{ "cells": [ { "cell_type": "markdown", "source": [ "# Deterministic Production Adjustment Model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demdoc05.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## About\n", "\n", "Profit maximizing firm must decide how rapidly to adjust production.\n", "\n", "* State\n", " - q current production rate\n", "* Control\n", " - x production adjustment rate\n", "* Parameters\n", " - 𝛼 production cost constant\n", " - β production cost elasticity\n", " - γ adjustment cost parameters\n", " - p price\n", " - 𝜌 continuous discount rate\n", "\n", "## Preliminary tasks\n", "\n", "### Import relevant packages" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "code", "execution_count": 1, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, OCmodel, NLP" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Model parameters" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 2, "outputs": [], "source": [ "𝛼 = 1.0 # production cost constant\n", "β = 1.5 # production cost elasticity\n", "γ = 4.0 # adjustment cost parameters\n", "p = 1.0 # price\n", "𝜌 = 0.1 # continuous discount rate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Approximation structure" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 3, "outputs": [], "source": [ "n = 10 # number of basis functions\n", "qmin = 0.2 # minimum state\n", "qmax = 0.7 # maximum state\n", "basis = BasisChebyshev(n, qmin, qmax, labels=['x']) # basis functions" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Steady-state" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 4, "outputs": [ { "data": { "text/plain": "Production 0.444444\nProduction adjustment rate 0.000000\ndtype: float64" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qstar = (p/(𝛼*β)) ** (1/(β-1))\n", "xstar = 0\n", "vstar = (p * qstar - 𝛼 * qstar**β)/𝜌\n", "\n", "steadystate = pd.Series([qstar, xstar],\n", " index=['Production', 'Production adjustment rate'])\n", "\n", "steadystate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Solve HJB equation by collocation\n" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 5, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving optimal control model\n", "iter change time \n", "------------------------------\n", " 0 1.3e+00 0.0040\n", " 1 8.8e-02 0.0040\n", " 2 4.1e-02 0.0050\n", " 3 1.6e-02 0.0050\n", " 4 3.4e-03 0.0060\n", " 5 1.9e-04 0.0060\n", " 6 6.2e-07 0.0070\n", " 7 1.2e-11 0.0080\n", "Elapsed Time = 0.01 Seconds\n" ] } ], "source": [ "def control(q, Vq, 𝛼, β, γ, p, 𝜌):\n", " return Vq / γ\n", "\n", "def reward(q, x, 𝛼, β, γ, p, 𝜌):\n", " k = 𝛼 * q ** β\n", " a = 0.5 * γ * x**2\n", " return p*q - k - a\n", "\n", "def transition(q, x, 𝛼, β, γ, p, 𝜌):\n", " return x\n", "\n", "model = OCmodel(basis, control, reward, transition, rho=𝜌, params=[𝛼, β, γ, p, 𝜌])\n", "data = model.solve()" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Plots\n", "\n", "### Optimal policy" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 6, "outputs": [ { "data": { "text/plain": "
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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['control'].plot(ax=ax)\n", "ax.set(title='Optimal Adjustment Policy',\n", " xlabel='Production Rate',\n", " ylabel='Adjustment Rate',\n", " xlim=[qmin, qmax])\n", "\n", "lb = ax.get_ylim()[0]\n", "ax.hlines(xstar, 0, qstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(qstar, lb, xstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$x^*$', (qmin, xstar))\n", "ax.annotate('$q^*$', (qstar, lb))\n", "ax.plot(qstar, xstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Value function" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 7, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['value'].plot(ax=ax)\n", "ax.set(title='Value Function',\n", " xlabel='Production Rate',\n", " ylabel='Value of the Firm',\n", " xlim=[qmin, qmax])\n", "\n", "lb = ax.get_ylim()[0]\n", "ax.vlines(qstar, lb , vstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$s^*$', (qstar, lb))\n", "ax.plot(qstar, vstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Shadow price" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 8, "outputs": [ { "data": { "text/plain": "
", "image/png": 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0adDV1cXWrVtx+vRpWbtUKsUXX3wh28yqLvACQKdOndCpUyeEhIQgPz9f7gNA7969AdSu8qOlpYV+/fo163W3lNGjR6NDhw44cOCA3EZiFRUVWLVqFYDaTcwAYM6cORCJRPjss8/kVniRSCRYtWoVYmJiUFNT0yKj0l26dIGWlhZiY2Pl9h5ITk7GunXrnvr8T/I+ALXTtCorKxtc5w+aM2cOgNpNrnJycmTtWVlZWLFiBQBg5syZT10/EbVdnK5DRK3agAED8O6772L16tX45JNPsG7dOnh7e8PY2Bi5ubmIjIxEZWUlhg4dildeeaXZzxMcHIyLFy/iww8/xOHDh2FpaYm7d+8iISEBFhYWEIlEKCoqQlVVFbS1tWFpaYlVq1bhjTfewIIFC9CrVy8YGBjg8uXLsLe3l40Q17GxscF///tfLF++HP/617/g7e0NGxsbxMbG4v79+7C2tsZXX33VYM573So7gPwof8+ePSEWiyGRSBAQECA3Nag1MDIywqeffoply5Zh8eLF8PX1hbm5OSIjI5GVlYX+/fvLlpz08fHBq6++ii+++AIzZsyAh4cHLC0tER0djfT0dFhYWODTTz9tkTr19fUxY8YMbNmyBfPmzZN9Q3PlyhX4+Pg89W67T/I+ALUf7Oo2cHNycsJnn33W6HnnzZuHa9eu4dSpUxg2bJhsZaIrV66grKwMI0eOxLx5856qdiJq2ziST0St3uzZs3H48GHMmzcP9vb2iImJwcmTJ3Hnzh0EBATgm2++wffffw8tLa1mP8fgwYPx448/wtfXF4mJibh06RKA2jB16NAhPPPMM5BIJHJTSkaPHo3ffvsNAQEBspHgwMBAbNy4UbZiSX1jxozBzp07MXz4cNy/fx+nT5+GhoYGnn/+eezfv7/RJSvrlvXU19eHu7u7rN3Q0FC2fKIidrltCYMHD8auXbswYsQI3LlzB2fPnoWenh6WLVuGH374Qe4DzaJFi7BhwwYEBATg7t27+Ouvv6Crq4vg4GDs378fDg4OLVbnypUr8cYbb8De3h6XL19GYmIi5s+fj19++aXB1K3meJL3YdWqVXB1dcXNmzdx4cIFFBYWNnpOsViMtWvX4j//+Q+6du2Ky5cvIywsDD169MCnn36Kb775psk3SRORehIJXDOLiIiIiEit8GM+EREREZGaYcgnIiIiIlIzDPlERERERGqGIZ+IiIiISM0w5BMRERERqRmuk/8YUqkUNTVcgIiIiIiIWo6WVsOll58GQ/5j1NQIKCgoU3UZRERERKTGLCyMFHo+TtchIiIiIlIzDPlERERERGqGIZ+IiIiISM0w5BMRERERqRmGfCIiIiIiNcOQT0RERESkZhjyiYiIiIjUDEM+EREREZGaYcgnIiIiIlIzDPlERERERGqGIZ+IiIiISM0w5D9GVkklckqrVF0GEREREVGTMeQ/Rm5pFSb8fAWfnryF9KIKVZdDRERERPRYmqouoC2oqhGwJzId+6MyMKqHJZ7r7YDOZvqqLouIiIiIqFEiQRAEVRfRmhWWVWHJ5jD8fTdf1iYCMNTZHPP6OMLF0lB1xRERERGRWrCwMFLo+RjyH6O6ugYFBWWIyyzGxivJOHMrR66/f1czzOvtAG87ExVVSERERERtHUO+ktWF/DpJuaXYdCUZx+OzUFPvnfOzN8GCPo7o3akDRCKRCiolIiIioraKIV/JHgz5dVIKyrE1LAWHojNQXS/t97AyxPw+jhjUrSM0GPaJiIiIqAkY8pXsYSG/TnZJJbaFpWLfjTSUV0tl7V066mNebwcMd7GAppiLGBERERHRwzHkK9njQn6dgvJq/B6eit8j0lBcKZG12xrrYG4vB4zzsIaOJsM+ERERETXEkK9kTQ35dUqrJNgXmY5t11KRW28TLTN9Lcz2t8ckbxsY6nDlUiIiIiL6B0O+kj1pyK9TKZHiSEwGNocmI62oUtZupKOJab62mOFrhw76WooslYiIiIjaKIZ8JWtuyK8jkQo4Hp+FTaHJuJP7z3l0NTUQ5GWD2f52sDbWVUSpRERERNRGMeQr2dOG/DpSQcBft3OxKTQZMRnFsnZNDRFGu1kiuJcDOnEXXSIiIqJ2iSFfyRQV8usIgoCr9wuwKTQZV+8XyNplu+j2doSLFXfRJSIiImpPGPKVTNEhv76Y9CJsCk3G2du5cu19O5tiXm8H+NmbcGMtIiIionaAIV/JWjLk10nMKcXmq8k4Fie/i66njTHm9XFA/65m3FiLiIiISI0x5CuZMkJ+nbTCCtkuupWSfzbWcjLXR3AvBwx3tYSmBsM+ERERkbphyFcyZYb8OrmlVdgZnord19NQWlUja7c11sGcXg4Y524FXS2xUmsiIiIiopbDkK9kqgj5dUoqJdhzPQ07wlORV1YtazfT18IMPztM8baFkS431iIiIiJq6xjylUyVIb9ORXUNjsRkYktYCtIKK2TtBtpiTPa2xUx/O5gbaKuwQiIiIiJ6Ggz5StYaQn4diVTAyYRs/BaajNs5pbJ2bbEIY92tMaenPRxM9VRYIRERERE1B0O+krWmkF9HEARcupOPTaH3cT21SNauIQKGOlvguV4OXGufiIiIqA1hyFey1hjy67ueUojfribjQlKeXDvX2iciIiJqOxjylay1h/w6t7Nr19o/Hi+/1r67tRGe6+2AQd06cq19IiIiolaKIV/J2krIr5NWWIFtYSk4+MBa+51M9RDcywGj3CyhJdZQYYVERERE9KB2G/KTk5Px6aefIjQ0FAAwePBgrFixAmZmZk0+R3x8PKZMmYLFixdj2bJlTTqmrYX8OvllVfg9Ig27r6ehqEIia7c01MZMf3tM9LKGgTaX3yQiIiJqDdplyM/Pz8fkyZNRVVWF4OBg1NTUYMOGDbCzs8Pu3buhrf345SMlEgmmTp2K2NhYLF26VO1Dfp3SKgkO3MjA9mspyCqpkrUb6Whiqo8NpvvZwUyfy28SERERqZKiQ36bGMrdtGkTMjIycPjwYTg5OQEAvL29MX/+fBw4cADTpk177DnWr1+PW7dutXSprY6BtiZm97THNF9b/BGXhS1Xk3E3rxzFlRL8eiUZ266lYqy7Feb0tId9By6/SURERKQO2sTk7JCQEPTu3VsW8AEgICAAXbp0QUhIyGOPT0hIwA8//IAXX3yxJcts1bTEGhjvYY3f5/XEZ+Pd4GFT+2mxUiLF3sh0TP71Kt46EoeEzBIVV0pERERET6vVh/zCwkIkJyfD3d29QZ+7uzuio6MfebxEIsHKlSsREBCA8ePHt1SZbYaGSITB3c3x60wf/DjNCwFdTAEAUgE4kZCNOVvDsWxPFELv5aMNzOQiIiIioka0+uk6mZmZAAArK6sGfRYWFigpKUFxcTGMjBqfx/Tzzz/j3r17+P777yGRSBp9THskEong79AB/g4dcDOrBJuvJuNkQjZqBODyvXxcvpePHlaGCO7lgCHdzSHW4PKbRERERG1Fqx/JLy0tBQDo6TWcL66jowMAKCtr/MbYW7du4bvvvsObb74Ja2vrliuyjXO2NMRHY3pg38LemOZjCx3N2ssiLrMEK4/EYerGq9gXmSa3JCcRERERtV6tPuRLpY8PlhoaDV9GTU0NVq5cCX9//ybdmEuArYku3hjaDYdf6I0X+jnCRLf2i57kggqsPnkb43++go1X7qOoolrFlRIRERHRo7T6kG9gYAAAqKysbNBX11b3mPo2bNiA+Ph4vPbaa8jLy0NeXh6KiooAAOXl5cjLy2vSB4j2yFRfG4sCOuPwoj54bYgTrI1qvzHJK6vG9xfuYtxPofjqbCIyixv+PyEiIiIi1Wv1c/JtbW0BANnZ2Q36srKyYGxsDH19/QZ958+fR3V1NaZOndqgb8OGDdiwYQNOnToFe3t7xRetJvS0xJjhZ4cp3jY4cTMbW66m4FZ2Kcqqa7D9Wip+j0jDyB6WmNvTHk7mDT9oEREREZFqtPqQb2xsDHt7e8TExDToi42NhYeHR6PHvfnmm7KR+zo5OTl44403MGHCBAQFBcHCwqJFalY3mmINjOphhZGulvj7bj62XE1GWHIhaqQCQmIyERKTif5dzRDcywE+dsYQiXiTLhEREZEqtfqQDwDDhw/H5s2bkZiYKFsr/9KlS7hz5w4WLlzY6DGNhf+UlBQAgIODAwICAlquYDUlEokQ0MUMAV3MEJNehC1hKTh9MwcCgAtJebiQlAdPGyPM7eWAgU4duSIPERERkYqIhDawGHpeXh7Gjh0LsViMBQsWoLKyEr/88gscHR2xc+dOaGtrIzk5GeHh4fDz84ODg0Oj50lJScHQoUOxdOlSLFu2rEnPXV1dg4KCxlfvIeB+fjm2haXgSEwGqmr+uZQcTfUwp6c9RrtZyVbrISIiIqLGWVg0vhx8c7WJ9GVmZoatW7fC1dUV3377LX777Tc8++yz+OWXX6CtrQ0AuHr1KpYvX46rV6+quNr2xdFUDyuHdcehF/pgQR8HGOnUfjl0P78c/z1xiyvyEBEREalAmxjJVyWO5D+Z0ioJDkZlYFtYCrJKqmTt+lpiBHlZY6afHayNdVVYIREREVHro+iRfIb8x2DIbx5JjRTHE2pX5LmdUyprF2uIMMLVAnN7OqCbBVfkISIiIgIY8pWOIf/pCIIgtyJPff06myK4lwP8HUy4Ig8RERG1awz5SsaQrzixGcXYcjUFp29lQ1rvquthZYg5Pe0R6GwBTa7IQ0RERO0QQ76SMeQrXkpBObZfS8Wh6AxUSv7ZddjWWAez/O0x3tMaelpiFVZIREREpFwM+UrGkN9yCsqqsft6GnZdT0NB+T+r75joamKyjy2m+9rCTF9bhRUSERERKQdDvpIx5Le8iuoaHInJxLZrKUgpqJC1a4tFGONuhdn+9uhkpq/CComIiIhaFkO+kjHkK0+NVMC52znYfDUFMRnFsnYRgEHdOmJOT3t425morkAiIiKiFsKQr2QM+conCAIiUgux5WoKLiTlyfV52hhjbi97DHTqCDFv0iUiIiI1wZCvZAz5qpWUW4rtYak4GpeJ6pp/LlVHUz3M9rfDaDcr6PImXSIiImrjGPKVjCG/dcgpqcTvEWnYG5mO4kqJrL2Dnham+dhiqo8tOuhrqbBCIiIiouZjyFcyhvzWpbRKgkPRmdhxLQXpRZWydh1NDYxzt8Isf3s4mOqpsEIiIiKiJ8eQr2QM+a2TRCrg9M1sbLmagvisElm7CMDg7uaY09MeXrbGqiuQiIiI6Akw5CsZQ37rJggCriUXYktYMi7dyZfr87I1xtye9hjAm3SJiIiolWPIVzKG/Lbjdk4ptoel4I+4LEik8jfpzvSzw1h33qRLRERErRNDvpIx5Lc92SWV2PWQm3SneNtgKnfSJSIiolaGIV/JGPLbrrKqGhyKzsCOaylIq3eTbt1OurP87dGZO+kSERFRK8CQr2QM+W1f3U26W8NSEJdZItc3oKsZ5vSyh6+dCUQiztsnIiIi1WDIVzKGfPVRt5Pu1qspOP/ATrpu1kaY7W+HQGcLaPImXSIiIlIyhnwlY8hXT3dzy7DtWgqOxmaiqt5OujbGOpjhZ4cJntYw0NZUYYVERETUnjDkKxlDvnrLLa3C7utp2HM9DYUV/9yka6gjxiQvG0z3tYOlkY4KKyQiIqL2gCFfyRjy24eK6hqExGZi+7VU3M8vl7WLNUQY4WqB2f72cLY0VGGFREREpM4Y8pWMIb99kQoCzifmYltYCiJSi+T6ejl2wOye9gjobMqbdImIiEihGPKVjCG//YpJL8LWsFScvpWNentroUtHfcz2t8PIHlbQ0dRQXYFERESkNhjylYwhn9IKK7AzPBUHozJQVl0jazfT18JUH1tM8bZFB30tFVZIREREbR1DvpIx5FOd4goJDkSlY2d4KrJKqmTtOpoaGONmhZn+dtxci4iIiJqFIV/JGPLpQdU1UpxIyMb2a6lIyGq4udbsnvbws+fmWkRERNR0DPlKxpBPDyMIAq4lF2LbtRRceGBzrR5Whpjlb49nnc2hKea8fSIiIno0hnwlY8inpribW4bt4Sk4GpuFSolU1m5pqI0ZfnYI8rSBkS431yIiIqLGMeQrGUM+PYn8sirsuZ6OPZFpyCurlrXra4kx3tMaM/xsYWeip8IKiYiIqDViyFcyhnxqjkqJFH/GZWLbtVTcyf3n+tEQAUO6m2OWvz28bI1VWCERERG1Jgz5SsaQT09DEAT8fTcf26+l4Mq9Ark+TxsjzPK3x+Du5tDU4E26RERE7RlDvpIx5JOi3MouwfZrqfgzLguSertr2RjrYLqvHSZ4WsNQh/P2iYiI2iOGfCVjyCdFyympxO7IdOy9nobCComs3UBbjAme1pjuawdbE10VVkhERETKxpCvZAz51FIqqmsQEpuJ7ddScT+/XNauIQIC/zdv35Pz9omIiNoFhnwlY8inliYVBFxIysOOaykISy6U6/O0McbsnnYY1I3z9omIiNQZQ76SMeSTMiVklWDHtRQci8+Wm7dva6yD6X52GO/BeftERETqiCFfyRjySRWySyqx+3oa9kWmc94+ERFRO8CQr2QM+aRKFdU1OBKTiR3hDeftD+lujpl+dvCyNYZIxKk8REREbRlDvpIx5FNrIBUEXEzKw/bwVITdL5Drc7c2wix/OwR2N4emWEM1BRIREdFTYchXMoZ8am1uZpVge3gqjj2w3r6VkQ6m+9oiyNMGRrqct09ERNSWMOQrGUM+tVY5pVXYcz0NeyPTUVBeLWvX09LAOHdrzPCzg4OpngorJCIioqZiyFcyhnxq7Sqqa/BHXBZ2hKfiTu4/16oIwACnjpjlbwc/exPO2yciImrFGPKVjCGf2gpBEHD5Xj62X0vF5bv5cn3OFgaY5W+PYS4W0NbkvH0iIqLWpt2G/OTkZHz66acIDQ0FAAwePBgrVqyAmZnZI487f/48fvjhB8TExEBDQwPe3t54+eWX4ePj06TnZcintigptxQ7rqXij7gsVEqksvaOBtqY4m2Dyd42MNXXVmGFREREVF+7DPn5+fmYPHkyqqqqEBwcjJqaGmzYsAF2dnbYvXs3tLUbDyuhoaEIDg5G9+7dMXnyZEgkEmzfvh1ZWVnYvn07vLy8HvvcDPnUluWXVWHfjXTsvp6O3NIqWbuOpgZG9rDEDD87dDM3UGGFREREBLTTkP/VV1/h559/xuHDh+Hk5AQAuHTpEubPn49Vq1Zh2rRpjR4XFBSEwsJCHD16FHp6tTcg5uTkYPTo0XB3d8fGjRsf+9wM+aQOqiRSnEjIxvZrKbiZXSrX16dTB8z0s0e/LqbQ4Lx9IiIilVB0yG8Tk3NDQkLQu3dvWcAHgICAAHTp0gUhISGNHlNYWIj4+HiMHDlSFvABwNzcHL169UJERESL103UWmhramCMuxW2zvXDj9O8MMipI+ri/JV7BXh5fzSmbQzDnutpKK+uUWmtRERE9PRa/WLahYWFSE5OxogRIxr0ubu74+zZs40eZ2hoiD///FMu4NfJz8+HWCxWdKlErZ5IJIK/Qwf4O3RASkE5doan4nB0Jsqqa3AvvxyfnrqNHy7eRZCnDab62MDaWFfVJRMREVEztPqR/MzMTACAlZVVgz4LCwuUlJSguLi4QZ9YLEbnzp0bHBcfH4/w8HD4+vq2TMFEbYR9Bz28HtgNIYv74OVBXWFjrAMAKKqQYPPVZAT9Eoq3j8QhOr1IxZUSERHRk2r1I/mlpbXzhxsbkdfRqQ0lZWVlMDJ6/Dym0tJSvPnmmwCARYsWKbBKorbLUEcTs3vaY7qfHc7dzsHO8FRcTy1CjQAcT8jG8YRseNoYYYafHQKdLaCpwXn7RERErV2rD/lSqfSxj9HQePwXEuXl5fjXv/6F+Ph4LF68GL1791ZEeURqQ1NDhKHOFhjqbIHYjGLsCE/FiYRs1EgFRKUXIyokHlZ/3cE0H1tM8LSGiZ6WqksmIiKih2j103UMDGqX96usrGzQV9dW95iHKSoqwoIFC3DlyhVMnjwZr7zyiuILJVIjbtZGWDXaFYdf6I0FfRxgols7HpBZXIm15+9g7E9X8MnJW7iby5WniIiIWqNWP5Jva2sLAMjOzm7Ql5WVBWNjY+jr6z/0+NzcXCxcuBBxcXGYPn06PvjgA4i4TCBRk1gY6uBf/btgfh9H/BGXhZ3hqUjKLUOFRIq9kenYG5mOfp1NMdPfDn07mfLfFhERUSvR6kO+sbEx7O3tERMT06AvNjYWHh4eDz22pKREFvDnzZuHlStXtmSpRGpLV0uMiV42CPK0Ruj9AuwMT8WFpDwAwN938/H33Xx0MdPHDD9bjHazgq4WV68iIiJSpVY/XQcAhg8fjr///huJiYmytkuXLuHOnTsYPXr0Q4/78MMPERcXh+DgYAZ8IgUQiUTo08kUX030wJ75PTHVxxZ6WrU/Ru7klWH1ydsY89MVrP3rDjKKKlRcLRERUfvVJna8zcvLw9ixYyEWi7FgwQJUVlbil19+gaOjI3bu3AltbW0kJycjPDwcfn5+cHBwQGJiIkaPHg0jIyO89dZbja6LP2HChMc+N3e8JXq04goJDkSlY/f1NKQX/XPvjFgEDOlugZn+dvC0MeJUHiIiokdQ9I63Txzy8/LycOnSJaSlpWH06NHQ19dHfn6+3G60LSEpKQmrV69GWFgYdHV1MWjQICxfvhxmZmYAgH379mHlypVYvXo1Jk2ahB07duA///nPI8+ZkJDw2OdlyCdqGolUwF//W4IzIlV+bX1369olOIc6m0NL3Ca+QCQiIlIqlYb8X3/9Fd988w0qKyshEonw66+/orS0FMuWLcOMGTPw3nvvqd1oHUM+0ZOLzyzGzvBUHIvPhkT6z48YcwNtTPWxxUQva5jqa6uwQiIiotZF0SG/yUNqhw8fxpo1azBs2DB88803qPts4O7ujmHDhmHnzp3YsmWLQosjorbJ1coI/xnlisOL+uCFfo4w069dUz+ntAo/XLyLsT9dwapjCbiVXaLiSomIiNRTk0fyJ06cCDMzM2zYsAH5+fno168fNm7ciH79+gEAlixZgtTUVBw+fLhFC1Y2juQTPb1KiRTH42uX4LyZXSrX5+9ggpl+dujftSPE3E2XiIjaKZWN5CcmJiIwMPCh/UOGDEFycrJCiiIi9aKjqYFxHtbYOtcPP07zwuBuHVEX568lF+L1g7GY9OtVbL+WgpJKiUprJSIiUgdNXiffwMAAxcXFD+1PS0t75KZUREQikQj+Dh3g79ABqYXl2BWRhkPRGSiprEFaYQW+OpuE9RfvYay7Fab52qKTGX+mEBERNUeTR/IHDBiA7du3Izc3t0FffHw8tm3bhoCAAIUWR0Tqy85ED68MdkLIor54I7AbHE31AABl1TXYdT0NUzaG4f/2ReHvu3loAyv9EhERtSpNnpOfmZmJKVOmoLq6Gr169cLJkycxYsQISCQSnD17FoaGhti9ezccHBxaumal4px8IuWQCgL+vpuPneGpuHw3X66vs5kepvvaYYy7FfS4my4REakhlS6hmZWVhS+//BKnTp2STd3R09PDwIED8frrr6tdwAcY8olU4U5uGX6PSEVITCYqJFJZu5GOJsZ7WGOary1sTXRVWCEREZFiqXwzLAAQBAH5+fmoqalBhw4doKWlpdCiWhOGfCLVKaqoxsGojAa76WqIgIFOHTHDzw5+9iZqtz8HERG1PyoN+adPn8aPP/6Ib7/9FtbW1gCAd999FzExMVi+fDn69u2r0OJaA4Z8ItWrkQr4KzEXO8NTEZ5SKNfX3cIA031tMcLVErqcykNERG2UypbQPHnyJF566SUUFBSgsvKfETV/f39UVVVh4cKFCA0NVWhxREQAINYQYUh3c6yf7o1tc/0w3sMK2uLa0ftb2aX46PgtjP3pCr6/cAeZxZWPORsREZH6a/JI/pQpU6Cnp4cNGzZAW1t+O3qJRILg4GCIRCJs27atRQpVFY7kE7VOBWXV2B+Vjj3X05BVUiVrF4uAQGcLTPe1hZetMafyEBFRm6DSzbDGjh3bIOADgKamJsaOHYv4+HiFFkdE9DAd9LUwv48jDj7fGx+PcYWnjTEAoEYATiRk4/mdkXhuWwRCYjJRVe/mXSIiovbgiTbDSklJeWh/VlZWox8AiIhakqZYA8NdLTHc1RKxGcX4PSIVx+OzIZEKiMsswX/+TMC3fyVhopcNJnvbwMJQR9UlExERtbgmj+QPHDgQW7duxfXr1xv0xcbGYuvWrRgwYIAiayMieiJu1kb4YJQrDi/qg0UBndDRoHbgIa+sGhsu38e4n0PxTkgcotOLVFwpERFRy2rynPysrCxMnToVWVlZcHd3R6dOnaChoYH79+8jKioK5ubm2L17N6ysrFq6ZqXinHyitqu6RoqTN7OxMzwNsRnFcn1u1kaY7muLZ50toK3Z5PEOIiKiFqHSJTQLCwvx008/4dy5c0hNTUVNTQ1sbGwwaNAgLF68GB07dlRoca0BQz6ReohOL8LO8FScvJmDGuk/P/bM9LUw2dsGk7xsYM6pPEREpCKtYjOs9oQhn0i9ZJdUYl9kOvbdSEdeWbWsXVNDhGddalfl8fjfTbxERETKwpCvZAz5ROqpSlI3lScVcZklcn3u1kaY7lc7lUdLzKk8RETU8pQW8nv06IE1a9Zg3LhxAABXV9fHrjctEokQGxur0AJVjSGfSL0JgoCo9GL8Hp6KU7c4lYeIiFRD0SH/oUtoBgUFwdHRUe7v3FSGiNSNSCSCl60xvGyN8XJJJfZGpmNfZDryy6uRV1aNn/++j41XkjHU2Rwz/Ow4lYeIiNqEJk/XuXXrFrp169bugj5H8onan0qJFCcTsvF7RONTeaZxVR4iIlIwlc3Jf+aZZzBx4kS8/vrrCi2gtWPIJ2q/HjeVZ5KXDSZxgy0iIlIApU3XeVBZWRns7e0V+uRERK3Zg1N56q/Kk1dWjV8u38fG0GQM7W6Oab628LI1bnffdhIRUevU5JH8r7/+GkePHsV///tf9OzZs6XrajU4kk9E9dWtyvN7RMMNtlwtDTHN1xbDXS2hw6k8RET0BFQ2Xef555/HtWvXUFFRAV1dXXTo0AEaGvK/xEQiEU6ePKnQAlWNIZ+IHiY6vQi/R6ThZEI2JPWm8nTQ08JEL2tM9raFlRGn8hAR0eOpLOTPnTu3SSfcsmXLUxXU2jDkE9Hj5JRWYX9kOvbeSEduaZWsXSwCBnc3x1QfW/jZm3AqDxERPRQ3w1IyhnwiaqrqGilO38zB7xFpiEovkuvrbmGAqT62GNXDErpaYhVVSERErZXSQ35WVhZu3LgBiUQCd3d3ODg4KLSA1o4hn4iaIzajGLuup+F4fBaqa/75MWusq4nxHtaY4mMDOxM9FVZIREStidJCviAI+Pjjj7Fjxw5IpVJZ+7Bhw7B69WoYGBgotJDWiiGfiJ5GflkVDkRlYM/1NGSV/DOVRwRggFNHTPOxRe9OHTiVh4ionVNayN+0aRM++eQT+Pj4YOTIkRCJRPj7779x9uxZjB8/HmvWrFFoIa0VQz4RKYJEKuDc7dqpPBEphXJ9nc30MNXHDmPcLWGg3eSVjYmISI0oLeQHBQXB0tIS69evlxthWrVqFX7//XdcvXoVenrq/1UzQz4RKdqt7BLsikjDH3FZqJT8802pgbYYY92tMMXHFp3N9FVYIRERKZuiQ/5DF3K+d+8ehg4d2uAr5EmTJkEikSAxMVGhhRARtRfdLQzx9nBnhCzqg/8b1BW2JroAgNKqGvwekYapG8OwbE8U/krMldtll4iIqKke+r1wRUVFoyP1NjY2AIDS0tKWq4qIqB0w0dPCnJ72mOlnh4t38rA7Ig2X7+UDAC7fy8fle/mwNdHFFG8bTPC0hrGuloorJiKituKhI/mCIDR6I1hdW/2bcenxwsPDsGHDelWXQUStkFhDhIFOHbF2iid2z++J6b62MNCuXWYzrbAC3/51B6PXX8FHx2/iZlaJiqslIqK2gPuut7AjRw7g2LGjsr/HxETj+++/UWFFRNSadTbTx+uB3RCyuA/eCOyGzma136hWSqQ4GJWB2VvCsWjndZxIyIakhoMtRETUuEcu45CUlISrV6/KtRUXFwMAEhISoKnZ8PBevXopsLzWZ8mSBUhIiEP37i744IP/wsbG9pGPHzVqHA4e3Id9+75DcXERyspK8dxzC5VULRG1VQbampjma4upPjYIvV+A3RFpOJ+UC6kARKQWISK1COYG2pjkbYOJXjYwN9BWdclERNSKPHR1HVdX14eu2/ywqTwAEBcXp7jqWoEHV9c5e/YUrlz5G4cPH8CkSVPx6qtvPvL4mpoaHDq0H3/+GYLi4iI888xABAcvgJGRYu+gJiL1l1ZYgb2R6TgYlY7CComsXVNDhKHO5pjqYwsvW2OuuU9E1AYpbQnNdevWNeuES5cufaqCWpvGltCUSCQYNSoQXbs6Yf36jY88/siRA9DU1IKlpRUiIq6hb99ncO7cKbz44v+1ZNlEpMYqqmtwPCEbuyLSkPDAHH0XS0NM87HFcFcL6GqJVVQhERE9KaWFfKr1sHXyFy+ej6SkRBw/fq5Jo2bh4WGIiLiGhQsXt0SZRNQOCYKAqPRi7IpIxambOZDUW27TRFcT4z2sMdnHBnYm6r+nCRFRW8eQr2SNhXxBELBw4VzcvBmPXbsOwtbWTkXVERHVyimtwoEb6dh3Ix3ZJVWydhGAZ7qaYZqvLfp0MoUGp/IQEbVKig753D+9Gfbv34ObN+MBAElJtxnyiUjlzA208Xy/TpjX2wHnEnPxe0QaIlIKIQC4kJSHC0l5cDTVw2RvG4xzt4aRLn/8ExGpM47kP8aDI/k5OdmYPXsKdHV1kZubixde+BdXyyGiVul2dil2X0/D0dhMVEj+WW5TV1MDo92sMNXHFt0sDFRYIRER1VH0SD7XyX9CX365BhKJBB99tAYAkJSUqOKKiIga183CACuHdcfRxX3xyuCucDStnZtfIZFi3410zNx8DYt+j+Sa+0REaqjNfF+bnJyMTz/9FKGhoQCAwYMHY8WKFTAzM2uR4xrz119n8ddfZ/Dii/+Gp6c3TE3NkJR0+8lfDBGREhnpamKWvz1m+Nnhyr187IpIw8WkPAgAIlIKEZFSWLvmvpcNJnpZw9xQR9UlExHRU2rydJ2xY8di8ODBGDRoEPz8/CAWK29ptvz8fEyePBlVVVUIDg5GTU0NNmzYADs7O+zevRva2o1vAtPc4+qrm65TWlqCOXOmwcysI376aRPEYjFefvlFRERcw8mTF6ClpaXol01E1GJSC8ux93o6DkVnyK25L9YQIbC7Oab52MLbTn7NfY3Cu9C//hN0EvZBVF0KQcsAlS6TUOazCFKTzip4FURE6kNlN946Ojpix44d2LBhA4yMjPDMM89g0KBBGDhwYLNGxZ/Epk2bkJGRgcOHD8PJyQkA4O3tjfnz5+PAgQOYNm2aQo9rzI8/foe8vFysWfOV7AOOk1N3hIWF4t69u+jWrftTvkoiIuWxM9HDvwd1xaKATjiekI3dEWmIzypBjVTAiYRsnEjIRncLA0zxscWoHpYwSTsH4z8XAzXVEAm1HwpE1SXQjdkO3fjdKBq5HlWdAlX8qoiIqM4T3XgrkUgQERGB8+fP48KFC4iLi4NIJIKHhwcGDRqEQYMGwcPDQ+FFPvvss7C3t8emTZvk2keOHAkrKyv89ttvCj2uvurqGly4cAUvvrgQs2YFY8mSfzb7+uOPI/j44//gvfdWYfjwUU/8uoiIWgtBEBCdXoxd19Nw6mY2qmv++dXQQycbBzXehLZQ8fDjNfWQN+MER/SJiJpJpTfeampqolevXnj11Vexb98+XLx4ER988AHy8/Oxbt26JxoZb6rCwkIkJyfD3d29QZ+7uzuio6MVetyDqqursWbNR7C1tcf8+S/I9Tk5dQMAJCZyXj4RtW0ikQietsZYNdoVRxb1wYv9O8PKqHZu/qyaw4C0+tEnqKmG/vWflVApERE1xRPfeFtSUoLw8HCEhYUhLCwM0dHRqKqqgpGREfz9/RVeYGZmJgDAysqqQZ+FhQVKSkpQXFwMIyMjhRz3oO+/X4ekpERMnz4Df/xxUNZubm6B3r2fgVgsRlLSbeTkZOHChbOPfT1BQfIfhA4c2PXYY/r3Hwxzc0vZ3y9cOIOcnOxHHuPq6g5X138+4MTHxyA+PuaRx5ibW6B//yGyv/M1/YOvqRZfU6328JpMASywAG7q62BS4QVoo+aR5xMJEujc3IeSQR8/tl4iImp5TQ75H3/8Ma5du4aEhARIpVIYGxvD398fr776Knr16gU3Nze5G7QUpbS0FACgp9dwW3YdndpRprKysgZhvbnHPWjWrFmyc6Wlpcj1aWtr49y5KwCA1NTkBv1N0ZRjKisr5f6ek5P92ONsbe3l/l5UVPjE9VVWVvI1/Q9fUy2+plrt6TUZA9DHw6fp1CeqKmnS44iIqOU1OeRv2bIFAGBtbY3nnnsOU6dOhaGhYYsVVkcqffzazRoaDWcdNfe4B2lpaTX4ZQjUjtLVp6Oj0+jjHqcpx9R9KHnYczfG2Nikwd8f91x8TQ/H19T4czeGr6nx87bl11SdpgNtobLRvvrKoIdDURkY7moBXS3lrcBGREQNNfnG2zNnziA0NBRXrlxBfHw8NDQ04Obmhl69eqF3797w9/dvkdAfHx+PCRMm4N1338WcOXPk+j755BNs3LgRERER0NfXV8hxD3pwx1siovbG8Nxb0I3ZLltVpzFVghg7agLxvmQ+jHU1Mc7dGlN8bGDfoeG3qURE1JDKltAcMmQIhgypnV9aVFQkC/yXLl2SrV7j4uKCffv2KbRAW1tbAEB2dsP5pVlZWTA2Nm40qDf3OCIiklfmswi68bsBycNDPsRa2CeeAEiAogoJtl1LwfZrKejXxRRTfWzRr7MZxBqKn9JJRESNa9aOt8bGxggMDIS5uTnMzMwgEokQGxuLuLg4RdcHY2Nj2NvbIyam4U1usbGxD12ys7nHERGRPKlJZxSNXN9gnXwAEESagFgL5SPX40f7wTh7Oxe7r6chPKUQAoBLd/Jx6U4+bE10MdnLBuM9rNFBn5sHEhG1tCcK+XFxcbh8+TIuX76MsLAwlJWVQV9fH/369cOMGTMwcODAFily+PDh2Lx5MxITE2WbWl26dAl37tzBwoULFX4cERHJq+oUiLwZJ6B//Wdoxu6CprQCEg1dSNymocznBUhNOkMTwLMuFnjWxQK3c0qx53oa/ojNQll1DdIKK7D2/B2sv3QXw1wsMNXHFu42xqp+WUREaqvJc/L79OmDoqIiCIKA7t27Y8CAARg4cCB69uwJTc1mfSHQZHl5eRg7dizEYjEWLFiAyspK/PLLL3B0dMTOnTuhra2N5ORkhIeHw8/PDw4ODk0+7nE4J5+IqPlKKiU4GpuFPdfTcCdP/mdpDytDTPGxxXAX3qhLRKToOflNDvkvvvgiBg8ejIEDB8La2lqhRTRFUlISVq9ejbCwMOjq6mLQoEFYvnw5zMzMAAD79u3DypUrsXr1akyaNKnJxz0OQz4R0dMTBAHhKYXYfT0NZ2/loN6GurIbdSd728DBlDfqElH7pLKQX6egoACXLl1CamoqtLS0YGNjg2eeeUYpy2mqAkM+EZFiZRVX4kBUOvbfyEBOaZVcX7/OppjiY4tnuvBGXSJqX1Qa8rdv347PPvsMFRUVqH+Yjo4Oli9fjtmzZyu0uNaAIZ+ISF5OThYqKyuho6Mjt9Puk5LUSHH2di72RKbhWnKhXJ+NsQ4medlgvKc1zPQfP7WSiKitU1nIP3nyJJYuXQo3Nzc8//zz6Nq1KwRBQFJSEjZu3IiYmBh8//33smU21QVDPhGRvAMHdiEtLQW2tvYICpqmkHMm5pRib2Q6jsZmorSqRtauJRZhqLMFpnjbwMvWuEV2Viciag1UFvKnT5+O6urqRm9Yra6uxvTp06Gnp4dt27YptEBVY8gnIpLXEiG/TmmVBH/EZmFPZBoSc+R/9na3MMAUH1uMdLWEvjZv1CUi9aLokK/R1AfW7SDb2Io0WlpamDBhQousk09ERO2HgbYmpvjYYkewP36e7o0RrhbQ/N/c/FvZpVh94hZGr7+Mz0/fxp1cDsAQET1Mk9e+1NbWRnl5+UP7S0tLIRZzZIWIiJ6eSCSCj70JfOxN8PLgKhyKysC+G+nILK5EaVUNfo9Iw+8RaejpYIIpPrYY5NQRmuImj1sREam9Jof8Xr16Ydu2bZg0aRIsLeVvtMrMzMT27dvh7++v8AKJiKh9MzfQxoK+jgju7YALibnYG5mOy/fyAQBhyYUISy6EuYE2JnpZI8jTBpZGOiqumIhI9Zo8J//mzZuYPn06NDQ0EBQUhM6dOwOoXYf+0KFDqKmpwY4dO9CjR4+WrFfpOCefiEheS87Jb6r7+eXYG5mGw9GZKK6UyNrFImBgN3NM8bZBL8cOvFGXiNoMlS6heePGDXz00Ue4ceOGXLuHhwfeeecd+Pj4KLS41oAhn4hIXmsI+XUqqmtwPCEbe66nIS6zRK6vk6keJvvYYqybFYx0W3ZndiKip6XyzbAAIDc3F6mpqRAEAXZ2djA3N1doUa0JQz4RkbzWFPLri0kvwp7IdJxIyEalRCpr19HUwEhXS0zxsYGrlWJ/iRIRKYqiQ36zhjY6duyIjh07KrQQIiKip+FuYwx3G2O8PKgrjsRkYm9kGpILKlApkeJgdAYORmfA3doIU3xs8KyzBXS1uFgEEamvh47kDx069MlPJhLh5MmTT11Ua8KRfCKitkkqCAi9l4+9ken4KzEX0nq/7Ux0NTHW3RqTvW3gYKqnuiKJiP5HaSP5tra2DdpiY2NRWloKFxcXdO3aFVKpFMnJyYiNjYWZmRn69++v0OKIiIiaS0MkQt/OZujb2QwZRRXYH5WBg1EZyC2tQmGFBNuupWDbtRT07WSKyd426O/UUbYmPxFRW9fkOflHjx7F22+/jfXr16N3795yfREREVi0aBGWLVuG4ODgFilUVTiST0SkPiQ1Upy9nYs9kWm4llwo12dpqI2JXjYI8rSGuSGX4SQi5VLZjbfDhw/HqFGj8MorrzTav27dOuzduxdnzpxRaIGqxpBPRKSe7uSWYW9kGo7EZKK0qkbWLtYQYXC3jpjibQt/BxMuw0lESqGyG2+zs7NhZmb20H59fX0UFhY+tJ+IiNRDa11d50l16aiP1wO74aUBXXAsLgt7ItORkFWCGqmAUzdzcOpmDjqb6WGSN5fhJKK2p8l7gLu4uGDPnj0oK2s4qp2Xl4dt27bB29tbocURERG1ND0tMYK8bLBlji82zvLBGHcraItrR+/v5pXjyzOJGLX+MlYdS0BsRrGKqyUiapomT9e5dOkSFi1aBEtLS4wdOxYODg6orKzE3bt3cejQIVRXV2PLli3w8PBo6ZqVitN1iIjkqctI/qMUlFfjSEwm9v1vGc76elgZYoq3LYa7chlOIlIclW6GdenSJXz++eeIjY395wQiEXr27IkVK1bA3d1docW1Bgz5RETy2kPIr1N/Gc7zibmoqfcb00hHE2PcrTDZywadO+qrrkgiUgutYsfbvLw8pKamQiQSwc7ODqampgotqjVhyCcikteeQn59mcWVOBiVjgNRGcguqZLr83cwwWRvWwzu1hFa4ibPhCUikmkVO96amZk1ehNubGws3NzcnrooIiKi1sbKSAeLAjpjQR9H/JWUh73X0xB6vwAAcC25ENeSC2Gmr4UgT2tM9LKBtbGuagsmonatySG/uroaP/30E44fP46ysjJIpVJZX01NDUpLS1FSUoK4uLgWKZSIiKg10BRrILC7OQK7m+NeXhn23UjHkZhMFFVIkFdWjV+vJGNTaDKe6WKGyd626NvZFGJuskVEStbk7xS//vprrF27FoWFhdDT00NqaipsbGygqamJjIwMVFdX4+23327JWomIiFqVTmb6eGWwE0IW9cH7I53hYVP7dbtUAM4n5eHl/dGYtCEUm67cR15Z1WPORkSkOE0O+X/++Sd69+6N06dP4+effwYAvPfeezh27BjWr18PiUQCLS2tFiuUiIiotdLVEmOsuzU2zvLF1jl+CPK0hq5m7a/YtKJKfHfhLsasv4K3j8ThWnIBmnE7HBHRE2nyjbceHh5YsWIF5syZAwB45pln8O9//xvTp08HALz77ruIjY3F3r17W65aFeCNt0RE8nJyslBZWQkdHR2Ym1uqupxWq6RSgqOxWdgbmYakXPnfI1066mOylw1Gc5MtIvofld14q6urKzdS7+joiJs3b8r+7uXlhWPHjim0OCIian0Y7JvGUEcT03xtMdXHBpGpRdgTmYbTt3JQXSPgTm4ZPj+TiHXn72CEqyUmedvAzVqxv+CJqH1rcsjv0aMH/vrrL9nIfdeuXRERESHrz8zMhEjEG4uIiIjqE4lE8LE3gY+9CfLLqnAkJhN7I9ORWliBCokUB6MzcDA6Az2sDDHZ2wbDXS2hx022iOgpNXm6zp9//omXX34Zfn5++Omnn3Djxg0sWLAAEydORNeuXbF+/Xr4+Pjgl19+aemalYrTdYiISNHqb7L1V2IupPV+ExvqiDHGzQoTvWzgZG6guiKJSKlUuhnW7t27sXHjRhw+fBhisRhffPGF7CZcW1tb/Pzzz3ByclJogarGkE9EJO/ChTPIycmGubkF+vcfoupy2rxHbbLla2eMyd62GNLdHNqa3GSLSJ21ih1v60tLS0NhYSGcnJygra2tqLpaDYZ8IiJ57XXH25YmkQq4kJiLvZHpuHwvX66vg54WxnvUju7bd9BTUYVE1JJaXchXdwz5RETyGPJbXkpBOfbfSMeh6EwUlFfL9fXtZIpJ3jYY4NQRmtxki0htqGx1HQDYvHkzTpw4gezsbFRXVzfoF4lEOHnypMKKIyIiao/sO+hh2cCuWBzQGaduZWN/ZDoiUosAAJfv5ePyvXxYGGpjgoc1grxsYGWko+KKiai1aXLI/+GHH/DNN9/A0NAQXbt2hY4Of6AQERG1JG1NDYzqYYVRPayQmFOK/TfScSQmE6VVNcguqcIvl+/j1yv30b9rR0zytkHfTqYQc3SfiPAE03WGDBkCOzs7rF+/HgYG7eduf07XISKSx+k6qlVeXYMT8dnYeyMdsRnFcn22xjoI8rLBeA9rdDRQv/vkiNSZyqbr5ObmYsmSJe0q4BMREbU2elpijPe0xnhPa8RlFmNfZDr+jMtChUSKtKJKfH/hLtZfuoch3WpH93s6dOA+NkTtUJNDfvfu3ZGcnNyStRAREdET6GFlhLeHG+H/BnXFH3FZ2BeZjts5paiRCjh5Mwcnb+bA0VQPE71sMNbdCh30tB5/UiJSC01edPfVV1/Fjh07cOrUKXBBHiIiotbDUEcTU31ssT3YD7/M8MYYN0toi2tH7+/nl+Obc0kYs/4y3jsaj+sphfw9TtQOPHRO/tChQxu01a2qo6urC1NT0wZf/6nj6jqck09EJC8+PgZFRYUwNjaBq6u7qsuhhygor8bR2EzsjUzH/fxyub6uHfUxycsGo92sYKT7RAvtEVELUdo6+XPnzm3WCbds2fJUBbU2DPlERNSWCYKA8JRC7I1Mx5lbOZBI//m1r6OpgeEuFpjsbQM3ayPO3SdSIW6GpWQM+UREpC5yS6twODoD+6MykFZYIdfnbGGAyd42GNHDEgbaHN0nUrZWFfILCwuhq6ur1mvmM+QTEZG6kQoCrtzLx77IdJxPzEVNvSSgryXGyB6WmORlAxcrQ9UVSdTOKDXkV1dXY+/evYiMjMTq1atl7WFhYXj//feRlJQEkUiEgIAAvPfee3B0dFRoca0BQz4RkTzOyVcvWcWVOBSdgQNRGcgsrpTrc7c2wiQvGwxztYCellhFFRK1D0oL+VVVVZg3bx7Cw8OhpaWFiIgIaGpq4u7du5gwYQKqqqowYMAAdOvWDceOHUN5eTkOHToEc3NzhRaoagz5RETyuBmWeqqRCrh0Jw/7bqTjYlIe6ocDA20xRrtZYZKXDbpZcL8copag6JD/0CU0f/vtN0REROCNN97A1atXoalZOz9v7dq1qKysxJgxY/DTTz9h+fLl2Lt3L8RiMX788UeFFkdERETKIdYQYYBTR3w10QOHXuiNhX0dYf6/XXNLq2qw+3oaZm6+hoU7riMkJhMV1TUqrpiIHuWhIf+PP/7AiBEjsHDhQujq6gKoHd0/ffo0RCIRFi5cKHtshw4dMGnSJJw9e7bFCt2+fTtGjhwJLy8vjBs3DiEhIU06rqSkBB999BEGDhwIDw8PBAYG4quvvkJVVVWL1UpERNSWWRvrYskznXH4hd5YM94NfTuZyvpupBXhP38mYMxPV/DFmUTcyeW33USt0UNvn7937x4mTZok13b9+nWUl5fD0tISPXr0kOtzdHREVlZWixS5YcMGrFmzBiNHjsS8efNw4sQJvPrqqxCJRBg9evRDjxMEAUuXLkVoaCimTZsGFxcXXL9+HevXr8ft27fx3XfftUi9RERE6kBTrIEh3c0xpLs5UgrKcSAqA4ejM5BXVo2iCgl2hqdiZ3gqfO2MMdHbBoHdLaCj2eR9NomoBT005EulUojF8jfZ/P333wCAgICABo8vLi6Gnp6egssDioqKsG7dOowdOxZffPEFAGDatGmYO3cu1qxZgxEjRjSos86pU6fw999/47333sPs2bMBADNnzoS1tTV+/PFHXLt2Df7+/gqvmYiISN3Yd9DD0gFdsDigE87dzsW+G+m4er8AABCRWoSI1CJ8oZuIMe5WmOhlg85m+qotmKide+jHbUdHR8TFxcm1nTx5EiKRCIMHD27w+AsXLrTI6jqnT59GWVkZZs6cKWvT0NDArFmzkJ6ejoiIiIceGxoaCgAICgqSax81ahQAPPJYIiIiakhLrIFnXSzw/VQv7F3QC3N72qODnhYAoLBCgu3XUjF1YxiW7IrE8fgsVEmkKq6YqH16aMgfM2YMDh48iJMnT6K8vBybNm3CrVu30LFjRwQGBso99tChQ7h48SKGDh2q8AKjo6MBAO7u8su0ubm5yfU35sUXX8SBAwdgYCC/EkB+fj4AyG4mJiIioifnaKqHfw/qipBFffDxGFf4O5jI+q4lF+LtkHiM+ekKvjmXhPv55SqslKj9eWjKnTdvHs6fP4+lS5dCJBJBEARoaWnh448/hrZ27d32J06cwNatWxEaGoouXbpg3rx5Ci8wKysLJiYmDaYCWVhYAADS0tIeemyHDh3QoUOHBu07duwAAPj6+iquUCIionZKW1MDw10tMdzVEnfzyrD/RjpCYjJRWCFBQXk1toalYGtYCno6dsAkLxsM7tYRWmLO3SdqSQ8N+dra2ti0aROOHj2K69evw8DAAOPHj0e3bt1kj4mOjkZ4eDjGjx+PFStWyFbhaYrs7OxH9uvr68PAwAClpaWNnreurbz8yUYGDhw4gGPHjqFPnz7w9vZ+omOJiAgwN7eQ+y9RfZ3N9PHKYCe82L8LztzKwb4b6YhIKQQAhN0vQNj9ApjqaWGchxWCPG3gYKr4+/mI6DE73j5OeXk5dHR0oKHx5J/GXVxcHtm/ZMkSvPLKK5g/fz6SkpJw7tw5uf6amhq4ublh+vTp+PDDD5v0nKdOncL//d//oUOHDti1axdsbW0feww3wyIiIno6d3L/N7ofm4miColcX2/HDpjoZYNBHN2ndk7Rm2E91aT0p1lN56OPPnpkf90SnQYGBqioqGjQXzeC/+B8+4c5cuQIVqxYAQMDA/z8889NCvhERET09Lp01MerQ5zw0oAuOHUzG/tvpON6ahEAIPR+AULvF8BMXwvjPKwR5GkN+w4c3Sd6Wiq783Tq1KlNepyNjQ0KCwtRVVUluxcAgGxNfisrq8eeY+fOnfjggw9gYmKCTZs2wdXVtXlFExERUbPpaGpgtJsVRrtZITGnFAeiMhASk4niSgnyyqrxW2gyfgtNRp9O/xvdd+oITY7uEzVLq19ext3dHYIgIC4uTm4Ofd3ynp6eno88/sCBA3j//fdhaWmJTZs2wcnJqUXrJSJSdzk5WaisrISOjg7MzS1VXQ61UU7mBnhtiBNe6t8Zp27mYP+NdESm1Y7uX7lXgCv3OLpP9DSeak6+MuTn52PQoEEYPnw4Pv/8cwC1G3XNnTsX6enpOHHixEM3w0pMTERQUBAMDQ2xY8cOdO7c+Ymfn3PyiYjkHTiwC2lpKbC1tUdQ0DRVl0Nq5HZOKQ7cSMfR2CwUV8rP3efoPqm7VjUnXxlMTU2xaNEirF27FoIgoG/fvjh27BjCwsLw9ddfywX8kydPAgCeffZZAMDatWtRVVWFAQMGIDIyEpGRkXLndnFx4dQdIiKiVqKbuQFeD+yGpQO6cHSf6Cm1+pF8ABAEAb/++iu2bduGnJwcdO7cGS+++CJGjhwp97i6TbpOnz4NAHjmmWeQk5Pz0PMuXboUy5Yte+RzcySfiEgeR/JJmRJzSrH/IaP7XJmH1ImiR/LbRMhXJYZ8IiJ5DPmkChXVNTh9Kwf7Iv8Z3a9jpq+Fse61o/tcd5/aqnY3XYeIiIhIV0sstzJP/dH9vLJqbL6ajM1Xk9Hrf6P73FWX2juGfCIiImpTnOrN3T99K0du3f2r9wtw9X+76o51t0KQlw0cObpP7RBDPhEREbVJD47uH4jKwNH/7aqbX16NLWEp2BKWgp4OJv8b3TeHtiZH96l9YMgnIiKiNq/+uvunb+XgwI10RPxvdD8suRBhyYUw0dWsnbvvZY3OZvoqrpioZTHkExERkdqoP7p/J7cMB6LSERKTicIKCQorJNh2LQXbrqXAz94EQV7WCOxuAR2O7pMa4uo6j8HVdYiIiNq2SokUZ2/lYH9UOq4lF8r1mehqYrSbFYK8rNG1o4GKKiTiEppKx5BPRESkPu7mleFgVAaOxGSioLxars/b1hgTvWww1Nkculrih5yBqGUw5CsZQz4REZH6qZJIcfZ2DvZHZSDsfoFcn6GOGKN71I7ud7cwVE2B1O4w5CsZQz4REZF6S84vx4GoDByJyUBemfzovoeNESZ62mCYqwX0OLpPLYghX8kY8omI5HHHW1JX1TVSnE/Mxf4bGbhyLx/1A5KBthgje1giyNMarlaKDWNEAHe8JSIiImoRWmINBDpbINDZAqmF5TgUlYFD0ZnIKa1CaVUN9kamY29kOnpYGSLI0xojeljCQJtRilonjuQ/BkfyiYjkcSSf2hOJVMDFpFwciMrApTt5kNZLTXpaGhjuYomJXtZwszaCSCRSXaHU5nEkn4iIiEhJNDVEGNTNHIO6mSOjqAKHozNxICodWSVVKK+W4mB0Bg5GZ6C7hQGCPK0xqocVjHQZr0j1OJL/GBzJJyKSx5F8au9qpAL+vpuHAzcycCEpFzX1kpSOpgaedTZHkKcNvO2MObpPTcaRfCIiIiIVEmuI0L9rR/Tv2hHZJZU4HJ2Jg1HpSCuqRKVEipDYLITEZqGLmT4meFpjjJsVOuhrqbpsamc4kv8YHMknIpLHkXyihqSCgKv3CnAgKh1nb+dCUm/yvpZYhCHdzBHkZQ1/hw7Q4Og+NYIj+UREREStjIZIhD6dTdGnsynyyqoQEpOJA1EZuJ9fjuoaAccTsnE8IRv2HXQxwcMaYz2sYW6greqySY1xJP8xOJJPRCSPI/lETSMIAsJTCnEgKgOnb2ajqt7kfbGGCAO6miHIywZ9O5lCrMHR/faOm2EpGUM+EZG8nJwsVFZWQkdHB+bmlqouh6hNKCyvxh9xWTgQlY7EHPlcYWWkg/EeVhjvYQ1rY10VVUiqxpCvZAz5REREpCiCICA6vRgHotJxPD4bFRKprE8EoF8XUwR52mBAVzNoijVUVygpHUO+kjHkExERUUsoqZTgeHwWDkRlIC6zRK6vo4E2xrpbIcjTGvYd9FRUISkTQ76SMeQTERFRS0vILMH+qHT8GZeF0qoaub6ejh0Q5GGNwd3NoaPJ0X11xZCvZAz5RETyLlw4g5ycbJibW6B//yGqLodIrZRX1+DUzWwcuJGByLQiuT4TXU2MdrPCBE9rOJkbqKhCaikM+UrGkE9EJI+r6xApR1JuKQ5GZSAkJhOFFRK5Pk8bYwR5WmOYqwX0tMQqqpAUiSFfyRjyiYjkMeQTKVeVRIqzt3NwICoDV+8XyPUZaIsx3NUCQZ426GFlCBE32mqzuBkWERERUTuiramB4a6WGO5qiZSCchyMysDhmEzkllahtKoG+29kYP+NDHS3MECQpw1G9bCEkS4jXnvHkfzH4Eg+EZE8juQTqZ5EKuBiUi4ORGXg0p08SOulOR1NDQx1NscET2v42plwdL+N4Eg+ERERUTunqSHCoG7mGNTNHJnFlTgSk4FDURlIK6pEpUSKo7FZOBqbBUdTPQR5WmO0mxU6GmirumxSIo7kPwZH8omI5HEkn6h1kgoCrt4rwIGodJy9nQtJveF9sYYIg5w6YoKnNfp0MoVYg6P7rQ1H8omIiIioAQ2RCH06m6JPZ1Pkl1UhJDYLB6PScTevHDVSAadv5eD0rRxYGelgvIcVxntYw9pYV9VlUwvhSP5jcCSfiEgeR/KJ2g5BEHAjrQgHojJwIiEblRKprE8EoG9nUwR5WmOAU0doibnRlipxCU0lY8gnIpIXHx+DoqJCGBubwNXVXdXlEFETlVRKcDw+CweiMhCXWSLXZ6avhTFuVhjvaY3OZvoqqrB9Y8hXMoZ8IiIiUjcJmSU4GJ2BP+IyUVJZI9fna2eMCZ42GOpsDl1utKU0DPlKxpBPRERE6qqiuganb9VutBWRUijXZ6AtxsgelgjytIarlWIDKDXEkK9kDPlERETUHtzNK8OhqAyExGYir6xars/F0hATPK0x0pUbbbUUhnwlY8gnIpLHOflE6k1SI8X5pDwcjMrA33cb32hrvIc1/Oy50ZYiMeQrGUM+EZE8rq5D1H5kFFXgSEwmDkVnIL2oUq7P0VQP4z2sMcbdCubcaOupMeQrGUM+EZE8hnyi9uefjbYycPZ2jvxGWyKgf9fajbb6dTGDJjfaahZuhkVERERESlV/o62CsmocjcvEgagM3MktQ40AnEvMxbnEXFgYamOcuxXGeVjDvoOeqstu1ziS/xgcyScikseRfCICajfaikovxsGodJxIyEZ5tVSuv6djBwR5WGNwd3PoaHKjrcfhSD4RERERqZxIJIKXrTG8bI3x6hAnnIjPxsHoDESnFwMAwu4XIOx+AYx1NTGqhyXGe1jD2dJQxVW3Hwz5RERERPRUDLQ1EeRlgyAvG9zOKcWhqAwcjc1EYYUERRUS/B6Rht8j0tDDyhBBntYY7moJQx3G0JbE6TqPwek6RETyOF2HiJqiSiLF2ds5OBSdgdB7BagfOHU0NfCsiwUmeFjDx86YS3FC8dN12swEqe3bt2PkyJHw8vLCuHHjEBIS0qzzvPzyy3BxcVFwdURERERUn7amBoa7WmLdFC8ceL43nu/rCCsjHQBApUSKkJhMLPo9ElM2hmFzaDJyS6tUXLF6aRMj+Rs2bMCaNWswcuRI9OvXDydOnMCFCxfw1VdfYfTo0U0+z/Hjx7Fs2TIAQEJCQpOO4Ug+EZG8CxfOICcnG+bmFujff4iqyyGiNqRGKuDKvXwcis7Audu58ktxaogwoKsZxnu0z6U42906+UVFRRg0aBACAwPxxRdfAACkUinmzp2L1NRUnDp1CmKx+LHnyc/Px5gxY1BUVITq6mqGfCIiIiIVyi+rwtHYLByMrl2Ksz4LQ22MdbfC+Ha0FGe7m65z+vRplJWVYebMmbI2DQ0NzJo1C+np6YiIiGjSeVatWgVTU1MMHz68pUolIiIioiYy1dfG7J72+P05f2yY6YMJHtbQ06qNptklVdh4JRkTN1zFkl2R+CMuExXVNSquuG1p9bc1R0dHAwDc3d3l2t3c3GT9PXv2fOQ5Tp48iT/++AM7duzAzp07W6ZQIiIiInpi9ZfifGVIV5xMyMbBqExEpRcBAK4lF+JaciGMdBIxwtUCEzyt4Wql2FFvddTqQ35WVhZMTEygpyf/VY2FhQUAIC0t7ZHHFxQU4D//+Q+ee+45+Pj4MOQTET2lnJwsVFZWQkdHB+bmlqouh4jUiIG2JiZ42mCCpw2ScktxMCoDR2OzUFBejeJKCfZEpmNPZDqcLQwwwdMaI3tYwlhXS9Vlt0oqC/nZ2dmP7NfX14eBgQFKS0uhq6vboL+urby8/JHnWbVqFfT09PDyyy83u1YiIvrHhQtnuYQmEbW4rh0N8MpgJywd0AXnE3NxMDoDl+/mQyoAN7NL8dnpRHxzLglDuptjvIc1ejp2gAaX4pRRWcjv37//I/uXLFmCV155BVKptNG1U+vaHrWu6qlTpxASEoLNmzc3+kGBiIiIiFo3LbEGAp0tEOhsgYyiCoTEZuJQdCbSCitQVSPgWHw2jsVnw9ZEF+PcrTDW3QrWxsx9Kgv5H3300SP7e/ToAQAwMDBARUVFg/66EXwDA4NGjy8sLMT777+PsWPHolu3bsjLywMAVFXVrsGal5cHHR2dhx5PRERERK2LtbEuFvbthPl9HBF2vwCHojNw5lYOqmoEpBVWYP2le/j573vo08kUEzytMdCpI7TErX6dmRahspA/derUJj3OxsYGhYWFqKqqgra2tqw9KysLAGBlZdXocfHx8cjOzsbhw4dx+PDhBv39+vXDxIkT8cknnzSjeiIiIiJSFQ2RCL07maJ3J1MUllfjWHwWDkZl4GZ2KaQC8PfdfPx9Nx8d9LQwqoclxntao5t5+xrYbfU33rq7u0MQBMTFxcHb21vWHhcXBwDw9PRs9DhXV1ds3LixQfuGDRtw4cIFbNy4EZaWvGGMiIiIqC0z0dPCNF87TPO1Q3xmMQ5GZeDP+CyUVNagoLwaO8JTsSM8Fe7WRhjvaY3hLhYw1Gn1EfiptfpXOGjQIOjo6GDLli2ykC+VSrF9+3bY2dnBx8en0eNMTEwQEBDQoP3QoUMA0GgfEREREbVdrlZGcLUywv8N6oozt3NwKCoDYcmFAICYjGLEZBTjqzOJGOpigfEeVvC1M3nk/Z1tWasP+aampli0aBHWrl0LQRDQt29fHDt2DGFhYfj666/ldrs9efIkAODZZ59VVblEREREpGK6WmKM6mGFUT2skFJQjsPRGTgSk4mskipUSKQIiclESEwmHE31MM7dCmPcrWBhqKPqshWq1Yd8AHjppZegp6eHbdu24cSJE+jcuTO++eYbjBw5Uu5x//3vfwEw5BMRERFRLfsOevhX/y5YFNAZl+/l41BUBv5KzIVEKuB+fjm+u3AXP168i35dzDDBwxr9u5pBUw1u1hUJgiCouojWrLq6BgUFZaoug4io1ThwYBfXySeiNi2/rApHY7NwMDoDd3Llc56ZvhZGu1lhvIc1unTUV1pNFhaK3cWXIf8xGPKJiIiI1JMgCIjJqL1Z90RCNkqrauT6PW2MMcHTCs+6WMBAu2UnwDDkKxlDPhEREZH6K6+uwamb2TgUnYmIlEK5Pj0tDTzrbIHxHtbwtjNukZt1GfKVjCGfiIiIqH25n1+OQ9EZCInJRE5plVyfo6kexntYY4ybJcwVeLMuQ76SMeQTERERtU8SqYDLd/NwMCoD55PyUCP9JzaLRUBAFzNM8LTGM12e/mZdhnwlY8gnIpLHG2+JqD3K+9/NuoeiMnAnT/E36yo65LeJJTSJiIiIiFTJTF8bc3raY7a/HaLTi3Eo+p+bdfPKqrE1LAVbw1LgaWOM8R61N+uqcmddhnwiIiIioiYSiUTwtDWGp60xXh3i1OBm3aj0IkSlF+GL/+2sO8HDGj4tdLPuozDkExERERE1g56WGGPdrTHW3Rr38//ZWTenVH5nXYcOuhjnYY0xblawNFLOzrqck/8YnJNPRCSPc/KJiB5OIhVw5W4+DkX/s7NuHQ0R0K+zGcZ7WGGAU0do1btZl3PyiYiIiIhaKU0NEZ7paoZnupohv6wKf8Rl4WBUBpJyyyAVgIt38nDxTh466GlhtJslxrlbo5uFgcLreLq1foiIiJopPDwMGzasV3UZREQtxlRfG7P87bHzOX9smu2LSV42MNAWAwAKyqux/VoqZm6+huCt4Qp/bo7kExGRUh05cgBaWtqwsLAEAMTEROPcuVN48cX/U3FlREQtQyQSwd3aCO7WRnhlcFecuZ2DQ9GZCLtfAACIyyxR+HMy5BMRkVKNGjUOBw/uw75936G4uAhlZaV47rmFqi6LiEgpdLXEGNXDCqN6WCG1sBxHojNxOCZT4c/DkE9ERE+kf//BqKyshI5O81eIqL+UnIaGGCIRZ48SUftjZ6KHxc90xgsBnRR+bq6u8xhcXYeISLGOHDkATU0tWFpaISLiGvr2fYbTdYio3ePqOkRE1KaNHRsEoPbGWwBwd/eAu7uHCisiIlI/HMl/DI7kExE93q1bN7Fhw4+IiLgGQQD8/XvitddWYubMiQgIGIAPPvivqkskImrVOJJPREQqdeHCGeTkZMPc3AL9+w9BWFgoli9/BdbW1njuuYXQ0dHB0aNH8Prr/0Z5eTm6d3dWdclERO0OQz4RET2RnJxspKWlAADy8/Px/vsr4ezsgm+++R46OroAgBEjxmDq1PEAgO7dXVRWKxFRe8XlDIiIqNm2bfsNhYWFePnl12UBHwAMDQ3h7OwKABzJJyJSAYZ8IiJqtlOnjsPHxw+urm6N9nfs2BFmZh2VXBURETHkExFRs5SWliA7OwsuLj0a9EmlUiQl3Ua3bpyqQ0SkCgz5RETULNXV1QDkN7aqc/78OeTn53GqDhGRijDkExFRsxgZGUMsFuP69XC59oyMdHz99WcAOB+fiEhVuLoOERE1i1gsxogRo3H06GGsWPEq+vXrj6ysTBw+fACmpmbIzs5iyCciUhGGfCIiaraXX34DmpqauHDhL1y7FgYPD0/897+fYePGX5Camgx7e0dVl0hE1C5xx9vH4I63RETy4uNjUFRUCGNjE7i6ujf6mEmTxsDCwhLr129UcnVERG0Td7wlIiKVeliwr1NcXIysrEwEBPRXUkVERPQg3nhLREQKlZR0GwDQrRvn4xMRqQpDPhERKVRiYm3I796da+QTEakK5+Q/BufkExEREVFLU/ScfI7kExERERGpGYZ8IiIiIiI1w5BPRERERKRmGPKJiIiIiNQMQz4RERERkZphyCciIiIiUjMM+UREREREaoYhn4iIiIhIzTDkExERERGpGYZ8IiIiIiI1IxIEQVB1EUREREREpDgcySciIiIiUjMM+UREREREaoYhn4iIiIhIzTDkExERERGpGYZ8IiIiIiI1w5BPRERERKRm2m3IT05OxtKlS9G7d2/07t0by5cvR15e3mOPO3/+PGbNmgVvb2/4+vpi3rx5uH79essXTErR3Ovi77//xsyZM+Hr64sBAwbg448/RmlpqRIqJmVo7nVRX3x8PDw8PLB27doWqpKUrbnXxZQpU+Di4tLgz7///W8lVE0trbnXRV5eHt555x0EBATAz88Pc+fOZb5QI096XaSkpDT6c6L+nytXrjzyOdvlOvn5+fmYPHkyqqqqEBwcjJqaGmzYsAF2dnbYvXs3tLW1Gz0uNDQUwcHB6N69OyZPngyJRILt27cjKysL27dvh5eXl5JfCSlSc6+Ly5cvY/78+XB3d8fEiRORnp6OzZs3w93dHdu2bYOGRrv9LK0Wmntd1CeRSDB16lTExsZi6dKlWLZsmRIqp5bU3OtCEAT4+fkhICAAw4cPl+uzs7NDz549lVE+tZDmXhclJSWYOnUqsrKyMG/ePBgbG2Pbtm3IzMzE7t274ezsrORXQorUnOuirKwMJ06caNBeWVmJVatWoWPHjjh48CBMTEwe/sRCO/Tll18KPXr0EG7fvi1ru3jxouDs7Cz8/vvvDz1uwoQJwuDBg4WysjJZW3Z2ttCrVy9h3rx5LVoztbzmXhcTJ04UhgwZIpSXl8vatm7dKjg7Owtnz55t0Zqp5TX3uqhv3bp1gru7u+Ds7Cx8++23LVUqKVFzr4v79+8Lzs7Owt69e5VRJilZc6+LL7/8UnBxcRFCQ0NlbVlZWYKXl5fwxhtvtGjN1PIU8XukzkcffSS4uroKV69efexj2+UQY0hICHr37g0nJydZW0BAALp06YKQkJBGjyksLER8fDxGjhwJPT09Wbu5uTl69eqFiIiIFq+bWlZzrovKykqYmppi2rRp0NXVlbX37t0bAJCQkNCyRVOLa851UV9CQgJ++OEHvPjiiy1ZJilZc6+L27dvA4DccaQ+mnNdCIKA/fv3Y/DgwejVq5es3cLCAsuXL+e3O2rgaX+P1ElISMDWrVsxceLEJl0X7S7kFxYWIjk5Ge7u7g363N3dER0d3ehxhoaG+PPPPzFv3rwGffn5+RCLxYoulZSoudeFjo4ONmzYgCVLlsi1x8XFAQBsbW0VXywpTXOvizoSiQQrV65EQEAAxo8f31JlkpI9zXVx69YtAP+E/LKyspYpkpSuuddFSkoKMjMzERAQAKA29Nfd0zV79mxMmzat5YqmFve0v0fq++qrr6Crq4uXX365SY9vdyE/MzMTAGBlZdWgz8LCAiUlJSguLm7QJxaL0blz5wbHxcfHIzw8HL6+vi1TMClFc6+LB6WmpmLfvn34+OOP4ezsjGHDhim8VlKep70ufv75Z9y7dw8ffvhhi9VIyvc018WtW7dgYGCA1atXw9fXF76+vnj22WefaDSPWqfmXhf37t0DAHTs2BGffvopevbsCT8/PwwbNgynT59u2aKpxSkqX8THx+PMmTOYMWMGLC0tm/Tcmk9WattX9+m4/pSbOjo6OgBqR1aMjIyadK4333wTALBo0SIFVknKpojroqCgAIGBgbLzvPPOO7JjqW16muvi1q1b+O677/Dee+/B2toaKSkpLVssKc3TXBe3b99GaWkpiouLsWbNGhQVFWHz5s149dVXUV1djaCgoBatnVpOc6+LoqIiAMA333wDTU1NvP3229DQ0MCGDRvw0ksvYcOGDbJRfmp7FJU7d+zYAbFYjDlz5jT5udtdyJdKpY99TFNWQykvL8e//vUvxMfHY/HixbI52NQ2KeK6EIlE+Oqrr1BVVYUtW7Zg/vz5+PLLLzFy5EhFlUlK1tzroqamBitXroS/vz+/aldDT/PzYtq0aZBKpZg9e7asbcyYMRg7diw+++wzjBs3jtM/26jmXhdVVVUAasP+sWPHZKulBAYGYtiwYfjiiy8Y8tswReSLiooKHDp0CIGBgbCzs2vyc7e76ToGBgYAam+YfFBdW91jHqaoqAgLFizAlStXMHnyZLzyyiuKL5SUShHXhYmJCUaPHo2goCBs27YNtra2+OSTTxRfLClNc6+LDRs2ID4+Hq+99hry8vKQl5cnG60rLy9HXl5ek37wU+v0ND8vZs6cKRfwAUBXVxcTJkxATk6O7MZcanuae13o6+sDAIYPHy63HKKxsTECAwMRExPDfVfaMEXkiytXrqCsrOyJBw3bXcivuxEyOzu7QV9WVhaMjY1l/+Aak5ubi+DgYISHh2P69On4+OOPIRKJWqxeUo6nvS4epKuri8GDByM9Pf2JN02i1qO518X58+dRXV2NqVOnol+/fujXrx8mTpwIoPYDQL9+/ZCWltayxVOLUfTPCwAwMzMDwBtx27LmXhd1c7XrroH6zMzMIAgCr4s2TBE/L86dOwctLS0MHjz4iZ673U3XMTY2hr29PWJiYhr0xcbGwsPD46HHlpSUYOHChYiLi8O8efOwcuXKliyVlKi510ViYiJeeOEFLFy4sMHoXGlpKUQiUZM2S6LWqbnXxZtvvikbua+Tk5ODN954AxMmTEBQUBAsLCxapGZqec29LjIzM7FgwQKMGjUKS5culeu7c+cOAMDe3l7xBZNSNPe66N69O7S1tRv9FiclJQU6OjqNfgCgtuFpcmed8PBweHp6wtDQ8Imeu92N5AO1X4n9/fffSExMlLVdunQJd+7cwejRox963Icffoi4uDgEBwcz4Kuh5lwXnTp1QnFxMXbu3CmbVwnUrrJz/Phx9OrV64n/UVLr0pzrwsPDAwEBAXJ//Pz8AAAODg4ICAjgTdltXHOuCysrKxQXF2P37t0oKSmRtaenp2Pfvn3o06cPP/y1cc25LvT19REYGIizZ8/KllgFgOTkZJw+fRpDhw7lfRptXHNzJwBUV1fj9u3bcHNze+LnFQmCIDzxUW1cXl4exo4dC7FYjAULFqCyshK//PILHB0dsXPnTmhrayM5ORnh4eHw8/ODg4MDEhMTMXr0aBgZGeGtt95q9B/chAkTVPBqSFGac10AwMGDB7F8+XL4+Phg/PjxyM/Px7Zt21BdXY3t27dzO/I2rrnXxYNSUlIwdOhQLF26FMuWLVPyqyBFa+51cfLkSbz00kvo3r07pk6ditLSUtnPix07dnCTrDauuddFSkoKpk6dCgAIDg6GlpYWNm/ejPLycuzbt++hP1eobXia3yP379/HsGHD8MYbb+D5559/sid+or101UhiYqLw/PPPCz4+PkLfvn2FN998U8jNzZX17927V27r8e3btwvOzs6P/ENt35NeF3VCQkKEiRMnCu7u7kKvXr2EZcuWCUlJScoun1pIc6+L+pKTkwVnZ2fh22+/VUbJpATNvS5OnDghTJkyRfDw8BB69uwpvPjii3Lb3VPb1tzr4v79+8KyZcsEf39/wc/PT1i0aBGvCzXS3OsiMjJScHZ2Fnbs2PHEz9kuR/KJiIiIiNRZu5yTT0RERESkzhjyiYiIiIjUDEM+EREREZGaYcgnIiIiIlIzDPlERERERGqGIZ+IiIiISM0w5BMRERERqRlNVRdARKSOVqxYgf3798u1aWhoQE9PD05OTpg1axYmTpzY4nUEBgbCzs4OW7ZsaZHz5+bmQk9PD/r6+gD+ed0JCQkt8nyN2bdvH1auXNmgXVNTE8bGxvD09MSyZcvg6enZrPOXlJSgqqoKZmZmT1sqEZHSMOQTEbWglStXwtTUFAAgCAJKSkpw6NAhrFixAvn5+ViwYIGKK2y+c+fO4fXXX8f+/ftlIX/69Ono16+fSuqZPn06/P39ZX+vqqpCQkICdu7ciatXr+LgwYNwdHR8onNGR0fjX//6Fz7//HP06dNH0SUTEbUYhnwiohb07LPPwt7eXq5typQpGD16NL777jvMmTMH2traKqru6dy4cQNFRUVybb6+vvD19VVJPT4+PpgwYUKDdj8/P7zyyiv49ddf8Z///OeJznnz5k1kZWUpqEIiIuXhnHwiIiXT1dVFYGAgSkpKcOvWLVWXo/ZGjRoFPT09REZGqroUIiKlYcgnIlIBkUgEAKipqQFQO3f+nXfewVtvvQVPT08MHDgQeXl5AICwsDDMmzdPNkoeHByMq1evNjjn0aNHMWHCBHh5eWHs2LG4fPlyg8cEBgZi7ty5TWqPjIzECy+8gF69eqFPnz5YtGiRbK79ihUrsG7dOgDA0KFDZceuWLECLi4ucudJTU3FG2+8gb59+8LT0xPjx4/Hrl275B6zYsUKjBw5Ejdu3MCcOXPg7e2NgIAAfPTRR6ioqHj8G/oIIpEIOjo6EARBrv3PP//EnDlz4O/vDw8PDwQGBmLNmjWoqqoCAKxdu1Y21z84OBiBgYGyYzMyMrB8+XLZawoKCsKhQ4eeqk4iIkXidB0iIiWTSqUIDQ2FtrY2nJycZO0hISHo0qUL3n77beTk5MDMzAynTp3C0qVL4ejoiH/9618AgN27d2PevHn49ttvMXToUAD/3Hzq6+uLN954A/fu3cOSJUsglUphZ2f3xDXWfbCwtLTEwoULoauri82bNyM4OBh79+7F9OnTUVJSghMnTmDlypXo3r17o+dJTk7GtGnTUFlZiTlz5sDCwgLHjx/Hu+++i7t372L58uWyx+bl5WHhwoUYNWoUxo8fj7/++gtbtmyBtra23OOeVFRUFAoKCuRC+u7du/HOO+8gMDAQr7/+Oqqrq3HixAls2LAB+vr6WLp0KYYNG4bs7Gz8/vvvWLJkiezG3czMTEydOhWCIGDu3LkwMTHBqVOn8MYbbyArKwvPP/98s2slIlIUhnwiohZUVFQkG5GvqalBamoqNm3ahPj4eMybNw8GBgayx1ZUVODrr7+W3RwqkUjw4YcfwsrKCnv37oWhoSEAYMaMGRg7diw++OADDBw4EBoaGvj888/h6emJLVu2QEtLCwDg5ubW6KozTfHpp5+iQ4cO2Lt3r+zG4UGDBmH06NHYvn07li9fDhcXF5w4caLR+w7qfPnllygoKMCePXvg7u4OAJg9ezZefPFF/Prrr5g4caLsA0JhYSHeeecd2bcC06ZNw+jRo3H48OEmhfyysjLZew0AlZWViImJwaeffgpdXV0sWrRI1vfrr7/C19cX33//vexblVmzZmHo0KE4duwYli5dCldXV/j4+OD3339HQECA7Mbbr776ClVVVTh8+DAsLS0BAHPmzMFrr72Gb775BhMnTkTHjh2f6P0mIlI0hnwiohbU2DKZ2tramDt3Ll577TW5dkdHR7nVX2JjY5GRkYHXX39dFvABwNjYGHPmzMEXX3yB6OhoiMVi5ObmYunSpbKADwATJkzAJ5988sQ15+bmIioqCvPnz5cFfADo0qUL9u7dCxsbmyadp6amBmfPnkX//v1lAR+oXUp0yZIlOHPmDE6fPi33LcCoUaPkzuHq6oo///yzSc+3atUqrFq1Sq5NQ0MDfn5++Pbbb9GlSxdZ+6FDh1BeXi4L+HWv29jYGGVlZQ99DqlUipMnT6JPnz7Q1NSU+1AxfPhwHDlyBBcvXsT48eObVDMRUUthyCciakGfffYZzM3NAdQGTmNjYzg5OUFHR6fBYx8c/U1JSQEAuXBap2vXrgCAtLQ0aGjU3l714PKQYrEYnTp1euKaU1NTIQhCo8e6ubk1+Tz5+fkoKytrtP66aUqpqaly7Q+uRa+trS27b+FxFi5ciP79+0MqlSI+Ph4//fQTOnXqhM8++wy2trZyj9XS0sLVq1dx5MgRJCUl4f79+8jNzQWAR05vys/PR3FxMU6ePImTJ082+pj09PQm1UtE1JIY8omIWpCfn99Dp7I8SCwWy/39wRtFG+vT0tKCVCoFUDs95UF1fY9TP0jXHVP34aG5HlV/3XM8uHzo0zxnt27dEBAQAADo378/+vTpg1mzZmHu3LnYvXu33AeIL774Aj/99BPc3NxkS2/6+vpi1apVjwzpde/TiBEjMGPGjEYf4+Dg0OzXQESkKAz5REStVN2IclJSUoO+O3fuAACsra1lHw7u3r0r9xhBEJCamio3HUZDQ0O2ekwdiUSC/Px82TcBddNx7t271+B5P/vsM5iYmMjNb38YMzMz6OvrP7b+luLp6YnXXnsNq1evxjvvvIPvv/8eQO23Bz/99BMmTJiANWvWyB2Tk5PzyHOamZlBT08PEolE9oGiTlpaGmJjY6Gnp6fYF0JE1AxcQpOIqJVyd3eHhYUFduzYgZKSEll7SUkJtm/fDgsLC3h4eMDNzQ12dnbYsWMHysvLZY8LCQlBfn6+3DnNzc1x584duWUpT58+LfctgJWVFVxdXRESEiL3vMnJydi8ebMsCNeNuj9sxF4sFmPAgAG4ePEiYmJiZO2CIODnn3+GSCTC4MGDm/HONN1zzz0HPz8/nDp1CkePHgVQe4MvUDvyX9+5c+dw9+5dSCQSWVvda6z75kFTUxMDBw7EuXPnEB8fL3f8J598gpdeeqnBe05EpAocySciaqW0tLTw7rvv4uWXX8bkyZMxZcoUAMCePXuQlZWFb7/9VhZC3333Xbz00kuYPn06Jk+ejMzMTGzbtg0dOnSQO+fYsWOxatUqPP/88xg/fjzu3buHXbt2NZiHvnLlSjz//POYPHkypk6dCg0NDWzduhXGxsZ44YUXAPwzf/6XX37BwIEDZct51vf666/jypUrmDt3LubOnQsLCwucOHECly9fxvz58xsEbUUTiUT48MMPMXHiRHz88cd45pln0K1bN9ja2uLHH39EZWUlrK2tcePGDezfvx86OjooLS2VHV/3Gnfs2IGcnByMGzdO9ppmz56N2bNnw9bWFmfPnsWZM2cwffr0hy4nSkSkTBzJJyJqxUaMGIFff/0VlpaW+O6777B+/XrY29tj8+bNePbZZ2WPGzJkCNavXw9dXV18+eWXOHnyJD7++GPZDbp1Zs2ahWXLliElJQWrVq1CaGgo1q1b1yCY9u3bF7/99husra3x3Xff4aeffoK7uzt27NgBCwsLAMCYMWMQEBCAffv24fPPP2+0fkdHR+zatQuDBg3Czp078dlnn6G4uBgff/wxVqxYoeB3q3Hdu3fHwoULkZOTg08++QTa2tr46aef4Ovri82bN+PTTz9FTEwM3nrrLbz++usoKSlBdHQ0AKBfv34YNWoUzp07h1WrVqGyslL2mgYPHoxdu3bhv//9L5KTk7Fy5Uq8//77SnlNRESPIxIedWcUERERERG1ORzJJyIiIiJSMwz5RERERERqhiGfiIiIiEjNMOQTEREREakZhnwiIiIiIjXDkE9EREREpGYY8omIiIiI1AxDPhERERGRmmHIJyIiIiJSMwz5RERERERq5v8BtVqVooK8GycAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data['shadow'] = model.Value(data.index, 1)\n", "\n", "fig, ax = plt.subplots()\n", "data['shadow'].plot(ax=ax)\n", "ax.set(title='Shadow Price Function',\n", " xlabel='Production Rate',\n", " ylabel='Shadow Price',\n", " xlim=[qmin, qmax])\n", "\n", "pstar = model.Value(qstar, 1)\n", "lb = ax.get_ylim()[0]\n", "ax.hlines(pstar, 0, qstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(qstar, lb , pstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$\\lambda^*$', (qmin, pstar))\n", "ax.annotate('$q^*$', (qstar, lb))\n", "ax.plot(qstar, pstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Residual" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 9, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.axhline(0, c='white')\n", "data['resid'].plot(ax=ax)\n", "ax.set(title='HJB Equation Residual',\n", " xlabel='Production Rate',\n", " ylabel='Residual',\n", " xlim=[qmin, qmax]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Simulate the model" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Initial state and time horizon" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 10, "outputs": [], "source": [ "q0 = 0.2 # initial production\n", "T = 10 # time horizon" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Simulation and plot" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 11, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PARAMETER xnames NO LONGER VALID. SET labels= AT OBJECT CREATION\n" ] }, { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "simulation = model.simulate([[q0]], T)\n", "\n", "# Time to midway adjustment\n", "qhalf = (q0 + qstar)/2\n", "thalf = np.interp(qhalf, simulation['$y_0$'], simulation.index)\n", "\n", "\n", "simulation['$y_0$'].plot(ax=ax)\n", "ax.set(title='Simulated Production',\n", " xlabel='Time',\n", " ylabel='Production',\n", " xlim=[0, T],\n", " xticks=np.arange(0,T+1,2))\n", "\n", "ax.axhline(qstar, ls='--', c='C0')\n", "ax.annotate('$q^*$', (0, qstar), color='C0', va='top')\n", "\n", "lb = ax.get_ylim()[0]\n", "ax.vlines(thalf, lb , qhalf, colors=['gray'], linestyles=['--'])\n", "ax.hlines(qhalf, 0 , thalf, colors=['gray'], linestyles=['--'])\n", "\n", "ax.annotate('$t_{0.5}$', (thalf, lb))\n", "ax.annotate('$q_{0.5}$', (0, qhalf),va='top')\n", "\n", "ax.legend([]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }