2. annealing_epsilon_greedy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1e350781",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import random\n",
    "import math\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9f5fdb5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02010651",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def ind_max(x):\n",
    "    max_value = max(x)\n",
    "    max_keys = [k for k, v in enumerate(x) if v == max_value]\n",
    "    return random.choice(max_keys)\n",
    "\n",
    "\n",
    "class AnnealingEpsilonGreedy():\n",
    "    def __init__(self, counts, values):\n",
    "        self.counts = counts\n",
    "        self.values = values\n",
    "        return\n",
    "\n",
    "    def initialize(self, n_arms):\n",
    "        self.counts = [0 for col in range(n_arms)]\n",
    "        self.values = [0.0 for col in range(n_arms)]\n",
    "        return\n",
    "\n",
    "    def select_arm(self):\n",
    "        t = sum(self.counts) + 1\n",
    "        epsilon = 1 / math.log(t + 0.0000001)\n",
    "\n",
    "        if random.random() > epsilon:\n",
    "            return ind_max(self.values)\n",
    "        else:\n",
    "            return random.randrange(len(self.values))\n",
    "\n",
    "    def update(self, chosen_arm, reward):\n",
    "        self.counts[chosen_arm] = self.counts[chosen_arm] + 1\n",
    "        n = self.counts[chosen_arm]\n",
    "\n",
    "        value = self.values[chosen_arm]\n",
    "        new_value = ((n - 1) / float(n)) * value + (1 / float(n)) * reward\n",
    "        self.values[chosen_arm] = new_value\n",
    "        return\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9e906243",
   "metadata": {},
   "outputs": [],
   "source": [
    "class BernoulliArm():\n",
    "    def __init__(self, p):\n",
    "        self.p = p\n",
    "    def draw(self):\n",
    "        if random.random() > self.p:\n",
    "            return 0.0\n",
    "        else:\n",
    "            return 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1f0f840e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_algorithm(algo, arms, num_sims, horizon):\n",
    "    chosen_arms = [0.0 for i in range(num_sims * horizon)]\n",
    "    rewards = [0.0 for i in range(num_sims * horizon)]\n",
    "    cumulative_rewards = [0.0 for i in range(num_sims * horizon)]\n",
    "    sim_nums = [0.0 for i in range(num_sims * horizon)]\n",
    "    times = [0.0 for i in range(num_sims * horizon)]\n",
    "    \n",
    "    for sim in range(num_sims):\n",
    "        sim = sim + 1\n",
    "        algo.initialize(len(arms))\n",
    "        for t in range(horizon):\n",
    "            t = t + 1\n",
    "            index = (sim - 1) * horizon + t - 1\n",
    "            sim_nums[index] = sim\n",
    "            times[index] = t\n",
    "            chosen_arm = algo.select_arm()\n",
    "            chosen_arms[index] = chosen_arm\n",
    "            reward = arms[chosen_arms[index]].draw()\n",
    "            rewards[index] = reward\n",
    "            if t == 1:\n",
    "                cumulative_rewards[index] = reward\n",
    "            else:\n",
    "                cumulative_rewards[index] = cumulative_rewards[index - 1] + reward\n",
    "            algo.update(chosen_arm, reward)\n",
    "    return [sim_nums, times, chosen_arms, rewards, cumulative_rewards]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "48e39f36",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_tests(means=[0.1, 0.1, 0.1, 0.1, 0.9],\n",
    "                   filename=\"anneal_greedy_standard_results.tsv\",\n",
    "                   num_sims= 5000, horizon=250):\n",
    "    \n",
    "    n_arms = len(means)\n",
    "    arms = [BernoulliArm(mu) for mu in means]\n",
    "    best_arm = ind_max(means)\n",
    "    print(\"Best arm is \" + str(ind_max(means)))\n",
    "\n",
    "    f = open(filename, \"w\")\n",
    "\n",
    "    algo = AnnealingEpsilonGreedy([], [])\n",
    "    algo.initialize(n_arms)\n",
    "    results = test_algorithm(algo, arms, num_sims, horizon)\n",
    "    \n",
    "    for i in range(len(results[0])):\n",
    "        #f.write(str(epsilon) + \"\\t\")\n",
    "        f.write(\"\\t\".join([str(results[j][i]) for j in range(len(results))]) + \"\\n\")\n",
    "    f.close()\n",
    "    \n",
    "    # Read this \n",
    "    df = pd.read_csv('./anneal_greedy_standard_results.tsv', sep='\\t', header=None, \n",
    "                     names=[\"Sim\", \"T\", \"ChosenArm\", \"Reward\", \"CumulativeReward\"])\n",
    "    \n",
    "    return df, best_arm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "686e3cfc",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be073026",
   "metadata": {},
   "source": [
    "## Probability of choosing best arm over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5ab5a5fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_prob_best_arm(df, best_arm):\n",
    "    df = df.copy()\n",
    "    xseries = df[df['ChosenArm']==best_arm].groupby(['T'])['ChosenArm'].count().to_frame()\n",
    "    xseries['ChosenArm'] = xseries['ChosenArm']/5000\n",
    "    xseries.plot( ylabel='Probability of selecting best arm', xlabel='Time', figsize=(15,8))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97e8181b",
   "metadata": {},
   "source": [
    "## Average reward over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9daf2a8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_avg_reward(df):\n",
    "    df = df.copy()\n",
    "    fig, ax = plt.subplots(figsize=(15,8))\n",
    "    xseries = df.groupby(['T'])['Reward'].mean().unstack().plot(ax=ax)\n",
