12-linearModel.ipynb 203 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "# Le modèle linéaire gaussien 2"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Les moindres carrés\n",
    "\n",
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    "On dispose de données: des inputs `x[i]` et des outputs `y[i]`. On cherche à expliquer l'influence des premiers sur les seconds. \n",
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    "\n",
    "ex: \n",
    "* `x[i]` est la surface du `i`-ième appartement\n",
    "* `y[i]` est le prix du `i`-ième appartement\n",
    "\n",
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    "Dans ce cas, il est naturel de supposer qu'il y a une relation affine entre `x` et `y`: \n",
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    "\n",
    "\ty[i] = w[0] + w[1] x[i] + bruit[i]\n",
    "\n",
    "Dans le programme suivant, on crée des données artificielles qui suivent parfaitement ce modèle. On estime `w` par la formule des moindres carrés (cf. explication plus bas).  "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 10,
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   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "% matplotlib inline\n",
    "np.set_printoptions(precision=2,suppress=True)"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 11,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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yN8EfXuCni94lNyk95OeFSnwKdR76u94eejEwxlq714GaRBJOxR704K4tWL4lP7ietLWw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\nQmCC\n",
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      "text/plain": [
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       "<matplotlib.figure.Figure at 0x10b627630>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def createData_one_input(nbData: int, sigma=0.3):\n",
    "    x = np.random.random(nbData) * 2\n",
    "    w1 = 3\n",
    "    w0 = 5\n",
    "    y = w1 * x + w0 + np.random.normal(0, sigma, size=[nbData])\n",
    "    return x, y\n",
    "\n",
    "nbData=100\n",
    "x,y=createData_one_input(nbData)\n",
    "x_ext=np.zeros(shape=[nbData,2])\n",
    "x_ext[:,0]=np.ones(shape=nbData)\n",
    "x_ext[:,1]=x\n",
    "\n",
    "\"\"\" ( X^T X )^(-1) \"\"\"\n",
    "XTX_1 = np.linalg.inv(x_ext.T @ x_ext)\n",
    "hat_w = XTX_1 @ x_ext.T @ y\n",
    "\n",
    "plt.plot(x, y, '.')\n",
    "xx=np.linspace(0,2,10)\n",
    "plt.plot(xx, hat_w[0]+hat_w[1]*xx);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*** Question: *** Est-ce que cela marche aussi avec les données suivantes ? "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 6,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7SKVxMXGxRFTL9YsL13EbtWtyGsfngw//Qllx3pmn1/1gjY4M4e5rL8Fgfw45YDHzTvKu\ne1ZxLXdgdGQId11zUWKBytU7A1Zz/S6BzLgNKkwV8VD+yOIKkr6+5h/+epm3i5lOlkNT1zMsn7hY\nIqrl4vxDNQZugyYOzS6uIhEAN4+2Xi0SZt7PvfxLzM2XISIYWjqYQmujyTpwWhi++8S1ElEt1y8u\nLJUYE05I9vcFQ80lAznctHZlpJ8dHRnC+MY1yOUEZVVseWS/M2WBrIemFobvlK6kS0bdYMZtSO2E\n5K3rTp2QbKX47hzKqs5lllkPTbPIsFxetUBuY+A2pDorbTYh2UzWAbIRF4amaQ7fsy4NkW0M3IbE\nEXSrA+TQ0sHFkoQLQcP1umecWFOnbjBwG3Pj2pWQyv87PdHDn2PGlx1XRz7VWMpxFwO3EbVD6xsj\nTkg24lrG12tBwoXSUDMs5biNgduIuAOtSxmfa0EirYuIy6WhpC7svXaBTgoDtxFxB9ow4wsfupAl\nl7J/1y4iWUniws73Nj4M3AaEWcr4xjWxP9Fm1+Q05krB/bqzOpFcyv5duohkKYlSjsX31tURAgO3\n45LMUlw5kVyq97p0Ecla3KUca++tyyOEloFbRC4A8G0AZyO4J/82Vf1K0g2jQJLB1aUTyZV6r0sX\nEd9Ye29dSWzqiZJxlwD8hapOisgyAAUReVxVX0i4bYRkg6u1EyktSV9EXB1+p8GVC3QULiU2tVoG\nblV9DcBrla/fFpEXAZwPgIE7JXGs3W4kPJHCW5qmHUx6LYi5PPymk7mc2LRV4xaRVQAuB7A3icbQ\nyeJeux3130krmPRiEHN5+E2ncnWEEPnugCLyPgA7Adytqm/V+fvNIpIXkfzMzEycbexZad0xL6s7\n82V9R8BmknqogrW7EPLhEm6KlHGLyACCoH2vqu6q9xpV3QZgGwCMjY01fuQ4RZZWjS2rWp6rNcQk\nRwIuD79r9eKIyIooq0oEwDcAvKiqX06+SQQku3a7VlabcVwNYkmXM1wdftdiWcddUTLuKwB8CsDP\nROT5yvc+r6o/SK5ZvS2rTCeLzTguBjFXRwJp4/vgriirSp4GMt8V3VOyyHSYXZ3g6kggbXG/D722\ngihJ3DnpoCwynSz+TZdPZBdHAlmI631gvTxeDNyOSnLtdj1pZ5m9eiK7fLFKkvURnWvHjYHbMWmt\n3a4nzc04Vk7kOE/YXr1YAbbr5S4eNwZux2Qd0NL6kFo4keN+L7I+tlmyPG/g4nFj4HZM1gEtrQ+p\nhRPZ54dXtCuOkYfVeQMXjxsDt0PSXLvdSJofUtdP5KQeXuHyxaoeF0sFaXLxuDFwO8KVk8PFD2lW\nkngvXL9Y1eNiqSBtrh03Bm5HuHRyhP9ueO+QuNvh2gx9M66dsFlwsVTQ6xi4HeHSyZFk9u/KyIKi\n63bkYelCbQUDt0PSXrvdSJLZv0sji3Z0G3ysB69ORx68UCeDgdsBWa7drifJ7N+lkUVU3QafXg5e\nVi/UrmPgdoBrH+4kJygtTn52e3xcO75psnihbsaVkRMDtwNc/HAnuYvS2oRft8fHxeObFosX6kZc\nGjkxcGfMhbXbjSTxQXUlY2lHt8HHl+DV6bGzdqFuxKWREwN3hly6gtcT9wfV9f42023wsR68LB+7\nuLg0cvI+cIdZwtDSQex79U0IgDXnneFEduvSFbyeuD+orveXGuOxc2vk5HXgvm/vYYzv3oeFsqL2\nIZgCoC8nuPPKD2DZ6QPeby/vRPhBjeuRZq73t5VOSwUWy0O1Oj12PvS9misjJ1GN/7m+Y2Njms/n\nY/+9URWmitg5OY0HnjuChXLr/oVBfMsNl+L29cPJNxAnjwRcyP4biXuIbPVE7vR98KnE0O6x86nv\naRCRgqqORXmtdxl3syy7EQVQKiv++ns/w/5X30x8A4ylD3RcQ+Tqk/6uay5KoKXJ6vR98KnE0G62\n6VPfXeNN4G6WZfdXSiJvHS9BACxb0o/tT//PKcF9QYPAn/TDci19oOMob1i6UDXS6ftgvTzUDV/7\n7sKo0YvA3SjL7hPg1nXDdTPo69acg4lDs3j7vfmTgrgCOD4fPOk8qYMytHQQOREA6vwHunpCZmjp\nYEc3nrJ0oWqk04kplya04hI1cPnadxeSENOBu1WW3axmXT3su27NOdg5OY0H80dQWggC+IP5I4nc\nN6QwVcSWR/ZjoazoywnGN65x/gMdtq/TD6wvmVenm5JcmdCKQ7uBy6e+A+4kIWYDd/gBOj5fjpxl\nNxJ+uARB9q4ASguaSNkkPPAKQFVRfHcult+btG4/sK7cQKtb7QQuF4bUcXMlcGXFlSTEZOAuTBWx\ndc+BxQAYapVlt3Lj2pXYOTm9eDFQAHPzZWzdcwB3X3tJLLsGXzn2Hvr7clhYsJV9hh/YufkyRARD\nSwcj/ZxrN9DqVtTA5cqQOm5RA5ePFy3AnfKPucBdW8/OSRCwPzl2QdfZXPW65R2FaZRKZZQBPP3z\no3jmF7NdXRSqT+T+nLQ9Ksja6MgQxjeuwfjufSirYssj+7H6nGUt2+9bhhY1cPnW71CUwOXrRSvk\nQvnHTOCuV88WAFdctDyWbDgUHpSb1q7E1j0H8PTPjy4uFxzfvS9SsKpnV1Umv1BWnHfm6Zkf/HYV\n351DWTVyMLI8wmgk6qYkV4bUSQiPeaOJal8vWrWyHFWYCNwNV43kJNagXW10ZAh3X3sJnvnFLEqV\nC8VCWTsqmxSmingof2Sx7X19Nk/k6mDUlxO8euw9FKaKLbMuiyOMVnZNTmOuVG46B+JLXb9Wq4za\n54tWKOtRRS61f6lDhakixnfvQ6kmaIf17CTfrNGRIWy54VL05wTB4r2gbHLL15/BfXsPR/odYT2+\nVDVKuHnU5okcZpu3rBsGRHD/s4exafsEClPFU15bnXVZHWE0Ui+jrBae1N95Npjc9k2z/lff7fKe\n61d7VyYJtfoMJK1lxi0i3wSwEcAbqnpp8k0KhKWR/a+8edJSv05WjXTj9vXDWH3OslPKJlF2Wdar\nxw/253CT4Qm60ZEhTByaRWkh+NA2WvNuaa16u1qNPHwvFTTqP9D5klFrsh5VtLxXiYhcBeAdAN+O\nGri7uVdJGLDDNdWL7UD69xOpbdctX39mMXMO1VvJ0qgef+XF8dbjs1KYKuK2bc9grnJ8BvtzuP+P\nNiyucQ4nd8MTO6tjlqTqfpYWTgQqAIvfD+v6Pgawev2/6uIVePyF16EIEqx7rl9t8vYGUYXvQVgO\nA9BVzTvWe5Wo6lMisqrtVnSg2X1Gsg56Ydmktn1h9v3kS29gxbIlDbfTJ1mPT9voyBA+OXbBiTXv\npTK2fH8/zn7/aXjywAzmq5ZpWlqr3o56I49/fPRF/PjwMZRVvazrV6vt///Nl7HnxdfNz+O0K5zr\neOC5w1AIVDWV0YYzk5PVtexag/05J4JeWDapzaYXFHjshdcb/lwa9fi0hWve5+aDJZM/mX4TwJsn\nvUYA78ok1TZceBb6c4K5ym7b514+UesveVbXr6e6/wAQnrqW53HaUV0SC/oevAFzKZTHYpucFJHN\nIpIXkfzMzEzbPz9xaPaUWvb1Hzwbm9YPLw7DXTA6MoS//70P4W+rJi0b6RNg0/phPPDHH/GuVBBO\nVF5x8fJT3gMBMNgnuH39sJdlglA48qj3GciJeHvBCtXrvwBYMmB7HieqsM5de/zTOPaxZdyqug3A\nNiCocbf78xsuPAtLBoKdeTkDddHq7Nu1enxawiWTew/NLmZd/X2CW2LYDGVF7cij+tj3Uv/D+Yw4\nNsJZUW/DXi6lYx/pQQqVGvcjSU9OWt0mWz1J4cpj0dJUO0nTK/0OWXkoRlKsnrdxiuM9aGdyMsqq\nkvsBXA1gOYDXAXxBVb/R7GeyfgIOEZE1ca8qua37JhERUVyc3zlJREQnY+AmIjKGgZuIyBgGbiIi\nYxi4iYiMibSOu+1fKjIDYKrDH18O4GiMzcmSL33xpR8A++IiX/oBdNeXEVVdEeWFiQTubohIPupa\nRtf50hdf+gGwLy7ypR9Aen1hqYSIyBgGbiIiY1wM3NuybkCMfOmLL/0A2BcX+dIPIKW+OFfjJiKi\n5lzMuImIqInMAreIfExEXhKRgyLyuTp/v0REHqj8/d60Hp/Wrgj9uENEZkTk+cp/d2bRzlZE5Jsi\n8oaI7Gvw9yIi/1zp509FZG3abYwqQl+uFpE3q47JeNptjEpELhCRJ0TkBRHZLyKfrfMa549NxH6Y\nOC4icpqIPCsiP6n05W/qvCbZ+KWqqf8HoA/ALwBcCGAQwE8AfLDmNX8K4GuVr28F8EAWbY2hH3cA\n+Nes2xqhL1cBWAtgX4O//20AjyJ4VsAGAHuzbnMXfbkawf3lM29rhL6cC2Bt5etlAA7U+Yw5f2wi\n9sPEcam8z++rfD0AYC+ADTWvSTR+ZZVxrwNwUFUPqeocgO8AuKHmNTcA+Fbl6x0APioizZ4UloUo\n/TBBVZ8C8MsmL7kBwLc1MAHgTBE5N53WtSdCX8xQ1ddUdbLy9dsAXgRwfs3LnD82EfthQuV9fqfy\nx4HKf7WThYnGr6wC9/kAjlT9eRqnHsTF16hqCcGTaF17iF+UfgDATZUh7A4RuSCdpsUual+t+Ehl\nqPuoiKzJujFRVIbblyPI8KqZOjZN+gEYOS4i0icizwN4A8DjqtrwmCQRvzg5mbzvA1ilqr8B4HGc\nuApTdiYRbC++DMC/APhexu1pSUTeB2AngLtV9a2s29OpFv0wc1xUdUFVPwxgJYB1IhLpsY5xySpw\nvwKgOvNcWfle3deISD+AMwDMptK66Fr2Q1VnVfV45Y/bAYym1La4RTlmJqjqW+FQV1V/AGBARJZn\n3KyGRGQAQbC7V1V31XmJiWPTqh/WjgsAqOoxAE8A+FjNXyUav7IK3M8BuFhEPiAigwiK9w/XvOZh\nAH9Q+fpmAP+llUq/Q1r2o6bW+HEEtT2LHgbw6coKhg0A3lTV17JuVCdE5Jyw3igi6xCcB64lBQCC\nFSMAvgHgRVX9coOXOX9sovTDynERkRUicmbl69MBXAfgv2telmj8avnMySSoaklE/gzAfyJYmfFN\nVd0vIlsA5FX1YQQH+T9E5CCCiaZbs2hrMxH78eci8nEAJQT9uCOzBjchVQ+FFpFpAF9AMOkCVf0a\ngB8gWL1wEMC7AD6TTUtbi9CXmwH8iYiUALwH4FYHk4LQFQA+BeBnlZoqAHwewDBg6thE6YeV43Iu\ngG+JSB+Ci8uDqvpImvGLOyeJiIzh5CQRkTEM3ERExjBwExEZw8BNRGQMAzcRkTEM3ERExjBwExEZ\nw8BNRGTM/wMZ8SrIS+Mb2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
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       "<matplotlib.figure.Figure at 0x10a631f60>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_deterministic_input(nbData:int):\n",
    "    x=np.linspace(0,3,nbData)\n",
    "    y=x*np.sin(10*x)+x+1\n",
    "    return x,y\n",
    "x,y=create_deterministic_input(200)\n",
    "plt.plot(x,y,'.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*** Exo théorique: *** \n",
    "\n",
    "Notons $X$ la matrice à deux colonnes définie par: \n",
    "* la première colonne est constante: $X_{i,0}=1$\n",
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    "* la seconde colonne contient les input: $X_{i,1}=$ `x[i]`.\n",
    "Notons $Y$ la matrice colonne contenant les output $Y_i$= `y[i]`. \n",
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    "\n",
    "La technique des moindres carrés consiste à trouver \n",
    "$$\n",
