2015 経済動学 講義資料 (2015-06-15)

2015-06-15.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import itertools\n",
    "\n",
    "import numpy as np\n",
    "import scipy.linalg as la\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearSystem:\n",
    "    \"\"\"Linear/Affine system\"\"\"\n",
    "\n",
    "    def __init__(self, A, origin=None):\n",
    "        self.A = A\n",
    "        self.origin = np.zeros(self.dim) if origin is None else np.asarray(origin)\n",
    "\n",
    "    def forward(self, x):\n",
    "        return np.dot(self.A, np.asarray(x) - self.origin) + self.origin\n",
    "\n",
    "    def reverse(self, x):\n",
    "        return la.solve(self.A, np.asarray(x) - self.origin) + self.origin\n",
    "\n",
    "    def eig(self):\n",
    "        \"\"\"Eigen values and eigen vectors\"\"\"\n",
    "        return la.eig(self.A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Ramsey:\n",
    "    \"\"\"One-sector Ramsey model\"\"\"\n",
    "\n",
    "    def __init__(self, A, α, ρ):\n",
    "        self.A, self.α, self.ρ = A, α, ρ\n",
    "\n",
    "    def f(self, x):\n",
    "        \"\"\"Production function\"\"\"\n",
    "        return self.A * x ** self.α\n",
    "\n",
    "    def U(self, x):\n",
    "        \"\"\"Utility from consumption\"\"\"\n",
    "        return np.log(x)\n",
    "\n",
    "    def u(self, x, y):\n",
    "        \"\"\"Reduced form utility\"\"\"\n",
    "        return self.U(self.f(x) - y)\n",
    "\n",
    "    def is_feasible(self, x, y):\n",
    "        \"\"\"Checks feasibility\"\"\"\n",
    "        return x >= 0 and y >= 0 and self.f(x) >= y\n",
    "\n",
    "    def steady_state(self):\n",
    "        \"\"\"Steady state for the model\"\"\"\n",
    "        A, α, ρ = self.A, self.α, self.ρ\n",
    "        koo = (ρ * α * A) ** (1 / (1 - α))\n",
    "        return np.array([koo, koo])\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"Forward evolution\"\"\"\n",
    "        A, α, ρ = self.A, self.α, self.ρ\n",
    "        return np.array([\n",
    "            x[1],\n",
    "            ((1 + ρ * α) * A * x[1] ** α -\n",
    "             ρ * α * (A ** 2) * (x[1] ** (α - 1)) * (x[0] ** α))\n",
    "        ])\n",
    "\n",
    "    def reverse(self, x):\n",
    "        \"\"\"Backward evolution\"\"\"\n",
    "        A, α, ρ = self.A, self.α, self.ρ\n",
    "        return np.array([\n",
    "            ((((1 + ρ * α) * A * x[0] ** α - x[1]) /\n",
    "              (ρ * α * A ** 2 * x[0] ** (α - 1))) ** (1 / α)),\n",
    "            x[0]\n",
    "        ])\n",
    "\n",
    "    def jacobian(self, x=None):\n",
    "        \"\"\"Returns jacobian matrix\"\"\"\n",
    "        A, α, ρ = self.A, self.α, self.ρ\n",
    "\n",
    "        def _jacobian(x):\n",
    "            \"\"\"Jacobian as a function of state\"\"\"\n",
    "            return  np.array([\n",
    "                [0, 1],\n",
    "                [-ρ * ((α * A) ** 2) * ((x[0] * x[1]) ** (α - 1)),\n",
    "                 (α * (1 + ρ * α) * A * x[0] ** (α - 1) -\n",
    "                  ρ * α * (α-1) * (A ** 2) * (x[0]**α) * (x[1] ** (α-2)))]\n",
    "            ])\n",
    "\n",
    "        if x is None:\n",
    "            return _jacobian(self.steady_state())\n",
    "        return _jacobian(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def linearize(diffsys, ss):\n",
    "    \"\"\"Linearize differentiable system around a steady state\"\"\"\n",
    "    if not np.allclose(diffsys.forward(ss), ss):\n",
    "        raise ValueError(\"Not a steady state\")\n",
    "    return LinearSystem(diffsys.jacobian(ss), ss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Simulation:\n",
    "    \"\"\"Simulation of a dynamical system\"\"\"\n",
    "\n",
    "    def __init__(self, system, x0=None, duration=np.Inf, inverse=False, domain=None):\n",
    "        self.system = system\n",
    "        self.x0 = x0\n",
    "        self.duration = duration\n",
    "        self.inverse = inverse\n",
    "        if domain is not None:\n",
    "            self.domain = domain\n",
    "        else:\n",
    "            self.domain = lambda x: True\n",
    "\n",
    "    def __iter__(self):\n",
    "        x = self.x0[:]\n",
    "        tick = self.system.forward if not self.inverse else self.system.reverse\n",
    "        t = itertools.count()\n",
    "        while next(t) < self.duration and self.domain(x):\n",
    "            yield x\n",
    "            x = tick(x)\n",
    "        del t\n",
    "\n",
    "    def reset(self, x0=None, duration=None, inverse=None):\n",
    "        \"\"\"Reset simulation parameters\"\"\"\n",
    "\n",
    "        if x0 is not None:\n",
    "            self.x0 = x0[:]\n",
    "        if duration is not None:\n",
    "            self.duration = duration\n",
    "        if inverse is not None:\n",
    "            self.inverse = inverse\n",
    "        return self\n",
    "\n",
    "    def __repr__(self):\n",
    "        text = \"Simulation({},\\n\"\n",
    "        text += \"           x0={},\\n\"\n",
    "        text += \"           duration={})\"\n",
    "        return text.format(\n",
    "            str(self.system),\n",
    "            str(self.x0),\n",
    "            str(self.duration)\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_initial_near_eqm(linsys, eps=1e-5):\n",
    "    init_vals = []\n",
    "    signs = [-1, 1]\n",
    "    lambdas, V = linsys.eig()\n",
    "    for i, lambda_ in enumerate(lambdas):\n",
    "        for sign in signs:\n",
    "            init_vals.append((lambda_, linsys.origin + sign * eps * V[:, i]))\n",
    "    return init_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def quiver_plot(ax, path, **kwargs):\n",
    "    options = {\n",
    "        'scale_units': 'xy',\n",
    "        'angles': 'xy',\n",
    "        'scale': 1,\n",
    "        'width': 0.003,\n",
    "        'color': 'black'\n",
    "    }\n",
    "    options.update(kwargs)\n",
    "    path = np.asarray(path)\n",
    "    return ax.quiver(path[:-1, 0], path[:-1, 1],\n",
    "                     path[1:, 0]-path[:-1, 0], path[1:, 1]-path[:-1, 1], **options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD7CAYAAAClvBX1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeYXVXVx/HPTm+EVAIJgZDQpUoLCEgnhA6h9yJIkSrY\n",
       "QEFeRUQREUWkCoihCBIQwQIoIkFQikjoNQklCZ0kpJ33j3WHDGGSzCQzt8zs7/PcJzNz9z1nzcmd\n",
       "311n7VVSURQymUwmU1u0q7QBmUwmk2k6WbwzmUymBsninclkMjVIFu9MJpOpQbJ4ZzKZTA2SxTuT\n",
       "yWRqkA7lOlFKKeckZjKZzCJQFEWa92dlE+/5GdCWSCmdVRTFWZW2o9Lk65CvAW37GqSUVsYO2Bbb\n",
       "4CX8A3/DPzG9tLQbnmvoGGUV70wmk2mLpJT6YHtzxbqLEOu/Yjy+29RjZvHOZDKZZial1BGbmivY\n",
       "q+DfQrAPx1P1lp+6KOfI4l1e7qu0AVXCfZU2oAq4r9IGVAH3VdqA5qQUCtlJiPUX8Brux48wFh/P\n",
       "56X/XKTzlau3SUqpaOsx70wm03pIKXUXQr2D8LC7CbH+O+7BlGY4TTc8V/ENy0wmk6lVUkoJa2Ik\n",
       "RmB9/E/cQRyFJ8tqT/a8M5lMpmFSSj2FUNdlhiThWd8rRPvDFjYhe96ZTCazMEre9Xrmetdr4TEh\n",
       "1Afi2YoZNw9ZvDOZTJsmpdRXeNZ13vVU4V3/SsSwp1XOuvmTxTuTybQpSt71+thZCPaqeFh415fg\n",
       "xYoZ1wSyeGcymVZPSqmHCIPsVPp3uohb/xQPmH8aX6XZYH5PZPHOZDKtklLe9S7YUYjg40Kw98IL\n",
       "FTStsWyBK+b3ZM42yWQyrYJSVeOWwrseiSVFr5C/iLzrls4MaU5G4hf4I3ZpSDuzeGcymZolpbS0\n",
       "ud71FnhFeNd/ElkitdjNdE9ciN/gHDybxTuTydQ0pc3GDcwV7GGivPweIdhvVc66ZuFgnItfCuHO\n",
       "ed6ZTKY2SSl1xnbYVQj2x0KsfyiEe2blrGtWjsEZohfKTxa2OIt3JpOpOkq517sJD3tL0dP6L9gf\n",
       "z1TQtJbiNJyEs3BZY16QxTuTyVQFKaVVsLsQ7DVFJ74/40xMrqBpLc3ZOEII+PWNfVEW70wmUxFS\n",
       "Su1E69TdRIZIHxEOuVwUzEyf74tbB+1E6GdvHI/fN+XFWbwzmUzZSCl1E1WNu5b+fUeEQ76K/6jN\n",
       "7JBFoQMuEtfgSLHZ2uQDZDKZTIuRUuqPPYSHvaloo/rn0vcvVdC0StFZZJNsJrJL7l+Ug2TxzmQy\n",
       "zU5KaTmMEqK9tihBv1uM/Hq3gqZVmm64EutgP9FTZZHI4p3JZJqFlNJqovR8N6wgimWuEWGR1h6/\n",
       "bgw9ca3ITR9lMYc3LFS8U0ojRLVPe1xeFMV58zzfD9dh6dLxflQUxdWLY1Qmk6l+6nXnGyVi2H1E\n",
       "7PbHIhQwq3LWVR198Fv0Fxk1zy3uARdYYZlSai9yKrfBBOHi71cUxbh6a85C56IovlES8mcwoCiK\n",
       "WfMcK1dYZjI1TkkTNhcl3LuIDcY/4Q9CH9rKhmNTWBo3iFj33ni1Ca9d5ArLDfF8URQvQ0pptPiE\n",
       "HVdvzeti2gRxWzBlXuHOZDK1S6nh0/ZCsHcSOdd3i9zk/1XQtFpgOSHcM4XH/XpzHXhh4j1IjK+v\n",
       "Yzw2mmfNZbgnpTQRS4hPlkwmU8OklDqJvtd7i5L0l0WHu7aaIbIorCiEe4rYnGyOafKfsDDxbswt\n",
       "0DfxWFEUW6SUhuHPKaW1i6L4YN6FpRBLHfcVRXFfoy3NZDItSkmwdxCCPVJMlLlTjAabWEHTapE1\n",
       "RIz7ZTH78r0mvHZjbFL6uuP8Fi1MvCdgcL3vBwvvuz6b4HtQFMULKaWXsAoemfdgRVGctZDzZTKZ\n",
       "MlIS7JHYRwj3C7JgLy7riSSO/+IwfNTE1z9YehAx7680tGhh4v0IVkopDRH/kfsI978+T4sNzQdS\n",
       "SgOEcNfEDLhMpi1S6tJXJ9gj8LwQ7B/Lgr24bIqrRLfDo7VgiuQCxbsoilkppePF5kR7XFEUxbiU\n",
       "0tGl5y/F93FVSulxUat/elEUb7eUwZlMpumUBHtHERIZIVLV7sT5mnETrY2zLS4VenmCFm5Vm4cx\n",
       "ZDKtlFKWyA6ijeoOIo33TozBGxU0rTWyq+hVcrPoDjinmY6bhzFkMm2BUqe+rYRg7yrGgt0uutdl\n",
       "wW4Z9hN3MFfiO8qU657FO5OpcUqVjsNFVsOeeBt3iDBJUwpCMk3nSNGP+6fiA7JsZPHOZGqUlNLa\n",
       "wsPeG0l42PtpnZNmqpETcbrItvtFuU+exTuTqSFKtRQHYl/0EmXpx4lJ6Zny8S0cK+pcfl0JA7J4\n",
       "ZzJVTikF9yDhVQ8RlY5nilzg3EukvCThaR8kZk7eVClDsnhnMlVIaeLMKNGsfwMxHuwi0WY19w6q\n",
       "DO1xgdgI/rK466kYWbwzmSqh1LFvW+HV7YTHcYso9phWQdMydMLPRSbPYeJDtKJk8c5kKkxKaR0c\n",
       "Iioe3xGCvQXerKBZmbl0wRXiDugAMdW+4mTxzmQqQEppkAiJHCga9d9W+vrpStqVaZAtxSi3vVXR\n",
       "xnAW70ymTKSUeggBOAifF0N4zxFTZ/LGY/XRB8eIfi9f0LTOgC1OFu9MpgUpFdBsJQYX7CSavd1S\n",
       "+j7PdaxOeosNycMxSYSwZlTSoIbI4p3JtAClTpxHiNDIxyKlbDMhBpnqpIfI3T4S3Us/O0cVCjdZ\n",
       "vDOZZiOl1FUUzxyKNUUTqGPxaAXNyjSeD8XwhDrh/qfIqa9KclfBTGYxKIVFviC87N3xBG4UOcAf\n",
       "V9C0TNNZFaNFi9wVRT73UxW1KHcVzGSal5TSQBETPVjkAN8khpLkYQa1yTr4jegLc7CYEFZp4V4g\n",
       "2fPOZBpJSqkDdhFFM8NF0/3RqiTvN7PIDMc1YjP5cNW1kZw970xmUUkpDRWCfbDoif1b0QxqaiXt\n",
       "yjQLW4gCnHvF/kRVbk42RBbvTKYBSlNoRuFL4pZ6jMjPrupb6UyTGClauY7ByZhdWXOaRhbvTKYe\n",
       "KaVVhJd9EF4SXvaRqutWOrP47CWaTF0n2rrWXJFUFu9Mm6c0nHdvHIXVcavwup+rpF2ZFuMQMTj9\n",
       "EvxfhW1ZZLJ4Z9osKaXVRJyzbvrMb8X4sJqJe2aazLFikML5uLDCtiwW7SptQCZTTlJKHVJKe6WU\n",
       "7hM9RTqKfN69RNl6Fu7Wy+lCuL+jBoT7L6z3PlfP7/nseWfaBCmlZUSToSNFxsg1ohIyi3XrJ4kh\n",
       "wYfjq+IOq2q5k7U257TubDV1AV0Ms+edabWkYKuU0u9Eq9WVxR/wTqIKMgt366cdfiTi3MepYuG+\n",
       "ldU/4Mod+GMH+j7Cgb3jjrBBsuedaXWklJYQIn2MCItcJ26X36+kXZmy01GMjtte3HH9ubLmNMxo\n",
       "VhrJqUuw8wyeeozDNuFPpdFJ3eb3uizemVZDSml1MRR2b1H1eDb+VlGjMpWiCy4VfWcOxj8qa85n\n",
       "+TVDd+PkJdh9Fs8/ydFf5A9vNzJtMYt3pqZJKbXDjkK01xbl6rnHSNumm9joW1N0eXykotbMwyUM\n",
       "3o+TezJqFq88zfHbMGYic5pynCzemZqkNJXmSBwvYtdXl77PnfzaNkviWqwg4sVPVtacuVzAwEM5\n",
       "sRf7zmbi83x1BL97cRErO7N4Z2qKlNIwnCjmPT6Cb+CBihqVqRb6ig3JvthDlRRZncNSx3JCbw6Y\n",
       "zeSX+Oae3PgYMxfnuFm8M1VPvVFip4hWnb/DDnitknZlqoplcINoz7s7Xq2sOXyTvidzXF8OmcN7\n",
       "r/DdffnNQ82U5ZTFO1O1pJQ6ic2mk8UG1NXC687d/DL1WV4I98fYTeTxV4yT6P1NjunL4QVTx3Pe\n",
       "YVzz12buj5PFO1N1pJR6i1j2cXgeP8Rf1GDzoEyLs5IQ7knYH1MqZciX6HkOR/XnSwUzX+eCE7n6\n",
       "dy3kbGTxzlQNKaXlcZqIZ/9NFFb8t6JGZaqZNUSM+0XRBbIiefz70P0nHDkgulGmN7nkdC6/LmZi\n",
       "thhZvDMVJ6W0vug7sR1uxraYUFGjMtXOBiKr5HEcpgKhtF3o+nMOW4ZjE50mcdnZ/OoS3ivH+bN4\n",
       "ZypCaRNypBDtVUQ8e7hcBZlZOJvhKlF4c7Qyp4duTZcrOWgQxye6T+Gq8/jFj3mnnHZk8c6UldKE\n",
       "mgNFg6COuExsSi5W2lSmzbCdqJz8I07ArHKdeCM6jWb/ZflKe3q/zTU/5eJzmFwuG+qTxTtTFlJK\n",
       "XYWXdKoIifxQlfaayFQtu+JnuEnsjTSpInFRWY0Ot7P38pzUnqXe4TeX8bOvVzirJYt3pkUpNYk6\n",
       "ofT4n8giebiiRmVqkf3FB/4VOEsZMo+G0v6P7LECJ3dg0LvccA0XnlQlrReyeGdahJRSX+FlH40H\n",
       "RTZA1ZQqZ2qKo8wdoHB+S59sIO3+wi4rckoHVnifm2/gJ0dXQeFPfbJ4Z5qV0tCDr4k0v7+IookX\n",
       "KmpUppY5WeyPfE9Mem8x+pD+xsiVObUjK3/Abbdx2MFV+v5d6DCGlNKIlNLTKaXnUkpfm8+aLVJK\n",
       "j6aUniyNl8q0MVJKQ1JKl2EceouNpRNV6Rs/UxOcIYT7G1pQuLviUbZ7nbvX4Fcf8/zv2HpJjqtW\n",
       "4WYhnndKqT0uFi02J+DhlNKYoijG1VvTCz/H9kVRjE8p9WtJgzPVRUppCM4UjYBuxBdFtVsms6gk\n",
       "nIsDxF7J71riJF3xN7ZYi9M6s85H/OkuTt419maqnoWFTTbE80VRvAwppdFix3dcvTX743dFUYyH\n",
       "oigqkjaTKS8ppeXwbYwS5cmbq2BpcqbV0F7EtncWse4/tsRJHuALn+e0LmwwlXvvZscRC5gXWY0s\n",
       "LGwyyKc7t40v/aw+K6FPSunelNIjKaWDmtPATHWRUhqcUvoVnhA7/puJiTVZuDOLSyf8ShRvHaoF\n",
       "hPs+NpzKTZtwY8HH97Jbdw6sNeFm4Z53Y9JxOuLz2FpMsHgwpTS2KIrP9NJNKZ1V79v7iqK4r5F2\n",
       "ZipMSmlZEYPcV9zGbq5CxQmZVklXXCm0ZH881JwHv5t1N+X0bmw+nX/9g1GbRRZUNbKxaH1M6GuD\n",
       "LEy8J2Bwve8HC++7Pq9hclEU0zAtpfR3MY7qM+JdFMVZCzlfpsooZY+cKf6gbsEWeKuSNmVaHUvg\n",
       "Gqws5o8+3lwHvp01tuS07mzzMY8+xH5b8vdpzXWCluFBcz9YuuErDS1aWNjkEaxUyiTohH0wZp41\n",
       "t2HTlFL7lFI3bISnFtnsTFWQUuqdUvqR+L/shi2F552FO9Oc9BYb3StgT80k3Dez6gdcvhN3d2Dp\n",
       "/3BIb3YaXv3C3WgW6HkXRTErpXQ87hYbCVcURTEupXR06flLi6J4OqV0l4iBzsFlRVFk8a5RSh/A\n",
       "p4j82r+KlL/c4S/TEiwlNrt7iOk3Ly3uAa9nxZ04dQl2mcHTT3DEcO5qLYJdn1QU5elvn1IqiqJI\n",
       "ZTlZpsmUGkZ9Gd8Smzc/wLMVNSrTmhkkPO5ChEoWu+T8RHr9mPvn8Paz/Hhzbn+79gd4dMNzDWln\n",
       "rrBs46SU2ol82u+KP6Aj8GhFjcq0doYKj/t9sQG+yHUB57DU/mw7gO2n8sytjDqR5yaWqWlVJcni\n",
       "3YZJKY0QvSIKfFNMr8lkWpLVMFokPhyAd5t6gO8z4BD26sP2XSI7xVTuH84PXmR285pbvSy0PD7T\n",