    "    xseries.set_ylabel(\"Average reward\")\n",
    "    xseries.set_xlabel(\"Time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ac7bd49",
   "metadata": {},
   "source": [
    "## Cumulative reward over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "eee6b616",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cumulative_reward(df):\n",
    "    df = df.copy()\n",
    "    fig, ax = plt.subplots(figsize=(15,8))\n",
    "    xseries = df.groupby(['T'])['CumulativeReward'].mean().unstack().plot(ax=ax)\n",
    "    xseries.set_ylabel(\"Cumulative reward\")\n",
    "    xseries.set_xlabel(\"Time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f355c8df",
   "metadata": {},
   "source": [
    "## Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "35cd83f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best arm is 4\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3gAAAHgCAYAAAD3xM9JAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAABtIUlEQVR4nO3dd3hUZfrG8ftNL6SQAqSSEHoJxQDSFRW7rB3L2nV1bVtd3abb1V1du/xce8OOvVFUpAmhQ+g9lfTe8/7+SIgBkjBAJpPy/VwXF5lzTs48icOYO295jLVWAAAAAIDOz83VBQAAAAAA2gYBDwAAAAC6CAIeAAAAAHQRBDwAAAAA6CIIeAAAAADQRRDwAAAAAKCL8HB1AccqLCzMxsXFuboMAAAAAHCJVatW5Vhrw5s71+kCXlxcnJKTk11dBgAAAAC4hDFmb0vnmKIJAAAAAF0EAQ8AAAAAuggCHgAAAAB0EZ1uDV5zqqurlZqaqoqKCleX0m34+PgoOjpanp6eri4FAAAAQIMuEfBSU1MVEBCguLg4GWNcXU6XZ61Vbm6uUlNTFR8f7+pyAAAAADToElM0KyoqFBoaSrhrJ8YYhYaGMmIKAAAAdDBdIuBJIty1M77fAAAAQMfTZQJeR5CZmalZs2YpISFBQ4cO1TnnnKPnnntO5513nstqmjt3rowx2rJli8tqAAAAANA+CHhtxFqrCy+8UKeccop27typlJQU/fOf/1RWVpZL65ozZ44mT56st956q9nztbW17VwRAAAAAGch4LWRb775Rp6enrr11lsbj40aNUpTpkxRSUmJLrnkEg0ePFhXXXWVrLWSpAULFmj06NEaMWKEbrjhBlVWVkqS7r33Xg0dOlSJiYn6zW9+I0nKzs7WxRdfrLFjx2rs2LFasmSJJOmBBx7QDTfcoFNOOUX9+vXTE0880fj8JSUlWrJkiV544YVDAt63336rU089VVdeeaVGjBihb7/9VtOmTdNll12mgQMH6t5779Ubb7yhcePGacSIEdq5c6fTv38AAAAATlyX2EWzqb98skkp6UVtes+hkYG6//xhrV6zceNGnXTSSc2eW7NmjTZt2qTIyEhNmjRJS5YsUVJSkq677jotWLBAAwcO1DXXXKNnn31W11xzjebOnastW7bIGKOCggJJ0t13361f/vKXmjx5svbt26czzzxTmzdvliRt2bJF33zzjYqLizVo0CDddttt8vT01IcffqizzjpLAwcOVEhIiFavXq0xY8ZIklasWKGNGzcqPj5e3377rdatW6fNmzcrJCRE/fr100033aQVK1bo8ccf15NPPqnHHnuszb6fAAAAAJyDEbx2MG7cOEVHR8vNzU2jRo3Snj17tHXrVsXHx2vgwIGSpGuvvVaLFi1SYGCgfHx8dNNNN+mDDz6Qn5+fJGn+/Pm64447NGrUKF1wwQUqKipScXGxJOncc8+Vt7e3wsLC1KtXr8ZpoXPmzNGsWbMkSbNmzdKcOXMOqalpi4OxY8cqIiJC3t7eSkhI0IwZMyRJI0aM0J49e5z+PQIAAABw4rrcCN7RRtqcZdiwYXrvvfeaPeft7d34sbu7u2pqahqnaR7Ow8NDK1as0IIFC/TWW2/pqaee0sKFC1VXV6dly5bJ19fXofvn5uZq4cKF2rhxo4wxqq2tlTFGDz/8sCTJ39+/xXu4ubk1PnZzc1NNTY2D3wUAAAAArsQIXhuZPn26Kisr9b///a/x2MqVK/Xdd981e/3gwYO1Z88e7dixQ5L02muvadq0aSopKVFhYaHOOeccPfbYY1q7dq0kacaMGXrqqacaP//g8Za89957uuaaa7R3717t2bNH+/fvV3x8vBYvXnxiXygAAACADouA10aMMZo7d67mzZunhIQEDRs2TA888IAiIyObvd7Hx0cvvfSSLr30Uo0YMUJubm669dZbVVxcrPPOO0+JiYmaNm2a/vvf/0qSnnjiCSUnJysxMVFDhw7V7NmzW61nzpw5uvDCCw85dvHFF+vNN99smy8YAAAAQIdjWpoq2FElJSXZ5OTkQ45t3rxZQ4YMcVFF3RffdwAAAKD9GWNWWWuTmjvHCB4AAAAAl6ira7/BpvZ8Llci4AEAAABod4u2ZWv4A19pe1ax05/LWqufvviD7nhzdYubHXYVXW4XTQAAAAAd3+zvdqqsqlazv9ulRy4b6dTnSt6bryU7ciVJUweE67KxMY3nDhRX6Nut2dqUVqiN6UUa3CdA/7hwhFPrcaYuM4LX1ZN4R8P3GwAAOOrRedv04uLdRxzPLq7UvtwyF1QEV9uWVaylO3MV1sNLH69LU2ZhhVOf7+WlexTo46GxcT31109TlFZQLknakFqocx7/Xve8t17vrUpVZmGF5qzYp9ySSqfW40xdIuD5+PgoNzeX0NFOrLXKzc2Vj4+Pq0sBAAAd3KJt2XpiwXY9Om+byqoO7a17+5urddGzS1ReVXvI8bzSKm1ILWyX+iqqa3Xb66u0YHNWi+ff+GGvTnvkW901Z41KKo+vP3BxRbW2Zhbrmy0HtGxnx/q59YkF2zU/pfmv/3Cp+WV66Mst+s9XW49Y05ZdXKmlO3Mc+tpeWbpHXh5ueuHasaqts3ppyZG/ACivqtWynbn636JdenvlPn2/PVu7c0pbvb+1Vr97b73eSd7feCyjsFxfbszUrHGxeuTSUapruOa7bdm6/Lll8vZw18d3TNKGB87U7KtPUp2Vvtma7dD3oyPqElM0o6OjlZqaquzszvsforPx8fFRdHS0q8sAAAAnqKSyRh+sTtVPRkcp0MezTe9dVlWj38/doJ5+nsovq9bnGzJ1yUn1Pz9sySzSit15kqR3kvfr2olxkup/QL9rzhol783Tmj/NkK+Xe5vUsi+3TBfPXqr/XDpS0waGNx5/d1WqvtiYqUXbsvXRHZPUv1dAYx0vLdmjZ77dqZySSg3qHaBP16crJaNIs68+Sf179XD4uR/9equeWLjjkGPj4kJ03zmDNTq2Z6ufm1lYoZeW7NZNU/opPMD7GL5iqaiiWu+srA86kcG+igr21YioILm5mcZrVu3N06PztikxOkinD+19yOff/dYafb89R8MiAzU0MlB7cko1LyVLVpK1UlVtnX5/Tv2O6vvzynTl88u1P69cI6KC9MszBujUQb1kjNHhCsuq9cHqNM0cGamRMcE6Z0SE3vxhn+6Y3l8BPp7amFaoBz7epLX7C1TTzMYopw/ppQcvTlRYjyO/H8l78/V28n69tzpVfUP8NL5fqN5Yvk911uqnJ/dVTIif7jtniP704UYt3pGjIRGBeuX6seoVWD9wMTwqUL0DvbVgc1bja7Wz6RIBz9PTU/Hx8a4uAwAAdBJfbcrUM9/s0JxbTpafV5f4cei4VFTX6qZXVmr5rjx9uzVbz1+TdMgP/8fqQFGFfLzcG4Pio19vU2p+ud752QTd+/56vb1yX+MPza8v3ytvDzclhPfQc4t26crxsfJ0d9O3W7O1eEeOJOmH3bk6ZVCvE/9CJT2/eJeyiyv1j89SNLn/VLm7GdXU1um5RTs1uE+Asosrdevrq/XR7ZPk4W50z3vr9dHadE3qH6onTh2lCf1CtWxXru58c41mPrVYf505XBeNiWo2wDRVXVun13/Yp3FxIbpmYl9FBvsqJb1Ij83frgufWarLkqL10MWJLd7nzx9t1NcpWfp0fYZevn6sBvQOOOR8YVm1NqUXakd2iaJ7+mp4ZJCC/Dz1xvJ9enLhduWXVR9y/eVJMXrokkRJ9SH24S+3SpLWpxYqq6hCvRuCTn5plT5dn6EhEQHKL6vSi4t3q4e3h26dlqCrT+6r2d/t1HOLdinU30tnDe+jK55brpLKGv3urMF6c8Ve3fBysoZGBOr0ob01dUCYRsYEy9O9fvLgu6v2q7y6tjHU/2xqgj5dn6E5K/Yp2NdLf/xoo0L8vHTz1H4aG9dTI6ODVVZVq/SCciXvzdfjC7brrMcW6aGLE3XakEND6RvL9yrA20PhAd66/c01mvvziZqzYp9OG9xbMSF+kqSrx8dq+c5cVVTX6r+zRh3yiw1jjKYP7q2P16apsqZW3h5t8wuG9tR939EAAEC39b9Fu7QutVBz16TpqvF9j/s+FdW1+n57jiYkhKqHt2M/Vm1ILVRFTa1GNfmB1xWqaup06+ur9MPuPJ0/MlKfrEvXY/O36VczBh3X/ZbuyNFNryarts7q3BERGt8vRC8u2a2rT47VuPgQXTY2Rg9+sUU7s0vUK8Bbc1en6bzESJ0zoo9ufCVZH69N18xRkfrn55vVN9RPWUX1G1+0FPD25pbqk3XpumVqgrw8Wv8+FpRV6d3kVMWH+WtbVonmrknTJSdF6/ONmdqfV67ZV5+kQB8PXf3CD/rVO2uVV1qllXvy9dszB+nnpyQ0hq+JCWH69K7JuuPNNfr1u+s0Z8U+PXDBMA2PCmrxub/bmq280ir97JJ+jWFkTGxPXTg6Sn//LEVzVuzXz6YlKCH8yBHBxdtz9HVK/UjSd9uyddGzS/XIpSNVXWv1/fZsLd2Zq315R65h9PZwU2VNnSb1D9V9Zw9RTE8/pRWU653k/Xp56R5NHRiucxMjtHhHjn7Ynacrx8fqzR/2acHmA7pyfKwkad7mLNXWWf3rwkSNiA5SVU2djFHja/aB84cpr7RK//pii579bqeMpDdvPlnDo4J005R4vb8qVW+t3K+nFm7XEwu2K9DHQ2cPj9AFoyL16rK9GhvXs/H7NiI6SBP6heo/X29TVUPdT8wardAmI3ShkmIaRuROH9Jbv3h7rW58JVl//8lwXX1y/b/hvNIqfb4hU1eOj9WV42M186kl+snTS5RbWqXrGsKkVB/inr5qTIv/zU4f0ktzVuzTD7vyNLXJaG9nQcADAADdyp6cUiXvzZcx9euArhwXe9RRmMMVVVTrjeX79MLi3copqdSIqCC9csM4hfh7SZJq66wWbjmgsXE9Fezn1fh5FdW1uuJ/9SMdPbw9NCEhVFeMi9H0wb1beqpD1NTWaV1qofJLq5RXVqWefl46bXCvYx51q62z+sXba/Tt1mz988IRumJcjHw93fTEwh0aGhmks4b3Oab7fb0pU3fMWaP4UH8lxfXUx2vT9cGaNPUO9NY9Zw2WJF00Jkr//mqr3kner+hgX5VW1eqnE/pqZHSQBvcJ0LPf7VRZda22HyjR7KtP0lsr92nRtuaX3xRVVOv6l1dqV3apjDG6/dT+jedW78vXXz5J0d9nDteI6PoA8cYP+1ReXatnrhqj372/Xv+dt03nJUZo9rc71S/cXzOG9pabm9Fvzhykh7/cKi8PNz15xWidPzLyiOeOCPLVuz+boPdWp+rhL7fo/KcW69oJcbr37MHy8TxytOeDNakK9fc6Iij4e3vo56f015wV+/X9tuwjAl51bZ3+8skmxYb46e8/Ga7c0ird8NJK3fLaKklSgI+HJvQL1RXjYjU8KlD9e/VQan65NqYVald2qU4b0kvTBoY3vraD/Dz1h3OHaO3+At33wXqNig3Wv7/aqqhgX91//lAt2patBZuzGgPelxsz60cEowIl6YgQ7eZm9Ohlo1RcUaNN6UV6/aZxGtyn/lpPdzfNGherWeNiVVhWraU7czQvJUufrk/X2w1r4+4569BfJNwxvb+ufXGFfn5Kgn49Y5DcW3lND+oToA9vn6ibXknWPz7brGkDwxUT4qf3Vu1XVW2drhwfq4G9A/TgxSN091tr1b9XD03qH9ri/Q43qX+YfDzdtGBzFgEPAAB0TAVlVbr3/Q0qr67V//30pGZ/EO1s3l65TzklVfrZ1H7yOIaRsA9Wp8oY6VenD9Qj87Zp2a5cTUwIk1S/3umjtWm6blJci1OzdmaX6OJnl6qgrFpTBoRp2sB++vdXW3XZ/y3T6zeOV15plX4/d4PW7i/QleNj9c8m260v25mrksoa3Tm9v3JLq/TtlgO64eUs/WRUpO4/f5h6+ns1+5wH3f32Wn22PuOQY2Nig/XABcOUGB3s8PfguUW79PmGTP3hnCGNP9D/deZwbc0q0a/fWau5a8Lk6+kuH093VdXWqaK6VpXVdeoV6KOEcH8lhPeQh7tReVWtduWU6t9fbdXwqCC9cv1YBft56Y/nDtXXKZka0CugcfpbrwAfnTa4l95flaqefl4aERWkkdFBMsbotlMSdPdba/W3T1I0Li5EZw7rrYzCcv3lkxTtyy1TbKhfY+11dVa/enut9uWWaWRMsJ5YsF3nJUaob6i/Csuqdeeba5RWUK6bX03Wx3dMUpCfp15eukdTBoRpSESgfnfWYF31/A+6c84apWQU6aGLRzQG5NumJcjL3U1JcSEaFdPy99PNzeiypBidNbyPHv16m15eukc/7M7T01eOVr8mQa2wrFrzUw40Tj89XEyIn/qG+un77Tm6btKhy41eX75X2w+UNP57jQr21Xu3TdAXGzKV0KuHRkYHHfG6jwjy1di4kBbr9nR30+OzRumcx7/Xpc8uVXphhR6+JFHeHu46fUhvzVmxT+VVtaqpq9Pi7Tm6ZkLfVn/54eXhppevH6vKmroW31OC/Dx19ogInT0iQhXVtVqw+YB2ZZforGGH/hJhUv8wbfzLmQ6/N3l7uOuhixM147+L9Lv31+u1G8frzYapsAMbprHOHBWl2jqrhPAex/RLHB9Pd03uH675mw/ogQvsMf8CyNUIeAAAdHEb0wp12xurlFlYoZo6q7vfWqNnrjqp1d+QW2u1Kb1IReXVmtg/rMXriiuqtWJ3nk4ddOyjSE3V1lnd//FG9Qrw0XWT4o662ceu7BL98cONqq61Wrw9R09eObrZDRcOV1dn9f7qNE3uH6abp/bTi0t265WlezQxIax+PdqrK7UxrUhVNXW687QBR3y+tVa//2CD6uqsPrljcuMI0bDIIN30ykqd9+T3yi+rVrCvp4ZHBeqLDRn6ywXDGn+4/zolUz28PXTH9P7y9nBXVU2dnvl2h55auEOLd+Tq1zMG6tzEiGa//g2phfpsfYaumdBXF4+JVoi/l5btytXDX27VzKeX6NoJcbr//KFH/WF0d06pHpu/TWcO662bp/ZrPO7j6a7ZV4/R797foD05ZSqvrlVFda28PNzk6+kuT3c3rdqXr4LD1nRJ0sSEUD13TVLjNFVfL3fNHBV1xHWXj43R1ylZyimp0sNN1p2dOyJCj87bpr25ZfrDuUNkjGncCOW77dn6aeiP02gfX7Bd8zcf0F8uGKazhvfRaY98pz9+uFGv3jBO936wXllFFXrwohH666cpuvm1VbrkpGhlF1fqkUvr+6xN6h+myf3DNC8lS70DvfWT0T/WaYzRTVP6yVGBPp564IJhmjowTL9+Z53Oe3KxHro4sXHk77MNGaqqrdPFY1rerGPKgDB9sDpNVTV1jaNkeaVV+u+8bZrcP0wzmmx8EuDjeUj/tuPRN9RfD1wwTL99b736hfvrooav//QhvfXy0j1asiNHpVU1qqqt09kjjj6Sa4xxOJT5eLrr3MSIVs8fi8hgX/3+nCH6/dwN+tU7a7Unt0y/PGPgIddc1Mr3vjWnD+ml+ZuztCWzWEMiAo/rHq5CwAMAoAv7bH2GfvXOWvX089LbP5ugtfsK9NdPU/S3T1OaDQNZRRV69tudmpeSpbSCchkjLb/vtMaNFw6qD0qpeujLrcopqdRDF4/Q5WNjj7vO2d/t1OvL90mSXli8W7dM7afrJ8W1uAHK3z5NkY+Hu+47e6Ae+nKLzntisZ65eozGHGVHwh925ymtoFy/PXOQfDzddcW4WM3+bqf255Xpv/O2aWNakYZEBOrpb3fowjFRiu7pd8jnv7cqVT/sztO/LhrRGO4kaUJCqObccrJuf3O1Th/SW/eePVjJe/J106vJWrw9R6cO7qXaOqt5KVk6ZVB44+igl4ebfnH6QM0Y2ke/e3+97vtgg+7/eJOmD+qlG6fEHzIa8+i8rQry9dRvzhzUGABjQvx09vA++vunm/Xy0j06NzGi1REca63u+2C9vNzd9NeZw484HxHkq1dvGNfq9zCvtEq7sktkJfl6usvXy13xof4OBfxpA8PVO9Bb5VW1h0x/9HB300MXJ2rHgRKNbBg5iw/zV0yIr77bmq2fNqyxWrglS48v2K6Lx0Q3ji7dc9Yg/fmjTfrZa6v0dUqW7j17sGaNi1Wwn5dufX2VNqQWaHCfAE0Z8OMvKn531mAtfXqxbp7Sr0020Zg+uLc+v3uK7nxzje6cs0a5JZW6blK8Plidqv69ejROc2zOlAHhen35Pq3Zl6/x/eqnET7//S4VV9bozw4E9uNxyUnRKquq1Ul9ezaOAo6LD1GAt4fmb85SQVm1egd6a3RM6/+eOoIrxsXo0/Xp+mhtukIaNnxpC9MH16/9XLA5q9MFvC7RBw8AABwpr7RK976/XkMjA/XpXZM1Jranbpgcr5smx+vlpXv0/PeH9p2ytn50780f9mlIRIDuPm2ArK2fVthUdnGlLnx2qX773nrFhvhqSESgHpu/XRXVh/Yyc9TGtEL9d942nZsYoU/umKykvj3176+26o8fbmz2+m+2HNA3W7N112kDdMPkeH3w84ny8nDTlf9brsXbc1p9rvdXp6qHt4fObJgedvXJ9SHhhpdX6oM1afrl6QP1/LVJMjL6+6ebD/ncvNIq/fPzzUrq21OXJx05ipIYHazv75muBy9OVLCfl6YMDFOgj4c+WZcuSVq7P185JVWaMezIH0CHRgbq4zsm6cPbJ+mq8bFK3puvq/73g77fXr8GbdXefH2zNVs/m9bviNG9gIZRpGA/T73w/ZG9xJp6J3m/lu/K033nDDkitDsqxN9LSXEhGhsXouFRQUoI7+Hw6K2Hu5seuXSU/nv5qCPaH5zcL7RxswxJjaN4S3fmqKqmTgeKKvSbd9drSESg/nHh8Mbgc9X4vhoZE6yvU7I0ZUCYbmkYgTtreB/9+oyBqrPSLVP7HRKURkQHadE9p+qGSW23C3tEkK9ev2m8zhjaWw98kqI/fbhRyXvzj7rT5oSEULm7GX3f8Notr6rVmyv2acbQ3o1TDduaMUbXTow7ZHMYLw83TR0Yrvmbs/TttgM6c1ifExqVby/GGD14UaJ6eHvoinExbbbrZa9AH42MDtL8zQfa5H7tiYAHAIADvtiQoee/3+XqMo7Jkwu3q7SqRv++5NB+Ub8/Z4jOGdFHD365Rav35Tce/zolS8t35elP5w3R89eO1V2nDVCQr6eW7jw0NL3xw16tTy3QI5eO1Hu3TtT95w9VRmGFXl2255hrrKiu1S/fXqsQfy/94yf1m2K8cN1YXTuhrz5Zl67s4spDrq+qqdPfPk1Rv3D/xi3Wh0UGae7PJyou1F83vLJS325t/geysqoafbEhQ+eM6NMYLiKDfTVjaG9tP1CiM4b21p3T+ysq2Fd3TO+vLzdlHrLJxz8+26ySyhr966IRDv3g6+3hrrOHR+irTZmqqK7V15uy5OludMqg5jdtMMZoVEyw7j9/mBb8apr6hfvrlldXaeWePD06b6tC/b107YS4Zj/X18tdV46L1dcpmdrfZFfFHQdK9Nt31+m3767Tnz/aqH98tlnj4kM06wSn+Z2IyQPCjtjaviXTBvZSWVWtVu7J06/fXaeyqho9ecWoQ6byubsZPXJpoi4cHaVHLxt1yH+bO6b31/xfTdWFo4+cLhrd06/NA4yPp7uevWqMLhodpdeW75Ux0k+amaraVKCPp0bFBDeG+fdXp6qgrFo3TnZ8qmhbOW1IL+WUVKmiuq7NRsLaQ2yon76/51T98vSBR7/4GJybGKGwHt6qqa1r0/s6GwEPANDtLdqWrdeX71VZVc0R58qranXfB+t12xur9ffPNmvt/oJm71FXZ/Xasj266ZWVKiw/co1Se9uXW6bXl+/V5WNjGhs3H+TmZvTgxYnqE+ijX729VmVVNaqsqdU/P9+sAb166Ipx9VMt3d2MxseHaNmuQ0fwFmw+oNExwbr4pGi5uRmd3C9U0waG6+lvdh7T115eVau/f5ai7QdK9O9LRx6y2+Q1E+NUXWv19sp9h3zOy0t3a1dOqf503tBDdvUL7eGtOTefrAG9euiWV1fpjR/2amNa/W6TOSWV+nJjpn7/wQaVVtUesR7qN2cO0k9P7qtHLxvZ+AP/TVPiFRfqp9/P3aBbXk3WpAcX6v3VqfrZ1IQj+pC15oJRkSqtqtXCLQf01aZMTUgIc6iZeJCfp167cbwignz00xd+0JIdubrtlAT5t9KK4ZoJcXIzRi8t2SNJKiyv1k2vrNRnGzK0eEeOPl6Xrp7+Xg4H1I5gQkKoPN2N7vtgg77fnqM/njv0iNezJPXvFaD/Xj7qiEbgxhj17xXQrptkeLi76T+XjtSd0/vr5in9FBnse9TPmTIgTOvTCpVXWqUXl+zWiKggjY1r/+mRpw7qJTdTP0o7rpWpvh1RT3+vY9psyRG3TE3Q89cmtfl9nY01eACAbu9PH23U3twyPfL1Vl03MV6nDg5XYXm1ckuq9Oy3O7U1q1i3TO2nd5L368kF2/XCdWMP+fy9uaW65731+mF3niTpn59tbmwkLEnzU7L0p4826t6zBx+