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    "\\hat w =  \\mathrm{argmin}_w \\| Y  -  X w \\|^2 =   \\mathrm{argmin}_w ( Y  -  X w)^T (Y -  X w) \n",
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    "$$\n",
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    "le minimum étant cherché parmi tous les vecteurs colonne $w=(w_0,w_1)^T \\in \\mathbb{R}^2$. \n",
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    "\n",
    "* Calculez la différentelle de $w \\to  ( Y  -  X w)^T (Y -  X w) $ en développant le produit matriciel. \n",
    "* Cherchez l'endroit où cette différentielle s'annule.  \n",
    "* Justifiez que ce point est un minimum global (une simple remarque sur la forme de la fonction suffit).\n",
    "\n",
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    "Vous aurez alors démontré que:\n",
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    "$$\n",
    "\\hat w= (X^T X) ^{-1} X^T Y\n",
    "$$\n",
    "\n",
    "\n",
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    "***Aide:*** Pour calculer la différentielle $Df_w$ d'une fonction à plusieurs variables, on peut: ou bien calculer les dérivèes partielles et les recoller dans une matrice, ou bien simplement essayer de trouver une formule du type: \n",
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    "$$\n",
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    "   f(w+\\epsilon) = f(w) + Df_w(\\epsilon) + o (\\epsilon) \n",
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    "$$\n",
    "Ici la seconde technique marche très bien. \n",
    "\n",
    "\n",
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    "***Question:*** Qu'est-ce qu'on aurait trouvé si on avait oublié de rajouter une colonne de 1 dans la matrice $X$ ? Supprimer cette colonne de 1 dans les programmes précédents et observer la dégradation de l'ajustement. Cela vous permettra de ne plus jamais oublier cette colonne de 1. \n",
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    "\n",
    "\n",
    "\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Des inputs plus nombreux\n",
    "\n",
    "\n",
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    "Les moindres carrés se généralisent immédiatement avec $n$-input. Seule la représentation graphique est moins sympa. \n",
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    "\n",
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    "Observez le programme suivant. Essayer de vous représenter le plot obtenu en 3D. Eventuellement, tracez-le avec matplotlib en 3D en utilisant [scatter 3d](https://matplotlib.org/gallery/mplot3d/scatter3d.html) et [plot_surface](https://matplotlib.org/examples/mplot3d/surface3d_demo.html) "
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 16,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "hat_w: [ 4.31  1.97  3.85]\n"
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     ]
    },
    {
     "data": {
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      "image/png": 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W/ulsX3GQdf/5nIv/OYOwuO5/jXfUuEhNaj2nQKdTiI/X47I78Hm8aLvBigSBUFWVZf8+\nxJcv5uP1qCgKzLwmhbNuTDvta6Gqqvzjtu1EDUvl8j8PQavXUra1gtfvXEJ8hpmMXGvbhYhO0yWD\nTG1sDJsWl7H144OEJ1sp21iKechgLEOO/FrWRUSgS4jHdagcU7Yfi+0G8GRdDSj1mP+/RvwtNpAs\nQmoAjfV3QlEgwxACmaQUSCYh1eff6xrIZUpVA8nO5GemiROck6uiju13vo512ijifjkDT0UNxW98\nhqO4lrRrpgSlflNOKoP+dSv2jQdxu9wMuSMdndWE5xSn6AvgsxJIdiBfADcLvzN4BJDBJJD6dX7e\nxH1e/7/X/mZQaa4/gPPy+dfWY7PIJM3MZv0Lb1H2+WbiZjavEVnyyXochypJmjIVp8+/SUla5ZjX\nQKvjjL/OYveHuzn02Tp0Jh2jbx1On6mpuP1sq/cU79XSx9aTee1Eks8ZDEDqeUPZ84/lfPePbUy7\nZ+wpy/X3MxBIxp9AMt54/bheJYxO5JW3C5g940hAvm2nk/wCF5kJNtY9+BVzfjcEp6/5tuwLIODU\nBHDN9ve8fMe+/6eq/yTfgdVvFbDszTLOePpsIrMisefb+ebepdRUeFC0GnxelSFnxpE1MvKEQaf2\nBOdVtLOOqhI3s346rKVHPT43lrzLBrLkjTIuv//ky1Z1pQF2Ppn4EzqKTkvcfbfi2leA216Pwbce\nXUpqqw+hz+3GU1GJLur4MUJChFLZB2uwjB1M1EXNqewMyXEYM5Io+MVfSLpwNDpbcHplNHotkaOy\nAkrrJ3o+g9XA1Cdns/rRbzj44lLwqYRnRjLt/85Ga2zfJV9r1DHg4oEMuHhgyzYlgCD7ZNyNbiq2\nVTLwT4NabU+eO4SNd7zR7vK7giGX9OOd6/K56OZSrpgfxv58Nw//rZqwvvEsue5NBs9NJ2Nsz3oS\nsfzVg4y7a/LhDFIQnh5OdG4cqz88wMAFA9FoFf5z9w6GnhHD/N9k+1VmbbmLiFTrcevQhqeFU7S1\nIOjnINqnSwaZ0DzZx9i3OVOlNtxK+f/9G2N6Oqa+ffA1Oah6/0OM/TLQxUW1UZIQnathTwlhs6e1\n2qaNsGJIjafpYAW2vLQTH9iF+FweXDWNGKLC0Oi7x3qP4oio/jGc9c/5NJbWo2gUzHE/9p753zvX\nmRStBhTwOTxorEc+b95GF1pTl71NBcQUbmDBv6az8Z193PtyGXqrgf7nZWGJNpH121xi+/a8DpOa\noiais6Nb/m7Pt3Pwq4PMf2M+5ujmH9s5Fw3go8s/YOQ5iaTltf0apOXaKN9RTWNFE5bYIz/YD3x9\ngNwRPe817O66xbfX2DeN6KvmUf7a6+Dx4XM4MA8bQOxNF4e6aUIcxxAfgftQCQw9knbP53LjLqk8\n4ezcrkT1qeS/toLiD9aj6HTg9ZK2YBSpF4+S2erdkCWhe4xP0xm1pE9JY/8rK+h3yzQURcHn8XLg\nlRVkz8nstHaoqtqhn3OjTc+Ya3LgmpwOq6MrSRoYTuH3hWTOzASgYEUBaVPSWgJMAKPNSJ+zsti6\ntNyvINMaZWDa1Wl88tPPGX7DUCyxZvYs2kvNrgomPjC8zeO7AhXwds3FfYKuWwSZAJbReZhHDsJb\nWYtiMR012UceFbaHr8lJw4Y94FOxDOsrk6iCIGHuCHbd+yaGjCRMeX3xNTRR9Z9F2PLSMCZ07TR3\nhW//QMXKg6Q98hP08VG4iiooevINtBYjyecOCXXzRA824ZejWHz7En64/hVs/ROo2VhA7IBIhl89\nqO2D20FVVTa/uYd1/9lJXVE9MdnRjLt5EDnTkzq03t5g1q19Wfib7/E4PCSOSKRqTxUuu+u4/TyN\nbvRR/j8xOeunmST1C2PFOztorPUwaEIE1/xmGJbwbhPS9Brd6h1RNBp5PB5E9Wt2UvrMexj6pKNo\nNJQ9/xFxN5xL5FTJm94eln6J9LljDode+BBPXROqx0vkhBwyfz4n1E07JVVVKXp3LUn3XI0+vvl7\nZkiOJe66cyl44X0JMkWHMkeZmP/ybErWl1GxswptYwRFq4p5eebbZJ2RwfjbhmOObl/GN5/Xx+7P\n89n9VSEoCjmzUqkvaWTTh/nk3juH8P7xVK7J56uHv8RoHEnmhNNb7kk06z8+hiv+PISvX9jJpufW\nEpVipmSnncqdlcTkNK+FXXuwlgNf7Of8N0f7Xa6iKAydFc/QWfEA6BVPh7S/48gSRqKH89obKH36\nPeJ+fj3GPs3LmrgKSyh7/FnCBqaij5fcv+0RMaYf4aP74qluQGM2oDUbUOjiCwb7VNw1DRhSW08+\nMGQk4Cqzh6hRojdRFIW43FiWP7SSqIk5jPvlvOYhHK+v4qNbvuKi/5x92ukrVVXli9+vpvxAIynz\nh6P6VL57YS2OkjrGPH0xtj7NQU/cuEwG/GwqK19aK0FmEGSNjiZr9JFxmdu/LOaNWxeTMCwBjVah\naE0J59/dn5hUeYrWE0mQ2UvVr9qGKS+nJcAEMKQkYhk9FPuKLcTMnxTC1vUMiqKgj7bSuLeUQy8t\npX7jfrQWE7FnDSH1qsloDO3/+qmqSvlXWyn9Yis+h5uoMX1Imj8SXZgx8PZqNZgz4mjcuJew4UfG\nkzau301YttxsRec4sCQfQ3wEWTccWeS+70+nsfHnC8n/rpDMqac3ca54QwVFm6sZ888r0R7+7kWP\nSGPFVa+0BJg/isxLYudTdad/EuKkhpwZT/9x0WxfXoHqVRnwUB/CIoOwQrvokiTI7KV8Tjca8/GP\nnjRmMz6H+6TH2b/bgv3dpTTkV2JJiSRi/hQipg/ryKZ2a87SWnb97g0iL5xJzG1X4a2po/r1Rez7\n8yf0u/u8dpd/8Lmvqd1YSOT509CEman5+geqfvUGeU9ehtYYeKaUzGsnsfvJ94i5fBam7DSatu6n\n6r9fMujec9vdViH8UXOgFuug1qk5FUXBlptCzX47TD29cg+tKiFuanZLgAlgjAlDY9BSt7cCW9/Y\nlu3Vm4uIzurak/S6M7NNx4hzeu8PVxXw9ZKJP73jLMVxwoZn07huM966hpZtviYHDavXYx114vXK\n6r7fSt3rn7Lg3j48uG4Wlz+UTeN7X1G7ZIPf9ao+ldplmyl5bCHFf3qdmiWbUL1d/DFyO5R/so6w\nicMInzkWjUGPPj6a2FsWYN9wEEdRdbvKdpbUUvnVVpLuvZ6wMbmYc7OI+9klYLVSsWT7aZUZPa4v\nOXefg3P1BkoeeQXPpm3kPXgekcO6/rJLomeI6hNB3dbCVttUVaVuSwGRWac/cc4UYcBV0bp3UtFq\nsCSFs+G+RVRvKcbr9FD23T52PrOccdf1jhngQnSkLtuTqZ4kg4SqqrgPFuJraMKQlYbG4udjwUCW\npQggM01HZBLqiCxC0DqTkC4pjvAzRlHy0F+xThmHotVQ/80qwkbnYOiThvcEy+nZ31vGxQ8MpN+4\n5l/8fUZGc+kjebx61zKsU0a0Wb+qqpQ98w7GkkPMuioVjUZhyavLKFm/i7jbLm61dIi/GXc6IosQ\n+P+6tpVFqDG/CvOEUa22aQx6jH2SacivRpsQc8LjTpRJ6Fj2bUWYcrPQWI70SCuKgmVMLjWb9xEz\nq3UPs7+vadiQTAYObZ1Fy32K5RUDyaLibyahjsgiBP5nPQqkTH+zCEHHZBLqiCxCADo/6z9VFp9j\nHZdF6ASSp2ax5oUt7H1uGWmXjEb1+chfuBrF7SZpXBruE3yP/WlDxplZrH7hI6o2HCL68I+mytUH\ncJTaGX1jHpsf+4z6wnqic6KZ8bsxJI5JwunnS+vv5yXYWYROp1x/M810RBYhCE4moWN5/TynrpRl\nxxtIasFurMsGmSfiKauk/OnXUB0utOHhuIuKibjoTGwzx4e6ad1SzIKZWIb2o/77Lag+lbib5mLO\n7XPS/RsPVZIxfGirbenDI2kqqkH1+poXVD6Fpt0FeLbv41efjENval6uIu/MeP40dxVNO/KxDPQj\nPaifVK8PX6MTjcXYZrs6kik9FsfOA4SNzm3Z5nO5ce4rwpg2q11l66OteIorjlvbz11SiTm6e6yP\nKMSxtAYtZ/39LNY9s4bVV/4TNAqZMzKY+syZpz3pB8Acbeashyfy5X2LMMZaUb0q7tpGzn58Mskj\nEhhy6YBjjui5T1iE6CzdJshUVZXyp1/DOmIkEVOnoigK7ooKiv/+LPrUREw5Jw+OxMmZB2RgHuBf\ncGdJi+HAumqyJx2ZfZy/vgZLcqRfgVzj5v0MnRXXEmAC6I1ahs+OY/Pm/UEJMlVVpfKDlVS+9z2q\n24PGZCD24klEnz2q7YM7QOyckey64yV0cVHYJo/AU1NH9cJPsY3IwpjYvhn81rx0UH3UfvQNEedM\nRNFqadq6j/pl60h/8sognUHPpHp9HPpoM0WLd+BpchE7JoOs/xmFIcoS6qYJwBJrYdofJsEfgltu\n6tgkrvx4PqWbylE0Cgl5se0KXIUQp9Ztgkz3wUJUh6slwATQx8YSMXUqDcvXSpDZCaznTeft33/E\nxX/Mpc+oaPI3VvPm77Zhm3+GX8drbRaq9h2/EG9VsQttUnBu7lUfr6ZmyRbif30jhpQEXAeLqHhu\nIYpBT/QZnb/OoyEunL4P/Q/FLy8lf+FitGFmos8cQuL/tH/2vqJR6H//Rex//CPyF32HxmQEn5es\nX56DKVnWkz2Vbf+3lJq91cRedibacAs1X65j9W1vM+4fC05rZr7oPrQ6DckjEkLdDNGLqSiS8aer\n8TU0oQ0PPy7lly4igqYDu0LUqt7FOi4XVJU3H/6axoNrMKdGYTv/TMKn+De73DZhEHsWfsGO5eUM\nmNLcG7prRSU7vqkk7a+5bRzdNlVVqXx/JXG3XYUhpfkmYshIJvqq86l87f2gBZkN2/Kp/eBbnAUV\nmFJjiDp/EmGDTj4xxpwRT9Z9l/g9JjIQxoRIBv35CpwlNXgdbsxpMSEdHtAdNBbVUrZ8D33/cTsa\nc/PSKYk3zqHw8TcpXLydjAtltQQhhAiGbhNkGrLScBcV466oQB/bPPFEVVXq1q3FNKRfiFvXe1jH\n52EdfyQjUCCBkzbMTMIvL+O1e98iLGIfiqJQX+0h4c4F6MLD2t84n4qnyo4+PbnVZkNGCu6y9s3k\n/lH9hn2U/t/bXPSLdPqO6M/edbW8/egbJN15IbZhoetNb++j996kblcZlkHpLQHmj8JGZlO7fWeI\nWiWEED1PtwkyNWYTERfOovjvzxIxdSq6iAjq1q3FW1dL2JTQjLcLBp/LjbemDm2EFY2x5y9IaxmU\nQfozd+DYUwSqSnT/FHyNTkqe+5i6ldtRAOv4QcT/z3S0tsAyQChaDYbUWBzb9mDOPbKYuGPrboyZ\nwVmTrXrhl1z1QF+Gn9n8Qycxy4LZpuPN577GNuz6oNQhOpYx3orzUPlxE6ac+aXY4mXClOhcjjoX\n3/xtCzs/O4TP4yNrSjJTbx9MRFLPyYBTU9xEfaWT+L42zJbeMau6LT5JK9n12GaOR5+WSMPyNTQd\n2IVpcD/Cpo7qlsGZqqrUfrgc+6JvUQwGVIcT25ljibxoJkoAS6J0R4pWizmn+fGy6vVy6A//Rp+Z\nQeJvfwaA/dOl5P/h32Q+dkPAj37jLptGyQtvEfU/czH2y8C5cx/VCz8m5fb2L3wOYN9VxuCp/Vtt\nGzw9hhfu3BGU8rsKt72Jwv+upGrVPjRGHfEzBpE4fwQanbbtg7u4iIGJGGwGyv/9JbELpqEYdNSv\n2YV9yUYGPrsg1M3rdqp2VbL/va04S+uwDUig34W5mGM6LkDyeXy4G9wYbIZuf61UVZV3//c7dKnx\njH/pcrQGHfnvbeS/1y/j2rfPwGDpVrfo4zTVunnrnk0c2lhNWEIYDSX1nHFLPyZcHryVRETX1u0+