02 - Exploring Differential Privacy with Laplace.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import e\n",
    "import scipy\n",
    "from cycler import cycler\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "np.random.seed(42)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we're going to explore a few different concepts:\n",
    "\n",
    "1. Differential Privacy using the Laplace Mechanism: a way to sample \"intelligent\" noise (e.g. error) and insert it into the results to reduce privacy loss.\n",
    "\n",
    "2. Composition: or the ability to combine differentially private responses to reason about privacy loss (or information gain, depending on how you look at it!).\n",
    "\n",
    "3. How we can calculate a privacy budget using the above concepts! A privacy budget (or privacy accountant) allows us to limit the amount of privacy loss for an individual over the course of several queries.\n",
    "\n",
    "To do so, we will first create an artificial dataset of ages and salaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mid_level_age = 45\n",
    "mid_level_salary = 50000\n",
    "\n",
    "age_scale = 10 #scale represents one standard deviation\n",
    "salary_scale = 10000\n",
    "\n",
    "salaries = [round(np.random.normal(mid_level_salary,salary_scale)) for _ in range(100)]\n",
    "ages = [round(np.random.normal(mid_level_age,age_scale)) for _ in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ages, bins=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nKC8vz9mXkpLi9mkAAECccT20bNmyRUOGDNHcuXO1Y8cO9ezZU9dee62uueaaZscHAgEFAgFn2+PxKDEx0fkarde0jqxn7KAnkdGa9WyLPbHxtpxYc1vsie2i3RPXQ0t1dbXWrVunMWPGKDs7W3v37tWiRYvk9Xo1YsSIk8YXFxerqKjI2e7bt6/y8/OVnJzsdmlxz+/3R7sE/EAs96Q82gWcgWDu/7bq+228zaeTmpoakXkjuU7N1RzLjxNJKh9zSUTmPfeNLRGZ1w3R6onroSUUCql///6aNGmSpO9DSFlZmdatW9dsaMnOzlZWVpaz3ZTeampqFAwG3S4vLnk8Hvn9flVVVckYE+1yIHqCs6OysjLaJbTYiTXH++MkFvt3up54vd6IX3BwPbT06NFD6enpYfvS09P1r3/9q9nxPp9PPp+v2WPxeCeNJGMMaxpj6Akiycb7VnM1x+vjJJZvc7R64vr7tJx//vmqqKgI21dRUcHTPQAAoFVcDy1jxozR7t27tWLFClVVVWnDhg1av369Ro0a5fapAABAHHH96aEBAwZoxowZWrp0qf7+978rJSVFt956q6688kq3TwUAAOJIRN4R9+KLL9bFF18ciakBAECc4rOHAACAFQgtAADACoQWAABgBUILAACwAqEFAABYgdACAACsQGgBAABWILQAAAArEFoAAIAVCC0AAMAKhBYAAGAFQgsAALACoQUAAFiB0AIAAKxAaAEAAFYgtAAAACsQWgAAgBUILQAAwAqEFgAAYAVvtAsAWur4tOujXUKLtXtxdUTmtXEtgNP54X263KV5I/UYxNnFlRYAAGAFQgsAALACoQUAAFiB0AIAAKxAaAEAAFYgtAAAACsQWgAAgBUILQAAwAqEFgAAYAVCCwAAsAKhBQAAWIHQAgAArEBoAQAAViC0AAAAKxBaAACAFQgtAADACoQWAABgBUILAACwAqEFAABYgdACAACsEPHQsnLlSk2YMEGLFy+O9KkAAEAbFtHQsmfPHq1bt059+vSJ5GkAAEAciFhoOXr0qJ566indfvvt6ty5c6ROAwAA4oQ3UhMvWLBAQ4cO1QUXXKAVK1acclwgEFAgEHC2PR6PEhMTna/Rek3ryHpGzw/Xnp7gbOD+9R82rkUs1hztn10RCS0bN27Uvn379Oijj/7XscXFxSoqKnK2+/btq/z8fCUnJ0eitLjm9/ujXYIryqNdwBlITU1tdn9re2LjWuDsCeb+b7RLiBmnegy6IVKPw0jW3FrR+n3iemg5cOCAFi9erPvuu0/t27f/r+Ozs7OVlZXlbDelt5qaGgWDQbfLi0sej0d+v19VVVUyxkS7nLhUWVkZtk1PgLPrh49BG8Rizaf72eX1eiN+wcH10FJSUqL6+nrNnDnT2RcKhbRz5069+eabWrp0qRIS/vNSGp/PJ5/P1+xc/DB3lzGGNY2SU607PQHODhsfZ7Fcc7R+drkeWgYPHqwnnngibN+zzz6rtLQ0jR07NiywAAAA/Fiuh5bExET17t07bF+HDh3UtWvXk/YDAAD8WFz2AAAAVojYnzyf6KGHHjobpwEAAG0YV1oAAIAVCC0AAMAKhBYAAGAFQgsAALACoQUAAFiB0AIAAKxAaAEAAFYgtAAAACsQWgAAgBUILQAAwAqEFgAAYAVCCwAAsAKhBQAAWIHQAgAArEBoAQAAViC0AAAAKxBaAACAFQgtAADACt5oFwDEg+PTrj9pX3kU6gAAm3GlBQAAWIHQAgAArEBoAQAAViC0AAAAKxBaAACAFQgtAADACoQWAABgBUILAACwAqEFAABYgdACAACsQGgBAABWILQAAAArEFoAAIAVCC0AAMAKhBYAAGAFQgsAALACoQUAAFiB0AIAAKxAaAEAAFYgtAAAACt43Z6wuLhYmzdv1v79+9W+fXtlZmbq5ptvVlpamtunAgAAccT10LJjxw6NGjVK/fv31/Hjx/Xqq6/qkUce0dy5c9WxY0e3TwcAAOKE66Hl3nvvDduePn26cnNzVVJSop/97Gdunw4AAMQJ10PLDx0+fFiS1KVLl2aPBwIBBQIBZ9vj8SgxMdH5Gq3XtI6sJ4B4ZePPv1isOdq/TyIaWkKhkBYvXqzzzz9fvXv3bnZMcXGxioqKnO2+ffsqPz9fycnJkSzNKuVjLmn9HC7U0RLnvrElYnOf7dsCwH6pqakRmztSP5MiWXNr+f3+qJw3oqFl4cKFKi8v18MPP3zKMdnZ2crKynK2m9JbTU2NgsFgJMtDBFVWVka7BABw2PgzKRZr9ng88vv9qqqqkjEm7JjX6434BYeIhZaFCxfq448/1uzZs3XOOeeccpzP55PP52v22A8XBPagdwBiiY0/k2K5ZmNMVOpz/X1ajDFauHChNm/erAceeEApKSlunwIAAMQh10PLwoUL9f777+uuu+5SYmKi6urqVFdXp2PHjrl9KgAAEEdcf3ro7bffliQ99NBDYfvz8vI0YsQIt08HAADihOuhpbCw0O0pAQAA+OwhAABgB0ILAACwAqEFAABYgdACAACsQGgBAABWILQAAAArEFoAAIAVCC0AAMAKhBYAAGAFQgsAALACoQUAAFiB0AIAAKxAaAEAAFYgtAAAACsQWgAAgBUILQAAwAqEFgAAYAVCCwAAsILHGGOiXURzampqFAgEXJ/3+LTrXZ9Tktq9uDoi80qRqxkAEJ/O9HeWx+NRamqqKisr9cP44PP5lJyc7EZ5p8SVFgAAYAVCCwAAsAKhBQAAWIHQAgAArEBoAQAAViC0AAAAKxBaAACAFQgtAADACoQWAABgBUILAACwAqEFAABYgdACAACsQGgBAABWILQAAAArEFoAAIAVCC0AAMAKhBYAAGAFQgsAALACoQUAAFiB0AIAAKzgjdTEb775pl577TXV1dWpT58+mjJligYMGBCp0wEAgDYuIldaPvjgAxUUFGjcuHHKz89Xnz59NGfOHNXX10fidAAAIA5EJLS8/vrruvrqqzVy5Eilp6dr2rRpat++vd59991InA4AAMQB158eCgaDKikp0Q033ODsS0hI0ODBg7Vr166TxgcCAQUCAWfb4/EoMTFRXm9knrlK6H9+ROZt5/NFZF4pcjUDAOLTmf7O8ng8kiSfzydjTNixSP3eDjuH2xMePHhQoVBISUlJYfuTkpJUUVFx0vji4mIVFRU528OGDdNdd92lHj16uF3a9/76SmTmjSQbawYAtFm9evWKynmj/tdD2dnZWrx4sfNv2rRpYVde0HpHjhzRzJkzdeTIkWiXgv9HT2IPPYk99CT2RLsnrl9p6datmxISElRXVxe2v66u7qSrL9L3l5h8EXxqBZIxRvv27TvpUh6ih57EHnoSe+hJ7Il2T1y/0uL1etWvXz9t377d2RcKhbR9+3ZlZma6fToAABAnIvKqmaysLM2fP1/9+vXTgAEDtGbNGjU2NmrEiBGROB0AAIgDEQktl19+uQ4ePKjCwkLV1dUpIyNDs2bNavbpIUSez+fTuHHjeBouhtCT2ENPYg89iT3R7onH8GQhAACwQNT/eggAAODHILQAAAArEFoAAIAVCC0AAMAKkf+gAJyRt99+W2+//bZqamokSenp6Ro3bpyGDh0qSTp27JgKCgr0wQcfKBAIaMiQIcrNzQ37C60DBw7oxRdf1Oeff66OHTtq+PDhmjRpktq1a+eM+fzzz1VQUKDy8nKdc845uvHGG0/60/Q333xTr732murq6tSnTx9NmTJFAwYMiPgaxLKVK1dq6dKlGj16tCZPniyJnpxthYWFYR8BIklpaWmaN2+eJPoRLd9++62WLFmirVu3qrGxUX6/X3l5eerfv7+k79+crLCwUOvXr1dDQ4MGDhyo3NxcpaamOnMcOnRIL730kj766CN5PB79/Oc/12233aaOHTs6Y7766istXLhQe/fuVbdu3XTddddp7NixYbVs2rRJy5cvV01Njfx+v2666SZddNFFZ2chYsT06dOd3yMnuvbaa5Wbm2vf48QgJn344Yfmo48+MhUVFWb//v1m6dKlJicnx5SVlRljjHnhhRfMb3/7W/PZZ5+ZvXv3mlmzZpn77rvP+f7jx4+bu+++2zz88MNm37595uOPPzZTpkwxr7zyijPmm2++MTfffLN5+eWXTXl5uVm7dq2ZOHGi+eSTT5wxGzduNL/+9a/NP/7xD1NeXm6ee+45M3nyZFNXV3fW1iLW7N692+Tl5ZkZM2aYRYsWOfvpydm1fPlyc/fdd5va2lrnX319vXOcfpx93333ncnLyzPz5883u3fvNt98843ZunWrqaysdMYUFxebW2+91WzevNmUlpaa/Px8M336dNPY2OiMmTNnjpkxY4bZtWuX2blzp/nd735n5s2b5xxvaGgwubm55i9/+YspKyszGzZsMDfddJNZt26dM+aLL74wEydONKtWrTLl5eXm1VdfNTk5Oearr746O4sRI+rr68MeI9u2bTPjx48327dvN8bY9zghtFhk8uTJZv369aahocHk5OSYTZs2Oce+/vprM378ePPll18aY4z5+OOPzYQJE0xtba0z5q233jK33HKLCQQCxhhj/va3v5m777477BxPPvmkeeSRR5ztP/zhD2bBggXO9vHjx81vfvMbU1xcHIFbGPuOHDli7rzzTrNt2zbz4IMPOqGFnpx9y5cvNzNmzGj2GP2IjiVLlpj777//lMdDoZCZNm2aWbVqlbOvoaHBTJo0yWzYsMEYY0x5ebkZP3682bNnjzPmk08+MRMmTDD//ve/jTHf92ny5MlOn5rOfddddznbc+fONY8++mjY+WfNmmWef/75Vt1G2y1atMjccccdJhQKWfk44TUtFgiFQtq4caMaGxuVmZmpkpISHT9+XIMHD3bG/OQnP1GvXr20a9cuSdKuXbvUu3fvsEt8F154oY4cOaLy8nJJ0u7du8PmkKQhQ4Y4cwSDQZWUlISNSUhI0ODBg50x8WbBggUaOnSoLrjggrD99CQ6qqqqdPvtt+uOO+7QX//6Vx04cEAS/YiWLVu2qF+/fpo7d65yc3N1zz336J133nGOV1dXq66uLuzx06lTJw0YMCCsL507d3aeTpKkwYMHy+PxaM+ePc6Yn/70p/J6//MKhyFDhqiiokKHDh1yxjTXu927d7t/wy0RDAb1/vvva+TIkfJ4PFY+TnhNSwwrKyvTvffeq0AgoI4dO2rGjBlKT09XaWmpvF6vOnfuHDa+e/fuzgdVNvcBld27d3eONf23ad+JY44cOaJjx47p0KFDCoVCJ82TlJSkiooK126nLTZu3Kh9+/bp0UcfPelYXV0dPTnLzjvvPOXl5SktLU21tbUqKirSAw88oD//+c/0I0qqq6u1bt06jRkzRtnZ2dq7d68WLVokr9erESNGOOva3JqeuObdunULO96uXTt16dIlbExKSkrYmKYe1NXVOWNPd554tHnzZjU0NDivNbHxcUJoiWFpaWl6/PHHdfjwYf3zn//U/PnzNXv27GiXFZcOHDigxYsX67777lP79u2jXQ4k50XpktSnTx8nxGzatIkeRUkoFFL//v01adIkSVLfvn1VVlamdevW8dlzMeDdd9/VhRdeqJ49e0a7lDPG00MxzOv1yu/3q1+/fpo0aZIyMjK0Zs0aJSUlKRgMqqGhIWx8fX29k2STkpJO+j+K+vp651jTf5v2nTgmMTFR7du3V7du3ZSQkHDSPM0l77aupKRE9fX1mjlzpnJycpSTk6MdO3Zo7dq1ysnJUffu3elJlHXu3FlpaWmqqqriMRIlPXr0UHp6eti+9PR052m7pjVpbk1PXPODBw+GHT9+/LgOHTp02t41bf+33sVjXySppqZGn376qa6++mpnn42PE0KLRUKhkAKBgPr166d27drps88+c45VVFTowIEDyszMlCRlZmaqrKws7I706aefKjEx0fmhct5554XN0TSmaQ6v16t+/fpp+/btYTVs377dGRMvBg8erCeeeEKPPfaY869///664oornK/pSXQdPXrUCSw8RqLj/PPPP+lyf0VFhZKTkyVJKSkpSkpKClvTw4cPa8+ePWF9aWhoUElJiTNm+/btMsY4fx6bmZmpnTt3KhgMOmM+/fRTpaWlqUuXLs6Y5np33nnnuXiL7fHuu++qe/fuYX/ybePjhNASo5YuXaodO3aourpaZWVlzvaVV16pTp066X/+539UUFCg7du3q6SkRM8884wyMzOdO8CQIUOUnp6up59+WqWlpdq6dauWLVumUaNGOZ/Oee2116q6ulpLlizR/v379dZbb2nTpk0aM2aMU0dWVpbWr1+v9957T19//bUWLFigxsbGuLvUm5iYqN69e4f969Chg7p27arevXvTkygoKChwHiNffvmlHn/8cSUkJOiKK66gH1EyZswY7d69WytWrFBVVZU2bNig9evXa9SoUZIkj8ej0aNHa8WKFdqyZYvKysr09NNPq0ePHrr00kslfX9l5sILL9Tzzz+vPXv26IsvvtBLL72kyy+/3Hla44orrpDX69Vzzz2n8vJyffDBB1q7dq2ysrKcWkaPHq1t27bptdde0/79+1VYWKi9e/fquuuuO/sLE2WhUEjvvfeehg8fHvbeKjY+TviU5xj17LPPavv27aqtrVWnTp3Up08fjR071nnVfdMbAm3cuFHBYLDZNwSqqanRggUL9Pnnn6tDhw4aPny4brrpppPeEOjll1/W119/fdo3BFq9erXq6uqUkZGh2267LW7/b+VEDz30kDIyMk56czl6cnbMmzdPO3fu1Hfffadu3bpp4MCBysnJkd/vl0Q/ouWjjz7S0qVLVVVVpZSUFI0ZM0bXXHONc9z8/5vLvfPOOzp8+LAGDhyoqVOnKi0tzRlz6NAhLVy4MOzN5aZMmXLKN5fr2rWrrrvuOt1www1htWzatEnLli1TTU2NUlNT4/LN5SRp27ZtmjNnjubNmxe2zpJ9jxNCCwAAsAJPDwEAACsQWgAAgBUILQAAwAqEFgAAYAVCCwAAsAKhBQAAWIHQAgAArEBoAQAAViC0AAAAKxBaAACAFQgtAADACoQWAABghf8DlYeG0vG4FvAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(salaries, bins=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is Differential Privacy?\n",
    "\n",
    "[Differential Privacy](https://desfontain.es/privacy/friendly-intro-to-differential-privacy.html) is a theory and technology used to better use and release data in a privacy-respecting way. It is a rigorous method to measure how much information any individual will leak when they contribute to a piece of data, statistic or even a machine learning model. By measuring and controlling the individual contribution, we can create rigorous definitions and guarantees that support individual privacy. \n",
    "\n",
    "We can tune this on a case-by-case basis and we can create a technical and data strategy around how we share this data in different contexts (i.e. more privacy for public releases, less privacy/more information for need-to-know internal use cases).\n",
    "\n",
    "To explain it a different way, differential privacy helps us *obfuscate* information from individuals in the dataset without completely destroying the statistical properties of the data. We do so by controlling how much information a person can contribute and by carefully adding controlled noise, to allow for uncertainty in drawing specific conclusions about individuals.\n",
    "\n",
    "To explore how this might work, we will start by understanding differential privacy using our dataset and the Laplace mechanism!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Laplace Mechanism\n",
    "\n",
    "Let's take a look at the Laplace mechanism and notice the properties it gives us. Our goal in evaluating Laplace is to understand, what can it offer in terms of providing controlled noise, and therefore, uncertainty in our results, so that it is less clear to a potential observer, who *exactly* is in our dataset and what attributes this person has (here, age and salary)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc = 0\n",
    "scale = 20\n",
    "\n",
    "x = np.arange(-50., 50., 1)\n",
    "pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)\n",
    "\n",
    "fig,ax= plt.subplots()\n",
    "ax.plot(x, pdf, linestyle='-');\n",
    "ax.set_title('Laplace Probability Density Function')\n",
    "ax.set_xlabel('actual number')\n",
    "ax.set_ylabel('probability density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the Mu and b values, we can see how the distribution changes, and how this might then affect our results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc75967f820>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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///vfz+nczlZXuel0lo++M8vNkfeD5ioqKiIgIKDORFSn0xEUFERubm6t5xr63YP96xBNJwmQcKqPPvqI1NRU5s6dW+s/3E2bNvH666/Xe2xOTk6dnWKto5Iam6vkySefxMXFhT///JPevXvbPff3v/+ddevW2W2zvqlkZGTQr1+/Bs9tvfbOnTvp379/g/u2lLpGlFjjqmvkFkBWVpbdfmeyjmg529nl/eeff/Ldd99x6aWX8tNPP9nedMEyouWll16qN+amXqO1nH/++QwaNMjWGfqnn37i5MmTPPLII+j1eqde68iRI6Snp6PT6Wydjq2vd/bs2bzyyitOvd6Z/P39efXVV3n11Vc5cuQI69at4/333+ett96isLCw3oEIjrj77rtZuXIlH374IS+++CIffPABbm5uTJ8+3QmvwJ5GYxmwbDQa63y+KbXDjTnz/aCl+Pr6UlBQgMFgqHW/GY1G8vPz66zpES1DhsELpzpy5AiArVr8TGcnIE15/ujRo5w4cYLY2NhG3+COHDlCUlJSreTHbDazYcOGWvtfcMEFAE2aedm672+//dbovq1p0KBBAPUua7FmzRqAOken1VXeRUVF7NixAzc3N1s5Wn+nV199tV3yA/DHH39QUVFRb3x1XcNkMtl+H9b4ncE6Kq6x/4bvueceKisrWbRoER988AGKonDnnXc6LQ6rZ555BoCrrrrKNkLuvPPOQ6PRtOp91L17d2677TbWrVuHl5cXP/zwQ6PHNKUsJ0yYQHR0NAsXLuTnn3/m0KFD3HDDDfj7+zstdivrOU+cOFHruSNHjjilJtH6u1m/fn2tZvu6NPV+O9OgQYMwm82sX7++1nPr16/HZDI5ZSSpaBpJgIRTWefBOPsDOTk5mRdeeKHBY19//XXS0tJsj81mM3PmzMFsNtc7f8vZ1z58+LCt2QEsfTDmzZvHvn37au1/88034+Pjw7vvvlvnG1J6errt51tvvRU/Pz+efvpp/vjjj1r7ms3mFl1bqz4jR46kZ8+ebNiwgW+//dbuuW+//ZbffvuNxMRERo0aVevY//znP7X6G8ybN4+ioiJuvPFGWxNXfb/T3Nxc/vGPfzQY3+rVq1m+fLndtrfeeouUlBTGjBnj1P4//v7+KIrC8ePHG9xv6tSp+Pr68tJLL7Fu3Touu+wy4uPjnRZHcXExM2fO5D//+Q9+fn68+OKLtudCQkKYNm0af/75J88++2ydH54pKSmkpqY2+/qpqakcPXq01vZTp05RVVWFu7t7o+cIDAwEaLAsNRoNd955J7m5ucyYMQNomX5UAL169cLHx4cffvjBromooqLCaTOmBwcHM2XKFLKysnjooYdqzclTWlpql2g1pYzOZi2nxx57zG6W6PLyctt8UbfddluzX4NwjDSBCYc0NLfHO++8w/Tp01mwYAH3338/a9asoUePHhw+fJjly5dz3XXX8fXXX9d7/MiRIxk4cCCTJ0/G19eXVatWsXPnToYMGcLDDz/caGyzZ8/mrrvuYtCgQVx//fXo9Xp+//139u3bx1VXXcWyZcvs9g8KCuKLL75g0qRJjBkzhssvv5z+/ftTXFzMrl27OHHihO2DKDAwkG+//ZaJEydywQUXcMkll9CnTx8UReHEiRNs2rSJkydPUllZ2bSCdBLrhGyXXXYZkydP5pprrqFXr14cPHiQ77//Hm9vbxYtWmRrQjjT5ZdfzsiRI7nhhhsIDw9nw4YNbNiwgdjYWLsP7WHDhjFy5EiWLl3KiBEjGDVqFDk5Ofz000/07NmTiIiIeuO76qqrmDhxIhMnTqR79+7s2LGDn376iYCAAN555x2nloWXlxfnn38+v/32G9OmTSMxMRGtVsvVV19t12zp4eHBzTffzBtvvAFwTn1WXnvtNfz8/FBV1bYUhrUGITExkc8//5zExES7Y9566y0OHz7MU089xX/+8x9GjRpFaGgomZmZ7N+/n61bt/Lll1/aJnZ01M6dO7nuuusYNmwYvXv3JiIigry8PH744QcMBoOtT1BDLrnkEhYsWMAdd9zB9ddfj7e3N35+ftx77712+91+++0888wztmbk4cOHNyvmxuj1embNmsWzzz7LoEGDmDhxIkajkf/7v/8jIiKiwXvQEW+99RZ79uzhvffeY+3atYwbNw4XFxdSU1NZtWoV//vf/2wdmJtaRmeaOnUqP/zwA0uWLKFPnz5ce+21KIrC999/T2pqKpMnT2batGlOeS2iCdp4FJroIGhgqKr169SpU6qqWuanuOqqq9Tg4GDVw8NDHTx4sPrhhx82OuQ2JSVF/fe//6327NlTdXV1VSMiItRZs2bVOfyzvmHwCxcuVAcMGKB6eHiogYGB6rXXXqvu2rXLNvR7zZo1tY7Zs2eP+re//U2NiIhQ9Xq9GhISol500UXq+++/X2vf1NRU9R//+IfavXt31dXVVfX29lZ79uyp3nTTTep3333XpLJsaB6gujQ23FZVLUO5b7rpJjUsLEzV6XRqWFiYOm3aNPXAgQO19j2zLKzl5ebmpgYFBam33HKLmpmZWeuYkydPqnfffbcaExOjurq6qvHx8epjjz2mlpWVNTgEeeHCheqyZcvUCy64QPXw8FB9fX3V6667rs75ds51GLyqqurhw4fVCRMmqAEBAaqiKHXOnaOqp4ebh4eH15rLpimsw+CtXzqdTvX391f79u2r3nTTTeo333yjVlVV1Xt8VVWV+uabb6rDhw9XfXx8VBcXFzUqKkodO3as+uqrr6r5+fm2fR0dAn7ixAn1scceU0eMGKGGhoaqLi4uardu3dTx48erK1assDu2oakDXn75ZbVXr16qi4tLg/frtdde2+AUEQ2x3if1TV1wJrPZrL7wwgtqfHy8qtfr1aioKHXOnDlNugfrAqgXX3xxre2lpaXqc889p/br1091d3dXvby81N69e6uzZs1Sc3Jy7PZtqIzqGgavqpa5mN5++211yJAhqru7u+ru7q4OHjxYfeutt2rNPdRQnKratPcGUT9FVWvGaQrRRm655RY+++wzUlNTa01nL0RL+PTTT7n11lt54oknePbZZ9s6nA7LbDbTvXt3cnJyyMrKkg68okORPkBCiC7FaDTyyiuvoNPp2t2Q7Y7m22+/JTU1lenTp0vyIzoc6QMkhOgSNmzYwLp161i7di27d+/m3nvvJTIysq3D6pBefPFFCgoK+OCDD/D09OSxxx5r65CEcJgkQEKILuGXX37h6aefJiAggDvuuKPB+YtEwx577DH0ej1JSUksWLDANru6EB2J9AESQgghRJcjfYCEEEII0eVIAiSEEEKILkcSICGEEEJ0OZIACSGEEKLLkVFgDTh16lS9qw93NcHBweTl5bV1GF2ClHXrkbJuPVLWracrl7VOp2vygrySADXAaDRiMBjaOow2pygKYCkPGTTYsqSsW4+UdeuRsm49UtZNJ01gQgghhOhyJAESQgghRJcjCZAQQgghuhxJgIQQQgjR5UgnaCGEEO2W0WikvLy8rcPoUCoqKqiurm7rMFqMh4cHOt25py+SAAkhhGiXjEYjZWVleHt7o9FIg0VT6fX6TjuC2Ww2U1JSgqen5zknQXJHCSGEaJfKy8sl+RF2NBoN3t7eTqkVlLtKCCFEuyXJjzibs+4JubOEEEII0eVIAiSEEEKILqfNO0GvXLmSZcuWUVhYSExMDDNmzKB79+517nvixAm+/vprUlNTycvL4+abb+bKK688p3MKIYQQAiZNmkRSUhLPPPNMW4fSKtq0Bmjjxo0sWrSISZMmMX/+fGJiYnj++ecpKiqqc/+qqipCQ0OZOnUqfn5+TjmnEEII0dmoqsqCBQsYNGgQCQkJTJ48maNHj7Z6HN26dav19cMPP7R6HHVp0wRo+fLlXHLJJYwZM4bIyEjuuOMOXFxcWLNmTZ37d+/enb/97W+MHDkSvV7vlHMKIbouc2VlW4cgRIt45513+OSTT3jxxRdZtmwZHh4eTJs2jco2uOdfeeUVkpOTbV/jxo1r9Rjq0mYJkNFo5OjRo/Tr1+90MBoN/fr149ChQ616ToPBQHl5ue2roqLC9pyiKPJVs7pwW8fQVb6krFvny/ztQjImj4H0Y20eS1f4as593RFNmjSJJ554gqeeeoqkpCQGDBjA4sWLKS8vZ/bs2SQmJjJy5EhWr15tO+brr7+md+/edudZuXIl3bp1a1YMqqry0UcfMWvWLMaNG0dSUhKvv/46OTk5rFq1qsFjTSYTjz/+OL169aJv37689NJL57yqvK+vLyEhIbYvNze3czqf1bneM23WB6i4uBiz2VyrKcvPz4/MzMxWPed3333Ht99+a3scFxfH/PnzCQ4OblYcnVVYWFhbh9BlSFm3vJyjB6k2GvAuyMFr2PC2DqdLcPS+rqiosKvtV1UVqqucHVbjXFyb/OGqKArffPMN9957L6tWreL777/nscceY9WqVVxxxRU88MADvPfee8yaNYvt27fbzWp85mvVarV22zZv3syUKVMavPa///1vJk2axLFjx8jNzWX06NG24wMDAxk8eDDJyclMmjSpwdinTZvGqlWr2LFjBw899BDR0dH87W9/A+Chhx6y+7ysy7Fjx+weP/7448yZM4eYmBhuvvlmbrzxxnNOcF1cXAgPDz+nc7R5J+j2YOLEiUyYMMH22PqLycvLw2g0tlVY7YaiKISFhZGdnX3O/wmIhklZtx7jqZMAFGWcoCQrq42j6dyae19XV1fbzWisVlVivveGlgixQZq3lqC4Nq3WQlVVkpKSuO+++wC45557eOONN/Dz87MlMLNmzeLTTz9l165dDBkyxPY5c+ZrNZlMdtuSkpL4+eefG7x2cHAwBoOB3NxcAPz9/e3OGRgYSHZ2dr2zRKuqSkREBE899RSKohATE8PevXt57733bLE/+OCD3HnnnQ3Gceb5H3roIUaNGoW7uzvr1q3jkUceobi4mNtuu63BczSmurqarDr+bnU6XZMrL9osAfLx8UGj0VBYWGi3vbCwsN4Ozi11Tr1eX2+fIvkQOk1VVSmPViJl3QpKSwBQS4ulrFtJV7mvz2zO0mq1+Pv7222zfkCfPHmyyed0d3cnLi7OeUHWY/DgwXa1M0OGDOH999/HZDKh1WoJCgoiKCioyeebPXu27ee+fftSXl7Ou+++e84JEJz753ObJUA6nY74+Hj27NnDeeedB1jW+NizZw/jx49vN+cUQnQ+qskEFWWWBzWJkOgAXFzRvLWkTa7riLPXqFIUxW6bNcEwm82Apa/q2R/mZ9fSbNmyhZtuuqnB686fP5/rrruOkJAQwNKKERoaans+Pz+fPn36OPRazvbII4+wdOnSBvc5fPhwvc8NGjSI1157jaqqKlxdHStXZ2vTJrAJEybw9ttvEx8fT/fu3VmxYgVVVVWMHj0agLfeeouAgACmTp0KWDo5p6en234uKCjg2LFjuLm52dqWGzunEEJQVlL3z6JdUxQFmtgU1ZEEBgZSWlpKeXk5Hh4eAOzdu9dun/79+zepCQwgJiaGkJAQNmzYQN++fQEoKSkhOTmZ6dOnN3iO5ORku8fbt28nLi7O1idpzpw53HXXXU1/cWfZu3cvfn5+bZ78QBsnQCNGjKC4uJglS5ZQWFhIbGws//znP23NVfn5+XZVcQUFBTz88MO2x8uWLWPZsmUkJSUxb968Jp1TCCHOTHrU0uI2DEQIS62Iu7s7L774IjNmzCA5OZlvvvnGbh9HmsAUReH222/njTfeID4+nqioKBYsWEBoaGijQ9AzMjKYN28eN910E3v27OGTTz7hqaeesj3vSBPYzz//TH5+PoMHD8bV1ZX169fz5ptvnlMC5Uxt3gl6/Pjx9TZPWZMaq5CQEJYsabz6s6FzCiGEXbOXNIGJNubv78+bb77Js88+y+LFixk1ahQPPPCA3T/8jrrnnnsoLy/n4Ycfpri4mGHDhvH55583OgR90qRJVFZWMmHCBLRaLbfddlujTW/10ev1fPrpp8ybNw9VVYmNjWXu3LlMmzatWedzNkXtCj3SmikvL6/e3vJdiaIohIeHk5WV1SU6MLYlKevWoSZvxvzOvywPvHzQvvp52wbUyTX3vi4uLsbHx6cFI+uc9Hp9p//squ/e0Ov1TR4FJouhCiG6HLtmr7JS1JrOqEKIrkMSICFE13Nmx2fVDBXlbReLEKJNSAIkhOh6zu73UyYdoYXoaiQBEkJ0PWcPfZeO0EJ0OZIACSG6HLVWDZAkQEJ0NZIACSG6nrOavGolREKITk8SICFE11OT8Gj8AmseSx8gIboaSYCEEF1PTcKj7xZd81hqgIToaiQBEkJ0KaqqQnkpADprAiSjwITociQBEkJ0LRXlYDIBoIuIsmyTGiAhmDRpkt26X52dJEBCiK7FOuLLxQVtUCgAqowCE52MqqosWLCAQYMGkZCQwOTJkzl69Girx/Hkk08yfvx44uLiuOyyy+rcZ9++fUycOJH4+HiGDh3KO++80yqxSQIkhOharLU9nj5ovH3ttwnRSbzzzjt88sknvPjiiyxbtgwPDw+mTZtGZWVlq8cyZcoUrrrqqjqfKykpYerUqURGRvLTTz/x5JNP8vLLL/P55y2/Pp8kQEKIrsXa38fLB62vX802SYCEc0yaNIknnniCp556iqSkJAYMGMDixYspLy9n9uzZJCYmMnLkSFavXm075uuvv6Z3795251m5ciXdunVrVgyqqvLRRx8xa9Ysxo0bR1JSEq+//jo5OTmsWrWqwWNNJhOPP/44vXr1om/fvrz00kvntDDzs88+yy233EJMTEydzy9duhSDwcDLL79Mz549ueaaa7jtttv44IMPmn3NppIESAjRpVgXQlW8vM+oAZJO0B2BqqpUGs2t/uVoAvDNN98QEBDA8uXLufXWW3nsscf4+9//ztChQ1m5ciUXXXQRM2fOpKKiosnn3LJlCz169Gjwa+nSpQCkpaWRm5vLqFGjbMf7+PgwaNAgtm3b1mjsWq2W5cuX88wzz/DBBx/wxRdf2J5/5JFHGo3DEdu2beP888/HxcXFtu3iiy8mJSWFwsJCh87lKF2Lnl0IIdobWxOYNxqfmgTIUI1aVYXi6tp2cYlGVZlUJn99qNWv+/XkRNx0SpP3T0pK4v777wfgvvvu4+2338bf359p06YBMHv2bBYtWsS+ffsYMmRIk87Zv39/fv755wb3CQ4OBiA3N9fusVVQUJDtufpERETw9NNPoygK3bt358CBA3z44Ye22OfMmcNdd93VpJibIi8vj6ioKLtt1rjz8vLw8/Nz2rXOJgmQEKJrsTZ3eXmjuHuCVmsZFVZWDK7BDR8rRBOc2Zyl1Wrx9/e322b9gD958mSTz+nu7k5cXJzzgqzH4MGDUZTTyd6QIUN4//33MZlMaLVagoKCCAoKavE4WoMkQEKIrsVaA+TlY3mj9/SG4kLL9gBJgNozV63C15MT2+S6jtDp7D9aFUWx22ZNMMxmMwAajaZWM5vBYLB7vGXLFm666aYGrzt//nyuu+46QkJCAEsNSmhoqO35/Px8+vTp49BrOdsjjzxia2qrz+HDh5t8vuDgYPLz8+225eXl2Z5rSZIACSG6lpoaIMXT2/LYqyYBko7Q7Z6iKA41RXUUgYGBlJaWUl5ejoeHBwB79+6128eRJrCYmBhCQkLYsGEDffv2BSyjrZKTk5k+fXqD50hOTrZ7vH37duLi4tBqtYDzm8CGDBnCSy+9hMFgQK/XA7B+/XoSEhJatPkLJAESQnQx1k7QeNUkQJ4+NdtL6HwfraIjGDRoEO7u7rz44ovMmDGD5ORkvvnmG7t9HGkCUxSF22+/nTfeeIP4+HiioqJYsGABoaGhjBs3rsFjMzIymDdvHjfddBN79uzhk08+sZsc0dEmsNTUVMrKysjNzaWyspI9e/YAkJiYiIuLCxMnTuTVV1/lwQcf5B//+AcHDhzg448/Zt68eU2+RnNJAiSE6FrKTjeBAShePqggy2GINuPv78+bb77Js88+y+LFixk1ahQPPPAADz/8cLPPec8991BeXs7DDz9McXExw4YN4/PPP8fNza3B4yZNmkRlZSUTJkxAq9Vy2223Ndr01pA5c+awadMm22NrArZ582aioqLw8fHhiy++4PHHH+fyyy/H39+f2bNnn9M1m0pRz2WAfyeXl5dXqx22K1IUhfDwcLKyss5pPgjROCnrlmd6ZAYU5KP958tEjLyY9Bf/ifrbzyjXTEUzYUpbh9cpNfe+Li4uxsfHpwUj65z0en2n/+yq797Q6/VN7jsk8wAJIbqW0tOjwABLJ+gztwshugRJgIQQXYZqqIbqKsuDmgRIqWkKk07QQnQtkgAJIboOay2PRgPunpafaxIhVWqAhOhSJAESQnQd1o7Ont6nJ3uzNoFJDZAQXYokQEKIruOMZTCsFGtfIFkPTIguRRIgIUTXUXZWB2iwzQMkNUBCdC2SAAkhugy1xDoJ4hnDZ71rfi4vQzWZWj8oIUSbkARICNF1nL0MBoCHV63nhRCdnyRAQoiu4+w5gABFqwWPmhFhkgAJ0WVIAiSE6Dpso8DOmkFWJkMUgkmTJtmt+9XZSQIkhOgy1DpqgCyPrR2hZSSY6BxUVWXBggUMGjSIhIQEJk+ezNGjR1s1hr1793LPPfcwdOhQEhISuPjii/noo49q7bdx40bGjRtHXFwcI0eO5Ouvv26V+CQBEkJ0HXX1AQJbDZBMhig6i3feeYdPPvmEF198kWXLluHh4cG0adOorKxstRh2795NUFAQb775JqtXr2bmzJm88MILLFy40LbP8ePHmT59OiNGjODnn3/m9ttvZ86cOaxdu7bF45MESAjRddRTA2SbC0j6AIlzNGnSJJ544gmeeuopkpKSGDBgAIsXL6a8vJzZs2eTmJjIyJEjWb16te2Yr7/+mt69e9udZ+XKlXTr1q1ZMaiqykcffcSsWbMYN24cSUlJvP766+Tk5LBq1aoGjzWZTDz++OP06tWLvn378tJLLzV7YeYpU6bwzDPPMHz4cGJiYrj++uuZPHkyK1assO3zn//8h+joaObOnUuPHj249dZbufLKK/nwww+bdU1HSAIkhOg6SusYBn/m4xJpAmvPVFXFaGz9L0cTgG+++YaAgACWL1/OrbfeymOPPcbf//53hg4dysqVK7nooouYOXMmFRUVTT7nli1b6NGjR4NfS5cuBSAtLY3c3FxGjRplO97Hx4dBgwaxbdu2RmPXarUsX76cZ555hg8++IAvvvjC9vwjjzzSaBwNKSkpwc/Pz/Z427ZtdnECjB49utE4nUHX4lcQQoh2QDWboKLM8uDsPkCyHEaHYDLBT