y8YS1VtuyShQf5t9qH6+dDQ2Mj2Xq0b+/3ip3N6NftPAb7UAfT/3n0pG68vnl9X3HQvy1N7dMr94w7pAfZiYmhOrrlCztzytTTEh9b7INaYX67ZmHbnF+z1mDdO4Ti/Xcop367ZmDW63ty40Z+mB1mhZtz1ZFdZ2undC3cUONgxLCe2jKgDC98cM+3TotQR7ubtqbW6r/ztuu0wb30qnN9Ebr6e+lN286Wde8tEJ/mHvk9E4vDzf9ZFTkEWvUEsJ76G8/OXQ9mreHu/46c7hufGWlvNzdNKZvT900Jf6Ye+ad3C9UYT289cSC7dqTW3ZMG3iEB3jr9ZvG69LZy1RbZw+ZvticPkE+Oi8xQu8k79cvzhig37y7Tqn55Zpzy8mtrsvryHp4eyipb/0vGU4f0ktXjT/+dZ7tyc3N6NfH0E9wyoBwPTZ/u/75+Wbtyi7V47NGuWTnxp7+XrosKUbRPX07XajBjwh4AIAOYfH2HN3+5mq9d+uEYxohOVFpBeXam1umK8bFKLu4Uv+dv03/nb+t8Xyov5deuWGcpg0MV6CPh/7z9TZtTCtsXLvy5cYM/fLtdfJwM3r4kkTtyi7V7O926ryREZoyIFw7DpToF2+vVVVNne5+a622ZhbrNzMGKSWjSPd/vEmr9uarT6CPbpoSryvGxR4yQmOt1VMLd+iReds0fXAvPX9NkkMjL+tTC/TJunTdOb1/q+usJiSE6sZJ8Xp+8W75eLrp1EHhR/R8OriD5rKduYoJ8dOChvUopx82xW5YZJAuGBmpFxbvlqe7m4ZHBikxOki9Dnv+pTtzdOvrqxUR5KPLk2J0xtA+mpjQfH+qn57cV7e8tkrzN2dpxtA++u276+XhbvT3C4/cHOSgID9PvXfrBKWkFymjsFxpBRWqq7Ma0zdYw6OCjikkTx0Yrm1/P/uEftB2dzM6LzFCLy/dI0k6Y6hjUxMPigz21ed3T1Flda1DOwzeOLmfPlybrqv+94M2pBXqT+cN7bTh7qCLxkTpQHGFHmqy62ZXMzI6SAE+HnpvVar6BPronBEt7zTpbA9enHj0i9ChEfAAAA7Zl1u/rqdpP6q2Uldn9c/PN6uwvFr/+36XHr5kZJs/R0sObiByzYQ4DYkI1I4DxdpxoFQh/l4K8fdUVLBf43qtaybG6blFu/TEgu167pokLd6eozvnrNHwqCA9c9UYRQT51q+1SsnUve9v0Pu3TdQtryXLx9NNn981RbMX7dQz3+7Ugs0HtO1AsUL8vPTbMwfp++3Z+vtnm/Xkwh2aOSpSM0dFakhEoH777np9tiFDI6ODtHDLAT02f5t+1cqoQHVtnT5dn67H5m9XiL+Xbpl69NGi35w5SIu2Z2tndqn+cO7QI84P6NVDYT3qt+O/bGyMFmzOUnRPXw3s3eOIa3975iDtyinR4wu2y1rJzUiPXjaqcRv6ujqrB7/YosggHy38zSlHDSynDemtqGBfvbJ0r9IKKrRiT57+c+lIRQS1PuXN091NI2OCG3djPBFtESjOHxmpl5fu0aiY4OPa2CTI11PyPfq0Tql+85BxcSFasSdP5yZG6IZJccf8fB3NpUkxurSZTW26Eg93N01MCNVXm7J0zcS+zfbMAxxFwAMAHJW1Vje8slIebkZf/mJqm9//840ZSskoUlyonz5cm657zhrsUE+zgyqqa/Xt1myNjw85aqPowy3bmauefp4a1DBq2L9XQLNrfKT6aY03TI7XY/O3652V+/WXTzapX1gPvXzdOAX51f8A7uPprn9fkqhLZi/TjP9+p7KqWr1x03jFhvrpnxeO0JCIQD38xRZdPzFed59ev4nJ7af21+p9+Xpx8W69vXK/Xl22V94ebqqqrdN9Zw/WLVP76Xfvr9cTC3doaGSQzhreRxmF5fp8Q6ZySuo3IamprdPnGzKVVlCugb176J9XjFaAA2u9fDzd9fqN47U/v1z9ex0Z2oypX2O3dGeOyqpqtHhHjq4YF9ts8IkJ8dOnd05RaWWNtmQW6V+fb9EfP9yoMbE9FRvqp083ZGh9aqEeuXSkQ6NR7m5GV50cq4e/3KpV+/J12uBeunhM6xtWdERjYoN1+pBerfb/aku/P3eIXlu2V3+ZOazLjnh1RReMjNLGtCJdOa5zTENFx2Wsta6u4ZgkJSXZ5ORkV5cBAN3Kmn35uvCZpZKkBb+epoTwI4PA8aqprdOMxxbJw83o6SvH6Iz/LtIvTh/Q4tqxpjIKy/X68r2as2K/8kqrNGVAmF69YVyzP9QWV1Tr/77bpdGxwY07+FlrNenBhRoVG6xnrjrJoXoLy6o1+aGFKq6sUVSwrz74+cRmR2X+9mmKXli8W3+5YFjjbo8HWWtb/MG7uKJa81KytHh7ji4YFalTGtaaVVTX6vLnlmtHVrGGRQVp5Z48WSt5NflNf2J0kG6dlqDpg0+s6fjh3vhhr/4wd6N+f85g/fPzLXr9xvGaPKDl5ucHpeaX6ezHv9eAXj30xk0na8Zj38nfy0Of3TWl1SbrTeWWVGrCgwvl6+mueb+cesSUTwDojowxq6y1Sc2dYwQPAHBU769OlZeHm6pq6vTFhgzdMX1A47lXlu7R/M1ZumJcrGYM7S0PdzfV1lltSCvUnpxSBft5KsTfS9E9/RTSzOjaB2vStCu7VP/305M0oHeATh0UrteX79Wt0xKaHeUpLK/WV5sy9fHadC3dmSMr6YwhvRUT4qcXFu/Wu8mpuuywLeAXbsnSH+ZuVEZhhSKCfDR1YLg83d20L69M6YUVuq1f82vAmhPk56k7T+uvV5bu1Ws3jmtxyt19Zw/WzFGRGtGkz9RBrY2qBPh46qIx0brosJ0efTzdNfvqMbrw6aXKLanUL08fqAtGRiouzN/h2o/XxIT6MPfkwh0K8PbQuHjH1nRF9/TTPy4cobvmrNHFzy7V/rxyvXLDOIfDnVS/O+YzV45RWIA34Q4AHEDAAwC0qqK6Vh+vTdfZw/soNb9+WuDBgFdSWaP/fL1V5VW1+n57jiKDfDQ8Kkg/7M47Yrt8L3c3/eHcIbpmQt/GgFNZU6vH52/XyOggzWjYfOLGyf109Qs/6ON16bosKUar9ubr9eV7tTunVOkF5couqZS1Ut9QP91+an9dlhSjmBA/1TWEyr99lqKpA8PVJ8hHOSWV+ssnKfpkXboG9Q7QFeNi9ei8bfpqU6bOS4zU0ob1dxMSjj4a1dQtUxN085R+rQY1D3c3JUYHH9N9jyYiyFdL750uY9pmbZij4kL91CfQR5lFFTp3RESrO34e7oKRkfp2ywF9sCZNk/uHaaoDI3+HO/0YNyYBgO6MgAcA7exAUYUyCivaZAOIg6y1Wr0vX4nRwUddnF9SWaOU9CJtzihSdW2dfDzd5evprskDwpodjVqw+YCKKmp08Zhobcsq1t8/26w9OaWKC/PX2yv3q7iiRu/fNlF5pVV6eelupWQUacbQ3poyMFxDIwJUWF6j/NIqvfHDXt3/8SYt25mrP5w7RF9tytQry/YoraBcD148ojGwTOofqsF9AjT7u536bH2GvtuWrWA/Tw2PDNIpg8IVFeynaYPCNTI66JCQ4+Zm9PDFiTrr8UX6w9wNOjcxQn/9NEVllbX61RkDdeu0BLm7Gb23KlUvLdmj8xIjtWxnrsIDvJUQfuyjYK5a2+SK/mXGGE1MCNUHa9J02pAj2xMczV9mDlOAj4eunRjHmjAAcDICHgC0o++3Z+uuOWuUX1atayb01X1nD2ncofFEvL86Tb95d53OHxmpxy8f1WwIyC6u1C2vJWvt/gI1t/w6wMdD/7hwhC4YGXnYveu37Z7UP0wJvXro759t1hcbM3XzlHi9uHi3xsb11El96xvytrYF/PTBvfTC4t166Mst+nJTpiRpbFxP/fHcoZoy4Met+Y0xumFyvO55b73yS6t079mDdc2EvvLzOvr/suLC/PWbGYP09882a8GWAzqpb089eNGIQ9ouXDcxTn/9NEXr9hdo6c5cTeofSuhwwLmJEVqyM0fTBx97wAvw8dRfZrbc2gAA0HYIeADgJHfOWaNlO3N0zogIzRwVqeW78vSfr7dqYK8AnZcYqVeX7dWSHTl67PLRGhF95DotR5VW1ujhL7coxN9Ln6xLV4ifpx644NDd80ora3TDyyu1/UCxfnHaQCVGB2loZKD8vNxVXlWrA8WV+vNHG3XXnDVasDlLD5w/TD39vZRdXKnvtmXr5in95O5mFBXsq5ExwfpiY4ZiQnyVVlCuP59/5Nb6zXFzM7p5aj+NjQ/R/JQsnTW8T2MvucNdMiZaYT28NC4+VD28j+1/VddPitf+vDL179VDV43ve0TYvTQpWo/O26Y/f7xJOSWVLfZgw6FOG9JbPwxhqiQAdHTsogmgy0kvKNcHq1N14+R+bTI6djyS9+TpktnLNDQiUDuzS1RZUydJmjkqUv+6aIT8vDy0eHuOfv3uWh0ortSMob1167QEjY7teczP9cjXW/Xkwh16/7aJ+mpTpp5btEu/PH2g7j69fp1cTW2dbn41Wd9ty9ZzP01qcT1TTW2dnvl2px5fsF3uxuiUQeHq4e2hD9akaf6vpja2Dvi/73bqX19sUVxDP7wFvz7lmDbN6Age+HhTY+PpRb891Sm9/QAAcBZ20QTQbWQUlmvWc8u1L69MVTV1rTaFbit7c0vl6+WuXgH169estXroyy0KD/DWe7dNUG2d1byULPl4uuvs4X0aR9YmDwjT17+YphcW79Iry/bqq01ZGhMbrMn9w5QUF6KRMcEK9PFodfpgWkG5nlu0SxeMjNRJfXtqdEywckuq9N/52zR3TaqGRQWpoqpW32zN1j8uHN7qZhUe7m6667QBOnNYH72TvF+frEvXgeJKjYoJPqQv3DkjIvSvL7ZoT26Z/jZzWKcLd1L9NM1Xlu1RZJCvYkJab5oNAEBnwggegC4js7BCs55bptySKg2LCtTqfQVa8KtpiglxzuhMWVWNHl+wXc9/v1uh/l568+bx6t8rQAu3ZOmGl5P1t58M109P7uvQvUorazRnxT59uDZNKelFqmt4a/bycFOIn5diQ/30/LVJCjyscfVdc9boq02ZWvibUxQVXB9Uqmvr9MrSPUrek6+N6YVKLyjXHdMH6FdnHL2vXFO1dVbJe/IUGex7xPfw/CcXa39+mZbde5rLRklP1L++2KzwHt66aUo/V5cCAMAxaW0Ej4AHoNOrqqnTD7tzdf9Hm3SguFKv3jhOEUE+mv6f7zRtYLhm/9SxBtaOqquzmrc5S3/7NEWp+eW6aHSUFm3PkWT12o3j9cu316q8ulbzfzXtqDtaNqekskZr9uUrJb1IeWVVOlBUqblr0vTn84bqhsnxjdetTy3QBU8t0V3T+7c6UllVU3dM29o7YntWscqqatt0J1AAAOAYpmgC6JIyCsv10BdbtGDLARVX1CjQx0MvXz9WYxrWsd1+aoL+8/U2Ld2Ro4n9j957y1qrNfsLNHd1miKDfTVjWG8lhPdoPF9YVq0P1qTqlaV7tCe3TAnh/nr7lpM1vl+odmaX6Mr/LdfMp5eoqqZOT1wx+rjCnST18PbQlAHhh+wsuTe3VK8t36vrJsY1bhry1MIdCvL11C3TElq9X1uHO0mH7EoJAAA6DgIegE7rTx9u0uId2To/MVIzhvXR5P5hh0wXvGlKP72dvF8PfLJJn945pdWg88m6dD3//S6