{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "d6d1bd10", "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import random as rn \n", "import matplotlib.pyplot as plt \n", "from sklearn.model_selection import train_test_split\n", "from sklearn.metrics import r2_score \n", "\n", "def vdw(V,R,T,a,b):\n", " return R*T/(V-b)-a/(V*V) \n", "\n", "a=1.37;b=0.0387;R=0.08314462; # parameters for O2 and gas constant\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "7253d0aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Use polynomials from 1 to 7\n", "Full data R^2 values [0.63812187 0.81745112 0.83459471 0.84173159 0.8453742 0.84558143\n", " 0.84581274]\n", "Full data sum |y-yfit|^2 values [292.27054652 147.43543617 133.58943032 127.82534149 124.88338382\n", " 124.71601809 124.52920047]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rn.seed(a=666)\n", "Pmax=150 # max Pressure\n", "T=200 # Temp \n", "N=50\n", "# for T in [200,300,400]:\n", "Vmin=R*T/Pmax\n", "Vmax=R*T/20. # Volume at 20 atm\n", "dV=(Vmax-Vmin)/float(N)\n", "PV=[]\n", "PvdwV=[]\n", "VV=[]\n", "#----------------------------------\n", "rnscale=0.9 # was 0.6 \n", "#----------------------------------\n", "for i in range(N):\n", " V=Vmin+i*dV \n", " P=R*T/V # ideal gas \n", " Pvdw=vdw(V,R,T,a,b)*(1.0+rnscale*(rn.random()-0.5)) # van der Waals pressure + noise\n", " VV.append(V) # vector of Volume\n", " PV.append(P) # vector of Pressure \n", " PvdwV.append(Pvdw) # P(vdw) vector\n", "\n", "#----------------------------------\n", "NP=7 # max order of the poly\n", "#----------------------------------\n", "Leave_one_out=False\n", "\n", "if Leave_one_out:\n", " P_train, P_test, V_train, V_test = train_test_split(PvdwV,VV,test_size=0.01)\n", " N_tr=len(V_train)\n", " N_te=len(V_test)\n", " print(' Leave one out ',N_tr,N_te,V_test)\n", "else:\n", " N_tr=N # full data \n", " V_train=VV\n", " P_train=PvdwV # noisy vdw data \n", " \n", "p_c=np.zeros((NP,NP+1))\n", "print(' Use polynomials from 1 to ',NP)\n", "for i in range(NP): # polynoms from 1 to NP\n", " p_c[i,0:i+2]=np.polyfit(V_train,P_train,i+1,full=False) # fit a poly to Pvdw\n", "# print('Polynomial coeff ',p_c[i,0:i+2])\n", "\n", "y=np.zeros((NP,N_tr))\n", "for i in range(NP):\n", " poly2=np.poly1d(p_c[i,0:i+2])\n", " y[i,:]=poly2(V_train) # y contain the poly fit data\n", "\n", "yave=np.sum(P_train)/N_tr # train data\n", "r2sk=np.zeros(NP)\n", "rb=np.zeros(NP)\n", "for i in range(NP):\n", " rb[i]=np.sum((y[i,:]-P_train[:])**2)/N \n", " r2sk[i]=r2_score(P_train,y[i,:])\n", "\n", "print('Full data R^2 values ',r2sk[0:NP])\n", "print('Full data sum |y-yfit|^2 values ',rb[0:NP])\n", "\n", "plt.title(\" Pvdw, polyP T=200\")\n", "plt.ylabel(\" P/atm\")\n", "plt.plot(VV,PvdwV,'o',label='Pvdw')\n", "for i in range(2,NP):\n", " R2lab = 'Poly'+str(i+1)+' R2= {: >6.4f}'.format(r2sk[i])\n", " if Leave_one_out: \n", " plt.plot(V_train,y[i],'+',label=R2lab)\n", " else:\n", " plt.plot(V_train,y[i],label=R2lab)\n", "plt.xlabel(\" V/L\")\n", "plt.legend()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "9e42a89e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Validation training point 35 test points 15 iteration 100\n" ] }, { "data": { "image/png": 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OHasty8/PLzOORCaTIS8vD+fOnavwtfTiqSlMJfBEC0pxcbFQKpVi6dKl2rL8/Hwhl8vFJ598IoQQ4uHDh0IqlYpdu3Zp6yQlJQkzMzMRFRVVpdetTgZGRFQf1boF5chiTatJRY8ji/Ub8GNPtqD8+uuvwsnJSbz++uvi0aNHQiqVih07dmiPFxQUCDc3N7Fs2TIhhG4LSsn55ubmIjExUQghRFpampBKpeLYsWM6rztnzhxhbW0tAIjnnntO3L9/v9I4AwIChFQqFTY2NsLCwkIAEGZmZuLLL7+s8JybN28Ke3t7sXHjRp3y33//vdLH3bt3K7zmBx98INq2bVumvG3btmLx4or/G+Xn54t//OMfAoBo0qSJsLCwENu2bauw/v3794W7u7uYP39+hXUGDx4sBg8erFP2ww8/CDMzM7Fz505RWFgo7t69K/r06SMAiJ07d5Z7HX21oFQ7QcnKyhIXLlwQFy5cEADEypUrxYULF8Sff/4phBDiww8/FHK5XHz99dfi8uXLYuTIkcLV1VWnKWjy5MmiRYsW4scffxTnz58X/fr1E507dxaFhYVVioEJChE1dLVOUDKTNV06iReEOLtFk5Sc3fJXWWay/oItZcyYMcLc3FzY2NgIS0tLYWZmJv7+97+Le/fuiUuXLgkAIiEhQeecv/3tb2LcuHFCiLIJihBCdOrUSSxZskQIIcTKlSuFp6enKC4u1rlGWlqauH79ujh06JDo3bu3ePHFF8vUKS0gIECMHTtW/P777+LcuXPi9ddfFxMmTKiwfmJiovDy8hLjx4+v7i2p1AcffCDatWtXptzLy0v7nsvz0UcfiXbt2ol9+/aJS5cuidWrVwtbW1tx+PDhMnVVKpXo1auXCA4OrrDb686dOxUmaCtWrBD29vbC3NxcWFtbiyVLlggAOg0NpRktQSn58Dz5GDNmjBBC04qyYMECoVQqhaWlpejbt6+4fPlymeCnTZsmHB0dhUwmEy+//LK4fft2lWNggkJEDV19HoPywgsviN9//10kJCTofCFevHhRAND+QVti6NCh4p///KcQovwEZdWqVdov8Y4dO4r333+/0hju3LkjAIhTp05VWOfJMSgFBQWibdu2YtOmTWXqJiYminbt2onQ0FBRVFRU5riNjU2lj+Dg4Arj2Lx5s5DL5WXK5XK5+PTTT8s9JycnR0ilUnHgwAGd8vHjx2vHe5bIzMwUfn5+on///pV+lhYtWiQUCkWFCUxxcbFITEwUOTk52nEzpccOlaavBKXaC7UFBgZCVLJ0ikQiQXh4uM5I6CdZWVlh9erVWL16dXVfnoiITJyNjQ28vLzKlHt5ecHCwgInT55ESEgIAECtVuPs2bOYOXNmhdcbPXo05syZg1WrViE2NhZjxoyp9PVLvqNKTxl+GqlUinnz5iEsLAwjR46EtbU1ACAxMRFBQUHo3r07IiMjYWZWdujmxYsXK722TCar8Jifnx9UKhViYmLQs2dPAMCvv/4KlUoFf3//cs9Rq9VQq9VlYjE3N0dxcbH298zMTAwaNAiWlpbYt29fhevpCCEQGRmJf/zjHxWOwZFIJHBzcwMAfP7552jZsiW6detW8ZvWA24WSETU0NkpgYC5mmcjsrGxwZQpUzB79mw4OjrC3d0dy5YtQ05Ojs701yc5ODjg1VdfxezZszFw4EC0aNFCeywmJgYxMTHo06cPHBwc8Mcff+C9996Dp6cn/Pz8qhVfSEgI5s2bp50WnZSUhMDAQLi7u2P58uVIS0vT1i2ZFAKg3GSsqry9vREcHIyJEydi/fr1AIA333wTL7/8Mtq3b6+t98wzz2DJkiX4+9//Dnt7ewQEBGD27NmQyWRo1aoVjh8/jm3btmHlypUAgKysLAwcOBA5OTnYvn27zhIdCoVCZ9X2I0eOID4+vsL/Bh999BGCg4NhZmaGr7/+Gh9++CF2795t+JXfn9rGYoLYxUNEDZ1eu3jqUHnTjEvLzc0V06dPF82aNXvqNOPSfvrpJwFA7N69W6f8t99+E0FBQcLR0VFYWlqK1q1bi8mTJ1c6MFWI8qcZC6EZE6JQKERWVpaIjIwsd0iDvr86Hzx4IEaNGiXs7OyEnZ2dGDVqVJn3D0BERkZqf09OThZjx44Vbm5uwsrKSrRv316sWLFCO+6mouEYAER8fLzOtUeOHCn8/f0rjC8oKEjI5XJhZWUlevXqJb7//vtK34++unhqtdS9sXCpeyJq6BrrUvcV2bFjB2bMmIGkpCRYWNR+rzQyHH0tdc8uHiIiMlk5OTmIj4/HkiVLMGnSJCYnjYheF2ojIiLSp2XLlqFLly5wcXFBWFiYscOhOsQEhYiITFZ4eDjUajV++ukn2NraGjscqkNMUIiIiMjkMEEhIiIik8MEhYiIiEwOExQiIiIyOUxQiIiIyOQwQSEiIiKTwwSFiIhMxrFjxyCRSPDw4UNjh0JGxgSFiKiBS8tJw7qL65CWk/b0yrU0duxYSCQSSCQSSKVStGnTBrNmzUJ2drbBXzs/Px9dunSBRCJ56g7DgYGB2jgtLCzg6emJsLAwnR2QExISMH78eHh4eEAmk8HT0xMLFixAQUGBXuPOyMhAaGgo5HI55HI5QkNDn5qgPXr0CNOmTUOLFi0gk8ng7e2NiIgI7fH09HRMnz4d7du3h7W1Ndzd3fH2229DpVLpXOf8+fMYMGAAmjZtCicnJ7z55pt49OiRTp0zZ86gf//+aNq0KRwcHDBw4MCn3l99YIJCRNTApeWmIeJSBNJyDZ+gAEBwcDCSk5Pxxx9/4P3339fuDmxoc+bMgZubW5XrT5w4EcnJybh58yaWLVuGtWvXIjw8XHv82rVrKC4uxvr16xEbG4v//e9/+OSTTzBv3jy9xh0SEoKLFy8iKioKUVFRuHjxIkJDQys955133kFUVBS2b9+Oq1ev4p133sH06dPx7bffAgCSkpKQlJSE5cuX4/Lly9iyZQuioqJ0dixOSkrCCy+8AC8vL/z666+IiopCbGwsxo4dq62TlZWFQYMGwd3dHb/++itOnjwJe3t7DBo0CGq1Wq/3oYynbidogribMRE1dPrczTj2fqzosKWDiL0fq4fIKlfebsYTJkwQSqVSCCFEXl6emD59ulAoFE/dzfjRo0fCzs5O7NmzR+d6+/btE9bW1iIzM1Nb9v3334tnnnlGxMbGCgDiwoULlcZZ3m7Gr776qujWrVul5y1btkx4eHhUWqc64uLiBABx+vRpbVl0dLQAIK5du1bheb6+vmLRokU6Zd26dRPvvvtuhefs3r1bWFhYCLVaLYQQYv369cLZ2VkUFRVp61y4cEEAEL///rsQQogzZ84IAOL27dvaOr/99psAIG7evFnu6+hrN2O2oBARNUBpOWmIexCHuAdxuPrgKgDg6oOr2rK66O4pIZPJtH9tz5kzB1999RW2bt2K8+fPw8vLC4MGDUJ6enqZ82xsbPDGG28gMjJSpzwyMhLDhg2DnZ0dAODevXuYOHEiPvvsM1hbW9coxkuXLuGXX36BVCqttJ5KpYKjo6NOma2tbaWPwYMHV3i96OhoyOVy9OrVS1v23HPPQS6X49SpUxWe16dPH+zbtw+JiYkQQuDo0aO4ceMGBg0aVGns9vb2aNJEs09wfn4+LCwsYGb2Vyogk8kAACdPngQAtG/fHs2aNcPmzZtRUFCA3NxcbN68Gb6+vmjVqlUld6r2uJsxEVEDtOfGHkRcitApC48O1/48pfMUTO0y1eBxxMTEYOfOnejfvz+ys7MRERGBLVu2aL+0N27ciMOHD2Pz5s2YPXt2mfMnTJgAf39/JCUlwc3NDffv38eBAwdw+PBhAIAQAmPHjsXkyZPRo0cPJCQkVDm2devWYdOmTVCr1SgoKICZmRnWrl1bYf1bt25h9erVWLFihU7508ZjlHzplyclJQXOzs5lyp2dnZGSklLheatWrcLEiRPRokULNGnSBGZmZti0aRP69OlTbv0HDx7gv//9LyZNmqQt69evH/71r3/ho48+wowZM5Cdna3tvkpOTgYA2NnZ4dixYxg6dCj++9//AgDatWuHH374QZvoGAoTFCKiBmh4u+EIbBkIQNNyEh4djnC/cHg7eQMAFDKFwV77wIEDsLW1RWFhIdRqNYYOHYrVq1fj1q1bUKvV6N27t7auVCpFz549cfXq1XKv1bNnT/j6+mLbtm2YO3cuPvvsM7i7u6Nv374AgNWrVyMzM7NGOx2PGjUK8+fPR2ZmJpYuXQp7e3u89tpr5dZNSkpCcHAwhg8fjgkTJugc8/LyqvZrlyaRSMqUCSHKLS+xatUqnD59Gvv27UOrVq3w888/Y+rUqXB1dcULL7ygUzczMxMvvfQSfHx8sGDBAm25r68vtm7din/9618ICwuDubk53n77bbi4uMDc3BwAkJubi3/+85/o3bs3Pv/8cxQVFWH58uV48cUXcebMmUqTr9pigkJE1AAprBVQWOsmId5O3vBx8jH4awcFBSEiIgJSqRRubm7abpOSv8qf/OJ92pfxhAkTsGbNGsydOxeRkZEYN26ctv6RI0dw+vRpWFpa6pzTo0cPjBo1Clu3bq3wunK5XJtcbN++Hb6+vti8ebPOQFJAk5wEBQXBz88PGzZsKHOdp+2y/Pzzz+PgwYPlHlMqlbh3716Z8rS0NLi4uJR7Tm5uLubNm4e9e/fipZdeAgB06tQJFy9exPLly3USlKysLAQHB8PW1hZ79+4t04UVEhKCkJAQ3Lt3DzY2NpBIJFi5ciU8PDwAADt37kRCQgKio6O1XUE7d+6Eg4MDvv32W7zxxhuVvvfaYIJSF7JSgLORQI9xgJ3S2NEQERmUjY1Nua0KXl5esLCwwMmTJxESEgIAUKvVOHv2LGbOnFnh9UaPHo05c+Zg1apViI2NxZgxY7THVq1ahffff1/7e1JSEgYNGoRdu3bpjOt4GqlUinnz5iEsLAwjR47UjmVJTExEUFAQunfvjsjISJ3xGiVq08Xj5+cHlUqFmJgY9OzZEwDw66+/QqVSwd/fv9xz1Go11Gp1mVjMzc1RXFys/T0zMxODBg2CpaUl9u3bBysrqwrjKEmGPv30U1hZWWHAgAEAgJycHJiZmekkkCW/l34tg3jqMFoTVO9m8SReEGKBveaZiKgK9DmLJzU7Vay9sFakZqfqIbLKlTeLp7QZM2YINzc3cfDgQREbGyvGjBkjHBwcRHp6uhBCdxZPaSEhIcLCwkIEBwdX+vrx8fE1nsWTn58vXF1dxUcffSSEECIxMVF4eXmJfv36ibt374rk5GTtQ5+Cg4NFp06dRHR0tIiOjhYdO3YUL7/8sk6d9u3bi6+//lonfl9fX3H06FHxxx9/iMjISGFlZSXWrVsnhBAiMzNT9OrVS3Ts2FHcvHlTJ/bCwkLtdVavXi3OnTsnrl+/LtasWSNkMpn4v//7P+3xq1evCktLSzFlyhQRFxcnrly5IkaPHi3kcrlISkoq9/3oaxYPE5S6wASFiKpJnwlKXXpagpKbmyumT58umjVr9tRpxqX99NNPAoDYvXt3pa9fmwRFCCE++OADoVAoRFZWloiMjBQAyn3o04MHD8SoUaOEnZ2dsLOzE6NGjSrz/gGIyMhI7e/Jycli7Nixws3NTVhZWYn27duLFStWiOLiYiHEX/exvEd8fLz2OqGhocLR0VFYWFiITp06iW3btpWJ79ChQ6J3795CLpcLBwcH0a9fPxEdHV3h+9FXgiJ5/MbrlczMTMjlcu2UKZOUlaJ5AEDyJWD/28CQVYBrZ02ZnZLdPURUoby8PMTHx8PDw6PSpvnGYseOHZgxYwaSkpJgYWFh7HCoEpV9dqvz/c0xKIZyNhI4/qFu2f63//o5YC4QVP1R50REjUlOTg7i4+OxZMkSTJo0iclJI8IExVB6jAPaP16cp6IWFCIiqtSyZcvwwQcfoG/fvjWaSkz1FxMUQynVhZOW/xB7msox3LEVFG5djBsXEVE9Eh4errM/DjUeXOq+DqTlP0SEgxxp+Q+NHQoREVG9wASlLlg76T4TERFRpdjFYyBpOWnarc2v5qX+9fwgDoBmmeknV3kkIiIiDSYopRQVC8TEpyM1Kw/Odlbo6eEIc7OKl1+ujKls1EVERFQfMUF5LOpKMhbuj0OyKk9b5iq3woIhPgju4Frt6xlzoy4iIqL6jmNQoElOpmw/r5OcAECKKg9Ttp9H1JXkal9TYa2Aj5MPfJx8tElJyUZdPk4+7N4hIirHsWPHIJFI8PDhQ2OHQkbW6BOUomKBhfvjUN5yuiVlC/fHoai43i24S0RU58aOHQuJRAKJRAKpVIo2bdpg1qxZyM7ONthrtm7dWvuaJY+5c+dWek5gYKC2roWFBTw9PREWFob8/HxtnYSEBIwfPx4eHh6QyWTw9PTEggULUFBQoNf4MzIyEBoaCrlcDrlcjtDQ0KcmaI8ePcK0adPQokULyGQyeHt7IyJCd1jBhg0bEBgYCHt7+6cmffn5+ejSpQskEonO5odbtmwpc29LHqmpqbV410/X6Lt4YuLTy7SclCYAJKvyEBOfDj/Pms3CUcgUmNJ5Crt1iMgo1KmpeLhrN5qOeB1SZ2eDv15wcDAiIyOhVqtx4sQJTJgwAdnZ2WW+QPVp0aJFmDhxovZ3W1vbp54zceJELFq0CAUFBThz5gzGjRsHAFiyZAkA4Nq1ayguLsb69evh5eWFK1euYOLEicjOzsby5cv1FntISAju3r2LqKgoAMCbb76J0NBQ7N+/v8Jz3nnnHRw9ehTbt29H69atcejQIUydOhVubm4YOnQoAM0qvMHBwQgODn7qIndz5syBm5sbLl26pFM+YsQIBAcH65SNHTsWeXl5cDbwZ6nRt6CkZlWcnNSkXnkU1gpM7TKV3TpEZBSFaWm4v3YtCtPS6uT1LC0toVQq0bJlS4SEhGDUqFH45ptvAGj+Un/77bfh7OwMKysr9OnTB2fOnCn3OtnZ2bC3t8eXX36pU75//37Y2NggKytLW2ZnZwelUql9VCVBsba2hlKphLu7O1577TUMGDAAhw4d0h4vSbQGDhyINm3a4JVXXsGsWbPw9ddf1+CulO/q1auIiorCpk2b4OfnBz8/P2zcuBEHDhzA9evXKzwvOjoaY8aMQWBgIFq3bo0333wTnTt3xtmzZ7V1Zs6ciblz5+K5556rNIaDBw/i0KFD5SZdMplM576am5vjyJEjGD9+fM3fdBU1+gTF2a5qm3BVtR4REemSyWRQq9UANH+pf/XVV9i6dSvOnz8PLy8vDBo0COnp6WXOs7GxwRtvvIHIyEid8sjISAwbNgx2dnbasqVLl8LJyQldunTBBx98UO1umEuXLuGXX36BVCqttJ5KpYKjo6NOma2tbaWPwYMHV3i96OhoyOVy9OrVS1v23HPPQS6X49SpUxWe16dPH+zbtw+JiYkQQuDo0aO4ceMGBg0aVMV3rHHv3j1MnDgRn332GaytrZ9af9u2bbC2tsawYcOq9To10ei7eHp6OMJVboUUVV6541AkAJRyzZRjIqL6Qp2aqm0xyYuL03kGgCYKRZ1098TExGDnzp3o37+/tptny5Yt2i/tjRs34vDhw9i8eTNmz55d5vwJEybA398fSUlJcHNzw/3793HgwAEcPnxYW2fGjBno1q0bHBwcEBMTg7CwMMTHx2PTpk2VxrZu3Tps2rQJarUaBQUFMDMzw9q1ayusf+vWLaxevRorVqzQKS89ZqM8MpmswmMpKSnldpU4OzsjJSWlwvNWrVqFiRMnokWLFmjSpAnMzMywadMm9OnTp9JYShNCYOzYsZg8eTJ69OiBhISEp57z6aefIiQkpNL3pC+NPkExN5NgwRAfTNl+HhJAJ0kpWQFlwRCfGq+HQkRkDA937cb9J75sU/7znvbnZm+9BcX0aQZ57QMHDsDW1haFhYVQq9UYOnQoVq9ejVu3bkGtVqN3797aulKpFD179sTVq1fLvVbPnj3h6+uLbdu2Ye7cufjss8/g7u6Ovn37auu888472p87deoEBwcHDBs2TNuqUpFRo0Zh/vz5yMzMxNKlS2Fvb4/XXnut3LpJSUkIDg7G8OHDMWHCBJ1jXl5eVbovFZFIyn6/CCHKLS+xatUqnD59Gvv27UOrVq3w888/Y+rUqXB1dcULL7xQpdddvXo1MjMzq7wJY3R0NOLi4rBt27Yq1a+tRp+gAEBwB1dEjO5WZh0UZS3WQSEiMqamI16Hbb8gAJqWk5T/vAflfxfByscHgKYFxVCCgoIQEREBqVQKNzc3bbdJcrJmyYYnv3if9mU8YcIErFmzBnPnzkVkZCTGjRtXaf2SMRc3b96sNEGRy+Xa5GL79u3w9fXF5s2by4yvSEpKQlBQEPz8/LBhw4Yy13naeJfnn38eBw8eLPeYUqnEvXv3ypSnpaXBxcWl3HNyc3Mxb9487N27Fy+99BIATWJ28eJFLF++vMoJypEjR3D69GlYWlrqlPfo0QOjRo3C1q1bdco3bdqELl26oHv37lW6fm0xQXksuIMrBvgo9baSLBGRMUmdnct04Vj5+EDm62vw17axsSm3VcHLywsWFhY4efIkQkJCAABqtRpnz57FzJkzK7ze6NGjMWfOHKxatQqxsbEYM2ZMpa9/4cIFAICra9X/uJRKpZg3bx7CwsIwcuRI7XiMxMREBAUFoXv37oiMjISZWdmhm7Xp4vHz84NKpUJMTAx69uwJAPj111+hUqng7+9f7jlqtRpqtbpMLObm5iguLq40ltJWrVqF999/X/t7UlISBg0ahF27dumMiQE005p3796tneFUF5iglGJuJqnxVOLK1PUUPyIiU2RjY4MpU6Zg9uzZcHR0hLu7O5YtW4acnJxKZ4U4ODjg1VdfxezZszFw4EC0aNFCeyw6OhqnT59GUFAQ5HI5zpw5g3feeQevvPIK3N3dqxVfSEgI5s2bh3Xr1mHWrFlISkpCYGAg3N3dsXz5cqSVmgWlVCq1P9emi8fb2xvBwcGYOHEi1q9fD0Azzfjll19G+/bttfWeeeYZLFmyBH//+99hb2+PgIAAzJ49GzKZDK1atcLx48exbds2rFy5UntOSkoKUlJScPPmTQDA5cuXYWdnB3d3d+39L62kJcjT01PnHgPArl27UFhYiFGjRtX4vVabqIdUKpUAIFQqlbFDqZKcK1dEXPtnRM6VK8YOhYjqidzcXBEXFydyc3Nrfa2Ce/dE6qrVouDePT1EVrkxY8aIoUOHVng8NzdXTJ8+XTRr1kxYWlqK3r17i5iYGO3xo0ePCgAiIyND57yffvpJABC7d+/WKT937pzo1auXkMvlwsrKSrRv314sWLBAZGdnVxpnQECAmDFjRpnyDz74QCgUCpGVlSUiIyMFNEMTyzz06cGDB2LUqFHCzs5O2NnZiVGjRpV5/wBEZGSk9vfk5GQxduxY4ebmpn3fK1asEMXFxdo6CxYsKDf20tcpLT4+XgAQFy5cKHPMz89PhISEVOn9VPbZrc73t0QIUe+WSM3MzIRcLodKpYK9vb2xw3mq3NhYJLw2DK2/+rJOmleJqP7Ly8tDfHw8PDw8YGXFZQ527NiBGTNmICkpCRYWFsYOhypR2We3Ot/f7OIxEFOZ4kdEVJ/l5OQgPj4eS5YswaRJk5icNCJMUAzEmFP8iIgaimXLluGDDz5A3759qzwdlhoGdvEYyJMtKOVN8WMLChFVhF08VF+xi8fEGXOKHxERUX3X6PfiISIiItPDBKUO5FtIcfflgci3qHwTKiIiItJgglIH8s3N8NudW8g35+0mIiKqCn5jEhERkcnhIFkDeZSRjuyMdADAnbjrOs8AYOPgCFsHxxpdu6hYcM8gIiJq0JigGMhvPx5E9Jef65Qd/yxC+7PfsJHwH179PQ2iriSX2XXZlbsuE1EDcezYMQQFBSEjIwNNmzY1djhkROziMZBOLwzG6CUfY/SSj+E3bCIAwG/YRG1ZpxcGV/uaUVeSMWX7eZ3kBABSVHmYsv08oq4k6yV2IqKaGjt2LCQSCSQSCaRSKdq0aYNZs2YhOzvboK/73XffoVevXpDJZGjWrBleffXVSusHBgZq47SwsICnpyfCwsKQn5+vrZOQkIDx48fDw8MDMpkMnp6eWLBgAQoKCvQae0ZGBkJDQyGXyyGXyxEaGoqHDx9Wek5J7E8+PvroI22dlJQUhIaGQqlUwsbGBt26dcOXX36pc50bN25g6NChaNasGezt7dG7d28cPXpUe3zLli0VvlZqaqpe78OT2IJiIBIzG5g10czakZinPX52hlkTl8fHq7dcc1GxwML9cShvVT0BQAJg4f44DPBRsruHiHRkq/IR+3MifPs2h43c0uCvFxwcjMjISKjVapw4cQITJkxAdnY2IiIinn5yDXz11VeYOHEiFi9ejH79+kEIgcuXLz/1vIkTJ2LRokUoKCjAmTNnMG7cOADAkiVLAADXrl1DcXEx1q9fDy8vL1y5cgUTJ05EdnY2li9frrf4Q0JCcPfuXURFRQHQ7GYcGhqK/fv3V3hOcrLuH6QHDx7E+PHj8dprr2nLQkNDoVKpsG/fPjRr1gw7d+7EiBEjcPbsWXTt2hUA8NJLL6Fdu3Y4cuQIZDIZPv74Y7z88su4desWlEolRowYgeDgYJ3XGjt2LPLy8uBs4MVG2YJiILE/J2L34jPYvfgMzn6fAAA4+32Ctiz258RqXS8mPr1My0lpAkCyKg8x8em1iJqIGqIcVQHOfJeAHJV+//KviKWlJZRKJVq2bImQkBCMGjUK33zzDQAgPz8fb7/9NpydnWFlZYU+ffrgzJkz5V4nOzsb9vb2Zf7q379/P2xsbJCVlYXCwkLMmDEDH330ESZPnox27dqhffv2GDZs2FPjtLa2hlKphLu7O1577TUMGDAAhw4d0h4vSbQGDhyINm3a4JVXXsGsWbPw9ddf1/zmPOHq1auIiorCpk2b4OfnBz8/P2zcuBEHDhzA9evXKzxPqVTqPL799lsEBQWhTZs22jrR0dGYPn06evbsiTZt2uDdd99F06ZNcf78eQDA/fv3cfPmTcydOxedOnVC27Zt8eGHHyInJwexsbEAAJlMpvM65ubmOHLkCMaPH6+3e1ARJigG4tu3OV6f9yxen/cseg/vDHOr59B7eGdtmW/f5tW6XmpWxclJTeoREdUVmUwGtVoNAJgzZw6++uorbN26FefPn4eXlxcGDRqE9PSyf1zZ2NjgjTfeQGRkpE55ZGQkhg0bBjs7O5w/fx6JiYkwMzND165d4erqisGDB2u/YKvq0qVL+OWXXyCVVr5elUqlgqOj7gQHW1vbSh+DB1fcpR8dHQ25XI5evXppy5577jnI5XKcOnWqSrHfu3cP3333XZmkoU+fPti1axfS09NRXFyML774Avn5+QgMDAQAODk5wdvbG9u2bUN2djYKCwuxfv16uLi4oHv37uW+1rZt22BtbV2lBLC22MVjIDZyy1JNqS0hlfmjpXdLKNztanQ9Z7uq7cVR1XpE1LBlq/K1LSZpt7N0ngHAWm5RJ909MTEx2LlzJ/r376/t5tmyZYv2S3vjxo04fPgwNm/ejNmzZ5c5f8KECfD390dSUhLc3Nxw//59HDhwAIcPHwYA/PHHHwCA8PBwrFy5Eq1bt8aKFSsQEBCAGzdulEkmSlu3bh02bdoEtVqNgoICmJmZYe0Tm7yWduvWLaxevRorVqzQKb948WKl90Amk1V4LCUlpdyuEmdnZ6SkpFR63RJbt26FnZ1dmXE3u3btwogRI+Dk5IQmTZrA2toae/fuhaenJwDNOJbDhw9j6NChsLOzg5mZGVxcXBAVFVXhAOVPP/0UISEhlb4nfWGCUk/09HCEq9wKKaq8csehSAAo5Zopx0REsT8n4sx3CTplR7df0/787Eut0XNIGxjCgQMHYGtri8LCQqjVagwdOhSrV6/GrVu3oFar0bt3b21dqVSKnj174urVq+Veq2fPnvD19cW2bdswd+5cfPbZZ3B3d0ffvn0BAMXFxQCA+fPna8dfREZGokWLFtizZw8mTZpUYZyjRo3C/PnzkZmZiaVLl8Le3l5nDEdpSUlJCA4OxvDhwzFhwgSdY15eXlW/OeWQSMqOGxRClFtenk8//RSjRo0qszHfu+++i4yMDPz4449o1qwZvvnmGwwfPhwnTpxAx44dIYTA1KlT4ezsjBMnTkAmk2HTpk14+eWXcebMGbi66s4MjY6ORlxcHLZt21bzN1sNTFDqgLXcAs++1BrW8uoNjC3N3EyCBUN8MGX7eUgAnSSl5CO8YIgPB8gSEQBNN7NHZwUATcvJ0e3XEDT6GW0rbm3+PXqaoKAgREREQCqVws3NTdttUjKw88kv3qd9GU+YMAFr1qzB3LlzERkZiXHjxmnrl3yJ+jzeKR7QjIFp06YNbt++XWmccrlcm1xs374dvr6+2Lx5c5mukqSkJAQFBcHPzw8bNmwocx1bW9tKX+f555/HwYMHyz2mVCpx7969MuVpaWlwcXGp9LoAcOLECVy/fh27du3SKb916xbWrFmDK1euwPfxJrWdO3fGiRMnsHbtWnzyySc4cuQIDhw4gIyMDO3OwuvWrcPhw4exdetWzJ07V+eamzZtQpcuXSrs/tE3jkGpAzZyS/Qc0qbWzanBHVwRMboblHIrKJCBmU2+hAIZUMqtEDG6G9dBISItG7klFO522gcAnd8N2b1jY2MDLy8vtGrVSmdMh5eXFywsLHDy5EltmVqtxtmzZ+Ht7V3h9UaPHo3bt29j1apViI2NxZgxY7THunfvDktLS50BpWq1GgkJCWjVqlWVY5ZKpZg3bx7effdd5OTkaMsTExMRGBiIbt26ITIyEmZmZb82L168WOlj06ZNFb6un58fVCoVYmJitGW//vorVCoV/P39nxr35s2b0b17d3Tu3FmnvOQ9PBmvubm5ttWpojpmZmbaOiUePXqE3bt318ngWC1RD6lUKgFAqFQqY4diFIVFxeLSr8eEWGAvLv16TBQWFRs7JCLSs9zcXBEXFydyc3Nrfa3UPzPFmkk/idQ/M/UQWeXGjBkjhg4dWuHxGTNmCDc3N3Hw4EERGxsrxowZIxwcHER6eroQQoijR48KACIjI0PnvJCQEGFhYSGCg4PLvWbz5s3FDz/8IK5duybGjx8vnJ2dtdcsT0BAgJgxY4ZOWX5+vnB1dRUfffSREEKIxMRE4eXlJfr16yfu3r0rkpOTtQ99Cg4OFp06dRLR0dEiOjpadOzYUbz88ss6ddq3by++/vprnTKVSiWsra1FREREmWsWFBQILy8v8fzzz4tff/1V3Lx5UyxfvlxIJBLx3XffCSGESEtLE05OTuLVV18VFy9eFNevXxezZs0SUqlUXLx4Ued6mzZtElZWVpXe0xKVfXar8/3NLp56yNxMgk4t5ACgeWa3DhFVQh/dzPry4Ycfori4GKGhocjKykKPHj3www8/wMHBodLzxo8fj507d+Kf//xnmWMfffQRmjRpgtDQUOTm5qJXr144cuTIU6/5JAsLC0ybNg3Lli3D5MmTcejQIdy8eRM3b95EixYtdOoKUd5owJrZsWMH3n77bQwcOBAA8Morr2DNmjU6da5fvw6VSqVT9sUXX0AIgZEjR5a5plQqxffff4+5c+diyJAhePToEby8vLB161a8+OKLAIBmzZohKioK8+fPR79+/aBWq+Hr64tvv/22TIvM5s2b8eqrr1b7ntaGROjzLgMoLCxEeHg4duzYgZSUFLi6umLs2LF49913tc1IQggsXLgQGzZsQEZGBnr16oW1a9dq+8meJjMzE3K5HCqVSttv1ihkpWgeAJB8Cdj/NjBkFeD6+INkp9Q8iKjey8vLQ3x8PDw8PMoMfmyMduzYgRkzZiApKQkWFsZPtKhilX12q/P9rfcWlKVLl+KTTz7B1q1b4evri7Nnz2LcuHGQy+WYMWMGAGDZsmVYuXIltmzZgnbt2uH999/HgAEDcP36ddjZ1WwabqNwNhI4/qFu2f63//o5YC4QFFa3MRERGVBOTg7i4+OxZMkSTJo0iclJI6L3BCU6OhpDhw7FSy+9BABo3bo1Pv/8c5w9exaApvXk448/xvz587Vztrdu3QoXFxfs3Lmz0ilhjV6PcUD7xwv+VNSCQkTUgCxbtgwffPAB+vbti7Aw/gHWmOh9Fk+fPn3w008/4caNGwA0q/OdPHlS2+cVHx+PlJQUbV8boJkSFhAQUOGqefn5+cjMzNR5NEp2SsCti+ZRkpS4dv6rjAkKETUw4eHhUKvV+Omnn546nZcaFr23oPz73/+GSqXCM888A3NzcxQVFeGDDz7QDuIpWRnvyfndLi4u+PPPP8u95pIlS7Bw4UJ9h0pEREQmSu8tKLt27cL27duxc+dOnD9/Hlu3bsXy5cuxdetWnXrVWagnLCwMKpVK+7hz546+w65/7JSaMSdsNSEiogZI7y0os2fPxty5c/HGG28AADp27Ig///wTS5YswZgxY6BUar5QS2b4lEhNTa1w1TxLS0tYWhp+z4h6xU7JAbFERNRg6b0FJScnp9KV6zw8PKBUKrUbPQFAQUEBjh8/XqVV84iIiKjh03sLypAhQ/DBBx/A3d0dvr6+uHDhAlauXKldXEcikWDmzJlYvHgx2rZti7Zt22Lx4sWwtrZGSEiIvsNpsNJy0rDnxh4MbzccCmuFscMhIiLSK70nKKtXr8Z//vMfTJ06FampqXBzc8OkSZPw3nvvaevMmTMHubm5mDp1qnahtkOHDnENlGpIy01DxKUIBLYMZIJCREQNjt4TFDs7O3z88cf4+OOPK6wjkUgQHh6O8PBwfb88ERHVY8eOHUNQUBAyMjLQtGlTY4dDRsTdjOuRtJw0xD2IQ9yDOFx9cBUAcPXBVW1ZWk6akSMkosZu7NixkEgkkEgkkEqlaNOmDWbNmoXs7GyDvN6xY8e0r/fk48yZMxWeFxgYqK1nYWEBT09PhIWFIT8/X1snISEB48ePh4eHB2QyGTw9PbFgwQIUFBTo9T1kZGQgNDQUcrkccrkcoaGhePjwYaXnVPSeP/roI22dlJQUhIaGQqlUwsbGBt26dcOXX35Z5lrfffcdevXqBZlMhmbNmmkXUX3SgwcP0KJFC0gkkqfGpw/cLLAe2XNjDyIuReiUhUeHa3+e0nkKpnaZWsdREZGpe5SRjt9+PIhOLwyGrYOjwV8vODgYkZGRUKvVOHHiBCZMmIDs7GxEREQ8/eRq8vf3R3Jysk7Zf/7zH/z444/o0aNHpedOnDgRixYtQkFBAc6cOYNx48YB0Ky9BQDXrl1DcXEx1q9fDy8vL1y5cgUTJ05EdnY2li9frrf3EBISgrt37yIqKgoA8OabbyI0NBT79++v8Jwn3/PBgwcxfvx4vPbaa9qy0NBQqFQq7Nu3D82aNcPOnTsxYsQInD17Fl27dgUAfPXVV5g4cSIWL16Mfv36QQiBy5cvl/ua48ePR6dOnZCYmFjbt1w1T93v2ARVZ7vmhiQ1O1XE3o8VsfdjxZfXvxQdtnQQX17/UluWmp1q7BCJSE8q27K+ulJu/S6Wv/6SSLn1ux4iq9yYMWPE0KFDdcomTJgglEqlEEKIvLw8MX36dKFQKISlpaXo3bu3iImJ0dY9evSoACAyMjLEo0ePhJ2dndizZ4/O9fbt2yesra1FZmZmmdcvKCgQzs7OYtGiRZXGGRAQIGbMmKFT9uqrr4pu3bpVet6yZcuEh4dHpXWqIy4uTgAQp0+f1pZFR0cLAOLatWtVvs7QoUNFv379dMpsbGzEtm3bdMocHR3Fpk2bhBBCqNVq0bx5c+3vlVm3bp0ICAgQP/30k/a/T0Uq++xW5/ubXTz1iMJaAR8nH/g4+cDbyRsA4O3krS3jYFkiMkUymQxqtRqAZpLEV199ha1bt+L8+fPw8vLCoEGDkJ6eXuY8GxsbvPHGG4iMjNQpj4yMxLBhw8qdWLFv3z7cv38fY8eOrVaMly5dwi+//AKpVFppPZVKBUdH3VYoW1vbSh+DBw+u8HrR0dGQy+Xo1auXtuy5556DXC6vcPuXJ927dw/fffcdxo8fr1Pep08f7Nq1C+np6SguLsYXX3yB/Px8BAYGAgDOnz+PxMREmJmZoWvXrnB1dcXgwYMRGxurc524uDgsWrQI27ZtK7OMiCGxi4eIqAF6lJGO7AzNl/69+Fs6zwBg4+BYJ909MTEx2LlzJ/r376/t5tmyZYv2S3vjxo04fPgwNm/ejNmzZ5c5f8KECfD390dSUhLc3Nxw//59HDhwQGctrdI2b96MQYMGoWXLlk+Nbd26ddi0aRPUajUKCgpgZmaGtWvXVlj/1q1bWL16NVasWKFTfvHixUpfRyaTVXgsJSUFzs7OZcqdnZ21W8M8zdatW2FnZ1dm7MiuXbswYsQIODk5oUmTJrC2tsbevXvh6ekJAPjjjz8AaPY7WrlyJVq3bo0VK1YgICAAN27cgKOjI/Lz8zFy5Eh89NFHcHd3155TF5ig1FMKmQJTOk+BQsZWEyIq67cfDyL6y891yg5vWK392W/YSPgPH2WQ1z5w4ABsbW1RWFgItVqNoUOHYvXq1bh16xbUajV69+6trSuVStGzZ09cvXq13Gv17NkTvr6+2LZtG+bOnYvPPvsM7u7u6Nu3b5m6d+/exQ8//IDdu3dXKc5Ro0Zh/vz5yMzMxNKlS2Fvb68zhqO0pKQkBAcHY/jw4ZgwYYLOMS8vryq9XkXK2+ZFVLL9y5M+/fRTjBo1ClZWVjrl7777LjIyMvDjjz+iWbNm+OabbzB8+HCcOHECHTt21C6gOn/+fO37joyMRIsWLbBnzx5MmjQJYWFh8Pb2xujRo2v1HmuCCUo9pbBWcEAsEVWo0wuD4dld021wL/4WDm9YjQFvToeLh+avZxsDtp4EBQUhIiICUqkUbm5u2m6TkoGd1dmLDdC0oqxZswZz585FZGQkxo0bV279yMhIODk54ZVXXqlSnHK5XJtcbN++Hb6+vti8eXOZrpKkpCQEBQXBz88PGzZsKHOdp+2y/Pzzz+PgwYPlHlMqlbh3716Z8rS0tAq3fyntxIkTuH79Onbt2qVTfuvWLaxZswZXrlyBr68vAKBz5844ceIE1q5di08++US73YyPj4/2PEtLS7Rp0wa3b98GABw5cgSXL1/Wzv4RQgAAmjVrhvnz5xt0I18mKEREDZBtOV04Lh6ecGlTu7/2q8LGxqbcVgUvLy9YWFjg5MmT2pXD1Wo1zp49i5kzZ1Z4vdGjR2POnDlYtWoVYmNjMWbMmDJ1hBCIjIzEP/7xj6eOIymPVCrFvHnzEBYWhpEjR8La2hoAkJiYiKCgIHTv3h2RkZHljsGoTRePn58fVCoVYmJi0LNnTwDAr7/+CpVKVaXtXzZv3ozu3bujc+fOOuU5OTkAUOnWM927d4elpSWuX7+OPn36AND890hISECrVq0AaGb55Obmas8/c+YM/vnPf+LEiRPariJDYYJCRER1wsbGBlOmTMHs2bPh6OgId3d3LFu2DDk5OWVaLUpzcHDAq6++itmzZ2PgwIFo0aJFmTpHjhxBfHx8pdd5mpCQEMybNw/r1q3DrFmzkJSUhMDAQLi7u2P58uVIS/trramSjW+B2nXxeHt7Izg4GBMnTsT69esBaKYZv/zyy2jfvr223jPPPIMlS5bg73//u7YsMzMTe/bsKTMmpqS+l5cXJk2ahOXLl8PJyQnffPMNDh8+jAMHDgAA7O3tMXnyZCxYsAAtW7ZEq1attOuoDB8+HADKJCH379/Xxm3ohfSYoBARNXA2Do7wGzbSoN06VfXhhx+iuLgYoaGhyMrKQo8ePfDDDz/AwcGh0vPGjx+PnTt3avd1e9LmzZvh7+8Pb2/vGsdmYWGBadOmYdmyZZg8eTIOHTqEmzdv4ubNm2WSopKuDn3YsWMH3n77bQwcOBAA8Morr2DNmjU6da5fvw6VSqVT9sUXX0AIgZEjR5a5plQqxffff4+5c+diyJAhePToEby8vLB161a8+OKL2nofffQRmjRpgtDQUOTm5qJXr144cuTIU/971AWJ0OddriOZmZmQy+VQqVSwt7c3djhERHqXl5eH+Ph4eHh4lBn82Bjt2LEDM2bMQFJSEiwsLIwdDlWiss9udb6/2YJCREQmKycnB/Hx8ViyZAkmTZrE5KQR4UJtRERkspYtW4YuXbrAxcUFYWFhxg6H6hATlHpKnZqKtNVroE5NNXYodaqoWCD61gN8ezER0bceoKi43vVQElE1hIeHQ61W46effnrqdF5qWNjFU08VpqXh/tq1sO0XBGk5qxA2RFFXkrFwfxySVXnaMle5FRYM8UFwB1cjRkZERPrGFhSqF6KuJGPK9vM6yQkApKjyMGX7eURdSa7gTCIiqo/YglKPqFNTUfh4Hn5eXJzOMwA0USgaZGtKUbHAwv1xKK8zRwCQAFi4Pw4DfJQwN6va0tBE9UU9nGhJjZy+PrNMUOqRh7t24/4TG1ml/Oc97c/N3noLiunT6josg4uJTy/TclKaAJCsykNMfDr8PJ3qLjAiAypZDTUnJ6fSlUiJTE1BQQEAzaq1tcEEpR5pOuJ12PYLAqBpOUn5z3tQ/ncRrB7vo9BE0TA3DkzNqjg5qUk9ovrA3NwcTZs2RerjgfDW1tZV3jyOyFiKi4uRlpYGa2trNGlSuxSDCUo9InV21nbh3L+XgV/b90R/J1c4PN4IqqFytqvaIlVVrUdUX5Qsp57ayGbrUf1mZmYGd3f3WifUTFDqqYz7mXhg9QAZ9zPR0tjBGFhPD0e4yq2QosordxyKBIBSboWeHsZfxptInyQSCVxdXeHs7Ay1Wm3scIiqxMLCotxNFauLCUo9ZW5vp/PckJmbSbBgiA+mbD8PCaCTpJTk5wuG+HCALDVY5ubmte7PJ6pvmKDUI6l/piA9UdPUe/fPJO2z+anfAACOzZ3h3EpZ4fn1WXAHV0SM7lZmHRQl10EhImqQuFlgPbLn/TW4fTmqwuPuHYMx/N2GN4untKJigZj4dKRm5cHZTtOtw5YTIqL6gZsFNlABocOQntgXAPDn5au4cuQzdOgXilYdNduLOzZveGugPMncTMKpxEREjQATlHrEuZVSpwvnyhGgVUdvPOPfyYhRERER6R+XuiciIiKTwwSlnnJs7gz3jsGNoluHiIgaHw6SJSIiojpRne9vtqAQERGRyWGCQkRERCaHCQoRERGZHCYoREREZHKYoBAREZHJYYJCREREJocJChEREZkcJihERERkcpigEBERkclhgkJEREQmhwkKERERmRwmKERERGRymKAQERGRyWGCQkRERCaHCQoRERGZHCYoREREZHKYoBAREZHJYYJCREREJocJChEREZkcJihERERkcpigEBERkclhgkJEREQmhwkKERERmRwmKERERGRymKAQERGRyWGCQkRERCaHCQoRERGZHCYoREREZHKYoBAREZHJYYJCREREJocJChEREZkcJihERERkcpigEBERkclhgkJEREQmxyAJSmJiIkaPHg0nJydYW1ujS5cuOHfunPa4EALh4eFwc3ODTCZDYGAgYmNjDREKERER1UN6T1AyMjLQu3dvSKVSHDx4EHFxcVixYgWaNm2qrbNs2TKsXLkSa9aswZkzZ6BUKjFgwABkZWXpOxwiIiKqhyRCCKHPC86dOxe//PILTpw4Ue5xIQTc3Nwwc+ZM/Pvf/wYA5Ofnw8XFBUuXLsWkSZOe+hqZmZmQy+VQqVSwt7fXZ/hERERkINX5/tZ7C8q+ffvQo0cPDB8+HM7OzujatSs2btyoPR4fH4+UlBQMHDhQW2ZpaYmAgACcOnVK3+EQERFRPaT3BOWPP/5AREQE2rZtix9++AGTJ0/G22+/jW3btgEAUlJSAAAuLi4657m4uGiPPSk/Px+ZmZk6DyIiImq4muj7gsXFxejRowcWL14MAOjatStiY2MRERGBf/zjH9p6EolE5zwhRJmyEkuWLMHChQv1HSoRERGZKL23oLi6usLHx0enzNvbG7dv3wYAKJVKACjTWpKamlqmVaVEWFgYVCqV9nHnzh19h01EREQmRO8JSu/evXH9+nWdshs3bqBVq1YAAA8PDyiVShw+fFh7vKCgAMePH4e/v3+517S0tIS9vb3Og4iIiBouvXfxvPPOO/D398fixYvx+uuvIyYmBhs2bMCGDRsAaLp2Zs6cicWLF6Nt27Zo27YtFi9eDGtra4SEhOg7HCIiIqqH9J6gPPvss9i7dy/CwsKwaNEieHh44OOPP8aoUaO0debMmYPc3FxMnToVGRkZ6NWrFw4dOgQ7Ozt9h0NERET1kN7XQakLXAeFiIio/jHqOihEREREtcUEhYiIiEwOExQiIiIyOUxQiIiIyOQwQaF6J1uVj5j9fyBblW/sUIiIyECYoFC9c//OPZz6cifu37ln7FCIiMhAmKBQvZN7LwFFeaeRey/B2KEQEZGB6H2hNiJDyFblI0dVAADIuPtA+5x2OwsAYC23gI3c0mjxERGRfjFBoXrhQlQcLhy+BgAoLkoFAMQcu42zJw4AALoOeAZ9RnQ1WnxERKRfTFCoXih8dBoFWd/pluUcLnX8JQBMUIiIGgomKFQv9HBJhXfr8wCAW9keiE5zgJ8iA5428QAAG5dny5yTrcpH7M+J8O3bnN0/RET1DBMUqhdsAybBtttQAMD9Az8BPx2FvNOrcHm5v6aCnbLMOSWzfVw8/gEbuXtdhktERLXEBIXqBzulNgmRWp99/CwH3LpUeEpu5kPNbJ/MVwAwQSEiqk+YoFC94+ggg1dKOhwdZGWO6cz2ScnWPnO2DxFR/cIEheoFdWoqCtPSAADm6Xlody8D5ul5yI2NBQA0USggdXYuf7bP/hic/T4BAGf7EBHVF0xQqF54uGs37q9dq1OW8sFy7c/N3noLiunTUFhwGQVZu3Xq6cz2KXgdnO1DRGT6JEIIYewgqiszMxNyuRwqlQr29vbGDofqQOkWlPiYnyBZGgHx7ynw6KkZJFvSgvIoIx3ZGekAgFvnYhH95Ub4DZsIz+6+AAAbB0fYOjga500QETVy1fn+ZgsK1QtSZ2dInZ01v6g0U4vRvg1kvr469WxLJSAZKTkAAMfmHnBp41VnsRIRUe0xQaF6IS0nDWm5j1tQVPFo8/gZD+IAAAqZAgprhc450keJpZ471WW4RERUS0xQqF7Yc2MPIi5FAACaPhIY0EeCw3+sx8PUDQCAKZ2nYGqXqTrnyNXp8EpJh1ydXufxEhFR7TBBoXpheLvhCGwZCAC4+uAqwm3DEe4XDm8nbwCaFpQn2dhYo929DNjYWNdlqEREpAdMUKheUFiX7cLxdvKGj5OPTpk6PhaFf94AAOSdPaHzDABNWrWD1EN33AoREZkeJijUoDxcswj3v/tNpyxl00Fg00EAQLOXOkGxYpcxQiMiompggkL1jkKmwJTOU8rt1mk67T3YDvmrBSVl00EoJwyGVY/nAWhaUIiIyPQxQaF6R2GtKDMgtoTUw1e3C2fTQVj1eB6ywL/XUXRERKQPZsYOgMhQHqqzdJ6JiKj+YIJCDVZGMwfs6SNBRjMHY4dCRETVxASFGi53T+x53hxw9zR2JEREVE0cg0INSukVZ68+uKrzDJS/4iwREZkeJijUoJRecbZEeHS49ufyVpwlIiLTwwSFGpQyK85GP33FWSIiMj1MUKhBqeqKs0REZNo4SJaIiIhMDhMUarAqW3GWiIhMG7t4qMGqbMVZIiIybWxBISIiIpPDBIWIiIhMDrt4iMjkFRULxMSnIzUrD852Vujp4QhzM4mxwyIiA2KCQmRkjzLS8duPB9HphcGwdXA0djgmJ+pKMhbuj0OyKk9b5iq3woIhPgju4GrEyIjIkNjFQ2Rk9+/cQ/SXn+P+nXvGDsXkRF1JxpTt53WSEwBIUeVhyvbziLqSbKTIiMjQmKAQGVneI7XOM2kUFQss3B8HUc6xkrKF++NQVFxeDSKq79jFQ2QEjzLSkZ2RDgBIT4zXPt/7wxoAYOPg2Oi7e2Li08u0nJQmACSr8hATnw4/T6e6C4yI6gQTFCIjOHvgAM4d2K1TFv3lRkR/qfm5+8uvIzD0H0aIzHSkZlWcnNSkHhHVL0xQiIygiUVHWNhJAQDFRakozDmMJtYDYGbu/Pj4M8YMzyQ421nptR4R1S9MUIiMoGuwD9r7eQEArh48ijNHgK7PecB7cBAAwFpuYczwTEJPD0e4yq2QosordxyKBIBSrplyTEQNDwfJEhmBRb4Ktlm3YZt1GzY5KQAAm5wUbZlFvsrIERqfuZkEC4ZodqF+csWTkt8XDPHheihEDRQTFCIjeLhrNxJeG4aE14Yh94svYW71HHK/+FJb9nDX7qdfpBEI7uCKiNHdoJTrduMo5VaIGN2N66AQNWASIUS9m6OXmZkJuVwOlUoFe3t7Y4dDVG3q1FQUpqUBADIuXMWF7dHoOtoPDl29AQBNFApInZ2NGaJJ4UqyRA1Ddb6/OQaFyAikzs46CUib9/8Dh67/hMzX14hRmS5zMwmnEhM1MuziISIiIpPDBIXIyJooFGj21ltoolAYOxQiIpPBLh4iI5M6O0MxfZqxwyAiMilsQSEiIiKTwwSFiIiITA4TFCIiIjI5TFCIjCwtJw3rLq5DWk6asUMhIjIZTFCIjCwtNw0RlyKQlssEhYioBBMUIiIiMjmcZkxkBGk5adoWk6uJp3WeAUAhU0BhzXVRiKjxYoJCZAR7buxBxKUInbLwC/8DLmh+ntJ5CqZ2mWqEyIiITAMTFCIjGN5uOAJbBgIArt46hPCrmxHuPR7engMBaFpQ6srD32/gzPq1eHbSW2jatl2dvS4RUWWYoBAZgaKoCIr8As0vBZpn74IC+JSUWRTVWSyZfybgtzu30P7PBCYoRGQymKAQGcPZSOD4h5qfLaRAc1fg52XAjx9oygLmAkFhdRJKXm6RzjMRkSlggkJkDD3GAe0HAwAUt3/BlNNLoei3EHDvrTlupzToyz/8/QYy/0wAANw5f1H7bCUzBwDYt2rN1hQiMiqDTzNesmQJJBIJZs6cqS0TQiA8PBxubm6QyWQIDAxEbGysoUMhMh12SsCtC+DWBQr33pj6UAWFe29tmaETlDPr12LPxlXYs3EVLsb9AgC4GPeLtuzM+rUGfX0ioqcxaAvKmTNnsGHDBnTq1EmnfNmyZVi5ciW2bNmCdu3a4f3338eAAQNw/fp12NnZGTIkIgLQYdQkuPyeAABIuHAFv//xM9q26YvWXTsAABRtWxsvOCIiGLAF5dGjRxg1ahQ2btwIBwcHbbkQAh9//DHmz5+PV199FR06dMDWrVuRk5ODnTt3GiocItNlp9SMOTFwq0lpd+5a4cQRzePPtJYAgD/TWmrL7ty1qrNYiIjKY7AWlLfeegsvvfQSXnjhBbz//vva8vj4eKSkpGDgwIHaMktLSwQEBODUqVOYNGlSmWvl5+cjPz9f+3tmZqahwiaqe3bKOhsQW8K3b3N4dNZMZb568CjOHAE6P2sD78HPAgCs5RZ1Gg8R0ZMMkqB88cUXOHfuHM6ePVvmWEpKCgDAxcVFp9zFxQV//vlnuddbsmQJFi5cqP9AiRopG7klbOSWAIAs39Y4f+o5tPBtDYU7u1iJyDTovYvnzp07mDFjBnbs2AErq4qbiSUSic7vQogyZSXCwsKgUqm0jzt37ug1ZqLGzM7dA1KZP+zcPYwdChGRlt5bUM6dO4fU1FR0795dW1ZUVISff/4Za9aswfXr1wFoWlJcXV21dVJTU8u0qpSwtLSEpaWlvkMlIgC5FllA9/uaZ7AFhYhMg95bUPr374/Lly/j4sWL2kePHj0watQoXLx4EW3atIFSqcThw4e15xQUFOD48ePw9/fXdzhE9BSPpA/xicV/8Uj60NihEBFp6b0Fxc7ODh06dNAps7GxgZOTk7Z85syZWLx4Mdq2bYu2bdti8eLFsLa2RkhIiL7DISIionrIKCvJzpkzB7m5uZg6dSoyMjLQq1cvHDp0iGugENWRtJw0pOWmAQCuPriq8wxoNitUWNfdhoVERE+SCCGEsYOorszMTMjlcqhUKtjb2xs7HKJ6Z93FdYi4FFHh8Smdp2Bql6l1GBERNQbV+f7mXjxEjdDwdsMR2DIQgKblJDw6HOF+4fB28gagaUEhIjImJihEjZDCumwXjreTN3ycfIwUERGRLoNvFkhERERUXUxQiBo5hUyBKZ2nsFuHiEwKu3iIGjlFURGmZqiAoiJjh0JEpMUWFKLGLisFOP6h5pmIyEQwQSEiIiKTwy4eosYoKwXISkGREEi4HA1PALd+O4XWQsBcIgHslJoHEZGRMEEhaozORgLHP4Q5AM/HRZ6nw4DTj38JmAsEhRkpuLpRVCwQE5+O1Kw8ONtZoaeHI8zNyt9RnYjqHhMUokboqO2LWJFvBwGgg1kClko34t/qiYgtbg0A+H+2zyPIqBGWpU5NxcNdu9F0xOuQOjvX6lpRV5KxcH8cklV52jJXuRUWDPFBcAfXSs4korrCMShEjUxRscC8H+/jivBArPDAlcdJyZXi1tqyeT/eR1Gxae2CUZiWhvtr16IwLa1W14m6kowp28/rJCcAkKLKw5Tt5xF1JblW1yci/WCCQtTIxMSnl/lyLk0ASFblISY+ve6CqoKHeRk6zzVRVCywcH8cyku9SsoW7o8zueSMqDFiFw9RI5OapZucpIqm+LjwVaSKppXWMwZ1aqq2xSTjt/OQPH5uauUAAGiiUFSru6c6yZmfp1NtQieiWmKCQtTIONtZ6fyeBgd8XDjsqfWM4eGu3bi/di0AoGT4qmRpBBKg2Ym52VtvQTF9WpWvV9WkyxSSM6LGjgkKUSPT08MRrnIrpKjyyu3qkABQyjWzWoyt+JX+EN1bAwCSz/8CtzXfIGna3+DarbfmeHPPSs4uq6pJlykkZ0SNHRMUokbG3EyCBUN8MGW7psukdJJS0kqxYIiPSUy5/SrjKCJ+17SWeGQLLAXwf9n7Ef/7AQDAFOspmNrKu8rXq0/JGVFjJxFC1LvRYJmZmZDL5VCpVLC3tzd2OET1Un2YapuWk4a0XM0YlKs//ICsXRdhN6ILvAcNAqDZ6FBhXb1NDktm8QDlJ2cRo7uZzPsnamiq8/3NFhSiRiq4gysG+ChNerEyhfVfCUiyZSwSrH5CS8sW8HHyqfE1gzu4ImJ0tzLJmdLEkjOixo4JClEjZm4mqT+zVWxtdJ9roSQ5O3T9dxz882sMbvUqBrZva1LJGVFjxwSFiExW6p8pSE9MBQA8upmmfb5m9xsAwLG5M5xb1WzPIHMzCVo5F+JozA5MfvYVJidEJoYJChGZrOOffYnbl6N0ym7+vAc3f94DAHDvGIzh71Z9mjER1R9MUIjIZAWEDkN6Yl8AwJ+Xr+LKkc/QoV8oWnXUzNxxbF79PXlKD7z9/fcYDD9RhN/bx2iP12TgLRHpHxMUIjJZzq2Uf3Xh5D7ElSNAKy9XPOPfqcbX3HNjDyIuPZ66nCKw9KTAv9suR/x1TRfPlM5TMLXL1FrHTkS1wwSFiOqHvIe6zzU0vN1wBLYMBADEx/wEYB0mdZoEj579AWhaUIjI+JigEFG94Ogih7udLRxd5LW6TtNHArZpj1dASdE8e6QIeDz+uYlCANa1egki0gMmKERkurJSNA8AzpIEDG9xEJAMBpIeJyl2Ss2jGvS9vw8RGQYTFCIyXWcjgeMf6pbtf/uvnwPmAkFh1bpk0xGvw7ZfEADg/sUYPPrvMtj+Zw6adekJQLNDMhEZHxMUIjJdPcYB7Qdrfk6+pElOhqwCXDtryqrZegIAUmdnSJ01s3+ss4vwW+sX8Vzb7pD5+uoraiLSAyYoREZUVCxMeql5oyuvC8e1M+DWRS+Xf5Cqwu8uDmibqkI9WU+XqNFggkJkJPVhs76GTl2UhaK801AXdTN2KET0BDNjB0DUGJXsqFs6OQGAFFUepmw/j6gryUaKzITZKTVjTmrQrVNatiofabezkHY7C5kP8wEAmQ//KstW5esjWiKqJYkQQjy9mmmpznbNRKamqFigz9IjZZKTEhJodtY9+e9+7O4xgJO7LuDC4WsAgOKiVBTmHEYT6wEwM9eMS+k64Bn0GdHVmCESGZUhu56r8/3NLh6iOhYTn15hcgIAAkCyKg8x8en1Z6fheqTw0WkUZH2nW5ZzuNTxlwAwQaHGyZS6npmgENWx1KyKk5Oa1KPq6eGSCu/W5wEAt7I9EJ3mAD9FBjxt4gEANi7PGjM8IqMp6Xp+slulpOs5YnS3Ok1SmKAQ1TFnOyu91qPqsQ2YBNtuQwEAGUdPAvui4Og3Ei5BfTQVajnGhag+KioWWLg/rkxyAmhadSUAFu6PwwAfZZ11PTNBoQbJlKfv9vRwhKvcCimqvHL/MSgZg9LTw7GuQ2scSk1dtnK7+/i5td6mLhPVR6bY9cwEhRocU+pDLY+5mQQLhvhgyvbzkAA6SUpJCrVgiI/JJFQNWTOlHH7N/kQzZe329yEydU/7o80Uu56ZoFCDYmp9qBUJ7uCKiNHdyiRSShNKpBoD2xZt4T8sBGjR1tihEBlMVf5oM8WuZ04zpgajPk7fNeWuKCKq/yr6o63kX5mSP9pK/v18Wtdzbf/9rM73NxdqowajOn2opsLcTAI/TycM7dIcfp5OTE6ISG+eNvAV0Ax8LSoW2q5n4K/kpYSxup6ZoFCDYYp9qESNRlYKcHSJ5plMQnX/aCvpelbKdbtxlHIro3SPcwwKNRim2IdK1GhkpQDHP9TsPq2vqdpZKcDZSM2u1pz+XW01+aMtuIMrBvgoTaLrmQkKNRicvkvUwDDpqZWa/tFW0vVsbOzioQbDFPtQiRq0rBQg6aLmkXxJU5Z86a8yU+zuKUl6TDE2PSv5o63kXzyHvEyMuvoDHPIyAWj+XXSt4I82dWoq0lavgTo1te4CfgITFGpQTK0PlahBOxsJbAgANgQg7fuZWNdUjrTvZ2rLcDay+tesj0lPddThWJ0n/2hzzMvE6OuH4ZiX+dQ/2grT0nB/7VoUpqUZPM6KsIuHGhxT6kMlatB6jNN0vwBI++MQIm59hsAe06BoM1BzvCZdKGcjNS0cpe1/+6+fA+YCQWHVu2ZWijYhePT7afyW5o5Ov5+GbcnxUqsLG5whuq0qUXrNJTz8q7w+rLnEBIUaJFPpQyVq0Ep/sWcmALcANGtXu20DSiU9j34/jd92r0Wn19+Cbdvn/nrN6iqV9GTn2iD6fjd4fr8ItrJszfGaJD31hDo1FQGSdPw4RIlrP98BjgHLOlnimb5KmEnSoU41h9TZWVu3pMUkLy5O5xkAmigU2rp1gQkKERHVSFpOGtJyNV9ol27dxItnu+NSs5uAQvOlppApoLBWVO+ipZKe+9fvIvp+K7gVt4CtnpKe3OjjQMJh5Pb8N+AX8NdrGpIRW3Ae7tqN+2vXAgCsH5dZr1qK26s0Pzd76y0opk8rU7dEyn/e0/5cum5dYIJCREQ1sufGHkRcigAAtElugb6p5vji8k9YfH8rAGBK5ymY2mVqja+fl1Os81xTjwotkJ2nSQeSVFbaZ9njMhuZxV/JgiGUasG5l+GG6PuecPn6/2Dr8G/NcQO24DQd8Tps+wUBAPLOn0bKB8uhnD8LVt00LVJNFIry68bFIeU/70H530Ww8vEpU7cuMEEhIqIaGd5uOAJbBgIAzh47hbQL3+C1tq+hR6A/AE0LSnU9ykhHdoZm4bD0jCzt870/bgIAbBwcYetQvaUCfvvxIKK//FynLPqH/Yj+YT8AwG/YSPgPH1XtWKusVAtO9u7vgJRoZHuMBl5/SXPcgC04Umfnv7pl0m4AAKxaOkLm61t53cesfHzKrVsXmKAQEVGNiLQimCUWAgAsE4u0z2bXNWWieRHQqnrXPHvgAM4d2K1TFr3/c0Tv1yQY3V9+HYGh/6jWNb169odj844AgD/Pn8eVE1+iw/PD0KpbNwCAY3PDjqso3YKToW6ifb5XVy04NZHzQPfZCJigEBFRjRz/7EvcvhylU3b3l/24+4umZcK9YzCGv1u9MQtNLDrCwk4KACguSkVhzmE0sR4AM3Pnx8efqXacCb/l4Mx39zXXLLQEANy4aImbVzRlz75kC+dqJlLVEbN7Ny4cOaBTdvbsCZw9ewIA0LXfy+g3abJhXrzU+JcmhUlo5puFJoVJminbQIXjX5pYFWnqWhUZJq4qYIJCREQ1EhA6DOmJfQEA1y9cwM2f98Cr73C079oVQM1aJroG+6C9nxcAIPrno/h9P+DR3wN+fTVjI6zlFtW+pm/f5vDorOluunn2Ck7tAnq82BpePTrU+JrVUZhgCQs7TRdSeUlXYYIB9wcrNf6loMgB8a1fhO/xjyA9OU9zvILxL1InByg6ZgFODoaL7SmYoBARUY04t1LCuZXmr++iTBVu/gx4ebbBM/6danzNHGkm0mw0M4MeylK1z2k2dwAACqkCNqje2BYbuSVs5JqWk6zbNjC3eg4uzjZQuNvVOM7q6DVhILxva97T77/k4sJloKOnHdr29gYA2LsbcPBpqfEv9389h1PfJMPlb/+BTa/umuOlW09KtbZk37qM2KwR8L11GTYlx+tyvRgwQSEiIj0oyszSea6p0jODmj9ogWCr3tj551f46MD/Aaj9zCCpuhhSmT+k6trNDKoOuWdzyD2bo6hY4LfrmsG+uc3s4RbQ2fALSJZKKnItbqMoby9yLd4sf62aUq0tOeo2OJO9Ah5R/w820j80x+t4vRgmKEREVGsOzezhlOcEh2b2tbpO6ZlB1y6dxa1rv+HNLiPxTOceAGo2M6g0dZMstE74Duomf6vVdaor6koyFu6PQ6v4NDxn9Rw+O5+G95ceMfhqrtmqfOSoCgAAGfeLtM9ptzWJpLXcQtu6VLq1JefXc1B/cwo5PaYB5bW21AEmKEREVCOlVx61fZCMXtdjYPvgZeTGxgKo2cqjCutSi7tZ/QHvn7+DGBsIHycfvcSZd/MC2iR8j7ybrZDr6FjjOKsj6koypmw/DwFAInNEl2yB200dkaLKw5Tt5w26T9iFqDhcOHwNgGb8CwDEHLuNsyc0g3a7DngGfUZoxgxlFzsgp1DToZOUGY+ivL1IyhwP60JPAIB1scVf3T11gAkKERHViKmtPFqR0nGWdKhIlkYgAZquJEPGWVQssHB/HMTj35Nktvik5V+TiiUAFu6PwwAfpUG6ewoLLqMgS3fadmHO4VLHXwegSVBif07Eme8SAADFhZqBu2dP5OF89BkAwLMvtUbPIW30HmNFmKAQEVGNGGLl0dKtHXbxaXj0+DlXXvNWmeJX+kN0bw0ASD7/C9zWfIOkaX+Da7femuPNPasdZ1XFxKcjWVXxLB0BIFmVh5j4dIPsH9bj5Zfh3VuzcN6tc7GI/nIj/IZNhGd3zeJrNqUWvWvdyRr2Ts0AANfP/I6bpwD3jplo/6ymrmNza9QlJihERFQjhlh5tLxWmUf/XYZHj3+uSWvHVxlHEfG7prXEI1tgKYD/y96P+N813RxTrKdgaivvGsdcmdSsqk0hrmq96rIttfJuRkoOAMCxuQdc2niVqXsz5qcyK+7ePLUfN0/9teKucysDrrj7BCYoRERkMgzRKlN64G18zE8A1mFSp0nw6NkfQO0H3lbG2c5K53dJk0xIm/4K9cNeEIX2FdYzhHxpts7zkzq9MBie3XsBAE6fOIab338Drxf/hueeDwSg29pSF5igEBFRrTVRKNDsrbdqvaGcIVpldAbetsnAnj4SDGvTrVYDb6uqp4cjXOVWSFHlaQbJNsmCpeInFD7ygSi0hwSAUm6Fnh6G//IvcpLgotdDBDmVP9Yl17IID+SaGT9ZimLtc0mZmWVRnS7JzwSFiIhqTersbBIDYp+qmQP2PG+OYc3qZoVUczMJFgzxwZTt5/FkWlDy+4IhPoZfDwWAldweF9upYCUvfyp46TVoHFUWeAWu2HhzPdLTVgOo/Ro01cUEhYiITJK+WmVKU8gUmNJ5ikG7dZ7UvU0TzH/VDht+/gMZhYkAAHOrRDjYWuDNvm3QvY3hvorTctKQlqsZdHz1wVWdZ0BzP0pal0p3hV1OOIcD99Zjau+Z6Ni6u7ZuXZIIIcTTq1XdkiVL8PXXX+PatWuQyWTw9/fH0qVL0b59e20dIQQWLlyIDRs2ICMjA7169cLatWvhW8UmvMzMTMjlcqhUKtjb125RICIiIkNad3GdtmWiPIZsmajpa8c9iMOIAyOw6+Vdeu0Kq873t97TtuPHj+Ott97Cs88+i8LCQsyfPx8DBw5EXFwcbGw0S7wsW7YMK1euxJYtW9CuXTu8//77GDBgAK5fvw47u7rZG4GIiKgulG6ZuPrgKsKjwxHuFw5vJ83MIUO2TBjztWtL7wlKVJTu1tuRkZFwdnbGuXPn0LdvXwgh8PHHH2P+/Pl49dVXAQBbt26Fi4sLdu7ciUmTJuk7JCIiqmeKigVi4tORmpUHZzvNINK6GKdhCDqDdB/zdvKuk0G6NX1tY3SFPcngY1BUKhUAwPHxksLx8fFISUnBwIEDtXUsLS0REBCAU6dOlZug5OfnIz8/X/t7ZmamgaMmIiJjKdm3pvQCZ65yK4PvW0N/UVgr6nRAbHnMDHlxIQT+9a9/oU+fPujQoQMAICVFs5Wzi4uLTl0XFxftsSctWbIEcrlc+2jZsqUhwyYiIiMp2bfmydVXS/atibqSbKTI9MOYLROm0CpSHQZNUKZNm4bffvsNn3/+eZljEoluU50QokxZibCwMKhUKu3jzp07BomXiIiM58l9a0orKVu4Pw5FxXqd21GnSlomnux2aeivXRMGS1CmT5+Offv24ejRo2jRooW2XKnUbNf8ZGtJampqmVaVEpaWlrC3t9d5EBFRw1KdfWuo4dN7giKEwLRp0/D111/jyJEj8PDw0Dnu4eEBpVKJw4f/2k2xoKAAx48fh7+/v77DISKiesLY+9aQadH7INm33noLO3fuxLfffgs7OzttS4lcLodMJoNEIsHMmTOxePFitG3bFm3btsXixYthbW2NkJAQfYdDRET1RFX3o6npvjUNaWZQY6D3BCUiQrMgTGBgoE55ZGQkxo4dCwCYM2cOcnNzMXXqVO1CbYcOHeIaKEREjdiT+9Y8qTb71nBmUP2j95Vk6wJXkiUiaphKZvEA0ElSSto5IkZ3q3ZCUXLNJ7/sanNNqpnqfH8bdBYPERFRdQR3cEXE6G5QynW7cZRyqxolEo1hZlBDxc0CiYjIpAR3cMUAH6VexotUZ2aQn6dTLaImfWOCQkREJsfcTKKXhIEzg+ovdvEQEVGDZeiZQWQ4TFCIiKjBKpkZVFHnkASa2Tw1mRlEhsUEhYiIaqWoWCD61gN8ezER0bcemNSAU3MzCRYM0ezc+2SSUvL7giE+XA/FBHEMChER1Vh9WF+kZGbQk3EqTSxO0sV1UIiIqEbq2/oiXEnW+Krz/c0WFCIiqranrS8igWZ9kQE+SpNJAvQ1M4jqBsegEBFRtXHnYTI0JihERFRtXF+EDI0JChERVRvXFyFDY4JCRETVxvVFyNCYoBARUbVxfREyNCYoRERUI/reeZioNE4zJiKiGtPnzsNEpTFBISKiWuH6ImQI7OIhIiIik8MEhYiIiEwOExQiIiIyOUxQiIiIyOQwQSEiIiKTwwSFiIiITA4TFCIiIjI5TFCIiIjI5DBBISIiIpNTL1eSFUIAADIzM40cCREREVVVyfd2yfd4ZeplgpKVlQUAaNmypZEjISIiourKysqCXC6vtI5EVCWNMTHFxcVISkqCnZ0dJJLGvSFVZmYmWrZsiTt37sDe3t7Y4Zgk3qPK8f48He/R0/EePR3vkablJCsrC25ubjAzq3yUSb1sQTEzM0OLFi2MHYZJsbe3b7Qf+KriPaoc78/T8R49He/R0zX2e/S0lpMSHCRLREREJocJChEREZkcJij1nKWlJRYsWABLS0tjh2KyeI8qx/vzdLxHT8d79HS8R9VTLwfJEhERUcPGFhQiIiIyOUxQiIiIyOQwQSEiIiKTwwSFiIiITA4TlHpg3bp18PDwgJWVFbp3744TJ05UWPfrr7/GgAEDoFAoYG9vDz8/P/zwww91GG3dq879OXnyJHr37g0nJyfIZDI888wz+N///leH0RpHde5Rab/88guaNGmCLl26GDZAE1Cde3Ts2DFIJJIyj2vXrtVhxHWvup+j/Px8zJ8/H61atYKlpSU8PT3x6aef1lG0da8692fs2LHlfoZ8fX3rMGITJ8ikffHFF0IqlYqNGzeKuLg4MWPGDGFjYyP+/PPPcuvPmDFDLF26VMTExIgbN26IsLAwIZVKxfnz5+s48rpR3ftz/vx5sXPnTnHlyhURHx8vPvvsM2FtbS3Wr19fx5HXnereoxIPHz4Ubdq0EQMHDhSdO3eum2CNpLr36OjRowKAuH79ukhOTtY+CgsL6zjyulOTz9Err7wievXqJQ4fPizi4+PFr7/+Kn755Zc6jLruVPf+PHz4UOezc+fOHeHo6CgWLFhQt4GbMCYoJq5nz55i8uTJOmXPPPOMmDt3bpWv4ePjIxYuXKjv0EyCPu7P3//+dzF69Gh9h2YyanqPRowYId59912xYMGCBp+gVPcelSQoGRkZdRCdaajuPTp48KCQy+XiwYMHdRGe0dX236K9e/cKiUQiEhISDBFevcQuHhNWUFCAc+fOYeDAgTrlAwcOxKlTp6p0jeLiYmRlZcHR0dEQIRqVPu7PhQsXcOrUKQQEBBgiRKOr6T2KjIzErVu3sGDBAkOHaHS1+Rx17doVrq6u6N+/P44ePWrIMI2qJvdo37596NGjB5YtW4bmzZujXbt2mDVrFnJzc+si5Dqlj3+LNm/ejBdeeAGtWrUyRIj1Ur3cLLCxuH//PoqKiuDi4qJT7uLigpSUlCpdY8WKFcjOzsbrr79uiBCNqjb3p0WLFkhLS0NhYSHCw8MxYcIEQ4ZqNDW5R7///jvmzp2LEydOoEmThv9PRE3ukaurKzZs2IDu3bsjPz8fn332Gfr3749jx46hb9++dRF2narJPfrjjz9w8uRJWFlZYe/evbh//z6mTp2K9PT0BjcOpbb/VicnJ+PgwYPYuXOnoUKslxr+vz4NgEQi0fldCFGmrDyff/45wsPD8e2338LZ2dlQ4RldTe7PiRMn8OjRI5w+fRpz586Fl5cXRo4cacgwjaqq96ioqAghISFYuHAh2rVrV1fhmYTqfI7at2+P9u3ba3/38/PDnTt3sHz58gaZoJSozj0qLi6GRCLBjh07tLvXrly5EsOGDcPatWshk8kMHm9dq+m/1Vu2bEHTpk3xt7/9zUCR1U9MUExYs2bNYG5uXiYDT01NLZOpP2nXrl0YP3489uzZgxdeeMGQYRpNbe6Ph4cHAKBjx464d+8ewsPDG2SCUt17lJWVhbNnz+LChQuYNm0aAM0XjRACTZo0waFDh9CvX786ib2u1OZzVNpzzz2H7du36zs8k1CTe+Tq6ormzZtrkxMA8Pb2hhACd+/eRdu2bQ0ac12qzWdICIFPP/0UoaGhsLCwMGSY9Q7HoJgwCwsLdO/eHYcPH9YpP3z4MPz9/Ss87/PPP8fYsWOxc+dOvPTSS4YO02hqen+eJIRAfn6+vsMzCdW9R/b29rh8+TIuXryofUyePBnt27fHxYsX0atXr7oKvc7o63N04cIFuLq66js8k1CTe9S7d28kJSXh0aNH2rIbN27AzMwMLVq0MGi8da02n6Hjx4/j5s2bGD9+vCFDrJ+MNTqXqqZk6trmzZtFXFycmDlzprCxsdGO9J47d64IDQ3V1t+5c6do0qSJWLt2rc4UtocPHxrrLRhUde/PmjVrxL59+8SNGzfEjRs3xKeffirs7e3F/PnzjfUWDK669+hJjWEWT3Xv0f/+9z+xd+9ecePGDXHlyhUxd+5cAUB89dVXxnoLBlfde5SVlSVatGghhg0bJmJjY8Xx48dF27ZtxYQJE4z1Fgyqpv+fjR49WvTq1auuw60XmKDUA2vXrhWtWrUSFhYWolu3buL48ePaY2PGjBEBAQHa3wMCAgSAMo8xY8bUfeB1pDr3Z9WqVcLX11dYW1sLe3t70bVrV7Fu3TpRVFRkhMjrTnXu0ZMaQ4IiRPXu0dKlS4Wnp6ewsrISDg4Ook+fPuK7774zQtR1q7qfo6tXr4oXXnhByGQy0aJFC/Gvf/1L5OTk1HHUdae69+fhw4dCJpOJDRs21HGk9YNECCGM2YJDRERE9CSOQSEiIiKTwwSFiIiITA4TFCIiIjI5TFCIiIjI5DBBISIiIpPDBIWIiIhMDhMUIiIiMjlMUIiIiMjkMEEhIiIik8MEhYiIiEwOExQiIiIyOUxQiIiIyOT8f7s8Zixw+jgRAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Validat average poly 1 - 7 : R2 values [0.52591035 0.73266722 0.74410654 0.74341028 0.72933788 0.70594779\n", " 0.6605303 ]\n", "Validat average poly 1 - 7 : sum |y-yfit|^2 values [358.35885361 197.00066855 187.79874283 187.81476318 201.75231429\n", " 219.71267567 261.85078136]\n" ] } ], "source": [ "tes=0.3 # 30 % of the data to test set\n", "P_train, P_test, V_train, V_test = train_test_split(PvdwV,VV,test_size=tes)\n", "N_tr=len(V_train)\n", "N_te=len(V_test)\n", "Nval=100 # num of validation cycles\n", "#print('V_test',V_test)\n", "#print('P_test',P_test)\n", "print('Validation training point ',N_tr,' test points ',N_te,' iteration ',Nval)\n", "aver2=np.zeros(NP)\n", "averb=np.zeros(NP)\n", "\n", "for iv in range(Nval):\n", " p_c=np.zeros((NP,NP+1))\n", " for i in range(NP): # polynoms from 1 to NP\n", " p_c[i,0:i+2]=np.polyfit(V_train,P_train,i+1,full=False)\n", "# print('Polynomial coeff ',p_c[i,0:i+2])\n", "\n", " y=np.zeros((NP,N_te))\n", " for i in range(NP):\n", " poly2=np.poly1d(p_c[i,0:i+2])\n", " y[i,:]=poly2(V_test)\n", "\n", " r2=np.zeros(NP)\n", " rb=np.zeros(NP)\n", " for i in range(NP):\n", " r2[i]=r2_score(P_test,y[i,:]) # R2 over test-set\n", " rb[i]=np.sum((y[i,:]-P_test[:])**2)/N_te # sum_test-set (y_fit - y_real)**2\n", " aver2[i]=aver2[i]+r2[i]/float(Nval) \n", " averb[i]=averb[i]+rb[i]/float(Nval) \n", "\n", " if iv == Nval-1: \n", "# this will show one test case, the + are the fits in this iteration\n", " plt.plot(V_test,P_test,'o',label='P_test')\n", " for i in range(2,NP):\n", " R2lab = 'Poly'+str(i+1)+' R2= {: >6.4f}'.format(r2[i])\n", " plt.plot(V_test,y[i],'+',label=R2lab)\n", " plt.legend()\n", " plt.show()\n", "\n", " P_train, P_test, V_train, V_test = train_test_split(PvdwV,VV,test_size=tes) # new test and train sets return for iv loop\n", "\n", "print('Validat average poly 1 -',NP,': R2 values ',aver2[0:NP])\n", "print('Validat average poly 1 -',NP,': sum |y-yfit|^2 values ',averb[0:NP])\n" ] }, { "cell_type": "code", "execution_count": null, "id": "1be45f67", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }