ExnerWentWrong.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Why did the solution of Exner went wrong on the problem?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding the exact solution\n",
    "Bueno pues, comencemos escribiendo Exner en 2D. Notamos $q_s(X,Y)=(U,V)$ para coordenadas $(X,Y)$, asi exner se escribe como\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\eta}{\\partial t}\n",
    "=-\\frac{1}{\\varepsilon_0}\\nabla\\cdot q_s\n",
    "=-\\frac{1}{\\varepsilon_0}\\left(\\frac{\\partial U}{\\partial X}+\\frac{\\partial V}{\\partial Y} \\right)\n",
    "$$\n",
    "\n",
    "Ahora, el vector field que escogimos es\n",
    "    $$U=-X$$\n",
    "    $$V=-Y$$\n",
    "Y si hallamos las derivadas parciales nos da\n",
    "    $$\\frac{\\partial U}{\\partial X}=-1$$\n",
    "    $$\\frac{\\partial V}{\\partial Y}=-1$$\n",
    "ademas el codigo de exner que usamos usa $\\varepsilon_0=1$, de modo que la equation queda:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\eta}{\\partial t}\n",
    "=-\\frac{1}{1}( (-1)+(-1) )=2\n",
    "$$\n",
    "es decir que la solucion exacta de Exner es $\\eta=2t+\\eta_0$. En otras palabras, por cada unidad de tiempo (e.g. una hora) que pase la cama del rio se eleva el doble en unidad de espacio (e.g. 2 milimetros)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### But we didn't use the exact solution, right?\n",
    "Sip, nosotros usamos euler, no la solucion exacta, de modo que discretizamos haciendo:\n",
    "\n",
    "$$\\frac{\\partial \\eta}{\\partial t}\\approx\\frac{\\Delta \\eta}{\\Delta t}$$\n",
    "$$\\frac{\\partial U}{\\partial X}\\approx\\frac{\\Delta U}{\\Delta X}$$\n",
    "$$\\frac{\\partial V}{\\partial Y}\\approx\\frac{\\Delta V}{\\Delta Y}$$\n",
    "\n",
    "Pero como $U=-X$ y $V=-Y$ entonces\n",
    "$$\\Delta U=-\\Delta X\\quad \\text{ which implies that}\\quad \\frac{\\Delta U}{\\Delta X}=-1 $$\n",
    "$$\\Delta V=-\\Delta Y\\quad \\text{ and therefore also}\\quad \\frac{\\Delta V}{\\Delta Y}=-1 $$\n",
    "\n",
    "de modo que al final, la version discreta de Exner que estamos resolviendo NUMERICAMENTE es:\n",
    "\n",
    "$$\\frac{\\Delta \\eta}{\\Delta t}=-\\frac{1}{1}((-1)+(-1))=2$$\n",
    "es decir\n",
    "$$\\Delta \\eta=2 \\cdot \\Delta t $$\n",
    "de modo que por cada unidad de tiempo que pase la cama del rio se eleva el doble en unidades de espacio... ehh?? es decir, obtuvimos la misma solucion del metodo numerico??\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So the solution is not only working but is actually an exact solution?\n",
    "Sip, por la forma que definimos a $U$ y a $V$ el sistema es lineal y euler resuelve de manera exacta este tipo de sistemas. Veamos un par de ejemplos con diferentes valores para $dt\\approx \\Delta t$ que efectivamente esto esta pasando."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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0Gjl48GAWKlTof8NZDKASgMOJfh8NYHQKr/8TQI9Ev/9rgYAUXzf4VFeuXKGrq6t58VFk1PBpMBA92M6dO0cHBwdev35deLSTeL0gucWxlLRv3z56e3vz4sWLwrfrpruC9evX89KlS8Lb/u2339isWTNu2LBBmDWVWpgyZYow+/DhQ7Zr147t2rUTvrDExsZy+vTpzJUrl1Qg2bBhA8uUKcN58+YJD1quXbvGgQMHslGjRlKZYUuXLqWDg4OUu3fPnj0cPHiw1N3AjRs3eOHCBampyPDwcL5+/ZoVKlQQTptVFIXv37/n4sWL6ePjI/x5x8XFSQcBo9HIuLg4tm7dmlWrVpUaoKakrxkIWgJYmej3DgB+S+a1NgBCTdNCH/72HMB1ANcA9ExhOz0BXAVwVTZtMCUlXjdYvHixEPvkyRN6e3tz5MiRHDZsmNBIN3EwaNmypfCIbdu2bXRzc2PFihWF7yxM6wXu7u7CBrr379+zfPnyzJw5s/B6w8uXL1mvXj0C4IwZM4TY2NhYNm7cmADYrFkzIZZMGOFpNBrmzJlTmH348KHZXCUzxVK6dGkCkFrfmTx5MgHQy8tL+Bi5fPkyAdDKykrqLi5jxoy0trbm1KlThVlfX18C4MiRI4UNVoMHD2bmzJk5bNgw4cHGH3/8QXd3d6l1gVOnTrFKlSp0dXXls2fPhFg/Pz/++OOPUkEgKCiIo0ePZvXq1dmiRQupu5DU9DUDQaskAsHiZF7bBsC+T/6W68O/Th+mlaqnts2v5SO4du0ac+fOTY1GI1z3/M2bN3RxcSEA4V4Ht2/fNhtRREvdnj171syKpkSeP3+ednZ2BJBsympyev36NYsXL04AHDp0qBCrKAqHDBlCAGzXrp0QSyZkUKRLl46+vr7CbEREBF1cXKQ9CA0bNiQAqUqWEydOJACpu6AdO3YQgFQ9/3v37km7uGNjYwmAHh4eDA4OFmIVRWHOnDmZPn16HjhwQHjbhQsXJgB26dJFOIiY/Dxly5YVdlM3atSIAFihQgXhkjEmg2atWrWEP6+OHTsSABs2bCg9hZea/iumhgDsAvBTCv/XJADDUtvm1woEjx8/No/acubMKVR3/t69e2ZDmIuLi1CvgfDwcI4dO5aZM2emu7u70EhAURRu3bqVLi4uUoaje/fusWjRoixYsKDwnH1ERATr1q3LYsWKCXFkwn53796dJUqUEGbJhHLSxYsXl2I3bNjAwoULS7FHjx6VTgG9evUqnZ2dpRcdc+TIITW18+LFC9rY2EgVT3vz5g0zZMggVWn27du3TJcunVR23qtXrwiAkyZNEj4unz59SgBs27atsKPZFDQrVaokPFV85coVc9Bcv3690Ll44sQJAmC2bNk4bNgwhoeHC23bUn3NQJAewDMAeRMtFhdJ4nU5PkwLZUn0tywAsiX6+QKA+qlt82sFAjLhAnXhwgV26tSJLVq0ED4IHz58yO7du0tlprx9+5a9e/eWapgTFhbGPn36SJVIjo2NZc+ePaXq7Ot0Onbu3FmqWYvBYJAuAW40GtmnTx9hjkz4jkXvYhKzY8aMkWZlF1z1er00GxISwmnTpkmxd+/ele4qduTIkSQ9J5Zow4YNXL16tRQ7e/Zsrly5UioZ4eeff+aSJUuEg7WpYdS8efOEp3S0Wi1r1KjBX3/9VapZlYi+WiBI+L/REIAfErKHxn74W28AvRO9pjOALZ9w+T4EjlsA7pnY1B5pCQQiC6OhoaGfjcAs7cwVGBiY5MFkSYvKlG5lUyshkdriUkqLypYchEm9RlEUiytifvp5xsfHCxUFS3ySyUzPmLKkZFgy4b3KZHmZlBY2Ojpa6uKm1+sZFxdHo9EofIFLvE2DwSBUA+fTY8JgMFg815/USN5gMFh0nCV3HOv1+lRLZaR0/uj1+mTPTa1Wm+ooXqfTJXn+hoaGWhQ8dDpdmstPfNVA8H/9SIuzuGjRouzQoYPUrZder2fhwoU5cOBAqaJQOp2OPj4+nDx5stQJrdPpWKBAAemevzqdjl5eXtLdkuLj4+np6Sndck+r1TJ37tz08/OT4mNiYujq6ipt6IqMjKSzs7N0Qa+goCDmyZNHiiUTBiEy02gmXbt2jZUrV5bmjx8/nqaGQNu3bxcubJhYy5YtS5MhbsqUKezYsaMUqygK+/Xrx27duknxer2ebdq0Ye/evaX4yMhI1qtXj/369ZPi37x5w8qVK3PgwIFSvElqIPigqKgo9uzZk3ny5OHp06eF+dDQUDZs2JCVK1eWMmS9efOGpUqVYrdu3aSmRPz8/Jg7d27pYGDqnyrbe3b79u3Mly+fVG16kpw+fXqaLiadOnXi9OnTpfly5cpJu2MVRaGNjY30e0+rj+Cvv/5i8+bNpflhw4ZxwoQJ0ryvr690v+fw8HA6OztLH3cXL16ko6OjRXfUSWnBggUsXLiw1NSLKQh89913Us7mN2/esGTJkuzevbvUOX/q1Cm6urpy8uTJ0oY+k9RA8In27t1LFxcXjhgxQrheudFo5OTJk+nq6irVMjEyMpL169dnvXr1pC4qaQ0GppRT2daB3bp1kx6ZxcXF0dPTU9ouf/XqVbq7u0vX+5kwYQKHDRsmxZJksWLFpC9maQ0EU6dOlS5zQJJFihSRvpu7efMmc+XKJXUhIxOCUNeuXaXYiIgI5suXT7gZkEl79uyRSgUl0x4E7ty5Qw8PD06bNk14FsDU3c3Z2Vm6x/enUgNBEgoMDGTjxo1ZsmRJ3r17V5j/+++/6eTkxFmzZgl/yXq93pw1I3Nn8WkwEN3+jBkzWLx4cUZGRgoHwqioKObPn5+bN2+WmqbZtm0bixUrxsePH0td0CtXrsyNGzdKNWK/ePEiixQpIpVPHxYWxubNm3PmzJnCpcJjY2O5a9cu6ZaPZ86cYZs2bbh06VLhzKGwsDDu2LGD9vb2UmmJly5dYrdu3aRMeE+fPuWDBw9ob28vXCLdaDQyODiYHTt2lJrS0Wq1vHbtGh0cHIRTdhVFSXMQOH78OB0dHaWMjxEREWzevDnLli37v+Es/jceXzJrSFEULl++nPb29lywYAENBoNQhzF/f3+WLVuWzZs3Z0hICM+fPy+07WnTptHDw4PXrl0TTrMzBYPffvtN2OxjSt9s0KCB1Oj+ypUrdHBwYLly5YTn3MPDw1miRAk6ODjw6tWrQuzr16/ZrFkzpk+fXvg9G41G9ujRgwBYunRpIZZMyOW3trYmgM9KJKcmRVHMzYdkeujOmTOHAGhnZyccfIOCgswp0cuXLxfedtWqVZk+fXpOnjxZOJBMmTKFDg4OHDRokHA2jakcSP78+aWCX6tWrejm5ibs5DYYDBw3bpx0EFi/fj3Xr19PR0dHnjhxQog9deoU7969ywIFCrBnz55f3FSmBoJU5OfnxwoVKrBSpUr08fERmrKJi4tjz5496erqSg8PD+F5yI0bN9LGxob29vbCJ/nZs2dpZWXFjBkzCk/17Nq1y3xhE82Z3rlzJ21sbAhA2Cxk6gcLQLgRvCmAAWCvXr2EWDLhjkCj0bB8+fLCrKk0Rrp06YTvosgEpywAqcqv+/btIwCpUg0hISHm/HYZH4KHhwcBSJXGqF+/vtlgJbrt/v37EwDz588vXN5i1qxZBEAfHx/hjnDr168nAObNm1e4Ic+BAweYPn16uru7C88ynDlzhra2tnRwcJBOnU1NaiCwQNeuXWP27NnN5QtEFmaOHj3KTJkyEQDbtGkjNFWzfft283ZFR+dHjx4193bt0qWLEBsWFmYeIYuy5H8CmEiNepMeP35MDw8PtmrVSpiNj4+nr68vGzZsKMySCQXUKlWqJMWuWLFCep7/+PHjzJo1q1QQefToEa2srCxOX06s8PBwAuDBgweFWYPBQCsrK6lpIYPBwOzZs7Nx48bCI1uDwUBnZ2fmz59feJCi0+mYO3duZs2alb/99pvQeRwXF2cOfG3atOHTp08tZqOjo5knTx4CYOHChYWy48LCwszbLViwoPSieGpSA4EFio+P54EDB9ilSxfa2dkJm3AePnzIESNG0NnZWbiTUEREBOfOnUt3d3fhrBaj0cg///yT3t7eFnUK+1QnTpxg0aJFhe30ZMJiWLly5aRuYV++fMmaNWtKpdIGBwcL95U2KTIyUrqaZVxcnPSip06nk05f1Ol07NSpkxQbHR0tVcqDTJiKa9u2rdR3dOvWLbZu3Vpqgfn48eP84YcfpNK8N2/ezIYNG0o5qefNm8datWpJ1ZIaPnw4K1WqxJ07dwpNoSmKwh9//JElSpTg4sWLv3ihucRSA4GgdDodjxw5ImU80ul0PHHihFSql06nk6