{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "314a6850",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # para cálculos numéricos\n",
    "import matplotlib.pyplot as plt # visualização, gráficos\n",
    "from matplotlib import rcParams\n",
    "\n",
    "\n",
    "rcParams['font.family'] = 'serif'\n",
    "rcParams['font.serif'] = 'Times'\n",
    "#rcParams['svg.fonttype'] = 'none'\n",
    "plt.rc('text',usetex=True)\n",
    "\n",
    "import matplotlib as mpl \n",
    "mpl.rcParams['figure.dpi'] = 400 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efabe803",
   "metadata": {},
   "source": [
    "# Distribuições discretas\n",
    "\n",
    "Estatística I - Aeronáutica - 2023/02\n",
    "\n",
    "Thomas Peron "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3eada4b",
   "metadata": {},
   "source": [
    "## Distribuição geométrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "5519e770",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import geom\n",
    "\n",
    "\n",
    "\n",
    "p = 1/6\n",
    "K = np.arange(0,30)\n",
    "Pk = geom.pmf(K,p)\n",
    "\n",
    "fig = plt.figure(figsize=(6,3))\n",
    "plt.bar(K,Pk,edgecolor='C0',facecolor='lightgray')\n",
    "plt.ylabel(r'$\\textrm{Pr}\\{X = k\\}$',fontsize=13)\n",
    "plt.xlabel(r'$k$',fontsize=13)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8354c5cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.16666667, 0.13888889, 0.11574074, 0.09645062,\n",
       "       0.08037551, 0.0669796 , 0.05581633, 0.04651361, 0.03876134,\n",
       "       0.03230112, 0.0269176 , 0.02243133, 0.01869278, 0.01557731,\n",
       "       0.01298109, 0.01081758, 0.00901465, 0.00751221, 0.00626017,\n",
       "       0.00521681, 0.00434734, 0.00362279, 0.00301899, 0.00251582,\n",
       "       0.00209652, 0.0017471 , 0.00145592, 0.00121326, 0.00101105])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "dacf210d",
   "metadata": {},
   "source": [
    "## Distribuição binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a3b1e03e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "N = 50\n",
    "p = 0.2\n",
    "K = np.arange(0,30)\n",
    "Pk = binom.pmf(K, N, p)\n",
    "\n",
    "fig = plt.figure(figsize=(6,3))\n",
    "plt.bar(K,Pk,edgecolor='C0',facecolor='lightgray')\n",
    "plt.ylabel(r'$\\textrm{Pr}\\{X = k\\}$',fontsize=13)\n",
    "plt.xlabel(r'$k$',fontsize=13)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.tight_layout()    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f2e7122",
   "metadata": {},
   "source": [
    "### Várias visualizações"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "f1238e73",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 4800x5200 with 35 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = [1/8,1/4,1/2,3/4,7/8]\n",
    "N = np.arange(1,8)\n",
    "\n",
    "fig = plt.figure(figsize=(12,13))\n",
    "\n",
    "i=1\n",
    "for n in N: \n",
    "    for p in P: \n",
    "        \n",
    "        ax = plt.subplot(len(N),len(P),i)\n",
    "        i=i+1\n",
    "        K = np.arange(0,n+1)\n",
    "        Pk = binom.pmf(K, n, p)\n",
    "        plt.bar(K,Pk,edgecolor='C0',facecolor='lightgray')\n",
    "\n",
    "\n",
    "for i in range(1,6):\n",
    "    ax = plt.subplot(len(N),len(P),i)\n",
    "    ax.set_title(r'$p = '+str(P[i-1])+r'$',fontsize=15)\n",
    "        \n",
    "for i in range(0,7):\n",
    "    ax = plt.subplot(len(N),len(P),5*i+1)\n",
    "    ax.set_ylabel(r'$N = '+str(N[i])+r'$',fontsize=15)        \n",
    "        \n",
    "for ax in fig.get_axes():\n",
    "=\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)        \n",
    "plt.tight_layout()        \n",
    "plt.show()        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79f037fd",
   "metadata": {},
   "source": [
    "### Lançando várias moedas"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b13d3202",
   "metadata": {},
   "source": [
    "Variando o número de moedas $N$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "bbea868c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4800x6000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = np.arange(10,110,10) # Faremos vários experimentos, lançando um número diferente de moedas em cada um deles. \n",
    "p = 0.5    # moedas não viciadas.\n",
    "i=1\n",
    "\n",
    "fig = plt.figure(figsize=(12,15))\n",
    "\n",
    "for n in N: \n",
    "    \n",
    "        ax = plt.subplot(len(N),1,i); i=i+1\n",
    "        K = np.arange(0,70)\n",
    "        Pk = binom.pmf(K, n, p)\n",
    "        plt.bar(K,Pk,width=1.0,edgecolor='C0',facecolor='lightgray')\n",
    "        plt.ylim([0,0.25])\n",
    "        plt.text(s='$N='+str(n)+'$',x=62,y=0.06,fontsize=13)\n",
    "        \n",
    "plt.ylabel(r'$\\textrm{Pr}\\{X = k\\}$',fontsize=16)\n",
    "plt.xlabel(r'$k$',fontsize=16)\n",
    "\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)     \n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4386a04a",
   "metadata": {},
   "source": [
    "Variando a chance de sucesso $p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5e21b17b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 4800x6000 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P = np.arange(0.1,0.91,0.1) # Faremos vários experimentos, cada um com uma taxa de sucesso distinta. \n",
    "p = 0.5    # moedas não viciadas.\n",
    "i=1\n",
    "n=100\n",
    "fig = plt.figure(figsize=(12,15))\n",
    "\n",
    "for p in P: \n",
    "    \n",
    "        ax = plt.subplot(len(N),1,i); i=i+1\n",
    "        K = np.arange(0,100)\n",
    "        Pk = binom.pmf(K, n, p)\n",
    "        plt.bar(K,Pk,width=1.0,edgecolor='C0',facecolor='lightgray')\n",
    "        plt.ylim([0,0.18])\n",
    "        plt.text(s='$p='+str(np.round(p,2))+'$',x=90,y=0.2,fontsize=13)\n",
    "        \n",
    "plt.ylabel(r'$\\textrm{Pr}\\{X = k\\}$',fontsize=16)\n",
    "plt.xlabel(r'$k$',fontsize=16)\n",
    "\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)     \n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "391ce614",
   "metadata": {},
   "source": [
    "## Distribuição Binomial e Gaussiana"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "aa6f29c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom, norm\n",
    "\n",
    "\n",
    "N = 100\n",
    "p = 0.1\n",
    "\n",
    "\n",
    "kmax = 50\n",
    "\n",
    "K = np.arange(0,kmax)\n",
    "Pk = binom.pmf(K, N, p) #Binomial\n",
    "x = np.linspace(0,kmax,1000)\n",
    "Gauss = norm.pdf(x,loc=N*p,scale=np.sqrt(N*p*(1-p)))\n",
    "\n",
    "fig = plt.figure(figsize=(6,3))\n",
    "plt.bar(K,Pk,edgecolor='C0',facecolor='lightgray',label=r'Distribuição Binomial')\n",
    "plt.plot(x,Gauss,'-',linewidth=1.0,color='r',label=r'Gaussiana')\n",
    "plt.ylabel(r'$\\textrm{Pr}\\{X = k\\}$',fontsize=13)\n",
    "plt.xlabel(r'$k$',fontsize=13)\n",
    "plt.legend(loc='upper right')\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.tight_layout()    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "828e1e3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6,3))\n",
    "\n",
    "plt.bar(K,binom.cdf(K, N, p),linewidth=0.6,edgecolor='C0',facecolor='lightgray',label=r'Distribuição Binomial')\n",
    "plt.plot(x,norm.cdf(x,loc=N*p,scale=np.sqrt(N*p*(1-p))),'-',linewidth=1.0,color='r',label=r'Gaussiana')\n",
    "plt.ylabel(r'$F_X(k) = \\textrm{Pr}\\{X \\leq k\\}$',fontsize=13)\n",
    "plt.xlabel(r'$k$',fontsize=13)\n",
    "for ax in fig.get_axes():\n",
    "\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "plt.tight_layout()    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bd522fa",
   "metadata": {},
   "source": [
