Files
ANum/QUESTION19.ipynb
2024-12-03 20:04:03 +01:00

147 lines
86 KiB
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "7a5c0139-3d42-4163-87e0-2c545af4a54a",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "84f76ae7-f53b-4a7e-af5f-6a979dcedfa9",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def fexamen(t, y, alpha = 1.1, beta = 0.4, gamma = 0.4, delta = 0.1):\n",
" y1, y2 = y[0], y[1]\n",
" \n",
" return np.array([\n",
" alpha * y1 - beta * y1*y2,\n",
" delta *y1*y2 - gamma * y2\n",
" ])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c3165e93-6475-40f7-b8c9-f72ad24c9793",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def RK2(fct,a,b,y0,h):\n",
" t = np.arange(a, b, h)\n",
" y = np.zeros((len(t), len(y0)))\n",
" \n",
" y[0] = y0\n",
" print(y0)\n",
" \n",
" for i in range(1, len(t)):\n",
" k1 = fct(t[i-1] + 0 *h, y[i-1])\n",
" k2 = fct(t[i-1] + 1 *h, y[i-1] + 1*k1*h)\n",
" \n",
" y[i] = y[i-1] + h * (.5*k1+.5*k2)\n",
" \n",
" return t, y"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "c36ba389-8ab4-4af1-a27d-c1c756e54274",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[10 10]\n"
]
},
{
"data": {
"image/png": 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YOnUqAGZymTdvHt544w1UV1dj1KhReP3119G/f3/JnyG4WjIyMkh8EARBEESSISVkIqyA044dO+LPf/4zdu3ahV27duHKK6/EDTfcgAMHDgAAXnzxRbz88st47bXXsHPnThQUFGDSpEmor6+P7C8gCIIgCEJ1RF1kLDs7G3/5y19wzz33oKioCHPmzMETTzwBALDb7cjPz8cLL7yA+++/X9L71dXVITMzE7W1tWT5IAiCIIgkIZz1O+JUW7fbjRUrVsBisWDMmDE4ceIEysvLMXnyZPEao9GIcePGYdu2bSHfx263o66uLuBGEARBEIR6CTvgtKSkBGPGjIHNZkNaWhpWrlyJfv36iQIjPz8/4Pr8/HycPHky5PstWLAA8+bNC7cZBEEQSYnb7YbT6Ux0MwgiIvR6PbRabdTvE7b46N27N/bu3Yuamhp8+OGHuOuuu7B582bx9aaBJjzPtxh88tRTT+HRRx8VfxaiZQmCINQEz/MoLy9HTU1NoptCEFGRlZWFgoKCqGpxhS0+DAYDevToAQAYPnw4du7ciVdeeUWM8ygvL0dhYaF4fUVFRTNriD9GoxFGozHcZhAEQSQVgvDIy8tDSkoKFVEkkg6e52G1WlFRUQEAAWt9uERd54PnedjtdnTt2hUFBQXYsGEDhgwZAgBwOBzYvHkzXnjhhWg/hiAIImlxu92i8MjJyUl0cwgiYsxmMwBmWMjLy4vYBROW+Hj66acxdepUFBcXo76+HitWrMCmTZuwdu1acByHOXPmYP78+ejZsyd69uyJ+fPnIyUlBTNmzIiocQRBEGpAiPFISUlJcEsIInqE/2On0xkf8XH+/HnceeedKCsrQ2ZmJgYNGoS1a9di0qRJAIDHH38cjY2N+PWvfy0WGVu/fr2kamcEQRBqh1wthBqQ4/846jofckN1PgiCUBs2mw0nTpxA165dYTKZEt0cgoiKUP/PcanzQRAEQRDR4nA40KNHD3zzzTctXvfYY4/hkUceiVOrImPp0qXIyspKdDOSAhIfBEEQhOyUlZVhxowZ6N27NzQaDebMmRP0ujfeeAOdO3fGpZdeCgAoLS0Fx3HYu3dvwHWPP/44lixZghMnTkTdtrlz54LjOHAcB61Wi+LiYtx77724cOFCVO9766234siRI1G3ry1A4oNIODzPw2J3JboZhERcbg88HkV5a4kW8PA8PAnwrtvtdrRv3x7PPPMMBg8eHPK6f/zjH7j33ntbfb+8vDxMnjwZ//znP2VpX//+/VFWVoZTp05h0aJF+PTTTzFz5syg17rdbng8nlbf02w2Iy8vL6p2tZWxReKDSDj/9/F+XPL8emw9Gt2ug4g9Hg+P29/6FsP/9AXO1TQmujlEK7jcHhwur8fR8w1hC5Bly5YhJycHdrs94Pmbbrop5CLtT5cuXfDKK69g5syZyMzMDHrN999/j2PHjuHaa68Vn+vatSsAYMiQIeA4DuPHjxdfu/7667F8+fKw/o5Q6HQ6FBQUoEOHDrjuuuvwyCOPYP369WhsbBTdJ5999hn69esHo9GIkydPorq6GjNnzkS7du2QkpKCqVOn4ujRo+J7BnO7fPrppxg2bBhMJhO6deuGefPmweXybbbmzp2LTp06wWg0orCoCHfe+wBOVVll+RuVDIkPIqG43B689+0pON083tlWmujmEK3wY3k9vj1RhSqLA2tKyhLdnKSG53lYHa6Y3s7X2VFvc6K20YHKBjusDhek5hjccsstcLvdWLVqlfjcxYsX8dlnn+Huu++W5TvYsmULevXqFRCc+N133wEAvvjiC5SVleGjjz4SXxs5ciROnz7d4pEdkWI2m+HxeERhYLVasWDBArz11ls4cOAA8vLyMGvWLOzatQurVq3C9u3bwfM8rrnmmpDl8tetW4c77rgDjzzyCA4ePIjFixdj6dKl+NOf/gQA+N///oe//e1vWLx4MY4ePYo3/70CPfr0Q43VAbcES0syE3WRMYKIBn+Ff6He3sKVhBL46UKD+PjERUsCW5L8NDrd6Pfsurh/7sHnpyDF0PrUbzabMWPGDCxZsgS33HILAOC9995Dx44dA6wR0VBaWoqioqKA59q3bw8AyMnJQUFBQcBrHTp0EH+vc+fOsrQBAH788UcsWrQII0eOFEtDOJ1OLFy4UHQZHT16FKtWrcI333yDsWPHAmDfR3FxMT7++GPxO/LnT3/6E5588kncddddAIBu3brhD3/4Ax5//HE899xzOHXqFAoKCjBx4kTo9Xo4zdno1HsQAMDu8iDFoF77gHr/MiIpOH7Bt4CdryPxoXT8BUdZrS2BLSHiwX333Yf169fj7NmzAIAlS5Zg1qxZstUraWxsDCv1WKiuabUGd0vMnz8faWlp4u3UqVMh36ukpARpaWkwm83o168fiouL8d5774mvGwwGDBo0SPz50KFD0Ol0GDVqlPhcTk4OevfujUOHDgX9jN27d+P5558PaNN9992HsrIyWK1W3HLLLWhsbES3bt1w3333Yc2nn4iWF6db3bEfZPkgEkqFn7Wjot4Gl9sDnZY0sVIpr/MJDhIf0WHWa3Hw+Skx/YzjFyywOthi1s5sQIdsM8x66RUphwwZgsGDB2PZsmWYMmUKSkpK8Omnn8rWvtzcXJSUlEi+vqqqCoDPOtKUBx54AD//+c/Fn5taVfzp3bs3Vq1aBa1Wi6KiomZnjJnN5gCRFcpd1dLhqR6PB/PmzcP06dObvWYymVBcXIzDhw9jw4YN2LBhA55/6rfoUPwK3v7vajjd5HYhiJhRZfGJDw8P1NtcaJdqSGCLiJaoanCIj+sa6Vj4aOA4TpL7Ixr0Wg4mr9jQ6zQRfd69996Lv/3tbzh79iwmTpwo66njQ4YMwaJFiwIWcIOBjX+3293s+v3790Ov16N///5B3y87OxvZ2dmSPtv/kFQp9OvXDy6XC99++63odqmsrMSRI0fQt2/foL8zdOhQHD58uMXPMZvNuP7663HNdddh0s0zccP4kTj240F0zBkV8nfUAIkPIqFUWhwBP9c2Okl8KJgqv/6qJfGheFx+pnt3hCmct99+Ox577DG8+eabWLZsWVi/K9TqaGhowIULF7B3714YDAb069cPADBhwgRYLBYcOHAAAwYMAMBSas1mM9auXYuOHTvCZDKJ2TJbt27F5ZdfLrpf4knPnj1xww034L777sPixYuRnp6OJ598Eh06dMANN9wQ9HeeffZZXHfddSguLsYtt9wCjUaDffv2oaSkBH/84x+xdOlSuN1ujBo1Clq9EZ99+AFMJjMKOxZH3F/JAtm3iYRS1UR81NloQVMyVVZffzXYXXCp3DSczLg9PNx+rgJ3hLU+MjIycNNNNyEtLQ033nhjWL87ZMgQDBkyBLt378b777+PIUOG4JprrhFfz8nJwfTp0wNiLXQ6HV599VUsXrwYRUVFAQv78uXLcd9990X0d8jBkiVLMGzYMFx33XUYM2YMeJ7HmjVroNfrg14/ZcoUfPbZZ9iwYQNGjBiB0aNH4+WXXxaDZbOysvDmm2/i0ksvxYhhQ/DtN1vw6pLlyGqXrXrxQWe7EAnljre+xdfHLoo/v/vLUbisZ24CW0S0xNA/bAgQjHt+P4ksVRJIxNkuDpcbP5bXiz8btBr0KYxsTp00aRL69u2LV199Va7miZSUlGDixIk4duxYi4eQrl69Gr/73e+wb98+6HTqM9rXNTpRWukL6M4w6dElNzWBLQoNne1CJD1N3S5k+VAubg+PamtzNxmhTJrunCPZSVdVVWHFihXYuHEjZs+eLVfTAhg4cCBefPFFlJaWtnidxWLBkiVLVCk8gCD9pSy7gOyosxeJpEEIWsxNM+Jig50WMwVT1+iEMB8K/UViUbkI4R5aDSe6YFrKzAjG0KFDUV1djRdeeAG9e/cOeK1///4hi30tXrwYt99+u+TPEepgtIR/FosaEcSG2F8qd7uQ+CASSr138SrIZIuZ1dE8wp1QBg3e83fMei0yzDpcbLCjkfpLsQhnhOi1Grg9rJ88PA9tGOKjJWvEmjVrQlb2zM/Pl95QAoDP8iH0VyLO44knJD6IhMHzvLigtU9jOfaNDjpgTqnU21jfpJl0Yq0Iq5PEh1IRFjOdhgMHgAdLZ5de5aNl5KwwSgSKD5vTDZUbPijmg0gcjX4DLC/dJD5HKBNBKKYZdUgxsCWMLB/Kxd+ML7ha2sqJqcmIKD40rK94lfcViQ8iYTR4d9IaDmLGBLldlEuDnZnY04w6mL3Fqkh8KBdBaGg5DhpBfKh7PUtqBDeLUOHZw4euqqoGSHwQCaPeu5NONeqQ6t1J28jyoVga7Kxv0ow6mPVs6iC3i3IRLB8aDQeNd6ZXexxBMuNzu3gtH+Ch5t4i8UEkDMHykW7UwewVH2T5UC4NfjEfKaLlg2J0lIqwmGk1PsuHmnfSyY5/zIeAmt1kJD6IhGGx+wUwUgyB4gl0uwj9RRVOlYrH2zUajoM3jIDcLgomIEYH6neTkfggEka9XwCjkD1BAafKJdDtImS7kOVDqQQNOCXLh2w4HA7Mnz8fhw4dkuX9BLGo9XOTqdlSReKDSBg+M76esieSgEC3C/WX0hHdLhwUHXDqcDjQo0cPfPPNNy1e99hjj+GRRx6JU6ta57HHHkNJSQn69OnT4nVLly5FVlZWq+8nCEMuoL8U2GEyQeKDSBhC6ma6USce+00xH8oluNuF+kupePwDTrnA5+LBRx99hEmTJqF9+/bIyMjAmDFjsG7dumbXvfHGG+jcuTMuvfRSAKywGcdx4om4Ao8//jiWLFmCEydORN22uXPnguOYRUir1aK4uBj33nsvLly4IOn3P/zwQ+zfvx/vvPNOWBVjQ8HzvK+/OA4TRw7Eu28tUqRYlAsSH0TCaBCzXbS+AEZyuyiWBnKTJRWeIAGn8RQfW7ZswaRJk7BmzRrs3r0bEyZMwLRp07Bnz56A6/7xj3/g3nvvbfX98vLyMHnyZPzzn/+UpX39+/dHWVkZTp06hUWLFuHTTz/FzJkzg17rdrvh8fjim2666SZs3LgRBoM8hyr6d4uGEyI+4tNfoarUxhoSH0TCECtmGvUw6ti/osNFAYxKxT/mw0D9FT08DzgsMbvxDgs4pxUapxValxWc0wreYQlc6Vpg2bJlyMnJgd1uD3j+pptuCrlI+/P3v/8djz/+OEaMGIGePXti/vz56NmzJz799FPxmu+//x7Hjh3DtddeKz7XtWtXAMCQIUPAcRzGjx8vvnb99ddj+fLlktrfGjqdDgUFBejQoQOuu+46PPLII1i/fj0aGxtFV8lnn32Gfv36wWg04uTJk3A4HHj88cfRoUMHpKamYtSoUdi0aVPA+y5duhSdOnVCSkoKfvazn6GysjLg9Z9++gk33HAD8vPzkZaWhhEjRmDDhg3i61ddOQFnz5zCX+Y9jQyzIcCysm3bNlxxxRUwm80oLi7GI488AovFdxIux3H4+OOPAz4vKysLS5cuBeCzKv3nP//B+PHjYTKZ8O677+LkyZOYNm0a2rVrh9TUVPTv3x9r1qyR5XsOBZVXJxKGaMY3+RYzu4t20kqlwebrL08jW8DsJD4ix2kF5hfF7O37+j0u8t4AAE+fAwytH9V+yy234JFHHsGqVatwyy23