Barrera rampa.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cálculo de coeficientes de transmisión y reflexión por una barrera tipo \"Rampa\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Fuera de la barrera, \n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar^2}{2m}\\frac{\\partial ^2 \\psi(x)}{\\partial x^2}  -E \\psi(x)=0\n",
    "$$\n",
    "\n",
    "de manera que las soluciones serán de la forma $A e^{{\\bf i}k x}+ B e^{-{\\bf i}k x}$, correspondiendo a una energía $E=\\frac{\\hbar^2 k^2}{2m}$. Si estamos interesados en un flujo de partículas que vienen desde $x\\ll 0$, esperamos que la forma asintótica de la solución en la región $x\\gg a$ sea\n",
    "$$\n",
    "\\psi(x)=A_{r} e^{{\\bf i}k (x-a)}\n",
    "$$\n",
    "\n",
    "En la zona de la barrera, \n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar^2}{2m}\\frac{\\partial ^2 \\psi(x)}{\\partial x^2} + (V_0 \\frac{x}{a}-E) \\psi(x)=0\n",
    "$$\n",
    "con la condición de que $\\psi(a)=A_{r}$ y $\\psi^{'}(a)={\\bf i} k A_{r}$.\n",
    "\n",
    "![](grafico-barrera.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para resolver la ecuación diferencia, conviene hacer el cambio de variables  $x \\rightarrow z= (x-x_0)/\\alpha$, con\n",
    "\n",
    "$$x_0=\\frac{a k^2}{k_0^2}$$\n",
    "$$\\alpha=\\sqrt[3]{a/k_0^2}$$\n",
    "$$k_0= \\sqrt{\\frac{2 m V_0}{\\hbar^2}}$$\n",
    "\n",
    "de manera que  $\\psi(x)=\\varphi((x-x_0)/\\alpha)=\\varphi(z)$. \n",
    "\n",
    "Aquí, $x_0$ corresponde al **punto de retorno clásico** de la partícula en el potencial para la energía dada, suponiendo que $a\\rightarrow \\infty$. Si $0<x_0<a$ diremos que el punto de retorno es *real*, mientras que si está fuera de la barrera tendremos un punto de retorno clásico *virtual*. Por otro lado, $\\alpha$ una escala de longitud efectiva, que depende del potencial. Observamos que $(a/\\alpha)^3=\\frac{2 m a^2 V_0}{\\hbar^2}=a^2 k_0^2$, de manera que esta cantidad será pequeña si $V_0$ es pequeño frente a la energía cinética mínima de un estado concentrado en la barrera.\n",
    "\n",
    "Con este cambio, la ecuación diferencial se reduce a \n",
    "$$\n",
    "\\frac{\\partial ^2 \\varphi(z)}{\\partial z^2} - z \\varphi(z)=0\n",
    "$$\n",
    "que se conoce como **Ecuación de Airy**. Las soluciones son combinaciones lineales de las **Funciones de Airy**  $Ai(z)$ y $Bi(z)$. Estas funciones pueden escribirse también como\n",
    "$$\n",
    "Ai(z)=M(z)\\cos(\\theta(z))\n",
    "$$\n",
    "\n",
    "$$\n",
    "Bi(z)=M(z)\\sin(\\theta(z))\n",
    "$$\n",
    "\n",
    "con $M(z)$ y $\\theta(z)$ dos funciones monótonas. Con la normalización usual, estas funciones tienen los siguientes límites:\n",
    "\n",
    "|     Función     |    $z\\rightarrow 0$    |  $z\\rightarrow \\infty$ | $z\\rightarrow -\\infty$ \n",
    "|       ---       |        ----            | ---  | --- |\n",
    "|    $M(z)$       |    $\\frac{2}{3^{2/3} \\Gamma \\left(\\frac{2}{3}\\right)}(1+\\frac{(\\frac{3}{2})^{1/3}\\sqrt{\\pi}}{\\Gamma(1/6)}z)$    |  $\\frac{1}{\\sqrt{\\pi}z^{1/4}}e^{\\frac{2}{3}z^{3/2}}$  |  $\\frac{1}{\\sqrt{\\pi}(-z)^{1/4}}$ |\n",
    "|    $\\theta(z)$  |         $\\frac{\\pi}{6}-\\frac{ 3^{5/6}\\Gamma(2/3)}{2 \\Gamma(1/3)}z$   |$\\frac{1}{2}e^{-4/3 z^{3/2}}$ |   $\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3}$  |\n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivando la identidad $\\tan(\\theta(z))=\\frac{Ai(z)}{Bi(z)}$ respecto de $z$, encontramos además que\n",
    "$$\n",
    "\\theta^{'}(z)=\\frac{-W(z) \\cos^2{\\theta}}{Bi(z)^2}=\\frac{-W(z)}{M(z)^2}\\,,\n",
    "$$\n",
    "donde $W(z)=Ai(z)Bi^{'}(z)-Ai^{'}(z)Bi(z)=\\det(^{Ai(z)}_{Ai^{'}(z)}\\;^{Bi(z)}_{Bi^{'}(z)})$ es el *Wronskiano* asociado a las soluciones. De la antisimetría,  la bilinealidad del determinante, y de la ecuación diferencial que define a $Ai$ y $Bi$, $\\frac{dW}{dz}=0$ y por lo tanto $W(z)=W(0)=\\frac{1}{\\pi}$. De esta manera,\n",
    "$$\n",
    "\\theta^{'}(z)=\\frac{-1}{\\pi M^2(z)}\n",
    "$$\n",
    "\n",
    "y \n",
    "\n",
    "\n",
    "$$\n",
    "Ai^{'}(z)= M(z)\\left(\\frac{M^{'}(z)}{M(z)}\\sin(\\theta(z)) - \\frac{\\cos(\\theta(z))}{\\pi M^2(z)}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "Bi^{'}(z)= M(z)\\left(\\frac{M^{'}(z)}{M(z)}\\cos(\\theta(z)) + \\frac{\\sin(\\theta(z))}{\\pi M^2(z)}\\right)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propiedades de las Airy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-08T11:29:43.009543",
     "start_time": "2018-09-08T11:29:42.071696"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4HNW5/7+z6rLaqvfeZVuW3LGxZUwxvjElF8glwQRy\nQwiQ/LghFQLBcEm7yQ0phBaSgMkllACGxDRjWxh3ybIkq7dVW/WyWvW28/vjeFZbZmZni+2V9X6e\nZx9JM7Nnzq52v+c97/ue93A8z4MgCIK4/FFd6g4QBEEQFwcSfIIgiCUCCT5BEMQSgQSfIAhiiUCC\nTxAEsUQgwScIglgiuETwOY77M8dxvRzHVUqc38pxnI7juLLzj0ddcV+CIAhCOZ4uauevAP4AYK/M\nNUd4nr/BRfcjCIIg7MQlFj7P80cBDNu4jHPFvQiCIAjHuJg+/I0cx5VzHLef47jci3hfgiAIAq5z\n6djiDIBEnucnOI67HsA+AJkX6d4EQRAELpLg8zw/ZvL7hxzHPctxXCjP80OW13IcR8V9CIIg7ITn\neZtuc1e6dDhI+Ok5josy+X0dAE5M7AV4nqcHz+Pxxx+/5H1whwe9D/Re0Hsh/1CKSyx8juNeA1AE\nIIzjuHYAjwPwZtrNvwjgFo7j7gMwC2ASwJdccV+CIAhCOS4RfJ7nv2zj/B8B/NEV9yIIgiAcg1ba\nujFFRUWXugtuAb0PC9B7sQC9F/bD2eP/uRhwHMe7W58IgiDcGY7jwCsI2l6stEyCIAhFJCcno62t\n7VJ3wy1JSkpCa2urw88nC58gCLfivLV6qbvhlki9N0otfPLhEwRBLBFI8AmCIJYIJPgEQRBLBBJ8\ngiAIF3Hffffhpz/9qfHvmZkZ5OXlobe31+Zzn3nmGfzoRz+6kN2joC1BEO7FYgnaFhUVobKyEr29\nvfDy8hK95plnnkFNTQ2effZZm+1NT08jPT0dZ8+eRXh4uOg1FLQlCIK4yLS1teHo0aNQqVR4//33\nJa97/vnnsXv3bkVt+vj4YOfOndi7V24fKecgwScIgrCTvXv3YuPGjbjrrrvw8ssvG4/ffffd+MlP\nfgIAaG9vh0ajwfr16wEAs7OzKCgowDPPPAMAMBgM2Lx5M5566inj87du3Yr9+/dfsH7TwiuCIAg7\n2bt3L773ve9h7dq12LBhA/r7+xEREWF2TVVVFVJTU6FSMbvay8sLf/vb37BlyxZcffXVePvtt2Ew\nGPDjH//Y+JycnBxUVFRcsH6T4BMEsejgXLBhqqNhgqNHj6K9vR233XYb1Go10tPT8dprr+HBBx80\nu06n0yEwMNDsWF5eHh599FHcdNNN6O/vR0lJCTiTFxMYGIiRkRHHOqYAcukQBLHo4HnnH46yd+9e\nXHvttVCr1QCA22+/Ha+88orVdWq1GqOjo1bH77zzTrS1tWHnzp1ITU01Ozc6Oorg4GDHO2cDsvAJ\ngiAUMjU1hTfffBMGgwExMTEAWHbNyMgIKisrza5duXIlNBoNDAaD0a0DAPfffz927dqFjz/+GMeP\nH8cVV1xhPFdbW4v8/PwL1n8SfIIgCIW8++678PT0REVFhVkq5m233WaVXRMXF4f09HScPn0aGzZs\nAAC8+uqrKCsrQ0VFBd577z3ceeedqKyshL+/PwDgs88+w/XXX3/B+k8uHYIgCIXs3bsXX/va1xAX\nF4fIyEjj44EHHsBrr72G+fl5s+vvvfde40DQ0dGBhx56CK+++ir8/f1x++23Y+3atfjOd74DgM0e\nPvjgA3z1q1+9YP2nhVcEQbgVi2XhlRJmZmZQWFiIgwcPIioqSvbaZ555Bp2dnfjFL34heY2zC69I\n8AmCcCsuJ8F3NbTSliAIglAECT5BEMQSgQSfIAhiiUCCTxAEsUQgwScIglgikOATBEEsEUjwCYIg\nlggk+ARBEC6Ctji0E1p4RRBLG3dfeJWcnIy+vj54enrCy8sLV1xxBZ5//nnExcVZXUtbHBIEQSxi\nOI7D/v37odfr0d3djcjISHz7298WvZa2OCQIgljkCFa2t7c3brnlFtTU1ACgLQ4JgiAuWyYmJvDG\nG29g48aNVudoi0OCIAgXwD3h/B6H/OOOxwluuukmeHp6YmxsDJGRkfj444+trnHHLQ5J8AmCWHQ4\nI9au4L333sO2bdvA8zz27duHLVu2oLa21uwauS0OH3nkEdxyyy0XfYtD8uETBEHYieDD5zgON998\nMzw8PHD06FGza0y3ODTFcotDUy70Fock+ARBEE7w3nvvQafTIScnx+y46RaHAsIWhy+//DJ+97vf\n4c4778TExITxPG1xSBAE4Wbs2rULQUFBCA4OxmOPPYa9e/daCT5AWxzahBZeEcTSxt0XXtkDbXFo\nAxJ8gljaXE6C72popS1BEAShCBJ8giCIJQIJPkEQxBKBBJ8gCGKJQIJPEASxRCDBJwiCWCKQ4BME\nQSwRSPAJgiAuAB9//DG++MUvKrp2/fr1VsXXLgQk+ARBEHaQnJwMX19fDA0NmR0vKCiASqVCe3s7\nAODRRx/Fww8/rKjN73//+3jsscdc3ldLXCL4HMf9meO4Xo7jKmWu+T3HcY0cx5VzHLfKFfclCIK4\n2HAch5SUFPz97383HquqqsLk5KSxtn1JSQn0ej3Wrl2rqM1du3bh8OHD6OvruyB9FnCVhf9XANdJ\nneQ47noAaTzPZwC4F8DzLrovQRDERWf37t145ZVXjH+/8sorZkXPPvroI2zdutX494kTJxAREQGt\nVgsAqKioQGhoKBoaGgCw/WxXr14tupGKK3GJ4PM8fxTAsMwlNwLYe/7aUwCCOY6TryREEAThpmzY\nsAGjo6Oor6+HwWDAG2+8gTvuuMN4/ty5c8jKyjL+vXHjRnzzm9/EV7/6VUxNTWH37t346U9/iszM\nTOM1F3p7Q+Di+fDjAHSY/K09f4wgCMJ+OM75h5MIVv6BAweQk5OD2NhYY2Ezse0NH3/8ceh0Oqxb\ntw4JCQm47777zM4HBgZCp9M53S853HKLwz179hh/LyoqQlFR0SXrC0EQbogbVNO84447sGXLFmg0\nGtx5550AYPThi21v6OnpibvuugsPPvggnn76aav2RkdHERISoujexcXFKC4utrvPF0vwtQASTP6O\nP39MFFPBJwiCcEcSExORkpKCDz/8EH/5y1/Mzq1cudLonxfQarV44okncPfdd+Ohhx5CaWkpvLy8\njOdra2uxe/duRfe2NISfeOIJRc9zpUuHO/8Q430AdwIAx3EbAOh4nu914b0JgiAuOn/5y19w6NAh\n+Pn5AVjY63bnzp1WFvjdd9+Ne+65By+99BJiY2Px6KOPGs9NT0/jzJkzuOaaay5of12VlvkagOMA\nMjmOa+c47m6O4+7lOO4bAMDz/AcANBzHNQF4AcD9rrgvQRDExYYz8f+npKSgsLDQ6lxBQQFCQkJQ\nUlICAPj973+P/v5+PPnkkwDYQPHyyy/j2LFjAID3338f27ZtQ3R09IXtu7vtLEM7XhHE0uZy2fHq\nwIEDeO655/DOO+/YvHbjxo3485//jNzcXNnraItDgiAuKy4Xwb8Q0BaHBEEQhCJI8AmCIJYIJPgE\nQRBLBBJ8giCIJQIJPkEQxBLBLUsrEASxdElKSjLLdScWSEpKcur5ZOETBOFWtLa2gud5xx/FxWjP\nisGew3uca8cNH62trU69tyT4BEFcXnz6KY5m+mBN7JpL3RO3gwSfIIjLCv7TT/H3qH6sjl19qbvi\ndpDgEwRx+TAyAsO5SjRmRyA64MLWpVmMUNCWIIjLh88+Q/fyJKxJJeteDLLwCYK4fPjkE5zI8scV\n8Vdc6p64JST4BEFcHvA88P77+Gv8ADYlbrrUvXFLSPAJgrg8OHsW896eOBYwhLyIvEvdG7eEfPgE\nQVwevPceNFvzsT5+HB4qj0vdG7eELHyCIC4P9u3DgRXLsCmB3DlSkOATBLH40WiA7m68EdiGKxIo\nYCsFCT5BEIufN9/E/I27UNp7Fuvj11/q3rgtJPgEQSxueB549VXUXLca6aHpCPIJutQ9clsoaEsQ\nxOKmshIYG8O+sH5sD9x+qXvj1pCFTxDE4uZvfwPuuAOH2ouxPZUEXw7O3XaH5ziOd7c+EQThpszN\nAUlJmPzwn4j41xZ0f7cbgT6Bl7pXFx2O48DzvM1NBMjCJwhi8fL++0BKCo4uG0R+dP6SFHt7IMEn\nCGLx8uyzwAMP4KDmILankDvHFiT4BEEsTurqgKoq4ItfJMFXCAk+QRCLkz/+Efj61zFsmEDdQB02\nxG+41D1yeygtkyCIxUdfH/B//wdUVeGzts9wRcIV8PH0udS9cnvIwicIYvHx298CX/oSEBuLgy