simulation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numba as nb\n",
    "import numpy as np\n",
    "import pickle as pkl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coupon Collector's Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$1$ coupon each time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "@nb.jit(nopython=True)\n",
    "def coupon(m):\n",
    "    coupons = set()  # coupon set\n",
    "    count = 0\n",
    "\n",
    "    while True:\n",
    "        x = np.random.randint(m)  # generate a coupon x randomly\n",
    "        coupons.add(x)  # add the new coupon x to the coupon set\n",
    "        count = count + 1\n",
    "        if len(coupons) == m:  # all m types of coupons have been collected\n",
    "            break\n",
    "\n",
    "    return count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test the average times for $m = 20$ coupons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71.5682 233\n"
     ]
    }
   ],
   "source": [
    "count_list = []\n",
    "\n",
    "for i in range(10000):\n",
    "    count = coupon(20)\n",
    "    count_list.append(count)\n",
    "\n",
    "count_array = np.array(count_list)\n",
    "print(count_array.mean(), count_array.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$k$ ($k\\ge 2$) coupons each time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "@nb.jit(nopython=True)\n",
    "def coupon_k(m, k):\n",
    "    coupons = set()  # coupon set\n",
    "    count = 0\n",
    "\n",
    "    while True:\n",
    "        x = np.random.choice(m, size=k, replace=False)  # generate k coupons (k >= 1, without repetition) randomly\n",
    "        # coupons = coupons | set(x)\n",
    "        for i in range(k):  # add the k new coupons to the coupon set\n",
    "            coupons.add(x[i])\n",
    "        count = count + 1\n",
    "        if len(coupons) == m:  # all m types of coupons have been collected\n",
    "            break\n",
    "\n",
    "    return count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test the average times for $m = 10$ coupons, and each time we choose $k = 3$ coupons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.0348 31\n"
     ]
    }
   ],
   "source": [
    "count_list = []\n",
    "\n",
    "for i in range(10000):\n",
    "    count = coupon_k(10, 3)\n",
    "    count_list.append(count)\n",
    "\n",
    "count_array = np.array(count_list)\n",
    "print(count_array.mean(), count_array.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complete Graph Covering Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of the complete graph covering problem are equivalent to the average sampling times of $\\pi$-SGD: Suppose we sample a permutation of $n$ nodes randomly at each time. How many times does it take on average before any two nodes have become neighbors at least once?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "@nb.jit(nopython=True)\n",
    "def cover(n):\n",
    "    edges = set()  # edge set\n",
    "    count = 0\n",
    "    num_edges = int(n * (n-1))  # 2 * the number of edges in a complete graph K_n\n",
    "\n",
    "    while True:\n",
    "        p = np.random.permutation(n)  # generate an n-permutation (Hamiltonian path) randomly\n",
    "        count = count + 1\n",
    "\n",
    "        for k in range(n-1):  # construct the corresponding edges in the n-permutation (Hamiltonian path)\n",
    "            e = (p[k], p[k+1])  # construct a new directed edge e\n",
    "            edges.add(e)  # add the new edge e to the edge set\n",
    "            ##### please comment out the next line for directed cases #####\n",
    "            e_rvs = (p[k+1], p[k])  # reverse the directed edge e\n",
    "            edges.add(e_rvs)  # add the reversely directed edge e_rvs to the edge set\n",
    "\n",
    "        if len(edges) == num_edges:  # the complete graph K_n has been covered\n",
    "            break\n",
    "\n",
    "    return count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test the average times for $n = 10$ nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.2659 55\n"
     ]
    }
   ],
   "source": [
    "count_list = []\n",
    "\n",
    "for i in range(10000):\n",
    "    count = cover(10)\n",
    "    count_list.append(count)\n",
    "\n",
    "count_array = np.array(count_list)\n",
    "print(count_array.mean(), count_array.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison of Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the results of coupon collector's problem, with the number of nodes $n$ taken from 1 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "coupon_result = []\n",
    "\n",
    "for n in range(1, 101):\n",
    "    k = n - 1\n",
    "    m = int(n * (n-1) / 2)  # m = int(n * (n-1)) for directed cases\n",
    "    coupon_list = []\n",
    "    for i in range(10000):\n",
    "        count_coupon = coupon_k(m, k)\n",
    "        coupon_list.append(count_coupon)\n",
    "    coupon_array = np.array(coupon_list)\n",
    "    coupon_result.append(coupon_array.mean())\n",
    "    # print(n, coupon_array.mean())\n",
    "\n",
    "# with open(\"coupon_result.pickle\", 'wb') as f:\n",
    "#     pkl.dump(coupon_result, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the results of complete graph covering problem, with the number of nodes $n$ taken from 1 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "cover_result = []\n",
    "\n",
    "for n in range(1, 101):\n",
    "    cover_list = []\n",
    "    for i in range(10000):\n",
    "        count_cover = cover(n)\n",
    "        cover_list.append(count_cover)\n",
    "    cover_array = np.array(cover_list)\n",
    "    cover_result.append(cover_array.mean())\n",
    "    # print(n, cover_array.mean())\n",
    "\n",
    "# with open(\"cover_result.pickle\", 'wb') as f:\n",
    "#     pkl.dump(cover_result, f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n \t Coupon \t Cover (avg times)\n",
      "---------------------------------------------\n",
      "1 \t 1.0000 \t 1.0000\n",
      "2 \t 1.0000 \t 1.0000\n",
      "3 \t 2.5016 \t 2.4903\n",
      "4 \t 4.3077 \t 4.1853\n",
      "5 \t 6.4788 \t 6.2963\n",
      "6 \t 8.9973 \t 8.8005\n",
      "7 \t 11.5271 \t 11.4270\n",
      "8 \t 14.3898 \t 14.2770\n",
      "9 \t 17.3706 \t 17.1989\n",
      "10 \t 20.4025 \t 20.3587\n",
      "11 \t 23.6067 \t 23.5219\n",
      "12 \t 26.9507 \t 26.9066\n",
      "13 \t 30.3139 \t 30.3203\n",
      "14 \t 33.6650 \t 33.6813\n",
      "15 \t 37.2587 \t 37.3975\n",
      "16 \t 40.9407 \t 40.9211\n",
      "17 \t 44.3883 \t 44.5882\n",
      "18 \t 48.2013 \t 48.3560\n",
      "19 \t 52.1807 \t 52.0115\n",
      "20 \t 55.8813 \t 56.0006\n",
      "21 \t 59.7106 \t 59.7283\n",
      "22 \t 63.8763 \t 63.8467\n",
      "23 \t 68.0442 \t 67.9674\n",
      "24 \t 71.8257 \t 71.8489\n",
      "25 \t 75.8020 \t 76.0521\n",
      "26 \t 80.0733 \t 80.1358\n",
      "27 \t 84.0834 \t 84.1769\n",
      "28 \t 88.4062 \t 88.6117\n",
      "29 \t 92.5969 \t 92.4745\n",
      "30 \t 97.5968 \t 96.6826\n",
      "31 \t 101.3657 \t 101.4580\n",
      "32 \t 105.4870 \t 105.7047\n",
      "33 \t 110.3723 \t 110.0195\n",
      "34 \t 114.0602 \t 113.6935\n",
      "35 \t 118.8359 \t 118.9461\n",
      "36 \t 123.9651 \t 123.9354\n",
      "37 \t 127.7166 \t 128.4499\n",
      "38 \t 132.0647 \t 132.0986\n",
      "39 \t 137.2611 \t 137.3284\n",
      "40 \t 141.6260 \t 141.4073\n",
      "41 \t 146.1905 \t 146.1698\n",
      "42 \t 151.2778 \t 151.0081\n",
      "43 \t 155.5902 \t 154.9680\n",
