{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE30338](https://jckantor.github.io/CBE30338)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE30338.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Manometer Models and Dynamics](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/03.08-Manometer-Models-and-Dynamics.ipynb) | [Contents](toc.ipynb) | [PID Control](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/04.00-PID_Control.ipynb) >

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Modeling and Control of a Campus Outbreak of Coronavirus COVID-19\n", "\n", "This Jupyter/Python notebook presents models for the outbreak of an infectious disease into a susceptible population using standard epidemiological models. Model parameters are taken from a rapidly evolving scientific literature documenting the global COVID-19 outbreak. A control policy based on 'social distancing' is included in the model.\n", "\n", "The notebook is organized as follows:\n", "\n", "1. Brief Background on the SARS-CoV-2 Coronavirus and COVID-19\n", "2. Model 1. SIR Model for an Infectious Disease\n", "3. Model 2. SEIR Model\n", "4. Model 3. SEIR Model with Control\n", "5. Model 4. An Improved SEIR model.\n", "6. Ideas for student projects.\n", "\n", "The executable Python code in this notebook can be edited and run Google's cloud servers by clicking on the \"Open in Colab\" button located in the header. Use the interactive sliders to adjust model parameters and perform 'what if' simulations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Brief background on the SARS-CoV-2 Coronavirus and COVID-19\n", "\n", "[COVID-19](https://www.who.int/health-topics/coronavirus) is caused by the human coronavirus SARS-CoV-2. First identified in the 1960's, there are currently four human coronaviruses endemic to populations around the world:\n", "\n", "* 229E (alpha coronavirus)\n", "* NL63 (alpha coronavirus)\n", "* OC43 (beta coronavirus)\n", "* HKU1 (beta coronavirus)\n", "\n", "These four common coronaviruses cause an upper respiratory disease that can progress to pneumonia. These endemic viruses cause about a quarter of all common colds. Most people will suffer from at least one during their lifetimes.\n", "\n", "In recent decades, three additional coronaviruses that normally infect animals have evolved to infect humans. These include:\n", "\n", "* MERS-CoV (the beta coronavirus that causes Middle East Respiratory Syndrome, or MERS)\n", "* SARS-CoV (the beta coronavirus that causes severe acute respiratory syndrome, or SARS)\n", "* SARS-CoV-2 (the novel coronavirus that causes coronavirus disease COVID-19)\n", "\n", "The last of these, now called SARS-CoV-2, first appeared in December, 2019, at a seafood market in Wuhan (Hubei, China). The rapid spread of SARS-CoV-2 in Wuhan, and subsequent appearance in other locations around the globe, has resulted in declaration of a [global health emergency by the World Health Organization (WHO)](https://www.who.int/emergencies/diseases/novel-coronavirus-2019). Most countries are mobilizing to track the virus and control new outbreaks. At this stage, it is too early to know if efforts to contain the mitigate transmission of the virus will be successful in preventing COVID-19 from becoming a pandemic, or later an endemic disease with a global footprint. \n", "\n", "The latest status on the global outbreak of COVID-19 can be found at the following links:\n", "\n", "* [Coronavirus COVID-19 Global Cases by Johns Hopkins CSSE](https://www.arcgis.com/apps/opsdashboard/index.html#/bda7594740fd40299423467b48e9ecf6)\n", "* [WHO Novel Coronavirus (COVID-19) Situation](https://experience.arcgis.com/experience/685d0ace521648f8a5beeeee1b9125cd)\n", "\n", "The purpose of this notebook is to demonstrate the modeling of an infectious epidemic using the latest available data for COVID-19, and to provide a framework for evaluating the performance of 'social distancing' and other mitigation strategies. The models and data used in this notebook have been extracted from a rapidly emerging and changing literature. Recent papers on COVID-19 can be found at the following links.\n", "\n", "* [Cell Press Coronavirus Resource Hub](https://www.cell.com/2019-nCOV)\n", "* [Lancet COVID-19 Resource Centre](https://www.thelancet.com/coronavirus)\n", "* [medRxiv preprint server search on COVID-19](https://www.medrxiv.org/search/COVID-19%20numresults%3A50%20sort%3Apublication-date%20direction%3Adescending)\n", "* [New England Journal of Medicine Coverage on Coronavirus (COVID-19)](https://www.nejm.org/coronavirus)\n", "* [WHO Database of publications on coronavirus disease (COVID-19)](https://www.who.int/emergencies/diseases/novel-coronavirus-2019/global-research-on-novel-coronavirus-2019-ncov)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 1. SIR model for an infectious disease" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Readings\n", "\n", "* Keeling, Matt J., and Pejman Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2008. JSTOR, www.jstor.org/stable/j.ctvcm4gk0. Accessed 25 Feb. 2020.\n", "* Boldog, Péter, et al. \"Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China.\" Journal of Clinical Medicine 9.2 (2020): 571. https://www.mdpi.com/2077-0383/9/2/571\n", "* Bedford, Trevor. Cryptic transmission of novel coronavirus revealed by genomic epidemiology. Accessed 4 Mar 2020. https://bedford.io/blog/ncov-cryptic-transmission/" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Introduction to SIR models\n", "\n", "The SIR model is deterministic compartment model for the spread of an infectious disease that describes key phenomena encountered in epidemiology. In the SIR model, a population is broken into three non-overlapping groups corresponding to stages of the disease:\n", "\n", "* **Susceptible.** The subpopulation susceptible to acquire the disease. For SARS-CoV-2, the assumption is that everyone who has not previously acquired the disease is susceptible to infection.\n", "* **Infectious.** The subpopulation that has become infective.\n", "* **Recovered.** The subpopulation that has recovered from infection, and presumed to be no longer susceiptible to the disease.\n", "\n", "Neglecting demographic processes of birth and death from other causes, and assuming a negligible death rate due to infectious disease at issue, the progression of an epidemic can be modeled by rate processesl\n", "\n", "$$\\text{Susceptible}\n", "\\xrightarrow{\\frac{\\beta S I}{N}} \n", "\\text{Infectious} \n", "\\xrightarrow{\\gamma I} \n", "\\text{Recovered} $$\n", "\n", "The rate processes are modeled as follows.\n", "\n", "* $\\frac{\\beta S I}{N}$ is the rate at which susecptible population encounters the infected population resulting in trasmission of the disease. $S$ is the size of the susceptible population. $\\beta$ is a the model parameters with units of 1/day. \n", "* $\\gamma I$ is the rate at which infected population recovers and becomes resistent to further infection. $I$ is the size of the infective population.\n", "\n", "A model for the spread of an infectious disease in a uniform population is given by the deterministic SIR equations\n", "\n", "\\begin{align*}\n", "\\frac{dS}{dt} & = -\\frac{\\beta S I}{N} \\\\\n", "\\frac{dI}{dt} & = \\frac{\\beta S I}{N} - \\gamma I \\\\\n", "\\frac{dR}{dt} & = \\gamma I\n", "\\end{align*} \n", "\n", "The model becomes more generic by working with population fractions rather than raw population counts. To this end, define\n", "\n", "\\begin{align}\n", "s = \\frac{S}{N} \\qquad\n", "i = \\frac{I}{N} \\qquad\n", "r = \\frac{R}{N}\n", "\\end{align} \n", "\n", "After substitution, this results in a system of four equations.\n", "\n", "\\begin{align*}\n", "\\frac{ds}{dt} & = -\\beta s i \\\\\n", "\\frac{di}{dt} & = \\beta s i - \\gamma i \\\\\n", "\\frac{dr}{dt} & = \\gamma i\n", "\\end{align*} \n", "\n", "where $s + i + r = 1$ is an invariant." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Key Properties of the SIR Model\n", "\n", "The SIR model describes key epidemiological phenemena. Here is a brief synposis of the relevant results.\n", "\n", "* The parameters $\\beta$ and $\\gamma$ have units of inverse time. \n", "* $\\beta$ is rate constant associated with transmission of the infection. The corresponding time constant $\\tau_{infect} = \\frac{1}{\\beta}$ corresponds to exponential growth of new infections in an initially susceptible population where $s=1$. \n", "* $\\gamma$ is the rate of recovery from infections. The associated time constant $\\tau_{recovery}=\\frac{1}{\\gamma}$ is average time to recover from an infection.\n", "* The infectious population can grown only if $\\beta s > \\gamma$, that is the rate of infection is greater than the rate of recovery.\n", "* The ratio $R_0 = \\frac{\\beta}{\\gamma}$ is the \"Basic Reproduction Number\" that describes the transmissability or contagiousness of an infectious disease. \n", "* $R_0$ is the average number of people infected by an index 0 case in an otherwise completely susceptible population. \n", "* The infectious population can grow only if $R_0 s > 1$. If $s=1$, then $R_0 > 1$ is sufficient for growth of the infectious population.\n", "* The infectious population decreases if $s R_0 < 1$ or, equivalently, $s < \\frac{1}{R_0}$.\n", "* The population has 'herd immunity' when the fraction of susceptibles is less than $\\frac{1}{R_0}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation\n", "\n", "The following Python code implements a simulation of the SIR model. The parameter values were selected from the recent survey by Boldog, et al. (2020).\n", "\n", "* $\\tau_{infectious} = \\frac{1}{\\gamma} = 8.4$ days.\n", "* $R_0 = \\frac{\\beta}{\\gamma} = 2.4$ " ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# parameter values\n", "R0 = 2.4\n", "t_infective = 5.1 + 3.3\n", "\n", "# initial number of infected and recovered individuals\n", "i_initial = 1/20000\n", "r_initial = 0.00\n", "s_initial = 1 - i_initial - r_initial\n", "\n", "gamma = 1/t_infective\n", "beta = R0*gamma\n", "\n", "# SIR model differential equations.