AAAuXryIzz77DGvXrg27PR6PB/X19cjOzhaf27JlC3r16hVw/Pp3332HkSNH4osvvkD//v0DrAsjR47E6dOncfLkSdnLu5vNZng8HrhcbFNktVqxYMECvPXWW8jJyUFeXh7uvvtulJaWYsWKFSgqKsLKlStx9dVXo6SkBD179sS3336Le+65B/Pnz8f06dOxdu1aPPfccwGf09DQgGuuuQZ//OMfYTKZ8M477+DGG2/Ax5u+Q1HHTvjoo4/Qf+AgTL/tLjzy6/uRmcL+/pKSEkyZMgV/+MMf8Pbbb+PChQt46KGH8NBDD2HJkiVh/a1PPPEEXnrpJSxZsgRGoxG/+tWv4HA4sGXLFqSmpuLgwYNIS0uT54sNAYkPImFYvDvpdKNOtHzQYqZc/N0uQj+R5UO9mM1mzJgxA0uWLBHFx3vvvYeOHTsGWCOk8tJLL8FisQScTltaWoqiokAB1r59ewBATk4OCgoKAl7r0KGD+Htyio8ff/wRixYtwsiRI5Geng6AuSMWLlyIwYMHA2AWi+XLl+PMmTNimx977DGsXbsWS5Yswfz58/HKK69gypQpePLJJwEAvXr1wrZt2wLE2uDBg8X3BIA//vGP+Oijldi04XPccc/9yM7OhlarRWpaGvLyC8Tqz3/5y18wY8YMzJkzBwDQs2dPvPrqqxg3bhwWLVoEk8kk+e+dM2cOpk+fLv586tQp3HTTTRg4cCAAoFu3buF+hWFD4oNIGILbJZXM+ElBg19/CX3ncFN/RYw+hVkhYoDbw+NgWR0AoF9hBi5a7KiosyMn1YAifYrk97nvvvswYsQInD17Fh06dMCSJUswa9assIMsly9fjrlz5+KTTz5BXl6e+HxjY2NYi6bZbAbArBLBmD9/PubPny/+fPDgQXTq1CnotSUlJUhLS4Pb7Ybdbsf48ePxxhtviK8bDAYMGjRI/Pn7778Hz/Po1atXwPvY7Xbk5OQAAA4dOoSf/exnAa+PGTMmQHxYLBbMmzcPn332Gc6dOweXy4XGxkaUnz0jxuYIePxqnO7evRvHjh3De++9Jz7H8zw8Hg9OnDiBvn37QirDhw8P+PmRRx7Bgw8+iPXr12PixIm46aabAv72WEDig0gYQin1FIPWJz7cHvA8L0sEOSEvQin1NKMWRj25yaKG4yS5PyKBd3vA671nJxlTwTl04PVauHUG9rkSGTJkCAYPHoxly5ZhypQpKCkpCYjZkMIHH3yAX/7yl/jvf/+LiRMnBryWm5uLkpISye9VVVUFwGcdacoDDzwQYFlpalXxp3fv3li1ahW0Wi2KiopgNBoDXjebzQHzkMfjgVarxe7du6HVBp4NLLgopNTl+N3vfod169bhr3/9K3r06AGz2YzpN90Ep9PZTHz4v53H48H9998fNN1YEFgcxzVrQ7CA0tTUwP+7e++9F1OmTMHq1auxfv16LFiwAC+99BIefvjhVv+eSCHxQSQMIVPCpNfCqGODmecBp5uHQUfiQ2kIabUmvRZGLVmqlIx/2qaQUgogorNC7r33Xvztb3/D2bNnMXHiRBQXF0v+3eXLl+Oee+7B8uXLA4JKBYYMGYJFixYFbDiEGA+3u7mw3b9/P/R6Pfr37x/087KzswNiSlrCYDCgR48eUv8UDBkyBG63GxUVFbj88suDXtOvXz/s2LEj4LmmP2/duhWzZs0SLSQNDQ04dfIkBo0YK+pCg8EAt9sdID6GDh2KAwcOtNjm9u3bo6ysTPz56NGjIa1ETSkuLsYDDzyABx54AE899RTefPPNmIoPynYhEoawmJkNWjHmAyBTvhLxeHgxzsOs1/oFCFNfKRGhPoSwmAn3kVTMvP3223H27Fm8+eabuOeeeyT/3vLlyzFz5ky89NJLGD16NMrLy1FeXo7a2lrxmgkTJsBiseDAgQPic3l5eTCbzVi7di3Onz8fcP3WrVtx+eWXi+6XeNKrVy/cfvvtmDlzJj766COcOHECO3fuxAsvvCBmhjzyyCNYu3YtXnzxRRw5cgSvvfZas+DcHj164KOPPsLevXvxww8/YMaMGWIar2D56FjcCd9/uw3nzp7BxYsXAbAg0e3bt2P27NnYu3cvjh49ilWrVgUIhCuvvBKvvfYavv/+e+zatQsPPPAA9Hp9q3/bnDlzsG7dOpw4cQLff/89Nm7cGJYbJxJIfBAJQ3C7mPVaGPwOU6LdtPKw+blXmFhklirqK2Xib/lg9+z5SMpGZGRk4KabbkJaWhpuvPFGyb+3ePFiuFwuzJ49G4WFheLtN7/5jXhNTk4Opk+fHhDHoNPp8Oqrr2Lx4sUoKirCDTfcIL62fPly3HfffeH/ETKxZMkSzJw5E7/97W/Ru3dvXH/99fj2229Fa9Do0aPx1ltv4R//+AcuueQSrF+/Hv/3f/8X8B5/+9vf0K5dO4wdOxbTpk3DlClTMOiSIQB8/fTYU8/i3JlTGHVJf9HFNGjQIGzevBlHjx7F5ZdfjiFDhuD3v/89CgsLxfd+6aWXUFxcjCuuuAIzZszAY489hpSU1mN83G43Zs+ejb59++Lqq69G7969sXDhQjm+spBwvMKKx9fV1SEzMxO1tbUB6VeE+hiz4EuU1drw6UOXYWDHTPR8Zg2cbh7bn7oShZnx39kQoalssGPYH78AAByffw2OVjRgyt+3ICfVgN2/n5Tg1ikfm82GEydOoGvXrmEFWEaKxe7CTxcaYNRp0bsgHdUWB05XW5Fm1KFb+/BTKCdNmoS+ffvi1Vdflb2tJSUlmDhxIo4dOyZmmgRj9erV+N3vfod9+/ZBp1NXxECVxY4z1Y3IMOnRJTcV52oacbHBjvbpRkXOhaH+n8NZv8nyQSQMIebDbGD/hgaKI1AsQl8ZdRpoNBylRiscn+WD/cxFaPmoqqrCihUrsHHjRsyePVvGFvoYOHAgXnzxRZSWlrZ4ncViwZIlS1QnPACfm0wOS1WyoL5eJJIG/wBGADDoNLA43CQ+FIjoIjP4+gogoahUmrtdIgs4HTp0KKqrq/HCCy+gd+/eAa/1798fJ0+eDPp7ixcvxu233y75c+66665Wr/HPYlEbQil8n1j09peK1QeJDyIhNA1gBOCNI3DSblqBNDqa9pUvNdrj4aHRUHaSkggVcBruWSEtWSPWrFkT8lyQ/Pz8sD6nrSNaPrzjyNdfCWpQHCDxQSSEpgGMACiDQsE0+gUHA76+ApgAMWm0QX+PSAy+nbR3MYOwk5bvM+Qub96WEUShKBZj0F9Kg2I+iITgfxS7SUemfKXjX5MFaC4+CGnEy4zeNIZAjPmIqNIHEWv4UNlJCu0vOf6PSXwQCaFpACPgCzilqpnKw78mC4CA1Gi7k8RHawi1FqQWfIoWvknAaVsIYExmfGKR3QsxH0p1uwj/x1JqiISC3C5EQmgawAhALNlNlg/lYWviduE4DgadBg6XhywfEtBqtcjKykJFRQUAICUlJaZHCNjtdvAuBzwuwGbTwOF0g3c54PJwsNlsMftcIjIcdht4lwsuhwY2G+B0OFh/Odyw2ZTj0uR5HlarFRUVFcjKympWZj4cSHwQCcHq3Umn6H3/vGKqLS1miqOp2wVgViuHywO7kyxVUhBOaBUESCypsTrRYHeh0aSDxayHy+1BRZ0dGg7QWZRXN6Ktc7HBDpvTA1eqHjUGHRodblRaHDDqNHDVGlt/gziTlZXV7MThcCHxQSQEMc3Wz/JBMR/KpanbBWDiox4kFqXCcRwKCwuRl5cXMktELl5efwSrSyowa2wX3NmvCyrqbXjgkx3Qajis/3/jYvrZRPi8+sEe7DtTi99f1w/ju+Zh27GLmPvVfvTOT8fCO/okunkB6PX6qCweAiQ+iITQNHsCgFiym7JdlIfQX0EtVdRfYaHVamWZvFviQqMHZ+vdgNYAk8mEVBfHfgagNxihpdRoRXGu3o2z9W4YjEaYTCbojUacrXcjPdUdl4q4iYACTomE0DSGAPCrHUGLmeIIavnQk1hUKk0tiwHZSdRfisPatOBiGxD2JD6IhNAYJODUV+eDYgiURrCYD72W7Z6dKp4gk5WmlkXBqgioe0FLVkTLooE5I9pCzSMSH0RCECpmmoKY8Z1uheaXtWGCucn0FCCsWJr2lyAUAcDuJnGvNJpagg069Y+tsMTHggULMGLECKSnpyMvLw833ngjDh8+HHDNrFmzwHFcwG306NGyNppIfoItZjphJ63iAZes2ES3i2/K0HnFh4vEouJobNJfHMe1CVN+siL2lygWhbGl3r4KS3xs3rwZs2fPxo4dO7Bhwwa4XC5MnjwZFosl4Lqrr74aZWVl4m3NmjWyNppIfoLFfOhpMVMswcSigcSiYvH1ly+nQLB+0PhSFjzPwyq4Nb1iUd8GrMBhZbusXbs24OclS5YgLy8Pu3fvxhVXXCE+bzQao84BJtRNsABGPS1miiVYzIdO450glVqGsQ0TbHwxS5UbLg+NLyVhd3nEyrNCzIdOo/65MKqYj9raWgBAdnZ2wPObNm1CXl4eevXqhfvuu6/Fojp2ux11dXUBN0L9BF3M2oDaT1aCikWvX5oCTpVHS5ZFGl/KwuZXpM/kHVNCzIdLxcI+YvHB8zweffRRXHbZZRgwYID4/NSpU/Hee+9h48aNeOmll7Bz505ceeWVsNvtQd9nwYIFyMzMFG/FxcWRNolIIloKYFSz2k9Wgi5m3t0Z7aSVR/Dxpf7ddDIi9JVBqxE3YILlw+3hxROK1UbERcYeeugh7Nu3D19//XXA87feeqv4eMCAARg+fDg6d+6M1atXY/r06c3e56mnnsKjjz4q/lxXV0cCpA0QLICRFjPl0nK2izonx2SF53mfZTEgQFgQH9RfSsJX48NvLvSry+L0eGDUKOd8F7mISHw8/PDDWLVqFbZs2YKOHTu2eG1hYSE6d+6Mo0ePBn3daDTCaFRe7XoitlhF8eEXECcWGaPJUWn4FrPm2UlqjshPRvxjCMiyqHwEl2aK/1yo8RMfbh5GFdYiD+tP4nkeDz/8MFauXIlNmzaha9eurf5OZWUlTp8+jcLCwogbSaiPoKm2ZPlQLEJdFnPQuizUX0pCWMyApm4yyiZTIsFO+Pavy6JWcR9WzMfs2bPx7rvv4v3330d6ejrKy8tRXl6OxsZGAEBDQwMee+wxbN++HaWlpdi0aROmTZuG3Nxc/OxnP4vJH0AkJ0FTN3W0mCmVYDEfZMZXJsFiCABAr/P2F4l7RREs+N7/7B21FhoLy/KxaNEiAMD48eMDnl+yZAlmzZoFrVaLkpISLFu2DDU1NSgsLMSECRPwwQcfID09XbZGE8mPT+37+aQ1FI2vRPxjCJqnbpJYVBq+xSxwbymOL8pOUhSiC9qvvziOg17LwenmVWupCtvt0hJmsxnr1q2LqkFE26DRESzVlqLxlYjTzcPtjbgPVg5frZNjshIsLRrwKzKm0uyJZMXmbB7zAbAYHafbrdrxRWe7EAkheMVMWsyUSKMzeAxBWyiElIwEc5EBFHCqVIJtxADf+FKr24XEB5EQggVZkeVDmQiTo07DBRzNLhYZI7GoKILFEABUxE+pBHNpAv6FxtQ5H5L4IBJC04OUANqZKZVgVirAV5eF+ktZhHK7GCg1WpEEi/kA/GN01CkWSXwQcScggDFIBUbySSsL0SzcLIZA3TuzZCWUWPQFdFN/KYmQMR8qz04i8UHEHYfbA0FfmAxBKmZSNL6iCLmYaakonBLxFa1qIhbJTaZIQsV86FWenUTig4g7NodvMJmDnJJKlg9lETqAkYrCKZFQMR90fIEyCenW1Kp7PiTxQcQdYbDpNJw4wAA6+EqptOZ2of5SFqEtVVQUTok0BjnnClB/AD6JDyLutKr0aXJUFL7+Cpwu6Ih2ZWILWeeDxKIS8WW7NK/zAah3fJH4IOKO1eEC0HxyFJS+WvPak5XWd9LUX0qiNXFP/aUsQveXurOTSHwQcSdYjQ/Av8iYOgdbstJ6f6lzZ5ashIz5EBcz6i8lEazsAOCLgVPrZozEBxF3gp2QClARJKUSsgIjWaoUiTVEtguNL2XSGOScK8CXnaRWsUjig4g7re3MyCysLFqP0aH+UhKhLFVUFE6Z+CwfTWI+VN5fJD6IuEM+6eSiNZ807aSVRci6EVQUTpGEKq8uzoeUaksQ8tBaNL6Hh3iKKpF4KHsiuWitKByJRWURqo6OjgJOCUJeWsueAGhBUxIhDyqjct2KpNEZPKaK3JrKJFTAqUHl4p7EBxF3Qldg9P07qrWqXzISajEz6OgsHiXSmqVKrQGMyQjP87CGcLuovSgciQ8i7oSq6Kf3s3yo1dSYjIQ6K0Sn8rMnkpXQAd3qTt1MRuwuD3ivtmhrbk0SH0TcCeXj1Gp84oMmSOXQ6AxeFE7tAXHJSuhUW3XHECQjwlwIACZd8ArCarVUkfgg4k6omA+O46hwlQIJnT1BMQRKpPWDAGlsKQVhLjRoNWJAsIDaxxeJDyLuhDqoDKCS3UokdAAjCUWlwfN8q6mbDnKTKQarKOybL8Vqz04i8UHEHWFyTNE3Fx9qP0wpGQlVtIoqnCoPp5sX09RDZSeR5UM5+OKpdM1eE4qMqbUuC4kPIu40hojGB9RvakxG2moqYDLS6BdDECo7ifpLOYQS9gAFnBKE7ISKxgfIlK9EQtb58PYVzwMe2k0rAmEx02q4gOwxwL8uC/WVUmhpLiS3C0HITKiAU4BM+UokVAyBf3aSU6Wm4WTD6mel4rgm4oOyXRSHr7+aL8VqtwKT+CDiTktuF2F3RuXVlYHbw4sBiqGyJ4TriMTT0tgiN5nyECxVwWI+dBp1ZyeR+CDiTqhUQMB/wNEEqQRsLcQQBFg+VGoaTjZatiqq24yfjIRKYwd8/aVWSxWJDyLutOTnFBY0ivlQBv4BjMamRZD8yuGT5UMZkLBPLkK5NAGfZVGtY4vEBxF3Ws52oWO/lUSjXx0CjSYwhkCj4SCEFah1d5ZstFRDh4K5lUdLMR9alQcIk/gg4o4tRNEqgCwfSqOlnTTgs36o1S+dbPjcLsGKVqk7gDEZaSnmgywfBCEjLrdHzGQJtqBRCWhl0VIMAUBiUWm01F8kFJVHSzEfwthSq1gk8UHEFZtfaeeWsl1oglQGLZnxAb/dNLnJFEFLFTN9qbY0tpRCiwHCKs/8I/FBxBVhcuS45gGMANUiUBpiKfxQ4kOjbtNwstFy0SoSikrDF/8WZC4ULB8qHVskPoi44h9D0LQIEqD+3PZko7WYDx3VjlAULS1mgtuF50ksKgVftktLlip1ji0SH0RcsYY4J0RAiPAm07AysLbgkwZ8h1/RYqYMWhKLWq1/XRZ1LmjJBrldCCJOtGQWBvwjvGlyVAKtBpyKGRTqnCCTDSkBpwBZFpVCqEMbAfVnJ5H4IOJKSzU+AP8Ib5oclUBr/aVX+e4s2WgpQFjnZ/lQqyk/2fC5XULHfKh1bJH4IOJKq3UjtLSYKYnW+suXakuLmRJo2YxP5fCVhs/yESzmg4qMEYRsSK0bQRH5yqA1N5l4/gSJRUXgS7Vt3l8cx1GJdYXRUnl1snwQhIy0VjdCT7UIFEWjw1sQrpVUW1rMlEHrYpHGl5Jo8SwerbrHFokPIq6Ik2OQGh8AFRlTGr7+osUsGWjNskhVTpVFiwGnKu8rEh9EXLG1UrSKYgiURWv9RXVZlEVrAcJqrx2RTPA8D6sEt4tahT2JDyKutJo9ofLDlJKNVsurq3x3lmxILwpH/ZVo7C4PeG83BBUf5HYhCPnwmYWbR3cD6j9GOtlozYxPO2ll0WodHYrRUQyCUASCu6F1Ki+4SOKDiCvWFso/A1RkTGm0lD0BqN80nGy07nYhca8UBKFo0GrEfvFH53fCN8+rr79IfBBxRWrdCLUeppRstG75ILeLkmj1IECyVCkGa2tC0a8uixrd0CQ+iLjSenl1b5Ex2pkpglZTN8mMrxicbo9o0aBsF+XTUqYLgABriBr7i8QHEVckl1enxUwRSDXjk9sl8QTEELQSo6PW80KSCVsLmS5AoOWjzYuPBQsWYMSIEUhPT0deXh5uvPFGHD58OOAanucxd+5cFBUVwWw2Y/z48Thw4ICsjSaSl1bN+Cqv6pdstJo9QZYPxSCMLY4DjKHq6JBYVAxSrYqAOt1kYYmPzZs3Y/bs2dixYwc2bNgAl8uFyZMnw2KxiNe8+OKLePnll/Haa69h586dKCgowKRJk1BfXy9744nkQ+rZLjQ5KgOpYlGNO7Nkw+atRmvSacFxXNBrKNtFOVhbCebWqtzyETzfMQRr164N+HnJkiXIy8vD7t27ccUVV4Dnefz973/HM888g+nTpwMA3nnnHeTn5+P999/H/fffL1/LiaSkpbMMAP9TbWlyTDQ8z/t2ZyGyk6jCqXKwOl0AQi9mgL/bhfor0bS2ERPO4nF5eFWOr6hiPmprawEA2dnZAIATJ06gvLwckydPFq8xGo0YN24ctm3bFvQ97HY76urqAm6EemktyIqKjCkH/yJIKYbg+xQqMqYcWovPAfwsi2T5SDhiAb8QcyGg7kJjEYsPnufx6KOP4rLLLsOAAQMAAOXl5QCA/Pz8gGvz8/PF15qyYMECZGZmirfi4uJIm0QkAa0HnHrrENBilnCEvgJCn8VD5fCVQ2suMsDnJiPLR+JpzQoMqLvQWMTi46GHHsK+ffuwfPnyZq819TfyPB/SB/nUU0+htrZWvJ0+fTrSJhFJQKsHX1GRMcXQWhEkgCxVSkKK5YMCTpWDGPMhyfKhvv4KK+ZD4OGHH8aqVauwZcsWdOzYUXy+oKAAALOAFBYWis9XVFQ0s4YIGI1GGI3GSJpBJCGtRXhraWemGHx9FXqPQhUzlYMUy4dexWb8ZKO1VFtA3dlkYVk+eJ7HQw89hI8++ggbN25E165dA17v2rUrCgoKsGHDBvE5h8OBzZs3Y+zYsfK0mEhaPB4eNicbRKFz271FxlSo9JMNSTtpDVmqlIK0/iKxqBQkxXyo2O0SluVj9uzZeP/99/HJJ58gPT1djOPIzMyE2WwGx3GYM2cO5s+fj549e6Jnz56YP38+UlJSMGPGjJj8AUTyYHf5FqhWUzcphiDhtBaND/gtZiQWE46kmA8qr64YpPSXVsWp7GGJj0WLFgEAxo8fH/D8kiVLMGvWLADA448/jsbGRvz6179GdXU1Ro0ahfXr1yM9PV2WBhPJS6NfBcZWT0lV4WBLNlpzkQG0mCkJSdkulJ2kGBpbOWQT8HOTqXB8hSU+pJysx3Ec5s6di7lz50baJkKlCIuZUaeBRhOiCBIFxCmG1oogAVRkTEmEY/mgOjqJx5ftEnoZVrPlg852IeKGlJ2ZVsUBVsmGlIA4X6qt+ibHZKO1GjoAiXslYW3j/UXig4gb0iZH9Sr9ZCOcxYwChBOPsJOWYqmigxsTj5T+UvNmjMQHETekBVipV+knG1JiPqgcvnIQsyeozkdSIEXcq7m/SHwQcUNSAKOKlX6yEU7dCLJ8JB5rGBVO1RjAmGxYHewsHml1PtQ3vkh8EHFDWgVGiiFQCrZw6kaocHJMNmxSAoSFgFPqr4Qj1DySFtCtPrFI4oOIGzZJPmlKBVQK4WRPUJGxxCPFsugLYKT+SjSi5aONxlSR+CDiRlhuF5ocE441jAqMVDEz8UjJntBRdpJikHKwnJqPmyDxQcQNaQFW6vVxJhvhROOrcWeWbPgsi6HrRohn8VB/JZSAoyYkxVSpbzNG4oOIG9KO/Ca3i1KQUudDzRUYkw3fTrr1iplqXMySCZvLV+25JbFIlg+CkIFwAk7dHl5SRV0idkg5+ErNFRiTDXKTJQ9CXwGs4nModBTzQRDRIykgTuP7l6QFLbFIS7VVbx2CZMOX7dKS24UsVUrA3wUd6qgJwK8onAr7i8QHETckxRBofQNRjWo/mWiU4JPWUsVMxRBOXRYS9olFSrApoG43NIkPIm7YwojGB9Sp9pMJKXU+qMiYMnC4POICJSWmisZWYpGSmQT45kM1ji8SH0TcEN0uEorqAOoccMmE1cnqEEiJISC3S2IRxhYgNUCY+iuRSIl/A9R9CjGJDyJuSDvbxd/yQRNkIml0tF6BUc0HXyUTQmaSVsOJAiMYVJFWGTR6hX1LYwsgywdByIKUOh8cx6m6pHAyYaOA06TB34zPcS2IDwo4VQSCsG/V7aJVb3YSiQ8ibkipQwDQ+S5KgOf5sCowqjEgLpmQasYnsagMpBwqB6j7+AISH0TckFI3AlB3hHey4HTzoqm35bNCaCetBKS4NAG/1E0VLmbJhJTMP8A/1VZ9cyGJDyJuNEoo/wyoW+0nCwEBjFRkTPFIcWkCPjM+WT4SS7gbMYr5IIgokBJDAFAVRiUgNYBRNOOrcHJMJqTWjSBLlTKwOsKzfKgx/o3EBxE3JO/OVBzhnSw0Sgxg9D9YjsrhJw7pbhfKdlECkjdiKrZUkfgg4oJ/AKNJYsCpGnPbkwWr1ABGKoevCBolBjCS5UMZ+MZXKy5oFbs1SXwQccHh9kAYP2T5UD5Sd9JUDl8ZSC9apd6ddDIh2VKl4o0YiQ8iLtgcvsHTapCVinPbkwXp8TlUDl8JSDmHB6BsF6XQGGbMhxqFPYkPIi4Ipbr1Wk4MUgyFmgdcsiBG40usGwHQbjqRiG6XVsQH1flQBlaJ/aXmjRiJDyIuSA02BfxMjbQ7Sxg+s3DLU4T/aeBq9EsnC5LrRvidaksBwolDanaSL6BbfXMhiQ8iLojBphLEh1bIbVeh2k8WpPqkOY7zO6ZdfRNksiB1fFGAsDKQ6nbRaynglCCiQhhsqcaWo7sBQK/i3PZkQWoAI+BXaIzEYsKQmp2k8wsQpv5KHJIDulV8ajSJDyIuWCJxu6hwwCULFodw6qYUsUiFxhKNLUy3C0BuzUQiPZVdvRsxEh9EXLDa2WKWapQgPlRcUjhZEC1VUiwfVA4/4Ugt1x3gdiFxnzBsEmM+dCquIEzig4gLUovqAOrObU8WLPYw+ovK4Sccq0TLokbDiUHCVGgscYjl1fUSi4ypcGyR+CDigpBaJmUnTam2iafRSf2VTEh1uwBUYj3RRFLtmSwfBBEhUn2cAE2OSkCwfKRICBAmS1XikRrACPgtaNRfCcHu8kDIcm4tpsoXzK2+viLxQcQFixhD0PpiJsYQqHDAJQtWMeC09cVMKFxFlo/EYZVYFA7wq3KqQlN+MiD0FSC9KJwaxxaJDyIuNIazmKn4MKVkQeqR34Bvd0aLWeIQ+itNSiq7GMRI4j4RCFYqg04jjp1QaFVcDp/EBxEXLOJiJsHyQambCSec/qKYj8RjsUsX9z63C/VXIpBaCh/wS2NXYV+R+CDigq/ImBQzvnr9nMlCYzgBwlQOP6G43B7YXey7l+LW1JG4TyiN3kM2w7EqqrGvSHwQcUHYmUkKOFVxhHey4Eu1lR4grMbdWTJgdfrFEEiK0SFxn0jEQ+XaeF+R+CDiguDnDGtnRotZwhD7S0q2i4oPv0oGBKuiVsPBqGt9SlfzSanJgDWMzCSyfBBElIRl+VBxkFWyEEkMAS1micG/rziu5QBGwK9wFY2vhNAYRuafGByswrFF4oOIC9aIUm3VN+CSAbeHF2MIpAWcqjcdMBkIZ2wB6l7QkgFRLEo5akKr3mBuEh9EXAinyBgdVJZYBJ80EK7lg3bSiSCcxQyg/ko0YW3EVGwFJvFBxAWxvLqECVJLZuGEIkyOGg7SYggo1TahhFOTBSBxn2gawnBpCn3F84BHZf1F4oOIC1IPUgL8I7zVNdiSBf+dmbQYAiqHn0gsYgE/aW4XsnwkFt9GTLoLGlCf9YPEBxFzPB7eJz4kWT5oZ5ZIwgkOBuiskETjE4tS+4tiPhKJkMYuqeaRxrdEq82ySOKDiDk2l68OgbSzQmgxSyThpNkC6j72OxmwijEfEgNOya2ZUKxhWKr8y6+rLZssbPGxZcsWTJs2DUVFReA4Dh9//HHA67NmzQLHcQG30aNHy9VeIgkRlD7HASad9FRbsnwkhnDSbAG/uhG0mCUES9iWD0qNTiTh9JfOT3y0ecuHxWLB4MGD8dprr4W85uqrr0ZZWZl4W7NmTVSNJJIbIa/drNdC08pBSgCgJbNwQgk7gJFSoxNKODtpwN/tQmIxEYRjqdJoOAhTptr6S9p/qx9Tp07F1KlTW7zGaDSioKAg4kYR6iLcgDg61TaxWMM4VA6ggNNEI1gWpWe70PhKJJYw67LotBo4XB7Vja+YxHxs2rQJeXl56NWrF+677z5UVFTE4mOIJCHcnTSl2iYW306aAk6TAd+hjeFZPsjtkhjE8SW1LotGnZbFsC0frTF16lTccsst6Ny5M06cOIHf//73uPLKK7F7924YjcZm19vtdtjtdvHnuro6uZtEJJhwFzOqwJhYwrV8iP2lsp1ZsmAJe3yRWEwkVnuYlg+VFhqTXXzceuut4uMBAwZg+PDh6Ny5M1avXo3p06c3u37BggWYN2+e3M0gFES4ZmGyfCQWa7gBpxqqG5FIwi2vTm6yxBKuWBQsVW0+4DRcCgsL0blzZxw9ejTo60899RRqa2vF2+nTp2PdJCLONDqlF9UBqMhYogmnJgtAdSMSTaTl1cnykRhEy0eYqexqE/eyWz6aUllZidOnT6OwsDDo60ajMag7hlAPguVDyhHSABUZSzSWMKrRAlQ3ItGEn51E4ytR8DwvWj6kpkbrVWr5CFt8NDQ04NixY+LPJ06cwN69e5GdnY3s7GzMnTsXN910EwoLC1FaWoqnn34aubm5+NnPfiZrw4nkIfyAOFrMEkk45/AAFMCYaMJOtVXpTjoZsLs8EDSE1PlQPFxOZeMrbPGxa9cuTJgwQfz50UcfBQDcddddWLRoEUpKSrBs2TLU1NSgsLAQEyZMwAcffID09HT5Wk0kFYLSl1quWzz4SmWDLVkIP+CUzPiJJOyYD3KTJQzBRQZItwSr1U0WtvgYP348eD70P+26deuiahChPhojrsCorsGWLISdaitG49NilgjCjfkgN1ni8A++l1JwEVDvKcR0tgsRc3yWjzB30iobbMlCuDEEVDEzcfA8H7HlQ21m/GQg3IKLgHo3YyQ+iJgT9qmb5HZJKFZ7pG4X6q9443B7RJEu2a2pUjN+MhBuPBWgXjcZiQ8i5ljDrPMhKH0HTY4JweoMtwIj1Y1IFMLYAsKvo0P9FX8sYQp7wOcmI8sHQYRJ2Ge7kBk/oYRbFE6tAXHJgNXJ+sqg04jjpjXITZY4rGGm2QJ+bheViUUSH0TMafAGxKWZwhUf6hpsyYLYX5KLwlF/JQqhGm04i5kYcEr9FXdEYS9xbAHq3YyR+CBijiXMxUytZxkkA063Bw4X+96pv5SPJcy0aMAv4FRlO+lkIBLLh1rFPYkPIuY02GgnnSz41yGQXg6f+itRhHsOD0ABp4kkIrGoUnFP4oOIOYIZP/wKp3yLNWUI+an3CkVjWDEE6gyISwYaxBof4SxmJBYThVW0ApPlg8QHEVPYWQZM7Uu2fGh8/5ZU6yO+CMHBUvsK8FvMqK/ijtBfGRLjqQA6viCRiJaPcMaXSsU9iQ8ipticHvFAJKkBp8JgA9Sn9pWO6CILYzEjM37iEPpLaoExgIr4JZKIsl1UKu5JfBAxpcEvhiAlzLMMAPX5OZWO6CKLJICRhGLcqQ8zkwzwq8tC/RV3IqrzoVJxT+KDiCn+mS7hnmUAkOUj3giTY3iLGZnxE0W4mWQA1WVJJJYIAoR9bhd1zYUkPoiY4gs2lT7YNBoOgk6hCTK+NNidAMJbzNQaEJcMhJtJBvj1l8rM+MlAuDWPAH9LlbrmQhIfREwJN9NFgGoRJIYGr+UjnP5Sa0BcMhCZ24X6K1GEW8APUG+MDokPIqYIZsb0MMWHrwojTZDxJCIzvkadk2MyYIlA3JOlKnEI4iM9rOwksnwQRNhEbflQ2YBTOg0R1CFQ66mbyUBDBOKeUm0Th89Nppf8O2oth0/ig4gpkYoPvUqDrJSOT3yEPzlSZlL8EdxkkdRlobEVfyJxk/lidNQ1vkh8EDElYrcL7aYTglg3IgLLB89DrOlCxIcGGwsQDs/tQi7NRGB3ucM+NwlQbyo7iQ8ipvgWs3DdLrSbTgTRpG4C5CaLN1HFEJBQjCtCGjsQYcCpysYWiQ8ipjREUDcC8NX6IMtHfIkkFdC/LgtZPuKLJYLsJArmTgzCRizFoIVWYs0jwP9gOXWNLRIfREyJZCcNUCGkRBFJjA6Vw08MHg8fUeqmYPnw8Ow9iPhQH0ENHcA/oFtdcyGJDyKm+Mp1S48hAPyC4mhyjCuRxOjoNFQOPxEIh8oB4bpdqL8SQSTnJgHqDb4n8UHEFJ8ZX3r2BKBeP6fSiaTIGMdxvlofKpsglYzgctFqOBh10qdyOr4gMUSSFg1QhVOCiAhLBHUjAPVGeCudSMqrA1TlNBH49xXHhRFDQG6yhBBJPBXg74JWV1+R+CBiSsRFxuiwsrjjcntgc4afCgj4BQiTmyxuRFLjAyA3WaKoj+AcHoDqfBBEREQSEAdQnY9EYHH4UgEjTY0mN1n8iORQOYDcZIkikgJ+gP9ZPOrqKxIfREyJNtuFzPjxQ5gcDToNDGHEEADkJksEotslTDM+QOMrEQhiMZzgYIAsHwQREZG7XWgxizeRCkXAr3aEyiZIJRNJcLAAucniD1mBAyHxQcQMu8stiodIz3ahxSx+1EdQWl2ALB/xRyitHm72BEBuskRQH2GqrVqtVCQ+iJghDDYgcrVPi1n8iNQnDdBilggi3UkDJBYTQaSZZL6NmLr6isQHETME8ZFu1IVVThigxSwR1Ht30hkRxBCQGT/+RON2oWyy+BPJOTyAzwVNbheCkEhdo9csTItZUlDXKEyOkVs+1GYaVjLyBJzS+IoXkWYnCX3lUNnYIvFBxAzB8pFhpsUsGRAtH+bIzfhq250pGd9iFn6Mju/gRhpf8aI+6oBTdfUViQ8iZtSJZvzwxYdaI7yVTFT9RWb8uFPnFR+ZUYh7sizGj0jPdlFrTRYSH0TMiMbt4jtGmhazeCG4XSKJ+SAzfvwRxlckYlGt54UoGd/ZLuGecyUcsqmuviLxQcSM6NwuZPmINz63SxSWKpVNkEommvGlV+l5IUrF7eFh9VYQprNdGCQ+iJghmPEjCjilbJe4UxdhBUZAvSWglUw0bjJR3JPbJS4IVg8g/Do6Or/ge55XT3+R+CBihrgzi8YsTJNj3KiXYzEj8RE35HBrkqUqPgh9ZdJrYNSFJz70/qcQq2g+JPFBxIyoJkeyfMSdaFJtqSJtfHG5PeJBgFG5yUgsxoXaaOJztL5lWk39ReKDiBl1UcUQqNPPqWTqokm1pbN44op/9eBoxD0FnMYHYWxFkpnkb/lQU9ApiQ8iZkQXQ8D+NdVWWEfJROUmI0tVXBEWsxSDVrRihIOOivjFFTEzKRLxofH1r9OlnvHV9sQHzwPfvAJ8dD9w8ViiW6NqokkFFNQ+57QB654BPvt/QGO1rO0jfLjcnojLPwO+CdLQWAF8PBvY+EfA7Wrlt4hI8aVFhz+2AN/4yqjaD/zvl8Dud2RrG9Ecob8isXxoNByE0ym0R9YA/70b+OkrOZuXEMKfZZKdg58AG55lj899Dzy4HdC2va8hHtRHYfkQdnNXV/0bOPE+e7KxGrhlqVzNI/zwj8aPprz6+MPPA9Xb2JP6FODyR2VpHxFINC4ygMUR6ODCFXufAGxlwP7/AZkdgB4T5Wwm4cUX8xF5f+W5zyNz9e8AtwM4vAZ4aCeQ1UnOZsaVtmf52Pue7/HFI8Dh1Ylri8qJJuaDBVnxGNuwzvfkgZVA5U8ytY7wRxCKJr0GBl0kZnwO7VGNLtXbfU9ufw1wOeRqIuFHNFZFgFWkvUyzH+m2Mt+TX/9dhpYRwYhmLgRYf12v2QbO7R1PLhuw459yNS8htC3x4XYBJ7ayx72msvt9/0lce1SMx8NHZ8bXcujNnUY7dyXbQXe+jL2w/0M5m0l4iSYaH2Bi8TLNfnDggcLBQFo+YK0Ejm+SsZWEQLSLmU7LYbTmIPuh23h2X7oVqDktQ+uIpgjjKxK3C8DG1xXafeyHnlPY/f7/AR63HM1LCG1LfFw8DLgaAUM6MO5x9tyxLwGHNbHtUiENDheEejiR1vnox51kPxReAlwygz0+9Kk8DSQCiKYgHMAWswGaUvZDpzFAvxvY44MfR984ohnRlMIH2GI2XHOE/TD4NqDTWPb4yFo5mkc0IXpLFXzz4fgnAVMW0HAeOLNTphbGn7YlPsp+YPeFg4CiIUBGRyZGTm5LbLtUiDDYDDoNTPrwT93UaTn01nh3Yfn9gZ6T2OPyfYClUq5mEl6iKdUNsIDT/oL4KBwM9PZaFo9vAlRUlVEpRG3G54Ae3Fn2Q/4AoMdV7PFPG+VoHtGEaA4BBIAOmipkcFbwnI71l2CtSmLLYtjiY8uWLZg2bRqKiorAcRw+/vjjgNd5nsfcuXNRVFQEs9mM8ePH48CBA3K1Nzoqvdkt7fsAHAd0G8d+Pvl14tqkUnxpm5HtzPRaDn25U+yH/P5AWh6Q15/9fGKzHE0k/Ih2Z6bTcujOnWM/5PUFikcDWgNQdxaoOi5XMwkv0fZXBl+HLM4CHhyQ090nPk5sAdxOuZpJeBHdmhEGCPf2Wj1sWT0AncFPfCTvXBi2+LBYLBg8eDBee+21oK+/+OKLePnll/Haa69h586dKCgowKRJk1BfXx91Y6Om2mu2ateZ3XfxxhGUkviQm6gXM40Gnbjz7IfcnuxeBWpfqURTkwUATHCgPVfLfsjqDBhSgI4j2c8kFmXHZ6mKrL/ynEzY1xryAb0ZKBgMmNsBjgZmXSRkJZo6HwBQjAoAQGNGF/aEMBee+Q5wWKJsXWIIW3xMnToVf/zjHzF9+vRmr/E8j7///e945plnMH36dAwYMADvvPMOrFYr3n//fVkaHBU1gvjowu47X8ruz34P2BsS0iS1Eu1iptMAhVwV+yGzI7vv4u2v099F2zyiCdGcaAsA7ZxMKNo0ZraIAUDXy9l96TdRt48IJJpD5QAg186sVJXGYvaERuMTi6e+jbp9RCDRBnQX4CIAwGYuYk9kdwUyOgAeF1u/khBZYz5OnDiB8vJyTJ48WXzOaDRi3Lhx2LYteFyF3W5HXV1dwC0W2F1uNJQzt4sz3Zsb3a4zkFkM8G7g7O6YfG5bJdrFzOyqgYlzwgMOSPcOOGFyvPAjYKuVo5mEF9+5LpGJxSxHOQCgSlfAXJoAUOztr7O7om4fEYgYcBrh+MpwXQAAVOvzfE92GsXuT5P4kJtoyqsDQD7P4tys5gLfkx1HsPszybkZk1V8lJezCSg/Pz/g+fz8fPG1pixYsACZmZnirbi4WM4m+XBYkOZiFTIb0zv6nu8wjN3TBCkrtVEcKgcAZiurP1CFLObjBIC09l6rFQ+cof6Sk2h30oL4uKjzW8yKhrL76lKg4UI0zSOaEG1/ZTjZTrpWm+t7sthPfFCQsGzYXW7YnKwseqRiMY9n48dq8hMfgrg/nZwZLzHJduE4LuBnnuebPSfw1FNPoba2VrydPh2bPHODBljgvA1LXFPg0GX4Xug4nN0nqelKqdRY2eSYlWKI6PfNjWwxO8/lBL4gWD+SOMVMifj6K7LJMd3OxOIFjZ/4MGcBub3ZYxL3slIXZQBjmoOJj2pttu/JoqGARgfUlwG1VO9DLgQrFccB6cbI+ivXw/rLEmD5EObC75JSLMoqPgoK2BfT1MpRUVHRzBoiYDQakZGREXCLBZwpA//C9ZjnuivwJMcOXvFxZldSdqBSESwf7SJczExey0c530R8iGo/OU2NSqW2kVVOzDJHJhZTHCw+p0qTHfiCaBomsSgndVEcAggAqQ6v20XjN74MKUDBIPaYxpdsiFZgow4aTfBNeIu4Xcj2sPFVb/RbRwsHsYwya2VSZpTJKj66du2KgoICbNiwQXzO4XBg8+bNGDt2rJwfFREG73khDv+TAQsHA5wWaChnaYGELNRYo1vMDDam9CuQFfiCaKnaBajoeOlEI1g+IhWLZidzaVYhM/AFob9IfMiG0+8QwEjN+IL4qNI2EYsdvK6yc3sibh8RSLQ1WdBYBQ088PAcGnTtfM/rjGz9ApJyfIUtPhoaGrB3717s3bsXAAsy3bt3L06dOgWO4zBnzhzMnz8fK1euxP79+zFr1iykpKRgxowZcrc9bPTeMysCLB+GFCC/H3tMQaeyUe1dzDIjXMz0draYXfSkB76QPwDQmVnAaRWd8yIX0faXUbB8oInlUrB8nP0+qUtBKwlhJ81xEQYwejww25m4v9DUrVlE4kNu6qIsrQ4rCzatQSqcniaWE8H1koRrV9jiY9euXRgyZAiGDBkCAHj00UcxZMgQPPssOyn28ccfx5w5c/DrX/8aw4cPx9mzZ7F+/Xqkp6e39LZxQbB82F1Ndsz+rhdCFmq8Ay4r0rMMbGwxu+hOC3xBq/dT+9RfcsDzvM/tEmGMjtHOJshKvon4yOsL6FNZ/YiLR6JqJ8EQrIoZJj20kZjxbTXQ8EwI1jQVi0VsXkfZDyQWZSLaNFtYvPE5fHqg1R7wWaqScC4MW3yMHz8ePM83uy1duhQACzadO3cuysrKYLPZsHnzZgwYMEDudkeEcEy7090ktkPMeEk+9ahUar0TZLvUyBYzUXzwGXC5mww40fVC/SUHVodbHBORul18lqomi5lG61vQqL9koTrK4GAhTd3KG2Hnmxx90L43O8jR0QBcPBpNMwkvdVEWhBMsH1VIb75xFubC8hLAZY+0iQmhTZ3tYtQFifkAfB14bi+pfZmI1vKhsQlm/PQgYtGr9imDQhaEvjJoNTBHcA4PnI3QOVmRvgt8WvPXk3h3pkSizSSDndVSqkNKoAsaYGJRsCyS60UWaizejVik/SWIDz6j+VyY1RlIyQE8TiZAkog2JT4MocRHbi/AkAY4LcCFwwlombrweHjfEdIR7s64RiY+gpsaBbW/H3DaIm4nwRDM+Jkp+pAp8S3iNQs7eC2qXebmr5NlUVaqBatixJYPJj7q+RS4mi5mgF/cB5UfkIMqa3QuTZ/4CDIXcpxvPkyy8dWmxIfP7RJE7ZNpWDbqbE4xazmibBePB7B6LR98OuzuJtaorE5AavukVPtKJNpMF1iZ+KhEJhyeIIuZID7OHwCcjZF9BiHiyySLzu1ShxQ4g/aXYFkk8SEH0Y8vJj6qkQ5H07kQ8I2vJLMstinxIVg+mvnNABIfMiIMtlSDVvzOw8JWA84bEFcdzO3CcVSZVkZEM36EadGweCfHYDszgJ3Nk5rHjjEoo0PLokUutwuzfLQwF5aX0Am3MuCzVEU6vrzing8yFwJAx+ScC9uU+NBrmUm5meUDINOwjIjxHhGbGb0FdXgznNAFX9CS1NSoRGoafW6XiLDVAABq+VQ4go0tjqMgYRmpFnfSEY4vr+WjHubgbpfsboApE3DbgYqDkTaT8CL2V4TB96LlI5S4F9xkVcfFuTMZaFPiw6BjwXTBFzMyDcuFGEMQZV57LccyJ4L3FwUxykXUZmFhJw1z8J0Z4GfKJ/ERLaLbJcqYjzo+Fc5ghfo4zs8STK6XaKm2RBmj01K2CwCkZAPZ3dnjJOqvtiU+WrJ8+JuGKY4gKsTS6qmRV/QDgDqO1YZpUSxWnxDN/kRk1EQbEGfziQ+3h4e7pbiPJDMNK5HqaMWHKBZTgvcV4BMflPESNdXRjq9GlsZeE8ryASSlZbFtiQ8h2yWUaZh2Z7IQdQyB1yxs4VIBhOgvcxaQ05M9pqj8qBD6K2JLlb0eAIshAEKIe2Exqy4lsRglNVG7XWoAAHWhsl0AyniRCafbg3pvnY/Is5P8AoSDjS0gKcV92xIfwc528YfiPmSh2hptDAHbmVk1XvHRWn+R6yUqahqjXMz8dtJAKLHYDsjpwR7TghYV0Z5ALLpdWlrMBLF4/iC5oaNA6KtoSuH7i/vQc6Gf5SNJDkhtU+JDSLUNOjkCZPmQiehjCJjSt2lYwaqQ/ZWEpkYlUivTYlbPsxofkiZIImKizp4QAk55M1yh3C6UoSQL/qXwddoIlltHPQDWR3VICT0XFgzwnXBbXRpZY+NMmxIfIYuMCSRp1LDSqG2M1u3CFrNGLbN8OEMuZn5iMUnUvhKpjrZuhNfy0eh1k7VuGibxESk2p1sMOow25qMOqaH7KiBDiSyLkVId7UbMOxd6OB3s0IfuL50RKBjIHifJ+GpT4iNkkTGBlGyWZgZQoFUUVFnkCYiza1uxfOQPBLRGFqBadTyyzyL8zgqJTiyG5SYjsRgRglDUaTikGSM8K8TPUhUy5gOgjDIZqI7yjCthLnTq0wFwwbNdBJJM3Lcp8RHybBd/BOtHEqUsKQ1BfOSkRbeYOQTxEaq/dAagcBB7TP0VER4PL06QEfeX4CbTtmL5KBgAaPRMLCaJaVhpVFt8LrKISuEDfnU+UuAKlmor0IEsH9FSHe25Lt650K1vIfNPIMncmm1KfIQ81dafJFOPSqSygZ2umJNqjOwNBMuHroVsF4EkjPJWErWNTjHdMtoJUojRCbk7S0LTsNKIuoYO4HO78Klwutmp5EHpMBQAB9ScAhouRP55bZioTyD29pXLyGoehRT2gM9NVvZDUlSmbVPio8Xy6gL+4oNMw2HD8zwqvWo/O1JTo3cxc+rUp/aVhtBXGSZdZKXwAXGCtHktVS2KezGOgCxVkVApWhUjFPZOG+Bm71EPFiAcstaHKZMdugnQ+IqQmqiDg70xHwYJc2F2N8CUBbhsrFimwmmT4qPFDiwcBHBawFIB1J2NU8vUg8XhC4iL3IzvVfuSTI1eN1nZPsDliOzz2jCilSrSxYznxVRAp66VmA+ALItRIvRXbsQuTeZy4TkNLDABQOiMF4Asi1FSFe1GzOvS5A3eas8tWT6S7MyrNiU+Wg04BQC9Gcjvxx7TBBk2VQ1ssJn1WqQYoguIc+qFnXQrat+czc6hOL8/ss9rw4jxOZFOjs5GwMOKKDl0EvpLmByTxDSsNETLR5QuTRjTwUPCfNiRaulEQ9RuF+9cyBtbOGrCHzGoW/lrV5sSH5IsHwDtzqLgooXtzCJW+oA4QUoyNQaofeqvcLkY9c7Mu5hxGrilWD6yuwPGTMDVSIeWRcDFhmiDudlOGt7FDEArGS9eN9m571nBKyIsKi1Rxr816a8WhSKQVLWP2pb4aOlsF3/ExYz80uEiWD4iNgt73ICjAYBfhLfU/qLdWdhUNUQZQ2Dz7aT1LR1fIKDRAB2EQ8uUP0EqjajdZN7FjDNlQeNNlmlxPszvD+hM7PeqforsM9swF6N1kwni3sTER4vxioBvLrx4xCdcFErbEh9SJkfA14Hn9rLFkJBM9D7OOvGhW4qfE0gqta80fDuzKPvLmEmWxTgguF1yo+0vUwaM3lO+W1zQtHqgcDB7TOI+bCrFzVh04p4zSXS7pOYCWZ0B8IqvVdWmxIe+tbNdBNr3AfSprLTtxaNxaJl68LldotxJ60zQGdh7tNpfQm2WyqPiCZCENCqjrsni3V2ZMqTFVAF+GUpkWQwXuSwfMGbAqJeQ/QdQvY8IsTpcsDrY5jXa4HtNShYACWMLSBpLcJsSH4bWznYR0Gh9ap92Z2ERtdtF3ElnSN9Jp+YA7bqyxwpX+0pDWMyitlQZM6QV8QN8GUoVh8RMGUIalVHHfAiWj0yxv+yuVqy7FHQaEUJfGXWaqKvRak2ZAAAPD7gkW4KVLe7blviQOjkCfqWFv4thi9RH9DU+IthJA74BlwRR3kpCcJNFbBYWxEM4/ZVeAGR0BDMN743sc9sgNqcb9XaWWZQbbQCjVLcL4LN8nN8POCyRfW4b5IIY72GMvBqtV9xrUzLFp1oPG/CzVCm4VlXbEh/hLGadRrP7Uzti2CL1EXURJFsEO2kgqfLblYSwO4u2IByM6dKK+AnQCdJhIwhFnYZDhjnCnbQ9iOXD2Up/ZXUC0otYSjVZPyRzsT7KYFNAHF86r9sFAJyuVgRF4SBAowMaziu6VlXbEh/hLGadxrD7Cz/SCbdh4CutHn1AnOQAYSCw0qmC1b6ScMtyrotPLEo6vkCAgk7Dxt/lEvm5Ln7iXi/R7cJxQGfvfEibMclURmtVBMTxpfOzfNjdrfSX3syylABFi8U2JT7CmhxTc4GcnuwxDTjJRJ3tYmu+mEkSiwUD2aFllgvsLAqiVWqsDgjFLaMt/xwgFqX0V8cR7P70dyQWJXIx2poRQGRuF8C3GTu1LfLPbmP4LB8R9pfHI7o1OVMY2WRAUoj7NiU+wjILA35qnwacFHiejz4gzu6bHH0BwhIWJ72JnZoKKHrAKQlBKGaa9aLQCxv/AOFw3JodhgJaA9BQDlQdj+yz2xhRjy0guNslHPFxeifgdkX++W2Ii2JmUoT95agH4J37/MaXNPGh/PIDbUp8hBXACACdxrJ7snxIosbqFF0k7dOjjfnwV/oSa60IA+7Mzsg+u41R4d2Z5UXaV0DATtogNXsCYKZhYXd28pvIP78NUdkQ5U4aCEy1FWM+JPRXXl9WmdZpAcr3Rf75bYiL0bpdhLlQawT0JnF8SbLc+2e8KPTMqzYlPiSnlgkIlo9zewCHNUatUg/CYpaVohdNumHjF/MRltsF8PVX6deRfXYb43ydDQCQlxG9TxrGTJjCtixeyu5PkmVRCpXRnsMDNEm1DcPtotECnUaxx7QZk4Todol4I+YT9gDCs3zk9gJSctkxBueUmXLbRsWHB7wUP3NWZyC9kEV5UxZFq1TUs8UsP90U+ZsEyXaRpPQBoPNl7L68hIqNSUAQi7L0lykDRj1bzGxSdtIA0NlrWSTLhyQEsZifEUV/iW7NTOlFxgTEDEASi1KIvhqtN43dyI6Z0OtYkLGjtYBTgAUJd/HOh6VbI/v8GNO2xId3cuR5iRkUHOcXaEVqvzUq6rxmfDl20uGa8QEgPZ8pfvDAye2Rt6GNIPRX+6j6S5ggM2ASxYfExax4FMBpWYBwzenI29BGiNpS5fEEFfeSx5e/G5qChFtFPNclUsuH39gCfJYPyWJRFB/KtAS3KfFh0vv+XMkTpLg7I7XfGue9lo+I4z2AJosZ6y/JfQUofsApCaG/8qKxfPgd0S4sZpItH8Y0oOgS9pjGV6v4YnQi7C9HA8QARn+3i9Tx1WEoiz+wXAAq6ZC5lrC73KixOgFEU8Av8FA5QdyHLT5OfavIuI82JT4MWg2E9HhJQVaAX5S3MjtQSYiWj6gWM5+pUZgcJS9mgOJNjUrigre/8qOxfPi5XUTLh9TJESDXSxhURNtfwmKmNQB6U3jZLgCgM/oCGUu3RNaGNoLQVwadBu1S9JG9iV8mGeAnPqTOh+37ACk53rgP5R070abEB8dxMOnCNA3n9WOBO04rxX20woV6GRYzv3LdpnBjCACK+wiDimgtHy474GZ97m+pkjw5Ar7+IstHizTYXWjwllbPizTmwy/TBYD0ImP+dB3H7o9vjqwNbQRffE40pdUDYz6E8dUodXwpPO6jTYkPwNeBNqkDTqMBul7BHh/fFJtGqYSoFzMgwCft66swdtIU9yEJnudxvi7KVFuhrwDAmO4T9uH0V6fRADh2InFdWWTtaANUeBezNKMu6kPK4D2kLKxsF4FuXvFxYguLISGCUu7tr4KogoObiI9wN86AT9wr0A3dBsVHBLvpbuPZPan9FjkfbcApzwfEEJi9feVweeDxhBHgRnEfrdJgd4k7qIj7S+grQzqg0YZvFgYAc5Yv7oPEfUiiHltAs9RNyWe7+NNhGGBIAxqrgPMlkbdF5ZTXypCZZGvidjFE4YZWYNhAGxYfEaj9s7voCPAQ8DwffaqtwwL/in5CXwFh7s6EAXeCxGIohODFdKMOKYZId9JNFjN9mAGnAt2vZPfHv4qsHW0AWdLYm8QQhJ3tAgBava8+C23GQiKmsSfa8iHEfSgwbKDNiY+wI/IBoF0XdvO4yDcdgnq7SxwUUe+kOS2gNweIj7D6q+s4ABw7Arz+fGRtUTmCTzq6NNsmO7NIJkcA6DaB3f/0FaVwhkCWNHabr8YH4Cs9EJawB3ybMbJUhUSwfETndvFZgQG/kIFw5kKNxje+jn0ZeVtiQJsTH2GnKwlQoFWLCD7pdJMuQDSEhb/S5zhoNRz0WhasJTlGB2CHAhYOZo9/2hhZW1TOBTkKjPkFBwO+yTGsnTQAFI8E9CmApQI4fyDy9qgYWQqMhXK7RDoXntquOFO+UhBiPvIz5bNU+bLJwhxfPa5i9z+R+EgoEalHgNR+K5yvk9HM6J0cAd9uutER4YA79kXk7VExspRWb+qTjsSlCbAUTsFVRq6XoJyX4xwesW5EFgBElsoOsAzA1PbMlE/nKAXlvJwBp03FfbjjS3BrntsLWCojb4/MtEHxEeGAE9R+xQGgvlzmViU/Z2saAQBFWebI36RJKiAAv5Ld4Q44r/g4/hVF5QfhXA2bHAszo+ivJmZho18mmaTjC/wRXS9kqQqGrJaPZjEfYY4P/wxA6q9m8DzvF3AqR8HFpjEfYa5d6QVA/gAAvKLEfdsTH5GkAwLMlF80hD0+ukHmViU/Zd7FrCgqM2PgYAMiSI0WKB7JsjCslUDZ3sjbpFLOecVihyx5znUBfDtpyccX+CPszk5uA5y2yNukUmTNnmgSIBxWdpJAj4ns/uj6yNujUuoaXaKgkyfbRYj58FqBI+kvYXwpKO6j7YmPaAZczyns/ug6GVukDs7JYflocpYBEIWlSqv3ucoU5utUAudq5eivpm6XCI4vEGjfG0gvAlw2qnbaBI+HR5m3vzq0k6G/mtT5kHxqtD89JgHggPJ9QN25yNukQoR4j6wUfeTxb0Bzy0ckqbYCYtzHRsUEdbdB8RFFB/aazO5/+opVdyRE5FnMmls+zGLtiAgmSAWqfaUguF1kcZP5HfktHl8QrqWK44Ce3t30kbWRt0mFVNTb4XTz0Go45EcT8yGX2wUA0tqzmh8AWT+aIAjFqOI93E5WFh3wyyaL4KwrgU5jWFB3Q7ligrrbsPiIoAMLhwCpeeyAJkq5DcAX8yFfahkQRYAw4FP7p78DrFWRt0tlNDrcqPIe9y2P5YPtpP2PL4hILPa+ht0fXquY3ZkSEMZWQYYJOm0UU3bTCqfRjC0A6OW1BB8h8eHPmWrWXx2jslL51ZNq4naJqL90RqDL5eyxQsR9mxMfEdX5ENBogJ5e6wepfRGe58WYjw5yWD5MQdwu4e6kAVabJa8fwLspTscPwUqVZtQhwxRhgTGgWQwBEOWC1nUcoDMBtaeAioORt0tlnBXjc6IYW0CzU1LN0SxmgE98HN9ElmA/ZOkvoa90ZuZCBiI7uNGf3lPZ/eE1kbdLRtqe+IhmMQN8rpcjFPchUGN1ikFQBbLktfssH0Yx1TbSAefdTf/4WeTtUhnn/KxUER96BTSLIQCiKDQGAIYU31EGCpkglcDZahniPYBmbhdBfFidEWQnAUDBICC9EHBa6CgDP3yWj5TI36SF4PuI4hUBn/g4u1sR5yjJLj7mzp0LjuMCbgUFBXJ/TMT4zPgRLmbdJgAaPVD1E3DxmIwtS14EpZ+bZhTFQkQ0qRsBROl2AYA+17L7Y19SFoWXMjnSbIGgqdERZycJiLszZZiGlcA5OXbSbierywGIYtFs8GUnRRT3wXFAz0nsMW3GRM5Ws+9ZFrdLMCtwpHNhegHQcQR7rABxHxPLR//+/VFWVibeSkqUcwBRxLnS4htkAF28Zxv8+KlMrUpuZEnbBFrOdol0MSsawrIonBY668WLLDVZgKBuF1M0AcIA0Otqdn92N5XG9yJPDR3/E4hZf/mf6WMNt4ifgL9lkerpAPBZPqKyVNmCxL9FY1UUEOOqVCo+dDodCgoKxFv79u1j8TEREVXAqUC/G9j9wU9kaFHyI0uaLdBynY9I+4vjgD7CBLk6mtapBvnEYnO3i1GO3VnREAA8cOTz6NqnEmRxu9i9Vip9KqBlokOr4WDwxsBZHa7I3rfbBFZPp+4sE4xtHJvTLR4qJ7fbxWyI0qoI+CzBJ7YECtIEEBPxcfToURQVFaFr1674xS9+gePHj4e81m63o66uLuAWSyI+f8KfPtcBnAY4tweoPilTy5IX2XbSwcSHmD0RRX+Jav9z2p3BtzOLqr9cdlaTAwisSKuTY4K8jt0f+Djy91AR8haEywx4OsUQ4fEFAnoT0NtrrTr4cYSNUw9l3mJwKQYt2qXoI38je3MXtDHSoyb8ye0FZHcH3I6EHz0hu/gYNWoUli1bhnXr1uHNN99EeXk5xo4di8rK4DXlFyxYgMzMTPFWXFwsd5MCiNpvBgBpeb5jpcn6gdJK5uPsnBOF0geaReMDPr90VP3V5XI2iC0VwOkd0bRQFZyqkqG/xF0TFzBBCkGMUU2Q/X/G7k9sASwXI38fFVDb6ES9nVkl5KzJIpASTdVMAdESvKrNp0if8cZ7dMgyyxPMHcQFbXd5IgsQBryWYK/141BiwwZkFx9Tp07FTTfdhIEDB2LixIlYvZqZut95552g1z/11FOora0Vb6dPn5a7SQGY5RhsALle/DjlFR+dsqMVHy1VOI3CYqEz+HbTJf+L/H1UgN3lFlNtO2WnRv5GYrBpOktB95JqlGF85XRnpxLzbuDQqsjfRwUIYys3zRgQoxE2ovgItHwI4j7imA+AlVrXp7IU6XN7In8fFXBWjhofQIsuaCDCAGGBfjey+yPrAGdj5O8TJTFPtU1NTcXAgQNx9OjRoK8bjUZkZGQE3GJJihyDDQD6TgPAAWd3ATWxFUxKhud5nKyyAAA650SxmHk8QQecYMaPWiwOvIndH/yYRf63UU5XNYLngVSDFrlphsjfyN480wXwBTE22COMIRDoP53dH1gZ3fskOaWVbGx1idaqKIqPrICnhf6KylKlN/tKELTxzdhpwfIRE/HhyySMyhLcYSirqTP6AZ/rNAHEXHzY7XYcOnQIhYWFsf4oSaQa2WCzRDs5phewkrVAm/Z1VtTbYXN6oNVw0aUCOhoAeE2JfgNO6K+IA+IEuo4HUnLZQXPH227WyymvUOyUkxqdWTjETjpVEPf2KMVi/xvZfenXQENFdO+VxJyslEHYA4Ctht3HwvIB+CzBB1a2adeL4ILuEnV/Nc920Ws1MHgr3Fqi6S+OA+5aBVz1LGBuF00ro0J28fHYY49h8+bNOHHiBL799lvcfPPNqKurw1133SX3R0WEuJhFOzkCvt30Dx9E/15JyknvYCvKMomR8xEhLGZaA6ty6cUnFqPsL63Ot6Dtb7uul9KL3niPaF1kQdJsAb/+ilYstuvCzg7hPW16N33C219dc6Psr8Yadm/OCnjaZwmOsr96TgEMaUDNSeBU242rOnGBicWuudGKjxDi3iiI+yj7SwHILj7OnDmD2267Db1798b06dNhMBiwY8cOdO7cWe6PighhZ2ZxuCIP2hHoP50VHDtfApQrp5ZJPBHMwp2jiR8A/HZmWYDfjty/v6JmwM3s/tBnCfV1JhIx2DTaxSxImi0gs7gXXC8/rIj+vZIU+SwfwRczMdslWremIcUXS/DD8ujeK0nhed7nJotafNSw+2ZiUSa3pgKQXXysWLEC586dg8PhwNmzZ/Hhhx+iX79+cn9MxKR4J0cPH2UQIwCkZPvSzNroBHlKrkyXEDszYTGTZbAVjwIyOgKOesUcrhRv5BOLoWI+ZBSLg34OcFoWV3XhcPTvl4TIZ8avYfdNYj7MesGtKYNYHPwLdn9gZZsU9xX1dlgdbmg1HIqjqfEB+ObDJv2VJpclWAG0ubNdUvyCdmSZIAfPYPcl/wXcya9Gw0VczKIOiKth9yEGmyw7aY2GLWgA8P2/o3+/JOSUuJjJ5XZpGvMh42KWluc7yHHPu9G/X5LRYHfhYgMrWBW1pSpktotQZEyG/up8KZDZiVnFFFBBM96cuMjmwo7tzNG5oIGQlg/B7SLL2pVg2pz40Gg4n59TjgWtx0QgJQdoOM9Od2xjnBTTbKPcmTVWs/sQPumoA4QFhtzB7n/a2OaylFxujxiN30m27Ikmlg+j3P11O7vf90GbE/el3sUsJ9WADFMUBauAFmI+hGwXGb5bjQYYfCt73AYtwYL4iNpKBYS0fMiWMKEA2pz4AGT2m+kMvliCPcuif78kwuPh8dOFBgBAj7y06N6sNTOjHDE6AKsh0eVyADyw973o3y+JOFVlhdPNw6TXoCjaQ+WCFEECZLZ8ACyQURD3Ca7IGG9OyuXSBEJbPuSqeyQwyOt6OfYlUHdOnvdMEgTxEXWwqcsOuLxuq6aWD4MwH5LbJSkRI4blMl0Nncnuf1wN1JfL855JwLnaRlgdbui1nHxul6Y7MzljdASGejOv9rwLeJJ/EEvlaIVPKGo0UaTZAq2W65bNLKwzAIO8u+k9bctVdrSC1Xro1j5KYQ+EdGvKVvdIILcHc7/wbmB38MKSakU28SFsxMABxuAB3WT5SFJkV48FA4Di0YDHBXzfdqwfwmLWNTcVem2U/0qiWTgw71z2GB0A6HsdWzRrTwPHv5LnPZOAY97+6pmX3sqVEhAXs+CptrK4NAWG3MnuD38O1J6R730VztHzrL965cshPryWjxDiXtb+Gn4Pu9+9tE0V9BOswNGn2dawe1NGQPVgwC/mg8RHchKTDhzxS3a/a0mb8U0fOx+LxSwr4GmNhvOl28rVX3qzbze981/yvGcScPQ820lH7SIDAGsVuzdnBzwtu+UDAPL7MVcZ72bjq41wxNtfPfOjHF9Om6+SZRNLVbpXfNTbZRQJfa8HUtsDDeVtJvDU5nSLbrLeBVH2VwgXNCBj3SMF0CbFhxDzIav46HcD803Xn2szaZyCWViWxSxEQBzg253Jmts+8lfs/vAaoCr0qctqQrBU9Yp2MQOARq/4SAkUH76KtG55YnQERt7H7ncvZYupynG4PKIZP+r+EoQ9pwEMge+VbvKKD5uMY0tn8Lmid74l3/sqmJ8uNMDt4ZFp1iMv3Rjdm4VwQQP+qbbJv8Ftk+LDF/Mho3rUGX3m4e8Wy/e+CkZYzHrKYhauYfdB1H6aUeYgRgDI7Qn0mASAB759Q773VShuD+/ndomyv3jeZ/lIyQl4SbB8uD18dIdfNaX3tUBGB8B6sU0cZ1BaaYHLwyPNqENRpqn1X2gJ/5osTcz46d4sGlnFBwAMm8XEzoktQMWP8r63AjlczjZivQvSozu2AGjR8iGMrwZKtU1OfDEfMnfgiF+yokgntgDn9sr73gqD53l53S4tWD4EsSh7Vb/RD7L7Pe/6HRGvTs5UW2F3eWDQaVAcbWl1RwPg8Zrpm7ldfCevyioWtTpfLMG3/1T9+SFH/Fxksi1mQcaWz/Ihc2xGVieg9zXs8fZ/yPveCuSwt796y2FVFC0fzc9d8cVUkfhISmIWMZzVCRjgLQm97VV531thnKu1od7ugk7DoUu0BZCAFi0fwoIma1AcAHS/EsjtzSqeqjyTQtiZdW+fBm20mS7WSnavM7Gy2n5oNZyYvin7gjZsFvvMc3uA0q3yvrfCOCJnsKngIguymAnio05uywcAXPobdv/DB0BdmfzvryCOeMdXr2jjPYCWN2IGivlIagQzvuymRgAY+wi7P7ASqC6V//0VwoGzzJTbIy8NRp22latbweNpccDFzM/JcT7rx/bXWX69Sjlwjll2+hVmtHKlBEIEmwpkmpkpv7ZRZvGRmutzbW59Wd73VhiHy1l/yRKfY7nI7lNym70kuF0cLg/sLpkXtOKR7ORvjxPYsVDe91YYgrjvI4v48BZcDBpwGiMrcAJok+IjZpMjABQOArpfxU7j3Paa/O+vEPZ7F7MBHTJbuVICthqWyQCEmCCF3VkM+mvwbUB6IVB3Ftj7vvzvrxAOnGNicUAHGcRHiGBTAWF81TXGYjf9CKDRsRTps7vlf3+FsP8sG1/9i2QYX1av+EhtPrYEYQ/EaDN26Rx2v2uJL/ZEZdQ2OnGulgVB95LDBW25wO5T2zd7SYzRkTM7KUGQ+IgFgrlxz79Va248KCxmRTIsZsLOzJTJIuWbkBXL/tKbfP319cuqrUsgLGayiEWrUAq/uRkfADLMbEGLSX9ldQIGes/nUan1o8riwNkaVuGyvxxiUbR85DR7SavhYmsJ7jkZaN+HuTZVGti932sF7tjOjMyUKMvgA35isbn4yPK+f601+eeptik+UmIsPrpewU5QddmArS/F5jMSjLgzk2MxE5R+EKsH4BOLNbEacEPvYgO95hQ7Q0RlXGywo7zOBo4D+srhdpFo+YjZ+LpsDgAO+PEzoLwkNp+RQEq8i1nX3NToz3QBfDE6QSwfQAyDTgGWXXPF79jjbf/wuRRUxA9nagAAgztmyfOGglhMbS4WRauizQW3J7mDrtum+DDHWD1yHHDl/7HHu5cC1Sdj8zkJ4kK9zItZC2ZGAMiI9WJmSAHGPsweb/kL4HLE5nMShBDv0TU3NcDMHjGtxHxkiBNkjPqrfW9fYPeXz8fmMxKIsJMeKIewB1qM+QBiVOvDn/7Tgbx+gL2WCRCVUXKG9degjnL1V+j5UFi7gBiJxTjStsVHrBYzgFk/uo5jwVabX4zd5yQAIX5AvsUstE8aALJSmCumJpb9NfyXQGoeCxLepa6qp8JiJkv8AODrryBmfCBO42vCMyz24+h6oPSb2H1OAhAWM9nERyvjy1frI0b9pdGw/gKAHf8EGi7E5nMSxD6hv+QQHx6Pn6WqufjQazVixeeYWYLjRJsXH7JWYWzKlb9n9z+8D1Qcit3nxJnvT9UAAAbJvTMLMTnGZTEzpgETnmKPN7/gd7hT8rPnFDN1y9ZfDRXsPi0/6MuCqyCm/ZXT3VdF84u5qqr7IbhdZInPAQCLdzFrxfIRk3RbgT7XAkVDAacF2KKezdjFBjvO1jSC42QSi7YadkYYELK/hM1YTMdXHGjT4sPl4eUthNSU4hFAn+tY5svaJ1UzQe4+yczuw7sEN7uHjSV0gBXgH2QVY3fIkJms7kdjFfD132L7WXGC53nsPsnEx/AuwQNEw0YUH3lBX46LWASAcU8AOjNw5jvg4Cex/aw4UVbbiLM1jdBwMu2kAT/LR3BLlSAW62LZXxwHTJzLHu98Gzh/MHafFUf2eeM9uuWmihakqBCsHsbgwfeAz60ZU0twHGiT4iPFoIXOW2gp5hPk5D8CWiNwfBPw4+rYflYccLk92OO1fMi2mEkMOI15X2l1wKR57PGORUDVidh+Xhz46YIF1VYnjDqNfG6XhnJ2H8Ly4Uu1jXF/pRew1FsAWPcM4LDE9vPiwHcnmLDvX5Qpj0vTYQWc7MCzUOMrO5UtclWWGIv7buOAvtNYWv3aJ1SxGfvuBBP2QzrJPBeGsAIDMc7+iyNtUnxwHBe/BS27KzD2IfZ43dNJfyjWj+X1sDrcSDfp5MlpB8Jyu3hiHeHd62oWq+O2A2seS/oJclcpW8wuKc6CQSfDcOd5n+UjPcHiA2B1JLI6AXVngC1/jf3nxZhdpWwxGyGXVbHhPLvXmQBj8PEaN/EB+DZjJ7YAhz6N/efFmO9OMEvFqK7xsQID/gkTyR0Y3ybFBxDH3TQAXPYokF4E1JwEtib3BLnTu5gN7dQOmmjLdAsIE2QrZnwPH4cDlTgOuPYlQGsAjn3BKtUmMbvkdrk4Gnw76dQQ/ZUSR7OwIQW4+s/s8bZ/ABePxv4zY4gwvkZ2lam/6r11htIL2f92EATxURkP8dGui89atfappD5TyepwicGmo7sFd2mFjTgXhhYfWbEuFREn2qz4EDqwOh4DzpgGXL2APf76b0DZvth/ZowQzMIj5FrMeB6oO8ceZ3QIeolJr4XRu2uPS3Gd3J5MMAIsVieJKzMK/TW8s1w7aa/Vw5DG/q+DIC5mDXHamfW+hhWz8jiBVY+wjIEkpNbqFA8oGyZXf4ljqyjkJTnxtHwAwGX/j4mQujPAF8/F5zNjwJ5TNXB5eBRlmtCxnVmeN607y+5DzIWAT9xXU7ZLctI+3QiARSvHhf43An2vZ5HMn8xOykqaLrcH3xxjZsFLe4T2SYaFrZZFwANsdxYCYYKMW39d9v+A7O5sJ7L2qfh8psycrLTgVJUVOg2HEXKZhetbjvcAfGOrwe5CYywDugU4Drjmr0wQndoGfLso9p8ZA7YfrwTPA93ap4rfYdT4Wz5CEFe3CwAYUoFp3oM3d/2LuWCSkG+PM5fLyK7Z0Z88LCBBLGanxLm/YkSbFx8X6uN4mNg1f2Ulqcv3JWVp6H1na1FncyHDpMMguar5CYPNnN3shFR/2meYAMSxv/Qm4IbXAU4D7H0POLgqPp8rI1uOsOC1YZ3byRO8CPgWsxbER7pRJ8aXxE0stuvM4gkA4It5wIUj8flcGdl8hFmVxvUKbXIPGymWjzTBUhXHubDbOGDY3ezxJw8lpftly1G2ERvTXSaXCwDUtm75yMtIwNoVA9qs+MhN83ZgvEzDAAvQm+rNcd/8Z+Dktvh9tgwIi9llPXOjP5ZdoBWXi0B7b39VxHPAdR7jOxjr09/4dv1JgjA5XiHnYlZ7mt1ndQp5CcdxYn9diOeCNmwWO9TRbQc+ui+pTinmeR6bD7PxFW/xkZ3K+qrO5oLTHUeX1aTngcxiFgv32f9LquDuyga7WFZ9fO/gsU8RIcHt0j6NbcQq6pM7eaHNio+EWD4AYOAtwKBfsNof//ulrwBQErBVWMx6yjk5CoMt9OQIJFDtj38KKBjEan98eC/gTo6jrJ1uD7b/xP63ZO2vmlPsvgXxAQC5glsznv3FccD1/2DWxbK9LLssSThW0YBztTYYdRr5ghcBSW6XLLMewl4iLjFwAqYM4Ka3AE4L7P8fO4gzSdh0+AJ4HuhXmIF8r1U2agLi30LPh8JcGNeNWAxou+IjETszwJdNkdMDqD8HrLwf8MTBLx4lF+rt+N5bKVPWnbRU8ZGeoAGnM7AJUp8KlG4Fvpwb38+PkB3HK9FgdyEn1YD+cpw8LCBRfLT3mvLjPr4yOwDT32SPd74FlPwvvp8fIRt/ZC6XUd1yYNJr5XvjGq+lKrNjyEs0Gk6M+4h7f3Ua7TsHa83jQPn++H5+hHx1mPXXlX1ktHpYK5nVDmhRLAprV43VCbtL+WtHKNqu+EjEzkzAmAbcspTlux/bwMpDK5x1B8rB88DgjpkoypIpshtgZ6kAQFZxi5clzFIFsIPMblzIHm/7B7D/w/i3IUzWlDAX0eT+BfKlRAN+4qPl/hLcmhfrExAU13MScPlj7PGqR5Li5Ns1+1l/Tewr42LmbGQbHADI7tbipQWZbPdeXpsAU/6lc5i7zNUILL9N8We/2F1ubPa6oCfIKT6EuTC9MGR1U4Blauq1bExfjGfYgMy0efFxod4e2/NdQlEwkAU0AsC2V4E978a/DWGw1js5Th0YWpFHROVP7D67e4uX5aULAacJ8nP2v9EX//HxbOD0zsS0QwIutwfrD7D+umZggXxvzPPSLR+ipSpB/TXhaaDbeJZJ9d7PfYF8CuR0lRU/nK6BhgOuHiBjfwmLmTGTuaJaoDCTbSjO1TTK9/lS0WiYdTG7G1B7ClgxQ9HFGDcfvoB6mwsFGSYMKc6S740lzoUBMVVJ7Hpp8+LD4fYkLl960C3AFY+zx5/OAX7amJh2tEKVxYHt3rSyqXJOjgBQ5R1wOS0POKG/ztclcLBd+XtWT8LVCLz/c8UWtPqutAqVFgeyUvQyxw+UAy4bywDKCG3GB3w76bJE7KQBQKMFbnkHaN+H7f7f/7liMyrWlLC4jFFdc0SRLQtVx9l9dteQBcYEOnitmecS1V8p2cCM/wCmTHZWz8cPKNYdveoHZk26blChvFZFcS5s2UoF+LL/ztcpV6S1RpsVH0adFvnewJ3TVdbENWT8U0D/6axA0vIZwMntiWtLCFbuOQu3h8eADhnonJMq3xtbq4BGFkfSmllYmBzP19vgcCWoiJRWx9xlRUNZAOq/pytyR/3hbtamKf0KoNfKOMQvHmb37bq2aBYGgOJ2LG06oWPLnAXc/l9WifX8fmD5LxR3/gvP8/h4L1vMrhkks1VRFB+tL2aFglhMhOVDILcn8PNlgEbPKgt/qryCcRa7C18eYvEe11/Scpxa2Ei0fABAhyzWX2erE9hfUdJmxQfgmyBPJXKC1GiAny0Gekz07ajP7k5ce5rA8zz+s5MFrd06vGU/f9gIk2N6ESs81AK5aQaY9VrwPHA2kROkIZUtaIKJeOm1vqA+BVBnc2J1CVvMfj5C5v664BUf7fu0emlxNhtbZ6obE+PWFMjqBNz+H8CYAZz8Bnj/VnbYmkLYd6YWh8rqYNBpME1u8VF5jN1nd2310kLB8lGT4J10t/HeDBgNc0Ur7DTwT384h0anG11yUjCwg0wHNQpItAIDvvGV0LUrStq0+Ojk7cDT1QnuQJ0B+Pm/gc6XAfY64J0bgBNbE9smLz+cqcXh8/Uw6jS4/pKWa3GETcUhdp/bo9VLOY4T+yvhAy41F5j5CZDVGag+ASy9Bqg+mdg2eVm19xxsTg965qVhaKcsed9cFB+9W720KMsEjgMane74nBnSYmOGAHd8BBjSWcbS8lsV44JZ/h2Lobl2YCGyUlq2JoXN+QPsPq9fq5cKO+lztQrYSfe/EbjBG+D93WKvBSTxLhie5/HvHWyczxjVSb6qpgD7+4TCeLm9Wr1cMXNhFLRp8dExWwGmYQFDCjBjBRMgjnrg3ZuAH1cnulVY8g07Vv6agYXiAW+yUfYDuy8YJOnyTjkKGnBZnYC71zALSM0p4F9TfH9PgvB4eLyzrRQAcOuIYnknRwC48CO7l2D5MOq0yPfGLyhifBWPAO74kJVgP7GFCcYEF42rsTrE+IHbRrYcwBs2HrdPfBQMbPVywQp8rqYRNmfiF3pcchur2cJpgO+XAf+dlfCicXtP1+DAOWalumWYzFbFyp9YcLQ+hZVhaIXO2cxSrIi5MELatPhQnHo0prMJsve1LN/7gztYameCzI6nq6z4bB8LhvvlZa2bbsOm3HvAXuFgSZeL/VWpEL99Zkdg1mpvUGMZ8K+pwOG1CWvOxh8rcLSiAWlGnfwuF4/bdyBifn9Jv1KczUz5ihlfnUYBsz5jx5WXlwBvT/JZ3xLAO9tOwupwo09BunwHNQpUHWenD+vMkhaz9ulGpJt08PBAqVLG19CZ3pIEBuDQKuCd64H68wlrzuLNzE08bVAR2qXKbKUq9xtbmtbrvPivXR6PctxS4dCmxUfXXKYej1U0JLglfuhNLOhq6ExWBXX9/wEf/Yrl7MeZN7ceh9vD4/KeuRggt3/T4/bVX5AoPrp4LR/HLyhkcgRYcbR71gFdx7Gdy4rbgC1/iXugHM/zWLSZ+YxvH9UJGSaZrVQXDjOLnD4VyOsr6Vd65LFTb4+eV9D4KhoC/HKDz2L15pUJKURmsbuwZBuzKs6e0EN+K5VghcvrK2kx4zhO7C9FzYf9bgBu/x9LFz69A3hjfEJi4n4sr8PaA+XgOOCBca0H8IZN2V52L3EuLMoyQa/l4HB5lOEqi4A2LT56F6QDYOmbijohUKtjpz5OfZGVHi75D5sk41gs6WSlRfRHPzCu9QCosCnfx3ZmxgxJOzMA6FPIKnUeKlOGv17EnMUsVkPvYoJx4x+Bd6f7jp+PA18eqsDuk9Uw6DS4JxZWqjPeuiYdhkpazACgTwHrrx/LFdZf2V2BX37hrQNiBT78JbDmd3EV+Eu+OYEaqxNdclJwjdy1cwAWXAuwCqIS6alE8QGwQ+h+9RWQ25ulTf/ramYRjqPAf+ULllZ/zcBC9MxPl/8DTu1g90VDJV2u02rQI4+141BZvfztiQNtWnykGXXo7N1NK25B4zhg1P0ssDG1PVBxkAmQb16NS/DVi2sPw+lmVo+xcp7aKCAco9350jAWMzbYztXa4nsGhRS0euD6V1mgnM4MHP8KWDSWpQzG2G3mcnuw4HPmPvjlZV3lO2vCH2Ex6zhC8q8I/aXIyTE1hwWhCpVQv3sD+OdlcSked77OhoWbmJXq/03qJd8hjf6Ufs3uu1wm+VcEy8eR8wrsr5zuwL1fAH2uA9wOZhFedn1cMs22/1SJz/eXQ8MBj1zZU/4PsNcDZ79nj7teLvnX+nk3YwfPKWztkkibFh8A0LdAobtpga6XAw9uB3pNZYNuw++Bt66Kqelx69ELWF1SBo4Dnr6mr/wmYQA4vondd71C8q+km/Sir1Ox/TXkduBXm4D2fQHLBRYot+J234FRMeDtr0/gpwsWZKca8OD4GFipPG7g6Ab2uMdVkn9NsHycrWlEbWOCCvm1hEYLXPV7ZtZPL2Spqf+aDKx9GrDVxuxj5685BKvDjaGdsnD9YJlrRQCs9szFIwA4oNMYyb82oIi5VveeqpG/TXJgygBufReY9goLzCzdCrw+im3I3LH5/3K6PZi7igXuzhjVSbSWy8rJbQDvZvVzWqkc7E8/75lNB8ti978aS9q8+BjYkQ044dA0RZLWHrhtORt0xgzg3B7gzau8x7zLG4BVb3Piif+x4KeZozujb6GMh5IJWKt8qcRhLGYAxEPS9pyukblRMpLXB7h/MzDuCUCjAw6vBv4xDPhqPmCX16R9rKIBL21gKXpPXt1H/lgPADizixVVM2YCxaMk/1pmil60LH5/UsHjq+ck4NfbgUG3MrfZjtdZf32/THbT/uclZfhk7zloOOC5af1jI+wPfcrui0exyqESGVycBQ3HLIsJOeNFChwHDJsFPPA1+/ucFrYh++dlwLEvZbcyvvLFURw+X4+sFD1+O6n1FPOIOPgJu49wLtx7uiaxtXQipM2Lj1Fd2eDccbxK2VHDwqB7aCebJMEDu5cCrwwG1v8esFRG/RE8z+PJD0twrtaGTtkpeGJq6ymVEXHoU1bRNX+ApJoR/gj9JRwXr1h0Rna+yP1bvJOkFdj8AvCPocC3b8hS6MrqcOGh97+Hw+XB+N7tccvwlkueR8wPy9l9rynMvRQGo7syl92O4wrvL3M7YPobwO0fAjk9mdVq1cPAojEsIFUGV+eZaiueXsnith4c3x2D5TwXxB/h4MP+N4b1a6lGnWit2q1ksQgwN8zda9n5WCk5LA383ems6F/pN7J8xI7jlXh9EyvU9qcbB8qf4QKwM2wOfcYeD7gprF+9pDgLBp0G5+vsOH5RQUH4Emnz4mNQxyyY9VpUWRw4rERfZ1PSC9gkOWsN0GE4q4q67VXg7wPZkdRCid4IeP2rY1hdUga9lsPfbh2MFINOxoZ74XngO++R5wNvDvvXL+2RCwDYWVqljHoErZHfn2XD/HwZM6s2nAc+/x3rry1/YVagCPB4ePzuf/vwY3k9ctOM+PP0QbHZRdtqfYvZ0DvD/vXR3ZlY3KZ0sSjQcyLw4DZgynx2zsiFH1lA6sLRwO53IhaNDXYX7n1nF6qtTgzskInfXNV6IamIOLeHnY2i0QH9fxb2r4/0ivvNR+IXLB0xGg0w5A7goV3A6F+zU8JPfsNquCy5Bji4KmLReOKiBQ++uxs8D9wyrCOulbv6rMC+FYC9FsgsBoqlBwcDgEmvxbBOLEV727GLsWhdTGnz4sOg02CMN6By3YHEFh0Kiy6XsgCsGf9hRbqcFlYN8B/DWAnpH1cDLulBmcu2l+Kv65n5ft71AzCss3RzbVgcWQucL2E+26F3hf3rPfLSUJBhgt3lwddHk2TAcRxLGZz9HXDNX5lf13qRZcW81IelUpd+I9lk7PHweObjEqzeVwadhsOiO4aKB7nJzvaFrOpubm9WAC9MLu2RC44DSs7WKqPYmBR0BmDMbGBOCTDhGcCUxWIoPn0EeLkPiwkRqlFKwGJ34Z6lO/FjeT3apxvxxsxhMOhiNPVu/gu77z+dbVTCZFK/fAAse8qtZEuwPynZwNULgEf2AMN/yc6GOfkN8J87gVcuAba+HNYZTGdrGjFryXeotjoxuGMm5t0gra5N2LjswDevsMejf83EVJhc1pNtxtYfTFz9k0hp8+IDYKcTAsAne88ll++M45gp/P4twJ0r2Ymr4NkCv2IG8FIv4LNHWeS72xX0LXiex+tfHcOzn7CgqgfGdceMUTJXWxSw1QGfP8Eej/xVWP5oAY7jxF3Iyj3KO9StRXQGYOR9wMN7gOlvscqTbjuw7wO2W/vHUOCLecC5vSGFiN3lxmP//QHLvzsNDQe89PPBGNElRkLxwhHf5DjhqYgmx7x0k+h6EQrWJQ2mTGDc40yETPoD0K4LswTteB14fQSLM/j67y1mXFxssOOuf32H705UIc2ow5szh4vH18vO4c9ZfBGnBS7/bURvMbJrNjJMOlRaHNh69ILMDYwxmR2A614G5uxjf785m52/9OU84G/9gXemsfNiLKE3Lccq6nHLom04WWlFcbYZb901IjYWYAD4+m+sGFxq+4isigAreAYA3xy7iIokO+GW4xW22tbV1SEzMxO1tbXIyIhBsGMQGuwujPzTF7A63FgyawQm9MmLy+fGhIvHgO+XAvv+CzT4WXJMWSywrtfVQJfLgfR81Fqd+L9P9uNTb4nn+6/ohien9omN+d5lBz64Ezi6jh3HPvtbwJgW0VvtP1uL6/7xNfRaDpt+N0E88Tbp4HmWYvf9UqDkQ2a9EsjqzMRkt3EsXdLcDicrLZjzwV7sOVUDrYbDizcNwk3DYhTn0XCB+c8vHmb1MO5YGZH4AIAPdp7CEx+WoCjThE2/mxC7XX+s8XiAY18Au95m9x4/QZ/XnwUM9pzEzOc6A3afrMbD73+Pc7U2pJt0WHbPSAzpJHMlU4Hy/UzA2mqBMQ8BU/4U8VvNXXUAS7eVYnzv9lh690gZGxlnnI0sXueH5b5UcQAABxSPZBu37lexTYBGi0/2nsXTH5XA4nCje/tUvHvvqNgJxUOfsvkQPNuIDLol4re6edE27DpZjYcm9MBjU2IUFCuRcNZvEh9e5q85hDe2HMfADpn4ePalscm9jyceN0tnLfkvs4Q0BgaQNaR2wkZrD2x19MAhdMVt107C7WNjkMMOsDiUT2YDp7Yzv+zdnwMdh0X1ljPe3IFtP1Xi58M74sWbpVUFVDT2euDIOhb5fnQDi+XxwnMaXEjri3W1xfje1RU/GXrhdzOuxeW98mPTllM7gJX3A9Wl7MTh+zYCGZH7vG1ON6548StU1Nsx7/r+uGtsF9mamjAslcChT5hoPPkNAN80yutMOGXsjc9rO2G3pydqsgZgwV2T0CM/BvMZz7OYnNWPMuHRcSQr+a+LPDiy9KIFE17aBJ4HPvjVaIzqFoM6P/Gm+iQr1nhwla+UuRePPg0HdX3weV037OW7I7X4Eiy4cwJy0ozyt8PlYDF6X/2JZVYNmwVc93dmxY6QdQfKcf+/dyPNqMPGx8YhLz1GLlgJkPiIgAv1dlz5102ot7swZ2JPzJkYo4CwROBxA2d2wvXj57Ds/xzpdUegQZNu1+iYXz+/P6s42q6L75aWF/7gaKxh7p4DK9mC6nGyQ71ufRfoPiHqP2n3ySrctGg7AOCNO4dhcv/w/duKxWEBfvoK9iMb0XhkI7IsJ5pfY8xgp1/m9mKnAuf2YtaS9EIW/R+OlYLnWR2SE1vYBP3TRvZ8Vidm8ZBw6nBr/Ht7KX7/yQGkGLT4ZPalsakSmSisVcBPG2E9uBb8sS+R6gwSRGzKYqfL5vVlGV5ZnViQYVYxc++Eg8fDTlM+9gXw/b9ZDBXALC4zPmAVd6Pk6ZUleP/bU+iSk4KPZ18q/4m7iaT2LHB0HRpKVkN7ejvMniCZImn5LBsvr2/gXJjViWWyhYPHzQTP0S+A798Bar1uukvuAKb9PewMsqbwPI8bXv8G+87UYlyv9nj7ruHQaRNjXVSE+Fi4cCH+8pe/oKysDP3798ff//53XH5569XbEiU+AODD3Wfw2/+yMxEendQLD03oAU2SW0CsDhe2HavExsMVWFNShhqrExmw4DLjT7i7uBzDNEehqdjfclEljZ4taCk5rDKkOZsNQK2eHfoEsCwARwObiKtPsIPW/Ol+FXDtX9mZGjIx79MDWPJNKYw6DV76+WBcNygGBZviTJXFgc1HKvDloQpsOHgedpcH+ajC1WnHcHtxJXo6j4Ar3xdgGWmGRs+CDdPy2GGFhjR2r09huy3ezSbExmp2smvtaZZaKsBpgEtuByb/UZaFDGBBsre9uQPfnqhCXroR/7xzGIbGygURR05XWbH5yAWsO1COr49dBM/z6MaV4dp2ZzCjsAyFdftYsCrfQtaFMQNIzWXpvqYsdq83sX7gvNV/7fVsjFoqmGvV30WnTwEunQNc9v+isnj4U2N14NpXv8bZmkYM6JCBxXcOT173phePh8fh8/XYcuQCVv1wDgfO1UEDD/pwp3Br/hlMzzmN9OoDQNUJoOnmzB9Tpnc+zGX9Zkhl86BWz8aey8Y2EPZ6dn5QdSmL7RJIyWVja/AvorJ4+HO4vB7TXvsaDpcHUwcU4MWbByE9FjV/WiHh4uODDz7AnXfeiYULF+LSSy/F4sWL8dZbb+HgwYPo1KnlYMZEig8A+Ou6w3jtK5bb3acgHb+8rCsm9ctXvPJ3e3iU19lwqtKK0koL9p+tRcnZWhwqq4PT7eviokwTfj6iGHeN6eLLW+d5oPYMcH4/O4a7+gQzU1afBOrOsAUrEnJ6sniBIXcARZdE/Tc2xen24MF3v8cXh1ik9+U9c3Hn6M64old7mPTSSrYnCofLg7M1jThVZcXxCw0oOVuLkjO1OHahISDWtE9BOm4f1Qm3DC/2/U1uF1vQLh4BLh4FKo+yx7VnvSIigiHNadnOvM+1wKCfszoKMlNtceDWN7bjyPkGaDjgxks64OcjijGiS7bi3ZwWuwtnaxpxusqKH8vrceBcrTeDJ1AEju6WjVlju2ByvwLfxsVpY31UcYjdKo+yINXa04A1whRkjZ6d29JrChOKEQRvt8aP5XWY8ea3qLI4YNZrccfoTpg+tCP6FKTHJi5MJnieR73dhXM1jTh6vgFHztfjx/J67CqtQrXVVwlVp+EwsW8+7h/XLTAWx97AjrMoL2Eu4+pS380ZxEoiBWMGO0qi3/UsE0kvv2tkw8HzePDd3XB5eOSlG3HPZV1x7cBCFHurQseDhIuPUaNGYejQoVi0aJH4XN++fXHjjTdiwYIFLf5uosUHAPx312nM