0H\ncVXyVZe6R4sCsvAJglhc6HTACy8ApaUAgIOag9h7895L3KnFAVn4BEEsLp5+GvjCF4CUFHSPdqNn\nrAcF0QWXuleLArLwCYJYPHR3A888A5SVAQAOaQ6hKLmI6t8rhCx8giAWD3v2AF/7GpCUBIC5c65K\nIf+9UsjCJwhicVBeDuzbx/LvAfA8j4Oag/j+Fd+/xB1bPJCFTxCE+zM/D9x7L/DznwNqNQCgebgZ\ns/OzyA7PvsSdWzyQ4BME4f48/zzg4wPcfbfx0CHNIWxP3Q6Os1kzjDgPuXQIgnBvmpqY7/7IEcBE\n3A9qDuL69OsvXb8WIWThEwThvszNAXfcAfzkJ0BOjvGwgTfgkOYQBWzthASfIAj35bHHgJAQ4IEH\nzA6f6z2HEN8QJAYnXqKOLU7IpUMQhHvy5pvA3/8OlJQAKnPb9JDmEFXHdACy8AmCcD8qKphVv28f\nEBFhdZrKITsGCT5BEO5FWxuwaxdbUbtqldXp2flZfN7+ObalbLsEnVvckOATBOE+9PYC11wDfO97\nrBqmCCVdJUgJSUG4f/hF7tzihwSfIAj3oK8PuPZa4CtfAf7f/5O87GALuXMchQSfIIhLT3s7cOWV\nwI03shRMGQ61sgVXhP2Q4BMEcWmpqmJif999wJNPmi2usmRidgKlXaXYkrTlInbw8oEEnyCIS8bU\nG+9h9spt6Lz/Z+Af/C+b1x9rP4b8qHwEeAdchN5dfrhE8DmO28FxXB3HcQ0cx/1Q5PxWjuN0HMeV\nnX886or7EgSxOOFn53Dy2scwdPsD+Hr0fmx+7itYtQo4dUr+ebS61jmcFnyO41QAngFwHYA8ALdz\nHCdWvu4Iz/OF5x9POXtfgiAWKS0taE+6EoYTpzFzvBSv1K6DRgM8+ihwww3A669LP/Vw62FsS6Z0\nTEdxhYW/DkAjz/NtPM/PAngdwI0i11FJO4JYyhgMwAsvYGrVerw6fRtyWj9E8oZoAMxtf+utwKef\nAt/5DvDBB9ZPH50eRVVfFTYmbLzIHb98cIXgxwHoMPm78/wxSzZyHFfOcdx+juNyXXBfgiAWC5WV\nwKZNmPvzK9jhdQjXf/IdqMOs5WfFCuAf/wDuugtobjY/93n751gbtxa+nr4Xp8+XIRerls4ZAIk8\nz09wHHc9gH0AMqUu3rNnj/H3oqIiFBUVXej+EQRxIejuBp54AnjnHeCpp/DD2q8jq0CF1auln7Jp\nE/CjH7HS98XFC2V0DmvInSNQXFyM4uJiu5/H8Tzv1I05jtsAYA/P8zvO//0jADzP87+UeY4GwGqe\n54dEzvHO9okgiEuMTgf8+tfAc8+xPWgffhh9c6HIymI7FEZFyT99fp5lat5xB3D//ezYmhfX4Onr\nnsaVSVde+P4vMjiOA8/zNt3mrnDplABI5zguieM4bwD/AeB9i85Emfy+DmygsRJ7giAWOV1dwA9+\nAKSlAVotcPYs8KtfAaGhePZZ5qe3JfYA4OEB/OUvbA1Wdzegm9KhfrAe6+LWXfjXcBnjtEuH5/l5\njuO+BeATsAHkzzzP13Icdy87zb8I4BaO4+4DMAtgEoB4kQyCIBYn584Bv/0t8O67wO7dQFkZkJRk\nPD0zw4x9e7wQ2dlscvDYY8CN3/8cG+I3wMfTx/V9X0K4xIfP8/xHALIsjr1g8vsfAfzRFfciCMJN\nGB8H3ngD+NOfgI4O4BvfABobgbAwq0s//BDIzDTbtEoRjzwCZGUB00Xkv3cFtAEKQRDKmZtjZvrr\nr7NA7ObNTJWvvx7wlJaTvXuBO++0/3YhIczCf6TyMO7f+qzj/SYAuCBo62ooaEsQbsb8PHD8ONuB\n6q23gIQE4PbbWfniOLEMbHN0OubdaWtjAm4vPSNDiP2fFHy2cwBXbvJy4AVc/igN2pKFTxCENcPD\nwMcfA/v3M39MfDyLuB49CqSn29XU/v3A1q2OiT0AnOj6DLmBV+CpJ73w8ceOtUEwSPAJggCmp1kh\nm8OHgUOHWHbN1q3AF74A/OxnzKp3kH37gJtucrxrh1sP48tXbMOLz7OJxhVXON7WUodcOgSxFJme\nBs6cYQJ/+DAT++xsYNs29ti6FfD3d/o2U1NAdDSL5YpsTauIlc+txEs3vISKD9bhrbeATz5xuluX\nHeTSIQiCwfOsTsHJk0zYT50CqquZwBcVAf/1X2yVU3Cwy2995AiQl+e42A9PDqNV14rCmEIU3AX8\n9KfsZWzY4NJuLhlI8AnicmJujpnTFRUYOnkY7Z/9E+ktw/APCodqwwZg/XoWbC0sdIkFb4uDB9kW\ntY5yovME1sWtg6fKE1ABP/whE/1//tN1fVxKkOATxGKE59kesLW1rDBZRQV71NYCsbGYycvBX6eP\nIPm2G/BiuB6dAQa89x9vgpPZTepC8OmnbD2WoxxtP4rNiZuNf999N/DUU0B5ObBqlQs6uMQgHz5B\nuDMzM8wdU1cH1NcDdXXQl9QBdXXgVZ7wK8yGd+EKID+fPVasAAIC8P1Pvo+R6RG8uOtFzM7PouCF\nAvx8+8+xK2vXRev64CCQkgIMDADe3o61seWvW/CTrT/B1alXG4/95jfMrfPmmy7q6GWAUh8+CT5B\nXGp0OkCjAVpaFh4aDRP6jg6WIZOdDWRnYzQuG19+MhsP/D4LxVXhOHOGBTFNDXf9tB4pv0tB+b3l\nSAhm2TVvVb+F3576LY597dhFe1n/+AerhyNW214J03PTCPufMHR/txuBPoHG4+PjQGoqW/9l78rd\nyxUK2hKEO8DzzMTt7Fx4tLaaC/zsLFOwlBT2My+PpUOmpLAiZD4L9WN+8WMg9lZgxx3A1XPAypXM\nbWLqJ3+//n1sSthkFHsA+GLOF/HtD7+NpqEmpIfal0fvKAcPAldfbfs6Kc50n0FWeJaZ2APAsmXA\ngw8CP/85W8FLKIcEnyAcZX7eTMzHWupRV34AmRP+COofYce1WhYcjY9nj4QEIDER+OIXF0Q+PNzc\nRJdgdhZ46SW29glglQweegh45hlzwf9HzT9wa+6tZs/1UHngltxb8EbVG/jxlh+78l2Q5NAh4Jvf\ndPz5R9uPYnPCZtFzDzzAxsLmZvaTUAa5dAjCFJ4HRkaAnp6FR28v0NOD0aYetJ7sQYJnD0KmepjY\nBwcD8fEwxMfh3bESjEeqUerRiz13vITQjJVM5F2UDfPBByxD5ZiJV0avZ7fo7ASCgtg2gHG/iUP7\nd9oR4mu+tPXzts/xwAcPoPK+Spf0R46+PlYsbWhoYQMTe7nh7zdg98rduDXvVtHzP/kJ+/e8+KIT\nHb1MIJcOQQDMCh8aYuJs+RgcXPi9v98o7PDxYauFoqLYz+hoGCKj8ZvTGYgujMbbR6PwP3ujsera\nSMCL1XZ5rfJveOGMHkfuOoLyT76LJwyf43eZt7j0pXz4IXCjxW7RQUGsftlHHwG33QZ82vIpNiZs\ntBJ7ANiUuAn9E/1oGW5BqjrVpX2z5ORJlgHqqNgbeAOOdRzD8194XvKaBx8EMjJYcTUnFgIvKUjw\nicXB/DyzvHU6YHgY/NAwmkp1iPUbxrKZYTPxHutqw3BnIyInVfAZm2RFXMLDrR/R0cDy5aycr/B3\nVJSoRf7+PmB/FHBqHzD/HPD4i8B7/7Zw/vnS5/GDTT8Ax3F4aONDWPncSvzi6l/Az8vPZW/BRx+x\nQKglN93EytDfdhvwWdtnuCr5KtHnqzgVtqdsx8GWg0hdfWEF39kSCPUD9QjxDUFsYKzkNWFhwH/+\nJ9tY63e/c/xeSwkSfOLiYDCAHxsD9Hpwo6NMuM+Lt/Fh+rfl76OjQGAgoFYDISHoGFOjvkONCt8Q\n3HiXGl7R4UBGBuZD1bjnyH9h29p78b+Nr+Bf95cgIzLb6e6//DLbao/j2AbbjzzC3BaRkUCnvhO1\nA7XYkb4DABAfFI/CmEJ81PQRbs652el7A8xXPTbGgrSW7NrFFiTNzzPBf3andBnhq1KuwoGWA7hn\n9T0u6ZcUx48Djz7q+POPth/FpoRNNq/77neB3Fz2/1Cyk9ZShwSfkGd2ljmKTR+jo9bHzj9mB/Vo\nPqtHlL8eao+F6/ixMUx6AWO+KoRGJsFTHWYUb6jV7BEZyXa7EP42PRcUxPa9AxO+wmTgZBX7wnen\nAd/+Nuvuv+reQ9twAr7xld+g7aAfnjv7In5z3W+cegvGx1m5mb/+lf3t7w/s2AG89x5wzz3Ah40f\nYkf6Dnh7LCSb70jfgU9bPnWZ4H/6KXDtteKx3ZgYJnbHy4bRNNSE1bHSO4RvT9mOhw8+DJ7nL9gi\nrNlZtuHV+vWOt3G0Q5ngR0cDX/kKy83/peQu2oQACf7lwtwcU6axMdmf/OgY6svGEeE/hjCfheNT\nukF0dNciBoEImOXY8dFR9u0NChJ/BAYu/J6UBAQF4S+vB6E7LggnqoPwyrtBiM5g1zxe8iu0j2vh\n4+GDEN8Q/PIax7+d77zD3AXp6UzoH354QfBfr34dd626CwBw16q7cOVfr8Svr/01VJzj2zd//jlb\n1alWLxy75hqWdnjPPcCBlgPYmbHT7DnbU7bj9rLbHb6nJSdOAJtk9G/zZuD/Pj+G9XHrzQYeS5JC\nkhDgHYDq/mosj1zusv6ZUl7Oko+cKc1zWnsaD214SNG13/8++//84Aeim20RJpDgX2h4nq2WnJgA\nJicV/xztm4CmZhI5SRPwmmXHDeNj0HRWIXBOhUiDn7mgz86yBOWAANmfNW0BOHB8GYbn4vCjJ5fB\nL4Id/2nJL2HwW4Hjw5XYf08x/NURTMj9/BSlDALM8/LD77JSLkP/DfyxGPjv7SwA95dzr+CjOz6C\nv5c/1r+0Hj/b/jN4qDwcekv/+U+W1Qiw2l9tbUB7OxAbP4dPmj/Br6/5NQAgIywDIb4hONt9Vtbq\ntcWhQ8D27ebHtm5lWSI8DxzrOIZfXP0Ls/P50fkYmBiAVq9FXJDtTUJsceoU8J3vSJ+/8krglyUn\ncUuBbcf5poRNONl58oIJ/okTzvnv9dN6dIx0IC8yT9H1Qpbr738PPPGE4/ddCiwtwZ+fZ2Vhp6bA\nT06Bm54y/j05OgyPmVl4zxpYTdephXPGh4Q492omMDk8iaSICXDnj0+N6WAYH4PfLMB5eDA/gJ+f\n4p9vvuOPzsEgNM/74+Yvs+MHuj7Hv7pa0Tjdhee+9AekxC9fEHRfX0XC/OV84NdvshWQL6qAB+9g\nPuhnGxvR8Z0O3PrWrXh7phy7o3fb/fZ+9BETnogINs3+z/8E/vu/gfKecgR4BxgFJi4wDsc7juPK\npCvtvofBwCzrP/yB/e3pyar5HjoErLi2AtEB0WYCe23atfi05VOnBP/4ceDJJ82PCbnfx85pMTM/\ng5SQFLPzKk6FbSnbcFBzEHfmO7C3nwkjI2zBbZ6M/l15JXDvkTMojLGd+L4+bj1Odp7E1wu/7lS/\npDh1ynqAtIczXWeQH53PCqYp5Ec/YhU0v/tdZqcQ4rin4L/1lpnQzo5Ooa58Cjmp0/CcY8d0uh5o\n+5qRG5QKbmraWpxNH8K5uTnwvr7QT/tiztMHobG+4Hx9MevticrhGqj8/LA6eRNUfn5MQE0fPj5M\njCMi2M/zwqyb8cf93/KDj9of/77DD/++2x/TXiqs/dsWFOXcDO3cEN75yvt2vfyKCuCJ14BjtSxI\nt3M/u/0jL/4Kv7jvtyhuLcYfJ4rx6+Qv2NWuRsOyDrdvZ+PV00+z1Lb9DfuxM2Mn/L388aW8L2Ff\n/T7szrdf8D/5BLjuOvb7mjUsy7GjAzjQdgDXpC6sDNqRvgOHNIccEvyaGjZtj45eOLZtG1tmr885\nZrVQZ33cerxb967d9xGYn2f/j8JC8+McB2zZArx+pARrY9eK+sM3xm9EibbEacEvKWH3l9kyFsnJ\nPGYiziCWX2OzvfXx6/H8Gel0R2cpK2NBZEcp6SrBmhjbr8OU9HQWV3n2WSb+hDjuKfhvvmkmtkdP\n+OLYGR9oN/tix40h4H188JuT70AbMoTbCtfgurwbrAVaEGnTv7288MILHN57j7kA/vAH4KqrgKcO\nP46+8c0o7y3Hjzbdjxuzb7Tdx/O8+gcg8N/Z7m8/+xnw7z8DDjT8C6HJ2fj5zc8g/jfxGJwYRJi/\ncufivn2sgm1CArPqDh8GCjb3onmoGUXJRQj2Dcbd792NX1/7a7ve1o8/ZoKsUrEl77ffzrxBBzUH\n8W8ZLMdwe8p2PPTxQzDwBrv93keOMAsLYPHVzZuZdXzMcMxM9DYnbsbvTjmWRyeW7rduHVttOt15\nAtelXWd+Lm4dHjn0iEP3Ali9sqgo8e35Nm0CXtKcxk3L14k+tzCmEG/Xvu3wvQVOn2avUY7O0Q54\neaigrYsFbNSXWRm1EpphDUanR63KFjjL6ChzsTlT46a0qxQ3ZN1g9/MeeYQN/t/+Npv0EtY4Hsm6\nkLz1FvDqq8Cf/oTZ3/wBt2h+hW1Hn8KXqx/F7IPfw/EbC/H2JjVu/dk+PBFRzfLSrrmGzWvXrmUV\nAzMymHMvMpLN8by9AY7D22+z5d533sluAwD/avwXbl9xO25ffrvd1uAHH7DbX3stcO4cW+Pzacun\n2JG2AwHeAdiYsBGftX1mV5tHjrAPLsDaLS4GiluLsTV5K7w8vLAmdg26R7vRM9ZjV7snTrC3CGAT\nlBUrgNJS5oMWrO24oDiE+Iagtr/WrraHhtjapWyTDMgNG4DjJ3ic1p7GurgFxboi4Qqc7DwJA2+w\n6x6AuLX6xtLyAAAgAElEQVSdl8fSFiu6K1EQXWB2Lj00HfppPfrG++y+F8A2hVot4Q1atQrQzJzG\n2ti1oucLogtQ2VuJecO8Q/cWEHvNVv3sOoNEz9UoK7Pt1vP28EZ+dD5Kukqc6pcYFRVsaYOXE3uN\nl3SVSL6ncuTmMiPjT39y/N6XO+4p+CYcP85KjmzaxPS7tBQ4pDmEnek7sT1lO6r7qzEwMaCorakp\ntgKwqIhN/4qLgcGJQTQNNWFj/EZcl3YdiluLFffNYGDL3IuK2Ad83Tomqp+1fYai5CIAQFFSkV1t\nzs0xH6iQkbFhA2uzvKfcOM1VcSqsjVuLEq19X1hLS3HjRuDj492Ympsy80GvjVuLM91n7Gq7tJSJ\nkodJHHbdOuBYpRY8eCQELSyFDPULRYhvCFp1rXbdA2Cl3y1z0X18gIycKbQMtyA73DznnuM4rIld\nY/d7JSAn+CtW8NAvK0NBlLj7Idg3GNEB0agfrHfo3gJVVUxE5SjrLkNBzGqUlSlrc3XMapztPutU\nv0T7USb9fimhf7wfw5PDyAjLcOj5P/4x8Ktfse86YY3bC/6JE8xXCiz4aj9r+8zM2lX6Za6oYIZ/\ncDCzCjs7geKGMyiILoCXhxcywjIwMj2C3rFeRe01NLAFmkIq2BVXAJ+fmEb9QD1WRbPdGdbHr0dZ\nt8JvIZgLITZ2IaVt3TomOhW9lVgZtaB062LX4bT2tOJ2x8fZVNs08JefDxzXnEFhTKGZD7owutCu\nPgNsdpOfb35s+XKgdrAaKyJXWPm4V0SuwLnec3bdg+eZ4K9YYX0ueW0twlRp8PH0sTq3Nnatw9as\nnICNq7qh4jyg75Ze8VMYY/97acr0NCuomZUlf925vnPYlrMCZ86w98kW+VH5qOitcLhfUpSV2Z6N\nyFHaVYrVsasdTqMtLGQzr5dfdrwPlzNuL/ilpSwACDBvzZkyHmd7zhqnfOvj1uOU9pSitsrLgYLz\nM35PT/bh2H/2DFbHsG+0ilPZJQ5nziz0DWAftOON1UgLTTMuqc+Pykdlb6Vi90VFhblwCmuPyrvM\nBT8/Oh9V/VWK2gTYQJKebh74y8sDGnTVWBlpbjKvil5ltxjU1lr7bSMiAC6yBgl+1g7dFZErcK7P\nPsFvb2dJSeHh1ueC0ivhpxdZhgrms67qU/5eCfA82/pVyrqu6a9B6FweKmTeqoLoAqcEv6GB5bT7\nWI9jZlT3V2NLTh7m54GuLtvtropehfKecof7JcWZM84JviMBW0sefZQtwpqddaqZyxK3F/yzZxc+\nQPn5QFljFzxVnogKYFZVQXSBYnEqLzcX0xUrmJAK1jgA5EXkoW6gTlF7tbXmFvOKFUDt4DkzYVb7\nqaH2U6NluEVRmxUV1i6LtOVD0E2NICkkyXgsKyxLcT+FvloKcnY20GeoQ0aoufmYHZ6N+gH73BA1\nNeKBuqDUGgRO5VodXxFlv+CLuXME5sLOYbpd/GROeA5qB+yLSQAsJsHzLAwkRnVfNVIC8lAuo5vL\nI5ejpr/G7nsLKHHnTM5OolPficywDKxcyWZbtsiLzEPTUBOm56Yd7pslExMslmKrv3KUdpVibZz9\n/ntTNm5kM6LnnnOqmcsStxb8mRnmdkk9X+cpMxPQzlUiN2xhTp8TkaM4wFhTYy7QeXlAx0QjMsMy\njccywzLRMNigqL2GBtYngdRUQOfRiKSATLPrcsJzFLfZ2Gge+ASAsJxziMRys2luRlgGNMMazM4r\nM2Pq6qzbDQwEPCLrETRrLvhxQXHQT+uhn9YrapvnxQcUAEBELQy94ha+vVa3lDsHAHpRiaG6FaLu\njMywTLQMt2DOMGfX/YTXJLW8obq/GqvicmUFNjci16HBRkCJ4NcN1CFNnQYvDy8sX85mJbbw9fRF\nqjrVqcHIknPn2GfM1mxECp7nHQ7YWvK//8v2vh0cdLqpywq3FnyNhqUmChF/Ly9AnV6PWK8FizEj\nNAOtulbMzM/YbK+5mbk1BHJzeQxzjWYBInsEv7GRxQQEPDyAZYmNWDZlHnBKD01H01CTojabmsz7\nCAAecZXwGzVXOl9PX8QGxkKj0yhqt65OXJD50HrM9ZiPBCpOhYywDMXvQ08Pe+0RERZt8zxGvGug\na7S28LPDs9Ey3GKXhVlfL53u16Kvh6cuG30iyTh+Xn6IDYxF81Cz4nsBMoPYeWr6a7A5Mw/1MpOh\npOAkDEwMYHR61K57CygR/Or+auOq1Lw89hwlOOK6k8NZ/712VIt5wzwSgxOd7kteHqseumeP001d\nVri14Dc1mQsqAPjGNcJ/akERfTx9kBicaFNQJydZ9dz4+IVjoQn9MMx7ItQv1HhMqeDzvLXgs0Yb\n4TFiLfiNg4022zQYrAclAJgLasS01rriY3Z4tl3uJ0sLf2BiACrPeWjrrX0WWWFZit06tbUsJc6S\nvvE+eHpwaD4XYXXOx9MH8UHxigcsQOL9BjA1N4XesV7kxCShQeJf54hbR2qQBNhgVt1fjatX5qGj\ngwVXxfBQeSAzLNMu95spigS/rxrLI9hFeXnKLHyAxZdc6cd32n+vLcHaOPFFbI6wZw/w+uvK34+l\ngFsLfmOjtfgZ1I3ghsy/9anqVJspfi0trL6Xadqg3rMJGErH2NjCsbigOOimdDYtsq4utrjDtEAU\nz/OY8GvEpNa80xmhGWgatm3hd3czN0ugxVqYMU8NBhqs65crFeW5OTaQZJp7mlA/UI9Y7yzU1Vl/\nweyJEUhZwrUDtcgOz0FDvfgX2J6ZDyA++wGA5qFmJIUkITvTU9LazglX7voTEBskBfon+qHiVIgN\niUBSEnt/pciNyHXIdTI+zj4Ttrbws7Twa2qY8WALVwdunbXwXRGwNSU8nIn+N7+p7P1YCri14ItZ\n+BM+TVaCmhySbFPwxfa+bBpqROBMBlpNniq4MxqH5C3yxkZrAe0d74W3ygc9GrXZcaXCJiVo2skW\nQJeCAYvlBkot/LY2Fni03NejfrAe6aFZaBGJJ2eFZynOH29pERclzbAGWZGpmJlh9WAsSVenK3az\n6HQst1qs5nnjUCMyQjOQmQlpCz/CtRZ+y3AL0tTsRWdns2ulyA13TPBraljw0cNGjbnq/mrkRTDB\nDwlhj7Y22+3nR7PUTFdsKTo3x94DqRiLElwRsLXkm99k5TFoG0SGWwu+pYVv4A0Y4TvR32zu41Mq\n+JZi2jjUiEjPDGgsvAqZYZk2LeeGBuvBqGmoCQnLMqysveSQZLSPtNsMsIoJPs/z0AxrkKJOMRuY\nACgamAD25U9Otj7eONiIFbHWrx9gFr5SH35bG1sUZ3V8pA1JwUlITYXooJIWmmZ3bENstt84yAQ/\nKwuSFn5GaAaah5X78KemWC2gpCTx881DzcZtArOzpe8LODbYAOwzZiv/fnxmHF2jXUgLXRhxlbp1\nIpdFwsfDB12jCvI4bdDYyNaPOFrSgOd5JvguCNia4uHBVt4+9hjbT36p49aCbymAfeN9CPIOQVuz\neRpAckiyTV+wuIXfhOTAdCvBS1fbtshFB5DBRmRHZFiJm4+nD2IDY9E2Im92ifmoe8Z6EOAdgLT4\nQCvBTw5JttkmwAqYiQlyu74dKxOS0d9v7YNOUacoXgnb3i4ujG0jbUgKYYIv5vJID01X5OoCpP33\nAPs/ZoTJC36qOtWuoG1bG4v3SFnXphZ+Vpa8hZ8RmmGX60pAasZnSt1AHTLDMs0qSyrN1AEcdzdZ\ncu6cc+mYzcPNCPAOMKZbu5K8POCBB4BvfEPZorTLGbcV/Lk5JlSmlqlWr0V8cBxaW819co66dFqG\nW5AVlWol+EkhSejQd8i2JyaiGp0GebEp0GqtF30oCdxK9TFFnYKkJOtpenxQPLpHu23OHNrbxQW/\nY6QDSeoEJCRYt632VcPAG6Cb0sm2DbDnigq+zoaFr05TLMJi8RzjufMunbQ0WH02BGICYzAyPYLx\nmXFF99NoFtKBxWgeXrDwbQl+WmgaNDqN3TV15AY5gYbBBmSFmU8D7MnUcZXgV1U5584p0ZZgTazr\n/PeWCFtSPiu9++OSwG0Fv7eXlSzwNtm8p1PficSQeISEsGCWQEqIbWtUo2ErFk3p1HciPznBSvAT\nghJsCn5np3nGj9BecmgCYmOZyJqSFJyE9hGLgxaIWcoanQap6lQkJ8PKwvf28EZUQBS0o/JzVSnB\nbx9pR2JwIlJSrAWZ4zgkhSShTSc/g5icZP5503LFAoKFn5YmLvgp6hS0jbQpyo+Xs3YFC9/Pj61K\nFltpquJUSAlJUZwV1NIiL/gtwy1GN0p6unzQ1t/LH+H+4TY/U5YoFXzTdSTApbPwnfbfu9idY4q3\nN/DaayyIq3QwvBxxW8HXaoE4i42CtKNaxAXGISUFZiIduSwS4zPjGJsZgxg8zwQ6YaF+F2bnZzEw\nMYBV6dFWYpQYnGhTnC3bA5jgxwfFW/UPcHwQaRluQWqIuOADymY37e3WfZ03zKNrtEv0/RRICk6y\n6TJqb2d9Vll8kuYN82yADk6UdOn4evoiOiDa5nsNSFvcM/Mz6B3vRXwQe+PEBi8Be9w6LS3WBoLZ\n+eEWo4UfGclcYmKBaQF7M5IAZS6dhiFrwRdiCkoyU3IjclEzcOkFv6SrxOUBW0syMlgR3tBQ29de\nriwqwRcENS7OPABjyxrV65kgme6E0z3WjchlkchI87QSUkHwpbIXDAb5/sXHM/E2JSE4AZ16i4Mm\nzM6ypfwxMebHNToNkkOSRV06wHk/vg0rXMzC7x7rRrh/OHw8fWQF39ZgIuXO6R7rhtpXzVZ0Srh0\nADY70wzbtrql7tMx0oG4wDijD1vqtQBM8JWWuJBz6UzOTmJgYgBxgewDwHGQHNQEMkIzFK3FEBga\nYm5Ny8VsljQMNiAj1HwaIGwzrCRImRuRi+q+aqcydcbH2azK1mxEinnDPM72nL2gLh2BHTtYcHmp\nsqgEXzuqFRV8QF6cOjulxTk4mM0ATK2zYN9gcOAwMi1usvX3sy+Ur691mwlBzCduJfg2LPzubmYp\nWu5q1DHSgcTgRKOFb/m9tGWF87x4vEFw5wDSIqnEpSPnv08OSQbA4jCdnUzARO9hYxYxO8tcfJaz\nHwBo1bWa1RiSE/w0dZpiwZdz6Qj3NN2TV25QA84LvoKMKgG5rCQBnufRONhoZeEDkA1gmxLhHwEV\np3J4vwCAuY+ysuR35JKjdqAWMQExCPEV2WWGcCmLSvA79Z2IC4wTt6CDpC1oKX97fFA8OI65Ozos\ntFjOrSPWnn5aDx48gnyCEB9v3V58UDw6RqQFv6PD2u1i2s+QEDZLGR42P2/LpTM8zL6Ilvt8KhF8\nJVlAUvEBwX8PMP9pZKS4xakkttHZyfLvxTbVaNW1GgcWwLaFryQ1k+flXTqmAVuBtDR5C99el44S\n/33/RD88VB6iu6kpFXyO45z24zvtzrnAAVtigUUn+FIWfnxQvGTwUquVFnwAogJtr+AvDCCcrEtH\nauos1ibP82zWEMxGgqQkaz++LQvfVsBWaNcyyCy07ahLR8jQEZCKQSiJE0itIwDOC37wwklXuHSG\nh5llrVaLnzdNyRSwJfhK10wIKPLfiwRsBZQKPnDerdPveP0BZzN0LnTAllhg0Qg+z/PQ6rWIC4oT\nFfy4oDhZC19s8BB2YRJzwSQGJ0pa5HKCD0BU8AO8A+Dj6YPBSfHyfWIWvm5KBxWnQpAPM88TE60H\npqQQeVEWC9gCC64igFnfej3LuLFsW4kYS+bgKxD8xOBEm26j1lbpBVCtI8otfGFtga29CQR3jpQ7\nxXTRlYAtwU9Tp6FV16o4NVOJhS8sOBPDXsF31sJ3Jgf/YgRsCcaiEfyR6RGj+ElZ+I64dABxl05C\nUIKk2Im11zHSYdaepeALbUoNIh0d4n0UrHuACb6lJZ4QlACtXispYpIWvr7dOOCpVKzPlm1HLovE\n2MyYbO66rOCHKLDwFQ4qUha+aawAYK+jr0+8mJm/lz9C/UKh1ctHM21m6Ojst/D9vPwQ4R+hODXT\n0ZRMgYst+I5a+DPzM6jqq7Lai5i4MCwawdfqtUZBjY1lQU5T74i9Lp0OfYesS0cuq0ZyAAlkB8PC\n2GYQExP2tWlpiZv2ERAfmPy8/BDkEyQZdJNcZWvi0gHYNZZZQCpOJTvwzc2x7AyxGYSYS0fM8k4M\nTkSnvlPW6pa18C18+J6e7HMj5qIClLl1bC66ErHwExPZZ3JGpkq30qqpgOMpmQLJyaxsteWsTQxn\nBL+vj71myxm0Uip7K5EWmoZl3g7WZCDswi0FX69nqY+mgcZOfSfigtinys+P1ewwLSYWF2i/S0fO\nIndmxsBx7H5WbQbGS1p4kha+yebfYoIPyLuflPjwAWk/vlzaZ1cXSxs0XRwHMPebZfaMlIXv6+kL\nta8a3aPd1ifPI2XhCzn4wudCwNnArZyFb+ANxsVwpnh5sf+52GsUUJqpozQlUypDB2ADX2oqmynY\nIiYgBjPzM+gf77d9sQWCde9oReMSrWs2PCGU4ZaCL1j3ph8iISVTwNKtE+IbgjnDnGhZY0sLf84w\nh96xXsQEsqR3MSG1W/BHO62scbHArVxcwMrCHzG38MVcOkK7UgFmMR/+2MwYJmYnEO6/sDmsmIUP\nyAdVpdw5AxMD8PX0NcYeACagUmJoy60jdZ9OfSdiAmLM6sgI95L04yvI+5dLyewZ60GwT7CoRSq1\noth4PlRZKQklKZkG3oCmoSakh0pPAy5Gpo67r7AlzHFLwe/qkk7JFBBbfCXm1pmcBMbGzDe+7h3r\nRZh/GLw9mGkqCL6pi0iYMVhm1Qirdm3526VSR8Us/JkZNluxLE/QOarQwg+SzigSs/CFgK3pRhOS\nmToyQWElKZkC8fHM5SGaix8sne8/Py8+GALW7hwBWxa+rfIKci6d5qFms8qUpihJzVSSFqrEf9+p\n74TaT40A7wDJa+zx4zu67+9iWGFLLOASwec4bgfHcXUcxzVwHPdDiWt+z3FcI8dx5RzHrRK7RkAu\nJVNANFNHxK2j1TKfv6m1ZNlWYCCbApvmuC/zXgZ/L3+rrJrBwQWXklz/pOICYoLf3c3yzMUWXVm+\n5p4ea9GUanduji1YsnwvLd05gLSFnxicKOmGUpqSCTC3T1SUeDBbbhbR3c1iIpaL3ADHBD9FLV9P\nRyjaJxUzMC2pYImSTB2l+yI4E7AVsDdwa+8GMYBzKZnjM+NoGmrCikgnRgzCLpwWfI7jVACeAXAd\ngDwAt3Mcl21xzfUA0niezwBwL4Dn5dqUq6MjEB+vLFPHVg6+gFI/vph1PzYzhum5aah9FxK3JS18\nEZeOmP9e6KfprMHLi/l1uy3c3VJrBrq6WMql5YKl9pF2JAaZC76UhS+3HkFpSqaAbKaOhIVvT8BW\nQM59ZMul09nJ3jOpjbibh5uRGuKg4Ieylb620kLlKoMar5FJyRSwy8J3oGa/wcBW2Tqaknm25yzy\nIvPg4+ngrueE3bjCwl8HoJHn+Tae52cBvA7gRotrbgSwFwB4nj8FIJjjOMnC10otfEcF2tI9BCj3\n44u1J2QQmbpIpAYQ7ah1CqWYy8K46CrI/ITUqmAxK1wyB1/fYTaQCO1qtcyFYtm23YKvs3bpAPKL\nr9r10veQXXQlIvhSGUEAEBsYi8HJQUzOiqev2MrQMa2SaYmtejoB3gEI8gmSDVADzqdkCgiCr6RM\nTk54jt0+fI2GFSIz3ebTHihge/FxheDHATBVm87zx+Su0Ypcs3BSzMLXywdtgfOCapFjbStDx/hc\niXIIYu0pmTGIWfh+Xn4I9A7EwIT5XoVSi648VB4I9DHf4FYsXz4hSDxoqzRDB2AWbWio9ewhLjAO\n3aPdoguG3NXCj44GRkdhtlexgIfKA4nBiZJxCVs5+GJlFQSEoK2cwKaFptn04zubkikQFsZmd30K\nyuQkhSRheGoY+mm97YvP43TAtpsCthcbB8sdXVhOn96DsDD2gSoqKsL6TesxNjNmllUi5cP/sOlD\ns2NarbXFph3VIj863+yYMxa+Zb48ID6ACG12jHQgclnkwvM7xGv1W1r3gPhq2+iAaAxNDmF6btps\nemyP4AMLbh3T1+fj6YNw/3B0j3WbvUael97aUM7yPnLE+vrE4ES0jbSB53mzWRLA7iG1MbbUfTgO\nxuqieXnWzxMCtzkR1hvWKqqDrxa38AMDgYAANmhKVWRMD2X7+G5J2iJ63hUpmaYIVr7YXsCmqDiV\nceP6dXHrbLYLuKaGzsObH3a8gSVMcXExiouL7X6eKyx8LQDTr338+WOW1yTYuMaEPXj88T3Ys2cP\nioqK0DXahdjAWDMxULra1h6XjqiLaFRZe5aCHxHBLEzLhS9ii6+ULLoy7ael4HuoPBAbGGuVoaR0\n0ZWAXODWcgYxOMhmBZZF2QDxLB1A2sIP8Q2BilNheGrY6pzULGJ2fpbl4AeKTxQdTc2Uc+mMTo9i\ndHoU0QEiu72cx9nArZKUzNn5WbSPtEvONEzJzLTPj2+PW8cZwddN6dA12oXs8GzbFxNWFBUVYc+e\nPcaHUlwh+CUA0jmOS+I4zhvAfwB43+Ka9wHcCQAcx20AoON5vleqwf5+8xRF00VXAmFhTExNV7OK\nuWDEgraWOf2Acxa+mODLLb6ybFMsaNsx0iFq4Yu5dABxt46YhW/gDZKzB3sCt1JCrJ/WY2Z+BmF+\n1hUcpQQfkE7NlHLpdOo7EbUsCl4eIiU0oUDwJTJ15Fw6woIry1mIKbZy8W2lZirx32t0GsQFxRnT\niuWwK1Mn3L5MHWcEv7SrFAUxBVZrKIgLi9OCz/P8PIBvAfgEQDWA13mer+U47l6O475x/poPAGg4\njmsC8AKA++XaFHyPAnKCamrlRyyLwMj0CKbmphaeayHQpkXYTJHy4SsVfClxVhpYFrPwLQOrgLhL\nBxBfbSsWtO0b70OQTxD8vPxE2xaz8MUGE1spmWKiKJuLL7L4iuelN0jX6DRIUUs72+UGlxR1imR5\nBTmXjlxKpoArLHxXBGwFsrPl99s1xZ5Mnakp9v5mO2ig04KrS4NL8vB5nv+I5/ksnuczeJ7/xflj\nL/A8/6LJNd/ieT6d5/l8nufL5NqzlZIpYBkYVXEqxATEoGuUbWo6N2c9WxicHISflx/8vfzN2hLE\n2bI+T8dIh3HxlbCZiBILX+if6CBi4iaamWHuEctFV1JuF6nFV0otfKl2AddY+FLuHEBBLr6Fhd/T\nw/zilmseAOa/TwmRFnxHFl+NjbGH2P68wPlFVxL+e2PbNjJ1hLr4UmWylaRkNgw2IDNUmeBfqCJq\ntbVscLMsq6GUki7K0LkUuOVKWyVZNYB4JoypW6enh/nSTRc0WWb7CCxbxhZUDZqsswryCYKKUxkz\nF3Q6wMPD2m8t1T8l5RW6upjAeHiYX9ehF3fpREay3bksYwOWojw6yipGhll4VkzLIltiz+IrexZd\nmWLP3rytrdLuFamArYAjufgaDeuflMfGFRZ+qB/bUHVockj0vKtSMk3709EhXj3U6lp1GrSjWrMZ\nshSuCNjSCtuLz6IQfDGfu3CdpaCa1sWXSsmUCvTZcuuIuXMmZyetMoiUtgdIL7rqGBF36ahU4gOd\npSgLAVtL8WofaRcdSAAXWvgOCH5KSApaR8xPtLZK5+ALe/3K3UfKwg/1C4WBN2B40jxIrCQlUyoH\nX8CW4HMcJ+vHd3bjE0u8vdnnQK5PAl4eXkgJSUHDYIPNa50R/N6xXozOjNqcLRGuZ1EIvpRIi662\nDZQXaKnBA7AduBXztWtHWTxAymdtNSBZ1OgRy8EXAqty/bTKxbcooCa16ErOpRMSwlZP6nTmx8UE\nX8q33jbSZlOI7bHw5RZdybl0wsKYS8/ytQBMdMX8+M3NTLClUGLhR0ezRAK9TDp7Wqi4H19xSuaQ\nspRMAXv8+ErdOs4IfkkX29JQLvhNXBgWheBLuWEkXTrn0xOlyipIWfi2gqxS2TT2DCCWNXrEBqX+\n8X4EeAdYxRnk2rUUZbmNT6QE3zR/3ZRw/3BMzE5gbGZhJZNcDr6UDx9wreDLDSwcZyNwK5KpIyf4\nc4Y5tI+0y95TuK+tDc3T1emiVTMF/72cDo7PjGNwYlB09idFdradRdQUZOo4m6FD/vtLg9sL/pxh\nDn3jfaK5z6IWtA2XjtTgIbQnZ+HbGwQV6x9gnosvWs1SL+1nB8QzdYJ92Pr2kakRY7v2WviAuFuH\n4zizLKDxcfaIjLR+vqM+/FC/UMwZ5qCbWjDJpQR/em4afeN9VplWltgM3Fr48VtapAW/Y6QDUQFR\n8PUUqeJmgZKaOk3D1hZ+QwMLssrRNNSEVHUqVJzyr25WlmszdYaGWIxIagW0LShge+lwe8HvGetB\nuH+4aL61rXo6UnXrpYTClktHbCGTWCEyAWHxleXOV0L2DyDuC5fy35v2U0yUTd06UjVobAm+ksVX\ngnVvaYlOzU1heGrYuM+AGFKCz3Ec8+ObWPlCENWSDn0H4gLjbOZw25uLL2fh26o9b4qSTB0xC7+h\ngS2UksMe/72APRa+EpeOsIetIx4ZnucpYHsJcUvBNxVAsZx5gagoZm2YbitnKtCii6704imegO3V\ntvZa+GJrBQDzOINUm1KBVcBGLv75wK2YdTwxOwH9tB5RAdLr7KUCt6Zpn1IB2/aRdsQHxctanwkJ\nLBd/dtb6nKlbx2CQjhPYcucY20uWz8U3Ffz5eXY/KRdS01AT0tXKBN/RXPwLJfiCha+kiFpWWBaa\nh5sxZxBZLHEeZ9w57SPtUHEqye8gcWFxS8E3zbuWKjEAsFTG6GiW2igQExCDvvE+zBnmxF06TgRt\nxdwkcj5xJW2KWvgSKZlybQLmoiwm+K26ViQGJ8oKspLUTCnBVyLEXl7sfybm6koOSTa6WXp6WBDZ\nXySMoRnWyAZsBWxZ+KZB244OtkmOn/V6NAD2Wfi2BD8mMAb6ab1ZTARQKPgKiqZZEh7OUpN7Jde2\nLy/AHEQAABuYSURBVODn5YeYgBjZfX+rqhwviSxseEIB20uDWwq+KbayMSwzdbw8vBDmH4ae0V6r\nnbPGZ8YxNTdlzIW2RLDGDSbViwVxNhjEs3SkSgGb9k80F1/fgZERlpURatEdWz58waVjabEJbpeZ\nGfGNT2y9l4Cy1EypejNyhcVMURK4dSZga3ofKcEX9uoVSlXL+e8BoGnYdYKv4lRsb10Ttw7Puz4H\n3xRXLsCigO3ixe0F31YQUMqPX9XRaVxMJSD4fqWsC39/Vu2w32QvZ7WvGtNz09BoxxAcbN4ez/M2\n3S9yGTWCO8eyO7Z8+MHB7DkjI9btdug70NkJxMRYb3yiRCjlLHyh9IFU+QElaYuAslx8WcEfaZUt\nq2Bs7/ziKzFXxjLvZQjxDTHWpreVkmmPhZ+UxGadYm4rAcsyyV1d7LNnq7a8o4JvV4kFmUwdnndu\nlysK2F5a3F7wW0fkRUoqNbOqTWvlv9cMa2wKkqUfX9grt6xRa+VrH5wchK+nr1XNesv+WQp+qjoV\nLcMtsr5wuUGE48QHEsGlIxWwVSL4sbFsf13LlZmmq1PlBF+Jq8VZC18zLL/oSiA4mC08GhgQP2/q\nx29ulq6hY+ANigczgN0zNlZ84BRIV6eb+fGVuHMGJwYxb5hHhL+NRH0R7A3cSmXqtLczl6vlCm4l\nGHgDSrtKsSZ2jf1PJlyC+wu+DZESE9S4wDjUdHZafYGVfGmlUjOr2jutBL9N1ybregHEc7Ljg+LR\nO96LptZpK8GfmZ9B/0Q/YgMlCqqfRyxTR0idlKowqUTwPTyYWImt5O0e68b03PQFs/AFHz7P85IZ\nOsJ9lAwswr2U+PHlLHytXotQv1As8xYp6iNBWhpbNSt5PjTNzKVjT8DWEf+3vamZUi4dZ9w5dQN1\nCPcPR8Qy+wcswjW4teDzPK9oIY/lFzo+KB7N/Z1WX2AlgiQVZK3v7bAO2I60y/YNEPfneqo8kRCU\ngOrONqtBpFXXivigeMmyvwJimTrCorOW1nmHLXxAfPGVl4cXEoISUNHeCoPBOu4AOC/4Ib4h4DgO\nQ5NDkv7skakRjM2M2RwQBZTW1HFVSqZAZiYTcSnSQ9PRONRo/FuJ4NcO1CIr3EaivgT2unTqBupE\n9951RvBPa09jfdx6x55MuAS3FvzhqWF4qjwR4hsieU1GhrUlxYRPRPB1ygTf0rpNVaeiaaDZqsaJ\nRqeRjS8ATNw6O639uSnqFNT3tVgJs5LNqYV+Wlr4Pp4+UPuqUdfR61Q6Y2KieOA2LTQNJ+qakZpq\nHXcYnhwGD14yIG6KXC5+mpr5tqUEsHGoERlhGYqtXLmceKFqJs/LB23tSckUsBUkFURVQIngV/VV\nYXmEY+kxqaksHXZ83Pa1wb7BCPYNtiq3DQAVFcDKlQ51Aac6T5HgX2LcWvBbda02BVXYcMI0syY9\nNB19840us/AzwzLRMdlg9YWsH6hHVpi8xSXlz00NSUXzcIvVykql1mRysvjy/cTgRNR2t1n1VT+t\nx/jsuNnWilKIWfgAyx8vb2+SdecoEeL4eJZ2KRbUzArPQnlnPXQ66ywjQPnWfgJyvmshltLXx4rS\nic1aAMcsfFsWdXxQPMZmxowF3OrrbWfoVPdXY3mkY4Lv6ckGoRqFG1rlReShur/a6vjZs9JbTtri\nlPaU4u0TiQuD2wu+LYt02TL2RTUV6aywLIz51iE1dSE9g+d5h334mWGZGOZEBH+wXtEUW8ytkxKS\nir5pjVWbjUONisRFSsgywzKh0TdYbUxRN1CHrLAsRUvypVIz00PT0TDQLCr4wpJ/Jcjl4meGZuJ0\ncz3S05kIW2JPLXhA3nedFc72cK2tBXJypFeOKv2fWN5XzsLnOM5YxmBqin3mbAp+XzXyIkU26VXI\nihUsw0YJK6NWoqKnwuzY6Cj7nzmy6cnk7CTqB+tREFNg/5MJl+HWgq80OJeRwXKYBfxVavAz/vAK\nXViRNTAxAC+Vl6x7CBB3Z8T6ZmA2qBEJCeb5fQ2DDTYtfIAVxLJ0OwUZUuEZ2YJAiwSfpqEmRS6d\nrCzmBjBYuFnj/bIxH1qLcItqzXUDdYr3D01JEXeDpKnT0D7aLCpMtQO1yAm33hRcCim3TlZ4Fqp7\nrAdXgYahBmSE2X5/BISBUSw1MyYgBtPz0yipHkSOTNer+6uRG5Gr+J4A+xwJNWekyI3IRXVfNerr\nmctFbjMR3ZQOI9MjNpME5Fi+nPnglZAflY/KvkqzYxUVrA3T/SWUUtZdhtyIXEW1iIgLh1sLfm1/\nLXIibIuIpeC3tgK+Y9loHlkwsVqGWxTlbicmAn195huM9HcEw9MQgN6JhQFEP63HyPSIzQJegLiF\nzw+mwiPCOo1DqTUZFMRWolpaycsmcuCfUGdlrdoj+Lm5QLX1bB5poWkYMDSJrrKs6a+xSxQlBT8s\nC5rReknBt9elEx7OZgp9fdbnOI5Ddng2TjXXIlei61NzU2jTtdk1yADsnrYCt7nhbIFTVRWQZ8Nw\nr+5jg449RdMsWb7cOQu/rAwocNBAP6Ul/7074NaCXzNQo8hqtLSgm5qAcD7bLChW06+sLU9PJtCm\n0/GGBiB4LtNsY4iGwQZkhGYo+gKKWfhT2ixML2vEvGHeeGxmfgad+k5FAxMg7ic29DIL3xJ7LPCY\nGLYC2FIkU0PSMeXThrRM6+2TqvurkReh3N0gNYvIDMvEgKER6RnWGSI8zxvfd3uQ8+PnhOegpq9W\n0sKvH6hHqjpV0YbhlmRlsa0ApciNyEXNQA2qq22XKqjqq7Lr/RVjxQrlFn5ORA40Oo3Z7lfO+O9P\na0+T/94NcFvB53neLgvf1JI6dw5IDc4yE/yqviqsiFSWT5aTY/5Fra8H4nzNBb9+QJn/XmjPMljW\n2hCAIFWUWc2S5qFmJAQlKBYXMf+0riUDE15tmJmfMTtuj4XPcUyALK38vi5feI6lonvOXMVm52fR\nPNRsl+W9YgVQWWl9PNAnEKppNdTJ1hkiHfoO+Hv5I8zfvlU/cn78nPAcdEzWSQp+db/jfvO8PPGZ\nkoBQwqC6WoGF70TAViAhgVVulVqIZoq3hzcyQjNQ3bfwApwN2JKFf+lxW8FvGW5BoE+g6NaBluTn\nsw+jQHk5sDYl22y14Lm+c4q/MJZiVFMD5ERkm2UtCEFQJaSns6Xzpv7cujogNSjXrM2K3gqsil6l\nqE1A3MJvrPNGpE+S2SrO2flZaIY1drklxMSquhoIn8u3muo3DTUhITgBfl4SlcdEyM9nPmFLZmeB\n+d5scJHWpnF5Tznyo/MV30PAcgA3JWlZDiaW1Ypu5gKcD5Q6aFmvXCn+Go33DknC0OQQKuv1NgXf\nFRa+1EAuRX50Pip72RdhepoZVY4UTesd64VuSme3W4xwPW4r+PakcKWmMsulm5VFQVkZcH3BKpzt\nPgsDb4CBN+BM9xkUxigzT9asAUpKFv4uKQF2rFyD0q5S47HS7lKsjlmtqD1PT+YXF6bTPA+cOQNc\nkbIKZd1lxuvKe8qRH6Vc0HJzrX2yFRVscDJdKdkw2ICE4AS7AmZ5edZtV1UB6YErjSIg4EhQMzWV\nBTWHzbeVRU0NEDJViJqhMqvnlPeUY1WU8gFRYNUqc4PAjP5ceMZUi2YEAcyt6KjQ5ueLz2IEVJwK\nWaE56J6ttbmPrTMzDVPsCdyujFyJil42YlVVsZm0rwMx12Mdx7ApYZNT8QfCNbjlf6BnrAeft32O\njfEbFV3PccC6dcCJE6za5eAgULQ6FkE+QagfqEdNfw3UvmrZjTlMWbMGKC1lGTBDQ8yXfdO61ajo\nrcDs/Cx4nmeLSOKVT1HXrAFOn2a/NzezQllXZa3Dae1p4zWlXaWKByUAWL2aCdn8+TBATw9bWLM5\nrdBscHKkYJWYhV9VBayJzzeKgEBlb6XdC4JUKnG3TlkZkBNkPrgKlPeU2zUDEigoYO+TZUYTAHRV\npwK+OgxMiPs5ynvKsSLKsaWlyclsVjc4KH1NBHIRW1Atm/mi1Wsxb5h3SQ15e/z4phb+qVPsM+wI\nR9uPYnPiZseeTLgUtxT816tex7t17+Km7JsUP2fnTuCf/wQ++QS46ipWE6YouQgfN3+MA80HsDVp\nq+K2IiPZop+SEuDAAWDTJiDEPxBZYVk42XkSlb2VUPupRbddlOLKK4EjR9jvx44BGzYA6+KY4M8b\n5jEzP4NT2lPYlLhJcZtqNVvUJQjz6dPsS7kxfgNOaU8Zr3MkYFZQwFxjcyb7YJw6BXxhLRN83iTP\n8ZTWvsFPQMytc/YscGX6apcKfng4y2gSW6h2plSFVD/x+/WN90E3pXOoOiXADBGpWIWAry4fAelS\n0w9GaVepy2rIFxSwQVUJ+VH5KO8pB8/zOHEC2KjM/rKCBN99cEvBf/jgwyiIKbBrscvNNwPvvgs8\n9hhwxx3s2FdWfAV/KvsTXix7Ebvzd9vVh127gLffZo8bbzx/LHMX3q17F+/UvoObspQPRgBQVAR8\n9hnzhe7fD+zYwTbCiA+KxyntKZzsPImM0Ayb6wQsufJK4PBh9vvBg8C2bWwgOdN1xphhUdxabPcX\nTq1mKaqCIPf3s5nO1sIYeKo8jVUmDbzB4RopYq6Ws2eBqwvTMDozir7xhTQh3ZQOfeN9di+AEigs\nZG40S0pLgQ2J4jOKU52nsDZ2rVOuCKlYhcBE01qMB5dIXwDXlhRetYoZCDMztq+NCohCoE8gmoaa\nHBb88Zlx1PTXUIVMN8EtBb/knhK8ccsbdj0nIQF49lnga18DbriBHduWsg2bEjZha9JWuyx8ALjv\nPuDpp4HiYuA//oMdu2vVXfhr+V/x9MmncXfB3Xa1FxfHgnjPPsuE+d/+jR2/MetGvHbuNbxa8Spu\ny7vNrjYB1s6//sXiAvv3A9ddB6j91MiPzkdxazFada0YnBy0y1UksGULcOgQ+/3QIWDzZsDTk8O2\n5G04rGGjTFl3GaKWRclumyjFpk3A558v/D01xWYVa9ZwKIwxd0sdaz+GdXHr4KHysPs+AHN/WVq2\nIyPMBXjdirUo6bIWXVeUAigsNI8HWdJ6ohDd8+essqpMcaXgL1vG0o6V5uOvi1uHA7WnMTAA2cVp\nUpzsPIlV0atowZWb4JaCvzxyOYJ8gux+3pe/DDz55MISeRWnwou7XsTzX3je7ulwUhKzhEpKFjal\nSFGn4O3b3sabt77pUIrck08CDz0EfOtbbD9eAPjWum9hb8VevFP3Du5eZd8gAjCBr6wEfv5z9mUW\nFsbcknML/nz2z3ip7CXcknOLQ1bqjTeyWRMA7Nu3MJBek3oN9jfuBwB80PgBdmbstLttgAWddbqF\nUhYnTrDYQXAwsClhE460HTFeW9xajKLkIofuAwBr1wInT5ofKylhFu/6+DUo0VqrsiuqO27axFx4\nYoyMAN1tAUgNTUFVn7gC8zzv8hryq1ezmY0S1sWuw4eVp7F+vXipC1uQO8fN4HnerR6sS5cvc3PW\nx7r0XXyXvsvhNv/v/3g+LY3nDx9eODY2Pcan/i6Vj/ifCL55qNmhdqeneT42ludff53n1Wqe7+tj\nx/9/e/ceHFV9BXD8ewA3YkIQ0UgKCISHqKBAQago8gahCEXL8BgKI8MgyOA4FQWpYpVRy7RU8YUD\nZdCBgYIMT6uSCNEiD3EQ0EKQVyCEx9RKeKk8ktM/fhuyWXaTTXazG7LnM8Owuffu3sNvL7/c+3uc\nX97PeZr8arLmnsnVxq831q1Ht5Y79pEjVWfPdq+ffFJ1+nT3+ssjX2rrd1qrqmpBQYG2fKulbs7Z\nXO7znD2rmpioev580bZnn1V9/nn3+fX+Wk/3/2//lX2X8i9p7Vdr68lzJ8t9TlXVggLVunVVc3Ku\n3rd2rWq3bqqjVozSOdvmBHz/3h/2asNZDcOKwd+bb6qOHRvasZ9nf66/eqHTle+lrHq830NXZ60u\n35tNyLz1Zqn1a6W8w6/KqgdokUitlRryCKJAhg93M3m7di3aluhJZNfju9g7cW/ISc38eTyuWWvs\nWHjxRbjFu25F7etrM779eNrMaUPLm1uG1ewxbBjMnw/nzsHixTBihNvesX5HN0b95C52ntzJ+Yvn\nw7rbTkpyd7aF/R0An3wCvXq5FAu90nqRfjD9yr4tR7fQpE6TkLKLlkTENYUFusvPyHDn79SgE5uO\nbgr4/s8Ofkb3Jt3DisFfhw6uAz4U7VLbcUJ30b5jCI3+fn65/Atbc7fSpVGXMr/XVAyr8KuwRE8i\ndWrWCeszhgyBM2dg0qTi22d0n8GSR5ew7PfLwvr8Pn0gIcENq+3ZsyhjZPVq1RnffjzT1k9jSsYU\nJnWcFPYolUcegaVL3eusLNcJfd997ud+zfuxMmvllWNXZa2if/P+YZ2v0P33w8aNV2/PyHD/5p5p\nPUk/kF5s5NOVYw5l0DOtZ0TiKNS2rRuxlJdX+rEekuDHpiSlhTiW08fGIxtpndKa2teXslCviRqr\n8E251KhWg+5NupPkSQrrc6pVg48/dqOr5s4tvu/p+54mOSGZlMQUJt47MazzgOt8X7PGddS+8QaM\nGlX0xDWgxQC2HN3CsbPHuJh/kYXfLmRE6xFhnxOgRw/3NOFbn5844eJo186lna55Xc2r2vHzC/LZ\ncGhDxO/wPR53l78p8ENFMZs3w00/38vuMyE+EvjIOJhBr7Re5YjQVJRyJDo1JrLq1HFNO/4SaiSw\naPCiiJ0nJcU9qXTp4obH+g6XTPQk8ljbx3jus+doUbcF99x6T0h5nELRpo07n2+StFWroHfvol84\nfZr2Yd2BdcUmeX197GtSa6WGvJxjWTzwgBsh1a+U/vaMDOiQ2olNOZlM6DChTOdIP5jO631eDyNK\nE2l2h2/iyvTpMGeOa8Ou65eD7YUHX+BQ3iEWfbuIt/u9HbFzirhfaAsWuJ9V3esRPg8QfZv1ZfX3\nq4u9b9nuZQxuOThicfgqrPBLk54OQ3/zIJnZmQGbnIL54acf2P/jfjo16BRGlCbSpCxfYjSIiFa2\nmIwJ18GDrp9i9273ZDFhgkvoVphS4cLlCzT4ewO2jNlC05uacuHyBRq/0Zj1f1gfsScNX+fPu1XH\ncnLcLORATp0qXB9Caf5uQzJHZ4Y88W3pf5bywc4PWDt8bQSjNsGICKpaaieX3eEbEwVpaTBunOuk\nHTkSZs8uvnJUQo0Exv16HK/8+xUA5m2fF9FmJX+Jie4u/9NPgx+zZo2Lt2ZNoVuTosl2oVj7/Vr6\nNusbgUhNJNkdvjFRouomsKWmulxK/k79fIq277Wld9PerMhaQeaozIhkyAzm3XfdcNGFCwPvHzDA\ndXSPGAHzv5lP+sF0Fj+yuNTPvZR/iXp/q8fOx3fSILlBhKM2gYR6h28VvjGVyOG8wyzYsYD+LfpX\neP6ZnBzXoXz8+NXr6Z4+7dKV5OS4mc+5Z3K5e87dnPjjCa6rfl2Jn7v+0HqmZEzhq7FflXiciRxr\n0jHmGtToxkZM7zo9KsnGGjZ02TxXrrx638KFblJYYVqR+sn1SauTxsYjASYU+Fm+e3mZMt2a6LEK\n35g4NmGCa9rxlZ/vZlg/9VTx7QNvH8jqvcVHEvm7cPkCS3cvZXjr4RGO1ESCVfjGxLFBg9zShb7J\n1D780A1Z7ey3NMOgloNYvmc5+QX5QT/vo30f0SqlFY1vbFwxAZuwWIVvTBzzeGDGDJcv6dw5OHrU\nZXSdObMo62yhVimtSElMKZZzyN+87fMYdc+oCo7alJdV+MbEudGjXU6hli1dnp3Jk+HBIMtHjG03\nlrnb5wbct+vkLnac2MHQVkMrLlgTFhulY4wBXOqHxES3Fm8wZy6coenspnwx+our5ggMWz6MtvXa\n8kznZyo2UHMVG6VjjCmTu+4qubIHSE5IZur9U5mcPrnY9nUH1rEpZxPj24+vuABN2KzCN8aUyRMd\nnuDAqQO8/ZXLN5Sdl82Y1WOYN2AetRJqxTg6UxJr0jHGlNn+H/fz0KKHSPIkceT0EV7u9nKZs2ma\nyInKTFsRqQP8E2gEZANDVPV0gOOygdNAAXBJVYMukWQVvjHXhov5F9mWu420OmlhrdhmwhetNvwp\nQIaq3g6sB6YGOa4A6KqqbUuq7E1xmZmZsQ6hUrByKFKZysJT3UPn2zrHrLKvTGVxrQi3wh8IvO99\n/T4QbD61ROBccccuaMfKoYiVRREri7ILtxJOUdWTAKp6Agi24rMC6SKyTUTGhnlOY4wx5VDqEoci\nkg7c6rsJV4H/KcDhwRrfO6vqcRG5BVfx71HV0rMwGWOMiZhwO2334NrmT4pIPWCDqpa4YoOITAfO\nquqsIPutx9YYY8oolE7bcBcxXw2MBv4CjAJW+R8gIjcA1VT1nIgkAr2BPwf7wFCCNsYYU3bh3uHf\nBCwFGgKHccMy80QkFZirqr8VkSbAClxzTw1gkaq+Fn7oxhhjyqLSTbwyxhhTMSrFUEkRmSkie0Rk\nh4gsF5Fkn31TRWSfd3/vWMYZDSLyqIh8JyL5ItLOZ3sjEflJRLZ7/7wTyzijIVhZePfF1XXhS0Sm\ni8hRn2sh7lYLF5G+IpIlIt+LyLOxjieWRCRbRHaKyDciUuK6kuG24UfKOmCKqhaIyGu4CVxTReRO\nYAhwB9AAyBCR5lV8Ku63wO+A9wLs26+q7QJsr6oCloWI3EH8XRf+ZgUb+FDViUg14C2gB3AM2CYi\nq1Q1K7aRxUzhxNZTpR1YKe7wVTVDVQu8P27B/ScGeBhYoqqXVTUb2AdU6Zm6qrpXVffhhr/6i6sO\n7RLKYiBxdl0EEFfXgp97gX2qelhVLwFLcNdEvAp5YmulqPD9PAb8y/u6PpDjsy/Xuy1eNfY+wm8Q\nkftjHUwM2XUBE71NoPNEpHasg4ky/+//KPH3/fsKeWJr1Jp0SpjANU1V13iPmYZLrrY4WnHFQihl\nEcAx4DZVPeVtz14pIneq6rkKDrdClbMsqrySygV4B3hJVVVEZgCzgDHRj9JUEiFPbI1aha+qvUra\nLyKjgX5Ad5/Nubghn4UaeLdd00oriyDvuQSc8r7eLiIHgBbA9giHF1XlKQuq6HXhqwzlMheIt1+M\nucBtPj9Xue+/LFT1uPfv/4rIClyTV8AKv1I06XhHGUwGHlbVCz67VgNDRcTjHc/fDCixF7qKudJO\nKyI3ezurEJE0XFkcjFVgMeDbZh3X14V3VnuhwcB3sYolRrYBzbwj1zzAUNw1EXdE5AYRSfK+LpzY\nGvR6qCyjdN4EPLjHEYAtqjpBVXeLyFJgN3AJmFDVR2KIyCBcedwMrBWRHar6ENAFeElELuJ65cep\nal4MQ61wwcoiHq8LPzNFpA3uOsgGxsU2nOhS1XwRmYgb3VcN+Ieq7olxWLFyK7DCm5KmcGLrumAH\n28QrY4yJE5WiSccYY0zFswrfGGPihFX4xhgTJ6zCN8aYOGEVvjHGxAmr8I0xJk5YhW+MMXHCKnxj\njIkT/weosIGzN0n7zwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60ddbe7eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:26: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:27: RuntimeWarning: invalid value encountered in sqrt\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEMCAYAAADHxQ0LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60ddae65f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:41: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:42: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEKCAYAAAACS67iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl4lOXV+PHvSSCALAGEkEBCkEUoiKDIMlRNwKqgVu2L\n1lawotVSF9RqffVn9SW0+L4u1aJV61Irm1aoUkAEBZUglQCyyRoF2RIMSyABQsh+fn88kyEJCZkk\nk8xk5nyuK1fmWWbmzKgnx/Pcz32LqmKMMabxC/N3AMYYY3zDEroxxgQJS+jGGBMkLKEbY0yQsIRu\njDFBwhK6McYECUvoJqSJyNUiMtfLc1eLyI/qOyZjassSuglKIrJHRPJEpH2F/RtEpEREurp3TQH+\nz8uXfR74ky/jNMaXLKGbYKXAbuCXpTtE5AKghfsYIjIYaKOqX3v5mh8BI0QkysexGuMTltBNMJsJ\n3F5m+3ZgepntUcDy0g0RcYnIYRHp4t4eICJHReR8AFXNB9YBV9d75MbUgiV0E8xWAa1FpLeIhAG3\nALPKHO8PfFu6oaopwOvAdBFpjvMH4Q+q+l2Z52wHBtR75MbUgiV0E+xKq/QrcZLxD4C4j7UFTlQ4\nf7J7/xogTVX/VuH4CfdxYwJOE38HYEw9mwV8CZwHzHDvK52RLgtoXfZkVS0SkWnAS8DvKnm91kB2\nvURqTB1ZhW6Cmqruw7k4OhqoODxxE3B+2R3u/vkk4B3gRRFpWuE5PwK+qZ9ojakbS+gmFNwJjFTV\nU+7t0pbLIiCxwrnvAG+p6l047ZkppQdEpBkwCFhar9EaU0uW0E2w8kz0r6q7VXV9xWOqugHIdg9f\nREQeADoC/+M+705gvIj82L19PbBMVQ/Ud/DG1IZUt8CFuyr5EojA6bl/oKqTK5yTAMwHdrl3zVXV\nKRgT4ETkSuAeVf0vL85NAX6tqtvqPzJjaq7ahA4gIueoaq6IhANfAQ+o6poyxxOAR1T1+voL1Rhj\nzNl41XJR1Vz3w2Y4VXplfwWkkn3GGGMaiFcJXUTCRGQDcABYWsWt0i4R2SgiH4tIX59GaYwxplre\nVuglqnoREAsMrSRhrwO6qupA4BVgnm/DNMYYUx2veujlniDyFHBSVV88yzm7gUGqerTC/pq9mTHG\nGABUtdq2drUVuoh0EJFI9+MWOLdQp1Y4p1OZx0Nw/lCUS+Zlggran0mTJvk9Bvt89vlC7bOFwufz\nlje3/sfgTFYUhvMHYLaqLhKRCU5+1jeBm0TkHqAQOIUzCZIxxpgGVG1CV9XNwMWV7H+jzONXgVd9\nG5oxxpiasDtFfSgxMdHfIdQr+3yNVzB/Ngj+z+etGl8UrdObiWhDvp8xxgQDEUG9uCgaENPnduvW\njb179/o7jJASHx/Pnj17/B2GMcaHAqJCd//1abA4jH3nxjQm3lbo1kM3xpggYQndGGOChCV0Y4wJ\nEpbQjTGNWkGB82MsoQec6dOnc9lll/k7DGMajYUL4eab/R1FYLCEHmBUFRGbWt4Yb61aBYMH+zuK\nwGAJ3QsZGRncdNNNREVF0aNHD1555RUArr32Wn7/+997zvvFL37BXXfdBcCuXbu44oor6NChA1FR\nUYwbN47jx497zk1PT2fMmDFERUXRsWNHHnjgAVJTU7nnnntISUmhdevWtG/fHoBFixZx8cUXExkZ\nSXx8PJMnl1sB0JiQtmoVDBvm7ygCRAPPGKaVqWp/ICgpKdFBgwbplClTtKioSHfv3q09evTQJUuW\n6IEDB7RTp066bNkynTVrlvbo0UNPnjypqqo7d+7Uzz77TAsLCzUzM1MTEhL0d7/7naqqFhcX64AB\nA/SRRx7RU6dOaX5+vn711Veqqjpt2jS97LLLysWwfPly3bJli6qqbt68WaOjo3X+/Pl1+lyB/J0b\n462CAtWWLVWzs/0dSf1y//dafY715iRf/dQloUPdf2pj9erVGh8fX27f//3f/+mdd96pqqpz587V\nuLg47dixo65cubLK15k3b55efPHFqqq6cuVKjYqK0uLi4jPOqyyhV/TQQw/pww8/XMNPUp4ldBMM\n1q5V7dfP31HUP28TekDc+u8Nf93UuHfvXvbv3+9pf6gqJSUlXH755QBcd9113H///fTu3RuXy+V5\n3qFDh3jwwQdZsWIFOTk5FBcXe14jPT2d+Ph4wsK863itWbOGxx9/nC1btlBQUEBBQQE321UgY6zd\nUoH10KsRFxdH9+7dOXr0KEePHiUrK4tjx47x0UcfAfDEE0/Qt29fMjIyeP/99z3Pe+KJJwgLC2Pr\n1q1kZ2cza9Ysz632cXFx7Nu3j5KSkjPer7ILorfeeis33ngj+/fvJzs7mwkTJtht+8ZgCb0iS+jV\nGDJkCK1bt+a5554jLy+P4uJitm7dytq1a/nyyy+ZPn06M2fOZNq0aUycOJGMjAwATpw4QatWrWjd\nujX79+/n+eefL/eaMTExPP744+Tm5pKfn8/KlSsB6NSpE+np6RQWFnrOz8nJoV27djRt2pQ1a9bw\n3nvvNeyXYEyAWrUKyvyPccizhF6NsLAwFi5cyMaNGznvvPOIiori7rvvJiMjg/Hjx/Pqq68SHR3N\npZdeyl133cUdd9wBwKRJk1i3bh1t27blpz/9KWPGjCn3mh999BE7duyga9euxMXFMWfOHABGjhxJ\nv379iI6OJioqCoBXX32Vp556isjISKZMmcItt9iCUMYcPgyHDkGfPv6OJHDYbIshyr5z09jNnw+v\nvQaffgpJyUkkJSb5O6R6Y7MtGmOC2n/+A5de6jyevNzuzQBL6MaYRuqrr2Bnq2nIZKdwlclCUnKS\nf4PyM2u5hCj7zk1jduoUdOjg9NBbtnSSuU4K3n+freVijAlaX38N/frB818nWYVehlXoIcq+c9OY\n/e//QmYmvPginoRuFboXFbqINBOR1SKyQUQ2i8ikKs57WUR2iMhGERlYm6CNMcYbX30F+9vO9iRz\nIOSrc/CyQheRc1Q1V0TCga+AB1R1TZnjo4H7VfVaERkKvKSqZ9y/ZRV64LDv3DRWJSVw7rmQmgqd\nOgV//xx83ENX1Vz3w2ZAE6Dit3cDMMN97mogUkQ6eR+uMcZ4Z+tW54Lo37Zb/7wirxK6iISJyAbg\nALBUVb+ucEoXIK3M9n73PmOM8amvvnLGn5e9kUgnaVDfWOQtr2ZbVNUS4CIRaQPME5G+qrqtNm+Y\nlJTkeZyYmEhiYmJtXqbRmz9/Plu3biU8PJzOnTtz2223+TskYxqF//wHjsfMRybf6NkXbHeKJicn\nk5ycXOPn1XiUi4g8BZxU1RfL7HsdWKaqs93bqUCCqh6s8FzroQPHjx9nxIgRrFu3DgCXy8XChQs5\n99xzGyyGUPvOTXBQhfh4WLoUevcOjf45+HaUSwcRiXQ/bgFcCaRWOG0B8Cv3OcOA7IrJPNj97W9/\n47rrruPRRx8tt9QcwKefflpu+8svv6Rfv36e7QEDBrBs2bIGidOYxmzXLigqgvd+sP55ZbxpucQA\n00UkDOcPwGxVXSQiE3BW0XjTvX2NiOwETgJ31GPMAWfz5s2Eh4ezcOFC0tLSePDBB7n77rsZPnw4\na9eu5ejRo+XOT09Pp23btp7ttm3bsmPHjoYO25hGJzkZEhNh8ogkJo9ICpkK3VvVJnRV3QxcXMn+\nNyps3+/DuM5QdrxpbdXlH/yCBQsIDw9nxYoV9O/fn08++YQnn3yS3r17k5WVxW9+8xvAWbzinXfe\n4fnnn+eZZ55hwIAB/OlPfyr3WllZWTRv3tyzHRERQU5OTq1jMyZULFsGI0Y4PfPSCblksjApYVJQ\n9dBry+4U9cK+ffsoKCigZ8+eDBo0iM8//5yvvvqKkSNH0qJFCwBmzpzJnDlz6NOnD0899RRt2rTx\nPP/TTz/l6quv9my/8sor7N2717PoxaOPPkp0dDSPPPJIg32mQP/OjalIFWJjYfly6NkzNO4QLWVz\nufhQ165d6dmzJ4cOHaJNmza0bduWa6+91pPMt2zZQn5+Ph999BETJ07k4Ycf9qxAtHbtWrKyssq9\nXo8ePTh8+LBn+8iRI3Tu3LnhPpAxjdDOnSACM9OS7A7RKliF7oXU1FTy8/PZsGEDu3fvZvLkySxc\nuJDrrrsOcC5yli4aXerPf/4zX375ZaUtl9zcXIYNG8amTZsAGDhwIEuWLPGsUNQQAv07N6aiN9+E\nFStg5kxnO5T6595W6JbQvfDyyy+Tk5NDTEwMqampuFwuunTpwuDBg2v9mrNmzWLPnj2oKt27d2fs\n2LE+jLh6gf6dG1PRrbfCFVdAWo+kcgtahEL/3BK6OSv7zk1jogqdOzt3iXbvHlr9c7AeujEmiHz3\nHTRtCtP3Wv/8bKxCD1H2nZvG5PXXISUFpk93tkOpfw5WoRtjgsjSpfCTnzgVud0hWjWr0EOUfeem\nsSgqgqgoZ9rcmJjQ65+DVejGmCCxdq1zQ9Eb31r/vDqW0I0xAW3pUrjqKn9H0ThYyyVE2XduGovL\nLoMnn4Srrw7NdgtYy8UYEwSOH4eNG+FLfdraLV6wCj1E2XduGoMFC+Cvf3XaLhB6wxVLWYVujGn0\nliyBK6+04Yresgo9RNl3bhqD3r1h9mwYODB0++cQghV6IP/FTklJ8XcIxjQ6e/ZAdjb8++hk6597\nqdEk9Or+IZadfS3QbN269Yxl6MratGkTv/3tbxk7dmy5tUU/++wzJk+ezGuvvca+ffsaIlRjAsai\nRTBqFEhY6FXktaaqDfbjvN2Zqtpf7pykys+ZtGySkoTnZ9KySVWeVxfz58/XhQsX6mOPPaazZs3S\ncePGaWpqqlfPLSws1KlTp2pxcfEZx3Jzc/X1119XVdW0tDQ9//zzddq0afqvf/1L3333Xc95M2fO\nrFP8FXnznRvjT9dcozp79untqnJAKHD/91ptjg3oHnrZdQNLVTX3cXVXv+tydby6Jej27NnD9OnT\nEam6xZWdnc3atWuZM2cO0dHRnv2ff/45l19+OU2bNgVg27ZtXHrppfz617/2LFEHsHv3bvLz8+nT\np0+tPkNF1kM3gSw3F6KjYd8+mLox9OY/r8jbHnqjr9BLna0yL1vBn62Kr87Bgwc1MTGxVs8dP368\nfvzxx2fsX7JkyRn7brnlFu3Xr5+eOnXKs+/QoUO6bt26Wr13Zbz5zo3xl4ULVRMSTm+X/rcbqgiG\nCr2spOSkOv1VrkuFXt0SdNVZvHgxubm5jBkz5oxjhw4d4vvvv8flcgEwb948Tp48yaJFiygqKuKf\n//wnYWFh/P3vf+eOO+4gPDy8Vp+hIqvQTSC791447zw4OdiqcwjCUS51/Yc4KWFSrZ+7ZMkSPv74\nY1SVvLw85s2bR6dOnbx+/urVqytN5gBRUVGcOnWKqVOnkpSUxMmTJxk7diwzZsyge/fujBw5krvv\nvptevXr5LJkbE8hUYeFC8LJeMmVUW6GLSCwwA+gElABvqerLFc5JAOYDu9y75qrqlEpeq9YVuvEt\n+85NoNq8GW64Ab7/HkRCe/x5KV9W6EXAw6raD3AB94lIZVfmvlTVi90/ZyRzY4zxxscfw7XXwuTl\nNl1uTVWb0FX1gKpudD/OAbYDXSo5tforsMYYU43ShG5qrkYXRUWkG5AMXOBO7qX7E4APgXRgP/Co\nqm6r5PnWcgkQ9p2bQHToEJx/Phw4AM2bW7ullLctlyY1eMFWwAfAg2WTuds6oKuq5orIaGAecH5l\nr5OUlOR5nJiYSGJiorchGGOC3IIFzrznz6wqP7qlrqPcGpvk5GSSk5Nr/DyvKnQRaQIsBBar6kte\nnL8bGKSqRyvstwo9QNh3bgLRtdfCbbdBarQNVyzL2wrd24Q+A8hU1YerON5JVQ+6Hw8B5qhqt0rO\ns4QeIOw7N4Hm+HFn7dD0dGjTxtotZflslIuI/BgYC4wUkQ0isl5ERonIBBH5jfu0m0Rki4hsAKYC\nt9QpemNMyFm8GC69FF5cb6NbaqvaHrqqfgWc9Y4WVX0VeNVXQRljQs+//w0/+5kzqsLUTqO59d/4\nln3nJpDk50OnTvDtt87v0on5rN3iCLpb/40xwevzz+GCC8onc7Dl5moqKCr0TQc3AXBhpwtr/Rqh\nxip0E0juvNNJ6McvttEtlQmqCn3RjkUUlRRVeXziook8sPiBBoyoZmwJOmOqVlAA8+bBzTc7k/CV\nTqRnybzmAj6hZ5zI4Lr3ruOzXZ+dceyFlS8QNjmMVftXkZKeQtjkMF5Y+cIZ56UdS2P428MpLilu\niJDPUN0SdLVhy9aZYLFkCfTtC3Fx5dstk5dPtnZLDQVsy0VVufD1C/nuyHcUlxQjIrSOaM13E7+j\nwzkdADhVeIqb5tzEkl1LALiqx1V8cPMHtGjaAoC8ojxmbZrF8r3LmbVpFn+47A9c2OlCbu5781lX\nF6rMggULCA8PZ8WKFfTv359PPvmEJ598kt69e1f73KKiIl599VUmTpxIWFjd/4aeOnWKGTNmMGHC\nBNLT07niiit44oknaNmyJQUFBdx6660AzJo1i3HjxlX6GtZyMYHitttgyBA40t/aLVXx6Y1FvlLT\nHvqq9FWMmD6CvKI8wiSM6TdOZ9yF5RPUte9dy/I9y1GUxG6JfHzrx55jJ/JPMPCNgezO2g2Aoozu\nOZpFYxfVKO76XIKurOeee468vLxy+1QVEeH2228nPj4e8M2ydZbQTSA4dQpiYiA11VlyrrRCt2Re\nXlAsQZd5MlPDJodp+2fbK0no57s+P+OcxTsWa9qxNN2XvU8X71h8xvGdR3YqSWizPzXTVk+30qLi\nokrfyxv1sQRdbfhi2bqqvnNjGtKHH6qOGOE89nbB91CEl0vQBXQPvXmT5rx2zWsceOQAH9z8Ad3a\ndjvjnFE9RxHbJpa4yDhG9Rx1xvEth7YQHxnPMz95hvCwcDJyMmocR2pqKt988w2LFi3i8ssvB2Dh\nwoVeP3/x4sVcd911XHPNNTV+78oMGDCg3IXWefPm8dOf/pQBAwZw++23U1JSAsD8+fMZMGCAT97T\nmPowezbccsuZC8JbhV47Ad1yCRQvv/wyOTk5xMTEkJqaisvlokuXLgwePNir5yclJZWbZdIXvvji\nCzZt2kR2dja9evVi7NixFBcX8+STT5KSkkKvXr0YN24cCQkJlT4/0L/zhpaZm+m5NmMaxsmT0Lmz\nszJRhw7WbjmboOihm/pj3/lpacfS6P5ydyYOmciLV7/o73BCxrvvwqxZzhwuVqGfnSV0c1b2nUNB\ncQG//PCXpGamsu2wsx7Lf/3ov3h/zPs0DW/q5+iC31VXwR13wLcxlsyrE1Q3FhlTHyLCI+jZrqcn\