472 lines
279 KiB
Plaintext
472 lines
279 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9b437a81-b193-48ae-91bf-48edcfb12e18",
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"metadata": {},
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"outputs": [],
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"source": [
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"#pip install numpy matplotlib scipy"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"id": "a4ea5fe4-eaa9-4cc4-8677-385a68577332",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"import scipy.stats as stats"
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]
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},
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{
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"cell_type": "markdown",
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"id": "df08071e-cd3c-49dd-8623-baf38082eab0",
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"metadata": {},
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"source": [
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"Generate a normal distribution with sample of an experiment"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"id": "280f78b3-4338-49ec-8929-732d429762db",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Generate 1000 random numbers from a normal distribution\n",
|
|
"mu, sigma = 3, 6 # mean and standard deviation\n",
|
|
"data = np.random.normal(mu, sigma, 1000)\n",
|
|
"mean_sample = data.mean().item()\n",
|
|
"# Create a histogram of the data\n",
|
|
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
|
|
"title = \"Histogram with random numbers from: mu = %.2f, std = %.2f\" % (mu, sigma)\n",
|
|
"plt.axvline(x=mean_sample , color='m', linestyle='--', label='mu sample = %.2f' % (mean_sample))\n",
|
|
"plt.legend()\n",
|
|
"plt.title(title)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "0df9c2e5-ae6d-48c0-93a4-12a6e70240c2",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Show the approximation with the normal distribution\n",
|
|
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
|
|
"xmin, xmax = plt.xlim()\n",
|
|
"x = np.linspace(xmin, xmax, 100)\n",
|
|
"p = stats.norm.pdf(x, mu, sigma)\n",
|
|
"plt.plot(x, p, 'k', linewidth=2)\n",
|
|
"title = \"Fit results: mu = %.2f, std = %.2f\" % (mu, sigma)\n",
|
|
"plt.title(title)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f3c0c504-e041-4d85-8da0-3ef766f8e87a",
|
|
"metadata": {},
|
|
"source": [
|
|
"Generate for the distribution of mu_sample"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"id": "f7118230-fc88-4a71-b813-2daa0c63c97c",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
|
|
"metadata": {},
|
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"output_type": "display_data"
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}
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],
|
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"source": [
|
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"# Generate 1000 random numbers from the first normal distribution\n",
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"mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n",
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"data = np.random.normal(mu1, sigma1, 1000)\n",
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"\n",
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"# Create a histogram of the data\n",
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"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
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"\n",
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"# Add a graph of the first normal distribution used to generate the data\n",
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"xmin, xmax = -1, 5\n",
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"x = np.linspace(xmin, xmax, 100)\n",
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"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
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"plt.plot(x, p1, 'k', linewidth=2)\n",
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"\n",
|
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"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
|
|
"mu2, sigma2 = 1, 0.4\n",
|
|
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
|
|
"plt.plot(x, p2, 'r', linewidth=2)\n",
|
|
"\n",
|
|
"# Add vertical lines at x = 1 and x = 3 with labels\n",
|
|
"plt.axvline(x=1, color='b', linestyle='--', label='mu theoretical distribution')\n",
|
|
"plt.axvline(x=3, color='m', linestyle='--', label='mu in sample')\n",
|
|
"\n",
|
|
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
|
|
"plt.title(title)\n",
|
|
"plt.xlim(xmin, xmax)\n",
|
|
"plt.legend()\n",
|
|
"\n",
|
|
"# Show the plot\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"id": "8b4766b1-6fb5-487b-b552-790f43f83707",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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2lGb79u0kJyfz1ltv4eXlZdk/atQoXnrppVLvm5GRwZAhQ/D19S12ZFthtnxfzMzMLBCvtfL8n12+fJk33niD119/nbCwsFKvA1X7fzZzqKSlU6dOxVar20pcXFyRfceOHWPv3r0lPuHJyckAPP3008ybN4/bb7+dOnXq0K9fP4YOHWr3BCYuLo7x48czdepUfvzxR3r06MFdd93FP/7xD8uHWWVYf4BB/gdj4WpM8/6rV69W+lqV5ePjQ9++fW16zvDwcEuzyP333897773HbbfdxrFjx4iIiCjxfr6+vmRnZxfZn5WVZbnd+md5ji2vqrwGLl68SGZmJo0aNSpyW5MmTWyetHTr1s0m5ynreazocwhqVfS4ceN48skn2bFjB927d7fL38taRf7PTCYTKSkp1KpVq9LXO3/+PAMHDiQ4OJhffvkFg8FQ5n0iIyOJjIys9DVtyVb/Z5X5mw0bNoxvv/2Wxx57jAkTJtCnTx/uvfde7r///jITmFOnTgEU+T/z9PQsNUE3Go088MADHDx4kD/++IOoqKgy47Tl+6Kvry85OTnF3lae5/G1114jJCSEZ555pszrgG3+Xg6VtNhbcU+MyWTitttu4+WXXy72Puaan9q1a7N7926WLVvGH3/8wR9//MHMmTMZMWIE33//PUCJE3WVp42/NJ988gmjRo3it99+Y/ny5Tz77LNMmTKFzZs3U7du3Uqds6Q3s5L2K1Zt+KU9zvK8SZaX0Wgs99wmISEhJX5jKM3999/Pq6++ym+//caYMWNKPC4yMpJVq1ahKEqBx5+UlARgebMxv/mb91tLSkoiJCSkQrUsZvZ4DdjDxYsXy/V6DwgIICAgoMTby3oey/PmXhxzsmDuE2D+e5R0HaDS14LK/59V5r0kJSWF22+/nWvXrrFu3bpyx52ZmUlKSkq5ji0tsbeFyMjIcv0trF8fhRPApKQkS1+zivD19WXt2rWsWrWKJUuW8OeffzJ37lx69+7N8uXLbfreZvb444+zePFifvzxR3r37l2u+9jyfTEyMhKj0UhycjK1a9e27M/JyeHy5culvoaOHTvG119/zbRp0zh37pxlf1ZWFrm5uSQkJBAUFERISIhN/58dYnK5yrDVTJ4NGjQgLS2Nvn37FrtZf1Py8vJi0KBBfPHFF5w4cYIxY8bwv//9j+PHjwNQs2ZNQJ0cyZo5C6/K42nZsiWvvfYaa9euZd26dZw9e5YZM2ZU8NHaRs2aNYs8Rijf46yIxMREy7fAsraNGzdW6hrmasmy3rTbtGlDRkYGhw4dKrB/y5YtltsB6tSpQ1hYGNu3by9yjq1bt1qOq4yyXgPFvYbCwsLw9fXl2LFjRW47cuRIpWMpSceOHcv19/r4449LPU+LFi3w8PAo8jzm5OSwe/fuSj+P5gnjzDWrer2eli1bFvv32rJlC/Xr1y/QXFpdKvpekpWVxaBBgzh69CiLFy+mWbNm5b7W3Llzy/1/Zm9t2rRh586dmEymAvu3bNmCn5+f5Uuk+e9f+O927tw5zpw5U+nXh16vp0+fPkydOpWDBw/y7rvv8vfff7Nq1Sqg5PfpevXqART5P8vNzSU+Pr7Y+7z00kvMnDmTTz/9lOHDh5c7Rlu+L5b0PG7fvh2TyVTq83j27FlMJhPPPvsscXFxlm3Lli0cPXqUuLg43nrrLcC2/89OW9Pi7+8PqP/U5rbIyhg6dCiTJ09m2bJlRfq7XLt2jYCAADw8PLh8+XKBalu9Xk+rVq2A/Cov82iNtWvXctdddwGQnp5uqYkp7+Oxlpqaip+fX4F27pYtW6LX6wtUtV26dIlLly4RExNToT4PldGgQQPWrVtHTk6OJYtfvHgxiYmJZfZVqAhbtt1eunSJWrVqFXnT+fbbb4GCvedTUlJISkoiMjLSUp1/991388ILL/DFF1/w+eefA+q34hkzZlCnTh3LCAJQ+wV9//33JCYmWr4Frly5kqNHj/LCCy+U6/FYK+9rwN/fv8jrx2Aw0L9/fxYuXMjp06ctSfihQ4dYtmxZhWMpi636tAQHB9O3b19++OEHXn/9dUviMHv2bNLS0hgyZIjl2IyMDE6fPk1oaKhldMvFixeLNPlev36dadOmERoaSvv27S3777//fiZMmMD27dstr4MjR47w999/889//rN8D9zGgoKCCA0NZe3atTz//POW/V988UWRY41GI8OGDWPTpk389ttvdOnSpULX0qpPS1JSEikpKTRo0MDS7+f+++/nl19+4ddff+X+++8H1P/d+fPnM2jQIEstZfPmzbnpppv4+uuvGTNmjKUW5Msvv0Sn01nuWxFXrlwhJCSkwD7zh6n5/6yk9+kOHToQFhbGjBkzGD16tOV9cdasWcV+wfvoo4/4+OOPeeWVVyo8+tSW74u9e/cmJCSEL7/8kjvuuMOy/8svv8TPz4+BAwda9hX+jGnRogULFiwocs7XXnuN69ev8+9//9vymViR/+eyOG3SYn7TefbZZ+nfvz8Gg4EHHnigwud56aWXWLRoEXfeeSejRo2iffv2pKens2/fPn755RcSEhIIDQ3lscce48qVK/Tu3Zu6dety6tQpPvvsM9q0aWMZBtuvXz9iYmJ49NFHeemllzAYDHz33XeEhYVx+vTpUuNo0KABNWrUYMaMGQQGBuLv70/nzp3Zs2cP48aNY8iQITRu3Ji8vDxmz56NwWDgvvvus9y/okOeq+Kxxx7jl19+YcCAAQwdOpQTJ07www8/WF6g1n7//Xf27NkDqN869u7dyzvvvAPAXXfdZUn8imPLttsffviBGTNmMHjwYOrXr8/169dZtmwZK1asYNCgQQWqZhcsWMDo0aOZOXOmZdmBunXr8vzzz/PRRx+Rm5tLx44dWbhwIevWrePHH38sUHX8yiuvMH/+fG699Vaee+450tLS+Oijj2jZsiWjR48uEJe5c3NCQkKJsf/999/leg20b9+ev/76i6lTpxIVFUVcXBydO3fmzTff5M8//6RHjx48/fTT5OXl8dlnn9G8eXP27t1b4Fp79+5l0aJFABw/fpyUlBTL36t169YMGjSo1OfZVn1aQJ0SvGvXrvTs2ZMnnniCM2fO8Mknn9CvX78Cfcm2bt3KrbfeyqRJkyyd0adPn87ChQsZNGgQMTExJCUl8d1333H69Glmz55doMr86aef5ptvvmHgwIH885//xNPTk6lTpxIeHs6LL75YIKZevXpVaMhzVTz22GO8//77PPbYY3To0IG1a9cWOzX/iy++yKJFixg0aBBXrlzhhx9+KHB7WUNWbV2L8vnnn3Pt2jVLk8Hvv//OmTNnAHjmmWcsXwQmTpzI999/T3x8vOX/4P777+fmm29m9OjRHDx4kNDQUL744guMRiNvvvlmget89NFH3HXXXfTr148HHniA/fv38/nnn/PYY48VmJogISGBuLg4Ro4cWeqSAm+99RZr165l4MCB1KtXj+TkZL744gvq1q1L9+7dgZLfp+Pi4njnnXcYM2YMvXv3ZtiwYcTHxzNz5swiCfqCBQt4+eWXadSoEU2bNi3y97rttttKnY7A1n1a3n77bcaOHcuQIUPo378/69at44cffuDdd98tkMQV/owJDQ1l8ODBRc5pniak8G3l/X8uU7nHGdlRRSeXUxRFycvLU5555hklLCxM0el0ZQ7HM08uV5zr168rEydOVBo2bKh4eXkpoaGhSteuXZWPP/7YMlzxl19+Ufr166fUrl1b8fLyUmJiYpQxY8YUmUl1x44dSufOnS3HTJ06tVxDnhVFUX777TelWbNmioeHh+Xxnjx5UnnkkUeUBg0aKD4+PkpISIhy6623Kn/99VeB+1Z0yHPhmULNz/FHH31UYL956Gbh4baffPKJUqdOHcXb21vp1q2bsn379mIfU0kTARb+e9rbtm3blCFDhigxMTGKt7e34u/vr7Rr106ZOnVqgRk1FSX/9Vg4PqPRqLz33ntKvXr1FC8vL6V58+bKDz/8UOz19u/fr/Tr10/x8/NTatSooTz00EPK+fPnixwXGhpa5vDM8r4GDh8+rNxyyy2Kr6+vQqHJ5dasWaO0b99e8fLyKnVyudKGv2oxMeC6deuUrl27Kj4+PkpYWJgyduzYIpNvmV+j1sOAly9frtx2221KRESE4unpqdSoUUPp16+fsnLlymKvk5iYqNx///1KUFCQEhAQoNx5553KsWPHihzXvn37cg3PLOn/pqT3OvPfwnq4bUZGhvLoo48qwcHBSmBgoDJ06FAlOTm5yGM1D8MuaatupQ17t34PNL83FJ688sqVK8qjjz6q1KpVS/Hz81N69uxZ4mfDggULlDZt2ije3t5K3bp1lddee63AEHNFUZR9+/YVmJagJCtXrlTuvvtuJSoqSvHy8lKioqKU4cOHF5kOo7j3abMvvvhCiYuLU7y9vZUOHToUO7mc+W9d0lbe6Rts6euvv1aaNGlimVz1008/tcxkXjjusuIraUZcRSnf/3NZdIpSDV8ZhBBFHDx4kObNm7N48eIC1bDCMV2/fp2QkBCmTZtmmZRROL4vvviCl19+mRMnTthlQkVRvZy2I64Qzm7VqlV06dJFEhYnsXbtWurUqcPjjz+udSiiAlatWsWzzz4rCYuLkJoWIYQQQjgFqWkRQgghhFOQpEUIIYQQTkGSFiGEEEI4BUlahBBCCOEUnGJyOZPJxLlz5wgMDLTZ9P1CCCGEsC9FUbh+/TpRUVEVWjm7JE6RtJw7d67IolhCCCGEcA6JiYk2WdzVKZIW8zoFiYmJBAUFaRyNcHfp6WBelPTcObixHIkQmjGmG9kYpS6O1/VcVwz+tl+RWIjKSE1NJTo62mYLjzpF0mJuEgoKCpKkRWjOeoX6oCBJWoT2jAYj/qgvxKCgIElahMOxVdcO6YgrhBBCCKfgFDUtQjgSDw8YOTK/LITWdB46wkeGW8pCuCqnmMY/NTWV4OBgUlJSpHlICCGEcBK2/vyW74lCCIemKAp5eXkYjUatQxFCFGIwGPDw8Ki26UgkaRGighQFMjLUsp8fyNRB9pOTk0NSUhIZ5idclEgxqZXmOr28IEX18vPzIzIyEi8vL7tfS5IWISooIwMCAtRyWpqMHrIXk8lEfHw8BoOBqKgovLy8ZHLJEihGhYxDamLn19QPnUGeJ2F/iqKQk5PDxYsXiY+Pp1GjRjaZQK40krQIIRxSTk4OJpOJ6Oho/Pz8tA7HoSlGhTzyAPDx8ZGkRVQbX19fPD09OXXqFDk5Ofj4+Nj1ejLkWQjh0Oz9zU0IUTXV+T8q7wZCCCGEcAqStAghhBDCKVQ4aVm7di2DBg0iKioKnU7HwoULy7zP6tWradeuHd7e3jRs2JBZs2ZVIlQhhBBlGf3IaAYPHqx1GBUya9YsatSoYbPzrV69Gp1Ox7Vr1yp0P+vPtISEBHQ6Hbt377ZZXGaxsbFMmzat2Ova+1rOrsJJS3p6Oq1bt2b69OnlOj4+Pp6BAwdy6623snv3bp5//nkee+wxli1bVuFghRBCqOz5oWpPxX2IDhs2jKNHj2oTUAmio6NJSkqiRYsWZR5b0b/Ftm3beOKJJ6oYYUElJX72uJaWKjx66Pbbb+f2228v9/EzZswgLi6OTz75BICmTZuyfv16Pv30U/r371/sfbKzs8nOzrb8npqaWtEwhbAbgwHuv88EChgM0sIqHIAOPGpqOxg0Jyen0vN0+Pr64uvra+OIqsZgMBAREWHTc5qfo7CwMJuetzTVea3qYPd33E2bNtG3b98C+/r378+mTZtKvM+UKVMIDg62bNHR0fYOU4hy81m3gvkb6zJ/VSg+C37WOhy3k55e8paVVf5jMzPLd2xF9erVi2eeeYbnn3+emjVrEh4ezjfffEN6ejqjR48mMDCQhg0b8scff1juU9y35IULF5Y6L01cXBwAbdu2RW/Qc/ujt+PbwBdu3OXjjz8mMjKSWrVqMXbsWHJzcy33zc7O5p///Cd16tTB39+fzp07s3r16gLn/7//+z+aN2+Ot7c3sbGxli+eZrGxsbz99tuMGDGCoKAgy7f59evX06NHD3x9fYmOjubZZ58l/cYT2atXL06dOsULL7yATqezPL7iHv/vv/9Ox44d8fHxITQ0lHvuucdy2+zZs+nQoQOBgYFERETw4IMPkpycXOJzVZxjx45xyy234OPjQ7NmzVixYkWB2wvXnly9epWHHnqIsLAwfH19adSoETNnzizyt9DpdPTq1QuAUaNGMXjwYN59912ioqJo0qSJ5bkrXNuUlJTE7bffjq+vL/Xr1+eXX36x3FZcc9fu3bvR6XQkJCSwevVqRo8eTUpKiuV5nTx5crHXOn36NHfffTcBAQEEBQUxdOhQLly4YLl98uTJtGnThtmzZxMbG0twcDAPPPAA169fr9Dzay92T1rOnz9PeHh4gX3h4eGkpqaSWfhd44aJEyeSkpJi2RITE+0dphBlUxT46CMYMACSkuDqVXjwQXjpJcjL0zo6txEQUPJ2330Fj61du+RjC1cYx8YWf1xlfP/994SGhrJ161aeeeYZnnrqKYYMGULXrl3ZuXMn/fr14+GHH67STL9bt24F4K+//iIpKYlff/3VctuqVas4ceIEq1at4vvvv2fWrFkF+hKOGzeOTZs2MWfOHPbu3cuQIUMYMGAAx44dA2DHjh0MHTqUBx54gH379jF58mRef/31Iv0RP/74Y1q3bs2uXbt4/fXXOXHiBAMGDOC+++5j7969zJ07l/Xr1zNu3DgAfv31V+rWrctbb71FUlISSUlJxT62JUuWcM8993DHHXewa9cuVq5cSadOnSy35+bm8vbbb7Nnzx4WLlxIQkICo0aNKvdzZzKZuPfee/Hy8mLLli3MmDGDf/3rX6Xe5/XXX+fgwYP88ccfHDp0iC+//JLQ0FCg9L/FypUrOXLkCCtWrGDx4sWlnv++++5jz549PPTQQzzwwAMcOnSoXI+na9euTJs2jaCgIMvz+s9//rPYx3333Xdz5coV1qxZw4oVKzh58iTDhg0rcNyJEydYuHAhixcvZvHixaxZs4b333+/XLHYnVIFgLJgwYJSj2nUqJHy3nvvFdi3ZMkSBVAyMjLKdZ2UlBQFUFJSUiobqhBVk5amKA88oChq6lJ069tXUS5d0jpKl5KZmakcPHhQyczMLLC/pD8BKModdxQ8h59fycf27Fnw2NDQ4o+rqJ49eyrdu3e3/J6Xl6f4+/srDz/8sGVfUlKSAiibNm1SFEVRZs6cqQQHBxc4z4IFC5TS3qLj4+MVQNm1a1eB/SNHjlTq1aun5OXlWfYNGTJEGTZsmKIoinLq1CnFYDAoZ8+eLXC/Pn36KBMnTlQURVEefPBB5bbbbitw+0svvaQ0a9bM8nu9evWUwYMHFzjm0UcfVZ544okC+9atW6fo9XrL37FevXrKp59+WuCYwo+/S5cuykMPPVTiYy9s27ZtCqBcv35dURRFWbVqlQIoV69eLfb4ZcuWKR4eHgWegz/++KPAZ1rh53fQoEHK6NGjiz1faX+L8PBwJTs7u8D+ws8BoDz55JMFjuncubPy1FNPlfh4du3apQBKfHy8oijFv4YKX2v58uWKwWBQTp8+bbn9wIEDCqBs3bpVURRFmTRpkuLn56ekpqZajnnppZeUzp07F/vYFaXk/1VFsf3nt90bQSMiIgpUPQFcuHCBoKAgh2vDFKJY8fEweDDs3QtAOn4EoFZ3pxmC8Temwl9/QceOsGABtG6tYbCuLy2t5NsMhoK/l9ZiUHg+rISESodURKtWraxiMlCrVi1atmxp2Weufa5ok0ZJFKNC2q4bT4wCzZs3x2D1ZERGRrJv3z4A9u3bh9FopHHjxgXOkZ2dTa1atQA4dOgQd999d4Hbu3XrxrRp0zAajZZzd+jQocAxe/bsYe/evfz444/5sSmKZUmGpk2bluvx7N69m8cff7zE23fs2MHkyZPZs2cPV69exWQyAWrTR7Nmzco8/6FDh4iOjiYqKsqyr0uXLqXe56mnnuK+++6z1JQNHjyYrl27lnmtli1blquvT+Hrd+nSxeadrM2P27rLRbNmzahRowaHDh2iY8eOgNqkFBgYaDkmMjLSZq/VqrJ70tKlSxeWLl1aYN+KFSvKfIEI4RDOnIFOneDSJfX3gAD45icYfuP2JUtgxH3qp2N8PHTtCps2gdWHlrCtiqz1ZK9jy+Lp6Vngd51OV2CfuS+H+cNWr9ejKEqB+1j3QbHF9c3XSktLw2AwsGPHjgKJDUBABdvD/As9aWlpaYwZM4Znn322yLExMTHlPm9pX2jT09Pp378//fv358cffyQsLIzTp0/Tv39/cnJyyh98Bd1+++2cOnWKpUuXsmLFCvr06cPYsWP5+