       "+kgprZVS+rPoi3wJRsjCnWl51hVpps+L5IcmCzdcy5TurFQn3DN56Wt8uS0JN1m82xQppaVTSlfi\n",
       "XowVudq/r6xVmTbCxiJU8h/hcS/SfMcRdLmfM3qy5xzencOHN3PoxYv4QVDL5LBJG6CUQfJ10Uv7\n",
       "FmyqTHP2MhlsJSYm3YPjMGNRDvJX1t+Mn7RnqRf46hxmfcDb+4cn3+bI4t2KKW1GHi42Ix/FTni5\n",
       "kjZl2hw7ieZ2t4kU1CaHNramy2hO68vR07j/F+xzEhNXo8O4Mo5BqzayeLdSUkqbiZFRBY7Fvypr\n",
       "UaYNsjd+LKa8f8sipO39mc9/kQvbs/RLfG0NflOXs92WhZsc8251pJQGlbo/3iQmsu8oC3em/ByG\n",
       "n+CXIpOpScK9GZ3f4ltbc9ssXv85Ww6rJ9yZ7Hm3GkrtC75aetwouv19VFGjMm2V48UAhfNwUVNf\n",
       "/EfW3pqftmfQy3xrfa5tBcU2zU4W71ZASmln0QP5VeyCFytrUaYN83XRSOnbYlhwo9mITmM4pT/H\n",
       "TWfsFRx0zKdbUmfqkcW7hkkprSQ8m9VET+27K2tRpg2TxMb4YWLw9OimvPhO1tqaCzuw3Ct8ez2u\n",
       "zt72gskx7xokpdQ5pXSO6Hn8X9GmNQt3plK0ExuTB4vN8UYL9zp0fIPTRnDHbN69kq1X4Kos3Asn\n",
       "e941RkppG1EV+aqojJy3v3omU046iqym7URfnL809oVjWGN7ftKBoa9x9rpcmUW78WTxrhFSSv3x\n",
       "U9FX+zu4o7IWZTK6iLFlGwuv+x+NedE6dPwjJwzghI959Bq2OawZ2sG2NbJ4VzkppYQv4XtCsDeX\n",
       "s0gylae7SEVdQ3QG/HdjXnQrq4/kJx1ZcTzfG87lbaEDYEuQxbuKSSl9TpQVL4FD1OCQ1EyrpBeu\n",
       "w3IYhf8t7AWr0eGvHL80J3/M49ex3cG80NKGtmayeFchpcEI3xZ9IC7C5bJ3kqkO+uG3YnzZ7hoh\n",
       "wDexys78tBMrT+DcjfhV9rYXnyzeVUZKaX1chbfFJtBiTxjJZJqJgSKTpKMQ7gXmYA+l/f0cuwyn\n",
       "zuDJ0WzXVptINYJ2orBub/QVoagFksW7SihVSH5XxLd/gN9U1qJM5lMsLyp3pwnhfmNBi0ez0m7h\n",
       "ba82kfM355dtrd92I1lJCPYeeFO0tWhUm+Ys3lVASmkjsfkzEdtayB9GJlNmVhYe9yTsJ+4KG2Qo\n",
       "7f/O0QM5bQZP38T2++RZqAvifDwsPO3nmvLCPIC4gqSUOosskkNxjvjUzWSqiTVFjPt5kQ74/vwW\n",
       "XsewPbmwM2u+zo834xfZ215s8gDiaiOltLYIjbyOrS3GENZMpoXYQLRzfUyUvTfY1G8g7R7iqEGc\n",
       "PoPnfs8OezCunIZWMZ/DXmJj99rmPHAujy8zKaV2KaWviaki14oUwCzcmWpjMxEqeVC8RxsU7l8z\n",
       "9AVuHcQ33uBn67JjFm79cBT+LJIPPsLfm/sk2fMuIyml5UR+bA/R/S9XlWWqke1FH+4/4gQNDD0Y\n",
       "SLsHOWIwX5/JC7czctdG5Hu3AZYTfYbuEpXQD2qhkv8c8y4TKaWDRHP6X4v2rTkWmKlGdhdtGG7A\n",
       "1zSQj30FQ/bnJ51Z701+ugMXPcbMchtaxXQ1nzuVRSDHvCtFSmkJUWSzvrj9fLSyFmUy8+UAMUDh\n",
       "MtFi+FP0If2HwwbzrVm89AdG7syTZbey8iwjUvvu1PDdc1kG/uSYdwtSKrh5TPQ63k4W7kz1cjR+\n",
       "KO4OPyPcl7LceG5ejrMmcenmbU+4u2A3kXnzF5H3XtG75+x5twClZlIniBL3c0RxQyZTrfQX02/O\n",
       "EbHuT+hD+jeHLMcZs3jtLnYayRMVsbJybI8LhCM2WmTeTK+oRbJ4NzsppV6i4GYV8Umdm+9kqpX2\n",
       "4vZ/E5Fd8k79Jy9h8CFc0IXhk/j5LlzwEDMqYWiFeQRbiQrIqiGLdzNSqpS8QfQ1HomPK2tRJtMg\n",
       "7cTG5EkYih3UE+6u+B8HLc+3ZzPxT+w8ovV3tOwuBPr2Bp6bUmZbGkWOeTcDKThRbGCcj9Nl4c5U\n",
       "J7viPtGtcqgI6X0SBrmIQZMZPYTvT+HqrdmuFQt3wqbiWjwi7kK6V9SiJpA978UkpdRVTMleT/xh\n",
       "5MntmWpmHPqUvp4qmqDpiv+y/wp8ZzZv3sNu2zRywEKNcrCI878tPsDOVqUe9vzI4r0YpJRWwG1i\n",
       "nuRIZUoRymQWka5CpDriGdyKNy9g4NH8qCubT+HSfTn/r1WwIdfCPCcEvGarQbN4LyIppR1wDS7F\n",
       "LypsTiazMJYQ7RhWFL02+nbmn0+y71DOms3k+9h9q+hw11poLyoeG8rFfrDMtjQ7OebdRErx7a+J\n",
       "SsmvyMKdqX56i46VQ7AnnvgB46Zw+TB+9A437MI2rUi4V8WZIo79jQrb0mLk8vgmUBqYcBmGi1uu\n",
       "BU4SyWSqgAEiN7k79sFLXfEOf2hH7wc5+Ys8VFELm4/DxO/YDzeLD6xaT9XN5fGLS0qpn4hvf4yd\n",
       "5AnumepnWbEZNxu77cI7P2bfAXzxT5x+OS+OaV37NL1Ff/wHtIEZmdnzbgSlKe5/wJ/EqLJW/8bI\n",
       "1DzDhMf93rmccRQ79WJUosf97Fnj3nZnbScVN3vei0pKaYRo4/rD0r+ZTLWzOn7bjtde4NEh/K7u\n",
       "iUlcUqPCvZSI1+8lWq6eV1lzKs9CNyxTSiNSSk+nlJ4rbdTNb90GKaVZKaU9mtfEypFSOkRMuzlO\n",
       "Fu5MbfB5Ee99bg77vMPfi1La3wye2TOKyGqFTthZZMncJzJlviEcqTbPAj3vlFJ7XIxtMAEPp5TG\n",
       "FEUxroF154kG5DUZGpmXlNI3RDbJPniqwuZkMo1hE5EFNbYnRz3Nl5fhq+9xYzfWvZsT7q+tcEMv\n",
       "7C82Ho/SuuLzi83CwiYb4vmiKF6GlNJoUUU4b2L7V8Sn/QbNbWC5SSm1w89EC9ddxET3TKba2Rq/\n",
       "wl/34Gu/5uLubPsKZ6zGVdey6iierrSRTeQtMa0+0wALC5sM8ul0uPGln31CSmmQEPRLSj8qzw5o\n",
       "C1Ca5n6T+NDKwp2pFXbClRjzK344mlu7suED7DOEq6ahSoW7q4hj34AvVNiWmmNhnndjhPhCfL0o\n",
       "iqLUx7omwyYppW6isdTH2Ftt3V5m2i774Ef49b+4dz1un8krv2D7k6rT+UiiTmIvjBCFNNeW/s00\n",
       "gYWJ9wQMrvf9YOF912c9jA7d1g87pJRmFkUxZt6DpZTOqvftfUVR3NdUg1uC0qiyu/EGTpTnS2Zq\n",
       "g8Pwf4mLx/PhMvz6A27Zg9OruDfJKDG15yaci0mVNacq2VjsXxB9aBpkgXneKaUOooHN1uJT/F/Y\n",
       "b94Ny3rrr8LtRVHc0sBzVZnnnVLqgz+L28rT1XDYJ9OmOB7f6M+PX2DVHox4je+uyuVVvqvXTq6T\n",
       "aArzzfNeYMy7KIpZ4k1yt8i4uKEoinEppaNTSke3iKllJKW0FP6Gx3GaLNyZ2uAb+Mbm/GQ8O3Zj\n",
       "k7Hsv3x1CHc7bC5COZ0aeD4LdzPRZissU0oDca/wur9fYXMymcaQxJzJQ07n8nPZZxbjL+fw4z4b\n",
       "ziw3K4q9oj1EKORGMay3WsM3tUKusKxPSmmA8LhvFx5CJlPttMf5iT1v5ve7c+QH3L4Pp9xVeYE8\n",
       "S2Rn/U7kZT9bUWtaD+18es/xU7Q5zzul1FcI971iwySTqXY6KuVtP8yjq7LhBL63Mr+sgjAJkajw\n",
       "jrzRv6j0FyPp6h7DSv8OUdqwbEg725R4p5R6ijLbR0W/30ym2umCy4ay8cO81YslH+aY4fy9zHas\n",
       "jlXE9J1M0+nhs+Jc9+hRWjNdtLB9sd5jIm5q02GTlFJ3sfE6ThbuTG3QHVdvx9q3MwtTr2S/L/FK\n",
       "mc7fV8Sw9xLtVq8p03lrlU5ics+8Aj1MeNfE3ckrQpjH4npzhfoNn02a6Da/k7UJzzul1EX0XXlb\n",
       "lPLnrJJMtdMrcd1prPwDun7InYdx8u9iaHA5uARbCIfnJvxT/rshNo0HatiDHmxuBt8bPu1B1z1e\n",
       "ER/EjWW+G5atXrxLTbNuExf1aDkul6l++nVn9JUM2YsuEzl3JX5e5vj2xnhC2x060ttnxXkoVhCh\n",
       "LHhfCPK8oY6XNPK6DaTdofRel34D6dc7/u/7daF/J/ollurF1m0ubFIq179E3P7tKwt3pgbYgc0u\n",
       "ZNBQZv+bgzaIzfWWYGkRmmloVFjND+htBF19VpzrHr1Kaz7Gy0KU72nHi9+i4yj6rh2tQT7D1nTZ\n",
       "lUEr0W8p+vekXzf6daZfR/p1KD3a078dfVK9epuCOXN4ezaTZzFpGu/Oz/hW7XmnlM7EAaJx1gfl\n",
       "PHcmswhsiq8+Rb9hzLyeww9rePL54tBF9BTZG2uLVs6tJZb9eRG6uK3ezzqUfjavOA/DMqU1hciT\n",
       "r/OcXzDXm56IOcfT6zRGLcOBHVlpKvd9wKOdQpD7d6Bve/q3p1+7uRuQdQefPpvJdYI8kykzmDSd\n",
       "yR8x6V2mTGTyf5h0Ne9M/HQhU9sLm6SUDhXz7HbB6+U6byazCGyc+OoXGH4SU2exz608c0Pzhiz6\n",
       "isrMHfCYKKK5W+VzxJuDL4pK8E1Ervlkc0V6eXMjDJN9WqBfxIu7MOVg+q/Asn1YtjuDurBsR5Z9\n",
       "g5t7s3ZPdksxfg3MYdpsJsyaK8iTP2byNCZ/wKQpTHmZyX9i0hg+WoyQV9sS75TSFqK/+D4+23s8\n",
       "k6kW2rfnuztz6OkiyHwDo/fl1BY4VxccKlL93myB45eDnuaK8hMiffE4rFFvzXQ8ryTO7XhxMyYf\n",
       "yqz16b0ky3Zj2c4s24lBHVi2HUvWvXgO789i/EzGf8yE/zLmTB4/g9VXZp3erN2NdQpmrsMO45q2\n",
       "+bgotB3xTimtIGb0nYq/tvT5MplF5QlGLs/ZPSN7wVN8tC2rTly8/h/dxN5OrbY07iyKUxoqWulb\n",
       "WjNLtLR4ozNDV2T1wQxbmmVX4aMjuacbAzsyqD2D2s3dYDSbSbMYP4Px0xn/ERPeYfzLjB/D+Ksb\n",
       "GV49kB6vM6sM3RvbRnl8SqkH7sClsnBnqpy9mD2GZXoKtb2e0xdRuJMIGeyF7cXIsPubz9Jmp50Y\n",
       "6jKvOA8r/bxOqCZ25+U1mbABT2/IzLVpP5glOrN9R5Ztz9IpWgcomD2Dd2eywkxe/YB/f8iESYx/\n",
       "lgmXM6G5xsBdx4fNcZzFodV43qXxZbeLPNgTW+o8mUxzsCq7/5KfbcDsxGOv88IwTmniYQbiQNEj\n",
       "+12Rj32riO1WA/00XFU4RKnjYB/eW4UJa/DO2kz7HMVQOvenVycGto9jgDmx8VcX0hg/jfHvM/4N\n",
       "xj/KhB8fip5hAAAbm0lEQVTxxmLetVQjbcLzPlukPu1ZaUMymQWxGYdfwjnLMO0udutD1ysWbW9m\n",
       "iEh3O1TlhmR3F7nP9b3noRiaWGJAPPnxqkxenQ9W4+NhPLc0PZaIdLkllWLOs3lnNhNmMGEqz01m\n",
       "/LuMH8/4vzH+It6ukl4uVUGr8LxTSjvgapECVaubMZk2wF6cdiEnzeGd37FdlY4qm5eOouz7U0Ur\n",
       "HRk6iAHLYwjFKuFFT1uRYhCde7Fk+5KDWFDM5s1SvHnCx4z/kPFvM/4Fxt/ChGbOrmkttF7PO6U0\n",
       "GL8WoZIs3Jmq5TjO+z4HTgwvcrtLeG8hL1lFxLF3wbYWvr6xbCa6AD65J93OZ6/fcPeZEYv+RJx7\n",
       "stIQVhrEMsvRbnmsyPSVmLks7fvQta66pGDWLN6r2wycxoQXGT+J8U9Fz/HXH2JGM9mfUeOed0qp\n",
       "o9iY+afclztTxfyQPU/iokd58gR2XoCQ9cZuooimv8hbvlHDVZBNoZ3I8T4ea23Ahaez2fashfbf\n",
       "YfZgOi6PFZgzhKJ3aSMQZjFtFuNn82pdvPk9JrzBhIcZ/0PefDv3PmkJWmeqYErpAjEAeX/5jZOp\n",
       "TtJ+HL4WW36eh/bj4oWI3NkiJe5G/MOibcB1wQoDWPVMXp7MqJnsXND3XpwkWgXWv+2eGoUkb8zh\n",
       "pcSLUxn/DuNfZcKfGH8F7+Z4c0VofWGTlNLWovR9G1m4M1XIERw1ipO3ouc3OWh77mnEy75T7+uO\n",
       "27Lpljzzzc+GBNt3YPAarPU51h3Eqkuz/AD6D6bbMKXk8RLvMv1/vHsrM0az1DTG7sGkLqzagaHj\n",
       "OGb9nF5bU9Sk551S6oX/4tuixDeTqRpG8bljuGmrUhbFTfx379hMh6WE4zukP2f3ZdbTzJznEF23\n",
       "44QDOHJvOp7C1zqyytKs0r8k0MvSfSiprjRwFibz0du89QGvzOTp9jz+Bs/9hlfmaSXbRWxAPgsb\n",
       "0WkUfU/LbSSqkdYVNkkp/VZ4219tjuNlMs3N9fx2PzZ/k2J3NnswSrj3xnoduOcQljmBz+3LGh/T\n",
       "8zAGfJc39uGM/dhzZGn8VX2mUbzBh1N4631emcbTc3hsEv/7EePLUKqdKT+tJ2ySUtpXtIHYptK2\n",
       "ZDLzshydT+F7r/P0zcx8mXf+FV37JvTj3m/TbW92G0B6H3fy0uDYTCze5O87s87ytJ9prnr/hwvv\n",
       "4Jof8GaOO2fqqCnPuzT1/UkciYebxbBMppnYln578M012eYMNh/JUVtw+Lu89zRPHsSIXvXWz8Et\n",
       "3P8W/53FP87j/roKwUH034aNh7LeJjy5bVRPZtoerSNsklIaLXoKfLt5rMpk5s8pHLw0g9/g0Yf4\n",
       "5wP1GuN/n3M6MfNNHislX39rJMvugrt55XFuWpr1+0ds+f0d2XFdem7OxoNYbylW78/yrzLmGM6v\n",
       "zG+YqQFqP2ySUtpeFBd8sdK2ZFoFSx5Avz/yYkOpe0NYoqDHCRxb18T5deZM4MOn+UdvNkLfm5j0\n",
       "CN1XZfauFK8x9TA2f6OB+POjvP9obLDnTfbMYlMT4l0aIHyJ8LjLNYA108pZhtsnsuQEPn6Ld9/m\n",
       "9fd58S90vpgdu8yz/h2mPcgVp/ObOdzdk/dncsu3WGo4a13E5nfxVkV+mUyboybEW4j2c/hjpQ3J\n",
       "1CRLr8maG7LhENZYliGDY9RYt84YSuehDHifvv/hmSe5/he89BFP7shF+PBvXPgtrqjbMBzGsWMZ\n",
       "nTj6Gn41ks0r9+tl2iJVH/NOKa0uKs22UxtNfDKVYcn2DF2HddZh3eVZeTkGLU+vVWm3dGnRdIoJ\n",
       "fPAGE/9Nh8NYcTYznuDay/hhvT7N7dqz9VEMuITr5j3ZTfx+FBvAA7z9S3a9LsZqZTLNSU3HvC/A\n",
       "L2Xhbqu0x2ViBNaLVzBgZ1aZxYQpvP0H1nqGXs/S42bRExg+YtZEpkzh348z7iEeeZOHz2Z8XUbH\n",
       "OnxpPXr9Hz+7a+5ElGEiH3vP2Uy6hK/Pa9ARfH6nknDfz3P3clIW7ky5qWrPO6W0lciR3VTuSNZW\n",
       "aIdlze0JPXQlvrAqK68txoPvVm/xbIp/8ugPuPY4luzBMw/wzDlNz4leX5SmLyuaQd2EZxpY1/5u\n",
       "/taPdg9w6gk82PRfMZNpNLWXKphSSnhE3LLe0GKGZSpFf/PMKezBsDVYfi06roXPM2tNUo9Sd7uX\n",
       "o5Dllc/TuwNLvM8tt3LhYbzUDPYsL7zuv4mpZJ9hHw7amq99wJmnxsSaTKalqcmwyb5iSsiNlTYk\n",
       "s8j0EFNW5p2wMnR5llgL6zJrQ6auTftl6N4Os/h4Os/M5IlJPHUmPW+k+0QuHcG00Zx7BxcfuGht\n",
       "Uodp+HWvlB4NsgOHX8A57zPlZP68COfNZJqVqvS8S326nxFZJo3pxJapHPWnrHxq0gqW6oa1mL0h\n",
       "7wxn+rp0HEKvLjEl3Cxem85TH/HUWzz1b8adysvN3Bu6L3YXgw36iMEG7y7wFfXYjGOu44xZTPke\n",
       "m13ZfEMRMpmFUXOe93FigzILd3WQsIzPivNQIdztxJOTN2HypsxYjynDKJZkqUT7OXSfwavTeOoN\n",
       "xr3M/37N01fzQQvavRkOx3D8CefgAU34YNiAk67mtMSUn/HFLNyZaqHqPO9SQc4rOAyPtbhhmfr0\n",
       "9llxHiZCH3U1Kx8swcubMWUrZgyn88r07cOQ9hEmqfOmx33E/1rQm24MdTMH/qBp8xE7Ycbn+MYt\n",
       "HN8zhHvL7zOlRazMZOZP7WxYppROELe4B7S8VW2SLj4r0HWP3jCcmdvy7izeLJiYeLUTL/bkuSM5\n",
       "YAl2TaQ5TJvBuGk89V75vOmG6KT5spFWwB7D6DWGw5diymVs28AwhEymHNSGeJdi3S/iK/hXWQxr\n",
       "PQzET0VD/ZfEdXyp9NgK+wkvum7ASoEJpXUv1P3blZdG03snftuuNEwAZvH6s5wznQ860fURnvoW\n",
       "r0xctDFdzUEXbC9ysnti5+Y46Ebc+Dwb/jXmOb59FdufkmsMMpWjZmLeB2O8LNyNZYBPhzeGYJN6\n",
       "z08TqZbjhFDfL0T6RRGamj6Qdpey+lps3IeDu7JR+5IHDgUz3uKSo/jZmDhepdlAbDzuiMdFNtJd\n",
       "zXHgUzlsH76Q0JdiJNc9mIU7U6VUjeddyut+Ej+UU7Hq01PDceih4lOZENUXxIfxqngHV+HK0tef\n",
       "sA4df8Raq7JRLzbuygbtWGIO703joXd46H+MXZftu7HKaM7+0gJS6CrAJeJ9covmHdvV/n6e3pRu\n",
       "M3EYV/+G78mN0DKVpSY8763ErfBfKm1IBegsikTqC3Pdv31La2YJEX1RZExca64X/UZpzTfxW1yv\n",
       "JDpb0+Us1h3G8F4M78z67egym8lTGfsa5z3KQ8fxdP0QyEVMOiG89WrjmJY46LF8e9PSh2EH5lyE\n",
       "V5l9f0ucLJNpBhrleaeURuBCUel2eVEU583z/AE4XaSUfYBjiqJ4Yp41C/O878BDuKKpv0SN0A6D\n",
       "fNZ7HipKsuuuzevminL9x6saMaNwH7qfwvpDGN4zxHqdRKdZTJzK2MmMfZCxX+KFaoiBzEMSYZ+9\n",
       "xO97QRnO2aMdu7zA8UNY/iPu+QPn7FMazpvJVJhF97xTSu1xsZgZOQEPp5TGFEUxrt6yF7F5URTv\n",
       "lYT+VyK3tlGklFYQf7QnNvY1VUxfDXvQQ0RWBJErXLdJ+JC5Av2SJt6mH8OSR7HRsmy0BMM7sWaK\n",
       "GYgvf8TYV7n+HsaewmtVKNZ1DBGCvZconrlJecrPe+E3OzF0Kd4cy74bx75AJlP1NCZssiGeL4ri\n",
       "ZT4ZRbar2AQDRVHUb87zkPAkm8KXcIfq2BBrDN1FSllDRSs9S2s+Njfr40/mCvQLeHtRT3wm/fZm\n",
       "+ECG92CjjqyWSDN49iPGvsCvbuehr88NpVQ7A/D70uMw/K9M5+2XGH0Rgwfz45W4vIKZM5lMk2mM\n",
       "eA/Ca/W+Hy9GQM2PI3BnYw0oefYHl15XTdSVfTe0UTigtGaOuDYv4t/CY6zzqCdqhqKUCxi4AxsN\n",
       "YOMeDO/IsIJiBv/7gH9O4ILreei8xfhAqDBvimaB5RTOgbjhbHofR7eHeSYLd6bWaIx4N1qAUkpb\n",
       "inLkL8zn+bPqfXtfURT3YYQII/y3sedpRurKvhsqWFlOqZsdJpnrOd9jrkC/ohlb1XbFxQzZnOH9\n",
       "Gd6d4R0YXDDrYx5/l7tfZeylPHwZ7zfXecvAyiIkcjueaOD5cgrnENy4L86k96t8Z6PoJJjJVAsb\n",
       "m5vy23F+ixoj3hMwuN73g4X3/SlSSmuJpvkjiqJ4Z97noSiKsxr48RHCY21Jepl/VWHX0pqPzBXl\n",
       "W+t9/ZIWqhjsiqtZeQOG92V4NzbqwNJFdNX7zxRufomHzuWRKsmxbgq9RevtvbGU6JE9uaIWsQpG\n",
       "r8+71zH4XUavyuUVtimTmZcHze0T300ULX6GhWabpJQ6iA5/W4tQwL+wX/0Ny5TScsIjPbAoirHz\n",
       "Oc5nsk1SSj1EdsVw8+QjLwJdzG0/Om+oo67oZKa56XZ14lz3aPHBsfUKYob3YXipIKbPHKZO55F3\n",
       "efA5xp7J4/dHzLxW2VbMfrxHFNHcr/JhibVw/UBeeokBc5i4BXs/lId8ZKqbRc82KYpiVkrpeNwt\n",
       "wghXFEUxLqV0dOn5S0Xr1t64JGptzCyKYsNGGLaraD7VWOFur96UFZ+OQw+qt66u7PtJjDFXoMeb\n",
       "T6P9lmA1OvyMtUsFMcO7smGpIOb9aTz0Oj//H2NP5slxjUgDrCH+KTa6y93jZH5siGs78+izdG6H\n",
       "szkiC3emlqlohWVK6TZxe3DNPMv7+3QmR93Xy5sbA3rHZ73nujDHdBVga7p8h3VWZOMl2ahLFMR0\n",
       "nc2UqYx9m7GPMnbegpgapZ/oJ/Jr1f27fBFXJu57i7f7sPsd7Lpr+bJaMpnFofoqLFNKy4jc8Qdw\n",
       "qk970z1Ky6abK9B/8GmBXtwwS7PQh/QUpy3JxvUKYl6fytiXOetBHqzSgphFobMIiewlvNm7sITq\n",
       "7XG9gyinv/1ZHuvHd5/gyCzcmdZAWT1vUT25culRl243W1TTNVRV+Lry94BeIJvR+URWWIUV+zJs\n",
       "Ou8OYPsZvD6Jh+5l7EkxdKC1cThOEcJ3k0gHrea+H3viJ7j+H9yxCde/wU8Gxs8ymVqhOlrC4j5R\n",
       "dvysiHc/KkqgZ5bFiMXgUbZbg7PbMziVStk/4i+jOPquCoVpysznRPVjNfY7mZeDcS5+eRXXHcwd\n",
       "H3H/AL7cCj9UM62b6gibFEWxJZ90EDxdNFKqeuEeSLsOdEr0qBPu97hhY05vZRuNXURXwoYmGNVK\n",
       "qOEYnIEfHcrlB3DHTMbvzUlZuDOtiXYVOu+aYqf/xQqdv1GsQ8dn2edl7luDS6eXRO0tLl6GU1qR\n",
       "cG+EH+M/olVBrfJVIdxnDeSnF/OLdiz5Cw5rI3dHmTZEpTYsR4iNyqpkBF1+yX6DOLY9A97nlrs4\n",
       "4h9MOo1Ry7eewo4TxISdaSKOvaXaHfd1Fo7Eabj+Mc7oxqb3MCpPwsm0RiqSKphS+rNoRFSOznGN\n",
       "5lCW+B6HDOCodvR4h9+O5pLjGqgobSUcJO4mKtGaoLloh/Owj6hEu+0Z9lqZC5/lpFVavno3k2lJ\n",
       "qmPDsiiKlFLqJKZwN0dVZbPwTfqeyJH9oqtdmsI1v+BXZ0VPk1qnnepO51scOohKzh1wNP70F9bb\n",