nmQPM3T6Xp1c87ceoQsP+/bB2Ldx4o78jCS5WoYco+84dB3MOEv3C6WGkBx45QKdWnfwYUWh49lnY\nuRPeesvZtsm4zs4qdGO8kJWXxbgLx7H9vu1cGHUhWXlZ/g4p6KnCjBnwq1852zYZl+9YhR6i7Ds3\n/rJ2Lfz8587olsnLrX/uDavQjTEBqbQ6r+HsG8YL1a5Y1BDi4+NrPLeKqZvSaQSMaUgFBfDPf8Lq\n1TZUsT4ERELfs2ePv0MwxjSAjz+GH/0IuneHpO5JAHYzkQ9Zy8UY02DefBPuust5bFPl+l5AXBQ1\nxgS/PXvgkksgLQ2eXW3tlpqwi6LGmIDy1lswbhy0aOHvSIKXVejGmHpXWAhdu8IXX8Dsg1ad15TP\nKnQRiRWRL0Rkq4hsFpFKF+8UkZdFZIeIbBSRgbUJ2hgTnBYsgF69nAuiSYlJnjtCLZn7ljctlyLg\nYVXtB7iA+0Sk3BI4IjIa6KGqvYAJwOs+j9QY02i98QZMmOA8TkpOQiY7xaZdDPWtahO6qh5Q1Y3u\nxznAdqBLhdNuAGa4z1kNRIqITYhhjOH772HDBhgzxt+RBL8aXRQVkW7AQGB1hUNdgLQy2/s5M+kb\nY0LQG2/A7bdD8+Z2M1F98/rGIhFpBXwAPOiu1Gul7Mo9iYmJJCYm1valjDEBLicH/vEP+Pprf0fS\nuCQnJ5OcnFzj53k1ykVEmgALgcWq+lIlx18HlqnqbPd2KpCgqgcrnGejXIwJIa++6oxs+fBDq87r\nwtfj0P8BbKssmbstAH7lfuNhQHbFZG6MCS0lJfDSS/DQQ/6OJHRUW6GLyI+BL4HNgLp/ngDiAVXV\nN93nvQKMAk4Cd6jq+kpeyyp0Y0LExx/D//yPM11u6dx7paNbbCGLmmlUa4oaY4LPlVc60+Tedpu1\nW+rKbv03xvjNli2wdSvccou/IwktltCNMT734otwzz0QEWHVeUMKiPnQjTHBY98+mDfPWQTaNCyr\n0I0xPvXCC/DrX0P79ladNzSr0I0xPnPoEMyc6fTPTcOzCt0Y4zNTp8IvfgExMf6OJDTZsEVjjE9k\nZ0OPHs648/POs3aLL9mwRWNMg3rtNbj2WieZG/+wCt0YU2fHjjkLWCxf7l7Ewqpzn7IK3RjTYP7y\nFxg92knmxn+sQjfG1MmRI9C7N6xZA927W3VeH6xCN6YGMnMz/R1Co/Xcc3DTTU4yN/5lCd2EvLRj\nacS8EMPDnz7s71AanYwM+Pvf4cknnW2rzv3LbiwyIauguIBffvhLUjNTKSop4i+r/sLeY3t5f8z7\nNA1v6u/wGoX//V9nebnYWH9HYsAqdBPCIsIj6NmuJ9sOb/Psm7t9Lk+veNqPUTUeO3bAP/8Jjz9+\nel/ynmS/xWPsoqgJcQdzDhL9QrRn+8AjB+jUqpMfI2o8fvYzGDYMHnvM2U6clsjyvcs9xxPiE0ge\nn+yf4IKMXRQ1xgtZeVmMu3Ac2+/bzoVRF5KVl+XvkBqFZctg40Z48EFnOyk5yZJ5ALAeuglpfTr0\nYebPZgLwzT3f+DmaxqG4GB5+GJ55Bpo3r/ycxG6JDRqTcViFboypkRkzoEUL+PnPnW0b2RI4rEI3\nxnjtxAlniOLcuacXfjaBwy6KGmO89rvfObMqvvOOs23VecPw9qKoVejGGK9s3Ajvvlt+8YqKwxRt\n2KJ/WQ/dGFOtkhJn0eenn4aOHZ19FUe2TEqYZCNb/KzahC4ib4vIQRHZVMXxBBHJFpH17p8nfR+m\nMcaf3n7b6Zn/+ten91k1Hni8abm8A/wVmHGWc75U1et9E5IxDSszN5MO53TwdxgB69Ah+MMfYOlS\nCHOXgJVV59Y7979qK3RV/Q9Q3d0Wdr3bNEqlE3OlH08HnERlTlOFe++FO+6AAQOcfRUvhJrA4auL\noi4R2QjsBx5V1W3VPcEYf6o4MdeoWaPo3aE3c7fPtUqzjH/9y7kIOmtW1edYdR44fJHQ1wFdVTVX\nREYD84Dzqzo5KSnJ8zgxMZHExEQfhGBMzZROzDV3+1wAth7eytbDzvANmSyWpHBaLQ88APPmnb4j\ntGJ1nhCfEPLfU31ITk4mOTm5xs/zahy6iMQDH6nqhV6cuxsYpKpHKzlm49BNwCg7MZcgZDySQfQL\n0egk+3cU4OabnQWfn3vu9D6bgMs/fD05l1BFn1xEOpV5PATnj8QZydyYQFN2Yq6xF44lKy+LSQmT\n/B1WQPjnP2HLFvjjH0/vs2GKga/aCl1E3gMSgXOBg8AkIAJQVX1TRO4D7gEKgVPA71R1dRWvZRW6\nMQFu924YMgQ+/RQuvvj0/orVubWlGo63Fbrd+m+M8SgqgssvhzFj4JFHTu/vNrUbe4/t9Wxbq6Vh\n2XzoxnjJFog+7Y9/hNatnTlbSiUlJ1kybyQsoZuQZuPQT0tOdhZ8nj69/A1EFcec21zngcsm5zIh\nycahl7d/P9x6K0ybBtHRVZ9nffPAZj10E7IeW/oYz618rtJjoZS4CgogMRGuvda5xb9UxYug8ZHx\n7HloT4PHZ6yHbky1HnY97HksCAceOQCATtKQSebgXPzs2BH+3/87+3njB45vkHhM7VnLxYSs0nHo\n915yL6+tfS0kx6HPnAmffAJff326bw6Vj2oJpT9yjZW1XExISzuWRveXu7P7wd3EtokFnAuBoZC8\nVqxwhid+8QVccMHp/XY3aOCxlosxZ1FQXMCYOWMY9e4oz0XRMXPGUFhcGBIzCe7c6dzaP3Nm+WRe\n8W5QsFEtjYkldBOSSifn2nbYmRh06+GtHMg5QMSUCMCZoCtYhzBmZcF118GkSXD11af3VzZEMZQu\nDgcDa7mYkFXZ5FydWnVCJkvQTtCVnw+jR8PAgfDii+WPVeyb26iWwGEtF2Oqse3wNgRh2e3LPJNz\ngdMzDkbFxTBuHLRtC88/X/5Y4rTEMy6CWjJvfGyUiwk5ZW8qUpT7F91P7w696dGuB8AZPeRgoAoT\nJjjtloULITz89LGKF0HB+uaNlVXoJuRU1j/v2a4nT694Gpns/F9tMPXQVeG//9uZDrfsYhVQ+UVQ\n65s3XtZDNyGpqv45BN+KRVOmwOzZsHw5tG9/en9lF0FtiGJgsh66MVUoKC7gtn/fRmSzSADaNGvD\nbf++jcLiQsCpUINl6OIf/wjvvgtLlpRP5gBTV00ttx0fGW/JvJGzhG5CTkR4BBdFX8Sx/GMAHMs/\nxkXRF9E0vGm5qrUxt11U4amnYM4cZxbFmJjyx9s+09bz+cFGtAQLa7mYkLT+h/UMemsQcGbLBWjU\nQxdVnXlZFi+Gzz5z5mkpq2Iyj2wWSfbj2Q0cpakJa7kYU4nSO0R//sHPAejZriexbWI5dPIQ4PSV\nG/OF0eJiuO8+WLrUuaW/YjLvNrWbJfMgZhW6CTkVp8397+H/zbNXPlvunMZYoZ86BWPHwvHjMHcu\ntGlT/rhV5o2XVejGVKKguIAth7eU27fl8BbPBdGyGlN1fvQoXHmlMyRx0aIzk3nFyhzgoWEPNWCE\n9csKRYcldBNSIsIjaB3Ruty+mJYxNA1vCpRvuUxePrlRJPWdO+HSS2HoUJg1CyIiTh9LSk6i7TNt\ny90FCo17rLmqsid7D+9tfo+JiyZyyZuXcPO/bvZ3WAHBWi4mZJTeIbrl0Ba+O/KdZ3/aQ2nERsZ6\ntiuOzw7k5PfZZ06bZfJk+O1vzzxe+seprED+PJXJK8pj3Q/rWJm2kpT0FFLSUwBwxboYHjccV6yL\nQZ0H0bz5pY9cAAAT+klEQVRJ82peqfHytuVit/6bkFF6h+jc7XM9+/p27EtOYU6580qT3eTlkwM2\n+anCSy/Bs886QxMTKkw/U9nt/JHNInlo2EMB+XnKSjuWRkp6iieBbzm0hR91+BGuWBc3972ZF69+\nkfjIeESqzW8hp9qELiJvA9cBB1X1wirOeRkYDZwExqvqRp9GaYwPVNY/79a2m2cOl1JlK/TS34GU\nBHNznZEs69dDSgp061b+eFXJPBAvgOYX5bPhwAZS0lJYmb6SlLQUCooLcMW5GB47nOevfJ5LOl/C\nOU3P8XeojYI3Ffo7wF+BGZUdFJHRQA9V7SUiQ4HXgWG+C9EY36iuf16qbIVe9ncgJPVt2+DnP4cB\nA+Crr6BVq/LHK45kgcBK5j+c+IGUtBRPBf7NwW84/9zzccW6uP7863nmimfo3q67Vd+1VG1CV9X/\niEj8WU65AXeyV9XVIhIpIp1U9aCvgjSmrkr75xsyNpTbHwhJ2huq8M478Nhj8NxzMH48lM15SclJ\nTF019Yxk7s87QAuLC9l4YKOn770ybSU5BTm4Yl24Yl1MGTmFIV2G0CqiVfUvZrziix56FyCtzPZ+\n9z5L6CagbDm0hd3Zuz3brSNak5WXVe6CaKmkRGdd0couKja07Gy4/37YuNG5jb9fv/LHK2uxQMNP\ntHUw56CTvN0V+PqM9XRv1x1XrIure1xNUkIS5597vlXf9ajBL4omJSV5HicmJpKYmNjQIZgQlVeY\nV267Y8uO9OnQp8rzyw5Z9FfbZfFi+M1v4PrrYc0aOKdCK7mqFkt9X/wsKili88HN5UaeHD11lGGx\nw3DFunjq8qcY0mUIkc0j6y2GYJacnExycnKNn+eLhL4fiCuzHeveV6myCd2YhlDabsk8lVlu/+DO\ng8/on59NQyb148fh4YedYYnTpsEVV5Q/njgtkY0HNjZYvzwzN5NV6as8CXztD2uJaxPH8LjhjOg2\ngicue4I+HfoQJnZriy9ULHYnT/Zu9k9vE7q4fyqzALgPmC0iw4Bs65+bQLMhYwO5hbnl9v12UCUD\nt8uoeHG0IajC/Pnw4IPOAs6bNpW/6zNxWiJQ+apKvmqxFJcUs/Xw1nIjTw6ePMiQLkMYHjucx378\nGEO7DKVdi3Z1fi/jW94MW3wPSATOFZF9wCQgAlBVfVNVF4nINSKyE2fY4h31GbAxNeGpznPLV+e9\n2vciunV0jV9v2sZp9Vah79oFDzzg3Pn5zjswcuTpY0nJSSTvSa40kde1xZJ1KotV6as8Fy6//uFr\noltFOzfuxA7n967f07djX8LDwqt/MeNXdqeoCWoFxQX0+msv9h3bV27/sl8tI/G8RK9eo+JFR1+3\nNfLz4c9/hhdfhN//Hh555PTt+2eryKHmo1hKtITth7d7Ll6uTF9J+vF0Bnce7LnzcljsMM4959w6\nfirjS3anqAl5BcUF3Pj+jWck85pW58njk+k2tZtnPpRj+cdoPqU5eU/mVfPMs1N1loZ74gm44AJY\nuxbOO8855k0i79a2W7UtlmN5x1i9f7Vn5Mnq/as5t8W5uOKcoYMTh07kgqgLaBJmqSAYWIVuglJB\ncQG3fHALC79dSJEWlTtWk+q8rMqmnx0YPbBWfesvv3Sq8ZISeP55GDHidBKHqhM5VN0rV1W+PfKt\nJ3mnpKewO2s3gzoP8oz9dsW5iGoZVeN4jX95W6FbQjdBqapWS6/2vVjwywVnHa54Ns2nNCe/OL/c\nvoT4BPZk72H8wPHV9rHXr4ekJOdi56BxH5LZ/RUkzPlv4mxJvPR9Erslet4jpyCHNfvXeEaerEpf\nRZtmbcol7wGdBtRoJI8JTJbQTcgqKC5g1KxRLNuz7Ixjta3Oy6ps7HephPjTs2Ttyd5Dt7bdADix\nuzfbP7yJ4v0DiRv9Pp1HfMSKH5Z69X4J8QkkxCdw24DbnL63O4HvOLqDgdEDGR473NNCiWkdU/0L\nmkbHEroJSWdL5vGR8Xwy7pNaV+dlle2pn1X6EFj+P3BgAFz6LFz8FjTNr/Zpl8ZdyomCE3Q4pwPn\nND2HVemraNakWbkpYwdGD6RZk2Z1/iwm8FlCNyHnbMkcYMX4FVwaf6nP3q/KC5clYZB6A6Q8DMdj\n4cfPw0Vve5XIO7fuzPH845RoCf2j+p9O4HEuYtucOUWBCQ02ysWElOqS+VXdr6JDyw4+fc/SC5OJ\n0xLZk72HvYeOwIY7YNVD0OoguF6EPv+G8OIqX6NDiw4cyz+GiNCjXQ/uvOhOhscN5+KYi4N6wQZT\nP6xCN41eQXEBI6aNYGX6ykqPX9X9Kl4a/ZJPWi2VWb8e3nwTpr97ilZ9VhN79Rwie27z9NDzivI4\nnn+c9OPpAJwsPEnLpi1p06wNz1/5PMPjhtM1sqtNWmWqZBW6CQmbD27mzvl3sjZjbaXH6yuZnzgB\n778Pb7wBmZlw112wM7UFHTq5WJ/RzDNsMCUthcKSQlyxLm4fcDuuOJct2GDqjVXoptGasXEGt8+/\nvcrjifGJ/O26v/ksmRcVOZNlvfcefPSRM3Z8zPgfiOiewqr9zsiTbw5+Q+9ze3uGDbpiXbZgg6kz\nuyhqglJmbib7svcxcvpIjhVUPnQQIKZVDH+//u9c0+uaOr2fqjNt7bvvwuwPCunYfyN9fpJCUcxK\nNmSmcLLgpCdxu2JdDO4y2BZsMD5nCd0EneTdyYyYMaLa8+raZikudtbqfHf+Qf79dQqFnVJo1Xcl\nmU020KN9d8+wQVeci17te1n1beqdJXQTFDJzM8k4kcH4eeNZf2D9Wc+NOieKflH9eO3a12qczHNy\ni3h74SbmrExh3eEUtMtKws7J4uJOw7i673CGx7kY0mUIbZq1qf7FjPExS+imUfs281syTmR4VZED\ndDynI9NunOZ1i+XwyUzmrklh7tcprDuUwpFmazmnoCv927n42SXDuf4iF7079LYFG0xAsIRuGp1v\nM78l61QWu7J2MfbfY716jjdVeemCDZ9/t5IFG1LYcDiF4yUHiTg0lD6tXIy+YDh3jRpKjy5tfflx\njPEZS+gm4GXmZnIk9wgA3xz4hls+vMXr50Y2i6R5k+b844Z/nFGVly7Y8Pl3K1mamkLqia+RkzEU\n73bRq4WLa/q7uG10Xy68IBxrf5vGwBK6CThlE3jGiQxGzhiJUrN/H9o3b0/T8KaeRF66YMPKtBSW\npq7kq30pHM7bT0TmYAp3ubgg0sXo/sMYlXAugwdDM5v6xDRCltCN3/kigZcqrcj/OvqvRDaP5Ivv\nUlj67Uq2HVtNWF4HivcMp9lhFxdHubhm0AWMSGjCwIHQxG6dM0HAErppcKvSVnkWDq5rAi/Vumlr\nNL8NfVpfQlruTo4U76HJ4UGU7BlO75YuEnoMY8SQKIYOhS5dfPEpjAk8ltBNvcnMzWTnkZ3lVn3/\nfNfn3Lf4vrq9cHE4HI9D8tsiTQuQ1hloXiRNMlzEhw1nUCcXV1xwIcOHNqV3bwi3NYtNiLC5XEyd\nlG2XgHOhsV2LdjUaSlilvNZw5Hw4FgvaFCJOQLu90CaNiIJozmtyKYOihjP6AheJl0TTpQt28dIY\nL1iFHsLKJu3ShA0+apcUNoPsbpDVA472gGNdQQVaHoZOmyFuJWg44bldSIy7kl8P+znXDhpIm5YR\nPvhkxgQXa7kYvs38FiifrEu384ry6pa0FTjV7nTCzupe/nHTXOi1CLolQ/RGaJ1BWGEbIpo05cHL\n7+D+offZgg3GeMmnCV1ERgFTgTDgbVV9tsLxBGA+sMu9a66qTqnkdSyh+0Bpoi5VWcLed2xfjcZ1\nn6GwmbPazrGuzs/xOPfjuNPbUgLtvocO2yH+PxC9HtrvghZHQUpoGt6UZk2aMSlhEvcPud8WbDCm\nlnyW0EUkDPgOuAL4Afga+IWqppY5JwF4RFWvr+a1LKFXoqrWR2XbK/au4O6Fd9f+zUoEcjvCiRjI\niSn/+0Tn08k6ry20SYc2aRC5DyLdv9vsc5J4ZDpEnPK8bLiEExEewcQhE7l38L22YIMxPuTLi6JD\ngB2qutf9wu8DNwCpFc6z/3opXz1Xl5wBUg+n8rM5P6tbv1qBvEgnUZ/sCCejICf6zISdE+Mcb34M\nWmVA6wxo/YPzuMO3Tnskcp/z0/IQhFUekyCce8653D7gXm7ofQODOg+yBRuMCQDeJPQuQFqZ7XSc\nJF+RS0Q2AvuBR1V1mw/ia1TmbJlTtzZHqRKBU+1PJ+hqf3eAJnnOBcdzDju/SxN2zHrnd+l2y4PQ\npLDaEJqFN6NESwiTMPp27Ftuytjz2p5n1bcxAchXwxbXAV1VNVdERgPzgPMrOzEpKcnzODExkcTE\nRB+F4D85BTnE/yWeo3lHT+9UoLAF5LVzkvMp9++y21Udy28DzY6fTs5lf7fbBbGrzzzWpKBGMQtC\nm4g29Dy3J1f1uIpdWbtISS+/YMPwuOEM7jyYlhEtffuFGWPOKjk5meTk5Bo/z5se+jAgSVVHubcf\nB7TihdEKz9kNDFLVoxX2B10PPacgh96v9OaH/4yEtRPKJ2lRaJ7lXCRs4f59tu3Sx82zz7pSfHUE\noYk0oU3zNsz42QzP5FUHcw6Skp7CyjRnubQNGRvo0b6HJ3m7Yl30bN/Tqm9jAowvL4qGA9/iXBTN\nANYAv1TV7WXO6aSqB92PhwBzVLVbJa8VdAkdYOhbQ1mz+YjTo/Yk6Sxomufz92rdtDWFJYVMHTWV\nCZdMqPK8opIiNh3cREpaCivTV5KSlkJ2XjbDYod5EviQLkNo3ay1z2M0xvhWfQxbfInTwxafEZEJ\nOJX6myJyH3APUAicAn6nqqsreZ2gTOhbDm6h/+v9a/XcJtKEMAljYMxApt84vdbLpmXmZpKSluKp\nwNdlrCM+Mr7cYsW2YIMxjZPdWNSAFu1YxP2L7ueVa17x/K7r4sRnU1xSzJZDW0hJP53AD588zNDY\noZ7FiofGDqVtc1uwwZhgYAk9iBw9dZRV6as8FfjXP3xNTKuYciNP+nbsa9W3MUHKEnojVaIlbDu8\nzZO8U9JT2H98P4O7DGZ47HBccS6GxQ6jfYv2/g7VGNNALKE3EsfyjrF6/2rPyJPV6avp2LJjuZEn\nF0RdQHiYzRVrTKiyhB6ASrSE745854w8cSfwvcf2MihmkCeBD4sdRseWHf0dqjEmgFhCDwAn8k+w\nZv8az4XLVemraNu8bbkbd/pH9adpeFN/h2qMCWCW0BuYqrLz6E6n7+0e+/390e+5KOYiz8gTV5yL\n6FbR/g7VGNPIWEJvYFO+nMJb698ql7wHRg8kItwWbDDG1I0l9AZWVFJEkzBb0c8Y43veJnQbuOwj\nlsyNMf5mCd0YY4KEJXRjjAkSltCNMSZIWEI3xpggYQndGGOChCV0Y4wJEpbQjTEmSFhCN8aYIGEJ\n3RhjgoQldGOMCRKW0I0xJkhYQjfGmCBhCd0YY4KEVwldREaJSKqIfCcij1VxzssiskNENorIQN+G\naYwxpjrVJnQRCQNeAa4G+gG/FJE+Fc4ZDfRQ1V7ABOD1eog14CUnJ/s7hHpln6/xCubPBsH/+bzl\nTYU+BNihqntVtRB4H7ihwjk3ADMAVHU1ECkinXwaaSMQ7P9S2edrvIL5s0Hwfz5veZPQuwBpZbbT\n3fvOds7+Ss4xxhhTj+yiqDHGBIlq1xQVkWFAkqqOcm8/DqiqPlvmnNeBZao6272dCiSo6sEKrxWc\nC4oaY0w982ZNUW8Wwvwa6Cki8UAG8AvglxXOWQDcB8x2/wHIrpjMvQ3IGGNM7VSb0FW1WETuB5bg\ntGjeVtXtIjLBOaxvquoiEblGRHYCJ4E76jdsY4wxFVXbcjHGGNM4NPhFURH5o4h8IyIbROQTEYlu\n6Bjqk4g8JyLb3TdYfSgibfwdky+JyE0iskVEikXkYn/H4wve3DjXWInI2yJyUEQ2+TuW+iAisSLy\nhYhsFZHNIvKAv2PyJRFpJiKr3flys4hMOuv5DV2hi0grVc1xP54I9FXVexo0iHokIj8BvlDVEhF5\nBqct9f/8HZeviEhvoAR4A/i9qq73c0h14r5x7jvgCuAHnGtGv1DVVL8G5iMicimQA8xQ1Qv9HY+v\nuQvCaFXdKCKtgHXADcHyzw9ARM5R1VwRCQe+Ah5Q1TWVndvgFXppMndriZMcgoaqfqaqpZ9pFRDr\nz3h8TVW/VdUdQLBc4PbmxrlGS1X/A2T5O476oqoHVHWj+3EOsJ0guwdGVXPdD5vhXPessgr3yzh0\nEZkiIvuAW4H/8UcMDeROYLG/gzBn5c2Nc6YREJFuwEBgtX8j8S0RCRORDcABYKmqfl3VufWS0EVk\nqYhsKvOz2f37pwCq+qSqdgXeBSbWRwz1qbrP5z7nD0Chqr7nx1BrxZvPZ0wgcbdbPgAerNAFaPRU\ntURVL8L5v/2hItK3qnO9GYdemwCu9PLU94BFQFJ9xFFfqvt8IjIeuAYY2SAB+VgN/vkFg/1A1zLb\nse59ppEQkSY4yXymqs73dzz1RVWPi8gyYBSwrbJz/DHKpWeZzRtxel5BQ0RGAY8C16tqvr/jqWfB\n0Ef33DgnIhE4N84t8HNMviYExz+rqvwD2KaqL/k7EF8TkQ4iEul+3AK4Eqjygq8/Rrl8AJyPczF0\nL/BbVc1o0CDqkYjsACKAI+5dq1T1Xj+G5FMiciPwV6ADkA1sVNXR/o2qbtx/hF/i9I1zz/g5JJ8R\nkfeAROBc4CAwSVXf8WtQPiQiPwa+BDbjXCxU4AlV/cSvgfmIiPQHpuP8uxkGzFbVp6s8324sMsaY\n4GCzLRpjTJCwhG6MMUHCEroxxgQJS+jGGBMkLKEbY0yQsIRujDFBwhK6McYECUvoxhgTJP4/aSNh\nkUOU3owAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60d7fe28d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.special as scpsp \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "xvals = np.linspace(-20,1,500)\n",
    "ai,aip,bi,bip=scpsp.airy(xvals)\n",
    "m=np.sqrt(ai**2+bi**2)\n",
    "plt.plot(xvals,ai,label=\"Ai(x)\")\n",
    "\n",
    "plt.plot(xvals,bi,label=\"Bi(x)\")\n",
    "\n",
    "plt.plot(xvals,m,label=\"M(x)\")\n",
    "plt.legend()\n",
    "\n",
    "plt.show()\n",
    "\n",
    "xvals = np.linspace(-2,2,500)\n",
    "ai,aip,bi,bip = scpsp.airy(xvals)\n",
    "m = np.sqrt(ai**2+bi**2)\n",
    "theta = np.arctan(ai/bi)\n",
    "theta = np.array([t+ 3.1415926 if t<0  else t for t in theta])\n",
    "\n",
    "thetaapp0 = np.array([ np.pi/6.-.63134 * t for t in xvals])\n",
    "thetaappp = np.array([ .5*np.exp(-4/3.*t**(3/2)) for t in xvals])\n",
    "thetaappm = np.array([ np.pi/4 + 2./3. * np.sqrt(-t**3) for t in xvals])\n",
    "\n",
    "plt.title(\"$\\\\theta(x)$\")\n",
    "plt.plot(xvals,theta,label=\"$exacta$\")\n",
    "plt.plot(xvals,thetaapp0,label=\"$x \\\\approx 0$\" )\n",
    "plt.scatter(xvals,thetaappp,color=\"g\",marker=\"+\",label=\"$x\\\\rightarrow \\\\infty$\" )\n",
    "plt.scatter(xvals,thetaappm,color=\"g\",marker=\"*\",label=\"$x\\\\rightarrow -\\\\infty$\" )\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "m0 = np.array([.71 +.1957*t for t in xvals])\n",
    "mp = np.array([ np.exp(2/3 *t**(3/2))/t**(1./4.)/np.sqrt(np.pi) for t in xvals])\n",
    "mm = np.array([1./(-t)**(1./4.)/np.sqrt(np.pi)  for t in xvals])\n",
    "\n",
    "plt.title(\"M(x)\")\n",
    "plt.plot(xvals,m,label=\"exacta\")\n",
    "plt.plot(xvals,m0,label=\"$x \\\\approx 0$\" )\n",
    "plt.scatter(xvals,mp,color=\"g\",marker=\"+\",label=\"$x\\\\rightarrow \\\\infty$\" )\n",
    "plt.scatter(xvals,mm,color=\"g\",marker=\"*\",label=\"$x\\\\rightarrow -\\\\infty$\" )\n",
    "\n",
    "plt.legend(loc=0)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cálculo de los coeficientes de transmisión"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conviene entonces escribir la solución de la ecuación de onda con energía $E=\\frac{\\hbar^2 k^2}{2 m}$ como\n",
    "\n",
    "$$\n",
    "\\psi(x)=\\left\\{\n",
    "\\begin{array}{l r}\n",
    "A_l e^{{\\bf i}k x}+B_l e^{-{\\bf i}k x}   &  x <a \\\\\n",
    "\\left.u Ai(z)+v Bi(z)\\right|_{z=\\frac{x}{\\alpha}-(k \\alpha)^2}             &  0 \\leq  x\\leq a\\\\\n",
    "A_r e^{{\\bf i}k (x-a)} +  B_r e^{-{\\bf i}k (x-a)}   & x>a\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Escribimos las condiciones de continuidad en $x=0$\n",
    "\n",
    "$$\n",
    "\\left(^{Ai(z_l)}_{Ai(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi(z_l)/\\alpha} \\right)\\left(^{u}_{v} \\right)=\n",
    "\\left(^{1}_{{\\bf i k}}\\;^{1}_{-{\\bf i k}} \\right)  \\left(^{A_l}_{B_l} \\right)\n",
    "$$\n",
    "\n",
    "y en $x=a$,\n",
    "\n",
    "$$\n",
    "\\left(^{Ai(z_r)}_{Ai(z_r)/\\alpha}\\;^{Bi(z_r)}_{Bi(z_r)/\\alpha} \\right)\\left(^{u}_{v} \\right)=\n",
    "\\left(^{1}_{{\\bf i k}}\\;^{1}_{-{\\bf i k}} \\right)  \\left(^{A_r}_{B_r} \\right)\n",
    "$$\n",
    "\n",
    "donde $z_l=\\frac{a}{\\alpha}$ y $z_r=\\frac{a}{\\alpha}-(\\alpha k)^2$. De esta manera,\n",
    "\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &=&\\left(^{1}_{{\\bf i} k}\\;^{1}_{-{\\bf i }k} \\right)^{-1}\\left(^{Ai(z_l)}_{Ai^{'}(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi^{'}(z_l)/\\alpha} \\right)\n",
    "\\left(^{Ai(z_r)}_{Ai^{'}(z_r)/\\alpha}\\;^{Bi(z_r)}_{Bi^{'}(z_r)/\\alpha} \\right)^{-1}\n",
    "\\left(^{1}_{{\\bf i }k}\\;^{1}_{-{\\bf i }k} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "   &=&\\frac{\\alpha^2}{2{\\bf i}k \\alpha W(z_r)}\\left(^{{\\bf i} k}_{{\\bf i }k}\\;^{1}_{-1} \\right)\\left(^{Ai(z_l)}_{Ai^{'}(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi^{'}(z_l)/\\alpha} \\right)\n",
    "\\left(^{Bi^{'}(z_r)/\\alpha}_{-Ai^{'}(z_r)/\\alpha}   \\;   ^{-Bi(z_r)}_{Ai(z_r)} \\right)\n",
    "\\left(^{1}_{{\\bf i }k}\\;^{1}_{-{\\bf i }k} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "   &=&\\frac{\\pi}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{{\\bf i} k \\alpha}_{{\\bf i }k \\alpha}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{Ai(z_l)}_{Ai^{'}(z_l)}\\;^{Bi(z_l)}_{Bi^{'}(z_l)} \\right)\n",
    "\\left(^{Bi^{'}(z_r)}_{-Ai^{'}(z_r)}   \\;   ^{-Bi(z_r)}_{Ai(z_r)} \\right)\n",
    "\\left(^{1}_{{\\bf i }k \\alpha}\\;^{1}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "con $W(z)=\\det\\left(^{Ai(z)}_{Ai^{'}(z)}\\;^{Bi(z)}_{Bi^{'}(z)} \\right)=W(0)=\\frac{1}{\\pi}$\n",
    "es el Wronskiano asociado a las funciones de Airy, y donde usamos que\n",
    "$$\n",
    "\\left(^{a}_{c}\\;^{b}_d\\right)^{-1}=\\frac{1}{\\det \\left(^{a}_{c}\\;^{b}_d\\right)}\\left(^{d}_{-c}\\;^{-b}_a\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideremos ahora el coeficiente de transmisión $T$ para una partícula que se mueve desde la izquierda. En tal caso, $B_r=0$, y $T=\\frac{|A_r|^2}{|A_l|^2}$.\n",
    "\n",
    "Consideremos varios límites."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bajas energías"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $k \\alpha\\ll 1$, \n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &\\approx&\n",
    "\\frac{\\pi}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{0}_{0}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{Ai(0)}_{Ai^{'}(0)}\\;^{Bi(0)}_{Bi^{'}(0)} \\right)\n",
    "\\left(^{Bi^{'}(a/\\alpha)}_{-Ai^{'}(a/\\alpha)}   \\;   ^{-Bi(a/\\alpha)}_{Ai(a/\\alpha)} \\right)\n",
    "\\left(^{1}_{0}\\;^{1}_{0} \\right)  \\left(^{1}_{0} \\right)\\\\\n",
    "&=&\n",
    "\\frac{\\pi Bi^{'}(a/\\alpha)}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{Ai^{'}(0)}_{-Ai^{'}(0)}\\;^{Bi^{'}(0)} _{-Bi^{'}(0)} \\right)\n",
    "\\left(^{1}_{-Ai^{'}(a/\\alpha)/Bi^{'}(a/\\alpha)}  \\right)\n",
    " \\\\\n",
    "&=&\n",
    "(Ai^{'}(0)Bi^{'}(a/\\alpha)-Bi^{'}(0) Ai^{'}(a/\\alpha)) \\frac{\\pi }{2{\\bf i}k \\alpha}\n",
    "   \\left(^{1}_{-1}\\right)\n",
    "\\end{eqnarray*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $a/\\alpha \\ll 1$ (barrera delgada), $Ai^{'}(a/\\alpha)\\rightarrow \\frac{1}{3^{1/3}\\Gamma(1/3)}\\approx -0.26$, $Bi^{'}(a/\\alpha)\\rightarrow \\frac{3^{1/6}}{\\Gamma(1/3)}\\approx 0.45\\, ,$ y \n",
    "$$\n",
    "\\left(^{A_l}_{B_l} \\right) \\approx\n",
    "{\\bf i}\\frac{a^2}{4 k \\alpha^3}\\left(^{1}_{-1} \\right)={\\bf i}\\frac{a^2 k_0^2}{4 k a}\\left(^{1}_{-1} \\right)\n",
    "$$\n",
    "\n",
    "de donde obtenemos, para el coeficiente de transmisión, $T\\approx \\frac{16 k^2 /k_0^2 }{a^2 k_0^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por otro lado, si la barrera es ancha, $Ai^{'}(z_r) \\rightarrow 0$, $Bi^{'}(z_r)\\rightarrow \\frac{e^{-2/3 (a/\\alpha-(k \\alpha)^2)^{3/2} }}{\\sqrt{\\pi}\\sqrt[4]{a/\\alpha}}$ y\n",
    "\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &\\approx&\n",