/8tavXrXn69LzoHPi2TkpK4//77Abjvvvt4++238ff3Z9q0aQDMnj2bRYsWsW/fPoYMGdKkc/bv35+ff/65wX2Cg4MByM3NtXtsFRQUZHuuPhERETz99NMoikL37t05cOAAH374oS32OXPmcNdddzUp5rNt3bqV//3vfyxatMi2LTc3t844S0pKqKiowN3dvVnXagpJgIQQXUNZGVj/k/c4uxO09AESznNmc5ZWq8Xf399um/UD/+TJk00+p7u7O3Fxcc4Lsh6DBw8+vU4eMGTIEN5//31MJhNarZagoCCCgoIcPu+BAweYMWMGs2fP5uKLL3ZmyM0mCZAQomuwjvBy90A5+995TxkF1hFotZbamLa4riN0Z91fiqLYbbMmGGazGQCNRlOrmc1gMNg93rJlCzfddFOD150/fz7XXXcdISEhAOTl5REaGmp7Pj8/nz59+jj2Ys7yyCOP2Jra6nP48GG7x4cOHWLy5MlMmzbNVjNmFRISQl5ent22/Px8vL29W7T2ByQBEkJ0FXUshGqleHmjnrmPaJcsiURbR+F8gYGBlJaWUl5ejoeHB2AZQn4mR5rAYmJiCAkJYcOGDfTt2xew9L1JTk5m+vTpDZ4jOTnZ7vH27duJi4tDW5MFOtoEdvDgQW644Qb++te/8uijj9Z6fsiQIXYdwgHWr1/f5KbBc9EJbyUhhKhDWf0JkPQBEm1p0KBBuLu78+KLLzJjxgySk5P55ptv7PZxpAlMURRuv/123njjDeLj44mKimLBggWEhoYybty4Bo/NyMhg3rx53HTTTezZs4dPPvnEbnJER5rADhw4wA033MDFF1/MnXfeaet/pNVqCQwMBOBvf/sbCxcu5LnnnmPKlCls2LCBZcuW2fUTaimSAAkhuoR6J0E8c1tZCaqq2vWBEKKl+fv78+abb/Lss8+yePFiRo0axQMPPMDDDz/c7HPec889lJeX8/DDD1NcXMywYcP4/PPPcXNza/C4SZMmUVlZyYQJE9Bqtdx2222NNr3V58cff+TkyZMsXbrUrtksMjKSLVu2ABAdHc2iRYuYN28eH3/8MeHh4SxYsIDRo0c365qOUNTmDvDvAvLy8mq1w3ZFiqIQHh5OVlZWs+eDEE0jZd1yzKu+Q/12Icr5F6O5/UG7sjZXVmK+968AaF7/EsW6Nphwiube18XFxfj4+DS+o7Cj1+s7/WdXffeGXq+vNaqsPjIPkBCiayirZw4gQHF1BReXmv2kGUyIrkASICFE19BAJ2jLdh/7/YQQnZokQEKILkEta6APEJzREVqGwgvRFUgCJIToGhqrAZLJEIXoUiQBEkJ0DdaV4OupAVJkKLwQXYokQEKIrsFWA1TPqCJrYiQ1QEJ0CZIACSE6PVVV618J3sq6vVT6AAnRFUgCJITo/KoqwGS0/FxfJ2gvaQIToiuRBEgI0flZm7V0enBxrXufmqYxVWqAhOgSJAESQnR+ZwyBr2+ZC0VqgEQXN2nSJLt1vzo7SYCEEJ1fY0Pgz3xOaoBEJ6CqKgsWLGDQoEEkJCQwefJkjh492qoxFBQUMG3aNAYPHkxcXBxDhw7l8ccfp6TE/p+MjRs3Mm7cOOLi4hg5ciRff/11q8QnCZAQotNTSwotP/j41b+Tt6/le0mxrMMmOrx33nmHTz75hBdffJFly5bh4eHBtGnTqKysbLUYNBoNf/nLX1i4cCG//fYbr776Kr/99huPPvqobZ/jx48zffp0RowYwc8//8ztt9/OnDlzWLt2bcvH1+JXEEKItlZUCIDi7Vf/Pj7+lu+Gaqgob/GQROc0adIknnjiCZ566imSkpIYMGAAixcvpry8nNmzZ5OYmMjIkSNZvXq17Zivv/6a3r17251n5cqVdOvWrVkxqKrKRx99xKxZsxg3bhxJSUm8/vrr5OTksGrVqgaPNZlMPP744/Tq1Yu+ffvy0ksvNfsfAj8/P26++WYGDBhAZGQkF154ITfffLNtJXiA//znP0RHRzN37lx69OjBrbfeypVXXsmHH37YrGs6QtfiV2jEypUrWbZsGYWFhcTExDBjxgy6d+9e7/6bNm3i66+/Ji8vj7CwMFv1mlVlZSWLFy9m69atlJSUEBISwuWXX85f/vKX1ng5Qoj2qLjQ8t3Xr95dFFdXcHOHygrL/rIifLujqipGo7HVr6vT6ertO1aXb775hrvvvpvly5fzv//9j8cee4yVK1cyfvx47rvvPj788ENmzpzJ1q1bcXd3b9I5t2zZwk033dTgPvPnz+e6664jLS2N3NxcRo0aZXvOx8eHQYMGsW3bNq655poGY58yZQrLly9n165dPPzww3Tr1o1p06YB8Mgjj7B06dIG4zh8+HCd27Ozs/npp58YPny4bdu2bdvs4gQYPXo0c+fObfAaztCmCdDGjRtZtGgRd9xxBz169ODHH3/k+eef57XXXsPX17fW/gcPHuT1119n6tSpDB48mA0bNrBgwQLmz59PdHQ0AJ999hl79uzhvvvuIzg4mF27dvHRRx8REBDA0KFDW/slCiHag+JTlu8NNYFZn6+ssOwf1rz/vkXLMRqNvPvuu61+3bvvvhu9Xt/k/ZOSkrj//vsBuO+++3j77bfx9/e3JRGzZ89m0aJF7Nu3jyFDhjTpnP379+fnn39ucJ/g4GAAcnNz7R5bBQUF2Z6rT0REBE8//TSKotC9e3cOHDjAhx9+aIt9zpw53HXXXU2K2eqee+5h1apVVFZWctlll7FgwQLbc7m5uXXGWVJSQkVFRZMTxOZo0yaw5cuXc8kllzBmzBgiIyO54447cHFxYc2aNXXuv2LFCgYOHMjVV19NZGQkU6ZMIT4+npUrV9r2OXToEBdffDF9+vQhJCSESy+9lJiYGI4cOdJaL0sI0c6o1hqgpiRAcLrGSIhmOLM5S6vV4u/vb7fN+oF/8uTJJp/T3d2duLi4Br+8vLzOOfbBgwfb1XYNGTKE1NRUTCYTYElOGovjbPPmzWPVqlUsXLiQtLQ0nn766XOO0xnarAbIaDRy9OhRrr32Wts2jUZDv379OHToUJ3HHDp0iAkTJthtGzBgAFu3brU9TkxMZNu2bYwdOxZ/f3/27t1LVlYWN998c72xGAwGDAaD7bGiKLas05Fqz87KWgZSFi1PyrqF1CQ0im9ArTI+s6wVX39UgJIi+R04kbPua51Ox9133+2MkBy+7rnsryiK3TZrOZjNZsDy2Xd2P5szP5PAsSawkJAQAPLy8ggNDbU9n5+fT58+fRx6LWdrThNYSEgIISEhdO/eHT8/PyZOnMj9999PaGgoISEh5OXl2e2fn5+Pt7d3o7U/53w/ndPR56C4uBiz2Yyfn5/ddj8/PzIzM+s8prCwsFbTmK+vL4WFhbbHM2bM4P333+euu+5Cq9WiKAp///vfSUpKqjeW7777jm+//db2OC4ujvnz59eqluvqwsLC2jqELkPK2rkySosxA8Hx3XEJD7d77syyPhXWjVLAy2TA96z9xLlz9L6uqKio1fTk4uLizJCcTlEUtFqtXdx1bQNs20JDQyktLaW6uhpPT0vfswMHDgDYjhkyZIhdx+m6hISEoNfriYmJISQkhE2bNjFo0CAASkpKSE5O5tZbb623OU9RFHbs2GH3/I4dO4iPj8fNzQ2Axx57jHvvvbfBOBpqLtRoLA1PZrMZvV7PsGHD+PXXX+2O2bBhA0OHDm3wPC4uLoSf499om3eCdraffvqJw4cP8/DDDxMcHMz+/fv5+OOP8ff3p3///nUeM3HiRLuaJWtWmZeX1yYd7tobRVEICwsjOztbhge3MClr51PNJsw1o8DyDSaUrCyg7rI26ywfriWZ6ZTX7CfOXXPv6+rq6lo1Ie2dqqqYTCa7uOvaBti29evXD3d3d5577jlmzJhBcnIyX331FXC6Jkin0xEVFdXo9Q0GA3q9nttvv51XX32VmJgYoqKiWLBgAaGhoVx66aX1lqmqqqSnp/P4449z0003sWfPHj766COeeuop2zF+fn61Ki7qigHg119/JT8/nwEDBuDp6cnBgwd57rnnGDZsGOHh4RgMBqZNm8bHH3/M3LlzmTJlChs2bOCHH35g0aJFDf7uq6uryarjb1Sn0zW58qLNEiAfHx80Go1d7Q1YannqK1w/Pz+KiorsthUVFdn2r66u5ssvv2TOnDm2kWExMTEcO3aMZcuW1ZsA6fX6ejNN+RA6TVVVKY9WImXtPGpJEahmUBRUT284q1zPLGvVx1LDrBYXSvm3ALmv6+bv78+bb77Js88+y+LFixk1ahQPPPAADz/8cLPPec8991BeXs7DDz9McXExw4YN4/PPP7fV5NRn0qRJVFZWMmHCBLRaLbfddlujTW/1cXNzY/HixcybN4/q6mrCw8O54oor+Mc//mHbJzo6mkWLFjFv3jw+/vhjwsPDWbBgAaNHj270/Od6L7VZAqTT6YiPj2fPnj2cd955gKVKbM+ePYwfP77OYxITE9m9ezdXXnmlbduuXbvo0aMHYOlXZDKZarUL1tW+KoToImpqf/DyQdFqG9xV8fGz9AEqOtXSUYlO6szuFFZnzntjlZGRYfd4/PjxtT77rCOvmkNRFObMmcOcOXOafMyZsb/44ovNvrbVyJEj+d///tfoftZJEFtbm44CmzBhAr/++itr164lPT2djz76iKqqKlvm99Zbb/HFF1/Y9r/iiivYuXMny5YtIyMjgyVLlpCSkmK7aTw8PEhKSuLzzz9n79695ObmsnbtWtatW2dLsoQQXUxTR4DB6ckQZRSYEJ1em/YBGjFiBMXFxSxZsoTCwkJiY2P55z//aWvSys/Pt6vN6dmzJzNnzuSrr77iyy+/JDw8nDlz5tjmAAK4//77+eKLL3jjjTcoLS0lODiYG2+8kcsuu6y1X54Qoh1Qi5o4B9CZ+xSfQlVVGQkmRCfW5p2g66r2s5o3b16tbcOHD7ebRfJsfn5+3HPPPc4KTwjR0dWsA6b4+je+rzUBMhqhogw8zn1eFSFE+yRrgQkhOjcHmsAUF1dw97A/TgjRKUkCJITo3BxpAgOwLphq7TwthOiUJAESQnRqp5fBaEITGNgWTFWlBqhdsM6WLISVs+4JSYCEEJ2bdRmMptYAyXpg7YaHhwclJSWSBAkbs9lMSUkJHh4e53yuNu8ELYQQLcqRYfCcMRdQscwF1NZ0Oh2enp6Ulpa2dSgdiouLC9XV1W0dRovx9PR0eH22ukgCJITotFSTCUqLLQ9qmrYaJXMBtSs6nQ4fH5+2DqPDUBSF8PBwsrKyZALgRkgTmBCi8yottix9oWjAq4kfojU1RdIHSIjOTRIgIUTnZR0B5u2Doml4GQwr23xBshyGEJ2aJEBCiM7Lwf4/dvvWTKAohOicJAESQnRaarGDcwCdua+sCC9EpyYJkBCi87INgW/iHEBgvxxGeZnTQxJCtA+SAAkhOq9mNIEpehdw97Q/XgjR6UgCJITovKzLWTR1CLyVdX+ZC0iITksSICFEp6VaOzI70gfojP1lKLwQnZckQEKIzsvRZTBqKNYFUSUBEqLTkgRICNF52VaCd6ATNIDMBSREpycJkBCiU1KNRigrsTxoZhOY1AAJ0XlJAiSE6JxKiyzLYGg04OXt2LHSB0iITk8SICFE52RNXrx9m7wMhpUiC6IK0elJAiSE6JxsCZCf48dKE5gQnZ4kQEKITklt7hxAZx4jy2EI0WlJAiSE6JyaOQQeOF1rZDJCeamzIhJCtCOSAAkhOifbMhgODoEHFL0ePLzszyOE6FQkARJCdE7NWQn+TNbjZC4gITolSYCEEJ2S2oyFUO3IUHghOjVJgIQQnVNNzY3i63gTmN1xsiCqEJ2SJEBCiM6puQuhWslQeCE6NUmAhBCdjmo0Qql1GYzm1QBJAiRE5yYJkBCi8ykpsnzXaMDTq3nnsPYBss4nJIToVCQBEkJ0PmfMAq1omvc2p0gNkBCdmsPvDGvWrGmJOIQQwnmsSUtzZoG28pX1wITozBxOgMaPH09CQgLPPfccJ06caImYhBDinKjnOgcQnJ4NuqQQ1Ww+15CEEO2MwwlQRkYG9957L99++y3x8fGMGzeOJUuWUF1d3RLxCSGE46zLYDRnIVQrH1/Ld5NJlsMQohNyOAEKCgpi9uzZ7Nixgy1btpCYmMg999xDREQEM2fOZOfOnS0RpxBCNJ119uZmzgEEoOj04Oldc77Cc49JCNGunFMn6MGDB/PYY49x7733UlpayieffMKQIUO48MIL2bt3r7NiFEIIx5zrLNBWto7QMhmiEJ1NsxIgg8HAt99+yxVXXEFMTAyrVq3irbfeIicnhyNHjhATE8Nf//pXZ8cqhBBNcs7LYFjJchhCdFo6Rw+47777+PLLL1FVlb/97W+89NJL9O3b1/a8p6cn//73v4mIiHBqoEII0WTWPkDnmAApPn6oIAuiCtEJOZwA7du3jzfffJPrrrsOV1fXOvcJCgqS4fJCiLZzKt/y3T/w3M5jPb7w5LmdRwjR7jjcBDZ37lz++te/1kp+jEYj69evB0Cn03HxxRc7J0IhhHCAWlEOlRWWB/5B53Yy6/GnJAESorNxOAEaM2YMBQUFtbYXFRUxZswYpwQlhBDNVlBT++PhheLqdk6nUmoSINVaoySE6DQcToBUVUVRlFrbT548iaenp1OCEkKIZrMmKwHnWPtz5jkkARKi02lyH6DrrrsOAEVRuOWWW+yawEwmE7t27WLEiBHOj1AIIRxgq6051+YvOKMPUAGq2YSi0Z77OYUQ7UKTEyBfX8usqKqq4u3tjbu7u+05FxcXLrjgAu644w7nRyiEEI6oaQJTnJEA+fiBVmuZDbrwlHNqlYQQ7UKTE6CFCxcCEBsby0MPPSTNXUKI9slZI8DAUuPjGwAFeZbzSgIkRKfRrFFgkvwIIdor1Zl9gM48j/QDEqJTaVIN0ODBg/n111/x9/dn0KBBdXaCttq+fbvTghNCCIfVDFl3ShNYzXlUQD11kvrf+YQQHU2TEqBrrrnG1un52muvbcl4hBCi2VRVPT0M3kkJkO08BVIDJERn0qQEaO7cuXX+LIQQ7UpFOVQ5aRJEK2tfImkCE6JTcbgP0IkTJ0hPT7c9/uOPP7j//vv54IMPnBqYEEI4zJqkeHqj1LNUj6OUAJkMUYjOyOEEaOrUqbZ1vrKzs7n00kv5448/ePzxx3nmmWecHqAQQjSZs5u/APyD7c8thOgUHE6A9uzZw3nnnQfAkiVL6NevHxs3bmTx4sV8+umnzo5PCCGaTHXiEHgb67mKTqGaTM47rxCiTTmcABkMBluH6F9++YWrr74agF69epGVleXc6IQQwhE1CZDizPl6rJMhqmYoqr0OohCiY3I4AerTpw/vvfcev/32G//3f//H+PHjAcjMzCQw0In/dQkhhKOcuQxGDUWjAT9rR2hZFV6IzsLhBGj+/Pm8//77jB49mhtvvJEBAwYA8L///c/WNCaEEG1BbYk+QGecT5V+QEJ0Gk1eCsNq9OjR5OfnU1xcjL+/v237nXfeiYeHh1ODE0IIh9gmQXRubbTiH4gKMhReiE7E4QQIQKvV2iU/YFkjTAgh2oqqqqcTlIBg555clsMQotNxOAHKycnhoYce4tdffyU3N9fypnMGk4OjJFauXMmyZcsoLCwkJiaGGTNm0L1793r337RpE19//TV5eXmEhYUxbdo0Bg8ebLdPeno6ixcvZt++fZjNZiIjI3nwwQcJCpKFDIXotMrLoKrS8rOfk/sjShOYEJ2OwwnQLbfcwvHjx3nyyScJDw9vcF2wxmzcuJFFixZxxx130KNHD3788Ueef/55XnvtNXx9fWvtf/DgQV5//XWmTp3K4MGD2bBhAwsWLGD+/PlER0cDlrmJnnrqKcaOHcsNN9yAu7s76enp6PX6ZscphOgArLUzXs6bBNHKuh6Y1AAJ0Xk4nABt2LCB3377jYEDB57zxZcvX84ll1zCmDFjALjjjjvYvn07a9asqXPNsRUrVjBw4EDb0PspU6awe/duVq5cyZ133gnAV199xaBBg7jppptsx4WFhZ1zrEKIds6anPi1QE2vvzSBCdHZOJwARUVF1Wr2ag6j0cjRo0ftEh2NRkO/fv04dOhQncccOnSICRMm2G0bMGAAW7duBcBsNrN9+3auvvpqnn/+eVJTUwkJCeHaa69tcISawWDAYDDYHiuKgru7u+3nrs5aBlIWLU/KuvlUawfogKAmlZ9DZR1Y06eo6BSYTCi6ZnWf7LLkvm49UtZN5/Bf8Wuvvcajjz7K+++/f04dn4uLizGbzfj5+dlt9/PzIzMzs85jCgsLazWN+fr6UlhYaDtnZWUlP/zwA5MnT2batGns2LGDl19+mblz55KUlFTneb/77ju+/fZb2+O4uDjmz59PcLCTO1J2cFKT1nqkrB1XZKikGPCIjCEgPLzJxzWlrNXQUNJ1OjAaCXHVowuR309zyH3deqSsG+dwAjR58mTKy8tJSEjAw8OjVt+agoK2mynVbDYDMHToUFtNUWxsLAcPHuTnn3+uNwGaOHGiXc2SNXPOy8vDaDS2cNTtn6IohIWFkZ2d7ZTaP1E/KevmMx0/BkCFq3uTZqV3uKz9AiA/l9yD+1BM8rtxhNzXraerl7VOp2ty5UWzaoCcwcfHB41GY6u9sSosLKxVK2Tl5+dHUVGR3baioiLb/j4+Pmi1WiIjI+326datGwcPHqw3Fr1eX28n6a54A9VHVVUpj1YiZe046zpgqn+QQ2XX5LL2D4L8XMwFeWjUXs0Ns0uT+7r1SFk3zuEE6Oabb3bOhXU64uPj7RZXNZvN7Nmzx7a8xtkSExPZvXs3V155pW3brl276NGjh+2cCQkJtZrQsrKyZAi8EJ1dzRB1Z0+CaGUbCSZD4YXoFBxeCgMgJSWFJ554ghtvvJHc3FwAfvrpJ/bu3evQeSZMmMCvv/7K2rVrSU9P56OPPqKqqorRo0cD8NZbb/HFF1/Y9r/iiivYuXMny5YtIyMjgyVLlpCSkmKXMF199dVs3LiRX375hezsbFauXMm2bdsYN25cc16qEKIDsJ8EsYX+2ZGRYEJ0Kg7XAK1bt47LL7+ckSNHsn79ep5//nlCQkLYuXMnH3/8sV1n4saMGDGC4uJilixZQmFhIbGxsfzzn/+0NWnl5+fb9WTv2bMnM2fO5KuvvuLLL78kPDycOXPm2OYAAjjvvPO44447+P7771m4cCERERE8+OCD9OolVdZCdFrlpVBdZfnZ2ZMgWlknQ5QESIhOweEE6NFHH+W5557jgQcewNvb27Z97NixvPXWWw4HMH78+HqbvObNm1dr2/Dhwxk+fHiD5xw7dixjx451OBYhRAdlmwTRB8XFuZMgWikB1skQZUV4IToDh5vAdu/ezcSJE2ttDwkJIT9f/jMSQrQB2yrwLVT7c+a5pQ+QEJ2CwwmQn59fnUNMk5OT6datm1OCEkIIR9jW6HL2IqhnsvYtKj6FajQ0vK8Qot1zOAGaMmUKjzzyCNnZ2SiKgtls5vfff+ehhx5i+vTpLRGjEEI0zDoLdEvWAHn5glYHqmqZEVoI0aE5nAD961//olevXkRFRVFaWkpSUhIXXXQRI0aM4IknnmiJGIUQomGn8izf/VtuugtFo5FmMCE6EYc7Qbu4uPDhhx/y5JNPsmfPHkpLSxk0aJBtLh4hhGht1nXAWmwIvFVAEOTnoJ7KR1ZaEqJja/aKftHR0XbDz4UQos3YJkFs2QRI8bOOBJMaICE6uiYlQA888ECTT/jKK680OxghhHCUqqpQaB0F1go1QCBD4YXoBJqUACUnJ9s93r59O0ajkZ49ewJw6NAhtFotQ4YMcX6EQgjRkLISqK62/NySnaDPOL9akNey1xFCtLgmJUBr1qyx/fzKK6/g7e3NZ599hr+/PwCnTp3i1ltv5cILL2yZKIUQoj7WDsnevih6lxa9lG0yROkELUSH5/AosJdffpkXXnjBlvwA+Pv789xzz/Hyyy87NTghhGiUtTmqpWt/4HQTW6E0gQnR0TmcABUXF5OXV7v6Ny8vj5KSEqcEJYQQTWVrjmrp/j9nXqPoFKpBJkMUoiNzOAGaOHEit956K0uXLiU9PZ309HT++9//ctttt3Hddde1RIxCCFG//GwAlKDQlr+Wty+4ull+PpnT8tcTQrQYh4fBv/feezz00ENMnToVQ81/QDqdjttuu40FCxY4PUAhhGiImmtJgAgOb/FrKYoCQaGQkQZ52RAW2eLXFEK0DIcTIA8PD9555x0WLFhASkoKAAkJCXh6ejo9OCGEaFSeZW1CJSSsda4XHA4Zaai52TIZohAdWLMnQvT09KR///7OjEUIIRyiqirk1zRFBbdOAqSEhFlGguXVXhRaCNFxONwHSAgh2o3iQqiqBEWBwFboAwS2REvNy26d6wkhWoQkQEKIjstaC+MfhKLXt8olFWtfI0mAhOjQJAESQnRYpztAt1L/nzOvlZeNaja33nWFEE7lcAJUVlbWEnEIIYTjamphlJCWHwFmExAMGg0YDVBY0HrXFUI4lcMJUGhoKDNmzGDDhg0tEY8QQjRdfuvXACk6HQSG2F9fCNHhOJwAff755xQUFDB27FgSExN58cUXyczMbInYhBCiQbaOyEGt2AQGlrmAkI7QQnRkDidA1157Ld9//z0ZGRncddddfPHFF8TExDBhwgSWLl2K0WhsiTiFEKK23FaeA6iGrSN0riRAQnRUze4EHRwczAMPPMCuXbt45ZVX+OWXX5g0aRIRERE89dRTlJeXOzNOIYSwo1aWQ0mR5UFrdoIGsCZcMheQEB1WsydCzMnJ4bPPPuPTTz8lLS2NSZMmcdttt5Gens78+fPZvHkzP//8szNjFUKI0/JqJkD09Ebx8GrVSyvBlskQpQlMiI7L4QRo6dKlLFy4kFWrVpGUlMQ999zDTTfdhJ+fn22fESNG0Lt3b2fGKYQQ9qy1L61d+wOn1x2TBEiIDsvhBOjWW29lypQp/P777wwbNqzOfSIiInj88cfPOTghhKiPtfZFaWYCpKoqJrPavIsH18w6XVaCWl7a6jVQQohz53AClJWVhYeHR4P7uLu7M3fu3GYHJYQQjTrHVeA/Tc7lx4OHWDA+hlg/V4eOVdw8wNvX0gcpLxtiujcrBiFE23G4E7S3tze5ubm1tp88eRKtVuuUoIQQojGqdQ6eZowAM5lV/u9IIdUmM6uPFjUvgBBpBhOiI3M4AVLVuquMq6qqcHFxOeeAhBCiSaxNYM2YA+jQyQpKqy3LWGzPLG3W5RWZC0iIDq3JTWBvvPEGAIqi8NFHH+HldbrN22QysX79enr16uX8CIUQ4iyq0Qgna2qim9EHaHvm6SV9ThRVk1tqIMTLwcVUpSO0EB1akxOgV199FbDUAL333nt2zV0uLi7Exsby3nvvOT9CIYQ4W0EemM2g04NfgMOHb6tJgLQaBZNZZVtmKZcn+jt2kprES82VuYCE6IianAClpqYCMGbMGJYuXYq/v4NvFkII4Sx5p9cAUzSOteQXVhhJKagEYNLAbny9PZ3tWWUOJ0BKiGUuIKkBEqJjcrgP0Jo1ayT5EUK0KfUc5gDanmWp/UkIcGNCX0sz1q7sMgwms2MnsjaBncpHNRgcjkMI0baaVAP0wAMP8Oyzz+Lp6ckDDzzQ4L6vvPKKUwITQoh6ncMcQNZOz0MiPEkM8cLPTUthpYl9eRUMCPNs+ol8/MDVDaoq4WQOhEU6HIsQou00KQFKTk7GUPMfTnJycr37KYrinKiEEKIBajPnADKZVXbU1AANjvBCoygMjvBi9dEitmeWOZQAKYpiWRU+I82SkEkCJESH0qQEaM2aNXX+LIQQbaJmDiBHV4E/fLKSkmozni4aega5AzCkJgHallnKrYNDHIsjOBwy0lDzspF//4ToWJq9GrwQQrQFVVXtOkE7YltN89fAME+0GkvKMjDcE41iGQ6fV+ZYXx5bAiYdoYXocJpUA3Tdddc1+YRLly5tdjBCCNGokkJLvxtFgcBQhw61zv8zOOJ0U5e3q5bEQHcO5FewLbOU8T0cGORRMwmjTIYoRMfTpATI19e3peMQQoimsfb/8Q9E0Td98sLCSiNHaoa/D46wX7x0SIQnB/Ir2J5Z5lACpATXDIWXuYCE6HCalAAtXLiwpeMQQogmsdW2ONgBOrmm9ifO35UAd/u3vsERXizelc/O7HIMJhW9tok9eqxNYPk5qGazw3MSCSHajvy1CiE6lpo5gBwdAm9t/hpyVu0PQHyAK75uWiqNZvbnlTf9pAEhoNGAoRqKTjkUjxCibTWpBmjw4MH8+uuv+Pv7M2jQoAaHu2/fvt1pwQkhRC3N6ABtMqskZ9fu/2OlURQGh3uyJrWY7Zll9G/icHhFp4OAYMjPsSRm/oFNjkkI0baalABdc801uLq6AnDttde2ZDxCCNGg5jSBHSmopKTKhKdeQ6+a4e9nGxzhxZrUYrZllnKLI8Phg8MsTWB52SiJfZt+nBCiTTUpAZo7d26dPwshRKur6XDsyBxAW06UAJYh79bh72cbVDMc/nhRNVkl1YR7uzTp3EpwOOr+nac7ZwshOoQmL4Z6tj///JP9+/cDkJSUxJAhQ5wWlBBC1EUtK4WSIssDB2qANqdb5v+5IMq73n28XbX0DfFgV045W9JLuLZ3E5uzQiMssWWnNzkeIUTbczgBSk9P58Ybb+T333/Hz88PgMLCQkaMGMFXX31FZKRMBy+EaCFZxy3f/YNQPJrWTye9qIqM4mp0Gstw94ZcEOXNrpxyNp8obXICpEREWYbCZ51o0v5CiPbB4VFgt99+OwaDgf3791NQUEBBQQH79+/HbDZz++23t0SMQggBgJpZkwBFRDX5mM0nLLU//UM98XTRNrjveZGWEWIH8ioorDA27QIR0ZbvuZmoRlkVXoiOwuEEaN26dbz77rv07NnTtq1nz568+eabrF+/3qnBCSGEnUxLLYtiTTqaYHO6pf9PQ81fVsGeeroHuKECf2SUNu0C/kHg5g4mE+TIhIhCdBQOJ0BRUVG2leHPZDKZiIiIcEpQQghRF1sNUHjTaoBOlhs4fLIShdO1O425IMqy3+aajtONURTFFo8tPiFEu+dwArRgwQLuu+8+/vzzT9u2P//8k1mzZvHvf//bqcEJIYSdLMdqgKzNXz2D3PF3b1qXx/Nraop2ZpdTbjA16RhbPFmSAAnRUTTpHcHf399u8sOysjLOP/98dDrL4UajEZ1Ox4wZM2SeICFEi1DLS6GwwPKgiTVAW2zNX02r/QGI8nEhwtuFzJJqtmWUcWGsT+MHRUgNkBAdTZMSoNdee62FwxBCiEZkOjYCrLTKxJ4cy7IWTen/Y6UoChdEebF0XwFb0kualAApEdGWkWCZMhJMiI6iSQnQzTff3NJxCCFEg1RrctHEEWB/ZpZiUiHG17XJkxpaXRDlzdJ9BfyZUYbBZEavbaS3wFkjwRRd01epF0K0jXNaDLWyspLi4mK7LyGEaBE1NUBKeFP7/1iav853oPnLqkegG/7uOiqMZnbnNGFxVBkJJkSH43ACVFZWxr333ktISAienp74+/vbfQkhREtQs5peA1RlNNtWf3ek+ctKoyicH2kdDdb4cPgzR4JJR2ghOgaHE6CHH36Y1atX8+677+Lq6spHH33E008/TUREBIsWLWqJGIUQ4nQNUBNGgO3ILqPKpBLsoSPe37VZl7MmTlvSSzCraqP7W+OSjtBCdAwOL4WxbNkyFi1axOjRo7n11lu58MIL6d69OzExMSxevJhp06Y5HMTKlStZtmwZhYWFxMTEMGPGDLp3717v/ps2beLrr78mLy+PsLAwpk2bxuDBg+vc94MPPuCXX37h5ptv5sorr3Q4NiFE23N0BJi11ub8KG+7EayO6BvigadeQ2GliYP5FfQO9mj4ABkJJkSH4nANUEFBAfHx8QD4+PhQUGB5Uxo1alSzZoLeuHEjixYtYtKkScyfP5+YmBief/55ioqK6tz/4MGDvP7664wdO5b58+czbNgwFixYwPHjtd90/vjjDw4fPixNc0J0dNYO0E0YAWYwqfzRjOHvZ9NrFYZ0sxy/8XjjkyLaaqZkJJgQHYLDCVB8fDypqakA9OrViyVLlgCWmiHr4qiOWL58OZdccgljxowhMjKSO+64AxcXF9asWVPn/itWrGDgwIFcffXVREZGMmXKFOLj41m5cqXdfgUFBXzyySfMnDnTNl+REKJjcmQG6B1ZZZRWm/F315HUWK1NI0bFWJrBNqSVYDI30gwWLmuCCdGROJwA3XrrrezcuROARx99lLfffhs3Nzdmz57NnDlzHDqX0Wjk6NGj9OvX73RAGg39+vXj0KFDdR5z6NAhu/0BBgwYwOHDh22PzWYzb775JldffTVRUU1fNFEI0U45MAP0+jTLaNRR0d5oNc1r/rIaHO6Jp4uGggoje3MbGQ0WcMZIsFwZCSZEe+dw1cjs2bNtP1966aXs37+f7du30717d/r37+/QuYqLizGbzbVqjvz8/MjMzKzzmMLCQnx9fe22+fr6UlhYaHv8ww8/oNVqufzyy5sUh8FgsFvfTFEU3N3dbT93ddYykLJoeVLW9bB2gO4W3WDZVBrNtuavi+J8G9y3KWXtotMyMtqHn48U8ltaCQPC629SUxQFc0Q0HD0IWSdQusU0+JK6ErmvW4+UddOdc9tQbGwssbGxTgjFOY4ePcqKFSuYP39+k2+A7777jm+//db2OC4ujvnz5xMcHNxSYXZIYWFhbR1ClyFlbS8zJxMTENRvEK7h4fXu9/P+HCqNKt183bi4b1yT3gMaK+trB7vy85EdbE4vZV5IaIOTIhYkJFJ29CBeJafwbSDOrkru69YjZd24ZiVAv/76K6+++ir79+8HoHfv3tx///1ceumlDp3Hx8cHjUZjV3sDllqe+voT+fn51eogXVRUZNt///79FBcXc88999ieN5vNLFq0iBUrVvD222/XOufEiROZMGGC7bH1TTMvLw+j0ejQa+qMFEUhLCyM7Oxs1CYMBxbNJ2Vdm1peiulkLgAnXTxQsupvXvphh6WpbESUJ9nZ2Q2et6llHa5TCXDXUVBh5KftRxgWWf+8QmY/yz9NJQf3Ut5AnF2N3Netp6uXtU6na3LlhcMJ0DvvvMOsWbOYNGkSs2bNAmDz5s1cccUVvPrqq/zjH/9wKND4+Hj27NnDeeedB1iSlT179jB+/Pg6j0lMTGT37t12Q9p37dpFjx49ALjoootq9RF6/vnnueiiixgzZkyd59Tr9ej1dU9d3xVvoPqoqirl0UqkrE9TM06vAYa7R73lUlplYnumZfj7hTE+TS6/xspao8DIaG+WHTzFumPFDO3WwMgy61D4jOPy+6uD3NetR8q6cQ4nQP/617949dVXuffee23bZs6cyciRI/nXv/7lUAIEMGHCBN5++23i4+Pp3r07K1asoKqqitGjRwPw1ltvERAQwNSpUwG44oormDdvHsuWLWPw4MH8/vvvpKSkcOeddwLg7e2Nt7f9f2g6nQ4/Pz8iIiIcfblCiDZmmwG6kRFgm06UYDRb1v6K8Wve5If1uTDWh2UHT/FHeglVRjOuunqawexGghlRZASqEO2Ww3+dhYWFddbO/OUvf+GRRx5xOIARI0ZQXFzMkiVLKCwsJDY2ln/+85+2Jq38/Hy7dvyePXsyc+ZMvvrqK7788kvCw8OZM2cO0dFNWx9ICNHBNHEGaOvorwtjHV/6ojGJgW6EeenJLjXwR3pp/SvEBwSBqztUVUBu5ulFUoUQ7Y7DCdDVV1/Nd999V2vI+w8//GDXj8YR48ePr7fJa968ebW2DR8+nOHDhzf5/HX1+xFCdAxNWQX+VIWRPTWLll4YU09ycg4URWFUjA/f7j3J+rTiehMgRVEscaYesgzdlwRIiHarSQnQG2+8Yfs5KSmJ559/nrVr19qSkM2bN/P777/z4IMPtkyUQoiuqwk1QBvSijGrNTU13i4tEsZFsZYEaHtmKaVVJrxctXXup0REoaYeQs04jjJkZIvEIoQ4d01KgF599VW7x/7+/uzbt499+/bZtvn5+fHJJ5/wxBNPODdCIUSXZVkD7KTlQQN9gH6raf66qL6mKSeI8XMlxteVtKIqNp0o4bLufnXvaFsSQ9YEE6I9a1ICZF36QgghWlVWuuW7X2C9a4DllFZzML/SMlqrBZq/znRhrDdpO6tYn1ZcbwKkhEejckbnbSFEu+TwUhhnkmF2QoiWZFsDrIHmr3WpltqfviEeBLi37Kgraw3Tnpxy8svrWe/LGmuOZSSYEKJ9alYCtGjRIvr164e7uzvu7u7079+f//znP86OTQjR1aUfA+rv/2NWVX45apkYdWy8b537OFOolwt9Qtwxq7D6aFHdOwVY5ivCZITs9BaPSQjRPA4nQK+88gp33303V1xxBUuWLGHJkiWMHz+eu+66q1ZfISGEOBdq2hHLD7Hd63x+T045OaUGPPQaRkQ7f/h7XS5N8APg15QizHXUgCuKAtEJAKhpKa0SkxDCcQ7XF7/55pu8++67TJ8+3bbt6quvpk+fPsybN89usVQhhGgu1WSCE0cBUGLqToB+SbHUwlwY41P/5IRONiLamw+25pBdamBfbgV9Qz1q7aPEdEc9uBuOHYaRl7RKXEIIxzj8jpGVlcWIESNqbR8xYgRZsvaNEMJZso5DdbWlOSmk9sKipdUmNp2wrPx+WfeWb/6yctNpbJMt/l9KYd071dRY2WqwhBDtjsMJUPfu3VmyZEmt7V9//bVtPS4hhDhX6rGa5CE6AUVT+63qt2PFVJtUYnxd6R7g1qqxWZvBNh4voazaVOt5W43ViVRUYz2dpYUQbcrhJrCnn36ayZMns379ekaOtEzy9fvvv/Prr7/WmRgJIUSz1NSeKPX0/7E2f13a3dduuZzWkBjoRpSvCyeKqvktrZjxPfztdwgOAw9PKC+zzAdU0ydICNF+OFwDdP311/PHH38QFBTE999/z/fff09QUBB//PEHEydObIkYhRBdkK0GKKZ2zfKxU5UcKahEp4HRLTj5YX0UReHSBEuzmzURO/t5amqBbK9DCNGuOFQDZDAY+Pvf/86TTz7J559/3lIxCSG6ONVogHTLBKx11QBZk47zIr3xcWubFddHx/myKDmPwycrSSusqrUCvRLbHXX/zpqarHFtEqMQon4O1QDp9Xr++9//tlQsQghhkXEcjEbw8IKgULunDCYza1Nrmr9aYe6f+vi56RgW6QXAL3V0hlZqaq6kBkiI9snhJrBrr72W77//vgVCEUIICzXtsOWH2O61+vf8kV5KSbWZQHcdA8PrXh6jtVxW0xl6bWoxBtNZcwJZa64y0lAN1a0bmBCiUQ7XHffo0YNnnnmG33//nSFDhuDpaf8GNHPmTKcFJ4ToompqTeqa/8fa/DU23hetpnU7P59tULgn/u46TlUY2ZpRwojoM/ojBQSDlw+UFkN6GsTJKFkh2hOHE6CPP/4YPz8/tm3bxrZt2+yeUxRFEiAhxDlT6xkBll1STXJWGQCXJLRd85eVVqNwSbwv3+49ycrDhXYJkKIollqgPdtR0w6jSAIkRLvicAIkK8MLIVqSaqiGjDTLg7NGgK04dAoVGBzuSbi3S+sHV4dx3f1Yuu8kO7PLOVFURZTv6c7QSkx31D3bbTVaQoj2Q1aDF0K0L+nHwGQCb1/LwqI1Ko1m28KnV/b0r+fg1hfipWdYN0tn6B8PnrJ7TpEZoYVot5qVAH388cf07dsXNzc33Nzc6Nu3Lx999JGzYxNCdEGn5/+x7wC9LrWYsmozYV56Bke0befns02oScjWpBbZzwxtrcHKPI5aVdUGkQkh6uNwAvTUU08xa9YsrrrqKr755hu++eYbrrrqKmbPns1TTz3VEjEKIbqSmhFgZ/b/UVXVVrtyRaI/mlae+bkx/UI9iPJ1odKosvroGRMj+gWArz+YzbZ5jYQQ7YPDCdC7777Lhx9+yAsvvMDVV1/N1VdfzQsvvMAHH3zAO++80xIxCiG6ELWOEWB7cstJK6rCVau0i87PZ1MUhSsTLbVAPx46hbmma4DMCC1E++VwAmQwGBg6dGit7UOGDMFoNDolKCFE16RWVUHmCcuDM2qArLU/Y+J98XLRtkVojRod54unXkNWiYEdNSPV4IxEzjq3kRCiXXA4Afrb3/7Gu+++W2v7Bx98wLRp05wSlBCiizpxFFQz+Aag+AUCkFdmYEt6KWBp/mqv3PUaxtbUTi0/ozO0rSO01AAJ0a40axGdjz/+mJ9//pkLLrgAgC1btnD8+HGmT5/OAw88YNvvlVdecU6UQoguwTZa6ozan5WHCzGrln42Z6+31d5cmejP8gOn2J5ZRlZJtWWovrUGKDsdtbICxc29bYMUQgDNSID27NnD4MGDAUhJSQEgKCiIoKAg9uzZY9vv7OnrhRCiUWf1/6k2mfn5SCHQvoa+1yfc24XBEZ5syyzjx0OnuH1IKIqvP/gHwal8OH4UEvu0dZhCCJqRAK1Zs6Yl4hBCiFozQK8/VkxxlYlgDx3n1cy1095dmejPtswyfk0pYmr/IDz0Wkst0Kl81LQjKJIACdEunNNEiEII4SxqRTlkp1sexCRgVlW+21cAwOWJ/m2+7ldTDYrwpJuPC+WG07VXtiH9qYfaLjAhhB1JgIQQ7cORfaCqEBKO4uPP1vRS0our8dBrGN/Dr62jazKNojCxdwAAP+w/hcFkRuneGwD18F6ZPV+IdkISICFEu6Ae3A2AktgXVVX5du9JwDLyy7OdDn2vz+g4HwLcdRRUGFmbWgxxiaDTQWEB5Ga1dXhCCCQBEkK0E+qhvZYfevZlT245h05WotcoXNUBOj+fTa/VcG1NLdDSfQWYdS4Q3xMA9dCehg4VQrQSSYCEEG1OrSwHawfoxL78d6+l78+lCb74uTdrto42d1l3X7xcNGSWVLMlvQQlsa/liZqaLiFE25IESAjR9o7st6yXFRxGKt4kZ5WhUWBiUkBbR9ZsHnqtbeLGb/cWQA9LAqQekn5AQrQHkgAJIdqcetDSLKQk9rH1/RkV40Ool0tbhnXOJvT0x0WrkFJQyS6vGNDqLPMB5WW3dWhCdHmSAAkh2py1X0xm3EA2nSgB4PoOXPtj5eum47LufgD893BNZ2ikH5AQ7YEkQEKINqVWVsAxy0KhPxCNWYUhEZ7E+ru1cWTOcW2vALQK7Mou50jCeZaNByUBEqKtSQIkhGhbNf1/8sMSWJ1ZDcCkPoFtHJTzhHjpuSjWB4Bv3awjwXZLPyAh2pgkQEKINmVtDvq2xxUYzSp9QtxJCvFo46ica1KfQDQK/FGk5bBvDBTkQ35OW4clRJcmCZAQok2ph/aQ7RbAr9pIAG4aENzGETlfpK8rF9fUAn3Z6xpA+gEJ0dYkARJCtBm1qhKOHebr2MswoTA43LPT1f5YTekXhFaBHe6R7PWNk35AQrQxSYCEEG0nZT/HXYNYHzoYgGmdsPbHKszbxTYi7Iu48ZilBkiINiUJkBCizagH9/JV3F9QFYXhUV50D+wcI7/qc0PfQFw0Cvv94khW/VClH5AQbUYSICFEmzmSmsnm4H4oqEzt33lrf6wCPfRcnugHwJdx4zFLM5gQbUYSICFEm1CrqvhCbxkWflG4C9F+rq0eg9FobvVrXt8nEDdMpHhHsvlIbqtfXwhhIQmQEKJN7Nt1kOSAnmhVE1OGRrbqtY0Glc3rSvj0nYOkpVS16rV93XRcFWIC4EtjFCazzAckRFuQBEgI0epUVeWzI5ZJDy8xZRDh03q1P1WVZjauKSU3y4jJpLJzazmH9la26sSE15wfj6ehghNuQazend5q1xVCnCYJkBCi1a0/VsxBsxdupiomx+pa7bplJSY2/FJK0SkTLq4Kvfv5AXBwTyW7t1WgtlJtjLePF5PKdgPw+b5iyg2mVrmuEOI0SYCEEK2q0mjms+2W0U/XHV9D4KDBrXLdwgIjG34tpbzMjIenhlGXenPRpRH0G+IOQFpKNX9uLMdkbJ0k6MpYD8LL8yg0a/lmz8lWuaYQ4jRJgIQQreq7fSc5WWkmuLKAq/Q5KD5+LX7NnEwDG9eUUl2l4uOnZeQlXnh5awGI6+HGkBEeaDSQnWFg09pSqipbvnO0y8DzuCVlOQD/O1BAVkl1i19TCHGaJEBCiFaTV2Zg6b4CAG5O+RG3fi1f+5N6uIo/NpRhMkJQqI4RY71wc7d/64uIcuGCi73Q6eHUSUszWWlxCzdLRUQxVClgQMEhjGb4LFlGhAnRmiQBEkK0mkU78qg2qSQVpTI8bzfKgPNb7FqqWWXP9nL2bK8AFaLiXDj/Qk/0eqXO/QNDdIy61BsPTw3lZWY2/FpKfq6hxeJTFAXNgPO49cgyNKqZTSdK2Z1T1mLXE0LYkwRICNEqDuRVsP5YMQoqtx7+H0pwGEREtci1jAaVrb+XkXrY0qzUq78bA4a5o9HWnfxYeftoGXWpF/6BWgzVKpvXlXEiteWappQB5xFdnsO4vO0AfLwtV4bFC9FKJAESQrQ4s6ry0TZLx+ex5gwSSjNQ+g9DURpOSJqjvMzM76tLyMk0otHCkBEe9Ojt1uRrubppGD7ai4goPaoZdvxRzr6dLTRCrEcfcPdkyqHleGkh9VQVv6QUOf86QohaJAESQrS4n48UcvhkJW46ham7vwUstR/Olp9r5Lf/K6G40IyLq8KI0V5ERLk4fB6tTmHwcA96JFnmJ0o5YOlHZKh2bhKk6HQofQfjbSxnsuYYAP/ZkUthpdGp1xFC1CYJkBCiRZ0sN/BZch4A07qp+J/KBHdPS+2HEx07UsXmtZaRXr7+Wi76izf+Qc2fY0hRFHr1c2fwcA80WsjNMvLbLyXO7xxdkwiO3/sjcf6ulFSb+WSbdIgWoqVJAiSEaFEfbcul3GCmR6Abl+dsAUDpOxhF55wJEM0mlV1/llsmMlShW7SeEWO9cPdwzttbt2gXRo71ws1DoazEzG+/lJCT6bzO0UrfIaDRoM1M4x+JejQKrDtWzPbMUqddQwhRmyRAQogWsyW9hI3HS9Ao8I/zw9Ds2mp5wknNXxXlZn5fXUpaiqWjcu/+bgy6wAOdzrl9i/wCdFx0mTcBQVqMBvjjtzIO7nHO8hmKp5etNizh2HYm9PQH4N0/cqhsg8VahegqWm8O+gasXLmSZcuWUVhYSExMDDNmzKB79+717r9p0ya+/vpr8vLyCAsLY9q0aQwebJlPxGg08tVXX5GcnExubi4eHh7069ePqVOnEhAQ0FovSYgur9xg4v0/LB2fr+0dQKzhFObM46DRWGo9zlFetoHtm8uprlLR6xUGXeBBaIT+nM9bH2vn6D3JFaSlVHNobyWnThoZfIEHLq7n9r+kMuA81IO7UXf+wdSZE9h0vITcMgNf7srn1sEhTnoFQogztXkN0MaNG1m0aBGTJk1i/vz5xMTE8Pzzz1NUVPdIiIMHD/L6668zduxY5s+fz7Bhw1iwYAHHjx8HoLq6mtTUVK6//nrmz5/Pgw8+SGZmJi+99FJrviwhurzPd+RxssJImJeeKf2CUHf9YXmiRx9LrUczqarKoX2VbF5XZpvZ+aK/eLVo8mOl0Sr0H+rBwPMt/YLyso2s/7mEwpPn1mnZ1iH88F7cDOXcdV4YYJkhOqWg8lzDFkLUoc0ToOXLl3PJJZcwZswYIiMjueOOO3BxcWHNmjV17r9ixQoGDhzI1VdfTWRkJFOmTCE+Pp6VK1cC4OHhwZNPPsmIESOIiIggMTGRGTNmcPToUfLz81vzpQnRZR3Mr2DFoUIA7j4vDFedBnWnpflLGdj85q+qKrOl+Wm3JSmIjndh1KVeeHhpzzlmR0TFunDhpd54emmoKFf5fXUpqYermt0kpoSEQ3gUmEyoe7YztJsXo2K8Mavw9pYsmRtIiBbQpgmQ0Wjk6NGj9OvXz7ZNo9HQr18/Dh06VOcxhw4dstsfYMCAARw+fLje65SXl6MoCh4eHs4JXAhRryqjmTc2ZaECY+J8GBjuiVpWCof3AqD0b14ClJ9rZP2qEnKzjGg0MGCYOwOGeaBtZHLDluLjp+XCy7wJ66bHbIY92yv48/dyqqub12/HVgu0w9JR/I4hoXi6aEgpqOK/+2SxVCGcrU37ABUXF2M2m/Hz87Pb7ufnR2ZmZp3HFBYW4uvra7fN19eXwsLCOvevrq5m8eLFjBw5st4EyGAwYDCcHtWhKAru7u62n7s6axlIWbS8zlDWn+3II724mgB3HbcNDUVRFNRtv4PJBN1i0IRGOHQ+1Wxp8jq4txJU8PLWMGSEJ77+5/b25YyydnFVGDbKk6OHqti3s4LsDANFq0wMGeFJgIND8DWDh2Na+V/UnX9AVQX+Hh7cMTSU1zZm8dWufAZHeNEj0L3ZsbalznBfdxRS1k3XLjpBtxSj0cirr74KwO23317vft999x3ffvut7XFcXBzz588nODi4xWPsSMLCwto6hC6jo5b1xtST/HjwFADzruxDz9hAAHK2baAa8B13DT7h4U0+X2mJgdUrM8hKtzR5JSb5MmpsOHq98yqvnVHWERHQs1cFv6xIp7jIwO+/ljBsRAgDhgai0TTtg0gNCyM7Ihpj5nF8U/bjeekEpoaFsTvfyK+H8nhjSy6fTx+Gm751m/ucqaPe1x2RlHXj2jQB8vHxQaPR1Kq9KSwsrFUrZOXn51erg3RRUVGt/a3JT35+Pk899VSDzV8TJ05kwoQJtsfWzDkvLw+jUWZkVRSFsLAwsrOznTLsV9SvI5d1caWRecuPAnBlT39i3arJyspCzcnEtG8nKBpKkwZTlpXVpPNlHK9m19ZyDAYVrQ76D/UgKlZDfn6OU+JtibIeeaknu7aWkXHcwB+/55JyqIBBF3jg4dm0pMV83kXw/eec+mkpxX0sI+VuHeBH8olTpBWU88KKXbYO0h1JR76vO5quXtY6na7JlRdtmgDpdDri4+PZs2cP551naf82m83s2bOH8ePH13lMYmIiu3fv5sorr7Rt27VrFz169LA9tiY/2dnZzJ07F29v7wbj0Ov16PV1jyDpijdQfVRVlfJoJR2trFVV5e0tWZyqNBHp48LNA4Nt8Zs3rbbslDQAfAMafV2GapXd28vJSLM0S/v6axk83AMvb22LlIkzy1qng0EXeBAUWs2e5ApO5hlZu7KYfoM96Bajb7xZ4oLR8P3nqAd2Yc7PQQkMwdtFy8zh4cxbfYIVh04xNMKTId2aP4quLXW0+7ojk7JuXJuPApswYQK//vora9euJT09nY8++oiqqipGjx4NwFtvvcUXX3xh2/+KK65g586dLFu2jIyMDJYsWUJKSootYTIajbzyyiscPXqU++67D7PZTGFhIYWFhVKbI0QLWX20iE0nStEq8MDICFx1lrcW1WxG3WQZ0akMH9voeU7mGlm3qtiS/CjQI8mVUZd64eXdcZp9FEUhOt6Vi8d54x9omTgxeUs52zeVU13VcAdpJTAEeloGeVjLDWBQuKdtgsQ3N2dRJGuFCXHO2rwP0IgRIyguLmbJkiUUFhYSGxvLP//5T1uTVn5+vt1/TT179mTmzJl89dVXfPnll4SHhzNnzhyio6MBKCgo4M8//wTg4YcftrvW3Llz6dPHuesPCdHVZZVU88GflrWrpvYPJiHA7fSTh/fCyVxw90AZdEG95zAaVQ7sqiD1sGVGZw9PDYMu8HC4I3F74umlZcRYL47sr+LQ3koyTxg4mWek/1APwrrVP2eRMmKsZVLETWtQr7zB9v43fWAwO7PLOFFUzVtbsvnnRd2ko6sQ50BRpY6sXnl5eXajw7oqRVEIDw+39OeQ26VFdbSyrjKaeXhVGscKq0gKdue5S6PRntHp1/zp66i//4py4V/QTL+3znOczDOy449yyksttSPRcS70GeSOTt+yH+6tWdaFBUaSN5dTWmJ5jd1i9PQd5F7nDNJqZQXmh26Gqko0j76EktDL9tzRgkrmrDqG0Qy3DApmYlJgi8btLB3tvu7IunpZ6/X6JvcBavMmMCFEx6SqKu9tzeZYYRW+rloeGhVhl/yoVZWof24E6m7+MhpV9mwvZ+PqUspLzbi5K5x/kScDzvNo8eSntfkF6LhonDcJvVxBgYw0A2tXlpCdUfsfLMXNHWXwcADUjavtnosPcOP2IaEALNqRx56c8pYPXohOShIgIUSz/HykiNVHi9Eo8NCoCAI97Jt11ORNUFUBwWHQvbfdc7lZlgTA2uQVHe/C6PE+hIS3/HIWbUWrVUga4M6oS7zw8tZQVamydUMZ2zaWUVlh3zfImjCqf/6Gaqi2e258Dz9Gx/pgVmHBhgxOlksttRDNIQmQEMJhh09W8MGfluHoNw0Ipn+YZ619rLUXygVjbH1VqirNbN9Uxpb1ZVSUmXH3qKn1GeaB3qVz1frUxz/QUhvUvZcrigKZJwys/amEtJQzltLo2Q8CgqC8DHXHH3bHK4rCPeeHEePnSmGliX9vyMQoS2UI4TBJgIQQDimuMvHSbxkYzSrnR3pxXVJArX3Ugjw4sAsAZfgYVFXlRGoVa34qIeO4ZYRXXKJrm9b6qKraZiNDtVqF3gPcufAyL3z9tRgMKrv+rGDjmlJKik0oGg3KBWMscW5aXet4V52GRy/shodew768ChYl57b2SxCiw+u4QyyEEK3OZFZ5+fdMcsssq7zPHB5e50gkdcs6UFVI7EOJPpjdq0spyDcB4OOnYcBQD/wC2+btp7y8nH379rF3716Ki4uJjo6mb9++xMXFodG07v+Evv46Rl3qRerhKg7urqQgz8S6VSUkJLrS/bwxaFZ8A3u3oxadQvH1tzs2wseFmcPDeXF9Bj8cOEX3QHcuivVp1fiF6MgkARJCNImqqnzwZw47sspw0So8elE3vFxqz8+jmkyo61dh0LpzuPfNpP1cgqqCVguJfd2IT3Rt8vIQzow9PT2dPXv2kJKSgtl8us9NWloaaWlpeHp60qdPH/r06dPo5KnOpNEoJPR0IzxSz+5tFeRmGTlyoIp0D29697uasN3/Q/1tFcqEKbWOHR7lzXVJASzdV8Abm7II9tTRO1gWfRaiKSQBEkI0yf8OnGLl4UIU4MGREcT5u9W5n7p9Exm6BA6MvJGqMsvCxeGRevoMcsfdo3VrWEpLS9m/fz/79u2zW0InNDSUfv360bdvX3777Tf27t1LWVkZf/zxB1u3biU6Opo+ffoQFxeHVts6kzB6eGo5/yIvsjMM7EmuoKLMTHLoJIK0iSRt/B8+465D0bvUOu6mAcFkFFezJb2Uf63L4KVxMYR7195PCGFP5gFqgMwDZNHV55VoTe21rDefKOHF9RmowK2Dg7m2d93zzxTkG9jz4yGK3LoB4Omloe8Qd0LCWq+fj8lk4tixY+zbt49jx47ZylGv19OrVy/69u1LcHCwXVkbDAaOHj3K7t27ycjIsJ3L3d2d3r17k5SUREBA7b5OLcVoVDmyv5KUA1WYzaCYjcR459PzL4m4uNROIiuNZv75f8dJKaikm48LL/0lBi/X9jN7dnu9rzujrl7WjswDJAlQAyQBsujqf1CtqT2W9ZGTlfzz/9KoMqmM7+HHXcNCa/X7qSg3s39nhaWDM6A1VtIjyY34/r5ota3T3JWfn8++ffs4ePAgFRUVtu0REREkJSXRo0cPuzX/6ivrwsJC9u7dy/79+ykvPz3PTmhoKElJSSQmJuLq6toqr6msxMTe/0slxxAEgN5FoWdfN2ISXGo1I54sNzBnVRony430C/Vg7pgo9K1U9o1pj/d1Z9XVy1oSICeRBMiiq/9Btab2VtZ5ZZYP1VMVRgaFe/Lk6Ei7yQ4NBpWUA5WkHKzCbAJUlcjM9fQMzsfjb7e1eHzl5eUcOnSIAwcOkJt7eiSUh4cHvXr1arDmprGyNplMpKWlsXfvXruaJK1WS0JCAr169SI6OrrFO06rFeXk/GsB+2Ovp9QrEgAvHw29+7sTGqGzS0aPnarkkZ+PU2k0Mzbel5kXhLWL5TLa233dmXX1snYkAZI+QEKIOp2qMPLkr8c5VWEkxteVhy88PdOz2aSSllLNoX2VVFdZ3mQDfE30/r+n8S0+hmbqOy0Wl9Fo5OjRoxw4cIC0tDTbm7xGoyEuLo6kpCSio6PPue+OVqslPj6e+Ph4ysvLOXDgAPv27aOgoIBDhw5x6NAhPDw8SExMpFevXrZmNWdT3D0IGRBN4M9PcGLQVA6FjaO02MzWDWUEBGtJGuCOf82Iulh/Nx4eFcFz69JZfbQIbxcNtw4OaRdJkBDtjSRAQohaSqpMzP31BFklBkI8dTw1NhIPvRZVVck8YeDA7krb2l2e3hqSBrgTvPpDKD4GA85DCYt0ajxms5n09HQOHjxISkoK1dWnZ0cODQ2lV69e9OjRAw+PlhkB5eHhweDBgxk0aBC5ubkcOHCAgwcPUl5ezo4dO9ixYwf+/v707NmTnj174uvr69TrK2OvQvPL/4jZ/jmRjwwmpbwbRw9VUZBnYsMvpYRH6unVzw0vHy1Dunlx7/lhvLE5mx8OnMJDr2VK/yCnxiNEZyAJkBDCTrnBxNNrTpBWVIW/u45nLokm0F1HdoaBg7srKC6yJD6ubgqJfdyIjndBKSvGXDNhn+Yv1zolDlVVyc7O5vDhwxw6dMiuP463tzc9e/akV69erdo5WVEUQkNDCQ0NZdSoURw/fpwDBw5w9OhRTp06xebNm9m8eTNhYWEkJibSo0cPPD1rz5Lt8HUDglCGXYi6eS261d/R+845xHZ35eCeSk6kVpOVbiArw0BUrAuJfVy5JMGPcoOZj7bl8uXufNz1Gq7p3XrlJERHIAmQEMKmymjm+bXpHD5ZiberlqfHRKIrU9iwuZTCAstEhjo9JPS0zOdjXbTUvGYFGKohtgf06NPs66uqSl5eHocOHeLw4cOUlJTYnnNzc6NHjx707NmT8PC6J2BsTVqtlri4OOLi4qiqqiIlJYWDBw+Snp5OdnY22dnZrF+/nm7dupGYmEhCQsI51VApl12Lunkt6rbfUfOn4x4UysDzPIhPdOXA7gpyMo2cSK0mPa2amHgXLkvyo8JoZvHOfD7Znou7XsNfuvs5rwCE6OAkARJCAJbk58X1GezJrcBDp+Gh/hGkbzdQkF8JWCYyjEt0JaGnKy6upzv+qtVVqGt+BED5y0SHExNr0nP48GGOHDliN1+PXq8nPj6exMREp/TraSmurq4kJSWRlJREWVmZrdYqOzubjIwMMjIyWLt2LZGRkfTo0YP4+HiHkyElOh56D4D9O1F/+R/KlDsA8PHTct6FXpzKN3JgTyX5OUaOHanmeGo1veM9uL5HAP89XMA7W7LRaxTGxDu3eU6IjkoSICEEFQYz/1qXzq6ccmK1rlzpE8CJZMsISI0GYhJc6N7bDTf32iOe1DUroLQYAkNQBg9v0vVUVSUnJ4cjR45w5MgRiouLbc/pdDpiY2NJTEwkNjYWna5jvU15enoycOBABg4cSHFxsS0ZysvL48SJE5w4cYI1a9bQrVs3unfvTkJCQpObyTR/mYh5/07U31ahjrsOxf/0fEz+QTqGj/YiP8fSR+vUSRPHDlcTqHFhin8Qy04V8PqmLKpNKuN6+LXQqxei4+hY7yxCCKcrqzbxzOp0KgvMXKsLJAg9VcUqGi3ExLuQ0Mut3hmc1dJi1B+XAKBcdSNKAzU0ZrOZjIwMUlJSSElJoayszPacTqcjJiaGHj16EBsbi4tL55jJ2MfHhyFDhjBkyBAKCws5cuQIhw8fJi8vj/T0dNLT01m7di3h4eEkJCSQkJDQcAfqPoMgoRekHED94XOUW2bV2iUoVM/IEB35OUYO7a2kIN+EV4mOKbpgDpkr+PyPPKpMZq7uJX2CRNcmCZAQXVhhhZEPfs6lb4UnflrL24FGC7EJriT0cq2zxudM6o9LoKIMImNRho+u9bzBYCAtLY2jR49y7NgxKisrbc/p9XpiY2Pp3r07sbGxdpMUdkZ+fn4MHTqUoUOHUlRUZKv9ysnJISsri6ysLDZs2EBQUJBt+P3ZQ+sVRUHz1xmYX3wYdeNq1EuvRomMq3UtRVEIDtMTFKrjZK6RQ/uqOJlrpKfGg0TFndTkKr4pyeevw2R0mOi6JAESogsyVJvZf7CSg/sr6a16gAIaHSQkuhLXwxVXt8Yn91NzsyzNX4Dmr7eiaCy1P6WlpRw7doyjR49y4sQJTCaT7Rg3Nzfi4+NJSEggKiqqwzVvOYuvr6+tZqikpISjR4+SkpJCRkYG+fn55Ofn88cff+Dl5WXraB0ZGYlOp0NJ6IUyZCTqtt8xf/sp2vufrvc6iqIQFKonKFRPQZ6RIwcqyck0Eq+4wVFYml3AyCFehITr27xTuRCtrWu++wjRRZWXmjh6qIq0o9WYTeCGhgpMJPR0ZUAfT9uorqZQly4CkxG1zyByAyNI3byZ1NRU8vLy7Pbz8fGx1WhERES0+MzJHY23tzcDBgxgwIABVFRU2JLH48ePU1payu7du9m9ezd6vZ6oqCji4uKIufyvuO/YAnuTUfcmo/QZ1Oh1AoJ1nBfsRXGhiTVbiuCUgr5cwx+/lePloyE+0ZXIWJdWW7pEiLYmS2E0QJbCsOjqU6u3ppYoa1VVOZlnJPVwNdkZBqg5bYFqIN2lilvHBhPh59jaVpUHdnPso9c57h1EWlgsFVXVds+HhYURFxdHfHw8AQEB7bJ2ob3f10ajkRMnTpCamkpqaqpdnymAYJ1CTGYKMW4uhD36PFqdY02Iq/YWsn1XGYmKOy6KJSl1cVWISXAhtnvjzZ+OaO9l3Zl09bKWpTCEEBiNKhlp1aQerqKkZvJCgHS1it3mMnwDtTw2OhKfJqwarqoqubm5HD9+nGPHjpGdmYka3d/yZFU1er2e6Oho4uLiiI2NbbEZmbsSnU5na/6yThVgTYZyc3PJM6rkhcTzJ+D2/gdEJyQQExNDdHR0k0aVjevjR7C/jld/yyLG5Ep/nSdUaTm8r4oj+6sIj9QT18MV/yBtu0xghThXkgAJ0cmUFJtIS6kmPbUag8G6gCeUe5lYfvIUpzByUawPMy8IQ6+t/7/80tJSjh8/zokTJ0hLS7PrwIyi4F9VRuygocT27EVERES7naOnM1AUhZCQEEJCQjj//PMpLy8nLS2N1M0bOF5YTCXY1icDCAoKIjo6mujoaCIiIurtazU4wotn/xLFM2vT2VNeTpKLB2O9fakosix5knnCgI+flpgEFyJjXBxqIhWivZMmsAZIE5hFV69SbU3NLWuTSSU73UBaShUn8053Ovbw1BAep+e77Hz+yLY0odzQN5Cp/YNq/VdfVVVFZmYmJ06c4Pjx4xQUFNg9r9frieoWQdSO34nOPobvuGvQXDPtHF5t2+oM97VqqMb45D1kV1RxYuAojrv7kpuba7ePVqslIiKC6OhooqKi6ly09WS5gWfXppN6qgqdBm7rHUpEtQsZxw2Ya24nrQ4iY1yISXDB19+x/507Q1l3FF29rKUJTIguorjQxPHUajLSqm2rsqNAaLiOmARXSl2NvLQhk+xSAy5ahbvPC2NszUzARqORrKws0tPTOXHiBDk5ObXeMENDQ4mKiiImJoawsDCUL99HPXHAMunhuImt/XLFWRS9C7rJtxPxzr+I2PQTwx+dT0VYlC2JPX78OGVlZbYJGMEyEq9bt25ERUURFRWFn58fgR56/nVZNG9symLTiVLe35vD2HhfZlweTG66kbSUaspKzKSlVJOWUo2vv5boeBe6RevRu0indtExSQ1QA6QGyKKr/0fRmppS1oZqMxnHDZxIrbatzwXg5q4QHe9CdLwr7h4a1hwt4p0/sqk2qYR66Xl4RBju1YW2Cfiys7PthqiDZXh2ZGSkrbbAzc3N9py6Lxnzq3MB0Dz4HEqv/i1QAq2nM93X5g9fRv1jHYR1Q/Pkaygulk7tqqpSUFBgS4gyMjJqvad5enoSGRlJt27diIyM5Nd0I5/vysesQry/K49e1I0QTz0ncy2JUFaGAbWmS5lGC+GReqLjXAgM0dXbV6gzlXV719XL2pEaIEmAGiAJkEVX/4NqTfWVtdmskpdtJP2YZSSX2WzdH0K7WT6AgsN0aDQKlUYzH2/L4ZfDBfgai+jtVkqcroT83ByMRqPd9Tw8PIiKiiIyMpKoqCh8fHzqjEstL8M87z44lY8y5ko0U//eYmXQWjrTfa2WlWCeex8UFaBcdg2aG26rcz+TyURubq6tRigrKwuz2Wy3j5eXFx4BofxR5EaW4ofGzYt/XBDOiGjLvVFVaSY9rZrjR6spLT59rLuHQrcYFyJjXfD2se8P1pnKur3r6mUtCZCTSAJk0dX/oFrTmWVtNpspLDCRkVZNxnHD6SYuwNtHQ1S8pWOqddLCyspKth08xqrkI+jKC/AxFqHB/vfl7u5u99++v79/k0b4mD99HfX3XyEkHM1Tr6O4ujV6THvX2e5rdddWzG8+C4qCZs4LKD2SGj3G2gyakZFhqxU8OyGqVvQU6v0JCQvn2mGJRIaHotFoUFWVwgITx49Wk3miGuMZb5V+AVoiY1yIiNbj6qbpdGXdnnX1spY+QEJ0YAX5lezfVUFGWjXlZac/jFxcFSJjXIiM1ePtq6G4uJijqalkZWWRmZlp67R85uIGnp6edOvWzfbV1ITnTOrOrZbkR1HQ3DKrUyQ/nZHSfxjKyEtQf/8V88LX0Mx9o9HflU6ns/UFAsvSJWeuYJ+dnY2LyUBIdS4cz+X74zvR6nSEh4URERFBeHg4vfqH0XeQLzmZBtLTqsnNMlJYYKKwoII9OyoICtHRLdqFAH9Tg7EI0dokARKijamqSmmxmcwT1WSdMFBSfMr2nFYHYRF6QrspmJUCcnKy+e33bLKzsykvL691rjKNB67+IYzpF09cdCS+vr7nNIeLWlaC+T9vA6BcenWTahVE21FuuB11307Iy0b976coU+9y6HjrbNPWhMhoNJKbm0vyoTSSDx3DveoUGI22fmRWgYGBhIeHExYWRnSPUMqKPMk8bqCwwER+jpH8HCO7tx0kOExPeKSesG466Twt2pw0gTVAmsAsunqVaktQVZXiQhNZ6QayThgoLTld06NowNuvDJ3bSSqr88nNzSE/P79W2Ws0GrTeARyt9uKU1pdKtwBmXBDNmDgfp0xcp5pMmF+fB/t3QlgkmidftXWu7Qw6632t7k3G/Jqls7py+4Nozr/YKectrTbx/pZsth3NxM9YSLhSTBjFVJSW1NrX1dWV0NBQAgNC0BBERYkfFaUutucVDQSH6giP1BPaTY+rqyRDztJZ7+umkiYwIdoh1axyMt9EdoaB7AwDFWVmVFXFZC6j2ngSrUsBBnMBxYX5VGVV1Tre09OTsLAwwsPDMbr782WKiaNFRtDBwHBP7jkvlFAvlzqu3Mx4v/nEkvy4uKK5c06nSn46M6XPIJTx16Ou/C/qZ2+ihkSgxPU45/N6uWh58MJu/B7tzft/5vBnpQkFGN/TlYuCjJzKzyUrK4vc3Fyqqqpsw/Ct/Hz9cXP1RzEHoFYHkp0RQG6WEf6sIDBIS1g3PWGRejw8ZUJN0TqkBqgBUgNk0dX/ozgXhmqVvGwD2ZkGcjINVFaWUWU4SbWxgGrjSQymAgzGilrH6XQ6QkJCCAsLIzQ0lLCwMLy9vSmtMvHl7nxWHDqFWQVvFw23DQlltJNqfazMv/2MuugtADR3P4YyeLjTzt1edOb7WjWbML/9L9i1FXwD0DzxMopfoNPOX1Jl4tPkXH5JKQIg0EPHjMEhjIz2xmw2c/LkSbKzLU21OTk5nDp1qo6zKLi5+KLTBOCiD8RVF4iL3h8/P1dCu+kJDdfjFyjLcDiqM9/XTSGjwJxEEiCLrv4H5Qhrf56czGpOHD9FTk4eVYYCqg0nqTIWYDZX1jpGURQCAwNtiU6fPn1QVdXujd9kVvn5SCGLd+VTUmXpTHpRrA+3DQnBz825Fbnqob2YX3kSTEaUa6aimTDFqedvLzr7fa1WlGN+8WHIPA6xPdDM+ZfTa/F2ZpfxzpZsskst75N9Qty5fUgo8QH2na+rq6sxGAzs27ePnJwccnJyai3uaqGg1/rgog/AVReIp0cgUVEhRER5EhSmw0X6DTWqs9/XjZEEyEkkAbLo6n9QjakoN5CaksuJ47nk5eVRVlFAtfEUqlr73lEUhYCAANu6TiEhIQQHB9vWaqqrrPfklPPRthxST1maxaJ8Xbh9SCgDwxtf8NJRan4O5ucfhNJilKGjUO6c02n/A+8K97Wal235fZaVoJx3McrtDzj991llNPPd/gL+u/ck1SYVjQKXJfgxbUAQvm7139dlZWXk5OSQm5tr+6qrYz+ATuOFi94fX59AwsJDiIsLISLSD00Da9l1VV3hvm6IJEBOIgmQRVf/g7JSVZWSkhLy8vLJOJFHdnY+hYX5VFYXA7XLRaNoCAgIJDTMkuQEBwcTFBSEXq+v9xpnlnXKyQo+35nHtkzLf8qeLhqm9g/i8h7+aDXOT0rUkiLM/37cUmMQnYDm4RdRXDtvv5+ucl+rB3ZZOkWbTChX/BXl2ptaJKnNKzPwaXIuG9IsnaLddRqu6e3PNb0D8HTRNamsS0tLycvLIy8vj9zcXHKy8ygrr93JGkCj6PH0DCAwMJBukcGEhwcTGBiIaye+Z5uiq9zX9ZEEyEkkAbLoan9QqqpSUVHByZMnbV+5ufmcKijAaKr7ftBqXPH2DiQkJJio6BBCQ4Px9/d3eIV0RVGodvXl9V/28VtaMQAaBf7S3Y9p/YPwcXJzl5VaXIj55ScsyY9vAJp/LkAJaNqbSEfVle5r87qVqJ+/8//tnXeUHNWZt5+qznGyNDMKM8pgUEAEywQDBhsZC4vgY4KxhFmDvxWsjVmv2YOxjXyQP1gHdr8FvNiAtWATHciWwQTbiCiBEsgaFJCENEKTuns6d1fd74/q7pnWzEgzoidp3uece+reW7errl7VVP3uexMA2rlfRjv/K4Pm2Xt3f5x7137EtnbLYxlw2fjSMVVc+emj6WjdP2BbJ5NJWltb2btnP3s+3E9beyuJRAiF2Wt5r8dPdXUVNeOqqay0BFJlZWXBy3qkM5ae694QAVQiRABZHKl/UEopYrEYHR0dtLe3097eTltbG+3t7SSTPcfqWOg47EHczgoqKqqor69hyrTxVNcEPvYH5cNIij+8187L2yMYOTt/uiHIpXOqqQ+WbnbXgahIB+ZPb4Lm3VBeif6vK9BqJwza/UYKR+pz3RfmX55APXIvwKB6ggBMpXhtVye/3dDKnkgagHF+F4uPKuez08pw2T9e11Umk2X3zjZ2frCfjz5qobOznXQ2hGH23oWmaRrBYJDKyspCqKqqoqKi4qAe2dHIWHuuD0QEUIkQAWQx2v+gDMMgHA7T0dFRCO3t7XR0dJBOp/v8nd0WwGkvx2Evx+Msp2ZcNRMnVzGu1kmwvHSzU7a1J/ndu228tquz0JF24gQ/X5lbzZSKwV11uVj8VKF/ZwXa+PpBvedIYbQ/14eD+cJTqId/BYD2+YvQLlgyqGO8DFPx0o4wD29spSVm7UMXdNk476gKzp1Zgd9Zminv2YyirSVL854Yez5sIRRqI50Nk8mGSGdDmKrnshJ5AoEAFRUVVFZWUlFRUQher3dUjn8bi891d0QAlQgRQBaj4Q8q780JhUKEQqGC0AmFQoTD4YPUW8Nh8+Owl+OwleUETxkedxk1491U1diprLFTVmFDL+G4G1Mp1jXHeOIfHaxr7poNc9JEP//n9FlUa/FBt7UKtWH+/AeW+KmoRv/OLWjjxob4gdHxXA8G5gtPox7+JQDaORegXXTFoH/os6ZiTSv8+rXthRljHrvOOTPK+cLMCsb5S+uFSadM2lsN2vZnad2foaM9RjoTImOESWdDZLJhMkYIw+xbGDmdTioqKigvLy8c88HpHDyP7MdlrD7XeUQAlQgRQBYj5Q8qL3LC4XBB6OQFTjgcPuj/lc1mx+0sw6YF0bUynPYgDnsZdlsQXbPh9mhU1tiprLZTWW0jWGZDG4SBxomMyUs7wjyzpYMPc10DuganNQS56JgqGivcQ2JrtX0L5i/+L4TaobLa6vYaVzdo9xuJjJTnejgwX3oG9eDdVmL+yehf+xaa2zNo98vb+sM9e/n7B2F+/247O8OW+NA1+OREP4tmVXLMOM+giLFMRtHRmqW9NUt7q0FHWxbTAMNMksmGLW+REUFpYTLZCMlUlN4mNuTx+XyUlZUVBFE+XlZWNuziaCw/1yArQQujmGw2S2dnZ0HUhMNhIpEIoVCISCRCNpvt87eapuHzBfC4y3DYgmAGMDMBHPYgNr3Lna1pECy3UVlto7zKEjwerz6oreAPOpI8vy3Mi9vDxDPW4E2PXefsaWUsmlVBbWDoXprmqy+gHrgTslmom4T+L99Hq6kdsvsLw49+5hcwnW7rOXj7VcyP9qBf871Bfw5susbpU8o4rTHI2j0xntrSzvp9cV7bHeW13VEay10snFHOaY3BknWPATgcGuPqHIyrszxNpqEIhww6Wt10tAXoaKslEe8SC0oZZIxODDOM7oiitE7SmQixeJhkMkEsFiMWi7F3794e9/J4PJSVlfUIwWAQn883KrvVjlTEA3QQxANkUcoWhWEYRKNRIpEInZ2dRCIRIpFIQej0vjhacV2CwSCBQBCPK4jdHkQz/WRTftJJL5rW86Xp8elUVNoor7JRXml1Z9ntg/8SimcMXtnZyXNbQ7zf1jWouj7gZNGsCs6cGsTrKK7vYLbelGGgfvdr1F+etDLmfRL9n76N5vaW9D6jhbHeUgZQWzdbnsBICPwB9Ku/i3b03JLf52C23hVK8UxTBy9tD5MyrHNOm8bJkwN8blo5nxgkr9CBJBMmHW1ZQm0GHe0GofYsRm/tLT2F0xPDZo9iEs0JowiRSJhEoueq7t2x2WwEg8E+g9vt/tj/1rH+XEsXWIkQAWQxkD+odDpNNBqls7OzELqLnVgsdshrOByOQospGCzD7Qxg0/1g+kmnvETDimSi92u4PRplFV1Cp7zShss9dIulZU1rbM9fP4jwxu7OwgvdrsOJEwJ8bnoZ8+p86H285Abr5aXaWjBX/hf8Y4N1n0WXoJ13CZo+dheSG+sfijyqvRXzrh/Dzq2g69bssM9dgDbAJRwORn9sHU0ZvLgjzF+2hgvdYwC1fgefbgxyemOQiWVDt8aPMhXRTpNQu0G4I0uo3SASMjCMnmU1DfxBHW/AwGaPobQoWaMzJ4ysBl5nZ2e/3n1+v78giAKBQFHw+Xzoh/ibHevPtQigEiECyCL/B7V79246OzuJRqOFkBc5+XTf08e7sNlsBAKBopZPIBDA6QigKR+ppJNoxKQzbBDtNFG9L/eBz68TrLBRVm4rHN2eof+gG6Zic0uCv++MsHpXZ2GrCoCJQSefnV7GGVPK+rVlRalfXkop1N+fszY2TSbA5Ub/2nVox5/8sa892hnrH4ruqHQK9cCdqNdftjKmzLTGBdVNKsn1B2JrpRRNbUn+si3E3z7oJJntegFMrXDx6cYgp0wOlnzgdH/Ii6Jwh0G4wxJE4ZBBJt37v8nh1AiU6QSCNvwB0B0JDBUlkejs4QU/lPcb8t38voIg8vv9hWM++Hw+6uvrx+xzLQKoRIwVAaSUIplMEovFiEajhf7tvKiJxWLE4/F+/YGCNXviwJZLXuR4vX6U4SEWNYlGTKIRwwqdJmYfQsdmh2CZjWB5t1Bmw+4Yvr70jGGyfl+c13d38uaHUcLdRE+528ZpDUFOawwys2pgLu1SfpRVWwvm/f8N762zMqYdhX7FN9FqJ36s6x4piAAqRimFevVF1CP3QCIGdgfaFy9D+9z5H9sbdLi2TmRM3vywk799EOGd5hhGt59Oq3SxYFKABZMCTAo6h21sjVKKRFzRGbbEUCQXYlGzz3HUTpeGP5gXRjr+oA231yRrxIqGCHQP0WgUs6+XZDd0XScYDOLxeAqCqLs4yocjbf2jPCKASsRoF0D5FY3zgiYvYrqHeDze7z8ssHYp797aOLAVEggEcDicxGMmsahJrNMk1mkJnFinUTTQ8EB0G9YLIagTLLMRyAWPVxsRAwfb4hneaY6xZk+Mdc0xEt1apn6nzkkTA5zeGGT2eO9hb1VRio+yymRQLz+LevJBy+vjcFrdGmefh6aXrltjtCMCqHdUeyvmb+6CjWusjIbp6Jd8HW36Jw77mqWwdSSZZfWuTv6+M8LmlgRmt8vUBxwcP8HPCfV+jhnnwTEC9ggzDEU0YtAZNomEjUI8Huv7XavbLM+2P2DDF9DxB3R8fitud1jv87wYOvCYb6z2F5fLVRBDXq8Xv9+P1+stpLsLpZHw/u0vIoBKxEgUQKZpkkwmSSQSBUETj8cL6QPzBvLf63a7i1oM3VsOjY2NpFIpnE6rpZXNqJzIMYhHLbETj1mCJxE3OdhtHc5c6ydgiR1/0EYgqOPxDe5MrIGSNkw2tyTYsC/O23ujbO8oXjOkwmNnwUQ/n5oc4JhxXuwlmDb/cT4UyjRRb/0d9ccHoG2/lSlenz4RAdQ3PbxBAPMWoF+4BK1u4M9SqW0dSmZ588Mor+/uZP2+GN3aIrjtGnNqfcyr9TGn1svEYfQO9UY2q4h1WmIo2mkUPOGxaN9ecAC7Hbx+Gz6/js+v480Fn1/H7dHRdQ3DMEgkErhcLnbu3ElnZ2eRZz9/PNhs2p73teP1eovEkcfj6TU9EsSSCKASMRQCKN/9lEgk+gzdBU4ymRzwC8Tj8fRQ9QcGr9dbtFdONqtIxEzicZNETKFrHlo+ihCPWUInnTp4HfItGV/AlmvFdLVqhnJQ8kDIGCZb25Js2h9nw744m1sSZMzif+eMKjfH1/uYX+9nRpW7z8HMh8vhfCiUUrB5Hebv74dd26zM8kqr++KUs8Tr0wcigA6NCrWjnnwQ9cpfQJnWIOlTP4e26GK0iqp+X2cwbR3PGKxrjrF2b4y1e6J0JItHKVd67MwZ72VOrZdPjPNS6x/+j3RvmKb1zo1GTWK5YQGWF/3gnnOwBmF7vDpenxXG15WRNWN4vDoer47boxUWclVKFSar5HsADuwdyKcH+v2z2WwFseTxeArCKB/vHtxu96AIJhFAJaLUAuj999+nqampSNykUqnDeiG43e7Cw9U95MVM93DgrAHTUCSTimTcJJGwPDbJeJfYScTNPgf1dcfh1KyWiK+rJZJvobg9I6Pb6mBEklma2pJsbknw3v4477clewieCo+dueO9zK3zMb/e16+BzB+HAQ0WzWZQa15BPf8E7NpuZbo9aAsvQjt78RG9k3spEAHUf9TeXZh/uB/Wv2ll2OxoJ56G9tnFaJOnHvL3Q2VrpRQ7OlKs3RvtsxFT4bZx9Dgvn6jxcFSNh8ZyNw7byH5XGYYqeNjzXvf8MINE7OCeI7AEktuj4fHpBVFkCSMdj1fD7dVxOnu+s9PpdKFnoXvvQveQb5wPxKuUZ968eXz6058e8O8OhgigElFqAbR27VpWr17d6zmXy1WkjPtS0F6vF7fb3esu40op0ilFKqlIJsxc6BlPJfv3X253kGtR2KiuCaC0BB6vVshzOEf2S6M78YzBBx0ptrYneb81SVNborAkf3fK3DY+UeNh9ngfc2u9TBhi93l/PhSqM4J65TnUi09bKzkDOJ1op52D9oUvowXKhqy+oxkRQANHNb2L+cRvoOndrsyj5qCfvRiOnd/nYOnhsnUqa7KlNcH6fXE2fRRna3uS7AGCyKFrTK10MaPKw4wqN9Mr3dQFnIc9jm+oUcpaFiTvnU/ETFBu2lqiVjrR90za7ug6uD06bq9mHT1WQ9bt0XG7rbjLo/e5hlomkykSRAf2YBwYDMNgwYIFnHTSSSW1hwigElFqAdTS0kJzc3MPN2BfggashzubgVTKEi6pZO/HZMIklVL9etCh+GH3ePQeLQOPVy8InNH0oVBK0ZbIsrMjxc5Qiu0dSba1p2juTPc6IWNC0Mmsag/HjPNwdI2X+sDwusf7srXKpGHDW5ivvQSb1lJYjKSsAu3ML6CdvhDNHxymWo9ORtNzPdJQO95HPf84au1qCu6Hsgq0T56OtuBMtElTisqPFFunsiZb25O8t9/yDjW1JuhM93xpumwaUyrcTK10MaXCTUO5i8llLjyOkdl9350DbZ0XSIl4l7c/kfP4J+MDaxSDNRbJ5dFxuTXcbuvo6uXodGnY+vCsKaUK39ZSbx0iAqhEDMYYIGUq0hnLU2MFs1tckeqWTiWteD8naBVwujRLrbuLVbzHaz2cHq/1cPb3Qz9SXl7dMZWiLZ5ldzjFnkia3eE0u8MpdoZTxHp5oYE1FmBapYuZVR5mVHuYUenG7xpZ42O629pMJeEfG1Dr3rA+NPFuMzwapqN95gtoJ34a7QidzjrYjMTnerSh2lpQLz6FevUFiHZ2nZjQYHWRzT0JJjSg6/qItLVSin3RDFtaE7zfluT9tgQ7OlKkjd7rON7voKHcxcSgk0llLiYEnUwMOvGVcNuOj8vhPNeGYX1vEvHeew9SuXhvi0AeDLsDXC7re+N0a11xlxXPL2tSSkQAlYhSC6Cm95Js2ZQ82B57fWKzU6yyXZaoyafdbg1n7qiXuD97uD4UhmmJnI9iafZ1Ztjbmaa5M0NzZ5rmznRhleUD0TXLszO5zMXUXCtuaqV70MfvlIT2FoIfbif0t+dRm9dBOt11rqK6q4U9YfKwVfFIQQRQ6VDZDGxai/nay7DhTWufuTxV49DmnEjVGefQUV0HzpE9Ns0wFXs702xrT7KjI8UHHUl2hlI9Bld3p8Jtoy7gpC7gpD7gpC7gYLzfyXi/A79zaGe3Dtpq8kqRzUIqYZLs3guR8yAd2EvRn1tPm+XiE/NKuwmvCKASUWoBtH1LknfXWSslOxwaDpeG09mlhp1uK+50dokcZ86VOBR7V/XFYP1BJbMmbfEsbfEMLbEMLfGsdYxl+CiaoTWeKZreeiA2DeoCTiaVOZkQdDGpzEljudUqGwnrgBwKpRS0NKOa3oWmTdYxP309T0U12twT0eafDLOOlRldJUQE0OCgYp2otatR6960tl7JdBPxNpvlvZx5LNrMY2DaUWhe//BVdgBEkll2hlPsCqW7PM+RNB2Jgw/+9Tl0xvkdjPc7qPE6qPE5qPbZqfY6qPbaKXfbSzreaCQ811YXlyKdVKS69WYUejbSVnxig4NJU0oriEUAlYhSC6BMWmGaCoeza0riaGCgy9jH0iahVJZwwqAjmaUjkQvJLO0Jg/Z4hrZEts+uqu7YdajxWa2p+oCj0MKqDTio9TtLsvbOUKBMA1o+gt3bUTu3oXZuhZ3bIB4tLqjrOGceQ/aouTDnRJjYOOJn041WRsKH4khH5btxN7yFvnkdRstHPQuNq0NrmG4Jo4ZpVvfZKBrIH00bOa903ktthY+iGUIH8Rrl0TUod9up8tqp9FihIh/cdso9NspcdsrcNlz2QzfsxvpzLQKoRIzEhRCHkqypiKUNYhkTd6CCD/buJ5LK0pkyiKYNIqmu0JkyCCcNIqnsQb02B+K2a1TlWkU1Xrt19DkY73Mwzu+g0lPa1tFgopSCzjC07EO1fgT7m6F5N6p5N+zbA9leniW7HRpnos08xmoVTz+a+ilTx+zLaygZ6x+KoSRv670b12Fu2QhN76KaNkHLvt5/4A9C/SRrL7LaiWg1tVBTC9Xj0UZ4F1p3UlmTj2IZ9ke7vNqtsSwt8Qz7Yxk6ElnMATx6HrtOmdtG0JULbhtBl52A00bAZcPv0gm47EypH08y0oHXoeFx6CVfr2wkM+oE0KpVq3jqqacIhUI0NDRw5ZVXMn369D7Lv/baazzyyCO0tLRQW1vLV77yFebPn184r5Ti0Ucf5YUXXiAWi3HUUUfx9a9/nbq6ugHVazQKoIyhSGVNkoZJMmuSzCjrmDWJZ6xjIpMLWZN4xiCeMYmnTWKZXDptEssYJLOH/2j4HDpBt40Kd3FrpsJjo8rroNJrp8pjx+sYWas/94XKZiAShs4QhDtQ4Q7oaINQG6qj1Yq37odUou+LOJ1QN9lq7TbmWrv1k9HsXYOY5aM8dIith44+ZzdGI7Brm+UV/WAr7N4OrR9x0AEkZZVQWW11D1dUWfGySrRgOZRVQLAcvH60Q+yaPhIwTEU4ZdAWz9AWz9Ke6OYxz3nNQ0mrcXng9P3+omvgdej4nDbr6NDx5uJeh47HruNx6HgdNjwOHbddw+OwWUe7jsuu47bruOwaLps+4huko0oAvfrqq9xxxx1cddVVzJgxg2eeeYbXX3+d//zP/6SsrKcbdMuWLfzwhz/ksssuY/78+bzyyis88cQT3HbbbUyebA0Mffzxx3n88ce55pprGDduHI888gi7du3i5z//+YCm3JVaALXGrVZA1lRkDEUmd8yn04ZZyMun07ly6awilUvn8/N5qaxJKid8+hgX/LHwOnSCHgdeG/hdNgJOG35n9xaIFQIuG+Vuy1XrHEFjcJRhQDoFqSSkk5BMWntkpZKoZMJa6j8Rg3gcElGIx1CxTmtWSywX4v3cY0fToLwKamrRasZDXa4VWzfJGgx6iJeyfJSHDrH10DGgbvRUCj76ELV3N+zdhdq/1/IUteyDRLx/N7TZwBfoCv4Ami8AHh94c8HjRXN7we0GlwfcueB0gdMNDseIEVFKKWIZk3DSIJzMFrzu3T3w0bR17EwbxLMQSWR6LAJZCpw2DZdNw2nXcdksYeS06VZeLt+Zizty+Q6bhkO3ytn1/DmNhnJrmYFSMhABNOzTYp5++mnOOusszjzzTACuuuoq3n77bV566SXOP//8HuWfffZZ5s2bxxe/+EUALrnkEjZu3MiqVau4+uqrUUrx7LPPcuGFF3LiiScCcO2113LVVVfx1ltvccoppwzZv+1AXtzSym/fCw/JvewauGzgtml4cke3Ddw28NrAk8v32rGONvDljl47+G0Knw5em4ldU1RVBWhrabFeXvmAstYASSgrmPlzZq6caZ1XCmXm4oVgdJ3Pp00TjFzcyFpr3Rx4zGYhm0UZmVy82zGTsQZcplNWOp2LGwNfobRXbDYIlFktzGA5WoXVCqWiyopX1kD1ODRHade1EISxhOZyweRpaJOnFeUrpazGSMtH0NGK6miDjlYrHmqHSMgK8aj1rsin87/v5V6HlAdOpyWI7E4r7sgFuwMcDmt6rt1hLUVhs+XSduuYT3c/6rq1T1A+runW0Wbrimsa6DZLfGlaoZxP1/BpGvWaDhpWeZsGPh38ABroGpqmU1VdTVtbGymlEctqRA2IGRpxAytkKcQThaMikYWkCUlDkTAgaVjxlNFlK6sRrqAfYzgPxUUzAkw5acLHvs7hMqwCKJvNsn379iKho+s6s2fPpqmpqdffNDU1sWjRoqK8uXPn8tZbbwGwf/9+QqEQc+bMKZz3er1Mnz6dpqamXgVQJpMp8vRomobH4ynES0XZB+9RF3fiMLM4lIHdzOIws9iVgdPMYDcN65yZxWlmcOaOVjqXZ2Ry5zK4jAwuM43TyODK5XmMFC4jjb2/KyL2AwPYf8hSowBNs1p2+Zaey4prHm+uRZhrFXp94At2tRr9AUv4DIFbPf+8jYZuwdGO2HroKIWtNU2z/g4DZcDMPssVuqtjnVYXW96bG42gEvGcxzdueXqTiZw3OHdMJorH6qXTxUtR9HXPw/5XDc418+9rO1CWCx+3LmndQdLmJGVzktYdpHQHKZuDlO4kbXOQ1h2kdbt1zuYgk4vn87O5dEa3kdXspHU7dTsdaJ8cvo2ah1UARSIRTNOkvLy8KL+8vJy9e/f2+ptQKNSja6ysrIxQKFQ4n8/rq8yB/PGPf+R3v/tdIT1lyhRuu+22frvR+stFtfDZF/5fH2cPeDH09qIo5Gk9f6JroGO1TOi2mrHWvWy3PE2z0oVL5hdGzJ3Ll+9WVtM1q9WhUWilWEX0ruvpViume+tF021d5XXNWi4/38LRdWtfoVwrKH8Omx3Nbs/l2a18h9OKO6wWluZw5oLDOud0ojld3YITze1Bc7nRXW6rzCj52NXW1g53FcYMYuuhYzTYWhkGKp1C5brIVTqFSqdR6WTumEJl0qhMxlqhPR/PeaKVkUVlMmBkrTzDQBk5z3Xe220YVte8aVozRLvHlcp5xFW3dM6rnsvPe99V7hx088wrhcqX6e6tVxTiXZ58KEit7mXz2bnuSqUUbsDqrMpYwVRgcoBS63atouze5VzgmK9SNsCxuaVk2LvARgIXXHBBkVcp/5FsaWk5rA3e+uTks7GdfHbprjdEaJpGbW0t+/bt67X//rBcy0NFxoRMHKL9HDswzBzK1kLpEFsPHaPX1jo4PFbwjY6p+ZqmUXcIW4+UZmAciDc3l/Sadrt9dIwBCgaD6LrewzMTCoV6eIXylJeXEw4Xj6MJh8OF8vljOBymoqKiqExjY2Ov13Q4HDj62E5gdP2xDi75fWWEwUdsPXSIrYcOsfXQIbY+NMM6xN1utzN16lQ2bdpUyDNNk02bNjFzZu99vDNnzmTjxo1FeRs2bGDGjBkAjBs3jvLy8qIy8XicrVu39nlNQRAEQRDGFsM+x2/RokW88MILvPzyy3z44Yfcc889pFIpzjjjDADuuOMOHnzwwUL5c889l/Xr1/PUU0+xZ88eHn30UbZt28bChQsBy/137rnn8oc//IE1a9awa9cu7rjjDioqKgqzwgRBEARBGNsM+xigk08+mUgkwqOPPkooFKKxsZEbb7yx0JXV2tpaNHB11qxZfPOb3+Thhx/moYceoq6ujn/7t38rrAEEsHjxYlKpFHfffTfxeJyjjjqKG2+8cUBrAAmCIAiCcOQy7AshjmRG40rQg4EsGDd0iK2HDrH10CG2HjrGuq0HshDisHeBCYIgCIIgDDUigARBEARBGHOIABIEQRAEYcwhAkgQBEEQhDGHCCBBEARBEMYcIoAEQRAEQRhziAASBEEQBGHMIQJIEARBEIQxhwggQRAEQRDGHMO+FcZIxm4X83RH7DF0iK2HDrH10CG2HjrGqq0H8u+WrTAEQRAEQRhzSBeYcEgSiQQ33HADiURiuKtyxCO2HjrE1kOH2HroEFv3HxFAwiFRSrFjx44xubHeUCO2HjrE1kOH2HroEFv3HxFAgiAIgiCMOUQACYIgCIIw5hABJBwSh8PBl770JRwOx3BX5YhHbD10iK2HDrH10CG27j8yC0wQBEEQhDGHeIAEQRAEQRhziAASBEEQBGHMIQJIEARBEIQxhwggQRAEQRDGHGNzsxBhwGQyGW688UZ27tzJf/zHf9DY2Fg4t3PnTu699162bdtGMBhk4cKFLF68ePgqOwrZv38/v//979m0aROhUIjKykpOO+00LrzwwqK9bcTWpWPVqlU89dRThEIhGhoauPLKK5k+ffpwV2tU88c//pE333yTPXv24HQ6mTlzJpdffjn19fWFMul0mvvvv59XX32VTCbD3Llz+frXv055efnwVXyU8/jjj/Pggw9y7rnncsUVVwBi5/4gHiChX/zmN7+hsrKyR348HueWW26hurqaW2+9lcsvv5zHHnuMv/zlL8NQy9HL3r17UUpx9dVX8/Of/5ylS5fy/PPP8+CDDxbKiK1Lx6uvvsr999/Pl770JW677TYaGhpYsWIF4XB4uKs2qnnvvfc455xzWLFiBTfddBOGYXDLLbeQTCYLZf73f/+XtWvXcv3117N8+XI6Ojr42c9+Noy1Ht1s3bqV559/noaGhqJ8sfOhEQEkHJJ33nmHDRs28NWvfrXHuVdeeYVsNsuyZcuYNGkSp5xyCp///Od5+umnh6Gmo5d58+axbNky5s6dy/jx4znhhBM477zzePPNNwtlxNal4+mnn+ass87izDPPZOLEiVx11VU4nU5eeuml4a7aqOZ73/seZ5xxBpMmTaKxsZFrrrmG1tZWtm/fDlgi/sUXX2Tp0qUce+yxTJ06lWXLlrFlyxaampqGufajj2QyyX//93/zjW98A5/PV8gXO/cPEUDCQQmFQtx9991ce+21OJ3OHuebmpo4+uiji7pp5s6dy969e4lGo0NZ1SOOeDyO3+8vpMXWpSGbzbJ9+3Zmz55dyNN1ndmzZ8vHocTE43GAwnO8fft2DMMosv2ECROorq4W2x8G99xzD8cddxxz5swpyhc79w8RQEKfKKW46667+OxnP8u0adN6LRMKhXr0KefToVBocCt4BLNv3z7+9Kc/cfbZZxfyxNalIRKJYJpmr7YUO5YO0zRZuXIls2bNYvLkyYD1nNrt9iJvBUBZWZnYfoCsXr2aHTt2cNlll/U4J3buHzIIegzy29/+lieeeOKgZW6//XbWr19PIpHgggsuGKKaHXn019YTJkwopNvb21mxYgWf+tSnigSQIIwm7r33Xnbv3s2PfvSj4a7KEUdraysrV67kpptu6tUzL/QPEUBjkPPOO48zzjjjoGXGjx/Ppk2baGpq6tHC+Pd//3dOPfVUrr322l5bzfm0zDbov63ztLe3s3z5cmbNmsXVV19dVE5sXRqCwSC6rvdqS7Fjabj33nt5++23Wb58OVVVVYX88vJystkssVisyDsRDofF9gNg+/bthMNhbrjhhkKeaZps3ryZVatW8b3vfU/s3A9EAI1BgsEgwWDwkOWuvPJKLrnkkkK6o6ODFStWcN111zFjxgwAZs6cyUMPPUQ2my2MTdmwYQP19fVF41fGKv21NXSJnylTprBs2TJ0vbiHWmxdGux2O1OnTmXTpk2cdNJJgPXx2LRpEwsXLhzm2o1ulFLcd999vPnmm9x8882MGzeu6PzUqVOx2Wxs3LiRBQsWANYMyNbWVmbOnDkcVR6VzJ49m5/+9KdFeb/4xS+or69n8eLFVFdXi537gQggoU+qq6uL0m63G4Da2tpCq+7UU0/lscce43/+539YvHgxu3fv5k9/+hNLly4d8vqOZtrb27n55pupqalhyZIlRCKRwrl8i01sXToWLVrEnXfeydSpU5k+fTrPPvssqVTqkN464eDce++9vPLKK3z3u9/F4/EUvGxerxen04nX6+Uzn/kM999/P36/H6/Xy3333cfMmTPlwzwAPB5PYVxVHpfLRSAQKOSLnQ+N7AYv9Jv9+/dz7bXXHnQhxEAgwMKFCzn//POHrZ6jkZdffpm77rqr13OPPvpoIS62Lh2rVq3iySefJBQK0djYyNe+9rWCZ1M4PL785S/3mr9s2bKCuMwv0Ld69Wqy2aws0Fcibr75ZhobG3sshCh27hsRQIIgCIIgjDlkGrwgCIIgCGMOEUCCIAiCIIw5RAAJgiAIgjDmEAEkCIIgCMKYQwSQIAiCIAhjDhFAgiAIgiCMOUQACYIgCIIw5hABJAjCEcEVV1wxYheFXLlypSxAJwgjDBFAgiAMGTfffDPz5s0b7moIgiCIABIEQRitZDKZ4a6CIIxaRAAJgtBvVq1axamnnkp5eTlVVVUsWrSIbdu2FZX58MMPufTSS6msrMTn83HCCSfwxhtvsHLlSpYvX8769evRNA1N01i5ciUffPABmqaxbt26wjVCoRCapvHyyy8DYBgG//RP/8SUKVPweDzMmjWL//qv/xpQ3fPdUH/+8585+uij8fv9LFy4kObm5kKZM844g+uuu67od+eff35hfyWAxsZGbrnlFpYsWYLf76ehoYEnn3ySlpYWFi9ejN/vZ86cOaxZs6ZHHR5//HFmzJiB2+3mnHPOYffu3UXnn3jiCebPn4/b7Wbq1KksX76cbDZbOK9pGr/4xS/44he/iM/nY8WKFQOygSAIXYgAEgSh38RiMa6//nrWrFnDCy+8gK7rXHDBBZimCUA0GuX0009nz549PPnkk6xfv57vfve7mKbJxRdfzL/+679yzDHH0NzcTHNzMxdffHG/7muaJhMnTuSxxx7jvffe4wc/+AE33nhj0Uax/SEej/PTn/6UBx54gL/97W/s2rWL73znOwO2w+23384pp5zCO++8wxe+8AW++tWvsmTJEi6//HLefvttpk2bxpIlS+i+1WI8HmfFihWFDSpDoRCXXHJJ4fzf//53lixZwre+9S3ee+897r77blauXNlD5Nx8881ccMEFbNy4kSuvvHLAdRcEIYcSBEE4TFpaWhSgNm7cqJRS6u6771aBQEC1tbX1Wv6HP/yhmjt3blHejh07FKDeeeedQl5HR4cC1EsvvdTnva+55hp10UUXFdJLly5Vixcv7rP8r3/9awWorVu3FvLuvPNONX78+EL69NNPV9/61reKfrd48WK1dOnSQrqhoUFdfvnlhXRzc7MC1Pe///1C3muvvaYA1dzcXHTv119/vVBm8+bNClBvvPGGUkqps846S/34xz8uuvcDDzyg6urqCmlAXXfddX3+GwVB6D/iARIEod+8//77XHrppUydOpVgMEhjYyMAu3btAmDdunUcd9xxVFZWlvzed955J8cffzw1NTX4/X5++ctfFu7bX7xeL9OmTSuk6+rq2L9//4DrMmfOnEJ8/PjxAMyePbtHXvdr2+12TjzxxEL6qKOOory8nM2bNwOwfv16fvSjH+H3+wvhqquuorm5mXg8XvjdCSecMOD6CoLQE/twV0AQhNHDeeedR0NDA7/61a+or6/HNE2OPfZY0uk0AB6PZ8DX1HWrHaa6dRcdOLj34Ycf5jvf+Q4/+9nP+NSnPkUgEOAnP/kJb7zxxoDu5XA4itKaphXdV9f1onRvdTnwOpqm9ZmX7xrsD9FolOXLl3PhhRf2OOd2uwtxn8/X72sKgtA3IoAEQegXbW1tbNmyhV/96lecdtppALzyyitFZebMmcM999xDe3t7r14gp9OJYRhFeTU1NQA0Nzdz3HHHARQNiAZYvXo1J598MsuWLSvkHTj4uhTU1NQUDYo2DINNmzZx5plnfuxrZ7NZ1qxZw0knnQTAli1bCIVCHH300QDMnz+fLVu2MH369I99L0EQDo10gQmC0C8qKiqoqqril7/8JVu3buXFF1/k+uuvLypz6aWXUltby/nnn8/q1avZvn07v//973nttdcAawbVjh07WLduHa2traRSKTweDwsWLODWW29l8+bN/PWvf+Wmm24quu6MGTNYs2YNf/7zn2lqauL73/8+b731Vsn/jZ/5zGd45plneOaZZ/jHP/7BP//zPxMKhUpybYfDwb/8y7/wxhtvsHbtWq644goWLFhQEEQ/+MEPuP/++1m+fDnvvvsumzdv5uGHH+5hC0EQSoMIIEEQ+oWu6zz88MOsXbuWY489lm9/+9v85Cc/KSrjdDp57rnnGDduHOeeey6zZ8/m1ltvxWazAXDRRRexcOFCzjzzTGpqanjooYcAuO+++8hmsxx//PFcd9113HLLLUXX/cY3vsGFF17IxRdfzCc/+Una2tqKvEGl4sorr2Tp0qUsWbKE008/nalTp5bE+wPW+KMbbriByy67jFNOOQW/388jjzxSOH/OOefw9NNP89xzz3HiiSeyYMECbr/9dhoaGkpyf0EQitHUgR3egiAIgiAIRzjiARIEQRAEYcwhAkgQBEEQhDGHCCBBEARBEMYcIoAEQRAEQRhziAASBEEQBGHMIQJIEARBEIQxhwggQRAEQRDGHCKABEEQBEEYc4gAEgRBEARhzCECSBAEQRCEMYcIIEEQBEEQxhwigARBEARBGHP8fzOde/n+E9vKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = [0, 0, 0, 0]\n",
    "b = [5, 10, 20, 30]\n",
    "linestyle_cycler = cycler('linestyle',['-','--',':','-.'])\n",
    "\n",
    "x = np.arange(-50., 50., 1)\n",
    "fig,ax= plt.subplots()\n",
    "plt.rc('axes', prop_cycle=linestyle_cycler)\n",
    "\n",
    "for mu_val, b_val in zip(mu, b):\n",
    "    pdf = np.exp(-abs(x-mu_val)/b_val)/(2.*b_val)\n",
    "    ax.plot(x, pdf, label='mu=%s b=%s' % (mu_val, b_val))\n",
    "    \n",
    "ax.set_title('Laplace Probability Density Function')\n",
    "ax.set_xlabel('actual number')\n",
    "ax.set_ylabel('probability density')\n",
    "ax.set_prop_cycle(linestyle_cycler)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making a \"Differential Privacy Mechanism\"\n",
    "\n",
    "You might have heard the term \"differential privacy mechanism\". This is a way to take data and to provide a \"differential privacy guarantee\" by controlling the contribution and the noise before releasing the data for further analysis.\n",
    "\n",
    "Let's create a very naive differential privacy mechanism, that samples from Laplace and adds the noise to the result. Please note, do not use this with any real data! Instead use a well-known and audited open-source library!\n",
    "\n",
    "NOTE: this is an incorrect usage of laplace, please do not use in a real problem! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 1.1\n",
    "\n",
    "def naive_laplace_dp_mechanism(value, epsilon):\n",
    "    # Please do not use this function, ever :)\n",
    "    orig_value = value\n",
    "    value =  np.random.laplace(value, 1/epsilon) # more on this choice of 1/epsilon later!\n",
    "    print(\"Noise: {}\".format(value - orig_value))\n",
    "    return value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's calculate a summary statistic and see the result. I'll start with a mean of the ages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 1.277692233946226\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "46.55769223394623"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_laplace_dp_mechanism(np.mean(ages), epsilon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45.28"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And what if you added an outlier?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 0.5971700616306563\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "46.51796214083858"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_laplace_dp_mechanism(np.mean(ages + [110]), epsilon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 0.45538840431066063\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "45.2969725627265"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "naive_laplace_dp_mechanism(np.mean(ages + [1]), epsilon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise:\n",
    "\n",
    "Try it out with salaries. What is similar or different? And what about if you looked at something like mode, or min, or max?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems here that the mean result for ages and salaries is unsafe.... What did we do wrong?\n",
    "\n",
    "\n",
    "Let's take a look at the \"noise\" we are adding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc = 0\n",
    "scale = 1/1.1\n",
    "\n",
    "x = np.arange(-6., 6., .1)\n",
    "pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)\n",
    "\n",
    "fig,ax= plt.subplots()\n",
    "ax.plot(x, pdf, label='mu=%s b=%s' % (loc, scale), linestyle='-')\n",
    "ax.set_title('Scale: 1/ε with ε=1.1')\n",
    "ax.set_xlabel('actual number')\n",
    "ax.set_ylabel('probability density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to figure out how to safely add noise, we need to better understand sensitivity!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring Sensitivity and Error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we want to release data in a differentially privacy way, we need to think about the sensitivity of the result. This is how much one person can change the result of a query. \n",
    "\n",
    "Our error / noise insertion needs to scale with this sensitivity in order for the differential privacy guarantee to hold (i.e. that with one addition or removal to the data, I cannot get \"too much\" more information based on the query result).\n",
    "\n",
    "Sensitivity is how much one person (or privacy unit) can change the results. As you can see, we've been using sensitivity improperly! Let's choose something that is easy to define. \n",
    "\n",
    "First, we can rewrite our mean as a SUM over a COUNT. \n",
    "\n",
    "We know that for SUM, the maximum one person can change the result is by + or - 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_ages = ages + [round(np.random.normal(mid_level_age, age_scale))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(new_ages) - len(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now our sensitivity is correct for our counting query!\n",
    "\n",
    "But what about our SUM query?\n",
    "\n",
    "If we want to use bounds in order to bound a previously *unbounded query*, such as a SUM, we can do so by determining those bounds and then enforcing those bounds on our existing and incoming data. \n",
    "\n",
    "Since I know this dataset is employees who are working, I can choose bounds of 20-70 for the ages. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write a function called filter_bounds, that takes a value, a lower bound and upper bound \n",
    "# and returns a number within the bounds (see usage below)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/filter_bounds.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "bounded_ages = [filter_bounds(age, 20, 70) for age in ages]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have bounded the amount that one person can contribute to a sensitivity of 50, we can appropriately scale the noise, so that we can calculate a safe sum. But first we need to figure out how we can run multiple queries and still keep the same guarantees!\n",
    "\n",
    "Remember, we use differential privacy so we can guarantee every individual some amount of privacy, no matter who they are and how much they are different than the others. As you can see, our bounding helps with that! But it also means when we increase the sensitivity - we also increase the carefully constructed noise. \n",
    "\n",
    "And, so far we've only measured sensitivity for ONE query at a time. When we want to run multiple queries (like a SUM and a COUNT), we need to track the privacy loss of those individuals for each query and make sure we know how much privacy loss they can expect in total. This is brings us to..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Composition\n",
    "\n",
    "So how do we reason about how much privacy loss there is when we answer a series of questions about the data? Differential privacy promises that we can track and measure privacy loss, so how do we do this?\n",
    "\n",
    "One amazing property of differential privacy is that the epsilon value (ε) is our privacy loss for one particular response and it has the property of being individual to each query and yet composable -- meaning if I answer two queries, I can add their epsilons to calculate the privacy loss!\n",
    "\n",
    "What does this mean in practice? \n",
    "\n",
    "1. Privacy budgets! I can budget my total epsilon appropriately over the course of a certain amount of queries. This means I can detemine how much information gain / privacy loss someone has when given multiple queries across the data.\n",
    "\n",
    "2. The privacy loss is only for the individuals contained in the query response. This means I could also count the budget per individual and stop including those individuals in the responses once their budget has been reached. Of course, this will likely than bias my data as more individuals \"drop out\" when their budgets are reached.\n",
    "\n",
    "3. Depending on what epsilon I come up with, I may want to spend more of it on a particular query than others. So if I know the queries in advance or if I am releasing data all at once, I may want to allocate my budget on a query by query basis!\n",
    "\n",
    "Let's now fix our differential privacy mechanism. It should be similar to the one above, but this time take sensitivity as a parameter. We scale Laplace by sensitivity / epsilon!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write a new laplace_dp_mechanism that takes the value, the epsilon and sensitivity as a keyword argument.\n",
    "# See usage below. If you'd like, you can add the print statement to observe the mechanism as you learn, but \n",
    "# in real life you'd never ever know the noise as it would immediately violate the guarantee!\n",
    "\n",
    "# Also please never write your own DP mechanism, use a trusted library that has been tested and audited. :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load solutions/laplace_dp.py\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: -53.24175804583501\n",
      "Noise: 1.928454653399541\n"
     ]
    }
   ],
   "source": [
    "epsilon_for_sum = 0.5\n",
    "epsilon_for_count = 0.5\n",
    "\n",
    "summed_ages = laplace_dp_mechanism(np.sum(bounded_ages), epsilon_for_sum, sensitivity=50)\n",
    "count_ages = laplace_dp_mechanism(len(bounded_ages), epsilon_for_count, sensitivity=1)\n",
    "\n",
    "average_age = summed_ages / count_ages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43.88135047434459"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "average_age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which means a relative error of..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.030888902951753706"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(average_age - np.mean(ages))/ np.mean(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![High Five](https://media.giphy.com/media/ujGfBmVppmgEg/giphy.gif \"Liz Lemon gives herself a high-five to celebrate and so should you!\")\n",
    "\n",
    "You did it! You built your first DP mechanism!\n",
    "\n",
    "Of course, this mechanism is really only a toy example to get you learning, please don't use it in production! I hope, however, that it has peaked your interest in learning more about differential privacy and privacy technologies! You can also check out a few other notebooks in this repository to learn more and read the References!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Homework\n",
    "\n",
    "So far we've investigated the ages dataset. Try answering some basic questions about the salaries dataset using the (very simple and slightly broken) Laplace mechanism we've defined here. Some starting points might be:\n",
    "\n",
    "- What is the average salary? \n",
    "- What is the average salary of people over 40?\n",
    "- What is the average salary for people under 40?\n",
    "\n",
    "To do so, you might first want to link the datasets. I have written some example code below to help you get started! \n",
    "\n",
    "_Note_: When you are first experimenting with differential privacy mechanisms and real data, you might end up using the budget just trying to figure out how you might want to release the data. This is not optimal, but it is necessary. The most essential task is to get the differential privacy mechanisms used working properly before releasing data outside of your organization or across trust boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_budget = 1.1\n",
    "\n",
    "# Try tracking your budget as you answer the above. Think about how you spend it wisely!!! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "linked_dataset = np.column_stack((ages, salaries))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "over_40 = linked_dataset[(linked_dataset[:,0] > 40)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_employees_over_40 = laplace_dp_mechanism(len(over_40[:,1]), 0.3, sensitivity=1)\n",
    "num_employees_over_40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "len(over_40[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#keeping my budget honest!\n",
    "my_budget -= 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_budget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recommended Reading\n",
    "\n",
    "- Ted on Privacy's Blog Series on Differential Privacy! https://desfontain.es/privacy/friendly-intro-to-differential-privacy.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix\n",
    "\n",
    "Below is a recreation of a graph by Damien Desfontaines in Python, to show the probability bounds of different choices of epsilon, to give you a visual idea of the privacy loss and attacker's information gain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb7613e62b0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "\n",
    "y = np.arange(0, 1.0, 0.001)\n",
    "x = np.arange(0, 1.0, 0.001)\n",
    "\n",
    "\n",
    "linestyle_tuple = [\n",
    "     ('loosely dotted',        (0, (1, 10))),\n",
    "     ('loosely dashdotdotted', (0, (3, 10, 1, 10, 1, 10))),\n",
    "     ('long dash with offset', (5, (10, 3))),\n",
    "     ('loosely dashed',        (0, (5, 10))),\n",
    "     ('dashdotdotted',         (0, (3, 5, 1, 5, 1, 5))),\n",
    "     ('dashed',                (0, (5, 5))),\n",
    "     ('dashdotted',            (0, (3, 5, 1, 5))),\n",
    "     ('dotted',                (0, (1, 1))),\n",
    "]\n",
    "\n",
    "for epsilon in range(8):\n",
    "    lower_bounds = (e**epsilon * y) / \\\n",
    "         (1 + (e**epsilon - 1)  * y)\n",
    "    upper_bounds = y / (e**epsilon + (1-e**epsilon) * y)\n",
    "\n",
    "    ax.plot(x, upper_bounds, label='ε={}'.format(epsilon), \n",
    "            linestyle=linestyle_tuple[epsilon][1])\n",
    "    ax.plot(x, lower_bounds, linestyle=linestyle_tuple[epsilon][1])\n",
    "\n",
    "ax.set_title('Probability Bounds of Epsilon Values')\n",
    "ax.set_xlabel('initial suspicion')\n",
    "ax.set_ylabel('updated suspicion')\n",
    "ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}