    "### Comparando as curvas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "9d55d72f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DHzxXHCLKWTtV5u21FISm7m62u3Yqpfj9vFEy+BLlJobNE7VJdbF2Kmq+WW9gBdihOgUtdzaam+PQuDXfVG2w+Udv3Wt4kvuiJp5ha6dSut8s9Vd+8enw+f/P/93N7Fly1k5NWzsFAAAAAI3xr20AwKk07quLpvq97lsFDlK4aqbJ41blp7u0OCnNN8U/R87KnzLHLwpNRaGr++qt2pkPgi9l1xxVCU7MT59s+KaX4gBQk+ue6pyxu60035T39t2MFWwVVT0+v/3W3UbnOBSvnRp929XPPpUWg/fWf/ndN9MPbq1nzbKzFzffjAoDAQAAAADlCd8AAGOj3Nqp9lc61bksuTAzVbs557icp4vWD0WtHW17bFKab84Xr53KMWoFzTDx2qk48BGvnSqeJ1z51HDwZdg8UQCobPtOWb1eHIRazwpCZarTfNNG+GbMmm+isMsov/NmO+GbKO/SLwi7XFiYSV/63FOFj98/SOk/+u9/L2uW3YxjMzPlnwMAAAAAoCn+tQ0AOJUGDa90atp8B2uxjjtIB90231QIFz22dDaab3KUOXzn5ovP270GVh1F4ww6Xvk0dO1UiwGg3GBJl803dbSydqpCGqjV8E3FcNLvvN1S8020dir40P+1L3y8sB0npZR+5dd/kG5vxMGqnOab6a7b2QAAAABgggnfAABjo0yYo4vmmzrVN/MthIOicQ4O4vVDTTbfVFo7pfnmgV6JIxg338RBi3pLp+L3dNutMynF4Zs6AaCcYElO883W7n7aq5oKqTDTKG0031QZp83wTdWj84/eutfYOToqCt9EbVdPXxqkP/upxwvvs7a9l77x698PZ8n5+Wb6/jkAAAAAAJriX9sAgFOpk/BNDVFIoA0bO3the0cUHCijylatS5pvfqLE8YvCN+vbe+HF9oNw71TxzdF7er1k8CVegzVkho7bd4aJGoBSam71VJU1T4fuZLSjlFVlnHfutRi+qXiAtnb30w9urTc8TRx4ycm6/Et/8uPhff7j//730/ZucbPNzl58bDTfAAAAAEBzhG8AgLFR5jLguK+daiMcFDUD5bSfDBptvqmwdmpxQppvOl47tZRx3qLWo0h0PqP39GYHzTdx+068ameUnBxHL/UywzfNHIs63Sx3N1tYO1Uh7NJq802NA/TbbzW/eioqm5mKdkqllJ59eiX93FPLhff58e3N9H//+z8svM+utVMAAAAA0CnhGwDgVBo02OAySpVwyaE21k5F7m3FF/xPuvnmsSYaY8bAymA2zdS8cF3m0TnnLQpf1V2y0/TKp2il0rDPXzTDZtvNN724hSil5sI3dbSxdqpK2OXu5m5r5yVa81TkH7URvomabzL+0Oz1elntN//hf/u7hQGb3Yy1U9PWTgEAAABAY/xrGwAwPkqkEeatnXpEzqqbxUabb8q7NCHNN/1+L32g5gqtnAvxh5bmGwjfVFjzdFTTK5+q5CYWZot/fakT8sgdJ6fVKqeFKkfVtUoppXRno4Xmm4qPa6v9JiNfMtJvv3WvuUHetxecr9zP/J/71OPpyeWFwvv8/rvr6W9958cjb9/RfAMAAAAAnRK+AQBOpS7WTlVpdjl0MuGbOHjQaGNQyePT76W0PJiM8E1K9Vt8yq2dis9bTvNRkWicsPmm6baXIQNFM+zuH2SFDobJCbr0Ul4LUdkg0ih12orGpfkmpZTeuddO+CZqTyrSSvNNGL7Je57pqX766xntN//Bf/27I9t2dvfiYzOj+QYAAAAAGuNf2wCAsVFmzdNg3JtvWpivThjoUKNrp0qmby4uzqap3KvPp8BjNZtvyhy/nFVHp27tVNTEM+R7Oevcmgq+jNJt8031x97ZbKP5ptpAbTXf1Dk+33vnXuWg1ijR2qkyf/795V94Oj22VBxW/Edv30v/1f/w5tDbstZOab4BAAAAgMYI3wAAY6NMuKSLtVN1LkvmhATKKht2GaaNUFCuixOycupQdGE80nTzzd0gbBE1u9ReO9V0882wGTI+V5sV58jJcfR6vazgXxfHInJ3Y4yab1oL31RP3+zsHaR//O5ag9OkFJXNlFk1Nz8zlf76n7wc3u8/+G9+d+hx2N3PWDs1QWFIAAAAADhpwjcAwKk09s03J7B2KjI71U+z08399a9sE8/khW/qNd+UMTfdD1sz6ratROGuMHxTtvkmmmfY2qmc4EvF5pucHEcvpTQz1U+zU8Wfo7WGwjfjt3aq2kRvtxS+ySh3KfRbbza7eipeO1XuD82/8ksfTcuDmcL7fPeHd9J/+9vvPPL9aO3UdL+Xek3UqQEAAAAAKSXhGwBgjJS5DDiYaW590ih1rksuzDb/16y610kX55oNBJUdR/jmYWXOZ6/XC9tv1rabXzN0VLh2akyab9peO5VSSoPgs7TR1Lmo0exyZ2O3VjPMMFWfra3mmyjsEvmtHzccvmlw7VRK9xuv/md//OPh/f79b/7OI+c6Wqk1SSsAAQAAAGAcCN8AAKfSSa5PyjGOzTeD2WYDS2VbEyYufHOuXvimbAtGFL65FzTfRDmFcO1U8J7e3T8IL/g/PE+wBmtIvCtnnVvlEFBO8837Iw2COcah+WZ7bz9t7eafjxzjt3aq3uN/88d3mhnkfXtB+KZfIfDyL3zhY+lc8Nn/zg9vp//3d9986Hu7wSwzQXsTAAAAAFCOf3EDAMZGmSxCF+GbaA1PkZyQQFl1ewoab74pu3ZqMGHhm6V6P0/Z8xmdv9prp4KB5hte+VQlN9Hm2qkyBkEYYr3muWhK06unDirGgd6511b4pmbzTeNrp4pvr1I2c2FhJv3VL3w0vN+/+1/9dto9En7bDYJw01OabwAAAACgScI3AMCpNI7NMkeNYzNP4803Je+/MmHNNx+ovXaq3BFcjNZObRWHTqoGJw5FbS8ppbTZ4OqpYYcn53O/WTF8k3N8DgN5g+Dzvd5U803NZpc7G82GgKrO84dtNd/UfPwPVzfS7fXmAkrRGqypirsD/8U/cTl8z918Zy39Fzd++ODrqPlmuu+fAgAAAACgSf7FDQAYG7lNM3PT/TRVpUKgpIrXSVNK7YSD6syT0hg030xY+OaxuuGbkveP1k7d3ay3diqaqPHWmWgN1pDv5a2dqrZqKSdY8mDtVHAsmls7VS9e0nzzTTXv3N2q3VIzTBR2yfFbbza3eqqNtVMp3f+z81/8Ex8P7/e/vf47D8Jnu3vR2inNNwAAAADQJOEbAODUiS58j4NxbOZpuvmmbHxkZcLWTl1YmEnTNUJgZcNLUfim7bVTOe/pphpfRpnq99LsdPGvMJ2snQo+SxvbzTTO1G++aTh8U3Ge7b39xlt4UornefriIHyO3/xxc+GbKAxUJzP613/5cloezBTe50e3N9N/+ne/n1JKaWff2ikAAAAA6JLwDQAwNnLDCF0FW+o0zcy3EBAqu6bouMWGZzrrzTf9fi9dWqr+MzW+dioIfNQNcmS1zpQIvkStLqOOT/T5rxq+yTk8hxN11XxT152gDam86m+id+5tNjjHfUHRTDo3Px0GcH7rzbsNzhOsnaqRvjk/P5P+xp96Jrzf/+G/+d10d3MnbL6xdgoAAAAAmuVf3ACAUydn/c1JG8vmmyC80baVCQvfpFR99VSVHFXUfHMvaL4Jwy7B6+c0Tm2WCJ1UDQPNzxT/ClNmhtIy105tNLV2qmZg6m7Ta6dqzPP23a3mBnlftMqq10vpZx4/V3ifJptvwrVTNQOUf/XzH0sfPFf8Z86tte30H/w3v5t294Lmmw5WNwIAAADAWSJ8AwCMjdxLgc2vTxql+sXJNsI3dS+VNt58U/L+Fyds7VRKNcI3FR6zOBe0rbS9dirj/dPkyqdR47TWfFMiWRL9GRS1EOWqmb1pfNVTnfDNO22Eb4Lb+71e+uSHzxfe57ffuhuGZnJFT1M3fLMwO5X+5hc/Ed7vP/7vfj997521wvtMT/mnAAAAAABokn9xAwDGR+aFyXFslTkuZ0VP16K1RWWVWZs0P9M/FY1FZVVvvil/ET46f/eCFUO1105Nx+dvvUzzTdU5TnTt1P3z1l3zTb2Tdqfp5ps6a6daCN/sB2mXXq+XPvnh4uabzZ399PvvFgdVmpqnztqpQ1/+3FPpo5eKV2lt7+2nv/WdHxfeZ2ZK8w0AAAAANEn4BgA4dboKcdQpKWglIFTzWuliw41BZcaZxNablFJ67Fy1n6vKqTxXe+1UsV4wVb/fS3PTxb8+NNl8M2qc6PPfVPClSBSEaqr5pq47G+Ozduqde9033/RSCptvUkrpt358t5F59oIDVLf5JqWUZqb66X/1/B+p/TzWTgEAAABAs4RvAICxkb92avwbVOZnm/9rVhSOiAyCtUVllbmOvLI4meGbD1Ruvin/mDjwsVerKSVnpij4slkifBONWnXtVJkZysyT0k+OUbj6qoMAUI67QRtSWXV6eN6500LzTRh2SemplUG4cu83f3ynoXmKb28q7/IXPvNE+vmnl2s9h7VTAAAAANAs/+IGAJw6nTXf1HjsOK7Gar75Jv8IXZzQ8M04rZ3a2z9IW7v7o+9Qc+1USikNxiB0EgZfmmzfOebwrC0GQba1rabWTtV7fONrp8at+SYKcPV6qd/vpZ9+vHj11G+92VD4poO1Uynd/7n+jX/6U7WeQ/MNAAAAADRL+AYAGBu5eYRxDLYcN9/CjHU3ljTdGFSq+WZS105VDd9UeMxSEL5JqXj11EGQvsmZaT54D62XCN+E84x4g0UzVA0ARfMctRAE2TZ29sIgRo4yMw3T+NqpGvO8c7eN8E3cfJNSvHrqN5taOxWc836DgZefe2o5/aWff7Ly4zXfAAAAAECz/IsbAHDqjPvaqZmpXpoZwwubUXNKmya2+eZctZ+rjbVTKaW0VhC+ieS08TS58qlqi0o4Q1H7T5GstVP3j1G0xiildht4ct1peO1UnSxQG+GbKN902M71M0H45oerG+l2A0GlnDVYTXr5z/1M5TDqjOYbAAAAAGjU+F0VAgDOrNw1RlHrRFOqNs200XqTUr01WCmdbPPNxIZvKjfflD+bOc03dwvCFnVXGKXU7cqnUe+vMHzTxeqrjM9SmRagUaJzFh2L5ptvqru1vp129ioGo0aI25Pu/79/9MPFa6dSSum3flx/9VQUvpmqW192zOMX5tO//E88U+mx01PCNwAAAADQJOEbAODUGffmm3Fdi9V0802ZAMnKhIZvVgazldosqlyDzwnfFDXfNJC9CUMnZVY+VZ0nnKFiAChnnsPztpgRAFzfrt86E810fqF4jqIwVhXRmqfix6Z0a227wWni5pv++yfspx8vbr5JKaXferP+6qku104d+uu/fDk9ubxQ+nHWTgEAAABAs/yLGwAwNnIDCV2FW6q0k6SU14pRRd3ShBNdOzWYzPDNVL+XLi6Wb7+pcioX5+L31VqNwEfO+yv67K032Xwz4vtRs1Tl8E3O2qn3/9+cAGAzzTfFQ11YmCm8fWNnL21XXcM1bJ6aj3/7TrOrp6Ljc/ieXpqbTk9fHBTe9zcbaL6J3kP9hptvUrr/efg3/uk/Wvpx1k4BAAAAQLOEbwCAU6etcEtTxrb55gTXTq0sFocETrPHlsoHi6pchM9pW7m3NTrwUae15FD02Su18ikMTgw/RuHqqw7WTg0ygmxNNN9EovBNSind3Wxu9VTdt9DbdzebGeR9ZcIuP/N48eqpJsI3e9HaqZYCL//kpx5P/+Qf/VCpx0z1/VMAAAAAADTJv7gBAGMj97JkV2unqpYURM0cVVVt4jk0yAhvlFHm+Fyc0LVTKaX0gXPlm2+qnMp+vxe+9+usncp5f4XBlwabb0bPUPwrzGbltVNxsuTwPT/I+Iw30nwT3H5+Pg7f3Glw9VTt5pu7zTbf7Gc236SU0ic/XLx66rfevJt29+q1BIVrp1povjn0b/6FT5UKWM5Mab4BAAAAgCYJ3wAAp864NsscGsf5ZqZ6aXa62b/6lQkDTeraqZRSemypm7VTKd1fn1PkXo2gRdbaqeDifpnwTRwGan+GqgY5K8AKWoiyBQfpfEbzzZ2NJptv6sVvml87VXz70fakKHyztbufbv7hWqvztLnp6YnlhfSv/dmfzr7/tPANAAAAADRK+AYAGBu5pQBdrZ2qemmyrfnqlCY03XqTUrl5lic6fFP+Zxu1UikShm+Kmm/qb51qdOVT1XmiZqmNnb1KIZG8h9w/b7NT/XCF0MZO/caZaKS8tVPj03zzVsNrp4KimYfCLp96ojh8k1JK3/3h7VrzRM03ba2dOvRXP/+x9MeevJB132lrpwAAAACgUf7FDQAYG7mBhDaCJE0ax+abMutIcuVeRj43N9146844qdR8U/Ea/GIQvqm3dirW5dqpUccomuHg4H6LSVk5wZLDmXq9nBVg7TfwnJ+P/yy8s9lc803d9E3zzTfB2qkj//sjKwthWOm7P7xTa569YJ42106ldD/c89W/9MeyGnasnQIAAACAZk3uVRAAYGJFF72bUrWdJGrmqKrOpdJBENqoIvfwrCxObutNStXCN1Uvwi8G647Wtk947VSp5ptqSY6cZqnNDlZPLQYhwDLHYpToGM1M9cMwUqNrp2qmb95uuPkmmubo56zX66VPP1ncfvPdH9VrvonOV8vFNymllD795IX00p96Jrzf0lzcmgQAAAAA5BO+AQBOnXFsljlqYbalv2LVaE1oo/kmNw408eGbcxWabyq+Vrx2qiDw0cDeqTB802joZfhRyvn8V5kjJwx0dKKw+aZGEOpQ2FbUS+lc0H7TZPPNfvlCoYc03XyzHzXfHHsLffqJ4pVM/8OP7qT9aJdVgZNeO3Xof/ncJ9InPrhUeJ9nP7rcySwAAAAAcFYI3wAAp05O88VJGsdwUBurunKzQBcHk92w8NhS+XBR1RxVFL6ptXYqY6jovV2mcSYnWDJMTrNUE60zkUHQQtRM803x7b1eL50PVind2agfAnowT83mm3fubYUBlTJyjs9Rf/SJ4uabe1u76fu31ivPE/1s/Y7CN3PTU+nf+9Jn0tyIdX9/7MkL6Rc+frGTWQAAAADgrBC+AQDGRm4goau1U1W1Fb6pc9l2sYW1U7kuLpZvhjlNPlBh7VTVsxmdx3ubNdZOZdwnem/v7B2knb2a9SjRDBmf/2rNN/F9joY5BjNBEKqB5psc54Pmm7sNNt9Exyhq4dnbP0i31rYbmydqvjmedfn0k8XNNynVWz0VHZ+q6+aq+NmPLKf/+H/6uUfOyc9+5EL6D//Ks2luerz//1EAAAAAOG1O7ioMAEBF8x1dNKx6nXR+DMNBi0FLRxW5h+fi4mQ331xcnE29XrmtTm0139wrar5poHAk5729sbOXZqbijH/YWjJqhoxwW5kGnjIeWjsVfKbWi1aAZcppmgmbb2oEso6LpvnQ+fl0d/Ne4X3evruZPlBhVVuVeXrH3kUfv7SYFmen0lpBK9F3f3gn/Y9+9olK8+wFb+qpDsM3KaX0hZ96LP36v/5c+tXffDvd2dxJH1lZSH/ipx7LarkCAAAAAMrRfAMAjI3jF0qHmZ/pd7a6o6rWmm9q/NjtrJ3KG2hlsfxaptNkeqqfVgblfsaqpzJqvilqWwmDHBlD5by3NzPXLVXNAuXMsLHdbvtOSiktBp+p9U7WTqV0bj5aO9Vd882HzsehmrfvbDU0TUoHUfNN//jXvXD11D+s0XwzLmunjpqfmUp//mc/nP7ZX3g6/clPfEDwBgAAAABaInwDAJwqbYRIRskJAw2T08zRtcUW2niym29KBlNOo8eWyv2MVdfPhOGbguabSM77PWflW5WVT8OMOkRZ4ZvW1k795H9Hx6KJtVNxO1AvXDt1p8G1U1Fk6uLiXJoOAiZv391sbJr9IGM17D39qSeKV09994e3w1DPKPHaqUpPCwAAAACcAsI3AMDYyMkjtNUq06TWmm8q96WkNAhCG1Xk5kcmvfkmpZQeWyq3Rqdq+cS5E147lfPezm18qRpwmJuOf4WpFL7J6OI5+