OOPS71f4eeoMswzzlq/Rqry+ihLaa8frVW4T0taWhq7d++2ZIDx8fHs3r2b06dPA2p/lBEjRliOf/LJJzl58iQvv/wyhw8f5osvvmDevHm88MILtnkEQtjTJ5/kJyyNGsGWLTBoUP7t3bvD9u1g/saZkQHvvFP9cQqnFhYWxvXr1y0dVoEyv2Wbv70bjcYKXatt27YYjUaSk5Np2LBhgc08WqZp06Zs2LChwP02bNhA48aNiyQ61tq1a8fBgweLnLdhw4aWeL28vMqMuVWrVqxcubLY2w4fPszly5d5//336dGjBzfddFOFawGaNm1KYmJigT41mzdvLvN+YWFhjBw5kh9++IFp06bx9ddfA5X/W1grfP3NmzdbaqbMI4Cs4y38+ijP82p+3Nb9RA8ePMi1a9fKVUPlCCqctGzfvp22bdvStm1bAMaPH0/btm154403APVJNScwoPaqXrJkCStWrKB169Z88sknfPvttyUOdxbCYaSlwY3RAXh7w7p1UNw/dnQ0rF0L5g7nv/6q1tAIUU6dO3fGz8+PV155hRMnTvDTTz+VOQln7dq18fX15c8//+TChQukpKWU61qNGzfmoYceYsSIEfz666/Ex8ezdetWpkyZwpIlSwB48cUXWblyJW+//TZHjx7l+++/5/PPPy+2c6e1f/3rX2zcuJFx48axe/dujh07xm+//WbpiAtq08PatWs5e/Ysl8xfCAqZNGkSP//8M5MmTeLQoUPs27ePDz74AFBrbLy8vPjss884efIkixYt4u233y7XYzfr27cvjRs3ZuTIkezZs4d169bx6quvlnqfN954g99++43jx49z4MABFi9ebEkqivwtUsr3t7A2f/58vvvuO44ePcqkSZPYunWr5Xlr2LAh0dHRTJ48mWPHjrFkyZJiR3OlpaWxcuVKLl26VGwn7759+9KyZUseeughdu7cydatWxkxYgQ9e/Ys0tTnqCqctPTq1QtFUYps5n+wWbNmFRk616tXL3bt2kV2djYnTpyoUC9vITTzww9gfvN58MH8pKQ4vr5gnsDJaISvvrJ/fMJlhISE8MMPP7B06VJatmzJzz//bBmyWhIPDw/+85//8NVXX1Enug7DXxxe6vHWZs6cyYgRI3jxxRdp0qQJgwcPZtu2bZYmnHbt2jFv3jzmzJlDixYteOONN3jrrbfKfO9u1aoVa9as4ejRo/To0cPyhda678hbb71FQkICDRo0KHEOkV69ejF//nwWLVpEmzZt6N27t2WETlhYGLNmzWL+/Pk0a9aM999/v8wmmsL0ej0LFiwgMzOTTp068dhjj/Huu++Weh8vLy8mTpxIq1atuOWWWzAYDMyZMwco+LeIiooq0h+oPN58803mzJlDq1at+N///sfPP/9sqf3w9PTk559/5vDhw7Rq1YoPPviAdwrV6Hbt2pUnn3ySYcOGERYWxocffljkGjqdjt9++42aNWtyyy230LdvX+rXr8/cuXMrHK9WdErhhlQHlJqaSnBwMCkpKQQFBWkdjnAHigItW8KBA+rvO3fCjdrF9PT8obBpaVZ9Ic6dg3r11OHPtWvD6dNqDY2olKysLOLj44mLi7P7cvfOzrojbkDbAHSGkud3EcLWSvtftfXnt0znKURxVq3KT1i6dbMkLKWKisqfKCQ5GebNs198QgjhhiRpEaI4n32WX37mmQI3GQxwxx3qVqRPolXbfYFzCGFPOjAEGzAEGywz4grhirRdrEIIR3TqFCxapJajouDeewvc7OOjjnQuVrdu0KYN7N4N27apo406d7ZntEKg0+vwa+SndRhC2J3UtAhR2JdfgnlOgiefhEJzFpRKpytYMyO1LUIIYTOStAhhLTMTvvlGLXt6QimzcpZo+HC4MbMo8+bB+fO2i08IIdyYJC1CWPv5Z7hyRS0PHQrFLE2fnq6OGPL3L2EVYF9feOwxtZybCzcmoBLCXhSjwvWd17m+8zqK0eEHhApRaZK0CGGmKKV2wLWWkaFuJXrqqfzFbWbMADtOLy4EAKYbmxAuTJIWIcy2bFE70IK6+GFVOtDWqwd33aWWk5Lgt9+qHJ4QQrg7SVqEMFu8OL/85JNVP99TT+WXSxxuJIQQorwkaRHCbMWK/PIdd1T9fD17qv1bzOd2/MmnhRNJSEhAp9OVubCis9LpdCxcuFDrMISDkaRFCICrV9XVmgFatCi2A26FeXvDLbeo5XPn4PDhqp9TiBuio6NJSkqiRYsWWociRLWRpEUIUKftN8/Ncttttjuv9bmsa3KEqCKDwUBERAQeHjJHqHAfkrQIAfDXX/nlvn1LPVSvV1t+evbMHyBUIutzWV9DVJox3VjylmUs/7GZ5Tu2onr16sUzzzzD888/T82aNQkPD+ebb74hPT2d0aNHExgYSMOGDfnjjz8s95k1axY1atQocJ6FCxei05U8J3+B5iEdbDi4gaCOQaz8eyUdOnTAz8+Prl27cuTIkRLPkZOTw7hx44iMjMTHx4d69eoxZcoUy+1Tp06lZcuW+Pv7Ex0dzdNPP01aWlqRuBcvXkyTJk3w8/Pj/vvvJyMjg++//57Y2Fhq1qzJs88+i9GY/1zGxsby9ttvM3z4cPz9/alTpw7Tp08v9XlNTExk6NCh1KhRg5CQEO6++24SEhJKvY9wPZKiCwH5tSCenvlNOiXw9YXVq8t53pYt1RWfk5PVO+XmVmyGXVHEuoB1Jd4WckcIrZa0svy+ofYGTBnFjwMO7hlM29X5C2Fujt1M7qXcIsf1UnpVOMbvv/+el19+ma1btzJ37lyeeuopFixYwD333MMrr7zCp59+ysMPP8zp06fx86v69Ps6vQ6fGHV13ddef41PPvmEsLAwnnzySR555BE2bNhQ7P3+85//sGjRIubNm0dMTAyJiYkkJiZabtfr9fznP/8hLi6OkydP8vTTT/Pyyy/zxRdfWI7JyMjgP//5D3PmzOH69evce++93HPPPdSoUYOlS5dy8uRJ7rvvPrp168awYcMs9/voo4945ZVXePPNN1m2bBnPPfccjRs35rZiajpzc3Pp378/Xbp0Yd26dXh4ePDOO+8wYMAA9u7di5eXV5WfQ+EcJGkRIiEBjh9Xy126QECA7c6t10OfPuqkddevw9at6vpEwqW1bt2a1157DYCJEyfy/vvvExoayuM3Zlh+4403+PLLL9m7dy8333yzTa/97rvv0rNnTwAmTJjAwIEDycrKwsfHp8ixp0+fplGjRnTv3h2dTke9evUK3P78889byrGxsbzzzjs8+eSTBZKW3NxcvvzySxo0aADA/fffz+zZs7lw4QIBAQE0a9aMW2+9lVWrVhVIWrp168aECRMAaNy4MRs2bODTTz8tNmmZO3cuJpOJb7/91lL7NHPmTGrUqMHq1avp169fJZ8t4WwkaRFi5cr8chlNQ5XSt6+atIDaRCRJS5X0SOtR8o2FVt3ullzKc12oae/mBNslD61a5df2GAwGatWqRcuWLS37wsPDAUhOTrbZNYu7dmRkpOU6MTExRY4dNWoUt912G02aNGHAgAHceeedBRKAv/76iylTpnD48GFSU1PJy8sjKyuLjIwMSw2Rn5+fJWExP7bY2FgCrJL/8PDwIo+1S5cuRX6fNm1asY9pz549HD9+nMDAwAL7s7KyOHHiRGlPh3AxkrQIYd1BthxJS3o6xMaq5YQEdTr/UhXu1zJpUkUjFFYM/oayD7LzsWXxLNQEqNPpCuwz1xaYbnT+1uv1KIWGxOfmFm2qKoliVMg8ngmAhz7/bb3wdQpr164d8fHx/PHHH/z1118MHTqUvn378ssvv5CQkMCdd97JU089xbvvvktISAjr16/n0UcfJScnx5K0lPVYzftKiqE80tLSaN++PT/++GOR28LCwip9XuF8JGkR7s1kyq9pCQpSZ8Ith0uXKnCNmBho3BiOHoXNm9VmokLfGIV7CwsL4/r166Snp+N/Iwuu6PwrlV1zKCgoiGHDhjFs2DDuv/9+BgwYwJUrV9ixYwcmk4lPPvkE/Y0e5/PmzavUNYqzefPmIr83bdq02GPbtWvH3LlzqV27NkFBQTaLQTgfGT0k3NuePfkZyK23gr2Gj5rb6fPyYM0a+1xDOK3OnTvj5+fHK6+8wokTJ/jpp5+YNWuW3a87depUfv75Zw4fPszRo0eZP38+ERER1KhRg4YNG5Kbm8tnn33GyZMnmT17NjNmzLDZtTds2MCHH37I0aNHmT59OvPnz+e5554r9tiHHnqI0NBQ7r77btatW0d8fDyrV6/m2Wef5cyZMzaLSTg+SVqEe7MehmzL+VkKs24ikvlaRCEhISH88MMPLF26lJYtW/Lzzz8zefJku183MDCQDz/8kA4dOtCxY0cSEhJYunQper2e1q1bM3XqVD744ANatGjBjz/+WGA4dFW9+OKLbN++nbZt2/LOO+8wdepU+vfvX+yxfn5+rF27lpiYGO69916aNm3Ko48+SlZWltS8uBmdUrgh1QGlpqYSHBxMSkqKvECFbfXrl59EHD4MTZqUeZf09PwBRmlp5ejTApCSAiEhanNUs2Zw4EDlY3YTWVlZxMfHExcXV+zIF5FPMSqk7VLnTwloG4DOUPL8Lo4gNjaW559/vsDoJOG8SvtftfXnt9S0CPeVlQXrbsz5Ubeu2u/EXoKDoVMntXzwoDqtvxBCiAqRpEW4r40b1cQF1KahUmYftQmZHVcIIapERg8J91XBoc5mej106JBfLrfbboN33lHLf/0FI0ZU4M5ClEIHej+9pezoZPp9UVmStAj3ZV3b0adPue/m6wvbtlXiejffrHaASU9Xr60o9q/dEW5Bp9fh36w8nauEcG7SPCTc0+XLsGOHWm7VCm7MUGpXXl7qKosASUlq3xZRJicYKyCEW6vO/1FJWoR7WrNGrekA+0zdXxLra1kvHyCKMM+qmpGRoXEkQojSmP9HC8+EbA/SPCTc05Yt+eUyVnUuLCNDHbUMamVJhRbpNde0gLp4oiiRwWCgRo0aljVr/Pz8LNPSi4IUo0LGcfWDw6+hn8MPeRauQVEUMjIySE5OpkaNGhgMtlsKoySStAj3tH17frmcU/ebKQqcOpVfrpAWLdRmopycgjGIYkVERAD2WVjQlSgmheykbAC8PbzR6SVpEdWnRo0alv9Ve5OkRbgfkym/P0tUlLpVFy8vaNNGrWU5cgRSU9U1j0SxdDodkZGR1K5du0ILCLqTN1a9gSHbwO3P3w7AvGnzMHobCxzz1q1vaRGacAOenp7VUsNiJkmLcD/Hj6sz1EL+2OXq1KFDftPQjh3qmkeiVAaDoVrfGJ1JSl4KhlwDplPqKsopuSkYDQWTFplRWLgK6Ygr3I91s4xWSUtxsQghhCiVJC3C/VShP4tNWF9TkhYhhCg3SVqE+7GeGa59++q//k035Q85qtQsdUII4Z4kaRHuxWiEnTvVcr16EBZW4VPodOqQ52bNKjmhrYcHtG2rluPj1YnuhKgKHaREp5ASneIU0/gLUVnSEVe4l8OH1YlWoNJNQ35+cOBAFePo0AE2bFDLO3ZAv35VPKFwZ0ZvI0unL9U6DCHsTmpahHuxbo7RohOumXXCJE1EQghRLpK0CPei9cih4q4tnXGFEKJcJGkR7sU6QahkJ9yMDGjeXN0qvSxOo0b5k8pJ0iKqyJBt4I6xd3DH2DswZMt8NsJ1SZ8W4T5ycmD3brXcqBHUqFGp0yhK/gLNlV7cVK9Xk6ZVq+DMGTh/HqppGmzhghQITgy2lAsb8/uYUu/+1aCv7BCUELYnNS3CfRw4ANnq+iyazM9SmDQRCSFEhUjSItyHo/RnKS4GSVqEEKJMkrQI9+EoI4fMZASREEJUiCQtwn2YazP0+vzJ3bQUGwshIWp5+/YqdJARQgj3IEmLcA9ZWbBvn1pu2hQCArSNB9TpdM01PsnJaodcIYQQJZKkRbiHPXsgL08tV7FpSKdTVwCoV6+S0/hbkyYiYQs6SKudRlrtNJnGX7g0GfIs3IMNV3b284OEhKqFY1G4M+6999roxMKdGL2N/P7t71qHIYTdSU2LcA+ONnLITEYQCSFEuUnSItyDuenFwwNat9Y2Fmt16uRPKiedcYUQolSStAjXl5YGhw6p5ZYtwcenSqfLzFRbmDp2VMtVYt0Z9+pVOHmyiicU7siQbaDf+H70G99PpvEXLk2SFuH6du8Gk0kt26BpyGRSK0W2b88/bZVIE5GoKgVqHa9FreO1ip3GXwhXIUmLcH07d+aXK7lIol1ZJy3WsQohhChAkhbh+vbvzy87Un8Ws1at8svWsQohhChAkhbh+syTygE0b65dHCWpWxeCb6zQax2rEEKIAiRpEa5NUfJrL2JjITBQ03CKpdNBixZqOTERUlK0jUcIIRyUJC3CtZ06pY4egvzEwBFZxyZNREIIUSxJWoRrs04AWra02WlDQ9XNZqxjkyYiUQlZQVlkBWVpHYYQdiXT+AvXZp0A2Chp8feHixdtcqp81rFJTYuoIKOPkQU/LNA6DCHsrlI1LdOnTyc2NhYfHx86d+7M1q1bSz1+2rRpNGnSBF9fX6Kjo3nhhRfIypJvBKIaWCctztI8JDUtQghRrAonLXPnzmX8+PFMmjSJnTt30rp1a/r3709ycnKxx//0009MmDCBSZMmcejQIf773/8yd+5cXnnllSoHL0SZzLUWHh7QpIm2sZQmJASiotTyvn0ynb8QQhSjws1DU6dO5fHHH2f06NEAzJgxgyVLlvDdd98xYcKEIsdv3LiRbt268eCDDwIQGxvL8OHD2bJlSxVDF6IMublw+LBabtIEvLxsctrMTLj9drX8xx/g62uT06q1LefOqdP5JyXlJzHCrY35fUyZxxiyDfR8sycAayatwehttHdYQmiiQjUtOTk57Nixg759++afQK+nb9++bNq0qdj7dO3alR07dliakE6ePMnSpUu54447SrxOdnY2qampBTYhKuzoUTVxAZt2wjWZYM0adbPJNP5m0hlXVFLWtSzC94cTvj+c46uOk5edp3VIQthFhWpaLl26hNFoJDw8vMD+8PBwDpu/0Rby4IMPcunSJbp3746iKOTl5fHkk0+W2jw0ZcoU3nzzzYqEJkRRduiEa1eFO+P2769dLMLhKYrChcMXOLj0IOfWn2MEIwBY98U6lNkKTfo0oemApgRHBWscqRC2Y/chz6tXr+a9997jiy++YOfOnfz6668sWbKEt99+u8T7TJw4kZSUFMuWmJho7zCFK3KWTrhm0hlXlNPpHaf5v+f+j0X/WsTxNccxGQtW+WVfz2bvwr3MfXIuSyct5WriVY0iFcK2KlTTEhoaisFg4MKFCwX2X7hwgYiIiGLv8/rrr/Pwww/z2GOPAdCyZUvS09N54oknePXVV9Hri+ZN3t7eeHt7VyQ0IYqy0xwtdtOsmTo7rqJI0iJKdG7fOZa9swzFmN9Z2yvAC27MoVi/R30ObzqMKU9NZM7sOsOS15dwzyf34F/LX4uQhbCZCtW0eHl50b59e1auXGnZZzKZWLlyJV26dCn2PhkZGUUSE4PBAKjVm0LYjfmD398f6tXTNpby8PWFhg3V8sGDYJTOlKKg1POprHh/hSVhCWsURq/ne/HAlw9Yjun5TE8emvkQnUZ2IqB2AAAZVzJY/u5y6esinF6Fm4fGjx/PN998w/fff8+hQ4d46qmnSE9Pt4wmGjFiBBMnTrQcP2jQIL788kvmzJlDfHw8K1as4PXXX2fQoEGW5EUIm0tLg/h4tdyiBRRTo+eQzDVCWVlw4oS2sQiHkpORw7J3l5F9PRuA6HbR3P3h3TTu3RiDd8H3Ut9gX9rc14Z7PrnHkrhcPH6RtZ+vlS+LwqlVeMjzsGHDuHjxIm+88Qbnz5+nTZs2/Pnnn5bOuadPny5Qs/Laa6+h0+l47bXXOHv2LGFhYQwaNIh3333Xdo9CiMIOHMgv26FpyM/P5qdUtWwJv/6qlvfvh8aN7XQh4UwUk8KqT1dx9ZTaNyW4TjC9/9kbvSH/vTbPu2gtim+wL/1f7c9v//qNvKw8jq85TkhsCG3ua1NdoQthU5Waxn/cuHGMGzeu2NtWr15d8AIeHkyaNIlJkyZV5lJCVI51fxYbd8L194f0dJueMl/hzrj33munCwlnsv2n7ZzacgoAL38v+r/aH++A/H5/Rh8j8+fPL/a+teJqcesLt7JiygoAtv5vKzWja1KvkxM0mQpRiJPUmQtRQc423NlM5moRhZxYd4Jd83YBoNPr6PNSH2rUrVGhc8R1iaPDgx3UXxT4+5O/uXL6io0jFcL+JGkRrsnZhjubNWgA5pFzsnCi27t06RJrP19r+b3z6M5Et4uu1LnaDmtL/W71AcjNzGXNtDXSv0U4HUlahGsyf+DXrq1uNpSVBQMHqpvN1/308FCHPgMcO6auGSDc1scff0xupjqrc8OeDWl5V/G1hvocPbe8dQu3vHUL+pzi39Z1Oh29nu9FzeiagNox99TWU/YJXAg7kaRFuJ7kZHUDuzQNGY2wdKm62WVUsjlmkyl/7SThdpKTk/nss88A0Hvo6TSyEzqdrthjdSYddbbXoc72OuhMxR8D4OHtQccRHS2/7/hpB4pJaluE85CkRbgeO3bCrRYyM64APvzwQzIyMgBoOqApAaEBNjlvvU71CG0YCsDl+MskbE6wyXmFqA6StAjX46ydcM2kM67bS0pKYvr06QAYvAw2HaKs0+nyO+UC23/ejsmmK38KYT+StAjX40o1LdIZ1y198MEHZN3oMNXs9mY2n34/un00tRurfb2unrrKL7/8YtPzC2EvkrQI12NdO9G8uXZxVFadOlCjhlqWmha3c/bsWWbMmAGAr68vre9tbfNr6HQ6OjyUX9syefJkjLJshHACkrQI12Iy5ddO1K8PAbbpB1CtdLr8JqKzZ+GqrNDrTqZMmUJ2tjpV/7hx4/CraZ/pl+u0qUN4U3Um80OHDjF37ly7XEcIW5KkRbiWU6fyp6t1xqYhM2kickunT5/mm2++ASAgIICXX37ZbtfS6XR0fCh/JNGbb75JXp4sqCgcmyQtwrVUQydcf39QFHXzt21Xg3zSGdctvffee+Tk5ADw7LPPEhoaWq77GX2M/LzoZ35e9DNGn/I380S1iiKyZSQAR48e5aeffqp40EJUI0lahGs5eDC/7Iz9WcysY7d+TMJlXbx4ke+++w6AwMBAXnzxxWq5bofh+X1bPvjgA5klVzg0SVqEazl0KL/ctKl2cVSVdezWj0m4rB9//JHcXHX22zFjxhASElIt141sEUm3bt0AOHjwINu2bauW6wpRGZK0CNdi/oDX6aBJE7tcIisLhgxRN5tP428WFga1aqllSVpcnqIozJw50/L7o48+WqH763P0dHu/G93e71biNP6leeSRRyxl6ziEcDSStAjXoSj5097HxoKvr10uYzTCL7+om11HiZprW5KSICXFjhcSWtu1axd79+4F4Oabb+amm26q0P11Jh0xG2OI2RhT6jT+JRkyZAh+fuoopZ9//plMWfNKOChJWoTrOHsWrl9Xy87cNGQmTURuw7p2Y/To0dV+/cDAQIYMGQJASkoKCxcurPYYhCgPSVqE63CV/ixmkrS4hezsbMuoHV9fX4YNG6ZJHNbJkjQRCUclSYtwHZK0CCe0aNEirly5AsC9995LcHCwJnHccsst1K9fH4C//vqL06dPaxKHEKWRpEW4DklahBPSumnITKfTMWrUKEDtGPy///1Ps1iEKImH1gEIYTOulrRER4OfH2RkSNLios6ePcufy/4EIKB2AHPT5jLv93maxTNy5EgmTZqEoijMmjWLV199FZ2u4h17hbAXqWkRrsP8wR4eDjVrahuLLej1YB5FEh9vx/HVQiuzZ89GMamTuTXu3RidXtsEISYmhj59+gBw4sQJ1q1bp2k8QhQmSYtwDVeuQHKyWrZzLYufH6SlqZuffdayy2d+LCYTHDtm54uJ6lR4bpbGvRtX+lxGbyPz5s1j3rx5GL2rNg5fOuQKRyZJi3AN1dg0pNOpaw75+6tlu5J+LS5r06ZNHD16FIDIlpEERQRV/mQ6df0ho48RqviavOeeeyydgefPn09aWlrVTiiEDUnSIlyDq/VnMZOkxWVZ12I06Wuf2Zsrw9fXl+HDhwOQnp7O/PnzNY5IiHyStAjXUI1JS3Y2jBqlbtnZdr2UJC0uKisri7lz5wLg6etJ/a71q3Q+fa6eztM603laZ/S5VX9bt24i+v7776t8PiFsRZIW4RqqMWnJy4Pvv1e3vDy7XgoaNgSPG4P8JGlxGStXruT6jdmb47rG4eFdtYGcOqOO+n/Xp/7f9dEZq95m2bFjR5rcWLtr3bp1XLx4scrnFMIWJGkRrsH8gR4YCFFR2sZiS56eauICcOSInRc7EtVlwYIFlnJclzgNIymeTqfjnnvuAcBkMvH7779rHJEQKklahPPLyIBTp9TyTTdVQ+/YamauOcrOhoQETUMRVWc0Glm0aBEAfn5+1GldR+OIijd48GBLWdYiEo5Ckhbh/I4cUVd4BtfqhGsm/VpcyqZNmyzNLQMGDKhy05C9dOzYkcjISACWL18uo4iEQ5CkRTi/w4fzy5K0CAdnXWthXZvhaPR6PXfffTegLuq4fPlyjSMSQqbxF67AVYc7m0nS4jIURbEkLQaDgYEDB7J+w3ptgwLG/D6m2P2JEYmW8sKFC7n33nurKyQhiiU1LcL5uXrSYp7KHyRpcXIHDhzgxIkTAPTs2ZOQkBCNIypdVMsoPP08AVi8eDG5ubkaRyTcnSQtwvmZP8i9vKB+1ea7KA8/P3XFgOTkapjGH9Spd2Ni1PKhQ/n9d4TTsVfTkNHbyK+zf+XX2b9WeRp/awZPAzHt1dfe1atXZS0ioTlJWoRzy8uDG1Oh06hR/pwmdqTTQViYulXbQCVzDVJKCpw/X00XFbZmnbSY+4vYhA6yg7PJDs6u8jT+hcXeHGspyygioTVJWoRzO3kSzFXWrtg0ZCb9WpxeYmIiO3bsAKBdu3bEmGvPHFx0+2g8PdUmooULF6JITZ/QkCQtwrlp0J8lOxvGjlU3u0/jb2b92KxHSwmnYc9RQ/pcPe1ntKf9jPY2mcbfmpefF3369AHUxGvnzp02Pb8QFSFJi3BuGiQteXnwxRfqZvdp/M2kpsXp2TNp0Rl1NF7amMZLG9tkGv/CZKI54SgkaRHOzdVHDpnJCCKnduXKFdasWQNA/fr1adGihcYRVcxdd91lKUvSIrQkSYtwbuYPcJ0Obizw5pLCwqBWLbUsSYvTWbJkCcYb60YNHjwYnZMtNREZGcnNN98MwP79+zl+/LjGEQl3JUmLcF6Kkt+/IzYWfH01DcfuzDVJ586po4iE03CWWXBLYx33b7/9pl0gwq3JjLjCeZ09C9evq2Xr5hNX1bQprL8xe+rhw9C5s7bxiHLJysrizz//BCA0NJSuXbtqHFHFjfl9DNeCrll+//i7jzna+GiBY74a9FU1RyXckdS0COflLv1ZzKQzrlNav349GRkZAAwcOBCDwaBxRJVTo24NgusEA3Dh8AVy0nM0jki4I0lahPNy9YUSC5OkxSktW7bMUh4wYICGkVRd3bZ1AVBMCmf3ntU4GuGOpHlIOC+NkhZfX4iPzy9XG+smsCNHqvHCoirMqyPrdDr69u1rl2sYvYws+maRpWwvddvW5cDiAwCc2XWGuC5xdruWEMWRpEU4L+ukpRpHDun1ar/fahcTAz4+kJUlE8w5iaSkJPbu3QtA+/btCQ0Ntc+F9JAenm6fc1uJahGF3kOPKc/Emd1n7H49IQqT5iHhvMy1DbVqgb0+DByJXp+fnJ04kb98gXBYK1assJT79eunYSS24enrSXjTcACun79OyjkZxSaqlyQtwjldv66OHoJqHzmUkwMvvaRuOdXdF9H8WPPy1HWXhEMzNw0B9O/f327X0efqaTOzDW1mtrH5NP6FRbeNtpSltkVUN0lahHOy7tNRzUlLbi58/LG6VXtlh3UzmDQROTSTyWRJWgICAiyTs9mDzqij6YKmNF3Q1C7T+Fszd8YFOLNTkhZRvSRpEc5Jo/4smrNO0CRpcWh79uzh4sWLAPTu3RsvLy+NI7KNWnG18An2AeDcvnOY8kwaRyTciSQtwjlpWNOiKRlB5DSshzq7Qn8WM51eR902am1LbmYuFw5f0Dgi4U4kaRHOybqWwZ2SlsaN88tS0+LQqqs/ixYKNBFJvxZRjSRpEc7J/IHt6QlxbjRXhL8/RN/oCHn4sLr+knA4aWlprL+x5EJcXBwNGjTQOCLbMte0gPRrEdVLkhbhfIxGOHZMLTdsCB5uNt2QuWbp6lW40WdCOJY1a9aQe6OXdv/+/Z1uVeey+IX4ERIbAsDFExfJSs3SOCLhLiRpEc7n1CnIzlbL7tQ0ZCb9Whyeq/ZnsWZpIlKkiUhUHzf7iipcgsb9WXx9Yf/+/HK1KzzsuUcPDYIQpTH3ZzEYDPTu3dvu1zN6GVny+RJLuTrUbVuXvQvU2X7P7JKkRVQPSVqE89E4adHroXnzar9sPhn27NBOnTrFkRs1YDfffDPBwcH2v6geUmNS7X8dKxHNIjB4GTDmGDmz6wyKorhcM5hwPNI8JJyPdZOIO83RYiZJi0Nz5VFD1jy8PIhqEQVAxpUMDh48qHFEwh1I0iKcj8YTy+XkwOTJ6lbt0/gDREVBQIBalj4tDkeL/iz6XD0tfmpBi59a2H0af2t12taxlK0ftxD2olMUxx8zmZqaSnBwMCkpKQQFBWkdjtBaeDgkJ0NEBCQlVfvl09Pzc4a0NHUUcrXr0AF27FDbqtLT1dWfheaMRiOhoaFcu3aNmjVrct9396E32D+JMGQZGDp0KADz5s3D6FM9/Vqunr7K/HHzATVBk8RFFGbrz2+paRHO5epVNWEB9xw5ZGZ+7CYTHD+ubSzCYufOnVy7dg2APn36VEvCoqUa0TXwr6Vm7evXrydHk6pH4U4q9R81ffp0YmNj8fHxoXPnzmzdurXU469du8bYsWOJjIzE29ubxo0bs3Tp0koFLNycu/dnMZN+LQ5p1apVlnJ1jBrSmk6nI7JlJAAZGRllfhYIUVUVTlrmzp3L+PHjmTRpEjt37qR169b079+fZPO330JycnK47bbbSEhI4JdffuHIkSN888031KlTp9jjhSiVu07fX5h1wib9WhyGddJy6623ahhJ9YlqGWUpWz9+IeyhwknL1KlTefzxxxk9ejTNmjVjxowZ+Pn58d133xV7/HfffceVK1dYuHAh3bp1IzY2lp49e9K6desqBy/ckCQtKqlpcTi5ubmsW7cOgIiICJq4SU2gJC2iOlUoacnJyWHHjh307ds3/wR6PX379mXTpk3F3mfRokV06dKFsWPHEh4eTosWLXjvvfcwGkvuKJadnU1qamqBTQjAfVd3LqxRIzDPiSFJi0PYtm0b6enpgNo05C5zlgRFBBFYOxCAjRs3kpUlU/oL+6lQ0nLp0iWMRiPh4eEF9oeHh3P+/Pli73Py5El++eUXjEYjS5cu5fXXX+eTTz7hnXfeKfE6U6ZMITg42LJFmxeIE8L8Ae3jAzEx2saiJR+f/IUiZeFEh+COTUNm5n4t2dnZJX6BFcIW7N613WQyUbt2bb7++mvat2/PsGHDePXVV5kxY0aJ95k4cSIpKSmWLTEx0d5hCmeQm5s/UqZxY3W4rwZ8fGDrVnXTdKSxufkhLU2Tod+iIC2TFpOniWWfLGPZJ8sweZqq9doAUa2kiUhUjwpN4x8aGorBYODChQsF9l+4cIGIiIhi7xMZGYmnpycGg8Gyr2nTppw/f56cnBy8vLyK3Mfb2xtvb++KhCbcQXw85OWpZQ2bhgwG6NhRs8vnu+km+OMPtXz4sDrpnNBEdnY2GzZsACA6Opr69etX6/UVg8KVRleq9ZrWpF+LqC4V+qrq5eVF+/btWblypWWfyWRi5cqVdOnSpdj7dOvWjePHj2My5Wf/R48eJTIystiERYgSSSfcgqQzrsPYsmWLpS/Hrbfe6jb9WcwCQgNo2LAhoD4XGRkZGkckXFWFF0wcP348I0eOpEOHDnTq1Ilp06aRnp7O6NGjARgxYgR16tRhypQpADz11FN8/vnnPPfcczzzzDMcO3aM9957j2effda2j0S4Po2n7zfLyYF//1stP/ccaJZ7F17tWWhG6/lZ9Ll6Gv/eGICjg45q0kTk0cADjqujqIZ8PIS6besWuP2rQV9Ve0zC9VQ4aRk2bBgXL17kjTfe4Pz587Rp04Y///zT0jn39OnT6K36GkRHR7Ns2TJeeOEFWrVqRZ06dXjuuef417/+ZbtHIdyDg9S05ObCyy+r5aef1jBpsX4OZK4WTf3999+WshadcHVGHW1ntQXg2B3HwLPaQyCqZRSHl6n/o+f2niuStAhhCxVOWgDGjRvHuHHjir1t9erVRfZ16dKFzZs3V+ZSQuSz/mBu3Fi7OBxF7dpQowZcuyY1LRrKzMy0vL/Vr1+fGDcd1Wbdr+XcvnMaRiJcmWsvjCFch6LAoUNqOTo6f8VCd6bT5de2nD6tLpwoqt3GjRsta+6421Bna341/agRXQOAi8cvkpMh6xAJ25OkRTiHS5fUxRLBvdccKsz6uTh6VLs43Jg7z89SmLm2RTEpnD9Y/NxdQlSFJC3COchMuMWTfi2ak6QlnzQRCXuTpEU4BwcZOeRwrJMWc/OZqDZpaWmWlY2bNGlClJvPlSNJi7C3SnXEFaLaWX8gN22qXRyORuZq0dTQT4aSd2PCQ32cnjG/j9E4Im35BPkQEhvClYQrXD55mey0bLwDZKJQYTuStAjn4CDDnUGdut/cIqDpNP4ADRqAh4c6U7AkLdXu3N782gTrqeyrm8nTxMp3V1rKWopqGcWVhCsoJoWk/UnE3hyraTzCtUjzkHAO5g/kwEDNp6s3GKBXL3WzWp1CG56ecGMmUo4ehVJWTxe2Z90EEtVCu9elYlBIbplMcstkFIO2i2dKE5GwJ0lahOPLzFTXHQK1lsXNpkgvk7nmKSsLTp3SNhY3kpqayqUTlwCoGVMT3xq+GkfkGCJbRMKNf1FJWoStSdIiHN+xY+o8LeAQ/Vlyc2H6dHXLzdU6Ggo+J9JEVG02bNiAYlJfl5EtIjWNRZeno9GSRjRa0ghdnrZJvXeAN6H1QwG4cuoKWdezNI1HuBZJWoTjs+6E6wDDnXNyYNw4dctxhPmzZASRJtasWWMpa9k0BKDP09Phqw50+KoD+jzt39YjmkeoBQWZr0XYlPavbiHK4kCdcB2SjCDSxNq1ay1ly4e0AAomcecPSNIibEeSFuH4ZLhz6aSmpdqlp6ezbds2AILrBONX00/jiBxLRLP8JC5pf5KGkQhXI0mLcHzm2gMPD3WIrygoKCh/RJXUtFSLTZs2WeZn0bo/iyPyCfKhZr2aAFw6eUnWIRI2I0mLcGwmU/709A0bqkN8RVHmGqjLl9V1moRdWTcNad2fxVFFNleTOcWkcOHQBY2jEa5Ckhbh2E6dUofygvRnKY00EVUr60640p+leNY1UNJEJGxFkhbh2KybO6Q/S8lk2HO1ycrKYsuWLQAERgQSEBqgcUSOyVzTApB0QJIWYRsyjb9wbA423BnA2xsWL84vOwSpaak2W7duJTs7Gyj4wawlk6eJNa+vsZQdgV9NP4LrBJNyNoWLxy+SkZGBn590WBZVI0mLcGwOONzZwwMGDtQ6ikJk2HO1se7P4iidcBWDwrmOjjf7bGTzSFLOpmDKM7F582Z69+6tdUjCyUnzkHBsDljT4pCiotR1mUBqWuzMuj+Lo9S0OCrr58f6eROisiRpEY7NXGsQFaUO7XUAubkwa5a6OcQ0/qCux2RO6k6dgowMbeNxUbm5uWzcuBGAunXrEhgeqHFEKl2ejriVccStjNN8Gn9r1jVR1jVUQlSWJC3CcV26lD9814E64ebkwOjR6uYQ0/ibmZ8jRVHXaxI2t2PHDjJuJIS33HILOgdZvFOfp+fmf9/Mzf++2SGm8TcLCAsgsLaa2G3evNnSF0iIynKcV7cQhTlgfxaHJp1x7c66iaNnz54aRuI8zLUtWVlZbN26VeNohLOTpEU4LhnuXDEy7NnurJs4JGkpH2kiErYkSYtwXNIJt2KkpsWujEYj69evByA8PJzGjRtrHJFzkM64wpYkaRGOS5qHKqZBA3U8NkhNix3s2bOH1NRUwLH6szi6wIhA/Gv5A7Bx40ZyHab3unBGkrQIx2X+4A0MzF8QUJTM01Ndnwng6FEwGrWNx8VY1xLccsstGkbiXHQ6nWWpg/T0dHbu3KlxRMKZSdIiHFNmJsTHq+WbblKH9IqymWuksrLUoc/CZqQ/S+VJvxZhK5K0CMd07Jg6dBccrhOutzfMm6duDjONv5l0xrULk8lk+bANCQmhefPmGkdUkMnTxPqX17P+5fUOM42/NenXImxFpvEXjsmBO+F6eMCQIVpHUYLCnXHvuEO7WFzIwYMHuXLlCgDdu3dHr3es73uKQSGxe6LWYZSoRt0a1K5dm+TkZNavX4/RaMRgMGgdlnBCjvWfJ4SZDHeuHKlpsQtpGqoanU5Hjx49AEhJSWHfvn0aRySclSQtwjE5cE1LXh7Mn69ueXlaR1NIkyb5ZRn2bDPWSYsjdsLVGXVEr48men00OqNj9v+yft6kX4uoLElahGMy1xJ4eKhDeR1IdjYMHapuDjcreVBQ/kgrqWmxCUVRLB+yAQEBtGnTRtuAiqHP1dP9w+50/7A7+lzHfFuXpEXYgmO+uoV7M5ngyBG13LChOpRXlJ+5iejy5fy1m0SlnThxgqSkJAC6deuGh4d0BayMli1bEhwcDKhJi2LuaC9EBUjSIhzPqVPqkF1wuKYhpyAz49qUozcNOQuDwUD37t0BuHjxIkfMX0yEqABJWoTjkU64VSOdcW1KOuHajvXzJ01EojIkaRGO5+DB/LLUtFSc9XNm/VyKSjF/uPr4+NChQweNo3Fu0q9FVJUkLcLxWH/QNmumXRzOyvo5k6SlShITE4m/MTPzzTffjLfDzSboXNq1a4efnx+gTjIn/VpERUnSIhzPgQP5ZWkeqriICKhZUy1bP5eiwqQ/i215enrStWtXAM6cOUNCQoK2AQmnI0mLcCyKkl87EBcH/v7axlMMLy+YOVPdvLy0jqYYOh2Yp5k/exauXdM0HGfmLEmLycPE5uc2s/m5zZg8HG8af2vSRCSqQpIW4VgSE+H6dbXsYOu7mHl6wqhR6uawo7GtnztpIqo084eqh4cHN998s8bRlEzxUIjvE098n3gUD8ducpGkRVSFJC3CsVg3Zzho0uIUrJ87aSKqlOTkZA7fGH3VoUMH/B2w1s8ZderUCa8bVZSStIiKkqRFOBYnSFry8mDJEnVzuGn8zSRpqbJ169ZZyo7cNATqNP5R26KI2hblsNP4m/n6+tKpUycAjh8/zrlz5zSOSDgTSVqEY7H+gHXQkUPZ2XDnnermcNP4m1k/d5K0VIqz9GcBdRr/nm/3pOfbPR12Gn9r1s+ndXIoRFlkPmrhWMz9L3Q6GTlUFeHhEBICV65In5ZKsiQtOpifOp9Fvy/SNiAnN+b3MZZyoleipfzW/97ib7+/+WrQV1qEJZyM46fkwn0UHjl0Yz4HUQnWI4jOnZMRRBV07do19uzZA0Ct2Fp4B8j8LLYUflM4Or3ajJV0IEnjaIQzkaRFOI7TpyEtTS07aH8WpyL9Wiptw4YNlonPIltEahyN6/Hy8yK0figAV09dJSs1S+OIhLOQpEU4DifohOtUJGmpNOv+LBHNIzSMxHVZP6/nD57XMBLhTCRpEY5DkhbbkqSl0qyTlshmUtNiD5HN859XaSIS5SVJi3AcTjByyKnICKJKSU9PZ/v27QDUqFsD3xq+GkfkmiKa5de0SNIiyktGDwnHYf5g1ekcenVnLy/4/PP8ssOqXRtq1YLLlyVpqYCNGzeSd2MCHmdpGjJ5mNg+Zrul7Ax8gnyoWa8mV09d5fLJy6SkpBAcHKx1WMLBSU2LcAwmExw6pJbr13fokUOenjB2rLo57DT+UHAE0fnz6vBnUaY1a9ZYylEtojSMpPwUD4VjA49xbOAxh5/G35r5+VVMChs2bNA4GuEMJGkRjuH0aUhPV8vSn8V2ZA2iClu9erWlLCOH7Mv6+bV+3oUoiSQtwjE4USdcoxFWr1Y3o1HraMognXErJCMjg61btwLQqFEj/Gs5x3pDOqOO2vtqU3tfbYefxt+adWdc6xouIUoiSYtwDE6UtGRlwa23qluWo08vIUlLhWzevJnc3FwAevbsqXE05afP1dPn1T70ebWPU0zjb+Zbw5ea0TUB2LFjB9fNK7wLUQLneXUL1yYjh+xDRhBViHUThTMlLc7M3ERkNBqlX4sokyQtwjGYP1D1eoceOeR0ateGUHXmUUlaymbdRCFJS/WIbClNRKL8JGkR2is8cshX5sWwKXMT0YUL6vBnUazMzEw2b94MQP369YmOjtY4Ivdg3a9FOuOKskjSIrR36hRkZKhlB+/P4pRkBFG5bNmyhZycHAB69eqlbTBuxK+mHzXq1gBg+/btpJtHEQpRDElahPacqBOuU5LOuOUiTUPaMfdrycvLY+PGjRpHIxxZpZKW6dOnExsbi4+PD507d7YMESzLnDlz0Ol0DB48uDKXFa5Kkhb7kqSlXKQTrnZkvhZRXhWexn/u3LmMHz+eGTNm0LlzZ6ZNm0b//v05cuQItWvXLvF+CQkJ/POf/6RHjx5VCli4ICdLWjw94cMP88sOT5KWMmVlZVn6s8TGxlKvXj2NI6oYxaCwa9QuS9nZWM88LJ1xRWkqnLRMnTqVxx9/nNGjRwMwY8YMlixZwnfffceECROKvY/RaOShhx7izTffZN26dVy7dq1KQQsXYz1yqEkTbWMpBy8veOklraOogNBQCAuDixclaSnB1q1bybox6Y4z1rKYPE0cvvew1mFUml+IH8FRwaScS2HTlk08+sujeHgX/Xj6atBXGkQnHEmFmodycnLYsWMHffv2zT+BXk/fvn3ZtGlTifd76623qF27No8++mi5rpOdnU1qamqBTbgo65FDDRqAj4+28bgqc21LcjJcuqRtLA7I+tu9dMLVhrmJyJRn4sLhCxpHIxxVhZKWS5cuYTQaCQ8PL7A/PDyc8+fPF3uf9evX89///pdvvvmm3NeZMmUKwcHBlk2GHrqwhATIzFTLTtA0BOrU/du2qZvDT+NvJiOISuXsnXB1Rh0hx0IIORbiVNP4W7Pu15K0P0nDSIQjs+vooevXr/Pwww/zzTffEGqe4KocJk6cSEpKimVLTEy0Y5RCU07WnwXUqfs7dVI3h5/G30z6tZQoJyfHMmIlJiaG2NhYbQOqBH2unv4v9qf/i/2dahp/a9ZJy7l95zSMRDiyCvVpCQ0NxWAwcOFCwaq7CxcuEBERUeT4EydOkJCQwKBBgyz7TCaTemEPD44cOUKDBg2K3M/b2xtvb++KhCac1b59+WUnSVqckvVza/2cC7Zt20bmjdq+nj17otM5Z02FswsIDSAoIojU86kkH00mLzuv2H4twr1VKCX38vKiffv2rFy50rLPZDKxcuVKunTpUuT4m266iX379rF7927Ldtddd3Hrrbeye/duafYRsGdPfrlVK+3icHUtW+aXrZ9z4fRNQ67Eul9L8tFkjaMRjqjCaez48eMZOXIkHTp0oFOnTkybNo309HTLaKIRI0ZQp04dpkyZgo+PDy1atChw/xo1agAU2S/clPkD1NvbKUYOOa2aNaFePXX24b171Q7QeudsRrA163lBpBOutiJbRnLkryOA2kQU1TKqjHsId1PhpGXYsGFcvHiRN954g/Pnz9OmTRv+/PNPS+fc06dPo5c3Q1EeGRlw7JhabtECPKQq2K5at1aTlrQ0iI9XR2u5sTG/j8GUZ2LVulUA+Nfy54MDH6A7KM1DWrGer0U644riVOpTYty4cYwbN67Y28qazXDWrFmVuaRwRfv3q9/4Qf1AFfbVujUsWqSW9+xx+6QFIPlYMnlZeYDaNCH9WbQVEBZAYHgg1y9cJ/mI9GsRRUmViNDO7t35ZUla7M/6OZZ+LQCc25M/SiWqlTRFOALz38GYa5T5WkQRksIK7Vh/cDpR0uLpCZMm5ZedhiQtRZzdd9ZSrtO6joaRVI1iUNj3wD5L2ZnVaVWHIyvUfi1n954t8HcZ8/uYUu8rM+a6PklahHacdOSQlxdMnqx1FJVQvz4EBKh9WqxrudxUXnYeFw6p3+QDIwIJrB2ocUSVZ/I0sf/B/VqHYRPWNV7n9pyDhzUMRjgcaR4S2jCZ1FEsADEx6ugWYV96ff7Q51OnwM3XADt/6DymPLVPVZ1WzlvL4mr8avpRM1p9P7h4/CI56TkaRyQciSQtQhsJCXD9ulp2oqYhUPOtAwfUzdyP2GlYP9fmpNFNndvrQv1ZTBB0Ooig00HgbK/JYkS1Vv8eikkh6aCMIhL5JGkR2rBuGmrTRrMwKiMzUx2h3aJF/rJJTsP6uXbzfi1n9+b3Z3H2+UAMOQYGjhvIwHEDMeQYtA6nyqxrvs7uOVvKkcLdSNIitOGknXCdnnTGBSAlJYVLx9XVrmvWq4lfTT+NIxLWIltEotOrw8+ta8SEkKRFaEOGO2ujZUswz0XixknLmjVrUEzqKBvpz+J4vAO8Ca2vLrJ7JeEKmdecrUpT2IskLUIb5g/MgAB1VIuoHv7+0LChWt6/H/LytI1HI3///bel7OxNQ66qwCii/VLbIlSStIjql5KidsQF9Zu/LPtQvcw1W1lZ+csouBlz0qLT6yyL9AnHYj0/izQRCTP5tBDVz3rUijQNVT8379eSnJzMvn3qRGyhDULxDvDWOCJRnPCm4eg91I8o6YwrzCRpEdVPOuFqy/o5d8NJ5latWmUpS38Wx+Xp40l4E3Uh3tSkVNIupmkckXAEMiOuqH5OnrR4esI//5lfdjpuXtOycuVKS9np52e5QTEoHLrnkKXsKqJaRZF0QJ2n5ezeszTp00TjiITWJGkR1c/8QanT5c/Q6kS8vOCjj7SOogqio9UZiK9edcukxdyfRe+hJ6JZhMbR2IbJ08Tu0bu1DsPm6rSuw46fdwBqvxZJWoQ0D4nqlZcHN/oT0LChOnpIVC+dLr+2JSkJLl7UNp5qdOrUKU6cOAFA+E3heHjL9zZHFtYozPI3Orf3HIriOrVIonIkaRHV69gxddQKOGXTEKhT9yckqJvTTeNv5qZNRAWGOrtI0xAAJvC/4I//BX+XmMbfzOBpsNSGpV9OJ+VsisYRCa1J0iKql5P3ZwF16v64OHVzumn8zSRpcalOuIYcA3c9fhd3PX6XS0zjb02GPgtrkrSI6uUCSYtLcMOkRVEUSydcf39/whqFaRyRKA/rGjHr9aKEe5KkRVQvSVocQ7NmYLjxjdxNkpZDhw6RlKSOROnRowcGT9eqkXBVteJqWebSObf3HCajC7V/iQqTpEVUL/MHZI0a6igWoQ0fH7jpJrV86BDk5GgbTzVYtmyZpdyvXz8NIxEVoTfoLbUt2WnZloUuhXuSpEVUn4sX4dyNNunWrfMX7hPaMNd05ebCwYPaxlINrJOW/v37axiJqKjodvlfcBJ3JWoYidCaJC2i+lg3Q7Rpo1kY4gbrv4GLNxFlZmayZs0aAOrWrUvTpk01jkhURN22dS3lMzvPaBiJ0JokLaL6WE8ZL/1ZtGf9N9i1S7s4qsHatWvJujHUfsCAAeikls+pBIQFUDO6JgDJR5PJTsvWOCKhFZlZSVSfbdvyy+3baxdHFXl4wNNP55edVrt2+eXt27WLoxq4etOQYlA4esdRS9kV1W1Xl6uJV1FMCmf3nKV+t/pahyQ04MxvucLZbN2q/vTzU0evOClvb5g+XesobCA0FOrXh5MnYedOtW+LUy6mVLY///wTAL1eT58+fTSOxvZMniZ2PLlD6zDsqm7buuz7TZ1NO3FnoiQtbkqah0T1uHhRnUIW1G/4Tl1F4UI6dVJ/ZmbCgQPaxmIniYmJHDqkLibYuXNnatasqXFEojIim0di8FKHqZ/ZdUam9HdTkrSI6mHdNGT+oHRSiqLmYBcvqmWn1rFjftn6b+RCrJuGBgwYoGEkdqSAd4o33ine4OyvyRJ4eHsQ2TwSgPRL6VxLvKZtQEITkrSI6mFuGgKnT1oyMqB2bXXLyNA6miqy/ltY/41ciLlpCFyzPwuAIdvAvQ/fy70P34sh23UnzavbLn8UUeJOGfrsjiRpEdXD+lu89bd7oa22bUF/423ABWta8vLy+OuvvwAICQmhQ4cOGkckqiK6bf58LWd2ydBndyRJi7A/Rcn/Fl+rlrrSoHAM/v7QooVa3r/fBaqOCtq6dSspKerKwH379sVgcN1aCHdQI7oG/qH+ACQdSCIvO0/jiER1k6RF2N+pU3DpxtTbHTvKTLiOxtxEZDS63HwtbtGfxY3odDrL7LjGHCNJB5I0jkhUN0lahP25UH8Wl2TdXOdi/Vqs+7PIekOuwXp2XOnX4n4kaRH2Z/1BKP1ZHI+Ldsa9fPky227002nRogV16tTROCJhC3Va10GnV2trpV+L+5GkRdifdMJ1bM2bq6s+g0t1xv3rr78sc3m46qghd+Qd4E3txrUBuJZ4jbSLaRpHJKqTJC3CvoxG2HFjps569SA8XNt4bMDDA0aOVDeXmCPP0zN/Sv8TJ+DyZW3jsRHrpiFX78+iGBRO9j7Jyd4nXXYaf2sy9Nl9SdIi7OvQIUhPV8suUsvi7Q2zZqmbt7fW0diIdRORC6xDpCgKy5cvB8DX15fu3btrHJF9mTxNbHl+C1ue34LJ06R1OHYnQ5/dlyQtwr6kE65zcLHOuHv27OHcuXMA9OrVCx9z85dwCaENQ/EOVL8xnNl9BmOuUeOIRHWRpEXYlwt2wlUUtfIoPd0FpvE3c7HOuIsWLbKU77zzTg0jqSYKGLIMGLIMLjuNvzW9QW8Z+pybkStDn92IJC3CvswdO3U6aN9e21hsJCMDAgLUzWXmYmvQAMwLCW7b5vTZmHXSMmjQIA0jqR6GbANDhw5l6NChLj2Nv7V6netZyqe2ntIwElGdJGkR9pOVBXv3quWmTSEwUNt4RMl0uvyasAsXINF5OzeeOXOGHTc6f7dt25bo6Ogy7iGcUXTbaPQe6kfYqa2nZNVnNyFJi7Cf3bsh78Y029KfxfFZ/42ceOjz4sWLLeW77rpLw0iEPXn5exHZQl31OS05jSsJVzSOSFQHSVqE/UgnXOfiIp1xrZuG7r77bg0jEfYW2znWUpYmIvcgSYuwH5lUzrlY/Y0UJ61pSUtLY+XKlQDUrVuXNm3aaBuQsKt6naRfi7txhamxhKMyf1v38oJWrbSNRZQtMpK8qGg8ziWibNuOzmgEJ1sVedmyZeTk5ABq05BOFud0aQFhAdSKq8Xl+MtcPHaRf8z6B/61/Es8/qtBX1VjdMIepKZF2Me1a3D0qFpu00ZNXITDy26l1rbo067DkSMaR1Nx1k1D0p/FPRQYRbRNaltcnSQtwj6sZ1V1sf4sBgPcf7+6OVlFRJmyWztvZ9y8vDyWLFkCQGBgIL169dI2oGqk6BVOdz3N6a6nUfTuNYpGmojcizQPCfvYtCm/7GL9WXx8YP58raOwjxyrpEXZuAndyJEaRlMxmzZt4vKNdZMGDBiAt8ussVA2k5eJDRM2aB2GJkIbhOJfy5/0y+mc23OO3MxcPH09tQ5L2InUtAj7WLMmv+zi6764kuzWncjTqd9lTKvWlHG0Y5GmIfek0+kstS3GXCNndstaRK5MkhZhezk5sHGjWq5bF+LitI1HlJvi5098rQ4AGI4dVieacxLmpMVgMHDHHXdoHI2oTtJE5D4kaRG2t307ZGaq5Z491dlWXUh6uvqQdLr8BaxdyeHaPfN/WbtWu0Aq4PDhwxy90fG7e/fuhISEaBxR9TJkGRh+13CG3zVcXX/IzUS1irI0CZ3edhqT0fVXunZXkrQI27NuGurZs+TjhEM6ZJ20rHGOJiKZUM69GTwN1G1bF4Cs1CySjyRrHJGwF0lahO1J0uLUjtXuhkmnvjWYVjtf0iL9WdyT9dDnhC0J2gUi7EqSFmFbeXmw4cYohogIaNRI23hEhWV6BpEY1g4A/YH9cOmSxhGVLjk5mY03+lA1a9aMBg0aaByR0EJM+xh0erUp+tQWWUDRVUnSImxr505IS1PLLtifxV0kxFjVkK1bp10g5fDLL79YPqAGDx6sbTBCMz5BPkQ0jwAg5VwKl+MvaxyRsAdJWoRtSdOQS4iPcZ5+LXPmzLGUhw0bpmEkQmsNuufXsp1Yd0LDSIS9SNIibMv6A86NZiR1NfF1e2BCrSVTHLhfy5kzZ1i/fj0ATZs2pWXLlhpHJLQU1zXO0kR0ct1JaSJyQZK0CNsxGvObEmrXhptu0jYeOzEY4I471M3VpvE3y/KpQVJYa/WXvXvg6lVtAyrB/PnzLR9Mw4YNc9sFEhW9wtkOZznb4azbTeNvzTfYlzqt6wBwPfk6F49e1DgiYWuStAjb2bMHUlPV8i23uGx/Fh8fWLJE3Xx8tI7Gfk7XV5uIdIoCN2ozHI00DalMXibWvrGWtW+sxeTl3nOUNOiR30R0fN1xDSMR9iBJi7Ad6c/iUk7Vc+x+LfHx8WzduhWANm3acJOL1uyJiom9ORa9h/rRdnL9SRST+9Y8uSJJWoTtSNLiUk7X62EpO+J8LXPnzrWU3bmWRRTkHeBN3XbqRHMZVzI4f/C8xhEJW6pU0jJ9+nRiY2Px8fGhc+fOlm87xfnmm2/o0aMHNWvWpGbNmvTt27fU44WTMpny+7OEhEDz5trGY0fp6eDvr26uOI2/WYZfKEmhLQDQ7dqZ3/TnIKRpKJ8hy8CQIUMYMmSIW07jX1jDHg0tZRlF5FoqnLTMnTuX8ePHM2nSJHbu3Enr1q3p378/ycnFT5u8evVqhg8fzqpVq9i0aRPR0dH069ePs2fPVjl44UD274crV9TyLbeA3rUr8TIy1M3VnY670a/FZMqfNNABHD58mD179gDQqVMn4mRRTjyyPfDI9tA6DIcQ0zEGg5eavJ3ceFLWInIhFf5kmTp1Ko8//jijR4+mWbNmzJgxAz8/P7777rtij//xxx95+umnLW3O3377LSaTiZUrV1Y5eOFApGnIJTlqvxbrpqEHHnhAw0iEI/Ly8yKmQwwAWSlZnNt7TuOIhK1UKGnJyclhx44d9O3bN/8Eej19+/Zl06ZN5TpHRkYGubm5pa7Cmp2dTWpqaoFNODhJWlzSqXq3WMqO0q9FURRL05BOp2Po0KEaRyQcUYNbZKI5V1ShpOXSpUsYjUbCw8ML7A8PD+f8+fJ1dvrXv/5FVFRUgcSnsClTphAcHGzZoqOjKxKmqG6KAmvXquXgYGjVStt4hM2kB4RzIUQdlaPbsd0hOvHs27ePw4cPA9C9e3fq1KmjcUTCEcW0j8HT1xOA+E3xGHONGkckbKFaOx68//77zJkzhwULFuBTygQXEydOJCUlxbIlJiZWY5Siwg4dgos3JnHq0cN1Z1xzU5Z+LXl5cGNhQi1Zd8CVpiFREg9vD+p1Uld+zknP4czuMxpHJGyhQklLaGgoBoOBCxcuFNh/4cIFIiIiSr3vxx9/zPvvv8/y5ctpVcY3cW9vb4KCggpswoGtXp1flqYhl7PD3+pvav231oB105Ber+f+++/XNB7h2Ao0Ea2VJiJXUKGkxcvLi/bt2xfoRGvuVNulS5cS7/fhhx/y9ttv8+eff9KhQ4fKRysc09Kl+eXevbWLo5ro9Wpu1rOnyw+S4tQpWJ57q+V34+KlpRxtfxs3biQ+Ph6A3r17U7t2bU3jcRg6uNDiAhdaXADXnIi6Uuq2qYuXvxcACZsTpH+kC6jw+Ljx48czcuRIOnToQKdOnZg2bRrp6emMHj0agBEjRlCnTh2mTJkCwAcffMAbb7zBTz/9RGxsrKXvS0BAAAEBATZ8KEITGRlgTmKjoqBtW23jqQa+vppXOFSLU6cgPh7imkSQmNCR6KRtGPbuhsRE0Kif2bfffmspP/zww6UeO+b3MfYOx2EYvY38/d7fWofhcAyeBhr0aMChPw+Rl53H3Llzefzxx7UOS1RBhb8nDhs2jI8//pg33niDNm3asHv3bv78809L59zTp0+TlJRkOf7LL78kJyeH+++/n8jISMv28ccf2+5RCO2sXAlZWWr5zjtddr0hd5OYeCNhiYN69eB4kzvzb1yyRJOYUlJSmDdvHgDBwcHSNCTK5aZ++cs7WCe9wjlVaiaicePGMW7cuGJvW13oK2hCQkJlLiGcxeLF+eU77yz5OOE0rl+HS5egcWM1YQE42vhObl09CQDl98Xonnyy2uOaM2cOGTdm9HvooYfw8/Or9hiE8wltEEqtuFpcjr/M1q1b2bt3b5n9KoXjcvEWeWFXipKftPj4QJ8+2sZTTdLTISxM3RxgBLDNXb+uJivmhAUgKaIt1/yj1F9WrtRkOmDrb8mPPfZYtV/fkRmyDNzzj3u45x/3yDT+heh0ugK1Lf/97381jEZUlSQtovJ27YJzN2aa7NMH3Oib76VL6uaKAgOL6bKi01maiHTZWfn9mKrJ7t272b59OwDt2rWjrRv0naoon1QffFJLnkrCnTXs2dAyrf/s2bPJMjdpC6cjSYuoPGkackmBgcXvP9rY6m9s/bevBtbfjqUjpago7wBv6nerD8DVq1dZsGCBxhGJypKkRVSe9QfXwIHaxSGqRXz9PuQY1G/ypt8Xq82D1SAzM5MffvgBAF9fX4YPH14t1xWu5abb8puIvvnmGw0jEVUhSYuonKQk2LZNLbdpo9kQWFF9cj39OBmr9lvSJ51Tmwerwf/93/9x7do1AIYOHUpwcHC1XFe4lojmETRq1AiAVatWcfz4cY0jEpUhSYuoHOsJ5aRpyG0cv6n6m4ikA66wBZ1OV+D1891332kYjagsSVpE5Uh/Frd0tFF+M6Dyu/2TlqNHj7LmxgriN910E926dbP7NYXrGjlyJB4e6kwfM2fOJC8vT+OIREVJ0iIqLisLli9Xy2Fh0LGjtvFUM70eOnRQN1efxr+w1OBozoW1BkC3fZvaTGhH1t+GH3vsMXQyeWHxdHC54WUuN7ws0/iXIjw8nLvuuguA8+fPs3SptstSiIpzs7dcYROrV+fP0zFwoNt9cvv6qt15tm1Ty+7mmPXsuHZ808/NzWXWrFkAeHp6ljltvzszehtZPnU5y6cux+ht1Doch2bdRCQdcp2Pe33aCNuwbhoaNEi7OIQmjjbJ/5vbs4lo7ty5lhXl77rrLlkcUdhEv379iL4xcGDJkiUcO3ZM44hERUjSIirGehZcT0+47TZt4xHV7lydjlz3DQNAWbEif+0pG1IUhY8++sjy+3PPPWfzawj3ZDAYGDt2LKC+zqZOnapxRKIiKrX2kHBj+/ery/8C9OpV8kxkLiwjA5o1U8sHD7rVRMAAKDo9xxsPpO2eWegz0tXmwgEDbHqNFStWsHfvXgBqN67N7Kuz+eH3H2x6DVdiyDZwx9g7AFg6fak0EZVhzJgxvPPOO6SlpTFr1izefPNNqclzElLTIirGeiZJNx01pChq3nbqVLXNr+ZwrGfHVf7vV5uf33oV+Fb3tJIOuGVRICA5gIDkAHDT12RF1KhRwzKzclZWFl988YXGEYnykqRFlJ+iwP/+p5Z1OrjnHm3jEZo50bA/2Z7+ACjz5kFmps3OvXv3blasWAFAUEQQsTfH2uzcQpg9//zzGAzqekSff/65ZQVx4dikeUiU34YNcOKEWu7TR2bBdWM5XgEcbHo/bfd+jz41BRYtgmHDbHJu61qWloNbojfIdythG2N+H1Pg97jucRxfc5zLly/T78V+NL+jOV8N+kqj6ER5yLuBKL8bw08BGDlSszCEY9jTJv81oMycZZNznj59mjlz5gDgHehNkz5NbHJeIYrT+t7WlvK+hfswGU0aRiPKQ5IWUT4ZGTBvnloOCJCmIcGp2J5cCaqn/rJiOZw7V+VzTps2DaNR7UTafGBzPLylMljYT624WtRpUweA1POpJGxO0DYgUSZJWkT5LFwI16+r5SFDwN9f03CE9hSdnn2t1QnfdCYT/Phjlc537do1y2RfPj4+NB/YvMoxClGW1vfk17bsWbAHxV171zsJSVpE+Xz/fX7ZzZuGdDp1yHOzZmrZne1pPcJSVmZ9X6XhVF999RVpaWkAjBo1Ct9gN5xuuLJ0kBKdQkp0ikzjX0F12tShVlwtAC4evcj69es1jkiURpIWUbazZ+Gvv9RybCz06KFpOFrz84MDB9TN3eZoKexKrUYk1OkKgO7gAdi5s1Lnyc7O5t///rd6Hp2O8ePH2yxGd2D0NrJ0+lKZo6USdDodrQa3svz+4YcfahiNKIskLaJsP/wAphsd1EaOdLu1hkTptjYdlf+LdY1cBUyfPp2kG4svDh48mEaNGtkgMiHKp0GPBviHqk3eixcvZtOmTRpHJEoinz6idIpS8INoxIiSjxVuJzUVfsgZSrbeBwDlx58gJ6dC57h27RrvvvsuoH7rnTRpks3jFKI0eg897Ya2s/z+8ssvS98WByVJiyjdtm1w6JBa7tED6tfXNh4HkJEBzZurmzvPR5WaCnv2AMHBHGoyGADdlcuwZEmFzvPBBx9w5coVAP7xj3/QunXrMu4hCjNP43/H2DswZBu0DscpNbmtCcF1ggFYv349ixfbbzFQUXmStIjSSQfcIhRFXXPo4EH3ncbfnLD4+0OrVrC/ndWcLbPK30R05swZpk2bBoCXlxdvv/22rUN1DwoEJwYTnBgs0/hXkt6gp9OITpbfJ0yYQF5enoYRieJI0iJKlp0NP/+sln191aHOwu0VTlg8POBE/dtI8Y9UD1i6BC5eLNe5Jk2aRNaNVaLHjRtHvXr17BW2EGWKvTmWrl3VjuUHDx7k+0r20RL2I0mLKNmiRXD1qlq+5x4ICtI2HqG54hIWAEVvYH/rfwCgy8sr15wtBw4cYNaNWZaDg4N55ZVX7BW2EOWi0+n44IMPLL+/8cYbsiaRg5GkRRRPUcBqDRhGjdIsFOEYSkpYzHa3GWUpG6dOg9zcUs83ceJETDdGpU2cOJFatWrZOGIhKq579+7cddddAJw7d47//Oc/GkckrEnSIor399+wdatabtUK+vbVNh6hqbISFoCLYc042uB2AAyJp/KbFouxbt06fv/9dwDq1KnDs88+a5e4haiMKVOmoL8xtcP777/P5cuXNY5ImEnSIop3YwgqAK+8IlO/urHyJCxm62/Jb+JR3puSP7+PFUVRePnlly2/v/XWW/j6yuy3wnE0a9aMRx55BICUlBTLkHyhPUlaRFGbNsGqVWq5YUO4/35t43EwOh3Uq6durp7LVSRhATgd0534uuqMybojh2HBgiLHfPvtt2zevBmA5s2bM1JGpVWdDtJqp5FWO02m8beRyZMnW5Lp//znP+zatUvjiARI0iKKM2VKfnnCBDDIvA/W/PwgIUHdXHka/4omLGYbelrVtrz7XoFx4YmJibz44ouW36dOnYpBXl9VZvQ28vu3v/P7t7/LNP42UqdOHf71r38BYDQaeeSRR8gto5+WsD9JWkRBe/fCjb4G1K0LDz+sbTxCE9evVy5hATjeoD9nwtXZRXW7dsLy5YDaLPTkk09y/cZq4aNHj6Zfv342j10IW5k4cSItWrQAYPfu3bIukQOowFuRcAvvv59ffukl8PLSLhahidxc2L8fatSoeMICgE7HhlteYdh8tVlRee89dP378+OPP7J06VIA/EL8MN1mYszvY2wbvBA25OXlxcyZM+ncuTMmk4m33nqLe+65h2bNmmkdmtuSmhaR7/hxmDtXLYeGwmOPaRuPg8rMhI4d1S0zU+tobO/yZbXZq1IJyw2Hm97DhZCbANCtXcvl334rMEKo+1Pd8Q7wtkW4AnUa/37j+9FvfD+Zxt/GOnTowEsvvQRATk4OjzzyCEajNMFpRZIWke/DD/NHe7zwgmt32KgCkwm2b1e3YgbHOD0PD3VdpcomLACKTs/GHhMsvyeMeZKrNyYqHD58OLGdY6sYpShAgVrHa1HreC2Zxt8OJk2aRJMmTQDYsmUL//73vzWOyH1J85BQnT0LN2YnJSgInn5a03CEdmrVqlrCAvD7kd/5wzuIzr61icpMpv2F87QGjgT74DnQ0yZxCmEPJTVZNhndhCMTj4ACL098ma3+WwmOCq7UNb4a9FVVQnRrUtMiVBMn5s9gOnas2qFBuCVbDePO03sws2F+R9tPgG5PdMUnyMc2FxCiGkU0i6DFnWqnXGOOkdXTVmPKc8GqVgcnSYuAv/6C2bPVco0aatOQEFVkMuYw9exmEm783gd4MEf6Agjn1fHhjgSGBwJw4fAFNn67UeOI3I8kLe4uMxOefDL/9w8/hLAw7eIRLkFRFBK3f8mVK8exbmgc8t0W/FOzNItLiKrw9PGkz0t90HuoH50Hlx7k8PLDGkflXiRpcXfvvgsnTqjl7t3h0Ue1jUe4hIvHlnA5fiUAfxq8WBreFoDA61nc/91mLUMTokpqN65Nj7E9LL+vn7Ge84fOaxiRe5GkxZ0dOADmZdg9PeHrr0EvL4nyCA1VN1FUfPwqzuz61vJ7vU7PMO3m50n18Aeg699HabLnrFbhuaysoCyygqQWqzo06dOEFoPU/i2mPBMr3l9B+uV0jaNyD/IJ5a5MJnjiCcjLU3+fMAGaNtU2Jifh7w8XL6qbv7/W0TiWa9cSmD9/CChqB8Xwm+4lpF5PLvvW5LPW+WsMPfjFejxy8rQK0+UYfYws+GEBC35YgNFH+g1Vh5tH30xUyygAMq9msnzKcvLkNW13krS4q2++gY03OpE1bqyu5CxEFWRlXWPOnMFkZl4GICiyHVGt8peBWNCwHztD1JlEI5JSuGOeLEAnnJfeQ0/ff/UloHYAABePXmTtZ2sxGWVEkT1J0uKOkpLgxkJgAMyYAT4yDFVUXmbmFf73v75cuLAHAO+ASGK7/BOdPn92VqPJg5ej3iIHdZ6W/v+3h6hTVzSJVwhb8Anyod8r/TB4qa/z42uOs+Y/ayRxsSNJWtxNZibccw+kpKi/jxoFt96qaUjOJjMTevVSN1ecxr+iMjIu87//9SEpaQcAfn5h1O/xGh5eAZZjTEY9VxLqcEjfjJmN1DWJPIwmxrz7l4wmsgFDtoHer/Sm9yu9ZRr/ahZaP5Q+/+yDzqBOcHRs1TF1DhdJXOxCkhZ3YjLByJGwZYv6e9268NFH2sbkhEwmWLNG3VxxGv+KyMi4xP/+14fz53cD4O8fzqhRq/ENjrYcY05Y8rK9CYk9w6w293E0OBaAiPPXGPPeCgy50g+jShQI3x9O+P5wmcZfA7E3x9L35b6WxOX4muOsmrpKEhc7kGn83cnrr8P8+Wo5IAAWL5YhMKJSfj/yO7lZKRxb9RpZKacA8PQJoV7PSWy+csJyXOGExcsvixy8eOGW1/h++UuEZl+lycEkHv58LbOe72W76XiFqGZxXeK4bcJt/PXBX5jyTJxYdwJFUeg9vrdlXpfyKmv1c3deBkBqWtzFrFnw3ntqWa+HOXOgdWtNQxLOK+v6OY79/Up+wuIbQqPe7+ITVNdyTHEJi9l5/9qMv+VVsvReAHRZdYzb50vHXOHcYjvHctvE2yxJysn1J1k+ZTk56TkaR+Y6JGlxB6tXq8ObzaZNg4EDtYpGOLlDhxZwePl4slITAfD0rUWj3u/hE1THckxpCYvZgVqNef3m/CUjBv+wnQ7rThQ5TghnUq9jPbVzrqfat+j0ttP8Ov5XLsdf1jgy1yBJi6vbvRvuvTd/McRx4+CZZzQNSTgnkymPFSv+xbx592LKzQDAJyiaxr3fwycwKv+4ciQsZn/HdOM/rUZYfh/56WqZeE44vZgOMfR/vT/eAd4ApCalsvClhRxddVTjyJyfJC2ubNEidWr+q1fV32+/HT79VNuYhFNKSzvP//7Xl40bP7TsqxnTgya3fYx3YKRlX0USFrPvm97Hwri+AHjlGXl20h90k/VchJOr26Yu9356L6EN1X6Dxhwjqz9dzbov1pGdna1xdM5LkhZXpCjw8ccweDCk35ha+uab1X4sHtL32hb8/NTN1SmKid27v2fGjNacOrUGAL3eg7rtniC2yz8xePpajq1MwgKATseUDk+xNrIjAB4mEyM+X8t9Mzejk9EX5ZbnnUeet8zI6kgCwwO56/27uKnfTZZ9h/48RMeOHVm7dq2GkTkvSVpcTU4OPP44vPSSmrwAPPAA/P03BAVpG5uL8PdXc8H0dNeexj8paSfffded334bRXp6MgCBgXUYNWoNtRvfic5qpE+lE5Yb8gye/LPHK/zUaJBlX78Fe3lyygq8M3Nt84BcmNHHyPz585k/f75M4+9gPLw8uGXcLfR8tqdlErp9+/bRs2dP/vGPf3Du3DmNI3QukrS4ksRE6N8f/vvf/H2TJ8NPP4Gvb4l3E8JadvYVli9/mq+/7sCZM5ss+5s1u58xY3YSHd21wPFVTVjMjHoDn7R/nHfbP0WeTn1zb7P1FP98eRHhZ65V+vEI4Qia9G3C4I8GE9YwzLLvxx9/pEmTJnz88cfk5kpyXh6StLiCrCx491246SZ1pBCAtzf8/DNMmiRzX4hyOXPmDFOmvMxvv8Wxe/eXmGcpCw29iYcfXsGQIfPx969d4D62Slis/drodp7t+YZlVeiYU5d545lfuHfmZrwzZOiocF614mpx90d389VXXxESEgJAWloaL730Eo0aNWLatGlcv35d4ygdmyQtzm7xYmjRAl57DTLUER2Eh6vJywMPaBqaq8rKUkeMDxyolp3d7t27efjhh4mLi+Prrz8iNzcVAE9Pf/r2/ZAnn9xD/fp9i9zPHgmL2ZaItozu9xGn/dVRSR5GE/0X7OWtp+bTedWx/KZPAYA+R88tb93CLW/dgj5H3tYdmd6g54knnuDo0aM8+eSTlmbWU6dO8cILLxAdHc2WWVtIv5yucaSOSacojv/fn5qaSnBwMCkpKQRJvwz1DXvVKrWz7R9/5O83GODpp+HNN6FmTe3ic3Hp6eqEwgBpaY7Xr6U8s2leuHCB//u//2POnDmsW7euwO16vRctWoygT5/JBFnNvWLtt4NL7JawWPPJy2bkwV8YefhXvE351efHmkSwfEhr9rePxmSQD2lDloGhQ4cCMG/ePOnX4uCsZ7TdsWMHr7/+On9Yv5cDOoOOep3q0aBHA2I6xODp41ns/R2drT+/ZSiJM7l0SZ3Z9uuv4dixgrf17AmffQYtW2oSmnB8GVczSNiSQJ9pfVi9ejWmQgsnhYSE8OCDT3Pu3FgaNowosRtUXh7VkrAAZHl481Wrh1hcvw8v7PyOW89tBqDRkfM0euc8V0IC2NC/Cetva8K10IAyziaE42nfvj1Lly7lwIEDTJ06lR9++IGcnBwUo0LCpgQSNiVg8DJQr2M96veoT902dcs+qQuTmhZHd/YsrFwJS5bAwoXq6CBrdeuqNS5Dh0rflWriLDUt6ZfTSdqfxLn950jan0TK2ZRij2/SpAnPPvssI0eO5OJFf157DerUKb7vdl4e7N0LO04dsnvCUpwuSTt5cce3xKWdKbDfpNOxr30M+zrFcLBNHS5HuNf7hNS0OJfSakrOnz/PHc/dweFlh8lMKbqMvE6vo2OHjvTs2ZOePXvSvXt3goOD7RlulThETcv06dP56KOPOH/+PK1bt+azzz6jU6dOJR4/f/58Xn/9dRISEmjUqBEffPABd9xxR6WDdlkmE5w6BXv2qM0/K1bAoUPFH9u7N4wZo87F4uVVrWEKx5Kbm8uxY8fYu3cve/fu5c+//uRKwhXSLqaVeJ+GDRsydOhQhg0bRsuWLS3t6hcvlnwdc8KSno4mCQvApsh23N7xR9qfOMzo9NncenkjBkzoFYXW20/Reru6FlJy7SAOt43icOs6JMbV4mJEEIo0IwknEBERQcd/dKT98PYk7U/i5IaTxG+MJytV/X9TTApbt25l69atfPTRR+j1eho3bkyrVq1o1aoVLVu2pFWrVsTExKDXu95rvsI1LXPnzmXEiBHMmDGDzp07M23aNObPn8+RI0eoXbt2keM3btzILbfcwpQpU7jzzjv56aef+OCDD9i5cyctWrQo1zVdqqYlNxeSkuDMGXVLTFQTk/374cAB9at7SUJDYdQodR2hRo2qLWRRUHXWtKSnp3PhwgWSk5MtP8+cOUNCQgLx8fEkJCRw9uzZIk09hekMOmo3qk1ky0i+m/gdbdq0KTDPillCAtw2ajN+Idfw8M7vQ2LPTrcVcT05hOsXQgkMv0Rg7SuEp1/krpN/MfjkCiIyL5V4vxxPD87VrUlSbA2SYmpyJTSAq6H+XK3lT0otf/JurBPjrKSmxbWZjCbO7T1HwpYEkvYncfX01TLv4+XlRUxMDHFxccTGxhIbG0tUVBS1a9cmPDyc8PBwwsLC8Pb2tmvstv78rnDS0rlzZzp27Mjnn38OgMlkIjo6mmeeeYYJEyYUOX7YsGGkp6ezePFiy76bb76ZNm3aMGPGjHJd0/ygj6xcSaD506K4sEvbZ/3zxqaz/t1ksvzUWe8zGtEZjerXTHM5NxfdjY2cHLWclYUuIwNdVhb6jAy1fP06+pQU9Neu5f+8fFk9fzkoBgM5bdqQ3b07WT16kNO2rVPVqlRHy2NJ1zDvt769pH2F9yuKgslkstxm3kwmEyaTifR06N69DQB//bUZL69cjEYjJpOJvLw88vLyyM3NJTc3l7y8PHJycsjOzi6wZWZmkpGRQXp6Ounp6WRkZHD9+nWuXbtGSkoKKSkpXLt2rdLTfXv6elIrrhaRLSKJbB5JeNNwS0e+0qqmi0taHDVhsaY3GWl69QSdzu+m8/k9tLl0CE+l/LPDpgb4kh7oQ0aAFxmBXmQEepPp70W2twc5Pp7keHtYtjwPPXkeBoweevI89Rg9DJj0OowGPSa9DpNBh0mvR9GBotOh6HXqT/PvOkCnQ0H9nRu5owKWJl6lmJZepZTmX0O2B7c9PRqAFV/MxFjJmXGLu65wPC+3e5ktW7awefNmtm7dytGjR8mp5Dwvvj4+BAcHExgYSFBQEEFBQfj5+eHn54evr6+l7OXlVWDz9vbG09MTDw8PPDw88PT0xGAwYDAY0Ov1lnJGVha3PPCANklLTk4Ofn5+/PLLLwwePNiyf+TIkVy7do3ffvutyH1iYmIYP348zz//vGXfpEmTWLhwIXv27Cn2OuY3drOUlBRiYmJIBJy8nqVUJ4FDwAFgF7AOkBH7jsgXOH+jHAEUbXeuLiEhIdSrV4+4uDiaNWtGixYt+OXiL/iH+hdbkwLw79v/XeL5Tp2CwU9tA70JvYcRk0nH9aQwjHkeBIVfwsNHm3lSMq8FknElGL+QFHxrlP1f4WvMpM21A7RMPUT9tFM0SDtNvawzGHD4LnyVYsSbjfwfAF25DwOyto1wDKlANHDt2jWb9L2pUJ+WS5cuYTQaCQ8PL7A/PDycw4eLX+Ds/PnzxR5//vz5Yo8HmDJlCm+++WaR/dEVCVYIu8kEHKPj25UrV7hy5Qq7du3i119/Ldd9ZjGrctc6Wam72dTVU+U/dp/9wnBA2cCdWgchRIkuX75c/UlLdZk4cSLjx4+3/H7t2jXq1avH6dOnHbqXtKNLTU0lOjqaxMRE5+8bpDF5Lm1HnkvbkOfRduS5tB1zS4l5BuCqqlDSEhoaisFg4MKFCwX2X7hwgYiIiGLvExERUaHjAby9vYvtHBQcHCwvIBswt1uKqpPn0nbkubQNeR5tR55L27HVSKYKncXLy4v27duzcuVKyz6TycTKlSvp0qVLsffp0qVLgeMBVqxYUeLxQgghhBDFqXDz0Pjx4xk5ciQdOnSgU6dOTJs2jfT0dEaPVnuujxgxgjp16jBlyhQAnnvuOXr27Mknn3zCwIEDmTNnDtu3b+frr7+27SMRQgghhEurcNIybNgwLl68yBtvvMH58+dp06YNf/75p6Wz7enTpwtUA3Xt2pWffvqJ1157jVdeeYVGjRqxcOHCcs/RAmpz0aRJk+w+ntzVyfNoO/Jc2o48l7Yhz6PtyHNpO7Z+Lp1iGn8hhBBCCNeb41cIIYQQLkmSFiGEEEI4BUlahBBCCOEUJGkRQgghhFOQpEUIIYQQTsHpkpZ3332Xrl274ufnR40aNbQOx6lMnz6d2NhYfHx86Ny5M1u3btU6JKezdu1aBg0aRFRUFDqdjoULF2odklOaMmUKHTt2JDAwkNq1azN48GCOHDmidVhO6csvv6RVq1aW2Vu7dOnCH3/8oXVYTu/9999Hp9MVWOxXlM/kyZPR6XQFtptuuskm53a6pCUnJ4chQ4bw1FNPaR2KU5k7dy7jx49n0qRJ7Ny5k9atW9O/f3+Sk5O1Ds2ppKen07p1a6ZPn651KE5tzZo1jB07ls2bN7NixQpyc3Pp168f6enpWofmdOrWrcv777/Pjh072L59O7179+buu+/mwIEDWofmtLZt28ZXX31Fq1attA7FaTVv3pykpCTLtn79etucWHFSM2fOVIKDg7UOw2l06tRJGTt2rOV3o9GoREVFKVOmTNEwKucGKAsWLNA6DJeQnJysAMqaNWu0DsUl1KxZU/n222+1DsMpXb9+XWnUqJGyYsUKpWfPnspzzz2ndUhOZ9KkSUrr1q3tcm6nq2kRFZeTk8OOHTvo27evZZ9er6dv375s2rRJw8iEUKWkpADYbCVYd2U0GpkzZw7p6emyvlsljR07loEDBxZ4vxQVd+zYMaKioqhfvz4PPfQQp0+ftsl5KzyNv3A+ly5dwmg0WpZaMAsPD+fw4cMaRSWEymQy8fzzz9OtW7cKLe8h8u3bt48uXbqQlZVFQEAACxYsoFmzZlqH5XTmzJnDzp072bZtm9ahOLXOnTsza9YsmjRpQlJSEm+++SY9evRg//79BAYGVuncDlHTMmHChCKddgpv8uEqhGsaO3Ys+/fvZ86cOVqH4rSaNGnC7t272bJlC0899f/t27FLalEAx/Hf48LBMCmqC4VxpZBocsjwH3AIh6BFpCGuukVGkEE0+S8Utjg55dASQQQFojgFEQhBkxEYSDpEkA0Oet7w4EEU79Hz+Y7H9/uAy0UOX8Th58W7Dtu2cXd3pzpLK4+Pj9ja2sLR0REcDofqHK2FQiGEw2H4fD4sLS3h/PwcLy8vOD4+7vrsvrjTkkwmEY1Gf/me2dnZfxMzgCYmJmAYBur1+rvr9Xodk5OTiqqIgEQigbOzM5RKJUxPT6vO0ZYQAl6vFwDg9/txfX2Ng4MDZDIZxWX6uLm5QaPRwMLCws9r7XYbpVIJh4eHaLVaMAxDYaG+RkdHMTc3h0ql0vVZfTFaTNOEaZqqMwaWEAJ+vx/5fB4rKysAftySz+fzSCQSauPovySlxObmJk5OTlAsFjEzM6M6aaB0Oh20Wi3VGVoJBoO4vb19dy0Wi2F+fh67u7scLF1oNpu4v7/H2tpa12f1xWj5imq1iufnZ1SrVbTbbZTLZQCA1+vF8PCw2rg+tr29Ddu2sbi4iEAggP39fby9vSEWi6lO00qz2Xz3a+Hh4QHlchljY2OwLEthmV42NjaQy+VwenoKl8uFp6cnAMDIyAiGhoYU1+llb28PoVAIlmXh9fUVuVwOxWIRFxcXqtO04nK5Pvynyul0Ynx8nP+1+qKdnR0sLy/D4/GgVqshlUrBMAysrq52f3hPnknqIdu2JYAPr0KhoDqt76XTaWlZlhRCyEAgIK+urlQnaadQKHz6/bNtW3WaVj77DAHIbDarOk078XhcejweKYSQpmnKYDAoLy8vVWcNBD7y/GcikYicmpqSQgjpdrtlJBKRlUrlr5z9TUopu58+RERERL3VF08PEREREf0ORwsRERFpgaOFiIiItMDRQkRERFrgaCEiIiItcLQQERGRFjhaiIiISAscLURERKQFjhYiIiLSAkcLERERaYGjhYiIiLTwHUrZZ0Rb1m6UAAAAAElFTkSuQmCC",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Generate 1000 random numbers from the first normal distribution\n",
|
|
"mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"data = np.random.normal(mu1, sigma1, 1000)\n",
|
|
"\n",
|
|
"# Create a histogram of the data\n",
|
|
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
|
|
"\n",
|
|
"# Add a graph of the first normal distribution used to generate the data\n",
|
|
"xmin, xmax = -1, 5\n",
|
|
"x = np.linspace(xmin, xmax, 100)\n",
|
|
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
|
|
"plt.plot(x, p1, 'k', linewidth=2)\n",
|
|
"\n",
|
|
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
|
|
"mu2, sigma2 = 1, 0.4\n",
|
|
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
|
|
"plt.plot(x, p2, 'r', linewidth=2)\n",
|
|
"\n",
|
|
"# Add vertical lines at x = 1 and x = 3 with labels\n",
|
|
"plt.axvline(x=1, color='b', linestyle='--', label='mu theoretical distribution')\n",
|
|
"plt.axvline(x=3, color='m', linestyle='--', label='mu in sample')\n",
|
|
"\n",
|
|
"# Calculate the 95% quantile for the second normal distribution\n",
|
|
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
|
|
"\n",
|
|
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
|
|
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
|
|
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
|
|
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
|
|
"\n",
|
|
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
|
|
"plt.title(title)\n",
|
|
"plt.xlim(xmin, xmax)\n",
|
|
"plt.legend()\n",
|
|
"\n",
|
|
"# Show the plot\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"id": "665a50fe-8404-4db3-b412-aec36d81016e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"T-statistic: 98.77295966495895, P-value: 0.0\n",
|
|
"The means of the two theoretical distributions are statistically different (reject H0).\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Define the parameters for the two normal distributions\n",
|
|
"mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n",
|
|
"\n",
|
|
"# Perform a t-test to compare the means of the two theoretical distributions\n",
|
|
"# Since we don't have samples, we use the means and standard deviations directly\n",
|
|
"# Calculate the t-statistic and p-value manually\n",
|
|
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
|
|
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
|
|
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
|
|
"df = n1 + n2 - 2 # degrees of freedom\n",
|
|
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
|
|
"\n",
|
|
"# Print the t-test result\n",
|
|
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
|
|
"\n",
|
|
"# Interpret the result\n",
|
|
"alpha = 0.05\n",
|
|
"if p_value < alpha:\n",
|
|
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
|
|
"else:\n",
|
|
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "63072dac-c7e6-4237-b5cc-b9832a2c7707",
|
|
"metadata": {},
|
|
"source": [
|
|
"Now with narrowed mu and alpha error"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"id": "aa9ea3d5-3559-4fd7-a2c7-f041486c090e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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33so3VPfwww/z4osvFvvY9PR07r33Xnx9fQud2XY9W74vZmRkFBhaNCvN79nFixcZN24cb7zxBuHh4cVeByr2+2zmVElLu3btCu1Wt5W4uLgC9x05coTdu3cX+YInJSUB6ljp/PnzufXWW6levTq9e/dm4MCBdk9g4uLiGDNmDFOmTOG7776jc+fO3HHHHTz44IOWD7PysP4Ag7wPxuu7Mc33X758udzXKi8fHx969uzp8OsW5q+//qJv3778/ffflp/R/v37ExQUxJtvvskjjzxiqQ8C8tUnmJnrKqzrX0qjIj8D58+fJyMjg3r16hX4XoMGDWyetNx00002OU9Jr2NZX0NQu6JHjRrFk08+ybZt2+jUqZNd/r+sleX3zGQykZycTNWqVct9vbNnz3L77bcTHBzMwoULMRgMJT6mWrVqltosrfn6+pbq/8IePx+DBg3iiy++4LHHHuOVV16hR48e3H333QwYMKDEBOa///4DKPB75unpWWyCbjQaue+++9i/fz+//fYb0dHRJcZpy/dFX19fsrOzC/1eaV7H119/ndDQUJ5++ukSrwO2+f9yqqTF3gp7YUwmE7169eKll14q9DHmnp+IiAh27tzJypUr+e233/jtt9+YM2cOQ4YM4euvvwYossizNGP8xZk8eTIPP/wwv/zyC6tWreKZZ55h0qRJ/P3339SoUaNc5yzqzayo+xWrMfzinmdp3iRLy2g0lnptk9DQ0CL/YrCFzz//nMjIyAJJ9R133MGECRPYtGkTjRs3trz5JyYmFjhHYmIioaGhZeplMbPHz4A9nD9/vlQ/7wEBAQQEBBT5/ZJex9K8uRfGnCyYawLM/x9FXQco97Wg/L9n5XkvSU5O5tZbb+XKlSts3Lix1HFnZGTkK+ovTkWKbEujWrVqpfq/sP75uD4BTExMpF27dmW+tq+vLxs2bGDt2rUsW7aMFStWMG/ePLp3786qVats+t5m9vjjj7N06VK+++47unfvXqrH2PJ9sVq1ahiNRpKSkoiIiLDcn52dzcWLF4v9GTpy5AizZs1i6tSpnDlzxnJ/ZmYmOTk5nDx5kqCgIEJDQ236++wSs4cKY6sZKXXq1OHq1av07Nmz0Jv1X0peXl7069eP6dOnc+zYMYYPH87//vc/jh49CkCVKlUAdTaSNXMWXpHn06xZM15//XU2bNjAxo0bOX36NDNnzizjs7WNKlWqFHiOULrnWRYJCQmWvwJLum3atMmm177euXPnCv3AyMnJAbAsaFW9enXCw8PZunVrgWO3bNlCy5Ytyx1DST8Dhf0MhYeH4+vry5EjRwp879ChQ+WOpSht27Yt1f+XeTitKE2bNsXDw6PA65idnc3OnTvL/TqaF4wz96zq9XqaNWtW6P/XP//8Q+3atfMNlzpKWd9LMjMz6devH4cPH2bp0qU0bty41NeaN29eqX/P7K1ly5Zs3769wMzNf/75Bz8/P8sfkeb//+v/386cOcOpU6fK/fOh1+vp0aMHU6ZMYf/+/bzzzjv88ccfrF27Fij6fbpWrVoABX7PcnJyOHHiRKGPefHFF5kzZw4ff/wxgwcPLnWMtnxfLOp13Lp1KyaTqdjX8fTp05hMJp555hni4uIst3/++YfDhw8TFxfHW2+9Bdj299lle1r8/f0B9ZfaPBZZHgMHDmTChAmsXLmyQL3LlStXCAgIwMPDg4sXL+brttXr9TRv3hzI6/Iyz9bYsGEDd9xxB4BlGmpZno+1lJQU/Pz88o1zN2vWDL1en6+r7cKFC1y4cIGaNWuWqeahPOrUqcPGjRvJzs62ZPFLly4lISGhxFqFstCqpiU5OZnExESqVatm6c6vX78+q1atYt26dflmZ/3www8AtGrVynLfPffcw9dff01CQoLlr8A1a9Zw+PBhnnvuuTLHU9qfAX9//wI/PwaDgT59+rB48WLi4+MtSfiBAwdYuXJlmWMpia1qWoKDg+nZsyfffvstb7zxhiVx+Oabb7h69Sr33nuv5dj09HTi4+MJCwuzzG45f/58gSHf1NRUpk6dSlhYGK1bt7bcP2DAAF555RW2bt1q6Uk7dOgQf/zxBy+88ELpnriNBQUFERYWxoYNGxg9erTl/unTpxc41mg0MmjQIDZv3swvv/xChw4dynQtrWpaEhMTSU5Opk6dOpa6nwEDBrBw4UJ+/vlnBgwYAKjvbQsWLKBfv36WXsomTZrQsGFDZs2axfDhwy29IDNmzECn01keWxaXLl0iNDQ0333mD1Pz71lR79Nt2rQhPDycmTNnMmzYMMv74ty5cwv9A+/DDz/ko48+4tVXXy3z7FNbvi92796d0NBQZsyYwW233Wa5f8aMGfj5+XH77bdb7rv+M6Zp06YsWrSowDlff/11UlNT+b//+z/LZ2JZfp9L4rJJi/lN55lnnqFPnz4YDAbuu+++Mp/nxRdfZMmSJfTt25eHH36Y1q1bk5aWxp49e1i4cCEnT54kLCyMxx57jEuXLtG9e3dq1KjBf//9x6effkrLli1p1KgRAL1796ZmzZo8+uijvPjiixgMBr766ivCw8OJj48vNo46deoQEhLCzJkzCQwMxN/fn/bt27Nr1y5GjRrFvffeS/369cnNzeWbb77BYDBwzz33WB5f1inPFfHYY4+xcOFCbrnlFgYOHMixY8f49ttvLT+g1n799Vd27doFqH917N69m7fffhtQh1bMiV9hbF3TUtpYFi1axLBhw5gzZ45lrZNRo0YxZ84c+vXrx9NPP02tWrVYv349P/zwA7169bIULAO8+uqrLFiwgG7duvHss89y9epVPvzwQ5o1a8awYcPyxWQubi5qDR+AP/74o1Q/A61bt+b3339nypQpREdHExcXR/v27XnzzTdZsWIFnTt35qmnniI3N5dPP/2UJk2asHv37nzX2r17N0uWLAHg6NGjJCcnW16jFi1a0K9fv2JfY1vVtIC6JHjHjh3p0qULTzzxBKdOnWLy5Mn07t07Xy3Zli1b6NatG+PHj7cUo0+bNo3FixfTr18/atasSWJiIl999RXx8fF88803+brMn3rqKWbPns3tt9/OCy+8gKenJ1OmTCEyMpLnn38+X0xdu3Yt05Tninjsscd47733eOyxx2jTpg0bNmwodGn+559/niVLltCvXz8uXbrEt99+m+/7JU1ZtXUvymeffcaVK1csQwa//vorp06dAuDpp5+2/CEwduxYvv76a06cOGH5PRgwYAA33ngjw4YNY//+/YSFhTF9+nSMRiNvvvlmvut8+OGH3HHHHfTu3Zv77ruPvXv38tlnn/HYY49Z3pNB/d2Ki4tj6NChxW4p8NZbb7FhwwZuv/12atWqRVJSEtOnT6dGjRp06tQJKPp9Oi4ujrfffpvhw4fTvXt3Bg0axIkTJ5gzZ06BBH3RokW89NJL1KtXj0aNGhX4/+rVq1exyxHYuqZl4sSJjBw5knvvvZc+ffqwceNGvv32W9555518Sdz1nzFhYWH079+/wDnNy4Rc/73S/j6XqNTzjOyopBVxC5v+l5ubqzz99NNKeHi4otPpSpyOV6tWrQKr/pmlpqYqY8eOVerWrat4eXkpYWFhSseOHZWPPvrIMl1x4cKFSu/evZWIiAjFy8tLqVmzpjJ8+HDL6o9m27ZtU9q3b285ZsqUKaWa8qwoivLLL78ojRs3Vjw8PCzP9/jx48ojjzyi1KlTR/Hx8VFCQ0OVbt26Kb///nu+x5Z1yvP1K4WaX+MPP/ww3/3mqZvXT7edPHmyUr16dcXb21u56aablK1btxb6nIYOHVrkdDxHr/5b2ljM/1/Xx3fw4EFlwIABSkxMjOLp6anUqlVLeeGFF5S0tLQC19q7d6/Su3dvxc/PTwkJCVEeeOAB5ezZswWOCwsLK3F6Zml/Bg4ePKjcfPPNiq+vr2U6ttn69euV1q1bK15eXkrt2rWVmTNnFjpFv7jpr1qsZrxx40alY8eOio+PjxIeHq6MHDky35R8Rcn7GbWeBrxq1SqlV69eSlRUlOLp6amEhIQovXv3VtasWVPodRISEpQBAwYoQUFBSkBAgNK3b1/lyJEjBY5r3bp1qaZnFvV7U9R7nfn/wnq6bXp6uvLoo48qwcHBSmBgoDJw4EAlKSmpwHM1T8Mu6uZoxU17t34PNP8+Wt+nKIpy6dIl5dFHH1WqVq2q+Pn5KV26dCnys2HRokVKy5YtFW9vb6VGjRrK66+/nm+KuaIoyp49exRAeeWVV4qNe82aNcqdd96pREdHK15eXkp0dLQyePDgAsthFPY+bTZ9+nQlLi5O8fb2Vtq0aaNs2LChwPui+f+6qFtZl2+whVmzZikNGjRQvLy8lDp16igff/yxZfXw6+MuKb6iVsRVlNL9PpdEpygO+JNBCFHA/v37adKkCUuXLs3XDSucU2pqKqGhoUydOtWyKKNwftOnT+ell17i2LFjdllQUTiWyxbiCuHq1q5dS4cOHSRhcREbNmygevXqPP7441qHIspg7dq1PPPMM5KwuAnpaRFCCCGES5CeFiGEEEK4BElahBBCCOESJGkRQgghhEuQpEUIIYQQLsElFpczmUycOXOGwMBAmy3fL4QQQgj7UhSF1NRUoqOjy7RzdlFcImk5c+ZMgU2xhBBCCOEaEhISbLK5q0skLeZ9ChISEggKCtI4GlHZpaWBeVPSM2fg2nYklY4xzcimaHVDto5nOmLwt/0uuEII15aSkkJMTIzNNh51iaTFPCQUFBQkSYvQnPUO9UFBlThpMRjxR33yQUFBkrQIIYpkq9IOKcQVQgghhEtwiZ4WIZyJhwcMHZrXrqx0Hjoih0Za2kIIYW8usYx/SkoKwcHBJCcny/CQEEII4SJs/fldif9OFEK4AkVRyM3NxWg0ah2KEOI6BoMBDw8Phy1HIkmLEGWkKJCerrb9/KCyLh2kKAqmdBMAej+9Xd60srOzSUxMJN38ggshnI6fnx/VqlXDy8vL7teSpEWIMkpPh4AAtX31auWdPWRKN7ExYCMAna92tvnsIZPJxIkTJzAYDERHR+Pl5SWLSwrhRBRFITs7m/Pnz3PixAnq1atnkwXkiiNJixDCKWVnZ2MymYiJicHPz0/rcIQQhfD19cXT05P//vuP7OxsfHx87Ho9mfIshHBq9v7LTQhRMY78HZV3AyGEEEK4BElahBBCCOESJGkRQgg38vDDD9O/f3+twyiTuXPnEhISYrPzrVu3Dp1Ox5UrV8r0OJ1Ox+LFiwE4efIkOp2OnTt32iwus9jYWKZOnVrode19LVcnSYsQQrgge36o2lNhH6KDBg3i8OHD2gRUhJiYGBITE2natGmJx5b1/+Lff//liSeeqGCE+RWV+NnjWlqS2UNClJHBAAMG5LUrLQOEDwi3tEXllp2dXe51Onx9ffH19bVxRBVjMBiIioqy6TnNr1F4eLhNz1scR17LEaSnRYgy8vGBBQvUm51n9zk1g4+BJgua0GRBEww+jsta0tKKvmVmlv7YjIzSHVtWXbt25emnn2b06NFUqVKFyMhIZs+eTVpaGsOGDSMwMJC6devy22+/WR5T2F/JixcvLnZdmri4OABatWqFTqeja9eu+b7/0UcfUa1aNapWrcrIkSPJycmxfC8rK4sXXniB6tWr4+/vT/v27Vm3bl2+x//00080adIEb29vYmNjmTx5cr7vx8bGMnHiRIYMGUJQUJDlr/k///yTzp074+vrS0xMDM888wxp117Irl278t9///Hcc8+h0+ksz6+w5//rr7/Stm1bfHx8CAsL46677rJ875tvvqFNmzYEBgYSFRXF/fffT1JSUpGvVWGOHDnCzTffjI+PD40bN2b16tX5vn9978nly5d54IEHCA8Px9fXl3r16jFnzhyg6P8L81DdO++8Q3R0NA0aNLC8dtf3NiUmJnLrrbfi6+tL7dq1WbhwoeV7hQ137dy5E51Ox8mTJ1m3bh3Dhg0jOTnZ8rpOmDCh0GvFx8dz5513EhAQQFBQEAMHDuTcuXOW70+YMIGWLVvyzTffEBsbS3BwMPfddx+pqallen3tRZIWIUSFDf91eLE3WwoIKPp2zz35j42IKPrYW2/Nf2xsbOHHlcfXX39NWFgYW7Zs4emnn2bEiBHce++9dOzYke3bt9O7d28eeuihCq30u2XLFgB+//13EhMT+fnnny3fW7t2LceOHWPt2rV8/fXXzJ07l7lz51q+P2rUKDZv3syPP/7I7t27uffee7nllls4cuQIANu2bWPgwIHcd9997NmzhwkTJvDGG2/kOweoiVGLFi3YsWMHb7zxBseOHeOWW27hnnvuYffu3cybN48///yTUaNGAfDzzz9To0YN3nrrLRITE0lMTCz0uS1btoy77rqL2267jR07drBmzRratWtn+X5OTg4TJ05k165dLF68mJMnT/Lwww+X+rUzmUzcfffdeHl58c8//zBz5kxefvnlYh/zxhtvsH//fn777TcOHDjAjBkzCAsLA4r/v1izZg2HDh1i9erVLF26tNjz33PPPezatYsHHniA++67jwMHDpTq+XTs2JGpU6cSFBRkeV1feOGFQp/3nXfeyaVLl1i/fj2rV6/m+PHjDBo0KN9xx44dY/HixSxdupSlS5eyfv163nvvvVLFYneKC0hOTlYAJTk5WetQhBCFeGLJE8XeyiMjI0PZv3+/kpGRke9+dSOFwm+33Zb/HH5+RR/bpUv+Y8PCCj+urLp06aJ06tTJ8nVubq7i7++vPPTQQ5b7EhMTFUDZvHmzoiiKMmfOHCU4ODjfeRYtWqQU9xZ94sQJBVB27NiR7/6hQ4cqtWrVUnJzcy333XvvvcqgQYMURVGU//77TzEYDMrp06fzPa5Hjx7K2LFjFUVRlPvvv1/p1atXvu+/+OKLSuPGjS1f16pVS+nfv3++Yx599FHliSfy/39v3LhR0ev1lv/HWrVqKR9//HG+Y65//h06dFAeeOCBIp/79f79918FUFJTUxVFUZS1a9cqgHL58uVCj1+5cqXi4eGR7zX47bffFEBZtGiRoigFX99+/fopw4YNK/R8xf1fREZGKllZWfnuv/41AJQnn3wy3zHt27dXRowYUeTz2bFjhwIoJ06cUBSl8J+h66+1atUqxWAwKPHx8Zbv79u3TwGULVu2KIqiKOPHj1f8/PyUlJQUyzEvvvii0r59+0Kfu6IU/buqKLb//JaaFiHKKC1NlvEHMKYZLcv4G+YbMPo4ZkPDq1eL/t71NUbFjRhcvx7WyZPlDqmA5s2bW8VkoGrVqjRr1sxyX2Rk5LX4yjakUVpNmjTBYPViVKtWjT179gCwZ88ejEYj9evXz/eYrKwsqlatCsCBAwe48847833/pptuYurUqRiNRsu527Rpk++YXbt2sXv3br777jvLfYqiWLZkaNSoUani37lzJ48//niR39+2bRsTJkxg165dXL58GZNJ3QMrPj6exo0bl3j+AwcOEBMTQ3R0tOW+Dh06FPuYESNGcM8991h6yvr370/Hjh1LvFazZs1KVetz/fU7dOhg8yJr8/OOiYmx3Ne4cWNCQkI4cOAAbdu2BdQhpcDAQMsx1apVs9vPallJ0iKEcCllSRLtdWxJPD09832t0+ny3Weu5TB/2Or1ehRFyfcY6xoUW1zffK2rV69iMBjYtm1bvsQGIKCM42H+171oV69eZfjw4TzzzDMFjq1Zs2apz1tcUW5aWhp9+vShT58+fPfdd4SHhxMfH0+fPn3Izs4uffBldOutt/Lff/+xfPlyVq9eTY8ePRg5ciQfffRRsY+7/jUqD/OKs9Y/IxX5+ShJcT8/WitzTcuGDRvo168f0dHRpZ5bvm7dOm644Qa8vb2pW7dugXFRIYSozMLDw0lNTbUUrAIl/pVt/uvdaCxbD1erVq0wGo0kJSVRt27dfDfzbJlGjRrx119/5XvcX3/9Rf369QskOtZuuOEG9u/fX+C8devWtcTr5eVVYszNmzdnzZo1hX7v4MGDXLx4kffee4/OnTvTsGHDMvcCNGrUiISEhHw1NX///XeJjwsPD2fo0KF8++23TJ06lVmzZgHl/7+wdv31//77b0vPlHkGkHW81/98lOZ1NT/vhIQEy3379+/nypUrpeqhcgZlTlrS0tJo0aIF06ZNK9XxJ06c4Pbbb6dbt27s3LmT0aNH89hjj7Fy5coyByuEEO6offv2+Pn58eqrr3Ls2DG+//77Ev+4i4iIwNfXlxUrVnDu3DmSk5NLda369evzwAMPMGTIEH7++WdOnDjBli1bmDRpEsuWLQPg+eefZ82aNUycOJHDhw/z9ddf89lnnxVa3Gnt5ZdfZtOmTYwaNYqdO3dy5MgRfvnlF0shLqhDDxs2bOD06dNcuHCh0POMHz+eH374gfHjx3PgwAH27NnD+++/D6g9Nl5eXnz66accP36cJUuWMHHixFI9d7OePXtSv359hg4dyq5du9i4cSOvvfZasY8ZN24cv/zyC0ePHmXfvn0sXbrUklSU9//C2oIFC/jqq684fPgw48ePZ8uWLZbXrW7dusTExDBhwgSOHDnCsmXLCp3NdfXqVdasWcOFCxcKLfLu2bMnzZo144EHHmD79u1s2bKFIUOG0KVLlwJDfc6qzEnLrbfeyttvv51v+llxZs6cSVxcHJMnT6ZRo0aMGjWKAQMG8PHHH5c5WCGEcEehoaF8++23LF++nGbNmvHDDz9YpqwWxcPDg08++YTPP/+c6OjoAjUoxZkzZw5Dhgzh+eefp0GDBvTv359///3XMoRzww03MH/+fH788UeaNm3KuHHjeOutt0qcodO8eXPWr1/P4cOH6dy5M61atWLcuHH5akfeeustTp48SZ06dYpcQ6Rr164sWLCAJUuW0LJlS7p3726ZoRMeHs7cuXNZsGABjRs35r333itxiOZ6er2eRYsWkZGRQbt27Xjsscd45513in2Ml5cXY8eOpXnz5tx8880YDAZ+/PFHoGL/F2ZvvvkmP/74I82bN+d///sfP/zwg6X3w9PTkx9++IGDBw/SvHlz3n//fd5+++18j+/YsSNPPvkkgwYNIjw8nA8++KDANXQ6Hb/88gtVqlTh5ptvpmfPntSuXZt58+aVOV6t6JTrB1LL8mCdjkWLFhW7ZPTNN9/MDTfckG+e+Jw5cxg9enSR2WhWVhZZWVmWr1NSUoiJiSE5OZmgoKDyhiuETaT9d4GAWHWq49X98fg3Kv1YvTuxLsSdP39+sYW4n/f7vMznz8zM5MSJE8TFxdl9u3shRPkV97uakpJCcHCwzT6/7b5Oy9mzZy2V8maRkZGkpKSQcf3qTtdMmjSJ4OBgy8260lkITf37L3TqlPd1p05w3aJUQggh7MMpF5cbO3YsycnJlpt10ZAQmvniC+jUCcOpk9zGMm5jGYZLSXDLLTBpEjhJdb3DGCD0tlBCbwtF0Ze7w1YIIUrN7lOeo6Ki8i0RDHDu3DmCgoKKnNbm7e2Nt7e3vUMTonQyM2HUKPjySwB8gGUd34UqVWBZFpiAV1+Ff/6Br7+G4GBNw3UUg4+B5svU9UhMv1ayhE0IoQm797R06NChwNS11atXl7iQjxBOIS0NunSxJCwAPP00rF0LS5bAxIlg3h/ml1+gbVu4LkkXQghhG2VOWq5evcrOnTstc8RPnDjBzp07iY+PB9ShnSFDhliOf/LJJzl+/DgvvfQSBw8eZPr06cyfP5/nnnvONs9ACHv67DO4NmsBX1/45hv45BPw8lKXVH39dVi+XO11AThyBK6r6hdCCGEbZU5atm7dSqtWrWjVqhUAY8aMsUxrA3XxG3MCA+rul8uWLWP16tW0aNGCyZMn88UXX9CnTx8bPQUh7CQnR01aQO1NWb8eHnyQtDR19VR//2u7AN9yC2zbBn5+6rFz5oDVbqzuyphmZIP/Bjb4b8CQ6bhdnoUQlVeZa1q6du1aYLlpa4UtiNS1a1d27NhR1ksJoa1Fi+DUKbXdt6869HNNgXWb4uJg6FCYMUPNZL76CsaMcVysGjGlSy2LEMJxnHL2kBBOwWptIUaPLvl46/1WPv0UKrCktxBCiIIkaRGiMFu2wObNartpU+jWreTHNGyoDhWBumXwkiV2C08IISojSVqEKMz//V9ee/TovBlCJXn22cLPIYSNnTx5Ep1OV+LGiq6qtBvyispFkhYhrnfmDMyfr7arVoX77y/9Y3v3VntcQC3cddMPFKG9mJgYEhMTadq0qdahCOEwkrQIcb3p0yE3V20/+aQ61bm09Pr8tS3S2yLsxGAwEBUVhYeH3dcIFcJpSNIihLWMDPj82uZ+Hh7w1FMFDtHr1fXmunRR2wUMGQIhIWr7++/dd7E5PQR3CSa4SzCUcvTMFoxpxqJvmcbSH5tRumPLqmvXrjz99NOMHj2aKlWqEBkZyezZs0lLS2PYsGEEBgZSt25dfvvtN8tj5s6dS4j5Z+aaxYsXoytmWPL64aF169ah0+lYs2YNbdq0wc/Pj44dO3Lo0KEiz5Gdnc2oUaOoVq0aPj4+1KpVi0mTJlm+P2XKFJo1a4a/vz8xMTE89dRTXL16tUDcS5cupUGDBvj5+TFgwADS09P5+uuviY2NpUqVKjzzzDMYrQrTY2NjmThxIoMHD8bf35/q1aszbdq0Yl/XhIQEBg4cSEhICKGhodx5552cPHmy2McI9yMpuhDWvv8eLlxQ2wMHQnR0gUN8fWHdumLO4e8Pjz8OH34I2dlqEnRtHSN3YvA10Gqdul6T8VfHzZQy7yxdmNDbQi1bCwD8FfFXkdOyg7sEW+IH+Dv2b3Iu5BQ4rqvStcwxfv3117z00kts2bKFefPmMWLECBYtWsRdd93Fq6++yscff8xDDz1EfHw8fub1fWzktddeY/LkyYSHh/Pkk0/yyCOP8NdffxV67CeffMKSJUuYP38+NWvWJCEhId9eb3q9nk8++YS4uDiOHz/OU089xUsvvcT06dMtx6Snp/PJJ5/w448/kpqayt13381dd91FSEgIy5cv5/jx49xzzz3cdNNNDBo0yPK4Dz/8kFdffZU333yTlStX8uyzz1K/fn169epVIM6cnBz69OlDhw4d2LhxIx4eHrz99tvccsst7N69Gy8vLxu+gsKZSdIihJmi5J/mbF1UW1YjR8LkyeomitOnw8svg+ynVWm0aNGC119/HVBXCX/vvfcICwvj8ccfB2DcuHHMmDGD3bt3c+ONN9r02u+88w5dunQB4JVXXuH2228nMzMTHx+fAsfGx8dTr149OnXqhE6no1atWvm+P9pqqn9sbCxvv/02Tz75ZL6kJScnhxkzZlCnTh0ABgwYwDfffMO5c+cICAigcePGdOvWjbVr1+ZLWm666SZeeeUVAOrXr89ff/3Fxx9/XGjSMm/ePEwmE1988YWl92nOnDmEhISwbt06evfuXc5XS7gaSVqEMNu4EfbuVdsdOkC7duU/V61acPfdsHChOjz0888weLBt4qzkOl/tXPQ3r1uY96akm4o+9rqhvRtP2i55aN48r7fHYDBQtWpVmjVrZrkvMjISgKSkJJtds7BrV6tWzXKdmjVrFjj24YcfplevXjRo0IBbbrmFvn375ksAfv/9dyZNmsTBgwdJSUkhNzeXzMxM0tPTLT1Efn5+loTF/NxiY2MJCAjId9/1z/X6/ec6dOjAVOs/Gqzs2rWLo0ePEhgYmO/+zMxMjh07VtzLIdyM1LQIYbZ0aV57xIgiD0tLg/Bw9ZaWVsz5rOthrM/tJoxpRv4K/4u/wv9y6DL+Bn9D0TcfQ+mP9S3dseXh6emZ72udTpfvPnNvgcmkDl3p9foCK43n5BQcqirrta+/zvVuuOEGTpw4wcSJE8nIyGDgwIEMGDAAUGtm+vbtS/Pmzfnpp5/Ytm2bpe4kOzu71M/VfF9RMZTG1atXad26tWXfO/Pt8OHD3F+W2X3C5UlPixBmq1ap/+p0cOutxR5qLnspVqdOEBgIqamwerU6VFRo5a7rKqwGRJRdeHg4qamppKWl4e/vD+Cw9VeCgoIYNGgQgwYNYsCAAdxyyy1cunSJbdu2YTKZmDx5MvprP7fzzUsB2MDff/9d4OtGjRoVeuwNN9zAvHnziIiIICgoyGYxCNfjXu+gQpTX2bOwa5fabt0awsIqfk5PT+jeXW2fP593fiGu0759e/z8/Hj11Vc5duwY33//faH7uNnalClT+OGHHzh48CCHDx9mwYIFREVFERISQt26dcnJyeHTTz/l+PHjfPPNN8ycOdNm1/7rr7/44IMPOHz4MNOmTWPBggU8W0Qd2QMPPEBYWBh33nknGzdu5MSJE6xbt45nnnmGU+b9wUSlIEmLEAC//57XtmVRn/W5zD05QlwnNDSUb7/9luXLl9OsWTN++OEHJkyYYPfrBgYG8sEHH9CmTRvatm3LyZMnWb58OXq9nhYtWjBlyhTef/99mjZtynfffZdvOnRFPf/882zdupVWrVrx9ttvM2XKFPr06VPosX5+fmzYsIGaNWty991306hRIx599FEyMzOl56WS0SnFbdnsJFJSUggODiY5OVl+QIV9DBkC33yjttetUxdhKUJaGphrDK9eVWc4F+noUahXT2136wZ//GGTcJ2BMc1omX48f/58jD5FT3v+vN/nZT5/ZmYmJ06cIC4urtCZL8J1xcbGMnr06Hyzk4TrKu531daf39LTIoSi5PWC+PurM4dspU4diItT23/+WULlrhBCiOJI0iLEnj15q9Z26wa2XKhKp8sbIsrJUfcjEkIIUS4ye0gI61qTUtSz6PXQpk1eu0S9e+dtDbBqFdx2W9ljdEZ6CGxzbd0MBy7jL1yfLL8vykuSFiHKmLT4+sK//5bh/N27q9mNyeRWxbgGXwOt/20NwKxfZ2kcjRCiMpDhIVG5ZWTAhg1qu2ZNqF/f9tcICYH27dX2gQNgtbeLKJkLzBUQolJz5O+oJC2ictu4EbKy1Hbv3moNij1Y9+CsXm2fa7gZ86qq6enpGkcihCiO+Xf0+pWQ7UGGh0TlVsahIYD0dGjcWG3v3w+l2qS3d2948828az7ySNnidELGdCNbGm8BwPCRAaO3bXd6NhgMhISEWPas8fPzsyxLL4TQnqIopKenk5SUREhICAaD/bfzkKRFVG7mpEWvhx49SvUQRYH//strl0q7dhAcDMnJak+L0QgO+AW3KwWy/suytO0hKioKsM/GgkII2wgJCbH8rtqbJC2i8kpMVKc7A7RtC6Gh9ruWh4eaFP38M1y6BDt25E1BEkXS6XRUq1aNiIiIcm8gKISwH09PT4f0sJhJ0iIqL+vaElsu3V+U3r3VpAXUHh5JWkrNYDA49I1RCOGcpBBXVF7lqGepENmHSAghKkSSFlE5mUx5PS2BgXlTku0pLg7q1lXbmzZBaqr9rymEEG5EkhZROe3eDebizu7dwQFT9YD8S/qvW+eYawohhJuQpEVUTuYF5QB69izTQ3U6dcpz48blWNalV6/CY3BFOvBr7IdfYz9Zxl8I4RCStIjKacuWvHbHjmV6qJ8f7Nun3kq1Rou1G2/Ma5dpLwDnY/Az0G5fO9rta2fzNVqEEKIwkrSIysmctHh7Q7NmjrtuVBTExKjtrVvV9VqEEEKUiiQtovK5fBmOHFHbrVo5rp7FrF079d+0NDh40LHXFkIIFyZJi6h8tm7Na7dtW+aHp6dDkybqrVzb4lhf03qYysUY041sabKFLU22YMiSNVSEEPYnSYuofKwTBXOvRxkoirrn0P79ZVjG35r1NV04aUGB9P3ppO9Pt9sy/kIIYU2SFlH5WBfAliNpqbDWrfOmHbl4Ma4QQjiSJC2i8jH3bgQH5y325khBQdCwodretQsyMx0fgxBCuCBJWkTlcvq0ulEiqLUleo1+Bcw9PLm5auIihBCiRJK0iMrFuoakHEW4NuMmxbhCCOFIkrSIyqWCRbg24y7FuEII4UAeWgcghEPZoAhXp4NatfLa5dK8OXh5QXa26xbj6sC7lrelLYQQ9iY9LaLyMJnyEoToaPVWDn5+cPKkeivzMv5m3t7QooXaPnQIrlwp54m0Y/Az0OFkBzqc7CDL+AshHEKSFlF5HDkCKSlqW8uhITPrGLZt0y4OIYRwEZK0iMrDWYpwC4tB6lqEEKJEkrSIysNGRbgZGWq+0bat2i43Fy/GNWYY2dZ2G9vabpNl/IUQDiGFuKLysC54bdOm3KcxmfK2LzKZKhBPgwYQGAipqa5ZjGuC1K2paluW8RdCOIAkLaJyyM6GHTvUdv36EBKiaTiAurBdmzawdq266N2ZM+UuDran4b8OL/R+Q6aBgQx0cDRCiMpMhodE5bBnj5q4gHMU4ZpZx+KKvS1CCOFAkrSIysHZinDNpBhXCCFKTZIWUTk4y0q413PxYlwhhHAkSVpE5WAeevHwgJYtNQ0lnxo1IDJSbW/dWsHKXiGEcG+StAj3l5oK+/er7ebNwcenwqcMC1NvFabT5fW2XLkCR4/a4KSOkxmUSWZQptZhCCEqCZk9JNzf9u2gXJuTa4OhIX9/OH++wqfJ064d/Pqr2t6yRZ3d5AKMPkYWfbtI6zCEEJWI9LQI97d9e167Auuz2I11TOZp2UIIIQqQpEW4v92789rmTQqdiXVM1rEKIYTIR5IW4f727FH/1euhceMKny4jA7p2VW8VWsbfLCoqr0DGHKsLMGQZ6P5qd7q/2l2W8RdCOITUtAj3lpsL+/ap7bp1wc+vwqc0mWD9+rx2hel0aoHwH3/AuXPqzTyjyJkpELk30tIWQgh7k54W4d6OHoXMa7NbmjfXNpbiNGuW13ah3hYhhHAkSVqEe7NOAJw5abGOTZIWIYQolCQtwr1ZF7a6StIixbhCCFGociUt06ZNIzY2Fh8fH9q3b8+WEpYfnzp1Kg0aNMDX15eYmBiee+45MjNlQSrhANYJgPUQjLNp3FitbQFJWoQQoghlTlrmzZvHmDFjGD9+PNu3b6dFixb06dOHpKSkQo///vvveeWVVxg/fjwHDhzgyy+/ZN68ebz66qsVDl6IEpmHWgICIDZW01CK5ecH9eqp7f371QJiIYQQ+ZQ5aZkyZQqPP/44w4YNo3HjxsycORM/Pz+++uqrQo/ftGkTN910E/fffz+xsbH07t2bwYMHl9g7I0SFpaTAiRNqu1kzdcqzjfj52WQiUn7mIaLMTJdZzj/XO5dcb0mwhBCOUaZ38ezsbLZt20bPnj3zTqDX07NnTzZv3lzoYzp27Mi2bdssScrx48dZvnw5t912W5HXycrKIiUlJd9NiDLbuzevbcOhIX9/SEtTb/7+NjutS9W1JO5NZPFbi7nT/04ebfYo25Zt49zBcxhzjFqHJoRwY2Vap+XChQsYjUYir1tDIjIykoMHDxb6mPvvv58LFy7QqVMnFEUhNzeXJ598stjhoUmTJvHmm2+WJTQhCnKVmUNm1097HjhQu1iKkHwmmX/m/sPJv09a7ou/FE/81ngADF4GqjevTofHOhAcHaxRlEIId2X32UPr1q3j3XffZfr06Wzfvp2ff/6ZZcuWMXHixCIfM3bsWJKTky23hIQEe4cp3JGrzBwyc+KelqyrWWz+cjMLRi3Il7AYvPKvhGvMNhK/NZ6lry8l5az0kAohbKtMPS1hYWEYDAbOnTuX7/5z584RFRVV6GPeeOMNHnroIR577DEAmjVrRlpaGk888QSvvfYa+kLqDLy9vfH29i5LaEIUZP3B37SpzU6bmQn33KO2f/oJfHxsdOLYWLVg+OpVp0pa0i6msfjFxaRdSLPc51vFlw73deCRLY+Qm5nL152+JuFQAqd3nibjSgZpF9JY9voy+k3qR0B4gIbRCyHcSZl6Wry8vGjdujVr1qyx3GcymVizZg0dOnQo9DHp6ekFEhODQf3rTFFk7W9hJ4qSNzwUEwNVqtjs1EYjLF+u3oy2LOHQ6/OSq5Mn1UJijeXm5rLmwzWWhMXgZeCGQTdw38z7aNCtAdW3VafWvlo07NGQ7mO6M+CTAYTEhACQmpTK0teXkn4pXcNnIIRwJ2UeHhozZgyzZ8/m66+/5sCBA4wYMYK0tDSGDRsGwJAhQxg7dqzl+H79+jFjxgx+/PFHTpw4werVq3njjTfo16+fJXkRwuYSEiA5WW27wtCQmXWs1oXEGpkwYQJn958FwD/Mn0EzBtHmgTZ4+noWerxviC99J/YlqFoQACmJKSx9Y2mRSyIIIURZlHnDxEGDBnH+/HnGjRvH2bNnadmyJStWrLAU58bHx+frWXn99dfR6XS8/vrrnD59mvDwcPr168c777xju2chxPVcZVG5611f19Kxo2ahrF69mnfffRcAnV5Hjxd7lGqoxy/Uj75v9+XXsb+SmpTKlYQr9OrVi7Vr1xIaGmrvsIUQbqxcuzyPGjWKUaNGFfq9devW5b+Ahwfjx49n/Pjx5bmUEOXjakW4Zk5SjJuYmMgDDzxgGcJt+1BbohoVXrdWmIDwAG5/+3Z+ffVX0i6ksXv3bkaPHs3//vc/e4UshKgEZO8h4Z5cbbqzmXXBsEYbJxqNRh544AHOnz8PQEzrGFrc1aLM5wmKCqLv233xDlCL6r/55hu2bt1q01iFEJWLJC3CPZl7KTw9oX59bWMpiypV1MJhUJ+DBsXqEydOZO3atQBER0fTdXRXdHpduc4VHB1M68GtLV8///zzUoAvhCg3SVqE+8nKgkOH1Hbjxmri4krMPUMpKRAf79BL792717KGkl6v54cffsA32LdC52x8a2PqX0scN2zYwOLFiysaphCikpKkRbifAwfy5iLbYWjI31/tAFEUGy/jb3b9yrgO9M4772AymQAYN24cN998c5HHGn2M/LDkB35Y8gNGn6Lnfus99HzwwQeWr1988UWys7NtF7QQotKQpEW4H1edOWSmUTHuoUOHmDdvHgDh4eG8+OKLNjv3HXfcQdeuXQE4duwY06ZNs9m5hRCVhyQtwv246swhM42SlkmTJlnqTZ5//nn8bLiNtU6nY/Lkyeh0am3MxIkTuXTpks3OL4SoHCRpEe7HzjOHMjPh3nvVW2amzU+vFg57ealtBw0PnThxgm+//RaAKlWq8NRTT5X4GH22npveu4mb3rsJfXbJbyU33HADQ4YMAeDy5cu89dZbFQtaCFHpSNIi3I+5d6JqVShiT6yKMBph4UL1ZtNl/M08PaFRI7V96JCdMqP83nvvPYzXnszo0aMJDAws8TE6k46am2pSc1NNdKbSzS5655138PVVC3unTZvG4cOHyx+0EKLSkaRFuJekJDirLjtP8+agK99UXc2Ze4iMRrWw2I5OnTrFnDlzAAgMDOTpp5+227WqV6/OSy+9BKj7GsnK2EKIspCkRbgXV11U7noOrGv58MMPycnJAeDpp5+mig03lyzMiy++SEhICADz5s2T2hYhRKlJ0iLci/Umg644c8jMOnY7bpx49uxZZs2aBYCfnx+jR4+227XM/P39efjhhwHIyspi7ty5dr+mEMI9SNIi3Iv1UEqTJtrFUVHWsdtxeGjKlClkXquZefLJJwkPD7fbtawNHz7c0p45c6askiuEKBVJWoR72b8/r20uZnVF1auDuRjW+jnZ0KVLl5g+fToA3t7evPDCC3a5TmEaNmxIt27dADhy5Ihl2wAhhCiOJC3CfSgK7NuntqtXh+BgbeOpCJ1O3YIA4ORJSEuz+SV++OEH0q6d99FHH6VatWo2v0ZxnnzySUt7xowZDr22EMI1SdIi3Mf582Au6jR/4NuBnx9cvarebLj+WkHm56AoeXsp2dDXX39taVsnEKVl9DYyf/585s+fj9G77HO/+/fvT2RkJACLFy8mMTGxzOcQQlQukrQI9+GgoSGdTt1zyN/fzjOqrZ+DjYeI9u/fz7///guoi741K0/Rsk7df8joY4RyvA5eXl48+uijgDr9+csvvyz7SYQQlYokLcJ9WH+w27GnxWGsn4ONkxbrXpahQ4fa9Nxl8fjjj1uW9p81a5ZlgTshhCiMJC3CfTgoacnKgocfVm9ZWXa7jN2SFqPRaFmy38PDg8GDB5frPPocPe2ntqf91Pboc8r3VhIbG8ttt90GQEJCAr/99lu5ziOEqBwkaRHuw0FJS24ufP21esvNtdtloFYtuLbkvS2Tlt9//50zZ84AcPvtt5d7mrPOqKP2H7Wp/UdtdMbyj5NJQa4QorQkaRHuw/zBHhGh7jvk6vT6vLqWY8dstgeRswwNmd16663UrFkTgN9++42TJ09qG5AQwmlJ0iLcw8WLcO6c2naHehYz83MxmcAGmwsmJyezaNEiAKpWrcrtt99e4XNWlMFg4IknngBAURS++OILjSMSQjgrD60DEMImrFeNdcekBdSepArup7RgwQLLCriDBw/Gy8urQuezlUceeYQ3xr2BYlL49KtPSWqXZCnQtfZ5v881iE4I4Sykp0W4B3ebOWRm42JcZxsaMqtWrRpRTaIASElM4eKJixpHJIRwRpK0CPdQGXpaKrgH0bFjx/jzzz+vnbYxrVu3rtD5bK32TbUt7RObTmgYiRDCWUnSItyDu/a0xMWBt7farmBPy//+9z9Le+jQoYUOv2gprkOcZZG6438dl00UhRAFSE2LcA/mD/TQUHX2kB35+UFSUl7brjw8oEED2L1bLcTNyQFPzzKfxmQyWZIWvV7Pgw8+WOHQjN5Gfv7mZ0u7ovyq+FGtcTUS9yWSfDqZSycvUTXODWaBCSFsRnpahOtLSYFTp9R248Z2XltfPX14uHpzSGeFuecoNxeOHi3XKTZv3myZStyrVy+io6MrHpcOsoKzyArOKtcy/oWJuynO0j7+13HbnFQI4Takp0W4PutaDzvuOaSZ6/cgKsdzXLx4saV9//33W9rDfx1ekchsrnbH2myavQkUNWlp80AbpxvGEkJoR3pahOtzcD1LVhaMHKne7LqMv1kFZxApimJJWgwGA3379rVJWPocPa1ntqb1zNblXsb/en6hfkQ1UmcRJZ9O5nL8ZZucVwjhHiRpEa7PwUlLbi5Mn67e7LqMv1kFk5YDBw5w9Nqw0s0330xoaKhNwtIZddRfXp/6y+tXaBn/69XulDeLSIaIhBDWZHhIuD53nTlkVreuWpCbm1uupMV6aOjOO++0YWClV5ZhqLgOcWyatQm4NkR0fxt7hSWEcDHS0yJcn/mDPDAQqlfXNhZ78PKCevXU9qFDZe7e+eWXXyxtrZKWsvCv6k9ko0gAriRckSEiIYSFJC3CtaWlgXmDPQfMHNKMuQcpKwtOlH7htdOnT7NlyxYAWrRoQWxsrB2Csz3rheZkiEgIYSZJi3BtBw/mtd1xaMisnHUtS5YssbT79+9vw4DsK66jTH0WQhQkNS3Ctbl7PYvZ9UlLKYd5rIeGXClpCQgLILJhJOcOnuNy/GUuJ1ymSkyVUtXGyKaKQrgv6WkRrs1d9xy6Xjn2IEpOTuaPP/4AoFatWrRo0cIekdmN9UJzJ/6SvYiEEJK0CFenQU+Lr69aVnLihNp2iPr1QX/t17WUw0MrVqwgJycHUAtwbb1Im9HLyJLZS1gyewlGr4ov43+92h3z6lr+2/qfzc8vhHA9krQI12b+APfzg5o1HXJJvR5iY9Wb3lG/QT4+UKeO2j5wAEymEh9i96nOekiLTCMtMs0u7yQB4QGE1lLXlDl/5DwZVzJsfxEhhEuRpEW4rsxMOHZMbTdq5MAMQiPmnqT0dIiPL/bQ7Oxsli9fDkCVKlXo3LmzvaOzi5g2MWpDgYQdCdoGI4TQnJu/ywu3dvhwXo+DA+tZsrPhxRfVW3a2wy5bphlE69atIyUlBYC+ffviWY6doUuiz9HTck5LWs5pabNl/K9Xs3Ve71nCNklahKjsJGkRrsv6g9uBGyXm5MBHH6m3ayUjjmH9HPftK/ZQR6yCqzPqaLSoEY0WNbLpMv7WIhtG4uXvBcCp7acwGUseFhNCuC9JWoTrcvfdna9n3dNivT7NdUwmk2V9Fm9vb/r06WPvyOxG76Gnegt1leOsq1kkHU7SOCIhhJYkaRGuq7IlLQ0a5LWLmfa8fft2Tp8+DUDPnj0JCAiwd2R2VbONDBEJIVSStAjXZf7g9vTMm1njzgICIOZaYeqBA6AohR62YsUKS7tfv36OiMyuYm6IsbQlaRGicpOkRbgmo1EtxAV1M0GPSrK4s7lH6coVSCp8qGTlypWWtisPDZn5hfoRVicMgAvHLpB+KV3jiIQQWpGkRbimEyfypu40bKhtLI5k/VwLGSJKSUlh8+bNANSvX99lNkgsSUxrq96W7dLbIkRlJUmLcE2VrZ7FzPq5FpK0/PHHHxiN6uq07tDLYpYvaZEhIiEqrUrSpy7cjoZJi68v7N2b13Yo6+dayAwiRw4NGb2MLPtsmaVtTxH1I/AO9CYrNYtTO09hyjWh95C/uYSobOS3Xrgm6w9sByctej00aaLeHL4IbzHDQ4qiWJIWT09Punbtat9Y9JBSM4WUmil2fyfRG/TUaFUDgOy0bM4dPGffCwohnJIkLcI1WX9gW08FdncREVClitq+Lmk5evQoJ06ouyF36tQJf39/R0dnV9ar48ZvK34bAyGEe5KkRbgeRcn7wK5ZExz84ZydDRMmqDeHLuMPoNPl9SydOgWpqZZvOXrWkD5HT9Pvm9L0+6Z2W8bfWo0basC1hXelrkWIykmSFuF6zp2D5GS1rUERbk4OvPmmenPoMv5m1kNEhw5ZmqtWrbK0HZG06Iw6mv3YjGY/NrPbMv7WfIN9Ca8XDsClk5e4euGq3a8phHAukrQI12M9LFKZpjubFTKDKDs7m7Vr1wIQGRlJ8+bNtYjM7mQDRSEqN0lahOuprNOdzaye8/JfpzD81+Hc89E9XL2q9jwENQ5ixLIRDP91uFYR2k1MG1mvRYjKTJIW4Xo0nDnkFKx6l6olXAHUHZDNarSs4eiIHCasdhjegd4AJO5JlF2fhahkJGkRrqey97TExoK3+sEddeoKAAk78nodzFOD3ZHeoCe6WTSg7vp88fhFjSMSQjiSJC3C9ZiTltBQCAvTNhYtGAyWad4Riclknb9q+fCuWrsqviGOXvHOsaq3qG5pn959WsNIhBCOJkmLcC0pKXD62gdVo0bqFODK6NoQkcGooGw8ark7plVMUY9wG/mSlp2StAhRmZQraZk2bRqxsbH4+PjQvn17tmzZUuzxV65cYeTIkVSrVg1vb2/q16/P8uXLyxWwqOSspvhqNTTk4wNbtqg3Hx9NQsj33AO2Wg0N3eC4oSGTp4mVk1eycvJKTJ6Oqy0JqhZEQHgAAGcPnCU3O9dh1xZCaKvMScu8efMYM2YM48ePZ/v27bRo0YI+ffqQlJRU6PHZ2dn06tWLkydPsnDhQg4dOsTs2bOpXr16occLUSwnmO5sMEDbturNYNAkhHxJS9Wj5wHw8PEgsmGkw0JQDAqX6l3iUr1LKAbFYdfV6XREN1frWozZRs4dkCX9hagsypy0TJkyhccff5xhw4bRuHFjZs6ciZ+fH1999VWhx3/11VdcunSJxYsXc9NNNxEbG0uXLl1o0aJFhYMXlVBlL8I1s3rudTPVnoboZtEYPLXKohzLeoaU1LUIUXmUKWnJzs5m27Zt9OzZM+8Eej09e/Zk8+bNhT5myZIldOjQgZEjRxIZGUnTpk159913MRqL3hU2KyuLlJSUfDchAKeY7pydDR9+qN4cvoy/Wb16mK6V85hfBUfPGtLn6Gn4c0Ma/tzQIcv4WzP3tACc3iVJixCVRZneaS5cuIDRaCQyMn8XdGRkJGfPni30McePH2fhwoUYjUaWL1/OG2+8weTJk3n77beLvM6kSZMIDg623GJi3L+4UJSSuafFxwdq1dIkhJwceOkl9abJMv4Avr5cjAwEwDxIVr25Y4dcdUYdrea2otXcVg5Zxt+aXxU/qtRSN468cPQCWVezHHp9IYQ2POx9AZPJREREBLNmzcJgMNC6dWtOnz7Nhx9+yPjx4wt9zNixYxkzZozl65SUFElchNqtcfTaTJkGDUBfuSe/JVYPIfxsKoFA3SAfQmJCChzjjqvimlVvUZ3L/11GMSkk7k0k9sZYrUMSQthZmd71w8LCMBgMnDuXv/Dt3LlzREVFFfqYatWqUb9+fQxWFYuNGjXi7NmzZBfRt+7t7U1QUFC+mxAcPQrmYcXKXM9yzXF/L0u7Y60q6CrZ9O98U59liEiISqFMSYuXlxetW7dmzZo1lvtMJhNr1qyhQ4cOhT7mpptu4ujRo5hMeVMiDx8+TLVq1fDy8ir0MUIUygnqWZzJ3uy8urAbQvw0jEQb1ZpUQ6dXEzVJWoSoHMrcvz5mzBhmz57N119/zYEDBxgxYgRpaWkMGzYMgCFDhjB27FjL8SNGjODSpUs8++yzHD58mGXLlvHuu+8ycuRI2z0LUTk4wXRnZ/LvhauWdmN95eplAfDy8yKifgQAV05dIe1imsYRCSHsrcw1LYMGDeL8+fOMGzeOs2fP0rJlS1asWGEpzo2Pj0dvVWsQExPDypUree6552jevDnVq1fn2Wef5eWXX7bdsxCVg0x3tsjMzGTTf5csX9espB/Y1VtW59xBdbj69K7T1O9eX+OIhBD2VK5C3FGjRjFq1KhCv7du3boC93Xo0IG///67PJcSIo95eEivh3r1tI1FY3///TcXckycAyKBqNNXNI5IG9WbV2f7j9sBSVqEqAzsPntICJswmfKSlrg4DdfPVy+9dm1e2x5KmvWz9butABxATVqCL2fgezWLjABv+wRUCJOniTXvrLG0tRDRIAIPbw9ys3I5ves0iuK4lXmFEI5XueeMCtdx6hSkXRsC0XhoyGCArl3Vm1bL+JtXgbUqTabaqSsOjUExKCQ1SyKpWZJDl/G3ZvA0UK1pNQDSL6VzxcGvgRDCsSRpEa5BZg5Z5GTkkHRY3evrZHBeV09UJf3Atl5UT2YRCeHeJGkRrsGJZg7l5MC0aepNixVxz+4/i2JUezYu1ouw3F8t4bJD49Dl6qi3rB71ltVDl6vd7KXqLfOSljO7z2gWhxDC/iRpEa5h//68duPG2sWBujDvqFHqTYu9h6w3CExrW9PSjkq44tA49Ll62nzehjaft0Gfq91bSWitULwD1VqexL2J+daEEkK4F0lahGuQ6c4WZ/bk9SZ4dowj09cTgGqnHNvT4ix0ep2lriXraha7d+/WOCIhhL1I0iJcgzlpiY6G4GBtY9FQ1tUsLhy7AEDVuKr4BPuSWCNE/fpcKp5ZuRpGp53oZnm7Phe27IIQwj1I0iKc3/nzcEH9oK7svSyJexPh2kSd6ObqB/XZa0mLXoHISrpeiyQtQlQOkrQI52c9NKRxPYvWrOtZzElLYs0qlvuqObiuxVlUiamCT5A6k2r9+vUYjcYSHiGEcEWStAjnZ12EW8l7WsyzY3R6HdWaqHUc5uEhcPwMImdhXddy5coVqWsRwk3JirjC+UkRLgDpl9O5HK8mJeF1w/HyU3dJPxuT19NSWddqAXWI6MSmEwA89dlTNO/fvNDjPu/3uSPDEkLYkCQtwvk52fCQtzcsXZrXdpTEvYmWtnUNx4XIQHI8DXjmGB3a02LyNLH+jfWWttaqNatmaZ/Ze6bIpEUI4bokaRHOzzw8FBoK4eHaxgJ4eMDttzv+utZTnc31LAAmg55z0cHU+O8SkWeS0eeaMHnYf+RXMSicaes8i7lViamCT7APmcmZnN13FpPRhN4gI+BCuBP5jRbOLSUFTl8rPm3cGHTarbyqNXNPi86gI7JhZP7v1QwBwGBUiEhMdnRoTkGn0xHdVE3mstOyuXjiosYRCSFsTZIW4dycsJ4lJwfmzlVvjlrGP/1y3maAEfUi8Ly2oJzZ2RqOn0Gky9URtyaOuDVxmi7jb8162CxxT2IxRwohXJEkLcK5OWHSkp0Nw4apN0ct429dz2KeJZPv+zEhlnaUg1bG1efqufH/buTG/7tR02X8reWra9njPENXQgjbcI53GiGK4kR7DmmpqCJcy/djZK0WgJAaIfiG+AKQuD8Rk1H7AmEhhO1I0iKcmxP2tGjhzN689Vmur2cBSIoOxqRXh2gq61otoNa1mHtbctJzuHD8gsYRCSFsSZIW4dzMSUtAAMTEaBuLRtIvp3PlWu9JeL3wAvUsALmeBpKqBQHqWi06k+LIEJ2KuRgXpK5FCHcjSYtwXhkZcPy42m7YsNLOHErcZzU01LTg0JCZeQ8ir2wjoUmp9g7LaVkPn5l7qIQQ7kGSFuG8Dh8G5VqPQWWuZ7HqLbAuNC1wnNS1ABBcPRjfKmpdi3m9FiGEe5CkRTgv2XMIyF/PEtUoqsjjrGcQVXPQDCJnpNPpLL0tORk5XDgmdS1CuAtZEVc4LyctwvX2hvnz89r2lHElI6+epW7h9Sxm+dZqibd/0mLyNPHnS39a2s4kumk0xzYcA9SpzxH1IzSOSAhhC5K0COflZHsOmXl4wL33OuZa+dZnKWZoCPJqWgCqOWDjRMWgkNApwe7XKQ/r1ypxTyIt72mpXTBCCJuR4SHhvMzDQ15eEBenbSwasS4kLa4IFyDL15OL4QHAtd2elco7gyg4Ohi/UD8Azh6QuhYh3IUkLcI55eTAkSNqu0EDtXvDSeTmwoIF6i03177XMhfh6vQ6IhsVXJ+lwPHXinH90rIJvpRu19h0Rh0xf8YQ82cMOqNzzezS6XSWlYOlrkUI9yFJi3BOx47lbezjRPUsAFlZMHCgesvKst91Mq5kcPnaQnHhdcPx8vMq8TFn8xXjXrFTZCp9jp5OH3Si0wed0Oc431uJ9XYH1sNsQgjX5Tx/vgphzUmLcB3Jen2WwvYbKvQx1nUtCZc52KK6rcNyGdbDaWf2nqHF3S0AGP7r8BIf+3m/z+0WlxCi/JzvzyMhwGmLcB3JesO/kopwzazXaomqxGu1wLX1WkJkvRYh3IkkLcI5yRotliGNktZnyfcY6+GhSrwHEVy3D1FGDhePX9Q4IiFERUnSIpyTuadFr4f69bWNRQMZVzK4fG2tlbC6YaWqZwFID/Qh+VrvQmVeFdcsuoks6S+EO5GkRTgfkykvaalTx/4ruDmhfPUsTUo3NGRmLsYNSs7APyXTlmG5nHzrtUgxrhAuT5IW4Xzi49XNEqHSDg1Z17NYbwBYGolWK+NGOWCROWcWUiME32C15ylxX6LUtQjh4mT2kHA+Tl6E6+UFc+bkte3B3NOi0+uIaly6ehbLY6+razlWxseXlsnDxN/P/m1pOyPzei3H/zpOTnoOl05eIqxOmNZhCSHKSZIW4XycvAjX0xMefth+5z9//jyX/7tWz1Kn9PUsZmetZhBF23EPIsVD4USPE3Y7v62YkxZQe7AkaRHCdcnwkHA+e/fmtZs21S4OjWzYsMHSLu36LNZO13TsxonOTupahHAfkrQI52NOWnQ6p+xpyc2FZcvUmz2W8V+/fr2lXdJ+Q4VJDfElNcgHgOrxl2wW1/V0Rh3R/0YT/W+00y3jb61KTBV8rr0eUtcihGuTpEU4F5MJ9u1T23Xrgq+vtvEUIisL+vZVb/ZYxn/dunVA+epZ1AfqOFNL7W0Jvmy/GUT6HD1dJnahy8QuTrmMv5n1PkTZadlcOmm/RE4IYV/O+04jKqcTJ/JmDlXCoaELFy6wZ88eAMJqh+HlX75K3zM1Qy3taDv2trgK2YdICPcgSYtwLtb1LE2aaBeHRjZu3Ghpl3bp/sKcrpVX11L9P6lruX4fIiGEa5KkRTiXSl6Eax4agvIV4ZpZ97RIMS5UqVkF70B1kcKz+86imBSNIxJClIckLcK5SNIClG2/ocKcqWnd0yLDQzq9zrKycNbVLC7JayKES5KkRTgXcxGupyfUq6dtLA528eJFdu/eDUDV2lXxDij/9gUZAd5cruoPXFurRZGeBalrEcL1SdIinEdODhw8qLYbNLDfcrNOKl89Sxn3GyqMubfF/2oWwZfSK3w+V2e9HYL1NglCCNchK+IK53HkiJq4gFMPDXl5wWef5bVtxbqepaz7DRXmdK1Qmuw4pZ4v/jLJ13pebMXkYWLr8