      "44 \t 160.1902 \t 160.2899\n",
      "45 \t 164.7853 \t 164.9146\n",
      "46 \t 169.8397 \t 169.7805\n",
      "47 \t 174.7032 \t 175.0513\n",
      "48 \t 179.6522 \t 179.4978\n",
      "49 \t 184.4197 \t 184.0066\n",
      "50 \t 188.6791 \t 188.8858\n",
      "51 \t 193.4494 \t 193.5360\n",
      "52 \t 198.4837 \t 198.5213\n",
      "53 \t 203.2985 \t 203.4180\n",
      "54 \t 208.5924 \t 209.0448\n",
      "55 \t 213.2313 \t 213.0806\n",
      "56 \t 217.5188 \t 218.0031\n",
      "57 \t 223.4606 \t 223.8205\n",
      "58 \t 228.1511 \t 228.3347\n",
      "59 \t 233.1696 \t 232.6600\n",
      "60 \t 238.2353 \t 238.7997\n",
      "61 \t 242.9412 \t 243.7219\n",
      "62 \t 247.7554 \t 247.4385\n",
      "63 \t 253.3868 \t 253.3714\n",
      "64 \t 259.0851 \t 257.9728\n",
      "65 \t 264.0284 \t 264.0104\n",
      "66 \t 268.4330 \t 268.6047\n",
      "67 \t 273.6828 \t 273.7295\n",
      "68 \t 279.2329 \t 278.9162\n",
      "69 \t 283.4486 \t 283.9280\n",
      "70 \t 289.3319 \t 288.7196\n",
      "71 \t 293.6898 \t 295.2743\n",
      "72 \t 299.7644 \t 299.9439\n",
      "73 \t 304.3790 \t 304.1154\n",
      "74 \t 310.1395 \t 310.0458\n",
      "75 \t 315.3243 \t 314.6226\n",
      "76 \t 319.6531 \t 320.2555\n",
      "77 \t 326.0600 \t 325.6762\n",
      "78 \t 330.6202 \t 331.2159\n",
      "79 \t 336.7426 \t 336.4346\n",
      "80 \t 342.7569 \t 342.1855\n",
      "81 \t 346.5362 \t 346.7003\n",
      "82 \t 351.9482 \t 352.3463\n",
      "83 \t 357.8231 \t 357.4453\n",
      "84 \t 362.5077 \t 362.0272\n",
      "85 \t 368.4160 \t 368.9085\n",
      "86 \t 374.0587 \t 373.7370\n",
      "87 \t 378.9175 \t 379.5188\n",
      "88 \t 384.2114 \t 384.7991\n",
      "89 \t 389.0430 \t 389.7624\n",
      "90 \t 395.7467 \t 395.2806\n",
      "91 \t 400.4921 \t 400.8710\n",
      "92 \t 406.2911 \t 406.0662\n",
      "93 \t 412.1532 \t 411.3619\n",
      "94 \t 417.0107 \t 417.1278\n",
      "95 \t 422.9036 \t 423.0884\n",
      "96 \t 427.2680 \t 427.6824\n",
      "97 \t 433.0829 \t 433.3556\n",
      "98 \t 439.1229 \t 438.7761\n",
      "99 \t 445.2973 \t 443.9343\n",
      "100 \t 450.2670 \t 450.2508\n"
     ]
    }
   ],
   "source": [
    "print(\"n \\t Coupon \\t Cover (avg times)\")\n",
    "print(\"-\" * 45)\n",
    "for i in range(len(coupon_result)):\n",
    "    print(i+1, '\\t %.4f \\t %.4f' % (coupon_result[i], cover_result[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot for Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3YULo+Ho5G4kk20IIIYQQwryKiyFqLdxM0s440jm08hrt0ol2APg0BehSL5PrsiTZFkIIIYQQ5mVhAV5+4N8NfCtPmP+4D9vOQ3pe6US74ZBkWwghhBBCmEfaTSjMh+ZtIKhvlc2v3YOfLkCxCmM7QJsmZoixlslsJKJRGzlyJOHh4br34eHhjBw5su4CqoGy1yCEEEI0SKoKR7fB8R2Vz6H9gOYmbDoLdtYwJahhJtogyfYj486dO8yePRsfHx9sbW3x9PRk8ODB7N27V6/drVu3eP3112nfvj12dnY0b96cJ554gk8++YSsrCxdu/DwcBRFQVEUrK2tad68OYMGDWLFihUUFBSY+/KM9tFHH7FmzRqTn2fgwIH85S9/Mfl5hBBCiAZBVbU12f0nwaCpldZnFxVD1GXYnwxtm8DkzuBqb75Qa5uUkTwiJkyYQE5ODl988QX+/v7cvn2bQ4cOkZqaqmuTnJxMaGgoLi4uLF68mC5dulBcXMyFCxf4+uuvadasGVOnTtW1HzJkCN988w1FRUXcuXOH/fv3s3DhQr755huioqJwdHSsi0utVJMmlX8szs/Px8am4imHhBBCCFENqgrxhyAzDULHgbNrpc2z8+HHi3A9E3p6wROtwaLivLxBkJHtBigwMFA3qlz2tWjRonLtMzIyiI6O5n//938ZPHgwbdu2pWfPnkRERDB58mRdu1mzZmFhYUFMTAyTJ08mMDCQoKAgxo8fz5YtW5gyZYpev7a2trRo0QJvb29CQkJ44403OHjwIL/99hsffPCB0ddjaBS4bLnHwIEDmT17NgsWLMDd3Z3mzZsTERFBcXGxrk1OTg7h4eE4OTnh6elJZGRkuXMZ6nfWrFlERETg4eFBaGgoAKqq8sEHH+Dn54e9vT3BwcF6I+KqqrJ06VLat2+Pra0trVq1Yv78+bpzHDp0iBUrVuj+XpKTk6vs09hrEEIIIRqEoiJt2YjmIKBoZyCpxJ1s+C4BbmfDcH/o26bhJ9ogI9s6B5PhTo55z+nhAAN9qn/cli1b6NChAzt27KBbt26oqoq/vz+ffPJJuYQYwMnJCScnJ7Zt20bfvn2xs7Mr1yYtLY3du3cTGRlZ4Yi0UslXPiWCgoIICwtj48aNvPPOO9W/uEqsXbuWuXPn8ssvvxAXF8fUqVPp3r277pojIiLYu3cvGzduxNvbm3feeYfDhw8zfvz4Svtds2YNr7zyCtHR0agPasjeeustfvjhB1asWEGHDh04evQof/7zn3F1dWXEiBEsWLCAzz77jGXLltG/f3/u3LlDbGwsoC1VuXDhAh07dtQlyx4eHlX2+TDXIIQQQtQr+ffh8Aa4fgm6DICuAystHUlKhx2XwNoSnukMnvXvy/Eak2S7Abp16xaKotCvXz+cnJy4dOkSOTk59O3bF3v78kVNVlZWrF69mj//+c/85z//oVu3boSGhjJp0iQef/xxAC5evIiqqnTo0EHv2FatWpGRkQHAc889x7/+9a8q4wsMDGTfvn21cKXl+3333XcBCAgI4PPPPycqKoopU6aQlZXFF198wapVqxg2bBgAX375Ja1ataqy33bt2rF06VLd++zsbJYtW8aePXvo16+frs3x48dZsWIFAwYM4MMPP+Sf//wn06ZNA8Df358+ffoA2lIVGxsbHBwcaNGihVF9jhgx4qGuQQghhKg3cjJh/1rIuA19RkP7xyptrrkJB5LB3QHGdABnW/OEaS6SbD9QkxHmuqLRaPD19cXJyQmAuLg4HBwc8Pf3Z+3atcyYMUPXdufOnfTr148JEyYwYsQIoqOjOXr0KLt27WLp0qX8/e9/Z8GCBRWeKzo6mqKiIl555RXy8vKMik9VVaNGwaurSxf9eTi9vLy4ffs2AImJieTn5+sSXtCO6AcHB1fZb/fu3fXenzlzhry8PMLCwvSuo6CgAB8fH86cOcP9+/cZPHiw0bFX1efDXoMQQghRL6Tf1iba+bnaByG9/StsWqzC4SsQexPaNYXh7cHG0oyxmokk2w1QfHw8Xbt21b2Pi4sjKCgICwsLRo8erRutBvD29tb9t52dHU899RRPPfUU/+///T9efvllFi1aREREBP7+/iiKwrlz5/TO1a5dOwAcHByMju/MmTP4+voa3d7CwkJXvlHC0Iwm1tbWeu8VRdHVbJc9vjrKls2U9Ll9+3batGlTLoabN29W+xxV9QkPdw1CCCFEnbuRBIfWg6UVDH0JmrWssGl+Eey8BJfToVsL6N+2cdRnGyIPSDZA8fHxeqO8cXFxuuTb2dkZf39/3ctQWUmJwMBACgsLycvLo1mzZgwdOpTly5frTfFXXQkJCezatYuJEycafYyHhwc3btzQ26bRaKp1Xn9/f6ytrTl27JhuW3Z2NgkJCdXqB7T3xdbWlitXrujdS39/f9q2bavbHxUVVWEfNjY2FBUVGd1nbV+DEEIIYVaqCrH7wMEZnn650kQ7Ox82nNHWaQ/y0VYXNNZEG2Rku8EpLi4mISGBefPm6bYlJibqlR6UlZqayqRJk5g2bRpdunTB2dmZmJgYPvjgAwYPHoyLiwsAn376KaGhoXTv3p1FixbRtWtXrKysOHnyJBqNhqFDh+r1e//+fW7evElxcTF37twhKiqKyMhIunfvTkREhNHX9OSTT/Laa6+xbds2OnTowL///W+uXbumK68whpOTE9OnT2fevHl4eHjg5eXFu+++q5fwGsvZ2ZmIiAgiIiJQVZX+/fuTlZXFsWPHsLCw4JVXXmHu3LnMnz8fW1tb+vfvT2pqKidPnmTWrFkA+Pj4cPz4cZKTk3FycsLNza3KPmvzGoQQQgizUFXtLCOWljBwsnZU27bigb70XNh0DnILYHQH8K18JsBGQZLtBiYxMZHs7Gy9ke3g4GD+8Y9/8Nhjj/H000+XO8bJyYnevXvz0UcfcenSJe7fv4+3tzdTp07lrbfe0rXz9fUlNjaW999/n7fffptr165hbW1Np06dmD17drnp+fbt20fLli2xtLSkadOmBAUFsXDhQmbMmKGbq3r16tW89NJLJCUlVZg8T5s2jfj4eN3DhrNnz2bcuHHcvXu3WvdmyZIlZGdnM27cOBwcHHj11VfJzs6uVh8lFi9ejKenJ0uWLGHWrFm4uLgQEhLCX//6VwDef/99XF1dWbx4MSkpKXh6evLCCy/ojo+IiODFF18kMDCQ3NxckpKSquyztq9BCCGEMLnjOyDnHgz4k3ZUuxI3MmHreUCBSYHg6WSeEOua0pjrRHv06KHGxMQY3Hf27Fk6depk5ogePQsXLuSHH35Ao9FgZSWf7UTjIr9HhBCPvHPHITcTQp6sdGq/y+nw00VwtIbxnaBp+VmIGzRFUU6qqtrD0D7JfoRJ7dixg+XLl0uiLYQQQjQWOZlwLxVa+EDHXlU2T7gNUUna9UXGdADHR2yhZsmAhEmdOHGirkMQQgghRG3JuKOd2q+oEMbNBSvrCpuqKhy/Dr9cg7ZNYWQjndqvKpJsCyGEEEKIqt1MhoPrtA9BPjm10kQ7rxD2JEJiOnRyh6d8wfIRnQNPkm0hhBBCCFG5pFPw8xZwdoXBz4FT0wqbXrsHuy5BTgH0awPdW1Zazt3oSbIthBBCCCEMU1U4/TP8tk9boz3gT/pT++XFQ+YmKLxKsWVbjmU+x/E7fjSxg8mdH50ZRyojybYQQgghhCivuFg7td+FGGgXDE+M0ZaQlMiLh7QlYOHKH0X+7Exqx43seAJbWTIowOeRrM82RJJtIYQQQgihT1Xh0Pdw7RwE9zM8tV/mJrBw5UqOLz9d7YwKPN06ho7NNGC5qC6irpck2RZCCCGEEPoUBdp0Am9/CDA4fTQUXuViVgg7rgXhZpfD6LYJNLHOgcIU88Zaz0myLYQQQgghtDLuQGYatO4Afl0rbXomsyd7r7WluUMW43zisbMqhKI/wKqNmYJtGB7RSViEEEIIIUQ5v+2FmF1QVFRps7ibsPv2eFrZX2NCm4PYWeZDUToUp4PzeDMF2zDIyLYQQgghxKOuuBgsLOCJsVCYD5aGn24svVCNn4cnw1v3wSr7BhRe1Y5oN50Odl3MHHz9Jsm2EEIIIcSjSlXhVDTcTNLOn23nADhU2PTIVYi5AR3dYagvWFp0AQdJrisjZSQN2Oeff46vry9WVlbMmDFDtz09PR1PT08SExON7mvixIksW7bMFGFWS3h4OCNHjqzrMIQQQojGr6gIjm2HuP3g4FJp02IV9iVpE+0unhDm9+iuCFldMrLdQJ07d45Zs2axYcMGevfujbOzs25fZGQkw4cPx8/Pz+j+Fi5cyIABA5g+fTpNmjQxRchCCCGEqC/y78PhDXD9EnQZAF0HVrjMY0ER7LykXXq9lzc80erRXhGyuuQzSQO1bds2goKCGDduHC1btsTJSbtEU05ODitXrmT69OnV6i84OBhfX1/WrFljinCFEEIIUV9k34Pdq+DmZegzGkIGVZg95xXC5nNwOR0G+kBoa0m0q0uS7QYoICCAefPmodFoUBSFcePG6fbt2LEDCwsLQkNDddtSUlJQFIWtW7cSFhaGo6Mjfn5+HDhwQK/f0aNH891339V6vMae35CBAwcye/ZsFixYgLu7O82bNyciIoLi4uJa6V8IIYR4pKTfgp0rISsDnnwW2j9WYdOsfNhwBm5kwdP+0K2FGeNsRKSMpLQ9q6tu4x0AnZ/4v/Z+IdpXXg4c/r7q40u3tzP8AEJVjhw5Qr9+/XjhhReYPn06Dg7/1090dDTdu3dHKfWxMy4uDoBly5bx9ttvs3z5cv77v/+bN954g9jYWF27Xr168d5775Gbm4u9vb3eOSMjI4mMjKw0rp07d9KvX79y2409f0XWrl3L3Llz+eWXX4iLi2Pq1Kl0796dKVOm1Er/QgghxCPheqJ2VUhrWwibBq6eFTZNz9WOaOcUwNgO0LapGeNsZCTZboBcXFy4fPkyoaGhtGih/zHzypUrtGzZUm+bRqPBxcWF9evX69pPnDiR+fPn67Xz8vKioKCA69evl6v3njlzJs8880ylcXl7exvcbuz5KxIYGMi7774LaEf1P//8c6KionTJ9sP2L4QQQjR6qgpnj4FTU+2ItmPFD0TeyoLN5wEVJgZCCyfzhdkYSbJd2tDwmre3c6je8TUc1QZISEigsLCQkJCQcvtyc3Px9NT/pBoXF8eIESP0EvNLly7h7++v165kNDs3N7dcv25ubri5udUoXmPPX5EuXfSnFPLy8uL27du11r8QQgjRaKkqFOSDjS30m6jdZmNbYfMLqbA7ERysYVxHcLOvsKkwktRsN0BxcXG0bduWpk3Lf6fj7u5Oenq63jaNRkOfPn30tsXGxpZL1tPS0gDw8PAo129kZCROTk6VvqKjow3Ga+z5K2Jtba33XlEUvZrth+1fCCGEaLSO/Qj7voaiQm2SXUGirarw6+/w00XwcIDJnSXRri0yst0AxcXFVZhIduvWjdWrV+veZ2dnk5iYSLdu3fTaxcbGMn68/nKqCQkJeHl5lRsZh5qXkVTn/DVh6v6FEEKIBs27PTg2AQvDK0KCdmq/vZfhfKp2sZqnfMFKhmNrjSTbDVBcXBxDhgwxuG/YsGHMmzeP1NRUmjVrRnx8PIBecp6amkpKSkq5hD06OpqwsDCD/da0jKQ6568JU/cvhBBCNDiZ6ZB6HXw6Q5uO2lcFsvNh2wW4maWd1q+nl0ztV9vkc0sDo6oq8fHxFSaSwcHB9OrVi3Xr1gHaEov27dvr5uEG7aivtbU1gYGBum15eXls3ryZP//5z7Uar7Hnr6/9CyGEEA3K3d+1U/sd36FduKYSt7PhuwS4mwMjA7QL1kiiXfsUVVXrOgaT6dGjhxoTE2Nw39mzZ+nUqZOZIzKPXbt2MXfuXM6cOYOlZcVfG5W2YsUKtm7dyp49e0wcnRCNR2P+PSKEaICunoMjG8HeSTvjSBP3CpuWPAhpZwWjO4CnoxnjbIQURTmpqmoPQ/ukjKQRCgsLY86cOaSkpNC2bVujjrG2tuaTTz4xcWRCCCGEMImzv0LMLmjmBYOmaBNuA1QVjqZoH4Zs4QSjAsDJxsyxPmIk2W6k/uu//qta7V955RUTRSKEEPRPu9QAACAASURBVEIIkykuhpN7tHNot+kEfceDlbXBpvlF2tHsS2kQ6AGD28mDkOZQJ7dYUZT2iqLkKYqyptS2qYqiXFEUJVtRlC2KoriV2uemKMrmB/uuKIoytS7iFkIIIYSoNwrytStCnj0GgX2g/6QKE+0/7sP605CYBv3bwlCZccRs6uo2rwBOlLxRFKUz8G/gecATyAE+LdM+/8G+Z4HPHhwjhBBCCPHoUVU4uA5SzkPPp6HHMLAwnNal3IPvTkHmfRjbEbq3lAchzcnsZSSKokwGMoBfgJIl/p4FtquqevhBm7eBs4qiOAPFwAQgSFXVLOCIoijb0Cbmb5o7fiGEEEKIOqcoENQXOj4OrTtU2OzcXW3pSBM7GBMArrJQjdmZNdlWFMUFeBcYDEwvtasz2uQbAFVVExVFyQcC0CbbRaqqXijVXgMMqOAcrwCvALRp06ZW4xdCCCGEqFM3kuDeXejQE1r6VthMVSHmBhy5Ct7O2hlH7ORJvTph7tu+GPhCVdVriv73F07AH2Xa/gE4A0WV7CtHVdX/AP8B7dR/tRCzEEIIIUT9cOk3SL8F/t3AslQalxcPmZug8CrFlm05mPECmrR2BDSDYX5Sn12XzJZsK4oSAgwBuhnYnQW4lNnmAmSiHdmuaJ8QQgghROOmqpCfB7b20Gc0FBeVT7TTlnAtsyXrz/ShmasjGQVx9Gin0tfPV+qz65g5P+cMBHyAq4qi3AQigAmKovwGnAa6ljRUFMUXsAUuPHhZKYrSvlRfXR8cI4QQQgjReBUVwc9bYPeX2tlHrKzBxk6/TeYmsHAl8Z4Xn8Q/TkK6DwO9kujX5GtJtOsBc5aR/AdYV+p9BNrkexbQHDiqKEo/4De0dd2bVFXNBFAUZRPwrqIoLwMhwBjgCfOFLoQQQghhZvdztVP73UyCkEEVTutH4VUyCtuz/2YwWNrS2/0k3TwyoDDFvPEKg8yWbKuqmoN2Sj8AFEXJAvJUVb0D3FEUZSawFmgG7ANeKnX4bGAVcBtIBWapqioj20IIIYRonDLT4cC3cC9Nu1CNb5cKm16/H8Sq053YfNYDclL48HATQtwKad9cJoqoD+qsXF5V1UWqqj5X6v23qqq2UVXVUVXVMaqqppXal6aq6tgH+9qoqvpt3UQtasP8+fO5f/9+tY9LTk5m2rRpTJ48Wbdty5YtHDhwoDbDE0IIIerWnRTYuRJys2DI85Um2hdSYfXlyayKbQU5Vwn1vkV2vgUjvu3NLXWMGYMWFZFnU4VJJScnM3ToUJYuXcrLL79Meno6xcXF2NralttXFR8fH1atWqW3bdSoUaxfv95U4QshhBDmdfUs7FkN1jYQNh1a+Bhspqpw8gbsuAi+zb1YPCiHAy/F8u34fURNS+D9UR54Njc0J4UwN5lxUZiURqNhwoQJzJgxgxdffJHY2Fg6dOhgcF/Jtr/97W96fWzbtg2LClbFsrS0JCsry7QXIYQQQpiaqsKZo/DbXnD3hoFTwN7RYNNiFQ4mg+YWtHfTTu1nbfk48DgA7sCEtmaLXFRBkm1hUhqNhueffx5VVbG0tCQtLY2mTZsa3AfQtWtXfvzxx2qfR1VVFHnkWgghREOWcRvadILQcRU+DHm/EHYlwuV07bLr/drI0uv1nZSRCJNKSkrCx8eHS5cu4efnR0BAAMnJyQb3VSUjI4OZM2cSExPDsmXLdNstLS0l0RZCCNEw5d+HrAxtxtx7FPSfVGGinZoD352G5AwY5AP920qi3RAoqtp4F1ns0aOHGhMTY3Df2bNn6dSpk5kjEqqq8uqrr7J8+fJa6e/atWt88803LFiwoFb6E6I65PeIEOKh7fsGsv+AkbPgwbe8hlxIhT2JYGUJI9pD67LL/Yk6pSjKSVVVexjaJ2UkwqwUReGZZ57h/v372NraPnR/t27dYubMmbUQmRBCCFEHug7Srg5ZQaJdrMKRq9qHIVs4wcj24Pzw/3wKM5JkW5hd//79a62vHj0MfogUQggh6q/fL0LaTQjuBx6tKmyWUwA/XYSUe9DVEwa0BUspAG5w5K9MmJSiKGZ/CfNLTEw0ar7zI0eO8Nxz2un116xZQ25urqlDE0KI+uX8Cdj/LVw5A0WFFTa7lQVrT8GNLO1sI0+2k0S7oZKRbWFS1XkmYOfOnWzcuJG7d+/y6quvMnjwYBNGJmqiqKiIzZs3c/v2bRwcHMjMzOTVV19lx44dWFpacuXKFd02Q/r27cuxY8cAeOKJJ9i3bx+jRo3S7d++fbveeyGEaDRUFU7uhTO/QKsA6DcRLA2nYRdSYXciOFjD5M7Q3PAMgKKBkM9Iot54+umnWblyJatXr+b777+v63CEAcuXL+epp54iNzeX8PBwioqKAMjPzy+3bcuWLYSHhxMeHs6WLVvK9eXl5cW1a9f0tvn4+LBhwwbTX4gQQphTYQEc+l6baHfsBQMnaxetKUNV4WiKtnSkuSNMCZJEuzGQkW1R77z//vvy0GM9dOHCBYqLi2nSpAk2NjYUFRVhY6P9x6Lkz9Lbxo4dy9ixY/X6OH36NNHR0YSEhODr60vr1q319gcHB7NmzRqGDx+Oo6P8CyOEaARys+DAd5B6HXqGQafeBpsVFMGey9pR7UAPGNwOrGRItFGQqf9EvfL222/Tv39/nnrqqboORZQxe/Zs3nnnHTw8PMrtS0xM5OrVqwwaNMjo/tasWcOECROwt7fX2/7LL79w6NAh5s+f/9Axm5r8HhFCVCrjDuxfC3nZ0HcCtOlosFnmfdh+AW5nQ2gb6NFS5s9uaCqb+k8+M4l6Y9WqVWzfvp2NGzfyn//8p67DEaWoqkpiYqLBRBvAz8+vWok2wHPPPVcu0QZtLffevXtrFKcQQtQbqgqHN2gfghz2UoWJ9u1s7UI1abkwqgP09JJEu7GRMhJRb0ybNo1p06bVdRjCgBMnTtC+fXvde1PM+lL6WzYHBweSk5Px8fGp9fMIIYTJqao2Y+43AWzswLGJwWbX7sG282BjCX/qDB5SPdcoSbIthKjSiRMnCAgI0L2vqvxsw4YNaDQaBg4cyJAhQ6p9vuDgYH799VdJtoUQDYuqQtx+7QORPcPA1bPCppfSYMclaGIL4zqCiyxU02hJGYmoU0uWLKnWHNojR46s65AfSbdu3cLV1dXo9pMmTWL27NkkJyfX6Hyurq7cunWrRscKIUSdURRtol1YoE28K3DqNvx4ATwc4JlASbQbOxnZFnWq9IwTrq6uuLm5Vdrey8vL1CEJA27fvk3Pnj2Nbp+fn89nn33G22+/XaPzNW3atNy0gEIIUW/lZmsfgnRtDj2GabcZKLdTVThxHX6+Bm2bapdetzG8SrtoRCTZFnXqlVdeYe/evWzevBlbW1t27dqFv79/XYclyrC1taWgoMDo9m+++SaOjo6cPHmSPn36VPt8BQUF2NrKUI8QogHIuAMHvgUUGPMXsDBcNKCqcOgKxN6Eju4w1FdWhHxUyF+zqFOWlpasW7eOYcOGcfPmTYYMGdKgRzQPHDjAkiVLanTs6NGjcXV1ZeLEibUc1cNr3rw5GRkZRrdftmwZixcvrlGiDZCeno6nZ8W1jkIIUS/cSIJdX0BBvvZhyAoS7bxC2HZBm2h3awFhfpJoP0rkr1rUORsbGzZv3kz//v25cuUKgwcPbrD1uoMGDSIiIsLgvoMHD7Jo0aIKj3399df5+uuvTRTZw2nTpg03btww2/lSU1Np1aqV2c4nhBDVlhgHUd+AgzMM/zO4extsdjML1p6C5AwY6AMD2srUfo8aSbZFvWBvb8+PP/5Iz549uXjxIk899RRpaWl1HVa1jRo1ilOnTtXo2EGDBuHs7FzLEdWOwYMHc/LkyWofV9mHi8qcPn2afv361ehYIYQwKVWF2Cj4eQt4+kDYdHBqarBZ3E1Yf1r7388Eake1JdF+9Eiy3YB9/vnn+Pr6YmVlxYwZM3TbS76CT0xMNLqviRMnsmzZMlOEaTRnZ2d27dpFcHAwp06dIiwsjMzMzBr1VZN7UF2G7tn58+fp0KGDyc5ZV7y8vMjLy6O4uNjoY5KTk2s0H3dBQQH29vY4OTlV+1ghhDCpwgKI3ginoqF9d3jyWe082iXy4uHOIu6nvMKO377nwKVbtGkCzwZDy/o5liLMQJLtBurcuXPMmjWLpUuXcu3aNZYuXarbFxkZyfDhw/Hz8zO6v4ULF/Lee+/xxx9/mCJco7m5ubF3714CAgI4ceIEI0eOJDc3t9r91OQelHb48GFGjx6Nt7c3iqKwevXqcm3K3rPMzEzs7OywsbHRazdo0CBCQkJ4+eWX+de//kVISAghISEm/SBgCpMnT2b37t1Gt9doNHTt2rXa54mKimLSpEnVPk4IIUyqqAj2fg3JCdD9Keg9EixLTSWSFw9pS0jLyee75NFcTHcm1PlzxraNx9667sIWdU+S7QZq27ZtBAUFMW7cOFq2bKkbBczJyWHlypVMnz69Wv0FBwfj6+vLmjVrTBFutXh6erJv3z7c3Nw4fPgw4eHh1Tq+pvegtKysLIKCgvjoo48MLikO5e9ZQkICnTt3LtfuwIEDxMXFsXLlSmbOnElcXBxxcXE1/iBQV5577jkOHTpkdPuaJtv79+9n8uTJ1T5OCCFMytISWgXAgGegc2j5epDMTfxR6MUPVwaQV2TDBL/z9PK8g5K1qW7iFfWGJNsNUEBAAPPmzUOj0aAoCuPGjdPt27FjBxYWFoSGhuq2paSkoCgKW7duJSwsDEdHR/z8/Dhw4IBev6NHj+a7774z23VU5qeffiItLQ17e3v+8pe/VOtYQ/eguoYPH05kZCQTJ07EooKny0H/niUkJBAcHFzjc9Z3FhYWPPvss+zZs8eo9klJSdVeAfLgwYNMnDgRKyuZlVQIUU/cuAy3H8ySFdwP2gYabJaTd5NNV/pRWGzJRF8NrZ0ywKIJFF41Y7CiPpJk+2E8qM3ixjTtn3nxZjntkSNHCAgI4L333uPGjRt89dVXun3R0dF0795dr1Y2Li4O0E7HFhERgUajISgoiDfeeEOv3169enH8+HGDZRuRkZE4OTlV+oqOjq6V69uwYQNz5szBysqK77//vtoPyhm6B6ZS+p6dOnWKoKCgGvc1ZMgQJk2axI4dO2jVqhVHjx6txUhrR3BwsNGzhHz55ZfV/jto0qQJvXr1qkloQghR+4qL4cROiIuqdEXI+4Ww+doIsgpUxvrE426X/eD4P8CqjZmCFfWVDB/V1IPaLCxcwbIVFKVr37tFgF0Xk57axcWFy5cvExoaSosWLfT2XblyhZYtW+pt02g0uLi4sH79el37iRMnMn/+fL12Xl5eFBQUcP369XIlDjNnzuSZZ56pNC5vb8PTHlXHvn37eO6551BVlVWrVtVoeXZD98BUSt+zjz/+uNK2AwcOZODAgRXu37dvXy1HZxqBgYZHdWpDt27dTNa3EEIYTVW1ibalJQyaCrb2FU4jUlisnUP7rtqT0d5L8bLLB7WJNtEuToemNS9pFI2DJNs1lbnpQaLtqn1f8mfmJpMn2wkJCRQWFhISElJuX25ubrnFQOLi4hgxYoReYn7p0qVyKzWW1CYbGtl2c3Orcin1hxUTE8O4cePIz8/nww8/5Pnnn69RP4buwVtvvcXf//73So87cOBApcmwIZXdMyGEEA1QYQH8vBksrSF0LDi7Vti0WIUdF+H3exDWoQXtnJ7X5gGFV7Uj2k2nmzwnEPWfJNs1VXhVO6Jdmplqs+Li4mjbti1Nm5af19Pd3Z309HS9bRqNhldffVVvW2xsbLlkvWReaw8Pj3L9RkZGEhkZWWlcO3furPHcyOfPn+fpp58mKyuLBQsW8Nprr9WoHzB8D1577TWee+65So9r06b6X/VVds9qiznKYUTV1Eq+QhZCNBK5WXDgO0i9Dt2HVtpUVWHvZUhMh0E+2iXYoYsk16IcSbZryqqNtnTEstQnXjPVZsXFxRkc1Qbt1/Clp6nLzs4mMTGx3NfzsbGxjB8/Xm9bQkICXl5eBpfJNmUZye+//87QoUO5e/cuM2bMqHIEuipl7wFoE3B3d/eH6teQyu5ZbZEkTwghzCD9NuxfC/dzYMCfoE3HCpsWFMHBK3DmDvRuBSEtKmwqhDwgWWPO47W1WEXpoBZr/yxO1243scqS7WHDhnH27FlSU1MBiI/XPrRZun1qaiopKSnl+oiOjiYsLMxgv25ubvj7+1f6qmiKvMqkpaUxdOhQrl69ysSJE/n000+r3UdZZe9BTWRlZemm6CsuLubq1avExcVx9ar+NxeV3bP6ruRno7TExMRys9QYcuTIEb1vCtasWVPjUpoLFy5Uq33ZuI2NGfTjNhRzdWMRQjQSv1+CXV9o/z0f9lKlifbdHPguARJuQ08v6P3wjyuJRk5GtmvKrov2YUgz12apqkp8fDwREREG9wcHB9OrVy/WrVvHnDlz0Gg0tG/fXm81vtjYWKytrfUedMvLy2Pz5s3VWrSkNsyYMYMzZ84A8MMPP2BZeoEAAxwdHcnKyqq0Tdl7UBMxMTEMGjRI937hwoUsXLiQF198UTdqXlf3rDZ8++23uuv79NNPcXBw0K3WOWfOHL1tZUuQAPr27cuxY8d075944gn27dvHqFGjqh3L5cuXKS4upmPHiv9xKxt3TWIuG7ehmKsTixCikTh/QjvjSNPmMGgKODYx2ExVIf4WHLoKNpYwriP4lK/mFKIcGdl+GHZdwGMRtFyl/dMMdVqKonDv3j3Gjh1bYZuFCxfy8ccfU1RUxMyZMzl37pze/iFDhpCfn6+30uEXX3zB448/Tu/evU0WuyE2Njb4+flV62WM0vegJgYOHIiqquVepctT6uqePazLly+TkZGhm7ElNzeX8PBwioqKyM/Px8LCQm8bwJYtWwgPDyc8PJwtW7aU69PLy4tr167VKJ6wsDC+/vrrasVtqpiNjUUI0QgUF0PMbvj1J/Dyh6EvVZho5xbA9guwPxlaucDzwZJoC+PJyHYjFBYWxpw5c0hJSaFt27ZGHWNtbc0nn3xi4sjKW7t2rUn6rck9qK66umcP68MPP9Sri7exsaGoqEj3p6qqetsAxo4dq/cB7/Tp00RHRxMSEsKQIUO4fv06rVu3NjqGRYsWsWjRIt377t27s3XrVsaMGWNU3DWJuWzcvr6+BmM2JhYhRCNQVKhdsKZTb+3DkBUsYHbtHuy6BDkF0L8tPNaiwlkAhTBIacwPX/Xo0UONiYkxuO/s2bN06tTJzBEJUbfy8/OZMmUKGzduNLg/MTGRq1ev6pXQGGPNmjVMmDDBqLr95ORkvvrqKxYuXKjbVlBQwJ/+9Cc2bTK8rHFlcdd2zFXFUpr8HhGiAcrJBBs7sLKGgnywtjHYTFUh9iZEXwUXWxjeHjwdzRyraDAURTmpqmoPQ/tkZFuIR8ihQ4fKPRhbW1MLlsyLrqoqGo2Gv/3tb3r7t23bhoWFBRqNhq5du+rts7a2Jjs7m8zMTJydnauMu7ZjLonbmFiEEA1YQT7sXAmePtB3XIWJdkERRCXB2bvg5wrD/MBWMiZRQ1KzLczuwIEDLFmypNrHjR49GldXVyZOnGiCqOq32rr2Q4cOlUt0DdWml359//33/O1vf2Pv3r1Vti1JWLt27cqPP/6o97J48BWtoWQbICgoiJ9//ln3fvLkybrnDcrGXdsxl/2Gr2wsQohGwtoGugyAzk9U2OTefdhwRpto924FowIk0RYPR5JtYXaDBg2qcDaVyrz++uuP7MNrtXXt169fr/ZKoJMmTWL27NkkJyc/9PkBkpKS8PHxKbfdw8OD69evA1BcXMzFixd1s4JUN+6Hjbl0LEKIBk5V4cxR7fR+AO0fA1fDayP8fg++TYD0PBjdAfq0kvps8fAk2RZmN2rUKE6dOlXt4wYNGvTIfq1fW9d+69YtXF0rXnrYkPz8fD777DNeeOGFhz4/wJdffmmwDMTV1ZXbt28DcPLkSbp3767bV924Hzbm0rEIIRqwoiLtbCMxu+HK6Uqbxt+CH86CrSVM7qwtHxGiNsgXI8Lszp8/T4cOHXTvH3/8ce7fv1+u3caNG42e6k8Yr7oPRb/55ps4Ojpy8uRJ+vTpY6KotKPZJUn47t27GTpUf6nk6sT9sDGXjkUI0UDl58HhDXA9EYL7QciTBpupKvx8DU5c107n97Q/2El2JGqR/DgJs8rMzMTOzk5vju9ff/21DiNqHIKCggxu37lzp970dp6enmRkZFSr72XLlj1UbMbKyMigRQvtmsdRUVF6CxJVN+6Hjbl0LEKIBigzHQ58C/dS4Ykx4N/NYLOiYth7WVuf3aU5DGoHFvI5W9QySbaFWSUkJNC5c2e9bTKy/fASEhKMauft7V1vyyPS0tJ47LHHyMzMpLi4WK9sxNxxl8QihGiAbl+Dg+u0S68Pfh5atjPY7H4h/HQRrvwBT7SGXl5Sny1MQ2q2hVklJCQQHByst+3XX38lLi6u3EsS7dr35JNPUtHc8w8rOTmZadOmMXny5Bodf+bMGZ544gmioqLKzZldW3EbG2NJLEKIBibpFOz9Cqxt4emXK0y0s/O19dnX7sFQP3jcWxJtYTqSbAuzOnXqVIUlD1UZMmQIkyZNYseOHbRq1YqjR4/WcnT1V21de79+/Th9uvKHhEokJyczdOhQli5dyssvv1xlex8fH1atWlWjuEpWfnR2dmbPnj0MGzasyrirG5+xMZaORQjRgGRlwM9bwN1bm2i7NDPYLC0X1p2G9FwYHQCdPcwcp3jkSBmJMKuPP/64xsfu27evFiNpWGrr2q2srOjSpQtJSUm0a2d4xKeERqNhwoQJzJgxgxdffFG3raLFah7G4cOHdUurHz9+nE8++aTKuA3FVxsxlo5FCNEAqKp2WNqpKQx5Hjxag6WlwaYX02DfZW3zSYHg6WTmWMUjSZJtIR4x//M//8Onn37Km2++WWk7jUbD888/j6qqWD74h6tksZratnfvXt555x2ACstFysZtKL7aiLF0LEKIei4vR1ufHdgH2nSCFj4Gm+UXwaErkHBbu+T6iPbQxM68oYpHV42GoxRFsVcUZYiiKG1rOyAhhGm5uLjw+OOPV/lQZcniM5cuXTKqfj4jI4OZM2cSExNTrdlAfv75Z8aOHYu1tXW14q5ufMbEaGwsQoh6wtoGLCy1o9ul5cVz7VIkH27+/4hN+Ji1sb9z+jb09II/dZZEW5iXYszctYqirAaOq6r6qaIoNsBJoDOQD4xTVXWnSaOsoR49eqgVjZKdPXuWTp06mTkiIeqPy5cv4+vrW9dhcO7cOd1KkcYwZdzVjUV+jwhRR24kQbOWYGP3f2UkJfLiIW0JP6f4MXX7U0zqdp8ObjcI69yN1h7y/6swDUVRTqqq2sPQPmNHtocBxx7892jAGWgBLHrwEkI0MPUh0QaqldyCaeOubixCiDpw/gREfQNx+7Xvy04jkrmJ3OLmHL7bC2zd8XLM4nn/32jNevPHKgTGJ9uuQMkkt2HARlVVbwPrgEBTBCaEEEIIoVNcDMd3apdf9/KHkMEGm/2Rc4flp4eyNqEN5N1iQ0wB1zKbQeFVMwcshJaxyfZNIEhRFEu0o9wlUyM4AQWmCEwIIYQQAoD8+3DgOzj3q/ZhyIGTwca2XLO7OfDFxbF8FtMKJe93Qr1SyCmwZMSaztzKk7UbRN0wdjaSVcB64DpQBEQ92P44cM4EcQkhhBBCaOfP3v8t3LsLvUdCgMGyWH6/B1vPg5NzZ97u8Q2j2t/F3cmeu1m5HEqyx7PlRDMHLoSWUcm2qqrvKopyGmgDbFBVNf/BrkLgH6YKztRUVUWRJaOEEDVgzMPlQoiHVLL0enERPPkseBkenU5M1y697mwD4zt50UR9GjI3QeFV3J3bMCF0PNh1MXPwQmgZPc+2qqobDWz7qnbDMR9ra2tyc3NxcHCo61CEEA1Qbm6uTBEohCndSdEuve7grE20m7gbbJZwG6KSwMMBxnYEB2uALpJci3rD6GRbUZTWQD+gOWVqvVVVNX5S3XqiefPm/P7773h7e2Nvby8j3EIIo6iqSm5uLr///juenp51HY4QjZdbS+jQC4L6gl35gTFVhV9S4Pjv0LYJjAwAG8MLRwpRp4xKthVFeRZt3XYhcAco/f2pCjS4ZNvFxQWA69evU1Agz3gKIYxnbW2Np6en7veIEKKWFBVCbBR07gv2jtBjqMFm+UWwOxEupUFnDxjcDixrtEyfEKZn7Mj2u8BS4G1VVYtMGI9Zubi4yD+WQgghRH3xx124EKMd1fY1XAbyx33Ydh5Sc2BAW+jWovxU20LUJ8Ym257AysaUaAshhBCinsjNAnsncGsBY/9LW6dtQMo9+PECFKswriO0bWrmOIWoAWO/dNmBdpo/IYQQQojak3IBtnwMl+O17ytItE/dgo1nwc4apgRJoi0aDmNHtvcC/1AUpTNwijIL2aiquqm2AxNCCCFEI6aqcPYYnNwDri3A06fCZtFX4eQNbYI93B/sjJ7eQYi6Z+yP678f/LnAwD4VkOd/hRBCCGGcoiI4vgMunoQ2nSB0HFjblGtW8OBByItp0NUTBvqAhdRniwbG2EVt5BlfIYQQQjy8+7lw6Hu4mQTB/SDkSYNPOOYWaFeEvJkF/dvCY/IgpGig5IsYIYQQQpjHvVTt0utZGRA6FvxCDDbLyIPN5yAzH4a3h4BmZo5TiFpk7Dzbb1S2vyEuaiOEEEIIM7p1Rbv0uqLA0BeheRuDzW5kwtYLgAoTOoK3zNArGjhjR7ZfLfPeGmgJ5AK3aYCL2gghhBDCjGzswKUZ9J0Azq4Gm1xMg12XwNFaO7Wfq72ZYxTCBIyt2W5XdpuiKJ7Al8DntR2UEEIIIRqB4mJIOa99CNLVE8KmGyy8VlXtbCNHroKnE4zpAA7WdRCvECZQ4wcfVVW9BfwN+KD2whFCytTqvgAAIABJREFUCCFEo3FZAwfXa0tIwGCiXVQM+5O00/u1bwYTO0miLRqXh31A0gLt6pJCCCGEEFqqqk2sfbuCnSN4tjXYLK8QdlyEK39ATy8IbS0zjojGx9gHJMeX3YS2ZnsOEF3bQQkhhBCigbp9VTuH9qCp4OgCrQIMNvvjPmw9B+l58JQvBDU3c5xCmImxI9s/lHmvAneA/cB/12pEQgghhGiYEjVwdBs4NYWiggqb3cyCLee1Jd3jOkKbJmaMUQgzk0VthBBCCPFwVBXi9sOpaGjRDgY8A7aGpxK5nA4/XdTOODKmEzRzMHOsQphZlcm2oijWwBHgBVVVz5s+JCGEEEI0GAX58PNmuHoW2neHXsPB0tJg01O3ICoJmjtqZxxxLL9CuxCNTpXJtqqqBYqitENbOiKEEEIIoZV9Dw58B+k3occw6NT7/55wzIuHzE1QeBXVsg1HM5/n1zt++DSFEe3BxnA+LkSjY2x5yFfAn00ZiBBCCCEakLu/w47/QGYaPDkVAvvoJ9ppS6AonSKlNXuvefPr5Xg6N01mdIAk2uLRYuwDko7As4qiPAWcBLJL71RV9b9qOzAhhBBC1GPXE8HKGoa8AK5lphLJ3AQWruTjzk9XA0nObMbjzU/Rx02DYrGoTsIVoq4Ym2x3An578N++ZfZJeYkQQgjxKFBVyMrQLrce3A869tIuw15W4f/P3p2HV31d9/5/L81CIBAICTEIgRAIBNgOso0N2Ay28TyPsdPEcZJOadqm03N708Rtb3552vjem/a2SZu0GRw3tROHxDbGYOMBY7ABATaTmSTQAAJJIKF5PPv3xz5gCQl0MDo6Gj6v5zkP53z3V+cs/kBabK29Vgmn2maypmwup5qTuGnyAealVEJHWf/HLBJhoXYjWRbuQERERGSA27EeCnfCXX8AiSN7TLSdgz211/LOsUnERsdxb9Zuskadho4zEJMZgaBFIutyJ0iKiIjIcJGzAEaM8lMhe9DcDm8UweHKe5ma+BtumVzEyPgEn2gHqmHMU/0csEjkKdkWERGRCzt1HI7shgW3QPJYSF7Y422ltbD2MDS2wZLp6SxIuR6rPwHtJX5He8xTkDC/n4MXiTwl2yIiItKzo3th82/9TnbeIl86ch7nYMsx+KAMRifAo3mQPhJgPiQquRZRsi0iIiJdOQe7NsBH70BaJtz4CCR2Lx1xDt46ArsqIDcVVkxTWz+R8ynZFhERkU+0t8Hml+DoHsi+EhbeCdHd04WOAKwrhAOnID8DFmd+0mZbRD4Ryrh2A24Crgcm4Fv9nQQ2AW8659T6T0REZChorPMTIU+Xw4KbYc71PWbQbR3w6iE4UgOLp8DVkyIQq8ggcdFk28wmAauB+cDH+CTbgBuAbwIfmtndzrlj4Q5UREREwujUcZ9ot7XA0kdhyqweb2tph5cPwrFaWJ4FV0zo3zBFBpvedra/D9QAU51zXTrRm9lk4FngX4F7wxOeiIiIhJ1zsPU1iIqGW5+ClPQeb2tqg9/sh8pGuHWGr9MWkYvrLdleASw+P9EGcM6VmdmfARvDEpmIiIiEl3MQ6PA12Tc8CFExPR6EBCivg7WFUNcKd82E6Sn9HKvIIBXVy3oTMPYi62OD94TEzJ4zs3IzqzWzg2b2pU5rK8xsv5k1mtnbZja101q8mf04+HUnzOzroX6miIiI9MA5eG8VvPuif540usdEu60D3i2GF/ZCewDuz1WiLXIpetvZfh541sz+HHjDOXcKwMzGATcD3wV+cQmf9x3gKedci5nlAu+Y2U6gGFgFfAl4Bfh74AXgbOf8p4EcYCr+kObbZrbPObf2Ej5bREREzjKD1Ml+Z/sCjtXC60VQ0wzz03zHkXj1MRO5JL39k/mz4D0/A2LM7Oy/yGigHfhP4C9C/TDn3N7OL4OPbGABsNc59ysAM3saqDKzXOfcfuB3gCedc9VAtZn9CPgCoGRbRETkUlSWQWszTJoBs6/t8ZbWDthUCh+dgFHx8MBsyBzdz3GKDBEXTbadc63A75vZXwH5wNkTEyeA7c652kv9QDP7Pj5RTgR2AmuAbwMfdfrcBjMrBPLM7CQwsfN68LkOZYqIiFyKol3w/sswOhUmZvfY1q+8Dl47DGda4MoJsGiKBtWIXI6QfhkUTKrf6osPdM79gZn9EXAdsBRoAUYClefdegYYFVw7+/r8tW7M7CvAVwAyMzP7ImQREZHBzTn48C3YvREmZMEND3dLtJ2DgnLYXAoj4+ChOTA5OTLhigwloQy1mQz8Pt2H2mwG/s05V3qpH+qc6wDeM7Mngu9dD5z/TzoZqAuunX3dfN5aT+/9Q+CHAPn5+Rq4IyIiw1tbqz8IWbofchbANbdDdNet6sY232mkuAZyxsJN0yFBtdkifaK3oTaLgdeAcuB1/O62AWnAg8AfmdltzrlNl/H52cBe4POdPjfp7HXnXLWZlQNXAG8Eb7ki+DUiIiJyIfU1flBNTQVcfRvkXtNtR7vkjE+0m9v9kJr56Rq7LtKXevt/6/eAnzjnvtbTopn9U/Ceq3v7IDNLA5bjJ1I24UfAPwZ8Fr9L/l0zewB4FT+dclfwcCT44TnfMLMCfN34l4Ene/tMERGRYauiBN55wXcbWfGEr9HuxDl4vwy2HoMxiXDfLBjfc4ttEbkMvSXbecDjF1n/AcH66BA4fMnIv+H7excDf+KcewkgmGj/C/AcsAV4tNPXfiv4WcX4RP0f1PZPRETkApob4c3nIHEULHvMH4jsxDl48wjsroA542FZlg5BioRLb8l2ObAIOHCB9UXBe3rlnKsEbrzI+nog9wJrLcAXgw8RERHpiXO+BiRhBNzwkO+jHZ/Y7ZZ3in2iffVE321EZSMi4dNbsv0M8G9mdg2+Xvokfod6An6ozReAPwlngCIiIhKC1hbY+CJkXwlZeTApp9stzsF7JfDhCfhMhhJtkf7QW5/t75vZKeBPgafww2wAOoDtwO84534Z3hBFRESkV9HR0NEGbS2fXGveBXWroL0EYjL5oO5zFFRkMz8dbshUoi3SH3pt7OOcewF4wcxigbNFX1XOubawRiYiIiK9O3EUUtJ9ucjNn/8kg27eBaefobQugxc/vpacCQEO1e0ib0o0y7OylGiL9JOoS7g3EHx0BP8UERGRSHEOPt4C65/1A2ug61Z13SqISqGsIY3vbZ/LW+VXMGtMNTeN/