{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Resolvendo numericamente equações diferenciais com R\n", "\n", "*Esta é uma breve descrição do que é integração numérica e um tutorial prático de como fazê-la em R.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Software necessário\n", "### R\n", "*Para executar os códigos R deste notebook em seu próprio computador, você precisa instalar o seguinte software:*\n", "\n", "* [R](http://www.r-project.org/), juntamente com os pacotes do [CRAN](http://cran.r-project.org/):\n", " * [deSolve](http://www.vps.fmvz.usp.br/CRAN/web/packages/deSolve/index.html), uma biblioteca para resolver equações diferenciais\n", " * [ggplot2](http://www.vps.fmvz.usp.br/CRAN/web/packages/ggplot2/index.html), uma biblioteca para plotagem\n", " * [reshape2](http://cran.r-project.org/web/packages/reshape2/index.html), para manipular data.frames\n", "\n", "Para instalar o R, baixe-o de sua página inicial (Windows ou Mac): http://www.r-project.org/. No Linux, você pode instalá-lo usando a maneira preferida de sua distribuição, por exemplo:\n", "\n", "* Debian/Ubuntu: `sudo apt-get install r-base`\n", "* Fedora: `sudo yum install R`\n", "* Arch: `sudo pacman -S r`\n", "\n", "Para instalar os pacotes, tudo o que você precisa fazer é executar o seguinte no prompt `R`\n", "\n", " install.packages(c(\"deSolve\", \"ggplot2\", \"reshape2\"))\n", " \n", "O código R apresentado aqui e alguns exemplos adicionais estão disponíveis em https://github.com/piklprado/ode_examples (obrigado, [Diogro](https://github.com/diogro), e todos mais que contribuiram para estes tutoriais).\n", "\n", "### Executando comandos este notebook\n", "Você pode executar os comandos neste notebook diretamente no R de duas maneiras:\n", "* Copie os trechos de códigos R neste notebook e cole-os no prompt R. Alternativamente, você pode salvá-los em um arquivo de texto puro com extensão .r ou .R e executá-los diretamente em um shell R, ou do R Studio.\n", "* Baixe o [script R](https://raw.githubusercontent.com/piklprado/ode_examples/master/Integracao%20numerica%20em%20R.R) e execute os comandos em um shell R.\n", "\n", "### Executando comandos R do Jupyter\n", "Este tutotial está em um Jupyter notebook, uma interface que combina texto e comandos em várias liguagens, e executa os comandos, se você tiver as linguagens instaladas em seu computador. *Para executar os comandos R neste notebook a partir de IP[y], você também precisa:*\n", "\n", "* A interface [Jupyter notebook](http://jupyter.readthedocs.org/en/latest/install.html) e\n", "* o [R Kernel para Jupyter](http://irkernel.github.io/).\n", "\n", "Para instalar o notebook no Windows e Mac, recomendamos instalar a [distribuição Anaconda](https://store.continuum.io/cshop/anaconda/), disponível em http://continuum.io/downloads. No Linux, ele deve estar disponível nos repositórios da sua distribuição.