diff --git a/bayesian/variation_inference_post.ipynb b/bayesian/variation_inference_post.ipynb new file mode 100644 index 0000000..cbe3932 --- /dev/null +++ b/bayesian/variation_inference_post.ipynb @@ -0,0 +1,525 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "lengths = np.array([195, 185])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# lets create a grid of our two parameters\n", + "mu = np.linspace(150, 250)\n", + "sigma = np.linspace(0, 15)[::-1]\n", + "\n", + "mm, ss = np.meshgrid(mu, sigma) # just broadcasted parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/_distn_infrastructure.py:1662: RuntimeWarning: divide by zero encountered in true_divide\n", + " x = np.asarray((x - loc)/scale, dtype=dtyp)\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "likelihood = stats.norm(mm, ss).pdf(lengths[0]) * stats.norm(mm, ss).pdf(lengths[1])\n", + "aspect = mm.max() / ss.max() / 3\n", + "extent = [mm.min(), mm.max(), ss.min(), ss.max()]\n", + "# extent = left right bottom top\n", + "plt.imshow(likelihood, cmap='Reds', aspect=aspect, extent=extent) \n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "prior = stats.norm(200, 15).pdf(mm) * stats.cauchy(0, 10).pdf(ss)\n", + "\n", + "plt.imshow(prior, cmap='Greens', aspect=aspect, extent=extent)\n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "unnormalized_posterior = prior * likelihood\n", + "posterior = unnormalized_posterior / np.nan_to_num(unnormalized_posterior).sum()\n", + "plt.imshow(posterior, cmap='Blues', aspect=aspect, extent=extent)\n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(unnormalized_posterior, cmap='Blues', aspect=aspect, extent=extent)\n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [], + "source": [ + "import pymc3 as pm" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Sequential sampling (1 chains in 1 job)\n", + "NUTS: [sigma, mu]\n", + "100%|██████████| 10500/10500 [00:07<00:00, 1402.54it/s]\n", + "The acceptance probability does not match the target. It is 0.8838815681167924, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "Only one chain was sampled, this makes it impossible to run some convergence checks\n" + ] + } + ], + "source": [ + "with pm.Model():\n", + " # priors\n", + " mu = pm.Normal('mu', mu=200, sd=15)\n", + " sigma = pm.HalfCauchy('sigma', 10)\n", + " \n", + " # likelihood\n", + " observed = pm.Normal('observed', mu=mu, sd=sigma, observed=lengths)\n", + " # sample\n", + " trace = pm.sample(draws=10000, chains=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3604: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAEYCAYAAABBWFftAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4XGeV+PHvGVWrWbZluchy5BqXxLETpzghgTiE9GQ3JEtYlhAWyAYIS1sCAX4sC8vSW4AlhISeAiQshPTeEyd24l7lLluyiq3epfP7496RR6OZ0Z3RNEnn8zzzaObOvTNn7oxm7rnv+55XVBVjjDHGGGOMMSPnS3UAxhhjjDHGGDNWWIJljDHGGGOMMXFiCZYxxhhjjDHGxIklWMYYY4wxxhgTJ5ZgGWOMMcYYY0ycWIJljDHGGGOMMXFiCZYxxhhjjDHGxIklWMYYY4wxxhgTJ5ZgGWOMMcYYY0ycWIJlTJoQkX0i8jkR2SgibSJyl4hME5FHRaRFRJ4SkUki8g4RqQqx7TtTFbsxxpixzX6jjPHOEixj0su7gQuBhcAVwKPAF4ESnP/Xf09daMYYY8Y5+40yxgNLsIxJLz9R1SOqegh4EVijqm+pahfwf8CK1IZnjDFmHLPfKGM8sATLmPRyJOB6R4jbBckNxxhjjBlgv1HGeGAJljGjTxuQ578hIhnA1NSFY4wxxgyw3ygz7lmCZczosxPIFZHLRCQL+DKQk+KYjDHGGLDfKGMswTJmtFHVJuBjwJ3AIZyzhVURNzLGGGOSwH6jjAFR1VTHYIwxxhhjjDFjgrVgGWOMMcYYY0ycWIJljDHGGGOMMXFiCZYxxhhjjDHGxIklWMYYY4wxxhgTJ5mpDiCeSkpKtKKiItVhGGOMidG6devqVXVMzpljv1HGGDO6ef2NGlMJVkVFBWvXrk11GMYYY2IkIvtTHUOi2G+UMcaMbl5/o6yLoDHGGGOMMcbEiSVYxhhjjDHGGBMnY6qLoDHxsuFgI39ed5BdR1rp7OljXmkB71w8jYuWTifDJ6kOzxhjTAz6+pWHNh7m5LKJzJ1akOpwjDFjlCVYxgSob+3ilvs38sz2WvKzM1g0o4jC3Cxe2FnPX948xNySfL59zTJOr5ic6lCNMcZEqbu3H4Bdta2WYBkzCrV391LX0sUJU/JTHUpElmAZ49pU1cSNv1/L0bZubrn4RN5/1gkU5mYBzlnPx7fU8O3HtnPdHa9x6yWL+PC5c1McsTHGmGiIdUAwZlR7pbKBtu5eyoonkJmRviOdLMEyBthR08L77nyNwtwsHvjo2ZxUNnHQ/Rk+4dKTZ/C2BSXc8ueN/PfD2+jq7efj589PUcTGGGNipZrqCIwxsehyW6HT/V84fVM/Y5LkcGMH1/9qDROyM7jvxrOGJFeBinKz+Nn7TuUfls/ku4/v4Dcv701ipMYYY4wxJt1ZC5YZ13r7+vnEvW/R1tXH/R9dRfnkvGG3yfAJ37v2FNq6+/jaQ1tZOK2Qs+eXJCFaY4wx8ZHu57+NGV/21LXS0NY9Zsa4WwuWGddue6aSdfuP8Y1/PIlF04s8b5eZ4eOH71nOnJJ8br73LaqbOhIYpTHGmHiwMVjGpKdNh5o43Dh2jqUswTLj1qaqJn76zC6uPrWMq5aXRb19QU4md1y/ks6ePm65fyNqnfqNMWZUsK9rk056+/o5eLQ91WGMKul+rsQSLDMu9fUrX/rrJibn5/CfVyyN+XHmTS3gi5cu5sVd9dy95kAcIzTGGBNvkvaHZaFVHWvnb+sPDZSZN2PLhqom3jxwjKNt3akOxcRJQhMsEblYRHaISKWIfCHE/SIit7n3bxSRUwPuKxaR+0Vku4hsE5FViYzVjC/3rNnPxqom/t/li5k4IWtEj/W+M2fztvkl/M8j2zg0hpq3jTFmrBptDVi769oAZw4gM/Z09fQBzslfMzYkLMESkQzgZ8AlwBLgvSKyJGi1S4AF7uVG4OcB9/0YeExVFwGnANsSFasZX5o7e/j+kzs5e94Urjxl5ogfT0T45tUn06/K1/++NQ4RGmOSSUTKReRZ92TeFhH5pLv8u+5Jvo0i8n8iUuwurxCRDhFZ715uT+0rMGOdv93Njr/jo69f6emz1kCTOIlswToDqFTVParaDdwHXBW0zlXA79TxGlAsIjNEpAg4D7gLQFW7VbUxgbGaceQXz++msb2HL166GInTiOfyyXl8YvUCHttSw7Pba+PymMaY6InIBBE5McrNeoHPqupi4Czg4+4JwSeBk1R1GbATuDVgm92quty93BSX4I0xSfHs9loe2VSd6jBMDHSUtD8nMsEqAw4G3K5yl3lZZy5QB/xaRN4SkTtFJD/Uk4jIjSKyVkTW1tXVxS96MyYdae7krpf2ctXymRHnu4rFR86dy9yp+Xztoa12ZsyYFBCRK4D1wGPu7eUi8uBw26lqtaq+6V5vwekxUaaqT6iqv0/Wa8CsxERuks2KXIxvbdbVMqV6+vppaO0a0WOk+79wIhOsUE0Dwfsj3DqZwKnAz1V1BdAGDBnDBaCqd6jqSlVdOXXq1JHEa8aBnz1bSV+/8tkLoz3BPbzsTB9funQxe+vbuPd1K3hhTAp8Faf3RCOAqq4HKqJ5ABGpAFYAa4Lu+lfg0YDbc9wTgM+LyLkRHs9OAhozBtSPMCEwx72x9ygvVdbTO4ZPRicywaoCygNuzwIOe1ynCqhSVf8P3P04CZcxMatp6uS+1w9yzWmzmD1l+AmFY7F6USlnzZ3Mj5/aRUtnT0KewxgTVq+qNsW6sYgUAA8An1LV5oDlX8LpRni3u6gamO2eAPwMcI/btX0IOwmYnkZLNyO/8T5/V29fP03tyflNDdUD5eDRdl6urLdS6nHS1OG8l2N5TGEiE6w3gAUiMkdEsoHrgOCuGg8C17vVBM8CmtyuGjXAwYB+9BcAVj3AjMgvXthNnyofe8f8hD2HiHDrJYtpaOvmjhf2JOx5jDEhbRaRfwYyRGSBiPwEeMXLhiKShZNc3a2qfwlY/gHgcuB96k52p6pdqtrgXl8H7AYWxvelmPGgs6ePZjsZN6y1+4/x3M7ahHe/r6xt5ZFN1XR09w1a3trldClsD1puYjOG86oBCUuw3H7rNwOP4/Rn/5OqbhGRm0TEPyD4EWAPUAn8EvhYwEN8ArhbRDYCy4H/SVSsZuyrb+3injUH+McVZZRPTkzrld8p5cVcccpMfvniHo40dyb0uYwxg3wCWAp0AfcCzcCnhttInGo3dwHbVPUHAcsvBj4PXKmq7QHLp7qVchGRuTiVcO2MyjBUNW0mZE+TMHhq2xErjORBY7szP1R/HN64SKXQq5ucqVasHP7otK++jS2HY+7EEFeZiXxwVX0EJ4kKXHZ7wHUFPh5m2/XAykTGZ8aPe9ccoKu3n5vePi8pz3fLRSfy2OZqfvjkTr717mVJeU5jxjs3CfqSe4nGOcD7gU0ist5d9kXgNiAHeNKtOPqaWzHwPOBrItIL9AE3qerROLyEtNLS2cOxtp64dal+YusRVJWLT5oRl8cbCxI571Fjeze7altZecKkuFXMHQuqjh3v5tfU3kNPfz8lBTmD1ukLk8h52Y3P7ails6efi0+aPqI4x7J4fBpDvUUbqpyC40tnxreIWSwSmmAZkw56+vr5/Wv7OW/hVOaXFiTlOcsn53H9qgp+/fJePnzuHOaXFibleY0Zz0TkWUL0PlHV1ZG2U9WXCP2b/0iIZajqAzjdCce053fW0devcUuwOnvSp3tVmjRgJdQb+47R3t1L+4wi8nPGxuFevFsen9vptB5etdwpci3u18Cruxu49OQZZGVE39HLP74oGuPh8zjeJHIMljFp4dHNNdS2dPHBsyuS+rw3nz+fvOxMfvDkzqQ+rzHj2H8An3Mv/w+nZPvalEY0iiWydcWYdNPU0TOoa2BXb/Iq3Pn/18bL/1y8X2U67jdPCZaInJToQIxJlN+8vJeKKXm8fWFyK3hNys/mQ2+bwyObath8KD36BBszlqnquoDLy6r6GeDMVMc1Hjy97Qiv7m5IdRhmzEp8F8fndtTSkaJW1mPuGLNdtS0pef7RJDiZ6uju46GNh9lb3xZy/Tf2HeVAQ/KrP3ptwbpdRF4XkY+JSHFCIzImjjYcbOTNA4184OwKfL7k90H/8LlzKM7L4ntP7Ej6cxsz3ojI5IBLiYhcBNhAiCRo7eqltmVsF/Vp7uzhb+sPUZuC4kX+Y0orvjBy6VLgJJ4e2VTNvjAJxljV2OEkpf4Kj4cbO0Kud7ixg7cOHktaXH6eEixVfRvwPpw5q9aKyD0icmFCIzMmDn77yj7yszO45rRZKXn+wtwsbnr7PJ7bUcfafWNuDLwx6WYdTpfAdcCrwGeBD6U0onFuw8FG/rb+UKrDCKmrd2hrRXVTB39bf4jK2lb+tv7QoHLdx9qcA7rDTclPsPxV9NYfbEz6c49UU3sP/WnYhStVjrZ18+yO2pDd2iSGljpVpaevn42jqKdMPE53t3X18crueo66/5fpljh7HoOlqruAL+OUrH07cJuIbBeRqxMVnDEjUdvSyd83HubaleUU5malLI4PrKpgamEO3318R9qUKDZmLFLVOao61/27QFXf5RawMAlQ29I5bIvKvob0PKuuqjy2uWbIVBoHjzpnwf2lngPnqGrrcpKt/Q1t7E/T15VuWrt6eW5nLVsONw+/chob7qdbVak61u7pN37L4SaaO3pCFsPIyYq9NEI0xxfxOBbp7evnqa1HqGnqDNt6FPb5R/zsTtGcupYuttc0u48Z+VGTffzldQzWMhH5Ic58VquBK1R1sXv9hwmMz5iY3bvmID19yvWrTkhpHBOyM7j5/Pms2XuUlyrrUxqLMWORiFwd6ZLq+MaqV3c38Mwon8PptT2Rx40FnmkPHB+TyJakju4+XtxVR3cSiiw0dfTwxr6jcWthqjrWzp661oHbXe6YJn93rlilosp8NE958GgH6/YfY4+Hbnr+VqrAA/6y4gkATC/KjSpG53GiW7+7t58HNxymcoTjvRo7emjr7mXN3gbe2Hc06VVCg1/3cK1/B44mdxyW11T5p8CbwCmq+nFVfRNAVQ/jtGoZk1a6e/v5w5r9nH/iVOZOTU5p9kiuO6OcsuIJfM9asYxJhCsiXC5PYVxp4W/rD7F1BC0Ikb6z4lG961hbN1sPN/PY5poRH/SNBbtqWzja1h120H60IiUnbx44xuHGDlo6w7dE7q5r5a0D3sawrNt/jE0BXdXGy/xb3X1OMhzYpXTIOr39g/5fAv9z/LvJy+5q7uwZUeEsf6z741z4Idbvgv5+jUs34uFasHqT3E3V68QIlwIdqtoHICI+IFdV21X19wmLzpgYPbKpmrqWLm44Z06qQwEgJzODT16wgFse2MiTW4/wrqU27t6YeFHVD6Y6hnTlT4521bawZGZRxHV7+/rp7Vee3V7LyorJCY+ts6ePrAwfL1XW0+/GueVwc9h5A3v7+smMYV6iRIt3XD3uAfD2mmZOnJ76ORT9B/MrZk+Karu2rl5e3FUHxG98TLSPc7ixg2lFuWQEFLkaSSjh8p9QiVFPX/+gebQe3VxNUW4W2Zkj+6w867YaL5hWQE5mRtSvxx/qSN+TuEwWjJKsavjJTvW9vstPARMCbue5y4xJS79+ZR9zp+Zz7vySVIcy4OpTy5hbks/3n9iZlnM2GDMWiMhlInKLiHzFf0l1TIlW39pFS2f0k5sGe3hTNY9vqaG7r39gXEO8hGoFe3xLDa/sPp5cBVu77+jAGKmapk4e3lQ9MKA9Gj19/eyoaaGnrz/qrmo9/Rrx+/pI8/G46lu7aGoP/z509fZ56oqXkk4OCTj6jNQqNhL+BNSvqaOHhtauIevVt3bxxr6jI2q99cq/+wI/y49sqh6yXnNnT8gEJ5b33Bdj66B/s3D/d2NVsltTvSZYuao60KnWvR6fqd2NibO3Dhxjw8FGbkhRafZwMjN8fPrChew40sJDGw+nOhxjxhwRuR14D/AJnGOea4HUDsJMgpcr61M6Fmp3wJibaEVKmA41dgyMkap3D6BjSbC2Hm5me00zj2yqjnqurrX7jvL8ztqw3STrWpy4jrV383JlPc/tDP8+PLa5hqe2HYnq+RMugcfYiTiePdTYziObqgcVH3luR23I8c3+RCwZpe1jOXgfrktbosRSqdCLZL+aaOcMS9cWrDYROdV/Q0ROA6IrGWJMkvzmlX0U5mRy9ampKc0eyWUnz2DxjCJ++OTOIWfhjDEjdraqXg8cU9X/AlbhTC9iEiiW8SCHoqw65h+P5D/rvqOmxfO8PyMde9HS2TtoXNFwGtu7w7Z6RTuRbVdv36DfisA8r66li/rWLp7dUcvTERK3eDVUbK9pHigXH6yzp29Ii02o593f0MYTW2qGfa699W28ETC1if/g+Eizk9BGaik8vk38D6m74/G7Heew0nlcd2ePMwmwl/crkuqmjrR+naF4TbA+BfxZRF4UkReBPwI3Jy4sY2JzpLmThzdWc+3KcgpyvA4xTB6fT/jshQvZ19DOA+uqUh2OMWON/6i9XURmAj1AegzETDNNHT30ejxYjPW4ZtCA/qDHeHN/dBN/+hMrf2W97TXNbKhK3pxQoSqQ7atvC7lvnt9ZF1VCFizwIR/bXBOyqxnAK7vrebmynuaOnoHJVkN5atuRgbLz4XhpgNlR08LzO/1jqgZ3naxr6Yp40lBxWjrXH2yko6dvyMFya1fvoKR7Y1Vj1KW/k6GytpXqpo6wXXKDPw/+MuahVx66KLglrLK2daD1Npi/9TTaf8/glrP1BxvZ39DG5kNNPLM9vi2sNU2d9PUre8NMa6A6fEveocYOXt97lN11Iyv6sre+LanzsXmdaPgNYBHwUeBjwGJVXZfIwIyJxd1rDtCnqS/NHskFi0tZXl7MbU/vSnpZU2PGuIdEpBj4Lk7l233AvSmNKA319yvP7ajljX3RJTnRitQdLp7jP3r7+vnb+kNh56ZK1FiTSAnesWG6MrZ29SZ8AubAJKaytnUgrm3Vx8ckxdpNbdOhJh7aeDiqVoXAls7gzZ7ZXsvagBarQP39GnXLXyReY/bnOt29/XT0HE9gX997dFCX3NqWzrAl9f1lzAc9rr9Me2BMYWLYcriJl8NM7/JGmP01nBd2Oo/nT+b2N7Sx/mAju+taQ46ba2rvYe2+o8Putx01LQNVFFWVHTUt9PY7+yXaRrv+fh1Ihvyl/iNVaPSiubNnRN2ZoxVNKZPTgWXACuC9InJ9YkIyJjZdvX3cs2Y/q08spaIkP9XhhCUifO6iEznc1Mk9aw6kOhxjxgxV/bqqNqrqAzhjrxap6pgqctHZ08f2muYRdZfxb9nQdvzMeNWx+M8RE3gCKZHnjbvcg9udR0IfPCWjJSTaA8jgogyByZaXt3bnkdjK2b+wqy7kttHE39LZM9BlM1Ksgclbc4hJdQetG+GBQrV+hFu9vbuXxzbXDO5WGfGZHaFapPzP8fS2I1QdC/0Z6utXXt3dEFVRmFjHptW3dkVsqfTbcLAxYvLe1RtdorJ2/1EONXYMee7g1raqY+0DYyYPN3WyvaY55gmm/77xME8mYLxiT1/yWrA89aESkd8D84D1gP+dUeB3CYrLmKg9vLGa+tZubjinItWhDOuc+SWsmjuF/32ukuvOKCcvO/26Mxoz2ojIBpwu7H9U1d1A6L41o9iGg43UNHdSUpBDSUFO3B53XVCXveEO8hM9CW64A+5QB6f+EtyJrIoWbeXX5jhUdQynrat3UCuU3yu761k0vYjJ+dlA4qqmxVJQZSTvTW8UB8Uv7Kyjq7efF3bWsXTmRM/bRXpN8Rh3Far7ZLS7JFxLVvDj7HMT0gMN7RTkZg58Ho62dQ96jEifjr31bRTmZlJSkBNVQuh/ncFd8cI9RmVtK7lZg9t6/MlhcA+fPfWtUSenqRy35bUFayVwjqp+TFU/4V7+PZGBGRMNVeXXL+9jfmkBb0uj0uyR/MdFJ1Lf2s2vX96X6lCMGSuuBHqBP4nIGyLyHyIyO9VBxVOfe8CQ6BLLTcO0OITrzhVO4FnzkUwmHOpl+w+6UtHlursv/HP2D1PiPZj/YHC4g8Jw99a1dA2aEDjS4zy19QgNrV2pKQk/AgMlzsPsBX8LRWtX74j/R+LZLfHRzccLe3jNEbxOveCfayzYWweP8eKuOrZVN9Pc2cOLu+qG7JNwk1lvrGocktDF86PiT8R217VG1coVbRe/1/fG1o0yHrwmWJuBqGdGFZGLRWSHiFSKyBdC3C8icpt7/8bASoXu/Rki8paIPBTtc5vx5c0DjWw61MQHzq4YNTPHn3bCJFYvKuUXz+8e9mDGGDM8Vd2vqt9R1dOAf8bp1r43xWHF1UBltBEc7QQfeIeq6DfcwWnLMF2V2oLuf3Lr8e4+sXYbguG7V430jHW02/u7joVq5Xhi65GQU3KsP9gYsatSpAgyh5l6xGv4bd297gTPzu1k/272q4Ys/qCqVDcN36Vzf0M7f1t/aEjLUODndmPAGLm+fo26G2y4FiO/kPGHWTfU50pROnv6BpWRD3wXvLYUBnbdCzXn184jLWGnJ9iYpEIxiSoNHyjUZ7+mefB7lMyPudcEqwTYKiKPi8iD/kukDUQkA/gZcAmwBGfc1pKg1S4BFriXG4GfB93/SWCbxxjNOPabV/ZRmJvJ1SvKUh1KVD77roU0d/Zy54t7Uh2KMWOCiFSIyC3AfTjFmW5JcUhxVdsSpiIZTgvOE1tqhiQ3gdt29vQNHAT6D0iibY3q6esftrUonvM9xTq4vS9goHyihSoOEG6sy/6GtoGiE4H870ekJGliXlbEOLr7+unu7Q/ZhTNUQuA/uO/u7Y/42QonXKjDPdb2mhbW7G0Ysp5q5FYH/8nIY265+EitTF0B+2DToSbW7T/mtNpFjMy74OIVXgUms49vqeHJrUfi1pIYbm6okbTuhkqOVHWgimEoXsaKpUIyEyyvAz++GsNjnwFUquoeABG5D7gK2BqwzlXA79RJ7V8TkWIRmaGq1SIyC7gM+AbwmRie34wTNU2dPLqpmhvOriA/DUuzR7J05kQuWzaDu17aywfOrojrmApjxhsRWQNkAX8CrvX//owXVcfa6ejpY299GyeVDR1/8uruBnKzMli9qBRwzvZ76cJW29LF9Im5A7dHUoLcq8ADzie2BnavGnyEtK++bVA1P1XnIOpAQztvHTzGlPzhv1N3Hmlh4bTCEcUbqZDG/oa2uFUvKy3MiThZck9fP49uDl3WPdJ8Za/srqevX7li2Ux8Aa1kXid2Dm7x3Hq4OeI+bXeT5uBEsDbooD04QQ5uKfSSmBwJaMU42tZNWxQJe7iTFceff3AAXrv1Odt6f9xoC1N4EW5sWbjxlYEhVda2hizs0dHTR21L55BCKiNJbOLZupqMljQ/r2Xan8cpd5vlXn8DpwRuJGXAwYDbVe4yr+v8COfMY8TRhSJyo4isFZG1dXWh+6Gase3uNfvd0uwVqQ4lJp9+50I6e/r4+XO7Ux2KMaPdB1T1VFX91lhPrhpDdCvWge5eQ5f5dfb0DU5ePEz6umZvw8CcWU3tPRwMMSdU4OMn4mAwnOBkz//SDrvdzAIrJYazrbp5xBOhRrL+YOOQFq5Qx4wDLYvDtLEEdimLRluE7fyJdvA64cb3BHrzwDHWHxzc1cxrC0bwwXNwi9ZbB49FPjiPsuVna3Vz2HL+oQzXEhv89F4S0uHyhbqWLh7cMLhr6YaD8T+pEW7esuHmTIPjCXIooU4AhJvLazj1rV1RJa1+u460hGwlTiZPCZaIfAS4H/iFu6gM+Otwm4VYFvxZDLmOiFwO1HqZa0tV71DVlaq6curUqcOtbsaYzp4+7llzgAsWTWP2lLxUhxOT+aUFXH3qLH7/2n5Pfc+NMaGp6vZYthORchF5VkS2icgWEfmku3yyiDwpIrvcv5MCtrnVHT+8Q0Quitdr8CpUFTmvAlsbvFZI82/x3M7I40Ie31LDY5uHT9rSTb2HRCyeYj2PPpLxa174x/109/azy0Mp+N7+/pAJ93Ato/6xMU3tgydJDj4hUNsc+X0J/DwmM7H3CzcJtBdvHQg9/ilU17toq1iOxJBJtd0Pa31rF+sPNsbU3TDW6F+urA9biCOSrdXNIRPFWJK1WHkdg/Vx4BygGUBVdwGlw2xTBZQH3J4FBI/2DLfOOcCVIrIPpx/9ahH5g8dYzTjy4IbDNLR1c8PZFakOZUQ+ecECVJWfPFOZ6lCMGY96gc+q6mLgLODj7pjhLwBPq+oC4Gn3Nu591wFLgYuB/3XHHSfdmweGThYc2A0m1IHN4x5arYKppuYANlhj++AWguDXp6psPtQ0qFuYF+lQTc/fLWykE6rGw+bDTWz1kMS/tCt8IYhIE+H6X+uu2haeDmglCm4BiqZE+nDJWLrwdyf1T8Ib6K0DjSHHUaWiQibAWweODUz0u/lQE/sb2nhuR/S9xbp6+hM6dYFXoQr6JIrXBKtLVQc+9SKSyfAJ6RvAAhGZIyLZOD9GwYUxHgSud6sJngU0qWq1qt6qqrNUtcLd7hlV/RePsZpxQlX51Ut7WTS9kHPmT0l1OCNSPjmP954xmz++cXBEJYyNMdFzf3fedK+34BRXKsMZJ/xbd7XfAv/gXr8KuE9Vu1R1L1CJM+440XEOWRbYenDM7ea2q7aFpvYejrZ189yO6OcsCqWlsydpLVM7aloGihgEqwvqahS8T7r7+mMa7+QlmYinUMUZ/K8kHQoEeJ17Kt6xhjoI95r87omhpSNd+HuvhEq6IPy8aqEKl8TTgaPtg4qFgHOiJdqEr6u3j2e313LwaPtAd+N4C/edkSpeKwI8LyJfBCaIyIXAx4C/R9pAVXtF5GbgcSAD+JWqbhGRm9z7bwceAS7F+XFqBz4Y28sw49HLlQ1sr2nhu9csGzWl2SP55AUL+L+3DvFff9/K7/71jDHxmoxJJhHJAz4LzFbVj4jIAuBEVfU81YeIVAArgDXANFWtBicJExF/z40y4LWAzUKNMfY/3o04VXKZPXtkU3INV1wisIvxcF35opXMg/5Qg+cDRToTHlgOPhqqSk+XrkCNAAAgAElEQVRf/5Cyzsk0ku5m8fTanoaYx8wkwnCfB7/g1s3xINZKhiMV6/9JqBb3scprC9YXgDpgE/BvOInRl4fbSFUfUdWFqjpPVb/hLrvdTa5Qx8fd+09W1bUhHuM5Vb3c6wsy48edL+2hpCCHK5fPTHUocTGlIIdPvXMhL+6q5+lt8T04Mmac+DXQBaxyb1cB/+11YxEpAB4APqWqkY7qvIwxdhbGcZxwddDZ6mR22evsScxZ51g863F+oGilS4KTakeaO5M65seYschrFcF+Vf2lql6rqte41+2/z6TMriMtPLejjg+sOoGczJQMfUiI61edwLyp+fz3w1vTYryDMaPMPFX9DtADoKodeKwnICJZOMnV3ar6F3fxERGZ4d4/A/Af2XsZY5xwySwm4bUVwRhjjPcqgntFZE/wJdHBGRPOr17eS06mj/eddUKqQ4mrrAwfX7liKfsa2vn1y/tSHY4xo023iEzAbU0SkXk4LVoRidMf9y5gm6r+IOCuB4EPuNc/APwtYPl1IpIjInOABcDr8XkJ4aVqoLsxxpjoeB2DtTLgei5wLTA5/uEYM7yG1i4eePMQ15w2i8n52akOJ+7evnAqFywq5SdP7+LqFWWUFuUOv5ExBuA/gceAchG5G6ci7Q0etjsHeD+wSUTWu8u+CHwL+JOIfAg4gPPbhzue+E/AVpwKhB9X1YRmP8HzAxljjElfnhIsVQ0eRfcjEXkJ+Er8QzImsj+8doDu3n7+9Zw5qQ4lYb58+RIu+uELfP3hbfzkvStSHY4xo4KqPikib+KUWhfgk6oavo708e1eInxXwgvCbPMN4Buxxhqtzu70GQNljDEmMk8JloicGnDTh9OiVZiQiIyJoK2rl9+8spfVi0qZX1qQ6nASZk5JPh87fx4/emoX7z61jHecONy0c8aMX0G/UQD+agWzRWS2vwT7aBaufLMxxpj047WL4PcDrvcC+4B/ins0xgzjD6/t51h7D59YPT/VoSTcR98xj79vOMyX/7qZJz59HnnZXv9djRl3vh/hPgVWJyuQRLGqbsYYM3p47SJ4fqIDMWY4Hd19/PLFPZy7oIQVsyelOpyEy8nM4JtXL+OffvEqP35qF7deujjVIRmTlsbDb5TPZ/PiGWPMaOG1i+BnIt0fVHXJmIS49/UD1Ld2c/P5Y7/1yu+MOZO57vRy7nxpL1cun8nSmRNTHZIxaUtEcoGPAW/Dabl6EbhdVUd9hYh+a8EyxphRw+tEwyuBj+LMVF8G3AQswRmHZWOxTMJ19vTxixd2c8acyZw5d0qqw0mqWy9ZzKS8bD7/wEZ6+mwchjER/A5YCvwE+CnO79TvUxpRnFQ1dqQ6BGOMMR55HdRRApyqqi0AIvJV4M+q+uFEBWZMoD+vq+JIcxffv3Z5qkNJuol5Wfz3P5zETX9Yx0+eqeQzFy5MdUjGpKsTVfWUgNvPisiGlEUTRxliXQSNMWa08NqCNRvoDrjdDVTEPRpjQuju7ef253azYnYx58wfX61XfhefNJ2rTy3jZ89Wsv5gY6rDMSZdvSUiZ/lviMiZwMspjCduMmwMljHGjBpeE6zfA6+LyFdF5D+BNThdMYxJuN+/tp9DjR186p0LkXF8FverVy5lWmEOn/nTejq6EzqnqTGj1ZnAKyKyT0T2Aa8CbxeRTSKyMbWhjUxultefa2OMManmtYrgN0TkUeBcd9EHVfWtxIVljKOpvYfbnt7FuQtKOG9BSarDSami3Cy+d+0p/POda/j2Y9v56pVLUx2SMenm4lQHkCinzCqm6piNwzLGmNEgmlNieUCzqv4YqBKROQmKyZgBP312F82dPdx6yeJx3Xrld/b8Ej54TgW/eWUfz2w/kupwjEkrqrofaAYmAlP8F1Xd7943amVmWAuWMcaMFp6+sd1ugZ8HbnUXZQF/SFRQxgAcaGjnt6/s59rTZrFkZlGqw0kbn794EUtmFPHpP26g6lh7qsMxJm2IyNeBjcBtOJMPfx/4XkqDMmYcufik6akOwYxSJ5WNrWlovJ4S+0fgSqANQFUPY+XZTYJ9+/HtZPiEz1x4YqpDSSu5WRn87/tOpa9fufmet+jutdLtxrj+CZinqu9Q1fPdy+pUB2Wid+ac8VnQaLTzjbGeJiUFOakOYUBOZkaqQ/Bk1bzY/nczYyjkk84JvdcEq1tVFWfiRkQkP3EhGQPr9h/j4Y3VfOS8uUyfmJvqcNJORUk+37lmGesPNvKtR7enOhxj0sVmoDjVQSTKjIkT4vZYk/Oz4/ZYiRDPoh5nzxvd43fnTS0Y8WPkZ3udlWd0ifa9nTe1gMJc7/sinY4/Fk1PfLvGO04sjXnbTJ/zP1tamLx95hNh1qS8pD1fNLx+g/1JRH4BFIvIR4CngF8mLiwznvX29fP//rqZaUU5/Nt5c1MdTtq69OQZ3HB2Bb96eS8Pb6xOdTjGpINv4pRqf1xEHvRfUh1UvDjnOYc6Z/7Qg8zsYcZsCZHPFkfbErG8PL55bXHe8QTwoqUjO0s9tTB9WiFikZMZXbI5t2RoQjazOH7JeSRZSR4rGMt7u2qu96QsHsltvET6n4z2MxLOSBogTymfyJWnzBy0LJoEONx3UqjvNxFh2axisjJ8nHbCpIHlRblZnp8v0Ty9I6r6PeB+4AHgROArqvqT4bYTkYtFZIeIVIrIF0LcLyJym3v/RhE51V1eLiLPisg2EdkiIp+M7mWZ0ew3r+xja3UzX71iKfk5Y/OsW7x88dLFrJhdzGf/vJ5NVU2pDseYVPst8G3gWxwfg/X9lEaUBKG6MZ2/qJT87EzOXTA15DZzp0buiDKnJLqOKpEO/lbN9dZl6Kww6+VmDe4addXyMu+BxdmsSRM4Y87khD7HlPzwSYOXA9aTZw0dy7J4RuTWj9FcRCr4oD6SBdOiT5iC982kvKGtv6n8TAIsmBaf1q2RTmju5XNUFmWyH2p/X3nKzEHfUf7rs6dEbs0qmpC8BGzYBEtEMkTkKVV9UlU/p6r/oapPetkO+BlwCbAEeK+ILAla7RJggXu5Efi5u7wX+KyqLgbOAj4eYlszBh082s4PntzJBYtK07pvbbrIzvRxx/tXMiU/hw//7g1qmjpTHZIxqVSvqrep6rOq+rz/kuqg4mVxQLEf/5n1C5dMC7lublYG71wyjaIw3aFmFk+IeFC4eEYRVyybyepFpSPumhiqleHkEAPa87LDjzEJdRY7UYpDHND5nXbCZArcE38FQScAo01Szpo7hWlFg7tTnVQ2MWICF67FJs/tAujvnhU8MfVwsQW2jkabLERKCP2CE/DzF5VyXpjk32/VvCmeurJGs99jGccUruU4nkYydi0vO5N5Uwu4fJn3RDOUDJ+QmRF7HKHeB2XwvsvNymB+aegkN9QuuOSkGcO0tQc9xjD3nz+CLpDRGjbBUtU+oF1Eoi3vcQZQqap7VLUbuA+4Kmidq4DfqeM1nC6IM1S1WlXfdJ+/BdgGpPb0gEm4/n7lc/dvwCfCf121dFSfUUumqYU53HXDSlo7e/nw796gvbs31SEZkyrrROSbIrJKRE71X1IdVLwU5WZx1fIyLlg8jZPKJnLV8rKBA+twMjN8LJsVvvteuGISAvh8QmFu1qAD/nDd9aYV5Q4cDAd3qwr1XX7ClKEtZJG+80sKcrhwybRBCeXEBJ2NnpQX+nHfFiLJCzwwXlY20XMXuQlZGUwryuX0isHJ1AmT88j22N0rcFzVDHesUKQkdU5JfkLGq5xUNnyV39LCnEGJW6aHg/nSwtwhLbDvWhLdidfg1s9ggWOOwiXxXhLIkVoWotVxOLMm5bF6USmrFzmvIcMnI+oKmp+TOWzX4WgF56bBt69YNpO87Mywrdxe/xfSkdfIO4FNInKX26XvNhG5bZhtyoCDAberGJokDbuOiFQAK4A1oZ5ERG4UkbUisraurm7YF2LS129e2cdre47ylcuXpO2gxXS1aHoRP/nnFWw93Myn7ltPb59VFjTj0gqcXg//wxgu0x7cchJo2aziIQeV091WklDJVPAZZnAOxH1hKnqFO2DNzvRx7oKpXLW8LGS55XMXTB20bXALC4Q++xz4W5CXnTmQUF55ykzevnDwwXeoQg5L4zjFx5QQXTEXzzj++LGcE8zwyaBuf6GSTP+i4Ja1k8omDuwPf6LnfzdXzJ405HOybFYxp50wiauWl3HZyTMGJcLRjuHxb/v2hVMpzsuOumhKrAfyEwISyMBW0NmTQx8zDNfyGfi6w0V05tzBSXB5mOeKVeCJglmTvCdIK8qLKczNCvm/FKvAj1/g/96ps51xThUhTowMbBti2XCNfz6fcOGSaZQW5Q5KDlfNm8L5buIY/C+xME7dIRPN6wCXh91LNELu62jWEZECnHFfn1LV5lBPoqp3AHcArFy5MvHtuCYhthxu4luPbWf1olKuXTkr1eGMSqsXTeMrly/hq3/fyhf+sonvvHtZ2IMkY8YiVT0/1TGk2pyS/CHjpyZkZ0TV7StSi1esJudn864l03hww+Eh903IyqCjp2/IgVSksTWhEpH8nEzeuWQaf1t/CHAKASWi6EJedibZGT6WzCyiratvxI83fKEG57UGl7GePjGXvJwMDjS0D2m5KiueQFnxBF7YWUdv/9ATbpkZPk4qm8juulYAcrIy6Bpmyo/zF5Xy7PZaAJbMKGLGxNyBpO+suVPo6Bl+X/jf60guPXmGp7FAcwMSxOK8bA4cHTov5HClv/sjZAD+ZCf4MzSnJJ+NVY0Dt4frbXPFspk8v6uO5o6eIfdNLczh7Hkl7G9oAyDD5/3zGur3PZpf/EyfL+RnA5z/19NOmDQw12b55DzKJ+ehqiyZWcQTW44M2TZUdcZQJ3DCCUwUi3KzBk7IBO5fL99jp50wCRGhtrmTA0fbWTKjiK3VzXErBOJVxARLRGar6gFV/W0Mj10FlAfcngUEf7OGXUdEsnCSq7tV9S8xPL8ZJVq7evnEPW8xKS+L716zzLoGjsAN58yhsaOHHz21i4KcTP7ziiW2P824IiKXAUuBgcEtqvq11EWU3qYV5lIxJZ/efqXqWPugFpl4COzCGO67aGnZRDYebCQ3aHyMl++uxTOK2FYd8vzroIPN3KwMOnv6WFkxmbX7joZcf/WiUvr6NeSBeqAMn3DJyTMAqKxtHXRffk4mje3dw8Yd7rVFesWhcoGi3CxOKps4cIAePF7ovIWRxzl5ed7A5/Lz+WRQi15Whm9IInLB4mk8ve3IoGXlk/PYeaSFzAzBFyKZWDVviqekOFJXOBGJOG4q8Gn91TYXzygakgpMnDB8q9xl7ucgEi8nOiO19Kwon0RGhtDXF10bworySWRn+lizt2HQ8gyfIEjIFtesDB+r5k4JOw5RRMjKkJCJU2GICn5Du1fqwGsNVek0O8NHdww9cPzJWWDZ9rLiCSwvL6art5+t1c1Jn6NtuBasvwL+yn4PqOq7o3jsN4AFIjIHOARcB/xz0DoPAjeLyH3AmUCTqlaL881zF7BNVX8QxXOaUUZV+fz9G9nX0MY9HzkrZBcME51PXrCA1s5e7nxpL4W5mXz2XTZRsxkfROR2IA84H7gTuAZ43eO2vwIuB2pV9SR32R9xKueCM79Wo6oud7uubwN2uPe9pqo3xellJJXPJ5xSXsyWw04V0ngfgoQrwhHI39oCsLIiugp9C6cVUjwhi1f3NAy/8jD8B4j7G5wEa9H0IrbXhE7ewjlr7mSOtfVQ7I7jenxLTcj1ohlb4uW4cKRjZ0SES0+eEdeD0FCtUIumF7JwWuHAAfFlJ89gV20rO4+0AN7mUArVilEc0M0uJ9PH8vJi9tW3hdw+sNCFiAw8Xn1rV9jnPGVWMRsCWq38MiMkg29fOJWGtsjJdqj3bUFpIa1dvVQ3dQDHK+MdDEj8vRTr8G9XWphLbcvxAliLphcxv7SARzeFnt6ltCh+81gFf84HdfmNY5XoE93PVHBXUREhNyuDRdOLmFmc3DnNhvsPD3zno5qQSFV7gZuBx3F+iP6kqltE5CYR8f8QPQLsASpx5tX6mLv8HOD9wGoRWe9eLo3m+c3o8NNnKnl4UzWfv3hR2BK9JjoiwpcuW8x1p5fzk2cq+d7jO5JSBcmYNHC2ql4PHFPV/wJWMbiXRCS/AS4OXKCq71HV5aq6HKdHRWBvit3++0ZrcpWOApOtaAWfVQ9sJTplVjEFOZmeugn5D9K8jYc5/pyZGT5yMjOYPjGX3KyMiAUWwo2jG2l+M5Jv+qwM30DiM7UwhxOmDO1uCk43P2+xDI1GRAZ1BcvM8FEWxbijcCblZw8Ue1B1iq6c6eGYInB3T8rLZmphDqvmTqGkIIfyySOLqzgve9h5tPzTJfhLkU8vymXJzKKBwjKhxhXmZmXwjhNDt0yGmrIh3GfK30oVy5j3WA4pLj15hucxkdH+H2Rm+Fg0vShsa+GJ0wtDtrAl0nDpo4a57omqPoKTRAUuuz3gugIfD7HdS8T/RJpJMw9tPMz3n9zJP64o40abUDiuRIRv/OPJAPz02UoaO7r52pUn2ZgsM9Z1uH/bRWQm0ADM8bKhqr7gtkwN4faq+CdgdRxiTKlw3af8i7wc2Fy0dHrYlploLCgtpGhCHM5ie4h5+sRcpk/M5ajbopCTmUFXr9NlsLOnj8kBXaIm5WfHNK9RVhQlriNV+wvmZTzS9Im5TD6azYkxFgAI/mkILLyxN6Al6KKl0z0XVQju8hlOvCaHzXT7/gXuruF2XeD9gQVHgltxojkAPmVWsacWyncunjYw1+fEvCyuWDZz0G/05ctmhvxolxTkhE3eZ0/OG9LSFm4XrKyYRGtnLz6fDIy18iqWRD6a8ZDxrmaYCsN9s50iIs04788E9zrubVXV+HbWNuPGK5X1fOaPGzijYjLfvPpkGyeUABk+4ZtXn8zEvCx+8fwemjp6+f61p4zqsqfGDOMhESkGvgu8iXMc8Ms4PO65wBFV3RWwbI6IvAU0A19W1RdDbSgiN+LM88js2bPjEMrIXHLS9JAD+/0tKhOGKfsODLTOdPX2x9Q67v++XxLHCn9AVEd9edkZnuZanFqYQ11L+K5jgS8/1JiSE6bkD4yPAqfVYOG0AqaF6QoX/Fu4onwS+TnOwbS/ReiipdPp7R/8Yv1VHGPl9YB2uLLngeJ1Qm+4MVV+/v0T+KyxzHs1UhUeJ+kOfkXB+yt8Iht+X4Q6lJozNZ+a5qFzZGZl+JiUn02Tv/hGiIddXl4cU2tVrMZSX5uI36SqmvxPphnz1u47ykd+t5Y5Jfn88gMro/rCNtEREW69ZDHFE7L59mPbOdbWzU/eu4JJUZbUNWY0UNWvu1cfEJGHgFxVbYrDQ78XuDfgdjUwW1UbROQ04K8isjRUtdt0q3Qb7ixyRUk++TmZHiraOS5c7Iyt+vvGoVUBIzl/UWnIRCQRQh2e+pd5fSMCW3IiKcjJDFkYYHl5McvLiwcqGxblZnqauHlKfg4NbV3MnpJHQ9DYoET8Zib6HOdIumdduHgaT2wdvsU0NzODnMyMkNMEhOP15K4/wQtVKc/T88S0VdBjeBmLF2KlkbQQhpqvDkY2+XJBbiYiwqLp3ltbT509iV21LTE/ZyrEb4SZMR68se8oN/zqdaYV5fL7D52RsIkizWAffcc8Sgqy+dL/bebKn73EHe9fGfdqYcakioicDhxU1Rr39vXAu4H9IvJVVQ1dNs7bY2cCVwOn+ZepahfQ5V5fJyK7gYXA2thfxcicv6jUU1eySLwmVxB760S8uoMFSofuRF6SJvBeAv/seVPoS2LTQaL3YDQH08EmeOxO6fOJp1bJWPjfCS9FOBIt3h8Lfyn7oiQdj2Vl+CJOwRCKv0z8aGJ9hUzSPLX1CP9y5xqmTczlvhvPimulGjO8a1eWc9+/nUV3bz9X/+8rPBTlmWdj0tgvgG4AETkP+BbwO6AJt/VoBN4JbFfVKv8CEZkqIhnu9bnAApyCTSlTlJs1MJ4jXSQimRrtvI5f8vlkoLUxkV3oL1rqJCReu7XFKt3G/4YqBhFJWfEE8rIzY95PoYqFRNsK5O/eP9IWzOAW5PycTM6eV8Ly8tjnvzsvQvfUBaWFnB5lddCxIL2+jc2YpKr8+uV9fOORbSydWcSvbzjdyrGnyKmzJ/H3m9/GR+9+k5vveYvnd9Tx/65YYgdCZrTLCGileg9wh6o+gNNVcL2XBxCRe4F3ACUiUgX8p6rehTPFyL1Bq58HfE1EeoE+4KaRtJKNBlkZPnpCzE/jEwk5puuyOJf89iI4ilBPH++QvB4in7dgasT9MW9qwcCkv8mUmxXdJNSJsnpRKf0JarBbOrOI/JzMQdUPz5wzmc5hJlYOlJuV4WnKgXBmT85DEGqaOwfKr0c7Hrq0MJfTTpjETI+tpX7+j51PhOXlxSGrY0bTej308SXisINYxlqOhWH5lmCZhGrr6uXzD2zkoY3VXLhkGj96z/K0O8s63pQW5XLvR87ix0/v5OfP7eaV3Q1855plnDPf21gDY9JQhohkutODXIBbVMLl6QtHVd8bZvkNIZY9gFO2fdxYvag0ZIJ1weJSWjt7hyyPND9QvMVyMJbsqSuGG/d6UtnEqMYOjTWJLKE9v3Ro98TMDB8Fcf6MLpxWGPazKCLOeLo2ZzzdKbOKYyrA4bWkevB8UE4MJKSbXaiXfOacKZ7L+QeaNWkCe+vbRtzdOR3Yka5JmMraVj76h3XsrmvllotP5Kbz5qVdN4HxKjvTx+cuWsQ7F0/js3/awPvuXMM1p83ilotOtK6bZjS6F3heROpxSrW/CCAi83G6CZoRCjevU152JnkeKg8mQyqn+0vG8aBNZ5jevIxrXjpzIhOyMzhhSuLGE12xbObgUvUpGKM4fWJsxxEnl01k8Yzw81mNJunxrWjGlJ6+fu54YQ8/fnoXBTmZ/P5DZ1rrSJpaMXsSD//7ufzoqZ386uW9PLKpmo+fP58PvW2OVXc0o4aqfkNEngZmAE/o8eYJH/CJ1EVmksHf9S7SRMMDy+J8sJmMpGe0HWpmZ/joDtHaORKr5k4ZE1OMZGc6E+ImUrKTk3ieXBCRqOaTS2eWYJm42ljVyC33b2R7TQuXnjydr16x1FpE0tyE7AxuvXQx7z1jNv/zyDa++/gO/vDafj5y7lyuO6M8bc5OGxOJqr4WYtnOVMRikqt4QhalhbkscVsQCnMzaQnRbTFQvPKiMdCTKe4uXDJtYDzVslnFdPX2jfgx0+044twFU+lL1KCxOEv0Z3RhjJNbj3V25GTi4kBDOz98aid/XX+I0sIcfvH+0waqE5nRoaIknzuuX8kru+v58VO7+NpDW/nps5V88OwKrjtj9ogGwRpjTKL4fMKqeVMGbp89r4Tmzp6kPPecknzau/uYX1qQ8OcaHYfzg8ffhaqeNxZMHkVzSQ7M/ZaAD1A6FEhJV5ZgmRGpaerkf5+r5N7XD+AT4d/Om8fHzp9nVelGsbPnlXD2vBLW7T/K/z67m+8/uZMfP72LC5dM47ozZnPu/JIx0T/aGDM2hRsvBsS9v11Whm9E5a29sFYyEw/x/BwtmVHE1uoh86qbAJZgmZhsrGrkrpf28vDGahR4z+nl/PvqBTEPbDTp57QTJnPXDZOprG3lj28c4P51VTy6uYbSwhwuOWk6l5w8g9MrJnue18UYY9LGaGkOMmaEEjGP2oJphSywroERWYJlPGvu7OHhjdXcv66KdfuPUZCTyfWrKvjgORWjboZt49380gK+dNkS/uOiE3ly6xEe2lDNfW8c5Lev7mdKfjZnzy/hbfOncM78Es8lZI0xxowOxXnZIec6M6NDsqckMA5LsExErV29vLCzjkc31/DElhq6evuZNzWfL1+2mH86vdy6Ao4jOZkZXL5sJpcvm0lbVy/P7qjl6W21vFxZz983HAagYkoeq+aVsLx8IstmFbOgtCCp8+EYY0wkhTmZTC/KTXglt0RI1YHy2xdOTcnzmvjwt2Bl229xUlmCZQZRVXbVtvLq7gae21HLy5UNdPf1Mykvi/ecXs67T53FslkTE9LkbEaP/JzMgWTL/5l5ubKelyvreWjjYe59/QAAE7IyWDqziJNnTWRBaSHzSwuYX1owqgYIG2PGDp9POHPulOFXNGaMyPAJy2YVU2qFqpLKEqxxrrG9m82Hmtl0qIlNhxp5fe9R6lu7AWcm8PevOoF3LZnGaSdMspYIE5KIsHBaIQunFfLBc+bQ36/sa2hjY1UTG6oa2VTVxH2vH6Sj53ip3sn52cybmk/5pDzKJk2grHgCs9zrM4tzY5rh3hhjxjJrgTCxGqvVHNOZJVjjgKpS19LF3vo29jW0sbe+nb31rWw53EzVsY6B9WZNmsC5C6ayau4UVs2bYuOqTEx8PmHu1ALmTi3gH1Y4JVz7+5VDjR1U1rWyu7aVytpW9tS18dqeBmqaOwmeTqSkIIephe7FvV5SkD2wrLQwh0l52UyckGWJvzFmTCvOy2bxjCJm22+yMaNGQhMsEbkY+DGQAdypqt8Kul/c+y8F2oEbVPVNL9uOd6pKZ08/jR3dHGvrobGjm7qWLmqbuzjS3Elty/G/NU2dg1oPMn3C7Ml5nDKrmPedeQInl03kpLIiivOs25ZJDJ9PKJ+cR/nkPM4/sXTQfT19/dQ0dVJ1rINDjR0cOtZBdVMH9a1d1LV0UXmkhfrWbrr7+kM+dmFuJpPysinOy6I4L5tJeVkUTwi47t5XmJtFYW4mBTmZFORmUpCdaeXmjTGjgk3maszokrAES0QygJ8BFwJVwBsi8qCqbg1Y7RJggXs5E/g5cKbHbUcNVaW3X+ntU7r7+unxX3qVrt4+2rr7aO/qdf5299LWdfxvW3cvTe1OAnWsvWfQ9e7e0AecuVk+phXlMq0wl6Uzi1i9qJTZk/OoKMlnzpR8Zhbn2ll/kzayMnwDyVc4qkpzR5zn8R8AACAASURBVC91rZ3UtXRT19rFsbZuGtt7ONbeTWO78z/R2NHD/oY2jrV109zZO+xzF+QEJFw5mQMJWH5OJrlZPnIzM9w5dXzkZmWQk5VBbqZv4K9/vp2cTB+ZGUJWho9Mn/M3K8Nd5nP++q9bUmeMMcaMbYlswToDqFTVPQAich9wFRCYJF0F/E6d0jiviUixiMwAKjxsG1ev7K7nB0/spF8VBfrVOajrV0X1+G3nug6sN+i2Ol2hevrVTaD66XGTqljlZvmYOCGL4gnZTMzLoqIkj+IJxQNn64vds/UT87IoLcxhamEuRbmZVoTCjCkiwsQ853M+v3T49QH6+pWmDn8C1kNLZw+tXb20dvbS2tVLi/u3tbOXlq6egds1TZ20dvXS2dNHZ08/nb19xLN4l08gM8NHlk+cvxlCppuE+UTwCfhEkCF/j9/nE4JuCwiDbkvAuv7b7t509+nxW8evB90nx5cF/UFEAq4fv+8715xCdqadwDHGGDN+JTLBKgMOBtyuwmmlGm6dMo/bAiAiNwI3ujdbRWSHx/hKgHqP66YLizk5LObksJiTJ2lx//i9I36IE+IQRlpat25dvYjsH8FDjNbPX6LY/jjO9sVgtj+Os31xXDz2haffqEQmWKGaUILPA4dbx8u2zkLVO4A7ogsNRGStqq6MdrtUspiTw2JODos5eUZr3GONqo5oQiF7Hwez/XGc7YvBbH8cZ/viuGTui0QmWFVAecDtWcBhj+tke9jWGGOMMcYYY9JKIjvKvwEsEJE5IpINXAc8GLTOg8D14jgLaFLVao/bGmOMMcYYY0xaSVgLlqr2isjNwOM4pdZ/papbROQm9/7bgUdwSrRX4pRp/2CkbeMcYtTdCtOAxZwcFnNyWMzJM1rjNoPZ+ziY7Y/jbF8MZvvjONsXxyVtX4jGszyWMcYYY4wxxoxjVkvXGGOMMcYYY+LEEixjjDHGGGOMiZMxm2CJyK9EpFZENgct/4SI7BCRLSLynYDlt4pIpXvfRcmPOHTMIvJHEVnvXvaJyPpREPNyEXnNjXmtiJwxCmI+RUReFZFNIvJ3ESlKs5jLReRZEdnmfnY/6S6fLCJPisgu9++kdIk7QszXurf7RWRl0DbpGvN3RWS7iGwUkf8TkeJREPPX3XjXi8gTIjIzXWI20RORi933q1JEvpDqeBIhnt9zInKa+31eKSK3iUio6V/SnohkiMhbIvKQe3s874tiEbnf/S7eJiKrxuv+EJFPu/8jm0XkXhHJHS/7QkIfw8XttYtIjjjH3pUiskZEKmIKVFXH5AU4DzgV2Byw7HzgKSDHvV3q/l0CbABygDnAbiAjHWIOuv/7wFfSPWbgCeAS9/qlwHOjIOY3gLe71/8V+HqaxTwDONW9XgjsdGP7DvAFd/kXgG+nS9wRYl4MnAg8B6wMWD+dY34XkOku//Yo2c9FAev8O3B7usRsl6jf4wz3fZqLM43JBmBJquNKwOuM2/cc8DqwCmdezUdxf5NG2wX4DHAP8JB7ezzvi98CH3avZwPF43F/AGXAXmCCe/tPwA3jZV8Q+hgubq8d+BjHfy+vA/4YS5xjtgVLVV8AjgYt/ijwLVXtctepdZdfBdynql2quhenquEZJFmYmAFwM+t/Au51F6VzzAr4W4AmcnwOs3SO+UTgBff6k8C73evpEnO1qr7pXm8BtuF8yV6F86OD+/cf3OspjztczKq6TVV3hNgknWN+QlV73dVew5mbL91jbg5YLZ/jk7WnPGYTtTOASlXdo6rdwH047+OYEq/vORGZgXOC4VV1jpJ+F7DNqCEis4DLgDsDFo/XfVGEc2B9F4CqdqtqI+N0f+BUAZ8gIplAHs5x1rjYF2GO4eL52gMf637gglha9sZsghXGQuBct8nveRE53V1eBhwMWK/KXZZOzgWOqOou93Y6x/wp4LsichD4HnCruzydY94MXOlev5bjE12nXcxuc/UKYA0wTZ2543D/lrqrpVXcQTGHM1pi/lecs12Q5jGLyDfc/8P3AV9xV0urmI0n4+49G+H3XJl7PXj5aPMj4BagP2DZeN0Xc4E64Ndul8k7RSSfcbg/VPUQzrHVAaAaZw7ZJxiH+yJAPF/7wDbuidUmYEq0AY23BCsTmAScBXwO+JOblYbKTNOtfv17Od56Bekd80eBT6tqOfBp3DNOpHfM/wp8XETW4XRN6XaXp1XMIlIAPAB8KqiFYsiqIZalJO6xFLOIfAnoBe72LwqxedrErKpfcv8P7wZu9q8aYvN0+T80oY2r9ywO3xmjfn+JyOVAraqu87pJiGVjYl+4MnG6hf1cVVcAbThdwcIZs/vDHV90FU6Xt5lAvoj8S6RNQiwbE/vCg1hee1z2y3hLsKqAv6jjdZyzQiXu8vKA9WZxvFtbyrlNwFcDfwxYnM4xfwD4i3v9zxzvfpS2MavqdlV9l6qehpPI7nbvSpuYRSQL56DjblX1798jblM37l9/t9e0iDtMzOGkdcwi8gHgcuB9bpcCSPOYA9zD8W6vaRGzicq4ec/i9D1XxfFuvIHLR5NzgCtFZB9Ol9DVIvIHxue+AOd1VKmqv0fB/TgJ13jcH+8E9qpqnar24Bxvnc343Bd+8XztA9u4x98TCTN8J5LxlmD9FVgNICILcQZJ1gMPAte5lUPmAAtwBr+li3cC21U1sDkznWM+DLzdvb4a8HdrTNuYRaTU/esDvgzc7t6VFjG7La13AdtU9QcBdz2Ik9Di/v1bwPKUxh0h5nDSNmYRuRj4PHClqraPkpgXBKx2JbDdvZ7ymE3U3gAWiMgcEcnGGXj9YIpjirt4fc+5XYRaROQs9zGvD9hmVFDVW1V1lqpW4Lzfz6jqvzAO9wWAqtYAB0XkRHfRBcBWxuf+OACcJSJ57mu4AGe84njcF37xfO2Bj3UNzv9e9C17mgYVQRJxwWmFqAZ6cLLRD+EkVH/AGW/zJrA6YP0v4bRa7CBFVVRCxewu/w1wU4j10zJm4G3AOpzKLWuA00ZBzJ/EqVi1E/gWIGkW89twmqg3Auvdy6U4/YKfxklinwYmp0vcEWL+R3e/dwFHgMdHQcyVOH2y/ctuHwUxP+B+120E/o5T+CItYrZLTO/zpe73027gS6mOJ0GvMW7fc8BK9/O/G/hp4Hf6aLsA7+B4FcFxuy+A5cBa9/PxV5whH+NyfwD/hXPSbDPwe5wqeeNiXxD6GC5urx3Ixel9VYlz8nFuLHH6H8wYY4wxxhhjzAiNty6CxhhjjDHGGJMwlmAZY4wxxhhjTJxYgmWMMcYYY4wxcWIJljHGGGOMMcbEiSVYxhhjjDHGGBMnlmAZY4wxxhhjTJxYgmWMMcYYY4wxcWIJljHGGGOMMcbEiSVYxhhjjDHGGBMnlmAZY4wxxhhjTJxYgmWMMcYYY4wxcWIJljHGGGOMMcbEiSVYxqSQiHxRRO5MdRzGGGNMMPuNMiY2ovr/27vzOLfq897jn2c2bxjvBmMbbIwDGJKwmMUhyQ0BEpYE2t6Q0NwUkqZNcrO0ae995ULabM3NqzRNe5M0bQjZytJCyIpDIcRhDxiMDTbed+NlPLtn3zTSc/84R2PNWDNzZkaaoxl936+XXiMdnSM9+o2kcx79fr/neNwxiIiIiIiITAjqwRIREREREckRJVgiY8TM/o+ZHTGzFjPbaWZXmdmXzez+jHVuNbPXzazezL5gZgfM7Orwvi+b2U/N7P7wMTab2RvM7A4zqzGzQ2b2rozH+oiZbQ/X3WdmH4/jdYuISOHTPkokd5RgiYwBMzsb+DRwibtPB94NHOi3zgrg34D/ASwAZgAL+z3Ue4H7gFnAq8DjBJ/jhcDfAd/LWLcGeA9wMvAR4P+Z2UW5fF0iIjL+aR8lkltKsETGRhKYBKwws3J3P+Due/ut8z7g1+7+e3fvBr4I9J8k+Zy7P+7uPcBPgXnAne6eAB4ElpjZTAB3/y933+uBZ4DfAm/L30sUEZFxSvsokRxSgiUyBtx9D/BZ4MtAjZk9aGan9VvtNOBQxjbtQH2/daozrncAde6ezLgNcBKAmV1nZi+aWYOZNQLXA3Nz8XpERGTi0D5KJLeUYImMEXf/T3d/K3AGwa9+/9BvlaPAovQNM5sCzBnJc5nZJODnwDeAU9x9JvAoYCN5PBERmdi0jxLJHSVYImPAzM42s3eGO5VOgl/ykv1W+xnwXjN7i5lVAF9h5DubCoLhHrVAj5ldB7xr8E1ERKQYaR8lkltKsETGxiTgTqAOqALmA5/PXMHdtwKfIRinfhRoIZgE3DXcJ3P3FuAvgIeAY8AHgdUjD19ERCYw7aNEckgnGhYpUGZ2EtAILHf3/XHHIyIikqZ9lMjA1IMlUkDM7L1mNtXMphGMTd9Mv1K5IiIicdA+SiQaJVgiheUmoDK8LAducXUzi4hIYdA+SiQCDREUERERERHJEfVgiYiIiIiI5EhZ3AHk0ty5c33JkiVxhyEiIiO0YcOGOnefF3cc+aB9lIjI+BZ1HzWhEqwlS5awfv36uMMQEZERMrPX444hX7SPEhEZ36LuozREUEREREREJEeUYIU6E0me3VWLin6IiIiIBFq7emhqT8Qdhsi4ogQr9PDGI9z6o3Vc963n+N226rjDERGRMWZmpWb2qpk9Et6ebWZrzGx3+HdWxrp3mNkeM9tpZu+OL2qR/HpiezVP76qJOwyRcUUJVugPL1zEP77vTSSSKT5+/wY2vN4Qd0giIjK2/hLYnnH7duAJd18OPBHexsxWALcA5wHXAv9mZqVjHKuIiBQoJVihirISbl65mF988gpOmzmZv3hgI43t3XGHJSIiY8DMFgE3AD/IWHwTcE94/R7gDzKWP+juXe6+H9gDXDpWsYqISGFTgtXPjCnlfOePL6KmpZOvP74z7nBERGRsfBP4HJDKWHaKux8FCP/OD5cvBA5lrHc4XCYiIqIEK5s3L57JzSsX87MNh6lp6Yw7HBERySMzew9Q4+4bom6SZVnWCklm9jEzW29m62tra0cco4iIjB9KsAbw5287k0QyxT0vHIg7FBERya8rgBvN7ADwIPBOM7sfqDazBQDh3/RM/8PA4oztFwGV2R7Y3e9295XuvnLevAl5/mQREelHCdYAls6dxnXnn8p9a1+ntasn7nBERCRP3P0Od1/k7ksIilc86e4fAlYDt4Wr3QY8HF5fDdxiZpPMbCmwHFg3xmGLiEiBUoI1iI++9UyaO3t49LWjcYciIiJj707gGjPbDVwT3sbdtwIPAduA3wCfcvdkbFGKiEhBKYs7gEJ20ekzOWPOVFZvquT9lyweegMRERnX3P1p4Onwej1w1QDrfQ342pgFJiIi44Z6sAZhZtz45tN4YW+dil2IiIiIiMiQ8ppgmdm14Vnu95jZ7VnuNzP7dnj/a2Z2Ub/7S83sVTN7JJ9xDuamC04j5WiYoIiIiIiIDClvCVZ4Vvt/Ba4DVgB/bGYr+q12HcHk4OXAx4Dv9rv/L4Ht+YoxirPmT+fcBSfz8KasBaJERKSAmNkUMzs77jhERKR45bMH61Jgj7vvc/dugtK3N/Vb5ybgXg+8CMzMKIm7CLgB+EEeY4zkPW9awKsHGzVMUESkgJnZe4GNBIUnMLMLzGx1vFGJiEixyWeCFeVM94Ot803gc0AqXwFGdeXZ8wF4eqdOEikiUsC+TPDjXiOAu28ElsQYj4iIFKF8JlhRznSfdR0zew9Q4+4bhnwSs4+Z2XozW19bm58E6NwF0zn15Mk8vbNm6JVFRCQuPe7eFHcQIiJS3PKZYEU50/1A61wB3GhmBwiGFr7TzO7P9iTufre7r3T3lfPmzctV7H2YGVeeM4/ndtWRSMbeoSYiItltMbMPAqVmttzM/gV4Ie6gRESkuOQzwXoZWG5mS82sArgF6D8WfjVwa1hN8HKgyd2Puvsd7r7I3ZeE2z3p7h/KY6xDuvLs+bR09bD+wLE4wxARkYF9BjgP6AIeAJqBz8YakYiIFJ28nWjY3XvM7NPA40Ap8CN332pmnwjvvwt4FLge2AO0Ax/JVzyjdcVZc6koLeGpnTWsWjYn7nBERKQfd28H/ia8iIiIxCJvCRaAuz9KkERlLrsr47oDnxriMZ4Gns5DeMMybVIZF58xi+f31MUdioiIZGFmT3HiXF/c/Z0xhCMiIkUqrwnWRHP5mXP45hO7aGzvZubUirjDERGRvv53xvXJwH8HemKKRUREilSkOVhmdn6+AxkPVi2bgzus298QdygiItKPu2/IuDzv7n8NXBZ3XCIiUlyiFrm4y8zWmdknzWxmXiMqYG9ePIPJ5SWs3VcfdygiItKPmc3OuMw1s3cDp8Ydl4iIFJdIQwTd/a1mthz4U2C9ma0Dfuzua/IaXYGZVFbKxWfMYu1eJVgiIgVoA8EcLCMYGrgf+GisEYmISNGJPAfL3Xeb2d8C64FvAxeamQGfd/df5CvAQrPqzDl847e7ONbWzaxpmoclIlIo3H1p3DGIiIhESrDM7E0EJdRvANYA73X3V8zsNGAtUDwJVlii/aX99Vx7/oKYoxERETP7o8HuL6YfAUVEJH5Re7C+A3yfoLeqI73Q3SvDXq2i8caFM5lSXsravUqwREQKxHsHuc8poh8BRUQkflETrOuBDndPAphZCTDZ3dvd/b68RVeAKspKWLlklgpdiIgUCHcv2JPUi4gUgs5Ekp1VLbxx4QxKSizucCa8qFUEfwdMybg9NVxWlFYtm8Ou6lbqWrviDkVERDKY2Q1m9jkz+2L6EndMIiJx23ykiQP1bVQ1d8YdSlGImmBNdvfW9I3w+tT8hFT4Lj8znIe1T+fDEhEpFGZ2F/AB4DMElQRvBs6INSgRESk6UROsNjO7KH3DzC4GOgZZf0J748IZTKsoZe2+urhDERGR497i7rcCx9z9K8AqYHHMMYmISJGJOgfrs8BPzawyvL2A4FfColReWsIlS2fzonqwREQKSfqHv/awym09oNLtIiIypqKeaPhlMzsHOJtg2MUOd0/kNbICd/mZc7jzsR3UtnQxb/qkuMMRERF4xMxmAv8IvEJQQfD78YYkIiLFJvKJhoFLgCXhNheaGe5+b16iGgcuWzobgJcPNHD9G1WuXUQkbu7+1fDqz83sEYL5w01xxiQiIsUn0hwsM7sP+AbwVoJE6xJgZR7jKnjnL5zBlPJS1u3XMEERkUJgZpvM7PNmtszdu5RciYhMLKmU09DWHXcYQ4rag7USWOHuns9gxpPy0hIuPmMWLynBEhEpFDcSzA9+yMxSwE+Ah9z9YLxhiYhILmytbGZfXStXnjOfkyeXxx3OgKJWEdwCnJrPQMajS5fOZkdVM03tRT0dTUSkILj76+7+dXe/GPgg8CZgf8xhiYhIjjR3Bsfc3T2pmCMZXNQerLnANjNbB/SeXdfdb8xLVOPEpUtn4x7Mw7p6xSlxhyMiUvTMbAnwfoKerCTwuTjjERGR4hM1wfpyPoMYry5YPJOK0hLWKcESEYmdmb0ElAMPATe7+76YQxIRkSIUtUz7M2Z2BrDc3X9nZlOB0vyGVvgml5dyweKZmoclIlIYbnP3HXEHISIixS1qFcE/B34GfC9ctBD4Vb6CGk8uXTqbLUeaaOvqiTsUEZGipuRKREQKQdQiF58CrgCaAdx9NzA/X0GNJ5cunU0y5bxy8FjcoYiIiIiISMyiJlhd7t5bdN7MygCVbAcuOmMWpSXGS/s0TFBEREREJN8K/cRRUROsZ8zs88AUM7sG+Cnw6/yFNX6cNKmM8xfO0AmHRURiZmZTzewLZvb98PZyM3tPhO0Wm9lTZrbdzLaa2V+Gy2eb2Roz2x3+nZWxzR1mtsfMdprZu/P3qkREZLyJmmDdDtQCm4GPA48Cf5uvoMaby5bOZuOhRjoTybhDEREpZj8mOJXIqvD2YeD/RtiuB/hf7n4ucDnwKTNbQbDve8LdlwNPhLcJ77sFOA+4Fvg3Myv6wk8iIhKIlGC5e8rdv+/uN7v7+8LrBd45N3YuXTKb7mSKTYca4w5FRKSYLXP3rwMJAHfvAGyojdz9qLu/El5vAbYTFHO6CbgnXO0e4A/C6zcBD7p7l7vvB/YAl+byhYiIyPgVtYrgfjPb1/+S7+DGi0uWzMYM1u6rjzsUEZFi1m1mUwjnCJvZMoIercjCExVfCLwEnOLuRyFIwjhe3GkhcChjs8PhsmyP9zEzW29m62tra4cTioiIjFNRTzS8MuP6ZOBmYHbuwxmfZkwt57zTTmbt3no+e3Xc0YiIFK0vAb8BFpvZfxBUv/1w1I3N7CTg58Bn3b3ZbMDOr2x3ZB3V4e53A3cDrFy5UiM/RESKQNQhgvUZlyPu/k3gnXmObVx5y7K5vHpQ87BEROLi7muAPyJIqh4AVrr701G2NbNyguTqP9z9F+HiajNbEN6/AKgJlx8GFmdsvgioHG38IiIyMUQdInhRxmWlmX0CmJ7n2MaVVcvm0J1MseF1nQ9LRGQsZe6jgDOAowQJz+nhsqG2N+CHwHZ3/+eMu1YDt4XXbwMezlh+i5lNMrOlwHJgXW5ejYiIjHdRhwj+U8b1HuAA8P6hNjKza4FvAaXAD9z9zn73W3j/9UA78GF3f8XMFgP3AqcCKeBud/9WxFhjccmS2ZSVGC/sreOKs+bGHY6ISDH5p0Huc4YecXEF8CfAZjPbGC77PHAn8JCZfRQ4SDA8HnffamYPAdsI9omfcncNXxARESBiguXuVw73gcOStf8KXEMwnOJlM1vt7tsyVruO4Je/5cBlwHfDv+mSua+Y2XRgg5mt6bdtQTlpUhlvWjSDF/aq0IWIyFgayT6q3/a/Z+Bqg1cNsM3XgK+N5nlFRGRiipRgmdlfD3Z/vyEVaZcCe9x9X/gYDxKUts1Mkm4C7g1Lvr9oZjPNbEFYrSlduanFzNIlcws2wYJgHtZ3n9lLS2eC6ZPL4w5HRKSomNlk4JPAWwl6rp4D7nL3zlgDExGRnBjyvBsFIuqJhlcC/5MgyVkIfAJYQTAPa6C5WFHK2A65Tr+SuScopBK4V5w1l2TKWateLBGRONxLcPLffwG+Q7Cfui/WiEREJpBjbd3oVLhDizoHay5wUXgCRszsy8BP3f3PBtkmShnbQdfpXzI325MUUgnci8+YxbSKUp7dXcu7zjs1zlBERIrR2e7+5ozbT5nZptiiERGZQGpbunhhbx3nnTaDs+afFHc4BS1qD9bpQHfG7W5gyRDbRCljO+A6A5TMLWgVZSWsWjaHZ3fVxR2KiEgxetXMLk/fMLPLgOdjjEdEZMLo6A5q+bR0JmKOpPBFTbDuA9aZ2ZfN7EsEw/XuHWKbl4HlZrbUzCqAWwhK22ZaDdxqgcuBJnc/OkjJ3IL39jfM42BDOwfq2uIORUSk2FwGvGBmB8zsALAW+G9mttnMXos3NIniN1uOsuVIU9xhiIiMStQqgl8zs8eAt4WLPuLurw6xTY+ZfRp4nKBM+4/C0rafCO+/C3iUoET7HoIy7R8JN89aMtfdH43+0uLx9uXzAHh2dy1L5k6LORoRkaJybdwByOh09aTYW9vK+QtnxB2KiMiIRZ2DBTAVaHb3H5vZPDNb6u77B9sgTIge7bfsrozrDnwqy3aDlcwtaEvmTuOMOVN5Zmctt65aEnc4IiJFw91fN7NZBEPPyzKWvxJfVCIiUmyilmn/EkElwbOBHwPlwP0EPU3Sz5Vnz+fBlw/S0Z1kSkVp3OGIiBQFM/sq8GFgL8cLJkU50bAUoVTKKSkZl7/lihQ9P6FuXmGJOgfrD4EbgTYAd69k4PLsRe/qc0+hM5Hi+T0qdiEiMobeDyxz93e4+5XhRcmVnOBoUwe/fq2SpnZN1heJqtCTmkISNcHqDofzOYCZaXLRIC5dOpvpk8pYs6067lBERIrJFmBm3EFI4atu7gKgsaN7iDVFRIYv6hysh8zse8BMM/tz4E+B7+cvrPGtoqyEd5wznyd2VGsIgojI2Pl7glLtW4Cu9EJ3vzG+kEREpNhErSL4DTO7BmgmmIf1RXdfk9fIxrmrz53PrzdV8uqhRi4+Y1bc4YiIFIN7gH8ANgOpmGMREZEiNWSCZWalwOPufjWgpCqid5w9n7IS4/GtVUqwRETGRp27fzvuIEREpLgNOQfL3ZNAu5nppBTDMGNKOW9/wzwe2VRJKqVJgSIiY2CDmf29ma0ys4vSl7iDEhGZSMw09WUoUedgdRKc9HcNYSVBAHf/i7xENUHc+ObTeHJHDRsOHuOSJbPjDkdEZKK7MPx7ecYylWmXca+5M8FTO2pYtWwO86dPjjsckfiMk9wuaoL1X+FFhuGaFacwubyE1RsrlWCJiOSZu18Zdwwi+dDQGlQ7rGzsVIIlMg4MmmCZ2enuftDd7xmrgCaSaZPKuOrcU3h081G+9N4VlJVGrYovIiIjYWY3AOcBvUeh7v538UUkhea1w40ca1d5dhHJn6GO+H+VvmJmP89zLBPSTW8+jfq2bp7eWRt3KCIiE5qZ3QV8APgMwUCSm4EzYg1KCkpPMsX+ujaaO4r7BMOdiSQ7qprjDiM2PckUbV09cYchE9hQCVbmSMcz8xnIRHXlOfOZN30SD6w7GHcoIiIT3Vvc/VbgmLt/BVgFLI45pgntud21PLWjJiePlRyDglCanB/Y8Poxdla1cKytOHvynt5Zy++2V4/JcyWSKdxV7KzYDJVg+QDXJaLy0hLev3IRT+2sobKxI+5wREQmsvSXbLuZnQYkgKUxxjPhNbR109yZm96gZ3dPvJEenYlkpIPrutYuthxpGvD+XOeF6WR2pAd2yZTT3TN+TzXX1j02vVfJlPPo5qNsOXK8t7AlR5+XTNXNnaPukWvt6qGpffDYlCdGN1SC9WYzazazFuBN4fVmM2sxs+LtWx6mWy45HQd+8vKhuEMREZnIHjGzmcA/Aq8AB4AHYo1IIivEYXutXT00tnfz261VbnZIGgAAFnxJREFUtEc4KHd39tW2kkw5yZTz+NYqNh0eOHFKe35PHXtrW3MR8gnx5MPze+p4bMvRPsvau3ty9nydiSStE2AIX08qSEIPH2sHYE9NK0/uqMl5z+GL++p5YpCe5G2VzTQM8ZxPbK/m6V256Y2WIRIsdy9195Pdfbq7l4XX07dPHqsgx7vFs6fy9uXzeGDdQbp6knGHIyIyIbn7V9290d1/TjD36hx3/2LccUnhsiFqPj+xvZpndtXSkUiyZls1lY0dNA2SCB5p7GDzkSZ2VDX3HlxXNY1+9MrGQ43A8BKmfbWtrN5UmfW4Y7Q9Yv2LhDR3JlizrfqEJLG6uXNE5wJds62aJ8ZoCF9UVU2dHBnmSKT0+yvpzu7qlt52y0cP2mDvjd01LXQmJtjxZ4H3pqms3Rj5s7ctpaali1++ciTuUEREJhQzu8TMTs24fSvwEPBVM9M5Mgrcc7tr2VOT+96bfHj5QANP7xz4V/700Luow+d2VDWzZlt+EomDDUGvSUd3bg+ss82VSz9HXevxxKu+tYsX99Wz7ejwBzylCnAs2kv761l/oGFE2yZTzrajzcOeKlLT3Nk7dNTd2VnVMuwf6jX/Kx5KsMbIW8+ayxsXzuB7z+4bk4m8IiJF5HtAN4CZvR24E7gXaALujjGuojHY/KGhNLR1s7Vy8O0TyRRVTZ0jfo5CtbOqJdLQw5HIV0GPF/fVR1qvK0wy23Oc4OVSZvKRSnnBJSNr99X39grWtXazo6qZTYeG91nrf8hZ19rFUztrRtSzmE1jezevHW7MyWMNS/j2dnde2FtHTUvf74fORDLWIi5KsMaImfHJdyxjf10bj24+OvQGIiISVam7p39a/gBwt7v/3N2/AJwVY1xFIx/zhzK9erCRl/bXR5rI39SR4OGNR9hX28re2lYe3nik92Cy/wF0c2ewbv9CHZWNHazeVDmqmEdyrN44BufnSiRTvfNxUu5srWwikYxesKKutWtYzzeaPG+w4ZiZDjW0DznHaCi/fq2S3++po62rh93VLaN6rKGkRlAfxMMxcT2DbNx/GODRpg6qmvsmHunTFLRGSOx/t6160B7bzkSSZ3bVsr+urU/xjv11bYNu119rV8/wE75w9UTSqW3pYv2BY33ufnpnTayFc5RgjaF3n3cqy+efxD/9due4rr4jIlJgSs2sLLx+FfBkxn1lWdYft1Jh8YThWL2pkhf21A26TiKZGvYcjf6/GA/XkcaOyBXV0olVT4TXnj6w23ykiV1VLYNul04M+w/d2lHVHEtvxnO7B/8/5aLTIbO38VBDO3tqWtlxNL8JxVCaOxPsrMoSwwCvtzORZHvG0MNXDh7juRwcTDe0dfPS/mBYY+bQyly/Fwbrse1MJHlud23kz2O6gAbA41ur+nym1u1vGPGwRgjmig2U5LZ39/D41qre25nfS68dbhw0Oe7uSfF6fRsAXT1JnthezabDjbR39wxZ3KS2JVqC3xXzcbYSrDFUUmJ8/oZzOVDfzr1rD8QdjojIRPEA8IyZPUxQqv05ADM7i2CY4ITx3J46HnlteD0r7k7tEL0OT+6o6XOwFMXavX2Hig0n8TtY3876Aw08GfUcWkP0gjR3JugZpBfGh5gR3//4ubtn8PX31rb2/lDq7kPMizHau3tOmAuVrb2yPWvmwX39MHuPsslMNtMHq1Eq9g3Ww5At/xhOSvL87rqgMEiEnrTunhSPb61iV/Xoz+OVLe62rhP/l3tr2yI/ZlVTJ3trW9lZ1XJCpcW07n6vszOR5OGNR+jqSbK3tpWGtu4+iVOf90q/mDe83rfnZrjVF7P94H+srXvQuXvG6IZ+bnj9GBsPNdLcmWBbZZAoH2xo71Pc5OGNR/ok0UMptDPcKcEaY1eePZ+3v2Ee335id06+KEVEip27fw34X8C/A2/140ekJcBn4oorH4YaQjbSeRXpX8szfzXfU9PK74ZRgOGpHTW0d/cM+Mt7ZyLZm4i8euhY1nWGNMDLe2pHDev2n/hLff/haQO1Tv8D7aEKCWw50sRjW47y3O5aXjvcxG+2VPU5CO7uSfUOuzMLquL9dtvxBLahrTtSotzUnuBA/fED7Wz/3g2vNww6B26wzpeO8H8VpTcyagW9F/bW9ZmTM9CBb08y1dtzOGDPZJaNM5OW/ls9uaOahzcewd1p7kxQ0zz8XtZ0gQ3HOdrUwaGG9j49TsmUU9nYwZM7qrP2bL20v54tYSXJqNI/bmx4/VjG/+v4i69u7hyy4mVaTzL6d0BTe4LHthxlT03f3sNnd9f2eb9mEyWagd5XneHnq6G1u7cYSza7IgzVzPzxJP3/yvTwxiNsOjT2c8SUYMXgCzecS0ciyRce3lJwEypFRMYjd3/R3X/p7m0Zy3a5+ytxxjUWEskUyZTTmUjy69cqOVif/YAlyvyex7dWsW5/A8lUMDdnOOWk27p7WLOtmse3VmXdtz2+tYrfbInWS3a0qYPKxuBgqaqp84SDuZcPNPSprgZQN4rejMyDtOEkqQ1t3b1JQmaCVdXcmbV3Lt1bMNB8of7t9vSumr7JSpaj2sPHOoY1B26kv/TXtHSecPCa7gHLTKprW7rYX9e3x6cnmaKmuZPORJJ9ta3sq21l0+EmXj7QQFN7orf1B2r5Qw3tvLivfsj/TUtn8H7dW9vGUztqWBsW5Gho6z4hiQCG7Nldt7+BVw72/THgkdcqeflAAy2dPVTmuPBKIiM5ymzTvbWtkRPc/vEOpKG1u3cY39bKaMlgdZiwNrR38/t+w47X7q1nw+t9f+TYcqSJDa83cCB8PzR3Jmjv7uk9592miMUxOhPJrMVg9tS00tl9vAcu2/8L4EB9G4ca2sf0mHtCjU0fL5afMp2/uuYNfP03O1m9qZKbLlgYd0giIjJOPbr5KNMnlzGtItilv3roGAtnTaG0pO+hdG1LF4ePdVDf1s0lS2YxuayUkpITD7ePNnXwu+3HE4BUyk9Yb6i5U6s3VTJ7WgVvWz7vhPuiFFTo7kn1nvspU1NHglcOHes9QDt/4Yw+PTQD9Z4NdVy1p6aV806bAUTvqemNNXw9LZ0JjrWf2C6ZMT225SiXnzlnyMfsTCSznnh58aypQPC/nFxewuTy0t77ntlVy6VLZjOlopRUymntPPGAdPPhpqyvb0p5sI0TtP2UiuBxM4ebHT7WweFjfbd9YW8dq5bN6T1Qrs7oMUofzB5p7KCstKR3zk1aRWnwG39bxgmKT/g/eRBP+qC5OkuPSLaey8wEz91752edNX96n/Ve3Fc/4DFYlPL5e2taKSsxtlU2s3j2lBMefzBrtlVz+ZmzmT65vHdZY3s35Vk+kw1t3b1JeUciSVVTJ/OmTxpVOftNhxtZNu+kE5YPVIa/tqWrt2BGtvdmdzLF4WMdXHxG3+Xp982SudN4KuKQ4P7DHNM9fJmfnZaunj49i0MVU3nlYNA7ePqcqZFiGC0lWDH5+NuX8cT2Gv72l1tYseBklp8S/UMpIiLFrakjwYwpxw/MWjp7en+9h+Cg9eTJ5X0OaJzjRR3SB49nnzq9zwFeWmZSsK+uja2VTSyYMYVl86bR2JGIVJa9oa2b1q4e2rv6/tIfpZLu0QF6BvoPLdx8uIl9dcd7b57e2bfQQXqi++Nbq3jHG+b3Jg7ZvHLwGIca2lk4c8qQ8WXT/xf9gUQpcz7QfLj0QeQLe4PnSifVEByc/3ZbFeecenKf4WnP7q7l6nNPYdqksj5tlckJquilXf/GBZSVWKST/dY0Z+8Fypwb1D+5Sj8n0GeeTcq9Ty/VoWPtfYoVHOmX4LkHw/j6y+ztyKwGWdvSRXlp3yPxhzceYdWyoZPebI61d/f+P7dWJqhvjd6L2t7dw9bK5hMS7nSvWvUAwxtbu3p4af/g76GHNx7hXStOHXQdyF79M9vQ1aGGC2bKfO+VZGQ9wzkfW+b7LrMHN/Ozc+Kw3uPvk2d2ZS94crixfcwSLJtIQ9RWrlzp69evjzuMyI40dnDTd55nSkUJv/rkFcw5aVLcIYmIxMrMNrj7yrjjyIfR7qPSCUDadecv4NCx9gGTnVVnzukdIiWBitKSEwoMFJpTT558QmntXFg4c8qwe+cmohlTyiOXfx8LM6dWjEl5/jicPLm89xQIk8pKYq/sB4x61FjUfZTmYMVo4cwp/OC2ldQ0d/EnP1w37HNLiIhI8eg//+WxLUcH7UlScnWiQk+ugLwkVzD8oY8TVSElVzA25z6LS+b55QohuYKRFwIaLiVYMbtg8Uy+9ycXs6+ulfd/b23vREARESlsZnatme00sz1mdns+n2s45YpFRCS7bPNO8/I8Y/IsMqh3nD2f+z56GfWt3Vz/7ef4z5cOjlmGLSIiw2dmpcC/AtcBK4A/NrMV+Xq+4Z7bRkRE4qMEq0BcsmQ2v/ns27hg8Uw+/8vN/NF3X+DlUZx9W0RE8upSYI+773P3buBB4KZ8PdnZpx4vhGRDlcsqQiVqk0HNnFoxqu0nlUU/XFw+jEp6xSRf79GTJpVxzqkn5+WxJ5rMqpv5piqCBWTBjCnc/9HL+MWrR7jzsR3cfNdaLjx9Jh9YuZh3n3cqs6aN7gtSRERyZiFwKOP2YeCy/iuZ2ceAjwGcfvrpI36ykyeXDzo5uyeZoqw0v7+ZuvuYJHfZnie9rDORpKK0ZMhhPsmUYwTDgXIVd3pkSfq5E8kU5Xlu82wxOJxQgj+Z8hOWjVU82f4XK07L7QF/ZyLJpLKSAd8XuZL5enqSKZLuVJSe+LyZ4mp7dyflx98LmT/CZMbVk0xhZpFiHKvP+EAGej9lk/7OyxZzIpnCHSrKSkimnEQyNabJFeQ5wTKza4FvAaXAD9z9zn73W3j/9UA78OH0SSGH2naiKikx3nfxIq5/46n8dP1h/v2FA9z+i83c8cvNnDXvJC48fSYXnj6Ls+afxKJZUzhl+uQxG08qIiK9sn3xnjC2293vBu6GoIpgvoLJd3IFY9dzlu150suiHiRlHkzmKu7++9qxTq6yxZAWxwE+jN18loH+77l+T2a+nrLSkkgHyXG1vZlROshTp+MazndD3L3jw3k/pV9XtpgzP5ulJUZpydgmV5DHBCtjfPo1BL/svWxmq919W8Zq1wHLw8tlwHeByyJuO6FNrSjjtrcs4dZVZ7C1spmndtTw6qFG1myr5qH1h3vXqygtYd70ScyaVs7MKRXMnFrOzKnlTJ9czuSyUiaXlzCpLDgZ4eTy0t7rk8pLKCspobTEKCux8A3Y93pwu4SSEnrXLbHgzWwE5+Ow8Bgj/f7uvyxYz3qPRMzi/wCLiOTAYWBxxu1FwIknkBERkaKTzx6s3vHpAGaWHp+emSTdBNzrwcm4XjSzmWa2AFgSYduiYGacv3AG5y8MzjDv7hxsaOdAfTuHGto5fKyD6uZOmjoSHGvvprKxg8aOBM0dCXoKvFBGb1JG36St2FjWH8InML3cCW3Tl9415kMxYvIysNzMlgJHgFuAD8YbkoiIFIJ8JlhRxqdnW2dhxG2BvuPbgVYz2znCeOcC0U7DLgNRG+aG2nH01IajN6I2nPK1UT/vGaN+hDHg7j1m9mngcYKh7D9y962DbbNhw4Y6M3t9FE+r93Vfao/j1BZ9qT2OU1scl4u2iLSPymeCFWV8+kDrRBrbDn3Ht4+Gma2PcmZmGZjaMDfUjqOnNhw9teHQ3P1R4NFhrD9vNM+n/0lfao/j1BZ9qT2OU1scN5Ztkc8EK8r49IHWqYiwrYiIiIiISEHJZwmc3vHpZlZBMD59db91VgO3WuByoMndj0bcVkREREREpKDkrQdroPHpZvaJ8P67CIZWXA/sISjT/pHBts1XrKFRDzMUtWGOqB1HT204emrDwqP/SV9qj+PUFn2pPY5TWxw3Zm1hQQE/ERERERERGa2xP0ueiIiIiIjIBKUES0REREREJEeKPsEys2vNbKeZ7TGz2+OOp5CZ2Y/MrMbMtmQsm21ma8xsd/h3VsZ9d4TtutPM3h1P1IXFzBab2VNmtt3MtprZX4bL1Y4RmdlkM1tnZpvCNvxKuFxtOExmVmpmr5rZI+FttWGBKoZ9VS6/H83sYjPbHN73bbPxeRr7XHxGJ1BbzDSzn5nZjvA9sqpY28PM/ir8jGwxswfC/WJRtIXl6Fh0oNduZpPM7Cfh8pfMbMmIAnX3or0QFNDYC5xJUBp+E7Ai7rgK9QK8HbgI2JKx7OvA7eH124F/CK+vCNtzErA0bOfSuF9D3BdgAXBReH06sCtsK7Vj9DY04KTwejnwEnC52nBEbfnXwH8Cj4S31YYFeCmWfVUuvx+BdcCq8PviMeC6uF/fCNtk1J/RCdQW9wB/Fl6vAGYWY3sAC4H9wJTw9kPAh4ulLcjRsehArx34JHBXeP0W4CcjibPYe7AuBfa4+z537wYeBG6KOaaC5e7PAg39Ft9E8KVH+PcPMpY/6O5d7r6foFLkpWMSaAFz96Pu/kp4vQXYTvBlqXaMyAOt4c3y8OKoDYfFzBYBNwA/yFisNixMRbGvytX3o5ktAE5297UeHCXdm7HNuJGLz+gEaouTCQ6sfwjg7t3u3kiRtgdBFfApZlYGTCU4V2xRtEUujkWHeO2Zj/Uz4KqR9OwVe4K1EDiUcftwuEyiO8WDc5cR/p0fLlfbDiHsdr6QoAdG7TgM4bCZjUANsMbd1YbD903gc0AqY5nasDAVXfuP8vtxYXi9//LxJhef0YnSFmcCtcCPwyGTPzCzaRRhe7j7EeAbwEHgKME5ZH9LEbZFhly+9t5t3L0HaALmDDegYk+wsmWkqlufG2rbQZjZScDPgc+6e/Ngq2ZZVvTt6O5Jd78AWETwa9T5g6yuNuzHzN4D1Lj7hqibZFlW1G04xoqq/XPw/Tju2yuHn9Fx3xahMoJhYd919wuBNoKhYAOZsO0Rzi+6iWDI22nANDP70GCbZFk2IdoigpG89py0S7EnWIeBxRm3FxF0s0p01WFXK+HfmnC52nYAZlZOcPDwH+7+i3Cx2nEEwiEiTwPXojYcjiuAG83sAMFws3ea2f2oDQtV0bR/jr4fD4fX+y8fT3L1GZ0IbQHB6zgcjlaAYOjWRRRne1wN7Hf3WndPAL8A3kJxtkVaLl977zbhEMwZnDgkcUjFnmC9DCw3s6VmVkEwmW11zDGNN6uB28LrtwEPZyy/JazGshRYTjChsKiF43h/CGx393/OuEvtGJGZzTOzmeH1KQQ7mx2oDSNz9zvcfZG7LyH43nvS3T+E2rBQFcW+Klffj+EQoRYzuzx8zFszthkXcvUZnQhtAeDuVcAhMzs7XHQVsI3ibI+DwOVmNjV8DVcRzFcsxrZIy+Vrz3ys9xF89obfszeSyhgT6QJcT1CpaC/wN3HHU8gX4AGC8b4Jggz/owTjUp8Adod/Z2es/zdhu+5kHFSmGaM2fCtBV/NrwMbwcr3acVht+Cbg1bANtwBfDJerDUfWnu/geIUytWGBXophX5XL70dgZfj9sBf4DmBxv75RtMuoPqMTpS2AC4D14fvjV8CsYm0P4CsEPyxuAe4jqJJXFG1Bjo5FB3rtwGTgpwQFMdYBZ44kzvSDiYiIiIiIyCgV+xBBERERERGRnFGCJSIiIiIikiNKsERERERERHJECZaIiIiIiEiOKMESERERERHJESVYIiIiIiIiOaIES0REREREJEf+Pw33xJ1HdzBsAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace);" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 15.0)" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize = (16, 6))\n", + "axes[0].imshow(posterior, cmap='Blues', extent=extent, aspect=1)\n", + "axes[0].set_ylabel('$\\sigma$')\n", + "axes[1].scatter(trace['mu'], trace['sigma'], alpha=0.01)\n", + "axes[1].set_ylabel('$\\sigma$')\n", + "axes[0].set_title('True posterior')\n", + "axes[1].set_title('Sampled $\\\\theta$')\n", + "plt.xlabel('$\\mu$')\n", + "plt.xlim(150, mm.max())\n", + "plt.ylim(0, ss.max())" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import pyro\n", + "import pyro.distributions as dist\n", + "import pyro.optim\n", + "from pyro.infer import SVI, Trace_ELBO\n", + "import torch\n", + "import torch.distributions.constraints as constraints" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "def model():\n", + " # priors\n", + " mu = pyro.sample('mu', dist.Normal(loc=torch.tensor(200.), \n", + " scale=torch.tensor(15.)))\n", + " sigma = pyro.sample('sigma', dist.HalfCauchy(scale=torch.tensor(10.)))\n", + " \n", + " # likelihood\n", + " with pyro.plate('plate', size=2):\n", + " pyro.sample(f'obs', dist.Normal(loc=mu, scale=sigma), \n", + " obs=torch.tensor([195., 185.]))\n", + " \n", + "def guide():\n", + " # variational parameters\n", + " var_mu = pyro.param('var_mu', torch.tensor(180.))\n", + " var_mu_sig = pyro.param('var_mu_sig', torch.tensor(5.), \n", + " constraint=constraints.positive)\n", + " var_sig = pyro.param('var_sig', torch.tensor(5.))\n", + " \n", + " # factorized distribution\n", + " pyro.sample('mu', dist.Normal(loc=var_mu, scale=var_mu_sig))\n", + " pyro.sample('sigma', dist.Chi2(var_sig))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[iteration 1] loss: 20.5714\n", + "[iteration 101] loss: 12.0774\n", + "[iteration 201] loss: 11.7402\n", + "[iteration 301] loss: 9.8967\n", + "[iteration 401] loss: 28.1990\n", + "[iteration 501] loss: 13.2090\n", + "[iteration 601] loss: 11.4618\n", + "[iteration 701] loss: 14.9521\n", + "[iteration 801] loss: 11.2410\n", + "[iteration 901] loss: 9.7651\n", + "[iteration 1001] loss: 9.7140\n", + "[iteration 1101] loss: 9.5427\n", + "[iteration 1201] loss: 9.0695\n", + "[iteration 1301] loss: 9.0411\n", + "[iteration 1401] loss: 10.2914\n", + "[iteration 1501] loss: 8.6590\n", + "[iteration 1601] loss: 9.7012\n", + "[iteration 1701] loss: 12.4810\n", + "[iteration 1801] loss: 8.0311\n", + "[iteration 1901] loss: 9.6596\n", + "[iteration 2001] loss: 10.1730\n", + "[iteration 2101] loss: 8.9640\n", + "[iteration 2201] loss: 9.5495\n", + "[iteration 2301] loss: 9.6852\n", + "[iteration 2401] loss: 10.8672\n", + "[iteration 2501] loss: 8.9980\n", + "[iteration 2601] loss: 8.3449\n", + "[iteration 2701] loss: 9.4454\n", + "[iteration 2801] loss: 9.4535\n", + "[iteration 2901] loss: 9.0612\n", + "[iteration 3001] loss: 8.6264\n", + "[iteration 3101] loss: 8.5423\n", + "[iteration 3201] loss: 7.1836\n", + "[iteration 3301] loss: 8.9224\n", + "[iteration 3401] loss: 8.8739\n", + "[iteration 3501] loss: 9.0185\n", + "[iteration 3601] loss: 38.2326\n", + "[iteration 3701] loss: 8.8873\n", + "[iteration 3801] loss: 9.0606\n", + "[iteration 3901] loss: 8.0937\n", + "[iteration 4001] loss: 9.1192\n", + "[iteration 4101] loss: 7.1300\n", + "[iteration 4201] loss: 9.4013\n", + "[iteration 4301] loss: 8.7548\n", + "[iteration 4401] loss: 9.2406\n", + "[iteration 4501] loss: 9.3022\n", + "[iteration 4601] loss: 8.9886\n", + "[iteration 4701] loss: 9.1033\n", + "[iteration 4801] loss: 9.0818\n", + "[iteration 4901] loss: 8.5367\n" + ] + } + ], + "source": [ + "pyro.clear_param_store()\n", + "pyro.enable_validation(True)\n", + "\n", + "svi = SVI(model, guide, \n", + " optim=pyro.optim.ClippedAdam({\"lr\":0.01}), \n", + " loss=Trace_ELBO())\n", + "\n", + "# do gradient steps\n", + "c = 0\n", + "for step in range(5000):\n", + " c += 1\n", + " loss = svi.step()\n", + " if step % 100 == 0:\n", + " print(\"[iteration {:>4}] loss: {:.4f}\".format(c, loss))" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "190.1922149658203 5.435718059539795\n" + ] + }, + { + "data": { + "text/plain": [ + "10.607619285583496" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(pyro.param('var_mu').item(), pyro.param('var_mu_sig').item())\n", + "pyro.param('var_sig').item()" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [], + "source": [ + "sigma = dist.Chi2(pyro.param('var_sig')).sample((10000,)).numpy()\n", + "mu = dist.Normal(pyro.param('var_mu'), pyro.param('var_mu_sig')).sample((10000,)).numpy()" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 15.0)" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize = (16, 6))\n", + "axes[0].imshow(posterior, cmap='Blues', extent=extent, aspect=1)\n", + "axes[0].set_ylabel('$\\sigma$')\n", + "axes[1].scatter(mu, sigma, alpha=0.05)\n", + "axes[1].set_ylabel('$\\sigma$')\n", + "axes[0].set_title('True posterior $P(\\\\theta|D)$')\n", + "axes[1].set_title('Approximated posterior $Q(\\\\theta)$')\n", + "plt.xlabel('$\\mu$')\n", + "plt.xlim(150, mm.max())\n", + "plt.ylim(0, ss.max())" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}