MLE_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "tfd = tfp.distributions\n",
    "\n",
    "tf.executing_eagerly()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to do maximum likelihood estimation (MLE), and for demostration purposes, data will be generated with two distributions. I encourage you try with your data instead.\n",
    "\n",
    "The main libraries we use for this tutorial are Tensorflow and Tensorflow Probability. Just because of the easiness with computing maximum likelihood.\n",
    "\n",
    "## Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "params_to_func = {'mu': tf.math.reduce_mean, \n",
    "                  'sigma':tf.math.reduce_std, \n",
    "                  'rate': tf.math.reduce_mean}\n",
    "\n",
    "colors_encoding=['b','m','g']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions to perform MLE\n",
    "def loss(model, data):\n",
    "    total_log_prob = -tf.reduce_mean(model.log_prob(data))\n",
    "    return total_log_prob\n",
    "    \n",
    "\n",
    "def grad(model, inputs):\n",
    "    with tf.GradientTape() as tape:\n",
    "        loss_value = loss(model, inputs)\n",
    "    return loss_value, tape.gradient(loss_value, model.trainable_variables)\n",
    "\n",
    "def mle_run(data, model, parameters, optimizer, steps=1000, verbose=False):\n",
    "    update_list = []\n",
    "    prob_values = []\n",
    "    value_range = tf.linspace(tf.reduce_min(data),tf.reduce_max(data), 100)\n",
    "    \n",
    "    for i in range(steps):\n",
    "        loss_value, grads = grad(model, data)\n",
    "        optimizer.apply_gradients(zip(grads, parameters))\n",
    "    \n",
    "        if i % 10 == 0:\n",
    "            update_list.append((\n",
    "                optimizer.iterations.numpy(),loss_value.numpy(), \n",
    "                *[p.numpy()[0] for p in parameters]))\n",
    "            param_str = \", \".join([p.name.split(':')[0]+\": \"+str(p.numpy()) for p in parameters])\n",
    "            iter_info = f\"Step: {optimizer.iterations.numpy()}, initial loss: {loss_value.numpy()}, {param_str}\"\n",
    "            if verbose:\n",
    "                print(iter_info)\n",
    "            prob_values.append(model.prob(value_range))\n",
    "    \n",
    "    return update_list, prob_values, value_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions for plotting\n",
    "# Code adapted from: https://alexgude.com/blog/matplotlib-blitting-supernova/\n",
    "from functools import partial\n",
    "from collections import namedtuple\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "def init_fig(f, ax, artists, data):\n",
    "    \n",
    "    freq, bins, _ = plt.hist(data, bins=50, density = True);\n",
    "    # Set axis and plot titles\n",
    "    ax.set_title(\"Fitting data with Maximum Likelihood\", fontsize=20)\n",
    "    ax.set_xlabel(\"Values of the distribution\", fontsize=14)\n",
    "    ax.set_ylabel(r\"$p(D|\\theta)$\", fontsize=14)\n",
    "    \n",
    "    ax.set_xlim((tf.reduce_min(data)-0.1*tf.math.abs(tf.reduce_min(data))).numpy(), \n",
    "                (tf.reduce_max(data)+0.1*tf.math.abs(tf.reduce_max(data))).numpy()\n",
    "               )\n",
    "    ax.set_ylim(0.,freq.max())\n",
    "    \n",
    "    \n",
    "    return artists\n",
    "\n",
    "def frame_iter(update_list, prob_values):\n",
    "    for i in range(len(prob_values)):\n",
    "        yield (update_list[i][0], prob_values[i])\n",
    "        \n",
    "def update_artists(frames, artists, value_range):\n",
    "    s, p = frames\n",
    "    artists.prob.set_data(value_range.numpy(), p)\n",
    "    artists.step.set_text(\"Step \" + str(s))\n",
    "\n",
    "# Function to plot learning curves\n",
    "def plot_curves(update_lists, data, params_list):\n",
    "    from pandas import DataFrame\n",
    "    param_names = [p.name.split(':')[0] for p in params_list]\n",
    "    learning_df = DataFrame(update_lists, columns=[\"Step\", \"Loss\", *param_names])\n",
    "    \n",
    "    f, ax = plt.subplots(1+len(params_list), 1, sharex = True, figsize=(16, 8))\n",
    "    learning_df.plot(x = \"Step\", y='Loss',style=\"r--X\" ,ax=ax[0])\n",
    "    for i, p in enumerate(param_names):\n",
    "        learning_df.plot(x = \"Step\", y=p, style=f\"{colors_encoding[i]}--*\",linewidth=3,ax=ax[i+1])\n",
    "        ax[i+1].axhline(params_to_func[p](data).numpy(), color=colors_encoding[i])\n",
    "        ax[i+1].legend([f\"MLE {p}\",f\"True {p}\"])\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MLE to Normal random variable\n",
    "The first example generates data sampling from a Normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data\n",
    "x = 0.66+tf.random.normal([5000])\n",
    "# Two variables\n",
    "mu = tf.Variable([0.], name=\"mu\") # Mean of the distribution\n",
    "sigma = tf.Variable([3.], name=\"sigma\") # Standard deviation of the distribution\n",
    "\n",
    "# The model is a probability distribution\n",
    "model = tfd.Normal(loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step: 1, initial loss: 2.099677324295044, mu: [0.00999957], sigma: [2.99]\n",
      "Step: 11, initial loss: 2.0641984939575195, mu: [0.10959134], sigma: [2.8898435]\n",
      "Step: 21, initial loss: 2.02828311920166, mu: [0.20712045], sigma: [2.7890012]\n",
      "Step: 31, initial loss: 1.9919394254684448, mu: [0.30047598], sigma: [2.687032]\n",
      "Step: 41, initial loss: 1.955170750617981, mu: [0.38740954], sigma: [2.583688]\n",
      "Step: 51, initial loss: 1.9179555177688599, mu: [0.46564385], sigma: [2.4788895]\n",
      "Step: 61, initial loss: 1.8802293539047241, mu: [0.5329764], sigma: [2.3726714]\n",
      "Step: 71, initial loss: 1.8418810367584229, mu: [0.58749294], sigma: [2.2651427]\n",
      "Step: 81, initial loss: 1.8027677536010742, mu: [0.6279548], sigma: [2.1564546]\n",
      "Step: 91, initial loss: 1.762769103050232, mu: [0.6542955], sigma: [2.0467935]\n",
      "Step: 101, initial loss: 1.7218703031539917, mu: [0.66800785], sigma: [1.9363881]\n",
      "Step: 111, initial loss: 1.6802476644515991, mu: [0.6721305], sigma: [1.825547]\n",
      "Step: 121, initial loss: 1.6383267641067505, mu: [0.67066795], sigma: [1.7147218]\n",
      "Step: 131, initial loss: 1.5968329906463623, mu: [0.6675432], sigma: [1.6046048]\n",
      "Step: 141, initial loss: 1.5568495988845825, mu: [0.66545004], sigma: [1.4962634]\n",
      "Step: 151, initial loss: 1.5199013948440552, mu: [0.6651632], sigma: [1.3913218]\n",
      "Step: 161, initial loss: 1.4879469871520996, mu: [0.66583323], sigma: [1.292193]\n",
      "Step: 171, initial loss: 1.4630918502807617, mu: [0.66625494], sigma: [1.2022939]\n",
      "Step: 181, initial loss: 1.4467984437942505, mu: [0.6661174], sigma: [1.125995]\n",
      "Step: 191, initial loss: 1.4387118816375732, mu: [0.66594326], sigma: [1.0677992]\n",
      "Step: 201, initial loss: 1.4362263679504395, mu: [0.66600215], sigma: [1.0303419]\n",
      "Step: 211, initial loss: 1.4360015392303467, mu: [0.6660534], sigma: [1.0121673]\n",
      "Step: 221, initial loss: 1.4360740184783936, mu: [0.66601795], sigma: [1.0076921]\n",
      "Step: 231, initial loss: 1.4360424280166626, mu: [0.66601217], sigma: [1.0099958]\n",
      "Step: 241, initial loss: 1.4359997510910034, mu: [0.666027], sigma: [1.0138243]\n",
      "Step: 251, initial loss: 1.435987114906311, mu: [0.6660229], sigma: [1.0166142]\n",
      "Step: 261, initial loss: 1.435986876487732, mu: [0.66601944], sigma: [1.0178548]\n",
      "Step: 271, initial loss: 1.4359866380691528, mu: [0.66602254], sigma: [1.0180049]\n",
      "Step: 281, initial loss: 1.435986876487732, mu: [0.66602224], sigma: [1.0176945]\n",
      "Step: 291, initial loss: 1.4359862804412842, mu: [0.6660213], sigma: [1.0173547]\n"
     ]
    }
   ],
   "source": [
    "optimizer = tf.optimizers.Adam(0.01)\n",
    "ul, pv, vr = mle_run(x, model, [mu, sigma], optimizer, steps=300, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting an animation of updates in the probability distribution fitted by the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(18,10))\n",
    "Artists = namedtuple(\"Artists\",(\"prob\",\"step\"))\n",
    "artists = Artists(plt.plot([], [], \"r--\",animated=True)[0], \n",
    "                  ax.text(x=0.9*vr[-1].numpy(), y = 0.05, s=\"\"))\n",
    "\n",
    "init = partial(init_fig, f=f, ax=ax, artists=artists, data=x)\n",
    "update = partial(update_artists, artists=artists, value_range=vr)\n",
    "frame = partial(frame_iter, update_list=ul, prob_values=pv)\n",
    "\n",
    "ani = animation.FuncAnimation(fig=f, \n",
    "                              func=update, \n",
    "                              frames = frame,\n",
    "                              init_func = init)\n",
    "\n",
    "ani.save(\n",
    "  filename='myvideo_new2.mp4'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the learning curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iBSSi5GSpX7/g/WbNbMWuBQtsmz/fpoV5L40fb0mc22+XnnnG6gGNHm3Fn4uKbArZ5MlxeykAAAAAgCPHFC2gvlq3TmraVGrdWvrHP6Tvfz/YlpQklZbafqSCzwAAAACAOokpWkBD06WLJXck6cILbUrXccdJKSnB5E56uhV/fuUVG+FTUGAFngEAAAAACaXSBI9z7knn3Bbn3IcVtLd0zr3knHvfOfeuc65v7MMEcMR27JC++MKmaAWUltrKXP/+t03VGjlSatHCVum67Tab4gUAAAAAqPMqnaLlnMuVtFfSVO99ueSNc+5PkvZ67+9wzvWWNNl7f3plT8wULaCW5eTYsuvFxVJGhlRSYjV4AlO0du+W3n7b6vfMn2/nLV9ufX/xC6v7M2yYNHSo1Lx5fF8LAAAAADRQ1Z6i5b1fIGnHYU45VtKcQ+eukdTVOde2uoECqCH5+VJeniV0pk6Vxo2z/RkzrL15c+ncc6V77pGWLLEtYPVq6YEHpPPOk1q1kgYOtKldAAAAAIA6Iaoiy865rpJerWAEzx8kpXvv/8s5d5Kkf0sa7L1fHuHcPEl5ktS5c+eB69atO7LoAdSeffts5a35822lrtNPl269Vfr2W5vSdeqpNsInN1dq0ybe0QIAAABAvVSTRZb/KKmlc26lpPGS/iOpONKJ3vsp3vtB3vtB2dnZMXhqALWmcWOr0XPHHVaM+dZb7fi2bVJWlvTkk9Kll0pt20rHHmsjhqSK6/gUFNi0sc2bw/cBAAAAAFWWcqQP4L3fI2msJDnnnKQvDm0AGoIuXaQ335QOHrSaPYEaPoEVvGbNkn79axvZM2yYbZ9/btO9ioqk0aNtZFBRkRV6njw5vq8HAAAAABJQLKZotZC0z3tf5Jz7iaTTvPdXV/aYFFkGGoi5c61+z8KF0q5ddiw11VbwKimxgs+BpdkDBZ8BAAAAABFVNEWr0hE8zrlpkoZLynLOFUr6naRUSfLePyapj6SpzrkSSaskjYth3AAS3ciRtpWUSB9+aKN7Fi2Stm61Qs779tl5ycnSJZdIa9dK3bpJzsU3bgAAAABIIFGN4KkJjOABGrCCApuiFUjulDVihI38kWxET3Y2CR8AAAAA0BGM4AGAmJswwWruSDZFq6TE7rdsKd11l5SWZm2lpVLv3lKTJtLw4cHt6KNJ+AAAAABAiFisogUAVZOfL+Xl2cicqVOlceNs/8UXpRtukH78Yzvv4EHp97+XTjnFCjn/+MdS9+7SnXdae1GR9NlnFa/UBQAAAAANBFO0ACQG76U1a6R586STTpIGDrTCzbm5UseO4SN8jjmGET4AAAAA6iWmaAFIbM5JffrYFtCjh/TnP1vS5623pOeft+OLFtmon/XrbZQPCR8AAAAA9RxTtAAkrnbtpOuuk6ZPlzZtklavtoTPwIHW/vDDlgTq1EkaPVp6/HHp00/LT+kqKJBycqTNm8P3AQAAACBBMEULQP31+edW72fePNu+/lpq3dpW5kpKsileX35pSaKiIpvutXix7eflSZMnx/kFAAAAAEC4iqZokeAB0DB4L33yiSV0zjzTjvXqZccCUlOtsLNkRZ+3bKn1MAEAAADgcCpK8DBFC0DD4JwldALJHUmaPVu65x6pTRu7H0juZGTY6J3nnpPWrav9WAEAAACgiiiyDKDh6tVLGjRI2rs3/HhJiTRrltX2kaRu3aQRI6SRIy1BlJVV+7ECAAAAwGEwggdAwzZhgtXckWzkTlqa3X/rLemDD6QHH5T69ZNeekm66ippwQI7d+1aacYMq+sDAAAAAHFGggdAw5afbwWVs7OlqVOlceNs/+9/l/r2tQTQSy9JW7dKy5dLZ5xh/WbNki6/3FbyOu44afx4O7Z/f3xfDwAAAIAGiSLLAFAdxcXSihW2rHpBga3IdfCgtGuX1Lix9M9/2v3cXKlFi3hHCwAAAKCeYBUtAKhJRUXSmjXS8cfb/REjbGn2pCRpwAC7f9ZZVscHAAAAAKqp2qtoOeeedM5tcc59WEF7c+fcK86595xzHznnxsYiYABIKGlpweSOZCN45s2TbrvNavs88IB0773B9gcesDo/+/YFjxUUSDk50ubN4fsAAAAAUIlKR/A453Il7ZU01XvfN0L7LZKae+//2zmXLeljSe2890WHe1xG8ABoUPbtk7Zvl446Stqzx1biOnhQSk2VhgyRunaVZs60qV+5udLixTYqKC/PlmwHAAAAAB3BCB7v/QJJOw53iqRmzjknqemhc4urGygA1EuNG1tyR5IyM6UdO2yUz89/Ln33nfTss5bQKS6W/v1vSwgVF1uxZwAAAACoRCxW0XpEUh9JGyV9IOln3vvSGDwuANRfTZtaTZ577pGWLpVWr5aGDrVEUOhKXHv3Suefb1O6tm+PX7wAAAAA6rRYJHjOlLRSUgdJ/SU94pzLjHSicy7PObfMObds69atMXhqAKgnNm2Sli0Lr8mTkiIdfbQVb77pJunAATv+r39Jjz8uff65FKdC+QAAAADqllgkeMZKmuXNZ5K+kNQ70one+yne+0He+0HZ2dkxeGoAqCcmTLApWpIVZU5LsylaW7dKn34qffWV1KGDtU+bZrV5uneXunWTxo2Tpk+PX+wAAAAA4i4WCZ71kk6XJOdcW0m9JK2NweMCQMORn29Jm+xsaepUS9pkZ0szZlh7ILkjSU89ZVO6Jk+WBg6UXnpJuu++YPvDD9uxnTtr9zUAAAAAiJtoVtGaJmm4pCxJX0v6naRUSfLeP+ac6yDpaUntJTlJf/TeP1fZE7OKFgDESEmJjfRp187227WTtm2TnJMGDJBOP1265BLpxBPjHSkAAACAI1TRKloplXX03l9RSftGSd87gtgAAEciOdmSOoH9r76SliyR5syR5s6V7r9fatbMEjx79ljB5pEjpcGDbZl2AAAAAAmv0hE8NYURPABQS779Vjp4UGrRQpo/XxoxwoozN2ki5eZasueqq4JJIkkqKLC6QPn5Nh0ssB96DgAAAIBaV9EInljU4AEA1GVNmlhyR5KGDbPpWy++KF1zjfTFF9LEidKWLda+aJH0859L55xjq3eNHi2dd57tT5oUv9cAAAAA4LAYwQMADd1XX0nt20tJSdIvfynde2+wLTnZ6vpIVvQ5kAgCAAAAEBeM4AEARNaxoyV3JOlPf7JRPL16hSd3MjKkRx+Vnn1Weu016Ztv4hcvAAAAgHIqLbIMAGhAnJMOHJA2bAgmdyTbnzNHeuMN6csvpZQUacgQadQo6fzzbbUuAAAAAHHDCB4AQLgJE6SiItvPyJDS0uz+iy9aweU5c6xuz4ED0h13SM88Y+cWF0sPPyx99JEVcQYAAABQa6jBAwAIt3mzFVSeOdOmZc2dK73wgjRjhq3AFWrHDkv0tG8vrVghDRxox9u3t9E9o0ZJ554rtW5d+68DAAAAqIcqqsFDggcAEDtffmkjfN56y7Zt2+z29NOljz+WPvnEVvLKzIx3pAAAAEBCqijBQw0eAEDsdO0qjRtnW2mp9P77Uu/e1vbss9Lvf2/FmwcPDo7wOeUUOwYAAACg2qjBAwCoGUlJUv/+Unq63b/tNqmgQLr5ZivafNdd0nnnBev1zJ8vffhh+fo9BQVSTo5NHQvdBwAAAPB/mKIFAIiPXbusaPPJJ9v9vn2tQHPbtsHRPY0bS2PHWpHn3Fxp8WLbz8uTJk+Ob/wAAABAHFCDBwBQt61fb/V78vOtbs/WrVLz5tK339oKXY0aWUFnScrOlrZsiW+8AAAAQBxUlOBhihYAoG7o3NlG6/ztbzYF6733pFmzbOROenowuZOUJA0fLr3zjiV+AAAAAJDgAQDUQUlJ0vHHS87ZtKz9+4Nt3tsS7qecYreSjfb57LPy9XsAAACABqLSBI9z7knn3Bbn3IcVtE90zq08tH3onCtxzrWKfagAgAZnwgSruSNJGRlSWpolcVq3lv7+d+l737O255+XevSQjj5auvZa6YUXpB074hc3AAAAUMuiGcHztKSzKmr03v/Je9/fe99f0q8lzffe879qAMCRy8+3gsrZ2dLUqbb8ena2jdy59FJL9EjSD35gRZf795emT7e29u2tfo8kFRYGE0UAAABAPRRVkWXnXFdJr3rv+1Zy3t8kFXjvH6/sMSmyDACoEcXF0rvv2opcP/mJHRsxQlq61Gr3nHGGjfzp3dumgAEAAAAJ5IhW0YomweOcayypUFL3ikbwOOfyJOVJUufOnQeuW7cuquABADgir70mvf66jQj69FM7dtll0owZtr9rl9SiRfziAwAAAKJUUYInJYbPcb6kRYebnuW9nyJpimQjeGL43AAAVOzcc22TpC+/tERPmzZ2f+dO2+/b10b2nHGGNHSordwFAAAAJIhYrqJ1uaRpMXw8AABir2tXm7p14YV233vpjjuk5s2l+++3BE/LlrZEu2RTvkpLpYICKSfHlnAP3QcAAADqgJgkeJxzzSUNk/SPWDweAAC1plUr6ZZbpHnzbOWt116TrrvOEjiSTeNq3doSP6tWSZdcIp13nrRmjTRpUlxDBwAAAAIqnaLlnJsmabikLOdcoaTfSUqVJO/9Y4dOu0jSm977b2soTgAAal7TptI559gW0KWLjfIpKbH7ixYF22bOlB55hGLNAAAAiLuoiizXBFbRAgAkjE2bpNGjpXfekfbvt2MZGbZ0++zZ0saNwfo9/fpJSbGcAQ0AAAAEVVRkmf+BAgBQmTVrpCVLgskdyUb0zJ0r9eghbdki/fd/SwMGSO3aSbfeGr9YAQAA0CDFchUtAADqpwkTpKIi28/IsOROUZH0wguW3LntNhvF89Zb0ptv2jmSdPCgdNpp0qmn2uie3FypceP4vQ4AAADUW4zgAQCgMvn5Ul6elJ1t07LGjbP9GTOC53ToIF19tfTcc9JvfmPHtm6VmjWTJk+Wzj7bVucaNUpasCA+rwMAAAD1FjV4AACoafv2SQsX2uieN9+0wszDhtmxv/wlWL+nfft4RwoAAIA6rqIaPEzRAgCgpjVuLJ15pm2hNmyw0UHPP2/3+/a1ZM/tt9vIHwAAACBKTNECACBerrzSVuj6z3+ke+6xAs3TpgXr9Dz6qB1fuVIqLQ32KyiQcnKkzZvD9wEAANBgMUULAIC6pLhYSjk0wPbCC20Zdklq08bq9/TsaUmfoiIr2rx4se3n5VmtHwAAANRrFU3RIsEDAEBdtnGjTePKz7f6PQcPSnv3BhNBxcV2Xna2regFAACAeq2iBA9TtAAAqMs6dJCuucZW59q82Ubs5OZK6enB5I5kI3zuvltauzZ+sQIAACBuSPAAAJAokpJsRM/ixdL+/cHjyclWy+eWW6QVK+zY559LTzwhrVsXn1gBAABQq1hFCwCARDJhgtXckaSMDKmkxO4nJ9sIn8DqW6+9Jv3sZ7bfo4ctw37GGdLZZ0uNGsUndgAAANQYRvAAAJBI8vOtoHJ2tjR1qjRunO3PmCG1bRtcgWv8eOmjj6T777cEzzPPSJddZjV8JGn+fGnRouB9AAAAJDSKLAMA0BAUFVnC54QT7H5urrRwoY34GTFC+t73bOvRI75xAgAA4LAosgwAQEOWlhZM7kjSyy9LM2dKV1whffCBdOONNuon4I03pG3baj9OAAAAVEulCR7n3JPOuS3OuQ8Pc85w59xK59xHzrn5sQ0RAADEXKtW0iWXSH/5i6289dln0v/8j7Vt2yadc46tzDVwoHTzzdKcOeGFnQMKCqScHKv/E7oPAACAWlXpFC3nXK6kvZKmeu/7RmhvIenfks7y3q93zrXx3m+p7ImZogUAQB1VUiItXWr1fvLzpXfesSXZJ0+WbrhB2rlT2rDBEkHnn2/Tv3JzbXWvoiKrETR5crxfBQAAQL1U0RStqGrwOOe6Snq1ggTPDZI6eO9vrUpAJHgAAEgQ33xjRZkHDJA6dJCefloaO9ZW7iotlbyX0tODI3yys6Utlf6tBwAAANVQkzV4ekpq6Zyb55xb7py7+jBB5Dnnljnnlm3dujUGTw0AAGpcs2bSeedZckeypdafekq64AIpJcWOBZI7GRnS734n7dgRn1gBAAAaqFgkeFIkDZR0rqQzJd3mnOsZ6UTv/RTv/es7LuYAACAASURBVCDv/aDs7OwYPDUAAKh1bdtKY8ZYUebU1PC2khLp3nulrCwb8TNxohVs3rs3LqECAAA0FLFI8BRKesN7/633fpukBZL6xeBxAQBAXTZhgtXckWzkTlqa3d+5U7rjDikzU3roIRvxc/rpwX4ffBDsBwAAgJiIRYLnH5JOc86lOOcaSxosaXUMHhcAANRl+flWUDk7W5o6VRo3zvZnzZJuu02aN8+SPW++adO2JOnAAWnwYKllS+nMM6V77pGWLbORPwAAAKi2aFbRmiZpuKQsSV9L+p2kVEny3j926JyJksZKKpX0hPf+gcqemCLLAAA0QEVF0j//acuuz5kjrVplx++6S/rNb6TvvpO++ELq00dyLr6xAgAA1EFHtIpWTSDBAwAAtHmzNHeuNHCg1KuX9Prr0rnnSu3bSyNH2tSukSOlLl3iHSkAAECdQIIHAADUfV9/Lb3yio3umTs3uNz6++9LOTnShg22JDuLNQAAgAaqJpdJBwAAiI22baUf/1iaNs1G93zwgfTww9Jxx1n7XXdJbdpI/fpJN90kvfqqtGePtRUUWBJo8+bwfQAAgAaAETwAACBxvPeeTeOaM0datEjav186+mjpiSek886zIs5Dh0pLl1q9n7w8afLkeEcNAAAQM0zRAgAA9cv+/dI770g7dki33y6tWSMVF4efk5kprV8vNW8elxABAABijSlaAACgfklPl0aMkC6+2JZiP+00qVGj8HP27LEl2yVL/rzwAtO2AABAvZQS7wAAAACO2Jo10pIlNkUrIC1NOuss6dpr7f7KldKll9p+jx5Sbq5tZ59N0WYAAJDwGMEDAAAS34QJVnNHkjIyLLlTVGRTuAIFmvv1kxYvlu65x5Zkf/FF6ZprrK6PZCt1PfaYtGqVFKcp7AAAANVFggcAACS+/HwrqJydLU2dKo0bZ/szZgTPSU2VBg+WJk60pdi3b7fkzqmnWvtrr0nXX28Joexs6aKLpPvuk/bti89rAgAAqAKKLAMAAEg2amftWmnBAmnhQrv9+mtp504pJcVG92zfbrV+TjrJagABAADUMoosAwAAHI5z0jHHSGPHSk8+KX32ma3AlXKoZOHcudKtt0rDhtmqXKedJt17b/nHKSiQcnKsmHPoPgAAQA2iyDIAAEBFWrYM7v/977Yk+6JFwVE+//lPsP2CC2wVr1desRW7Ro+2mj9FRdKkSdLkybUfPwAAaDCYogUAAFBd3tvIn2+/lc47T5o/P1ig2bngflaWtGED07oAAMARY4oWAABArDlnt02a2HSstWulAQOsoHMguZORIf3qV1KzZtLAgdJ110l//aut2lVcHL/YAQBAvVJpgsc596Rzbotz7sMK2oc753Y751Ye2n4b+zABAAASwBdfSGvWSAcPBo+VlNhqXb/8pU35mj5d+vGPbdn2OXPsnDVr7Pjnn7NEOwAAqJZoavA8LekRSVMPc85C7/15MYkIAAAgUU2YYDV3JBu5U1Ji9998U9qyxY6XlloB56VLpSFD7NisWdJvfmP7rVpJJ55oW2DkDwAAQCUqHcHjvV8gaUctxAIAAJDY8vOlvDwpO1uaOlUaN872Z8wInpOUJPXsaUWYmze3YxMnWsHmv/xF+sEPbNWtBx4I1uyZNMmO33239NZb0q5dtf/aAABAnRZVkWXnXFdJr3rv+0ZoGy7pRUmFkjZK+qX3/qMKHidPUp4kde7ceeC6deuqGzcAAED9duCArcolSXfcIT33nI38CRg2TJo3z/Y//VTq1MlGDYUqKLBRRfn50urVwf127WrlJQAAgNirqMhyLBI8mZJKvfd7nXPnSHrQe9+jssdkFS0AAIAq2rlTWrbMpnclJUk332zHjz5aWr9eysmxqV0nnWSFnm+4waaI5eYGl2zPy2PJdgAAEliNJXginPulpEHe+22HO48EDwAAQAx4L73yivTuu5b4WbrUEkEtW0rffGMrdaWkBFfsatVK2rYtuAIYAABIKDW2TLpzrp1z9j8E59xJhx5z+5E+LgAAAKLgnHTBBdJdd0n/+pe0fbtN2XrtNRu5k54evhz7jh2W5HnqKbu/Z4/0z39KX35pBaABAEBCqnQVLefcNEnDJWU55wol/U5SqiR57x+TdImk651zxZK+k3S5j2ZYEAAAAGLPOal7d2nDBpuWtX9/sC0lRRo82KZyHXOMHVuxQjrnHNtv3Fjq3Vvq08dW8Dr+eKsFlJxsfQEAQJ0V1RStmsAULQAAgBqUkyOtWWOjd0KXbM/ODi7ZLkl799oKXqtXB7dVq6QXXrBaPs89J/3oR7byV58+we2881jCHQCAOKhoihZ/igEAAKiP8vNtefWZM6VHH5XmzrWkTeiS7ZLUtKl02mm2RXLssdJ//ZclflaulGbNsqlcX31lCZ4nnpBmzw5P/vTpI2Vmhj8OK3oBAFCjGMEDAACA6O3fbzV++va16WCTJ0uPPSZ98omNEJJsBa99+2xa1wsvSIsWSX/+s40mys2VlixhRS8AAKrpiFbRqgkkeAAAAOqR4mJp7VobnbN5s3TttXb8nHOsiHMk2dnSH/5gyaCOHaVOney2XTtq/gAAUAGmaAEAAKDmpKRYnZ6ePcOPv/qqtHy59JOfWG2fgwfteEaGTR2bNEl6//3wPsOH25QuSbrxRrvt2DG4de8udelSvTiZKgYAqKdI8AAAAKDmJCVZIedPPw0mdyQr+jx3rhV43r5dKiy0uj5ffSW1bh08b/lyKxa9a1fw2FVXSc8+K3kvDRoktWwZHP3TsaM0ZIg0YIC1e28xSJbcOe88mx42erStMlZUZEkmpooBABIcU7QAAABQs6Jd0etw9u0LJoBatJD697fHuPJKO1ZYKG3aZI99883S3XdbUig7W2rf3hI/q1ZJ33xjSZ/Gje0xJXu8d9+1otGZmRajczX3fgQwmggAUA0VTdFKikcwAAAAaEDy862gcna2NHWqNG6c7Zdd0etwGjeWevSw6Vv9+9uxtDQr4vzOO9KGDdKBA9LGjbbql2SJnIkTpREjpCZNpDZtbDRPoAh0wK5dNrWsfXs776mn7PjKlVZM+uSTpTPPlC65xJaMX7HC2tevt+LRzz8vvfKKNG+ete3da+2lpRZDJIHRRGvW2GiiwP6kSdG/J7FUUGCJuM2bw/cbcix1JQ5iqdtxEEvdj6WuxFELGMEDAACAhiGQVAlN7qSkSKNGWZLlm2+kPXukc8+1xM6qVdJttwWPB26ffFI64wxbHv7CC8s/z9y5llSaNk364Q9tZFBgdFCzZpZAuvRSG7VTUmIxFBdb38aNbTRSy5Y2PW3JEktIpaQEt4suktLTpY8/lr74IrwtJUU68UQpOdl+gdm9u3x727b2XIFVzxYulC64wO7n5ganrsVjlbPQaXTxjKWuxEEsdTsOYqn7sdSVOGKsohE88t7HZRs4cKAHAAAAak3fvt6npFhlnowM79PSbD87u3qPd+CA9xs3ev/xx94vXer93Lne/+Mf3m/bZu3/+Y/3t9zi/fjx3o8Z4/0PfuD9GWd4v3at9evdO1AlKHxbu9b6/+EPkdu3brX2X/86cvt331n7+PHl21JSgvGPGRO5f2Br1Mjep8DWuLHFHHDhhd43bRrcmjXzfvDgYPsZZ3ifmWlb8+bet2hhxwJOPdX7li1ta9XK+9at7dzAZ+RcMBbnrP3qq4P9e/SwY6HbDTcE29u1s8cN3SZODH52gecO3e64w9r79In8njRpYu3r19vrKbs99pi1r1oV+fGfe87a3303cvvLL1v73LnBmJOSwj+T0Pek7OtbvNj6T5tW/r1p3dr7Dz+09scfj9z+5ZfWfv/93mdlld969w5+PqGbc9a+f7/1v/nm8n3btw9+NuPH289d6NajR7B97Njy7SecEGzPzIz8+QR+ls85p3z/s88O9h82rHz7JZcE2wcOLN9+zTXB9l69gseTk4PP37hx+HsS2v+//zt47ZV97Oxs7ydNsvYdOyK3339/8NqL1D5lin3HhcYTGsvf/ha89iL1nz3b2gsKIrfPnWvtr74auX3JEmufPr38+xK6NW0auX/g2nvggcjtge/Vu+6K3B649n796/DjFX0+1f3eryMkLfMR8iwUWQYAAEDDkJ9vU6BmzrQVvObOtSleVZkqFiotzaZ1tW8fub1//+B0srIKCmyKV9nHGzMmuELYz35mU8KKi8O3li2t/frrbeRN2fa0NGsfM8aml4W2lZYGn+/ii23a286d9j4UFgZHEmVk2FS6jAy7Hxj136JFsP8550jHHBPeHhgdJNlIqOOOC/5qJ4WvfnbuueHFsCV7L+fOtb+yB0ZaJSfbKKvu3aV+/YL9L7pI+vbb8PfwpJOC+5dfHnw9ASeeaLdJSVasu6wTTrDbV16x6YCbNwcfIyVFuukm22/SRLr66vL9e/e22+bNIz9+4P3KyorcHnh/2rWz+lKSvcY335S+/tqmIUpSo0Y2Sqx79/D+2dl2262bvf6yAp9fjx6R25s0sds+faTLLivfftNN0rXXSosWBWMJfD7HHBMsaD5gQPn+ycnB/UGDyn82jRsH908+2UaphWrVKrg/caL02GP2noR+Po8+avvDh5dfaa9bt+D+qFHSsceGt/fpE9w/+2wr/h4q9Gf5/POD196330pz5khbt4Zfs6efHvy8peC1lZRk0z3L6tvXbtPSIrcHrq3GjSO3d+9u18mll9rIv8D7Eoila1e737p15P4dO9ptmzaR2wM/2x06RG7PyrLbLl2sPfC+hH5GGRnSL39px8oKXHu9e0d+/EaN7LZv38jtgWuvf//w9kAcO3cGP5/AKo71EFO0AAAAgNoWi8LTsRJp6lpamiV4avuXoLoSS12Jg1jqdhzEUvdjqStxxFhFU7RI8AAAAAC1bfPmikcTjRhRu7HUpWRTXYmlrsRBLHU7DmKp+7HUlThijFW0AAAAgLqiXTsr8Llli00nePRR26/t5I4Um1XO6lssdSUOYqnbcRBL3Y+lrsRRSxjBAwAAAAAAkCAYwQMAAAAAAFBPkeABAAAAAABIcHGbouWc2yppXVye/MhlSdoW7yCAKuK6RaLhmkUi4rpFouGaRSLiukUiiuV128V7n132YNwSPInMObcs0nw3oC7jukWi4ZpFIuK6RaLhmkUi4rpFIqqN65YpWgAAAAAAAAmOBA8AAAAAAECCI8FTPVPiHQBQDVy3SDRcs0hEXLdINFyzSERct0hENX7dUoMHAAAAAAAgwTGCBwAAAAAAIMGR4AEAAAAAAEhwJHgAAAAAAAASHAkeAAAAAACABEeCBwAAAAAAIMGR4AEAAAAAAEhwJHgAAAAAAAASXFQJHufcWc65j51znznnbo7Qfr9zbuWh7RPn3K7YhwoAAAAAAIBInPf+8Cc4lyzpE0lnSCqUtFTSFd77VRWcP17SCd77H8U4VgAAAAAAAESQEsU5J0n6zHu/VpKcc9MlXSgpYoJH0hWSflfZg2ZlZfmuXbtGGSYAAAAAAACWL1++zXufXfZ4NAmejpI2hNwvlDQ40onOuS6SukmaW0F7nqQ8SercubOWLVsWxdMDAAAAAABAkpxz6yIdj6YGj4twrKJ5XZdLesF7XxKp0Xs/xXs/yHs/KDu7XLIJAAAAAAAA1RBNgqdQ0lEh9ztJ2ljBuZdLmnakQQEAAAAAACB60SR4lkrq4Zzr5pxLkyVxZpc9yTnXS1JLSe/ENkQAAOqGTZukYcOkzZvjHUndigUAAADxV2kNHu99sXPuRkn/kpQs6Unv/UfOuTslLfPeB5I9V0ia7itblgsAgCratEm6/HJpxgypXbvYPKb3UlGRdOBAcMvMtC3Uu+9KW7ZY+5//LC1cKI0eLf3oR1JyspSUFLwdOFDq3Ll8/+++s/bQc8veJiVJXbpITZqUf+3OlT/3ttukt9+Wbr/d4nKRJlTXkpr4fFA/1ZVrpa7EAQBALFW6THpNGTRokKfIMgCgMosWSTffbLeDBknf+154UiZ0O/98aezY8P433ST94x/h5xUV2VbWfffZ+aFOO80SKdF45hnp6qvDjx13nLSqonUny8jPl0aNCj/WsqW0a1d0/d9/X8rJCd4/eNCePzU1uKWlVXz/L3+RmjUL9t+5U7rnnvJ9yvabOlWaM0e67jrp0UeD/Xfvlt57zxJTKSmHv23UqPwv2iUltgUSW9EkserKL+51JY6aiCXwX0fvg/tlP59AAjX0HO+ln/1MevJJS5A++GDw/IyM8P6lpeV/Rst+/qH309LC20pLbSsr0OenP5Uef1zKy5MmT7b446U+Xyv1IZa6Egex1O04iKXux1JX4ogV59xy7/2gcg3e+7hsAwcO9ACAhqG42PvNm71//33v8/O9f+457++91/tf/cr7a67x/qyzvD/hBO9vvjm8X3p64NfD6Laf/az8c48eHX3/u+8u3//006Pv/9xz5fv36hV9/zlzyvfPzIy+/6pV4X337q3a+7dzZ3j/zz6rWv/Alp5u/RcsiL7P0UeXf+3Tp4efk5zsfaNG3jdubO9Ly5beZ2V5366d9xddZH2uv977pCS7feIJ73v0sK1nT9t69QpuvXvb1qeP97/8Zfnn/9OfvM/Jse34423r1y+49e9v2wkneH/ffeF9r7/ee+csvhNOsPP69bPH6tvX++OO8/7YY+25e/f2/qmnyj////t/3nft6n2XLt537ux9p07ed+zofYcO3rdvb6+7bVvv27Txftas8v0HDLD3KTXV3r+UFO+bNLH3LyPDtvR02xYsKN+/eXN7L52z7XCf3yefhPfdvbtq18w334T3X7Mm+r5Nm5aPfe7c6l2zAc8/X3mfwPsyYkT557/3Xnu/Q7fU1OCWlhbcevYMXrMBv/pV+DmH2371q/LPP3p0+eevaAu9dgM/Px062M9bNNu0aeWfv1ev4PtT2VZQUL5/06aR3+tI28cfh/fds8deQ7Tbnj3h/desCW8v+x0UujVvXj72efOif+/69Cnf/29/q/j8srGMHFm+/733Rv/8o0eX7/+LX0T3vgXiCL1uvff+iiuif+/vvbf8848YEX3/adPCv/O9t2sv2v6Rrr3mzaN//8pee+PGVXytRNoqu/YOt2Vmlo+9oCDydRupf+/e5fv/7W/RP39F33uHu1ZCY7nyyvL9o732kpLs3LKuvPLw73fgu6TsNZuoZLOpVHaL2wieZs0G+YEDGcEDAHVVUZGNPDn22PJ/HZfsn+qDB4OjYYqKbKRF2UUSv/pK+uyz6J6zdWupb9/wGN57T9q3L7r+7dtLPXuGH/v444rr1DgXnP6UlCQddZTUqVP4OV98Ie3dK337rY3+CUhPt9EugX9Gvbe+LVqE91+92vqFnhe6H3qsT5/wETSStGSJjWIJPbe0NHg/1Ekn2UiIgOJiG/kUrdNOCx/JsG+ftHRp9P2TkqSsLOmYY+ya2bXLPr9oZGRY/KG2bLH3rza0aWPvf6jPP5cKC6Pr36mTve4FCyJ/NpU5+mi7/kKtXGmjoKLRp4+9hlDz50f//P36lb92Fy6MPAomkrLXXklJ9CPfJGnoUPv+CKjKtZeUZNduqKpce8nJFn/o91xVrr3mzaX+/cOPbdggrV0bXf+ynJM6dqz6tRdq1Spp69bo+h99tH3PVfdXgkjXXmBqajTKXntV/RlK5GsvFt97w4aF36/KtXek33uhnJNyc6t+7R3J996RitX3XnW/9xP52jvS771Y/ZsbqirXnhS8ZhPV/PmRR/BUWoMHANAwrVtn/8n67DP7xSeQxAkkdYqLy/dp0qR8gielCv/SlJ2SkZZmiZTQBE+zZvYcoYmZwH7of/IDunWzujhlz412Ska3bnb70UeWgGrf3ob5FhVZ8qsyZf8DU1WDB5c/9tFH9t4EYjlwwGIp+5qSk6UTTwwmkAKJoUj3S0vLT4FJTbXXX/a80P09e4K/yJWW2ucd+EU5Odn+E1jZWAip4iRitDIz7VrZts3iSEqSGje25FxtGjLE/pMaiCOe0tOl/ftr57kifVZlr6dI51T0cxhIvkYjFtOrIl1/tS00QbphQ+0+d126bocMkd5hyZaolK0ZFw+h121ty8y07/jAd35Wlv2bVFvfewF16ecHlYvnNVsb4pbg6dVLmjcvXs8OAJCk7dstWfDhh7bt2iW99FL4f46q8teQpk3Lf7f/61/SWWdJrVrZX2zatq1469Ch/AiaH/zAEhl5edKUKZbQmDWr2i8ZMVZbn09pabAmT3Fx+dvUVOm3v7UY0tMtAXfppVa/qeyIqdD9wG1mZvlrb+NG+w97NP3btAn2v/56i6NRI4vj4oulX/86mGCMtLVtawnEss+/f38wKVlRX+cskVY2wbl7t9WUeuaZYJJ27FjpgQfCEyjOWXvoX5IlS+aGPkfg3OoW9K4rP8vViaNscqrs/bJJppKS8F/0Il07kjR+vPTXvwY/n4svtjpWBw9G/4tioJZVqOLi6BOkgQLuges28PPzk59IjzwSXf9Irz/a6yTSNXXddVYjKfC+BGolRdM/kHyOVqT6UYH+gVpNgTgivSdl33vv7fVHq2z/iupH/fSn0hNPhMcyeXL5n9uK+kfiXOT+lV07Zd+XwHUbbf/Q54907UQrEEfgmr34Yunhh6PvH6m2W6Q/XlUkOTnYvzo/P6H9papfu2U/u0D/SNdtpJ+f6nz2Ve1fUSyRPvtYXDsV9S/78xN6zSaqir5jGcEDAA3AN9/Y0NVAIieQ1Nm0Kfw852zEzm23SS+/bCNnKhoF4Jz9BaRsgqaskSNthEl1/0Ie+otXRf/BR/zU1ucT+CUyNbXic77+2n4xDP3FveyUvaro0CHyNV2ZSHEMGFC95z8SzZtb0rZsLE2bRtf/cO91ddSVn+XqxHG4As+RJCeX/+Unkm3byn8+0pG/91UZORkQ6bqtzuNI0b32w9mypXws0Y7UipS0qIrQ/pHiqOw9ca7675tU8QjTrVvLxxLpdVZlhGpFz1+ZSO9LVfofTlU+u0hxHOm1V93PLhY/P7G6dqv7vhzpZxepf1ViqclrJ9LPT33FKloAUI8cOFD+r7m7d5efY344y5fbX1umTAn+pWPwYOmGG4KJnDZtLLlzJP+JBQAAAFB1Fa2ixX/NASABFRfbfO/AiJzA9umnUkFBeOG95s1tJMDGjeUfJz3darf07RvcuneP/Jeoq66qvdcHAAAAoGpI8ABAHbJpk3T55dKMGVK7dsHj8+dLixcHEzmBlZki+fDD8isr9O9vo3hCEzl9+9oKFpGGtNaVqRQAAAAAokOCBwDqiOJiKwK3cKF0553hxd8eeMBq4kTjq6/KH3v11eoXRgUAAABQ95HgAYA48d5G4rz1lq10E7pywp//bFt6ui1B3bdv+QRPx47BkTjHHWe3xx5rS5WXRXIHAAAAqN9I8ABALSoslObMsaTOnDkVV/Fv3Fi66CLpf//X7o8cKe3cGZ7Qadmy9uIGAAAAULeR4AGAWvDOO9LYsdLHH1d+bnKyLUuemRmswzNihG0AAAAAEAkJHgCIoe++s2TO8OFSUlLweIcOkZM7LVta4mbUKOmll2wFq2uvDa5cBQAAAADRcN77yk9y7ixJD0pKlvSE9/6PEc65TNLtkryk97z3Vx7uMQcNGuSXLVtWnZgBoM4oKZFWrAhOuXr7bVvd6r33pOOPDz+3e3crgDx0qCV0Tj9dOuGEyKtYAQAAAEAkzrnl3vtBZY9XOoLHOZcsabKkMyQVSlrqnJvtvV8Vck4PSb+WdKr3fqdzrk3sQgeAusN76ZNPggmdggJp167y5731VvkEz+uvS507W+FkAAAAAIilaKZonSTpM+/9Wklyzk2XdKGkVSHn/ETSZO/9Tkny3m+JdaAAEG93321LlxcWHv68Xr2sSHJZPXvWTFwAAAAAkFT5KeooaUPI/cJDx0L1lNTTObfIObf40JSucpxzec65Zc65ZVu3bq1exABQAzZtkoYNkzZvlnbvltasKX/Od99FTu60by/98IfS009LGzZY3+uuq/GQAQAAAOD/RDOCx0U4VrZwT4qkHpKGS+okaaFzrq/3Pmzigvd+iqQpktXgqXK0AFADiostIbNwodS/v7RtmzRggPTuu+HnnX66NGmSrW41fLjV0Rk1SurdW3KRvikBAAAAoJZEk+AplHRUyP1OkjZGOGex9/6gpC+ccx/LEj5LYxIlAMSY99KSJVbwuKQkePzrr+126VJp505b5Srg5JNthaxBg6QU1iAEAAAAUIdEM0VrqaQezrluzrk0SZdLml3mnJcljZAk51yWbMrW2lgGCgCx8PHH0m9/K/XoYQmb0OROqJwcaWOZVHZamjRkCMkdAAAAAHVPpb+meO+LnXM3SvqXbJn0J733Hznn7pS0zHs/+1Db95xzqySVSJrovd9ek4EDQFUVFVmCJtKqV5ItV15aKo0ZIz35ZK2GBgAAAABHJKq/Q3vvX5f0epljvw3Z95L+69AGAHG3Z48VSz4qZIJpWpp08cXSX/9q9zMzpUsusWXP+/a1OjxTpljBZQAAAABIJEw0AFBvFBVJb7whPfec9Mor0oUXStOnh59z9dXSjh3S6NHSuedK6enh7ZMn1168AAAAABArJHgAJLTSUmnRIun556WZMy15EzB7tvTNN1KzZsFjubm2AQAAAEB9QoIHQEL64ANL6kybJq1fH/mcnj2lDRukY4+t3dgAAAAAoLaR4AGQUIqLpcGDpRUrIrd36SJdeaVNwTruuNqNDQAAAADihQQPgISSkiK1axd+rFUr6dJLpauukk45RUpKik9sAAAAABAvJHgA1Dn790uvvmpTsHr1kv74x/D20aOluXOlCy6w/bPOshWyAAAAAKChcrbCee0bNGiQX7ZsWVyeG0DdU1IizZtnSZ0XX7RlziUbrVNYKCUnB8/dv99WzMrMjEuoAAAAABA3zrnl3vtBZY8z5LvDbQAAIABJREFUggdA3GzcKJ1/vnTiibas+caN5c/ZvFlassSmXgWkp5df3hwAAAAAGjISPABq3cGD0pQp0q23Srt2RS6YfMwxNv1q9GhbDQsAAAAAUDESPABqXWamTbOKZPx4S+qcdJLkXO3GBQAAAACJirVmANS43bvD769dKw0cGLyfnCyNGCFt2CA99JAtg05yBwAAAACiR4IHQI04eFCaPl0aMkQ6++zwtvbtpf79LYmTni55L/XuLXXqFJ9YAQAAACDRMUULQEzt2CE9/rj0yCO2+lXAkiU2Mif0vOuvl/LyrB7Ppk21HysAAAAA1BckeADExJo1Nr3qmWekffvC29LSpJUrwxM8s2YF9ydPrp0YAQAAAKC+imqKlnPuLOfcx865z5xzN0doH+Oc2+qcW3lo+3HsQwVQ13gv5edL55wj9ekj/fnP4cmdNm2k22+X1q+Xrr02bmECAAAAQL1X6Qge51yypMmSzpBUKGmpc262935VmVNneO9vrIEYAdRRd9xhW1nHHy/ddJN0xRVSo0a1HxcAAAAANDTRjOA5SdL/Z+/ew6uqzsSPf9fJnZAE5CJgQFCochU1CiL1bkc73lstWjtarSj11nao2v46HbWt06tOW6kWe7G2U7U6arV22qotKipiFESEKogggYCIkBBMQi7r98fBXEiQACEnId/P8+TJ3muvvc97wgGfvK71vktjjMtijFuA+4Az92xYkrqCz3ym8TgEOP10+Pvfk9uxLr7Y5I4kSZIkdZS2JHj2A1Y2OS/ZOratT4UQFoQQHgwhDG7tQSGEqSGE4hBC8bp163YhXEmp8Mor8PnPw7Z/bUeOhHPPhauvhjfegEcfTbY7t8W5JEmSJHWsthRZbu1XtbjN+WPAvTHG6hDCFcBvgBNa3BTjTGAmQFFR0bbPkNSJ1NUlEzb//d/wzDPJsQMPhG98o/m8++83oSNJkiRJqdaWFTwlQNMVOYXA6qYTYozrY4zVW0/vAg5vn/AkdbTy8mRSZ8QIOOecxuQOJLtd1dQ0n29yR5IkSZJSry0reF4CRoQQhgGrgCnABU0nhBAGxhhLt56eASxu1ygl7XHLlsFPfwq//CVs2tT8Wno6nHceXHstZGSkJj5JkiRJ0vbtMMETY6wNIVwF/BVIA34VY3w9hHAzUBxjfBS4JoRwBlALvA9cvAdjltSO3nsPLrsM/vjHZNvzpvbZJ9ne/ItfhMLC1MQnSZIkSdqxELf9ja6DFBUVxeLi4pS8ttSdlZbClCnJ2jkDBiRr7QwfDsuXN84ZORK+9CW48ELo0SNloUqSJEmSthFCeDnGWLTteFtq8EjaS5SXw3XXwezZcPPNybG0tGQXLIB/+Rf4y19g4UKYOtXkjiRJkiR1Fa7gkbqBigro3Rtqa1tey86GtWuhpARGjer42CRJkiRJbecKHqkb+uADuPVWOOCAlsmdHj3gs5+Ft9+G/HyTO5IkSZLUlbWli5akLqaqCu66C265BdasaXk9MzM5Jz8/WYdHkiRJktS1meCR9iJbtsCvfgXf+U5yy1VTQ4ZAnz5w5JEwbRrMnJksuCxJkiRJ6vpM8Eh7iSeeSBZGbtoNC2DQIPh//w8uvRSyshrHZ8zo0PAkSZIkSXuQCR5pL9GnT/Pkzr77wte+BpdfniykLEmSJEnae1lkWeqC6uuhpqb52GGHwVlnQd++8IMfwLJlcO21JnckSZIkqTswwSN1ITHCQw/BIYfA7be3vD5jRjKxM316skuWJEmSJKl7MMEjdQExwmOPweGHw6c+BQsXwne/C5s3N583aBDk5aUmRkmSJElS6pjgkTqxGOEvf4EJE+CMM2DevMZrmzfDyy+nLjZJkiRJUudhgkfqhGKEp56CyZPh1FPhpZcar+XkwFe/Cm+/Dccck7oYJUmSJEmdh120pE7m+efh61+Hp59uPp6VBdOmwfXXw4ABqYlNkiRJktQ5meCROpmnn26e3MnIgMsuSyZ99tsvdXFJkiRJkjqvNm3RCiGcEkJ4I4SwNIRww0fM+3QIIYYQitovRKl7ufpq6NcP0tOTiZ2lS5PdsUzuSJIkSZK2Z4cJnhBCGjADOBUYBZwfQhjVyrw84BrgxfYOUtobvfoqnH02vPZa8/GePeG3v4U33oCZM2HIkNTEJ0mSJEnqOtqyRetIYGmMcRlACOE+4Exg0TbzvgV8H5jerhFKe5nXX4cbb4QHH0yeJxLwv//bfM6//EuHhyVJkiRJ6sLaskVrP2Blk/OSrWMNQgiHAoNjjH/6qAeFEKaGEIpDCMXr1q3b6WClrqq0FI48Es45B8aObUzuADz8MCxfnrLQJEmSJEl7gbYkeEIrY7HhYggJ4Dbg33f0oBjjzBhjUYyxqF+/fm2PUurCSkvhhBOSrc4ffjjZAv1DZ50F8+fD0KEpC0+SJEmStBdoyxatEmBwk/NCYHWT8zxgDDArhAAwAHg0hHBGjLG4vQKVuprKSsjPh9raltcSCZg7Fw4/vOPjkiRJkiTtfdqyguclYEQIYVgIIROYAjz64cUYY1mMsW+McWiMcSgwBzC5o27v/PNbJncSiWR9nVWrTO5IkiRJktrPDhM8McZa4Crgr8Bi4A8xxtdDCDeHEM7Y0wFKXdVXvtL8PDMz+f2AA2DAgI6PR5IkSZK092rLFi1ijH8G/rzN2De3M/e43Q9L6lpKSmDgQEhLaxw75hi4/HJ48UWYOBGuuCLZ9ry0NHVxSpIkSZL2Tm1K8EhqXUUFfO978MMfws9+Bp//fPPrd97Z/HzGjI6LTZIkSZLUfbSlBo+kbdTXw69/DR/7GHz721BVBV//ejLhI0mSJElSRzPBI+2kp5+GoiK45JLm260GDYI1a1IXlyRJkiSp+zLBI7XRW2/Bpz4Fxx0H8+Y1jg8cCHffDS+9BMOHpyo6SZIkSVJ3Zg0eaQfKypLbsH7yE9iypXE8JwemT4frroOePVMXnyRJkiRJJnikHfj+95NFlJv67Gfhv/4LBg9OTUySJEmSJDXlFi1pB776VejTJ3l81FEwZw787ncmdyRJkiRJnYcreKQmFi+GgoJkweQP9eqV3J6VSMBnPgMhpC4+SZIkSZJa4woeCVi/Hq6+GsaOheuvb3n9ggtgyhSTO5IkSZKkzskEj7q1LVvgttuS3a9uvx3q6pLbr+bOTXVkkiRJkiS1nVu01C3FCI89luyCtWRJ82vHHQe5uSkJS5IkSZKkXeIKHnU7r74KJ50EZ57ZPLkzfDg8/DD8/e8wenTq4pMkSZIkaWeZ4FG3sXYtXHYZHHpoMonzoYIC+NGP4PXX4ayzrLMjSZIkSep62pTgCSGcEkJ4I4SwNIRwQyvXrwghvBZCmB9CmB1CGNX+oUo7r7QUjj0W1qyB4mL4xS+S27MA0tLgyith6VL4ylcgMzO1sUqSJEmStKt2mOAJIaQBM4BTgVHA+a0kcH4fYxwbYxwPfB+4td0jlXbBt74Fs2fDzTfDJz8JJ5+cHD/lFFiwIFlYuW/f1MYoSZIkSdLuakuR5SOBpTHGZQAhhPuAM4FFH06IMZY3mZ8LxPYMUtpZWVnJDlkfuuOO5FdmJvzf/yUTPJIkSZIk7S3askVrP2Blk/OSrWPNhBCuDCG8RXIFzzWtPSiEMDWEUBxCKF63bt2uxCt9pIoKuP76ZLvznj0hJyc53qMHfPazsGKFyR1JkiRJ0t6nLQme1krOtlihE2OcEWM8ELge+EZrD4oxzowxFsUYi/r167dzkUofIcZkB6xRo+D7308meCoqoKoKsrOT3/PzYcCAVEcqSZIkSVL7a0uCpwQY3OS8EFj9EfPvA87anaCknbFsGZx2GpxzDqxsstasTx847zyYMweuuCJZaFmSJEmSpL1RW2rwvASMCCEMA1YBU4ALmk4IIYyIMS7ZevqvwBKkPayqCn7wA7jlluTxh/r2hR/+EP7t3xpbns+YkZoYJUmSJEnqCDtM8MQYa0MIVwF/BdKAX8UYXw8h3AwUxxgfBa4KIZwE1AAbgIv2ZNDS3/4GV10FS5qkEkOAyy+H73wH9tkndbFJkiRJktTRQoypaXhVVFQUi4uLU/La6trWr4f994fNmxvHDjss2SXryCNTF5ckSZIkSXtaCOHlGGPRtuNtqcEjdSp9+sB//mfyuKAAbr8d5s41uSNJkiRJ6r7aUoNHSqmSEigsbD72pS8lV/J8+cuw776piUuSJEmSpM7CFTzqtN57Dy69FA48EBYtan4tIwO++12TO5IkSZIkgQkedUL19TBzJhx0EPzqV7BlC3zxi5CiclGSJEmSJHV6btFSpzJvHkybBi++2Hx8n32SRZV79kxNXJIkSZIkdWau4FGnUFYG11wDRUXNkzsHHACPPw4PPWRyR5IkSZKk7XEFj1IqRvj97+Hf/x3Wrm0cz8yEG25IfuXkpC4+SZIkSZK6AhM8Sqlrrkm2OW/qE59Ijo0YkZqYJEmSJEnqatyipZS68EIIIXk8aBD84Q/wl7+Y3JEkSZIkaWe4gkcdKsbGhA7AhAnJDllZWXDjjZCXl7LQJEmSJEnqskzwqEO8/TZcey2cfjpcdlnzaz/9afOkjyRJkiRJ2jlu0dIeVV0N3/kOjBoFjz0G118P69Y1n2NyR5IkSZKk3WOCR+2utBSOPTZZT2fcOPjGN6CqKnltwwb4v/9LbXySJEmSJO1t3KKldnfDDfDMM8mvpsaPhzvugIkTUxOXJEmSJEl7qzat4AkhnBJCeCOEsDSEcEMr178SQlgUQlgQQngqhLB/+4eqzi4nJ7nd6p57Wl77yU/gpZdM7kiSJEmStCfsMMETQkgDZgCnAqOA80MIo7aZNg8oijGOAx4Evt/egapzW74cRo9uOT50KMyfD1dfDemuF5MkSZIkaY9oywqeI4GlMcZlMcYtwH3AmU0nxBj/EWP8YOvpHKCwfcNUZ9erF6xa1XgeQvLr1FPhkENSF5ckSZIkSd1BWxI8+wErm5yXbB3bnkuBVsvohhCmhhCKQwjF67ZtpaQurVevxnbnRUUwZw5MmwZr1qQ6MkmSJEmS9n5t2TTTWhPr2OrEEC4EioBjW7seY5wJzAQoKipq9Rnq/DZuhD/+ES66qPn4pz4Fy5Ylt2UBHHlkh4cmSZIkSVK31JYVPCXA4CbnhcDqbSeFEE4C/h9wRoyxun3CU2cSIzz4IIwcCRdfDE8+2fx6CI3JHUmSJEmS1HHakuB5CRgRQhgWQsgEpgCPNp0QQjgU+DnJ5M677R+mUm3lSjjrLDj33MZtV5dfDtWm8iRJkiRJSrkdJnhijLXAVcBfgcXAH2KMr4cQbg4hnLF12g+AnsADIYT5IYRHt/M4dTF1dXD77TBqFDza5E914ED4wQ8gMzN1sUmSJEmSpKQ2Na6OMf4Z+PM2Y99scnxSO8elTmDhQrjssmTB5KYuvxy++91kYWVJkiRJkpR6bUrwqHupqoJvfxu+9z2orW0cP/hgmDkTPv7x1MUmSZIkSZJaMsGjFr70Jfj5zxvPMzLga1+Dr38dsrJSF5ckSZIkSWpdW4osq5u54Qbo0SN5PGkSzJ8PN91kckeSJEmSpM7KFTzdXIxQXw9paY1jQ4fCj36UvHb55ZAwDShJkiRJUqdmgqcbW7kSrrwSDj00uUKnqSuuSE1MkiRJkiRp57k2oxtq2vr8scfgv/4LXn891VFJkiRJkqRdZYKnm1m4ECZPhquvhoqK5FhNDTzxRGrjkiRJkiRJu84tWt3ER7U+v+uuZNJHkiRJkqQ9oaamhpKSEqqqqlIdSpeRnZ1NYWEhGRkZbZpvgqcbePppmDoV3nyzcSwjI9n2/GtfszuWJEmSJGnPKikpIS8vj6FDhxJCSHU4nV6MkfXr11NSUsKwYcPadI9btPZiFRVw2WVw3HHNkzsftj6/8UaTO5IkSZKkPa+qqoo+ffqY3GmjEAJ9+vTZqRVPJnj2YllZMHdu43l+PvzsZ/Dss8kCy5IkSZIkdRSTOztnZ39eJnj2YhkZyfo6IcDZZ8OiRTBtGiT8U5ckSZIkdTMhBD73uc81nNfW1tKvXz9OO+00AO6++26uuuqqFvcNHTqUsWPHMn78eMaPH88111zTYTHvDGvw7CVKSuATn4CnnoKBAxvHjzwSXn0Vxo5NXWySJEmSJO2s0lKYMgXuvx8GDNj95+Xm5rJw4UIqKyvJycnhiSeeYL/99mvTvf/4xz/o27fv7gexB7VpLUcI4ZQQwhshhKUhhBtauX5MCOGVEEJtCOHT7R+mPsqiRXD44bB4MVxwQcvrJnckSZIkSV3Nt74Fs2fDzTe33zNPPfVUHn/8cQDuvfdezj///HZ57sUXX8y0adM4/vjjOeCAA3j66ae55JJLGDlyJBdffHHDvJ49ezYcP/jgg82u7a4dJnhCCGnADOBUYBRwfghh2wou7wAXA79vt8i0Q1u2JLdhjR4N776bHJs1K7klKycnpaFJkiRJkrRdN96Y/N31o77uuAPq65Pft/09d+rU5nNvvLFtrztlyhTuu+8+qqqqWLBgARMmTGjTfccff3zDFq3bbrut1TkbNmzg73//O7fddhunn346X/7yl3n99dd57bXXmD9/ftsC3A1t2aJ1JLA0xrgMIIRwH3AmsOjDCTHG5Vuv1e+BGNWK4mK49FKorW0+np4On/40bOfzJkmSJElSl5KWltyq9cMf7v6zxo0bx/Lly7n33nv55Cc/2eb72rJF6/TTTyeEwNixY9l3330Zu3U7zejRo1m+fDnjx4/frdh3pC1btPYDVjY5L9k6phSorITrroMJE2DBgubXsrKS2c3evdtnf6IkSZIkSalWV5fsCt1ev+eeccYZTJ8+vd22Z30oKysLgEQi0XD84Xnt1tUZTTtj7UwL9LZoS4Kntb5ccVdeLIQwNYRQHEIoXrdu3a48olt7+mkYNw5+8INkIgeSS9TGjoUrroAXX0x+X7MmtXFKkiRJkvRRbrwRYtz+19lnwxe/CPPnJ79v+3vuzJnN57d1ixbAJZdcwje