\n", "\n", "Para instalar o Kernel do R no Jupyter notebook siga as instruções que estão em http://irkernel.github.io/\n", "\n", "### Executando da web\n", "Se por algum motivo você não quiser instalar nada em seu computador, você pode usar um serviço que executa notebooks na nuvem, por exemplo, [SageMathCloud](https://cloud.sagemath.com/) ou [wakari](https://www.wakari.io/). É possível visualizar notebooks disponíveis publicamente em http://nbviewer.ipython.org, mas nenhum cálculo pode ser realizado (apenas mostra os resultados pré-calculados salvos)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Como funciona a integração numérica\n", "\n", "Digamos que temos uma equação diferencial que não sabemos (ou não queremos) derivar sua solução (analítica). Ainda podemos descobrir quais são as soluções por meio da **integração numérica**. Então, como isso funciona?\n", "\n", "A ideia é aproximar a solução em pequenos intervalos de tempo sucessivos, extrapolando o valor da derivada em cada intervalo. Por exemplo, vamos tomar a equação diferencial\n", "\n", "$$ \\frac{dx}{dt} = f(x) = x (1 - x) $$\n", "\n", "com um valor inicial $x_0 = 0.1$ em um momento inicial $t=0$ (ou seja, $x(0) = 0.1$). Em $t=0$, a derivada $\\frac{dx}{dt}$ é igual a $f(0.1) = 0.1 \\times (1-0.1) = 0.09$. Escolhemos um pequeno passo de tempo, digamos, $\\Delta t = 0.5$, e assumimos que esse valor da derivada é uma boa aproximação ao longo de todo este pequeno intervalo de $t=0$ até $t=0.5$. Isso significa que neste tempo $x$ vai aumentar $\\frac{dx}{dt} \\times \\Delta t = 0.09 \\times 0.5 = 0.045$. Portanto, nossa solução aproximada para $x$ em $t=0.5$ é $x(0) + 0.045 = 0.145$. Podemos então usar este valor de $x(0.5)$ para calcular o próximo ponto no tempo, $t=1$. Em resumo, calculamos a derivada em cada passo, multiplicando o resultado da derivada pelo passo de tempo, e aí somamos o resultado ao valor anterior da solução, conforme tabela abaixo:\n", "\n", "\n", "| $t$ | $x$ | $\\frac{dx}{dt}$ |\n", "| ---:|---------:|----------:|\n", "| 0 | 0.1 | 0.09 |\n", "| 0.5 | 0.145 | 0.123975 |\n", "| 1.0 | 0.206987 | 0.164144 |\n", "| 1.5 | 0.289059 | 0.205504 |\n", "| 2.0 | 0.391811 | 0.238295 |\n", "\n", "Claro, isso é terrivelmente tedioso de fazer à mão, então podemos escrever um programa simples para fazer isso e fazer um gráfico da solução. Abaixo, comparamos com a solução que obtivemos na tabela acima com intervalos de tempo $0.1$ com a solução analítica conhecida desta equação diferencial (a *equação logística*). **Não se preocupe com o código ainda**: existem maneiras melhores e mais simples de fazer isso! Os pontos são os valores aproximados para alguns momentos, e a linha mostra a solução analítica." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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}, "metadata": { "image/png": { "height": 300, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# intervalos de tempo: uma sequência de zero a dez em passos de 0,5\n", "time <- seq(0, 10, by = 0.5)\n", "# condição inicial\n", "x0 <- 0.1\n", "## A função a ser integrada (expressão à direita da derivada acima)\n", "f <- function(x){x * (1.-x)}\n", "## Um vetor vazio para armazenar os resultados\n", "x <- c()\n", "## Armazena a condição inicial na primeira posição do vetor\n", "x[1] <- x0\n", "\n", "\n", "# loop ao longo do tempo: aproxima a função a cada passo de tempo\n", "for (i in 1:(length(time)-1)){\n", " x[i+1] = x[i] + 0.5 * f(x[i])\n", "}\n", "\n", "## plotando com ggplot2\n", "library(ggplot2)#carrega cada biblioteca uma vez por sessão R\n", "p <- ggplot(data = data.frame(x = x, t = time), aes(t, x)) + geom_point()\n", "analytic <- stat_function(fun=function(t){0.1 * exp(t)/(1+0.1*(exp(t)-1.))})\n", "print(p+analytic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Por que usar bibliotecas científicas?\n", "\n", "O método que acabamos de usar acima é chamado de *método de Euler* e é o mais simples disponível. O problema é que, embora funcione razoavelmente bem para a equação diferencial acima, em muitos casos não funciona muito bem. Há muitas maneiras de melhorá-lo: de fato, existem muitos livros inteiramente dedicados a isso. Embora muitos estudantes de matemática ou física aprendam a implementar métodos mais sofisticados, o tópico é realmente profundo. Felizmente, podemos contar com a experiência de muitas pessoas que já criaram bons algoritmos que funcionam bem na maioria das situações. Estes algoritmos estão já disponíveis na maioria das linguagens de programação. Aqui vamos usar uma ótima implementação disponível em R." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Então, como... ?\n", "\n", "Vamos demonstrar como usar bibliotecas científicas para integrar equações diferenciais. Embora os comandos específicos dependam do software, o procedimento geral é geralmente o mesmo:\n", "\n", "1. Defina os valores dos parâmetros e a condição inicial \n", "2. Escolha um intervalo de tempo ou uma sequência de tempos em que deseja a solução calculada\n", "3. Definir a função derivada na linguagem computacional (o lado direito da equação diferencial)\n", "4. passar a função, seqüência de tempo, parâmetros e condições iniciais para uma rotina de computador que executa a integração.\n", "\n", "### Uma única equação\n", "\n", "Então, vamos começar com a mesma equação acima, a equação logística, agora expressa com os parâmetros para taxa de crescimento ($r$) e capacidade de carga ($K$):\n", "\n", "$$ \\frac{dx}{dt} = f(x) = r x \\left(1 - \\frac{x}{K} \\right) $$\n", "\n", "E vamos usar o caso em que $r=2$, $K=10$ e a condição inicial $x(0) = 0.1$. Mostramos como integrá-lo usando R abaixo:\n", "\n", "#### 1. Defina os valores dos parâmetros e condição inicial" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "# paramentros: devem estar em um vetor\n", "parameters <- c(r = 1.5, K = 10)\n", "\n", "# condições iniciais: também devem estar em um vetor, mesmo que seja um só valor\n", "state <- c(x = 0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Escolha um intervalo de tempo ou uma sequência de tempos em que deseja a solução calculada\n", "Note que estes são momentos no tempo para os quais você quer a solução. **Não são os intervalos de integração**, que são definidos internamente pela função de integração." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "## seqüência de tempo\n", "time <- seq(from=0, to=10, by = 0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3. Defina uma função em R para a EDO ser integrada\n", "\n", "Vamos definir uma função em R para o lado direito da equação diferencial.\n", "Para esta função ser reconhecida pelas rotinas de integração da biblioteca que vamos usar (*deSolve*), esta função em R deve calculas os valores da derivada em um tempo $t$.\n", "Há muitas maneiras de fazer isso, mas o formato recomendado é:\n", "* Faça uma função com três argumentos: seqüência de tempo, variáveis ​​de estado e parâmetros, nesta ordem.\n", "* A função deve retornar uma lista com resultados da função a ser integrada.\n", "Para fazer isso use `with(as.list(c(state, parameters){ ... }` dentro da função R.\n", "Inclua entre parênteses a(s) função(ões) a ser(em) integrada(s)\n", "e então feche retornando a lista dos valores calculados." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "## A ODE logística a ser integrada\n", "logistic <- function(t, state, parameters){\n", " with(\n", " as.list(c(state, parameters)),{\n", " dx <- r*x*(1-x/K)\n", " return(list(dx))\n", " }\n", " )\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 4. Integrar a função\n", "\n", "Agora chame a função da biblioteca \"deSolve\" `ode`. Para realizar a integração, os argumentos básicos da função 'ode' são\n", "* `y`: o vetor de condições iniciais\n", "* `times`: o vetor com a sequência de tempo\n", "* `func`: a função R como descrito acima\n", "* `parms`: vetor de valores de parâmetro (nomeado)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "library(deSolve)# Carrega a biblioteca para integração, basta chamar uma vez por seção do R\n", "## Executa a integração\n", "out <- ode(y = state, times = time, func = logistic, parms = parameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "O objeto resultante tem os valores da integração\n", "em cada ponto de tempo no vetor de tempos" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A matrix: 6 × 2 of type dbl
timex
0.000.1000000
0.010.1014960
0.020.1030141
0.030.1045547
0.040.1061181
0.050.1077046