tSy2Ut4ebKmvq9NCXW9Qv3F8+Hu5KLyxXQVl94+4xscH61YxBOnt4n8YQlxDeQ2/fMkFX/m+5wgN9dN6IiDb9Wq+dGKe731qrxTtyNHVguLZnFevrlCzdfdqAY95lEgAAdF38VACgU0rek6f5m7P02zMH6fZT+zd7jY+nu/507lDd8toqXfDUYv3n0pHNbst/cFfIhHB//W3mMF00JloF5dWan5Klb7YekLsxGtM3WBFBvprcP6zFaYlxYf5a+JtTVGdtmzejPmt4H4X18NKry/Zo6sBwPfvtTvl5ueu6iXFt+jwAAKBzI+AB6HSa7lJ5/aS4Vq+dMayPnr8mSb+fu0Ezn16i26Yl6NZTEhpHvd5J3q9/fbHliAbh/t4eunZinK49xgDl4+mcDUe8Pdx1xbhYPfXNDi3dmaOP1qXruolx6unv5ZTnAwAAnRMBD0Cn883WA1q5J19/+8lw+Xkd/W3s9KG9NTYuRH/7LEVPfbNDryzdo0uTYtS/Vw/98cMNmjIgTI9cOrLNR93a2pXjY/XMtzv1s1dXyc1IN7P7IwAAOAwBD4DT1NZZGemEg9OHa9L05cZMTeofqulDeuvhL7eqb6ifZo2NcfgeQX6e+s+lI3XV+Fi9vHSPXl22RzV1ViNjgjX76pOcshFJW4sI8tWMob31xcZMzRoboz5BPq4uCQAAdDBObZNgjDlL0uOS3CU9b6198LDzQZJelxSr+rD5H2vtS63dkzYJQOeQW1Kpi59dquKKGk3qH6YpA8IUH+avgz27B/cJlL8Dm4O8tmyP/vTRJgX6eKiooqbx+BNXjNYFIyOPu76sogrNS8nSeYkRCvbrPNMc1+4v0C/eWqNXbhinvqH+ri4HAAC4gEv64Blj3CVtk3SGpFRJKyVdYa1NaXLN7yUFWWt/Z4wJl7RVUh9rbVVL9yXgAa6zN7dUMT39jjoiV1VTp6tf+EFr9xfozGF9tGxnrnJKKg+5pn+vHvr0zsmtrll7YfFu/e3TFJ0+pLeevmq09ueV6+uUTBWV1+ieMwd1+CmVAAAAzuCqPnjjJO2w1u5qKOItSTMlpTS5xkoKMMYYST0k5UmqOfxGAFzvo7VpuvuttUfsWllVU6drX1yhPkE+uuu0AYoL9dP9H2/Sit15enzWKM0cFSVrrbZkFiu7uD7k7c0r058+3KjHF2zX784a3OzzvbykPtydPbyPHp81Wl4eburfq4f692p+x0wAAAA4N+BFSdrf5HGqpPGHXfOUpI8lpUsKkHS5tbbOiTUBOA7r9hfonvfWyxjppSV7dOPk+MaRt7lrUrVsV6483Y0+XpeucXEhWrYrVz8/JUEzR0VJkowxGhIRqCFNWsNtSC3Qc4t26ezhfZQYHXzI832z9YD++mmKZgztrSevGC2P42wYDgAA0N0486em5uZOHT4f9ExJayVFShol6SljTOARNzLmFmNMsjEmOTs7u63rBNCKrKIK3fxqssJ6eOvxWaOVU1Kpj9emS6rfRGX2d7s0LDJQS+6drusmxmn1vnzNGNpbv5kxqNX7/uHcoQrr4aV73luvqpoff6+z40Cx7npzjQb3CdRjs0YR7gAAAI6BM39ySpXUdIu7aNWP1DV1vaQPbL0dknZLOmK+lrX2OWttkrU2KTw83GkFA11FaWWNNqQWnvB9KqprdcurySqtrNEL1yXp/MQIDYkI1POLd8laqy83Zmp3Tql+fkp/9Qrw0Z/OG6pVfzpDz1590lHXxwX5euqfF47Qlsxi/eqdtZq7JlUr9+TpxleS5e3ppv9dm+RQCwQAAAD8yJkBb6WkAcaYeGOMl6RZqp+O2dQ+SadJkjGmt6RBknY5sSagy6urs/rZa6t0/lOL9fryvSd0r399vlnrUgv16OWjNLhPoIwxunlKvLZllejbbdl6+psd6hfmr7OG92n8nB7eHnJ3cPOT04b01vWT4vTFxkz98u11unT2MmUUVOj/fnqSooJ9T6h2AACA7shpvx631tYYY+6Q9JXq2yS8aK3dZIy5teH8bEl/k/SyMWaD6qd0/s5am+OsmoDuYPainVq8I0cJ4f7644cb5eFmNGtc7DHf5+tNmXpl2V7dODleZw77McCdlxiph77covve36DMogo9fHGiw4GuOfefP0z3nT1E+/LKtONAiWJD/DQ08oiZ2gAAAHCAU+c/WWs/l/T5YcdmN/k4XdIMZ9YAdCer9+Xrka+36dwREXr08pG69bVVum/uBrm5GV2W5HhT8PSCct3z/noNjwrUPWcdupbOy8NN102M10NfblFEkI9+MjrqhOv+cYfMHid8LwAAgO6M3QuALqKoolp3zVmjPoE++udFI+Tt4a5nrz5Jk/uH6Xfvr9dLS3Yfcn1VTZ02pBYessGJJOWVVukXb61VdU2dnrxijLw9juxTd+W4WEUE+egXpw+QlwdvIwAAAB0FOxgAnVxpZY3mrNin57/freySSr176wQF+XpKknw83fW/a5L0i7fW6i+fpCizqEK/O3OwFu/I0V8+2aSd2aUK8vXUOSP6aHx8qOZtztLXmzJVXWv12OWjFB/m3+xzBvl5atl9p7XnlwkAAAAHGGsP71zQsSUlJdnk5GRXlwE43Y4DxdqYViQfT3f5erlrcJ8A9Q70OeSarzZl6p731quwvFoT+oXq7tMH6OR+oUfcq7bO6v6PN+r15fvUL9xfu7JL1TfUTzdNjteqvfn6OiVLZVW1Cvbz1EWjo3X52BgN6hPQXl8qAAAAjoExZpW1Nqm5c4zgAR2QtVY3vpKsvblljcfiw/w175dTG/vC1dTW6a+fpKh3oLdevn6sRsf2bPF+7m5Gf5s5XH0CffTC4t2656xBunFyvLw93PXTCXEqq6rR5owiDY8KanZKJgAAADoHAh7gYh+tTVO/sB4aER3UeGz1vgLtzS3TH84Zokn9w7Rid64e+CRFn2/M1AUjIyVJX6dkKa2gXLOvPqnVcHeQMUZ3TB+g20/tL2MO3fXSz8tDJ/UNadsvDAAAAO2O3REAF/p8Q4bufmut7n57jerqfpwuPXdNqnw83TRrXIyGRgbqmglxSgj31zPf7NDBadUvLN6t2BA/nTG09zE95+HhDgAAAF0HAQ9wkorqWl30zBLd8PJKvbVin7KLKw85vze3VL97b71C/L20K7tUC7YckFS/u+Wn6zN0xtA+CvCp3yzFzc3otlP6a0tmsb7ZekBr9xdo1d58XTcx7oR60AEAAKBrIeABTvLlxkyt3legjWmFuveDDRr3z/m66ZVkrdqbr4rqWt3+5mq5uRnN/flERQX76rlFOyVJ323LVkFZtS46rL/czFGRigr21dPf7NQLi3crwNtDl411vLcdAAAAuj4CHuCggrIq/fPzzSqprHHo+neS9ys2xE/L7ztNX9w9Rbef0l/Je/N08bNLdep/vtXGtCI9culI9Q31142T47VyT75W78vX3DWpCvX30uQBYYfcz9PdTbdM7adVe/P16fp0XT42Rj28WUYLAACAHxHwAAe9sHi3nlu0S59vyDjqtfvzyrR0Z64uPSlabm5GQyIC9ZszB2npvdP15/OGysvDTXdN76/TG9bPXT42RkG+nnr0622av/mAzh8ZKU/3I/95Xj42RmE9vGQkXTsxro2/QgAAAHR2/PofcEBFda3e/GGfJGnh5gO6LOnHqZH5pVX69bvrdOu0BI2Lr9+J8t1VqTJGuvik6EPu4+floRsmx+uGyfGHHPf39tDVJ8fq6W/qp2leeNj0zIN8PN31jwtHKC2/XDEhfm329QEAAKBrYAQPcMDH69KVW1qlwX0C9P32bFXW1Dae+2htmhZuOaCfv7FKmYUVqq2zei95vyb3D1NksK/Dz3HtxDh5ebipX5i/Epu0TDjcmcP6HBEQAQAAAImABxyVtVYvLdmjQb0D9NszB6m0qlY/7MprPD93TZpiQnxVVlW/ccqibdlKL6w4ZJTPEb0CfPTIpSP19wuH08oAAAAAx4WABxzF8l152pxRpOsnxWlS/zD5eLppYUNLg53ZJVqXWqhrTo7TQxcnatXefN05Z42CfD2PuT+dJJ0/MlITE8KOfiEAAADQDAIecBQvLdmtnn6e+snoKPl4umtSQpjmb86StVYfrUmTm5EuGBWp80dG6vpJcSqprNFPRkXKx9Pd1aUDAACgm2GTFaAV+/PKNH9zlm47JaExsE0f0ksLthzQtqwSzV2bpkn9w9Q70EeS9Ptzhiimp58uGBXpyrIBAADQTTGCB7Ti/dWpspKuGt+38dhpg+unXv77qy3an1eun4z6ccdLT3c33TA5XmE9vNu7VAAAAICAB7TEWqtP1qVrXFzIIbth9gny0bDIQM3ffEC+nu46a3gfF1YJAAAA/IiAB7QgJaNIO7NLm51uedrgXpKkGcN6y9+bmc4AAADoGAh4QAs+WZchDzejs4dHHHHu7BER8nQ3mjU21gWVAQAAAM1j6AFoxsHpmZMHhCnE3+uI80MiArXhgTPZKRMAAAAdCiN4gKS6Oqu80qrGx6v35SutoFwXjGx5N0zCHQAAADoaAh66vQNFFbrq+R809h/z9fz3uxpG7zLk7eF2XM3KAQAAAFdhiia6tUXbsvXLt9eqrKpWSX176u+fbdaa/QX6YVeepg/upQAfT1eXCAAAADiMgIduqbq2To/O26Znv92pQb0D9NSVo9W/Vw/N/m6X/v3VFtVZtTo9EwAAAOiICHjodtIKynXXnDVatTdfV4yL0Z/PGyZfr/r1dLedkqCR0UH6alOmTm1ohQAAAAB0FgQ8dBvWWn28Ll1//miTamrr9PisUZo5KuqI6yb2D9PE/mEuqBAAAAA4MQQ8dAsp6UV64ONNWrEnT4nRQXp81mjFh/m7uiwAAACgTRHw0CVZa7U7p1Tfb8/Rom3Z+mbrAQX7eelfF43QZUkxcnczri4RAAAAaHMEPHQ5WzKL9Me5G5W8N1+S1DfUTzdP6aefn9JfQX7sigkAAICui4CHLqO8qlZPLNyu/y3apQAfD/3pvKE6fUgv9Q1lKiYAAAC6BwIeuow73lytBVsO6NKTonXfOUMU4u/l6pIAAACAdkXAQ5ewKb1QC7Yc0K/PGKg7Txvg6nIAAAAAl3BzdQFAW/jfol3y93LXNRPjXF0KAAAA4DIEPHR6aQXl+mR9hmaNi1WQL5uoAAAAoPsi4KHTe3HxbknSDZPjXVwJAAAA4FoEPHRqheXVemvFPp2fGKGoYF9XlwMAAAC4FAEPnZa1Vs9/v0ulVbW6ZWqCq8sBAAAAXI5dNNHp1NTW6fONmZr97U6lZBTp9CG9NTQy0NVlAQAAAC5HwEOnsjunVLe9vkpbMovVL9xfD1+cqJmjI11dFgAAANAhEPDQaXy9KVO/fmed3N2NnrpytM4eHiF3N+PqsgAAAIAOg4CHDi2vtEqr9uZr4ZYDmrNinxKjg/TMVWMU3dPP1aUBAAAAHQ4BDx3Skh05evjLLVqXWihJ8nJ301XjY/Wn84bKx9PdxdUBAAAAHRMBDx3KruwS/fPzzZq/+YCie/rqt2cO0ti4ECVGBxHsAAAAgKMg4KFDKCir0uMLtuu1ZXvl4+mue84apBsmxRPqAAAAgGNAwINL1dVZvbZ8rx6dt03FFdW6fGysfnXGQIUHeLu6NAAAAKDTIeDBZQrLq/Xrd9Zp/uYsTeofqj+eO1RDIuhnBwAAABwvAh5cYktmkW59bZVS88t1//lDdd3EOBlDywMAAADgRBDw0G42ZxRpfkqWvt+eo9X78hXi76W3bjlZSXEhri4NAAAA6BIIeGgXO7NLdP6Ti1VTZzUiKki3TO2n6ybFqVeAj6tLAwAAALoMAh7axeLtOaqps/r6l1M1sHeAq8sBAAAAuiQ3Z97cGHOWMWarMWaHMebeZs7/1hiztuHPRmNMrTGG+Xpd0IrdeYoM8tGAXj1cXQoAAADQZTkt4Blj3CU9LelsSUMlXWGMGdr0Gmvtv621o6y1oyTdJ+k7a22es2qCa1hr9cPuXI3vF8pGKgAAAIATOXMEb5ykHdbaXdbaKklvSZrZyvVXSJrjxHrQDgrKqvSXTzapqKK68diunFLllFRpXDyDswAAAIAzOTPgRUna3+RxasOxIxhj/CSdJen9Fs7fYoxJNsYkZ2dnt3mhaDtfb8rSS0v26N3k1MZjP+yqH5QdT8ADAAAAnMqZAa+5uXi2hWvPl7SkpemZ1trnrLVJ1tqk8PDwNisQbW9taoEk6d3k/bK2/j/3it25CuvhrfgwfxdWBgAAAHR9zgx4qZJimjyOlpTewrWzxPTMLmF9aoE83Iy2ZBZrQ1phw/q7PI3vF8L6OwAAAMDJnBnwVkoaYIyJN8Z4qT7EfXz4RcaYIEnTJH3kxFrQDiqqa7Ulo1izxsXI28NN7yTvV2p+uTIKK5ieCQAAALQDp/XBs9bWGGPukPSVJHdJL1prNxljbm04P7vh0gslfW2tLXVWLWgfKRlFqqmzmtw/TCUVNfp4bboG9wmUJI2PD3VxdQAAAEDX59RG59bazyV9ftix2Yc9flnSy86sA+1j/f4CSdLImGAF+njqw7Xpemz+dgX7edL/DgAAAGgHTg146F7WpxYqPMBbfQJ91DvAR9E9fZWaX64ZQ3vLzY31dwAAAICzOXMNHrqZdakFGhkdJGOM3NyMLjkpWpLofwcAAAC0EwIe2kRRRbV2ZpdqZHRw47Erx8Vq2sBwnT0iwnWFAQAAAN0IAQ/Hpbq2TinpRY2PN6YWSpISY4Ibj/UK9NErN4xTVLBve5cHAAAAdEsEPByXV5ft1TlPfK8vN2ZKktYdDHhRQa4sCwAAAOjWCHg4Lh+vTZMk3fvBemUVVWh9aoH6hvqpp7+XiysDAAAAui8CHo7Z3txSrUst1BXjYlRZXadfvbNW6/YXKLHJ+jsAAAAA7Y82CThmn67PkCTdfmp/JUYH674PNkiSbohmeiYAAADgSozg4Zh9uj5DY2KDFd3TT7PGxmjG0N6S6hucAwAAAHAdRvBwTHYcKNHmjCL9+byhkiRjjP596UiduiFDJ8X2dHF1AAAAQPdGwMMx+XR9uoyRzk38sbddkK+nrhgX68KqAAAAAEhM0cQxsNbqk3XpGh8fot6BPq4uBwAAAMBhCHhw2JbMYu3MLtV5iZGuLgUAAABAMwh4cNhXmzLlZqSzh/dxdSkAAAAAmkHAg8O+356jEdHBCu3h7epSAAAAADSDgAeHFFVUa+3+Ak3pH+bqUgAAAAC04Ki7aBpj4iXdKSmu6fXW2gucVxY6muU7c1VbZzV5AAEPAAAA6KgcaZPwoaQXJH0iqc6p1aDDWrwjR76e7hodG+zqUgAAAAC0wJGAV2GtfcLplaBDW7w9R+P7hcjbw93VpQAAAABogSMB73FjzP2SvpZUefCgtXa106pCh5JWUK5dOaW6cjzNzAEAAICOzJGAN0LSTyVN149TNG3DY3QDi7dnS5KmDAh3cSUAAAAAWuNIwLtQUj9rbZWzi0HH9P32HPUK8NbA3j1cXQoAAACAVjjSJmGdpGAn1wEX+3hdum59bZW+2XpAdXW28XhdndXSnbma3D9MxhgXVggAAADgaBwZwestaYsxZqUOXYNHm4QuZPa3O5WSUaQvN2UqPsxfl5wUrcF9AlRbZ5VXWkV7BAAAAKATcCTg3e/0KuBSGYXlSsko0m9mDFRMiJ9eXrpH//5q6yHXTKbBOQAAANDhtRrwjDFukp621g5vp3rgAgs2H5AknTW8j/r3CtDMUVEqLKvWzpwS7TxQIl8vd/UK9HFxlQAAAACOptWAZ62tM8asM8bEWmv3tVdRaF8LtxxQbIifEsJ/3EQlyM9TY2J7akxsTxdWBgAAAOBYODJFM0LSJmPMCkmlBw+yBq9rKK+q1ZIdObpiXCybqAAAAACdnCMB7y9OrwIus2RHjipr6nT6kN6uLgUAAADACTpqwLPWftcehcA1Fmw5IH8vd42LD3F1KQAAAABO0FH74BljTjbGrDTGlBhjqowxtcaYovYoDs5lrdXCLVmaOjBcXh6OtEQEAAAA0JE58lP9U5KukLRdkq+kmxqOoZPblF6krKJKTR/cy9WlAAAAAGgDjqzBk7V2hzHG3VpbK+klY8xSJ9eFdrBg8wEZI51KwAMAAAC6BEcCXpkxxkvSWmPMw5IyJPk7tyy0h++3ZysxKkhhPbxdXQoAAACANuDIFM2fNlx3h+rbJMRIutiZRcH5yqtqtS61QCcnhLq6FAAAAABtxJFdNPc2fFghWiZ0Gav35au61urkfgQ8AAAAoKtg68RuavmuXLkZKalvT1eXAgAAAKCNEPC6qR925WlEVJACfDxdXQoAAACANuJIH7xLHTmGzqO8qlZr9xcwPRMAAADoYhwZwbvPwWPoJNbsy1dVbZ3G9wtxdSkAAAAA2lCLm6wYY86WdI6kKGPME01OBUqqcXZhcJ7lu/Pq19/FEfAAAACArqS1XTTTJSVLukDSqibHiyX90plFwbmW78rV8KggBbL+DgAAAOhSWgx41tp1ktYZY9601lZLkjGmp6QYa21+exWItlVRXau1+wp07cS+ri4FAAAAQBtzZA3ePGNMoDEmRNI6SS8ZYx51cl1wkjX7ClRVW8cGKwAAAEAX5EjAC7LWFkm6SNJL1tqTJJ3u3LLgLI3971h/BwAAAHQ5jgQ8D2NMhKTLJH3q5HrgZIt35GhYZJCCfFl/BwAAAHQ1jgS8v0r6StJOa+1KY0w/SdudWxacIbOwQqv25mvG0N6uLgUAAACAE7S2i6YkyVr7rqR3mzzeJeliZxYF5/h8Q4Yk6ZzECBdXAgAAAMAZjjqCZ4wZaIxZYIzZ2PA40RjzR+eXhrb2+YYMDe4ToITwHq4uBQAAAIATODJF83+S7pNULUnW2vWSZjmzKLS9zMIKJe/N17kjGL0DAAAAuipHAp6ftXbFYcdqHLm5MeYsY8xWY8wOY8y9LVxzijFmrTFmkzHmO0fui2P3xUamZwIAAABd3VHX4EnKMcYkSLKSZIy5RFLG0T7JGOMu6WlJZ0hKlbTSGPOxtTalyTXBkp6RdJa1dp8xptexfwlwxGfrmZ4JAAAAdHWOjODdLun/JA02xqRJ+oWkWx34vHGSdlhrd1lrqyS9JWnmYddcKekDa+0+SbLWHnC0cDju4PTMc5ieCQAAAHRpjuyiuUvS6cYYf0lu1tpiB+8dJWl/k8epksYfds1ASZ7GmG8lBUh63Fr7qoP3h4Map2cS8AAAAIAu7agBzxgTKul+SZMlWWPMYkl/tdbmHu1Tmzlmm3n+kySdJslX0jJjzHJr7bbDarhF0i2SFBsbe7SS0YS1Vh+uSdOg3gHq34vpmQAAAEBX5sgUzbckZau+990lDR+/7cDnpUqKafI4WlJ6M9d8aa0ttdbmSFokaeThN7LWPmetTbLWJoWHhzvw1Dho2a5crUst1NUT+rq6FAAAAABO5kjAC7HW/s1au7vhz98lBTvweSslDTDGxBtjvFTfWuHjw675SNIUY4yHMcZP9VM4Nx9D/TiKZ7/dqbAe3rr0pGhXlwIAAADAyRwJeN8YY2YZY9wa/lwm6bOjfZK1tkbSHZK+Un1oe8dau8kYc6sx5taGazZL+lLSekkrJD1vrd14vF8MDrU+tUDfb8/RTVPi5ePp7upyAAAAADiZsfbwZXENJ4wpVv2aOSPJX1Jtwyl3SSXW2sB2qfAwSUlJNjk52RVP3enc+toqLd2ZoyX3TleAj6erywEAAADQBowxq6y1Sc2da3GTFWttgPNKgrPtOFCir1Iydfsp/Ql3AAAAQDfhyBRNdEL/991OeXu46fpJca4uBQAAAEA7IeB1UQu3HNA5IyIU2sPb1aUAAAAAaCcEvC4op6RSuaVVGhYZ5OpSAAAAALQjRxqdhzRzuNhaW+2EetAGtmYWS5IG92EZJQAAANCdODKCt1r1zc23Sdre8PFuY8xqY8xJziwOx+dgwBvYm4AHAAAAdCeOBLwvJZ1jrQ2z1oZKOlvSO5J+LukZZxaH47Mtq1gh/l4K6+Hl6lIAAAAAtCNHAl6Stfargw+stV9LmmqtXS6JHTw6oK1ZxRrUO0DGGFeXAgAAAKAdORLw8owxvzPG9G34c4+kfGOMu6Q6J9eHY1RXZ7Uts1iDWH8HAAAAdDuOBLwrJUVL+lDSR5JiG465S7rMaZXhuKQVlKu0qpb1dwAAAEA3dNRdNK21OZLubOH0jrYtBydqW1b9BiuD+vRwcSUAAAAA2psjbRIGSvqNpLim11trpzuvLByvLeygCQAAAHRbRw14kt6VNFvS85JqnVsOTtS2rGJFBfsqwMfT1aUAAAAAaGeOBLwaa+2zTq8EbWJrZrEG9mZ6JgAAANAdObLJyifGmJ8bYyKMMSEH/zi9Mhyz6to67cou1aA+ga4uBQAAAIALODKCd23D379tcsxK6tf25eBE7MkpVVVtHRusAAAAAN2UI7toxrdHIThxW7PYYAUAAADozloMeMaY6dbahcaYi5o7b639wHll4XhsyyyWu5tRQjgjeAAAAEB31NoI3jRJCyWd38w5K4mA18FsySxWXKiffDzdXV0KAAAAABdoMeBZa+9v+PCv1trdTc8ZY5i22QFtzSrWsEg2WAEAAAC6K0d20Xy/mWPvtXUhODE5JZXam1umkdHBri4FAAAAgIu0tgZvsKRhkoIOW4cXKMnH2YXh2CTvyZckJcXRwQIAAADorlpbgzdI0nmSgnXoOrxiSTc7sSYch+Q9efL2cNPwKKZoAgAAAN1Va2vwPpL0kTFmgrV2WTvWhOOwck+eRsYEy9uDDVYAAACA7sqRNXi3GmOCDz4wxvQ0xrzovJJwrMqqarQxvUhj43q6uhQAAAAALuRIwEu01hYcfGCtzZc02mkV4Zit3Veg2jrL+jsAAACgm3Mk4LkZYxqHhowxIWp97R7a2co9+TJGGhPLCB4AAADQnTkS1B6RtNQY857qG5xfJukfTq0KxyR5b54G9Q5QkK+nq0sBAAAA4EJHHcGz1r4q6WJJWZKyJV1krX3N2YXBMTW1dVq9N1/j4pmeCQAAAHR3jkzRlKQQSaXW2iclZRtj4p1YE47B5oxilVbVsv4OAAAAwNEDnjHmfkm/k3RfwyFPSa87syg4buWePEliB00AAAAADo3gXSjpAkmlkmStTZcU4Myi4LjkvXmKCvZVRJCvq0sBAAAA4GKOBLwqa61V/QYrMsb4O7ckOMpaq5V78pXE6B0AAAAAORbw3jHG/J+kYGPMzZLmS/qfc8uCI7KKKpVdXKlRMcGuLgUAAABAB3DUNgnW2v8YY86QVCRpkKQ/W2vnOb0yHNWGtEJJ0oioIBdXAgAAAKAjcKhheUOgI9R1MBvTCmWMNCQi0NWlAAAAAOgAWgx4xphiNay7O/yUJGutJVW42Kb0QiWE95C/t0M