZdG0KddhuaLs4OfnGnr0/fdeBKLlgmrKG3bWWS4m88EH9kHVYcPqutbuuIOCzHO/dOxodnlWVDB9+c8/mUDw889Mq7V7LVtGJpKXB7z/Pv/9+uvahZCDB7PB3yuvUFi4t/eIjqbV8fzzjHO5IyjIWY/RojOKm/RFgI0rSilWLo8Y4bsWw4LWPL/Bg83Zev7+FL49e5qHFDVuzPVGRppnezdrRqHWtKlMU//9d35HUre0Zw+VI4klcvgwLXVJ25HcXAogyXHLyrhW6Tzy5OT/jyq4lVIfKqWylVK7fHw+Uym1Qym1Uym1VinVz+2zJOf725RSPmpM60LKTCsq6leVm5cnn9mdkSFvDihtyQHUv4Lb6voqwf79MssCcDUIlKI+873//JO9iKT47TeP7JDsvXRD9aobZa2qopYvCcBa+PFHMp/6rMlCcTFjYpMncxSmRMuzMHo03Wdz5zIY7w2BgcyQWriQGrU19tfSwB94oC7jvvRS10yOgL4XoHPQJnz9rvecZqsdSOPGfNm1/Bg2jNlskmpvK7YRF0cXol2GYYcOZL7dunGP2iVrBATwcytuYbIaIiLoikpJMdNGR3MfpKWZadu0oVDOyjLTRka6LAsTWrXi+Uksi5YtKVyOtxvqRFoWHwOwy006BOA0rXUfAE8CeNfj89O11v211oYcHRf8/GTFOzk5vPhpabLjOhxmzcZCRoZcWlvZRZLNkpzMh0dCW13Nh0e6Wfbv5wMpaWhmCQtJoC0ri9dZKdm8c6sXEWA2jw8fpjCsFfPZvRiAAnrWTXP74QcyQKmSUFHBYrcXXpDRuyM5mRbNpZcyPjJ9ev2P0a8fa3CuuopasC9ERdFasuZOK0VXVNeuddOs+/XjdSsoAPYHTAIAFG/wnj41aBCFzf79jFXZxWWs1h0//UT353ff+aZt1Yp7+JdfGHuxewb9/bkP1q9n3MmU2desGS3ZWbPs6QBa9Tt2yMYUhIZSsN18s1kANGpES+Suu8xV2Y0asebnscfM1lDTpvQWvPaaOS4TGEhl8csvZWn5UpwwYaG1/gOAT3altV6rtbaSL9cDqIfe7B0VFfT3mpCTw4348cdm2poaPoCSORIAGeSbb7o0PTukpfHGr1xppk1OpmB59FEzbUoK/dpPPilr+ZGTQ7r33jPTWsJizhzzg2ONSi0rM88l19oVQE9P58AhO/zwgytFsrraqfnuXgx0GA40q2vavf9+bYZXWWnv3371VQ4Uklp+FjZtYk3Cq6/KB9X4QpcutG7uu8/3lDyAFsb8+S53Rps2dCF5E/4XXcQ2EP3O6Ios9MbwMO8H9vfnvaiqYgzELlbm58eU0VNO4XU1uSnbteMeKiw0T+Dr3p2MPTjYPHuid2/uI0lX5N69yS9CQuS0QUFmRbBXL14Dpczr7daNe7C83Dx6oF078qKMDPM18/Pj/XNvt3M88N8Ss7gawE9u/9cAliultiilbGW/UupapdRmpdTm4uIcUVV2djaZr68mau7Iy+MGXLJEFgwqK6NElxTPpabyuJKUw+RkmterVplpDx7kA/vee+aivLIyPjDPPy+r4N69m9r866+bTWIrXjF3rrlI8dAhBp6VolZmsuR++MEVr3jmGSBpcwKQHe8c9FMbKSkUhj178v9aU6v19eCnpQFffcV4hSfsBOR33zGov3ChvNLWhDZtGOt45RVWZXtDcDBTd91nl/tq9zJjBrV/AIg4bRJ6N1sPHPFeMTl2LC2Ap54yuxKHD+c1njnTLCz69qXrqlcvM0ONjaVFKHGTdunCeJbETRoTwzV4m37oifbteUyJK7FNG3oATDVLAN1Q4eGyam9/f1rSdRI6bI49YMDx6yQA/BcIC6XU6aCwcNfdR2mtBwKYAOAmpdSpXr8MQGv9rtZ6sNZ6cE1NK1FVdmoqmZ5EWGRlMVh15Ih5CIvVFbK8XNbC4+BBNmuTVmUvW0ZtwZTGd+gQGWRpqVkAHDjADf7RR+bz05oMYe5capymFh5bt/KhfOYZcxBv9Wq6oFasIKO2s8xKS3lPOnemq+SJJ4Du1Yv4oRcX1Mcfs7bCwty5FDa+hMV993mfppee7r3NidbMjHr/fWr0kpTl+iA8nBbGd9/57jt2ySXsSOB+D71l2ERH002RlAT493YGcHZ7d0WNHcvspRYtqEzYYfhwZuw88YQ5ttavH/foyy/b0wEUFlrLxrV27sy1SgriOnZk3MJKlrBDu3a8lpIarjZtuG8kldahoWTmkvUCdEVddJGMtkOHv9cE0w7/qLBQSvUF8D6AC7TWx+L8Wus057/ZABYCEMhemp833mimy8xkodYtt5gZb2YmJfSVV5qbfeXmcsP26ydvtT1mjKztQVISKz1vvtnsWjp0iJt12DAz40pIoEY2apS5kjQ9nVlOAwaw5sCk4SQkUMOJja1b0OYJK7hdWUlNzi6lcuVKV9X7n3/yvnepWAxEDwXCavuNHA66aKyHbMMGxiJ8mfJ//kn3iGeW1fbtvJ6eWXGVlbx/hw/TdfafNg/0hcaNabFs385OqZ4Wjp8f3Y4PPWQ+1syZzkB3q+5A617OWE9ddOrEe15RwRiIHYYOZWyhUydzgkffvjwPyexpa6qeJDGhSxfufUnlcseOPDdTGxOAwi8rS0YbFuZqKSOBn5/cXdm8uazrBMDYkLQ1iBT/mLBQSnUAsADAZVrr/W7vhyqlmlp/AzgbgNeMKk9oLeuzYgVnzzzTbAZnZdGf2LeveRZCejqZSfv25gZlVVVkckVFsk2Ym8vzO+88c2aW5YYaMMA8TGj/fprX+fmsP7GDFa+orKRgsasOLyjg5o6Joatrzhz7Y2/ZwnX4+/NBs9Mk3VNmw8KAF+4/gJZVO48V4rnj11/pS7eET69eFOjelIqaGrbitoLFFpKTeY8KCmr3KMrPp1bYty/jVMezJ5Q3d1dgIAf8lJXx+rz9du3PzzqLazRZzFOnMniuNZg5lrwOKPae6zlypDl1FiBzKiiQjQitz1jVHj1k7lHANdpV4qZp147uRglt06ZU0CS0Fo20QLhRI1khI8BrLB3vWp8RrFKcyNTZLwGsA9BDKZWqlLpaKXW9Uspq/PAogJYA3vRIkY0E8KdSajuAjQB+0Fr/LPtN2U2yWh5L6gWysqidStJhMzKoAUpSXK0UW1OxEeCa75CUJHNxJCXRjWPSBgE+iB07yoJ3lrCQjEq14hVWvYfdOebkUCAHBdENdcYZvum1puvOUgoWLACm9HRqxj3rSt33368teD75hJk13kz0996jW8Kz5iQggK6ghx92uaYOHaKb5rbb2ILDNAp20yYW2W3cyL/tXuvWMbNo9Gi68HbtcgkPPz+2I1+/HrjpprruzmefZdqsXWylaVNae5s3wxnj0cAe7xkFVtxCAqvnkwnWXpNkyFlzWSQFdE2ayBJLAApeaQEfwPsrLeILDZW35YiKkmdaWplkEkREyKu9pThhFdxaa9uEQa31bAB1EvK01gcBGFiRd0il+UMP0S1Rp4WzF8ycSYYqERannMJYgeSGtm5NbVvaU+jLL8nkTJkQAIu0vvxSFmR76CFqK5IA4vTpZJZvvWUOIg4eTIa0apXZJdesGQvmANKbMs++/poPe3ExrblW2YuAdoOB5nUvzqOPuvpAORy8Nr/+6v24Y8d6L768+WZ2t3V3mzRrxmOZhKbWFBLXXUdLy9Sry+Gg5TR0KIViRoZr+I+V2dKkCQXb00/TOk5KogAAePyoKMa3xo2r/UzMnMl716wZ03o/+wwY8losENGDrqihLql61110055+et0OvJ54/XVeh+HDKcTsgsaLF5ORWkV5dtdj2zYKzVatyPjs2vMUFDBl2GLUpjY606e7BJF17XzhiitcrTZMLYLmzOHxMjLMha6ffEKBmZVlVgJXraKFKy0MXL1aVhvWUMFtQKdONJdNMQiAD15BgUxYhIXRpJRYFlbKnqTXk1KuNEaT2wzgg5iQILMsLNPd1OsJ4LVo2pQamWnMbFgYTX3JqNTgYPqbi4rIXO1aiSjlymr66Sdg5jmHgIztXgvxgNoNA3/5hULMV7Fily51mcyCBXzPk/G2bGkWFADw73+T4TZvznjIO+/Yv957j26f5GQGgBMS6BbzTIEcMYJC5brr6gpXK3bhGUDu08c1e/rss2nFVVSA1+7wGqDEpeV06uQa4BQYaK+lRkYyjmQFue3QujWFp6TxYGQka0xiY80Dwpo3p6Cy9rMJ+/e7iv5MKC7m8U0JHYCr4NfUkh8gD5LWcPn7cx0SYREaSmElsSz+Kyq4/wlImD9Qv1GCQP2qslNT5bn5VqGdBNaQIimk7T4AangWAzZh37765W5v3iyzcABqQ6ZAuDsWLACm9XFm8vgQFu54/XVqy1IUFrIDriRrxxvWrqUbbOJEBpSl+7NTJzLJZcuo1dvt1yefpMvPfRZJUhKz/Tzblc+a5aotKi5mPGnMGDDWox21XFHnnkthUV1Nt+Azz/j2gY8aRUFojVe1Y+xWcLtvX9LaWeFRUUwwiY2lK87OtaMUGWpMDAWBycUVHU0BcOiQuXiuQwe6l5OTza6rdu2otGZkmGktN3RWljnWExnJc8rONtO2aEGlNS+vfpaDCSeVsAgIkHWoLCigD1oaODt6VDauFWDQLCRE5rO0hIVkzVa8QtJVU2tuLD8/mSZiCQuJ+8yKVzgc5r46lZWugiNJEM+KVwDmTV5eznW3LVgEtB0AhNtnHyQmcg2SKWoW7rmHWntEhPw7AK//66/z+0uWMBtL0nvLHWFhzK5KTrafVe3vz3TaO+90vTdmDNNsd+2qzViioqjZb9/uuifr1wM1LXsBLbvWyorq1IlMrKSErqOXX/Z9T9q25d754gv+5r//7fu8QkPJnOfNYzWyXS8ppWjJfvkla15Mwd3oaJ731VebBYBVv3L11Wbm26oVLafrrzcft0ULxpzuuMPMA1q2ZOHqY4+ZLZFWrciv3niD19gOStGq+OorWcdgKU4qYVFVJRt/mpXFh1EyR9rS6m65RWaRpKUxJ14S6EtJ4UZ95x0z7aFD1Jpuu81Mm5dHBvfpp7KK9sREPmgPPmimtYTFN9+Yj+0eCH/8cfOxrXYfWtuPPQUYd5h2djJU+lag1ySsWWNP/8YbjD24w07zW7mSD3B9W3UcPcp4wK5d7F1lJQ/8HQQEMMuqXz/OPLHT7Js1oyVg4ZxzyLw9FZHZsxkf8ventdO6NVBcohjoTloNHHX5Ls48k/fEuhd2rVL696fC0aGDWbjGxXHNNTXmGFzv3jz/mhqzezcujkIuLMwcs+jViwy4ZUtz4VpsLI8ZHm52v3brRiskNNTcmdnaG5Jzs9yBBQXmeKFSXKc15O144aQSFkePymZUW4V2kgI+q2fLsmUyP2RREQvcJIV2yck8rkSwHDpEbXrRInPGR0ICXVDPPsuiOztUV5M5f/IJjAwXoADo2ZOZQabOmla8Yv16e20ToIALCeFD9t139v2FAH4+YwD9LKnNzsfdd/umLSmhEuGeo56S4gqqe6KsjAHet96q3+S7/fsZnzjrLCoAx6N6VilmW91+OwPwvkbfPv88+1C5u1/Gj68753r8eLq4ysqoXX/+ubNup9cFdEXt/f4Y7bnnMi4yciSFjJ2wGDWK9/vZZ83CYuBAV/dgk7CIi3ONPzV1iu7WjYJFEn/r1Il03oZgeaJDB9JLYlTt2lEISaq9W7WiUBsyxLzPlKJgGzRIFpvt2JHndzzrfk4qYVFRIZt9nZpKv+q+fWbGm5Hh6rFjasqlNWlzcmTC4sABWiG+Oou649AhV0M5k/ssMZGpwQcOmIXFoUN8GJ55hsLLZD1lZFCDPXDAHJjbuJHxittv53W2M+F//53uk4ICWnF2Wn9VFWMhMUcXQUf2xUXXdbal//RTZgJZD1lBATV1X1riE0+wCNNbPCkhwbtLctEi9pJ6++3a1eLHCxMnUrhddJH3li/t2vH3PXtweTIhf38WrS1YwP+PHevUaqP6AOGdnPNACGusqtbMBrOLuYwezZjTlCnmYruBA/mcvviimZnFxTH+Jokbde/O5+/++820nTuTX0gaCXboQFpJg0IrtiCh9fPjHjRNkbQQFsZnSYL27ZlafTxxUg0/atq07khMb8jKoobVr585CJWezodm0CCz+ZefTw2keXPZjaqsZDrs8OHmeotDh+i77tuX5rAdEhLohti501wdumcPA9adO9N8Li/3zUSzs6kNnXUW3Q4mrWzXLmZkDR5MTefoUd+m+YoVZIQFBWbN7I8/gPPHpEKlbUJ6z0eQluY7BVNrMtnly/n/qiq6ieLjvacL//WXa/6EJxYvZg2Du8+4uppW1s6dPAdpW/i/g/79qVxceCGZ3NixtZMp7riDWVKXXmqfZHHVVXxZ85y57xQD3WteA47mAaEtERhIK9KaemiHHj1cgW1TfKZ/f15HifYdF0dFxjQDHOD93L9f1pbDamUumcFtTdUbN85MGxDA2I60hUdAgOy4AF2G0mSRVq3qF5+T4KSyLBwOWZuN3FzS9u5t1mwyMugaiYkxV3CnplKiBwSY6xasNNikJG4skxmank7hMmSIualbYqKr941pFviePWQEiYl0Ndj5ZHfsIG1mJl0Tdu0ECgpoYoeF8Ryff97eh7t+PYVmZCQ12LlzfdMuWABcMYTB2EaDJ6NNG98dhH/9lUzJyjkPDOS9ufjiuveoupqV3W+/Xdfl8dxz1MjHjnWlG2ZnuyyUpUuPr6CorPRu5bVtyxTgJUu4192FWnAwlSVT7U5MDK9DHQu11yRA19RyRZ13Hl1RJihFl5fJkgUYXyktlRXFtW4tL0Srz9jR0FDZOAOA99sqjJUgONh+Toc76lOUJxkCZaF1a/nYWCmMwkIpdYtSyqDL/nfA4TAX2AC84GVlfPBMsFwOktqJtDQ+CFJaq+eMqThQa57bwYOy2okDB7hZY2PNtHv20Ld5+LBZGFoBa0k67MaNLCxzOMwpwhkZtJZCQuhiOf10+wru1auBrhWLgKg++ObXLrjoIt+M+o03aqfL5uXxN774ou533niDWp43C9LPj+9Pm8b/791LwXHnnSzEsstXdzgo4KSvzz5jLKFTJ7Yf//HH2swnNJQKxpEjFPDumWbnnsu4mbdhRe5ZP1aguxba9APCY4Ddi44xx/HjmTVkgtZ0RdkNSXKnldROANwH4eFUPiS0ISHy9hmNG8sFRn3aZ7RrJ4tvAowbSWnrIyzqM2NcCollEQlgk1LqG6XUeKXqE/L7v4dkdXPn8uGT1E7cdBOlv0QAjB1L37KkdqJ9e1YA+/nJ1rxyJbV/ibD4+Wea2BJh8dpr1DSbNDGv46abyCy3bDELizPPZPX07t1ksnbHjorijAVr7eNtRmYpBaxakgq/tI1Ar0n46iv77prvvVfbhfL667QevAVLL72U7hFPbNtGJr5+vav1ePv2dEtNmOD7ty1ozWv22WcMAu/Z4/u1axfdWosXU4hasTVPJjF7NoP01jm545VX2OPKc7DQBRe4lJ/zz6cQqhVHUgqImwwcXIU7r8/H7t1kOg6Hfdrqs88yjmXVW9jh22+Z7GDFLeywZQuFcVycOa5XUEDLr2tXPicmjBlDYSxJWz/nHCqWkrT1226jZSEp4HvjDa5bkpa/fDmVNYmwOHiQ6doSi6w+NWdGYaG1fhhANwAfAJgFIEEp9S+lVBfbL/4DkFYjNm0qK90H6GLIzpYJC6vSVSIs/P2p1UgElqVdSQv+wsOp+UoK7Zo1I60kKyQkhNdj926zIAoI4LGt1uN2sM4PIL1pjGl4Bl1QGS0mQyn7e+N+j0tKyPQvu8w7bcuWdTN+ysrImD/8kALV2mOWa9KE1FQy5uef5/147jlWV/t6Pfoo4ykBARReP/3EWIQ3qy8sjAxn3bra77dtS6upX7/amvPUqa407eBgWlGLF3tozE5X1CX9lx4Lgk+YYG9dDBhAZWbAAHM2Ymws1ysRFl260IqV9Jxq3pzuTituYUJZGQW+RFiEhZFnSIRFWBjdy5IpnGFhFMQSYdG8OdcsERaWFSSxLOqj+ovYq9ZaA8h0vqoBhAOYr5QydLn/v4W0QhbgTTKl4lmoz/zr+lRlWwN/JLBcCFKBaE2dk0ASwLRQVESmKW2tUp+52la9h3H0afwiIKoPPvuxS73qIN5/n31+6jN//d57GQyWVri7Q2sy++3b2RJfknwB8PrOn897cuaZLgvCG8aNIyNzTzVu3JgJGXl5tQXJ9OkUllY8JCSEWTu1uso6XVEDQxYdi1XExtIaWLbM+xpGjaKQr64mU7OGK3lDr15UNix3pl3WYPPm3G89e9K6s7sOSvG6RUfTOjPFLjp3Jv3evebiUivGc/CgeTyAlQqcnGymbduWll16urmAr00bCv6sLHMGZ7NmrmpvqZtNAknM4jal1BYAzwNYA6CP1voGAIMATD1+S/nPERgoS521RiRKCtYASv7MTJnJdvgwN8GePWZaS1hIUmet4PnBg7LAoGWFSDSnHTuYOSHRhrZuJSMCZMHEXbtcMQDTJl+2rLYLymvFcFEqkEoX1Pz51JYlqKxk/YskVdLCTz/x+t1wg/w7FnJzmUa6dSsF5pdfypUTgMzvttvo4jnvPBb4+cLLLzPd1/LrK0XB9MorZOIWQkJ4rPnzSTN2LN2xtTRQpysqMHkVYiLzceAAhfj69b5dUdYQn127KJzsRuj6+9OKnDuX1+XHH+2vQ0wMz+Ott8xtzWNjaWk9/rhZA+/cmSnVDzxgnj3foQNTo++/3xw7iY5mAsKcOWY3UHQ0r+uLL5pdZ1FR5BMffADjNFCl+NtLlnAPHy9I9NQWAKZorcdprb/VWlcBgNbaAeC847eU/xxacwOYkJnJoLI0Z7mmhm4EO83GQnIytSVfnU3dcegQg1aSzrNWvMKqh7BDeTm15/h4PmQm7NxJYXH33eZhUJs3U1hkZgIvvGBPm5xMgeXvT5+rO+Pyhp9+csUAVq70IXCdLSkSgiYfc7cAFKB2dTBffEGfvSQBAiADvf9+Ppz1jdItX06L4Moref1jYmQuT28YNYouoKee4r33JkAjIrhWz310++2ugLyFG25gVThAa+eFF7y4K5yuqJvPXIqFC1mgOGiQvVU7Zgyfj1tvNWcYDh1Kqykiwpxk0q+fK23W5Pbr1culyHgWI3oiNpbpvsHB5sLAbt1I06iRmbZTJ55XUJDZaxAdTSuwpsaclh8YyL1bViZLOW7RglaFKRuyPpDELOZorb32ZtRaC/Tn/zuUlsrGmWZk0Oxbs8ac4lZeTmbx3XeyQrvMTPq3pYV2W7bIKskTE+mL/OQTc1fNhARu8Mcfpx/XDlYhYVISe8mYqrKt4PYjj5g7dq5ZQ2ZXXs7guF2WSnk5LZvOnWm+X3WVDyYdvxCI6oOPl3bBjBmutx9+2Lc1V1NDN4pnE8Fff/V+DtYYz6ef9t6y3O4cbr+dmvWyZbKhVhK0aUMBlJNDa8Wb2+SSS7ivV66s/b5nNXP79jyeteduv51Co/YP0hU1tMkiLF5Ml+MHH9i77844g7/98MPmRpPDhtEKefBBc8yuXz96AsaNM7t3e/akoBo92lw937UrmfqwYWbXrtVCRFJp3b49r9PQoebjNm5MV9iwYTIXeosWfPaaNTPTdu/O6yEZaSDFSVVnUVFBbdrkLkpLc2nnJqZu1Tf4+ZmFhdYUQnv3ytICrQrunByzeZuYyAesqsqcy753L039H34wM3RrVOpjj/H/pmDb3r28zh99ZE4ltILbL7zgauTnC+6xjbvvds6I9nTbFKUCqZuge03C99/TpQLQD//cc76198WLuQ73z1etAmbM8B6Lev99MrHzfNjNVgsYd+zcyY65XbrwuksGa9UHgYF0N82YwdTinTtr73OlaDHcdZc5dfTWW10ZVEp5qU1yuqKCU1ehZaN8pKeTaXuOmnXH8OF0QTVr5tpLvjBsGLPCbrjBnFjRrx8txldfNceaevZkcNszO8wbunWjJWSyjgEy3KwsWS85q1HiU0+ZaQHe12eekdFGRVFJk6BtW2aSHc/c1RMqLJRSHyqlspVSXvskKuI1pVSiUmqHUmqg22dXKKUSnK8rJL8XFsZsD0lV9nnnkSmZTNvUVJrY1hxuOxQV0e0yZAhTUk04coQPzCuvmLWQhARqxmefba463buXRXOjRpk3uOWCuvxyatN2fX0KCmgKd+tGDcfky9+0iRrWkCFkpHZapJUyW1VFrXDQIC/CwtmKYlvlZPTvT82supqzqYODvQsLrYGXXiITtbBmDRlft251f2P/fhblvfii93X+9BMzliw4HPS/WxlTt9xyfB9QT0ybxhqMK6+kv929DXmHDnzf1LRx1Ciep60V6XRF3TKWrijAviFiSAgVlIwMc28oa6RpcLBZqFrzKSTJGh06UAmUJGtYBXwSl05QEPel1KXj7+9yh5nQurXZZWahbVu5pRAZefwVlhNtWXwMwCZrHhPAtNxuAK4F8BYAKKVaAJgDYBiAoQDmSAoDa2q4qUwmXUYGmUhMjLnqNjWV2kKHDmaXhJUJlZ9v9kFWVXGdiYncWCY/b3IyA8TWDGk7WKmwWVmult++YGVCxcdTENlt3K1bKST8/MgkJ0/2TVtQQAYSEsL1XHopNWJfsHpDBQbSqvjiCy9riV8AtOmHDxa5XFABARQYP/zg/bqsWEGh4O7C6NyZrgXPeo6qKjLbd991zey2UFZGQXDOOS6LIyODQufwYVoqkvRjKUpKfGey9OpF62fuXLbYdmf6N97I7Ca75A2lODTp3XdtFtCmH9CiM0aGLTgmLEw4/XTvbVK8oVs3300R3eHnR1eNN2vOG21goGxcq1L1q7QOCzMHwi3UpyjPEpwSnKgCPilOaG8orfUfSqkYG5ILAHzqTM1dr5RqrpRqA2AMgF+01vkAoJT6BRQ6X9r9Xk2NrCo7P5/MTpIOm5NDTUGSDpuRwWPGx5u1y4wMMqzERHMvHa25sRMSZBpWSgq1vBYtzOtISKCQmD+fDN0O8fEUbJIK7r/+cgUmf/vNvn2HVcXeuDEFYkqKF793/iEgbQv0WY9j4weujJu8PF5DX3O73367rqb94osMCHum3b7xBgWBN62wvJxxiB49+Fvx8XQJvfhibUtPa420wjJsSynE9pRCHMothdbamZWmEB4QiqjA5ogKbI6m/t57q+TkkEE+9RQZ8MSJfLnv7b59aVW8+SYb0S1YQGbp78+g+uzZdAO6pzgXFbmUkunT6Q66/37vFsPRUoXGcVMQ8ufLCKnJRm5ua58WQ1UV9+gZZ9C6sktndjjIzC1XlF1bHK153fv0oVJjzV33hbIylxAyCe7yciojhw6Z06LLyvisJiWZx+JWVVH7T042d0SoqaEASEszWyIOBy1nSU2G1nz2JZmQ9cE/HbNoB8A9xyjV+Z6v9+tAKXWtUmqzUmpzRUWOqCXv229zw0pMuttuoyZquvEAg3BXXSUTLB06cMRlZqbZYlGK2qK0dmLVKjJQSSOxd94h45HUfNx6KxnkunXmxm7WdLXqaj44dtZQZCR7KwEM5Hqt4I6neqviJmPtWhcT/OwzFtn5EopffFE7yJuaykaEl1xS1/V3/fW+M9Oef57CdOlSfq97d1otlqAoKq3Ce38cxJgXf8eo51bi5nl/4ZN1h5FaUIrMonKUqXKUoBR/HT2EHwq34oOcFfg8/3fsxyE0DqtCixZ8wJs3Zxxr+XJaNy1b8uU5n8HPjw0d8/N5X9zz9OPiuBfvv792RfX06a4kgEaNaBX5agV/663A9uqpgHbg1rMWH7s/3vDcc3QFDh5sTuv8+msK+mHDzIkdmzdzBkm/fuYRrEVF3DfWbG8TRoxgkFti3YwbR6YuYb433sh7Iynge/VVWgqSau+ffuK9lAiLgwdpNUosi+Nawf3fDq31u1rrwVrrwQEBrcT+YqtuQQKJlmDBmmgnQVUVmZ5kzUrxIZAIC6VcsQgJbU4O/cySdfj5UVhYbS9MtJs2yTplWrGDRYvYtqEOdi0AoocA4R2PCQqt6b+3s4g8teYnn2TGjreah5AQ7+8vXOhqw2FZgYGBZOJZR8rxwIKdGPbMr3j6xz2IbBqCJy6Iw5KbR2LXY+Pw022n4l9jRmNSo9EI/eNUPN5nHBbeeAoePa8XoiMD8WPmbsw99BsOhO3CuVMqMGsW3X0TJ3LP3X03u8x6y4BRisL+3nvrFkl27cpYzTffuN674w4KPQtWGq23Fh0XXwy8t6QX0KonRjVfgAULfMcCx44lMwsMpPVjl1Rxyin8PctCtUOfPhQSVpDbDpabKDZWJizCwrhWSWuQrl0pXCXColMnubDo0IHXVOKGio6mhSMRFm3a0G1nymwETkAF9wlEGgB3lh3tfM/X+7aoT9FTfr651bcFSZM9C/WZfV0fwQLImg5a2LlT7kP/6y9ZoA8gg67POf72m313WndUVbniIrWQsx/I2gn0rl2Bt2ED3ULSbq9WRll9Ulr37qWA+fTT2pZIjUPjk7VJOPOlVfhuayom9W+HH24dhW+uH4HLR8Sgb3RzBAX4oaaGDP/++xnkv2ymPwZ0CMdVozph0U0jsfimkRjXOwrzNibjjJdW4auNydBa48472Ul39mxqoL5GmsbGMm7haRFdfDHjEu5FWWedxfOxGFlSElPNn3227nHPOIMWWE3PKWiUsw6Z+9Nw333e1zB4MFOqS0ro2rntNt8FfB070s1YVkZXkNVSxBtCQsjMIiO5LzZs8E0L0P/fqBFpTQIjNpZuoB07zOnlXbsyI3LvXrMV0KkTY00HD5rjCx068JodPmymjY5mHDAtzSwwrMSPzEyZwJDinxYWSwBc7syKGg6gSGudAWAZgLOVUuHOwPbZzvdsERTkfTCMJ6zZEZIOmQBvZlhY/aqyTRsbcMUrJNP9SkrolnA4ZJP14uPpjpCk8G7dSmGhtTnV1hIUlkVigvtcbVPrAasvlMWUj5nI8QsAKGbouOG998hMpXjsMcYvpNpUcTGtlo8+qq1Y7M08gslvrsGcJfEY0KE5frnjVDw7tS/i2tb2gW7bRgExYgT7PnlLKe3XvjlentYfP902Gj0im+L+BTtx8bvrcDCnBHFxZNgpKQys+2Io11/P++ZeDR0YyNjFdde5Uq2VYlaYNUho9GgKFW/FpgEBvG9/Fk6Bgsa49ot8atb+/rQCEhKopCxebJ/m2rs3azK2bbNvDQLQqpg7lxaq6Xnt25eW0uLFMmHxySd8SYTFggXcb6bno1MnVnC//77ZaunQgRXcX3xhTstv0YIZbEuWyPhWdjbpFi8200pxolNnvwSwDkAPpVSqUupqpdT1SqnrnSQ/AjgIIBHAewBuBABnYPtJAJucryesYLcd/P1rpzX6Qn4+L/7dd8syHAoL2a5BwtQPHuRDKcnfTkigJmZNkrPD/v3Uor/+2r71A0AmW1xMLctz7rQ3WMJiwQLzsd1dULffbu/zLC2lORwVRU3niSfsj71okSvDSmsyaWgN7PoO6DgSaObKvT1yhPfDvaAsPd13JszOndSypFaO1tTYb7+99jjN73ekY/Iba5FeWIa5l/THp1cNRceWtVOnSkuB++5j9tS77/K8n3zSXkh1bd0UX107HM9P7YuE7BJc8O81+G1PFoKD6U66+25Wty9aVPe7SpE53X9/7RYTSvF77lbx5MkUQLm5rtoMXxlwM2YA7y3oCkT1xR1jF9hOOhw/ngkAb7xBQWM3F2XUKFoel15qTrMdPJhZi5LOz336UEHy9zdbvlYFN2CePdO1q8tlbQqGd+rksnRNbuDISFfWnSlwbjXb1FrmBYiJIa10WJIEJ1RYaK2na63baK0DtdbRWusPtNZva63fdn6utdY3aa27aK37aK03u333Q611V+frI8nvWWNVfZnsFlJTaYVs3Gguyqupoab7+uvm3jQAtZRvv5XRWuNP//zTrN3s3cvN/cQTZn9oSgq1lg8+oLZuCmIlJJCh3HeffStqgIH2U06hZjhvnn3q4Zo1rgyWV16xt7a0Ztqlxfzff9+pKWfFA7n7gd6183S//rp2kProUTI3X7UAjzzinWH7Csi+/DIfZiseUuPQeP7nvbh53l/o1bYZfrxtNC7o3w6eHft/+43n3L49z8dyBcriQQrThrTHD7eORseIxpj96Wa8sTIRWmucdRattM8+Y38rT+UiMpI1NddcU/d+u8cz/P1ZTW8VrgUFUaB5e2aGDqXbrrL7VLQs24xrLkzyufZx4ygs4uIotOxcwtbci6eeMscNBw2iq+jBB820ffpQYZgxQyYsiotpsZmqyLt25fUeN87s8mzdmorRmWea3dx+fhQWp58u6xTQti0FrcQF3L0779/xTOf+p91QxxVWXyOTqZiSQs20USOzuZqRwY1fXm4+LsBNtXo1BZJJaCUk0AwNCDC38Nizh8dOSzMHxHbu5MNgZX3ZWU8FBQyeWua4qTngli3UtO+4g/+3s4iseMX+/bT47K7H1q182IOCKMBvu83Zxyl+AaD8gZ4X1KL/+GN2kAUo0GfOdGnLntiwgb/tGZT/+mvvFuDvvzPr6aWX+P+yyhpc++lmvPn7AUwf2h7zrhmG1k1r95PIy2ONxty5dBXcfHP9YmjuaNe8Eb697hSc368tXli2Dzd/+Rcqqx1o2ZIpzsOH0721aVNtYXfeefTb29ZPgAJw4UJXBlVEhPeiUKUY31mWSkE9sbPvgovISMYhiorocrNDXByFUMeOzB6yg5U2e+21Zq0+NpZK1VNPmVtidOjA5/n1182CvFkzXitJZbhSvJaSolyAwufpp2W07dvTUpQoHm3b0jKuT4dlE04qYdG8OdM1TZWLKSk06cePN8+oPnyYErpjR/YXskNJCWMbEycyIGqqJM/MpL959mwyADvs3csU0c6dfVcXW9i1i2btRRdxg9tVh1vB7Zkz+a97vyVPlJTwWI0bs9vrvffab9xVq2gptGrFB91uSJF7FlRlJRlYl85OF1SnU4EmrvLs7dt5TEsj3LSJAtpXsoBlVbjjnXeYSuopQFJTKajmzaPgKq2sxlUfb8KKfdl44oI4/GtyH2Rn+B+b76A1XZRnnME9tXjx8enH0yjIH69e3B/3T4jFDzsycP3nW1BeVQOlmJ799de0EMaOrR3DevFFCgu7WFVwMFuTm4QKwGv07rcdgeghULt85Nk6ceaZtH5MfZn8/Fy1CCbtOziYQremxkwbFMT7IZkR4+dHJU16r0JDZccFyKglKfwAhVbjxjJaK4AvXYNdxf3fwUklLBwOMnXTBU1J4WaxJsTZ4fBhbih/f/MGsILb+/ezPYjdzbLSZvfuZR2AqSvpwYPUQpo1Mw9Asqqyt26l6Wy3bitesXUr2xm4++c9YY1KDQigILjtNtdsa08UFPAah4XR+mjZ0r49iPuEvPR0Nsx74PJNQEES0OeiWrQffEB3i4WwMLor3NNCLaxYwd92Py+Hg/cqIoIauoWKCjLH11/nw1ZSUY1ZH27ChkN5eHlaP8wYEoO5cxX69KGZf/iwq33477+zFcfxavVRUAAkJytcf1oXPD25N1bszca1n1FgANy7553HPTFliqvCuXFjCoGrroJtjOGaa2idmaqde/ZkIsPRzhcxIy3btyk+fry8JbY1A0OC/v3NqbMWevSQDT8C5DPDAbqipLTSCXyAq0WJBNHRspoMgPtXWu0txQmt4P6/RnW1fPBQTY0sbbW8nMxGooEUFHBjf/aZmaFnZ5Px7tlDv6kdtOZG2btXVjtRUcGHJjHR3HcmN5ca8fffm62b5GRaChUVdLvYVcvv3u06rx9/tD/H3Fy6EKz24fPmsSjMf9c3QEAI0HPiMVqtyQysjB6Arp/bb/fupvjss7oV3CUlXNOWLbXP4f33aTGdeipQXF6FWR9twraUQsy9ZAAm9muLL7+k+23aNArAK66gq8qujQnAfSlpQ2/Bmonyxhv0OU+c2BF3jvLDK2t24OpPNuH9y4egUZA/Hn2UgqK83JV5BVBwTpzI7Kv773ddV/exvE2bMtj9+ed0V3hbQ7t2VAwuugiYv3cKrlAPADu+Ac6aU4s2J4cWwIgRtHasbENvKC7m/hk9mllAM2f6vg7l5UxGGTyYNRl2tT3V1WSOltvK1G4nKclVk2GqXUpK4nOUkGCvTAGuLg6HDpknRObnU0mUuLdLSuTT+iored8kwqI+RXnQWp80ryZNBumCAi3CI49ovWSJjPbXX7W+4w4ZbWWl1gMHymi11nr8eK1TU2W0b77JlwS5uVqfdpp8HZMmaZ2QIKP94w+tr71Wfuzzz9d63z4ZbUmJ1v37a+2oqtT6uU5af325LX1uLq93TY33zx2Ouu/ddZfW771X9/2aGtJXVNXoGe+t010e+EH/uCNda837On48v7tpE2lLS2XnVFOj9cqVstdvv2l94YVax8Vp3auX1g8/rPWGDTzG/M0pOub+7/XVH2/SVdU12uHgtf3uu7q/WV2t9ciRWg8f7ro206ZpvWKFiyYnR+sBA0jridtucz0fKSlajxmjtf5sitYv965zsV96Seu33+bfU6dqHR/v+1osXKj1gw9qXVam9aBB9tdt506tL7lE661btb7cfhvokhKthw3TeulSHt+Evn21njdP63/9y0x71lk8v2eeMdPeeKPWTz2l9eOPm2nnziVfueceM+2yZVpfeqnW11xjpj18WOszz9R68mQzrcOhNYDNWsBfTyo3VE2N3Fd46JBshjJA81PaGbK+hXZWi3AJpFXZQP0L7SRWiIXffzdr0xasxABTeqKFJUsYVFUHVwKleUDfabb077xDl4qvuIynhrt3LzO6rrqqLq2fH5Wne+dvx5rEPDw3tS8m9GkDrRlgPessxgSsZopS/7GfH5sk9uhB63PAAP7f2+uMM5hN98EH9JMHBdFa9fMDpg6KxuPnx+HXPVmYsyQegMYnnzCg65l9V1xMF+v69a7Rqk88wQluljbZsiU1/HPPrTvWc/Zs1hUA1JT9/IADjS8CipKBlNppbZMmuVJ6x4+nS9FXMsOYMdw/1jx3u9b81ghWKyBuh9BQatSxsbK5M9HRdOFJshZjY3n+kmrvbt1o5UjcUJ07MxtSYi107MjkAYkbqk0bXldJtff/TxXcxx3Sk09KkguLgwfljHT/fjljPHqUm1y65l275KlwVixCgsOHeS2k67A6xEpppYIFoAtq+nQAO78FQpoDXX33Y6+s5MCmyy+XHVtruqteftm3cHl+2T4s2paOe8b1wNRBTOx/7DHGiu68U34e7vjzTyoQbdvS/ShRaIYNY+pxQABTcdev5/uXj4jB9ad1wRcbkvHm7wfQvDljD5deWnvmc/Pm7MT7yCPMoAIorLp2dRXvVVYyOL5sWd0eSb17002SlsZ4SFUVMPSKc6EDGvHeuKFzZ7oSjxzhHnr9dd4Xb2jenPchKYlM7YorfAsWPz9mWW3fTgb84Yf21ywujueRmIhjCQi+0Ls3Y5c7dvA62yE2lox3505zi5KuXUm7d695EFunTkxyOXDA3PuqfXsqlunpZmEYGMh7W1ZmFrL1wUklLAID+YBIUFLClFJJNbRlWUhGpVpT6iStmvft4wN89Kh5Y2lNzaJ5c1lxoCUsjh41aznr1rniFaZ6j/Jyai1WxpmpLuOHH2oPzbEb25qb64xfdD4K7P0BiJsEBPjOEvj2WwZ5pdkkS5Zw3b5iM5+tS8Lbqw5g5rAOuHEMtYP33+cD9/LLfy94vXYt4wY1NTzGddfJvxsYyJkV8+axL9Wtt1Ig3DuuByb1Z1rtgq2p6NuXguyqq2r7oP39aU1cdpnrvTlz+J7DwTjDggX0w3sLCl95JVOqmzXjdc4vaYrKTuewqWNN7ej5OecwuB0ezj1UU+P7vE47jZbv/v0sELTL1jvlFArK+Hhz8HzgQMbe9uzhdbdDnz7cD9u2mZ+92FgKn40bzYy6WzcG7tevNwflO3Xic7p5s7njQ+PGFELbt5sLZwE+99u3+24U+XdwUgmLoCBqjp4mtScqKlyTxyTCIimJEv399820+/dT07rxRnPq7J49DMq+8QY3jR2sxod5ecA995jXYRXxvfSSueXH+vUMHpaXM8PJDhs2uJhtfLx9+qXWZAZW4HXTJmqxvjB/PoOp2PsjUHUUR7tMwx9/+D72G28woOoOX3UfZWVklN76IAHAugN5eGzpbpzVszWeuKA3lFL46ScGyD//vP41E4cPM1X4mWe4b37/3VWbUl9068YWEv37M2j6448Kz1/YD6d0aYn7v9uJbSmFmDGDlotVG+IOdwuzY0daLd86jYNmzciEvWVOXXwxGxE6HMzvHzsWKOo4DSjLBxJrc6xJk1i7MWUK//ZsbOiOM87g9Xj1VSo/dhgxgs/f1VebU+IHDqRA79vXnOjSpw/ddBERZq9Bz55k1o0bm0fGdupE3hIcXHekrScaN+b1DwqSuZejoui6M1V7A7wGTZrQ5Xm8cFIJC4eDJqiJOaak8MK/956ZVms+SC++KPNZ7t9PP+uePd577rhj9266f55/3uyLtOIVzzxjXvORI3RvZWWxfbRp/OnGjUybfekls5ZluaBqaujXtuv3tGcPH8SgIArwmTPtme5XXznrXnZ+A90sGjMfGOGzoPDPPymU3bPOsrN9F4S99BI1bG8MJzGjDDfP24qYlo3xysX94e+nsGULtfnvvpPHJgBq/g8+SKF39dUs7ouNlTde9AWrvmLZMmdb9pl+eGzsQEQ0Ccb1n21BTnEFXniBmrXnHG5PPPgg94WlzLRp472+pkkTZuytXEnt/9NPgeqYM4FGLYCd39Si7d+f+7migvVIvlKqAbrV1qzhPjL19rLmXjz6qDkW2L8/9+9jj5mFRWwsvQB33GEWFm3a0OKdPdssLKx0+UsvNRcRAhQWF19szt4CeP4TJ5ozsizasWPlrmgJTiphUVPDoJWpR31SEjd/cLC5Yjk/nw9NYqKZ6QJMI1y3jt8xuXT27CFDr6qq3dPHG3bu5Ab48Ue6geyqobdto0bx8cfUqO3WXVbG3y8pYcW3qUeVJSzee89VGe0LP/zgmip35528L74Ktg4fpjbarnkukPgb1h6ZisVL/Hy2QXjlldqaemEha0q8TUlMTmYA9pZb6n72x5oaXPz6FlRUO/Du5YPRNCQQhw6RMX/7rbl3kYWaGloQI0dSe1+71jz+9u8gKooFeZddBlx0QRAqfhuE/JJK3DRvK5S/A19+SevaTlGJimIg+pNPXO/5cgW5B7qjooC20YFA3GRafxWuIIlStBhWrqQAtzt3S6POzDSnFDdvzj0aEcEkAzuEhXEfT5zoZa64B4KDec+uu87cUVop7ts77rAXghZat6bL0FTDBfCZvuIKV3qzHTp2pNUm6Zbdvj2TF0wp/PXBSSUswsKYOz51qj1dUhI3c/v23gu53HHgAM3JwYOp+drlJZeVcVNNmkSz3TSz99AhPgBdupgHvO/cSZN89Gi6Bux8wlu2MNf+ggs4C8Fi2N6wdStp27ThA2bX0qC8nFZL69Y8x2HD7JmCVV+hNc3iCRN8b/SvvrIC2/MBXYNlmRejbVvvlsDBgxSY1nQxrdkyYds27+b83XfTIvMskvz4Y40Ln92FPEcRXrm4P7q0aoK8PF6zDz4wWwNW/GXFCvrWExLor77uOns3zPHAeedR2/5rRRgKf+mLjYfy8fQPe9CmDd1zM2bYF9zdcw9bUpiK8oYM4fWupVT1vRioLgN2L6lF654VZYrvWIJFUmVsFY1KmG9sLK17SRJBt25U7iRr6N5dNtrVOq57soEdOncm35CgY0c5rTX/4njOgz+phIXWZLymGdyHDuHYZDJT75QDB3hD9+8nI7K7+FbLcas9uN3mrqqiNnfwIL9j8t1aMYht2/ig2Z2jFdy2JtrZZX1Z8QqHg79h15LDvePsL78wxdVXVlRBATdrVBSv2cqVFMy+fKjffecU8tvnAW36YcWuOKxZ410zeu01am4WrHnKDzxQV6NcuZLX2lOo5eQAz3ydgsZxqbjptG4Y2ysSZWVcw5NP2nfrPHyYlscvv1Agv/kmW34895w8dduEvDy62uziXlOn0iJ99Y526OXfCR+vTcL3O9IxahQFnl38KTyc7o933rFfh1K0Yj7/3O3N9kOBFl2A7V/Woh01iu4lU080gK1BJIFagHvOSv81wRIsEvTuLc8WsvpOSdC1q8xlDdCyMPWFs9Cxo6yAD6AiLK32luKkEhY1NTLfcHg4NT/T7GuATHnQIGrVJt91eTnTRC1hYYe8PGYJbd9u9kFarYa15jmasn+aNaM1JBl/WlND14m1ZjthaK0ZoNUwYYJv2kOHXB1bi4tpzfm6Jvn5ZDTNK+KBjO1IazUTEREUcp4autakdx9glJdHl9fjj9f1KS9dWrva28LqHcWo7B2PXi1b4s5x3Ajz5jGu4qvavKaG/v7u3alpP/UU50PMn2+/76qqyLwlr6lTud9mzWJiQGQkU4O9xam0Zrxp+nRg8ROxGNChOR74bieS80qPZU49+aQrM2jVqtqM/NZb6TrzlhCyebNLi505k8LimFWtFNB/OpC0GihIwv79FFoBAdyndpk9GRncG0OGmNNQi4q4LyXCoqKCFrVUWKxb56r2NmH9eu4ribDYtYsKjmRca1ISlQtJTYY1O0bazLSkxBwzBf6HK7gjIgbpjRvNVYtaa/3pp1q/8IKMNi2N1btSDBrEil8JHnhA6++/l9Fu3qz1rFnydQwYoHVFhYz2tde0fustGW1Vlda9e3uvjvaGefO0njNHQPjzg1o/3lLffWOu/vFH2bG15jX88EM5fX5Rte580++635zlOutImfh75eXcB23bap2U5Ltq3BMOh9YHDsheCQlaP/mk1l27spL97be5/3wd99Zb2Y1Aa62T847q3nN+1ue/vlpXVNXoBQu0Blj5qzWrsj/+uPYx5s7V+umntc7MrP3+449r/e67rv/PnKn12rVuBAXJWs8J03rls/qDD1zVzYsXa33vvb6vxa+/an3TTfz7vPN4zr5w6JDW557L69ynj/1+q6jgfs/Lk3Uu6N9f6717tZ4yxUx73nla//KL1tOnm2nvvJN78eKLzbRvv631E0+wCt+ElSvZNWHMGDNtRobWZ59trpC3gP/FCu6KCnnxnFUPIcHevbLZ14ArBdHkCrMgsSwsbN7s8tObkJ/vqgCWYOVKeaHdxo1090j9od9840yJtUNNNbDjG1R3Hoflf7bE2WfLjp2by9RP91oCE6Y+vRs1TUowd0b/Oq3GfaG8nGmh559PrbRjR/v6AHcoRctD8uralVlYmzcDZ5/NQjRfGq1SrvTv994D2rdojOen9sX21CK8uHwfzj2XrrmFC+kWfOwx0hcVuY4xbBgzxR57rPaxr7+eCQ+W5mmNdz1WwNa8PdBpNLB9HqZM1sfy+ceOBZYv911/M3q0a8aK5Yry5WqLiaF27HDQB2+nKQcFcb/7+ZkTQAA+z5WVMhdQnz7U1CWupZ49mWwhOW737rQYJDO4u3QhnV3Fu4XISB7XLq75d3BChYVSarxSap9SKlEpdb+Xz19RSm1zvvYrpQrdPqtx+2yJ53e9obraNU3KBEtYSGiteIEE7s3aJEhLk2csbN4sn3y1YYN94zV3OByuSXwSmBoDuuPIET7kxtTAA78BR7OxIn8GLr5YXtfw4ovM/pEGlF+en4GDKhnXndoFp3U3tPp1wl1Q3HCDvFmlhdJSMsXXXmNCgym1FaB74rnnGAt56y0Gj70Vzvn700X0+edO12CfNrh0eAe8+8dBrDmUjX/9i8J0zRrGxW67rXa79k6dyFw8Cz1bt2Z8afly/n/nTgr9WmvvPxMoSELzI+vQvj1p4uPJqKxZI54ICnLF9QoLmZjwyy++r8PAgczACw5m0N6uk+6wYWwR37gxCyHtMGgQr0tFhSvbyxf69GG90JEjvAZ26NmTylRJCYv+7NCtGyu3y8rMxcRt29JdVVVlLk5UintWKbphjxdOmLBQSvkDeAPABAC9AExXStUqU9Fa36G17q+17g/gdQAL3D4usz7TWp8PAZQiY5LMv7YC197GVHpi3z5qIt9/b6a1fP8lJeYq0rw8BtmVgs/iM3dYVkhRkbkNs3sw2jTgyarhsCwFk6bzyy/skwRQ0Nil2y5dWju+APgQ0NvmAY1b4smvxnrt2+QNOTlkZnadS91xKLMcr6/bgdhWzXH3OFlPlrIyZthNnly/6mt3HD7MNd5+O5lffdqfdO7MFN677mIc44476mqXjRqxEvuRR6hQPHxuL/SIbIp7vt2B/KOVx/o/ATzG+vWuPdG6NQVZRUVdRnz77bQmAJ77Kad4zF3vOREIagJs+wIzZzLmM2AAg6t2mUPnnkvBZg0gsksyGTOGMYi8PO5TO4t9+HCe1759ZNh2GDiQz+q+feZ2H336uGhNz3TPnlzDnj3m47ZtS361e7e544O/Py2h3btlbeDDwlglv2CBmVaKE2lZDAWQqLU+qLWuBPAVgAts6KcD+NLmcyOCgzn5zMQctebDsXGjc86zAXv3ymdlx8czuDx3rrnAzWL+mZkcaWqH8nKuu1EjBlZNvfXXrqWwKCw0Vw6792/6+We6LXwhI4PmvjWJ7PXX7d0Dni6or77y4qIozQf2/YisyGmIbBtUK122pMR3o7UXXuC5SawKh0Pj4pe3IyBI460r+iPQ37z1S0up0V94Ye35GVLs3Ushcf31rPH44gv+/XdgjSK1mhC+/jqZu3tTwPnzWQiYnuKPVy/pjyNlVXhgwQ5orY8pAn5+dDvdcYfru23aULN1d08BzBZyOPg8BQVRaNWy+IJCgV6TgPjFOOeso/jhByocH39sLwAmTKCwmDWLAsguccRqPPjyy+YahxEj+Mzdf795UNGAAdTUZ840W4o9etDdecYZZjd3ixauhBRTjzg/P1p7ffuaq70BWiJ9+sj6w/XvT1qpi1uCEyks2gFwZyOpzvfqQCnVEUAnACvc3g5RSm1WSq1XSk3y9SNKqWuddJurqnLw/vtmRpqbyz7yTz5pLpwDyMyXLeNxTRkG8fF0K73wgrnr4/bt3CiPP27OiLAGGiUkUBB5PtjuqKnhOUZFUds0HXvlSgqL4mJqkHb+3p9/dmVB7dxJIeer0K6oiG1SrErW+Hgev84c4/gFQE0l3t0wvRYzraqioPHme83OZq+u6dNrv19VRdeNJx79PAnZfrl47IJe6BQR6vsEnbAExcUXe5/3YIfdu7muG27gd3//nVlUnmutL/z8mBm1di0F7vDh3MNW645OnVgfctFFQOugZrh7XHcsi8/Ct1tq51AOG0Zmunix673oaO8FiO7WRdu23E+10H86UFmMRklLMWgQ19ajR90ZIu6IiqKWXFREF5tdQVrHjtxD/fubW9G0a0faG280u2vDw2n9PPigOYMyMJBC8N57ZTHR8HCuQeLW7dyZAksiLLp2ZcGhpDVITAwFbd++Zlop/lsC3JcAmK+1dmcLHbXWgwHMAPCqUsrrbdJav6u1Hqy1Hty4cSuEhdn7NQEy3LZtGQR21868obSUPtAtWyhgTLnLiYncsP7+5h5V27fzYVi/npaDHZO2gttWINFurrblCktKIkOwK7xyOCgEu3Zlm4bkZPvrYaXMlpfTL11R4VtYLFnCOgSAjGHyZGqcdQLDWz9FTas++G5tX5xxBt/SmkHVFSu8a37PP0/XjLtVYdVJeKYXbk8qxuc792JEx9aYMazuFCuHo7bL4OhRrnvmTO+tzH1h1y4Kl1tuoVBcuZLaqFLHtzgqNJQB6a+/ZhxkxgyXi3TwYAqQKVOAGYM6Y1inFnh8STxS8mv3ZXn2WR7DVOQ1bhz3nlWUV6eossMpQHgMsPWzY64owJyyPW4cFbC+fc3xrEGD+PzdfLM9HUAGnZrqvVrfE926cS9Os++CD4Bu6DZtak9W9IWePfk8SXo4de/OdUishS5dyC8kAiAmhi5GaYxTghMpLNIAuD+Z0c73vOESeLigtNZpzn8PAvgdgLElVlgYtZZ//cueLiGBN7JrV1f7Zl+wWo6fdhq1LLvNUlnJzXfOOdQYTIPYd+/mQ9WnDx92OyZtBbfHjKF2OXmyb9q1a13FeF26uB5gb7BcYUox++bCC32fY1UVXStxcXRLnHkmtedQH4r6N9+4HkQr+cC9Ay0AIP0vIGM71pRfgRkz1DFBcvAgz6NXr7rB7sxMMmL3AsKyMloCS5fWXn9VjQOXv7kNjQMD8NqlfaE8uHZqKjN4rOwVS1BcfrnvIK0ndu6kNn/HHWxs+Ntv8syy/wRt29KqmDOHFoVVt3DOOaxxmXWFwgtT+8FPKdz5zTbUOFwbzKrfMM1z9/NjUN5n8Z6fHzDwcuDwnzi9byJWrzYrawD3gRXUNQlSyxUlSXqwajLqUxku6Vrcpw+VAUkVec+ejG9IaLt3p1Ln6xlyR+fOVOYktFYmmeUuPh44kcJiE4BuSqlOSqkgUCDUyQ9QSsUCCAewzu29cKVUsPPvCAAjAew2/aCfH81p06ayMqESE6mJ2G1WK23WYqp2m9A67q5d3Fx2m7Cqiu6VkBDSDx9uv+4dO6hR/Pkn/de+eiYBruB2aSldS3ZantXrCeDDO2WK7yrrtWtZwGdpysuX05fszY1QWEhXkeW3LSmhb/qDDzwIt3wCHdAIjy+4CLNmud4ODKRm5C0B4bnn2MLD/Xo1asQH46yzamtT93yUiCK/I3hlRh+0alrbkR4fz+KwLVsoJK2+QrNmyVJxN2wg/d1300Xyyy8yzVOC3FwKebu+Xo0b03348MOMM7mf9zXXUNC+9GRj3DwyDpuSCvDRmtr+yFtuoeVpKvS67DJaMT7by/e/FPALgP+2T3Dmma4MKjsMHMgArCS9c8wYWQYZwOfImv0hWYO02ltawAe4gtwSdOt2YmaGd+okc7HXBydMWGitqwHcDGAZgD0AvtFaxyulnlBKuefHXALgK2dxiIWeADYrpbYDWAngWa21UVg4HLJ6iM6deUOVMgdHw8NpVVjM2g5ak9lKBg8dOULNtaCAGojdOrSmthgSQmFhmu3bpQvXumaNmdZisADjEePG+aatqHD53Tdt4m/4ckGlp9d2BXz0EV06tVxQFSXAzvmo6j4ZZ57bHK1buz566SW6mTybvGlNIeHpOrDy9X/+2SXQd6UVYXFiIs7u3g7jetdtMnX0KP3c11xDYbNkCV1fVuW5L2RkMFA9YQLXuGyZ/XWuqmL3VslryBC6O8aM4Tpat2YfKF+dht96y7cr6fHHqYk+PLMdRnWKxLM/7sPuFJdvNDCQPbO8tbz/+WeXoGrcmELRV9ro5n2ROBo9Htg2D5dOr7S1ZBMTKST8/Hi+dpmLOTnMEmzf3tVw0xfKy6nsSAXAggVUiiSzYRYvpuCVCIvVq6nISYTFzp3cyxJhkZLC+yGp9i4qIr8yNScF/ocruNu3H+R1trI3xMdzvq8UffvKK5avu07rNWtktD//zKpPCWpq6lc5fd998jnjmZn1m9l9113yY1dXswL36FGPD7Z8ovWcZlofXlfr7exs+7nanqis1HrwYK0PHnS9V1FVo8e9skoPeeoXXXC0bhl7drbW/fqxglha5W59r0MHrZWS32OHg1Xv0teKFVqfeiqruN96i5XjvvDee1qPG+d9HnhlJSvng4K0vvnuMt3j/mV64H1/6uqa2hto8mStb79d68LC2sd9+GHX/9PSas/zdsfixVq/eecvWs9pph07F+j+/bUuLva+3q1bXdXN331nPy87O1vr0aP59+zZHhXkHnCv8h4+XOsjR3zTaq310KGc2y15rqdNI7/o29eeTmutH3pI60WLuLdM+OQTrZ9/Xka7bh0ruCW0+fl8lvv3lz1D+F+s4C4vl1daS/o3WcjPp4UhDVLWpyrbqoaWwKr3kK5j1SpaRRL89JN9ryd3aE1Xg7TKevlyus7quOW2fAJE9ADa174Ar7/OYKa0QvrNN2l5uc87eH1FAvZmFuOZKX3QvHFt32F1NYPXzzxDK1Na5V5Tw+8MGcL4lSmIa8GyYKWv00/nvfvoI7qXZs70PXZz9mxaWZMm1Z0tEhjIIPaOHUDy/hA8em4c8lCIR75wlRdbvcZqVWeDVu/SpS7rovn/a+/Kw2ys+/f9zIx937JmLKnsywhJ2mwtKKmkpH152zciESJSUVmiKET2irGE7LJvY2cYzGqYGbPPOXPO8/n9cc/jbM/m/eUVzn1d5zJzfOdZvstnX8oyWirA5wTO/eRV90AtfSOU3T+jWzeWkNeLBmzWjPs4J8eT7X32rP67VarEtUpN9fgt8vL0x4aEUKOOjqbGsmOHecDIbbdxjGauMZOwNQd7mTLmgSUAz31UFDVVs14vAOnPoUP2xmq1qUqXNo+EBEir0tKooSYlmY+9FFyTzMKOauXNLKzG2zFBacjPp23XjhMKoBpul1lo/go7SEujimvXweXf/tQM27ZRhbeq2Kvhxx91mtwkHQDidwIRz/pwv8xMqv12E+2Sk1kSwztPJSruAiauO4GeETVwX/1A586gQTQb2WWOAP0ZPXrQPzN/vnVpezOI2KvM2q4dTVzvvcewzR499HN3nn+ezv7u3fWJzi230PfTtWk1tKtVBbP3H8P+M6yhHRrKiKrWrcmgNBQqxEKDWuc9RaEfZcWKwIS7sDDgkUdDsS+kD3ByHRIPxWDwYJoi/aEoZC7LltEhf/KkeR5Q585kKKdOkQGZZUXffTf9RsnJDLwwys8B6NNbtYqm1d69zdejZUtG5YWGWidmNm3q6Z1u1bO9fn2a5MLCjJt2aShXzlOs0b80ix5CQ8lorYJ9LgXXFLNwuSj9mNlMNWjJcxs2WNv2oqK4Cdxu67T8Q4c8MdNmZQwAEo3Tpxka6nJZZ516+yus7KfejmvA/OA4nZT2vJmnmfTiHeWkweiwnT1LohHgNN89HQgtDDT1rYk+ZQp7P9uV9gcOZOy/prU4XG58OD8KFUsWxicPBQavL1rEtR80yN71AU/E1GOP0Q9gx9flj++/p5ZXty7vfSm24rZtSaQ//JDv+/DDgXb5556jj6NbN/3EUUUBSpVSMO7pRigWFopnxkfB5eailS/PnBV/5t+nD4n6+fOUfv/4g1E2eg7xF14APlv6NKCEYMSjM1G0qHHo+OOPcw/dcQd9Rma+CK23d/Pm9GGYBY3ccw/PSPny9AOYJfG1bUsLQEYG38csuKRFC17v9Gnr+lB163K/Hz1q7bcoXpw05eBBY83RGxUqcN337LEee8stZMZWlX0vBdcUswgN5QIZ9Vn2hlbuo39/a1VNS56bOZOHygyaczs7m9KNGWJiqAYrCk0pVmVKtOdwOKwziv/6i6GtAK9r1itb01g0Af+HH8j09KCqnAPv/hCTJxsThunTA0NQD+3LhuybC9TvBhT3ZOg5HByv12pTj6Ds2EGJ07vZ1YQ10Th6luanMsV8a0McOcIchBkz7Ju4du2ixjVmjLXjWw9nz/KeEyZQGBg0iCHVl9rTG6A0vGwZiwMOHkxNYtcuZoYDnOe+fY0ZBgBULFkEnz/WEGkhFzDoF4+3tGRJhuB6o1AhRnlp2sUNN1BY0jPF1KgBuIpXR0blTqgUOxPfjnUa7gktuTQ/n1qhWQkPzQTUpQvfyywcVetPMWQITVhmYzWmN3KkdbZ32bKczwEDrLO9Q0N539dft9cuoXZtatFW2d4Ahbnu3e2Z2uvX5/m3k+xnF9cUsyhalBvFKhRQy4dYupRhdlbM4uBBLuqgQdZtWDVm8cUXZEhGNlbA469ITKR0bFZKJCGBhzUsjHZzK81CK/eRm2udL+Btgjp4kATCKKt261YeYE3y37yZJhK98SLMpvbOXI6NBeZ9PBeKIx24zZcrzJxJU4v/IZ87N1DrUlWq+d9842FyB+LTMXHdCfRoXh2tb/Q1P2VmUlKePt1eW0qApptXXqE2YhVV5o/t23m/rl1JjLZtIwN/7rlLu44eWrdmXs6gQTThPP0094QI7/ncc7yvEbHu3qwa7qhVGXMOHMOB055Begzs6aep1Wg1oRo0MJ6LV14BZh59EchOxottFxsmhCkKI7yWLqWJx8wMFRLC87RrF/0qZm1uQ0IYipqWxvwRM9+eojDPqlo1exn69evzWe3U9WrcmFqTVadMgAzg9tvt+ThvvZUalp1kv3r1yICCPbgNULgwzSeVK5u3NdQS7Y4eZRKfWSy7202JVwtdtDI/7NnDRd22zdohpvkrVq+mGcosm1YzQZ0/zyxuMzNGfDxV8aJFSYCPHTOXZNes4SFwOJiAlZdnLJV5m6ASEpifoBVD9MeGDdzYWve4tDSgSxfB0zdPAao0Bmq2uTjW7aZ25Z95+/PPZHb+ZqyZM8m0NNOZ06XiwwVRKFeiMHrWbeBTdVSEdv2337bnexKhND1xIk2JdsveOxys/nrHHdREXnqJa/ziizQ52HWI20XLliTQL71EZ/TIkXz2p5/mPbt21T8HiqJgbO9GKFqI5ijvZD1/hIWRmHsn7xkR4c6dgR/W3Ae1XF0o2yeb5gJppijAmqhqPo7ata0znTVHuJ08mbZtKVTZKRDZsiVNRf/5j/XYpk1prtLTkP3RsCHNnHaEiFtuoaZqJ1m0Xj0KwZdSgcAK1xSzKF6ccfkzZpg7mDXndpMmBY3vTXotaK1Sb7+dRPH7743Hut3UDipX5sLOnWveLnXHDm7CVq140LxbhfpDMxVVrEj11qz08Jo1HhNUu3aU4nr0MH6/6tVpky5ShITuvff024Oqqu+1S5WiZGZULsHfsR0bC9xaZCNuKn0YaPWKD9VZtIg2fW878+7dJPD+CY7p6YE9GCatO4HDiRnoXL4ROrQv7CN9ffUVhQIzM1J6On1d+fkkHkeOUPK1o4XEx1MzbNmSfzdnDp3g7dv/s2U+/KEoNGFMmUKiN3Cg5/969+Z7aAzDXxC5oXRRjHi0AVJD0/DJjFOm9+nd2+M4NkNoKPDY4yHYLi8BcduZnW+ARo3o3LYqiQMw6s5Ooh9AoWftWnvzrmV72zEJRkTQ/m/HV6VFRNnxuzVsSHpkJ1hEa+1q1bETIM06ftxedrpdXFPMomhRT+SSmU1aYxa7dvGAm20ALQz2+HEyALNF9e4JsXUrCa9R0prTyciVsmVJgO+919wht20bmYrTSTu9VkNJD97+it9/p03fSM31NkGpKk0OI0fqE8nNm/kM2iE4fpy2Xz0fUVqap5yJhpMngcGdJ0MtWh5o3PPi9yLMBH//fd9rFC3KtfQ3UwwfTiaiMeIjSRkYv/Y4HmhYDetnV4HbTScwQMKxZInH7u4Pt5tZ5TffzOd48EH+PGWKuS1dhAz8iScobNSrR+b/2WdMIvv/4tw5ZqofPGjfGe5fg6pXL/rNOnXSj8zp0aI6bg+/AbMPHsGhM8Y2UC2yx04E2PPPA4N/6w0UKgFsM3aUKQoZmZ2y/+XL8zz7lEc3QIMG3Hd25kzzh9jBpWR7N2liP9v7Unp7h4fbz8ouU8a8TPx/g2uKWRQuTFOAVdhqRASJnp3OczfeSAKydat1iGvhwrR/ZmbyMJg52HJyWCYC8BScM4IIS1CUKOHJyjaTnNq08dgqIyOpWRihZk1Pv4mNGzkvRgwxLMy3xPbkyZRe9Z7lwgX6j7T/EwFmfheLJkWXISTiGaCQRzzKzqYaXqOG7zU+/JDmnN69Pd+JUHPT1HaXW8WH86NQumghPFq7IURohtAY75Ej9JsYSXk7dpCgVqvG9XrtNa6LlWR6+DCzp196iVLvM88YCwb5+dxndj4tWpA43nYbHaqNGlHrNMrgHjTIvLhlmzY0XUyZwut5E1yaoxqjSKEQPP1tFM7Eeijs7Nm+vr8nn6RQo+ffW7vWQ0irVgVKVSyDc9V7AQcWAtm+Tr4DBzxBIt6mKD0kJnoq6nbpwjBiI+TlUZMNCbHXL3vCBErohQpZE9UffuDa5uQYd/XTsHgx935WlnV49JYtfE6Hw3rs8eOc/5AQ69pbaWnUbkuUMDfHA9dxBnfDhhG2et9qsOrr641XXxXZuNHe2JUrmRFrB5ealf3hh/Yzp2NjRe69195YEWaIrlljb2xGBrNJ7WZZr1kjsvitISKflhVJO205fsUKez2PJ6w9LuH9I2XBtgRp3pw9rO3C6RTp3p19kJcssf93GRkis2bxb594wv7a2UVsrMi774pUqcJqALGxxmM3bmRm8c6dxmPS09mn+557RDp2ZJa4N35cc1rC+0fKLQ/FXHyXVatEevb0HTdrFp/r6FHf73fs4FxoWLlSZMh/DjM7f8OXPmNPn/atFNCihXG2dXY295iqMvPbbD+oKufB4RAZP15k4kTjsSI8FwkJ7Eu+apX5WC17vHdvkX37zMeOGiUycyaz4qOjzccuXMgM++7dfasP6CEqivfv2TNw/v2Rnc0s9meeEdmzx3ysyHWawZ2TY1wEzx9JSYwusmtT3rXLfmTBxo32k+cOHKD0aPc5tN4TdvDHH54S4VZwOinp2C2EN2sWpU27Iahjv8jF/ZWnA7c8AJQ1jz90uSgxf/65+TWjkzMxbtVx3N+oClZOrYrXX7ff0lZVaTJp25b+BjPtyx+bN9P/cfAgtat/2i9RowbNcjExfL7HH6e5a9OmQEmwXTtmeb/yinHXx9KlgWHDqGHdfntgAljvNjeinKMicuodwZptzOrr0IFz9NdfnnFVqtBnN2aM79+3bEmfiBZu3bIlMG/trTiJu4Ad09hfvQA1a9KOrmlK3brRjKmnsRQvTjPN3r0MlNi/nxK2HhTF099b81uYBa7cey/HaH4Ls+CSdu049y1bkg6YaRetW9Nk3LQpTdhmGoNm2tL8FmZSvmausmO2Kl6cmtZNNxnP13+Da45ZaI5NK/VK81fYva6i2HcWbdpEf4UdaP4KO4iPpy3STuljgMRDs91bYcUK2rbtOPtEWIrCbhjorl1AxyrzEeZMBVpbh578+COfxb+IoDfcquDDBVEoUSQUbYs0wrlz9iM/RFhOpGZNhv3ahQjzAgYOZJ7DokX6gQD/FIoWpXlr82b6bSZNollp6lRf4lanDk07EyeSkBvt/cqVaRo8csTTFwUAihVTsGRwExQpAgyO3A8puMBXXzEPSTN7tG5NAqdnj+/fnz4WgBF7CQnAhJ2vABlxwGHftOsXX+Qau1x8t5EjdbonFkAzVe3cSXOaWYSRVvZ8xw7+O2GC8dj77iMj3LePIbkrVhiP1ZjQ/v1cd7OkuJYtGTZ9+DA79pkl8YWH04937BhNhGaN1TT/2eHDDOywasJWvTrP3Zgx9ooP2sE1ySzy8qybpXszi0sZe+GCuVMsP582Qy1s0Cor21tTcLnMN9eff9J2q8EsPyQtjfZK7yQis/ozs2f7+gYAY6KzY4enuYodfDFaxQv1vwWqNAFqmatc6ekket6hr3qYuukk9py5gLfbN8SXnxXBlCn2JfyBA6kRffaZvfEAidljj1EK3bCBRNdOxzINbjffLS6OxNpORVANikImMWsWtcX4ePqW+venX+Hvv8m0li6lJPnyy8Z27ZAQ5pqMGOErodYoVwxDutdHvOs8ft1OSlSrFjWuiRM5pkQJ3qNIkUCJ+Z57uHdPn6azf/Zs4LeDXYDydYHN3/hspoceInFWVWpQRYoY5yPdfz8zuCMiqAWYrfHdd/M83XeftXDXsiUZUOvW1EACujd6QasfVa8e18+77a8/SpbkWleowLXw98N5Q1Ho4wkJIROoVs14LEANJCuL1girsU2akFbt3k3G8U/gmmIWLheJ9Nix1inxmnM7Pt5auvR2bg8caF46Y88ej7nq9GnfcEa9542J8cTxjx5tnDkN+Bb7y883j/letsy31lNiIudFD5mZlG68TXinTxtLW5MnB/aSzsnRV3mPHwfqqctRPOc4cMfbPqddr5fByJEMITZrtRmdnIUvVx5DxwaVMW9MNXzxhXmyljdGjeKaf/utfeayejW1v6eeorOzZMlLMz2J0OFYtiwDJr75xvz9zFClCqXbXbu4Xn36MA/hqae4nyZPpqnigQcoMOihbFnmrzz9tK8DtHermmhbtwJGLD2EuDRKFv36UYvUmFuZMmwY5i94KAoDA7SoswceAP7zeiik7ZtA4l7g1MaLYwsX5v8vWUIT7OjRxsyiWDFGOO3ZQ6ZlRtSLFeP85uZyjswCXcLCKNk3bEhGZ3ZdReGcdupEIm0lJDVrxverXt3aGtGiBash1KplHZbbtClNYnXqWFsAGjbkc1xKoUxL2HFsXC2f0qUjJD5epEQJOq7MoDm3e/USKVPGfGyPHnQqbdnC0tS//mo89quvRKZN47U7dRK57Tbjsdu3i/Tty5937xYJCxNZulR/bH6+r0O+f3+Rm282vvajj4rs38+fHQ6RO+4Q+fRT/bEzZtDJq+HCBTrd9ZzdaWkizZv7OnUdDpH779d3/r34okjqmI4iYxuLuDye1ZUrA9/15EmWjna59J8zOVnE5VblkQmbpOnQP2XUuFx56y39sXqYMIGOR38HrxHy8liKvXNnlui+VJw8KfLZZ3Ti9uwp0rq1yIIFl34dM+zezblv3FikSxc6bUVEfvuN9zVzss6axefyXsszKdnS4JPl8vSPW0Ut+I8FC0ReeMH6Wdxu3jM5mb+rqojqzBX54iaRGY/4jD16lM+r/d3588bX/e03kX79+PPBg+bP8P33ImPHck9u22Y+dtw4kcmTOYfavBnhm284dv5883EiIlOmcPyMGdZj58wRGTFC5McfrceuXMn9OGmS9dg9e+jg/u4767Gw6eC+rMQbQBcARwFEA/hI5/+fBXAOwN6Cz4te/9cXwPGCT18796tSJULWrGEUyUcfGU9OfDyjQs6dE2nXTqRGDfPJ1Ij055+LlC7NOvRGePhhkWPHSDhr1iSRNsKoUbyWqpKoKgo3hB42beIYEUZGVKjAg6mHnBxPFIkIa+wDJJZ66NLFE0WUn0/iCLDXgz+++07kS68Al/x8MqawsMC+EHFxIi922sKomG1TLn4/fz57LCQm+o5/7DGR1av1n/Gnn8jQJq+PlvD+kTJ+SZy0bKnfx0GDqnoibWbOJPM26w3hjQMHyLjGjrUf8SVCQjl+PPswdOzI59b6RBj1ePgn4c1od+3iPti40ZhBvvUWeyp4Y+aWUxLeP1JmbWXUmqqKdOhA4cYKP/3k2wdDRBgRNaS0SGKUz9d33y1y6pT1NXNz7feTOXOGz2oHUVHsVWEHu3aJ9Olj7xn27RN56il7Y48dozBqZ48lJfHd7IzNzTUXvLxxxZkFgFAAJwDUAVAYwD4ADfzGPAtgvM7flgdwsuDfcgU/l7O6Z506EZKczMYxZtLj4sUiAwbwZ41QGi1sbKxHApo3j6FuRqF+quoJg9VCYs0kls6dublFSJS+/NJYgh00yCOVuly89tq1+mOXLKEEomHZMjKx9esDx549K9K2ref33FxqO7ffHkj8VZVNhs6d83x36hQ1nDZtAq/9/vsisWN6iYyqJeJg56MDB0TKlw/UijZtEunaNfAaeXkMWwZElqzPlHofL5MXftohrVqrsnev/vuLcE27dyfx/v137omsLOPx3u/43Xd8T6swSQ1ZWZTSH3iA8/b119aS6v8KcXFcm0ceoWbsD4eDoax//eX5TlVV6f3DFmnwyXKJTfWs2x13WBMqh4OEPT3d68ucVJER1UQWvOgzduZMnic7eOope8xKhGtn1fxIxHNe7RDf/Hx7zY+0sc2a2RvrdttraKTB7jOIXF3Nj1oBiBaRkyLiBDAHgM1ATnQGsEpEUkUkDcAqUEsxRbFidPa1a2du/9Mc1vn5tOXfdJOxDdq738SqVbQvGtmbtQxuRaFjqWlT44qWTicd1Fq27++/08Fs5LhavdrT/nTDBoZUepcg98bvvwOPPOL5/Ycf6JDVC4udN49hmd7PtXcvexv42zq3bOH7efsHLlygvfW333zHpqYCJ7cdQY2sZYyAKkzjbVgYM6S9S4SrKm3j/iGZAJ3CK1cCDRqp+CFqH4oXDkWxQ43w+GOKbla6203nbaNGnMuoKIbg/vGHdbJmYiLn9fBhzrFZHan8fPqFnnqKkW9Hj9JZ+/ffjFzyXncRjr+UT2IiI7aWLzcvRmmF6tWZ3Pjbb0wYdTh8/79wYYbUvvsuI2wcDibrjX6UL99vQRRUVdCwIRMFZ8wwv1/hwoxK86lyXKwc+5YcWAikeTL9Hn2UEWV2+nBbJfB5o1Mn6/YAAM9po0b2sq3DwugvMkuA9B5bpoxxhJc3QkLoQzIL8/VG5cr2GxrVqvUP9+G2w1H+mw+AngB+9Pq9D/y0CFCzSAQQBWABgBsLvv8AwCCvcZ8A+MDgPi8D2AlgZ82aNeWDDyhJm2HjRkqcW7ZY22IPHBA5coRSSNOmTOQyQny8yNat/PnTT0VmzzYem5kp8uef/DkpydM+Ug+qygQeDS+8ILJunfH4RYs86mdiIqVdI6xfT+1Cw9df86OHgwc5H9545BH99qKJiSIJk14TGV5ZJOv8xfd44AFqEd7IyfF9P298+y0THIfMOybh/SNlyb54+flnY4lJVZm8Vb48tYu5czm/ZsjNpfmkbl2+jx0cO0YTzrZt1uYGp5MmAbuf0qVFKlemNhUSIvLQQ9yDenj5ZeukMlVlUlnDhiL/+Y/+mI0bKZFrbU6//15k5Bwm603bxIyxtDSaZC9c8DVvLF3q63/KyuI4H5PfhViRoeUl+ecPfGz5r79ufF7j4qhxi3CNzJJo8/JEBg/mz5s3izz/vP44DQMH8lo//GC83zV8/jk1lWHD6GMww8yZIocPM3l2+XLzsatX0y/47rvG5lcNBw+Snrz/voduGOH8eb7Txx9bJ/Cq6r/DDGWHWVQAUKTg51cArJFLZBben4iICGnblpvaDkaO5OLawbFjvlmqVrj9dpGUFHtjJ0+mY9wO8vJ4aOza0UeP5sG3A5dLx4Rggj17aErTxflokU/LiSz3OI8WLxZ5+ml71xbx+A12nbwgdQcslTdm77b8m5EjSUDt2MI17NolUqSISJ069kxVlxtOJ81abdtyrYcM4f7TQ3w81+D99639MceOidSvr894du+mH6xSJZqSjh8XadZclT4/bJebP14m0cl0uEydyr3tbbaKj2fQg7fZcuhQOmI1M6uIiPz+H1GHVZIOreIvjt2719hmr/Vu19akTx+PMKaHO+6gYOBykTGanZHHH+e9T54UefBB43EiDCb54w8S9jfeMB87ZQoZ3Pz5xgElGv76S+TNN0mD/P1G/jhzhoEM06eLjBljPlYzg82eTUZnBbvM4nKaoeIBeJdUq1Hw3UWISIqIaIrxjwAi7P6tHlSVZhSzSq/eWLvW2JTjD80EZQdJSVTHzcLxvLFoka/ZyAzLlzPXwk7mtEhgPwkz/P47Q0TttmL99FOTFo8bvmQnvDveAUBTyuDBnsQtKzgcNGdMmuzGgN/3oXyJwhjevaHp3/zyC81AEyaYJ/R54/hxJnqNHk1znd12uCdPMl/hlVdYANHptPd3dlCoEE2SmzfzferVY+HEtm2ZQOZthqhWjeawGjVYtffgQePr1qvHSshPPBEY/t28OcPJb72VIa033QS88boCZUdjFCscivfm7YPLreLsWZojvVuwVqvG5M9Jk3y/e+stP/Nk+w+hiBvDOo+92M2yShXme/gXkQQKqtg+xmcGaLYaM4Z5Pnp44gmaqkJDGTaq5Yfo4ZFHuN9r1/bkvhhBy/Vo1Yph9EY9wwFPZriWyW3WcVIbo2Vym+VB1ajB52zShImE/uZEb4SFcR/XrMn9YFXPyjbscJT/5gMgDHRM14bHwd3Qb0xVr58fAbC14OfyAGJA53a5gp/LW93z5psj5PXXrTmpCKWgS3Esde9uLN35Y9o0RjrZQVoapWe76NnTXr0XEZqqnnvO/rXvusu6Ro2GXbso6eji3HHWgFox8OJXI0ZQy7GLDz6gKj1y2SEJ7x8paw6fNR2/ejUl8UuJOFq3jnvA7nxqUFVK8gAd59nZl/b3/y3OnmWkVbt2nkir9HTuS6eTDvnbbqPpzsw0tnUrI+n0zHMuF01WIrxGjx4in/wQL+H9I+Xb1TwAX33FSCZvZGdTK9W06ZgYRiUGnMc/3hR1aEW5v22suN18hmrVRBo00H/W+HhPAIYW6DBvnv7YpCRqFykpDKBQFOM5uHCBc7V9O02W7dsbj9Wc9gsWiJQqxecwglaj6scfGcJvpV3cfjvns2RJhvKa4ZFHaFoqU8Y6fPbNN6kFlS9PbccMuNKahYi4ALwB4E8AhwHME5GDiqIMUxSloM4p3lIU5aCiKPsAvAX6MCAiqQCGA9hR8BlW8J0psrJ8u3j9/bfx2B07KCloiI42rg+Tn8/kOe+6Q2bd+LzLfgOUOo3q9kdGslSzN4yk1IwMSrR2umoBlJTtNGABKFVWqEBJyw5MtYr1o4Gwohe1irg4JnK98469a69ZQ8d0664pmLLhJJ5sdSPuudU4EyoqiglhixbZL4Xy889MmFy+3F7nMQ1bt1KCz8ujUzgy8p/tGWCGG25gu86NG1mjKT6eCWXdu7MkRalSdMyfOMEsaSNHaOvWbGbUrVtg4l5oKDOlATqAJ08G/viuGjreXA3f/HUc+2Iv4L33qFF5Z4kXL841GDaMv9eqxbkNeIb2H0CBYMCdX+OPP+iwXbDAWAKvVo1j9uyhVnHTTcYO/8qVuf5paax/ZZY4WaYMNf+KFUkzzFoPFC7M5La6dVm630z7VBRqaZUr09JhZV24/XY+c3Y2W8GaoXVrWhS0Bm9maNmSGkVqqnnG+SXBDke5Wj6lS0dcrNC5aJGYJmx99pnHAa05IP1DRTVs2iTy0kue3zdsIIfXg8MR6Ih