hmMglBNNN9Eer147dTdJtdOBYdoqpfClVJvNdl8E5yzYZ+zTwXNN++t76Qf364WEArXTknfAAAAAMDEEr4BAE6VhRYaXEapGpA4O803eQfoovDNI9paO7W5s59294bXgeSsMIrkvLcba74ZcZT6/V6anyn+NSZ39VUdYfNNjRaiMs53uXYquL3X66UPBuGbRptvwqaZR99Dn36yuPkmpfvtN1WEa6esfAIAAACAiSV8AwCMjZzLkjlrb05aWwGhOtdtT7T55kysnSrbfFN17VT83lrbqhY8yZko573dVPCl6BBFDTxdrJ3qovkmagfqpZTOL0Rrp5psvonn+eD5+cL7NNp8UyFQ9lMfXEqzQXvSd390p8Is8RtI+AYAAAAAJpfwDQAwNsZt7VTVy6TjuBqrjeabXGei+eZcNz/jUkaI6t728LBFA1unssJvTTXfFIk+Y5tjMMP6iPNQRtw0k9K5oPnm3tbuyDakpudJvZTRfNNk+KZ808zMVD998vFzhY/7hxWab6LWm5RSmvLbNwAAAABMLP/8BwCcKqei+aal8E2dzoTB7Mk131xYKA4HTILyzTfVXidqW0lp9LqjsLUkZ+3UdPzezm18CVtLiuYI/hyo1HxT8v5RC1HVBqIyeqmXzs9nBLIaWoEVn7Ne+uC54uabd+40uXYqbuIZ5lPB6qnv/qhC+EbzDQAAAACcacI3AMDY6GXES9pa6dSkhdnx+ytWTmNKW6b6k3/B+QMlwzdVL8JnNd9UDFrkfP76/V6aC1b25AZfDmp08bSzdiqe5+hpiwJtGzt7WW0oxTPF9zmfEW6729DqqZwmng+dj5tv9msel/x5hr+nP/XE+cLHvXVnK71TsqEn51wJ3wAAAADA5Bq/K0MAAAUWZroLkVS9TjrfVvNNjeu2g6Clo4pRF7bPorKrtaoeupzwzajmm6ZEAbimVj4Vvb/CtVOZ7Tt1RM03KdVfwRUFlHq9lM4Ha6dSSun2xk6tOR7Mk9E088EgfLO7f5DeW99uZJ4owzMq9/fpJ4qbb1JK6R+WbL/JWzvlz0wAAAAAmFTCNwDA2MgJJJzptVM1wi6LbaydyrnPGbnWXDp8U/F1ctZO3RvRchKuDMocahC1zjS0dqpIFABqa+3U0XagnFVu6zWDUHnNN/EcdzabCd9Eer0Urp1K6X6zTBOqrlL76cfPhUGY7/6wZPgmZ+2U8A0AAAAATCzhGwDgVOkyfFM17DKOq7HaOG45h+fioFwo5bQq33xT7b01O91Ps1PFf4WvvnYqz3wLwZeyonapjZ391mfICbSttdzA0+v1sppv7mw0tHYqCnClXth8k1JKb9/d7GSeUWue5mem0ic+uFT42N/4g3Lhm4OMt5zsDQAAAABMLuEbAOBUaWulU5Pmp8dvxpzGlLJ6GXGN5UEcDJgEg9mpNDed/1frOtfgo3VHo9ZORSuMckXNTtnNN8HtRfmkpmZ4aJ6Mw3N0ppxVbnVXgOWcsbmMQFZTzTc5a7AuLc6FrTJvN9R8s1+x+SallD79ZPHqqX/wB6ulZslpvpk6K1VgAAAAAHAGCd8AAKdKp803FR4zN90fy9UiJ9V8s3JGmm96vV66VKL9ps41+KX54iDVqLaVMBuQOVQYfOmg+SaaYbPSDHF44ughymm+Wa/ZfBM3zbzffhOsnro7YhVZ4/P0Uprq99JjS8Wfha6ab4oapj7z1HLhY9+6s5XeupM/ZxQESsnaKQAAAACYZMI3ELh58+ZJjwBwZuSs4ukyfFNFmyunqgY2pvq9Uq0suXLGWT4j4ZuUUlopFb6pfhE+Cn20vXYqeo9nN99kBDkqz9BBACir+Wa7buglr9klWj11Z6Oh5pswX3J/oA+emy+819t3u2m+Kcq6fOYjxc03KaX0Gz9YzZ9lPyN8o/kGAAAAACaW8E3LVldX0+uvv56ef/759Mwzz6Rer5dWVlbSlStX0tWrV9ONGzdOesQHup513I/N6upqunbtWnr++edPdA4AHtbp2qkK10mjRo6TMJidqhX2qGPljKydSimli2XCNzVeZylYIXZvRMtJM0unmmu+qbMGK/pzoLW1U0fO3CDjs76+1W4I6HCac0EbUpdrp1JK6UPn5wrvV6ZRpnieYkWr8X7m8fPhuq7fKLF6KmvtlN++AQAAAGBi+ee/Fr3yyitpZWUlvfTSS+n69evp8uXL6eWXX05f+tKXUkopXbt2LV25ciVduXLlxIMmXc96EsfmpZdeSr1eL/v/VlZW0tWrV9MLL7zQyOsDEDvIuHg5yFj1cpLaDN8UXUguEoU1qtrJaHr4wLnii/CTpKu1U4vB+Vwb0XwTfb5yZ2qq+SZS9H5vZ+1UOdNT/bBRqm7zTU4gKKWUzi9EzTfdrJ06bJr5QEfNN9F7uqj5Zna6nz75xPnCx/+DP7idPUvGH4eabwAAAABggo331atTanV1NX3xi198EBq5fPly+uY3v5kuX7780P2uXbv2oOHlypUr6Y033ug86NH1rCd1bA5bdqp46aWXKr8uAOXkXDDvcu1UlbBLp808mdo6Zh86N5cGs1NpvSBs8ZeefbKV1x5HpdZO1ei+CZtvKq+dypupseabWmunikMvVdZO5eRcjs+0ODedtna3R89RM4gUNru8P1C0dupuY803wTzvv4ei5pu37zQVvgnmCcIun/nIhcLVUr/xg9V0cHCQ1Rxm7RQAAAAAnG2ab1pwtK1leXk5ffvb334kXJJSSi+88EJ64403Hnx99erVygGRqrqe9aSOzVe/+tVKj3vuueeGzgdAO3IumEetGyetzfmqXreNmlKqmp7qpysfXRl5+0cvDdIzH1hq5bXHUVfNN1H4ZlTbSlNrp8KVTx20zjQVADoqb+3Uw6JgW/3mm7y2ovML3aydit5Eh/N8MGy+2cxqOovs12xz+tmPLBfefmdzN/3+u+tZs+xlhG+miqp4AAAAAIBTTfimYVevXk03b9588PUbb7yRlpeXR97/hRdeeKjR5aWXXupsBVXXs57ksaka3HnllVcqPQ6AaooaVA61udbpuCoBiS7ny9VmW9C/9Rc+NTQMMt3vpX/rL3wqqzFiUlxczF+xVee4RGGqe1sjPkc1mmaOit5Pza2dGm0uCt80NENkMViDtz7qXDTk8BhFzTeNrZ0K3kSH80TNNzt7B+m99fqBoCjvErU5/dxTF8LX+Ad/sJo5i+YbAAAAADjLrJ1q0LVr19K1a9cefP3ss8+m5557Lnzcq6+++tDjrl69mr73ve+1MuOhrmc9yWPz+uuvp9XV1bS8vJy+/vWvZz9ueXk5a0YAmjNua6eqaHPtVNXLtlFAoI7LH1hK33jpl9K/8//57fTf/vY7KaWUPvexlfSv/plPpD/1Rz7Q2uuOo4uLxQGIo+pcgl+aC9pWKq+dytNG60xZ0Qxbu/tpf/8g9Us0jUTBkpQeDSgNonNRt/km837n5rtpvsld8xQ136R0v/3mYom2qKHzBLdHp//yY0tpaW66cFXbb/zgdvqLPxevz8sK3/hPXwAAAABgYgnfNOh4S8pXvvKVrMddvnw5Pffcc+n69esppZRu3ryZXn/99fTiiy82PuOhrmc9yWPz6quvPnjNo006AIyfnLaKLtdOVQlIjONarEFLa6cOfeqJC+n/8td+IR0cHKSt3f1WA0jjrFzzTfXXCZtvNttdOxW9x3NbZ+KVSqMPUk7D1ObuXhqUCJ7lbUF6eKa2m2/Cmd4/RucXouabhsI3mff7YNB8k1JKb9/ZSj/zeM15ggMUha/6/V769JPn09+5eWvkfX4js/lmbz++z5TmGwAAAACYWP7bu4Zcv379oZVKKaVSQY+rV68+9HWb6466nvUkj821a9fSzZs30/Lycnr55ZezHwfAychpzChzMf0kzE+399erqtdtFzsKBPV6vTMbvEkplWrxaDN8M6r5Jg675L1+dI5zm2/ywi7D5YTculg9FTVx1W6+ic7Z+/9vtHbq3tZu2o92NGWI2l0O30OXFmfD1pm37mzWnids4sl4js88tVx4+z/80e20m5GsyWu+Eb4BAAAAgEklfNOQr33taw99XXZd0Ze+9KWHvl5dXU2vv/567bmG6XrWkzw2X/3qV1NK+U07AJys9Zzmmw7DHVUCEuPYfDOOM02iS2XCNzUWT0Urhta2d4eGNuISlbyZosBJzvq4HEXT5IS8cv48OSonDHT8EEVBqLIzlHU4z/mF4jn2D+oHgVLKCbvcH2h6qp8uLRW337x9d6v2PHEYKH5Pf+Yjy4W3b+7sp9956174PHsZ4aa+5hsAAAAAmFjCNw1YXV1N165de+h7zz77bKnnWF5eTsvLyw9974033qg72iO6nvUkj82NGzfSjRs3UkpJ6w3AKZFz0X5+Zrz/+tJmOKhqYGOp5bVT3HdhYSZs+zhUq/kmaH/aP8hvn6kieo/v7B2knYymkDCqUHCMcj5nW7tj0HwzooUoV25Xzbmg+SallO6MWEdWRuYWrJRSSh8KVk+93UDzTZR3yfmc/exHLoT3yVk9ldN8Y+0UAAAAAEyu8b56dUr8yq/8yiPf+9znPlf6eT772c8+9PX169fT6upq1bGG6nrWkzw2R9dTXb16Nb322msPwjgAjKecwEBuO0cTqoRd2ly7VPVH13zTjX6/l1YGee03dd7HUdtKSvfXDB1XZ83TUfM5K59aDP+klLt2Kg4AHXWQEXU5ftZab77JbJqJ1k6llNKdjZ16s6QUvomOHp8PnpsvvG8TzTfRWq6cMNyTywvpsaXiz+0/yArfxK/V99s3AAAAAEws//zXgG9+85uPfK9su8uox1y/fr3STKN0PetJHZubN28+dPu1a9fSK6+8kq5cuZJ6vV56/vnn0+uvv954uAmAev6lP3H5pEeobRyDLlFTCs25mLl6qk6ELKfJ6N6QlpMoXJKbB8ppndnMCJ3EK4xGixpnUiofAMpbO/XwVGHzTc1VT7lNM9HaqZSaCd802XzzVgPNN9E5y1nz1Ov10s8Gq6d+4we3w+exdgoAAAAAzjbhmwYMC4Fcvlz+4uEzzzzzyPeGhVfq6HrWkzo2r776auHzXb9+Pb300ktpZWUlPf/88xpxAMbEZz+2Unj7lz77kY4mua/KddI2105VNY6BoEm1khu+qbN2ai4+n7UbVwo0FXzJaZoZJadhqu32nZTiY7G+1e4Mh2+jnOabu02snQrXPP3kjf2BoPnmrTsNNN9EgbLM54lWT/32W3fTRvCZylo7lbuXDgAAAAA4dYRvalpdXX2kPWV5ebnScw0Lpdy8ebPScw3T9awndWxWV1fT66+/nv3c169fT1euXElXr17VhANwwp5cXhgZsBnMTqW/9sc/3vFE5Y1j+EbzTXcujUnzzVqFtVO5a9Zy3uNNBF+KVnNlzVCzdWaY4xMNgs9W7eabzF1hg9mpMNhxZ7OJ5pv8sEvUfPP23c20n7OrqUD08Nz1bp95arnw9r39g/SdHxa33+T8LJpvAAAAAGByCd/UNKzZ5eLFi5Wea9jjvvWtb1V6rmG6nvWkjk3VVV3Xrl1LV65caTTwBEA5vV4v/dt/8dPp6pWPPHQh+amLC+n/+M9dSZ/88PkTnC7PfIstM7kXko/LaSqhGdlrp2pchB/khG+GhD7i1pK8189pnclp3snMlQw1M9ULwyZdNN9ELUTr23vZAZphctc89Xq9dG6++H3RyNqpcKCf/M/Hzxc33+zsHaRb69u15onaZnLf058J1k6llNKN779XePtexnlWfAMAAAAAk8t/Bl3TrVu3HvlelbVKKQ1vhTlsj6naGHNU17Oe1LF54YUX0sHBQbp58+aD//vmN7+Zrl+/Hjbb3Lx5M125ciV9+9vfrjwrAPXMz0ylf+fqZ9Lf/OIn0j9+dz1NT/XS5z528UTWdVR5xXFsvhG+6U5u+KbO23mQ8R671+K6o5w1ZpsNrL0qOkS9Xi8tzEyle0Mafg5tbO+Xer2cjMzxMEfUfLO3f5C2dvezAktVZjraVnR+fiatro8O2NzpYu3UkXk+FIRvUkrprTub6bGl4oac4oGKb85tmrm4OJs+dmmQfv/d9ZH3ufGPi8M3+xlvN2unAAAAAGByCd/U1OSaolGtMLdu3WokfNP1rCd9bC5fvvwgQPPiiy+mlFK6ceNG+sY3vpFef/31kfOtrq6m559/Pn37299u5LiX9bf/9t+u9fjvfOc7DU0CcLKeujhIT10cnPQYpbUZvql62TYKCNCc7OabGoun+v1eGsxOFbbLrBeEUkbPlKeptVO5rS4j55gNwjclm2+ilUopPXrecla6rW/vVQ7fZAz0wPmF4lnuNrJ2KhjnaPPNhbzwzaeeuFB5nqj5pkzW5dmnV4rDN99/Lx0cHIxsrYpmSen+ZxcAAAAAmEyuxNT07rvvPvK9pgMbTYVYup51HI/Ns88+m5599tn06quvptdeey199atfHfocN2/eTH/9r//19MYbbzQzaAlf+MIXOn9NAEaosBpoYXb8tnoOgtU4NCc3fFMje5NSSmlxbrowfDMslBKtP8p9uzcVvqkrmmOzgxlyPltrW7v574tjcgJBh87PzxTefmejieab4D105H9fHMymmale2tkb/Zg3b2/Vmye4vcx6t5//6Er6L/7+D0fe/of3ttMPbm2kpy8ND4XmrZ0SvgEAAACASTV+V4dOmZs3bzb2XG23rHQ967gfm5dffjn93u/9XnrhhReG3n7t2rV048aNxl8XgMnWWsNFqpQFSilZO9Wl/OabepbmijP0ay2uner3e2luuvjXiKJg0ANhkKP4KEXhm/XtcmGTKmuncptvqorXPP1EGL5poPkmcvT49Pu99MFzxe03b97ZrPV6UdtMmT8zrzy9Et7nxvdHr57a34/fQFPCNwAAAAAwsYRvToFbt26d9AjZup617ustLy+nN954I7366qtDb3/llVdqPT8Ap1uVy6Rtrp2qytqp7mSHb2peg48CVcOCJ2FLSIl3/ELw+jmtM/mdLsPNBzNsbO/XfIVYTrBtrWQI6KgyzS7n5os/57c3Glg7FYaBHn4Pfej8XOH937pdM3wTnOIy7+mffvxcWgzOZ2H4pkJ4CwAAAACYHMI3NV28ePHUvEbXs56mY/Pyyy+nl19++ZHvX79+vZHnB+DsiEIJdVS9bqv5pjuXFovDBofKhAKGWQyab4avnSp+zjLBgChktlGj7eVQNM/CTPGvMmVXX1UJA0XnIaVmjsUoDzXfLLTffBOtwTp+zh6/0G7zTaRf4j091e+lzzy1XHifovDNXk7zTZmBAAAAAIBTxX8GXVPbq6KafI2uZz1NxyallF599dV0/fr1R1ZNXb9+PT333HONvU7k137t12o9/jvf+U566aWXGpoG4Gyr0lIwbs03s1P9NDMlb92VlcXiAMShfs1TEjV01Fl1lCMKmeUEX3LWPBWJGp1y2neOOsgY6PifCVnNN0OCUNlKHKMLQfimm+abh33ofHH45q2W1071S/4h/uzTK+nXvvfuyNt/88d30/r27tD3XjRLStZOAQAAAMAkE76p6dKlS498b3V1tdJzjXpcU+0uXc96mo7NoVdffTU9//zzD33vxo0bnYZvPv/5z3f2WgA0b77F8E2vwoXbNpt4eNTc9FRampse2jxz1Ik039Re9PQTXTTfnIYZ5qb7aarfK2w9qROEKtM0E4Zv1ptovgkc+zPq8ZbDN022OaWU0pWPrhTevrd/kH7jB7fT55959PecnPCN7A0AAAAATK6x/8+gb9y4kVZWVlKv1zux/3vmmWfSzZs3h853mtpdNN/EnnvuuXT58uWHvvfuu6P/61cAJlvZgESvd/9ifFuqXLiNGlJo3sXF2fA+dS/CLwXhm2FtK3FQIX+oMPiS03wTBkuK54mCbustrJ06PlOv1wvbb9a2qzfflAmXROGbu1u7aT9jNVLxPME5O/Z1tHbqvfWd0g1FR0WBl7KBxZ9/ejm8z6jVU9HaqX6vWoASAAAAADgdxj58c+vWrcptKU25efPmyBk++9nPPvK9W7duVXqdYY9rMlzS9ayn6dgcdbzl5qTffwCcHgszU2N3cVXzTfdWMsI3dUUrl9YqtK2UeeeGa6e6aL6ZLf5VZrPkDDlrsIYdo8XgXKxvtXcsjgYEzy8Uz3FwcD+AU0d0iI7/8RetnUoppbfvbLU3T8nnWx7MpssfWCy8z98fEb6JgkBT/fH6/xsAAAAAgGaN/dqp5557Lr333nsjm2e6cPny5ZFBj2efffaR71WdddjjhgVYqup61tN0bI66cuXKQ1930eADwHgqm6OJ2kDqqnLpNlpPRPMuZTXf1LsQvzQXtK0MXTvVnEaab6JWlw5maMIgOhd1mm9K3DdqvkkppTsbO1n3qzpQ/9j7Oid88+adzfT0pUG1cYI3UZW8y7NPr6Sb76yNvP3G91fTwcHBI5/h/f3i5x23YCYAAAAA0KxTcTVmeXl5aJBjXFy+fPmhcEjVppRhj3v++ecrTjVc17OepmNz6OLFiw99fenSpVZeB4DJE63BOQltB4J4VNbaqZqvEYWqqq2dyn/9qPkmZ5VQ3TDQQtA4Uz58E0807BiFzTc1WoDCNU8l1k6llNLtjZ30VOVpyjfNPJ4Zvqkq2qLVr5C+efbplXTt238w8vZba9vp999dTx9/7OGGnL2o+Ub4BgAAAAAm2tivnToNjq8pSqlayGRYu0vToaOuZz1Nx+bQ8aYbzTcAZ1fZS6XzMy3/1arCxVvNN93LCd/U3UAzqBC+iZRaOxWEuuoETg5Fb/ew+aaD1VcppTQIgkhVzsWhMgGl85nNN3WUCQOldD+kdX6++L361u3q4ZtwngrPeeWjK+F9bvzjR1dP7QdJIGunAAAAAGCyCd804PiaopRS+ta3vlX6eX7913/9ke8NC6/U0fWsp+nYHDoeDmrrdQCYPFEbyEkYx5kmXVbzTdtrp7b3hgQTmls8FbU8NbF2KrIQhN3KNt/kzNMbEueIAm5NBJFGOfo+Oj+f13xTR9h8M+R9/fiF4vabNptvqnzOPvHBpXQuOKff/v6Q8E2DzVIAAAAAwOkjfNOAF1988ZHv3bhxo/TzHH9MG6GPrmc9Tcfm0NGWneXl5XT58uXWXguA8Vb2YmnbK56qXLtdFL7pXE74pq5BsOpob/8gbe3uP/S9eO1U/jssantponUmbL5peIacLNCwmVptvikRUJqfmUpz08W/3tUO31QITH0oWD31Vo3wTdkmnhz9fi/93NPLhff59u8/Gr4J105pvgEAAACAiSZ805AXXnjhoa+HNbVEjq9Weumll2rNNErXs56mY5NSSt/85jcf/O8vfelLrb0OAJMnagM5CVFIg+ZdHMThm3ub1QMZKaW0lLFOrGzoo0xQIQqabeY03wRxl2EtM0fltO9E4YwmLAafsVabb459fSFYPVW/+aZ82OXxVsM3xbf3K9bNPPt08eqp337rbnpvbfuh74Vrp1TfAAAAAMBEE75pyPEwyPXr10s9/tq1aw99vby8/EhopSldz3qajs3q6upD873yyiutvA4Ap0PZlSWtN99UuHYbtXLQvItLcfjm1vp2eJ8i0aqjlFJa23o49NFkDCVqnWkzcHIoJ1h2vP2nSN7aqSFzhCvAqgWtcoJDx/9MiMI3dzbbbb4ZFpiKmm/qrZ0qHqhq2cznPnYxvM+3/vHD7TfRLHVXzQEAAAAA4034piHPPfdcWl5efvD18RBH5Bvf+MZDX3/lK1/Jfuwrr7ySrly5kq5evfpIQ8w4zHqSx6aso2GbF1980copAEqJAgknQfime5cy1k6t1g3fZJzX46GPcEVPidfPaZ0JhWuwim/PCbs1sf4qEjbfbLXZfPPwQWq9+abCOfvQhaj5ZqtyQ1H0qKg9aZSff3o5XBP1937v3Ye+3ouab/zmDQAAAAATzT8BNujrX//6Q19/7Wtfy3rc6urqQ+0uy8vL6cUXX8x67PPPP59ee+21dOPGjXTt2rX0zDPPZAVwup61q9dbXV1Nr7322oNjUsbNmzfT66+/nlJK6dlnn82eEQAOtd58U+FCsrVT3VvJCN+8t14vBJHXfFOycaVEM0cza6fqWZiNf5VZzwkBvS8rADLkELXXfFP+MefD8E29dWdVAlzR2qnt3f3Kn4e4babS06bFuen06ScvFN7n7/1+ueYba6cAAAAAYLIJ3zTohRdeSM8999yDr69du5YVhPnqV7/60Ndf//rXH2qKGeXmzZtDG2SOr2kah1m7er2Pf/zj6ZVXXnnQBvTMM89kh3CuXr2aUrof8PnVX/3VrMcAwFFRG8hJ0HzTvXMZwZioJSMSta2klNK9Y+GbJtdORe+rnb2DtLOXv/JpmCiqkPN5K9N8k3N8hgXgBsEcVVdwZc1Tcu1U7eabkvOkFIdvUkrpzdvVVk/FTTzVAy+/8LGVwtu/+8PbDwXcoo+0tVMAAAAAMNmEbxr2xhtvPLSq6DDQMcr169fTa6+99uDrl19+Ob3wwgu1Znj33XfjO6XuZ2379W7evJlWV1cf+d6VK1ceWid13Orqarpy5Uq6ceNGevbZZ9Pv/d7vZQWKAOC4ttdOVbl2O8gIgtCsLi6yLwZtKyk9GvoIgwolXn8+470erZ6qumroUE7TVE4DT13RZ6x0A9H7co7P8XMWhW/utL12asi76EMX5sLnfetuO+GbYHNUoV/4+KXC2/f2D9Lf//7qQ18XidZYAQAAAACnm/BNw5aXl9O3v/3tByGTGzdupCtXrjwSCknpfrjk+eeff/D1yy+/nF599dXs17p8+XJ69tlnH/n+l7/85bGbtYvXu3z58sjQzGuvvZaeeeaZ9Prrrz8I6dy4cSO98soraWVlJd24cSO9+OKL6dvf/rbgDQAPlM1QtL92qryolYPTaXqqn+ami/8qf7z5JlLm/Z4VfKnY+PJAMFDOSrUoAHRU1tapISNFLURbu/tpt2YLUO480dqp2uGboPtm2PF5bHEuDJ68VbH5Jlr11K8RhPvsR4ubb1JK6e/93k/+o4d94RsAAAAAONP8p9AtWF5eTt/73vfSK6+8kl577bV048aNtLKykl544YX0uc99Lr377rvp+vXrD9YhXb58OX3ta197aC1Trl/91V9NV69eTdevX3/wPMMCOeMwaxev96u/+qvpi1/84tBAz82bN9NLL730yPdffPHF9OqrrwrdAFBb2+GbKgYZDSmcTotz02lrd3vk7evH107VbJo5Kue9HjffFD8+iipkzVA3AJQh5zO2vrOXzk+V++8eqpyt8/PFv97VXjtVYah+v5c+eG4u/bggYPPmnYrNN8HtdUqoVhZn009/6Fz67bfujrzP3/v9Ww/+d7x2qvosAAAAAMD4E75p0auvvpq+8pWvpF/5lV9Jb7zxRrpx40a6du1aSul+qOSFF15IX/7yl2utmVpeXk7f/OY3T8WsXbze4dqo69evp2984xvpxo0b6datW2l1dTUtLy+nixcvpuXl5fTcc8+l559/vnKICICzYdgKlSI5q3jqqLR2KqMdhOZ9+bNPpW986wcjb/9rf/xjtV9jcW4q3Vobffva8bVTwfOVeb8PGlg7Vdf8bBxmOb56q0jU6pLS8EBQ1HyTUkrrW3vp/HxxK80j82QFXR6eKFo7dXtjJx0cHFRejRaHXYY/74fOzxeGb96qGL6Jmm/qroD73MdXCsM3f//7q2lrdy/NTU+lvWCWKekbAAAAAJhorsa0bHl5Ob344ovpxRdfPOlRQl3P2tbrLS8vpxdeeKGxoBAA5BrH5pvFlgNBDPenf+aDheGbX/jYxdqvEYU+2lw7NZ/xXo+CL3VbS2an+qnfK24c2SwTAMpaO/XoUDlBpPXtcufi/jgZYaBj40Thm939g7Sxs1c5lFe1rejx8/OFj3uz4tqpuu1JkV/4+KX0n/yd74+8fWt3P333h7fTlY9etHYKAAAAAM64ct3nAABnSNmigrbDN2WbeFJKaUH45kT8mZ/5YPrCM5eG3vbLf+QD6Z/81OO1X2NxrjhAcXztVKU9RiPkvK82o/BNzXl6vV74mWu7fSel+DykVK6Bp4zjfyJE4ZuU6q6eippmhn//8QtB+ObOVvlJMt5A/ZptMzkhub/7e/dXT7XdwgMAAAAAjDfhGwCAhixkrMHpWs5KHJo3O91PX/vnr6S//Lmn0vzM/ffFzFQv/Quf/2j63//ln2+kBSMKfdzbKrt2Kl9O0Kxu8CVnnoXg/b1Rau1UbPjaqfhYrJVsIUqpWjjpfMvhm6pNMx8Kmm+qrJ0Kimbuz1PzY/b4hfn09MVB4X1+/f3wTbh2avz+vwcAAAAAoEGuxgAAjFD2um3OKp5aKlxI1nxzcs7Nz6T/zT/zs+lf//OfTGtbe+nc/HRWS0quKPRRNvBRJqjQRPgmZ61SOEcQeCsTAMoJuww7RoOTbL45NlBW8816jfBNyXkOPX5hrvBxt9a209buXpqbzv/zKq/5JvvpRvrcxy6m799aH3n7t37/vbS3fxCvndJ8AwAAAAATzX9/BwDQkLbXTpU11e+luWl/3Ttp5+Zn0uMX5hsN3qQUN9+sbT8cvskJK+TqZ7y3yrTODJOzpif6zG12sHYq53N//FzkyAoDHfs6J3xzZ7P8LIei99CoUxY136SU0tslV0/lNd/UD7z84seLV0/d3dpNv/njO+E81k4BAAAAwGRzNQYAYISy10rbbpkpe+l2MDPlgu8EW4rCN8eab+K1U+XeK9H7PWy+qbjC6KEZguBLmcaZnCaeYcdoqt+L59hqq/nm4a8Hs1NpOqh7qbV2KppnxPdzwjdlV0/lna/6PheEb1JK6e/cfDftRc03TdTwAAAAAABjS/gGAKAh49Z8M5gbr3lo1iAIv5RedVQ2bBa83+s23+SIVr2VWTtVx2LwWavUfFNhLVev10vng/abWuGbeO/U0G8/nhG+ebNs+Cbj8PQbCB9+7NIgfeBc8dqsv/29d9N+MJC1UwAAAAAw2YRvAABGKNsEEgUB6irbYjOYbXbNEeMlWjt173jzTXNbp1JK9ZtvIjlv9yiAtFmm+Sbn+IyYKfqslQ5CZc4z7BhFq6fqhW+CtVMjvr84N53OBe/XN283H75pIu/S6/XS5y9fKrzP3/29W2lnb7/1WQAAAACA8SV8AwDQkLbDN2VFwQROt8Xg/D66dqpacGKUsPkmXDtVPw3UZAAoK3szMnxT7lw0Ns+QsxY139xpc+1UwZvo8QvF7TdlwzdR00xKzTTfpJTSF54pDt/c29pN/78f3C68j7VTAAAAADDZhG8AAEYoe9227bVTZS/dCt9Mtqj5Zq1k20rZZqW2107lNE+Nz9qp5ptvslRovqkTvonSN0Vhlyh88+MWwjdNtc184ZnHwvv85o/vFN4ufAMAAAAAk034BgCgAVP9XpqZavfiatkLydZOTbalIPCxvbv/0CqcztdOBYGTJsaJAkBlQi85TTyjPoKtNN9UPGGtrp0Kbi/6I+rDYfhmo9FZUiofKBvlqYsL6cnlhVrP0dQsAAAAAMB4Er4BAGjAwszU2F1c1Xwz2QZB+Calh0MfdYITw7TeOpMxUBS+2eyq+SYIulVpvslbO/Wo8/PFs9QK3wSBoKI/Aj98oTi8Unbt1MF+fJ+mymZ6vV64eirScjYTAAAAADhhwjcAAA2IgghN0HzDUUtz8XuuzOqp8u+vesGXqNglZ5y67TsPzZNxn1EBu0FwLta2qzTfVJsnXDu12WbzzeizFjXfvHV3K+3t57f9HGScsZzVZbm+8FM1wzfWTgEAAADARBO+AQAYoUyTzcLs+P21SvPNZFss2XzTyJ6nI5pc+VR5hih8U6b5JifsMuL7YfPNVjvHYtg8ra6dqlGf9HgQvtnbP0jv3N3KniUnp9Nk3uXzlx+r9fhxa0YDAAAAAJo1fleJAABOoSiI0ISyLQ5RGwenWxT4SOn42qnqK4OGqbt2qol5xmXtVBvNN1XDUq2Gb6JzVnDbE8vFa6dSSulHtzeyZ9nPqAZqMvDy+IX5dPkDi5UfPyV8AwAAAAATTfgGAKABXYRvyhrMWDs1yfKab0qsnSoZ7qq78ilnrVI4Q4PtO1lrjEYcorD5pkILUNV5zgfhm82d/bS1Wy2UFK4KKwiYRM03KaX05u3Nxma5P0/202X5wjPVV09ZOwUAAAAAk034BgBghDKXSqMWkCaUvZC8qPlmouWsFbt3tPmm4bVTg5ZbZ3LCQDlrpw6a/sGHiM7FQ+u/MmWFS4Yco6j5JqXq7Tc1tk6l8/MzaSkIjP24VPgmPkD9htM3f/yZ6qunFN8AAAAAwGQTvgEAaEAUAjgJ4zgTzZmb7qfpoE1jffvo2qliZcMBOcGXIk3ME4XeDg5S2trdj58oVQ+7pJTSoIXmmxzDjlFO+ObORoU1WCmFJy06Z1H7zY9X89dO5USqmg68/NJlzTcAAAAAwHDCNwAAI5S5cDuOa6eiVTicbr1eL1w9VaVxJVcUfGkrcHJUTvtPbgNPnTVGUcvU2vZu6Qaeqn09bTbf7Ac/Q/Rn5oej8M2d/OabaJaUUmo677KyOJv+6IfPV3rslOobAAAAAJhowjcAAA0Yx/BNTjCB020xOMf3tn4SPGl6/VL0no9CL9E4OVmFnM9d1MDThKj5pkwDz08eE5+vYYfo/HxO801ba6eKT1oYvinRfLOfFZZqPvDyhWeqtd+0MQsAAAAAMD6EbwAARihzqXS+g6BL2Yu3USCA0y9qvim3dqrs+6v4Pb+zd5B29ooCJ/XDQFH7Tkr5DTx1polCUCmVbyHKmmfIKTs3Px0Gl6o230SBoHjt1ELh7W/ezm++qRpOqusLP1UtfDPlN28AAAAAmGj+CRAAoAFj2XwTrMLh9BsE4Zt7JQIfZYMKOYGz3JVPw0QtKimltJAxw0Zu+CYnzDFipOg8pFR+DVfWGqwhx6jf76VzwTx3NttpvolEzTdv3d1KezmVNinv+PRbaJv5xY9fSjNT5Z93qukdWAAAAADAWBG+AQAYoUwTSBfhm7KXbq2dmnxLQcBq/aG1U82+dtbKp4LASRPz5MxQJwCUK6v5Zrtc800dFwbFq6dur1dtvim+PfozMwrf7O0fpHfubjUyy/15sp6qlMW56XTloyulH2ftFAAAAABMNuEbAIAG5DRw1FX22u2itVMTLzrH90oEPsq+v7LCN3WabzLmyQmY5c6QkwUa1caT03yztlWy+SZjolHH6Px8EL6puHYqEp2yDwdrp1JK6ce3N7Jeaz8jfdNG801KKf3yH/lA6cdMCd8AAAAAwEQTvgEAGKHMtdL5MVw71UUgiJO1GIQ+1kqtnSoXDqgbfGmi+Sbnc5e7dqqOnOab9bLNN1lrp4a7sNB8+KbOWq5DH14ubr5JKaUf397MmicnfNNW3uWXP1EhfGPtFAAAAABMNOEbAIAGdLN2qtzFW803k28xc+1UTnCirHEIvsxN98OARXbzTY01RoOMz1r55puceYYPFIVv7mxWCd9kzBP8GXVubjoMKuWGb+o0FdX1Rz98Pj22NFfqMYpvAAAAAGCyCd8AAIxQ5lrpwux4/bWq10tpfma8ZqJ5UfPNvfebb+oES0bJaVYqCt9Ea5VGBUuO3ycKvuUHgDKaVEZ8f3a6n2amiuct3XxTQyvNNxn3iU5Zr9dLj18obr95M3PtVE6grN/SH4H9fi/98iceK/UYa6cAAAAAYLK5IgMA0ID56Q6ab0pcux3MTGWFFzjdonajtRKBj7Lvlpy2p7bXTuXMkdt8U1fUfrNWsgWoTmAqDt+UDwJlrZ3KeJ4nlhcKb/9RbvNNA008dfzyHym3esraKQAAAACYbMI3AACjlAivzGe0gHRpwcqpMyFqvjlcddT80qnMtVM1gi+5n76ogafZtVOjp4rWKa1vlQu8RM1AKY0+RuejtVMn1HyTUkqPn4+ab/LCN/sZA7WZd/kTJZtvhCEBAAAAYLIJ3wAANCCnBaSuMpduF+fGKwxEO6LAx9qDtVMZQY6S2YCpfi/NTRf/OlG8dqoZ0Wdvs2TjTFWDKAjVYfNNK+GbrBMWv4k+HKyd+vFq5tqpnHBSi4GXx5bm0qefPJ99/ym/eQMAAADARPNPgAAAI5S5bNtF+KaMcZuHdkTNNxs7e2kvpyIkpVR+8VRzrTPD5OYmohnWM0MvWc0uBbc13XxTR7R26u7Wbon3xX15YZf4eT4crJ166+5W1mz7+/FrtV0286dKrJ6a0nwDAAAAABNN+AYAoAFRAKAJZa7dRqEMJsNSxnle395tZe1USnHIq7D5Jhgq9+0erb9qdu3U6NsGwaq30s03WfcaPlAUvkmpfPtN1vHJeJ7Hg+abvf2D9If3tsLn2c8YqN9y4OWXP5EfvrF2CgAAAAAmm/ANAMAIZa6VjlvTzKCDMBAnL+c8r23t1Q6WjBKGb2o035ymGVKKV72tb5drvqmzKuz8fBzKul1h9VQkJ2DyxIXi5puUUvpR5uqpSNtxl2c/upIVgEvp/po2AAAAAGByCd8AADQgat9oRv7FW+GbsyGn4WgtM/RRJRoQve83d0bvBorWGOU2hUTv9c3c5pustUqjZwqbb7ZKNt/UaJrJar7ZbL75JidfEjXfpJTSm7c3w/uMQ/PNzFQ/ff6ZS1n3Fb4BAAAAgMkmfAMAMEKvRByhi7VTZURBACZDVvhmazcrWFJF9L4vDL40NFKd1VdNarr5po6c8E3Z5pu8cFL8POfnp8PA1I8ywjdttTmV9ad/+oNZ97N1CgAAAAAmm/ANAEAD5qfb/2tVmYu3mm/OhijwkVJK97Z2M4MK5dMBbQZfcqeZD97r65kz5ByjImHzTQshoFHn7Hwb4ZusJp74rPV6vfThoP3mzdvx2qmc5ptOwjc/84Gs+01J3wAAAADARBO+AQCoaXaqn6anxuuvVcI3Z8NSRvPNeua6ozbWTm0UNN801cUTBYDy104Vi7ITi1EIaKtc802dtVMzU/3wz4DyzTcZMt9EH76wUHj7j7PWTsWv0/baqZTu/yyf/PD5sZgFAAAAADg543WVCABgjOReK52f6eavVGUu3Vo7dTYszEyF79O1FtcdRWunisI3kdzPX9i+U2OGMgZBECq3gedQ3TVP0eqpOxtlw0AZ82Q+V9R8kxO+yYkDdZV3+eLPxKun3rqT8zMBAAAAAKeV8A0AQE1RAKEpZdYCab45G3q9XloMglb5a6fKv/5CEDwrap2Jwxx5AzUVAIrmiaaJPnPrLYSgitY8ReGbNppvcv+MitdOnZ7mm5RS+tMZ4ZuPrBS3/QAAAAAAp5vwDQDACLmXbaPmjZMQtXAwOcLQR+7aqUrhmyD4UrLtpYp4hv3WZ0gpbptaK9t8U3Mv1/mmwzc11mAd93iwdurNO5tpL0jXNDlPXT/31HK6uDhbeJ+nLw06mgYAAAAAOAnCNwAANc13FL4ptXZqDANBtGMpCFrd29rNWmFUxXyN1pmw9yZ37VQ0Q0ONM1Gry2Iwx/buftrZyw8C5TXNjL7t/Hy0dqpc+CZnoNxz9uHl4uabvf2D9M7drcL77Oesweqo+Waq30tf/txThbd/7mMXO5kFAAAAADgZwjcAACM0dfH/JCzOjd9MtGMxCN+sb2eunarQExK2zhSunSr9cpVniFdcxfOEa6cy2qbWS7Tf5MxcJFo7dWez7NqpjLBL5nvoiaD5JqWUfri6UXh7Tvim31X1TUrpX/nTPzVynda//Rc/lc4FYSgAAAAA4HQTvgEAqKmrtVNlShwWghU4TI5o7dS9zLVTVXb0RO/9zRprp3LHiZqn9g9S2i7ROFNV1HyT0v0gVJOK/kyIwjetrJ3KPGlPBM03KaX0oyB8k9fE0136ZmluOv2tv/kn01/6+ScftFF98sPn07/zws+mv/KLH+1sDgAAAADgZLgqAwAwQm6LQ1fhmzJyggBMhmjt1NrWbktLpzJWPtVYO5UrCh+llNLm9n6amy6+X9TsEuU4BhmBt7XcIFSqf3waD99k3Cc36nJufiadm59OdzdHh5Gi8M1+xkBdNt+klNLFxdn073/551JKKW1s76X5mX6nASAAAAAA4ORovgEAqGm+o6BLueYb4ZuzIm/tVM7KoPKi1pmi8E2kybVvOXPEa6eKB8pZ9Vam+abuqrALC8Xvi7Lhm5w1T2XeRE8uF6+eisI3Ta7BasPC7JTgDQAAAACcIcI3AACj5F78H8vmGwWHZ0UU+ri3lRf4qBIUCNdO7eyn/REVJVEgqMnmqTohoFxNN9/kdM0UnbLzQfPNnY2dkedm6DQ1w0DHPRGEb364ull4e87oPb/tAgAAAAAd8c+RAAA1zc9081eqMhe2c1bxMBmioNX69l57a6cygi9bu/stvfp9UftOSnmNM2G4JPj4Nd18k6MofBOtndo/SGmtTBNPzTDQcU8szxfeHq+diufpa54BAAAAADoifAMAMELuZdtxbL4ZBKuImBzRuV7b2s1sLSmvzsqnMOvS4NqpzQ6ab+anp8KZ17bz58g5Z0Wi8E1KJVdPNfweenJ5UHj7j24Xh2+angcAAAAAoA7hGwCAmjoL35S4kjyOgSDasRiET9YzAx9VSkJyWmdGrnxqqI4na+3Udty+U7P4JvX7vTQIZlnPXAGWM8/9mUZP1XT4JmueEm+iqPlmdX0nrRUcL803AAAAAMA4Eb4BABgh90Ly/JiteJqf6aepvovOZ0VO801be6fygi/VWmdycxM5K9ZGBoCOOAjCHDnzhOei4eabopnONx2+qTnPcU8uL4T3+XFB+03T8wAAAAAA1CF8AwBQU1ctM7nXkQezVk6dJTnNNwcZ6ZuiFpVR6qx8ypkpx9x0/CtNTvimCeG5KNF8k6PojOU039zZKNPEk/MeyvdERvjmh6ubI2/Lab4RvgEAAAAAuiJ8AwAwQu51287CN5lXknOaQJgcUdhqd/8gbe/Ga5eqBBWymm8qBl9yw0C9Xi+cY2M7DpnEa6fieaJzUar5pmY4aX5mKs0GwaQ7J9h888Fzc2FD149WC5pvMl7D2ikAAAAAoCvCNwAANeW0f3RJ+OZsWZyLz/e9hhtXDtVZOxWGOUrkJqLPYNbqqwaKeKJzsZ4RAjrURNglar8ptXYq6175J216qp8ePz9feJ/C8E1O8032NAAAAAAA9QjfAACMkFuaMG/tFCco53yvbcXhkypBhfnZ8Vj5FDbf7MTNP5GcPw/C5puM83AoJ3wTnbXz88XzlArftLDm6Ynl4vDNDwvCN/sZx0fzDQAAAADQFeEbAICaulo7lUvzzdmS03yzltO4UiGnMDvVT8HmoLQ5InwTZTnKjBM232QEgKI1TznzNNl8k6Nu882dzYbXTmU/231PLC8U3l7cfJMxj+wNAAAAANAR4RsAgBFyL9x2tXYqdx7NN2fLYlbzTTtrp3q9Xtw6M2rtVBN7nt4XzTAqANS0sPkmZ/3V+5o4Pk2uncrRK5l2icM3myNv289q4pG+AQAAAAC6IXwDAFCT5htOUs75vpcRvulVWjzVTOvMMGWCE9FnMKdxJmziyZhnMToWJZpvmmiaaTJ8cxLNNz++vZH2R+yXisaJGpkAAAAAAJokfAMAUNN8R+Gb3HBEzhoiJsfiXNx8s57RuFK1JCR6/48K3+SEObJnCEMv++FzNDHOIDgXa1vNNvBEgaDzTYZvMo5Qv+Sb6Mnl+cLbd/YO0h/e2xo+T/AG0noDAAAAAHRJ+AYAYITcsEtXa6dyLcxYO3WWzE33w5aPttZOpZSx8qnEqqWjykQnFmaKf61pYu1UzjxR801OA08ZdZtv7jTdfFMy7xI136SU0g9XN4Z+P1o7pfkGAAAAAOiS8A0AQE1drZ3KvbCt+eZs6fV6aXG2OHCVt3aqmqprp6IsR5kgxyD4+XNWX4Xhkox5ojnWSgSRmmgGitdOlViDVXeYIXLCNz9a3Rz6/XBNWOV3NAAAAABAecI3AAAj5F787yp8k2vcmnho3yAIXOWtnaoWVqi6dqpJ4QwV23fKGkTNNyUaiHLWPEWnLFo7dWdjJ1zf9GCejPuVfQudn59J54JVXT8a2XzT7CwAAAAAAHUI3wAA1DQ33c1fqXKvJUctKEyeJppvqorCZxvb+0O/HzeXNDfDek7zTRB2yZlnEARJ1nf20n6UGjmcJ2fNUzDV+fni8M323n7a3Bl+fh6ZJ+M+VdpmovabUWunojBQX/oGAAAAAOiQ8A0AQA3zM/3U74/XRV7NN2dP1HyzlrN2quLbOAq+bI4MvjS3yGhhtvjXms2M5pswDJRxgBaDz97BQbNNQNFI0dqplFK6s7mT9VpZYaAK76EnlucLbx/VfBOfr/KzAAAAAABUJXwDAFBDpyunMi8ma745ewbBOV/bylg7VfG1o7BX1bBJmTVYYftOB6uvUkppMWi+SSmlte28FqImokk54ZvV9bzwTc5E1cI3xc03P7o9au2U5hsAAAAAYHwI3wAAjJBz8b/L8E3uSpeB5pszJ2pcyWm+qWo+XDs1PPiS06SSayEIH+WEb6JxcrIcOcG39YwgVErxWqUcy4M4fHN7o8HmmxbWTv1odXP4POEsAAAAAADdEb4BAKhhfgyDLsI3Z88gaFzJaVtpa+1U5eabBmfIWTvVhGj9V0op3csMQuVEb5pYO7W6vt3ZPMM8GYRvbq1tp/Uh79+o+UbxDQAAAADQJeEbAIARcq7dzk932HyTeTE5WkHE5Gmm+aZaWmFhtvhXis0R4ZswzFFinGiG9Z29uEkmCnNkzLGUsXZqvcEgUNTONZidSjNTxfdptvmmvKj5JqXh7TfRPGXWlgEAAAAA1CV8AwBQw8IYtszktG8wWaLA1VrmqqMqqjbfNLFWKXeGvf2DtLNX/Hrx2qk4zJHTOpW7AqyJw9Pr9dKFhdnC+2SHbzK6b6rkXZ5Yng/v86PVjUfnCQ5QX/YGAAAAAOiQ8A0AwAg5F5Kji/5Nyr2WbO3U2bMYBK5yAh9Vi0Lmo/BNxaaXXokelWiGlKqvvyojp3UqZwXYfRlhl4xnubBQPNPqenPNN1W6bx4/Px8GZYaFb/aDefqabwAAAACADgnfAADUkHPRv2vWTp09YfNNRuCjalQhan8a2XxT8fWGyXnPj1p/dShcY5Qxx1S/Fwbymmy+ycmXLA+aab7ZzxioSt5leqqfHj9f3H5TpflG9gYAAAAA6JLwDQDACDnNG12uncpZe5OS5puzaDE451FLSB1R2CQKvYxSJjyR00AVNfA0tQZrca67FWA5f0YtL8wU3r6au3YqJwyU9UyPemJ5ofD2P6jQfJP75yUAAAAAQBOEbwAAaliYGb+/Ts1Mjd9MtGsQBD5yVA0rRMGXnb2DtLO3/8j3G8q63J9hNn7Pr1dcf3Uo9/A0sQIspeaagS5E4Zv17YZeqfp7KArfDG2+iWapNAkAAAAAQDWuzAAAjJBzHTmncaMpihwYZbGBVWNV317zGU1LVdpvysyTs/5t1PqrQxlLlbJmic7FWmYIqKm1UxcGxeGbO2PQfPPkStB88175tVN9f2ACAAAAAB0SvgEAqCEneNClvuvNZ9IgaFtpU9bKpyHBl7C5pOG1U1XXX5UVNd+sb2c232SkXXIO0fLCbOHt2WuncuJJFf/8+UgQvvnx7c20e6w9KTo8/iwEAAAAALokfAMAMELOtdtOm28y7jNooAGF06eR5puKYYWs4Mv2sLVTze2dynnfbwSNM9E4uccnmuVe5tqpLDnNNwvF86yuN9l8U+1N9JGVQeHte/sH6c07mw99bz8YqOoKLAAAAACAKoRvAABq6DJ8k2NhzJp46MaggfNeNTiR856LVj4NU2aeuen415r6a6fyLM0Vh13WtzLXTjUxTEppeVDcfHNncyft78evljNPW803KT26eioaWfYGAAAAAOiS8A0AwAg5F2+7DLvkzNNECIPTZzEIfLSp6tqpJvX7vTQ/U/yrTdR8E8nNckSfwbXstVPxfXICShcGM+Hr3N2MZ2qyqei4J5fLh2+iNVjCNwAAAABAl4RvAABqmO+0+Sa+mjxuTTx0Y7GJ5puKYYWcz0CV4EvZeaL3fth8E64xypsjCkKtZa6disIlKeXNdGGhOHyTUkqrG9sZ88TqvIc+cG6u8D5/8N76w/MEA/WlbwAAAACADgnfAADUMG5hF803Z9PgJJtvMt5zm0OCL1F4ouvwTVMW54Lmm8y1UzlyDtFyRvjm9sZOeJ+sJp4agZdo9dQjzTfBQMI3AAAAAECXhG8AAEYar6aZvLVTJxfC4OScZAhsfjr+laKL4EsUAqq/diovzBE232SuncqqmsmwPJgN77O6HodvcgaqE3eJVk/98Fj4Zj8Kb9WYBQAAAACgLOEbAIAaclo/ujRu89CNqX6vdgCnalHI9FQ/zU4V/1oxLPgSr1UqN1D03h/WvvPQPA018SwGAbj8tVOxnKaZ8/NxIG+1seab+D6jfGRlUHj7H6w+vHZqv6E1YQAAAAAATRC+AQAYIefi7XyXzTcZ97F26uyK1h1FcptdhpmfCcI3FdZOlRWFj9ZrNt/kij6Da5lzZIVdMp5neqqfzgVtPFlrpzJeq86qp2jt1I9XN9Pu3v5P5gnDUtI3AAAAAEB3hG8AAGo4yXU/wwjfnF0nuXKsbuvMMGWzE1EQLlp9FTXx5I6zFARdtnf3086REEkducfowmCm8Pbb69vhczQVBholCt/s7h+kt+5uHZmneKC+7A0AAAAA0CHhGwCAEXKu3Xa55imnyWFh5uQCGJysusGrOkUhUQht6NqpjptvovBNUwZB+CallNa34lnitVz5LiwUh29W13PWTrWbvonWTqWU0h/c+snqqWiaOi08AAAAAABlCd8AANSg+YZxsZgR+ihSJ6tQt3VmmLLjRO/9zWDdU1NrjJYy1n+tbe+G98nLuuTNtBw13zS0dqrO6rKo+SallP7gvY0H/3u/6fQWAAAAAEANwjcAACPkNc10F3bJaZ7osomH8XKSwavofTcsfBOueSqZ46gyw8PzNCNn/dfaVkb4JufFMo/R8sJs4e2rOeGbnDBQzQDXY0tzhfd5OHxT/HyabwAAAACALgnfAACMMD9T/Felfi+l+dnu/jq1ubMf3kfzzdm1mBH6KFKntWR+Omid6WDlUxvtO1UsZTQQrQUtPLly8yXng7VTt3PWTmXEgerGXaL2mz9478jaqbCpqOYwAAAAAAAlCN8AAIzw6ScuFN7+xz6ynOaC0EGTNnbitgzhm7NrkLHuqEidsELYOjMkbBKGJ0pGOaIWqmEzlJonc5ycz2BW802Da5WaWDuVU8WTu5prlCeD8M0PV3/SfBMdH803AAAAAECXhG8AAEZYWZxNf+5Tj4+8/eqVj3Q4TUrrGW0ZCzXbTzi96jbf1BEGX4aunTr5GY7KaXbJsZjTfNPQ2qnceMly0HyzurHd6TyjxM03R8I3wXP1ZW8AAAAAgA4J3wAAFHjt6s+mn3tq+ZHv/7U//rH0V37x6U5nyWkCWdR8c2bVbr6p8dh45VO8Mu24ssUlVdp3ysidZ266n6aC5Mfadhy+abJp5kIUvslZO5U1T9Y4I31kZVB4+49WN9Le/v1B9vftnQIAAAAAxof/NBoAoMD5+Zn0f/uXv5D+6996O33nh7dTSin9+T/24fSJD53rfJbPP3Op8Papfi/9wscvdjQN46Zu8029tVPFmf7NYcGXhqtvwvBN1HzT0BqsXq+XBrNT6e7m6IDN2la9INBPZsoTrZ3a2t1Pmzt7hSGqnGagsqvCjouab3b3D9JbdzbTE8sLmm8AAAAAgLEifAMAEOj1eumLn/xQ+uInP3Sic1xcnE1/5ENL6Xfeujf09p9/ajmdmy++yM7kGpxg61HdlU/DlM1ORDNsVpihqqW56SB8k7N2qrl00oWF2fA+tzd2isM3HeydeioI36R0f/XUE8sLaT8YSPYGAAAAAOiStVMAAKfIV//Sz6aZqUcvKy/MTKV/8y986gQmYlwsztXN1VePK1QJ30ThktyVSrkz7OwdpJ298uuvfjJP/n2jINRaxgqsJtc8RWunUopXT2Vlb2omXp5cLl47lVJKf/De+v15goH61k4BAAAAAB0SvgEAOEWufHQl/V//xV9Mn/3oyoPv/clPPJb+k3/pF9Onn7xwgpNx0uo239TJKsxHK58ywiZ1RTOkVNzAc5BV7ZJnKQhCZTXf5IRvMgNT0dqplO433xTPk7N2qp6F2an02FJxS88fvLeRNY/wDQAAAADQJWunAABOmV+6fCld+xtfSHv7B2l3fz/NTZ/cuiHGRxT4aFOVlU8NZl2yZkgppc3tvXS+4mq2MlGOwWzxuVjfjsM3OXLzJTnhm9X17cLb85p46gdenlwZpD+8N3qWw+ab/Wge2RsAAAAAoEOabwAATqmpfk/whgeiwEekTlah2tqpZuU0/xQ33xQ/tkywJFoBtraVsXYq+9ViCzNTQ9fVHbUaNd9kTNRE3uUjKwuFtz9ovgnm6QvfAAAAAAAdEr4BAIAJsDhXd+1U9bTCQrR2amev9FqnsuPkNN8UhW+aFJ2LvLVTzcVver1eurBQvM7pTrh2Kud1ykw13EeWi8M3P1y9H76Jmm9yV3IBAAAAADRB+AYAACZA3eabOuaD4MvBQUpbu/vHvtds9000Q0oprW8XNN8Ejy0T5QibbzLWTuUcnTJhl2j11Op6A+GbBgIvUfPNj1Y30t7+Qfj+6ftNFwAAAADokH+SBACACVC7+abGY3NaZzZLts6UDXJE7TsppbRZFL5pMH2zGMySs3YqR5ljdGEhCN9sbBfe3nQYaJSPrAwKb9/ZO0hv392M14RpvgEAAAAAOiR8AwAAE6Bu802d4ERO8OX4yqcw63KK105F5yKr+abZYqC0HIRvbm8Uz9R0U9EoUfNNSin94NZG2g/maSIIBAAAAACQS/gGAAAmwCAjANOWrOBLQetMZzMUhG8OgjhQmSzHUrR2aisO3+R0zZQJmFwI106NR/PNk1nhm/UwnNSXvgEAAAAAOiR8AwAAE2Bmqp9mp6v/9b7Omp75CsGXeG1QOf1+L80FP3/bAaBDg2AF2HrG2qmcopkyxyhaO3V7Y6eBeeoHXgaz0+mxpdnC+/zgvfW0H71/ZG8AAAAAgA4J3wAAwIRYrNF+0/baqc2Sa6famKOw+SYMc+QfoLD5Znu3kTVOZWZaXigOtEThm6abeIo8dXFQePv3b62Hx0/zDQAAAADQJeEbAACYEIPZ4tBHW/LWTu2Xes4q2YlojqLmmyhaUmac6DzsH6S0uVN8PJoOJ11YKJ5pdb2J5ptmPB2Eb35wa73R8wUAAAAAUJfwDQAATIjFYN1RW7LCN8dbZxpofik7R1HzTZNyzsPa9m7h7U2HXZYHxc03dzZ30n7BLqecs1WmiadIFL75/q31tB8coKZmAQAAAADIIXwDAAATok7zTZ2swtx0/GtF2eBLlfBEnbVTUdqlzDiLGedhbSsI3zS85unCYKb49Q5Surs5eqacMFC/o7VTb93ZKmwxanIWAAAAAIAcwjcAADAhTqr5pt/vpfmZ4l8tNo8FX9pYGxQ132zWWDtVxuJcTvimfgtPmYDShYXi8E1KKa1ubI+8LS8M1Ezi5amV4vBNSvfbb4pnaWQUAAAAAIAswjcAADAh6jXf1EsrhMGXDlY+Rc0360FbSpFeiThQV2unyljOCd+s74y8rYUtYSM9fal++KYvfQMAAAAAdEj4BgAAJsRiED4pUjeqEIVvjq8JCsMcFQaaj2YoCABF85TJcuSEoOK1U81aHsyG97m9URC+CR7bZNbl8fPzaWaq+AmjIJXsDQAAAADQJeEbAACYEIOMdUdtmQ+CP8eDLzlrjMoah/adlPJCUNHaqYMgDVQ2XHJ+Pn5vrBaFb6J5yo1TaKrfSx/JWD1VpKkVWAAAAAAAOYRvAABgQtRqvqmZVQibb0oGX8qseTo0KBkAOqrJMND0VD/NTRf/qhWtnYqUPTrTU/10Lghn3V7frj5Pw2GXpy7WC99YOwUAAAAAdEn4BgAAJkTOuqNRqoRdjgpbZ8qunaogXDtVsKqo6XmWgqBLtHaqDRcGM4W3F66ditZyVRmowFMrC7UeL3oDAAAAAHRJ+AYAACbE4lz15pu6Fmq0zgxTpbgkmmG9IHwTKdvsMgjORTRLGHapcIAuLBSHb1bXC8I3QTNQ00UzT9duvmloEAAAAACADMI3AAAwIWo139QMK4StMzv7D33dRpNK2L5TuHaq2XkWg3NxL2i+CcMuJedJKaXloPlmtVbzTbNpl7rhm6bXYAEAAAAAFBG+AQCACVGn+aZuVCEKvhxf+dTC1ql4hpLtO3UsBmun1muunaqSLVlemC28vc7aqab3PD1VO3zT0CAAAAAAABmEbwAAYELUab6pq07rzDBtrJ06HgA6Kl7zVG6WKHyzVnPtVBXnw7VT2yNv6zh7k56+VHftlPQNAAAAANAd4RsAAJgQ0aqjQjWzCmHw5Vj45qCFdEkcANofeVu05qmsxeB4rEVrp1pY8xSunVovar4J1mA1nHU5Pz+TLgRhoSKiNwAAAABAl4RvAABgQgxqrZ2qF1eYL7l2KlJlnigAtL23n3b3RgdwCucpOU7UQhQ234QDlZsnpZRWovBN0dqpcJzm4y5P11g9pfkGAAAAAOiS8A0AAEyIWs03NTW9dqqNGVJ6tIHngYabZpaCIFTUfBOpEi1ZXpgtvH11fXt0w03Da7ly1AnfyN4AAAAAAF0SvgEAgAkxCJpfitQNKyzMFv9qMTL0MkKVeaL2nSpzVDWYC5pvwrVTza/litZO7ewdpPURjTz70dqpylON9lSt8I30DQAAAADQHeEbAACYEItB4KNI3ahC1DpzPPQSZUuqzJMTPtrcHr52KlyrVHKgpSh8sx2EbxqeJ6WUlgfFzTcppfTe+nbFecZt7VSDgwAAAAAABIRvAABgQtRpvqkrap3ZONaochDGOcpbyPj5RzXfRE0zZbMc0blY3woaeBpeg5VSSitB801KKa2u7wwfp4WwVMTaKQAAAADgtBC+AQCACTE33U9TFSs/6jaXRMGXrd39tL9fInBTYZ6ofSellNaDxpmmRC1E94K1U5Eqp+tCnfBNnAZq3FMXFyo/ti99AwAAAAB0SPgGAAAmRK/Xq9x+0/baqZRS2tz9SdtL1KRSRdS+k1JR803wwJJhjsXZ4vDN1u5+2t0bvgIrpXaagZYX4rVTqxsj1k6dQPPNE8sLlddHid4AAAAAAF0SvgEAgAkShT7akhO+Ob56qkiV8ETO2qnNUeGbCq9XZHEunmWt4Hi0EXaZne6nxeAYjW6+CeZpoWlmZqqfnliu1n7TxjwAAAAAAKMI3wAAwAQZZIQ+hqmbVZjPCL4cbZ1pofgmMwA0um2mSNnDE62dSql4BVZbYZflQXH7zer68OabKA3UVtbl6YuDSo+zdgoAAAAA6JLwDQAATJCqzTe9mot6stZOjWidGaZKdmKq30uz08W/4lRdO1V2npz1X2tb+cfjuKpna3kwU3h75eabivNEqoZvZG8AAAAAgC4J3wAAwATJCX20oWzrzEHUpFIxzhHNsVHQNtOkpYzmm7WtguabNqqBUkorQfPNe6PCN2E4qZ20y1OVm28aHgQAAAAAoIDwDQAATJCcdUdD1QwrLIzB2qmUMsI3o5pvgonKHp5BRgPRWuHaqSjtUnKg910Imm9ubwxfOxWHpdpRvflG+gYAAAAA6I7wDQAATJCqzTd1swrzOc03La+dSikOAR1t3zmq6aaZvOab0ccjbJopO9D7VoLwzcjmm+B52wq7fOzSYqXHyd4AAAAAAF0SvgEAgAmymNG40oa8tVNHwiYtVd9EIaAyAaCjyoZL5mf64eqj9RorsKqGXZYXitdOra6Par6J5qk0TujpS1XXTknfAAAAAADdEb4BAIAJMpir2HxT83VnpnppKkibbJZpvqk4R9T8U2aGo8rO0+v1wiDUva2itVPtWA6ab1arNt9UnCdyYWEmXVwsDgwNI3oDAAAAAHRJ+AYAACZI1eabumuDer1e2H5ztHWmrXBJOMN2tfBNFVEQar1g7VRUNVP1dC0PguabjZ10MOS1h32viXlyfLRC+43mGwAAAACgS8I3AAAwQao23zQhXPlUIvhSNTsRzbA+ovmmjXBJm803VaMlywvFzTd7+wfpbsFco+dpL+zysUuLpR8jewMAAAAAdEn4BgAAJkjl5psGXnthtvjXi4eab8KwS7WJFoK1U6MCQG008SzOFZ+L9e3yIZdDVY/PymJx+CallG4PWT0VnK6xa76p2+QEAAAAAFCG8E3LVldX0+uvv56ef/759Mwzz6Rer5dWVlbSlStX0tWrV9ONGzdOesQHxmHWGzdupOeffz698sorjT/3OPx8AABtGwThk1GayCpEK582O1k7VfwrzuaI5ptIlWaX6FzcK1g7FYVdqrqwULx2KqWU3lvffuR7B8EZazPqUqn5poU5AAAAAABGEb5p0SuvvJJWVlbSSy+9lK5fv54uX76cXn755fSlL30ppZTStWvX0pUrV9KVK1dOPPhx0rMehm6uXLmSrl+/3vjzn/TPBwDQlahtpU1R+KbM2qmqBkHzz8bItVPBE1dIcyzVaL4Jm4HKj5NSSmllEDffrFZqvmkv7lKl+aav+QYAAAAA6NDJ/cv8BFtdXU1f/OIXH4Q4Ll++nL75zW+my5cvP3S/a9euPWhcuXLlSnrjjTfSCy+8cKZmvXHjRnrllVdaCdykdPI/HwBA1yo33zTQFTIfhW8eWjtV++WqzTBy7VTzAw2C8M1aUfNN8NxVsyUXFjLCNxtDwjfVXq4RVZpv+rI3AAAAAECHNN+04Gh7yvLycvr2t7/9SNgjpZReeOGF9MYbbzz4+urVq+n111/vbM6UTm7WtptuDp2mcwEA0ISqzTeNrJ0Kgj+jWmeGqTpP2L5Tee1UeUtzxbOsbY1uvolVO0DTU/10br74PbI6bO1U2HxTaZwsy4OZdD6Y+TjFNwAAAABAl4RvGnb16tV08+bNB1+/8cYbaXl5eeT9X3jhhYcaVl566aXO1h6dxKyHoZsvfvGLaXl5udV2mdN0LgAAmlK1+aYJUfBl82jzTdClUrWJZ2G2+Feckc03LYRLohVYxWunyr9eruVg9dTQtVPR+Wox7NLr9dLHHivXftPmGiwAAAAAgOOEbxp07dq1dO3atQdfP/vss+m5554LH/fqq68+9PXVq1cbn+24k5r1G9/4Rnr11VfTe++9l9544430xhtvpJdffrnUc+Q4TecCAKBJi0Hgo01h68yI4EunM1RsvqkiaiG6V9B809baqZRSWhnMFt7+XpXmmwbWlhX5aMnVU7I3AAAAAECXhG8a9Morrzz09Ve+8pWsx12+fPmhYMjNmzdbX3l0UrO++uqr6dlnn33oe88//3z243OdpnMBANCkQbDqaJQmwgrzJdZOtbXGaCEIH40K34RhlwrhksXgeKwXhJEOggNU53RdWChuvrk9pPkm0nbY5WOXBqXu35e+AQAAAAA6JHzTkOvXrz+04iilVGql0vGGlePhkSaN26wXL16s9fjjxu3nAwDo0lg33+zsP/jfba1VimbY3t1Pe/uPvngb8wxqNN9Eum++aS8MlKNs801f9gYAAAAA6JDwTUO+9rWvPfR1zoqjo770pS899PXq6mprjSunadYqJv3nAwAoEoVPRmlibVD02psl1k5VnWZhNv4Vp8rqqSphl6WghWh9ey8MtbRheVDcfLO68WjzTdxU1G7apWzzTdtrsAAAAAAAjhK+acDq6mq6du3aQ987vlopsry8nJaXlx/63htvvFF3tEecplmrmPSfDwAg0u/30iBYdzRME9mJhRJrp9oynxE+2hgaAgqaXSocn0HQQrS3f5C2dveH3haGXWqES5aD5pvVIWunhpQFHZunXWWbb2ydAgAAAAC6JHzTgF/5lV955Huf+9znSj/PZz/72Ye+vn79elpdXa061lCnadYqJv3nAwDIEYU+2hIFX8qEb6qGJ3KafzY7CAGllNJSsHYqpZTWRqyeOmghDHRoeSFovhm2diqYp+30zWNLs2mxRKis7SYeAAAAAICjhG8a8M1vfvOR75VtWxn1mOvXr1eaaZTTNGsVk/7zAQDkWAzWHQ3TRFShzNqpaN1S1WaXnODRsBBQG00zOQ1Ea1vVgkB1ztfKYnH45vbGTto/VnUTH5929Xq9Uu03fdkbAAAAAKBDwjcNGBbKuHz5cunneeaZZx753rAwSR2nadYqJv3nAwDIUaX5pommkIXZ4l8vulg7ldN8M2ztVBQuqSKr+WZ7RPNNC/McWl4oXju1f5DS3c2H54rG6aJp5mOPDbLv29d8AwAAAAB0SPimptXV1UfWES0vL1d6rmEhkZs3b1Z6rmFO06xVTPrPBwCQq8x6niZFwZfd/YO0s7efUsoJc1SbYT4IAKWU0vqQ8E2kyjyDjPDN+qjwTThP9XDJ8qC4+SallN47vnoqbCpqX5nmG9kbAAAAAKBLwjc1DWtauXjxYqXnGva4b33rW5Wea5jTNGsVk/7zAQDkygl9HNdEVmE+p3Xm/fabtppdcppvNoetnQrjLuUtZTQQ3RuxdqrV5ptBcfNNSimtbuw89HVbYakyPnYpv/mmiyYeAAAAAIBDwjc13bp165HvVVlzlNLwlpZhbS5VnaZZq5j0nw8AINfSXPnmmyayClnBlwqtM03P0MX6q5RSWshoIFrfGt58E6lzvlYymm9WjzXfRGGgXgfdN6Wab1qcAwAAAADguPL/SSwPaTKMMaql5datW5XXJx11mmatYlJ+vr/9t/92rcd/5zvfaWgSAOC0GmQ0rrQhJ2zyoPmmhaaZlFKanuqn2al+2n5/vdXQGYYEgMJwSYW0y+x0PMu9EeGbto5PSimdm59JvV7xz7y6frz5Jlg71UnzTX74pq/5BgAAAADokPBNTe++++4j32s6nNFUqOQ0zVrFpPx8X/jCF1p/DQBgsi1mhGCOa2JNT5OtM3XmmZ8JwjdD1061Y3FuKm2vj55lfUQTUBwGqj7TVL+Xzs/PpNvHVksdVbb5pgsfPDeX5mf6aXNn9PE81Je9AQAAAAA6ZO1UTTdv3mzsudpuVDlNs1Yx6T8fAECuwdzJZOznc8I374dN4jVG1UUNPMOabyJV54laiEY130TqrnmKVk+990jzTbEummb6/V766MW89hvFNwAAAABAl4RvToFbt26d9AjZTtOsVUz6zwcATIYqzTdNKLd2qsU5ghDQ0OablppmloIg1Pp2xfBNzXDJhcFs4e3HW3HabOIp42OPDbLu10STEwAAAABALuGbmi5evHhqXuM0zTqur32SPx8AQK6obeW4pnIKOWunNrPXTlWfI2rgGb52qp040GCueJa1rVFrp9rd8xQ33xxbOxUcn+7CN5nNNy3PAQAAAABw1Mn00U+QLtYTNfUap2nWcX3tLl7j137t12o9/jvf+U566aWXGpoGADiNFoPAx3FNBRXy1k7tp5TiJpU6BmO0dipqvlkbsXaqzbVcKaW0vFAcvlk9tnYqyibVXYOV63Jm+KaLNVgAAAAAAIeEb2q6dOnSI99bXV2t9FyjHtdU28ppmrWKSfn5Pv/5z7f+GgDAZCvbfNOUqX4vzU730/bu/sj7DGudGaZOdCJafzW0fSdcq1RtoigItDZi7VSUTaq7Vmk5WDu1+kjzTTRPrXGyffyxpaz79XW8AgAAAAAdGvt/krxx40ZaWVlJvV7vxP7vmWeeSTdv3hw632lqWzlNs47ra5/kzwcAkKt0802DyYlo9dRPwjftVd9EM6xXaL6pajFsvqk2S+3mm2Dt1OrGw8030RqsrnpmPvbYIOt+XTXxAAAAAACkdArCN7du3arcXtKUmzdvjpzhs5/97CPfu3XrVqXXGfa4JsMep2nWKib95wMAyFW2+abJmEIUfNnMDL7UCQRF66+Gte+EzS4VZ1kMzsX6qOabFtdypZTSStB8897aseabMam++cDSXLjKK6XumngAAAAAAFI6BWunnnvuufTee++NbJ7pwuXLl0cGL5599tlHvld11mGPGxYoqeo0zVrFpP98AAC5osBHm+ZnivP9h8GXKMxRJzwRBoCGhW9aSrsMghaieyOabw7CPVhVJ7ovar65s7mb9vYP0lS/9/48rY6TrdfrpY89Nkjf/eGd8H4AAAAAAF0Z+/BNSvcbR4YFK8bF5cuXHwprVG3qGfa4559/vuJUw52mWauY9J8PACDHwmzZtVPNvXZu60ybxS6D4OffqLB2quoxWmqp+ab+2qni5puUUrq9sZMuLs7mzdNh1uXjjy2F4Zu+7A0AAAAA0KGxXzt1Gjz33HOPfK9K6GNY20rToaPTNGsVk/7zAQDkWAzaVo7rNdhbEgV/coMvdSaaj2aosHaq6kSDYEXS2tbw8E2kbrPL8kJx801KKa2u/2T1VNTE02XW5eOXBuF9+ppvAAAAAIAOCd804MqVK49871vf+lbp5/n1X//1R743LExSx2matYpJ//kAAHIMZk6u4DJ35VNba55yZqjSfFPVUhCEWhu5dqpdKxnNN6sbOw/+d9x8013Y5aOXFsP73DkyOwAAAABA24RvGvDiiy8+8r0bN26Ufp7jj2kj7HGaZq1i0n8+AIAcZddONVlbEgZfhrTODFUjzFFlhrbWKg2CtVMbO3tpb3/IiwcD1T1lFwblmm8iXfbMfOyxuPnmx7c3O5gEAAAAAOA+4ZuGvPDCCw99Paw5JXJ81dFLL71Ua6ZRTtOsVUz6zwcAEJmd7qeZqfw4RJPBiXDl0/utM202u4SrryqtnapmKVg7lVJK69uPrp6K5qlbNHN+fjpN9Yuf5L21o803QRiow/TN5ceWwvv83NPL7Q8CAAAAAPA+4ZuGHA9nXL9+vdTjr1279tDXy8vLj4RImnKaZq1i0n8+AIAcUeNKW5pqvqmT5ZhvYe1U1XkGGS1Eo1ZPFenVjEz1er10YaG4/ea9I803YRiow+6blcXZ9DOPnyu8z6efuNDRNAAAAAAAwjeNee6559Ly8vKDr1dXV0uFPr7xjW889PVXvvKV7Me+8sor6cqVK+nq1auPNLaM26xdmPSfDwAgR07o41CTrSVR+Gbz/fBNW2ueUop/9q3d/bR/bNVTW80uixnNN2vDmm/arAZ630qwemp1/WjzTfBkXe6dSin9s7/w9Mjb/vRPfyB94Nxch9MAAAAAAGed8E2Dvv71rz/09de+9rWsx62urj7UtrK8vJxefPHFrMc+//zz6bXXXks3btxI165dS88880xWAOckZh0lZ96yxunnAwA4CaXCNw0mJ3JXPkVhl1ozBAGgo3O0LSt8szVs7VT7a55WBrOFt996qPkmmKf+OKX81c9/NP3zv/TRR77/yQ+fT//el36u42kAAAAAgLNO+KZBL7zwQnruuecefH3t2rWsYMlXv/rVh77++te//lBzyyg3b94c2uhyfG3SOMxaZNjrrq6u1nrOcfr5AABOQk7oow1NrXyqEwiqEr5pa63SYsW1U1003ywH4ZvVo+GbFpuKquj1eunf/oufSv+Pf/WPp5f+1OX0N/6JZ9L/7i//XPp//i/+RLq4WPxzAQAAAAA0TfimYW+88Ua6fPnyg6+vXr1aeP/r16+n11577cHXL7/8cnrhhRdqzfDuu+9m3W8cZk3p0TVPKaX0rW99q/bzjsvPBwBwEnICKIe6XTu1n1KKwy51zGcEXh4JAbU0UE4Ian3I2qlIr4GTdnGxeO3Ue2s/WTu1H4VvOu++uX8MfvYjy+kr/9Qn0yt/7mfSX/y5J9NUv/s5AAAAAACEbxq2vLycvv3tbz8Ifdy4cSNduXJlaJPL9evX0/PPP//g65dffjm9+uqr2a91+fLl9Oyzzz7y/S9/+ctjN+swN27cSFevXk03btwYettLL71UayXVSf98AAAnqUzzTZNxhYWZ4l8xctc91cmW5ASPNkuunao6T84s94aunWpftHbqvSPNN9FEXTffAAAAAACME+GbFiwvL6fvfe976eWXX04p3Q99rKyspKtXr6bXXnstvfLKK+nKlSsPwh6XL19O3/zmNyuFPX71V3/1wXqlw+cZFsgZh1lTSun1119PzzzzTOr1eunKlSuFK7KO3veZZ54Jm2vG4ecDABgXCxntLyfxug8aZ1pMlwxymm8eWTvVTrik3++Fq6fWh6ziCtc8VRvnIdHaqffGeO0UAAAAAMA4yf/PYSnt1VdfTV/5ylfSr/zKr6Q33ngj3bhx40HY5PLly+mFF15IX/7yl2utNlpeXk7f/OY3T8WsKaX04osvphdffLH2vGV19fMBAIyLKPBxVBMrjA7NB00vGzt76SBKcqR64ZKctpnja6cyRqpsMDed1oYEbA6tDW2+ab9pJlw7tb6TDg4OUq/XywgDSd8AAAAAAGeX8E3LlpeXTyxwUtZpmrWKSf/5AACOGsye1NqpOPiytbsfFt/UCZfMZwSP1suunapxlJbmptM7d7dG3j5s7VQ4TwMnLWq+2d7dT+vbe2lxbrqTMBAAAAAAwGll7RQAAEygnNVLbchZd7Wxndd+U3mGjADQZtnmmxrhksW54nmGNd+0uZbr0EoQvknpJ6un2mwGAgAAAAA47YRvAABgApUK3zTYWpK18imjdaZO08zMVD9N94sfnzNDUxaDFqJ7W4/OEmeB6p+0aO1USimtru/kzaP6BgAAAAA4w4RvAABgAp3U2qn5zPBN20UqUQPP8fBNuFapxixLc8XnYljzTdQM1MXaqZRSurWW13wTZJ0AAAAAACaa8A0AAEygcV87FaoZ5ogaeI7P0OZapcUK4ZtIE1mX5YW4+ebB2qkWw0kAAAAAAKed8A0AAEygQRD4OKrJlUE5a6c2d/ZaDbuklNF8kxMAOqLOMYrCN/eGNt9Ufrls01P9dH6+eLbDtVNRVZG1UwAAAADAWSZ8AwAAE2iQEYI51GRuIi98sx/ep+5IYfPNI2un2ptnaa54lrXtIeGb6EkbOmkri8Wrpx6snYrGaWQaAAAAAIDTSfgGAAAm0CAIfLQla+3Uzl68xqhmuGS+ZPimTfHaqUdniZpvmgq7LA+Kwzerh2ungoEU3wAAAAAAZ5nwDQAATKDBbIm1Uw2+7tx0/CvGRgdrpwZBCGjzePNNuFap+ixLFdZORZoKu1wczBTe/t77a6fi0yV9AwAAAACcXcI3AAAwgRYzGmgO1W2ZOf5c0cqnze24dab1tVOPzNBeGihuvhm2dqrldNL7VoLmm/ceNN8UP4/mGwAAAADgLBO+AQCACTQIAh9tilZP3V871a75YIb1jADQUXWyJVH4Zn17L+3vP3xExmXt1IPwTfA8sjcAAAAAwFkmfAMAABNoEDS/HNV0cCJsndnJaL6pOVTZGeJml+oDLc3F52Jtu9zqqabaii4uBmun1t5fOxUcIM03AAAAAMBZJnwDAAATaJAR+DjUdHBifqb414yN7b02tzyllOLwzWZGAKgpi7NxC9HaVndNPEc113wjfQMAAAAAnF3CNwAAMIFmp/ppqn8ygYho7VRO8KVuIGiQsfrqqDbXKkVrp1JK6d7Ww803UdNMU1aC8M369l7a2o3DUppvAAAAAICzTPgGAAAmUK/XCwMoR+7d6GvnrHw6CNIcdZtU5qMZto+vnWov7LKUEb5ZOx6+Ce7fVNhlJVg7lVJKq+s78fkSvgEAAAAAzjDhGwAAmFC54Zvm107FwZe2i12i9p3j4ZtQjWOU03zzSPgmapppKDAVNd+klNKtte3O5gEAAAAAOI2EbwAAYEItzsahjzbkNN9E6gaCys4Qr52qPlBO883xtVOhpppvMsI3763H4RvZGwAAAADgLBO+AQCACRW1vxxqOjcRve7mzl4Ydqk9Q9nwTYsDzc/0Uz84yGvbx9dOtX2E7lseNLR2qqmBAAAAAABOIeEbAACYULnNN02vnWqi+ab2DGEAaD/t7+cHXOoco16vF66eurdVLgzU1Cmbn5kK15NlrZ1q+k0EAAAAAHCKCN8AAMCEym2+adp8FL7Z3ksHbVbNpDgAlFJKW7v7D/532z0z0eqpta3jzTfFmsy6RKunVte3M9ZyAQAAAACcXcI3AAAwoRbnctdONRudiEI/Gzv7hbenVL9JJSd4tH5s1VORukcoar45Hr6JNHnOVhaLV0+9t76T0XzT2DgAAAAAAKeO8A0AAEyohZnxXDu1ubPXepNK1L6T0sPrr6ImnrrHKF47daz5pu0qniOi5pv31rbj49PkQAAAAAAAp4zwDQAATKjc5pumReGb+2unTnaGwzm6shSci0ebb9oNAx21HIVvctZOqb4BAAAAAM4w4RsAAJhQg9nM5puGX3c+XDsVh17qZjkGGWuncuY4VHfN02JwLta2Hp6lyzVPFwfFa6dure9ovgEAAAAAKCB8AwAAEyongJJS860lYfNNidBL5RlywjfbR9dOFd+37iFaKrl2KlI3DHRU1HyzmtF8I30DAAAAAJxlwjcAADChcsM3TYvCN9u7++Fz1A2X5IRv1jsIAR1aDMI3x9dOtb2W66iVoPnmvbXtOJwkfQMAAAAAnGHCNwAAMKFy1041bWG2/q8ZdZtmogBQSiltHm2+Cbpd6s4ThW+ON9+0Pc9RK4vFzTd3NnfT7n5xYKovewMAAAAAnGHCNwAAMKEW53LXTjX7uvMZwZe2zUz108xU8Q+2XmLtVF1LwblY2z7J5pvi8E1KKa2u7xTe3vR7CAAAAADgNBG+AQCACZXT/jKur9tEliMKAW2UWjtVb6J47VS5FVi9BtMuOeGbW2vbhbdbOwUAAAAAnGXCNwAAMKGiwMehpltLFmZPvvkmpZQGwRwbJZpvul871Z2VxZnwPmH4RvYGAAAAADjDhG8AAGBC5YZgmm4taaT5poGRojnKNd/UsxSEb7Z399PO3v6Dr8MwUBNDvS+n+WZrd7/wduEbAAAAAOAsE74BAIAJtTib13zTtJNad3XcQvDzrx9tvgm6ZupmS3JaiNaOtN+E8zQYdhnMTqXZqbq/GkrfAAAAAABnl/ANAABMqGjt0qGmW0vmG1k7VX+ohZniX3c2d/LXTtW1NBcfk+Orp4o0ecp6vV7W6qni52hoGAAAAACAU0j4BgAAJlR2+Kbh1x2XtVODsPmmRNil5jx5zTdH1mC1HAY6Lmf1VBHZGwAAAADgLBO+AQCACRWFT9oyM9VP0/2Tj2PMByGgjZ39B/87yrr0asZLclaA3Xto7VQwT8NVM8sDzTcAAAAAAFUJ3wAAwISan+lnhSKaDnKkVL/9pomJouafjaPNN62vncppvjkSvgn2YDV9xi4u1m2+kb4BAAAAAM4u4RsAAJhQvV4vDTJCMG3EJuYzV161KQoAbezsFd5+VDdrp7pbg3Xcct21U7I3AAAAAMAZJnwDAAATbJAR+mhD7eabBtIcC0EAaH37J+Gbg5arb2an+2l2qvjXrzJrp5q2UnftVENzAAAAAACcRsI3AAAwwRZzGmhaSE7UDd80MkO4dqpE803dYVJKi3PF8zy8dip6tmZP2krt5hvxGwAAAADg7BK+AQCACbYwGzffjOPaqSZmilZuHV07FYVdmgiXRKun1h5q4onmqT3OQ+qGbwAAAAAAzjLhGwAAmGBZzTctWJip96tGE+GSMs03Xax5WgrCN0fXTkWaDkxdXKzbfNPQIAAAAAAAp5DwDQAATLAogJJSOyuDJm3tVBPC5puH1k51EQf6iZW64ZtW+pMAAAAAAE4H4RsAAJhgiye0dion9FOkkeabUmunisMuTcwThW+ONt90vXbqYs21U5pvAAAAAICzTPgGAAAm2OCE1k7Nj0HzTfSz7+4fpO3d/Y6mSWlprnieo803Ufqm6aaZi0t1m28AAAAAAM4u4RsAAJhggyDwkVI7rSV11041ES7JCQAdtt+ETTMNzBO1EK1t5a/BavqcLc5Opdmp6r8ear4BAAAAAM4y4RsAAJhgg6y1U80nJ+qGb5qQ87NvbL8fvonSNw0ot3aqg4GO6PV6aWVxptbjAQAAAADOKuEbAACYYCe1dmqh7us2kOXICQAdNt9EmsiWLAXhm6Nrp6IwUBtZl5VB9dVTojcAAAAAwFkmfAMAABMsJ3zTRpAjZ+VTkSZGygkArW/fD7zEa6fqi5pvSoVvWoi7XFqqHr6RvgEAAAAAzjLhGwAAmGA5q5faMA5rp3LCN5uHzTcd7J1amiuep9TaqbFrvpG+AQAAAADOLuEbAACYYKd17VSvgTqeQUYAaH27u7VTYfPN9l466CAENMrFxRrhG9kbAAAAAOAME74BAIAJltN8s7vffODjtDTfbLwfvuki8hKFb/b2D9LW7v79ebovvqnVfNMXvgEAAAAAzjDhGwAAmGA5zTcbme0vZczXDN80keWYm+6HjSwbO7nNN/UnWgrCNyn9ZPVUFAZqYp7jajXfWDsFAAAAAJxhwjcAADDBFufiEMza9m7jr1t37VQTer1e2MDzoPmmg6aZqPkmpZTube52Ns9x1k4BAAAAAFQjfAMAABMsZ+1UG803dddONRXmiJp/1h+snWp/8VSZ5puTUK/5BgAAAADg7BK+AQCACZazdmprd7/x160dvmkozhGtv8pdO9XEODnhm7UH4ZviMFAbTTMrg+rhG9U3AAAAAMBZJnwDAAATLKf5pg0Ls+Pxq0YUPspdO9WEMivATt3aqQbnAAAAAAA4bcbjX8QBAIBW5DTftCFqnIk0VaQSNfDkNt800cSzmBGEurd1uAYrmKeFppmVxZnKj1V8AwAAAACcZcI3AAAwwequfzptr3vcQhA+Ws9svmkiXNLv98Iw1E/WTnVvbnoqazXWME2tCQMAAAAAOI2EbwAAYIL1+ycTiohCL5Gmpo5CQJs7eU0zTVkMwi2H4ZuDIA3U1lmt2n6j+QYAAAAAOMuEbwAAgMbNT49H880gWPW0vp3XNNNUtiRqlrl3GL6JnqilsMvFwWylx8neAAAAAABnmfANAADQuH6/l+ama/y60VCaYz5ovtnY2U8pZTTNNDTP4lze2qlwDVZLcZeLixXDN9I3AAAAAMAZJnwDAAC0Igq+FGkqXDII1l9tZDbfNGUxaOK5t7WX9TxthV1WKodvpG8AAAAAgLNL+AYAAGjFQo3wTWMzROGbncywS0NhoGjt1Fru2qmWVF07BQAAAABwlgnfAAAArYiCL0WaKlKJAkDr2/fDN9Gap6Ys5oZvojVYjU30sOrNNw0PAgAAAABwigjfAAAAraizdqopUQBoc7vbNU9R+ObeVt4arLbCLpeqhm9aiwMBAAAAAIw/4RsAAKAVCzPVf91oKsoxCMI36++vnToIFj01Nc/SXPE8a9uZ4ZuWwi6abwAAAAAAyhO+AQAAWlFn7VRTovadjbFbO9XtPMddrNx8AwAAAABwdgnfAADAhPtX/vQzhbf/uU893srrLtRYO9VrqEolar7Z2t1Pe/sZSZeG5lnKXDsVNvG0lHZZGWi+AQAAAAAoS/gGAAAm3J/5mQ8V3v7Zj6208rpR60yRpsIcOQGgzZ29IOrSnLj55v3wTTBQW2GX6s030jcAAAAAwNklfAMAABPu559aTn/+j3146G0//aFz6X/yi0+38rp1mm8amyFj9dXGzl54n6aiJVH4Zn17L+3nNPG0FHa5sDCT+hWeWvMNAAAAAHCWCd