diff --git a/Projects-ML/Reg-models/Project-2_Advertising.ipynb b/Projects-ML/Reg-models/Project-2_Advertising.ipynb index 79b9640..907dfff 100644 --- a/Projects-ML/Reg-models/Project-2_Advertising.ipynb +++ b/Projects-ML/Reg-models/Project-2_Advertising.ipynb @@ -55,7 +55,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -66,6 +66,106 @@ "import matplotlib.pyplot as plt" ] }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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5br/9dm3YsEGjR492F8tjx46pRYsWmjhxoq6++uoS7ae0LBaLvv32W40fP17x8fFKSkpSdna2JkyYoJ9//rnIRXW95bHHHtPy5ct18803KyQkRBs3bpTdblenTp3073//W+3bty+y/WeffaZRo0YpPDxca9eu1eLFi7Vy5coSPdd9992nJUuWaOjQoXK5XNqwYYNCQkJ0++23a926dRo0aJDXX1958OTfyKV+jwKAJyyGJ3OfAgB8ygMPPKA33nhDL7/8Mn+JBwCgnDAyBQAVXFZWlr766itJhSflAwCA8kGZAoAK4pVXXjnnkKXk5GTdeOONOnLkiNq3b69OnTqZEw4AgCqIw/wAoILo06ePFi9erIiICDVo0EB5eXnavn27XC6XoqOjtXDhQrVs2dLsmAAAVBnenRMWAFBm/v73v6t69epat26dtm/fLsMw1LBhQw0cOFCPPPKIEhISzI4IAECVwsgUAAAAAHiAc6YAAAAAwAMc5ifJ5XIpJSVFYWFhslgsZscBAAAAYBLDMJSZman4+HhZrRcee6JMSUpJSVGdOnXMjgEAAADARxw8eFC1a9e+4DaUKUlhYWGSCt+w8PBwk9MAAAAAMIvdbledOnXcHeFCKFOS+9C+8PBwyhQAAACAEp3+wwQUAAAAAOAByhQAAAAAeIAyBQAAAAAeoEwBAAAAgAeYgMIDTqdTBQUFZseo8vz8/GSz2bg2GAAAAExBmSoFwzB05MgRpaenmx0Fp9lsNsXExCgiIoJSBQAAgHJFmSqFM0UqJiZGISEh/PJuIsMw5HA4ZLfbdfjwYZ06dUpxcXFmxwIAAEAVQpkqIafT6S5SUVFRZsfBaWFhYQoMDFRaWppiYmJks9nMjgQAAIAqggkoSujMOVIhISEmJ8GfhYaGyjAMzmMDAABAuaJMlRKH9vkeviYAAAAwA2UKAAAAADxAmQIAAAAAD1CmAAAAAMADlCl4zdSpU9W+fXv5+/tr4sSJZscBAAAAyhRlCl4TFxenSZMmaejQoWZHAQAAAMoc15mC15wpUbNmzTI3CAAAAFAOGJkCAAAAAA9QpgAAAADAA5QpAAAAAPAAZQoAAAAAPOBzZerXX3/V4MGDFR8fL4vFou++++6ij1m8eLE6dOigoKAgNWjQQG+99VbZB8U5HA6HcnNz5XQ6i9wGAAAAKiOfK1PZ2dlq06aN3njjjRJtn5SUpGuuuUY9e/bU+vXr9fjjj+vBBx/U119/XcZJ8WfPPfecgoODNX36dD3//PMKDg7Wxx9/bHYsAAAAoExYDMMwzA5xPhaLRd9+++0Fr1v06KOPavbs2dq2bZt73b333quNGzdqxYoVJXoeu92uiIgIZWRkKDw8vNhtcnNzlZSUpMTERAUFBZXqdaBs8bUBAACAt5SkG5xR4a8ztWLFCg0YMKDIuquuukrvv/++CgoK5O/vf85j8vLylJeX51622+0eP//g15fqWGbexTcsJzXDAvX9Az3MjgEAAAAf4nIZyne6VOB0qcBpKN9ReNu9zmGowOWS02XI4TTkdBlyGoacLteflove73AZcjpdcrgMudzLRtHlsz4cp5+j8LYhl8uQ05BcRuHtfk1jNKxjHbPfrhKr8GXqyJEjio2NLbIuNjZWDodDaWlpiouLO+cxkydP1qRJk7zy/Mcy83TEnuuVfQEAAKBycjhdyilw6lR+4Ueew6XcAmfhx1m38wpcynWcXl/g+uOz44/78goKH1/gdJ0uRca5xejs5dPlpyKoFVGxjjKq8GVKKjwc8Gxnjlz88/ozJkyYoPHjx7uX7Xa76tTxrAHXDAv06HFlxdfyAAAAVFROl6HM3ALZTzlkzy2Q/VTB6c+Fyzn5TmXnO5ST51R2nqPwdn7h7bPvy8pzKM/hMvvlVAi+ewJS8Sp8mapVq5aOHDlSZN3Ro0fl5+enqKioYh8TGBiowEDvlI7KcEjd+Uqnr/Hh0/sAAIAPy3e4lJ6Tr+PZ+TqZffpzTr6OZ+Ur49S5Jalw2aGsPIfZ0UvEZrXI32aRv82qAJtV/jar/P0s7tsBfqfXnbNN4bozy36n77daLPKzWmSzFn62Wosu26wW2azWs27/+b4zy9bz3n9mvzZL4bLVapHVIoUGVqx6UrHSFqNr1676/vvvi6z7+eef1bFjx2LPl8K5fK2kHDt2TMOGDZMkbdu2TW+//fYFJyEBAABVT4HTpbSsPKXa83TUnqujmXmFH/ZcHcvM04mcfJ3ILvzIzC3/UhTkb1W1QD+FBPgpJMCm0MDCzyEBNgX72xToZ1OQv1VB/jYF+p++7WdTkP9Z6/2s7uXAP90X4PdHKbJZK8YfxisjnytTWVlZ2r17t3s5KSlJGzZsUI0aNVS3bl1NmDBBycnJ+uijjyQVztz3xhtvaPz48br77ru1YsUKvf/++5oxY4ZZL6FCmjp1qt59911t2rRJTzzxhCZOnGhalpo1a2rRokX6+eef9csvv1CkAACoYgqcLh1Oz1Vy+qnCj5OnlJyeo1R7nlLPKktl8ffgQD+rwoP9FR7kd/qzv3s5Itjfva5akJ+qBdoUEuB3ujSdXZj8KDhVhM+VqTVr1qhv377u5TPnNo0cOVLTp0/X4cOHdeDAAff9iYmJmjt3rh566CG9+eabio+P12uvvaYbb7yx3LNXZHFxcZo0aZK7pF7MqFGj1KdPH40aNcqj5zty5IiGDx9eZJ3NZtMvv/wiqfDizXPnztXLL7/s0f4BAIDvcrkMpWScUlJatvYfzzmrMBV+Ts3M9UpRCg/yU1S1QFUP8VeN0EDVCD33c0RwwOmS5KfwIH8F+dsu/YlRZfhcmerTp88FDzubPn36Oet69+6tdevWlWGqyu/M6M+sWbO8tk+Xy6VXXnlFb731lo4dO6brrrtO7777rgICAlSrVi0tWrSo2MetWrVKM2bM0JtvvllhzucCAABFGYahkzkFSkrL0t5j2UpKK/zYeyxb+45nezwhg7/NopiwINUMC1RMWKBiwgMVExak2NOfz6yvHhogf5vVy68KKMrnyhQqj6eeekpLlizRwoULFRERoSFDhujdd9/V2LFjL/i4IUOGqGHDhurXr5/69eunp556qpwSAwAATxzPytOOI5nafiRTO45kakdqppLSspVxqqDU+4oKDVDt6sFKqB6shMjTH9VDlBAZrLiIIEWG+PPHVvgMyhTKxOHDh/Xqq69qx44dio+PlyTdeuutWr58eYkeCwAAfI/LZWhvWrY2JadrS7Jd208XqLSsvBLvw99mUd0aIUqMrqYGNUNVLypEtU+XpYTIYAUHcJgdKg7KFErs2muv1dKlSyVJOTk5+vLLLzVu3DhJ0mOPPabHHnvMve2CBQuUm5ur5s2bu9c5nU7ddddd5ZoZAAB4xuUytO94tjYlZ2jToQz9npyhLckZys53lujxCZHBSowO/eOjZqgaRIcqITJYfhx+h0qCMoUS++GHH9y3LzYBxYkTJ3T77bdr2rRp5ZQOAABcitwCp34/lKE1+09o7b6TWnvgpNJzLn6YXo3QADWJDVOTWmFqWqvwc+PYsAp3vSDAE3yXQ5LkcDjkcDjkdDrlcDiUm5srf39/2WyeDbW3b99e//rXv7Rt2zY1a9ZMx48f1+rVq3X11Vd7OTkAAPBEVp5Dq5KOa+XeE1qz74Q2J9uV77zwpBAJkcFqlRChVrUj1CohQk3jwlSzWiDnMKHKokxBkvTcc89p0qRJ7uXnn39e06ZN83jq8549e+qhhx7SgAEDdPLkScXGxuqee+6hTAEAYJJ8h0sbDqZr2e40Ldudpg0H0+VwnX8G5eoh/upQr7ra1I50l6eoaoHlmBjwfRbjQvOQVxF2u10RERHKyMhQeHh4sdvk5uYqKSlJiYmJCgoKKueEuBC+NgAAFO/giRwt2JaqX3ce029JJ5RzgfOdGkSHqkO96upYv7o61q+hBtGhjDihSipJNziDkSkAAIBKwukytOFguhZsS9Uv21K1MzXrvNs2qBmqHpdFq1vDKHWsX0PRjDoBpUaZAgAAqMDyHE4t3nFMP29N1cLtR3U8O7/Y7WqGBarHZdHqflm0ul8WpbiI4HJOClQ+lCkAAIAKxuF0afme4/p+Y4rmbTmizFzHOdtYLFK7OpG6olmsrmgWoyaxYRy2B3gZZQoAAKACcLkMrdl/Ut9vTNHcTYeLHYEK9repV+NoXdEsVv2axnDoHlDGKFMAAAA+LCX9lL5cc1Az1xxScvqpc+6vFuinAc1jdW2bOHVrGK0gf88uawKg9ChTpcTkh76HrwkAoLIpcLr0y7aj+nz1AS3eeUx//lEX6GdV/2axGtwmTn2axFCgAJNQpkrI399fkpSTk6PgYE7Y9CXZ2dmyWCzurxEAABXVvrRsfb76oL5ae0hpWXlF7rNapF6Na2po2wT1bx6raoH8GgeYjX+FJWSz2RQZGamjR49KkkJCQjiJ00SGYcjhcMhut8tutysyMlI2G3+VAwBUPIZh6LekE3pvyV4t2Hb0nPsTIoN1S6c6uqlDbcVH8gddwJdQpkqhVq1akuQuVDCfzWZTXFycIiIizI4CAECpFDhdmrvpsN5dslebk+1F7vOzWjSgRaxu6VRXPS6Lls3KH3ABX0SZKgWLxaK4uDjFxMSooKDA7DhVnp+fn2w2GyOEAIAKJeNUgT5fdUDTl+/T4YzcIvfFRQRpRNf6GtaxNjPxARUAZcoDNpuNQ8oAAECpZOQU6L2lezVt2T5l5RW9LlTLhHDd3bOBrmkVJ3+b1aSEAEqLMgUAAFCG7LkF+mBpkt5fkqTMP5Wo/s1idFfPBuqSWIMjLYAKiDIFAABQBrLyHPpw+T698+teZZz64/QAf5tFN3Worbt6NlDDmtVMTAjgUlGmAAAAvCi3wKnpy/fp7cV7dDLnjxJls1o0rENtje17merUCDExIQBvoUwBAAB4gWEYmrvpiF6Yu03J6afc660W6Yb2tfVAv8tULyrUxIQAvI0yBQAAcIm2pGRo0vdbtSrphHudxSINbZugB/pdpgYczgdUSpQpAAAAD6Vl5emln3fq89UHZBh/rO/ZKFpPXttcjWPDzAsHoMxRpgAAAEqpwOnSh8v36dUFu4rM0Fc/KkT/HNRcVzSLYXY+oAqgTAEAAJTC+gMnNeGbTdp+JNO9rlqgnx684jKN7FZfgX5cixKoKihTAAAAJZCV59B/ftqhD1fscx/SZ7FIN3eoo39c1UQ1wwLNDQig3FGmAAAALmLJrmN69KvflZKR617XIj5ck29opda1I80LBsBUlCkAAIDzyMpz6IW52/TZbwfc64L9bRp/ZWON7l5ffjariekAmI0yBQAAUIyVe4/r/77cWOSaUd0vi9L/u6E1F90FIIkyBQAAUESB06VXFuzUlEV73OdGhQTYNOGaZrq9S11m6QPgRpkCAAA4bf/xbD34+QZtPJjuXtc5sYb+c1Mb1Y1iNApAUZQpAAAAST/8nqLHvt6krNPXjfKzWjR+QGPd06uhbFZGowCcizIFAACqtDyHUy/M2aYPV+x3r6sfFaJXh7dTmzqR5gUD4PMoUwAAoMo6dDJHYz9dp42HMtzrhraN1/PXt1JoIL8mAbgw/pcAAABV0vI9aRr76TqdzCmQJAX4WTVxcAvd2rkOk0wAKBHKFAAAqFIMw9D05fv03JxtcroKp+urFxWiN29rr5YJESanA1CRUKYAAECVkedw6olvN+urtYfc63o3rqnXbm2niGB/E5MBqIgoUwAAoEo4mZ2vez5eq1X7TrjX3denof4xoAmz9QHwCGUKAABUeklp2RozfbWS0rIlSUH+Vv37pjYa3Cbe5GQAKjLKFAAAqNRWJZ3QXz9eo/TTE03UDAvUeyM6Mu05gEtGmQIAAJXWT1uO6IEZ65XvcEmSmsSG6YPRnZQQGWxyMgCVAWUKAABUSjNWHdAT327S6Qn71LNRtKb8pb3CgphoAoB3UKYAAEClYhiG3vjfbr00f6d73Q3tEvSvm1rL32Y1MRmAyoYyBQAAKg3DMPTcnG16f2mSe909vRro0aubysqMfQC8jDIFAAAqBZfL0JOzNuvT3w641z1xTTPd3auBiakAVGaUKQAAUOE5nC498vXv+mZdsiTJYpH+dUNr3dypjsnJAFRmlCkAAFChOZwujftig374/bAkyWa16L83t9GQtgkmJwNQ2VGmAABAheV0Gfq/mRvdRcrfZtHrt7bX1S1rmZwMQFVAmQIAABWS02Xo4ZkbNWtDiiQpwGbVW3e0V7+msSYnA1BVMD8oAACocFwuQ499/bu+WV94jpS/zaIpf6FIAShflCkAAFChGIahid9v0cy1hyRJftbCQ/v6N6dIAShflCkAAFChvDx/pz5asV9S4WQTr93ajnOkAJiCMgUAACqM95bs1Wv/2+1efvHG1rqmVZyJiQBUZZQpAABQIcxcc1DPzdnmXn56cHPd2KG2iYkAVHWUKQAA4PMW7jiqx77Z5F4e17+RRndPNDERAFCmAACAj9t0KENjP10np8uQJI3qVl9/v6KRyakAgDIFAAB82METORo9fbVy8p2SpEGt4vTUtc1lsVhMTgYAlCkAAOCj0nPyNXLaKqVl5UmSOtWvrpdubiOrlSIFwDdQpgAAgM/Jd7h07ydrtfdYtiSpYc1QvTuio4L8bSYnA4A/UKYAAIBPMQxDT8/erJV7T0iSoqsFaProzooMCTA5GQAURZkCAAA+ZdqyfZqx6qAkKcDPqndGdFSdGiEmpwKAc1GmAACAz1i446iem7PVvfzija3Vvm51ExMBwPlRpgAAgE/YeyxLD362XqdnQNf9fS/T0HYJ5oYCgAugTAEAANNl5Tl0z8drlZnnkCRd1SJW469sbHIqALgwyhQAADCVYRh65KuN2nU0S5LUOLaa/ntzW6ZAB+DzKFMAAMBUby3eq7mbjkiSwoL89PYdHRUa6GdyKgC4OMoUAAAwzZJdx/Tvn7a7l1+5pa0So0NNTAQAJUeZAgAApjiSkau/f77BPeHEuP6NdEWzWHNDAUApUKYAAEC5czhdenDGep3Izpck9W1SUw/2a2RyKgAoHcoUAAAod/+dv1Or9p2QJMVHBDHhBIAKiTIFAADK1cIdRzVl0R5Jkp/Votdva6/qoQEmpwKA0qNMAQCAcpNqz9X4Lza4lx+5uok61KtuXiAAuASUKQAAUC5cLkPjv9ygkzkFkqT+zWJ0d88GJqcCAM9RpgAAQLl4d8leLdt9XJIUGx6of9/URhYL50kBqLgoUwAAoMxtTs7Qf37eIUmyWKSXb27LeVIAKjzKFAAAKFM5+Q49OGO9CpyFF5T6a68G6nZZtMmpAODSUaYAAECZem7ONu1Ny5YktUqI0P9d2cTkRADgHZQpAABQZhbtOKrPfjsgSQr2t+nV4W0V4MevHwAqB/43AwAAZSIjp0CPfv27e/mJQc3UoGY1ExMBgHdRpgAAQJl4evZmpdrzJEk9G0XrL13qmpwIALyLMgUAALzux02H9d2GFElSWJCfXrypNdOgA6h0KFMAAMCr0rLy9MR3m93LzwxpobiIYBMTAUDZoEwBAACvmjh7i05k50uSrm5RS0PbJpicCADKBmUKAAB4zc9bjuiH3w9LkiJD/PXc9S05vA9ApUWZAgAAXpFxqkBPzvrj8L6nBzdXdLVAExMBQNmiTAEAAK/4fz9uc8/e17dJTQ7vA1DpUaYAAMAlW747TTNWHZQkhQbY9Pz1rTi8D0ClR5kCAACXJLfAqQnfbnIvP3ZNM8VHMnsfgMqPMgUAAC7JlIW7tf94jiSpU/3q+ktnLs4LoGqgTAEAAI/tPpqlqYv3SJL8bRa9cH0rWa0c3gegaqBMAQAAjxiGoSe+3aQCpyFJ+muvBmoUG2ZyKgAoP5QpAADgkW/WJeu3pBOSpDo1gnV/30YmJwKA8kWZAgAApZaek6/n525zLz87pKWCA2wmJgKA8keZAgAApfbvn3boRHa+JGlQqzj1aRJjciIAKH+UKQAAUCqbkzP02aoDkgqvKfXktc1NTgQA5qBMAQCAEnO5DD01a7OMwjkn9OAVjVQrIsjcUABgEsoUAAAosW/XJ2vdgXRJUoOaoRrdPdHcQABgIsoUAAAoEXtugSb/uN29PHFwCwX48asEgKqL/wEBAECJvLZgl9Ky8iRJV7eopV6Na5qcCADMRZkCAAAXtedYlqYv3ydJCvSz6p/XNjM3EAD4AMoUAAC4qMlzt8nhKpx14t7eDVW7eojJiQDAfD5ZpqZMmaLExEQFBQWpQ4cOWrJkyQW3//TTT9WmTRuFhIQoLi5Oo0eP1vHjx8spLQAAldvSXWlasO2oJKlWeJDu6d3A5EQA4Bt8rkx98cUXGjdunJ544gmtX79ePXv21MCBA3XgwIFit1+6dKlGjBihO++8U1u2bNHMmTO1evVq3XXXXeWcHACAysfpMvTcnK3u5UeubqKQAD8TEwGA7/C5MvXf//5Xd955p+666y41a9ZMr7zyiurUqaOpU6cWu/3KlStVv359Pfjgg0pMTFSPHj10zz33aM2aNed9jry8PNnt9iIfAADgXF+sPqjtRzIlSa1rR2ho2wSTEwGA7/CpMpWfn6+1a9dqwIABRdYPGDBAy5cvL/Yx3bp106FDhzR37lwZhqHU1FR99dVXGjRo0HmfZ/LkyYqIiHB/1KlTx6uvAwCAysCeW6CXft7hXn7y2uayWi0mJgIA3+JTZSotLU1Op1OxsbFF1sfGxurIkSPFPqZbt2769NNPdcsttyggIEC1atVSZGSkXn/99fM+z4QJE5SRkeH+OHjwoFdfBwAAlcFbi/boeHa+JGlQ6zh1ql/D5EQA4Ft8qkydYbEU/auXYRjnrDtj69atevDBB/XUU09p7dq1mjdvnpKSknTvvfeed/+BgYEKDw8v8gEAAP5wOOOU3l+aJEkKsFn12NVNTU4EAL7Hp84gjY6Ols1mO2cU6ujRo+eMVp0xefJkde/eXQ8//LAkqXXr1goNDVXPnj313HPPKS4ursxzAwBQ2bw8f6fyHC5J0oiu9VSnBlOhA8Cf+dTIVEBAgDp06KD58+cXWT9//nx169at2Mfk5OTIai36Mmw2m6TCES0AAFA6O45k6qu1hyRJYUF+Gtv3MpMTAYBv8qkyJUnjx4/Xe++9pw8++EDbtm3TQw89pAMHDrgP25swYYJGjBjh3n7w4MH65ptvNHXqVO3du1fLli3Tgw8+qM6dOys+Pt6slwEAQIX1r3nbdfr6vBrb9zJVDw0wNxAA+CifOsxPkm655RYdP35czzzzjA4fPqyWLVtq7ty5qlevniTp8OHDRa45NWrUKGVmZuqNN97Q//3f/ykyMlL9+vXTv/71L7NeAgAAFdaKPcf1v+2FF+iNiwjSqG71zQ0EAD7MYnAsnOx2uyIiIpSRkcFkFACAKsswDA19c5k2HsqQJP1nWBvd1KG2yakAoHyVphv43GF+AADAHD9tSXUXqaa1wnR9Oy7QCwAXQpkCAAByugz9d/4fF+h9+KomsnGBXgC4IMoUAADQ7I3J2pmaJUlqXzdS/ZrGmJwIAHwfZQoAgCou3+HSy/N3uZcfvqqpLBZGpQDgYihTAABUcV+uOagDJ3IkST0ui1bXhlEmJwKAioEyBQBAFZZb4NRrv/wxKvWPq5qYmAYAKhbKFAAAVdjHK/braGaeJGlA81i1rRNpbiAAqEAoUwAAVFE5+Q69tXiPJMlikf5vAKNSAFAalCkAAKqoj1fs1/HsfEnSoFZxalIrzOREAFCxUKYAAKiCsvMcevvXvZIKR6X+fkUjkxMBQMVDmQIAoAr6aMV+nTg9KjW4dbwaxTIqBQClRZkCAKCKyc5z6J1fC8+VslqkBxmVAgCPUKYAAKhiPlyxTydzCiRJ17WJ12Ux1UxOBAAVE2UKAIAqJDvPoXdPnytltUgPMCoFAB6jTAEAUIXMWHXAPSo1pG2CGtZkVAoAPEWZAgCgishzOPXOWTP4je3b0OREAFCxUaYAAKgivl6brKOZeZKkq5rX0mUxzOAHAJeCMgUAQBXgcLr01uI97uW/MSoFAJeMMgUAQBUwZ9NhHTiRI0nq2SharWtHmhsIACoByhQAAJWcy2VoysI/RqXG9r3MxDQAUHlQpgAAqOR+2X5UO1IzJUkd6lVXl8QaJicCgMqBMgUAQCVmGIbeWLjbvTy2b0NZLBYTEwFA5UGZAgCgElux57g2HkyXJDWtFaa+TWLMDQQAlQhlCgCASuzNRX+MSv2t72WMSgGAF1GmAACopNYfOKllu49LkupHhWhQqziTEwFA5UKZAgCgkpqy6I8Z/O7t3VA2K6NSAOBNlCkAACqhHUcyNX9rqiSpVniQrm+fYHIiAKh8KFMAAFRCU886V+ruXg0U6GczMQ0AVE6UKQAAKpmDJ3I0e2OKJKl6iL9u7VzH5EQAUDlRpgAAqGSmLdsnl1F4e1S3RIUE+JkbCAAqKcoUAACViD23QF+sPiBJCvSz6o6u9UxOBACVF2UKAIBK5ItVB5Wd75Qk3dihtmqEBpicCAAqL8oUAACVRIHTpWnLktzLd/ZINDENAFR+lCkAACqJHzcfUUpGriTpiqYxalizmsmJAKByo0wBAFAJGIah95bsdS/f2ZNRKQAoa5QpAAAqgTX7T+r3QxmSpOZx4eraIMrkRABQ+VGmAACoBM4elbqrZ6IsFouJaQCgaqBMAQBQwe1Ly9bPW1MlSbHhgbq2dbzJiQCgaqBMAQBQwU1bliTj9EV6R3arrwA/frwDQHngf1sAACqwjJwCfbnmkCQp2N+m2zrXNTkRAFQdlCkAACqwz1Yd0KmCwov0DutYW5EhXKQXAMoLZQoAgAoq3+HS9OWFF+m1WKTR3ZkOHQDKE2UKAIAKas6mFKXa8yRJ/ZvFKjE61OREAFC1UKYAAKiACi/Sm+RevqsHo1IAUN4oUwAAVECrkk5oS4pdktS6doQ6J9YwOREAVD2UKQAAKqCPVux33x7TnYv0AoAZKFMAAFQwRzJyNW/LEUlSdLUADWxVy+REAFA1UaYAAKhgPlt1QE5X4VV6b+1cV4F+NpMTAUDVRJkCAKACyXe49NlvByRJNqtFt3XhIr0AYBbKFAAAFciPmw8rLatwOvQBzWMVFxFsciIAqLooUwAAVCBnTzwxomt984IAAChTAABUFJuTM7R2/0lJUuPYarq8AdOhA4CZKFMAAFQQH/9pVIrp0AHAXJQpAAAqgPScfH23IVmSFBbop+vbJZicCABAmQIAoAKYueaQ8hwuSdKNHWorNNDP5EQAAMoUAAA+zuky9PHKPw7xu6NrPRPTAADOoEwBAODjFu88qgMnciRJPRtFq2HNaiYnAgBIlCkAAHzeh8uZDh0AfBFlCgAAH7YvLVuLdx6TJCVEBqtf0xiTEwEAzqBMAQDgw/58rpTNynToAOArKFMAAPionHyHvlxzUJIU6GfVLR3rmJwIAHA2yhQAAD7q+40pysx1SJIGt4lX9dAAkxMBAM5GmQIAwEd99tsB9+3bL2c6dADwNZQpAAB80ObkDG08lCFJah4Xrja1I0xOBAD4M8oUAAA+aMaqP0albutSVxYLE08AgK+hTAEA4GOy8xyatSFFkhQSYNOQtvEmJwIAFIcyBQCAj/l+Y4qy8gonnriuTbzCgvxNTgQAKA5lCgAAH/PZnw7xAwD4JsoUAAA+ZHNyhn4/PfFEi/hwtUpg4gkA8FWUKQAAfMifR6WYeAIAfBdlCgAAH5Gd59Cs9cmSCieeuK4NE08AgC+jTAEA4CNmb0xRdr5TkjSkLRNPAICvo0wBAOAjilxbqnM9E5MAAEqCMgUAgA84e+KJlgnhalWbiScAwNdRpgAA8AGfMSoFABUOZQoAAJNlnTXxRGiATde1ZeIJAKgIKFMAAJjs+7MmnriubYKqBfqZnAgAUBKUKQAATPbZb2cf4lfXxCQAgNKgTAEAYKLNyRnalFw48USrhAgmngCACoQyBQCAiT5f/ceo1K2MSgFAhUKZAgDAJLkFTs3akCJJCva3aXCbOJMTAQBKgzIFAIBJ5m0+osxchyRpUOs4hQX5m5wIAFAalCkAAEzy5ZqD7ts3d6xjYhIAgCcuae5Vh8OhHTt2KD09XU6ns9htevXqdSlPAQBApXTwRI6W7zkuSUqMDlWn+tVNTgQAKC2PypRhGHrqqaf0+uuvKzMz84Lbnq9kAQBQlc08a1RqWMfaslgsJqYBAHjCozL17LPP6vnnn1dkZKRGjBih2rVry8+PCwwCAFASTpehr9YekiRZLdKN7WubnAgA4AmPGtAHH3ygevXqac2aNYqKivJ2JgAAKrWlu9OUkpErSerbJEax4UEmJwIAeMKjCShSU1M1dOhQihQAAB74ssghfkw8AQAVlUdlKjExUXa73dtZAACo9E5m52v+llRJUlRogPo1jTE5EQDAUx6Vqfvvv18//PCDjh496u08AABUat9tSFa+0yVJuqF9ggL8uEoJAFRUHp0zde2112rRokXq1q2bnnrqKbVr104RERHFblu3bt1LCggAQGVhGIa+WM21pQCgsvCoTNWvX18Wi0WGYWj06NHn3c5iscjhcHgcDgCAymRzsl3bjxReUqRd3Ug1ig0zOREA4FJ4VKZGjBjB9TAAACilsyeeYFQKACo+j8rU9OnTvRwDAIDKLbfAqe82JEuSgv1turZ1nMmJAACXirNeAQAoBz9tOaLM3MJD369pFaewIH+TEwEALpVHI1NnW758uTZs2KCMjAyFh4erbdu26t69uzeyAQBQaRSdeKK2iUkAAN7icZn67bffNHLkSO3atUtS4QxFZ86jatSokaZNm6auXbt6JyUAABXYwRM5Wr7nuCSpflSIOifWMDkRAMAbPCpT27ZtU//+/ZWdna2rrrpKffr0Ua1atZSamqpFixZp3rx5uuqqq7Ry5Uo1b97c25kBAKhQvlp7yH17WMc6TOIEAJWER2Vq0qRJys/P108//aQrr7yyyH2PPPKIFixYoEGDBumZZ57R559/7pWgAABURC6Xoa/XFZYpq0W6sT2H+AFAZeHRBBQLFy7UTTfddE6ROqN///668cYbtXDhwksKBwBARbdq3wkdOnlKktSjUU3ViggyOREAwFs8KlMZGRmqX7/+BbdJTExURkaGJ7sHAKDSOPsQvxvbJ5iYBADgbR6Vqfj4eK1cufKC2/z222+Kj4/3KNSUKVOUmJiooKAgdejQQUuWLLng9nl5eXriiSdUr149BQYGqmHDhvrggw88em4AALwlJ9+hHzcdliSFBfrpqha1TE4EAPAmj8rUkCFDtGjRIj355JPKzc0tcl9ubq6efvppLVy4UEOGDCn1vr/44guNGzdOTzzxhNavX6+ePXtq4MCBOnDgwHkfc/PNN+uXX37R+++/rx07dmjGjBlq2rRpqZ8bAABvmrf5iLLznZKka9vEKcjfZnIiAIA3WQzDMEr7oBMnTqhLly7au3evoqKi1LlzZ8XGxio1NVWrV6/WsWPH1KBBA61atUo1apRu+tcuXbqoffv2mjp1qntds2bNNHToUE2ePPmc7efNm6fhw4dr7969pX6uM+x2uyIiItzXygIAwBtue3ele0r0r+/rqg71mBIdAHxdabqBRyNTNWrU0G+//aZRo0YpOztbc+fO1bRp0zR37lxlZmZq9OjRWrlyZanLTX5+vtauXasBAwYUWT9gwAAtX7682MfMnj1bHTt21IsvvqiEhAQ1btxY//jHP3Tq1KnzPk9eXp7sdnuRDwAAvOnQyRyt2FtYpBKjQ9W+bnWTEwEAvM3ji/bWqFFD77//vt566y1t375ddrtd4eHhatq0qfz9/T3aZ1pampxOp2JjY4usj42N1ZEjR4p9zN69e7V06VIFBQXp22+/VVpamv72t7/pxIkT5z1vavLkyZo0aZJHGQEAKIlv1yXrzLEfN7RL4NpSAFAJeVymzvD391erVq28kcXtzz9wDMM47w8hl8sli8WiTz/9VBEREZKk//73v7rpppv05ptvKjg4+JzHTJgwQePHj3cv2+121alTx4uvAABQlRmGoW/WJ0uSLBbphg5cWwoAKqNLLlPeFB0dLZvNds4o1NGjR88ZrTojLi5OCQkJ7iIlFZ5jZRiGDh06pEaNGp3zmMDAQAUGBno3PAAAp607cFJJadmSpK4NopQQee4f9gAAFV+JylS/fv1ksVj04Ycfqnbt2urXr1+Jdm6xWPTLL7+UOExAQIA6dOig+fPn6/rrr3evnz9//nlnBuzevbtmzpyprKwsVatWTZK0c+dOWa1W1a7NXwIBAOXv7GtL3cSoFABUWiUqU4sWLZLFYlFOTo57uSQ8OT58/PjxuuOOO9SxY0d17dpV77zzjg4cOKB7771XUuEhesnJyfroo48kSbfddpueffZZjR49WpMmTVJaWpoefvhhjRkzpthD/AAAKEu5BU79sLHw2lKhATZd3ZJrSwFAZVWiMuVyuS647E233HKLjh8/rmeeeUaHDx9Wy5YtNXfuXNWrV0+SdPjw4SLXnKpWrZrmz5+vBx54QB07dlRUVJRuvvlmPffcc2WWEQCA8/lpyxFl5jkkSQNbxSkkwKeOqAcAeJFH15mqbLjOFADAW0Z8sEq/7jwmSfr8r5fr8gZRJicCAJRGmV9nasyYMZo9e/YFt5k7d67GjBnjye4BAKiQjmTkaumuwiJVu3qwOtfnIr0AUJl5VKamT5+uDRs2XHCbTZs26cMPP/Rk9wAAVEjfrk+W6/TxHje2ry2rlWtLAUBl5lGZKonc3Fz5+XGcOACgajAMQ1+v+2MWvxvbM4sfAFR2Hred883Ud+b6TnPnzlV8fLzHwQAAqEh+P5Sh3UezJEmd69dQ3agQkxMBAMpaiUemrFarbDabbDabJGnixInu5bM//Pz8VL9+fa1evVrDhw8vs+AAAPiSs0eluLYUAFQNJR6Z6tWrl3s06tdff1XdunVVv379c7az2WyqUaOG+vXrp7vvvttrQQEA8FUFTpe+35giSQr0s2pgK64tBQBVQYnL1NkX6rVarRo9erSeeuqpssgEAECFsnjHMZ3MKZAkDWhRS2FB/iYnAgCUB4/OmSrLi/YCAFDRfLsh2X37+nacLwwAVYVHs/kdOnRIs2fPVnp6erH3nzx5UrNnz1ZycnKx9wMAUFnYcws0f2uqJCkqNEA9G9U0OREAoLx4VKaef/55jR49WsHBwcXeHxISojFjxmjy5MmXFA4AAF83b9MR5TsKj9gY3CZe/rYyu+oIAMDHePQ//i+//KIBAwYoMDCw2PsDAwM1YMAALViw4JLCAQDg675d/8dRGEPbJZiYBABQ3jwqU8nJycXO5He2evXqcZgfAKBSS0k/pZVJxyVJDaJD1aZ2hMmJAADlyaMyFRAQILvdfsFt7Hb7eS/sCwBAZTBrQ4oMo/D20HYJ/NwDgCrGozLVunVrff/998rLyyv2/tzcXM2ePVutWrW6pHAAAPgqwzD07fo/LtQ7tC2H+AFAVeNRmRozZowOHTqk6667Tnv37i1y3549ezRkyBClpKTorrvu8kpIAAB8zdbDdu1MzZIkdaxXXXWjQkxOBAAobx5dZ2rkyJH68ccf9eWXX6pp06ZKTExUQkKCkpOTlZSUJIfDoVtuuUWjR4/2dl4AAHzCt+vOurZUe0alAKAq8qhMSdLnn3+uXr166c0339S2bdu0a9cuSVLz5s01duxY3XfffV4LCQCAL3G6DM3amCJJ8rdZNKhVnMmJAABm8LhMSdLf/vY3/e1vf1NOTo7S09MVERGh0NBQb2UDAMAnLd+TpmOZhecN920So8iQAJMTAQDMcEll6oyQkBCFhHCsOACgajj7EL8bOMQPAKqsSy5T2dnZSk9Pl9PpLPb+unXrXupTAADgM3LyHZq35YgkKTzIT32bxpicCABgFo/L1Pvvv6+XXnpJO3bsOO82FotFDofD06cAAMDn/LwlVTn5hX9AHNQ6XoF+NpMTAQDM4lGZmjp1qsaOHSs/Pz/16tVLtWvXlp+fV44YBADAp327/qxZ/NpxiB8AVGUeNaBXXnlF0dHRWrp0qRo3buztTAAA+KSjmblasuuYJKl29WB1rFfd5EQAADN5dNHe/fv36+abb6ZIAQCqlO83HpbLKLw9tG2CrFaLuYEAAKbyqEzFx8efd8IJAAAqq+/OOsRvKIf4AUCV51GZGj16tH788UdlZ2d7Ow8AAD5p99FMbUrOkCS1rh2hy2KqmZwIAGA2j8rU448/rs6dO+vKK6/Ur7/+qszMTG/nAgDAp5w98cTQtoxKAQA8nIAiIKDwSu+GYahv377n3Y6p0QEAlYHLZei79SmSJJvVosFt4k1OBADwBR6VqZ49e8pi4aRbAEDVsHrfCSWnn5Ik9WwUrZphgSYnAgD4Ao/K1KJFi7wcAwAA38W1pQAAxfHonCkAAKqK3AKn5mw6LEkKDbBpQPNaJicCAPgKyhQAABewcPtRZeYWnv97VctaCg6wmZwIAOArPDrMr1+/fiXazmKx6JdffvHkKQAA8AnfnHWI3w3tapuYBADga8rknCmLxSLDMJikAgBQoZ3MzteiHUclSbHhgeraMMrkRAAAX+LRYX4ul6vYj/T0dP3vf/9Tly5ddOONNyo/P9/beQEAKDc/bDqsAqchSRrSNkE2K38kBAD8wavnTIWHh6tPnz766aeftHr1aj3//PPe3D0AAOXqOy7UCwC4gDKZgCIsLEwDBw7UtGnTymL3AACUuf3Hs7V2/0lJUtNaYWoeH25yIgCArymz2fysVqsOHz5cVrsHAKBMfbc+xX17KNeWAgAUo0zK1N69ezVz5kzVq1evLHYPAECZMgxD364/JEmyWKQhbeNNTgQA8EUezeY3ZsyYYtc7HA4lJydr6dKlKigo0MSJEy8lGwAApthwMF37judIkro2iFJcRLDJiQAAvsijMjV9+vQL3t+4cWONHz9ef/3rXz3ZPQAApioy8QSH+AEAzsOjMpWUlFTseqvVqsjISIWFhV1SKAAAzFLgdOn73wvP+Q30s2pgy1omJwIA+KoSlakxY8Zo6NChuu666yQVXpQ3MjJS4eHMbAQAqFx+3XlMJ7ILr5N4ZfNYhQX5m5wIAOCrSjQBxfTp07Vhwwb3cmJiol555ZUyigQAgHm+OesQvxvac4gfAOD8SlSmwsPDlZmZ6V42DKPMAgEAYBZ7boEWbE2VJNUIDVDPRjVNTgQA8GUlOsyvWbNmmjFjhjp37qzY2FhJ0r59+/Trr79e9LG9evW6tIQAAJSTeZuOKM/hkiQNbh0nf1uZXY4RAFAJWIwSDDPNmzdP119/vfLzC48hNwxDFoulRE/gdDovLWE5sNvtioiIUEZGBueBAUAVdus7K7Vi73FJ0ndju6ttnUhzAwEAyl1pukGJRqauvvpqbdu2Tb/88ouSk5M1ceJE9e7dW7179/ZKYAAAzJaSfkorkwqLVGJ0qNrUjjA5EQDA15V4avT69evrzjvvlCRNnDhRffr00VNPPVVmwQAAKE+zNqTozLEa17dLKPERGACAqsvj60xFRkZ6OQoAAOYwDEPfrj/kXh7alln8AAAX51GZqlevnrdzAABgmq2H7dqZmiVJ6livuupGhZicCABQETBNEQCgyvvurGtLDW3HqBQAoGQoUwCAKs3pMjRrQ4okyd9m0aBWcSYnAgBUFJQpAECVtnxPmo5m5kmS+jaJUfXQAJMTAQAqCsoUAKBK+/asQ/yu5xA/AEApUKYAAFVWTr5D8zYfkSSFB/mpb9MYkxMBACoSj8qU0+mU3W6Xy+Uq9n6XyyW73S6n03lJ4QAAKEvzt6YqJ7/wZ9Wg1nEK8reZnAgAUJF4VKYmTZqkmJgYHT9+vNj7jx8/rtjYWD3//POXFA4AgLL0zbqzD/GrbWISAEBF5FGZ+uGHH3TFFVeoZs2axd5fs2ZN9e/fX7NmzbqkcAAAlJVjmXlasuuYJCkhMlgd61U3OREAoKLxqEzt3btXTZs2veA2TZo0UVJSkkehAAAoa7M3pshlFN4e2i5eVqvF3EAAgArHozLlcDhktV74oRaLRbm5uR6FAgCgrH3HLH4AgEvkUZlq2LCh/ve//11wm//9739KTEz0KBQAAGVp99FMbUrOkCS1SojQZTFhJicCAFREHpWpG2+8URs2bNBTTz11zox9TqdTTz75pDZs2KBhw4Z5JSQAAN7EtaUAAN5gMQzDKO2DsrKy1KVLF23fvl0NGzZU3759lZCQoOTkZC1cuFB79uxRs2bNtHLlSlWrVq0scnuV3W5XRESEMjIyFB4ebnYcAEAZcrkM9XxxoZLTT8lmtWjlhCtUMyzQ7FgAAB9Rmm7g58kTVKtWTb/++qvuu+8+ff3119q9e7f7PqvVqptuuklTpkypEEUKAFC1rN53QsnppyRJPRtFU6QAAB7zqExJUlRUlL788ksdPXpUa9asUXp6uiIjI9WxY0fFxHAFeQCAb/puA4f4AQC8w+MydUZMTIyuueYab2QBAKBM5RY49cPvhyVJIQE2Xdk81uREAICKzKMJKAAAqIgWbj+qzFyHJOnqlrUUEnDJf1MEAFRhJfopMmbMGFksFr3wwguKjY3VmDFjSrRzi8Wi999//5ICAgDgLcziBwDwphLN5me1WmWxWLRt2zY1btz4ohfsde/cYjln6nRfxGx+AFD5nczOV+cXFqjAaSgmLFArJlwhm9VidiwAgI/x+mx+SUlJkqSEhIQiywAAVBRzNh1WgbPw74dD2sZTpAAAl6xEZapevXoXXAYAwNcVPcSvtolJAACVhUcTUDzzzDP69ddfL7jNsmXL9Mwzz3gUCgAAbzpwPEdr95+UJDWJDVOzuDCTEwEAKgOPytTEiRO1aNGiC26zdOlSTZo0yZPdAwDgVWePSg1tlyCLhUP8AACXrsymRs/Pzy/xRBUAAJQVwzD0zfpDkiSLRRraLt7kRACAysLjtnOhv+rl5+dryZIlio3lYogAAHOtO3BS+4/nSJK6N4xWXESwyYkAAJVFia9W2KBBgyLLL7/8sqZNm3bOdk6nU2lpacrNzdXdd9996QkBALgEX6/j2lIAgLJR4jLlcrnco1EWi0WGYai4S1T5+/urRYsW6tevn5588knvJQUAoJTyHE79sDFFkhTsb9PVLWuZnAgAUJmUuEzt27fPfdtqteqhhx7SU089VRaZAADwiv9tOyp7rkOSNLBlLYUGlvjHHgAAF+XRT5WkpCRFRkZ6OQoAAN519iF+N7Tn2lIAAO/yqEyd76K9SUlJWrBggYKDg3X99dcrNDT0ksIBAOCp41l5WrTjqCSpVniQujaMMjkRAKCy8Wg2v3/9619q1KiRTp486V63aNEitWrVSvfee69GjhypDh06FLkfAIDy9P3GFDlchef2DmkXL5uVa0sBALzLozI1a9YsJSQkqHr16u51Dz/8sFwulyZNmqT77rtPO3fu1Kuvvuq1oAAAlMbZF+q9oR2H+AEAvM+jMrV37161aNHCvXzw4EGtXbtWY8eO1T//+U+98cYbuuKKK/T11197LSgAACW1+2imNh7KkCS1TAhXk1phJicCAFRGHpWp9PT0IhNQLF26VBaLRYMHD3ava9++vQ4cOHDJAQEAKK1v1jEqBQAoex6VqdjYWO3fv9+9PH/+fAUGBqpLly7udbm5ue7rUgEAUF5cLkPfnT7Ez2a16Lq28SYnAgBUVh7N5tepUyfNmjVLc+bMUVBQkL788kv16dNHgYGB7m327t2r+Hh+gAEAytfKpONKyciVJPVuXFPR1QIv8ggAADzj0cjU448/LofDoeuuu04DBgxQbm6uJkyY4L4/MzNTCxcuLDJSBQBAeShyiF/7BBOTAAAqO49Gptq3b6+VK1fq448/liTddNNNuvzyy933b9y4UVdeeaVuu+0276QEAKAEcvId+nHTYUlSWJCf+jeLNTkRAKAy86hMSVKbNm3Upk2bYu/r0aOHevTo4XEoAAA88fOWVGXnOyVJg1rFKcjfZnIiAEBl5tFhfgAA+KJvzr62VHtm8QMAlK0SjUx99NFHkqTrr79eYWFh7uWSGDFihGfJAAAohVR7rpbuOiZJqlMjWB3rVb/IIwAAuDQlKlOjRo2SxWLR5ZdfrrCwMPfyhRiGIYvFQpkCAJSLWRuS5TIKb1/frrasVi7PAQAoWyUqUx988IEsFovi4uIkSdOmTSvTUAAAlFbRC/Uyix8AoOyVeGTqbCNHjiyLLAAAeGRril3bj2RKktrXjVT96FCTEwEAqgImoAAAVHjfrDvkvs3EEwCA8kKZAgBUaA6nS99tSJEkBdisurZ1nMmJAABVhUdlymq1ymazXfDDz89PNWrUUNeuXfXiiy/q1KlT3s4OAICW7E5TWlaeJOmKZjGKDAkwOREAoKrwqEz16tVLrVu3lmEYslqtql+/vrp06aL69evLZrPJMAy1atVKtWvX1u+//64JEybo8ssvl91u93Z+AEAV9+1ZE09cz8QTAIBy5FGZ+uSTT3Ty5EmNGjVK+/bt0549e7R8+XLt2bNHSUlJGjlypNLT0/Xjjz8qNTVVd999tzZt2qQXXnjB2/kBAFVYZm6BftpyRJJUPcRffZrEmJwIAFCVWAzDMEr7oOHDh+vgwYNatmzZebfp3r276tatqxkzZsjlcql169YqKCjQjh07LilwWbDb7YqIiFBGRobCw8PNjgMAKKEvVx/UI1//Lkka2bWeJg1paXIiAEBFV5pu4NHI1IIFC9SnT58LbtO7d28tWLCg8EmsVvXs2VMHDhwo0f6nTJmixMREBQUFqUOHDlqyZEmJHrds2TL5+fmpbdu2JdoeAFCxfc0sfgAAE3lUpnJzc3XkyJELbnPkyJEik06EhYXJz+/il7X64osvNG7cOD3xxBNav369evbsqYEDB160iGVkZGjEiBG64oorSvYiAAAV2oHjOfot6YQkqUHNULWuHWFyIgBAVeNRmWrfvr0+//xzrVmzptj7V69erc8//1wdOnRwr9u7d69iY2Mvuu///ve/uvPOO3XXXXepWbNmeuWVV1SnTh1NnTr1go+75557dNttt6lr166lezEAgArp7FGpmzrUlsViMTENAKAquvhQUTGeffZZXXnlleratauGDh2qrl27qmbNmjp27JiWL1+uWbNmyWq16plnnpEkZWVl6aefftLNN998wf3m5+dr7dq1euyxx4qsHzBggJYvX37ex02bNk179uzRJ598oueee+6i+fPy8pSXl+deZpZBAKhYXC5DX60tLFNWi3Qjh/gBAEzgUZnq3bu3fvjhB/31r3/V119/ra+//loWi0Vn5rKoW7eu3nrrLfXu3VtS4TlTS5cuVULChaesTUtLk9PpPGcEKzY29ryHFe7atUuPPfaYlixZUqLDCCVp8uTJmjRpUom2BQD4npV7jys5vfBQ8l6Nayo2PMjkRACAqsijMiUVjhbt3btXS5cu1caNG2W32xUeHq42bdqoR48eslr/OIIwJCREbdq0KfG+/3yohmEYxR6+4XQ6ddttt2nSpElq3Lhxifc/YcIEjR8/3r1st9tVp06dEj8eAGCumWuLHuIHAIAZPC5TUuGIU69evdSrVy+vhImOjpbNZjtnFOro0aPFnm+VmZmpNWvWaP369br//vslSS6XS4ZhyM/PTz///LP69et3zuMCAwMVGBjolcwAgPKVmVugHzcfliRFBPurf7OLn48LAEBZuKQyJUkOh0M7d+50z8PepEmTEh9u92cBAQHq0KGD5s+fr+uvv969fv78+RoyZMg524eHh2vTpk1F1k2ZMkX/+9//9NVXXykxMdGjHAAA3zXn98PKLXBJkoa0jVeQv83kRACAqsrjMnXy5Ek9+uij+uyzz4pMgR4cHKzbbrtNkydPVlRUVKn3O378eN1xxx3q2LGjunbtqnfeeUcHDhzQvffeK6nwEL3k5GR99NFHslqtatmy6AUaY2JiFBQUdM56AEDlcPYhfsM6cIg2AMA8HpWpkydPqmvXrtq5c6eioqLUs2dP1apVS6mpqVqzZo3ee+89LV68WCtWrFCNGjVKte9bbrlFx48f1zPPPKPDhw+rZcuWmjt3rurVqydJOnz4cIkv/gsAqFz2HMvS2v0nJUlNYsPUMuHCV6YHAKAsWYwzU/CVwvjx4/XKK69owoQJeuKJJxQSEuK+79SpU3rhhRf0/PPPa9y4cfrvf//r1cBlwW63KyIiwn2oIgDAN704b7umLNojSfrnoGa6q2cDkxMBACqb0nQDj8pUgwYNlJiYqF9++eW82/Tv31979+7V3r17S7v7ckeZAgDf53QZ6v7//qcj9lz5WS1a+fgViq7GZEIAAO8qTTewXvDe80hJSdHll19+wW26dOmilJQUT3YPAMA5luw6piP2XElS36YxFCkAgOk8KlMRERHav3//BbfZv3+/IiIiPAoFAMCfcW0pAICv8ahM9enTRzNnztSCBQuKvf+XX37RzJkz1adPn0vJBgCAJCkjp0Dzt6RKkqJCA9SvaYzJiQAA8HA2v6efflpz5szRVVddpWuuuUa9e/dWbGysUlNTtWjRIv34448KCQnRU0895e28AIAqaPbGZOU7C68tNbRdgvxtHv0tEAAAr/KoTDVv3lw///yzRo0apTlz5mjOnDmyWCw6M5dFw4YNNX36dLVo0cKrYQEAVVORa0t15BA/AIBv8Piivd26ddOOHTu0bNkyrV+/Xna7XeHh4WrXrp26d+8ui8XizZwAgCpqx5FM/X4oQ5LUKiFCTWsx6yoAwDd4XKYkyWKxqEePHurRo8c5973++utauHChvvnmm0t5CgBAFffV2oPu20w8AQDwJWV20Pm6des0a9assto9AKAKKHC69O36ZElSgM2qIW3jTU4EAMAfOIMXAOCzftl2VGlZ+ZKkK5vHKjIkwOREAAD8gTIFAPBZX6w+4L59S6c6JiYBAOBclCkAgE9KST+lxTuPSZISIoPV47JokxMBAFAUZQoA4JNmrjkkV+EVN3RLpzqyWpklFgDgWyhTAACf43QZ+nJN4Sx+Vguz+AEAfFOJp0a/5pprSrXjTZs2lToMAACStHR3mpLTT0mSejeuqfjIYJMTAQBwrhKXqXnz5pV651y4FwDgibMnnhjeua6JSQAAOL8Sl6mkpKSyzAEAgCQpLStP87emSpKiqwWqX9MYkxMBAFC8EpepevXqlWUOAAAkSd+sO6QCZ+HMEzd1qC1/G6f3AgB8Ez+hAAA+wzAMfb76oHuZa0sBAHwZZQoA4DNW7zupvceyJUmXN6ihxOhQkxMBAHB+lCkAgM/4/OyJJzox8QQAwLdRpgAAPiHjVIHmbjosSYoI9tfVLWuZnAgAgAujTAEAfMLsDcnKLXBJkq5vl6Agf5vJiQAAuDDKFADAJzDxBACgoqFMAQBMtzk5Q1tS7JKkNnUi1Swu3OREAABcHGUKAGC6GavOnniCUSkAQMVAmQIAmCon36HZG1IkSSEBNg1uE29yIgAASoYyBQAw1ewNKcrMc0iSBreOV7VAP5MTAQBQMpQpAIBpDMPQJ7/tdy//5XKuLQUAqDgoUwAA02w8lKHNyYUTT7SuHaHWtSPNDQQAQClQpgAApvlk5R+jUrd3qWdiEgAASo8yBQAwRXpOvr7fWDjxRHiQHxNPAAAqHMoUAMAUX609pDyHS5J0Y4faCg6wmZwIAIDSoUwBAMqdYRj67Lc/ri31Fw7xAwBUQJQpAEC5W77nuPamZUuSujaI0mUx1UxOBABA6VGmAADl7uyJJ5gOHQBQUVGmAADlKtWeq5+3pkqSoqsFakDzWiYnAgDAM5QpAEC5+nzVQTldhiRpeKc6CvDjRxEAoGLiJxgAoNw4nC7NWFU48YTVIt3ahUP8AAAVF2UKAFBuftl+VEfsuZKkfk1jlBAZbHIiAAA8R5kCAJSbohNPMB06AKBio0wBAMrFvrRsLdmVJkmqUyNYvRvVNDkRAACXhjIFACgXn6364yK9t3WuJ6vVYmIaAAAuHWUKAFDmcgucmrnmoCQpwGbVzR1rm5wIAIBLR5kCAJS52RtTdDKnQJI0sFUtRVULNDkRAACXjjIFAChThmFo2rJ97uWR3eqblgUAAG+iTAEAytRvSSe07bBdktSmTqTa161uciIAALyDMgUAKFPTzxqVGs2oFACgEqFMAQDKzMETOfp56xFJUkxYoK5pFWdyIgAAvIcyBQAoMx+v3C+XUXj79svrKcCPHzsAgMqDn2oAgDKRk+/Q56evLRVgs+q2LnVNTgQAgHdRpgAAZeKbdcmy5zokSde1jVc006EDACoZyhQAwOsMw9D05fvcy6OYeAIAUAlRpgAAXrdkV5p2H82SJHWuX0MtEyJMTgQAgPdRpgAAXjdtWZL79uju9c0LAgBAGaJMAQC8au+xLC3ccUySlBAZrCubx5qcCACAskGZAgB41Ucr9rtvj+haT342ftQAAConfsIBALzGnlugmWsOSpKC/W0a3onp0AEAlRdlCgDgNTPXHFJ2vlOSdH37BEWE+JucCACAskOZAgB4hdNl6MOzpkMfzXToAIBKjjIFAPCKBdtSdeBEjiSpZ6NoNYoNMzkRAABlizIFAPCKd37d6749pnuiiUkAACgflCkAwCVbs++E1u4/KUlqEhumPk1qmpwIAICyR5kCAFyytxb/MSr1114NZLFYTEwDAED5oEwBAC7J7qOZWrAtVZIUFxGkwW3iTU4EAED5oEwBAC7J2edK3dkjUQF+/GgBAFQN/MQDAHgs1Z6rb9cnS5LCgvw0vDMX6QUAVB2UKQCAxz5YlqQCpyFJuuPyeqoW6GdyIgAAyg9lCgDgEXtugT5beUCSFGCzalT3+uYGAgCgnFGmAAAemfHbAWXmOSRJN3ZIUExYkMmJAAAoX5QpAECp5Tmc+mBZkiTJYpHu6tnA5EQAAJQ/yhQAoNRmbUhRqj1PkjSgeawa1qxmciIAAMofZQoAUCoul1FkOvR7ejc0MQ0AAOahTAEASuV/249q99EsSVLn+jXUvm51kxMBAGAOyhQAoFTe/nWP+/Y9vTlXCgBQdVGmAAAltnb/Ca3ed1KS1Cimmvo2iTE5EQAA5qFMAQBK7I3/7XbfvrtXA1mtFhPTAABgLsoUAKBENidnaOGOY5KkhMhgDW2bYHIiAADMRZkCAJTI2aNS9/ZpqAA/foQAAKo2fhICAC5qZ2qm5m05IkmKCQvUsA61TU4EAID5KFMAgIt6c+Efo1J/7dVAQf42E9MAAOAbKFMAgAtKSsvW9xtTJEk1QgN0W5e6JicCAMA3UKYAABc0ddFuuYzC23f2SFRIgJ+5gQAA8BGUKQDAeR04nqOv1yVLksKD/DSiaz2TEwEA4DsoUwCA83r9f7vkPD0sNaZHosKC/E1OBACA76BMAQCKtS8tW9+s/2NUakyPRJMTAQDgWyhTAIBivbFwt3tU6q6eDRTOqBQAAEVQpgAA59iXlq1vT49KRQT7a3T3+uYGAgDAB1GmAADneO2sc6Xu7sm5UgAAFIcyBQAoIiktW9+dHpWKDPHXyG71zQ0EAICPokwBAIp4ef5O93Wl7u7ZgFEpAADOgzIFAHDbdtiu739PkSTVCA1gVAoAgAugTAEA3F76eaeM06NSf+vTUNUC/cwNBACAD6NMAQAkSesOnNSCbamSpLiIIN1+eT2TEwEA4NsoUwAASdJ/ftrhvv3gFY0U5G8zMQ0AAL6PMgUA0LLdaVq+57gkqX5UiG7qUNvkRAAA+D7KFABUcYZh6MWzRqUeurKx/G38eAAA4GL4aQkAVdyPm49o48F0SVLTWmEa3Dre3EAAAFQQlCkAqMIKnC69OG+7e/nRq5vKarWYmAgAgIqDMgUAVdiMVQe073iOJOnyBjXUp0lNkxMBAFBxUKYAoIrKynPo1QW73MsTBjaTxcKoFAAAJeWTZWrKlClKTExUUFCQOnTooCVLlpx