\n", "def deriv(x, t, beta, gamma):\n", " s, i, r = x\n", " dsdt = -beta * s * i\n", " didt = beta * s * i - gamma * i\n", " drdt = gamma * i\n", " return [dsdt, didt, drdt]\n", "\n", "t = np.linspace(0, 180, 2000)\n", "x_initial = s_initial, i_initial, r_initial\n", "soln = odeint(deriv, x_initial, t, args=(beta, gamma))\n", "s, i, r = soln.T\n", "e = None\n", "\n", "def plotdata(t, s, i, e=None):\n", " # plot the data\n", " fig = plt.figure(figsize=(12,6))\n", " ax = [fig.add_subplot(221, axisbelow=True), \n", " fig.add_subplot(223),\n", " fig.add_subplot(122)]\n", "\n", " ax[0].plot(t, s, lw=3, label='Fraction Susceptible')\n", " ax[0].plot(t, i, lw=3, label='Fraction Infective')\n", " ax[0].plot(t, r, lw=3, label='Recovered')\n", " ax[0].set_title('Susceptible and Recovered Populations')\n", " ax[0].set_xlabel('Time /days')\n", " ax[0].set_ylabel('Fraction')\n", "\n", " ax[1].plot(t, i, lw=3, label='Infective')\n", " ax[1].set_title('Infectious Population')\n", " if e is not None: ax[1].plot(t, e, lw=3, label='Exposed')\n", " ax[1].set_ylim(0, 0.3)\n", " ax[1].set_xlabel('Time /days')\n", " ax[1].set_ylabel('Fraction')\n", "\n", " ax[2].plot(s, i, lw=3, label='s, i trajectory')\n", " ax[2].plot([1/R0, 1/R0], [0, 1], '--', lw=3, label='di/dt = 0')\n", " ax[2].plot(s[0], i[0], '.', ms=20, label='Initial Condition')\n", " ax[2].plot(s[-1], i[-1], '.', ms=20, label='Final Condition')\n", " ax[2].set_title('State Trajectory')\n", " ax[2].set_aspect('equal')\n", " ax[2].set_ylim(0, 1.05)\n", " ax[2].set_xlim(0, 1.05)\n", " ax[2].set_xlabel('Susceptible')\n", " ax[2].set_ylabel('Infectious')\n", "\n", " for a in ax: \n", " a.grid(True)\n", " a.legend()\n", "\n", " plt.tight_layout()\n", " \n", "plotdata(t, s, i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How many people will be infected following an outbreak?\n", "\n", "Given an outbreak in a susceptible population, the final state is reached when $i$ returns to a near zero value. A formula for the final state can be found by taking the ratio \n", "\n", "\\begin{align}\n", "\\frac{di}{ds} & = \\frac{\\frac{di}{dt}}{\\frac{ds}{dt}} = -1 + \\frac{1}{s R_0} & \\\\\n", "\\end{align}\n", "\n", "Integrating,\n", "\n", "\\begin{align}\n", "\\int_{i_0}^{i_f} di & = \\int_{s_0}^{s_f} (-1 + \\frac{1}{s R_0}) ds & \\\\\n", "\\end{align}\n", "\n", "\n", "\\begin{align}\n", "i_f - i_0 & = -(s_f - s_0) + \\frac{1}{R_0} \\ln\\frac{s_f}{s_0} & \\\\\n", "\\end{align}\n", "\n", "The starting point of an outbreak begins with a very small value $i_0 \\approx 0$ and ends with a very small value $i_f \\approx 0$. Setting $i_0 = i_f = 0$ gives\n", "\n", "\\begin{align}\n", "s_f - \\frac{1}{R_0}\\ln s_f & = s_0 - \\frac{1}{R_0} \\ln{s_0} & \\\\\n", "\\end{align}\n", "\n", "For the special case of an initially susceptible population, $s_0 = 1$ which gives \n", "\n", "\\begin{align}\n", "s_f - \\frac{1}{R_0} \\ln s_f & = 1\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import brentq, fminbound\n", "\n", "def f(s, R0):\n", " return s - np.log(s)/R0\n", "\n", "def g(s0, R0):\n", " rhs = f(s0, R0)\n", " smin = fminbound(lambda s: f(s, R0), 0.0001, 1)\n", " return brentq(lambda s: f(s, R0) - f(s0, R0), 0.001, smin)\n", "\n", "R0 = np.linspace(1.01, 4.0, 100)\n", "sf = [g(0.8, R0) for R0 in R0]\n", "\n", "plt.plot(R0, sf)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 2. SEIR model\n", "\n", "The SEIR model extends the SIR model by adding an additional population compartment containing those individuals who have been exposed to the virus but not yet infective.\n", "\n", "* **Exposed.** The subpopulation that has been exposed to the disease but not yet infective. \n", "\n", "The compartment model can be diagrammed as follows.\n", "\n", "$$\\text{Susceptible}\n", "\\xrightarrow{\\frac{\\beta S I}{N}} \n", "\\text{Exposed} \n", "\\xrightarrow{\\alpha E} \n", "\\text{Infectious} \n", "\\xrightarrow{\\gamma I} \n", "\\text{Recovered} $$\n", "\n", "The rate processes are modeled as follows.\n", "\n", "* $\\frac{\\beta S I}{N}$ is the rate at which susecptible population encounters the infected population resulting in trasmission of the disease. $S$ is the size of the susceptible population. $\\beta$ is a the model parameters with units of 1/day. \n", "* $\\alpha E$ is the rate at which exposed population becomes infective, where $E$ is the size of the exposed population. The average period of time in the exposed state is the incubation period of the disease, and equal to $\\frac{1}{\\alpha}$.\n", "* $\\gamma I$ is the rate at which infected population recovers and becomes resistent to further infection. $I$ is the size of the infective population.\n", "\n", "An elementary model for the spread of an infectious disease in a uniform population is given by the deterministic SEIR equations}\n", "\n", "After substitution, this results in a system of four equations.\n", "\n", "\\begin{align*}\n", "\\frac{ds}{dt} & = -\\beta s i \\\\\n", "\\frac{de}{dt} & = \\beta s i - \\alpha e \\\\\n", "\\frac{di}{dt} & = \\alpha e - \\gamma i \\\\\n", "\\frac{dr}{dt} & = \\gamma i\n", "\\end{align*} \n", "\n", "where $s + e + i + r = 1$ is an invariant." ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "image/png": 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VOEtfZYlV4yxdlSVOKJ1Y169ff9IYk9c7xCq1WrVqmSZNmng6jAqnMu3j5UW3SW66TXLTbZJbaW2Twp6LLpoKVVhYGOvWrStRHrGxsURHR5dOQGWsssSqcZa+yhKrxlm6KkucUDqxisifpRNNxVOnTp0Sn68uRpVpHy8vuk1y022Sm26T3EprmxT2XKRN/pRSSimllFKqmLRCpZRSSimllFLF5JEKlYh8IiLHReS3POaLiEwUkT0iskVE2pR3jEoppZRSSilVEE89QzUVeA/4NI/5NwNX258OwAf23zKR5sjkwOkkDidmsvdEIgJ4iSACgvUXQCT3dAFEcgzbad1N9xLB20vw9RYkK2OllFJKKVVhpKenExcXR0pKiqdDKVBgYCDbt2/3dBgVSlG3iZ+fH6Ghofj6+harPI9UqIwxy0QkLJ8k/YBP7TdY/yIitUTkSmPMkbKI52h8Cj3fWWaNrFhaFkW4VcXbC19vwdfHyx72ooo97O/ng39VH/z9fKiZNVzVlyD/KtQJqMqh+Ayan0shxL8q3l5aMVNKKaWUKi1xcXEEBAQQFhZW4S+AJyQkEBAQ4OkwKpSibBNjDKdOnSIuLo6GDRsWq7yK2stfPeCgy3icPS1bhUpEHgIeAqvXpNjY2GIVdjw5s1jLlVRaRiZpGWD9r+heWb0YH4Eragh1/b2o6+9FPX8vGtfyIsivYjwel5iYWOzvpTxVljih8sSqcZauyhInVK5YlVLKnZSUlEpRmVIlJyIEBwdz4sSJYudRUStU7vZek2uCMR8CHwK0a9fOFLd7xENnz9No+xqSk5KpVr06xhgMkGkMxoAxzvLINGCwp5M1z55uL2eyhp1pLkzPNIZMY0jPyLU6xeIwEJdoiEvMAC5UzOrVqsZ1TUK4vtnldA+/jGpVvEulvKKqLF15VpY4oeBYMzIzSM1IJS0jjbTMNFIzUknPSCfDZJBpMnP/zcxjuv0301gXHAzG+a/Q2APG/sdh7P9cp23fvp3m9Ztnm54zTRbr35TJnnceaUvbrl27CL8yvEzLKA2VJU6wYn3w2ge5osYVng5FKaWKTStTl46SftcVtUIVB9R3GQ8FDpdVYfVqVePnEdHl+qM6M9OQnplJeoYh3ZFp3a1yZJKekUlKeiZJaQ4SUxycS0knMdVBQoqDhJR0TiWmcexcCnsPnyIp04dTSWlu8z909jxfrTvIV+sOUqOKN7e0upK72l9F2wa1y2X9VNEZY0h2JHPq/ClOpZyy/p4/xenU0ySlJZGYnkhieiIHjh1g8veTSUpPIsWRkq3ilJaRRoYp3h3PMrHC0wEU0i+eDqCQKkucwA3xN2iFSiml1CWholao5gCPi8iXWJ1RxJfV81Oe4uUlVPXypqoPULXoy2dV/s6lpLP3eCK7jyey93giWw/Fs/HAWc6nX/hRnZSWwTfr4/hmfRztGtTmsR5NiA6/TK+8eECmyeRQwiF2nd3FwXMHiUuMIy4hjrjEOI4lHSMlo5APv1b8Z2SVUkopVU4mTZpE9erVue+++7JNnz17NuHh4bRo0aJI+c2ZM4dt27YxatSoIsfyxhtv8OKLLxZ5ucrMIxUqEfkCiAZCRCQOeBnwBTDGTAK+B24B9gDJwP2eiLMyqOnnS+uratP6qgt3nhwZmWyOO8vPO47zw9aj7DuZ5Jy37s8z3D/lV7qFX8bovi1ocrm/J8K+ZBxNOsqvR39l84nN7Di9g91ndpPsSC7TMgWhqndVqnhXcf719fLFW7zx8vKy/kref92lcc07qyIuZP+LuEwT4dixY1xR54rsaV0q8TmnucvbmbYMK/9HDh/hyrpXlln+Bcm5rnk5fPgwdevWLeNoSsfhw4epU72Op8NQSqlLxvDhw91Onz17Nn379nVboXI4HPj4uK8KxMTEEBMTU6xYilqhsh6TMXh5VYzn/4vDU7383V3AfAM8Vk7hXHR8vL1o2yCItg2CGNmrKZvj4vnfL3/y3aZDzme3lu06wc3vLuP53s0Y2qUhXtpTYKlITk9m+aHlrDq8il+P/srBhIMFL+SiqndVgv2CCa4W7Pwb5BdEQJUAavjWIKBKAPt27KNTm07U8K1BNZ9q2SpOVbyr4CM+FeLuY2xsLNFdoz0dRoFiY2OJ7hTt6TAKVFniBCvWRrUaeToMpZSqtJKSkvjLX/5CXFwcGRkZ/P3vf+fOO+/MM/2YMWPw9/dn5MiRzmmrVq1izpw5LF26lLFjxzJjxgweeOABOnfuzMqVK4mJiSE8PJyxY8eSlpZGcHAw06dPp06dOkydOpV169bx3nvvceLECYYPH86BAwcAmDBhAl26dCExMZEnnniCdevWISK8/PLL/Prrr5w/f56oqChatmzJ9OnTeeedd/jkk08AePDBB3n66afZv38/N998M9dffz2rV6/mtttu4+zZs/zrX/8C4KOPPmL79u288847ZbiVS09FbfKnSomIEFW/FlH1azGiVzj//nkPX6w9gDGQnmEYO387K/acZMKdUdSqXsXT4VZKqRmprIhbwYL9C1gat5TzjvP5pg/yCyK8djiNAhsRGhBKqH8ooQGhXFHjCvx9/QusDMX+GUubOvqua6WUUqo8hI2aX2Z573+rj9vpCxYsoG7dusyfb5UdHx9f5Lw7d+5MTEwMffv2ZeDAgc7pZ8+eZelS6zVBZ86c4ZdffkFEmDx5Mv/4xz/45z//mS2fp556imeeeYbrrruOAwcOcNNNN7F9+3Zee+01AgMD2bp1qzOv22+/nffee49NmzYBsH79eqZMmcKaNWswxtChQwe6d+9O7dq12blzJ1OmTOH9998nKSmJyMhI/vGPf+Dr68uUKVP473//W+R19hStUF1Crgysxhv9WzGow1W8MHMrW+Ksf5yxO09wx6TVfPpAe64MrObhKCuPA+cO8MWOL/huz3ckpCe4TePn7cc1l19DuzrtiAiJoGntpoRUC6kQd5CUUkopVTG1atWKkSNH8vzzz9O3b1+6du1aanm73umKi4vjzjvv5MiRI6Slpbl9D9OiRYvYtm2bc/zcuXMkJCSwaNEivvzyS+f02rVzd3y2YsUK+vfvT40aNQAYMGAAy5cvJyYmhgYNGtCxY0cAatSoQY8ePZg3bx7NmzcnPT2dVq1aldo6lzWtUF2CWtYN5Nvhnfnnwp38d9k+AHYfT+T291fx2YMdaHyZPleVn11ndvHhlg9ZuH+hs2tvV40CG9ErrBedruxEREgEVbz1zp9SlZWIfAL0BY4bYyLczBfgXaznfpOBIcaYDeUbpVLqYhMeHs769ev5/vvveeGFF+jVqxejR48ulbyzKjcATzzxBM8++ywxMTHExsYyZsyYXOkzMzNZvXo11aplv+hujCnwAnF+rz5xjQOs5oBvvPEGzZo14/77K1f3CVqhukRV8fHihVua07JeICO+3kR6huFwfAr3Tl7DzEe7cEWgn6dDrHCOJh3l3Q3vMm/fvFzzQv1DubnhzfRu2Jura12td6CUunhMBd4DPs1j/s3A1fanA/CB/VcpdZHIq1leWTp8+DBBQUHcc889+Pv7M3XqVABeeOEF2rdvT//+/QuVT0BAAAkJ7lvRgNWUsF69egBMmzbNbZpevXrx3nvv8dxzzwGwadMmoqKinNMnTJgAWE3+ateuja+vL+np6fj6+tKtWzeGDBnCqFGjMMYwa9YsPvvsM7fldOjQgYMHD7Jhwwa2bNlSqPWrKCpvdxqqVMRcU5dPhlxLdfvFv4fjUxgyZS3nUtI9HFnF4ch0MHnrZG6ddWuuylSXel34oOcHzB8wnyfbPEl47XCtTCl1ETHGLANO55OkH/CpsfwC1BIRz3UbqZS6KGzdupX27dsTFRXF66+/zksvveScfsUVhX/H31133cW4ceNo3bo1e/fuzTV/zJgx3HHHHXTt2pWQkJBs87J+z0ycOJF169YRGRlJixYtmDRpEgAvvfQSZ86cISIigmuuuYYlS5YA8NBDDxEZGcmgQYNo06YNQ4YMoX379nTo0IEHH3yQ1q1b5xnvX/7yF7p06eK2+WBFpneoFF2vvoz3B7XhwWnrcGQadhxN4KkvNvLx4Gsv+d7/dp3ZxUsrXmL76e3ZpkfXj2b4NcNpGdzSQ5EppSqIeoBrd55x9rRs704UkYeAhwAuu+wyYmNjyyu+SiMxMVG3Sw66TXIrr20SGBiY752dspbVE5+rhIQEzp8/T0RERLbYMjIyGDFihDONq8jISNasWeMcnzt3brZ0PXr0YPPmzbnKOXz4MDVq1CAhIYGqVasyefLkXGkA3nvvvVzTX3rpJWcFMCEhgWHDhjFs2LBsaYKDg1m9enWueGNjY3nsscdKvO0zMjKKnEdKSkqx9y2tUCkAoptezlu3RzLyG+sf1ZKdJ/hk5R882PXS7PrYGMOM3TN4c82bpGWmOac3C2rGX6/9K9deca0Ho1NKVSDurjrlemjAGPMh8CFA06ZNTXR0dBmHVflkvbC+2Ja8eWH4+hdKHE9FUOJtchEqr22yfft2AgICyrycolq8eHGuaQkJCaUa66RJk/jiiy+YOXNmuW2Ds2fP0r59e6655hpuvfXWEudXnG3i5+eX792z/GiFSjkNbBvKrmMJfGh3VPH2gh10bBRMRL1AD0dWvtIy0nhl9SvM2TvHOa2KVxUea/0Y97W4Dx8v/WejlHKKA+q7jIcChz0Uy6Vt6VsXhi+SCpVSnjB8+PA8XxRcVmrVqsWuXbvKtczSpM9QqWxG9mpKZKhVgUrPMDz15UbSHJkejqr8xKfG89BPD2WrTDWp1YRvbv2GoRFDtTKllMppDnCfWDoC8caYIwUtpJRS6uKhFSqVTRUfLybe1ZoadicVe08k8fGKPzwcVfk4lnSMe3+4l/XH1jun9Wvcj8/7fE6jWpdm00elLnUi8gWwGmgqInEi8oCIDBeRrMu33wP7gD3AR8CjHgpVKaWUh+jldpVLWEgNnu3VlNfmWS9x+/fPu7mtdd2L+qW/ZxxnGPrjUA4kHHBOe6btM9zf8n7ttU+pS5gx5u4C5hvgsXIKRymlVAWkd6iUW4M7NaBpHethvuS0DMbO217AEpXXieQT/PvYv52VKR/x4R/d/sHQiKFamVJKKaWUUvnSCpVyy8fbi1f7XegSfP7WI2w+eNaDEZWNpPQkHlv8GCccJwCrMjU+ejw3N7zZw5EppZRSSlnGjBnD+PHjARg9ejSLFi1yzvvmm294/fXXcy0TFhbGyZMnOXv2LO+//36pxJGamsqdd95JkyZN6NChA/v37y+VfKdOncrjjz8OZF9Xd/bv309ERAQA69at48knnyyVGEpCK1QqTx0aBdOn1YX3U05cvNuD0ZS+9Mx0RsSOcL5jylu8+Wf0P7nhqhs8HJlSSimllHuvvvoqPXv2dI4vWrSI3r1755m+NCtUH3/8MbVr12bPnj0888wzPP/886WSb3G1a9eOiRMnejQG0AqVKsBTPa8mq9Xb4h3H2RJ38dylGv/reFYevvDSvNGdRtPjqh4ejEgppZRSyvL666/TtGlTevbsyc6dO53ThwwZwrfffgtY783cunUrbdq04dSpU/Tq1YvWrVvz8MMPYz3iCaNGjWLv3r1ERUXx3HPPlSim7777jsGDBwMwcOBAFi9e7CwnS9a7wgYOHEizZs0YNGiQM03WXTOw7i4V9E6xPXv20LNnT6655hratGnD3r17c5XVt29fwLqzNXToUKKjo4mMjMxW0frf//5H+/btiYqK4uGHHyYjI6NE2yEn7ZRC5Su8TgC3tLqS+VusXoAnLt7N5MGV/6W28/fN5/MdnzvHewf2ZsDVAzwYkVJKKaUqrCVvZn/XWX7aDIaYHHdN5jwJG6ZdGO8+Kt/3pa1fv54vv/ySjRs34nA4aNOmDW3bts2VbuPGjURERCAivPLKK1x33XWMHj2a+fPn8+GHHwLw1ltv8dtvv7Fp0ya3ZXXt2pWEhIRc08ePH5/tThjAoUOHqF/fevWej48PgYGBnDp1ipCQkFxx/f7779StW5cuXbqwcuVKrrvuujzXNy+DBg1i1KhR9O/fn5SUFDIzMzl+/Hie6Xfs2MGSJUs4cuQIbdu25ZFHHmHPnj189dVXrFy5El9fXx599FEhPSZYAAAgAElEQVSmT5/OfffdV+R48qIVKlWgJ3tczfdbj2AMLNp+nO1HztH8ypqeDqvYdp/ZzSurX3GO39jgRm4xt3gwIqWUUkqpC5YvX07//v2pXr06ADExMW7TLViwgBtvvBGAZcuWMXPmTAD69OlD7dq1C11WYeW8GwW47cCrffv2hIaGAhAVFcX+/fuLXKFKSEjg0KFD9O/fHwA/P78Cl+nTpw9Vq1YlODiYyy+/nGPHjrF48WLWr1/PtddaNwTOnz/P5ZdfXqRYCqIVKlWgplcE0LvlFfzw21EAPl39J28OaOXhqIonLSONvy77K+cd5wEIqxnGa11e49eVv3o4MqWUUiXSZrCnI1CqVBWmp+GFCxcyderUIi2TU1HuUIWGhnLw4EFCQ0NxOBzEx8cTFBSUa9mqVas6h729vXE4HIB1VyszMxOAlJSUfONyV3kriLtyjTEMHjyYN998s8j5FZZWqFSh3N+lobNCNXvjIUb1bkZgdV8PR1V07218jz1n9wDg5+3HhOsnUMO3hoejUkopVWI5m1gpVZqufyHfJnoFiplYpH20W7duDBkyhFGjRuFwOJg7dy4PP/xwtjTx8fE4HA6Cg4Ody0yfPp2XXnqJH374gTNnzgAQEBDgtsKUpSh3qGJiYpg2bRqdOnXi22+/pUePHkWqxIWFhbF+/XpuvvlmZsyYkW/amjVrEhoayuzZs7nttttITU0t1rNPN9xwA/369eOZZ57h8ssv5/Tp0yQkJNCgQYMi55UXj3RKISK9RWSniOwRkVFu5l8lIktEZKOIbBERbY/lYdeG1abZFdZ7qc6nZ/DN+oMejqjo1h9bz9TfpzrHR7QbQeNajT0XkFJKKaWUG23atOHOO+8kKiqK22+/na5du+ZK89NPP2W7g/Tyyy+zbNky2rRpw8KFC7nqqqsACA4OpkuXLkRERJS4U4oHHniAU6dO0aRJE9555x3eequQz5W5xPjUU0/RtWtXvL29C0z/2WefMXHiRCIjI+ncuTNHjx4tcswtWrRg7Nix9OrVi8jISG688UaOHDlS5HzyZYwp1w/gDewFGgFVgM1AixxpPgQesYdbAPsLyrdt27ampJYsWVLiPMqLJ2L9fM2fpsHz80yD5+eZ7v/42WRkZBa4TEXZpimOFNNnZh8TMTXCREyNMMN+HGYyMy/EX1HiLIzKEqvGWboqS5zGlE6swDpTzuen8vqEh4eXePtcjCrTPl5edJvkVl7bZNu2beVSTkk88MADZvXq1ebcuXOeDqXCKc42cfedF/Zc5Ik7VO2BPcaYfcaYNOBLoF+ONAbI6vUgEDhcjvGpPPSLqkuAn9VKdP+pZJbvOenhiArvk62f8Oe5PwHw9/Xn1S6vFqudsVJKKaVURTB58mQ6duzo6TAUnnmGqh7g2l4sDuiQI80YYKGIPAHUAHrihog8BDwEUKdOHWJjY0sUWGJiYonzKC+eirVjHfjJqpcw6Yf1mMP597hSEbbpifQTfHj4Q+f4zQE3s+PXHexgh3NaRYizsCpLrBpn6aoscULlilVdROY8eWFYn6dSSpUjT1So3N0WyNmNx93AVGPMP0WkE/CZiEQYYzKzLWTMh1jNA2nXrp0p6OVgBcl6EVll4KlYQ66O56d/rwBg00m4ttN11Kia925UEbbp8EXDcWD1LtMyuCV/u+VveHtlb7dbEeIsrMoSq8ZZuipLnFC5YlUXEdd3/GiFSilVjjzR5C8OqO8yHkruJn0PAF8DGGNWA35ACMrjWtatSXgdf8DqnOLH34v+cGB5WnloJSsPrQTAS7z4e6e/56pMKaWUUkopVVyeqFD9ClwtIg1FpApwFzAnR5oDwA0AItIcq0J1olyjVG6JCLe1ruccn7XxkAejyV9GZgb/XP9P53j/Jv1pGdzSgxEppZRSSqmLTbk3+TPGOETkceBHrB7/PjHG/C4ir2L1pDEHGAF8JCLPYDUHHGL3tKEqgNui6jHux50YAyv3nOTYuRTq1Cz47dXlbc7eOew+sxuAaj7VeCzqMQ9HpJRSSqmLzcFzB5m2bRrz9s0jOT2Z6r7V6duoL4NbDKZ+zfoFZ6AqPY+8h8oY870xJtwY09gY87o9bbRdmcIYs80Y08UYc40xJsoYs9ATcSr36taqRseG1kvkMg3M3VzxOmFMzUjlvU3vOceHtBzCZdUv82BESimllLrYLI9bzoC5A5ixawZJ6UkYDEnpSczYNYMBcwewPK7wL83Nyd/fv8A0Dz74IDt2WJ1svfHGG9nmde7cudhlHD16lLvuuovGjRvTokULbrnlFnbt2lWIqPMXGxtL3759AZgzZ47zPVazZ89m27ZtznSjR49m0aJFJS6vvHikQqUqv35RdZ3DFfE5qm93fcvx5OMABPsFM6TlEM8GpJRSSqmLysFzB3l26bOkOFJwGEe2eQ7jIMWRwrNLn+XguYN55FBykydPplmzZkDuCtWqVauKlacxhv79+xMdHc3evXvZtm0bb7zxBseOHStxvK5iYmIYNWoUkLtC9eqrr2Z7aXFFpxUqVSw9W9TBy+6vcd2fZziRkOrZgFykZqTyydZPnOPDIodR3be6ByNSSiml1MVm2rZpODIc+aZxZDj4dNunJSonq+fUgQMH0qxZMwYNGkTWkzDR0dFs2LCBUaNGcf78eaKiohg0aBBw4e5TYmIiN9xwA23atKFVq1Z89913+Za3ZMkSfH19GT58uHNaVFQUXbt2xRjDc889R0REBK1ateKrr74qMMYFCxbQrFkzrrvuOmbOnOnMc+rUqTz++OOsWrWKOXPm8NxzzxEVFcXevXsZMmQI3377LQCLFy+mdevWtGrViqFDh5Kaav3mDAsL4+WXX3auV9adOk/QCpUqlhD/qrQLCwLAGPhpW+letSiJGbtmcPy8dXcqpFoIt199u4cjUkoppdTFZt6+ebnuTOXkMA7m7ZtX4rI2btzIhAkT2LZtG/v27WPlypXZ5r/11ltUq1aNTZs2MX369Gzz/Pz8mDVrFhs2bGDJkiWMGDGC/Lom+O2332jbtq3beTNnzmTTpk1s3ryZRYsW8dxzz3HkyJE8Y0xJSWHYsGHMnTuX5cuXc/Ro7lZNnTt3JiYmhnHjxrFp0yYaN27snJeSksKQIUP46quv2Lp1Kw6Hgw8++MA5PyQkhA0bNvDII48wfvz4gjdkGdEKlSq2m1pe4RyuKM3+0jLS+Pi3j53jD0Q8gJ9PxeswQymllFKVW3J6cqHSJaUnlbis9u3bExoaipeXF1FRUezfv7/QyxpjePHFF4mMjKRnz54cOnSo2M33VqxYwd133423tzd16tShe/fu/Prrr3nGuGPHDho2bMjVV1+NiHDPPfcUqbydO3fSsGFDwsPDARg8eDDLli1zzh8wYAAAbdu2LdI2KW1aoVLF1qtFHefwqr0nOZeS7sFoLPP2zXM+OxVSLYSB4QM9HJFSSimlLkaFfZyghm+NEpdVtWpV57C3tzcOR/53xlxNnz6dEydOsH79ejZt2kSdOnVISUnJM33Lli1Zv36923n53dnKK0YRKXSsRSnPtcyibpPSphUqVWz1g6oTUa8mAOkZhiU7jns0nkyTybTfpznH721xr96dUkqpS0X3URc+SpWDvo364iP5v4HIR3zo26hvucTj6+tLenrui9vx8fFcfvnl+Pr6smTJEv7888988+nRowepqal89NFHzmm//vorS5cupVu3bnz11VdkZGRw4sQJli1bRvv27fPMq1mzZvzxxx/s3bsXgC+++MJtuoCAABISEtwuv3//fvbs2QPAZ599Rvfu3fON3xO0QqVK5KYWF5r9efo5qhWHVrAvfh9gXQ26I/wOj8ajlFKqHF3/woWPUuVgcIvB+HgXUKHy9uG+FveVSzwPPfQQkZGRzk4psgwaNIh169bRrl07pk+f7uwVMC8iwqxZs/jpp59o3LgxLVu2ZMyYMdStW5f+/fsTGRnJNddcQ48ePfjHP/7BFVdckWdefn5+fPjhh/Tp04frrruOBg0auE131113MW7cOFq3bu2sfGUtP2XKFO644w5atWqFl5dXts4yKopyf7Gvurjc0LwO//zJei/B8t0ncWRk4uPtmXr61N+nOodvv/p2AqoEeCQOpZRSSl386teszzvd3+HZpc/iyHBk66DCR3zw8fbhne7vFPvlvomJiYDVk190dLRz+nvvXXjPZmxsrPPOzttvv83bb7+da/mQkBBWr16dbxk51a1bl6+//trtvHHjxjFu3Lhs0/KLsXfv3m574BsyZAhDhgwBoEuXLtm6TZ86dapz+IYbbmDjxo25lnd9Zqpdu3bExsa6jbc86B0qVSLNrwygTk2r/Wr8+XQ2x531SBzbTm3j16PWQ5He4s09zYv20KNSSimlVFF1De3KzFtnMjB8IP6+/giCv68/A8MHMvPWmXQN7erpEFU50DtUqkREhO7hl/H1ujgAYneeoG2DoHKP44sdF9rk3hR2E1f6X1nuMSillFLq0lO/Zn3+1vFv/K3j3zwdivIQvUOlSiy66eXO4aW7TpR7+WdTzvLDHz84x/+v+f+VewxKKaU87PM7L3yUUqoc6R0qVWJdmoTg7SVkZBq2xMVzMjGVEP+qBS9YSmbvmU1qhvXW7OZBzYkMiSy3spVSSlUQuxZ4OgKl1CVKK1SqxAKr+dL2qtqs3X8agGW7TjCgTWi5lJ1pMvlq51fO8bua3VWi9x2o0pWenk5cXFy+77vwtMDAQLZv3+7pMApUWeKEosXq5+dHaGgovr6+ZRyVUkopVTa0QqVKRfemlzkrVLE7y69CterwKuISree3alapyc0Nby6XclXhxMXFERAQQFhYWIWt6CYkJBAQUPF7hKwscULhYzXGcOrUKeLi4mjYsGE5RKaUUqUv7cABTk2Zwrk5c8lMTsarenVqxtxK8P33U+WqqzwdnioH+gyVKhXdwy9zDq/ae6rAN1uXlhm7ZjiH+zXpRzWfauVSriqclJQUgoODK2xlSnmWiBAcHFyh72AqpVR+EpctY1+/2zj7zbdkJiWBMWQmJXH2m2/Z1+82EpctK3be3t7eREVFOT/79+9n3bp1PPnkk8XOMywsjJMnT+Zej8REHn74Yed7p7p168aaNWuKXU6W/fv3ExERAZAt9tjYWFatWuVMN2nSJD799NMSl+cpeodKlYoWV9YksJov8efTOZmYyp7jiVxdp2yvpp88f5LYg7HO8YHhA8u0PFU8WplS+dH9QylVWaUdOEDcU09jzp/PPdPhwDgcxD31NI2+m12sO1XVqlVj06ZN2aaFhYXRrl274oacpwcffJCGDRuye/duvLy82LdvX6k3M2/Xrp0z9tjYWPz9/encuTNAhXxZb1HoHSpVKry8hI6NLnSXvnrfqTIvc97eec6X6EVdFkWjwEZlXqZSSimlFMCpKVMw6en5pjHp6ZyaOq3UyoyNjaVv374AjBkzhqFDh3LLLbfQqFEjJk6c6Ex322230bZtW1q2bMmHH36Yb5579+5lzZo1jB07Fi8vq2rQqFEj+vTpA8A777xDREQEERERTJgwAbDuPDVv3pxhw4bRsmVLevXqxXm7Yrl+/XquueYaOnXqxH/+859cse/fv59Jkybxr3/9i6ioKJYvX86YMWMYP348AJs2baJjx45ERkbSv39/zpw5A1gvD37++edp37494eHhLF++vDQ2aanQCpUqNZ0bhziHV+0p2wqVMYaZe2Y6xwdcPaBMy1OVl7smEyU1e/bsbG90Hz16NIsWLSpxvsnJyQwaNIhWrVoRERHBddddl+db7MtDfuuZV7ORMWPGZDupK6XUxercnLngcOSfyOHg3Jw5xcr//PnzznNX//793abZsWMHs2bNYu3atbzyyiuk2xW8Tz75hPXr17Nu3TomTpzIqVN5/y77/fffiYqKwtvbO9e89evXM2XKFNasWcMvv/zCRx99xMaNGwHYvXs3jz32GL///ju1atVixgzrMYz777+fiRMnsnr1arflhYWFMXz4cJ555hk2bdpE167ZX35833338fbbb7NlyxZatWrFK6+84pzncDhYu3YtEyZMyDbd07TJnyo1nRsHO4d/+eMUmZll9xzV5hOb+SP+DwCq+1TnprCbyqwsVbm5azLhylHQydCN2bNn07dvX1q0aAHAq6++Wuz4XL377rvUqVOHrVu3ArBz506P9n5XVuuplFIXg8zk5MKlS0oqVv4Fnb8A+vTpQ9WqVQkICODyyy/n2LFjhIaGMnHiRGbNmgXAwYMH2b17N8HBwfnm5c6KFSvo378/NWrUAGDAgAEsX76cmJgYGjZsSFRUFABt27Zl//79xMfHc/bsWbp37w7Avffeyw8//JBn/jnlXH7w4MHccccdzvkDBgzIVl5FUeIKlYiEA88BDVzzM8b0yGeZ3sC7gDcw2Rjzlps0fwHGAAbYbIzRt7VWcE0u9yfEvyonE1M5m5zO9qPnyqys2XtmO4d7N+xNdd/qZVaWKh1ho+aXWd773+pTpPRTp05l/vz5pKSkcO7cOebPn0+/fv04c+YM6enpjB07ln79+gHw6aefMn78eESEyMhIHnnkEebMmcPSpUsZO3YsM2bM4LXXXqNv374MHDiQxYsXM3LkSBwOB9deey0ffPABVatWJSwsjMGDBzN37lzS09P55ptvaNasWba4jhw5QoMGDZzjTZs2tdZv/35uueUW592i8ePHk5iY6LwbNGnSJHx8fGjRogVffvkliYmJPPHEE6xbtw4R4eWXX+b2229n4cKFvPzyy6SmptK4cWOmTJmCv78/YWFh3HnnnSxZsgSAzz//nOPHj+e7ngDjxo3LtkyTJk2yrc/evXt57LHHOHHiBNWrV+ejjz7Ktc5KKVVZeVWvXqjKkpddGSkLVateeO+nt7c3DoeD2NhYFi1axOrVq6levTrR0dH5dv7TsmVLNm/eTGZmprPJX5b8OhnLWfb58+cxxpTps7FZZWata0VRGk3+vgE2AC9hVayyPm6JiDfwH+BmoAVwt4i0yJHmauAFoIsxpiXwdCnEqcqYiNDJ5S7V6r1l0+wvLSONhX8udI7f1uS2MilHXRzyajKxevVqpk2bxrx58/Dz82PWrFls2LCBJUuWMGLECIwx/P7777z++uv8/PPPbN68mXfffZfOnTsTExPDuHHj2LRpE40bN3bmmZKSwpAhQ/jqq6/YunUrDoeDDz74wDk/JCSEDRs28MgjjzjbirsaOnQob7/9Np06deKll15i9+7dBa7fW2+9xcaNG9myZQuTJk0C4LXXXiMwMJCtW7eyZcsWevTowcmTJxk7diyLFi1iw4YNtGvXjnfeeceZT82aNVm7di2PP/44Tz/9dL7rmdcyOT300EP8+9//Zv369YwfP55HH320wPVRSqnKombMreBTwL0JHx9qxsSUT0C2+Ph4ateuTfXq1dmxYwe//PJLvukbN25Mu3btePnll50VqN27d/Pdd9/RrVs3Zs+eTXJyMklJScyaNStXEz1XtWrVIjAwkBUrVgAwffp0t+kCAgJISEjINT0wMJDatWs7n4/67LPPnHerKrLSaPLnMMZ8UHAyp/bAHmPMPgAR+RLoB2xzSTMM+I8x5gyAMeZ4KcSpykGnRsHM3XwYsCpUTcJKv4zlcctJSLP+Edbzr0fUZVGlX4i6aOTVZOLGG28kKCiIhIQEjDG8+OKLLFu2DC8vLw4dOsSxY8f4+eefGThwICEh1vOBQUFBufJxtXPnTho2bEh4eDhgNVX4z3/+46xsuDZVmDlzZq7lo6Ki2LdvHwsXLmTRokVce+21rF69mmrV8n4dQGRkJIMGDeK2227jttusiwuLFi3iyy+/dKapXbs28+bNY9u2bXTp0gWAtLQ0OnXq5Exz9913O/8+88wz+a5nYZZJTExk1apV2ZpqpKamFipfpYql7wRPR6AuMcH330/87O8w+dwpEV9fgocMLseooHfv3kyaNInIyEiaNm1Kx44dC1xm8uTJjBgxgiZNmlC9enWCg4MZN24cbdq0YciQIbRv3x6wegNs3bp1vs3tpkyZwtChQ6levTo33eT+kYxbb72VgQMH8t133/Hvf/8727xp06YxfPhwkpOTadSoEVOmTCn8yntIaVSo5orIo8AswHm2NMacziN9PeCgy3gc0CFHmnAAEVmJ1SxwjDFmQc6MROQh4CGAOnXqEBsbW8xVsCQmJpY4j/JSUWP1Tsp0Dq/cfZyYYFPqcU49MdU5HOEVwdKlS0ucZ0Xdnu5UllgTExMJDAx0XoHa+rduZVaWu6tc+c1PSUnB19eXhIQEMjIy+Pjjjzly5AixsbH4+voSERHByZMnOX/+PGlpabmWT09P5/z5887pWeOJiYlkZGQ4pycnJ+NwOJyVtvT0dBISEkhJSSE1NTXPuG+88UZuvPFGHA4Hs2bNYsCAAWRmZjrTx8fHO/P98ssvWblyJd9//z2vvPIKa9euJSMjg6SkpGz5JycnEx0dnevElBVbVvqsB5qzht2tZ37LpKam4u3tTXx8PIGBgbl6YXK3zikpKZVin1YVXLv7PR2BusRUueoqQt+dYHWdnp6evYMKHx/E15fQdycU++W+7jolio6OJjo6GrA6AYILx9XffvvNmS6v55byqgjVrFmTjz76yO28Z599lmeffTbbtLCwsGzljRw50jnctm1bNm/e7BzPitM19vDwcLZs2eJM43rXKyoqyu1dNdfzREhIyMX1DBWQVe12beZngLz6sHbXsDJnA00f4GogGggFlotIhDHmbLaFjPkQ+BCgXbt2JutLKq7Y2FhKmkd5qaixGmOYsOVnjsSnkJIBpzKq0a8U40xIS2DEVyOc449e/yiNapW8u/SKuj3dqSyxxsbG4ufnR0BA2b6PrDByxuDn50eVKlWcTQ5SU1OpW7cuQUFBLFmyhAMHDuDv70+fPn3o378/o0aNIjg4mNOnTxMUFERQUBAOh8OZr6+vL9WqVaNt27YcPHiQY8eO0aRJE2bMmMENN9xAQEAAIoK/vz8BAQHUqFEDb2/vXHGtXLmSFi1aULt2bdLS0tizZw+9evWicePGnDhxgrS0NPz9/fnpp5/o3bs3NWrU4MCBA/Tp04devXoRGhqKiNC7d2+mTp3q7N72zJkzXH/99YwcOdIZW3JyMnFxcYSHhyMizJ8/n1GjRvG///2Pzp07ExAQkOd6Zq2Pu2WqVq2Kl5cX9erVo1GjRixYsIA77rgDYwxbtmzhmmuuyfX9+Pn50bp167L46pVSqkz5d+tGo+9mc2rqNM7NmUNmUhJeNWpQMyaG4CGDi12ZUpVLiStUxpiGRVwkDqjvMh4KHHaT5hdjTDrwh4jsxKpg/VrsQFW5yHqOauaGQwBsO51Rqvkv+nMRaZlpADQPal4qlSmlBg0axK233kq7du2IiopydpzQsmVL/va3v9G9e3e8vb1p3bo1U6dO5a677mLYsGFMnDiRb7/91pmPn58fU6ZM4Y477nB2SlGUlxXu3buXRx55BGMMmZmZ9OnTh9tvvx0R4fnnn6dDhw40bNjQGV9GRgb33HMP8fHxGGN45plnqFWrFi+99BKPPfYYEREReHt78/LLLzNgwACmTp3K3Xff7Wx6N3bsWGfzxNTUVDp06EBmZiZffPEFQJ7rmcXdMq6mT5/OI488wtixY0lPT+euu+5yW6FSSqnKrMpVV3Hl6L9z5ei/ezoU5SGSX+8dhcpAxBd4BMhqzxML/NeuDLlL7wPsAm4ADmFVkv7PGPO7S5rewN3GmMEiEgJsBKKMMXn2ctCuXTuzbt26Eq1LZbnyDxU71m/WHeS5b63buBHB3sx7rnep5f3gjw+y5ugaAEa2G8nglqXTLrkib8+cKkussbGx1KlTh+bNm3s6lHwlJCRUiLtoBSnLOMPCwli3bp3zWbGSKmqs27dvz7WfiMh6Y0y7UgmogmnatKnZuXOnp8OocCrLsa086TbJrby2yfbt22nWrFmZ9lhXWirLeaw8FXWbGGPYsWNHsc9FpdHk7wPAF3jfHr/Xnvagu8TGGIeIPA78iPV81CfGmN9F5FVgnTFmjj2vl4hsAzKA5/KrTKmKxbWnv11nMkhzZFLFp+QdSh5LOsbao2sBEITeYaVXUVNKKVXJ/dflOc2Hl3kuDnVR8PPz49SpUwQHB1eKSpUqPmMMp06dws/Pr9h5lEaF6lpjjGsbjp9FZHOeqQFjzPfA9zmmjXYZNsCz9kdVMqG1q3NVUHUOnE4mLRM2HTxL+4b5945WGAv2L8DYj9u1v6I9dWrUKXGeSqm8H1JWqlI5ku9PD6WKJDQ0lLi4OE6cOOHpUAqUkpJSosrAxaio28TPz4/Q0NBil1caFaoMEWlsjNkLICKNsO4qqUtY58bBHDhtvUF89d5TpVKhmr/vwoth+zQq2otclVJKKaUKy9fXl4YNi9pNgGfExsZqxz45lPc2KY0X+z4HLBGRWBFZCvwMjChgGXWRc232t2rvyRLnt+/sPraf3g5AFa8q9GzQs8R5KqWUUkopVVKl0cvfYhG5GmiK1SX6DmOMvr3xEtep0YUK1cYDZ0lJz8DP17vY+c3bN8853L1+dwKq6MOXSimllFLK84p9h0pEeth/BwB9gCZAY6CPPU1dwi6v6Uejy2oAkJaRycYDZwtYIm/GGBbsv/Be5z4NtbmfUkoppZSqGErS5K+7/fdWN5++JYxLXQQ6NLxwl2rNH8XvpHH76e0cTDgIgL+vP11DuxawhFIXeHt7ExUV5fyURgcMs2fPZtu2bc7x0aNHs2jRohLnGxsbS9++BR8+J06cSPPmzRk0aFCRy5gwYQLJycnO8VtuuYWzZ4t/wUMppZS61BW7yZ8x5mV78FVjzB+u80SkcjzFp8pUx0ZBfLH2AABr9p0udj4L9y90DkfXj6aKd5USx6YuHdWqVWPTpk15znc4HEXOc/bs2UN/7JgAACAASURBVPTt25cWLVoA8OqrrxY7vuJ4//33+eGHH4r1wPSECRO45557qF69OgDff/99AUsopZRSKj+l0cvfDKBNjmnfAm1LIW9Vibneodpw4Aypjgyq+hTtOSpjDAv/vFCh6tWgV6nFp8rZmMAyzDu+SMmnTp3K/PnzSUlJ4dy5c8yfP59+/fpx5swZ0tPTGTt2LP369QPg008/Zfz48YgIkZGRPPLII8yZM4elS5cyduxYZsyYwWuvvUbfvn0ZOHAgixcvZuTIkTgcDq699lo++OADqlatSlhYGIMHD2bu3Lmkp6fzzTff0KxZs7xXacwYDhw4wL59+zhw4ADDhw/nr3/9K8OHD2ffvn3ExMQwdOhQHnroIZ544gm2bt2Kw+FgzJgx9OvXj4yMDJ5//nl+/PFHRIRhw4ZhjOHw4cNcf/31hISEsGTJEudLfceNG0eDBg149NFHneUHBAQwYsQIxo0bx9dff01qair9+/fnlVdeKf53pZRSSl1kil2hEpFmQEsgMMczUzUB7QxfcUWgH3WqC8eSDamOTDYfjC9y9+k7Tu9wNver4VuDzvU6l0Wo6iJ2/vx5oqKiAGjYsCGzZs0CYPXq1WzZsgVfX1/8/PyYNWsWNWvW5OTJk3Ts2JGYmBi2bdvG66+/zsqVKwkJCeH06dMEBQURExPjrEC5SklJYciQISxevJjw8HDuu+8+PvjgA55++mkAQkJC2LBhA++//z7jx49n8uTJ+ca+Y8cOlixZQkJCAuHh4TzzzDNMmjSJBQsWsGTJEkJCQnjxxRfp0aMHn3zyCWfPnqV9+/b07NmTTz/9lD/++IONGzfi4+PjjP2dd95xLuvqrrvu4umnn3ZWqL7++msWLFjAwoUL2b17N2vXrsUYQ0xMDMuWLaNbt27uQlZKKaUuOSW5Q9UU61mpWljPTWVJAIaVJCh18Wga5M2xZKtJ1Zp9RX8flevdqej60VT1rlqq8amLX15N/m688UaCgoJISEjAGMOLL77IsmXL8PLy4tChQxw7doyff/6ZgQMHOisfQUH57787d+6kYcOGhIeHAzD4/9m78/iqynPt4787AyRACKMok+AACgKCyCAqUbFgRayKglKLQ4taW23tcPS1DsfqObbaWlF6WrVOSKUUraJVQCxxFgEBmURGJYyBACZAyHS/f6ydZGeCQHb2TsL1/Xy2WcOz1r72Q5DcWc961vjxTJo0qaSguvzy4HdPZ5xxBq+++uohs1988cU0btyYxo0b07ZtW7Zt21bhwYOzZ89mxowZPProo0BQ1H3zzTfMmTOHm2++mYSEhGpl79u3L9u3b2fz5s1kZmbSsmVLOnfuzMSJE5k9e3bJ8zxycnJYvXq1CioREZGQmtxD9TrwupkNdvdPIphJGpDuLeN4PyNYnrc+i58exrHuXub+KQ33q+cOc1hebWvatGnJ8pQpU8jMzGThwoUkJibSpUsXcnNzcXfMrNrndPeD7m/cOPiFQHx8fLXu3Spuf7Bj3J1XXnmF7t27V9h+ONkBRo8ezfTp09m6dStjx44tOc9dd93FTTfddFjnEom6q6fGOoGIHKUi8WDfm82sRfGKmbU0s2cjcF5pAE5pVXrP1MKvd5FfWFTtY7/a9RXfZAeTWjRJaMKQDkMink8EYM+ePRxzzDEkJiYyd+5cvv76awAuuOACpk2bxs6dwSyVWVnB5CopKSlkZ2dXOM8pp5zChg0bWLNmDQCTJ09m6NChFdpF0vDhw3niiSdKirlFixYB8J3vfIe//OUvJUXYobJDMOxv6tSpTJ8+vWQ44/Dhw3n22WfJyckBYNOmTWzfvr1WP5PIEel+UelLRCSKIlFQ9Xb3kjl33X0X0DcC55UGoHVyHB1bJgOwP7+QLzKqf5Vi1oZZJctDOw3VcD+pNePGjWPBggX079+fKVOmlEwW0bNnT+6++26GDh1Knz59uOOOO4Cg8HjkkUfo27cva9euLTlPUlISzz33HFdeeSW9evUiLi6Om2++uVaz33PPPeTn59O7d29OO+007rnnHgB++MMf0rlzZ3r37k2fPn34+9//DsCECRO46KKLOO+88yqcq2fPnmRnZ9OhQweOO+44ICjMrrnmGgYPHkyvXr0YPXp0lQWZiIjI0cgONUTlkCcwWwKkhQopzKwV8J6794pAvmrr37+/L1iwoEbnSE9PJy0tLTKBall9yZqens4b21vyyufBuL9fj+jOj9NOOuRx7s6o10ax4dsNAPwp7U9ccPwFtZqzPvQn1J+s6enptGvXjlNPPTXWUQ4qOzublJSUWMc4pPqSEw4/68qVKyt8n5jZQnfvH+lsdUH37t191apVsY5R59SX/7dFk/qkIvVJReqTiiLVJ9X9tygSV6j+AHxsZr81s98CHwO/j8B5pYEYeELpzfDVfR7VV7u+KimmNNxPREREROqqGj+Hyt1fNLOFwHmAAZe7+4oaJ5MGY/AJpc+jWrAhi4LCIhLiD17Lh8/uN7TjUJISNBO/iIgcxKNhE7P8UlcARSR6InGFCndfDkwDXgdyzKxzJM4rDUPHlsm0Tw0Kor15hSzf/O1B21eY3a+LZvcTkdgwsxFmtsrM1pjZnZXs72xmc81skZl9YWbfjUVOAXK2lr5ERKKoxgWVmY0ys9XAeuA9YAPwdk3PKw2HmTEw7CrVvPU7D9p+9e7VJcP9khOSObvD2bUZT0SkUmYWD0wCLgJ6AFebWY9yzX4DTHP3vsBY4M/RTSkiIrEWiStUvwUGAV+5e1fgAuCjCJxXGpCBYQ/0/fQQ91GFX53ScD8RiaEBwBp3X+fuecBU4NJybRxoHlpOBTZHMZ+IiNQBNb6HCsh3951mFmdmce4+18x+d7ADzGwE8DgQDzzj7g9X0W408E/gTHev2RR+ElPhV6jmr8+isMiJj6v40FF3L3P/lIb7iUgMdQA2hq1nAAPLtbkfmG1mPwWaAsMqO5GZTQAmALRt25b09PRIZ633cnJyatQvaWHLDaV/a9onDZH6pCL1SUXR7pNIFFS7zawZ8D4wxcy2AwVVNQ4bQnEhwT9O881sRvmJLMwsBbgNmBeBjBJjXVo34ZiUxmzPPkD2gQJWbvmW0zqkVmi3Zvca1u9ZD2i4n0RGfHw8vXr1oqCggK5duzJ58mRatGhx6APrmO9+97s89thj9O/fIGcSr6sq/tYnuCIV7mrgeXf/g5kNBiab2WnuXuYp5u7+FPAUBNOma4rjimo8zXF66WJD6V9Nh12R+qQi9UlF0e6TSAz5uxTYB/wcmAmsBS45SPvqDKGAYCjh74HcCGSUGDMzBoVdpfp47Y5K273z9Tsly+d0OIfkhORazyYNW3JyMosXL2bZsmW0atWKSZMmxTpSiYKCKn/3JHVDBtApbL0jFYf03UgwKRPu/gmQBLSJSjoREakTanSFKnS16XV3HwYUAS9U47BDDqEws75AJ3d/08x+WZOMUncMOak1M5YEP4t8tGYnE849sUIbze7XcPV6ofae9b10/NJqtRs8eDBffPFFyfojjzzCyy+/TEFBAZdddhn//d//DcCLL77Io48+ipnRu3dvJk+ezNdff80NN9xAZmYmbdu25bnnniM1NZU+ffqwbt064uLi2LdvH927d2fdunV888033HrrrWRmZtKkSROefvppTjnlFK677jpatWrFokWL6NevHw888AA//elPWbp0KQUFBdx///1ceuml7N+/n+uvv54VK1Zw6qmnsn///lrpOzmo+cDJZtYV2EQw6cQ15dp8Q3Dv8PNmdipBQZUZ1ZQiIhJTNSqo3L3QzPaZWaq776nmYQcdQmFmccBjwHWHPFHYmPR27drVeKxkfRqDWl+yhueM21c6AuaTtZnM+c9cEsLuo9qSt4W1e9YCkGiJsA7SN6RHPWddV1+y5uTkkJqaSnZ2dq2/16HeIzs7m8LCQmbNmsW1115LdnY27777LitWrODdd98lLi6OMWPGMHPmTFq1asVvf/tb3nnnHVq3bk1WVhbZ2dncfPPNXHnllYwbN47Jkyfz4x//mJdffpmePXvy9ttvc+655/LKK69w/vnnk5uby4033shjjz3GSSedxPz587npppt48803yc/PZ8WKFfzrX/8iPj6e++67j8GDB/P444+ze/duzjvvPAYOHMhzzz1HYmIiH330EcuWLeOcc85h7969UenPmiosLDysnLm5uXXye9rdC8zsJ8Asgnt+n3X35Wb2ALDA3WcAvwCeNrOfE/xbdp27lx8WKCIiDVgk7qHKBZaa2TvA3uKN7n5bFe0PNYQiBTgNSDczgGOBGWY2qvzEFOFj0vv371/jMen1aQxqfclaPufEZf9hY9Z+8goh9YQ+nNmldPa/Jxc9CVuC5bTOaQxPGx6znHVZfcmanp5OUlISKSkptf5eB3uP/fv3c84557BhwwbOOOMMLr30UuLj4/nwww+ZO3cuQ4cOJS4ujpycHDZt2sTq1au56qqr6NKlS5lzz58/nxkzZpCYmMiPfvQj7r33XlJSUhg3bhxvvPEGF198Ma+//jo//vGPMTPmzZvH9ddfX5LjwIEDpKSkkJiYyNVXX11yH1d6ejozZ84sGYqYl5fHrl27mDdvHrfddhspKSkMHjyY0047jaZNm0alP2sqOzv7sHImJSXRt2/fWkx05Nz9LeCtctvuDVteAQyJdi4REak7IlFQ/Tv0qq6DDqEIXekqGX9uZunALzXLX8Mw5MQ2TM0KRnx+tGZHSUHl7szaMKuk3UVdL4pJPqk91R2WF2nF91Dt2bOHkSNHMmnSJG677TbcnbvuuotrrrmmzA//EydOJPTLnIMqbjNq1CjuuususrKyWLhwIeeffz579+6lRYsWLF68uNJjmzZtWrLs7rzyyit07969yvcQERGRuuuIJ6Uws84A7v5CZa+qjnP3AqB4CMVKggciLjezB8xs1JHmkfph8IlhE1OsKX3A75dZX5Y8zLdJQhPO6XBOtKNJA5eamsrEiRN59NFHyc/PZ/jw4Tz77LPk5OQAsGnTJrZv384FF1zAtGnT2Lkz+P7Mygqem3bWWWcxdepUAKZMmcLZZwczUDZr1owBAwZw++23M3LkSOLj42nevDldu3bln//8JxAUTUuWLKk01/Dhw3niiScoHiW2aNEiAM4991ymTJkCwLJly1i2bFltdItIwzEhvfQlIhJFNblC9RrQD8DMXnH3K6p74KGGUJTbnlaDjFLHnHVi6eRXizbuYl9eAU0aJTBzw8yS7ed1Pk8P85Va0bdvX/r06cPUqVO59tprWblyJcOGDSMuLo5mzZrx0ksv0bNnT+6++26GDh1KfHw8ffv25fnnn2fixInccMMNPPLIIyWTUhQbM2YMV155ZZn7gKZMmcItt9zCgw8+SH5+PmPHjqVPnz4VMt1zzz387Gc/o3fv3rg7Xbp04c033+SWW27h+uuvp3fv3px++umcccYZ0egikfqrfd0cNioiDV9NCqrwsSgn1DSIHB3apjSme7sUVm3LJr/Q+Wx9FkO7tS0z3G9ElxExTCgNTfEVqGJvvPFGyfLtt9/ODTfcUOF+n/HjxzN+/Pgy27p06cJ//vOfSt9j9OjRlJ+HoGvXrsycObNC2+eff77MenJyMn/9618rtEtOTi65IgaHf1+SiIiIREdNnkPlVSyLHNRZJ5UO+/tg9Q6W7ljKppxNAKQkpnBW+7NiFU1ERERE5LDUpKDqY2bfmlk20Du0/K2ZZZvZt5EKKA3P0G5tS5bTV20vM9zvguMvoFF8o1jEEhERERE5bEc85M/d4yMZRI4eg05oTeOEOA4UFLE2M5u31pUWVBru1/C4u2arkyrpkU0SMfenhi1X99GYIiI1V5MrVCJHJCkxnkEnBMP+4pO/ZmduJgAtG7dkwHEDYhlNIiwpKYmdO3fqh2aplLuzc+dOkpI0CY2IiNRfkXgOlchhS+velve+yiSheelU0sOOH0ZiXGIMU0mkdezYkYyMDDIzM2MdpUq5ubn14gf6+pITDi9rUlISHTt2rOVEIiIitUcFlcREcB9VIQnNS5+to4f5NjyJiYl07do11jEOKj09nb596/50y/UlJ9SvrCIiIjWlIX8SE13bNOW4YzcTlxBMad08sRX9jukX41QiIiIiIodHBZXEhJnR6pjSq1Pt4gcQH6d5TkRERESkflFBJTGxL38f2wo/K1nfsqmHJi4QERERkXpHBZXExLvfvMuBov0AFB5oy5btbVm5JTvGqUREREREDo8KKomJGWtnlCwX7OkHGLOWb41dIBERERGRI6CCSqJu696tzNsyDwDDyN8TTEahgkpERERE6hsVVBJ1b657Eye4X6p/uwEk0hKAL7dm883OfbGMJiIiIiJyWPQcKomqIi/i1dWvlqxfdvKl2NY2vPvldiC4SvWjc0+IVTwREamv7vgy1glE5CilK1QSVfO3zmdj9kYAUhqlcOHxFzK857El+2cs2RyraCIiUp81P670JSISRSqoJKqmfzW9ZPmSEy4hKSGJ4T2PpVF88K24dNMeVm/TbH8iIiIiUj+ooJKoycrNYs43c0rWr+h2BQCpTRIZ1uOYku2vLtoU9WwiIiIiIkdCBZVEzYw1MygoKgCgT9s+dGvZrWTfZX07liy/vmgTRUV6yK+IiByGb7eUvkREoigmBZWZjTCzVWa2xszurGT/HWa2wsy+MLN3zez4WOSUyCksKmTqqqkl66O7jS6zf2i3trRskgjA5j25fLp+Z1TziYhIPffHU0pfIiJRFPWCyszigUnARUAP4Goz61Gu2SKgv7v3BqYDv49uSom09I3pbMoJhvKlNk5leJfhZfY3SohjVJ/2JevTF2ZENZ+IiIiIyJGIxRWqAcAad1/n7nnAVODS8AbuPtfdix9I9CnQEanXXlzxYsnyVd2uIjkhuUKby/uV/jG/+cUWsvbmRSWbiIiIiMiRisVzqDoAG8PWM4CBB2l/I/B2ZTvMbAIwAaBdu3akp6fXKFhOTk6NzxEt9SVrTk4OL856kc+3fw5AHHF0zupcaXZ3p2vzONZ/W0ReQRH/MzWdkSc2ilrO+tCfUH+yKmdk1ZecUL+yioiI1FQsCiqrZFulMxCY2feB/sDQyva7+1PAUwD9+/f3tLS0GgVLT0+npueIlvqSNT09nQ/jPyxZv+iEi/jeOd+rsv2u1AzumLYEgA+3xfO/151LYnztX0itL/0J9SerckZWfckJ9SuriIhITcViyF8G0ClsvSNQ4WmuZjYMuBsY5e4HopRNIiwzP5OZ62eWrF976rUHbX9x7+No06wxAFu/zWXW8q21mk9EREREpCZiUVDNB042s65m1ggYC8wIb2BmfYG/EhRT22OQUSJk9p7ZFHohAAOPG0jPNj0P2r5xQjzjBnYuWX/mg/W4awp1EREREambol5QuXsB8BNgFrASmObuy83sATMbFWr2CNAM+KeZLTazGVWcTuqwjOwMPtv7Wcn6LX1uqdZx4wZ1plFomN/ijbuZu0o1tYiIiIjUTbG4hwp3fwt4q9y2e8OWh0U9lETcM0ufoYgiAM489kzOaHfGwQ9wh51rOGbbMh47YSnL12WQRQrvv/Elae3HEdf82CikFhERERGpvpgUVNLwrduzjtfWvFayftCrUztWw7y/wqq34dvg+VMXAxcnhvbvBf74ALTpDt0vgn4/gNYn1lp2EREREZHqUkElteIPC/5Qcu/UmceeSf92/Ss22rEG3rkXVv27eifdsSp4ffQnOCENhv4XHH9WxDKLiIiIiBwuFVQScR9v/pj3M94HwDB+1f9XmIXNlp+fC+//Hj6aCEX5ZQ9u3Bw6D4bUDuTGNWHmvGW09y30sbU0toLSduvSg1fXoTDiYWjXo9Y/l4iI1GH374l1AhE5SqmgkojKL8rnkfmPlKwPbDqQU1ufWtpg+0qYfiNsX172wG4XwaCb4fizIT74tkwCdqWu52dvrCCJA6QlLOfRk76g2ddzwIN7s1j/HvzlbBgwAc67C5JSa/kTioiIiIiUisW06dKAPbv0WdbsXgNAckIyI1uMLN25+O/wVFrZYqrjALjpfbhmajCML75sjf+DwV04vVMLcmnMzIJ+XJ/7cwpvXQh9vw8WHzTyQpj3f/DEGcF7aJp1EREREYkSFVQSMWt2reEvX/ylZP3HfX5MakIqFBXCrLvhtVugIDfYmZAE330UbpgFx/Wp8pzxccbDV/QiIS4YMjh/wy7+sCAPLp0Et3wMXc4pbbw3M3iP5y+GzK9q5TOKiIiIiIRTQSURkV+Uzz0f3UNBUXCfU682vbi2x7XEF+yFv4+BT54sbdz2VJiQDgN+BHGH/hY85djm/OT8k0rW/5y+lpnLtsIxp8D4N2D0c5DSvvSArz+CvwyBuf8b3K8lIiIN3+ZFpS8RkShSQSUR8fjCx1m2cxkAiXGJ/HbIb4nftYF+n/8a1rxT2rD7xfDDd+CYU6s4U+V+ev7JDO3WtmT9F9MWs2TjbjCD0y6Hn8yHIbeXDgMszIP3Hg4Kq/Uf1PjziYhIHfdUWulLRCSKVFBJjc3eMJsXVrxQsn7r6bdyYtZGePp8mu7LKG14zi9gzEvQOOWw3yM+znh87Ol0apUMwN68Qq792zyWbQrN6tS4GVz4QHA/VoewKdp3roEXRsJrt8K+rCP6fCIiIiIiVVFBJTWyKmsV93x0T8l6WsehXL83HyZfDrm7g40JSXD5M3DBvdUa4leVFk0a8cwPzqRlk+CJv9/mFjDumXnMW7eztNGxp8GNs4P7sxo3L92++CV4sj8s+YcmrRARERGRiFFBJUfs62+/5qZ3bmJfwT4AOjXrwENZ3xI387+CmfeAA41awvVvQe8rI/Ke3Y9N4aUfDiQ1OSiq9uzPZ9wz85j86dd4caEUFx/cn3XrZ3DqqNKD9+2Ef02AFy7RGHsRERERiQgVVHJENuVsYsLsCezMDa4OpSQ04U9bt9N8+euljdr3Y+EZf4AOZ0T0vXu2T2XKDwfSplkjAAqKnHteW8aPXlzI1j1hk1A0Pw7GTIarp0LzjqXbN3wQjLGffgNkrYtoNhERERE5uqigksO2cudKvv/W99m8dzMASZbApE2b6Ja5trTRGdfB9W+T17h1rWQ4rUMqM35yNqd1KB3WN2flNi7843tMmruGfXkFpY27XwS3zoNBt5ZOWgGw7BV4cgD8+5ck7d9WKzlFREREpGFTQSWH5Z2v3+G6mdexY/8OABIx/rhlM333ZQcNEpvAZU/BJY9DYlKtZmnfIpl/3nQW4wZ2LtmWfaCAR2at4tzfz+XxOavZ/m3oilXjZjDif4LC6tRLSk9SlA/zn2bgvJuDK1YaCigiIiIihyEh1gGkftiXv49HFjzC9K+ml2xLKXIe37aNM3MPBBvadIOrXjzsKdFrIrlRPA9d1otL+rTnrleXsn7HXgB25OTx2JyveOI/qznn5DZ8t9dxpHU/hrZtTg5mGtz4GbxzL3zzCQBGUXDFatkrwcOC+42HUy6GRk2i9llEREREpP5RQSUH5e7M2jCLRxc8yrZ9pcPi2ucXMGlbJifl5wcbzrgOvvNQcCUoBgad0JrZPz+X6QszmPjuaraE7qUqKHLmrspk7qpMAE5o25SBXVsxoGt7+oz8J8fv/pT4T56A9e+VnmzDB8GrUTPo8T3oMxaOPyuY7EJEREREJIwKKqlUkRcx95u5PL30aZbvXF5m33dy9nLvzixSixxanRAM7+t6boySlkqMj+PqAZ25ol9HZi7fyuRPNjB/w64ybdZl7mVd5l5e/mwjAI3i4+ja5pf0bnYR1yfN5ZSdc4gLzVBIXk4w3frilyC5FZw0DE7+Dpx0ATRpFeVPJyIiIiJ1kQoqKWPDng28tf4tXl/zGpv3bimzr1VhIXdk7WZUzl6scXMY+msYMAESGscobeUaJcQxqk97RvVpz8asfby1dAvvrtzO4o27ySssKtM2r7CIVduyWUVn/sl4jmMkl8V/wBXxH3BiXNjn358FS6fB0mkUEcfmpBPZ1KwXW1N6saNlH3KbdSa5UQJJifEkN4qjcUI8CXFGQrwRHxdHQpwRH2ehbWXXg69xxMWBmWGAGRgW+gqE1uMMsvOcXXvzStpglLQzC9oUH0u5c0VCdU9TWOQUlOvvCueKUKianKXInaIiD+WJSJyIfS4ROQzNjo11AhE5SqmgOoq5O5n7M/ki8wsWbv6EDze+x4ZKZrtrVOSMyc7m5t17aN6oOQy9EwbeVC+u0nRq1YSbhp7ITUNPJDe/kMUbd/PZ+izmb8jiq23ZbPv2QJn2W2jNnwu/x58LL6WPreWK+A8YET+fY2x3SZs4iuiYu5qOuathx6uwHnZ5M77yjqwu6sAi78hq78hGP4Yt3opCamGo4H/eifw5a8Pst2OdoHpmvRXrBNUz89+xTlBtkztkcs7JbWMdQ44mv1wV6wQicpSKSUFlZiOAx4F44Bl3f7jc/sbAi8AZwE5gjLtviHbOhqCwqJCs3Cy2793K1qw1bNu9lnW7VrMm+2vW7N/OHs+v8tjUwkKuyM7h2m+zadP6FBjxG+g9BpKaV3lMXZaUGM+gE1oz6ITSqdy/zc1n7fYc3nx/AU3bHc/WPfvZsieXrXtyWf/tKdx34CTuKxhPD/ua8+IWc178YvraGuLMy5y7peUw0L5kYNyXZbYXeBxbaUWGt2W7t2CnN2eHp7KD1JLlPTQlx5PIIZn9NKZm11tEREREJJqiXlCZWTwwCbgQyADmm9kMd18R1uxGYJe7n2RmY4HfAWNqK1Pu/l0sXfUvtmSu5rNFa3APhim5O47j7oBD8ToerJbsAygKtQdC292LStZxLzlfcO5gn4f2gZc5X/G5CryQ/KIC8ovyyC/MC33NZ3tWJgv/9Wfyi/LJLyogtyif7MI8coryyC46QHZRATkUkoNTeBg/nycXFTFofy4X5+zlvKadadTzTH6SlQAAIABJREFUKuh5ORzbK3LjoeqQ5kmJ9O3ckj0dE0lL61Zhf1GRk51bwO79eezZn8/uffnM2rOTJpmLSd25mNa7FnPMnqU0Lsyp9PwJVkRHdtDRdlQrTyFx7CeJfSSRQxP2WTL7SCKfBPI8kTziyS2KpzCuEXkkhG1PIM8TKCCeQoxCj6MQw4kLrRtFxIVeRiFxOMG2QuJwD7YVBQMHKf6u9rDizstsL1Z2P2H73YNvmeLt5fcXnyS8NK2ybSXvUdl+qTsSDnQHdIVKREQavlhcoRoArHH3dQBmNhW4FAgvqC4F7g8tTweeNDPz0uolojJ3fMkNSx4LVr6ojXeoJd8eZF81a58mRUV0z8ujX24+ZzRuw5kdziKpaxp0ORuaHROJlPVaXJyR2iSR1CaJYVvbAqcAY4NVd9izEbZ/CZkrg68718DubyBn