       "ipuncGV/zqmseZnMYlMdG5YlNhSpgRUX7gsZeCDH9Gb/gmlvcsk5XH1J6xC6YSIfe08xMuzcyprT\n",
       "7HTGL7GZyC65/wIGbsEVU/nH2jHCLJNptVRKvBvqLFc2rmHYzhy7JKNmM2k8536F39Rg86d56Wru\n",
       "UINlhWgfhKcraVQL0E3M51xHxOwfHkGXY7lyDu8dz7GtoII1k1kglRDvz4ueI2VnDGtswfE92GkW\n",
       "r7zI1w/gd62ox0V78eH4E9HmtGx9XMpITzG/cxhG4cmuuJGfdGTwNex0dfX0VMlkWoxKiPe6GF3O\n",
       "E97Hhuvzle5sNYNx4zhuZ+54sfWJ24c4vtJGtCB9xIDl/tgdz8ELnNSDHR/igMOidUIm0+opa553\n",
       "SqmL6F3S4gUfXfEwW07j1i9ya3t6/odDerHN57itRoW7j+h/frdIt2wLdBA95JcW2UlLij7hz8Hj\n",
       "7LAMp73Kd/L8yUxbotye9zrCM2qxXtUDaXc3I1fiK51ZYyp/u589t2dsjQa0O4oGXnuLDJ0/4/9U\n",
       "cZ58M3OQCLWtL6pxdxc9b9zK6mvws3e5fjWuqqCNmUzZKbd4r4+nWuLA69DxRvYYwnEdGfYhd97D\n",
       "aSMrvDnaDGwjik9uFCGRjyprTlnpJTpO9hazQncXaaa+Sd+duPpjntiSb9boB3Mms8iUW7zX08yb\n",
       "lfOrhty3dFvdCvhj6dEWqRNuogvlDrhuHTqeGVWuxdkc+VgN9MfJZJqbcov3umKyzWJzaOuphuyC\n",
       "7UUc9wQ5U6KOlXCIyAS6Hhfj9a64l3M7scZt7HIeb1fSyEymUpRbvAfh5cU5QKka8kv9OFRtV0Ou\n",
       "L/KxdxKhnRu1npTF5uCb+A1+pl5vkqc5ohf7PcERezBuvq/OZFo55RbvnqIndJNpZdWQZ2Er3CBi\n",
       "2q9X1JrqYltReHOWGBb9CWPZfDBnvc4P144pPplMm6XcwxhmiAnvjWbeasiJ/LIVVEN2U91TaCrF\n",
       "rqJXyc2iO+AnVZK/ZuiBMVThvgEcW8v/+ZlME6ia3ibvN3ZhjVdDJmyM1TXcPjYL92fZD+eLsvfv\n",
       "qDf+7kv03I+rZ/LK3pyShTuTqULxvq+2qyGHiDj2KPG7/rai1tQOR+Js/BQ/rP/EUNpfyCXtWOKn\n",
       "7JOHKmQyQdWI9/WsuDvnd2HD6TzyHw7ZlL/UkJd1lSgmuVUM662VsWGV5iQRIvk+fj7vkw9xRlc2\n",
       "/iujTst7A5nMJ5RbvOebBjeOd3fh/X8wajserCHRruM8PK/1jEYrB9/CsaV/r573yefYtx9HPcMJ\n",
       "28aItkwmU6LcG5Z/wFFlOWHLsCK64/FKG1LjJOFpH4hTNDDt5h422IKbJnPZUrk3d6btMt8Ny3IP\n",
       "IG70hmUV0VvklP9B5GKvUVFrap/2uFBsUH5ZA8J9IQM35/Kp/G2d1jdEIpNpFrJ4z5/euAz/FD2y\n",
       "z8cGonAks2h0EtNvdhIj5/5Q/8lH2W4fuh/D1XN458scl4cqZDINUzUx7yrkPdHB7xS1ZXe10gVX\n",
       "iA/AAzC2/pN9SJ/jO9cwowNLXc2O10V/8kwm0wDlFu9qrIbsJ1rUzivQc0SYJLP49MA1WEW0tn1s\n",
       "3gV38cWOkWppOg+vzDIWs5VCJtOaaathk07YEb8WDfzXq6w5rZre4kOwbmzZZ4QbVo8wCpjKkxfm\n",
       "TeFMZoG0Nc97CL4kyrCfEqJyjFzx2FL0FyPveope3C82tOhSluvG1rN47V+c+oW2M2gik1lkyi3e\n",
       "i9SUqhnpIboPjlB7rWNrjUGi8VYS7W4nzG/h7hz0Ltcew//d0LaGTWQyi0xr9bw7abgHypMqNLm+\n",
       "jbGCuKv5APvirQUtHsttu+T/l0ymSZQ75t3SnvdG+LGoxuvXwufKNMyqokXAJOxpIcINWbgzmaZT\n",
       "bvFuCc97sEjn+yd+IErUt8bkFjhXZsGsg9+J2PbeeKey5mQyrZdyh01aYmr8LugjqvVqfdhwLTNc\n",
       "pAM+Ihpz5e5/mUwLUu7eJoPKcrJMudlCFODcKxpN1ULP9UymFqia3iaLwlB8TQNd5zJVwUjxf/MH\n",
       "HC0LdyZTFqpVvHuKjnNjcAs6i5armepiFC4VQydOVBsDMzKZVsFCxTulNCKl9HRK6bmU0tfms+ai\n",
       "0vOPp5TWbQa7rsemYrLKeviuPCm82jhE/P9cim+oN7Ysk8m0PAsU75RSe1wsilpWx34ppdXmWTMS\n",
       "KxZFsZLo1X1JM9i1i9iA/KvW5c1tXGkDmoljRT/u8/F/i/D61nIdFod8DfI1qGORrsPCPO8N8XxR\n",
       "FC8XRTFTlDrvOs+aXUSPEEVRPIReKaUBCzluHxwhCjgaorW2Ad2k0gY0A6eLyTffEX25F4XWcB0W\n",
       "l3wN8jWoY5Guw8LEexBeq/f9eJ/NGGlozbLzOd4IMR38AZET/EKjLc1UmiTCVyfgq7i8suZkMm2b\n",
       "heV5NzaOOW8ay/xe92WxAfl1c3s1d2vkOVoDHdXm79tOhEf2EAVRd1i836NWr0Nzkq9BvgZ1LOg6\n",
       "fCZF8JMnFpTnnVIajrOKohhR+v4bmFMUxXn11vwS9xVFMbr0/dP4YlEUb85zrLyhlclkMotAQ3ne\n",
       "C/O8H8FKKaUhmIh9xOzB+ozB8RhdEvt35xXu+Z08k8lkMovGAsW7KIpZKaXjcbcYHHtFURTjUkpH\n",
       "l56/tCiKO1NKI1NKz4t2noct4JCZTCaTaQbKVh6fyWQymeaj2SssK1TUU1Us7BqklFZNKT2YUpqe\n",
       "Ujq1EjaWg0ZchwNK74EnUkoPpJTWqoSdLUkjrsGupWvwaErp3ymlrSphZ0vSGE0ordsgpTQrpbRH\n",
       "Oe0rF414L2yRUnqv9F54NKV0xgIPWBRFsz1EaOV5MW6so5hXuNo8a0biztLXG2Fsc9pQ6Ucjr0F/\n",
       "rC8yOE6ttM0VvA4bY8nS1yPa6Huhe72v1xR1FRW3vZzXoN66e0Qm056VtrtC74UtMKaxx2xuz7ul\n",
       "inpqiYVeg6IoJhVF8QhmVsLAMtGY6/BgURR1Pd4fMv/6gFqlMdeg/ti3HlpfH/rGaAJ8BTeLIR6t\n",
       "kcZeh0YndjS3eDd3UU8t0phr0BZo6nU4Ane2qEXlp1HXIKW0W0ppHP4oiqBaEwu9BimlQULI6lpr\n",
       "tMaNuMa8FwpsUgqj3ZlSWn1BB2zuYQzNXdRTi7Sm32VxaPR1SCltKQY4fKHlzKkIjboGRVH8Hr9P\n",
       "KW2Ga7FKi1pVXhpzDS7E14uiKFJKSRO8zxqiMdfhPxhcFMXUlNIO+D1Wnt/i5va8J4ixZHUM9tkp\n",
       "7fOuWdYCJovXII25Bm2BRl2H0iblZdilKIrWNjatSe+FoijuR4eUUt+WNqyMNOYarCfqRF4Sc09/\n",
       "kVLapUz2lYuFXoeiKD4oimJq6es/omNKqc/8Dtjc4v1JUU9KqZMo6hkzz5oxOJhPKjgbLOqpYRpz\n",
       "DepojR5GHQu9Diml5US7hAOLoni+Aja2NI25BsNK3qaU0uehKIopZbe05VjoNSiKYmhRFCsURbGC\n",
       "iHsfUxTF/P5mapXGvBcG1HsvbChSud+e3wGbNWxS5KKeRl2DlNLSeFgMnZiTUjoRqxdF8eF8D1xj\n",
       "NOY64NvojUtK79mZRVFsWCmbm5tGXoM9cXBKaabo9zO/Tps1SSOvQaunkddhFI5JKc3CVAt5L+Qi\n",
       "nUwmk6lBqnUMWiaTyWQWQBbvTCaTqUGyeGcymUwNksU7k8lkapAs3plMJlODZPHOZDKZGiSLdyaT\n",
       "ydQgWbwzmUymBvl/IpicyV13gQ4AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1069cdda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ramsey = Ramsey(A=1.2, α=0.4, ρ=0.98)\n",
    "linearized = linearize(ramsey, ramsey.steady_state())\n",
    "\n",
    "sim_ramsey = Simulation(ramsey, domain=lambda x: ramsey.is_feasible(*x))\n",
    "sim_linear = Simulation(linearized)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "kmax = 1.8 * ramsey.steady_state()[0]\n",
    "k = np.linspace(0.0, kmax, 200)\n",
    "ax.plot(k, ramsey.f(k), color='black')\n",
    "ax.fill_between(k, ramsey.f(k), 0.0, color='black', alpha=0.1)\n",
    "ax.plot(k, k, color='black', linestyle='dashed')\n",
    "\n",
    "init_vals = find_initial_near_eqm(linearized, eps=1e-6)\n",
    "for lambda_, inits in init_vals:\n",
    "    if abs(lambda_) < 1:\n",
    "        path = list(sim_linear.reset(inits, 15, inverse=True))\n",
    "        path.reverse()\n",
    "    else:\n",
    "        path = list(sim_linear.reset(inits, 20, inverse=False))\n",
    "    quiver_plot(ax, path, width=0.004, color='black')\n",
    "\n",
    "for lambda_, inits in init_vals:\n",
    "    if abs(lambda_) < 1:\n",
    "        path = list(sim_ramsey.reset(inits, 16, inverse=True))\n",
    "        path.reverse()\n",
    "    else:\n",
    "        path = list(sim_ramsey.reset(inits, 16, inverse=False))\n",
    "    quiver_plot(ax, path, width=0.004, color='red')\n",
    "\n",
    "ax.set_xlim([0, kmax])\n",
    "ax.set_ylim([0, ramsey.f(k[-1])])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_ramsey(A, α, ρ):\n",
    "    ramsey = Ramsey(A, α, ρ)\n",
    "    linearized = linearize(ramsey, ramsey.steady_state())\n",
    "\n",
    "    sim_ramsey = Simulation(ramsey, domain=lambda x: ramsey.is_feasible(*x))\n",
    "    sim_linear = Simulation(linearized)\n",
    "\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "\n",
    "    kmax = 1.8 * ramsey.steady_state()[0]\n",
    "    k = np.linspace(0.0, kmax, 200)\n",
    "    ax.plot(k, ramsey.f(k), color='black')\n",
    "    ax.fill_between(k, ramsey.f(k), 0.0, color='black', alpha=0.1)\n",
    "    ax.plot(k, k, color='black', linestyle='dashed')\n",
    "\n",
    "    init_vals = find_initial_near_eqm(linearized, eps=1e-6)\n",
    "    for lambda_, inits in init_vals:\n",
    "        if abs(lambda_) < 1:\n",
    "            path = list(sim_linear.reset(inits, 15, inverse=True))\n",
    "            path.reverse()\n",
    "        else:\n",
    "            path = list(sim_linear.reset(inits, 20, inverse=False))\n",
    "        quiver_plot(ax, path, width=0.004, color='black')\n",
    "\n",
    "    for lambda_, inits in init_vals:\n",
    "        if abs(lambda_) < 1:\n",
    "            path = list(sim_ramsey.reset(inits, 16, inverse=True))\n",
    "            path.reverse()\n",
    "        else:\n",
    "            path = list(sim_ramsey.reset(inits, 16, inverse=False))\n",
    "        quiver_plot(ax, path, width=0.004, color='red')\n",
    "\n",
    "    ax.set_xlim([0, kmax])\n",
    "    ax.set_ylim([0, ramsey.f(k[-1])])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAXgAAAD7CAYAAABgzo9kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJztnXeYU3X2h98zhTL0Ih1EwAKCDQUREQQERIodUFfFhiiW\n",
       "lbWXZa3r2iuLFV0LrPqzg10sq9JsoICg0osMvcMw398f50bCkJnJZJLc3OS8z5OHyeTm5nBhPnPu\n",
       "qeKcwzAMw0g/svw2wDAMw0gMJvCGYRhpigm8YRhGmmICbxiGkaaYwBuGYaQpJvCGYRhpSk6yPkhE\n",
       "rB7TMAwjBpxzEsv7kibwELuRfiMio5xzo/y2I1aCbH+QbYdg2x9k2yE17ReRysBRwDFAF+Bw4A9g\n",
       "KjAF+ApYBIwE7gPygLmxfl5SBd4wDCOTEJGaQDdU0I8G2gK/ANOBccBlwJpEfb4JvGEYRpwQkQZA\n",
       "D1TUjwaaAj+iHvoDqJe+JVn2mMBHxyS/DSgnk/w2oBxM8tuAcjLJbwPKwSS/DSgnkxL9ASLSBOjO\n",
       "Li99L2AaKuTXAD8ABTGc+qu42JesWTQi4oIagzcMwwAQkb3Z3UOvhXrnk4H/ATOBwjh+ZB4wNxBJ\n",
       "VsMwjCAhIvuwS9C7ANVQ7/wb4D/Az0DKVgiawBuGYQAiIkALoCfQFRX0yuwS9GeAOaSwoBfFBN4w\n",
       "jIxFRFoAvYBj0ZBLLhpumQw8gVa8BBYTeMMwMgYRaYR66CEvPQ/4GvXQHwV+9c+6+GMCbxhG2iIi\n",
       "dVAx74566fXY1VD0HDDLP+sSjwm8YRhpg4hURYW8h/dnC+A7VNCvRGvS41nlktJYmaRhGIFFRCqi\n",
       "9ec9UC/9QLRU8SvgC7RjdIdvBpYfK5M0DCMzEJFsoAOaGO0OtAfmoTH0h9B4+lbfDEwxSvXgRaQP\n",
       "8CCQDTzlnLu7yOt/A870nuYArYG6zrm1RY4zD94wjDIjIi2B41FRPwYdzvU/7/ElsN4/6xJOuTz4\n",
       "EgXe+205B01SLEE7toY45yImJkSkH3Clc65nhNdM4A3DKBURqYWKeS809FIFDbl8DnwKLPfPuqST\n",
       "0BBNB2Cec24+gIiMAwZSfOb5DODlWAwxDCMzEZFcoDPQGxX1/dHE6BfAhcBP/lkXbEoT+MbobOIQ\n",
       "i4GOkQ4UkTz0H+iS+JhmGEY64nWMtgb6AMeh4r4IFfR70Xj6Nt8MTCNKE/iylNj0B74sGnsPR0RG\n",
       "hT2d5JybVIbzG4YRULx69FAcvTu6LvRLYAJwNbDaP+tSjk7oUhDQztqYKU3gl6DzjEM0Rb34SAym\n",
       "lPBMqm1XMQwjMYhIFnAk0Bf11PdHc3hfoEUZMW8pygC+9h6gv/xiprQkaw6aZO0BLEU7wPZIsopI\n",
       "DeA3oIlzLuIwe0uyGkZ6IyL1gX6ooHcHVgGfAZ+ggrXdP+sCydVoc1ZidrI65wpEZATwPlom+bRz\n",
       "bpaIDPNeH+MdeiLwfnHibhhG+uE5gJ3Z5aXvg1a7fAbcjTqFRmzcgOYzbwDujPUk1slqGEbUeBuM\n",
       "Ql56N1TEPwM+Ru/wY9leZOzOKOAC4K/AuySqDj6emMAbRvDwvPQuaBFFb6AR2mD0GfARsMI/69IO\n",
       "AW4HzkaXcb+BjSowDCOeeBUv/bxHT9RL/xS4Ed03mjHDupKIoGGtwcBw4J14nNQE3jAyHK8u/SDU\n",
       "S++HDuyajIZd/gks88+6jCALrf8/GbgIeC9eJzaBN4wMREQqod55f7Q+PRutdnkcLWW0RqPkkI0O\n",
       "STsBjbt/FM+Tm8AbRoYgIo3RUSP90PV0v6CiPpQ0X3yRouQAj6DNX+eieY24f4BhGGmIF3o5HDgJ\n",
       "9RD3Rr3zD9Aa6zX+WZfx5AKj0Uqks9HEddwxgTeMNMIb3NUD7U3pB+wEPgTuQGe8WBmj/1RAF3p3\n",
       "Rrt6Jyfqg0zgDSPgiEg1YAAafukFzEdjuedgoZdUoxLwFHAEMAStSkoYJvCGEUC8ePrJqKh3RMfr\n",
       "foCW2lnVS2pSCRgLHAwMAr5P9AeawBtGAPDi6QeyS9RboQsw3kBb2jf6Z50RBXnA88ABwGno3tiE\n",
       "YwJvGCmKJ+odUEE4CRWJj4D70VG7QV4mnUlUBV4AWgKnAz8n64NN4A0jhfDG7B6NivpAtGv0PeBy\n",
       "NAxjBIvqwIvoqPVT0NLUpGECbxg+4+0+7g6cior6elTUz8fW1QWZmuiOjPqouP+abANM4A3DB7xy\n",
       "xl6oqPcD/gAmosk3W4YRfGoB470/TwF+98MIE3jDSBIiUhGdnX4aOh5gAeqpD/C+NtKDuqi4V0WT\n",
       "4otKPjxxmMAbRgIRkQpoF+lgdIb6HNRTvx9biJGO1ANeQTtVT0bXnvqGCbxhxBlvhnovtJGlHxp7\n",
       "fQedzGjz09OXhsB/va9PIQX6EUzgDSMOeInSY1FRH4h6528Dx2GeeibQGPXcd6AhuD/8NUcxgTeM\n",
       "GPHq1I8GzkBvx1ehnnp/LKaeSTRDxX0jmiTP99ecXZjAG0YZ8ET9CHRI1CnAVtRTPw2Y56Nphj/s\n",
       "g4ZlVqN5lpSa0JlV2gEi0kdEZovIXBG5tphjuonIdyIyU0Qmxd1Kw/AZEWkpIv9Ak6Svos7RucAx\n",
       "wD2YuGcirYDXgJWo555S4g6lLN324opz0M0vS4CpwBDn3KywY2qis4x7O+cWi0hd59wetyi2dNsI\n",
       "GiJSFw2/nAHsB0xAxX2Kn3YZKcH+qOe+AL2b25Cgz0no0u0OwDzn3HwAERmHJpDCR5CeAbzmnFsM\n",
       "EEncDSMoiEhlNJ5+Fjqv+3N0dvdH2Cx1QzkQrXOfC/yFFB70VprAN2b3Iv3F6GjScPYFckXkU6Aa\n",
       "8JBz7j/xM9EwEot3p9oT/WHth076ewO4ghT+4TV8oR0wDh0Ydg6w2V9zSqY0gS8+frOLXOAwdItM\n",
       "HvC1iHzjnNuj3VpERoU9neScmxSlnYYRd0TkIOA8NH66GngdnQmz3E+7jJTlUOAl4Ac0/7I1QZ/T\n",
       "CTjK+zq3PCcqTeCXoFPQQjRFvfhwFgH5zrktwBYR+RwdaL+HwDvnRsVuqmGUHxGpg+7APAdogHrq\n",
       "ZwKz/bTLSHmOQEf+TgEuALYl8LO+9h6gTvNlsZ6otCqaacC+ItLca7keBLxV5Jg3gaNFJFtE8tAQ\n",
       "TtLmHRtGaYhIjogMFJE30KFP3YH70IXUt2LibpTMkajn/hU64TOR4h5XSvTgnXMFIjICeB/IBp52\n",
       "zs0SkWHe62Occ7NF5D3gR3R29ZPOORN4w3dEpC36A3kG2jb+KnAdOo7XMKLhaOA54BN0c1aglqyU\n",
       "WCYZ1w+yMkkjCXhlu38BhqJFAm+gM7mTumjBSAu6AU+jDu7l+FNFldAyScNIebzu0mOBYegY3i+B\n",
       "h1Cva6ePphnBpSfwJNql/FcC+v/IBN4ILCJSDw3BnO9962XgNrQixjBipQ/wb7RL9Wo09BxITOCN\n",
       "QOHtLO0NXISW5n4EXAN846ddRtrQH3gMdRauI7pS8ZTFBN4IBCLSCBX1ocAmtNnkeixhasSPk4CH\n",
       "0aTqTT7bEhdM4I2UxfPWTwAuRqsZJqKVDN/5aZeRlpwGPIDG3f/hsy1xwwTeSDm8ZqSL0KTpJrTB\n",
       "5Erva8OIN2cA/wIeB+702Za4YgJvpAwi0hHt2usPfIrOgpnqq1FGunMOKuoPAPf6bEvcMYE3fEVE\n",
       "KqGjAi5BRwe8iIZjVvlpl5ERXICGY+4BHvTZloRgAm/4goi0AEagc2FmAaOB9whwSZoRKIajidQ7\n",
       "0NBMWmICbyQNryHpeLQrsCM6vfEk4Fc/7TIyjsuBa4G/A0/5bEtCMYE3Eo63RONc9AcrG3gWuBTY\n",
       "4qNZRmYyErgKuBEY668piccE3kgYXu365Win6UzgdjR5ahh+cD3qWFyNTodMe0zgjbgjIoejXtIJ\n",
       "wDvAqUTYD2AYSeQWtPT2KnSXakZgAm/EBa8p6SR0MFMr4Hl0M81aP+0yDPTO8Ry0BPd1n21JKibw\n",
       "RrkQkYpoCGYk2oj0FDqi1xZUG34jwF1oI9Ml6GTIjKK0jU6GERERqSkiNwML0U1fN6BT+F7FxN3w\n",
       "nyy0cWkwGpoJpLiPgf3K835b+GGUCRFpjHrrQ4HP0cl7M301yjB2JxvtTO2PivuH/ppTdv4PWveE\n",
       "v1aDEwSIVTvNgzeiQkRai8hY4CegDuqtD8fE3UgtcoBHgH6oExIocX8d2myAJ0+CjypCi6/KsXAb\n",
       "LAZvlII3H+ZGoDM69KszsMZXowwjMrnoHWUPNKn6hb/mRM/r0KYn/LUq9N0Os2bAhd1g4mqoXJ7z\n",
       "msAbERGRLmin34HoCNW/Yo1JRupSARiDzjE6k4AsgHkTDuyuwn78dvj5R7jgWHhvdZwWjZQaohGR\n",
       "PiIyW0Tmisi1EV7vJiLrROQ775EWg/IzFRHpISKfoRttPkVLHf+NibuRulREl2MfhVbMpLy4vwkH\n",
       "boCnBsAHFWDvH+GChtDrYPXa45YYLdGDF5Fs4FF0Ae0SYKqIvOWcm1Xk0M+ccwPiZZSRXLwZMb1Q\n",
       "j70xeps7DquGMYLBvkA1YAjwrc+2lIjnsV9VFfp4Hvv5x8L78RT1cEoL0XQA5jnn5gOIyDhgIDr9\n",