74w1fJ7I3HnnEN9EoO9vjqPPHzz/zub2RlKTvIExNpfToL2GeO+dnRy5A7976VXXd7kBb+M6dJnbe5CPUKlZ+cvGrXr2snX0aUlIomR0+4ZQ2I1fL3WPWSrbDOA76zBlqB1aVODW43XRu9uhxaf6J06fpOH/gAc96XUq12awskV9+oYN0wQJz2/ulIDubod316onceqvH0bxiBefRzMG5eDG1FCtt7M8/RTo95JTbC9YjK09/PdxuagHea3H4sM7AJe+IOrSCPHLv6Ytz+P33xjkBK1aw+q4IAwqmTTN+1unTRYYP59rohWJ7Q0vgi4nhHrUaO24cAya8E1iNnmH0aO4zswReEdKpQYPoy7Oq+LxuHTW1Ll1Y6dcMBw7QL3PnncwnMQOutIP7SnyKFYsQEUY6VarEKAMjdOjgiYX/5BOqrEaHf8gQj+p77pxI9ep0pOph9WrfiJOZM3ltvYOQleWbDa2qXGBvxuSNTp18E+UyMsgQ9KIjvvsuMMojJYX38w8AiIvjIfd/f6eTkVf+zKJrV+OY9/PfPyfqZ1UvRkCtXy/SrZv+WA3e7//YYyLz56vyn1m7pO6ApbL3TJrh36Wl0ZSgF42lh5wcXr9fP/sBApmZFAxatiTRulSoKh2po0aJlCvHE/fii2TmlxvJycyvefVVMpXc3MAxs2bRpKX3f954+22RD8ecl1ofRUr/BcYJKBs22AgEuRArMqyi/PXuWxcd5apqfP7cbjI+LXfCjLmlp3uEpLg488dISPCY03SZmhdOnWIggaqal4MXoQDTuTOfxSwXSIRC5N1381xbldfPymIVgG3bjIVPDS4XhahVq6wDVuwyi2uqNpTWbnDzZqqqRjVRHA7GQFetymYwixdThTdSW707z02bRvXfyAnsbYKKj6c6XL68fi0XrTCgdt+vvqKDTq/TWlISVdU6dfi708n+17t3M2/BGyKMh/fuQ5yeziY6Fy4EBgCMH0/zhvf75+TQaXnypK+KrjkX9fomR07dj3IJi6C0fhkoUQEuF2P8v/46cCxANf3bbzlPAPtqlywJKLXjsTQqEe92vBlNbywb8HcifP/HHmPBQTu9rZOSGKDQuTOd2VYBAm4317ptW+YqbNnCv7WDtDQ27Xn+eTokR42iKaBfPzo/f/jBXrvW/y8qVaJprkULmqkefpgVYb3Ruzcdx716mTfVGTUKWDevAno2qIs5O2Kx4oC+jevOO+mgX7PG5MHK1ABa9MU9ZX7BzG9OAAjs8ueNkBA+36+/8nczU2Pp0jQX7d1rXUCvalW+87lzdOybITyc4/Ly7DVMO3uWVYOtTMY33MAzWaOGdXn9EiV4Zho3tq5PFRrKuWjRwn7AiiXscJSr5VOzJjULrVGKUb2ZDRs8aq0IVXEjaSEtzTdPYeFCxv0bSSLNmnlKUKgqzVtG+Ra9e/ved/16ag969aG++ca3zktuLrWQNm0CtZbt2yWgCdSBA4zd91e3tZh4//yRSZMoBftn2D74YOBcqarIoEGqrOrTVbKHhDNjV+iMNTLXJSTwXTXJ7uRJzt3B01nS4JPl8tj3f4vL7Stqut0M3YyMZEbvt9/qX9sfUVG8tne4pxnWrqUE98EH9sKw3W7OyfDhVPtvv52mxC1b7JVbuNxQVWoGALUIvWcaPZpz6nYbVz/Yt0/kttZueWDcBmk69E9JuKBfa+XECc6f6btnJImMqCZ/v93bUlIXYd6OXpUAPfz+O9fODkaPNjdreePdd+2bU19+OTCfyAgvvGDfLPnKK/av+/bb1vkbItepZqFJHL/9RinKqKe1d1nwM2coARhJC/4tT3/5hRKjniSilSTWNJxdu+jo0wtddTiYOerdUOm771g2+4EHAsfPncssVg1paZT6N24M1Fr0HNt791KK/OYb3+9nzODz+febjo9nUyCt5SrAML/Q0MC5UhSgUZGV6FBnPVIbfwQUK4fz5z2tPP0hQkfoypVsS+pysTfGN9+50e+P3QgNUfD1400RGuIRNbX+3yNH0olbtSrw5puB1/bHokV8h9mzrfuGxMQAPXpQ2/nlFzpUjcKws7Io6T7zDKXHceMYHLBwIQMrhg5lWfHQUL7viRP2P4cOca67daODOd4kaNxO9rOiULvbuBGoX5/X9Ee/fpSeH3yQIcF6aNIE6PV4CG6Maw6nS8Vbv+6Byx3Y3adOHVYLMLoOAKBUZeCOd3B72Uj88e1my3eoUoUS+86dlkMvtmC1alUKkE74Vx8wghZCawf33muhXXmhXTuujR1o4bZ2oDVr+sdgh6NcLZ+ICGoWLVua2+kOHvRIjF9+yaQ4I8TGehzCKSnmVWRTU0UOHfL8/sorxoUB8/J8JfQzZ4yLDqpqoF2+Xz86TPXw99++Nnmnk5K1Vg3UGwcOBNrPT5zge/pLmHFx+lVMo/Y6Jeb9luIe10LUfKoo6ekMr9VDSgqfZ8wYakj5+ZTmh/xxQML7R8qfBxID/mbwYPp+fvqJvgMrn0N0NCWrYsUYGGAHu3cb19vyR2wsHZ3bt1s/i9PJkGe7n6pVmSAHMEzymWeMM7j79KH2ZidkuF8/zp+Rb2DLFhZ4rFWL/i69qqluNzXCJ/rHSnj/SPlixWFZvDhQy7twgRprRobv/OzZ46WtOrJFvqovR95rL0cOB05iUpJvEtzq1cYVF5xO30J/L75ovpbPPecJaGnRwnz++venJpyba13zadIkzmNSEtvYmmHpUvpCtTpmZti/n2ty6BD9bmZITWVot52x/4oM7ivxiYiIkOhoRqzYRdu2+kRUD5MmWWdPasjMpFPOriN1wAA6G+0gLY3Xtltqe/JkOvHtont3+0TT6RT54rEprCp6ONJyvNvN9fntN9/vl+9PkPD+kTJ0cWAN6pUraYJYtcr+Oy9cyN3t30faDA4HTVX9+1uXwr7cOHKEDPKpp1jsrk8f7g/vIo4inI+JE0mYp041N/1kZ7NC8IABxvty717m24wfz7PhX0pEVVnKAhDpOnyv1PooUlbtT5ZWrTwl8TVMnMhreBcwdLm4lheZ395fRYaUlilvzNEt3Nihg+e6bjeJtX+1Yg29e9PELML9+9JLxoyxXz9PufGBA43LzYhwLrQciAce0K/GrCEyUuS99/hzRIR5VeSDBxmV512A1AgZGTTtac5+M2jX0/JDrHDdMosvv7ROQtEQE0Mbrl20b2+/r8G0abRh20FOjmdx7WDkSONy43rXbtLEUybbCitW2C/bLCIyeugFyR5SW+SnB23Fkg4Z4qn4q+FMSrY0GrJCun23URz5vlRs0yYeOqvoD2/Mn0/NaM4cY8Lij+RkkfBwngi7pVf+V3C7GSo5bBj9a23bch41n0hyMjWdDz4gQTFj9G43mWHPnsbJhFrET1ISibN/RE96OpnOXfe5pOPX66TFsJWydmuutGrliZxTVd5Hbz7//psJnarKB7rwRXs5804DefWFQMq6caOH4WdlkbhWraof9rxjh6e2V2wsw4mNEkGPHvWUqlm3jnTAaN7OnqUfSlWpQb39tn74uYhvOfU33+R4o0gzLYEvL4/z+ccf+uM03HUX17pjR2sfx1NPUVNu397X2qGH65ZZtG9vXThOwxdfsJCYHZw4QfXbLu68Uy7mfFhh2jTrTE8NGmMxk1i88dVX9rPJHQ6q5EYHwR979ojMfnYgtYr4PZbjIyM5h97Sb67TJQ9+u0EaDVkhZ1J8qdfu3Qz/szuPqkpGev/99pmjCMMiH3hA5N57GfZsN3/C6WT+xebNlMAvJe/i/4OUFMb7P/ss98J995HRLVtG81uPHgyZNQvFnDqVZk8rZnr0KAma/55QVZpwtx3OkFsHLZeekzbLl1+7fUrjqypNZI8+GnjdZ57x5IA4jm0SGVJapj2jH4/eqZOnXPwbb4hhrxUREtQTJ2heLVbMPNfinnsoMA4axGuaNSDq0oVBLffey7H+BTW90asXNZxbb+VYs+Kjr7/OXIwbbxSpWNF4nAiFz6+/JrOsV8987I8/UgOsWtXadHZdMoumTSN0q7caqdxt2ph36PLG0KHmTY+8ceAAK4XagRYxZVcCnjCBpTPsICPDtxCbFcaMsa8NORwifTrsFfXTsiKL37YcHx1Nwu9tRlFVVd6ft1fC+0fK6kO+HP7IERIpq9hz7+d59lkSe7umKpeLSVnNm1OqzM62/7cOB6V4gETB7nP+01BVRt7UqiVy001cP6eT0nKbNrRdG0V0rVnDNbFK2tq8mX5Aveuoqsjve+IkvH+kDP79gHTuHBiBo3WO9EZCAomYJnU7Zz8vzk8qipwLrKmzebNHY3A6KS0b5dYsXOjpkjl5srnfYOZMmvq00j9mBTdnziQN2L9fpFAhYx+SCP0QgwbRVxYWZjxOhAz+nXfYrK1uXfOxW7fS1/L009x7ZoiOJqN88EEKE2a4LplFeHhEgE8hI4O2U3+cOKFfMXX37kAnrqpyY+s5wfTqCr37LsP39ODvTN6wgSqjEbwPmdaAxW5V3WHDaG+1g4QEHhir5CwNQwa7JGHoXWyZmWOeYZadTYbon3U64+8YCe8fKV+v9E2/PnXKHhHTcP48Jb5vvrEv3e/dS3POwIH2tTQRmgFGjCAT7tOHEuelaDH/S7jddGg3aUIhIysrMFHtyBEyS6uy/osWkegYVbYdtuSghPePlB9Xx/rUiDLDmDFegk/mWXGPuFHUafrmzC5dPGft7FnjpFAtGe3CBV7GzMeYk8N1dLmouZhZGTIyPAm0gwaZt6vNzKSG7nZbV7TNzeXzZmRYC5haFd5Tp6x9carKsbt3c5+a4bpkFmXKRPhIeA4H7Xt6dstRo6iKe+PQIRY/8yceW7fqE/T58wML9eXl0TSgp3qOHctD543HHjO2P06c6Ot8/+UXTy9iPeza5Tln589zE5r5QbzNQc88Y8zg9O4z7slJND/tX2A6VlUpCfmr+DtiUqTugKXy/E/bxe2VT5GYyENp1T9Zw7FjPJhLltgbn5NDKa5tW/ud8ETI6Pr2pYQ9eTIJb06OfU1EhITrnXdIIH/99X+Xg5GZSQLXsCG1IH//z7lzzHexylv59lvmL+lp6vkutzwx+W+5+eNl8s2MC/LYY9aMO8DsufMn7qndgWF+W7fabxEwdqzHT2I1x2+84clrstLAn3iCvpzcXOtOfN260Wx1+rT183btSnOfnZI1jz5KOmVHkOrTh89rlcdyXTKL4sUjLk6A200iBQRG3ohQjfOWfk6eZPXLW24JHPv664HJOPPmiYSGBh6wOXMCHbiaNAL4mmHOnPFtaarB5SJRad7c9xq33abfrlOToPr29XzXr595yOiOHZ4a+ps3U3IzO9yqys2flyfy4J2x4h5eTWRmD0uK8N13nt7hGuLTcqTlZ6vk7jFr5UKOh6umpFADsaqRo0GrGmtVUkHDmjWc03Hj7BFqh4MRSO3a0Q+wdq19zUVV6WtZsIBrcffd9CuEhrL8hl2z4z+FvDzuj2LFRFfyz8sjcXnjDUrlRhrmBx/Qca2Hc5l50mbkamn7+V/y1At5tkKWly/3ShR1u0V+7CQyKlwk61zA2AceMA7H9kZ6uv1owb177Te8WrzYE+lkhZ9/Ni4J5I/vv7duwKRh8mTr6rQapk2zF715XTKLqlU9zEJzwHXqFBgNcPx4YHnthATafN980/d7h4OagvfGc7tpCy5dOlAr6NAh0H597BjrSTVs6Pv9wIH6zZfGjuXKaF3LRCg5e2eda9DqHQEezSAhgRFEegTR5aJkGxbmiaZp08a8Ns6xY3yvJUtEBg5U5fjwXuyAlxpj+DcnT9Is1LatL+HJzMuXzmPXS6PBK+RYkkc8y8ggUbbq7KXhp594bTu9rlNS2DntwQftNUVKSGC0UePGZPx2pMP0dIbdjhxJ53LjxtxjQ4bQxHPuHLUlq8gUDXZDri8VDgdNOHpFI1WVPo+bbzbOvHe7KWEbmTejYi/IrYOWS9dvN0mzCJdpmKmG7t29Oj+ePSQytILIwsACadu2WdcZ0/Duu56e9VZo29Ye89ZogR1BIyXFfsZ5bKy1X0GDnWZNlzr2umQW9et7mIVmDsrICJQGR44ksfHGpEl0YPmbbRYvppTvjfx8EuODB30J4YkT+ou+eTMJh7edNTeXz6dnA/7kEzprtb4CInTq6dlJtValTZp4nuX1140PyrFjrHHfsKGnraRZaYTly0WKFmW/gW3bREY9MYOmgs36NouzZ1ntt0wZ/o03oc13ueXZadukzoClsuGYx77mdHI+jSRWfwwZYr9q7JIlJNyzZ1trBYcP08zSpg33h5n/JiWFZsJnn6Up5Y476FidNYvr5H0vt5tajd3PL7/QTNWsGQWGLVuMmcelFCS0M19RUYzMCQujvVsPeXn0Eb37Ls+AqvoKUysOJEqtjyLliW92yZ3tVcnP950Pf2IbkAS6ZgT32IHfAt77oYeMK6563+PkSfMeFd5jJ082jxj0Hvvyy9ZlY7TxHTva79h42232O1Q2a2Y/zL5xY2sN67pkFloGtwht5EalvpOTfQ9OXp5xLkJGRmDS3g8/0O7tD4cjMMwzIAmpAG63fqOhqCjGdPsvsJGENmUKNQ5vG6o/sfLG4MEkQJqpJzHR3P46dixNPdOmiWSdiRb38KrMqTCgXkOGeLQi/3fWMrRnbSUHUVWq602aMMTPbuOibdtIMOzUvdm9237E29GjZOx2TE1nz9JpvHOn9cHNz6f5wu6naVOGUQKsntyjB9dL77nee48a2axZ1s8xfDi1UCsp2uFgpvTNNxszmB9/5PM99xyTJp980pcJTF4fLeH9I6Xrx0ekVy9PJYMjR0jw/bfPxx9TW0lNFRGXU2TKPeIeWVMe6xzn4//bsUPfEexykYF5P2+PHsaO8B49PPOQkUECbLTub77pca6vX2+cRS5Cs7SW4DdpkqeHuB6WLqX1Q4TnxUwTOnTIY/V47TUvTUwHmZke01rfvsZzIHKdZ3CLcOM0bx6Y7WqE8ePth4xmZ5Nb241ImjKF8c524HLx4Nu1wWvOXbuhsUuWMALMrmN1/nxKRzk5Io4cp8iUe0U+v5ElpnWwaxcJ3ejRgVLSDxtOSHj/SBm+xJMa7XKRyISFWTeh18aPGMEQw1q17Pc4F+GhuJTEviuNtDQ64P/8k1FtDz3EfffQQ9yrf/7p0SoOH6ZW06gRhQEz01xkJJnzDz9Y+6jGjaOvRY/ZOp30eZUtywirQYMotHjKzavSf8E+Ce8fKSWbnvbxWw0YECjIHT0qUqMGzYUiwh7un1WRk592leHDfDlLt258X/997F+4cuNG7i+9bPy5c31Nzs8/T41BT2DZsMHjV3G7uQ5GCY3R0Z5w3YQE5n0YIT3dw6T+/tu8q6V235wc+mC9TdR6uPtursvPP1t3qPxXMAsAXQAcBRAN4COd/38PwCEAUQD+AhDu9X9uAHsLPovt3E9jFvPne2KtrZCby0WwqwKOGGHfGZWa6luH3wrjxgU6x43gdNL0YdUERcPx44F5DmbYuJHO5ovalmYaMIh+2rmT19czlc3fyTpCr/2y82Il2YwMRoEMHWq/iubJk9S6Spe25+h0Ouk3eeQRkdq1zaWxqwGqyiSyuXPpM7vzThKbJ5+k2W/oUDpL27QhcTPSkjIyaCq8917rVsFLllDwMorUiYmhhqdlLPfr57mn0+WWvlO3Sa3+kVK1VcJFDcHlotDiHcF25gwjtW680euZC6Kjvu317UUBKieH5iUg8Jny87lntT24apVI8eK+gR8a3G4GuZw6xfv168d+I0Z7pH17nqHUVO5b7+ATfzz0EBl9YiLXZ9Ag47HPPcd7nj0rUr++fj0uDR99xMCa+HgKiWbhzuPHc+8fP06GZdbz5YozCwChAE4AqANPD+4GfmPuAVC84OfXAMz1+r+sS71nRESEqCoPix2npAjVRrtJbufOkSAaxZr74403zBffGzEx3IB2Y/4HDbL/3Fqeg51S0CKUVH0yp2M2svvdwpd1x+/YwfF6prI/DyRKnQFL5akftkpePkXBM2d4UI1Kt/tDVTmPzZpx05up1f7P1agRi+PZaVzkdPJwrVnD+9kxc11p5OdTeAkPZ1jvyy+T8Pz9t7X/ZcsW2spHjDDPMt67l+u7dq35s7jd9OF478sch0t6TNwsdQcsk59XeCQV7Sx5CxfnzvEdLppnVVVk9pPiHlpR+nbcddHMdvo0mYqe2WbdOk+IrcNBQmkk3S9d6pHmFywgNdTqRflDCzBxu8noAGOz38qVjABMTGRBSC/reAA2b2bU5saNLJRplhNx8CAZ1dSpvL9REIII733nnfTPAubmsH8Ds7gdwJ9evw8AMMBkfHMAm71+/6+YxcqV3LB2oCXl2JX8337buNKrP6KiuFh27N+qSge4Xcl30yaqmXbMSarKHBH/nBIjJCbyEF8sCpd2RmR0HZFvI0RyA9Wv7ds5Xs//8nf0ean38TLpNn7TxVacO3ZQ27Lb3S41ldE3ffva1/7i4pg30qkTGaTd/JGYGIZPAyxKdynJev9WaJFdjRpRMv3sM18zp8PB7267zTy3JSGBUUNWvR/y85kL4N175UK2UzqPXS/1P1kuu097PPI7d1KI8TbpZGT4+bqyzot83UjSh9SX0YM9dsRjx/STbUV82/impBiX6VFVagxaJOCHHxrXXFNVMrKEBJYTqlzZ2AyqqpT8z58n8zEr5qeNTU2lcKmnBXmjTRsKA+3bU5M0wz33UPipW9e8Xt6/gVn0BPCj1+99AIw3GT8ewCCv310AdgLYCuBhk797uWDczpo1a0qHDvbDE8eNE/n8c3tjtYYudkIaVZUqvh1TiQgZkFErVX+kp5M4x8TYG//tt/avnZlJM8/FPAdnjsj3d4qMrKFbhmHrVkr7es+y5cR5qf/Jcrnvq3WSmkURbOFCP8nRAmvX8qDNnWtvfHY2a2xpSXp2GfWGDXT83n47cyBGjLD3t3FxLC/y5puMDDKKHvo3wOGgtlS4sEiJEoEM9MgREpe33+Y+0Hv/7Gw6hj/6yPwc5OUxb8e7PM7Z9Fy5c/QaaTRkhezxapU7dSola9P5Ttgr6vDKsvetzrJ7h0ecN9KGYmO5BzTJPybG+Prr13vKeOfn83cjeCfFrlxpXkNtwgSPr8DKAvD112SumZnWNeLGjqWJ6dAha3P4xIkcHxlprsVfVcwCwNMFTKGI13fVC/6tA+AUgLpW97z11gjbCTaaVmE3AufJJ417U/hj7lyaA+wgOfnSSng884x+boYeNm2iX8OO2czpZAjuxTLpqspY9yFlRI4Etgf7+28yCr3QwM3R5+TWQWQUZzNyRVV5cDp3tveeDgcJ0n332Stq6HaTEDZpQjutmUlFQ04OI3pataLmpeXLWIUZqirt0aNGkbiWLEl/iB0H/ZVGUhKTRrVMcv8MdrebEmjTpnSi6+W82KlaK8Kgi7vu8q1YEJeWQ4YxeIXs8tIwXnrJVxPRRdR8kSGlZV7f92zt5xEjPEmnVujSxR6j9y+3Y8bgtBYF+fnWe+rcOe5DVbXWZhMTPX1vrMrMJCUxYEbEvA3Dv4FZ2DJDAegA4DCAG0yu9TOAnlb3LFs2wlaZiMxMlgOwihLQsHOnfh0pPWRlcZPY7ZHx1FOBJUCMMHcuVWw7Um9ion61UD2oKsMBfeZj0zg6tNcFnrjNm8ko9PxCm46fk1sGLZOOX6+T5Iy8i2GYr7xij4gfPkwJ/4sv7GlxmzbRPPLWW/aio2JiKB02akQ13k4yVloazQnPP8+/e+IJ+gESEqgt2YlG07SeO++kPXvcOPvmz/81Dh0SKVWKzmEj7XjqVM57fLxxLkFaGs0m3kJWfFqOtP9ijTQcvEJ2nuKC5eWRAFoGOvw5SGRIafl90I8WAz2Niuwkbe7caT/R7VIKeb7zjv2z/cQT9n1x999vHZig4b77rP23/wZmEQbgJIDaXg7uhn5jmhc4wev5fV9O0zIAVARw3N85rvcpVcrEkySeHs6vvmqvGquq0vZ52232TQxvvmnuTPLGsmVU6+0gNpYSn50kLKeTPg27DtqhQ5nId5EJ7ZlFRjH3mQCKvWkTHfF6TGjFgUS5+eNl0nnsejmXmSepqcz8/uorawanqoxLj4iwN9cxMey70bWreQVQ7dqrV9Px2b49pWuznAS3m0Tys89I3Nu0YaLk5s3mUmJWFqX1BQuoebz4IqXrpk15jY4daQJ6913rA5ybe+X6d+fkMCDgnXeoPRkJHGvWsFT2XXcZM/azZ7mmmzZ5QnATL+TK3WPWSoNPlsv6o5SqzpyhcGPKvN0uUWf2FNfgsnL8j98t32PxYusiehoefVQ/q90fWosAM61Kw/Hj9jOzV62yb42YNcs4h8wf339v3Z/lijMLPgMeAHCsgCF8XPDdMADdCn5eDeCsf4gsgLYA9hcwmP0AXrBzv3r1jJnFkSPctIpCE4dVzZStW0lwq1enCcoKJ09SS6hQwV5NmqwsRrCYtXT1RrdutMPbSTAbNMh+D4sFC1ie4iJhOhwp8mk5kendRfJ99f39+8ko/CuXiojM3HJKan8UKd3Gb5KULIekpdFubNXQRYTEvEcP2v/tHMLRo8nA/bu46WHJEq77c89ZM6GoKJr5GjXiWs6caZybcfYsI02ef54MqGlTakR9+jAvYvZsSoqpqZzb6dNpY544kT+bffr1Ywh1xYq058+da2xy2LvXvgkzJsa+0/7cOc9aGGWyJyTQeQyY289jYynlt2vHuTh3jj6MzmPXS90BS2XhLobd/fUXz5x3XkSAcOTIlpzvOopjUEVxHF7j81/+c6QFjugFU/hrdQcP8t56Qk1Wlu/3I0calzvJz/cVRB580Ljon7fZye3mHjIzi2vrkJXFsWYCmDY2OVm//pw3/hXM4n/9iTCJUduzR6ROHUqjeXnmpRxUlcQFoBRqFYVz/DiTk4oXD2wtqXft8eMZdVOnjvXhVVVGST3+OKU8O4woKYnO4alTrSX69HQPUXBFbxAZVklkyj0ieYG71ukMJJ6qqsqYFUckvH+kPPfTdsl25F98brvhyyKX1g/i0CH7UveRI/ZzS06fJoG3W/tnzhyaMKxsxy4XzU52P927kymHhDCnpF49mh9HjmSc/Z49HmI3YQK1llatqAnt2mUs5f/yCzXqfv2sAyRWrKCkP2OGtTlwzhwyNrOy/B078jxNnszrbt8ukp7rlF6Tt0h4/0iZuDZanE5Vnn6a5WUOHeLZaNFCxzyTkyrnht0uuZ9UlY2/Mh5cVUns/bWDo0c5P/6mst69AysVP/MM39t//T/+2DeaSGtrrGdW/ekn37yKFSuMNYYNGygMaPjsM+OoxdhYX2b2zDPGEYV5eRSQNKbVoYP5egeZhRe8G+nYaYs6fTqjmebPtya2bjfNCg8/bK/KZG4uoy9KlzaPvNBw4gQTrkqWNK+hr2HqVJZZL1/emiBo5pYRI0Q+fGyDuIZXExnfSiTb3PjvdrPBU1qGS976dbeE94+UfvP3Sb7rMlW/uw6Rmelh4hcukCnNmUOC0rcvbfxNm/Lfvn25n9q2ZZBCo0YkJrNnB2qiTiev0749mZKWUKeHlBRGR7Vta+1PiI0lUerfX9/Ep6o8T127ch+3bEl/T16+S96YXbCHFuyTH6a6pGRJT3XXmBhqJf6+yKVzEiX6zSaSOaimSCwzU+PiOCfeRTEvXCCRrVDBN9BDK+HvLaRoXQH9zTZZWWRa3kmA/fvTT+bPhFwuzpemTbjdZPx69aQ0zUeb27g4al9GfpYXX/Qw5FWraE430kSGDKFZV4SMbswYY59hkFkU4PTpS2uk8/PP3PR2nJZOJ80OWtaqldSfnMxDOmGCvfBeLWP5k0+s49tFaPe97z6RG26wl4QWF8ex3W5ZJq5PK5FRpBt7BJcsYeRImTIin4zKli7jNkitjyJl/JrjoupQHFXlYYqMpBQVxD+P9HQ6UevUYRDG22/TpLJ9O31R7dqRoXz6KQmuVh1XhGa5558nIZwwwZjwHDlCIv/44+YCiNvNwASzKsY5OWSCaWk0YY0aJeJyqTJ6+WEJ7x8p3cdvkq1RudK9u4e4nzpFhuFd4VlVRSaPPiUn3m4q6mdVRU6sFRFq9s2aeXwfqkr7PhDI8HbupDlTO+vLlzO0WK+y7Y4dZAJOJ9+zTx9e0791gQhNg3fc4emP3rixSJEi+kz5yBHOl8vF9ahalQxfD3FxXKv8fPqLKlQw7m+Tlsb75uXR1FyjhnEnwCCzEJpjWrSw30hn2jSqy3bs5tnZTOu3G5536BA3sd7m0sOyZWRyW7dyk1lpOHPmcPy6dfZMOsuXc/ycgXPEPaScyOS7TTWK6GhKokWLirw0KFmaDv1TGg1ZIWsO6xv1s7JYdRYgEbNivseOsebNd98xbPNSqqle77DaG+fPc3/07UutQysAqEWPnT9Pot2kCZmNFmnjb35atYrE9aOPzE2zu3fTDDJpkvmzOZ2Mknv+eWojS6MSpP4ny6XlZ6tky/EUnz1z+jTPj3clZhGR1b8lSvaXbUSGVRQ5xFjftWspZHn7Jb75Rj+naupUmqS051y8mIxXDyNGeExM58+zPIlRb4mBAz3/pxVdNPJ/ffghCXl+Pi0ajRvrjxOhL2vKFGpyFSqY15MaOpRCwLp19NUa+TGve2aRmnppjXR+/JGSjh1GkZZG1dZuVvSqVX5Z0SZwuykFduxoL/w2PZ0mh1697Dk6k5N5OHr0UCV96deMevrpQZE8/TjOCxdYwrxVK5E/V7vktcmHpNZHkdLhq3Vy8lwgB3C7aV5o1YpMomdP62qoWVlU6wGRmjWtO9jl5vLgvvsuVXO95lZB6GPhQjrv+/YlQfMm+i4X57JDB5pH3nsvcI+7XPQ7NG5MomXk38nOZsBCt27m+1hVafa57z4yryOJGdL+izVSZ8BS+XrlUR/T5pkzNOn42+rV7BSRH+5jSZqtk0VUVWbP5jt4m16MhKiXX/ZtYrZwof5Zcrl8/SKnThmH0ebmUlDVNLF33zUut5ORwflMSeFctWqlP06E51GL5IyMNG+vqo3NzeX5Mkr4u66ZRWYmQx7tNtKZMoWEzU6kSGIiF9MugZoyhaaApCTrsSkpVEEHDLDnZNXyHWbOtBeaOn06pcfFCzJF5vYho5j3rIgz0Nufn8/IncaNyUiPJGTI/eM2SHj/SPloYdRFR7YGt5s26dtuI5E4c4aEyOw9oqN5iJo0odT3yivWlWH37+f83HADu75ZVU8VoZ23a1cWFHznnaDWYgf79nGOATIN/3VMTycBatWKfg8js+eSJVxfqx7ff/xB4nrsGB3f78zZI+H9I+XhCZvk1HmPUBIbS4YR4EPJyxSZ9QT39KJXRZw5Mno0tRar/aHledgJnY2JoeCnMVkzmrF+vacDpctlnvMxcybD10WomZk989ix9F2JWCeDDh9Obd3hMK57dd0yi9xcSuV2i9RNnswFtcMoTpwgcbajrbhcrAz6+OP2rr17N69tp45Rfj4dWHfdZa/sx4kTZIavvSaScSpaZEIbSmGbvtHdlStW0AE5cKBISppbJq6Nlps/XibNh62UPw/4BsK73QztbNmStW38+3n4w+2mCezBBylNLlzo8fUYHZDTpz3hsg8/zIigP//ULz2tIS6OUnHPnmR4oaF8f6vIpdOnaUJp146x91a+liuVC3G5kZND8+3ChTThGO35kyfJiMPCjEvnJCVxvd98kwKCEbPevZuMRQv8+GNvvDQaskIafLJcpm48ebFicVwcGUbA2rjdIms/J8P4vr2oaWfk9detayiJePI87CTxzZxJbd4OXnnFXsUFrU6Vnb7weXlkWHYtD5p2YXS+rktm0aJFhHTvbj93YdIkSvJmYbQa9u3jZrJT7ykri/b9QYPsZSFPm0ZCaCcrMzqaWtPw4dYO9fx8RkFERIhs3KCK7JgqMqKayKhaItGBp//QIc5Hr15UsXfEpEjHr9dJeP9IeWn6Djmb7pkol4sMOSKCUSFWUWbp6SQ6zZvzAFmZ5FJSuI53382Q4SlTzDUCh4O26n79yLg6dGBjmQMHeLj0pEaHg6aBCRNolmnenE7MWrXIyMzWOjub79ClC0NbH3rIutRIWtrla5d6JbFgAfNkKlfmHOhBCxmvUoWMw2ge4uLo8J0+nSHCcWk50mfqNgnvHykPfrtB9sWmXRzXooVBROGRZaxnNvJGce+aLQ8/rNoKEPnrLwpgVpUGVJVnxE7NsgsX7Fd02LWLe91OhYZZs+y3YRg50nhdRK5TZlG+fIRth/OECdy0dhjFxo3k5EY1/b3hvdmtkJvLuji9e9vLJv/pJxI0/77feti1i88xZIhIXnKsyIyHKXFN78ZKsl44f55awR130LQVl5Yj783dK+H9I+X2katl5UGPDc3lYrx+ixY06VhJYocOUb1u2pS2aTOCn53NA9itG80bX3xhXq7k9GkylIcf5oF87TWaHvWielSVjHb2bE84aPPmZBITJ/p2vDt0iOO1jOyFC6nZvPgimZeWkf3UU7SLN2rEfARvIpObSwa6fz8djIsW8b5lylDLGzbMnICkp1995jJVpaZhJMScPEnmGhrK9zdCVhaZfalSjGJUVVUW742Xlp+tktofRcqARVFyNj33Yl+HH37QaRiWckJkameRIaUlf2Yv6X5fkqxYYe0/Gz3aHhHWetVYadIiNFn37m09ToSC1Jw51uPcbu5BOz3ONZ+IkYXDLrNQOPbaQNWqLSUxcafluOXLgYkTgQULgCJFzMcePw707g389htQo4b52Kws4M47gW++Adq3Nx8rAtx/P/DQQ8DrrwOKYj7+/feB9HRg3DigZEnzsT/9BEyfDkz6zoH6mVOA9V8AqhvoNAxo+YLPzTZuBN54A+jXD3jg4Xx8vz4aP/19ChDguTtq4a376qFEkTAAwKlTQI8ewD33AB9+CFSpYvwMeXlA9+5ASAiv36ULEBpqPP7NN4ENGzgfvXsDDRsajx0/nu9YqRKve//9UQEY3AAAFM5JREFUwM03689hZCTXOi4OqFMHaN0aaNUKaNkSKFPGd+yePcCECVzz9HSgRAmgbl3gppv4qVePv5cvDyQmci3i4oDcXCA1FcjI8FyraFGOK18eKFsWOHgQcDqBAweA5s35KVdO//127gRcLmDFCqBRI+C++4CePYGmTYFixXzfc8kSwOEAwsKAjh35zEbYsgXIzARuu8343hqOHuU7tm0LFC5sPvb8eWD/fu55szUG+F6//QZcuAB06wZUrhw4xu0GvvqK81umDBAVBRQqBKTn5mPsqmP4ZetpFAoNwYt31sZNrjp45KFC6NQJGD6c8xoWVnAh1Q1snQT8NQxqWDGM2fkxtjifw7yFhXDsGNe0aFHfe4twrh9+GGjQAIiIAGJigAoVgNKlfceuWweMGAH88QdQvDi/S0nhOlet6ju2Z0/g+eeBBx7wfJefD5w5wz3lPZf33Qf8/bfvWooA0dHcgxpWrwamTQNmzw6cwxMnfK87ejRp3TvvBI5VFGWXiLQM/B+/cdcSs2jZsqXs3GnNLPLzAVW1ZhQAFyk725pAa8jMBEqVsjc2PT2QYBkhLc36gF8cmyookxSJkFWfAGkxwE0dgQfGAOVrB4zNygJScxyYszsGM7eeRpbDhR7Na+DdjvVQo1xxn7FuNzez3gHXQ2wscOON9saeOEFibsU0AR6aatU8B9QMp06RgNWoYX3tpCQgPp6HrGxZ87EZGcC2bWQGFSrw31Kl9O+hqiQoubnccyEh5tfevp1MKDISCA8nUyxcmAQ2J8czrnRpEt/cXDKhIkX43DVrArfeSsKiMbq6dUnQFy0ikVEUMiKNeTZt6nse9u8HJk0CNm/mumhMuWbNwOc9cwb47DMyo86dgaeeApo105+L9HSgf3/O3bPP8mN0BnJzgUceIbEeOhR47DGu5anz2fhy5VFERiWiTLFCqOWshbVTaqFn18LYv5/P0rmz14XOHYUa+T5CTm/E4XM3I77xSJwu1BETJ5Ih3Xmn7323bQPuvpvv/NtvwNKlwKBBFCTatvUd278/12nRIuCWW8joX3iBAo33dZOSeL3XXgNeeYXfnT5NpjRmDNChg2fshAlAQgLw5JNcI4B0pWNH3u+RRzxj77+fTLJePc88qirw4IPA448Dzz3H77Ky+OxbtlDg8N6DdpnFFTcd/ZMfs3If1wXcbtZ2mnIPTU7jW4kcNy6gdDQpQwYsipJ6Hy+TWh9Fyn9+2SWHEmx2GArissLptO6RnZ7OAId162gSefZZmuV27PBkfA8f7pvx3a4dfQsNGtAUNGECI4YiImjWeOMNOmSPHuU9li2jKWjsWJrPWrRgdNTKlYGl7/PyGKDx2GMcN3y4sZkkNZX1pJo2ZfScWZJqQgJNni1a0FavBRXsi02TF6fvkPD+kXLLx8vl8dEHZOPeTOnVi743n2uqquTvj5TUT5uJDCkt6tTOkrhhpXTurMrLL/uGyqanc85CQz3JfTEx9GcMHuwbkKGFfA8f7vn72FjO89ixnjVMTmbb1EKFfPM/tDLi3n7WLVtYcPKJJ3znQS9k/6efRCpVCuzImZPD9fqxoECv283k3oiIwDXB9eizuG6ZhSNbZPcvZA5DSouMbSyyY5qIK9B4nOt0yYKdsfLoxM0S3j9S6g1cJh8t3KebMxHE1QE7DlENcXF03vftS8end8JqRgaDBEaPpsO6SRP2pa5blxFoqkq/0rJljGxq1oyO/fHjSYCmT/cQwvR0VkPo1InE8Lvv9H00bjfzBbp0oZ/i99+NI8wSE8momjcnQ9OI9rGkDHlv7l6pO2CphPePlF6Tt8iX8+Lljjtd8sYbfiVP8h2SsnyyuMY0INOYdIdsnDhPWjbLlYULfe83b54vEc/PJ1No1843Z2PmTDZG80ZeHpngE094fGhbtzIc2T/iMSeH495/n++enU1/apUqgWubnc3oM62dwOrVDCF/883A+crJ4bxOZuqJvPQSKb5/2L9dZnFdmqGuCYgAiXuB3TOB/fMBRwZwQwOg3XtAw0eA0LCLQx0uNzYcO4/IqASsPnQW2U43alcsgSdb3YhHW9RAhZI27HFBXHdISQHefpvmtUqVaNpo3dp3zIkT9K0sXw6sWgXccAN9RF27esYkJQFz5wLz5tFU0rs3zVzvvedr0jx6lCaY9euBp5+mOad8efpkvE1kZ88CX34J/PUXbfC9e9NPkZyRh/m74vDr9jOIS8tFqaJhqFesCo6srIrnH6yIt94I8fhfXE5g/zxg0zgg5TjUImWx6mwvLD/bBx9+2QjVq3OY0xnos9m+HXj1VfrZnn2W5rZ9+4BatQJNajNnAt9+y39vvZVm0SVL+LfeUFVgyBDOy6xZvOdzzwGDB9Mf5438fM5NlSr0RaxdS9PbmjWBa5iXRz9j9+7Aiy8CzzzD5/jkE8+YoM/iWoSqAgl7gMN/AIeXAKkngbCiQIPuQItngPA7LhqKE9Nzsf7oOaw7eg6bo88j0+FC2eKF0KVhFXRrVg2316kAxY6DIIggbOD0aeD770m0w8KARx/12Nu9cfw4MHkyHdiVKwMzZgCdOvmOycxkgMa0aUCLFsDJk8CUKfS9eCM5mddZuZJM7emnSYzr1BFsij6PP/YmYOWhJGTmuVAYYUBSJfS8oxLefrwSKpcp8GyrKhCzHtg9AzgSCbidOJFxCy5U7YrmvbsipFpTXedLVhYZVXo636d8eeO5iYoiU/n4Y86Lqhr7rWbMoK9owQI6yc+fJwP2h6oy6CUjg/ffsQNo00bfT5SXx/s+9BAZxrx59CtpCDKLawEiZAinNgIxG/jJPgeEhAG12wP1uwINe0AtUganUrKx63QadpxKxc5TaTh5PhsAULVMUdx1cyV0blQF7W6qiEKhFt7VIIK4zDhyBNi1i0whOxvo1QsXJXlviDDq7quvSIwXLGAknj/On+eY5cupxSxbRiYDUKveeOw8VhxMwroj53A+2wEAqFq8JOqWLo8e7cshIrwcapYvDiUnFTi4CO4Di4HTmxGquJFftAqUOu0RetNdUGq3A8qG+1DkRYvofP/6a0YxGeHCBaBvX2oJn3/uFbGlg40bqXn89BOju4wgwmvt3MmIKP/ILm84HIzI6tKF0ZfeCDKLqw3ufDKGc0eApANAwm4gfjeQm8r/L1kFqHMXsmu0x9Eyd+BoeiiOnc3EwYQMHErIQJbDBQAoU6wQbqtVDq1ql8ddN9+AmyuXDGoQQVy1yM5mhFpsLM1P3bvrhweL0IwzeTIl6cjIwCgnEcGhxAz8uvYcflmZCrV8GkKK8NyUKhqGRtXKoGG10qhXuSRuKe1E0ajNOL1qA1pV2oByhZJ5keIVgeoRQPUWQOWGQKX6SMirjedeCEXjxny+227TJ9yqCowaRfPZ7NmMbjQKS46OBp54gu/UrZv5HE2eDMyfT8blH97rDYeDEWUdO/qawf4VzEJRlC4AvgEQCuBHERnl9/9FAMwAEAEgBcATInKq4P8GAHgBgBvAWyLyp9X9/tXMIj8PyE4GMhKBzEQgIwG4cBpIOwWknYKknICi5gMARAlBZul6SCzRACcK34Idcit2ZlbEmbRcpOfmX7xk0UIhaFC1NBpV5yZvXrMcbqpUEiEhQeYQxPWL5GSG27ZqpW+Wyc0Ffv4Z2LRZsOdkJnq/eQG5RdNxICEDRxIz4HCpF8eWLlIIqbHFUCsnGS+3OIw2ZY+hatYhlMyIhgLSTgktApSvg+jU2li2pRYq3xKOXi9VBUpVA0pVAUreAIR5nC6rVlFjuvFGEvpq1fTfIy2N4a9dujAU2UxzmT8fGDsW+P13+neMwpEdDjKhe+6h6Q74FzALRVFCwZaqHQHEAdgB4EkROeQ15j8AmojIq4qi9ALwiIg8oShKAwC/AmgFoBrYfvVmEXGb3dOQWTAIABAVQMG/ouLgQRVVK7tQprQKUV1Q3W6Img9R3RB3PlRXPlSXE+LKR3ycA4VDHShb0gHV5YDk50J15kLycyHObMCZBTj4rzsrHUpeBoorGSjkSEMRZxoKu3MCHitXKYZ4pQrOqJUQrVbGEVd1HJMaiJbqyAM3V+GwENQoWww3li+OG8sVg2SVwD0tSuKWqiVRvWwxU8awYwfQuLG5eqohKoox/XbyPo4d4zg7+Rbx8dygdepYj01Pp+27cWPrnAi3m+93223WiWAAnZL+uQRG2LuXeQl28mWOHGGeRaVK1mPPnOE2DA+3HpuayqS4Bg2s5yI/nwmFLVta53AAzCNo3tw62Q4Adu9m/oBZsp+GQ4e4JypUsB4bE8NEO6tEVwA4d47O9ltusZ6LvDzmnLRoYT0XIsDWrbyu5nNwq4K4tBxEJ2chOjkLp1NzcPJsDqITc5GSlwtRyEiKIw83KfG4OSQO9UPjcVNoMmpIMqpKEooreQH3coaWgKNwOeQXKQdX4dI4lVQaUdFlUKJcSTRvVQKhxUuiZLniUAoVQ0jhYvw3rAhUpQgGDy2CPVFFMH5CYdxQtRBy8gqhVp1CUEJCoYQUQkhoKJSQMKxbH4LBn4bhhhtCsOi3EOTkhuDYcQXNmofQulAweU4nTX8NG/Lz5JNXnlncDuBTEelc8PsAABCRz73G/FkwZouiKGEAkgBUAvCR91jvcWb3jKgWJtteKgUFAgVAiPK/NbFlSVHkoCgypDgyUByZUhypKIVUKY0UKYVUKYtzakWcV29AinoDzmaWgzu3MDLOF0JIfmGULlIY1SsUQYWShVFELYoialEUkkJQoODoUUpMp09Tnb3xRto/9Wy9sbF09CUm0hFXowaJn17SW0oKD3lqKg9l1apA7do8QP5EOCeHtuasLCaNVapEwtewoT7h2biRG/PkSSaLaWP1CM+uXTQ5HDvGZLvwcKB+fX3H4eHDtFPHxPD3mjX5vP5ZswDn68wZMq3cXM7FTTcxcsV/Ls6dI/E/f57zUbUq5+zmmwMJT1YWCXRmJq9duTKfuUEDEkFvqCqT2xwOPnO5cp650Ess3LGDc33sGBlWzZq8rl6i4IEDlEBPnOB6aQl5eoz85Ek+a1wcn6VGDSZz1awZOBdJSXRGJyfT3l69OveFXqZ8RgajgdLTueeqVOH81q8faJvPzyeBzs3l2lSo4JkLPaFm61YygOPHaWKpWZNj9cwtUVF8huhorkHNmnwGPUYeHc1nPXOGiY01avDd9JJI4+M5d2fPCrLy81G1Th6q1M5DxRoOOEOccCpO5Ic44VLyket2onB+CiqEJaNKofOoWvgcKoako4KSgfJKBsohC6WUHJRGDsoo2SiOPJRQHIE3vYxwi0YhAYGCwsPSrjiz6Amgi4i8WPB7HwCtReQNrzEHCsbEFfx+AkBrAJ8C2CoivxR8PxXAchFZoHOflwG8XPBrIwAHLssLXXlUBHD+Sj/EZUTw/a5uBN/v6sUtImKpR5v45K8OiMgUAFMAQFGUnXY45NWIa/ndgOD7Xe0Ivt/VC0VRbDl6L2ccZTwAb6WuRsF3umMKzFBlQEe3nb8NIoggggjif4TLySx2AKinKEptRVEKA+gFYLHfmMUA+hb83BPAmoL088UAeimKUkRRlNoA6gHYfhmfNYgggggiCBNcNjOUiLgURXkDwJ9g6Ow0ETmoKMowsBbJYgBTAcxUFCUaQCrIUFAwbh6AQwBcAF63ioQqwJTL8S7/ElzL7wYE3+9qR/D9rl7YerdrKikviCCCCCKIy4Ng7YcggggiiCAsEWQWQQQRRBBBWOKaYhaKogxXFCVKUZS9iqKsVBTFIJH+6oSiKGMURTlS8I6/KYpS9ko/0z8JRVEeUxTloKIoqqIo10SYoqIoXRRFOaooSrSiKB9d6ef5p6EoyjRFUZILcqauKSiKcqOiKGsVRTlUsC/fvtLP9E9CUZSiiqJsVxRlX8H7DTUdfy35LBRFKS0iGQU/vwWggYi8eoUf6x+DoiidwIgxl6IoowFARPpf4cf6x6AoSn0AKoDJAD4QkX9poS97sFPy5mqHoijtAWQBmCEiOkXJr14oilIVQFUR2a0oSikAuwA8fK2sn8IKoyVEJEtRlEIANgF4W0S26o2/pjQLjVEUoASAa4cTAhCRlSLiKvh1K5h/cs1ARA6LyNEr/Rz/IFoBiBaRkyLiBDAHQPcr/Ez/KERkAxjJeM1BRBJFZHfBz5kADgPQKbBzdaKgUV5Wwa+FCj6GNPOaYhYAoCjKCEVRYgE8BWDwlX6ey4jnASy/0g8RhCmqA4j1+j0O1xCxuZ6gKEotAM0BbLvCj/KPQlGUUEVR9gJIBrBKRAzf76pjFoqirFYU5YDOpzsAiMjHInIjgFkA3jC/2r8PVu9XMOZjMP9k1pV70v8Odt4viCD+TVAUpSSAhQDe8bNeXPUQEbeINAOtFK0URTE0JV51taFEpIPNobMALAMw5DI+zj8Oq/dTFOVZAA8BuE+uQofTJazftYBg2ZqrHAW2/IUAZonIoiv9PJcLInJBUZS1ALrAoBjrVadZmEFRlHpev3YHcORKPcvlQEEzqX4AuolIYIOMIP5tsFPyJoh/KQocwFMBHBaRr6/08/zTUBSlkhZRqShKMTAQw5BmXmvRUAsB3AJG1JwG8KqIXDOSXEFZlCJgsUWAZdyvpWivRwB8B/Y0uQBgr9YP5WqFoigPABgHT8mbEVf2if5ZKIryK4C7wRLeZwEMEZGpV/Sh/iEoitIOwEYA+0GaAgADRWTZlXuqfw6KojQBMB3cmyEA5onIMMPx1xKzCCKIIIII4vLgmjJDBRFEEEEEcXkQZBZBBBFEEEFYIsgsgggiiCCCsESQWQQRRBBBBGGJILMIIoggggjCEkFmEUQQlxGKopRVFOU/V/o5ggji/4sgswgiiMuLsgCCzCKIqx5BZhFEEJcXowDULeixMuZKP0wQQfy3CCblBRHEZURBtdLIa63XQxDXH4KaRRBBBBFEEJYIMosggggiiCAsEWQWQQRxeZEJoNSVfogggvj/IsgsggjiMkJEUgBsLmjwFHRwB3HVIujgDiKIIIIIwhJBzSKIIIIIIghLBJlFEEEEEUQQlggyiyCCCCKIICwRZBZBBBFEEEFYIsgsgggiiCCCsESQWQQRRBBBBGGJILMIIoggggjCEv8Hy1zRl1hDEjIAAAAASUVORK5CYII=\n", "text/plain": ["
"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["plt.plot(tt,Y1,label='y(0)=1')\n", "plt.plot(tt,Y2,label='y(0)=2')\n", "t=np.linspace(-3,3,31)\n", "y=np.linspace(0,2.2,23)\n", "T,Y=np.meshgrid(t,y)\n", "U=np.ones(T.shape)/np.sqrt(1+f1(T,Y)**2)\n", "V=f1(T,Y)/np.sqrt(1+f1(T,Y)**2)\n", "plt.quiver(T,Y,U,V,angles='xy',scale=20,color='blue')\n", "plt.axis([-3,3,0.,2.2])\n", "plt.title('champ de vecteurs et solution')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q4)** Refaire le m\u00eame exercice pour l'\u00e9quation 3, en repr\u00e9sentant les solutions qui v\u00e9rifient $y(0)=1$ et $y(0)=-1$"]}, {"cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0.5, 1.0, 'champ de vecteurs et solution')"]}, "execution_count": 3, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["# Fonction f d\u00e9finissant l'EDO\n", "\n", "def f3(t,y):\n", " return t*y**2\n", "\n", "# Solution de l'EDO\n", "\n", "def y3(t,y0):\n", " return -1/(-1/y0+.5*t**2)\n", "\n", "plt.figure(1)\n", "tt=np.linspace(-2,2,100)\n", "Y1=y3(tt,1)\n", "plt.plot(tt,Y1,label='y(0)=1',color='r')\n", "plt.title('Solutions de y\\'=ty^2')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "\n", "t=np.linspace(-2,2,31)\n", "y=np.linspace(-10,10,23)\n", "T,Y=np.meshgrid(t,y)\n", "U=np.ones(T.shape)/np.sqrt(1+f3(T,Y)**2)\n", "V=f3(T,Y)/np.sqrt(1+f3(T,Y)**2)\n", "plt.quiver(T,Y,U,V,angles='xy',scale=20,color='blue')\n", "plt.axis([-2,2,-10,10])\n", "plt.title('champ de vecteurs et solution')\n", "\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["### Calcul d'une solution approch\u00e9e d'une EDO : votre premier sch\u00e9ma num\u00e9rique.\n", "\n", "On consid\u00e8re le probl\u00e8me de Cauchy pour l'\u00e9quation diff\u00e9rentielle $(E),$ \n", "\\begin{equation}\n", "(4)\\ \\ \\ \\ \\left\\{\\begin{aligned}\n", " y'(t) & = f(t,y(t)), \\\\\n", " y(t_0) & = y_0,\n", "\\end{aligned} \\right.\n", "\\end{equation}\n", "o\u00f9 l'instant initial $t_0\\in\\mathbb{R}$ et la valeur initiale $y_0\\in\\mathbb{R}$ sont donn\u00e9s. \n", "\n", "On suppose que ce probl\u00e8me a une unique solution $y:J\\longrightarrow\\mathbb{R}$ d\u00e9finie dans un intervalle $J\\subseteq\\mathbb{R}.$ On s'int\u00e9resse ici \u00e0 trouver num\u00e9riquement une solution approch\u00e9e de $y$, dans un intervalle de la forme $[t_0, t_f]\\subseteq J.$ \n", "\n", "Pour ce faire, on se donne $\\Delta t>0$ *petit* et on consid\u00e8re une subdivision uniforme de pas $\\Delta t$ de l'intervalle $[t_0, t_f].$ On peut le faire en se donnant $N\\in\\mathbb{N}$ *grand*, en posant $\\Delta t=\\frac{t_f-t_0}{N}$ et en consid\u00e9rant les $(N+1)$ points \n", "$$\n", "t_0,\\ t_1:=t_0+\\Delta t,\\ \\cdots,\\ t_N:=t_0+N\\Delta t=t_f. \n", "$$\n", "\n", "On cherche alors des valeurs $y^0,\\ y^1,\\cdots,\\ y^N$ qui approchent la solution exacte de (PC) respectivement aux points $t_0,\\ t_1,\\cdots,\\ t_N.$ On va d\u00e9finir ces valeurs par un *sch\u00e9ma num\u00e9rique*.\n", "\n", "On pose $y^0=y_0.$ Soit $n\\in\\{1,\\dots,N\\}.$ Une id\u00e9e pour calculer une valeur $y^n$ approchant $y(t_n)$ (la solution exacte \u00e0 l'instant $t_n$) est d'approcher la d\u00e9riv\u00e9e de $y$ par un taux d'accroissement au point $t_n$ et d'utiliser l'\u00e9quation $(E).$ La solution exacte de $(E)$ v\u00e9rifie\n", "$$\n", "y'(t)=f(t,y(t)),\n", "$$\n", "en chaque point $t$ et \n", "$$\n", "y'(t)\\approx \\frac{y(t+\\Delta t)-y(t)}{\\Delta t},\n", "$$\n", "on remplace alors l'\u00e9quation $y'(t)=f(t,y(t))$ par l'\u00e9quation\n", " $$\\frac{y(t+\\Delta t)-y(t)}{\\Delta t}=f(t,y(t)),$$\n", "en chaque point $t_n$ de la subdivision consid\u00e9r\u00e9e, puisque l'on a alors\n", " $$\n", "\\frac{y(t_{n+1})-y(t_n)}{\\Delta t}\\approx f(t_n,y(t_n)).\n", " $$\n", "\n", "\n", "On obtient ainsi tr\u00e8s simplement un premier sch\u00e9ma num\u00e9rique : le sch\u00e9ma d'Euler explicite, pour lequel $y^0,\\dots,y^N$ sont d\u00e9finis comme suit\n", "\n", "** Sch\u00e9ma d'Euler explicite** : \n", "$$\n", "\\begin{cases}\n", "y^0=y_0,\\\\\n", "y^{n+1}=y^{n}+\\Delta t f(t_n,y^{n}),\\ \\ \\ \\textrm{pour }\\ n\\in\\{0,\\dots,N-1\\}.\n", "\\end{cases}\n", "$$ \n", "\n", "\n", "**Q5)** \u00c9crire sur papier le sch\u00e9ma d'Euler associ\u00e9 \u00e0 l'\u00e9quation (1).\n", "\n", "> **R\u00e9ponse:** \n", "\n", "$y^{n+1}=y^{n}+\\Delta -2t_ny^{n}$"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q6)** \u00c9crire une fonction python de la forme\n", "\n", "`euler_exp(t0, tf, y0, deltaT)`\n", "\n", "prenant en argument les extr\u00e9mit\u00e9s **t0** et **tf** de l'intervalle de temps $[t_0,t_f],$ la donn\u00e9e initiale $y_0$, le pas de temps $\\Delta t$. Cette fonction `euler_exp` devra retourner deux vecteurs : \n", "\n", "- $[t_0,\\, t_1,\\, ...,\\, t_N],$ tableau `numpy` unidimensionnel de taille $(N+1)\\times 1,$ repr\u00e9sentant la subdivision de l'intervalle $[t_0,t_f]$ de pas $\\Delta t$ consid\u00e9r\u00e9e, \n", "\n", "- $[y_0,\\, y_1,\\, ...,\\, y_N],$ tableau `numpy` de taille $(N+1)\\times 1,$ repr\u00e9sentant la solution approch\u00e9e aux instants $t_n,\\ n=0,\\dots,N.$\n"]}, {"cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": ["def euler_exp(t0,tf,y0,dt):\n", " T=np.arange(t0,tf+dt,dt)\n", " N=T.size\n", " Y=np.zeros(N)\n", " Y[0]=y0\n", " for n in range(N-1):\n", " Y[n+1]=Y[n]-2*dt*T[n]*Y[n]\n", " return T,Y\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q7)** Tracer sur une m\u00eame fen\u00eatre graphique pour la donn\u00e9e initiale $y(0)=1$ :\n", "\n", "- La solution exacte sur l'intervalle $[0,1]$ discr\u00e9tis\u00e9 avec un pas de temps de $10^{-4}$ ;\n", "\n", "- Les 3 solutions approch\u00e9es sur le m\u00eame intervalle obtenues avec la m\u00e9thode d'Euler avec des pas de temps $\\Delta t$ \u00e9gaux \u00e0 $1/4,\\ 1/10,\\ 1/100.$\n", "Rajouter des l\u00e9gendes \u00e0 votre graphique."]}, {"cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0.5, 1.0, 'solution exacte et solutions approch\u00e9es pour diff\u00e9rents valeurs de $\\\\Delta t$')"]}, "execution_count": 5, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", "text/plain": ["
"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["# solution approch\u00e9e de l'edo1 obtenue par le sch\u00e9ma d'EE \n", "\n", "t0=0.\n", "tf=1.\n", "y0=1.\n", "\n", "# solution exacte\n", "tt=np.arange(0,1+0.0001,0.0001)\n", "yy=y1(tt,y0)\n", "\n", "\n", "dt1=1./4\n", "dt2=1./10\n", "dt3=1./100\n", "\n", "T1,Y1=euler_exp(t0,tf,y0,dt1)\n", "T2,Y2=euler_exp(t0,tf,y0,dt2)\n", "T3,Y3=euler_exp(t0,tf,y0,dt3)\n", "\n", "plt.figure(5)\n", "plt.plot(tt,yy,label='sol ex')\n", "plt.plot(T1,Y1,label='dt 1/4')\n", "plt.plot(T2,Y2,label='dt 1/10')\n", "plt.plot(T3,Y3,label='dt 1/100')\n", "plt.legend()\n", "plt.title('solution exacte et solutions approch\u00e9es pour diff\u00e9rents valeurs de $\\Delta t$')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q8)** Modifier la fonction `euler_exp` (ou d\u00e9finissez une nouvelle fonction) de fa\u00e7on \u00e0 ce qu'elle prenne la fonction $f$ d\u00e9finissant l'\u00e9quation diff\u00e9rentielle $y'=f(t,y)$ en argument. \n", "`euler\\_exp(t0, tf, y0, deltaT,f)`"]}, {"cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": ["def euler_exp(t0,tf,y0,dt,f):\n", " T=np.arange(t0,tf+dt,dt)\n", " N=T.size\n", " Y=np.zeros(N)\n", " Y[0]=y0\n", " for n in range(N-1):\n", " Y[n+1]=Y[n]+dt*f(T[n],Y[n])\n", " return T,Y\n", "\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q9)** Reprenez la question **Q7)** avec votre nouvelle fonction.\n", "\n", "**Remarque** Pour programmer le sch\u00e9ma d'Euler, on peut aussi construire une fonction python de la forme `euler_exp(t0, tf, y0, N,f)`, en donnant comme argument le nombre de points $N$ que l'on consid\u00e8re dans la subdivision de l'intervalle $[t_0,t_f].$ Dans ce cas, il faudra d\u00e9finir le pas $\\Delta t$ \u00e0 l'int\u00e9rieur de la fonction."]}, {"cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0.5, 1.0, 'solution exacte et solutions approch\u00e9es pour diff\u00e9rents valeurs de $\\\\Delta t$')"]}, "execution_count": 7, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["T1,Y1=euler_exp(t0,tf,y0,dt1,f1)\n", "T2,Y2=euler_exp(t0,tf,y0,dt2,f1)\n", "T3,Y3=euler_exp(t0,tf,y0,dt3,f1)\n", "\n", "plt.figure(5)\n", "plt.plot(tt,yy,label='sol ex')\n", "plt.plot(T1,Y1,label='dt 1/4')\n", "plt.plot(T2,Y2,label='dt 1/10')\n", "plt.plot(T3,Y3,label='dt 1/100')\n", "plt.legend()\n", "plt.title('solution exacte et solutions approch\u00e9es pour diff\u00e9rents valeurs de $\\Delta t$')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["## 2. Mod\u00e8les de croissance d'une population\n", "\n", "**Mod\u00e8le de Malthus** \n", "\n", "Consid\u00e9rons une population d'individus isol\u00e9e dont on note $P(t)$ sa taille \u00e0 l'instant $t.$ \n", "\n", "Le mod\u00e8le le plus simple pour d\u00e9crire l'\u00e9volution de cette population est donn\u00e9 par l'\u00e9quation diff\u00e9rentielle\n", "\\begin{equation}\n", "P'(t)=(n-d)P(t),\n", "\\tag{M}\n", "\\end{equation}\n", "o\u00f9 $n$ et $d$ sont des constantes positives qui repr\u00e9sentent respectivement les taux de naissances et de d\u00e9c\u00e8s de la population.\n", "\n", "**Q1)** Soit $P_0\\in\\mathbb{R}^+$ la population \u00e0 l'instant initial $t=0.$ Donner la solution $P(t)$ de $(M)$ qui v\u00e9rifie $P(0)=P_0.$ Comment \u00e9volue la population lorsque $n>d$ ? Et lorsque $d>n$ ? Interpr\u00e9ter. \n", "\n", "\n", "**Mod\u00e8le de Verhulst** Un deuxi\u00e8me mod\u00e8le suppose que la croissance de la population est inhib\u00e9e par la limitation des ressources et que la population ne d\u00e9passe pas une taille critique donn\u00e9e par une constante $K>0.$ Si on note $P_0\\ge0$ la population \u00e0 l'instant initiale, l'\u00e9volution de la population est mod\u00e9lis\u00e9e par les \u00e9quations \n", "\n", "\\begin{equation}\n", "\\begin{cases}\n", "P'(t)=(n-d)P(t)\\big(1-\\frac{P(t)}{K}\\big),\\\\\n", "P(0)=P_0.\n", "\\end{cases}\n", "\\tag{V}\n", "\\end{equation}\n", "\n", " **Q2)** Montrer que le probl\u00e8me de Cauchy $V$ admet une unique solution maximale d\u00e9finie dans un intervalle $J\\subseteq\\mathbb{R}$ tel que $0\\in J.$\n", "\n", "> **R\u00e9ponse:** \n", "\n", "La fonction $f(t,x)$ est $C^1$ donc loc. lip. On peut appliquer le thm de Cauchy-Lipschitz et on obtient qu'il existe une unique solution maximale $P:J\\to\\mathbb{R}$\n", "\n", "\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["\n", " **Q3)** Quelle est la solution de $V$ lorsque $P_0=0$ et lorsque $P_0=K$ ?\n", "\n", "> **R\u00e9ponse:** \n", "\n", "Si $P_0=0$, la solution de $V$ est la fonction $P(t)=0,\\ t\\in\\mathbb{R}.$\n", "Si $P_0=K$, la solution de $V$ est la fonction $P(t)=K,\\ t\\in\\mathbb{R}.$\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q4)** Soit $P_0\\in (0,K)$, montrer que la solution maximale est globale \u00e0 droite et calculer $\\lim_{t\\to\\infty}P(t)$\n", "\n", "> **R\u00e9ponse:** \n", "\n", "la solution est born\u00e9e par $0$ et $K$, on applique le thm d'explosion en temps finis et on obtien que la solution est globale \u00e0 droite. On verifie facilement que $\\lim_{t\\to\\infty}P(t)=K$.\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Q5)** On consid\u00e8re dans cette question $n=1,\\ d=0.75$ et $K=200.$ Utiliser le sch\u00e9ma d'Euler explicite pour obtenir une solution approch\u00e9e du probl\u00e8me $V$, de donn\u00e9e initiale $P_0=10,$ dans l'intervalle de temps $[0,50],$ avec un pas $\\Delta t=1.$ Repr\u00e9senter graphiquement la solution obtenue. \n", "\n", "Illustrer, dans un nouveau graphique, l'\u00e9volution de la population lorsque la donn\u00e9e initiale est telle que $P_0>K.$ Interpr\u00e9ter le r\u00e9sultat obtenu.\n"]}, {"cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [{"data": {"text/plain": ["Text(0.5, 1.0, 'solutions du mod\u00e8le de Verhulst')"]}, "execution_count": 8, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["# Mod\u00e8le de Verhulst\n", "\n", "n=1\n", "d=0.75\n", "K=200\n", "\n", "def fV(t,P):\n", " return (n-d)*P*(1-P/K)\n", "\n", "P0=10\n", "P0til=300\n", "t0=0\n", "tf=50\n", "dt=1\n", "\n", "T1,Y1=euler_exp(t0,tf,P0,dt,fV)\n", "T2,Y2=euler_exp(t0,tf,P0til,dt,fV)\n", "\n", "plt.figure(6)\n", "\n", "plt.plot(T1,Y1,label='P_0=10')\n", "plt.plot(T2,Y2,label='P_0=300')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('P')\n", "plt.title('solutions du mod\u00e8le de Verhulst')\n"]}, {"cell_type": "markdown", "metadata": {"deletable": false}, "source": ["**Un mod\u00e8le d'\u00e9volution d'une population de saumons**\n", "Le mod\u00e8le suivant d\u00e9crit l'\u00e9volution du nombre d'individus d'une population de saumons :\n", "\n", "\\begin{equation}\n", "\\begin{cases}\n", "P'(t)=(2-\\cos(t))P(t)-\\frac 12 P^2(t)-1,\\\\\n", "P(0)=P_0,\n", "\\end{cases}\n", "\\tag{S}\n", "\\end{equation}\n", "\n", "o\u00f9 $P_0$ est la population \u00e0 l'instant initial. Le terme positif p\u00e9riodique $2-\\cos(t)$ correspond \u00e0 un taux de naissances saisonnier. Le mod\u00e8le suppose que les d\u00e9c\u00e8s sont proportionnels au carr\u00e9 du nombre d'individus dans la population et le terme ind\u00e9pendante avec signe n\u00e9gatif $-1$ mod\u00e9lise une proportion d'individus p\u00e9ch\u00e9s.\n", "\n", "**Q6)** Utiliser le sch\u00e9ma d'Euler explicite pour obtenir une solution approch\u00e9e du probl\u00e8me $S$, de donn\u00e9e initiale $P_0=5,$ dans l'intervalle de temps $[0,10],$ avec un pas $\\Delta t=0.01.$ Repr\u00e9senter graphiquement la solution obtenue. \n"]}, {"cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [{"name": "stderr", "output_type": "stream", "text": ["No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n"]}, {"data": {"text/plain": ["Text(0.5, 1.0, 'solutions du mod\u00e8le Saumons avec P0=5')"]}, "execution_count": 9, "metadata": {}, "output_type": "execute_result"}, {"data": {"image/png": 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\n", 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"]}, "metadata": {"needs_background": "light"}, "output_type": "display_data"}], "source": ["\n", "# Mod\u00e8le d'\u00e9volution population de saumons\n", "\n", "def fS(t,P):\n", " return (2-np.cos(t))*P-(P**2)/2-1\n", "\n", "P0=5\n", "t0=0\n", "tf=10\n", "dt=0.1\n", "\n", "T,Y=euler_exp(t0,tf,P0,dt,fS)\n", "\n", "plt.figure(7)\n", "\n", "plt.plot(T,Y)\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('P')\n", "plt.title('solutions du mod\u00e8le Saumons avec P0=5')\n", "\n"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": []}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": []}], "metadata": {"kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.0"}, "celltoolbar": "None"}, "nbformat": 4, "nbformat_minor": 2}