pFQyYEMplAQCYsZoqMfhIrIiJCulFNYGCg9DxoWkZNMk5ok0QXPRNLJtimdbs6nU643o5J79+/l24G8/LlS+maOU+ePJEuU37v3j1p9tq1a1JsfHy8VBkOMuEzvnr1qvQ+iyi5QKBJeO5/S2XLluXVq1f/7d1QpUqVqv8paTSaayTLfvr3dP/GzvxbMhqN+O6777Bt2zbIBECj0YjGjRvj8OHD0tv/4YcfcPHiRWm+TZs2uHv3rhRvMBjQoUMH+Pv7S/Ndu3bF+/fvpXidTofevXsjOjpaitdqtRg0aBD0er0UHxMTgxEjRkh99wAQERGBSZMmSbEA8P79e8yYMUOaf/36NebMmSPNP336FPPmzZPm79y5g/nz50vzly9fxty5c6X5EydOYPbs2dL8nj170vT5b9y4EVOnTpViSWLJkiXSx4/BYMCsWbMwbtw4KT5VJXWb8N/+SMvU0KlTp1ikSBHWrl1bqufwkSNH6OHhwe7du0vNX+7evZuOjo6cPXu21NTRhg0b6OjoKN1zeNGiRcyTJ4/UoiNJjh49mlWrVpVa8CQTSu327dtXiiXJWrVqSRcyUxSF+fLlkzaExcfHM2PGjNJTJWk1lO3evZv169eX5qdOnSpd4oBMaB4/a9YsKTYuLo4FCxYULtFukp+fH52cnKRd4bt376aTk5PU3L+iKJw4cSLz5MkjNfUaHh7Oli1bsmTJklLlVe7fv8/y5cuzVq1a0uetSVDXCP4jnU7HefPm0d7eniNGjBBOa4uIiGDPnj3p7u4u5fh7/vw5K1SowMaNGwvXLCcT0sycnZ2l2xamJRgYjUY2a9aMnTt3pqIowvOaoaGhdHNz4/Hjx6UuqKdPn6anpyeDg4Ol+FGjRnHkyJHS6yGFCxfm8ePHhRf0tFotr1+/znz58kl950+fPuWUKVOkq6Y+efKExYsX56lTp4TZwMBA3r59m05OTlJrZrGxsRwxYgSbN28u5a4NCwujj4+P9PGeliCg1WrZrl07litXTmqN5tq1a/Ty8mKfPn2E18L0ej1nzJhBe3t7qYqoSUkNBEno7du3bNeuHXPnzs2//vqLiqIILW6Z7g66devG8PBwRkVFWXygx8fHc8iQIfTw8OCFCxcYEBAglF3h5+fH/Pnzc+jQoXzy5InwYqApGJw/f1645lJUVBRLlCjBiRMnCrcBJMn9+/fT09OTLVq0EGYjIiJYoUIF5s2bV/jEjoqKYq9evZg1a1apdNnFixfT0dGR1tbWwou+RqORXl5ezJAhg1Tm0Jo1a2htbU1vb2+pO5r8+fMzffr0Uv1zJ0+ezLx583L06NHCF7Nnz56xfv36dHZ2Fv7MFEXh6NGj+d1330n5J7Zs2SIdBP755x++f/+eVatWZfPmzYWqxr569YqKovD333+ng4OD0F2QaVD6Je8CEksNBCko8XTRggULhCzhERER7NGjB93d3dmnTx/h2u2mqaI6depw9OjRQmxwcDCrV69Od3d3qfTAuXPnMn369KxQoYLQSE1RFP7xxx8EQAcHB+GLw6pVq5gxY0YCEC7VcPv2bXNXNRnTzciRI81NS0T17t072tjYMHPmzFIZHl27dpU2Zp08eZIApLqykaStrS01Go2w05UkW7VqZW7WInr3vHDhQrOZTbQkyNmzZwmA9vb2wuzr16+ZOXNm5siRQ7jPRmRkJD08POju7s7hw4cLjcTj4+NZrlw5NmjQgCVKlBCaCjIYDGzUqBEnTJjwRe8CEksNBKlIp9Nx7ty5tLKyYvr06YXNNxs2bCAApkuXTmj+XlEUc/kAjUbDI0eOCLFjx44199EV2WfTvGeGDBkIQLihzaVLl1ioUCGp9poGg8HcqnL27NlCrGnbWbJkkWr+Ex8fz5IlS0p7EIYOHcpChQpJsTt37mSGDBmkCg36+/sTgHSxvkyZMkkX2ytUqBBLlCgh7LIlE9Z0bGxspArGmdo+Nm/eXPhuwuQ+d3JyEna+Dxw4kACYKVMm4anfoUOHEgCzZMkinAY+fPhwcykQkTI3IlIDgQU6cuQIq1SpwvTp09PGxkaoUuPff//NDh06MGfOnMyRI4dwvaKpU6eyQIECdHJyEpqLNBgM3L17N319fenh4WFxgxiTnj59yp9++okFCxYULgAXFxfH0aNHs3z58lIj5FWrVrF27drCHJlggvv++++l2Hv37klNS5EJufyybFRUFBs3bizF6vV6+vr6Sn3OiqKwVKlSUgv8Wq2WhQsXlvI/hIaGMm/evLx+/bow+/r1a7q6upqnbEV0//592tra8pdffhG+g7lw4QIzZcrETp06Cd+F7N+/n+nSpWPNmjW5Zs0aoXNx7dq1BEBvb28OHTpUDQSWPL62oSwqKop///03Z82aJdxRSq/X8/Tp01yxYoVUu7tLly5x586dQpxJ165dk+qxQJLXr1+XqsBKJhSgkzVKXbhwQbpRjExrTZNu3rwpzcp+TiSFi9V9ie3q9Xppo2FAQICUQ5ckHzx4IG2Cu3z5srQJ7vDhw9IGxy1btkiZDXU6HVesWCFVKTQkJIQLFizggwcPvrqpLLlA8EUMZRqNpj6AhQCsAKwkOeOT52sA2APg+Yc/7SQ52RI2KamGMlWqVKkSV3KGsvRf4D+2AvA7gLoAXgO4otFo9pK8/8lLz5JsLMmqUqVKlaqvpC/hLC4P4AnJZyR1ALYAaPp/wEpp06ZNePfunTS/detWhIeHS/O7du2SdtYCwIEDB6DVaqX5o0ePSjtzAeDMmTNQFEWa/+eff5CWu9Bbt25JsyTx4MEDad5oNOLp06fSvE6nk3Z1A0BcXBxevnwpzUdHR+PVq1fSfGRkJJ4/f576C5NRWFgY/Pz8pPng4GDcu3dPmg8ICMDNmzel+ZcvX+LKlSvS/JMnT6SrCgDAgwcPcPbsWWk+JX2JQOAGIPHR9frD3z5VJY1Gc0uj0RzSaDRFBFloNJqeGo3mqkajuSpb4oAkLl68iIIFC2LEiBHCAYEkTpw4AR8fHyxatAg6nU6Y37NnD4oUKYJ9+/YJsQCgKArWrVuH8uXLS5WZUBQFCxYsQIMGDRAWFibMG41GjB8/Hj179pQKBgaDAb169cLChQuFWQDQ6/X44YcfcOTIERiNRmE+Pj4eVatWxfPnzxETEyPMx8TEoHjx4ggPDxfevqIo8Pf3R+3ataX2PTIyEufPn0e7du2EWSBh3zdt2oRBgwZJ8UajEZMmTcKvv/4qzf/0009YtWqVFB8cHIxatWph9+7dUvz169dRvnx5nDp1Sor/66+/ULZsWVy7dk2Y1el0mDZtGipUqID798UnO4KCgtCnTx9Ur149TQORFJXUwoHIA0ArJMztm37vAGDxJ6/JDiDrh58bAnhsKZvUI62LxS9fvmSfPn1oZ2fH4cOHCy8s3b59m/Xr16e3tzd37NghvMBz9OhRent7s3nz5nz9+jVJy1tNmnL47e3tuXjxYiqKIrTYqtfrOWjQIObPn58PHz4UXsyLiopi1apV2a1bN965c0c4K+PZs2d0cnLitm3buHv3biGWTOg/W6BAAakyFSEhIWzfvj1LlCjBTZs2CfPLli1jjhw56O3tLfyda7Vali9fnlmyZJHqUHbixAnmzp2bZcqUkSqz0KdPH+bLl48rVqwQzh568+YNO3ToQAcHB6lF2FWrVnH06NH09fUVLkl97do1vn37lsWKFePo0aOFPvfY2FiGh4dz27ZtdHBw4NatW4W2HR8fz8jISHbq1Ine3t5CyQmm/Tx79iwLFy7Mhg0bChvDYmJiOHXqVObMmZODBw+WcqR/KnytrCEAlQAcTvT7aACjU2H8ATjIsPyCWUNJBYQLFy5YfLAePnyYxYoVY5UqVXjp0iXu2LHD4rIHcXFxHD9+PO3t7blo0SLOmTNHqGzBo0ePWKZMGTZq1IhdunQRLpmwYsUKOjo6snLlysK56aZg4OzsLNywxGAwcObMmQTA6tWrC7FkwsXY1FVNtJtbYGAg3dzcCIDz5s0T3vbhw4cJgHny5BFmSbJFixYEIFUr6f79++ZWlaId8Eiybt26BMDvv/9eOJtt48aNZlOYaKnl4OBgZsyYkRkzZhRKxyYTLqaVK1ems7OzcBAgyWHDhrFBgwbMnTu3cEvUTZs2cdSoUfTy8mLXrl2FBjznz5/npk2b2L17d+bKlYvbtm2zeN8fPnzIy5cvc926dcydOzdbtGjBx48fC+17SvqagSA9gGcA8gKwBnALQJFPXuMCmDOUygN4CUBjCZvU40unjyYOCD4+Pvz+++8tdssaDAauWrWKuXLlop2dHevXry804rp//z6rVatGjUbD6tWrC7Hx8fFm12fJkiWFau9ER0ezadOmBEBPT0+hAz0mJsbMZsuWTeiCbLLeZ86cmQCE2wjGxsaaty1jUrp06RKtra05cuRIYVZRFNaqVYsVKlQQZsn/5IrLpFSGhoZKG/BIsnjx4vTx8ZEqlNitWzfp4Dlv3jwCYL58+Xju3Dkhds+ePWaz5Ny5c4UCwaVLl5guXTop9s6dO+Y2rEuXLhXa50ePHtHe3p7p0qVjv379hD7vJ0+eMFeuXMyZMycrVKgg/HlZoq8WCPif6R4/AE8BjP3wt94Aen/4uT+Aex8u9JcAVE6JTe3xtXwEa9asMR94tWrVstgQoigKJ0yYYGabNGli8XSNyWVrujC2adPG4hGbVqvltGnTWKRIEQIQ7px1+fJltm/fnhkyZBCuSqnT6bh8+XK6uLhw8ODBQiyZcMKUL1+egwYNEmb1ej27du0qXUnzjz/+kKo1RCZ8Zk2bNpVi3717x4oVK0qxiqLQy8tLuvJp/vz5hYOuST4+PkJlV0xSFIU+Pj7s0aOH8BSiXq9n4cKFWb58eZ48eVKIjYuLY6FChejo6MixY8cKNTCKiIgw96WuU6eO0HRSUFAQ8+XLZ3Y0i7DPnz83t6rMkCGD8Hu2VF81EPxfP75WIAgMDOTRo0c5f/58du3alQMHDrT4xFMUhU+ePOHGjRvZv39/Tp8+XbhX6rFjxzh8+HBu3LhReN/v3r3L8ePHS1eXnDp1qnDdHzLhzmL27NlS85d6vZ6//fabVCtDRVGkLk4m7dmzR5oVKQPyqWRLRKRlu4qicO/evVLs+/fvhUs0mPTgwQPu27dPij179iy3b98uZbDatm0b161bJ9X5btGiRfz999+FDZI6nY5jx47lzJkzefPmTaFzPywsjD179uS4ceO4f/9+4SlPESUXCNQOZapUqVL1jUjtUKZKlSpVqpKUGghUqVKl6hvXNxcI0uIKBhKMPWlRWlzFQIK7NC2Kj49PE58WVzIAKTNVYn2Jqcy0/h9pcVanZZtp2e8v9bmldR/S8v2TTNPxRzJNxz/JNJ1/JKWMjIn5qKgoaT4lfVOBgCSqV6+OmjVrYvPmzcIHBUn4+vqicePGOHHihPBJYeLbtm0r5TA07X+fPn2kGsib+IkTJwq7ohPzf/zxBwDxoKAoCqpXr46jR4/i9evXwts3Go2oXr06Lly4gH/++UeY1+l0qFmzJoYOHSr83RmNRhw5cgT16tXD4MGDhbdtMBgwdepUtGzZEps2bRLmY2Ji0KhRI3Tu3BnXr18X5i9duoQhQ4Zg6NChwiwA/P3331i1ahVGjhwpzMbGxiIkJAQTJkzA2LFjhXm9Xg+tVouuXbti4sSJwjyQUF6iadOm+OWXX6T4GzduoGbNmpg8ebIwSxIHDhxA+fLlMWXKFGFeq9Vi1apVKFasGKZOnSrMW6SkVpD/2x9pyRrSarX866+/WKtWLTo4OHxW+zu1mvyxsbFcsWIFCxYsyOLFi3Pt2rXm3H9L0k0jIyM5ffp0Ojo68scffzSXJba0fG1wcDAHDBhAe3t7zp07l/Hx8Txz5oxFLJlQ571hw4YsXrw4r1+/ziVLlljMkgmZID4+PuzVqxc7deokXEL6zJkzdHBwYLFixYTr1BuNRo4ZM0a63eO6deuYPXt2ApAqrdyzZ08C4HfffSfMkmSdOnXMee2iMhgM5vTkXbt2CfPLli0jAObPn1+4JLXBYGDu3LmZMWNGqbTG6dOns1y5cixatKiwM/nBgwfs27cvy5Urx5YtWwqlocbGxnL16tVcv369OZXUUp+Ooig8c+YMAwMD2b17dzo5OXHp0qUW9+zw9/enoijcv38/y5Yty6JFi3Lbtm0WZROZriNBQUGcOHEinZ2dWb9+fR45ciTNZaqhpo9+Lj8/P44YMYJOTk709fXln3/+yU6dOllUM95oNPLgwYOsU6cOXVxcOGXKFFatWpW3bt2yaNufBoS8efMKWdjv379vLnORLVs2obRERVG4du1aOjg4UKPRcP369RazZIK5KX/+/ATAMWPGCLFv3rxhyZIlpS6ocXFx7N+/v9nIJppTr9Pp2LhxYwKQSol8//497ezs2Lx5c2GW/E/bRpH2hYmVOXNm1qtXT+piYPrcFixYIMweO3bM3HVr3bp1QmxwcDBz5Mhh9rmIpArrdDqWK1eOANihQwfhdqo//fQTra2tWbRoUeGexWPHjqW7uzvt7e05ZMgQITf34sWLWa5cOeEAQCaYDlu3bs1u3brR1taWPXr0SFMPi0+lBoIUZLpL8PX1JQBmzZpVqHXjrVu32KBBA/MF6tChQxazkZGRrFmzpnm7IiOukJAQFitWjABoY2Mj5ER89eoVS5UqRQDC9v+XL19ywIABzJEjB9OlS8fz589bzJIJzs0mTZoQAI8ePSrEkuSOHTtoa2sr1BTcpNjYWNaoUYMzZswQZklyyZIl7NixoxT77Nkz+vj4SLEk6ebmJt25ytfXl7/88osU27FjRxYvXlxq20OHDmXGjBk5bNgwoRIqJDlp0iQCoJeXF2fOnCnkC5g+fbr5Dko0ACVme/ToYfFFXFEUTp061cxOmDBBiB0/fryZHT16tHRznZSkBgILtGzZMlasWJF58+ZllixZOHr0aBoMhlQ5o9HIuXPnsk2bNixfvjxz5crFZcuWWbTNuLg4/vnnnxw9ejSbNGnCQoUKWTxaVRSFjx8/5tq1a9mjRw9WqlRJaLpFURRev36dkyZNYsOGDYUcmGRCqYnVq1ezXbt2ws5RMmGaaMCAAVINup8/f87JkycLc2RC8F20aJEUazAYpGoFmbR27Vppdvny5VKcoiicNm2a1J1EdHQ0R4wYIWXOevXqFXv37i01DXfz5k22bduWR48eFT4+Dh06xIYNG3LJkiXCx/Qff/zBypUrc8SIEdyzZ4/F5i5T//BixYqxbdu2/PXXXy0e5MTFxbFDhw7MkycPfX192blzZ2kTX2pKLhCohrIUFB0dDWtra1hbWwuzMTExyJw5M9KlE1+Pj4uLQ+bMmYU5IGFBVGZ/gYRFuQwZMkixBoMB6dOL9zkyHYgyn5OiKFLct8aaznGNRvN/tk0gYYHdyspKipU9noC0Hcey54/BYICiKFKsVquFlZWV9D6L6Kt1KPv/WVmzZpVms2TJIs3KBgEA0kEAQJoORNmTVqPRSF2gAEhfoL41VvbzTcs2AUgHAUD+eALSdhzLnj9p2d9MmTJJs19K31T6qCpVqlSp+lxqIFClSpWqb1xqIFD1P6e0uDOBL+Oy/V9UWt93Wj93Vf+9+uYCQZ8+fTBr1iw8ePBA6sQYOHAgFi9ejLdv30ptf9iwYVi1apV0qYrRo0dj69atZlev6HuYNGkSjh07BpKIjo4W5n/99VfcuHEDr1+/RkREhBALAPPmzcPt27exfft2YZYklixZgjZt2kiVCiCJTZs2Yfbs2cKsid+3bx8uXbokxQcEBODkyZPCvbJNOnz4MM6cOSPFksSQIUNw4sQJKf7mzZto3749/v77byl+1apVOHr0KPbv3y/M3r9/HyTx559/YteuXUJsTEwMyITSEkuXLsXWrVstZk2JDAAQGhqKWbNmSbnCAcDf3x+TJ0/GunXrhFmSuHnzJsaMGSPd89mijfyvPdKSPnrw4EH27t2bbm5u9PLy4uDBg3n8+HHqdDrqdDpeunQpRX7//v3s0KEDbW1tWbVqVS5cuJCvX79mUFAQT58+ner2d+/ezaZNmzJHjhxs3749jx07xjt37nD//v0W7f/27dtZrVo1urm5cerUqdy6datQOuOmTZtYoEABc4rcsGHDhNIKV6xYQScnJ1avXp01atQQSitUFIWzZs2ijY0Ns2fPzmfPnlnMkgn+AxcXFwLgwoULhVgy4bvPmDEjc+fOLZVKuWHDBmo0Gk6fPl2YJckpU6YQgLC5yaTq1aszZ86cUq0Lb9++TQD09vaWSuesX7++2QQo6gfYtGkTrays6OrqyhMnTgixfn5+dHZ2Zo0aNViiRAleuHDBYjYsLIyVK1fm4sWL6e7uzvr161v82Wu1Wnbr1o23bt1ijx49zOfrjRs3UmUNBgPnzJnD6Ohorlu3jjVr1qS9vT379euXquHUaDSa+6Bfv36do0ePpre3Nz09PTl8+HDevn3bov1PTlB9BB/L9EH/8ssvLFu2LG1tbdm6dWva2Nhw6NChqbpWtVot9+7daw4K5cuXp0aj4ahRoywquxAUFMT58+ezRIkStLe3JwCOGjXKYgv79evX2aVLF2bKlIkAOGTIEIs8D2TCgbphwwZzV7SePXtazJLkqVOnmD59egJg8+bNhdgjR47Qzs6OAFi+fHmhEhWxsbGcPXs27ezs6ODgwIiICItZMuE7nzt3LtOlS8dr164JsSa+fv36nDhxojBLJuTGu7q6SvkmSLJ8+fJSzmCSnDp1Kh0cHHj27Flh9vjx4wTAIkWKcO/evUJB1M/Pj1mzZiUAlipVii9fvrSYffPmDT09Pc2mMpGGLUFBQWYHe+HChYUMk+/evWOVKlUIgC4uLpw0aZLF7UUDAwNZu3ZtWltb09bWlo0aNeK2bdssKm3x5s0bfvfdd7S3t//o4n/lypU0l5Yw6asGAgD1ATwC8ATAqCSebwfg9ofHBQAlEj3nD+AOgJvJ7eSnj69hKHv79i179Ohhdvblz5/f4pNGq9WancWmA97StoAREREsXLiwma1evTrfvHljEfvixQtWqlTJbOFv2LChxRfHGzdusHv37qxYsSKzZs3KH3/80WL35bt377h161b26dOHBQsWZO/evYUO1NjYWP71119s1KgRR40aZTFnUlhYGEeNGiU9Mj9w4IBU/10y4TiRqRVEJgSSKVOmSLEkOXz4cOkg0r17dz5//lyYUxSFLVq04Jo1a4QCPplwXtSqVYs9e/bkuXPnhI6RsLAwlilThpUrV+bYsWN57Ngxi0uKvHz5kj4+PnRxcWGdOnU4bNgwi0tE3Llzxxx8nJ2dheppnT59mq6urh+5ki19z9u3b2fOnDnN7OzZs7/YxT+xkrvGptlQptForJDQc7gugNcArgBoS/J+otdUBvCAZJhGo2kAYBLJCh+e8wdQlmSwpdv8Woay06dPfzTvnS5dOtSpUyfVPF+j0YiHDx8iPj4eWq0W8fHx0Gg08PX1tSiH22AwICIiAmFhYQgNDUWGDBlQqlQpoX2PiorCq1evkDFjRnh5eQmxiqLg5cuXsLGxgZOTkxALJMx9Z8uWTcp38e7dO9jb20vlnIeHh8PW1laYAxLmjmW9HlqtVjr3+99gSSI2Nlbq/Wq1WgByue7h4eHIlCmTFJuWY+rJkyewtbWFg4ODMHvjxg3kyJEDbm5uyJgxo8WcwWDAhQsXkC1bNtjZ2SFnzpzIli2bRed/ZGQkLl68iEyZMiFjxozIlCkTcuTIgbx58wrvf2pKzlD2JQJBJSRc2Ot9+H00AJCcnszr7QDcJen24Xd//JcEAlWqVKn6/1lfs1WlG4BXiX5//eFvyakbgEOJfieAIxqN5ppGo+mZHKTRaHpqNJqrGo3mqkwtflWqVKlSlbS+RImJpO59krzN0Gg0NZEQCKom+nMVkm81Go0TgKMajeYhyc9y5EiuALACSLgjSPtuq1KlSpUq4MvcEbwG4J7o99wAPkuy12g0xQGsBNCUZIjp7yTffvj3HYBdAMp/gX1SpUqVKlUW6ksEgisA8ms0mrwajcYawI8A9iZ+gUaj8QCwE0AHkn6J/p5Fo9FkM/0M4DsAd7/APqn6L1Zae/6mdV1LlZzS+rn/G72eVVmmNAcCkgYA/QEcBvAAwFaS9zQaTW+NRtP7w8smALAHsESj0dzUaDSmlV5nAOc0Gs0tAP8AOEBSzrpooQ4fPozbt2/DYDBI8cePH8ejR48+OyksPUlOnToFf3//j/4m4pI9d+4cAgICzL8HB1u8xg4AuHz5MsLCwgAAd+7cEWKBhKyK2NhYbNu2TeozvH//PkaOHCnVsxgAnj17Ju0MBoCQkBD4+fml/sJkpNfr09QAPS0yuWRldePGDXMWkKj0ej0mTpyI0NBQKf7w4cNYtGgR3rx5I8wGBQXhxIkTePPmzWfnTmqKj4/Ho0ePACRkEz158sRiliRCQkLMP9+9excPHz4U2rZJRqMR169fx7179yze9qf/16VLl3D79m2Lty+kpHJK/9sfafER9OvXjwUKFKCNjQ0rVqzIfv36cfXq1bx16xZv3brFUaNGMTQ0NEXew8ODOXPmZIMGDTh58mQePXqUmzZt4ujRo1PN4+/Xrx+dnJyYJ08edurUiWvWrOHIkSM5YsQIi5q79O3blzly5GCpUqU4ZswYNmnShAMHDrS4MUyvXr2YLVs2NmjQgMWKFWOHDh0YHh5uEUuS3bp1o52dHR0dHVmrVi2+e/fOYpYk27RpQwDMkyePsEPWaDSyVKlS1Gg03Lt3rxBLJrRN9PLyYosWLYRZMsE/kSdPHmln8K1bt1i+fHnhfHyTpk6dyubNm0t5CaKioujs7My2bdtK8aZWlzK+j+3btzNDhgxMly6dcFOfS5cu0c3NjXnz5qWtra1Qq8x79+6xZMmSbNSoEUuVKkUnJyeL27L6+fmxZs2aHDFiBHv27El3d3d6eHhYtP3Hjx+zUaNG3LRpE+fOncsmTZrQ1taWBQsWTJX38/NjixYteO/ePW7bto1DhgxhpUqVaGNjY+6RnhZBdRZ/rPDwcJ48eZJz5sxh27ZtWaBAAbPT1s7OjjNnzmRMTEyy/Js3b7h9+3YOHTqUVapUMTt8nZycuGzZshQdwoqi8P79+1yyZAlbt25tbqieK1cubt68OVUjiU6n4+nTpzlq1Cjzdj08PHjw4EGL3ntERAQXL15sNq/kyZOHZ86csYglyblz55pZDw8PXr161SJOURROnz6d+fLlM7s2RSzz79+/59y5c+nr60tbW1vhJuyKovDgwYMsXrx4qqVEktMff/zBNWvWSLF6vZ59+vSRYkmyd+/e0iUGfvnlF7Zs2VKq3eSyZcuYLVs2tmrVihs3bhQKZGvWrGG6dOlobW3NEiVKCPXW/uOPP2htbW1up2qpG1xRFC5atMh8bjg6OvLYsWMWufZ1Oh2nT59uZr28vDhnzhzeu3cv1fMyJiaGY8eONe+zp6cne/fuzS1btqTqTA4JCeGgQYPMjn17e3s2atSIU6dO5fHjx80N7dOq5AKB2qEskcaOHYtt27bBxcUFLi4uKFOmDAYNGmSRoaxHjx548uQJcubMCXt7e/j6+qJDhw6pGkrCw8PRt29fKIqCrFmzIlu2bGjUqBHq1KmT6v76+flh+fLlsLKyQvr06WFlZYU2bdqgaNGiqbLXr1/H7du3zQY4nU6HDh06wMXFJVU2PDwcgYGBePfuHYKCghAZGYm2bdvCxsYmVdak6Oho3L9/H2/fvsX3338v3AAlJCQEDx8+RJUqVYQ4IOH7evz4MQoWLCjMAglmJ1dXVyk2ODhYyuiUlu2SxIMHD1C4cGFhVqfT4fz586hcubKQwQpIKNR2/PhxFC1aFN7e3kINY549e4Zjx47B2dnZ/HBxcbGoadPly5dx5swZs5ktY8aM+O677yw6tnfv3o2rV6/CaDTCYDAgY8aMGDt2bKrbNRgMWLlyJe7du4fo6GhER0ejYMGCmDx5cqrXgKioKMyfPx9PnjxBSEgIQkJC0KVLF/Tq1SvV/RXVVzOU/RtSDWWqVKlSJa6vaShTpUqVKlX/w1IDgSpVqlR941IDgSpVqlR941IDgSpVqlR941IDgSpVqlR94/rmAkFKWVKBgYEwGo1S/PPnzy1yfSb1mtu3b1vsGE38OpI4c+aMkNvU9Nro6GgcPHhQ2KlKEs+fP8eff/4pVTLgypUr+PXXX6XduU+ePJFyp5oUFxcnzf6vKz4+PtXjOyWdPXtWmn/79i169eolxUdGRmLhwoX/MT8JKC4uDnv3/qfijQiv1Wpx+fLlj/5mKa/VapN0sFvCx8bGflQ9QGb7wkrKXPDf/kiLoaxYsWJ0cXFh6dKl2bhxY/bo0YMTJ07k8uXLOW7cOObJk4fTp09nUFBQknyZMmWYO3duVqxYka1ateLPP//MuXPnsk2bNvTx8eHixYtTNH9UrFiRnp6erFGjBjt37sxJkyaxQoUKLF68OFevXp1qD+Bq1arR29ubDRo04MCBA5k7d26WKlWKmzdvtsgwU7t2bRYpUoStW7dmxowZWaZMGe7evdvibkj169c3twAsUaIEDx48KNRJqXHjxubeuZYa4BKra9eutLOz47Zt24RZMsHZPXnyZKnuT6YOY5Z2ykqKP3z4sBRLkleuXOHOnTul2OjoaNapU0fKkR0fH89Ro0Yxffr03Lx5szA7a9YsZs2alenSpRNqtanVajl//nw6ODgwR44czJ8/P2fPnm0RGx0dzTlz5tDZ2Zne3t5s2LCh+dxOTWFhYfz111/p7OxMX19fduvWjb6+vsyVKxd/+eWXFNnAwEBOmDCBjo6O7NSpE0eOHMk2bdqwQoUKdHZ25vjx45Nlnz17xmHDhtHOzo5TpkzhtGnT2KdPHzZp0oQlS5akg4ODlLM7saA6ixOk0+n46tUrXr58mbt27eKSJUs4btw4du3alWXKlDE7ZjNlysQpU6Z81ms0Pj6ez58/59mzZ/nnn39y1qxZHDBgAAsWLGhmnZycuG7duiQvNlqtlo8fP+bRo0f5xx9/cOzYseaG7PjQXzWlBt9xcXG8d+8ed+/ezRkzZjBDhgwEQI1Gw9q1a6faIjM2NpbXr183N1IHwGzZsrFjx47JBr/EioqK4sCBAwmANjY29PLy4pgxYyy6OCqKws6dO9Pb25slS5Zk1apVuXTpUotLHiiKwlmzZrFr165s166d8EVNURT+/fffnD59urSz+PHjx8KO5sTy8/OTZo8dOybcp5lMeN/r16/n4sWLU22e/qlMTtsOHTqwe/fu3L9/v8VseHg4Bw4cyEqVKrFYsWLMmzevxa7sFy9esGXLlsydO7fZbbtjxw6LBjtXrlxh5cqVzQ7frFmzctu2bfTz80vVFb179256eXl91LJ2yZIlPHr0KJ8/f54sbzAYuHjxYtra2prZChUqcOrUqdy4cSPPnTvH169fJ3msR0VFcfjw4eb3CYB16tTh8OHDuWjRIu7cuZNXrlxhQECAdKtSk5ILBKqhLJE2bNiA8PBwlC5dGiVKlLC4TR5JLF68GE5OTihevDgKFCiA9Okta/UQHR2NtWvXolChQihSpAicnZ0tam8HJExH3bhxAwUKFIC3t7dQS8D79+9Dq9XC09MTdnZ2Fm8TAF69egU7OzupNoKqVIlKURSEhYVBURQ4OjoKcQEBAXj+/DkKFCgg1IY1LCwMfn5+ePr0KVq2bAlra2uLOKPRiOfPn+PevXuIiopC+/btLd5mTEwM7t69i1u3bsHFxQXff/+9xaylUp3FqlSpUvWNS3UWq1KlSpWqJKUGAlWqVKn6xqUGAlWqVKn6xqUGAlWqVKn6xvVFAoFGo6mv0WgeaTSaJxqNZlQSz2s0Gs2iD8/f1mg0pS1lValSpUrV11WaA4FGo7EC8DuABgAKA2ir0Wg+7YDRAED+D4+eAJYKsP9n+vvvv3Hs2DHodDphdtOmTbhy5Yqw29ZoNGLZsmVSfXTfv3+PlStXJutCTEm3b9/Gtm3bEBkZKcweO3YMR44ckXIHnzhxApcvX5ZuZB4aGvr13JWqUpTBYJA6XoAEt+y+ffuEegabFBISgo0bN+Lp06fC7MuXL7F06VLExMQIcSRx584drFy5Uvh4MxqNOHfuHHbu3CnEAQlO6AMHDuDMmTPCbFpkWbJ7yioP4AnJZwCg0Wi2AGgK4H6i1zQFsP6DoeGSRqOx1Wg0rgA8LWC/qMaMGYO3b98m+dyLFy9w6tQpZM+eHfXq1UOTJk3QunXrjzozTZgwAS9fvvyMvXHjBm7fvg0XFxc0btwYzZo1Q8OGDT/Lz//ll1/w/Pnzj/527Ngx9OnTBwUKFDBvs3z58knu49SpUz86mf766y/06NED5cqVQ5MmTfDjjz8if/78yb7/6dOn49GjR4iLi8PWrVuRIUMG+Pr6okmTJmjbtm2qedqzZs3CkSNHcPz4cWTNmvWjz8mS7lF79uzBokWL4OTkhEaNGqFZs2Zo3LixxR3KJkyYgL///htNmjRBq1atULlyZYs4k+bMmYPo6Gi0bdsWPj4+QiwAnDlzBj4+PnB2dhZm4+PjsXbtWunOU7du3ULmzJlRoEABIY4kjh8/jp07d6Jly5aoVauWxazBYMCOHTuwd+9eHDp0COvXr0fjxo0tYiMjI7F582bs378fx44dg1arxYEDB+Dt7Z0q++bNG/z555/Yt28fzp8/D5Jo164d2rZti4YNG6bI3r17F1u2bMG+fftw+/Zt2NnZmUtFtGzZMsX9P3XqFHbs2IF9+/bhxYsX8Pb2xrlz58zP//DDD2jatOlnnNFoxO7du7Fnzx4cPHgQISEhKF++/EflLQDg+++/R/PmzT/6W3R0tHl/jx07htjYWDRo0ACrV6/+bDuNGjVCq1atUnz/MvoSgcANwKtEv78GUMGC17hZyAIANBpNTyTcTcDDw0N6Z8uVK4fw8PAknzt37hwuXLiAypUrw9fXF9WrV/+sPV+ZMmWQN2/ez9jXr18jR44c8PX1ha+vLypWrJikSat06dKf7f/58+fh6upqZlNqNVmyZEm4ubkBSDhJt27dioIFC5rZpPYtsUqUKAEXFxcEBARg27ZtKF26tJm1pIVi8eLF8fTpU5w5cwaVKlUyf06WBAEAyJ49O7Jly4bq1aujRo0aqFSpklCbSjc3N9SoUQM1atRAiRIlLOZMKlKkCDJnzox8+fIJswBQqFAh6VaT1tbWKFWqlBQLAD4+PlJ3YRqNBuXKlUNoaKhwq8v06dOjWrVqiIyMRHR0NLJly2Yxmy1bNtSoUQNRUVGIjIzE+fPnkT17dotY0/kQGRmJyMhI3L59G+XKlYO7u3uqbP78+T9io6KiUL16dWg0mlSvHaVLl0ZwcDAiIyNx8OBBZM+eHb6+vubn8+TJkyRnZWWFKlWqIDw8HJGRkTh69Cjc3Nw+YgHA09PzMzZr1qzm/Y2KijIPNooXL/7Za1M7v6WVlN1Y5AGgFYCViX7vAGDxJ685AKBqot+PAyhjCZvU40s0r09K9+7dY1RUlBR748YN6nQ6Yc5gMPD69etS1vHQ0FA+fvxYmCMTLPyBgYFS7IMHD6SbaT99+pTx8fFSrKr/bYWEhEgfcy9fvuTbt2+FOUVRePfuXUZHRwuzBoOBV69elapLFRcXJ1zOw6SwsDA+evRIik1N+FolJjQaTSUAk0jW+/D76A8BZnqi1ywHcIrk5g+/PwJQAwlTQymySUl1FqtSpUqVuL6ms/gKgPwajSavRqOxBvAjgL2fvGYvgI4fsocqAoggGWAhq0qVKlWqvqLSvEZA0qDRaPoDOAzACsBqkvc0Gk3vD88vA3AQQEMATwDEAuiSEpvWfVKlSpUqVZZLLTqnSpUqVd+I1KJzqlSpUqUqSamBQJUqVaq+cX0JH8H/N5o7dy4uXryI0qVLo3Tp0ihVqpRFxiGSGDhwIPR6PUqUKIESJUqgWLFiFuVcR0dHY8CAAcidOzeKFi2KIkWKoECBAhY1wnj8+DF+++03FChQAD4+PihQoABy585tUV7+6dOncf36dXh6eiJv3rzw9PSEra1tqhwAHDlyBHq9Hi4uLnBxcYGTkxMyZMiQKkcSjx8/RtasWZE1a1ZkyZIFVlZWFm1T1f+udDodoqOjER0dDcByH1BsbCwCAwPNjwIFCqTosTFJURQEBQXh+fPn8Pf3x/Pnz9GlSxfkypXLon19+vQp/Pz88OjRI7x//x7Tpk2z6HyMjIzE/fv3cffuXdy7dw92dnaYMGFCqhxJBAYG4tatW7h9+zZu3bqFunXronPnzqmyX0xJ5ZT+tz/S4iM4e/YsN2zYwJkzZ3Lw4MFs3bo1q1WrRi8vL2bOnNncKq5EiRJcvnz5Z60qz507x7Vr13LKlCns1asXGzVqxOLFizNr1qxmtnr16tyxY0eS+cfnzp3jypUrOW7cOLZv355Vq1ZllixZzO0mv//+e549ezbZ/T937hyXLFnCn3/+mU2aNDG3t0ufPj07dOjABw8epPj+z5w5w3nz5rFt27YfteUcMGCARa0qT506xR9//NHMZsmShRMnTrS4j2+LFi0+apEp2qqyU6dO9PLyYqFChaRaVc6bN49NmzaValWpKAo3bNjAq1evCrMmHTt2TJrdsGEDr1y5IswpisKlS5eyZcuWPHLkiBCr0+k4efJkenh4MH/+/Pzjjz8sZsPDw9m7d2/z9w3AYv7Fixds3br1R+y0adMsavV59epVNmjQwMxlzZqVgwcP5ooVK1LlDx48yKpVq5pZZ2dntmnThuPGjePatWuT5Q0GA9euXcvixYubWVdXV9atW5c9evTgtGnTuGnTpiT5qKgozpkzh3nz5v1ou+XLl2eLFi04aNAgzp49m1u2bEmzvwDJ+Ai+uTuCNWvWIDY2Frly5YKbmxvKlSsHV1dX5MqVC1evXsXhw4fRp0+fZJ3BGzZsQHR0NNzd3VGsWDE0bNgQuXPnxvbt2xEcHIz+/fsn6Qg0afPmzYiOjoanpydq164NT09PLF68GLly5cLAgQNTLA8BANu3b0d0dDS8vb1RtWpVvHjxArVr18bgwYMtGmnt378f0dHRqFy5Mg4fPozOnTtj2LBhFjtOjx49ihw5ciBDhgzo3bs3xo4dK1RuweSM7NChA2bOnCnkdNVoNHB3d4eTkxM2bNgALy8vi1kTbzQa0a9fP1SokKSBPVXexcUFpUuXTv3FSYgkcufOLcUCQM2aNZN1xackjUaDXr164c2bNxY7e03KkCEDxo8fjzJlyqBnz56pHp+JlSNHDixduhSdOnVC//798eDBA4vbRXp4eOCvv/7CiBEjMGbMGNy5cwf+/v64fft2qvtQpkwZHDx4EFevXsWUKVMQEBAAV1dXnDt3DtmyZUuRb9CgARo0aIALFy5g1qxZyJw5Mxo1aoTHjx/jyJEjsLKySpK3srJCp06d0LFjR5w8eRLz589HuXLlUK5cOfj7+8Pf3x979uxBfHz8Z3zWrFkxdOhQDB48GIcOHcLixYvRq1cvuLi44PXr13j16hVev36NS5cuITIyUrjEiCVSs4YSSVEUoXIHiWUwGCzuU/yp4uLiLC7RkFgkER4eDjs7O2E2NjYW0dHRQn1cTQoICIBWq5Wyu9+/fx+hoaGoWrWqMAsAwcHBsLW1lf6sSQr1Z/7/TWl5/+/fv0fOnDmlpvOMRiPWr1+Pjh07SvEXLlxApUqVpPbd398/ydIOligsLEzq/ALkz2sgbdeTlKT2LFalSpWqb1xq+qgqVapUqUpSaiBQpUqVqm9caiBQpUqVqm9caiBQpUqVqm9caiBIpIcPH+Lt27cwGAxCnNFoRHBwMIxG41faM1WqVH0rio+PR0hIyP/pNtVA8EEBAQGYM2cO3NzcYG1tDScnJ0ycOBFarTZVVqfToUWLFkifPj3s7Ozg4+OD1atXW9TrNDw8HEWKFIGrqyvy58+PSpUq4dixYxbts5+fHypXrowKFSqgcuXKaNKkCe7evWsRe+LECXTp0gVt27bFDz/8gG7duiEwMNAi9syZM1i+fDkmT56Mfv36YcyYMYiNjbWIJYlXr17h0KFDmDVrFhYuXCjcvzg2NhZ79+7F1q1bhTiTXr9+jRMnTkixRqMRaclYu39fvgvrP//8I8WRxNatWxEXFyfM6nQ6LFy4EJcuXRL+nkJDQzFmzBgsXboUZ8+eRVhYmMXss2fP0KNHD/z888+YMWMG1qxZg8ePH1vEXrp0CT/88ANatGiBdu3aoUePHsm2p/1U27dvR/Xq1VGpUiWUL18erVq1suhzMxgMmDdvHooVK4Z8+fLByckJHTt2tOgaEBUVZfYBZc2aFZkyZcJvv/0m3ddbSkm5zP7bH2ntUPb27Vvu27ePkyZNYuPGjenq6ko7Ozuzo9DX15cXL15MklUUhc+fP+eff/7JAQMGsFy5csycObPZFVi/fn3euXMn2W0risIHDx5w6dKlbNOmDZ2dnWljY0MA/P777/n06dMU991oNPLKlSucPHkyK1WqxHTp0hEAmzdvzjdv3qT63vV6PY8ePcpu3bqZXYzNmjXj+/fvU2XJhM5LEyZMMLMNGzZkWFiYRayiKBw+fLiZrVatGsPDwy1iSfLdu3ds0aIFM2fOzAIFCjA0NNRilkzo/DRixAja2try5cuXQiyZ8Nl37dqVf/31lzBLJjhIGzduLMWSZNeuXbl582YpdsOGDcydOzdXrVol3A3v/PnztLa2prOzM8eOHUuDwWAxe+PGDTo6OhIArayshJzNN2/eNJ9XGTNm5KFDhyzuFnb16lX6+PgQAHPmzMkJEybw7t27FrHnzp1joUKFzM75Jk2acMmSJXz+/Hmq7JEjR1iwYEEzW6hQIfbp04d//fVXit3ZFEXhrl276O3tzXTp0tHLy4s5cuRg3bp1OWHCBB46dEj4eE9KSMZZ/K9f1GUeaQkEFStWpJ2dHevUqcORI0dy27ZtfPbsGRVF4ePHj1M92KpUqUInJyc2bdqUM2bM4OnTpxkTE8PTp0/z77//TnX71apVo4eHBzt27MjVq1fz2bNn3LhxIw8cOGDR/levXp0+Pj4cPHgwjxw5wrFjx3LHjh0Wv/8aNWqwTJkynDlzJhs3bsxVq1YJteKrVasW69Spw4IFC3L8+PHCF5U6deowe/bsrF+/PmNiYoRYkmzSpAlz5MjBhw8fCrN6vZ7Nmzfn8OHDhVmSfP/+PVu3bs179+5J8Y8ePWLfvn2FLqSJtWrVKo4bN06qranRaGTFihU5Z84cqW2vWbOG1tbWnD9/vjD78OFD5s6dm3Z2dpw5c6YQGxwczLp167JOnTr08fER4mNiYti3b18OHjyYP//8M3Pnzs0ZM2ZYxGq1Wk6cOJEbN27kpk2b2L59ezo4OPDXX39NlY2Pj+fs2bN569YtXr16lXPmzGHjxo2ZI0cOTps2LVV2wYIFDAsLY1BQEPfs2cNRo0bR19eXWbJk4S+//GLR/icnNRB80Lt376R6kJoUHBycJj40NDRNfERExEe/i14UEvdkluk7bKopJHsxjI+P5/r166X7FsfHxwvXy0ksvV5v8R1MckrL9/dvbtfSu77kdODAAel98Pf355EjR6S+d4PBwIcPH1JRFMbFxQnzpuPcaDQK9y5OfH4ZjUbpnuZkwvv49PwVkV6vF7qDTkrJBQLVWaxKlSpV34i+irNYo9Hk1Gg0RzUazeMP/35WlEOj0bhrNJqTGo3mgUajuafRaAYlem6SRqN5o9Fobn54NEzL/qhSpUqVKnGlNWtoFIDjJPMDOP7h909lADCUZCEAFQH002g0hRM9P59kyQ+Pg2ncH1WqVKlSJai0BoKmANZ9+HkdgGafvoBkAMnrH36OAvAAgFsat6tKlSpVqr6Q0hoInEkGAAkXfAAp1jTWaDSeAEoBuJzoz/01Gs1tjUazOqmppURsT41Gc1Wj0Vx9//59GndblSpVqlSZlGrBa41GcwyASxJPjRXZkEajyQpgB4DBJCM//HkpgClIyCufAmAugK5J8SRXAFgBJCwWi2zbUq1Zs+YjQ5aLiwsGDBiATJkypcgZjUasW7cOERER0Gq15lr9nTp1SrV+enR0NK5cuYKwsDCEhoYiLCwMxYsXR7169VLdX5IIDQ3Fq1evzI/KlSujZMmSFr1fIMGcZWqvV7duXbi5id2sBQUF4ezZs6hfvz6yZs0qxMbHx+P06dOoXbu2cI16krh27RrKlv1s3csiPX36VLixjUlv3rwR/pxMCgwMhItLUqfT19suSTx79kzq/cbFxeHp06cWtYj8VEFBQfD390f58uWF+wg8evQIL168QJUqVZAlSxYh9vz58wgICECxYsXg5eUlVNd/165dCAsLg7u7u/lhyfYNBgNWr16N2NhY2NnZwc7ODo6Ojsk2uEqsqKgo/Pbbb9DpdMiUKRMyZcqEwoULo27duhbvd5qVVCqRpQ8AjwC4fvjZFcCjZF6XAcBhAENS+L88Ady1ZLtpNZR9qvDwcP71118ftbfr0KEDg4ODU2UVReGlS5dYo0YNM9uvXz+Lc+SDgoLM5hUAHDNmDPV6vUXs8+fPzWYdjUbDGTNmWJzed/36dRYqVIgajYYA+Pvvv1vEkeSlS5fYr18/836vWbPGYlZRFF68eJF9+vShnZ0dN2zYYDFr0pkzZ1ixYkWh7ZpkNBo5evRoLl68WJglycuXL3PChAlSrE6nY9euXaVYkmzVqpV0+mKbNm24b98+KfbHH39kp06d+OLFCyFOURT+9NNPLFCgAKdOnUp/f3+LWaPRyLZt2zJDhgysWrUqx48fz7dv31rExsfHs2XLlmYjmojpMTIyko0bNzafj7Vr17Y45TUoKIh16tQxs127dv2s1W1yevbsGStXrmxmBw8ebJGBTVT4Gj4CALMBjPrw8ygAs5J4jQbAegALknjONdHPPwPYYsl2v0QgePLkCefPn89atWoxa9asrF+/Pn///Xd6eXmlesKYLv5Dhw5lnjx5WKBAAQ4aNIjOzs4WGcN0Oh13797NZs2aMUeOHKxTpw5z5sxpsaksPDycCxYsoLe3N3PlysUsWbJw165dFrFkQgDp0aMHra2taWVlJXwxPnToEDNkyEAAnDVrlhB7+PBhWltbEwA7deokxN67d898khYpUkTYmBUVFcWmTZsSgNBFyaTo6Gjmz59f2tRz/PhxZs2a1eKLw6eqWLEiu3fvLsUuW7aMGo2Gs2bNEvYC+Pn5MX369MyYMSOHDh0q5MOIiIigl5cXATB//vxCju74+Hh+9913BMB8+fIJBSK9Xs8uXboQAJ2cnDhr1iyLPQQGg4HDhw+nRqOhi4sLa9asyV27dll0vBkMBk6cOJHZs2dnjRo1aG9vz379+vHKlSupfu56vZ5Tp06lt7c3u3XrRnt7e5YvX56zZ8/+YkHhawUCeyRkCz3+8G/OD3/PBeDgh5+rfohytwHc/PBo+OG5DQDufHhub+LAkNIjLYFgwoQJLFSoEJ2dndm1a1fu2rXLPMqyxGw0btw488V/7NixvHXrFhVFYXh4ON+9e5fq9seMGUMnJydWrVqVK1euZEREBP39/S2+MA0fPpx2dnZs3bo1z507x+vXr/PGjRsWsSQ5aNAg2tnZcfTo0dyyZYtQACHJ7t27M3fu3Bw4cCCHDh0qxCqKwpYtW9LLy4s+Pj7Co9vo6Gh6eHgQgNTo9syZM7SxsWGJEiWEWZLcvn07ra2thd2xJk2ZMoXZsmXj8ePHpfg6deowd+7cfPz4sTD7+vVrAmDp0qWlymv07dvXfKcsamK8evUqHRwc6OLiwuXLlwuxUVFRrFy5MidMmMCcOXNy/fr1FrNGo5GDBg3ijRs32KpVKzo5OQmV6Fi7di21Wi03bdrEChUq0NPTk1u3brWIPXPmDMmEkf6kSZOYN29eFi1alNu3b0+VNX2/Op2Of//990dBwRI+JX2VQPBvPdISCNauXctLly5J2fRJcuPGjeaLv4y2bt1KPz8/KZYkd+3axVevXknzBw4cMDtMZd7DsWPHGBUVxcjISKnP8Ny5c4yMjOStW7eEWZK8du0aJ06cKP35P3/+3OI7r6T0/v17vn79Woo1Go0MDQ2VPvZevnzJkJAQKZYkd+zYwYCAACk2ICCA06ZN47Nnz6T4f/75h2/evJEqDWJy4z558iTFOl5JSVEU87Fy+/ZtXrt2TXj7Jl2+fJmXL1+WYo1GI0+fPs3z589L8aagcPr0aSnepOQCgeosVvU/J/LbbkD/b0n93P/3pfYsVvX/jdSL0b8j9XP//1dqIFClSpWqb1xqIFClSpWqb1xqIPhE8fHxePXqFa5evYpDhw4Jd3WKi4vDw4cPcebMGeEOQyTx8uVL3Lx5U4gz6f3793jy5IkUGxoaanGHsk8VFhaGyMjI1F+YhEJCQoRbgyberqyioqKk2ZiYGGnW0k5uX3K7JKXfb2xsLOLj46XY0NBQ6PV6Kfbt27fS7JMnT6DT6aTYW7duSX1HBoMBFy5ckDomIyIicOrUKbx48eJfa3erBoJEmj17NjJlygQPDw+zqy9z5sypcoqiYPjw4XB1dYWNjQ1q1qwJGxsbpEuX+ser1WoxbNgwVKlSBba2tqhRowayZ89u0f6GhYVh1apV6Nq1K3x8fFCrVi3Y2SVbpeMzPXv2DAsWLEDNmjXRtGlT2NraWsySxMWLF9G5c2d07txZ2FUcExODadOmYcSIEULOT5P27t2LqVOnCnNAQm/q2bNnS7ERERHSrKIomD59uhQLAOPHj5fiNBoN+vfvL9Wq0traGi1btrS4TWRiZciQAbVr18b27dshmpSi0WhQpkwZjB8/Hi9evBBiDQYD8ufPjx9//BF//vmn0MU5Ojoabm5uqFChAoYOHYrdu3dbNKBLnz493r17BxcXF7i5uaF+/fpYuXKlRdvMkSMHHj58CC8vL2TKlAn58uXDzp07Ld7nL6KkUon+2x9f2ll88+ZN9u3bl3Z2drSxsWHRokUtztWOjo7mb7/9Rm9vbwJg0aJFhcxKFy9e5IeSGSxcuLBQamJ4eDiLFStGAPT29rbYeUmSr169Mht9cufOLZRW+Pz5c5YrV44AaGtrK5TOqtPpuHTpUrq4uNDKyko4nVCr1XLQoEEEIJWP7+/vz9y5c0s7i3/++We2a9dOir1y5QqdnJyk00dz5szJw4cPS7ENGzZko0aNpBrDDBs2jFmzZuWmTZuE2d9++40AWL58eZ44cUKI3bZtm9k137lzZ6GmNIcOHTK3cW3dujV1Op3F7NGjR82mx969ewt9X0ePHjW3nu3cubPQ+Xzo0CFmy5aNAFirVi3u379f+lhJTlB9BB8rOjqaq1atYvny5enm5saJEyfy5cuXnD9/vkVGp1evXnHkyJG0t7fnDz/8wLNnz3LAgAEWdxC6cOEC69WrR3d3dy5dupT169e3uIOUwWDgH3/8QRcXF3bs2JEFCxYUCj5hYWHs0qUL8+TJQ1tbW+Hc6ps3bzJPnjxMly6d8MUhKCiIlSpVIgD26tVLiI2JiTE7i93d3YVPkoCAAHPAPnXqlBBLknfv3qWVlRWbNm0qzJI093pOrh92arK2tqaPj4/UxXzkyJEEwDZt2gg7sm/fvm0ufSDqJI+PjzcPOAYNGiR0QSbJ9u3bM126dKxXr55wZ7l58+bR3d2d9vb2XLhwodDxsmfPHlasWJHlypVj2bJlee7cOYvZCxcusH379hwyZAjt7OzYv39/iwPCrVu3OH36dG7YsIElS5akj48Ply1bJtXWNSmpgeCDEo/+GzduzL1791pc24dMcEm2a9eOdnZ2HDhwIJ88eWJ+zhKT06cBwFRuwNLRzqlTp1iyZElWrlyZ//zzD0la1LTepAMHDjB37tzs3bs3IyMjeeHCBYtZkty8eTMdHBz4559/8vfffxc2ds2fP5958+ZlmzZthO5gTOrbty89PDw4ZswYYXb//v3MmTMnAVhURyqxFEVhvXr1CIB16tQR3jZJlipVylxPSlQ6nY4AmD59es6ePVuY37BhAwGwUqVKvH//vjBfrlw55sqVi3v27BFmt2zZwl69etHR0ZGXLl0SYsPCwrh27Vr279+f3t7eFjegJxO+swsXLvDhw4esVKkSq1WrJuTKfvPmDY1GIzds2EA3Nzf++OOPFpe5MJ3PgYGBHDp0qFBAMJ1TiqLw5MmTbNKkCR0dHTl27Fipcyax1EDA/5zMEydOFC6gZeIbN27MWbNmSfW9VRSFzZs3/ygAiPI//vgjN2/eLOWsVRSFHTt25LFjx4RZE9+9e3ehkhaJZTQa2a9fP/r7+0v1njUYDBw6dCjfvXsn9f3Fx8dzzJgx3Llzp9S2Q0NDOW3aNK5YsUKY1+v1PH78OBctWsSrV68K85GRkZwxYwaXL19u7hstoocPH3Lnzp38448/hFkywdV7/vx5qfduNBqp1Wq5b98+LlmyRGr7JLlmzRrpKT2DwcC5c+dy/vz5Unx0dDQnTJggfEdkkikg/Prrr1L8o0eP2LdvX06ePFmKNym5QKA6i1WpUqXqG5HqLFalSpUqVUlKDQSqVKlS9Y1LDQQpKCYmBlqtVoqNiooSNpQl3q6sZPcXgLRxCIC0+UdRFGkTjawRDUCajDv/ayxJ6WMxLZ9xWljZ4wlI23Ese/4YDAbp7cbGxqbp/X4JqYEgkU6ePInx48fjhx9+gLe3N0aNGgVra+tUOZJ48OABVq9ejZ49e6J48eJYuXKlRYYyIOGgP3v2LMaPH49KlSrh8OHDQvsdFBSE33//HXXq1MGtW7eEWKPRiD179qBZs2YICAgQYgHg+vXraN++vZRZ6fXr1+jXr59UMbPIyEhMmjRJmAMAnU6H+fPnS7GKomDZsmVSLACsWrVKml26dKk0O3PmTCkuKioKkyZNgsxa4vPnzzFy5EipC+Q///yDgQMH4t27d8Ls3r170a1bNymH/tKlS9GmTRvs3LlT6Ji2srLCyJEj0ahRIyxcuBAPHjyw+DOzsrJC27ZtUb16dYwYMQI7d+6UdvlLK6kV5P/2x5c2lJEJmQ0LFy4050uPGjVKKDNn0qRJZnbatGkWcwaDgV27djWzc+fOtZjVarXs3Lmz2TizaNEii9mYmBjOnj2bnp6eBMDffvvNYpYknz59yrZt2xIAFy5cKMQqisJNmzbR1taWM2bMEGLJhAyMUqVKcezYscIsmZCC2rNnTynW1NJURn5+fvTy8pLK+DIYDMyWLZt0+mCePHmkUj9JsnTp0uzZs6ew/4AkfX19WaxYMan+E/Xr12fWrFk5adIkRkZGWswpisJGjRoRAKtWrcrt27db/JkbjUY2bNiQAJgtWzYuXbrU4u3qdDrWr1/ffC7/+eefFrOxsbHmNpfp06c3N7b50oKaPpq0jEYjt27dyiJFirBcuXL87rvvOH36dIv5ly9fskOHDnR2dmaRIkWE+tkqisJVq1bR0dGRjo6OHDhwoNBF4vnz56xcuTLTpUvHtm3bCrGKorBVq1YEQF9fXyGzTUxMDJs3b04AzJs3r1AqrF6vZ/fu3QmAGTJkYFBQkMUsmRCATAYlmTTY1atXEwDHjx8vzOp0OubPn5+lSpUSZkly7ty5BCCVxx8YGEgA7Nu3r9S2y5Yty2zZskk1hhk6dCgBsHnz5sJpv5s3bzZ/1+vWrRNib968ae6pvWDBAqHj+/Xr18yRIwcBcNWqVULbDQkJoaenJ9OlS8d+/foJpetGRkayVKlSdHV1ZYkSJYR8EzExMfT19WW1atWYM2dOTps2TSpVOCV9lUAAICeAo0hoVXkUgF0yr/NHQkvKm4l3xFL+08eXCASfBoADBw5QURSLR1wREREcPXo07ezsOHbsWEZERPD27dsWH6z3799n9erVWbZsWV67do2HDh0SGnFt2rSJDg4OnDVrFpcsWSLU9jEuLo7t27dnmTJl2KtXr49McZbo4cOHzJUrF6tVqyZVdmD27Nm0tbVlmzZthNkdO3bQ2tqa1tbWwifJgwcPmCtXLqk7IDKh7y8Aurq6CrMkWaNGDQKQanV58+ZN82hRplWlaYRcu3Zt4c9t//795j7RoiN7rVZLV1dX5syZU8o/0b59e9aoUYN16tQRdteuXr2aEyZMoJOTE5ctWybEXrt2jTt27GCrVq1YpEgR3r5922L27du3vHbtGjdu3EhnZ2f269fP4ooDUVFRfPbsGf38/Ni8eXO6u7tz/fr1X6zUxNcKBLPwcfP6mcm8zh+Agyz/6SMtgSBxAChbtqw5AFgqvV7PJUuW0NnZmR07dhTu/xoXF8fx48ebbe+it9sRERFs3749CxQoIHViBQQEsGLFimzVqhVjYmKELf+mILBq1Sq+e/dO+AA9evQonZ2d+ejRIylj2pw5c1i3bl2uWbNGmCXJVq1asUOHDty7d68we/LkSdrZ2bFZs2bC31tsbCy7detGBwcHoem/xNuuW7cu69WrJzXNMn36dFavXp2rV68WZiMiIrh8+XI6OjpKbfvy5cvcunUrPTw8LOrrnViBgYHU6/X86aefhIOBoijU6XT08/Ojj48PBwwYIFRFwPR/rFmzhg4ODsJ3JWTC3UX37t2ZK1cubtu2TZg/e/Ysy5cvz1KlSgnXakpKXysQPMKHhvMAXAE8SuZ1yQUCi/hPH2lxFlesWJFly5bl/v37hb8URVFYvnx51qxZU6r3qaIoLFu2LH/44QepvsNGo5GlSpVijx49GB0dLcWXKFGCEydOlBphGAwGFi1aVPhW2yS9Xs+CBQtKN2/X6XT09vaWmt4gE4Kwp6cnw8LCpObpw8LC6O3t/VEfXBE9ffqUFStWFObIhGPn0qVLbNiwoTS/Z88etm7dWoonySVLlrBLly7S/KhRo9inTx8p1mAw8KeffuLgwYOl+LCwMNatW5fDhw+X4h8/fsxy5cpx1KhRUvyZM2dYqFAhjhs3TphVFIVbtmyhp6enFJ9YyQWCNDmLNRpNOEnbRL+HkfysDrJGo3kOIAwJiyjLSa4Q4T881xNATwDw8PAoI1qa1qRHjx6hQIEC0m33nj17hrx580rzL1++hIeHhxQLJNRpz5UrlzT//v17ODo6SvNhYWFCpa4/VXR0tHDJ6sTSarXIlCmTNG80GmFlZSXN/y9LURRoNBrpY9doNEJRFGTIkEGaj4+Ph42NjTQfExNjcZn2T2UwGBAVFSV9/Or1eoSHh0ufPzqdDqGhoXBxcZHi4+PjERwcDDc3NykeSN5ZnGog0Gg0xwAktedjAayzMBDkIvlWo9E4IWEtYADJMyKBILHUEhOqVKlSJa7kAkGqHUFI1knhPw3SaDSuJAM0Go0rgCSTfkm+/fDvO41GswtAeQBnAFjEq1KlSpWqr6e0Gsr2Auj04edOAPZ8+gKNRpNFo9FkM/0M4DsAdy3l/68VGxuLo0ePYsyYMejbt69Q2zqSuHXrFqZMmYJffvlF2M355s0bzJo1S8p0FBkZiQULFuDvv/8WZuPj47Fo0SJhMxqQMN2wePFiKQMMSSxdulS6reD69eulOADYsWOHNLt//35p9uDBg//n2zUYDNizR+7Uev36NY4fPy7F3rhxA2fOnJFijxw5glOnTkmxGzduxOHDhyEz7T1nzhzs2rVL2MWt1+sxcuRIbNq0SbgyQGhoKHr27Inly5fj7du3QuwXU1ILB5Y+ANgDOI6E9M/jAHJ++HsuAAc//JwPwK0Pj3sAxqbGp/b4GoYykjx8+DAzZ85MAMyXL59Q167169fTw8PD3GksIiLCIk5RFP7111+sW7cuNRoNy5QpI5SX//z5c/7888/Mli0bq1SpIrQIbDQauWnTJubNm5d169a1mDPp0aNHrFKlChs3bizMarVadurUic2aNRNmyYQUVFl27969UvtMJjQOqVWrlhQbEBBA2WM3NjaWefPmFc7yMsnFxUXoeDbJYDDQyclJqpmOVqulvb29VOnrqKgo2trask+fPkJmMpIMDg5m9uzZWatWLXPPDkv16tUrZsuWjfny5ePChQuFtv3w4UNmyZKFWbNmZefOnYUSSv755x9mypSJAFiuXDmhdFURQTWUpaznz5+zadOmtLGxobOzs1BuvVar5ZgxYwiA9vb2fPr0qdC2Te38smXLJrRdRVH4yy+/EACtra354MEDIXbUqFFmF6TIQasoCufPn28+cEXbJwYEBJi7lMmkMy5fvlzaFBYYGEhHR0e2aNFCmCUT0k/z5s0rxa5cuZIAhNoXmvTw4UPpz4skbWxsWL9+falsp7Jly9LW1lYqddRkWhw0aJBw6ubgwYMJgHny5OHp06eF2F9//ZUAmDlzZh44cECIXbJkCQEwU6ZMwimb69atIwDa2Njw5s2bQqzJfGdnZ8ft27cLsZZKDQTJKC4ujpMnT2bOnDk5ZcoUnjlzhtevX7eYv3r1KosWLcomTZpw5cqVPHnypMVsfHw8hwwZQnd3d/7888/cvHmz0L5fvnyZrq6ubNiwIadMmSLE6vV6/vjjj3R3d2fbtm2FWDJhVJ0+fXr6+PgIp6Lu2rWLmTJlokajEc4rP3fuHO3t7QmAf/31lxCbuPSATN/hu3fvUqPR0MrKSviiRpJNmzYlAGFzE5nQzxYAvby8pLZt6swmY6Tr3LkzAbBs2bLCnd02btxIfOjlfefOHSH28ePHtLa2pr29vXBpjZiYGHp4eNDNzU34jsRoNLJ69eps1KgRq1WrJvyeO3XqxOnTp9PBwYFbtmwRYsePH8/jx4+zQIECbNOmjcXtay2VGgiS0MGDB+nl5cVmzZrx+fPnQqxWq+W4cePo6OjI9evXC+eW+/v7s0KFCmzUqBGDg4OFO5Zt376dDg4O3L17N0NDQ4X62JqCQN26dfnu3TvhO5gnT57Q2dmZf//9t5Qxa9asWfT19ZXq1qTX61mgQAE2a9ZMuFRDVFQUZ82axbx580rlo//111/09vamt7e3UI9oMmHA4evry2zZsnHIkCHC216xYoV5Ck90pEmS3333HTNlyiQ8sibJRYsWsWHDhuzXr58wGxISwvHjx9PR0VFogGXSrl27OGLECFavXl24V/OtW7f46NEjqWAQFBREo9HIYcOG0dvbm48ePbKYNZ3LV69eZb58+di7d2+LS3OYriGxsbEcMmQIXVxcvujdgRoIEsk0DeTt7c2DBw8K84nvAmSKgO3Zs4eOjo6cNWuW8GhaURTOmjWLbm5uUs7ixEFApo5JeHg4CxUqxN9//12YJRNKa5imz2SmKTZs2MCqVavSaDRKFUHr1q0b58yZI90M3NPTkw8fPhSuuaMoCv38/JgvXz6p9x0XF8cFCxZIG7JiYmJYu3Ztbtu2TZjV6XQMDAyknZ2dlBFSURSuXbuWxYsXF76YkwnrFN9//z27d+8u9dnJBgOTli9fTicnJ6kgGh4ezhYtWrBkyZL08/MT5s+fP/9F7w7UQMCEA2rKlCnmaSDRk9lgMHx2FyDKm6aCzp8/L8Sa+B49erBYsWLCpS1MfFqCgMFgYIMGDaQLnxkMBlaoUEFqeoL8z92AbM9lnU5He3t74dG8SVFRUcyUKZPU1AxJcyCQ1dGjR1m9enVpftmyZWlyFg8dOlTqroD8z7ScSFHGxIqMjGSxYsWkew6bgsHKlSul+MOHD9PBwYEbN24UZhVF4eLFi+ng4CAViBPfHezevVuYTyw1EDDhC5k6darwNFBifubMmdKlgBVF4bx584TnHBPzixcvtjgjKSletvm5iV+7dq105orBYOCff/4pXUBLr9cLlRT+VPHx8dy3b58USyackKIL44kVFRUlHcTIhNFlWurNBAcHC61hfarAwEDp8iAk+ebNGx49elSa9/f3T9Pn7+fnJ7xwnFh37tyRLuVNJswk7Ny5U5o/f/48t27dKs2TyQcCtXm9KlWqVH0jUpvXC4gkrl+/jlmzZkm1jbx37x6WLl0q1R7w4cOH2Lp1qzAHJNRRkjX/PHjwQKqjEwDcvHkTr169kmIvXrwo3R7wwoULUhwApGUgcePGDWlW9jNOy3bj4+Nx+/ZtKfbVq1fS3+2dO3fw/v17Kfb8+fMICwuTYg8ePIiIiAgpdtOmTVKsTqfD8uXLpfY5ODgYixcvlv6svoTUQJBIDx8+xMiRI+Ht7Y2yZcuiSJEiyJIli0VsZGQk/vjjD1SsWBElS5ZE2bJlLW5VSRLnzp1D06ZNUaZMGZQpU0ZovwMCAtC7d29UqlQJxYsXF2J1Oh0mT56MunXrwsfHR4gFgLVr16JNmzZShbCOHTuGAQMGSBWRu3nzJsaOHSvMAYC/vz/GjRsnxb5//156u5GRkRg5cqQUGxsbi8GDB0uxer0ePXr0kOp5nDlzZjRp0gTR0dHCbLZs2eDr6yvlls2ePTvKli0rFTizZcuGwoULS7mps2bNCi8vL8yfP1+oxaa1tTXSp08Pd3d3DB48GCJFMR0cHBAdHQ03Nze0bNkShw4dSlNvayklNV/03/74Ws7i+/fvM3v27ATAX375RYg9efIkM2bMKNyqkkxotpI+fXopduPGjWY3tKiX4OLFiyxSpIiUOSsuLo49evQgAA4dOlSIJRMyp6ytrdm9e3dhNiAggO7u7vzhhx+EWUVRWK9ePely0OPHj5duTLN161ZaWVkxNDRUmDU1prlw4YIwGxYWZu7yJSpFUZgpUyY2a9ZMKsPNzc2N+fLlE16XUxSFhQsXZqZMmYRNdKZy7wDYsmVLIUe1oiisXLmyubrA3bt3LWaNRiOrVatmNsGJZAkZDAZWr16dAFioUCG+efPGYlZEUBeLU9bmzZvp6OjIESNGsHHjxkIH/ZMnT1iiRAnWq1eP1apVE0pr1Ov17NmzJz09PVmkSBHh9Lo9e/YwW7ZsdHZ2Fu5RcP78eXO3L9HyAwcPHqStrS0BCNv4L1y4QDs7OwIQbjATFxfHChUqEAAHDhwoxJIJ6af4YOMXVVRUlHm/ZRbsO3ToINzL1qS//vqLAKTKagQHBxMAs2TJIpUokT9/fgLg6NGjhdnWrVtLm9FMrvnSpUsLe102bdpkvqiKmhbPnj3LTJky0cPDQ/jzun//Pl1cXOjo6Cjcve/FixcsWrQoixQpwk6dOkmnOKek5AJBqtVH/39XeHg4+vXrh6tXr+LgwYMoW7YsoqKiLJ7W2b9/P7p27Ypx48ZhwIABePv2rcX17qOjo9GmTRsYjUbcvHkTz58/h7W1tcX7vnfvXnTv3h3Hjh3Du3fvLJ7GAhKmGn7++WeMGDEC9vb2wjXSQ0ND4ezsjJYtW6Js2c/WnlJUqVKlYGtri0KFCqFKlSpCbGxsLMqUKYO3b9/C3d1diFUUBS9fvoSVlRUyZ84sxAIJ33XWrFkRHx+Px48fC03hGY1GXLp0CRkzZsSJEyfQtm1boW37+fnBxsYGz549g7+/Pzw9PYW2nSNHDmTPnh03btwQYgGgYMGCCAkJQeHChYX7OVSpUgWvX79GoUKFYG9vL7TdNm3a4OXLl9izZ49wD4VWrVohICAAu3btwty5czFjxgyL2apVq2Lr1q3w9/dHzZo1cfLkSYs/s0KFCuHgwYNInz49GjdujBcvXmDUqFEW7b+HhwcOHToEW1tb9OzZE5UrV8aOHTvg5eVl8b5LK6no8N/++FJ3BCdOnKCHhwf79OkjPJo2GAwcO3Ys3dzceO7cOeFtv337lqVLl2bXrl2l0jFNpjTR0TiZcAvbokULc8N70XTMZ8+e0cHBgdevX5fKqZ8xYwa///57RkVFSXkx8ubNywsXLgg3vifJAwcOsFq1alI+DJJs0KABt2/fLjzKjI+P5507d5gvXz6h/tImvX79mr179+aiRYuE2ejoaD59+pRZs2aVGmUGBQVxwoQJ7N27tzAbFRXFsLAwOjs7SzmL9Xo9Z8+ezcqVK0u1mXz37h29vLy4YsUK4W2TCa5qT09PqTup169fs0SJEuzZs6fUvi9cuJCOjo5pSnn+VFCnhv4jrVbLoUOH0tXVVSqv+P3796xbty59fX0ZGBgozN+7d4958uTh5MmTpXLi0xIESHLkyJGsUqWKsKGOTDgxK1euzNmzZ0ttOyAggPb29lIuSzKhxlHZsmWlvQT9+/eXKm1hkre3t3BpC5PSaiibO3cuBwwYIM1Xq1ZNOo/+7du3tLW1ZVhYmBS/bNkyVq9eXep7MxqNrFOnDidNmiS17YcPH9LJyUnaw5CWYBAZGcl69eqxYcOGUgOAc+fO0c3NjWPHjpVy0n8qNRB80O3bt1m8eHE2bdpUeFRHJpSL9fDw4PDhw6VGwydPnqSjoyPXrVsnzJJpDwJ//PEHvby8pN47SU6aNIm1a9eWNoV169ZNanHZpDp16nD9+vXSvJeXF2/cuCHF6nQ6WltbSwVQMu2BYO/evWzQoIE0/+uvv7J///7SfNu2bTl37lwpVq/Xs1ixYtJ1c968eUMnJycpRz75n/Pu3r17UnxagoFOp2O3bt1YunRpKTNqYGAgfX19Wbdu3TSXmVADAf9zMK5cuVJqZKLX61myZEnpg1mv17NcuXJpKpFQsWJF6SCg0+lYtWpV6ebv8fHxrFGjhlQZZTJhobdu3brSo8qYmBg2aNBAuECfSZGRkWzWrJn03URwcLBU1VKTXr9+zW7duknzT548kS7vQSYMggYNGiTNX7p0Sbp5PEkeO3aMP//8szS/a9euNO3/unXrpBIMTFq0aJF0IFUUhVOmTJH+/vR6PYcPHy41PZdYaiD4IEtH8UajkUeOHPmsMYUlt2dGo5HHjh1LctSc2kjaYDCkOOpJ6SKm0+lSHe0mx8fFxQlVWEys8PBw6XS3t2/fCq/PmCRbKoRMyNCQlUzhtX+T1Wq1Uk1pyITRqGxJkmfPnklPZzx48EA6YN+6dStZNrX/88qVKyk+nxyv1Wp56dKlVPctqfM/MDDQ4rvUtE4PJRcIvjlDWfr0KSdKBQUFYfr06fD29saRI0eQLVu2j55PKWMiPj4eK1euRKFChXD//v0kM4+Sy0YiiX379qFEiRIICgpKdhvJZR9cunQJZcqUSdWlmxT/8OFDVKpUSShjyaTXr1+jdu3an31OligkJAStWrWCjY2NMBsZGYk+ffoIc0BC5tGQIUOk2Pj4eGlTWHx8PMaMGSPFxsXFYfTo0VJsZGQkRo0aJcWGh4ejf//+Uuzbt2/Rq1evhBGnoB4+fIiuXbtCr9cLsxcvXkTHjh0RFRX12XOpZe/s27cPP/74Y7KtV5PjM2bMiFWrVqFZs2a4f/9+sv9/Uue/k5MTxowZg3r16uHEiRMpfl4iGVtCSio6WPoAkBPAUSS0mjwKwC6J1/gAuJnoEQlg8IfnJgF4k+i5hpZs92sZyh4/fkxPT09zIw2RueCbN2+aW1WWKVNGKHJfu3aNVatWJQBWrFhRaCQUHh7Ovn37UqPRsGrVqhZzJq1du5Y2Njb09fUVZm/fvk03NzepipiRkZEsV64cK1euLMwqisI2bdqwdOnSwixJTpgwgT4+PlLsmjVr6OzsLMUePnyYNjY2UmsM169fZ/r06aWynZ49e0YAUvPrQUFBUn4PMuHYBMCff/5ZeHQfHh5OKysr1q1bV9izERoaSmtra+bPn184U+ndu3fMlCkTc+TIwWXLlgmthb1+/ZqZMmViunTp2K1bN6H5/KdPn5o7/tWrV4/h4eFC+22p8DWmhgDMAjDqw8+jAMxM5fVWAAIB5OF/AsEw0e1+rUCwbNkyOjo60tbWVnhB8eLFi3R2dqa1tXWqt5ef6s2bN3R0dCQAnjp1Soi9efMmnZycCEC4MuL58+fp6upKAFy1apXwdk37PHXqVCE2NjaWvr6+BMCePXsKseR/WnvWrl1bmH369CkzZsxINzc3YVZRFBYvXpwApBbt+vfvTwBSmTvr168nAI4YMUKYvX37NgGwVKlSwlMLOp3O3PJRpo+uu7s7AUhl/FSpUoUAWK1aNeFg0LJlSwJg1apVhRMjevfuTQCsU6eOMGtq/1q3bl3hz3ratGnMmDEjK1So8MU7k5mUXCBI69RQUwDrPvy8DkCzVF5fG8BTkpYX4vg/UHx8PHr27ImFCxfi3Llz2Lt3L0qWLGkxv2/fPjRp0gSrVq3Cxo0bhQxWwcHBqF+/Prp3747Zs2fD19dXaN83bdoEb29v9OzZE40bNxZira2todfrUbt2bbRs2VKILVKkCHLlyoX8+fPju+++E2Kjo6Ph7u4OW1tbFCtWTIiNi4vDnTt3kD59euTMmVOIBRJqI2k0GqligidPnsTjx48BJBQWFBFJHDhwAEDC8SIq0/Y2btwoXPfH9Pp3797h4MGDQmyGDBlgZ2cHRVGkCvUVL14c2bNnh4ODg/A0z3fffYf8+fOjQoUKyJ49uxDbsWNH1K9fH+/evROuZTVkyBD06dMHt2/fxvXr14XYkSNHYt68eYiLi0OvXr2ECk8OGzYMmzdvRo0aNVClShU8e/ZMaNtpUlLRwdIHgPBPfg9L5fWrAfRP9PskAP4Abn947rOppUSv7QngKoCrHh4eXyxCvnnzhhUrVuQPP/zw2cKwJVq2bBldXFx4+fJlYfb9+/csVqwYR48eLWXs+u2335g/f36+f/9eOJU1LCyMefPm5datW6Xym+fMmcPatWszMDBQeOQTERFBBwcH3rx5k8+ePRPe9vjx4zlgwADhOy8y4X1nyZJFqq5+ZGQke/fuzcmTJ/PBgwdCbFxcHI8cOcJ8+fIJs2RCf+r69etzx44dwou3T5484dq1a6WmDsmElOn8+fNL1Tl6+PAhFy5cyO+//16YDQgIYEBAAB0cHITv0HU6HbVaLbt27cqffvpJ+NzS6/U8c+aM1LYVRWFkZCSrVq3Kbt26SaVaL168mK6urlJdCFMSZKeGABwDcDeJR1ORQADAGkAwAOdEf3NGwnRROgDTAKxObX/4BaeGzp8/z1y5cnHKlClSBbXGjx9PLy8vPn78WHjbnwYBUe3du5cuLi588uSJMKsoCps3by7dbcrf3z9NprBp06bxp59+kmKNRiM9PDykXKokuW/fPtaqVUuKJcn69etLOz3T6iPo27cvFy5cKMVGRUXRxsZGun7NtGnTpKbxyISpwFy5cvHatWtS/IoVK1i+fHmpjJmYmBgWKVJEuk3lli1bmDt3bqm1mbQGgx07dtDBwYGHDh0SZpOTdCBI6QHgEQDXDz+7AniUwmubAjiSwvOeAO5ast20BgJFUczrAfv37xfmdTodu3TpwrJly0qVOUhrEPjnn3/o4OBgUbpaUlq0aBFLly4ttWhpajkoWunUJNPdgMyomCSPHz/O4sWLS6cWDh06lJMnT5ZiSbJgwYK8c+eOFJvWQDBr1qw05fFXqlRJ2sPy8uVL2tnZSaeSyt4VkAnBv0qVKtItTu/fv08HBwfeunVLip81axaLFSsmtYCb1mBw9uxZOjk5SS3WJ6WvFQhm4+PF4lkpvHYLgC6f/M010c8/A9hiyXbTEgi0Wi27d+/OQoUKSeXNR0VFsX79+tKW8bQGgWfPntHV1ZW7du0SZsmEPGkHBwepOwmS3L59OwsVKiRt6krL3QCZUMFz3rx50nzZsmV55swZKVZRFGbOnFlqCpFMeyDYunWrVPVRk0aPHs1x48ZJ83Xr1pWqnEqm/a7g7t27tLe3l/arrF+/nj4+PlLfnaIo7Nu3L+vUqSNcHZhMezC4f/8+8+TJw6lTp0oPgEz6WoHAHsBxJKSPHgeQ88PfcwE4mOh1NgBCAOT4hN8A4M6HNYK9iQNDSg/ZQBAfH89KlSpZvB4QHBz80evi4+NZtmxZduvWLdU5+devX3/2pcfHx7NEiRKpBoHkbOharZYFCxZMsfBYSncoWq2W+fLlS7bvaWqZCnFxcXRzc+Pp06c/+rvRaLSoxn5sbCwdHR0/uhvQarUWjzKjoqKYI0cO83sUHaGFh4cza9as1Gq1UmWkAwMDaW9vn6ZA4OnpKcWSCWUSSpYsKczpdDrGxMTw8OHDrFKlihAbERFhPlY3bdrEevXqWcx+6iBfuHChxT0kQkJCPvvbmDFjLHJ2J3ccd+vWLdX+F8mdP3q9nk2aNEl2OjUuLi7JfTbJFAySclYHBwenOmX35s0blihRQiprLLG+SiD4tx5puSM4ceJEqlH51atXHDx4MBs3bvzZBfvs2bMpXsSDg4M5dOhQ9unTJ8nnL168mCwfHR3N4cOHc/r06cn+/8mNqLRaLYcNG8YNGzYky5JMMgVQr9dz0KBBFqWufjqlYzQa2aNHD4sXfROvpyiKwvbt2wvdXZjcxIqisGvXrhZzJubly5dUFEWqVIDBYOCrV684ZMgQYZZM+I5kSwRotVoOHz5cqsjh27dvOXXqVGq1WmH+6tWr/P3330kmXOxEHMp79uz5qKZWbGysxe7o5cuXc8uWLR/9LTY21iI3+S+//JLkYCcmJibV9bw+ffp8tl2ToqOjky3PoigKmzVrxvXr1yd7fkdGRiY5rajValm5cmWuWLEixQFmREQEb968meL+pyY1EFigoKAgdu3alRkyZGD69OmFClTFxMRw+vTpzJEjBzNmzCi8uLRnzx56eHgwS5YsKY4sktL9+/dZsmRJZs+eXXgxMCwsjN999x1z5swpnHlkMBjYuXNnOjk5Sd2yTpgwgbly5RLmyIRsLXd3dyl2+/btzJ07txR77Ngxuri4SLGXLl2ivb291KLnjRs3aGtrK1WO486dO8yaNatUmYm7d+8yU6ZMUhVXb926xQwZMgh7Y8iEAU+6dOlSHdgkpfPnzxMAJ06cKDwVc/ToUQJgx44dhe8ad+/eTQCsUaOG8BqYySfi4+PDnTt3pnkKKDmpgcACabVas4ll5MiRQuz79+9ZpkwZAuDw4cOF2CdPnphbRoouBvr5+dHLy4sA2KtXLyH22bNnLFCgAAGwQ4cOQqxer+dPP/1EAFKLgOvWrSMA4akKMiElMXPmzMyfP78wGx8fTy8vL9rY2AizJNm0aVMCkEoSGDt2LAFI9a9Yu3YtAXDZsmXC7OnTp6XNe0+ePDF3CROdH4+MjCQA2tnZCRc61Ol0zJw5MzUajbDZ0WAwmE2WrVq1ErrjNBqN5uoCTZs2FVocNxqNLFSoEAGwbdu2QqzBYDCbFQcMGCC1FmGJkgsE31ytoeQUGRmJhg0bwsnJCRMnTsT48eMtZkli4cKF0Gq16Ny5s3BdlxcvXuDdu3eoU6eOcA0cOzs76PV6FClSBN26dRNiPT094eXlBQcHB3z//fdCbFhYGDQaDTJkyICKFSsKsdHR0Thy5AgAIG/evEIsSbNhR6bp/ZIlS+Dv74/Y2NhU6zJ9Kn9/f7MZ7Pbt28LbNrEyhjLT9hYvXpwwghNQSEgIAGDdunW4e/euEGv6jJ89e4aNGzcKsdmyZYO9vT0iIyNx7NgxITZDhgwoW7Ys0qdPj5iYGKFm7lZWVmjcuDEcHBxQtWpVZMyY0WI2Xbp06NKlC4oWLYr06dMLHWPp0qXD8OHD8f333+Py5cuIjIwU2ufp06dj0KBB2Lx5M06fPm0x+0WUVHT4b3986TuCt2/fsmTJkuzduzcNBoPQbZmiKBw3bhyLFCnCoKAg4W5jplINJ0+eFL4VNRgMrFOnDocPH87Xr18L305u2rSJRYoU4ePHj4W3HR4eTicnJ546dUqq9EDPnj05atQoHjx4UJg9f/48CxUqJDVtEBkZSS8vL06dOlW4h+6zZ8/Yv39/tmvX7rMF89QUGxvLxYsXM3fu3FIlJrZs2cIiRYpw7dq1wtlqp06dYq9evdivXz9hNiwsjL/99hvt7e2lO+mVK1dOKsvt7NmznDFjBps2bSrM3r9/n3fu3KG9vT39/f2F2KCgIEZFRbFMmTLCDZji4+MZFxfH8ePHs0yZMkKft6Io1Ol0PH36NB0cHHjkyBGhbVsiqFNDSevRo0fMmzevVLewT4OAqF68eEE3N7dkF6dS09ixY1mjRg2pBjkBAQF0cnKScueSCTVVOnfuLMW+e/eOtra2UgufJDl48GBOnDhRig0KCmKOHDmkG+t07dpVanqGTHv6aNOmTblt2zYp9uzZs0zLeVO+fHn+/fffUuzmzZtZrVo1KTYuLo558uSRWmcgE5rx1KlTR2rO3d/f3zzYEZWiKOzSpQsbNGggFUC/VjBQA0ESunz5Ml1cXKRch2kNAiEhISxUqJB0x6e9e/cyd+7cUhdTRVHYtGlTjh49Wmrb/v7+zJkzp3R9/MmTJwtn/JhkNBrp5ubGu3fvSvF79uxh3bp1pViS/O6776RMiGTaA0G/fv04f/58KTY2NpaZM2eWdhbPnj1buqmOTqeju7u79KBj06ZNLFOmjFTw1uv1LFu2rHTwPnz4MF1dXaX8CzqdjvXr12eXLl2kAtHXCAZqIPhEBw8epIODg3DFTjLtQSAuLo7VqlWT7tb0+PFjOjo6Srft27RpEwsXLixtCmvXrp20MUmr1dLFxUXanWuaFpLVqFGjOH78eGm+UKFC0g7VtAaCGTNmSKeukmS5cuWEp7RMMpUVkRndkgmBJC1lRcqWLcuNGzdK8bJTRCZNnjyZlStXllrANU0xTZgwQWrbXzoYqIEgkdatW2dR/1NFUT4rw2BpENDpdEmmCRoMBrZs2ZKtW7dOdoST0gU6JiaGxYsXT9ZUltrBapoSSqrdpSUH+pUrV+ji4vKZqcrSC8SaNWs+GpGb5kUtVeJpIZkpMV9fXx48eFCKJcls2bJJBX8y7YFg3bp1bN26tTBnNBppNBo5YMAAzpgxQ4hN/DmJTg8l/l7DwsJoZ2dncVr1p8fE6dOn6eHhYVEmTlLH8bRp0yyaIkqKNRqNbNSoUYptLnU6XbLnc2BgIPPly8fly5cn+XxqA7IvGQzUQMCEi86MGTPo4eGRal70yZMn2bJly48CgaVB4NSpU+zZs+dnB52iKBwwYAB9fX2TrfNz8uTJZOe/FUVhx44d2bZt2yQP6CNHjqR4C5zSlNCePXtSvTtSFIW+vr6fHdAbNmywqHSAoigsVqzYR0W0FixYYPGi7afTQtOmTbOIM0mv1zNLliwMDQ3lnDlzhFgywdBjY2MjPT3z6NEj2tvbS7Em059MI5+3b99y06ZN/PPPP4UXXi9evGiu1Co6PbRjx46PigMOHDjQYmfs8uXLP0s5bdasmUWBbOrUqZ8ZHPV6PcuUKZPqFNHPP/+cZBvT0NBQ5s2bN9kSG3q9np06dUo20Pn5+dHFxSXJgoWBgYFs165dikHySwUDNRAwYUqmffv2Kc5t37x5kw0aNEiyK1NcXBy7dOmSbBAIDAxkhw4dCCDJLzwuLo49evRIsnl7XFwcf/75ZwLgxYsXk93/fv36fWYqUhSF06dPZ7p06VKsnxQbG8tBgwZ9NgJZvXo1raysUl1viImJ4bBhwz4aJe7evZvW1tYWzT1HR0dzzJgx5iB28uRJZs6c2eK536ioKHODk3/++Yd2dnYWcSZFRETw119/5a1bt+jq6irEkgkXg6FDh0qb0S5cuEA7Ozup+eI7d+7Qw8NDKghdv36d+fLl4/Pnz1MsT5KULly4wLx58zI6OpovXrwQqn565MgR5smTx1zy4enTp1ywYIFF7K5du5g7d+6PpnMePXpk0Zra2rVr6eLi8tkU3p07d1LNAlqwYAEdHBySLFN+/fr1FAPRhAkTmCNHDm7cuDHJ7/jSpUvJDl769u1LGxsbzpw5M9k75NOnT/OXX35Jcf9TkxoILFBUVJTZMFSkSBEhB2hYWJi561axYsWETvbg4GBWrFiRAIQra0ZGRrJ58+bm7YrIdIcEgIULFxZiyQSXrbW1Nb29vYXZFy9e0NHRUcpZrNVqWaRIEWbPnl2YJcnGjRszXbp0Ug7fgQMHEoBw5yqSnDlzJgFIpduanKcyJYkPHjxIAOZSESK6cOECAaQ4LZKcbt26Ze4kJzoV9/jxYwKgt7e3sCP6xYsXBMAcOXIIr4m8evWKAJguXTrOnj1b6Fx8+fIl06VLRwAcNGiQ0OL28+fPaWVlRQDSBSktUXKBQDWUJZKfnx8uXryIOnXqYMaMGUKNog0GAwIDA1GkSBGMGjUq1SbZiWVnZwcHBwc4Ojqid+/e/6+9cw+Oqsrz+OcHGAsUQkISEiBZiKGoGVA007ITNsrggBoecUZMKVqY1R0ULR/zh2vx0BUdNA5Vu1pjiajZLcCackrK+IoiMruZwjDOFOERHQoZYSGaFTXLJiQQkEr6t3/c204bOknfc9LNo8+nqqvv63vPr8899/76nHPP+QXSpqWlkZ6eTlpaGhUVFXHrAI4ePfpdoO2ZM2cG0nZ2dlJdXc2pU6cCRxnr7u5m+fLltLS0MHr06EBagFWrVgWOEBahvr6e2tpawuEwLS0tgbTHjx9n3bp1AOzatStw2rW1td/7DkIkUtaaNWsCayOB2J944gmjyGzgDWSrr68PpIlc248++oiXX345kLawsJChQ4dy6NAhNm7cGEhbUFBAYWHhd+Xbe/7Fx7hx4ygpKWHIkCHk5eUF0ubn5zN37lyys7MpKiqKGai+N8aPH8/ChQuZPHkyzc3NcesGiiFJT/EsZefOnZSVlbF27VpmzJhBRkZG3Nrjx48zb948ysvLeeCBB8jNzQ2U9sqVK2lra6O+vj6wdvfu3bz77rts3bo1cOjGCy+8kPr6el555RXGjh0bSDts2DBGjhzJPffcQ0lJSSDt4MGDWbhwIXv37g3svADuvvtunn32WW677bbA2hEjRlBSUkJeXh5HjhwJlN9NTU2Ul5dz8OBB2traAqV78uRJpk6dyr59+0hPTw9oNWRnZzN69GimTZvGt99+G3i07FVXXUVxcTGtra1cdNFFcWuHDBnCrbfeSktLC1OmTAlkc1ZWFg8++CDr168PfK0GDRrE6tWrqa6upqCgIJAWoKqqim3bttHQ0MCSJUsCaZ988kna2tp46KGHKC8vZ/jw4XFrV61axbBhw5g+fTqXXXYZV199daB0MzMzmTVrFsuWLePpp58OZLcVsaoJZ/tnoJuGduzYoTk5OVpTUxNYe+rUKZ07d64uWrTI6D3nmpoaHTdunNGEYB0dHVpUVGQ8yGjlypVxTwvck6amJs3IyDBqIlFVLS8v1+rqauPobDNmzDDShsNhzc7O1qamJiP9smXLjAPb2L41NH36dKNYCuFwWF988UW9/fbbjbSR6btN4m+Ew2FdsGCBvvDCC4G1qt79cfnllxtdq7a2Ns3Nze21z60/7rzzTuPxLps2bdLc3FyjyGYtLS06adKkuPtTgoDrI4iNjROIjB687rrrjN6v3rNnj1WkscWLFxvd3Kpex11mZqbxu9VLliwJPDFfhC+++EIzMjKMHiyq3u8OOvQ/wueff65ZWVnGbbCVlZVaXV1tpLV1BDfddJPxKPSGhgadPHmycdrXXHON0T2i6g3KMn2Yd3d369SpU/XNN980SnvDhg1aXFxs1B/U3t6uhYWF+vrrrxulXVVVpaFQyCiq28GDB3Xs2LH66quvGqXdG84RxMDGCah6UzyEQiGjB1pra6tOnDgx8MyKEd566y0dP368Ufg8VdX58+frqlWrjLS2tYHHH3/ceF7+7u5uzcvLCzybZYQ33ngjUHCVnsyePdtofiRVe0dw//33G0dnO3nypA4dOtRoGmtV1WeeeUbvuOMOI213d7dOmDAh5tiVeLCpFYTDYS0tLdU1a9YYpb1t2zbNycnpNVhUf2lXVFRoZWWlke2NjY2anZ0d8w0mU5wj6IGtE3juuee0qKjIaHBRZIDKvffea5T2V199pbm5ucYhF9955x0tKioyHllsUxvo6urS/Px83bVrl5F++/btRtNPR3jkkUd0xYoVxvopU6YY227rCKqqqgJPcR5NcXGx8Wj0/fv3a05OjvEcTU899ZTxFBW2tYLGxkbNysoy/uOyYsUKLSsrM3qYd3R06KWXXhr4td0IdXV1mp2d/b3xGDYkxBEAFcAeIAyE+jjuerxA9/vxYxz72zOBLXihLrcAGfGka+sIbJ3Axo0bNS8vTw8cOGCkf/TRR7W0tNRoyHo4HNZ58+bp0qVLjdLu7OzUwsJCo9cQVe1rA7W1tXrllVcaaVVVH3vsMatpFsrKyoyvu6pqZmbmGRtZvG7durhCNfbG4sWLjR9Iqt70GqbNmIcPH9b09HSjEKGqdrUCVe+1X5u5kkKhkNHrt6p/c6KmE+e99tprOmbMmLijAPZFohzBD4BJwB96cwTAYOAAUAikAY3AD/19qyOOAVgK/DqedG0cga0TqKur06ysLOMg3JHOYdOZN9euXatXXHGFceAKmw5iVbvagKrXJGUyyV+E4uJiraurM9JGdxSbcOLECb3ggguM/xXbOoIPPvhAZ86caaw37TCO8PDDD1vVpm688UbjJhrbWkFra6tVx/Gnn36qo0aNChx5LML7779v3Hms6rVATJw40fgPWISENg314whKgM1R68uAZf7yPvyA9UAesC+e9EwdQWdnpxYUFBg7gePHj2tBQYFu2bLFSm/6ryqiDxJCM5pjx45pfn6+cQdxRG9aGNvb2zU/P9+4k7i1tVULCgqMJz5raWnRSy65xPhfZXNzs06ZMsVIq+p10IdCIWP9nj17tLS01Fjf0NBg5Ug+/PBDvfbaa431mzdv1jlz5hjra2pqjKLhRdiwYYPVn6Dnn39eFyxYYKyvqqrSiooKY/3y5cv15ptvNtar9u4IxNtnh4j8AXhIVRti7LsJuF5Vf+GvLwL+XlXvE5E2VR0ZdWyrqsZ8gV9E7gLuAigoKPhRU1OTka1Hjhxh1KhRRlrwInMFGWPQk/b2dkaMGGGsP3bsGBdffLGx/sSJEwwdOtRYH/Qd9p50dXUxZIj58JVwOBxooE5PVDXQgL3zCdvfHnlWmJ4jHA6jqoEGavbUd3V1kZaWZqRXVU6ePGlc/lWVzs7OQOMweuo7OjqM739V5ejRo4wcOdJIDyAiO1Q11HN7v3ekiPweiDXqZoWqvhVP2jG2BfY+qvoS8BJAKBQy9l42TgCwcgKAlRMArJwAYOUEACsnAFg5AcDKCYD5Q+x8wPa32+ptr92gQYOMnQB49tuUfxExdgIRvc39LyJWTqAv+r0rVXWWZRrNQH7U+jjgS3/5axHJU9XDIpIHfGOZlsPhcDgCkoy5hrYDE0VkgoikAbcAb/v73gYq/eVKIJ4ahsPhcDgGECtHICI/F5FmvA7hd0Vks799jIi8B6CqXcB9wGZgL/CaqkZmDHsamC0inwGz/XWHw+FwJJEB6SxONqFQSBsaTuuXdjgcDkcf9NZZ7KahdjgcjhTHOQKHw+FIcZwjcDgcjhTHOQKHw+FIcc7JzmIRaQHMhhZDFvC/A2jOQOPss8PZZ4ezz56z2ca/U9XsnhvPSUdgg4g0xOo1P1tw9tnh7LPD2WfPuWBjT1zTkMPhcKQ4zhE4HA5HipOKjuClM21APzj77HD22eHss+dcsPF7pFwfgcPhcDi+TyrWCBwOh8MRhXMEDofDkeKcl45ARCpEZI+IhEWk19e4ROR6EdknIvtFZGnU9kwR2SIin/nfdtFoTk+33/OLyCQR2R31aReRX/r7VorI/0Ttm5Ns+/zjDonIJ74NDUH1ibRPRPJFpE5E9vpl4cGofQnJv97KU9R+EZHf+Ps/FpHieLVJsu82366PReSPIjI1al/Ma51k+34iIkejrtu/xKtNkn3/HGXbX0SkW0Qy/X0Jzz8rYsWvPNc/wA+ASfQdS3kwcAAoBNKARuCH/r7VwFJ/eSnw6wG2L9D5fVu/whsMArASLzRoovIvLvuAQ0CW7e9LhH14MbCL/eXhwF+jru+A519f5SnqmDnAJryofT8G/hyvNkn2TQcy/OWyiH19Xesk2/cToNZEmwz7ehw/H/ivZOWf7ee8rBGo6l5V3dfPYdOA/ar636p6CvgdcIO/7wZgvb+8HvjZAJsY9Pw/BQ6oqulo6qDY/v4znn+qelhVd/rLHXixMMYOsB3R9FWeItwAbFCPPwEjxYvMF4824fap6h9VtdVf/RNeNMFkYZMHZ0X+9WAh8OoA25AwzktHECdjgS+i1pv524NitKoeBu+BAuQMcNpBz38Lpxeq+/wq/H8MdNNLAPsU+EBEdojIXQb6RNsHgIiMB64A/hy1eaDzr6/y1N8x8WiTYV80/4RXe4nQ27VOtn0lItIoIptEZHJAbTLsQ0SGAdcDr0dtTnT+WWEXSfwMIiK/B3Jj7FqhqvGEvIwViXvA3qXty76A50kDyoFlUZtfAH6FZ++vgH8F7jwD9v2Dqn4pIjnAFhH5VFW3BrEjwfYhIhfj3ZC/VNV2f7N1/sVKKsa2nuWpt2MSWhb7Sfv0A0Vm4jmC0qjNCbvWAezbidc8eszv13kTmBin1pYgacwHtqnq/0VtS3T+WXHOOgJVnWV5imYgP2p9HPClv/y1iOSp6mG/6v7NQNonIkHOXwbsVNWvo8793bKIvAzUngn7VPVL//sbEXkDr/q8lbMk/0TkAjwn8FtVrYk6t3X+xaCv8tTfMWlxaJNhHyJyGVANlKnqkcj2Pq510uyLcuSo6nsiskZEsuLRJsO+KE6rwSch/6xI5aah7cBEEZng/+u+BXjb3/c2UOkvVwLx1DCCEOT8p7U1+g+/CD8H/jKg1sVhn4hcJCLDI8vAtVF2nPH8ExEB/h3Yq6r/1mNfIvKvr/IUbfft/ttDPwaO+k1b8WgTbp+IFAA1wCJV/WvU9r6udTLty/WvKyIyDe/5dSQebTLs8+1KB2YQVSaTlH92nOne6kR88G7uZuBb4Gtgs799DPBe1HFz8N4mOYDXpBTZPgr4T+Az/ztzgO2Lef4Y9g3DK+jpPfSvAJ8AH+MVxrxk24f39kSj/9lztuUfXrOG+nm02//MSWT+xSpPwBJgib8swPP+/k+IeqOtt7I4wPnWn33VQGtUfjX0d62TbN99fvqNeJ3Z08+m/PPX/xH4XQ9dUvLP5uOmmHA4HI4UJ5WbhhwOh8OBcwQOh8OR8jhH4HA4HCmOcwQOh8OR4jhH4HA4HCmOcwQOh8OR4jhH4HA4HCnO/wP9C4cSxhOF1QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We first define the range of the x and y values\n",
    "xrange=np.arange(-1,1,0.1)\n",
    "yrange=np.arange(-1,1,0.1)\n",
    "\n",
    "#then we make them into matrices\n",
    "X,Y=np.meshgrid(xrange,yrange)\n",
    "\n",
    "#define functions of the vector at every (x,y) location\n",
    "def Ucomp(xmatrix,ymatrix):\n",
    "    return -xmatrix\n",
    "\n",
    "def Vcomp(xmatrix,ymatrix):\n",
    "    return -ymatrix\n",
    "\n",
    "#assing them\n",
    "U=Ucomp(X,Y)\n",
    "V=Vcomp(X,Y)\n",
    "\n",
    "#Let's plot\n",
    "axis=plt.quiver(X,Y,U,V)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exner function\n",
    "def ExnerCalculator(X,Y,Uq,Vq,eps=1,dt=0.1):\n",
    "    \"\"\"\n",
    "    ExnerCalculator takes in the X and Y locations and the vector field defined by U and V and returns the\n",
    "    deposition/erosion happening at the current time.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    X: matrix \n",
    "        x locations of the flux\n",
    "    Y: matrix \n",
    "        y locations of the flux\n",
    "    Uq: matrix \n",
    "        first components of the flux\n",
    "    Vq: matrix \n",
    "        second components of the flux\n",
    "    eps: float\n",
    "        1-porosity of the bed\n",
    "    dt: float\n",
    "        time delta for the method\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    Xs: matrix \n",
    "        x locations with n-1 locations corresponding to dh\n",
    "    Ys: matrix \n",
    "        y locations with n-1 locations corresponding to dh\n",
    "    dh: matrix\n",
    "        The difference in elevation in dt time units based on the flux\n",
    "    \"\"\"\n",
    "    m,n=X.shape\n",
    "    dx=X[0][1]-X[0][0]\n",
    "    dy=Y[1][0]-Y[0][0]\n",
    "\n",
    "    #gradient\n",
    "    dUq=[ [Uq[j][i+1]-Uq[j][i] for i in range(n-1) ] for j in range(m-1) ]\n",
    "    dVq=[ [Vq[j+1][i]-Vq[j][i] for i in range(n-1) ] for j in range(m-1) ]\n",
    "    \n",
    "    #exner\n",
    "    dh=(-dt/eps)*(dUq/dx+dVq/dy)\n",
    "\n",
    "    #new Xs and Ys\n",
    "    Xs=np.array([ [X[j][i] for i in range(n-1) ] for j in range(m-1) ])\n",
    "    Ys=np.array([ [Y[j][i] for i in range(n-1) ] for j in range(m-1) ])\n",
    "\n",
    "    return Xs,Ys,dh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora corramos Exner para diferentes valores de $\\Delta t$. Vamos a usar $1,\\ 0.5,\\ 0.2,\\ 0.01$ y lo que deberiamos ver es un aumento de elevacion constante de el doble de este valor, es decir $2,\\ 1,\\ 0.4,\\ 0.02$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#We will use Exner for different time delta values\n",
    "T=[1, 0.5, 0.2, 0.01];\n",
    "for deltat in T:\n",
    "    #find the solution with Exner\n",
    "    newx,newy,deltah=ExnerCalculator(X,Y,U,V, dt=deltat)\n",
    "\n",
    "    #plot the heatmap\n",
    "    erosion=pd.DataFrame( {\"x\": newx.flatten() ,\"y\":newy.flatten(),\"erosion\": deltah.flatten()} )\n",
    "    erosion_table=erosion.pivot_table(columns=\"x\",index=\"y\",values=\"erosion\")\n",
    "    sns.heatmap(erosion_table,cmap=\"RdYlBu\",xticklabels=False,yticklabels=False)\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entonces que son esas formas tan raras que vemos en el fondo?? Floating point arithmetic error, son numeros muy cercanos pero que el computador no puede guardar con perfecta precision. Podemos verificar diciendole de donde a donde queremos la colorbar en la grafica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MvpTOcJbUf4azJDXIcJakBhnOktSghYXx2/SN4Syp99Zk1tkGM5wl9Z5lDUlqkOEsSQ0ynCWpQYazJDXI2RqS1CBHzpLUoBn88m3DWVL/OXKWpAYZzpLUoFm8Ibg2L9uXJJ0Wv0NQkhpkOEtSgwxnSWqQ4SxJDTKcJalBhrMkNchw1ppKcmGSB5KckeQHkxxNcv5G90tqnfOcteaS/B5wBvADwHxV/cEGd0lqnuGsNZdkC3AY+Dbw0qpa3OAuSc2zrKH18Azgh4AfZjiCljSGI2etuSQHgQPAduDcqtq7wV2SmueLj7SmklwFLFTVXyQZAP+S5OVV9Y8b3TepZY6cJalB1pwlqUGGsyQ1yHCWpAYZzpLUIMNZkhpkOEtSgwxnSWrQ/wE/rV70Zgls5QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T=[1, 0.5, 0.2, 0.01];\n",
    "for deltat in T:\n",
    "    #find the solution with Exner\n",
    "    newx,newy,deltah=ExnerCalculator(X,Y,U,V, dt=deltat)\n",
    "\n",
    "    #plot the heatmap\n",
    "    erosion=pd.DataFrame( {\"x\": newx.flatten() ,\"y\":newy.flatten(),\"erosion\": deltah.flatten()} )\n",
    "    erosion_table=erosion.pivot_table(columns=\"x\",index=\"y\",values=\"erosion\")\n",
    "    sns.heatmap(erosion_table,cmap=\"RdYlBu\",xticklabels=False,yticklabels=False, \n",
    "        vmin=1.99*deltat,vmax=2.01*deltat) #a small 1% range around the main value 2*deltat\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So is Exner wrong??\n",
    "Si... y no. Para entender todo con detalle tendriamos que ver uno o mas cursos. \n",
    "\n",
    "La version resumida es que Exner esta resolviendo una equacion de conservacion de material entre la cama del cuerpo de agua y el agua. Pero una de las assumciones para poder llegar a la formula de exner es que el sedimento en el cuerpo de agua encima es constante, de modo que \"nunca se acaba\" el material que puede depositar.\n",
    "\n",
    "\n",
    "\n",
    "### An \"example\" of situation like this\n",
    "Imaginen que estamos en una isla y que el agua __siempre se mueve hacia el centro de la isla__ de todas las direcciones y que esa __agua siempre tiene la misma concentracion de arena__. \n",
    "\n",
    "Entonces como el flujo de agua se desacelera hacia la isla (quiver plot), todas las partes en donde este cubierta de agua la isla siempre se esta depositando mas y mas arena, haciendola mas y mas grande.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "axis=plt.quiver(X,Y,U,V)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "135e24ee289c60ba69d5004678bf472a320b24bde767457479ce4e07bf7a1633"
  },
  "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": 2
}