K2WtrMLrRWKd4A3WVezSNyXiGJS0Omdd30ZIURBkrQI5+Ei9SyenjBypO3Pa6ln0ZVzfZbrnKmVv67lQKsaFT6nNcVD4cjtR2x6TnvS6dX1Wk7+fZKsVLWupWpcVa3DEkKUgQwPCefhIkmLPVy6dMlSz9KqVasK1bOY5VurRQpPgeuGiHbLEJEQrkaSFuE8XGSNFqMR1q1Tb0ajbc65ceNGlGvFsl26dLHJORNjQjBdG/2ITrD9tGedUUfEnggi9kQ49TL+1qyLcWW9FiFcjyQtwnmYkxZfX4iL0zaWYmRmQrdu6i3TRivkW9ezdO3a1SbnzPbx5EJkEKCu1aKz8dok+hw9PV7rQY/Xejj1Mv7WQmuFWtZrSdwr+xAJ4Wpc451GuL+MDDh6VG03bgwGg7bxOJh5k0SdTkfnzp1tdl5zXYtPZi6hSak2O6+rMte1gOxDJIQrkqRFOIcDB/LWEqlk9SyXL19m586dALRs2ZIqVaoU/4AyOFMrr66luqyMC8jUZyFcmSQtwjmYF5WDSpe02KOexey01cq4Uoyrype0SF2LEC5FkhbhHCrxzKE//vjD0u7WrZtNz51/t2fpaQF1HyKfIB9A3YdI6lqEcB2StAjnUImTlrVr1wKg1+u5+eabbXruc9WDMRrUmT3S06LS6fLXtVw8cVHjiIQQpSVJi3AO5qQlOBiqV9c2Fgc6f/58vvVZQkJCbHp+o6eBc9HqOaNOXUEvvQoARDeXuhYhXJGsiCu0l5IC8fFqu0kT0Dn3mh+envDBB3ntijDPGgLo3r17xU5WhDO1qhCdcBnPXBPhiSmcqxFik/MqBoUdD++wtF1JdNO8pCVxTyIt7mqhYTRCiNKSpEVoz8WKcL284MUXbXMu89AQ2L6exex0zVDacBxQl/O3VdJi8jRx8O6DNjmXo4XEhOAb7EtGcgaJ+9T1WvQG6XgWwtnJb6nQXiWuZzEX4Xp4eNCpUye7XMN6DyKpa1HpdDqqNVPrWnIycrhw/ILGEQkhSqNcScu0adOIjY3Fx8eH9u3bs2XLllI97scff0Sn09G/f//yXFa4KxdLWoxG+Pdf9VaRZfwTExM5eFDtqWjbti2BgYE2ijA/67VabDmDSGfUEXoklNAjoS6zjL812YdICNdT5qRl3rx5jBkzhvHjx7N9+3ZatGhBnz59SEpKKvZxJ0+e5IUXXrDpap/CTbhY0pKZCe3aqbeKLOPviKEhgPORgWR7qSsMV7dhT4s+R0+f5/vQ5/k+LrOMvzXrpCVxb6KGkQghSqvM7zRTpkzh8ccfZ9iwYTRu3JiZM2fi5+fHV199VeRjjEYjDzzwAG+++Sa1a9cu8RpZWVmkpKTkuwk3Zk5aIiIgPFzbWBzIOmmxVxEugGLQkxijDhFFJKbgkZ1rt2u5kuDqwfhW8QXg7P6zmHJlZpUQzq5MSUt2djbbtm2jZ8+eeSfQ6+nZsyebN28u8nFvvfUWERERPProo6W6zqRJkwgODrbcYmJiyhKmcCXnz4O5l84FellsyZy0eHl50bFjR7te68y1lXH1JoWo08l2vZar0Ol0lllEORk5XDgmdS1COLsyJS0XLlzAaDQSGRmZ7/7IyEjOnj1b6GP+/PNPvvzyS2bPnl3q64wdO5bk5GTLLSEhoSxhClfiYjOHbCU+Pp5jx44BcOONN+Lr62vX6+Wra5FiXAvZh0gI12LXgejU1FQeeughZs+eTVhYWKkf5+3tTVBQUL6bcFN79uS1mzTRLg4Hc9TQkNkZqz2IasjOxhbmGUQAp3ef1jASIURplGmdlrCwMAwGA+fOnct3/7lz54iKiipw/LFjxzh58iT9+vWz3GcyqePGHh4eHDp0iDp16pQnbuEuru1uDECLyrPAlz33GyrMqbiqlnYNWbbeIjg6GP8wf9IupHF2/1mMOUYMngatwxJCFKFMPS1eXl60bt2aNWvWWO4zmUysWbOGDh06FDi+YcOG7Nmzh507d1pud9xxB926dWPnzp1SqyLykha9Hpo10zQUR1EUxdLT4uvrS/v27e1+zSuhfqRe2yRQkpY8Op2O6s3VbSOM2UbOHTxXwiOEEFoq84q4Y8aMYejQobRp04Z27doxdepU0tLSGDZsGABDhgyhevXqTJo0CR8fH5peV6dg3lvl+vtFJZSTkzdzqH598PPTNp5S8vSE8ePz2mV1/PhxS53WTTfdhLe3tw2jK4JOR0JcVRrvOk3wlQyCLqWTElqx11sxKOy5b4+l7aqiW0Rz+I/DAJzedTpfnYsQwrmUOWkZNGgQ58+fZ9y4cZw9e5aWLVuyYsUKS3FufHw8er3rrdkgNHDgAGRnq+1WrbSNpQy8vGDChPI/3tFDQ2YJtdWkBSDmxAX2hdas0PlMnib23r+35AOdnLmnBWSROSGcXbn2Hho1ahSjRo0q9Hvr1q0r9rFz584tzyWFO7KuZ2nZUqsoHM7RRbhmCbXziuFjjl9kX+uKJS3uwr+qPyExIVxJuELS4SSy07O1DkkIUQTpEhHacdGkxWRSZ2rv26e2y0JRFEtPS0BAAK1bt7ZDhIWzLsaNsUVdiwmC4oMIig8CF1+XzdzbopgUWR1XCCcmSYvQjosmLRkZ6pIyTZuq7bI4ePCgZfZd586d8SxPUUw5na0ebFnOP+Z4xZMWQ7aB20fdzu2jbseQ7dozbqq3yBsiOr1Lpj4L4awkaRHaUBTYsUNtR0erS/hXAr///rul7ch6FlCX8z8dqy4yF56YjLcMg1hUa1oNnV7d9FHWaxHCeZWrpkWICouPhytX1LYL9bJUlHXS8rfX3wz/dbhDr58QV5W4w+fRK+rmiccbFVxfqTLyDvAmrG4Y5w+f5/J/lzl79myha08JIbQlPS1CGy46NFQROTk5liJcn2AfqsZWLeERtpcQl1eMW9MGQ0TuxHoWkfUMLyGE85CkRWjDOmlxoenOFbFlyxZSU1MBtYbCPBzhSAm1ZWXcoljXtVgvoCmEcB6StAhtmOtZoNL0tKxevdrSrtGyhiYxnI4NxXQtV7JFMa47iWwYaVnC//fff0dRXHfBPCHclSQtQhvmnpaAAKhdW9NQHMU6abH+q96Rsn08SYoOVmP47xJ6o4vPVbYhD28PohqrdSzWu3ALIZyHFOIKx7t8Gf77T223aKHuO+RCPD3hhRfy2qWRnJzMP//8A0Bw9WACwgPsFF3JEmpXJep0Mp45RqJOXeFMrdBynUcxKBy464Cl7Q6im0dbpjyvWbOGunXrahyREMKaa31aCPewa1de2wXrWby84MMP1ZuXV+kes27dOoxGI6Dd0JDZ9SvjlpfJ08TOYTvZOWwnJk/36LGRuhYhnJskLcLxKnk9S/WW2gwNmSXESTFuUcLqhOHlr2aif/zxB6ayLnkshLArSVqE47n4dGeTCU6eVG+l/Uwzr89iMBg030XYOmmpefxC+U9kAv9z/vif83f5ZfzN9Aa95f/n4sWL7LLuFRRCaE6SFuF45qTFYIAmTTQNpTwyMiAuTr2VZhn/hIQEDh06BMCNN96Il18px5TsJLWKH8lVfIFrPS3lnCVjyDZwx+N3cMfjd7j8Mv7WopvnJZUyRCSEc5GkRThWVhbs36+2GzcGHx9t43EA66GhXr16aRhJnvhrdS0BqVlUuZCmcTTOxbquxfr/TgihPUlahGPt2we5uWrbBYeGysMZkxab7/jsRkJqhFCjhlosvWHDBjLKuiumEMJuJGkRjuXi9SxlZTKZLPUsgYGBtG3bVuOIVNYr48ZUpK7FDel0Om655RYAMjMzWb9+vcYRCSHMJGkRjlXJkpZdu3Zx4YKaFHTr1g3P0i7sYmfWxbiyMm5B5qQFYMWKFRpGIoSwJkmLcKxKlrQ449AQwPlqwWT6qGtLyrTngnr06IHBoBYXS9IihPOQpEU4jsmUl7TUrAmh5VuJ1ZWYh4bAuZIWRa/j1LVdpsPPpeJ7NUvjiJxLSEgIHTp0AODQoUOcPHlS24CEEIAkLcKRTpyAa7scu3Ivi4cHPPWUevMoZiOMzMxMNm7cCEBMTAz169d3UISlc8p6x+eTZe9tUQwKh287zOHbDrvNMv7WrIeIVq5cqWEkQggzSVqE47jJ0JC3N0ybpt68vYs+buPGjWRmZgJqL4tOp3NQhKWTb5G5Y2VPWkyeJrY9uY1tT25zm2X8rUldixDOR5IW4Thbt+a1XXDPobL67bffLO3evXtrGEnhrPcgqnnsvIaROKdWrVoRHh4OqIvMZWdnaxyREEKSFuE413Y5BqBdO+3iqCBFgfPn1Vtxi8kuX74cUJfud8ak5VRsKDmearFp3OFyJC0KeCd7453sDe43OoRer7f8v6WmprJ582aNIxJCSNIiHMNohH//Vds1akC0tvvvVER6OkREqLf09MKPOXbsmGXp/o4dO1KlShUHRlg6Rk+DZb2WyDPJ+KVmlunxhiwDdz90N3c/dDeGLPdZxt+aDBEJ4VwkaRGOceAAXL2qttu31zYWBzD3sgDcdtttGkZSvBP1IyztcvW2uDnrHjJJWoTQniQtwjGsh4YkaXEa+ZOWJA0jcU4RERG0bt0agJ07d3L27FmNIxKicpOkRThGJUpa0tPTWbt2LQA1atSgWbNmGkdUtBMN8pKWWElaCmU9RLRq1SoNIxFCSNIiHMOctBgMcO0vV3e1du1asrLUxdpuu+02p5vqbO1CZCCpQepO23GHk4qvLK6kpK5FCOchSYuwv6tXYe9etd20Kfj7axuPnS1btszSduahIQB0OssQUUBqFuGJKRoH5HxuvPFGgoODAbWnxWg0ahyREJWXJC3C/rZtU5fwB7cfGlIUxVLP4unpSY8ePTSOqGQn64db2rFHpBj3eh4eHvTs2ROAixcvsm3bNo0jEqLykqRF2J+b1bN4eMDQoert+mX8Dxw4wH///QdAly5dCAgI0CDCsilvMa5iUDje/TjHux93y2X8rfXp08fSliEiIbRTzM4pQtiImyUt3t4wd27h37OeNXT77bc7JqAKOmmdtBwqfdJi8jTxz+h/Sj7QDVjXtSxbtoxx48ZpGI0QlZf0tAj7MyctAQHQsKG2sdiZq0x1tpYe4M3Z6mrNRszxC3jkSM3G9WJiYmjRogUAW7ZsITExUeOIhKicJGkR9nX6tHoDaNtWnT3k4hQF0tLUm/Vkm+TkZMuuznXq1KFevXoaRVh25iEiz1wTNU6UcvNEBQyZBgyZBrdcxv96d9xxh6X966+/ahiJEJWXJC3CvtxsaAjUpfsDAtSb9TL+v//+O7m5uYDzT3W+3sly1LUYsgwMHDiQgQMHuu0y/task5YlS5ZoGIkQlZckLcK+tmzJa7tJ0lIUV6xnMTtRzrqWyqR169ZEX9sz6/fff+eqeVsKIYTDSNIi7MsNe1oKYz3V2dfXly5dumgcUdlY7/gsK+MWTqfTWXpbsrKyWL16tcYRCVH5SNIi7MdohK1b1XZMDFSrpm08drRjxw7LvjQ9evTAx8dH44jKJt+Oz4kp+KeUbcfnyuLOO++0tH/55RcNIxGicpKkRdjP/v2VZmdn6w8wV5k1dD3rISJZZK5w3bp1s6y9s3TpUlkdVwgHk3VahP1UkqEhgJ9//hlQhxD69++vbTDldP0ic/tax2gYjbaG/zq8yO+FNw/n6qarXLx4kU2bNtG5c2cHRiZE5SY9LcJ+KknScvjwYfZe21upQ4cOVHPRYTDZ8bl0arWvZWnLLCIhHEuSFmE/brqzs8EAAwaoN4MBFi1aZPneXXfdpWFkFXMhMpCUAF8AYg+dL3HHZ0WvEN8xnviO8Sj6SrBQyzU1W9dEp1ens//yyy8osjO2EA4jw0PCPq5ehX371HazZuDnp208NuTjAwsW5H1tHhoC105a0Ok4GhfNDXuOEXg1k/DEFM5HBxd5uMnLxF+v/OXAAJ2DT5APUY2jSNybyJEjRzh06BAN3XylZyGchfS0CPvYujVvZ+d27bSNxY5OnTrFlmtr0bRo0YI6depoHFHFHKsdbWmXZfPEyqZWu7whIplFJITjSNIi7GPz5ry2G9ezLF682NK+++67tQvERo7F5iUttQ+c0zAS5xbbPtbSlroWIRxHkhZhH+vW5bXdbHZFWhrodOptwYK8VXBdemjomiN1qpOLushcvT3FJy2GTAOD7xjM4DsGq/sPVSJB1YJo3LgxAJs3b+bcOUnwhHAESVqE7WVnw59/qu3q1aFuXW3jsSPzBol169aladOmGkdTcRm+3uwLbABAjVMXCbySoXFEzsu80JyiKCxbtkzjaISoHCRpEba3dWveToJdu6pdEm5KUdS6nbvvvtulNkgszj8hN1ja9fYmahiJc7PeQNF6BpkQwn4kaRG2t3ZtXrtbN+3icCB3qGcx+9sqaWmw54yGkTi3du3aWTZQXLlyJZcvX9Y4IiHcn0x5FrZnXc/StatWUThM9erVadu2reXr4lZTdQXbg5qTqzPgoRipv1t6Woqi1+sZOHAgU6dOJScnh8WLFzNs2DCtwxLCrUlPi7CtrCz469raHTExULu2tvE4QP/+/dHr3edXKc3Dn73B9QGIPn2ZoMvpGkfkvAYNGmRp//jjjxpGIkTl4D7vtMI5/PsvZFwr3nTzehYzdxoaMtsa0dzSri91LUVq3749tWqpa7asWbOG8+dlo0kh7EmSFmFblaCeJScnE4NhBbCMKlWCufnmm7UOyea2hjWztOsXUdei6BVOtznN6TanK9Uy/tZ0Oh333XcfAEajkZ9++knjiIRwb5K0CNuqBPUs69evxGi8FehL//634OHhfqVhO6s2IUenrr3SoIi6FpOXiQ3jNrBh3AZMXiZHhudUrIeI5s2bp2EkQrg/SVqE7WRlwaZNartWLYiL0zYeO/nuu+8s7QEDBmgYif1kePiwt4q6XkvUmSsEX0zTOCLn1bJlS+rXV2uA1q9fz5kzMuNKCHuRpEXYzj//QGam2nbTXpbk5GTLsu3h4eH06tVL44jsZ1tU3mJ5UtdSNJ1OZ+ltURSFhQsXahyREO5LkhZhO9ZDQ25az/LTTz+RlWUArnL5cgLZ2Z5ah2Q32yLykpbC1msxZBq49957uffeeyvdMv7XM9e1gMwiEsKeJGkRtmNdhOumPS3ffvvttZY/ubnemsZib7vDGpGtU+t1ilqvxSPLA48s96vpKavGjRvTrJlavLx582b+++8/jSMSwj2VK2mZNm0asbGx+Pj40L59e7Zs2VLksbNnz6Zz585UqVKFKlWq0LNnz2KPFy4qMzNvZ+e4OLWmxc0kJCSwzro3yc1lenizN1Sta4k8m0zIhasaR+TcrAty58+fr2EkQrivMv+JNG/ePMaMGcPMmTNp3749U6dOpU+fPhw6dIiIiIgCx69bt47BgwfTsWNHfHx8eP/99+nduzf79u2jevXqNnkSwgn8/bdaiAtu28vyww8/oCiVa2rvtqim3HBxHwAN9iTyT7d6GkfkPK5f+Tg5LNnS/uDzDzja8Cif9/vc0WEJ4dbK3NMyZcoUHn/8cYYNG0bjxo2ZOXMmfn5+fPXVV4Ue/9133/HUU0/RsmVLGjZsyBdffIHJZGLNmjVFXiMrK4uUlJR8N+HkKkE9S97QUOVhXddSf6/MiilOcHQwYXXDALhw7ALJZ5JLeIQQoqzKlLRkZ2ezbds2evbsmXcCvZ6ePXuy2Tw0UIL09HRycnIIDQ0t8phJkyYRHBxsucXExJQlTKEFN69n2b17N3v27AGgXbv2GkfjOLurNiRbpxYb198lM4hKUqdzHUv72MZjGkYihHsq0/DQhQsXMBqNREZG5rs/MjKSgwcPluocL7/8MtHR0fkSn+uNHTuWMWPGWL5OSUmRxMWZZWSow0MAdeqoew65GeteFn0zPVwry3p6+dN4+mRrFJX9ZXl4szOoCe2SdxKRlEKV81e5HB6gdVhOq06nOvwz5x8Ajqw9gqIo6CrBVhZCOIpDZw+99957/PjjjyxatAgfH58ij/P29iYoKCjfTTixzZsh+9oHtxv2shiNRr7//nsAdAYdtW+KpVrTQ1Rregidzr1rXFKTQtngdZPl63xTn3Vwruk5zjU9B/K5DEBAeADRzaMBSD6TzMaNGzWOSAj3UqaelrCwMAwGA+fOnct3/7lz54iKiir2sR999BHvvfcev//+O82bNy/2WOFiVq3Ka7th0rJ+/XpOnz4NQEzrGALCDPR7d4rGUdlfalIoqefC2FGjIVzbB7Dx9lP83V1d/dXobeSPd//QMELn1LBXQ87sVpO7L774wi33phJCK2XqafHy8qJ169b5imjNRbUdOnQo8nEffPABEydOZMWKFbRp06b80QrndG2FWHQ66NNH21jswHpoqH7X+hpG4jhXL1Qh9VwYgZEXOFo3mlQPPwCabk1An1t59xkqjdgOsXgHqGv4LFy4kCtXrmgbkBBupMzDQ2PGjGH27Nl8/fXXHDhwgBEjRpCWlsawYcMAGDJkCGPHjrUc//777/PGG2/w1VdfERsby9mzZzl79ixXr8qaD27hyBE4cEBtd+wI4eHaxmNjGRkZlmXZg4KCqNm2psYR2V92hg9Xk0IJjLxAYMQlcg2ebKrWGgD/9CzqHjircYTOzcPLg7pd6wLqz88PP/ygcURCuI8yJy2DBg3io48+Yty4cbRs2ZKdO3eyYsUKS3FufHw8iYl5swxmzJhBdnY2AwYMoFq1apbbRx99ZLtnIbTz66957Tvv1C4OO1m0aBGpqamAujmih7cHOZle/O/Bj/jfgx+Rk+mlcYS2l5PhTUDEJQIjLlnu21C9naXdYou62qsh08BdD97FXQ/eVemX8b9ew14NLe0vvvhCw0iEcC/lWn971KhRjBo1qtDvXb9i6MmTJ8tzCeEqzENDAHfcoV0cdjJjxgxLe+jQoXyXrO7wnJkSqFVIdufpm0VA2OV89/0V3ZocnQFPxUizv+NZ8MiNAPikFF1QX5lVjatKeN1wzh89z/bt29mxYwetWrXSOiwhXJ7sPSTK7+JF+PNPtV2/PjRooG08NrZnzx7+vPb8mjRpQufOnTWOyDG8fDML3JfqFcD2MHWhuchzyVRLuOLgqFxPg955vw9ffvmlhpEI4T4kaRHlt3w5GI1q2817WUaMGFHp19vYWKOtpd18i2wIWJK6N9fFz08tYP7222/JyMjQOCIhXJ8kLaL83HhoKDU1lW+++QYAf39/HnroIY0j0l6+upZ/JGkpiZefFwMHDgQgOTmZn376SeOIhHB9krSI8snKghUr1HbVqlDMlHdX9O2331pmuD344IOywCFwOiCKI4GxAMQdPkfgFek5KMmjjz5qacsQkRAVJ0mLKJ9168A8bf3228GjXDXdTklRFKZPn275esSIERpG41w2XBsi0ivQZHuCxtE4v5tuuokG12q91q1bx5EjRzSOSAjXJkmLKB/roSE3m+r8559/snfvXgA6duxIixYt8n1fp1MIr3uS8Lon3X4Z/+ttqJE3RNRs239crHuRi3UvyjL+RdDpdDz22GOWr6W3RYiKkaRFlJ2i5CUtXl7Qu7e28diYdQHuU089VeD7Ht453DVlEndNmYSHd44jQ9PcvtB6XPCuAkDjXSdZO2k5q6aswuht1Dgy5zVkyBA8PdWdsmfPnk1aWprGEQnhuiRpEWW3cyecOqW2e/SAAPfZ9ffcuXOWFXDDwsIYMGCAxhE5F0WnZ0O0OkTknZ1Lo12nNY7I+UVERHDfffcBcOnSJebOnattQEK4MElaRNn98kte281mDX355Zfk5Ki9J48++ije3t4aR+R8rIeIZOpz6Tz//POW9scff4zRKD1TQpSHJC2i7KzrWfr21S4OGzMajXz++eeAWoswfPjwQo/LzfLk+8fe4fvH3iE3y9ORITqFfyNbkKH3xog3+tUTuOPRfhiyZBn/4rRo0YJevXoBcOzYMX6xTvyFEKUmSYsom4QE2LFDbbduDTVqaBuPDS1ZsoT4+HgAbr31VuLi4go9TlF0XE0K42pSGIpS+SpQMz28+SeqJaAjR4nE/3wAVK565HJ54YUXLG3Ze02I8pGkRZTN4sV5bTcaGlIUhXfeecfy9ciRIzWMxvltqN625INEPr169aJZs2YAbN68mU2bNmkckRCuR5IWUTbWRYR3361ZGLa2atUqtm3bBkDLli259dZbNY7Iua2v3p4c8oaE9EaThtG4Bp1Ol6+2RXpbhCg7SVpE6e3aBdu3q+02baBpU23jsaG3337b0n7ttdcq/T5DJbniE8zmqLxdixvuOqNhNK5j8ODBREdHA7B48WKOHj2qcURCuBZJWkTpzZmT1x42TLs4bGzDhg2W3ZwbNWrE3W7Ug2RPy+O6Wto3rj2sWRyuxMvLi2eeeQZQhyQ//vhjjSMSwrVI0iJKJzsbvv1WbXt7w+DB2sZjQ9a9LGPHjkWvl1+L0thc7QZLu9m/CfinZGoYjesYPnw4AdfWNpozZw4XLlzQOCIhXIf7bBgj7OvXX+HiRbV9111QpYq28djIli1bWL16NQCBkYFsCNzAn7/+WexjdDqFKjFnLO3KKlfvQbbXRUKyU/EwGWm3/ihr+7nPkKG9hISE8NhjjzF16lQyMjKYPn0648aN0zosIVyC/EkpSsd6aOiRR7SLw8asZwy1HNASvaHkXwkP7xzunfYm9057s9It428txwNm9zhLO4ZhIIuOvx/SOiSX8eyzz2IwqIXMU6ZM4dKlSxpHJIRrkKRFlOzMGfjtN7UdEwPdu2sbj43s3r2bJdcWyqtevTr1u9fXOCLXczy4JruCGwJQ88RFYo7JUEdpxMbGMnToUACSk5OZNGmSxhEJ4RpkeEiU7JtvwHRtSuvDD4PBPVY/fffddy3tl156iX2e+zSMxjVlp/vwfcAgWiS/CUDHNYeYVydM46icx/BfC19VGSDzpky8v/MmKyuLTz/9lGeeeYaYmBgHRieE65GeFlE8RYGvvsr7+uGHNQvFlg4ePMj8+fMBdUO7xx57rNSPzc3yZMHI8SwYOb5SLuNvpqT48PJKH1pe7EqaLhCAduuO4ZEj++qURkB4gGUmUVZWFhMmTNA2ICFcgCQtonibN8Pha9NZu3aF2rU1DcdWXnjhBRRFLaIdM2YMfn5+pX6soui4nBDN5YToSrmMP6g9LFfiq1Mjy0i1TFhX/UYAAq5m0vwf2USxtF555RVCQkIAmDt3Lvv379c2ICGcnCQtonjWvSxusjbLihUrWLZsGaDWsowaNUrjiFxLdroPl07WwOCVZbnPes2WjqulILe0QkNDefnllwEwmUy89tprGkckhHOTpEUULS0N5s1T24GBcM892sZjAzk5OTz33HOWrz/44AP8/f01jMi1mBMWD+8sQmvlrYK7I6IJp30jAGiy8xQhF65qFaLLeeaZZ/Ktkrt582aNIxLCeUnSIoo2bx5cvfbhM2gQuMGH+4wZMzh48CAAHTp0YLAbLZJnb/kSltjT6A15+w0pOj1La6uzyvSKwk0y/bnU/Pz8GD9+vOXrV155xTJ0KYTIT5IWUTijEd5/P+/rRx/VLhYbGP7rcIZ+N5QXX33Rcl/kgEieXPokw38dXuwsD1F8wmL2a1wPjNfeUrot2Y93RuVdw6asHnnkEerXV6fcb9iwgd/MSwwIIfKRpEUUbv78vALcLl3gxhu1jccGtn6/ley0bADqd69PRL0IjSNyDaVJWAASAyJZWaszAIFXM7h5hRSVlpaHh0e+hQ5Hjx5NRkaGhhEJ4ZwkaREFmUxg9QbKG29oF4uNXPrvEgdWHADAw8eDtg+1Lfe5dDqFgIgLBERccPtl/IsdEgIu+Zm45GfC/Cp82XggJtQZVb1+3oNnVq7jg3ZR99xzDx07dgTgyJEjvPXWWxpHJITzkaRFFLRoEey7ttBahw4uvwKuoihs/mIzikn9aG11byv8q5a/PsfDO4f7v3iN+794za2X8S+phyXHA965I4137kgj59oylSeDY/i9xk0ABCen02nVQUeH7bJ0Oh2zZ8/Gy8sLgA8//JAdO3ZoHJUQzkWSFpGfooDVrse88QboXHstknnz5nF612lA3RSx2Z3NNI7I+WVneJdqSKgwXza919Lu/dMuWWyuDBo3bmyZ9mw0Gnn00UfJzZXeKiHMJGkR+S1dCjt3qu02beCWWzQNp6JOnTrFiBEjLF/fOOxGPLxk94riGHMNXImPLlfCAnA0JI610WoNVOilNNlIsYxeeeUVmjZVd8vesWMHkydP1jgiIZyHJC0ij6LAxIl5X7/+ukv3sphMJh5++GGuXLkCQJ3OdYjrGFfh8+ZmebJozFgWjRnrlsv4Z6UGYPDOLjFh8ciFZ1f58ewqPzyu6wz4oulAS7vPwl3oc8uW+FRmXl5efPnll+j16tvzhAkTOHLkiMZRCeEc5E9OkWfVKvj3X7XdvDnccYe28VTQJ598wpo1awDwD/On04hONjmvoug4fzTW0nY3eoORkJqJJfaw6IGalwyWtrWDoXX5M7INnc5tJex8KjeuPcymXg3tE7ALK26qfZN+Tdjzyx4yMzN5/PHH+eOPPyyJjBCVlfwGCJWb9bLs3buXV155xfJ112e74h3grWFErsM7MA29vuI9I180y+ttuWX+LvRG6W0pizYPtCEwUt2Icv369Xz++ecaRySE9iRpEao1a+Cvv9R2o0YuvWR/VlYWDz74IFlZ6t44zz33HNVbVNc4Ktdhq2nce8Ia8k9ECwAizyXTbt1Rm5y3svD08aTzyM6Wr5977jm2bt2qYURCaE+SFgGZmTByZN7Xr70GLtwN/cYbb7Br1y4AmjZtyrvvvqtxRJXXF00HWdr3fPUP/imZGkbjemq0rGHZ0DMrK4u7776bpKQkjaMSQjuu+8kkbOett/JWv73xRrjvPm3jqYDffvuNjz76CFALGr/99lt8fHw0jqry2h7RlDXVOwAQlJrBgC9lM8Cymjx5smXRuYSEBAYNGiTToEWlJUlLZbdzJ3zwgdr29IQvvgCDQdOQymvnzp0MHDjQstnc22+/TYsWLTSOSnzQ5glSPNTF/DquPULj7QkaR+RavLy8WLBgAVFRUQCsW7cuX72WEJWJJC2VWW6uuhGi8driX6+9Bk2aaBtTOT0w5wFu6nETV6/tSh3XMY4j9Y/YbTNEn6BUfIJSbX5eV3PV28RV7+ILbC/4VmVqy2GWrx+Y9qdsplhG0dHRLFy4EA8PdcLn5MmT+fHHHzWOSgjHk6SlMvv4Y9i+XW03aQJjx2obTzmlpqaycuJK0i+lAxDRIIJuz3VDp7fP7CdPn2yGfPsCQ759AU+fbLtcwxVke8D4u9IYf1ca2SUsnvBLnV5sCW8OQNj5VO789l8HROhebrrpJv7v//7P8vWjjz7K7t27NYxICMeTpKWyOnoUxo1T2zqdOix0bc8TV5Kbm8vAgQO5eOIiAIFRgfR5rQ8e3rIEkVPR6Xin3VNk6tWfsW5L9xJ38JzGQbmeESNG8PDDDwOQnp5Onz59OHRIVhwWlYckLZWRosATT6izhgCeeUYtwHUxiqIwatQoVqxYAYB3gDe3jrsV3xBfjSMThYn3q8Hk6KcA0Cvw0KcbMci+RGWi0+mYMWMGbduqu5SfPXuWbt26cdhcSC+Em5OkpTKaPBnWrlXbtWrl3yDRRZhMJkaPHm1ZcEvvoafXq70IqRFi92vnZnny66tj+PXVMW65jH9peeTCiDW+jFjjW2AZ/+uZjHounazO51UeYW9QfQCqJ1zi7rn/OCBS9+Lj48OKFSto2bIlAImJiXTr1o2jR2UdHOH+JGmpbBYuhBdfzPv6888hIEC7eMohJyeHIUOG8Mknn1ju6/J0F6KbRjvk+oqiI3FvAxL3NnDLZfxLSw/UPe9B3fMexb6RmBOW3CxvguPO8naHkeTo1BlqPX/dS7elex0SrzsJDQ3l999/p3lztU7ozJkzdOvWjWPHjmkcmRD2JUlLZbJpEzz4YN7X48dDnz7axVMO6enp3HnnnXz33XcAGAwG5syZQ71u9TSOTBTGOmEJjT2Fl18mR6rE8X6bJy3HDJy9iRZ/n9QuSBdVtWpV1qxZQ7NmzQB1R3NJXIS7k2rFyuLIEXUDxGtL2zN0qJq0uJBLly7Rr18/Nm3aBIC3tzfz58/njjvuYPOvsmiZsyksYTFbVKcPUWnneWz/fPQKPPrRH0x5py8nG0RoGLHrCQsLY82aNTRo04DL8ZdJSEigSasm9HixBzVa1sh37Of9ZO8i4fqkp6UyOH8ebr0VLqozbOjZE2bNcqkNEY8ePUqXLl0sCUtQUBArV67kDhffidpdFZewmM1o9gDLanYFwDs7l5ETVxKWmOLgSF1feHg4fd/uS5WaVQDISs3itwm/sfOnnZaFFoVwF5K0uLu0NLWHxdxl3KyZWtfiItObFUVh7ty5tGzZkr171dqHiIgI1q1bR5cuXTSOThSmNAkLADodE9s/zb/h6vBGUEoGT09YIfsTlYNviC93vHcHNdvUBEAxKWz5egtrPlhDjizkJ9yIDA+5s4QEuPNO2LFD/To6GpYtg+BgbeMqpStXrvDkk08yb948y3316tVj+fLl1K1bV8PIRFFKnbBck2Pw5MXOY/ly9cvUSU0gKvEKLz//CzPe6EVizVAHRe3cSruis3eAN31e78O2H7ex/Ud10cjjfx3ncsJler7c054hCuEw0tPirjZtgjZt8hKWoCA1YYmJ0TauUvrzzz9p0aJFvoTlkUceYfv27U6RsHh4Z+HhnaV1GJrLMihkGdQhiLImLGapXgE803U8ST5qkhJ5LpmXX1hCs3//s1vc7kqn19Hm/jb0fq03nn7qdPzL8Zf56dmfeO2110hPT9c4QiEqRqe4wKBnSkoKwcHBJCcnExQUpHU4zm/OHHjySci+tsR8nTqwZAk0bqxtXKVw6tQpXn/9df73v/9ZxuNDQkKYNWsW9957b5GPs8f+QpVR6rmq/PvtHfiFXsHDu/TDCuVNWKxFpp1n8sZ3aXRFHco06WDxkHasvLuFS9VfOYsrp66watIqriRcsdwXGxvLZ599xu23365dYKJSsfXnt/S0uJPsbBgzBh55JC9h6d4d/vnH6ROWlJQUXnvtNerVq8fXX39tSVg6d+7Mrl27ik1YhLZskbAAnPMP57Gek1hVoxOgrpp799dbeGTyWtlgsRxCaoRw95S7aTWwFXoP9a3+5MmT9O3bl7vvvlumRguXJD0t7kBRYOlSeP55dWqz2ahRMGUKeDrvqq1paWl89dVXTJw4kfPnz1vuDwkJ4Y033uDZZ5/lqeVPaRhh5VLWnhZbJSz5KAqP7JvPyL3fWe66XMWfRQ+3ZUuXeih22gjTnV1OuMz5BedZt26d5T69Xs+9997Lyy+/TKtWrbQLTrg16WkR+e3fD7fcos4QMicsHh7qSreffuq0CcuhQ4d49tlniY6O5plnnrEkLF5eXowZM4Zjx44xZswYDAaDxpEWlJvtwW9vjeK3t0aRW9L2xm5Mn61n6KpgRh9MJyLGRgkLgE7HV00H8UKnsaQbfACocjmNRz5ex0sv/ULsoSTbXKcSqRJThT/++INvvvmGiAh1LRyTycS8efO44YYb6NOnD3/88YdMkRZOT5IWV3X0qNqT0rw5rFqVd3/nzrBli7ohopNJT0/np59+olevXjRs2JBPPvmElJS8dTkGDRrEgQMHmDx5MqGhzjtzRDHpSdjajIStzVBMlfNXyGTUc+VkNC2Tc2mVmo2Pr+2nKa+t0YHBt0xlfbV2lvtqH05i7IuLGTZ5LdWv7ewtSken0/Hggw9y6NAh3nnnHcLDwy3fW7VqFT169KB+/fqMGzeOAwcOaBipEEWrvH8muqLMTPj5Z/jii7wND81q1YIPP4QBA5yqaDEpKYlff/2VX375hdWrV5OZmf/DzcfHh/vvv59Ro0ZJF7WLMA8JGbLtv9bPqcBoxnR5nRsTd/Dc9i+pmxoPwI3rj3Dj+iMcrxfBn30asrVTbbL8XGPtIa2FhITw6quv8txzzzF37lw+/PBDTpw4AaiLOE6cOJGJEyfSsmVLBg8ezG233UaTJk3Q6XSlKniXlXeFPUnS4uxSU2HDBvjtN/j+e7h8Of/3/fxg7Fi1nsXXV5sYrZw9e5ZNmzaxadMm/vzzT7Zs2VJol3OdOnV46qmnePjhh526V0XkZ13DElbzFOx1zPDj39Vacf+t/8c9R3/jyT3fE5xzFYDaR5KofSSJgbM3s7Vzbfa2ieFQs2jSA30cEpcr8/X1ZcSIETz++OMsXLiQWbNmsW7dOsvv686dO9m5cycvv/wyERERdOvWjTNVzxDdPJqgakHonOiPI1F5lCtpmTZtGh9++CFnz56lRYsWfPrpp7Rr167I4xcsWMAbb7zByZMnqVevHu+//z633XZbuYN2a+fPw+7dsG4drFmjDvUYjQWPq18fHntM3UMowvH7tWRnZ3P06FH279/PgQMH2LdvH1u2bLH8xVaYqKgo7rjjDu655x569uyJXl85h1ZcVYGiW69MwHE1U0a9gfn1+zIv4G56H9nEQyk/0iTtMAA+WTl0+v0QnX4/hEkHCXHhHGxRjUPNozkVW5XkUD+n6oF0Jh4eHtx3333cd999nDlzhnnz5vHDDz/w77//Wo5JSkrKt2aSl78XVWOrEhoXStW4qlSNq0pwdDBe0tsl7KzMScu8efMYM2YMM2fOpH379kydOpU+ffpw6NAhS4GXtU2bNjF48GAmTZpE3759+f777+nfvz/bt2+nadOmNnkSLsVkgqQkOH0aTp1SbwcPwr59sHevmrQUxcdHHf55/HG1dsUOb8KKopCens758+e5cOEC58+f5/Tp0yQkJBAfH2/598SJE+Tm5pZ4vpCYEGLbxVKrfS0i6keAHn7K+omflv1k89iF/RQ6S6jk/36bS00KJfViGD83CmB1eGsaXT5K/2OrueW/DQTkqgun6RWodfw8tY6fp8+i3QCk+XlzplYVztSqwtkaIVwOC+BymD9XqvqTHOKLYpAEGiA6OprnnnuO5557jqNHj7JkyRLWrl3L+vXrSU1NtRyXnZZN4r5EEvcl5nu8d6A3OxruoHbt2sTFxVGtWjWioqIst8jISIKCpJdGlF+Zpzy3b9+etm3b8tlnnwFqBXpMTAxPP/00r7zySoHjBw0aRFpaGkuXLrXcd+ONN9KyZUtmzpxZqmuap0wdWrOGwIAA9c5CwlZMpoIPNh9n/a+ioLNq57uZTOiu/YvJBEYjOqNR/ddkQsnJQZebiy4nB7Kz8/7NzESXmYk+IwNdRga69HT0qanok5PzbikpGC5cQFeKD3uzzNhYUtu1I7VtW67ccAM5/v4YjUZMJhNGoxGj0UhOTg65ubmWW3Z2dr5bVlYWmZmZZGRkkJ6ebvn36tWrpKSk5LtdvHixQN1JaRm8DETUiyCiYQSRDSOJbBiJb7D2Q1a2lpPpxZyBnwIwbP7TePpkaxyR7RQ25bmoac1euTBpYSAAYwekYu+JVKlJoaSeCyMw8gKBEZfyfc8nN5M2SXtoe3Y3bc7toWHy8VKf16TTkRzsR1qADxkBnqQHepEe4E2GvxdZ3p5ke3tYbjneBnI9DBg99OR66DF6GMj10GMy6DDp9Zj0Oktb0esw6XQoelB0OpRrH9SKDtDpUFDv59rntwKWP0SUQj7TlQp+0L/X672SDyriGrm5uezZs4dxX48j6UgSlxMuk345o1xx6HU6goODCQoKstz8/Pzw8/PD398fX19f/Pz88PLywtvb23Lz8vLCw8MDT0/PfP8aDIYCN51Oh16vt9x0Op3ldv3X1glUYV9b/1vUfcWxdYLmaglf6tWrNOje3WZTnsv0NpOdnc22bdsYO3as5T69Xk/Pnj3ZvHlzoY/ZvHkzY8aMyXdfnz59WLx4cZHXycrKIisrb4n05ORkAPx69MC/LAFrzHTtVlrngAPXbjuA9cDZkyfh5EmYP9/m8ZWXv78/sbGxpAelE1IjhOAawYREhxBULciyiJVZdrr7fKCb5WQCqLOestOzUUzu8xxzMrIw5aZx9YIBvQeYTDpSE8Mx5uoJikwkM9VIZqo6JORlVEgjDYCUJA+yDfZ7M824Ekj6pWD8Qi+gKKmknMs/LJWCJ8sNHVlevSNUh5DsZNpc3kmzlEPUTosn7up/VMu5UPjJFQXDlTSCrqThzqtApfB9hR5fB/iuxKNKQVHgyhX1JtyeubjBVtPpy5S0XLhwAaPRSGRkZL77IyMjOXjwYKGPOXv2bKHHnz17tsjrTJo0iTfffLPA/a6xa477S0tLY9++fVqHobFZAHz3sLZR2MeUQu+9VEjnRV9zY4Pdgsnnchm2I9pqvzCEEGV08eJFgm2wWa9Tzh4aO3Zsvt6ZK1euUKtWLeLj423ypCurlJQUYmJiSEhIkJWFK0heS9uR19I25HW0HXktbSc5OZmaNWvabJZomZKWsLAwDAYD586dy3f/uXPniIqKKvQxUVFRZToesIxhXs88DioqxjyOLCpOXkvbkdfSNuR1tB15LW3HVrNFy3QWLy8vWrduzZo1ayz3mUwm1qxZQ4cOHQp9TIcOHfIdD7B69eoijxdCCCGEKEyZh4fGjBnD0KFDadOmDe3atWPq1KmkpaUxbNgwAIYMGUL16tWZNGkSAM8++yxdunRh8uTJ3H777fz4449s3bqVWbNm2faZCCGEEMKtlTlpGTRoEOfPn2fcuHGcPXuWli1bsmLFCkuxbXx8fL5uoI4dO/L999/z+uuv8+qrr1KvXj0WL15cpjVavL29GT9+fKFDRqL05HW0HXktbUdeS9uQ19F25LW0HVu/lmVep0UIIYQQQguyDKQQQgghXIIkLUIIIYRwCZK0CCGEEMIlSNIihBBCCJcgSYsQQgghXILLJS3vvPMOHTt2xM/Pj5CQEK3DcSnTpk0jNjYWHx8f2rdvz5YtW7QOyeVs2LCBfv36ER0djU6nK3bjT1G0SZMm0bZtWwIDA4mIiKB///4cOnRI67Bc0owZM2jevLll9dYOHTrw22+/aR2Wy3vvvffQ6XSMHj1a61BczoQJEwrspN2wYUObnNvlkpbs7GzuvfdeRowYoXUoLmXevHmMGTOG8ePHs337dlq0aEGfPn1ISkrSOjSXkpaWRosWLZg2bZrWobi09evXM3LkSP7++29Wr15NTk4OvXv3Ji0tTevQXE6NGjV477332LZtG1u3bqV79+7ceeedsqlpBfz77798/vnnNG/eXOtQXFaTJk1ITEy03P7880/bnFhxUXPmzFGCg4O1DsNltGvXThk5cqTla6PRqERHRyuTJk3SMCrXBiiLFi3SOgy3kJSUpADK+vXrtQ7FLVSpUkX54osvtA7j/9u7v1f29zgO4M/zXX0iFmH52UR+5YJCJMnFVpKUGy1Jw51GEwpX8h8QN664oeVmKSm0tnaDRCtLCqkpTBJtCjXvc6Hj5Ph2Tr7jvPf2fT5qN+/Wq2drbc+9+3z2VlIoFBKFhYViY2NDNDQ0CLvdLjuScsbHx0V5efmXzFZup4U+7unpCbu7uzCbza9rP378gNlsxubmpsRkRC/u7u4A4NNOgv1dRSIROBwO3N/f83y3X2Sz2dDc3Pzm85I+7ujoCFlZWcjPz0dHRwcCgcCnzP3w3/iTeq6vrxGJRF6PWvhLeno6Dg8PJaUievH8/IyBgQHU1dV96HgP+tv+/j5qa2vx8PCAxMREOJ1OlJaWyo6lHIfDgb29Pezs7MiOorSamhrMz8+juLgYFxcXmJiYQH19Pfx+P/R6fVSzY2KnZXR09N1FO/988MuV6Huy2Wzw+/1wOByyoyiruLgYPp8P29vb6O3thdVqxcHBgexYSjk7O4PdbsfCwgLi4uJkx1FaU1MT2traUFZWhsbGRqyuruL29hZLS0tRz46JnZahoSF0dXX963Py8/P/nzDfUFpaGnQ6HYLB4Jv1YDCIjIwMSamIgL6+PqysrMDr9SInJ0d2HGVpmoaCggIAQGVlJXZ2djA1NYXZ2VnJydSxu7uLq6srVFRUvK5FIhF4vV7MzMzg8fEROp1OYkJ1JScno6ioCMfHx1HPionSYjAYYDAYZMf4tjRNQ2VlJVwuF1pbWwG8bMm7XC709fXJDUe/JSEE+vv74XQ64fF4kJeXJzvSt/L8/IzHx0fZMZRiMpmwv7//Zq27uxslJSUYGRlhYYlCOBzGyckJOjs7o54VE6XlIwKBAG5ubhAIBBCJRODz+QAABQUFSExMlBsuhg0ODsJqtaKqqgrV1dWYnJzE/f09uru7ZUdTSjgcfvNr4fT0FD6fDykpKTAajRKTqcVms2FxcRHLy8vQ6/W4vLwEACQlJSE+Pl5yOrWMjY2hqakJRqMRoVAIi4uL8Hg8WFtbkx1NKXq9/t01VQkJCUhNTeW1Vh80PDyMlpYW5Obm4vz8HOPj49DpdGhvb49++Jfck/SFrFarAPDu4Xa7ZUeLedPT08JoNApN00R1dbXY2tqSHUk5brf7p+8/q9UqO5pSfvYaAhBzc3Oyoymnp6dH5ObmCk3ThMFgECaTSayvr8uO9S3wludfY7FYRGZmptA0TWRnZwuLxSKOj48/ZfYfQggRffUhIiIi+loxcfcQERER0X9haSEiIiIlsLQQERGRElhaiIiISAksLURERKQElhYiIiJSAksLERERKYGlhYiIiJTA0kJERERKYGkhIiIiJbC0EBERkRL+BEXi2/fAnqEFAAAAAElFTkSuQmCC",
|
|
"text/plain": [
|
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"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Generate 1000 random numbers from the first normal distribution\n",
|
|
"mu1, sigma1 = 1.8, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"data = np.random.normal(mu1, sigma1, 1000)\n",
|
|
"\n",
|
|
"# Create a histogram of the data\n",
|
|
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
|
|
"\n",
|
|
"# Add a graph of the first normal distribution used to generate the data\n",
|
|
"xmin, xmax = -1, 5\n",
|
|
"x = np.linspace(xmin, xmax, 100)\n",
|
|
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
|
|
"plt.plot(x, p1, 'k', linewidth=2)\n",
|
|
"\n",
|
|
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
|
|
"mu2, sigma2 = 1, 0.4\n",
|
|
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
|
|
"plt.plot(x, p2, 'r', linewidth=2)\n",
|
|
"\n",
|
|
"# Add vertical lines at x = 1 and x = 3 with labels\n",
|
|
"plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n",
|
|
"plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n",
|
|
"\n",
|
|
"# Calculate the 95% quantile for the second normal distribution\n",
|
|
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
|
|
"\n",
|
|
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
|
|
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
|
|
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
|
|
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
|
|
"\n",
|
|
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
|
|
"plt.title(title)\n",
|
|
"plt.xlim(xmin, xmax)\n",
|
|
"plt.legend()\n",
|
|
"\n",
|
|
"# Show the plot\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 39,
|
|
"id": "0db5895c-28ab-4617-ad67-7ad8311d0341",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"T-statistic: 39.50918386598358, P-value: 8.942863909656787e-253\n",
|
|
"The means of the two theoretical distributions are statistically different (reject H0).\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Define the parameters for the two normal distributions\n",
|
|
"mu1, sigma1 = 1.8, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n",
|
|
"\n",
|
|
"# Perform a t-test to compare the means of the two theoretical distributions\n",
|
|
"# Since we don't have samples, we use the means and standard deviations directly\n",
|
|
"# Calculate the t-statistic and p-value manually\n",
|
|
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
|
|
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
|
|
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
|
|
"df = n1 + n2 - 2 # degrees of freedom\n",
|
|
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
|
|
"\n",
|
|
"# Print the t-test result\n",
|
|
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
|
|
"\n",
|
|
"# Interpret the result\n",
|
|
"alpha = 0.05\n",
|
|
"if p_value < alpha:\n",
|
|
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
|
|
"else:\n",
|
|
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 51,
|
|
"id": "ab987426-9a37-4c22-b561-d2870b856071",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Generate 1000 random numbers from the first normal distribution\n",
|
|
"mu1, sigma1 = 1.03, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"data = np.random.normal(mu1, sigma1, 1000)\n",
|
|
"\n",
|
|
"# Create a histogram of the data\n",
|
|
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
|
|
"\n",
|
|
"# Add a graph of the first normal distribution used to generate the data\n",
|
|
"xmin, xmax = -1, 5\n",
|
|
"x = np.linspace(xmin, xmax, 100)\n",
|
|
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
|
|
"plt.plot(x, p1, 'k', linewidth=2)\n",
|
|
"\n",
|
|
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
|
|
"mu2, sigma2 = 1, 0.4\n",
|
|
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
|
|
"plt.plot(x, p2, 'r', linewidth=2)\n",
|
|
"\n",
|
|
"# Add vertical lines at x = 1 and x = 3 with labels\n",
|
|
"plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n",
|
|
"plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n",
|
|
"\n",
|
|
"# Calculate the 95% quantile for the second normal distribution\n",
|
|
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
|
|
"\n",
|
|
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
|
|
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
|
|
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
|
|
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
|
|
"\n",
|
|
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
|
|
"plt.title(title)\n",
|
|
"plt.xlim(xmin, xmax)\n",
|
|
"plt.legend()\n",
|
|
"\n",
|
|
"# Show the plot\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 50,
|
|
"id": "9c019dea-d687-4dc1-b48f-fe629e54172e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"T-statistic: 1.4815943949743855, P-value: 0.13860593668122914\n",
|
|
"The means of the two theoretical distributions are not statistically different (fail to reject H0).\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Define the parameters for the two normal distributions\n",
|
|
"mu1, sigma1 = 1.03, 0.5 # mean and standard deviation for the first normal distribution\n",
|
|
"mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n",
|
|
"\n",
|
|
"# Perform a t-test to compare the means of the two theoretical distributions\n",
|
|
"# Since we don't have samples, we use the means and standard deviations directly\n",
|
|
"# Calculate the t-statistic and p-value manually\n",
|
|
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
|
|
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
|
|
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
|
|
"df = n1 + n2 - 2 # degrees of freedom\n",
|
|
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
|
|
"\n",
|
|
"# Print the t-test result\n",
|
|
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
|
|
"\n",
|
|
"# Interpret the result\n",
|
|
"alpha = 0.05\n",
|
|
"if p_value < alpha:\n",
|
|
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
|
|
"else:\n",
|
|
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
|
|
]
|
|
}
|
|
],
|
|
"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": "3.10.12"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|