Week3_4-RoughFit.ipynb

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    "# Setting up a custom stylesheet in IJulia\n",
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   "source": [
    "<h1> Using the data: a rough fit of the model parameters </h1>"
   ]
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   "source": [
    "<h2>In this lecture</h2>\n",
    "\n",
    "- [Outcome](#Outcome)\n",
    "- [Total cases data: observation vs model](#Total-cases-data:-observation-vs-model)\n",
    "- [Interactively fitting the model to data using the notebook](#Interactively-fitting-the-model-to-data-using-the-notebook)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to the top](#In-this-lecture)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "<h2>Outcome</h2>\n",
    "\n",
    "After this lecture, you will be able to\n",
    "- Extract total number of cases per epidemic day from a a run of our EVD model\n",
    "- Use a plot to compare model values to observed values\n",
    "- Use the interactive notebook to adjust $\\lambda$, $\\gamma$ and $S(0)$ \n",
    "- Estimate quickly a fairly good set of values by improving the fit of the model to the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to the top](#In-this-lecture)"
   ]
  },
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   "metadata": {},
   "source": [
    "<h2>Total cases data: observation vs model</h2>\n",
    "\n",
    "When one fits data to a model, the first thing is to ensure that the numbers from the model and the numbers from observation really represent the same thing.\n",
    "\n",
    "In this case, the data reported in Wikipedia are of two kinds: total cases to date, and total deaths. Our model does not include deaths, so we cannot use that data. Moreover, in our model there is no explicit record of the number of cases. Therefore we have first to work out how to get our model to tell us what the total number of cases are.\n",
    "\n",
    "Fortunately, that is not hard. The total cases to date is the number of people who have ever been infected. But every such person is either in the infected group currently or has moved to the removed group. So the total number of cases at time $t$ is $I(t) + R(t)$. We will use $C(t)$ to denote the modelled number of cases, and $W(t)$ for the reported number of cases from Wikipedia."
   ]
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   "source": [
    "Let us rerun the model as we left it at the end of the previous lecture, with the estimates from there:"
   ]
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       "updateSIR (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
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   "source": [
    "using Plots  # might as well start by loading Plots and choose to use the PyPlot backend\n",
    "pyplot()\n",
    "\n",
    "# now lets get the total cases data\n",
    "EVDdata            = readdlm(\"wikipediaEVDdatesconverted.csv\", ',')\n",
    "tvalsfromdata      = EVDdata[:,1]  # the epidemic day values\n",
    "totalcasesfromdata = EVDdata[:, 2]    # we'll extract individual countries when we need them\n",
    "\n",
    "# here's the function that drives the changes that happen every time step\n",
    "function updateSIR(popnvector)       # exactly the same function as before\n",
    "    susceptibles = popnvector[1];\n",
    "    infecteds    = popnvector[2]; \n",
    "    removeds     = popnvector[3];\n",
    "    newS = susceptibles - lambda*susceptibles*infecteds*dt\n",
    "    newI = infecteds + lambda*susceptibles*infecteds*dt - gam*infecteds*dt  \n",
    "    newR = removeds + gam*infecteds*dt\n",
    "    return [newS newI newR] \n",
    "end\n",
    "\n",
    "# this cell we need to run only once"
   ]
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   "execution_count": 19,
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OTo60tixY+nmzZsF2l+5coXefPNNqlmzJtWpU4eGDh1K0dHRNHr0aJLJZFIdrOzsbFqyZAn179+fbGxsyMTEhKytrcnd3Z127dpVqpiEhIRQ586dydTUlBo2bEgffPABJScnqz2u1NRUmjlzJjk4OJCpqSm1aNGCFi5cSNnZ2Wp/JnK5nD777DOys7MjIyMjEkWRxowZI+0/fvw49erVi2rXrk316tWjwYMH06VLl2jevHkkiiIdP368VMfCWGXDI1iMMcYYY1rGc7AYY4wxxrSMEyzGGGOMMS3jBIsxxhhjTMs4wWKMMcYY0zJOsBhjjDHGtKzaLpWTmJiIw4cPw87ODqamprruDmOMMcYqifT0dMTGxqJfv36wtLRU26baJliHDx/GyJEjdd0NxhhjjFVS27Ztw7vvvqt2X7VNsOzs7ADkBKcsi9D6+PggJCREy72qfjiOmuMYao5jqB0cR81xDLWjvON48+ZNjBw5Usol1Km2CVbuZcFWrVpJy1mURp06dcr0PKaK46g5jqHmOIbawXHUHMdQOyoqjkVNMeJJ7mVkb2+v6y5UCRxHzXEMNccx1A6Oo+Y4htqhD3GstiNYRYmPj0diYmKRbZKTk3Hx4sUK6lHVxXHUnCYxtLS0hI2NjZZ7xBhjjBOsfOLj49GqVSukpaUV29bV1bUCelT1cRw1V9YYmpmZ4ebNm5xkMcYqDYVCgZMnT+LRo0ewtrZGr169IJPJVLYnJiZCoVAAQLFt827XJk6w8klMTERaWlqZJ78zVlnkTtJMTEys9glW7969dd2FKoHjqLnqFMOSJEr5k599+/Zh+rSPERt/X3odO5umeGfYcOzetVNleyPrhiAiPEtMKratnU1TLFvxPYYOHaq14+MEqxBlnfzOGKt8jh8/junTp+u6G5Uex1FzlSWGpR0Byt/+2bNn+HTG9BIlSrnJDwD4+fnB094KK/3d0MKiJm4nvcbqC9FYsmQJ2jcwR0ie7avO3cPR2CR81r05RnewKbLt6gsx8PPzw549e7SWZHGCxRir9tasWaPrLlQJHEfN6VsM1SVSISEhakeRChsBUjfqJBMEtKlfK1+SU3TyY2lRD572VtgwqCNEQQAAuFjXwYZBzhj72yXcSXqNDg1qQyYKcLGug43eLhj32yVsv/YAE1zti2y7YVBHjDsQiRmfTIOPj49WLhfyXYSMsWqvul8i1RaOo+Z0EUMlEbKVhNeZcvzxVyg2/LwdIUdCseGXINjb28PDwwMBAQHw8PBAwwYN8fbbb8PRIBMh/m64NdETIf5ucDTIhJ+fH/67fg9CE5Q4+lCJPx8oMef/9sDPz69Ae3c7S1x98hJPUjNRw8hASn487a3wIj0bHRrUzrO9IzztrPA86Tk+dLGTkqtcoiBgSmcH3H+ZjnMJL1S2T+7sgPg824ts28keMXHxOHnypFbiyiNYlYCdnR0yMjLw8OFDKasODQ2Fp6cnPv74YyxfvrxUrzdz5kzUqlULc+bMKbLdmDFj4OzsjKlTp5a573nNnz8fKSkppe4vY4xVVkSEbCWQrgAy5Dlf0//5mqGgnO+lx7nf52zPVADZSiDrn3/ZSiBLQf9+rwSyFPm+p3xtFP8+V06AQglkKxSQ3z4FxYtHUNa2Bpr3BCL3Q7Z7BhRJqqNMra1qYU3ey27no3E0CfBraQ0X6zoAICVBY3+LxH8/+wQKxSBAlAFKBWRffoI+dgVHnTYOdsa43y5hwcnb6OtQHzJRkJIf36BwnEt4gW5N6gHITZTs8VfMU7zKkquNcwuLmgCAJ6mZxW4vru2jR4/K9sPOhxOsSkAQBNjY2GD//v0YMmQIAGDjxo3o3LmzjnvGGGNVj1xJSM4CkjOBF1mEF5nAq+ycf6+z6Z+vxTyWA6nZOYmTkkr3/qYywNQAMBIBY1nOV0MRMJIBRqKQ8730GDAzAOr8831OWxFGMsCAFHhy5STSkx6jTv2GcHTthVth+3Fg6SdIevRvIlW7niVSnifCw6E+pniqJlPHYp7hSWomXKzrqCRGC0/dQf9mDSATc5KmnOTIHkeDwrGtyRl07+WO8FOnMCLpPqZ6uqkddZqsJpkqLvm58jQFfeytCsTsdtJrAECDGsbFbi+urbW1dbE/o5LgBKuSGDNmDDZs2IAhQ4bg5cuXOHv2LAICAvDq1SsAgFKpxKxZs3Do0CEIggB3d3csX74cBgYGePz4MUaPHo0HDx6gUaNGsLCwkO6QlMvl+OqrrxAaGoqsrCw4OTnhxx9/RO3atQvty8KFC/Ho0SOsXr0aAJCamgobGxvcuXMHjx49wsSJE5Geno6MjAwEBATgiy++KPAaW7ZsQXBwMH799VcAwMGDB7F06VKEhoYCyFnCaM2aNZDL5ahZsyZWrVqF9u3bIzw8HJMmTYJSqYRcLsekSZPwwQcfaDXWrPpZtGgRZs2apetuVHr6GMd0OeFpOvA045+v6cDTdMKzDOBFJuFFFvAiU/X7V9mFv56xDKhpANQyBGoaArUMhX++AvVNgVqGovS4hkFOomQqE2DyT9JkaoCc72XCv98b5CRVJjLg+2WL8VkRMSzp5HJ1857qW1ni6bNEeDnUx5T8o1LPC45KFTbKpC4xAv5NgsSXj2FvLuBsymOV7fmpS6aKS35C45IwtUszlYRNSYTV56PR1NwUXRrVVdm+5nw0bPJsL7LthRjY29qgV69e6oNfSpxglVL0y5y/bMqqjhHgYC4U3zAPQRDQo0cPrFu3Do8fP0ZISAj8/f0hiv9Oofvxxx8RERGBS5cuQRRFDB48GCtWrMDMmTMxdepUuLm54dChQ0hISEDHjh2lBGvJkiWoWbMmzp49CwBYsGABvvzyyyInWr733nvo1KkTli9fDkNDQ+zevRt9+vSBhYUFTExMcOzYMRgaGiIjIwPdu3eHl5cXunTpova41D0+ffo0duzYgZMnT8LQ0BCnTp1CQEAArl27hm+//RYzZ87EsGHDAAApKSmliiVj6pSk7h0rXkXG8WUW4UEq8DA15+uDVMLDVOBROklJ1NOMnJGl/OoaA5bGQF1jAXWNgYZmQKs6Iuoa5+yrayT8+72xgLpGgLlRTkJlKJbu87u00v+JoSaTy/ft26f2brtV56Nx9FnhiZS6UanSjDLlHwHK/Xo76bX0fura5yZTxSU/DayscPHRM4w7EInJneyl41pzIRpHY56hfQNzRD5J+Xdy/Ll7OBqbiFndmyNdriiy7ZoLMTga8wx79uzRWj0sTrBKITGD0DxIXurh3rxkAvB4pAEsTUr+S0qU84aBgYHYtGkTQkJC8Msvv2Dbtm1Sm6NHj2L06NEwMMj5kY4fPx7r1q3DzJkzcfToUSxbtgwA0KhRI3h7e0vPCw4OxsuXL7Fnzx4AQHZ2drFLDDRp0gTOzs7Yv38/3n77bWzevBmffvopgJwP2IkTJyIyMhKiKOLBgweIjIxUm2AVJiQkBFeuXIGbm5t07MnJycjMzISHhwe+/vpr3LlzB3369EGPHj1K/LqMFWb+/Pm67kKVoK04EhGSMnP+oI1+lfuVEPf630Qq/yhTfVOgsRlgbSagVR2gt7WI+iZAfVMB9U3/+WoCWJoARrLyTZI0MX/+/GJHn1YWUV5AoVBg+rSP1d5tV9pECij5KJO6EaBevXrBzqYpVl+IUelLbvvV56PRsIYxWlvWQsSj5BIlPwAwfdrH8A0Kl17L3tYGM2fOxO5dO1W2N7CygpWlBRadjsKi01FFtrW3tdFqiQaAE6xSsTQREOVvoPEIVmmSq7wCAwPh4uKCli1bolmzZkW2zT86VNg+IsLq1avh5eVVqr6MGTMGGzduhIuLC+7du4f+/fsDAL744gtYWVnh8uXLEAQBb7/9NjIyMgo838DAQKqyC0ClDRFh1KhRWLBgQYHnffTRR/D19cVff/2FL774Am3btsXatWtL1XfGmH5IySLcfEG4mQzcSiZEvSQpqcqbQNUzBhxqCbCtBbStK6JxDaBJDQFNagCNzQQ0qgEY63HSlKskl/dKO/qUv7zAyZMnERt/Hyv9Sz7vCSh+VEpllOncPdQwlEEmCHidJS90BEgmk2HZiu/h5+dX6KgTALT98RiAkic/uceZP47ffvttge2A+kru6tpyJXcdK+3lPW2ytrbGd999h5YtWxbY5+Xlha1bt2LEiBEQBAHr169Hv379AABvvvkmNmzYgHnz5uHRo0fYv38/Jk2aBADw9fXFihUr0KNHD5iamiI9PR0xMTFo3bp1kX3x9fXF5MmT8e2332LkyJHS5coXL16gdevWEAQBt2/fxp9//qm2MrGjoyOuXLmCzMxMyGQybN++Xdrn7e2NkSNH4oMPPkDTpk1BRLh48SJcXV1x584dODk5Ydy4cWjSpAm+/PLLMseTMVYxXmYRLicRrjzPSaZuJhNuJhMe/XNFUQBgWxNwqi2gewMRI5vnJFT2tQTY1wLqGOtn8lSaYpuFVSDPe3mvzKNPnezhGxQu9QUo3bwnoPBRqYKjTDE4FpcES4t6eHvPOaltYSNAQ4cOxZ49e9SOOu3evRuWlpalTn5kMhnc3d0LHFth20vTVps4waoE8o44jRo1Sm2b999/H9HR0XBxcZEmuX/00UcAgO+//x6jR49G27Zt0bhxY3h6ekrPmzVrFr7++mu4ublBEAQIgoBZs2ZJSVJhjIyM4O/vjx9++AE3b96Uts+ePRuBgYHYsmULmjVrpvJeebm5uWHgwIFo06YNGjVqhB49eiA8POeXr2fPnli8eDGGDBkChUKBrKwsvPXWW3B1dcWaNWtw7NgxGBkZwcDAgEs+MK1ITEyEpaWlrrtR6SUmJkJuZoFLSYRLiYTIJMKlJMLdlzn7DUWguTnQqq6AcS1EtKojoFUdAS3qAGYG+pFElXT5lsIqkasrtlnYqFT+y3uajj7l9g0o+bwnoKhRKfWjTHv27Cl0FEmdoUOHlqq9NpIfffidFih3kks1kzsiEhERobIkTmHbGatq+Fz/l7e3N/bv36/rblQ6WYqcJOrMU8KZJ4T9154i3SznFvraRkBHCwEdLQQ4//OvZR39mf9Umknk6pZvya1E/nXvVioJU+5lsryjUo4O9nA0yFQ7D2ncgUjcU5gg6l40goKCEBAQgFsTPVHDqOD4x+ssOVr9cBSr+7eHb4t/SwlEPEqGb1A4QkND0atXryLfb+z+izj78AW2+riitVUtlct7lhb1VNbts7e1weKly9SOMum78v6dLsnnJ49gMcaqvXnz5um6C5VCajbh7yeEYwmEU48JEYmEDEVO6QJXSwFv2wM+bWVwscy5tFfUKLgulW4SeSHr3KmpEaVuuZViR6XyXN4r6+hT3snlRc97KvryXmlGmfSdPvxOc4LFGKv2qvsIXmEyFYTwpzkJ1bEEwtmnOVXJrc2AXg0F+NmL6NYgZ3QqZ2Sqka67rFbe0aqoqCjMnTu3QCJV+CTyQta5K6xGVJ6Eyd3dvcRzoh49egR/f/+i77or4eTyouY9FZdIlfe8pIqiD7/TnGAxxhiTJKQSfr9POBCvxF8PCanynHpQHtYCVnQV0aeRiJZ19Hd0Kj91o1U1DGWlqgVV+PIthdeIyk2sSjoqZW1trdHok7rJ5dUhkdJnnGAxxlg1RkSITAJC4pQ4EJ9z2U8UgG71BXzpLKJfExEd6kFKOPRBaaqZq51cfj4aE3+/jB/fEjDAsQGAspUwKKpGVG5iVVwtqPy1ozQZfcqvIu6UY4XjBIsxVu1t2LAB48aN03U3KgwR4epzIChaiaBoJaJe5tTo699UwLR2MvRvIsCiDPX6KiKOJSl3ABRd8mCDmst7QOlKGKjbri5hKm5UKv/lvdwY8uiTZvThd1osvgljjFVtFy9e1HUXKkRUCmFuhAKtdsvRYZ8ca28o0auhgEP9ZXgaaIAdfQzwrqNYpuQK0CyOCoUCYWFh2LFjB8LCwlQKEefKHZFyNMhEiL8bbk30RIi/GxwNMuHn54d9+/ZJbXMnl0/pZF9oyYP4l+k4l/BC2l5ULSh1y7fkrxE17kAkjsY8w9LlK1RGlXJHpe53t16AAAAgAElEQVTKjeEbFI5WPxyFb1A47ilMClzey41h7ujTiBEj4O7uXmknm+uKPvxO8wiWlsjlcpw/fx5paWlo2bIlGjdurLXXtrOzg6mpKUxMTJCRkYHRo0dX+IKq8+fPx+effw4jI6NSP/edd97B4MGD8d5775VDz4oniiKSk5Nhbm5eYe85d+5cBAUFoU6dOjhz5kyFvS8rm6q8GsDrbMKeGMLG20qcfEwwNwSG2AlY3lWEV2NBq2UTyhpHTYtwqrt7r7QFN4urBVVw+ZbCa0SpW26lpLWgqvK5WJH0IY6cYGmIiLB27Vp8t/AbPHyUs3K4KIrwHjwYK1etgo2NjcbvIQgCgoKC0K5dOyQkJKB169bw9PREp06dNH7t4igUCshkMsyfPx/Tpk0rU4Kla9qYjJsbh5JasmQJYmJi0KBBA43fm7GyCH+qxE83ldgVnTNR3auxgO0eMvjaCTDVk6KegBaLcOa7e6+kk8vNjQyKrVBe2PIthVUiLwzPiape+BKhhubOnYspU6agex0RIf5uODmqF75xb4nzYX+hZ/du0l9RmsqtB9uoUSO0bNkScXFx0r5t27aha9eu6NSpE9zd3XH16lUAwJYtW+Dp6QkfHx+0adMG7u7uiI+PBwAolUrMnDkT7dq1Q/v27TF16lTI5XIAOesMjhs3Dr1790a7du0wceJEADmTNV1cXJCYmIjXr1/j/fffR9euXdGxY0dMmDBBev7t27fRo0cPtGvXDkOGDMHLly/VHlNcXBzq1q2LefPmoVOnTnBycsIff/wh7RdFUeW5VlZWUv/t7e3x1VdfoUePHrC1tcWPP/6IzZs3o3v37nBwcMCuXbtUYrdkyRJpHce8y/JcuHABnp6e6NKlC1xdXaXFRHP79tlnn8HV1VXtX0OHDx+Gq6srOnbsCA8PD9y6dQsA0KNHD2RmZqJv3774+OOPCzwvISEB77zzDtq3b4+OHTti7ty5AIAdO3aga9eucHV1hbOzMw4cOCA9Z8GCBWjTpg1cXFzg4uKC+/fvF9n/xMRE9OvXDx06dEDHjh11PheBVYxMBWFblBJdguXoGqLA0QTCzPYiYoYb4M+BBhjhKOpVcpV/VMrFug5qGBlIo1Ke9laY8ck0KBSKUpU7AFQnlyvz1dPOvbwnEwSM2n9R5XLdo8dPEBoaiu3btyM0NBRR96KxePFi3I2OKbDdz8+PL+OxwlE1FRERQQAoIiKiRNvViY2NJVEUaXrXZnT/o34q/86N6031apjQ5MmTNe6rnZ0dXb58mYiIbt68Sc2bN6fExEQiIvr7779p4MCBlJWVRUREJ0+epDZt2hAR0ebNm8nExIRu375NRESLFy+mvn37EhHRunXryMPDg7Kzs0mhUNDAgQNp8eLFREQ0evRo6tixI6Wmpkp9EASBXr58KT1+//336eeff5Ye/+c//6GlS5cSEVHnzp1p06ZNRER09epVMjY2pi1btqiNnyAI9OuvvxIR0aFDh6hFixbSflEUKSUlRXpsZWVFcXFxUkw++eQTIiK6e/cumZqa0jfffENEROfPnycrKyuVvs+dO5eIiKKjo6levXoUFxdHycnJ5OzsTI8fPyYiosTERLKxsaGEhASpb9u2bVP7M3n69ClZWFjQ9evXiYjol19+odatWxcar7w8PDxo0aJF0uPcn+Xz589VYtOwYUPKysqiFy9eUJ06dSgjI4OIiNLT0ykzM7PI/q9YsYImTJggvd6LFy8K9KM05zrTb49SlTTngpzq/5xF+CmL3jyYTb/FKkiuUOqsT3K5nEJDQ2n79u0UGhpKcrm8QJvQ0FACQCH+bgU+Q+9/1I+C/d0IAIWGhpaqba69e/eSIAjk5VCfgv3d6OZETwr2dyMvh/okCALNnz+/yP4xVpiSfH7yCJYGtmzZghpGBnjfxa7APuuaJni3dSNs2bwJ2dnZBZ9cSsOGDUPr1q3Rtm1bTJkyBRYWFgCAkJAQXLlyBW5ubnB2dsaUKVOQnJyMzMyceQXdu3eHk5MTgJz1Co8fPw4iwtGjRzF69GgYGBhAFEWMHz8ef/75p/R+77zzDszMzFT6QHn+CgwODsaSJUvg7OwMZ2dnnDp1Cvfu3cOrV68QGRkprZnYtm1b9OzZs9DjMjU1ha+vLwCgW7duiI6OVvt+6h4PGzYMANCsWTOYmJjAz88PANCpUyc8f/5cZfTrP//5D4Ccka/evXvjxIkTOH36NKKjozFgwAA4OzvDy8tLWqQayFlv8d1331Xb7/DwcLRv315aFDsgIAAJCQlISEgotL8AkJqailOnTmH69OnSttyfZW5f2rVrB19fX7x48QIxMTEwNzeHk5MTRo4ciZ9++glJSUkwMjIqsv9du3bFH3/8gZkzZ2L//v0FfpZMlbe3t667UCaxrwiT/lbAbqccy64o4Wcv4oafAY4MNMAgW7HCSyvkxnHfvn1wdLCHh4cHAgIC4OHhAUcHe5VJ6ABKNSpV3IhU/rv3gOInl8+ZM0fvRp8q67mob/QhjjwHSwNxcXFwrFcTZobqw9i+gTlenY9GcnIyrKysNHqv3DlYR48exeDBg9GnTx+0adMGRIRRo0ZhwYIFxb6Guv/wc+Wfp1SzpvoPvLz27t0LR0dHlW2vXr0q8FpFzYEyNv73bp3cBVULe5yRkaHyXBMTE5W2eR8LgiBdsgRUj52IIAgCiAht27bFqVOnCvQrLi6u3JKS3PfOb/jw4dIi10BO4pWRkQFRFHH27FmcPn0aoaGh6Nq1K3bu3Flk/wEgMjISf/31F/bt24evvvoKkZGRlaY4ZEWbPHmyrrtQKjdfEL67rMAvdwl1jIDZHUVMaiOirrFuf76TJ08u8ZwqQLtFOPOXO8hV2oWGda2ynYv6Sh/iyCNYGrC0tMSDl+nIVijV7o9NToOhgYFW7l7L/Q/Z09MTH374Ib788ksAOVn6tm3bpDk5RISIiAjpeWfOnMGdO3cAAOvXr4eHhwcEQYCXlxe2bt2K7OxsyOVyrF+/Hv369Sv0/c3NzZGSkiI99vX1xaJFi6QEKDk5Gffu3UOtWrXg7OyMLVu2AACuX79eaAKQ97jUPW7evDnCw3Mmle7btw9paWnFRKlwmzZtAgDExsbi1KlTeOONN9C9e3fExMTg6NGjUrvLly9LiVlRCWnXrl1x9epV3LhxAwCwc+dONGnSBI0aFb1USI0aNfDGG29g2bJl0rbExEQAOTG0s7MDkDOvLjk5GQDw+vVrPH78GD169MDs2bPRs2dPXLp0qdD+Z2dnIzY2FjVq1ICfnx9WrVqFqKgovH79uqThqnb69u2r6y6UyN0UQsAxOdrskeNoAmGpm4i4EQaY7SLTeXIF5Hw+lXROFVD8PKnCinCWpNxBXpWp5EFlORf1nT7EkUewNPDuu+9i8eLF2HfrEYa1US3LkJolx7brOZOZ847SlEX+UYfZs2ejefPmuHTpEnr27CmNeigUCmRlZeGtt96Cq6srgJxLhLNmzUJUVBQsLS2xdetWADmXC6Ojo+Hi4gJBEODu7o6PPvpI7fsBwPTp0+Hl5YUaNWrgyJEjWL58OT777DN07NgRoijC0NAQixcvRrNmzbBlyxaMGTMGy5cvR/PmzdG7d+8SH1vex8uXL8fUqVNhbm6Ot956S7qUVtzz8j8WBAEKhQIuLi5IS0vD6tWr0bRpUwDAwYMHMX36dMyYMQNZWVmwtbVFcHBwoXHIZWlpiV9++QWBgYFQKBSoW7cudu/eXWh/8vr5558xefJktG3bFkZGRvDx8cHcuXPx/fff4+2330bdunXRp08f6Q7UlJQU+Pn5SQmmk5MTRo0ahVq1ahXa/7CwMCxfvlwaBVy6dClq1apVaJ+YfktIJXx9SYn1t5Sobwr80FPEaCcRxlossaANpb3TryyjUpVtRIpVXwIV9Wd6FXbx4kW4uroiIiJCZVHIwrYX5t2AAOzZHYSZXZthRNsmMDcywLmEZHx7+i5up2TgbPg5tGnTpjwPpVBbtmxBSEhIgXkPjAGlP9dZxUvJInwXqcTKa0qYGABfdBQxqbV+3QmY144dOxAQEIBbEz1Rw6jg3++vs+Ro9cNRbN++HSNGjJC2q6uDZW9rg6XLVxQ6KsWYLpXk85NHsDS0afNmmNeujUXr/w8L/46CkUxEplyBFs0d8de+bTpLrhhjJRccHCzdbKEPlETYfIfw+XkFXmcDn7QTMaO9iDo6vgxY3BqA9+7dA1CyOVV58ajUv/TtXKys9CGOPAdLQ0ZGRvjhhx9w//4DrF+/HktXfI9jx47h5u07cHNz02nfRo0axaNXjJXAjh07dN0FydknSnQNUWDcCQW8Ggm4/Y4BFnSW6Ty5KsmdgZcvXy71nX65KtM8qfKkT+diZaYPceQRLC1p2LAhxo4dq+tuMMbKIG9hWl15nkGYEa7ApjsEZwvg5GAZejbUj7+BS3pn4O7du6W2pbnTj/1LH87FqkAf4sgJFmOM6RARYXc0YcoZBTIVwP96ivhPi4qvYVWY0q4BmHun3/RpHxdYWqaoO/0Yq2o4wWKMMR15mEr48G8F9scRhtoJWNNDBmsz/UiscpX2zkCA51QxBnCCVaibN2/quguMlSs+x3WHiLA1ijD1tAJmBsBeLxmG2uvH5cD8SrsGYC5e2JhVd5xg5WNpaQkzMzOMHDlS111hrNyZmZnB0tJS193QuTFjxkjFaMvb8wzChFMK7I4hBDoKWNldt0VCi7szsDTV1isyjlUVx1A79CGOnGDlY2Njg5s3b0rVtQtz6NAh9O/fv4J6VXVxHDWnSQwtLS2lgqbVWUVVfT76UIlRxxVIkwO7+sjg30y3o1bq6k/Z2TTFshXfS3Ol8lZbzzsHCyh4Z2D+USxWevpQgbwq0Ic4cqFRLrLIGCtnciXhy/NKLL6iRJ9GArb0lqFJTd2XXci9M3BKnrv9Vue52y83ycrbtrA7A3nyOqtOSpJDcILFCRZjrBw9SiMMP6rA308I33YWMb29WGCyeEVTKBRwdLCHo0Gm2lGpcQcicU9hgqh70dLlQq62zti/uJI7Y4zp0IlHSgw7qoAgAGGD9KeuFd8ZyFj5K9ff9szMTAwZMgQtW7aEs7Mz+vXrh+joaACAu7s7HBwc4OLiAhcXF6xcuVJ6Xnp6OgICAtC8eXO0bNkSe/fulfYREaZMmQJHR0c4OTlh7dq1Ku+5YMECODo6onnz5pg9e3a5HdupU6fK7bWrE46j5jiGmtN2DIkIS68o0OegAi3rCLg4xEBvkitA8zsDC6u2zuei5jiG2qEPcSz33/gPPvgAt27dwqVLl+Dt7Y3//Oc/AABBELBy5UpcvHgRFy9exEcffSQ9Z+nSpTAxMUFUVBQOHTqEDz/8EC9evAAA/Pzzz7h16xbu3r2L8PBwLFmyRLrd/MSJE9i1axeuXbuG69ev4/Dhw/jjjz/K5bgWL15cLq9b3XAcNccx1Jw2Y5ghJwSGKTAzXIkZ7UX8OVCGhnpW2yrvnYHqFLZmYHH4XNQcx1A79CGO5ZpgGRsbq9zd1LVrV8TGxkqPlUql2uft2rULEyZMAADY2dnB3d0dv/76KwAgKCgI48ePBwDUrVsXw4YNk9YcCgoKQmBgIExMTGBkZISxY8eW23pEO3fuLJfXrW44jprjGGpOWzF8mk7oc1CBvTGEnX1k+K6LDAYVXJFdoVAgLCwMO3bsQFhYGBQKRYE2ee8MLO2agUXhc1FzHEPt0Ic4VuiY9cqVK1VWt541axY6dOiAESNGICYmRtoeHx8PW1tb6bGdnR3i4+M12qdtZmZm5fK61Q3HUXMcQ81pI4ZXnxO6BMsR84pwfJAMw3RQgqEkCzIDOZf6lq34HkdjnmHcgUhEPErG6yw5Ih4lY9yBSByNeYaly1eUen4Vn4ua4xhqhz7EscI+ARYuXIh79+5h4cKFAIBt27bh1q1buHz5Mnr27IlBgwZVVFcYY0yr/nygRI/9ctQxAs75GqBLfd0kV35+fnA0yESIvxtuTfREiL8bHA0y4efnVyDJyl0z8K7cGL5B4Wj1w1H4BoXjnsKEyy4wpgUV8imwdOlSBAcH49ChQzAxMQEANG7cWNo/adIkREdHS/OsbG1tERcXJ+2PjY2ViiHa2NiUaV9hBg4cCG9vb5V/3bp1Q3BwsEq7I0eOwNvbu8DzJ02ahA0bNqhsu3jxIry9vQsUK507dy4WLVqksi0+Ph7e3t64deuWyvbVq1dj5syZKtvS0tLg7e1dYPLejh07MGbMmAJ9GzZsGB8HHwcfRzkfx0+XUvDWYQV6NRRwytsA65fMq/Dj2Lt3r8qCzC7WdVDDyEBakNnT3gozPpmGiRMnqhzH0KFDEbRnL7p164Yff/wRoaGhiLoXjaFDh1ban0dVOa/4OPTnOFxdXdG/f3+VPGHIkCEFnl8AlbNly5aRq6srJScnS9vkcjk9efJEerxnzx6ys7OTHs+bN4/GjBlDRETR0dHUoEEDSkpKIiKizZs3k5eXFykUCkpKSiJbW1u6du0aERGFhYVR27ZtKS0tjTIyMqhTp0508OBBtf2KiIggABQREVGm45oxY0aZnsdUcRw1xzHUXFlj+P1VOeGnLBoVmk1ZCqWWe1VyoaGhBIBC/N3o/kf9CvwL9ncjABQaGlqu/eBzUXMcQ+0o7ziWJIco1zpYDx8+xIwZM9CsWTN4eHiAiGBiYoKjR4/irbfeQlZWFgRBgJWVFfbv3y89b+bMmRg7diwcHR1hYGCAtWvXol69egCAwMBAXLhwAc2bN4coipgxYwbatGkDAOjduzeGDRuGtm3bQhAEDB8+HAMHDiyXY+PlRbSD46g5jqHmShtDIsKXF5T4NlKJT9uL+K6LCEGHxUPLWnZB2/hc1BzHUDv0IY5cyZ0ruTPGSkFJhCmnlVh3Q4mlbiKmty//QpvFLcgcFhYGDw8PhPi7qV2QOeJRMnyDwhEaGioVDmWMlV1Jcgj9qXzHGGN6TkmED04q8MMNJdb3klVIclWSOwPLq+wCY6zsOMFijLESUCgJ404osOE2YVNvGca1LP+Pz5LeGVheZRcYY2XHCVYZ5b/bgZUNx1FzHEPNFRdDuZIw+rgCW6MI2zxkGOVU/h+dCoWiRHcG5hYS1YeyC3wuao5jqB36EEdOsMro008/1XUXqgSOo+Y4hporKoZKyhm52nGPsMNDhgDHivnYzF2QeUon+0IXZI6Ji8fJkyel7UOHDsXd6BiEhoZi+/btKmUXKgKfi5rjGGqHPsSxXO8irMrWrFmj6y5UCRxHzXEMNVdYDOmfCe0/RxF+8ZDBvwKrs2u6ILMu8LmoOY6hduhDHHkEq4z04RbQqoDjqDmOoebUxZCI8Pn5nLsFf+olw4gKGrnKVV4LMpcnPhc1xzHUDn2IIydYjDGmxreRSiy6rMSKriL+o+UJ7bpckJkxVjE4wWKMsXzW3VDgywtK/NdVxMfttHvnna4XZGaMVQxOsMoo/1pKrGw4jprjGGoubwyDY5WY/LcSH7cVMdtZux+RVX1BZj4XNccx1A59iCNPci+jtLQ0XXehSuA4ao5jqLncGJ55osSIYwr42QtY1lW7y9/kL7uQe2dgbtmFcQciMeOTafDx8VEZlRo6dCh8fHyKrOSuL/hc1BzHUDv0IY68VA4vlcMYA3AnmdB9vxyt6gj4c6AMJgbaXVuQl7NhrOrgpXIYY6wEnqYTBhySw8oUCOmr/eQK0J8FmRljFYMTLMZYtZapIPgeUSBVDvzR3wD1TLSfXAGVs+wCY6zsOMEqo8TERF13oUrgOGqOY1h2RIQJpxS4mKjE/r4y2NUqn+QKqB5lF/hc1BzHUDv0IY6cYJXR2LFjdd2FKoHjqDmOYdmtuKrE5juE1hdWokv98v04rA5lF/hc1BzHUDv0IY58F2EZzZs3T9ddqBI4jprjGJbNH/eVmHlOiVkdRPi7elbIe+aWXZg+7WP4BoVL2+1tbfSy7EJp8bmoOY6hduhDHPkuQr6LkLFq51YywS1YjjesBQS/KYNM1PzSoEKhKHEphdK0ZYzpn5LkEDyCxRirVl5lEXyPyNGkBvCLh3aSq3379mH6tI8RG39f2mZn0xTLVnyvdlRKlwsyM8YqBs/BYoxVG0SEcScUSEgD9r1pAHMj7SRXpanOzhirHjjBKqMNGzbougtVAsdRcxzDklt1XYndMYRNvWVoUeff5KqsMcxfnd3Fug5qGBlI1dk97a0w45Npahdzror4XNQcx1A79CGOnGCV0cWLF3XdhSqB46g5jmHJ/P1YiRlnlfiknYi37VU/+soaw5MnTyI2/j6mdLKXlr7JJQoCJneyR0xcPE6ePFnmflcmfC5qjmOoHfoQR06wymjt2rW67kKVwHHUHMeweE/SCP5HFehaX8B3XQp+7JU1hlydXRWfi5rjGGqHPsSREyzGWJWmJMLIMAUUBOzylMFQC5Pac3F1dsZYYdQmWPfv38fp06eRmppa0f1hjDGtWnpFiaMPCb94yNCohnYrtVeH6uyMsbJRSbB++uknNG7cGHZ2dujVqxdu374NABgyZAhWrlypkw4yxlhZnX+mxJfnlfi0gwjPxtofsK8O1dkZY2UjfeJ8//33mDJlCt577z0cPnwYeeuPuru7Y/fu3TrpoL7y9vbWdReqBI6j5jiG6r3KIow4poCzpYCvOxWdXBUWQ4VCgbCwMOzYsQNhYWFq7wbMrc5+V24M36BwtPrhKHyDwnFPYVIlqrOXBp+LmuMYaoc+xFEqNLp69Wp89dVXmD17doEPkRYtWkijWSzH5MmTdd2FKoHjqDmOoXqTTyvwJB04PKD4eVfqYlia4qFDhw6Fj49Pta/Ozuei5jiG2qEPcZQSrIcPH6J79+5qGxkaGuL1a/WTOKurvn376roLVQLHUXMcw4K231ViaxRhq7sMzcyLn3eVP4a5xUM97a2w0t8NLSxq4nbSa6y+EAM/Pz+1I1NcnZ3PRW3gGGqHPsRRGje3tbXFuXPn1DYKDw+Hk5NThXWKMcbKKvYVYcIpBd51FBDYvPTzrrh4KGNMG6RPn/Hjx2PBggXYsGEDXr58CQDIzs7GwYMHsWTJEnzwwQc66yRjjJWEkghjjitQzxhY16Nsl+e4eChjTBukBGvGjBkYO3Ys3n//fVhZWQEAevToAR8fHwQGBuLDDz/UWSf1UXBwsK67UCVwHDXHMfzX2utKhD3KWQqnNOsM5o0hFw8tOz4XNccx1A59iKPK+PmqVasQFRWFdevWYcGCBVizZg1u3ryJVatW6ap/emvHjh267kKVwHHUHMcwx51kwqxzSkxuLcKjUekuDeaNIRcPLTs+FzXHMdQOfYijQP/UYzhx4gRcXFxQs2bBv9pSU1MRERGBN954o8I7WF4uXrwIV1dXREREwMXFRdfdYYxpQKEk9PpNgWcZhMihBqhhWPaCogqFAo4O9nA0yMSGQR1VLhMqiTDuQCTuKUwQdS+62t0lyBjLUZIcQvozz8PDAzdu3FDb6NatW/Dw8CifXjLGmIaWXVXi7FPC5t4yjZIrgIuHMsa0QyrTQPmWecgrNTUVpqamFdIhxhgrjevPCV9dUGJ6exE9GhZ9aVChUJSoVlVu8dDp0z6Gb1C4tN3e1qbaFQ9ljJWNwfLly6UH27dvx6lTp1QaZGRkICQkBK1atarovjHGWJEUSsKYEwo0Mwe+di06uSpN4VCAi4cyxjQkCAIJgkCiKFLu93n/GRkZUYcOHejvv/+mqiQiIoIAUERERJmeP3r0aC33qHriOGquOsdwxRU5CT9l0enHiiLb7d27lwRBIC+H+hTi70a3JnpSiL8beTnUJ0EQyMPDo4J6XLVV53NRWziG2lHecSxJDmGgVCoBAKIo4uzZs+jSpYtOE77KQh+qxFYFHEfNVdcYxr4ifHlBiUmtRXRrUPjoVf7CobmT1nMLh447EIkrV69CoVDw6JSGquu5qE0cQ+3QhzhKdxFWN3wXIWOVFxFh4CEFrr0g3PAzQK0ial6FhYXBw8MDIf5ucLGuU2B/xKNk+AaFIzQ0tNovdcMYK5mS5BAG+TdkZGQgOjoaGRkZBRpzIsIY0wc77hEOPSD81ldWZHIFcOFQxphuSAlWVlYWJk6ciG3btkEul6ttzGtvMcZ0LTGD8NEZBfwdBAyyLb6gaN7CoepGsLhwKGOsPEifTvPnz8eRI0ewefNmEBHWrFmDTZs2wdPTE3Z2dvjtt9902U+9k/9uS1Y2HEfNVbcYTj+rgIKAVd1KNl+qV69esLNpitUXYqDMNyNCSYQ1F2LQqGED9OrVqzy6W61Ut3OxPHAMtUMf4iglWLt378a8efPg7+8PAOjSpQvee+89HDlyBD179uQEK5/FixfrugtVAsdRc9UphsceKrE1irDUTYYGZiUrKFqSwqGNmjTlCe5aUJ3OxfLCMdQOfYijlGA9ePAATk5OkMlkMDExwYsXL6RGI0eOxO7du3XSQX21c+dOXXehSuA4aq66xDBLQZh8WoGeDQSMcSpdtfbcwqF35cbwDQpHqx+OwjcoHPcUJtizZw+OHz9eTr2uXqrLuVieOIbaoQ9xlOZgWVtbIykpCQBgb2+PsLAweHl5AQDu3Lmjm97pMTMzM113oUrgOGquusRw5TUl7qQAF4fIIAilXw6HC4eWv+pyLpYnjqF26EMcpQTL3d0dp06dgq+vL8aPH48ZM2bg5s2bMDIyQnBwMAICAnTZT8ZYNfbgNWH+RSUmtxHR3qLsaw3KZDIuxcAYqxBSgvXNN98gMTERAPDxxx+DiLBnzx6kp6dj6tSpmDNnjs46yRir3j45q0BNQ2C+muVwSrq+IGOMVSTp06phw4Zo27attGPatGn4+++/cfHiRSxatAg1atTQSQf11cyZM3XdhSqB46i5qh7DPx8osTsmZ2J77Xw1r/bt2wdHB3t4eHggICAAHh4ecHSwx759+0r1HlU9hjc2sIMAACAASURBVBWF46g5jqF26EMciy8io4HMzEwMGTIELVu2hLOzM/r164d79+4BAJ49e4YBAwbAyckJ7du3x8mTJ6XnpaenIyAgAM2bN0fLli2xd+9eaR8RYcqUKXB0dISTkxPWrl2r8p4LFiyAo6MjmjdvjtmzZ5fbsdnY2JTba1cnHEfNVeUYZv4zsf2NhgLedSyYXPn5+cHRIBMh/m64NdETIf5ucDTIhJ+fX6mSrKocw4rEcdQcx1A79CGOgr29fYmXyomOji7Vi2dmZiI0NBT9+/cHAKxduxZ79uxBaGgoxo4dCzs7O8yZMwcXLlzAkCFDEBsbC5lMhq+//hoxMTHYuHEjYmNj4ebmhlu3bqFu3brYunUrfv75Z/z555948eIFnJ2d8ccff6BVq1Y4ceIEJk2ahPPnz0MURfTo0QP//e9/MWDAgAJ946VyGNN/30UqMPuCEpFDDdC23r8JlkKhgKODPRwNMlXWFwRyaluNOxCJewoTRN2L5suFjDGtK0kOIfr4+CD3X3Z2NpKSkuDs7Iz+/fvD2dkZSUlJkMvl8PX1LXUHjI2NpeQKALp27Yq4uDgAOXW3JkyYAADo1KkTGjduLN0qvWvXLmmfnZ0d3N3d8euvvwIAgoKCMH78eABA3bp1MWzYMOzYsUPaFxgYCBMTExgZGWHs2LHSPsZY5fLgNeHrS0pMbSOqJFcAcPLkScTG38eUTvYqyRUAiIKAyZ3sERMXrzIyzhhjFclgxYoVAIAlS5agadOmOHToEMzNzaUGKSkpGDBgABo0aKDxm61cuRK+vr54/vw55HI56tevL+2ztbVFfHw8ACA+Ph62trbSPjs7uyL3hYeHS/vyVmO2s7PDrl27NO43Y6zifXE+Z2L7PDUT23l9QcaYvpM+uVatWoXPP/9cJbkCgNq1a+Ozzz7D6tWrNXqjhQsX4t69e1i4cKFGr6Mvbt26pesuVAkcR81VxRiee6rEz3cJCzrJYK5mMee86wuqU9r1BatiDHWB46g5jqF26EMcpQTr+fPnSElJUdsoJSVFpbJ7aS1duhTBwcE4dOgQTExMUK9ePRgYGODp06dSm9jYWGlSmq2trXQpMf8+GxubMu0rzMCBA+Ht7a3yr1u3bggODlZpd+TIEXh7e0uPP/30UwDApEmTsGHDBpW2Fy9ehLe3t1T2ItfcuXOxaNEilW3x8fHw9vYucDKsXr26wF0QaWlp8Pb2LrDG0o4dOzBmzJgCxzZs2LBijyOXro4jN46V/Tjyqujj8PHxqRLHkfvzICJ8fEaJ9vUAL9MHao/j8uXLqGNuXuT6gva2NujVq1eJjiP3POTzSrPjyPv7XJmPI6+KPo7333+/ShyHrn8eueeiNo7D1dUV/fv3V8kThgwZUuD5BdA/Bg8eTI0aNaKwsDDKKzQ0lBo1akSDBw+msli2bBm5urpScnKyyvYxY8bQvHnziIjo3Llz1KRJE5LL5URENG/ePBozZgwREUVHR1ODBg0oKSmJiIg2b95MXl5epFAoKCkpiWxtbenatWtERBQWFkZt27altLQ0ysjIoE6dOtHBgwfV9isiIoIAUERERJmOKy4urkzPY6o4jpqrajHcHqUg/JRFxx4qimy3d+9eEgSBvBzqU7C/G92c6EnB/m7k5VCfBEGgvXv3lvg9q1oMdYXjqDmOoXaUdxxLkkNICVZCQgJ16tSJRFGkunXrkpOTE9WtW5dEUSRXV1d6+PBhqTvw4MEDEgSBHB0dydnZmTp27Ehdu3YlIqInT55Q3759qXnz5tS2bVs6fvy49LzU1FQaNmwYNWvWjFq0aEF79uyR9ikUCpo8eTI5ODiQo6MjrV69WuU9v/76a3JwcKBmzZrRl19+qVFwGGMVKzVbSU1/ySLfw9klar93716ys2lKAKR/9rY2pUquGGOstEqSQwhEquPrhw4dwrlz56SqyF26dFG5E7Cq4DINjOmfry8q8PUlJW74GcCxdsmWxOFK7oyxilaSHMIg/4b+/ftXyYSKMabfHqYSvrusxEdtxRInVwCvL8gY00/lWsm9Kss/SY+VDcdRc1Ulhl+cV6CGATDbueI/lqpKDHWN46g5jqF26EMcC4xgsZJJS0vTdReqBI6j5qpCDC8lErZGEX7oIRZYb7AiVIUY6gOOo+Y4htqhD3EsMAeruuA5WIzpj36/yxH7mnDdzwAGYsUnWIwxVhplmoPFGGMV6a+HShx5SNjrJePkijFWZfAcLMaYziiJ8Gm4At3qCxhix8kVY6zqUEmwUlNTsXbtWowYMQL9+vXDiBEjsG7dOqSmpuqqf3orf3VaVjYcR81V5hjuvEe4lAQsdhMhCLpLsCpzDPXJ/7N352FRXOkawN9eVNzGFQxRliYsGo0CkjBGSUDiGoNIiEQmxIAxqxr3bDouURN3jZqZO3NJzKJERMSMxsSEQGwz4wIIrqCyNaOtAi4RUbS7zv3DS8WWRpuu6q7q5vs9j88j1dXw1WuBH1WnzqEchaMMxSGHHPkGq6KiAn379sWUKVNQVFQEpVKJoqIiTJkyBf369UNFRYWUdcpOUlKS1CU4BcpROEfNsM7I8OEhI6K8FBj00B+/6xmNRmRnZyMlJQXZ2dkwGo02r8VRM5QbylE4ylAccsiR/6k2ffp0AMCJEyeQl5eH3bt3Iy8vD8ePH4dCocCMGTMkK1KO5s+fL3UJToFyFM5RM/zbCQ6668DHj/8xKWh6ejp8fTSIiIhAfHw8IiIi4OujQXp6uk1rcdQM5YZyFI4yFIcccuQbrJ9++glLlixBQECAyQ4BAQH46KOPsGfPHrsXJ2f05KE4KEfhHDHDq7cYFh3mkOSvwKOd7twaTE9PR2xsLHzVddgxNhSFb0Zix9hQ+KrrEBsba9MmyxEzlCPKUTjKUBxyyJFvsAwGA1q3bm12p9atW9vlMj0hpHlYVsCh1gAs6H/n6pXRaMSMaVMRqXFF8qhABLt3RNuWagS7d0TyqEBEalwxc/o0+jlECHEYfIM1cOBALFq0CFevXjXZ4erVq1i8eDEGDhxo9+IIIc7n3HWG1Uc5THtMiYfb3rl6pdVqUaarwOQQDZT3DHZXKhSYFKJBabkOWq1WipIJIaTJ+AZr5cqVOHPmDDw8PBAdHY3XX38dY8aMgYeHB4qLi7FixQop65Sd5ORkqUtwCpSjcI6W4eJ8Di5qYHa/Pwa26/V6AEBAl3Zm31O/vX4/sTlahnJFOQpHGYpDDjnyP+H69OmDI0eO4NVXX8W5c+fwyy+/4Ny5c5g4cSIKCgrQp08fKeuUnby8PKlLcAqUo3COlGHZNYZ/FnKY3dd0SRx3d3cAQFF1jdn31W+v309sjpShnFGOwlGG4pBDjrRUDi2VQ4jdJP1qwK4KhpI4Ndq2+KPBMhqN8PXRwFddh+RRgSa3CTnGMGFnPoqNLjhdXAKVSmXuUxNCiN1Y0kPwV7B8fHxQUFBgdqdjx47Bx8fHNlUSQpqFoisMX55m+CBQadJcAYBKpcLK1WuQWVqJCTvzkau/gppbBuTqr2DCznxkllZixarV1FwRQhwGvxZhWVkZ6urqzO5UW1tLE40SQgSZn2fEw22A13uaX6ErJiYGaWlpmDFtKqJTD/DbNV6eSEtLQ0xMjL1KJYQQwdSXLl1C/V3C33//HZcuXTLZ4ebNm8jIyMDDDz8sRX2EECdwpJrh22KG/xmkgou68SVxYmJiMHr0aGi1Wuj1eri7uyMsLIyuXBFCHI7S1dUVbm5uUCgUGDZsGFxdXU3+eHh4YOnSpXj11VelrlVWoqKipC7BKVCOwjlChn/NNcKnPZAY8OD1BlUqFcLDwzFu3DiEh4fbpblyhAwdAeUoHGUoDjnkqP7888/BGENSUhLmzJmDRx55xGSHli1bolevXggMDJSoRHmaNGmS1CU4BcpROLlnePAihx3lDF+Fq9BCKd2Czvcj9wwdBeUoHGUoDjnkyD9F+OWXX2LUqFHo0qWL1DXZBT1FSIh9DPvegIrrDEefV0Ml0waLEEKawpIegh/kPn78eLsVRghpHvbqOew5y7A1UkXNFSGkWTH/OA8hhAjEGMOcHA5BXYAYDTVXhJDmhRosK2VkZEhdglOgHIWTa4Y/nWXQnmf4KEQFxnHIzs5GSkoKsrOzZbdos1wzdDSUo3CUoTjkkCM1WFZKSUmRugSnQDkKJ8cMGWNYkMfhCVcFbh7aDl8fDSIiIhAfH4+IiAj4+miQnp4udZk8OWboiChH4ShDccghR1oqhwa5EyK6n89yGPK9ER9wO/Dxm2MRqXHF5BANArq0Q1F1DdbllCKztJImECWEOKQmLZVz7do1VFVVmby4adMmzJkzB1lZWbatlBDiNBhjWJDLoX8nDpuXTEekxhXJowIR7N4RbVuqEezeEcmjAhGpccXM6dNkd7uQEELEwDdYL730EubOncu/sHDhQiQkJODvf/87hgwZgtTUVEkKJIQ4lqxzDPsuMDxv+A1lugpMDtGYLN4MAEqFApNCNCgt10Gr1UpUKSGE2A7fYB06dAhDhw4FcOc30A0bNuCDDz5AVVUVpkyZguXLl0tWJCHEcSzI49C/qwJe3HkAQECXdmb3q9+u1+vtVhshhNgL32BdunQJXbt2BQDk5uaiqqoKSUlJAO5MOV9UVCRNhTKVmJgodQlOgXIUTk4ZZp/jsPc8w1+Dlfz6pUXVNWb3rd/u7u5ut/oaI6cMHRnlKBxlKA455Mg3WN26dcOJEycAALt27YK3tzd8fHwAANevX4darTb/GZqp+qt9RBjKUTg5Zbgg7868V895KhAWFgZvTw+syykFd8+zNBxjWJ9TCo2XJ8LCwiSq9g9yytCRUY7CUYbikEOOfIM1duxYzJ49Gy+88AKWLVtmMrP74cOH4efnJ0mBcjVu3DipS3AKlKNwcslwr55Dtp7hr8EqKBQKqFQqrFy9BpmllZiwMx+5+iuouWVArv4KJuzMR2ZpJVasWm2XxZwfRC4ZOjrKUTjKUBxyyJG/LPXxxx+jffv2OHToEGbOnIn33nuP3yk3Nxdjx46VpEBCiGNYkMehX2dgtNcfA9pjYmKQlpaGGdOmIjr1AL9d4+VJUzQQQpwa32Cp1Wr89a9/NbvT9u3b7VYQIcTx7DvP4ZdzDOnP3Ll6dbeYmBiMHj0aWq0Wer0e7u7uCAsLk8WVK0IIsZUGM7mfPHkSX3/9NZYsWYLz5+88BXTmzBlcu3bN7sXJ2b59+6QuwSlQjsLJIcMFeRz6dgZGe5tfc1ClUiE8PBzjxo1DeHi47JorOWToDChH4ShDccghR77Bqq2tRXx8PPr06YOkpCTMnTsX586dAwC8//77+OijjyQrUo6WLVsmdQlOgXIUTuoM/32Bw89n74y9une+K0chdYbOgnIUjjIUhxxy5BusmTNn4pdffsHu3bvx+++/4+4VdEaOHIkffvhBkgLl6ttvv5W6BKdAOQondYYLcjn06QSMaeTqlSOQOkNnQTkKRxmKQw458mOw0tLSsHz5cgwdOrTB0hXe3t4oKyuzd22y1qZNG6lLcAqUo3BSZnjgIoc9ZxlSIx336hVA56FYKEfhKENxyCFH/gpWTU1NoxP+Xb9+3W4FEUIcx+LDHHp2BJ7XOG5zRQghtsA3WH379sW2bdvM7rRr1y6EhITYrShCiPwdqWb4l47h/X6OffWKEEJsgW+w5s6di+TkZCQkJGDXrl1QKBQ4ePAgZs2ahc8//xwffvihlHXKzqxZs6QuwSlQjsJJleHHBUZ4twPG+Tp+c0XnoTgoR+EoQ3HIIUe+wXr22Wfx7bffYt++fYiOjgZjDG+99Ra2bNmCTZs2ITIyUso6ZcfT01PqEpwC5SicFBmevsqQWsIwu58SLZSO32DReSgOylE4ylAccshRwdg9i4QBOHXqFKqqqtC5c2f07NlTirpsLi8vD/3790dubi6Cg4OlLocQh/LqXgO+r2AoiVPDRe34DRYhhDSFJT2E2RWc/f394e/vDwC4desWWrZsabsqCSEOpaKG4avTDB8/rkQLBYfsbJqhnRBC7sXfIvz666+xbt06/oVjx47Bz88Pbdq0QXh4OC5evChJgYQQeVlxhEP7FsBDhRnw9dEgIiIC8fHxiIiIgK+PBunp6VKXSAghkuMbrOXLl0Op/GPlnMmTJ6Nly5ZYs2YN9Ho9PvjgA0kKlKvCwkKpS3AKlKNw9szw4g2GfxZyGHJxBxJefAG+6jrsGBuKwjcjsWNsKHzVdYiNjXW4JovOQ3FQjsJRhuKQQ458R1VWVoZHH30UAFBVVQWtVouVK1di0qRJWLhwIX788UfJipSj2bNnS12CU6AchbNnhquPclDCiP98Oh2RGlckjwpEsHtHtG2pRrB7RySPCkSkxhUzp09rMGGxnNF5KA7KUTjKUBxyyJFvsJRKJW7dugUAyMrKQosWLRAREQEAcHd3R3V1dZM/+TvvvAONRgOlUokjR47w28PDw+Hj44Pg4GAEBwdj7dq1/Gs3btxAfHw8/Pz80LNnT5O5uRhjmDx5Mnx9feHv748NGzaYfL1FixbB19cXfn5+mDNnTpPrbYr169fb9PM3F5SjcPbK8Eodw4YTHJ67+Rt0FRWYHKJpMP+VUqHApBANSst10Gq1dqlLDHQeioNyFI4yFIcccuQHuffr1w+fffYZevTogU8//RSDBw9Gq1atAAA6nQ5ubm5N/uQvvPAC3n33XQwaNMhku0KhwNq1a/Hcc881eM+KFSvg4uKC06dPo6ysDKGhoRg8eDA6deqEr7/+GoWFhThz5gwuX76MoKAgDB48GL169cLevXuxZcsWHDt2DEqlEgMHDsTAgQMxYsSIJtdtCTk8AuoMKEfh7JXh+uMcbnHAU20u4FsAAV3amd2vfrter7dLXWKg81AclKNwlKE45JAjfwVryZIl2Lt3L/r27YujR49iwYIF/E7bt2/HE0880eRPPmjQIDz88MMwMxMEOI4z+54tW7bgjTfeAHBnDcTw8HBs374dAJCamoqJEycCADp16oS4uDikpKTwryUkJMDFxQUtW7ZEUlIS/xohRJjrtxnWHOPwaoASvbwfBgAUVdeY3bd+e2NLbxFCSHPAN1gDBw6ETqfDwYMHUVZWZrI0zoQJE7Bo0SJRv/C7776Lfv36Ydy4cSgtLeW363Q6eHl58R97e3tDp9MJeo0QIsw/CjlcvQXM6qtEWFgYvD09sC6nFNw9vzxxjGF9Tik0Xp4ICwuTqFpCCJGe8u4P2rdvj/79+6Njx44mO40cOZKfF0sM33zzDQoLC1FQUIBBgwZh1KhRon1ue1m6dKnUJTgFylE4W2dYZ2RYcYTDS34KeLVXQKVSYeXqNcgsrcSEnfnI1V9BzS0DcvVXMGFnPjJLK7Fi1WqHmg+LzkNxUI7CUYbikEOOJg0Wx3H4+eef8dlnn2HVqlUmf1avXi3aF+3evTv/97fffhslJSW4fPkyAMDLywvl5eX862VlZfy9VE9PT6teu5+RI0ciKirK5M+AAQOQkZFhst+ePXsQFRXFf1xbW8vXn5ycbLJvXl4eoqKiUFVVZbJ93rx5Df7RdTodoqKiGjxSum7dugZrKdXW1iIqKgr79u0z2Z6SkoLExMQGxxYXF/fA46gn1XHU5+jox3E3ex/H999/b9Pj+PIUg74WeK+fij8OpVKJtLQ0nDG0QnTqAfT6WyaiUw+g2OiCtLQ0xMTENPk4pPz3qD8P6bwSdhx3fz878nHczd7HUVxc7BTHIfW/R/25KMZx9O/fH8OHDzfpE8aMGdPg/Q2w/6fX61lAQABTKBRMqVQyhULB/73+j7W8vb1ZQUEBY4wxg8HALly4wL+WlpbGvL29+Y/nz5/PEhMTGWOMlZSUsG7durHq6mrGGGMbN25kzzzzDDMajay6upp5eXmxY8eOMcYYy87OZn369GG1tbXs5s2bLCQkhO3atavRmnJzcxkAlpuba/VxEeLsbhs55pNyi73w022zrxsMBpaVlcU2b97MsrKymMFgsHOFhBBif5b0EPxThNOnT0eXLl1QUVEBDw8PHDhwAN26dcM333yDr776Crt27Xpwt3aPN954A7t27cKFCxcwbNgwtG/fHgUFBXj22Wdx69YtKBQKuLq64rvvvuPfM2vWLCQlJcHX1xdqtRobNmxA586dAQAJCQnIycmBn58flEolZs6cid69ewMAnn76acTFxaFPnz5QKBR48cUXMXLkyCbXTAj5w5YShpJrwLYh5m/3qVQqhIeH27coQghxAPxiz/XTM0RHR0OtVmP//v38k4OLFy/Gvn37sHv3bkmLFRMt9kzI/XGM4bE0A7zbK7BruNllSwkhpFmypIfgx2BdvXoVXbt2hVKpxJ/+9CeTtQcHDBjQ4H5nc3fvfWViHcpROFtl+F05w4krwIdBygfv7ODoPBQH5SgcZSgOOeTI/+TUaDQ4e/YsAKB37974+uuv+Z22b9/O36YjdyQlJUldglOgHIWzRYaMMSw+zOFpdwWe7Ob8DRadh+KgHIWjDMUhhxz56/7PPvssfvrpJ4wbNw5z5szB6NGj4ebmhhYtWuD8+fOyeORRTubPny91CU6BchTOFhn+dJYhp4phzwjHmWpBCDoPxUE5CkcZikMOOfJjsO6Vk5OD7du348aNGxgyZIjNlpyRCo3BIqRx4TsNuH4bOBitguKe9QYJIaS5s6SHaHTkakhIiMls7oSQ5uG38xx+1TNsH0LNFSGEWIsfXJGZmYkvvvjC7E4bN25EVlaW3YoihEhnST6H3p2AKC9qrgghxFp8gzVnzhxcuHDB7E6VlZWYM2eO3YpyBPfO9kqsQzkKJ2aGh6sYvq9geD9QBWUzunpF56E4KEfhKENxyCFHvsE6fvx4o7cEg4ODcfz4cbsV5Qjy8vKkLsEpUI7CiZnhknwjfNoDcT7Np7kC6DwUC+UoHGUoDjnkyI/BUigUuHr1qtmdLl++DKPRaLeiHMGGDRukLsEpUI7CiZVh4RWGbaUMfx+kglrZvBosOg/FQTkKRxmKQw458lewQkNDsWHDBtz7UCFjDJ999hlCQ0PtXhwhxH6WFhjh3gYY79+8mitCCLEF/grWggULEBERgb59++KVV16Bu7s7zp07h6+++gqnTp1Cdna2hGUSQmyp/BrDN6cZloUq0UpFDRYhhAjFN1gDBgxAZmYmZs+ejXfffRccx0GpVPLb//znP0tZJyHEhlYc4dChJTCxp/PP2k4IIfZg8tN04MCB+O2333Dt2jX897//xe+//w6tVouBAwdKVZ9sRUVFSV2CU6AchROa4YVahv8t4vBOHyXatWieV6/oPBQH5SgcZSgOOeRodqLR1q1bo3Xr1vauxaFMmjRJ6hKcAuUonNAMVx/j0EIJvNmTITs7G3q9Hu7u7ggLC4NK1TyWyqHzUByUo3CUoTjkkGOjS+U4O1oqhxDgch2DV4oBkRd2IP+z6SjTVfCveXt6YOXqNYiJiZGwQkIIkR9LeggacEFIM7bhOIebh7Zjx/tj4auuw46xoSh8MxI7xobCV12H2NhYpKenS10mIYQ4HGqwCGmmrt9mWH3kNtpsm4lIjSuSRwUi2L0j2rZUI9i9I5JHBSJS44qZ06fRPHiEENJEyosXLwIAdDodbt++LXE5jiMjI0PqEpwC5SictRn+s5DDleP7cPVCBSaHaBosjaNUKDApRIPSch20Wq0YpcoWnYfioByFowzFIYccleXl5QAAjUaDw4cPS1yO40hJSZG6BKdAOQpnTYZ1RoYVRzkMdDkPAAjo0s7sfvXb9Xq99QU6ADoPxUE5CkcZikMOOSqLi4sB3JmxXdGMFncVasuWLVKX4BQoR+GsyfCr0wznrgOvhnYHABRV15jdr367u7u79QU6ADoPxUE5CkcZikMOOapffvllvPfee1AoFIiOjkarVq3M7qhQKFDfjBFCHJeBY1haYMTzGgX+EvEU5nl6YF1OKZJHBZrcJuQYw/qcUmi8PBEWFiZhxYQQ4njUf/vb33Dy5EmsWrUKTz31FB566CGpayKE2NDWEobi34HUSBVUKgVWrl6D2NhYTNiZj0khGgR0aYei6hqszylFZmkl0tLSms18WIQQIhb1hAkTAADbtm3De++9h379+klcEiHEVjjGsCTfiOE9FAjueudqVUxMDNLS0jBj2lREpx7g99V4eSItLY3mwSKEECvw0zSUlpZSc9UEiYmJUpfgFChH4ZqS4S4dw7HLwAeBpjO0xMTE4ExJKbKysrB582ZkZWXhdHFJs2mu6DwUB+UoHGUoDjnkaLJUztmzZ7FmzRrs27cPly5dQufOnREWFoZ33nkH3bt3l6pGWRo6dKjUJTgFylE4SzNkjGFxPodB3RQIc284BZ5KpUJ4eLjI1TkGOg/FQTkKRxmKQw458kvlHDt2DE899RRu376NIUOGoFu3brhw4QJ+/vlntGjRAnv37kXv3r2lrlc0tFQOaW5+Ocsh8nsjvh+uwggPmmOYEEKsZUkPwV/BmjlzJh555BHs2bMHnTp14ne4fPkyhg4dipkzZ2L37t22r5oQYhNL8jkEdQGG96DpWAghxNb4Bmvfvn3YtGmTSXMFAJ06dcKHH36IhIQEuxdHCBHHgYscMs8xbI1U0Xx3hBBiB/x9ArVajbq6OrM71dXV0WPa99i3b5/UJTgFylE4SzL8OJ9DQAdgjDc1V+bQeSgOylE4ylAccsiRb7CeeeYZfPjhhzh16pTJDqdPn8bcuXMxZMgQuxcnZ8uWLZO6BKdAOQr3oAyPXWLYUc7wXqAKKiU1WObQeSgOylE4ylAccsiRH+Su0+nw9NNPo6KiAn369EG3bt1w8eJFHD16FJ6envj111/h4eEhdb2iETrIvba2Fm3atLFBZc0L5SjcgzIc94sB/77AcCZOjRbUYJlF56E4KEfhKENx2DpHS3oI/gqWp6cnjh49ilWrVsHfI3PqUgAAIABJREFU3x8cx8Hf3x+rV6/GkSNHnKq5EgN9A4iDchTufhkWXmHYUszwfj8lNVf3QeehOChH4ShDccghR5N5sNq1a4cpU6ZgypQpUtVDCBHRksNGPNwWSAygaRkIIcSe6KcuIU7qzFWGzcUM7/ZVopWKrl4RQog9UYNlpVmzZkldglOgHIVrLMOP841wdQFe7Unf5g9C56E4KEfhKENxyCFH+slrJU9PT6lLcAqUo3DmMiy7xvDVaYZZfZVoraarVw9C56E4KEfhKENxyCFH/inC5oaWyiHO7A2tEellHEpfVKNtC2qwCCFETBY/RXjz5k2sWrUKx44ds2uBhBDxVdQwfH6Kw4zHlNRcEUKIRJQA4OLigjlz5qC6ulrqegghAi0r4NC+BfDWozQCgBBCpML/BA4MDMSJEyekrMWhFBYWSl2CU6Achbs7w3PXGf5ZxGH6Y0q0b0lXryxF56E4KEfhKENxyCFHvsFau3YtVq9ejbS0NNTW1kpZk0OYPXu21CU4BcpRuLszXH6EQ2sVMKk3Xb1qCjoPxUE5CkcZikMOOfKD3Nu3b49bt27BYDAAuDMLqkLxx2/ACoUCV69elaZKGxA6yF2n08niKQVHRzkKV5/hhVoGzbcGzO6nxPz+tDh7U9B5KA7KUTjKUBy2ztGSHoKfyX3GjBkmDRW5P/oGEAflKFx9hiuPclArgXf60NWrpqLzUByUo3CUoTjkkCPfYM2fP1/CMgghQlTdZPjsBId3+ijRqRX9okQIIVIz+6tuRUUF/v3vf+P69ev2rocQYoWVRzgAwLTH6OoVIYTIgclP43/84x/o3r07vLy8EBYWhqKiIgDAmDFjsHbtWkkKlKulS5dKXYJToByFm7vsU3x6nMOUPkp0daGrV9ag81AclKNwlKE45JAj32CtWbMGkydPxssvv4w9e/bg7gnew8PDsXXrVkkKlCt60lIclKNwP6sDoVIAM+nqldXoPBQH5SgcZSgOOeTI/0Ret24d5s6di48//hgREREmOwUEBPBXs5rinXfegUajgVKpxJEjR/jtlZWVGDFiBPz9/dG3b19otVr+tRs3biA+Ph5+fn7o2bMntm3bxr/GGMPkyZPh6+sLf39/bNiwweTrLVq0CL6+vvDz88OcOXOaXG9TLFiwwKafv7mgHIXR1zLkdxyAaY8p0ZmuXlmNzkNxUI7CUYbikEOO/CD3s2fP4sknnzS7U4sWLVBTU9PkT/7CCy/g3XffxaBBg0y2v/feexgwYAB2796NnJwcjBkzBmVlZVCpVFixYgVcXFxw+vRplJWVITQ0FIMHD0anTp3w9ddfo7CwEGfOnMHly5cRFBSEwYMHo1evXti7dy+2bNmCY8eOQalUYuDAgRg4cCBGjBjR5LoJcRRLCzi0UgHTGnly0Gg0QqvVQq/Xw93dHWFhYVCpaAoHQgixNf6nspeXFw4ePGh2pwMHDsDf37/Jn3zQoEF4+OGHce960qmpqXjjjTcAACEhIejevTt+/fVXAMCWLVv417y9vREeHo7t27fz75s4cSIAoFOnToiLi0NKSgr/WkJCAlxcXNCyZUskJSXxrxHijM5eZ/j7yTtrDnY08+Rgeno6fH00iIiIQHx8PCIiIuDro0F6eroE1RJCSPPCN1gTJ07EokWLkJycjN9//x0AcPv2bezatQvLly/H66+/LsoXvHTpEgwGA9zc3PhtXl5e0Ol0AO5MDubl5cW/5u3tLfg1W6iqqrLZ525OKEfrLcnn0EYNvOR+ucFr6enpiI2Nha+6DjvGhqLwzUjsGBsKX3UdYmNjqcm6B52H4qAchaMMxSGHHPkGa+bMmUhKSsJrr70GV1dXAMDAgQMxevRoJCQk4K233pKsSDlKSkqSugSnQDlaR1fD8M9CDrP6KvHO66YZGo1GzJg2FZEaVySPCkSwe0e0balGsHtHJI8KRKTGFTOnT4PRaJSoevmh81AclKNwlKE45JCjycCNTz/9FKdOncKGDRuwaNEirF+/HidPnsSnn34q2hfs3Lkz1Go1Ll68yG8rKyvjZ1318vJCeXm52dc8PT2teu1+Ro4ciaioKJM/AwYMQEZGhsl+e/bsQVRUFP9x/cSsb7/9NpKTk032zcvLQ1RUVIMOet68eQ0eHdXpdIiKimqwMOW6deswa9Ysk221tbWIiorCvn37TLanpKQgMTGxwbHFxcU98DjqSXUcd09w68jHcTd7HMfiwxw6tAQm91bioYceMjkOrVaLMl0FJodooLxndQalQoFJIRqUluv4h0uc8bxq6nHUn4eOfhz1pDqOu7+fHfk47mbv44iLi3OK45D636P+XBTjOPr374/hw4eb9Aljxoxp8P4GmB14e3uzgoIC/uPExEQ2f/58xhhjBw8eZD169GAGg4Exxtj8+fNZYmIiY4yxkpIS1q1bN1ZdXc0YY2zjxo3smWeeYUajkVVXVzMvLy927Ngxxhhj2dnZrE+fPqy2tpbdvHmThYSEsF27djVaU25uLgPAcnNzbXLMhNhKyVWOqf95iy0vMJh9ffPmzQwAK3wzklW8M6zBn5NvRjIAbPPmzXaunBBCnIMlPYT67mbr9u3b2LhxIw4cOMA/dfTnP/8Z48ePR4sWLR7crd3jjTfewK5du3DhwgUMGzYM7du3x6lTp/DJJ58gISEB/v7+aNWqFTZt2sQ/2TRr1iwkJSXB19cXarUaGzZsQOfOnQEACQkJyMnJgZ+fH5RKJWbOnInevXsDAJ5++mnExcWhT58+UCgUePHFFzFy5Mgm10yI3H102IguLsBbj5p/ctDd3R0AUFRdg2D3jg1eL6quMdmPEEKI+BSM3XnE79SpUxg+fDh0Oh369euHbt264cKFCygoKICHhwd++OEHBAQESF2vaCxZCZsQuSm6wtA7zYAVoUpMfcz8dAtGoxG+Phr4quuQPCrQ5DYhxxgm7MxHsdEFp4tLaMoGQgixgiU9BP8r8Ouvv46WLVuiqKgIubm5+P7775Gbm4vCwkK4uLjgzTfftFvhjuDe+7TEOpRj08zNMeLhNsAbvf64enVvhiqVCitXr0FmaSUm7MxHrv4Kam4ZkKu/ggk785FZWokVq1ZTc3UXOg/FQTkKRxmKQw458j+lDxw4gMWLF+ORRx4x2cHX1xcLFy7E/v377V6cnOXl5UldglOgHC2XW8mwtZRhfn8VXNR/XJUyl2FMTAzS0tJwxtAK0akH0OtvmYhOPYBiowvS0tIQExNjz9Jlj85DcVCOwlGG4pBDjvwtQl9fXyxbtszsD960tDTMnj0bJSUldi/QVugWIXE0w743QHed4ejzaqiVli2LQzO5E0KI+CzpIfhB7vPmzcPcuXMRGBgIHx8ffoeSkhLMmzcP8+bNs33FhBCzfjnLYc9Zhm3PqMw2V401UiqVCuHh4fYvmBBCmjn13XNBXLlyBQEBAejTpw/c3Nxw8eJFHDt2DN26dcO2bdswfvx4CUslpHlijOH9Qxwed1VgjLf5JXFmTJuKMl0Fv83b0wMrV6+hW4GEECIR9bVr1/gP/P39+TUHb926hY4dO/ILNd+9HyHEfjLKGA5WMmSOVEFxz8Sh9UviRGpcsXZsKAK6tENRdQ3W5ZQiNjaWxlsRQohE+DFYzY3QMVhRUVH47rvvbFBZ80I53p+BY+i7zYAebRXYM9Jk2ro/pmNQ3UTyc0E0HYMAdB6Kg3IUjjIUh61zbNI0DaRpJk2aJHUJToFyvL+vTzOcvAIsebzhtyq/JM7jPhYtiUMaR+ehOChH4ShDccghR5NfiSsqKpCRkYGKigrcvHnTZEeFQoG1a9fatTg5Gzp0qNQlOAXKsXE3DQzzco14QaNAiGvDBkuv1wMAArq0M/v++u31+5HG0XkoDspROMpQHHLIkW+wUlNTkZCQAI7j4ObmhpYtW5rsSA0WIfa14QSHc7XARyHmb+/RkjiEECJffIP1wQcfIDo6Gv/4xz/QoUMHKWsipNmrvsmw6DCH13oqEdDR/JxXYWFh8Pb0wLqcUrNL4qzPKYXGyxNhYWH2KpsQQsj/4+87VFZW4rXXXqPmykIZGRlSl+AUKEfzPjrMwciA+f0bHyZJS+KIh85DcVCOwlGG4pBDjvxP7+HDh9NyOE2QkpIidQlOgXJs6PRVhg3HObwfqIRb6/vP2B4TE4MBAwbQkjgC0XkoDspROMpQHHLIkZ+m4fLly4iLi8Pjjz+OyMhIdOzYcEyHMy0pQ0vlELmK+cmA3CqGwhfUaK2mJXEIIURumrRUzrVr11BbW4uPP/4Yn3zyiclOjDEoFAoYjUbbVkxIM6fVc9hexvBNhMri5goALYlDCCEywzdYL7/8MnQ6HdatWwd/f/8GTxESQmyLYwwzDnAI6arAuEcsb64IIYTID99gHTx4EJs3b0Z0dLSU9RDSbG0pZjhUyfDrKFWDiUMJIYQ4Fn6Qu5+fHwwGg5S1OJTExESpS3AKlOMdNw0M7x8yItpLgafcm7bAAmUoHGUoDspROMpQHHLIkf9JvmrVKixevBiFhYVS1uMw5DBLrDOgHO9YeZTD2evA0ieaPjCdMhSOMhQH5SgcZSgOOeTIP0X42GOP4fz587h8+TIefvjhBk8RKhQKFBQUSFKkLdBThEQuKmoYem414K1HlVgeSk/+EUKI3DXpKcL+/ftDQeM+CLG72QeNaN8CmBtEa68TQoiz4BusjRs3SlgGIc3TXj2Hb4sZNj6twp9a0i84hBDiLOhXZivt27dP6hKcQnPO0cAxTP63EaFuCiT4Wd9cNecMxUIZioNyFI4yFIcccuSvYCUlJT1w588//9ymxTiSZcuWYdCgQVKX4fCac47/KORw5BJwMFppdloGS2dnb84ZioUyFAflKBxlKA455MgPcg8KCmrw4uXLl1FRUYGuXbuie/fuyMvLs3uBtiJ0kHttbS3atGljg8qal+aaY/VNBr9UA8Z4KZD8tLrB6+np6ZgxbSrKdBX8Nm9PD6xcvabB+oLNNUMxUYbioByFowzFYescmzTI/fDhw2Z3OHnyJMaNG4eVK1fapkoHRd8A4miuOc7J4WDkgI/NTMuQnp6O2NhYRGpcsXZsKAK6tENRdQ3W5ZQiNja2wSLOzTVDMVGG4qAchaMMxSGHHB84BqtXr1549913MW3aNHvUQ4jTO3CRw/+c5LAwRAm31qa3Bo1GI2ZMm4pIjSuSRwUi2L0j2rZUI9i9I5JHBSJS44qZ06fRuqCEECJzFg1y79ChA86cOWPrWghxegaO4XWtEUFdgUmPNvz202q1KNNVYHKIpsG4LKVCgUkhGpSW66DVau1VMiGEECvwP+EvXbrU4M/58+eRlZWFDz74AH369JGyTtmZNWuW1CU4heaW46fHOBy9DPzPIBVUyoYD2/V6PQAgoEs7s++v316/H9D8MrQFylAclKNwlKE45JAjPwara9euZicaZYzBw8MDGRkZdi1M7jw9PaUuwSk0pxwrahj+msvh7UeVCHE1f/HY3d0dAFBUXYNg944NXi+qrjHZD2heGdoKZSgOylE4ylAccsiRf4pw48aNDRosFxcX9OjRA6GhoVCrGz7p5MhoqRxib2P2GHCgkuHkC2p0aGRSUaPRCF8fDXzVdUgeFWhym5BjDBN25qPY6ILTxSVmp2wghBBie016ivCVV16xV12ENDvflXPIKGdIjVQ12lwBgEqlwsrVaxAbG4sJO/MxKUTDP0W4PqcUmaWVSEtLo+aKEEJkzrkuSxEiQzW378zYPsJDgVjNg2dsj4mJQVpaGmZMm4ro1AP8do2XZ4MpGgghhMiT2sfHx6IdFQoFiouLbVyO4ygsLETPnj2lLsPhNYccPzjEoeomsP5JlcULqsfExGD06NEWzeTeHDK0NcpQHJSjcJShOOSQo3r06NH33eHIkSPIysqy+D+G5mL27Nn47rvvpC7D4Tl7jlo9h3XHOawZoITPn5r2PaRSqRAeHv7A/Zw9Q3ugDMVBOQpHGYpDDjmqV69ebfaF/Px8LFy4ENnZ2XjkkUfw/vvv27k0eVu/fr3UJTgFZ86x1sCQtNeIgd0UmNzbduuqO3OG9kIZioNyFI4yFIcccmzwUz8nJwdRUVHo378/Tp48iS+//BJFRUUWLQbdnMjhEVBn4Mw5/jWHw3+vA8lPqcwu5iwWZ87QXihDcVCOwlGG4pBDjnyDtX//fowYMQKhoaEoKyvD5s2bceLECbz00ktQKm332zchzmj/BQ6rj3FY2F+JgI50e50QQpob5d69ezFkyBA8+eSTuHjxItLS0nDkyBHExcXRuCtCrHDz/28N9u+qwLTH6JcTQghpjpQRERGoqanBzp07kZubizFjxkhdk0NYunSp1CU4BWfMcUEehzO/A188pYLazHI4YnPGDO2NMhQH5SgcZSgOOeSoZozh2LFjePHFF++7o0KhwNWrV+1UlvzV1tZKXYJTcLYctXoOSws4LApRondn+1wBdrYMpUAZioNyFI4yFIccclTMnz+fWbrzvHnzbFmLXdFSOURsv99i6LvNgB5tFfh1lPnFnAkhhDg+i5bKcaamiRApTfm3EZfqgKxnqbkihJDmjpbKIUQEaSUcvjzNsPFpFTSNTChqNBotmpmdEEKI46NHnKxUVVUldQlOwRlyPHud4fV9RjyvUeBlP/PNVXp6Onx9NIiIiEB8fDwiIiLg66NBenq64K/vDBlKjTIUB+UoHGUoDjnkSA2WlWjiVXE4eo5GjmF8thGtVMD/DDK/1mB6ejpiY2Phq67DjrGhKHwzEjvGhsJXXYfY2FjBTZajZygHlKE4KEfhKENxyCFHBWPM4kHuzkToIPe8vDwaHC8CR8/xozwj5uVy+GmkCpHdG/6+YjQa4eujga+6DsmjAk1mdOcYw4Sd+Sg2uuB0cYnVtwsdPUM5oAzFQTkKRxmKw9Y5WtJDSHoFy9vbG7169UJQUBCCg4OxdetWAEBlZSVGjBgBf39/9O3bF1qtln/PjRs3EB8fDz8/P/Ts2RPbtm3jX2OMYfLkyfD19YW/vz82bNhgs9rpG0Acjpzjr3oO8/M4zA1Wmm2uAECr1aJMV4HJIZoGy+UoFQpMCtGgtFxnco43lSNnKBeUoTgoR+EoQ3HIIUdJB7krlUqkpqbiscceM9n+3nvvYcCAAdi9ezdycnIwZswYlJWVQaVSYcWKFXBxccHp06dRVlaG0NBQDB48GJ06dcLXX3+NwsJCnDlzBpcvX0ZQUBAGDx6MXr16SXSExFldvMEw7hcjnnpIgb8GNf57il6vBwAEdGln9vX67fX7EUIIcQ6SXsFijMHcHcrU1FS88cYbAICQkBB0794dv/76KwBgy5Yt/Gve3t4IDw/H9u3b+fdNnDgRANCpUyfExcUhJSXFHodCmhGOMSRkGWFkwObB95+Swd3dHQBQVF1j9vX67fX7EUIIcQ6SD3JPSEhAv379MHHiRFRXV+PSpUswGAxwc3Pj9/Hy8oJOpwMA6HQ6eHl58a95e3tb9JrYkpOTbfJ5mxtHzPGTfA4/nWX4JlwF9zb3n+8qLCwM3p4eWJdTCu6eXyY4xrA+pxQaL0+EhYVZXY8jZig3lKE4KEfhKENxyCFHSRssrVaLgoIC5OXloUuXLhg/fjwAmL2qJTd5eXlSl+AUHC3HHys4zMnh8GGQEkN6PPjbR6VSYeXqNcgsrcSEnfnI1V9BzS0DcvVXMGFnPjJLK7Fi1WpB82E5WoZyRBmKg3IUjjIUhxxylLTB6tGjB4A7/wlNnToVWq0WnTt3hlqtxsWLF/n9ysrK4OnpCeDO1azy8nKzr3l6ejb6WmNGjhyJqKgokz8DBgxARkaGyX579uxBVFQU/3H9APq33367Qaecl5eHqKioBvNwzJs3r8EClDqdDlFRUSgsLDTZvm7dOsyaNctkW21tLaKiorBv3z6T7SkpKUhMTGxwbHFxcQ88jnpSHcfdDyLI/TgmfvAxXvzFiOEeCswPVlr87xETE4O0tDQcuFCD6NQD6PW3TESnHkCx0QVz5szBxo0bBR1H165d6bwSeBz156GjH0c9qY7j7u9nRz6Ou9n7OCZMmOAUxyH1v0f9uSjGcfTv3x/Dhw836RPGjBnT4P33kmyahtraWty+fRsdOnQAAKxatQrfffcdsrOzkZSUBC8vL8ybNw+HDh1CTEwMP8h9wYIFKC8vx+eff47S0lIMGDAAJ06cQOfOnfHll1/im2++wY8//ogrV64gODgYu3btQu/evRt8fVqLkDRFzW2GATsMuGkEDkWr0bFV05fCoZncCSHEOVi0FqGda+JduHABzz//PDiOA2MMPj4++OqrrwAAn3zyCRISEuDv749WrVph06ZN/H9Es2bNQlJSEnx9faFWq7FhwwZ07twZwJ3xXDk5OfDz84NSqcTMmTPNNleENAVjDBP2GlF6DTgw2rrmCrhzpTY8PFzc4gghhMgSTTRKV7DIAyzNN+K9QxzSnlHheY3kz4UQQgiRmOwnGnVk5u7fkqaTe47bSzm8f4jDh4FK2TZXcs/QEVCG4qAchaMMxSGHHOX5P4YDmDRpktQlOAU553ioksNfsoyI1SiwMES+3ypyztBRUIbioByFowzFIYcc6RYh3SIkZpRfYwjdYYCmvQK/PKtCa7V1464IIYQ4H7pFSIgVrt5iePZHA9qogR1DqbkihBDSdJKuRUiI3NQZGWJ/NuLsdeDfUWq4tabmihBCSNPRFSwr3TtxGbGOnHI0cnfWGNyrZ0gfokKvTo7RXMkpQ0dFGYqDchSOMhSHHHKkBstKtIi0OOSSI2MMb/3GYVsZw5ZIFSIetuxbw2g0Ijs7GykpKcjOzobRaLRxpQ3JJUNHRhmKg3IUjjIUhxxypEHuNMidAPjgkBEf53P4/CkVEgMsa67S09MxY9pUlOkq+G3enh5YuXoNYmJibFUqIYQQidEgd0IssPLIneZqRaiySc1VbGwsfNV12DE2FIVvRmLH2FD4qusQGxuL9PR0G1dNCCFEzqjBIs3aumNGzDzA4f1AJWb0tWxdQKPRiBnTpiJS44rkUYEIdu+Iti3VCHbviORRgYjUuGLm9GmS3C4khBAiD9RgkWbr02NGTPkPh5l9lVjchIlEtVotynQVmByigVJhOhBeqVBgUogGpeU6aLVasUsmhBDiIKjBslJiYqLUJTgFqXL89JgR7/yHw6y+Six7QgmFwvInBvV6PQAgoEs7s6/Xb6/fz9boXBSOMhQH5SgcZSgOOeRIDZaVhg4dKnUJTkGKHO9urpY2sbkCAHd3dwBAUXWN2dfrt9fvZ2t0LgpHGYqDchSOMhSHHHKkpwjpKcJmgzGGJfkc5uRY31wBd8Zg+fpo4KuuQ/KoQJPbhBxjmLAzH8VGF5wuLoFKZdm4LkIIIY6DniIk5P9xjGH6/jvN1cL+1jdXAKBSqbBy9RpkllZiws585OqvoOaWAbn6K5iwMx+ZpZVYsWo1NVeEENKM0VI5xOnd5hiSfjVi0xmGzwYq8eajwhufmJgYpKWlYca0qYhOPcBv13h5Ii0tjebBIoSQZo6uYFlp3759UpfgFGyd4/XbDDE/GbGlhOHbwSpRmqt6MTExOFNSiqysLGzevBlZWVk4XVxi9+aKzkXhKENxUI7CUYbikEOO1GBZadmyZVKX4BRsmePZ6wxP7TQgW8+wc5gKYx8R/3RXqVQIDw/HuHHjEB4eLsltQToXhaMMxUE5CkcZikMOOdIgdysHudfW1qJNmzY2qKx5sVWOeVUMz/1ogEoB7BymRt8ujrFwszXoXBSOMhQH5SgcZSgOW+dIg9xtiL4BxGGLHDPKOIT9y4DubRU4EO3czRVA56IYKENxUI7CUYbikEOO1GARp8ExhgW5RsT8ZMRIDwWyR6ng3sa5mytCCCHyRE8REqdQfZPhpSwjfvwvw4L+SnwYpGywjA0hhBBiL3QFy0qzZs2SugSnIEaOuZUM/bcbcLCSYfdwFeYGq6xuroxGI7Kzs5GSkoLs7GyHWLCZzkXhKENxUI7CUYbikEOO1GBZydPTU+oSnIKQHBljWHfMiIH/MsDVRYG8MWoM87D+lE5PT4evjwYRERGIj49HREQEfH00SE9Pt/pz2gOdi8JRhuKgHIWjDMUhhxzpKUJaKschna9lSPzViB/+yzDpUSWWhyrhorb+lmB6ejpiY2MRqXHF5BANArq0Q1F1DdbllCKztJImDyWEEMKjpwiJU9pZzqHvNgPyqhl2DVNh3UCVoObKaDRixrSpiNS4InlUIILdO6JtSzWC3TsieVQgIjWumDl9mkPcLiSEECIP1GARh3GljmHCrwY8t8eIJ1wVOPq8GiM9hZ/CWq0WZboKTA7RNBi7pVQoMClEg9JyHbRareCvRQghpHmgBstKhYWFUpfgFCzNMaOMw6NpBqSVMvzPIBX+NUwFt9bCrlrVD2bPzMwEAAR0aWd23/rter3e6q9nS3QuCkcZioNyFI4yFIcccqQGy0qzZ8+WugSn8KAcz9cyjP3ZgDE/GdG/qwLHY9V4rZcSCgFTMNw7mH3RokVQKRTYWKAzu39RdQ0AwN3d3eqvaUt0LgpHGYqDchSOMhSHHHKkebCstH79eqlLcAqN5XjLyLDuOIcFeRxaqYCUwSrE+SgENVaA6WD2tWND+cHsnx4qwSf/Pg3vjm3wrN9D/P4cY1ifUwqNlyfCwsIEfW1boXNROMpQHJSjcJShOOSQIzVYVpLDI6DOwFyOe/7L4Z3/GHHqKvBWLyUWhijRqZXwSUPvHcxeP94q2L0jPn8uCEnf5WHGT8fg2qYVHnVtj6LqGqy/6ylCKRZytgSdi8JRhuKgHIWjDMUhhxypwSKyceIywweHjNhRzvDUQwpsGayyeh1Bo9EIrVYLvV4Pd3d3hIWF8YPZ144NNTuYffITjyAz9QCeTzvIb9d4edIUDYQQQpqMGiwiufJrDPPzjPjqNINnW+Fn6JqZAAAYwElEQVS3A9PT0zFj2lSU6Sr4bd6eHoiOeR7Agwezz5kzB48++ijfmMn1yhUhhBD5okHuVlq6dKnUJTi8C7UMg9bth3+qAd9XMKwdoEThWDVefMT6Qez1Y6x81XXYMTYUhW9GYsfYUPiq67B27VoAfwxav1f99sjISIwbNw7h4eEO0VzRuSgcZSgOylE4ylAccsiRrmBZqba2VuoSHFb5NYblRzgkF3HgWvbB3CAlpj6mRLsWTW+q7r4V6ObmhulT3zE7xip5VCAm7MyHtuISPj1Ugs+fCzK5TegIg9kbQ+eicJShOChH4ShDccghR1oqh5bKsZuTlxmWFhix6QxDh5bA1D5KvN3b+gHs5m4FqhQKzBrgi7cf92mwf67+CqJTDwAAnvFxw6S7lsRZT0viEEIIsZAlPQRdwSI2xTGG73V3plzYc5bh4TbA8lAlJvZUoq2FV6zMDVjfsWOH+ekWDhZj6b9Pw6dTW4zw7WbyeerHWE2dOhUZ6dv4ZgugweyEEELERQ0WsYkrdQxfnOKw/jiHkmvA464KfBWuwlgfBVqpLL9iZe4qlZeHB2pv1JqfbiEqGBP+dRiLtEUY6uMGlfKPr1U/xmr06NFYsWJFg6bNEcZbEUIIcQzUYFmpqqoKXbt2lboMWTFyDJnnGDae4rC9jMHIgBc0CmwerESoW8PnKYxGI3bu3Ina2lqzTU5jk4KuyynFzxXVCPH3M7924OM+iE49gIPnLmNAj84AGo6xUqlUCA8Pt2ke9kLnonCUoTgoR+EoQ3HIIUd6itBKSUlJUpcgG6euMHx4yAjvbw0YttuIw9UMC/oroRunxqbBarPNVf1yNdHR0YiPj0dERAR8fTRIT08H0HBS0GD3jmjbUs0PWI/07opvjlbAyDUcQlh/K3D/2UuouWVArv4KJuzMR2ZpJVasWu10V6roXBSOMhQH5SgcZSgOOeRIV7CsNH/+fKlLkNSpKwxbSzlsLeFQcAno0BIY94gSr/gr8ITr/eewut+VqdjYWKSlpaFz584PnBT03qtU9epvBa7aX4xV+4sBOPcYq+Z+LoqBMhQH5SgcZSgOOeRIDZaVmtuTh4wxHLkEfFfOYWsph6OXgLZqYJSnAnOClHjWU4GWCg5a7V58e59xTfdbrqZ+KoWZ06fho8VLADx4UtDzNTdNttffCvT29MT/fv45Ll686PRjrJrbuWgLlKE4KEfhKENxyCFHarBIo36/xfDzWYbvKzjsrmA4Vwu0bwE856nAgmAlhnso0Fp9p0FqbPb0lavXmFw1etByNZNCNIhOPYDKykoAd65GBbt3bFBb/VWqjUcq4NmhjdnpFiIjI0XPhBBCCLEENViEd9PAsP8iw696hiw9w2/nGQwM6NXxzu2/kR4KDHpIgZb3PAVoyS2/+iZLr9cDePCVKVdXV3h7emBdTqnJlS7gj6tU3VxdUa1uRdMtEEIIkR0a5G6l5ORkqUu4L6PRiOzsbKSkpCA7OxtGo7HBPr/fYsg8y2FerhFPZdThTx9kImLeJqxIy0IHlRGfPqlE6YtqnHihBVb8WYXB3ZUNmqsHDkbXuGLm9Gn813d3dwfw4OVqunfvjpWr1yCztBITduYjV3+lwYD1z/7+dxSXliErKwubN29GVlYWTheXNLvmSu7noiOgDMVBOQpHGYpDDjlSg2WlvLw8wZ/DkibImvfVP6EXERHBP6H3iEaD5V9sw99OGJH4qwG9t95Gxy8NeOZ7I1Z9uQ2HX/fD7eVDgP99GTWfDMGRN/zQrXAHvNvff86q+lt+k0M0jd7yKy3XQavVAgDCwsL4K1PcPYsI3DuVQkxMDNLS0nDGcOcqVa+/ZSI69QCKjS78Var66RYcae1AsYlxLjZ3lKE4KEfhKENxyCFHWipHxKVyzM043th/+JaOWWrq++6+XTf5rqVgPj1UisyySijf+BZBQ2LwhKsCT7gpcHX/dkx75YUG+6+zcOmYlJQUxMfHo/DNSLRt2fCOc80tA3r9LRObN2/GuHHj+GOor9GS5WqakishhBBia5b0EE7XYJ05cwbjx49HVVUVOnbsiI0bN6JXr14N9rO2wWrsP/umNEyNNUEPamoe9L4+76ag6H9nIax9HT5/ruG4pQk783HG4IIzJSVQqVQwGo3w9dHAV11ndpzThJ35KDa64HRxSaMNTXZ2NiIiIrBjbKjZwej16/9lZWWZTOxpLi+NlydWrFrd7G7xEUIIcSzNssGKjIzEK6+8goSEBGzbtg1Lly7FwYMHG+xnTYPVWBP1QtyLWLFihUUNk6VNzakzxbhmVKG8BtDVMJRdNWDeMF+EtDH/vqSd+fjPZaD28kWLmx1rm6O7CWnS6MoUIYQQR2RJD+FUY7AqKyuRm5uLv/zlLwCA559/HhUVFSgpKRH8ueuvHvmq67BjbCgK34zEjrGh8FXXYfny5XjMrb1Fg7wtHbPUfk42On9lQFC6AaP3GDHj6724cr7x900O0aD28kUAD35Cr/5JPkuf6KvfzxyVSvXAweiNzZ5O46cIIYQ4K6dqsCoqKuDu7g6l8o/D8vT0hE6nE/R5LVm25WJNHe69Fnh3wxSyLBuPbr2NUVvuXP16UFPzfKcLSI1UYf9oFfR/UWNjkGXNE/DgJ/Tqn+Sz9Im++v0aY8lg9MZERUXd93OTB6MMhaMMxUE5CkcZikMOOTpVg2UrD7rqNPmJR3D+eh0Onrvc4L31jU/r63oM7aFEfP+HATy4qXk1tDte8LmzSPJDbRTo/rBl7+vm5mrRE3pA057oe5CYmBicKSlt8pQJkyZNeuDnJvdHGQpHGYqDchSOMhSHHHJ0qgbLw8MDer0eHMfx23Q6HTw9PRt9z8iRIxEVFWXyZ8CAAcjIyOD3sfRW2oXrdQ1eq298ljzTAx1+WAhN5UGLmpqCggLMmjWLfy0sLAxeHj2w7lCJ+fcdKoHGyxPr1m+47+26l14ejzFjxgC45/bevw6b3b+LqxsuXzZtHOfNm4elS5eabNPpdBgzZgweeughk1t+69atMzkOAKitrUVUVBT27duHoUOH8ttTUlKQmJjYIMO4uDiTfw8A2LNnj9nfUN5+++0G85/k5eUhKioKVVVVFh1HVFQUCgsLTbY/6DjuZu/j+O2335ziOKT896g/Dx39OOpJdRx3fz878nHczd7H0bVrV6c4Dqn/PerPRTGOo3///hg+fLhJn1D//+j9ON0g98GDB2P8+PEYP3480tLSsGzZMsGD3C0dDP5tTAgGenThtzc2yLup0xTUs/R9TX1Cj57oI4QQQizXLJ8iPHXqFF555RVUV1ejQ4cO+OKLL9C7d+8G+zWlwXrwk3KHkVVahXDvrpj8uI9FDZO1TY2l72vqE3r0RB8hhBBiGYt6CNZM5ebmMgAsNzfXov23bdvGFAoFe8bHjWWMDWUn34xkGWND2TM+bkyhULBZs2Yxb08PBoD/o/HyZNu2bWv0cxoMBpaVlcU2b97MsrKymMFgsKgWa98nR9u3b5e6BIdHGQpHGYqDchSOMhSHrXO0pIdwuitYlhJrHqy7rx7RVaCmGzBgAP7zn/9IXYZDowyFowzFQTkKRxmKw9Y5WtJDNFzbhDQqJiYGo0ePhlarxYwZM7By5UqTJqp+XidiOVdXV6lLcHiUoXCUoTgoR+EoQ3HIIUdqsJqovonq3r07NVOEEEIIMcuppmkghBBCCJEDarAIIYQQQkTWbG8R3rhxAwBw8uRJq95/8OBB5OXliVlSs0Q5CkcZCkcZioNyFI4yFIetc6zvHep7CXOa7VOEmzZtwksvvSR1GYQQQghxUN988w3+8pe/mH2t2TZYVVVV+PHHH+Ht7Y3WrVtLXQ4hhBBCHMSNGzdQVlaGYcOGoWvXrmb3abYNFiGEEEKIrdAgd0IIIYQQkVGDRQghhBAiMmqwmujMmTMYOHAgAgICEBoaavVTiM7unXfegUajgVKpxJEjR/jtlZWVGDFiBPz9/dG3b19otVr+tRs3biA+Ph5+fn7o2bMntm3bJkXpslFXV4cxY8agZ8+eCAoKwrBhw1BcXAyAcmyKYcOGITAwEEFBQXj66aeRn58PgDK01hdffAGlUonvvvsOAOXYFN7e3ujVqxeCgoIQHByMrVu3AqAMm+rWrVuYPHky/P390a9fP7z88ssAZJijTVdDdEKDBw9mX331FWOMsbS0NPb4449LXJE8abVadvbsWabRaFhBQQG/PSkpiS1YsIAxxtihQ4dYjx49+MWqFy5cyBITExljjJWWljI3Nzd26dIl+xcvEzdv3mS7d+/mP16/fj0LDw9njDGWmJhIOVro6tWr/N+3b9/O+vXrxxijDK1RVlbGnnzySfbkk0+yHTt2MMboe7opNBoNO3LkSIPtlGHTTJ06lU2ZMoX/+MKFC4wx+eVIDVYTXLx4kXXo0IEZjUZ+20MPPcSKi4slrErevL29TRqsdu3a8d8MjDEWGhrKMjMzGWOM9e7dmx04cIB/LS4ujiUnJ9uvWJnLyclhGo2GMUY5WuuLL75gwcHBjDHKsKk4jmPPPPMMy8vLY+Hh4XyDRTla7t6fh/UoQ8tdv36d/elPf2LXrl1r8Jrccmy2E41ao6KiAu7u7lAq/7iz6unpCZ1OBx8fHwkrcwyXLl2CwWCAm5sbv83Lyws6nQ4AoNPp4OXlZfY1AqxduxbR0dGUoxXGjx+PrKwsKBQKfP/995ShFVatWoWwsDAEBQXx2yjHpktISAAAPPHEE/jkk0+gUCgowyYoLi5G586dsXjxYvz8889o06YN5s2bh8DAQNnlSGOwCHEAS5YsQXFxMZYsWSJ1KQ7pyy+/hE6nw6JFizB79mwAAKMZaix2/PhxbNu2DR9++KHUpTg0rVaLgoIC5OXloUuXLhg/fjwAOhebwmAwoLy8HH369MGhQ4ewdu1avPjiizAYDLLLkRqsJvDw8IBerwfHcfw2nU4HT09PCatyHJ07d4ZarcbFixf5bWVlZXx+Xl5eKC8vN/tac7ZixQpkZGTghx9+gIuLC+UoQEJCArKzswEALVq0oAwtpNVqUV5eDj8/P2g0Guzfvx+vvfYaUlNT6Vxsgh49egAAVCoVpk6dCq1WS9/PTeTp6QmVSoX4+HgAQGBgILy9vXH06FH5fU/b9AakE4qIiGAbN25kjDG2detWGuT+APeOOUhMTGTz589njDF28OBBk0GI8+fP5wchlpSUsG7durHq6ur/a+/+Q6o6/ziAv8+5aXrd9ccozbKozBtOyx+lqDHszmxBtFo1ZGyWssmWlMSybtBEt5WryBg0XFjdhbURLNBZ7B/Zln/ElqZu4EaCu8O2vP2y+SNTu3o/3z+iw05XW353UmnvF9w/no+f5/E5Dygfnufcc8Z/0pNIWVmZLFmyRLq6unRxruOT6erqko6ODq1dVVUls2fPFhGu4b+xfPlyqampERGu45Pq6+vT/R2XlZVJenq6iHANx+rll1+Wb775RkQerMn06dOlo6Nj0q0jC6wxam1tldTUVLFarZKUlCQtLS0TPaVJ6Z133pGIiAjx8fGRGTNmSFRUlIg8+LbHypUrJSoqSmJjY6Wurk7r09fXJ1lZWRIZGSkLFy6Us2fPTtT0J4U///xTFEWRBQsWSEJCgsTHx0tKSoqIcB2fVHt7uyQnJ8vixYslLi5OMjMztYKfa/j/s9ls2k3uXMcn43Q6JSEhQeLi4mTx4sWybt06aW9vFxGu4Vg5nU6x2WyyaNEiiY+Pl6qqKhGZfOvIV+UQERERGYz3YBEREREZjAUWERERkcFYYBEREREZjAUWERERkcFYYBEREREZjAUWERERkcFYYBEREREZjAUWERERkcFYYBGRoT744AOoqur1MZlMOHjw4JjGqqurg6qqaGpqemzeJ598AlUd339n8+bNQ0FBwVMZe926dXjppZeeythEND6mTPQEiOjZYzab8f3333u93X6sL1ddsmQJfvzxR0RHRz82T1EUKIoy5nn+G9XV1QgJCXkqY4/3tRCR8VhgEZHhVFVFUlLSvx7nueeeQ3JysgEzMl5cXNxET4GIJjEeERLRhFBVFQcOHIDdbkdoaCgCAwORm5uLu3fvajkjHRH29vZi06ZNCAwMRFhYGOx2O4aGhrzG7+7uRn5+PmbOnAk/Pz8sXboUtbW1uhybzYY1a9bgzJkzsFqtCAgIwCuvvILu7m60t7dj1apVsFgsiI2NRV1dna7vSEeEP/zwA1auXImgoCAEBgYiNTUV33777WPX4cqVK0hPT4e/vz+ioqJQWVnpldPa2orXX38dc+bMQUBAAGJiYnD48GHdDuHSpUuRnZ3t1ddutyMiIsJrN5GIni7uYBHRUzE8POwVM5lMuvann36KxMREVFZW4vfff4fdbsfg4CC+/PJLLefR47Lc3FzU1tbi4MGDmDt3LsrLy3X5AOB2u7FixQrcunULH3/8MWbOnIlTp05h9erVaG5uRkxMjJbb3NyMzs5OlJWVobu7GwUFBXj77bfR3t6OzZs3o7CwEKWlpdiwYQOuXr0Ks9k84vVevHgRGRkZSEtLg8PhQFBQEC5fvoyrV6+OukaDg4PIzMyExWLBF198ARFBUVERenp6YLVatbxr167BarXijTfeQGBgIH766ScUFxejr68PRUVFAIC8vDzs2LEDvb29sFgsAACPx4PTp08jNzeXx45E402IiAxUUlIiiqJ4fVRVlYsXL2p5iqJIZGSkeDweLeZwOMRkMklra6uIiFy4cEFUVZXGxkYREfn1119FVVU5efKk1md4eFjmz58vqqrqxvH19ZUrV67o5paSkiJZWVlae/ny5WKxWOTOnTtarLCwUBRFkYqKCi3W0tIiiqJITU2NFps7d65s27ZNa6elpUlsbKzuev7JZ599JlOmTJHffvtNi7W1tYnJZBKbzTZqv6GhISktLZVZs2ZpsZ6eHgkICJCjR49qsZqaGlFVVdra2p54TkRkDB4REpHhzGYzGhsbcfnyZe3T0NCA+Ph4Xd6aNWt0OysbN26Ex+NBfX39iOM2NDQAePAtu4dUVdW1AaC2thaLFi3CggULMDw8jOHhYQwNDSEzM1Mb46H4+HjdzepWqxWKoiAjI0MXA4A//vhjxHn19/fj0qVLyMnJGdNOUX19PWJjYzF//nwtFhkZ6XV/1+DgIIqLixEVFYWpU6fCx8cHe/bsgcvlwr179wAAFosFWVlZcDgcWr+TJ0/ixRdfRGRk5BPPiYiMwSNCIjKcqqpISEj4x7zQ0FBd22KxwM/PDy6Xa8R8l8sFHx8fBAUF6eJhYWG69u3bt9HU1AQfHx+vMR6NBQcH69q+vr5e8Yd9BgYGRpzXX3/9BY/Hg/Dw8BF/PhqXy+W1BsCD6/n779q1axdOnDiBkpISJCYmIjg4GNXV1di3bx8GBga0Y8u8vDwsW7YMLS0tmDFjBs6fP4/jx4+PaU5EZAwWWEQ0YW7evKlr9/b2YmBgYNRCJTw8HG63G93d3boi6/r167q8559/HnFxcXA4HONyc3dwcDBUVUVHR8eY+oWHh6O5udkrfuPGDd31nT17Fu+++y4KCwu12Llz57z6paSk4IUXXoDD4cDs2bPh7++PjRs3jmlORGQMHhES0YQ5d+6crgD66quvHvuIh6SkJIgIqqqqtJjH40F1dbUub8WKFXA6nQgPD0diYqLXx2hmsxmpqamorKwcU0GXnJyMlpYWOJ1OLdbW1oaff/5Zl9ff36/befN4PDhz5syIY+bl5eH06dM4ceIEsrKy4O/vP8arISIjcAeLiAzn8Xhw6dIlr3hoaCjmzZuntQcHB7F27Vrk5+fD6XRi9+7deO2117Bw4UIt5+8FS3R0NF599VVs374d/f392rcI3W637vds2rQJFRUVSE9PR2FhIaxWK7q6utDc3Ay32419+/YZfs379+9HRkYGMjIykJ+fj5CQEDQ1NWH69OnIyckZsU9OTg727t2L1atX46OPPoKIoLi42GsHLzMzE8eOHUN0dDSmTZuG8vJy3L9/f8Qxs7OzYbfb0dnZqbsfi4jGFwssIjJcf38/0tLSvOJvvfUWKioqtPa2bdtw69YtvPnmm3C73diwYQOOHDmi6/PoTeOff/45tm7dCrvdDj8/P2zevBk2mw07d+7Ucnx9ffHdd9+hpKQEpaWlcLlcmDZtGhISEpCfn//Y8Ufz6NPiH20vW7YMFy5cwPvvv4/c3FyYTCbExMRg7969o47p5+eH2tpabNmyBdnZ2Zg1axaKiorw9ddfo6urS8s7cuQItmzZgoKCApjNZuTk5GD9+vXIy8vzGjMkJATp6em4du3apH1IK9F/gSLjcYMCEdEjVFXFoUOH8N577030VJ4pPT09iIiIwIcffojt27dP9HSI/rO4g0VE9Ay4e/cufvnlF5SXl0NV1VGPJYlofLDAIqIJMREvaH6WNTY2wmazYc6cOaisrPR6/AQRja//ASjM8Oqr4vJvAAAAAElFTkSuQmCC\" />"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set parameter values\n",
    "lambda = 1.47*10^-6.   # infection rate parameter (assumes rates are per day)\n",
    "gam = 1/8.      # recovery rate parameter  (ditto)\n",
    "dt = 0.5         # length of time step in days\n",
    "tfinal = 610.;    # respecting community values: lowercase only in the names \n",
    "\n",
    "# set initial values (originally s0, lambda, gam, i = 22.*10^6., 2.3*10^-8., 0.05, 4. )\n",
    "s0 = 10.^5.     # initial susceptibles, note that we use the  type Float64 from the start\n",
    "i0 = 30.          # initial infecteds; set this to 1. to  mimic an epidemic with an index case\n",
    "r0 = 0.          # not always the case, of course\n",
    "\n",
    "# initialise \n",
    "nsteps = round(Int64, tfinal/dt)    # note the use of round() with type Int64 to ensure that nsteps is an integer\n",
    "resultvals = Array(Float64, nsteps+1, 3)  #initialise array of type Float64 to hold results\n",
    "timevec = Array(Float64, nsteps+1)        # ... ditto for time values\n",
    "resultvals[1,:] = [s0, i0, r0]  # ... and assign them to the first row\n",
    "timevec[1] = 0.                 # also Float64, of course.\n",
    "\n",
    "# the main loop over time steps\n",
    "for step  = 1:nsteps\n",
    "    resultvals[step+1, :] = updateSIR(resultvals[step, :])  # NB! pay careful attention to the rows being used\n",
    "    timevec[step+1] = timevec[step] + dt\n",
    "end\n",
    "\n",
    "# make the plot\n",
    "ivals = resultvals[:, 2]\n",
    "rvals = resultvals[:, 3]\n",
    "cvals = ivals + rvals     # assemble the model values for the case\n",
    "\n",
    "plot(timevec, cvals,       # first the model's output s plotted as a line\n",
    "label = \"Model values\",\n",
    "xlabel = \"Epidemic day\",\n",
    "ylabel = \"Number of cases to date\",\n",
    "title = \"Model versus data\")\n",
    "\n",
    "plot!(tvalsfromdata, totalcasesfromdata,\n",
    "#legend = :right,\n",
    "line = :scatter,\n",
    "label = \"Reported number of cases\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There's quite a lot wrong here! Obviously the epidemic is going to far, too fast. We might also like to add \"legend = :right\" to stop it blocking things ... but we don't know where it is going  to be needed, so that would premature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to the top](#In-this-lecture)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Interactively fitting the model to data using the notebook</h2>\n",
    "\n",
    "We now interactively use the notebook, changing the values of $S(0)$, $\\lambda$ and $\\gamma$. In fact, it makes a difference what we set $I(0)$ as well, because that influences the  start of the modelled epidemic quite a bit. While in principle also $R(0)$ also matters, it is very small and hence it's influence is minimal.\n",
    "\n",
    "It turns out that we have to adjust $S(0)$ especially, and accordingly the value of $\\lambda$ needs to be adjusted as well.\n",
    "\n",
    "No need to write out new code, we just navigate up to the cell where the model is run and plotted, and play there.\n",
    "\n",
    "(The values of using $S(0) = 10^5$, $I(0) = 30$, $\\gamma = 1/8$ and $\\lambda = 1.47 \\times 10^{−6}$ were found by extensive experimentation of this kind)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to the top](#In-this-lecture)"
   ]
  }
 ],
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   "display_name": "Julia 0.4.6",
   "language": "julia",
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   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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