/+c2GFTYdad9992Xx4sXU19fz8MMPt+uz27JFqwQY3OS8EFi9Ky8WY5wJzAQoKirapSRRd/U//wMXXth87IQTkm3QDzigcWzGjI6NS5IkSZKk9vbQQ43H7f17bmFhIddee22r1+6++24eeeSRhvM5c+YAyRo8aWlpQHKb1z333LNLr/3d736X0047jcGDBzNmzBgqKip26TmtCTF+dJ4lhJAOvAmcCKwCXgIuiDG+3srcu4E/xRgf3NELFxUVxeLi4l2JuVvauBFGjUq2icvPhx/9KFmDJ7S2vkqSJEmSpE5k8eLFjBw5MtVhdDmt/dxCCC/HGIu2nbvDLVoxxlrgKuCvwGLgDzHG10MIN4cQztj68CNCCCXAucDPQwgtkj/aPb16JSuHn3FGsi36F75gckeSJEmSJCW1ZYsWMcY/A3/eZuybTY5fIrl1S7spRrj/fnj55WStnabOPDOZ4DGxI0mSJEmSmmpTgkcdY9UqmDYNHnsseX7yyfCJTzSfY3JHkiRJkiRtqy1dtLSHxZgsljxqVGNyB+Bb30pdTJIkSZIkqeswwZNib70FJ54IU6dCeXnj+LRp8PjjqYtLkiRJkiR1HSZ4UqSuDm69FcaOhX/8o3F8xAiYNQt+9rNktyxJkiRJkqQdsQZPCixcmGxxPndu41giAdOnw403Qk5OykKTJEmSJGmvs379ek488UQA1qxZQ1paGv369QNg7ty5ZGZmpjK8dmGCJwW+9rXmyZ1x4+CXv4SiFl3sJUmSJEnS7urTpw/z588H4MYbb6Rnz55Mnz692ZwYIzFGEomuudmpa0bdxf30p5CbC5mZyULKxcUmdyRJkiRJ6mhLly5lzJgxXHHFFRx22GGsXLmSXr16NVy/7777+MIXvgDA2rVrOeeccygqKuLII49kzpw5LZ73i1/8gnPOOYfTTjuNYcOGcccdd/CDH/yAQw89lEmTJrFx40YAJk+e3JBwWrNmDcOHD9/t9+IKnj3sgw8gLQ2yshrHhg6Fe+6Bgw9Ods6SJEmSJKm7+NKXYGtuo92MHw///d+7du+iRYv49a9/zZ133kltbe12511zzTVcd911TJw4keXLl3PaaaexcOHCFvNef/11XnnlFSoqKhgxYgS33nor8+bN4+qrr+Z3v/sdV1111a4FugMmePagWbPgC1+Az34Wbrqp+bVzzklJSJIkSZIkqYkDDzyQI444YofznnzySd54442G8w0bNlBZWUnONoV0TzjhBHJzc8nNzaVnz56cfvrpAIwdO5Y333yzfYNvwgTPHlBWBtddBzNnJs9vuQU+9alkrR1JkiRJkrqzXV1ps6fk5uY2HCcSCWKMDedVVVUNxzHGNhVkzmqyhSeRSDScJxKJhhVC6enp1NfXt3iN3WENnnb2pz/B6NGNyR1I1ttZsSJ1MUmSJEmSpB1LJBL07t2bJUuWUF9fz8MPP9xw7aSTTmLGjBkN5/N3Y5/Z0KFDefnllwF48MEHdz3gJkzwtJN16+CCC+D002HVqsbxs86CRYuS45IkSZIkqXP73ve+xymnnMKJJ55IYWFhw/iMGTN47rnnGDduHKNGjeKuu+7a5df46le/yo9//GMmTZrEhg0b2iNsQtOlRx2pqKgoFhcXp+S129Pq1XDiifDuu/D++43j/fvD7bfDpz8NIaQuPkmSJEmSUm3x4sWMHDky1WF0Oa393EIIL8cYW/TitgbPbnj/fZg0qeX2q899Dm67Dfr0SU1ckiRJkiSpe2nTFq0QwikhhDdCCEtDCDe0cj0rhHD/1usvhhCGtnegnU1OTjKBs21yJyMj2QLd5I4kSZIkSeooO0zwhBDSgBnAqcAo4PwQwqhtpl0KbIgxDgduA77X3oF2NsuWJWvufFgcOz0dzj0X3nkntXFJkiRJkqTupy0reI4ElsYYl8UYtwD3AWduM+dM4Ddbjx8ETgxh7648M3Ag5OdDTU0yyVNfD337woABqY5MkiRJkqTOJ1U1gLuqnf15tSXBsx+wssl5ydaxVufEGGuBMqDFJqUQwtQQQnEIoXjdunU7FWhntHYtXHEFvPhi8vuaNamOSJIkSZKkzic7O5v169eb5GmjGCPr168nOzu7zfe0pchyaytxtv0TacscYowzgZmQ7KLVhtfu1B56qPF4xozUxSFJkiRJUmdWWFhISUkJe8Nij46SnZ3drE37jrQlwVMCDG5yXgis3s6ckhBCOlAAvI8kSZIkSer2MjIyGDZsWKrD2Ku1ZYvWS8CIEMKwEEImMAV4dJs5jwIXbT3+NPD36LorSZIkSZKkDrHDFTwxxtoQwlXAX4E04FcxxtdDCDcDxTHGR4FfAr8NISwluXJnyp4MWpIkSZIkSY3askWLGOOfgT9vM/bNJsdVwLntG5okSZIkSZLaIqRqJ1UIYR2wIiUvvvv6Au+lOghpJ/m5VVfjZ1ZdkZ9bdTV+ZtUV+blVV9Sen9v9Y4z9th1MWYKnKwshFMcYi1Idh7Qz/Nyqq/Ezq67Iz626Gj+z6or83Kor6ojPbVuKLEuSJEmSJKkTM8EjSZIkSZLUxZng2TUzUx2AtAv83Kqr8TOrrsjPrboaP7Pqivzcqiva459ba/BIkiRJkiR1ca7gkSRJkiRJ6uJM8EiSJEmSJHVxJngkSZIkSZK6OBM8kiRJkiRJXZwJHkmSJEmSpC7OBI8kSZIkSVIXZ4JHkiRJkiSpizPBI0mSJEmS1MWlp+qF+/btG4cOHZqql5ckSZIkSepyXn755fdijP22HU9Zgmfo0KEUFxen6uUlSZIkSZK6nBDCitbG3aIlSZIkSZLUxe0wwRNCyA4hzA0hvBpCeD2EcFMrc7JCCPeHEJaGEF4MIQzdE8FKkiRJkiSppbas4KkGTogxHgKMB04JIUzcZs6lwIYY43DgNuB77Rtm51VdWs28Y+dRvaY61aFIkiRJkqRuaoc1eGKMEajYepqx9StuM+1M4Matxw8Ct4cQwtZ792rLb1pO2ewylt+8nIN+dlCqw5EkSZIkaY+pqamhpKSEqqqqVIey18vOzqawsJCMjIw2zW9TkeUQQhrwMjAcmBFjfHGbKfsBKwFijLUhhDKgD/BeWwPvap7JeYb6qvqG89I7Sim9o5SQEThq5VFk7puZwugkSZIkSWp/JSUl5OXlMXToUEIIqQ5nrxVjZP369ZSUlDBs2LA23dOmIssxxroY43igEDgyhDBmmymt/am2WL0TQpgaQigOIRSvW7euTQF2VhOWTaD/Bf0J6c3feqyJPD/geeYMm8Oi8xdR8uMSyl8sp766fjtPkiRJkiSpa6iqqqJPnz4md/awEAJ9+vTZqZVSO9UmPca4MYQwCzgFWNjkUgkwGCgJIaQDBcD7rdw/E5gJUFRU1KW3b2UNzCItP41Y2/rbqFpeRdXyKt69710AQmZgyHVDGPattmXeJEmSJEnqjEzudIyd/Tm3pYtWvxBCr63HOcBJwD+3mfYocNHW408Df+8O9Xdq1tYw6IuDGPvXsfT+l97kDM+hYHIBieyWP9a4JZLRr+W+uZU/WsmK765gwz82UFtR2xFhS5IkSZKkvUxbVvAMBH6ztQ5PAvhDjPFPIYSbgeIY46PAL4HfhhCWkly5M2WPRdyJjHmocadan0/0aTiur6ln84LNlM8pT369WE7lkkryJ+a3eEbJT0uoXrG1A1cCcsfkkj8xv+Grx0E9CAmzo5IkSZKkrqm6tJpFUxYx6v5RZA3I2u3nhRC48MIL+e1vfwtAbW0tAwcOZMKECfzpT3/i7rvvpri4mNtvv73ZfUOHDiUvL4+0tDQAjjnmGH7yk5/s8PWKi4u555572jQ3ldrSRWsBcGgr499sclwFnNu+oXVdiYwEeYfnkXd4HvtduR8AW97bQnqv5j/u6tLqxuQOQD1sXrCZzQs2UzqzFIC0gjTyJ+STPyGfwmumaw0jAAAgAElEQVQLyejTturZkiRJkiR1Bsu/1b7dp3Nzc1m4cCGVlZXk5OTwxBNPsN9++7Xp3n/84x/07dt3p16vqKiIoqKiXQm1Q7WpyLJ2X2bfTBLpzX/caT3SOOhXBzFw6kByx+W2+qdRV1bHhr9tYMW3V7Qo6FxXWcemlzdRX1NPdWk1846dR/Wa6pYPkSRJkiRpD3j7xreZFWZ95FfpHaVQn+w+PSvM4pmcZxruf2PqG83mvn3j22163VNPPZXHH38cgHvvvZfzzz+/Xd7PAw88wJgxYzjkkEM45phjAJg1axannXYaAOvWrePkk0/msMMO4/LLL2f//ffnvffeY/ny5Rx88MF84QtfYMyYMXz2s5/lySef5Oijj2bEiBHMnTsXgLlz5zJp0iQOPfRQJk2axBtvvNEucYMJnpRKL0hn4OcHctDPD+KIV49g8sbJHPL3Qxh2yzD6nNGHjP6Nq3V6jOxBekHzFUDlc8p5uehlZufP5uXDXqbsmTL+edE/qV5lkkeSJEmS1MmkQf/P9mfC2xN2+1FTpkzhvvvuo6qqigULFjBhQtueefzxxzN+/HjGjx/Pbbfd1uL6zTffzF//+ldeffVVHn300RbXb7rpJk444QReeeUVzj77bN55552Ga0uXLuXaa69lwYIF/POf/+T3v/89s2fP5oc//CG33HILAAcffDDPPPMM8+bN4+abb+brX//6Lv4EWtqpLlras9Lz0ul9fG96H98bSPa9r1peRfmL5a00nU8meADqq+rZsmYLABv+toEXCl8AoN+5/Rpq+fQ8rCdp2Wkd80YkSZIkSdpWHaTlp7VLHZ5x48axfPly7r33Xj75yU+2+b4dbdE6+uijufjiiznvvPM455xzWlyfPXs2Dz/8MACnnHIKvXv3brg2bNgwxo4dC8Do0aM58cQTCSEwduxYli9fDkBZWRkXXXQRS5YsIYRATU1Nm2PfERM8nVgIgZxhOeQMy2n9ekYgc79Mtqza0ur1dQ+sY90D64Bksmf0H0bvsVglSZIkSd3PsBuHMezGYdu9vvCchWQOzGTQ1EGsnrmaLaXNf389aOZBHDRz1+rynHHGGUyfPp1Zs2axfv36XXrGtu68805efPFFHn/8ccaPH8/8+fObXf+ohuFZWY2Jq0Qi0XCeSCSorU12zf6P//gPjj/+eB5++GGWL1/Occcd1y5xgwmeLm3I9CEMmT6Exf+2mLW/W5vccFcHpG393kT+hJYdvJZ+eSmVbye7exUcVUBeUR5pua7ykSRJkiS1j6bdpz8242Pt+uxLLrmEgoICxo4dy6xZs9rlmW+99RYTJkxgwoQJPPbYY6xcubLZ9cmTJ/OHP/yB66+/nr/97W9s2LBhp55fVlbWUBD67rvvbpeYP2SCZy9QV1HHoGmDGjKi1aurGfqfQxvbtM8pb7VF+/o/radyaSXr/7g105kGPcf2JP+oxjbtOSNyCME27ZIkSZKkzqWwsJBrr7221Wt33303jzzySMP5nDlzgGQNng/bpI8bN4577rmn2X1f/epXWbJkCTFGTjzxRA455BCefvrphuv/+Z//yfnnn8/999/Psccey8CBA8nLy6OioqJNMV933XVcdNFF3HrrrZxwwgk79X53JHzU8qI9qaioKBYXF6fktQVb1m3h+f7P73Be+j7p5E/IZ/hPhtNjeI8OiEySJEmS1FktXryYkSNHpjqMlKmuriYtLY309HReeOEFpk2b1mIbV3tq7ecdQng5xtiib7sreLqpjD4ZHPH6EZS/0LjKZ/Prm1sUc659v5b3/+990ns1/6jUVdax9ndryT8qn9yRuYQ0V/lIkiRJkvZu77zzDueddx719fVkZmZy1113pTqkBiZ4uqmQCOSOyiV3VC4DLx0IQG15LeVzy5tt7apdX0vOiBwy+2Y2u3/Ty5t4c+qbAKTlpZF3ZF5DLZ+s/bNYcuUSRt0/ql2qo0uSJEmS1BmMGDGCefPmpTqMVpngUYP0/HT2OWkf9jlpHyBZHbxyaSVb1rbs0vVhi3aAuk11bHxqIxuf2thszvxj51P4pUJ6HdOL3NG5ezZ4SZIkSZK6sUSqA1DnFUKgx4ge9Jrcq8W1HiN60PesvmTsm7Hd+yvfrGTJF5fw0riXWlyLdamp/SRJkiRJ0t7IFTzaJX3P7EvfM/sSY6T6nWrK55Sz4akNrHtoHbXra5vNHXz94Bb3v3H5G5Q9XZbs2LX1K3dMLol0c46SJEmSJO0sEzzaLSEEsvfPJnv/bPp/pj+kQenMUkJ6INZEsodl0/eMvi3uK3++nMqllVQurWTtb9cCkMhNkH9EY8Inf2I+mf0yW9wrSZIkSZKaM8GjdlWztoZBVwxi0NRBrJ65mi2lWyiYWNBsTt3mOqrermpxb/3mejbO2sjGWY21fHKG5zDqvlHkHZ63x2OXJEmSJHVu69ev58QTTwRgzZo1pKWl0a9fPwDmzp1LZuaeWyRQV1fHcccdx7PPPrvHXmN3mOBRuxrz0JiG44/N+Firc9Jy05i8cTKbXtmUbNP+QjllL5SxZVXLYs6VSyvJ3K/5X9D6LfUsv2k5+RNd5SNJkiRJ3UmfPn2YP38+ADfeeCM9e/Zk+vTpzebEGIkxkki0bwmQtLS0TpvcARM8SpFEVoKCowooOKpxdU9VSVVDwqf8hXI2vbKJrEFZLVqtV8yr4J1b3mk4zxmes91aPtWl1SyassiW7ZIkSZLUzpZ8aQkV8yva9Zk9x/dkxH+P2On7li5dyllnncXkyZN58cUXeeSRRzjkkEPYuDG5Q+S+++7jySef5Be/+AVr165l2rRpvPPOOyQSCX7yk58wceLEZs977bXXuOSSS6ipqaG+vp5HHnmEIUOG0LdvXzZu3EhdXR1XXnklzz77LAcccAA1NTVcccUVnHXWWRQWFnLRRRfx1FNPUVdXx89//nNuuOEG3nrrLW644QYuu+wyysvLOeuss9i4cSO1tbXccsstnHbaabv1szPBo04juzCb7HOz6X9ufwDqq+upWtlyK1fZC2XNzj+qlk/FaxWUzS5j+c3LOehnB+35NyFJkiRJSolFixbx61//mjvvvJPa2trtzrvmmmu47rrrmDhxIsuXL+e0005j4cKFzeb87Gc/Y/r06XzmM5+hurqaGJt3gn7ggQdYtWoVr732GmvWrGHkyJFcccUVDdeHDh3KnDlzuPrqq7n00kuZPXs2FRUVHHLIIVx22WXk5OTwxz/+kby8PN59912OPvpoEzzaeyWyEvQY3qPFeP6EfAq/XNiwyiduaf4XrbVaPqV3lFJ6RymJ7AST1k4iLTeNkBb2+HuQJEmSpL3Vrqy02ZMOPPBAjjjiiB3Oe/LJJ3njjTcazjds2EBlZSU5OTkNY5MmTeLb3/42K1as4JxzzmH48OHNkkazZ8/mvPPOI5FIMGjQII499thmr3HGGWcAMHbsWGpra8nNzSU3N5dEIkFFRQWZmZlcf/31zJ49m0QiwcqVK3nvvffo27dlk6K2MsGjLqfp1q766vqPrOUTMpLdvBI9EvQ9uy8H/vBA3rruLd69991kDZ+j8imYVED+hHzSC/zrIEmSJEldVW5ubsNxIpFotuqmqqpxd0iMcYcFmT/3uc9x1FFH8fjjj3PyySfzm9/8hkmTJjV7xkfJyspqiOPD4w/Pa2true+++ygrK+OVV14hPT2dwsLCZjHuivatOCR1sA9r+Qz+ymBGPzCaSSWTmLhyIqP+MIrcsbnE2kgiO0F9VT1p+WlkDcii/IVy6srr2PC3Day4aQUL/mUBs3vP5qWxL/HG5W+w5jdr+ODND3b4F1aSJEmS1DklEgl69+7NkiVLqK+v5+GHH264dtJJJzFjxoyG8w+LNje1bNkyhg8fzrXXXsu//uu/smDBgmbXJ0+ezIMPPkiMkdLSUp555pmdiq+srIz+/fuTnp7OE088wapVq3byHbZkgkd7nezCZB2fnOE5DJo2iMPmHMagKwZRs6aG+i311KyvaXlThM0LN1M6s5R/XvxP5h40l+f7P8/GZza2nCtJkiRJ6vS+973vccopp3DiiSdSWFjYMD5jxgyee+45xo0bx6hRo7jrrrta3Pv73/+e0aNHM378eJYtW8aFF17Y7Pp5551H//79GTNmDFdeeSUTJkygoKCgxXO253Of+xzPP/88RUVFPPDAA4wYsfvb3UKqVikUFRXF4uLilLy2urcYI1XLkx27yp4vo/z5cioWVEBdy7kT35lI9uDshvP62nremv4W+ROSW7uyhmQRgrV8JEmSJHUPixcvZuTIkakOo1OoqKigZ8+erFu3jgkTJvDiiy/Sr1+/dn2N1n7eIYSXY4xF28616Ii6nRACOcNyyBmWw74X7AtAbUUtm17aRPnzyTo+5S+Uk9YjrVlyB2Dzgs2s+vEqVpFcPpc5MJP8SVvr+ByVT95heSSyXBgnSZIkSXu7U089lfLycmpqarjpppvaPbmzs0zwSEB6z3R6H9+b3sf3BiDWR7as3dJiXvkL5c3Ot5Ru4b3/fY/3/vc9AEJmIK8oj/yj8ul9fG/6/GsfAKpLq1k0ZRGj7h9F1oCsFs+VJEmSJHUtzz77bKpDaMalBlIrQiKQNbBlIqZgcgH7f3N/ep/Um7SeaS2uxy2R8ufLKflRCStvXdkwvvxbyymbXcbb33ib+tr6PRq7JEmSJO1JNqTpGDv7c3YFj7QTeh7Sk56H9AQg1kU2v765oY5P+QvlVC6tbJhbMKmAZ3Keob6qMaGz5pdrWPPLNZCA/b+xf3Jr10RbtEuSJEnqGrKzs1m/fj19+vSxHukeFGNk/fr1ZGdn73jyVhZZltrRlne3UD4nWby571l9yd4/m7emv8V7j7xH/Qf1EIBt/8oFyB2Tm6zlc3QBBZMKyD4g238sJUmSJHU6NTU1lJSUUFVVlepQ9nrZ2dkUFhaSkZHRbNwiy1IHyOyfSd8z+tL3jL4NY2n5adRX1ZPITjRbzdMgwubXNrP5tc2U/rwUgIx9Mxh176iGmkCSJEmS1BlkZGQwbNiwVIehVpjgkfawmrU1DLpiEIOmDmL1zNVULqtkwEUDkh27niuj4tWWLdpr1taQPaT5UrxYH3n7P94m/8h88o/KJ7N/Zge+C0mSJElSZ7bDBE8IYTBwDzAAqAdmxhh/vM2c44A/Am9vHXooxnhz+4YqdU1jHhrTcPyxGR9rON53SpMW7XM3JWv5PJds057ITpB9wDYt2hdt5p1b3mk4zxmR09CiveDoAnqM7EFIuK1LkiRJkrqjtqzgqQX+Pcb4SgghD3g5hPBEjHHRNvOejTGe1v4hSnu39J7p9D6hN71PaGzRXr2qukUNnvLnm7dor1xSSeWSStb+Zm3yOb3SyT8qn/xJ+fQ6phe9junVMW9AkiRJkpRyO2yTHmMsjTG+svV4E7AY2G9PByZ1VyERyB7cslJ63uF5DP7qYPKPzidktlypU7uxlvf/732W/8dy3v7G2y2u19ck6/9Ul1Yz79h5VK+pbv/gJUmSJEkpsVM1eEIIQ4FDgRdbuXxUCOFVYDUwPcb4eiv3TwWmAgwZMmRnY5W6tbzD88g7PA+A+up6Nr2yibLnyhpq+dS8W9MwN39Sfov7l31tGev+sI6QGahaVsWSq5cw6t5RJNJ3mOeVJEmSJHVybW6THkLoCTwNfCfG+NA21/KB+hhjRQjhk8CPY4wjPup5tkmX2k+MkaplVZQ9V0bZ82Xse/6+9Dq2+RatWYlZLVu0AyRg///Yn4KjC8ifmE96nrXXJUmSJKmz2l6b9DYleEIIGcCfgL/GGG9tw/zlQFGM8b3tzTHBI3Wc+tp6nuv7HHVldR89MQE9x/VkxM9GUHBUQccEJ0mSJElqs+0leHa4NyMkK73+Eli8veROCGHA1nmEEI7c+tz1uxeypPaSSE9w9HtH0/dTfSGw/b/59VAxv4L03s1X8cQYWf3z1Wyav4lY17ZVf5IkSZKkjtOWvRhHA58DXgshzN869nVgCECM8U7g08C0EEItUAlMiW3d+yWpQyTSE1APg6YNYtDUQayeuZrKtyoZcNGAZC2f58qpWJBM7vQ4qEezeyvfrOTNK94EIC0vjfyJ+RQcXUDB5ALyJuSR3tNtXZIkSZKUSm2uwdPe3KIldT615bVUvlVJ3qF5zcZLf1XKG5e+0fpNadDzkJ7JhM/RBeQfnU92YcsuYJIkSZKk3bfLW7QkdR/p+ektkjsAWUOy6HdePzIHZba8qQ4qXqlg1U9XsWjKIl7/dIsGepIkSZKkPcx9FZJ2aJ+T9mGfk/ZJdutaUUX5c+WUzS6j7LkyNi/c3Kw7V8HRLYszr7hlBRuf2diwrSv/yHzSctOoLq1m0ZRFjLp/FFkDsjrwHUmSJEnS3sUEj6Q2CyGQMzSHnKE57PvZfQGo2VhD+QvlDXV8eh3fq8V97//lfcqeLWPDXzckB9Ig79A86qvr2bxwM8tuWMbIu0d25FuRJEmSpL2KNXgk7VH1W+qZXTCb+qr6HU9OgyNeO4Lckbl7PjBJkiRJ6oKswSMpJUJG4IiFR3Dwbw5m4NSB9BjdY/uT6yDWNk86xxgpf6mc+i1tSBBJkiRJUjflFi1Je1QIgZwDc8g5MIcB/zYAgJr3a1h84WLe/8v7EICtuZu0gjRyRzdfvVO1oopXjnyFRE6C/An5FEzeWsdnYj7pBf4TJkmSJElggkdSCmTsk0EiO8GgaYMYNHUQq+5YxQf//ID9rtyPkAjN5pbNLgOgvrKejbM2snHWxuSFALnjchsSPgWTC2zPLkmSJKnbMsEjKSXGPDSm4figOw/a7rxYG8k+IJuqZVXbXIDNr25m86ubWT1jNQD7/Os+jPvTuD0SryRJkiR1ZiZ4JHVqAy8eyMCLB1K9upqy58qS7dlnl1Exv6Jha9eHcg7IaXH/2nvXUrWiioLJBeQV5ZGWndZBkUuSJElSxzHBI6lLyBqURf9z+9P/3P4A1G6qpXxOeUPCp3xOOQWTC1rcV/rLUjY+ldzWFTIDeUfkNW7rmlRAxj4ZAFSXVrNoyiJG3T+KrAFZHffGJEmSJKkd2CZd0l6hvqYeIiQyE83GZveeTf3m7Xfg6jG6BwWTC6hcUsnGWRsZePlADvrZ9reMSZIkSVIqba9NugkeSXutuqo63r333YZVPpVvVrb53kR2gmMqjyHWxxaFnyVJkiQpVbaX4HGLlqS9Vlp2GgM/P5CBnx8IwJZ3tzSv4/NKBbG2eZI70SNB37P7cuAPD6SqpIriscXkH51sz97r473IK8ojkZVo7eUkSZIkKWVM8EjqNjL7Z9Lv7H70O7sfAHWb6yifW85b171FxcsVJLIS1FfVk5afRtaALNbet5bajbW8//j7vP/4+wCErED+kfkUfLyxjk96gf+USpIkSUotfyuR1G2l5abR+/jeZA/OJv/IfAZNHcTqmavZUroFgIpXKlrcE6sjZc+WUfZsWXIgAT3H9aT/lP4MuX5IR4YvSZIkSQ2swSNJ2xFjpHJpZXJL17Nb6/gsab2Oz8DLB3LQnc2LM1e8WkEiO0HOx3IIwTo+kiRJknafNXgkaSeFEOgxogc9RvRoqONTvaa6oYZP2bNlVMyvgHro9fFeLe5fdsMy3v/L+2T0y0hu5/p48qvn+J4k0q3jI0mSJKn9uIJHknZDbXkt5XPK6XlYTzL7ZjaMx7rI7H1mU1de1+KeRG6CgqMKGpI++RPySctNA6C6tJpFUxYx6v5RZA3I6rD3IUmSJKlr2N4KHv8XsiTthvT8dPb5xD7NkjsAtRtr6XVsL9J7t1woWb+5ng1PbmD5jct59cRXmd1rNhULkvV+ln9rOWWzy1h+8/KOCF+SJEnSXsIVPJK0B8X6yAeLP2DjsxsbtnVVv1PdbE4iO5lrr6+qb3F/yAhMWDqB7CHZHRKvJEmSpM5teyt4TPBIUgereqeqIdmz8dmNZPbPZOT/jOSt6W/x3iPvUf9BPSEzELc0/vucNSSLgo8X0OvjvSj4eAE9RvawcLMkSZLUDVlkWZI6iewh2WRfkM2+F+wLQH1NPYmMBGn5adRX1ZPITrRYzVP9TjXv/s+7vPs/7wKQ3iedgsnJhE/vk3vTc1zPDn8fkiRJkjoPa/BIUoolMpL/FNesrWHQFYM4bM5h9P10X3JG5tD7pN4kclv+U127vpb1f1zPW9PfouS/S1pcT9XqTEmSJEmp4QoeSeokxjw0pvH4gcbj+pp6KuZXUPZs47au2vW1DdcLPl7Q4lmLPrOI6pLqhtbsBUcXkNE7Y8++AUmSJEkpY4JHkjq5REaC/CPyyT8in8FfGZws3PzPDxqSPb2O69VsfqyPbHhqA7Xv11L+Qjkrv78SAuSOzW1WxydrkG3YJUmSpL2FRZYlaS/zwZIPmPuxuTucl31ANgUfL+DA7x1I5r6ZO5wvSZIkKfW2V2TZGjyStJfpMaIHk96dxOiHR1P45ULyivIgreW8qmVVvPv7d0nLb36xtqKWTfM2UVVSxbxj51G9prrlzZIkSZI6FbdoSdJeKLNfJv3O6ke/s/oByaRN+QvlDXV8yueUU19VT94ReaTlNE/wbPzHRhaesRAygBpYeNZChv9oOHlFeSSy/P8CkiRJUmdkgkeSuoH0nunsc/I+7HPyPgDUb6ln08ubiFtabtNdePbC5EFN8tumFzcxb/I8AAqOLaDXMb0oOKaAgqMKSMttZWmQJEmSpA63w/8VG0IYHEL4RwhhcQjh9RDCta3MCSGEn4QQloYQFoQQDtsz4UqS2kMiM0HBUQX0OrZXi2v7XbMfITu0el/Z02Ws+NYKFpy8gGcLnuXtb769p0OVJEmS1AZtWWtfC/x7jHEkMBG4MoQwaps5pwIjtn5NBe5o1yglSR1mxK0jGHDRAAgQMpKJnm3r9ABQB1mFLTtxlf6ylLX3raV6lbV7JEmSpI6ywy1aMcZSoHTr8aYQwmJgP2BRk2lnAvfEZEuuOSGEXiGEgVvvlSR1MTXv1jBo2iAGTR3E6pmr2VK6hREzRiRbsz+zkbJnytj82mYKPl7Q7L4YI29/4222rNkCJDt1NWzp+ngBOQfmEELrq4MkSZIk7bqdapMeQhgKPAOMiTGWNxn/E/DdGOPsredPAdfHGIu3uX8qyRU+DBky5PAVK1bsbvySpBSpeb+G9N7pzRI2O2rRnjkwk4JjCuj18WTSJ3d0LiFhwkeSJElqq91ukx5C6An8L/ClpsmdDy+3ckuLzFGMcWaMsSjGWNSvX7+2vrQkqRPK2CejxWqctB5p7P/N/el1XC8S2S3/E7OldAvr7l/HkquWUHxoMXWb6zoqXEmSJGmv1qYuWiGEDJLJnf+JMT7UypQSYHCT80Jg9e6HJ0nqSrL2y2LYTcMAqK9Odupq2NY1u4y68saETt6heaTnNf/P0IZZG1jx7RUNK3zyJ+ST1iON6tJqFk1ZxKj7R5E1oGXdH0mSJKm722GCJyT/9+wvgcUxxlu3M+1R4KoQwn3ABKDM+juS1L0lshIUTCqgYFIBQ64fQqyLVLxWQdmzZZQ9U0buIbkt7tn41MaGL0gWec4ryqOuso7Nr27m7f/3Ngf/8uCOfiuSJElSp7fDGjwhhMnAs8BrQP3W4a8DQwBijHduTQLdDpwCfAB8ftv6O9sqKiqKxcUfOUWS1M3MO3YeZc+U7XhiGhw6+1AKJhbseK4kSZK0F9leDZ62dNGaTes1dprOicCVux6eJEkw8ncjm3Xq+mDxB61PrINNL21qkeCp2VhDRq+MDohUkiRJ6lzaVINHkqSOkD04m+wLstn3gn0B/n979x4e91XfefzzndFII81NV9uSE8eu49ixncRxnDixEydkC4TQQmkpDWwb7qaQdMtT2m7b5QEKu9uyT4FCISHeEiAsGwJtmrJdKLBAyM25OLaTOHZsx7EcX0a2fNGMbnM/+8dvPNJoJFu2dRv7/XoePTO/M+f85vzk45+k75zzPcp0Z7TjD3boxE9OeB81DJt02riusaytc06brtgk+b3XYjfF1LiuUfWXsTU7AAAAzn8EeAAAM1ZtW638DX51fKxDHes7dOAfDmhgx4Cafr1JoeXlOXxS+1JKH0hLkg5/57AOf+ewJCkwK+AFfNbFFLsppvAVYZmfgA8AAADOL6fNwTNZyMEDAJhIx396XNvesU2FgcIp6/ljfjWua9Syh5fJV1O5lTsAAAAwk511Dh4AAKpB85uadWPPjerb0lfK4ZN4PKFcT66sXj6RV2pfqiK4M7h3UKl9KW9r9nr/VHYdAAAAOGcEeAAA5w1fwKfodVFFr4tKfyq5glP/tn4v4FPcnj3TlanI3yNJh//XYXV+qtPbmv3ayNCyrjUx1cS8H5fpeFrb79iupQ8tVd2cuqm+PAAAAGBMBHgAAOct85nCV4YVvjKsi+6+SM45Db46OGoOnpPbs7usU/KppJJPJaW/leSTwivCit0U08ArA0o8kVDnZzu1+J7FU3w1AAAAwNgI8AAALhhmpoZFDaO+FroypPShtAa2j9iavSD1be5T3+a+UlH83rji98blC/q0bnDdZHYZAAAAGBcCPAAASLr0C5dKX/C2Zk884S3n6nmsR31b+6QReZutztT2zjYt/LuFpbJXP/GqGi5v8LZmX8TW7AAAAJhaBHgAABimtq1Wbe9oU9s72iRJuWROiacS2vtXe9W3xZvF47JO/qi/lIcnfSitA188UDpHYHZxa/abYmpc16jQFSGZj4APAAAAJg8BHgAATqEmWqOW21oU3xBX9Iao5rx/jrq+2aVMPFOqk3g8UdYmezir7h90q/sH3d45GmsUuzGm2Dov4BNdHZ3SawAAAMD5z5xz0/LGq1atcps2bZqW9wYAYCIN7hlU98Pd3rKux3uUT+THrNuwpEHX7bhuCnsHAACA84mZPe+cWzWynBk8AACco/qF9Zr3Z/OkP5Ncvrg1++M9pWQ68AcAAB5kSURBVDw+2cPZUt3YulhF+/1f2q/uf+4u35o9yo9oAAAAjB+/PQIAMIHMbwpfFVb4qmFbs+8eVM9jPUo8nlDLW1sq2pz4fyeUfDKp5JNJ6W9U2pq9FPC5MabattqpvxgAAABUDZZoAQAwjVzB6YnmJ065rEuSGpY2KHZTTHPvnqvw8rDS8bS237FdSx9aWkr2DAAAgPPfWEu0fNPRGQAA4DGfafWu1Vr2z8s094/nKrwyPOpP54HtA4rfFy8Fgjo/16nEEwl1frZTg3sHNV0f2AAAAGBmYAYPAAAzTC7hbc1+ModP73O9clknX9CL/BRShVHbtf5Oa2l79vCVYZmfrdkBAADON2PN4CHAAwDADJcfyCv5bFKpvSk139asPX+6R0cfOarCQEFWa3KZyp/l/qhfsbUxxW7ytmaPrIrIV8fEXQAAgGrHLloAAFQpf4NfTbc0SbcUj6N+FVIF+YI+FdKjB3nyybyO//i4jv/4uCTJF/Sp7XfbdPkDl09x7wEAADAVCPAAAFBlsoez6vjDDnWs79ChDYeUOZTR/L+er8TjidL27Jl4pqxNIVUYdclWz696lOvJKXZjTIGWwBRdAQAAACYaAR4AAKrM8oeXl55f9rXLSs/DV4Y19665cs4p9VqqtDV7z2M9Su1JKXZTrOJcB/7+gI4+clSS1LCsQY03eTl8YutiCl4UnPyLAQAAwIQgBw8AABeA9KG0/CG/amJDn+045/Rk25PKHcuN2iY4P6jYuqE8PvWL6mVG4mYAAIDpxDbpAABcwOo66sqCO5JUGCyo/QPtil4fldVUBm5SnSkdfuCwdn14l55d/KwSjyVGPXc6ntaWm7co3ZWelL4DAADg9FiiBQDABcrf4NfC/7FQkpTvzyv5TLK0pCu5ManC4NB27BYwRa6NlLXP9mS14z/uUPZYVr3P9qrz051afN/iKb0GAAAAeAjwAAAA+UN+Nd3apKZbmyRJhUxBvZt7lXg8ocRjCbmCk7/BX9bmqVlPyWWHlnrHN8QV3xCX/NIVP7xC0TVRBRpJ3AwAADAVyMEDAADOyq67d+nQ1w6NXcGk0BUhxW6MqeX2FrW8tWXqOgcAAHCeGisHDzN4AADAWZn3Z/PU/3K/Eo8mJJM08jMjJ/W/2K/+F/uVS+QqAjy5ZE7+iJ/EzQAAABOAAA8AADgrwUuCCjQF1PGxDnWs79D+L+3XwI4BRW+IKvFEQn1b+qRiGp/YjZVbtO/80E6d+MUJxdZ6O3XFbowpsjIiXy17QAAAAJwplmgBAIBJkevNKfl0UoknEppz5xzVL6wvveac08aOjcp0Zcra+Op9iq6OKnajF/SJXh9VTZTPowAAAE5iiRYAAJhSNZEaNb+xWc1vbK54LdudlctVfshUGCyo59Ee9Tza4xX4pPBVYS393lI1XNYw2V0GAACoWqedA21m95vZETPbNsbrt5hZwsy2Fr8+NfHdBAAA55PaWbVac2SNrt1xrS7bcJlm3zlbwQXByooFqe+FPtW215YV5/pyin8jroFdAxo+GzkdT2vLzVuU7kpP9iUAAADMKOOZwfMtSV+V9MAp6jzunPuNCekRAAC4IJiZQktCCi0JqePDHZKk9MG0Ek8kSl99L/QpfHVYNZHyX1mSG5Pa+aGdkqTArIC3pOvGmBJPeu06P9upxfcsnvJrAgAAmC6nDfA45x4zs/mT3xUAAHChq5tbp1m/N0uzfm+WJCmXyCkdr5yNk3g8UXqePZLV0YeP6ujDR0tl8Xvjit8blwVMaw6vUaApMPmdBwAAmEYTtU3FDWb2gpn92MyWjVXJzNab2SYz29Td3T1Bbw0AAM5XNbEahZaEKspDy0Nq+c0W1TSd+rMql3Xa9dFdk9U9AACAGWMikixvlnSJc67PzG6X9IikRaNVdM5tkLRB8nbRmoD3BgAAF6BZ75qlWe+aJVdwGtgxoJ7He7T/i/uV2p2qqBtbW7lF+667dyl9IK3Ymphia2MKXxOWP+ifiq4DAABMinMO8DjnksOe/8jM7jGzVufc0VO1AwAAOFfmM4WWhRRaFtKJn55Q8xub1fpbrdr/d/s1uGdQgSYvP89Ix/7PMaVfT+vYvx7zzlNrilwTUXRNVLG1McXWxFQ7u7aiHQAAwEx1zgEeM5sj6bBzzpnZdfKWfR07554BAACcgeUPLy89H21r9pNSB1JKv16e18dlnJIbk0puTOrAFw5IkoILg4qtiWnBf1+g4EWj7PAFAAAwg5w2wGNmD0q6RVKrmR2Q9GlJAUlyzn1d0jslfdTMcpIGJd3hhu9XCgAAMIPUddTp2pevVeKphJJPJpV4KqHBXYMV9VJ7Ukq9ltKlX7m0rDw/kFdyY1KR1RHVhCditTsAAMC5s+mKxaxatcpt2rRpWt4bAABguEx3RsmNSSWeTCj5VFLJ55JyaafQ8pCufenasronfnlCL9z6guSXwleFFVsTU3RtVLE1MQXneTN90vG0tt+xXUsfWqq6OXXTcUkAAOA8ZWbPO+dWjSznYycAAHDBq22rVevbWtX6tlZJUiFdUO+WXuV78xV1E08Wt2jPS32b+9S3uU8Hv3pQklR3UZ2ia6JKH0wr+VRSnZ/p1OKvL56y6wAAABcuAjwAAAAj+Op8il1fmZxZkgJNAYWuCKl/W780YiJ0+kBa3d/vLh3H74srfl9cvqBP6wbXTWaXAQDABY4ADwAAwBmYe9dczb1rrrI9WfU+06vEkwkvn8/TSRX6C2V1LWBqe1ebFv7dwlLZ7j/erdS+lKLXRxVdHVVkVUQ1EX4lAwAA54bfJgAAAM5CoDGg5jc3q/nN3o5dhVxB/S/1a/cf7VbyyaQkyeWc/FF/WR6eY/92TKnXUqUt2uWTQktDiqyOlII+oaUhmd+m/JoAAED1IsADAAAwAXw1PkWujqh2Vq06PtahjvUdOnTfIWW6MqU6me6MUq+lyhsWpP5t/erf1q+ub3RJkvxhvyKrIrpsw2VqWNQwlZcBAACqFLtoAQAATBFXcBrYMaDkM0nv6+mkl8unMHr9tcfWKtAcKB3n+/M69PVDil4fVXhlWP56/xT1HAAAzBTsogUAADDNzGcKLQsptCyk9g+0S5JyfTn1Pd+n5NNDQZ9MPKP6RfVlwR1J6n2+V3v+dI93rhpT6MpQaVlXdHVU9YvqZT6WdgEAcCEiwAMAADCNasI1ary5UY03N0qSnHNKH0grE89U1E0+kyw9dzlX2qb90D2HvHM11ShyXUTR1VE1vqFRTbc0KR1Pa/sd27X0oaVluYAAAMD5xTfdHQAAAMAQM1Pw4qCi10UrXgtfGdbs985Ww5LR8/LkTuR04icntO+z+3TwywclSZ2f61TiiYQ6P9up9MG0concpPYfAABMD3LwAAAAVKHsiax6n+sty+eTOzYUvLEak8uN/ntecGFQkZURRa6JKLwyrPDVYdW21k5V1wEAwDkYKwcPAR4AAIDzgHNOqddSpYBPy+0t6nqgS0cfOarCQEG+Bp+sxpRP5kdtXzevTpGVXsAnsjKi6NqoAo2BUesCAIDpQ5JlAACA85iZqX5hveoX1mv2e2ZLkrof6VYhVZAv6FMhVVBNc40sYHLZyg/40q+nlX49raOPHJUkXfHjK9RyW0t5nXhatXNqZUYiZwAAZhoCPAAAAOep7OGsOv6wQx3rO3RowyFl4hktfXCp+rf1q3dzr/o293mPL/TJpcuDPpGrI2XH+YG8Nl600UvkPGymT+SaiIK/FiToAwDANGOJFgAAwAWukC1oYMdAKeiT2pfSFf96RVmdxNMJbblhy6jt/TG/IlcPBX3CK8NqWNJA0AcAgEnAEi0AAACMyhfwKXxlWOErw9L7Rq+TiWfkj/pHzeGTT+TV82iPeh7tkSTVttdqzaE15XUG88oczeiV33+FLdsBAJgEBHgAAABwWm3vaFPr21uV2psqW97V+3xv2e5dkhS5JlLRvuvbXdp9924pL21dt1VzPjBHoaUhhZaFFJwflPmZ7QMAwLkgwAMAAIBxMd9QIudZvztLkrd7V3p/uizo03hrY1m7x+ofUyFVKB0P7h7U3r/cWzr2BX1quLxBDUsbFFoWUtMbmxRdFZ2aiwIA4DxBgAcAAABnzcwUnBdUcF5Qbb/VNmqd1a+t1vOrnlfmUGbU1wupgvq29KlvS58kyeVdRYCn+5FuSVJoWUj1v1bPjB8AAEYgwAMAAIBJVddep5a3tSi+IS6r8bZpDy0LKTA7oIGXB5TpKg/8hJaGKs7R+ZlO9b/QL0myOlPDkobSEq+TM3/qFxL4AQBcuAjwAAAAYNKNtmX78oeXe68dz6p/e78GXh5Q//b+ihw+Lu808MrA0HHaqf+F/lLA5ySrMzUsbtDl37ncSxg9hnQ8re13bCfZMwDgvMI26QAAAJjRcr057f3kXg1sH1D/y/3KxEdf6nXS9fuvV/CiYOk4P5DX5jWbFbo8pIZlDUo8kdCJn55Q+4fbtfi+xZPdfQAAJhTbpAMAAKAq1URqtOjLi0rH2RPZUrCnNPOnGPjxR/2qm1s+K2fglYFRZ/zEN8QV3xCXTJr1nlmqX1Cv+kX1mnPnnCm5LgAAJhIBHgAAAFSVQFNAsbUxxdbGysqzJ7JK70/LrDwPT//L5YGdCk468t0jkqTgwmBFgCfxVEKH7juk4IKggvODql9Qr+D8oOouqiPnDwBgxiDAAwAAgPNCoCmgQFOgorz1Ha26+smr1b+9Xwe/clD9L40d8AnOD1aU9W7q1eEHDleUW42p7uK6UuAnuCCo6HVRNb+p+dwuBACAs0CABwAAAOe1mnCNYmtiiq2J6fiPjit2U0wd6zt08N6DSu1Nad5/nqfU3pRSnSnVXVKZdDnVmRr1vC7nvHZ7h16f/fuzKwI88W/GlXw6WQoCnZwFFJgVUKYrQ8JnAMCEIMADAACAC8bJnbskafHXx5dgefads9WwpKEUBBrcO6hUZ0rZw9mKusEFlTOAjv/kuLof6q4o99X7ZHWmfE9eW9dtVctbW9T2rjbFbihfepbry8nf4Jf5WA4GABgbAR4AAADgFCIrIoqsiFSU5wfySu1LlQI/qb0pNd7SWFFvrBlAhcGCNOg9H9w9qAN/f0AHv3ZQN2duLqu3dd1W9b3Yp0BrQLVttQq0BUpftW21CrQOHYevDivQWLlMDQBw/iPAAwAAAJwFf4NfoctDCl0eOmW9BZ9boIEdA6UgUKozpYE9Ayr0FirqXvaPl1WUZbuzUl7KHs6OOmtouKt+cZWa3tBUVvbiW16Ur95XFggaLVCUPZ5luRgAVDECPAAAAMAkan5js5rfWJl4+ZUPvKKub3XJakwu5xRZHVHTzU0V9QqZykDQWAJt5bN3CtmCjv/78XE2lpSXOj/bqcX3eMvXMocz2vmRnfI3+OVr8J3y0R/2q+X2lor3LwwW5GvwyVfjG/d1pOPpGRFsmin9oC8zux/0Zeb3Zab0Y7KZc+7UFczul/Qbko4455aP8rpJ+rKk2yUNSHqfc27z6d541apVbtOmTWfVaQAAAKDabfvtbaptr1XH+g4d2nBImXimLEfQcPlUXtmjWWW7h74y3ZmKsmUPL1NtW22pXborrY3tG8+qf76gT9dsvkbPLX1uXPX9Yb9u6r2prKznVz3aestWSZIFbPTgUMgvf4NfwQVBLfrKIknSzo/tVPy+uFp/u1WhJSHJL5nfvDxEfsl85m1R71PpMTg/qNbfaC17/75tfep/sb9Uz3zlbYafs25uXcVsrO1/sF1HvntErb/dqnl/Pk9ykis4yanied0ldaqfX1/WvndzrzJHMlKhWN8V6xeGPS+eJ7IyovpfK29/7MfHlD2alZzU9a0u9Tzao9jNMc1+z2zvHAUnl3dSQWr5zRbVLyhvf+DLB5RL5kp1yx7zrqzs4k9crODFQzmknHPa+aGdo7ZNPpdUak9KdQvqFFkRkSs4Lbl/iQLNQwHG7LGstr9n+9D36eT3oPg9G1l2zTPXlPW9f3u/tt9R3t658jbZ7qzyvXkF2gJae2RtWfvjPzuuV973Sul7fPKavCdDZXJS6MqQVvx8RVn7+LfievXjr1bULTtH8bH5Lc0KzA4ofl9c7R9p1+J7Fmvff9unzs91ajza39+uy+4tn72362O7FP/H+LjaX/LJSzT/U/NLxzs/tlPxe+OSebv9lRklldeiry5Sx4c7yso2r92svs19lZVHab/sB8vU8tby4O7Tlz6tTDyjQrog5SXVSL46L8jrhRCGrPjVCkVWli+DfTz6+Knfd9jxdTuuU137UNAmczijZ5c8W1Y9P5CXyzq1/2F7KYBdzczseefcqorycQR41knqk/TAGAGe2yX9kbwAz2pJX3bOrT5dh5ZGlrrvXvPdcXYfAAAAwBkrSLlkTi7r5LJOhUxh6Hm2+DzjHZf4pEBrQPUL61VIF0b/I28UFjBF10TLynLHc6fcln44X4PPy0t06j9PxlTTXKPQFeUBmtS+lNKd6XG1D8wJqGFxgyQp8VjijPtRd0mdgvPLk2z3v9Sv3PHcuNrXL6pXbUdtWVnv870q9I1vBlfD8gYFWspncCWfSpb/255CeGVY/oi/rCzxq8S42kpS9IaorHbor26XcUpuTI67fezm8uTi+d78uMdeiUmxdd55sseyGtg2MK5mvrBPkWvKAwyZeEaDuwbP7P3PUu2cWtUvLg/ODe4aVCaeGVf7k2PvbMatNDlj70zGzrSMvWFjpRqt/NXKUQM8p12i5Zx7zMzmn6LK2+UFf5ykp82s0czanXPjCzcCAAAAmBw+qabx9FkZSn9MmqSC96m/1Zp8Pp8aljUMzfjIj5j9kR+aRWL+yo/2nXOSX94n+KdhflP0+qgG9wx6s1YK8vpzlgEfrwPjr2rDpgSU+nHk1DmPxnHSc2x+BicY7VqncOM159yZ9fd0zvBUgVleUHI6WK23zFIFlQKkVmvKHBhfgGaiVPz/mUYWsHEHF6fUsAD2+WgicvDMlbR/2PGBYllFgMfM1ktaL0nz5s3T1Y9ePQFvDwAAAOBcnMlysbPhnDdTKD+QV2GgUPaY7/ee+8N+Nd3apJ0f3an4hrh8QZ8K6YLCq8Jebp8xAksny0PLQ5r70bll73vkn47o6MNHh+qNaDP8nC23t+jiP7m41HbnR71lYt4FePmNgguC3rIX85Z4DX8+5845av9ge9n77/3MXiWfTnp1rFjfN/R8+HHH+g41v7k8V9PeT+3V4GuD6n22V4O7B0vBsoYlDYqti5UtOWv/ULvCV4bL2r/++deV682VL08b/ugfOp51x6yK3CTx++NDfSy2iX8zrp5f9JRyRzW9qUkdH+lQ823N8tcPzcIopAvqebRn6PtUvM7S9fvKv4/R1dGypTv5wbw3g2Z4+2Ft9n56r7q/1+0FVzJOrb/TWrb0Jj+YH5o9dfL7raHH0r+JvGBEoGlE/qp0QfnBfEXd4ec62d/dH9+trvu7vDGbKaj1d1q16MuLvDE2DuY3+QLlOaoKucL4gzQ+lXJclf3/yRTU/qF2LfoHb+njmAFPvypyZOVT+cr6Y7S3WqtsP5DX7v+0W13f7Cr9G815/xxd+qVLK9++wV8RIM4lh818G/G+I1ch1URrvPFx8vWCUy4x1H7PJ/ao69td8tUO/ftU/TKtMQKgp12iJUnFGTz/NsYSrf8r6W+cc08Uj38u6c+dc8+f6pzk4AEAAAAw0mQHm6qtH/RlZveDvsz8vsyUfkyks87BU2w8X2MHeO6T9Khz7sHi8U5Jt5xuiRYBHgAAAAAAgDMzVoBn/HsVju2Hku40z/WSEuTfAQAAAAAAmDqnzcFjZg9KukVSq5kdkPRpSQFJcs59XdKP5O2g9aq8bdLfP1mdBQAAAAAAQKXx7KL17tO87iTdNWE9AgAAAAAAwBmZiCVaAAAAAAAAmEbjSrI8KW9s1i1p37S8+blrlXR0ujsBnCHGLaoNYxbViHGLasOYRTVi3KIaTeS4vcQ51zaycNoCPNXMzDaNlrEamMkYt6g2jFlUI8Ytqg1jFtWIcYtqNBXjliVaAAAAAAAAVY4ADwAAAAAAQJUjwHN2Nkx3B4CzwLhFtWHMohoxblFtGLOoRoxbVKNJH7fk4AEAAAAAAKhyzOABAAAAAACocgR4AAAAAAAAqhwBnjNkZreZ2U4ze9XM/mK6+wOMxsw6zewlM9tqZpuKZc1m9jMz2118bJrufuLCZmb3m9kRM9s2rGzUcWqerxTvvS+a2crp6zkuVGOM2c+Y2cHi/Xarmd0+7LW/LI7ZnWb25unpNS50Znaxmf3SzHaY2ctm9sfFcu63mJFOMWa532LGMrOgmT1rZi8Ux+1fF8sXmNkzxXvtQ2ZWWyyvKx6/Wnx9/kT0gwDPGTAzv6SvSXqLpKWS3m1mS6e3V8CY3uCcW+GcW1U8/gtJP3fOLZL08+IxMJ2+Jem2EWVjjdO3SFpU/Fov6d4p6iMw3LdUOWYl6UvF++0K59yPJKn4+8EdkpYV29xT/D0CmGo5SZ9wzl0u6XpJdxXHJ/dbzFRjjVmJ+y1mrrSkW51zV0laIek2M7te0ufljdtFkk5I+mCx/gclnXDOXSrpS8V654wAz5m5TtKrzrnXnHMZSd+T9PZp7hMwXm+X9O3i829L+q1p7Asg59xjko6PKB5rnL5d0gPO87SkRjNrn5qeAp4xxuxY3i7pe865tHNur6RX5f0eAUwp51zcObe5+LxX0g5Jc8X9FjPUKcbsWLjfYtoV75l9xcNA8ctJulXSPxXLR95rT96D/0nSfzAzO9d+EOA5M3Ml7R92fECnvtkA08VJ+qmZPW9m64tls51zccn7wSlp1rT1DhjbWOOU+y9msruLS1nuH7b8lTGLGae4BOBqSc+I+y2qwIgxK3G/xQxmZn4z2yrpiKSfSdojqcc5lytWGT42S+O2+HpCUsu59oEAz5kZLaLGPvOYidY651bKm2Z9l5mtm+4OAeeI+y9mqnslLZQ3HTsu6QvFcsYsZhQzC0v6Z0kfd84lT1V1lDLGLqbcKGOW+y1mNOdc3jm3QtJF8maRXT5ateLjpIxbAjxn5oCki4cdXyTp0DT1BRiTc+5Q8fGIpH+Rd4M5fHKKdfHxyPT1EBjTWOOU+y9mJOfc4eIvdAVJ/1NDywIYs5gxzCwg7w/l7zrnHi4Wc7/FjDXamOV+i2rhnOuR9Ki8HFKNZlZTfGn42CyN2+LrMY1/GfiYCPCcmeckLSpmwq6Vl8zrh9PcJ6CMmYXMLHLyuaQ3Sdomb6y+t1jtvZL+dXp6CJzSWOP0h5LuLO7ucr2kxMmlBcB0GpGb5B3y7reSN2bvKO6SsUBewtpnp7p/QDGnwzck7XDOfXHYS9xvMSONNWa532ImM7M2M2ssPq+X9Ovy8kf9UtI7i9VG3mtP3oPfKekXzrlznsFTc/oqOMk5lzOzuyX9RJJf0v3OuZenuVvASLMl/UsxR1eNpP/tnPt3M3tO0vfN7IOSXpf0u9PYR0Bm9qCkWyS1mtkBSZ+W9LcafZz+SNLt8hInDkh6/5R3GBe8McbsLWa2Qt606k5JH5Ek59zLZvZ9Sdvl7Qhzl3MuPx39xgVvraQ/kPRSMTeEJP2VuN9i5hprzL6b+y1msHZJ3y7u4OaT9H3n3L+Z2XZJ3zOz/yppi7zgpYqP3zGzV+XN3LljIjphExAkAgAAAAAAwDRiiRYAAAAAAECVI8ADAAAAAABQ5QjwAAAAAAAAVDkCPAAAAAAAAFWOAA8AAAAAAECVI8ADAAAuGGb2X8zsZTN70cy2mtlqM/u4mTVMd98AAADOBdukAwCAC4KZ3SDpi5Jucc6lzaxVUq2kpyStcs4dndYOAgAAnANm8AAAgAtFu6Sjzrm0JBUDOu+U1CHpl2b2S0kyszeZ2UYz22xmPzCzcLG808w+b2bPFr8una4LAQAAGIkADwAAuFD8VNLFZrbLzO4xs5udc1+RdEjSG5xzbyjO6vmkpF93zq2UtEnSnww7R9I5d52kr0r6+6m+AAAAgLHUTHcHAAAApoJzrs/MrpF0k6Q3SHrIzP5iRLXrJS2V9KSZSd4Sro3DXn9w2OOXJrfHAAAA40eABwAAXDCcc3lJj0p61MxekvTeEVVM0s+cc+8e6xRjPAcAAJhWLNECAAAXBDNbbGaLhhWtkLRPUq+kSLHsaUlrT+bXMbMGM7tsWJvfG/Y4fGYPAADAtGIGDwAAuFCEJf2DmTVKykl6VdJ6Se+W9GMzixfz8LxP0oNmVlds90lJu4rP68zsGXkfko01ywcAAGDKsU06AADAOJhZp9hOHQAAzFAs0QIAAAAAAKhyzOABAAAAAACocszgAQAAAAAAqHIEeAAAAAAAAKocAR4AAAAAAIAqR4AHAAAAAACgyhHgAQAAAAAAqHL/Hz0Tze3R72fRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x576 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curves(ul, x, [mu,sigma])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MLE to Poisson random variable\n",
    "The second example tries to estimate the parameter from data generated with a discrete distribution like Poisson."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fake_samples = tf.random.poisson([300], 1.4)\n",
    "fake_samples = tf.cast(tf.math.ceil(fake_samples), tf.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The model is a probability distribution\n",
    "rate = tf.Variable([5.], name=\"rate\") # Give the parameter an initial value\n",
    "model = tfd.Poisson(rate=rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step: 1, initial loss: 3.3020403385162354, rate: [4.9900002]\n",
      "Step: 11, initial loss: 3.23081374168396, rate: [4.8900356]\n",
      "Step: 21, initial loss: 3.1602823734283447, rate: [4.790227]\n",
      "Step: 31, initial loss: 3.090550184249878, rate: [4.690694]\n",
      "Step: 41, initial loss: 3.0217032432556152, rate: [4.5915265]\n",
      "Step: 51, initial loss: 2.9538094997406006, rate: [4.4927883]\n",
      "Step: 61, initial loss: 2.88692045211792, rate: [4.394528]\n",
      "Step: 71, initial loss: 2.821084976196289, rate: [4.2967854]\n",
      "Step: 81, initial loss: 2.756347417831421, rate: [4.1995964]\n",
      "Step: 91, initial loss: 2.692753791809082, rate: [4.1029973]\n",
      "Step: 101, initial loss: 2.6303486824035645, rate: [4.0070257]\n",
      "Step: 111, initial loss: 2.5691795349121094, rate: [3.9117212]\n",
      "Step: 121, initial loss: 2.5092968940734863, rate: [3.817127]\n",
      "Step: 131, initial loss: 2.450749397277832, rate: [3.723288]\n",
      "Step: 141, initial loss: 2.393590211868286, rate: [3.6302533]\n",
      "Step: 151, initial loss: 2.3378727436065674, rate: [3.5380754]\n",
      "Step: 161, initial loss: 2.283651828765869, rate: [3.4468107]\n",
      "Step: 171, initial loss: 2.2309834957122803, rate: [3.356519]\n",
      "Step: 181, initial loss: 2.179926872253418, rate: [3.2672658]\n",
      "Step: 191, initial loss: 2.130537986755371, rate: [3.17912]\n",
      "Step: 201, initial loss: 2.0828752517700195, rate: [3.0921555]\n",
      "Step: 211, initial loss: 2.036996364593506, rate: [3.0064514]\n",
      "Step: 221, initial loss: 1.9929590225219727, rate: [2.9220922]\n",
      "Step: 231, initial loss: 1.9508174657821655, rate: [2.8391676]\n",
      "Step: 241, initial loss: 1.910627007484436, rate: [2.7577732]\n",
      "Step: 251, initial loss: 1.8724350929260254, rate: [2.6780088]\n",
      "Step: 261, initial loss: 1.8362876176834106, rate: [2.5999815]\n",
      "Step: 271, initial loss: 1.8022247552871704, rate: [2.5238013]\n",
      "Step: 281, initial loss: 1.7702771425247192, rate: [2.4495842]\n",
      "Step: 291, initial loss: 1.7404718399047852, rate: [2.3774495]\n",
      "Step: 301, initial loss: 1.712819218635559, rate: [2.3075202]\n",
      "Step: 311, initial loss: 1.6873241662979126, rate: [2.23992]\n",
      "Step: 321, initial loss: 1.6639748811721802, rate: [2.1747735]\n",
      "Step: 331, initial loss: 1.642746090888977, rate: [2.1122038]\n",
      "Step: 341, initial loss: 1.6235970258712769, rate: [2.0523295]\n",
      "Step: 351, initial loss: 1.6064695119857788, rate: [1.9952626]\n",
      "Step: 361, initial loss: 1.59128999710083, rate: [1.9411064]\n",
      "Step: 371, initial loss: 1.577967643737793, rate: [1.8899503]\n",
      "Step: 381, initial loss: 1.5663957595825195, rate: [1.8418679]\n",
      "Step: 391, initial loss: 1.5564552545547485, rate: [1.796914]\n",
      "Step: 401, initial loss: 1.5480151176452637, rate: [1.7551198]\n",
      "Step: 411, initial loss: 1.5409350395202637, rate: [1.7164923]\n",
      "Step: 421, initial loss: 1.5350698232650757, rate: [1.6810114]\n",
      "Step: 431, initial loss: 1.5302746295928955, rate: [1.6486287]\n",
      "Step: 441, initial loss: 1.526405692100525, rate: [1.6192676]\n",
      "Step: 451, initial loss: 1.5233262777328491, rate: [1.5928245]\n",
      "Step: 461, initial loss: 1.5209083557128906, rate: [1.569171]\n",
      "Step: 471, initial loss: 1.5190356969833374, rate: [1.5481572]\n",
      "Step: 481, initial loss: 1.5176044702529907, rate: [1.5296155]\n",
      "Step: 491, initial loss: 1.516525387763977, rate: [1.5133651]\n",
      "Step: 501, initial loss: 1.5157220363616943, rate: [1.4992172]\n",
      "Step: 511, initial loss: 1.515131950378418, rate: [1.4869794]\n",
      "Step: 521, initial loss: 1.5147037506103516, rate: [1.4764605]\n",
      "Step: 531, initial loss: 1.5143970251083374, rate: [1.4674742]\n",
      "Step: 541, initial loss: 1.5141794681549072, rate: [1.4598423]\n",
      "Step: 551, initial loss: 1.5140267610549927, rate: [1.4533974]\n",
      "Step: 561, initial loss: 1.5139204263687134, rate: [1.4479841]\n",
      "Step: 571, initial loss: 1.5138479471206665, rate: [1.4434615]\n",
      "Step: 581, initial loss: 1.5137981176376343, rate: [1.4397018]\n",
      "Step: 591, initial loss: 1.5137648582458496, rate: [1.4365911]\n",
      "Step: 601, initial loss: 1.5137429237365723, rate: [1.4340298]\n",
      "Step: 611, initial loss: 1.5137277841567993, rate: [1.4319304]\n",
      "Step: 621, initial loss: 1.5137183666229248, rate: [1.4302167]\n",
      "Step: 631, initial loss: 1.5137121677398682, rate: [1.4288238]\n",
      "Step: 641, initial loss: 1.5137078762054443, rate: [1.4276965]\n",
      "Step: 651, initial loss: 1.5137053728103638, rate: [1.4267879]\n",
      "Step: 661, initial loss: 1.5137038230895996, rate: [1.4260583]\n",
      "Step: 671, initial loss: 1.513702630996704, rate: [1.425475]\n",
      "Step: 681, initial loss: 1.5137017965316772, rate: [1.4250103]\n",
      "Step: 691, initial loss: 1.5137017965316772, rate: [1.4246416]\n",
      "Step: 701, initial loss: 1.513701319694519, rate: [1.4243503]\n",
      "Step: 711, initial loss: 1.5137007236480713, rate: [1.4241209]\n",
      "Step: 721, initial loss: 1.5137012004852295, rate: [1.423941]\n",
      "Step: 731, initial loss: 1.5137006044387817, rate: [1.4238005]\n",
      "Step: 741, initial loss: 1.51370108127594, rate: [1.4236909]\n",
      "Step: 751, initial loss: 1.5137008428573608, rate: [1.4236059]\n",
      "Step: 761, initial loss: 1.5137012004852295, rate: [1.4235405]\n",
      "Step: 771, initial loss: 1.513701319694519, rate: [1.4234903]\n",
      "Step: 781, initial loss: 1.5137007236480713, rate: [1.4234517]\n",
      "Step: 791, initial loss: 1.5137007236480713, rate: [1.4234222]\n"
     ]
    }
   ],
   "source": [
    "optimizer = tf.optimizers.Adam(0.01)\n",
    "ulp, pvp, vrp = mle_run(fake_samples, model, [rate], optimizer, steps=800, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(15,10))\n",
    "Artists = namedtuple(\"Artists\",(\"prob\",\"step\"))\n",
    "artists = Artists(plt.plot([], [], \"r--\",animated=True)[0], \n",
    "                  ax.text(x=0.9*vrp[-1].numpy(), y = 0.05, s=\"\"))\n",
    "\n",
    "init = partial(init_fig, f=f, ax=ax, artists=artists, data=fake_samples)\n",
    "update = partial(update_artists, artists=artists, value_range=vrp)\n",
    "frame = partial(frame_iter, update_list=ulp, prob_values=pvp)\n",
    "\n",
    "ani = animation.FuncAnimation(fig=f, \n",
    "                              func=update, \n",
    "                              frames = frame,\n",
    "                              init_func = init)\n",
    "\n",
    "ani.save(\n",
    "  filename='myvideo_poisson2.mp4'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we plot the learning curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_curves(ulp, fake_samples, [rate])"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}