322+++UZXXnmlatasqfDwcHXt2lU//fRTOaYFgIrpncV7dDw7X5J0bes4takTaW4gAAAqGJ8rU1988YXGjRunJ554QuvXr1fPnj01cOBAHThwoNjtf/31V1155ZWaO3eu1q5dq759+2rw4MFav359OScHgIrjqD1X7y5JkiT52yx6+KomJicCAKDisRiGYZgd4mxdunRR+/btNXXqVPe6Zs2aaejQoZo8eXKJ9tGiRQvdcssteuqpp0q0vd1uV0REhDIyMhQeHu5RbgCoSB77+nd9vvqgJGlUt/qaeF0LkxMBAOAbStMNfGpkKj8/X2vXrtWAAQOKrB8wYICWL19eon24XC5lZmaqRo0a590mLy9Pdru9yAcAVBVbUjL0xZrCIhUW6KcH+l1mciIAAComnypTaWlpcjqdio2NLbI+NjZWR44cKdE+XnrpJWVnZ+vmm28+7zaTJ09WRESE+6NOnTqXlBsAKgrDMPTcD9t05piEB664TFHVAs0NBQBABeVTZeqMP88mZRhGiWaYmjFjhiZOnKgvvvhCMTEx591uwoQJysjIcH8cPHjwkjMDQEUwf2uqVuw9LkmqFxWikd3qmxsIAIAKzM/sAGeLjo6WzWY7ZxTq6NGj54xW/dkXX3yhO++8UzNnzlT//v0vuG1gYKACA/lLLICqJd/h0gtzt7mXJwxspkA/m4mJAACo2HxqZCogIEAdOnTQ/Pnzi6yfP3++unXrdt7HzZgxQ6NGjdJnn32mQYMGlXVMAKiQPlqxz32B3i6JNXRViwv/kQoAAFyYT41MSdL48eN1xx13qGPHjurataveeecdHThwQPfee6+kwkP0kpOT9dFHH0kqLFIjRozQq6++qssvv9w9qhUcHKyIiAjTXgcA+JK0rDy9+kvhBXotFunJa5tzgV4AAC6Rz5WpW265RcePH9czzzyjw4cPq2XLlpo7d67q1asnSTp8+HCRa069/fbbcjgcGjt2rMaOHeteP3LkSE2fPr284wOAT3px3nZl5jokScM61FbLBP7YBADApfK560yZgetMAajMNhxM19A3l0mSwoL89L//66OaYZw3CgBAcSrsdaYAAN7lchl6atZm9/JD/RtTpAAA8BLKFABUYl+uOajfD2VIkprEhmlE13omJwIAoPKgTAFAJZWRU6AXf9rhXp54XQv52fhvHwAAb+GnKgBUUv/5eYdOZOdLkq5tHaeuDaNMTgQAQOVCmQKASmjDwXR98tt+SVJIgE2PX9PM5EQAAFQ+lCkAqGQcTpce/2aTzszV+lD/xoqPDDY3FAAAlRBlCgAqmenL92nrYbskqVlcuEZ3r29uIAAAKinKFABUIsnpp/Tf+TslSRaL9ML1LZl0AgCAMsJPWACoRCbO3qKcfKck6S9d6qpd3eomJwIAoPKiTAFAJfHjpsOavzVVkhRdLVAPX9XU5EQAAFRulCkAqATSc/L15Kwt7uWnBjdXRLC/iYkAAKj8KFMAUAk8N2eb0rLyJEn9m8VqcOs4kxMBAFD5UaYAoIL7decxfbX2kCQpLNBPzw1tKYvFYnIqAAAqP8oUAFRg2XkOTfhmk3v58UHNVCsiyMREAABUHZQpAKjA/jVvu5LTT0mSujaI0vBOdUxOBABA1UGZAoAKatnuNH20Yr8kKcjfqv93YysO7wMAoBxRpgCgArLnFujhmRvdy49d3VT1okJNTAQAQNVDmQKACuiZ77cqJSNXktStYZRGdK1vbiAAAKogyhQAVDDzt6a6Z++rFuinF29qLauVw/sAAChvlCkAqECOZ+UVmb3vqcHNVbt6iImJAACouihTAFBBGIahR7763X1x3iuaxmhYh9ompwIAoOqiTAFABfHJyv36ZftRSVJUaIAmM3sfAACmokwBQAWwMzVTz83Z5l7+97DWignj4rwAAJiJMgUAPi63wKkHZ6xXnsMlSRrZtZ76NY01ORUAAKBMAYCP+38/btf2I5mSpCaxYZpwTTOTEwEAAIkyBQA+bd7mw5q+fJ8kKcDPqldvbasgf5u5oQAAgCTKFAD4rAPHc/TwV7+7l58c1ExNa4WbmAgAAJyNMgUAPijP4dTYz9YpM9chSbq2dZxuv7yeyakAAMDZKFMA4INemLNNm5IzJEmJ0aGafAPToAMA4GsoUwDgY2ZvTNGHK/ZLKjxP6o3b2iksyN/kVAAA4M8oUwDgQ7YdtuuRrza6lycObqEW8REmJgIAAOdDmQIAH5GRU6B7Pl6r3ILC60nd1KG2bu1cx+RUAADgfChTAOADnC5Df/9ivQ6cyJEktUqI0HNDW3KeFAAAPowyBQA+4OX5O7VoxzFJUo3QAL11RweuJwUAgI+jTAGAyWZtSNYbC3dLkqwW6Y1b2ykhMtjkVAAA4GIoUwBgovUHTha5MO/j1zRTt8uiTUwEAABKijIFACZJST+lv368VvmOwgknhneqozt7JJqcCgAAlBRlCgBMkJ3n0F0frtGxzDxJUpfEGnpmCBNOAABQkVCmAKCcOZwu3f/ZOm09bJck1a0Rordu76AAP/5LBgCgIuEnNwCUI8Mw9OSszVp4eua+sCA/vT+yo6qHBpicDAAAlBZlCgDK0ZsLd2vGqoOSpACbVe/c0VGNYsNMTgUAADxBmQKAcvLV2kP6z8873cv/HtZaXRtGmZgIAABcCsoUAJSDBVtT9ejXf0yB/tjAphrSNsHERAAA4FJRpgCgjK3Yc1x/+2ydnC5DkjSiaz3d06uByakAAMClokwBQBnadChDd3+0xn0tqevaxGvi4BZMgQ4AQCVAmQKAMrL7aKZGTlulrDyHJKlf0xi9dHMbWa0UKQAAKgPKFACUgT3HsnTru7/pRHa+JKlz/Rp687b28rfx3y4AAJUFP9UBwMuS0rJ16zsrdSwzT5LUKiFC743qqOAAm8nJAACAN1GmAMCL9h8vLFJHTxep5nHh+vjOzgoP8jc5GQAA8DbKFAB4SVJatoa/s1JH7LmSpKa1wvTpXV0UGRJgcjIAAFAW/MwOAACVwc7UTP3lvd/ch/Y1jq2mT+/qouqhFCkAACoryhQAXKLNyRm64/3fdDKnQFLhiNQnd3VRVLVAk5MBAICyRJkCgEuwdv8JjZq2Wpm5hdOft6kdoQ/HdObQPgAAqgDKFAB4aMHWVI39bJ3yTl+Qt1P96vpgVCeFMdkEAABVAmUKADzw5ZqDmvDNJjldhiSpZ6NovX1HB4UE8N8qAABVBT/1AaAUDMPQ1MV79OK8He5117WJ13+GtVGAHxOkAgBQlVCmAKCECpwuPfndZn2++qB73ahu9fXUtc1ltVpMTAYAAMxAmQKAErDnFuhvn6zT0t1p7nUPX9VEf+vTUBYLRQoAgKqIMgUAF3HwRI7GTF+tXUezJEkBflb9+6bWGtI2weRkAADATJQpALiAZbvTNPazdUo/fQ2pGqEBeueODupYv4bJyQAAgNkoUwBQDMMw9MGyfXph7jb3jH0NaoZq2qhOqhcVanI6AADgCyhTAPAnOfkO/fPbzfpmfbJ7Xb+mMXpleFuFcw0pAABwGmUKAM6y+2iW/vbpWu1MzXKvu7/vZXroysayMWMfAAA4C2UKAE6btSFZE77ZpJx8pyQpJMCmf9/URoNax5mcDAAA+CLKFIAqLyffoWe+31rk+lFNYsP05l/a67KYaiYmAwAAvowyBaBK25ycoQdnrNfetGz3uhvb19ZzQ1sqOMBmYjIAAODrrGYHAAAzOF2G3l68R9dPWeYuUsH+Nr14Y2v9Z1hrihSASi0nJ0eTJk1S06ZNFRQUpKioKN166606efKk2dF8OltlxvvuGUamAFQ5SWnZenjmRq3Z/8cPiFYJEXp1eFs1qMlhfQAqN8MwdOutt+rXX3/VU089pbZt2+r333/XQw89pIYNG+q5554jWxXD++45yhSAKsPlMvThin3617ztyi1wSZIsFumeXg01/srGCvBjsB5A5bd48WLNnj1bM2fO1E033SRJ6tu3ryZPnqzs7OyLPLrk+vTpo/r162v69Ok+l80bPHl9Zc3TTBXpffc1/OYAoErYfTRTt7yzQpO+3+ouUvWiQvTFX7vqsYFNKVIAyt22bdtksViK/YiIiJBhGGXyvDNnzlT16tV1/fXXu9f9+uuvSk1NVb9+/crkOUvKG9kOHz6satWqafjw4UXW//DDD/L399cTTzzh1cyVAe+75/jtAUClludw6r/zd2rgq0u0et8fh/WN7FpPP/69pzon1jAxHYCqLD4+XitWrCjy8eyzz0qSxowZI4ul6LXtDMOQw+Eo0ceFLF++XF26dJEkpaSkaNq0abrxxht1xRVX6Nprry2bF1tC3sgWFxenRx55RF9++aXWrl0rSVq0aJGGDRum++67T88//3yZ5a+oeN89R5kCUGkt2XVMA19dotd+2aUCZ+FfeOtHheizu7to0pCWCgngSGcA5omIiNDll1/u/jhy5Iiee+45/eMf/9DLL798zvaLFy+Wv79/iT727dtX7HPm5uZq8+bN6tKli1544QUlJCRozJgxCgkJ0fTp090F7tixYxo0aJBCQ0PVuHFjzZ8//4KvpbiiZxhGsevPp6TZpk6dqvbt28vf318TJ04sdl//+Mc/FBcXp0cffVSrV6/Wddddp1tvvVWvvvqqe5uS7Mebr8/bvJWppO97SZTkfa9sLEZZjSFXIHa7XREREcrIyFB4eLjZcQBcouT0U3ruh636cfMR9zo/q0X39G6gB/o1UpA/M/UB8C0ff/yxxowZo6efflr//Oc/i90mMzNTO3bsKNH+WrdurYCAgHPWL1++XN27d9ecOXPUtGlT7d69WytXrtQrr7yiyMhI/f7776pWrZpuvvlmhYWF6fXXX9eCBQs0cuRI7d69W1FRUcU+36JFi9S3b98SZUtKSlL9+vU9zvbdd9/JZrPpo48+UosWLc5bhKZNm6YxY8YoNDRUgwYN0meffSab7Y///0u6H2+9Pm/zVqaSvu8ldbH3vSIoTTfgz7IAKo2cfIfe/TVJUxfvdp8XJUnt60bqhRtaqWkt/lgCwPe88cYbGjdunF555RXdf//9592uWrVqatu2bYn26edX/K94q1atkiR17txZ0dHRatCggQYMGKDGjRvr1ltv1cqVK3X55Zfru+++0549exQSEqLrrrtObdq00axZszRmzJhi99uhQwetXr26yLp77rlH8fHxevrpp4usj4+P9zhb//79NXToUEnSrFmzLvgeNG7cWJJksVg0ffr0c36hL+l+vPX6vM1bmUr6vr/00ktas2aNgoOD9c033yg+Pl6zZ8/WZZddVmR/F3vfS7qfioIyBaDCc7kMfb3ukP7z8w6l2vPc66OrBeixgc10Q7sEWa0lP0wBAMrL888/r4kTJ+qDDz7QiBEjLrjt4sWLL3kkYtWqVWrQoIGio6OLfVx8fLx27dqlatWqqU6dOu71rVq10pYtW877fGFhYerYseM566Kios5Zfz4lyVZSGzZs0LXXXqvu3btr2bJl+uCDDzR27NgSP/7PvPH6vM1bmUr6vm/atElLlizRzJkz9d5772nEiBF699139a9//cu9bUne95LspyKhTAGosAzD0P+2H9VLP+/U1sN293qb1aI7Lq+nh65srIhgfxMTAsD5Pfzww3r99dc1c+ZM9yjJhRQ3EnE+Fxr9iYuLK7LOMAy99957atmypZo3b64lS5acc2hTeHi40tLSSvTcnipJtpLYsWOHrrrqKnXt2lWzZs3SsGHDNHHiRN1+++2KiIgoi+gVWknf902bNmnixInq2rWrJKlhw4Y6deqU+zElfd8vtp+KhjIFoMIxDEOLdx7Ty/N3auOhjCL39W8WqwnXNFVDLr4LwIeNGzdOr776qp599lnVqlVLK1eudN8XFxenevXqnfOY4kYiSuPEiRPas2eP9uzZo7vuuku33nqrcnJy9MEHH2jp0qVauHChpMLDCe12e5HH2u32Up03U1bZLmbfvn3q37+/mjRpoq+//lr+/v76f//v/6lly5Z64YUXTB392L9/vxo2bKiRI0fq/fffd6+/88479eGHH2rPnj3ur/v5tvW2kr7vTqdTW7du1TXXXON+7JYtW9zLJX3fL7afiojZ/ABUGIZhaOmuNN04dblGTVtdpEi1SojQZ3d30XsjO1KkAPg0wzA0bdo0SdKTTz6prl27Fvn49ttvy+R5z5wbM2LECM2bN08DBw7U/fffLz8/P/3222/ukYJGjRopKytLhw4dcj928+bNatGiRZnkKk22Czl8+LD69++vmJgY/fDDDwoODpYkNW3aVGPGjNGrr7563lkOy4NhGHI6nXI6nUXWn1l39pxw59vW20r6vu/evVthYWFFRjx///13tW7dulTv+4X2U1ExMgXA5xmGoZV7T+jlBTu1KulEkfua1grT+Csb68rmsaWavhUAzGKxWJSRkXHxDb1s1apV8vf319tvv62goKDzbletWjUNGTJEEydO1Ouvv65ffvlFGzZs0MyZM0v1fIsWLfJ6Nknu6b6dTqccDodyc3Pl7++vuLg47d69u9jHvPPOO3rnnXdKtJ+SzjxXmtcnSfXr1y/2QszTp0/X9OnTS7SttzOV9H3ftGlTkclPcnJytG/fPrVo0ULBwcElft8vtJ+KipEpAD7L4XTp+40pGvrmMt367soiRapRTDVN+Ut7zX2wpwa0qEWRAoCLWLVqlVq1anXRsiJJU6ZMUUpKiqKiovTQQw/piy++OO8EBeWd7bnnnlNwcLCmT5+u559/XsHBwfr4449L/Zze2k9FVtL3fdOmTWrTpo17ecuWLWrYsKF7FKqkvLUfX8J1psR1pgBfY88t0JerD2rasn1KTi96UmqDmqEa17+xBrWKk40Z+gCgxGJjY3XDDTdo6tSpZkc5hy9nq8x434vHdaYAVEiHTuZo+rJ9+nz1QWXlFb1ie/O4cP21VwMNbhNPiQIAD6Smppod4bx8OVtlxvt+6ShTAEzlcLq0cMcxfb7qgBbuOCrXn8bK+zWN0V09EtW1YRSH8gEAAJ9CmQJgigPHc/TFmgOaueaQjmbmFbkv0M+qG9rX1p096uuymDCTEgIAAFwYZQpAucktcGr+1lR9vvqAlu0+fs79cRFBGt6prm6/vK6iqgWakBAAAKDkKFMAylS+w6Wlu4/p+42H9fOWI8rOL3rNDJvVov7NYjS8U131alyT86EAAECFQZkC4HVOl6Hf9h7X7I0p+nHzEWWcKjhnm3pRIbqlUx3d1KG2YsIuPhUuAACAr6FMAfCKU/lOLdudpl+2p2r+1qNKy8o7Z5vwID9d3bKWhrZL0OWJUbIyCgUAACowyhQAjx215+qX7Uf1y7ZULd2dptwC1znbhATYdGXzWA1uHa+ejaMV6FeyK8sDAAD4OsoUgBLLczi1/kC6lu1O0687j2njoYxitwv0s6p345q6rm28+jWNUUgA/9UAAIDKh99wAJyXy2Vo62G7lu9J09Ldx7Uq6Xixo0+SVDMsUFc0jdEVzWLV47JoBQcwAgUAACo3yhQAtzyHU5uT7Vq7/4TW7DupNftP6kR2/nm3bxYXrv7NCgtU64QIzoECAABVCmUKqMLSsvK04UC61uw/qbX7T2jjoQzlO4ofeZKkWuFB6n5ZtLpfFqXul0UrNpxZ+AAAQNVFmQKqiBPZ+dqUnKFNh9L1+6EMbU7OUEpG7gUfEx7kp8sbRKlHo2h1axithjVDZbEw+gQAACBRpoBKx+F0ad/xbG0/kqkdRzK1/UimtqbYlZx+6qKPrRcVog71qqtjvRrqWL+6LqtZjUP3AAAAzoMyBVRQuQVOHTiRo73HsrQ3LVu7j2Zp++FM7T6WdcFD9c4IDbCpZUKEWteOUPu61dWhfnUungsAAFAKlCnAhzldhlLST2lvWraSjmUpKS278HZatpLTT8kwSrafkACbWsZHuMtTq9oRSowKZdQJAADgElCmABPlO1w6kpGrQ+k5Sj55Ssnpp/74nH5Kh9Nzle+8+CjTGVaLlBgdqqa1wtWkVpia1ApT01phqlM9hOIEAADgZZQpoAwYhiH7KYeOZubqaGaejmbmKtWep6P2wtuHM3KVfPKUUjNzSzy6dLawQD81qBmqxOhQJUZXc9++LKaagvy5vhMAAEB5oEwBJZTncOpkdoGOZ+ed9TlfJ7LzdSInX8ez8t3F6ag9T3klOG/pQqoF+ikhMlj1o0MKC1N0qBJPl6ao0ABm1QMAADAZZQpVSm6BU/ZTBbLnFijjlEP23ILTyw73evupAtnPuu9ETr5OZhcoK8/h1SzR1QKUEBmshOrBhZ8jgxV/erl2ZIjCg/0oTAAAAD7MJ8vUlClT9O9//1uHDx9WixYt9Morr6hnz57n3X7x4sUaP368tmzZovj4eD3yyCO69957yzExvMkwDDlchnILnMpzuHQq36mcfKey8x3KyXMqJ9/xp+XCdWeWs0/fn5PvVHaew32/PddRolnuLlVEsL9iwwMVExakmLBAxYSf+Vy47sx9wQEcjgcAAFCR+VyZ+uKLLzRu3DhNmTJF3bt319tvv62BAwdq69atqlu37jnbJyUl6ZprrtHdd9+tTz75RMuWLdPf/vY31axZUzfeeKMJr6BicLkMOQ1DTlfhh8NpKN/pksPlUoHj3NsFTpccTkMFTlfhfcXcLu6+vAKX8hzO059d7oKU53Aq98x9jsLtct3bOeXy4DyismCxFJajGqEBqhESUPj5Tx/VQwMUFRqg6iEBqhkWyDlLAAAAVYTFMDw5/b3sdOnSRe3bt9fUqVPd65o1a6ahQ4dq8uTJ52z/6KOPavbs2dq2bZt73b333quNGzdqxYoVJXpOu92uiIgIZWRkKDw8/NJfxCX47887tPtYlhxOQ67TIzTOsz7OrHO5/nSfUXS7Iuudf7rfMDya9KAiCvSzKjTQT8H+NoUH+ys8yO/0Z3+FB/ud/nzu+ojgwvXVAvyYBQ8AAKAKKU038KmRqfz8fK1du1aPPfZYkfUDBgzQ8uXLi33MihUrNGDAgCLrrrrqKr3//vsqKCiQv7//OY/Jy8tTXl6ee9lut3shvXcs33Nca/afNDtGubBapCB/m4L8bQr0s57+sCnIv/BzoH/huuAAP4UG2BQcYFNogJ9CAm0K8bcpJNCvyHJooJ9CAgo/BwcUrvOzWc1+mQAAAKikfKpMpaWlyel0KjY2tsj62NhYHTlypNjHHDlypNjtHQ6H0tLSFBcXd85jJk+erEmTJnkvuBfZSjgKYrUUbmuzWmSzWP64bbXKZlXhOtt57rNaZbNIflarrNbC/fhZrfK3WRXgV/xtfz+LAmzWwmX3bYv8/U7fb7Oc/lz09tlFyX3b36YgPytFBwAAABWaT5WpM/48g5lhGBec1ay47Ytbf8aECRM0fvx497LdbledOnU8jetVr9/WTk6XIZvFIqvVIj/rWZ8thZ9tVguzvAEAAAAm86kyFR0dLZvNds4o1NGjR88ZfTqjVq1axW7v5+enqKioYh8TGBiowMBA74T2spiwILMjAAAAACgBnzrOKiAgQB06dND8+fOLrJ8/f766detW7GO6du16zvY///yzOnbsWOz5UgAAAADgDT5VpiRp/Pjxeu+99/TBBx9o27Zteuihh3TgwAH3daMmTJigESNGuLe/9957tX//fo0fP17btm3TBx98oPfff1//+Mc/zHoJAAAAAKoAnzrMT5JuueUWHT9+XM8884wOHz6sli1bau7cuapXr54k6fDhwzpw4IB7+8TERM2dO1cPPfSQ3nzzTcXHx+u1117jGlMAAAAAypTPXWfKDL50nSkAAAAA5ilNN/C5w/wAAAAAoCKgTAEAAACAByhTAAAAAOAByhQAAAAAeIAyBQAAAAAeoEwBAAAAgAcoUwAAAADgAcoUAAAAAHiAMgUAAAAAHqBMAQAAAIAHKFMAAAAA4AHKFAAAAAB4gDIFAAAAAB6gTAEAAACAByhTAAAAAOAByhQAAAAAeIAyBQAAAAAeoEwBAAAAgAcoUwAAAADgAcoUAAAAAHjAz+wAvsAwDEmS3W43OQkAAAAAM53pBGc6woVQpiRlZmZKkurUqWNyEgAAAAC+IDMzUxERERfcxmKUpHJVci6XSykpKQoLC5PFYjE7TqVht9tVp04dHTx4UOHh4WbHgfia+Bq+Hr6Hr4nv4WviW/h6+B6+Jt5nGIYyMzMVHx8vq/XCZ0UxMiXJarWqdu3aZseotMLDw/nH7WP4mvgWvh6+h6+J7+Fr4lv4evgevibedbERqTOYgAIAAAAAPECZAgAAAAAPUKZQZgIDA/X0008rMDDQ7Cg4ja+Jb+Hr4Xv4mvgevia+ha+H7+FrYi4moAAAAAAADzAyBQAAAAAeoEwBAAAAgAcoUwAAAADgAcoUAAAAAHiAMoVyM2fOHHXp0kXBwcGKjo7WDTfcYHYkSMrLy1Pbtm1lsVi0YcMGs+NUWfv27dOdd96pxMREBQcHq2HDhnr66aeVn59vdrQqY8qUKUpMTFRQUJA6dOigJUuWmB2pypo8ebI6deqksLAwxcTEaOjQodqxY4fZsXDa5MmTZbFYNG7cOLOjVGnJycm6/fbbFRUVpZCQELVt21Zr1641O1aVQ5lCufj66691xx13aPTo0dq4caOWLVum2267zexYkPTII48oPj7e7BhV3vbt2+VyufT2229ry5Ytevnll/XWW2/p8ccfNztalfDFF19o3LhxeuKJJ7R+/Xr17NlTAwcO1IEDB8yOViUtXrxYY8eO1cqVKzV//nw5HA4NGDBA2dnZZker8lavXq133nlHrVu3NjtKlXby5El1795d/v7++vHHH7V161a99NJLioyMNDtalcPU6ChzDodD9evX16RJk3TnnXeaHQdn+fHHHzV+/Hh9/fXXatGihdavX6+2bduaHQun/fvf/9bUqVO1d+9es6NUel26dFH79u01depU97pmzZpp6NChmjx5sonJIEnHjh1TTEyMFi9erF69epkdp8rKyspS+/btNWXKFD333HNq27atXnnlFbNjVUmPPfaYli1bxgi6D2BkCmVu3bp1Sk5OltVqVbt27RQXF6eBAwdqy5YtZker0lJTU3X33Xfr448/VkhIiNlxUIyMjAzVqFHD7BiVXn5+vtauXasBAwYUWT9gwAAtX77cpFQ4W0ZGhiTx78FkY8eO1aBBg9S/f3+zo1R5s2fPVseOHTVs2DDFxMSoXbt2evfdd82OVSVRplDmzvxVfeLEifrnP/+pH374QdWrV1fv3r114sQJk9NVTYZhaNSoUbr33nvVsWNHs+OgGHv27NHrr7+ue++91+wolV5aWpqcTqdiY2OLrI+NjdWRI0dMSoUzDMPQ+PHj1aNHD7Vs2dLsOFXW559/rnXr1jFS6yP27t2rqVOnqlGjRvrpp59077336sEHH9RHH31kdrQqhzIFj02cOFEWi+WCH2vWrJHL5ZIkPfHEE7rxxhvVoUMHTZs2TRaLRTNnzjT5VVQuJf2avP7667Lb7ZowYYLZkSu9kn5NzpaSkqKrr75aw4YN01133WVS8qrHYrEUWTYM45x1KH/333+/fv/9d82YMcPsKFXWwYMH9fe//12ffPKJgoKCzI4DSa7/3979g1TZ9nEA/52UDpUW0RmKyj+1VDRUGmY1KA0NFRXSHzChhkhIoRyKaAhEXGyIqMWGiiCICKuhQCHKIaJoaqkwiIZTGELQkCHpM/Q+8vr6vM8TN4/exvl84AznOmf4wr3c33Ndv3OPjsaGDRuis7Mz1q9fH8eOHYujR49OOKrM9ChOOwC/r5aWljh48ODffqeioiK+fv0aERFr1qwZX89ms7FixQrD3f+yX70mHR0d8ezZs8hmsxM+q66ujsbGxrh+/fpUxiwov3pN/pTP56O+vj5qa2uju7t7itMREZHL5aKoqGjSLtTg4OCk3SqmV2tra9y/fz/6+/tj2bJlaccpWC9fvozBwcGoqqoaX/vx40f09/fHpUuX4vv371FUVJRiwsKzZMmSCfdVET/nPO/cuZNSosKlTJFYLpeLXC73j9+rqqqKbDYbb968ia1bt0ZExMjISLx//z7Ky8unOmZB+dVrcvHixejo6Bh/n8/nY/v27XHr1q2oqamZyogF51evScTPv7mtr68f372dNcvhgekwe/bsqKqqir6+vti7d+/4el9fX+zevTvFZIVrbGwsWltbo6enJx4/fhyVlZVpRypo27Zti1evXk1YO3LkSKxatSpOnz6tSKVgy5Ytkx4X8PbtW/dVKVCmmHLz58+P5ubmOHfuXCxfvjzKy8ujq6srIiL27duXcrrCVFZWNuF9SUlJRESsXLnSr78pyefzUVdXF2VlZXH+/Pn4/Pnz+GeLFy9OMVlhaGtri6ampqiurh7fFfzw4YOZtZQcP348bt68Gffu3YvS0tLxXcMFCxbEnDlzUk5XeEpLSyfNq82bNy8WLVpkji0lJ0+ejM2bN0dnZ2fs378/nj9/Ht3d3U40pECZYlp0dXVFcXFxNDU1xbdv36KmpiYePXoUCxcuTDsazAi9vb0xMDAQAwMDkwqtJ1hMvQMHDsTQ0FC0t7fHx48fY+3atfHgwQO/8qbkz7mPurq6CetXr16Nw4cPT38gmGE2btwYPT09cebMmWhvb4/Kysq4cOFCNDY2ph2t4HjOFAAAQAIO5AMAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAEAACSgTAFQ8CoqKiKTyfzf17Vr19KOCMAMVJx2AABI24kTJ+LLly+T1q9cuRL5fD7mzp07/aEAmPEyY2NjY2mHAICZ5vLly9HS0hK7du2Ku3fvxqxZDnMAMJEyBQD/o7e3N3bs2BGrV6+Op0+fRklJSdqRAJiBlCkA+C+vX7+OTZs2RTabjRcvXkRZWVnakQCYocxMAcB/DA0Nxc6dO2N4eDgePnyoSAHwt5QpAIiIkZGRaGhoiHfv3sWNGzeitrY27UgAzHCmaQEgIpqbm+PJkydx9uzZOHToUNpxAPgNmJkCoOB1dXXFqVOnoqGhIW7fvh2ZTCbtSAD8BpQpAArap0+fYunSpZHJZKKtre0vnym1Z8+eWLdu3fSHA2BGMzMFQEEbHh6O0dHRiPi5Q/VXKioqlCkAJrEzBQAAkIA/oAAAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEhAmQIAAEjgD4SRfl8t6MGHAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Define the logistic function\n", + "def logistic_function(z):\n", + " return 1 / (1 + np.exp(-z))\n", + "\n", + "# Generate values for z\n", + "z_values = np.linspace(-7, 7, 200) # Adjust the range as needed\n", + "\n", + "# Calculate corresponding function values\n", + "logistic_values = logistic_function(z_values)\n", + "\n", + "# Plot the logistic function with LaTeX representation\n", + "plt.figure(figsize=(10, 8))\n", + "plt.plot(z_values, logistic_values, label=r'$\\frac{1}{1 + e^{-z}}$', linewidth=2)\n", + "plt.title('Logistic Function Plot', fontsize=16)\n", + "plt.xlabel('z', fontsize=14)\n", + "plt.ylabel('Logistic function', fontsize=14)\n", + "plt.legend(fontsize=12)\n", + "plt.grid(False)\n", + "\n", + "# Adding equation at the bottom right\n", + "equation = r'$z = \\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n$'\n", + "plt.text(7, 0.05, equation, fontsize=12, ha='right')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Define the logistic function\n", + "def logistic_function(z):\n", + " return 1 / (1 + np.exp(-z))\n", + "\n", + "# Generate values for z\n", + "z_values = np.linspace(-7, 7, 200) # Adjust the range as needed\n", + "\n", + "# Calculate corresponding function values\n", + "logistic_values = logistic_function(z_values)\n", + "\n", + "# Plot the logistic function with LaTeX representation\n", + "plt.figure(figsize=(10, 8))\n", + "plt.plot(z_values, logistic_values, label=r'$\\frac{1}{1 + e^{-z}}$', linewidth=2)\n", + "plt.title('Logistic Function Plot', fontsize=16)\n", + "plt.xlabel('z', fontsize=14)\n", + "plt.ylabel('Logistic function', fontsize=14)\n", + "plt.legend(fontsize=12)\n", + "plt.grid(False)\n", + "\n", + "# Adding equation at the bottom right\n", + "equation = r'$z = \\beta_0 + \\beta_1 x_1 + \\ldots + \\beta_n x_n$'\n", + "plt.text(7, 0.05, equation, fontsize=12, ha='right')\n", + "\n", + "# Adding a vertical dashed red line at z=0\n", + "plt.axvline(x=0, color='red', linestyle='--')\n", + "\n", + "# Adding a dot at x=0, z=0.5\n", + "plt.scatter([0], [0.5], color='black', marker='o')\n", + "\n", + "# Adding the value '0.5' in the vicinity of the dot\n", + "plt.text(0.2, 0.5, '0.5', fontsize=12, ha='left')\n", + "\n", + "plt.savefig('logistic_function_plot.png', dpi=300)\n", + "\n", + "plt.show()\n" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/Projects-ML/Reg-models/logistic_function_plot.png b/Projects-ML/Reg-models/logistic_function_plot.png new file mode 100644 index 0000000..8f5ab64 Binary files /dev/null and b/Projects-ML/Reg-models/logistic_function_plot.png differ