\nwabsPpiyj3os2QHj3DpD3VeraVyxhaQ7b0MfF4unuobyV/5DrfEbos6fEurmdZr6NbtAZyDq8vkt\nvUpRV5xP2aPPUL92F7Yxxy4rcmoREwaiMWipePdbqv/zAcb0OFLunI91aBYBLWp6EuZ4K0W7G0jP\ntbVsK9rZgLkH9YB5HW62/vK/6PtlEHvrAnwOJ2XvLqF+dynZd3f/zD+KojD8oXPZ+sTX7LnuCRSD\nDkOEmaFczNuVAAAgAElEQVT3z8GSfPqLffdGhd/ls+GRJVx3g4mcuTq++mofX1y/i+nPzSMsIbjf\nCZ/Xx6YX17PznZ34PD7MkQYG3zSSvrP7BrWezlSwtpxGu5fxv5rZcv3rd+046veWs/3TfIZemBXi\nFrbPO/duQo2J5pz3zkFr1FFXUMuyOz4mJs1MzpT4UDcvZFSQiT+iY9Ut/p6YSxegj2t+7KqLiiRm\nwUWUPvMckfMnHzfBqady5pdhzM46ZiF2BWNOX5wHywIOMgFso7KxnSRrUXtFnDOOl+9dzS1/yyE2\n1URFQROv3LePqHPHdkh9oVC1dBua6Ehibziv5X0x/iqVgtv/QsP+csL6xLVRQtdnjA5jxMNzcdsd\neB1ujHHWkH/nfB4vzspGDJFmtMauf2lWfSpb/vYdf33KxvhJzTPyp59hIuLROr57ZT0jfz25jRIC\ns/H5dSjb9vLpJxGkpmlZt9bNT25ZhcFmJGNSctsFdEGV++xEDk4+7rMXMTiFin2lIWpVcNSVOziw\nropz3j+n5fNsS41g4HWjWfHGtl4dZPYmXf9K1kN5qmoxJLVeRkOfEI/XXg9eH/SAx5L+MCRF07Bp\n43HbXfsPYZ0zPAQtOrXouWOpdDh58MJV6I0a3E4fMfPGEjN3TKibFjT1O0swD8tpdePTGPSY87Jo\n2F3SI4LMH+nDTejDTW3veIyK1Qc59Mk2XHYH8aNSyDx/MHrr6S99tO+dTex6dS1oNKguDxnzcsm9\ncVSXXimgsbwBb6OLcRNtrbafd76JD24oCmpdHqeXne/s5PPPo0hJab42jhxl4L57Lfz55U3dNsiM\nzgyn5s3Nx40Prt1SRNrk7j2Zr6HKhTnajO6YH0zWlHAOVR6/lJ3ombpmkKkCXr9zMPpXZCDX6kCe\nqp6i90P1ePFUVKOxWtBaLa3SVRr6pNK4ZTvW0UfSMTZt24EhLQkUHaq/WboCOC9/0yqebqrKNus/\nQRoty6hcKhYupeaDzwmf1TxMwP7ZMrw1NVhGDcTXRpvVAFKfBTIT/uTpKhWiL55G5HmT8NTUo48K\nQ2PQ4VVp83OjDaD+jjgvf1JVAujjIqg/1LoXRVVVXPml6GYPxHPMexLI69oRaR39TVUJ/qerPFX9\nB99Yy6EPNhFz4WRsUTZKl22k8Nb3GPPURW2usXmicos+38Hed7aR+eBVmNLjcFfYKfjLeygvryPn\nurZ7yDsiVSWAr63xjmYTToePhnoVq+3IvqXFXgwRRly+428v/qaqhNapIhtrnOgNtASYP8rL02Mv\nrD9hXSfiC6D+QF4rvZ/7Hvv5ix+RhMm8lW1/+Zp+14xDY9SR/+5G6naX0veh4Tj9Pq/gp2Ftb6pK\nW2YEzloHNXsriex7JH1uwdd7SR8RjcOnD1ob/E1VeaJ7UCioKJJWUrRP/bfrqHnrMxStDm9jI5Zh\nA4i+7rzmBbOByItmUv7X1/E5mjD164vzQD41H39K9I3nh7jlnUvR60i57xrKX15M4Z0PAmAZmUPq\nH65Go++6H0+NQYchPrJD1r4MtdhZQyi99Z+YBvUhbFweqsdLzQfLUPBhG9pzBuyrXh/l3+6h4vv9\naAxaEs8YQOSQ1FMe4653cOC1VfT5y0/RxzWP37SO7E/h429S8MlWMi8ZccrjT+TA2xtJvPEsTOnN\nPcT62HBSbpvH3l++SP+rRgclI42zupGa7WWYYkxE5sQFZWiA3mokeUIaD/+xgj88aMVgUKis8PKn\nPzWRfF5we/ZNUSZURcv27W4GDjwSnHzzjYuo/tFBraszKRqFuU9N5bu/buCbK17B5/aRMSWVC56f\ngSGs7SCsK9MZtMy4bSBLf7mIAVePxJYWQeGyfZR8e4BzXmt/MgrRPXTdu3g35ti+l5q3Pyf+xusw\npqXia3JQ+c57VL74HnE/uxQAU04f4n9xFfaPl2Nf/i36xBhi//dSTAP6EIwJKt2Jp7oOXVwE4WeM\nImzMQMyDMtH2jtECXZI+2kr2Hy7iwNOfU/mvj1C9Pqy5qeQ8eHG3n837I9WnsvWPi2goqiN85ki8\nDhdbH/mMlHPzyLz85L2HdTtKMWUmtASYP7JNyqNq+drTCjIdpXZMGa3Hp+kTIvG5vHgdbjTteAyv\nqio7X1rN/nc2Y8lJxlVcjTHcwNiHz8Ic1/6JOXm/mMbaBz5n8thy0rL07N3hJOv8XDLPyWl32UfT\n6DQMvHY4N960jgfvD2PgQB1Lljh57IlGJv15alDr6mymcAMz7x3DjN+NBjjqB0D3vw8MvyCDqFQL\nP7yxj5LPnaSPiGLu65OwxgY+RKWn8XXhiT+KorwEnAuUqaqad9T2/wVuBbzAJ6qq/rqtsnpMkOmp\nqsH+0RIc2/egsZixThlN2JTRKJrOfyPrvvieyNmzMKY194pozCZiLr6Agvv+2LwmZmTzGCZj3zTi\nfn55p7evK6l8awn2r9ZhnTQGRauh7O/vYx03iPirZ4W6ab2adUAyuU9djbu6AY1eiy7ANUu7uqof\n9lN/qJa0R25q6TEPnzyEA7c/TeKsQVhOslqAPtKMu9yO6lNbBdzushoMkaf3GoUPSKBuzR6iZx0Z\ng9y4NR9jTBi6sPYtz1a8bC8FS/aT/Y9b0EeGofpUSv+7nLV/XMKkv85tV9nQ3Js55vFzqTtUS1NZ\nA1l9ozFGdkwA0e+CQehsJn73+EbqSmqJHRjDxCemEjMojp4QkIV64llHyRwTR+aYI+O4NT3gveoF\nXgaeBl79cYOiKNOB84Chqqo6FUXxa+ZWjwgyvfZ6Sh9+FuvwkSRefR0eu53qxYtwl1YQteCcTm+P\np9qOPqH1pB6N0Yg2IhxvbX1LkNnbuYoqqF28muT7foE2vPmmbp02nuIHniR8ch6mrO45mL+nUBQF\nQ3TPWZrpaJWrDmCbMrTVkAxdlI2w4f2oXnsQy9knTnNq7RuHIdJE5TvLiblgMopWgzO/jOqPvmfY\nA3NOqy39rh7D2rs/QnV7sA7LomlPESUvf0nezya2O/A4+MkO4i6dgj6yOaOWolFIuGQS269ZS2Ox\nHUtSeLvK/5EtLQJbWscv/5R5ZhaZZ3bvZX2E6OpUVV2uKErmMZt/Cjyqqqrz8D5l/pTVI4LM+qUr\nseQMIGZOc0BpSEzEmJrKoUceJnz2FLQRnRvUGfum0bh5C6aszJZt7vIKvHV16JJiO7UtXVnjul1Y\nRg5uCTABtGEWwsYMo37NLgkyRYfRWgw47I3HbffaG9FZTt57qCgKQ+4/ly0PLmLvZ2vRRYXhLq8l\n++ZJRA5KOq22RA5KZNSf5rH3tbXkf7QSS3I4Q+6aSeLYtNMq72jueldLgNlyDjotOpsJd4PM8BXd\nU3VhI5/+ZSe7lpag1WsYOieZ2XdkYw7vHuNYVRW8oc34E6soypqj/v68qqrPt3FMNjBZUZSHAAfw\nS1VVf2iroh4RZDr3FRAxclyrbVqLBUNqCq5DxZg7OcgMP3syJff/HbQawoYOwVNeQfUnnxIxfwYa\nQ/f4EnQGxaBDdTiP2+5zOtEYpLdXdJzEMwey/o63CJ82DGNq86O8+nW7cR4sIXrsqZ9+mOJtjHpq\nAQ35VXjqHET0j233upYRAxIY8eCxPaH+z24+mfjRqVR+tRHrkMyWbQ07C/E1ubBlRrW7fCE6m6Pe\nzYvXrCLzvIGc98sz8Do8bHlxDS/fso6f/HtMjx12EGQVqqoGmo9bB0QD44DRwJuKomSpbSyF0iOC\nTF1sFM7iYsLyBrdsU71e3GVl6GI7/0Kqi4kk8d6fUvvJMipe/y/aSCtRl52NZfSgTm9LVxY2ZhCV\nC7/CdagIQ1pzr6W7uIzGHzYSd8nNQanD2+igYc0ufE431uF9j5uwIXqnsIwY+t48mT2/fQFz/xR8\nDhfushoGPzAPrVGPP2P8wtKbZzVrA1jqprNlXTyEolvf5+AjbxE+YRCu4ioqP/6BoXdO6vAUoTW7\nKtj9zjbqi+uJGRRL/4vysMXJhA/RPhs/KiRyUDyDrjk8yc5mZNRdU/js8rc4sLaaPqO6w2oDygmX\nferiCoB3DweVqxVF8QGxQPmpDuoRQaZ1+jjKHnseU2oa5gEDUB0OKhd9jD4tCX1iaBaO1sVFEXPN\n/GO2yoDno+kircTdPI/SP/+jOeuPRsGxYy+x185BH9/+HwcNG/dS9Je3MfbLRGM2Uf7vL4m+YCKx\n508MQutFd5d0Vi5xE/tRs/EQGoOOyGFpaPQ9a1kDg83E5GcvIH/RdipXbcIUY2bik+cQ0a9jh+0U\nf5fPqoeWE3/+GKJGxVO9Zg9fXv8+s547h7AkeUohTl/ZgQZiBie22qYoCrGDEyjbV99Ngsxu6X1g\nOrBEUZRswABUtHVQjwgyDSkJxNy4gMqFH+L970JUrwfzkIHE3nxpqJsm2mAbl4tlcBaN63eDTyXh\n1rlobRbaG5D7HC6KnnyH2FuvxtS/Ode9p8ZO6cNPE5aXibl/ShBaL7o7ndVI7MR+oW5Gh9KHGeh7\n8VD6Xjw0oAXGT5fqU1n31+/p8+vzCB+WCUDE6L4UWkxsfnkj4+6WNRLF6YvvY2XT9yVw6VFPLn0q\nFZtLib8g8DTE4niKoiwEptE8drMAuA94CXhJUZQtgAu4uq1H5dBDgkwAc142pj/egbemDo3JgMbc\nvR/LqL7mm0EolmDqbNowM7ZJQ4JaZsOGPRjSU1oCTABdZDjWKWOwf7O5U4JM1evr0mkBhTiZhiI7\nnpoGIvpFozMFNo7cUdmIu9593ML90dMGceCht4LZTHGY6lMp2lSJo8ZF0pBoLNHd+/53KkPPTWb5\nS9+y9aV19L8oF4/DzdYX12KL1JI5snuMM1YJ+cSfU1JV9bKT/NMVgZbVNYPM00wrqaCgCz885u7Y\nbFQBpYr0f9dgp6t0l5RTs3ARTZt3oei0WMYOJeqyOWjDTrwGX2DpB/3csQNSVUJg6SpV1b8el5MN\n8vY6fSgnmGSl6PX4Gn1BS1d5oow/tcs2UfHWN7iLK9HFRRJz/kQiZ41A1fr/CgSSScjfdJUdlYLT\n33SVAKrfKTADSH/o9f8Rt78p9ToiVSUEllaxI1Jw6tpYTN9Z08T6Bz7HvrcSfWw4rpIaBlw/hj4X\nDD7pMcf2jvqMJnwuD94GJzrrkWDHVW5HH27C5fPv/dL4mSoQ/H9dvQG8V9oA6vc3XWVHpKq0F9Tx\n1S+/xqK4SUnR8cXvHQy7ciDDrz/xe+bv56UjUlVC+9NVKmE6rnppIl8+uY0P5m1Aq9eQNyeFM54e\ni1PVn/I+2w3HQXZ7XTPIDAHV7cbncKGxWvwPxoLM19BE2aMvEj5tCvFXXIXqclG9aDHlf3mFhN/d\nLLPmAmAZ2o/yFz/GXVqBPqF5/JnP6aLhux+Iv252h9Vb++1Wyl9fSswNl2Dsn4lrfwGV/3wTgJiz\nA88GI0RnWv/AF2hSkxlwzxUoOi3Ooip2//41rOmRxI3yb0klfZiBxImZFLz4Fem3noVGr8Nd00DR\nK0vJuWRgB59B76KqKkt/u4yfXaHjlhsiUBSF0jIvZ56/i6icGDInnXwZOGedi4byJmxJYejN3SsU\niEyxcNETRyZHd8cF3r1dOONPMHWvT1YH8Dld1Lz5CQ2rNoACusgIIi85G/OQzh/bUf/tOkx9+xI5\nfVrzBoOBmIsvpPDRJ3DuPHA45aTwh9ZmIebKsyh99O+ETRiJxmykYeV6LIPSsQzt2yF1qqpK5VvL\nib7qfEzZze+VMSuNmOsvoeK51yXIFF1aY5Ed+54Kcn57OcrhmefG5GhiL57E/g+2+R1kAgz9xWTW\n/vFrNl/9DKaUKJoOVtCnA9JN9nZVe2vx1Dbx0+uP5KNPiNfyq5+F8ezHu08YZHrdPlY9uZbtnxwg\nJlZHdZWXYVcOYNi1udKRIYKu1weZVa++i+Lwkf6bu9BYrTTt2knZSwuJv/0aDJmpndoWT0kFxszW\n45gURcGYkY67pEKCzABFzByJeUA6dd9uwudsIPEn52LOzeyQC2nj9nxKnv0YV3EVxr7prf7N0CcV\nT3kNqsfbcvMWoqtx1TShj7EdN8PekBBBw/KmgMrShxkY98hsGorsNJXWEZ4VgyHChNKFl3vqjtwN\nbqKitGiOGQYRG6PB0+A+4TFrnt2ItbiYLSsSiInWcvCQh4uu2c32aDOD5nfMD3DRe/WO/tqT8NTY\ncWzeSdwlC9DabCiKgiVnAJHTZ1D35YpOb48+NR7Hnr2ttqk+H459+zCkJpzkKHEqhpQ4YhbMJO6q\n2Vjy+nRIgOmprqfgT28Sft5sDOnJOHbub/Xvzt0H0SdGS4ApujRb3xhc5bU4DjWvSqKqKpWL1nLo\nzx9g31HKdz//gMpNRQGVGZYcTuzwFAwRXWsiiqqqVO2spGRNEe7GEwdj3UHsgGgKCj1s2XYke5Oq\nqrzyhoP4scdPbvR5fGx9by/PPB5BTHTz9SgjTccT94ez480dndbu3k5FwaeG7k9n6tU9md6qGnQx\n0WiMxlbbjckpNGzf3OntCZswHPun31L1yaeET56I6nRR/eln6OKiMPRtf4o50TFqlmzAMjwXy4g8\n0GioevU9AEwDsnDuzafq1feIXTAlxK0UXZHX4aZmS1HzOp25SSFdjUBr1DHgxnHs+sPrxF00kcZd\nRTTuLCTjtxdhSo/Dvno3P9yzmHGPn0vkgPiQtbO96ovqWHbXEpz1bgzRVhoPVjD8lpH0P7/7LX+j\nM2oZ94vRzLtsNTdfayEjVcvC95zsLdcz557jl+byOLx43T5Sk1v/4M3up6euvKazmi16kV4dZOoT\n4/BUVOKx29GFh7dsb9y1E0NG5+fN1phNJNx9I7Vvf0bBw4+h6HWEjR9G9IXze+xYGZ/DibukCl10\nONrwsLYP6II8lXXoEptvupZhzVmdaj/8mvJn/oMuOpy4y2cQMTkPWYxfHK34q53sfGopxtRYvE0u\n1EYHQ++fQ3h26J5aZJyXR1hqJAfe3UztD/lkP3UThsTmZWGipg/G29DE7tfXM/qBs0LWxvZQVZWl\nv/maiGlDSLygOQWho7CKjXe9TkRWFPFDu98To/6z+xCdFc7iD3bj3uwgdkJfzpnT54STefRhOiIT\nzSz9xsn0KUd6lz9a3EjS4JjObHavJxN/egGNxYx15gRKXnqRmHPmoouOpn7jBurWrCbxnltC0iZd\nTCSxP1kQkro7k6qq1Ly/jNpPvkMbGY63uhbLmFxirz232+V3twxIpXLRemxnTmoecjFsEObc/hTd\n/Ripdy/AlNH9blyiYzXkV7HzqaWk3HcNpszm7CV1329lwz0fMem1a9AYQndpjh2ZijnRRs3tFS0B\n5o+sgzMp+HRNiFrWflU7K3E1elsCTABTSjQJ549hz0e7u2WQCRCXE0Xcr8e0uZ+iKIz83+Fcd9sq\n7v2FlRHDDCxZ7uTPz9ZzzjNjO6Glorfp1UEmQMR5Z6KLiqBy0Ud46+oxZvch4Tc3o4uV1FQdqW7Z\neupXbCXp7jvQRUfha2qi4tU3qHr9c2KvOSfUzQuIbdwgqj5aReXzC7HOGI/qdGFftATL4EwJMMUJ\nFX2+nfAZI1oCTADb+FxqF6+i4oeDxE8M7QQMU4wFb6MDd6UdfcxRT3l2FmJNiwhhy9rHVevEEGM9\n7smQITacxu3OELWqc2VNTcUUbuT517dR93I9Uf2jmPv8eGL6dt/3VXRdvT7IVBQF69SxWKce9Ssu\ngIVlxemxf76KqPPPRRfd3FOiMZuJufQCCh94jJjLz0Ixdp9HCYpeS9r9V1L14Upq3/wQRaclYkoe\nUWeNavtg0St56l1oo4//IauNsuGpc4SgRce0w6Qn47w8Dj3+Lsm3nosxJYa6tXso/c8SRj/YPR+V\nA8TkxtGwrxxHSQ2mxEjg8CSgJVvoMz4pxK3rPMnD40gePjXUzei1VMDXhTP+BFOvDzJFaHhr69HH\nx7bapglvnuHva3KiMZ44w1FXpTUbiVswlbgFcuEWbYsYkMDul1eiMRuxjs5BF2HFY2+gYcMeom9p\n+7FnZxh4/Rh0r61j/z2v4qptwpYVy/C7ZxAzpPPHqweLwWpg6E3D2frr10i4aByGaCuVX2/GV1VD\nv7njQ928HqW2sIGynTWEJ1mIHxDZY+cViFPrukGmv8uptZEmrYX/mawCW9ipA9JVBjtV5ZH6/WtA\nh6SqhFavqzE7ncb1mwg/Y1rLNseuvWgirCjWMHx+vv8dkaoSTp6u8liaQFIqdlBaR9XPNrQnVaWq\nqtSu2EHN8m2oXi8R43OImjYYRavpkPMKZJmNQFLa+ZsusiNSVQL4NAqlX23jwLNLGDbaBLuWsvGV\nRZjGDMKx8xDJ84ahiYvC5fO/3I5IVQnNaR0zrxhLxuVjUL0+NIeX4HIdU11bqSpb1e8NIFWkJoD0\ng/5+XxUNWRcNwZoVy76PdmFf7yRtTDJZcyfjM+pbnVsgr6u/6Sr1AVwwfQGkteyIdJWBpJU8OlWk\nz+vjq4fXs/vrAqLzEqnbX0V4opl5T4zHHGkMerpKZ70bxeXBEm1o87qtSlrJTtd1g8wewud04diy\nC9XtxjSoL9oIW6ib1CVEXTCd4gf/ic/pwjwwG1dBEbWffknMdfMOXyhCP2RBVVWcewtxHixFnxiN\neVDHLOTeHRT+YzH1WwuxnTUJRael/NOV1K7cRebdF6HI8p9+c1bUcfCZL/m/t9NJ7988u7dgn5Pb\n5m0l87ZZJJ4xKMQtPJ6iKD1ujdf4EcnEj+i+PbJd2Yb/7qFkXyNT/nstOosB1aey46llfP3oes55\ndFzQ6mmscrLskTXsW1GKVqsQnWph6l3DSR3aHWbJK3h7ScDbOwYFhIhj5z5KfvsImh+WYNq9mtJ7\nn6Du6+9C3awuwZCaQPIfbsLbVEPVux/g2L+H+DsuI2x017jJ+pwuih7+DyVPvk3j5kLKX1xEwW9f\nwGtvCHXTOp3jYBm13+8i4Z6fYJ08krDxw0i46wacRdXUb9zfdgGiRcU3uxk/y9YSYAKkZhmZMi8S\nT3VjCFsmRHBs/eggfa+fgM5iAEDRKPS/YTz7vy3CdZIsRIFSVZVFd3zDjD5NFG3MoHJ7Bo/+3MKH\nt3+PvUS+R12J9GR2EJ/TRdVz/2b6w1NIGt38i7m+uJ6Pr/sEY99MDBnHZ2PobfRJscTdMD/UzTih\nqreXoehMJN//KxStFlVVqX7zQ8pfXkzibRd2WL2qqoLPh6LrOr//6jcfxDxiIBrzkaQFik6HefQQ\n6jceIHyEpDv1l8/lxWQ+vgfDZFLwuQMZ0yNE5/F5fOxcdIA9XxeCAtlnppI9OxPlBEMlXA1uDBGt\nx9RrzQYUrQaP0wvW9ocdxZuroK6JP/8hpeXp0sXzrHyz2smmdw8w6Zau0VlxMr1p4k/vOMsQcGzd\nRVT/6JYAE8CaZCXn/GwaV60PYcuEP+q/3UTEubNQtM2PCRVFIeLcM2lYvQ3VE/xgQPV4KV/4NXuu\nfZxdC/7Igd/8k4YtB4Jez+nQWk14q2uP2+6trkVr614TtEItZnwWyz+po6bC07KttsrD0o/txIyX\nvNGi61FVlc/u+Z717xwkfNpgwqfkseb1fXz5h1Un3D9jXAKFn25tta30272EJ4VhjjKe8JhA2Ysa\nyR1oPG740og8PQ1F9UGpQwSH9GR2ENXlxhh2/KLiRqse3K4THCG6Ep/Lg8ZkaLVNY9Cj+nyoPh8K\nwR2jVvavz3AcqiLhrlvRxUbRtH4rhU+8Tfp9V2Dqk9h2AR0ofGwORS99SeParVhG5gLg2LmfxjVb\nSbvqhpC2rbuxpMeQMG8EPz13PbMvDkejgcVv2Yk9exhhfWLbLkCITla0rpyyXXbGvHBFS5KAuEn9\nWHXNy5RurSQht/UYyHE3DeKNa5fgqmwgZmwm9XvKKVy8jXlPTAjaePuEgZG8+3gjjY0+LJYjfWUf\nfeUgZlBor5eiNQkyO4hpYD9KF75HfXE91iQrAF6nh50f7sE0b17A5bkOFtKweCnugmJ0CbFYzpyC\nKScr2M0Wh4WNzKFu6fdEXTCnZVvdt6sxD+oT9IxE3rpG7Ms3kfTwb9BaLQBYRg3BU1VD1YcrSf55\naIcUaM0G+txzCQcff4/adz9H0enwVNtJv3Pe4YW6Qz9JqztJvWIiEWP6sfKbHaBCn9/lYBsgN0bR\nNRWuKSV2cv9WWai0Rh2xk/pRuKb0uCDTGmfm8tfPYMt7+yhZtYOoZAtTX51JRKo1aG2KyrCRMSmJ\ns68s5aFfRxIdqeX5/9SxcpOHK+7OCFo9Ham3TPyRILODaCNs2M47i4+v+4Sc87MxWvXs/HAvamIq\nprzsgMpy7s2n6m//YsSNg0keNYHyrRWsfuY/hF91EZbhAzvoDHq3mEtnUHDfS7hLyzDl9Md18BCO\nHbtJ+f3VQa/LXV6DNjaqJcD8kTErndp1G4Ne3+mw5KQw4LlbaNxdBD4fluyUHjfjuDPZshOwhTBH\nufBf7YFqdr+6jurtZVjiw8i8eBgpk9JD3axOY4o04jpgP267s7wO06ATz+Q2hRsYdfWADm3XjHtH\ns37hbq78zX7cTR4yJiay4F8Dm58Wii5DgswOZJsxEWO/TA6uWg8uF6Z5czHlZaNoAhsKW//hZ4z7\n+XCy5/UHILpfFGHxFpY9sRjzsAG9dlmdjqSLDif98Z9iX74JV34xpux44m+adVwgGAz6hCi8FdV4\n7fVow4/82nfs2ocxIy7o9Z0uRashbEBqqJshRKepPVDN8ls+5IabzUy/08KeXW7+9MhSnFVjyJrX\nsUFUV9F/Vgarn/uEyh8OEjO6uZewfMU+ajYV0vf+YSFrl0anYeSVOYy8MqfVOp3dgaoqvWbijwSZ\nHcyQnoIh/fBM8tNMV+ncV0j6lNYpClPGJeMsWoLq9qAE+fGtaKYxGYmcNbrD69GGmYk4cyQVf3+V\nyEvnoY+PoXHtZuq++IaMP14TtHp8TjcoSqvHXqLj+VweVFVFa5TvaXez+9V13HCzmRtvaf7x1y9H\nT7LvPPUAACAASURBVJ9+Oq6+4gcy52Sj6UKrQHQUc5SRsx+byOe//xxdmBFVVVGdbs758ySMNkPb\nBYherc27jaIoLwHnAmWqquad4N9/BVx+VHkDgThVVasURTkA1NGcb8ejqqqfyZwVFJ+/6XH83C2g\nAK+Degb9vR4d01RdlI3qfTUkjTgybquuoA6txYCi6MDrZyaf06z/lAK4xqoqOPcV0LBiI6rbg2X4\nAExD+p+wZ9fvztlA6vcFkkHDvxfBG8Brdaoe5+jLzkTz8fdUvvAa3pp6zAPSSb3nCvQpCW1mP2or\n446zoJzSFz/FsSMfFAXryP4k3nQ2usiTj5EK5PvSnkxCJ62/g7Ij+ZvxJhhZhJxldvY/8yW16w4A\nED4sg6xbZ7bkzA5WG3wBZNwJ5Lz8zXjT1mvq8zaXo9FqAsuOFMB1WOPnRSvQLEJV28uYfmfrpxc5\nA/UYdCq1pQ7CkpqTa2j8zM7jCyAzT2BZfIKfSejo+mNHpHDp+/Op2F4JGoXYAdFotBqcvsDKPLbc\ntvjbQ+lvFiE1gIxXIjj86dJ4GXgaePVE/6iq6uPA4wCKoswF7lBVteqoXaarqlrRznb2apbpk/nu\nsWXMemIq4ak2GiuaWPbgSqzTJgT86N1fqteLc8d+fA1NGHMyg5KpyP7pt9g/+RbrhHFoIkxUL/wM\nw/ebiPnJRb3+kb+i0RA1byJR8yYCgaWrPBVvQ9P/s3fe8VHU6R9/z2zv6b0SQgkkoQQIRUApgoIN\nBeztTvHUs513p3fqFc/T8/xZz957L4ioIKAivXcEQhKSkF42ySbb5/fHakJMkF1Isinzfr3yUr47\n8/0+Mzuz88z3+zzPh6K/vY75rNOJvOlaJLcb65KVHPnbW6T+33Ud1rnrbJrzSnEUV6FJjMSY1nvj\nEN02O82FVajDjWiif91R9Drd7P3jexhOG0nKDReDANYv17Hnj+8z4oWr+8Wspr2ygf1PraZq3WEA\nIiYMIOOm09BGdl4CSFejjzJy6ICTgYNbv6+aag9NjV7U5s4px9MbaCyzUbSmBFEpkDwlEVHR92dw\nuxqPvFzuQ5Kk7wVBSPGzv4uBd07FIJn2GE4bS6OtiU+u+BKVUYWr3oHhtLGY50w/pX6dBSU0bduL\noFKiH5uFKsoXxO0sKafqsdcRdQYUZhM1r3yC+ewpmOdMOemx3HX1WD9dRdyf7kAZ6ntAmyaOp/SR\nx7DvOoguK7BkKBn/sH63E82gAZin+ZxXQaUk5MLZlP3zELadhzGO6LrajJ5mJ0UPfoijpBr1gESc\neavQJkeS8qcL2pWH6slIkkTpe+sp/XAD6rgIXOU1GIfEMeDOOSiN2g73qVl7EEVECKHzTm9pCz1v\nCvb9BdT8cIDIacO6y/yg4HG62XzbJxgmZTLo9XkgQfUnP7Dx9k+Y9PIliKrekTSWMG8EDz6witSB\nSgYPVVFb4+HuPzaQOGMgKkPvuYZPhd3v7mPLC7uIGD8Ar9PD+se3cdrd4xgwvXdkccsEl04LzhIE\nQQ/MAm46plkClgm+9aznJEl6/lf2vw64DkAR5t9yUn9BEARMs0/HMG2SrwC2xYSo/fkt+uRmvGrf\n/5KmddsxjBqF12mj/B//I2T+bAyTRlP1xJuETJ+BaexYANxWK6VPPoV6QDzajIEnNZ591yG0Qwa1\nOJjgqztpGJtD8/YfZSezi3CV1aBJbpusIwgC6pQEXGU1QNc5meWvrwS9ibj/XIsgikgeD1XPvUvZ\nW98Rd+2MLhu3s6ldvZ/Kb/aS8NDvUYZbkFxuql9fQv4TX5N+97kd7uMorUM9oL2qlyY1HntpXVeb\nHHQqVuehiAwh6uJWJzvq0mkc+bGIijWHiZmaHkTr/CduUgqu2nFceelG1CqJpkYvSTMHknHTpGCb\n1i3U5tWx7ZU9jH72crTRZgAa8ypZfft7xOXEoA3pP7O5nYlEYOEgvZnOzACYC6z5xVL5JEmSSgRB\niAKWC4KwX5Kk7zva+ScH9HkATXKiXHivA0S1CjH61As2Ow4V0rRhJ/F/+AMKvS/eyHLaJI4+9jii\nxYQgKjCOaU14UVosmKdMxvbD1pN2MgWNCq/d3q7d22xvl7jkrqqjefs+BFFEn5OBwtIzltc89TZq\nPliJbfN+BIUC44ThhM6b0qNn5bQpMVhX78M8a3JLm+T14tifR/iZXTebJkkS1m93Efuv21pCOgSF\ngpALZ1H+z//1Kiez/IvthM6fgTLcAvhmg8Munc2RGx/CZW1CEdp+NlM/IIrK19YhSVJLKIgkSdh3\n5xF1cdcnkwWbpuJatOntKxFo0hOwFfUuJzt5bgaJswfTXNmE2qzpNzOYAIe/KSR6xrAWBxPAmBZJ\nWE4yhd8XMficjp8HrmY3G5/fxcEvC/A4PSRPiif3xmyM0Z1fnUOmZ9OZQQEL+cVSuSRJJT/9twL4\nBBjbiePJnCRNW/ZgGjOmxcEEUEVGoh0yGMe+PESDoV2MpMJgwGs/eaUiXfZgnEeKaT5wqKXNVV1N\n4/oNGCa2lsFo+PoHKu59nMiavYSW7qT0T/9H47rg14r0Ol2U/P1lJJeS6FtvIHLRNTiP1lP2n7cD\nSlLpbkwTh+OurqXm7cW4KqpxFpdR9dzbqKLM6AZ3bTkir8OJqG/rgIkGHV67q0vH7Wzc1maUEW1X\nV0StBtGgxdPY/sUJICQnFYUSKp/9BGdJJc6jlVQ9/xmC103ouL4vH2lMjaB5T0Gbe0OSJJp3F2Aa\n0HFtxZ6MqFRgiDX1KwcTfJrlQgehDYJKgdfdcQKPJEl8+YfvKS9xk/3IfMa8eAWu0Ag++e1ynLbe\nde/LnDqd4mQKgmABpgCfHdNmEATB9PP/AzOB3Z0xnsypIQgCUkcpyx4PypgIXKVlOMvLW5olr5eG\nDRvRZQ8+6TFFjZrImxdS+doblD39HOUvvUrpw48ScsE01Im+rHlnSTmNS1Zx2XszOfPvYzjrgXEs\nePl06l77DI81uHq0tg17UJgthC04H1VUBOr4GCKuvgR3dQP2fYVBte3XEDUqkv55JaLgoPyhZ6h8\n8hV0iRYS717YpclWgiBgHDmQxm83tmlv/HYjptHBdbLc1iZqVu2h9of9eJpP/OJkykygcd3ONm32\nQ0UIkoTmOJnigkJk6L8vwhCmoOyBVyn71yvoLDDswfkI/SBpInJCKjjslD2/FGdFHc7yOsqe/QLR\n6yIyNyXY5sn4SfLURCqW78HV0PoyZS+vp3p9PkmTOn5JrdhTTW2xjYy7ZqNPDEUTYWTAtRPRp0Vz\nYGl+d5newxHwSGLQ/roTf0oYvQNMBSIEQSgG7gNUAJIkPfvTZucDyyRJsh2zazTwyU8PMiXwtiRJ\nX3We6TIni35sFpWPvYZ54kSUZt8yiKPkKPaDhwi77nwEpYLSp5/GPGECCrOFxi1bQAWGCSN/tV/b\nhp00LN+Ax9qAJj0JyzlTUcW0Lu9rM9KIf/RO7LsOIrnchF9/LgqToeXzpg27yJibjCmmtS18YAjJ\nE2Kp27oP0+nBW2Z0FJShHdI2jkwQRTSDB+IsLEOXkRIcw/xAaTESs2gOonh2t44bc/U08v/6Bq6S\nMtQDU3AcyMex9yBpD1zerXYcS+VX2yl+aRW6jFS8TjeFT35F6h/PwTL6+BKtcfNz2Xv7m0hOF/rR\nQ3GVVGD9/HuSrp/2k8PY8YyO0qAh5fozSLn+jJa2/hGF5Zv5y3nkfA69vJ6CO58HBKKnDGTQI+f1\nCye7rxA1LIK0mclsue51omZkILk8VCzfS871WRiiOl76rj5UR0hmQrvvOWREElWHSrrDbJkehD/Z\n5Rf7sc2r+EodHdt2GMg+WcNkug51SjzG6RMoefhh9JmZSC4XzXv3EXb1BYgGPcbTRqNOisX2wxZc\nxZUYp+WgH5uJoDz+5VL/5Q80rtxM6JyzUUVGYNu5i7L7nyfm3kWoosJathM1avQ5x4kF9HpRdFDc\nWFSKHc+8diOq6DCadhS0a3ceKcY4vv3MnLvaSsPqHXjqm9ANS0U/Mr3fPVw1CREMfPw6ar/ZjqPg\nEIa0CJIX/RalOThxWfaiKkpe/Y7Yv9+IKsa3ZGs/UEj+Q6+T+coiFIaOM8XVkWaGPX4FZZ9tofGL\nb1FHGEm/53yMQ9sn9si0orboyLjtdDJua03+CaROpkzPIPf3o0iblkTBt0WIOpGxz80gNNVy3O1D\nkkzUv3mgTTwyQMP+o6QOP/VSeH0BCf9r9vZ2ZOmPfoplzlT0YzN9CTYqFSFXnNVG0lCdHIc6Oc6v\nvrwOJ9bF3xJ3262oInwPb3VMDJLLRf3S1YRf1XEG7i/RjR7Gnic2Meryweh+ylqsP9pIweoSou+/\nMMAj7FyMk7Ko/eQ76leuxnRaLpLHg/WrleB2os9uG/zetP0g5U9+hH5UNsqwEGreXYV12Sbi/rjw\nVx31vojSYiBy3sSWf/tbjL0rqP12D4ZJo1ocTADtoGQ0g5Op23CI8DPaaU20oAozknj1yZfwkpHp\nzUQOiyBymH9Jp7Ejo9CZlBx8YiUpV01AoVFydMlO6rYVMfjPZwU0bkNZE/WlNsJSzS3PBJneRf96\n4sm0QRUVjmrmqZficJdXozCZWhzMn9EPG0b1px/73Y8mNR7txBzemL+MjDlJeJxe9i09gvmC1sze\nYKHQa4m75yqqXllK3adLQRDQZw8i9i9XtCmIL7k9VDz7KZHXXYk23bcEa54+hfInX6D+2+1Ypvsp\neiXT6XidbkRd+0oFok7rk9yUkZE5ZQRBYM5jU1jz2DbWXfwiXreX+LGxnPvsNLQWDccLLzkWV7Ob\nH/65juKNZSSnqjh8yMnwC9LIvSm7WwQkZDqPnulkSvgtleivHnhAF2YAky1Bl6sMZAXWX1MDOVWS\ngGiy4LHW47XbEbWtS47O0lIUYRYkz09G+nGuzOfPQjsqi7xtu0EUibjrLFSxkUjH+V0KJLE7kDyX\njqT6lDHRxNx1NV6HEwQBye6kbtk6HAeLUISYMM8YC5KEaDS2OJjgK91jmjyBxg0bMJ/hX1xpZ8lV\nHktXSTUGok7k7/3SFVKVpjGDKHpiKebZp7WUnXLX1tO0/UcSrzkNt6f1ZlIEcEyBLHt1hlxlu/E9\n/hc2V/rZJ/gv1dcVUpXQNee1K6QqwX+5Sn/PKfgvVenrt/PlKk9FqlIwKZl0zyQm3D0BJFo03h1e\n/8bf8OhGBmhq+WpTJHqdSFW1hwsvP8K2Dy0Mu7B9TWV/j6kn1ab0dGpxn55Lz3QyZXoVCrMR3cih\nVL73AREXXoDCYMBeUEjd18sIv35+wP2pk+PQpMZ2gaWdg6hR465roPS+59AOSsc8aTKuikoqHnkb\n48xxSC53u3gkyeXqsBSITPdhGJaEMSuR0nufwjg5B8nlonHVJqLmjUcdaT5xB37QfKSKyqXbcFY1\nYhgcS+SsbJQmXaf0LSPT2zgZ+UmP08Ohrwt4f43PwQSICFfwr3uM3PCX/R06mTI9F9nJlGnBa3fg\nsTagDDcjqALTVg694jxq315C0T8fQNSoQSESMn822iF9syag9Ysf0GUMJWz++QDoGIomLZWK515B\n1Klp2rIDQ46v/qfXbqd+xfeEXdA/VEJ6KoIgkHjTWTRuz8e64SCCUkHqX+ahH+Rf7PGJsG7OI/+/\nSzBNH4d69EDqt+2j6svXGPLfy1CF9QxBARmZno6r2Q0SRIS3dVATExRYS2x89+9NZF86mJCkznkx\nlOlaZCdTBsnjof6TL2lcvRGVUYO72YVp1lSMMyf7vRQratSEX30BoQvPxtvUjCLU3CZWsa9h35tP\n2AXntWnTJCciajSEzp9GzeuLaVy3EWVoKM2796Efm4Eh9/iJJTLdgyAImEYOwDTy+CWLTgbJK3Hk\nmeVE3rgA3XBfIpgxN5Pq1z6n7MP1JF43vVPHk5Hpq2jMaixxepavcDBzemv41UefNmMaGkuzMYyP\nr1nOOU+fQcSg0CBaevJICHJ2uUz/oeHz5agrDnPBB+ejC9dTX1TPijtXYjPoMU4KrDalqNMg6vp+\nFqBo1OOurePYI/U6XXgbbWiHpJDw+O00bdmPt6EJy3m5qBOiAooz7A7ctQ1Uf/Adti0HEDQqzJOz\nCDt3IoJK/lkIFGeFFa/djXZY25l74+RRVD//AYlBsktGprchCAIjfj+WRbd9x83XuxiZpWL5Sidv\nfexk+P9dgD4xFJVFx4ZndnL2o3LFh55O351qOkkkrxf7j4do+GE99ryCHi0Z2BlIXi+N365j0j0T\n0IX76heaE83k/mEsTat+6PzxJKlPnFPztDHUfbEMd61Ph1nyeKhbvBTNkGSUoSZEtQrj+EzMM8eh\nTogKsrXt8TY7KLrnZbySlshbryPsqoux7Smh9HH/qwHItKLQqfE6nEjOtlnqHmsjCkPff+nqCzhq\nm6jcWEjD4epgm9LvSciNY9qTZ/LZ7lCuXVTDsroBZD11GfpE38xl1JRBlG2vDLKVp4YXMWh/3Yk8\nZXEMnkYbFU+/BA432vhEGpZ9hyI8lMhFV/niDPsgktOF1+XGGNs2ZiwkNQR3TX2njeNtaqb2vaU0\nbdiB5PagyxpMyMLZqKL9q73W0zCMHYaztIrSBx5BFRuNu6oGVVI0UTcHnugUDKzf7UAZE0Po/Lkt\nbZE3XMnRux/EUViONqXnOcY9GaVFjykrmdoPviHsklkIooinsYm6j74heu6IYJsn8ytIksSPL6yn\n4NPd6NNicRytxhBnZsw/z0QTIidtBYvwQWFE/XUCL08vJeP8HLTRrTGYzaVWtGEdiyfI9CxkJ/MY\naj/6HF1sMpFnnd+i71320VtYlywjdN6cYJvXJQgaNeqIEMo2lxI7pjUBomh1EZoBnbPIJ0kSlY++\nhioimoS77kLUaKhfs4aKB18k9v5bEA2984c89NwpWGaOxVFYijLEhCq29zjMjev3oh3RViZUUCnR\npKf4JDRlJzNgkm+ZTd79n1B8+39Rx0ViP1RMxMwsImZmBds0mV/h6PIDHF1TRPrTN6G0GJA8Xspf\n/4ZtD64i98HAiof3BCSvROmGYkrWFqPSKUmdNRDLgN4ZuygqRIaeN5CDT64g4+6zUBo0OGubyHt6\nFcPnDTxxBzJBR14u/wnJ66Vp207CTz+zJdlFEEXCTz8T26ZtQbau6xAEAeN5s/nu3tUcWnKQ2rxa\n9r6zh83/24rx7BmdMobjYAHexiYiLroIpdmMqNEQcsYZaFNSsa3t3edW1GvRDU3tVQ6mJEm4ikrx\nHClq1+44XIQqKiRIlvVuVBY9Qx6+lPT75hF3/kiGP/dbEn87ze/kOZngULhkH5ELp6K0GAAQFCJR\nl5xOzc6jOGqagmxdYEheibV/+45NT2zBbomizqnnmxu/5NBn+4Nt2kmT+7ssIqKVrLv4RbYsepMN\nV71Cck4EWQsHB9u0k0aSwCMJQfvrTuSZzJ+RJCSvt13pHlGtRnK7g2RU1+Iqr0JyONBlDUXUXcrO\nJd/hfnkfysRYIm77Leqkzint4i6tRJOU3O5hq0lJwXm0rFPGkPEfyeXG0+jAuXMXjWtTMYwbieR0\n0bBkGV6bDe2QpGCb2KvRD4iGAdHBNkPGT1wNDpRhbTW1RY0KhV6Dy+ZEE6YPkmWBU7LmCNV5VoY+\nfjWi2vd4j5iZxbZbXiVxagoaS+9bYlaoFJz+13GM+102DUcbCUkyoTHLcc69BdnJ/AlBoUA3OB3r\nprWETpja0l67/gd0mRnBM6wLcFfVUPvS23iqa1AZNTgbXVguPp+wG68BwHEon9r3luIsKEIZasE0\nfSKGKWNPekZGFRdN/dLVPif+mLJG9sOH0WSldMYhyQSAoFKiCTcy5/Y01ry9kqPvfgKSRNywUNyx\nlp++596fnCUj4w+RYxKwfrsT/aD4ljbbnkJEEQxxvasWY/EPRYTPHNHiYAJo48IwDU+gfPNRkqZ1\nbumu7kQfpkXfh+Iw5RJGwUQCwT+VLvBTLtKfhObQC86l/MlnsZcUoU1Ipjn/EI6KUqJvvQGOY48g\nCjiOFNO8ay+CWoVhVDbK8LDjGOGXqUgBSNrhDexClbxeqp96hSHnpjD0khmICpHKneV8e+eHqCIj\n8TqcVD71BhFnn4N+4ZU4y8uo+uwTvDY75tlTO+jwxGOqU5NRhJqpfPddQs88syUm01FURNhvL+hQ\nQlTy9wYMpCxQAMEh/ibAn6pU5fE7DkDW0c9tW6UqBUxzTmPl82tY8MBwQhP1lOyu46O/7cW4cA4e\njxDQC0VXyFV2hVRlION3lQRnV8hVBiLr2BUiuF0hVQldI1fZ0TlNvGg0G2/+kOLH7JjGDsFRXEnN\nFxvJuvN0PKLSr5Pm9fN3uCukKqH1vApqJZ5mR7vPPc1OvCoVTq8CpZ/fwS+lIn8Nf2Ud4dTkKo/b\np5/nSn517n56ppMZJFRRkcTedQe2TVtwVFSiyRpM2JiFiJqOp+YlScL6yRKat28jccZA3M1uSv6z\nCssF52Acl9PN1vuHI68QlcpDxmWZLY5EZFY06ecNonjtRlyVdYROn4lptM9+XeoAYi6/kuL/PYFp\n+qSTqqEoCAKRN1+J9dOvOfr440guF7rsoUT/6TpEXd95M+1NmGaOo0EQeOX332OvakQXF4LpwlkY\nc4cF27Q+QXN+OZVLNuMst6IfGEPk3BxU4b1rVqy/oAkzkPvMAoo/30Xt6q1oIwzk/Pc8QtPDg21a\nwCTNGMi6v35DxIws1OG+EADrtnzsR6qIHpMQZOtk+iOyk/kLFHo95qn+yf858vJx7N7BtNcXoDL5\nHNEB84bz/aJP0A0bisJo6EpTTwpvfQPGOHO7mSpTohnpQD2ukjL0Z8xq85kqPAJBpcJTV48y8jiz\ntCdA1GoIvXguoRfPPfHGMl2OIAiYZ47DPHMcktuDoOz5uurNB0toXLcHJDCOz0A3qGc+NOu35nHk\nkcWYZ5+GMXsEzTsPcOC2Vxj40BXo4+Wkqp6Iyqwl9dIxpLZp9X92rqcQPjya9IuGseeGF7CMSsXT\naKcpr5zcf01HoZEf9z0Fn+JP/8i7lq+6U6B55y5S5g5pcTABTClhhI+Ip3nvfoxjRwfRuo5RD0ii\n4u0PcVjtLUHgkiRRsLwA1cAcXA0O7EeOoI6OadnHXVeH5HAgmvu3/rLH1kzd+8to2rgLvBL6nGGE\nLpiBwtK7z0tnOpiexmY81kaUkSGIatWJd/CT6vdXYVuxmfEXxoIA6/9vB7rJo4i4ZFqnjdEZSJLE\n0RdXEH79fPRZgwDQZQ1CNOgof/cHUu/om6XQ+iuO2iYKXl9P1drDKNQKIs8YwoBLc4Lq0A2+dARJ\nM9Mp31iMUq8iZvwZKLWddy/KyASC7GSeCoKA5Gkf5SF5pR6r260MDcEwaRzLFn1J5jVZaC1aDnx6\nAGu5i4jLRqGMiaT6hbdRmEzoBw3GVVVJ5UcfYJw6vs8WpPcHyeul4sGXUccnEveH20AUsa78lrJ/\nvUTcAzciKPv3reR1uqh5ZQkNa/eiC9Vgb3ARcuFUQmaPP+W+HcVV1H+1kT99nosxzHcNTro0kYfm\nrsc4MRNdSuQpj9FZuK1NuGoa0WWmt2k3TBhBxUMvBskqma7AY3ex7dYPmDpF4KK3wrA3Szz/6H52\n/b2cEQ+cG1TbdJEGUs7uvSV++gMev6Oeezf9+8l4iuhHjqDgtVdJOW8YmlBfmQvrgUpqdh4lbt6Q\nIFt3fMznnUXTlgR2fLgJyW5HPTSDiFsnIKrVaAelEXbFPKo//YKyV19GNOgxTZvYcdJPP8K+8yBI\nIuHz57WEGoRfcC5lTz1D0+a9GHL7d8Htmte/JMJTzg3LpqKzqKjMb+TV362hIdSCKffUqjM0bvqR\nEbOiWxxMAEOImlFnR3Ng0489yslUaNXg9eBtbEZhai19466qRWHuPaVwZE7M0RUHSUuR+MPfW2M3\nH3o2gnmnl1K3v5yQIcEtY+Ww2mkub8QQb0Zl6L8TBDLBRXYyTwFNShK63FxWXPYecVPTcDc5KV9X\nSNglFyHqeq6KjSAIGHKyMeRkd/i5LnsouuyhvvqgCoVcTBpwFpejTUttdy60aWk4i8ox5AbJsB6A\nt9lBw+pdXP/VFHQW37JcZKqRs/8wiCUvrD1lJ1NQKXE0tM8edTR5EYw9K5ZU1KqwTMyg9u0lhF19\nPqJahae+kbr3vyZiliwv2ZdoOlTGtMltl6GVKoHR47UcPVgVNCfT6/aw/bF1FC0/hDrShLOygbQL\nhzPsN6Pl33KZbkd2Mk8Ry+yZ6EeNpGHPPoQIFbH3LERh6t0xej/TX5aAPfWNNHzxLY6d+xE1ajS5\nozDNHI+gaHVgVLER1G9a3W5fR2Ehhsn9exbTY7Oj1CowhLadLYlMNeKuOXTK/ZvGD2XP7asou6qR\nmHTfvVVx2MbOZRUk/XfeKfff2cRfN4Mjj35OyW3/QRUbjrO4gvBZowifNfLEOwcRe2kdRz/ajO1g\nOZoYC3Hnj8I0pHMEGfoi6pgQ9uxur5q1f7eLmPHBqySw54Ut1BQ1M/TFG1GadLiqG8j/5/toQ7UM\nvHB40OySaUVCrpMpEwCq6EhU0T1nyU7Gf7x2B1UPPk/KuDCGPzweR4OTjc9to66ohNDrFrRspxsx\nmLoPllPz2edYZkxDEESsq77DVVWJfmz/LvujDDUhKZQU76ojIbM1e3rvynI0g05dPUgVbibiN2fz\nxKVLSMsNRxAEDq2rIvLas1BFWjhe9Tuvy42joByFUYc69uSqIpwMCp2a1Lvn4Syvw1lZjzYxAqXl\n56Xynlmpr/lINXvufBfj1BzMC0bjLCxl/32fkHbrTMLGp5+4g35I/JlDWXfNZj57u56zLzLhcEi8\n+pSVRo+G8FHBqXwgebwc/mwvgx7/DUqTbzVNFW4i7rqZ5P1vSb9yMt12N8XrS/G4vSSMjZFVgoKE\n7GTK9Gtsa7YRkaJjyl1jW9rmPBHOG3MX4zpagSouCvApQkXfdQ21b31J8T3/QJIk9COHEvOXJYbg\negAAIABJREFUazs1i7o3IihEQhfO4I1bvuLMW9KJSTex77sK1rxVRNzfr+2UMSynZWLITsO65SBI\nEimXDUL5ixhHyeXBuno3jdsP47Y2YT9UgjI8BE99I+r4CBLuOB91ePetMqijQ1BH946SRUVvrcM8\neyIh50wBQDckBXV8FAUvfEpo7kB5mbUD1CE6Rjx8Aa8/uZJH/3EEgJjcJEY8dDpCIMILnYjH5cFj\nd6OOtLRp18SFYa+2BcWmYFC8sZRv7l6DYUAkolrJd/dvYOIdPanai1zCSKaf4CqrwFVehSo2ClVU\nRLDN6XbchUWkTm67JKjUKokdHU1j/tEWJxNAYTER8bv5SN4LARBEMSC1l76MaXI2YoiRFZ+uwVNd\ngmpAAnH/+A3quM67ppRmPSGndxxH7HW5OfL3t/G6RfS5oxDq6rHnl2OcOgHjaTlYF39D0UMfkvaf\nqzrNnr5Ew55iYs5rWx9XO2wAbmsTbmsTqpCeV/O3J2BOi2DkY/PxNDkQRAGlLrgvnEqtClNKGPWb\nD2EZ2zoDXbdmP+GZsZ0yRuWOMva/sIGyXdWYIjWkXjCcIRcPD5pj/UucjU6W3/UDg+89j5DsRACa\nimpYe+vbmOPk5Lvupsc6mUIHUoMd4rf+XwCDB3CzBKA+57dUoBBIrEYAmx4rV+l1Oql99R1c+QVY\n0iOp+rECzZCBhF62EEHdRZdFIC9u/p7XgKQi258sMSSMqoPFv9hOouZQHboxIUgdXoe+WE3JE+j4\n/m8bgKKb/1J9XSBVCa1yldphA9EOG9j2s1/k6/hb2ctvWVF8so51K3fj9SqIvOM3LeXD9GOzKb//\nKQzjsrGcO4Ojf95KU34l2uQTJ2R0hVQldI1cZWdIVSpDjLjKa1FFt2ZKe6w2JK+EpNHi9h7/i+sK\nqUroGrnKgCQ4A7kGtTokwHkCdcOAjikAyeBj5SqHXp/L1vuX4FgwEcOgeBq251P1+UbG/3cuTo8S\nr58SjB2dq7oDVWy462v+ep+BabOiKMhzc99fd7Oz3sGw68f51W9XyFUee13nfVeIOSO+xcEE0CeG\nETVzGM27CvweW6Zz6B/ztTLtqF/8JRaLgzmfXMKUR2cx55NLMCjqqV+6PNimdSv6SWM49PURDn9T\niOSVcNndbPjfDtyCBs2glGCbJ+Mntm15GCbktKlPq4qOQJUUh+NgAYIooogIxVPXf5YMAyHq7JHU\nvP0l7mor4KsYUP3qYsKnZiBq+nc4SG8jamwSuQ+dhTevkLLnv0RZU8nEJ87DMujU8wby393Koht1\nzL1Aj14vkpGp5n/Pmcn7eC8um7MTrD913M1uFMb28ZcKY8+SMPYiBO2vO+mxM5kyXYckSdjWbWHS\n6/MQVb5ZOYVGSfZN41h14xdYzpsdVPs8dfXYtuxEcjjRZQ5BndR1Ga7K8BDCbrqKH579mG8f2ITk\n9qIdkkrYLdfIcWi9CFGnxtPY1oGUJAlvow1Bp8VdU4frSCnagXK2dEeEz8jEWVlP8Z+eQBUZgquq\njpBxA0m67oxgm9YleF0eqtbm0fBjGdoYC1FnDEbVw5yQUyFkaDQ5987o9H5tBTWMualtFYmoGAVh\nUUqayhuxDOi+BLvjEZ8bz+ant+KssaEO84V5eOwuqr7Zi9Ygz6t1N7KT2R+RJDzNDjShbWt5akP1\neJocQTLKR9PW3dS89hH64cMRtVoqH38V/ZhMQhbM6TKnT5OeTMS9t+Kpa0BQKVEY9QEtLcsEH8vp\n2Rx9/FP0ozNRhvmSbWxrtuBtsuMqq6T65fcJm3caCkPfcSQ6E0EQiLt0EtHnj8FeUoM6wowmrG/G\nr7ka7Wz/w0dIKg26EenUbS6j4I0NjHj4Agwp/S8uPRAMyaFs21LD8OxWR7Oq0kNNhRt9dM8o3WeM\nNTL8kmHsuPlNYuZkI2pUVHy5k+iscKx5tcE2D/CFTnnkEkYyfRVBFNFnpFHw5QHSzmstlF3w5Y/o\nMgb+yp5di9fuoOa1D4n97SI0Cb4SIGHTZ1L85GPosoeiHdp1tgmCgDI0eLXt+jvumnoavtuOt7Ye\nVXoSpvEZiCr/f570w1IImzOOsvseRTMwGY+1AU+tFWW4GceePURfeybG0YPoqSWEegoKvQZD+s8J\nIt1zrmz5lTQXVqFLDMOQ1vUFzAvf2ogiIZboG89reXGtW7aJHx9dyajH53f5+L2ZlPmjeOqPnxMV\npeCMM7UUHnZzz18aGXDOkB6lKpR9dRaxo2PI+zofj8vDuJtGkDAhgSVXLwm2af0O2cnsp5jPm8Ou\nJ1/Aml9HZFYUFdvKKFpVQOQt1wfNJvveg2gSk1ocTABRp8M8Lpemzbu61MmU6X4kr5emnYdpWL0D\n+9b9DJ8VR3SmgV3ffE/pV2uJvedqRJ3/te3CzhmPeWoWzfuOoNBr0WUkIygCXx7zNDRjXbkVT3EZ\nYkwkIdNHoZSzqzsdj93FgX9/TuPBCrTpCTgOfY8+OYzB95yLQtd1DkvVmjyib1/YZmXEcsYoqt5Y\njsvajMrSc9Xagk3o0EhG/u1MHn5mHXfcWIoxXEPKvEwyLuu46sOJsNc0s+P5LRR/X4ggCiRPH0DW\nb0d1isMalRVFVFbUiTeU6VJkJ7Ofok6II+pPt1C9eh0Vi0tRRMcQ9edzUYa0ra9m33cQ24ZtSC43\nuuyh6EdntVHC+TUkSaJp8w4cW7YiuT2os4ZhnDgGIYAZKl9HgW0u0/PxutxU/vctFNZqpHo7Fz6Q\nzZDTYwDIvSyV9/6wncov1hJ24ekB9as0GzCNG3rSdjnLaym552UGjbMweIqFw9sOsfv2DcT/7Qq0\nSfIDqzMpemMNbjQkPXE7glKB5PFQ+czHFL70PQNumt51A4sikrtthrXk9frWMBX9YwnzVIgaHU/U\n6AuRvFJL2SJ/s8CPxeP08M1NS9FnDWDIo1chub2UvruGVbctY8azZ/eYkkhdRX+pk9k/jlKmQ5Rh\nIVjOnU3Yb67EMvfMdg6m9fPl1LzxMdrwBIzJQ2hcvpaq5970/SD7gfW9T3B9u5xh58Yx4pJUFPu3\nUP30K8fdX5uRjqPoCI7iVqk2T3Mz9RvWo8/JPPkDlelx1H+zmRCVjYsfGYmoEBg8tXWZVBAExl+S\nhGPLvm63q/bt5Zy2IIbL/zOMsfMSWHj/UGYtSqLmta+63Za+TuXyPYRdPANB6XtpFRQKwi6eSeWK\nPQGVegqU6NMHUfPR90ie1t+huiXrMA+L65TkH1ejg6Nf7eXIx9uxFfWMGMCu4FSdwKJV+YghZpIW\nzUQTHYI2PoyU2+Zgt3ko33y0k6yUCTbyTKZMh7hramlYuYakW/+E0mgCwDRiNEXPPIp99350WRm/\nur+rtJzmbTuZ88GClqWP2EnJLLv2M5p37kM/or0Uo6jVEHbVRZS+8Dz6jAxEnQ7bzh3ox2ajGZLW\n+QcpEzQcm3YzY1EKar0St9OL1yOhULY+tJxN7q6r1/qzDSXV1H3yHY4fi1CGmTDOyqVhSx7j7x/f\nZrtxF8az+KGVxHq8J7X83hNpyq+g5NXvaNhZiNKkI2JWNrELJnTr8XntTkRj26Vp0ajD63B16epF\n0sIcrPd+zpHbnkKXnYazoAyvtYERD8875b6rtxxh3z+/IHOcnpBQkbW3riN69nBSr50kV6v4BXWH\najBmpbRpE0QBU2YSdXk1xIyND45hMp2K7GT2cdx1VuoWf03zrr0IKiX6sSOxzJmOqP71mBf7/jz0\n6YNbHEzwzTSYsnNo3nPghE6m/cBhYicktYmtERUiKdNTKTiQ16GTCaAfOQxNWhJNW3bhtTuIvPUa\n1Imdo1Qh04MQRbweCUusnogUIxvezmfCFb4XCZfdw8rnD6Od4F9x55PBWVpDyT0vMfmyBDJ/P5zK\nAhufP/IViNDc4MYU0RoLam90+0p99REnwVFWx4G73sFy/jQSrr0YT42V2re/wFn1NSm/777yZZac\nVOpXbCb03MktbfUrt2AZlfrTLFnXeJoKjYrsB8/HuquEhoMVaMeNIDw3FVHpXxjQ8fA43ex/YCn/\nfDaGrHG+zPz6P4Wz6Ny91IxMJnx0UmeY32cwJVoo/7akXbvtYCmmiR0/H/oKEsJxhRH6Gj3TyZTA\n7xAPf7+oQL7PgKRZAujXz+WFzlIR8joclD/yDMaMLCJvuB3J6aR65VdUPf06UTf95vhv1gIo1Fo8\ntsZ2H3lsDYh6XYsik3QctRGF0YhtX/vC142ljQj6BPgVNQuF0YxpysRjBj3upl0nN9IFyjQBlUUK\nZFN/b4GuUBGCAI/Lt61mTDbfv7KOtImRnHf/SN68YT27lpYQmmDg8OZaNJnphJ0xBo8fyl/+qgj5\nhvf1V/vpGiYsiGf6Ip9jGz3QSEy6kccuWs/i/x7i6scyUahEvF6JJY/mYZk8HK+k6PBaFANQ3AlE\nSchfdZpAVYTKPtuKYXIO5um+GVuFQUfk7y+l+Lb/EL1wMqpw34ulv0pCgTwsFcco3iReM4W9d76D\n62gV2qEpOA4coWnrfoY+uBCPJCD9ispQu+Pyc7tjFXdMw5MwDfc5fhLg+cUzJ5B7QBQkqrcUkjBA\n3eJgAphDFMy7wszSVT9iHpkasJKVv3SFkpAYwI+QvypC0Hpdx56Rzq6Xt1P6/jqizslB8ngoe28d\nNNsJH5eC0yui9PM78FdFSOrmQuQyckxmn8a2aSua6DgiZ85FZQlFHRlNzEWX466sxllQ9Kv7aocN\nwVlRhm3f7pY2R1kp9Vs2Yhw36oRj6zKHUF9YR8FXB1oegpXbjnLkm8MYckef2oHJ9HpMp4/Cpovk\n8TnfsfbNfMwJJioK7Rw1DCL8z9cSfsOFbdR7OhtXXhHDprZVQIlINmCI0FFSqeb+mWt55bY9/OvM\ndRw6rCDs8lnH6an3YT9ShXZwaps2UadFnRiDo6S62+zQxoeR+fTVWFLNeH48gCnBQObTV6NL7p21\nKiWPhErV3olRqQXwM469P6HUq5j85BxcP+azff6j7LjkCcTqKiY/fjaisu+7JrLij0yvx1lSij61\nbdkfQRTRpaThPFqKJvX4yzeiWkXkoquoeP4NlKuWI2g0OEtLCJt/PqroE2fZCioV4b+7lh0vvsmu\nF7eh0ChxWB2EXnVJS7Fsmf6LoFAQfvNCHIeKyd9fiGKEkcTfZiBqfw6v6NqSAoqIEMoONZCY2Zrs\n1tzgwlZtJ+lvN+CusVJ7pILQM8LRpMX1qXg6TVwojrwj6EcMbmnz2p04i8tRx3avYosqRE/cgtxu\nHbOrCBmRyOb/2snbZydtqC+ByN7s5dO3Ggi5vG8cY2djjDcz6eFZeF0eEDjlkAWZnofsZPZhVJGR\n2A8fadMmSRKO4iPoJ514NlKTkkT8P/+M41A+ksuFZuAARK3/dQvVCXFE3XMnruJSJLeb0OR4v8sf\nyfR9BEFAm56INj2x28c2zprAl098QMxAE4mZFmx1Tj782z5M44agMOlRmnVoU2K63a7uIPKcMRy8\n8zVU0eEYcrNw19RT+9YSzDkDUUfKggQni1KvZsAtM7j9kmWcPtdEaKjAssVNaIYmE547INjm9Wh+\nljeW6XvITmYfxjBuNKUrvqV23fdYcnKRXC6qV30NWjWadP9+9ASFAu3gky+CLggC6sSf9KL7zmSQ\nTC9HnzkA98JZvHjzMkS8uJrcmCZkEHbNnGCb1uVo4sJIvXc+pa+uour5j1AYtITNHEHMZZNPvLPM\nrxI1ZTDmIbHsW7EPb5WT+FtTsWTG96mZcJlTRyKwWObejOxk9mEUBj3RN19P7UeLqfr6c5+c5IhM\non53jfyjJ9PvMU/OxjQxE3dNPQqjLiB1od6OYXA8A/99ma9WpCjIvwedgCRJ1O0opm5zAaJBTezc\nbLTR8szwyWCvbWbX0xso+fYwSJAwNZURN45BG6Y/8c4yPYq+H13bz1HFRBF5wzWEL5yHdnA6XruD\n5r37/S6oLiPTlxEUIqrIkD7jYEqShLOsFldt+8oQHSEoRNnB7AQkr8Shh76g9MklTIgsYHDzfnbc\n8BqVqw8E27Reh9ft4ftbvsCuMpHx/A1kvPQ77LoQVty0FI/L/yz2no5XEoP2153IM5l9HEmSqH79\nXdwV1YSOOw2A2hWrse89QPiVC+UHjIxMH6FxZwHFz3yFp8mB5HSjHxRH4u/PRhXeM2bTbAdKqfhs\nE45SK/q0KGLn5aCNCw22WZ1C1Q8HUZSU8OTSFDRa30N89gILf7p8GWFjUlFoVUG2sPdQuvYIaLXE\nXzej5fkU/5vpHPpzKSXfF5A0TRbm6E30iplMd0M9jqMleJ3OYJvS63DkF+LIP0LiVTdizhqNOWs0\niVffiCOvEGd+YbDNk+mjuEqrqHt/OTWvfoZt01555ryLcZbVUvjQx1jmzyH+0btJePwvKJJTyP/H\n+10q0egv1k15HLzvA0hIxnzRbFxqC3tve4umgspgm9YpWNce4JxLzS0OJsDA4TqSBmup21EcRMt6\nHw35tegzEttNgOgzEqkvqAuSVTInS4+eyfTa7VR++AHNB35EaQ7B3WgldPpMLJNOC7ZpvQbHwTxM\nGVmIqtY3aVGlwjg0E/uBPDQDUoJnXC/HWVKO7buNeOoaUKcnYTwtB1F36trHvR3b+l3UvfoZmeck\nYx6gYdcXX1P17UYibrscVL3ivbbXUb18O/qJo9CPGOJrUCmxnDedsi27adpbhGFY8NRmJEmi6OVV\nRFx/IfrsQQBoh6QgGrSUvLmW9L+eGzTbOg2FiNvV3pl3OyW0fUSKtLswJYdwZM1eJElq42g27S8m\n9YKTT0LtUUj9R/GnR1/9VR9/jNKrZNAN9zLw6jsZcNkt1K/+AdvuXcE2rdcg6nW46tu//bnr6xAN\nchD1ydK0bS8VDz2PQtBjHJSJc+8Ryv/5NJ7GpmCbFlS8The1r3zGwucmcsYdmeRcPogr35yCUaqn\ncc2OYJvXZ3FVN6KKi27TJggCyphIXNUNQbLKh8fmwFVuRZeV3qbdMHY4DXv6xixf2NQMPn7NSoO1\nNWZw+5pGyopchGQnBNGyrqc+r5riFYew5nVOIf/YScnQ1MzRl1bgstpw1zdR8spKvDX1xE9J6ZQx\nZLqPHjmTKQDexiaa9u0h/YZ7EdW+oHx1aCRRp51FzZq1GDMyWzf2t1N/CeQNIwBJOb/rS3eiVKVh\nxEjqlnyN7eB+DOm+WQ7bwX00HT5IyKUXQEeyfQEckxCQrKL/mx5PrrIdfkqkBcyvDC95vdS+uZiY\nK69Cm+orBWUcNYqK99+j4es1hJw3s+MdT0L+0Pf/Es079tG0djuSy41uxBAME0chKH+6ff2Vn+sC\nqUpoK1dp319EaIqZ6CGtsXaiUmT0hSmsXrwX72Q/1Z5OQqqyM/s9GalKv4YP4Lj8vQe8goQ2PR7r\npr2Ypoxpbbc7sO8/jPqaqbh/kmj0V6oS/JerPNExeZUaEAU8dQ0oQ1vjQ10VtSgtBtyejmskBnKu\nFH7KKnaFVCWAeVQq1jEZ/Gb6LnKnm6it8bJnUxPpfz0XSaFqkawMRKoyEKlIyQ/51Z/x97yeaHyP\n3cWef3xB06Fyho7Usu0ZO/q0aIbfexZK3fFjUJXCCZJ3RJEJj81lzzPr2XP1/0CCuKkDOO2JuXgU\n6nbyn+D/de0NfuQI8FMJo35S069HOpkAniYbCp0ehabt8qM6NAJPY3DfzHsTCoOeqGuvpOyNd1Bo\ndQB47M1EXnsFCr08k3kyuMsqffVDU9vWGjXljKF66WI4npN5klg/+IrmbfuwTJmCoNHQsGYdTZt2\nE3nblT2uuL2gUuKwudq1O5tcCCo5+aGrCJmaRc3STVS//BHGKWPw2pqxLl6BefzQblfx+SWiSkHY\ntCyqX11M5PUXIuq1uGvrqX17KVFnjwyqbZ2FIAgk/fZ0Is7M4vDWQpRJakbemI7S0DuqFnicbip/\nOIy9ogHL0BhCsuJOuE/eS2sZGFLHP9bEoVQKuN0S991aTd5Laxl805RTskcbpmf0X84g5y9TAeQE\n1V5Mj3UyVaFheD1umsuL0UW3LjfUH9iBNjkleIb1QrQD00i49y4cRUWAgDopocc5J70JQavB22xH\ncrtbZxMBT2NjQIpI/uCuqKbx+00k3HUXip/CGwxZWRx94kmat+1DnzO8U8c7VTTpidQ2evlxWTGD\nZ/ru2+Y6B+tfz0O38LwgW9d3EXVqUh+4iqpP11L72scIWhWh07IInXliZa/uIPaqMyh++iuKbn0Y\nVWQorspaouaOJmJ233Ayf0afFI4+KTzYZgSErbiWLX/4FFVsOJqkKI58sQpDnImc+2ej0LR3ERy1\nTdTtKaPoiz38e2kMSqXPAVQqBW76k4XL5+w/ZSfzZ2TnsvfTY51MQaEgfNbZFH38EpETzkQTHk3D\nod3U7d1C/A03B9u8XoXX4cB+MA8UAtr0gbKDeYoow0JQJ8ZSu+IbQmfMRBBFPDYbdd8sx3R256qm\n2H/MRzdkSIuDCb57wzhyJPZ9eT3OyRREkbCbL+WrB19n07sFGCM1FKwtwzhtHLqfkj5kugaFSUf0\n5dOIvnxasE1ph6hWknTrHLz1U3FV1qOJC0VhkJPkgo3X5WHXA8uwnDWOiHMnABB1pZfiB98l/4Pt\nDLwsp832h9/YQOF7Wxk6Sk9YqMCd11Twn5eiSUjxrVKYQxU4m9zdfhy9kf6S+NNjnUwA0+gclCEh\nWNeuwb17PdqkZOJv/D2qkL5RW607sG3fRfV7H6CJiQOvl6o33iXiqkvRDZYf+KdC2LULqHrqNRq3\nb0MVEYGjoBDj1HHox47o1HFEgw6P1dqu3W2tQzTpOnWszkKTGk/s/91J844D1NiaiZo9AFWkfM/K\ngCrEgCrEEGwz+j2SJFHw7hYK3t2K1+2lqWQNeCTCz5+AoBAJP38SpS8taeNkVq4voG75Tt5ZEU94\npBJJkvjwFSv33FjBy0viEASBxe82EJvbtxOd+gOCILwMzAEqJEka/ovP7gD+C0RKklR1or56tJMJ\noEsbiC6tj5Qt6GbctXVUv/cBiZctQhvnu/GbCvIoeeUV4u79sxyTeQooQ8xE/+UmnIXFeKwNhKXM\nQxHS+UWvdZmDqX3jMxq3bsMwcgSCIOA4UkTj5i1E//WGE+7/yzIg3YWgUqLPyej2cWVkZE7MkY93\nUPLNIZL/fS3quHAcJdWUPPIhgkZF+NljQSki/SJLpuLr3Vx5g4nwSJ/bIAgC866y8Pbzdbz6ZB0l\nxRLfr3SQ8+jsYBxSr6IXaJe/CjwFvH5soyAIicBM4Ii/HfV4J1Pm5LFt3YYpI7vFwQTQp6ShT02n\naccuTOPHAeCqrqb+m29x5heisJgxTZ2IbtiQYJndaxAEAU1qYteOoVISedtVVP3vLeqWL0fQanBX\nVxN25fmooiOOu59tzVasn3+Lu6wSZWwUlrlTMU7q3FlWGRmZ3knhh9uJvWM+6jhf/KgmPpzYRXMo\nefQjwmaPoeazdcRMbpvY6GlyYAltG2oligLGEBVLftATkp3I+JeGoQnt3skLySshicF5me6rSJL0\nvSAIKR189CjwR+Azf/uSncw+jNfuQKFvvzSl0BuQ7A7A52CW/99TWEaOI2zOApzVFVS9+wnmM8/A\nNGlcd5ss0wHqpDhi/30HzvxiJJcbTVrir2Zq29Zsw/rJSiIWLkCbmoo9P5+qd99FEMEwQXY0ZWT6\nO46KerTJbeuqalKjcVXUUfjnF1GqYMDCtqIn5tEDWPzBDibN0Lc4dHn7HFSUe5ny1DkdJgl1JZVb\nStj93Ebq9pWjDtUzcN4whlw+AkEuft8lCIJwLlAiSdKOQBx62cnsw+iGDqb6jXcJnzStpdaop7mJ\nxv27iJ6xCID6b77FPHIcEdPOAkAbn4gmOo7iN57FmDu6Tfa0TPAQRBFNmn+qLdYl3xKxcAG6NJ/G\nry4tjYj5C6j+7GPZyZSR6SfYKxup+P4gXpeHiNxUjCmtWe/G9Ggatx3CNHZwS5tt6yE0UWbSrxhN\nZG4Kyl+8xybMHc62Vfu59cpKZp+ro/Sohw9fayD9pind7mDW7qtgw33fEHfDWST9ezCOozUUPf0F\nzoaNZN+c2622nCxBXi6PEARh8zH/fl6SpOePt7EgCHrgbnxL5QEhexB9GE1qCpr0NApfeoKQ0ROQ\nvB7qNq/BMGY0qhjfW6wzv5CwOQva7hcdi6jW4K6qQRUTFQTLZU4WSZJwl1WiTUlp065NTcFV2jd0\nonsSkiThLCzHXdeINi0OhUmOc5YJPmUr9nPoyRVMnGlCbxBYdedGYs7OJuWqiQCkXzOOXf/+HI/N\njn5oEk37jlD5+nIy75pBxNjkn3ppW/VcqVMx6rGLOLpsP299XYjCrCfroRmY0yMJSOmhEzjwzk4i\nF5xGyMShAGgTI0j84zwOLHqGjGtGoTKou9WeXkiVJEk5J96shTQgFfh5FjMB2CoIwlhJksp+bUfZ\nyezDCIJA+MILad6zj6adu0AUCb3oPLRDWjPLFRYzzuoKtPGtsYUeux2PrRHRKGeBniqu8ipsqzfh\nsTagSU9GP34EoqbrfgAFQUAVG4X9cD669NaEOfvhw6ji5BeGzsRd20Dlo+8g1dYRkmDkyP5aQuZO\nIOSCqf0yPsxRWkvtt7vxNDsxjx6AMSulX56HYOO0NnPoiRU89kEiKYN8K1iX3hTGork7CR2XRkhG\nNBFjU8i+bxb5b2+h5r2VGJLDyL5vFmEjfj0zXKFRkjh3OMwNbum0hiIrMXPb2qoKNaIKM9Bc3ohq\nQHAFCE6ERO/SLpckaRfQ8gARBKEAyOm92eUSnEh5qmVTP8MvAvqt6yoJSn837USpSgERQ8YwDBnD\nWk095gXVNGkiVR9+giYmHk1UDB67nYovPkQ3fBhKnRFO8D0EdJ90hVxlV0hVgv9ylb8iZ9a8az/V\nL7+PacxY9PFpNG7cSeOq9UT94TpE/QnKDwV0Xtv+0zznDKrefZeI+fPRDEjFcTifyvfNTXJOAAAg\nAElEQVTfJ2T+bCRP68aS20Pzzv24K6pRJ8WhGTIA4Sc9RSGAc3U89UFJkrCt3krD8vV46upRpyUS\ncsEZqJNPrCYiBBBWFYhUn/8SnCferup/H5I10cD0m0chiAINlXZevmYD9bExGMd1nFnfFXKVXSFV\nCT65Sn8QBYm673Zz9IWvMYwficJkpujp5egHxpBw27kIx0jf+itVCQEeVxecK3+lKsF/ucqAHi0n\nKVdavv4ImeONLQ4mQEi4krPmm/jhu4OYhsYCYMlOYkR22xAczzGnpyukKgG8J5BCPpbjyUUak8Ow\n7TmCPr31t8RVVY+r1oYqytwio/pLpH4i5XiqCILwDjAV37J6MXCfJEkvnUxfPdPJlOk29BlD8Uy3\nUvzaM4gaDR6bDd3wDMLnXxBs03o1ktdLzVufEnPZFS0luExjxlLx7ls0rFyLZU7XFcw25GYDUL1k\nMa7SClSxUYTMn41hXFbLNu5aKxUPv4RCZ0CdkEDt6iWIRh2Rt16FqPM9nCRJwl1aieRyo0qMaXFA\n/aX+i9XYfthO2PnnoIqKomnXbsoffIXov/wGdUL0iTvowbiq6nAWlnHGK9NbnChTpJZpvxvI8vc2\nHdfJ7It4mhwcfe4rou++HnVCDADmWadRdv/TNGz8EXNu91WqaMqvoPlwOZrYEAxDE/rnTOpxHHnf\nuegZ4t2uBgdepxt1mP6kvqO0i0ew4fbFKMx6LOOH4Cip5uizX5J6/nBUenmp/FSRJOniE3ye4m9f\nJ3Qyf60o50+fT8WXzp7/U9PHkiT946fPZgGPAwrgRUmSHvTXMJnuwzQhF+PYHFzV1SiMRhQmeZn8\nVHGVViCIijY1XgVBwDwml+rlS7vUyQSfo/mzs9kRtW8uxpCZRdhsX007yeul8u13sC5eQeiCs3Ad\nraD2+XfA1ohCp8LZ5CHkynnoMv0r4u91uqj/4nti77gFVYQv4cA8eRJeh5P6Jd8TseiiUz/IIOK1\nNaO1aFCo2jrexggNUmNTkKwKDrZdBahT41scTABBrcI4ZRzWDQe6xcn0utwUP/wxjkMlpOdYKPy4\nkXKdkeR7F6I096842bBxA9j6zAoKDzpITve9MFpr3Cx9v57ku4Nbms5RY2PbIyup3VYMChF9nJnh\nt00hJCPmxDsfgyU9kpwHzuLHFzdQ8tRSNOEGBswbRtpFWSfeuYfg7Sezqv7MZL5KB0U5f8FqSZLm\nHNvw/+ydd5gV5dn/PzNzet/eK70tvYOAIijYe8FuLLEk0Wj0fZM3v8SYxGiMRqPGEmOLGhuKgoCA\ndASkSO8L2/vZcnqZ3x+LC+sucI6cs+csO5/r2ku8z8zz3DNnZs49z3M/91cQBAn4B3AuUApsEATh\nM1mWd/5IXxWiiKBSoUnr3qNL8YSo1RB0u5EDgXYyngGXE0EX2zdt2efDvW0vqY9d32YTRBHb9HOo\nfPVVbJfPpPZvrzPmtr4MvLQPgihQtrGShQ+/i/q396NKPrV6T6C2AdFoaAswv0ffvy+O9zZH/Ji6\nGk1WKq5mP+U77GQOsrXZN39Whnpwnxh61vUIKgl8HaUEZZ+39bMuoPqD1aSp7dz/1TBUGhFZlnnn\n8WJ2vPIl2Q/2rFkZtVVP/r3T+dmVXzHpPDMGg8Cyz5tJPm8YlgEZ/HBBD0DA7cNV0Yg22YTaHB25\nT1mW2fTIZ+iK+tDnZ9cgqFU0rdnBxkc+Z9Jr16BLMYXVXuKQDMY/ewkAqlDz6xS6nFPOf8myvAKo\n/xFtjwH2y7J8UJZlL/AecPGPaEchhvhqa6n/+DOqXnyV+rnz8NXVxdqlboEqORF1egr2FV+35aEF\nXC4aln2FccKImPrWquQhd0h8FCQJAgHc2/diSdMy6PK+bVPBWaPS6XNePo7V34bUh2SzEGhuIdDc\n0s7uLS1DdQZITAoqiYQbZvPW3RtY+dp+di4u578PbWbfhmYs50+ItXtdirEoH19lLa4d+9tsgWYH\nzUvWYps8qEt8aPp6G1f8PAuV5mhOsSBw2f051K/ZR7CTAPhMJ+2cgQz95y0cTCziO3EAff98LTk3\nT+6wnSzLlLz3Dd9c+0+K//ARG+a8yoFnFxH0RT5oa9haht8nkzLnHEStGkEUsE4ajHnCIErn74p4\nfwrxQaRyMscLgrAVKAd+KcvyDiALKDlum1LghNW9BUG4A7gDQGXt/j9CZwKeklKqXnwF2/BxmIdP\nxHn4IBV//Tvp99yJJuvUizfCxVdTi7/ejiYzHckS3lttPJJ029XUPPfvNn1z14EDGMePwDB2eEz9\nErUatP0KaVq9Ctu0aUDrj03j8uXoRwwi0NSCLavj+bflmCjb2hxaHwYdponDqXnnXZKvvhLJZsW9\nbz/2+V+SfO81ET2eWGEaPwR1WiKblq1HXmNH1bs/aY+NQjLGp6Z8tBDVKnIeupSSJ/6DtncuosmA\nc8tukmaNxFSU3yU+BNw+9Kb2P2canYgsgxwIwom1C85YtClmsq8YedJtKhftxLlsCy99lkt6joZm\ne4A/PlBC8Wsr6H3X1Ij6465qRpuX2iEHU5ufhuPwoRPsdYYix7xOZpcRiSBzE5Any