    "{\\bf i} (0.23 \\frac{e^{2/3 (a/\\alpha-(k \\alpha)^2)^{3/2} }}{\\sqrt[4]{a/\\alpha}k \\alpha})\n",
    "   \\left(^{1}_{-1}\\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "de manera que $T\\approx 18.9 (k \\alpha)^2 \\sqrt{a/\\alpha} e^{-4/3 (a/\\alpha-(k \\alpha)^2)^{3/2}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Límite de altas energías"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para altas energías, $z_l < z_r \\ll 1$, por lo que podemos usar la aproximación asintótica para las funciones de Airy:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "Ai(z)&\\rightarrow &\\frac{1}{\\sqrt{\\pi}(-z)^{-1/4}}\\sin(\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3})\\\\\n",
    "Bi(z)&\\rightarrow &\\frac{1}{\\sqrt{\\pi}(-z)^{-1/4}}\\cos(\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3})\\\\\n",
    "Ai^{'}(z)&\\rightarrow &- (-z)^{1/2} Bi(z) \\\\\n",
    "Bi^{'}(z)&\\rightarrow & (-z)^{1/2} Ai(z)\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De esta manera, definiedo $\\theta_{^l_r}=\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z_{^l_r}}$,  podemos escribir la ecuación matricial como\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "(^{A_l}_{B_l})&\\approx&\\frac{1}{2{\\bf i}k \\alpha (z_l z_r)^{1/4}}\n",
    "   \\left(^{{\\bf i} k \\alpha}_{{\\bf i }k\\alpha}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{1}_{0}\\;^{0}_{\\sqrt{-z_l}} \\right)\n",
    "   \\left(^{\\sin(\\theta_l)}_{-\\cos(\\theta_l)}\\;^{\\cos(\\theta_l)}_{\\sin(\\theta_l)} \\right)\n",
    "\\left(^{\\sin(\\theta_r)}_{\\cos(\\theta_r)}   \\;   ^{-\\cos(\\theta_r)}_{\\sin(\\theta_r)} \\right)\n",
    "\\left(^{\\sqrt{-z_r}}_{0}\\;^{0}_{1} \\right)\n",
    "\\left(^{1}_{{\\bf i }k \\alpha}\\;^{1}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{1}{2{\\bf i}k \\alpha (z_l z_r)^{1/4}}\n",
    "   \\left(^{-{\\bf i} k \\alpha}_{-{\\bf i }k\\alpha}\\;^{-\\sqrt{-z_l}}_{\\sqrt{-z_l}} \\right)\n",
    "   \\left(^{\\cos(\\theta_r-\\theta_l)}_{-\\sin(\\theta_r-\\theta_l)}\\;^{\\sin(\\theta_r-\\theta_l)}_{\\cos(\\theta_r-\\theta_l)} \\right)\n",
    "\\left(^{\\sqrt{-z_r}}_{{\\bf i }k \\alpha}\\;^{\\sqrt{-z_r}}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{\\sqrt{k \\alpha}}{2{\\bf i}   \\sqrt[4]{1 - k_0^2/k^2}}\n",
    "   \\left(^{-{\\bf i} }_{-{\\bf i }}\\;^{-1}_{1} \\right)\n",
    "   \\left(^{\\cos(\\theta_r-\\theta_l)}_{-\\sin(\\theta_r-\\theta_l)}\\;^{\\sin(\\theta_r-\\theta_l)}_{\\cos(\\theta_r-\\theta_l)} \\right)\n",
    "\\left(^{\\sqrt{1 - k_0^2/k^2}}_{{\\bf i }}\\;^{\\sqrt{1 - k_0^2/k^2}}_{-{\\bf i }} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{-\\sqrt{k \\alpha}}{2   \\sqrt[4]{1 - k_0^2/k^2}}\n",
    "   \\left(^{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}+1)}_{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}-1)} \\;\\;^{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}-1)}_{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}+1)}\\right)\n",
    "  \\left(^{A_r}_{B_r} \\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "Finalmente, \n",
    "$|A_l|^2 \\approx |A_r|^2\\frac{k \\alpha}{4 \\sqrt{1-k_0^2/k^2}}(\\sqrt{1 + k_0^2/k^2}-1)^2$, \n",
    "$|B_l|^2 \\approx |A_r|^2\\frac{k \\alpha}{4 \\sqrt{1-k_0^2/k^2}}(\\sqrt{1 - k_0^2/k^2}-1)^2$\n",
    "y por lo tanto,\n",
    "$$\n",
    "R= \\frac{|B_l|^2}{|A_l|^2}\\approx \\frac{(\\sqrt{1 - k_0^2/k^2}-1)^2}{(\\sqrt{1 - k_0^2/k^2}+1)^2}\n",
    "\\approx \\frac{k_0^4}{16 k^4}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-17T12:26:59.961217Z",
     "start_time": "2018-09-17T12:26:57.194930Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: divide by zero encountered in cdouble_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: invalid value encountered in cdouble_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: divide by zero encountered in cdouble_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: invalid value encountered in cdouble_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: divide by zero encountered in cdouble_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: invalid value encountered in cdouble_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.special as scpsp \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def theta(z):\n",
    "    ail = scpsp.airy(z)\n",
    "    ml = np.sqrt(ail[0]**2 + ail[2]**2)\n",
    "    thl = np.arctan2(ail[0],ail[2])\n",
    "    mllnp = (ail[0]*ail[1]+ail[2]*ail[3])/ml**2\n",
    "    thlp = 1./(np.pi*ml**2)\n",
    "    return thl \n",
    "\n",
    "def coeftransm(k=0.,a = 10.**(1./3.),alpha=1.):\n",
    "    zl = -(k * alpha)**2\n",
    "    zr = a/alpha + zl\n",
    "    ail = scpsp.airy(zl)\n",
    "    ml = np.sqrt(ail[0]**2 + ail[2]**2)\n",
    "    thl = np.arctan2(ail[0],ail[2])\n",
    "    mllnp = (ail[0]*ail[1]+ail[2]*ail[3])/ml**2\n",
    "    thlp = -1./(np.pi*ml**2)\n",
    "    \n",
    "    air = scpsp.airy(zr)    \n",
    "    mr = np.sqrt(air[0]**2 + air[2]**2)\n",
    "    thr = np.arctan2(air[0],air[2])\n",
    "    mrlnp = (air[0]*air[1]+air[2]*air[3])/mr**2\n",
    "    thrp = -1./(np.pi*mr**2)\n",
    "    \n",
    "    u = (1.j*k*alpha-mrlnp)*np.cos(thr)/thrp + np.sin(thr)\n",
    "    v = -(1.j*k*alpha-mrlnp)*np.sin(thr)/thrp + np.cos(thr)\n",
    "    al = (u*np.sin(thl)+v*np.cos(thl))*(1.j*k*alpha+mllnp)\n",
    "    al = al + thlp * ( u * np.cos(thl) - v * np.sin(thl) )\n",
    "    al = al/(2.*1.j*k*alpha)\n",
    "    t = mr**2/ml**2/(al*al.conj()).real\n",
    "    return (t,u,v)\n",
    "\n",
    "\n",
    "def coeftransm_app(k=0.,a = 10.**(1./3.),alpha=1.):\n",
    "    t=.5\n",
    "    k0 = np.sqrt(a/alpha**3)\n",
    "    if k > k0:\n",
    "        t=1- (.5*k0/k)**4 \n",
    "    elif k<k0:\n",
    "        if a/alpha>1:\n",
    "            t = 18.9\n",
    "            t = t * (k*alpha)**2*np.sqrt(a/alpha)\n",
    "            t = t * np.exp(-4./3.*(a/alpha)**1.5 * (1-(k/k0)**2)**1.5)\n",
    "        else:\n",
    "            t= 16.*(k/k0)**2/(a*k0)**2\n",
    "    if t>1:\n",
    "        t=np.nan\n",
    "    return (t,1-t)\n",
    "\n",
    "\n",
    "\n",
    "ks = np.linspace(0,4.,100)\n",
    "ens = ks**2\n",
    "\n",
    "a=1.\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a= \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=False)\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.title(\"Barrera intermedia\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "ks = np.linspace(0,4.,100)\n",
    "a=(10.**(1/3.))\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\sqrt[3]{10} \\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a=\\\\sqrt[3]{10} \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=False)\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.title(\"Barrera ancha\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "ks = np.linspace(0,3.,100)\n",
    "a=(.1**(1/3.))\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\sqrt[3]{.1} \\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a=\\\\sqrt[3]{.1} \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=False)\n",
    "plt.title(\"Barrera delgada\")\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.legend(loc=4)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generación de gráficos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-20T11:19:44.215647Z",
     "start_time": "2018-09-20T11:19:44.051003Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('text', usetex=False)\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "x3s=np.linspace(-3.2,-1.4,100)\n",
    "wf=.1*np.exp(-(x3s+2.4)**2/.25)*np.cos(20.*(x3s+1.8))+1.\n",
    "plt.plot(x3s,wf,color=\"b\")\n",
    "\n",
    "x3s=np.linspace(-1.2,.7,100)\n",
    "ks = np.array([ 20.*(1-x) if 0<x<1 else 20. for x in x3s])\n",
    "wf=.095*np.exp(-(x3s+0.2)**2/.25)*np.cos(ks*(x3s))+1.\n",
    "plt.plot(x3s,wf,color=\"orange\")\n",
    "\n",
    "x3s=np.linspace(1.1,2.9,100)\n",
    "wf=.03*np.exp(-(x3s-1.8)**2/.25)*np.cos(20*(x3s+1.8))+1.\n",
    "plt.plot(x3s,wf,color=\"green\")\n",
    "\n",
    "\n",
    "\n",
    "xs=np.linspace(-3,3,100)\n",
    "vs=np.array([1.3*x if 0.<x<1. else 0 for x in xs])\n",
    "plt.xlabel(\"$x/a$\")\n",
    "plt.ylabel(\"$V(x)$\")\n",
    "plt.text(1.2,1.2,\"$V_0$\")\n",
    "plt.plot(xs,vs,color=\"red\")\n",
    "plt.arrow(-2.2,1.15,.5,0.,color=\"b\",shape=\"right\",head_width=.05,head_length=.15)\n",
    "plt.arrow(.1,1.15,-.5,0.,color=\"orange\",shape=\"left\",head_width=.05,head_length=.15)\n",
    "plt.arrow(1.7,1.15,.5,0.,color=\"green\",shape=\"right\",head_width=.05,head_length=.15)\n",
    "\n",
    "plt.savefig(\"grafico-barrera.png\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "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": "3.5.5"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "toc": {
   "toc_cell": false,
   "toc_number_sections": true,
   "toc_threshold": 6,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}