\n" ], "text/latex": [ "A matrix: 6 × 2 of type dbl\n", "\\begin{tabular}{ll}\n", " time & x\\\\\n", "\\hline\n", "\t 0.00 & 0.1000000\\\\\n", "\t 0.01 & 0.1014960\\\\\n", "\t 0.02 & 0.1030141\\\\\n", "\t 0.03 & 0.1045547\\\\\n", "\t 0.04 & 0.1061181\\\\\n", "\t 0.05 & 0.1077046\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 6 × 2 of type dbl\n", "\n", "| time | x |\n", "|---|---|\n", "| 0.00 | 0.1000000 |\n", "| 0.01 | 0.1014960 |\n", "| 0.02 | 0.1030141 |\n", "| 0.03 | 0.1045547 |\n", "| 0.04 | 0.1061181 |\n", "| 0.05 | 0.1077046 |\n", "\n" ], "text/plain": [ " time x \n", "[1,] 0.00 0.1000000\n", "[2,] 0.01 0.1014960\n", "[3,] 0.02 0.1030141\n", "[4,] 0.03 0.1045547\n", "[5,] 0.04 0.1061181\n", "[6,] 0.05 0.1077046" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(out) # primeiras 6 linhas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Que podemos plotar" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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UBxgo4dvGQ0Gnft2mWbD5sVN0Hh1bmxObp79y4RlStXzrZHr9dnnff6qo8//piI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}, "metadata": { "image/png": { "height": 300, "width": 420 } }, "output_type": "display_data" } ], "source": [ "#### Para o jupyter notebook apenas\n", "options(jupyter.plot_mimetypes = 'image/png', repr.plot.height=5)\n", "####\n", "\n", "plot(out, lwd=6, col=\"lightblue\", main=\"\", ylab=\"N(t)\")\n", "curve(0.1*10*exp(1.5*x)/(10+0.1*(exp(1.5*x)-1)), add=TRUE)\n", "legend(\"topleft\", c(\"Numerical\", \"Analytical\"), lty=1, col=c(\"lightblue\", \"black\"), lwd=c(6,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Temos uma aproximação muito melhor agora, as duas curvas se sobrepõem!\n", "Obtenha o mesmo gráfico com o uso do pacote *ggplot2*:" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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P9CChsrpEtUa4EEJOX4FtJXhqM21u8o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\n3BB7JXGcMh5DentUjVY7emajcUbmk8H7NG1x+Dt9XDtoaVMvjkl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}, "metadata": { "image/png": { "height": 300, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## Plotando com o ggplot2\n", "p <- ggplot(data = as.data.frame(out), aes(time, x)) + geom_point()\n", "analytic <- stat_function(fun=function(t){0.1*10*exp(1.5*t)/(10+0.1*(exp(1.5*t)-1))})\n", "print(p+analytic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Um sistema de equações\n", "Agora, e se quiséssemos integrar um sistema de equações diferenciais? Vamos tomar, por exemplo, as equações para o sistema predador-presa de Lotka-Volterra:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dV}{dt} &= r V - c V P\\\\\n", "\\frac{dP}{dt} &= ec V P - dP\n", "\\end{aligned}$$\n", "\n", "Tudo o que você precisa fazer é escrever uma função R que retorne os valores de ambas as derivadas, e definir os valores dos parâmetros e das condições iniciais:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1. Defina valores dos parâmetros e condições iniciais" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "# Paramêtros: vetor\n", "parameters <- c(r = 2, k = 0.5, e = 0.1, d = 1)\n", "\n", "# condições iniciais: vetor\n", "state <- c(V = 1, P = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Escolha um intervalo de tempo ou uma sequência de tempos em que deseja a solução calculada" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "# sequência do tempo\n", "time <- seq(0, 50, by = 0.01)\n", "\n", "# Paramêtros: vetor\n", "parameters <- c(r = 2, k = 0.5, e = 0.1, d = 1)\n", "\n", "# condições iniciais: vetor\n", "state <- c(V = 1, P = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3. Defina uma função em R para o sistema de EDOs a ser integrado" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "# Função R para calcular o valor das derivadas a cada valor de tempo\n", "# Use os nomes das variáveis conforme definido nos vetores acima\n", "lotkaVolterra <- function(t, state, parameters){\n", " with(as.list(c(state, parameters)), {\n", " dV = r * V - k * V * P\n", " dP = e * k * V * P - d * P\n", " return(list(c(dV, dP)))\n", " })\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 4. Integrar a função" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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/Bguvitg8ej7zsg0B2hmWnINTtIsML8O7ct85TtHxLLPkXNh+Cx0azNsPOINZEd\n6QnrDWW+RLEoHsghr+gjVM3m5Vg/r8C7bwh0QHLP/iPDCL7zunLntmf2SIqLdOw8RenpAnuw\nYb4hDo2Phf7j38QqD1LPnnR5F3GWQ+HFbzCm9HSlvc7Yvjkh7OGD+kP7vbWpIHJOqOOhkFjl\nQfbsv90nMjdu8caY4hDM3UbAcym8+Apa35jzGiTO+BauaXRpm/s1eHoKuSagfQWrqePllamX\njg6pdvwzz+yRFBfp2HkKyVXMhGJRweY7uVYNotmZ0M//U6RWA85djt2IUnzyKMnw/PwOD4Wd\n3yAEMOYVVbFnnuMVlc7X+BL3IDEA6Hv2i1X3bazf5H4Bq6k11230xpiiQHNIJ3IgJOfn6CM4\nR5FcZbUIgSJMIJ/0dKHZ6dRLx3Axns5dES7xJ9Kx85Y8YvV4bNQDQ4pGRQ4xKhSNKOIo83FC\naIOr1qChh15/RaBgA6tvgFonyWVKgTE0MxX+6b+Tnm6HC/wKa2zmqk2td/6ZysNlrHmJ1zYV\nBhkZclpGAAAcWFNL7Mvf4Gp2JXD/oWYdbpvcAJH+8EGBBFzw2AieyLEt0+WrBPqMyGjuIlSW\nSw9F4lukY+cpebURCCXvZGzYnPMaHBGpPIjXN7hfgGZn8KAw851QNAIz9/77Ox4sgu+94Zk9\nhaNePu9Qdz+fn0XRSOC1n5Fc43F9hXLrutMyB+CAAI2Nkv4er20qBMbwpIO8JVcUIAoPlyX2\nP5bYI1I9A2SV+J6Dl1fEnnrWG1uKgrtmUBJjh2AF35IU0rHzFFZbd68IN0vwTt8gUnmQ0nUn\n5zWsusYDS4oC0vX09sOs8VVxGvqUnu50TXznnMvoSPbpFL7DfewEACBqakcPe2NMccj6dUIA\ngEwj8O6bZNgxqudLMLb5DRySxZGUokgk8NlH2UN6foTX1jvq0XAtwDFhlVWJg5/juRSMfYW5\nsp07DKmbHxZCSOLhRw2hnkSSdKRj5ynqmZP3srEOM1yI/sjjVCgdO9KVo3OK1TeYa9Z7Y0zh\noJlpSEuzOncqEsLEKQ/KqQwCAIAQiDOqgWWrGkwDT+RoGfEVOb9OiJrK5fPeGFMUzNWWGkdk\n+TPw4Tvu5bm+ggeDrMFhsATSE4hRPD0VfP1n6oUz3hu2YFAshuYUdu6dXrk27+oRAnn8yiS+\nRTp2noJnppxWMSeEE0JbWg1xfKAkyLVqkC5ti/3y152Ohj6FhcM51ZsS+x8TaGOXYFUAACAA\nSURBVBoSa84hNMgB6IpVAs3gMjdsBpRj4+K5BCN9ReacBucfFHYfO+Yz8PSUS