3KLIAizgLlA\n2PNFRwuBvgygy8qJj+zkHk7Dp1+QcvZsbCNai9ua+g5CbUukYd580u66PWL9BN1u6t/6D97iwxhy\nEqk7WINp4jisF8/u1on7qqQE0v/vZ3j2FRNobMJ6/WxUSfHxApUw5yKqn3gFz6FitDk5uPbuJeB2\nkvqr2wm2OCn9ZD5ehw+NsfXXWQ7K7F1Ugnry2aH3cd0s7B8upvyJp5CDMlKChcSbL0bXvyBah9Xl\naAuz0Pa6JNZuxBzTkHz6vnwvzev3EnR5yZwzAU16113rltG9WfpuFVc/nNdmWz23Gku/dKTTSE8J\nuL04D1SjshrQZ3d9WRy/00vdqr34mtzYhuVg6h3ZlKbqT7/lwV8nkZ7Teo7MNokH/5jKbTN3UHjr\nJERN5NYGW/ql4nx5DUGvv127jm/3kT0pK2L9KMQXp30FybLcdNy/5wuC8IIgCMlAGXC8sHP2UZtC\nN0CWZdz795NzVftg0lo0kppFIcuWhoT9o7lYMwSGPHUzkkbCa3fxzcOf07IqEfPk7j31KIgiun5H\nNYDjKF5WpyWT8ccHcK7/Dn91HcbpYzCMHISgUiGZjOhHFzH3jiWMvGUAar2KbR/sx+nTkjwy9OlP\nQSWRcM152K44l6DHi2jQtStno3BmIRm02KYOiUnfKddNZdUjb1BVso+iiWYObHOyaamd/N9d96Pb\nrJq3mdI3VqJKSyTQ0IQuK4Hej16IJrFrZlmadpaz47dz0fXJQUqyUfrRpySMyqPvL2ZE7D5y1znI\nLmz/MpCUpkKQZfwuH5oIBpmm/CQSR2RT+vg7JF01Fcmoo2HhRvyVtWTNCP3l9UxARhnJDBlBENKB\nKlmWZUEQxtCa51kH2IE+giAU0BpcXgP8+DteoUsRBAFRr8ff3IQm4djiDV9TI6Ihcqs1gx4vji3b\nGPfBTUia1kUCGpueAXeN47tnv+n2QWY8I+q0mM4a3eln1usuwrFuK+ve24Ts86EpGkLSjWN/1EIO\nQSUhqXrWFLJC16JJMtPn2Z9Qt+Q7Fq2tRJWWTZ+/D0Wd8OMCwqYtxZS9/w0Zv7sLdXoyciBAw0dL\n2P+neQx88qTVXSKCHAiy+49fkHz7JRhHt6raBK+dQcXvXqXm692knj0gIv1YB2WyemEzl956bJT2\nu3VOtIkG1JbILwAa/Mi5lH68mbJ/fUHA7Sd1Qh69nrsMlb4H5jP0EEIpYdShKCdHM1xkWX4JuAK4\nWxAEP+ACrpFbVzr4BUG4F1hIawmjfx3N1VToJpjHj6N64SdkXn4jolpD0OuhetGnmMafMLU2bGSP\nB0ESUZm07ey6FBMBR88qBRNPCKKIacJwTBNimz+qoBAqkkFL6oWdvzSFS82CLVgvmoI6PRloXRSX\ncPk5lP7sL7hK66M+dd6yrwo0mrYAE0DUabDMmkj111sjFmRmz5nIWw+9j8sVZPRZRvZtd/P6M/Xk\n3zsjKqlKoiRSePVwCq9Wnis9hVMGmSEU5Xye1hJHnX02H5j/YxwTQlUbCFVBItTmgkGCAR+CRhPS\nTXb8JrIsE2hqbJ1yNHbyBh3qPRsNFSEIXXHn6GYJM2dQ+/4HHHjm92hTM/BUVWAYMpiE6dOPKTKd\npjqSZDCjslqo+eYwqePy2+xli/ag690bTnUdRENFCEK/XsKpTx6W6lQ4qk9RUEc6QffuvcW4129C\n9vvRDh2Mfmh/BCn0kxCqklAYwjDh3S4huhqOilBYaifhHFioijsieI5U0fjeQpq3FKMyaTFPG4Ht\nimmI6vaP+HBUZMQQFW/kMM5VqCpCcGK1l059CPG8hnpMPrsL7Q9KdQmShJRoxdPgQUwI4Kmwo0k0\nobIaQr4GQlURCgRk6OS+EiSRYFDG9wNFmx+rJKTNS2PAU9ez5MN1fDGvCk26lYJHL8M6JBtvMPTz\nrwpHHSkKSkKhqgjFk+KPMl3ew5CDQewrv8a+egVBjxuVxUrC9JmYh4dWbsZVfIi6eR/ib25G9vnR\n5eeTcunVqCzWKHsePQSVipTrr8Xf0ICvphZ1agoqm+3UO4bThyBgu+hitjz+DgVXFmHpnUz1uiNU\nrCgm7f57I9qXQquWesuytfir61HnpGOaNh6VzRLSvk1fLMWzai2Dr+qLSqdm58df4Pl2C7bbr+3W\nC7S6O77aRiofe51z7u7F8Odm0FzjZsFTu6l9qYGU+66KtXvdEvPQXFrWfYdh6DHxAV9FLb7KOpq2\nHOLA7z5ASjDjr2/CNqEfeffMiOgiGVO/DIItTpzbD2IY3JrTLfv9NC1cR8bsyJaFMuQmUfjA7Ii2\nq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UMLeFyIam2X+66g0J1wbd6Be/s+cn/1a6SjxfObN29k3R8XMOWJaSy+dxGWC85tv8/2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\n5EJ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/oa2sTCw/3wTh2fQRZQ8uxVg2sDRKbTMw7R9W8+lX/4z5mqsnz9S5yJSJZEpO5kWO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cs+MzEhyZe5hN0HHierZA3GFCmnWCAWUFrJaPou1gOntda1WusA8DRw3wX73Ac8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\n1NPqlUaCgIsAAAAASUVORK5CYII=\n",
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      "text/plain": [
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       "<matplotlib.figure.Figure at 0x10d104cc0>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def createData_two_output(nbData: int):\n",
    "    x = np.random.random([nbData, 2]) * 2\n",
    "    w = np.array([2., 4])\n",
    "    w0 = 5\n",
    "    '''y[i] = sum_j x[ij] w[j]  '''\n",
    "    y = np.sum(x * w, axis=1) + w0 +  np.random.choice(a=[2,-2],p=[0.3,0.7],size=[nbData])\n",
    "    return x, y\n",
    "\n",
    "nbData=500\n",
    "x,y=createData_two_output(nbData)\n",
    "x_ext=np.zeros(shape=[nbData,3])\n",
    "x_ext[:,0]=np.ones(shape=nbData)\n",
    "x_ext[:,1:]=x\n",
    "\n",
    "\"\"\" ( X^T X )^(-1) \"\"\"\n",
    "XTX_1 = np.linalg.inv(x_ext.T @ x_ext)\n",
    "hat_w = XTX_1 @ x_ext.T @ y\n",
    "#hat_Y= x_ext @ hat_w\n",
    "\n",
    "print(\"hat_w:\",hat_w)\n",
    "\n",
    "plt.figure(figsize=(12,12))\n",
    "mini,maxi=np.min(y),np.max(y)\n",
    "xx=np.linspace(0,2)\n",
    "x_1, x_2 = np.meshgrid(xx, xx)\n",
    "hat_Y= hat_w[0]+hat_w[1]*x_1+hat_w[2]*x_2\n",
    "plt.imshow(hat_Y,\n",
    "           origin='lower',\n",
    "           extent=[0,2,0,2],\n",
    "           norm=plt.Normalize(vmin=mini, vmax=maxi))\n",
    "\n",
    "\n",
    "plt.scatter(\n",
    "            x[:, 0],\n",
    "            x[:, 1],\n",
    "            marker='o',\n",
    "            c= y,\n",
    "            edgecolors=\"k\",\n",
    "            norm=plt.Normalize(vmin=mini, vmax=maxi)\n",
    "        )\n",
    "\n",
    "plt.xlim(0,2)\n",
    "plt.ylim(0,2)\n",
    "plt.colorbar();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Énigme:*** Pourquoi le `hat_w` trouvé est plus petit que le vrai `w=[5,2,4]` ? Si vous trouvez la réponse, demandez-vous ce que doit vérifier un \"bruit\" pour mériter son nom... "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Le bruit est maintenant gaussien (ou pas loin)\n",
    "### on peut faire des stats\n",
    "\n",
    "Maintenant on suppose précisément que nos observations $y_i$ (petit $y$) sont des réalisations de v.a $Y_i$ (grand $Y$) telles que: \n",
    "$$\n",
    "    Y_i = w \\cdot x_i  + Bruit_i\n",
    "$$\n",
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    "et que $Bruit_i$ ce sont des v.a gaussiennes centrées de variance $\\sigma^2$ (qui ne dépend pas de i). En d'autres termes:\n",
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    "$$\n",
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    "    Y_i \\sim \\mathrm{Normale} (esp = \\mu_i , var = \\sigma^2 ),  \\qquad  \\mu_i =  w \\cdot  x_i\n",
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    "$$\n",
    "La densité de probabilité des $Y_i$ est, à une constante près: \n",
    "$$\n",
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    "      L(y_0,y_1,...) =  \\prod_i \\exp - (\\frac{ y_i - w \\cdot x_i}{2 \\sigma}  )^2\n",
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    "$$\n",
    "Donc le paramètre $w$ qui rend le plus vraisemblable les observations $y_i$ (petit $y$) c'est tout simplement\n",
    "$$\n",
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    "  \\hat w= \\mathrm{argmax}_w \\prod_i \\exp - (\\frac{ y_i - w \\cdot   x_i }{2 \\sigma}  )^2\n",
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    "$$\n",
    "\n",
    "\n",
    "*** Exo: *** Par une habile utilisation de la fonction log, montrez que l'on retombe exactement sur le $\\hat w$ des moindres carrés ! \n",
    "\n",
    "\n",
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    "La conclusion de cet exercice est décourageante: à quoi bon avoir supposer autant de chose sur nos données, pour au final retomber sur l'ajustement des moindre carré? \n",
    "\n",
    "Réponse: on peut faire des stats maintenant! \n",
    "* estimer la variance du bruit\n",
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    "* estimer la variances des estimateurs $\\hat w_i$\n",
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    "* faire un test pour savoir si l'un des $w_i$ est nul. Ce qui revient à dire que le i-ième input n'a aucune influence sur l'output. Ce genre de considération est importante, car on cherche à expliquer l'output de la manière la plus simple possible.  \n",
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    "\n",
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    "Au travail:"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 8,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "sigma_hat:  0.289163491185\n",
      "T_scores: [ 44.64   0.8   43.99  21.17  -0.43]\n",
      "pValues:  [ 0.    0.42  0.    0.    0.67]\n"
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     ]
    }
   ],
   "source": [
    "\"\"\" observez la génération des données: parmi les inputs, deux n'ont aucune influence  \"\"\"\n",
    "def createData_four_input(nbData: int, sigma=0.3):\n",
    "    w0 = 5\n",
    "    w = np.array([0., 2, 1, 0])\n",
    "    x = np.random.random([nbData, 4]) * 2\n",
    "    y =  x @ w + w0 + np.random.normal(0, sigma, size=[nbData])\n",
    "    return x, y\n",
    "\n",
    "\n",
    "nbData=100\n",
    "nbInput=4\n",
    "x,y=createData_four_input(nbData)\n",
    "x_ext=np.zeros(shape=[nbData,nbInput+1])\n",
    "x_ext[:,0]=np.ones(shape=nbData)\n",
    "x_ext[:,1:]=x\n",
    "\n",
    "\"\"\" ( X^T X )^(-1) \"\"\"\n",
    "XTX_1 = np.linalg.inv(x_ext.T @ x_ext)\n",
    "w_hat = XTX_1 @ x_ext.T @ y\n",
    "Y_hat= x_ext @ w_hat\n",
    "\n",
    "\"\"\"\"    Estimateur de la variance du bruit\n",
    "Au dénominateur, le ( - nbDescriptors -1)  c'est pour rendre l'estimateur sans biais   \"\"\"\n",
    "sigma_hat = np.sqrt(np.sum((y - Y_hat) ** 2) / (nbData - nbInput - 1))\n",
    "print(\"sigma_hat: \",sigma_hat)\n",
    "\n",
    "\n",
    "\"\"\"  Estimateur de la variance des w_hat\n",
    "(c'est la variance du bruit multipliée par un coefficient qui dépend de la matrice X\"\"\"\n",
    "std_err= sigma_hat * np.sqrt(np.diag(XTX_1))\n",
    "\n",
    "\n",
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    "\"\"\" T-scores. Se sont  les w_hat[j] renormalisé: \n",
    "quand le vrai w[j] est nul, T-score[j] est une 'petite' variable aléatoire (de loi de Student).\n",
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    "* T_score[j] petit  =>  hypothèse H_0[j]  :  w[j] est nul\n",
    "* T_score[j] grand  =>  hypothèse H_1[j]  :  w[j] est non-nul\"\"\"\n",
    "T_scores= w_hat / std_err\n",
    "\n",
    "\"\"\"p-values associées. Attention, l'ordre de grandeur est inversé:\n",
    "* p-value[j]  petite => hypothèse H_1[j]  => w[j] est non-nul\n",
    "* p-value[j]  grande => hypothèse H_0[j]  => w[j] est nul \"\"\"\n",
    "pValues=2*stats.t.sf(np.abs(T_scores),nbData-nbInput)\n",
    "print(\"T_scores:\",T_scores)\n",
    "print(\"pValues: \",pValues)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour bien comprendre les calculs précédents, il faut connaitre les tests statistiques. Nous n'entrons pas dans les détails, mais expliquons simplement la recette: \n",
    "* On choisit un niveau de test, disons $\\alpha=5\\%$.\n",
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    "* Quand `p-value[j]`$>\\alpha$, on choisi l'hypothèse H0 c.à.d qu'on décide que `w[j]` est nul, donc les input `x[:,j]` n'ont pas d'influence sur l'output, on pourrait supprimer cette colonne de notre base de donnée.\n",
    "* Quand `p-value[j]`$<\\alpha$, on choisi l'hypothèse H1 c.à.d qu'on décide que `w[j]` est non-nul. \n",
    " \n",
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    "\n",
    "\n",
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    "La théorie nous indique que notre décision est rarement fausse:\n",
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    "* sous H0   `p-value[j]`$<\\alpha$ dans seulement $\\alpha$=5% des cas.\n",
    "* sous H1   `p-value[j]` est \"presque-toujours\" proche de zéro (il converge p.s vers zéro quand nbData devient grand). \n",
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    "\n",
    "*** Le jeu des 5%:***  Transformez le programme précédent en une fonction qui vous indique si vous gardez ou pas le `j`-ième input. Lancez un grand nombre de fois votre programme. Constatez que dans 5% des cas, le programme se trompe pour `j=1` et `j=4`. Par contre, il devrait quasi jamais se tromber pour `j=0`, `j=2` et `j=3` \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pas que linéaire\n",
    "\n",
    "\n",
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    "Le modèle linéaire permet de modéliser des relations non-linéaires entre l'input et l'output. Et c'est à vous même de deviner comment on procède! Observez cet exemple. Une aide supplémentaire est donné plus loin. \n",
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    "\n",
    "\n",
    "Dans le jeu de données suivant: \n",
    "* l'input est le nombre de followers de youtubers\n",
    "* l'output est son revenu\n",
    "\n",
    "Essayer d'ajuster une fonction `f` telle que `y[i] ~ f(x[i])`. Pour cela, vous n'avez besoin que des outils présenté dans cette fiche.  "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 9,
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   "metadata": {
    "scrolled": true
   },
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   "outputs": [
    {
     "data": {
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TuMSEpkpna6Cz87fXaKDOYGI/gJrEQKCJ1G/8f7uykofeT/ndUj+mg9QkLkOtiVeO6+8V\nDHop5wxY6WtauWexptKgkUDt1qxcNm/iV/s+wm4cLz3FQKCJ0pneuejDXwS6p4Z27n+463c4QUya\nzz4CTYRuQ0Srjuzp7Pg1CEjzGQg0Vrrl7C/68BfnPd2XT/9rVi7r+dTfea6jgKTeDAQaK712BOtm\nUOrHxeGkauwj0NBV6fDdvH0Pm7fv6TsstJctO/Yevm5mbhszc9sW1MksNY0tAg1d+1P/5u17+NK+\nh7qmfgZ9R6c1K5dx7RVnz/seWwTSYLYINFJbduxl5/6H5z3hl5V3+3DPbp91vtceBCRV54QyDcXR\nLPsM/TuGe00Mc7KYms4JZRorG9et5sCm9QsavbNh7SoObFp/OOXT3kLo/C6XiZAWz0Cg2pSTveCp\nzt+yVVAlKJQVebeWwMzctnkLy9khLC2encVaUu3pmJ37Hz583G1p6G7vt+s3Yqi8hx3C0tGzRaAl\n060fYMuOvfNaBu3vb96+54hWQa9WQvtTvykfaWnZWayjNmhHsMUqn/T7PfUbGKTe7CzWkuuVg9+y\nY28tO3pVyfsbBKSjZx+Buup80m5P+2xct/rw5y9536e7Xl9lHaBOVVoAkpaeLQJ11f6E3x4E2v/O\nzG3je99/csnu2evp36d+qV4GAh3WrSK+6MNfPCLtU2VFz26tgc5Zwe2bxLSPBHKlUGm47CxuoF6z\ncJciz1+mhMqtI/ttIVnuJ2waSKqHncXqqTPt0/ne0ShbAu2rf8JTs4ThqclkG9et9ulfGgN2Fjdc\nHSN+Tjv5BL4wt7Zvp2/ZIjH/L42egaAheu3y1U+Zuqmqyl7AtgCk8WMgmDALmUDV3vm70KGcsPB0\nUWe5ulX6tgCk8WMfwYQpK+dyEbd25VIO7Xn/OlI/a1Yu65ry6Vz8zUpfmgy2CCZUt8ld5VP/lh17\n+dK+h2q79879D8/rBHZ/YGmy2SIYQ92e9MunbTgyv9/+xF+2ChaTChqkcxexKn0CksafgWCJLNVa\n+J3j+Tdv33N4XP6alcuOOL8zONQRAKCVDmovV7kfQBl47ASWJpeBYIn0y8N3y+d3ft7re9qP66rk\nqzjrzFPmbSZT7hZW7hNsy0CaXPYRLKFeI3o68/mdr8ucfr/hnVWGey6VA5vWHx5u2pn+GbSZjKTJ\nYyBYpG4zcssROuUeu90CQ3tQGJenfXgqtVOW6dorzmZmblvXwNYtRSVpcrnWUAXdKvTOUTLlE3u5\nts5pJ5/AA4/+c8/vXOhkrWEpgxi46Ys06VxraAm1j91v/1u+bk/blK/LINBrSOU4BIEyz9/+ugwC\nYN5fagpTQz10mxTVOTmrfSx9r4p9mLn9TscfE/zSuS9gy469juqR1FNjA0G3Hbg6K/32v/0q9MVM\n3lrMDl5VlYFpz+/9DND639Dv6d4gITVbo1JD7amdLTv2HjFs85xNOxb1vYup0OsMAp3LOw+q6E0B\nSc3WiM7i8ml/Zm7bEU/i7fvkTqI1K5dx1pmnHD62UpdUqtpZPJLUUES8HtgCHANcmZmb6rxfe2qk\n80l8UgJAWeG7ro+kpTb0QBARxwB/DKwDDgK3RsSNmXlXHfcrl0CYlAq/G9f0kVSnUfQRvBK4JzP3\nZebjwCeBC5b6JuWwzlFP1OqnX+6+/KxbELBzV9JSGkUgOA24v+34YPHektq4bvXYp082rlvNmpXL\nWLNyGaedfMK8z/rNM7B1IGkpje3w0Yi4HLgcYMWKFQu6tnMFz3HSvvwEMG8C18zctsNDP8c9iEma\nHqNoETwAnNF2fHrx3jyZuTUzZzNzdvny5Qu6QdkaaK9MO487tX9WJfXS77s2rF11xHeU5/dbrdO+\nAEmjMIpAcCuwKiJWRsTxwMXAjSMoR1eDKuPO8fmdKZ3y+s6x/J3XdlPe1z4AScM09NRQZj4REb8M\nfIbW8NGPZOaddd2vs1JtH3f/pX0PcdaZpxyeGdweBNasXMbBR/4JgAtf8VQDZuO61YfPLyv8zdv3\nHP6uziWb21V92rdVIGmYGjGhTJKayNVHJUmVGAgkqeEMBJLUcAYCSWo4A4EkNdxEjBqKiEPAvYu4\n9NnAd5a4ONPC36Y3f5ve/G16G8ff5nmZOXBG7kQEgsWKiF1Vhk41kb9Nb/42vfnb9DbJv42pIUlq\nOAOBJDXctAeCraMuwBjzt+nN36Y3f5veJva3meo+AknSYNPeIpAkDTCVgSAiXh8R34iIeyJibtTl\nGScRcUZE3BQRd0XEnRGxYdRlGjcRcUxEfCUi/mbUZRknEXFyRFwXEV+PiLsj4uzBVzVDRGws/nv6\nWkR8IiJOGHzV+Ji6QBARxwB/DPxb4EXAmyPiRaMt1Vh5AvjVzHwRcBbwDn+fI2wA7h51IcbQFuDT\nmflC4MfxNwIgIk4D3gXMZuaLaS2vf/FoS7UwUxcIgFcC92Tmvsx8HPgkcMGIyzQ2MvPBzLyteP09\nWv8xL/me0ZMqIk4H1gNXjros4yQingm8BrgKIDMfz8xHR1uqsXIs8PSIOBY4Efi/Iy7PgkxjIDgN\nuL/t+CBWdF1FxAzwMmDnaEsyVj4I/Drww1EXZMysBA4BHy3SZldGxEmjLtQ4yMwHgD8E7gMeBL6b\nmX832lItzDQGAlUQET8CXA+8OzP/cdTlGQcRcT7w7czcPeqyjKFjgZcDf5qZLwMeA+x/AyLiWbSy\nDiuB5wInRcTPj7ZUCzONgeAB4Iy249OL91SIiONoBYFrMvNToy7PGDkHeENEHKCVUjwvIv5itEUa\nGweBg5lZth6voxUYBK8F9mfmocz8AfAp4CdHXKYFmcZAcCuwKiJWRsTxtDptbhxxmcZGRAStPO/d\nmfmBUZdnnGTmb2Tm6Zk5Q+v/N5/NzIl6sqtLZn4TuD8ifqx4ay1w1wiLNE7uA86KiBOL/77WMmEd\n6UPfvL5umflERPwy8Blavfcfycw7R1yscXIO8Dbgjoi4vXjvP2Xm346wTJoM7wSuKR6w9gGXjbg8\nYyEzd0bEdcBttEblfYUJm2XszGJJarhpTA1JkhbAQCBJDWcgkKSGMxBIUsMZCCSp4QwEmmgRMRMR\nX+t4bzYi/qh4fWlE/I8Ffue/L1bXvKnPOeeWq5Mu5h7SOJm6eQRSZu4Cdh3FV7wd+MXM/PslKtKS\niIhjM/OJUZdD08cWgaZGRJxZLIj2nm57CRSth89GxFcjYkdErOhyzm8BrwKuiog/iIgTIuKjEXFH\n8d0/NaAMR9yj2N9gf7ScHBFPRsRrivNvjohVEXFSRHwkIr5c3OeC4vNLI+LGiPgssCMiTi2uub1Y\n+/7VS/LjqdEMBJoKxdIH1wOX0lpmpJsPAVdn5kuBa4A/6jwhM3+HVmvirZn5HuAdrbfzJcCbgasH\nbDpyxD0y80ngG7T2x3gVrRmor46IfwGckZl7gf9Ma0mLVwI/BfxB2+qeLwcuzMx/A7wF+Exm/gSt\nPQFuRzpKBgJNg+XADbQq73/oc97ZwF8Wrz9Oq1Ie5FXAXwBk5teBe4HVi7jHLbTW838N8PvF+/+a\np4LW64C5YtmPzwEnAGWLZXtmPly8vhW4LCJ+G3hJsaeEdFQMBJoG36W18FeVin2eIm1ze/Hvd5a+\naIfdDLya1sZJfwucDJxLK0AABPBzmfkTxb8VmVkuXPZY+SWZeTOtYPIA8OcR8Qs1llkNYSDQNHgc\n+FngFyLiLX3O+988tYXgW4FbMvPJtsr3t7pcc0txLhGxmtZT+jcWco/i9ZdpLU38w8z8Z1opnSto\nBQhoLZL4zmL1SiLiZd2+PCKeB3wrM/+M1i5qLgWto2Yg0FTIzMeA84GNwI/2OO2dtNIqX6W1AuuG\nCl/9J8DTIuIO4Frg0sz8fp/zu96juOZ+4EvFebcAzwDuKI7/G3Ac8NWIuLM47uZc4B8i4ivARbT2\nEZaOiquPSlLD2SKQpIYzEEhSwxkIJKnhDASS1HAGAklqOAOBJDWcgUCSGs5AIEkN9/8BhSV91EHX\nOOYAAAAASUVORK5CYII=\n",
      "text/plain": [
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       "<matplotlib.figure.Figure at 0x10aa36cc0>"
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_y=np.loadtxt('data/youtuber_incomes.csv', delimiter=',')\n",
    "x= x_y[:, 0]\n",
    "y= x_y[:, 1]\n",
    "\n",
    "plt.plot(x, y, '+', label='train')\n",
    "plt.xlabel(\"kilo-followers\")\n",
    "plt.ylabel(\"kilo-euros\");\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "*** Aide: *** Précédemment, nous avions ajusté des fonctions affine en utilisant le modèle linéaire: en rajoutant un input `x[:,0]` partout constant. A vous d'ajouter un input maintenant!  "
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   ]
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  },
  {
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   "cell_type": "markdown",
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   "metadata": {},
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   "source": [
    "\n",
    "| Tables   |      Are      |  Cool |\n",
    "|----------|:-------------:|------:|\n",
    "| col 1 is |  left-aligned | \\$1600 |\n",
    "| col 2 is |    centered   |   \\$12 |\n",
    "| col 3 is | right-aligned |    \\$1 |\n",
    "|$\\int_0^1$ |  $$\\frac {\\exp^{-x^2}}{5} $$  |       |\n",
    "\n",
    "\n"
   ]
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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  }
 ],
 "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",
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   "version": "3.6.5"
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  }
 },
 "nbformat": 4,
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 "nbformat_minor": 2
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}