ZkSbZF+1GuybWb3mdkmoBE4jj8Q2Whmm8xMI9NFRET6W0cHfLAatr3ma7Ovuqn7Pe0lBGwMu6unQPx4JiWe4tbMYqI6ivs/XpFh7KLJtpn9LvACsA/fAnApsCz4fC/wvJl9OcwxioiIyFnNjX43+9B2mLcElj4KcfHdbqt3M/j+rnn884550HaGF7e3UVjVBjGZEQhaZPjqrWb7L4A/cM79Rw9rL5rZVuB/AD/q88hERESkq+qTfiJkUz0seQCmzevxtpIz8KtDn+dft9YyoqOcRWkn2Fsxgjt+sZCNfzyF9H4OW2Q46y3ZngRsvMj6e8DEvgtHREREelSyHzatgth4WPkkpE7qdkvA+YmQH5RB6phJ/M0Nx7krczOpcUVUtU5nQ/kK0tOuikDwIsNXb8n2XvzUxwv10v7d4D0iIiISLscL4Z3nfYK99FEYMarbLY1tsPYwFJ+B3FRYMQ3ioq8GrgZ8O7EHpvZv2CLSe7L9Z8CrZnYb8Dpdh9rcBEwGbg9rhCIiIsNdehZ85ibIvRZiYrstn6iH1QehsR1umg5zx6uHtshA0dtQmw1mNhe/u70Qn2QDnABeAv7NOXc0rBGKiIgMRw21sHUNLLwLEpNg7uIeb9tTAW8dhaRYeCQP0pP6N0wRubhQhtocBf4q/KGIiIjIOc0NUFUGtVU+2T5PewA2HIVdFZA5Gm6fAYndN71FJMJ6TbZFRESkH1Ud87XZ4zLgvj/usWykrgVWH/LlI1dPhOunQJTKRkQGpEuZINkjMysys++bWUpfBCQiIjIsBQJQsA7W/AhKD/hrPSTax2rhF3vgVCPckQOLM5VoiwxkfbGz/S4wB9+VRG0ARURELlVLE2x80Xcdyb0WJs7o8bbdJ319dnI8PDgbxo3o3zBF5NJddrLtnPsCgJklX3Y0IiIiw82ZKj+opr4Grrsbcj7T7ZaOAGwoho9OwtQxvj47QYWgIoNCn/1Tdc7V9tV7iYiIDAvHDsG7L0J0DNzyeUjrPkq9qQ1ePQSltbAgQ2UjIoNNr8m2mU3Gt/67Ht/6z+H7bW8C/t05VxrWCEVERIYa52DfZtixHlLS/aCakWO63VbVCC8fgPo2WJkNc8ZHIFYRuSwXTbbNbDHwGlCOH2rzFmBAGvAQ8DUzu805tyncgYqIiAwZO9+EPe9BVh5cdw/ExnW75fBpPxEyLgYemg0Z3YdGisgg0NvO9veAnzjnvtbTopn9U/Ceq/s6MBERkSFr2nyIjfeDas4b9egcbDkG75fBhJFwZw6Mio9QnCJy2XpLtvOAxy+y/gPgK30XjoiIyBBVWQal++GqFZCS5h/naWmH14v8rvbsVD96Peaym/SKSCT19k+4HFh0kfVFwXtERETkYo4dguK9vs1fD2qa4YW9UFQNN071NdpKtEUGv952tp8B/s3MrgHewB+MdPiDkjcDXwD+JJwBioiIDFqBgG/plzwWrlgKsxdCfGK324prYM1h//y+XD9+XUSGhosm286575vZKeBPgaeA6OBSB7Ad+B3n3C/DG6KIiMggdHZQTfVJuOerEJfQLdF2DgrKYVOJH1Bz90wYnRCheEUkLHpt/eecewF4wcxigdTg5SrnXFtYIxMRERmsair9oJqGM3DtHT7RPk9DK6wr8rvaOWPhlmyIi+7hvURkUAt5qE0wuVZ9toiIyMWUHYSNv4aY2AsOqjlaA2sLobUDVkyDeWndmpKIyBBxWRMkzSwb+JFzbnkfxSMiIjI4Oed7Z3/4FozNgKWPQFKw+Lp5F9Stor21jE1VN7Kj7hbGjUrnwdmQOiKyYYtIeF3uuPaRwI19EYiIiMig1dYK778MR/fAtHlw3d1+Zxt8on36GarbJrHm2N1UNMZyRcrPWTLjFmJHzI9s3CISdr1NkPxmL18/oQ9jERERGXw6OmDdT6D6BCy4GeZc37UmpG4Vx5un8duSJZg57so6wIyRpdC4CpKUbIsMdb3tbD8NFAE9NwUFnZkWEZHhLToaps+H0cthUk635ZKaRl4uu4Wk2Fbun7aL0XHN4EZDe0kEghWR/tZbsn0E+IZz7vmeFs3sSnwLQBERkeHDOThYAMnjIGM6zLmux9uKqmF12a2MiTnFA9MPkRTb6hcCZyCm+8FJERl6eptNtQP4zEXWHaDz0yIiMrwEOuDAVij88IK3HDwFrxyE1NEzeWjqOpKiToILQEc1BKph1P39GLCIREpvO9vfAi52TnofMK3vwhERERnAmuohNt4ffrz58xDf84/IvZXwRiFkjIJ7Zk0mof1rULfKl47EZMKYpyBB9doiw0FvEyT39bLeBhT3aUQiIiID0anj8Pbzvmxk0b2QOLLH2z48AW8f9SPX75oZHFQTM1/Jtcgwdbmt/0RERIa+ol2+tV/iSJi9sMdbWtrhnWLYVwnTU+COHIjprVhTRIY8JdsiIiIXEgjAjvWwbzNMyIIlD0FiUrfbTtbDmsNwphmunQQLJ0OUTjSJCEq2RUREetbSBBtfhOOFkHsNLFjp2/x14hxsL4dNpTAiFh6YA1OSIxSviAxISrZFRETOV10B7/w3NNT6aZA53RtzNbTCuiIoroEZY+Hm6ZCgn6oicp5evy2YWSzwHPDXzrnC8IckIiISQZVlsP5ZiImDW74AaVO63XKyAX67H1o6YMU0mJfWdWikiMhZvSbbzrk2M7sF+B/9EI+IiEhkpaRD1lyYvxSSuteElNXCSwcgPhoey4Px3Uu4RUTOCfWc9CpA3fdFRGRoam2BbWv9nzGxvnSkh0T7SDWs2g9JcfCIEm0RCUGo1WUlwDfMbAlQADR0XnTO/Z++DkxERKTf1Jz049czpsPkmT3ecqAK1hZC6gi4L9cfiBQR6Y0553q/yezIRZadc25634XUd/Lz811BQUGkwxARkYGqrhpGpfjnjXUwYlSPt+0+CW8egYmj4O5ZOggpIl2Z2XbnXH5PayF9u3DOaSS7iIgMHc7Bnvfgo7dhxRN+R/sCiXbBcdhYAllj4M4ciI3u8TYRkR5d8v/NzSwdqHTOBcIQj4iISHi1tcLm30LxPpg2D8Z37zYCUN0EG4rhSA3MHAe3ZkO0JkKKyCUKKdkOtv/7NvD7QCIwEygys38Aip1z3w9fiCIiIn2krhreeR5qKmDBLTDnum49+1o7YOsxP6wmJgqWZMJnMjQRUkQ+nVB3tr8F3AU8Afyi0/WtwF8BSrZFRGRgO17oJ0I6B8sfh0kzuiw7B/urYGOpH1gzZzwsnuI7j4iIfFqhJtuPAV90zm0ws87lI3vwu9wiIiIDk3Ow733Y8QaMHg9LH4XksV1uOd0ErxdCeT2kJ8FdOZDRcwm3iMglCTXZnggUX+DrdSZbREQGroJ18PEHMHUOXH8vxHbdqj54yifaMVF+5HreeE2DFJG+E2qivBe4ATh63vWHge19GZCIiEifmjoHEpJg7uIuWXTAwXslvjZ7wki4IweS4yMYp4gMSaEm238LPGdmU4Bo4CEzywU+C9wRruBEREQ+lfIjcOqYT7DTMv2jeRelZat5cXcst8+Gj5of5VjzFOanw41T/c62iEhfC7XP9itm9jDw10AAf2ByB3CXc259GOMTERG5dMV7oaIYcq/149ebd8HpZyirns73tl1LlbUzYdQH3JrbxOxJOnokIuETcr21c24dsC6MsYiIiHx67W3QVO8nQl59K3R0+EQboG4VRKVQ1JgNIyYTHX2MR7M/YnzcXuDpSEYtIkNcSL80M7PfmNn9ZqYGSCIiMvDU18DaH8P6n/skOzoG4joVYLeX8MrRq/jO1nzoaOKNXbXUNCVBe0nkYhaRYSHUCrUm4FngpJn9yMxuCGNMIiIioSs/Amt+CHWn/Y52dPd56m8cv4E/fus6OlobuD51P41txh3P5XGyOTsCAYvIcBJqzfZnzWwEcD/+UOR6MyvHD7h5zjm3N4wxioiIdOcc7N8C21+H5HHB/tnjut225RjsabqNx3Pf4atXbCd9VAJV9U1sOJJIesaDEQhcRIYTc85d+heZjQceAX4PyHXODche2/n5+a6goCDSYYiISF9rb4MPXoGiXTAlFxbd17VsBJ+Lby7zo9dnp8Itk3YRVb/Kl47EZMKo+yFhfoT+AiIylJjZdudcfk9rl5wkm1kCsBxYiZ8eWXp54YmIiFyC+hp453moPglXLod5S7pNoXEONgZ7aM9NgxXTIMrmQ6KSaxHpXyEl22YWBdwEPA7cC3QALwI3OefeDV94IiIinTTV+/rsQACWfxYm5XS7pbkd3jkKH1fBFemwLEsTIUUkckLd2T4OjAZeA54EVjvnWsMWlYiISE8SR0LeIpgyG5LHdlsuOeNHr9e3wsLJsHCSEm0RiaxQk+1vAr90ztWEMxgREZFu2lph6xrIvQbGTfTJ9vm3dMB7pfDhCRiTAI/kQcaoCMQqInKeULuR/BDO1WvPABxQ6JxrDmNsIiIi/jDkyaMwfrJPts9TXgdrC6GmGa6cAIunQGz37n8iIhERas12DPAd4KtAHGBAi5n9P+B/OufawheiiIgMSxUlMG4SJCbB3X/4yTTIoI4AvF8GBcdhZBw8MBsyR0coVhGRCwi1jOQfgcfwrf7eC15bgk/Ao4A/7/vQRERkWHIO9rwHH74FV62AuYu7JdrVTX43+0Q95I2HG6dC/IBsQisiw12o35o+C3zRObem07VCM6sE/gMl2yIi0hdaW2Dzb6HkY5g2D3Kv7bLsHOyt9N1GoqPgjhyY2X2OjYjIgBFqsj0aKOzheiEwpu/CERGRYetMFWx4AWpPQf5KmL2wSyuR5nZYXwSHTsOUZFiZDaPiL/J+IiIDQKjJ9kfA14A/PO/6HwMf9mlEIiIy/JTsh02/gehoWPE5yJjWZbm0FtYehsY2WJwJCzIgSi39RGQQCDXZ/ktgjZndDLyP70ZyHTARuC1MsYmIyFAXCMBH78Dud32nkaWPQFLXU477q2BdISTHw6N5kD4yMqGKiHwaobb+e9fMZuJ3tnPx3Uh+BXzfOXc8jPGJiMhQtmejT7RnXAXX3gHRXX8s7Tzh67MnJ8NdMyFBhyBFZJAJ+dtWMKn+n2GMRUREhgvnfD32rGv8Tvb0K7rUZzvn2/ptOQbZKXB7DsRERTBeEZFPSd+6RESkfx3dC+t/Dh3tEJ8I2Vd2SbQDDt464hPtvPFw50wl2iIyeOkXciIi0r/MINDhx7CfVzbSHvD12QdPQX6GPwxpOggpIoOYkm0REQm/pnqoLIPMXJg6BzJnd8uim9pgzWEoOQNLMiG/+2R2EZFBR8m2iIiEV2WZ75/d3gYT/gTiErol2ifrYfUhqG+FW7J9+YiIyFDwqZJtM0sEFgGHnHPFfRuSiIgMCc7BoR2wdQ0kJcPyx32ifZ7dFb5GOykWHsmDCWrtJyJDSEjJtpn9FNjqnPu+mcUBW4E8oNXM7nPOvRbGGEVEZLDpaIctr8LhnTBxBix5wB+GBGjeBXWraGs9xtsVy9nbsJyp49K5bQYkxkY2bBGRvhbqzvZK4J+Dz+8GRgETgC8CTwNKtkVExKuvgQ2/hFPHYf6N/hEVbCfSvAtOP8OZ9omsLruLisZYrkn9Mddl3UFU7PzIxi0iEgahJtspQEXw+a3Ar51zFWb2POq9LSIiZx0vhPd+7SdDLnsMpszqsuxqV7GnZh4bK64C4J5pHzM96QTUr4JEJdsiMvSEmmyfAOaaWTl+l/srwesjgbZwBCYiIoNMawtsfBESR/mx68njuixXN8H6w1Moa5rOpKQz3DL5AGPim8CNhvaSCAUtIhJeoSbbPwZeAI4DHcCbwevXAvvDEJeIiAwWba0QEwtx8bDiCRg9HmLjzi13BGB7OXxwDGJap3JTRgFzUxs+aUgSOAMxmZGJXUQkzEJKtp1zf2dme4FM4FfOudbgUjvwD+EKTkREBrimBnj9JzAzH2YvhNRJXZZP1MMbRVDVCDljYWnuBEbW74ZACkSN9ol2oBrGPBWhv4CISHiF3PrPOffrHq79rG/DERGRQSVhBKRNhZQJ3ZY+PAHvHIURcXDXTJgxFmAuxP051K3ypSMxmT7RTlC9togMTSEn22Z2G/CHwHRgpXOu1My+BBxxzr158a8WEZEho6MDdm2AnM/AyDFw3V1dlp2DTaWw7ThMGwO3zoCEzj9tEuYruRaRYSMqlJvM7HHgl8AhYBpwthNqNPCX4QlNREQGnKZ6WP8s7H4XSj7uttwRgHWFPtGelwZ3zzov0RYRGWZCSrbxCfWXnXN/iq/TPusD4Mo+j0pERAaeilJ49d99/+zF98Oc67ost7TDbw/Ax1Vw/RRYMQ2i7ALvJSIyTIS635ADvN/D9Xogue/CERGRAcc5OLANCtZB0mi47QlISe9yS30r/HY/nGqCW7Ihb3yEYhURGWBCTbaPAzOB4vOu3wAU9mlEIiIycLS1wpbVULTLD6hZdB/EJXS5pbIBXj4ITW1wzyzIGhOhWEVEBqBQy0h+CPyzmS0Kvp5iZp8H/hH4QShvYGbxZvafZlZsZnVmtjN46PLs+goz229mjWb2tplNPe9rf2xmtWZ2wsy+HmLcIiLyadWegtf+A47shiuXw9JHuyXa+yrh+b3Q4eChOUq0RUTOF2qf7X80s9HAG0AC8DbQAjzjnPvXS/isUuBGoAS4Hfilmc3Dl6OsAr4EvAL8PX6IzsLg1z6NL2WZCkwA3jazfc65tSF+toiIXKpjh6Cpzg+qmZjdZak9ABuOwq4KmJwMt8+ApLie30ZEZDgz51zoN5uNAObgd8T3OefqL+vDzXYBfwuMA77gnLs+eD0JqAKucs7tN7NjwJPOudeD638P5DjnHr3Y++fn57uCgoLLCVFEZHgJBPyO9pjxvla7uQESR3a55UwLvHoQTjbA1RP9YUgdhBSR4czMtjvn8ntaC7WMBADnXKNzrsA5t7UPEu10fB34XiAP+KjT5zTga8HzzCwFmNh5Pfg87wLv+xUzKzCzgsrKyssJUURk+ClYB2v/00+GNOuWaB+tgV/shupmP6hmcaYSbRGRiwmpjMTM4oE/AJYBaZyXpDvnrrmUDzWzWOC/gJ8Fd65HAudnxmeAUcDITq/PX+vGOfdDfI05+fn5oW/bi4gMZ8755HrOdTAuAxKTui1/cAy2lMG4EXBnDqQkRihWEZFBJNRuJD8C7gReAvYBnzqJNbMo4OdAK/DV4OWeWggmA3XBtbOvm89bExGRy3G2rV9FCSx5wE+EHNl1fEJzO6w9DEdqYHaq758dGx2heEVEBplQk+27gXuccxsu58PMzID/BNKB251zbcGlvcDnO92XBGQDe51z1WZWDlyBP6BJ8Pney4lFRGTY69zWb/JM6GiHmNgut1Q2wOpDUNsCy7NgfrrfABcRkdCEmmxX4A8sXq4fALOBm5xzTZ2u/wb4rpk9ALwKfBPY5ZzbH1x/FviGmRXgE/UvA0/2QTwiIsNT7SnY8EuoqfBt/eYt6ZZF76+CN4ogPsa39ZvYY/GeiIhcTKgHJP8a+P+ChxU/lWDf7N/Fj3c/YWb1wcfjzrlK4AHg20A1cC3QudPIt/AHJouBDcB31fZPRORTKvkYXv0hNNbC8sdh/g1dEu2OALxzFF47