From 3faf2fcfc29c1d3444d2ae45a679747eb726cb46 Mon Sep 17 00:00:00 2001 From: snoopy0328 Date: Sat, 22 Mar 2025 17:35:57 -0400 Subject: [PATCH] num 4 --- HW03/hw3.ipynb | 49 ++++++++++++++++++++++--------------------------- 1 file changed, 22 insertions(+), 27 deletions(-) diff --git a/HW03/hw3.ipynb b/HW03/hw3.ipynb index 18dab9e..863c1ff 100644 --- a/HW03/hw3.ipynb +++ b/HW03/hw3.ipynb @@ -9,7 +9,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -24,22 +24,22 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Sample Mean (ybar): 4.84 hours\n", - "Posterior Mean (µ_n): 4.89\n", - "Posterior Standard Deviation (σ_n): 0.15\n" + "Sample Mean (ybar): 4.66 hours\n", + "Posterior Mean (µ_n): 4.70\n", + "Posterior Standard Deviation (σ_n): 0.21\n" ] } ], "source": [ "np.random.seed(42)\n", - "n = 100 #sample size\n", + "n = 50 #sample size\n", "mu_true = 5 #avg sleep time\n", "sigma = 1.5 #standard deviation\n", "data = np.random.normal(mu_true, sigma, n)\n", @@ -47,7 +47,7 @@ "print(f\"Sample Mean (ybar): {ybar:.2f} hours\")\n", "\n", "# Prior parameters (initial belief about sleep time)\n", - "mu0 = 7\n", + "mu0 = 5.5\n", "sigma0 = 1.0\n", "\n", "# Posterior parameters\n", @@ -60,12 +60,12 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "metadata": {}, "outputs": [ { "data": { - "image/png": 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9nqe5769Zdt30+OOPAzBr1qwWx9Mes2fPJjc3l1dffdXT5nQ6efzxx4mOjmbq1KmAO0DZbDaffWl//etfj/i1SktLfb7nI0eOxGq1tvtYABGRpjTjJCLSjKysLF5++WUuvPBChg4dyty5cxkxYgS1tbWsXLnSU1IZYNSoUVx66aU8/fTTFBcXM3XqVL7++mv++c9/MmfOHKZPn96m137iiSeYPHkyI0eO5KqrrmLQoEHk5eWxatUq9u7dy/r16wF3uHvxxRc55ZRTuP766z3lyPv3709hYaFn9sThcPDkk0/yy1/+krFjx3LRRReRnJzM7t27ee+995g0aRJ/+ctfWhzP/fffz+rVqzn33HM9YWHNmjU8//zzJCQkeBVuGDduHE8++ST33nsv2dnZpKSkcNJJJ3HqqafSv39/rrjiCm655RZsNhvPPvusZxym5ORkbr75ZhYuXMgZZ5zB7NmzWbt2LR988AFJSUle47rlllt45513OOOMM5g3bx7jxo2joqKC77//ntdee42dO3f6POZwxo0bB8BvfvMbZs6cic1m46KLLuLKK6+ksLCQk046ifT0dHbt2sXjjz/O6NGjvWYZD7V48WLuuOMOzjrrLE444QSio6PZvn07zz77LDU1Ndx5550tPjYrK4t7772XBQsWsHPnTubMmUNMTAw7duzgzTff5Oqrr+bmm2/GarXyj3/8g1mzZjF8+HAuu+wy+vXrx759+1i2bBkOh4P//ve/Xs+9Y8cOzjrrLE477TRWrVrFiy++yCWXXMKoUaPa9PU6nKuvvpqnnnqKefPmsXr1agYOHMhrr73GihUrePTRRz0FWGJjYzn//PN5/PHHsVgsZGVl8e6777bpgOWlS5dy3XXXcf7553PUUUfhdDp54YUXsNlsnHfeeX59XyISpAJY0U9EpNv76aefjKuuusoYOHCgERYWZsTExBiTJk0yHn/8ca9y4XV1dcZdd91lZGZmGqGhoUZGRoaxYMECr2sM48jKkRuGYWzbts2YO3eukZaWZoSGhhr9+vUzzjjjDOO1117zum7t2rXGiSeeaNjtdiM9Pd1YuHCh8ec//9kAjNzcXK9rly1bZsycOdOIjY01wsPDjaysLGPevHnGt99+2+rXYMWKFcb8+fONESNGGLGxsUZoaKjRv39/Y968eca2bdu8rs3NzTVOP/10IyYmxgC83uvq1auN448/3ggLCzP69+9vPPzwwz7lyA3DMOrr64277rrL6NOnjxEREWFMmzbN2LBhgzFgwACvcuSG4S61vmDBAiM7O9sICwszkpKSjIkTJxoPPvigUVtb6/U1/r//+z+f9wYYd9xxh+dzp9NpXH/99UZycrJhsVg85cFfe+0149RTTzVSUlI847/mmmuMnJycVr9227dvN26//XbjhBNOMFJSUoyQkBAjOTnZOP30073K1BtGyyXbX3/9dWPy5MlGVFSUERUVZRx99NHG/Pnzjc2bN3tdt3btWuPcc881EhMTDbvdbgwYMMC44IILjCVLlvi8xg8//GD87Gc/M2JiYoz4+HjjuuuuM6qqqlp9L4bhLgUeFRXVYj+HlCM3DMPIy8szLrvsMiMpKckICwszRo4c6fPfu2EYxsGDB43zzjvPiIyMNOLj441rrrnG2LBhQ7PlyJsbw/bt243LL7/cyMrKMsLDw42EhARj+vTpxieffHLY9yUiciQshnEEu2JFRKTHuPHGG3nqqacoLy9vsSCCBKc777yTu+66i4MHD7Z5Nk5EJNhpj5OISA9WVVXl9XlBQQEvvPACkydPVmgSERHxI+1xEhHpwSZMmMC0adMYOnQoeXl5PPPMM5SWlrZ4BpSIiIi0j4KTiEgPNnv2bF577TWefvppLBYLY8eO5ZlnnmHKlCmBHpqIiEivoj1OIiIiIiIih6E9TiIiIiIiIoeh4CQiIiIiInIYQbfHyeVysX//fmJiYjyHQ4qIiIiISPAxDIOysjL69u2L1dr6nFLQBaf9+/eTkZER6GGIiIiIiEg3sWfPHtLT01u9JuiCU0xMDOD+4jgcjgCPRkREREREAqW0tJSMjAxPRmhN0AUnc3mew+FQcBIRERERkSPawqPiECIiIiIiIoeh4CQiIiIiInIYCk4iIiIiIiKHEXR7nEREREREmmMYBk6nk/r6+kAPRfwoNDQUm83W4edRcBIRERGRoFdbW0tOTg6VlZWBHor4mcViIT09nejo6A49j4KTiIiIiAQ1l8vFjh07sNls9O3bl7CwsCOqsibdn2EYHDx4kL179zJ48OAOzTwpOImIiIhIUKutrcXlcpGRkUFkZGSghyN+lpyczM6dO6mrq+tQcFJxCBERERERwGrVr8a9kb9mD/Vfh4iIiIiIyGEoOImIiIiIiByGgpOIiIiISBAZOHAgjz76aKCH0eMoOImIiIiI9FDz5s3DYrFgsVgICwsjOzubu+++G6fT2eJjvvnmG66++uouHGXvoKp6IiIiIiI92GmnncZzzz1HTU0N77//PvPnzyc0NJQFCxZ4XVdbW0tYWBjJyckdej3zeYKNZpxERERERFpQWets8VZdV+/3a9vDbreTlpbGgAEDuPbaa5kxYwbvvPMO8+bNY86cOdx333307duXIUOGAL5L9Xbv3s3ZZ59NdHQ0DoeDCy64gLy8PE//nXfeyejRo/nHP/5BZmYm4eHh7RpnT6cZJxERERGRFgy7/aMW+6YPSea5y47zfD7unk+oOiQgmY7PTODVayZ4Pp98/zIKK2p9rtv5p9M7MFq3iIgICgoKAFiyZAkOh4PFixc3e63L5fKEpk8//RSn08n8+fO58MILWb58uee6rVu38vrrr/PGG2906CyknkzBSURERESkFzAMgyVLlvDRRx9x/fXXc/DgQaKiovjHP/7R4tK6JUuW8P3337Njxw4yMjIAeP755xk+fDjffPMNxx57LOBenvf88893eJlfT6bgJCLSjRmGwU9FP+F0ORmaOBSrRSusRUS60g93z2yxz3rIwaqr/zjjiK/94nfTOzawJt59912io6Opq6vD5XJxySWXcOeddzJ//nxGjhzZ6n6kTZs2kZGR4QlNAMOGDSMuLo5NmzZ5gtOAAQOCOjSBgpOISLdV76rn9pW38862dwCY2Hcij01/jPCQ4FxbLiISCJFhR/7rcmddezjTp0/nySefJCwsjL59+xIS0vjcUVFRfnkNfz1PT6Y/XYqIdFPP//C8JzQBrNy/koe+fSiAIxIRke4oKiqK7Oxs+vfv7xWajsTQoUPZs2cPe/bs8bT98MMPFBcXM2zYMH8PtUdTcBIR6YZKakp4cv2TANw54U6enOH++N8//ZsdJTsCOTQREelFZsyYwciRI/n5z3/OmjVr+Prrr5k7dy5Tp05l/PjxgR5et6LgJCLSDb2+5XWqnFUMiR/COYPPYXK/yUxJn4LLcPGvH/8V6OGJiEgvYbFYePvtt4mPj2fKlCnMmDGDQYMG8eqrrwZ6aN2OxTAMI9CD6EqlpaXExsZSUlKCw+EI9HBERHwYhsGZb53JrtJd3D3xbs4ZfA7gXqp3zeJriA6N5tMLPyXMFnyHD4qIdIbq6mp27NgR1GcU9WatfX/bkg004yQiEkguF9RVNX5eW8nm9c+zq3QXdpudUwee6uk6oc8JpESkUF5Xzpc5XwZgsCIiIsFLwUlEJJDWPg9/PxkKtkFlIfz9JJZ9ejsAk/tNJiq0sYqR1WJlxgB3qdvFu5o/yFBEREQ6h4KTiEig1DvhswfhwEb46SOIiIf4AXxldy/Bm9xvss9DpmVMA2DlvpUE2UprERGRgFJwEhEJFFsIzHsPTr4dxl8OFgvVU2/lu3A7AMfGDPR5yNjUsdhtdg5UHWB7yfYuHrCIiEjwUnASEQmk+AFw4m8h1L1Zdb3VSZ3FQorTSf+tn/tcbrfZGZMyBoBvcr/p0qGKiIgEMwUnEZFu5OvcrwE4troGy4//bfaa0SmjAfg+//uuGpaIiEjQU3ASEQmErUvglZ/Dxre8ms1ZpOOqqmHfaijN8XnoyKSRAHx38LtOH6aIiIi4KTiJiATC5vfhx3dhx2eepjpXHRvzNwIwNjbb3bhtqc9DzeC0s3QnJTUlnT9WERERUXASEelyhgFbGsqJDz7F07yjZAe1rlqiQqPoP2Cqu3H3Sp+Hx4fHkxGTAcCG/A2dPlwRERFRcBIR6XoF26B4F9jCYOCJnuYfC38EYEj8EKwDG0qR71rV7FN4luvla7meiIg0z2Kx8NZbbwGwc+dOLBYL69at65TnW758ORaLheLi4g6NuT3uvPNORo8e3emvo+AkItLV9nzlvu83HuzRnuZNBZsAGJo4FDKOByxQuA3K8nye4pjkYwD4/qAKRIiIBLN58+YxZ86cZvtycnKYNWtWp7xuRkYGOTk5jBgxolOevztScBIR6Wr7Vrvv08d5NW8qdAenoxOOhog4SG34x6iZ5XrDEocB8FPRT502TBER6dnS0tKw2+2d8tw2m420tDRCQkI65fm7IwUnEZGuZganfo3ByWW42Fy4GYChCUPdjQMmuO+bWa6XFZcFQF5lHqW1pZ03VhGRYFdb0fZbvbPx8fVOd1td1ZE9rx81XVp3qPr6ei6//HKOPvpodu/eDcDbb7/N2LFjCQ8PZ9CgQdx11104nc5mH9/S0r/Vq1czfvx4IiMjmThxIps3b/bqf/LJJ8nKyiIsLIwhQ4bwwgsvePXv3r2bs88+m+joaBwOBxdccAF5ed4rL/70pz+RmppKTEwMV1xxBdXV1W34qrRf8EREEZHuoK4a8hoKOjQJTvvK9lFeV06YNYxBcYPcjdkzoGQfpPkug3CEOUiNTCWvMo9txds8h+KKiIif/W/ftj/m/EUw/Bz3xz/+F/4zDwZMhsvea7zm0ZFQWeD72Ds7v1pqTU0NF198MTt37uTzzz8nOTmZzz//nLlz5/LnP/+ZE088kW3btnH11VcDcMcddxzxc//hD3/goYceIjk5mV/96ldcfvnlrFixAoA333yTG264gUcffZQZM2bw7rvvctlll5Gens706dNxuVye0PTpp5/idDqZP38+F154IcuXLwfg3//+N3feeSdPPPEEkydP5oUXXuDPf/4zgwYN8vvX6VAKTiIiXSn3e3A5ISoZYjM8zZuL3H+Ry4rLItQa6m48aqb71oLs+GzyKvPYWrxVwUlERI5IeXk5p59+OjU1NSxbtozY2FgA7rrrLm677TYuvfRSAAYNGsQ999zDrbfe2qbgdN999zF1qrsy7G233cbpp59OdXU14eHhPPjgg8ybN49f//rXANx00018+eWXPPjgg0yfPp0lS5bw/fffs2PHDjIy3P9GPv/88wwfPpxvvvmGY489lkcffZQrrriCK664AoB7772XTz75pEtmnRScRES6UtNlehaLp3lHyQ4AsuOyj/ipBscNZsW+FWwt2urXIYqISBO/39/2x9ia7Cs6+kz3c1gO2SFzY2CK+1x88cWkp6ezdOlSIiIiPO3r169nxYoV3HfffZ62+vp6qqurqaysJDIy8oie/5hjjvF83KdPHwAOHDhA//792bRpk2cWyzRp0iQee+wxADZt2kRGRoYnNAEMGzaMuLg4Nm3axLHHHsumTZv41a9+5fUcEyZMYNmyZUf4FWg/BScRka60f637vu9Yr2YzOGXGZnpfbxhQug8sNnD08eoyQ9bWYgUnEZFOExbVscfbQtw3fz9vO82ePZsXX3yRVatWcdJJJ3nay8vLueuuuzj33HN9HhMeHn7Ezx8aGur52NLwB0KXy9WBEXcfKg4hItKVDmx03x+yb2l7yXagmeD00e/hkeHw1d98nkrBSURE2uraa6/lT3/6E2eddRaffvqpp33s2LFs3ryZ7Oxsn5vV6p/IMHToUM9+J9OKFSsYNmyYp3/Pnj3s2bPH0//DDz9QXFzsdc1XX33l9RxffvmlX8Z3OJpxEhHpKq56ONhQPjxlqKfZMIyWZ5wSs92zTdW+m4UzYzOxYKGwupCCqgISIxI7begiItJ9lZSU+FS3S0xs+d+E66+/nvr6es444ww++OADJk+ezO23384ZZ5xB//79+dnPfobVamX9+vVs2LCBe++91y/jvOWWW7jgggsYM2YMM2bM4L///S9vvPEGn3zyCQAzZsxg5MiR/PznP+fRRx/F6XTy61//mqlTpzJ+/HgAbrjhBubNm8f48eOZNGkSL730Ehs3blRxCBGRXsVVD2c/AQd/hLgBnuYDlQeodFZis9joH9Pf+zGjLobRP4dQ32USkaGR9I3uy77yfewo2aHgJCISpJYvX86YMd5FgsziCS258cYbcblczJ49mw8//JCZM2fy7rvvcvfdd3P//fcTGhrK0UcfzZVXXum3cc6ZM4fHHnuMBx98kBtuuIHMzEyee+45pk2bBriX9r399ttcf/31TJkyBavVymmnncbjjz/ueY4LL7yQbdu2ceutt1JdXc15553Htddey0cffeS3cbbEYhiG0emv0o2UlpYSGxtLSUkJDocj0MMREeHLnC+56uOrGOgYyH/P+W+bHnvN4mtYuX8ld028i3MH+65LFxGRw6uurmbHjh1kZma2aT+P9AytfX/bkg0Cusdp4cKFHHvsscTExJCSksKcOXN8Dsk61KJFi7BYLF43/QcuIj2ZuUxvYOzANj/WnKHaVbrLn0MSERGRQwQ0OH366afMnz+fL7/8ksWLF1NXV8epp55KRUXrpyY7HA5ycnI8t1279AuDiPQAP30MW5dAVbFXc4v7m0yrnoC/nwTrX/HpGuBwL/nbU7bHp09ERET8J6B7nD788EOvzxctWkRKSgqrV69mypQpLT7OYrGQlpbW2cMTEfGvT+6AAz/AJf/2Oth2Z8lOADIdLQSnkn3u859yvoNRF3l19XdoxklERKQrdKty5CUl7qpRCQkJrV5XXl7OgAEDyMjI4Oyzz2bjxo0tXltTU0NpaanXTUSkyxkGpAyDxMFeFfWgcbYoIyajuUdC0mD3ff5PPl3mUr09ZXsIsi2rIiIiXarbBCeXy8WNN97IpEmTGDFiRIvXDRkyhGeffZa3336bF198EZfLxcSJE9m7d2+z1y9cuJDY2FjPrelJxCIiXcZigZ89A9d/C3GNlfOcLic5FTkApMekN/9YMzgVbPHp6hfdD6vFSpWzioNVB/0+bBEREXHrNsFp/vz5bNiwgVde8V3D39SECROYO3cuo0ePZurUqbzxxhskJyfz1FNPNXv9ggULKCkp8dyaHqglIhJouRW51Bv1hFnDSIlMaf6ipKPc90W7oK7aqyvUFkrfqL6AluuJiIh0pm4RnK677jreffddli1bRnp6C39xbUFoaChjxoxh69atzfbb7XYcDofXTUSkyzlr3Mv1DmEu0+sX4545alZUMthjAQMKt/t0mwUidpfu9ttwRURExFtAg5NhGFx33XW8+eabLF26lMzMFjZGt6K+vp7vv/+ePn36dMIIRUT85OM/wsIMWPVXr+a95e5lxunRrfzRyGJpdZ+TuTdqV5lmnERERDpLQIPT/PnzefHFF3n55ZeJiYkhNzeX3NxcqqqqPNfMnTuXBQsWeD6/++67+fjjj9m+fTtr1qzhF7/4Bbt27fLrqcYiIn5XuA1qyyAs0qt5b1lDcGppf5PJE5x89zmZlfX2le3r+DhFRESkWQENTk8++SQlJSVMmzaNPn36eG6vvvqq55rdu3eTk5Pj+byoqIirrrqKoUOHMnv2bEpLS1m5ciXDhg0LxFsQETkyBdvc9wlZXs2e4NTajBNAYsPjinb4dPWNdu9xMotMiIiIdDd33nkno0ePDvQwOiTgS/Wau82bN89zzfLly1m0aJHn80ceeYRdu3ZRU1NDbm4u7733HmPGjOn6wYuIHKn6Oihu2H+U6B2cDluK3BTfsJS5aKdPV7/ofgDsK9eMk4hIsJk3bx4WiwWLxUJYWBjZ2dncfffdOJ3ODj3v8uXLsVgsFBcX+2WcN998M0uWLPHLcwVKQA/AFREJCsW7waiHkAiI8d6P6dnjdLilevED3ffNBCdzxqmwupAqZxURIREdHbGIiPQgp512Gs899xw1NTW8//77zJ8/n9DQUK/tLoFiGAb19fVER0cTHR3doeeqq6sjNDTUTyNru25RVU9EpFczK+ElDHIXemhQUlNCWW0Z0Dhr1CIzOJXu9ylJ7ghzEB3q/scop1zL9URE/MEwDCrrKgNya+uB5na7nbS0NAYMGMC1117LjBkzeOeddygqKmLu3LnEx8cTGRnJrFmz2LKlca/srl27OPPMM4mPjycqKorhw4fz/vvvs3PnTqZPnw5AfHw8FovFsyLM5XKxcOFCMjMziYiIYNSoUbz22mue5zRnqj744APGjRuH3W7niy++8Fmq53K5uPvuu0lPT8dutzN69Gg+/PBDT//OnTuxWCy8+uqrTJ06lfDwcF566aV2fCf9RzNOIiKdzdzflDjIq3l/+X4AEsITiAyNPPRR3iITISwaasuhZE9jsYgGfaP78lPRT+wr38eguEEtPImIiBypKmcVx798fEBe+6tLvjr8vwutiIiIoKCggHnz5rFlyxbeeecdHA4Hv/vd75g9ezY//PADoaGhzJ8/n9raWj777DOioqL44YcfiI6OJiMjg9dff53zzjuPzZs343A4iIhwr2ZYuHAhL774In/7298YPHgwn332Gb/4xS9ITk5m6tSpnjHcdtttPPjggwwaNIj4+HiWL1/uNcbHHnuMhx56iKeeeooxY8bw7LPPctZZZ7Fx40YGDx7s9TwPPfQQY8aMITw8vN1fE39QcBIR6WzFDWXC472PXDCLOfSJOoLjFCwWmLbAXZUvIsGn2wxOZhgTEZHgYxgGS5Ys4aOPPmLWrFm89dZbrFixgokTJwLw0ksvkZGRwVtvvcX555/P7t27Oe+88xg5ciQAgwY1/uEtIcH9b01KSgpxcXEA1NTU8L//+7988sknTJgwwfOYL774gqeeesorON19992ccsopLY71wQcf5He/+x0XXXQRAPfffz/Lli3j0Ucf5YknnvBcd+ONN3Luuef64avTcQpOIiKdzSwMEdffq7lNwQlg4nUtdnkKRFSoQISIiD9EhETw1SVfBey12+Ldd98lOjqauro6XC4Xl1xyCeeeey7vvvsuxx/fOGuWmJjIkCFD2LRpEwC/+c1vuPbaa/n444+ZMWMG5513Hsccc0yLr7N161YqKyt9AlFtba1Psbbx48e3+DylpaXs37+fSZMmebVPmjSJ9evXH/HzdDUFJxGRzmbOOMUN8Go29yP1ie74Ad59o/p6PaeIiHSMxWLp0HK5rjR9+nSefPJJwsLC6Nu3LyEhIbzzzjuHfdyVV17JzJkzee+99/j4449ZuHAhDz30ENdff32z15eXlwPw3nvv0a+f995cu93u9XlUVFQ73403fz2PP6g4hIhIZ/PXjFN1KexaBTs+8+kyZ5y0VE9EJPhERUWRnZ1N//79CQlxz4sMHToUp9PJV181zpoVFBSwefNmr/NPMzIy+NWvfsUbb7zBb3/7W/7+978DEBYWBkB9fb3n2mHDhmG329m9ezfZ2dlet4yMwxyr0YTD4aBv376sWLHCq33FihXd+mxWzTiJiHSmqmKoLnF/HOf9j0puRS7QhuC052t46TxIHQHXev9jY5Yk11lOIiICMHjwYM4++2yuuuoqnnrqKWJiYrjtttvo168fZ599NuDePzRr1iyOOuooioqKWLZsGUOHDgVgwIABWCwW3n33XWbPnk1ERAQxMTHcfPPN/L//9/9wuVxMnjyZkpISVqxYgcPh4NJLLz3i8d1yyy3ccccdZGVlMXr0aJ577jnWrVsX8Mp5rVFwEhHpTOZsU2QShHkvN/DMOB3pUr2ETHdZ8ljfM5/M4FRQXUBNfQ12m93nGhERCS7PPfccN9xwA2eccQa1tbVMmTKF999/33MWUn19PfPnz2fv3r04HA5OO+00HnnkEQD69evHXXfdxW233cZll13G3LlzWbRoEffccw/JycksXLiQ7du3ExcXx9ixY/n973/fprH95je/oaSkhN/+9rccOHCAYcOG8c4773hV1OtuLEZbC8X3cKWlpcTGxlJSUoLD4Qj0cESkt6utgJz17mV2Q05rbK6vZdyL4wD49MJPSQj3rZTXFoZhcPzLx1PlrOL9c94nw3HkSyZERIJddXU1O3bsIDMzM+Alr8X/Wvv+tiUbaI+TiEhnCouCARO9QhNAXkUeAHabnXh7fIdfxmKxkBqZCkBuZW6Hn09ERES8KTiJiARA08IQFovFL89pBqe8yjy/PJ+IiIg0UnASEelM61+Bb5+F4j1ezW2uqGdafAc8OAS+/rtPV0pkCtA4myUiIiL+o+AkItKZVv4F3v1/cGCTV3ObC0OY6muhPLex6EQTqVGacRIREeksqqonItKZsk9yV8FLzPJqNsONubzuiJkV9Ur2+nSZz3Wg8kDbxykiIgRZzbSg4a/vq4KTiEhnOuXuZpvNcGMurztisQ3V8kr2+HR59jhpqZ6ISJuY5bkrKyuJiIgI8GjE32prawGw2Wwdeh4FJxGRAGh/cGplxklL9URE2sVmsxEXF8eBA+6fzZGRkX4r3COB5XK5OHjwIJGRkYSEdCz6KDiJiHSW2gqor4PwWDjkH2AzOLV9qV7DjFNZLjhrISTM02U+V35VPnWuOkKtoe0fu4hIkElLSwPwhCfpPaxWK/379+9wGFZwEhHpLD+8DW9dC0edBpe86mmura+lsLoQaMeMU1QShISDsxrK9kP8QE9XfHg8odZQ6lx15Ffmt73whIhIELNYLPTp04eUlBTq6uoCPRzxo7CwMKzWjtfEU3ASEekspfvc95FJXs35VfkAhFpDibPHte05LRb3cr2Cre4S502Ck9ViJSUyhX3l+8irzFNwEhFpB5vN1uG9MNI7qRy5iEhnKd3vvo/t59XcdH9Tu5YNOBqer5XKermVuW1/XhEREWmRgpOISGcpaZhxcvT1ajaLN7R5mZ7JDE5l+326VFlPRESkcyg4iYh0FnPGydHyjFO7OBqW4JXm+HSpsp6IiEjnUHASEekspc3POJnBKTkiuX3PG9MQnMqaCU6acRIREekUCk4iIp2hrgqq3JXzWgpObS5FbjKfr7SZpXqacRIREekUqqonItIZzFATGgnhcV5dHV6q12c0nP4wJAzy6fLMOCk4iYiI+JWCk4hIZ2i6TK+Fw2/bHZxi+8GxVzTbZQang5UHqXfVY7OqpK6IiIg/aKmeiEhnaKEwhGEYHV+q14qkiCRsFhv1Rr3nvCgRERHpOAUnEZHO4Jlx8g5OpbWlVNdXA5Ac2c7iEAB7V8N3//GprGez2kgITwAgv1rBSURExF8UnEREOoNnxsm7MMTByoPu5jAH4SHh7X/+D26FN66Efd/6dCVFJAGQX6ngJCIi4i8KTiIinaGFw287vL/J1G8cDDzRXXziEOZM1sGqgx17DREREfFQcQgRkc5w+oMw8XpIyPRqNqvddXh/0+wHWuwyz4dScBIREfEfBScRkc4Qm+6+HcJvM06tSIxIBKCgqqDTXkNERCTYaKmeiEgXMoNThwpDNOVy+TR5ZpwqNeMkIiLiLwpOIiL+VpEPS+6B1Yt8uszlcykRHZxx2rcGHjwKnpzo02UGJ5UjFxER8R8t1RMR8bfCHfD5gxCbAePmeXWZy+eSIpM69hp2B5TnQW2lT5f53NrjJCIi4j8KTiIi/hYRB8deCWFRPl3mLJBZMrzdHH3c97VlUF0K4Q5PV9MZJ8MwsFgsHXstERERUXASEfG7pMFw+kM+zYZh+C84hUWBPRZqSqAsxys4mcUh6lx1lNaWEmuP7dhriYiIiPY4iYh0lbK6MmpdtQAkhid2/AnNWSfzsN0GdpsdR5g7SKlAhIiIiH8oOImI+FtZLlQWgmF4NZuzTTGhMYSHhHf8dWIaglNZjk+XznISERHxLwUnERF/e+d6eCAT1r7g1ey3whAmR1/3/SEzTk1fQ5X1RERE/EPBSUTE38py3ffRaV7N5rK5Du9vMkWnuu/LD/h0ma+h4CQiIuIfCk4iIv5Wnue+j0n1avYUhgj3d3DK8+nSUj0RERH/UnASEfGnemfjDJC5B6lBfrU7OJlV7zos5ghmnCo14yQiIuIPCk4iIv5UcRAwwGKDQ/YyefY4+X2pXq5Pl+csp2oFJxEREX9QcBIR