62G9XzxFNGMfzdjHMWRVXi2Uf3qclfsqUhck9wdOinUKERGRWheLgqoDsDFsPQMYWFUbdy8wsz1Aa6DMr/nNbAIwAaBdu3akp6cfUaDsnJVHdFx9kVpYSLuCQo4pgtaeyLHWhE7WguMaHUeTJiez75jO7E8+jsK4RD6FoJd3rKBsjXtkcnJyjvjPJZoik7MR0Ada9oGWwZa4wgM0PpBJUm4mjfL2kJi/h0Z5u0nM302jvGA5oWAv8YX7g1dRXg0ziNQNS5YsYddGVfkSRavC7tnsflHscojIUScWBVVl/8KW/z18ddrg7k8BTwH079/f09LSjihQ5va2nPHW3ygoKCAxISE06CkUJDTMrfi/xfssLGLxcslsauW3F68Vz8RWZm/4e1iFcydaHIkYiZZAYlw8iXGJNIpLZG/2Xtq2aktiXCKJ8Yk0im9MSkITmiU2IyW5FSnJbWjWtC0pzY4jMbl1cN9TDGbjS09P50j/XKKpzuQsLAimaz+QHfqaE3wtzAteBQdYufwLTj35BCjMh4IDZfZRVABeVPoqKgxbDy0XFVWyrbidB1+BMn/lvOzAuyq3hW3PysqiVauW1Wpb9XnDd9fO4L7du3fTokWLWjl3JNWXnBBk7TPwXOjQL9ZR5Gjy8tjS5fv3xC6HiBx1YlFQZQCdwtY7ApuraJNhZglAKpBVW4HaHtOT569bUHd+qK6G+pRVDkN8AiS3CF5V2LazDaeekRa9TEfoi3ryPbpYOSNucXo6aSqmRETkKFH+boxomA+cbGZdzawRwY0oM8q1mQGMDy2PBv5TW/dPiYiIiIiIHKmoX6EK3RP1E2AWwbTpz7r7cjN7AFjg7jOAvwGTzWwNwZWpsVWfUUREREREJDZi8hwqd38LeKvctnvDlnOBK6OdS0RERERE5HDEYsifiIiIiIhIgxCTK1S1YeHChTvM7OsanqYN5aZmr8PqS1bljLz6klU5I6u+5ITIZD0+EkFqysxGAI8TDFF/xt0frqTNVQTPTnRgibtfE9WQIiISUw2moHL3tjU9h5ktcPf+kchT2+pLVuWMvPqSVTkjq77khPqV9WDMLB6YBFxIMPvsfDOb4e4rwtqcDNwFDHH3XWamJ6KLiBxlNORPRESkcgOANe6+zt3zgKnApeXa/AiY5O67ANx9e5QziohIjDWYK1QiIiIR1gHYGLaeAQws16YbgJl9RDAs8H53n1n+RGY2AZgA0LZtW9LT02sjb72Wk5NTo35JC1tuKP1b0z5piNQnFalPKop2n6igKuupWAc4DPUlq3JGXn3JqpyRVV9yQv3KejBWybbyz0RMAE4m+Hm+I/CBmZ3m7rvLHOT+FKF+6d69u9eXhzRHU40fWL+qT8liQ+nfGvdJA6Q+qUh9UlG0+0QFVZjQP3j1Qn3JqpyRV1+yKmdk1ZecUL+yHkIG0ClsvSOwuZI2n7p7PrDezFYRFFjzoxNRStz0fqwTiMhRSvdQiYiIVG4+cLKZdTWzRgQPmZ9Rrs1rwHkAZtaGYAjguqimFBGRmFJBJSIiUgl3LwB+AswCVgLT3H25mT1gZqNCzWYBO81sBTAX+JW774xNYhERiQUVVCFmNsLMVpnZGjO7M9Z5iplZJzOba2YrzWy5md0e2t7KzN4xs9Whry1jnRWCaYbNbJGZvRla72pm80I5/xH6LW/MmVkLM5tuZl+G+nZwXexTM/t56M99mZm9bGZJdaVPzexZM9tuZsvCtlXahxaYGPr79YWZ9YtxzkdCf/ZfmNm/zKxF2L67QjlXmdnwWOYM2/dLM/PQFZA615+h7T8N9dlyM/t92PaY9GekuPtb7t7N3U9094dC2+519xmhZXf3O9y9h7v3cvepsU0sIiLRpoKKMs8auQjoAVxtZj1im6pEAfALdz8VGATcGsp2J/Cuu58MvBtarwtuJ/hNbrHfAY+Fcu4CboxJqooeB2a6+ylAH4LMdapPzawDcBvQ391PI5hBbCx1p0+fB0aU21ZVH15EcF/JyQQznf1flDJC5TnfAU5z997AVwTPESL0d2ss0DN0zJ9D/3+IVU7MrBPBc5C+Cdtcp/rTzM4jmE68t7v3BB4NbY9lf8rRZsFzpS8RkShSQRWozrNGYsLdt7j756HlbIIf/DsQ5Hsh1OwF4HuxSVjKzDoCFwPPhNYNOB+YHmpSV3I2B84F/gbg7nmhGbnqXJ8STByTbGYJQBNgC3WkT939fSCr3Oaq+vBS4MXQb/M/BVqY2XGxyunus0PDuQA+JZhsoDjnVHc/4O7rgTUE/3+ISc6Qx4BfU3Z2uTrVn8AtwMPufiDUpvhZTDHrTzkKvfmz0peISBSpoApU9qyRDjHKUiUz6wL0BeYB7dx9CwRFF3BM7JKV+BPBD35FofXWwO6wH1zrSr+eAGQCz4WGJz5jZk2pY33q7psIftP/DUEhtQdYSN3s02JV9WFd/jt2A/B2aLlO5Qzdp7PJ3ZeU21WnchJMxHBOaCjqe2Z2Zmh7nclpZk3M7B4zezq0frKZjYxFFhERaVhUUAWq86yRmDKzZsArwM/c/dtY5ykv9IPJdndfGL65kqZ1oV8TgH7A/7l7X2AvdWfIZInQ/UeXAl2B9kBTgqFe5dWFPj2UOvm9YGZ3EwyrnVK8qZJmMclpZk2Au4F7K9tdybZY9mcC0JJgWPKvgGmhK9R1KedzwAFgcGg9A3gwRllERKQBUUEVqM6zRmLGzBIJiqkp7v5qaPO24iE+oa/bqzo+SoYAo8xsA8GQyfMJrli1CA1Xg7rTrxlAhrvPC61PJyiw6lqfDgPWu3tm6Bk3rwJnUTf7tFhVfVjn/o6Z2XhgJDDO3Yt/yK9LOU8kKKaXhP5edQQ+N7NjqVs5IcjzamgI4mcEV6nbULdynujuvwfyAdx9P5UXfCIiIodFBVWgOs8aiYnQb3n/Bqx09z+G7ZoBjA8tjwdej3a2cO5+l7t3dPcuBP33H3cfRzCN8OhQs5jnBHD3rcBGM+se2nQBsII61qcEQ/0GhYYqGaU561yfhqmqD2cAPwjNTjcI2FM8NDAWzGwE8F/AKHffF7ZrBjDWzBqbWVeCSR8+i0VGd1/q7se4e5fQ36sMoF/o+7dO9SfBs5jOBzCzbkAjYAd1qD+BPDNLJnSFzMxOJLhiJSIiUiMJh27S8Ll7gZkVP2skHnjW3ZfHOFaxIcC1wFIzWxza9v+AhwmG1dxI8IP3lTHKdyj/BUw1sweBRYQmgqgDfgpMCRXQ64DrCX7BUGf61N3nmdl04HOCYWmLgKeAf1MH+tTMXgbSgDZmlgHcR9Xfl28B3yWYlGAfQX/HMuddQGPgnaBW5VN3vzn0jKFpBIVrAXCruxfGKqe7V/VnW9f681ng2dBU6nnA+NBVv5j1ZyXuB2YCncxsCsH/W6+LURYREWlArHSki4iISMNlZq0J7vMygiJ6RyxydO/e3VetWhWLt67T0tPTSUtLO/IT3J8atrynxnnqghr3SQOkPqlIfVJRpPrEzBa6e/9DtdMVKhERafDMbAbwMjDD3ffGOo+IiDQcuodKRESOBn8AzgFWmNk/zWy0mSXFOpSIiNR/ukIlIiINnru/B7xnZvEEE2j8iODer+YxDSYiIvWeCioRETkqhGb5uwQYQ/CohBdim0giqtuIWCcQkaOUCioREWnwzOwfwECCmf4mAenuXhTbVBJR1/wj1glE5CilgkqkhkIzh70bWj0WKAQyQ+v73P2sWnrfhcBgd88L23Yd0N/df1Ib7ylSjz0HXBPDadtFRKSBUkElUkPuvhM4HcDM7gdy3P3R2nxPM+sCbAovpkSkIjM7393/AzQBLg09d6yEu78ak2AiItJgaJY/kVpkZjmhr2lm9p6ZTTOzr8zsYTMbZ2afmdlSMzsx1K6tmb1iZvNDryFVnPoigqFLmNn1oXO+R/Cw0uL3vsTM5pnZIjObY2btzCzOzFabWdtQmzgzW2NmbczsSjNbZmZLzOz9Wu0YkegZGvp6SSWvkbEKJSIiDYeuUIlETx/gVCALWAc84+4DzOx24KfAz4DHgcfc/UMz6wzMCh1T3gjg52Z2HPDfwBnAHmAusCjU5kNgkLu7mf0Q+LW7/8LMXgLGAX8ChgFL3H2Hmd0LDHf3TWbWolZ6QCTK3P2+0OID7r4+fJ+ZdY1BJKktc/+3dPm8u2KXQ0SOOiqoRKJnvrtvATCztcDs0PalwHmh5WFAj7BhSc3NLMXds4s3mFkjoKO7rzOz7xHcXJ8Z2vcPoFuoaUfgH6GiqxFQ/MPks8DrBAXVDQT3lgB8BDxvZtMADYOShuYVgpn9wk0n+GWENATvPVy6rIJKRKJIBZVI9BwIWy4KWy+i9O9iHMFEE/sPcp5zCK4+FfMq2j0B/NHdZ5hZGnA/gLtvNLNtZnY+waxn40LbbzazgcDFwGIzOz10f5hIvWVmpwA9gVQzuzxsV3NAD/YVEZEa0z1UInXLbKBkhj4zO72SNiOAt0PL84A0M2ttZonAlWHtUoFNoeXx5c7xDPASMK141jMzO9Hd57n7vcAOoFNNP4xIHdCd4F6pFpS9f6ofwcN9RUREakRXqETqltuASWb2BcHfz/eBm8u1SQPuBXD3LaGZBT8BtgCfA/GhdvcD/zSzTcCnQPj9IjMIhvo9F7btETM7GTCCaeCXROpDicSKu78OvG5mg939k1jnERGRhkcFlUgEufv95dabhb6mA+lh29PClkv2ufsOYExV5zezjsCO8CGB7l6+MCre/jrBvVKV6UMwGcWXYe0vr6KtSENws5mtdPfdAGbWEviDu98Q41wiIlLPqaASqUfcPYNgyvQjZmZ3ArcQundK5CjRu7iYAnD3XWbWN5aBRESkYdA9VCJHGXd/2N2Pd/cPD91apMGIC12VAsDMWqFfKoqISAToHxMRETka/AH42MymE8yMeRXwUGwjiYhIQ6CCSkREGjx3f9HMFgDnE0y8crm7r4hxLBERaQA05E9ERI4WrYC97v4EkGlmXQ91gIiIyKHoCpWIiDR4ZnYf0J/guVTPAYkEz2IbEstcEkH9yj9uT0QkOlRQiYjI0eAyoC/Bs9pw981mlhLbSBJRoybGOoGIHKU05E9ERI4Gee7uBBNSYGZNY5xHREQaCBVUIiJyNJhmZn8FWpjZj4A5wNMxziQiIg2AhvyJiEiDZWaN3f2Auz9qZhcC3xLcR3Wvu78T43giItIAqKASEZGG7BOgn5lNdvdrARVRDdWM20qXdT+ViESRCioREWnIGpnZeOAsM7u8/E53fzUGmaQ2fP5C6bIKKhGJIt1DJUcdM2tnZu+bWbaZ/SHC515uZmmRPGesmNn9ZvZSDY5vMH0h9drNwCCgBXBJudfIGOYSEZEGQleopEEwsw3AD919TjWaTwB2AM1Ds34d6Xs+D2S4+2+Kt7l7zyM930HepwuwHtgb2rQD+Iu7Pxzp9zpS0eoLkcPl7h8CH5rZAnf/W6zziIhIw6OCSo5GxwMralJMxUgLdy8ws8HAu2a22N1nxjqUSH3g7n8zs7OALoT92+fuL8YslIiINAga8icNjpldZ2YfmtmjZrbLzNab2UWhfc8D44Ffm1mOmQ0zszgzu9PM1prZTjObZmatws53tpl9bGa7zWxj6PwTgHFh53kj1HZD6JztzWx/ufP0NbMdZpYYWr/BzFaGMs4ys+Or8/nc/RNgOXBa6Dxnmdl8M9sT+npW2Humm9n/mtlnof2vF2cyszQzyyjXdxvMbFgV/fpPM9saOs/7ZtYztP2gfRFabmxmfzKzzaHXn8yscXgOM/uFmW03sy1mdn11+kKkusxsMvAocDZwZujVP6ahRESkQVBBJQ3VQGAV0Ab4PfA3MzN3vw6YAvze3ZuFhgjeBnwPGAq0B3YBkwDMrDPwNvAE0BY4HVjs7k+VO88l4W/u7psJZhe7ImzzNcB0d883s+8B/w+4PHTeD4CXD/WhLDAE6AksChVH/wYmAq2BPwL/NrPWYYf9ALgh9NkKQm2PxNvAycAxwOcEn59D9UXI3QT3sZwO9AEGAL8J238skAp0AG4EJplZyyPMKVKZ/sAQd/+xu/809LrtkEeJiIgcggoqaai+dven3b0QeAE4DmhXRdubgLvdPcPdDwD3A6PNLIHgysscd3/Z3fPdfae7L65mhr8DV0NQCAFjQ9uK3/N/3X2luxcA/wOcfoirVDuALOAZ4E53fxe4GFjt7pPdvcDdXwa+JLjhvthkd1/m7nuBe4CrzCy+mp+hhLs/6+7ZYX3Ux8xSq3n4OOABd9/u7pnAfwPXhu3PD+3Pd/e3gByCZwWJRMoygsJdREQkonQPlTRUW4sX3H1fUM/QrIq2xwP/MrOisG2FBAVYJ2DtEWaYDjxhZu0Jruw4wZWo4vd8vNwsg0ZwhebrKs7XJlR8hWtfSfuvQ+cptrHcvkSCK3fVFirAHgKuJLiiVtxXbYA91ThF+Zxfh7YV21nus+2j6j8vkSPRBlhhZp8BB4o3uvuo2EUSEZGGQAWVSFBw3ODuH5XfYWYbCYanVeagk1q4+24zmw1cBZwKvBw2EcZG4CF3n3LksQHYTFCchesMhE9W0ancvnyCq117gSbFO0JFU9sq3uca4FJgGLCBYHjeLoIiEA7RF2E5l4fl2HyIY0Qi6f5YBxARkYZJQ/5E4C/AQ8XD7cysrZldGto3BRhmZleZWYKZtTaz00P7tgEnHOLcfye4h+kKSof7Fb/nXWETO6Sa2ZVHkP0toJuZXRPKNwboAbwZ1ub7ZtbDzJoADxDcx1UIfAUkmdnFoYkyfgM0ruJ9Ugh+q7+ToAj7n3L7D9UXLwO/CfVtG+Be4IifcSVyuNz9vcpesc4lIiL1nwoqEXgcmAHMNrNs4FOCSS1w92+A7wK/ILh/aTHBpAoAfwN6hGb/e62Kc88gGO63zd2XFG90938BvwOmmtm3BPd3XHS4wd19J8HDSX9BUOz8Ghjp7jvCmk0GnicYBplEMAkH7r4H+DHBPVmbCK5YlZn1L8yLBMP0NgErCPoo3KH64kFgAfAFsJRgUosHD+OjihwRCx7g/W0lr+zQ3z1pKIbeWfoSEYkiq3+P4hGR6jKzdOAld38m1llEJNC9e3dftWpVrGPUOenp6aSlpcU6Rp2iPqlIfVKR+qSiSPWJmS1090M+YkNXqERERERERI5QrRZUZjbCzFaZ2Rozq3AN3sxuNrOlZrbYggex9gjbd1fouFVmNrw2c4qIiIiIiByJWpvlLzRj2CTgQoL7Muab2Qx3XxHW7O/u/pdQ+1EEDyUdESqsxhI8vLQ9MMfMuoVupBeRanL3tFhnEBEREWnIanPa9AHAGndfB2BmUwmmXS4pqNw9/IbgppROvXwpMDX0ANH1ZrYmdL5PajGviIiI1Fd/H1O6fM0/YpdDRI46tVlQdaDsA0UzCM2cFs7MbgXuABoB54cdGz6LWAZlH1RafOwEYAJAcnLyGZ06dSrf5LAUFRURF1c/biurL1mVM/LqS1bljKz6khMik/Wrr77a4e5VPRdNpKKvZh66jYhILajNgsoq2VZhSkF3nwRMMrNrCJ6DM/4wjn0KeAqgf//+vmDBghoFrk+zpNSXrMoZefUlq3JGVn3JCZHJamZfRyaNiIhI7arNX3dmAOGXjDoCmw/SfirwvSM8VkREREREJOpqs6CaD5xsZl3NrBHBJBMzwhuY2clhqxcDq0PLM4CxZtbYzLoSPBj1s1rMKiIiIiIicthqbcifuxeY2U+AWUA88Ky7LzezB4AF7j4D+ImZDQPygV0Ew/0ItZtGMIFFAXCrZvgTEREREZG6pjbvocLd3wLeKrft3rDl2w9y7EPAQ7WXTkQkMvLz88nIyCA3N7fW3iM1NZWVK1fW2vkj6XCyJiUl0bFjRxITE2s5lYiISO2o1YJKRORokJGRQUpKCl26dMGssjl1ai47O5uUlJRaOXekVTeru7Nz504yMjLo2rVrFJKJiIhEXv2Yg1dEpA7Lzc2ldevWtVZMNVRmRuvWrWv1yp6IiEhtU0ElIhIBKqaOjPpNRETqOxVUIiIiIiIiR0gFlYhIA9CsWbNDtvnggw/o2bMnp59+Ovv37z+s87/22musWLGiZP3ee+9lzpw5h51TpNaM/FPpS0QkilRQiYgcJaZMmcIvf/lLFi9eTHJy8mEdW76geuCBBxg2bFikI9Y5ZjbCzFaZ2Rozu/Mg7UabmZtZ/2jmkzD9ry99iYhEkQoqEZEGJD09nbS0NEaPHs0pp5zCuHHjcHeeeeYZpk2bxgMPPMC4ceMAeOSRRzjzzDPp3bs39913X8k5XnzxRXr37k2fPn249tpr+fjjj5kxYwa/+tWvOP3001m7di3XXXcd06dP5+233+aqq64q8/7F67Nnz2bw4MH069ePK6+8kpycnOh2Rg2ZWTwwCbgI6AFcbWY9KmmXAtwGzItuQhERqQs0bbqISAR1ufPftXbuDQ9fXK12ixYtYvny5bRv354hQ4bw0Ucf8cMf/pAPP/yQkSNHMnr0aGbPns3q1av57LPPcHdGjRrF+++/T+vWrXnooYf46KOPaNOmDVlZWbRq1YpRo0aVHBvuwgsv5KabbmLv3r00bdqUf/zjH1x++eXs2LGDBx98kDlz5tC0aVN+97vf8cc//pF77723itR10gBgjbuvAzCzqcClBA+dD/db4PfAL6MbT0RE6gIVVCIiDcyAAQPo2LEjAKeffjobNmzg7LPPLtNm9uzZzJ49m759+wKQk5PD6tWrWbJkCaNHj6ZNmzYAtGrV6qDvlZCQwIgRI3jjjTcYPXo0//73v7nnnnv49NNPWbFiBUOGDAEgLy+PwYMHR/qj1rYOwMaw9QxgYHgDM+sLdHL3N82syoLKzCYAEwDatm1Lenp65NPWczk5OeqXctQnFalPKlKfVBTtPlFBJSLSwDRu3LhkOT4+noKCggpt3J277rqLm266qcz2iRMnHvZU5mPGjGHSpEm0atWKM888k5SUFNydCy+8kJdffvnIPkTdUFlHeMlOszjgMeC6Q53I3Z8CngLo3r27p6WlRSZhA1I8XPWI/fXc0uWb3q9xnrqgxn3SAKlPKlKfVBTtPlFBJSISQdUdlne4srOzI3q+4cOHc8899zBu3DiaNWvGpk2bSExM5IILLuCyyy7j5z//Oa1bty4Z8peSklJlhrS0NG688UaefvppxowZA8CgQYO49dZbWbNmDSeddBL79u0jIyODbt26RfRz1LIMoFPYekdgc9h6CnAakB4qQo8FZpjZKHdfELWUEtiyJNYJROQopUkpRESOQt/5zne45pprGDx4ML169WL06NFkZ2fTs2dP7r77boYOHUqfPn244447ABg7diyPPPIIffv2Ze3atWXOFR8fz8iRI3n77bcZOXIkEAxre/7557n66qvp3bs3gwYN4ssvv4z656yh+cDJZtbVzBoBY4EZxTvdfY+7t3H3Lu7eBfgUUDElInKU0RUqEZEGoHgGvbS0tDLDHJ588smS5eeff77MMbfffju33357hXONHz+e8ePHl9k2ZMiQMtOmlz/Xk08+WfJexVeyzj//fObPn3/Yn6WucPcCM/sJMAuIB5519+Vm9gCwwN1nHPwMIiJyNFBBJbG1bQUUFcBxvWOdRESkAnd/C3ir3LZKpyp097RoZBIRkbpFBZXERlEhzLkPPn4iWO82AkY8DK26xjaXiIiIiMhh0D1UEn0HcuDvV5UWUwBfzYRJA2FdesxiiYiIiIgcrlotqMxshJmtMrM1ZnZnJfvvMLMVZvaFmb1rZseH7Ss0s8Whl8apNyTvPgBr5lTcXngA3vgZFOZHP5OIiIiIyBGotYLKzOKBScBFQA/gajPrUa7ZIqC/u/cGphM8ab7Yfnc/PfQaVVs5Jcr2ZcHnL5aun/1zuHEOJLUI1neth89fiE02EREREZHDVJtXqAYAa9x9nbvnAVOBS8MbuPtcd98XWv2U4Bkf0pDN/xsU7A+Wj+0FF9wHnc6Ec+4obfPe7yFvb2zyiYiIiIgchtqclKIDsDFsPQMYeJD2NwJvh60nmdkCoAB42N1fK3+AmU0AJgC0a9eO9PT0GgXOycmp8Tmipb5kDc8ZV5jHoE+fpFFo34qWw9j+3nuhfacwsFErGudlQc421r38X3xz/OiY5Kzr6kvWoylnampqxB+8W15hYeFB36NFixb07NmzZP2KK64oeYZUtJXP+t3vfpcHH3yQfv36Vdo+Nze3XnyviIiIVKY2CyqrZJtX2tDs+0B/YGjY5s7uvtnMTgD+Y2ZL3b3M0yTd/SngKYD+/ft7+LNXjkR6ejo1PUe01JesZXJ+/iLk7w6Wm3egx+i76RGfWNq4xX3wRvBMnBOy3uOEHzwBVtm3US3nrOPqS9ajKefKlStJSUmJTKAqZGdnH/Q9kpOT+eKLL2o1Q3WVzxofH0/Tpk2rzJ+UlETfvn2jFU8aqqunxjqBiBylanPIXwbQKWy9I7C5fCMzGwbcTfB0+QPF2919c+jrOiAd0L+29d2il0qXB97zWjGZAAAgAElEQVQM4cUUQJ9rSu+l2vMNZCyIXjaRBmjPnj10796dVatWAXD11Vfz9NNPA9CsWTN+8Ytf0K9fPy644AIyMzMBWLx4MYMGDaJ3795cdtll7Nq1C4CJEyfSo0cPevfuzdixYwHYu3cvN9xwA2eeeSZ9+/bl9ddfB2D//v2MHTuW3r17M2bMGPbv3x/tjy5Ho+4Xlb5ERKKoNq9QzQdONrOuwCZgLHBNeAMz6wv8FRjh7tvDtrcE9rn7ATNrAwyh7IQVUt/sy/r/7N13eFzVtfj975pR77Yky1Zx70WuGEyzTWihQ0JwAgnthnATUshN7i95k5AAIZebAiSEJBBKCDeEHjAGQrUwuIBt3LtcVWxJlqxeZ2a/f5yjmVEfWxrNSFqf55lH+5zZ58zSkaas2Q0K19sbAnOu71gnIgqmXQ6bnrG2t79sja9SaiD5RXJQTpsI8IuqLu