DGlJ8PhcJdoiIp9WqDvbrwNfASrM7ATQ1nnROTe9tzdwzhUDF/zlo3NuPZB7gbUW4IvBh4iIfBqBAOx8E/ZugtRJcMNDvka7k9oWWHMIyuvhqgmwJBOiL6lvlYiIdBZqsv0svtXsLP10AAAgAElEQVTe94CTXMYBSRERiYDmRtjwApwshllXQ/5KiO76I+DQaXij0H+Dv30GzEqNTKgiIkNJqMn2zcBy59yWcAYjIiJhEhvnS0UW3QfZV0DzLkqPrObF3bHcm9dOkXuUXdXTSE+C23NgTELvbykiIr0LNdkuwY9nFxGRwcI5OLQdpuZBfCLc/HmfcDfvgtPPUFY9ne9tu5ramBaSEz5kQZZjUfZ0lY2IiPShUL+l/inwj2Y2I5zBiIhIH6o9BVtfg8M7/OuzhyDrVkFUCkcap8OITJoCydybtZcbxjyrRFtEpI+FurP9KyAeOGBmLUB750Xn3PkDaUREJFKa6v2Y9dGpcNuXYOyELsvtrWX81+GVfHfrXOho5p09NTw1MxraiyIUsIjI0BVqsv3V3m8REZGIK/zID6pZ/ABk5vrR652caYZfHLyf776fTUKgiutTS9hXOYI7nstj45cCpEcobBGRoSqkZNs597NwByIiIpehox22rYWDBTAhC8ZP7nZLYTWsOwwkXMVfXPlLHsotI3VkIlX1TWw4kkh6xoP9HraIyFB3wWTbzMY6506ffX6xNzl7n4iIREBdNbz7Kzh1HOYu9hMhoz4pvg442FwK2477ITV35mQwmmW+dru9hNRRmTyw6H5ImB/Bv4SIyNB0sZ3tSjPLcM6dHdXeU29tC16PDkdwIiLSi7KD8N4q/3zZYzBlVpfl2hZYVwhltTAvDZZmQUwUwHwl1yIi/eBiyfZy4HSn5xpkIyIyUAQC8NHbsHsjjM2AGx+GUSldbjl4CtYX+Z3tldkwZ3yEYhURGcYumGw75zZ0ev5Ov0QjIiKh2fwSFH0EOQvgmtu6TINsaYcNxbC3EiaMhNtmaEiNiEikhHRA0sw6gLMlJZ2vjwMqnHMqIxER6U+510DGNMi+ssvl8jpYW+i7jlw7yT/UO1tEJHJCbf1nF7geD7T2USwiInIxezf5Htr5KyF1kn8EBZw/APlBGYyMg4fmwCRNQBARibiLJttm9vXgUwf8npnVd1qOBpYA+8MUm4iIdNZYB011vl67U7eRM83w2mEor4dZ42D5NEgIdStFRETCqrdvx38U/NOALwEdndZagaPA7/V9WCIiAvh2fgDjJsKCW/zI9eDYded8XfY7RyHKfG12bmrkQhURke4ummw756YBmNnbwP3Ouep+iUpEZLhzzg+o2bbWl4usfLLLbnZTG6w/AodPw+Rk320kOT6C8YqISI9CnSC5LNyBiIhIUFsrfPAKHNkNE2fA4vvP7WYDHK3xvbOb22FJJizI6LIsIiIDiKr6REQGkuoKePeXUHvKT4Kct6RL2ci247CpFMYlwn25fiKkiIgMXEq2RUQGisKPYMtqiI2Hm37Ht/YLag/AG0Wwv8ofgrx5OsSq6aqIyICnZFtEJNLa22Dba3BoB0zIgsUPwIhR55YbWuHlg3CiHq6fAtdMVNmIiMhgoWRbRCTSThbD4Z2+ZOSKZV0OQp5sgFcOQFM73DkTcsZGME4REblkISfbZpYOfA7IBv7GOVdlZouA4865I+EKUERkyKqrhlEpMGkG3P2HMLpr375Dp2HtYd8z++E8SFd9tojIoBPSEF8zWwAcAB4HngLOziW7Gfh2eEITERnCDu+El/4FTp/wrzsl2gEH75XA6oOQOgI+O1eJtojIYBXqzvYzwD85575lZnWdrq8Dnuz7sEREhijnfMH1lFxorIXR47ssN7T6aZCltTA3DZZlQUxI2yIiIjIQhZpsL8DvaJ+vHEjvu3BERIaw0gNwYCssewziE2FmCpz+e2gvgZhMyniENaWzaW6HW7Ihb3zvbykiIgNbqMl2E5DSw/VcoKLvwhERGYI6OmDnm7BvM4zNgJYmiDoCp5+BqBRc1GS2nxzNphP7SB6dzL15k9Q/W0RkiAg12X4J+JaZPRR87cwsC/gH4NdhiEtEZGhoOAPvvgiVpTDrashfCdExULkKolJoZjxvlM7i8JnxzEg+ys1TfkJC0jciHbWIiPSRUJPtPwfWAJXACOA9fPnIJkA/FUREenLsEGz6jd/ZXvIgTJv7yVp7Cceb5/Ba2Vzq2+JZklHIgnHFWKAscvGKiEifCynZds7VAovNbDnwGXwXkx3OufXhDE5EZFAKBODDt2DPezB2AtzwECSP+2TZQcHpxbx/YgIj4+Dh7J1kjKiFjjMQkxnBwEVEpK9d0lAb59xbwFthikVEZPBrbYG3/gsqSmBmPlx9qy8bCapvhXWFUFJ9BzNH/pIVk4+SEJvkE+1ANYzp6Sy6iIgMViEl22b2zQssOaAZOAysdc419VVgIiKDUmwcjEzx9dnT5nVZOlLtE+22ANw0M525o27E6k+d60bCmKcgYX6EAhcRkXAIdWf7ISATSAKOB69NBBrwddxTgAozu9E5V9TnUYqIDGSBAOzaANlX+omQi+/rsuwcvF8GW475ITW3z4BxIwDmQ6KSaxGRoSzUUQn/G9gGZDnnMp1zmUAWsAX4O3zifRD4v+EIUkRkQGuqg/1boGRft6W2Dlhz2Cfac8bDo3lnE20RERkOzDnX+01mR4B7nHO7zrt+JfBb51yWmS0EXnLODZghN/n5+a6goCDSYYjIUFV1DMZN9BMhG+tgxKguy/Wt8PIBqGiARZmQn+FvFRGRocXMtjvn8ntaC3VnOx1I6OF6PJAWfH4S3xZQRGRoCwRgx3pY8yMo/NBfOy/RPtkA/70HTjfBXbPg6olKtEVEhqNQa7bXA/9uZl8BtgevLQB+ALwRfD0PONK34YmIDDANZ2Djr323kZwFkDW32y2HTsPaw5AYAw/noWmQIiLDWKjJ9peAZ/E12h3Ba1HA68CXg6/r8MNvRESGprKDfkhNoAOWPNCt20hbB3xQBgXlMGEk3D0TkuIiFKuIiAwIoQ61qQBuNbNZwCzAgI+dcwc73fN2eEIUEYmwjg7Y+Sbs29zjkBrwbf3eOgq1LTA3DZZOhdjoyIQrIiIDx6UOtTkAHAhTLCIiA099DWx8ESrLfO/s/JXdhtRsKIaDpyAlER6cA1OSIxiviIgMKCEn22Y2E3gQ32+7yy9GnXNf7OO4REQGhg9WQ02l383Oyjt32TnYXQHvlUC7g+smQ/5EiAn12LmIiAwLoU6QvAP4NbATfzByG5CN70ayMWzRiYhEQke7f8QlwMI7ffeR5LHnlhta4bXDUFrrd7FXTPO72iIiIucLdWf774C/dc59x8zqgM/hJ0n+HHg/XMGJiPS7QABe/xkkJMHSR2DkmC7LpbWw5hC0dsBN02HueLX0ExGRCws12Z4FvBB83gaMcM41m9nfAa8C/yccwYmI9LuoKMi+AhJHdcminYOC47CpFEYnwP25MF4t/UREpBehJtt1fDLUphyYAewJfn1KGOISEek/7W2wbS1MmgGZs2Fm1yFgze2+b/aRGpg5Dm6aBvGXdLxcRESGq1B/XGwBFgP78DvZ/9vMrgDuQ2UkIjKY1VTCu7+CmgpIGu2T7U5O1sPqQ77ryLIsuCJdZSMiIhK6UJPtrwMjg8+fBkYBDwAHg2siIoOLc37U+tY1EBMHN30OJmZ3Wf7wJLxbDEmx8PAcyBh1kfcTERHpQa/JtpnFALn43W2cc43A74c5LhGR8GltgS2r4chuyJgOi+6DEZ9k0s3tsL7Ij12fNgZWZkNibATjFRGRQavXZNs5125mq/AJ96nwhyQiEkanjsO7L0J9NVy5HOYuhtY9lB5ezYu7Y1maE8fOpgepC0xicSbkZ6hsREREPr1Qy0g+wh+KPBq+UEREwqzwQ3j/Fd/Wb+WTkJYJzbvg9DOUnp7O93bcwDHXyqyxG3ho7lVMTJ3d+3uKiIhcRKizzp7GH4q818ymmNnYzo8wxici0ndGj4cps+DO3/OJNkDdKho60nn/9AKITyMtsYknZuxgonvh4u8lIiISglB3tl8N/rkKcJ2uW/B1dF8GJSLSZ04chYpimH8jpE6CGx8+t+Qc7Kt0rDp6Oy/sSYeWKn6zo4X7ssaRE30ocjGLiMiQEWqyvSysUYiIhEvZASg7CLOvg9i4c5fPNMObR2Bv8Qp+un0UIwLFLMqoYW/FCO54Lo+NXwqQHsGwRURkaAgp2XbObQh3ICIifaahFloaYewEuGoFzF96LtEOONh5AjaX+l/N3ZWXQW7sz1k2vYnUkYlU1Tex4Ugi6RkPRvSvICIiQ0PIM9DMbB7wu0A28EXnXLmZ3QsUO+d2hitAEZFLUnoANv/Wj1u/6/chOsY/gLoWePUQlNdD1hhYMQ2S43O4Mu1BqFsF7SWkjsrkgUX3Q8L8CP9FRERkKAgp2TazW4CXgdeA5UBicCkb+AJwbziCExEJWUc7bH8d9m+FsRlww4NdevaV18HLB6GtA27NhtzUTssJ85Vci4hIWIS6s/33wNedc983s7pO198B/qzPoxIRuRRnqmDji3D6BMy5zpeORH/y7e3jSnjjiJ8E+cBsSB0RwVhFRGRYCTXZzgPW9HD9NKDWfyISGV1GrsfCisdhUk6X5U2lsO04TE6GO3M0CVJERPpXqMl2NTCJ7kNtPgOU9WVAIiIhaW2GD1bD0T0wYRosvr/LyPWWdlhbCEXVMD8NlmZBdKiTBURERPpIqMn2L4DvmtnD+L7aMWZ2I/AM8JNwBScickGVpVCyz5eM5C2CqE8y6WO1sP4I1DTDsiy4Il0j10VEJDJCTba/AfwUKMZ3y9oX/PMXwLfDEpmIyPkCAag6BmlTfLnIvV+DkWPOLde2wMYSOHgKRsbBfbmQOTqC8YqIyLAXap/tNuBxM/smcBV+zPtO55xGrIlI/9mzEXZtgLv/EJLHnUu02zqgoBwKjvtfvV07CfInQpxm24qISISF2vrvHuBV51whUBjekEREztPe5g9AzroGRo31D/wByAOn/G52fSvMHAeLM2F0fITjFRERCQq1jOS/gUYz+xXwc+fc5jDGJCLitbf53tlVx+DWpyA+EabNA6CpDd4ogsJqSEuC22b4jiMiIiIDSajJdjrwIPBZ4F0zKwH+C3jOOXcgXMGJyDBWfRI2/hpqKmDO9V2Wimt8p5HmdrhhKlw1AaJ0AFJERAagUGu26/BdR35iZhnAY/jE+6/NbLtz7powxigiw4lzcGCb39GOS4AVT8CkGQC0B3zf7B3lMDbRH4BMS4pwvCIiIhcR6s72Oc65cjP7F3xnkm8AC/o8KhEZnpob4f2XoPSA7zZy/b2Q6LPpU43w2mGobIT56XBDJsTqAKSIiAxwl5Rsm9ky4HHggeCl3wBf7+ugRGQYOl4Im34DLU1w9a2Qe+255th7KuCtoxAXBffMgukpkQ1VREQkVKF2I/ku8CiQBqwDfhd4yTnXEsbYRGS4qCiF9T+HMeN92cjYCYAvG9lwFHZVwJRkfwgyKS6yoYqIiFyKUHe2FwHfAZ53zp0OYzwiMpx0tEN0DIyfDAvvhOlX+BZ/QF0LrD4EJ+ohPwMWZeoQpIiIDD6hHpC8vve7REQuQekB2LIaVn4RRqVAZhxUfxvaSyhtns+rJx+hPSqDO3J8/2wREZHBKOSabTOLAa4BMoEuv8h1zj3bx3GJyFCXkg6pk/3OdvMuOP0MzlLYUX0d75VPIjlmPQ/N/wzjUvIiHamIiMinFmrNdi7wCjANMKAj+LVtQAugZFtEeldeBEf3wMK7/Kj1pY/465WraGccb5QvZH91OtnJVaycuJP49kJAybaIiAxeoe5sfw/YDlwJnAj+ORr4Ab79n4jIhXW0w863YN9mGJ3qW/wlftIgu6HpJC8fW8mJxjFcl36Ea9OKMUZCe0kEgxYREbl8oSbbVwM3OucazCwAxDjndpjZXwL/D5gftghFZHCrqYT3fg2nT8Csq2HBLecOQQKcbICXj95Lc3sbd07dQ87oKr/QcQZiMiMUtIiISN8INdk2oDH4vBKYBBwAyoAZYYhLRAY75+BgARSsg9g4WPYYTJnV5ZaDp2BdISQmzOOR1O+QNiIK3GgInIFANYx5KkLBi4iI9I1Qk+09wBVAEbAV+Csz6wC+DBwOU2wiMlg1NfhJkGUHYWK2nwQ5YtS5ZedgyzF4vwwyRsJdMyeSFPgy1K3ypSMxmT7RTtAvzUREZHALNdn+NnC2wPIbwGrgbaAKeDgMcYnIYFVTCa//FNpauk2CBD92fUMxFJ+B2alw03SIiQKYr+RaRESGnFD7bK/r9LwImGNmY4Fq55wLV3AiMgiNGgsTZ0De9b69X1BzO3xQBh+dhNgoWJ4F89O75OEiIiJDTsh9ts+nSZIick71Sdj+Oix5EOITYfF955YCDvZUwOZSn3DPS4PrpsCI2Iu8n4iIyBDxqZNtEZFzAgGoPQX1NT7ZDjpWC28fhcpGmDQKlmZBWtIF30VERGTIUbItIp9OfQ2U7ofZC2FcBtzzRxAdDUB7wO9k7yiHkXFwRw7kjFXJiIiIDD9KtkXk0hXtgi2v+udT83ynkWCifbIe1hbC6SaYnwZLpkJcdARjFRERiSAl2yISupYm2LoGjuyG8VNg8f3nWvp1BHw7v23HfT32fbmQNSbC8YqIiESYkm0RCU35Edj8W2iqgyuXw9zFEBUFQFWjH05T0eDb+S3NggR9dxEREVGyLSK96GiHnW/CvvdhdCrc+hSkTgJ8p5GC4344TXwM3DnT12aLiIiIp2RbRC6s9jS88zzUVEDuNfCZmyHG9+w71QivF8GJepg5DpZlqZ2fiIjI+ZRsi8iFJSRBXAKseAImzQD8bvb2cr+bHRflO43MHBfhOEVERAaoqP78MDP7qpkVmFmLmf30vLUVZrbfzBrN7G0zm9ppLd7MfmxmtWZ2wsy+3p9xiwwr9TXw/su+fCQuHlY+eS7RPt0EL+yF90pg2hj43Hwl2iIiIhfTr8k2cBz4X8CPO180s1RgFfA3wFigAHih0y1PAznAVGAZ8Jdmdms/xCsy/JypgqN7/VRIONcce28l/NduqGmG22bAnTmQFBfBOEVERAaBfi0jcc6tAjCzfGByp6X7gb3OuV8F158Gqsws1zm3H/gd4EnnXDVQbWY/Ar4ArO3H8EWGrqYGOHkUsvJgXCPcUA9tfwOVmbSNuJ+3TsxnXyVMSYZbZ/hBNSIiItK7gVKznQd8dPaFc67BzAqBPDM7CUzsvB58fm9Pb2RmXwG+ApCZmRm2gEWGjNIDwbKRNkiph4Z/pbQ+gxc/vpYV2Sf5sHonp6PSuHbqBBZOhihNgRQREQlZf5eRXMhI4Mx5184Ao4JrnLd+dq0b59wPnXP5zrn88ePH93mgIkNGawtsfgne/m8/mObWL0HraxCVQllDGt8rmM1zhctpDIzhvokvcP0UJdoiIiKXaqDsbNcDyeddSwbqgmtnXzeftyYin8aJo35ATcMZmLcE5i/149bLS2hhKtuqsiFhAmPiingiZzcjo4oiHbGIiMigNFB2tvcCV5x9YWZJQDa+jrsaKO+8