8SczxESngNX7R6zfznAytbLHKTmyYameypGLiIj4hYKTiIg/lTXsN4pO9enqtOBUWw415V5d5nJAFYcQERHxj5BAD0BEpFcxZ5xi0ny6/B6c7NFw1uMQlQK2UK8uc6leeV05Vc4qIkIi/POaIiIiQUrBSUTEn1qYcXK6nBRVFwF+DE4AY+c22xwdGk24LZzq+mryq/LJiMnw32uKiIgEIS3VExHxp7Ic9/0hFfWKqoswMLBZbMTZ4zp9GBaLRWc5iYiI+JGCk4iIP7VwhpN5nlJCeAI2q81/r5e3Eb77N+xf59Nl7nMyq/mJiIhI+yk4iYj4U5lZVc97j5Pf9zeZVi+CN66CH9726UoITwCgsLrQv68pIiIShBScRET8qYUZJ3PWx2+H35pSh8PAEyHOdw+TZpxERET8R8UhRET86bL33bNOyUd7NXfajNO4ee5bMxLDG4JTtYKTiIhIRyk4iYj4U/xA9+0QnRacWqGleiIiIv6jpXoiIl2g04NTvdOnSUv1RERE/EfBSUTEXw5uhiX3uKvcHcIMTn7f41RZCA9kwX2p4Kr36tJSPREREf9RcBIR8Zfc7+HzB2HN8z5d5nI5M8z4TXgsVBWCywkV3uc1JUQ0LNWr0lI9ERGRjlJwEhHxl/hMOO5qGDLLp6uopgho3HfkN1YbRCW7Py7P9eoyQ1pZXRk19TX+fV0REZEgo+IQIiL+kj7OfTtEnauOkpoSAOLD4/3/utEp7jLo5Qe8mh1hDkKsIThdTgqrCukT3cf/ry0iIhIkNOMkItLJzNBktViJDYv1/wtEN5wZVeY942SxWFRZT0RExE8UnERE/KVkH1QUgMvl1WxWtYuzx2Gz2vz/utFp7nvz8N0mVCBCRETEPxScRET85T+Xwv8Ngs3vezV32v4mU3SK+76Z4GQWiFBJchERkY5RcBIR8ZeKg+57s1hDA7OqXafsb4LG4GS+fhOacRIREfEPBScREX8xy4FHeR9y2+kzTp6qes0EJx2CKyIi4hcKTiIi/lBbCbXl7o8PmXEyQ0u8XTNOIiIiPZWCk4iIP1Q2zDbZ7GCP8eryzDhFdPKMU8UBny5V1RMREfGPgAanhQsXcuyxxxITE0NKSgpz5sxh8+bNh33cf/7zH44++mjCw8MZOXIk77///mEfIyLSqZrub7JYvLrMPU4J9s4KTg0zTlVFUF/n1eWZcdJSPRERkQ4JaHD69NNPmT9/Pl9++SWLFy+mrq6OU089lYqKihYfs3LlSi6++GKuuOIK1q5dy5w5c5gzZw4bNmzowpGLiByihf1N0AUzThHxYLF5j6OBucdJM04iIiIdExLIF//www+9Pl+0aBEpKSmsXr2aKVOmNPuYxx57jNNOO41bbrkFgHvuuYfFixfzl7/8hb/97W+dPmYRkWa1UFEPGkNLp+1xslrhnKcg3AHh3gfsmsGpuKaYeld955wjJSIiEgS61R6nkpISABISWv6r7KpVq5gxY4ZX28yZM1m1alWz19fU1FBaWup1ExHxuyMITp024wRwzPlw1EwIi/RqjrPHYcGCy3B5Zr5ERESk7bpNcHK5XNx4441MmjSJESNGtHhdbm4uqampXm2pqank5uY2e/3ChQuJjY313DIyMvw6bhERoMWlenX1dZTVlgGduMepFSHWEOLscYCW64mIiHREtwlO8+fPZ8OGDbzyyit+fd4FCxZQUlLiue3Zs8evzy8iArQ442TO8tgsNhx2R+e9ft5GWP8K7Fvt06WznERERDouoHucTNdddx3vvvsun332Genp6a1em5aWRl5enldbXl4eaWlpzV5vt9ux2+1+G6uISLNaCE7mLE+cPQ6rpRP/VrXuZVj1F5h4PfQb59VlliTXWU4iIiLtF9AZJ8MwuO6663jzzTdZunQpmZmZh33MhAkTWLJkiVfb4sWLmTBhQmcNU0Tk8A4TnDp1fxNAyjDInArxA326zJLkZll0ERERabuAzjjNnz+fl19+mbfffpuYmBjPPqXY2FgiIiIAmDt3Lv369WPhwoUA3HDDDUydOpWHHnqI008/nVdeeYVvv/2Wp59+OmDvQ0SEi16GsjxIGuzV7AlOnb2/aczP3bdmmKFNM04iIiLtF9AZpyeffJKSkhKmTZtGnz59PLdXX33Vc83u3bvJycnxfD5x4kRefvllnn76aUaNGsVrr73GW2+91WpBCRGRThfXHzKOhYg4r+ai6oYznMK7vjCESYfgioiIdFxAZ5wMwzjsNcuXL/dpO//88zn//PM7YUQiIv7lOcMpvJPOcDpUvRNs3j/adQiuiIhIx3WbqnoiIj1WWS58chd8+6xPV5fNOJUfgPsz4b40cLm8ulQcQkREpOMUnEREOqpwO3zxMKz8i0+XGVY6fcYpPA6qCsFVB1XeB91qqZ6IiEjHdYty5CIiPVpkEhx3DYTH+nSZM05meOk0IWHu8FRd7K7wF9X4ek2X6hmGgcVi6dyxiIiI9EIKTiIiHZV8FMx+oNmuLt3jFJXcEJwOAEd7ms2lenWuOsrqynCEdeJBvCIiIr2UluqJiHSiLq2qF53ivi8/4NUcHhJOZEik13hERESkbRScREQ6qiwXyg+Cq96ruba+lvK6cqALZ5wAKvJ9uszXV3ASERFpHwUnEZGOev8WeDAbvnnGq9lcphdiCema5XGe4HTAp0uV9URERDpGwUlEpKPMGZ7oZK/mpvubuqQgg7lUr+KgT5dmnERERDpGwUlEpKPMoBLlHZy6dH9T09cvbyY42RWcREREOkLBSUSko1oITl1aUa/p6zcz45QQkeA1JhEREWkbBScRkY5w1rpLgEOLwanLZpw8S/Wa2eNkd4+hqEYzTiIiIu2h4CQi0hGVDcUWLDb3AbRNdHlwarpUzzC8usxZr8IqzTiJiIi0h4KTiEhHeJbpJYHV+0dqwPY4OaugtsKry1McQjNOIiIi7RIS6AGIiPRoLexvgsbg1GV7nOzRMOdJiEwCW6hXV2J4IqA9TiIiIu2l4CQi0hFmKfKoJJ+uLl+qBzD6kmabm5YjNwyja8qji4iI9CJaqici0hGtzDgFJDi1wAxOda46yuvKAzwaERGRnkfBSUSkI7pbcNq/Dtb9C3K/92qOCIkgIiQC0FlOIiIi7aHgJCLSES0s1at2VlPprAS6cI8TwLfPwFu/gs0f+nSZh+Bqn5OIiEjbKTiJiHRECzNO5qxOqDWU6NDorhtP2jGQdRLEpvt0mTNfmnESERFpOxWHEBHpiDMfhdIciMvwai6scc/qxIfHd20hhuOuct+aoZLkIiIi7afgJCLSEY6+7tshzINmzTLg3YHnEFwt1RMREWkzLdUTEekE5qxOl+5vaqre6dNkLtVTcBIREWk7BScRkfaqrYDFd8CqJ8Dl8uoyZ5y6PDjlb4U/DYCHhvh0aY+TiIhI+2mpnohIe5XnwYpHITQSJsz36jL3OHX5GU7hsVBdDFjcs062xh/zTQ/BFRERkbZRcBIRaa+QcDj+WjBcPl3mjFOXB6fIBMACGFBVCNEpni4t1RMREWk/BScRkfZy9IVZf2q2y9zj1OXByWqDyESozHeXSm8SnHSOk4iISPtpj5OISCfw7HGyB6A4hHmmlHnGVIOmS/UMw+jqUYmIiPRoCk4iIu1VkQ9lec1WsPPMOEV08YwTQFSS+74i36vZnP2qddVS6azs6lGJiIj0aApOIiLt9dn/wUNHwbJ7fbrM5XAJ9kAEp+ZnnCJDIwm3hQNariciItJWCk4iIu1VfsB9H5Xi1VxZV0mVswoI0IyTua/JHF8TOgRXRESkfRScRETay5zRMWd4GpjL9MKsYUSGRHb1qJos1Tvo06WS5CIiIu2j4CQi0l7mHiIzqDQwQ0lCRAIWi6WrR9VkqV6+T5cOwRUREWkfBScRkfZqYcbJXAYXkIp60OIeJ9BZTiIiIu2l4CQi0h6ueqgscH/cQnAKyP4maDU4mWFOM04iIiJto+AkItIelYVAw1lIkYleXQGtqActliMHFYcQERFpr5BAD0BEpEcyZ3MiEsDm/aPUs8cpPEDBKaYvnPOUO0AZBjTZZ+VZqlej4CQiItIWCk4iIu3Rwv4maLLHKTxAe5xCw2HURc12qTiEiIhI+2ipnohIexxBcArYjFMrVI5cRESkfRScRETao4VS5NBNgtPuL2HtS1Cwzau56R4nwzACMTIREZEeScFJRKQ9WplxCvgeJ4DPH4K3fw27Vng1m2Oqqa+hylkViJGJiIj0SNrjJCLSHi0EJ8MwAr/HCaDfeDBcPuOLDInEbrNTU19DYXUhkaGRARqgiIhIz6LgJCLSHif9D4yb5xNMqpxV1NTXAAGecZr2u2abLRYL8eHx5FbkUlRdRHpMehcPTEREpGdScBIRaY/oFPftEAXV7kNxw23h3XY2J97eEJxqVCBCRETkSGmPk4iIH3WL/U1N1Tt9msyxFVQVdPVoREREeiwFJxGR9lhyN6z4M9SUeTV3i/1NALtWwsL+8NQUny5PSXLNOImIiBwxLdUTEWmruip31TqAcZd6dXWbGaewaKgpgQq7T5cOwRUREWk7BScRkbZyOeGE+VBZAHaHV5e5xyngM05m0YrKfHC5wNq4wKDpWU4iIiJyZBScRETayh4Dp/1vs13mLE5ieGJXjshXZMPrGy6oKoKoxvGYM04KTiIiIkdOe5xERPyo2+xxCgmD8Dj3x+aZUw3i7Q17nLRUT0RE5IgpOImItFVVEZTmQH2dT1e32eMEjcv1DglOCRHa4yQiItJWCk4iIm21+p/w8NHw9nU+Xd1mxglaDk72huCkqnoiIiJHTMFJRKStzCASnezTZQangO9xAohKct9X5Hs1m6GuyllFZV1lV49KRESkR1JwEhFpKzM4RaV4NRuG4Vn+1i1mnKIbxnfIjFNUaBSh1lBAs04iIiJHSsFJRKStPMHJe8apoq6CWlct0E2CUwtL9SwWS+MhuNrnJCIickQUnERE2qqF4GSGkIiQCCJCIrp6VL48S/UO+nSZSwlVklxEROTIKDiJiLSVuWfIDCYNzMNvu0VFPWgy45Tv06UZJxERkbZRcBIRaQvDOOyMU/cLTr4zTmZw0oyTiIjIkQkJ9ABERHqU6mJwOd0fHzLjZIaQbhOcko+Gc54GRx+fLh2CKyIi0jYKTiIibWEue7PHQojdq8usUNctCkMARCbAqAub7UqM0B4nERGRttBSPRGRtvAs00vy6Sqo6mZ7nFrhmXFSOXIREZEjouAkItIWLexvgsYQ0q2C0/blsOYFKMv1alZxCBERkbZRcBIRaYtWZpwKq7rZHieAj/8H3rkOcr/3ajbHqKV6IiIiR0Z7nERE2sJTirzlGadus8cJoP9EiOkDYdFezaqqJyIi0jYKTiIibXHc1XDUTLA7fLq65YzT7AeabTbHWOWsospZ1T0O7BUREenGFJxERNoiMsF9O4RhGBTWdMPg1ILo0GhCrCE4XU6KqouIiFZwEhERaY32OImI+EFZXRnOhvOdutVSPZOr3utTi8XiCXgqECEiInJ4Ck4iIm3xxaOw4jEoy/NqNsNHVGgUdpu9mQcGyA9vw/+mw0vn+3SZwamguqCrRyUiItLjaKmeiEhbrHgUqopg8EyISfU0m0UWzPORuo3QSKgta6wG2IRmnERERI5cQGecPvvsM84880z69u2LxWLhrbfeavX65cuXY7FYfG65ubmtPk5ExC8MA8b8Ao65yCs0QWNwSojoZvubzLLpZjXAJlRZT0RE5MgFdMapoqKCUaNGcfnll3Puuece8eM2b96Mw9FY0SolJaUzhici4s1igVPvbbbLE5zs3S04NZRNrzjoDn4Wi6dLM04iIiJHLqDBadasWcyaNavNj0tJSSEuLu6Irq2pqaGmpsbzeWlpaZtfT0TkcMzw0e1mnCIbZpxcdVBdAhFxni7tcRIRETlyPbI4xOjRo+nTpw+nnHIKK1asaPXahQsXEhsb67llZGR00ShFpNepKYOSfeCs8enqvnucwhvPnDpkuZ5mnERERI5cjwpOffr04W9/+xuvv/46r7/+OhkZGUybNo01a9a0+JgFCxZQUlLiue3Zs6cLRywivcqP78Mjw+Cln/l0eZbqdccznDz7nLwLRJghT3ucREREDq9dS/W2b9/OoEGD/D2WwxoyZAhDhgzxfD5x4kS2bdvGI488wgsvvNDsY+x2O3Z7NyoNLCI9lxk8onz3VXpmnLrjGU5RyVC4HSoOeDWbywo14yQiInJ47Zpxys7OZvr06bz44otUV1f7e0xtctxxx7F169aAjkFEgoQZPKJ9g5MZPhLDE7tyREemaYGIJsxCFppxEhERObx2Bac1a9ZwzDHHcNNNN5GWlsY111zD119/7e+xHZF169bRp0+fgLy2iAQZc4+QufStie4949R8SXJzxqm6vprKusquHpWIiEiP0q7gNHr0aB577DH279/Ps88+S05ODpMnT2bEiBE8/PDDHDzoe9Bic8rLy1m3bh3r1q0DYMeOHaxbt47du3cD7v1Jc+fO9Vz/6KOP8vbbb7N161Y2bNjAjTfeyNKlS5k/f3573oaISNt4luolezW7DBfF1cVAd93j1PyMU2RIJHabeymzZp1ERERa16HiECEhIZx77rn85z//4f7772fr1q3cfPPNZGRkMHfuXHJyclp9/LfffsuYMWMYM2YMADfddBNjxozh9ttvByAnJ8cTogBqa2v57W9/y8iRI5k6dSrr16/nk08+4eSTT+7I2xAROTItBKey2jKchhPorjNOzQcni8XiGa/2OYmIiLSuQ+c4ffvttzz