       "LxyrjgkgnrCfgHb51UGF/RUCukHeyDgaoItgAE7005DSeAvaHquhmD7b4adEC3uI0gS+MbAo7Pli\n",
       "dApgOA44SkR+QL38vznnfo6fiUYiEJHj0A6/OsBDaIefjeo1gkAtdNT0uaj+HO2rNSXgCftVVaH3\n",
       "dvjpBzivO3yQaGEPUZrAR2PEt0BT59xmETke7WIsV3G+kThE5Gh0BnZzdMnBK5iwG8FhGDpPpqr3\n",
       "/AFguX/mRKaIsM9MtrCHKE3glwBNw543Rb34P3HObQj7eqKIPC4itZ1zq4ueTERGhT2d5JybVGaL\n",
       "jZjwBoDdAbRD64RfxGLsRvB4E50IWRVYiS6KSRnehrbdYGRV6LUdZn4PQ4+CD8pYodAJTRiDln7G\n",
       "TImdrCKSA8xB60qXAlOAIeFJVhGpD/zhnHMi0gH4r3OueYRzWSerD4hIWzQUcxT6wzAW2OanTYYR\n",
       "I7XQ5H8ddDrpO6ij4jtFhf1nuC8GYY9EHjA3Vu0s0YN3zhWIyAjgfbT992nn3CwRGea9PgYdBTtc\n",
       "RAqAzejsB8NnRKQpuky4LzoAbCRW6mgElzromN9qwMmoBz/HV4uAd6FdV7iqCvTaFrvHnjBsFk2a\n",
       "ISLVgZvRhcLj0Dj7hhLfZBipTT1U3CuiDuUSf83ZU9hnxc9jL0riPHgjOIhIBbSy4Hp0CNhxaFjN\n",
       "MIJMQ3Yt6DgZWOajLUyAg45RYT9uG8z4Ds7tDB+misdeFBP4gOPVsg9GwzGL0DZtGwBmpAON0Sqv\n",
       "HcDpwAq/DAmasIcwgQ8wItIVuA+9jbsJ23dqpA9N0d0Cm1Bxz/fDiIlwcBcV9p7b4Mdv4Zyj4aNU\n",
       "F/YQJvABRET2RoW9M7rUYBxJrq81jATSHPXc16B3p3uUXCeaoAt7CBP4ACEildHNSSPQ0b1HY5Ux\n",
       "RnrREhX3FehsmaTu9H0PDjlahb3HNvhhOpzdBT4O6g+ZCXwA8OLsQ4C70YUbx6Or8gwjndgPTaiG\n",
       "cknrk/XB6SbsIUzgUxwROQSd6LkXcA3wmb8WGUZCaAOMB34FzgI2JuND34dDO6uwd98G30+Hv3SB\n",
       "T4Iu7CFM4FMUEamKVsaciQ4Dexab8mikJ+3QPNIs4Gy0YTKhpLuwhzCBTzG8cMzpwP3oaIju6MwN\n",
       "w0hHDgVeAn5Ap0NuTeSHfQiHHQVX5cGx2+C7aXDWMfBpugl7CBP4FEJEWqLzYlqiK/K+9Nciw0go\n",
       "R6DFAlPRzuuEiXumCXuIUlf2GYlHRCp4kzanAd+jXruJu5HOdEQ996+A80iQuH8E7TfBiz3h7Syo\n",
       "MRXOrAX9jsgAcQfz4H1HRI4EngH+QAeDLfDXIsNIOEcDz6GNecPRTtW48hG076Qee7et8O1UOLMr\n",
       "TMoEUQ/HBN4nvJr2u9CKgdvZNW/DMNKZrqhD8wFwGXHeSeAJ+8g86LoVvp0CZ3SDzzJN2EOYwPuA\n",
       "iPRAR/j+DBwLrPLXIsNICj2BJ9E57lcSx6qwj+HwI9Vj77oVpme6sIcwgU8i3ijf+4H+6Ejfd/y1\n",
       "yDCSRm9gDPB/wN+I05pIT9hH5sExW2H6ZBhyLHye6cIewpKsSUJEeqEee3WgGybuRubQD3gCDUOO\n",
       "JA7i/gkcsQle7g5vZkGVyTCkNgw40sR9N8yDTzAiUgm4B61tvwb40F+LDCOpnIjuAH4OvWst11C8\n",
       "T+CIjuqxd9kK08xjLxkT+AQiIu3ROt8FaOnjGn8tMoykchoaknwaGFWeE30KR3QIE/ZvYHB3+MKE\n",
       "vWRM4BOAiGQD1wFXoeMGXvbXIsNIOkPQO9fRwB2xnqSIsE81YS8bJvBxRkT2QTe956J17Yv8tcgw\n",
       "ks7ZaAnwg6jIlxkT9vhQapJVRPqIyGwRmSsi15Zw3BEiUiAiJ8fXxOAgIoPQtuvPgZMwcTcyj/NR\n",
       "cb+HGMV9NDRtDxdmQaVvYHBtOLGTiXtMlOjBe6GGR9H61SXAVBF5yzk3K8JxdwPvATFt/w4yXiL1\n",
       "IdRjHwpM99ciw/CF4ejqyDuBx8ryxnug4SDoXw8GbIfFf4HLP4CtJurlo7QQTQdgnnNuPoCIjAMG\n",
       "omM9w7kM3Z94RLwNTHVEZH/0774EOI4kLikwjBTicuBa4B9oSWSpHAK5r8OZDWBgJdUadsCvl8Df\n",
       "3kzwVMlMobQQTWN2DzMs9r73JyLSGBX90d63MmY3qIichQ5L+i86MMnE3chERqLifhNRijvA97Bj\n",
       "I+SHxL0QtrwOF7yQpGUfmUBpHnw0Yv0gcJ1zznmzzNM+RCMiucADwAB0IceP/lpkGL5xHXoHfw1a\n",
       "XBA1M6F/a7i7AJblQMM5MHIQ/JIQKzOU0gR+CdA07HlT1IsPpz0wTrWdusDxIrLDOfdW0ZN5I3FD\n",
       "THLOTSqrwX4jIg3QduvtaPv1On8tMgzfuBkYhpYDj4/2TYOgyhi4rQYMWgMvXgW3/QuuaANvJszS\n",
       "YNEJOMr7Orc8JxLninfSRSQHmAP0AJaiG4aGFE2yhh3/LPC2c+7/IrzmnHOB9u5FpDO68f01NKkc\n",
       "l3kahhFAbkM3MF2BOjxR8R4c0h0ey4IaP8HfDtbCDGqDrM6g8G4ZyAPmxqqdJcbgnXMFwAjgfXSO\n",
       "ynjn3CwRGSYiw2L5wKAiIpcCbwG3oGVgJu5GJiLo//9zgEuJUtwbQdYSuKwXvFkAi++FniFxBzBx\n",
       "TwwlevBx/aCAevBeCejDQB+0BHKevxYZhm9kobXtpwIXAxOjedP90OhieKQSHL4E7j4YRpugR025\n",
       "PHjrZC0BEamGhmOqohPxLN5uZCpZ7CosuIAoh+bNgH5t4F87IX8i9DsBZiTSSGN3bFxwMYhIc+Ab\n",
       "YDUwGBN3I3MJNTz2R8uBSxX3UyBvDdzXFsasg3dOhd4m7snHPPgIiEgn4HV069LjPptjGH6Sg/4M\n",
       "9EDj7l+U9gYvkfpoNtT6ES44OMpQjhF/zIMvgoiciC7juAkTdyOzqYA2Lh2L7g4uUdyLJFKX3K+J\n",
       "VBN3HzEPPgwRuQCtEBgKTPPZHMPwk4ro/tQjgTPQIXrF4iVSH64ER1giNXUwgfcQkRvQsq/TsG46\n",
       "I7OpBDwLHIrmn74t6WBLpKYuGR+iEZEsEXkITR4NxMTdyGwqA88DB6NrJosV9/BE6np41xKpqUdG\n",
       "e/BejfvzQBtU3G2lnpHJVEFXTO6LivvM4g6cCAf3gMcskZraZKwH741hGAc0Rxs3TNyNTKYaulqy\n",
       "JfrzEFHcvUTqiN7wVgEstURqapORHrwn7uOB+sBfsNnTRmZTAxX3hsApwNxIBxVNpHaEfy+1kR2J\n",
       "oiZamtqgPCfJOIH3xP2/6OTLszFxNzKbWuidbB1U3H+LdJAlUpNOX1Tg3yvtwJLIqFk03hz3V9D/\n",
       "1OcC2/y0xzB8pg56J1sdrR5bUPSAUyDvKbitJgxeCy+dA7e8BbZJLz4Iete0tIRjbBZNNHie+yvo\n",
       "rc+5mLgbmU099E62EnAye+552C2ROgMuPAgmJNvINKQi0BndJXEc8Cv6yzUhZESSVUSygOdQj+Vc\n",
       "TNyNzKYBukc4lwjiHimRauJebgTtjP8B3YD1O5rMTpi4QwaEaLw1go+gG1JOw24vjcymEXonuxP9\n",
       "eVgR/mJ4InUp3N3BEqnxpAfwHTrAMFosRFMK/0BvhU7ExN3IbJqi4r4ZrXPPD39xBpzgJVJXvwf9\n",
       "+9qu4bIgaHNYL+BTIo92+DipFpHmIRoRGYFOwLNxv0am0xzdvrQBDQ38Ke5hHalPrIcJQ6C3iXtU\n",
       "VAS6A/8EpgMPoU5zfklvSiZp68GLSH/g78BJFLkNNYwMoyWaUF0JDCGsqc9LpD6aDbUtkVpmBqCD\n",
       "2N5Hf2lGLDH1k7SMwYtIe/SiX4Qu7TCMTGVfNCyzGBWj9aCJ1CkwvBFcsxUmPwZXXA3L/DQ0hamF\n",
       "f53uFoMPR0SaoMuxR2HibmQ2rdE699/Qju0NAPdAw0s1kdrBEqkRCcXTe6Mx9VzgGF8tipG0EngR\n",
       "qYwu63iJKLe9G0aa0hbtUJ2DdmxvAvgR+h4I91gitVj+ga4mXA98AFxDKeOSU5lSk6wi0kdEZovI\n",
       "XBG5NsLrA0XkBxH5TkSmi0j3xJhaqp0CPAMsQpcDG0amcggac/8J3cS0KZRIbQdProeJlkgtlino\n",
       "yIZuwJ1o8jSwi0tKjMF743TnAD2BJWjpzxDn3KywY6o45zZ5X7cDXnfOtYpwroTG4EVkJLrtvR9W\n",
       "DmlkLocDL6LCdB6wdQIc1FM7Umv/BFdneCK1GRp2+REV81SnXDH40jz4DsA859x859wO9JZvYPgB\n",
       "IXH3qIoPJUIi0gO4HjgfE3cjc+mIhie/AYY2gu2L4dI+8HYBLH8IjstAcRf0juYatA79beAAtBcg\n",
       "7SktBt8YDXmEWIz+J9oNb1H1XejgnF5xsy4KRKQR+p/6r8D8ZH62YaQQndFxHJ8BF98DdS2RCuhU\n",
       "xmvQqrpQPD2wIZeyUprAR3UhnHNvAG+ISBfgP8D+kY4TkVFhTyc55yZFc/7i8GbMvIzeWSS9S8ww\n",
       "UoRj0B2qHwIjfoReoUTq+zDgeJ1/ku5UIvLo73e9R5DohI5WAa3giZnSBH4J2t4coikRps6FcM59\n",
       "ISI5IlLHObcqwuujYrKyeG5E14zdG+fzGkZQyELvqif2h+ufh3/WhCFr4eUL4JbX0jsU0QwtZewN\n",
       "tALaozN2gs7X3gM0Bn9ZrCcqTeCnAfuKSHN0ZvEgtBPuT0SkJfCbc86JyGEAkcQ93ohIZ+BKoA/p\n",
       "8Y9qGGWlNxqaHDYBavSECRnSkXopOgWzLnrXMgb4AtOBPShR4J1zBd48l/eBbOBp59wsERnmvT4G\n",
       "LSk6W0R2ABvRuS8JRUSqo5UCN6J3GYaRSXQBrgUOzYGn5kM/ryN1yqMw6KqSF0ikA8vIwHh6LARy\n",
       "VIGIPA9UAK6Kx/kMIyDsgw62OhpAYN1qmFkDOi6Ff3WA0WmSSK2FDvFagnWjJ7RMMuUQkT5oXf4t\n",
       "fttiGEnmd7xdqFWAh+DLtfDu+zCgCTwWcHFvBlyILiL5BjgBjRoY5SBQowpEpArwBFrzvtFncwwj\n",
       "2QxpDBffDr+cCPtuhHlNtTQy6BwNPMbu8fRIFTFGGQlUiEZERqPrxi6Nj1WGEQxOgmsGwhVnQmEO\n",
       "ZK2Hxf3gmC+CtX4ym8iJ0FAkIch3IIkiM6ZJisgxaObcl1k3huEXWXD+NrjiVNiao/Xe/ABXBETc\n",
       "a6Kr6nqj9d0d2bN004Q9QQQiBi8iOeit2634N5fZMPzg4my49XqYmQcVCmHdWnjpmNRPPg5G59CH\n",
       "4ukfA11J77r8lCMoHvylqLC/7rchhpFELqsJ102G+a2gxbdwTkM48HZ43m/DosCh+TKLp/tIysfg\n",
       "RaQW8Au6jeanuBtmGKnJyL3hqimwsjbsnAjnDICZtUFWp0btd0V0/s1mUv9uIsikfZnk7cBHmLgb\n",
       "mcO17eGqmbCxJuQ/Av0HwEwAn8W9JtrY+AQ63+YyoLaP9hilkNIhGhFpjcbyuvlsimEki5sGwMWv\n",
       "wvYd8O0wuGist2rPZ9qhNer/QzvbrwNW+2pR+pONVg3GTEqHaETkPbQd+dHEWGUYKcWtl8F5DwHr\n",
       "YPxRcO0sKPDbKI9sdLKhxdPjQyVUvBugY9bDH6Hv1cOLsqRdmaS3+q8NcLHfthhGgpEcuPMe+MuV\n",
       "IEvh7lbwcBI311RA4+m90ZLGPkDRgYE7sWFe0VKd3YU6knjXCjt+J7ACnbGzHN3GtRydKbQW3XcR\n",
       "Eykp8N5+1duBh4HtPptjGIlEasD9Y+G0/rBzNlzZOnnVYr2AU9F58rPR0Mtg9hR3QxF0gmVIqBux\n",
       "S7BDfzYCKoe9Zysq3CHxnlXk+TJgJcX3AuSVx+CUFHjgOPRijffbEMNIIFn7wGPjoP9BsPkrODvJ\n",
       "9e110fr0dI2n5wI7ynBsfSJ72yExr8/umrlOYFlP2NwD3HXwJnuK99qiH1QZ6At5R0D1ZlCtDjSq\n",
       "AdWqQLVKUK2C98iBqoVQq35Mf3UlJWPwIvINKu4m8Ea6kt0BnhkHPepA/ttwylnwa5w/Q4CDUfGa\n",
       "GudzpypV0LuS073HJtQLLi5UEnrUDTuHQ73qkFAvBZZnwbJsWL4Dlv0Tcs+BE+rAybmwzyb4YBV8\n",
       "mQvVcqFatifQ2VA9C6pmQbXQQ6CqFFPBWAhbHWwohPWFsHE7bK4OnWKNwaecwItIV3TtX2cs5mek\n",
       "JzknwctPw1E7YN5DcPKd8QuLVETXvfVGQzAb0C7wmOO4KU4eWovfEjgXFfWqqLAvQcW7WtjxO9jl\n",
       "XS+rBCv2hw0HweaDoeBgcC0htyrUzoU6uVA3B+pmQ90sqLsY7qoNR1aF48ONcLC9ENYVqjhvLIQN\n",
       "O3c9NhbAhu2wYQds2AobNsOGjbBhDWxcDht+gg0fw8YISfVy1cGnosBPBL4Cnk68VYaRdHIvh7fu\n",
       "gYMWw5RLYch78atMaQ68x654+vvAb3E6d7LJRqtIIoVKwp//gt7pXww0AS3Wrw+Fh8Eb+8OW/WDn\n",
       "PiCNIbfB3I3iAAAaFklEQVSmetYh0a6TpYf/iYOdhZC/E/ILYFUB5G+H/G2QvwVWTYKvL4cFj8M+\n",
       "R0PHvaBjFThyOyyoC4MTkBhPH4EXkXbAp0AHrBzLSEN6QcfX4b8/w8SBcEmcZ7gL2niU6knSUIlg\n",
       "pFDJHiWClYD6sLYprGoO6/eBLc1hRzNwTUGaAjlQR6BeNtTOKpJbLIR1O1W0VxVA/g5PsLfCqo2Q\n",
       "vwbyF0P+FFj1PKyNpZnsHmj4IuR/H33MP1rSSuCfBdYDdyfFKMNIEtVg7/Ph/i7QZBmcNKLsa/UE\n",
       "OIhdoZehwKJ42xkHipYI7lFpkgW16qAKXh8Km8C6prCxGWxrCgUNQepCbg3IqwzVc4pUkjjYthNW\n",
       "eV52fpiXvWoz5K+FlStg1c+Q/zqsnhzsSrz0GBcsIjXQccDdfDbFMOJGDWhwEdx/LnRtA9wKw/5e\n",
       "NnE/Ah0PcBy65CbURZrsXcTFlggKNKwGDetBo7pQqR4q3g2goClsbgzbG4KrB9k1oUIVcKLnA8hy\n",
       "ULMQ3E7YshNWF8DK7Z53vRLyN0D+Klg1H/I/hfzXYGMSewQCTcoIPLqu60u04N8wAk1l4A64/Xg4\n",
       "9wBPzCbCr3+Hd8p4qv2BBcBpxB5Pr4vOYn/7Sqh1AXRpC2+Fvb5HiWAlaNQYmtWDxrWhfi2otRdk\n",
       "19t1YEEjKKgHUhtyKhRZr7cTNhfCyqKx7NWQv0i97FVLIf8HyH8R1vxmBRUJIaoQjbcH9UH0H/Ep\n",
       "59zdRV4/E91yLmjWfrhz7scixxQbovEam+aiq/j+F8PfwzBSjmfgyFPgleq6gYlLoMeLmgAtSjNU\n",
       "hL+NswntgaEC/U6BKTdA5XZw8GRY8jysqQl7VYeatSAv5HV7Au5q7fKwASiEwq2wrgBWCSx38Ed4\n",
       "8nG9523/Cvnvw6q3wJzs+JDYEI2IZKOzYHqit4VTReQt59yssMN+A45xzq3zfhk8ARxZBjuO9f40\n",
       "cTfSgq7QsDU850CWwfp34bswcQ+Pp/dGxf0pPIEfCIctgBlRJOxqNYa928L+TaBVbWjWCVZWhKab\n",
       "oP0bUKsRemu8n5YdA9AZmnWGZptg+2Yt21taACsFlubConWwcgmsDHnb38Cql2BdiowpNspANCGa\n",
       "DsA859x8ABEZBwxEW24BcM59HXb8ZLxypTJwDvBaGd9jGCnLADivBeQ9ABd0hBr3wETvpbq58Llo\n",
       "E8ubwLXAtxUg7zy49XgYdBhs7AYnnwptGkGrWtC8JjSpAfVqQu1aUHUvqNgApE6Rz90Mm7dC/nJY\n",
       "/TnM/gTqrYbm3WDdabC4IrTZDrOPgwEBWflnlINoBL4xu2frF6N7FYvjfGBCtAaISCX0F0bPaN9j\n",
       "GKnK6dD6NHgkH+YNhYMneCMADoCq98CdXeHU6lDldRhTFaaPhYJB8Go/6NDaC4sUQNV52gvyJ6th\n",
       "52rYsg7Wb4S5C2DFHFi0A35z8MtK+P1FWBmpYuRbqPAM7Hc2LOoCW2+CNgdARRP49CcagY/6tkxE\n",
       "jgXOI+x2sMjro8KeTnLOTUIrZ36i7GVjhpEUhkPX6fD9FFhX0nHXQ7fqcNFUaPUIFAyDO2rDmN4w\n",
       "qicc3iAsrn0dXDMT5u6EVQfCvnn6cyYA22Dnc3D/Rpi9AWa/BkvKWV+9HW9hyBdAb/iuHOcyEk8n\n",
       "tBsZNAEeM9EI/BKgadjzpqgXvxsichDwJNDHORdxMbZzblSEb5+N7Vo1/KX6zTACmD4RPptWpMlu\n",
       "XzjxEXjpd9gxH/5YCnOXwdQ5MOlUeHwqrF4OB70D2SuAY8FdDnUHQLN34cst8Md0+H1vaLgvVK4I\n",
       "PAFjn4Tbwj+rD7RuD71aQvuq8NkFJsSZytfeAzTJelmsJyq1ikZEcoA56JzopcAUYEh4klVEmgGf\n",
       "AGc55yJOw4tURSMi1bxztkdrfA0j2eS2hmZDYfzV0LAAmA9bF8HyFfDLNFh7K5we3mmzDfgMfv8S\n",
       "HmwBpz8ACw+FU/tCYTVY1Be6FvdhB0LlvnBsNah9C7yQ6L+cEXgSW0XjnCsQkRFog0U28LRzbpaI\n",
       "DPNeHwPcgg6wH60Vj+xwznWI4vP7oV6KibsRLdXRmulN50K18bChhHq8vKrQuAMc0BIOaAD77AWN\n",
       "60C9ulCzPuQ1hpzwMYI5QCuoJFA7H+Z+BO/uC5VPgf7fws58+Hwi3PLCrpr0V5+DF/fWrskrH9Je\n",
       "jmL5Cbb8VIYclWGUB19HFYjIeDQ2aIPFjGipgd4tbr0EVt8LbdfB4gL4+SvgHdhnOuTdDU3bQk5j\n",
       "dgUxC4GVsH0VbFoNq9fCivWwcD38Ogs63w/dvoV5P8O/hsO7W7Q+vVc1OGMLtHDwwk64qQJU3Q7b\n",
       "BsNBl8NLn8CDN8Fon66Hkd4EcxaNiOQCf6DVM8uSYoQRBEJTBP+cX1IDmrSBls2hSTOo1whq7gNZ\n",
       "LYADi7z5K1g6Gr4aANXzYP1m+HU7zF4Ns0bDsuJ2nF4AJ+8H310Dv6M/VG+j9ekfAh8An+PFy5+A\n",
       "V8bAV+PhrwIFt0OvZ2FeIi6GkfEEVuB7Afei+x+NzKAiEfZUCjRoCk33gYbNoM4+IC3QAd8tobBh\n",
       "2HKEjbDldyicCVXWwsKhULsi5K6FVybAE3FcmtEW+Jki0x6HQ/sH4a21wGbY/i84brSJu5E4Ajts\n",
       "rB86GthID4pbNNwAaFgZGu4NtVoALYBW4PaHbS2BppBbyZtlshMKN8PybbDQwbxt8PuPMH8+LHwd\n",
       "Fo7VURgXAx9eqWGW8x6BsWVcmFET6I52kT4G/BjhmJmR3tgfHq6A3mK8CVn5WiBgAm+kJH568D8A\n",
       "t1GkocNIOaJZNNwQyKvPn+K9ozVsPAB2tISsplC5lq5SA6BAZ5r8vgMWbIGFG2DBClj4PSy4D5Yl\n",
       "aPBUI6AvKuoHoWMxPkA7TEusbw9xCfR9GJ7MBlbAlqlw7zkwxlr4jQQSPA/eGw3cEpjmx+cbf1Km\n",
       "RcMVgZawvjWsawtbW0NhK6AJrK8N2bl6CA6kANbtgIXbYMEmWLAYFsyHhW/Dwid15n+y6QocgPZq\n",
       "/BlPLwsnwV1boOA7GPsPuOtjW0pjpDh+hWi6ATMI9iD+VGEAsDcaL/4J3TcZoiXFe9x7LBrOgpWv\n",
       "Qu4BkLUO1m2CPzbDD1tgYQ4sPRluRUMx1Qth7Q5YsN3zwhfCgj9g4XcwP4FeeGlUQCtfIoVMXvYe\n",
       "ZaY1dD4E+tSBr0fB9fdBxEY+w0g1/BL4Y9GGKSM2arFLpJujA6tCrEaF/hVgFLrCbbdFw2h4Yhmw\n",
       "PBuWDYXCizTB2aYGHF1Jl0zUAJrthOZLYdp98Np+sHw+LJgAi0ZHGdZIAjXRJrzewDHAJDRGHxdq\n",
       "Q6dH4OUKsOYwOAQLxxgBwi+BPwb4p0+fncpkA3uxZ7ik6POKYe/ZjHrL2WgJ4BfAs8BU4AfU21wN\n",
       "uNog98DeHaFdPWhXBXpUhHbZ+guDHTB/K/xUCSiETX/AmKthzAteI9pD8G6iL0AZyAFeREU3FE+/\n",
       "njjuI82GTg/C+M7AOzpjycTdCBRJT7J64wmWo2VomTTNLmKJILuHT+oTVhKICnPI6w73wMO/VwFN\n",
       "FI5HW99XADSCrPuh5cHQrq6KebuK0DYLqjko3AHztsKMtTBjAcx4Bn4aCxtegf27weB74ZG7vUmI\n",
       "KcyRwPckJhbe5Q544VrIngxDO2s9vGEkm2DVwYtIT+BfaJlkulCdksW7IZ6X7FGIinNItCOJ9wqi\n",
       "+wVYrQ3s/Ce0aA1ta0O7PGhXAQ7MgkoOCnbA7M0wcy3M+BVmPAw/B2DjTgV0KmkvdFdAMhPy3S+G\n",
       "Z0dDzi9w7f42M8bwj8BV0RxM5LVlqUioRLC4UMmfJYJh79nK7qI9Bx2oFi7mK4kxCdkDKl0DrfeF\n",
       "drWgXWUV8wMEch1s2w4/b4YZS2DcHJhxK8wJ0Fb5GuweT5+DzkDaY3ppAunVD558FHKWwYMm7kaQ\n",
       "8UPg25EaAl+0RDBSpUl9dp/HvI5dQr0ITRSHi/ly4lhhMQiqDIcD94F2NTwxz4V9BbILYfN2mLkR\n",
       "pqyCp2fAjJthXnGt+AGhN9rZ/D5wA3GMp0dJ3w7w71eADfBKS7gnyZ9vGHHFjxDNNOBuErt/NY+S\n",
       "Pe4GaDIzhEO96uLi3KGvExbWGAE1z4C2TaFddRXztjnQQkAKYe1WmLEJZuTDzGkw80r4LaANNoKW\n",
       "bi7x25AiDGwJj0yHHbkw5XD4S8B/WRrpQXBCNCKSBexPMW3gURJeIlhc3Lt62PGhEsHlaKjkK3YX\n",
       "7qXo0LOk/TDfrMsg2jXyxLwStMvxlqrshPyt8ONqeGcFzPgSZvwNFqd6wLwUQvH03sBx6N3Pib5a\n",
       "tDun7AUPfgkbK8PC8+FCE3cjHUh2iKY5sInINdR7TBEksngXLRFcyi4P+wd2iXfo+6vxydOtDNwB\n",
       "jY6Ftg2gXTWtZGmXo38PCmDpVpixEsYvgxnvw4zbYEXAxbwoj6Jx9VA8/XTiNxAsHgzOg3v/B3/U\n",
       "hYJ74OwXbD+BkSYkNUQD3AyciVZFRFMiWDQ5WTR0siEpxkdBhBrztl6NeW34s8Z8xnqYsRhmvA4z\n",
       "A1CGGA+6o794kx1Pj4azsuDub+C39lDnFRg4GOb6bZRhhBGcMknvS8eegh3yuEPfi7ZE0BdKqTF3\n",
       "BTBvC8xY59WYPw8/+TR/JdEIOrirF9pgFXFdY4oyFLh9AnzfB9p8AYO7wmS/jTKMIgQnBo+uKvsU\n",
       "eCnJnxszh0DuP2C/NtCuNrQNqzGvHF5jvgLeCVCNeXmogG58740K+yY09LLST6PKyEXA35+GScdD\n",
       "t5kwzMTdSEeSLfAt0PnbKc906HkgjPRqzCsUqTEfH8Aa83jRFziX1IynR8OlwA23wevnwUkLYVQ7\n",
       "eMdvowwjESQ7RJOPen0rkvKhUdIHKl0B+7eC1rWgTUVotADebABHrIIZaVJjXlZqkT5TE5sD84G/\n",
       "An+7GJ59HM5aDWPr6kA2w0hVEh+DF5E+wINopctTzrm7i7x+ADrg6lDgRufcfRHO4dCql4O9P32n\n",
       "C1R8Fx6uCieIxpPZCasnwJAB5SvlDCKheHpv71EZLW0MYq19OJWAj4D3gOED4cH/g/M3wWfN4eKA\n",
       "9hIYmUNiY/Aiko2WuvVEm1OmishbzrlZYYetAi6j9NrmSqRQfPo0qFsIW0PiXgDLX4FBZ2TeCrab\n",
       "0X+7UDz9WuBb0kP8LgL2AYYfCg+8CoO2w6wT4HITdyPdiSYG3wGY55ybDyAi44CBwJ8C75xbCawU\n",
       "kRNKOddWUuCH6n5odC5cVhOG7NSlFl9UgL2fgUHDYKHf9vnANDTxHbR4emnUBUaAdr69DMN3wLJr\n",
       "YOgXKVylZRjxIhqBb4x2HoZYDHSM8fN8Dc38ExpcCCNqwZk7IX8+3DwExo+Grh/DzKu1RDMdaYrm\n",
       "PmYTeUTExOSakzSuAqpUgN++hx3NoNYYGPworPXbMMNIBtEIfDw97k1xPFfU3Ab1hsOI2nDWTliz\n",
       "AG49G14KeXGHpees7/B4+l7o3zGTduC26gp9voa/rYDO1aH3BDjp0uROpjQMX4lG4JfgzUnxaErs\n",
       "PyRVgJHe118BX8d4nqi4GepeDpfWgbMLYf0iuOM8eDEDliX3Am5C4+nXofH0Ql8tSh5ZwJ1ZMGMi\n",
       "/OGgX2XoMg3O7p95iXMjmHRCe01g92m2ZSYagZ8G7CsizdFu00HAkGKOLS3TOx/Yo8Im3lwLtUfC\n",
       "JXVgqIONi+Hui+D599JP2CsTOWn9gffINLKBh4ATboAllXU0NZvgk+npl18w0pev2eX85qEFLDFR\n",
       "qsA75wpEZATqDWYDTzvnZonIMO/1MSLSAN0BWh0oFJErgDbOuaJDmxIaohkJta6F4Z6wb10K914K\n",
       "Y9Oss7Qpu0IvBwDtybxmq0jkAI+gdy/nXq/VMwAI5Fbyb/+wYfhGshudJgIXxPvcI6DmzTCsLpzv\n",
       "YPtyePwKGPtaitTbx4nhwCnoxM0P0V+4n5N+dyWxkAuMBroB57wOa06ED3dC/i/w9/bwRjr9hjcy\n",
       "ikDNoomr4A6HGn+HC/eCC4GC5fDIVfDMeJ+SuQlmKXA9MJ3MiadHQwXgCTRmeSYwuTs8vAb+cyPc\n",
       "NTryaGrDyAiSLfBxmbN9LlS7Cy6sp8LOChh9Azw9NoXGB8dATXS07goilzK+mVxzAkEl4Gk0THUG\n",
       "MK015HwFTx+vI4oNI6MJlAd/FlT9F5xfH4YBWX/Ak7fAkwEexRuKp/dCyxq/Qkc+GKVTGRiLJlIH\n",
       "A98DzIICE3fDUJIt8DGFTgZBlfthaH24WKDCSnjydngy4A0rHYAn0TkpT2Hx9LJQBXgeXf94Olb+\n",
       "aBgRSWkPfgBUfgyGNoRLBCrmw9N3wZgHgzXlMBvYGeH709DhbBZPLxtVgReAlsBphI3MMAxjd1Iy\n",
       "Bt8HKj0B5zSCSwXyVsGz98HoAK24C8XTe6MTGTuxZ37AhL3sVEdn5jRBK4p+8dccw0htUipE0wMq\n",
       "PQNnNYYRAtVWw9gH4PE7U3OfZyROR73KUDz9feAGgp38TRVqAuPQsQunYI1LhlEqKSHwXaDif+CM\n",
       "JnBZFtRYDf95FB4bFaw1cKBe+ZNYPD3e1EbFvRYq7vN9tcYwAkKyBX43T7YjVHgZhjSFy7Khzmp4\n",
       "4Ql49IYU2/gURmgf6XbUQy/Kq8k1JyOoC/wXTayezO6TTQ3DKAFfYvCHQO5rMKgZXJENe62BF5+B\n",
       "R1N0XG8NoAdaytgVmINWvRiJpz4q7rnASWizl2EYUZL0EM0pkDcOPs6GRmvh5efh4StT9wf3AOAN\n",
       "1Fv/ALiR4OQDgk4jVNwLUc99ub/mGEbwSLoHPwSa/QEvvgFvBGA29y/AIVg8Pdk0AV5B5/WfDvzh\n",
       "rzmGEUyykvlhFWBDX7h9MnycAuJeAR1OdRdak14/wjGFmLgnm2bA/6EJ+VMwcTeMmEmqBz8VelWG\n",
       "TjW1WcUveqKljMeg8fQP0Bn3qZrYzSRaoGGZVej4gSA1tBlGypFUgW8DNwNU0RGYflEH+BStT7d4\n",
       "eurQCg3LLEMHhwV5DIVhpARJFfgcTZyRl3gP/iB0GNXkCK+NT/BnG2XnANRzn4+O/LXGMMOIA75s\n",
       "uamoNc3xJFSfHprMuAktZYwk8EZqcSD6S3cu8BfiNFLaMAwfBH4R3LoTdsTxlI3RiYxz0NEAp2Nt\n",
       "7EHhIOBl4GfgHNJrA5dh+E5SV/bthI37QptlsDPOK9TqYPH0oHEYOjjse+BcrFrJMCJRrpV9SS2T\n",
       "3AJTfiu7uB8EXI166S2LOcbEPVgcgXruU1HP3cTdMBJAqQIvIn1EZLaIzBWRa4s55mHv9R9E5NDi\n",
       "zrUWvo7SrsPR+vTpwKNojP164Pco32+kLp1Qz/0r4Hy0mckwjARQosCLSDYqsH2ANsAQEWld5Ji+\n",
       "QCvn3L7AReh2+4j8FL3At0KHSp2O1qvfgXp7fs1Q7+TT58aLVLG/C7qsYxL6f2V7FO9JFdtjJcj2\n",
       "B9l2CLb9cbG9NA++AzDPOTffObcDHdk6sMgxA4DnAJxzk4GaIhKpK5QrYUbY0yaopx6JccDjpE6y\n",
       "9Ci/DSgnqWB/N/T/yfvAcKJPtKeC7eUhyPYH2XYItv1xsb00gW/M7uNZF3vfK+2YJpFONkvvAkLx\n",
       "9AmoR2ekP8ehy8TfAS4DCvw1xzAyg9LKJKMtsSma4S3ufY+j4j4KrZ4oxN+u1mjJJRh2Foef9vcC\n",
       "HkKnct4IVCzj++3a+0eQbYdg2x+yPabqmRAllkmKyJHAKOdcH+/59UChc+7usGP+DUxyzo3zns8G\n",
       "ujrnVhQ5V3LqMQ3DMNKMWMskS/PgpwH7ikhzdGb7IGBIkWPeAkYA47xfCGuLint5DDQMwzBio0SB\n",
       "d84ViMgINDGWDTztnJslIsO818c45yaISF8RmYeOCBiacKsNwzCMUklaJ6thGIaRXMrdyVqeRqho\n",
       "3ptoymn/fBH5UUS+E5EpybP6z88v0XYROUBEvhaRrSIysizvTQbltD/Vr/2Z3v+XH0XkfyJyULTv\n",
       "TQbltD/Vr/1Az/bvRGS6iHSP9r3JoJz2l+3aO+difqBhm3lAczTr+z3QusgxfYEJ3tcdgW+ifW+i\n",
       "H+Wx33v+O1A7mTaX0fa90F6D24GRZXlvKtsfkGvfCajhfd0ngP/vI9ofkGtfJezrdmgvT5CufUT7\n",
       "Y7n25fXgY22EahDlexNNPBq5/Eoel2q7c26lc24aezYVBeLal2B/iFS+9l8759Z5TyezqzckKNe+\n",
       "OPtDpPK13xT2tCqQH+17k0B57A8R9bUvr8DH2gjVGF3+Udp7E0157Aet9/9IRKaJyIUJszIy0die\n",
       "iPfGi/LaEKRrfz7a2BfLexNBeeyHAFx7ETlRRGYBE4HLy/LeBFMe+6GM17688+BjbYRKFcpr/9HO\n",
       "uaUishfwoYjMds59ESfbSqM82fFUyKyX14bOzrllqX7tReRY4Dygc1nfm0DKYz8E4No7594A3hCR\n",
       "LsB/ROSAxJoVNTHZD+zvvVSma19eD34J0DTseVP0N1JJxzTxjonmvYkmVvuXADjnlnp/rgReR2+/\n",
       "kkV5rl9Qrn2xOOeWeX+m7LX3EpNPAgOcc2vK8t4EUx77A3HtQ3jilwPU9o4LxLUPEbJfROp4z8t2\n",
       "7cuZMMhBB4I1R0f6lpakPJJdyaZS35uEhEd57M8DqoWSIsD/gF6pZHvYsaPYPckaiGtfgv0pf+2B\n",
       "Zmgy7chY/94pan8Qrn1LdpWAHwb8GrBrX5z9Zb728TD4eHRd3jzgeu97w4BhYcc86r3+A3BYSe9N\n",
       "9iNW+4EW3j/O98BMP+wvzXagARrvWwesARYCVYNy7YuzPyDX/il0Ec133mNKkP7fF2d/QK79NZ5t\n",
       "3wFfAEcE7NpHtD+Wa2+NToZhGGlKUlf2GYZhGMnDBN4wDCNNMYE3DMNIU0zgDcMw0hQTeMMwjDTF\n",
       "BN4wDCNNMYE3DMNIU0zgDcMw0pT/B/o03zRTX9IJAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10752b080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ramsey(1.1, 0.35, 0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD7CAYAAABzGc+QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeYnGX1//HXnU0ngRQCIUUgoffQey9BuoBU6UgRv6Kg\n",
       "gIrytYIiTVAREFB+GkBF/AqigDQVkBJ6KJGSBkIgBQjpz++Pe2I2y2Z3s21mds/7uubanZ2nnH32\n",
       "2c+cOfcpqSgKQRAEQfXRpdwGBEEQBM0jBDwIgqBKCQEPgiCoUkLAgyAIqpQQ8CAIgiolBDwIgqBK\n",
       "6dpeJ0opRb5iEARBMyiKItX383YT8IaM6CyklC4oiuKCcttRTuIaxDWg816DlFIvbIsdcQwG4m08\n",
       "hn/hn5hYa5feeGVpx2tXAQ+CIOhMpJT6YWdZsLfHBngZT+A5nItpzT1+CHgQBEErkVIajN1k0d4e\n",
       "w/GM7GFfKnvZH5U2P0sLxJsQ8Pbm/nIbUAHcX24DKoD7y21ABXB/uQ1oDVJKw7CrxV72IDwuC/VX\n",
       "8DTmL2X3f7b4/I31QkkpjcZlqMG1RVFcVM82O8vvLt0wtSiKnevZpujsMfAgCKqblNKqlvSw+8ve\n",
       "9aP4hxwWWdiKp+yNV5amnQ0KeEqpBi9hd0wuGXpEURTjam3TTzZ8r6IoJqWUViyKYmo9xwoBD4Kg\n",
       "qkgprW6xYO+AvrJ3/Yisey+gLTPsGhTwxkIoW2J8URSvQ0ppDA7AuFrbHInfFUUxCeoT7yAIgkon\n",
       "pZQwQnZYd5IFu5fFgv0L2aGtmJToxgR8qCVTWiZhqzrbrIluKaX75Heny4ui+FXrmRgEQdA2pJRG\n",
       "YE/sIodEusnhkEfxczljpGJpTMCb8k7TDZvKHzN64+GU0iNFUSw1dzEIgqAcpJSGyB72Ii+7Nx6W\n",
       "Pewr8e/yWbfsNCbgk+U0mEUMl73w2kyUFy4/wkcppQexsXqSz1NKF9R6en9RFPcvq8FBEARNJaU0\n",
       "UBbrXWUveyWLC2ZutGQ4uFLYRi72ITvIS6WxRcyucsxnN0yRf/G6i5jryO9ce6GH/NHjsKIoXqhz\n",
       "rFjEDIKgTUkp9ZGFerfS1xEYKwv2g3JOdmtmibQ1zV/ELIpifkrpDPxFTiO8riiKcSmlU0qvX10U\n",
       "xYsppbssvjDX1BXvIAiCtiCl1EPOv95N9rLXl1P5/on/lSse55XNwDam0TzwVjtReOBBELSQUmrz\n",
       "lvLC467YDOPlGPZDcjx7dtkMbH2anwfemoSAB0HQHFJKI7G3LNo7ys2f/lF6/B0zy2ddmxMCHgRB\n",
       "9ZBS6i+L9Z5yaGQ5i2PY9+Gt8lnX7rSokCcIgqBNSSl1w3ZyIsSeWFteeHwIJ+P58llX2YSAB0HQ\n",
       "rpQqHtfFaOwhi/dEWbAvluPZc8pmYBURIZQgCNqcUj72ojj2rvI4x7/Lon0f3iufdRVNhFCCIGhf\n",
       "UkpdsDU+KXvaa8vN8B7CURqYMhM0nRDwIAhahZTSythXFuxd8S4ewI/k9L655bOuYxICHgRBsyhV\n",
       "am9nsZe9upwt8gAukqu3gzYkBDwIgiZTmkCzyMveWRbpB/BtudXG0qbPBG1ACHgQBEul5GXvgP3k\n",
       "NL8hcgHNA3Kp+n/KZ10QAh4EwRKUMkb2LT12l73s+/A1ed5jNTWD6tCEgAdBJ6eUl72R7GXvKzeE\n",
       "ehT34kK8WT7rOj3rNfRi5IEHQSckpdRT9q73k/Oza/A33C2n+kUhTfnZBL/B8tELJQg6OSmlofJM\n",
       "233l8WEvy6L9F5U52KAzszn+n9xSYIcQ8CDoZJRCI5vjIOyDVWXv+l7Z055WPuuCBtgKv5JTMs/E\n",
       "8yHgQdAJKDWG2g0Hyp72Alms/yr3GIk0v8pmO3nU2/04TR6pFqX0QdBRSSn1xf5yeGRPvI57cKwI\n",
       "jVQTO+J6+Q33DPnNtsGZmCHgQVCFlOLZn5JFeys5VvpXuQIyskaqj91wLe7AF+RPTo0SAh4EVUAp\n",
       "nr2+xaK9hjzg4A84HR+Uz7qgheyFq3EbzrIMefYh4EFQoZREe0scKi9E9pZDI5fIrVg77LDeTsS+\n",
       "uAq34CtYpkXJEPAgqCBKbVi3l0X7ANkbuwv/I4dJgo7DgfgxfomvW0bxJgQ8CMpOadL6rjhEFu2Z\n",
       "smifKMaJdVQOlT9J/QLfbO5BQsCDoAyU0v32lEV7X3nS+p9xmBh20NE5Aj/ET/HdlhwoBDwI2omU\n",
       "Ug+5d/ahcvn6G7KnvX/p+6Djcwy+j8tkEW8RIeBB0IaklLrLVZCHyz20X5I97UvEwIPOxon4lizc\n",
       "l7XGAUPAg6CVKfXQ3lP+qLwv/o0/yZ39on925+RUnI/vyVknrUIIeBC0AqWFyF1k0T5A9q7/D3sI\n",
       "T7uz83mcKw/A+HlrHrhLYxuklEanlF5MKb2SUjqnntd3TinNSCmNLT2+3poGBkGlkjI7pJR+Kov0\n",
       "FfIg3/3kcMlVQrw7O2fJ4v11rSzeNOKBl7yKK+W+wZPxWErpj0VR1O2v8EBRFPu3tnFBUGmUimu2\n",
       "wFE4GLNlT/tQjC+jaUHlcY6cv38ObmqLEzQWQtkS44uieB1SSmPkj4d1BTy6DAYdmpTSSDmD4Aj0\n",
       "lEX7OLxQRrOCyuXrctz7LIxpq5M0JuBDMbHW80ly45zaFNg2pfS07KWfXRRF3NRB1ZNSWhFHlh5r\n",
       "4U653Plf5bQrqHi+heNl7/v3bXmixgS8KaWdT2J4URSzUkp7y8111qpvw5TSBbWe3l8Uxf1NMTII\n",
       "2ouUUi+5YdTRcm/mB+XY5T2il3bQMEkuzDlabgd7ezOPsw22LX3fYDvZBgc6pJS2xgVFUYwuPT8P\n",
       "C4uiuKiBfV7DZkVRvFfn5zHQIahISms9u+Mzctrfc7Ij8kfR5S9oGknO7z5UHsRwZysdt7cWDHR4\n",
       "HGumlFaTV9MPk2OA/yWltDLeLoqiSCltKb8pvFf3QEFQaaSUNsIJ8n39ntzOc1e8VU67gqqji1yY\n",
       "dSBOlvuytwsNCnhRFPNTSmfIQ09rcF1RFONSSqeUXr9a7uVwWkppPmbJFWdBUJGklAbKi5HHYrDs\n",
       "aR+FF8tpV1C11Mjpo3vLzsDf2vPkMRMz6PCUKiP3kReWdsUDcv/l+yxD8/wgqENXOdd/dzkj6aE2\n",
       "OEeLQihBULWklDaQ+08cKY8Z+61cVDGznHYFHYLu+Jk8x/Iz8gT5dicEPOhQpJT6yf9Qx8tpsH+Q\n",
       "Y9wvl9OuoEPRQ85M2kZ2DsqWVhoCHlQ9perIXXCKHIv8Oy6X45FNGg4bBE2kpzyEYVM5oeOJchoT\n",
       "Ah5ULSmlleQQyYmlH/0G35YzSoKgtemFG7AhPo1nymqNEPCgyijNjNwLn8VucoHNV/BIOe0KOjzL\n",
       "4VdykeKn5VqBshMCHlQFKaUhsmgfjw/l/hLniQXJoO3pKzejWl1Om66YlNMQ8KBiKXnb+8hNgbaX\n",
       "J9mcLqazB+3LWnJY7mwVNq80BDyoOErFNp+VFyU/lL2fM0vfB0F7saYcnpsif/KrOELAg4ohpbSV\n",
       "PL1kP7nI5gt4rKxGBZ2R4XIb2EPkXjjblNecpRMCHpSVlFJPuZT9dLm0/f/J4ZJ3y2lX0Gn5vCze\n",
       "i7oAXoFp5TOnYaKUPigLKaURcsvNY+QBITfiLlHaHpSXIXLvpwHyfIMdMKeM9kQpfVAZlApu9pYb\n",
       "3W8ld/87SJ7aHgTlZghulT3uf+FPyivejRICHrQ5pSEJx8nCXYPr8Tl8VEazgqA2w+ReOR/Jed59\n",
       "8VpZLWoCIeBBm1HK3f4fuVLyOXxHXpwMgkpiNdnznm5xb/h3ymlQUwkBD1qdlNLm+JKcw/0neTW/\n",
       "ovJng6DESLm18FR5lkHFLljWRwh40CqUim4OwhexBn4pp19NL6ddQdAAa8qe92S5q+CM8pqz7ISA\n",
       "By0ipdRDDpGcJRfaXCu3cI0BwEElsy5uluPcR+P98prTPELAg2ZR6rv9eTkV8EV8VdtMJAmC1mYD\n",
       "uZfOy3Lv+Kqt8A0BD5aJlNJQ2ds+Hg/K/wAV0ZktCJrAxnLb4efkuahVnQnVpdwGBNVBSmndlNIN\n",
       "eB4DMRqnCfEOqofN5LDJU3IBWVWLN+GBB41Q6k/yNWwnN5XaTpWt1AcBtpTv30dwsgov0Gkq4YEH\n",
       "9ZJS2iGldI+8IPmU/A9wkRDvoPrYFr+WR+2dpIOIN+GBB3VIKe2Gb8j5sT+Vb/i5ZTUqCJrPjnLl\n",
       "7z1y9W+Hyo4KAQ8W9SjZE9+UJ7lfJa/Sd6ibPeh07Cqntf5ZrgjucAOuQ8A7MSXh3kf2uAfKwn2r\n",
       "DnijB52OPfFz3C4Xl1Vll8uBdGmor3LEwDspKaU95AWdy+RhrTvJXneId1DtfBLXyM2pqlK8j6bP\n",
       "G5w0hbsb2q5RAU8pjU4pvZhSeiWldE4D222RUpqfUvpUcwwO2oeU0vYppQfkj5ZjsDN+pwpv8iCo\n",
       "hwPwM3nR8suq7L6+jtWm8q0beWIY503jHw1t3+BAh5RSDV7C7nK/gMdwRFEU4+rZ7m7MwvVFUfyu\n",
       "nmPFQIcyUmow9V1siB/Lk28ixh10JA7BpfKi5TfKbEuT6YV72X4jTuzNHgt48y2uv4hfX5kTCJo9\n",
       "0GFLjC+K4nVIKY2R3+HG1dnu8/LHlS1a8osErU9KaQO5jeu2clbJqTpQGlUQlDgcF8ve93fKbEuT\n",
       "2I2eV3PQcE7qzjqzeex5Tj2AP7+6OJTZu6FjNCbgQzGx1vNJ8iSV/1IqrT5AXvHdAu0zoy1okJTS\n",
       "cHxPjgdeK5e/V33lWRDUw2dwoTy/8qIy29IoFzL4eI4dyGe60Od9/ngvX/wkzyzrsRoT8KaI8WU4\n",
       "tyiKopTVEGGSMpJSWh7ny/nbY2TPuyo7rQVBEzgB38aPcEmZbWmQu9hkG07uy74LmTmVG67hl+fz\n",
       "dnOP2ZiAT8bwWs+Hy154bTbDmKzdVsTeKaV5RVH8se7BUkoX1Hp6f1EU9y+rwUH9pJS6y50Bz5Ob\n",
       "TO2BKWU1KgjallPkWPeF8rpOxbEuXW/lkyM5qSebzeX58XzlRP7w0NJDmdvIjhd0a+j4jS1idpUX\n",
       "MXeTxeBf6lnErLX99fi/oih+X89rsYjZBpQ+9Rwuh0smyvG/aDAVdHQWOSvfluPeFcWZ9P8yR63E\n",
       "cTUM/pC/PMW1e/LwMsYxmz+VviiK+SmlM/AXeRjtdUVRjEspnVJ6/eplsyVoTVJKO8kfHXvj62Le\n",
       "ZNA5+JK8pnM+flFmW5bgZtbag5P6cXDBvPf4ze+5/hQmtMX5GvTAW/VE4YG3GimlVWXh3k5eeR8j\n",
       "Fo+DzsFX8AXZ+/5lmW0BA0h3s9s6nNSbHebx2hSuO4dbbm75sIjme+BBZZFS6iVPvjlDbo25vcgs\n",
       "CToPX5N70J8lOy1l5TCWu4hPD+GEboyYxUNPcuwe3PteOzlUIeBVQCnOfYScIvU89tZGH8mCoEL5\n",
       "Xznj5Ey55qRs/JThh3DCAI5IdJvO7+7lpEPzemG7EgJe4aSUNsGVGCR/fHygvBYFQbuS5Ario+WC\n",
       "wT+Uw4he+Atbj+Lk5dhzAW+/xZWX8P9+VMYe+SHgFUpKqY+cWXIULpfLg6PRVNCZSPgBPo3T8af2\n",
       "NmAHelzHgatyYnfWn82T4zjjEO4YVwGtKELAK4xSuOTTclHCv+QK13fKalQQtD9d5IX6g/BZOROu\n",
       "3fg2K53MMStyTBdWeJ87HuTcPXiyPe1ojBDwCiKltGgKzki5Debfy2tREJSFGvlT5z44Efe214nv\n",
       "YMPtc7Xk/gv54F1+dT03nstb7WXDshACXgGUqii/KqdHXSMPXZ1XVqOCoDx0ldd89sBx2mHNZwQ1\n",
       "tzN6DU7uyRZzefFVzjuF2+5ldlufvyWEgJeZlNLWcjHC23LjqTfKa1EQlI3uclXljjhGI72wW8pp\n",
       "rPBVjhzM8TUMmcXdD3PYbvy9WnJzQ8DLRCmn+/vy6vp3cEt5LQqCstJDHoG2rbxw/2hbnejXrDGa\n",
       "E1fgUCycxpjb+cWJvN5W52wrQsDLQGny+7V4AbugobF3QdDR6Sl/Ct1Mrnd4vLVPMIB0Fzutz8m9\n",
       "2Xk+EyZx4Te5+YYq7tYZAt6OlFq9XoL95D4O7Z4WFQQVRi/cIE+KOgxPtcVJnuMLq/Dlj/jHUxy/\n",
       "D/dMqbJxa/URAt5OpJT2lL2Mf8pzKGeU1aAgKD/LyQO115JTZ1uti2Yv3MwGW7DXCmz9Ty58lL8e\n",
       "lD/1dhhCwNuYlFJP/FC+Qb+ikSnTQdBJ6Cv38xkhx6LrbVG9LPTCX9lmXUavwOiuDCtY+ChH7s4T\n",
       "LT1+JRIC3oaklDaTb9I35IKcspXcBkEFsYI8VHsYDsbLrXHQj9CNbgM4OuW4uon87zY81BrHr0S6\n",
       "lNuAjkhKqSal9DX8VV6sPEGIdxBAf9yMVbSieMNtrDeK8xe1AZzBzevk/78OSwh4K5NSWl1+xz9Q\n",
       "zuv+TXktCoKKYYCcLjtQFu9/t8ZBR1AzhS8cwJ0LmXUTe3zAX/fi3GrJ524uMdChFUkpHYar5Hf9\n",
       "K3WAVe4gaCUGyeLdG4fI4/9azBjWPJDLu7PuZH6wFVdPYeEO9Ghg5mQ1EQMd2prSQuXlssd9vA66\n",