9vaGhgzpw53u0f//jHXHfddfzxj3/kpptu4rvf/S4nTpzg61//OmAlQ/PmzeN3v/sd99xzD3fffTd//OMf+drXvsbDDz/M4sWLueuuu7j77rt56KGHuP/++zl48CDR0dFUVlotzffddx/nnXceTz75JJWVlSxcuJDzzz+fJ554gri4OLZu3crWrVu77OqnlFJKDQZBS6iMMS4RuQN4G3ACTxpjdojIPcAGY8xy4DdAAvCiWF27jtgz+k0DHhURD1Yr2v3GmJ3BilX1g/0fgPFY5ewFEJ/aeb2Z1/gSqp2vwkW/Aocul6ZUT2JjY9m8eXOH/RdccAEvvvgi3/rWt9iyZYt3v8Ph4LrrrgPghhtu4JprrqGqqorKykoWL7Z6X994441ce+21AOTm5nL99ddz1VVXcdVVVwHwzjvvsHz5cn77298C1lioI0eOsHr1au/4rdzcXHJzc4P3iyullFIhFswWKowxbwJvttt3l1/5/C6OWwPMCmZsqp/te9dXnnRh1/XGngtxaVB/HGqOwpG1MPas4Men1CDl8XjYtWsXsbGxVFRUkJ3d+WSq0sN4xTfeeINVq1axfPly7r33Xnbs2IExhpdffpkpU6ac9PmUUkqpwSKoCZVSAHg8bRfyndhpHm1xRsD0K2DDk9b2jlc0oVIDSzfd8nqjpqaGU5n24sEHH2TatGn86le/4pZbbmHt2rVERkbi8Xh46aWXWLZsGc8++yxnn302ycnJDBs2jI8++ohzzjmHZ555hsWLF+PxeCgoKGDp0qWcffbZPPvss9TW1nLRRRfx8MMP8/DDDyMibNq0iblz53LWWWfxj3/8g6VLl7J9+/awmSxDDXK/9Uvsf7AndHEopYYcTahU8B3dZLU4AcSnw6g53defcY0vodr1Olzy236b7U+pgar9GKqLL76YW265hccff5xPP/2UxMREzj33XH75y19y9913Ex8fz44dO5g/fz7Jyck8//zzADz99NPcfvvt1NfXM378eJ566incbjc33HADVVVVGGO48847SUlJ4Wc/+xnf+973yM3NxRjD2LFjWbFiBbfeeivf+c53yM3NZc6cOSxcuDBUl0UNJbXHQh2BUmqI0oRKBd++dq1TPY2JGnMmxA6DhhNQWwKluyBjenBjVGqAc7vdne7ftWuXt/zAAw+0ue/ee+/l3nvvbbNvzpw5rFu3rsN5Pv744w77YmNjefTRRzvd/9xzOoW1UkqpoUFH+6vgy/cfP3VBz/UdThh3rm/7wMq+j0kppZRSSqk+oAmVCiqHuwmKN/l2jF8a2IH+9fZrQqVUX6utrQ11CEoppdSgoAmVCqrEmnzwuKyNtCkQNzywAyf4JVSHV4Orue+DU6oPGWNCHcKApNdNKaXUQKcJlQqqpGq/mZZOZpHeYWNh2Dir3FIPhZ/2aVxK9aWYmBjKy8s1OThJxhjKy8uJiYkJdShKKaXUKdNJKVRQJVXv9m1kn+RMX+OXwMaDVnn/Shh7dl+FpVSfys7OprCwkLKysqA9RmNj44BJPE4m1piYmC7XxlJKKaUGAk2oVPAYQ3KVfwvVSSZUE5bCxqes8oE8+NzP+iw0pfpSZGQk48aNC+pj5OXlMXfu3KA+Rl8ZSLEqpZRSvaVd/lTwVB4mqqXSKkcnW2OoTsa4c0Hsf9Hiz6AxOAumKqWUUkopdao0oVLBU7DeV86e3/P6U+3FDoOMmVbZeNqeTymllFJKqTCgXf5U8PhPJHGy46dajTkTjm21ykfWwqTzex+XUkqpwee2vFBHoJQaorSFSgVPwSe+8snM8Odv9CJf+cja3sWjlFJq8Mqc67sppVQ/0oRKBUdLIxzb7tvOWnBq5/FPqIo2gqupd3EppZRSSinVhzShUsFRugOM2yqnToTYlFM7T2IGDB9vlV2NULy5b+JTSimllFKqD2hCpYLj6BZfeWRu787Vptvfmt6dSymllFJKqT6kk1Ko4PBPqEbN7t25Ri+Czf+wykfW9e5cSimlBqdfJPuVdZkNpVT/CWoLlYhcLCJ7RCRfRH7Uyf3fF5GdIrJVRN4XkTF+990oIvvs243BjFMFwdGtvvKoXrZQjTnTVz6yDjye3p1PKaWUUkqpPhK0hEpEnMAjwOeB6cCXRWR6u2qbgAXGmFzgJeDX9rHDgZ8DpwMLgZ+LyLBgxar6mLsFSnb4tkf2soVq+HiIH2GVGyuhbHfvzqeUUkoppVQfCWYL1UIg3xhzwBjTDDwHXOlfwRiz0hhTb2+uA7Lt8kXAu8aYCmPMCeBd4OIgxqr60vG94LZm42uMToP41N6dTwRy/Nax8l/fSimllFJKqRAK5hiqLKDAb7sQq8WpK7cCb3VzbFb7A0TkNuA2gIyMDPLy8noRLtTW1vb6HP0lnGPNOPYB0+xyZewYdvdBnDnNqUywy0fXv8aemrG9Pqe/cL6e7Q2UWDXOvjVQ4oSBFatSSinVW8FMqKSTfabTiiI3AAuAxSdzrDHmMeAxgAULFpglS5acUqCt8vLy6O05+ktYx/rWW95iQ8rkvonzSAwceBqAUS0FjOrj3z2sr2c7AyVWjbNvDZQ4YWDFqpRSSvVWMLv8FQI5ftvZQHH7SiJyPvAT4ApjTNPJHKvClN+EFLUJ4/vmnKPmgCPSKpfvg/qKvjmvUkoppZRSvRDMhGo9MElExolIFLAMWO5fQUTmAo9iJVOlfne9DVwoIsPsySgutPepcOfxwDFfQlWTOKGbyichMqbt9OuF6/vmvEoppZRSSvVC0BIqY4wLuAMrEdoFvGCM2SEi94jIFXa13wAJwIsisllEltvHVgD3YiVl64F77H0q3J04CM21Vjkujeao4X13bv+JKQo+6bvzKqWUUkopdYqCurCvMeZN4M12++7yK5/fzbFPAk8GLzoVFMe2+cojZ1kz9PWVnIWw7k9WuUBn+lNKKaWUUqEX1IV91RDUZv2pmX177my/FqqijeB29e35lVJKKaWUOklBbaFSQ1DJdl85Yxac6MNzJ2dBUjZUF0JLPZTuaDuuSiml1ND1fV30XSkVGtpCpfrWMf+Eakbfnz/nNF9Zu/0ppZRqlTTKd1NKqX4UUEIlIpNF5K8i8o6IfNB6C3ZwaoBpqISqI1bZEQlpk/v+MXL81obWhEoppZRSSoVYoF3+XgT+AvwVcAcvHDWgle70ldOnQkRU3z+G/ziqQk2olFJKKaVUaAWaULmMMX8OaiRq4PPv7tfXE1J4zzsLImLA1QgnDkFtKSSMCM5jKaWUGjiqj/rK2u1PKdWPAh1D9bqIfFNERonI8NZbUCNTA0+J35TpwRg/BVarV+Zc37Z2+1NKKQXwwFTfTSml+lGgCdWNwA+BNcBG+7YhWEGpAcp/yvSMILVQgS7wq5RSSimlwkZAXf6MMeOCHYga4DxuKPEbQzVyVvAeq804qvXBexyllFJKKaV6EFBCJSKRwH8C59q78oBHjTEtQYpLDTQVB8DVYJUTRkJ8WvAey7+FqugzcDUHZwIMpZRSSimlehBol78/A/OBP9m3+fY+pSzH+mH8VKuEETBsrFV2N7V9bKWUUkoppfpRoLP8nWaMme23/YGIbAlGQGqA8k9qRuUG//GyF1qz/IE1jip7fvAfUymllFJKqXYCbaFyi8iE1g0RGY+uR6X8tWmhCuKEFK1ydD0qpZRSSikVeoG2UP0QWCkiBwABxgA3By0qNfCU+K9B1Q8tVG1m+tOESimllFJKhUags/y9LyKTgClYCdVuY0xTUCNTA0dtGdTYCypGxELqhO7r94URMyAyHlrqoLoIqgohOTv4j6uUUkoppZSfbrv8ich59s9rgEuBicAE4FJ7n1IdF/R1OIP/mM4IyJrn29ZWKqWUUkopFQI9jaFabP+8vJPbZT2dXEQuFpE9IpIvIj/q5P5zReQzEXGJyBfb3ecWkc32bXlAv40KDf/xU32w/lR5bRMvbCjgd+/s4f1dJTS7PJ1XzDndV9b1qJRSSimlVAh02+XPGPNzu3iPMeag/30i0u1ivyLiBB4BLgAKgfUistwY47f6K0eAm4AfdHKKBmPMnO7DV2GhTUJ16hNSNDS7+X8vb2XF1mI8xrc/OTaSO5ZO5D/OGYeI+O5oM47qk1N+XKWUUoPAL6pCHYFSaogKdJa/lzvZ91IPxywE8o0xB4wxzcBzwJX+FYwxh4wxW4EumiDUgNAmoTq1CSnqm13c/LdPWb6lbTIFUNXQwn1v7uLu13fi8b8z+zRf+ehWaGk4pcdWSimllFLqVHXbQiUiU4EZQHK7MVNJQEwP584CCvy2C4HTu6jbmRgR2QC4gPuNMa92Et9twG0AGRkZ5OXlncTpO6qtre31OfpLuMTqcDdxTtleBDAIH+8px70/z3t/IHE2uw2/29DInhO+vHpSioOcJAdbSt2UN1pJ1N/WHGL/4UJumRnlbalaGJtFXEMReFrY9MZTVKVMP6XfI1yuZyAGSqwaZ98aKHHCwIpVKaWU6q2eZvmbgjVWKgVr3FSrGuDrPRwrnewznezrymhjTLG95tUHIrLNGLO/zcmMeQx4DGDBggVmyZIlJ3H6jvLy8ujtOfpL2MRa9Bl8ZCVCkjqBc87/fJu7A4nzgXf3sufEPu/2jz4/ldsXWzMFNrs83Pn8Zt7YZs0i+FGRi0tPn8ayhaOtypVLYfP/ATA3rRnO7v6xuhI21zMAAyVWjbNvDZQ4YWDFqpRSSvVWT2OoXgNeE5FFxpi1J3nuQiDHbzsbKA70YGNMsf3zgIjkAXOB/d0epPpfLyekOHi8jr/k+f6sP7hwsjeZAoiKcPCHL88lOsLBK5uKALhnxU7OGJ/K2LR4axyVnVBxZN2p/Q5KKaUGvuJNvnLm3NDFoZQacgIdQ3W7iKS0bojIMBF5sodj1gOTRGSciEQBy4CAZuuzzx9tl9OAs4Cd3R+lQqIXCZUxhrte206z22rhmp2TwjeXTOxQz+kQ7rt6FhPS4wGob3Zz5wubcXsMjDnLV/HIGvDocDyllBqSHlviuymlVD8KNKHKNcZUtm4YY05gtRh1yRjjAu4A3gZ2AS8YY3aIyD0icgWAiJwmIoXAtcCjIrLDPnwasEFEtgArscZQaUIVjvwTqoyTS6je2VnCR/uOA+AQuO+qmTgcnfUUhdgoJw9dN5cI+/5NRyp5cUOBtYhw/AirUmMVlOq/iVKq7wSw/Mf3RWSniGwVkfdFZEwo4lRKKRU6gSZUDhEZ1rohIsPpefwVxpg3jTGTjTETjDH32fvuMsYst8vrjTHZxph4Y0yqMWaGvX+NMWaWMWa2/fOJk//VVNB5PFCy3bd9Ei1Uxhj+5NfV76tnjGFmVnK3x8zKTuZbS30tWA+8u5f6FjeMOdNX6fCagGNQSqnu+C3/8XlgOvBlEWk/880mYIExJhdr9ttf92+USimlQi3QhOp3wBoRuVdE7gXWoG8a6sRBaK61ynFpkDgy4EM3HD7BlgKr0TPK6eCO8yYFdNztiyeQkRQNQGlNE39ddbBdQrU64BiUUqoHgSz/sdIYU29vrsMaL6yUUmoICSihMsb8HfgiUAKUAtcYY54JZmBqAGg/fko6767XmcdWHfCWr5mXRXpidEDHxUY5+a8Lpni3H121n4q0Bb4Kh9eAOZnJJJVSqkudLf+R1U39W4G3ghqRUkqpsNNjt71W9vinMuz1p0RktDHmSNAiU+HvFLv77S+r5b1dJd7t/zhn3Ek97BfmZ/PExwfZU1JDfbObR3dH8+OYZGsMVV0pVBywxlYppVTvBLz8h4jcACwAFndxv3fdxPT0dF2nqxO9Xb9siV95sFxfXdOtI70mHek16ai/r0lACZU9icTvgEysFqoxWBNNzAheaCrsneIMf39fc8jbiHTe1BFMHJF4Ug/rdAj/deFkbntmIwDPfFLIDyadTuT+d6wKh1drQqWU6gsBLf8hIucDPwEWG2OaOjuR/7qJU6ZM6fW6iYNRr9cvy/MVB8v11TXdOtJr0pFek476+5oEOobqXuAMYK8xZhzwOUAHqwx1p5BQNba4eXWz7/PIrWefXOtUq/OnZTAlw0rE6pvdrHNP9d156ONTOqdSSrXT4/IfIjIXeBS4whhTGoIYlVJKhVigCVWLMaYca7Y/hzFmJTAniHGpcFdXDtXWQrs4oyE1sEkl3t9VSlVDCwDZw2JZND71lB7e4RC+udTXCvXoYb8JMQ6u0nFUSqleC2T5D+A3QALwoohsFpGA1ltUSik1eAQ6hqpSRBKAVcA/RKQUcAUvLBX2SvzXn5oOzsD+lV7c6Bvf/YV52V2uOxWIS2eN4nfv7OVIRT1rGkbTlJBAtKsWao5CeT6kBZbkKaVUV4wxbwJvttt3l1/5/H4PSimlVFgJtIXqSqAeuBP4N7AfuDxYQakB4BS6+5VUN7Jqb5l3+4vzeze7cITTwTcWjwfAg4NPjd/yMAfyenVupZRSA0zCSN9NKaX6UY8Jlb2w4WvGGI8xxmWMedoY8we7C6Aaqoo3+cojcwM65JXPivDYPfHOGD+cnOFxvQ7jmrnZpMRFAvB+o984qoMf9vrcSimlBpAf7PHdlFKqH/WYUBlj3EC9iCT3QzxqoCja6CtnzQvokNc2F3nL187P6aZm4GKjnCw7bTQAqz0zfXcc/Ag87j55DKWUUkoppboSaJe/RmCbiDwhIn9ovQUzMBXG6ivgxCGr7IiEjJndVgdr7andx2oAiI5wcNHMvuuS8dVFY3A6hH0mi1KTYu1srIRjW/vsMZRSSimllOpMoAnVG8DPsCal2Oh3U0NR8We+8shZEBHd4yFvbj3qLS+Zkk5CdMBrSvcoKyWWi2ZkAMIaj/84Ku32p5RSSimlgqvbT7UiMtoYc8QY83R/BaQGgCK/hCrA7n5vbPMlVJfMGtXXEXHzWeN4c9sxVntmcpVzjbXz4Idw9vf6/LGUUkqFoT1v+cpTPh+6OJRSQ05PzQSvAvMARORlY8wXgh+SCnttEqr5PVY/4NfdLyrCweemZfR5SAvGDGNGZhJrimdApL3z0Gporoeo3k9+oZRSKsz9c5mv/Iuq0MWhlBpyeury579I0PhgBqIGCGPaTkiR2XML1Zt+rVNLJvdtd79WIsLNZ42jiHT2ebKsne4mOPRxnz+WUkoppZRSrXpKqEwXZTVUVRdBXalVjkoIaPHcN7Yd85Yvze377n6tLp89irSEKFZ65vh27nsnaI+nlFJKKaVUT00Fs0WkGqulKtYuY28bY0xSUKNT4ce/u1/mXHA4u61+rM7DrqN1QPC6+7WKjnDylYWjycubzW28Ye3Mf9dqVRPp/mCllFIBa2h2c6y6kbomF3VNLuqb3dQ2uahvdlHb5Ka+yUVts4v6JjeNLW6iIhzERjqJiXQSE+mwf1q3WHvfnnI3iYdPEBPpYHh8FGkJ0UQ6A507SymlQqfbhMoY0/2n5R6IyMXA7wEn8Lgx5v52958LPATkAsuMMS/53Xcj8FN785c6MUaYaNPdb26P1T895vKWFwepu5+/G84Yw+N5U6kz0cRLkzW9e3l+QC1pSiml2qpqaCG/tJb9pbXsK60hv7SWfaW1FFU2YILRb2X9Gm9RBIbHRTEiKYYRidHWLSmaDHs7PTGGjKRo0hOjiY7o1ccVpZTqlaB9uhURJ/AIcAFQCKwXkeXGmJ1+1Y4ANwE/aHfscODnwAKsroYb7WNPBCteFaDC9b5yABNSrD/mW1z30iDM7tfeiKQYLsgdzeodM7nQaSd/+97VhEoppQJQVNnAeztLWLmnlJ3F1ZTWNIUsFmOgvK6Z8rpmdh3tvm5KXCSb/bYf/+gAY1PjGZsWT87wWE24lFJBFczmgoVAvjHmAICIPAdcCXgTKmPMIfs+T7tjLwLeNcZU2Pe/C1wM/DOI8aqeuJratlCNPqPb6geP11FQY/1pre5+I4IZnddNZ47lxW1zvAlV8+5/E7Xom/3y2EopNZAYY9hRXM17u0p4d2cJO4qrez4IcAhkpsSSGBNJQrSTuKgIEqIjiItyEh8dQXy0/TMqgphIB80uD40tHhparC6AreWmFrd339GycmLik2hodlNe10R5XXPArWCV9S0Q49v+5Ru7vGURyEyOZVxaPGNS4xibav0clxZPzvA4YiI12VJK9U4wE6osoMBvuxA4vRfHZrWvJCK3AbcBZGRkkJeXd0qBtqqtre31OfpLKGJNqtrNPFcjAA0xI/lk425gd5f1X9/f7C3PGC5sXLc62CF6HYifC/bDOw6v5qP33sQd0fX06fq373saZ98aKHHCwIp1qCqtbuSJjw+yYutRiiobuqwX5XQwPj2eiSMSvLdJIxIZmxbX560+eXl5LFlylne7xe2hvLaZkupGSmuaKK1ppLTa/6dVLqtpwtNN4mWM1fJWVNnAx/lt7xOBUUkxjLFbs8baidaUkYnkDIvD4dDxt0qpngUzoersVSjQHtcBHWuMeQx4DGDBggVmyZIlAQfXGevFvHfn6C8hiXX1Fm8xdsp5PT7+r7d8BLQA8LWlM1kyNzuIwbVVmVzEjn+NYYbjMBG4WJReR8TsS7qsr3/7vqdx9q2BEicMrFiHmuLKBv7y4X6eW19As6t95xCIdApnjE/lwukZnDUxjdHD44gI0cQQkU4HI5NjGJkc0209t8dQXtcEv/Ptu/700Rwqr+PQ8XqKq7oe72UMFFc1UlzVyNoD5W3ui4l0MGlEIpMzEpmckcDkkYlMyUhkVHIMohMdKaX8BDOhKgRy/LazgeKTOHZJu2Pz+iQqdeqOrPOVA+jut/Oo1XUkyhnc2f06c8msUTz5+iJmeA4DUPLpS2TNvrZfY1BKqXBRUFHPn/LyeWljIS3uttlFYkwE500dwQXTMzh3cjpJMZFdnCU8OR3CiMS2Sdd9V8/ylptcbgoqGjh0vI5D5XUcLq+3kq3yOopONHTZutXY4mFbURXbitouEpwYHcGkjAQ70UpkyshEJmUkkJ4QrYmWUkNUMBOq9cAkERkHFAHLgK8EeOzbwK9EZJi9fSHw474PUQXM42mXUC3qtrr/Yr6heIOOinAQP/tq2PQcAMOL86ClASJj+zUOpZQKpRa3h9+/t48/f7gfd7vMYXZ2Mt9aOpGlU0cMjunJR83udHd0hNPbXbG9ZpeHwhP13tasQ+V15JfWsrekluO1nU/IUdPk4rMjlXx2pLLN/mFxkUzKsFqxJo9MZPKIBKaOSiI5dmAlqEqpkxe0hMoY4xKRO7CSIyfwpDFmh4jcA2wwxiwXkdOAfwHDgMtF5G5jzAxjTIWI3IuVlAHc0zpBhQqR8n3QYP8JYof3OGveiq2+hOqyIC7m252Lly7h4GcjGSfHiDWNHPz0Dcad9cWQxKKUUv1tf1ktdz6/ma2FbVtYFowZxrc/N4lzJ6UNrhaVb6w66UOiIhyMT09gfHrHZKu8tom9JdZ08XuO1bCvpJY9JTVUNbR0eq4T9S18erCCTw+2/biSPSyW6aOSmJ6ZxPRRSczISiZTuw0qNagEdVEgY8ybwJvt9t3lV16P1Z2vs2OfBJ4MZnzqJBxZ6yuPXtTtQrkHymrZZXf3i3DQb7P7tZeeFMPWtPMYV/4sAGWfvqgJlVJq0DPG8OynR/jlil00tPiWrlgwZhjfv3Ayi8an6of5AKQmRLMoIZpFE1K9+4wxlNY0sbfESrL2ltRYSVdJDXXN7k7PU3iigcITDbyzs8S7Lzk20ptkzci0fk5ITxgcLYVKDUHBXWVVDR4nMX7Kv7tfbpqTxBD2x8856zpYbiVUkyo/pvREDSOGJYYsHqWUCqYml5vvP7+FN/xeh6OcDn540RRuPXuczlrXSyJCRlIMGUkxnDMp3bvf4zEUVzXYiZaVYO0+VsO+0poOY9bAWjB57YHyNhNhREU4mJKR6GvNykyiwRWM1ZOVUn1NEyrVM2Pg4Ee+7R7GT/l391s4MrT/YpPnnEvZinTSPWUMk1pe/PfzXPvl/whpTEopFQwNzW6+8X8bWbW3zLtvckYCD103l+mZSSGMbPBzOITsYXFkD4vjvKm+SZiaXR72l9Wyo7iancXV7Dxaxc7iaqobXR3O0ezqfBKMsZtW2i1ZyUwflcTMrGTSE6OD/jsppQKnCZXq2fF9UF1olaOTIHNul1XzS2vZfawGsL5tmz0ixAsmOhzUTLyS9L2PA5Cw52Vqm24iIVr/9ZVSg0dtk4tb/ra+zfidG84YzU8vnT50Fq7d8JSvvODm0MXhJyrCwbRRSUwblQTzrX3GGApPNLDzqJVk7SiuZtfR6i7XAztUXs+h8nre3HbMu29kUgwzs5KZlZXMrGwryWo/06FSqv/op0rVswMrfeWx54Cz638b/+5+S6ekExtRG8zIAjJm6c1gJ1RLzXpeXLuLry6Z1cNRSik1MFQ3tvC1Jz5lc4Fv1rk7z5/Mdz43cWiNlVrxPV85TBKqzogIOcPjyBkex0UzRnr3V9Y3e5MsqzWrmr0lNZ1O636supFj1Y28t8s3LisjKZpZWcm+RMHCfbEAACAASURBVCsrmRFJmmQp1R80oVI92++XUE1Y2m1V/4Tq0txMOLE3WFEFzDlqJicSJzOsZi8x0sLh1c/Tcs4MHfyrlBrw3B7Dd/+5qU0y9f9dMpXbzp0QwqjUqUiJi+LMCWmcOSHNu++d91cyaso8dh6tYkdxNduLqth5tJrGlo6LMpdUN1FSXcp7u0q9+0YktkuyspPJ0CRLqT6nCZXqnrsFDvmNn5pwXpdV80trvN39oiMcfG7qCNavDX1CBZBw2lfgg18AcG5jHq9vKeaaeZ1OMKmUUgPG797Zw8o9vjFT9145g68uGhu6gFSfinIKs7KtRKiVy+1hf1kd24qq2G6PudpZXN1mRsdWpTVNvL+7lPd3+5Ks9PZJVlYyI5M1yVKqNzShUt0rXA/Ndre95NEwfHyXVd/Y6uvffd7UEcSH0TilyNlfwnxwN4LhLMd2vvz+J1w5JwunznillBqgVmwt5k95+73bty+eoMnUEBDhdDBlZCJTRibyxfnWF4Nuj2F/WS3bCqu8idaOLpKsspomPthdyge727Zk5WanMDs7mdwc62dKXFS//U5KDXTh84lXhac23f2WdLv+1Bvbir3lS2aFZjHfLiVn4R5zDhGHV+EUw6LKN3hr+yIuy80MdWRKKXXSDpfX8cMXt3q3F09O54cXTQlhRCqUnA5hckYikzMS+YJfknWgrNY7c2BrklXfyXpZpTVNvLerpM2YrDGpcb4kKzuFmVlJxEXpx0alOqPPDNU9/wkpxnc9fqp1cUOAmEgH500NzWK+3Yk47WY4vAqAZRErufX9PVwyc5Suy6KUGlCMMfzo5W3e1oexqXH8YdlcbXFXbTgdwqSMRCZlJHq7uLs9hoPH7SSrsJptRZVdJlmHy+s5XF7P61usL0sdApNGJJJrt2LNyU5hyshEoiJ0PLJSmlCprtWUQOEGqywOGL+ky6ovf1boLX9uakZYdffzmnoZnrh0HPVljJIKsspW8c7OqVw8M8xa05RSqhvPry/wLgjrEHj4y/NIjgvdAupq4HA6hIkjEpk4IpGr7RVQ3B5DfmktWwor2VpYydbCKnYdre6wILHHwJ6SGvaU1PDiRus9P8rpYFpmkrcVa3Z2MuPTEzS5V0NOGH7qVWFjzxuA/YI6+kyIG95pNbfH8OqmIu/2NfOy+iG4UxARhWPeV+HjBwC4wfkev3xnCRdMH9nDgUopFR5Kqxu5781d3u2vnzO+zYQFSp0sp0O8Y7K+tCAHgCaXm91Ha9haWMmWwiq2FFSSX1aLaTeFe7Pbw5aCSrYUVAKHAYiPcjIzK5k5OSnkZqeQm51M9rDYoTWFvxpyNKFSXdu1wleednmX1T7aV0ZJdRMAaQnRnDs5PdiRnbr5N2E+fhDBsNi5lbvK8nlt8wQ6TxWVUiq8PPjeXmoaXYA1xuV7508OcURqMIqOcDI7J4XZOSl81d5X2+Rie1GVN8naWlhJQUXHxYjrmt18crCCT/wWmR4eH2V1FcxOYU6O9TMtIbqffhulgk8TKtW5hko4+KFve+qlXVZ9+TNf69RVczLDe32nYWOQSRfAvncAuNX5Fg++N46fL9BvzpRS4W1/WS0vbPB1r773ypnERjlDGJEaShKiIzhjfCpnjE/17quoa/Z2E9xSYCVax2ubOhxbUddM3p4y8vym+M9KifUmWbOzk5mZnUxSjHZdVQOTJlSqc/veAY/1LSiZcyElp9NqVQ0tvL3DN1166+xCYe2Mb3oTqi858/h9xTWsPJLO+SEOSymluvPAO3txe6w+V2dNTA3v3gChMPniUEcw5AyPj2LJlBEsmWJNRGWM4WhVY5tWrK2FVd5WVX9FlQ0UVTbw1nbfZ4jx6fHMsbsJ5uakMH1UEjGR+qWBCn+aUKnO7XrdV556WZfVlm8uotllrdg+IzOJaaOSgh1Z741fAqNmw9EtxEgLN0a8zaP7v8QP65t13Q2lVFjafayaN7Yd9W7/90VTQxhNmPrK86GOYMgTETJTYslMifVO+OTxGA6W11lJVoGVZO0orqbJ/uzg70BZHQfK6njFHpcdYY/v8p++vfVLBaXCiSZUqqOmWsh/z7c97YpOqxlj+Pvaw97t1sGsYU8Ezr4TXrwJgK853+UvTVfw0Hv7+MUVM0Ibm1JKdeLxjw56yxdOz2B2TkoIo1EqcA6HMCE9gQnpCVw91+rF0uL2sLekhq12K9bmgir2ltR0SJZcHsOO4mp2FFfzz0+tfVEOyN2zxkqy7PFYY1PjdNILFVJBTahE5GLg94ATeNwYc3+7+6OBvwPzgXLgOmPMIREZC+wC9thV1xljbg9mrMrPzlehpd4qp0+D9M4HPa87UMG+UmvtqbgoZ/jO7teZaVfA8PFQcYAUqeNG5zs8ti6W608fzaSMxFBHp5RSXqXVjby22TdW9fYlE0IYjVK9F+l0MCMzmRmZyXx54WgAGprd7Dxa5W3F2lpYxYHjdR2ObfbAhsMn2HD4hHdfUkxEmwRrdnYKI5Nj+u33USpoCZWIOIFHgAuAQmC9iCw3xuz0q3YrcMIYM1FElgH/C1xn37ffGDMnWPGpbmz6h6889/ouqz2z7pC3fPXcLBIH0mBShxPO+h68/h0Abo9Yzj+azuOnr27nudvO0G+6lFJh45l1h71rAs0bncK80cNCHJFSfS82ysn8McOZP8Y3725VQwvbi6rYXOBbI+toVWOHY6sbXXycf5yP8497941IjPZ1Fcyxfmq3fhUswWyhWgjkG2MOAIjIc8CVgH9CdSXwC7v8EvBH0U+yoVW+H46sscrihNzrOq12rKqRt3eUeLe/tmhsPwTXx+Z8BVb/Hir2kyz1fDPide4/+GVe3FDIl04bIN0XlVKDmsvt4YUNBd7t/zhnfAijCXMr/8dXXvrj0MWh+kxybCRnTUzjrIlp3n2vvv0BCTkz2kx8caK+pcOxpTVNvLerhPd2+T6rjEmNazMea2ZWEnFROvpF9V4w/4uygAK/7ULg9K7qGGNcIlIFtM7HOU5ENgHVwE+NMR+1fwARuQ24DSAjI4O8vLxeBVxbW9vrc/SXYMU67sAzjLHLx4fPZ/uGnbTNgS0v7W329nWeMszB0d0bObq7/+LsK+kjr2FGxW8AuMn5b55yXcTdy7cSU5FPUnR45vbhfk1baZx9a6DECQMr1nC3qs06f1FcMD0jxBGFsQ/9RhVoQjVopUQ7WDI9g/Pt54IxhoKKBrYUVnqTrO1FVdQ3uzsce7i8nsPl9by+pRgAh8CkEYnkZidb625lpzBlZCJREWG8/IsKS8FMqDr7NNp+apau6hwFRhtjykVkPvCqiMwwxlS3qWjMY8BjAAsWLDBLlizpVcB5eXn09hz9JSixetzw2Te9m2nnf5cl0zo+RnVjC99e+YF3+7uXzGHJrFH9F2df8pwLf30Xjm4mRlr4UeQ/ubPlW/z7eBKPfGVeWHb9C/tratM4+9ZAiRMGVqzh7oX1vnWnvjAvO7zX+VMqBESE0alxjE6N4/LZmQC4PYb9ZbVsKbDXyCqsZNfRam/X2VYeA3tKathTUsOLG63nWpTTwbTMJG8r1uzsZCakJ+BwhN/nARU+gplQFQL+/aaygeIu6hSKSASQDFQYYwzQBGCM2Sgi+4HJwIYgxqt2vQ7V9sDnuDSYfFGn1Z5Ze5iaJmtNifHp8Vw0Y2R/Rdj3HA644B74uzWT4dXO1bzgXsKb2+CVz4oGxrpaSqlBqa7Jxco9pd7taxfo65FSgXA6hMkZiUzOSORaewbiJpeb3Udr2nQV3Fdai2n3VX+z22MtUlxQCVgzGSdERzAzK4nZ2Snk2utkZQ+LDcsvXVVoBDOhWg9MEpFxQBGwDPhKuzrLgRuBtcAXgQ+MMUZE0rESK7eIjAcmAQeCGKsyxhpP1Gr+TeDsOMlEQ7ObJz/2Td/7n4sn4Bzo39qMX0zJiHPIKLV6lf4y4kk+33w/P1++g4XjhpMzPC7EASqlhqK8PWXetXqmZCQycYTOQKrUqYqOcFrd+nJS+Kq9r67JxfYiqwWrNckqqGjocGxtk4t1BypYd6DCu294fJS1ALHdijU7J4W0hOh++m1UuAlaQmWPiboDeBtr2vQnjTE7ROQeYIMxZjnwBPCMiOQDFVhJF8C5wD0i4gLcwO3GmIqOj6L6zKGPofgzq+yMhtM7n6X+n58eobyuGYCslFiumjuApkrvxv4Jt5BRtQWaqpngOMq3Il7lwaZr+fY/N/H8N84gOkJXaldK9a+3tvsW8r145gDuCaBUmIqPjuD08amcPj7Vu6+irtk7o2DrGlnHa5s6HFtR10zenjLy9pR592Umx1gtWDnJzM5OYWZWMsmxA2gGZHXKgjq1iTHmTeDNdvvu8is3Atd2ctzLwMvBjE214986Nfd6SEjvUKWqoYWHP9jn3b7t3PGDpj9/c/RwOO9n8NYPAbjD+SofumfzWcFk7nl9J/ddPSvEESqlhpLGFjcrd/u6+31+liZUSvWH4fFRLJkygiVTRgDWpBdHqxrbdBXcWlhFTaOrw7HFVY0UVx3j3zuOefeNS4v3tmTlZiczI1NnFhyM9C+qoHgz5L9rbwgsuqPTao+szPdOTZo9LJbrBtvU4qfdai1qfHg1TjE8FPkIlzT/D//45Aizc1L40oJB9vsqpcLWR/uOU2fPUjYuLZ4puuC4UiEhImSmxJKZEsvFM60JuDwew6HyOu+EF1sKKtlRXO3touvv4PE6Dh6v47XNvpkFJ2ckMivLtz7W1JFJOrPgAKcJ1VBnDLzzU9/29CsgdUKHagUV9fxt9SHv9v+7eCoxkYOsG5zDCVc/Cn8+C5qqGO0o4/7Ix7mj5dv85F/byEqJbbMWhlJKBYv/ZBQXzRipg9+VCiMOhzA+PYHx6QneoQ8ut4e9JbXelqxtRZXsPlqDy9NxZsHdx2rYfaztzIJTRyW2acmaNCJx4I9RH0I0oRrq9rwJh+wlvhwRVre3dowx3LNiJ81u65uXuaNTuCy382nSB7yUHLj8QXjpFgAuc65jjyebh93X8I1nNvLCNxYxPTMpxEEqpQa71fnHveUlUzp2wVZKhZcIp4PpmUlMz0xi2UJrX2OLm11Hq+3xWFZ3wfyyzmcWbK0DRwCIjXQyMyvJm2DlZqcwNjVOv1wJU5pQDWWu5ratUwtuhbRJHaot31LMuzt9K43/9NJpg/sJPfMLcHgNrH8cgP+KfIl8k8VbTafztSc/5bnbTtfZtpRSQVNQYS0+CtaHqrmjU0IckVLqVMREOpk7ehhzRw/z7qttcrGjqMrbXXBrYRVHKuo7HNvQ4mb9oROsP3TCuy8pJoLc7BRmZSd718kalRzTL7+L6p4mVEPZxw9AhT0bfUwyLPlRhyplNU38fPkO7/ZXTh/N/DHD+yvC0Ln4fji+Fw6uAuD3kY9Q2xLLR7W5LHvsE/759dOZpGMalFJB4N86tXDccJ1lNFDzbgx1BEr1KKGTmQUr65u9LVhbCqvYVljFserGDsdWN7r4OP84H/u9RqQlRJMV62Kza6+3JUunb+9/mlANVYUb4MNf+7YX/wji2iZKHo/hx69spdKeiCIrJZYff35qf0YZOs5IuPZpePxzUHGAKHHxWOQD3Nzy36yrnc6yx9bxxE2nMSdHvzlWSvWtNfvLveWzddxm4K74Q6gjUOqUpMRFce7kdM6d7OveW1rdaCdXvtkFWycG83e8tonjtbDlPd8szFkpseRmJ9stWTp9e3/QhGooaq6DV24DY80gxegz4fRvdKj28Af5vLfLNzD6f7+QS2LMEHpCxg2Hr70GT10CVQXESjNPRf6ab7d8m/fq5rPssbX8ftlcLpqh0xkrpfrOpgJfF5+F44ZAjwClVAcjkmK4YHoMF0zPAKzx7IUnGvxasirZXlRNbVPH6duLKhsoqmzgre2dT98+OzuZ6Tp9e5/SKznUeDzwr9uhYr+1HZUIV//FmuHOz7s7S3jwvb3e7VvPHsfZk4bgN6Upo31JVe0xYqWZR6Me4OctN/F/LRdw+/9t5NtLJ/Ld8yfrbDxKqV4rq2mioKIBgOgIB9NG6SQ4Silr+vac4XHkDI/j0lzf9O0Hjtfx/LtraUnMZEthJTtPcvp2/5kFdfr2U6cJ1VDz3l2wa7lv+5Jfw7Axbap8cqCc7/xzk3f7zAmpQ6erX2dSJ8DNb8L/fQFOHMSJ4ZeRTzFb9vMz18384YN8Nhw+wW+vnU1mSmyoo1VKDWCbCyq95ZlZyfrhRinVJYdDmDgigbOyIlmyZAYALW4Pe0tqvC1ZWwur2HOs++nbX9jgm7592qhEZnlbslKYOCJBvzAOgCZUQ8nq38Oah33bp/8nzPlKmyobDlVw89/W09BidQfMSonlj1+ZR4RziL+pp06AW9+FZ6+FYivZvDZiFbMd+/lBy+2s2Q8XPbiKn1w6jetOyxncsyAqpYJm0xFfd7+5Okbz5Cz/jq+s46nUEBXpdDAjM5kZmcl8eeFowJq+fefRarb5zSy4v4vp27cUVrGlk+nbZ2YlW+OyspIZl6ZJVnuaUA0FxsD7d8PHD/r2TbkULrqvTbV/bz/Gnc9v9iZTIxKjeebWhQyPj+rPaMNXQjrc9Aa88V+w5Z8ATHYU8a+ou3jCfQl/aLqaH72yjec3FPDzy2fohBVKqZO26Yivhcp/qmUVgM+e9pU1oVLKKybSybzRw5jn95pS09jCjuLqNjMLBjp9e3yUkxmZyXZLVjIzs5IZlxqPYwgnWZpQDXaN1bDie7D9Zd++MWfBF/7qHTfl9hgeWZnPA+/6xkylJUTx7NfPYHx6Qn9HHN6i4uGqP8PoRfDvH0FLPU4x3BbxBtc4P+Ih1xd44cgSrnpkNZ+fOZLvfG6SjoFQSgXE4zFsLfRPqPRLGaVUcCTGRHLG+FTO8Ju+/URdM1uLqthaUGn9LKykpLqpw7F1zW4+PVTBp4cqvPsSoiOYkZnkTbBys1MYMzxuyCRZmlANZkc+gX99A04c9O2bcgl88UmItMb67C+r5YcvbuEzv29Fx6TG8cSNpzFxhCZTnRKB+TfCuHPh9e/CwQ8BSJNqfhn5FHdEvMrjrkt4YfsS3tp+jCVT0rnxzLEsnpQ+ZF5YlFIn70hFPXXNVg+BtIQoXbBTKdWvhsVHsXhyOov9pm8vqW5kW2EVW4uq2G4vSHy8tmOSVdvk4pODFXxy0JdkJUZHMDPLasmalWXdxqTGDcphEZpQDUbVxfD+Pd5uaV7zb4ZLfgvOCE7UNfPIynz+vvYwzW7fbDCLxqfyp+vnMUy7+fVs+DhrBsBtL1rXu6oAgJFygp9G/oP/iniRFe4zWL7vTG7bM53UpAQuyx3FFXMymZWVPChfUJRSp25PSY23PGVkor5GKKVCLiMphozpMZzvN317SXUTWwsrrQSryOouWF7X3OHYmiYXaw+Us/aAb229pJi2SVZuVgo5w2MH/OudJlSDSclOWPcn2Po8uP3+saMS4fKHYNYXOXi8jqfX7OGljYVt1i6IcAjfPm8S31w6gcihPgHFyRCB3C/BtMvh07/C2j9CbQkAsdLMtRGruJZVVJs43m+Yy7/XnMb1H89keGoaF07PYNGEVE4bO3xore+llOrUnmO+hGpyRmIII1FKqc6JCCOTYxiZPJIL7XU4jTEcrWpkm51cbSuybhWdJFnVjS7W7C9vs4B5cmwks7KS20x8kT1sYCVZmlANZMZA2R7Y97Y1Rurolo5Vpl7GkdN+yrvF0ax4ZHWbKXlbzclJ4b6rZzIjM7k/oh6cImPhrO/AwtuslsH1T0DJNu/dSVLP1c7VXO1cjccIe2qy2bh2MstXT+FXTCAxczILxqUxI9NabG98WrzOrKjUENF85AjlTz3F4pdf43PNDTRERNNQcwHNs79N1OjRoQ5PKaW6JSJkpsSSmRLLRX5JVnFVI9sKK9lmdxXcXlTFifqWDsdXNbTwcf5xPs4/7t2XEhfp7SY4y27RykrpPskqqC7g6Z1Ps+LACupa6oh/Np7Lxl/GjdNvJCcpp+9/cT+aUA0UHg9UF0LZXijbzfQdb8Fn34Tqok6rH03K5YWEr/L8wQkUbz7QaZ2JIxL4wYVTuGhGxoD6FiCsRcbAgpth/k1QtNFKdHe97u0OCOAQwzQpYJqjgBt4H4CmsggOlI4i32TxpsnkmIxAUnKIGj6GxIwxZKelMDo1joykGOpbDMYY/ZspNQjUrlpF4Xe/h2lpIcpl9RqIdzURl/dvDqx5n+zfP0TCueeGOEqllDo5IkJWSixZKbFcPNNaiNgYQ+GJBm9XwdYxWVUNHZOsyvoWPtp3nI/2+ZKsYXGRzMpOYVZWErOyUpiVnUxmcgwiwkeFH/H9D7+Py+3CZazX0rqWOl7e+zKv7X+NBxY/wDnZ5wTt9w1qQiUiFwO/B5zA48aY+9vdHw38HZgPlAPXGWMO2ff9GLgVcAPfMca8HcxY+5Ux4HFBSz001Vi3xmq7XA2NlXiqj+GpPoapOQo1R3FW5ONwNXhPMaKT0zaZSN71zOdvrgvZUDoVSgEa29SJcAhLpqTztUVjOXtimk6SECwikL3Aul30K6v1cPcK2Ps2pmQ7YtquYh4tLivJwpd4UWPfDkO1iaPcJHKCRCJNEi9/9BCNkcMgOomI2Hic0Qk4ohNwxiQQGZtIVGwCUbFJRMXFExUVQ2RUNNHR0URFRRMVHUNMVCTRkU5iIhw4HaLJmVJd6M37WE+ajxyxkqmGhg73iduFaXBR+N3vMf61V7WlSik14IkIOcPjyBkex+dntU2ytnq7ClayrbCK6kZXh+NP1Lewam8Zq/aWefelxkcxKauJPc5f4KLjZBku48LlcvH9D7/PK5e/ErSWqqAlVCLiBB4BLgAKgfUistwYs9Ov2q3ACWPMRBFZBvwvcJ2ITAeWATOATOA9EZlsjHEHI9bjxYco+fstpLQ0s2NdBBiD9fHSIMYA1k0w9n12GQMGb1ns+k5cRBgXEfZPJ24iaCHCuInARSQd/0nac9i3ntSYWD7yzGKlZw5vu0+jmvgOdRKjIzhjQirnTR3BxTNG6oQT/U0EMudYt/N+ijTVWK1XRz6Bgk/wlOzEUXu021MkST1JUs84Snw73UC9fTtJbiO0EEE9Ebhw0kIEbpyA4BHB4LD/ox2Y1m2x94nffQhGBA8OsJ8ZHrHKyS4321Zb57SuA75yu8vTyiC+Gl0keabdOdpv+z2YX52uzxPf0sLmdZHWMR1OFT6JZlxzM5s/+Z9QhxGQuOZm8odFMnH2WaEOpVd68z4WyPnLn3oK09Lxm1l/pqWF8r89zai7fnZKv4NSSoUz/yTr0lxfknWkor7DmKyaTpKs8rpmaqteI3JYS1cfGwBwuV38feff+ckZPwnK7xHMFqqFQL4x5gCAiDwHXAn4vxFdCfzCLr8E/FGsr8qvBJ4zxjQBB0Uk3z7f2mAE2tTYwIzGjdZGUFK2vlFhEsg3WeR7MtltRrPRM4XdJsf+IGyJi3IybVQSMzJbb8lMGZmoE02Ek+hEGL/EumEnzg2VcHwvlO6CEwdpKj9Cc/lhnNWFxDSW4sDT5elOhVMMTlqIofsPc4AvG+ksK+lJAKcPC2H8vG+jY0NG2NpWVRrqEPrCKb+PGWN6fMZUL38dXD18weZyUb18uSZUSqkhQ0QYkxrPmNR4LsvNBKx1+rxJlp1obS+qoqbJRWTyJkS6/5zkMi5WHFgxIBOqLPDvv0QhcHpXdYwxLhGpAlLt/evaHZvV/gFE5DbgNnuzVkT29DLmNOB4j7VCphoobt3oMtZdwCv9FFEAwvyaeg2UOGHgxKpx9q2BEidAGndf09tYx/RJJL3Tm/exNr9/u/erJhHZPiM6Zn6ggewQ2XiSsQ9Effc/fnf4tC730kB63vcXvSYdDelrEjM28NdSuf6kX0sDei8KZkLV2atZ+2/suqoTyLEYYx4DHjv50DonIhuMMQv66nzBNFBi1Tj73kCJVePsWwMlThhYsfagN+9jbXf4vV8NouvTp/S6dKTXpCO9Jh3pNemov69JMPuBFQL+I7+y8WteaV9HRCKAZKAiwGOVUkqpYOrN+5hSSqkhIpgJ1XpgkoiME5EorEkmlrersxy40S5/EfjA7ne+HFgmItEiMg6YBHwaxFiVUkqp9nrzPqaUUmqICFqXP7sv+R3A21jTzT5pjNkhIvcAG4wxy4EngGfsSScqsN6ssOu9gDXw1wV8K1gz/LXTZ90H+8FAiVXj7HsDJVaNs28NlDhhYMXapd68j/VgUFyfINDr0pFek470mnSk16Sjfr0mol+kKaWUUkoppdSp0bm0lVJKKaWUUuoUaUKllFJKKaWUUqdIEyqbiFwsIntEJF9EfhTqeFqJSI6IrBSRXSKyQ0S+a+8fLiLvisg+++ewUMcKICJOEdkkIivs7XEi8okd5/P2wO6QE5EUEXlJRHbb13ZROF5TEbnT/rtvF5F/ikhMuFxTEXlSREpFZLvfvk6voVj+YD+/torIvBDH+Rv7b79VRP4lIil+9/3YjnOPiFwUyjj97vuBiBgRSbO3w+p62vu/bV+zHSLya7/9Ibme4aCn9xV74qXn7fs/EZGx/R9l/wrgmnxfRHba/9fvi0g4rEcWVIF+/hCRL9qvA0NieuxArouIfMn+f9khIs/2d4z9LYDnz2ixPjNusp9Dl4Qizv7U3XunfX//vF8aY4b8DWuw8X5gPBAFbAGmhzouO7ZRwDy7nAjsBaYDvwZ+ZO//EfC/oY7VjuX7wLPACnv7BWCZXf4L8J+hjtGO5WngP+xyFJASbtcUa8HQg0Cs37W8KVyuKXAuMA/Y7rev02sIXAK8hbVmzxnAJyGO80Igwi7/r1+c0+3nfzQwzn5dcIYqTnt/DtakCIeBtDC9nkuB94Boe3tEqK9nqG+BvK8A3wT+YpeXAc+HOu4wuCZLgTi7/J96Tbz1EoFVwDpgQajjDofrgjUD9CZgmL09QjIKBgAACwhJREFUItRxh8E1eaz1M4H9+nso1HH3w3Xp9L3T7/5+eb/UFirLQiDfGHPAGNMMPAdcGeKYADDGHDXGfGaXa4BdWB+0r8RKCrB/XhWaCH1EJBu4FHjc3hbgPOAlu0q4xJmE9QR8AsAY02yMqSQMrynWTJyxYq1vEwccJUyuqTFmFR3X2+nqGl4J/N1Y1gEpIjIqVHEaY94xxrjszXVY6wu1xvmcMabJGHMQyMd6fQhJnLYHgf+m7WKxYXU9sT743m+MabLrlPrFGZLrGQYCeV/xf768BHzOft0crHq8JsaYlcaYenvT/7k5WAX6+eNerC+sGvszuBAK5Lp8HXjEGHMC2rzuDFaBXBMDJNnlZIbAGq7dvHe26pf3S02oLFlAgd92ob0vrNjdQeYCnwAZxpijYCVdwIjQReb1ENYHP4+9nQpU+n1wDZfrOh4oA56ym8UfF5F4wuyaGmOKgN8CR7ASqSpgI+F5TVt1dQ3D+Tl2C9a3VxBmcYrIFUCRMWZLu7vCKk5gMnCO3W3tQxE5zd4fbnH2p0B+d28d+zldhfW6OVid7P/Drfiem4NVj9dEROYCOcaYFf0ZWIgF8r8yGZgsIqtFZJ2IXNxv0YVGINfkF8ANIlIIvAl8u39CC2v98j6kCZWls28Ew2o+eRFJAF4GvmeMqQ51PO2JyGVAqTFmo//uTqqGw3WNwGoe/rMxZi5Qh9U9LazY44+uxOoqlQnEA5/vpGo4XNOehOX/goj8BGutu3+07uqkWkjiFJE44CfAXZ3d3cm+UF7PCGAYVneKHwIv2C0t4RZnfwrkdx9q1yfg31dEbgAWAL8JakSh1+01EREHViv1f/VbROEhkP+VCKxuf0uALwOP+4+HHYQCuSZfBv5mjMnG6ur2jP0/NJT1y+vsUL/IrQqxxim0yiaMmklFJBIrmfqHMeYVe3dJa5Ol/TPUTd1nAVeIyCGsZujzsFqsUuzuahA+17UQKDTGfGJvv4SVYIXbNT0fOGiMKTPGtACvAGcSnte0VVfXMOyeYyJyI3AZcL2xO1oTXnFOwEqmt9jPq2zgMxEZSXjFCVY8r9hdKj7FaqVOI/zi7E+B/O7eOvZzOpnuu64MdAH9P4jI+VhfJlzR2o10EOvpmiQCM4E8+3XgDGD5EJiYItDnz2vGmBa7S/EerARrsArkmtyKNc4aY8xaIAbrtXgo65f3IU2oLOuBSWLNnhaFNTh4eYhjArzjkJ4AdhljHvC7azlwo12+EXitv2P7/9u72xgrrjqO498fsUha0KQPmibUIBtpbWLYBhSqErYVa6EVmwDBhGif3myjqC+aWkNCtu0bfAjaqA1q02KsUUAb3LSCBNulFS2UloWlKA9StKA0XY21pIha/r4457rj9i67vXBn7tbfJ5nsnbnnzJz7z509c+45c6YoIr4UERMjYhIpfo9FxBLgcWBhTlZ5OQEi4hjwgqRL86aPAHtpsZiShvrNlHRu/h7UytlyMS0YKobdwKfzbDszgZdrQwOrkIeGfJF0wfZq4a1u4JN59rV3kyrn7VWUMSL6IuIdETEpn1dHSBPUHKPF4gmsJ/2IgqQppBum+2mheFZgJPVK8XxZSPq/+WbuoRo2Jnl423dI52bVP2qV4bQxiYiXI+LCwv+Bp0ix2VFNcUszkvNnPWkSE5RmQJ0CHCq1lOUaSUz+SLpWQNJ7SQ2ql0otZespp75sxkwXo3EhdY3uJ82gsqzq8hTK9WFS1+RuoDcv80jj7H8JHMh/z6+6rIUydzAwy99k0gXUQWAdeRawqhegHdiR47qeNFyp5WIK3AX8DtgD/IA0W1pLxBT4Eenern+RLvZvHSqGpC73b+fzq48SZ6kaopwHSWOqa+fUqkL6Zbmc+4C5VZZz0PuHGZjlr9XiORZ4KH9PnwWurjqerbDUq1eAu0kXxJAudtbl7+N2YHLVZW6BmGwGXiycm91Vl7nqmAxK21Pm+d7Kccn/B1eSfmjsI89++2ZeRhCTy4GtpBkAe4Frqi5zCTGpVyd1Ap2F70nT60vlg5mZmZmZmdkb5CF/ZmZmZmZmDXKDyszMzMzMrEFuUJmZmZmZmTXIDSozMzMzM7MGuUFlZmZmZmbWIDeozM6QpAsk9eblmKSjhfVfN/G4z+RnURS33STpW806ppmZjR6Slkl6TtLuXCfNqKgc7ZLmFdbnS7ozv14taWGdPB2SHimznGaNekvVBTAb7SLiL6TnWiGpCzgeEV9r5jElTQKORsQ/m3kcMzMbnSRdCVxPeiD4yfzw27HDZGuWdmA68HOAiOjm9Q+lNRu13ENl1kSSjue/HZK2SForab+kFZKWSNouqU9SW053kaSfSno6Lx8aYtdzgY05z815n1uA/6aX9HFJ2yTtlLRZ0jsljZF0QNJFOc0YSQclXShpkaQ9knZJeqKpgTEzs2a7GOiPiJMAEdEfEX+SdDg3rpA0XVJPfj27MLpip6QJefsduZ7aJWlF3tYmaWMeKfGkpMvy9tWSVuVt+yVdn0dS3A0szvteXGc0xZxinsEfRNJ5kh7I9eJOSZ9oYtzM3jA3qMzKMxX4PPA+4FPAlIj4AHA/sDSnuRf4ekS8H1iQ36vnWmCjpIuBu0gNqY+SnpJe8ytgZkRcAfwYuCMiTgEPAUtymjnArojoB5YDH4uIqcD8s/B5zcysOpuAS3Ij5T5Js4dJfzvwmYhoB2YBJyTNBW4AZuS64Ss57XeBpRExLee7r7CfScBs4DpgFelaczmwJiLaI2JNnWP/Tx5J4wa9vwx4LNeNVwFflXTesBEwK4mH/JmV5+mI+DOApN+TKjuAPlIFAamBc7mkWp63SZoQEa/UNuRf+yZGxCFJNwA9EfFSfm8NMCUnnQisyY2uscDzefsDwM+AbwC3AA/m7VuB1ZLWAg+fvY9tZmZli4jjkqaRGkdXkeqDO0+TZSuwUtIPgYcj4oikOcCDEfFq3udfJY0HPgisK9RVby3sZ23+8e6ApEPAZSMo7nB5rgHmS7o9r48D3gX8dgT7Nms6N6jMynOy8PpUYf0UA+fiGODKiDhxmv3MIvU+1cQQ6b4JrIyIbkkdQBdARLwg6UVJVwMzyL1VEdGZb1i+DuiV1J7vDzMzs1EoIl4DeoAeSX3AjcC/GRihNK6QdoWkR4F5wFO5MSVeX8eMAf6We7LqHnaY9UbyCFgQEftGsC+z0nnIn1lr2QR8trYiqV6FdS2wIb/eBnQozTR4DrCokO7twNH8+sZB+7ifNPRvba5wkdQWEdsiYjnQD1xyph/GzMyqIelSSe8pbGoH/gAcBqblbQsK6dsioi8ivgzsIPUSbQJukXRuTnN+RPwdeF7SorxNkqYWjrMo35/bBkwG9gGvABNOU9x6eYp+ASxV7hKTdMWIA2FWAjeozFrL54DpSlPc7gU666TpALYA5CGEXcBvgM3As4V0XaQhGU+SGkhF3cB4Bob7QRqT3idpD/AEsOtMP4yZmVVmPPB9SXsl7SbdY9tFuu/23lw3vFZI/4XaxETACWBDRGwk1Rc7JPWS7peCNLLh1pz2OaA4ScQ+Uh21AeiMiH8Aj5OGs/dKWlynrPXyFN0DnAPsznXUPQ3Ew6xpFDGSnlgzawWSJgLfi4i5Z7if6aTJL2adnZKZmdn/O0mrgUci4idVl8WsTL6HymwUiYgjpCnTG5ZvSr6NgZn+zMzMzKxB7qEyMzMzMzNrkO+hMjMzMzMza5AbVGZmZmZmZg1yg8rMzMzMzKxBblCZmZmZmZk1yA0qMzMzMzOzBv0HO6LyeejVdBoAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# parameter values\n", "R0 = 4\n", "t_incubation = 5.1\n", "t_infective = 3.3\n", "\n", "# initial number of infected and recovered individuals\n", "e_initial = 1/20000\n", "i_initial = 0.00\n", "r_initial = 0.00\n", "s_initial = 1 - e_initial - i_initial - r_initial\n", "\n", "alpha = 1/t_incubation\n", "gamma = 1/t_infective\n", "beta = R0*gamma\n", "\n", "# SEIR model differential equations.\n", "def deriv(x, t, alpha, beta, gamma):\n", " s, e, i, r = x\n", " dsdt = -beta * s * i\n", " dedt = beta * s * i - alpha * e\n", " didt = alpha * e - gamma * i\n", " drdt = gamma * i\n", " return [dsdt, dedt, didt, drdt]\n", "\n", "t = np.linspace(0, 160, 160)\n", "x_initial = s_initial, e_initial, i_initial, r_initial\n", "soln = odeint(deriv, x_initial, t, args=(alpha, beta, gamma))\n", "s, e, i, r = soln.T\n", "\n", "plotdata(t, s, i, e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The addition of an exposed population compartment slows the outbreak, but doesn't appear to reduce the number of people ultimately infected by the disease.\n", "\n", "* What are the campus policy implications of these results?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 3. Mitigation and Social Distancing\n", "\n", "* Pan, Jinhua, et al. \"Effectiveness of control strategies for Coronavirus Disease 2019: a SEIR dynamic modeling study.\" medRxiv (2020). https://www.medrxiv.org/content/10.1101/2020.02.19.20025387v3.full.pdf\n", "\n", "The lack of a vaccine reduces the options for controlling the COVID-19 outbreak. Current efforts are focused on 'social distancing' designed to reduce transmission of the virus from individuals in the infective state to susceptible individuals.\n", "\n", "For the purposes of modeling, we introduce a control parameter $u$ indicating the effectiveness of these efforts. $u=0$ corresponds to no controls, $u=1$ corresponds to perfect isolation of infective individuals. The purpose of this model is to explore how a social distancing stragtegy affects the outcome of an epidemic.\n", "\n", "* **Exposed.** The subpopulation that has been exposed to the disease but not yet infective. \n", "\n", "The compartment model can be diagrammed as follows.\n", "\n", "$$\\text{Susceptible}\n", "\\xrightarrow{(1-u)\\frac{\\beta S I}{N}} \n", "\\text{Exposed} \n", "\\xrightarrow{\\alpha E} \n", "\\text{Infectious} \n", "\\xrightarrow{\\gamma I} \n", "\\text{Recovered} $$\n", "\n", "The rate processes are modeled as follows.\n", "\n", "* $(1-u)\\frac{\\beta S I}{N}$ is the rate at which susecptible population encounters the infected population resulting in trasmission of the disease. $u$ describes the effectiveness on any public health interventions to control transmission of the disease. $u=0$ means no effective public health interventions, $u=1$ means total elimination of disease transmission..\n", "\n", "After substitution, this results in a system of four equations.\n", "\n", "\\begin{align*}\n", "\\frac{ds}{dt} & = -(1-u)\\beta s i \\\\\n", "\\frac{de}{dt} & = (1-u)\\beta s i - \\alpha e \\\\\n", "\\frac{di}{dt} & = \\alpha e - \\gamma i \\\\\n", "\\frac{dr}{dt} & = \\gamma i\n", "\\end{align*} \n", "\n", "where $s + e + i + r = 1$ is an invariant." ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# parameter values\n", "u = 0.2\n", "R0 = 2.4\n", "t_incubation = 5.1\n", "t_infective = 3.3\n", "\n", "# initial number of infected and recovered individuals\n", "e_initial = 1/20000\n", "i_initial = 0.00\n", "r_initial = 0.00\n", "s_initial = 1 - e_initial - i_initial - r_initial\n", "\n", "alpha = 1/t_incubation\n", "gamma = 1/t_infective\n", "beta = R0*gamma\n", "\n", "# SEIR model differential equations.\n", "def deriv(x, t, alpha, beta, gamma):\n", " s, e, i, r = x\n", " dsdt = -(1-u)*beta * s * i\n", " dedt = (1-u)*beta * s * i - alpha * e\n", " didt = alpha * e - gamma * i\n", " drdt = gamma * i\n", " return [dsdt, dedt, didt, drdt]\n", "\n", "t = np.linspace(0, 160, 160)\n", "x_initial = s_initial, e_initial, i_initial, r_initial\n", "soln = odeint(deriv, x_initial, t, args=(alpha, beta, gamma))\n", "s, e, i, r = soln.T\n", "\n", "plotdata(t, s, e, i)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Social distancing has several beneficial effects:\n", "\n", "* Slows down the progress of the epidemic.\n", "* Seduces the fraction of the population infected at any point in time, thereby reducing strain on health care resources.\n", "* Reduces the number of individuals ultimately experiencing the disease. For a disease with a non-zero mortaility, this saves lives." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Social Distancing Strategies for the Campus\n", "\n", "The basic strategy is to slow transmission through 'social distancing' with the following goals:\n", "* Reduce the number of individuals acquiring the virus.\n", "* Slowing progress of any outbreak long enough to complete the semester.\n", "\n", "[CDC Social Distancing](https://www.cdc.gov/coronavirus/2019-ncov/community/guidance-ihe-response.html)\n", "\n", "* Replace large section courses with streaming lectures. Close the largest lecture halls for the remainder of the term.\n", "* Bring food to the dorms rather than the dorms to food.\n", "* Locate an area to isolate and quarantine students with potential infectious state.\n", "* Hold Saturday classes, move graduation up one week.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model 4. Improving the fidelity of the model.\n", "\n", "Boldog, et al." ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "u = 0.3\n", "mu = 0\n", "alpha = 1/5.1 # incubation period\n", "R0 = 2.4\n", "gamma = 3.3\n", "beta = R0*gamma\n", "\n", "N = 331000000\n", "\n", "def SEIR(x, t):\n", " S, E1, E2, I1, I2, I3, R = x\n", " dS = -(1-u)*beta*S*(I1 + I2 + I3)/N\n", " dE1 = -dS - 2*alpha*E1\n", " dE2 = 2*alpha*E1 - 2*alpha*E2\n", " dI1 = 2*alpha*E2 - 3*gamma*I1 - mu*I1\n", " dI2 = 3*gamma*I1 - 3*gamma*I2 - mu*I2\n", " dI3 = 3*gamma*I2 - 3*gamma*I3 - mu*I3\n", " dR = 3*gamma*I3\n", " return [dS, dE1, dE2, dI1, dI2, dI3, dR]\n", "\n", "\n", "IC = [N, 1, 0, 0, 0, 0, 0]\n", "t = np.linspace(0, 180, 1000)\n", "\n", "\n", "soln = odeint(SEIR, IC, t)\n", "\n", "s = soln[:, 0]\n", "e = soln[:, 1] + soln[:, 2]\n", "i = soln[:, 3] + soln[:, 4] + soln[:, 5]\n", "r = soln[:, 6]\n", "\n", "plotdata(t, s, i, e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Additional Modeling Opportunities. Transportation, power law kinetics, etc.\n", "\n", "* Ziff, Robert M., and Anna L. Ziff. \"Fractal kinetics of COVID-19 pandemic.\" medRxiv (2020). https://www.medrxiv.org/content/10.1101/2020.02.16.20023820v1\n", "\n", "* Peng, Liangrong, et al. \"Epidemic analysis of COVID-19 in China by dynamical modeling.\" arXiv preprint arXiv:2002.06563 (2020). https://arxiv.org/abs/2002.06563\n", "\n", "* Wu, Joseph T., Kathy Leung, and Gabriel M. Leung. \"Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study.\" The Lancet (2020). https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)30260-9/fulltext\n", "\n", "* Tuite, Ashleigh R., and David N. Fisman. \"Reporting, Epidemic Growth, and Reproduction Numbers for the 2019 Novel Coronavirus (2019-nCoV) Epidemic.\" Annals of Internal Medicine (2020). https://annals.org/aim/fullarticle/2760912" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Manometer Models and Dynamics](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/03.08-Manometer-Models-and-Dynamics.ipynb) | [Contents](toc.ipynb) | [PID Control](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/04.00-PID_Control.ipynb) >

\"Open

\"Download\"" ] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }