{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Week 6: Section\n",
    "Adapted by Misha Gupta (2024), from Aoyue Mao 2021, Danylo Lavrentovich 2020, Irina Shlosman 2019 and Kevin Mizes 2018\n",
    "Slightly updated by Kepler Mears (2026)\n",
    "\n",
    "### What's in this notebook\n",
    "\n",
    "- A concrete example of computing a p-value under a null hypothesis with a binomial problem\n",
    "- General overview of estimating parameters from data and building new hypotheses given data\n",
    "- Maximum likelihood estimation of parameters for binomial, normal\n",
    "- How T distribution arises from estimation of normal parameters\n",
    "- Practice problems\n",
    "\n",
    "We encourage you to run the examples here and try different parameter settings. To be able to run the code, make sure you download this [helper python file](w06_section_utils.py)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "from w06_section_utils import set_font_sizes, viz_coin_flip_H0_H1, estimate_normal_from_sample, get_dist_of_xbar_and_S\n",
    "set_font_sizes() # override matplotlib default plotting settings with bigger font sizes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Null hypothesis & computing a p-value\n",
    "\n",
    "Example: You are at a fair and you encounter an intriguing booth offering you 15 dollars straight up if you enter their game. What's the catch? You are also given a coin with an ominous cartoon face on it. You are asked to flip the coin $N=30$ times -- each time it lands on heads, your cash reward goes down 1 dollar. \"It's a fair coin, I promise you!\" the booth manager says...\n",
    "\n",
    "You take them at their word, the immediate cash on hand is enticing... and you flip heads 25 times out of 30. You suddenly owe the booth manager 10 dollars.\n",
    "\n",
    "You know you're a pretty unlucky person. But this seems like an especially embarrassing episode. If the coin really was fair, as the booth manager asserted, what is the chance we'd be this or MORE unlucky?\n",
    "\n",
    "The number of heads we'd expect to observe out of $N=30$ flips is well modeled by a binomial process ($N$ independent trials/flips, each flip has some probability of heads $p$, and we're interested in knowing the total number of heads we record). For any $p$:\n",
    "\n",
    "$$P(\\text{$k$ heads out of $N$ trials} \\mid p) = {N \\choose k} p^k (1-p)^{N-k}$$\n",
    "\n",
    "Let's plot out the probability mass function and the cumulative distribution function of $k$, the number of heads in $N=30$ flips, assuming $p=0.5$, and mark our unlucky $k = 25$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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inxOBQMDOnj0rcT3/mjVp0iSx4/zj3b59e7H3Ai9fvmRWVlZMS0uLPXnypML78GEMZX8vyjtvRbfJzMxkpqamTCgUij0upaWlbPz48QwACwwMFOuH/72fPXs2KykpER3fsmULA8Bmzpwp9fwfonG39sbd7du3S/x9yuLD8bc8W7duZQDYxIkTRcf459fV1VXquHv//v0q3RdCSNXQsqN6qk2bNvD19RU79vXXX8PS0hJ79+5FYWGhxG2+//576OnpiR3bvXs3iouL8eWXX6Jp06ai4zo6OqIlKdKm1pqZmUnUfJg4cSIcHBxw/vx5sSmTNjY20NTUFGsrEAjwxRdfAIBoyc2HAgMDRZ8uAty6eV9fX6Snp+PIkSNSb1MTZs6cCeD9LBfejh07UFRUhOnTp8vV38qVK2FgYCD6edSoUdDW1kZ6ejrWrFkDLa33E9rGjRsHgFtjXFbZGh48LS0tfP755ygpKUFYWJjE9R8+9wDQoEEDmdopa80/APznP/9BmzZtRD/r6elh3LhxEktqNm7ciJKSEgQFBUl8QikQCNCkSZNqxcH/HaxevVrs02Fra2ssWLAARUVFEp8IAsD48ePRvXt30c+ampqYNGkSACA6OrpaMfHWrFkDf39/LF++HBMmTIC7uzvy8vIwd+7ccj+tnTJlCm7fvi16DLdv346SkhKJ1xVpzp07h4CAAInLq1evFHJ/SN1S039bADdNf9iwYaKftbW1MWrUKDDGMGTIELi5uYmuMzIywuDBg/H27VupS22r66OPPpI6A2TOnDkAyh+zZCUQCDB+/HikpaVJLJ34448/AEBUlBPgZqtkZmYiODhYoi7GuHHj4OLign379lV63r/++guZmZnw9fVF69atRce1tbWxcuVKue+HrGNKZYYPH46+ffvKfbulS5fCyMhI9HPjxo2xcOFCFBcXY8+ePXL3Vx1//fUX0tPT4evrCycnJ9FxgUCAb7/9VmKpN8/AwADfffcdNDTev52fNGkStLS0FDY+VAWNu9LxY5y1tXWV+6gI/3h9uCQY4JbwSxt3Hzx4UCOxEEKko+RLPdW9e3eJpUB8/ZC8vDw8evRI7Dp+PfSHbt68CQBSt4Ls0qUL9PT0cOvWLYnrnJ2dxRIIADfQ8lPPyyYLCgsLsXbtWri7u8PY2BgaGhoQCARwdXUF8L5YXFna2tro0qWLxHF+ira0mGqKo6MjunbtioMHDyIjI0N0fNu2bTA0NMTYsWPl6s/Z2VnsZ01NTTRs2BCmpqYSb6z53RSeP38udjwrKwt+fn7o0KEDDA0NReunP/nkEwDij+moUaOgoaGB4cOHY8qUKdizZw+ePXsmEdfgwYOhr6+PL774AmPGjMG2bdskfo+UwcXFReIY/8YnPT1ddOzq1asAgP79+9dIHDdv3hTVHvoQ//cj7fdS1vir44cffkBAQABWrlyJEydOwM3NDdu3b8dPP/1U7m0mTpwIbW1tUY2E7du3o3Pnzmjfvn2l5wsODgZjTOJS3anupG6q6b8tQPJ1EXj/+ift96q810ZFYIxh27Zt6NWrF8zNzaGpqQmBQCBKLEgbs+Q1ceJEAO+TLQC3ZfDevXvRuHFjsWTElStXRF/9/f0lLvn5+UhNTZX6D1tZ/LgsbalT165dxRL/FRkzZgwAoHPnzvjiiy/w559/IiUlRabbSiPtNVUW0u6HMt4jABW/l2ratClatmyJJ0+eSCypsrOzg6GhodgxLS0tNGrUSGHjQ1XQuKscjLFyr5s5c6bUcbfs0jhCSM2jmi/1VMOGDaUe5+u4lE0S8O2lFTLLzMwUu52080h7cyvP+UeNGoVjx46J1rM2bNhQNNNj3bp1KCgokOinQYMGYp8EVXb/atqMGTMwZcoU7N69G7Nnz0ZUVBQePHiA6dOnS7xxqkzZ2i08LS0tqbsn8G+GyxYmLiwshKenJ27cuAFnZ2dMnDgRDRo0gJaWFhISErBjxw6xx7Rr1644f/48goODsXfvXtEnSa6urvj+++/h5eUFgJtNc/nyZQQEBODkyZM4cOAAAG6WVWBgIEaPHi3X/VSUih6XsgU309PTIRAIamz7z8zMTLHZYWXxu0xI+72UNf7qePnypdw7XTRs2BADBw7E3r17MXToUDx+/BhfffWVQuIh6qWm/7aA8l8XK7uuoqLtVTVv3jxs2LABTZs2xdChQ2FlZSWq3xAQECB1zJKXvb09nJ2dceLECaSnp8PU1BRnz57F69evsXDhQrHZou/evQPA1daoSE5OToWzFPnXJ2njt6ampsyzVsaOHQttbW389NNP2LRpE3799VdR8di1a9fKnYQt7/1HZaTdD2W9R6jsvVTjxo3x8OFDZGZmis3WKW/XJC0tLYWND1VB4650/DlrIukLcGM5AFhaWtZI/4SQ6qOZL/VUeZ8yvX79GoDkwCMt8QK8f1PL307aeaS98ZX1/NHR0Th27Bi8vb0RGxuLzZs3Y+XKlfD394ePj4/UPgDg7du3KC0trbT/2jJ27FiYmpqKlh7xX+VdcqQIR44cwY0bNzBt2jTcuHEDv/32G4KCguDv748BAwZIvY2HhwdOnTqFtLQ0hIWFYeHChbh37x4GDRqEJ0+eiNo5OTnhzz//xLt373D58mWsWLECr1+/xtixY3Hx4sVqxa2hoYHi4mKp1ynijbKpqSkYY6I3L4pmbGxc7t8Jf1za30pd5uvri7S0NEydOlU0rZyQD8nzt8UnzaX9rdf0P8SKOHdKSgp++eUXODk54cGDB9i+fTuCg4Ph7++Pzz//XKHxTpw4EQUFBTh48CCA97Ng+FkxPP515c6dO1I/+eYvNjY2FZ6PHzeljd8lJSVy7QQzcuRIREZG4t27dzh58iSmTZuGiIgIeHt7yz2zoLz3J5WRdj+kvUeojd/Jyt5LKWuMoHFXsfilTOHh4VLfo1YXv0NS2WWWhJC6hZIv9dTFixclpifm5eXh+vXr0NPTE1vPXRF+qre0LfGuXr2KvLw8qZ9i3bx5Ezk5OVLjAoAOHToAgOgf+0GDBknUfSlvm02A+zSTn2ot7TaKXt6goaFR4achenp6+PTTT3Hz5k1ERETgwIEDcHJyUsoAyT+mQ4cOlbiuoscU4O6Hp6cnfvjhByxZsgR5eXlS6xfwy74CAgLw888/gzGG48ePVytuMzMzpKSkSLwRzMnJQVxcXLX6Bt5PXT9z5kylbfnfRXk+AXN2dkZeXp5omnVZ/FazqrbsZuDAgWjcuDGeP3+OTz75ROWSR6R2yPO3xe+4I+2TYX5pRk1RxLnj4+PBGEPfvn2hr68vdl15r69VeT0BuHotmpqa+OOPP5CTk4O//voL9vb2Eq8jnTt3BgBcvnxZrv4/xI/L0u7H5cuXy/0nvSLGxsYYMGAAfv/9d0yePBkpKSn4999/RddXNrZWh7T7Ie09gry/F1UdHwDp76WeP3+OJ0+eoEWLFmKzXmoDjbuK1apVK/Tq1QtJSUnYsWNHhW3lnSH36NEjhIaGQigUiu10RgipWyj5Uk89fPhQVKuB9/333+PNmzcYN26cTNtFAlxRMi0tLaxdu1ZsHXtRUZGooG7ZLSJ5aWlpooK8vJ07d+LOnTvo3bu3aJoo/0nch1v73bt3D8HBwRXGtnz5crEp5Q8ePMC2bdtgYmIiVphREczNzSst3MgX3h0/fjxyc3OVMusFKP8xjYiIwObNmyXaX7hwQTQluiz+UyO+aGJ0dHSFnyRKK64oj06dOkkUx2OMYfHixVITefL6/PPPoampiWXLliExMVHsug8/mTM3NwcAuYp18sX6Fi9eLPZ7+fz5c6xduxZaWlrV3gJ98uTJEAgEUgsz1gQtLS0cPXoUhw8frlLBTVI/yPO31alTJwCShdoPHjwo+meppvDn3rlzp9in0pcvX5ZalFMa/vX10qVLYn0kJydLFJnnVeX1BICotktkZCTWrVuHnJwciVkvAFcc28jICEuXLsW9e/ckrs/NzZX6YcWHhg0bBmNjY4l6XkVFRVi2bJnMcZ87dw75+fkSx/nxo+xYIcvYWlUrV64Uq6Hy+vVr0Wvx+PHjRcfl/b0wMzODQCCQK+5hw4bBxMQEISEhYs8RP8YVFRVJfS9V02jcrZy84+7PP/8MPT09zJkzB/v375fa5sKFC+jdu7fMMURFRcHb2xsFBQVYvHgxPvroI5lvSwipXVTzpZ7q378/Zs+ejRMnTqBt27a4ceMGTp8+jaZNm2LVqlUy99OyZUt89913+PLLL+Hk5IQxY8bAwMAAx48fx4MHDzBs2DCxXRd4PXv2xM8//4wrV67Azc0Njx49wuHDh2FiYoINGzaI2rm7u8Pd3R2hoaF4+fIlunTpgmfPnuHo0aMYNGiQaLr1h6ysrJCeno6OHTti0KBByMjIwN69e5Gfn4/Nmzcr/NOj3r17IzQ0FKNGjYKzszM0NTUxaNAgsSLFDg4O6NatGy5dugRdXV2pj0ttGDJkCGxtbbF69WrcvXsXDg4OePjwIY4fP47hw4fjzz//FGv/ww8/4OzZs/Dy8kKLFi2gq6uLGzdu4Ny5c2jVqpXoE5bdu3fj119/haenJ1q1agVjY2PExsbi77//hoWFhUy74FRkzpw5CAkJwbRp03D27FlYWlriwoULSE9PR4cOHSR2dJKXo6MjfvrpJ8ybNw/29vYYPnw4bGxs8OrVK0RGRmLQoEGiArReXl4QCARYunQpHjx4ABMTE5iYmGDWrFnl9j9x4kQcOnQIR44cgZOTEwYPHoycnByEhobi7du3+OGHH9CiRYtq3Qf+HwNZC18qgpubG01xJhWS529r+PDhaN68ObZv346kpCQ4Ozvj/v37OH/+PAYOHIi///67xuLs0qWLqMZV165d0atXLyQmJuLo0aMYMmQIDh8+XGkfVlZW+OSTT/Dnn3+iU6dO6NOnD16/fo3jx4+jd+/eiI+Pl7hN7969cfDgQYwePRoDBw4UFbgfNGhQpeebOHEiTp8+DX9/f2hoaEj9R5LfxXD06NHo0KEDBgwYgLZt2yI/Px+JiYmIiIhAt27dcOrUqQrPZWJigp9//hmTJ0+Gm5sbfHx8YGJiguPHj0NPT0/muh1ffvklnj17Bk9PT9ja2kIgECAqKgpXr15Ft27dxHaZkWVsraoWLVrAwcEBn3zyCYqKihAaGoqUlBSsXLlS7LVY3t8LQ0NDuLm5ITIyElOmTIGdnR00NDQwfvx4iaL4PGNjY2zevBnjxo1D586dMXbsWFhaWuLcuXO4du0a3N3d8fXXX1f7PsuLxt3KyTvudujQAceOHcOYMWPg4+OD//73v6Li3O/evcPFixdx584dtGrVSuK2jx8/hr+/PwCufh8/U+zu3buiJNaKFSuqdX8IITWspveyJnVLWFgYA8D8/PxYREQE69mzJ9PX12empqbMx8eHPXv2TOI2NjY2zMbGpsJ+jxw5wjw8PJiRkRETCoXM0dGR/fDDD6yoqEis3dOnTxkANmnSJHb79m02YMAAZmRkxAwNDdmgQYPY3bt3JfpOSUlhvr6+rEmTJkxXV5c5OjqyX375hcXHx4v6khbv27dv2bRp01jDhg2ZUChknTp1YkeOHJHoPyQkhAFgISEhld7v8tq+fPmSjRkzhllYWDANDQ2pbRhjbNOmTQwA+/TTT8t9LMvj4eHByvuTreg5AsA8PDzEjsXHx7NPPvmEWVpaMn19febm5sb27dsn9vvBO3XqFPvss89YmzZtRM9V+/bt2bJly1hqaqqo3ZUrV9jMmTOZg4MDMzU1ZXp6eszOzo7NmzdP6u+VNNLOX9a5c+dY586dmVAoZA0aNGATJ05kr169kvrY+Pn5MQAsLCxMop/ynkc+hsGDBzNzc3Omo6PDrK2t2SeffMIuXrwo1m779u3M0dGRCYVCBkDs8S/vuSoqKmJr1qwR3c7IyIh5eHjI9XtZ0ePk7OzMjIyM2Lt37yRuIw0f58uXLytty//tent7y9Q3ANamTRuxY/x9Cg4OlqkPol5k/duKj49nw4YNY0ZGRszAwID16dOHRUdHS/2brug1o6K/ofJeH968ecMmTpzIzM3NmZ6eHuvSpQs7ffp0uX1Je33NyspiX375JbO1tWVCoZDZ2dmxwMBAVlhYKLV9UVERW7RoEWvWrBnT0tKSGNek3YaXk5PDDA0NGQDm5eUltQ3vwYMHbOrUqczGxobp6OgwMzMz5ujoyObNm8euXr1a4W3LOnz4MHN1dWVCoZA1bNiQTZs2jb17907qOCTtcd63bx8bM2YMa9myJdPX12cmJiasY8eObPXq1Sw7O1vs9hWNrRU9v4yJv98oi3/dy83NZV999RX76KOPmI6ODrO3t2dbtmyR2pe8vxcPHz5kAwcOZKampkwgEIg9BhXFHRkZyT7++GNmamrKdHR0WOvWrdny5cslHhfGKv69kOV9G4/GXdljVMS4y3v79i0LDAxkXbp0YWZmZkxLS4s1aNCAeXp6snXr1ok95/zvctmLnp4es7KyYl5eXmz58uXs8ePHUs/Dxz1z5ky54iOE1AwBYxXsS0bUTnh4OLy8vODn5yfKnpPaM3v2bPz222+IiIhAr169lB0OUSOZmZkwMzPDl19+idWrVys7HFINRUVFiI6ORlRUFBITE/HmzRvk5eXBwsIClpaWcHFxQc+ePWlqOSGEKBGNu4QQedGyI0JqyZs3b7Bz5060a9eOEi9E4S5evAhtbW0sXLhQ2aGQKgoLC8OWLVvw119/iWpiSPt8hN/dpV27dvD19cVnn31W4RbBhBBCFI/GXUKIvCj5QkgNO3HiBG7cuIGDBw8iJycHfn5+yg6JqKGPP/5YahFLUvcdO3YMixcvxv3798EYg5aWFjp27Ag3NzdYWVnB3Nwcenp6ePfuHd69e4fY2FhER0cjNjYWX331FZYsWYIZM2Zg+fLlsLS0VPbdIYSQeoHGXUKIvCj5QkgNO3DgAHbs2IEmTZpg1apVGDt2rLJDIoTUEb169cLFixehp6cnKsDo7e0NXV3dSm/75MkT7Nu3D3v37sWGDRuwY8cO7Ny5U+G7uRFCCCGEkOqjmi+EEEKIkpibm2PevHmYP38+TE1Nq9xPWFgYAgMD4eXlheXLlysuQEIIIYQQohAayg6gqqKjozFw4ECYmZnBwMAA7u7u2LNnj8y3T0lJQXBwMEaNGoXmzZtDIBCI1tGXh98SUdrl888/l3qbzMxMLFy4EDY2NhAKhbCxscHChQuRmZkp1/0lhBCifhITE+Hv71+txAvAbcN6/vx5zJ8/XyFxEUIIIYQQxVLJZUfh4eHw9vaGjo4OfHx8YGJigkOHDmHChAlISEjAkiVLKu0jNjYWS5YsgUAggJ2dHfT19ZGbm1vp7UxMTKS+ue3UqZPEsZycHHh4eODWrVvo168fxo0bh5iYGPz4448ICwtDVFQUDAwMZLrPhBBC1I+RkVGd7o8QQgghhCiGyi07Ki4uRtu2bZGcnIzLly/D2dkZAJCVlYWuXbvi4cOHiI2NhZ2dXYX9vH79Gg8fPoSzszOMjIzQtm1bPHz4UOrOEjxbW1sAQEJCgkyx+vn54b///S8WLVqE7777TuL4ihUrEBAQIFNfAFBaWooXL17AyMio0lk6hBBSHzHGkJWVhSZNmkBDQ2UndxLQmEcIIZVR9JhXUlKCoqIiBURGSP2gqakJbW1tmdurXPLlzJkz8Pb2xpQpU7Bt2zax6/bv3w8fHx8sXrwYq1atkqtfRSdfGGOwtrZGZmYmXr16JTbDJT8/H02aNIG+vj6SkpJkflOZnJyMpk2bytSWEELqs6SkJFhbWys7DIXJyMhAfHw8iouLYW1tDSsrK2WHVONozCOEENlUd8xjjOHVq1fIyMio8H8hQogkoVAICwsLGBsbV9pW5ZYdhYeHAwD69+8vcR1/LCIiosbOX1BQgB07duD58+cwMzNDt27d0KFDB4l2cXFxePHiBby9vSWWFunq6qJXr144cuQIHj9+XOksHR4/nTwpKUmmJ5cQQuqbzMxMNG3aVKWW3xQWFkJDQwNaWpJD8o0bN/DNN98gPDwcpaWlouPt2rXDihUrMGbMmNoMtVbRmEcIIRVT1JiXkZGB9PR0WFpawsDAgGYbEiIDxhiKioqQkZGB58+fA0Cl71dULvkSFxcHAFITFmZmZrCwsBC1qQmvXr3C5MmTxY4NGDAAu3btgoWFhUxxlj0eFxdXbpuCggIUFBSIfs7KygLAPan0RpQQUlZubi7c3NwAcAXJ9fX1lRyRcqnSG0c9PT306NFD4oOD06dPY8SIESgoKJD4JDI2Nhbjxo3Dw4cP1XZ3I/45pDGPEPIhGvPEVWfMY4whJSUFxsbGYv/LEEIqp6enByMjIyQnJyM1NbXS9ysqtyA+IyMDAFf4VhpjY2NRG0Xz9fVFeHg43rx5g8zMTFy5cgUff/wxTp06haFDh4q9OZYlzrLtpAkODoaJiYnoQtOvCSHlYYwhNjYWsbGxNGVYxTDGJJ6zzMxMjB8/Hvn5+XBzc8Pp06eRmZmJvLw8XLt2DT4+PmCMISAgANHR0UqKnBBClIPGPMUpKSlBSUkJJbkJqSKBQAATExMUFBRUWjNJ5ZIvyrRixQp4eHjAwsICRkZG6Ny5M44fP44ePXrg8uXL+PvvvxV6vsWLFyMjI0N0SUpKUmj/hBBC6qadO3ciLS0NXbp0wYULF9CvXz8YGhpCKBTCxcUFe/bswZw5c1BaWorffvtN2eESQghRUcXFxQAgdekrIUQ2fNHdkpKSCtupXPKFn0lS3oyRzMzMcmeb1AQNDQ1MmTIFAHDx4kXRcVniLNtOGqFQKJpuTdOuCSGk/rh48SIEAgECAwPLraIfFBQEHR0dREZG1nJ0hBBC1I0qLdclpK6R9e9H5ZIvZWulfCgtLQ2pqakyF7BVFH59ZG5uruhYRXGWPV7bsRJCCKn7UlJSAABdu3Ytt42xsTHat2+Ply9f1lZYhBBCCCGkilQu+eLh4QGA23L6Q/wxvk1t+ffffwG834oa4JIqTZo0wcWLF5GTkyPWPj8/H5GRkWjSpAlatWpVm6ESQghRAfxMx8pqGWhra9OnlYQQQgghKkDlki99+vRBixYtsGfPHty6dUt0PCsrC4GBgdDS0hLbjSg1NRUPHjxAampqtc4bGxuL9PR0ieNRUVFYu3YthEIhRo4cKTouEAgwbdo0ZGdn47///a/YbYKDg5GWloZp06bRm2ZCCCFISUnBzp07RRd+Df7Tp08rvN2LFy9gaWlZ7fP/8ccfmDlzJjp16gShUAiBQIDt27fL3U9paSk2bNgAJycn6OnpwdLSEmPGjKnRXQgJIYQQQlSBylVW0tLSwpYtW+Dt7Y2ePXti3LhxMDY2xqFDh/D06VMEBQWhdevWovYbNmxAQEAA/Pz84O/vL9ZX2SQNP2277LE1a9aIlhSFhoZi9erV6NOnD2xtbSEUCnH37l2cOXMGGhoa2LhxI5o1aybW/6JFi3D06FGsXr0aN2/ehKurK2JiYnDy5El07NgRixYtUuyDQwiptwQCAWxsbETfE9USFxcnqh8GcDNeBAIBTpw4AQcHB6m3SUhIwPPnz9GnT59qn3/ZsmVITEyEhYUFrKyskJiYWKV+Pv/8c2zevBnt27fH3Llz8fr1a+zfvx9nzpzBpUuX0L59+2rHSgghNOYRQlSRyiVfAMDLywtRUVHw8/NDaGgoCgsLYW9vj8DAQEyYMEHmfnbs2FHhMX9/f1HyxcvLC/fv38eNGzcQERGB/Px8NGrUCGPHjsWCBQvg7u4u0ZeBgQHCw8MREBCAgwcPIjw8HI0bN8aCBQvg5+cHAwODKtx7QgiRpK+vj4SEBGWHQapg0qRJ5V7Hz4CR5vfffwdQcV0YWW3ZsgV2dnawsbHBt99+i8WLF8vdR1hYGDZv3oyePXvi7NmzEAqFAIDPPvsM/fr1w6xZsxAREVHtWAkhhMY8UhOcnJxw584dJCUlwdraWmobc3Nz5ObmIisrq9yC+OouOjoafn5+uHz5suj/8Pnz52P8+PEy92Fra1vuBz0zZ87Exo0ba+zcyqSSyRcAcHd3x8mTJytt5+/vLzHjhVfZWvqyPDw8qlRLxsTEBGvXrsXatWvlvi0hdV1yMhAXB9jZAeWMUYSQSoSEhFTpdr1790bnzp3h6upa7Rj69u1b7T42b94MgNuFiU+8ANxyYW9vb5w6dQqPHj0Sm51KCFF9sr4XoHbVa0dqVn5+Pu7fvw8rK6tyEy9xcXFIS0uDq6trvU28hIeHw9vbGzo6OvDx8YGJiQkOHTqECRMmICEhAUuWLJG5LxMTE8yfP1/ieKdOnWr83MqisskXQohybd0KzJgBlJYCGhrA778DU6cqOypC6g9FJEwUKTw8HAYGBujevbvEdXzyJSIigpIvhKgRWd4LMAZs3AjMmfO+XUAAMHw4UFwsfjlyBFi7lmsnEADz5gH9+3N9lL2cOQP8+iv3vUAAzJoFSHtJ/Ocf4Lff3rf7/PPy223cqNx29F5KuWJiYlBcXIzOnTuX2+bq1asAABcXl9oKq04pLi4W1SyNjIyEs7MzAMDPzw9du3aFn58fRo8eLfNuvqampuVOkqjpcysNIyojIyODAWAZGRnKDoXUc0lJjGloiL8V0tTkjhPlyM3NZZ06dWKdOnViubm5yg5Haeh1svqCg4MZABYSEiLzbbKzsxkA5uDgIPX648ePMwDs66+/LreP/Px8lpGRIbokJSXRc0mIEiUlMXb+vPSxPT2dsaNHGRMIPkyLMObiwpiDA2PNmjFmair5fkExl1wGdPrfJbcG+lfORd73UooY8/Ly8lhsbCzLy8urch/q4Ndff2UA2KpVq8pt85///IcBYBs3bqyVmI4ePcoAsNWrV7P169czFxcXpq+vzwwNDdmIESNYcnJyrcTBO336NAPApkyZInHdvn37GAC2ePFimfqysbFhNjY2Sjl3TZD174hmvhBC5PboEfepVFklJcDjxzRlVllKS0tx7do10feE1KaMjAwA3BRiafits/l20gQHByMgIEDxwRFC5FZ2RotAAIweDZiaAg8fAg8eAK9fl3/bGzdkO4epKaCvD2hpcZfCQm4JzodatwaMjbk4BAIgMxN48KAUwLX/teDGPHt7gH8JEgiA9HTg3j3J/hwc3rcD6lY7dX8vVZeXWF2/fh0AamXmi6enJyIiIhAWFgZPT89y2/E7+27duhXPnj3DyJEj4enpiTNnzuDw4cN4+fIlLl++XK1Y5BEeHg4A6N+/v8R1/DF5arsVFBRgx44deP78OczMzNCtWzd06NChVs6tLJR8IYTI7dkzyWMaGkCrVrUfCyH11aJFi5CamgqBQICtW7cqO5xqW7x4MRYuXCj6OTMzE02bNlViRITUT+fOAdOnc3MxAO5raKhkO0tL4M0b8WMaGtwymhYtuISJkRGQnQ107iz+oY2mJnDnjvg/4MnJgI2NZLtz5yTbNWv2Pj6+3alTsvV38mTdbldX3ksxBuTmKq6/HTuAuXPfLz1bvx6ooN68zPT1uWRbdd34X9Zww4YN2LZtW7lttLS04OTkVP0TyuDmzZsAgJycHMTExIiW1BQWFsLNzQ1XrlzBpUuX0K1bt3L7kHVZD2/+/PkwNTWVel1cXBwASF3aY2ZmBgsLC1EbWbx69Upsp2EAGDBgAHbt2iXa9Kamzq0slHwhhMilsBAIDua+Fwjev/mxt697n2IQos4OHDiAxMTEOpF84We8lDezJTMzU6ydNEKhUKxQLyGk9rx9C+zdy/2DfO2a9Daffgp4ewNt2nCzUUxMuBkyM2dyMzY0NYFNm6TXLPn9d8l2H75nsLaWvd2GDcAXX3A/a2hUv7+63E5ZcnMBQ8Oa6bu0lHv++OewOrKzgepuIFtYWIi7d+8CAA4fPlxh2w4dOlR7rNq5cydyc3PRrFmzCtvxyZfdu3eLJR10dHQwYcIE3L59Gw8ePKgw+SLvjNLJkyeXm3yRZZZrsrTpa1L4+vrCw8MD9vb2EAqFiI2NRUBAAE6ePImhQ4fi4sWLYtvIK/LcykTJF0KIXH79lVt21LAhEB7OvUnz9eU+wTp9mntjRgipeaNGjUJqaqqywwAAGBgYwMrKCk+fPkVJSQk0NTXFrq/oEytCSO3il37Y2gJ373IJl6NHgaIi7npNTS4ZUJamJvfBy4eJgalTuXH/8WNuxkZ5iQNFt5s06f0/7vfvc8mg2jivstqRmnX79m0UFRVh1KhROHDggNQ2u3btwmeffSax5OjHH3/E2rVrkZqaiq5du2Ljxo2VFpavLOkCAOnp6UhISEDnzp3Rq1cviesbNGgAACji/3DLweTY3bc2rVixQuznzp074/jx4/Dw8EBUVBT+/vtvDBo0SEnR1RxKvhBCZJaayu1QAAArVwLt2nGXW7e43QkWLgRiYri124SQmvX9998rOwQxHh4e2LdvHy5evCjxRvH06dOiNoQQ5Slby+VDzs7A5MnAuHFcMkbWGRnW1rIlDRTdjvfRR7V7XmXf39qir8/NKlGE58+594sfLrGKja38+auMvn71bg+8X3LUsWPHctvw9VfKJl/27NmDJUuWYOvWrXBycoKfnx8GDBiA+/fvV3t2DD/rxbucTzWf/a8GQG0uz5VllmtFM1wro6GhgSlTpiAqKgoXL14US77U9LlrC/2LRAiRmb8/VyCuQwdgypT3x5cv5z45i43l3qApYhopIaRuSk1NRWpqKiwsLMTWZM+YMQP79u3DsmXL8M8//0BHRwcAcO7cOZw+fRq9evWibaYJUaLkZPFaLrzp07ltoMuWsaAZGUQgqP5yHl7r1tKXWNWVIYEvtltR8oVPhpRNvvz444+YPXs2xo8fDwDYvn07GjZsiCNHjmDMmDHViolP9pQ3S+bUqVPQ0dFBz549K+xHkTVf+NmrcXFxcHV1FbsuLS0NqampFS6BkgX/viL3g4JDtXHu2kDJF0KITO7d44roAcCPP3IDJ8/UFAgMBGbPBlasAMaPB8zMlBJmvfZhcTJCZLVlyxZERUUBAO7cuSM6xu8uMHz4cAwfPhwAV4wwICAAfn5+Ym/qvLy8MG3aNGzZsgXOzs4YNGgQXr9+jf3798PY2Bi//fZbbd4lQkgZhYVcgkXaCoTx48UTL7y6OiODR2OeaqnLCT1ZZr7ExMRAU1NT1KawsBA3b94UGweNjIzQuXNnXLlypdrJFz7ZI22mR0REBK5evQpfX18YGRlV2I8ia754eHggODgYZ86cgY+Pj9h1Z86cEbWpjn///RcAYGtrW+vnrg2UfCGEVIoxYMEC7tOKESMALy/JNtOnA7/8wiVp/vtfLkFDao+BgQHefLjtBFE5JSUlCAsLw7///ou4uDikpaUhLy8Penp6MDMzg52dHTp37gxPT09oKXB9X1RUFHbs2CF27OLFi7h48SIA7k0Qn3ypyKZNm+Dk5IRNmzbh559/hqGhIYYMGYKVK1fSrBdClOTFC26r6EuXJK+rS7vryIPGPNVUFxN6RUVFuHPnDiwsLPBROWugEhMT8e7dO7Rv3x76/1vnlJqaipKSEjRs2FCsbcOGDfG6or3YwS0Z4gvu6pezbopPvuzduxfz5s0TjfkJCQmYNGkSLCws8N///rfS+6fImi99+vRBixYtsGfPHsybN0+UiMrKykJgYCC0tLQkdi968uQJioqK0LJlS2hrawMAYmNj0aRJE4kkT1RUFNauXQuhUIiRI0dW+9x1ESVfCCGV+vtv4OxZQEcHKK/MhJYWl3Dp35/bhWDmTKBt29qNkxBVtnbtWnz77bd4+/YtAOlvmPjK/w0aNMA333yDhQsXiu0GUFXbt2/H9u3bZWrr7+9f7jRmDQ0NzJ07F3Pnzq12TISQ6ouIAMaOBV6/5mapTpzIFc6vi7vrEKIM9+7dQ0FBQYXLd6TVe6mOzz77DBEREQgLC4Onp6fE9fn5+aJdjB4+fAhXV1f069cPqampOHToEEpLS3H8+PFyk0U1RUtLC1u2bIG3tzd69uyJcePGwdjYGIcOHcLTp08RFBQk8UFLnz59kJiYiKdPn4pms4SGhmL16tXo06cPbG1tIRQKcffuXZw5cwYaGhrYuHGjxHKrqpy7LqLkCyGkQkVFXCFdAJg/H2jZsvy2/foBQ4YAx44BX30FHD9eKyESotIYYxg5ciSOHj0KxhiMjY3h5uaGFi1awMzMDEKhEAUFBUhLS0N8fDyio6ORmpqKRYsWITIyEn/99ZdCEjCEEPXBGPDTT8DXX3OJFicn4NAhbgxftKhuLv0gRBmqWu/FwsICmpqaSElJEWubkpJS7STNnTt3UFxcDE9PT/z8889YsGABfv31V+jp6WHgwIHw9/dHWyV9wunl5YWoqCj4+fkhNDQUhYWFsLe3R2BgICZMmCBzH/fv38eNGzcQERGB/Px8NGrUCGPHjsWCBQvg7u5eY+dWNgGr5lykoqIiREdHIyoqComJiXjz5g3y8vJgYWEBS0tLuLi4oGfPnrWemVNHfBXnjIwMGBsbKzscUk+sW8clXRo25LamrOxX79EjwN4eKC4GTp2iradrS15eHj7++GMAwMmTJ6Gnp6fkiJRDFV8nN2zYgHnz5qFRo0ZYu3YtRo8eXeGSouLiYoSGhuLLL79ESkoK1q1bhzlz5tRixLVDFZ9LQuqC7Gxg2jRg/37u5wkTuGKnitgVpq6gMY+jiNfJ/Px8PH36FM2bN4eurq6CI1Rvbm5u8PDwwJo1awAA2dnZsLS0xI4dO6pV82Xz5s2YMWMG9u/fX+3aMaR2yPp3VOWZL2FhYdiyZQv++usv5OfnA6h4inS7du3g6+uLzz77jApkEaIi3r7ldjgCgKCgyhMvAFe5fu5cbgkSbT1de0pLSxERESH6nqiOkJAQaGpq4syZM3B0dKy0vZaWFsaPHw97e3u4urpi27Ztapl8IYTIJzkZOH8eWLmS+yCEXw78xRfczjXqhMY8UhfMnz8f06dPR6dOneDg4ICAgABYWVlh6NCh1eqXn2lT0Wwcoprk/pfo2LFjWLx4Me7fvw/GGLS0tNCxY0e4ubnBysoK5ubm0NPTw7t37/Du3TvExsYiOjoasbGx+Oqrr7BkyRLMmDEDy5cvh6WlZU3cJ0KIgvj5cVtLOzkBvr6y3275cmDnTm7r6d9/53ZBIoRI9/DhQzg4OMiUeCmrQ4cOcHBwQFxcXA1FRghRFVu3im8jbWICnDgBdO+u3LgIUWcTJkxASkoKvvrqK6SmpqJr1644efJktWcQ3bx5EwYGBmilitWwSYXkSr706tULFy9ehJ6eHsaMGQMfHx94e3vL9Av25MkT7Nu3D3v37sWGDRuwY8cO7Ny5E8OGDaty8ISQmlN2a+mffhLfWroyZmbcjkdffMFtPT1uHG09TUh5hEIhsrOzq3Tb7Oxs0e4BhJD6KTkZmDFDfBvp7GzAxkZ5MRFSXyxYsAALFixQWH+lpaW4ffs2nJycoKGhobB+Sd0g1zN69+5dLF++HMnJydi7dy+GDRsmc2avZcuWWLp0Ke7evYtz587B1dUVt2/frlLQhJCalZQETJ5c8dbSlZkxg6v98vYtV/AvLIx7g0gIEefs7Iz4+HiEhobKdbt9+/YhPj4erq6uNRQZIUQV3LsHfLjypqSEK6pLCFEtGhoayMnJweXLl5UdCqkBciVfEhMT4e/vL7Ent7y8vLxw/vx5zJ8/v1r9EEIUb+tW7tOya9e4n93cqtYPv9ac77N3b67frVsVEych6mLhwoVgjGHChAmYPXs2rl27Vm4Ng9LSUly7dg2zZs3CxIkTIRAIFPqJGyFE9fz1l+QxTU1uNyNCCCF1h1zLjoyMjBR6ckX3RwipHmlTl5cvByZOrNp2lO3aif9cWgrMnMntgETbWxLCGThwIFatWoWlS5di06ZN2LRpE3R1ddGsWTOYmZlBR0cHhYWFSEtLw7Nnz0RF7gEgKCgIAwcOVGL0hBBlCgsDNm3ivtfQ4MZZTU3uGI2zhBBSt9AeJIQQkbi48qcuV+VNnLQ6oNXpj1RMX532Ea1n/u///g8eHh4ICgrCuXPnkJeXh4cPH0ptq62tjb59+2Lp0qXo1q1bLUdKCKkr0tOBSZO4D0ymTeOK5D9+zM14qQ9jLI15hBBVQ8kXQoiInR23HWXZmS/VmbpsZ/f+kzhF9EfKZ2BggJycHGWHQaqha9euOHHiBLKysnDz5k3ExcUhLS0N+fn50NXVhZmZGezs7ODs7EwzRwkh+OILrkZby5bcMl9Dw/qRdAFozCOEqKYaSb5kZGQgPj4excXFsLa2hpWVVU2chhCiYNbWQOfOwJUr3M/Vnbpsbc1tNc1vfykQ0FRoQipjZGSEXr16oVevXsoOhRBSR+3dC+zZw43Tf/zBJV4IIYTUbXLvX1VYWIji4mKp1924cQP9+vWDhYUFOnXqhC5dusDa2hoODg5y7+JACFGOd++4r8HBQEICMHVq9fqbOhVYupT7vl+/6vdHCCGE1GfPngGzZnHfL1sGdOmi3HgIIYTIRu7ki56eHvr06SNx/PTp0+jRowfOnz+PkpISMMZEl9jYWIwbNw6BgYEKCZoQUjPS0oBHj7jvp09X3AyVAQO4r7dviy9pIoqTn5+PQYMGYdCgQWIFWQkhhKiP0lJg8mQgIwNwd3//4UZ9Q2MeIUQVyZ184RMqZWVmZmL8+PHIz8+Hm5sbTp8+jczMTOTl5eHatWvw8fEBYwwBAQGIjo5WWPCEEMW6epX72qoV0KCB4vp1ceG2nn71ilufThSvpKQEf//9N/7++2+UlJQoOxxCCCE14McfuR2O9PW55Uba2sqOSDlozCOEqCK5ky/S7Ny5E2lpaejSpQsuXLiAfv36wdDQEEKhEC4uLtizZw/mzJmD0tJS/Pbbb4o4JSGkBvC1Xjp3Vmy/enqAk5P4OQghhBAiu9u3gSVLuO9/+okrak8IIUR1KCT5cvHiRQgEAgQGBkK7nBR8UFAQdHR0EBkZqYhTEkJqwL//cl8VnXwp2yd/DkIIIYTIJj8fmDABKCwEhg7ltpYmhBCiWhSSfElJSQHAbZNZHmNjY7Rv3x4vX75UxCkJIQrG2PtlRzVRvI/vk5IvhBBCiOySk4GJE4G7d4GGDYHNm7ndAwkhhKgWhSRfjI2NAUCiFsyHtLW1IaDRgpA66ckT4O1bQCgEOnRQfP/8zJfr14GiIsX3T4i6iYmJkZgtKu0YIUR9bd0K2NgABw9yP/v4cAkYQohyhIeHQyAQwN/fX9mh1GkCgQCenp7V7sff3x8CgQDh4eHV7qsuqFLyJSUlBTt37hRd+K2nnz59WuHtXrx4AUtLy6qckhBSw/haLM7OgI6O4vu3swNMTbmp07dvK75/QtTNnDlz0Lt370qPEULUU3IyMGMGt8MR75dfuOOEEEJks337dggEAmzfvl3ZoUCrKjeKi4vDlClTRD8zxiAQCHDixAk4ODhIvU1CQgKeP38udZtqQojy1WS9FwDQ0OC2xTxzhjuXq2vNnIcQdSJtRmlls0wJIeohLk488QIAJSXA48eAtbVyYiKEEFJ1cidfJk2aVO51/AwYaX7//XcAFdeFIYQoD598qYl6L7wuXd4nX2bPrrnz1EcGBgb0TzkhhKiRVq0kj2lqSj9e39CYRwhRRXIvOwoJCSn3snTp0nJv17t3bxw+fBgzZsyoVsCEEMXLzwdu3eK+r6mZL2X7pqK7hBBCSMWSksR/1tQENm2iWS+E1IQdO3agS5cuMDQ0hKGhIbp06YIdO3ZUeJvIyEh4eHjA0NAQ5ubmGD9+PJKlrAvkV400b94curq6sLCwgIuLC7788kuJtllZWfDz84O9vT309PRgamqKAQMGICoqSqKtp6cnBAIBCgoKsGLFCrRq1Qra2trw9/eHr68vBAIBLly4IDX2lStXQiAQYNeuXWLHb9++DR8fH1hZWUFHRwc2NjaYO3cu3r59K7WfLVu2wMHBAbq6umjatCkWLVqE/Pz8Ch83aZKSkjBu3DiYm5vD0NAQHh4e5da4KywsxPr16+Ht7Y2mTZtCKBSiYcOGGDlyJG7evCnWdvLkyaIVO1OmTIFAIBBdeNevX8ecOXPg4OAAExMT6OnpwdHREd9++y2KFFyoskrLjqqib9++tXUqQoicbt7kiuBaWgK2tjV3Hnd37uvDh0BaGmBmVnPnIoQQQlTZ2rXcVx8fYOZMbsYLJV5IbcvJySn3Ok1NTejq6srUVkNDA3p6elVqm5ubK3Wmk4GBQbl9yGPBggX46aef8NFHH2Hq1KkQCAT4888/MXnyZMTExGAt/8dYxpUrVxAcHIxBgwZh3rx5uHHjBvbu3YuoqChER0ejUaNGALiap+7u7sjJycGgQYMwduxYZGdnIy4uDuvXr8cPP/wg6vPdu3fo1asX7t27h549e8Lb2xsZGRk4cuQIvLy8cODAAQwfPlwilpEjRyImJgbe3t4wNzdHixYt4OHhgZCQEPzxxx/o2bOnxG12794NAwMDjBgxQnTs6NGjGDNmDDQ1NTF06FA0bdoUsbGx2LBhA06fPo1///0XZmXevAcGBmLFihVo1KgRpk+fDm1tbezfvx/379+X6/F/+fIlunbtiufPn8Pb2xsuLi64f/8++vXrBy8vL4n27969w/z589GzZ08MHDgQZmZmiI+Px9GjR3Hy5ElERkbCzc0NADB8+HCkp6fjyJEjGDZsGDp27CjR3+bNm3Hs2DH06tULAwcORG5uLsLDw7F48WJER0fjzz//lOv+VIipqKtXr7KPP/6YmZqaMn19febm5sZ2794t8+1fv37NVq1axT755BNma2vLALCKHo7k5GT2448/sn79+rGmTZsybW1t1qhRIzZy5Eh25coVqbfx8/MT9fvhRSgUyn2fMzIyGACWkZEh920JqciPPzIGMDZ4cM2fq2VL7lynTtX8ueqTvLw8NmrUKDZq1CiWl5en7HCURp1eJ3v06ME0NDQqPaau1Om5JERe8fGMaWhw4+WdO8qOpu6hMY+jiNfJvLw8FhsbW+7jWN7/MgDYwIEDxdrq6+uX29bDw0OsrYWFRbltO3XqJNbWxsZGajtFiIyMZABYu3btWHp6uuh4eno6a9u2LQPALly4IDoeFhYmOv+WLVvE+goICGAAmK+vr+jYzz//zACwdevWSZz7zZs3Yj+PHz+eAWDbtm0TO/7q1SvWtGlTZmlpKfY8eXh4MACsY8eO7O3bt2K3KS0tZU2bNmVmZmasoKBA7Lpr164xAOzTTz8VHUtNTWXGxsbM2tqaJSYmirXfs2cPA8DmzJkjOhYXF8e0tLTYRx99xF6/fi06npGRwdq0aSP1OS/PpEmTGAAWFBQkdnzTpk2ixzosLEx0PD8/nyUnJ0v0c/fuXWZoaMj69u0rdjwkJIQBYCEhIVLPn5CQwIqLi8WOlZaWMl9fXwaARUVFVXofKvs74ilkq+naFh4ejh49euDChQsYNWoUZs2ahdTUVEyYMAGrVq2SqY/Y2FgsWbIEhw4dgo6ODvT19Stsv379eixYsADx8fHo168fvvzyS/To0QNHjhxBt27dEBoaWu5tJ02aBD8/P7HLsmXL5LrPhNSk2qj3wuPPQUuPFKukpAQHDx7EwYMHUVJSouxwCCGEVMPPP3PFdvv3B8rZy6JeozGPKAq/A46/vz9MTExEx01MTODn5yfWpqw2bdrA19dX7NjXX38NS0tL7N27F4WFhWLXlZ3Jw7OwsBB9n5qaiv3796NPnz5iG9sAQKNGjfD111/jzZs3+OeffyT6CQgIgLm5udgxgUCA8ePHIy0tDSdOnBC77o8//gAAfPrpp6JjO3fuRGZmJoKDg9GsWTOx9uPGjYOLiwv27dsnOrZnzx4UFxdj4cKFaNiwoei4sbGxXP/nFhYWYv/+/WjYsKHEMqxp06ahdevWErcRCoX46KOPJI7b29vDy8sLkZGRci0XsrGxgaamptgxgUCAL774AgCkPuZVVWvLjhYtWoTU1FQIBAJs3bq1yv0UFxdj2rRpEAgEiIyMhLOzMwDAz88PXbt2hZ+fH0aPHg07O7sK+2nXrh0iIiLg7OwMIyMjtG3bFg8fPiy3vbu7OyIjIyWmbV24cAF9+vTBrFmzMGzYMAiFQonbTp48WSH7nBNSU2p6p6OyOncGdu+m5AshhBAiTUYGwL9VXrBAubEQkp2dXe51H/7DmpKSUm5bDQ3xz/wTEhJkbhsbG1tjBZb5GiHS/lfjj93iCyOW0b17d7G6IQCXYHF1dcWpU6fw6NEjODg4YPDgwfi///s/fPHFFzh79iwGDBiAHj16SCQVoqOjUVJSgvz8fPj7+0ucLy4uDgDw4MEDDB48WOw6d35d/wcmTpyI7777Dn/88YdoeVFJSQn27t2Lxo0bi5UFuXLliujr48ePJfrKz89HamoqUlNTYWFhgZiYGACQuqRJ2rHyPHz4EPn5+ejdu7fYEjaA+z3o1q0bHj16JHG7W7duYfXq1YiKisKrV68kki2pqamwsrKSKYbCwkJs2LAB+/btw4MHD5CdnS32+/bixQuZ709lai35cuDAASQmJlY7+XL+/Hk8efIEU6ZMESVeAMDIyAjLly+Hj48PQkJCKp0B06hRI9FaPFmMHDlS6vGePXvCy8sLZ86cwZ07d9CpUyeZ+ySkLkhJAZ4+BQQC4H/LI2tU2aK7jHHnJYQQQghn61YgKwto1w7w9lZ2NKS+k6euSk21rWyFQnVkZmZCQ0MDlpaWEtc1atQIGhoayMjIkLiu7GyPD28DQHSb5s2b4/LlywgICMDJkydx4MABANzMmcDAQIwePRoAV8cEAC5evIiLFy+WG6+0Wjnl/U9rb28PZ2dnnDhxAunp6TA1NcXZs2fx+vVrLFy4UCx5xp//l19+Kffc/PktLCxE90/a4yDP/9gV9VNeX5cuXULv3r0BAP3794ednR0MDQ0hEAjw119/ISYmBgUFBTLHMGrUKBw7dgytW7fG2LFj0bBhQ2hrayM9PR3r1q2Tq6/K1FryZdSoUUhNTa12P+Hh4QC4B/pD/LGIiIhqn0ce2traAAAtLekP54ULF3D16lVoamqibdu26Nu3r9QZMh8qKCgQe7IzMzMVEzAhZfAzUNq2BcrMtqwxHToAOjrA27fAkye0ZSYhhBDCKy7mlhwB3KwX+oCCkJplbGyM0tJSvHnzRiIBkJKSgtLSUhgbG0vcrrxZPq9fvwYAsSVMTk5O+PPPP1FUVITr16/j5MmT+PnnnzF27Fg0adIE3bt3F53jyy+/xJo1a+S6Dx/OwClr4sSJWLhwIQ4ePIhp06aJlhxNnDhRrB1//jt37sBBhrWO/P1LSUmBjY2N2HX8YyCLsv1II62vlStXoqCgAFFRUejevbvYdVeuXBHNypFFdHQ0jh07Bm9vb5w4cUIsIXXlyhWsW7dO5r5kUWs1X77//nvRltTVwU+5krasyMzMDBYWFqI2teHZs2f4559/0LhxYzg6Okpts2LFCnzzzTf46quvMHjwYDRv3hxnz56ttO/g4GCYmJiILk2bNlV0+ITUar0XABAKARcX8XMTQgghBPjrLyAxEbCwAMqUYyCE1BB+JQX/AX9Z/Af60nbIuXjxosRSqLy8PFy/fh16enpSa5Voa2ujS5cuCAgIwM8//wzGGI4fPw4AcHNzg0AgwOXLl6t5j8SNGzcOmpqa+OOPP5CTk4O//voL9vb2Evep8/+mpst6/g4dOgCA1K2sy9veWpo2bdpAV1cX165dk9iiurS0FJcuXZK4zZMnT2Bubi6ReMnNzcWNGzck2vMJFWn1oZ48eQIAGDRokMQyOnnuh6xUruAuPzXJpJyP6I2NjaVODasJRUVFmDhxIgoKCrB69WqJJ6xjx47YsWMHEhISkJeXh7i4OAQGBiI9PR1Dhw6tNCu3ePFiZGRkiC5JSUk1eXdIPVWb9V54ZZceEUIIIYTD72g7axYgpT4nIUTBJk2aBIArWlt2lUFmZiYCAgLE2pT18OFDbNu2TezY999/jzdv3mDcuHHQ0dEBwM2skDarg5/RwRfibdy4McaMGYNLly7h+++/l1rj5t9//0Vubq5c94+v7RIZGYl169YhJydHYtYLAEyZMgVGRkZYunQp7t27J3F9bm6uqC4MAIwfPx6amppYu3at2P3LzMxEUFCQzPHp6OhgzJgxSElJEdt2GwC2bNkitd6LjY0N0tLSxOIsKSnBV199hTdv3ki054sRJycnS+0LAKKiosSO37t3D8HBwTLfD1nV2rIjdVNaWgpfX19ERkZi+vTpUn+JP9yHvVWrVli2bBkaNWqEGTNmICgoSLTuTxqhUCjT8iRCqqq0FLh6lfueki+EEEKI8ly5Aly+zC3NnT1b2dEQUj/06tULc+fOxfr16+Hg4IBPPvkEjDEcOnQISUlJmDdvHnr16iVxu/79+2P27Nk4ceIE2rZtixs3buD06dNo2rSpWO3R3bt349dff4WnpydatWoFY2NjxMbG4u+//4aFhYXYjkm//vorHj58iEWLFmHXrl3o2rUrTExMkJSUhOvXryMuLg4vX76UuwbOxIkTcfr0afj7+0NDQwMTJkyQaMPv0jR69Gh06NABAwYMQNu2bZGfn4/ExERERESgW7duOHXqFADu/9oVK1bAz88PTk5OGDNmDLS0tPDnn3/C0dGxwo1sPvTtt9/i3LlzWLZsGaKiouDs7Iz79+/j77//Rv/+/XHmzBmx9nPnzsWZM2fQo0cPjBkzBrq6uggPD8fz58/h6ekpMYupa9eu0NPTw08//YTMzExRfZ//+7//g7u7O9zd3REaGoqXL1+iS5cuePbsGY4ePYpBgwbh4MGDcj3Wlap00+oKFBcXs7Nnz7KgoCA2adIkNnToUNavXz82dOhQNmnSJBYUFMTOnj3LioqKqnMaMaNGjWIA2LVr16Reb2FhwSwtLeXul9+PXBZl9/3+9NNPWUlJiVznKigoYFpaWszKykqu22VkZDAALCMjQ67bEVKee/cYAxjT12dMgX+mlXryhDuvtjZjeXm1d151VlpayrKzs1l2djYrLS1VdjhKo06vk6tWrWKTJ0+u9Ji6UqfnkhBZjBnDjY315E+8WmjM4yjidTIvL4/FxsayvHr+hmzbtm3Mzc2N6evrM319febm5sa2bdsm0S4sLIwBYH5+fiwiIoL17NmT6evrM1NTU+bj48OePXsm1v7KlSts5syZzMHBgZmamjI9PT1mZ2fH5s2bJ9GWMcZyc3PZ6tWrmaurKzMwMGB6enqsefPmbPjw4Wznzp1i/1d7eHjI9P9rTk4OMzQ0ZACYl5dXhW0fPHjApk6dymxsbJiOjg4zMzNjjo6ObN68eezq1asS7Tdv3szat2/PdHR0mLW1Nfvqq69Ybm4uA8A8PDwqjY2XmJjIxo4dy0xNTZm+vj7r2bMni4iIYH5+fgwACwsLE2t/8OBB5uLiwvT19ZmFhQUbM2YMe/LkCZs0aRIDwJ4+fSrW/sSJE8zNzY3p6ekxAGKPW0pKCvP19WVNmjRhurq6zNHRkf3yyy8sPj6eAWCTJk2qNH5Z/44EjFVt3661a9fi22+/xdu3b/kkjkQbvvhPgwYN8M0332DhwoUVFgSSxZIlSxAcHIy9e/fCx8dH7Lq0tDSYm5ujW7duFVaJlobfarqyh6O0tBTTpk1DSEgIxo0bh127dkksN5KFubk5SktLkZ6eLvNtMjMzYWJigoyMDKmFnwiRV0gI4OsL9OwJREbW3nkZAxo2BFJTuU/5aqveDFF/9DqpPui5JPVJYiLQsiVQUgLcusUVpyekMop4nczPz8fTp0/RvHlzia1+CSGykfXvSO5lR4wxjBw5EkePHgVjDMbGxnBzc0OLFi1gZmYGoVCIgoICpKWlIT4+HtHR0UhNTcWiRYsQGRmJv/76q1oJGA8PDwQHB+PMmTMSyRd+SpKHh0eV+69I2cTL2LFjq5x4iYuLQ1pamqhQESHKUtvFdnkCAXfO48e5GCj5QgghpD5bv55LvPTuTYkXQghRV3InX3755RccOXIEjRo1wtq1azF69Ohyt1gGgOLiYoSGhuLLL7/E8ePH8csvv2DOnDlVDrhPnz5o0aIF9uzZg3nz5okqNWdlZSEwMBBaWlqYPHmyqH1qaipSU1NhYWEBCwuLKp+3tLQUU6dOxfbt2zF69Gj88ccfFSZesrKy8PTpUzg5OYkdT0tLw9SpUwFw1acJUSZlFNvlde78PvlCqq+goAAzZ84EAGzatInqRRFCiIrIygI2b+a+X7hQubGoChrzCCGqSO5lR66urrh9+zZu3LhR7tbK0sTExMDV1RVOTk5St4CSR1hYGLy9vSEUCjFu3DgYGxvj0KFDePr0KYKCgrB06VJRW39/fwQEBMDPzw/+/v5i/ZRN0hw+fBiZmZli1azXrFkjStjw/RgaGuI///mP1ITT8OHDRcmghIQENG/eHJ06dYKjoyMaNmyI58+f4+TJk3j79i369euH48ePiyphy4KmYBNFyskBjI25ortJSYC1de2e/+xZoH9/oHlzID6+ds+tjnJycmBoaAgAyM7OhoGBgZIjUg56nVQf9FyS+mLdOmD+fKBNGyA2FtBQub1Iax+NeRxadkRI3VBjy44ePnwIBwcHuRIvALcXuIODA+Li4uQ9pQQvLy9ERUXBz88PoaGhKCwshL29PQIDA6VWby7Pjh07Kjzm7+8vSr4kJCQA4F7gV65cKbU/W1tbUfLF3NwcX3zxBa5cuYJjx44hPT0dBgYGcHR0xKeffopp06ZVackSIYpy/TqXeGnSpPYTLwDg5sZ9ffoUePMG+F/hcUIIIaTeKCnhki8Al4ChxAshhKgvuZMvQqEQ2dnZVTpZdnY2tLW1q3TbD7m7u+PkyZOVtvP395eY8cKTZ9LP9u3bsX37dpnbGxsbY8OGDTK3J6S2KaveC8/UFGjXDrh/n4tl8GDlxEEIIYQoy5Ej3IcQ5ubAZ58pOxpCCCE1Se78urOzM+Lj4xEaGirX7fbt24f4+Hi4urrKe0pCSA1QZr0XHn9uqvtCCCGkvklOBvz8uO8//xzQ11duPIQQQmqW3MmXhQsXgjGGCRMmYPbs2bh27RpKS0ulti0tLcW1a9cwa9YsTJw4EQKBAAsWLKh20ISQ6rtyhftaF5IvfCyEEHGMMaSnp6O4uFjZoRBCFGjrVsDGBrh7l/vZ3Fy58RAiZxlQQkgZsv79yJ18GThwIFatWoXS0lJs2rQJnTt3hpGREdq1a4du3brB09MT3bp1Q7t27WBkZITOnTvj999/R2lpKYKCgjBw4EC57wwhRLGeP+cuGhqAMiej8cmXq1e5+jOEEM7ly5fh7e0NAwMDNGjQAEKhEFZWVpgwYQKOHTum7PAIIdWQnAzMmCE+7n3zDXeckNrGbyJCSX5Cqq6oqAgAKq3pWqWyXv/3f/+HqKgoDBgwANra2sjLy8PDhw9x5coVREZG4sqVK3j48CHy8vKgpaWFAQMG4MKFC1i8eHFVTkcIUTB+mY+jI/C/zQKUwtER0NMDMjOBhw+VFwchdcn58+fh6emJf/75B/n5+aJPU16/fo29e/di+PDhcHV1xb179xR63ujoaAwcOBBmZmYwMDCAu7s79uzZI1cf6enpWLFiBZycnGBkZAQLCwu4ublhw4YNyM/PV2i8hKiquDjJDxxKSoDHj5UTD6nfNDU1oampiczMTGWHQohKYowhIyMDQqGw0vq2chfc5XXt2hUnTpxAVlYWbt68ibi4OKSlpSE/Px+6urowMzODnZ0dnJ2dYWRkVNXTEEJqQF2o9wIAWlpAp07AhQtcTO3aKTceVaavr4+UlBTR90R1LVu2DEVFRXBxccEPP/wANzc36Orq4unTpzh79iw2b96MmzdvonPnzti/fz8GDRpU7XOGh4fD29sbOjo68PHxgYmJCQ4dOoQJEyYgISEBS5YsqbSP9PR0uLq6Ij4+Hj169MDMmTNRUFCAkydPYu7cuTh8+DDOnj0LDdrOhdRzdnaAQACUnaWuqQm0aqW8mFQNjXmKIxAI0LBhQ7x8+RJCoRAGBgYQCATKDouQOo8xhqKiImRkZCA7OxsfffRRpbcRMFrgpzIyMzNhYmKCjIwMGBsbKzscosI8PYGICG7Nua+vcmP5+mtgzRqu2OBvvyk3FqL61OF1Ul9fHwKBAAkJCbAsZw/233//Hf/5z3+gqamJmJgYtGzZssrnKy4uRtu2bZGcnIzLly/D2dkZAJCVlYWuXbvi4cOHiI2NhZ2dXYX9rF69Gt988w0WLFiAtWvXio4XFhaiR48eiI6ORkREBHr16iVTXOrwXBJSHjc34No17ntNTWDTJmDqVOXGRFSPol4nGWN49eoVMjIyqPYLIXISCoWwsLCQ6W+wyjNfCCGqqbgYiI7mvlf2zJeyMVDRXUI4Ojo6aNGiRbmJFwCYMWMGNDU1MX36dAQFBSEkJKTK5zt//jyePHmCKVOmiBIvAGBkZITly5fDx8cHISEhWLVqVYX9xMfHA4BEbTcdHR3069cP0dHRok+qCanP8vKA+/e57zduBAYNAqytlRsTqd8EAgGsrKzQsGFDUe0KQkjlNDU1K11qVBYlXwipZ+7dA3JzAWPjurHMp0sX7uudO1xcNHu4agoKCrBw4UIAwNq1ayEUCpUcEakqfhZKZaZMmYIlS5bgzJkz1TpfeHg4AKB///4S1/HHIiIiKu3H3t4eAHDq1Cn07dtXdLyoqAj//PMP9PT00LVr12rFSog6OHsWyMkBmjblCu/SCg/50ZhXM/j6L4SQmkELrwmpZ/h6L25u3G5HymZtDTRpwhUbvH5d2dGoruLiYvz666/49ddfaccCFTd+/Hi8ePECoaGhFbbT0NBA06ZNkZaWVq3zxcXFAYDUZUVmZmawsLAQtanItGnT4Obmhh9++AGenp74+uuvMW/ePNjb2yM+Ph579uypcD10QUEBMjMzxS6EqKNDh7ivI0ZQ4qWqaMwjhKiiOvCvFyGkNtWVYrtl8bHwsRFSnw0bNgz9+/fHjBkz8M8//5TbLi8vD48fP0aralbpzMjIAACYmJhIvd7Y2FjUpiJ6enoIDw/Hp59+ioiICKxZswbr16/HkydPMH78ePTo0aPC2wcHB8PExER0adq0qfx3hpA6rqgIOHqU+37kSOXGQgghpHZR8oWQeoavrVIXky9U94UQoEWLFrhy5QoyMzPh7e0NHx8fnD9/HoWFhaI2KSkpmDhxIjIzM7FgwQIlRvteamoq+vXrhytXruDEiRNIT0/Hq1evsHHjRoSEhKBz584VztJZvHgxMjIyRJekpKRajJ6Q2hERAaSlAZaWQCX5SEIIIWqGar4QUo9kZr4v8leXki983Rea+UIIYGVlhRcvXgDgdqAIDQ3FgQMHoK2tjcaNG6O4uBivXr2ClpYWfvjhB0yZMqVa5+NnvJQ3u4XfTaMyCxcuxKVLlxATEwMnJydR39OnT0dJSQlmzZqFn376CQEBAVJvLxQKqW4DUXuHD3Nfhw3jdjkihBBSfygs+RITE4OMjAyxLSSlHSOEKE90NMAYYGsLNGqk7Gjec3Xl6s8kJwMvXnA1YAipr5KTk5GWlobbt28jJiZG9DU2NhbPnj0TtSssLMRXX32Fn376CY6OjnBwcBBd2rdvDx0dHZnOx9d6iYuLg6urq9h1aWlpSE1NRbdu3Srt58SJEzA3NxclXsrq3bs3AOA6FXYi9Vhp6fvkCy05IoSQ+kdhyZc5c+bg8uXLYkWvpB0jhChPXaz3AgCGhoCDA3D7NhfjiBHKjogQ5TIzM4OHhwc8PDxEx0pLS/Ho0SOxpMzt27eRlJSEpKQk/P333xD8r3qnpqam2DKlinh4eCA4OBhnzpyBj4+P2HX8Tkpl4yhPYWEh8vPzUVhYKJH4efPmDQDQzBZSr/37L/DyJbfb4P/ykYQQQuoRhdZ8YYzJdIwQohxhYdzXNm2UG4c0fEJo/35uBgwhRJyGhgbatm2LMWPGYOXKlTh27BgSExPx7t07hIeHY926dfD19YWLiwu0tbVl7rdPnz5o0aIF9uzZg1u3bomOZ2VlITAwEFpaWpg8ebLoeGpqKh48eIDU1FSxfrp3747i4mIEBgaKHS8oKBAd8/Lykv+OE6Im+F2OBg8GKA9JCCH1D9V8IaSe2LIF4DdOCQoCmjUDpk5VbkxlFRVxX/fvBw4cAH7/vW7FV9fp6enh6dOnou9J/WFqaopevXqJLfGV54MPLS0tbNmyBd7e3ujZsyfGjRsHY2NjHDp0CE+fPkVQUBBat24tar9hwwYEBATAz88P/v7+ouPffvstLl26hKCgIJw5cwbdu3dHfn4+Tp8+jfj4eLi6umLatGkKuc+EqBrG3idfaMlR9dGYRwhRRbTbESH1QHIyMHPm+59LS7mf68oMk+RkYOfO9z/XtfhUgYaGBmxtbWFrawsNDXppr+/45Uey8vLyQlRUFHr06IHQ0FD8+uuvaNCgAf744w8sXbpUpj46duyI69evY8qUKXj16hU2bNiA7du3w8DAAAEBAYiMjISurm5V7g4hKu/2bSA+HtDVBQYMUHY0qo/GPEKIKqKZL4TUA3FxXEKjrJIS4PFjwNpaOTGVVdfjI6Q+cHd3x8mTJytt5+/vLzbjpSw7Ozts27ZNwZERovr4WS8DBgAGBsqNhRBCiHJQqpiQesDODvjwg3BNTaBVK+XE8yE7O263o7LqUnyqoLCwEF9//TW+/vprmQutEkIIqR205EixaMwjhKgiSr4QUg9YWwNld4rV1AQ2bao7s0qsrbkaL3yCSCCoW/GpgqKiIqxZswZr1qxBEV9AhxBCiNI9egTcvQtoaXHFdkn10ZhHCFFFlHwhpJ7g35v4+QEJCXWvmO3UqcCCBdz3n3xS9+IjhBBCquLwYe6rlxdgZqbcWAghhCgPJV8IqQcYA2Jjue/HjKm7M0r42TmJicqNgxBla9GiBVq0aIEePXqU26ZXr15o0aIFWrZsWYuREULkxSdfaMkRIYTUb1Rwl5B6ICkJyM7mpjzX5Toq7dtzX2NjuQK8tIEBqa8SEhIAAMXFxeW2SUpKQmJiotw7GxFCak9yMvDvv9xy2mHDlB0NIYQQZaLkCyH1AD/rpXVrQEdHubFUpFUrQFsbyMnhEkY2NsqOiBDlCAkJAQAYVLAtypo1a5CdnV1bIRFCquCvv7iv3boBVlZKDYUQQoiSUfKFkHrg3j3uq729cuOojLY20KYNV5jw3j1KvpD6a9KkSZW2+eSTT2ohEkJIddAuR4QQQng0qZ+QeoBPvvDLeuoyPkY+ZkIIIUQVpaYCERHc9yNGKDcWQgghyqewmS8DBw5Eqw+KSUg7Rgipffyyo7o+8wV4HyMfM5GNnp4e7t69K/qeEEKIch09ytUvc3YGmjdXdjTqhcY8QogqUljyZfHixTIdI4TUrrI7HdHMF/WloaEBe1XIrhFCSD1BS45qDo15hBBVRMuOCFFzyclAVha305GdnbKjqVzZmS+MKTcWQgghpCoyM4GzZ7nvKflCCCEEoIK7hKg9fgZJXd/piFd2x6Nnz6jorqwKCwuxatUqAMCSJUugowpPNiGEqKm//wYKC7ki8u3aKTsa9UNjHiFEFdHMF0LUnCoV2wW4xEvr1tz3tPRIdkVFRQgICEBAQACKioqUHQ4hhNRrZZccCQTKjUUd0ZhHCFFFlHwhRM2pUrFdHhXdJYQQoqry87mZLwAtOSKEEPIeLTsiRM2p2swXgIruEiLNkSNHcOzYMdy/fx/v3r0DAJibm6Ndu3YYOnQohg4dquQICSEAsHcvt3TWygpwdVV2NIQQQuoKhc58YYwhPT0dxcXFiuxWqujoaAwcOBBmZmYwMDCAu7s79uzZI/PtU1JSEBwcjFGjRqF58+YQCAQQyDAvVN7zZmZmYuHChbCxsYFQKISNjQ0WLlyIzMxMmWMlpKrK7nREM18IUU1v375F165dMWLECERFRaFx48bo0aMHunfvjsaNG+PixYsYPnw4unXrhrdv3yo7XELqta1bgalTue9fvQK2bVNuPIQQQuoOhcx8uXz5Mvz9/XHhwgUUFBQAABo2bIjevXvDx8cHQ4YMUcRpRMLDw+Ht7Q0dHR34+PjAxMQEhw4dwoQJE5CQkIAlS5ZU2kdsbCyWLFkCgUAAOzs76OvrIzc3V6HnzcnJgYeHB27duoV+/fph3LhxiImJwY8//oiwsDBERUXBwMCgWo8FIRVRtZ2OeB/ueETr5Ul9tmDBArx58wZXr15Fp06dpLa5fv06fHx8sHDhQuzYsaOWIySEANyYO2PG+536GANmzgS8vQFra+XGRgghpA5g1XTu3Dmmo6PDNDQ0mEAgYAKBQOJ7FxcXdvfu3eqeijHGWFFREWvZsiUTCoXsxo0bouOZmZnM3t6eaWlpsUePHlXaz6tXr1hERATLzMxkjDHWpk0bVtHDUZXzrlixggFgixYtknp8xYoVMt1nXkZGBgPAMjIy5Lodqb9OnmQMYKxdO2VHIp/CQsa0tbnYExKUHY1qyM7OZgAYAJadna3scJRGHV8nzczM2MGDByttd/DgQWZmZlYLEdUOdXwuiXo7f54btz68hIUpOzL1Q2Meh14nCVEt1V52tGzZMhQVFcHZ2RlhYWHIzs5GUVER4uLi8Ouvv6Jjx464efMmOnfujBMnTlT3dDh//jyePHmC8ePHw9nZWXTcyMgIy5cvR3FxMUJCQirtp1GjRujVqxeMjIxq5LyMMWzZsgWGhoZYsWKFWF+LFy+GmZkZtm7dCsZ/PEJIDVDFJUeA+I5HtPSI1HfFxcXQ19evtJ2enl6tLPslhEhnZyc5U1NTE2jVSjnxEEIIqVuqnXy5desW9PT0cPLkSXh4eEBfXx8aGhpo2bIlPv/8c1y/fh0bN25ESUkJxo4diydPnlTrfOHh4QCA/v37S1zHH4uIiKjWORRx3ri4OLx48QLdu3eXWFqkq6uLXr164fnz53j8+LHCYyWEp4rFdnlUdFc+urq6uHr1Kq5evQpdXV1lh0MUyMvLC35+fkhJSSm3TUpKCgICAtC7d+9ajIwQUpa1NdCu3fufNTWBTZtoyVFNoDGPEKKKql3zRUdHBy1atIClpWW5bWbMmAFNTU1Mnz4dQUFBMs1MKU9cXBwAwE5KAQszMzNYWFiI2iiSvOetqH3Z43FxceW2KSgoENXQAUBFeoncVHXmC8DFfOAAzXyRlaamJtzc3JQdBqkBP//8Mzw9PWFrawsvLy/Y29vD1NQUAoEAaWlpiI2NRVhYGBo3bozQ0FBlh0tIvVVQADx9yn2/bRvQrx8lXmoKjXmEEFVU7eRL27ZtkZycXGm7KVOmYMmSJThz5ky1zpeRkQEAMDExkXq9sbGxTPHU9HllaV+2nTTBwcEICAioUryEqOpORzw+Zpr5Quo7Gxsb3L17Fxs3bsSJEyewc+dOpKWlAeCS//b29ggKCsL06dNhaGio5GgJqb8uXwby8oBGjYDJk6lYPCGEEHHVXnY0fvx4vHjxotJP2zQ0NNC0aVPRG0ZSucWLFyMjI0N0SUpKUnZIRIUkJwOZmaq30xGPX3bE73hEKlZYWIjvv/8e33//PQoLC5UdDlEwAwMDfPnllzh//jxevXolmhn56tUrnDt3DgsWLKDECyFKdu4c97VPH0q81DQa8wghqqjaM1+GDRuGv//+GzNmzIC5uTn69u0rtV1eXh4eP36MVtWsOsbPJClvxkhmZma5s01q87yytC/bThqhUAihUFileAnhZ73Y2QE6OsqNpSrs7LjEUXY2kJQENGum7IjqtqKiIixatAgAMHv2bOio4pNeTxUVFUFbW1vZYRBCqumff7iv5bwVJgpEYx4hRBVVe+ZLixYtcOXKFWRmZsLb2xs+Pj44f/68WBY6JSUFEydORGZmJhYsWFCt85WtlfKhtLQ0pKamlltDpTbPW1H7ssdrIlZCANUutguI73hES4+IOjM0NESHDh3w2Wef4YcffsC5c+eQmpqq7LAIIXLIyACio7nv+/RRbiyEEELqpmonX6ysrESzOBhjCA0NRb9+/WBsbAxbW1tYW1ujSZMmOH78OH744QdMmTKlWufz8PAAAKm1Y/hjfBtFkve8dnZ2aNKkCS5evIicnByx9vn5+YiMjESTJk2qPROIkPKocr0XHh87Fd0l6qyoqAh37tzBH3/8gUWLFqF///5o1KgRrK2tMWjQICxduhShoaF49OgRGK3BI6ROiogASkq4WZs0U5MQQog01V52lJycjLS0NNy+fRsxMTGir7GxsXj27JmoXWFhIb766iv89NNPcHR0hIODg+jSvn17macL9unTBy1atMCePXswb948dOzYEQCQlZWFwMBAaGlpYfLkyaL2qampSE1NhYWFBSwsLKp8P+U9r0AgwLRp0/Df//4X//3vf/Hdd9+JrgsODkZaWhrmzp0LAS0KJjWEny2i6smXAwdo5gtRbzdv3hSNnfwlNTUVL168wMuXL3Hq1ClRWz09PTg6OqJDhw7o2LEjOnToACcnJxgYGCjxHhBCytZ7IYQQQqQRsBr6GK20tBSPHj0SS8rcvn1brGgsn3jQ1NSUq1hWWFgYvL29IRQKMW7cOBgbG+PQoUN4+vQpgoKCsHTpUlFbf39/BAQEwM/PD/7+/mL9lE2WHD58GJmZmZg0aZLo2Jo1a8QSNvKcFwBycnLQo0cP3Lp1C/369YOrqytiYmJw8uRJdOzYEVFRUXK9YebrymRkZIh2SyJEGsYAU1Ou4O6dO4CDg7IjqpoDB4AxYwB3d+Dff5UdTd2Wk5MjKrianZ1db/8ZV5fXyZcvX+LWrVsYNGgQdHR00Lx5c8TFxaG0tFTUhh9DNTQ0UFRUpKxQa4y6PJekfrC352ZpHjwIfPKJsqNRfzTmceh1khDVUmPJl/Kkp6eLJWRu3bqF2NhYiaU5lbl69Sr8/Pxw+fJlFBYWwt7eHvPnz8eECRPE2lWUfKls1snTp09ha2tbpfPyMjIyEBAQgIMHD+LVq1do3LgxRo0aBT8/P7kLA9MLLJFVcjLQtCmgqQnk5qpmwV2AeyNrbw8YGnKJJJooVj56I8pRt9dJDQ0NWFhYICUlBXl5eaJxk7/cvn0beXl5YkkZdaFuzyVRXy9fAk2acGNUaipgbq7siNQfjXkcep0kRLXUevJFGsYYLb+RAb3AElmdPg0MGAC0bQvcv6/saKqusBAwMACKi4HERFpHXxF6I8pRt9fJsskXaRhjePToEdq0aVPLkdU8dXsuifravRv49FPAxQW4fl3Z0dQPNOZx6HWSENVS7ZovikCJF0IUSx2K7QLcjJ3Wrbn7ExtLyZeK6OrqIiwsTPQ9qR8EAoFaJl4IUSW0xXTtozGPEKKK6kTyhRCiWOpQbJfHr6O/d4+bzUOk09TUhKenp7LDIISQeoUxKrarDDTmEUJUUbW3miaE1D188qV9e+XGoQj8faAdjwghhNQ1cXFAUhI3U7NHD2VHQwghpC6jmS+EqBnG1GfZEfD+PvD3iUhXVFSE33//HQAwY8YMaGtrKzkiQghRf/ysl27dAH195cZSn9CYRwhRRZR8IUTNPH/O7QykqQnY2Sk7murjZ77ExnKJJSoRJV1hYSHmzJkDAJg8eTK9EVUhrVu3RocOHcQuzajAESEqgeq9KAeNeYQQVUTJF0LUDD9DxM4OEAqVG4si2NkBWlpAVtb7LbQJUSePHz/G48ePcejQIdExY2NjODk5AeD+ybh58ybs7e2ho6r7xhOihkpKgP/VfKV6L4QQQiqlkORLixYtAABNmjRBVFSU1Da9evVCcnIyBAIBnjx5oojTEkKkUKdiu4D4jkf37lHyhaifvXv34tatW4iJicGtW7fw6tUrZGRk4MKFCwCArKwsdOrUCVpaWmjTpg06duwodjE3N1fyPSCkfrp5E0hLA4yNgU6dlB0NIYSQuk4hyZeEhAQAQHFxcbltkpKSkJiYSNtKE1LD1KnYLq99e9rxiKivsWPHYuzYsaKf37x5I5aMiYmJwcOHD1FUVIS7d+/i7t272L17t6i9tbU1EhMTlRE6IfUaX+/F05OboUkIIYRURCFDRUhICADAwMCg3DZr1qxBdna2Ik5HCKmAOhXb5dnbAwcPUtFdUj9YWlqiX79+6Nevn+hYQUEB7t27J5aUuX37NjIyMpCcnKzEaAmpv6jeCyGEEHkoJPkyadKkStt88sknijgVIaQCjKnvzBeAtpsm9ZdQKISLiwtcXFzEjickJCAmJkZJURFSf+XnA/xKe6r3QgghRBY0SZIQNfLixfudjlq3VnY0ilN2u2na8YiQ92xtbWFra6vsMAipdy5d4hIwVlZAu3bKjoYQQogq0FB2AIQQxeFnhqjLTke8D3c8IpKEQiGOHz+O48ePQ6hOTz6pNdHR0Rg4cCDMzMxgYGAAd3d37NmzR+5+srKy4OfnBwcHB+jr68PU1BQuLi4ICAiogagJUQ6+3kufPvSBgDLQmEcIUUU084UQNaKOS44AbscjOzvg/n3a8ag8WlpaGDRokLLDICoqPDwc3t7e0NHRgY+PD0xMTHDo0CFMmDABCQkJWLJkiUz9PHv2DL1790Z8fDz69u2LQYMGoaCgAI8fP8aff/4JPz+/Gr4nhNQOqveiXDTmEUJUESVfCFEj6lhsl2dvzyVfYmNpxyNCFKm4uBjTpk2DQCBAZGQknJ2dAQB+fn7o2rUr/Pz8MHr0aNjZ2VXYT0lJCUaNGoUXL17g3Llz8PLykjgPIeogPR24do37nuq9EEIIkRUtOyJEjajrzBeAiu5WpqioCNu3b8f27dtRVFSk7HCICjl//jyePHmC8ePHixIvAGBkZITly5ejuLhYtKthRQ4ePIjo6Gh89dVXEokXgPukmhB1EB4OlJZytdWsrZUdTf1EYx4hRBXROyFC1ARj6j/zBaDtpstTWFiIKVOmAABGjx4NbW1tJUdEVEV4eDgAoH///hLX8cciIiIq7Wf//v0AuN+/pKQknDhxAunp6WjZsiU+/vhjGBoaKi5oQpSIr/dCS46Uh8Y8QogqouQLIWrixQsgI0P9djri0Y5HhNSMuLg4AJC6rMjMzAwWFhaiNhW59r91GFFRUViwYAEKCgpE11laWiI0NBSenp7l3r6goEDsNpmZmbLeBUJqFV/vhZYcEUIIkUeNLTs6cuQIpk2bhu7du6Ndu3Zo164dunfvjmnTpuHo0aM1dVpC6i1+OU6rVuq10xGP3/EoM5N2PCJEkTIyMgAAJiYmUq83NjYWtalISkoKAGDu3LmYP38+kpKS8ObNG/z888/IyMjA8OHD8fLly3JvHxwcDBMTE9GlKVXWJnXQ8+fAgwfcBwBSVtcRQggh5VL4zJe3b99i8ODB+Pfff9G6dWvY29ujffv2YIwhLS0NFy9exLZt29ClSxccO3YMDRo0UHQIhNRL6rzkCBDf8Sg2lnY8Iupj586dCu/T0NAQI0eOVHi/FSktLQUADB48GN9++63o+Ny5c/H8+XN899132Lp1K5YtWyb19osXL8bChQtFP2dmZlIChtQ5/JIjV1fAzEy5sRBCCFEtCk++LFiwAG/evMHVq1fRqVMnqW2uX78OHx8fLFy4EDt27FB0CITUS+pcbJfXvv377aa9vZUdDSGKMXnyZAgEAjDGFNanra2tzMkXfsZLebNbMjMzy50V82E/qampGDp0qMR1Q4YMwXfffSdamiSNUCiEUB2n7RG1QvVeCCGEVJXCky/Hjx/H5s2by028AICrqyu+/fZbTJ8+XdGnJ6TeUveZLwB33/78k4ruEvWya9cuhfcpT3FbvtZLXFwcXF1dxa5LS0tDamoqunXrVmk/bdq0QWpqKkxNTSWu44/l5eXJHBchdQ1jVO+FEEJI1Sk8+VJcXAx9ff1K2+np6aG4uFjRpyekXmLs/cwXdU++ALTdNFEvEyZMUOr5PTw8EBwcjDNnzsDHx0fsujNnzojaVKZ37964ePEiYmNjJWbdxP4vY2pra6uYoAlRgogIrri9jg7QvbuyoyGEEKJqFF5w18vLC35+fqLCe9KkpKQgICAAvXv3VvTpCamX1H2nIx6/pIrf8Yi8JxQKERoaitDQUFq6QeTSp08ftGjRAnv27MGtW7dEx7OyshAYGAgtLS1MnjxZdDw1NRUPHjxAamqqWD9TpkyBUCjE+vXr8fz5c7F+Vq1aBQAYM2ZMjd4XQmrK1q0A/7a1sBDYs0e58dR3NOYRQlSRgClykTmAxMREeHp64vXr1/Dy8oK9vT1MTU0hEAiQlpaG2NhYhIWFoXHjxjh//jxsbGwUeXq1xq+7z8jIgLGxsbLDIXXI2bNA//5AmzbcLgzqqrAQ0NcHSkqApCTA2lrZEZG6hl4nqyYsLAze3t4QCoUYN24cjI2NcejQITx9+hRBQUFYunSpqK2/vz8CAgLg5+cHf39/sX7Wr1+PefPmoUGDBhgxYgSEQiFOnDiBhIQEzJgxA5s2bZI5JnouSV2RnAzY2AD/qykNgPuwIyGBxiGiXPQ6SYhqUfiyIxsbG9y9excbN27EiRMnsHPnTqSlpQEAzMzMYG9vj6CgIEyfPl2uNemEkPLVh2K7wPsdjx484O4zveklRDG8vLwQFRUFPz8/hIaGorCwEPb29ggMDJRrWdTcuXNha2uL77//Hvv27UNxcTHs7e2xZMkSqvNGVFZcnHjiBeA+BHj8mMYhQgghslP4zBdScyi7TcozYwaweTOwbBkQGKjsaGrWqFFc0d21a4EFC5QdTd1RXFyMw4cPAwBGjBgBLS2F59ZVAr1Oqg96LkldQTNf6h4a8zj0OkmIapG75ktRUVFNxEEIqYYbN7ivjRsrN47awBfdPXuWe0NMOAUFBRgzZgzGjBmDgoICZYdDCCFqw9oaGD36/c+amsCmTZR4USYa8wghqkjuNLGhoSHatm2LDh06oEOHDujYsSM6dOgACwuLmoiPEFKJLVuA69e57+fNA3R1galTlRtTTXr1ivt68iT3SeTvv6v3/SWEEKJ8/P/306cDK1ZQ4oUQQoj85F52pKHxfrKMQCAQfW9lZSWWjOnYsSPs7OzE2pDqoamF5EP1bSp0fbu/8sjJyRHV0crOzoaBgYGSI1IOep1UH/RckrqitBSwtATevQMuXwa6dFF2RITGPA69ThKiWuSe+XLz5k3cvn0bMTExoktqaipevHiBly9f4tSpU6K2enp6cHR0FEvKODk51dsXSEIUrb4VAaxv95cQQojy3b3LJV4MDABXV2VHQwghRFXJnXzhlxtNnDhRdOzly5e4desWBg0aBB0dHTRv3hxxcXHIzc3Fv//+i3///Vc0A0ZDQ4PqxhCiIHZ2gEAAlJ2/pqkJtGqlvJhqkp0doKEhOfNFXe8vIYQQ5YuI4L527w5oays3FkIIIapLIaXBraysYGVlBQAwNjbG/fv3kZeXh9u3b+PWrVuiy+3bt5GXl6eIUxJCwM326NoVuHSJ+1ndiwBaW3M1XqZP5xJOAoF6319CCCHKxydfPDyUGwchhBDVVmP7sunp6aFz587o3Lmz6BhjDI8ePaqpUxJSL/FFAAMCAF9f9U9ETJ0KPHwIfP89MHw4FdslhBBScxij5AshhBDFkHur6eoQCARo06aNQvqKjo7GwIEDYWZmBgMDA7i7u2PPnj1y9VFaWooNGzbAyckJenp6sLS0xJgxYxAXFyfRdvv27RAIBBVe+vTpI3Ybf3//ctvq6upW6/4TAnD1Tu7d474fN079Ey+8Hj24r/Hxyo2jLtHR0UFISAhCQkKgo6Oj7HAIIUQtxMYCqamAnh7g5qbsaAiPxjxCiCqqsZkvNSk8PBze3t7Q0dGBj48PTExMcOjQIUyYMAEJCQlYsmSJTP18/vnn2Lx5M9q3b4+5c+fi9evX2L9/P86cOYNLly6hffv2orYdO3aEn5+f1H4OHjyIe/fuwdvbW+r1kyZNgq2trdgxLS2VfOhJHRMfD+Tnc28KW7RQdjS1x8GB+3r/PlBcDNCfE6CtrY3JkycrOwxCCFEr/KyXbt0A+h+/7qAxjxCiilTuX5bi4mJMmzYNAoEAkZGRcHZ2BgD4+fmha9eu8PPzw+jRo2FnZ1dhP2FhYdi8eTN69uyJs2fPQigUAgA+++wz9OvXD7NmzUIEP+KCS7507NhRop/CwkJs2LABWlpamDRpktRzTZ48GZ6enlW7w4RU4M4d7mv79ly9l/rC1pbbdSInh9sBqV07ZUdECCFEHdGSI0IIIYpSq8uOFOH8+fN48uQJxo8fL0q8AICRkRGWL1+O4uJihISEVNrP5s2bAQBBQUGixAsA9OnTB97e3oiMjJSpPs3hw4fx9u1bDB48GI0aNarCPSKk6u7e5b7yM0HqCw0NwN6e+55/DOq74uJinDhxAidOnEBxcbGywyGEEJVH9V7qLhrzCCGqSO6ZL61btxZtN81fmjVrVhOxSRUeHg4A6N+/v8R1/LGyM1Yq6sfAwADdu3eXuM7b2xunTp1CREQEWrduXWE/W7duBQBMmzat3DYXLlzA1atXoampibZt26Jv375iCR9Cqoqf+eLoqNw4lMHREbh6lXsMRo9WdjTKV1BQgMGDBwMAsrOzaWmjmsrMzMTJkyfx4sULuLi4wIP+IySkxjx6BLx+DejqAu7uyo6GlEVjHiFEFcn9SvX48WM8fvwYhw4dEh0zNjaGk5MTAG4Zzs2bN2Fvb18jBbD4YrjSlhWZmZnBwsJCasHcsnJycvDy5Us4ODhAU8paDb7vyvpJTEzEuXPn8NFHH2HAgAHltluxYoXYz1ZWVtixYwf69etXYf8FBQUo4LeyAfemm5Cy6uvMF+D9faaZL0Td7N+/H9999x1mz54tlth/8OAB+vfvj+fPn4uOTZw4Edu3b1dClISov/993ocuXbgEDCGEEFIdci872rt3L7755ht4e3ujUaNGYIwhIyMDFy5cAABkZWWhU6dOMDIygpOTEz777DOsXbsW58+fx7t376odcEZGBgDAxMRE6vXGxsaiNtXpo2y78oSEhKC0tBRTpkyRmsTp2LEjduzYgYSEBOTl5SEuLg6BgYFIT0/H0KFDERMTU2H/wcHBMDExEV2aNm1aYXtSv+Tnc/VOgPo78wWg5AtRP/v370dMTAx69eoldnz+/PlITk5GixYtMGzYMBgaGmLXrl34+++/lRQpIeqNlhwRQghRJLlnvowdOxZjx44V/fzmzRvcunULMTExoq8PHz5EUVER7t69i7t372L37t2i9tbW1khMTFRM9EpUWlqKkJAQCAQC+Pr6Sm0zfPhwsZ9btWqFZcuWoVGjRpgxYwaCgoJw4MCBcs+xePFiLFy4UPRzZmYmJWCIyIMH3FbTZmaAlZWyo6l9/MyXx4+B3FxAX1+58RCiKDExMTA3Nxdb9vry5UucPXsWzZo1w507d6Crq4vIyEh4enril19+wcCBA5UYMSHqh+q9EEIIUbRqL5C0tLREv379xJbQFBQU4N69e2JJmdu3byMjIwPJycnVOh8/W6W8WSmZmZnlzmiRp4+y7aQ5e/Ysnj17hj59+qB58+aVxl3WpEmTMHv2bFy8eLHCdkKhkGrDkHLxMz4cHQGBQLmxKEOjRoClJfDmDbfltKursiMiRDHevHkjsbQ2LCwMjDGMHz8euv9b/9CrVy/Y2Njg/v37ygiTELX25Anw4gW3vXSXLsqOhhBCiDqokepUQqEQLi4ucHFxETuekJBQ6VKbypStx+L6wX9baWlpSE1NRbdu3Srsw8DAAFZWVnj69ClKSkoklgxVVFeGJ0uh3fLo6OjAyMgIubm5ct+WEB5fbLc+1nvhOTgAYWHcY0HJF6IuCgsLUVJSInbswoULEAgE8PLyEjveqFGjao+rhBBJfL2Xzp0BPT2lhkIIIURN1OpW07a2thg2bFi1+uB3djhz5ozEdfwxWXZ/8PDwQE5OjtTZJ6dPn66wn7dv3+LIkSMwNzfHiBEjZI6dFxcXh7S0NNja2sp9W0J4ZWe+1FdU94Woo48++ghPnjwRS9CfOnUKWlpaEjv0ZWVlVTrbkxAiP1pyRAghRNFqNfmiCH369EGLFi2wZ88e3Lp1S3Q8KysLgYGB0NLSwuTJk0XHU1NT8eDBA6Smpor1M2PGDADAsmXLUFhYKDp+7tw5nD59Gr169Sp3m+ldu3ahsLAQn376abnLgrKysnD79m2J42lpaZg6dSoAYNy4cTLdZ0KkoZkv7+87/1jUZzo6OtiwYQM2bNhQIzvNkdrTt29f5ObmYu7cubh79y78/f2RmJiI3r17Q79McSO+kDvVAiNEsajeS91HYx4hRBUJGGNM2UHIKywsDN7e3hAKhRg3bhyMjY1x6NAhPH36FEFBQVi6dKmorb+/PwICAuDn5wd/f3+xfqZPn44tW7agffv2GDRoEF6/fo39+/dDV1cXly5dQvv27aWe39HREXfv3sXt27fhWM60g4SEBDRv3hydOnWCo6MjGjZsiOfPn+PkyZN4+/Yt+vXrh+PHj8s1YPD1bDIyMkQ7MpH6KSMDMDXlvn/3jiu6Wx9dvgx06wY0aQKU2X2X1GPq8Dr57NkzuLq6inYIZIxBW1sbFy5cgLu7u6hdaGgofHx8MH/+fKxdu1ZZ4dYYdXguiWp6+hRo0QLQ1gbS0gADA2VHRIh09DpJiGqpkZovNc3LywtRUVHw8/NDaGgoCgsLYW9vj8DAQEyYMEHmfjZt2gQnJyds2rQJP//8MwwNDTFkyBCsXLmy3FkvV69exd27d+Hu7l5u4gUAzM3N8cUXX+DKlSs4duwY0tPTYWBgAEdHR3z66aeYNm2a1O2pCZEFv8zG2rr+Jl4AwN6e+/riBZeEMjdXbjyEKEKzZs1w7do1rFmzBo8fP0bTpk3xxRdfoEOHDmLtwsPD0aFDh2ov5yWEiOPrvbi5UeKFEEKI4qjkzJf6irLbhLdpE/D558CAAcDJk8qORrlsbYHERG6KeK9eyo5GeUpKSnDhwgUAQM+ePettcpdeJ9UHPZdEWSZPBnbsABYvBlatUnY0RBoa8zj0OkmIalHJmS+E1Hd8jZP6XGyX5+jIJV/u3KnfyZf8/HzRTjjZ2dkwoI9rCSGkSqjeS91HYx4hRBVR8oUQFcQvO6rPxXZ5Dg7A8eO04xFRTc+ePVNIP82aNVNIP4TUd4mJQEICoKkJfLC5GCGEEFItlHwhRMUwRjNfyuIfA9rxiKgiW1tbCASCavUhEAhQXFysoIgIqd/4WS+dOgGGhsqNhRBCiHqRO/myc+dOhQdhaGiIkSNHKrxfQtTRq1dccVkNDaBtW2VHo3z87J+7d7nEVDX/jyWkVjVr1qzc5Mvz589FSRUtLS1YWFjg7du3KCoqAgBoa2ujSZMmtRYrIfUBLTkihBBSU+ROvkyePBkCgQCKrNNra2tLyRdCZMTP8LCzA/T0lBtLXdC2LaClxW2/nZwMNG2q7IgIkV1CQoLU43PmzMHmzZsxb948zJ49G3Z2dqKx9/Hjx/jll1+wceNGDB48GOvXr6/doAlRY5R8IYQQUlPkTr7s2rVL4UEY0rxOQmRG9V7E6egArVsDsbHcY0PJF6Lqfv31V/z222/Yu3cvxowZI3adQCCAnZ0dfvrpJ3Tr1g3jxo1D+/btMWvWLCVFS4j6eP4cePKEm1nao4eyoyGEEKJu5E6+TJgwoSbiIITIiOq9SHJ05JIvd+4AH3+s7GgIqZ5NmzahWbNmEomXD40ZMwbffPMNNm3aRMkXQhSAn/Xi4gLQrr2EEEIUjQruEqJiaOaLJAcHYP/++r3jkba2NlavXi36nqiux48fw97eXqa2lpaWuHfvXg1HREj9EB7OfaUlR3UfjXmEEFVEyRdCVEhJCcD/n0UzX96jHY8AHR0dfP3118oOgyiAoaEh7t27h/T0dJiampbbLj09Hffu3YOBgUHtBUeIGuNnvnh6KjUMIgMa8wghqkhD2QEQQmT39CmQlwfo6gItWyo7mrqDnwV0/z5AO+4SVdevXz/k5eVhwoQJePfundQ2aWlpmDBhAvLz8+Ht7V3LERKifl6+BB494nbMo3ovhBBCagLNfCFEhfAzO9q3BzQ1lRtLXdK8OaCvD+TmAo8f188tuEtKSnDjxg0AgIuLCzTpF0RlrVq1CqdOncKpU6fQrFkzjB49Gu3atYOlpSXevHmDBw8e4MCBA8jJyUGDBg0QFBSk7JAJUXmRkdzXjh2BCiackTqCxjxCiCqi5AshKoTqvUinoQHY2wPR0dxjVB+TL/n5+XB3dwcAZGdn01IUFdasWTNcuHABn376KW7evIkdO3ZAIBCIrmeMAQCcnZ2xa9cu2NjYKCtUQtQG1XtRLTTmEUJUESVfCFEhtNNR+RwdueTLnTvAqFHKjoaQ6mnXrh2uX7+O8+fP4/Tp03j06BGys7NhaGiI1q1bo3///ujTp4+ywyREbVC9F0IIITWNki+EqBCa+VI+/jGpzzseEfXTu3dv9O7dW9lhEKLWUlK4mmECAdCzp7KjIYQQoq6o4C4hKqKggCsGCNDMF2n4x4SSL4QQQuRx+DD3tU0bwNxcubEQQghRX5R8IURFPHjAbTVtago0aaLsaOoefubL48fcjlCEEEJIZbZuBWbN4r5/+JD7mRBCCKkJtOyIEBXBz+hwdOSmRhNxjRoBFhZAaio3fdzFRdkREVI9OTk5OHbsGGJiYvDu3TsUFRVJbScQCLCV/mMkRG7JycCMGcD/aliDMWDmTMDbG7C2Vm5shBBC1A8lXwhREXyxXar3Ip1AwD024eHcY0XJF6LK9u3bh1mzZiEzM1N0jN/l6MOdjyj5QkjVxMUBpaXix0pKuBmUlHwhhBCiaJR8IURFlJ35QqRzdOSSL/Wx7ou2tjb8/PxE3xPVdfnyZUycOBF6enpYunQp9u/fj8ePH2Pz5s1ISkpCTEwMjh07BqFQiGXLlqEJrUMkpErs7LjEPT/zBQA0NYFWrZQXE5ENjXmEEFVEyRdCVATNfKkc/9jwj1V9oqOjA39/f2WHQRRgzZo1KC0txe7duzFkyBCEhYXh8ePHmDp1qqjNgwcPMHr0aPzyyy+4fv26Qs4bHR0NPz8/XL58GYWFhbC3t8f8+fMxfvz4KvVXVFQENzc3xMTEoE2bNnjw4IFC4iREUaytge7dgago7mdNTWDTJpr1ogpozCOEqCIquEuICsjMBJ49476n5Ev5aMcjog4uX74MCwsLDBkypNw2bdu2xZ9//omXL1+KPv2tjvDwcPTo0QMXLlzAqFGjMGvWLKSmpmLChAlYtWpVlfoMDAzE48ePqx0bITWFMSApifv+u++AhASgTI6TEEIIUShKvhCiAvhkwkcfAWZmyo2lLrO3574+fw6kpSk3ltpWWlqKe/fu4d69eyj9sIgBUSlv375Fs2bNRD/r6OgA4ArwltW6dWvY29vj5MmT1TpfcXExpk2bBoFAgMjISGzevBlr1qxBTEwM7O3t4efnh7i4OLn6vHHjBoKDgxEcHFyt2AipSfHxQGIioK0NfPEFzXhRJTTmEUJUUY0mXzIzM7F//378+OOPiIiIqMlTEaLWqN6LbIyNARsb7vv6NvslLy8PDg4O/9/efcc3Ve5/AP+kK91llF3asqWlgz1LBYSiXgVFyh5Ki4gTnKBSlvKD60W9goiMqiBTKoKC7ELZy5Yho0ALpSBQoHs3z++PcxMaks6kPUn6eb9eeTU958k53+Yk5zn9nmegXbt2yOFc22atbt26WsfQ3d0dAHD16lWdskVFRbhz545B+9u7dy+uXr2KkSNHon379prlLi4u+PTTT1FYWIjIyMhyby8/Px/jx49Ht27d8MYbbxgUG1FV2r1b+tm9O+DkJG8sVDGs84jIHBmcfFm/fj06dOiA5cuXay2/ePEi2rVrh5EjR+K9995D3759MX78eEN3R1QjcbyX8qvJ476QZfD29sbt27c1v3fo0AFCCPz8889a5eLi4nD58mXUq1fPoP1FR0cDAAYMGKCzTr2sIjdQZs6cifj4eKxYsUJrZiYiU7Nnj/TzqafkjYOIiGoGoyRf4uLi0Lt3b63l77zzDm7evInmzZtj0KBBcHZ2xqpVq7Bt2zZDd0lU46hbcTD5Ujb1e1TTWr6Q5ejfvz9SU1Nx/vx5AMDIkSNhb2+PL774AqNHj8bixYsxY8YM9OvXDyqVCkOGDDFof+ouRa1atdJZV7t2bbi7u5e729GJEyewYMECzJo1C61bt65QHHl5eUhPT9d6EFUVlQrYu1d63q+fvLEQEVHNYHDyJS4uDnXq1NG6yLp9+zZ27doFT09PnD17FlFRUdi6dSuEEFi8eLGhuySqUYR41IqD3Y7Kpn6P2PKFzFVoaCj69u2LS5cuAQCaNm2KJUuWwMbGBmvWrMFbb72Fzz77DA8ePEDXrl0xd+5cg/aXlpYGAHBzc9O73tXVVVOmNHl5eRg/fjzat2+Pd999t8JxzJs3D25ubppH06ZNK7wNovKKiwPu3wdcXIDOneWOhoiIagKDp5q+d++ezt2yffv2QQihuVsHAL1794aXlxcuXLhg6C6JapQ7d6QLRCsroG1buaMxfcVbvggBsNcDmRtfX1/s2rVLa9m4ceMQFBSEDRs2IDExEQ4ODujVqxcGDx4Ma2trmSLV9umnnyI+Ph6nTp2qVEzTpk3D1KlTNb+np6czAUNVRt3lKDhYGnCXiIioqhmcfMnPz0dRUZHWspiYGCgUCvTp00dreYMGDRAXF2foLolqFHULjpYtAQcHeWMxB088AVhbA6mp0qxHnL2CLEXz5s3x0UcfGX276hYvJbVuSU9PL7FVjNrp06excOFCfPrpp/CrZBM9pVIJpVJZqdcSVZR6sF2O90JERNXF4G5HTZo0wdWrV5Gdna1Z9ueff8LGxgY9e/bUKpuRkVHmBRwRaeN4LxWjVALqXpAc94WobOrWq/rGdXn48CFSUlL0jgdT3JkzZ1BUVISZM2dCoVBoPQDg0qVLUCgUqFWrltHjJ6qovDwgJkZ6zvFeiIiouhjc8uWpp57C8uXL8eabb2LKlCn45ZdfcP36dYSEhMDR0VFTLicnB/Hx8QgICDB0l0Q1Csd7qTg/P+DCBem9GzhQ7miqh62tLd577z3Nc7IMSUlJiImJQXJyMnJycjBjxgzNuoKCAgghYGdnZ9A+goODMW/ePOzcuRPDhw/XWrdz505NmdK0bt0aEyZM0LtuxYoVcHNzw0svvaR1XUAkl6NHgexsoEEDwNdX7mioMljnEZE5UgghhCEbuHHjBjp27IgHDx4AAIQQsLW1RUxMDLp06aIpt2HDBgwfPhzvvPMOFi5caFjUNZS66XdaWhpcXV3lDoeqSZcuwIkTwMaNwEsvyR2NeZgzB5gxAxg7FvjxR7mjoepkKefJlJQUvP7669i0aROKV9PFu/mOHj0aa9euxfHjx9GxY8dK76uwsBBt2rRBcnIyjh49isDAQABSa9Xu3bvj0qVLOH/+vGZg/ZSUFKSkpMDd3R3u7u5lbl+hUKBNmza4ePFiheKylGNJpmfGDKmeGDkSeGwGdyKzwvMkkXkxuNuRp6cnTp48icmTJ2PAgAEICwvD8ePHtRIvABAdHY2AgAAMGjTI0F0S1RgqFfC/2WbZ8qUCOOMRmbOMjAwEBwdj48aNaNKkCcaPH48mTZrolAsLC4MQAlFRUQbtz8bGBsuXL4dKpUJQUBAmTpyI9957DwEBATh//jxmzpypNaPhokWL0LZtWyxatMig/RLJRT3eC7scERFRdTK42xEAeHl54Ztvvim1zLfffmuMXRHVKAkJUtNopRJo0ULuaMyHenycv/8GioqkAXgtnUqlwo0bNwBISXErK4Nz6ySTBQsW4MKFCxgyZAh++uknODg4ICgoCMnJyVrlevfuDQcHB+zbt8/gffbp0wcHDx5EREQENmzYgPz8fPj6+mLOnDkYNWqUwdsnMhXp6cDx49JzDrZrvljnEZE5MkryhYiqhrrlho8PYMNva7k1by7NDJWTA1y5ArRpI3dEVS8nJwfNmjUDAGRmZsLJyUnmiKiyfvnlFyiVSixfvhwOpUxxZmVlhZYtW2r+ATFUly5dsH379jLLzZw5EzNnziz3dg3s3UxkVPv3S0n5li0BT0+5o6HKYp1HROaoQmniGzduGOVhDCdOnMAzzzyD2rVrw8nJCV26dMGaNWsqtA2VSoVFixbB398fDg4OqFevHkJDQ/XO+AAA3t7eOrM4qB+TJk3S+5r09HRMnToVXl5eUCqV8PLywtSpU5Genl7hv5lqHs50VDlWVo8GUeSMR2RuEhMT0bp163LNDujo6IiUlJRqiIrIMuzZI/1kqxciIqpuFbqXrk4+GEKhUKCwsNCgbURHRyMkJAR2dnYYPnw43NzcEBUVhVGjRiExMRHTp08v13YmTZqEZcuWwcfHB2+++Sbu3LmD9evXY+fOnTh8+DB8fHx0XuPm5oZ33nlHZ3mnTp10lmVlZSE4OBixsbHo378/RowYgbi4OHz55ZfYt28fDh48yEw9lerYMeln06byxmGO/PyAkyeBLVuArl0BDw+5IyIqH3t7e2RkZJSr7O3bt8uVpCEiCcd7ISIiuVQo+eLp6Vli8iU5OVmTVLGxsYG7uzvu37+PgoICANI0cI0bNzYwXGlWhrCwMCgUChw4cADt27cHAERERKB79+6IiIjA0KFD0apVq1K3s2/fPixbtgxBQUHYtWsXlEolAGDs2LHo378/XnvtNezfv1/ndbVq1Sp3c+sFCxYgNjYWH3zwAebPn69ZHhERgdmzZ2PBggWYNWtWOf9yqmlWrAB+/116Pm+e1JWmhJlcSY+sLOnnTz8Bq1cD33/P94/Mg6+vL44dO4br16/Dy8urxHKxsbG4ceMGBtaU+dSJDPTPP9Ig9goF0KeP3NEQEVFNU6FuR4mJiUhISNB5PPvss1AoFHjrrbdw8eJF5OXl4datW8jNzcWlS5fw1ltvQaFQ4F//+hcSEhIMCnjv3r24evUqRo4cqUm8AICLiws+/fRTFBYWIjIyssztLFu2DAAwd+5cTeIFAPr164eQkBAcOHAAly9frnScQggsX74czs7OmDFjhta6adOmoXbt2lixYgX7wpNeN28CEyc++l0I4NVXpeVUtps3gV9+efS7SsX3j8zH6NGjUVRUhIkTJyI7O1tvmYcPH2LChAlQKBQYO3ZsNUdIZJ7UXY7atwfq1pU3FiIiqnkMHsLz22+/xZIlS7B27VqEhoZqrVMoFGjVqhW++uor9OjRAyNGjICPjw9ee+21Su8vOjoaADBgwACddepl+lqs6NuOk5MTevbsqbMuJCQEf/75J/bv3681vSYA5OXl4ccff0RycjJq166NHj16ICAgQGcb8fHxuHXrFkJCQnS6Ftnb26N379747bffcOXKlTJb6VDNEx8vJQyKKyqSBo9l95my8f0jcxYeHo61a9di165d8PPzw9ChQ3Hnzh0AwMqVK3Hu3DmsXr0aKSkpGDBgAIYPHy5zxETmgeO9EBGRnAxOvixduhSenp46iZfHhYaG4sMPP8TSpUsNSr6oB8PVl7CoXbs23N3dSxwwVy0rKwu3b99Gu3btYK1nDlr1tvVt559//sH48eO1lg0cOBCrVq2Cu7t7ueJ8fB8llcnLy0NeXp7mdw7SW3O0aiU1iy7eMMraWpqdgcrWqpU06G7xBAzfPzIX1tbW+P333zFx4kSsX78e//73vzWtJMPDwzXPQ0NDsWLFCjlDJTIbQnC8FyIikpfByZcrV67AVz2tSBnq1auH8+fPG7S/tLQ0AChxgEFXV1fcLKNvQXm2Ubyc2iuvvILg4GD4+vpCqVTi77//xqxZs7B9+3Y8//zzOHTokGZMnMruo7h58+ZxTJgaysMD6NhRGjAWkBIHS5ey1UZ5eXhIY7yEh0sX3AqF5b9/NjY2mDx5suY5mTcXFxesXbsW06dPx6+//oqzZ88iLS0Nzs7O8PHxwQsvvICOHTvKHSaR2bhyBUhKAuzsgF695I6GDMU6j4jMkcFnK2dnZ5w/fx6pqamoVatWieVSU1Nx/vx5s57d5/GxW7p27Yrff/8dwcHBOHjwILZt24Znn33WaPubNm0apk6dqvk9PT0dTTntTY3xzz/Szy+/BF56ybITB1VhwgTgzh3g44+lC21LH2xXqVRi8eLFcodBRubn5wc/Pz+5wyAye+ouRz16AI6O8sZChmOdR0TmqEID7urTv39/5OTkYNSoUXjw4IHeMg8fPsSoUaOQm5uLkJAQg/anbklSUouR9PT0MqfdLM82ipcrjZWVFV5++WUAwKFDh4y6D6VSCVdXV60H1QxJSdLgsNbWUusNJl4q55lnpJ9xcdKYL0REVDOxyxEREcnN4JYvn3/+Of7880/8+eef8PT0xNChQ9G2bVvUq1cP9+7dw8WLF7Fx40ZkZWWhbt26mDt3rkH7Kz5WyuNNrh8+fIiUlBT06NGj1G04OTmhUaNGSEhIQFFRkc64L2WN1/I49VgvxWelKG3cmMrsg2qWI0eknwEBgBk3FpNdu3aAszOQng78/TdgyQ0IhBBISUkBIJ2T1F0gyfw9fPgQmZmZpc6O5+npWY0REZmXoiJg3z7pOQfbtQys84jIHBmcfPH09ERMTAxGjx6Nv/76Cz/++KPWCVB9sdi+fXusWrUKXl5eBu0vODgY8+bNw86dO3VmeNi5c6emTHm2s27dOhw6dAi9e/fWWrdjx45ybwcAjh07BgDw9vbWLGvVqhUaN26MQ4cOISsrS6u7VW5uLg4cOIDGjRujJUcAJT0OH5Z+lpFHpDLY2ABdugB790rvqSUnX7Kzs1G/fn0AQGZmpll38STg8uXLmDlzJv78889SxwYDpJkFCwsLqykyIvMTGws8eAC4ugKdOskdDRkD6zwiMkcGdzsCgLZt2+LUqVPYvXs33n//fTz//PPo27cvnn/+ebz//vvYtWsXTp06BR8fH4P31a9fPzRv3hxr1qxBbGysZnlGRgbmzJkDGxsbrdmIUlJScPHiRU12XG3ixIkAgE8++QT5+fma5Xv27MGOHTvQu3dvrWmm//77b6SmpurEc/DgQSxcuBBKpRIvvviiZrlCoUBYWBgyMzMxe/ZsrdfMmzcPDx8+RFhYGDP1pJe65Uv37vLGYQnUCSz1e0pk6mJjY9G5c2esX78eqampUCqV8PDwgKenp94HxwIjKp16vJcnn5SS8kRERHIwahXUt29f9O3b15ib1GFjY4Ply5cjJCQEQUFBGDFiBFxdXREVFYWEhATMnTtXK2myaNEizJo1CxEREZg5c6ZmeZ8+fRAWFobly5ejffv2ePbZZ3Hnzh2sX78erq6uWLJkidZ+N2zYgAULFqBfv37w9vaGUqnEuXPnsHPnTlhZWeG7777Tafb9wQcfYMuWLViwYAH++usvdOzYEXFxcdi+fTsCAwPxwQcfVOl7ReYpJwc4fVp6zpYvhlO/h+rWRESmbvr06cjIyEC/fv3w5Zdfol27dnKHRGTWON4LERGZArPM//fp0wcHDx5EREQENmzYgPz8fPj6+mLOnDkYNWpUubezdOlS+Pv7Y+nSpfjvf/8LZ2dnPPfcc/jss8+0EjjqfV64cAGnT5/G/v37kZubiwYNGmDYsGGYMmUKunTporN9JycnREdHY9asWfjll18QHR2Nhg0bYsqUKYiIiGATSdLr5EmgsBBo1AgwsJceAejWTfoZHw+kpAD/G6KJyGQdPnwYzs7O2Lx5M+sJIgPl5gIHD0rPOd4LERHJSSFKG8GPTIp6Jqe0tDTOfGTBFiwAPvwQePFFYNMmuaOxDD4+wIULwJYtwHPPyR1N1cjKyoKzszOAmt3/3RLOk66urmjTpg1OnDghdyiysoRjSfLbtw/o21e6oZGcDLC3t2VgnSfheZLIvBit5UtWVha2bt2KuLg4PHjwAAUFBXrLKRQKrFixwli7JbI4HGzX+Hr0kJIvhw9bbvKFLEdgYCCuXbsmdxhEFkE93kvfvky8EBGRvIySfFm3bh1ee+01pKena5apG9Q8PvMRky9EJROCyZeq0L07sGIFB90l8zBt2jT861//wqpVqzBmzBi5wyEya+rxXtjliIiI5GZw8uXIkSMYM2YMHBwc8PHHH2P9+vW4cuUKli1bhqSkJMTFxWHr1q1QKpX45JNP0LhxY2PETWSRrl0D7t0D7OyADh3kjsZyqBNZx48DBQWAra288VQFGxsbjBs3TvOczNfTTz+Nb7/9FpMnT8bp06cxYcIEtGjRAg4ODnKHRmRW0tIAde89DrZrWVjnEZE5MnjMlyFDhmDz5s3YvHkznnvuOQQFBeHw4cMoKirSlLl48SKGDh2Khw8f4tSpU2jQoIHBgddE7Ndp+VatAsaOlVpqcHYe41GppIF2Hz6ULsQ7dZI7Iqoq5naetLa2NngbCoUChYWFRojGtJjbsSTTs2IFEBYGNGsm3dwgsjQ8TxKZFytDN3DkyBG4u7vjuVIGUnjiiSewadMm3L59GxEREYbukshisctR1bCyejTrEbsekSkRQhj8UKlUcv8ZRCZnxQogPFx6npgo/U5ERCQng5Mv9+/fh6enp+Z3Ozs7ANIAvMW1bt0avr6+2L59u6G7JLJY6sRA9+7yxmGJ1AktS21RJIRAVlYWsrKywEnszIdKpTLKg4geuXkTmDhRGkcNkH6++qq0nCwD6zwiMkcGJ1/q1q2LnJwcze/u7u4AgKtXr+qULSoqwp07dwzdJZFFSk8Hzp6VnjP5YnyWnnzJzs6Gs7MznJ2dkZ2dLXc4RESyiY+XupsWV1QEXLkiTzxkfKzziMgcGZx88fb2xu3btzW/d+jQAUII/Pzzz1rl4uLicPnyZdSrV8/QXRJZpOPHpYtFb2+A41IbX5cuUvejGzeA5GS5oyEioqrSqpXutNLW1kDLlvLEQ0REBBgh+dK/f3+kpqbi/PnzAICRI0fC3t4eX3zxBUaPHo3FixdjxowZ6NevH1QqFYYMGWJw0ESWiF2OqpazM+DvLz3nuC9ERJbLwwPw8nr0u7U1sHSptJyIiEguBidfQkND0bdvX1y6dAkA0LRpUyxZsgQ2NjZYs2YN3nrrLXz22Wd48OABunbtirlz5xocNJEl4mC7VU+d2LLUrkdERCS1cExMlJ5v2iQ9nzBBzoiIiIgAG0M34Ovri127dmktGzduHIKCgrBhwwYkJibCwcEBvXr1wuDBg40yrSaRpVGpHrXGYPKl6vToASxZwpYvRESWbPNm6WdQEPDii7KGQkREpGFw8qUkzZs3x0cffVRVmyeyKBcvAmlpgKPjo64xZHzqxNapU0BuLmBvL288RERkfFFR0k8mXoiIyJQYNfmSlJSEmJgYJCcnIycnBzNmzNCsKygogBBCMxU1ET2i7gbTpQtgU2UpUWrWDKhfH7h7Fzh9mq2MiIgszd27QEyM9PyFF+SNhYiIqDij/JuXkpKC119/HZs2bYIQQrO8ePLl5Zdfxtq1a3H8+HF07NjRGLslshgc76V6KBTSe7x5s/SeW9L7bW1tjZdeeknznMzXtWvX0Lx5c7nDIDJLW7ZIXXk7dtQedJcsC+s8IjJHBg+4m5GRgeDgYGzcuBFNmjTB+PHj0aRJE51yYWFhEEIgSt0WlIg0ONNR9VEnXCxt0F17e3ts3LgRGzduhD37U5m1QYMGITs7W+4wiMwSuxzVDKzziMgcGZx8WbBgAS5cuIAhQ4bg4sWLWLFiBbz03Gro3bs3HBwcsG/fPkN3SWRR7t+XxnwBgG7d5I2lJlAnuI4cAYo11CMyGefPn8eoUaPKXf7ChQtVGA2R+UhLA/bskZ4z+UJERKbG4OTLL7/8AqVSieXLl8PBwaHkHVlZoWXLlrhx44ahuySyKEePSj/btAHc3eWNpSbo2BGwtQX++efRVKREpiQ8PBxbtmzR6rpbkt9//x3d2WSOCACwbRuQnw+0bQs88YTc0RAREWkzOPmSmJiI1q1bw83Nrcyyjo6OSElJMXSXRBaFXY6ql4MD0KGD9NySuh5lZWVBoVBAoVAgKytL7nDIAIsWLULXrl3x2WefYdOmTSWWmz9/Pl544QVkZmZWY3REpotdjmoO1nlEZI4MTr7Y29sjIyOjXGVv375driQNUU3CwXarX/GuR0SmxtbWFlFRUWjQoAHGjx+Pc+fOaa3Pz8/HmDFjMH36dDg6OuLXX3+VKVIi05GTI7V8ATjLERERmSaDky++vr5ISkrC9evXSy0XGxuLGzducKYjomIKC4Fjx6TnbPlSfSx10F2yHA0bNsQvv/yCgoICDBo0CPfv3wcg3cQICgrCzz//jGbNmuHIkSN47rnnZI6WSH47dwLZ2YCn56PWjURERKbE4OTL6NGjUVRUhIkTJ5Y4O8PDhw8xYcIEKBQKjB071tBdElmMs2eli0VXV8DHR+5oag51oisuDmCPDTJVPXr0wNdff42EhASEhobi8OHD6Ny5M06cOIG+ffvixIkT8OGJgwiAdpcjhULeWIiIiPSxMXQD4eHhWLt2LXbt2gU/Pz8MHToUd+7cAQCsXLkS586dw+rVq5GSkoIBAwZg+PDhBgdNZCnULS+6dwesDE6FUnl5eABNmwJJScCJE0CfPnJHRDWVi4sL/Pz84Ofnh4CAAAQEBMDf3x8uLi4AgFdffRWnTp3C8uXLERQUBCEE3nzzTSxcuBDW1tYyR09kGgoKgC1bpOcc74WIiEyVwckXa2tr/P7775g4cSLWr1+Pf//73xD/m781PDxc8zw0NBQrVqwwdHdEFqV48oWqV48ewPr10jFg8oXkkp2djaNHj+Lo0aNQFLtd7+XlBX9/fwQGBqJPnz7YuXMn7ty5g8WLF+OVV16RMWIi0xMdDaSmAvXrc/w0IiIyXQYnXwDpzt3atWsxffp0/Prrrzh79izS0tLg7OwMHx8fvPDCCxzrhUgP9YCvvFisft27P0q+EMklMzMT586dQ1xcHOLi4nDmzBmcOXMGiYmJSExMxJYtWzRJGXt7e0RGRuLUqVPw9/eHv78//Pz84OzsLPNfQSQvdZejwYMBNggjIiJTZZTki5q66TQRle32bSAhQeqb3rWr3NHUPOqE19GjgEpl/t2+rK2t8cwzz2iek3lwcHBA586d0blzZ63l169fx5kzZ7SSMlevXsWhQ4dw6NAhTUJGoVDA29sbV65ckSN8ItkVFQHqCb/Y5ajmYJ1HROZIIdT9gsjkpaenw83NDWlpaXB1dZU7HDJQVBQwZAjg5wecOSN3NDVPQQHg5iZNT3rhAvDEE3JHRMZgyefJ7OxsnD17Vicpk5mZiaKiIrnDMzpLPpZkPIcOAb16Sefzu3cBOzu5IyKqPjxPEpkXo7Z8AaSZjTIzM1FaTsfT09PYuyUyO+xyJC9bW6BTJyAmRup6xOQLmTpHR0d07doVXR9rKpeYmGiU7Z84cQIRERE4cuQI8vPz4evri3feeQcjR44s1+sPHjyIX3/9FdHR0UhMTERWVha8vb0xaNAgTJs2DbVq1TJKnETFqbscPfccEy9ERGTajJJ8uXz5MmbOnIk///wTaWlppZZVKBQoLCw0xm6JzJp6rBEmX+TTo4eUfDlyBOAYpmSuvL29Dd5GdHQ0QkJCYGdnh+HDh8PNzQ1RUVEYNWoUEhMTMX369DK38dJLLyElJQW9evXC2LFjoVAoEB0djQULFmDTpk04fPgw6tevb3CsRGpCaE8xTUREZMoMTr7ExsYiODhY09rF3t4e9erVg5W5D6BAVIXy8oCTJ6XnnOlIPurElyUMupuVlaX5x/bu3btwcnKSOSIyF4WFhQgLC4NCocCBAwfQvn17AEBERAS6d++OiIgIDB06FK1atSp1O1OmTMHYsWPRqFEjzTIhBF5//XUsWbIEs2bNwuLFi6v0b6GaJTYWSEwEHByAkBC5o6HqxDqPiMyRwRmS6dOnIyMjA3379sWZM2eQnZ2N69evIyEhocQHUU33119Afj7g7g60bCl3NDVXt27Sz7//lqYpNXfZ2dnIzs6WOwwyM3v37sXVq1cxcuRITeIFkGYy/PTTT1FYWIjIyMgyt/Phhx9qJV4AqbXrp59+CgDYv3+/cQOnGk890O7TTwOOjvLGQtWPdR4RmRuDky+HDx+Gs7MzNm/ejHbt2hkjJiKLt22b9LN9e2m2I5JH/fqPkl9LlwI3b8obD5EcoqOjAQADBgzQWadeZkjixNbWFgBgY2P0YeaohmOXIyIiMicGJ19UKhXatGnD5n5E5bRiBTBnjvR8927pd5KPu7v086OPAC8vHg+qeeLj4wFAb7ei2rVrw93dXVOmMlauXAlAf3KnuLy8PKSnp2s9iEpy6RJw/rw0ePqzz8odDRERUdkMTr4EBgbi9u3bxoiFyOLdvAlMnPjodyGAV19liwu53LwJHDv26HeViseDah71QPlubm5617u6upY5mH5JYmNjMWvWLNSvXx8ffPBBqWXnzZsHNzc3zaNp06aV2ifVDOouR/36AZxIi4iIzIHByZdp06bh9u3bWLVqlTHiKbcTJ07gmWeeQe3ateHk5IQuXbpgzZo1FdqGSqXCokWL4O/vDwcHB9SrVw+hoaF67/AlJyfjq6++woABA+Dp6Qk7Ozs0bNgQQ4YMwbHi/70VM3PmTCgUCr0Pe3v7Sv3dZN7i46V/8IsrKgKuXJEnnpouPl5KgBXH40FkHAkJCfjXv/6FoqIirFu3Du7qZmYlmDZtGtLS0jSPpKSkaoqUzJG6y9ELL8gbBxERUXkZ3AH76aefxrfffovJkyfj9OnTmDBhAlq0aAEHBwdjxKeXMabEBIBJkyZh2bJl8PHxwZtvvok7d+5g/fr12LlzJw4fPgwfHx9N2W+++Qbz589HixYt0L9/f9SvXx/x8fHYvHkzNm/ejLVr1yI0NFTvfsaNG6czFSj7vtdMrVpJY7wU/4ff2pqD7sqlVSvAyko7IcbjQabm8uXLuHz5MjIyMuDi4oLWrVujdevWRtu+usVLSa1b0tPTS2wVU5Lr16+jT58+uHfvHjZt2oQ+ffqU+RqlUgmlUlmh/VDNdOwYcOKE9HzQIHljISIiKjdRAVZWVgY/rK2tK7JLHQUFBaJFixZCqVSK06dPa5anp6cLX19fYWNjIy5fvlzmdvbu3SsAiKCgIJGbm6tZvnv3bqFQKETv3r21ym/atEkcOHBAZzsHDhwQtra2ok6dOlrbEUKIiIgIAUDs27evgn+lfmlpaQKASEtLM8r2qPqpVEK4uwshpV+EsLYWYvlyuaOq2ZYvF0KhkI6HQmG+xyM7O1sEBweL4OBgkZ2dLXc4srGk8+R3330nmjVrprcubd68ufj++++Nsp9p06YJAGLt2rU66x48eCAAiB49epR7ewkJCcLb21vY2tqKzZs3VzouSzqWZDzFz9mA+Z6zyTCs8yQ8TxKZlwp1OxJCGPxQPd7nooKMNSXmsmXLAABz587VutPWr18/hISE4MCBA7h8+bJm+YsvvoigoCCd7QQFBaFPnz548OABzp49a8ifRjXA8eNASgpgby/NeJSYCEyYIHdUNduECcCePdJzKytg8GBZw6k0BwcHREdHIzo6ukpbHlL1ePnllzF58mQkJibCzs4OLVq0QI8ePdCiRQvY2dkhISEBkyZNwssvv2zwvoKDgwEAO3fu1FmnXqYuU5bExEQ8+eSTSE5Oxvr16zGIzRLIiNTjphVvPcpxumom1nlEZI4qlHxRqVRGeRjCWFNiRkdHw8nJCT179tRZFxISUu7tAGVPoxkTE4MFCxbgP//5D/744w/k5eWVa7tkedTDEr34IvD004CHh7zxkKRPHyAwUBrv5Zdf5I6Garo1a9bgxx9/hKOjIxYsWIB79+7h8uXLiImJweXLl3Hv3j0sWLAATk5O+Omnn7B27VqD9tevXz80b94ca9asQWxsrGZ5RkYG5syZAxsbG4wfP16zPCUlBRcvXkRKSorWdoonXtatW4cXOBgHGRnHTSMiInNmdgOPGGNKzKysLNy+fRvt2rWDtbW1znr1tsszteaNGzewe/duNGzYEH5+fnrLzJgxQ+v3Ro0a4ccff0T//v1L3XZeXp5WoobTbpq3wkJg/Xrp+ciR8sZCukaOBGJjpQTZq6/KHQ3VZMuWLYNCocCmTZv03mhwdnbGe++9B39/fwwcOBDLli3DiBEjKr0/GxsbLF++HCEhIQgKCsKIESPg6uqKqKgoJCQkYO7cuVpjzCxatAizZs1CREQEZs6cqVn+5JNP4vr16+jWrRvOnDmDM2fO6OyreHmiiuK4aUREZM7MLvlSnikxb5bR/rQ82yheriQFBQUYM2YM8vLysGDBAp1ETmBgIH788UcEBwejQYMGuHnzJtatW4fPP/8czz//PI4ePYqAgIAStz9v3jzMmjWr1BjIfOzbB9y5A9StC+j5f4pkNmIE8OGHwIEDQFISYG6z3GZlZWkG9k5MTISTk5O8AVGlxcXFoXnz5noTL8UNGDAALVu2xF9//WXwPvv06YODBw8iIiICGzZsQH5+Pnx9fTFnzhyMGjWqXNu4fv06AODo0aM4evSo3jJMvpAh7OykZEthofS7tTWwdClbkdZErPOIyByZXfLFVKhUKrzyyis4cOAAwsPDMWbMGJ0ygx8bPKJly5b45JNP0KBBA0ycOBFz587Fxo0bS9zHtGnTMHXqVM3v6enpaGpu/xGShrrL0dChwP96qpEJ8fAAevcG9u8H1q0D3n9f7ogq7vFuIGSecnNzUatWrXKVLc8Nh/Lq0qULtm/fXma5mTNn6k2iiMfnbScysiVLpMRLYCCwcKHUEoaJl5qLdR4RmZsKjfliCowxJWZ5tlG83OOEEAgPD8fq1asxevRofPfdd+WKXW3cuHGwsbHBoUOHSi2nVCrh6uqq9SDzlJMDbNokPWeXI9OlPjbqRBmRHDw9PXHu3Lky/7G4d+8ezp8/D09Pz2qKjEg+ubnAt99Kzz/6SBqri4kXIiIyJ2aXfCltPJaHDx8iJSVF73gwxTk5OaFRo0ZISEhAUVGRzvrSxpVRqVSYMGECVq5ciREjRuCHH36AlVXF3kY7Ozu4uLggOzu7Qq8j87VtG5CRIXVl0TPGM5mIIUOkVkmxscDff8sdDdVUzz//PPLy8jBs2DDcu3dPb5m7d+9i2LBhyM/P54xCVCOsWQPcvSvVo0OGyB0NERFRxZld8sVYU2IGBwcjKytLb+uTHTt26N2OSqVCWFgYIiMjMWzYMKxatUrvgL1liY+Px8OHDzV9VcnyqVtSjBghTWdMpqluXWDgQOm5gRPIEFXaRx99BA8PD0RHR8PLywvjxo3D/PnzERkZifnz52PcuHHw9vZGdHQ0PDw88OGHH8odMlGVEgL46ivp+ZtvAiVMLklERGTSzO7fQGNNiTlx4kQAwCeffIL8/HzN8j179mDHjh3o3bu31uwO6hYvkZGRGDp0KFavXl1q4iUjI0PvTA8PHz7EhAkTAMCg2SnIfKSmAn/8IT1nlyPTV7zrEYewIDnUqVMHe/fuRYcOHZCbm4tVq1Zh+vTpCAsLw/Tp07Fq1Srk5uaic+fO2Lt3L+rUqSN3yERVas8e4OxZwMkJCA+XOxoiIqLKMfjewbVr19C8eXNjxFIuxpoSs0+fPggLC8Py5cvRvn17PPvss7hz5w7Wr18PV1dXLFmyRGu/s2fPxg8//ABnZ2e0bt0ac+fO1Ylt8ODBCAwMBADcv38fAQEB6NSpE/z8/FC/fn0kJydj+/btuH//Pvr3748pU6ZUyXtEpuXXX4G8PMDHB/D3lzsaKstzz0kX+NeuAcePA127yh0R1UQtW7bEiRMnsGfPHuzcuROXL19GZmampg4KCQlB37595Q6TqFosXCj9fOUVoJxjURMREZkcg5MvgwYNwrFjx+Do6GiMeMrFGFNiAsDSpUvh7++PpUuX4r///S+cnZ3x3HPP4bPPPtNK4ADSNHYAkJmZic8++0zv9ry9vTXJlzp16uD111/H0aNHsXXrVqSmpsLJyQl+fn4YPXo0wsLCKtVlicyPusvRyJGAQiFvLFQ2Jydg8GDg55+lh7kkX6ysrNCpUyfNc7IM/fr1Q79+/eQOg0g2Fy4A27dL9efbb8sdDZkK1nlEZI4UwsC5Ia2srDBo0CD8+uuv5Sp/4cIFtG3b1pBd1ljqmZzS0tI485GZuH1bmo1BpQKuXgWqsZEYGWDbNuDZZ4H69YHkZI4vYE4s4Tx54MABuLm5ISAgoMyyZ86cQWpqKnr37l0NkVUvSziWZLhXXwW+/15KipfzUpOoxuB5ksi8GJwqDg8Px5YtWzBjxowyy/7+++/o3r27obskMhsbNkiJl27dmHgxJ/37S4Pv3r0L7N0rdzRU0zz55JN46623ylX27bffZvcjslgpKcBPP0nPp06VNxYiIiJDGZx8WbRoEbp27YrPPvsMmzZtKrHc/Pnz8cILLyAzM9PQXRKZDXWXowr0hiMTYGsLhIZKz9XHkKg6VaRRqoENWIlM1tKlQG4u0LEj0KuX3NEQEREZxuDki62tLaKiotCgQQOMHz8e586d01qfn5+PMWPGYPr06XB0dCx39yQic3flijRgq7U1MHSo3NFQRalnPYqKAnJy5I2lPLKzs+Ht7Q1vb29kZ2fLHQ5Vk/v378PBwUHuMIiMLi8PWLRIej5lCsdMI22s84jIHBllJIOGDRvil19+Qd++fTFo0CAcP34cdevWxe3btzF48GCcOHECzZs3x5YtW+Dj42OMXRKZvLVrpZ9PPQU0aCBvLFRxPXoAnp7AjRvSVOEvvSR3RKUTQuD69eua52Q+0tPTkZqaqrUsLy8PSUlJJR7LnJwc7N+/H+fOnSvX2DBE5mb9euCff4AmTXgDg3SxziMic2S0YSR79OiBr7/+Gq+99hpCQ0MxZ84chIaG4tatW+jbty82btyI2rVrG2t3RCZNCGmmHOBRCwoyL1ZWwIgRwPz5UtcjU0++kPn68ssvMXv2bK1lJ0+ehLe3d7leP2HChCqIikg+QjyaXvqNNwA7O3njISIiMoYKJV9cXFzg5+cHPz8/BAQEICAgAP7+/nBxcQEAvPrqqzh16hSWL1+OoKAgCCHw5ptvYuHChZxWmWqU2Fjg0iXA3l6aoYHM08iRUvLljz+A1FSgVi25IyJLVKtWLXh6emp+v3HjBuzs7NCwYUO95RUKBRwcHNC8eXMMGzYMo0ePrq5QiapFdDQQFwc4OgITJ8odDRERkXFUKPmSnZ2No0eP4ujRo1AU63zr5eUFf39/BAYGok+fPti5cyfu3LmDxYsX45VXXjF60ESmTj1I63PPAZz5z3z5+QG+vsD589LYLzydUVV4++238fbbb2t+t7KyQufOnXHgwAEZoyKSz5dfSj/Hjwfq1JE1FCIiIqOpUPIlMzMT586dQ1xcHOLi4nDmzBmcOXMGiYmJSExMxJYtWzRJGXt7e0RGRuLUqVPw9/eHv78//Pz84OzsXCV/CJGpUKkejffCLkfmTaGQjuHHH0sJNSZfqDpERkaiAQeKohrq8mVg61bpebGcJBERkdlTCCOMUnX9+nWcOXNGKylz9epVqFQqaSf/S8goFAp4e3vjypUrhu6yRkpPT4ebmxvS0tLgyuYUJmv/fuDJJwE3N+DOHUCplDsiMkRCAtC8uZSISU4GGjWSOyL9srKyNMntzMxMODk5yRyRPHietBw8ljXT668D334rtRzdskXuaMhUsc6T8DxJZF6MMuCul5cXvLy88Nxzz2mWZWdn4+zZszpJmYSEBGPskshkqbscvfQSEy+WoFkzoHt34MgRafaNd96ROyL9FAqFZjY5BedkJSIzdPYssGKF9HzKFHljIdPGOo+IzJHRZjt6nKOjI7p27YquXbtqLU9MTKyqXRLJLj8f2LhRes4uR5Zj5Egp+bJmjekmXxwdHXH+/Hm5wyAiqpQVK4DwcGmmIwC4ehXo00femMh0sc4jInNkVd07LO/UmUTm6OefgYcPgfr1geBguaMhYwkNBaytgRMngFWrgJs35Y6IiMhy3LwpzWpUvCP8pEk81xIRkWWp9uQLkaVaseLRgKz37gE//CBrOGRE9esDbdtKz8eOBby8HjWNJyIiw1y+LA1WX1xREcAhAomIyJJUKPkyefJk3DTSbYh169ZhjXpwDCIzp75rpyYE8OqrvGtnKW7elKabVlOpTO/4Zmdnw9fXF76+vsjOzpY7HCKicjt2THeZtTXQsmX1x0LmgXUeEZmjCiVfvv/+e7Rs2RJhYWE4cOBAhXd27949LFq0CG3btsWoUaM4+C5ZDN61s2zx8drN4QHTO75CCPz999/4+++/YYRJ7IiIqsWlS8CcOdJz9bip1tbA0qWAh4d8cZFpY51HROaoQgPuxsbG4sMPP8TKlSsRGRmJxo0b4+mnn0aXLl3QsWNHNGrUCHXq1IGdnR3S0tLw4MEDXLhwASdPnsTBgwcRHR2NoqIi1K1bF19++SVee+21qvq7iKrVpUu6y3jXznK0agVYWWkn2KyseHyJiAxRUACMHg3k5ABPPSV157x2TTq3MvFCRESWpkLJl3bt2uGPP/5ATEwMFi1ahN9++w3Lly/HijIGP1BnpFu2bInw8HBMmjQJLi4ulY+ayITcuwdEREjPFQqphQTv2lkWDw/g+++lrkZFRdKyxo2lsWCIqkpeXh7WrVuHHTt24PLly8jIyICLiwtat26NAQMGYPjw4bC3t5c7TKJKmz0bOHkSqF1bGietSRPA01PuqIiIiKqGQhjQVi8lJQVRUVGIiYnB4cOHkZSUhMLCQs16V1dXBAYGolevXhgwYAB69+5tlKBrqvT0dLi5uSEtLQ2urq5yh0P/M3IksHYt0K4d8NtvwI0bvGtnqW7elGY8euUVIDVV+sfh00/ljkqSlZUFZ2dnAEBmZiacnJxkjkgelnKePHz4MEaPHo3r16/rbVKvUCjg6emJ1atXo2fPnjJEWPUs5ViSfocOAb17Sy0KN24EXnpJ7ojInLDOk/A8SWReDEq+6JOamorc3FxN9yMyHp5gTc+WLcCgQVIXlKNHgc6d5Y6IqsOaNcCoUYCtLfDXX4Cvr9wR8UJUzRLOk+fPn0eXLl2Qk5ODhg0bIiwsDG3btkWDBg1w9+5dXLhwAStWrMCtW7fg4OCAY8eOoV27dnKHbXSWcCxJv/R0IDAQSEiQZpD78Ue5IyJzwzpPwvMkkXmpULej4u7evYsTJ04gLy8PHh4e6NSpE6ysrFCrVi0jhkdkulJTgUmTpOfvvcfES00yYgSwbh2wdSvw8svA4cOATaXPpkTaPvnkE+Tk5GD06NFYsWIFbG1t9ZYJCwvDqlWrMGPGDERFRckQKVHlvPOOlHjx9ga++UbuaIiIiKpHhWY7Uvvoo4/g4eGB559/HkOHDkX37t3RoEEDLFq0yNjxEZmsd98Fbt+WBmOdOVPuaKg6KRTAkiWAq6vUDemrr+SOSOqG4uXlBS8vLyjUU4aQWTpw4ABcXV3x/fff6028AICtrS2WLl0KV1dXREdHV2+ARAaIigIiI6Xz6E8/SedRoopinUdE5qjCyZeVK1diwYIFKCwshBACVlZWEELg/v37ePvttzFt2rSqiJPIpOzaBaxcKV08rlwJODjIHRFVtyZNgIULpeeffipNRy0nR0dHJCYmIjExEY6OjvIGQwbJz89HmzZtyhxM197eHm3atEFBQUE1RUZkmFu3gPBw6flHHwFBQfLGQ+aLdR4RmaMKJ1++//57KBQKjBgxArdv30Z+fj6uXbuG6dOnw9bWFv/+979x8uTJqoiVyCRkZDy6eHzjDaBXL3njIfm88oo0PWpuLjBhgvZU1ESV1bZtW9y8ebNcZZOSkuBrCoMOEZVBpZK6aT54AHTowBajRERU81Q4+XL+/HnUqlULK1euRIMGDaBQKODt7Y25c+diyZIlUKlUWLp0aVXESmQSpk0Drl+X+qp//rnc0ZCcFApg2TLAyQmIiZG6IhEZ6p133sHt27fx9ddfl1ruv//9L/755x+888471RMYUSXdvAm8/Tawcydgbw+sXg1wTgYiIqppKpx8ycrKQuvWraFUKnXWjR8/HrVr10ZMTIxRgiMyNTExwOLF0vNly4D/DbRPNZi3N/B//yc9//BDIDFRnjhycnLQuXNndO7cGTk5OfIEQUYxcuRIzJ8/Hx9++CFefPFF7N69G8nJySgoKMCtW7ewZ88eDBkyBB988AEWLFiA4cOHyx0yUYlWrAC8vAD1sIAvvgi0bStvTGT+WOcRkTmq8FTTVlZW6NWrFw4cOKB3fbdu3XD+/HlkZGQYJUB6hNPJySs7GwgIAK5cAcLCpOQLESA1pw8OBg4eBPr3B3bskFrFVCdOuymxhPOktbW1wdtQKBQoLCw0QjTysYRjWdPdvCklXop3ybS2lpLUHh6yhUUWgHWehOdJIvNSqdmOSmNra4vs7Gxjb5ZIVjdvSn3Vr1wBGjcGvvhC7ojIlFhZSXd37e2lwZj/8x9g3z7pc0NUUUIIgx8qDkBEJuD773XHwioqkupSIiKimqZSyZdr167hP//5D3bt2oW7d+8aOyYik6JuMr1hg/T7kCGAm5u8MZHpad0amD1bev7++0DfvtLnZsUKeeMi86NSqYzyIJJLQQEwdSowZ47uOmtroGXL6o+JiIhIbpXqdgRITZrV6tWrB39/fwQEBCAqKgqJiYkoKioybqTEpoUyYJNpqojERKBZM+1l1fV5YRNsCc+TloPH0jzduQOEhgLq3ulPPy0NtFtUJJ0Ply6VZocjMgTrPAnPk0TmxaaiL1i7di1iY2MRFxeH2NhY/PPPP7h79y52796NPXv2aMq5uLjA19dXk5Tx9/eHv78/3NhkgMyEEFL3opKaTDP5Qo9LSNBdxs8LEdUUhw8DQ4cCt24BLi7Ajz8CL7wg3ci4ckVq8cJzIRER1VQVTr4MGzYMw4YN0/x+7949rWRMXFwcLl26hKysLBw/fhzHjx/XaiXTtGlTJMo1HQhROSUnS3fmduzQXccm01SSVq2k8V8eT9h99x3QoQPAm1JEZImEAL79FpgyRepy5OMDREUBbdpI6z08mHQhIiKqcPLlcfXq1UP//v3Rv39/zbK8vDycP39eKylz5swZpKWlISkpydBdElWpdeuAyZOBhw+lAVQHDwY2btRuMs2LSNLHw0MaYPLVV6XPi0Ih/VOyfj1w7Jh0F7h376rbv7u7e9VtnKpNRWc7soSZjcg83bwJnD0LLF8uJVsAqeXLypXA/3qEEFUZ1nlEZG4qPOaLIRITExEXF4dBgwZV1y4tCvt1Vq0HD6Sky/r10u8dOwKrVgFt27LJNFVM8c/L1avAuHHA9etSMubdd6VBKO3t5Y7SMlnCeVI9tlpFWOIAu5ZwLC3ZihXAxImPWvopFMC//y0NtFuswTMRVSGeJ4nMi9Gnmi6Nt7c3Ey9kUm7elKYEXrUKaNdOSrxYWwMREcCRI1LiBZASLk8+ycQLlU/xz0twMHDmjNSNTT2OUOfOQGzso88fp6Sm4kqbwSgzMxOxsbF4/fXX4ejoiO+++84iEy9kujIypPNYWJh2F0uFAhg2jIkXIiKiklRr8sWYTpw4gWeeeQa1a9eGk5MTunTpgjVr1lRoGyqVCosWLYK/vz8cHBxQr149hIaGIj4+3mj7TU9Px9SpU+Hl5QWlUgkvLy9MnToV6enpFYqVjE89hXTfvsDYscDt21L/9CNHgJkzAVtbuSMkS+HqKjXL/+03oH594Nw5oFMnwNOTU1JTxTg6OsLf3x/ffPMNFi9ejNdeew3bt283yrblqlfJ9DyeGFapgD17gDFjgIYNgfff132NSiW1+CMiIiL9qrXbkbFER0cjJCQEdnZ2GD58ONzc3BAVFYWEhAR89tlnmD59erm2M3HiRCxbtgw+Pj549tlncefOHaxfvx729vY4fPgwfHx8DNpvVlYWevXqhdjYWPTv3x8dOnRAXFwc/vzzTwQGBuLgwYMVmhqPTQuNIyEB+OUX4IMPtJcrFMClS9KgqURV5d496R+YxwdztrICTp4E2rev3HZzcnLw9NNPAwC2b98OBwcHAyM1TzXtPNmkSRO0aNECB9Tz+laSXPVqaWrasTQVxbsTWVlJU0WfOQMUH7KveXOpLi1+BWltDSQmsoUoVQ/WeRKeJ4nMjDAzBQUFokWLFkKpVIrTp09rlqenpwtfX19hY2MjLl++XOZ29u7dKwCIoKAgkZubq1m+e/duoVAoRO/evQ3e74wZMwQA8cEHH+hdPmPGjAr97WlpaQKASEtLq9DrLElSkhB790o/y1vun3+EWLtWiLAwIZo1E0K6XNT/2LevWv4MquH27Cn5M9iunRBvvSXEb78JkZoqlS/P5z4zM1MAEADEpUuZ1fOHmKCadp7s2LGjcHFxMWgbctWrZalpx7I6lHYuycoSYscOIRQK/eemWrWEmDRJiKNHhVCphFi+XAhra2mdtbX0O1F1KV7nZWayzuN5ksg8mF3yZceOHQKAePnll3XWrVu3TgAQ06ZNK3M7I0aMEADE/v37ddYNHDjwf//AXKr0flUqlWjcuLFwdnbWqRRycnJE7dq1RZMmTYRKpSozVjVDTrCVSVqYWrnly4WwspIu9KystC/0cnKEuHFDiFOnhHjnnZIvHgEhbGyE6NRJt4y1ddlxEhlDUtKjz3JpDysrKWGo/qxaWQkRESFEcrIQeXna21y8+NGFqEKRWeo/Qqb8Pa9IOX1q0oVoZmamcHZ2Fm5ubgZtR656tSw1vc4zdrnH69CRI4V44w0h+vcXwtOz9HPRjBlSPatvv/v2se6k6sfki6Qm1XlElsDgqaarW3R0NABgwIABOuvUy/bv31+u7Tg5OaFnz54660JCQvDnn39i//79aN26daX2Gx8fj1u3biEkJESna5G9vT169+6N3377DVeuXEGrKu7nsmyZNPWtEFLXmkmTgKee0i23ezfw3XeVK9evn7SueBPkPXukaZnV5cLDpUFIH7+si44GIiMflRsxQpppqKBAeuTnA/fvA0uWPNq+SiUN9jdrljQldGZm6e+Bjw8wcKAUZ1AQ4OIiNa1WTwnMKaSpOj0+JbX68zdokDTOwt690vcnPl5q2q+mUkmf+VmzpN/d3IB69aQxZU6fflROCOn7du4c4O4ujV9kawvY2UlTXq9e/ej79sorQJ8+0vPij337pBjV5V599dH3vPiAmnv2VP68UVY5KysphgkTDH/PLc2FCxcwdepUZGdnY+DAgQZtS656taoU7zZTVXWesevGPn30140rVz4qN3o00LUrUFio/Th+HNi69VG5zp2lsaXS06XBcdPTpXrywYNHMahUgL7hfNzcgLQ07WXW1lKM+mZo8/BgvUlERFRucmd/Kuqll14SAMTJkyf1rnd3dxf16tUrdRvqbHm7du30rv/9998FAPH+++9Xer/qbbzxxht6y7/33nsCgPjjjz9KjDM3N1ekpaVpHklJSRXObpf3DrslPGxthahbV/+6kroT8a4dyamsz9+6dfo/z/pbdj26Cyg9l/87aYxHRVukWcJdwGbNmpX48Pb2Fk5OTsLKykooFArh4uIiYmNjDdqfXPXq41jnVf9j2DCpRUxMjBB377I7EZkPtnyRWEKdR1STmF3Ll7T/3ZJxc3PTu97V1RU3y5i3tTzbKF6uMvutzD4eN2/ePMxS3+KupPh47akg1dq1k+5wqaWmAufP6y9Xq5Z2uXPndMv5+emWO3tWt1xgIFCnzqO76w8fAqdO6ZZ76inpbpqdnXTHPi9PupspxKMyVlZAVBTg6/vo7n9ysjRzTPG/2doaaNlSdx8A79qRvMr6/PXsKX3OH/88X7sGODtLg/feuwdcuCDd6S9OoZAG9lUqH7UgS04G9DVg6NABqF370b9kDx4AcXG65cr7PS/veaM856GiImkGlZr0PU1MTCyzjJubG0JCQjBr1iy0adPGoP3JVa8+zlTqvKqqGxUKqdyZM7rlyls3BgcDjRsDNjbS4+5d4I8/dMu9957UAsbVVWrpmZ0ttf58/FzyxRe6360JE4CQEOl717JlzfruERERVSWzS77UJNOmTcPUqVM1v6enp6Np06YV2karVvr/edu+XfuC6uZN/UmL8pbbtq185bZuLV+5yEjdC75u3fR30yiupO4cvHgkc1TS59nTU1pfp440PXqvXlKC5fXXpeUlddcp6fv222/G/Z4b+/xSUvLUUiUU72v2GIVCAScnJ9StW7caI6oe5lTnyVU3rl5dvnJvv61b71WkbuSNCSIiIuOzkjuAilLfVSvp7pl6yjVDt1G8XGX2W5l9PE6pVMLV1VXrUVHqf96sraXfS7rgMvVygPSPZGKiNBZFYmLJ40CUtxyROSjv53ncOMDBwRH29o64cEF/OVP/nlfkfGDJvLy8Snx4enoaPfEiV736ONZ5VVcOYN1IlsfR0RGOjo5yh0FEVG5m1/JFPThtfHw8OnbsqLXu4cOHSElJQY8ePUrdhpOTExo1aoSEhAQUFRXBWn3V8j/x8fFa+6rMfouX10ffPqpKeZsQm3o5oPx343jXjixJeT7PTk5OyM7OKnNbpv49Z5eH6idXvVpVTP2zaw51KJGpc3JyQlZW2XUeEZEpMbuWL8HBwQCAnTt36qxTL1OXKWs7WVlZOHTokM66HTt26Gynovtt1aoVGjdujEOHDulUDrm5uThw4AAaN26MltXUnt7DQ5ppqKyLLlMvR0SGM/XvOc8H1UuuerUqmfpnl98ZIiKimsfski/9+vVD8+bNsWbNGsTGxmqWZ2RkYM6cObCxscH48eM1y1NSUnDx4kWkpKRobWfi/0an/OSTT5Cfn69ZvmfPHuzYsQO9e/fWmg6zovtVKBQICwtDZmYmZs+erbXvefPm4eHDhwgLC4Oi+JytRERUo0yePLnMwWzLa926dVijb/7gMshVrxIRERHVKHJPt1QZe/fuFba2tsLZ2VmEh4eLd999VzRr1kwAEHPnztUqGxERIQCIiIgIne2EhYUJAMLHx0e8//77YuzYsUKpVAo3Nzdx/vx5g/YrhDQNXmBgoAAg+vfvLz766CPx9NNPCwAiMDCwwlPjcTo5IipJTk6OeOaZZ8QzzzwjcnJy5A5HNuZ2nrS2thZKpVJMmDBB7N+/v8Kvv3v3rvjmm2/EE088IaysrPTWReUhV71aGnM7lkRUfVjnSXieJDIvZpl8EUKIY8eOiYEDBwo3Nzfh4OAgOnXqJFavXq1TrrSLxKKiIvHf//5X+Pr6CqVSKerWrSteeuklcenSJYP3q5aamiqmTJkimjZtKmxtbUXTpk3FlClTRGpqaoX/Zp5giagkmZmZAoAAUOHEriUxt/Pk2bNnxTPPPCMUCoWwsrISHh4eIjw8XCxbtkycPn1a3L59W+Tl5QkhpPrk2rVr4o8//hCzZs0S/fv3F7a2tsLKykrUq1dPfP311yI/P7/SschVr5bE3I4lEVUf1nkSnieJzItCCCGqsaENGUA940RaWlqlZoEgIsuVlZUFZ2dnAEBmZiacnJxkjkge5nqejImJwaJFi/Dbb78hPz+/zC6p6qq7ZcuWCA8Px6RJk+Di4lIdoVYbcz2WRFT1WOdJeJ4kMi9mN9sRERGRpQkKCkJQUBBSUlIQFRWFmJgYHD58GElJSSgsLNSUc3V1RWBgIHr16oUBAwagd+/eMkZNREREROXF5AsREZGJcHd3x8SJEzWD1wJAamoqcnNzUadOHdjZ2ckYHRERERFVFpMvREREJuDu3bs4ceIE8vLy4OHhgU6dOsHKygq1atWSOzQiIiIiMhCTL0RERDL76KOPsHDhQhQVFWmW1alTBxEREXjjjTdkjIyIiIiIjIHJFzOiHmAxPT1d5kiIyNRkZWVpnqenp2v9E1+TqM+P5jSW/MqVK7FgwQLN79bW1igqKsL9+/fx9ttvIzk5GfPmzZMxQnmwziOikrDOk5hjnUdUk3G2IzNy8+ZNNG3aVO4wiIhMXlJSEjw8POQOo1y6deuGEydOYPjw4Vi4cCHq16+P69evY/ny5fjiiy9QWFiIo0ePolOnTnKHWq1Y5xERlY851XlENRmTL2ZEpVLh1q1bcHFxKXMa0selp6ejadOmSEpK4lR0JoDHw7TweJgWQ46HEAIZGRlo3LgxrKysqihC43JxcYGdnR1u3boFpVKptS4yMhITJkzAhAkTsGzZMpkilAfrPMvB42FaeDxMS02r84hqMnY7MiNWVlYGZ7VdXV1Z0ZoQHg/TwuNhWip7PNzc3KogmqqTlZWFdu3a6SReAGD8+PF47733EBMTI0Nk8mKdZ3l4PEwLj4dpqSl1HlFNxhQpERGRzGxtbfUuVygUaNWqFZKTk6s5IiIiIiIyJiZfiIiITJitrS2ys7PlDoOIiIiIDMDkSw2hVCoRERGht1k7VT8eD9PC42FaauLxuHbtGv7zn/9g165duHv3rtzhmL2a+BkyZTwepoXHw7TweBDVHBxwl4iISEbqQRKLDypbr149+Pv7IyAgAFFRUUhMTKyxU6kSERERWQImX4iIiGS0fv16xMbGIi4uDrGxsfjnn38064onZBwdHeHr66tJyvj7+8Pf35+DLRIRERGZASZfiIiITMi9e/e0kjFxcXG4dOkSCgsLNWWKJ2WaNm2KxMREGSIlIiIiovJi8oWIiMjE5eXl4fz581pJmTNnziAtLQ0KhYJdkoiIiIhMHJMvREREZioxMRFxcXEYNGiQ3KEQERERUSk425GFO3HiBJ555hnUrl0bTk5O6NKlC9asWSN3WBZt9erVePXVV9GpUycolUooFAr88MMPJZZPT0/H1KlT4eXlBaVSCS8vL0ydOhXp6enVF7SFSk5OxldffYUBAwbA09MTdnZ2aNiwIYYMGYJjx47pfQ2PR9VJTU3FW2+9he7du6Nhw4ZQKpVo0qQJ+vbti02bNkHfvQAej9J5e3sz8VIM67zqxzrPdLDOMy2s84jocWz5YsGio6MREhICOzs7DB8+HG5uboiKikJCQgI+++wzTJ8+Xe4QLZK3tzeuX78Od3d3ODk54fr164iMjMT48eN1ymZlZaFXr16IjY1F//790aFDB8TFxeHPP/9EYGAgDh48CCcnp+r/IyzERx99hPnz56NFixYIDg5G/fr1ER8fj82bN0MIgbVr1yI0NFRTnsejal25cgWBgYHo1q0bWrZsiTp16uDu3bvYunUr7t69i/DwcHz//fea8jweVBGs8+TBOs90sM4zLazziEiHIItUUFAgWrRoIZRKpTh9+rRmeXp6uvD19RU2Njbi8uXLMkZouXbt2iUSExOFEELMmzdPABCRkZF6y86YMUMAEB988IHe5TNmzKjqcC3apk2bxIEDB3SWHzhwQNja2oo6deqI3NxczXIej6pVWFgoCgoKdJanp6cLHx8fAUCcO3dOs5zHg8qLdZ58WOeZDtZ5poV1HhE9jskXC7Vjxw4BQLz88ss669atWycAiGnTpskQWc1S2oWoSqUSjRs3Fs7OziIzM1NrXU5Ojqhdu7Zo0qSJUKlU1RRtzTJgwAABQJw4cUIIweMhtylTpggAYvPmzUIIHg+qGNZ5poF1nulinWdaWOcR1Uwc88VCRUdHAwAGDBigs069bP/+/dUZEj0mPj4et27dQs+ePXWakdrb26N3795ITk7GlStXZIrQstna2gIAbGxsAPB4yCk3Nxd79+6FQqGAj48PAB4PqhjWeaaP32l5sc4zHazziGouG7kDoKoRHx8PAGjVqpXOutq1a8Pd3V1ThuRR2jEqvjw+Pr7EMlQ5N27cwO7du9GwYUP4+fkB4PGoTqmpqfjqq6+gUqlw9+5dbNu2DUlJSYiIiNB6nwEeDyof1nmmj99p+bDOkxfrPCJSY/LFQqWlpQEA3Nzc9K53dXXFzZs3qzMkekx5jlHxcmQcBQUFGDNmDPLy8rBgwQJYW1sD4PGoTqmpqZg1a5bmd1tbW/z73//Gu+++q1nG40EVwTrP9PE7LQ/WefJjnUdEaux2REQ1hkqlwiuvvIIDBw4gPDwcY8aMkTukGsnb2xtCCBQWFiIhIQGzZ8/Gxx9/jCFDhqCwsFDu8IiILALrPNPAOo+I1Jh8sVDqzHlJGfL09PQSs+tUPcpzjIqXI8MIIRAeHo7Vq1dj9OjR+O6777TW83hUP2tra3h7e+Ojjz7C3Llz8euvv2LZsmUAeDyoYljnmT5+p6sX6zzTwzqPiJh8sVCP9yEt7uHDh0hJSWGfUZmVdoyKL+dxMpxKpcKECROwcuVKjBgxAj/88AOsrLRPfzwe8lIPiqoeOJXHgyqCdZ7p43e6+rDOM32s84hqJiZfLFRwcDAAYOfOnTrr1MvUZUgerVq1QuPGjXHo0CFkZWVprcvNzcWBAwfQuHFjtGzZUqYILYNKpUJYWBgiIyMxbNgwrFq1StPnvTgeD3ndunULwKOZOHg8qCJY55k+fqerB+s888A6j6hmYvLFQvXr1w/NmzfHmjVrEBsbq1mekZGBOXPmwMbGBuPHj5ctPgIUCgXCwsKQmZmJ2bNna62bN28eHj58iLCwMCgUCpkiNH/qu3+RkZEYOnQoVq9erfciFODxqA6xsbF6m1Q/ePAA06dPBwA8/fTTAHg8qGJY55k+fqerHus808I6j4gepxBCCLmDoKqxb98+hISEQKlUYsSIEXB1dUVUVBQSEhIwd+5cfPzxx3KHaJGWL1+OgwcPAgDOnj2L06dPo2fPnpq7FYMHD8bgwYMBAFlZWejVqxdiY2PRv39/dOzYEXFxcdi+fTsCAwNx8OBBODk5yfWnmL2ZM2di1qxZcHZ2xttvv625w1Tc4MGDERgYCIDHo6q98847WL58Ofr06QMvLy84OTnh+vXr+OOPP5CZmYkhQ4Zgw4YNmubxPB5UEazz5ME6z3SwzjMtrPOISIcgi3bs2DExcOBA4ebmJhwcHESnTp3E6tWr5Q7Loo0bN04AKPERERGhVT41NVVMmTJFNG3aVNja2oqmTZuKKVOmiNTUVHn+AAtS1rEAICIjI7Vew+NRdWJiYsT48ePFE088IVxdXYWNjY2oX7++GDhwoFizZo1QqVQ6r+HxoIpgnVf9WOeZDtZ5poV1HhE9ji1fiIiIiIiIiIiqEMd8ISIiIiIiIiKqQky+EBERERERERFVISZfiIiIiIiIiIiqEJMvRERERERERERViMkXIiIiIiIiIqIqxOQLEREREREREVEVYvKFiIiIiIiIiKgKMflCRERERERERFSFmHwhIiIiIiIiIqpCTL4QEREREREREVUhJl+IiIiIiIiIiKoQky9UpuzsbFhbW8PJyQkqlarS21EoFFAoFEaMTB7e3t5QKBRITEyUOxSzFxcXh3/961+oU6cOrKysoFAoEB0dLXdYZqmk97K0zys/y0S6WOdp43nCeFjnGQ/rPCIyRzZyB0Cm79y5c1CpVGjXrh2srJivszRfffUVUlNT8c4776BWrVrVtt+7d++iT58+ePjwIZo0aYK2bdtCoVDAzc2t2mKorM2bN2P79u04efIkbt26hfv378PR0RE+Pj4YNmwYXnvtNdjZ2ZX4+m3btmHhwoU4ffo08vLy0KZNG7z88st4/fXXK/UdM+f3ksjUsM6zbKzzKo51HhGRcTD5QmWKi4sDAPj7+8scCVWFr776CtevX8f48eOr9UJ03bp1ePjwIQYNGoSoqCiz+ifniy++wKFDh6BUKtG4cWMEBATg9u3bOHLkCI4cOYJVq1Zh9+7det/P//u//8O0adMAAM2bN4ezszPi4uLw1ltvYffu3fj1118r/F5U9r1s0aIF7O3tYWtrW6H9EVky1nmWjXVexbHOIyIyDvM585Ns1BeiAQEBMkdCluTixYsAgJCQELO6CAWAsLAw7Nu3DxkZGbh27RpOnDiBmzdv4siRI/Dw8MCpU6fw8ccf67zuyJEjmD59OqysrLBmzRpcvXoVcXFxOH36NBo0aIAtW7Zg4cKFFY6nsu/lnj17cPHiRTRp0qTC+ySyVKzzqCqwzmOdR0RkXmd/ksWZM2cA8EKUjCsnJwcA4ODgIHMkFTd+/Hg8+eSTOnfPunXrprmQ3Lx5s87r5s6dCyEEwsLCMGLECM3ygIAAzev+7//+DwUFBRWKx5zfSyJTwzqPqoI5n6dZ5xERGYkgKoObm5sAIFJTU7WW5+XliYkTJwoAwsfHR8THx5e6HQBC/ZHbtm2bCAoKEs7OzsLV1VUMHDhQnD59utTXFxQUiCVLloiePXsKNzc3oVQqRZs2bcTHH38s0tLSdMqfPXtWzJgxQ3Tr1k00bNhQ2NraioYNG4oXXnhBHDp0qNR9JSYmilGjRol69eoJBwcH4efnJxYtWiRUKpXw8vISAERCQoLOayZOnCiaNWsm7OzshLOzs2jWrJkYPHiwWLt2ban70yclJUW8//77onXr1sLe3l7UqlVLBAcHi9WrVwuVSqVVNiEhQQAQXl5eJW6v+PsvhBCRkZGaZfoe+/btq5JYIyIiStxncHBwmfsy9HNU1c6cOSMAiFq1amktT0tLE3Z2dgKAOHbsmM7r8vPzhaurqwAgduzYUa59lee9LOnzWtq64u/xzz//LDp37iycnJxE7dq1xaBBg8TZs2f1xmPs7wCRHFjnsc4zZqys81jnERGpMflCpSrpAufWrVuie/fuAoB47rnnRHp6epnbUlduS5YsEQqFQjRq1Eh06NBBODk5CQDC2dlZXLhwQe9r09LSRO/evQUAYWVlJby8vES7du00FXvbtm3FnTt3tF7Tr18/zQVB27ZtRYcOHYS7u7sAIKytrcXPP/+sd19///23qFu3rgAg7O3tRceOHYWnp6cAICZPnqy38k5ISNBs29HRUfj5+YnAwEBRp04dAUAEBASU+f4UFx8fL5o2bSoACDs7O9GhQwfRvHlzzXs4duxYrQu8ylyIbtu2TfTs2VMolUoBQHTq1En07NlT8yjvBV1FY12xYoXo2bOnqF+/vgAgWrVqpdnnG2+8Ueb+DPkcVYelS5cKAKJv375ay6OjozWfqYKCAr2vVX9mZ8+eXa59lee9NORCdP78+QKAaNiwoejUqZNwcXERAISDg4OIiYnReo2xvwNEcmCdxzrP2LGyzmOdR0SkxuQLleq3337TXGyqHTp0SDRq1EgAENOnT9e5y1MSdeXm6OgoIiMjNcvT09M1FfCwYcP0vnb48OECgOjXr5+4evWqZvmDBw/Eiy++KACIl156Ses1GzduFGfOnNFaplKpxObNmzV3jR6/gFapVKJDhw4CgAgJCRH379/XrFu7dq2wtbUVNjY2OpX3G2+8IQCIcePGiYyMDK1tXrhwQSxdurRc75E6hk6dOmnu5Pzzzz+addu3b9dccH377bea5ZW5EFUr7UKlKmJVGzdunACg9VkoD0M+R5999pnWxXZ5H2VdlBcWFoqkpCSxePFi4eLiIpycnHTu9C1btkwAEK1bty5xO+Hh4QKAGDNmTPnfEFH6e2nIhaitra34z3/+I4qKioQQQmRlZYlRo0ZpPmvZ2dma1xjzO0AkF9Z5rPOMHasa6zxdrPOIqKZh8oVKNXv2bAFAfPLJJ0IIIb777jthZ2cnHB0dxfr16yu0LXXl9uabb+qsUzdbdXNz01kXFxenqfj03W3MysoSTZs2FQqFQiQmJpYrlk8++UQA0LkTuHv3bs1djnv37um87q233tL8HcUr75CQEAFAxMXFlWv/pdm1a5cAIJRKpbh9+7bO+gULFmjeD/U/AXJdiFYmVjVDL0Qr+jkqvs+KPkpqjv7ll1/qlB08eLDeJsrq96Jr164l/m0ffPCBACD+9a9/leu9ePzvMvaF6PPPP6/zmry8PNGwYUMBQKxcuVKz3JjfASK5sM7TxjrP8FjVWOfpYp1HRDUNB9ylUqlnfXjiiScwceJETJo0CY0aNcLhw4cRGhpaqW2GhYXpLPPz84O9vT3S0tJw//59rXW//vorACA0NBQuLi46r3V0dMRTTz0FIQRiYmK01t24cQP/93//h9DQUPTt2xe9evVCr169sH79eq2/T23Hjh0AgKFDh8Ld3V1nX5MnT9b7NzVt2hQA8Msvv0AIobdMee3cuVMTQ8OGDXXWT5o0CUqlEtevX8elS5cM2peh5Iy1op8jAPjhhx8gpKRzhR5PPvmk3hiaNGmCnj17okuXLmjQoAEAYN++fVi7di2Kioq0yubm5gIA7OzsSvyblEolgEeDCcrt9ddf11lmZ2enee/V3xfAuN8BIrmwztPGOk8b6zzWeWqs84ioMmzkDoBMm3rWh+nTp+PGjRsIDg7Gxo0bUa9evUpvs0WLFnqX16tXD0lJScjMzETdunU1y8+ePQtAuiA9fPiw3tdev34dAJCcnKxZ9uOPP2LSpEmaCwB9Hjx4oPX75cuXAQBt27bVW75Vq1awsbFBYWGh1vLXX38dP/74I+bMmYOffvoJAwcORFBQEPr06YPGjRuXuH991DH4+PjoXe/i4oKmTZviypUruHz5Mp544okKbd+Y5Iy1op+jqjB06FAMHTpU8/uxY8fw6quv4vPPP8eDBw+wZMkSzTp7e3sAQH5+fonby8vLA2A6MziU9D1QL1cff8C43wEiubDO08Y6TxvrPNZ5aqzziKgy2PKFSpSVlYWrV6/C3t4e//zzDwBp2kBDLkIBwMnJSe9yKyvp4/j4HYS0tDQAwJUrV3Do0CG9j5s3bwJ4dPfk6tWrCA8PR25uLt5991389ddfSE9Ph0qlghACy5YtAwCd6Q0zMzMBoMS/0crKSu/dwcDAQBw4cAADBgxAcnIyli5ditGjR8PDwwMhISG4cOFCud6b4jHUr1+/xDLqO04ZGRnl3m5VkDPWin6OqkPXrl2xbds2KJVKfP/995p/kACgdu3aAICHDx+W+Hr1OnVZuZV0XPUdU2N+B4jkwDpPf4ys8x5hnaeNdR7rPCKqGLZ8oRKdPXsWKpUKHTp0wMsvv4zw8HCEhobixIkTaNKkSbXF4ezsDABYtmyZ3ma3+mzYsAEFBQUYPnw4vvjiC531SUlJpe7r3r17eterVCq9TXsBoFu3btixYwcyMzNx6NAh7Nu3D2vWrMHOnTvRv39/nDt3DrVq1SozdnUMd+/eLbHMnTt3AEDTJF2hUAAo+eIrKyurzP1WRmVildPnn3+Obdu2Vfh133zzDdq3b1+uso0bN0ZgYCCOHTuGuLg4eHl5AZDuIANSt4DCwkLY2Oiefq9du6ZVVm737t2Dh4eHznL18X78mBrrO0AkB9Z5uljnaWOdp4t1Hus8Iio/Jl+oROrm1/7+/ggLC8OZM2fwzTffYPDgwYiJidE0Ka1qPj4+2Lx5M86dO1fu1yQmJgIAevTooXf94/3e1Vq3bg0AuHjxot71V65c0blz+DhnZ2eEhIQgJCQEM2bMgL+/P65evYrt27djxIgRZcaujuHvv//Wuz4jI0NzIa0uq74jVtIF9JUrV0rcn/oitjIqE6ucLl++jEOHDlX4deo70eWlbqJfvKl++/btYWtri9zcXJw+fRpdunTRek1BQQFOnDgBQLqbaAouXLig90JUfUevpGNq6HeASA6s83SxzjM8VjmxzqsY1nlEVNXY7YhKpL5Y8/f3BwAsXLgQffv2xcmTJzFhwoRqi+OFF14AAKxevbrEO3CPU/cfVt+BKu7ixYvYunWr3tcNGDAAALBx40a9+/r222/LtX81R0dH+Pn5AQBu3bpVrteEhIRoYlA3fS9u6dKlyMvLg5eXF9q0aQMAqFu3Ltzc3JCTk4Pz58/rvGb58uUl7k/9XlVmwLvKxConYw8+qE9iYqLmuxMQEKBZ7urqiqeeegoAsGLFCp3Xbdy4Eenp6ahbt26F9leV9H3e8/PzNfGrvy+lqcx3gEgOrPNY51VFrHJinVcxrPOIqMoZOl0SWa6ePXsKAOLgwYOaZffv3xfNmzcXAMTnn39eoe2hhGkf1UqbHjA0NFQAEO3btxenT5/WWldYWCj27dsnRo4cKXJzc4UQQmzcuFEAELVr1xZ//fWXpuylS5dEu3bthL29vQAgxo0bp7UtlUol2rdvLwCIp59+Wjx48ECzbv369cLOzk7Y2NjoxDlp0iSxbt06kZWVpbW9/fv3CxcXFwFA7N27t4x36FEMnTt3FgDEk08+Ke7cuaNZt2PHDuHs7CwAiCVLluh9jwYMGCAyMjI0y3/44Qfh6OhY4vv/7LPP6t1eVcYqhOHTbpbEkGlEy+PkyZNixowZ4urVqzrrtm/fLp544gkBQDzzzDM66w8ePCgUCoWwsrISa9as0SyPjY0VDRo0EADE/PnzKxxTVU27aWtrK7766ivNlKnZ2dli7NixAoBo2rSp1ufdmN8BIjmwzmOdV1WxCsE6j3UeEZGU4SbSy9XVVSgUCpGWlqa1/Ny5c8LFxUVYWVmJLVu2lHt7hlxAZGRkiP79+2u24enpKbp27Sr8/PyEg4ODZnlOTo4QQoiCggLRrVs3AUBYW1uLtm3binbt2gmFQiEaNWok5s6dq/dCVP331alTRwAQDg4OolOnTprYJk+erDfOgIAAAUDY2NiItm3bii5dumjKARCjR48u9/skhBDx8fHCw8NDABBKpVJ06NBBtGzZUrO9MWPGaC4O1C5cuKC58HNychIdOnQQjRo10lwIlvT+//TTT5p17dq1E8HBwSI4OFjrAt7YsQphvhei+/bt08TQsGFD0alTJ+Hv7y9q1aqlWd65c2dx7949va9Xf/YAiObNmwt/f39hZWUlAIhnn31WFBYWVjimqroQnT9/vubv7Ny5s3B1dRUAhL29vdi/f7/Wa4z9HSCqbqzzWOdVVaxCsM5jnUdExOQLleDatWsCgPD29ta7/rfffhMKhUK4uLiIc+fOlWubhl5AFBUViZ9//lmEhIQId3d3YWtrKxo1aiS6du0qPvzwQ3H8+HGt8mlpaeLNN98UjRs3Fra2tsLDw0OEhYWJW7duicjIyBIvRNV//8iRI0XdunWFvb298PPzE998841QqVR649y7d694++23RYcOHUS9evWEnZ2d8PLyEiEhIWLLli16L8TKcu/ePfHee++JVq1aCaVSKVxdXUXv3r3FqlWrStze6dOnxcCBA4WLi4twcnISPXr0EFu3bhVClP7+f/3118Lf31/ron7fvn1VGqu5Xog+ePBAfP311+L5558XLVq0EM7OzsLOzk40atRIPP300yIyMlIUFBSUuo2tW7eKvn37Cjc3N+Ho6CgCAgLEV199VamLUCGq7kJUCCF+/vln0blzZ+Ho6Cjc3NzE888/L+Li4nS2VRXfAaLqwjqPdR7rPP1Y57HOIyLjUQghw9x0RERkssqaSYSIiMhSsM4jourCAXeJiIiIiIiIiKoQky9ERERERERERFWIyRciIiIiIiIioirE5AsRERERERERURXigLtERERERERERFWILV+IiIiIiIiIiKoQky9ERERERERERFWIyRciIiIiIiIioirE5AsRERERERERURVi8oWIiIiIiIiIqAox+UJEREREREREVIWYfCEiIiIiIiIiqkJMvhARERERERERVSEmX4iIiIiIiIiIqhCTL0REREREREREVej/AVp8B0kxCFTTAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_flips = 30\n",
    "p_fair = 0.5\n",
    "unlucky_k = 25\n",
    "viz_coin_flip_H0_H1(k=unlucky_k, n=n_flips, p_null=p_fair, show_h1=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call $H_0$ the null, or \"fair\" hypothesis that the booth manager's coin's chance of heads is $p = 0.5$. The p-value of the data is the probability that you would observe data at least as extreme as the data you observed, given the null hypothesis is true. In our case, we'll consider \"extreme\" to be one-sided -- the higher $k$ is, the more money we lose.\n",
    "\n",
    "The total area under a PMF is 1. Graphically, the p-value for our observed data is the area to the right of the dashed line on the PMF plot. A convenient way to compute this value is with the CDF:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\text{p-value} &= P(X \\geq k \\text{ heads} \\mid H_0: p = 0.5) \\\\\n",
    "&= \\sum_{q = k}^n P(X = q \\text{ heads} \\mid H_0: p = 0.5) \\\\\n",
    "&= 1 - \\sum_{q = 0}^{k-1} P(X = q \\text{ heads} \\mid H_0: p = 0.5) \\\\\n",
    "&= 1 - CDF(k-1 \\text{ heads} \\mid H_0: p = 0.5)\n",
    "\\end{aligned}$$\n",
    "\n",
    "The p value can be computed as $1 - CDF(25-1)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00016245711594820023"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - stats.binom.cdf(unlucky_k - 1, n=n_flips, p=p_fair)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be more safe, use the \"survival function\" `sf`, which is optimized for dealing with small probabilities that `1-CDF` might just call 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00016245711594820025"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.sf(unlucky_k - 1, n=n_flips, p=p_fair)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oof, if the coin was indeed fair, the chance that we'd be this unlucky or even unluckier is 0.00016. This seems quite unlikely. So unlikely, in fact, that why don't we formulate a new, better hypothesis given our observed data?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specifying a new hypothesis / parameter estimation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will demonstrate maximum likelihood estimation (MLE) on two specific probability distributions. A discrete distribution, the binomial; and a continuous distribution, the normal. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLE for a binomial distribution\n",
    "\n",
    "Let's come back to the coin flip example, where the data is some observed $k$ heads out of $N$ flips. We will try to find the per-trial chance of heads $p$ that maximizes the likelihood:\n",
    "\n",
    "$$P(D|p) = P(k,N|p) = L(p) = {N \\choose k}p^k (1-p)^{N-k} $$\n",
    "\n",
    "What can we do here? We could plug in a bunch of $p$'s, evaluate this function, and then store the $p$ with the highest likelihood. \n",
    "\n",
    "Or, with this rather simple equation, we can solve by hand by taking a partial derivative of $L(p)$ with respect to $p$ and finding the $p$ that satisfies $\\frac{\\partial}{\\partial p} L(p) = 0$.\n",
    "\n",
    "So, taking the derivative:\n",
    "\n",
    "$$\\frac{\\partial}{\\partial p}L(p) = {N \\choose k} kp^{k-1}(1-p)^{N-k} - p^k{N-k}(1-p)^{N-k-1} $$\n",
    "\n",
    "This is a little gross. There's a lot of chained $p$'s and exponents to deal with.\n",
    "\n",
    "A convenient trick that comes up frequently with this kind of problem is to maximize the log likelihood instead of the likelihood. This is okay to do because the logarithm is a monotonically increasing function (the $x$ that maximizes $f(x)$ also maximizes $\\log f(x)$). Exponents come up a lot in statistics formulas, and taking the log helps to separate them out.\n",
    "\n",
    "The log likelihood:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\log L(p) &= \\log \\bigg[ {N \\choose k}p^k (1-p)^{N-k}\\bigg] \\\\ \n",
    "&= \\log {N \\choose k}+ k \\log(p) + (N-k)\\log(1-p) \n",
    "\\end{aligned}$$\n",
    "\n",
    "Now it's a little easier to take the derivative with respect to $p$:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial}{\\partial p} \\log L(p) &= \\frac{\\partial}{\\partial p} \\bigg[ \\log {N \\choose k}+ k \\log(p) + (N-k)\\log(1-p)  \\bigg] \\\\ \n",
    "&= \\frac{k}{p} - \\frac{N-k}{1-p}\n",
    "\\end{aligned}$$\n",
    "\n",
    "Setting it to zero to find our maximizer, $\\hat{p}$ (you should check it's a maximum by taking the second derivative too):\n",
    "\n",
    "$$\\frac{k}{p} - \\frac{N-k}{1-p} = 0 \\implies k - kp = Np - kp \\implies \\hat{p} = \\frac{k}{N}$$\n",
    "\n",
    "Rather unsurprisingly, if we observe $k$ heads out of $N$ flips, the maximum likelihood estimate of the probability of heads is just $k/N$.\n",
    "\n",
    "So, we can set a new hypothesis, $H_1$, that explains our observed data. Let's plot it on the same plot as $H_0$ for comparison. This new distribution predicts the data much better -- it must be true, right? $H_0$ is just wrong!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6nU757bffjO7Xvq/Gjh1rsF17vR977DGD44Br164pXl5eio2NjXLu3Llcn8PDbcj+f5FTvbk9JikpSXF3d1fs7e0NXpesrCxl1KhRCqDMnj3boBzt//7FF19UMjMz9dsXLVqkAMrkyZNN1v8w6XNLrs9dtmyZ0eczPx7ue3OyePFiBVDGjBmj36a9v+3atTPZ5546dapQz0UIUXgyzaecaNKkCRMmTDDY9vrrr1O1alVWr15NWlqa0WM+/vhjHB0dDbatXLmSjIwMXn31VerUqaPfbmdnp58CYmo4q4eHh1HOhDFjxtC8eXN27dplMEyxXr16WFtbG+yr0+l46aWXAPRTXB42e/Zs/RlAUOeeT5gwgYSEBDZs2GDyMcVh8uTJwINRKJrly5eTnp7O888/X6Dy3nvvPZydnfV/DxkyBFtbWxISEvjkk0+wsXkwgGzkyJGAOk83u+w5MDQ2Njb8+9//JjMzk5CQEKP7H37vAapUqZKv/Sw1bx7glVdeoUmTJvq/HR0dGTlypNEUlm+++YbMzEzmzJljdBZRp9NRs2bNIrVD+xx89NFHBmdwa9euzfTp00lPTzc6awcwatQounbtqv/b2tqasWPHAhAREVGkNmk++eQTZs2axTvvvMPo0aPp0KEDycnJTJkyJcczquPHj+f48eP613DZsmVkZmYafa+YsnPnToKCgowu//zzj1mejyg9ivtzBeqw+IEDB+r/trW1ZciQISiKwlNPPYWPj4/+PhcXF/r378/NmzdNTmstqlq1apkcofHyyy8DOfdX+aXT6Rg1ahTx8fFGUxV++OEHAH2SSlBHkyQlJTF37lyjvBIjR46kbdu2rFmzJs96f/nlF5KSkpgwYQKNGzfWb7e1teW9994r8PPIb3+Sl0GDBvH4448X+HFvvfUWLi4u+r9r1KjBjBkzyMjIYNWqVQUuryh++eUXEhISmDBhAi1bttRv1+l0fPDBB0bTqjXOzs58+OGHWFk9ODQfO3YsNjY2ZusbCkP6XNO0/q127dqFLiM32uv18PRbUKfLm+pzT58+XSxtEULkTIIp5UTXrl2Npt5o+TeSk5P5+++/De7T5hQ/7MiRIwAmly/s1KkTjo6OHD161Oi+Nm3aGAQEQO08teHe2X/8p6WlMW/ePDp06ICrqytWVlbodDratWsHPEiglp2trS2dOnUy2q4NizbVpuLSokULOnfuzE8//URiYqJ++5IlS6hUqRLDhw8vUHlt2rQx+Nva2ppq1arh7u5udLCsrRhw5coVg+23b98mMDCQVq1aUalSJf0c5GeeeQYwfE2HDBmClZUVgwYNYvz48axatYpLly4Ztat///44OTnx0ksvMWzYMJYsWWL0f2QJbdu2NdqmHcwkJCTot/35558A9OnTp1jaceTIEX3unodpnx9T/5f5bX9RfPrppwQFBfHee++xZcsWfHx8WLZsGZ999lmOjxkzZgy2trb6PAPLli2jY8eOPPbYY3nWN3fuXBRFMboUdXi5KH2K+3MFxt+J8OC7z9T/VE7fi+agKApLliyhR48eVK5cGWtra3Q6nT5QYKq/KqgxY8YAD4InoC5xu3r1amrUqGEQXDhw4ID+etasWUaXlJQU4uLiTP4Ay07rk01NLercubNBED83w4YNA6Bjx4689NJLrFu3jtjY2Hw91hRT36f5Yep5WOL4AHI/jqpTpw6PPPII586dM5rC1KhRIypVqmSwzcbGhurVq5utbygM6XMtQ1GUHO+bPHmyyT43+1Q0IUTJkJwp5US1atVMbtfyoGT/0a/tbyq5V1JSksHjTNVj6oC1IPUPGTKETZs26eeEVqtWTT8S4/PPPyc1NdWonCpVqhicrcnr+RW3SZMmMX78eFauXMmLL75IeHg4p0+f5vnnnzc6GMpL9twnGhsbG5MrBGgHuNkT9aalpeHn58fhw4dp06YNY8aMoUqVKtjY2BAdHc3y5csNXtPOnTuza9cu5s6dy+rVq/Vne9q1a8fHH3+Mv78/oI522b9/P0FBQfz666/8+OOPgDoKavbs2QwdOrRAz9NccntdsiehTEhIQKfTFduSlUlJSQajt7LTVlIw9X+Z3/YXxbVr1wq8mkO1atXo27cvq1evZsCAAZw9e5bXXnvNLO0R5Udxf64g5+/EvO7LLYF5YU2dOpUFCxZQp04dBgwYgJeXlz7/QVBQkMn+qqC8vb1p06YNW7ZsISEhAXd3d3777TeuX7/OjBkzDEZy3rp1C1BzU+Tm7t27uY4g1L6bTPXd1tbW+R5VMnz4cGxtbfnss8/49ttv+eqrr/TJVOfNm1fggGpOxx55MfU8LHV8kNdxVI0aNThz5gxJSUkGo2lyWhXIxsbGbH1DYUifa5pWZ3EEcUHtxwGqVq1aLOULIcxDRqaUEzmdCbp+/Tpg3JmYCqTAgwNV7XGm6jF1MJvf+iMiIti0aRMBAQFERkaycOFC3nvvPWbNmsWIESNMlgFw8+ZNsrKy8iy/pAwfPhx3d3f9VB/tuqBTfMxhw4YNHD58mIkTJ3L48GG+/vpr5syZw6xZs3jiiSdMPsbX15dt27YRHx9PSEgIM2bM4K+//qJfv36cO3dOv1/Lli1Zt24dt27dYv/+/bz77rtcv36d4cOHs3fv3iK128rKioyMDJP3mePg193dHUVR9Ack5ubq6prj50TbbuqzUppNmDCB+Ph4nnvuOf1QbiGyK8jnSguAm/qcF/cPXHPUHRsby5dffknLli05ffo0y5YtY+7cucyaNYt///vfZm3vmDFjSE1N5aeffgIejFLRRq1otO+UEydOmDwzrV3q1auXa31an2mq787MzCzQSieDBw9m9+7d3Lp1i19//ZWJEycSFhZGQEBAgc/853RskhdTz8PU8UFJ/E/mdRxlqf5B+lzz0qYOhYaGmjw+LSptBaDs0xqFEKWPBFPKib179xoNCUxOTubQoUM4OjoazInOjTa82tQybn/++SfJyckmzzQdOXKEu3fvmmwXQKtWrQD0P9T79etnlDclp6UhQT3jqA1vNvUYc08nsLKyyvWMhaOjI//61784cuQIYWFh/Pjjj7Rs2dIinZ72mg4YMMDovtxeU1Cfh5+fH59++ilvvvkmycnJJnMAaNOsgoKCmD9/PoqisHnz5iK128PDg9jYWKODu7t37xIVFVWksuHBcPEdO3bkua/2v1iQs1Rt2rQhOTlZP7Q5O2151LI2zaVv377UqFGDK1eu8Mwzz5S5YJAofgX5XGkrypg6c6tNhSgu5qj7/PnzKIrC448/jpOTk8F9OX23Fua7BNR8J9bW1vzwww/cvXuXX375BW9vb6PvkI4dOwKwf//+ApX/MK1PNvU89u/fn+OP7ty4urryxBNP8N133zFu3DhiY2P5448/9Pfn1a8WhannYer4oKD/F4XtG8D0cdSVK1c4d+4cDRs2NBiVUhKkzzWvRx99lB49enD58mWWL1+e674FHcH2999/ExwcjL29vcFKXkKI0keCKeXEmTNn9LkONB9//DE3btxg5MiR+VriENREXTY2NsybN89gLnh6ero+wWz2ZQ018fHx+gS1mhUrVnDixAl69uypH5qpnS17eDm6v/76i7lz5+batnfeecdgGPfp06dZsmQJbm5uBskKzaFy5cp5JjPUEtGOGjWKe/fuWWRUCuT8moaFhbFw4UKj/ffs2aMfhpyddmZHSyQYERGR69k+UwkHC6J9+/ZGCeMURWHmzJkmA3MF9e9//xtra2vefvttLl68aHDfw2fPKleuDFCgBJZaAruZM2ca/F9euXKFefPmYWNjU+Qlu8eNG4dOpzOZrLA42NjYsHHjRn7++edCJaEU5V9BPlft27cHjJOW//TTT/ofP8VFq3vFihUGZ433799vMkmlKdp36759+wzKiImJMUq4rinMdwmgz42ye/duPv/8c+7evWs0KgXURNEuLi689dZb/PXXX0b337t3z+SJh4cNHDgQV1dXo1xY6enpvP322/lu986dO0lJSTHarvUd2fuJ/PSrhfXee+8Z5CC5fv26/nt41KhR+u0F/b/w8PBAp9MVqN0DBw7Ezc2NpUuXGrxHWv+Wnp5u8jiquEmfm7eC9rnz58/H0dGRl19+mbVr15rcZ8+ePfTs2TPfbQgPDycgIIDU1FRmzpxJrVq18v1YIUTJk5wp5USfPn148cUX2bJlC02bNuXw4cNs376dOnXq8P777+e7nEceeYQPP/yQV199lZYtWzJs2DCcnZ3ZvHkzp0+fZuDAgQYrC2i6d+/O/PnzOXDgAD4+Pvz999/8/PPPuLm5sWDBAv1+HTp0oEOHDgQHB3Pt2jU6derEpUuX2LhxI/369dMPcX6Yl5cXCQkJtG7dmn79+pGYmMjq1atJSUlh4cKFZj/D07NnT4KDgxkyZAht2rTB2tqafv36GSTtbd68OV26dGHfvn04ODiYfF1KwlNPPUX9+vX56KOPOHnyJM2bN+fMmTNs3ryZQYMGsW7dOoP9P/30U3777Tf8/f1p2LAhDg4OHD58mJ07d/Loo4/qz4KsXLmSr776Cj8/Px599FFcXV2JjIxk69ateHp65muVl9y8/PLLLF26lIkTJ/Lbb79RtWpV9uzZQ0JCAq1atTJasaigWrRowWeffcbUqVPx9vZm0KBB1KtXj3/++Yfdu3fTr18/fUJWf39/dDodb731FqdPn8bNzQ03NzdeeOGFHMsfM2YM69evZ8OGDbRs2ZL+/ftz9+5dgoODuXnzJp9++ikNGzYs0nPQDvbzmwzSHHx8fGRYschRQT5XgwYNokGDBixbtozLly/Tpk0bTp06xa5du+jbty9bt24ttnZ26tRJnx+qc+fO9OjRg4sXL7Jx40aeeuopfv755zzL8PLy4plnnmHdunW0b9+eXr16cf36dTZv3kzPnj05f/680WN69uzJTz/9xNChQ+nbt68+2Xu/fv3yrG/MmDFs376dWbNmYWVlZfKHobZC39ChQ2nVqhVPPPEETZs2JSUlhYsXLxIWFkaXLl3Ytm1brnW5ubkxf/58xo0bh4+PDyNGjMDNzY3Nmzfj6OiY77wXr776KpcuXcLPz4/69euj0+kIDw/nzz//pEuXLgarqOSnXy2shg0b0rx5c5555hnS09MJDg4mNjaW9957z+B7uKD/F5UqVcLHx4fdu3czfvx4GjVqhJWVFaNGjTJKEK9xdXVl4cKFjBw5ko4dOzJ8+HCqVq3Kzp07OXjwIB06dOD1118v8nMuKOlz81bQPrdVq1Zs2rSJYcOGMWLECP7v//5Pn6z61q1b7N27lxMnTvDoo48aPfbs2bPMmjULUHPfaSO5Tp48qQ9Kvfvuu0V6PkKIElDcay+L4qWtOR8YGKiEhYUp3bt3V5ycnBR3d3dlxIgRyqVLl4weU69ePaVevXq5lrthwwbF19dXcXFxUezt7ZUWLVoon376qZKenm6w34ULFxRAGTt2rHL8+HHliSeeUFxcXJRKlSop/fr1U06ePGlUdmxsrDJhwgSlZs2aioODg9KiRQvlyy+/VM6fP68vy1R7b968qUycOFGpVq2aYm9vr7Rv317ZsGGDUflLly5VAGXp0qV5Pu+c9r127ZoybNgwxdPTU7GysjK5j6IoyrfffqsAyr/+9a8cX8uc+Pr6Kjl9BHN7jwDF19fXYNv58+eVZ555Rqlatari5OSk+Pj4KGvWrDH4/9Bs27ZNefbZZ5UmTZro36vHHntMefvtt5W4uDj9fgcOHFAmT56sNG/eXHF3d1ccHR2VRo0aKVOnTjX5f2WKqfqz27lzp9KxY0fF3t5eqVKlijJmzBjln3/+MfnaBAYGKoASEhJiVE5O76PWhv79+yuVK1dW7OzslNq1ayvPPPOMsnfvXoP9li1bprRo0UKxt7dXAIPXP6f3Kj09Xfnkk0/0j3NxcVF8fX0L9H+Z2+vUpk0bxcXFRbl165bRY0zR2nnt2rU899U+uwEBAfkqG1CaNGlisE17TnPnzs1XGaL8yO/n6vz588rAgQMVFxcXxdnZWenVq5cSERFh8vOc2/dFbp+fnL4bbty4oYwZM0apXLmy4ujoqHTq1EnZvn17jmWZ+m69ffu28uqrryr169dX7O3tlUaNGimzZ89W0tLSTO6fnp6uvPHGG0rdunUVGxsboz7N1GM0d+/eVSpVqqQAir+/v8l9NKdPn1aee+45pV69eoqdnZ3i4eGhtGjRQpk6dary559/5vrY7H7++WelXbt2ir29vVKtWjVl4sSJyq1bt0z2QaZe5zVr1ijDhg1THnnkEcXJyUlxc3NTWrdurXz00UfKnTt3DB6fW7+a2/urKIbHGtlp33n37t1TXnvtNaVWrVqKnZ2d4u3trSxatMhkWQX9vzhz5ozSt29fxd3dXdHpdAavQW7t3r17t/Lkk08q7u7uip2dndK4cWPlnXfeMXpdFCX3/4v8HLNppM/NfxvN0edqbt68qcyePVvp1KmT4uHhodjY2ChVqlRR/Pz8lM8//9zgPdf+l7NfHB0dFS8vL8Xf31955513lLNnz5qsR2v35MmTC9Q+IUTx0SlKLmtviVIvNDQUf39/AgMD9RFuUXJefPFFvv76a8LCwujRo4elmyPKkaSkJDw8PHj11Vf56KOPLN0cUQTp6elEREQQHh7OxYsXuXHjBsnJyXh6elK1alXatm1L9+7dZTi3EEJYiPS5QojCkGk+QhTSjRs3WLFiBc2aNZNAijC7vXv3Ymtry4wZMyzdFFFIISEhLFq0iF9++UWfV8LU+QttBZNmzZoxYcIEnn322VyXtRVCCGFe0ucKIQpDgilCFNCWLVs4fPgwP/30E3fv3iUwMNDSTRLl0JNPPmkysaMo/TZt2sTMmTM5deoUiqJgY2ND69at8fHxwcvLi8qVK+Po6MitW7e4desWkZGRREREEBkZyWuvvcabb77JpEmTeOedd6hataqln44QQpR70ucKIQpDgilCFNCPP/7I8uXLqVmzJu+//z7Dhw+3dJOEEKVEjx492Lt3L46OjvqkhAEBATg4OOT52HPnzrFmzRpWr17NggULWL58OStWrDD7amVCCCGEEKLoymzOlIiICAIDA9m/fz9paWl4e3szbdo0gyXwchMeHs7PP/9MaGgo0dHR3L17l/r16zNw4EBmzpyJu7t7sdQrhBCi/KpcuTJTp05l2rRpOfYj+RESEsLs2bPx9/fnnXfeMV8DhRBCCCGEWZTJYEpoaCgBAQHY2dnpl/Nbv349Fy5c4L333uPNN9/Ms4waNWoQFxdHt27daNOmDTqdjtDQUI4cOcIjjzzCvn37qFatmtnrFUIIUX7dvn3brEu1m7s8IYQQQghhHmUumJKRkUHTpk2JiYlh//79tGnTBlAPODt37syZM2eIjIykUaNGuZbz4Ycf8uyzz+Ll5aXfpigKL730El9//TUvvvgiX375pdnrFUIIIYQQQgghRNlW5oIpO3bsICAggPHjx7NkyRKD+9auXcuIESOYOXMm77//fqHKv3btGjVr1sTb25uTJ08Wa71ZWVlcvXoVFxcX/WoOQgghVIqicPv2bWrWrImVlZWlmyOKSPo8IYTInbn7vfT0dDIzM83QMiEqBmtra2xtbfO9f5lLQBsaGgpAnz59jO7TtoWFhRW6fO3Fs7ExfGmKo96rV69Sp06dQrRSCCEqjsuXL1O7dm1LN8OsEhMTOX/+PBkZGdSuXdtglGR5JX2eEELkT1H7vaSkJOLi4khNTTVjq4SoGOzt7fH09MTV1TXPfctcMCUqKgrA5HQaDw8PPD099fsUhjbq5OGgiTnqTU1NNfhS0wYFXb58OV9vlhBCVCRJSUnUqVOnzOUMSUtLw8rKyigoD3D48GH+85//EBoaSlZWln57s2bNePfddxk2bFhJNrVEae+j9HlCCGGaOfq9pKQkrly5QqVKlfD09MTW1lZGAwqRD4qikJ6eTmJiIleuXAHI83ilzAVTEhMTAXBzczN5v6urKzExMYUq++jRowQFBVGtWjXeeOMNs9c7d+5cgoKCTD5WDiyFEJp79+7h4+MDqCuIOTk5WbhFllXWDgIdHR3p1q2b0WjF7du38/TTT5OamsrDM2wjIyMZOXIkZ86cKber92jvo/R5QoiHSb9nqCj9XlxcHJUqVaJ27dplrv8UwtIcHR1xcXEhJiaGuLi4PI9XZBL6fRcuXKB///5kZmayZs0aPD09zV7HzJkzSUxM1F8uX75s9jqEEGWfoihERkYSGRlp9KNblH6Kohi9b0lJSYwaNYqUlBR8fHzYvn07SUlJJCcnc/DgQUaMGIGiKAQFBREREWGhlgshhGVIv2ce6enppKam4ubmJoEUIQpJp9Ph5uZGamoq6enpue5b5kamaCNDtJEiD0tKSspx9EhOLl68iL+/Pzdu3GDdunX4+/sXS7329vbY29sXqG1CCCHKvhUrVhAfH0+nTp0ICwszSG7Wtm1bVq1ahaenJwsWLODrr7/Wn6EVQggh8ktLNluQBJpCCGPaZygzMzPXz1OZG5mi5SwxlZ8kPj6euLi4Ai1PHB0djZ+fH1evXiU4OJj+/fuXSL1CCCEqjr1796LT6Zg9e3aOnfKcOXOws7Nj9+7dJdw6IYQQ5YmMShGiaPL7GSpzwRRfX19AXar4Ydo2bZ+8aIGUK1eusHbtWgYOHFgi9QohhKhYYmNjAejcuXOO+7i6uvLYY49x7dq1kmqWEEIIIYQopDIXTOnVqxcNGzZk1apVHD16VL/99u3bzJ49GxsbG8aNG6ffHhcXx+nTp4mLizMoJ3sgZc2aNTz99NNmrVcIIYTQaAnM8soFIKsuCCGEEEKUDWUuZ4qNjQ2LFi0iICCA7t27M3LkSFxdXVm/fj0XLlxgzpw5NG7cWL//ggULCAoKIjAwkFmzZum3+/n5cfHiRTp16sTx48c5fvy4UV3Z9y9ovUIIISqu2NhYVqxYof87IyMDUJOdN2/ePMfHXb16lapVqxap7h9++IE9e/Zw6NAhTpw4QVpaGkuXLi1wwD8rK4uvvvqK7777jqioKCpVqoS/vz/vvfeeTGsVQgghRIVX5oIpAP7+/oSHhxMYGEhwcDBpaWl4e3sze/ZsRo8ena8yLl68CMCBAwc4cOCAyX2yB1PMVa8QQuRFp9NRr149/W1R9kRFRTF+/Hj934qioNPp2LJlS47BlOjoaK5cuUKvXr2KVPfbb7/NxYsX8fT0xMvLS9/fFdS///1vFi5cyGOPPcaUKVO4fv06a9euZceOHezbt4/HHnusSO0UQgiN9HtCiLKoTAZTADp06MCvv/6a536zZs0yCopA3kOti1qvEEIUlpOTE9HR0ZZuhiiksWPH5nifNkLFlO+++w7IPa9KfixatIhGjRpRr149PvjgA2bOnFngMkJCQli4cCHdu3fnt99+069E9+yzz9K7d29eeOEFwsLCitROIYTQSL8nzK1ly5acOHGCy5cvU7t2bZP7VK5cmXv37nH79u0KuwJSREQEgYGB7N+/Xz9QYNq0aYwaNSrfZdSvXz/HEzeTJ0/mm2++Kba6La3MBlOEEKJci4mBqCho1AhyOAgQpdPSpUsL9biePXvSsWNH2rVrV6T6H3/88SI9HmDhwoWAusKQFkgBNX9YQEAA27Zt4++//5bprUKUQ/ntfmQ/065FxPDPnihqdG+El4/035aQkpLCqVOn8PLyyjGQEhUVRXx8PO3atauwgZTQ0FACAgKws7NjxIgRuLm5sX79ekaPHk10dDRvvvlmvstyc3Nj2rRpRtvbt29f7HVbkgRThBCitFm8GCZNgqwssLKC776D556zdKtEMTNHEMRcQkNDcXZ2pmvXrkb3acGUsLAwCaYIUc7kp/vJzISvvoJp0x7sN2sWDBwIGRmGl40b4X//U/fT6WDKFOjTBxTF8PLbb2qZiqLu98ILYOor8fff4euvH+z373/nvN8335h3v01fx/AoUZylEU+9UNtwP0XB7s4tdF/M58lDs/FCIRMr9oz9ju7LpP8uaceOHSMjI4OOHTvmuM+ff/4JQNu2bUuqWaVKRkYGEydORKfTsXv3btq0aQNAYGAgnTt3JjAwkKFDh+Y7R5q7u7vJ2SAlUbclSTBFCCFKk5gYkp9/nh73pyLuzsrCcfJkCAiQESqiRNy9e5dr167RvHlzrK2tje7XDm6ioqJyLSc1NZXU1FT930lJSeZtqBCiQHIaWZGVBVeuQHg4PP+8GljQtk+cCPPnQ2oqJCWpl7t3DcvNyoJ331UvuVEUtaz5803dmwz0uL/fbr76ypGvvsq7vK+/Vi/Fvd8EFhPNJKzJIgsdG74eyI2vq1KXS/pLJQxfGGuy6Lx8MtdeCpARKiXs8OHDgJqeIScREREARR4Nml+bNm1iwIABfPTRRzg6OrJ06VJOnz6NlZUVvXv35osvvqBWrVol0haAXbt2ce7cOcaPH68PZgC4uLjwzjvvMGLECJYuXcr7779fruo2NwmmCCFEaRIVRZaicPD+n1mgngb8+28JpogSkZiYCKhDdk3RlnnW9svJ3LlzCQoKMm/jhBCFkn3EiU4H/fuDkxOcOaN2L/fu5fxYEwtemuThAc7OYGOjXlJT4fJl4/0aNwZXV7UdOp0aoDl9OgsMez68vcHNTd0HICEB/vrLuLzmzdX9NOber9L1syw8+zxWqFEmKxSe5hfTL8JDbMjk+t6z5TKYUppnIx86dAigREam+Pn5ERYWRkhICH5+fjnud/ToUQAWL17MpUuXGDx4MH5+fuzYsYOff/6Za9eusX///iK1pSBCQ0MB6NOnj9F92raC5EZLTU1l+fLlXLlyBQ8PD7p06UKrVq1KpG5LkmCKEEKUJo0aqUeODyfJXr0a/P0fHFWKcueNN94gLi4OnU7H4sWLLd2cIps5cyYzZszQ/52UlESdOnUs2CIhKp70dFixQh1holEU2LTJcD8bG6hTBy5cMNxuZaUGYho2VAMgLi5w5w60basGZjTW1mrQJfuP6pgYqFfPeL+dO433q1vXsNuztoZt2/JX3q+/FuN+f/1Fet8B+kBKdneGjqXSk75q4+vV49o1qNajCdY8KDADa6p3fdTosZagKLkHzQpi+XJ1ypY2zeuLLyCX3OsF4uRU9EMdbWTKggULWLJkSY772NjY0LJly6JVlk9HjhwB1NGfx44d04/yTEtLw8fHhwMHDrBv3z66dOmSYxn5nUajmTZtGu7u7ibv00aXmppK4+HhgaenZ54jULP7559/GDdunMG2J554gu+//x5PT89irduiFGExiYmJCqAkJiZauilCiFLkzsyZCqAAyh2d7sG08jlzLN20ElXRviPr16+v6HQ6xcrKymxlzp07VwGUpUuX5vsxd+7cUQClefPmJu/fvHmzAiivv/56gdpS0d5PISzpyBFFmTZNUapWfTg7yYPL5MmKsmGDopw+rShpaerjFi1SFGtr9X5ra/VvU8y935df3tH3e1ZWd0qs3hz3y8pSlPnzFcXeXlFAyXroxcu0slaUy5eNyts9dpGSjlpgOtbK7rE5VJyDon5PJicnK5GRkUpycrLRfXfu5Py/UJoud+4U6qnrpaamKra2tvr/p9wurVq1KlpliqJcvHhROXXqlHL37t1c96tfv74CKGFhYUb3ffjhhwqgLF68ONcy8vOcsl8uXLiQY1m9e/dWACUqKsrk/Q0bNlTs7OxybY8mKChICQ0NVW7cuKEkJSUpBw4cUJ588kkFUDp37qxkZWUVW93FJbfPUnYyMkUIIUqbmjUf3D59Wj1NNm0avP02VK6sZuYT5c6QIUOIi4uzdDNwdnbGy8uLCxcukJmZaZQ3JbczSkKIkqdNt/DwgJAQddTAsWMP7vf0hJs3jUd+vP228fSM555TU3SdPQuPPprz9A1z7zd2LLz0knr71Cl1KlBJ1Gtyv3/+gfHj1aExAE88ga53b5Q33kCXmYlibY3Vt9+aLLT7sue49lIA1/eepXrXR+leDqf3lHbHjx8nPT2dIUOG8OOPP5rc5/vvv+fZZ581muLzv//9j3nz5hEXF0fnzp355ptv8ky0Xrdu3TzblJCQQHR0NB07dqRHjx5G91epUgWA9PT0XMtRHh61XEq8+1DCpI4dO7J582Z8fX0JDw9n69at9OvXz0KtK14STBFCiNLmflI0AGrVgldeUY+EZ89Wjzbd3WHkSIs1TxSPjz/+2NJN0PP19WXNmjXs3bvX6MBv+/bt+n2EEJa1aJGaC+Xh31h2durqOuPGqavnLF8OkyerKbisrSGHWACgbs9PDgxz76fJKwdnsbZv40Y1whIXBw4O8PHHar+r06EbNgzOnkWXW3QG8PKpXSpzpDg5qVO0iurKFWjWzHh6VGRk3u9dfjg5Fe3x2hSf1q1b57iPlr8kezBl1apVvPnmmyxevJiWLVsSGBjIE088walTp7C3ty9Sm7QpPgEBASbvv3TpEkCJToXV8qLllP8sKSkpx9xp+WFlZcX48eMJDw9n7969BsGU4q67JEkwRQghSpuDB423BQXBrVvw5Zfw7LNqdry+fUu+baJciYuLIy4uDk9PT4M5zZMmTWLNmjW8/fbb/P7779jZ2QGwc+dOtm/fTo8ePWRZZCEs7MwZdfWdh733nrrEb+XKD7bld6RGhRQToyZ8WbUKVq5Ut7Vsqf7t7f1gv4JGhUoZnU5NEFxUjRurS2Y/HJwrLV2Clnw2t2CKFtzIHkz53//+x4svvsioUaMAWLZsGdWqVWPDhg0MGzasSG3Sgjc5jWLZtm0bdnZ2dO/ePddyzJkzJfvKfA+vaBQfH09cXFyu+VvyQzuuuPdQsp6SqLukSDBFCCFKk9u3ITISTzA8Etbp1PUk4+PVA7whQ2DHDujWzVItFaXUokWLCA8PB+DEiRP6bVr2/EGDBjFo0CBATc4XFBREYGCgwUGav78/EydOZNGiRbRp04Z+/fpx/fp11q5di6urK1/ntcaoEKJYRUXBE0+Yvq9LF8PuQ1PaYwEPJ6ksEdmXOdK8+qoakSriaITyrDQH5/IzMuXYsWNYW1vr90lLS+PIkSMG/aCLiwsdO3bkwIEDRQ6maMEbUyMxwsLC+PPPP5kwYQIuLi65llPQFfLGjRuXYzDF19eXuXPnsmPHDkaMGGFw344dO/T7FMUff/wBQP369Uu87pIiwRQhhChNDh3CGbhRpw7cH/apZ2UFy5ZBYiJs2aKubRkcDLa2pXNtQkFmZiYhISH88ccfREVFER8fT3JyMo6Ojnh4eNCoUSM6duyIn58fNjbm6ZLDw8NZvny5wba9e/eyd+9eQD2o0YIpufn2229p2bIl3377LfPnz6dSpUo89dRTvPfeezIqRQgL2rBBHaCYlGR8n7W1+uO2rHF2dubGjRslW2lMjHEgxcpKzVEmgZQ8lcbgXHp6OidOnMDT05NaOcw5unjxIrdu3eKxxx7D6f6cori4ODIzM6lWrZrBvtWqVeP69eu51nnp0iXu3btH3bp19eU9TAumrF69mqlTp+r7++joaMaOHYunpyf/93//l+fzM2fOlF69etGwYUNWrVrF1KlT9YGl27dvM3v2bGxsbIxW5zl37hzp6ek88sgj2NraAhAZGUnNmjWNgjbh4eHMmzcPe3t7Bg8eXOS6SysJpgghRGlyP4pPx46m77e1VQMoTzwBe/aop4ZAPQD87jv1dJEoFebNm8cHH3zAzZs3AdMHQbr76z9WqVKF//znP8yYMUO/rbCWLVvGsmXL8rXvrFmzchw2bGVlxZQpU5gyZUqR2iOEMI/MTHj3XXj/ffXv7t3VvCj/+U/+cqGIh0RFGQZSQP377Fl5Ecuov/76i9TU1Fyny5jKl1IUzz77LGFhYYSEhODn52d0f0pKCqdPn6ZLly6cOXOGdu3a0bt3b+Li4li/fj1ZWVls3rw5x+BPcbGxsWHRokUEBATQvXt3Ro4ciaurK+vXr+fChQvMmTPH6MRJr169uHjxIhcuXNCPNgkODuajjz6iV69e1K9fH3t7e06ePMmOHTuwsrLim2++MZreVJi6SysJpgghRGmSVzAF1Oxs33xjOJc7K0udwBwQIAeBFqYoCoMHD2bjxo0oioKrqys+Pj40bNgQDw8P7O3tSU1NJT4+nvPnzxMREUFcXBxvvPEGu3fv5pdffilyQEUIUb7ExcGoUfDbb+rfr7yi5ka1tYXhw0vndItSLyHBeFtZHdojgMLnS/H09MTa2prY2FiDfWNjY4scdDlx4gQZGRn4+fkxf/58pk+fzldffYWjoyN9+/Zl1qxZNG3atEh1FJa/vz/h4eEEBgYSHBxMWloa3t7ezJ49m9GjR+e7jFOnTnH48GHCwsJISUmhevXqDB8+nOnTp9OhQ4diq7s00ClFHC+Unp5OREQE4eHhXLx4kRs3bpCcnIynpydVq1albdu2dO/evcSjbWWBlqk4MTERV1dXSzdHCFEa1KpF8tWrPNm6Nbi58euvv+Lo6Gi8X0gI9OxperuJMyNlUVn9jlywYAFTp06levXqzJs3j6FDh+Y6hScjI4Pg4GBeffVVYmNj+fzzz3n55ZdLsMUlo6y+n0JY2qFD8MwzcPGiGktftKj8LeiWnJzMk08+CZBzv2duTz6pLn+s06nLIWlDeyw4wrOo35MpKSlcuHCBBg0a4ODgUAwtLL98fHzw9fXlk08+AeDOnTtUrVqV5cuXFylnysKFC5k0aRJr164tcu4VUXLy+1kq9MiUkJAQFi1axC+//EJKSgqQ+xDmZs2aMWHCBJ599lnLJJgSQojSLiYGrl4ly8qKsPvDULMeHoKsadRIndrz8NqEckbN4pYuXYq1tTU7duygRYsWee5vY2PDqFGj8Pb2pl27dixZsqRcBlOEEAUTE6PmHf/8c0hLU7/e16+HfHytlDlZWVmEhYXpbxe7gwfVQIq1NYSGQkaGDO2p4KZNm8bzzz9P+/btad68OUFBQXh5eTFgwIAilauNhMlttIwouwocTNm0aRMzZ87k1KlTKIqCjY0NrVu3xsfHBy8vLypXroyjoyO3bt3i1q1bREZGEhERQWRkJK+99hpvvvkmkyZN4p133qFq1arF8ZyEEKJs0qb4PPYYnDyZ+761a6s5UrInz5PJ8qXCmTNnaN68eb4CKdm1atWK5s2bExUVVUwtE0KUFd99py5vrJ2nbNVK/c2fw8IcoqDmzFGvR42SVfEEAKNHjyY2NpbXXnuNuLg4OnfuzK+//lrkET5HjhzB2dmZR+VkV7lUoGBKjx492Lt3L46OjgwbNowRI0YQEBCQr3+yc+fOsWbNGlavXs2CBQtYvnw5K1asYODAgYVuvBBClCt//qle+/jkHUwBdShyo0bg6wsODjBhQvG2T+SLvb09d+7cKdRj79y5o8+QL4SomGJiDAMpoHYJd+5IMMUsjh9Xl0TS6eDNNy3dGlGKTJ8+nenTp5utvKysLI4fP07Lli2xsrIyW7mi9CjQu3ry5EneeecdYmJiWL16NQMHDsx3tO6RRx7hrbfe4uTJk+zcuZN27dpx/PjxQjVaCCHKJW1kio9P/h/TqZM6TDklBa5dK552iQJp06YN58+fJzg4uECPW7NmDefPn6ddu3bF1DIhRFnw88+GgRRQV+s5e9Yy7Sl33ntPvR46FCyU+FNUDFZWVty9e5f9+/dbuimimBRoZMrFixdxcXEpcqX+/v74+/tz+/btIpclhBDlQmamOocboH37/D/Ozg7q1YPz59VlHmvWLJ72iXybMWMGu3btYvTo0YSGhjJhwgTatm1r8qxUVlYWhw8fZvHixSxatAidTmfWs2JCiLLl9m11lZ6HSUosMzl1Cn78Ub399tuWbYsQoswrUDDFHIGU4ixPCCHKrL/+grt3wcUFmjQp2GMbNVKDKWfPqlN+hEX17duX999/n7feeotvv/2Wb7/9FgcHB+rWrYuHhwd2dnakpaURHx/PpUuX9EncAebMmUPfvn0t2HohhCW98gpcvgyVK0Niohpn1xaZkZRYZvD+++qwn0GDymcmXyFEiSr0aj5CCCHMSJvi0749WFvj5OSU/8c2agTbt6sjU0Sp8N///hdfX1/mzJnDzp07SU5O5syZMyb3tbW15fHHH+ett96iS5cuJdxSIURpsX49LF2qpvL45Rdo0ECNkVeURWYK1O8VxrlzsGqVeltGpQghzECCKUIIURpoyWc7dsTZ2Zm7d+/m/7Ha2G8JppQqnTt3ZsuWLdy+fZsjR44QFRVFfHw8KSkpODg44OHhQaNGjWjTpo2M1BSigrt6FZ5/Xr39n/9A9+7q7YoQRAEK3u8Vxty56up3Tz4JkptKCGEGxRJMSUxM5Pz582RkZFC7dm28vLyKoxohhCg/tJEpHTsW/LGNGqnXkp2wVHJxcaFHjx706NHD0k0RQpRCiqIuxnbrFrRpA0FBlm5ROXTxIixfrt6WUSlCCDMp8BpNaWlpZGRkmLzv8OHD9O7dG09PT9q3b0+nTp2oXbs2zZs3L/CqBkIIUWHcuaPmTIGiB1MeXgJCCCFEqfbll+pMTQcH+OEHNa+4MLOPPoKMDOjZE2Q6pRDCTAocTHF0dKRXr15G27dv3063bt3YtWsXmZmZKIqiv0RGRjJy5Ehmz55tlkYLIUS5cvCgOvS4Th3w8iIlJYV+/frRr18/g+SkOapfX81QeO+eOlZcCCFEmRAZCa+/rt7+6CN47DHLtsdSCtzvFcTVq7B4sXr7nXfMW7YQokIrcDBFC5Bkl5SUxKhRo0hJScHHx4ft27eTlJREcnIyBw8eZMSIESiKQlBQEBEREWZrvBBClAsPTfHJzMxk69atbN26lczMzLwfb2urBlRApvoIIUQZkZYG//oXpKRAQAC89JKlW2Q5Be73CuKTTyA1Fbp2lRXvhBBmVeBgiikrVqwgPj6eTp06sWfPHnr37k2lSpWwt7enbdu2rFq1ipdffpmsrCy+/vprc1QphBDlhxZM6dCh8GVoU30kCa0QQpQJgYFw5AhUqQJLloCVWY7KhYHYWPjmG/X2O++oSyUJIYSZmOVre+/eveh0OmbPno2tra3JfebMmYOdnR27d+82R5VCCFF+ZFvJp9BkRR8hhCgz9uyBDz9Ub3/3HdSsadn2lFvz5kFyMvj4QJ8+lm6NEKKcMUswJTY2FlCXgcyJq6srjz32GNeuXTNHlUIIUT5cuaJerK2LtlSjrOgjhBBlQmQkDB2q5gsfPx4GD7Z0i8qpW7fU7L6gruAjo1KEEGZmlmCKq6srgFEulYfZ2tqiky8yIYR4QJvi07w5ODsXvhyZ5lPqHTt2zGh0pqltQojya/Fi8PaG69fVv4sSQxd5mD1bXS2vWTN46ilLt0YIUQ7ZFOZBsbGxrFixQv+3tlTyhQsXaN68eY6Pu3r1KlWrVi1MlUIIUT49lHy20LRpPmfPqisDyeT7Uufll19m//79+j4zp21CiPIpJgYmTTLc9sorMHAg1K5tmTaVW198AZ99pt4+fVpNSvPccxZtkhCi/CnU0XZUVBTjx4/XX7Zs2QKgvzYlOjqaK1eu8Kh2wC+EEMI8yWfhwfLIyckg0ylLLVMjOPMa1SmEKB+iotRYd3aZmTI70+xiYtQolUZRYPJkdbuoMFq2bIlOpyMml/e9cuXKODg4kJ6eXoItK10iIiLo27cvHh4eODs706FDB1atWlWgMhRFYf369fj7++Pl5YWTkxNNmjRh8uTJnD9/3mDfhIQEpk6dSufOnalRowb29vbUqlWLnj17sm7dujJ3TFTgkSljx47N8b7czqx99913QO55VYQQokLJzISDB9Xb2UamODs7F7wz0ZZHPndOPWKvVct87RRCCFFkpr7Wra0fDCysyArV7+UkKsr4xdaiVjIEqEJISUnh1KlTeHl5UTuH9zwqKor4+HjatWuX4wIq5V1oaCgBAQHY2dkxYsQI3NzcWL9+PaNHjyY6Opo333wzX+W89tprzJs3Dy8vLwYNGoSrqyvHjh1j4cKFrF69mn379ulnr8TFxbFkyRI6derEoEGDqFy5MrGxsWzatIkhQ4bw/PPP6+MGZUGBgylLly4tVEU9e/akY8eOtJPJoUIIoYqMhLt3oVIldU53UTVq9CCY4udX9PKEEEKYzZo16rVOp/7Wt7aGb7+V3/dm98gjxtskalWhHDt2jIyMDDrmMoX6z/srKbZt27akmlWqZGRkMHHiRHQ6Hbt376ZNmzYABAYG0rlzZwIDAxk6dCiNtJx8Ofjnn3/47LPPqF+/PseOHdPnUgX47LPPmD59OvPmzWPJkiUANGjQgISEBGxsDMMQt2/fplOnTixcuJBXXnkFb29vMz/j4lFik+off/xxBg4cmGN0UAghKhxtio+Pj3qgV1Syoo8QQpRKN26Alm7wp58gJASioyWNR7FITDT8W6JWxSMmRv1HLoXTpw4fPgxAh1ymUEdERACU2In+TZs2odPp+Pjjj1mwYAHt2rXD2dkZFxcXBg8ezJUrV0qkHZpdu3Zx7tw5Ro0apQ+kALi4uPDOO++QkZGRr0EU0dHRZGVl0bVrV4NACkC/fv2AByv/AlhbWxsFUrR6AwICADhbho5jC5WAVgghhBnkkHw2JSWFMWPGAPD999/j4OCQv/K0s26yoo8QQpQq33wDqanQvj08/bSs0vuwQvd7puzcqV77+UFgoNo3SiBFHQ517555ylq+HKZMeZDw/osvIJdUEAXi5FTkD8ihQ4cASmRkip+fH2FhYYSEhOCXy6jgo0ePArB48WIuXbrE4MGD8fPzY8eOHfz8889cu3aN/fv3F6ktBREaGgpAnz59jO7TtoWFheVZTqNGjbCzs2Pv3r3cvn0bFxcX/X1bt24F1BkqeUlJSWHXrl3odDoee+yx/DyFUkGCKUIIYSk5BFMyMzP56aefAFi2bFn+y5PlkYUQotRJTYUvv1Rvz5ghgRRTCt3vmaIFU/r1kymv2d27p04rNresLHjpJfViDnfugLNzkYrQRqYsWLBAP73E1D42Nja0bNmySHXl15EjRwC4e/cux44d00+fSUtLw8fHhwMHDrBv3z66dOmSYxmzZs0qUJ3Tpk3D3d3d5H1R948VTU3j8fDwwNPTU79PbqpUqcJ7773H66+/TrNmzRgwYAAuLi6cOHGC33//nUmTJjFlyhSjxyUkJPDZZ5+RlZVFbGwsW7du5fLlywQGBuY5tag0KbFgyhtvvEFcXBw6nY7FixeXVLVCCFE63bkDf/2l3i7qSj4arfM5d06WRxZCiFJi9Wq4fl0dHDFkiKVbU85lZIB2Nj0fZ8NF+ZOWlsbJkycB+Pnnn3Pdt1WrVtjb2xepvhUrVnDv3j3q1q2b635aMGXlypUGwQI7OztGjx7N8ePHOX36dK7BlKCgoAK1bdy4cTkGUxLvT4dzc3Mzeb+rq2uuKyFl99prr1GzZk0mT57M119/rd/epUsX/vWvf5lM8JuQkGDwfGxtbfn444959dVX81VnaVFiR9o//vgjy5YtK3q0WQghyoODB9WAR+3aULOmecqsV+/B8shXr5qnTCGEEIWmKDBvnnr75ZfVhddEMYqIgNu3oXJlaN3a0q0pXZyc1BM5Rb2cOWN8ssbaWt1ujvKdnIr0NI8fP056ejpDhgxBURSTlxX3Exhln+Kzfv16evfuTeXKldHpdERHR+ervrp169K0aVOccml3QkIC0dHRdOzYkR49ehjdX6VKFYA8l2jO6fnkdKlfv36+nkNRzZkzh3HjxjFz5kwuX77MnTt3CA8PJyMjA39/f9avX2/0mPr166MoChkZGVy4cIH/+7//46233uKZZ57JdYXg0qbERqYMGTKEuLi4kqpOCCFKt/tzdR+e4lMktrbQoIGagFaWgBRCCIvbtQtOnFB/H06aZOnWVAC7dqnX/v4yOvNhOl2Rp88A0LgxfPcdTJ6sLjmtJfht3LjoZZuBNsWndS7BNC1/SfZgyt27d+nevTuDBw/mxRdfNGubtFEpWoLVh126dAmAOnXqmLXe3GgjUhIfTth8X1JSUo6jVrLbtWsX77zzDtOnTzdYSrlr165s3ryZhg0bMn36dAYPHmzy8dbW1tSvX5///ve/WFtb88Ybb7Bw4UJeeOGFQjyrkldiwZSPP/64pKoSQojSL4d8KUXWqJEaSJHlkYUQwuL+9z/1evx48PCwbFsqBC1fSq9elm1HeffccxAQoB5vlLIEv1ry2dyCKVpwI3swRUuAfPr0abO3SQve5DQVaNu2bdjZ2dG9e/dcyzFnzhRtqlFUVJTRikbx8fHExcXlOuVIs2XLFgD8/f2N7qtatSotWrRg//79xMXF4enpmWtZffr04Y033iA0NFSCKUIIIXJRXMEUWdFHCCFKhdOnYcsWdUDAK69YujUVQHIy7Nun3pZ8KcWvdu1SFUTR5GdkyrFjx7C2ts51H3PSgjemRoGEhYXx559/MmHCBIOVcEwxZ84UX19f5s6dy44dOxgxYoTBfTt27NDvk5e0tDQAbty4YfJ+bXt+ctNcvT9F3dTSyaWVjH8TQoiSduWKerGygiIuyWdES2p29qx5yxVCCFEgn3+uXj/11IOvZlGM9u5Vl06qVavUTDkRJSs9PZ0TJ07g6elJrVq1TO5z8eJFbt26RZMmTXLNc5Jfly5d4vTp09zLZdlpLZiyevVqg3wg0dHRjB07Fk9PT/7v//4vz7rMmTOlV69eNGzYkFWrVulHzgDcvn2b2bNnY2Njw7hx4wwec+7cOU6fPm2Q26Vr164AzJs3zyhYtHz5cs6ePUu7du30gaKjR4+aDCrdunVLP03oySefzPO1KC2KFPbJzMwkJCSEP/74g6ioKOLj40lOTsbR0REPDw8aNWpEx44d8fPzK1MRJiGEKFbaqJTmzU0uU+jk5MSdO3f0twtERqaUWn379uVR7f3JZZsQouy7eROWL1dvz5hh2baUBUXq9zTZp/jI+tMV0l9//UVqamqu02VM5UspimeffZawsDBCQkLwMzG9OiUlRb9Kz5kzZ2jXrh29e/cmLi6O9evXk5WVxebNm3MM/hQXGxsbFi1aREBAAN27d2fkyJG4urqyfv16Lly4wJw5c2j8UFCyV69eXLx4kQsXLugDNUOHDuXbb78lNDSURo0aMWDAADw8PDh27Bi//fYb9vb2fPbZZ/oyli1bxqJFi/D396devXo4Oztz8eJFtmzZwp07d3jmmWcYNWpUCb4SRVPoCMe8efP44IMPuHnzJqBGyh6mu/9FVqVKFf7zn/8wY8YM/TYhhKiw8pjio9PpcC5skrjsI1NkeeRSZebMmfnaJoQo+779Vp110qYNmFi8QzykSP2eRks+K/lSKqzC5kspTidOnCAjIwM/Pz/mz5/P9OnT+eqrr3B0dKRv377MmjWLpk2blkhbHubv7094eDiBgYEEBweTlpaGt7c3s2fPZvTo0fkqw9ramm3btvH555+zdu1aVq9eTVpaGtWrV2fUqFHMnDmT5s2b6/cfMmQIiYmJHDhwgN27d3Pv3j0qV65Mt27dePbZZxkxYkSZihfoFFNRkFwoisLgwYPZuHEjiqLg6uqKj48PDRs2xMPDA3t7e1JTU4mPj+f8+fNERESQlJSETqejf//+/PLLL2XqBSpOWpbkxMREXF1dLd0cIURJ8feH0FBYtEhN4mZOGRng6KheX75cKucz55d8R5Yv8n6KiiItDerXh2vXYMUKuJ/XUhSnhASoUkU9iVCG+76ifk+mpKRw4cIFGjRogIODQzG0sPw7ffo0zZo1Mxh9URQLFy5k0qRJrF27lmHDhhW9gaJE5PezVOCRKV9++SUbNmygevXqzJs3j6FDh+Y6hScjI4Pg4GBeffVVNm/ezJdffsnLL79c0GqFEKJ8uHgRDhxQb+cwMiU1NZXJkycD8O233+YraZeejY16FK+t6FNGDyiFEKKsWrtWDaR4ecHw4ZZuTdlQpH4PICxMDaQ0biz9niiUW7ducenSJaKjowGIjIwkISGBunXrUrly5UKXq42EKalkt6JkFXj899KlS7G2tmbHjh2MHDkyz1woNjY2jBo1im3btqHT6ViyZEmhGyuEEGXa4sXQsCGkpKh/799vcreMjAyWL1/O8uXLDRKV5Zs21UfypgghRIlSFJg3T7398stgZ2fZ9pQVRe73ZElkUUQbN26kTZs2PP300wD069ePNm3asHHjxiKVe+TIEZydnSU/WjlV4GDKmTNnaN68OS1atCjQ41q1akXz5s2JkoN7IURFFBMDkyapZ840L7ygbjc3WdFHCCEsIiwMjh5VZ1veH2ghSoIEU0QRjRs3zuSKOA+vaFMQWVlZHD9+nBYtWmAlOezKpQJP87G3t9dn2y6oO3fuYGtrW6jHCiFEmRYVZRhIAcjMVAMe5h6SLCv6CCGERWijUsaOVVN4iBLwzz8QGamu4OPvb+nWCKFnZWXF3bt3Ld0MUYwKHCJr06YN58+fJzg4uECPW7NmDefPn6ddu3YFrVIIIcq+Ro2MV9axtn4Q+DB3XSDBFCGEKEF79sCmTertadMs2pSKRVvFp00bKEJuCyGEKKgCB1NmzJiBoiiMHj2aF198kYMHD5L18NnW+7Kysjh48CAvvPACY8aMQafTMX369CI3WgghypzateG77x78bWWlrp1ZHInytGDKuXPGo2GERSmKQkJCQuFyAgghSq3Fi8HX98Hf4eGWa0uFo03x6dnTsu0QQlQ4BQ6m9O3bl/fff5+srCy+/fZbOnbsiIuLC82aNaNLly74+fnRpUsXmjVrhouLCx07duS7774jKyuLOXPm0Ldv3+J4HkIIUfqNHauORgHYt8/8yyJr6tVTV/VJSYErV4qnDlEg+/fvJyAgAGdnZ6pUqYK9vT1eXl6MHj2aTdqpbCFEmaSlxFKUB9smTy6elFjiIYoi+VKEEBZTqEw4//3vfwkPD+eJJ57A1taW5ORkzpw5w4EDB9i9ezcHDhzgzJkzJCcnY2NjwxNPPMGePXuYOXOmudsvhBBlx+XLap4UOzto37746rGxgQYN1Nsy1cfidu3ahZ+fH7///jspKSko939xXb9+ndWrVzNo0CDatWvHX3/9ZbY6IyIi6Nu3Lx4eHjg7O9OhQwdWrVpVoDISEhJ49913admyJS4uLnh6euLj48OCBQtI0VakEkLkmhJLFLPz5+HiRbC1he7dLd0aIUQFU+AEtJrOnTuzZcsWbt++zZEjR4iKiiI+Pp6UlBQcHBzw8PCgUaNGtGnTBhcXF3O2WQghyqbz59XrBg0ejFAxwcnJidjYWP3tQmnUSD3CP3tWhj5b2Ntvv016ejpt27bl008/xcfHBwcHBy5cuMBvv/3GwoULOXLkCB07dmTt2rX069evSPWFhoYSEBCAnZ0dI0aMwM3NjfXr1zN69Giio6N588038ywjISGBdu3acf78ebp168bkyZNJTU3l119/ZcqUKfz888/89ttvsjqBEDyYWZldcaXEKq8K3e9p+VI6dQJn52JomRBC5KzQwRSNi4sLPXr0oEePHuZojxBClF/nzqnXjzyS6246nY6qVasWrS5Z0afUOHr0KI6Ojvz6668G7+sjjzzCI488wr///W++++47XnnlFYYPH86xY8d4JI//kZxkZGQwceJEdDodu3fvpk2bNgAEBgbSuXNnAgMDGTp0KI1M/frL5rvvvuP8+fNMnz6dedryJEBaWhrdunVj165dhIeHS98vBFCpkpoGSxudYm1dfCmxyqtC93syxUcIYUFySkkIIUpKPoMpZiEr+pQadnZ2NGnSJNcfCpMmTWLBggXcu3ePOXPmFLquXbt2ce7cOUaNGqUPpIB64uOdd94hIyODpUuX5lnO+fujqB7Oc2ZnZ0fv3r0B9GeRhajoNm9WAymNG0NICERHF19KLJFNVtaDkSkyAlMIYQESTBFCiJKSz2BKamoqL730Ei+99BKpqamFq0sbmSKT9i2uadOm+Qo8jB8/nqpVq7Jjx45C1xUaGgpAnz59jO7TtoWFheVZjre3NwDbtm0z2J6ens7vv/+Oo6MjnTt3LnQ7hShP1q9Xr4cPBz8/GZFSGIXq906ehBs3wMkJOnYs3gYKIYQJZTaYUtTkerGxscydO5chQ4bQoEEDdDodOp0u18fUr19fv9/Dl3//+99FfUpCiPIun8GUjIwMvvrqK7766qvCL6EryyOXGqNGjeLq1asEBwfnup+VlRV16tQhPj6+0HVF3R+JZGoaj4eHB56envp9cjNx4kR8fHz49NNP8fPz4/XXX2fq1Kl4e3tz/vx5Vq1aRa1atXItIzU1laSkJIOLEOXN3bugxRyfftqybSnLCtXvaaNSevRQE7sLIUQJK3LOFEswR3K9yMhI3nzzTXQ6HY0aNcLJyYl79+7l+Tg3NzemTZtmtL19ca7MIYQo+xTlQTClYcPiry/78sgxMVC3bvHXKUwaOHAgW7duZdKkSVSuXJnHH3/c5H7JycmcPXuWR4uQtTIxMRFQ+ypTXF1dicnHeq2Ojo6EhoYyefJkfvjhB/1oFisrK15++WW6deuWZxlz584lKCioAK0XouzZvh2Sk6F+fWjd2tKtqWAkX4oQwsLKXDDFXMn1mjVrRlhYmH61oaZNm3LmzJk863d3d2fWrFnmeCpCiIokLg5u31Zva8sWFydteWRtRR8JplhMw4YNcXFxISkpiYCAAIYOHcqkSZPo1q0bdvfPpsbGxvLiiy+SlJTE9OnTLdxiiIuLY+DAgcTGxrJlyxa6du1KSkoKGzdu5NVXX2Xz5s0cPHgQDw+PHMuYOXMmM2bM0P+dlJREnTp1SqL5QpQYbYrP4MGQxwBnYU4ZGaBNWZR8KUIICylz03zMlVyvevXq9OjRQ5ZtFkKUDG1USq1a4OhYMnVKEtpSwcvLSz/FRVEUgoOD6d27N66urtSvX5/atWtTs2ZNNm/ezKeffsr48eMLXZc2IkUbofKwpKSkHEetZDdjxgz27dvHunXr6Nu3L25ublSvXp3nn3+ejz76iPPnz/PZZ5/lWoa9vT2urq4GFyHKk7Q0NfksqMEUUYIiItQTFJUry5AgUWihoaHodDo5UZ4HnU6Hn59fkcuZNWsWOp1On9+tPDBbMOXYsWPs3r07z21FZa7keoWVmprK8uXLef/99/n66685duxYsdUlhChH7q+OUiIr+Wi0YIokobWomJgYbt68SUhICJ999hkTJkygbdu2WFtbc+nSJa5evUpWVhZpaWm89tpr1KtXj/79+/Pf//6XH374gaNHj5KWlpavurRRmabyosTHxxMXF5fnyE2ALVu2ULlyZVq2bGl0X8/7Z4EPHTqUrzYJUV6FhEBiItSoAZKPuYRpU3z8/dV1qYUQFcKyZcvQ6XQsW7bM0k0BzDjN5+WXX2b//v0GSaNMbSsqcyXXK6x//vmHcePGGWx74okn+P777/H09Mz1sampqQYZyiUZnxAVSEkui6zRcm/IyBSL8/DwwNfXF19fX/22rKws/v77b44fP86xY8c4fvw4x48f5/Lly1y+fJmtW7fqE6NbW1vnK6Di6+vL3Llz2bFjByNGjDC4T1slKHsbcpKWlkZKSgppaWn6qUiaGzduAOrIEyEqMm2Kz6BB8nu+xGnJZyVfihDCgsz61a8oSr62FUV+kuvlNLy5qCZMmEBoaCg3btwgKSmJAwcO8OSTT7Jt2zYGDBiQ53OdO3cubm5u+ovMHReiArFEMEWm+ZRqVlZWNG3alGHDhvHee++xadMmLl68yK1btwgNDeXzzz/Xj2KxtbXNV5m9evWiYcOGrFq1iqNHj+q33759m9mzZ2NjY2NwQiAuLo7Tp08TFxdnUE7Xrl3JyMhg9uzZBttTU1P12/z9/Qv3xIUoBzIz4Zdf1NsyxaeEJSfDvn3qbQmmCCEsSOLoBfDuu+/i6+uLp6cnLi4udOzYkc2bN9OtWzf279/P1q1bc338zJkzSUxM1F8uX75cQi0XQlhcAYIpjo6OXLhwgQsXLuBYlPwqsjxymeTu7k6PHj2YMmUKCxcuJCIigjt37uTrsTY2NixatIisrCy6d+/OpEmTeO2112jVqhV//fUXs2bNonHjxvr9FyxYQLNmzViwYIFBOR988AEuLi7MmTOHjh07MmPGDF588UUee+wxtm/fTrt27Zg4caJZn7cQZcm+fRAbC+7uYIZUAhVegfq9vXshNVXNQZaPaYui4lm+fDmdOnWiUqVKVKpUiU6dOrF8+fJcH7N79258fX2pVKkSlStXZtSoUSZXv4uKimL8+PE0aNAABwcHPD09adu2La+++qrRvrdv3yYwMBBvb28cHR1xd3fniSeeIDw83GhfPz8/dDodqampvPvuuzz66KPY2toya9YsJkyYgE6nY8+ePSbb/t5776HT6fj+++8Nth8/fpwRI0bg5eWFnZ0d9erVY8qUKdy8edNkOYsWLaJ58+Y4ODhQp04d3njjDVJSUnJ93Uy5fPkyI0eOpHLlylSqVAlfX98cU3+kpaXxxRdfEBAQQJ06dbC3t6datWoMHjyYI0eOGOw7btw4fV658ePHo9Pp9BfNoUOHePnll2nevDlubm44OjrSokULPvjgA9LT0wv8XPJS5lbzMVdyPXOxsrJi/PjxhIeHs3fvXvr165fjvvb29jIsWoiKqgDBFCsrK+rXr1/0OuvWVVf1SU2V5ZHLOF0Blgnx9/cnPDycwMBAgoODSUtLw9vbm9mzZzN69Oh8ldG6dWsOHTrE3Llz2blzJwsWLMDGxoZHH32UoKAgXnvtNRwcHAr7dIQo87QpPgMGQD4HjolcFKjfy74ksiyhVGB3797N8T5ra2uD7/bc9rWysjIIfBVk33v37pkc0e/s7JxjGfk1ffp0PvvsM2rVqsVzzz2HTqdj3bp1jBs3jmPHjjFv3jyjxxw4cIC5c+fSr18/pk6dyuHDh1m9ejXh4eFERERQvXp1AK5evUqHDh24e/cu/fr1Y/jw4dy5c4eoqCi++OILPv30U32Zt27dokePHvz11190796dgIAAEhMT2bBhA/7+/vz4448MGjTIqC2DBw/m2LFjBAQEULlyZRo2bIivry9Lly7lhx9+oHv37kaPWblyJc7Ozjz99NP6bRs3bmTYsGFYW1szYMAA6tSpQ2RkJAsWLGD79u388ccfBivyzZ49m3fffVefbN7W1pa1a9dy6tSpAr3+165do3Pnzly5coWAgADatm3LqVOn6N27t8kRrbdu3WLatGl0796dvn374uHhwfnz59m4cSO//voru3fvxsfHB4BBgwaRkJDAhg0bGDhwIK1NJJ9euHAhmzZtokePHvTt25d79+4RGhrKzJkziYiIYN26dQV6PnlSzKRbt26KlZVVntuKaubMmQqgrF692ui+W7duKYDSpUuXApfbpEkTpbAvx4YNGxRAeeWVVwr0uMTERAVQEhMTC1WvEKKMuHtXUUC93LxZsnU3bqzW+/vvJVuvGch3ZPki76coL7KyFKVuXfWr9ZdfLN2aCqhVK/XF/9//LN0Ssyvq92RycrISGRmpJCcn57gPkOOlb9++Bvs6OTnluK+vr6/Bvp6enjnu2759e4N969WrZ3K/otq9e7cCKM2aNVMSEhL02xMSEpSmTZsqgLJnzx799pCQEH3dixYtMigrKChIAZQJEybot82fP18BlM8//9yo7hs3bhj8PWrUKAVQlixZYrD9n3/+UerUqaNUrVrV4H3y9fVVAKV169bKzYeOFbOyspQ6deooHh4eSmpqqsF9Bw8eVADlX//6l35bXFyc4urqqtSuXVu5ePGiwf6rVq1SAOXll1/Wb4uKilJsbGyUWrVqKdevX9dvT0xM1P9Gfvj9zsnYsWMVQJkzZ47B9m+//Vb/WoeEhOi3p6SkKDExMUblnDx5UqlUqZLy+OOPG2xfunSpAihLly41WX90dLSSkZFhsC0rK0uZMGGCAijh4eH5eh75+SwpiqKUuWk+WuI8LZFedgVJrmdOf/zxB4B5ziQLIcofbSUfNzfIdhYgJ2lpabz++uu8/vrr+V7FJUdaElpZ0UcIIczi8GG4dAmcnMDE4pKiEPLd733xBWgrab76KixeXDINFGWCtsLLrFmzDGYquLm5ERgYaLBPdk2aNGHChAkG215//XWqVq3K6tWrjf4nTU1Fy74QSVxcHGvXrqVXr176aSma6tWr8/rrr3Pjxg1+//13o3KCgoKoXLmywTadTseoUaOIj49ny5YtBvf98MMPAPzrX//Sb1uxYgVJSUnMnTuXug+NSh45ciRt27ZlzZo1+m2rVq0iIyODGTNmUK1aNf12V1dX3n77baM25iQtLY21a9dSrVo1o2lPEydONJhmrLG3t6dWrVpG2729vfH392f37t0Fmp5Tr149rK2tDbbpdDpeeuklAJOveVGUuWk+2ZPrTZ06VT+8J7fkenFxcXh6eua52k5uIiMjqVmzJu7u7gbbw8PDmTdvHvb29gyWDGSijIuJUXOVNmoEtWtbujXlSPYpPvkYkpyens4nn3wCqAcED6+mUiCShFYIIcxKm+LTty8UJa2VeCBf/V5MDLzyyoO/s7Jg8mQICJCDlgLILQfXwz9CY2Njc9zX6qElrKKjo/O9b2RkpNkXKQH0OTb8TCQy0rZlT86u6dq1q9F0WkdHR9q1a8e2bdv4+++/ad68Of379+e///0vL730Er/99htPPPEE3bp1MwoSREREkJmZSUpKCrNmzTKqT1t59vTp0/Tv39/gvg4dOph8bmPGjOHDDz/khx9+0E/nyczMZPXq1dSoUYPHH39cv++BAwf012dNnExLSUkx+I187H6A0tQUIlPbcnLmzBlSUlLo2bOn0VRgKysrunTpwt9//230uKNHj/LRRx8RHh7OP//8YxQ8iYuLw8vLK19tSEtLY8GCBaxZs4bTp09z584dg/+1q1ev5vv55EeZC6ZoyfUCAgLo3r07I0eOxNXVlfXr13PhwgXmzJljlFwvKCiIwMBAo3/m7EGXa9euGW375JNP9AGY4OBgPvroI3r16kX9+vWxt7fn5MmT7NixAysrK7755hujyJ8QZcnixTBpknpsYmUF330Hzz1n6VaVE5ZYyUcjwRQhhDArLZiSLT2BKAlRUeqE2ewyM9WRlxJMybeC5CUprn2dnJzyvW9BJCUlYWVlRdWqVY3uq169OlZWVibzbmYfjfHwY+BBrs4GDRqwf/9+goKC+PXXX/nxxx8BdWTL7NmzGTp0KKDmAQHYu3cve/fuzbG9pvLMaHU+zNvbmzZt2rBlyxYSEhJwd3fnt99+4/r168yYMcMgEKbV/+WXX+ZYt1a/p6en/vmZeh1yao8puZWTU1n79u2jZ8+eAPTp04dGjRpRqVIldDodv/zyC8eOHSM1NTXfbRgyZAibNm2icePGDB8+nGrVqmFra0tCQgKff/55gcrKjzIXTAHzJNcDTGZ1zr5t1qxZ+mCKv78/p06d4vDhw4SFhZGSkkL16tUZPnw406dPzzGKKERZEBPzIJACcrLH7LRpPpYIpsg0n1KhYcOGANSsWdNkFn+AHj16EBMTg06n45wWgBNClCqnTsHp02rS2VzWHBDFwdTKPdbWD/o5UeG5urqSlZXFjRs3jH7Qx8bGkpWVhaurq9HjchqBc/36dQCDKUMtW7Zk3bp1pKenc+jQIX799Vfmz5/P8OHDqVmzJl27dtXX8eqrr+pHXOVXbgnnx4wZw4wZM/jpp5+YOHGiforPmDFjDPbT6j9x4gTNmzfPs07t+cXGxlKvXj2D+7TXID+yl2OKqbLee+89UlNTCQ8Pp2vXrgb3HThwQD9qJj8iIiLYtGkTAQEBbNmyxSDAdODAAT7//PN8l5VfZS5niqZDhw78+uuvJCQkcO/ePSIiIkwGUmbNmoWiKCaHWCmKkuslew4UX19f1q5dS1RUFElJSaSlpXH58mVWr14tgRRR5u3bZ7xyrnayR5hBaRiZIssjW1R0dDTR0dFcunQpx30uX76s308IUTr9/LN6/fjjahosUYJq1zZ80a2t4dtv5ayP0GvTpg0AoaGhRveFhYUBmFwBZu/evUbTjpKTkzl06BCOjo4mc33Y2trSqVMngoKCmD9/PoqisHnzZgB8fHzQ6XTs37+/iM/I0MiRI7G2tuaHH37g7t27/PLLL3h7exs9p44dOwLku/5WrVoBmFx6OaflmE1p0qQJDg4OHDx40GhJ5aysLPbt22f0mHPnzlG5cmWjQMq9e/c4fPiw0f5agCQzM9NkWQD9+vUzmrJWkOdREGU2mCKEMI/0dDAVNJeTPWZkyWBK3brqKdTUVLh8ueTrFwAsXbqUpUuXmlySUfPJJ5+wdOlSlixZUoItE0IUhDbFR9LkWcD166BN0di6FaKjZT6yMDB27FhATeKalJSk356UlERQUJDBPtmdOXPGqO/9+OOPuXHjBiNHjtTn8ImIiDA56kIbcaElpq1RowbDhg1j3759fPzxxybzw/zxxx/cu3evQM9Py42ye/duPv/8c+7evWs0KgVg/PjxuLi48NZbb/HXX38Z3X/v3j19XhWAUaNGYW1tzbx58wyeX1JSEnPmzMl3++zs7Bg2bBixsbEGy0QDLFq0yGS+lHr16hEfH2/QzszMTF577TVu3LhhtL+WnDcmJsZkWYDRCOC//vqLuXPn5vt5FESZnOYjhDCft9+GiAhwcIC0tAeDFzp0ABPJtUVBZWaqB3xgmWCKjQ00aAB//60ONXpo+KYoGaYO3h72zDPPlEBLhBCFdfEiHDqk5hUbMMDSramA7icXpUkTePJJy7ZFlEo9evRgypQpfPHFFzRv3pxnnnkGRVFYv349ly9fZurUqfTo0cPocX369OHFF19