       "YBIEzWRl3CrrzUFaYdj2ELo8ymeH8pW5vHQrex1WKxzTQcS7UULAW0hKaW25wfxkuX/DzPJaFAQV\n",
       "xRDZ816IT2mFplDXs/rhXNqDUW9x6W5cWQmtXctBxMBbQErpaDmv+xZ5oTLEOwgWMwy/k8X1EC0U\n",
       "7wGk1zj+GO7pQp8/sc8QLuus4k144M0ipdQNl2J/uW/DM+W1KAgqjlXlsMlMucKyRe0irmLY8VzS\n",
       "k23e4cr9ufRR5raGodVMCPgyklIajN/LN89eoqIyCOoyUk4VfBeHa0EKbS88y5Grc8EC3vwr+41u\n",
       "o3L7aiRCKMtASmk7eSLHE3IXwRDvIFiSNeU1obdlz7vZ4n0hg6dy0wh+8B437c1eId5LEh54E0kp\n",
       "fQ7fwjm4s8zmBEElso68HvS6HFpsVpe/XhjLwWvy7QVMe5BP7ZzHCwZ1CA+8EUpVlVfhS3IKVIh3\n",
       "EHycDWTP+984UjPF+3xWfJtfrM0V0/n9Iey+c4j3UgkPvAFSSn3lVfQ+2FeETIKgPjaWK46fx7GY\n",
       "1ZyDPMu+63JhwayHOWzbmAnbKOGBL4WU0mp4BO/JCzEh3kHwcTaTFyyfwWc0Q7zPpP9MfrIBV7/P\n",
       "Xceza4h302hUwFNKo1NKL6aUXkkpnVPP6weklJ5OKY1NKT2RUtq1bUxtP1JK28jifZscOum0eaZB\n",
       "0ABbyJ73Y7LnvcwDgMey58Xc15utn+Az/Tn7Jj5obUM7Kg0KeEqpRu7pMRrr4YiU0rp1NrunKIqN\n",
       "i6IYJU+R/nlbGNpepJQOlCflfB0/KbM5QVCpbCOL9z9womUsXT+Z5adz6SZc/yEPncmum/O3tjC0\n",
       "I9NYDHxLjC+K4nVIKY3BAWo1Xy+K4sNa2/fB1Fa2sd1IKZ0kDxo+XhvM5QuCDsIO8hi0e/E5zFuW\n",
       "nR9lp025ONHjGU7cmLvawMZOQWMhlKGW7Bo2qfSzJUgpHZhSGoc/439az7z2I6X0VfyvPB0kxDsI\n",
       "6mcX3Ii/4DTLIN6Hsdx7XLQlv/6IsV9j5xDvltGYB96kXrNFUfwBf0gp7SDPuFu7vu1SShfUenp/\n",
       "URT3N+X4bUlKqYtcFr+P/OmixZ3SgqCDsieuxh/ltaEFTd3xIbbZmku70Hccp2/G7R29V3cL2Abb\n",
       "lr7v1tCGjQn4ZAyv9Xy47IXXS1EUD6WUuqaUBhZF8bHeB0VRXNDI+dqVUoz/l3J8/wAxNScIlsYn\n",
       "8VM51/vLmtjrfjQ9b+K8gZz0IXdfylfOz1WawdJ5uPQg9wP//NI2bEzAH8eapZS6KXJp7BG1N0gp\n",
       "jcSrRVEUKaVNoT7xrjRSSl3lRZghcqe0cAiCoH72l5MZfo3zNPGT+T1stiOX1TDoFb60MTfHP1nr\n",
       "0qCAF0UxP6V0hhzvqsF1RVGMSymdUnr9ank00jEppXly+s/hbWxziymJ981yo/nPaEb6UxB0Ej4l\n",
       "Dyu5Aec3ZYcd6PE7zl6RUz/i71dy2JciNNkmdLqRaiXxvgUrymmPId5BUD+H42I5NfhbTdnhDjbc\n",
       "nSu6MuwNvrU+vwqvu0U0OFKtU1Vilvp4/1YeqtqswoMg6CQcjR/JM14bFe9N6PYmZ+3NHQt471p2\n",
       "GxHi3eZ0ml4oJc/7VvSTPe9OMTMvCJrB8fgOLpFFvEF+yzr7cXk31pjIt0Zx3XtNjJMHLaNTeOCl\n",
       "VMEbZc/7OCHeQbA0PiuL9w80It4jqJnMGZ/iroXMuYk9V+XaEO/2o8N74CmlhCuwrlyk0+nHMAXB\n",
       "UvgcvorvaqSNxE2MPITLu7P+FH64Iz97dRnywoPWocMLuFxduQcOFKmCQbA0voiz8U1cu7SNBpDG\n",
       "ctJwzp3L+N8x+lBeajcrgyXo0AJeSoE8VhbvaAcbBPXzZZyJr8npgvVyDasexaU92ew/XL4rV3Tm\n",
       "ifCVQIcV8JTSfrI3cRD+U2ZzgqBS+Zrc0+TLcqHOxxhAepxjVuX8+Uy4g33247l2tTKolw65iJlS\n",
       "2gzX4xS8WmZzgqBSuUAW7y9ZinhfxpCJ/GY1vjOV63ZkdIh35dDhPPCU0jC52c4F8lCGIAiWJMmZ\n",
       "JsfIfTZuq7tBLzzD4SO4YAFv38sBe/BkO9sZNEKH8sBTSr3kYQy/xu/LbE4QVCIJF8ktJE5Xj3h/\n",
       "j5Xf4caRXDyNMfuzZ4h3ZdJhPPBSuuAv5P7ll5bZnCCoRLrIpfGfkvO9l+jF3QtPcODafHchMx/i\n",
       "4J14tAx2Bk2kI3ngX8Im8mp6EARLUiPXQxyEk9QR768y8G2uWZerZvDHw9ktxLtd6Iu98D3ZAV0m\n",
       "OoQHnlLaTW5zub/I9Q6CunTFj+WBDMfhgdovPs3e63NRwZxHOHwbHiqDjZ2JGnly2U7yLILH5b/J\n",
       "L5f1QFUv4CmlIXLM+4t4vbzWBEHF0U0exLCLXBPx90UvnEG/7/Kd5TloOmO+yAU38H6Z7OxMLJDb\n",
       "DVyCf2lBU72qbidb6nFyH56SF2aCIFhMD7kV7LbyouV/s7IeZ7dN+CHS03x5M+4pk40dkT7yNd9R\n",
       "9qpfbsGxOnQ72a9hOXlhJgiCxfSUY6pb40gl8T6OvtP40Wb88kMePptdQ7xbhbXwBTn77UmcIA+x\n",
       "aNMK8KoNoaSUtpMXLEeLJjpBUJteckn8RvJQhrHwMDtsziWJns9y8kbcWUYbOxqbyq2qr5DfLNtl\n",
       "1kBVhlBSSsvjGVwoF+0EQZBZTv7Yvo4s3s8eTO+f8/UBHPsBf/4+53yPip9bW2H0lsMiPXBHO593\n",
       "qSGUavXAr5Tf5UK8g2BJ1sMKcuvkF+5ny23zYOF+L3LGptwWaVpNImED7Cxni2wkr7VVVIFg1Ql4\n",
       "Smk0dpcvbBAEmVXkkOI07LEbPcbwzYGcPIu/XcGXvxpN3ZaFleXUy/vlsXKPqMAU5aoKoaSUlsM4\n",
       "eTr23a1iWBBUNwNwhpzfPQvb/YURu3B5DSu/yjc3YkzFKU9l0Ete5H1Q5a6jdagQysV4Qoh3EHSR\n",
       "i0FOl+Pe+nLheE4bxOdm88+fccT/MLmsVlYWCevL6X07YZS8lvY83i6jXc2magQ8pbSj3MNh13Lb\n",
       "EgQVwEL8Wfa+4fXn6L0iJ73B+ZtxY8ym/Bg/k0crPoBr8DA+LKtFLaQqQiilifLPyouXH+ueFgSd\n",
       "kJVxC7ptw9yf8u4sLnmeSSfzRrmNKyM95UKaqUt5rV3S+1qRDhFC+Zy8OBPiHQQM6cItn6LXz5nU\n",
       "n82n80R//lFuw8rEenJIZCc5H/sy9Q9lrjbxbpSK98BTSv3lUtQj5VhVEHRmhu3I7dczcETuc2IB\n",
       "U89kpyuZXm7j2plN5WrT9+WwyIP4Jz4op1GtTIMeeJMEvJS6d5ncRevaoiguqvP6UfiKvEjwPk4r\n",
       "iuKZOts0V8Cvklfaz1rWfYOgg/EJ/LYr7/+HdwewHTzPqRvwf2W2rS2pUX+WSG8MlGcAdFRaJuAp\n",
       "pRq8JOdeT8ZjOKIoinG1ttkGLxRFMaMk9hcURbF1neMss4CnlNaVu6ftLCrHgs7N6ri1H9Ne5b1+\n",
       "bP4B93ah+yCO64BpgutYHBZZD5tjflktKg8tjoFvifFFUbwOKaUxOEDOxwZFUTxca/tHMay51tbh\n",
       "UlwtxDvo3KyBW0bw3nN07c46d3PIq0z9iAUdTLy/g09ijlxE80s5LNIZxbtRmiLgQy35EWUStmpg\n",
       "+xO1QpOclNKu8jvvqS09VhBUMWvjlu2Z+jdWxPRr2Pe0jhs2+Juc4teZM2maTFMEvMmrnCmlXeQ2\n",
       "its12yL/nW/5Hbmz19yWHCsIqpj1cfNRTP0lq87hiS9w8jXMLLdhzWQti8MiN6s/bv+3drWoymmK\n",
       "gE/G8FrPh8te+BKklDaS3zlHF0Uxrb4DpZQuqPX0/qIo7l/KOfeQezvc3AT7gqAjsmFizDeY9k3W\n",
       "mMHNu3DuU8wrt2HLyEbyJKCd5DDIA/IErb83tFMnZxu58yGlTKOl0ZRFzK7yIuZucoPyf/n4IuYn\n",
       "5HfOo4uieGQpx2nyImZK6RFZvEPAg87IqK78+no+OJohU/j+GlxZpbHuTbGhLNyvl9eUqqRli5hF\n",
       "UcxPKZ2Bv8jpPNcVRTEupXRK6fWr8Q30x09z9MO8oii2bI61KaWdMAS/bc7+QVDlbNGHm+5kznas\n",
       "+DynbVDZbZNHyt71SnJ//ro8WXoEbUDFFfKklP4srzpf1/ZWBUFFsfVQbvob80cy7wGO3y1PLK8k\n",
       "umJvi2PZ5GyRe3FXmWzqyFRPKX1KaUNsIZfOB0FnYvtR/PIvFCvw9vV8pkJ7miyUBfwxedr9v8tr\n",
       "TuemojzwlNL18gp7TJgPOhM778v1t1BT8Ng5nFjmsvgRsnf9Z7xVRjuqnWE4CmN8/M24m5wWulIT\n",
       "Ht0r3gNPKa0gt4vducymBEF7svsZXHcZXd/nt7twdhkyTVbA9haHRbrIfUXua2c7OgJd5JbXn5ET\n",
       "P2bLOltXlAfU2e9DuSf5osfY0tfpGnBoK0bAcbKcWhRjn4JOQQ/2vpCfn0mXyVy8JpeWKdPkZDnd\n",
       "7wH8HOMIESlLAAAZQ0lEQVTLY0bFUqNxb3m23C31LDkJYxG95DfFt/EmnrakUC96zFJnpz3otT6r\n",
       "fL8BwyoihFIq3HkF5+m8LTGDTsQqHPwzLt+bYjxfWK/th+WuJnvaT7fxeaqJ3nJf9UFL+bpInAfK\n",
       "jfoWMVt2NGsL8AT5zW8l+c1wIzmXf8PVuejLPPIJ+g2gX1/696ZfD/p1p183+tXQvyv9uuTv+3Wh\n",
       "X6K70okrPYSyS+lriHfQ4dmS437Cd9dizsMcsVPuH9TaLC9XRC8Ki/TA9Tq+gHeRwxMNCfOir73r\n",
       "7PueJUX5hUXf92TqFnw4mrmb0X0g/fvQr1cW4v7dGNaNK2pKAlwS4f5dWCHlTq5LsJAZC5i+kOkL\n",
       "mD6f6bOYMo/pc5g+m+kfMv21PEh5qfUwleKB3ygvllzeLsYEQZk4kzW/xH3deP+v7HMsr7bBaVaV\n",
       "58Y+JodFHpCL8aqZnrJ325gwryiHPBYxVy1R7sE7n+D9Nfhwbeasw/w1KValpg99u9Gva8kbrqnl\n",
       "EacsxEvoV8HChVmEpy0oCfECps8rPeYw7SOmf8D095g+helPM/0WZkzJ2TxNoeX9wFuDpQl4Sqmn\n",
       "LN67y5WeQdAhWY3tD+MLRzDuV1z6ozxlqiUMt/SmVj3kjn6VTJILAJuSidG39o49mD6Id1dhxlDe\n",
       "H85Hn2DucOYPxcp07U/33ixXQ/9FYtwlj1tbgoJ5C2t5wwuYNr+WEM9m+kdMf59p7zH9DaY9yvQ/\n",
       "8kE7zB2t+DzwT8mTdkK8gw7JSDY7iUtOYI0/8YtNcuVyc+gr98hYFBZZTnZ86pv/WE7x7iF7ww2K\n",
       "cmJQL7oOkGMeA1kwmBmD+XAIs1dh7srMGsQb/em6PD16sVw3+nahn/z4LwuZvZBptYR4+lwmzePZ\n",
       "uaXQxCymz2T61ByemPYQ0+9kVpW2KagID/wu3CM3uAmCDsM6rH8ilx3DeivhOT7cibWb6bVdhIPk\n",
       "ysxFYZEXW9HcRfTFwbJnfOmiH97K2ltwzLO8tV9OcastxCv1Y5WBrNyPQSvQZ5EoD8Ag5g5mzkrM\n",
       "G0QxgC7L0603PbvW40Qu5MPaoYn5pce8LMjTZzNtFtNnMP1tpr/MtHuZcW8HnHmpkkMoKaW+sue9\n",
       "mY41xy7o5Ayhyxh+vAUH9iz97Juc9a1c1NEQSxsftqqc+dBWIrVB4tjlOGgQvSbxr/68fzxrHcbg\n",
       "UaWueH8qbVwS5gUD0I8uNXXiwzCf9xcyrVhSiKfVXaibzvS3mDaO6f/HjCrsuNiWVHQIZV/53TzE\n",
       "O+hQTGHhk/TeTlbje5i0FPFezuKwyI5y46qL62zTayvefHTZeuP3xUrLs8rarD6EVQcytD+DV2DF\n",
       "fqywAn035bUaBvdihZUsTss4ihHn0mW9HD/+r3hsy7i5vNqVt+cz7QOmvVMS4mmlhbpnmHYbM1+t\n",
       "/40oaEXKLeAHyqvlQdChuIYxJ7HDrdwzgq438aM6m2xYw/cW5Ik7T8qVj6fJqWugLxsfyTnHsM7K\n",
       "/HANbunGihuw+uqMHMSq/Rm6PCsvz4rLZ1Hu04+eg+iyKIG5NgsoZjLnAz6YxcReTFiOB9/kowdZ\n",
       "biwDXmDI3yl+zVH7k85m45FsvgKbFbyxChe05bULmk7ZQigppW5yas/ucoVSEHQIDmW9A/naPGYe\n",
       "x2mj6XlXKfTRi3QGJ27AqW/gG2y/Jj02Y+1t6Xk9T/XhqIM5+RBWHlo65sss6E3NSkrVHbWYyYIZ\n",
       "zH4/i/KMj5g6l//MZ3JiQlde+w9v/4t3f5lT2pr9T99LTkwO2o2KDaHsIqdAhXgHHYbL+OEuHLoL\n",
       "Z85gq0E8sT4nzePdg/jmruy2bimePJXiNP69Yq39J3HfLmyxMX1WqfXz2Yx/mufmMHkebyzk31OZ\n",
       "eBvvLWNopUWEeFcW5fTAr5A9geg8GFQkO/GJb/DH93hzCk++zr1jeOBNFpzGgRuy60Qe6EK3FVlv\n",
       "LifeKZdVrsasT9HrYNLz/LEXa63LamvnzAvwb+Y8yJ8/YNKHvDGXF27j+aeY14Neu7DT5uy2Bpts\n",
       "x8Mb8Y0Q0E5HZWahpJSexrfl4Q1B0J6M+Aa/3IWF7/DcNP4+nrt/yDs92PACPt2PYcuz8hasv2at\n",
       "T6of4hHeeIanvsgB/2LGa/x7FYY+ycojWHgv507j8Q+Zsymf/Ihx3y119tuSFXZn70+w0zDWHsPR\n",
       "N0UNRLB0Kk/AS61jJ2MDMXU+aDt6dGXQOqy2HmsOZcSKDBvAyv1Z97A64eS3mfltnvk+28/J4j63\n",
       "KzVr0O19/JTpNzD+31y0NzNXZ8XLuP90tjuTm27m++fnhkZB0FpUZAx8ZzwrxDvI62KFWvnN+9Pr\n",
       "ceY00C+iHwb1ZPAmjFyVEaswbEUGD2TgwJwS12swXYdasnZ6LsU7zJ0oj0jviv/wwTh+czuXX8ms\n",
       "e1kwLr+86iH88Wm6j6dbkQtnHsCk25nUjy638dC7vLEv67xc+aXrQQejXAK+izzdPggKOZV0Lp7B\n",
       "M7OZ8gYXzWDWMyx8hvlPUPMEy+3BwCNKwjzYkjfwTOa/xwczePd9pr7BlHFMnM34Obz8LG/8JDcY\n",
       "Sjsy5mcMmsyPjuXPtd8sxi0+5Dq/409Fnvn4TzmC4gLO+BEvX8M39mH1n3B7iHdQDsoVQnlSnmD9\n",
       "93Y5eVBO+lpKL4xeDF6dVYYzbFV6rC43rR7Jwo1Y2KOWPr/FzN/ycOLdLRgwl4kL8jzG8f/mzVt5\n",
       "665lqFIcQpcpOYSyldzJ7pam7Lcq3e/lpUnUbEfNNVx6+scLb4KgtaisEEqpfH5tudVlUJ00ZULJ\n",
       "SjWsNISeq2N1jKBYkzlrsHBValakR5fSAT/AZObM49X+PFawLrb4iEde4up9uGcZWnA2xHrYaUqu\n",
       "fNxUbqR2Z1N3PpuLRtJ9JG7nwx/nQSRBUBbKEULZSu5NHB85K49lnlCyMkYydy1mrsPstShGUDOU\n",
       "3v3pvqgx80LmzWfifCbMYeIsJoxj4kQmnMHur3P/Ap5YZMgUvvAU3/hkDqu0Fj3xYzyCX+Aky9DG\n",
       "YWP6Hcghi54PZ+IpvHRmKxoYBMtCOQR8Y23TRS2on5ZMKHl3IFPX54MNmLMB09bkg1V5a1AeDTWo\n",
       "JrcO7V4wYEGeKDJxDhM+YtJ4JrzJhEeZ+AP+00AF4MemxAxp/nCPHtgST+H9Oq/NlgfNNovPctUw\n",
       "uoxnyljO+nQufw+CslEOAd9QCHhr0NwJJXPUmlDSn1c257ktsAnd1soVgP1WYKVuDO+Sw11gAW/P\n",
       "Y8JcXvmICVOZ8A6TnmXCZXnBcH57/OL1sLbFPbK3kNchz/ZxAW8uvddk2z1Z6298cV9uiYKaoBIo\n",
       "h4BvgDvKcN5qoNkTSuTpLrXn+b2Mt/vy7l4Ue9B9C/oMzU30h3fnE13ZoiYLPChNIpk0lwkzefAD\n",
       "Jr7LhJeYcD2TK7Tf8rflfjr341dyQ6iZrXj8Pufx1x1Y6Ug2fqyUiRIElUC7ZqHInuAM+SPujHY5\n",
       "cduxutzHpSmi1qQJJaVtar+pzsM7ch/oul/fxttdefsNTujHuvN5d27p8RHvvsdbm/OrRbP8FjJr\n",
       "PhPm5dS6iR8yYRoTXmPi7Uy8ofU81tamuxwGeque19pydNjyR/CnXzHyCa7fiq+30XmCYGm0PAsl\n",
       "pTRanqxcg2uLoriozuvryBOvR+FrRVHUbZ25iNVkD6baxRs2kmOgL8tFSc+Uvr4g93epLcwr1Nl3\n",
       "piW95UfrPF/0WOrMxAGkKxixBdv2YZXeuTgKFMx+h2sv5o7enDaJifcx4Qreq6KP/mtZ3CN7S3li\n",
       "0//Ws11biXe/7fnDNYx8gzt3DvEOKpBGPfCUUo2cNbK7XP7+GI4oimJcrW0GyRNDDsS0+gS85IF/\n",
       "CmfiiNb6BdqAbrIn3NiC3yBLlmIvlEfD3SD/fu+rX5Tf0YxQxAUMOoBRQxjVh1E92bgLyxfMm8vz\n",
       "3Vgz0Xsmt/yCi79Uvf01Vset8jCA++XKx39o3zf9/mvy+7+zRuLJnTi4jPH9oHPTYg98S4wviuJ1\n",
       "SCmNwQFqFawVRfEO3kkp7dPIsTaWPdZysNSCEksKc/86+31gSQF+svT1A3xXFuRf4/9ZLJoPtMTQ\n",
       "g+n9P2w4gk1XYJNejOrKUJjHqx8xdiI/eImnvsHzw+h6Iz+5mx8cVGsgQIXTVf2iOBGH4rX2Nee/\n",
       "rDiQW//EiN689nmODvEOKpWmCPhQ+Z9qEZPkXO7msKHW7T7YpIKS0qNnrf0WypO8F4nyZHm0W30e\n",
       "89KiDuvhFPxFC/7BR1BzMWttxKiBjOrNqG6sneiygHdn8+Q7/HoiY3/F01cyve4xXmFeH45rrg3t\n",
       "yEiLs0W2wjY+Hiaar3zivVJ3br2d4asx/SoOv6Fy1wWCoEkC3pqrnDvK4YMhspA/vJTtltM0Uf5v\n",
       "QUmJjyy50Pes+hcA39Xyqr4XLKO32wvfZ8hubLoym/RhVI8cCum1kNlzeWYmD/6HKx7gybOZ1JSY\n",
       "dUsmrLQTZ+Ow0vcP4LdyKG2pMf4ysErill+x0tYsuJOjqjgMFVQ328hzUikN/1gaTRHwyRhe6/lw\n",
       "2QtvDkke2toVn8Dm6hfmjxWUWFKAn1e/MFdUitfJLH8CG3+CUcszqhejahhUUMzjpVk89Sa3PcfY\n",
       "c3mpA39U/yduk3uXVCJDcesPWP5Qej3BsfvzXLmNCjotD1vs3PbG55e2YVME/HGsmVJaTfZIDrP0\n",
       "Rch6A+21GGjxZO5FBSWLBPgF2TurK8xTVYGwbUK377PeOozqzya92bRbDhmYz5TZPPUWP3+NsVfy\n",
       "zM0V9mbTAkZYnC3ykFyiXpdKHtrxCdx6Bl3Ppv+rfGWL0vCFIKh0mpQHnlLa2+I0wuuKovh+SukU\n",
       "KIri6pTSYDk7ZXk5NPE+1iuK4oNaxyjkj/o7y8LdmsUW7UovXMlq2zJqEKOWy6GQDRLdF/LBHJ56\n",
       "P3vXT97JU1/Nb0YdiTXwWVm4a+Q33gdLj0oKizTG6rhlf+b+gWHv8LOV+X65jQqCWlTORB7Mwprt\n",
       "csJW5BwGHMqooWyyPJv2ZJMu9CuYP5dxsxg7lbFPMvZL/LuVuuZVMiPlnu4PqN5ufCNx6+bMeISh\n",
       "H3LP6nyuCtYTgs5FRQn4VDmVsGLZjZ5fY8ORbNK/FLfumj9mm8cbH/HUdMaOZ+z3eK5Cy8tbyqqy\n",
       "d70OvlpmW9qCtXHLarz5MoMWMGFPDn8oOmQGlUdF9QOvqLjvELpcyhqjGLViKW7dnXUTNQuYNoen\n",
       "pvLbyYy9lacu4r1y29yGjLY4xa+nxWGRjsZ6uLkfr72Qs50+PI8TQryDaqS9BXxWO59vCS5k8N5s\n",
       "MphRfRen8PUpmDOH5z7g0bf56cM8dQavV1HZeWuwi5wlcoNcedsR2RBjuvPSG8zpzmrXse9l1RW3\n",
       "D4L/0mE98MNY7vNsvBqbrFCKW3dlFZjH+FmMfYs7XmTsVxn3VG4c1ZEZLnvXj6o/bn1O+5rT7ozC\n",
       "rxNPT2RyXw68l0NPYUK5DQuC5tLhBPwNThzMUd1YK5EW8M5HjH2bGyfw1C94+poqzoBZBvrIxQCL\n",
       "wiJ95LDI2HIaVSa2wE14fDyPDeLsZzlpj9wWIQiqlg4RQhlCl1vZZi12/ZCJM7j3P/zoXsaex5RO\n",
       "FgpZxCHYSxbtky0xbL1TsZUs3v94gj+N4PIJfHNj7iq3YUHQUqpWwAeQbmWzjTmgH/vWsNJznLIh\n",
       "f2qtc1QBQzFMDovU5YbSozPSB5vJHQ1vxH13cf0obnqX61bl2vKaFwStQ3sLeJMHyDbEunT9B9/t\n",
       "z9GLfvYu13QC8V7O4rDIjugn9xWpT8A7M6fLnz5Ww93Xcuke/P5D7tuIC8pqWRC0IlXpgc+hmMN/\n",
       "CopEms1jO/Cd1jh2BbOcPLX9aTkscrrcEyYKT5ZkFblLZE+8uzM3HcsN83j9UE7vBEVWQSei6hYx\n",
       "r2LYCVzZg42n8P3BnHQ5p3agRlBD5B4wdbNiPpSLoCJfuWG+rNQ6eDne/k2pNP67HHtXxyy6Cjox\n",
       "VeWBP88B63DRAt76P/Y9gOd/z9/OrX9WYrXQW24fuShbZIC8AFlfLnaId8Osj0/jtR5c/Bb79Wab\n",
       "37Dft3MVcBB0KLq08/maFQM/jOWmc9l6/GQGt+3P6ANy+MCnqju74st4CqfKDb7OkGdtdtRCmrak\n",
       "D06Qr+nOk3OTsV3/wQlHV24b2yBoERUfQrmLTXblqi6s8DQnbJIn4FQbSxsf9v9wlTJXqHYADsX5\n",
       "W3PYjWzQk2MHctI4Prcjj5TbuCBoKypWwIfQ5TE+twpnz+aRKzi4ikIlPbG1xWGRJ+WpNHWJiS8t\n",
       "5wj8ED+9hR2H8LkuDJjChevxh3IbFwRtSXsLeJPmC17CkFO5oidbTObCjflZlbT5XBUXYVN5nNsD\n",
       "+GLp+6D1OUZepLxsXS5dhYdrGFgwryt9dqBHNKkKOjIVlwf+LPusxw8W8N6f2Xef6hK/qbgOJ6qw\n",
       "zosdkBPxLdn7vuz3HNQ1Z/CYzeN/4ZYQ76Cj096LmEsVtf3pNY2LN+DnM/nzEexVYeLdUy6eOV+O\n",
       "w9ed20n+/e4W4t3WnCqL9/dwWS+M4NSFTB/PWQM55JhYuAw6ARXhgd/BhntwVQ0rPsdnN+SOdrar\n",
       "IY7CvnJp9vNyWORckVNcLj4vX///xc/hHrabzSsXceT38gDsIOgUlDUGPoD0NKcO5ZzZPH4lh3+p\n",
       "8hb2FuB6eQZkk2L4QZtxFr6Er8t/E/BHxm2XUzCDoFPR3iPVhi56/j1W/gKX92LbN/nhFlxVhjLn\n",
       "HthSDo08ITrUVTLnyt73OXJ3wSDoDFTUSDUwlj035JKFzLybA/Zq3x7Vq2A/Ob1vC7kQ6EERM61k\n",
       "zpf7m5yFMWW2JQgqhnYV8NH0/DXf7M8xM7jlFL5+c/sv+A3DCNmLO03nGO5QzXwbx+F/8PvymhIE\n",
       "lUW7hlDm8koNg1/knPW5vY1O1V32rNdSK04aVB1JzjI5Sg6dtNX9EgSVTOWEUBYw/RqO/hyTWvnQ\n",
       "a1pc9bglXsZ9rXyOoP3oIud3HyKnDN5ZXnOCoDJpVw98CMPbaKHydrkB1AP4B6a3wTmC9qELLsUB\n",
       "cubPX8trThCUlcrxwLeh5++a17ipm5yH/Rr+U8/rB7TIsKBSqMGPMVruLPi38poTBJVNo5WYKaXR\n",
       "KaUXU0qvpJTOWco2V5RefzqlNGppxzqd9ZbBtpE4Xp7r+Cy+geHLsH9QXXTFT+VRaMcK8Q6CRmlQ\n",
       "wFNKNbhS9ojWwxEppXXrbPNJrFEUxZryR96fLu14I9iwiXZ9Tk4XWx+/kwcefBKPN3H/SmWbchtQ\n",
       "AdR3DbrLVZW74jN4qF0tan/iPohrQCtcg8Y88C0xviiK14uimCeLat1wxf7y5G9FUTyKfimlles7\n",
       "WD82qPW0q1qFPXW4Rs4kORv/h2mN2FktbFtuAyqAuteghzwlfnsciX+2u0XtT9wHcQ1ohWvQmIAP\n",
       "xcRazyf5uOjWt82w+g42Pgv4cXJ633M4bynnnduIXUHHoKccIttS7uv9r7JaEwRVRmOLmE1NUam7\n",
       "QlrvflszGKPktLDz8Z76u/p1VLrpXL9vfSy6Br3ksMl6csx7nM5zbeI+iGtA065Bvdkn/32xoTTC\n",
       "lNLWuKAoitGl5+dhYVEUF9Xa5me4vyiKMaXnL2Knoij+U+dY1TCQIQiCoOJobhrh41gzpbSa3CXw\n",
       "MPmjbm3+KHeCG1MS/Ol1xbshA4IgCILm0aCAF0UxP6V0hjzAoAbXFUUxLqV0Sun1q4uiuDOl9MmU\n",
       "0ni5r8nxbW51EARB0H6VmEEQBEHr0uKRai0p9GnKvtVAC6/B6ymlZ1JKY1NKVZuF0dg1SCmtk1J6\n",
       "OKU0O6V01rLsWy208Bp0lvvgqNL/wDMppX+klDZq6r7VQguvwbLdB0VRNPshh1XGYzV5RfUprFtn\n",
       "m0/iztL3W+GRpu5bDY+WXIPS89cwoNy/Rztcg0HYHN/BWcuybzU8WnINOtl9sA1WKH0/upPqQb3X\n",
       "oDn3QUs98OYW+gxu4r7VQGsUO1X7Am+j16AoineKongc85Z13yqhJddgEZ3hPni4KIoZpaePWlwz\n",
       "0pnug6Vdg0U0+T5oqYA3t9BnKIY0Yd9qoCXXgJwzf09K6fGU0sltZmXb0pRr0Bb7VhIt/T06431w\n",
       "osWtgjvrfVD7GrCM90FLuxE2t9CnI9HSa7B9URRTUkqDcHdK6cWiKKqtF0hLVsI7yip6S3+P7Yqi\n",
       "eLOz3AcppV3kjpPbLeu+FU5LrgHLeB+01AOfbMkOgcN9fFhD3W2GlbZpyr7VQHOvwWQoimJK6es7\n",
       "uE3+CFZttORv2Znug6VSFMWbpa8d/j4oLdpdg/2Lopi2LPtWAS25Bst+H7QwYN9VHga8mtxRrrEF\n",
       "vK0tXrRodN9qeLTwGvRG39L3y8nDKPYs9+/UFteg1rYXWHIRs9PcBw1cg05zH+AT8iLf1s29fpX8\n",
       "aOE1WOb7oDUM3luehjMe55V+dgpOqbXNlaXXn8amDe1bjY/mXgN5uPJTpcdzHfkayH1wJmKG3F1y\n",
       "Avp0pvtgadegk90H1+JdjC09/tXQvtX4aO41aM59EIU8QRAEVUqLC3mCIAiC8hACHgRBUKWEgAdB\n",
       "EFQpIeBBEARVSgh4EARBlRICHgRBUKWEgAdBEFQpIeBBEARVyv8Hg4ORvBnZ2MAAAAAASUVORK5C\n",
       "YII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10752b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ramsey(1.01, 0.35, 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
       "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD7CAYAAAClvBX1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xe4XGXV/vHPk14IJCEhkCIEQg31pUmH0EJv0hEpLyJV\n",
       "BCkiKqKiWBCFV0RE9GejKGJABVSqiAgqICF0Qie0hEAgIWX//lhzyEk4JzlJzpk9M+f5XtdczMns\n",
       "s2dlM7nn2etZ616pKAqZTCaTqS+6lB1AJpPJZBadLN6ZTCZTh2TxzmQymToki3cmk8nUIVm8M5lM\n",
       "pg7J4p3JZDJ1SLdqvVFKKdckZjKZzGJQFEWa/8+qJt6tBZAJUkrnFkVxbtlx1CL52iyYfH0WTC1d\n",
       "n5RSb2yOrbEVNsKruA//xN/xfLNf6YMnWjpXVcU7k8lkOhMppf7YVoj1llgbj+NfuAonYfLinDuL\n",
       "dyaTybQTKaXlsb0Q7C0xAg+JlfV3xer6vfZ4ryzetcPtZQdQw9xedgA1zu1lB1Dj3N5RJ04pDccY\n",
       "c1fXg3G/EOkz8CBmdch7V8vbJKVU5Jx3JpOpZ1JKK5p3ZT1ArKrvxd14GHPa8S374InSNywzmUym\n",
       "nkgpjTRXrLdCP7Gq/gd+jkdQSiVdFu9MJpNBSilhZeyAbYRY9zZXrH+Cx5Qk1vOTxTuTyXRaUkor\n",
       "YydsJ9Ig3UUK5F78SFSG1CRZvDOZTKchpTRUrKybVtd9cI9YWV+Cp8qLbtHI4p3JZBqWlNKyQqjH\n",
       "iNX1cuY2w/wME8qLbsnI4p3JZBqGlNJSQqS3r/x3ZfxHiPUpoua6PatBSiOXCmYymbolpdRT1Fdv\n",
       "L1bXo0W53t9xl+hknFlagEtOLhXMZDL1T0qpKzYRm4xjsCGeFDnr74n89fTSAmx/Nm3thbzyzmQy\n",
       "NU1KaRXsIgR7a2HkdHfl8TdMLS+6DmUr/BS9WtLOLN6ZTKamSCkNEEK9k0iH9BVpkDtxG14pL7qq\n",
       "sR2uwJ+xexbvTCZTc6SUumML7CwEe3WxyXiXEOvx5UVXCjvhMozD5/FYFu9MJlM6lU7GNTEWOwrh\n",
       "fl6I9R0ifz2jtADLZVdcimuFsVUvrWxYZvHOZDIdTqXeuilvPUaMYPybuavrN8uLrmbYUzQK/RJn\n",
       "izb8XG2SyWSqR0qpCz4qVpJjRSrkPiHWh2plOkwnZl9RLXMlvtiWX8jinclk2oWU0hDsLsR6DN4Q\n",
       "aZDviBK+98uLrqY5UFyjy/CVtv5SFu9MJrNYpJS6iXx10+p6pKgKuQMX4KXyoqsbDsU3cTG+sSi/\n",
       "mMU7k8m0mcrkmKbV9bZCoO8QK8Z/6qCpMQ3KkfgqLhQr70Uii3cmk2mVyup6K+whSvmGiuaYO/Bl\n",
       "TCovurrmGJwr7lC+vzgnWKh4p5TG4iJ0xY+LorhgvtcH4RdYvnK+bxdF8dPFCSaTyZRPpTJk98pj\n",
       "B7G6vk3UHN+vQYydSuR4cS2/KsoCF4sFlgpWfAQeE/8DXxS7xQcXRTGh2THnomdRFJ+rCPljGFIU\n",
       "xaz5zpVLBTOZGqRSd72uWF3vLsyd7sVfcQteLi+6huMUnC4qSq5ow/GLXSq4CZ4simIipJSuwl7m\n",
       "9cB9WfyPh6XxxvzCnclkaouUUi+xKNtD1F93xa34gSjn66xNMh3J6UK8zxZe4kvEwsR7mOh8auIF\n",
       "H3a5uhy3ppReEsM5D1jSoDKZTPuTUhomFl+7i5FfjwvBPlIdDyWoEz6P4/BZ/Lo9Trgw8W5L++XZ\n",
       "eKAoim0r7l9/TimtVxTF2/MfWEmxNHF7URS3tznSTCazSFTSIRthH+yGFcWq+haxCpxcXnSdinPx\n",
       "v/iMaHtfGJth88rz7q0dtDDxfhEjmv08Qqy+m7M5vgZFUTyVUnpGdFPdP//JiqI4dyHvl8lkloCK\n",
       "ydP22FussGcLZ7qvCc+QnNKsHklsSh6OE3F9G3/vnsqDyHmf1NJBCxPv+7FqSmklseN8IA6e75hH\n",
       "Re7s7kqH1ep4uo1BZjKZJSSl1E/4YuwlvEMm4i/4hJwOKYskygAPFOmSG9v7DRYo3kVRzEopnYib\n",
       "xYbGFUVRTEgpHVt5/TKcjytTSg8Ks5kziqLIJjOZTAdSyV/vKwR7U2GheosQjFwdUi5d8G3x/+eT\n",
       "Qj/bnewqmMnUAZX89WhzBXuUGE5wsxDtd8qLLtOMrsJgajeR5/7rEp4vuwpmMvVGRbA3wf5i07GP\n",
       "SIdcKOxU63mwbiPSTXiU7IQjRBdqh75ZJpOpESpWqlsKwd5LdDPehJNFaiRTm3QX3ZLbig3Kuzv6\n",
       "DbN4ZzIlU+lkHoOPCcGeKgT7aJ1vBFg90gM/Eg6Lh4ru1A4ni3cmUwKVkr6dhGDvLiai/0lUJ+RB\n",
       "BfVDL/wYG4tKvA+VSHcUWbwzmSqRUuopvK/3Fy3pz4oV9p6V55n6ohd+ivXEl+4D1XzzLN6ZTAeS\n",
       "UuohKg8OEh7Yj4kV9oXysIJ6pg/+H9YQX8YPVzuALN6ZTDtT8cDeSdxG746nRJPGN2T/60ZgKWGD\n",
       "vYrwcnqkjCCyeGcy7UBl03E7Idh7iVX1DdhRXmE3EkuL6e4jsJ8w9yqFLN6ZzGJSqcPeEoeI5pk3\n",
       "xAp7DzmH3Yj0F46AQ4RwP1VmMFm8M5lFoCLYG4uSsP0wXayw98eTJYaW6VgG4ioMEP/fnyk3nCze\n",
       "mUybqNgdHy7SIr2EYB+hpHxnpqoMwjXoK+6wnl/w4dUhi3cm0wqVsX6HVB6r4Y84Q0xJz3QOhgjh\n",
       "7i6E+8Vyw5lLFu9Mphkppd7iH+lhomPuTtE99xfZC7uzMVQI9xzxmXil3HDmJYt3ptNTqRTZAR8X\n",
       "pX0PC+P8T8tufZ2V4WLqzQxRDvhqueF8mCzemU5LSmldHCW6497E74THSE2tsDJV5yP4jfCYOVBU\n",
       "EdUcWbwznYqU0rJi4/ETWF6ssA8VE6EymZFixf2G6Iqt2TmfWbwzDU+l43E3MSV9jPBZ/g5uE/nM\n",
       "TIYYcHGNuPM6BFPKDWfBZPHONCwppbWFreohYjTYb3CWuB3OZJqzuhDuZ8Wd2NvlhrNwsnhnGoqU\n",
       "Un+x8Xgkhom0yIFKbGPO1DyjcbWw4v24OtmkzuKdqXsqXY/b4Vhhtfo3MUfwVswuMbRM7bOO6Jx8\n",
       "ROyDvFtuOG0ni3embkkpLSfSIkdX/ujX+IqoHMlkFsYG+BUeFN2y00uNZhHJ4p2pKyozHnfGJ7G9\n",
       "aJ45A/8oM65M3bGxsHX9p5jyPqPccBadLN6ZuiClNFQI9pGYJm51PydvPmYWnY/i5yK9dizeLzec\n",
       "xSOLd6Zmqayyd8OnhPXqn3C8PEU9s/hsiZ+J/ZDjMbPccBafLN6ZmqPSSPNJsSqaJm5vT6k8z2QW\n",
       "l21xBW7GyercqyaLd6ZmSCltipPEMIPbhLfIfaUGlWkUdhQGY+NwqgaoQupSdgCZzk1KqVdK6eiU\n",
       "0r9wnRgZtqW4pc3CnWkPdsGPxefrM+pIuC+Jrs8WSUVRVCWIlFJRFEWqyptlap6U0so4UfiMTBB5\n",
       "yJvkdvVM+7InLhElgZ9DdQRvCTmXwSfz2f4c0oUuLWlnXnlnqkYKdk0p3YR/iZmA+4gOyD/Kwp1p\n",
       "X/bF/4mFwVnqQLj3pPfLnPoF/t6PHR7k7NaOzSvvTIdTGXBwhNgk6oorhY/EeyWGlWlsDsCFIs99\n",
       "XsmxLJShdLmTA1fi9MRSr3DJ0fzoplhgP9GSduYNy0yHUanNPll0QD6Mr4qNyEymIzkU3xTpkq+X\n",
       "HMsC6Y27GLMO53Rn1GR+cREXfoXXK4f0ae13s3hn2p2U0kZiR3833IiPCdOfTKajOQJfE6vu75Qb\n",
       "yoIZx9rbc04ftnqHm6/lmMN4qq2/n8U70y5UGmr2Ebv5o/D/sJka90TONBTH4Fyx6v5euaG0zkUM\n",
       "PYIzl2a/93nwTvbdhnsX9TxZvDNLREqpp0iLnCaaaH4sbFjrugEiU3ccj8+LVfcPSo6lRY6g3wWc\n",
       "OJhjZvPqBE7YinFvLuZGahbvzGJR8c0+SZT7PSp2xe8qNahMZ+XTwpzsS2LxUFOsT/frOWw4pya6\n",
       "vsAF+3PlvUvoqZLFO7NIpJSGiVX2kbhTmNc/XGpQmc7MZ0Wq7vP4abmhzEtv3Muua3B2N4a9wZVf\n",
       "5vuXtFMqMYt3pk2klNbEmdgbv8dYPF9qUJnOzudwAk4XTTg1w1/YcAu+0IuN3+b3v+aQY3muPd8j\n",
       "i3dmgVT8Rj6PLYRB1BZqeKJ2ptPwRWFedqroGagJrmCl/flcP3Z/j3tvZrexPNAR75XFO9MiKaWt\n",
       "RA5xNC4Xt6a5qSZTC3xVjCw7Cb8rORZwCgPO4ZSBfGIWzz3AkZtzS0f+g8ninZmHlNL2YlWzCi4V\n",
       "U0bq0qw+03Ak0XRziKguuaHccNiKnr/i6KGcVDBzIl/ajV9OqEK11UK9TVJKY1NKj6aUnkgpndnK\n",
       "MdumlP6TUno4pXR7u0eZ6VAqniM7p5T+jp/gD9hctLFn4c7UAl3wbRwk0iWlCvdA0gT2uZW7hnHa\n",
       "a1x5BJuvzM+qIdwsxNskpdQVj2EHvCgsOg8uimJCs2P6427sXBTFCymlQUVRvN7CubK3SY1Rmbq+\n",
       "m1hpLytMfK5VR5aZmU5BV3xX+LwfI+aWlsbf2HwjvtiDtadyzeV863Re7qC362MxvU02wZNFUUyE\n",
       "lNJV2EtYeDZxCH5bFMUL0JJwZ2qPlNKOIne4rOhG+53s6pepPbrh+2Lo9BG4o6xArmLV3TmnLzu8\n",
       "yx2/Z6d9eKSseBYm3sPMWw72Ajad75hV0T2ldBv64XtFUfy8/ULMtCcppS1FF9pKuEistLNoZ2qR\n",
       "7qJbcozYoPxbGUF8heVOCG/tg2fy2D85ZNMSv0SaWJh4t6Vtszv+B9uLJf49KaV/FEXxISOilNK5\n",
       "zX68vSiK29sYZ2YJqZhFfQ3r4GL8Um5hz9QuPXCZmKp0KP5R7QD2o88lfGo5jpvD1Cf57LZc+1LH\n",
       "L3Y2E3tOhL62yMLE+0WMaPbzCLH6bs7zeL0oivfwXkrpTqynBRe5oijOXcj7ZdqZlNLaIj2yuage\n",
       "+RRmlBpUJrNgeok2941FWraq4/BWpustc721+77CxRVv7elVCuGeyoNYEJ/U0kELqza5H6umlFZK\n",
       "KfUQE0/GzXfM77FlSqlrSqmPSKuUlgfKBCmlESmln4vbu8fEt/llsnBnapteos19Q1FZUjXh7o37\n",
       "GTOBP6/MN97iT+ey+TC+X0XhbjMLXHkXRTErpXQibhY7vlcURTEhpXRs5fXLiqJ4tDLW6iFxO3F5\n",
       "URRZvEsipbQ0viDqs68SK+63Sw0qk2kbfcTIsrXEJJz/VuuNbwhv7S/0ZsvF8dYugzwGrUGo3Bmd\n",
       "KPwe7hTNDC+VGlQm03aWEvYLq4g7/KosAC9i6JGctTT7zeCBezlvcby1O5DFLhXM1DiVWu2DcL7Y\n",
       "fzhUdvnL1BdJCPdIMXXpsY5+wyPo901OGsT/zubVRzh+Sby1yyCvvOuYlNI2YtRTH1FJkudDZuqR\n",
       "nTFYbNJ1aKqi4q398Yq3dpcX+V57eGt3IHnl3UiklFYUor2FaBm+Sh2tGDKZClvhLJHeO6Yj36ij\n",
       "vbXLIIt3HZFS6i0m1pwobjO3lJ3+MvXHhkK0Nxe9Bid25JtVw1u7DLJ41wGVvPbBuADjsYsG+PBl\n",
       "OiVjhE/JoMrPP8MzHfFG1fTWLoMs3jVOSml9XCJygmeogbbcTGYJmICpQrzfFkLerpzGgM/xmYEc\n",
       "Xi1v7TLI4l2jpJSWEhUkhwrjqCtlt79MfTNMeOnMFMM9BmnHqUxlemuXQRbvGqOSIjkAF+Kf4jbz\n",
       "tVKDymSWnI8I4Z4mPt9vacM8gbYwkHQ3+4zirK4s+yqXfZYf/IJ32uP8tUoW7xoipdQ0vWYVsTIp\n",
       "xUUtk2lnRoo5k5NFT8Kb7XXiu9liQ75QJW/tmqJdvvkyS0ZKqUfFcfF+saEyRhbuTGOwCn6L18WK\n",
       "u12E+ypWfYefbc41s3nz9+zUn1M7i3CTV96lk1L6qBg99ip2xbPlRpTJtBurixX3c2LvZuqSnrBW\n",
       "vbXLIIt3SVRqtr+Ow4Rl6zXlRpTJtCtr4WrRMXmYJcw/l+itXbNk8S6ByoT2Hwvzne3wRrkRZTLt\n",
       "yjqi6/dRfBzvLu6JasBbu2bJ4l1FKnatF4pBql/AjeVGlMm0OxvgV3gQR1rMDuDeuIsx63BOd0ZN\n",
       "5hcXceFXIneekcW7aqSUdhK57b9jW1Eqlck0EhsL24b7hJ/8Yq2O69FbuwyyeHcwKaVe+JbYaT8D\n",
       "fy43okymQ9hUCPffcKzFcOmb31v7TvatMW/tmiKLdweSUtpQfKCfFeV/7dZNlsnUEFsKj5LbcJzo\n",
       "oGwzRzSAt3YZZPHuAFJKXYVr2qmixf3X5UaUyXQY24h04C1iUG6bW9Hn99Z+gQtq3Fu7psji3c6k\n",
       "lEbil+gu6rafLzeiTKbD2AGXi433U7TRe6cRvbXLIHdYtiMppQPFZs2d2EcW7kzjsrMod/0dPq2N\n",
       "wv0XNnyT69fh8uk8dDnbDOa8LNyLTl55twOVTcnviZX2kfhXuRFlMh3K7vg/0YRzpjbkphvdW7sM\n",
       "sngvISml1fEbvIgdtUMLcCZTw+yNi8UG5RcsRLhPpP+5nNro3tplkNMmS0BK6TBRt30NjpKFO9PY\n",
       "7C+E+wqcYyHCvT29jmTDZdh5Il9ajzEbZOFuN/LKezFIKXUXE0D2FIY7D5UbUSbT4Rws+hUuxdda\n",
       "O2gg6Xo2XYeP9WPsbRy+Ipt1Zg+SjiKL9yKSUloe14lypp3lTslM4/MJUfJ6kRDwD3EZH9mbQway\n",
       "b7eYmOMFvroj/65inJ2KnDZZBFJKW4gP47+EU1oW7kyj879CuL+lFeGGW3i9L2s0Cfc0/roeP6xS\n",
       "jJ2SvPJuIymlE3Ce2F3/Y8nhZDLV4DiR2z5fVJe0yPp0v5RT+7LjbF4rmPUlPp07JDuWLN4LodIt\n",
       "+X2MFbXbT5YbUSZTFU4WC5Uv40etHfR/DD+KS3uw1pOcNoNprzPpO9kKYknojq3FntrA1g7K4r0A\n",
       "Ukr9xAinpURta06TZDoDpwlrh3NwZWsHPcgua/OdWUz6DbscyOMDSXnFvdisLfpEdhaLxN/jVlHR\n",
       "9iGyeLdCSmkl/AH/FXm/Nns2ZDJ1zFnCo+QMYfPwIbai5/V8YSBHTuGqT3DOuIpvdxbuJWIZMcDi\n",
       "2+bO4uzT2sGpKKpzrVNKRVEUqSpvtoSklDYTbb8/xg9KDieTqRZfEHaup4nuyQ9xBSsdymXdWflx\n",
       "zlwzKq8ybacLRuHxNh7fB0+0pJ155T0fKaW9RRNC3pjMdCa+giNErrtFQR7PXmvwzVk8+wt2/gRP\n",
       "VzPAOiZhI+yF3cRA5r0t4V1KFu9mpJT+VwwFPhL3lxxOJlMNkqgmORQnYNz8B4yl1684bwCHvslP\n",
       "9+a8u5hR7UDrlNNxoNgvG4f9tNOXXhbvCimls8WHd39tv6XJZOqZLqJ2+2MiXfKn+Q/4FaP247Ju\n",
       "DHuYT64T+0CZtvOI6E59or1P3OnFO6XURbS67yZua14qN6JMpio0fe73FBvyHxrP9xj7j+LrM3ns\n",
       "x+x0bNzuZz7MaHEH83ALr3XYl12nFu9KDff/w1pCuHNtaqYz0FUYTI0Vhmq3NX9xP/pcwdeX4WOv\n",
       "86MdOf+BRRxt1glYXXzx7YEeokKkJfHuMDqteKeUuonxZEPFbWM2O8t0BrqJCqrthWfJXc1fvI41\n",
       "d+eyriz7AEduEOPNMnMZKca+LSVy2CfhwTIC6ZSlghXhvhpDcDimlxtRJlMVegi/ka3E5/6ephd6\n",
       "42EOG8l5M3joMo4/JacQW6IH1hX+RtUQz1ZLBTudMVVFuK/BYFm4M52HnqJvYUscoplwH0G/SVy6\n",
       "Mhe8xo/+h491cuEegePRv4XX3heVaKU3Iy1UvFNKY1NKj6aUnkgpnbmA4zZOKc1KKe3bviG2HxUf\n",
       "7t9gWXHLmIU70xnohZ9iExwk5qyCP7Luj7i5D1v8k0OG8I0JnbObeKiouLlRbDJ+RFy3mmWB4l3Z\n",
       "0LtEbGyshYNTSmu2ctwFuEnsutYclRX3teLb9Ai5TjXTOegtNuXXwwEq/tq9MZGjxjJuFi98kx03\n",
       "5Y7ywiyVk0Ruf1V8ExsIm4BXygxqYSxsw3ITPFkUxURIKV0lqjImzHfcSWJFu3F7B9geVMoBfyZW\n",
       "3B8Xtz6ZTKPTFz/HakK4HybmSn6dC/uy4ytcuBHf6+STbn4h9gLqqqJmYeI9DM83+/kFbNr8gJTS\n",
       "MCHoY4R4l54Lak5KKQlL1zVFA04W7kxnoJ8QpZGimupR+AsbbsOliW53c8BWzXLfDcwA7IqVtDzC\n",
       "rS5LhBeW826LEF+Es4ooW0lqL23yZTHV/VC5HDDTOVgGV4m87X54dCDpeY4fw+/e54kvsmODC3d/\n",
       "kd//lbBU3UKzXH8jsLCV94ti57WJEWL13ZwNcVUscA3CLimlmUVRfMgjIaV0brMfby+K4vZFDXhR\n",
       "SCmdKDYm95a9uDOdgwFCuJdV8dE4k4Ff5Pu92folvrEul3YC69YbRWv6r3G0+lq4bYbNK8+7t3bQ\n",
       "Auu8K5t8j4mC/pfwTxxcFMX8Oe+m46/EDUVRfMiVrNp13imlPUQx/T6y+1mmc7Cs6F9YWqQIn72T\n",
       "j24WI8zm3Mlx23cew7WumF12EO3A4tV5F0UxCyfiZvEtdnVRFBNSSsemlI7tkFDbgZTShmICyLGy\n",
       "cGc6B4NF0UBf7DuU51/ilC25djoPfYYdG0i4e4vW9MtFaqQlGkG4F0jDdVimlIbjXmHtmo3iM52B\n",
       "5UXjWRcc8BVmncbFvdj0eb66Bj+up5xBK/QSRRF7YlvR4ThOlCc3ckq0cwxjSCn1FrmuX8nCnekc\n",
       "DBX9C7Ox3z2stjGXzGHaTey5Kw+VHF97sa7oiL4Bn1OnFSLtScOsvCslgb8ShjE1m9LJZNqREUK4\n",
       "3x3EweM5YjAnvcMfTuazP+XtkuNbHBolV91edIqV96lYX0x5z2QaneXF3eWUE/n0t/hhT9abyOdG\n",
       "8/M6S5N0E6V8e2InbIM3S42oDmgI8U4pbS9upfZUXyVBmczi0FWU6F77Bx7bmWvm8Obv2X2fKCyo\n",
       "FzYWVTG7YKLIYX9bFu42UffinVIaKtIlnxEfgEymUUnizvL0vlw9kZ6D+MFUfnsUZ/2Wd0uOb1FZ\n",
       "V/yb3cWH+0cyC6Guc94Vz5Lb8IAwxspkGpUxOBNrr8LL/+XVnqz+FGevx9U1fLuZRP3562UHUqc0\n",
       "rJ/350Vd67fLDiST6UA+I4zV1u6KY7ihC3OuZexqtSvcG+BLorHv3HJDaUzqNm2SUtoCpwi72rw7\n",
       "nWlkbl2KY45kmdN5/xn+PIAv16Bo98JpYu9pBn4vPIUeLzOoRqUuxTultDR+KVbeL5YcTibTYWzL\n",
       "DmO5/Di6LI1H+Ns2YbRUi0zHVBypvjZO65K6FG8xIOIfYnc6k2lItmfsl7l8i0p6cxaTL+fksuMS\n",
       "/uBvajmPfXGVY+m01J14p5TGYgfRIpvJNCpb3MMls0Igl4On+NJF5XUWriLSIXsIr/DP4G8lxZJR\n",
       "Z+KdUuqLH4ma7ndKDieT6Si2Xo4rb2f6avR8iP8dxeEb8NsSYtkM54mKkRtxhupNTu+sDBSDcIaJ\n",
       "YRotUlfiLapK/oU/lx1IJtNBbL86V9zG+4OYehWHHcZTp/GPkjYon8c5omokC/aS0x0rCGEebq5I\n",
       "N3/efPBxqw1LdVPnnVLaWvg4jJFNaTKNyU5bcvkfmdOdR87nE1+pTn30UGwthjhkloxlzCvGQ80r\n",
       "zEPMnTY2U8xJeLHyeKHZ86ZHF/XsbVIZCnGZuH3Lwp1pRHbbn0t/QXqf2w7kuHEda/UwBLuJPPYo\n",
       "4dl/nTzjdUF0FdettRXzcNF30sQUc0X4IfzJvCL9moUPfu7T2gt1Id44QYj278oOJJNpb7qw16lc\n",
       "8i26vMnP1uGcDp7m/h3RH3GLGM59lzqbnN5B9LVgYV7e3MbG2XjFXDEeb15hfsli7MutT/e96b8G\n",
       "/ZdnQGLINq0cW/Npk5TSAFHkf4i4QJlMw9CD/S/kuyeQXuArq/HDKuS2VxYi05lW2UmsmpuL8VDz\n",
       "ivQyzY6fJq5R81RG8+eTLKA5cChdDmaZdRkwjAEDGLAU/XsxoCf9uzOgO/27MrArA7rSvwsDusy7\n",
       "cv8g8Ja0sx7E+//E7utp7R9VJlMeQzj8R3x9F2Y/zglrx6CB9qC/WFm/r/MMJentw2Lc/PkK5g7z\n",
       "LYT4tpRjbhLpqU0nPYylN6L/RxiwbEWE+4QID2gS4W4hwAO6hCAP6DLvF0HTm86aw+TZTJ7DlFlM\n",
       "nsXkmUx+n8kzmDKNyVOZ8iqTn2LK1Uy/n4frTrxTSmuKWtJt8UZHxJXJlMHaHPcTzlkz/nEetB33\n",
       "LeEp+2FnkcPeRKRCfoE7lvC8Hc3SKkK5EAZpJsarMWokK98cw1eGiQVeE9PNFeYX8GIXXlyRN7bl\n",
       "7Z2ZtSL9+s0V4f495hPhigAP6MIyKXLdH1AwZw5vzeHN2UyZHSI8ZVZFhKcz5V0mv83k15n8HFPu\n",
       "ZPI4pi3GXVWrxlS1Lt434d+iozKTaQh24owf8ul+vPUn9jicp5bwlEOESP9ddB3/Wdz21yo9sQ+O\n",
       "xtliM69p1dxSSmMoenYXfrif5P0d6PENHp7A06swbRQzVmL2CNIAejcT4aaVcP9Ej/kDmcPUppVw\n",
       "RYQnz2JKZSU8+T0mv8OUN5j8IlPuZ/LVTH2zemWT9SfeKaUx+KkoYepMublMA7MHg37Gv97i1csZ\n",
       "e3773VH2VbuCPUAUHAzBJ/Bxc1fKr2PQUiKvMZyZI5m8Mu+szMwV8Wv+/HFGrs8WPSIl9CHm8O6c\n",
       "EOHJsyqpiSYRfp8p7zF5GlMmhwhPHs/ka3nr6do3tauvMWiVeZRfFTvhWbgzjUDXj3LMdhzxMCec\n",
       "z19uitv7ttA0OX0P4R3SkulTWcLdzdymk/nzzcOWYtgK9NmHb77FPkuz4hB6rCCW06vSczAzesRq\n",
       "HLoXDJrNnNm8OotXXuS3sxj8Og8vw4a92LArA17jB5dx+Y1MubcT6kRNrrxTSjuJuu6t1f43Yyaz\n",
       "INI2fPyWjiGiAAAYpElEQVQIPncIS1/Jzz4VqYKF0UPs9eyJ7fGg2NC8QdtyxO3F0loQ5qUZMYzh\n",
       "yzF4BdJQDGXOSkwfwayhpEH06jV3k1ARgvzau0x+lenP4jWmbsKNU5j0Eq88wKuX8vqCSiV744es\n",
       "PJqRG/HXDv3bl099pU1SSv/A1ZVHJlOX7MpeB/PVAxjYA//l3W1ZrY350k8JA7Zx+KOO6bRsajr5\n",
       "YKU8kBVHMHJ5hg9i8HL0HiqW1iOYNZw5Q+jat9kmXsGcmbxZ8PIsXnmfSTN49V1emcKkV5j0byYt\n",
       "TJQzLVI/aZOU0jbijuo3ZceSySwuvfFl+qzC0k27ZFfx5UXY6Pph5dEWNunNJv/kmTnMXo+bKn/e\n",
       "R2XFvBwrjWK1Iaw0mKHLMmggyzStmit5j6Lf3NZtcyimR974VbxY8NIMJk3ilbd49WVeeZBXf8zr\n",
       "dZA7bjhqbuWdUvqT2DW/ouOjymQ6ht74ATcewQZvM+suJu0WJXzEqnUzkRIZLdrUF5Ue2Gskn/oE\n",
       "axzPzMF0v5rn36T3QJYeTI9KOsPSzX5xDt5h2jTenMmkgue7M3F6iPKkV5j0AJOyKNcE9ZE2SSmt\n",
       "IwYKb6LtmzmZTM3xCdb9GjfcwjXr8PK3uOuaaK3eU4j1yyopkU+xx17s8z12a9rE7Emv9Vl9NKOH\n",
       "sPpAVhzAsLV5ZymW/yL9D2XpPc17+/wW709m6ju8MYNX5vBcV57qwrMvR045i3J9UTfifaXYjMmT\n",
       "4DN1ydosfQLfXZl1LmTMzbwzkLQVI5/lN925/z7OX5VpR3DeWHb5H7q/zMz7mDSQ/oPpPYyuSzU7\n",
       "7zSK13hvNs/24IkTue0lVt6ADVdn1Nr0G8PUadw2IHcjNxK1n/NOKS2DfeUJOZk6Zie22pGdLueU\n",
       "m3nn0+y+PWfuwMq9cTsD/8t3D2CTIc1+b1m6D6X3ZF4czyv3MvFdnnyX8Y8y4RdMbak77/65T7ui\n",
       "+9n07a1j7QgztUHNiDeOEa3wk8oOJNN52Y41NmDFm7lz/HwaeArnbcMWr/Doy9z7H/7yNyZ9hk9O\n",
       "YdsubHktXuKtz3H+QNbcjkNH0a/33NPM+iIHP8AWq7L1MNYfzsiVGfBfzjlq8eeyzsbs83O6sdNQ\n",
       "E2mTSlPOE2K82d1VCSiTaYFBDPkL961F12d5/zlem8TTr/PANDY8i82bjr2bGcfxn5f5HziGHvsy\n",
       "+3L2vYUHJzHzPbF5eTDrrsp2y9H1aC5s6b2H0iWX0mXmo+bTJttV/puFO7OkrIhVrqBPTyZ8jWcn\n",
       "MKvZ6/02YrX1WHcoawxmpUGssBzLLs9Sw+nWZAc3ih6jGPYgvf/B3fdw87ts/h9ev5MffpHrZ3HU\n",
       "WXQ7i41OYszGPDZ/QO/hJ+Hf8dCCAs/CnVkUamXl/TNhbP69qgSTaVS6YERi3KcZ9F2h2q8ydTIv\n",
       "PECX37BG84kerzN7Eu+8weTJvDyFif3ZaVeWvYfH7+erpzERT2/JOhuzzHfDsc/K9N2T3cZw9J85\n",
       "5+IldwbMZOandqtNUkq9hHDvIKZPZDKt0dR0Mqwbw9dmjdVY5SMMH87gESy1MmmU8AltzlQev5Hr\n",
       "j+WR77L8VB66g8dbGjX2Lb7yF266OdIhewg70r3xHBzKmX/gt1fxmzUZOJY1J9SuKVSmvqlp8T5E\n",
       "jDnbvyqBZGqVJESyyT9jeC+Gr86oVRgxguVWpM8oMXBxpLkjtqcz+3XeeIuX3+GZ37HWcwz4JYOm\n",
       "cvcELhnDXW2swNgDx4velhuFl8g/VVIaH2OFS7jvHmbuTI9LOOsMft5+lyGTmYeaznkfLs+m7Az0\n",
       "1MxDo+nRh+GjWGkkQ0bSrUmcVwtv5q5NH9D3mD6VZ95l4hwee57HXuSZO5h4Aa/NJ8xb/YgXb6D3\n",
       "Xos+Ou91fA33aKGRZX9+MIS0Nz2+xnNfCsOoTKbqlLryTin1E6mSDS3GsM5Mh5O00YtjfYa+zPKT\n",
       "WM58Y6iWYtgqDGoS5lWZvSbvr0KXwfRsmuj6HlNm8PwcHp/B01OY+BwTb2TiJTGJu70YglWEDUOb\n",
       "OYjRP+aWpiGD/2HCtRz19Uo6JZPpAGp25b07/iMLd61yqRDgRzGh2X/74STNRPoFev1bLK9fYfZr\n",
       "TJvMlDeZNJzHd42UiPd5ZTZPz2DiNJ4Zz8RnePZXTLy6Y/PGy4rP2x5YC9dYRPHej//ri6d56QFO\n",
       "24872z/MTKZtlC3ee4uRTZlyWcZ8JvqVxxpYVaWOucLt+FlPVtqCd8bw5Ga8uDqDhjCyG72Xi26/\n",
       "pd/m9hv5ziNMe5ulLuf5v1a/iaSLyEn/j/B+/pEYGTZjEc4xYB+23JxBd3DqLlydOxgzZVNa2iSl\n",
       "1F1YTe4gTHoyHUNXLK/lSSdNz/s2O36KGNr6khC4PQby3s7ceTxPrMOQ3qzVndVSTD15/30ee4/x\n",
       "XVmqH7tP45a/8u3FyDd3FJuK3PTifHEM/Da3zuLd37FtZ5zYkimVJas2SSmNxUVCCH5cFMUF871+\n",
       "KM4QOdK3cVxRFA/Nd8z84r0Tvo2xi/zXyTSnaXp2S6I8TAh3U1p5tviifFGzydpNz3vw0sUs+9Fw\n",
       "shv9FtsPDje7ZSq/PHkGD7/L+Dd45GHGf4Enm5pgJrDvczyzc6TCqknT5PTHLaQRZhEZfCo3f4ch\n",
       "t/O17fhBO547k2kLiy/eKaWuomtsB/GP/D4cXBTFhGbHbIZHiqJ4qyL05xZF8dH5zjO/eH9fbIZl\n",
       "B8HW6eLDG4DNH8PNa9X8jrmC3FyYmx6TVCootqLnWay2GqMHsnZv1urJWl1CCM3kmemMf5vxr/DI\n",
       "rYz/Ii/XULqgL3bEXsIb+x5cgn+10/mHHMQff8Hyj3DZupzXTufNZBaFJdqw3ARPFkUxEVJKV4l/\n",
       "MB+Id1EU9zQ7/l4hKgtjG3ylDcc1Mr19WIybP1/B3P9HhWhmakpp3O7DIt3ibMMzGbg3o4ez59KM\n",
       "7hVpj1UTXQumv8+j7zJ+EuOeYfxlPNLBm4dLyla4XNRfj8PJ4o6vvRi6Hb+/kiEvct2mWbgzNUhb\n",
       "xHsYnm/28wsih9gaR4uZe61SsX9dxTyOlg1HU9PJgnLNA5od/565Yvy0aMFuLswvm9ej40MMJH2H\n",
       "lTZi9HKM7svonqzVLb4EzA6D/off4tbXufghxp/N03VozH8/Pqp9ywebGL4O11/HkGncuR2n1NDd\n",
       "RibzAW0R7zbvaKaUtsNR2KKV18+tPF0dz6rvzZ+eoguvuRgPne95z2bHv2quEN/tw2mNyYvy5mPp\n",
       "dQprrMro/ozuw+gekfboU1DM4unpPDyJK1/mkZsYfz6v1okQNU1O31k4Tc7/OXlPx1hWrzic6/7E\n",
       "st14+GCOqsMvtkz9s5m57pXdWzuoLeL9IkY0+3mEEJ55SCmtK25lxxZF0aIQFUVxbuXYi/CXNrx3\n",
       "mQzQ+ibgMAxuduwM824C3mvelMbLFq00bR6+wKDdGT2M0f0iPz26Gysnuszhvfd55D3Gv8S1T/PI\n",
       "xUxoybOjxumOrUUd9o6ipnycuZutHc0q/bn2zyyzLC+dwyE3ZW/sTDncU3kQOe+TWjqoLRuW3cSG\n",
       "5fYi1/pPH96w/AhuxWFFUfyjlfN8sGGZUvo3viGGL5RBdx8MzG41pdGr2fFvaqE6o9nz19sjqKF0\n",
       "+SYjN2DtwXPTHqO7Vr4oZjNpOuOnMf41xv+bR87imQaxEv2BuFsZhz+o7lCOVXtwze302YjpV7D7\n",
       "cfOmCjOZsljiUsFdzC0VvKIoiq+nlI6FoiguSyn9GPuY2yY8syiKTeY7R1EURaq0xL+CtS3BanQh\n",
       "LGNeMZ4/vTFE5KSJPPJLWhfmF3XACmw/+hzHmis3S3t0Z80u9CqYM5MnpzN+KuNf4OEbeOR83mjv\n",
       "OGqIbhaS0+8g1ujCNdeTdqXnn9h3Dx4uIY5MpiVqx1UwpbQDvilalReHrkJ8F1Tb3NwR9C0tl801\n",
       "ifRrOnjlej5DdmL0CpH2GN0r0h4jE2kO097nkXd5eDLjn+CRb/NYCZ2IHUkXbCwmp8/Cl8oN5wPW\n",
       "xlWXMf0YBt/LYZtVvLozmRqhprxN1hP5zNboa+FNJ10rx84Wq/gmMR5vXmF+SZV9U3pjP5bajkEr\n",
       "Mag//dfi+F5sOouXZjD+Tca9yvj7eOR0nn1zETaF64iEjUQOe3eRWrrB4s9obG/Ww6/P5c1PMvIx\n",
       "Ts7CnaknqrryFqL7a1GP/C8tN50s0+zXpmm56aTp+QdNJ2VzGxtvyfe7slyq5Mtn88Y9HPskrzzM\n",
       "lO8sYkVJndMXv8XNQrCfKjccxB3ZCLGa+eUnef6HrPkS5w/P3ZOZ2qRmVt7TzS19OVqIb5MQ3+HD\n",
       "KY0Wm05qjSPotyJrJXo2CfcM/nMxx5zeOXxbWrKOnab2rA9OwPrYcC8e/SHrTOanq2bhztQh1V55\n",
       "HyFsRvcU0+JnVuXNO4DeuIENN+LQfuyV8C539mWnKfxqT865q+M2ZGuBtURKZA/RgXhLueEslKEi\n",
       "LdJrA16+j6Xe5c41+FSDVOtkGpOaWXnfJVbTj1T5fduN41jmTPZbgUN7sMb7PPo8X72A6z7Kslvy\n",
       "l1X4ZdlxdhAfwQHiy7enSIcch/+WGVQbOQO9huNGhrzAMx/npCzcmXql2uK9nqgZryt6409ssj6H\n",
       "Ls3uBaZy/Z2cvif/buqGuTQqW54uL9IOZ2WRy/606jsHLglrj+RjbzH5PmYNYMpn2KvB74wyDU4Z\n",
       "4v14ld9zsTmFAZ/hYytwWHdGvc/4iZx3Htf9tH2NkGqNgaIxaX5urzzqiS4bcvZVvLQ8L/Vi+MUc\n",
       "UvmizWTqlmqL9zoWcfRUtemNP7P5OpHL3rVg1lv87l5O3pcH663nfBEYLvLXewrx3lyNVPIsAbvi\n",
       "5Ot4+iMMKxh6LwefGiWkmUxdUy3fiCbW0sxKtpY4m2Wf57i3uGsLru3JyGc45xDWH8gZuzSucB8m\n",
       "6q//hJFicnojCPde+OEaPDYiRFwircVBh83bxJXJ1CXVXnkPUkOlcwNJf2DL0Ry6FGMLZrzFdXdz\n",
       "XCdqkS7ERKO7ldOe3hHsJ+wcrryT9xPdZ/LMv/hcbsTJNArVFu8+aiBXfC6Dj+HAwRzSnRWn8++n\n",
       "OOssxv2Wd8uOrwNYVjQ/tbSZ2miVMQeJL6PLjuP7A/nbK3znAP4vb1BmGolq13nPEeVmVW8HH0qX\n",
       "69l6TQ7ry44F707ht3fwy31rNJWzhAzALiKHvZ5YiV5WakQdz2FirN73ccFf2eg53jiSZ0qOK5NZ\n",
       "XGrDmEqsaletyhtW+AbLH85BgzmkG8Omc99z/OLT3Nigfs3L4zvYELeJfPatGvPv2pwj8VXxd7+w\n",
       "5FgymfaiZpp0qpKSGEqXGxizOof2YYeCqZO59i/88qDo7Gxk3sDV+F/1N5BhcfmkcCr8Bi4uOZZM\n",
       "pipUW7w7dKjtRQw9kIMHcVA3hr7HPY9x8if5Y4PlO/tiB+EHM/8cx5lqx7mvGpyAs8Uw6x+WHEsm\n",
       "UzXqfuW9Jt1+zfajYpU9Zg6T3+Tqm/j14bXhZNde9BaCvYcYF/ZPPKRjhvDWC5/BZ/EF/KTkWDKZ\n",
       "qlK3K+9LGbFPZZXdlSHvctcjHH80N91b34ONW+IwfF60pI8TPh2dWbThdJwiBhT/v5JjyWSqTl2J\n",
       "9/p0/zk7rcyhvdl6Dm+8ydU38KujmdhOMdYit+KPWm5Z74x8XhhinYarSo4lkymFukibXMFKe3DI\n",
       "QA7swrLvcefDfPJw/vxAHdvKNqM7tsIaWvaWzu3cc/kyjhKr7t+UHEsmUxo1K96b0uMKxlZW2VvO\n",
       "ZtLr/PJ3/LpBJnt3E23oe2FnPInrS42otkmidf8wnCRfq0wnp9rivdB5kv+PVXbhkAEc0IUB73Lr\n",
       "Axy5H399uv79Nppzi0gj3SBqk/PqunWSGFp9AI7HjeWGk8mUT82svO9nzFqc0JuPzuKl1/jp1fz6\n",
       "lMYVtb3UgFVAHdBFfLntI+q5by43nEymNqiJDcveGM6Gs5n6bz6xP7fV+So7iQ7HPfEArmvhmCzc\n",
       "C6crvofdxMzTv5YbTiZTO9TEyvspTnmTJ5bnW1WOp71ZXwj2HiJFNA7/KjWi+qUbLsGOYvbpHaVG\n",
       "k8nUGKXnvB/ngBU4/aFYXdUzG4vb+3E4VB1NDKpBuotuyW1wuLCrzWQyzSg1bXIv24yqrLZ/X//O\n",
       "b/eJzsfMktETPxKVOIfi3nLDyWRqk2pP0vlAvMex9kZcnug2m8l1MFNwNdEUcjtWKDeUhqWXaHP/\n",
       "KA6WhTuTaZVqr7zfJibYbMSOc3irC31n1W535EhRFbInlhZlfZ9RQ9OAGoje+KmYc3qg2OjNZDKt\n",
       "UErO+02KS/n5lznpDX7SpfpxtJXdxRSaM3G/EoZIdBL6Cn+S1UUtd2cZQZfJLDal5bxP4Mg5vHsU\n",
       "51c5hpbopeVhBdkbuuNZCr/AKthfY041ymTanVJW3vvRZzBHvMpPxpU3MGAFsbLesxLXwSXF0ZlZ\n",
       "Gr/CcDE0OFfoZDJtpJSc94UhlL0u4soqv383fFzksUeJbr2myemZ6tJfOAIOFsLdSN7rmUyHU23x\n",
       "nr4m3YZy7BSuuqD6FqezsJJIh9ypMRwJ65GBQrgHCOGeWGo0mUwdUvWNwt+ye1dWuC5qeTuKAWJz\n",
       "saWBBV/qwPfNLJxBuEZsUu6rMRwiM5mqU9U6795YhePf4cZjeLadT7+MKDH7Je7BZu18/sySMwS/\n",
       "FRvE+8jCncksNlUV79vYugej/8al7XjatfEz0dCxo5icvgH+1I7vkVlyhgrhTmLF3ahukZlMVUhF\n",
       "UZ3S5ZRSMY27EqlPrJDbi5HCEKrJHztTewzHtZgh6rhfLTecTKZu6IMniqJI879Q1Zx3H7a6L/wq\n",
       "FpXeIg1yawuvPaP+fVEamY+IcWVTxZf2G+WGk8k0BlUV7/eZsE14g7SFnthO1GGPEZPT71FeXXhm\n",
       "0RkpVtxv4CBMLjecTKZxWGjOO6U0NqX0aErpiZTSma0c8/3K6w+mlDZo7VxP84M2Ku8ZQqyPwt+F\n",
       "w9zBsnDXE6NEjvtVseLOwp3JtCMLFO+UUldhiD8Wa+HglNKa8x2zK0YVRbGqGFPV6mbkvuF13RZu\n",
       "Fl7OB4jW6WrXg5dBI1XHrC6E+wUh3C2VbC4KjXRtOoJ8fRZMQ16fha28N8GTRVFMLIpipmis2Gu+\n",
       "Y/YU1R6KorgX/VNKQ1o62YRokiHGW22NnVp53wfx2sLDbyg2LzuAdmK0EO6ncYj2GffWKNemo8jX\n",
       "Z8E05PVZmHgPM28t7guVP1vYMcNbOd8WuEDYfZ6Jfm2ONFMPrCMacCaIjekPTU7KZDLtw8I2LNta\n",
       "Rzh/GUtrv/cl/FG0RL9Q+bM+bXyPRqe7+r4W6wmvmofwqcqftdffp96vTUeTr8+Cqefr86ESwQ9e\n",
       "WFCdd0rpozi3KIqxlZ8/hzlFUVzQ7Jgf4vaiKK6q/PwotimKYtJ858pe2JlMJrMYLE6d9/1YNaW0\n",
       "kuiIO9CHrVPH4URcVRH7KfMLd2tvnslkMpnFY4HiXRTFrJTSiaL6oyuuKIpiQkrp2MrrlxVF8ceU\n",
       "0q4ppSdFh+ORHR51JpPJdHKq1h6fyWQymfaj3Y2p2rOpp9FY2LVJKa2RUronpTQ9pXRaGTGWSRuu\n",
       "z6GVz8xDKaW7U0rrlhFnWbTh+uxVuT7/SSn9K6U0pow4y6It2lM5buOU0qyU0r7VjK/dKYqi3R4i\n",
       "tfKkGHjQXZQErjnfMbvij5Xnm+If7RlDrT7aeG0GYyN8FaeVHXMNXp/NsEzl+djO8tlZhOvTt9nz\n",
       "dUSPRumx18r1aXbcrbgR+5Ud95I82nvl3a5NPQ3GQq9NURSvFUVxv8454act1+eeoijeqvx4r9b7\n",
       "CRqRtlyf5q6aS+H1KsZXNm3RHjhJGKXVfRNge4t3ezf1NBJtuTadmUW9PkeLnoHOQpuuT0pp75TS\n",
       "BOFnf3KVYqsFFnp9UkrDhKA3WXjU9YZfe4t3ezf1NBKd4e+4JLT5+qSUthOmZa3mNRuQNl2foiiu\n",
       "L4piTeyBn3dsSDVFW67PRTiriPxJsoAGmHqgvS1hX8SIZj+PMLeTsrVjhlf+rNFpy7XpzLTp+lQ2\n",
       "KS/H2KIoOpNT4SJ9foqiuCul1C2ltGxRFJ3BQ70t12dD0Y9CzFLdJaU0syiKthrm1RTtvfL+oKkn\n",
       "pdRDNPXMf2HG4XA+6OBssamnAWnLtWmirlcEi8lCr09K6SO4DocVRfFkCTGWSVuuzyqpokwppf+B\n",
       "TiLctOH6FEWxclEUI4uiGCny3sfVq3DTzivvIjf1tEpbrk1KaXnch6UxJ6X0aaxVFEXDGzy15frg\n",
       "ixiASysaNbMoik3KirmatPH67IfDU0ozhSnYQaUFXGXaeH0aitykk8lkMnVIVafHZzKZTKZ9yOKd\n",
       "yWQydUgW70wmk6lDsnhnMplMHZLFO5PJZOqQLN6ZTCZTh2TxzmQymToki3cmk8nUIf8fDxOyH3yU\n",
       "HfgAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106a419e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ramsey(1.2, 0.35, 0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}