5HQAAAEAX12IysNayU2YHtyGtUBP6hbq6DAAAAAAdhEONzo0xk40x1zd8HEajc9c7UFyhrKJKDWf9HQAAAIAGx9Po3Es0One5TWlFkkTAAwAAANCIRued1MaGHTSHRbIUEgAAAEA9Gp13UhvSChUf5q8AH09XlwIAAACgg6DReSe1Kb2I6ZkAAAAADkGj804or7RKaQXlumZCX1eXAgAAAKADOWrAa5iSudBaO88YM0jSIGOMp7W22vnloTkH19+NYAQPAAAAQBOOTNFcJMnbGBOl+umZ10t62ZlFoXUb0w9usELAAwAAAPAjRwKesdaWSbpI0pPW2gslDXVuWWjNxrRCxYb4KciPDVYAAAAA/MihgGeMmSDpKkmfNRw76tROOM/GtCINj6I9AgAAAIBDORLw7lZ9k/O51tpNxph+kr5xblloye6cUu3LK9PomJ6uLgUAAABAB+PILpqLVL8O7+DjXZLucmZRaNl7q/bLzUgXjIp0dSkAAAAAOhhHRvDQQdTWWb23KlWnDOql3oE+ri4HAAAAQAfj1IBnjDnLGLPVGLPDGHNvM+dPMcYUGmPWNvz5szPr6ewWbc9WVlGlLkuKdnUpAAAAADqgFgOeMeahhr8vPZ4bG2PcJT0t6WzV77p5hTGmud03v7fWjmr489fjea7u4t3k/Qrx99L0wb1dXQoAAACADqi1EbxzjDGeqt9g5XiMk7TDWrvLWlsl6S1JM4/zXt1eXmmV5qVk6SejouTlwcxaAAAAAEdqLSl8KSlHUqIxpsgYU9z0bwfuHSVpf5PHqQ3HDjfBGLPOGPOFMWaY46V3Lx+tTVN1rdVlY5meCQAAAKB5LQY8a+1vrbVBkj6z1gZaawOa/u3AvU1ztz3s8WpJfa21IyU9KenDZm9kzC3GmGRjTHJ2drYDT921WGv19sr9SowO0uA+9L8DAAAA0LyjzvWz1s40xvQ2xpzX8CfcwXunSopp8jhaUvph9y6y1pY0fPy5JE9jTFgzNTxnrU2y1iaFhzv69F1HTkmVtmQW67zECFeXAgAAAKADO2rAa9hkZYWkSyVdJmmFMeYSB+69UtIAY0y8McZL0ixJHx927z7GGNPw8biGenKP7Uvo+jIKyyVJcaH+Lq4EAAAAQEd21Ebnkv4oaay19oAkNYzgzZf0XmufZK2tMcbcIekrSe6SXrTWbjLG3NpwfrakSyTdZoypkVQuaZa19vBpnN1eekGFJCky2NfFlQAAAADoyBwJeG4Hw12DXDnYP69h2uXnhx2b3eTjpyQ95ci9urODI3h9gmhuDgAAAKBljgS8L40xX0ma0/D4ch0W2uBcGYUV8vJwU6i/l6tLAQAAANCBHTXgWWt/a4y5SNJk1e+M+Zy1dq7TK0OjjMIKRQT5qGG5IgAAAAA0y5ERPFlrP5D0gZNrQQsyCsoVwfRMAAAAAEfh0Fo6uFb9CB4brAAAAABoHQGvg6uts8osqmAEDwAAAMBROdIH7zxjDEHQRXJKKlVbZxVBiwQAAAAAR+FIcJslabsx5mFjzBBnF4RDpRfUt0iIZAQPAAAAwFEcNeBZa6+WNFrSTkkvGWOWGWNuMcYEOL06KKOwvsk5PfAAAAAAHI2jDcuLJL0v6S1JEZIulLTaGHOnE2uDmo7gMUUTAAAAQOscWYN3gTFmrqSFkjwljbPWni1ppKTfOLm+bi+zsEI+nm4K9vN0dSkAAAAAOjhH+uBdIum/1tpFTQ9aa8uMMTc4pywclFFYocggX5qcAwAAADgqR6ZoZhwe7owxD0mStXaBU6pCo/TCctbfAQAAAHCIIwHvjGaOnd3WhaB5GQU0OQcAAADgmBanaBpjbpP0c0kJxpj1TU4FSFri7MIg1dTW6UBxhSKDGcEDAAAAcHStrcF7U9IXkv4l6d4mx4uttXlOrQqSpAPFlaqzYgQPAAAAgENaC3jWWrvHGHP74SeMMSGEPOfLKKxvkRDBGjwAAAAADjjaCN55klZJspKabuNoJfVzYl2QlF5Q3+Q8gimaAAAAABzQYsCz1p7X8Hd8+5WDpjILGwIeUzQBAAAAOKC1TVbGtPaJ1trVbV8OmkovLJe/l7sCfRxpVwgAAACgu2stOTzSyjkraXob14LDZBRUqE+QD03OAQAAADiktSmap7ZnIThSRmG5IoOZngkAAADAMa1N0ZxurV1ojLmoufPW2g+cVxYkKaOwQoP6BLi6DAAAAACdRGtTNKdJWijp/GbOWUkEPCeqqqlTdkml+rDBCgAAAAAHtTZF8/6Gv69vv3JwUGp+mayVopmiCQAAAMBBbke7wBgTaox5whiz2hizyhjzuDEmtD2K687WpRZIkhJjglxbCAAAAIBO46gBT9JbkrIlXSzpkoaP33ZmUZBW7y1QD28PDejFGjwAAAAAjnGkwVqItfZvTR7/3RjzEyfVgwZr9udrZEyQ3N1okQAAAADAMY6M4H1jjJlljHFr+HOZpM+cXVh3VlZVo80ZxRod09PVpQAAAADoRFprk1Cs+t0yjaRfSXq94ZSbpBJJ9zu9um5qQ2qhauusxvQNdnUpAAAAADqR1nbRZPGXi6zeVyBJGsUIHgAAAIBj4MgaPBljekoaIMnn4DFr7SJnFdXdrdmXr/gwf4X4e7m6FAAAAACdyFEDnjHmJkl3S4qWtFbSyZKWSZru1Mq6KWutVu8r0NQBYa4uBQAAAEAn48gmK3dLGitpr7X2VEmjVd8qAU6Qml+unJJKje7L9EwAAAAAx8aRgFdhra2QJGOMt7V2i6RBzi2r+1q9L1+SNDom2LWFAAAAAOh0HFmDl2qMCZb0oaR5xph8SenOLKo7W7OvQL6e7hrchz1uAAAAABybowY8a+2FDR8+YIz5RlKQpC+dWlU3tmZfvhKjg+Th7sjgKgAAAAD8yKEUYYwZY4y5S1KipFRrbZVzy+qeKqprtSm9SGNYfwcAAADgOBw14Blj/izpFUmhksIkvWSM+aOzC+uOdhwoUU2dVWJUkKtLAQAAANAJObIG7wpJo5tstPKgpNWS/u7MwrqjjMIKSVJUT18XVwIAAACgM3JkiuYeNWlwLslb0k6nVNPNZRaWS5L6BPkc5UoAAAAAOFKLI3jGmCclWUmVkjYZY+Y1PD5D0uL2Ka97ySiskIebUZi/t6tLAQAAANAJtTZFM7nh71WS5jY5/q3TqunmMgsr1DvQR25uxtWlAAAAAOiEWgx41tpXDn5sjPGSNLDh4VZrbbWzC+uOMosqFMH0TAAAAADHyZFdNE+RtF3S05KekbTNGDPVuWV1T5mFFepNwAMAAABwnBzZRfMRSTOstVslyRgzUNIcSSc5s7DuxlqrjMIKTR/cy9WlAAAAAOikHNlF0/NguJMka+02SZ7OK6l7KiqvUXl1LTtoAgAAADhujozgrTLGvCDptYbHV6l+4xW0oYyi+hYJEUH0wAMAAABwfBwJeLdKul3SXZKMpEWqX4uHNnSwyTkjeAAAAACOV6sBzxjjJmmVtXa4pEfbp6TuKbMh4LGLJgAAAIDj1eoaPGttnaR1xpjYdqqn28oorJCbkcIDaHIOAAAA4Pg4MkUzQtImY8wKSaUHD1prL3BaVd1QZmG5wgO85enuyL43AAAAAHAkRwLeX4735saYsyQ9Lsld0vPW2gdbuG6spOWSLrfWvne8z9eZZRRWqA8brAAAAAA4AS0GPGOMj+o3WOkvaYOkF6y1NY7e2Bjjrvrm6GdISpW00hjzsbU2pZnrHpL01bGX33VkFlaoX7i/q8sAAAAA0Im1Nh/wFUlJqg93Z6u+4fmxGCdph7V2l7W2StJbkmY2c92dkt6XdOAY79+lZBZV0CIBAAAAwAlpbYrmUGvtCElq6IO34hjvHSVpf5PHqZLGN73AGBMl6UJJ0yWNbelGxphbJN0iSbGxXW+/l5LKGhVX1NAiAQAAAMAJaW0Er/rgB8cyNbMJ08wxe9jjxyT9zlpb29qNrLXPWWuTrLVJ4eHhx1FKx0aLBAAAAABtobURvJHGmKKGj40k34bHRpK11gYe5d6pkmKaPI6WlH7YNUmS3jLGSFKYpHOMMTXW2g8drL9LOBjw+gQS8AAAAAAcvxYDnrXW/QTvvVLSAGNMvKQ0SbMkXXnYc8Qf/NgY87KkT7tbuJOkjMJySWINHgAAAIAT4kibhONira0xxtyh+t0x3SW9aK3dZIy5teH8bGc9d2dzcASvVyBNzgEAAAAcP6cFPEmy1n4u6fPDjjUb7Ky11zmzlo4so6hCof5e8vE80UFTAAAAAN1Za5usoJ1kFlawgyYAAACAE0bA6wAyCivYQRMAAADACSPgdQCZheXqzQ6aAAAAAE4QAc/FKqprlV9WzQgeAAAAgBNGwHOxxh54tEgAAAAAcIIIeC6WWVQf8BjBAwAAAHCiCHgu9uMIHgEPAAAAwIkh4LlYxsGAxyYrAAAAAE4QAc/FMgvLFejjIX9vp/acBwAAANANEPBcrL4HHhusAAAAADhxBDwXyyyqYP0dAAAAgDZBwHOxjMIK1t8BAAAAaBMEPBeqqqlTTkklI3gAAAAA2gQBz4UOFFfIWnrgAQAAAGgbBDwXogceAAAAgLZEwHOhgz3w2EUTAAAAQFsg4LkQI3gAAAAA2hIBz4Uyiyrk5+WuQB+anAMAAAA4cQQ8F8osrO+BZ4xxdSkAAAAAugACngtlFJazgyYAAACANkPAc6HMwgr1psk5AAAAgDZCwHOR2jqrrOJKRvAAAAAAtBkCnovklFSqts6qDy0SAAAAALQRAp6LNPbAY4omAAAAgDZCwHORzMJySfTAAwAAANB2CHgu0jiCR8ADAAAA0EYIeC6SWVghL3c3hfh7uboUAAAAAF0EAc9FMmhyDgAAAKCNEfBcJLMh4AEAAABAWyHguUhmUQXr7wAAAAC0KQKeC1hr60fwaJEAAAAAoA0R8Fwgr7RKVbV1TNEEAAAA0KYIeC5AiwQAAAAAzkDAc4GDAa9PkK+LKwEAAADQlRDwXCA1v0ySFN2TgAcAAACg7RDwXCA1v1y+nu4Kpck5AAAAgDZEwHOB1PwyRff0pck5AAAAgDZFwHOB1PxypmcCAAAAaHMEPBfYn1em6J5+ri4DAAAAQBdDwGtnheXVKqqoYQQPAAAAQJsj4LWztPxySWIEDwAAAECbI+C1M1okAAAAAHAWAl47S20YwYsJYQQPAAAAQNsi4LWz1Pxy+Xm5q6efp6tLAQAAANDFEPDaGT3wAAAAADgLAa+d1ffAY3omAAAAgLZHwGtnB0fwAAAAAKCtEfDaET3wAAAAADgTAa8d/dgigSmaAAAAANoeAa8dNbZIIOABAAAAcAKnBjxjzFnGmK3GmB3GmHubOT/TGLPeGLPWGJNsjJnszHpc7WDAY4omAAAAAGfwcNaNjTHukp6WdIakVEkrjTEfW2tTmly2QNLH1lprjEmU9I6kwc6qydVS88vk7+WuYHrgAQAAAHACZ47gjZO0w1q7y1pbJektSTObXmCtLbHW2oaH/pKsurCDLRLogQcAAADAGZwZ8KIk7W/yOLXh2CGMMRcaY7ZI+kzSDU6sx+XqAx7TMwEAAAA4hzMDXnPDVEeM0Flr51prB0v6iaS/NXsjY25pWKOXnJ2d3bZVtiN64AEAAABwJmcGvFRJMU0eR0tKb+lia+0iSQnGmLBmzj1nrU2y1iaFh4e3faXtoLC8WsUVNbRIAAAAAOA0zgx4KyUNMMbEG2O8JM2S9HHTC4wx/U3DgjRjzBhJXpJynViTy+zPq++BFxPCCB4AAAAA53DaLprW2hpjzB2SvpLkLulFa+0mY8ytDednS7pY0jXGmGpJ5ZIub7LpSpeSVlDfIiEqmBE8AAAAAM7htIAnSdbazyV9ftix2U0+fkjSQ86soaPILamSJIUFeLm4EgAAAABdlVMbneNH+WX1Aa+nHwEPAAAAgHMQ8NpJQVmVfDzd5OPp7upSAAAAAHRRBLx2kl9WrRBG7wAAAAA4EQGvnRSUVSmYgAcAAADAiQh47SS/rFo9/T1dXQYAAACALoyA107ySxnBAwAAAOBcBLx2kl9WpZ5+jOABAAAAcB4CXjuoq7MqLK+mRQIAAAAApyLgtYOiimrVWTFFEwAAAIBTEfDaQX5ZtSQxRRMAAACAUxHw2kF+WZUkMUUTAAAAgFMR8NpBQUPAC2YEDwAAAIATEfDaQX7pwSmajOABAAAAcB4CXjtgiiYAAACA9kDAawcFZdVyM1KAj4erSwEAAADQhRHw2kF+WZWC/bzk5mZcXQoAAACALoyA1w4KyqrZYAUAAACA0xHw2kF+WZVCWH8HAAAAwMkIeO0gv6xawQQ8AAAAAE5GwGsH+aVV6skUTQAAAABORsBrB/llVerpzwgeAAAAAOci4DlZeVWtKmvq2GQFAAAAgNMR8JyMJucAAAAA2gsBz8l+DHiM4AEAAABwLgKekxWUVUsSu2gCAAAAcDoCnpMxRRMAAABAeyHgOVl+wwgeUzQBAAAAOBsBz8kKSutH8JiiCQAAAMDZCHhOll9WLX8vd3l58K0GAAAA4FykDicrKKti9A4AAABAuyDgOVl+WZV6+rP+DgAAAIDzEfCcLL+smh00AQAAALQLAp6TMUUTAAAAQHsh4DlZflm1QmiRAAAAAKAdEPCcqKa2ToXl1YzgAQAAAGgXBDwnKiynyTkAAACA9kPAc6L8soaA588IHgAAAADnI+A5UUFZlSQxRRMAAABAuyDgOVHjCB5TNAEAAAC0AwKeE+WVVkoSffAAAAAAtAsCnhNtzSyRj6ebIoJ8XF0KAAAAgG6AgOdEG9MKNTQiUB7ufJsBAAAAOB/Jw0lq66w2pRdqRFSQq0sBAAAA0E0Q8Jxkd06JSqtqNZyABwAAAKCdEPCcZENaoSRpRDQBDwAAAED7IOA5yYbUIvl4uql/eA9XlwIAAACgmyDgOQkbrAAAAABob6QPJ6its9rIBisAAAAA2hkBzwl255SorKpWI6KDXV0KAAAAgG6EgOcEjRusMIIHAAAAoB0R8NpAZU2t1uzLb3x8cIOVhHB/F1YFAAAAoLtxasAzxpxljNlqjNlhjLm3mfNXGWPWN/xZaowZ6cx6nOXBL7Zo1nPLtWpvfchjgxUAAAAAruC0BGKMcZf0tKSzJQ2VdIUxZuhhl+2WNM1amyjpb5Kec1Y9znTHqf0VEeSjm15ZqR0HSrQxvVCJrL8DAAAA0M6cOcQ0TtIOa+0ua22VpLckzWx6gbV2qbX24NzG5ZKinViP04T28NbL14+TMUaX/98ylVXVajjr7wAAAAC0M2cGvChJ+5s8Tm041pIbJX3hxHqcKi7MXy9cm6TSqhpJbLACAAAAoP15OPHeppljttkLjTlV9QFvcgvnb5F0iyTFxsa2VX1tbnRsT82++iTNXZOm/r16uLocAAAAAN2MMwNeqqSYJo+jJaUffpExJlHS85LOttbmNncja+1zalifl5SU1GxI7ChOGdRLpwzq5eoyAAAAAHRDzpyiuVLSAGNMvDHGS9IsSR83vcAYEyvpA0k/tdZuc2ItAAAAANDlOW0Ez1pbY4y5Q9JXktwlvWit3WSMubXh/GxJf5YUKukZY4wk1Vhrk5xVEwAAAAB0ZcbaDj3j8QhJSUk2OTnZ1WUAAAAAgEsYY1a1NDBGJ24AAAAA6CIIeAAAAADQRRDwAAAAAKCLIOABAAAAQBdBwAMAAACALoKABwAAAABdBAEPAAAAALoIAh4AAAAAdBEEPAAAAADoIgh4AAAAANBFEPAAAAAAoIsg4AEAAABAF0HAAwAAAIAugoAHAAAAAF0EAQ8AAAAAughjrXV1DcfEGJMtaa+r62gQJinH1UWgS+M1BmfjNQZn4zUGZ+L1BWfrqK+xvtba8OZOdLqA15EYY5KttUmurgNdF68xOBuvMTgbrzE4E68vOFtnfI0xRRMAAAAAuggCHgAAAAB0EQS8E/OcqwtAl8drDM7GawzOxmsMzsTrC87W6V5jrMEDAAAAgC6CETwAAAAA6CIIeMfJGHOWMWarMWaHMeZeV9eDzs8Ys8cYs8EYs9YYk9xwLMQYM88Ys73h756urhOdhzHmRWPMAWPMxibHWnxNGWPua3hP22qMOdM1VaMzaeE19oAxJq3hvWytMeacJud4jeGYGGNijDHfGGM2G2M2GWPubjjOexlOWCuvr079PsYUzeNgjHGXtE3SGZJSJa2UdIW1NsWlhaFTM8bskZRkrc1pcuxhSXnW2gcbfpHQ01r7O1fViM7FGDNVUomkV621wxuONfuaMsYMlTRH0jhJkZLmSxpora11UfnoBFp4jT0gqcRa+5/DruU1hmNmjImQFGGtXW2MCZC0StJPJF0n3stwglp5fV2mTvw+xgje8RknaYe1dpe1tkrSW5JmurgmdE0zJb3S8PErqn/TARxirV0kKe+wwy29pmZKestaW2mt3S1ph+rf64AWtfAaawmvMRwza22GtXZ1w8fFkjZLihLvZWgDrby+WtIpXl8EvOMTJWl/k8epav3FADjCSvraGLPKGHNLw7He1toMqf5NSFIvl1WHrqKl1xTva2hLdxhj1jdM4Tw4dY7XGE6IMSZO0mhJP4j3MrSxw15fUid+HyPgHR/TzDHmuuJETbLWjpF0tqTbG6Y+Ae2F9zW0lWclJUgaJSlD0iMNx3mN4bgZY3pIel/SL6y1Ra1d2swxXmdoVTOvr079PkbAOz6pkmKaPI6WlO6iWtBFWGvTG/4+IGmu6of8sxrmhx+cJ37AdRWii2jpNcX7GtqEtTbLWltrra2T9D/9OH2J1xiOizHGU/U/fL9hrf2g4TDvZWgTzb2+Ovv7GAHv+KyUNMAYE2+M8ZI0S9LHLq4JnZgxxr9hca+MMf6SZkjaqPrX1bUNl10r6SPXVIgupKXX1MeSZhljvI0x8ZIGSFrhgvrQyR38obvBhap/L5N4jeE4GGOMpBckbbbWPtrkFO9lOGEtvb46+/uYh6sL6IystTXGmDskfSXJXdKL1tpNLi4LnVtvSXPr32fkIelNa+2XxpiVkt4xxtwoaZ+kS11YIzoZY8wcSadICjPGpEq6X9KDauY1Za3dZIx5R1KKpBpJt3e0XcHQ8bTwGjvFGDNK9dOW9kj6mcRrDMdtkqSfStpgjFnbcOz34r0MbaOl19cVnfl9jDYJAAAAANBFMEUTAAAAALoIAh4AAAAAdBEEPAAAAADoIgh4AAAAANBFEPAAAAAAoIsg4AEAujVjTKgxZm3Dn0xjTFrDxyXGmGdcXR8AAMeCNgkAADQwxjwgqcRa+x9X1wIAwPFgBA8AgGYYY04xxnza8PEDxphXjDFfG2P2GGMuMsY8bIzZYIz50hjj2XDdScaY74wxq4wxXxljIlz7VQAAuhsCHgAAjkmQdK6kmZJel/SNtXaEpHJJ5zaEvCclXWKtPUnSi5L+4apiAQDdk4erCwAAoJP4wlpbbYzZIMld0pcNxzdIipM0SNJwSfOMMWq4JsMFdQIAujECHgAAjqmUJGttnTGm2v64iL1O9f8/NZI2WWsnuKpAAACYogkAQNvYKincGDNBkowxnsaYYS6uCQDQzRDwAABoA9baKkmXSHrIGLNO0lpJE11aFACg26FNAgAAAAB0EYzgAQAAAEAXQcADAAAAgC6CgAcAAAAAXQQBDwAAAAC6CAIeAAAAAHQRBDwAAAAA6CIIeAAAAADQRRDwAAAAAKCL+H85Ft1ZYrLSoQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df, best_arm = simulate_tests()\n",
    "\n",
    "plot_prob_best_arm(df, best_arm)\n",
    "#plot_avg_reward(df)\n",
    "#plot_cumulative_reward(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5cbca9a",
   "metadata": {},
   "source": [
    "# Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b056d6d",
   "metadata": {},
   "source": [
    "## Only 2 arms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02361b9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# With only two arms\n",
    "df, best_arm = simulate_tests(means=[0.1, 0.9])\n",
    "\n",
    "plot_prob_best_arm(df, best_arm)\n",
    "plot_avg_reward(df)\n",
    "plot_cumulative_reward(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48487543",
   "metadata": {},
   "source": [
    "## 200 arms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f3dcf81",
   "metadata": {},
   "outputs": [],
   "source": [
    "means = [0.1 for x in range(199)] + [0.9]\n",
    "df, best_arm = simulate_tests(means=means)\n",
    "\n",
    "plot_prob_best_arm(df, best_arm)\n",
    "plot_avg_reward(df)\n",
    "plot_cumulative_reward(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5fdf30f",
   "metadata": {},
   "source": [
    "## When all arms have probabilities close to 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6b20e34",
   "metadata": {},
   "outputs": [],
   "source": [
    "means = [0.05, 0.06, 0.07, 0.08, 0.09, 0.1]\n",
    "df, best_arm = simulate_tests(means=means)\n",
    "\n",
    "plot_prob_best_arm(df, best_arm)\n",
    "plot_avg_reward(df)\n",
    "plot_cumulative_reward(df)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}