77LO88sorREVFcfPNN3PFFVewd+9e7rrrLs4+++xWl/BNmzYNwzBa7F+0aJHX57feeiu33nprR4YsItJ+nqV63sHJnK2JCY0hzBbW1aM6vBaW6oF7hiy3IlczTiIiIofRruD08MMP89xzz7F582Zmz57N888/z+zZs7Fa3RNYmZmZLFq0iIEDB/pzrCIigWMYTWacvPc4dev9TQAZx8O5/4D4AT5d5pgVnERERFrXruD05JNPcvnllzNv3rwWCzOkpKTwzDPPdGhwIiLdRm05OBuqiB4y42Quc+uW+5sAYtPhmPOb7TKrACo4iYiItK5dwWnx4sX079/fM8NkMgyDPXv20L9/f8LCwrj00kv9MkgRkYAzZ5tCIyEsyqur2884tcI8BFd7nERERFrXruIQWVlZ5Of7rpUvLCwkMzOzw4MSEel2jqAUebedcQL46SNY/U+oLvVqNkuSa8ZJRESkde2acWqpoEN5eTnh4eEdGpCISLfUQkU96CHB6e3r3Af49hsLaSM9zeaMU2GNgpOIiEhr2hScbrrpJsBdwvb2228nMjLS01dfX89XX33F6NGj/TpAEZFuoZXg1O33OAFkToGaMrB6/9hPjGjY41Sl4CQiItKaNgWntWvXAu4Zp++//56wsMayu2FhYYwaNYqbb77ZvyMUEekOhp8DfceCLdSnq0fscfpZ88V6PHucarTHSUREpDVtCk7Lli0D4LLLLuOxxx7D4XB0yqBERLqd8Fjoc0yzXT1iqV4LPHucqgoxDAOLxRLgEYmIiHRP7drj9Nxzz/l7HCIiPVaPCk6uerDaPJ+aM061rloqnZVEhUa19EgREZGgdsTB6dxzz2XRokU4HA7OPffcVq994403OjwwEZFu5Zt/uPcIDZsDCY3VQ12Gi+KaYqCbB6ev/w6L73AvOZzzhKc5MjSSiJAIqpxVFFYVKjiJiIi04IiDU2xsrGcJR2xsbKcNSESkW/rmGTjwA/QZ7RWcSmpKcBkuAOLC4wIztiMRYoe6isYiF03E2+PdwammkAwyAjA4ERGR7u+Ig1PT5XlaqiciQWf4OdBnFMQP8GouqCoAIM4eR6jVt3BEt2FWA2wmOCWEJ7C/Yr8q64mIiLSiXXucqqqqMAzDU458165dvPnmmwwbNoxTTz3VrwMUEekWpt7abHOP2d/kCU6+h5eb1QBVWU9ERKRl1vY86Oyzz+b5558HoLi4mOOOO46HHnqIs88+myeffNKvAxQR6c56TnBKct9XHIRDDjE3x26+FxEREfHVruC0Zs0aTjzxRABee+010tLS2LVrF88//zx//vOf/TpAEZGAq6uC4j1QV+3TVVDtXqrX/YNTw4yTswpqK7y6FJxEREQOr13BqbKykpiYGAA+/vhjzj33XKxWKyeccAK7du3y6wBFRAJuz1fw6Ah4eqpPV4+ZcQqLglD38upD9zkpOImIiBxeu4JTdnY2b731Fnv27OGjjz7y7Gs6cOCADsUVkd6nvCFomLM2TXiCU0Q3D07QZLme9z4nzx6nau1xEhERaUm7gtPtt9/OzTffzMCBAzn++OOZMGEC4J59GjNmjF8HKCIScOYMTXSKT5dZiS4xPLErR9Q+UQ3jrzjg1awZJxERkcNrV1W9n/3sZ0yePJmcnBxGjRrlaT/55JM555xz/DY4EZFuwQwarc04dfeletBiSXIFJxERkcNrV3ACSEtLIy0tzavtuOOO6/CARES6nVaW6vWY4hDgXVmviabByTAMz2HnIiIi0qhdwamiooI//elPLFmyhAMHDuByubz6t2/f7pfBiYh0C60t1WuYpUmM6AlL9Zo/y8nc4+R0OSmrK8MRpr2qIiIih2pXcLryyiv59NNP+eUvf0mfPn3010kR6d1aWKpX7aymos5d2rtnzDg1v1QvPCScyJBIKp2VFFUXKTiJiIg0o13B6YMPPuC9995j0qRJ/h6PiEj341mq5z3jZFahC7WGEh0a3dWjarvBp7hnzRKzfbriw+OpLK+ksLqQAY4BARiciIhI99au4BQfH09CQg/466qISEcZRpOlet4zTk0LQ/SImfekwe5bMxLDE9lXvk8FIkRERFrQrnLk99xzD7fffjuVlZX+Ho+ISPdSUwr1Ne6PD1mq16MKQxyGuc9JwUlERKR57Zpxeuihh9i2bRupqakMHDiQ0NBQr/41a9b4ZXAiIgFnLtMLi4HQCK+uHnX4LUB9HWz52D2DNuaXYLV5uszwp0NwRUREmteu4DRnzhw/D0NEpJtqYZkeNKmo1xMOvwXAAq9c4v7w6DMay5OjGScREZHDaVdwuuOOO/w9DhGR7qm1w2+retDhtwC2EMg6CWx29+xTEzoEV0REpHXtPgC3uLiY1157jW3btnHLLbeQkJDAmjVrSE1NpV+/fv4co4hI4GSdDL/6wl0k4hA9co/TL99stlnBSUREpHXtCk7fffcdM2bMIDY2lp07d3LVVVeRkJDAG2+8we7du3n++ef9PU4RkcCwR0PayGa7etTht4ehPU4iIiKta1dVvZtuuol58+axZcsWwsPDPe2zZ8/ms88+89vgRES6s6blyHsUwwBXvVeT9jiJiIi0rl3B6ZtvvuGaa67xae/Xrx+5ubkdHpSISLex9kX4/CE4uNmnq8ftcQJYeh/c1weW3efVbL6H4upiXIYrECMTERHp1tq1VM9ut1NaWurT/tNPP5Gc7LuBWkSkx1rzAuz5EhKyIHmIp9kwjJ4542QLBWdVY7XABuZ7cBpOymrLiLXHBmJ0IiIi3Va7ZpzOOuss7r77burq3FWZLBYLu3fv5ne/+x3nnXeeXwcoIhJQR58Oo38OSUd5NZfWluI0nEAPC05mCfKKfK/mMFsY0aHRgJbriYiINKddwemhhx6ivLyc5ORkqqqqmDp1KtnZ2cTExHDfffcd/glERHqKSb+BOX+F1GFezWa4iAmNIcwWFoiRtY9ZVv2QGSdoDIAFVQVdOSIREZEeoV1L9WJjY1m8eDErVqxg/fr1lJeXM3bsWGbMmOHv8YmIdEueZXoRPWi2CQ4bnHaX7daMk4iISDPaHJxcLheLFi3ijTfeYOfOnVgsFjIzM0lLS8MwDCwWS2eMU0Sk6zlroDzPHTZCI7y6zFmZHrVMD5oEp3yfLrOsunk+lYiIiDRq01I9wzA466yzuPLKK9m3bx8jR45k+PDh7Nq1i3nz5nHOOed01jhFRLpe3gZ4dCQ8Ps6nq0cWhoDGPU615VBb6dWVGN4QnLRUT0RExEebZpwWLVrEZ599xpIlS5g+fbpX39KlS5kzZw7PP/88c+fO9esgRUQCorxhOVuUb7VQz+G34T3s8Fu7A2xhUF8LlfkQ1t/TpRknERGRlrVpxulf//oXv//9731CE8BJJ53EbbfdxksvveS3wYmIBJS5Dyg6xaerx+5xslggquH9HLLPKSnCPRulGScRERFfbQpO3333HaeddlqL/bNmzWL9+vUdHpSISLdQccB938qMU49bqgctliTXUj0REZGWtSk4FRYWkpqa2mJ/amoqRUVFHR6UiEi30MpSvR5bHAJarKynpXoiIiIta1Nwqq+vJySk5W1RNpsNp9PZ4UGJiHQLR7JUrzcFpyYzToZhdPWoREREurU2FYcwDIN58+Zht9ub7a+pqfHLoEREuoUjWKrX44pDQMtL9RpmnKrrq6l0VhIVGtXVIxMREem22hScLr300sNeo4p6ItJrtLBUr66+jtLaUqCHzjiN/Bn0HQMpw7yaI0MjiQiJoMpZRUFVgYKTiIhIE20KTs8991xnjUNEpPtpYameOdtks9hw2B1dPaqO6zPKfWtGQngC+8r3UVBdQH9H/2avERERCUZt2uMkIhI06p1Q2VAk4ZAZJzM4xYfHY7X0rh+jngIRqqwnIiLipXf9iy8i4i+VBYABFitEeu9j6tH7mwBqymHTf2Hdyz5dKkkuIiLSvDYt1RMRCRrmMr3IRLDavLp6dEU9gOoSePUXYA2BYy4Ca+Pf0FSSXEREpHkKTiIizTmCinrx4fFdOSL/iUqC9OPc781ZDWGRni7NOImIiDRPwUlEpDkZJ8C1K6G+zqcrv8pdxjspIqmrR+UfIXa4cnGzXZpxEhERaZ6Ck4hIc8IiIXV4s109Pji1QjNOIiIizVNxCBGRNuo1wckwwFXv1aQZJxERkeYpOImINGf9K/DZ/0HuBp8uMziZIaNH+u8NcF8afPusV7MZBjXjJCIi4k1L9UREmrP+Fdi+DGIzIG2EV5cZKnr0jJPF6i4MUZHv1Wwu1at0VlLlrCIiJCIQoxMREel2FJxERJozZDbE9oPko72a61x1FNUUAT08OJnVAs3qgWZzaBR2m52a+hoKqgpIj0kPwOBERES6HwUnEZHmHH91s82FVe5S5DaLjTh7XBcOyM88wemgV7PFYiExPJH9FfspqFZwEhERMWmPk4hIG+RXN+xvCk/EaunBP0I9wSnfp8tTIEL7nERERDx68L/6IiKdpK4aCndAXZVPlxkmenRhCGhxxgka9zmZRTBEREREwUlExFfeRvjzaHh8nE9XrylF3lpwUklyERERHwpOIiKHKs9z30en+nT1nuDUMP7qEvcMWxMJ4QmAluqJiIg0peAkInKo8lz3fW8OThHxYLO7PzaDYgNzxqmwurCrRyUiItJtKTiJiByqvKFEd0zLwanH73GyWBqDYQvBSTNOIiIijRScREQOVWbOOKX5dPWKw29NZjA0328DsziE9jiJiIg0UnASETmUZ49Tik9Xr1mqBxDTEAw14yQiInJYCk4iIocyg0RMMzNO1b1oxsmcUSvL8Wo231t5XTnVzupDHyUiIhKUQgI9ABGRbqes+ap6lXWVVNRVAL0kOI2+GAZOgtSRXs0xoTGEWcOoddWSX5VPekx6gAYoIiLSfQR0xumzzz7jzDPPpG/fvlgsFt56663DPmb58uWMHTsWu91OdnY2ixYt6vRxikgQMYwWy5Gbs00RIRFEhkR29cj8r984GH4OJGV7NVssFpIj3ec86RBcERERt4AGp4qKCkaNGsUTTzxxRNfv2LGD008/nenTp7Nu3TpuvPFGrrzySj766KNOHqmIBI2qInDVuT8+ZI+TuecnMTwRi8XS1SPrUuaM2sEq3wNyRUREglFAl+rNmjWLWbNmHfH1f/vb38jMzOShhx4CYOjQoXzxxRc88sgjzJw5s7OGKSLBxJxtioiHELtXV68qDAFQWwFbP4GqYhh3qVdXSqQ7NB6sVHASERGBHlYcYtWqVcyYMcOrbebMmaxatarFx9TU1FBaWup1ExFpUSulyHtfcKqEf8+F/94A9U6vLs04iYiIeOtRwSk3N5fUVO89B6mpqZSWllJVVdXsYxYuXEhsbKznlpGR0RVDFZGeyjz8tpVS5D3+8FtTZCJknABDz4C6Sq+u5Aj3HifNOImIiLj1+qp6CxYs4KabbvJ8XlpaqvAkIi0begb0+bLZrl4XnKxWuKL5PaLmjJOKQ4iIiLj1qOCUlpZGXp73QY15eXk4HA4iIiKafYzdbsdutzfbJyLiIywKUoY222UWh+g1S/VaYVbV01I9ERERtx61VG/ChAksWbLEq23x4sVMmDAhQCMSkWDi2eMU3suCk2GAs9aryVyqpxknERERt4AGp/LyctatW8e6desAd7nxdevWsXv3bsC9zG7u3Lme63/1q1+xfft2br31Vn788Uf++te/8u9//5v/9//+XyCGLyK90ZdPwqcPQOF2n6786l5WHALgkzvh3hT4/CGvZnPGqbC6kLr6ugAMTEREpHsJaHD69ttvGTNmDGPGjAHgpptuYsyYMdx+++0A5OTkeEIUQGZmJu+99x6LFy9m1KhRPPTQQ/zjH/9QKXIR8Z9vn4Vl90HxHq9mwzB6X1U9AJsd6muhPNerOc4eR4jFvZrbPPhXREQkmAV0j9O0adMwDKPF/kWLFjX7mLVr13biqEQkqI26CAp3QMIgr+bS2lKcLnfJ7l5THAIgpqHsepn3/lGrxUpiRCJ5lXkcrDxIWpRveXYREZFg0qOKQ4iIdLoTf9tssznb5AhzEGYL68oRdS4zOB0y4wTufU55lXkqECEiIkIPKw4hIhIova4UuSm64Wy8Mt/glBSpkuQiIiImBScREVN1KRRsg5pyn64Dle6DcVMifA/G7dE8M04HwFXv1WW+V/O9i4iIBDMFJxER0/bl8PhYeGGOT5e5XC0lspcFp6gUwAJGPVR6F4HQjJOIiEgjBScREZO5XC2mj0/XwUp3cDLLdPcathCIaqgSeMhyPfMsJ+1xEhERUXASEWlUtt9930xw8izV620zTtBkuZ53ZT1PcKpUcBIREVFwEhExlea47x0tByczTPQq0WZJcu8ZJy3VExERaaTgJCJiKmsITjF9fbp67R4ngJiGynqHlCQ3i0MUVBdQf0jhCBERkWCj4CQiYiprfsbJMIzevVQvuvlDcBPCE7BarLgMF4XVhQEYmIiISPeh4CQiYjKX6h2yx6mkpoQ6Vx0ASRFJXT2qztfCIbg2q42E8ARABSJERERCAj0AEZFuoaYMasvcHx8SnA5UuWeb4u3xhNnCunpknS/7ZLjgeUjM9ulKjkgmvypf+5xERCToKTiJiEBjYQS7A+zRXl29thS5KWGQ+9YMc4ZNlfVERCTYaameiAhA6eFLkffa4NQKc0+XOesmIiISrBScRESgSUW9NJ8uT2GIiF5YGMK06V348m9QVezVbM445VdqqZ6IiAQ3LdUTEYHGGSdHkJUiN71/szs8ZhwH/cZ6mj2H4Ko4hIiIBDkFJxERaNzj1MpSvV4dnLJnuAtkhNi9mnUIroiIiJuCk4gIwMm3w7FXQFi0T5enOEREL97jdPZfmm02lyfmVeY12y8iIhIsFJxERMBdSS95SLNdZmGEXj3j1ALzPRdUFVDvqsdmtQV4RCIiIoGh4hAiIq2od9VTUFUABEFVPZfLvVyviaSIJGwWG/VGPQXVBQEamIiISOApOImIuOrh3f8Hy++HuiqvrqKaIuqNeqwWKwnhCQEaYBfY9F+4NwX+dbFXs81q81TWy6vQcj0REQleCk4iIhUH4dtn4dM/gTXUq8vc25MUnkSItRevbo6IB1ddY3XBJlKjUgHtcxIRkeDWi38LEBE5QtZQmPo7qCkHm/ePRU9hiN6+TM+sJli6HwwDLBZPV2qkgpOIiIiCk4hIVCJM/32zXWYp8l5dUQ8az69yVkF1sXsGqoEnOGmpnoiIBDEt1RMRaUVuhft8J3O5Wq8VGtEYlg5ZrpcWlQZAbmVuV49KRESk21BwEhEp3AH5W6Gu2qfLXJ5mhodezdHPfV+a49VsliQ3Z99ERESCkYKTiMjyP8FfxsFXf/PpMmecgiM4NSzXK93n1ayleiIiIgpOIiJQstd9H5vu02XOOJnhoVdrWiCiiaZV9QzD6OpRiYiIdAsKTiIipQ3ByVyq1sAwjCCbcWp4/2XewSklwr1Ur85VR1FNUVePSkREpFtQcBKR4OZyNc6wxHoHp5KaEmrqa4AgmXHyLNXzDk6htlASwxMBLdcTEZHgpeAkIsGt4iDU14LF2rhUrYFZRS4hPIEwW1ggRte1HOZSvRyfLh2CKyIiwU7BSUSCm7lMLzoNbKFeXUG1TA+aVNXb69Nlzripsp6IiAQrBScRCW6ewhD9fLrMZWlpkUEWnKpLoKbMq8ssSW6GSRERkWATEugBiIgEVElD6e1mKuqZS/V6/eG3pnAHXPCCO0CFhHt1mbNuWqonIiLBSsFJRIKbeWaRw3fGKeiW6gEMO6vZZs9ZTgpOIiISpLRUT0SCW8ke930rZzgFzVK9VugQXBERCXaacRKR4NbaUr2KIFuqB5DzHez8AhKz4ahTPc2HHoJrsVgCNUIREZGA0IyTiAS3FpbqGYbRWBwimJbqbVsKHy2A7//j1WzOOFU5qyitLQ3EyERERAJKwUlEgld9HZQ1VIk7ZMapqKaIWlctFiykRKQEYHAB0mcUDJsDGcd5NYeHhJMQngDA/vL9zTxQRESkd9NSPREJXrZQWLDXPesUmeTVZS7TS4xIJPSQ8516tazp7lsz+kb1pbC6kP0V+xmaOLSLByYiIhJYmnESkeBmj4bkIWD1/nHoqainwhAefaL7ADrLSUREgpOCk4hIMzwV9YJpf5PJ5YLSHHDWeDX3iXIHJy3VExGRYKTgJCLBa+Ob8M5v4Mf3fLpyKnKAIKuoZ3riOHj4aNi/1qu5b3RfoPFrIyIiEkwUnEQkeO34HNb8E/at9ukyZ1X6RfsejNvrxTTMshXv8WrWjJOIiAQzFYcQkeA19EyIToGBk326csrdsyp9o/p29agCz6wwWOIdnDTjJCIiwUzBSUSCVysV5PaVu893MsNCUPEEp71ezeaMU2F1IdXOasJDwrt6ZCIiIgGjpXoiIoeodlZTUF0ABGtwynDfHzLj5AhzEBkSCWjWSUREgo+Ck4gEp5py2LYUCrb5dO2vcO/hiQ6NxhHm6OqRBV4LM04Wi6VxuV65gpOIiAQXBScRCU4HNsEL58A/z/LpMosf9I3ui8Vi6eqRBV5cf/d98R4wDK8uT4GIChWIEBGR4KLgJCLBqXiX+z5+gE9X0+AUlBwNlQRry6CqyKvL/Jqosp6IiAQbBScRCU5mcDJnV5owC0MEZSlygLBIiG44v8r8OjUwZ5y0x0lERIKNgpOIBKciMzi1PONkhoSgZH5dihScREREQMFJRIJV8W73fTMzTkF9+K0pfqD7vminV7OKQ4iISLBScBKR4NTKHqegPsPJ1EJwMmec8irzcLqcXTsmERGRAFJwEpHg46p3V4wDnxmnpmc4acYJn+CUHJlMiDWEeqOeA5UHunxYIiIigaLgJCLBpywXXHVgDYEY71kls8x2VGhUcJ7hZBp8Cly5BM57xqvZarF6AuXesr3NPVJERKRXUnASkeBjLtNz9ANbiFdX0J/hZIpOgfTxEJXo05Ue4z4gd0/Znq4elYiISMAoOIlI8DELQ7RyhlO/qCBepncYGdEZAOwt14yTiIgEDwUnEQk+RS2f4RT0h9829d2/4cMFkLvBq1kzTiIiEoxCDn+JiEgv4ylFPtCny5xFUXACvnsVtn4CKUMhbYSnOSOmYcZJe5xERCSIKDiJSPCpKnTfN7NUz5xFMcNBUBt6pjs0pQzzataMk4iIBCMFJxEJPhf/C6pL3VX1mjAMgz2l7jDQP8Z3GV/QGTev2eb0aHdwKq0tpaSmhFh7bBcOSkREJDC0x0lEglO4A8IivZqKa4opqysDGmdVxFdkaCSJ4e5qeyoQISIiwULBSUSkwe4y996n1MhUwkPCAzyabsAwoCwP9nzj02UuZdRyPRERCRYKTiISXLZ+As/PgRV/9unaXeoOTv0dWqYHQE0ZPHQUPDPD/XETKhAhIiLBRsFJRIJLznewfRnkbfDpMmdPtL+pQbgDIhsOwC3c4dVlLmVUcBIRkWCh4hAiElyGngXRKRDrWzXPXKqninpNJGRBZQEUbIU+x3iatVRPRESCjYKTiASXpGz3rRmeinpaqtcoMRv2fg0F27yaNeMkIiLBplss1XviiScYOHAg4eHhHH/88Xz99dctXrto0SIsFovXLTxcm7hFpOPMGSct1WvCDJkFW72azRmn3Mpc6urrunpUIiIiXS7gwenVV1/lpptu4o477mDNmjWMGjWKmTNncuDAgRYf43A4yMnJ8dx27drVhSMWkR6rthK+fQ62f+quGNdESU0JxTXFgJbqeUk0g9MW7+bwRCJCInAZLvaV7wvAwERERLpWwIPTww8/zFVXXcVll13GsGHD+Nvf/kZkZCTPPvtsi4+xWCykpaV5bqmpqV04YhHpsQq3wbs3wn/mgcXi1WUuOUsMTyQyNNL3scEqscmMU5OwabFYPMv1zJk6ERGR3iygwam2tpbVq1czY8YMT5vVamXGjBmsWrWqxceVl5czYMAAMjIyOPvss9m4cWOL19bU1FBaWup1E5EgZe7TSczy6fJU1NP+Jm8JgwALVJe4i0Q0kenIBGBHyY5mHigiItK7BDQ45efnU19f7zNjlJqaSm5ubrOPGTJkCM8++yxvv/02L774Ii6Xi4kTJ7J3b/MblBcuXEhsbKznlpGhJTgiQauwITglDPLpUkW9FoRGNFYgzPderjcwdiAAO0t3du2YREREAiDgS/XaasKECcydO5fRo0czdepU3njjDZKTk3nqqaeavX7BggWUlJR4bnv2qHSuSNAq3O6+T/CdcfIcfqvCEL7MGbpDCkRkxmrGSUREgkdAy5EnJSVhs9nIy8vzas/LyyMtLe2IniM0NJQxY8awdevWZvvtdjt2u73DYxWRXqCgITg1s1RvV6m7yIyW6jUjMdt9aPChwalhqd7Okp0BGJSIiEjXCuiMU1hYGOPGjWPJkiWeNpfLxZIlS5gwYcIRPUd9fT3ff/89ffr06axhikhvkb/ZfZ/ofY6TYRhsL3GHKnMWRZpIbL4k+QDHAHdzdQGltdo/KiIivVvAl+rddNNN/P3vf+ef//wnmzZt4tprr6WiooLLLrsMgLlz57JgwQLP9XfffTcff/wx27dvZ82aNfziF79g165dXHnllYF6CyLSE1TkNxQ3sEDSUV5d5i/+FiwMdAwMyPC6NfMsp1LvsuPRYdGkRKQAmnUSEZHeL6BL9QAuvPBCDh48yO23305ubi6jR4/mww8/9BSM2L17N1ZrY74rKiriqquuIjc3l/j4eMaNG8fKlSsZNmxYoN6CiPQEBxtmm+L6Q5h3uXFzj07f6L6Eh+hAbR8DJsFvN0O079EPA2MHcqDqADtLd3JM8jEBGJyIiEjXCHhwArjuuuu47rrrmu1bvny51+ePPPIIjzzySBeMSkR6lYM/uu+Th/h0bS92L9MbFOtbbU9wV9YLjWi2KzM2k69zv1aBCBER6fUCvlRPRKRLmDNOzQWnhv1NWXG+RSOkdebSRi3VExGR3k7BSUSCg2fG6WifLjM4acapFRteh39dAmtf9GrWWU4iIhIsFJxEJDjk/+S+T2p5xkkV9VqRvxU2vwe7Vno1m1+zXaW7qHfVB2JkIiIiXaJb7HESEelUzhqIzYDaSkj2rqhXXlvOgcoDAAyK04xTi46aCRFxkH6sV3OfqD7YbXZq6mvYX76fDEdGYMYnIiLSyRScRKT3C7HDlYvBMMBi8eoyixokRSThCHMEYnQ9Q9/R7tshrBYrAxwD+KnoJ3aU7lBwEhGRXktL9UQkeBwSmkD7m/whK9ZdVGNL0ZYAj0RERKTzKDiJSO9nGC12mTNO2t90BA5uhvWvwIFNXs2D4wcDsKVYwUlERHovLdUTkd7vXxdB/haY9QAMnuHVpRmnNvj8IfjuVTjpj5Ay1NN8VLx739hPRT8FamQi0k7FlbXklFRTWVtPVW09lbVOqurMj+s5bUQafePc57it2V3EB9/n4HQZ1LsM9329Qb1hYLXAL08YyMj0WAA27Cvh9TV7sVks2GwW7DYr4WE2wkNsRITZOGFQIplJUQCUVNaxs6ACR0QojvAQHBGhhNr0t33pfhScRKT3y/sBSnY3e4irJzipMMThmWGphRmnHSU7qKuvI9QW2tUjEwlqRsOsuqVhOfIP+0v5ekcBB8trKKyoo7SqjuKqWkqq6iiurONvvxjHiH7ugPPa6r3c+96mFp87OyXaE5w255bx989bPuz6pKNTPcFp28Fynluxs8VrH7lwlCc4fbWjgKtfWO3VHxlmwxEeiiMihBtOPorTj+kDwL7iKj74PoekaLv7FhNGYpSdhKgwbFbf5dgi/qTgJCK931VLIPd76DPKq7myrpLdpbsBGBw3OBAj61lShrnvDwlOfaL6EB0aTXldOTtKd3hmoETEf/YXV7Fxfyn7iirZX1LNvuIqcoqrOFhew8GyGl771URPGPp8y0EWfvBji89VWFHr+Tg2IpSkaDsRYVYiQ0OICLMRGWYjItQ9M5QQFea5dmgfB9dMHUSI1YLNam24t2C1WHAZBkelRnuuzU6J5tppWbgaZqdq611U1dZT7XTf94uL9FwbarPSJzacsmon5TVOACobZrxyS6HG2XjUwab9pc0GPasFEqPt/O60o/nZuHQADpbV8OX2AvrGhdMnNoKUGDshmsmSDlBwEpHeLzoFsk/2ad5SvAUDg+SIZBIjEgMwsB7GnHHK/wnq66BhZslisTA4fjBrD6xlS9EWBSeRNqp1uthbVMnOggp25Feyq6CC3YWV/PGMYWQlu8PIO+v386dWwtDBshrPx0f3cXD6yD4kRYeREGUnLjKU2IiGW2Qo2SmNAef88RmcP/7IqmGOzohjdEbcEV07vG8sw/vGHtG1049OYdUC989oZ72L8honpVVOSqvds2VNx5sQHcaZo/pSUF5DfnkNBeW1FFbW4jLcX4NQW+Os0/o9xVz/r7Wez21WC2mOcPonRDIgMZKfjUtn/MAEwD1rZ2mmgJBIUwpOIhK0NhduBmBIgu+huNKM2AwIi4bacijcDsmNX7fBcY3BSUR8GYZBbmk1sRGhRIa5f/16e90+Hvr4J/YVV1Hv8i1i84vjKzzBKSs5mpH9YukXF0HfuAj6xoXTLy6CFIed5OhwUmPtnsdNPSqZqUcld80b87MQm5W4yDDiIsOa7R/bP56x/eO92pz1LgorazlQWkO/uMYl2fZQK8cOjGd/cTW5pdXUuwz2FVexr7iKVdsLmJCVyPiGa5dvPsgtr61nQGIUAxIjyUqOZnBKNINTY+ifEKllgAIoOIlIb7fqr1BxEEaeD6nDvLp+LHT/9XZIvILTEbFYIPlo2Pct5G30Ck4qECHiZgakn/LK2ZJXxpa8cn46UMbWvHLKapw8N+9Yph+dAoDVYmF3YSUAEaE2BiRGkpkUxcCkKAYkRDK0b+PZcqcMS+WUYakBeU/dXYjNSkpMOCkx4V7tJw5O5sTB7gBZ7zI4WFbDvuJKdhW4b6PS4zzX7iyoIL+8lvzyWlbvKvJ6nrAQK49fPIaZw9MAyC+vobCiloGJUYSFaOlfMFFwEpHebd3LkPc9pI/3CU6bi9wzTkcnHB2IkfVMaSPcwSn3OxhxrqdZJcklGFXV1vNjbil94yJIdbh/aX973X5ufHVds9fbrBbySqs9n0/MSuSVq08gMymKlBi7lop1IpvVQlpsOGmx4YwbkODTf8H4DI4dmMDOggp25lew9UA5Ww+Ws/VAOdV1LtIcjaHs/e9zuP3tjYRYLWSnRDOsj4OhfRwM6+u+b7ovTHoXBScR6b2ctXCwYU9A2kivrnpXvWdZ2VEJ2pNzxMwCG/vXeTVnx2cDkFuRS0lNCbH2I9vbINJTFFXUsnF/KT/klLBxfykb95ey/WA5LgPuPHMY8ya5z4LLTonGZrUwMDGSo1JjGJwaw+CUaI5KjSEzyXuGIjHaTmK0vaWXlC4UZQ9hRL9YT4ENk6theV+Ko/H7VFVbT4w9hLIaJz/mlvFjbhms3efpf+1XEzx7p/YWVeKsNxiQGKlg3AsoOIlI73XwR3DVQXise39OE3vK9lDlrCLcFs6AmAEBGmAP1Ge0+z5nvftg4YZfBBxhDvpE9SGnIoetxVsZlzoucGMU6aCSqjpqnS6SY9y/LK/dXcQ5f13Z7LVJ0WE4m+xPGtrHwQ93z8QeYuuSsUrnslotZCREerVdMzWLq6cMYn9JNZv2l7Ipp5QfGm67CysZnBLjuXbRip3844sdOMJDOCY9jmPSYzkmPY5RGbGkOcIVpnoYBScR6b1yv3ffpx3j+QXf9GOReyZqcPxgbFb9gnPEUoeDNRSqCqFkD8T193QNjh9MTkUOPxX9pOAkPUaNs55NOWWs31PM+j3FrNtTzPb8Ci6flMntZ7qX9w5OjcFqgYyESIb3dTC8byzD+jgY3tdB8iFL7GxWi36mBAGLxUK/uAj6xUUwo8nes4oaJ1H2xl+va5wuwkKslFY7+WJrPl9szff0JcfY+ejGKZ6lfbUN10r3peAkIr2XJziN9On6qdBdxEAV9dooxO4uS577nXu5XpPgdHTC0Xy29zM25m8M3PhEjlB5jZOf/+MrNu0vpbbe5dOfU1Ll+TjaHsL3d870+oVYpDmH/jdyz5wR3H7mMDbnlvHd3hK+21vM+r0l/JRXhstlEB/ZeGD4/JfX8FNeGeP6xzN2QDzjBsRzVGqMKvp1I/oJICK9V9MZp0Oool4H9B3tDk4562DYWZ7mEYkjANhYoOAk3UNdvYuN+0v5dmch3+4sIi4ylD+d5/55EBVmI6e4itp6F/GRoYxqOKNoVEYco9LjfDb4KzRJe4XarJ79U5cc7/5jU1VtPfuKK71mKzfsKyGnpJpdBZW80bBnKtoewpj+cZwwKJH507MDMn5ppJ8CItI7GUarM06qqNcB/cbBnm8gwvsslRFJ7uC0vWQ7lXWVRIZGNvdokU71xZZ8vtxewDc7C1m/t5jqusbZpMSoMBae6z7o1GKx8PjFY+gTG0FGQoT2mkiXigizkd1kLxTAhzdOYf2eYlbvKmLN7iLW7i6mvMbJ51vyqahxegWnxz7ZQr/4CI4dGE//BBWe6CoKTiLSOxVuh5oSsNkhybtq3sHKgxyoPIAFi+f8IWmDcfPct0MkRyaTEpnCgcoD/FDwA+PTxvtcI+JPOSVVbNxX6rXH5NFPfuLbJufwxEWGMq5/POMHJjB+YHzTmiYcPyixq4cs0qLYiFCmHJXMlKMaz576Ka+M1buKiAlv/JW9vMbJY0t+wqxJkuYI57jMBI7LTOCEQQlkJUcrSHUSBScR6Z32fuu+7zMKQryX3GzI3wBAVlyWZkX8bETiCJZWLmVjwUYFJ/G7/cVVfLm9gK+2F/LljgJ2FVRiscD6O07FEe7eK3LaiDQGJEYxfmA84wfEk5UcjVV7RKQHslktDG04I6qpWqeLq04cxLe7ivhubzG5pdW8s34/76zfD8CF4zO4/2fuJamGYWAY6P8BP1FwEpHeaV9DcEr3/eX9+3z3Er6RSb5L+KQN6p3grAZ7tKdpRNIIlu5Z6gmnIv7wr6938+TybewurPRqt1pgRL9YDpbVeILTlScOCsQQRbpMQlQYC2YPBdx7pdbuKeLrHYV8tb2QNbuLGJHeeBbVtoPlnPvXlRyXmcDxmYkcl5nA8L4OQmyq3tceCk4i0juZM079fMtim8HJ3JMj7fDZ/8FnD8EJ18KMOzzNw5OGAyg4SbvsLarky+2FfLW9gGunZTEo2R3KDQN2F1ZitcDIfrGcMCiREwYlMn5gPDHhoYd5VpHeKyLMxsSsJCZmJQHu8vquJkUiv9pRSGm1k082HeCTTQcAd8GJ4zITmJiVyKyRfegXFxGIofdICk4i0vvUVTcWhjhkxslluDzlsjXj1AFRKeCsgjzvCnrDE93BaW/5Xoqri4kLjwvA4KSnOFBWzcqtBXyx1V3QYW9RYwnwY9JjPcFpxtAU+sQdy/gBCkoirTn04OULx2cwvG8sX+9wL3H9emchZdVOlv54gKU/HmBQcpQnOO0vrqKqrp5BSVHaI9UCBScR6X1cdTD993DwR4gb4NW1q3QXZXVl2G12suNV2rXdhp4J/U+AxMFezbH2WPrH9Gd32W42FmxkUr9JARqgdEeGYXh+IVu5LZ9L/v6VV7/NavHMKI3p31i1McURToojvEvHKtIbhNisjG4otX/1lCzqXQabckpZuS2fVdsKOC6zsUDKC1/u4snl20hzhDMxK5EJWYlMzE7SjFQTCk4i0vvYY+DEm5rtMpfpDU0YSqhVf7lut8gE960Zw5OGs7tsNxvyNyg4Bblap4u1u4tYsTWfFdsKmJSVyE2nus9OOyY9jjCblaPSopmUlcSErETGD0wgWucliXQam9XiOVPq6ilZXn0VNU7CQqzkllbzxtp9nrOkBiZGMiEriT+cPjTo//8M7ncvIkFnTd4aAEanjA7sQHqxY5KO4YMdH7Du4LpAD0W6mGEYbMopY8XWfL7Yms/XOwqpqqv39DvrXZ7gFG0PYfUfZ2jpnUg3cffZI/j97KGs3lXEym35rNxWwHd7S9hZUElZdS73zWncF/zW2n3EhIdw/KDEoApTwfNORSQ4GAZsfBMyjoPYdJ/utQfWAjAmZUxXj6z3yVkPKx6D8Dg442FP89jUsQCsO7COelc9NquthSeQ3qC4spa4SHfJf8OAXzzzFYUVtZ7+xKgwJmYnMTk70bOB3aTQJNK9hIfamJSdxKRs9/+rZdV1fLOzkMKKOk9Jc8MwWPjBJvJKawixWhidEcfkwUlMzk5iVEYcob24Yp+Ck4j0LgVb4bXL3AffLtgDIXZPV1F1EdtLtgMwNmVsoEbYezhrYMPrEJkEpz/kOVV0SPwQokKjKK8rZ0vxFo5OODrAAxV/KqyoZeW2fPfyu60FVNfV89XvT8ZisWC1WjhlaCoHyqo9v3wNSY3RGTIiPVRMeCgnHZ3q1VZd5+Lkoal8sSWf3YWVfLuriG93FfHoJ1uItodwwfgMbj9zWIBG3LkUnESkd6kugb5j3WcLNQlN0DjblBWbpWpv/tBnlDugVuZDwTZIchfbsFltjE4ezYr9K1idt1rBqRdYvauQjzbm8cWWfH7IKfXqC7Fa2FtURUaC+zBp8+BNEemdIsJs/O857qq0uwsqWbHNvTR35dZ8iirraPp3kuq6ev7nrQ1MzEpkcnZSjy/youAkIr1L+ni4ehleB1k0MPc3jUnVMj2/CLG7z8navRJ2r/IEJ3Av11uxfwVrD6zl50N/HsBBSls5612s31vC8L4OwkPdyyw/+D6Xf3yxw3PN0WkxTMxKYvLgRI7LDK49DiLSqH9iJP0T+3Pxcf1xuQx+yCklJrzx58E3Owt5bfVeXlu9F4CjUqOZlO1e1jcxK4mIsJ61lFs/6USkd7L6rrFenbca0DI9v+p/QmNwGvtLT7O5h2x13mqvEtTS/RiGwbaDFazYms/nW/L5ansBZTVOXrjiOE4cnAzAjGGplFbXMSnbXf0uJaZn/9VYRPzP2lCxr6l+cRFcOy2LL7bks2F/CT/llfNTXjnPrdjJ4v83hcGpMQEabfsoOIlI71FT5r63+/4gLqkp4YfCHwA4Nu3YrhxV7zZwMnzxMGxf7q4M0BCQjkk+BrvNTn5VPjtKdjAoblBgxyk+th4o48nl21mxNZ/c0mqvvtiIUA6U1ng+P2FQIicMSjz0KUREWjUoOZrfnXY0vzsNiipqWbnNfeD1T3llZKdEB3p4babgJCK9x/pX4MPb4NgrYdb9Xl3f5n6Ly3CRGZtJWlRagAbYCw2Y6N7nVLoP8rdA8lEA2G12xqSM4cucL1mVs0rBKcDKa5x8vaOA+Mgwz8GyTpfB62vcy2fCQqwcOzDes4RmeN9YbCroICJ+FB8VxunH9OH0Y/oEeijtpuAkIr3H9uXgckJUkk/XqpxVAJzQ54QuHlQvFxrhXq6341PYvswTnAAm9J3Alzlf8uX+L7XPqYvV1btYv6eYL7a6q9+t3V2M02UwZ3RfT3AakhrDb04ezHEDExg/MN6zn0lERJqn4CQivUO9E3Z87v540Ek+3V/lfAUoOHWKrOnu4LRtGRx/jafZ/Fp/k/cNda46Qq06s6ezOetd/OrF1azaVkBFbb1X34DESPrFR3g+t1gs3HTKUYc+hYiItEDBSUR6h/1roKYEwmOh72ivrpzyHHaW7sRqsWp/U2cYNB24E3Z+Ds5aCHEfhnp0wtHE2eMorilmQ/4GHTrsZ7kl1XyxNZ/ckiquO2kwACE2Kzkl1VTU1pMQFeYpATwpO8lTLlxERNpHwUlEeoefPnTfZ50EVu8lR5/t/QyAY5KOISasZ1Xw6RHSjoGoFKg44K6wN2gaAFaLlRP6nMCHOz/k872fKzh1UGFFLV9uL2DVtgJWbstn28EKAMJsVi6fnElkmPuf9D+eMYxoewjD+jh08KyIiB8pOIlI77D5A/f9kNk+Xcv3LgdgasbULhxQELFa4ahTYe2L7u9DQ3ACmJI+hQ93fsjyvcv5zdjfBG6MPdyd72xk0cqdXm1WC4xMj2NydiK1TheR7ok+Vb8TEekkCk4i0vMV7YQDP4DFBtkzvLoq6yr5OudrAKalT+v6sQWLIbPdwemnj7wqGk5Jn4LNYmNL0Rb2l++nb3TfAA6yeyuvcfLNzkJWbXPPKv3152M9y+v6N9wPSY1hQpa7NPiEQYnERmrfmIhIV1FwEpGeb3PDMr3+EyAywatrVc4qal219IvuR1ZcVgAGFyQGTYM5T8LgmV7NsfZYRqeMZnXeapbvWc4lQy8JyPC6o+q6er7dWcSq7fms3FbAd3tLqHcZnv5V2wo8wem8semcNbovSdH2QA1XRCToKTiJSM+36b/u+yGn+XQt270MgGkZ07BYtN+j04RFwejmQ9H0jOmszlvNsj3Lgjo4VdXWU+t0eWaJlm8+wK9eXON1TUZCBBMGJTIxK4nJgxvL6mtmSUQk8BScRKRnK82BXSvcHw8726urtr6WpXuWAnBy/5O7emTS4KSMk3jw2wf5JvcbCqoKSIwIjj04JVV1rN5VyFc7CvlmRyHf7S3h19OzPSXAj89MpF9cBMdnJnBClnvpnSrfiYh0XwpOItKz/fAWYEDG8RDX36tr5f6VlNWWkRKRwtiUsQEZXtD55hlY/y8441FIGwFAhiOD4YnD2ViwkU92fcKFR18Y2DF2ovIaJw9+tJmvdxSyKbcUw/Du33qgzPNxfFQYK27zPXNMRES6JwUnEenZNrzuvh9xnk/Xhzvde59OHXgqtkNKlEsn2bYU9n7j/r40BCeAWZmz2FiwkQ92ftBrgtPeokq+3lGI02VwwfgMACJCbby+Zi9l1U4AMpOiOHZgPMdlJnJ8ZgLpTQ6gFRGRnkXBSUR6rnonxGdC3kYYNserq7Ku0rO/aebAmc08WDrFcVdD5hSf78fMgTN58NsHWZO3htyKXNKi0gIzvnaqq3exKaeU1buKWL2riDW7ithfUg249yWZwclmtXDraUcTHxnKcQMTSHGEB3LYIiLiRwpOItJz2ULgvL9DbYW7OEETH+/6mEpnJenR6YxKHhWgAQahQVPdt0OkRaUxLnUcq/NW89bWt/jVqF8FYHBHrqy6jpjwxoIM5/9tFev2FHtdY7NaGNEvluMzE6irdxFqswLwyxMGdOVQRUSkiyg4iUjPd0hoAnhjyxsAnHfUeaqm102cN/g8Vuet5s0tb3L1MVdjtVgDPSQAXC6DLQfKPbNJa3cXsbe4iu/vPBV7iHuJ54h+DnbkVzC2fxzjBsQztn88ozLiiLLrn1ERkWChn/gi0jPlfu8+8DZ1mE/X9uLtrD2wFpvFxllZZwVgcEHOMGDdS7DuZTj/nxCdDMApA05h4VcL2V+xny/3f8nEfhMDOsx31u/n1W92893eEs+epKZ+yi1nZHosAAtmDeXus0ZgtSqEi4gEq+7x5z4Rkbb6cAE8OQG+esqn65XNrwBwYvqJpESmdPXIxGKBb591l4lf/ZynOTwknNMHnQ40fo86W3FlLZ/9dJC/LN3Clf/8lt0FlZ6+3JIqVmwtoKzaSWSYjYlZiVx/UjbPXXYs624/xROaAKLsIQpNIiJBTjNOItLzOGsgKhlCwuHo0726SmpKeGvrWwD8fOjPAzA4AeCEX8PrV8DXT8PE30Cou0jCxUdfzCubX2H5nuXsKt3FAId/9wPtKazk4x/yWL+nmO/2FrOzSVACOHNUH/onus9KOnloKjHhoRyTHsuQ1BhCbPpbooiItEzBSUR6nhA7nP8cVBZCZIJX139++g9VziqGxA/h+LTjAzRAYdjZsPgOKN0L370K4y4FYFDcIKakT+GzvZ/xwg8v8D8n/E+7nr6oopaN+0vZuL+ESdlJjOjnnh3auL+Ue979wevagYmRHJMex6iMOEZnxHnas5KjyUqObt/7ExGRoKPgJCI91yGhqbKukhd/eBGAucPnqihEINlC4YRr4eM/wBcPw+hL3G3AvOHz+GzvZ7y19S2uOeYakiOTW32qsuo6Vm0raAhKpfywv8RTChzgplOO8gSnMf3jmDE0lVHpsYzKiOOY9FjiIsM6732KiEjQUHASkZ7lq6ch6yRIyvbp+teP/6KguoB+0f2YlTkrAIMTL+MvgxWPQtFOWPui+3NgfOp4RiWPYv3B9Tz93dP84YQ/AFBZ62RLXjmbc8tIT4hgYlYSAPuLq7n6hdU+Tz8gMZLhfR0MTmmcNUp1hPOPS8d3+lsTEZHgo+AkIj1HznfwwS1gDYEbvwdHX09XWW0Zz254FoBfj/41odbQlp5FukpYFJz4W/jwNvj0ATjmQgiLxGKx8KtjruPaJVfx782v8ePmcew+YGd3YSWG4X7ouWP7eYJTVnIUx6THMjglhuF9HQzv62BoXweOcH2PRUSk6yg4iUjPYBjw/i3uj4ed7RWaAP667q+U1pYyKHYQp2ee3swTSFerq3exu//59I38MxFl+/nh33cy7BcPADA+9VjqK7IhaivflD5PdYG7kEdSdBhD0mIY1sfheZ4Qm5V3rpsckPcgIiJiUnASkZ5h/b9gz5cQGgmn3O3VtblwM//68V8A/O7Y32Gz2gIxwqBnGAYPfLSZrQfK2XawnN0FlThdBjOtF/BU2KMM3voMFFwDiVmEh9o4NvZS1jrvINTxPTefYGXO0JNIirYH+m2IiIg0S8FJRLq/0v3uc5sAptwCsemerjpXHXeuvJN6o55TBpwS8ENVe6uq2np2F1ays6CC3QWVbM+vYNvBchKjwnjyF+MAsFgsvLNuP/uKqzyPiwqzkZM8g03VKxha8Q289Wu47H2w2vjnz+dw/9ebeXHTi7y2+zEuHj0FUHASEZHuScFJRLo3l8v9y3Z1MfQZDROv9+p++run2VCwgZiwGG499taADLG3KKmqY1dBBeXVTiZmJ3naz/7LF6zfW9LsYw6dIbp6yiAslsZS36kOu7u6YdEz8OQk96zhFw+7AzAwf/R8lu5eyr7yfSz8aiH3Tr63896giIhIByg4iUj3tuw+2L7MfdjtuX/3lLQGWLFvBU9/9zQAt59wO2lRaYEaZY/z1tp9bMopZW9xFXuLqthVUEFxZR0AaY5wvvz9yZ5rw0PdSx8d4SEMTIqif0IkAxOjyE5xhyPDMDyl3y+dOLD5F4wfALMfgLeuhTUvwITrIDSC6LBo/vfE/+WyDy/j7W1vMy51HOcMPqdT37uIiEh7KDiJSPf13b/h8wfdH5/xKCQf5enaXrydWz69BZfh4tzB53Ja5mmBGWM3UlhRy96iSvYVVbGvIRDtK65iX1EVTpeLj//fVM+1L3+9m693FPo8R3KMnf4JkdS7DGxWdxh68PxRxISHdPw8pFEXQ8VB931ohKd5XOo4rh11LX9d/1fu/vJu+jv6My51XMdeS0RExM8UnESke9r0X3jzV+6PJ1wHoy/2dO0u3c2VH19JWV0ZY1LG8Ifj/xCgQXaNylonuSXV5JZWc6C0htzSanJLqqmsdfLAz0Z5rvv1S6v5crtvGAKwWKDW6SIsxArArBFpDO/roF9cBOnxEQxIdM8kRdl9/1nISIj0zxuxWGDSDd5tddUQGs41o65hS/EWFu9azHVLruPvp/6dEUkj/PO6IiIifqDgJCLdz5oX4L83gFHvnp045R5P14+FPzL/k/kcrDpIdlw2j01/jDBbB2dCAqCu3kVhRS355TXkl9dSUF5DfnkN5dVObjp1iOe6KxZ9w5IfDzT7HBYL3HfOSEJt7jDUJzaClBg7/eIj6BcXQb/4CNLjI0lv+NicQQK4bFJm577BI7H+FfjkTrjoZaz9xnLf5PsorC5kdd5qrv74ah6e/jAn9Dkh0KMUEREBFJxEpLvJ2wjvXOf+eNTFcNZfwOoOBu9vf5+7Vt1FpbOS7Lhs/n7q34kPjw/gYBtV19VTUlVHUWUtRRV1FFfWUlRZR0F5DeU1ThbMHuq59poXvuWjjXktPtf1Jw/2hCFHhHtPV1SYjdTYcNIc7luKI5w0h516l0HDFiQevmCUZ69Rt+eshVVPQFkO7PgM+o0lIiSCJ05+gl9/8mvWHFjDtYuv5cZxN/LLYb/EarEGesQiIhLkLIZhntMeHEpLS4mNjaWkpASHw3H4B4hI1/vgd2CPgel/AIuF3IpcHvz2QT7a+RHw/9u78/ioyrvv458zk0wy2QlJCEsSWaIg+yIYKLe4UEREXG4XioKIrY+iiLRUoWKkgECxQF2Koj7AS6X4aGWpFa3Yiix6y74ICER2SAIhIRvJTGbO88eQgTGJw9y1nkS+79crL+Zcc53r/OacK2F+5zrnOtCraS9m95tNnOOH/R32ek1sF4zK7D5RzPGisxSWVydCLorK3RSVu6lwe3jj/qv8dUf8369YvfdknW3vmzbQnwyNXbKFZVuPY7cZJEY7aBztIDk2gsbRDpJiIhj388uJcvjOa50uc+EIsxFTyyV0DV5FMax/AfpNgOpnb1VVUmnApLWTWHlwJQA9U3uSnZVNely6hcGKiMhPUSi5gRInEbHW4f+BL16EGyZD49a+MtMEwyC/PJ+/7PkLb+16iwpPBTbDxq86/YqHOj1EmO18IuH2eCmv9FDurqKs0sNZl4cyVxVllVW4PV5u7NDUX3f+5znsPFZMSYWbkoqqcz9uiiuqANg5eYC/7v0LvuKzb+pOhvZOHei/Z+jxJVv4YPsJEpzhxEeF0yjKQaOocBLPJUOPXZeJ0+FLDk6WVGK3GSQ4wwMStUue+yz8+Wq4/EbMXg/z3qkNzNowi7NVZwkzwrgt8zZGdRxF85jmVkcqIiI/EQ0ucXr55ZeZNWsWubm5dO7cmRdffJGePXvWWf/dd99l0qRJHDx4kMzMTGbOnMlNN910UdtS4iTy47lwmmqAY0VnKavwjdZUekwq3B4yP3+c1CN/J79pP1IeWk65u5w1x9Ywf9NS9pV+iYkHgBgzk2TX3eBqTmSYnf/3f7L87f73vPVsPFRYawxRDju7fn9+xr1gydD+aQMJOzcyNOWDXWw4eJqEKAcJznAaRYWTcC4hSohycFPHpv7EqcLtwWG3KRH6d+x4D/466tyCAZn9OdzmGqYXbWVt7v+cKzXo3aw3g1oN4mfNf1ZvLtUUEZGGKZTcwPJrP9555x3GjRvHK6+8Qq9evZg7dy4DBgzgm2++ISUlpUb99evXM3ToUKZPn87NN9/M4sWLufXWW9m8eTMdOmgGJvlpMk0Tj9fEBP/lXgCnSivxeE2qvCbec/96vF48XogMt5HRONpf98tvC6hwe3B7TNweL26PF1eVF7fHpFFUOAM7nh+VeWV1DoXlLtxVF9T1+OqmxkXwu0FX+uuOXryZQwVlVLi9VFZ5fP+6PVRWeUlPCOeTkS3h1D4o2M/ef31MW9dOJrsfYp23I9jOkhnRmqucPVjnTqDpB/ew5/QePKbH335V+WW4C/pSUnolJzCAMzUuW4s6txxmM4iOCCPKYSfKYSc6Ioy4yPCAS/Du6pHGz9okERcZTmxkGLH+f32vL5xAYdLNV3Kxqp91JP+Gjv8NUY1h3Z98z+7a9w/S9/2DeYaNTU0yeSU2ki+rCll3fB3rjq/DZti4otEVdEjqQIekDrSKb0WzmGYkOZN0T5SIiPzgLB9x6tWrF1dddRUvvfQSAF6vl7S0NB577DGeeuqpGvXvvvtuysrK+OCDD/xlV199NV26dOGVV14Jur36NOK0t3AvG3b9i+L8Q9R+GEyaN4rCee6MdmG5i1OlLqpsERTFtz1XxSS++BvsngpS23QmNiERgFMnDnP66D7MgNZMqgtaNHL6v3wWnXVz/MxZTCOMgrj25+pCQul+wqtKSb6sPY2TfV+qT508Qf6BnYFtcu7KKqBZQiQJTt8MZ8UVbg6fLgcgL64TGIav3fKDRLqLSGyRSWrzy3wxFBZw9JtN59s1AyNPjYskOTYSE5Nyl4f9J0sByI25Eq/hu3k+7uwRol2nSEhtSXor36xkJSXF7Nu27oL2TMzq3WCaNImPpEUj3/NkKt1eth4tAuBIRCaVhm97jVx5NKrKIy65BR06dAWgvKKCTWt999t4L9wTXt/rlPhI2jaJBcDjNVm9zzfCccCWQQnReE2TRt4CmnpyiU1MoffVfXxteU3+/ve/+mI8F6jXv5chNS6Cq1s19u+Zv207jseEHLMpp01ff25kFJNpHCcqthH9r7vB/9n/9uEyzCo3tUmICqdvmyT/8qo9+ZS7qjhsNiEPX5+KpYx2xmEczmj633B+BOeLf7yLzVVMOB4cRhVRnMVhVBJmqwSbC7cBFYZBhc1GqWFw2m7nYFgcxXYTDFet8aTFptEsrCdJtl6kRWf6kiBHGE6HnegI3+teF+yHclcVYTabf/RHfgIKcmD7O7DnQ8jb4S8+EhbG8phoPoty8k1E7bMpOrDRJLopCc5E4hxxxFW5iXOdJcIejsMIw2ELw2HzvY6whWGz2bEZNgwMMAxshh3DEYOR0g7DMDAwsOXuxPC4MZpc6XvPMODMcSg+FtrnCouApp3OL+d9Da5ySMoEZ4KvrDQfCg+F1q7NBs0vePbVyW9895AltoToc7/bZ4t8JzFC1by7f4IWCnKg/DQkpEHsuQdOV5ZC/u7Q223aybc/AAoPQ2kexDaFhBa+MncF5O6oe/26NGkHjhjf6+ITcOYoRnQSJLbylXmr4NiW0NtNvhwi432vS09C4UFwxkPS+efLcXSj7z/EUAQco0I4tR8ioiHlghM3J7b5JlQJRW3HKDwCUmvpf6GITfW1DeePkc0Ozbudr1Pd/0IR3bj2Y9SiO1SfCDmdA2W1P3KhTnUdowv7X9FhKKl7wp5a1XWMaul/IanrGNXW/0JR1zGqrf+FqrZjdDF/I5p3pW/6tUTYI0Lf5g+owVyq53K5iIqK4r333uPWW2/1l48YMYKioiKWL19eY5309HTGjRvH2LFj/WXZ2dksW7aMbdu21ahfWVlJZWWlf7m4uJi0tLR6kTjN3jibBV8vsDQGEaulRKVwWdxltE5oTZfkLnRN6UrTmKbBV5RLR/EJOLbR94Und7vvC0PRYXINk+2tstjZ9np2FeziSPERckuP4W0oMwuKiFzi/nXXv0hyJgWv+B/UYC7VO3XqFB6PhyZNmgSUN2nShD179tS6Tm5ubq31c3Nza60/ffp0Jk+e/MME/ANrFtOMTHsq9vLa77cwgIhwO9VXDlVVX2JlhJMbfn52qabuI4SZLmyNWxEZHYeBQVlhPkbJ8VrbBIgIs/kvSarymriqvHgNO8cdrfwVU1xHifCehUbpRMclA1BeXID5nTOhF35FcYTZ/PeHeLwmrirfJVdHIy/3127sOo7TWwJxLYhu5DsbUVF2Bu/3nOVw2G3+S9S8pu/eGIBcZxu8hq8bJ7jyiK4qwoxpQnSy72yYu+IsVSe+BqM6zsAvVGE2g/AwGwa+E1DV7RbGtMFrjwQguvIkUZX5eKOSiErxPfvGW+XGdXQr1d/PjO+0a7MZOM6doTXx7V+As3Gt8ThisRkQXlFAZOlRTGcjwlPa+Nf1HtkU0JZxwQsbBrV+J0xshRF1bgSm/LTvjI8jFlLano/v+Fbw1hxxqm2/+DXKgJhzl8xWlkD+Hgh3QmqH85+5IAc8Lt/ZLJsd7BE4wqOIjIjz/TgbExEWiTPMSVR4FI0jG9PY2ZjEyEQaRzYmKvwHeriq/HTFNYW4wdBu8PkyTxWpxUdJNU1+ntjSX+b+/A/kVRaR134wxWYVZ1xnKP72XxTn78SFicv04sIb8K/vt970je6avt9Z0xGNmXwFXtM35mvmfY3pcWM2boO3+ix12UnfKEko7I7As98F+6GqAhpddv4s9dnC0EeyDFvg2e/Cg+AqhfgWEJngK6ssgaIQR7LA12712eQzR6GiyHcmOerclx13OZz+NvR2ky737Q/wTUtfXuBrs/ostafyfzdCltja93cKoOwkZmmebx/En5tUxOuBk7V/x/heCRkQceExOu5bTsg4XydvFxDi+ei45udHGyuK4cwRX/zVoy/gGx3wVoXWbkyT8yMJrnIoPAD28O/0vxxf/wtFVBLEnvseVuWCgn3n+t/5Ry74+l9ZaO3WdYxS2n2n/50Jrd26jlHS5b79AVCS6+t/oajrGCW2Cuh/lNb+HL461XWMaut/oajrGNXW/0JV2zGqrf99V3JbwgzL7xoKScOK9n9hwoQJjBs3zr9cPeJUH9zT9h7uaXuP1WGIiDQ89jBfsvGdsvBrJ9ICaHFheZtbf7SwRETkp8vSxCkpKQm73U5eXuAZu7y8PFJTU2tdJzU1NaT6ERERRERYe+2kiIiIiIg0bJbeSe1wOOjevTuffvqpv8zr9fLpp5+SlZVV6zpZWVkB9QE++eSTOuuLiIiIiIj8uyy/VG/cuHGMGDGCHj160LNnT+bOnUtZWRkjR44EYPjw4TRv3pzp06cD8Pjjj3PNNdfwxz/+kUGDBrFkyRI2btzI/PnzrfwYIiIiIiLyE2Z54nT33Xdz8uRJnnnmGXJzc+nSpQsfffSRfwKIw4cPY7OdHxjr3bs3ixcv5umnn2bixIlkZmaybNkyPcNJRERERET+Yyx/jtOPrT49x0lERERERKwTSm6gp0WKiIiIiIgEocRJREREREQkCCVOIiIiIiIiQShxEhERERERCUKJk4iIiIiISBBKnERERERERIJQ4iQiIiIiIhKEEicREREREZEglDiJiIiIiIgEocRJREREREQkCCVOIiIiIiIiQShxEhERERERCUKJk4iIiIiISBBhVgfwYzNNE4Di4mKLIxEREREREStV5wTVOcL3ueQSp5KSEgDS0tIsjkREREREROqDkpIS4uPjv7eOYV5MevUT4vV6OX78OLGxsRiGYXU4FBcXk5aWxpEjR4iLi7M6HKnn1F8kVOozEir1GQmV+oyEqj71GdM0KSkpoVmzZths338X0yU34mSz2WjRooXVYdQQFxdneceRhkP9RUKlPiOhUp+RUKnPSKjqS58JNtJUTZNDiIiIiIiIBKHESUREREREJAglThaLiIggOzubiIgIq0ORBkD9RUKlPiOhUp+RUKnPSKgaap+55CaHEBERERERCZVGnERERERERIJQ4iQiIiIiIhKEEicREREREZEglDiJiIiIiIgEocTJAvPmzaNTp07+h35lZWWxcuVKq8OSBmTGjBkYhsHYsWOtDkXqqWeffRbDMAJ+2rZta3VYUs8dO3aMe++9l8aNG+N0OunYsSMbN260Oiyppy677LIaf2cMw2D06NFWhyb1lMfjYdKkSbRs2RKn00nr1q2ZMmUKDWWuujCrA7gUtWjRghkzZpCZmYlpmixatIghQ4awZcsW2rdvb3V4Us9t2LCBV199lU6dOlkditRz7du3Z9WqVf7lsDD9yZe6FRYW0qdPH6699lpWrlxJcnIy+/bto1GjRlaHJvXUhg0b8Hg8/uWdO3fSv39/7rzzTgujkvps5syZzJs3j0WLFtG+fXs2btzIyJEjiY+PZ8yYMVaHF5T+F7XA4MGDA5anTZvGvHnz+PLLL5U4yfcqLS1l2LBhvPbaa0ydOtXqcKSeCwsLIzU11eowpIGYOXMmaWlpLFiwwF/WsmVLCyOS+i45OTlgecaMGbRu3ZprrrnGooikvlu/fj1Dhgxh0KBBgG/U8i9/+QtfffWVxZFdHF2qZzGPx8OSJUsoKysjKyvL6nCknhs9ejSDBg3ihhtusDoUaQD27dtHs2bNaNWqFcOGDePw4cNWhyT12IoVK+jRowd33nknKSkpdO3alddee83qsKSBcLlcvPXWWzzwwAMYhmF1OFJP9e7dm08//ZS9e/cCsG3bNtauXcvAgQMtjuziaMTJIjt27CArK4uKigpiYmJYunQpV155pdVhST22ZMkSNm/ezIYNG6wORRqAXr16sXDhQq644gpOnDjB5MmT6du3Lzt37iQ2Ntbq8KQe+vbbb5k3bx7jxo1j4sSJbNiwgTFjxuBwOBgxYoTV4Uk9t2zZMoqKirj//vutDkXqsaeeeori4mLatm2L3W7H4/Ewbdo0hg0bZnVoF8UwG8rdWD8xLpeLw4cPc+bMGd577z1ef/11Vq9ereRJanXkyBF69OjBJ5984r+3qV+/fnTp0oW5c+daG5w0CEVFRWRkZDB79mxGjRpldThSDzkcDnr06MH69ev9ZWPGjGHDhg188cUXFkYmDcGAAQNwOBz87W9/szoUqceWLFnC+PHjmTVrFu3bt2fr1q2MHTuW2bNnN4gTNBpxsojD4aBNmzYAdO/enQ0bNvCnP/2JV1991eLIpD7atGkT+fn5dOvWzV/m8Xj4/PPPeemll6isrMRut1sYodR3CQkJXH755ezfv9/qUKSeatq0aY2Td+3ateOvf/2rRRFJQ3Ho0CFWrVrF+++/b3UoUs+NHz+ep556invuuQeAjh07cujQIaZPn67ESS6e1+ulsrLS6jCknrr++uvZsWNHQNnIkSNp27YtTz75pJImCaq0tJScnBzuu+8+q0OReqpPnz588803AWV79+4lIyPDooikoViwYAEpKSn+G/5F6lJeXo7NFjjFgt1ux+v1WhRRaJQ4WWDChAkMHDiQ9PR0SkpKWLx4MZ999hkff/yx1aFJPRUbG0uHDh0CyqKjo2ncuHGNchGA3/zmNwwePJiMjAyOHz9OdnY2drudoUOHWh2a1FNPPPEEvXv35rnnnuOuu+7iq6++Yv78+cyfP9/q0KQe83q9LFiwgBEjRuiRBxLU4MGDmTZtGunp6bRv354tW7Ywe/ZsHnjgAatDuyjq4RbIz89n+PDhnDhxgvj4eDp16sTHH39M//79rQ5NRH4ijh49ytChQykoKCA5OZmf/exnfPnllzWmDxapdtVVV7F06VImTJjA73//e1q2bMncuXMbzE3bYo1Vq1Zx+PDhBvPFV6z14osvMmnSJB555BHy8/Np1qwZDz30EM8884zVoV0UTQ4hIiIiIiIShJ7jJCIiIiIiEoQSJxERERERkSCUOImIiIiIiAShxElERERERCQIJU4iIiIiIiJBKHESEREREREJQomTiIiIiIhIEEqcREREREREglDiJCIidTIMg2XLllkdRlD9+vVj7Nixlm3/v/7rv1i8eLF/ub7ut1OnTpGSksLRo0etDkVEpMFR4iQicok6efIkDz/8MOnp6URERJCamsqAAQNYt26d1aH5HTx4EMMwvvdn4cKFvP/++0yZMsWSGFesWEFeXh733HOPJdsPRVJSEsOHDyc7O9vqUEREGpwwqwMQERFr3HHHHbhcLhYtWkSrVq3Iy8vj008/paCgwOrQ/NLS0jhx4oR/+fnnn+ejjz5i1apV/rL4+HicTqcV4QHwwgsvMHLkSGw2689Fut1uwsPDv7fOyJEj6d69O7NmzSIxMfFHikxEpOGz/q+8iIj86IqKilizZg0zZ87k2muvJSMjg549ezJhwgRuueWWOtc7cuQId911FwkJCSQmJjJkyBAOHjwYUOf111+nXbt2REZG0rZtW/785z/736seQVqyZAm9e/cmMjKSDh06sHr16lq3Z7fbSU1N9f/ExMQQFhYWUOZ0OmtcqnfZZZcxdepUhg8fTkxMDBkZGaxYsYKTJ08yZMgQYmJi6NSpExs3bgzY3tq1a+nbty9Op5O0tDTGjBlDWVlZnfvj5MmT/POf/2Tw4ME13jt16hS33XYbUVFRZGZmsmLFioD3V69eTc+ePYmIiKBp06Y89dRTVFVVBXyGuXPnBqzTpUsXnn32Wf+yYRjMmzePW265hejoaKZNm0ZhYSHDhg0jOTkZp9NJZmYmCxYs8K/Tvn17mjVrxtKlS+v8XCIiUpMSJxGRS1BMTAwxMTEsW7aMysrKi1rH7XYzYMAAYmNjWbNmDevWrSMmJoYbb7wRl8sFwNtvv80zzzzDtGnT2L17N8899xyTJk1i0aJFAW2NHz+eX//612zZsoWsrCwGDx78g490zZkzhz59+rBlyxYGDRrEfffdx/Dhw7n33nvZvHkzrVu3Zvjw4ZimCUBOTg433ngjd9xxB9u3b+edd95h7dq1PProo3VuY+3atURFRdGuXbsa702ePJm77rqL7du3c9NNNzFs2DBOnz4NwLFjx7jpppu46qqr2LZtG/PmzeONN95g6tSpIX/OZ599lttuu40dO3bwwAMPMGnSJHbt2sXKlSvZvXs38+bNIykpKWCdnj17smbNmpC3JSJySTNFROSS9N5775mNGjUyIyMjzd69e5sTJkwwt23bFlAHMJcuXWqapmm++eab5hVXXGF6vV7/+5WVlabT6TQ//vhj0zRNs3Xr1ubixYsD2pgyZYqZlZVlmqZpHjhwwATMGTNm+N93u91mixYtzJkzZwaNOTs72+zcuXON8muuucZ8/PHH/csZGRnmvffe618+ceKECZiTJk3yl33xxRcmYJ44ccI0TdMcNWqU+atf/Sqg3TVr1pg2m808e/ZsrfHMmTPHbNWqVY1ywHz66af9y6WlpSZgrly50jRN05w4cWKNffnyyy+bMTExpsfj8X+GOXPmBLTbuXNnMzs7O2A7Y8eODagzePBgc+TIkbXGW+2JJ54w+/Xr9711REQkkEacREQuUXfccQfHjx9nxYoV3HjjjXz22Wd069aNhQsX1lp/27Zt7N+/n9jYWP+IVWJiIhUVFeTk5FBWVkZOTg6jRo3yvx8TE8PUqVPJyckJaCsrK8v/OiwsjB49erB79+4f9PN16tTJ/7pJkyYAdOzYsUZZfn6+//MtXLgwIPYBAwbg9Xo5cOBArds4e/YskZGRQbcfHR1NXFycf1u7d+8mKysLwzD8dfr06UNpaWnIM9716NEjYPnhhx9myZIldOnShd/+9resX7++xjpOp5Py8vKQtiMicqnT5BAiIpewyMhI+vfvT//+/Zk0aRIPPvgg2dnZ3H///TXqlpaW0r17d95+++0a7yUnJ1NaWgrAa6+9Rq9evQLet9vt/5H4v8+FkyRUJyi1lXm9XsD3+R566CHGjBlTo6309PRat5GUlERhYWHQ7Vdvr3pbF8Nms/kvI6zmdrtr1IuOjg5YHjhwIIcOHeLDDz/kk08+4frrr2f06NE8//zz/jqnT58mOTn5omMRERHd4yQiIhe48sor65wMoVu3buzbt4+UlBTatGkT8BMfH0+TJk1o1qwZ3377bY33W7ZsGdDWl19+6X9dVVXFpk2bar1P6MfUrVs3du3aVSP2Nm3a4HA4al2na9eu5Obm1pk81aVdu3Z88cUXAYnRunXriI2NpUWLFoAvGb1wRsHi4uI6R76+Kzk5mREjRvDWW28xd+5c5s+fH/D+zp076dq1a0gxi4hc6pQ4iYhcggoKCrjuuut466232L59OwcOHODdd9/lD3/4A0OGDKl1nWHDhpGUlMSQIUNYs2YNBw4c4LPPPmPMmDH+y8smT57M9OnTeeGFF9i7dy87duxgwYIFzJ49O6Ctl19+maVLl7Jnzx5Gjx5NYWEhDzzwwH/8c3+fJ598kvXr1/Poo4+ydetW9u3bx/Lly793coiuXbuSlJQU8rOvHnnkEY4cOcJjjz3Gnj17WL58OdnZ2YwbN84/rfl1113Hm2++yZo1a9ixYwcjRoy4qJG7Z555huXLl7N//36+/vprPvjgg4CktLy8nE2bNvHzn/88pJhFRC51ulRPROQSFBMTQ69evZgzZw45OTm43W7S0tL45S9/ycSJE2tdJyoqis8//5wnn3yS22+/nZKSEpo3b871119PXFwcAA8++CBRUVHMmjWL8ePHEx0dTceOHQOmCgeYMWMGM2bMYOvWrbRp04YVK1bUmPntx9apUydWr17N7373O/r27YtpmrRu3Zq77767znXsdjsjR47k7bff5uabb77obTVv3pwPP/yQ8ePH07lzZxITExk1ahRPP/20v86ECRM4cOAAN998M/Hx8UyZMuWiRpwcDgcTJkzg4MGDOJ1O+vbty5IlS/zvL1++nPT0dPr27XvR8YqICBjmdy+gFhER+Q85ePAgLVu2ZMuWLXTp0sXqcH4Qubm5tG/fns2bN5ORkWF1OEFdffXVjBkzhl/84hdWhyIi0qDoUj0REZF/Q2pqKm+88QaHDx+2OpSgTp06xe23387QoUOtDkVEpMHRiJOIiPxofoojTiIicmlQ4iQiIiIiIhKELtUTEREREREJQomTiIiIiIhIEEqcREREREREglDiJCIiIiIiEoQSJxERERERkSCUOImIiIiIiAShxElERERERCQIJU4iIiIiIiJB/H/+uGVdA00OUgAAAABJRU5ErkJggg==", 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" ] @@ -78,31 +78,26 @@ "# Define x-axis range\n", "x = np.linspace(3, 8, 1000)\n", "\n", - "# Prior distribution\n", - "prior = norm.pdf(x, mu0, sigma0)\n", + "# Generate random samples for histograms\n", + "prior_samples = norm.rvs(loc=mu0, scale=sigma0, size=1000)\n", + "likelihood_samples = norm.rvs(loc=ybar, scale=sigma / np.sqrt(n), size=1000)\n", + "posterior_samples = norm.rvs(loc=mu_n, scale=sigma_n, size=1000)\n", "\n", - "# Likelihood distribution (centered at sample mean)\n", - "likelihood = norm.pdf(x, ybar, sigma / np.sqrt(n))\n", - "\n", - "# Posterior distribution\n", - "posterior = norm.pdf(x, mu_n, sigma_n)\n", - "\n", - "# Plot\n", + "# Plot histograms\n", "plt.figure(figsize=(10, 6))\n", - "plt.plot(x, prior, label=\"Prior\", linestyle=\"--\")\n", - "plt.plot(x, likelihood, label=\"Likelihood\", linestyle=\"-.\")\n", - "plt.plot(x, posterior, label=\"Posterior\", linestyle=\"-\")\n", - "plt.title(\"College Students Sleep Hours\")\n", + "plt.hist(prior_samples, bins=30, density=True, alpha=0.5, label=\"Prior\")\n", + "plt.hist(likelihood_samples, bins=30, density=True, alpha=0.5, label=\"Likelihood\")\n", + "plt.hist(posterior_samples, bins=30, density=True, alpha=0.5, label=\"Posterior\")\n", + "plt.title(\"Hours College Students Sleep\")\n", "plt.xlabel(\"Sleep Time (hours)\")\n", - "plt.ylabel(\"Density\")\n", + "\n", "plt.legend()\n", - "plt.show()\n", - "\n" + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -112,7 +107,7 @@ " Prior Data (Sample Mean) Posterior\n", "0 Precision 1.0 44.444 45.444\n", "1 SD 1.0 0.150 0.148\n", - "2 Mean 7.0 4.844 4.892\n" + "2 Mean 5.5 4.844 4.859\n" ] } ],