flip-to-freedom.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Riddler Classic \n",
    "\n",
    "For proper formatting I recommend viewing this notebook using [nbviewer](https://nbviewer.jupyter.org/github/Booleans/riddler-538/blob/main/flip-to-freedom.ipynb).\n",
    "\n",
    "## Can You Flip Your Way To Freedom?\n",
    "\n",
    "**2020-05-01**: https://fivethirtyeight.com/features/can-you-flip-your-way-to-freedom/\n",
    "\n",
    "From Bart Wright comes a rhetorical question from a famed soliloquy, “To flip, or not to flip?”:\n",
    "\n",
    "You are locked in the dungeon of a faraway castle with three fellow prisoners (i.e., there are four prisoners in total), each in a separate cell with no means of communication. But it just so happens that all of you are logicians (of course).\n",
    "\n",
    "To entertain themselves, the guards have decided to give you all a single chance for immediate release. Each prisoner will be given a fair coin, which can either be fairly flipped one time or returned to the guards without being flipped. If all flipped coins come up heads, you will all be set free! But if any of the flipped coins comes up tails, or if no one chooses to flip a coin, you will all be doomed to spend the rest of your lives in the castle’s dungeon.\n",
    "\n",
    "The only tools you and your fellow prisoners have to aid you are random number generators, which will give each prisoner a random number, uniformly and independently chosen between zero and one.\n",
    "\n",
    "What are your chances of being released?\n",
    "\n",
    "*Extra credit:* Instead of four prisoners, suppose there are N prisoners. Now what are your chances of being released?\n",
    "\n",
    "Initial thoughts: The prisoners' ideal scenario is to have only one person flip. This generates a release probability of 50%, which is the maximum value possible when your freedom is determined by a single flip of a fair coin. The prisoners need to choose a threshold and if they receive a number from the guards that is under this threshold they will agree to flip the coin. This is a binomial distribution with 4 \"trials\" with some probability of \"success\" equal to their threshold value. There are 5 possibilties for how many prisoners end up flipping the coin (0, 1, 2, 3, or 4) and altering this threshold changes the relative plausibilties of each scenario."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "from scipy.optimize import minimize_scalar\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_neg_prob_release_for_threshold(threshold, n_prisoners=4):\n",
    "    '''\n",
    "    Function that returns the probability of the prisoners being released when prisoners choose\n",
    "    to flip a coin only if their number from the guards is above a certain threshold.\n",
    "    \n",
    "    Args:\n",
    "        threshold (float): Threshold below which a prisoner will choose to flip a coin. For example,\n",
    "        a threshold of .70 means a prisoner will decide to flip the fair coin if his randomly assigned \n",
    "        number was less than .70.\n",
    "                            \n",
    "        n_prisoners (int): The number of prisoners involved in this \"game\".\n",
    "\n",
    "    Returns:\n",
    "        float: Returns a float between 0 and -1 that represents the negative of the probability\n",
    "        of the prisoners being released. The purpose of this negative is to be able to pass the\n",
    "        function into scipy optimize.\n",
    "    '''\n",
    "    # We can ignore the probability of 0 coins being flipped because that leads to a loss.\n",
    "    num_flips = np.arange(1, n_prisoners+1)\n",
    "    dist = stats.binom(n_prisoners, threshold)\n",
    "    # Calculate the probability of 1 to n coins being flipped given the current threshold.\n",
    "    p_num_flips = dist.pmf(num_flips)\n",
    "    \n",
    "    dist = stats.binom(num_flips, 0.5)\n",
    "    # We want the probability of every flip coming up heads, given the number of flips. This leads to release.\n",
    "    p_all_heads = dist.pmf(num_flips)\n",
    "    \n",
    "    return -1*np.sum(p_num_flips * p_all_heads)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize how the probability of the prisoners being released changes depending on the threshold selected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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EtmzS7pgm7X5HMV94J8eZV/5oW93+QxNssx1FQrOjH0RbxPhH4DkTHOeU2jY/p8kPy5X2W7V7vEn7w2r7P22C9tP1PC7r9PVCj5PybZ7rAV2c17+tbXtEh9v9c227F3d6zA72/de1fd9LmwReuc0ZtW1+Bcxv0/6AWvtjehX/BK+Rjv4+wMm1bVbSJCHRZLtnMr7Tzs3UEnBNtmmM8qwe7/lt2neTlH97bb9fpNYhpsk2G1KMhmxs8wdggzbt23bQadL+hFpM7a6H3660uwdY2MVx1hnkeenynCyiuD429n1lh9sFxajb6ufZap2+KEbEN9r8tN17s5vzOB0Lqyfwul3aJdqnKynfWCb6vrAXRce16jbPmqbz3K+kfFJ0aJnoOnhBbZvXTeL8HtdFnEfWtv0BE3QCoxg1/73KNitp8tlIMSK9uu+PdRHXvFbXohbPeyVw6AT7/PPaNm2vL9S+KwGX077z1ALgyto25/bovbRh7T2xAjhsgviPavH6MCnv4uLi4uLiMisW55SXJEnSjFXOX/mR2upvZObvOtzFmzLzlx22fSHFyNaGnwJt51jPzJ9TzOFb9eYOj9fw75l5+QRt/oWiHHzDU4AXtInrN5m5stMAMvO/gC9XVh3e6bYVPX8ec8BnKUYFNrxmog0iIhhf9v63FCODe+Xvavf/X2beNsE2J1KMlm54IkWliFkhIoYiYsuIOLScY/yUWpOPZub1Hezq7awqnz4KvDQz72m3Qfk+fC1F552GKU/bEBHrUIxeb7gNeFVOULY4Mx+k6JjRsF4ZX6v2/9dlaKdTVIhoaHctqZaN/25mLu30INm6rPS0nJduZOYSilLRDftHRNOS2zUHMH6Kic9m5oom7arn8euZOdZFbE3Po7p2CxN/X7iOosNVVf37w2z01xNdB1n9mvsnXR7jK5n5iS7av71y+wHgkMz8Q7sNyvfCXwGN90TQ/PtcfbqNr3QaVGaunOhaVHNmZn65XYPMvIjx36v2iYh1m7WNiMdTVLJpeBj4q8z8Y5v9P0xRQr/a5oiI2KzFJt04imKKh4ZPld9HW8rM8yg6WkmSJM1KJuUlSZI0KPMjYtsmy64RcVhEfJ5iTuDqfKR/BN7R4f7voIsfSyl+jK16VyfJjfIHxGrC8qkRUZ+vupU/Au/v4BhJUb60qh7vVH2tcnubLn9wnUnPY8Yok4znV1YdFBFPmmCzgymqSjSc0yIR17UyEfiMyqqbMnPCH7fL459SW/3XTZrOBN+LiKwuwAhF54b/Ag6qtf8sHSTJI+KJjJ/z9jMddGYAHktqnF1ZdXBE1Ofy7dYrKObZbTg1M0c6jOc6itGRDfW5fCetfI//d2XVM8o5gyfy+ImbdGRGnhfg3Nr9ozrYpt6mvo9menUe1Z1/77AzxH9SlLFvOLRVAnWW+F5m/miiRpl5E0WFlYbduzzOGZ02jIjnAE+rrPpgZt7fqn1V2eHzS5VVnVwD+vWeS4pOTp24qHJ7LYp57Jt5BePnkf9kJx2vMvNO4JOVVcPlvqaq+v0vgXd3uN2/9uDYkiRJA2FSXpIkSYPyBIp5SOvLT4ALKcqPrlVpP0ox4vHGDvf/jTJB1KlnVm4/zPjE0kQ+32Zf7Vycmcs6bUtR5rNh/w63e0xEzIuIRRGxVb0zBEXZ0Kqdutj1tD6PWebjldv1UfDNHFe5nYz/IXyq6q/L85u2au4i4KE2+5ptfgD8RWZOOIq69DxWjZKHIsHf7fEahoGnd7l93YGV2ysZPxK723j2iYihbjaOiLUiYsOI2LrJteTRStOFwBYtdnNr5fYBEdGLJPhAz0sb36YoP9/wqrIqRlMRsQB4eWXVtZn5sxbNq+fxiIjYe/JhDtwK4EldLB8eTJjjjDG+0kxL5bWm2llwbYp5u2erb3XR9pbK7W4S2Q9k5pVdtD+wdn8q1+ptImKr2uON6SIa3h4RG3V5jE7ckpm/mrhZ0bZ2v9X5rX9uf6GLeCb7PbepsqpJtQPrj8rk/4TKTh4/ncrxJUmSBmX+oAOQJEmSOrAYeE1m/riLbW6YuEkhIjZmfJngxV2W9b2qdr/TpMiEI8waMnM0IhYDzylXPSkiNizLLjdVjsZ9EcWc8XsCOzC+o0M7G3YaG31+HrNZZl5dPt/GyMBjI+KUZtMLlK/Daln4S7uYfqET9dfl1Z1uWP7drmNVwuPxEbF1Zv66Z9FNrw2AbmJ/Vu3+Q2UCulP1DvFPBq7oYvt28fwW2Lh8/XSqOnp8XWBz2pyPiFgfOBT4C4pEypMY30mhnQ3LGOvOB15S3l4L+O+I+ArwGeA7mbm8w/1XTet56VRmroiIzwInlKueSFGe/nstNjmM8VVi2o2SP59VI4PXA66MiM9RJNx+kJmPttxyBuo0MTeD3NpFpzQoPi+rna/2ppizeza6uYu2Syq3F3axXcff5UrVa8AY8GiX1+r6Z/OTgN807mTmfeU0KM8vV+0C3BIRn6AYZX9Dlx1CW5nsuYXW57f6HWAUuK6LY/y43KbRUWmqnX+eVtkXdPE9stJ+1ynGIEmSNO1MykuSJGmmeZjiB8Y7KJKGX8vMH7TfpKnfd9G2Pqro9i6PdWvtfqejwH7R5XF+zqpkNsCmQNNkdjnq9COML4XejW5+NO/b85gjzgLOLG9vBbyA8eVmG46iGEXd0M0cup3oxeu8Ogrx8fQgYdljRzK+k8xaFFU5dgTewKpRqbsBl0fEgZ2UX6b4u1VNJaEOMNWRldV4tqaoMjIVG9HibxkRrwFOA7pJble1upacTzENwgvL+/MoktGHAaMR8WOK8/x9iuRyPfHUzLSdl0k4h1VJeYCjaZ2Ur5auH6H9iNYPUoyqb7y2hykqchwLPBIRV7HqPF5RTqeg3pnM51/Vpr0KZAA6eU82VCuSdFOBopvvcjD+GjCf1c93t5pdq/+O4nNmUXn/8RTz2L8duD8irgD+F7gMuG6SU9BM9txC6/Nb/Q7w62467GTmSETcCWzfZF+TUZ8iaarvI0mSpFnB8vWSJEkalF9lZjRZ1svMLTPz2Zl5/CQT8gB/6KLtBrX7S5u2aq3+42mno8ynepx63ABExKuBrzP5hDx093+FvjyPOeRzQHXU72tatKuuv4/xZY57YVCv8+l0d2beWVl+kZk/yMyzM3Mv4O8rbR8HfKXDkdS9Lk/8uImbNFdWwOj1PNRN44mId1N0DplsQh5aXEvKahGHUJQgr8/HPQTsBxxPMZXI7yPivyOiXpq6Guu0nZfJyMybGT8a9OURsV69XVkuu/o8v9FuTuwyyf48isR9fYTuOhQj8t8B/A/Fefx8ROw1qSehZtbkz7/VKr70QTff5WAartWZeQtF+fZrm7TfmKKiyHuBa4DfRMQZEdFqGo9W+nFuF1Vud/u6hfGv3UXtpuDoQK+/j0iSJM0KJuUlSZKk1fWi9Gg/jjPhD6ARsT3w0VrbnwH/BBwEbEcxcnXtamcIiqTOZPX8ecwlmbmU8fO3vyQixo2OjIj9gadWVn0mM6ultPsSWpftZ/3fLTM/SFFBouEJwAc62LRXc4s3TOVcDk/cpGurxRMRB1FcN6qupOjY8ByKTj/rA8O1a8lrOz1oZj6amX9HUcngVIqpSpq9LocoSt1fGhEXRESzZPm0nJcpqpahX4+iKkDdqxj/W805E+00M5dk5l9STJPxAVav3tKwgKKaxI8j4iMRYfXEqVvjrqMz3LRcq8t5zfehqHzzWeDuFttvTtG56OcRcWyPY5uKyXzP7edr1/eRJElaI/gfMEmSJAkeqt1f1LRVa/X2nZZi7/Y49TLQ9bgBTmR8cuoM4IQO5jhdv8tYqvrxPOaas1g1En6IonT16ZXHj6u173Xpemj+On+gi+3rf7fZOuXA24GXsarM8asi4szMvKrNNtXzNAKsW470nnaZuSwiqnP7XpqZB/fhUCfV7v9tZn60g+26vpZk5h3l8U6KiA2B/YHnUnQk2pvxCZhXUCSXX1zbx3Sdl6n4AvB+Vl2jjwbOq7V5VeX2vcDFne48M38C/APwDxGxGcX82s8FDmZ8px+AN5b/vqnT/aspP/9mlgdYNVr+F5m5Xb8OVH6vuqRciIgdKEbQ/wlFsn7zSvMFwKci4g+Z+aV+xTSBJayqetLt6xbGv3aXdPC9sp2pfu/uZoolSZKkGcOR8pIkSdLqc5Z2+yPuDhPsr5WndHmcelz3Nmnzosrt24ATO/zhdPOJm7TUj+cxp5Tzll9fWfVYqfpy1O8rK4/9sByF12uDep3PKJn5B4pR2VX1+3X3VG4PA9v0NKjuVd8z27dsNUkRsQh4dmXVtzpMyMPUriVk5oOZeVFm/mNmPoNiRP4HGF/O+UUR8fwmm/f1vExVZj5AMbVIw/Mi4omNOxGxD7Bz5fHPZ2a9tH+nx7onM7+cmW/JzF2BXRg/Uh/gDRGx42T2r8f4+TezVK/V20REr0fOt5SZt2XmOZl5LLAlRaeiH9aavS8iBvVbbPUze+uI6Li6SNm2+rk31c//e2r3p/o+kiRJmhVMykuSJGmNV87X+6vKqt3L+Yk7tV/t/o873O4ZnR6g/GF598qqX2bmg7U2CxifEPt2F6N568+hGz19HjNML6cy+Hjl9o4R0Uh6HsH4eWvP7uExq+qvy3073bAsc713ZdXvM/PXPYlqMD4FVOM/KCKe1aZ9fRT9Qb0PqSvVeJ4YEb1OUGwLrFW5f0kX207lWrKazPy/zPwH4F9rD72kSfN+n5deOKdyOxg/Mv7oNm2nJDNvzsxjavucx/iOXOrejhHRTXWI+udlp98X1JnqNWA+xaj1aZeF71JUqah2stsa2GMQMTH+tTYE7NXFtnsxvgrTVF+3PwFGK/c7/h45yfaSJEkzgkl5SZIkqXBl5fZ61EojT+Ava/frI6NaeWEXP+a/kPHlOpsdY4Pa/aWd7LhM5r+swzia6fXzmEkerd2fyrzVnwOWV+43RstXS9cvAy6YwjHaubJ2//Autv1zxr++Zvrfra3MHAXeV1tdL9de9Z3a/WN6GlD3+h1PvZRwp9eSbShKpvdDfZT3tk3azLS/UzPfYvwo0aPgsZGo1ffk4sxc3Ifjd3Ie1bn5wKGdNCw7pR1SWfUo4yuoaOpm1DUgMx8G6uXqtx1AKDC17wCT/Z7bVGY+AtxQWfWMiNi2k20jYhdg16kcX5IkaVBMykuSJEmFz9fuv6OTEqMR8TJgz8qqn2Vmpz+yr0sx/+9ExwjgnbXVn2vStD5HZ73ceCtvZdUcrJPR6+cxkyyp3Z90ae7MXEYxp3TDKyPimYwfsf6FzFxOH2TmbcC1lVW7RsQhrdo3lO+Df66t/mwvYxuQsxlfgvfPIqLp6LvMvAX4fmXVsyKim4RGr53P+NfmmyOi2/K/7Uz2WvIuxo+w76V6x4CRJm36fV6mrCxHX73u7RAR+1F0BNu4sv6cPoXQyXlUd04sq4lM5I2M/xt/OTP/2KeY1lTfBn5RuX9kROw/qGBKM+U9d2Ht2MdFxJYTbVROsfGayqoRVu9oMBnV62AA7+hwu/r3EUmSpFnDpLwkSZJUuIjxP+TuCfx7uw0i4slAfZ7lD3d53H+slDFv5WTGl+q8g2K05TjliKw7KqteHBFt51WOiBfTfoRwp3r2PGaYW2v3nzfF/Z1Vub2AIolY1a/S9Q311+eZ5eu4nX9jfOn6XwNf6WlUA1C+Xz5UW13vNFJ1cu3+pyLiwG6OGRFbRsQLu9mmmcx8iGKe9YbHAd8oR6p3E89eEdGshPHtwCOV+8dExIYT7OuNjC/F3q7tvIh4S0Q8buLWj/mr2v36e3M6zkuv1EerH005Yr40xuodxVYTEZtGxLHdzA1NB+ex3Pd2EZGVZVJz268hdgbOaNcgIvZk9SkYzuxbRGuozFxB0TmoYR7wlYjYvcUmTUXE9hHx3CbrnxkRB3exn7VYfUR60/dcv2XmvcAXK6seB3y23XRNEbEuRfJ8QWX1BZl5dw9COo+iOlDDqyOibdWJiHgV3Y3wlyRJmlFMykuSJElAOff66xk/h/jbIuLciNis2jYKLwUuZ/zI6R8Cn+jisA8B6wAXRcRry9K21eNsGBFnsnoy8I1t5oq/sHJ7beB/miXLI2JRRLyLIrk6H7ivi/wQ2OcAACAASURBVLjr+vE8ZoTMvAP4TWXVURFxekQ8p0xabVtZNulgf9cyvlzx1pXbi8vH++mzjB/xvTlweUQcUlYyeEyZ8Ps0cEJtH39TjvadC/6T8aMY/6JV8iYzvw+8t7JqAfDtiPhIu7nLy9f/4RFxAXAnqydFJ+s9wP9W7u8E3BARb2uXQI+IbSLiTRHxA4p5gVdLPpejdy+qrNqM4rk+tcn+No+Is4CPlKs6uZbMo0ie/zoizoqI50fEOi3iXRARxzM+6bmS1knrvp2XXsnMGxl/HTiSYoqIhovKBNpEFgKfAn4VEe8vE4ZDzRpGxAYR8W/A31dWPwx8ubvoVdOoKvHmiDivyfeFtSLiryjKqleneflsZlZfp+qRzDyX8cnnzYCrIuLUdiPDI2KziHh1RFwE3AL8aZNmu1BcC38SEW+PiJ3rn52V/W1H8R1rn8rqazLz9m6fUw+dCNxfuf884HsRsVu9YUTsQfF9ofod8n5W/04wKZn5IPBPlVXzgC9ExIn1z4OIWC8iTqG43sHq1VwkSZJmhU7Ka0mSJElrhMy8NCL+lfHJ46OAv4qIq4H/o5hvfk9gq9rmvwP+uhyl1al/okjyrQ98HPi3iLiG4sfGLYH9WX0O8w9lZrvR5WdQlBltlMjdliLpegvwU2AF8ASKkumN5M19FCXsz+ki9n4/j5nkI6yqmjCP4ly9tUm7c+ls/tqzgI81Wd9Nh45JycyVEXEURdKy0SFgS4rE3G8j4nrgD+Vj+7L6/xlPy8yLmCMy86GI+ChFoqLhncArWmzydopzc2R5fx5FSeo3RsSdwM3AgxTvrQ2A7enT/MGZORoRL6co1/y0cvUGFO/Ff4+In1J0AlhKcd3amCKhNGHnkdIpwIsoOvdAUS3hJxFxA3AbxXPftlzf6PB/G8Xr+30dHmMD4HXlMhYRN1FUYniI4rW3FUVyfN3adu/PzJ812+E0nJdeOZdVU58savJYNzanSLb/PfBo+Rx/R1HKf21gm/JY9YT9CZl5P5qKrwBPAg6gqBRxZERcRdGZa32K90d92pPbgLdMY4xroldTJOMPKO+vQ1Ee/R0RcStFNZAl5foNKTrvTFjKvWJXig5A7wEeKt9zvweWU4xA35GigkLVo8AbJvFceiYz74qIoyk+8xvfy/YHFpfPoTGKf0dWn7d9BDgqM+/qYUhnAn9GMX0HZUz/DvxT+T66H3h8GeN6ZZvfUlT9aVvNSpIkaSYyKS9JkiRVZOYpEbGM4se+xvfltYBnlkszNwEvysw7uzzczcBhFD+ONpJD7Upbf4zxoxxXk5m/j2Ke8G9QjKJs2Klc6u6hSLyt3+SxTvX8ecwwZ1AkVlolarv1+XKf1dLdjzBN87Rn5v9FxLOAb7IqaQlFZ40ntNhsBXBSZv5bv+MbgA8Ab6ZIzgAcFhG7ZOZN9YZlZYe/jIjFFKWoq51NtqWzBPyDU4p2fDz3RDFf8tms6igARZJ8t3JpuwvGz8Fe3fdPIuIYihLDjWRuUCR392yyyS3AC4Dndxp/zXwmjjmB9zPBSM1+npce+hxwOqsnyu+nuH5P1toU16u927QZBU7MzP+cwnFUWEnx+fc/FOd8PuNHFtfdChxkZ4j+ysyHI+L5FO+xv2N8pdAdy2UinY7G3oD2f3MoOj++IjOv63CffZOZ34yIF1HMC79B5aFdWT0R3/AgRfyX9jiWlWUnqi8zvlrIQppXKrinbLdPk8ckSZJmPMvXS5IkSTWZ+T6KZOWFjJ9Xue6XFKPd9phEQr5xrMYP+f9FkShp5mbgLzLzDZmZLdpU93k58HSKxE6r9g9QlO5+Wmb+uOvAVz9mz5/HTJGZKzLzlRTJxk8Biyl+oG71PCfa3zLgC7XVF5bzYU+LzPw1xQjkNwG/aNP0UeCrwO5zNCFPZt7DqpK4UCSe3zHBNqcBTwH+gyJJMJFbyrb7Zeb/m2SorWJZnpl/CTyD4v33hwk2WUEx1cZJwJMz80tt9n0+8BzGl4Ov+y1wKvD0zPxVhzGPAc+l6JyymCKx2c4Ixetw/8x8a4fXwb6dl17IzPsYP0VAwxcyc6TD3fySYpTpf1K8xiY6L8spOv/slpkf6DRWtZeZD1AkZf8VaDXX9kMUnf32zMzfTldsa7LMHMvMv6eohHEOE3eISuAGir/TUzPzjCZtvkgxBckXgE5GjP8OOA3YITMv6yzy/svM7wDbAR+k+D7YygNlm+16nZCvxPIoxUj511NUSmlmOfBJiu/bN/YjDkmSpOkQs+i3MEmSJGnaRcQCiqTUEynKG/8RuBe4PjNv7vGxNgGeRVGyeX2KH/evz8zFU9jnlhTxb0Uxgu9uijL8V3SR+On2mD1/HnNNRJzO+BL4B5Rzlg8qnh0pkvSbUZQKv5/idXJ5Zi4fVFyzRTnX+tMorhGLKDrzLAF+DtzU4fzgvYpliCIR/ZQynvUoEtL3U4zSvSkzJ0pQN9vvUyiqhWxBkby6C7gDuKqsIDCVmBdSjNB8MrApsICiQ8iDZczXTybm2jH6cl5mkojYiFXncROK9/LDFIm1m4DFmdmuo5kmEBHzGd8h65OZeVzt8WdTlLTfnCIZfwdwWZl81IBExDyKKh87UVT0Wciq98ftwM+67RwXEduU+9uWYtT5EMV15R7gRuDmqV4f+y0i1qIYeb4jxfU3KUrx3wpc0+W0TFONJShK1e9CUbb+AYpE/Q9m+/VZkiQJTMpLkiRJ0rQqkza/ZtU8w7dn5g4DDEmS1IGJkvKSJEmS1Irl6yVJkiRper2EVQl5gE8MKhBJkiRJkiT1n0l5SZIkSZpef1+5/Sjw6UEFIkmSJEmSpP4zKS9JkiRJ0yQiXg48p7Lq/Mz8/aDikSRJkiRJUv/NH3QAkiRJkjQXRcQ6rCpT/3jgBcA/VpqMAadOd1ySJEmSJEmaXiblJUmSJKk/9gO+1+bx92Xmz6crGEmSJEmSJA2G5eslSZIkafpdBPzzoIOQJEmSJElS/zlSXpIkSZL6L4GlwI3AecCnMnPlYEOSJEmSJEnSdIjMHHQMmkZLlizxDy5JkiRJkiRJkiRJU7Bo0aLotK3l6yVJkiRJkiRJkiRJ6hOT8pIkSZIkSZIkSZIk9YlJeUmSJEmSJEmSJEmS+sSkvCRJkiRJkiRJkiRJfWJSXpIkSZIkSZIkSZKkPjEpL/XZ7bffzu233z7oMCRp1vN6KklT57VUknrD66kkTZ3XUknqDa+ns4NJeUmSJEmSJEmSJEmS+sSkvCRJkiRJkiRJkiRJfWJSXpIkSZIkSZIkSZKkPjEpL0mSJEmSJEmSJElSn6wxSfkoHB4R34iI30TEoxFxV0RcGhHHRcT8Hh1nQUS8ICJOioj/joifRsTdETESEcsi4vaI+GJEvCIi1upiv0MR8doy3rvK+H8TEV8vn1f0In5JkiRJkiRJkiRJUu/0JBE900XEhsCFwIG1hzYvlwOBN0TEIZn5f1M83HOBi1s8NgRsVy6vBG6MiMMz85Z2O4yIbYEvA3vWHnpCubwYOC4iXpGZD00+dEmSJEmSJEmSJElSL835pHxEDANfA55Trvo18HHg58BWwKuBnYG9gIsjYv/MXNqDQ98EXAPcCdwFPAAsKo9zBLARsBvw/YjYPTPvbhH/BhRJ/p3KVTcDnwJ+Q5Hcfx2wNXAw8OWI+NPMHOtB/JIkSZIkSZIkSZKkKZrzSXngDaxKyF8HHJyZDzYejIiPAF8F/gzYBTgJeNsUjvcjYMvMvKvF45+MiJOAi4B9gU2Bk8s4mzmZVQn5bwGHZOYjlfjPBL5DMYr+ecDrgf+cQvySJEmSJEmSJEmSpB6Z03PKl/PEv6O8m8BR1YQ8QJngPgpYXq76fxGx8WSPmZn3t0nIN9o8wPgk/IuatYuITYG/Le8uB46uJuQr+zqK4vkBnNTNXPWSJEmSJEmSJEmSpP6Z00l5irniH1/evjQzf9asUWbeC5xf3l0beOk0xHZT5fZmLdq8DBgub3+hjHM1mflT4LuVff1JTyKUJEmSJEmSJEmSJE3JXE/K/2nl9rcmaFt9/AV9iKXuKZXb97RoM5PjlyRJkiRJkiRJkiRNYK4n5Xet3P7xBG2vbbFdz0XEesB/VFZ9uUXTGRm/JEmSJEmSJEmSJKkz8wcdQJ/tULl95wRtfwOsANYCto+IyMycYJu2IuJxwMGNu8BCYDfgSGCLcv0NwClNtp3HqtH0K8r42vlV5fYOLVtJkiRJkiRJkiRJkqZNTDHvPKNFxAPAhuXd9TPzD71s38HxdwJubvHwA8C5wDsz8+Em2y4ElpR378/MTSY4VkftlyxZ0vQPfvvtt7fbvSRJkiRJkiRJkiStcbbffvum6xctWhSd7mOul69/XOX2Ix20/2Pl9vo9jqXuSuD7tWNWzeTYJUmSJEmSJEmSJEkdmOvl6wcqM2+hKFtPRKwFbAzsA7wJeHG5XBgRx2Tm8na76uRwU4m1VQ8PTV2jCoHnWJKmxuupJE2d11JJ6g2vp5I0dV5LJak3vJ7ODnN9pHy1/Pw6HbRft3J7WS8DycwVmXlvZn4jM18AnFo+9HLg0002qca+bpPH6xZUbvc0dkmSJEmSJEmSJEnS5Mz1pPxDldsbt2sYEfOBheXdMaDdyPVeOBm4rbz9iojYpfb4H8o4ADYoR9q3U31+D7VsJUmSJEmSJEmSJEmaNnM9KX9b5fa2E7TdCmgkvm/PzCmVg59IZq4Evl1Z9SdNHv9FeXetMr52tqncvq1lK0mSJEmSJEmSJEnStJnrSfmfVm4/fYK21cd/2rJVb1XLzG/Q5PGZHr8kSZIkSZIkSZIkqY25npS/pHL7zyZo+4LK7W/1IZZmtqvcvq/J4zM9fkmSJEmSJEmSJElSG3M9Kf894Pfl7YMj4qnNGkXEpsAR5d1HgK/1O7CI2Ar488qqK5s0+yowUt4+soyz2b6eChxY3r0b+H6v4pQkSZIkSZIkSZIkTd6cTspn5hjw7vJuAOdFxIbVNhGxDnAusF656iOZeX+z/UXEORGR5XJKizanRcQ2zR6rtHkK8A1gQbnq+5n5sybx/x44s7z7OOCcMt7qvjYEPlM+P4BTM3NFu+NLkiRJkiRJkiRJkqbH/EEHMA0+ChwGPAfYC1gcEWcBPwe2Al4D7Fy2vQk4dYrHez3wtoi4CrgCuBVYQnGutwSeTTFCfrhsfzfw2jb7+xeK0vQ7AS8ErouITwC/pSh//3pg67LtZcDHpxi/JEmSJEmSJEmSJKlH5nxSPjNHIuKlwIUUJd63pnni/TrgkMxc0oPDBrB/ubRzGXBcZv6iVYPMfCgiXgh8GdiTogPB+5o0/Q7wiswcnVTEkiRJkiRJkiRJkqSem/NJeYDMfDAiDgZeCbyKIrm9CfAg8DPgfODTZbn7qdoVOKBcngZsBmxKMVXAEuAXwI+ACzLzig7jvzMi9gWOAY4AngpsCNwHXE9Rvv6CzMwexC9JkiRJkiRJkiRJ6pE1IikPUCasv1guk93HMRSJ8XZtfgN8tlx6phwBf3a5SJIkSZIkSZIkSZJmgXmDDkCSJEmSJEmSJEmSpLnKpLwkSZIkSZIkSZIkSX1iUl6SJEmSJEmSJEmSpD4xKS9JkiRJkiRJkiRJUp+YlJckSZIkSZIkSZIkqU9MykuSJEmSJEmSJEmS1Ccm5SVJkiRJkiRJkiRJ6hOT8pIkSZIkSZIkSZIk9YlJeUmSJEmSJEmSJEmS+sSkvCRJkiRJkiRJkiRJfWJSXpIkSZIkSZIkSZKkPjEpL0mSJEmSJEmSJElSn5iUlyRJkiRJkiRJkiSpT0zKS5IkSZIkSZIkSZLUJyblJUmSJEmSJEmSJEnqE5PykiRJkiRJkiRJkiT1iUl5SZIkSZIkSZIkSZL6xKS8JEmSJEmSJEmSJEl9YlJekiRJkiRJkiRJkqQ+MSkvSZIkSZIkSZIkSVKfmJSXJEmSJEmSJEmSJKlP5g86AEmSJEmDkZmMLb6Nh8/+L0a/ew2Mjg06pKlbe4jhA/dh3eMOZf5uOxARg45IkiRJkiRJaziT8pIkSdIcMyeT7Z16dJSRi69g5OIrJm47bx7z930aC44/iqHdTeBLkiRJkiSpP0zKS5IkSbPIuIT7934EI6ODDmn2WrmSsR8uZunLj2/dxpH3kiRJkiRJmiKT8pIkSdIMlJmM3nArD7/vPMau/glkDjqkNdNEI+8dbS9JkiRJkqQJmJSXJEmSBsTE+xzQbrS9CXtJkiRJkiRhUl6SJEmaFibg10DNEvYm6iVJkiRJktY4JuUlSZKkHjMBr5ZM1EuSJEmSJK1xTMpLkiRJk5SZjC2+jYfP/i9Gv/cjGBkddEiajUzUS5IkSZIkzWkm5SVJkqQuNBLxy8/6EmPfudpR8OqPVnPVrz3E8IH7sO5xhzJ/N5P1kiRJkiRJs4FJeUmSJKmFcSPhv3sNjI4NOiSt6R4dZeTiKxi5+IpV60zUS5IkSZIkzWgm5SVJkqSKxnzwy08/lxXX/GTQ4UgTM1EvSZIkSZI0o5mUlyRJ0hrN0fCak6qJ+nnB0PP3Z8HrDoN1A0zQS5IkSZIkTSuT8pIkSVrjOC+81igrk9FLrmTJJVeyQbnqvnnzmL/v01hw/FEM7e5IekmSJEmSpH4yKS9JkqQ5z9HwHVhrHvP33Y313noUQ7vtMOhoOpaZjN14Gw+f/WVGv3cNPDo66JBmtMdS7ytXMvbDxSx9+fHF/eEhhg+y3L0kSZIkSVI/mJSXJEnSnORo+NLawwwftC/rHnfIrEq2dyoiGNp9RxZ95O0dtTeJ38JI83L3JuglSZIkSZKmzqS8JEmS5ozMZPSGW1l++rmsuOYngw5neszxpHuvdZLEz0xGF9/Kw+/7DGNX3bjmdeiolLsHmL/fbix469GWuZckSZIkSZokk/KSJEmatdaYsvQm3qdVRDC8x04Mf+bdTR9f00bbj111o2XuJUmSJEmSpsCkvCRJkmallSOjLH3tvzD2w8Wwcg6MZDbxPmu0G20/LmH/3athZI51FKmWuW9Ye4jhA03US5IkSZIktWJSXpIkSbPCuFHxl14NYysGHdLkmYCfs5ol7Od8ov7R8Yl6y91LkiRJkiSNZ1JekiRJM9acmCPeBPwab01L1DfK3cfmm7D+h05gaK+dTc5LkiRJkqQ1mkl5SZIkzTiZyeiPb2bpm0+De+4fdDidW3uI4YP2MwGvCU2YqJ8Dc9Xn3fex9PATAEfPS5IkSZKkNZtJeUmSJM0Is3JU/FrzmL/vbqz31qNMwmvK5nKivjF6HoDhIYYPcg56SZIkSZK05jApL0mSpIGaNaPiA+bvtzvrve1oE/CaNnMyUT/iHPSSJEmSJGnNYlJekiRJ027WjIqfN4/hP92fdV93mIl4zRhzbY56R9FLkiRJkqS5zqS8JEmSps2sGBXvvPCaheqJ+lZJ+my0H1CcE6qOop8XDD1/fxa87jAT9JIkSZIkaVYzKS9JkqS+m9HJeEfDaw5qNZr+l9+8lHUuuJThq34KK7PNHmaAlcnoJVey5JIriS02Yf0PnsDQXjubnJckSZIkSbOOSXlJkiT1xYwuUe9oeK2BIoIVO27D8pNezRbbbTeryt3nXfex9PATHD0vSZIkSZJmJZPykiRJ6qkZOSo+YP5+u7Pe2442CS/RvNz96OJbWX76eay4+sYBR9dGZfQ8wPz9dmPBW49maHcT9JIkSZIkaeYyKS9JkqSemHHJeMvSSx2LCIb32Inhz72n5Xz0M9HYVTey9OXHF3eGhxg+aB/WPe5QR9FLkiRJkqQZxaS8JEmSJi0zGVt8G8vP+hJj375q0OEAEFtswsIPncjQXjsPOhRpVmo1iv7h932GsatuhJyhc9GPjDJy8RWMXHyFc9BLkiRJkqQZxaS8JEmSutYYFb/sLe8l775v0OE4R7zUR4+Nov/Mux9bN9PL3TsHvSRJkiRJmklMykuSJKkrK0dGWXLcKay4cvHggnCOeGmg6uXuR68rp664ewZMXVFVmYPe0fOSJEmSJGlQTMpLkiSpI5nJyLU3sezYk+CRkYHEEJtvwsL/sDS9NJNEBMN778LGl5/j6HlJkiRJkqQmTMpLkiSppcxk9IZbWX76uay45ieDCcJR8dKsUB89P3bjbTx89pcZ/e7VMDI26PBWcfS8JEmSJEmaZiblJUmStJrGnPFL33wa3DOYctSOipdmr4hgaPcdWfSRtwMzdw56R89LkiRJkqTpYFJekiRJjxl4Mt5R8dKc1GwU/fKzLmTsO1fByhx0eONGzwMwPMTwQfuw7nGHmqSXJEmSJElTZlJekiRJA0/GxxabsPBDjoqX1gSNUfQbnPmO8WXuL70KRlcMOrzCyCgjF1/ByCU/ZP7+u7Hw7JOZNzw06KgkSZIkSdIsZVJekiRpDbdyZJQlx53CiisXT/uxLVEvrdnqZe5Xjoyy9HX/wtiVi2fICPqVjF1xAw/scoij5yVJkiRJ0qSZlJckSVpDZSYj197EsmNPgkdGpu/AlqiX1MK84SEWffpdq0bPf/dqGBkbdFgFR89LkiRJkqRJMikvSZK0hhlYqfp1hll47qkM773L9B1T0qxTHz2fmYwuvpXlp5/HiqtvHHB0rBo9v9fhLDznXQztvYuj5iVJkiRJUlsm5SVJktYAmcnY4ttYftaXGPv2VdN78HnzmP/M3Vl09snEkF8/JXUnIhjeYyeGP/eemTUH/SMjLD3iRADm77cbC956NEO7W9ZekiRJkiStzl9FJUmS5rDGqPhlb3kvefd903vwtYcYPmg/1j3uEMvUS+qJmToH/dhVN7L05ccTm2/C+h86gaG9djY5L0mSJEmSHmNSXpIkaY5aOTLKkuNOYcWVi6f1uPOfvaej4iVNi9XmoB/w6Pm8+z6WHn5CcWd4iOGD9mHd4w5l/m6OoJckSZIkaU3mL6WSJElzTGYycu1NLDv2JHhkZNqOG1tswsIPncjQXjtP2zElaaaOnmdklJGLr2Dkkh8yf//dWHj2ycwbHhpcPJIkSZIkaWDmDToASZIk9UYjGX//s49h2ZEnTltCPjbfhEUXnM7Gl59jQl7SwDVGzy/60hkMveBZMLTWYANauZKxK27ggb0OZ+Tan5E5wI4CkiRJkiRpIBwpL0mSNMs15o1f+ubT4J77p+egAfP325313na088VLmnFm5Oj5R0ZYesSJAMzfbzcWvPVohna3rL0kSZIkSWsCk/KSJEmz2HTPG2+Jekmz0Wpzz3/3ahgZG1g8Y1fdyNKXH09svgnrf+gEhvba2eS8JEmSJElzmEl5SZKkWWja541fZ5iF557K8N679P9YktQH9dHzmcnYjbex/KwLGfv2D2EAA+jz7vtYevgJgKPnJUmSJEmay0zKS5IkzSKDKFU//9l7sujsk4khvzpKmjsaSfoNznxHcW297maWveW95F33DSQeR89LkiRJkjR3+cuqJEnSLGGpeknqj4hgeO9d2OgHn54xo+dji01Y/4Mm5yVJkiRJmgtMykuSJM1wlqqXpOnRbPT80jefBndPT2WSqryrLG0/Lxh6/v4seN1hzN/N0vaSJEmSJM1G8wYdgCRJkpprJOPvf/YxLDvyxP4n5OfNY/6z92Tj6y8wIS9pjdcYPb/x5eew8Ivvhc03HkwgK5PRS65kyWHH88Bzj2XkxzeROYAh/JIkSZIkadIcKS9JkjQD5egYS9/6Pka/dQWsWNnfg609xPBB+7HucYcwtNsO/T2WJM0y1eT86OJbWX76eay4+saBxNIYPW9pe0mSJEmSZheT8pIkSTNMZrLsbe9n9JIr+5qQn//sPVl09snEkF8JJWkiEcHwHjsx/Ln3PFbaftlb3kvedd+0x9JIzs9/1h4sPPtk5g0PTXsMkiRJkiSpc/4CK0mSNINkJn88/xJGvvkD6FN14thiExZ+6ESG9tq5PweQpDmuMXp+ox98mrEbb2P5WRcy9u0f9u263crYFTfwwC6HwPAQwwftw7rHHeq885IkSZIkzUAm5SVJkmaAzGT0xzez9M2nwT339+UYJuMlqbcigqHdd2SDM9/x2Oj5pW8+De7uz3W8pZFRRi6+gpFLfsj8/Xdz9LwkSZIkSTPMvEEHIEmStCbLTEauvYn7n30MS484oT8J+XWGWfjF97Lx5eeYkJekPqnOPb/wi++FzTee/iBWrixGz+91OCPX/ozMaR66L0mSJEmSmjIpL0mSNCArR0Z56Oh39i8ZTzFv/MbXX8Dw3rv0Zf+SpPHGJecvPIO19t1t+oN4ZISlR5zIA889lpEf32RyXpIkSZKkAbN8vSRJ0jRrjI5fduxJ8MhIX45hqXpJGqyIYHiPnRj+3HsGVto+77qPpYefAPOCoefvz4LXHeac85IkSZIkDYBJeUmSpGkyHfPGs84wC8891ZHxkjSDVEfPjy6+leWnn8eKq2+cvgBWJqOXXMmSS64kttiE9T94AkN77WxyXtL/Z+/+w6O+63zvv97zC2jNTJqAW7rqcX+UCuwhkHKvtonspdbSWq/jbVcNVu3CHqw/Wy2WwNqbwhFagQjLuZbtrsazRLu2pFaPrqcC1rpnCyn2XsDACmzpnl291Ua3EMhE2vQ7k+/n/mNm7MAmJJn5fifJ5Pm4Lq7MTL7fz+eDey1N5jXv9xsAAABAhRDKAwAAVIDvZdS3coMGnz4a2h6x5kVKta+XxfkRDwAmoour573DJ9S/PLyuKUMpVM8TzgMAAAAAUDnMlAcAAAiZ72V09oY7QgvkbfZMpR5tU23HRgJ5AJgkzEzTFs9X3ZFOxZoXSpHKBuOFcL5v+Tr5XqaiewMAAAAAMNXwri0AAECIfN9X37JWuedfCGX9y++/UzNaloayNgAgfJFEXKldG5U9dkovtn9TmR88I3nZiu2f7epW77x3S4m4Em/7Q81YeStz5wEAAAAACBihPAAAQAh+Mz/+4/dLvX3BbxCLKnFTk6a/78bgnsUF/AAAIABJREFU1wYAVJSZKd5wjVI7/0ySxqe1vZeRt6dL3r6Dil23QMn29Yok4pXZGwAAAACAKkf7egAAgID5Xkbn/uT/UXpZaziBfDSixE1NqmlbRSUjAFSh4tb20aaGym7u+7nq+cYWeYeOyzlX2f0BAAAAAKhChPIAAAABcc7p5X88rt7GlnDnxz+yRckdrcyPB4AqF0nEVduxScnOrbLZMyu7+YCn9LI16l2yQt7hE4TzAAAAAACUgXdyAQAAyvSbVvWf2iL96kwoe9jsmUr+9zWKN84NZX0AwMRkZkpcO091T+1S9tgpnf/iY8o+cVCqUEbuek4r3dKqWNNCWtoDAAAAAFAiQnkAAIAyuExW6Xu2KbO3Sxr0g99gekLJr2xS4tp5wa8NAJg0CnPnax+8N/dhsCP5D4P9MpwPg10s29Wt3nnvlhJxJd72h5qx8lbFFsxhjAoAAAAAAKNA+3oAAIAS+b6vvpUblPnugVAC+VjzItX/6FECeQDABQrV8/X7O1Sze4s0PVG5zb2MvD1d6vvjz9DaHgAAAACAUSKUBwAAKIHvZdT3ns8o29UtBRxG2OyZSj3aptqOjcyNBwAMy8w0bfF81R3pVKx5oRSpbNV6obV93/J18r1MRfcGAAAAAGAyIZQHAAAYA+ecXv7H4+ptbNHgseeCXXx6QsnOrarf38HseADAqEUScaV2bVTq619Q/KYmKVHZD3Rlu7rV29gi79BxquYBAAAAABgCpVcAAACj4JxT5nB+fu+vgp/fG22Yo9rdW6mMBwCUpDBzPrXzzyTl/rvlHT6h/uXrpAEv/AMMeEovWyObPVM1O1oVb5zLvHkAAAAAAPKolAcAABiBy2SV/vRWpT+wNvhA3kyx5kWqfWwbgTwAIDDFre2jTQ0V25eW9gAAAAAA/EeE8gAAAJfgnFP/6u3K7HtaGvSDXTxiStzyZqXa11NNCAAIRSQRV23HJiU7t8pmz6zYvtmubvXOe7dOz3u30nd+Xpmjz9LaHgAAAAAwZVGOBQAAMAznnF7avU/e409JQecI0xNKfmWTEtfOC3hhAAAuZGZKXDtPdU/tUvbYKZ3/4mPKPnEw+P+2DcXLyNvTJW/fQcWuW6Bk+3pFEvEKbAwAAAAAwMRBpTwAAMBFnHPyDp3QmeblenHdzsBDi1jzItX/6FECeQBARRXmztc+eK/qT31Hyc6t0pX1ldnc93PV840t8g4dp2oeAAAAADClUCkPAABQxGWySt+zTZm9XYG3q7fZM5X872sUb5wb6LoAAIxVoXq+fn+HvMMn1L98nTTghb/xgKf0sjWy2TNVs6NV8ca5jHABAAAAAFQ9KuUBAADywpofbzNrlXq0TfX7OwjkAQATiplp2uL5qjvSqWhTQ8X2dT2nlW5pVe+SFfIOn6ByHgAAAABQ1QjlAQAAdNH8+OxgYOtGG+ao7uBDhPEAgAktkoirtmOTkp1bZbNnVmzfQjjft3ydfC9TsX0BAAAAAKgkQnkAADClhTk/3q6apdQjW2jLCwCYFAot7eue2qXUN7YpflOTFI9WZG/mzQMAAAAAqhmhPAAAmLJcJqv0p7cq/YG10q/OBLp2rHmR6p5sVyQRD3RdAADCZmaKN1yj1M4/08yT31bdif9Zmdb2+XnztLQHAAAAAFQbQnkAADAlhTY/fvZMpR5tU23HRlk8Fti6AACMl+LW9rqyPvT9aGkPAAAAAKg2vFMMAACmnAvmxwdYhHf5/XdqRsvS4BYEAGCCKLS2r9/fIe/wCfUvXycNeKHume3qVu+8d0uJuBJv+0PNWHmrYgvmMBYGAAAAADDpUCkPAACmjNDmx8eiSrxziaa/78aAFgQAYGIyM01bPF91Rzor09JekryMvD1d6nvvaqrnAQAAAACTEqE8AACYEkKbHx+NKHFTk2raVlG5BwCYMopb2tvsmZXZ1Pdz1fONLfIOHWfmPAAAAABg0iCUBwAAVc/3ffWt3KDMdw8EPz/+kS1K7mhlfjwAYMoptLSve2qXUt/YptiN10mV+HzagKf0sjXqXbJC3uEThPMAAAAAgAmPd48BAEBV872M+pa1avDYc4Guy/x4AAByzEzxhmtU++C9cs4pc+Sk0p/aIv0ywM40Q3A9p5VuaVWsaaGS7esVScRD3Q8AAAAAgFJRKQ8AAKqW72V09oY7gg3kmR8PAMCwCtXz9fs7lOzcKl1ZH/qetLQHAAAAAEx0UyaUt5wWM/tfZvZzM3vZzHrM7EkzW2lmgXUNMLPXmdlHzOxrZvZjM0ubmWdmL5jZATP7nJm9bpRr/cTM3Cj//O+g/g4AAEx2vu+rb1mr3PMvBLco8+MBABiV4nC+ZvcWaXoi3A1paQ8AAAAAmMCmRChvZldI+r6k3ZJukfTbkhKSrpT0Vkntkp4ZbVA+wl7fkvQTSX8t6TZJ8yXVSIpLmimpSdI6SafM7J5y9wMAABdyzsk7dEK9b/pQoBXyzI8HAGDszEzTFs9X3ZFORZsaQt+v0NKecB4AAAAAMJFU/TvKZpaQ9G1Jb86/9DNJX5L0L5JeI+lPJc2V1Chpj5ld55xLl7HlH0gqlM79o6S/l3RKUjq/3x8rF8xPk9RmZtOcc/ePYt0XJN0xwjWnSzoxAABVwmWySt+zTZm9XdKgH9i6zI8HAKA8kURctR2bmDcPAAAAAJiSqj6Ul/QxvRLIH5F0g3PubOGbZrZT0rckLZU0T7kq9tVl7Dcg6S8l/YVz7tkhvv/nZvZpSX+ef77BzL7unDs1wrovOue+Vca5AACoas459a/ersy+p4ML5GNRJW5qYn48AAABKG5p7x0+of7l66QBL9Q9C/Pmkx0bFb92HuNnAAAAAADjoqrb1+fnxN+bf+ok3V4cyEuSc25A0u2SzudfutPM6svY9s3OuU8OE8gX9twh6Rv5pzFJHyhjPwAApjznnF7avU/e409J2cFgFmV+PAAAoah0S3vmzQMAAAAAxltVh/LKzYuflX/8pHPu+FAXOef+Xbl581Kurfy7St3w4tD/Er5e9Pg/l7ofAABTnctklf70Vr24bmfuI3gBYH48AADhK7S0T3Zulc2eGfp+hZb2fcvXyfcyoe8HAAAAAEBBtYfyxb1m945wbfH3bwrhLBfrL3o8owL7AQBQdXzfV9/KDcp890Ag69nMWqUebVP9/g7FG+cGsiYAABheoaV93VO7lPrGNsVuvE4KuUFNoaW9d+g4VfMAAAAAgIqo9lD+D4oeHx7h2kPD3BeW4j1+Oorr683s+2b272bmmdkLZvb/mtkWM/u9sA4JAMBE5XsZ9b3nM8p2dUsBvKEebZijuoMPEcYDADAOzEzxhmtU++C9qj/1HSU7t0pXljNZbgS0tAcAAAAAVFC1h/Jzih7/ZIRrfy6pMIT2agtxeGx+1v2KopceH8Vtr5L0NuXa8cclzZT0f0lqlfSsmX3ezKJBnxUAgInI9zI6e8MdGjz2XCDr2VWzlHpkC7PjAQCYAArV8/X7O1Sze4s0PRHaXrS0BwAAAABUglXzp8HNrFfSFfmnNc65Xwd5fRnnWivp8/mn/yRpoXPOH+banygXwu+V1C3pV5ISkn5f0q26cB79V5xzyy+1d19f35D/B3/uuWBCDQAAQuf7qrl7h6KnflZ2d1snafCa16n/C3dJMT7bBgDAhJTJ6lXrv6TYj3K/t4bxETonySXi+vUDH9XgvN+R+KAeAAAAACDv6quvHvL1VCo16l8eqz2U95QLtCUp7pzLjnD9LyRdlX96lXOuJ4QzvUXS9yTFJGUlLXHOHbzE9c2Snr5EaP8xSX8hqZAkfNA597Xh1iOUBwBMWs4peuLfdPnGXYr0/br8QN5MmYVX6/z9H+WNdwAAJjrnFD35b7r8819V5HSfpODD+Qt+WY7HlHnjfA285y0anPM6flYAAAAAgCmMUH4EEy2UN7M3SDogqTAYr9U51xbAup+VdH/+6T8754YdhjtcKI/wFD7wMNz/wwIARuYyWT3/kQ1KHDgq84P5T1ninUtU07ZKFo8Fsh4ATAb8bIrJzjmnzJGTSn9qi/TLM+FvGIkodt0CJdvXK5KIj3w9pgz+PQWA8vFvKQAEg39Px89YQvlqnylf3H5++iiun1H0uD/Ig5jZ70h6Qq8E8juCCOTztkvqyz9+g5n9bkDrAgAw7nzfV9/KDUrs7w4skL/8/juV3NFKIA8AwCRTyXnzkiTfV7arW72NLfIOHVc1FzYAAAAAAMJT7aH8uaLH9cNeJcnMYpKS+adZSeeDOoSZvVbSDyS9Jv/SXzvn7g5qfefcgKQfFr10TVBrAwAwnnwvo773fEbZrm5ZEO+Bx6JKvHOJpr/vxgAWAwAA48XMNG3xfNUd6VS0qSH8DQc8pZetUe+SFfIOnyCcBwAAAACMSbWH8qeKHr9+hGtfo1fmsj/nAvoN28yuUi6QL+z/N5I+HsTaFynu23dFCOsDAFBRvpfR2Rvu0OCx54JZMBpR4qamXMt65sICAFAVIom4ajs2Kdm5Vbrykp/FD4TrOa10S6v6lq+T72VC3w8AAAAAUB2qPZT/cdHjxSNcW/z9Hw971RiY2ZXKBfK/n3/pa5I+HFTgf5Hidx/ODXsVAACTgO/76lvWKvf8C4GsZzNrlXpkCy3rAQCoQhVvaS/R0h4AAAAAMCbVHsrvK3q8dIRrbyp6vLfcjc1slqQn9Uor+U5Jf+Kc88tde4i9pkl6U9FLp4a7FgCAicw5J+/QCfW+6UOBVchHG+ao7uBDijfODWQ9AAAwMdHSHgAAAAAwUVV7KP/3kgoldjeY2fyhLjKzV0taln86IOnb5WxqZnWSvi9pXv6lb0r6oHNusJx1L2GVpFT+8XPOuX8JaR8AAELjMlmlP71V6Q+slXr7AlnTrpql1CNbaFcPAMAUQkt7AAAAAMBEU9WhvHMuK+n+/FOT9FUzu2DeuplNl/QVSZfnX9rpnCuez158bYeZufyfDcNck5L0PUkL8i/9naRl+bOMiZnda2aXLOszs49K2lj00v3DXQsAwETlnFP/6u3K7HtaGgymqUy0YY7qnmxXJBEPZD0AADB50NIeAAAAADCRTIWhqn8l6Y8lvVlSo6SjZvZFSf8i6TWS/qukQvB9QtKmMvfbI+na/OPnlZsjf8sIFXovOue+N8Tr75W0ycx+JOkfJJ2UdFZSQrk59bfqlfBfkv5W0lfLOj0AAOMgc/ikvD0HggnkzRRrWqjUrs9RIQ8AwBRXaGkfP9Kpvg9v0GDX0XA3zLe0t9kzVbOjVfHGufw8AgAAAACo/lDeOeeZ2bskPSbprZJeq6GD9yOS3u2cK7df7nVFj69Sbpb8SH4q6fWX+P6i/J/hZCVtlvTfHB/HBwBMMr7vq/8TDwQTyEcjStzcrJq2VbwBDgAAfqPQ0j5z5KTSn9oi/XLIBnmBKbS0J5wHAAAAAEhTIJSXJOfcWTO7QdL7JH1IuYB7pnJV58cl7Za0q5QW8yH7kKQlygX985U7c71yYwd6lavs/wdJf+Oc+8V4HRIAgFI455Q5fFLpj98fyAx5m1mr5IP3Kt54yckvAABgiipuaZ85clL9n94q13M61D0L4XysaaGS7esZqwMAAAAAU9SUCOUlKV9B3qnRVa4Pt8ZySctHuCawj7475/5J0j9J+sug1gQAYCJwmazS92xTZm9XIBXy0YY5qn1sGxVoAABgRIVwvu6pXcoeO6XzX3xM2ScOSiH2nSvMm092bFT82nn8zAIAAAAAU0xkvA8AAACmFuec+ldvV2bf04EE8nbVLKUe2cKb2wAAYEzMTPGGa1T74L2qP/UdJTu3SlfWh7dhft5875IV8g6fENPnAAAAAGDqIJQHAAAV45zTS7v3yXv8KSk7WPZ60YY5qnuynVawAACgLMWt7Wt2b5GmJ0Lbq9DSvm/5OvleJrR9AAAAAAATB6E8AACoCJfJKv3prXpx3c7y28OaKda8KNeyPj5lpvEAAICQmZmmLZ6vuiOdijY1hLpXoaW9d+g4VfMAAAAAUOUI5QEAQOh831ffyg3KfPdAWesU3q5O3PJmpdrX07IeAACEIpKIq7ZjEy3tAQAAAACBIJQHAAChcpms0ivuU7arWwrgjebL779TyR2tVMgDAIBQ0dIeAAAAABAUQnkAABCaQoV8tqu77LWcSd4fLdL0991Y/sEAAABGiZb2AAAAAIByEcoDAIBQ+F5Gfe/5TCCBvCRlF83Ri/d8gJb1AABgXNDSHgAAAABQKkJ5AAAQON/L6OwNd2jw2HPlL2amWPMi/XrTR6VYtPz1AAAASlTc0j7scL7Q0p5wHgAAAAAmP0J5AAAQKN/31besVe75FwJZL3HLm5VqXy9RIQ8AACYI5s0DAAAAAMaCUB4AAATGZbJKr7gvmAp5SZfff6eSO1pl8Vgg6wEAAASJefMAAAAAgNEglAcAAIHwfV99KzcEM0M+FlXinUs0/X03lr8WAABAyJg3DwAAAAC4FEJ5AABQtkKFfCCBfDSixE1NqmlbJaNlPQAAmCQq3tL+trXqv7tNLpMNbR8AAAAAQDAI5QEAQFmcc+pfvV3Zp4+WvZbNrFXqkS20rAcAAJNWxVraD/ry9nYpfc82KuYBAAAAYIIjlAcAACVzzuml3fvkPf6UVOabwbHmRao7+JDijXMDOh0AAMD4qUhL++ygMo/v18Cj+wjmAQAAAGACI5QHAAAlcZms0p/eqhfX7ZTKfA841rxQqfb1tKsHAABVpVIt7c/fu5M58wAAAAAwgRHKAwCAMfN9X30rNyjz3QNlrxVtmKPUro20qwcAAFWrEi3tXc9ppVta1bd8nXwvE8oeAAAAAIDSEMoDAIAxcZms0ivuU7aru+yW9XbVLKUe2UKFPAAAmBIq0dI+29Wt3sYWeYeOUzUPAAAAABMEoTwAABg155z6V29X9umjZa8VbZijuifbFUnEAzgZAADA5FDc0j60cH7AU3rZGlraAwAAAMAEQSgPAABGLXP4pLw9B8qukI81L1LtY9toWQ8AAKasSsybp6U9AAAAAEwMhPIAAGBUfN9X/ycekAb9staJNS9Uqn09LesBAABUmXnztLQHAAAAgPFFKA8AAEZUmCPvzpwrb6H6WqV2baRCHgAA4CKhz5unpT0AAAAAjBtCeQAAcEm+76tv5QZlu7rLWygaUfLBz1IhDwAAMIzilvaXbfqkFMKPTYWW9oTzAAAAAFA5hPIAAGBIzjl5h06o900fKj+Qj0WVuLlZ8ca5wRwOAACgipmZZrQsVeKWJVIsGsoezJsHAAAAgMohlAcAAP+By2SV/vRWpT+wVurtK2+xaESJm5pU07aKKnkAAIBRMjPVtK1SfOn1UjS8t2+YNw8AAAAA4SOUBwAAF3DOqX/1dmX2PS0N+mWtZTNrlXpki5I7WpkjDwAAMEYWjym5o1XJhzeHM2e+gHnzAAAAABAqQnkAAHCBzOGT8vYckLKD5S1UX6u6gw/Rsh4AAKAMxXPma3ZvkaYnQtuLlvYAAAAAEA5CeQAA8Bu+76v/Ew+UXSGvaETJBz9Lu3oAAICAmJmmLZ6vuiOdijY1hLoXLe0BAAAAIFiE8gAAQFJ+jvyK++TOnCtvITMlbm6mQh4AACAEkURctR2blOzcSkt7AAAAAJgkCOUBAIB831ffyg3KdnWXvVasqUE1bauokgcAAAgJLe0BAAAAYHIhlAcAYIorVMgHEsg3L1Jq10ZZPBbAyQAAAHAptLQHAAAAgMmBUB4AgCnMOaf+1duVffpo2WvFmhcq1b6eCnkAAIAKq2hL+9v+TP13t8llsuHtAwAAAABVhlAeAIApLHP4pLw9B6Ryqp3MqJAHAAAYZ8Ut7UMN531f3uP71bdyg3zfD2cPAAAAAKgyhPIAAExRvu+r/xMPSIPlvZmauOXNVMgDAABMEBWZN++csl3dOnvd7fIOn6CdPQAAAACMgFAeAIApqDBH3p05V9Y6l99/p5I7WqmQBwAAmGAqMW/enTmndEur+pavk+9lQtkDAAAAAKoBoTwAAFOM7/vqW7lB2a7u0hcxU+KdSzT9fTcGdi4AAAAErxLz5rNd3eptbJF36DhV8wAAAAAwBEJ5AACmkEKFfFmBvKRYU4Nq2lbRsh4AAGASqEhL+wFP6WVr1LtkBS3tAQAAAOAihPIAAEwRzjn1r96u7NNHy1on1rxIqV0baVkPAAAwyVSkpX3PaVraAwAAAMBFCOUBAJgiModPyttzQCqjainWvFCp9vVUyAMAAExitLQHAAAAgMoilAcAYArwfV/9n3hAGvRLX6S+lgp5AACAKkFLewAAAACoHEJ5AACqXGGOvDtzrvRFohElH/wsFfIAAABVhpb2AAAAABA+QnkAAKqY7/vqW7lB2a7u0hcxU+LmZsUb5wZ2LgAAAEwsF7S0r0+Fsgct7QEAAABMVYTyAABUKd/LqO89nykvkJcUa2pQTdsqquQBAACqXKGlfd3BhxRrXiiF8fMfLe0BAAAATEGE8gAAVCHfy+jsDXdo8NhzZa0Ta17EHHkAAIApJhKJKNW+QfF3NEuRcD6YWWhpTzgPAAAAYCoglAcAoMr4vq++Za1yz79Q1jqx5oVKta+nQh4AAGAKsnhMyR2tqnl4szQ9Edo+rue00retVf/dbXKZbGj7AAAAAMB4IpQHAKCKuExW6RX3lV0hr/paKuQBAACmODPTtMXzVXekU9GmhvA2GvTl7e1S+p5tVMwDAAAAqEqE8gAAVAnf99W3ckPZM+QVjSj54GepkAcAAIAkKZKIq7Zjk5KdW6Ur68PZJDuozOP7NfDoPoJ5AAAAAFWHUB4AgCpQqJAvO5A3U+LmZsUb5wZzMAAAAFQFM1Pi2nmq39+hmt1bQmtpf/7encyZBwAAAFB1COUBAJjknHPqX71d2YPHyl4r1tSgmrZVVMkDAABgSJVoae96Tivd0qq+5evke5lQ9gAAAACASiKUBwBgkst0PyvviR9Kvl/WOrHmRcyRBwAAwKhUoqV9tqtbvY0t8g4dp2oeAAAAwKRGKA8AwCTmMln137VZetkra51Y80Kl2tdTIQ8AAIBRq0hL+wFP6WVraGkPAAAAYFIjlAcAYJIqtK13PafLWifaMIcKeQAAAJSMlvYAAAAAcGmE8gAATFKZwyfl7TlQ1hp21SylHtlChTwAAADKRkt7AAAAABgaoTwAAJOQ7/vq/8QD0mDpc+SjDXNU92S7Iol4gCcDAADAVFbc0j60cJ6W9gAAAAAmGUJ5AAAmGZfJKr3iPrkz50peI9a8SLWPbaNlPQAAAEJRHM5ftumTUgiNmWhpDwAAAGCyIJQHAGAS8X1ffSs3KNvVXfIaseaFSrWvp2U9AAAAQmdmmtGyVIlblkixaCh7ZLu6dfaGOwjmAQAAAExYhPIAAEwShQr58gL5RUrt2kiFPAAAACrGzFTTtkrxpddL0XDeinLPv6C+97fK90sf7wQAAAAAYSGUBwBgEnDOqX/1dmWfPlryGjZ7FhXyAAAAGBcWjym5o1XJhzeHM2de0uDR53T2utuZMw8AAABgwiGUBwBgEsgcPilvzwGpjDcXkzvXUiEPAACAcVM8Z75m9xZpeiLwPdyZc0q3tKp3yQrCeQAAAAATBqE8AAATnO/76v/EA9Jg6a04bfYsxRbMCfBUAAAAQGnMTNMWz1fdkU5FmxpC2cP1nFa6pVV9y9cxax4AAADAuCOUBwBgAivMkXdnzpW+SDSimh2raVsPAACACSWSiKu2Y5OSnVtDa2mf7epWb2OLvEPHqZoHAAAAMG4I5QEAmKB831ffyg3KdnWXvoiZEjc3K944N7BzAQAAAEGpREt7DXhKL1tDS3sAAAAA44ZQHgCACahQIV9WIC8p1tSgmrZVVMkDAABgQqOlPQAAAIBqRigPAMAE45xT/+rtyj59tKx1Ys2LlNq1URaPBXQyAAAAIFy0tAcAAABQjQjlAQCYYDKHT8rbc0Aq4w3CWPNCpdrXUyEPAACASadiLe1v+zP1390ml8kGvz4AAAAAFCGUBwBgAvF9X/2feEAa9EtfpL6WCnkAAABMehe0tG+4OvgNfF/e4/vVt3KDfL+Mn78BAAAAYASE8gAATBCFOfLuzLnSF4lGlHzws1TIAwAAoGpEEnGlvr5NseaFUtA/5zqnbFe3+t77GebMAwAAAAgNoTwAABOA7/vqW7lB2a7u0hcxU+LmZsUb5wZ2LgAAAGAiiEQiSrVvUPwdzVI0+LezBo8+x5x5AAAAAKEhlAcAYJwVKuTLCuQlxZoaVNO2iip5AAAAVCWLx5Tc0arkw5ulK+uD32DAU3rZGvUuWSHv8AnCeQAAAACBIZQHAGAcOefUv3q7sgePlbVOrHkRc+QBAABQ9cxMiWvnqX5/h2p2b5GmJwLfw/WcVrqllXAeAAAAQGAI5QEAGEeZ7mflPfFDyfdLXiPWvFCp9vVUyAMAAGDKMDNNWzxfdUc6FW1qCGWPQjjft3wd8+YBAAAAlIVQHgCAceIyWfXftVl62St9kfpaKuQBAAAwZUUScdV2bFKyc2s4Le0lZbu6mTcPAAAAoCyE8gAAjINC23rXc7r0RaIRJR/8LBXyAAAAmNIq0dL+4nnzIpwHAAAAMAaE8gAAjIPM4ZPy9hwofQEzJW5uVrxxbnCHAgAAACaxirW0v22tLtvykJQdDGUPAAAAANWHUB4AgArzfV/9n3hAGixjjnxTg2raVlElDwAAAFzkgpb29angNxj0lThwTJe1/S3t7AEAAACMCqE8AAAV5DJZpVfcJ3fmXMlrxJoXMUceAAAAuIRCS/u6gw8p2nB18OsPDirxVLcGHt1HMA8AAABgRITyAABUiO/76lu5Qdmu7pLXiDUvVKp9PRXyAAAAwChEIhGlHtkqu2pWKOufv3fnb+bME84DAAAAGA6hPAAAFVCokC8vkKdCHgAAABirSCKuK77/pcDnzBc+Jut6TitIusDXAAAgAElEQVTd0qq+5evke5lA9wAAAABQHQjlAQAImXNO/au3K/v00ZLXsNmzqJAHAAAASnTBnPkr60PZI9vVrd7GFnmHjlM1DwAAAOAChPIAAIQsc/ikvD0HpDLemEvuXEuFPAAAAFCGwpz5+v0d4YXzA57Sy9bQ0h4AAADABQjlAQAIkXNO/XdvlQb9ktew2bMUWzAnwFMBAAAAU1dxOF+ze4s0PRH4HoWW9oTzAAAAACRCeQAAQpXpflau53TpC0Qjqtmxmrb1AAAAQMDMTNMWz1fdkc7A580XuJ7TSt+2Vv13t8llsqHsAQAAAGDiI5QHACAkLpNV/12bS1/ATImbmxVvnBvcoQAAAABcIPR584O+vL1dSt+zjYp5AAAAYIoilAcAIAS+76tv5YayquRjTQ2qaVtFlTwAAAAQsuKW9pdt+qQU9I/g2UFlHt+vgUf3EcwDAAAAUxChPAAAAXOZrNIr7lO2q7vkNWLNi5TatVEWjwV4MgAAAACXYmaa0bJUiVuWSLFo4Oufv3cnc+YBAACAKYhQHgCAADnn1L96u7JPHy15jVjzQqXa11MhDwAAAIwDM1NN2yrFl14vRYN/68z1nFa6pVV9y9fJ9zKBrw8AAABg4iGUBwAgQJnDJ+XtOSCVWvVSX0uFPAAAADDOLB5Tckerkg9vDmfOvKRsV7d6G1vkHTpO1TwAAABQ5QjlAQAIiHNO/XdvlQb90haIRpR88LNUyAMAAAATQPGc+ZrdW6TpieA3GfCUXraGlvYAAABAlSOUBwAgIJnuZ+V6Tpd8f+LmZsUb5wZ4IgAAAADlMjNNWzxfdUc6FW1qkCQFHZ3T0h4AAACoboTyAAAEwGWy6r9rc8n32+xZqmlbRZU8AAAAMEFFEnHVdmxSsnOr/JmpwIN5KdfS/uwNdxDMAwAAAFWGUB4AgDL5vq++lRtKr5KfFldy51rmyAMAAAATXKGlffqr69W/7c5Q5s27519Q3/tb5fsljsUCAAAAMOEQygMAUAaXySq94j5lu7pLWyASUeLt1ym2YE6wBwMAAAAQHjMNzvtd1e/v0GWbPikF3PBq8OhzOnvd7cyZBwAAAKoEoTwAACUqVMiXHMhLil2/gLb1AAAAwCRlZprRslSJW5ZIsWiga7sz55RuaVXvkhWE8wAAAMAkRygPAEAJyq6Ql6T6WqV2baRtPQAAADCJmZlq2lYpvvR6KRr8W22u57TSLa3qW76OWfMAAADAJEUoDwDAGDnn1L96u7IHj5W+SDSi5IOfpUIeAAAAqAIWjym5o1XJhzeHMmdekrJd3eptbJF36DhV8wAAAMAkQygPAMAYZY+ekvfkM5Lvl7xG4uZmxRvnBngqAAAAAOPJzJS4dp7q93eoZvcWaXoi+E0GPKWXraGlPQAAADDJEMoDADBGL335m9JLL5d8v82exRx5AAAAoEqZmaYtnq+6I52KNjWEsofrOa30bWvVf3ebXCYbyh4AAAAAgkMoDwDAGPi+L+97T5e+wLS4kjvXMkceAAAAqHKRRFy1HZuU7NwaTkv7QV/e3i6l79lGxTwAAAAwwRHKAwAwSi6TVXrFfZJf4htekYgSb79OsQVzgj0YAAAAgAkp9Jb22UFlHt+vgUf3EcwDAAAAExihPAAAo+D7vvpWblC2q7vkNWLXL6BtPQAAADAFXdDSvuHqwNc/f+9O5swDAAAAExihPAAAIyhUyJcVyDcvUmrXRtrWAwAAAFNYJBFX6uvbFGteKAX8YV3Xc1rpllb1LV8n38sEujYAAACA8lQslDezpJnNNrPLKrUnAADlcs6pf/V2ZQ8eK3mNWPNCpdrXUyEPAAAAQJFIRKn2DYq/o1mKBv/WXLarW72NLfIOHadqHgAAAJggQgvl8yH8GjPrMrMBSWcl/VzSR4e49mNmdpeZ/ZewzgMAQCmyR0/Je/IZyfdLWyBiVMgDAAAAuIDFY0ruaFXy4c3SlfXBbzDgKb1sDS3tAQAAgAkilFDezG6R9K+SHpD0JkkJSZcqD7xO0p9L+oqZTQ/jTAAAlOKlL39Teunlku+P33g9FfIAAAAA/gMzU+Laearf36Ga3Vuk6YnA93A9p5W+ba36726Ty2QDXx8AAADA6AQeypvZOyV9S9IVygXxA5J+NMJtX8xfm5R0U9BnAgCgFL7vy/ve06UvMGOaLvvwrcEdCAAAAEDVMTNNWzxfdUc6FW1qCH6DQV/e3i6l79lGxTwAAAAwTgIN5c2sVtJXJUUlZSStklTnnLv2Uvc557ok/Sr/9O1BngkAgFK4TFbpFfdJfolvWkUiSrztjYotmBPswQAAAABUpUgirtqOTUp2bg2+pX12UJnH92vg0X0E8wAAAMA4CLpS/qOSaiU5SSucczucc6Pt+fuMctXyCwM+EwAAY+KcU//q7coePFbyGrHrF6imbRWt6wEAAACMWnFL+8s2ffLSwyBLcP7encyZBwAAAMZB0KH8O/Jfu51zj4zx3n/Of/29AM8DAMCYZbqflffEDyXfL+n+WPMipXZtlMVjAZ8MAAAAwFRgZprRslSJW5ZIsWiga7ue00q3tBLOAwAAABUUdCh/jXJV8k+WcO+5/NdUcMcBAGBsXCar/rs2Sy97Jd0fa16oVPt6KuQBAAAAlMXMVNO2SvGl10vRoN/CeyWc71u+Tr6XCXx9AAAAAK8I+if62vzX0yXcm8h/La0sEQCAMhXa1rueUv4zJiliVMgDAAAACIzFY0ruaFXy4c3Bz5nPy3Z1q7exRd6h41TNAwAAACEJOpQvVLvXXvKqob0+/7XEJOTSLKfFzP6Xmf3czF42sx4ze9LMVppZYAmKmb3OzD5iZl8zsx+bWdrMPDN7wcwOmNnnzOx1Y1wzbmYfzp+3J3/+n5vZd/J/L0oyAaBMmcMn5e05UPL98Ruvp0IeAAAAQKCK58zX7N4iTU+MfNNYDXhKL1tDS3sAAAAgJEGH8j/Nf712LDeZWVTS25VrfX8y4DPJzK6Q9H1JuyXdIum3lavMv1LSWyW1S3pmrEH5MHt9S9JPJP21pNskzZdUIykuaaakJknrJJ0ys3tGuebrJT0j6Uv5816ZP/9vS3pn/u/1PTMr5cMQAADlq+Tv3ioNltiwZcY0XfbhW4M9FAAAAADkmZmmLZ6vuiOdijY1hLKH6zmt9G1r1X93m1wmG8oeAAAAwFQUdCj/pCST9BYz+50x3LdSuYC5sEZgzCwh6dvKhdmS9DPlQvH3S1qtVz4E0Chpj5kly9zyD5T730CS/lHSVuX+fu+TtEpSV/570yS1mdm9I5y/VtIeSYvyL53Mn/v9+b/Hz/Kv3yDpm0FW/APAVJLpfraMtvURJd72RsUWzAn2UAAAAABwkUgirtqOTUp2bg2npf2gL29vl9L3bKNiHgAAAAhI0KF8h6RBSVFJf2tml490g5m9Q9L2/NOXJO0K+Ewfk/Tm/OMjkhqcc5ucc7udc19QLozfl//+POWC7nIMSPpLSW9wzv2hc26Nc+5/OOe+7pz7c+dcs6S7i67fYGaXSnHWS3pD/vFeSY3OuS/kz79J0kJJP8p//y2SPlLm+QFgynGZrPrv2lzy/bHrF6imbRWt6wEAAABURHFL+8s2ffKV8pCgZAeVeXy/Bh7dRzAPAAAABCDQUN4596ykv1LuV4E3SfqRmd1uZlcWX2dmrzKzpWbWKenvJM1QrnX9VudcYDPl81XjhUp0J+l259zZi848IOl2SefzL91pZuV8zPjNzrlP5v+3GJJzboekb+SfxiR9YJjzv1rSx/NPz0v6k/x5i9fqzZ+/8BvSuvw4AADAKPi+r76VG0quko81L1Jq10ZZnEYlAAAAACrLzDSjZakStyyRYsG/HXT+3p3MmQcAAAACEHSlvJRr0f6EcsH87ylX+f4LvRIa3y+pT9J3Jb2n6Azfcc59LuCzvFXSrPzjJ51zx4e6yDn378rNZZdybeXfVeqGF4f+l/D1osf/eZhr/m/lZsdL0iP5cw61548l/SD/9Lck/dEozwAAU5rLZJVecZ+yXd0l3W+zZynVvp4KeQAAAADjxsxU07ZK8aXXS9Hg3+pzPaeVbmlV3/J18r1M4OsDAAAAU0HgP6k757KS3iGpTVJWuXC+OK1IFL1m+Wu2Sbo16LNIurHo8d4Rri3+/k0hnOVi/UWPZwxzzUQ+PwBMaoUK+VIDeUlK7lxLhTwAAACAcWfxmJI7WpV8eHM4c+YlZbu61dvYIu/QcarmAQAAgDEKo1JezrlB59wa5SrlN0k6qNy8+EIQ/7KkY8qF8W9wzq12zvkhHOUPih4fHuHaQ8PcF5biPX46imsm2vkBYNIqt0JeylXJxxbMCfBUAAAAAFC64jnzyc6t4YTzA57Sy9bQ0h4AAAAYo1BC+QLn3M+dc/c555qcc69SriK8xjk3wzm3MB/G/2uIRyhOS34ywrU/lzSYf3y1hdiLOD/rfkXRS48PcU1EuQ81KH+un4+wbHGwT0oEAMNwzql/9XZlDx4rfZFoRDU7VtO2HgAAAMCEUxzO1+zeIk1PjHzTGLme00rftlb9d7fJZbKBrw8AAABUG6vmT7SaWa+kK/JPa5xzvw7y+jLOtVbS5/NP/0nSwos7BZhZUlJf/ukZ59zMEdYc1fV9fX1D/h/8ueeeG+XpAWByi/7zT1Wz9kHZy15J9ztJ3h8t0otrPiQRygMAAACY6DJZvWr9lxT7Ue69nyB/i3Fmyiy8Wuc3fUSKhFr7AwAAAIybq6++esjXU6nUqH+8rvafll9V9HhgFNe/VPS4JuCzSJLM7C2SNuafZiV9ZJjW/RPu7ABQDaY/9gOpjEDen1WrF+/5AIE8AAAAgMkhHtOv7/+Y+rfdKX9mSk65322CYM4p/qNTqlm1Q6JiHgAAABjWuFTK59u3v13SG5QLk59yzp0IYR9PUjz/NO6cu+RvB2b2C0lX5Z9e5ZzrCfg8b5B0QFJhqFerc65tmGuvkvSL/NOfO+deO8LaMUmZ/FPPOTdtqOuGq5RHeApdCIb7FA2AynHO6cwb3iUNDvVZqFGYFlfq4c2KN1wT7MEwKvx7CgDl499SAAjGZP331Dmnlzr36cV1O4NL5gumJ5Ts2Kj4tfMY9QVgVCbrv6UAMNHw7+n4GUulfCzIjfMt1Nfmnz7lnNs7xDVzJH1H0u9f9PrfSlrpnMtcfE8Zfq1X2tFPzz+/lBlFj/sDPIfM7HckPaFXAvkdwwXyecVnnTHsVa+4rOhxoGcHgGqR6X629EA+ElHi7dcptmBOsIcCAAAAgAoxM81oWarsD4/J29slZQeDW3zAU3rZGtnsmarZ0ap441zCeQAAACAv6Pb1NygXyq/RK/PNf8PM4pK+Lelq5UZYFf/5oKQHAz7PuaLH9cNepd9UmifzT7OSzgd1CDN7raQfSHpN/qW/ds7dPcJtv86fQ5JqzSw6wvXFf79zw14FAFOUy2TVf9fmku+PXb9ANW2reFMJAAAAwKRmZqppW6X40uulaPCTLV3PaaVbWtW3fJ18L8jaGwAAAGDyCvon77fnv/7SOXdwiO/fLuka5RpknZP05fyfF5UL5v/UzBYFeJ5TRY9fP8K1r5FUCL6fcwH19c+3of9B0f5/I+njI92XnzP/f/JPo3ol0B/Ofyp6fGrYqwBgCvJ9X30rN8j1nC7p/ljzIqV2bZTFA20wAwAAAADjwuIxJXe0KvnwZunKS9axlCzb1a2zN9xBMA8AAAAo+FB+kXKB+1CBvJQL5SXpZUnXOefucM7dIekdQ1wThB8XPV48wrXF3//xsFeNgZldqVwgX2jV/zVJHx5D4D+u5weAauAyWaVX3KdsV3dJ98eaFyrVvp4KeQAAAABVxcyUuHae6vd3qGb3Fml6IvA93PMvqO/9rfL9EseIAQAAAFUi6FB+Vv7rsxd/w8xeJek65UL7/+mc+801zrmnJD2jXLV8U4Dn2Vf0eOkI195U9HhvuRub2SxJTyrXGUCSOiX9Sb4CfrTG7fwAUA2cc+pfvV3Zg8dKWyBiVMgDAAAAqGpmpmmL56vuSKeiTQ2Brz949Dmdve52eYdPKKDGlAAAAMCkE1Yo/x/myUt6o6RCqvF3Q3z/mfzX3w3wPH8v6YX84xvMbP5QF5nZqyUtyz8dUG7ufcnMrE7S9yXNy7/0TUkfdM4NjnGpb0ny8o/fnz/nUPvNl/TW/NNfSvqHMe4DAFUpe/SUvCefkUqsyojfeD0V8gAAAACmhEgirtqOTUp2bg28pb07c4458wAAAJjSgg7lC32u4kN8701Fj58a4vu/yn9NBnUY51xW0v35pybpq2Z2RfE1ZjZd0lckXZ5/aadz7sxQ65lZh5m5/J8Nw1yTkvQ9SQvyL/2dpGX5s4z1/C9IejD/9FWSOvLnLd7vCkkP5f9+krSphPAfAKrSS1/+pvTSy6XdPGOaLvvwrcEeCAAAAAAmsOKW9snOrVJ9KtD1s13d6m1skXfoOFXzAAAAmFKC7sd7VtKrJf2nIb73lvzXf3PO9Qzx/UKgP+bwegR/JemPJb1ZUqOko2b2RUn/Iuk1kv6rpLn5a09I2lTmfnskXZt//Lxyc+RvGaHS8kXn3PeG+d5/U641/Rsk3SzpiJl9WdIvlJtV/xFJr81f+78lfamcwwNAtfB9X973ni75/sTb3qjYgjkBnggAAAAAJodCOF938CH1vfczGjz6XHCLD3hKL1sjmz1TNTtaFW+cS4cyAAAAVL2gQ/kTkn5L0o1mZi7/kVczu1LSEuXmyQ9VJS9JV+W/ng7yQM45z8zeJekx5Vq8v1ZDB+9HJL3bOTdU6/2xuK7o8VXKzZIfyU8lvX6obzjnzpnZzcq1wF+k3AcItg1x6fclvdc5Rw8wAFOey2SVXrlB8kurvLDZs1TTtoo3hgAAAABMaZFIRKlHtursDXfIPf/CyDeMges5rXRLK+E8AAAApoSg29d/N//1tZL+wsySZvZbkv6HXvkAwHeGuXeRcqH9/wn4THLOnZV0g3Jz4x9XroLdU65l/g8k3SHpjc65/y/ovYPgnPuJpDcqd84fKHduT7m/x+PK/b1udM6dG68zAsBE4ZxT/+rtyh48VtoC0+JK7lwriwf9uTUAAAAAmHwiibiu+P6XFG1qCGV913Na6dvWqv/uNrlM0A00AQAAgIkh6MThbyStlVQn6WP5PwVO0r8qN2P9Amb2auVay0vSoYDPlNs8V7XfqdFVrg+3xnJJy0e4JpSP9OYr4NvzfwAAw8h0PyvviR9Kvj/2myMRJd5+HW3rAQAAAKBIJBFXbccmZY6cVPpTW6Rfngl2g0Ff3t4upZ1TckcrFfMAAACoOoFWyucr0lsknZdkF/05L+lDzrnBIW5dVnSWfwjyTACAqcNlsuq/a7P0slfS/bHrF9C2HgAAAACGUJgzX7+/QzW7t0jTE8FukB1U5vH9Gnh0n/ITMQEAAICqEXT7ejnnfiBpvqTPS9or6QlJX5C0wDn3w2Fue7ekX0j6iXKz0QEAGJNC23rXc7q0BSKm1K6NtK0HAAAAgEswM01bPF91RzoVbbg68PXP37tTvUtWyDt8gnAeAAAAVSOU5ME59zNJ947h+reEcQ4AwNSROXxS3p4DJd8fv/F6KuQBAAAAYJQiibhSX9+m9J/ep2zXUSnAAN31nFa6pVWxpoVKtq9XJBEPbG0AAABgPAReKQ8AQKU559R/91ZpsIQ58pI0Y5ou+/CtwR4KAAAAAKpcJBJRqn2D4u9oliLBf8g529Wt3sYWeYeOUzUPAACASY1QHgAw6WW6ny2jbX1Eibe9UbEFc4I9FAAAAABMARaPKbmjVTUPbw5+zrwkDXhKL1tDS3sAAABMaoTyAIBJzWWy6r9rc8n3x65foJq2VbSuBwAAAIASXTBnvqkhlD1cz2mlb1ur/rvb5DLZUPYAAAAAwhLKTPkCM5smabGkayTVSpo+mvuccw+EeS4AQHVwzql/9faSq+RjzYuU2vU5AnkAAAAACEAkEVdtxyZljpxU+lNbpF+eCXaDQV/e3i6lnVNyRyu/ywEAAGDSCCWUN7OZkjZK+qCky0pYglAeADCiTPez8p74YUn32uxZSrWv500cAAAA/P/s3Xt0nGd57/3fNdKMbCeSHCtubQq7lBBKYhoHO61R7BqaxLgkuxBCUzmhO9iEpKUrTVZMLZsGB7/F6fah8fLe9buhObyIBhI7AVPaBkKMORnVCThGApzUNrShG6JAZDmSCJKeGc31/jGjeGziwzxzP9JI+n7WmjWjmec+ENaSNXPN/bsABGRmysy/UE172pIpzueGlX10jwYvnaspf7KU93QAAAAYF4LH15vZGyV1SLpZ0lmSrMwbAACn9XJs/VAUa3zDtjWydKKBMQAAAAAwaZUW56etvyX4p34v3bGNPvMAAAAYN4JWI8ysVtIXJL2q+NT3JD0iaa6kP5bkkv5MUqOkN0m6StK5kvKStkp6JuR+AAATU6Wx9TZ7pmovekPgXQEAAAAATmRmmtqyVLknvqfosXYpNxxsbu/qVl9Lq2z2uarf2qr0vAs4OQ8AAICqFPqk/J9KOl+F4vtnJM1z97skPTlygbvf5+53u/sKSa9RIareJN0k6Ufufn/gPQEAJpjsU88o+tK34g2uSal+6yo+qAEAAACAUWJmqt+8Uumll0o1wYM7Xy7O9y5fq3yUDT4/AAAAUKnQfwW/q3jfJ+mD7p4/1cXuPuTuH5F0p6R6SQ8W+9EDAPCK3F39t2+Shk/5T8xJZd6xSOl5FwTeFQAAAADgVCxdq4atrWp4cIM0qymRNXLtHeqZ16Jo3wEi7QEAAFBVQhfl56lwSv4xd/9FGeM2SHpW0q9LujHwngAAE0i242BFsfX1m1dySh4AAAAAxkBpn/n67RulKZnwiwxG6rv+w+q/fbM8mws/PwAAABBD6KL8yCn3fz/h+ZebRZnZlBMHufuwpEdViLF/d+A9AQAmCM/m1H/rhniD69Jq2LZGlq4NuykAAAAAQFnMTHWXzNGM/TtUs3Bu+AXyeUWP7lHvB9Ypn4+XsgYAAACEFLooX1O8Hzjh+dJT8zNPMva54v1rQ24IADAxuLv6V22JfUo+s6RZtRe9IfCuAAAAAABxpTJpTW9br4Ydm8JH2rsr196h3ms/RJ95AAAAjLnQRfme4n39Cc//vOTx+ScZ++vF+3OC7ggAMCFkOw4q2vVErLHE1gMAAABAdSqNtJ+2/pZCjmZAw52H6TMPAACAMRe6KH+oeP+6E57/fsnjJScOskKV5PLijz0nvg4AmNxejq0fimKNJ7YeAAAAAKqbmWlqy1Jlrlos1dacfkA5BiP1LVutnsUrFD31NMV5AAAAjLrQRfknVfg+6yWlT7r7f0o6WHztg2Z20Qnj1kmaI8klfTvwngAA41ilsfU2eyax9QAAAAAwDpiZ6jevVHrppVJN6I8tJe/qVl9Lq3qXryXSHgAAAKMq9F+3jxfvX29mJ1ZAthXv6yV928y+ZGafMbOnJX2k5Lp7Au8JADCOVRJbr5qU6reuIrYeAAAAAMYJS9eqYWurGh7cEL7PfFGuvUNHr7iZwjwAAABGTeii/Ncl/UxSXtLNJ7z2cUm7VDgtn5H0dknLJP22jnWLanP3RwPvCQAwTlUaW595xyKl510QeFcAAAAAgCSV9plv2LEpkeK8P/eCeq9rVT6fDz43AAAAcKKgRXl3H3b32e6edve/OuG1vKR3SdokqVeFQvzIrVvSane/MeR+AADjV4jY+vrNKzklDwAAAADjVGlxvn77RmlKJuj8w52HdbT5BvrMAwAAIHHhmzOdgrsPuvsaSTMlzZX0Nkm/I+nX3X3zaO4FAFDdsk89o+hL34o3uC6thm1rZOnasJsCAAAAAIw6M1PdJXM0Y/8O1SycG3RuP/IifeYBAACQuFEtyo9w95y7f9/dv+nuB5yvogIASri7+m/fJA3HixHMLGlW7UVvCLwrAAAAAMBYSmXSmt62vhBp39QYdO5ce4d65rUo2neAU/MAAAAIbkyK8gAAnEq24yCx9QAAAACAXzESaT9j7wOqmXt+2MkHI/UtW62exSuItAcAAEBQo1aUN7MGM5ttZtNGa00AwPjj2Zz6b90QbzCx9QAAAAAwKaRSKTU+tEn2qpnB5/aubvW1tFKcBwAAQDCJFeWLRfjVZtZuZoOSjkr6iaQ/f4VrP2hmt5rZO5PaDwCg+rm7+ldtiX1Knth6AAAAAJg8Upm0zvnKPcH7zI/wrm71Xb9G/bdvlmdziawBAACAySGRo4RmdpWkT0k6Z+Sp4v3JvlbaLOm9kvrMbLa7DyaxLwBAdct2HFS064lYY4mtBwAAAIDJZ6TPfHb/M+q7baP0/JGwCwznFT3Wrj53NWxt5T0nAAAAYgl+Ut7M/rukf1KhIG+SBiV99zTD/qF4bYOkPwy9JwBA9Xs5tn4oijWe2HoAAAAAmJxG+sw37WlT/faN0pRM2AVyw8o+ukeDD3+ZKHsAAADEErQob2bTJf2jpBpJWUkrJc1w9/mnGufu7ZJ+VvxxScg9AQCqX6Wx9TZ7JrH1AAAAADDJmZnqLpmjGft3qGbu+cHnf+mObfSZBwAAQCyhT8r/uaTpKsTUr3D3re4+dIZjn1ThtPzFgfcEAKhyuc5DinY/GW9wTUr1W1cRIQgAAAAAkFSItG985G7VLrpYCvxe0bu61dfSqt7la5WPskHnBgAAwMQVuih/ZfG+w90fKnPsvxfvzwu4HwDAODBw305p4Ey/w3W8zDsWKT3vgsA7AgAAAACMZ6lUSo33rlP6ykVSKvyXuHPtHeqZ16Jo3wFOzQMAAOC0Qhflf1uFU/K7Y4x9sXjfGG47AIBql8/nFT3+b7HG2uyZqt+8klPyAAAAAIBfYelaNWxtVf2DG8L3mZekwUh9y1YTaQ8AAIDTCl2Un168j9MUeOQv43ygvQAAqpxnc+pbcaeUj/HBRV1aDZI1S8EAACAASURBVNvWyNK14TcGAAAAAJgQjuszv3BuImt4V7f6rl+j/ts3y7O5RNYAAADA+Ba6KD9y2n36Ka96Za8t3scp6AMAxhl3V/+qLcrt/V6s8Zklzaq96A2BdwUAAAAAmIhSmbSmt61Xw45N0qym8AsM5xU91q6+v7qbE/MAAAD4FaGL8j8u3s8vZ5CZ1UhaokL0/TOB9wQAqELZjoOKdj0h5csPSCG2HgAAAABQLjNTZv6FatrTlkxxPjes7KN7NPjwlynMAwAA4Dihi/K7JZmkPzCz3ypj3Ack/UbJHACACcyzOfXfukEaimKNJ7YeAAAAABBXaXF+2vpbCp9mBvTSHdvoMw8AAIDjhC7Kt0kallQj6dNmdtbpBpjZlZK2FH8ckPTJwHsCAFSRkdh674rZraQmRWw9AAAAAKBiZqapLUuVuWqxVFsTdG7v6lZfSyvFeQAAAEgKXJR394OSPq7C90vfIum7ZnaDmc0qvc7MzjazpWa2Q9I/S5qqQnT9JnenpzwATGC5zkOKdj8Ze3x6STOx9QAAAACAIMxM9ZtXKr30Uqkm9PmlY8X53uVrlY+ywecHAADA+BD+L01ppaRdKhTmz1Ph5PtPVSi6S9JdknolfVHSH5fs4V/c/W8S2A8AoIoM3LdTGhiKN3hqnabddE3YDQEAAAAAJjVL16pha6saHtwQvs98Ua69Q0evuJnCPAAAwCQVvCjv7jlJV0raLCmnQnG+9EhjpuQ5K15ztySqLAAwwbm7ol174w1OpZS5fAHR9QAAAACA4Er7zNdv3yhNyQRfw597Qb3XtSqfzwefGwAAANUtiZPycvdhd1+twkn59ZL2qtAvfqQQPyTpeyoU49/o7qvcnb9GAWCCy3YclIbj/bqvvfQi1W9eSXQ9AAAAACAxZqa6S+Zoxv4dqlk4N/j8w52HdbT5BvrMAwAATDKJFOVHuPtP3P1Od1/o7mer0Du+3t2nuvvFxWL8fyS5BwBAdfBsTv23bog1tnbRm9X4yY/J0rWBdwUAAAAAwK9KZdKa3rZeDTs2BY+09yMv0mceAABgkkm0KH8idx9y95dGc00AwNhzd/Wv2iLv6i57rM2eqcZ7P8oJeQAAAADAqCqNtJ+2/pbjG3QGkGvvUM+8FkX7DnBqHgAAYIIb1aI8AGByynYcVLTriVhjG7at4YQ8AAAAAGDMmJmmtixV5qrFUm1N2MkHI/UtW62exSuItAcAAJjAKMoDABL1cmz9UFT+4JqUai96Q/hNAQAAAABQBjNT/eaVSi+9VKoJ/5Gqd3UTaQ8AADCBxTp6aGavCr2RUu7+XJLzAwBGRyWx9ZKUXtJMbD0AAAAAoCpYulYNW1uV3f+M+m7bKD1/JPgaufYOHb3iZp3zlXuUyqSDzw8AAICxETcP+CeSkspScsXfFwCgilQSW6+pdZp20zVhNwQAAAAAQAVK+8wnVZz3515Q73WtanzkbqVSBJ0CAABMBJX8VWcJ3gAA41xFsfWSMpcvILoeAAAAAFCVSovz9ds3SlMyQecf7jyso8030GceAABggoh7Iv3flNxJeQDAOFdpbL3Nnqn6zSuJrgcAAAAAVDUzU90lc5Tev0O917VquPNwsLn9yIvqa2mVzT5X9VtblZ53Ae+TAQAAxqlYRXl3XxR6IwCAiSPXeUjR7ifjDa5Lq2HbGlmaTiYAAAAAgPEhlUmr8ZG71ff+O5Vr75QCnm73rm71tbSqduHFarj3o/SaBwAAGIdoSgQACG7gvp3SwFCssZklzcTWAwAAAADGnVQqpcZ71yl95SIpFf5Ee669Qz3zWhTtO0CkPQAAwDhDUR4AEJS7K9q1N9ZYYusBAAAAAOOZpWvVsLVV9Q9uCN5nXpI0GKlv2Wr1LF5Bv3kAAIBxhKI8ACCobMdBaThf/kBi6wEAAAAAE8BIn/kZ+3eoZuHcRNbwrm71Xb9G/bdvlmdziawBAACAcBKvfJjZ+ZIukTRT0lmSdrv7t5NeFwAw+jybU/+tG2KNJbYeAAAAADCRpDJpTW9br+z+Z9R320bp+SNhFxjOK3qsXX3uatjaSuocAABAFUusKG9mfyrpryX99gkvDUn69gnXflHSLEnfd/f3JbUnAEBy3F39q7bIu7rLHktsPQAAAABgIjIzZeZfqKY9bYqeelr9y9dKg1G4BXLDyj66R4OXztWUP1nK+2oAAIAqFTy+3sxqzewhSZ9SoSBvJbeT+aakiyW918x+M/SeAADJy3YcVLTriVhjia0HAAAAAExkx0Xazz0/+Pwv3bGNPvMAAABVLIme8n8vqUWFIvwvJX1S0m2nGfNpSV4c898T2BMAIEEvx9YPxfi2f02K2HoAAAAAwKSQyqTV+Mjdql10sRT4VLt3dauvpVW9y9cqH2WDzg0AAIDKBC3Km9l8SX+mQoH9e5Le6O43uvvfn2qcu/9E0veLP7415J4AAMmqJLZektJLmonXAwAAAABMGqlUSo33rlP6ykVSTfgzU7n2DvXMa1G07wCn5gEAAKpE6L/6PlC8z0q62t1/WsbYp1Q4KX9h4D0BABKU6zykaPeT8QZPrdO0m64JuyEAAAAAAKqcpWvVsLVVDQ9ukGY1hV9gMFLfstVE2gMAAFSJ0EX5t6pwSv5Rd3+2zLEjBfzfCLojAECiBu7bKQ0MxRqbuXwB0fUAAAAAgEnJzJSZf6Ga9rSpfvtGaUom+Bre1a2+69eo//bN8mwu+PwAAAA4M6GL8iMF9c4YY18q3p8VaC8AgIS5u6Jde2ONtdkzVb95JdH1AAAAAIBJzcxUd8kczdi/QzUL54ZfYDiv6NE96v3AOuXz+fDzAwAA4LRCF+XTxftsjLENxftfBNoLACBh2Y6D0nCMN/R1aTVsWyNL14bfFAAAAAAA41Aqk9b0tvVq2LEpfKS9u3LtHeq99kPKR3E+ugUAAEAlQhflXyjevzrG2IuL9z8LtBcAQII8m1P/rRtijc0saSa2HgAAAACAE5RG2k9bf4sUOFxuuPOweua1KNp3gD7zAAAAoyh0Uf57KvypeFk5g8zs14tjXNITgfcEAAjM3dW/aou8q7vsscTWAwAAAABwamamqS1LlblqsVRbE3bywUh9y1arZ/EKRU89TXEeAABgFIQuyn+xeP8GM7u2jHF/L6mu+Phfw24JABBatuOgol3xvkNFbD0AAAAAAKdnZqrfvFLppZdKNaE/xpW8q1t9La3qXb6WSHsAAICEhf5rrk3S88XH95nZ0lNdbGbnmtl2SX+swin5H0raGXhPAICAXo6tH4rKH1yTIrYeAAAAAIAzZOlaNWxtVcODG8L3mS/KtXcQaQ8AAJCwoEV5dx+Q9GcqFNjPlvRFM/uqma0puewiM7vFzB6S9J+SRk7U5yS93/nLDwCqViWx9ZKUXtJMbD0AAAAAAGUo7TNfv32jNCUTfpHBSH3Xf1j9t2+WZ3Ph5wcAAJjkguceufu/SLpJUqRCf/m3SrpLhUK9JP0PSf9L0p9IOqt4zZCk5e7eHno/AIBwcp2HFO1+Mt7gqXWadtM1YTcEAAAAAMAkYWaqu2SOZuzfoZqFc8MvkM8renSPej+wTvl8Pvz8AAAAk1j4ZkSS3P2Tkpol7VKh6H6ymyR9XdJCd38oib0AAMIZuG+nNDAUa2zm8gVE1wMAAAAAUKFUJq3pbevVsGNT+Eh7d+XaO9R77YfoMw8AABBQbVITu3uHpKVmdp6kyyTNldRUXPOIpH+XtMvdDyS1BwBAOO6uaNfeWGNt9kzVb15JdD0AAAAAAAGURtpn9z+jvr+4SzrSG2z+4c7D6pnXooa2jyk9/0LezwMAAFQosaL8CHf/kaQfJb0OACBZ2Y6D0nCM+Lq6tBq2rZGlE/8nBwAAAACASWWkOD9j7wPqvfZDGu48HG7ywUh9y1bLZp+r+q2tSs+7gOI8AABATInE1wMAJhbP5tR/64ZYYzNLmomtBwAAAAAgQalUSo0PbZK9ambwub2rW30trepdvpZIewAAgJiqrihvZsvGeg8AgGPcXf2rtsi7usseS2w9AAAAAACjI5VJ65yv3KOahXMTmT/X3qGeeS2K9h2QuyeyBgAAwERVNUV5M3uPmX1f0mfGei8AgGOyHQcV7Xoi1lhi6wEAAAAAGD2pTFrT29arYccmaVZT+AUGI/Vd/2H1375Zns2Fnx8AAGCCGvOivJm908z2S3pY0pyx3g8A4JiXY+uHovIH16SIrQcAAAAAYJSN9Jlv2tOm+u0bpSmZsAvk84oe3aPeD6xTPp8POzcAAMAEFawob2a/a2Y3m9kaM/tLM1tsp8grNrMlZvZtSZ+XNFfSyLW/CLUnAEB8lcTWS1J6STOx9QAAAAAAjBEzU90lczRj/47wkfbuyrV36GjzDYqeepo4ewAAgNOouChvZm83s0OSnpD0cUl3Sdoq6WuSDprZW064/rVm9kVJj0mar0Ix3lQoxm+Q9LpK9wQAqFwlsfWaWqdpN10TdkMAAAAAAKBsx0XaNzUGnduPvKi+llb1Ll+rfJQNOjcAAMBEUlFR3syulvSvks7TsZPupfevl/RlM5tfvP5KSd+VtFTHivH9kv5W0mvd/a/d/UglewIAVK6i2HpJmcsXEF0PAAAAAECVGIm0n7H3AdXMPT/4/Ln2DvXMa1G07wCn5gEAAF5B7KK8mTVIukdSbcnTg5KekzRU/Nkl1Uvaama/J+lzkhpUKMb3SVqvQjH+I+7eE3cvAIBwKo2tt9kzVb95JdH1AAAAAABUmVQqpcaHNsleNTP85IOR+patVs/iFUTaAwAAnKCSk/LXSTpXhcJ7l6Q/ktTg7q9WofD+bkk/K75+qaTtkuqKYz8h6Tx3v9Pdj1awBwBAYLnOQ4p2PxlvcF1aDdvWyNK1p78WAAAAAACMulQmrXO+ck/4PvNF3tVNpD0AAMAJKinKLy3e5yW9w90fdfdhSXL3nLt/QdJVKhTlJem1krKS/sTd/4KYegCoTgP37ZQGhk5/4SvILGkmth4AAAAAgCp3XJ/5WU2JrJFr79DRK26mMA8AAKDKivIXqVBw/6q7f/+VLnD370r6mgpx9S7pE+7+uQrWBAAkyN0V7dobayyx9QAAAAAAjB8jfeab9rSpfvtGaUom+Br+3Avqva5V+Xw++NwAAADjSSVF+XOL9/tOc923Sx5/soL1AAAJy3YclIZjvFEmth4AAAAAgHHJzFR3yRzN2L8jkUj74c7DOtp8A33mAQDApFZJUb6+eH+6nvClr/9HBesBABLk2Zz6b90Qayyx9QAAAAAAjG/HRdo3NQad24+8SJ95AAAwqVVSlB/JJz7dkcqXv/7o7n0VrAcASIi7q3/VFnlXd9ljia0HAAAAAGBiGIm0n7H3AdUuulgK/F4/196hnnktivYd4NQ8AACYVCopygMAJohsx0FFu56INZbYegAAAAAAJpZUKqXGe9cpfeUiKRX4S/iDkfqWrVbP4hVE2gMAgEmDojwATHIvx9YPReUPrkkRWw8AAAAAwARk6Vo1bG1V/YMbpCmZ4PN7V7f6WlopzgMAgEkhxNHGt5vZ2ad4/dKRB2Z255lM6O5/U/GuAACnVUlsvSSllzQTWw8AAAAAwARlZqq7ZI7S+3eo96Z1Gm7vDL7GSHG+duHFarj3o0pl0sHXAAAAGGshivJLirdTGfma40fPcE6K8gAwCnKdhxTtfjLe4Kl1mnbTNWE3BAAAAAAAqk4qk9b0tvXK7n9GfbdtlJ4/EnyNXHuHjl5xs875yj0U5gEAwIRTaXy9JXADAIySgft2SgNDscZmLl9AdD0AAAAAAJOEmSkz/0I17WlT/faNyUTaP/eCeq9rVT6fDz43AADAWKrkpPyngu0CADDq3F3Rrr2xxtrsmarfvJLoegAAAAAAJpnjIu2va9Vw5+Gg8w93HtbR5htU/3/+Wul5F/DZAwAAmBBiF+XdfUXIjQAARle246A0HOOb53VpNWxbI0uH6IACAAAAAADGo1QmrcZH7lbf++9Urr1Tcj/9oDPkR16kzzwAAJhQKo2vBwCMQ57Nqf/WDbHGZpY0E1sPAAAAAACUSqXUeO86pa9cJKXCn2jPtXeoZ16Lon0H5AGL/gAAAKONojwATDLurv5VW+Rd3WWPJbYeAAAAAACUsnStGra2qv7BDYn0mddgpL5lq9WzeIWip56mOA8AAMYlivIAMMnkOg8p2v1krLHE1gMAAAAAgBON9JmfsX+HahbOTWQN7+pWX0urepevVT7KJrIGAABAUijKA8AkM3D/TmkwKn9gTYrYegAAAAAAcFKpTFrT29arYccmaVZTImvk2jt09IqbKcwDAIBxhaI8AEwins0penyvFCPqLb2kmdh6AAAAAABwSmamzPwL1bSnLbHivD/3gnqva1U+nw8+NwAAQBIoygPAJDHSS17DMd6wTq3TtJuuCb8pAAAAAAAwIZUW5+u3bwzeb36487CONt9An3kAADAuUJQHgEmikl7ymcsXEF0PAAAAAADKdly/+bnnB53bj7yovpZW9SxeQXEeAABUNYryADBJDNy3UxoYKnuczZ6p+s0ria4HAAAAAACxpTJpNT5yt2oXXSwF/ozBu7rV19Kq3uVr6TUPAACqEkV5AJgE3F3Rrr3lD6xLq2HbGlm6NvymAAAAAADApJJKpdR47zqlr1wkpcJ/+T/X3qGeeS2K9h3g1DwAAKgqFOUBYBLIdhyM1Us+s6SZ2HoAAAAAABCMpWvVsLVV9Q9uCN5nXpI0GKlv2Woi7QEAQFWhKA8AE5xnc+q/dUP5A2tSxNYDAAAAAIDgjuszv3BuImsQaQ8AAKpJrKK8mX21eLs29IYAAOG4u/pXbZF3dZc9NrN0IbH1AAAAAAAgMalMWtPb1qthxyZpVlMia+TaO3T0ipspzAMAgDEV96T82yS9VdJrSp80s7yZ5cxsZaUbAwBULttxUNGuJ2KNnXrj1YF3AwAAAAAAcDwzU2b+hWra06b67RsTibT3515Q73WtyufLb+0HAAAQQhLx9eQcA0AVeDm2figqf3BNil7yAAAAAABg1BwXaT/3/ODzD3ce1tHmG+gzDwAAxkTcovxQ8b4+1EYAAOFUElsvSeklzfSSBwAAAAAAoy6VSavxkbtVu+hiKfBnE37kRfrMAwCAMRG3KP/z4v3vhNoIACCcXOchRbufjDd4ap2m3XRN2A0BAAAAAACcoVQqpcZ71yl95SKpJnzYa669Qz3zWhTtO8CpeQAAMCpqY47bp0I/+Xea2cckfUvSQMnr55nZ4ribcvdvxh0LAJAG7v98vNh6SZnLFxBdDwAAAAAAxpSla9WwtVXZ/c+o77aN0vNHwi4wGKlv2WrZ7HNVv7VV6XkXkBoIAAASE7cof7+kd0uqkfTXJ7xmkv68eIvDK9gXAEBS9LXvSPnyv+lts2eqfvNK3oQCAAAAAIAxZ2bKzL9QTXvaFD31tPqXr5UG4x1COBnv6lZfS6tqF16shns/qlQmHXR+AAAAKWZ8vbt/UdLG4o9WctMrPBfnFpwVtJjZv5rZT8xsyMy6zGy3mX3AzIJ9EcDMpplZs5n9pZm1mdkPzCxnZl68va2MuZ4tGXe629dD/W8AMH65uzQ4VP7AurQatq2RpfleFAAAAAAAqB5mprpL5mjG/h2qWTg3kTWItAcAAEmKXXlx9w+b2aclvVPSf5M0RdL7VDjp/pSkA0F2GICZnSPps5IuO+GlWcXbZZI+aGbvdvf/CrDk/5U0I8A8AFC2bMfBWOMyS5qJrQcAAAAAAFUrlUlrett6Iu0BAMC4U9FxSHc/oJLiu5m9r/hwu7tvqWTuUMwsI+kLkn6/+NT/lXSPpB9KerWk90u6QNI8SV8ys2Z376tw2ZoTfv4vSRkVvgAQ1wuSbj7NNd0VzA9gAvBsTv23bih7HLH1AAAAAABgPBi1SPvr1yjzjkWFz0tIFQQAABWaDH9NfFDHCvL7JV3h7kdHXjSzbZL+SdJSSRdKWitpVYVrfkHSIUn7JD3l7t1m1qZCkkBcv3T3f6pwXwAmMHdX/6ot8q7yv59DbD0AAAAAABhPRiLt0/t3qPe6Vg13Hg67wHBe0aN71Hu0Tw2f/BulUrE6wQIAAEiK2VP+FFaocPL8scDzxlLsE39H8UeXdENpQV6S3H1Q0g2SXio+9Zdm1lTJuu7+Pne/y92/7O6cXgcwKrIdBxXteiLWWGLrAQAAAADAeJTKpNX4yN2qXXSxFDoB0F259g71Xvsh5aNs2LkBAMCkErQo7+6fKt6eDjlvBS6TNLP4eHcxbv9XuPvPJW0v/lgn6V2jsDcACObl2PqhGHFtUzLE1gMAAAAAgHErlUqp8d51Sl+5SEqF/4xjuPOweua1KNp3QO4efH4AADDxjVrmjpmdZWavMbNXm9lZo7Ts20sen+70funrf5jAXgAgEZXE1itlyly2IPymAAAAAAAARpGla9WwtVX1D26QpmTCLzAYqW/ZavUsXqHoqacpzgMAgLIkWpQ3s6vM7GEz+6mkPknPSvqxpD4z+2nxtXckuIU3lTx+6jTX7jvJuGrRZGZfMbOfm1lkZi+Y2bfNbKOZnTfWmwMwdiqJrVddRlNvvDrshgAAAAAAAMbASJ/5Gft3qGbh3ETW8K5u9bW0qnf5WiLtAQDAGUukKG9mrzOzvZL+WdJ7JM2SZCfcZhVf+1cz+zcz+60EtlLaJPnZ01z7E0nDxcfnW/VlOZ8t6XIV4vjTks6V9LuSWiUdNLP/aWY1Y7g/AGOgoth6SZnLF9BPHgAAAAAATCipTFrT29arYccmaVZTImvk2juItAcAAGfMQv/BYGbnS/qWCkXj0sJ2JOlo8fE5kk7MEPq5pIXu/qOAe+kpriVJ9e7+i5DXl7mXNknvK/74B+7+9TMc96wKRfjHJHVI+pkK/+1eL+kaSb9Tcvmn3H35qebr7e19xf/DDx8+fCbbAVBN3DVt4wPKfOO7KvdbRC4pP3O6+v6/j0i1fJ8HAAAAAABMUO6qefo/dPYd/yAbypb9Gcoppy7e58+drpc+fIOGL3itVHVnvQAAQKXOP//8V3y+sbHxjP/hD3pS3sxSkj6nwmluk9Qv6S5JcyVNc/fZ7j5b0jRJF0laL6m3OPzXJO0MfEL97JLHg2dw/UDJ4/qA+6jEn0p6jbvf6O5/7+4Pu/un3X2du18k6S907IT/+8zsvWO3VQCjqebgfynzxIF4bybTNXrpjuUU5AEAAAAAwMRmpuE556n3kb9V7s3ny3WsmF7x1MVbqvtF1a/apmkbH5Byw6cbBgAAJqHawPNdp0I/dpd0QNI73P2nJ17k7nlJP5D0AzP7hKQvqXDi+03FOR4MvK9xy92/dZrXP25m56jw5QdJ+oikz5S7zsm+4YHKjaQQ8N8YofX9788pysbrXVa3dKHOvepyVV+nDuDk+H0KAJXjdykAhMHvU2B88oe3KLv/GfXdtlF6/kiweU2S8nnVtX9PZ599thq2tvKZyxngdykAhMHv0/EhdE/5a4r3A5Le+UoF+RO5+3OS3qVjp9TfE3A/pfHzU87g+qklj/sD7iNpW3QsceCNZva6sdwMgNERfe07Ur7873bb7Jmq37ySN4cAAAAAAGBSMTNl5l+opj1thX7zTY1hF8gNK/voHg0+/GX6zAMAgOOELsrPV+GU/L+4+7NnOqh47T+r8KXC+QH382LJ46ZTXWhmtZIaij/mJL0UcB+JcvdBSU+UPPXbY7UXAKPD3aXBofIH1qXVsG2NLB06KAUAAAAAAGB8GCnOz9j7gGrmhj9V+NId29SzeIWip56mOA8AACSFL8r/WvH+QIyxI2N+7ZRXledQyePXnubaV0saaa582MffX0uleUvnjNkuAIyKbMfBWOMyS5pVe9EbAu8GAAAAAABg/EmlUmp8aJPsVTODz+1d3epraaU4DwAAJIUvykfF+0yMsXUnzBHCD0oeX3Kaa0tf/8FJr6pepUkAL570KgDjnmdz6r91Q9njiK0HAAAAAAA4XiqT1jlfuUc1C+cmMv9Icb53+Vrlo2wiawAAgOoXuijfVbxfFGPswhPmCOHLJY+XnubaPyx5/FjAPSTOzOokvaXkqUMnuxbA+Obu6l+1Rd7VXfZYYusBAAAAAAB+VSqT1vS29YU+87NO2QU1tlx7h3rmtSjad4BT8wAATEKhi/LfVKEv/FvN7IozHWRml0t6mwr96L8ZcD9fk/RC8fEVZjbnJOv/mqRlxR8HJX0h4B5Gw0pJjcXHh939h2O5GQDJyXUeUrT7yVhjia0HAAAAAAB4ZSN95pv2tKl++0ZpSpww2NMYjNS3bDWR9gAATEKhi/L/WPL4c2b2rtMNMLM/kvTZk8xREXfPSbprZClJ/2hmx/VbN7Mpkj4l6aziU9vcvbQ/e+m1bWbmxdu6UPs8GTO7w8wuOM01fy7pYyVP3XWyawGMfwP375QGY3T5mJIhth4AAAAAAOA0zEx1l8zRjP07iLQHAADBBM0xdvd2M/uspD+WVC9pp5l9W9Ijkr4rqVuF0/DnSnpz8bq3qFAwd0mfdff2kHuS9HFJ75H0+5LmSeo0s3+Q9ENJr5Z0o6SRwvfTktZXuqCZXSbpshOefnPJ4xtfIUng79z9xF7w10pab2bflfQNSc9IOiopI+n1kq6RdFHJ9Z9WwC81AKguns0penyvVO63qFOmzGULktkUAAAAAADABDQSaZ/d/4z6btsoPf+K57gqMhJp39D2MaXnX8iBCgAAJrAkmgsvV6HYPdLj/PeKt5MZ+UvjieLYoNw9Kp7Y/6wKhfLX6JUL7/slvdvdewMsu1jSHad4/U9f4bn7JJ1YlB/xZh1f1D9RTtIGSf+Pk3kETEgjveQ1nC9/cF1GU2+8OvymAAAAAAAAJrDSSPuBHV/WL9duKxwtC2kwUt/1H1bmykWq37xSlk7iI3sAADDWQsfXy91/KemtkjZKGlCh6H6qCFHp8wAAIABJREFU2y8l/U9Jb3P3gdD7Ke7pqKQrVOgb/6ik5yRFkn4m6auSbpa0wN3/K4n1K/A/JN0i6TOSOiT9RIX/pkOSuiTtlnSnpNe6+9piXD+ACaiSXvKZyxf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emeTv0n3xf88kT0xyUpLvSvL6qnpAW+QStL3Tk/xSumTJPyV5e7ovvW+X5LtHC1bVLZK8K8kD+10z6RIs+9J9eXqHJI9JckaS70zyzqr6f1o3m26uS5M8sl8/1Pf74XRfzk8nObXv518vEf+sNXldqurn0yV7Zn06yf9Il8C6Q5IfSpcoOTnJS6vq5q21Fy4zxvn6u0+6537Lftf1Sd6U7r24RZIfSPc6vCbJS1fazxp4+Mj6J1prhxYqWFVPSfInOXqv4Y8meUe6hO3WJPdPl1yZSnJeklPS/ehgRarqrkn+Nslt+10Hk7wlyYeSbEt3ieWz0iVmfyTJd1XVw+d5DnvT3SM56ZJI75mnu7kzzx9UVbdsrX1zTkynpHueSfJ/W2tfHfd5jcQ0a1d/vH17Tl9bc/Qe8u+a8+9szK+ap+2zFuhnIWs99iyoqn40yWvTvX9Jl7x8R7oE2fXpkqc70yXup7P0fa1/K8mv9PG+Nd1Yk3S3BHh0v/7wJBcnecZK4+7doo+ppfthxj+k+4HKt5PcOt39289J91l4TJK/qqofaK0dWWW/4zp5ZP3bC5bqjq1z08X7vnTHytfTjdG3XLjavC7N2oz7r03yYyPb70tyebofjJye5PFJbpUuiX15//r+7RJtbk3y+hz9kdqb0yX1d6T7kdH9+nLnV9X7WmuvWaihqnpZkqeP7HpPv3ylb+/70x27JyX5o6ra1lr7/5aI76Qkb0x3/Hwp3Rj3iXTH2/elO97GcU6Ovn8tw/192ZnkxemOtyvTjU3Xpvs7+sR0n4lbpvsc3Lu19vX5Gqmq3enen9nP+pfT/a28Jt3fkMemO2fZluTCqrp1a+2XFmhrKt25y+gtQd6V5P+kO6+5T7q/9dPpfmTzN1X10NbaR+dp7veSPLlfvzHd2PiBJF9Ld1WZO6Q7nndlkXGqqh6Z7lxjdkb0Z9N9Pq7pt++V5IfTvd8/mOR/9edXM3PaOTV90r7f9Zl0PzS5Jl3S91bpztEemu48baV+p2/rWUlmr+bzu+nGhkWt93nWceCHkpzfr//vJO9Odxzer39se7ofHr6zqh7SWvvcRKIEABjXpH8VYLFYLBaLxWKxZPUz5Vu6hMFNZvKm+9J2dBbZTy7Q3rlz2rsx3SydWiKO0RnylyX5znnKVLok/+yM1I9lzkzodF/gzrbz8SR3WaTP70zy7HV6Xe6XLlE0W+5FSabmlNmW5IUjZWaSPGCB9q4YKXfaPI9vSfL3I2Xem3lmNSd5Zv8ejc7yvXCVx+HoMXDFEmXvlm6W1mz5X1ik7M50CdSW5FtJfmq+4yrdZdP/YaTNn1nha1jpEvKzZT6S5B7zlDsnx87Ku2ieMvcYefwdS3x+R2cz/uA85XaPPP6Hq3yvRmc0P3Kex79n5PEnj7wuX+33vXyJ59KS/NA6fcbOGilz6QJl7p0u8T5b7o1J7rBA2ZPTJdHvu8Tza/1xcsd5yv3YyGfrxixwZYEx3q97J/nVJLdb4jP1vpHYnrKaPud5ry5couwD57w2PzTn8QvnPH4gyY8t0eZpI+WvWOA5r8W4/8yRdm5I8tR5ytwux44dn0hy8hIxzy4vSTI9p1zl2HH/nxaJ/ekj5a5O8pAFyp2TLnE7+3fkJleYWCC+S+d7Lis4Xv7rSJsfWW17Sxw/1809xkbe538eKffcBdq7w8hr1dIl5285z3t0wZx+bzI292WfPye2Ry9wvH5opNyVmfO3LN34M3s1hK8nuf8ir8kp6c6zbnKVmSR3zNGZ7YeT/GKSm81T7rbpfnwyG9NvzVPmt0Yef1mSrQvEU+kS8/O+RmO816Ofs9OWUX5Nz7NWeExeuop2zlqqnYw/U/5IfxzNdy5xRo49/3rTal4Hi8VisVgslvVc3FMeAIDN4EiSx7fWbjKLt7X2T0n+08iu5d7H+vmttRe11tpCBarqwekSrEn35fQPt9Y+P08MrbX2h0n+sN91t3SXvB41el/V/9Za++RC/bbWPt9ae9FCj49Yi9fleelmbyfJm1trz25zZqG11m5orf1ikj39rm1J/uMy4pvPY5LM3lf9G+m+kP3sPPG/NF0SoVbYz1LuVFW/Mme5oKp+u6rekuQf0yWsk+5y8y9ZpK3np5vRmXSJ2dfMd1y11j6Rbvbp9f2u51bVSp7fo3J0tuP1SR7T5pnN2Fq7PMlPj+z6+aq67ZwyH003qzBJvreqto8+XlV3y9H7L/9humRO0s2qn2t0395lPI/FXDGyPt894s+aW7Z/zd+9UJ3q7j89+1xuzNF70C9miLFnPr+do7O4L0vyI621L8xXsLX2rdbay1prH1qizc8keVybZ4Zha+316S5jnXQ/lNm9srD/pb1/bK39XmvtS4uU+Xi6GZAH+l2rnZ2/bP0s4T8Y2XUgxx5j83l2/zqtxqrH/f6qEL82sus/tNb+dJ76X0r3+n6q33VaustlL+WtrbVntdYOjO7sP08XpJvRmyT37K9yMje+6XQziJNuNvgjWmtXzddRPyY9td/c1re/lHcneVpr7VvLKLuUe4+sv38N2lvM01prb567sz+HeM7IroXGjeekS2on3Sz0J7U5Vyfpzz0uytFzj6RLxB6jv4rJL4zsempr7e3zxPbxdH+jZ8f5XelmqI+6V47ObH9Va23fAvGntfb1/jxrvqvM/FqSf9Wv/1Jr7YWttRvnaePL6a4CMXtc/0J/BaNRo5+z57bWDi8QT2utvae19paFYh7Iep9nzeepc+97P8/yjTXsbymV7jYWN3kvWmv70x13s6/RD1fVznWMDQBgxSTlAQDYDN7cWrtykcdHEycPWLDUUQeS/P4yyv3cyPqvt6UvTT2a9PnhOY+NXsJ1OmtjVa9LVZ2cYy+h/h+W6G/08cdX1a2XDvEmRpPEL1oo8dj73RxNDqy1u6W73/bo8vvpEgWzl5n/YJJzWmtPX+i97xO9j+03/7a19j8W67RPkL72/2/vzqPmqMo8jn8flrAYiMiOQZDFhUWQTbbBNyqjjqAgg4qAgMKwjOgg43gGdURRHI8R9QjKwaMiCGJQQJFFoiSAYGAwiSxCBDIgCMgSBpAtLM/88dymblequ6vfrn7fN/j7nPOeVHffrrpdfft2pZ/73JtubkJpuYSaDsq2T3H3P3cqmOpzdbq5IrFOdlkrgL4SkYGey4PbM+kS9M7ue4F6Ae9u8qB+t2PdURrU0ZrCfiMze1WH5wDMdfdHa9Sj6b5nCWa2LrB3uvk8cJQ3M63719y9W5Bl4Lr3K7X/VtvYoTwIpElmtoyZrWlmexMzBoxkD0939259y93A9xuoRhP9/luA9dP2vUS2d6X0mk7I7jqoU9lMx8Bf6vfyPq2qnbyPYhmNU9z97ooy+T4vJLJgIQYR9PKFboPn+rR6tv1QQ/us8oceAzouo/hu29LMqqZ4/1C2fVynQHNyPMVyDNua2Ralx/cFVk7b17n7eZ125O73APmyAuU2NHCbTgM5Dkk37wZO6Vbe3f9GsdTAFNqXlinXaWUmkHG6zloa/KlqcFGLuy8AzsjuqtOXiYiIiIw7BeVFRERE5KXgkm4PuvtDFGt6rlVjf1eVM846eGv6dzG9sypbAacH083tSg/fkG0fm9ZSHdSg52UHivWYfv7NAAAUgUlEQVSrb3b3W3rs7zYiYw/iR/ByALeOXbLt8zuWiuM9CVw6imM0ZUvgPDP7TMpWrfIWimz+JTIPO5ifbZfbSR35OayTyTsj29614vE8AF7OgG8Fsu9OWfWtsluZ2YsBrpSB38qindcjGFxHXqftUmCjdax8PfnZpefl68qPlB7Lb9fN5G+676kyjaINzXb3O0e5n7KudSeWI2gZbd2XYGbLmtmWZvZ+MzvCzI7NZ6SgyI6dRCzp0JTP5VmfxACHB4DzgG2zcj8FPt9jX5c0NDCiiX6/rc+syiYuOZeY8hlg6/yzU+F+d5/f5XHo3U7emm332weuaWYbdCn3FIPPupFbNdse1oAv6N1vvAC0ZjdZgQg0v8jMXk1M7w6xBMnMHvt7jPZzX+7n8zZ0brd9Jfl3xi6lx24hllAAONDMPmBm/f72uBNFQP/XNT9r3b4382z975nZekwc43GdVeV6YmaKbn9NZub3ckGNMvngkZ2HVRERERGRJnX64UhEREREZGnSccrfzOPEVK/laU2r3NqrQJrutZWdOAlY3OdM4+Vpwm81s58T07C+HJhpZrcTP6RfDcxJ05v3Y9Dz8ppse17F41XmUmRLbkofQfOUFdvKXn6eWLu2lz8QWX5Nu8LdR8p3mtnKxPu+O/CfRGDkBOBNZrZXRUBsq2z782bWK9hXtmbvIm31y8/hC7QH/TrJp2netOLxclb650q3AS4v/WtEtmLrR/MRisDywEE0d7/dzO4BphIBjV0pgk7bU0z1Prv01PnEFNpTUt3zTLuRbLtuHZvue6rksyVcN8p9VOlV9zwoOdq6v8jMphAzTRxE/SD/WGaB3gic5O6n1yjb8zuijob6/b76aXd/1MwWAhsTQb2NiNdepW77bqlqJ3kfeMUoVuRYs0s9bqsxCKEf+WC8gdt8F6M5r4uy2/l7fkPNczCXYsaNcj/f73f9zcRgxEnAOma2SmtmCXd/3My+TUyvP4mY+WW6mV0K/Ba4tlfgmfY2c4iZHdKxZLXy9+apwFHEoIvdgbvM7Cqin59DfM6GOQijmzG9zuriZnef3sB+mtJrMBC0X9+8dlgVEREREWmSMuVFRERE5KXg6RplWpmBdSICdaatXr13ka6qshMPBM7Jbm9CTJF/NrDQzO40s+k9Mgdzg56X1bLtulP55uVeUfM5Vcd7rMZyAOXjDZ27P+nuC9z9ZOJH8dbU8HsAn6h4yjDaSTflc7i4Y8lC1/csZWbfmW6+KQ1MwMxeQ5Gt2Qpiz6fIDM+z6vOp4ZvKbO00hX2+PTt/Qsq4XGKKfTPbiGIww3NE8KiOpvueKnkb6rgme7/cvVfd8ynBB/rtIC3jMI/Ituwn637FQY5bMpP2rM9jgcOBvYAN3f0NNQPyUO87oq5B+/1h9tP9tG+obifD7AObfB8AHs62B613N4Oe16bf8772lwYBPJLdVd7fJ4FvEYPrAF4JfAT4AfBHM7vfzL5jZptTrdE24+53AW8H7kh3LUf0/18glgp4xMyuMrPDzGwSY2usr7OWFg/3LtJ2HqbYKEb8iIiIiIw1ZcqLiIiIiCypzlSp+bX0g9Rbg76rlKm1n5l9Cfggkbm7HcXUphsQgaSjzewYd//2oMfsp3pj9Jx+jduPsO7+gJl9hWK920+Y2fTS+sZ5OzmLetlfuWsGqWKDz5lFrPE7iZiueCbtQffLIYLeZnYlkfmbB8dbZZ+jCIoPahYR0IT2LPfW9sK0/nHZFcQgig3MbMM06CB//nVpjeKJaCw+U8NwJsVU9HcRn5mriMEejwJPtz43ZvZD2tfLbso1DWaCNjF1PdB4vz8R++m8D/wC/U8Lv7DLY429D8mtRCY1wDYN73tYmn7PB95fGlD3MTP7OrA/0f/vSDEl/drAEcDhZvZld/90aX95m7mY/gdyLTHLjrvPMbPXAXsC7wZ2I2aJgJgxYtf090kze0+NbP5hmIifXxERERFpkILyIiIiIiKjk2fxrNDktJ/ufhNwHICZrUSsOfqPwAFENu8k4BQzu93dL2vquBXy6XLX6FiqXV7ukY6lquXlVzWz5Wtkyw8zm7GOPGi+DpHlelt2X95O5rr7SUOuT/6eTal5Duu8Z5cTQXmIAMtMiqD7He5+d6nse4DNzGwdYuBEa2rZ6xucJjgP1GxrZqsQGaid1pNvydeVn0Zkbw4jk78peRtae9xqMUpmtg3FGtZ3Am909//r8pQpXR57yRqg3x/rfrpfD1O025+7+9xuhcfZLODotL2Zma3r7veNZ4U6aPo972t/ZrYs7RnelW0oLb3wReCLZrY8sC3wNmLwyeuJ74bjzOxOd/9u9tS8z7ujqesrd38OOD/9kdaW340I1O8DrEBMB/9LM9vM3Z9p4rg9TPTP73ipc22Xn4dHSwMiRURERCYkTV8vIiIiIjI6D1FMnbmqmW05jIO4+1PufkXKJNuE9GNycuQwjpnJg8tv7FiqXV7uT/0cLP0A3poOflmg09S2ua16FxmqJ0u3y2vZ5mtP78KQpenqW+dwGeANNZ5W5z2rmip+JP17eXvRtrIjDCngXZpWfzki8LsDsHK6b3aHp86lyNYdSf++OXt8ogXlb862dxi3Wozejtn293sE5AG2GGZllgZ99vt99dNmNoUiQ/h5umeiN2FM+8AB/YZiXXkjljeYiPL3/A1mVue3vW79fL/f9ZsRg0QA7q8z0Mrdn3X3Oe7+ReK7/VvZw0eVio9Jm3H3e939HHffn7iWaAXINwLeMazjlozpddZSpM61XX59s2BYFRERERFpkoLyIiIiIiKjkDJyfpPd9eExOOazwFeyu1435ENeB7SyrLcws9d2K2xmG1P8WPw8cO0ojplnnu/d43grM3Y/nHfyqtLtctbazGz7nSlzfNiuzrb/uUb5fTs890Xu/heK4MF2ZrYTxdrg5aD8TcSSDhBZ9cPMQi8PFhjJbl9BhbQecut1Tkvtdv10ezGDLRkwDLMopuke6bK2+ESVZ9Qu6lgKMLOtgY2HW52lS41+P//M7pWymLvZh2LZj/nu/sSAVewl7wM/PJHXfXb3xyiWIwE41sw26Xc/Zja5uVotKWWg35tuTqGYcr9TfVYh1lRvKffzjX9ndJOun76U3VVu01dQXHtsk/qFoXL3BcCMLnXqRz47Ta/P43hcZy0N9qpRJr9GnGjf2yIiIiKVFJQXERERERm9PNPrSDOrncXaUGDiqQb20VEK1vwsu+vLPZ7y3xTBngtqZMRWOTPbPtrM1upYEj4FrDKKYzRpv2z7MeCO/EF3vxX4dbq5EvDtuu/9AG3kh9n2v5rZ1C7HeBfwD+nm08A5XfbbCoAvC3yu4n7gxYDL7HRzGkVQ/llGEcDpoRyUbx3rf939zxXlW1oB+/WBQ7P757j7UD9X/XL3+ykypZcFvlMzM3aiyKei3rZTofSavjb86iz1yu3zcqC1fMRU4KOdnmhmLwM+m911eqM1q3YWxWCMrYGP1X3iOAXwp1PMNjIZuKBbH1qWrgOuGkbFSs7Itk8ws27LU/4X8LK0/fu0VELuXIpZX3Y0s/d02lGa8j1/D0+vV92u2tp0GhyRf4+damYr1NlRg21mkO+BR7PtV3QrOE7XWUuD15rZgZ0eNLNNgQ9ld53ZqayIiIjIRLI0/UdeRERERGRCcfergZ+kmysAvzKz93X6UdjMljOz3c3sAkpZ4Gb2KTM7zcy273Q8M3s57T/YXjnYK6jlRCJ7GGBvM/uGmU3KC5jZ8mb2NYoMu2eJdWRH41Lg92l7NWJt1/XKhczsUOAzwLisIWrh4xTrrAOcmaaPL/skEfCGeN9/Zmbrdtn3VDP7FHEuRuMyiqyxVYBLzWyjciEzm0YEzFpOdveHyuUyeQC8lXX5R3f/a5eym1BkPl/r7uXp/geV1+mNwM5pe3aP5+VZ9HkQs5z1P1F8liJo9k6iDVXOumBmk83scDObKNPA5wHKD5nZHuUCqW/7MTGzwt/NusBN9Ptpney8v/2qme1fsZ81gF8AG6a77gR+MLqa15emNv90dtdJZna8ma3U6TlmtpWZfYsIQI4pd19E9NOtoOzmwP+Y2aHdAt9mtpmZnUH0va8efk35JsVgh+2Bs8oZ+ul76hjg2OzufEAVAO7+SNpfyxlm9rZyOTPbELiEyM6HyPK+qFRmfzM7x8xGOg0eSu/917O7qq5lPk+xRNCbgJndZi0wszXM7EhieZLyY5eb2THdZqoxs12BA3rUqa58KvVpHUsVxvo6a2ngxGCMd5YfSO3gl8R1N8CF7j5/LCsnIiIiMlrdRtKKiIiIiEhvHwY2INZNfjkRpD/RzFrZiy8QweXNiB+WW1lTPyrtZyXgMOAwM7uHmJL0NiLjagoR2HwXxXrZi4CvDuclFdz9RjM7lmJWgI8TUyRfCNwHrA3sSXsQ4j9G+wOpu79gZocQGdWrEMGGBWZ2PvFD92Riqt5tiR+xT6NLZugA1jezf6+4f0Viyvq30f6aF9Cegfoid59vZgcTmVzLEwGffzKzWcB84j1+GfBKYBtinVSjfS3x2tzdU4bZHGKN+82Bm9N7dlOqw05EALQ1gORaYpBDN1VTz3cKYleVbXytdne/x8xuJ4L/yxKfI+gwdX3meuAJ4rzngayJtp48AO5+S/pcnEX8P34v4O1mNhO4EfgbsDrRdnYj2mmdYNDQuXur7e1JvEcXpv7xeuBxYNP02GrAH4FbiCnW/x400u+7+2lmtjsRsFse+JGZ/RuxxMrjxOdjL+I7CiLgvP8YTF3fqt+pZvZ6IsN6GSIw/NHUfm8jBpy0Xu8OxHcqtE8lP2bcfW4atHQ+sC6wDvBdYLqZzSbqvIjoO9YlZhvJA8bPjUEd7zezjwA/JT5X7yOWt/g5MeBiNWIAz+bZ077h7heV95UcTyz/sROwKhEEn018Fz+T9vNuij72IaINlQfRLA+8P/09aGZziDXiHyH621cRn/dWW1xM9UCBe8xsHyLoP5k4xwvM7CpiMMCiVJd1iBkYtk3noapNbwScRLx/84B5wF/Ssdcirs12zMrPGDDIexFwXNo+IbX9m4jz2Hp9J2fbY3qdtZT4BnAMcHFqh78l3q8tiHa4Yip3P3DkeFRQREREZDQUlBcRERERGYC7P2lmI8SUt0cQ19gb031d5IeJH1pzeYb11PTXyZ+AfdM630Pn7ieb2VPEj6STiYBJVSD8CeAT7n7agMe7MWVH/Yz4MXoyUJ7G9AngYNoDqk3aiPqDHi4GPpKyDSu5+09S0O0HRBByBeAd6a+T8hTDtbn7QjPbGTgP2JL4AXtf2tcCbrkAONDdn6l4LN/nX83sFuD12d2VQWx3v9XM7iMCVl3LNmAW7QEx6JEp7+7PmtnviMEVLU8xgdfndfcZZvYw0YbWJwJS705/VZ7tcP94OBj4FbBduv2W9JebRwTjlwjQvYQ12e/vB/yVCFAtQ5zr7SrK3Q28391/1391R8/dP25mNxPZ76sRg0g+0OUpzxCveVy4+7Vmtg2RsX0wMIkYONBxanciGP9T2mcGGBp3vyBNNX86sAYRYD6souizwInufnyXfS1OAztOp8jGHkl/ZTcD73X32ysey9v0mkQwec8Oh70POMDd/9ChTlem5QDOINryMsCb018nN3ap0zJE8L7jMhrpWP/S5fGe3P0aMzsb+CDRbg6uKHZy6Tljep21FPgFcBdxbT1CdTtcCOwxVtfCIiIiIk1QUF5EREREZEApmHm0mU0nfnydBryGIiv+EeB2Ylr2y4Bfl6c5d/cTzewSIgt8JyLwuR6RWfY0kQ00j8jcm+HuYxpwc/fvpaytI4hA8iZEptujxDrqlwKnpvWvmzje1Wb2OiJjbG+KQQ73pGOd4u63pwz0sbSYWDt+IZGJfk7d4Fb2mt4L7EFk5q1NzAjwBHAvEey4Eviluy8cpKLp/GxNBL72IYIaaxGBo/uIacXPdPfZfex2FkVQPl87vlPZD6btZ4BhBQFn0R6IutPd76rxvCtoD8pf02tgwnhz99+kqXsPIAJd2xCBr+WIzNEFRPuZ4e5Vwalx4e6LzGwX4n3aj8h2XAl4kMiMnwH8MAUGx6+iY6zJfj9NY/9RMzsNOJQY9DCVOM8PAzcQga7vu/vTnfYzTCmj/8fEWtC7ExnOaxCDlB4jMrxvIDL8L+o20GkspO+zw83sBCIY/1Zi1ps1iAD934g2PJ/oT3/i7g+McR0vMrONic/WHkQbekWq213ATOC0DgH08r6eAPY1s38g3qPdiIFVk4AHiGuY84Cz3f35Dvs428x+T1wn7Eycr6nE99xi4nzdSEw/fmav2Rrc/RZgezN7O3EtsAvxGZlCDKS6n+hDfgtc7O5Vg9m2Jt67ESIgvzHxHi5HzCSxkFh24Ax3v77rSarvAOJ6bz9iBpPVifPY0VhfZ0107v7NNDPCUcR7tx7RhhYA5xLXgU913oOIiIjIxGNLzjQlIiIiIiIiIiIiIjJ8ZnY6cFC6Oa3PAYMiIiIiS4VlxrsCIiIiIiIiIiIiIiIiIiIiL1UKyouIiIiIiIiIiIiIiIiIiAyJgvIiIiIiIiIiIiIiIiIiIiJDoqC8iIiIiIiIiIiIiIiIiIjIkCgoLyIiIiIiIiIiIiIiIiIiMiQKyouIiIiIiIiIiIiIiIiIiAyJuft410FEREREREREREREREREROQlSZnyIiIiIiIiIiIiIiIiIiIiQ6KgvIiIiIiIiIiIiIiIiIiIyJAoKC8iIiIiIiIiIiIiIiIiIjIkCsqLiIiIiIiIiIiIiIiIiIgMiYLyIiIiIiIiIiIiIiIiIiIiQ6KgvIiIiIiIiIiIiIiIiIiIyJAoKC8iIiIiIiIiIiIiIiIiIjIkCsqLiIiIiIiIiIiIiIiIiIgMiYLyIiIiIiIiIiIiIiIiIiIiQ6KgvIiIiIiIiIiIiIiIiIiIyJAoKC8iIiIiIiIiIiIiIiIiIjIkCsqLiIiIiIiIiIiIiIiIiIgMiYLyIiIiIiIiIiIiIiIiIiIiQ/L/TBjO9aTkIikAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 508,
       "width": 1010
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "thresholds = np.linspace(0, 1.0, 1001)\n",
    "p_release = np.zeros(1001)\n",
    "\n",
    "for i, threshold in enumerate(thresholds):\n",
    "    p_release[i] = -1*get_neg_prob_release_for_threshold(threshold)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.scatter(thresholds, p_release, color='crimson')\n",
    "ax.set_title('Probability of Release vs. Flip Threshold', fontsize=20)\n",
    "ax.set_ylabel('Probability of Release', fontsize=16)\n",
    "ax.tick_params(axis='y', labelsize=15);\n",
    "ax.set_xlabel('Threshold Below Which a Prisoner Chooses to Flip', fontsize=16)\n",
    "ax.tick_params(axis='x', labelsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write a function that will return the ideal threshold along with the probability of being released at that threshold. I was originally just testing 1000 different threshold values between 0 and 1 but switched to using the `minimize_scalar` function from `scipy.optimize` for a quicker, more precise result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_best_prob_release(n_prisoners=4):\n",
    "    result = minimize_scalar(get_neg_prob_release_for_threshold, bounds=(0, 1), args=(n_prisoners), method='bounded')\n",
    "    # Let's return both the probability of release along with the threshold above which a prisoner should flip.\n",
    "    return -1*result['fun'], result['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.28484236891760556, 0.34203573002489845)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_best_prob_release()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There we have it, the prisoners should flip the coin if their number from the guards is below `~.342`. This yields approximately a `28.48%` chance of being released. \n",
    "\n",
    "Let's experiment though and see how the threshold and probability changes when we change the number of prisoners."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_prisoners = np.arange(1, 101)\n",
    "p_release = np.zeros(100)\n",
    "threshold_best = np.zeros(100)\n",
    "\n",
    "for i, n in enumerate(n_prisoners):\n",
    "    prob, threshold = get_best_prob_release(n_prisoners=n)\n",
    "    p_release[i] = prob\n",
    "    threshold_best[i] = threshold    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 508,
       "width": 1010
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.scatter(n_prisoners, p_release, color='crimson')\n",
    "ax.set_title('Probability of Release vs. Number of Prisoners', fontsize=20)\n",
    "ax.set_ylabel('Probability of Release', fontsize=16)\n",
    "ax.tick_params(axis='y', labelsize=15);\n",
    "ax.set_xlabel('Number of Prisoners', fontsize=16)\n",
    "ax.tick_params(axis='x', labelsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, a single prisoner has a 50% chance of being released due to being guaranteed to be the only prisoner flipping a coin. As more and more prisoners are added the probability begins dropping and converging to what appears to be 25%. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 508,
       "width": 1000
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "ax.scatter(n_prisoners, threshold_best, color='crimson')\n",
    "ax.set_title('Ideal Threshold vs. Number of Prisoners', fontsize=20)\n",
    "ax.set_ylabel('Ideal Threshold', fontsize=16)\n",
    "ax.tick_params(axis='y', labelsize=15);\n",
    "ax.set_xlabel('Number of Prisoners', fontsize=16)\n",
    "ax.tick_params(axis='x', labelsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This chart also matches our intuition. A single prisoner will choose a threshold of 1.0, meaning he will always flip. As we add more prisoners the threshold will drop lower and lower in an attempt to have just 1 prisoner flipping."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation\n",
    "\n",
    "Before deciding to find an exact solution I wrote a simulation of the prisoner's scenario. The code is included below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_release_probability(n_prisoners=4, threshold=0.75, n_sims=5*10**6):\n",
    "    # Each of the 4 prisoners is assigned a random number between 0 and 1.\n",
    "    nums = np.random.random(size=(n_sims, n_prisoners))\n",
    "    # Prisoners flip the coin if they're above a certain threshold.\n",
    "    is_flipping = nums > threshold\n",
    "    # For every prisoner flipping, see if they got a 1 (heads) from a fair coin.\n",
    "    flip_results = np.random.binomial(is_flipping, .5)\n",
    "    # For each simulation we need to make sure at least 1 prisoner flipped.\n",
    "    someone_flipped = np.any(is_flipping, axis=1)\n",
    "    # Every prisoner who flipped must have gotten heads in order for the group to be released.\n",
    "    all_heads = np.all(np.where(is_flipping, flip_results, 1), axis=1)\n",
    "    \n",
    "    released = someone_flipped & all_heads\n",
    "    \n",
    "    return np.mean(released)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
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