8AAMCE6/d76d/70mfSP/9LH03zMz/5FeCf+vTj6f/0L3w2DWaLAyFV5QRfRmkqy5ETANrY3ksHQdVMU+GSpbl4nrXt3bD5pi1T/V5arrh6CgAAAADgrGrnX9kBAICxMj8zlf7X/+NPp3/tz/50em9tOw3mptIHz823+prj0HyTEyza6HLtVMY8a1t76SCYqM2mmZXBTLq1tl3qMT3VNwAAAADAGSZ8AwAAZ8iFhZl0YWGmk9earxG+aSrLkRMAWt/OWTvVzEDR2qmUUrq3FTfftBl1ubg4m773zlqpx4jeAAAAAABnmbVTAABAK+qsnepyho3tvdRV9c1SRvhmbWs3vE+bRTMXF8uvnVJ8AwAAAACcZcI3AABAK+qtnWomzZEVvtnpLuyS03yztrXb2RqsYaqEb/rSNwAAAADAGSZ8AwAAtKJO+KbLtVMb2/th2KWpaElO8829rd2wiaepNVjDrAw03wAAAAAAlCF8AwAAtGJ+DNZOTfV7aXa6+Nee9e3ddHDQTdfM/Ew/9YOgytr2bjoI0jdjt3aqhTkAAAAAAE4L4RsAAKAVtZpvGpxjEISANnf2wudoKuzS6/XC1VP3tjLmaWacoaqEb1TfAAAAAABnmfANAADQijrhmyZFc6xv78VrpxoMl0Srp9a2dlNHRTxDrWi+AQAAAAAoRfgGAABoxcJs9V83mgy7LATNNxsZzTdNippv1rZ2Ow0DHXdxUCF8I30DAAAAAJxhwjcAAEAr5k9J883G9l6nTTPx2qnddHCC1TdV1k71dN8AAAAAAGeY8A0AANCKOmunmoxyDDKabw7CrpnmLM0Vz7O2tRs+R5tNM5XWTsneAAAAAABnmPANAADQimjdU5EmwxxRA8/6drx2qsl5FmejtVN7HUaBHrU4O5Vmp8v9qih7AwAAAACcZcI3AABAK+o03zQpq/kmSLs0uVZpKWvtVHfzPPLcvV66OCjXfqP5BgAAAAA4y4RvAACAVkSNM0WaDJdEIaCN7Th806TFIHyztrUbNt+0HXYpu3qqzTAQAAAAAMC4E74BAABaMTfdH4tGlIVgzdNG12unMppvIm0f1ouLM+UeMAbnGQAAAADgpAjfAAAArej1epVXTzUZdolmWN+JwzdNWpornmdtezd1WsUzxMXFuVL3l70BAAAAAM4y4RsAAKA1VcM3TRrMFs+wmdN809QwKWft1N6Jr526VHbt1DhUHAEAAAAAnBDhGwAAoDXzYxC+WQjCN+s7u+kgaJrpeu1UVHzTdtildPimpTkAAAAAAE4D4RsAAKA1UfBllC7XTm1s74dNM01aCsI327v7aWdvv/A+bYddLi6Vbb5paRAAAAAAgFNA+AYAAGjNOKydigJAG9u74XP0Goy7RM03KaW0ljFTm8qvnWppEAAAAACAU0D4BgAAaE3V8E2TYZdBFL7Z2QvXPDVpaS4+Jvc2g/BNy2GXS0tzpe7f5PkCAAAAADhthG8AAIDWzFdcO9XoDEEAaP8gpa3dvcL7NNnsktN8c2+rOHzTdtjlouYbAAAAAIBswjcAAEBrFmaq/crRZJgjar5JKaX17eLwTZMWZ+Pwzc5ecRVP22GXsmunAAAAAADOMuEbAACgNZXXTjUYLsmZYWt3v7kXDCxlNN+ctPPzM2mqn38SeqpvAAAAAIAzTPgGAABozcIYrJ1qYoYmwyU5a6cibUdd+v1eqdVTojcAAAAAwFkmfAMAALRmvmrzTYNxjqrtO22Zne6n2al6v4p1UTRTZvWU4hsAAAAA4CwTvgEAAFozDsGXwez4Nc0sztU7Lk2Gk0Yp13wjfQMAAAAAnF3CNwAAQGuqhm+abFJpIgDUdLNLE6un2lYmfNOXvQEAAAAAzjDhGwAAoDULsyfffDMOMxy3VDN808Wap8eW5rLva+0UAAAAAHCWCd8AAACtma/afNPgDDNTvTRVs5ql+bVTNcM3Dc1RpEzzTTcTAQAAAACMJ+EbAACgNeOwdqrX66VBzdVTvYarXWqvneqgaqZM+EbzDQAAAABwlgnfAAAArRmXlU/zYzLHoaW58ZpnmEtlwjctzgEAAAAAMO6EbwAAgNZUbb5pOs4xqBm+abrZZXF2/NdOXVqay75v081AAAAAAACnifANAADQmvma656aUj0E1I66a6e6yLqUWjvV4hwAAAAAAONO+AYAAGhN1bVTTYdL6q6/ajpcslQ3fNNB3KXU2inpGwAAAADgDBO+AQAAWjMujTO152g4XbI0Xy9804ULCzNpqp/3cwvfAAAAAABnmfANAADQmqqhl6azHIOazTdNOw1rp/r9XloZ5LXfdNHEAwAAAAAwroRvAACA1szPVvuVo9dwumS+ZvNN09GSc7XXTnUje/WU7A0AAAAAcIYJ3wAAAK0Zl7VT49Z8s3QKmm9SSuliZvhG9gYAAAAAOMuEbwAAgNZUbZxpOsxRNwTUdNil7tqprlxcygzfdJUGAgAAAAAYQ8I3AABAa2am+mlm6uSDGQuzddc8NfsznJuv23zTzTF9TPMNAAAAAEBI+AYAAGhVlfabprMl47L+6lDdtVNdubg4l3U/xTcAAAAAwFkmfAMAALRqHIIvg9nJWjvVVdgle+2U7hsAAAAA4AwTvgEAAFq1UCH40nSYY75m+KZpdddOdeVS7top2RsAAAAA4AwTvgEAAFpVpfmm6TDHoGb7TtPZkrnpfpruV3/WrppmssM3Lc8BAAAAADDOhG8AAIBWzY/B2qkq7TtHNR0G6vV6tVZPddU0cylz7ZT0DQAAAABwlgnfAAAArarSfNP4DGO2diqllJbqhG8anKPIxcW5rPt11cQDAAAAADCOhG8AAIBWjUPwpW4AqI1wybn56uGbriwvzGTdr6smHgAAAACAcSR8AwAAtKpK8KXpMMegbgCohXDJaVg71e/nvZDsDQAAAABwlgnfAAAArZofh7VTYzDDcfXWTnUXd1kZxO03PdU3AAAAAMAZJnwDAAC0amG2/K8dTYc56q6+aiNaslRj7VSXWZeVwWx4H9kbAAAAAOAsE74BAABaVWnt1BjM0Lal2erhmy6tLMbhm8ztVAAAAAAAE0n4BgAAaNU4BF8GNYMubaxVqtN806WLGeGbdrqBAAAAAABOB+EbAACgVfMVVj41nXWZm673q08b0ZLFuTprp7oLu1y0dgoAAAAAoJDwDQAA0KpxaL7p93tjMcdR5+qEbxqcI5Kzdkr2BgAAAAA4y4RvAACAVlUJvfRaiHMsVGjgOdRGs8vpWTs1E95na3e/g0kAAAAAAMaT8A0AANCqOqGXJo1b8029tVMNDhK4uDgX3md1fbuDSQAAAAAAxpPwDQAA0Kr5Ks03LYRLxq355rSsnXpieT68z7n5uB0HAAAAAGBSCd8AAACtqrZ2qnmDOuGbFiaqs3aq12H1zbNPrxQeu34vpZ97armzeQAAAAAAxo3wDQAA0KpxWTtVpYGnTYuz1cM3XZqfmUp/5mc+OPL2X7p8qdYKLQAAAACA0074BgAAaFWV5ps2qm9qNd+0sXaqVvNNg4Nk+Df/wqfSxy4NHvn+xcXZ9O9e/Uy3wwAAAAAAjBn/eSIAANCqcWmcqRQCatFSjbaYjrM36bGlufSf/40vpP/0734/ffN/eCtNT/XSZz+6kv7nf+qZdGlpruNpAAAAAADGi/ANAADQqiprp3otxEvGZf3VoVqrmrquvkkpXVqaS3/zi59If/OLn+j8tQEAAAAAxpm1UxC4efPmSY8AAHCqjUvjTJ05ei2EXWan+2l22q9kAAAAAACnnX/pbdnq6mp6/fXX0/+/vbuJbSxh84X+uLo+UtXVd5z0MHd47wfzOgx3QLzDYFdz1a17EVA2QjAICewuBBK7tmHFLFCsWrAuOUKCbVxbNt22WI3YxLWkG6krllBvb9y6EppdpY9Ar8SM5k6x6E4mTuzknBN/HJd/P6mkPic+9pNK60nZ/vt5Go1G7O/vR6lUit3d3ajVatFqtWI8Hq+7xAtFqHU8Hkej0Yhut7v0x7pNkiQxHA6j0WisuxQAgI228yD7045lDHZ5UrDJNxERn+ScfrP6uTcAAAAAAMwjfLNE3W43dnd3o9PpxGg0ikqlEgcHB/Hll19GRMRwOIxarRa1Wm3tIZx113oeuqnVajEajRZ+/xERnU4nSqVS6j+7u7vRarWi2WwupR4AgG2xcz/P2qnFu9PkmwXWcVne1VNr2DoFAAAAAMAc+V7p5UZJksTz588vQiqVSiWOj4+jUqlM3W44HF5MlKnVajEYDFYe9Fh3rePxOLrd7tICN+fOp/rk0el0FlwNAMB2uXevFI/u34u//Ou/WWsdjx/mf/qzrLDL09yTb6RvAAAAAACKwuSbJbg8HaZcLsfJycm1MEtERLPZjMFgcHHcarVyB0TyWletq5h0c9mrV69yXVev12f+fQAAkM3jjCufSktIuzzOsf5q2Z7u+DwEAAAAAMCmK96rzxuu1WrFZDK5OB4MBlEul+fevtlsTk2Q6XQ6K1tBtY5az0M3z58/j3K5vLJJP3mDQt1ud8GVAABsp7usfFqUJ3eZfLOkSTO5J98YfAMAAAAAUBg+ZrlAw+EwhsPhxXG1Wo16vX7rdb1eb+q6VqsVp6enS6nx3Lpq/frrr6PX60W1Wr041+124/DwMPV9ZNXv9yNJkiiXy/H69evU15XL5VR/JwAA3C5r+GYZ2ZKdjNN3ViH/2ikAAAAAAIpC+GaBrk5JefnyZarrKpVK1Ov1i/VLk8kk+v1+tNvthdd4bl219nq9a+cajcZSwzfnj/ny5cuVTdoBAGDaThEm39yhhmVNmsm7dsrkGwAAAACA4rB2akFGo9HUCqeIyBT0aLVaU8fLXHdUtFr39vbudP1NhsNhTCaTKJfLcXBwsLTHAQDgZo8zTp1ZRrgkaw2XLSvrknfyDQAAAAAAxSF8syBHR0dTx1nXFX355ZdTx0mSRL/fv3Nds2xSrXf16tWriEg/2QcAgOXIvnZq8XGXu4RvliX/2imjbwAAAAAAikL4ZgGSJInhcDh1rlqtZrqPcrkc5XJ56txgMLhraddsUq13NR6PYzweR0SYegMAsGY7D9b/1CNrAOiypa2dyjv5RvYGAAAAAKAw1v8K+Afgm2++uXbus88+y3w/z549mzoejUaRJEnesmbapFrv6vI6rFarFYeHhxdhHAAAVmsna/BlCeGSJx/U5BsAAAAAAIpC+GYBjo+Pr53LOk1m3jWj0ShXTfNsUq13MZlMpuoZDofR7XajVqtFqVSKRqMR/X6/cIEhAIAP1V2mzhSjhuXEXZ7u5Jx8AwAAAABAYQjfLMCs0EmlUsl8P/v7+9fOzQrL3MUm1XoXvV7vxq+PRqPodDqxu7sbjUbDRBwAgCV7nHHqzDLWPGWt4bKirZ0qLasgAAAAAAAyE765oyRJrk1PKZfLue5rVghmMpnkuq9ZNqnWu0iSJPr9furbj0ajqNVq0Wq1TMIBAFiSzZ98sxwfWzsFAAAAALDxhG/uaNYkmb29vVz3Neu6t2/f5rqvWTap1rvIu/5qOBxGrVYrTIgIAOBDspMx+LKMcMn9j+7Fw4/yPQVaVtjlk5xrpwy+AQAAAAAoDuGbOzo7O7t2Ls8ap4jZU2hmTavJa5NqvYtmsxnv37+P09PTOD4+jqOjo2g2m6mm/EwmEwEcAIAlyL52ajnpkp0HxXoKlHftFAAAAAAAxeGV3jtaZNhk3hSas7Oz3OuhLtukWhehUqlchIva7XZERIzH4/j666+j3+/P/ftIkiQajUacnJys5Xv57rvv7nT9Dz/8sKBKAAAWpygrn548vB//z//315mvW1YYKPfaKZNvAAAAAAAKQ/jmjt69e3ft3KIDG4sKzWxSrctSrVajWq1Gr9eLw8PDePXq1cyaJ5NJfPXVVzEYDFZe4xdffLHyxwQAWLas4ZtlZUuyTuA5t6x68k6+KS2tIgAAAAAAsirWzPUNtMj1RMuesrJJta7CwcFB/Pjjj9FsNmd+fTgcxng8XnFVAAAfpkcFWfdUlAk85z66V4onOQJBJt8AAAAAABRHMV4B50ZnZ2frLiG1Tao14ucQ0WAwiF6vN/Pr3W53xRUBAHyYMk++WVK4JPfkmyWGXfKungIAAAAAoBiEb+5ob29vYx5jk2pdtYODgzg4OLh2fjQaraEaAIAPT9bQy7LWKuWZMhOx3PDNJ8I3AAAAAAAbzau8d7SK9UuLeoxNqnUder1ejEaja6umRqNR1Ov1ldXx7bff3un6H374ITqdzoKqAQBYjKKse9opSB2XPd3J/rSsZO8UAAAAAEBhCN/c0aeffnrtXJIkue5r3nWLmiazSbWuS6/Xi0ajMXVuPB6vNHzz+eefr+yxAABWJWvoZVnZktyTb5Y0iSci4uOHOcI3S6gDAAAAAIB8Cr92ajwex+7ubpRKpbX92d/fj8lkMrO+TZoms0m1rku9Xo9KpTJ17t27d2uqBgDgw5F17dSyFGUCz2V5Jt8AAAAAAFAchQ/fnJ2d5Z7OsiiTyWRuDc+ePbt27uzsLNfjzLpukWGWTap1na5OuVn3/38AAB+CooRecoeAljhq5umjPGunllAIAAAAAAC5FP4jlvV6PX766ae5k2dWoVKpzA2WVKvVa+fy1jrrulmBmbw2qdZ1qtVqU8cfSqgIAGCdChO+yVnHMrMuucI3Fk8BAAAAABRG4cM3ET+HH2YFR4qiUqlMhVHyTkqZdV2j0chZ1WybVOu67O3tTR1/+umna6oEAODDkXXizLImuzwpyPqry/KsnTL5BgAAAACgOAq/dmoTXF1TFJEv1DJrmsyiQ0ebVOu6XJ10Y/INAMDdPbqf7anHsia77OSdfLPEtEueyTcAAAAAABSH8M0CXF1TFBHx9u3bzPfz/fffXzs3KyxzF5tU67pcDSN9KN8XAMA6lUql2Hmw/qcfTx4WL+iSb+0UAAAAAABFsf5Xvz8A7Xb72rnxeJz5fq5es4zQxybVui6Xp/qUy+WoVCprrAYA4MPxOMPUmWUNmnn8MN9ToGWGXXKFb6RvAAAAAAAKQ/hmQZrN5tTxrMkwt7m6yqnT6dyppnk2qdZ1OD4+vvjvL7/8co2VAAB8WLKEb5ZXQ77JN8sMu3yca+2U9A0AAAAAQFEI3yzI1fDJaDTKdP1wOJw6LpfL10Iyi7JJta5akiRTfx/dbneN1QAAfFh2HmaYfLOkGh5nqGFVPtkp3iosAAAAAADSE75ZkHq9HuVy+eL4aojjNl9//fXU8cuXL1Nf2+12o1arRavVujaRpmi1Ft3lsE273bZyCgBggYow+eZJzvBNaYmTZqydAgAAAAD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      "text/plain": [
       "<Figure size 2560x1920 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = np.linspace(0.05,1.0,400)\n",
    "\n",
    "values_binom = binom.ppf(alphas, N, p)\n",
    "values_gauss = norm.ppf(alphas,loc=N*p,scale=np.sqrt(N*p*(1-p)))\n",
    "\n",
    "Pk = binom.pmf(np.int_(x),N,p)\n",
    "Gauss = norm.pdf(x,loc=N*p,scale=np.sqrt(N*p*(1-p)))\n",
    "\n",
    "#plt.plot(x,Pk)\n",
    "plt.plot(x,Gauss-Pk)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b64df91",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}