Hny+t18jFBkKOtqh4HV442dgUbDyi3DVCp9oAyXNV/B/P1zADz+cCa2neWVnI+U1jRCjkiwREZFPo79b/8WYWQIQDUSbWYKZxQC/Aeaa2QPB9W8Cu4KHIwGeBb5hZilmlgt8Gfhpf8YuMujVVMKr/w77NsPMfLjz9yBtCgAt7fBmEfys6GF+tH0q1lTKovQiGlujuOMXCznp7olw8CIiIoNTf5eRfAP4VqfXTwB/65x72sweAP4FeA7YAjza6b5vAT8AioEm4B+cc+pEInIp4hL8bnanATUAxTXwRhHUt8KNMzKYmVjMiknbSI0roqp1OhvKV5CedlUEAxcRERm8zDkX6RjCJj8/3xUUFEQ6DJHIqamEgwVw9a2+X7Zz5/pmN7f74TS7KyAlEW6ZDhN7PHYsIiIiF2Nm251z+T2tDZQDkiISDlVlcHQ35F4DyePADOfg4yp4twSa2yA/AxZOhtjoSAcrIiIy9CjZFhlq6qrhTCVMngnZV8LkWZAwAoCqRnjrCByrgwkj4f5cSEuKcLwiIiJDmJJtkaHCOTi0Hba/DrEJcN/XIDoGEkbQ2gFbymDHCYiLhpumwdy0cxUlIiIiEiZKtkWGgoZaPwXy+GHImA7X3+MTbT45AFnXCnnjYXEmjIiNcLwiIiLDhJJtkcHMOSj6CLathUAHXHuHb+tnRlsHvFcKH56AsYnw8ByYdP7oKBEREQkrJdsig1VjHWxZDaUHIH0qXHcPJI8F4GQDrD0Mp5vgygmweIoOQIqIiESCkm2RwejYYXjv19DeBvkrYfZCMCPgYPtx2FwGibH+AOTUMZEOVkREZPhSsi0yGI1IhpR0uPZOGJ0KwJlmWFfoO43kjIUV03zCLSIiIpGjZFtksCjeByePwjW3Q0oa3PIFAAIOdpTD+2UQZbAyG2anqtOIiIjIQKBkW2SwOFMJVcegrRVi4wBfm72+CCoaIDsFlmXBqPiIRikiIiKdKNkWGciK90FsPEzMhrzFMHcJREXR1uF3sneegIQYuCPHl45oN1tERGRgUbItMhA1NcC2NXB0L0yZ5ZPtaN9OpOSM380+0wLz0nzf7AT9SxYRERmQ9CNaZKA5uhe2vgqtLXDlcshbBEBzO7xbDHsrYUwCPDgHpqhvtoiIyICmZFtkoGiqh61rfOlIcgA+0wRJP8WdeotDHY/x9vFZNLfD1RNh4WSIiYp0wCIiItIbJdsikeac383etsbvZs/NgrQ3IWYs9R3Teat0MoVn9pE2Lon75k4mLSnSAYuIiEiolGyLRNq2tbB/C4yf7KdAtv0rrn0se87MYWN5Nu0uisUTdrEgfRdRSd+KdLQiIiJyCZRsi0SCcxAI+EOPU3IhKRlmXwdRUdQWV7L+xHKK68cxeWQNN086wJi4Bugoi3TUIiIicomUbIv0t44OeOd5GJMGC26GjGmQMQ3nYM9JePfIfbhAM8snHWT+2OO+nV/HGYjJjHTkIiIi8v+3d+fBbZ/3ncffX9wgCAI8QVKiRFKHacmW5MRx4jiurzh2rtatM9s0TY8dt5lJJtvpdLPd7Ux3J5N2t9Npt3v02N3OpDnqptt01226OZo0Tez4ji3HlixblnVStEiKFG8SJK5n//gRCEiRsiQTAgl+XjMcAj9QPz1fAiI/evD8vs8VUtgWudb8fmhohvpk6dDkgtfOr38Suhqv497EfyQRCQMJL2gXxiH5UPXGLCIiIldFYVvkWpga89r53XQPNHfCO+4HvK3WDw3DE/3el93TAze2dWELn4LpRyDX781oJx+CyL4qFiAiIiJXQ2FbpJIKBXj1GXjp+2A+mJ30wjYwPAP/fMrbcn17Au7phURxq/XIPoVrERGRGqCwLVIp4+fh6a/B6BveLpC3fBBiDczn4Kmz3ox2NAjv3wnXNWurdRERkVqksC2y1vJ5ePlxOPw4hCJw+0egey8O47VReOwMpLOwLwXv7tJW6yIiIrVMv+ZF1tLIADz9DzBxHnr3wc33Q6SOyXn47invAshUDB64DlL11R6siIiIVJrCtshayWXh+18BXwDu/hhs3U3BwYuD8ORZ8Bnc3Q03przbIiIiUvsUtkXequEz0LYNAkG462OQaIVQmNE5+KeTMDQDPUmv00g8/OanExERkdqhsC3yVgyfgW9/AW57AHYcgNat5Avw3AA8+waE/boAUkREZDNT2Ba5Us7B1AVItHgz2rc9AN03AF47v++chNE52N0Md3VDXbCqoxUREZEqUtgWuRLT4/Ds12HkLPzkpyHWADsOkM3DM2fg4CDUheDDu2FnU7UHKyIiItWmsC1yOQoFePVpeOlRb3Oam94LUa+dyMCUtzZ7Yh5uaIPbt6mdn4iIiHgUCUTezIVzXju/sSHo6oNbPgCxBhZy8MQZb3OaRBgevB62Jao9WBEREVlPFLZFVpPNeNusv/qMN4t9589CVx8O4/UL3uY0sxl4WwfcuhVC/moPWERERNYbhW2RlQyfgScegdlJRjpu5K9zu/np+u1E08ajp+HsFLTUwYd2QUe82oMVERGR9UphW2Ql4TqIxOCWvRwfOcx//modgeAxstHbCIXbtTmNiIiIXBZftQcgsm4cex6e+pp3O9kKd78T53uYk5P1EOvm+FQzN0T+il++7jD72xW0RURE5M0pbIsUzc/B3BTkcwCMjn6HPz7yU/ze8z8BhQxPHp1jW+QC0fn/W+WBioiIyEahsC2bV2YBfvgt6D/q3b/hPXDPx8kS4Mmz8OeH+/ivz12Pmx/i3S2vMJ/J8sGv3MrwxPnqjltEREQ2DK3Zls3HOeh/FZ77FqRnIByFbX3g89E/Cf98yuuZ/bb2WX73nd/ifbvStNTlGJ0L8NiJAKlkW7UrEBERkQ1CYVs2l+lx+OE34Y3Xoakd7vwotGxhLguP98MrI5CMLPbMDu+BsW+CrxFcgpbwCA/2jUP8M9WuQkRERDYIhW3ZHPI5OPIUHP4B+HzwjvvhulvI4+PFQXhmAHIFeEcnvHMLBP0A+6DpMzD9COT6IbANkg9BZF+1qxEREZENQmFbat/gSXj2GzB1Abr3wtvvw9U1cGrC25hmYh66k3DHdmiKLvuzkX0K1yIiIlXmnAPAzMhms8zPz5PP58nn8zQ3N1d5dJemsC21rVDwgrZzcM/HYctOLszBY6/BmQlojMID10FPY7UHKiIisnkUCoVSWM7lcks+F2+3tLQQjUaZmppiYGCA3t5eIpEI09PTnDt3rnSupqYmzNZvP16Fbak9hQK8fhB690MwBHd/DGIJ5l2AZ8/Ai0MQ9MFPbIcDKfCrJ4+IiMhVc85dFJzz+TyRSIRoNEomk2FwcJCWlhZisRjT09OcOXNm1fP5/X4CgQD5fB6AcDhMU1MTPp/3Czsej9Pb21v6uvVu/Y9Q5EqNDXqz2T4/7HobLt7Mq6PeBZDpLNzQBu/ugrpgtQcqIiKyvjjnSrPOZkYwGKRQKDA2NkY0GiUWi5HNZhWfHlAAAB1sSURBVBkYGFgSrIvLPMqlUimi0ShmRi6Xo1AoAF54TqVS+P3+UmAu/7x8ljocDtPe3l66HwwGCQY3zi9xhW2pDekZOHcCduyHli3wwU9AUwfnZ+F7p2BwBtrrvSUjqfpqD1ZEROTamp+fx8wIh8M45xgZGVl1CUcxFDc1NdHZ2YmZMTw8XJqZNjPMjEgksiQkr3QbvHC8Y8eO0lhCoRCtra1V+T5Ug8K2bGyFArz2Q3jx++AK0LkTojHmE508eRoOD0MkCPf2wt5WWMdLukRERC7JOVea9Z2bmyOXy120zrn8cyQSYdu2bQD09/dTV1fH1q1bMTMuXLgAUArHoVDoosAciUQA76LEvr6+0jKOQCBAd3f3tf8GbFAK27JxDZ32NqYZH/ZC9i3vpxCJcXgInhqAhRzsb4dbt0JEr3QREVlHypdrrBSYi+uVOzs7AS8s53I5ent7ATh37hzz8/Ol8/l8vlJQDgQChMPhUlgunqd8fXNfX98VXVTo9/vfUr2bmSKIbDyzk3DwO3D6CNQn4c6fha4++qeMRw/BhTR0NXit/Fpj1R6siIhsBqt11yh2yhgbG2N2dpauri4Azp49y9TU1IrnMrPSbHNRPB4vLe8A2LJlC/DjiwmLs86rqa9fuoZyPXfvqDUK27Jx5HPwytPexjTOwf47Ye9tTOaC/OB1OD4GDWH40G7Y2aglIyIicnWK3TVyuRyhUAifz0c6nWZmZobm5mZ8Ph9jY2OMj4+XAnZxJnq5RCJBIBCgUCiQy+WWHK+rq1vxIkGfz3dRGG5sXNqjNhpdvjGErFcK27JxvPQovPwEbLsebr6PhUiS587BC0NgwG1d8LYOCKiVn4iILJPP51lYWCAcDuP3+0mn00xNTa14gWB5d40dO3YQjUZJp9MMDw+TSCQIhUKYWWm5xkodNcpvA7S0tNDS0lIaTyKRqMr3Qa49hW1Z3yZHvYsgG9vg+luhvYdCxw4OD8PTr3mt/Ppa4D1dEA9Xe7AiIlJpxYsE8/k86XR61TXPxc8dHR00NDSQTqc5ffo0PT09xGIxFhYWGB0dveiCwOWBudhiLplMkkwmS8s1GhsbL5ptFlmJwrasX/k8/NOXITYPN2dw2X5OpW/iBwd/hvHcFrbE4Q618hMR2bBW2gxleXCOx+MkEgkymQzHjx+no6ODxsZGFhYWOH369JLzlQflYneN4kWBkUiE7du3Ew57MzOJRIJEInHZa5ffbE20yGoUtmV9KRTgzBHYtgf8fnjnXsh9keGZnTw+/CHOzkRJBr/Hh3ffwo7267QuW0RknVitu0YgEKC+vh7nHGfPniUej9PY2Eg2m+XYsWMrboYCXrgNBAKltcl+v5/GxsZSWA6Hw/T09FxyM5RygUCAeDxeuq8LBOVaUdiW9WPoNDz/jzA2BLcb9NxAOvA8T56/i5cndxHx57hry2luTBzBHzgB9tlqj1hEpGYVg7NzrtQVY2JiAp/PR0NDAwBnzpwhm82WAvZKwTmRSFBfX3/RLoJ+v5/W1tZVN0NZPpPs9/vp6OhYcj8WU8spWf8UtqX6psbghX+C/lchloDbP0Jh+14ODcFTr15HliZuah7gnakzRPw5cA2Q66/2qEVENpxMJkM+ny/NFo+NjZHJZFa9SBC8rhfF3f8uXLhAIBAohW0zW7Jc41K7CAKlHtHgzVy3tbVdq9JFqkZhW6onMw+HfgBHn/WWjBy4G/bcytm5II++DKNzsC3m587Ud2mO/bjXKIVJCGyr3rhFRKqofBfBhYWFUoBeHpiLnwF27doFwPDwMPPz86X7k5OTpNPpJZ00lnfXKF4gCNDd3b1kxrm4O6GIrE5hW669QgGOv+Btsb4wBzsOwIG7Gbc4T52CYxfK+mVHd2Djfwf5RvAlvKBdGIfkQ9WuQkRkTbzZLoK5XI7Ozk78fj/nz5/nwoULpd3/RkZGmJiYKJ2r2I6uGJaDwSCBQKAU0Jubm5cs9eju7tYugiIVprAt197AMXjm65DaDjffz3R9B8++AUdGwG/e9upv74CgH2Af2Gdg+hFv6Uhgmxe0I/uqXYWIyEXKN0NZ3lEjGAwyMzPDhQsX2LJlC4FAgJGREYaHh1c9XzE0FwoF/H4/0WiUpqam0uMtLS00NTVdcjOUcnV1dUvu6yJBkcpT2JZrY2wIpi5A917oug7e+wvMt/by3DnjRye8DSH3peCWTihfMQJ4wVrhWkSusfLuGsXOGNlslsnJSRoaGgiFQszMzHD+/PkVN0Mp193dTTAYxDm35CLBuro6UqnUqmuel4fheDy+pKNGJBKp7DdBRN4yhW25Nl56FCaGYdv1ZJyPF90Onn8RMnlvU5pbt0JCvzNEpMIKhQILCwulJRbZbLa05fZKa56Lwbmzs5OmpiZyuRxDQ0OEQqHSLoI+n49gMHhZuwguD8uxWEwdNURqnMK2VEZmHo48BTv2Q0Mz3PIBCv4gR0Z8PP0GzGagtxHevRVa9XtGRK5QcQ2yc465ubk33UUwmUzS1tZGoVDgxIkTdHR00NzcTD6f5/z586tuhlIMzMXlF+FwmOuvv750kaDCsoi8GYVtWVv5PBx7Hg4/BvNzEInh4s0cX2jgiX6YmIeOevjgTtjSUO3Bish6sNJmKMuDczgcpqWlBYBjx44Rj8fp6OjAOcepU6eWnK+45KO8u0ZxIxS/309XV1ep9V04HGbv3r3aRVBEKkZhW9aGc3D6CLz4zzA9Du098PZ7ORvs5IkjMDQDTVH4yeugN4l2fhSpYSt11wBvcxOAoaEhzIxUKgV44Tmbza54rmJ3jfIwnEgkSmuVfT4f3d3dS2aiLxWIzaw0juJ9EZFKUtiWt27wJLzwXbhwDhpTcM/HOZ/YwZMDxukJqA/Bvb2wpxV8+r0msqEUu2vk8/nS7PDMzAyZTKbUFWNoaIjZ2dlSwC5e/FcuFAqVQm4+n18ScpubmwFWXPO8UneNYkgvqq+vX7uCRUTWmMK2XL2pC/DsN7ywHUvAbQ8w2bGPp875eO0shPzwnm1wIFVs4yci60EulyOTyZTWIU9PTzM3N7fqLoLF9dF79uzBzJicnGR6enpJC7rico3L2UVwy5YtS8ZTXB4iIlKLFLblyhUK4POBPwCTo/CO+5nruZlnBgMcPuzNXt/c6X1E9AoTqbhsNsvCwsIl1zzn83l6enoIhUKMj48zPDzMnj178Pl8zMzMMDY2dtFmKMtnmova29vp6OhYcl9ERFamKCRX5vnvwMR5eO/HIZYg/eFf5+CwjxcPQd7B3lZ411Zv6YiIXL7VNkMpv93S0kIkEmFqaoqBgQF6e3tL9wcHB0vnMrPSjHJ5d43icoyGhoYl/ZlTqRTt7e2XvX5ZuwiKiFw+hW15c3PTwAnOnvsmjx8c4t6Oaeonb+Tg5H5eHPKRK8CuZq9XdlO02oMVqb5id43lYTkajRKJRMhkMgwNDdHS0kJdXR3T09P09/evuBkK/Li7Ri6XA7z1z01NTaULAePxOJFI5JKboZQr785RPL+IiFSGwrasLj0DLz8Br3wddp9mIHAzv3Xq/cz0jpB5/hi5cIpdqXbetQWa6978dCIbVbG7BkAwGKRQKDA+Pk40GqWuro5MJsO5c+dW3AylXHt7e2lGOZPJlM4ZCoVobW1ddTOU5WE4EoksWbpR3GBFRETWH4Vtudj8HLzyFBx9Fgp5aBtlrqmHQwN7IdbD0ZkE92w9yrvav0xz129We7QiV2VhYQEzIxQK4ZxjdHR01U1Rit01mpqa6OzsxMwYHBykra2Nuro6fD4fhUJhxc1Qytc8F9c9h0Ihdu7cWRpLOBymra2tKt8HERGpLIVt+bH0LLz6NLz2Q8hlofsG5vbcycH+L/C94zfzt0faID/Lk6+M8cm+YZoDr1d7xCIl6XSaXC53yV0EI5EIXV1dAJw+fZr6+vpSZ4yRkRGAizZDKQ/OxVlpM6Ovr6+0djkQCNDb21uFqkVEZL1T2BYvZL/yFBx7zgvZ2/cyt+cODs628uIJmBy7hS8fjFLnznBb2wRHztfxwYf38vivFEi9+dlFLtub7SJoZqUuGP39/RQKBbq7uwEYGBhgYWGhdK7iZijl3TWKuwYCdHZ2lmaai+H5StYul3fnEBERWY1+WwicO+6F7Z4bmd59Oy+kWzl0EvIF2N0M79zVTF/wb7izJ01LfZTRmTSPnYqS6vhItUcu69jy7hrFz42NjZgZY2NjzM3NsXXrVsALz1NTUyueq9hdo3xdcn19/ZJ10cUZ6ktthlIuHo8vua+LBEVEpBIUtjejQgGe+xY0NMP174KeG7kQ28pzM828dsr7kt3NcEtn8cLHvXzkto/A9COQ66clvo0Hb/sZiOyrZhVyDZV31wgGg/h8PtLpNLOzs6WuGGNjY0xMTCxZ57zSRYKJRAK/308+nyeTyZSONzQ0EI1GV9xFcKXuGuUbqgClDVpERETWE4XtzSQ9A9F6b0Oa2UlcIMzAFDx/zsfpiWYCPtifgps6IBFe9mcj+xSua0wx7BYv6kun00xPT1+0dKN4vxicd+zYQTQaJZ1OMzQ0RCKRKM0K+3w+gsHgJXcRLH5ta2srra2tpfEkk8lr/00QERGpMIXtzWD0Da+F38Ax+Olfo1CX4PUbf44Xho2hVyAa8Hpk709BNFjtwcrVyufzzM/Pv+kugh0dHcTjcebm5jhz5gy9vb3U1dUxPz/PyMjIRZuhRKPRJYE5GPReJMlkcknQbmpqumi2WUREZLNT2K5Vznnh+pWnYPgMhCJkrn8PR0ZDvDAGUwtGMgJ3d8OeVghqQ7h1YbXNUMo/x+NxGhoayGQynDhxgo6ODpLJJPPz85w6dWrJ+cqDc7G7RrGDRjQaZdu2baV10IlEgmQyedm7CGqNs4iIyJtT2K41+RyceMlr4Tc5CrEEs/vv40ext3FoPMzCIHTG4Y7t0NsIvsvLVXKVVuquEQwGicViOOcYGBggHo+TTCbJZrMcO3Zs1V0Ei901iu3n/H4/yWSyFJYjkQjd3d1LZqEvFYgDgQANDQ2l+wrPIiIia09hu5a8/AS88jTMz+KaOhg68CDPh/ZwctKPS3tbqr+9A9rrqz3QjanYXaO4eQnAxMQEfr+/1Nmiv7+fbDZ70WYo5ZLJJLFYDDNbsoug3++npaXlkrsIls86+/3+Uhu84v36ej25IiIi64nC9kY3MQLJxYvMJs6TaezkWOrdPJfvZmLOiGa8gH1jaoWLHqUUjIuzxePj4ywsLKy6hAO8rhfFDUxGR0cJhUKlsO2cW3EzlJV2EQTvYsMin89HKqXO5SIiIrVEYXujmT9UasHHQAgOG+6BzzIcSnG4/QGOjvnIzUFHPbxrqzebHdhEqwMWFhbIZrOXXPMMlLbKHhwcJJPJlO6Pj4+TTqcv2gylPDiX93ru7u5esvxi+/bt17BaERERWe8UtjeSkcfhxc9BUwq6eplvmaA/Ncdzr89w3qUI+Hz0tcC+FKRi1R7s1VttM5Ty252dnfh8Ps6fP8/Y2Bh9fX2At+X2xMRE6VzFzVDKg3L5zHJLS8uSpR7d3d2Y2WVfJKhdBEVERORSlBTWu3wO+l+F11+Ak1/AuXlGu3dy0Pbw+mQruXCGtvwr3LNjB9c1Q3idPaPLu2uUd9QIBALMzMwwNjZW2jp7ZGSE4eHhVc9XDM35fB6fz0ckEiGZTOKcw8xoaWmhsbHxkpuhlFu+EYouEhQREZG1tM6imQBe276xITj5Epx8CbeQZjLYyMnWG3kpfhcT/iZCUzn2NA5zQ+MAqdBRSH34mgytGJyLQTabzTI1NUU8HicUCjEzM8PIyMiSYL1Sd42enh4CgQCFQoFMJlOaXa6rq6Otre2SFwmWa2hoWNJRo7j2WkRERGQ9UNheb04dhkOPUZgYZTrn52yij8Mdb2Oovhf//PfpjvVza+MQvfELhPx5yI+Df9tV/3XOORYWFkoX7mWzWSYmJlZd81wMxVu2bKGxsZFsNsvg4CChUKi0ltk5RygUoq6ubtVdBIvLL5aH5VgsRiy2gdfAiIiIiJRR2K62hTScOozbtocx6hkZKZCeiPF64laGmvdAOEp3At7fDD3RVsKTXwRfI/gSkJ+EwjgkHyqdrlAoMD8/v2JYLr+dTCZpbW0ln89z/PhxOjo6aG5uJp/PMzw8jM/nW3KR4PLuGsXlF5FIhL6+vtJGKfX19Wo/JyIiIrJow4RtM2sCPg+8DxgFfss595XqjuoqOAdjgzjzMxFNMXRuluC3v8mh3iBnWm8C9pPcv5+t8QJ7Yzm21qfx44XkmflOJgufJDf5JGHfGzQ3NULyIY71R0gkhkmlUjjnOHny5JK/srgZSnl3jeIstN/vp6uri2g0CkA4HGbPnj2XvXbZ5/NpnbOIiIjIKjZM2Ab+FMgAKeAA8A0ze8k5d6S6w1oqnYV0ruyAczA9hhs+TW7wNOkzrzMzMc2Zxhs4duPPAS0Edv0yzW2NvLcLtiVguP8YmXQGl4azo0vPb9aA3/8h4vVxaN0CQEPDUGmtss/nY/v27ZfcDGXp+YxEIrHk/uV24hARERGRS9sQYdvMYsCDwA3OuRngCTP7B+AXgH9X1cEt89Iw/PDZV4iNnSI+NUB8+g2C2TQAOX+IsUQ3s6mbCXf18N4e2NIAs6MB/P5ZOlNe6M00NgKseIHgSt012tvbS7fNrLTBioiIiIhU14YI28BuIO+cO1Z27CXgjiqNZ1U7m6Bp6rsEJk6Ti7eS7dpJrmkLuaYu/I0pbkr4SdR5wTkY9P5MU9fWJedobW2twshFREREZK1tlLBdD0wuOzYJXDSFa2afAD4BsG3b1XfpuFotddDy4M9DJAYhtaETERER2cw2ypVtM0DDsmMNwPTyL3TO/blz7mbn3M1VmyFuaFbQFhEREZENE7aPAQEz21V2bD+wri6OFBEREREptyHCtnNuFngE+JyZxczsNuCngL+s7shERERERFa3IcL2ok8BUeA88NfAJ9db2z8RERERkXIb5QJJnHNjwAPVHoeIiIiIyOXaSDPbIiIiIiIbisK2iIiIiEiFKGyLiIiIiFSIwraIiIiISIUobIuIiIiIVIjCtoiIiIhIhShsi4iIiIhUiMK2iIiIiEiFKGyLiIiIiFSIwraIiIiISIUobIuIiIiIVIjCtoiIiIhIhShsi4iIiIhUiMK2iIiIiEiFKGyLiIiIiFSIwraIiIiISIWYc67aY6gYMxsBzlThr24BRqvw914LtVzbpWzGulXz5qCaN4fNWDNszrpVc3Vsd861rvRATYftajGz551zN1d7HJVQy7VdymasWzVvDqp5c9iMNcPmrFs1rz9aRiIiIiIiUiEK2yIiIiIiFaKwXRl/Xu0BVFAt13Ypm7Fu1bw5qObNYTPWDJuzbtW8zmjNtoiIiIhIhWhmW0RERESkQhS2RUREREQqRGF7DZnZp83seTNbMLMvVns8b8WlajGze8zsqJnNmdn3zWx7lYa5pswsbGafN7MzZjZtZj8ys/eXPV6rdT9sZoNmNmVmx8zsV8oeq8mai8xsl5nNm9nDZcc+tvgamDWzvzezpmqOca2Y2aOLtc4sfrxW9lhN1lxkZh81s1cX6zthZrcvHq+513fZ81v8yJvZH5c9XnM1A5hZt5l908zGzWzIzP7EzAKLjx0ws4OLNR80swPVHu9aMLPrzex7ZjZpZsfN7KfLHquJ5/lqs8ji7/O/WPy9NmRmv3HNB19GYXttnQN+F/iLag9kDaxYi5m1AI8A/x5oAp4H/uaaj64yAsBZ4A4ggVfjVxd/iNdy3b8HdDvnGoCfBH7XzN5e4zUX/SnwXPGOme0F/hfwC0AKmAP+rDpDq4hPO+fqFz+ug9qv2czuBX4f+JdAHPgJ4GStvr7Lnt96vOczDfwt1PzP7z8DzgMdwAG8n+OfMrMQ8DXgYaAR+BLwtcXjG9bifyS+Bnwd77n8BPCwme2usef5arPIZ4FdwHbgLuA3zez+azDelTnn9LHGH3gvjC9WexyVqAXvH/RTZfdjeD/M+6o91grVfwh4cLPUDVwHDAL/otZrBj4KfBXvh/LDi8f+E/CVsq/ZAWSAeLXHuwb1Pgr8ygrHa7bmxXqeAh5a4XhNv74Xa/ol4CQ/boZQszUDrwIfKLv/B3j/iXwf8Ebxe7D4WD9wf7XH/BbrvQGYWVbXd4DfqcXn+UqzyOJz/r6yx38H+N/VGr9mtuVK7QVeKt5xzs0CJxaP1xQzSwG7gSPUeN1m9mdmNgccxQvb36SGazazBuBzwL9e9tDymk/gBc/d1250FfV7ZjZqZk+a2Z2Lx2q2ZjPzAzcDrYtvsw8sLi+IUsOv7zK/BHzZLaYNarvm/wZ81MzqzGwL8H7gH/FqO1T2PQBvEmWj12yrHLuB2n6ei1at0cwagc7yxxdvV61+hW25UvXA5LJjk3hvz9YMMwsCfwV8yTl3lBqv2zn3Kbxabsd7a26B2q75d4DPO+fOLjteyzX/W6AX2ILXk/b/mdkOarvmFBAEPoL32j4A3AT8NrVdN2a2DW8pxZfKDtdyzY/hhakpYABvWcHfU7s1H8VbNvNvzCxoZu/De77rqN2ay12qxvqy+8sfqwqFbblSM0DDsmMNwHQVxlIRZuYD/hJvdu/Ti4drvm7nXN459wSwFfgkNVrz4sVR7wX+ywoP12TNAM65Z51z0865Befcl4AngQ9QwzXjva0M8MfOuUHn3CjwR9R+3QC/CDzhnDtVdqwma178mf1tvImCGNCCtz7796nRmp1zWeAB4IPAEN67dF/F+49GTda8zKVqnCm7v/yxqlDYlit1BNhfvGNmMbw1nkeqNqI1ZGYGfB5vRuzBxR9oUON1LxPgx7XVYs13At1Av5kNAZ8BHjSzF7i45l4gDBy79sOsOIf3tnPN1uycG8cLHyvt3larr++iX2TprDbUbs1NQBfwJ4v/mbwAfAHvP1VHgH2LP9uL9rHxa8Y5d8g5d4dzrtk5dx/eO1c/pHaf53Kr1rj4736w/PHF21WrX2F7DZlZwMwigB/wm1mk2Hpoo7lELX8H3GBmDy4+/h/w1sMdreZ419D/AK4HPuycS5cdr8m6zaxtsS1avZn5zew+4OeA71GjNeMtodiBt6TgAPA/gW8A9+EtHfqwmd2++MP7c8AjzrkNPSNkZkkzu6/479jMfh6vK8e3qdGay3wB+FeLr/VG4NfxOjjU6usbM3s33nKhv132UE3WvPiOxSngk4uv7yTeevWX8C4MzgO/ttgOrvhu5feqMtg1ZGb7Fv9N15nZZ/A6sXyRGnqe30IW+TLw22bWaGZ9wK/ifW+qo9pXmNbSB15XA7fs47PVHtda14L3FvxRvLdoH8VrG1f1Ma9BzdsX65zHexuq+PHztVo30Iq31nECb63jYeBXyx6vuZpX+B58lsVuJIv3P4bXrWAWr7VWU7XHuEbP83N4b6NOAM8A99ZyzWW1BfHawk3gvd3+34HI4mM1+frG68Lxl6s8Vqs1H1isZxwYxfuPRtviYzcBBxdrfgG4qdrjXaOa/2Cx3hngW8DOWnuerzaL4L079xeLv9eGgd+oZh3FdkAiIiIiIrLGtIxERERERKRCFLZFRERERCpEYVtEREREpEIUtkVEREREKkRhW0RERESkQhS2RUREREQqRGFbRERERKRCFLZFRERERCpEYVtEREREpEIUtkVEBDPbambOzH7KzP7RzGbN7ISZ3VXtsYmIbGQK2yIiAnBg8fNvAH8I7AdeBv6oaiMSEakBCtsiIgJeuJ4CftY5913n3HHg/wCt1R2WiMjGprAtIiLgzWx/wzk3VHZsJ3C8SuMREakJCtsiIgLezPbTy47dBLxYhbGIiNQMhW0RkU3OzGLADuBHyx5S2BYReYsUtkVEZN/i51KwNrNmYCsK2yIib4nCtoiI7Aded87NlB27CcgCr1RnSCIitcGcc9Ueg4iIiIhITdLMtoiIiIhIhShsi4iIiIhUiMK2iIiIiEiFKGyLiIiIiFSIwraIiIiISIUobIuIiIiIVIjCtoiIiIhIhShsi4iIiIhUiMK2iIiIiEiF/H9Z7wkYCngWowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "coupon_label = r\"$f\\,(n) = \\sum_{i=1}^{\\frac{n(n-1)}{2}} {(-1)^{i+1} \\frac{\\binom {\\frac{n(n-1)}{2}} {i}} {1-{\\binom {\\frac{n(n-1)}{2}-i} {n-1}} / {\\binom {\\frac{n(n-1)}{2}} {n-1}}}}$\"\n",
    "dicoupon_label = r\"$f\\,(n) = \\sum_{i=1}^{n(n-1)} {(-1)^{i+1} \\frac{\\binom {n(n-1)} {i}} {1-{\\binom {n(n-1)-i} {n-1}} / {\\binom {n(n-1)} {n-1}}}}$\"\n",
    "\n",
    "plt.figure(figsize=(12, 9))\n",
    "\n",
    "plt.plot(range(1, 101), [i/2 for i in range(1, 101)], color='darkgray', alpha=0.5, linestyle='-.', label=r\"$f\\,(n) = n/2$ (ours, undirected)\")\n",
    "plt.plot(range(1, 101), cover_result, color='dodgerblue', alpha=0.5, label=\"$\\pi$-SGD, undirected\")\n",
    "plt.plot(range(1, 101), [i * np.log(i) for i in range(1, 101)], color='orangered', alpha=0.5, linestyle='-.', label=r\"$f\\,(n) = n\\,\\ln n$\")\n",
    "\n",
    "# plt.scatter(range(10, 101, 10), [i/2 for i in range(10, 101, 10)], color='gray', marker='2')\n",
    "plt.scatter(range(10, 101, 10), cover_result[9:100:10], marker='2')\n",
    "plt.scatter(range(5, 101, 5), coupon_result[4:100:5], color='gold', alpha=0.5, label=coupon_label, marker='o', zorder=0)\n",
    "# plt.scatter(range(10, 101, 10), [i * np.log(i) for i in range(10, 101, 10)], marker='2')\n",
    "\n",
    "plt.xlabel(\"$n$\", fontsize=14)\n",
    "plt.ylabel(\"average times over 10,000 runs\", fontsize=14)\n",
    "plt.xticks([1,10,20,30,40,50,60,70,80,90,100], ['1','10','20','30','40','50','60','70','80','90','100'], fontsize=12)\n",
    "plt.yticks(fontsize=12)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}