+/QgGuwsoIzj2Am4fQrSUZhpRn6GEVkpBqQYtEg16GA2aGHWa6HVcOA4QKvhoOU4aLz3wsTq4Xl4eCYUeO9j9hwPj8f32OHywObywOZ0w+Z0w+70wOZijxsdHtQ0OlBjdaLa6kC1xYEqqwPltbYAkeFPx3ZmXNknD1f1zcdlPXLDm+hdDrbbslxkE6W1ku2Y3Q7vzcnEiSGV7bBNmayeRXbXmEyIzZrn9uCVL49i4aafxNRAvZZDz7x09MpPQ36GCXkZJmSZ9UgxaGE2aJFi0MGk10Dj7Rt2D2g4TnwOYP3h9rB+4nke7ib9JPSl0y30la/PbE43bC4PrA43aq0OVFmdqLE6UGVht/N1NoTKZOxTkI4r++RhSv8CDOqYGd5E73ayWiJ1Zazf7A3sNFp7AwvA4zTMJcNp2Q47LZ9ZSfL6AvrY72zrbE7838r9WPWDr9y8Wa9F/6IMdM5JRWGmCXkZRqQZdUgx6JBmZONLp2H9otVw0GnY2NJ5+w7wjS0Pz8YWzyNgfPHevnK4PbA7PbC73LC7vPdOD+ze8Vbb6ERNoxO1VidqGh2otjhRXmcLefCkTsNhaKd2uKJXLq4f3AGdcsKc6B0WJhqtlYCtho2txmq2e+Y9zMXCe5jlypzF+iynJxtfUZrrpXC6yor/98Fe7PIrOtYuRY9+RRnolJ2CokwzMlP0yDDpkWHWwaTTQq/TQK/VQKfhYNBpAvpJ+Jf3X3b8h4HH20dONw+X2yM+dro8cHp/trs8aLC5UG9zod7mRIOdPa62OlBeZ8P5WhssjuCWphSDFsO7ZGNK/3xcM6AwvMJhPM8su1bvXGi5yB47G71zoYvd64xsLjSksgyc7G7MxSbxDKto2H2yGv/vg7045ZfWXphpQt/CDHRsZ0ZeuhHt043IMOmRZtLh0u65slr3Eyo+HA4HUlJS8N///hc/+5mvyM1vfvMb7N27F5s3bw643m63w273maTq6upQXFycUPEBMLPjv7efxGf7ypKj+BjYotuxXQo6tjOjX1EGBnXIwqCOmejYzqzonYocnKq0Yum2UqzdX4ZzSi0N3QSzXotO2SnolJOC/kUZGNQxEwM7ZKF9egwC3RTGD6dr8O8dJ7H+QDnqbMHTwJVGhkmHDu1S0DMvDQM6ZKB/USYGdcxMiHk7nvA8jy8PVWDFztP4+tgF2JzxO002GjLNenRvn4reBenolZ+OQR0zMahjFvQJioeIFw6XByv3nMHKPWfx3YmqkJscrYbDsT9NlXVtSKj4OHfuHDp06IBvvvkGY8eOFZ+fP38+3nnnHRw+fDjg+rlz52LevHnN3ifR4sOfiw12HDhXh2MVDaios6G8zobaRiesDjesDhesDjdsDjfbGfNMvbuFXbP3MQcOGs67u9b4HnNNdt0cxwqfmXRamPQaGL33Jr3We9Mg02xAdqoeWSkGZKcY0C5V77XImBRvvo41PM/jTHUjDpyrw8lKC87X2XG+3oa6RicaHW5YHW40ei0TzLLh2x0L/eXhAR48s1759RezbHmtWhy8z3PQaTmY/fqH9Z3v56wUPdqlGJCdakC7VAPapRhQlGVC+zSj6kVha7g9PE5cbMCBc3U4U92I8lobLtTbYXG4YLG7vGPMDbeH9Y/Lw/rK5fbAwwMujydg7HDw9QsHVhfGN9YAo46NJaOOjS2jXhPwONOsR5bZgKwUPbJS9Mgw65GfbkKHdmZkmtUtMqTgcHlw4Fwtjl+w4FSVFeW1NtTZnOzW6ILd5WaWCrfHe2NWiwC4gDv22DsONByg1zLLiUGngV7LMSuKVgOD97FBp0GaUYd0kx4ZJp33sQ6ZKXrkZ5hQkGFCQaYpdvU5koh6mxM/ljO30/laG87X2XCxwS5a9f/7wNhW3iE8FCE+tm3bhjFjfCcq/ulPf8K///1v/PjjjwHXK9XyQRAEQRCEdMIRH7JLw9zcXGi1WpSXB5Yqr6ioQH5+87oERqMRRqP6zcwEQRAEQTBkd34ZDAYMGzYMGzZsCHh+w4YNAW4YgiAIgiDaJjFxij366KO48847MXz4cIwZMwZvvPEGTp06hQceeCAWH0cQBEEQRBIRE/Fx6623orKyEs8//zzKysowYMAArFmzBp07d47FxxEEQRAEkURQeXWCIAiCIKImnPVb3QnPBEEQBEEoDhIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHEFRIfBEEQBEHElZiUV48GoeBqXV1dgltCEARBEIRUhHVbSuF0xYmP+vp6AEBxcXGCW0IQBEEQRLjU19cjMzOzxWsUd7aLx+PBuXPnkJ6eDo7jZH3vuro6FBcX4/Tp03RuTCvQdyUd+q7Cg74v6dB3JR36rqQTq++K53nU19ejqKgIGk3LUR2Ks3xoNBp07Ngxpp+RkZFB/5wSoe9KOvRdhQd9X9Kh70o69F1JJxbfVWsWDwEKOCUIgiAIIq6Q+CAIgiAIIq60KfFhNBrx3HPPwWg0Jropioe+K+nQdxUe9H1Jh74r6dB3JR0lfFeKCzglCIIgCELdtCnLB0EQBEEQiYfEB0EQBEEQcYXEB0EQBEEQcYXEB0EQBEEQcaXNiI+FCxeia9euMJlMGDZsGLZu3ZroJimCLVu2YNq0aSgqKgLHcfj4448DXud5HnPnzkVRURHMZjPGjx+PAwcOJKaxCWTBggUYMWIE0tPTkZeXhxtvvBGHDx8OuIa+Kx+LFi3CoEGDxCJGY8aMweeffy6+Tt9VcBYsWACO4zBnzhzxOfqufMydOxccxwXcCgoKxNfpuwrk7NmzuOOOO5CTk4OUlBRccskl2L17t/h6Ir+vNiE+PvjgA8yZMwfPPPMM9uzZg8svvxxTp07FqVOnEt20hGOxWDB48GC89tprQV9/8cUX8fLLL+O1117Dzp07UVBQgEmTJoln8LQVNm/ejNmzZ2PHjh3YsGEDXC4XJk+eDIvFIl5D35WPjh074s9//jN27dqFXbt24corr8QNN9wgTmz0XTVn586deOONNzBo0KCA5+m7CqR///4oKysTbyUlJeJr9F35qK6uxqWXXgq9Xo/PP/8cBw8exEsvvYSsrCzxmoR+X3wbYOTIkfwDDzwQ8FyfPn34J598MkEtUiYA+JUrV4o/ezwevqCggP/zn/8sPmez2fjMzEz+n//8ZwJaqBwqKip4APzmzZt5nqfvSgrt2rXj33rrLfquglBfX8/37NmT37BhAz9u3Dj+N7/5Dc/z9H/VlOeee44fPHhw0NfouwrkiSee4C+77LKQryf6+1K95cPhcGD37t2YPHlywPOTJ0/Gtm3bEtSq5ODEiRMoLy8P+O6MRiPGjRvX5r+72tpaAEB2djYA+q5awu12Y8WKFbBYLBgzZgx9V0GYPXs2rr32WkycODHgefqumnP06FEUFRWha9eu+MUvfoHjx48DoO+qKatWrcLw4cNxyy23IC8vD0OGDMGbb74pvp7o70v14uPixYtwu93Iz88PeD4/Px/l5eUJalVyIHw/9N0FwvM8Hn30UVx22WUYMGAAAPquglFSUoK0tDQYjUY88MADWLlyJfr160ffVRNWrFiB77//HgsWLGj2Gn1XgYwaNQrLli3DunXr8Oabb6K8vBxjx45FZWUlfVdNOH78OBYtWoSePXti3bp1eOCBB/DII49g2bJlABL/v6W4U21jBcdxAT/zPN/sOSI49N0F8tBDD2Hfvn34+uuvm71G35WP3r17Y+/evaipqcGHH36Iu+66C5s3bxZfp+8KOH36NH7zm99g/fr1MJlMIa+j74oxdepU8fHAgQMxZswYdO/eHe+88w5Gjx4NgL4rAY/Hg+HDh2P+/PkAgCFDhuDAgQNYtGgRZs6cKV6XqO9L9ZaP3NxcaLXaZkquoqKimeIjAhGiyOm78/Hwww9j1apV+Oqrr9CxY0fxefqummMwGNCjRw8MHz4cCxYswODBg/HKK6/Qd+XH7t27UVFRgWHDhkGn00Gn02Hz5s149dVXodPpxO+DvqvgpKamYuDAgTh69Cj9XzWhsLAQ/fr1C3iub9++YqJFor8v1YsPg8GAYcOGYcOGDQHPb9iwAWPHjk1Qq5KDrl27oqCgIOC7czgc2Lx5c5v77niex0MPPYSPPvoIGzduRNeuXQNep++qdXieh91up+/Kj6uuugolJSXYu3eveBs+fDhuv/127N27F926daPvqgXsdjsOHTqEwsJC+r9qwqWXXtqsHMCRI0fQuXNnAAqYs2Ie0qoAVqxYwev1ev7tt9/mDx48yM+ZM4dPTU3lS0tLE920hFNfX8/v2bOH37NnDw+Af/nll/k9e/bwJ0+e5Hme5//85z/zmZmZ/EcffcSXlJTwt912G19YWMjX1dUluOXx5cEHH+QzMzP5TZs28WVlZeLNarWK19B35eOpp57it2zZwp84cYLft28f//TTT/MajYZfv349z/P0XbWEf7YLz9N35c9vf/tbftOmTfzx48f5HTt28Ndddx2fnp4uzuX0Xfn47rvveJ1Ox//pT3/ijx49yr/33nt8SkoK/+6774rXJPL7ahPig+d5/vXXX+c7d+7MGwwGfujQoWKKZFvnq6++4gE0u9111108z7N0rOeee44vKCjgjUYjf8UVV/AlJSWJbXQCCPYdAeCXLFkiXkPflY977rlHHG/t27fnr7rqKlF48Dx9Vy3RVHzQd+Xj1ltv5QsLC3m9Xs8XFRXx06dP5w8cOCC+Tt9VIJ9++ik/YMAA3mg08n369OHfeOONgNcT+X1xPM/zsbevEARBEARBMFQf80EQBEEQhLIg8UEQBEEQRFwh8UEQBEEQRFwh8UEQBEEQRFwh8UEQBEEQRFwh8UEQBEEQRFwh8UEQBEEQRFwh8UEQBEEQRFwh8UEQRFA4jmvxNmvWrEQ3kSCIJEWX6AYQBKFMysrKxMcffPABnn322YCDqsxmcyKaRRCECiDLB0EQQSkoKBBvmZmZ4Dgu4LktW7Zg2LBhMJlM6NatG+bNmweXyyX+PsdxWLx4Ma677jqkpKSgb9++2L59O44dO4bx48cjNTUVY8aMwU8//ST+zty5c3HJJZdg8eLFKC4uRkpKCm655RbU1NSI12zatAkjR45EamoqsrKycOmll+LkyZPx/GoIgogSEh8EQYTNunXrcMcdd+CRRx7BwYMHsXjxYixduhR/+tOfAq77wx/+gJkzZ2Lv3r3o06cPZsyYgfvvvx9PPfUUdu3aBQB46KGHAn7n2LFj+M9//oNPP/0Ua9euxd69ezF79mwAgMvlwo033ohx48Zh37592L59O371q1+B47j4/OEEQchDXI6vIwgiqVmyZAmfmZkp/nz55Zfz8+fPD7jm3//+N19YWCj+DID/v//7P/Hn7du38wD4t99+W3xu+fLlvMlkEn9+7rnneK1Wy58+fVp87vPPP+c1Gg1fVlbGV1ZW8gD4TZs2yfnnEQQRZ8jyQRBE2OzevRvPP/880tLSxNt9992HsrIyWK1W8bpBgwaJj/Pz8wEAAwcODHjOZrOhrq5OfK5Tp07o2LGj+POYMWPg8Xhw+PBhZGdnY9asWZgyZQqmTZuGV155JSA2hSCI5IDEB0EQYePxeDBv3jzs3btXvJWUlODo0aMwmUzidXq9XnwsuEaCPefxeEJ+lnCNcL9kyRJs374dY8eOxf9v535VFQbDOI7/zkAQr0AHtjGsM+kVCEMMgkYtgkXsFoOYxGywWQSbwXvQKFqcRTDYNHgDO+HA6eJ8LN9PHs/et31592e1Wsn3fe12u+Q2B+Dj+NoFwMuKxaKiKJLneYnPvl6vut1ucl1XkrTdbuU4jnzf/78mCAIFQaDBYKByuazlcqlSqZT4WgB8BvEB4GXD4VDValX5fF6NRkOO4+hwOOh4PGo8Hr81O51Oq91uazqd6vl8qt/vq9lsKpvN6nK5aD6fq1aryXVdRVGk8/msVquV0M4AWCA+ALysUqlos9loNBppMpkolUqpUCio0+m8PdvzPNXrdYVhqMfjoTAMNZvNJEmZTEan00mLxUL3+125XE69Xk/dbvft+wKw8xPHcfztRQCA9Pefj/V6rf1+/+2lAPggXjgFAACmiA8AAGCKxy4AAMAUJx8AAMAU8QEAAEwRHwAAwBTxAQAATBEfAADAFPEBAABMER8AAMAU8QEAAEwRHwAAwNQvq3nM5W44gR0AAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"a, b = 0, 60\n",
"y0 = np.array([10, 10])\n",
"h = 0.01\n",
"\n",
"t, y = RK2(fexamen, a, b, y0, h)\n",
"\n",
"plt.plot(t, y[:,0], label='y_1(t) - Proies')\n",
"plt.plot(t, y[:,1], label='y_2(t) - Prédateurs')\n",
"plt.legend(loc='upper right')\n",
"plt.title('Evolution des population')\n",
"plt.xlabel('Temps')\n",
"plt.show()\n",
"\n",
"plt.plot(y[:,0], y[:,1])\n",
"plt.title('Orbite')\n",
"plt.xlabel('y_1(t) - Proies')\n",
"plt.ylabel('y_2(t) - Prédateurs')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "70f5eab2-dede-4497-a69a-52389cdb9562",
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}