ky5YtNG3alMOHD7N9+3bq1KnD+++/r99v5cqVfPXVV/j5+fHoo4/i6upKZGQkW7duxdPT02BFoK+++oozZ87wxhtv8P3339O5c2fc3Ny4fPkyhw4dIioqimvXrhU4f8yYMWPYvn07s2bNwsrKyuTMDG0VoqFDh9KqVSueeOIJmjZtSkpKChcvXiQsLIwuXbqwbds2AB599FHeffddAgMDadmyJcOGDcPGxoZ169bRokULzpw5k+/2ffDBB+zcuZO3336b8PBw2rRpw6lTp9i6dSt9+vQxWpF3ypQp7Nixg27dujFs2DAcHBwIDQ3lypUr+Pn5GY0y6ty5M46Ojnz22WckJSXp8+P897//pUOHDnTo0IHg4GCuXbtGp06duHTpEhs3bqRfv3789NNPBXqt8yVfCy3nQ7du3RQrK6s8t4kHirqWvBBFtWGDoqjZ3BTlp58U5fJlRfnf/xRFp1O3LVpk6RaWAxcuqC+mnZ2iPLTufU7u3LmjAAqg3Llzp+ht6NdPbcPXXxe9rBIk35Hli7yfoqz73//Ur1JfX0u3pPzJV7/3/vvqGzByZMk2rgQV9XsyOTlZiYyMVJKTk83csrJlyZIlio+Pj+Lk5KQ4OTkpPj4+ypIlS4z2CwkJUQAlMDBQCQsLU7p37644OTkp7u7uyogRI5RLly4Z7H/gwAFl8uTJSvPmzRV3d3fF0dFRadSokTJ16lSjfRVFUe7du6d89NFHSrt27RRnZ2fF0dFRadCggTJo0CBlxYoVSnp6un5fX19fJT8/ze/evatUqlRJARR/f/9c9z19+rTy3HPPKfXq1VPs7OwUDw8PpUWLFsrUqVOVP//802j/hQsXKo899phiZ2en1K5dW3nttdeUe/fuKYDiW4AvvosXLyrDhw9X3N3dFScnJ6V79+5KWFiYEhgYqABKSEiIwf4//fST0rZtW8XJyUnx9PRUhg0bppw7d04ZO3asAigXLlww2H/Lli2Kj4+P4ujoqP/e0MTGxioTJkxQatasqTg4OCgtWrRQvvzyS+X8+fMKoIwdOzZfzyG/nyWdophnXaq5c+fy999/s3Tp0ly3iQeSkpJwc3MjMTHRZDIkIYpTdDS0aQMJCepKg5999uC+uXPhzTfV0SoHDsD9qZSiMHbuVCfXN2miZi3Mh6ysLE6dOgVAs2bNjJYULLDp09U3eMYMeGjYZWkm35Hli7yfoqzr0QP27IHPP4epUy3dmvIlX/3e0KHw00/w0Ufw+usl3MKSUdTvyZSUFC5cuECDBg2MlqYVQuRffj9LZpvmM3PmzHxtE0JYXmqqekySkAAdO6rHJdn95z8QHq5OSR46FA4eBPntU0havpT7q7nkh5WVFd7e3uZrg6zoI4QQRXL9utovgiyJXBzy1e9p03zati3+BgkhRD5IAlohKqDXXlMDJJUrQ3Aw3M+rpWdlBStWqLlLo6Jg4kR1MpAoBEsmn9VoK/pERVmuDUIIUYZt2KD2gz4+UKeOpVtTASUmPuhP76/YIoQQlibBFCEqmOBgWLBAvf3992rAxJQqVdR9bW3hxx/hyy9Lro3lyvnz6nUBgilpaWnMmjWLWbNmkZaWVvQ2aCNTzp1TE+IKIYQoEFnFp3jl2e8dPape16unngkSQohSQIIpQlQgf/+tjjIBmDkT+vbNff+OHeHjj9XbM2bAn38Wb/vKpUKMTElPTycoKIigoCDS09OL3oa6ddVVfdLS1KWbhBBC5FtCgpr+CiSYUlzy7PcOH1avZVSKEKIUkWCKEBVEcjIMGQK3b4OvL/zf/+XvcVOnwjPPQHo6DBsGt24VbzvLFUUpHdN8li+HjAz1dteusHix5doihBBlzJYt6leotzc0bmzp1lRQki9FCFEKmS0BrRCi9IqJgUmT4MQJqF4dVq9WByrkh06n/vY+dkzNXzp2rDrl59w5NRVH7drF2/Yy7eZNSEpSbzdoYJk2aG++JisLJk+GgAB58yxsw4YNbNq0iVOnTnHrfpSycuXKNGvWjAEDBjBgwAALt1AIAfDDD+r1449bth0VmoxMEUKUQmYdmaIoCgkJCWRoZ0CFEBa3eLE6y+PXX9W/x4wBL6+CleHmpuZNsbeHzZuhfn3o2VOduiyDHHKhjUqpVQscHS3ThqgoNYCSXWamrOxjQTdv3qRz5848/fTThIeHU6NGDbp160bXrl2pUaMGe/fuZdCgQXTp0oWbN29aurlCVGhffw3btqm3v/hC+jyLSE6G06fV2zIyJV8UWTVAiCLJ72fILMGU/fv3ExAQgLOzM1WqVMHe3h4vLy9Gjx7Npk2bzFGFEKIQtEEJ2b8P/vc/dXtBtW79YGqQVp42yKEw5VUIpWGKT6NG6vJM2VlbP0hKK0rc9OnTuXHjBn/++SenT59m3bp1LFy4kEWLFrFu3TpOnTpFREQEN27cYMaMGZZurhAVVkwMvPTSg7+lz7OQEyfUkwDVqhX8bFAFY21tDWCefGtCVGDaZ0j7TOWkyMGUXbt24efnx++//05KSoo+inP9+nVWr17NoEGDaNeuHX/99VdRqxJCFJC5ByW0b2+8TQY55EILpjRsaLk21K4N331nGFD59luZ4mNBmzdv5sMPP6S9qQ/Ufe3ateODDz6QExJCWFBUlOHJCJA+zyKyT/HR6SzbllLO1tYWe3t7EhMTZXSKEIWkKAqJiYnY29tja2ub675Fzpny9ttvk56eTtu2bfn000/x8fHBwcGBCxcu8Ntvv7Fw4UKOHDlCx44dWbt2Lf369StqlUKIfDI1+KAogxIaN1Z/k2cP0Mggh1yUhpEpAM89B+7uagbiunXVv4XFZGRk4OTklOd+jo6OMm1WCAtq1Mh4m/R5FiDJZwvE09OTK1euEBMTg5ubG7a2tugkCCVEnhRFIT09ncTERO7cuUOtWrXyfEyRgylHjx7F0dGRX3/9lapVq+q3P/LIIzzyyCP8+9//5rvvvuOVV15h+PDhHDt2jEcs/cNCiArizh3Dv62tizYooXZt+OabB/lMraxkkEOuChlMcXBw4M/761A7ODiYpy3aQej16+qpVjmwshh/f38CAwNp164d1apVM7lPbGwsQUFB9OzZs4RbJ4TQmJohKX1e8ci135PkswXi6uoKQFxcHFeuXLFwa4Qoe+zt7alVq5b+s5SbIgdT7OzsaNiwoUEg5WGTJk3C2tqa559/njlz5rB06dKiViuEyAct6WyPHhAUpJ5NK+pB4PPPq8n41q9X547LIIdcnD+vXhcwmGJtbY2Pj49521KzpnqdmqquMuTpad7yRb7Nnz8fPz8/6tevj7+/P97e3ri7u6PT6YiPjycyMpKQkBBq1KhBcHCwpZsrRIW1a5d63aIFzJ9vnj5UmJZjv5eeruZMARmZUgCurq64urqSnp5OZmampZsjRJlhbW2d59Se7IocTGnatCkx+cjENX78eN5880127NhR1CqFEPm0dat6/fTT4OdnvnKHDFGDKXv2mK/Mcic5Ga5eVW+XhtF49vZQtSrcuKFmT5RgisXUq1ePkydP8s0337BlyxZWrFhBfHw8AB4eHnh7ezNnzhyef/55KlWqZOHWClFx/f67et23r3n7UFEAp06pJwFcXaFBA0u3psyxtbUt0A9DIUTBFDkB7ahRo7h69WqeZ8+srKyoU6eO/oBRCFG87tx5EOzo29e8Zffpow5/PnkSLl82b9nlhjYqxc0NKlcu0EPT0tL4+OOP+fjjj0lLSzNfm7RTqjLs1+KcnZ159dVX2bVrF//88w+pqamkpqbyzz//sHPnTqZPny6BFCEsSFFg5071dq9elm1LRZBjv6flS2nTxnjelRBCWFiRv5UGDhxInz59mDRpEr9rIXwTkpOTOXv2LI9K1i4hSsSuXZCWpi4kYyqJXlFUqQIdO6q3t20zb9nlRvZ8KQXMT5Kens4bb7zBG2+8Yd7lDbVgiqzrWaxkSUohyr6//1a/Ku3toVs3S7em/Mux35N8KUKIUqzIwZSGDRty4MABkpKSCAgIYMSIEezatcsgqhwbG8uYMWNISkpi+vTpRa1SCJEP2hSfJ58snlyjTz5pWI94SGlZySc7LSu5BFOKVaVKlWjVqhXPPvssn376KTt37iQuLs7SzRJCFIA2KqVLF3B0tGxbKjRZyUcIUYoVOWeKl5cXV+/nBVAUheDgYH788UdsbW2pUaMGGRkZ/PPPP9jY2PDpp58yfvz4IjdaCJE7RXmQfNbcU3w0ffvCu++qc8rT0sDOrnjqKbNKYzBFpvmUiPT0dE6cOMGJEydYuXKlfruXlxetWrWidevW+utGjRrJkpVClELaYOvHH7dsOyq0rCzDaT5CCFHKFDmYEhMTQ3x8PMePH+fYsWP668jISC5duqTfLy0tjddee43PPvuMFi1a0Lx5c/3lsccew05+iQlhNpGRcOmSOjy5uJLmtWkD1apBbCyEh4Os4PoQLZjSsKFl25GdjEwpEUeOHNH3hdolLi6Oq1evcu3aNbZlmxvn6OhIixYtDIIsLVu2xNnZ2YLPQIiKLTMTQkLU25IvxYLOnVMTwDk4QNOmlm6NEEIYKXIwBdTVB3x9ffH19dVvy8rK4u+//zYIshw/fpzLly9z+fJltm7dqj8bZ21tbd4ki0JUcNqoFH9/cHIqnjqsrNSpPsuXq/VJMOUhMjKlwmrVqhWtWrVizJgx+m3Xrl3j6NGj9OvXDzs7Oxo0aEBUVBT37t3jjz/+4I8//tD3iVZWVpJ3RQgLOnwYEhLU/OHt2lm6NRWYli+lZUuwMctPFiGEMKti+2aysrKiadOmNG3alGHDhum3JyQkGARYjh49SmRkZHE1Q4gKKXu+lOKkBVO2boWPPy7eusqUzEyIjlZvl8ZgioxMKXFeXl54eXkB4OrqyqlTp0hOTtb3g9rl+PHjJCcnW7i1QlRsWr4UPz/5DW9RMsVHCFHKlXgX4e7uTo8ePejRo4d+m6IoJd0MIcqt27fVaTdQfPlSNNoSydq0orp1i7e+MiMmBtLTwdb2QQCjNNCm+SQlqf8oLi6WbU8F5+joSMeOHemoLY2F2h/+/fffFmyVEEKWRC4lJPmsEKKUKxULtkvyPSHMZ+dO9Xf8o4+ql+Lk4QGdO6u3talFggdTfBo0AGvrAj/cwcGBkJAQQkJCcHBwMF+7XFzA1VW9LVN9SiWdTkeTJk0s3QwhKqyUlAcnJCT5bMkx6vcURZZFFkKUeqUimCKEMJ+SmuKjkSWSTShivhRra2v8/Pzw8/PDuhDBmFzJVB8hhMjRvn1qQMXLS3KeliSjfu/KFYiLU09ItGhh6eYJIYRJEkwRohwpiSWRH6bVs3MnpKaWTJ2lXmlMPquRFX2EECJH2ZdEloHTFqSNSnnsMXU1HyGEKIUkmCJEOXLypPob2cEBsi2uVaxat4YaNeDuXdizp2TqLPWKGExJT0/nyy+/5MsvvzT/qi6yoo8QQuRI8qVYhlG/J/lShBBlgOQoF6Ic0Ual9OwJjo4lU6dOp071WbpUrV/mmFPkYEpaWhovv/wyAOPGjcPW1tZcLZNpPiWgcePG+uWRtUtdyc4sRKmXkAAHD6q3JZhSsoz6PcmXIoQoAySYIkQ5UtL5UjRaMGXrVvj005Ktu9RRlAfBlIYNLdsWU2SaT7E7e/YsZ8+eZf369fptrq6utGzZElB/NBw5cgRvb2/s7Ows1UwhxENCQyErC5o0KV0LsVVIMjJFCFEGmCWY0vD+D4aaNWsSrqVAf0iPHj2IiYlBp9NxTvuhIYQwm6Qk2LtXvV1S+VI0vXurOeJOn4boaKhfv2TrL1Vu3VLfDCidwRSZ5lPsVq9ezdGjRzl27BhHjx7ln3/+ITExkT3358Hdvn2b9u3bY2NjQ5MmTWjdurXBpXLlyhZ+BkJUTNnzpQgLiouDy5fV261aWbYtQgiRC7MEU6KjowHIyMjIcZ/Lly9z8eJFWQZZiGLy+++QkQGNG5f8b3h3d+jSRc2Z8uuv8MILJVt/qaIFi2vWLLm5VgUhI1OK3fDhwxk+fLj+7xs3bhgEV44dO8aZM2dIT0/n5MmTnDx5kpUrV+r3r127NhcvXrRE04Wo0CRfSilx7Jh63agRuLpati1CCJELswRTli5dCoCzs3OO+3zyySfcuXPHHNUJIUyw1BQfzZNPqsGUrVslmAKUzpV84MHIlBs31OWX7O0t254KoGrVqvTu3ZvevXvrt6WmpvLXX38ZBFmOHz9OYmIiMRLoEqLEXbmijq60sgI/P0u3poLTgimSL0UIUcqZJZgyduzYPPd55plnzFGVEMIESyyJ/LC+feHNN2HXLkhJqcArGZb2YEqVKmoAJTUVrl6FBg0s3aIKyd7enrZt29L2oXwA0dHRHNN+SAghSow2KqVdO/DwsGxbKjwJpgghyghZGlmIcuD4cfV3sZMT9OhhmTa0bKnObLl3D3bvtkwbSoXSHkzR6WSqTylWv359Bg4caOlmCFHhSL6UUuToUfVaks8KIUo5CaYIUQ5kXxLZUiNCtCWSs7enQjJDMMXe3p7NmzezefNm7ItjGo4koS33IiIi6Nu3Lx4eHjg7O9OhQwdWrVpV4HJu375NYGAgzZs3x8nJCXd3d9q2bUtQUFAxtFoIy1AUyZdiafp+LzgYe60flZEpQohSToIpQpQDWvDCUvlSNBJMwSzBFBsbG/r160e/fv2wsSmGFey1YIqMTCmXQkND6datG3v27GHIkCG88MILxMXFMXr0aN5///18l3Pp0iXatGnD7NmzqVmzJlOmTGHcuHHUrFmTdevWFeMzEKJknT6tju50cICuXS3dmopJ3+95eak5CGrXhqpVLd0sIYTIVTEcpQshSlJCwoMlkS0dTHn8cbCxgTNn4Pz50rkycLFKTlaPyKH0TvMBmeZTjmVkZDBx4kR0Oh27d++mzf0zu4GBgXTu3JnAwECGDh1Ko0aNci0nMzOTIUOGcPXqVXbu3Im/v79RPUKUF9qolK5dK3C+r9Li8GH1WkalCCHKABmZIkQZ9/vvkJkJTZtaPpeom9uDs3oVcnTK+fPqtasrVK5c6GLS09NZtmwZy5YtIz093UyNy0am+ZRbu3bt4ty5c4waNUofSAFwcXHhnXfeISMjQ78CX25++uknIiIieO2114wCKUDxjJgSwkK0fCkyxcdy9P1ecDDpIPlShBBlghwNCVHGaUsiW2oVn4f17QthYWq7XnrJ0q0pYVow5ZFH1CQyhZSWlsb48eMBGDp0KLa2tuZo3QMyzafcCg0NBaBPnz5G92nbwsLC8ixn7dq1gPr/d/nyZbZs2UJCQgKPPPIITz75JJUqVTJfo4WwoIwMuP+xkeSzFmTQ7wG2MjJFCFEGSDBFiDIs+5LIlp7io3nySfjPfyAkRJ314uho6RaVoNK+ko9Gm+YjI1PKnaioKACT03g8PDzw9PTU75ObgwcPAhAeHs706dNJTU3V31e1alWCg4Px8/PLtYzU1FSDxyUlJeXnKQhRog4dgsREcHeXwRClirwZQogyoNim+WzYsIGJEyfStWtXmjVrRrNmzejatSsTJ05k48aNxVWtEBXK0aPwzz/g7Azdu1u6NarmzdXf6snJ6giVCqWsBFO0kSlXr6pzxES5kZiYCICbm5vJ+11dXfX75CY2NhaAKVOmMG3aNC5fvsyNGzeYP38+iYmJDBo0iGvXruVaxty5c3Fzc9Nf6tSpU8BnI0Tx0/Kl+PuDtbVl2yLuq1z5QT8lhBClmNlHpty8eZP+/fvzxx9/0LhxY7y9vXnsscdQFIX4+Hj27t3LkiVL6NSpE5s2baJKlSrmboIQFYY2KqVXLyiOFXQLQ6dTp/osXKi274knLN2iElRWginVq4OVlRpIuX4data0dIvKlRUrVpi9zEqVKjF48GCzl5uTrKwsAPr3788HH3yg3z5lyhSuXLnChx9+yOLFi3n77bdzLGPmzJnMmDFD/3dSUpIEVESpI/lSSqHWrYs0VVYIIUqK2YMp06dP58aNG/z555+0b9/e5D6HDh1ixIgRzJgxg+XLl5u7CUJUGL/8ol536mTRZhh58kk1mLJxIwwaBI0aVZCTTGUlmGJjA15e6jSfK1ckmGJm48aNQ6fToSiK2cqsX79+voIp2oiUnEafJCUl5Thq5eFy4uLiGDBggNF9Tz31FB9++KF+KlBO7O3tsS8tUV4hTLh378FqeJIvpRRp2dLSLRBCiHwxezBl8+bNLFy4MMdACkC7du344IMPeP75581dvRAVxvz5EBGh3n77bahWDZ57zrJt0vTqpQ6Xjo6Gnj3VQRDffVd62lcsMjPhwgX1dmkPpoAa3bpyRU1C6+Nj6daUK99//73Zy8xvwlctV0pUVBTt2rUzuC8+Pp64uDi6dOmSZzlNmjQhLi4Od3d3o/u0bcnJyflqkxCl1d69kJamTk1t3NjSrRF6rVpZugVCCJEvZg+mZGRk4OTklOd+jo6OZGRkmLt6ISqEmBiYNu3B31lZMHkyBASUjhEgSUmGqThKW/uKRUwMpKeDrW3ZeJJaElpZ0cfsRo8ebbG6fX19mTt3Ljt27GDEiBEG9+3YsUO/T1569uzJ3r17iYyMNBoRExkZCaijZYQoy37+Wb3u3FlmlVhc9t8EXl6Wa4cQQhSA2RPQ+vv7ExgYqE9eZ0psbCxBQUH07NnT3NULUSFERakr+WSXmQlnz1qmPQ8ztVhIaWpfsThwQL2uVavIWQzt7e0JDg4mODi4+KZJaAEfWdGnXOnVqxcNGzZk1apVHD16VL/99u3bzJ49GxsbG8aNG6ffHhcXx+nTp4mLizMoZ/z48djb2/PFF19wJdv/yO3bt3n//fcBGDZsWLE+FyGK0+LF8PXX6u1169S/heXYz5tHMBAM2D/5pLwhQogywewjU+bPn4+fnx/169fH398fb29v3N3d0el0xMfHExkZSUhICDVq1CA4ONjc1QtRIZhY9RRra3j00ZJviymNGqlTe+7nsARKV/vMbvFi0KYtRkerfxdhTpONjQ1Dhw41T9tyogVTZGRKuWJjY8OiRYsICAige/fujBw5EldXV9avX8+FCxeYM2cOjbPNZ1iwYAFBQUEEBgYya9Ys/fYGDRrw8ccfM3XqVFq1asXTTz+Nvb09W7ZsITo6mkmTJtFLMnaKMiomBiZNevC3olSA0ZOlWUwMNrNno+/15A0RQpQRZg+m1KtXj5MnT/LNN9+wZcsWVqxYQXx8PAAeHh54e3szZ84cnn/++XzPARdCGPLwUIcka6NTrK3h229LzzFH7dqwYAG8+KL6d2lrn1lpR+XZhwqVhYNAbZqPjEwpd/z9/QkPDycwMJDg4GDS0tLw9vZm9uzZBZqCNGXKFOrXr8/HH3/MmjVryMjIwNvbmzfffFNynokyLSrKMNgPD0ZPluav7XIrt+G28oYIIUoxnWLO5QZEgWirKiQmJuLq6mrp5ogyJDQU/P2hRg1YvVod8VEajzdatoQTJ+DLLx8EVsqdkBA1y66p7X5+hSoyIyODn+9P5n/66aexsTF73Bt27wZfX/Wfx9S8rFJAviPLF3k/RWkREwN16xr+fteSppfGvrTci4kho04d7qew4WnApoK+IfI9KUTZUuAj9PT0dGxtbYujLUKIfNLSc3TvXujf6yXC11cNppTS3+rmUQxzmlJTU/X5KO7cuVM8wZTs03wURbIvCiEqjNq11cF52izHcj16siyoVYtUZ2eG3b0LwB0rK2zkDRFClAEFPkKvVKkSTZs2pVWrVrRq1YrWrVvTqlUrPD09i6N9QggT9u9Xrzt1smw78tKpkzrdR2tvuVS7NnzzzYMJ+FZWZeOovGZN9TolBeLjoXJly7ZHCCFKSHz8gxmO69ZBhw6l/yu7XLt2De4HUgA4dUrWqhZClAmFGply4sQJTpw4wcqVK/Xbvby8DIIrrVu3plGjRujkbKcQZqUoD4ITnTtbti150dp3+LD6m93BwbLtKTZPPKFeW1nBuXNQFpaMdXAAT0+Ii1NPz0owRQhRQezZo/alTZrAQyt/C0vItvIY8CCnlxBClHIFDqYcOXKE48ePc+zYMf0lLi6Oq1evcu3aNbZt26bf19HRkRYtWhgEWVq2bImzs7NZn4QQFcmFC3DjBtjZQdu2lm5N7ho0gGrVIDYWjhwp/cGfQvv7b/W6UaOyEUjR1Kr1IJjSsqWlWyOEECUiNFS99vW1aDOE5uFgihBClBEFDqZo03vGjBmj33bt2jWOHj1Kv379sLOzo0GDBkRFRXHv3j3++OMP/vjjD/0IFSsrK9LT0833DISoYLRRKW3agL29ZduSF51OneqzcaPa7goRTClLateGY8dkRR8hRIUSFqZel+acYxXKsWOWboEQQhSKWbIaenl54eXlBYCrqyunTp0iOTmZ48ePc/ToUf3l+PHjJCcnm6NKISqssjLFR9O584NgSrmlZdgta3O8syehFUKICiAx8cFACBmZUkrIyBQhRBlVDEtEqBwdHenYsSMdO3bUb1MUhb+1M7hCiELRVvIpS8EUeNDuckn7XitrwRRtXrqMTBFCVBDh4eria48++iAPt7Cgu3fL+ZJ/QojyzKokK9PpdDRp0sQsZUVERNC3b188PDxwdnamQ4cOrFq1Kt+Pj42NZe7cuQwZMoQGDRqg0+nylSy3qPUKURT37j0YDVvaV/LRtG+vLjsZE1OOB0BoB4JmmuZjZ2fH0qVLWbp0KXZ2dmYp0yQZmSKEqGAkX0opc+IEKAp21auXTL8nhBBmVGwjU4pTaGgoAQEB2NnZMWLECNzc3Fi/fj2jR48mOjqaN998M88yIiMjefPNN9HpdDRq1AgnJyfu3btX7PUKURQHD0JGhno2rU4dS7cmf5yd1dymR46oU32GDrV0i8wsPR3On1dvm2lkiq2tLePGjTNLWbmSYIoQooKRfCmlzP0zRLatW5dMvyeEEGZUoiNTzCEjI4OJEyei0+nYvXs3Cxcu5JNPPuHYsWN4e3sTGBhIVD6GCzZr1oywsDASExM5c+YMdfL4ZWqueoUoiuxTfMrSquPleqpPdLQa4XJ0LHtjxmWajxCiArl9Gw4fVm/LyJRSQsuX0rq1JVshhBCFUuaCKbt27eLcuXOMGjWKNm3a6Le7uLjwzjvvkJGRwdKlS/Msp3r16vTo0QMXF5cSrVeIotCSuJaVKT4arb3lMglt9ik+Vub5Ss3IyGDLli1s2bKFjIwMs5RpkjYyJSEB7twpvnqEEKIU2LsXMjOhQYOyM7qz3LsfTMlo0aJk+j0hhDCjAk/zady4sX55ZO1St27d4mibSaH3J7v26dPH6D5tW5g2hrMc1CuERlHK3ko+Gq29hw5BamrpX9K5QIoh+Wxqair9+/cH4M6dO9jYFNOMTFdXcHFRT9deuQJmymkl8i8pKYlff/2Vq1ev0rZtW3zldLkQxUam+JQymZlqzhQgtWlT+rdvDxRzvyeEEGZU4G+qs2fPcvbsWdavX6/f5urqSsuWLQFIS0vjyJEjeHt7F0sCKW0qTSMTiR49PDzw9PQsluk25qg3NTWV1NRU/d9JSUnmbaQo1y5ehOvXwdYW2ra1dGsK5pFHwNMT4uLUk1DZFvkq+7RgipmSz5a4WrXg9GkJphSjtWvX8uGHH/Liiy8yceJE/fbTp0/Tp08frmSbZjVmzBiWLVtmgVYKUf5J8tlS5tw5dTUfR8ey24cKISq0Ao9JX716Nf/5z38ICAigevXqKIpCYmIie/bsAeD27du0b98eFxcXWrZsybPPPsu8efPYtWsXt27dKnKDExMTAXBzczN5v6urq34fczJHvXPnzsXNzU1/yStPixDZaaNSWrdWjzvKEp2uHE/10YKoZW1ZZI0koS12a9eu5dixY/To0cNg+7Rp04iJiaFhw4YMHDiQSpUq8f3337N161YLtVSI8uvuXTWJO0gwpdTQlids3lxd9k8IIcqYAo9MGT58OMOHD9f/fePGDY4ePcqxY8f012fOnCE9PZ2TJ09y8uRJVq5cqd+/du3aXLx40TytL2NmzpzJjBkz9H8nJSVJQEXkW1md4qPp3Bk2b1afx7Rplm6NGRXDNJ8SpQVTJAltsTl27BiVK1emcbb/kWvXrvHbb79Rt25dTpw4gYODA7t378bPz48vv/ySvn37WrDFQpQ/+/apucLr1oX69S3dGgFI8lkhRJlX5AmJVatWpXfv3vTu3Vu/LTU1lb/++ssgyHL8+HESExOJKeLZT21kSE6jQJKSknIcPWLpeu3t7bEvV8kiREnKvpJPWVQuV/RJTobLl9XbZXWIsraij4xMKTY3btwwmiIaEhKCoiiMGjUKBwcHAHr06EG9evU4deqUJZopRLkm+VJKIW1kSqtWlm2HEEIUUrFkd7K3t6dt27a0fSixQ3R0NMe0L85C0g5Io6KiaNeuncF98fHxxMXF0aVLlyLVUZrqFQLU3+xHjqi3y9pKPhofH3Wxm0uX4OrVsreKsEnnzqmZgd3d1aQwZZFM8yl2aWlpZGZmGmzbs2cPOp0Of39/g+3Vq1cvcj8phDAm+VJKIRmZIoQo40p0aeT69eszcODAIpWhrXSwY8cOo/u0bcWxGoKl6hUC1FVwMjKgRg2oV8/SrSmcSpWgRQv1drnJm5I9+axOZ9m2FJY2MkWm+RSbWrVqce7cOe7du6fftm3bNmxsbOjatavBvrdv3y6W0ZVCVGT37sGff6q35VCtlIiLe9Dv3F/EQgghypoSDaaYQ69evWjYsCGrVq3iqBbRRj0AnT17NjY2NowbN06/PS4ujtOnTxMXF1ei9QphTtmn+JTV3+xQDqf6FFPyWTs7OxYsWMCCBQuKZVU0AzIypdg9/vjj3Lt3jylTpnDy5ElmzZrFxYsX6dmzJ05OTvr9kpOTiYqKklxaQpjZgQOQnq7Gjhs2tHRrBPBgis8jj4CLS8n2e0IIYSZlbhF3GxsbFi1aREBAAN27d2fkyJG4urqyfv16Lly4wJw5cwyS/C1YsICgoCACAwOZNWuWQVnZgx/Xrl0z2vbJJ5/geX/ofkHrFcKctJEcZXWKj6ZTJ/jmm3I4MsXMn31bW1teeukls5aZIy2Ycv06pKWBHMSa3VtvvcX69etZtmwZy5YtQ1EUbG1tCQoKMthv06ZNZGRk0L17dwu1VIjyKXu+lLJ8QqJceWiKT4n2e0IIYSZlLpgC4O/vT3h4OIGBgQQHB5OWloa3tzezZ89m9OjR+S5n+fLluW6bNWuWPphiznqFKAhFKfsr+Wi09h86VE5+t2ef5lNWeXqqb0RaGly7VnbnkZVidevW5eDBg3zyySecPXuWOnXq8NJLL9HqoaSLoaGhtGrVqsjTYYUQhiRfSikkyWeFEOWATlEUxdKNqKi0FYASExNxdXW1dHNEKXXpkvr71sYGEhMh26yAMkdR1N/ut26p89d9fCzdoiKqUUMd0XHwIDyUmLooMjMz2bNnDwDdu3fH2trabGWb1LAhXLgA4eHwUA4PS5LvyPJF3k9hCSkpao7w1FQ4c6bsrmJf7rRsCSdOwMaN8NRTJd/vlVLyPSlE2VLmcqYIUdFoo1JatSrbgRRQh1drU5XK/FSfpCQ1kAJmH5mSkpKCv78//v7+pKSkmLVsk7SpPpKEVghRzvzxhxpIqVGjbA8iLFdSU0FbAv7+yJQS7/eEEMIMyuQ0HyEqkuzJZ8uDzp1h61b1eU2daunWFIGWfLZ6dSjrZ4+0FX0kCW2RXbp0ySzl1K1b1yzlCFHRSb6UUigyUl2i0MMDJOG2EKIMk2CKEKVcecmXotGeR5kfmVJMyWctQlb0MZv69eujK+IvNp1OR0ZGhplaJETFJvlSSiEt+WyrVhLhEkKUaQUOpqxYscLsjahUqRKDBw82e7lClHUpKXD4sHq7rK/ko/HxUY+doqPhn3/UoddlUnlIPquRaT5mU7du3RyDKVeuXNEHSWxsbPD09OTmzZukp6cD6moWNWvWLLG2ClHepaY+CNxLMKUU0ZLP3l/JRwghyqoCB1PGjRuHTqfDnHlr69evL8EUIUw4cuT/27vv8Ciqtg3g96b3UEInRaqQQi/SixAsCHxKR0Hpdn1t8PoCCjZURAWRrqIUESwgXUIHCSUBIiWUYAIIBEgndc/3x3E22WQTstlNZnZz/65rr93Mzs482Un2zD5zznOAnBygZk3gvvvUjsY6fHyAkBBZd+7QIWDgQLUjKiNlmI899EzhMB+riYuLM7n8+eefx+LFi/Hiiy/i2WefRePGjQ1t6fnz5zF//nx8/fXXePTRR/Hll19WbNBEdioyUl6UqFkTuP9+taMhg0LTIhMR2SqzkykrVqywehBeXl5W3yaRPVCuqHXsaF89YTt2lMmUgwdtOJnCYT5USl999RUWLFiAVatWYciQIUbP6XQ6NG7cGHPnzkWnTp0wfPhwNG/eHJMnT1YpWiL7odRL6d7dvtpQmyYEp0UmIrthdjJl5MiR5REHEZlgb/VSFA88ACxebMN1U4Swr2E+Ss+Uq1cBvR5w4ERv1rRw4UIEBAQUSaQUNmTIELz55ptYuHAhkylEVlAwmUIa8fffQFIS4OwMNG+udjRERBZhAVoiDbO3mXwUyu9z5IgcxuTsrG48ZktMBJKT5aXOhg2tvnlnZ2fMnj3b8Ljc1a4tEyi5ucCNGzZcyEabzp8/j+Dg4FKtW6NGDcTExJRzRET2LycH2L9fPmYyRUOUXinNmgEuLobFFd7uERFZAZMpRBqVkCBvjo5A27ZqR2NdTZoAVarIi1MnTgBt2qgdkZmUXikBAYC7u9U37+Ligtdff93q2y2Ws7NMoFy9Kv/omEyxKi8vL8TExCApKQlVqlQpdr2kpCTExMTA09Oz4oIjslNHjgAZGYCfHztAaEox9VIqvN0jIrIC9uUm0ihlCExYGGBv360cHPJnJ7LJoT5K8Vl7GOKjUIb6cEYfq+vTpw/u3r2LkSNH4vbt2ybXuXPnDkaOHInMzEyEh4dXcIRE9kcZ4tOtG0cuakrBaZGJiGwce6YQaZS9DvFRPPAAsGWL/D2ff17taMxUzsVn8/LycOzfObFbt24NR0fHctmPkfr15dQXLEJrde+//z62bNmCLVu2ICAgAIMHD0azZs1Qo0YN3Lx5E2fOnMHatWuRnp6O6tWrY9asWWqHTGTzWC9Fo4qZFlmVdo+IyEJMphBpVMGZfOyRTfdMKefis5mZmWjfvj0AIC0trWKGfSgz+rBnitUFBARg7969GDVqFI4fP45vv/0WugJTiwghAACtWrXCihUrEBgYqFaoRHYhNxfYt08+ZjJFQ1JSgIsX5eNCPVNUafeIiCzEZAqRBmVlAUePysf22jOlQwdZv/XiRVnztGZNtSMygzLMxx6mRVYow3zYM6VcNGvWDEePHsXOnTuxdetWnDt3DmlpafDy8kKTJk3Qt29f9O7dW+0wiezCsWNAWhpQtSoQGqp2NGRw4oS8r18fqF5d3ViIiKyAyRQiDYqKArKzZeG8cpgsRhN8fWVRwJgYOdTnscfUjqiU9Hr7TKYoPVOYTClXvXr1Qq9evdQOg8iusV6KRhVTfJaIyFaxiSHSoIJDfAqMBrA7NjnU58oV4O5dwMkJCApSOxrr4TAfIrITW7bIe9Y41RilXgoPDBHZCSZTiDRISS7Y6xAfhfL72VQyRemV0qCBTKjYi4LDfP6t4UFEZGsWLwZ27pSPZ80Cli5VNx4qgD1TiMjO2NE3ASL7oRTOa9RI3TjKm5JM+fNPYMcO4P778ztIaFY5z+SjGiWZkpEBJCXJYgNkVenp6diwYQOio6Nx+/Zt5OTkmFxPp9NhKb8BEpktIQGYNCn/Z70emDgRCA+3gbbF3uXmAidPysfsmUJEdoLJFCKN+fRT4OpV+Xj4cCA1FRg7Vt2Yysv99wPu7nLUTJ8+cmz7okUa/32VninlNJOPatzdgWrVgNu35VAfJlOsavXq1Zg8eTJSUlIMy5RZfArP7MNkClHZxMbKBEpBeXnA+fNMpqju3DlZXd/T036LwRFRpcNkCpGGJCQAr7+e/7O9X1W7elUmUhQ28ftWQM8UZ2dnTJ8+3fC4wtSvL5MpCQlASEjF7dfOHTx4EE8++STc3d3x3//+F2vWrMH58+exePFixMfHIzo6Ghs2bICrqyvefvtt1K1bV+2QiWySqRy3o6P99/K0CcoQn7Awk1WBVWv3iIgswGQKkYbExhYtV2HPV9WUTh4Faf73VZIp5dgzxcXFBTNmzCi37Rerfn05dSWL0FrVJ598Ar1ejx9++AH9+/dHREQEzp8/j7EFumCdOXMGgwcPxvz583FUmRfdApGRkZg+fToOHjyI7OxsBAcH4+WXX8aIESPKtL2cnBy0a9cO0dHRaNq0Kc6cOWNxjETWVqMG4OwMKCPoHB2BhQs13J5UJkrx2WLqpajW7hERWYAFaIk0pLJdVWvcuOgFKk3/vrm5wMWL8rG91UwBjIvQktUcPHgQfn5+6N+/f7Hr3H///Vi3bh2uXbtmuDpbVrt27UKXLl2wd+9ePPHEE5g8eTISExMxcuRIvP/++2Xa5syZM3H+/HmL4iIqbwcPykRKjRqyCG1cnMaHjVYmLD5LRHaIyRQiDaleXSYTFPZ+Va1+feCLL/J/1vzvGxcnEyru7vmJh3Kg1+sRExODmJgY6AsXAChPyhvPZIpV3bp1CwEBAYafXVxcAMiCtAU1adIEwcHB2Lx5c5n3lZubi3HjxkGn02HPnj1YvHgxPvnkE0RHRyM4OBjTp09HrKkuYSU4duwYPvjgA3zwwQdljouoIvzxh7zv2xfo2VPDbUlldI9pkVVr94iILFCuyZSUlBSsWbMGn332GXbv3l2euyKyC5GRcphLzZqV56rac88BzZvLx/Pmafz3VYb4NGpkcsy3tdy9exchISEICQnB3YJFZcqb8s2Dw3ysqnr16kbH0c/PDwBw4cKFIuvm5eXh+vXrZd7Xzp07ceHCBYwYMQKtWrUyLPf29sb//vc/5ObmYvny5aXeXnZ2NsaMGYOOHTvi+eefL3NcRBVhxw5537u3unFQIf/8A1y/LtvN0FCTq6jW7hERWcDibwNr1qxB69atsWTJEqPlZ86cQUhICEaMGIHXXnsNvXr1wpgxYyzdHZFd279f3nfrVrmuqvXsKe81X4ZBuaJvj0N8AA7zKSdBQUG4du2a4efWrVtDCIEffvjBaL3o6GicO3cONWrUKPO+du3aBQDo27dvkeeUZeZc3JgxYwZiY2OxdOlSo1mHiLQmOVlekACYTNEcZYhP48aAh4eqoRARWZNVkinR0dHo1q2b0fKXX34ZCQkJaNCgAQYMGAAvLy+sWLECmzZtsnSXRHZLSaZ07qxuHBVN+X2V31+zKmAmH1VxmE+56NOnD5KSkhATEwMAGDFiBNzc3PDJJ59g1KhRmD9/PqZNm4bevXtDr9fj8ccfL/O+lCE8jU0UYKpatSr8/PxKPcwnMjISs2fPxjvvvIMmZfibz8rKQkpKitGNqLzs3i17djZuDBQYVUdacI/is0REtsriZEp0dDSqVatmdKJ17do1bN++HQEBATh58iTWr1+PDRs2QAiB+fPnW7pLIruk1wMHDsjHlTWZcvw4UKiMhLYoX0LLcSYfVSnJlDt3gIwMdWOxI0OGDEGvXr1w9uxZAIC/vz8WLFgAJycnrFy5Ei+++CLee+893L59Gx06dMCsWbPKvK/k5GQAgK+vr8nnfXx8DOuUJCsrC2PGjEGrVq3wn//8p0yxfPDBB/D19TXc/P39y7QdotJQ6qU8+KC6cZAJSs+UYuqlEBHZKounRr5582aRK2AREREQQhiuvgFAt27dEBgYiNOnT1u6SyK7dOaM/A7r4VH5Lt4EBMjv8QkJwOHD+cN+NMfee6b4+ACenjKjdeWK/SaNKlhwcDC2b99utGz06NHo2rUrfvzxR8TFxcHd3R1dunTBwIED4ViwCrVK/ve//yE2NhZHjx4tczxTpkzBq6++avg5JSWFCRUqN0oyhUN8NOjIEXlfWcYuE1GlYXEyJTs7G3l5eUbL9u7dC51Oh56FvhHVqlUL0UpXPyIysm+fvO/QAXB2VjcWNXTpAqxeLd8HTSZTMjOBv/+Wj+01yaDTAbVqyemfo6Ls9/fUiAYNGuCtt96y6jaVHinF9T5JSUkptteK4tixY5gzZw7+97//IbSYYpGl4erqCldX1zK/nqi0rl0DYmLkR5gm24/KbMECQJlWfcwYIDtb45XmiYhKz+JhPvXq1cOFCxeQUaBL+JYtW+Dk5ITOhcYqpKam3vMkjqiyqqz1UhSar5ty4QIgBODrC1hQIFTTli6ViRQAGDpU/kw2Rekpaqouyp07d5CYmGiynkpBJ06cQF5eHmbMmAGdTmd0A4CzZ89Cp9OhSpUqVo+fqCx27pT3rVsD1aqpGwsVkJAAFJwFTK8HJk5kXS4ishsW90x58MEHsWTJErzwwgt45ZVX8NNPP+Hy5csIDw+HR4GK3Xfv3kVsbCxacLwkkUlMpsj7gwdlEUENjHQwVnCITznPauLs7IzXXnvN8LhCJCQAEybk/yyEPOkND2fXbCuKj4/H3r17ceXKFdy9exfTpk0zPJeTkwMhBFxcXMq8/e7du+ODDz7Atm3bMGzYMKPntm3bZlinJE2aNMHYYq4cL126FL6+vnjiiSeM2ngiNSlTIrNeisbExsoESkF5ebKnSqF2RZV2j4jIQjohhLBkA3///TfatGmD27dvAwCEEHB2dsbevXvRvn17w3o//vgjhg0bhpdffhlz5syxLGo7oXS3Tk5Oho+Pj9rhkIquXwdq15bf0e/ckZ0fKpvcXKBqVSAtTRb+DwtTO6JCPvoIeOstYMQIoNCUtnYhIgLo1cv08h49KjwcwL4+IxMTE/Hcc89h3bp1KNjsFhwmO2rUKKxatQqHDx9GmzZtyrSf3NxcNG3aFFeuXMGhQ4fQ8t8CTKmpqXjggQdw9uxZxMTEGIrGJyYmIjExEX5+fvDz87vn9nU6HZo2bYozZZjH3J6OJ2mHEEBgIBAfD2zbBvTpo3ZEZJCQABSuk+ToCMTFMUlfDH5OEtkWi4f5BAQE4MiRI3j22WfRt29fjBs3DocPHzZKpADArl270KJFCwwYMMDSXRLZHaVXSkhI5UykAICTE9Cxo3ysyaE+yrAJey0+27gx4FCoSXB0BBo1UiceO5Kamoru3btj7dq1qFevHsaMGYN69eoVWW/cuHEQQmD9+vVl3peTkxOWLFkCvV6Prl27YsKECXjttdfQokULxMTEYMaMGUaz782bNw/NmjXDvHnzyrxPIjXFxspEiotL5e3ZqVn16wM1a+b/7OgILFzIRAoR2Q2Lh/kAQGBgIL788ssS1/nqq6+ssSsiu6QkD7p0UTcOtXXuLLtr798PTJ6sdjSFVOBMPnq9Hn//W+w2ICAADoWTHOWhfn1g0SI51Efpls2TXquYPXs2Tp8+jccffxzfffcd3N3d0bVrV1y5csVovW7dusHd3R0REREW7a9nz57Yt28fpk+fjh9//BHZ2dkIDg7GzJkzMXLkSIu2TaQ1yiw+nTvL2fBIQ27eBG7ckI9/+w1o1arYNkWVdo+IyEJWSaYQkWUqe70UhaaL0Co9Uypghpu7d+/ivvvuAwCkpaXB09Oz3PcJQM6w0L59/hir4cMrZr927qeffoKrqyuWLFkCd3f3YtdzcHBAo0aNDF8oLNG+fXts3rz5nuvNmDEDM2bMKPV2LRwZTGR1Sr0UTomsQYcOyfv77wf69y9xVdXaPSIiC5iVTLHGCR4gM85EJGVkAEePyseVPZnSsaMcaRIXB1y5ApgYCaGOlBTgn3/kY3ufLjgkBKhSBUhKkjP7hISoHZHNi4uLQ5MmTUo1m52HhwfOnj1bAVER2b68PFnWCWDxWU06eFDeP/CAunEQEZUTs5IpQUFBhqkRy0qn0yE3N9eibRDZk8hIWXy1bl1ZRK8y8/YGWrQAjh+XvVOGDFE7on8pvVJq1rT/ojY6nUwYRUbK35vJFIu5ubkhNTW1VOteu3atVEkXIpJtxZ07gI8PUMaazVSelGRKp07qxkFEVE7MGpAYEBBQ7M3R0RFCCAgh4OjoiFq1asHJycmwzMnJCQEBAfAvXNWbqJIrOMSnnGfctQmaHOpj78VnC1OKzp4/r24cdiI4OBjx8fG4fPlyietFRUUZZsgjontT6qX07CmLmJOG5OYChw/Lx+yZQkR2yqxkSlxcHC5dulTk9sgjj0Cn0+HFF1/EmTNnkJWVhatXryIzMxNnz57Fiy++CJ1Oh0cffRSXLl0qr9+FyCaxXooxTSZTKrD4rCYoQ5mUJBJZZNSoUcjLy8OECROQkZFhcp07d+5g7Nix0Ol0eOqppyo4QiLbxHopGnbypBzH7OsLNGumdjREROXC4jz+V199hQULFmDVqlUYUqhPvk6nQ+PGjTF37lx06tQJw4cPR/PmzTFZc9N0EKlDrwcOHJCPmUyRlPchKgpISwO8vFQNR6rA4rOawJ4pVjV+/HisWrUK27dvR2hoKAYPHozr168DAJYtW4ZTp07h+++/R2JiIvr27Ythw4apHDGR9mVmAvv2ycesl6JByhCfDh1kMTQiIjtk8afbwoULERAQUCSRUtiQIUMQEBCAhQsXWrpLIrtx+rSs8+npCbRsqXY02uDvL295efk9hFXHnilkAUdHR2zcuBFDhw7FpUuX8PHHH+P8+fMQQmD8+PGYO3cuEhMTMWTIEKxbt07tcIlswoEDMqFSp46cLIY0hsVniagSsLhnyvnz5xEcHFyqdWvUqIGYmBhLd0lkN5ShLB06cLx3QZ07A6tXy/enVy+VgxGiwpMpTk5OePbZZw2PK5zSMyUhAbh7FyhhOl8qHW9vb6xatQpTp07Fzz//jJMnTyI5ORleXl5o3rw5Bg0axFopRGZQ6qX07s16Y5pkZjJF9XaPiKgMLP608vLyQkxMDJKSklClSpVi10tKSkJMTAznjScqQOmizCE+xpRkivL+qOrWLdl9CAAaNqyQXbq6umL+/PkVsi+TqlfPnx75wgXO6GNFoaGhCA0NVTsMIpunJFM4xEeDbtyQbQcgrxaVgurtHhFRGVg8zKdPnz64e/cuRo4cidu3b5tc586dOxg5ciQyMzMRHh5u6S6J7AaLz5rWpYu8P3hQDvdRldIrpWZNmVipDJTpkQEO9SEizUlKkrO3Ayw+q0lKr5TmzWVinojITlncM+X999/Hli1bsGXLFgQEBGDw4MFo1qwZatSogZs3b+LMmTNYu3Yt0tPTUb16dcyaNcsacRPZvH/+AS5elN9bO3ZUOxptCQ0FvL2B1FTg1CmgRQsVg1myRN7fuAEEBgKLFgFjx5brLoUQSExMBAD4+flBp0Yf9kaN5LcVFqG1ujt37iAtLQ1CiGLXCQgIqMCIiGzL7t2ygHvTpkD9+mpHQ0WUoV6KJto9IiIzWZxMCQgIwN69ezFq1CgcP34c3377rdEHoHKy2KpVK6xYsQKBgYGW7pLILii9UkJD5cyBlM/RUSaYtm+X75NqyZSEBOCbb/J/1uuBiROB8PByPYPPyMhAzZo1AQBpaWnqDI9kzxSrOnfuHGbMmIEtW7YgOTm5xHV1Oh1yc3MrKDIi28MpkTWuDMkUTbR7RERmskqFp2bNmuHo0aPYuXMntm7dinPnziEtLQ1eXl5o0qQJ+vbti95s8YiMKMkUZUgLGevcOT+Z8m9NuooXGysL0BaUlyd7a9j75VBOj2w1UVFR6N69u6E3ipubG2rUqAEHThdKVCasl6JhOTn5Y7A4kw8R2Tmrlsvu1asXeqk+9QaRbWC9lJIp74vyPqnCVMFZR8f8RIM9Y88Uq5k6dSpSU1PRu3dvfPbZZwhhQV+iMrtyBTh9GnBwAHr0UDsaKuLECTkLXJUqnLOaiOwe5x4jUkFGBnDsmHzMZIppHTrIk+XLl+VoG1U6gmRkGP/s6AgsXGj/vVIATo9sRQcOHICXlxd++eUXdl0nstDOnfK+TRugalV1YyETlCE+HTvKRpyIyI7xU45IBYcPA7m5QL16AOtMmubtnV8rRbXeKYcPy/t27YCICCAurtyLz2qGMj0ykD/FJZWJXq9H06ZNmUghsgLWS9G4MtRLISKyVVbrmZKeno4NGzYgOjoat2/fRk5Ojsn1dDodli5daq3dEtmkgkN8WLC+eJ07A8ePy/dr6FAVAvjzT3nftWvl60+u08neKUeOyLopHJpSZi1btsTFixfVDoPI5gmRXy+FyRSNYjKFiCoRqyRTVq9ejcmTJyMlJcWwTJnFp/DMPkymELFeSml16QLMm6eBnikdOqgUgMoaN5bJFNZNsciUKVPw6KOPYsWKFXjyySfVDofIZp09K2umuLqy/dSk69eBS5dkMr6ytptEVKlYnEw5ePAgnnzySbi7u+O///0v1qxZg/Pnz2Px4sWIj49HdHQ0NmzYAFdXV7z99tuoW7euNeImsll6ff6FG54Mlkx5f6KjgbQ0wMurAneemSl3DADt21fgjgEnJyeMHj3a8Fg1ShFazuhjkYceeghfffUVnn32WRw7dgxjx45Fw4YN4c46NERmUXqldO7MMk6apJzcBAcDPj5mvVQz7R4RkRks/rT65JNPoNfr8cMPP6B///6IiIjA+fPnMbZAXYEzZ85g8ODBmD9/Po4ePWrpLols2l9/AUlJgKdnfk0QMq1+fVlT5u+/5YibCu3WHRUlp3isUQMIDKzAHQOurq745ptvKnSfJilFaNkzpdQcHR1LfP6LL77AF198UeI6Op0Oubm51gyLyC5s2CDv27VTNw4qhgVDfDTT7hERmcHiArQHDx6En58f+vfvX+w6999/P9atW4dr165h+vTplu6SyKYpQ1Y6dgR48eXeVJsiueAQn8pa2IbTI5tNCGHxTa/Xq/1rEGnO4sXA1q3y8ccfAxwxrkGsl0JElYzFyZRbt24hoMB0JC4uLgBkQdqCmjRpguDgYGzevNnSXRLZNNZLMY9qyRSl+GwFD/EB5Bfy9PR0pKenG+pPqaLw9Mh0T3q93io3IsqXkABMmpT/s14PTJwol5NG5OTIGltAmZIpmmn3iIjMYHEypXr16rhb4CTbz88PAHDBxFSaeXl5uH79uqW7JLJpTKaYR3mfDh4E8vIqcMcqFp/NyMiAl5cXvLy8kJGRUeH7N+D0yESkAbGxMoFSUF4eyzlpSnS0TLpXrQo0aWL2yzXT7hERmcHiZEpQUBCuXbtm+Ll169YQQuCHH34wWi86Ohrnzp1DjRo1LN0lkc26dg24eBFwcJDDfOjeQkMBb28gNRU4ebKCdnrrVv5Zetu2FbRTDVKmRwb4rYWIVKN8DBXk6Gh6OalEGeLTsaM8ySEiqgQs/rTr06cPkpKSEBMTAwAYMWIE3Nzc8Mknn2DUqFGYP38+pk2bht69e0Ov1+Pxxx+3OGgiW6X0SgkNNbvQfaXl6JjfY7jChvpERsr7xo2BatUqaKcaxbopRKSy1FTjnx0dgYULZZFy0gjWSyGiSsjiZMqQIUPQq1cvnD17FgDg7++PBQsWwMnJCStXrsSLL76I9957D7dv30aHDh0wa9Ysi4MGgMjISDz88MOoWrUqPD090b59e6xcudKsbej1esybNw9hYWFwd3dHjRo1MGTIEMQW86UhKCgIOp3O5G1SwcG8RMVQkgFduqgbh62p8LopSr0UFYb4aA57phCRytavl/e9egEREUBcHFBg0kjSAiWZ0qmTunEQEVUgi+cSCQ4Oxvbt242WjR49Gl27dsWPP/6IuLg4uLu7o0uXLhg4cOA9p40sjV27diE8PBwuLi4YNmwYfH19sX79eowcORJxcXGYOnVqqbYzadIkLF68GM2bN8cLL7yA69evY82aNdi2bRsOHDiA5s2bF3mNr68vXn755SLL21bmoQBUaqyXUjYVnkxR6qWoUHxWc9gzhYhUpiRTRo4EevRQNRQy5do1meFycGC7SUSVik7YWMns3Nxc3H///UhISMDBgwfRqlUrAEBqaioeeOABnD17Fn/99RcaK18AihEREYFevXqha9eu2L59O1xdXQEAf/zxB/r06YOuXbti9+7dRq8JCgoCAMTFxVnld0lJSYGvry+Sk5PhwzEfdi8jQw7tycsDDh1ipwdzpKXJOqh5ecCaNfLCV7l17xYCqFkTSEyUPVRUODFMT0+Hl5cXACAtLQ2enp4VHoPBwYPyDff3B/7+u0J3zc9I+8LjSWVx6RLQoIH8nn79OvDvPAekJevXA48/DoSFyUK0ZaCpdk9F/Jwksi1WrRAVHx+PlStX4uOPP8a7775r9FxOTg6ys7Mt3sfOnTtx4cIFjBgxwpBIAQBvb2/873//Q25uLpYvX37P7SxevBgAMGvWLEMiBQB69+6N8PBw7NmzB+fOnbM4XiLF9On5s9F06gQsXapuPLbEywuoV08+HjoUCAwsx/fv0iWZSHF2Blq0KKed2BAlMR0fz+mRiajC/fyzvO/enYkUzWK9FCKqpCwe5gMAiYmJeO6557Bu3TqjueGnTZtmePz0009j1apVOHz4MNq0aVPmfe3atQsA0Ldv3yLPKcsK9ygpbjuenp7obGK8RXh4OLZs2YLdu3ejSaHp3bKysvDtt9/iypUrqFq1Kjp16oQW/MJF95CQAHz6af7Pej0wcSIQHs4CeqWRkCC/yyvK9f1Thvi0bAkUSLRWJEdHRzzxxBOGx6pSpkdOSpJTUQUHqxuPDbp48SIaNGigdhhENkkZ4vN//6duHFQCKyRTNNXuERGVksXJlNTUVHTv3h2nT5+Gv78/HnzwQWzfvh1XrlwxWm/cuHFYuXIl1q9fb1EyRSkOa2oYT9WqVeHn51dsAVlFeno6rl27hpCQEJMf2Mq2TW3nn3/+wZgxY4yW9evXDytWrIDfPS6ZZGVlISsry/BzSkpKieuT/YiNlaNHCsrLkzU9mUy5twp9/zRQfNbNzQ1r165Vbf9GlOmRjxyRB4LJFLMNGDAAf/75Jzw8PNQOhcim/PMPcOCAfDxwoKqhUHGys2X7AFiUTNFUu0dEVEoWD/OZPXs2Tp8+jccffxxnzpzB0qVLERgYWGS9bt26wd3dHRERERbtLzk5GYAsBGuKj4+PYR1LtlFwPcUzzzyDXbt24ebNm0hJScGhQ4fw0EMPYcuWLXjsscdwr/IzH3zwAXx9fQ03f3//Etcn++HtXXSZo2P+RClUssaN5Xj5gsrt/WPx2aKU5DVn9CmTmJgYjBw5stTrnz59uhyjIbIdv/4qE+kdOvDCg2ZFRQFZWbIX4z3qFRIR2RuLkyk//fQTXF1dsWTJEri7uxe/IwcHNGrUCH9XcAFDa5o2bRq6d+8OPz8/eHt7o0OHDti4cSO6dOmCgwcPYtOmTSW+fsqUKUhOTjbc4guOWyC7dvy48c+OjsDChTw5LK369YFFi2QnCUDel8v7l5MDHDsmH7NCcD4la8UZfcpk/Pjx+O2334yGvhZn48aNeIB1B4gAcIiPTVCG+HTsmN9IExFVEhYnU+Li4tCkSZNie3kU5OHhgcTERIv2p+ynuN4nShVsS7dRcL2SODg44OmnnwYA7L/HvK2urq7w8fExulHlsGGDvH/9dSAiQs4gOHasqiHZnLFjgQ8/lI9btCin9+/kSSAzU9YIUbHbUHp6OnQ6HXQ6HdLT01WLw4DTI1tk3rx56NChA9577z2sW7eu2PU++ugjDBo0CGlpaRUYHZE23bkD7NwpHw8apG4sVAIrFZ/VXLtHRFQKFidT3NzckJqaWqp1r127VqoERUlKqmdy584dJCYm3nNaZE9PT9SpUweXLl1CnjK9SgEl1WUxRamVkpGRUar1qXK5exfYsUM+HjUK6NGDPVLKatQoeR8dLafItLqCQ3wKjyuqzJTEEof5lImzszPWr1+PWrVqYcyYMTh16pTR89nZ2XjyyScxdepUeHh44Gdl+hKiSmzjRiA3FwgJ4egRTeNMPkRUiVn8bSE4OBjx8fG4fPlyietFRUXh77//tqj4LAB0794dALBt27YizynLlHXutZ309HSTvUm2bt1a6u0AwJ//FqwMCgoq1fpUuezcKRMq/v5AaKja0di2unWBNm3kGPrffy+HHSjFZ1kvxRinR7ZY7dq18dNPPyEnJwcDBgzArVu3AMiLDF27dsUPP/yA++67DwcPHkT//v1VjpZIfRziYwOuXgX+/ltefGC7SUSVkMXJlFGjRiEvLw8TJkwotmfGnTt3MHbsWOh0Ojz11FMW7a93795o0KABVq5ciaioKMPy1NRUzJw5E05OTkaz7SQmJuLMmTNFhhdNmDABAPD2228jOzvbsPyPP/7A1q1b0a1bN6Npkf/66y8kJSUViWffvn2YM2cOXF1d8X9s8ckEZYhP//4cTmwNyvfMjRvLYeMsPmta9eqA0qvw4kV1Y7FhnTp1wueff45Lly5hyJAhOHDgANq1a4fIyEj06tULkZGRaN68udphEqkuPR3YskU+5qmVhim9UsLCAC8vdWMhIlKBxcmU8ePHo2vXrti+fTtCQ0Px1ltv4fq//e+XLVuGV199FU2bNsXx48fRp08fDBs2zKL9OTk5YcmSJdDr9ejatSsmTJiA1157DS1atEBMTAxmzJhhlASZN28emjVrhnnz5hltp2fPnhg3bhz27t2LVq1a4Y033sDo0aPxyCOPwMfHBwsWLDBa/8cff0TdunXRv39/vPDCC3jttdfQr18/dOvWDTk5OZg3bx4CAgIs+t3I/giR/6WfF5utQ3kft22T5U2sJiUFUGZRYTLFmE7Huiml5O3tjU6dOmHixIn46quvsH//fqOhsBMnTsS4ceMQERGBrl274urVq3jhhRewdetWVK1aVcXIibRjyxb5+d6ggfyeThrFIT5EVMk5WboBR0dHbNy4ERMmTMCaNWvw8ccfG6YIHj9+vOHxkCFDsHTpUkt3B0AmQvbt24fp06fjxx9/RHZ2NoKDgzFz5kyzpp9cuHAhwsLCsHDhQnzxxRfw8vJC//798d577xklZJR9nj59GseOHcPu3buRmZmJWrVqYejQoXjllVfQnl++yISoKODKFcDTU9ZKIcu1aiWH+1y9CuzaBfTrZ6UNHzkis1+BgUCtWlbaqB1p3Fi+R6ybUqKMjAwcOnQIhw4dgq5AV7TAwECEhYWhZcuW6NmzJ7Zt24br169j/vz5eOaZZ1SMmEh7Cg7xYY9ODdu1S943bapqGEREatEJJdthBSdPnsTPP/+MkydPIjk5GV5eXmjevDkGDRpkca0Ue6TMPJScnMyZfezUu+8C06cDAwcCrClpPRMnyqmSn3sOKNTprOw+/BCYMgUYMgRYs8ZKGy2b9PR0eP3bZTotLQ2enp6qxgMAmDYNmDkTmDBBzktdAWzxM/Lu3bs4deoUoqOjER0djRMnTuDEiRNGs8cpSRY3Nze0bt0aYWFhhltoaKjh2NsbWzyeVPGysoCaNWVnwQMH2OlBsxYuBCZNko8dHGSjbME0e5ps91TAz0ki22Jxz5SCQkNDEcoKm0QGyhCfRx9VNw5707+/PG/bsAH48ksrXbnUUPFZR0dHPPzww4bHmqAM82HPlBK5u7ujXbt2aNeundHyy5cv48SJE0ZJlgsXLmD//v3Yv3+/IcGi0+kQFBSE83yfqZLauVMmUurUATp0UDsaMikhAXj22fyf9Xp5lSM8vMzTFWqy3SMiugerJlOIKN+1a0BkpHz8yCPqxmJvevUC3NzkJAInT1ppTL2Gis+6ubnh93KZrsgCyvTIrJlSJoGBgQgMDDSaqScjIwMnT54skmS5dOmSipESqUsZ4jNoEGeo16zYWJlAKSgvTybby5hM0WS7R0R0D1ZPpty5cwdpaWkoafQQC7VSZaCcE7RvD9SurW4s9sbDA3jwQdnzZ+NGKyRTEhJkERZHR6B1a6vEaHcKT4/s7q5uPHbAw8MDHTp0QIdCl9/j4uIs3nZkZCSmT5+OgwcPGuqKvfzyyxgxYkSpXr9v3z78/PPP2LVrF+Li4pCeno6goCAMGDAAU6ZMQZUqVSyOkaiwvDzgl1/kY87io2FKe1CQo2N+0p2IqJKwSjLl3LlzmDFjBrZs2WI0LtwUnU6H3Nxca+yWSNOUKZE5xKd89O8vEykbNgBTp1q4MaVXSkiIrBZMRSnTIycny+mRg4PVjshuBQUFWfT6Xbt2ITw8HC4uLhg2bBh8fX2xfv16jBw5EnFxcZhain+YJ554AomJiejSpQueeuop6HQ67Nq1C7Nnz8a6detw4MAB1KxZ06I4iQrbtw9ITASqVQO6dVM7GipWerrxz46OsoZKGXulEBHZKouTKVFRUejevbuhN4qbmxtq1KgBB/bNpErs7l1gxw75mFMilw9l6NSffwI3bsiChWWm1EvRyAD99PR0wxfVGzduaKMQnzI98pEjsos3kymalJubi3HjxkGn02HPnj1o1aoVAGD69Ol44IEHMH36dAwePBiNTV1ZLuCVV17BU089hTp16hiWCSHw3HPPYcGCBXjnnXcwf/78cv1dqPJRhvg89hjg7KxuLFSCdevkfY8essp+o0YWJ1I02e4REd2DxRmPqVOnIjU1Fb169cKJEyeQkZGBy5cv49KlS8XeiOxdRASQkSHPLVq0UDsa+1SvnhyRIwSwaZOFG9NQvRRFRkYGMjIy1A7DmNKFm8VRNWvnzp24cOECRowYYUikAIC3tzf+97//ITc3F8uXL7/ndt58802jRAoge5b+73//AwDs3r3buoFTpSdE/qx3HOKjcT/9JO9HjpQJFSv1SNFku0dEVAKLkykHDhyAl5cXfvnlF4SEhFgjJiKbV3CIj1VmmiGTlF4/yvtdJnl5srcFoKlkiiYpvRlYhFazdu3aBQDo27dvkeeUZZYkQpz/7S7g5MT69WRdR4/KkkyenkCfPmpHQ8W6eBE4flxWBx4wQO1oiIhUZXEyRa/Xo2nTpuyOR/QvIfKnROYQn/Kl1KPZtg3IyirjRk6fBtLS5Bl88+ZWi80usWeK5sX+m+gyNYynatWq8PPzM6xTFsuWLQNgOllTWFZWFlJSUoxuRMVRhvg88oicrY00SjlQPXoANWqoGgoRkdosTqa0bNkS165ds0YsRHYhOlpODuPhIafwpfLTujVQp47MhZT5YrsyxKdtW1lEj4rHnimapxSB9/X1Nfm8j4/PPQvFFycqKgrvvPMOatasiTfeeOOe63/wwQfw9fU13Pz9/cu0X7J/QuSX4eAQH41TDtTjj6sbBxGRBlicTJkyZQquXbuGFStWWCMeIpunDDl58EFeXStvDg75vVPKPNRHY8VnNa3w9MhUaVy6dAmPPvoo8vLysHr1avj5+d3zNVOmTEFycrLhFh8fXwGRki06fRo4dw5wcQEeekjtaKhYCQnAoUNy/PKgQWpHQ0SkOouTKQ899BC++uorPPvss3jllVdw6tQp3OVJNlViHOJTsQrWTRGiDBvQYPFZzVKmRwbkuHkqk3PnzmHjxo1YtWoVNm7ciHPnzllt20qPlOJ6n6SkpBTba6U4ly9fRs+ePXHz5k389NNP6NmzZ6le5+rqCh8fH6MbkSlKTeQuXQD+mWiYMsSnUyfZLZSIqJIzq4Kc4z26wH/xxRf44osvSlxHp9MhNzfXnN0S2Yx//sn/bq5M3Uvlq3dv2QPo8mUgJgYwqw52RgZw8qR8rKFkioODA7p37254rBkFp0c+f57TI5tp4cKF+Oijj3D58uUizwUFBeGtt97C+PHjLdqHUislNjYWbdq0MXruzp07SExMRKdOnUq9vbi4OPTs2RNXr17F2rVr8ajSFYzISpYuBT75RD6OiJA/jx2rbkxUDGWIzxNPWH3Tmm33iIhKYNanlRDC4ptery+v34VIdb//Lu/btuVFm4ri4SETKkAZhvocOyZn86lTx2pTO1qDu7s7du3ahV27dsHd3V3tcIwpRWhZN8UsTz/9NJ599lnExcXBxcUFDRs2RKdOndCwYUO4uLjg0qVLmDRpEp5++mmL9qN8Gdm2bVuR55Rlyjr3EhcXhx49euDKlStYs2YNBnDmDrKyhARgwoT8n4UAJk6Uy0ljrl8H9u6Vj8uhsI2m2z0iomKYlUzR6/VWuRHZK+XLPIf4VKwyT5FccIgP57AuHaVuCmf0KbWVK1fi22+/hYeHB2bPno2bN2/i3Llz2Lt3L86dO4ebN29i9uzZ8PT0xHfffYdVq1aVeV+9e/dGgwYNsHLlSkRFRRmWp6amYubMmXBycsKYMWMMyxMTE3HmzBkkJiYabadgImX16tUYxPoIVA5iY4HCp4V5efx40aSff5bZrnbtgIAAtaMhItIEs4b5EFHxMjOB7dvlY/aEr1jKkKpDh4CbN82YrZHFZ83HnilmW7x4MXQ6HdatW2dySmEvLy+89tprCAsLQ79+/bB48WIMHz68TPtycnLCkiVLEB4ejq5du2L48OHw8fHB+vXrcenSJcyaNQtNmjQxrD9v3jy88847mD59OmbMmGFY3qNHD1y+fBkdO3bEiRMncOLEiSL7Krg+UVnUrVt0maNj/scMaQhn8SEiKoLJFCIriYiQJTjq1QNatVI7msqlfn35nh8/DmzaBIweXcoXarT4bHp6OoKCggDIHgKenp7qBlQQp0c2W3R0NBo0aGAykVJQ37590ahRIxw/ftyi/fXs2RP79u3D9OnT8eOPPyI7OxvBwcGYOXMmRo4cWaptKHVdDh06hEOHDplch8kUslTh0WiOjsDChZoadUkAcOuWPMkByi2Zoul2j4ioGEymEFmJMsTk0Uc5YkQN/fvLZMqGDaVMpty4AcTFyccaLHBTeNiFZiiXjJXpkTm2/Z4yMzNRpUqVUq3r4+ODBCsUjGjfvj02b958z/VmzJhhMikiyjQ1FlHp5eUBc+fKx++9JyeIadSIiRRN+vVXecBatCjXbkOabfeIiIrBctlEViBE/pTIHOKjDuV937oVyM4uxQtmzcp/HBoqp5Cge/Pz4/TIZgoICMCpU6fu+UXh5s2biImJQQDrEVAlsGGD/AipVg146SWgRw8mUjSLQ3yIiExiMoXICk6ckBfq3d3zZ5ahitWmDVC7NpCWBuzefY+VExKAefPyf9brOYVEaSnTIwOsEllKjz32GLKysjB06FDcvHnT5Do3btzA0KFDkZ2dzVlzqFKYM0feT5wIcESHhiUn5xeEK4cpkYmIbBmH+RBZgTLE58EHOepBLQ4OsnfKkiXyePTpU8LKZ87I7kQFKVNI8NLovTVqBBw5wroppfTWW29h9erV2LVrFwIDAzF48GA0b94cNWvWxI0bN/DXX39h7dq1yMzMhL+/P9588021QyYqV0ePyll2nZyA555TOxoq0caNQE4O0KyZvBERkQGTKURWoPSA7dxZ3TgqOyWZ8ssvwMCBQJMmxeRGrl0ruoxTSJQee6aYpVq1ati5cyeGDx+Oo0ePYsWKFdAVKKyk1Cdp164dVq5ciWrVqqkVKlGF+OwzeT9smCzaThr200/ynkN8iIiKsDiZcvHiRTRo0MAasRDZpM8+A6Ki5OOpU2VJibFjVQ2p0nrwQXmlMz5eDrdycAAWLTJxPH77Td7rdLKHCqeQMA+nRzZbo0aNEBkZiT/++APbtm3DuXPnkJaWBi8vLzRp0gTh4eHo1auX2mESlbsrV4A1a+TjV15RNxa6h7Q0YMsW+ZjJFCKiIixOpgwYMAB//vknPDw8rBEPkU1JSAD+85/8n5XSG+Hh/F6uhjt3gNzc/J9NHo/ERDkzASBPEl1cNDeFhIODA9q2bWt4rDnsmVJmvXv3Rm8WVqJKbN48+TndvTvQurXa0VCJNm8GMjOBhg3lTD7lSPPtHhGRCRZ/WsXExGDkyJGlXv/06dOW7pJIM86eLb70BlU8Ux0lihyPH36Q479btwb69tXkFBLu7u6IjIxEZGQk3LVYhKfg9MiZmerGYgP27NmD6OjoUq174sQJ7Nmzp5wjIlJHerrsBAiwV4pNKDiLT4GhieVB8+0eEZEJFidTxo8fj99++w3Tpk2757obN27EAw88YOkuiTTj8uWiy1h6Qz2NG8uhPQUZHQ8h8qdAfuaZCo3Nrvj5Ad7e8v08cEDtaDSvR48eePHFF0u17ksvvcThPmS3vv1W9iBs1Ch/OnvSqLt3ZfFZgEN8iIiKYXEyZd68eejQoQPee+89rFMy2CZ89NFHGDRoENLS0izdJZEmCAEsXiwfKxdsWHpDXfXryxopBS+gLVhQ4HgcOwacPAm4ugLDh6sSo11YtgxITZWPH3wwP0FFxRKFu7BZaV0iW6HXA3PnyscvvSTbS9KwbdtkVyJ/f6BdO7WjISLSJIuTKc7Ozli/fj1q1aqFMWPG4NSpU0bPZ2dn48knn8TUqVPh4eGBn3/+2dJdEmnC3r3AoUPye3lkJBARAcTFsfis2saOBU6fBry85M9VqxZ4ctkyeT9oEKDhGVMyMjIQFBSEoKAgZGRkqB2OsYQEYMKE/J+FkIVpEhLUi8mO3Lp1i13cyS79/rscilmlCjBmjNrR0D1V4BAfQOPtHhFRMawyNXLt2rXx008/oVevXhgwYAAOHz6M6tWr49q1axg4cCAiIyPRoEED/Pbbb2jevLk1dkmkuo8+kvdjxgBt2qgaChXStCnw6qvAu+8CH37477lg5l1g5Uq5gsaH+AghcPnfMWSa66UQGysvMRekFKZhlywAQEpKCpKSkoyWZWVlIT4+vtjjeffuXezevRunTp1Ci3Iu9EikBmU65AkT8pPdpFHZ2fmz3lXQEB9Nt3tERMWwSjIFADp16oTPP/8ckydPxpAhQzBz5kwMGTIEV69eRa9evbB27VpUNbpETGS7TpwANm2S9Tlee03taMiUF14APv4YOHoU2LkT6H3jFyApCQgIkPMmU9kohWkKJlRYKMjIZ599hnfffddo2ZEjRxAUFFSq149l9zayM1FRsvemoyPw/PNqR0P39McfQHIyULs20KmT2tEQEWmWWckUb29vhIaGIjQ0FC1atECLFi0QFhYGb29vAMDEiRNx9OhRLFmyBF27doUQAi+88ALmzJkDRw6OJTui9EoZPJjfIbXKzw8YNw748kvZO6U3/h3i8/TTRavUUukphWkmTpQ9UgBgxAj2SimgSpUqCAgIMPz8999/w8XFBbVr1za5vk6ng7u7Oxo0aIChQ4di1KhRFRUqUYVQeqUMGSJLcJDGffedvO/Th+0lEVEJdMKMvnSOjo6Grne6AuMnAwMDERYWhpYtW6Jp06aYMmUKrl+/jvnz5+MZjXenV1NKSgp8fX2RnJwMHx8ftcOhUrp0SSZQ9HpZz7RVK7UjouJcvgw0bAjUz4vDJV0D6ISQB7CUPQTUkp6eDq9/+8GnpaXB09NT5YhMSEiQ46gWL5Yn3Nu2WX0X9vIZ6eDggC5dulT6KY/t5XiSea5dAwID5Yz0hw+zlqnmKclyQCZSFi2qkGJwNtHuVQB+ThLZFrN6pqSlpeHUqVOIjo5GdHQ0Tpw4gRMnTiAuLg5xcXH47bffDEkWNzc3LF++HEePHkVYWBjCwsIQGhpq+KAkslWffioTKX37MpGidYGBstPEfSu+lYmU3r01n0ixGfXrA2+8IZMpO3cCt24B1aurHZUmLV++HLVq1VI7DCJVzJ8vEymdOzORonkJCcCkSfk/6/UysRIezt6HREQmmJVMcXd3R7t27dCuUGt4+fJlnDhxwijJcuHCBezfvx/79+83JFh0Oh2CgoJw/vx56/0GRBXoxo38WWDfekvdWKh03nhND68VywEA1x56BnVUjseuNGoEtGgBREfLYoVPP612RJo0evRotUMgUkVGBvD11/Lxq6+qGwuVwpkzcoa2glhgnIioWFYpQBsYGIjAwED079/fsCwjIwMnT54skmS5dOmSNXZJpIovvgAyM4H27YEePdSOhkoj5MZOAJeRBF/MihmE+WoHVAo6nc4w85muAqaktMjjj8tkyrp1TKYQkZEvvpCd1vz9gQED1I6G7uno0aLLKqjAuE21e0RE/zKrZoo1xMXFlXpGA3vHcZG2JTVVTgSTlASsXw8MGqR2RFQqI0YAq1bhK0zGKy5f4dIloG5dtYOyI3/9BQQHA87OwM2bgK+v1TbNz0j7wuNZuSxeLKdBBgCdTv7Miao0LCVFztZ244Y8YELIRMrChTxwFYifk0S2pcJLdDORQrZq0SKZSGnalFfYbMadOzLzBeBYi2eQnQ3MnatuSHaneXOgWTNZFGHjRrWjISINSEjIr2EKyO/lEyfK5aRRH3wgEymNG8thPRERQFwcEylERCXgfGdEpZCVBcyZIx+/8QZnCrQZq1bJgxcaioEz2wAAFiyQORayoscfl/fr1qkbBxFpwu7dxZfeIA2Ki8ufv/qTT4AGDeRYZtZJISIqkVlfCZ999lkkWOmywurVq7Fy5UqrbIuovH3/PXD1KlCvHjBypNrRUKktWybvn3kGDz+iQ0gIkJYmEypalpGRgeDgYAQHByMjI0PtcO5NSaZs3izfYCKqtHJz87+XF1RBpTeoLN58U1546NULKFD/sCLZXLtHRAQzkymLFi1Co0aNMG7cOOzZs8fsnd28eRPz5s1Ds2bNMHLkSBajJZuQlwfMni0fv/oq4OqqbjxUStHRspieszMwciQcHOT5IgB8/jlw96664ZVECIG//voLf/31Fyq4rFXZtGgBNGwoqzNv3qx2NESkog8/lB+9bm4ygQLkl95gRwcNOnAA+PFHWSdlzhx5rwKba/eIiGBmMiUqKgq9e/fGsmXL0LNnT/j7+2PChAlYsmQJjh8/jn/++QfZ2dkAgOTkZFy6dAmbNm3Cu+++i759+6JevXp46aWXcOvWLXz22Wd44403yuWXIrKmX38Fzp0DqlQBxo9XOxoqteVyOmQ89hhQowYAYOhQIDBQDgv/5hv1QrM7Oh2H+hARIiOBGTPk48WL5egRlt7QML0eeOUV+fiZZ2RinIiISq1Ms/ns3bsX8+bNw6+//ors7Ox7TmGm7KJRo0YYP348Jk2aBG9v77JFbEdYsVv7hAA6dJAniG+/DcycqXZEVCpZWXJM1q1bwO+/Aw8/bHjqyy+BF18E7rtPJsmcrDJBvHWlp6fDy8sLAJCWlgZPT0+VIyqFw4flP4unp5zVx93d4k3a22dkVlYWVq9eja1bt+LcuXNITU2Ft7c3mjRpgr59+2LYsGFwc3NTO8xyY2/Hk4ylpwOtW8vP1aFDZckqznCrcT/8AIwaBXh5AbGxQO3aqoVik+1eOeDnJJFtsWhq5MTERKxfvx579+7FgQMHEB8fj9zcXMPzPj4+aNmyJbp06YK+ffuiW7duVgnaXvADU/vWrAGGDZPdlf/+29DBgbTup5+AwYPlHMiXLxtlTDIyZO+UxESZWAkOlpMXaKn7uU2eVAoh39j4eOCXX6wy5ZU9fUYeOHAAo0aNwuXLl012YdfpdAgICMD333+Pzp07qxBh+bOn40lFTZ4MfP21/Cw9cQKoWlXtiKhEGRlyesKEBOC994CpU1UNxybbvXLAz0ki22LRNVk/Pz9MmDABEyZMMCxLSkpCZmYmqlWrBhcXF4sDJFLL0qXAuHHycVYW8Ntv7KZsM+bPl/eDBhXpeuLhIXumTJsGvPCCXObgIKe+5vG1gDLUZ+5cOdSH84cbxMTEoE+fPrh79y5q166NcePGoVmzZqhVqxZu3LiB06dPY+nSpbh8+TL69u2LP//8EyEhIWqHTVRqGzfKRAogh1AykWID5syRiZSAgPyhPkREZJYy90y5ceMGIiMjkZWVhfr166Nt27Zw4HyxZmH2WbsSEuRFdr0+f5mjoxz3raUeDGTCJ58Ar78uHxeTJTl5EggLM36Zlo6vzV6h27cP6NoV8PWVhWksTKjby2fkoEGD8Ouvv2LUqFFYunQpnJ2di6yTk5ODcePGYcWKFRg4cCDWr1+vQqTly16OJxm7cQMIDZX3r74KfPqp2hHRPV29CjRpIsdmrVwJDB+udkS22+5ZGT8niWxLmbIfb731FurXr4/HHnsMgwcPxgMPPIBatWph3rx51o6PSBWHDhknUgA5q8/58+rEQ6WUkAAULGyt1wMTJ8rlBSQmFn2plo6vTqdDYGAgAgMD71mTSlM6dQLq1AGSk4E//lA7Gs3Ys2cPfHx8sGjRIpOJFABwdnbGwoUL4ePjg127dlVsgERlJITswakkVN57T+2IqFTeflsmUjp2lGOZNcBm2z0iqtTMTqYsW7YMs2fPRm5uLoQQcHBwgBACt27dwksvvYQpU6aUR5xEFSYtDXjnnaLLHR2BRo0qPh4yw5w58uy+IBNZksaNZaeVgrR0fD08PBAXF4e4uDh4eHioHU7pOTjIoVUAZ/UpIDs7G02bNr1ncVk3Nzc0bdoUOTk5FRQZkWWWLAE2bJCd0L7/XtYXI407dix/OrvPPtNMlWCbbfeIqFIzO5myaNEi6HQ6DB8+HNeuXUN2djYuXryIqVOnwtnZGR9//DGOHDlSHrESlbvcXHmR5tQpWdxe+cLt6AgsXKiNISBUjIgI4Isvii43kSWpX1+O/nF0zF8WGAhUr17OMVYGyhTJv/wi/6EIzZo1Q0Kh3lHFiY+PR3BwcDlHRGS52Fjg5Zfl4w8+KDp0kjRICOA//5H3w4bJnilERFRmZidTYmJiUKVKFSxbtgy1atWCTqdDUFAQZs2ahQULFkCv12PhwoXlEStRuRJCFib9/Xd5dW37djkRTESErKXB4qQadv68/BKflwe0b5+fJSkhCzZ2rDyu33wD+PgAFy8CTz5ZdHgXmalbN8DPT05LvXu32tFowssvv4xr167h888/L3G9L774Av/88w9eVr6hEmnUpUvAY4/JCWF69cpPqpDGLV0K7NoFuLoCH36odjRERDbP7GRKeno6mjRpAldX1yLPjRkzBlWrVsXevXutEhxRRfrkE2DBAtnjdeVKecGmfn2gRw/2SNG05GR5Vn/nDtCunTxRjIsrVRasfn1g9Gg5U5OLixyZUrDkilru3r2Ldu3aoV27drh7967a4ZjHyQkYOFA+5lAfAMCIESPw0Ucf4c0338T//d//YceOHbhy5QpycnJw9epV/PHHH3j88cfxxhtvYPbs2RimkRoGRKYsXQo0bAicOSN/7tev6LBJ0qCvvwbGj5ePs7OBHTvUjacQm273iKjSMns2HwcHB3Tp0gV79uwx+XzHjh0RExOD1NRUqwRoz1ixWzvWrgWGDJGPP/uMV9lsRm4u0L8/sGULUK8eEBkpC6CWwcqVwMiR8vG8ecBzz1kxTjPZ/KwGW7YADz0E1KoFXLliPJ7KDPbyGelYxt+/IJ1Oh1wbHzZlL8ezMouPl0MiC545amkmNCpGTAxQeLp1jR04m2/3rISfk0S2xerXEpydnZGRkWHtzRKVm/375fAOAHjhBeCll9SNh8zw+uvyi7u7u+xeUsZECgCMGAHMmiUfv/iiLKpIZdSrF1ClCnD9OnDggNrRqE4IYfFNz/FnpLKMDNnRrxQ1vklL4uKAhx8uupwHjojIYmVKply8eBGffvoptm/fjhs3blg7JqIKExsLDBgAZGXJew0Vtqd7WbIEmDtXPv7uO6B1a4s3OXWqnOZTr5e1+VhLu4xcXOTQK4BDfQDo9Xqr3IjUcvGinPl8+/aiz2lpJjQq5PBhoEMH4O+/iz7HA0dEZLEyJVOuXr2KN954A/369UOdOnVQu3Zt9O3bF6+//jquXr1q7RiJysXNm3Ikwq1bstTGypVlHo1AFW33bmDyZPn4nXeAJ56wymZ1OuCrr4DwcHkV9tFH5UU9KgNlVp9161jVl8iGbdoEtGkDREcDNWoAr71WqhrfpLZffpFF327cAFq2BD7+mAeOiMjKzK6ZsmbNGkRFRSE6OhpRUVH4559/8jdW4JK+h4cHgoODERYWhhYtWiAsLAxhYWHw9fW1XvQ2juMi1aP0SDl9GrjvPuDgQVnegWzAxYtyxp5bt4ChQ4FVq6zenSglBejaFThxAmjWDPjxR5l8a9y4Ys497WLseGam/OaVlgYcOiSvjpqJn5H2hcfTtuj1wMyZMl8thCzKvnat/AxMSJAjRBo14vdxzREC+Pxz4NVX5eOHHgLWrAG8vTV94Oyi3bMCfk4S2RYnc18wdOhQDB061PDzzZs3jZIr0dHROHv2LNLT03H48GEcPnzYKMni7++POF7qJRUtXgxMmJD/8zPPMJFiM06fzu9O1LYtsGxZuYzL8vGRU2R37Ch3GRoqlzs4AIsWcZrsUnFzk117Vq+WvVPKkEwhInXcuSNrif3+u/x58mQ5DFaZyLF+fc19FydAFmV/5RVZRR0AJk0CvvxSzrIG8MAREVmZ2T1TSiMrKwsxMTFGSZYTJ04gOTkZOp0OeXl51t6lTWL2uWIJIctsFEykAJoraE/FKZwF+/hj2d+8HG3fDvTta7ysIv5e0tPTERQUBACIi4uz3St0P/0EDB4M1K4tx+77+5v1cnv5jDR3Nh97mLnHFHs5nvYsIUHW9J45U5bZcHOTM+qOHq12ZFSihATZlXLOHOCPP+Syjz8G/vMfmykEZzftnoX4OUlkW8zumVIarq6uaN26NVoXKggZFxeH6Ojo8tglUbGEALZtA95+23RBUaWgPZMpGpWbCyxYIKfYKeitt2SV2HI8cE4mPiHz8oClS4Fp08rvHNXT0xM3b94sn41XJKVA+T//AEFBlbZbj7nXLMrhGgfRPS1eDEycmD9bT/XqMqHcqpW6cdE9LF0qLzQotamcnOTwVyvVEqsodtPuEVGlYvWpkUsSFBSEAQMGVOQuqZLbswfo3h3o108mUtzdi34BZkF7jbp7V1aDbdy4aCIFqJBpHRs3lkN7CpsxQ44y2ry56DSh9K+EBDnXuEKvl9/UEhLUi0klJc3Qk5aWhqioKDz33HPw8PDA119/zZl7qEKdPQs8/7z8Pl7w8ywpSZY9Ig2LjATGjzcu8q3XyzGqRERU7io0mWJNkZGRePjhh1G1alV4enqiffv2WLlypVnb0Ov1mDdvHsLCwuDu7o4aNWpgyJAhiI2NLdf9UvlJSAAiIoCNG+WMLN27A3v3ynHer74qh2csXsyC9pqWlAR88IHsyfDcc/KgVa2qShasfn3ZmaLg30v//oCXF3DsGPDww7JQ7a5d+X97lTBXYFpsbNFZfCogAWZrPDw8EBYWhi+//BLz58/H5MmTsXnzZou3q1YbSdpU+PMpKUm2fQ88ANx/PzB/ftHX8N9Vo1JTgW++AXr3lsXYC2f09XoeOCKiiiJsUEREhHBxcRFeXl5i3Lhx4j//+Y+47777BADx3nvvlXo748ePFwBE8+bNxeuvvy6eeuop4erqKnx9fUVMTEy57VeRnJwsAIjk5GSzX0tFLVkihIODEPLMQt6cnISYNEmIhATjdePjhYiIkPekAfHxQqxdK8TkyUJ4e+cfwMBAIb78Uoj0dHmAHR3lckdH+XMFhlfw7+XmTSFee00INzfjvzdA/g1aGlpGRobo3r276N69u8jIyLA4flXExxf9h3R0NOufrjJ+RtatW1d07drVom2o1UbeS2U8nlpQsG3U6YRo104IV1fjf8teveRzFvy7UnmIjxdi504hLl0SYtMmIYYPF8LdvWjDYwcHzi7aPSvg5ySRbbG5ZEpOTo5o2LChcHV1FceOHTMsT0lJEcHBwcLJyUmcO3funtvZuXOnACC6du0qMjMzDct37NghdDqd6NatW7nstyB+YJaecj6hnB/o9fLxr78KMX26EA8+WPR8QqcTYv9+VcOmwgeuoLQ0IY4dE2L8+KJn8cHBQqxYIUR2dtHtaSgLdvWqEKNHmz6ffeEFIdatk+fAen3+a0p6SxRpaWkCgAAg0tLSyvvXKD8WJsAq42dkmzZthLe3d5lfr1YbWRqV8XiWt+I+T/R6Ia5fF+Knn4p+vCq3kBAhPvlEiGvX5GtUzFdXPqVpCL74omhCWrk1aSLEzJlCXLxoNwfObto9C/Fzksi22FwyZevWrQKAePrpp4s8t3r1agFATJky5Z7bGT58uAAgdu/eXeS5fv36CQDi7NmzVt9vQZZ8YF49HC+OfbpTXD1c8pdKW18vL0+eT/jr4kUP7BT1ES9CQoSoWdP0+UU9yPXqIV4A8nu3SaU5keF6lq1X8HKog4MQo0YJ8dJLQoSHCxEQUPxVNQcHIS5fLnn/GrJzZ8kXCQEhqlYVondv+asrX2wcHIRYtMj0NgueVJ49W/JJpZb/BIT49398TsQ9PwtMqWwnlWlpacLLy0v4+vqWeRtqtZGlwTbPuustXmzcNg4aJMRTTwnRoYMQVaqU3DYuXGic5C243+Nz7h2f5j94tLxe4bbx1VflAXnrLSGGDBGibduiB1C5jRkjxJ9/Fj14GrvQUBZMpkiVrd0jsnXlMptPedq1axcAoG/h+UoLLNu9e3eptuPp6YnOnTsXeS48PBxbtmzB7t270aRJE6vu1xoi+n2I7lunog4E9NBhd/AkuD78YJH1sjbtQNeYr8u0nstDRdfL3my83q7mk+DU70FA5A/ZFQDytu5A99P56+1oMgk53R5EXh6Qpwf0eXIstvuBHXjocv56a6pNwslaDyIjA0hPl7eMu0Bv7EAcvobDv+stODUJf+BBODgA/vWBBg2AWrWAxDU7MKnAel/rJiEk9kHgdqFfZMcOOdejELIOx6RJwINFf1+bXK9376Lr/fGH8XoTJgA9e/57wAocvIgIOXe0st6TTwKdO8uDVfB28CCwbl3+el26yOIiaWnylp4O3Lkja2Yo9Hrg+++LxubjA6SkGC/T64GLF4GAgKLra5BSpLZgeRAHB2DoUFnY8eRJ+XYos1Uq9Hp5KF55BahWDfD1BapUkbfr1/PXa9oUGDgQ6NBBTtKg3Jyd5aH47rv8QzFuXP6h1enybxERsj6CuX8q1vkTrQ8h6sPBodJO5lMqp0+fxquvvoqMjAz069evzNtRq40sT7ue+BLd1r1Urm2eOW2jKLRe9qYd6PZXobYx/EH58QoY2kj99kJtY+NJyO72oFG7mJcHeBw0bht/9JuEs/Vl23j3rrylpwMP3C3UNv4s28a6AOoC0AGoVh1oeWsHJhdqG/9P9yB0Pxf6RXbsQJ2vv0YdLbRl5dE2Fq4t8scfxh+M48cDvXoZpy8A+QG6dKlx29ipU9G28dAh47axWzfZjhU8qblzBzh1Kj8GvV5OZ1xao0fLOimF1a/P4m9ERCrQCWFbc1EMHjwYP/30E44cOYI2bdoUeb5GjRrQ6XS4oUzJaUJ6ejq8vLwQEhKCkydPFnn+999/x6OPPorXX38ds2fPttp+s7KykJWVZfg5JSUF/v7+Zs0lfy0yAbXaB8ChyOkckQ0YMgTo00dWPLz/fiAzEwgMNM5EODrKorM2dGK4dKmcqCYvL7+osZI0yMoCYmKAlSuBTz8t7RbTAXj9+zgNgKfVY1aDuYc2JSUFvr6+Zn1GalGDBg2KfU4IgZs3b+Lu3bsQQsDLywt79+5FixYtyrQvtdpIU6zV5tVsHwhHcIYjsmMdOgDt2smrQ/fdB3h6ymkIbbxtNIfyuQMAaWlp8PS0j3bPXPbS7hFVFjbXMyU5ORkA4Ovra/J5Hx8fJNxjOo3SbKPgetba7wcffIB33nmnxHXu5Z+9sahjIpFyzjUEmS75sbllJ6FJVozp9VwLrJdl2XqxriHIdJPr6QC4ZiWhcWbR9S56hCDHw9dwpdwpIwn3pRVd73qNELjU9IWTo7z6juQkuF8oul520xC4+BU4FklJ8htrYSEh8pK/PaxXpYrxegWvbilCQ4uuZ+LLEFq0MJ4hJykJOH686HqdO8tuP46O8nbzZtEuFoCcdadlSznNjaenvHQ6fHjRE8FPPy16IrhoUdFMhI2dLI4dK2ePOn9eTjBUMHxXV6B1a6BmTeCzz4q+JRERgJsbkJwsD8OhQ6aTLv36yWlKc3Pl7do1YN++ouu1bi3/BJQLq7dvAydOFF2vtH8qpf3TK82fsjI7iI0dXovFxcXdcx1fX1+Eh4fjnXfeQdOmTcu8L7XaSFOs1+YVTaSY1eaVY9vonpWExqbaRje5njIHmVtWEhoV1zZ6yvV0OsA5IwlBJtrGf/xC4OznKz+KnQBdchK84tg2lkvbWK1aftt4507xbWPt2vlt440bptvGiROBsDDAwyO/bXz66aINwU8/2WXbSERk99QdZWS+Pn36CAAiNjbW5PMNGjQQLi4uJW7jypUrAoDo3Lmzyef37NkjAIgJEyZYdb+ZmZkiOTnZcIuPjzd7XOTVw/EiF8YFyXLgWGR8s72sJ+LjRZ7OeL08BxOV6ks7cwjXq5j1hDCvKJ4djPcujdK8JfHxQuh0+WPHgTRNHdry+FMpjr2MHY+Liyv2dvnyZZGYmGi1fanVRprCNq/81mPbaKPrCcG2sRismSLZS7tHVFnYXDLliSeeEADEkSNHTD7v5+cnatSoUeI2lA/skJAQk89v3LhRABCvv/66VfdbWFk/MPeMXiJy4Gg4ydoz2nRDbC/riSVLhP7fEw99SScepT1B4XoVs54QlepEsLRK85bMn58mAA8BeAgHhzTNHdry+FMxhSeV5lOrjSwNtnlsG7nev9g2FpGWliY8PDyEh4cHkyls94hshs0lU6ZMmSIAiFWrVhV57vbt2wKA6NSp0z23U6dOHeHp6Slyc3OLPPfZZ58JAGJRgak2rLXfgiyd2eD4Z/eeIcNe1iv1iQfX09Z6VGZaP7QV8afCk0rzqdVGlgbbPLaNXI+oZGz3iGyLzSVTtmzZIgDLp30cNmyYAEo/7aO19lsQPzCJiIrHz0jzqdVGlgaPJxFRyfg5SWRbHKxbgaX89e7dGw0aNMDKlSsRFRVlWJ6amoqZM2fCyckJY8aMMSxPTEzEmTNnkJiYaLSdCRMmAADefvttZGdnG5b/8ccf2Lp1K7p162Y05aO5+yUiosrn2WefvWeB19JavXo1Vq5cadZr1GojiYiIiCobm0umODk5YcmSJdDr9ejatSsmTJiA1157DS1atEBMTAxmzJhhdII3b948NGvWDPPmzTPaTs+ePTFu3Djs3bsXrVq1whtvvIHRo0fjkUcegY+PDxYsWGDRfomIyiozMxOPPPIIHnnkEWRmZqodDplh0aJFaNSoEcaNG4c9e/aY/fqbN28a2q2RI0fi0qVLZr1erTaSiMgSbPeIyBbZ3NTIgDzJ27dvH6ZPn44ff/wR2dnZCA4OxsyZMzFy5MhSb2fhwoUICwvDwoUL8cUXX8DLywv9+/fHe++9ZzIxYq39EhGVJC8vD5s2bTI8JtsRFRWFN998E8uWLcPy5ctRt25dPPTQQ2jfvj3atGmDOnXqoFq1anBxcUFycjJu376N06dP48iRI9i3bx927dqFvLw8VK9eHZ999hkmT55sdgxqtZFERGXFdo+IbJFOCCHUDqKySklJga+vL5KTk+Hj46N2OESkEenp6fDy8gIApKWlwdPTU+WI1GHLn5F79+7FvHnz8OuvvyI7Oxs6na7E9ZWmuFGjRhg/fjwmTZoEb2/vigi1wtjy8SSi8sV2T+LnJJFtscmeKURERFrWtWtXdO3aFYmJiVi/fj327t2LAwcOID4+Hrm5uYb1fHx80LJlS3Tp0gV9+/ZFt27dVIyaiIiIiEqLyRQiIqJy4ufnhwkTJhgKugJAUlISMjMzDcN9iIiIiMj2MJlCRERUDm7cuIHIyEhkZWWhfv36aNu2LRwcHFClShW1QyMiIiIiCzGZQkREZGVvvfUW5syZY1RIsVq1apg+fTqef/55FSMjIiIiImtgMkVFSsHBlJQUlSMhIi1JT083PE5JSam0Mxson422Vid92bJlmD17tuFnR0dH5OXl4datW3jppZdw5coVfPDBBypGqA62eURUHLZ7kq22e0SVFWfzUVFCQgL8/f3VDoOISNPi4+NRv359tcMotY4dOyIyMhLDhg3DnDlzULNmTVy+fBlLlizBJ598gtzcXBw6dAht27ZVO9QKxTaPiKh0bK3dI6qsmExRkV6vx9WrV+Ht7X3PaTMLS0lJgb+/P+Lj4zl1mgbweGgLj4d2WHIshBBITU1F3bp14eDgUE4RWp+3tzdcXFxw9epVuLq6Gj23fPlyjB07FmPHjsXixYtVilAdbPPsB4+HtvB4aEtlbPeIKisO81GRg4ODxVlnHx8fNpwawuOhLTwe2lHWY+Hr61sO0ZSv9PR0hISEFEmkAMCYMWPw2muvYe/evSpEpi62efaHx0NbeDy0pTK1e0SVFVOeREREVubs7GxyuU6nQ+PGjXHlypUKjoiIiIiIrInJFCIiogrk7OyMjIwMtcMgIiIiIgswmWKjXF1dMX36dJPdyKni8XhoC4+HdlTWY3Hx4kV8+umn2L59O27cuKF2ODavsv4daRWPh7bweGgLjwdR5cECtERERFakFA0sWGS1Ro0aCAsLQ4sWLbB+/XrExcVV2qk/iYiIiOwBkylERERWtGbNGkRFRSE6OhpRUVH4559/DM8VTLB4eHggODjYkGQJCwtDWFgYiw8SERER2QAmU4iIiMrRzZs3jZIr0dHROHv2LHJzcw3rFEyy+Pv7Iy4uToVIiYiIiKi0mEwhIiKqYFlZWYiJiTFKspw4cQLJycnQ6XQcAkRERESkcUymEBERaURcXByio6MxYMAAtUMhIiIiohJwNh8bExkZiYcffhhVq1aFp6cn2rdvj5UrV6odlt36/vvvMXHiRLRt2xaurq7Q6XT45ptvil0/JSUFr776KgIDA+Hq6orAwEC8+uqrSElJqbig7diVK1cwd+5c9O3bFwEBAXBxcUHt2rXx+OOP488//zT5Gh6T8pOUlIQXX3wRDzzwAGrXrg1XV1fUq1cPvXr1wrp162AqV8/jUbKgoCAmUgpgm1fx2O5pB9s8bWGbR0SFsWeKDdm1axfCw8Ph4uKCYcOGwdfXF+vXr8elS5fw3nvvYerUqWqHaHeCgoJw+fJl+Pn5wdPTE5cvX8by5csxZsyYIuump6ejS5cuiIqKQp8+fdC6dWtER0djy5YtaNmyJfbt2wdPT8+K/yXsyFtvvYWPPvoIDRs2RPfu3VGzZk3Exsbil19+gRACq1atwpAhQwzr85iUr/Pnz6Nly5bo2LEjGjVqhGrVquHGjRvYsGEDbty4gfHjx2PRokWG9Xk8yBxs89TBdk872OZpC9s8IipCkE3IyckRDRs2FK6uruLYsWOG5SkpKSI4OFg4OTmJc+fOqRihfdq+fbuIi4sTQgjxwQcfCABi+fLlJtedNm2aACDeeOMNk8unTZtW3uHavXXr1ok9e/YUWb5nzx7h7OwsqlWrJjIzMw3LeUzKV25ursjJySmyPCUlRTRv3lwAEKdOnTIs5/Gg0mKbpx62e9rBNk9b2OYRUWFMptiIrVu3CgDi6aefLvLc6tWrBQAxZcoUFSKrPEo6qdTr9aJu3brCy8tLpKWlGT139+5dUbVqVVGvXj2h1+srKNrKp2/fvgKAiIyMFELwmKjtlVdeEQDEL7/8IoTg8SDzsM3TBrZ72sU2T1vY5hFVTqyZYiN27doFAOjbt2+R55Rlu3fvrsiQqIDY2FhcvXoVnTt3LtJl083NDd26dcOVK1dw/vx5lSK0f87OzgAAJycnADwmasrMzMTOnTuh0+nQvHlzADweZB62edrH/2l1sc3TDrZ5RJWXk9oBUOnExsYCABo3blzkuapVq8LPz8+wDlW8ko5PweWxsbHFrkNl9/fff2PHjh2oXbs2QkNDAfCYVKSkpCTMnTsXer0eN27cwKZNmxAfH4/p06cbvc8AjweVDts87eP/tHrY5qmLbR4RKZhMsRHJyckAAF9fX5PP+/j4ICEhoSJDogJKc3wKrkfWk5OTgyeffBJZWVmYPXs2HB0dAfCYVKSkpCS88847hp+dnZ3x8ccf4z//+Y9hGY8HmYNtnvbxf1odbPPUxzaPiBQc5kNENkuv1+OZZ57Bnj17MH78eDz55JNqh1QpBQUFQQiB3NxcXLp0Ce+++y7++9//4vHHH0dubq7a4RER2QW2edrANo+IFEym2Agls11cBjslJaXY7DeVv9Icn4LrkeWEEBg/fjy+//57jBo1Cl9//bXR8zwmFc/R0RFBQUF46623MGvWLPz8889YvHgxAB4PMg/bPO3j/3TFYpunPWzziIjJFBtReAxmQXfu3EFiYiLHXKqopONTcDmPkXXo9XqMHTsWy5Ytw/Dhw/HNN9/AwcH444zHRF1KkVClkCiPB5mDbZ728X+64rDN0z62eUSVE5MpNqJ79+4AgG3bthV5TlmmrEMVr3Hjxqhbty7279+P9PR0o+cyMzOxZ88e1K1bF40aNVIpQvuh1+sxbtw4LF++HEOHDsWKFSsMY8YL4jFR19WrVwHkzzTB40HmYJunffyfrhhs82wD2zyiyonJFBvRu3dvNGjQACtXrkRUVJRheWpqKmbOnAknJyeMGTNGtfgqO51Oh3HjxiEtLQ3vvvuu0XMffPAB7ty5g3HjxkGn06kUoX1Qrs4tX74cgwcPxvfff2/ypBLgMakIUVFRJrsw3759G1OnTgUAPPTQQwB4PMg8bPO0j//T5Y9tnrawzSOiwnRCCKF2EFQ6ERERCA8Ph6urK4YPHw4fHx+sX78ely5dwqxZs/Df//5X7RDtzpIlS7Bv3z4AwMmTJ3Hs2DF07tzZcCVh4MCBGDhwIAAgPT0dXbp0QVRUFPr06YM2bdogOjoamzdvRsuWLbFv3z54enqq9avYhRkzZuCdd96Bl5cXXnrpJcMVoIIGDhyIli1bAuAxKW8vv/wylixZgp49eyIwMBCenp64fPkyfv/9d6SlpeHxxx/Hjz/+aOiOzuNB5mCbpw62e9rBNk9b2OYRURGCbMqff/4p+vXrJ3x9fYW7u7to27at+P7779UOy26NHj1aACj2Nn36dKP1k5KSxCuvvCL8/f2Fs7Oz8Pf3F6+88opISkpS5xewM/c6HgDE8uXLjV7DY1J+9u7dK8aMGSPuv/9+4ePjI5ycnETNmjVFv379xMqVK4Very/yGh4PMgfbvIrHdk872OZpC9s8IiqMPVOIiIiIiIiIiMzAmilERERERERERGZgMoWIiIiIiIiIyAxMphARERERERERmYHJFCIiIiIiIiIiMzCZQkRERERERERkBiZTiIiIiIiIiIjMwGQKEREREREREZEZmEwhIiIiIiIiIjIDkylERERERERERGZgMoWIiIiIiIiIyAxMphARERERERERmYHJlEomIyMDjo6O8PT0hF6vL/N2dDoddDqdFSNTR1BQEHQ6HeLi4tQOxeZFR0fj0UcfRbVq1eDg4ACdToddu3apHZZNKu69LOnvlX/LREWxzTPGzwnrYZtnPWzziMhWOakdAFWsU6dOQa/XIyQkBA4OzKXZm7lz5yIpKQkvv/wyqlSpUmH7vXHjBnr27Ik7d+6gXr16aNasGXQ6HXx9fSsshrL65ZdfsHnzZhw5cgRXr17FrVu34OHhgebNm2Po0KGYPHkyXFxcin39pk2bMGfOHBw7dgxZWVlo2rQpnn76aTz33HNl+h+z5feSSGvY5tk3tnnmY5tHRGQ9TKZUMtHR0QCAsLAwlSOh8jB37lxcvnwZY8aMqdATy9WrV+POnTsYMGAA1q9fb1NfWj755BPs378frq6uqFu3Llq0aIFr167h4MGDOHjwIFasWIEdO3aYfD8//PBDTJkyBQDQoEEDeHl5ITo6Gi+++CJ27NiBn3/+2ez3oqzvZcOGDeHm5gZnZ2ez9kdkz9jm2Te2eeZjm0dEZD228+lPVqGcWLZo0ULlSMienDlzBgAQHh5uUyeVADBu3DhEREQgNTUVFy9eRGRkJBISEnDw4EHUr18fR48exX//+98irzt48CCmTp0KBwcHrFy5EhcuXEB0dDSOHTuGWrVq4bfffsOcOXPMjqes7+Uff/yBM2fOoF69embvk8hesc2j8sA2j20eERHAZEqlc+LECQA8sSTrunv3LgDA3d1d5UjMN2bMGPTo0aPI1a2OHTsaTgx/+eWXIq+bNWsWhBAYN24chg8fbljeokULw+s+/PBD5OTkmBWPLb+XRFrDNo/Kgy1/TrPNIyKyIkGViq+vrwAgkpKSjJZnZWWJCRMmCACiefPmIjY2tsTtABDKn8+mTZtE165dhZeXl/Dx8RH9+vUTx44dK/H1OTk5YsGCBaJz587C19dXuLq6iqZNm4r//ve/Ijk5ucj6J0+eFNOmTRMdO3YUtWvXFs7OzqJ27dpi0KBBYv/+/SXuKy4uTowcOVLUqFFDuLu7i9DQUDFv3jyh1+tFYGCgACAuXbpU5DUTJkwQ9913n3BxcRFeXl7ivvvuEwMHDhSrVq0qcX+mJCYmitdff100adJEuLm5iSpVqoju3buL77//Xuj1eqN1L126JACIwMDAYrdX8P0XQojly5cblpm6RURElEus06dPL3af3bt3v+e+LP07Km8nTpwQAESVKlWMlicnJwsXFxcBQPz5559FXpednS18fHwEALF169ZS7as072Vxf68lPVfwPf7hhx9Eu3bthKenp6hataoYMGCAOHnypMl4rP0/QKQGtnls86wZK9s8tnlERAUxmVKJFHfCcvXqVfHAAw8IAKJ///4iJSXlnttSGqsFCxYInU4n6tSpI1q3bi08PT0FAOHl5SVOnz5t8rXJycmiW7duAoBwcHAQgYGBIiQkxNBQN2vWTFy/ft3oNb179zY08M2aNROtW7cWfn5+AoBwdHQUP/zwg8l9/fXXX6J69eoCgHBzcxNt2rQRAQEBAoB49tlnTTbGly5dMmzbw8NDhIaGipYtW4pq1aoJAKJFixb3fH8Kio2NFf7+/gKAcHFxEa1btxYNGjQwvIdPPfWU0QlbWU4sN23aJDp37ixcXV0FANG2bVvRuXNnw620J2jmxrp06VLRuXNnUbNmTQFANG7c2LDP559//p77s+TvqCIsXLhQABC9evUyWr5r1y7D31ROTo7J1yp/s++++26p9lWa99KSE8uPPvpIABC1a9cWbdu2Fd7e3gKAcHd3F3v37jV6jbX/B4jUwDaPbZ61Y2WbxzaPiKggJlMqkV9//dVw8qjYv3+/qFOnjgAgpk6dWuQqTHGUxsrDw0MsX77csDwlJcXQoA4dOtTka4cNGyYAiN69e4sLFy4Ylt++fVv83//9nwAgnnjiCaPXrF27Vpw4ccJomV6vF7/88ovhqk7hE2K9Xi9at24tAIjw8HBx69Ytw3OrVq0Szs7OwsnJqUhj/PzzzwsAYvTo0SI1NdVom6dPnxYLFy4s1XukxNC2bVvDlZZ//vnH8NzmzZsNJ1BfffWVYXlZTiwVJZ14lEesitGjRwsARn8LpWHJ39F7771ndPJc2tu9TrJzc3NFfHy8mD9/vvD29haenp5FrsQtXrxYABBNmjQpdjvjx48XAMSTTz5Z+jdElPxeWnJi6ezsLD799FORl5cnhBAiPT1djBw50vC3lpGRYXiNNf8HiNTCNo9tnrVjVbDNK4ptHhFVRkymVCLvvvuuACDefvttIYQQX3/9tXBxcREeHh5izZo1Zm1LaaxeeOGFIs8p3UR9fX2LPBcdHW1oyExdDUxPTxf+/v5Cp9OJuLi4UsXy9ttvCwBFrtTt2LHDcBXi5s2bRV734osvGn6Pgo1xeHi4ACCio6NLtf+SbN++XQAQrq6u4tq1a0Wenz17tuH9UE7q1TqxLEusCktPLM39Oyq4T3NvxXX//uyzz4qsO3DgQJNdgpX3okOHDsX+bm+88YYAIB599NFSvReFfy9rn1g+9thjRV6TlZUlateuLQCIZcuWGZZb83+ASC1s84yxzbM8VgXbvKLY5hFRZcQCtJWIMqvB/fffjwkTJmDSpEmoU6cODhw4gCFDhpRpm+PGjSuyLDQ0FG5ubkhOTsatW7eMnvv5558BAEOGDIG3t3eR13p4eODBBx+EEAJ79+41eu7vv//Ghx9+iCFDhqBXr17o0qULunTpgjVr1hj9foqtW7cCAAYPHgw/P78i+3r22WdN/k7+/v4AgJ9++glCCJPrlNa2bdsMMdSuXbvI85MmTYKrqysuX76Ms2fPWrQvS6kZq7l/RwDwzTffQMiEsFm3Hj16mIyhXr166Ny5M9q3b49atWoBACIiIrBq1Srk5eUZrZuZmQkAcHFxKfZ3cnV1BZBfXE9tzz33XJFlLi4uhvde+X8BrPs/QKQWtnnG2OYZY5vHNk/BNo+IyspJ7QCo4iizGkydOhV///03unfvjrVr16JGjRpl3mbDhg1NLq9Rowbi4+ORlpaG6tWrG5afPHkSgDzBPHDggMnXXr58GQBw5coVw7Jvv/0WkyZNMjTopty+fdvo53PnzgEAmjVrZnL9xo0bw8nJCbm5uUbLn3vuOXz77beYOXMmvvvuO/Tr1w9du3ZFz549Ubdu3WL3b4oSQ/PmzU0+7+3tDX9/f5w/fx7nzp3D/fffb9b2rUnNWM39OyoPgwcPxuDBgw0///nnn5g4cSLef/993L59GwsWLDA85+bmBgDIzs4udntZWVkAtDNDQXH/B8py5fgD1v0fIFIL2zxjbPOMsc1jm6dgm0dEZcWeKZVEeno6Lly4ADc3N/zzzz8A5DR3lpxUAoCnp6fJ5Q4O8k+rcIY/OTkZAHD+/Hns37/f5C0hIQFA/tWNCxcuYPz48cjMzMR//vMfHD9+HCkpKdDr9RBCYPHixQBQZDq+tLQ0ACj2d3RwcDB59a5ly5bYs2cP+vbtiytXrmDhwoUYNWoU6tevj/DwcJw+fbpU703BGGrWrFnsOsoVodTU1FJvtzyoGau5f0cVoUOHDti0aRNcXV2xaNEiwxceAKhatSoA4M6dO8W+XnlOWVdtxR1XU8fUmv8DRGpgm2c6RrZ5+djmGWObxzaPiMzHnimVxMmTJ6HX69G6dWs8/fTTGD9+PIYMGYLIyEjUq1evwuLw8vICACxevNhkN1dTfvzxR+Tk5GDYsGH45JNPijwfHx9f4r5u3rxp8nm9Xm+yKy0AdOzYEVu3bkVaWhr279+PiIgIrFy5Etu2bUOfPn1w6tQpVKlS5Z6xKzHcuHGj2HWuX78OAIYu4DqdDkDxJ1Pp6en33G9ZlCVWNb3//vvYtGmT2a/78ssv0apVq1KtW7duXbRs2RJ//vknoqOjERgYCEBe4QVkN/zc3Fw4ORX9KL148aLRumq7efMm6tevX2S5crwLH1Nr/Q8QqYFtXlFs84yxzSuKbR7bPCIyD5MplYTS3TksLAzjxo3DiRMn8OWXX2LgwIHYu3evoQtneWvevDl++eUXnDp1qtSviYuLAwB06tTJ5POFx40rmjRpAgA4c+aMyefPnz9f5MpeYV5eXggPD0d4eDimTZuGsLAwXLhwAZs3b8bw4cPvGbsSw19//WXy+dTUVMOJsbKucsWquBPi8+fPF7s/5aS0LMoSq5rOnTuH/fv3m/065UpxaSld4gt2jW/VqhWcnZ2RmZmJY8eOoX379kavycnJQWRkJAB5tU8LTp8+bfLEUrniVtwxtfR/gEgNbPOKYptneaxqYptnHrZ5RFQROMynklBOvsLCwgAAc+bMQa9evXDkyBGMHTu2wuIYNGgQAOD7778v9gpZYcr4W+UKUUFnzpzBhg0bTL6ub9++AIC1a9ea3NdXX31Vqv0rPDw8EBoaCgC4evVqqV4THh5uiEHpal7QwoULkZWVhcDAGuW4nAAABXBJREFUQDRt2hQAUL16dfj6+uLu3buIiYkp8polS5YUuz/lvSpLAbiyxKomaxfjMyUuLs7wv9OiRQvDch8fHzz44IMAgKVLlxZ53dq1a5GSkoLq1aubtb/yZOrvPTs72xC/8v9SkrL8DxCpgW0e27zyiFVNbPPMwzaPiCqEpdMBkW3o3LmzACD27dtnWHbr1i3RoEEDAUC8//77Zm0PxUxTqChpOrshQ4YIAKJVq1bi2LFjRs/l5uaKiIgIMWLECJGZmSmEEGLt2rUCgKhatao4fvy4Yd2zZ8+KkJAQ4ebmJgCI0aNHG21Lr9eLVq1aCQDioYceErdv3zY8t2bNGuHi4iKcnJyKxDlp0iSxevVqkZ6ebrS93bt3C29vbwFA7Ny58x7vUH4M7dq1EwBEjx49xPXr1w3Pbd26VXh5eQkAYsGCBSbfo759+4rU1FTD8m+++UZ4eHgU+/4/8sgjJrdXnrEKYfk0kcWxZNrL0jhy5IiYNm2auHDhQpHnNm/eLO6//34BQDz88MNFnt+3b5/Q6XTCwcFBrFy50rA8KipK1KpVSwAQH330kdkxldc0kc7OzmLu3LmGKT4zMjLEU089JQAIf39/o793a/4PEKmBbR7bvPKKVQi2eWzziIgkJlMqCR8fH6HT6URycrLR8lOnTglvb2/h4OAgfvvtt1Jvz5ITgtTUVNGnTx/DNgICAkSHDh1EaGiocHd3Nyy/e/euEEKInJwc0bFjRwFAODo6imbNmomQkBCh0+lEnTp1xKxZs0yeWCq/X7Vq1QQA4e7uLtq2bWuI7dlnnzUZZ4sWLQQA4eTkJJo1aybat29vWA+AGDVqVKnfJyGEiI2NFfXr1xcAhKurq2jdurVo1KiRYXtPPvmkobFXnD592nAi5+npKVq3bi3q1KljOLEr7v3/7rvvDM+FhISI7t27i+7duxudkFs7ViFs98QyIiLCEEPt2rVF27ZtRVhYmKhSpYphebt27cTNmzdNvl752wMgGjRoIMLCwoSDg4MAIB555BGRm5trdkzldWL50UcfGX7Pdu3aCR8fHwFAuLm5id27dxu9xtr/A0QVjW0e27zyilUItnls84iIJCZTKoGLFy8KACIoKMjk87/++qvQ6XTC29tbnDp1qlTbtPSEIC8vT/zwww8iPDxc+Pn5CWdnZ1GnTh3RoUMH8eabb4rDhw8brZ+cnCxeeOEFUbduXeHs7Czq168vxo0bJ65evSqWL19e7Iml8vuPGDFCVK9eXbi5uYnQ0FDx5ZdfCr1ebzLOnTt3ipdeekm0bt1a1KhRQ7i4uIjAwEARHh4ufvvtN5MnVvdy8+ZN8dprr4nGjRsLV1dX4ePjI7p16yZWrFhR7PaOHTsm+vXrJ7y9vYWnp6fo1KmT2LBhgxCi5Pf/888/F2FhYUYn6REREeUaq62eWN6+fVt8/vnn4rHHHhMNGzYUXl5ewsXFRdSpU0c89NBDYvny5SInJ6fEbWzYsEH06tVL+Pr6Cg8PD9GiRQsxd+7cMp1UClF+J5ZCCPHDDz+Idu3aCQ8PD+Hr6ysee+wxER0dXWRb5fE/QFRR2OaxzWObZxrbPLZ5RGRdOiFUmH+NiIgqxL1myiAiIrIXbPOIqCKxAC0RERERERERkRmYTCEiIiIiIiIiMgOTKUREREREREREZmAyhYiIiIiIiIjIDCxAS0RERERERERkBvZMISIiIiIiIiIyA5MpRERERERERERmYDKFiIiIiIiIiMgMTKYQEREREREREZmByRQiIiIiIiIiIjMwmUJEREREREREZAYmU4iIiIiIiIiIzMBkChERERERERGRGZhMISIiIiIiIiIyA5MpRERERERERERm+H+8B0NtTIk1ywAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "viz_coin_flip_H0_H1(k=unlucky_k, n=n_flips, p_null=p_fair, show_h1=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's pause here to think about the flow of logic in these conclusions.\n",
    "\n",
    "- Does the fact that our data reject the null hypothesis validate $H_1$?\n",
    "\n",
    "- the $H_1$ PDF describes this particular experiment very well (because it's the MLE!). Does it mean that it is the correct model?\n",
    "\n",
    "- How many alternative distributions are potentially consistent with our observed data?\n",
    "\n",
    "- What happens if our null hypothesis is poorly formulated or incorrect? Or our experiment does not directly test the null hypothesis?\n",
    "\n",
    "- Finally, what if the priors on our two hypotheses - $H_0$ and $H_1$ - are not equal?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLE for a normal distribution\n",
    "\n",
    "Now let's switch gears to something a little more involved. Suppose we observe $n$ data points $x_1, \\dots, x_n \\sim N(\\mu, \\sigma)$. Just as we did for binomial distribution, let's try to maximize the likelihood of the observed data with respect to the parameters that describe it.\n",
    "\n",
    "For a single point $x$, the normal probability density function is\n",
    "\n",
    "$$P(x| \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
    "\n",
    "The joint probability of $n$ points, assuming they are all independently, identically distributed:\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "P(x_1, \\dots, x_n \\mid \\mu, \\sigma^2) &= P(x_1 \\mid \\mu, \\sigma^2)\\cdot P(x_2 \\mid \\mu, \\sigma^2)\\dots P(x_n \\mid \\mu, \\sigma^2) && \\text{assume data is IID} \\\\\n",
    "&= \\prod_{i=1}^n P(x_i \\mid \\mu, \\sigma^2) && \\text{use index notation} \\\\\n",
    "&= \\prod_{i=1}^n \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\big(-\\frac{(x_i-\\mu)^2}{2\\sigma^2} \\big) && \\text{plug in PDF}\\\\\n",
    "&= \\bigg(\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\bigg)^n \\times \\bigg[ \\prod_{i=1}^n \\exp\\big(-\\frac{(x_i-\\mu)^2}{2\\sigma^2} \\big) \\bigg] && \\text{pop out the constant from the product}\\\\\n",
    "&= \\big(2\\pi\\sigma^2\\big)^{-\\frac{n}{2}} \\times \\bigg[ \\prod_{i=1}^n \\exp\\big(-\\frac{(x_i-\\mu)^2}{2\\sigma^2} \\big) \\bigg]&& \\text{rewrite constant a little bit} \\\\\n",
    "&= \\big(2\\pi\\sigma^2\\big)^{-\\frac{n}{2}} \\times \\exp\\bigg( -\\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\bigg) && \\text{product of logs is log of sum}\\\\\n",
    "\\end{aligned}$$\n",
    "\n",
    "At this point it will be convenient to take the log again:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\log P(x_1, \\dots, x_n \\mid \\mu, \\sigma^2) &= \\log \\bigg[ \\big(2\\pi\\sigma^2\\big)^{-\\frac{n}{2}} \\times \\exp\\bigg( -\\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\bigg) \\bigg] \\\\\n",
    "&=  -\\frac{n}{2}\\log\\big(2\\pi\\sigma^2\\big) + \\log \\bigg[ \\exp \\bigg( -\\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\bigg) \\bigg] \\\\\n",
    "&=  -\\frac{n}{2}\\log\\big(2\\pi\\sigma^2\\big) - \\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\\\\n",
    "\\end{aligned}$$\n",
    "\n",
    "#### MLE of $\\mu$\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{d}{d\\mu} \\log P(x_1, \\dots, x_n\\mid \\mu, \\sigma^2) &= 0 \\\\\n",
    "\\frac{d}{d\\mu} \\bigg( -\\frac{n}{2}\\log\\big(2\\pi\\sigma^2\\big) - \\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\bigg ) &= 0 \\\\\n",
    "\\sum_{i=1}^N \\frac{-\\frac{d}{d\\mu} (x_i-\\mu)^2}{2\\sigma^2} &= 0 \\\\\n",
    "\\sum_{i=1}^N \\bigg( \\frac{x_i-\\mu}{\\sigma^2} \\bigg) &= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "Multiplying both sides by $\\sigma$ and rearranging gives us our likelihood-maximizing $\\mu$:\n",
    "\n",
    "$$\\hat{\\mu} = \\frac{\\sum_{i=1}^n x_i}{n}$$\n",
    "\n",
    "The maximum likelihood estimate of the mean given some observed $x_i$'s is the sample mean.\n",
    "\n",
    "#### MLE of $\\sigma^2$\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\log P(x_1, \\dots, x_n \\mid \\mu, \\sigma^2) = \\log L(\\mu, \\sigma^2) = -\\frac{n}{2}\\log\\big(2\\pi\\sigma^2\\big) - \\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2\\sigma^2} \\\\\n",
    "\\end{aligned}$$\n",
    "\n",
    "Taking derivative wrt $\\sigma^2$:\n",
    "\n",
    "\n",
    "$$\\frac{\\partial}{\\partial\\sigma^2} \\log L(\\mu, \\sigma^2) =  -\\frac{n}{2\\sigma^2} + \\sum_{i=1}^n \\frac{(x_i-\\mu)^2}{2(\\sigma^2)^2} = 0 $$\n",
    "\n",
    "Skipping some steps here (it is a good exercise to do these calculations by hand), we arrive at our estimate:\n",
    "\n",
    "$$\\hat{\\sigma^2} = \\frac{1}{n}\\sum_{i=1}^n (x_i-\\mu)^2$$\n",
    "\n",
    "This expression is not too surprising -- it's the average squared distance from the mean over all data points. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimation of Gaussian parameters only given data... the road to the T-distribution\n",
    "\n",
    "\n",
    "Let's say we observe some small number of data points $x_1, \\dots, x_n$ (around $n=5$) that we assume are generated by a Gaussian process, $x_1, \\dots, x_n \\sim N(\\mu, \\sigma^2)$, and we'd like to use the data to estimate $\\mu$ and $\\sigma$.\n",
    "\n",
    "From our analysis above, \n",
    "- the maximum likelihood estimator for the mean is the sample mean: $\\hat{\\mu} = \\bar{x} = \\frac{1}{N} \\sum_{i=1}^n x_i$\n",
    "- the maximum likelihood estimator for the variance is: $\\hat{\\sigma^2} = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\mu)^2$\n",
    "\n",
    "Wait a second. The MLE for the variance includes $\\mu$, something we're trying to estimate with $\\bar{x}$!\n",
    "\n",
    "If we plug in $\\bar{x}$ for $\\mu$ to get a new estimator for the variance, $\\hat{\\sigma^2} = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\bar{x})^2$, it turns out that this estimator is biased. An estimator $\\hat{\\theta}$ of a parameter $\\theta$ is a function of data and is biased if the expected value of $\\hat{\\theta}$ over all possible data is not exactly $\\theta$. A small correction is needed to yield an unbiased estimator of the population variance: $\\frac{1}{n-1}$ rather than $\\frac{1}{n}$. This is the Bessel correction -- you can read more about it [here](https://en.wikipedia.org/wiki/Bessel%27s_correction) and [here](https://en.wikipedia.org/wiki/Bias_of_an_estimator#Sample_variance), and it you want to see a proof you can find that [here](https://gregorygundersen.com/blog/2019/01/11/bessel/).\n",
    "\n",
    "So, given some data, an unbiased estimator of the population variance is the (Bessel-corrected) sample variance, $S^2 = \\frac{1}{n-1}\\sum_{i=1}^n (x_i - \\bar{x})^2$\n",
    "\n",
    "Let's see this in action. In the notebook you can use the function below to specify the true mean and standard deviation of a Gaussian, specify a number of data points $n$ to sample from that Gaussian, and visualize what an \"estimated\" Gaussian would look like, with mean $\\bar{x}$ and standard deviation $S = \\sqrt{\\frac{1}{n-1}\\sum_{i=1}^n (x_i - \\bar{x})^2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "random seed: 290\n",
      "inputs:\n",
      "\tn: 4\n",
      "\ttrue mu: 2.00\n",
      "\ttrue sigma: 4.00\n",
      "estimates:\n",
      "\tXbar: -0.65\n",
      "\tS: 1.30\n",
      "4 generated data points:\n",
      "\t[-1.75485318 -1.5817379  -0.3070837   1.03787662]\n"
     ]
    }
   ],
   "source": [
    "estimate_normal_from_sample(n=4, true_mu=2, true_sigma=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spend some time playing around with this. If you like the result from a particular random seed, you can input it into the function. Roughly how big does $n$ need to be to make the estimated PDF overlap with the true PDF?\n",
    "\n",
    "#### The distributions of $\\bar{x}$ and $S$\n",
    "Now, let's fix a true $\\mu$ and $\\sigma$ for a Gaussian and set a number $n$ of datapoints. We will generate a sample of $n$ datapoints, compute $\\bar{x}$ and $S$ as our estimates for $\\mu$ and $\\sigma$, store them, and then repeat this sample generation some large number of times.\n",
    "\n",
    "Our goal is to make histograms for $\\bar{x}$ and $S$ to see what their distributions look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 4\n",
    "true_mu = 35\n",
    "true_sigma = 5\n",
    "all_Xs, all_Xbars, all_Ses = get_dist_of_xbar_and_S(n, true_mu, true_sigma, n_experiments=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we should see here is that the distribution of $\\bar{X}$ looks like a normal centered around the true $\\mu$. This is consistent with the expression for $\\bar{X} = \\frac{1}{n} \\sum_{i=1}^n x_i$. A sum of normals is [still a normal](https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables), and any multiplicative factor on a normally distributed variable is still normally distributed, the distribution is just scaled.\n",
    "\n",
    "The distribution of $S$, the sample standard deviation, looks a little different. It's rather skewed, and it's not symmetric around the true $\\sigma$ (at low $n$ at least -- though you should test what happens if $n$ is large). At low $n$, the bulk of the $S$'s are lower than the true $\\sigma$, indicating that most of the time, the sample standard deviation underestimates the population standard deviation. \n",
    "\n",
    "What is up with this shape? Recall that $S = \\sqrt{\\frac{1}{n-1}\\sum_{i=1}^n (x_i - \\bar{x})^2}$ -- it is the square root of a sum of *squared* normals. In general, the sum of $K$ independent squared standard normal random variables follows a [$\\chi^2$ distribution](https://en.wikipedia.org/wiki/Chi-square_distribution) with $K$ degrees of freedom. In our case, there are $n-1$ independent terms (given $\\bar{X}$ and the first $n-1$ $X_i$'s, you can always compute what the $n$th one is), so $n-1$ degrees of freedom. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scoring data\n",
    "\n",
    "Given a sample of data $X_1, \\dots, X_n$ and a computed $\\bar{X}$, if we assume the underlying population is $\\mu_0$, how likely is it that we'd observe this particular $\\bar{X}$?\n",
    "\n",
    "To figure this out, $\\bar{X} - \\mu_0$ is of key importance. I would be willing to reject the hypothesis that $\\mu_0$ is the mean of $X$ if my $\\bar{X}$ is much larger than $\\mu_0$. But how large is large? How far off would I expect $\\bar{X}$ to be from the population mean by chance? The distance needs to be put in context. \n",
    "\n",
    "A natural unit is the standard deviation of $\\bar{X}$, which is a \"typical\" distance a particular $\\bar{X}$ is away from the population mean. We can find the standard deviation of $\\bar{X}$ by working with its square, variance: $[SD(\\bar{X})]^2 = Var(\\bar{X})$:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "Var(\\bar{X}) &= Var\\big( \\frac{1}{n} \\sum_{i=1}^n X_i \\big) = \\frac{1}{n^2} Var\\big( \\sum_{i=1}^n X_i \\big) = \\frac{1}{n^2}  \\sum_{i=1}^n Var( X_i ) = \\frac{1}{n^2} \\big[  n Var( X ) \\big] = \\frac{1}{n} \\sigma^2\\\\\n",
    "\\end{aligned}$$\n",
    "\n",
    "So, $SD(\\bar{X}) = \\frac{\\sigma}{\\sqrt{n}}$.\n",
    "\n",
    "With this unit in place, we now have a \"standard score\" describing the number of standard deviations away $\\bar{X}$ is from a putative mean $\\mu_0$: \n",
    "$$\\text{standard score} = \\frac{\\bar{X} - \\mu_0}{SD(\\bar{X})} = \\frac{\\bar{X} - \\mu_0}{\\sigma / \\sqrt{n}}$$\n",
    "\n",
    "Note that this score depends on $\\sigma$! \n",
    "\n",
    "**If we know $\\sigma$**, then the denominator is a constant, and the only randomness that's left is within $\\bar{X}$, a sum of normal random variables, making the entire term a normal random variable. This kind of score is called a Z score: \n",
    "\n",
    "$$ Z = \\frac{\\bar{X} - \\mu_0}{\\sigma / \\sqrt{n}}$$ \n",
    "\n",
    "Z scores follow a standard normal distribution, $N(0, 1)$, making it easy to set quantiles to determine cutoffs for p-values and do other calculations.\n",
    "\n",
    "**If we don't know $\\sigma$**, we need to estimate it with the sample standard deviation, $S = \\sqrt{\\frac{1}{n-1}\\sum_{i=1}^n (X_i - \\bar{X})^2}$. We replace $\\sigma$ with $S$ to get what's called a T score:\n",
    "\n",
    "$$ T = \\frac{\\bar{X} - \\mu_0}{S / \\sqrt{n}}$$ \n",
    "\n",
    "T scores follow [Student's t distribution](https://en.wikipedia.org/wiki/Student's_t-distribution) with $n-1$ degrees of freedom. If $Z$ is a standard normal random variable, and $V$ follows a $\\chi^2$-distribution with degrees of freedom $\\nu$, then $\\frac{Z}{\\sqrt{V/\\nu}}$ follows Student's t-distribution with $\\nu$ degrees of freedom. The T score written above follows this exact form, as $\\bar{x}$ is a sum of normals, and $S$ is the square root of a sum of $n-1$ independent squared normals, divided by $n-1$. \n",
    "\n",
    "So, some takehome messages:\n",
    "- if $\\sigma$ is known, we can do hypothesis testing on $\\bar{X}$ by computing a Z score, which follows a standard normal ($N(0, 1)$) distribution\n",
    "- if $\\sigma$ is unknown, we compute a T score with our sample standard deviation $S$ in the denominator instead. Such scores follow Student's t distribution with $n-1$ degrees of freedom. $S$ depends on the data, and has considerable spread, as seen in the histogram above -- it's not a constant!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### T vs Z distributions\n",
    "\n",
    "Let's actually compare the distribution of Z scores vs. the distribution of T scores by taking the samples above and building histograms of $ Z = \\frac{\\bar{X} - \\mu}{\\sigma / \\sqrt{n}}$  and $ T = \\frac{\\bar{X} - \\mu}{S / \\sqrt{n}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# uses the samples computed in previous code cell\n",
    "\n",
    "# compute Z scores with true mu, true sigma\n",
    "all_Zs = (all_Xbars - true_mu)/(true_sigma / np.sqrt(n))\n",
    "\n",
    "# compute T scores plugging in S for true sigma\n",
    "all_Ts = (all_Xbars - true_mu)/(all_Ses / np.sqrt(n))\n",
    "\n",
    "# find min/max for nice plotting\n",
    "totmin = min((min(all_Zs), min(all_Ts)))\n",
    "totmax = max((max(all_Zs), max(all_Ts)))\n",
    "\n",
    "# plot histogram\n",
    "plt.figure()\n",
    "b = np.linspace(totmin, totmax, 200)\n",
    "plt.hist(all_Zs, bins=b, density=True, alpha=0.5, label='Z')\n",
    "plt.hist(all_Ts, bins=b, density=True, alpha=0.5, label='T (df = {})'.format(n-1))\n",
    "plt.xlim(-8, 8); plt.ylabel('density'); plt.xlabel('score')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the distribution of T scores has fatter tails, giving more weight to outliers, than the Z distribution. \n",
    "\n",
    "The T distribution allows for $\\bar{X}$ to be \"far away\" from $\\mu$ because we had to estimate the true variance. The data could have had a small sample variance, making us underestimate the true variance, making us overestimate the \"distance\" between $\\bar{X}$ and $\\mu$. The T distribution gives more probability to large magnitude T scores that the Z distribution would say is unlikely.\n",
    "\n",
    "Try changing $n$ around a bit. How does the distribution of T scores compare to Z scores at large $n$? Why? Hint: does more data help us estimate the true variance better?\n",
    "\n",
    "We've made it! \n",
    "\n",
    "We have arrived at a t distribution through computing a standard score of a sample mean of normally distributed datapoints with an estimate of the population variance. The homework will show us another way the t distribution arises in a Bayesian setting, where we find the marginal distribution of the mean of a normal distribution, marginalizing over different possible variances."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "seq_analysis",
   "language": "python",
   "name": "seq_analysis"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