7wbAJBpCiSL\njUdH8FCO6ovAB+8gU5hAvnrj6rwaw73tLhW2R7oeeP8t5cqFUpgmKQLSsfMUXubUasAYohRR\nSnq7w//+T2jayfnzK6ajCsB82gIl4iBOSywAQChsti6zPJO4ovLySiAEqmvoM8/pDz1cKusW\nAKuq5u7T1sNlsSdFKg8iI0PAmfs1+pbt3hhTFLSTR9NeOZ8rWI1TB4wvQbEY6enOqcznIPzk\nV8io23jiJMjQRep7S7hOtgQAgMARoeoZJGlIx85T9K3b3C9AsVjgs488saU4OGsWzCvz4dGR\n8M/+XSBlPkSpMj5meSYh00Sz00ApTE6QTz4QqzBfvXXdrm3LMWF19by8grYuj37922KVBxHH\n4U5p6Lv3mZs7vDGmKOBcLYq8rFzfJsx8J5SfdCVb0vqgLSkW+bQaAIBAuuXuAsVJ8OSEQJLL\nknSkY+cpxK7lbRu8g4cGvTKnYDjXzpxwvwRFI9rFc96YUzh4sB9sbihP/5BmZ0K/eFmkVgOn\nKAJiFI+NotkZ0tsd/re/J+I0+QKA4ygqTggPl/Ng0Fy+SiyvDgB40GFORio5TpuXxL72QlY9\nQv/Byisc7ygdY9su2uhQteZPaNsynktEmtXU5uMt+QS6biPPpbrHw2VyqpigSMfOUxzmCdoH\n1WjCiCGhRBzlUfqDnLQPfIrh4LFZP6KZadLV6Y05hcNyPWKRoQdf+5lAR3Pa6CA0iChF0VkU\njyvdnaF//Qc8kjt35h/MdU4CxampaNR0/Fr6F0LoMmsHGA+FWFMLBIKsujbx2JPxQ0+XxLQF\nYpruPxCuafFnvyyQG6RcOGuf4GJB37rDG2MkRUc6dp6CzNzCtgL1kHJVyyf7wNxrvPwEa2zO\n1DVw3s1RXJhKdnPNelBzfEZ4YsxReMyfmOs2uj9BkWkEP3jbM3sKx/F0lJo6T0aGQy//SKAP\nCMVj5LZVmQ/FYnhoABJxPDmunT5OekXSxFZuXUf2ojSE6NI2VlNnrmyP/uqv0ZYcXUq+Aueq\nJzHWb9L3HfDGGEnRkY6dp7BcP35z5Wp95x5vjCkChNA169wv4apqbhImNcbDZSxDoDhLJbvj\nLAdfgqMRyGdMRh5HDp8QOHUsZ3wx53PLR3CuXL6Qo4c0kdCOH/HMogLBI8Puo1nQzHT41ZdF\nKr2dd7Iz4Jz09eCJMeXO7fCPfiiWq+o8/UzTaMsSXl1jrt2oH3hCIAkkiQXp2HmKYZV3AsBY\n33uALm2jLUv1vQdiX33eUQnTtzj08KK07SAUjn/hy0yc+eVksB/nUoKlK9vp0mXe2FM4yrXL\nwHLkXHgwJJCrigYHMl47ekS5gpT+AZkmMo2cPaR4XJyOy3xGpsai6tVLD96U4sBztSSjeDz0\n2k8Fkjuhq1Y7rOo6GehHkxPKjSvhH/6tWKW3knRE8iEWAdrxz6xLjGnHPiF9PWSgTzv2Sfjl\nH4E4c0jR1KRDiyindMUq2thCW5cl9h2wSZX6GjycpXMl6W0jxLdsjz37FYGKaRzSfDZPKPG5\npwU6nSMtUxbR6aOgK9c4rPoSrqo818BlAOBhYZonaGMzzzlmlIO9Wdu3mO1rM5snHA4TaGYG\n9971zKQCYRVV7hcg0wy+9ao3xkiKjnTsPAU7T/u+B7lzO3DkY2+MKRyccNY1IF2dZHiA9N4N\nfPB2+OUfpdRPBMA+XR4AkoPnQyFe38Dr6kETRm8ZAFitrVMPAQ+FaGMTD4bo0rbY174p1uwg\nY3WO7D+rqo4/8XlvjCkKxoatua8Rp54BEMrZFQsImDgiO6TrNoqn63E6n+uwOM3y2uljOa/B\nI8MCpcsl6UjHzlNQHnpI6pWLHlhSFFh1Tc6JBaSrU6C5kObyVdzJt8OD/SgWQ8PD+KN3g6++\nLFAPqbGpIyMaxwEAWGMzHhtF8RgeHCBdnQKlkADAQXgC4cSjh2j7Grq0Td+7P/rSbwk0GgQ4\nV665JCU5ACT2PmLmcmf9A+npzinVyyurzA2bvbGncEh37onYAEAbGh+0JcUCTU66VnVKxEaY\nSpTFgbFmfe6RgnlogvsErml0xWrF1gFnQblz29i+2xuTCoQjhIiSdSg7AgBQbl1X7twyV4mR\n7FMvn89I7iOAuQcVB0CImtqpYygRjz/9pVJZeL84SCdyph3/LNm3SPp6UCQaf/ILoiSX8dQk\ndho2Y27cAroOCBlr15sbc4f0/IPj7QAAIJQ8EdGGxsQzz+VUhvMRuSadAICxbZdA00F4eTnk\nUgRiNXW5U+oSXyIjdt6Sx9RUXi/MsQ9iUdJtk1y2w4SpGlSvX4F47hlouL/PA2OKAsk6kfNe\nOkm9eA5PiKOmMeXgN6SrUagXzwY+/cg7gwokS/RXuXJRuXVduXkt9PoroddfEShInK1kUN/x\nkLl8lbluo77/MeeJNX6FtS63L/KKCh4uAwAeCuv7DybEyv537LIuZX6/OCHxp3/JM3skxUVG\n7LwDUapcOJ2MlLhcFj/whGcmFYgy0J9T5RIAmOM8WV+Cp6fzuQzl0/fnF/JyCPDYiCjNy7yi\nAo2PuV+jnjmReOQxIYJ2rKqaV1SgGbdOAuXKBa25RRQhJNq2glVU4pnMn5KiaKePz/15/Yqx\neVv8GWGCxGbbClCIRRJI37qDDA/h0RFeUUkrq7lQagZ40HY0RaBv30XGx1AkQhsajb2PUIFC\nDJJMRPouCk8sikzT7tXxyspk0yWrrYt95Ru0zeF0KC6srl7fva/UVuQLy6M/EQDMle0P2pJi\nkefXSaCJVUYegvjINFAekVdfgDFtyT01Vbl03gNbigKanXHoxc48AaqXzim5Zv76B+3U0XT7\nk0elwGcfKzev4YkxcvdO6M2fB4TSxHbUmiE9d/HIMB4dJv29+G6XQEFiiQXp2HlIKOw4ns9c\nsdpct9FcscpYu4GKMxgbAGjLUvsdcULMdRtZdQ2rb9R37ok+/xLPIwHtE4z1m0C1jnTjhKTH\nvfT9BwVKJJkrVucUZ2E1dbR5iTf2FA7u68l5DVdUUUq40My0cvNa5prDAxWL4qcm5zTkEchX\nbt/wwJiigIeH0g/kjj8n7cwJMjTg9I4fcRQ0IKPDSSlmPDkZfP+twLFPPbdLUhwEyigJDyfE\nXL9JtZy8CUm1Uyhdndr509Ff/TVWLUhSLBhkNXUkqeEyn2Gmy1fycBkoKjCKDB3y2OL9Axkd\nts/lNNdvZpVVZGSQVNXQjVsS4vhAABA4dtjh5K2qqQYRXlER/9JXhchaAgCippqHQ2Ds2C3K\nHZHREdsH5OA5ULtsjV9xmL7liDg7Aw/kVjMAANJ7V5QjH62rJy6qewgAQDt6WN+2S6QGc8k8\n0rHzEM7xkE3/NlOOGMViwbdei37jW95ZVQCkp5uklPnmH0bKnVupiAMeH1Nu3Yi89L1klbH/\nUa9dsS8qt67yymo8OgKKgqMRdOAJLo4EFx5xaH5j9Y36pg5ldMisazC3bHdUePEnXNcdZRF5\nIIDmgxDG5o7EI497a9fC4Zo1QuxwDVES+x978LYUB+ZQm+VQWJx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Kmb7TaeZRzB4MBjHGD9psF0jHztDZUxm6BgiD7Sllfvbx9K59fN6N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FQT4/JCZ2qLktKycHerpxXFYHAGTwTtap\nT8Xjh+w/KaUA4PP5iEzNuajriiOrAwDfzIyalQWcoz/+J7p5HQAQQABA7HhIPPHkg1jmCkBn\nncKqwFnW1YvRD4JzdOMajI9CVrZobgMpz80ppX6/X7XPiGdnbG/leBCzAncHhS38lpUFBZsB\n4IHXHu1veCAQEJ+v2h93dhz/Gw6EQ1BZBbv2ijWdoq8HGbqorMHVNSlIGTDGX7zs5CDPixHn\nWZofdu4R05Po/JKcJyFi9yO+zo1fiwi7fQ2/HzcIlJ0DrrYTnJMbyM2Ftevh4vI8nABAqko3\nbKIrWQZC6D7d15IhyiuRK8Om9Y0kSSe0ml+geq0QY3yfVv5g7mh/X6RTYme57rtfC3Z6wTm/\nT/99AECGQftvO4IiuMBCIRwKemY3LBj8QicA+wdw/5b9OeDLn+HggjN6+TPr8UP0ykX369GV\ni+a+J6KPEVIUhTH2QFaeDHqzy+NycvO6tf8gOf4xTtRqRyePscpqvuTNJSfKlMcWXExOWJYF\noaDy21+hsVE7iBTFOvgsl698QilljDHGAADpuqdELzcNZlkAgAwD3biGZmdEfoFY3fEAe9gV\nRQEAxhj3rI4sgTXN8x0xTRP2TyMrG9YsmW6l5MeiqqplWfec2OGKKvcdRZSWWwgDY3DgGbRh\nKxq6A5iIugZRVPx1vSk79b8f1xPcuTGqeh2H1bmJWxbaf5BOTaLYEJKqWoee47n5K31TKb4M\n4va11JHYBTRzTScgpJSUoaW+WxtRUGhVVXu+IyHEfb0jZ/gqpFNip+v6F79o5dhXYcuy7tN/\nHwBIf4/iashAkYjV1wP5RW49BqEoela2+KL1IIQwxvdv2Z+Dz1U7AQBkGsb0FAqF3LcrEQ7H\n1hnLRx/IypNBvCYugVm6rmdd9UhV4cpnemPz/V7VV4EGAmjOWQxmmqbruvbWa7GsDgDANMnh\n1/WSMtnml1VVNU3TtD8aLaD4NXCpcOkl5UzXydiI9uof0GJ0syE+ei/83HcflJ+vqqqUUl3X\nPz+xQxVVWa6ZD15eEcnNB10HALSwQPtuoVCIl5SmplFV0zTDMD5/2Z8Dqm/KptSRB0S27rRi\nv/SCQoh9x76+n7+maXB/bhDqzLT7HmlkZTNdB0Dwne+TO31kYkxoAauhSWRlr/RNZWVlpfQy\nKER2orcEAEAobN2+yeqbzEPPaa/+PqbHLnJyw089zxgH5lxhdna2EOI+rdwnsZdmupBOiV36\ngrzUqgAALMtqbmV1DeROdP7c7lAxdj8i+WCs91goxqAFeHEJdHc5npFfHMQqryD9Tl1lq6Ia\nADxdQ1BY9hEKq2OdGj9qAAAARkcnMg3qcihGlkm7u4xtu1K1upVDiFXfSG9ci4+xohJWUweM\n+d98JZbVge0w9uYroR//k9RaXLrulPgG4Fk5dgKn3Ljme/fNmMILK68MfetFkHvaQL1wxl3d\nUbquWku1bTw5QYbuIMZYVU1aNKq6PVrsoD37Dwix+kZW35jqZd0reGHesZGwoSN3WX0TLykN\nvfzPtKcbzUyL/AKrqSUtZqoyuJE6e/i7gZVVAMbg2AdjzMorAKHwU9/yHTtCr19FpgE5OZGt\nu8wNWx7QSr8sZstq9ZMPHbclq61DKIqxcat65aJDxEGX3kvDWr3Wd/p4giUDQsb23QDAi0s8\nJD2lT1XRwryjk10QCnZRwVWSEUnyV3lAoaDbIY1MTeDZGbQw7zYjxrPTeHiQ1dSnaH0rh3Z3\nuQs8tPcWikSQHonP6gCAjA77P3g78vS3UrvGlYFdzVsAQJZMQdTjR5d1ywGsjs7wgacln3Fx\ny0QDQPzkLx4eoqMjQqGsrpHLLa8DACKJ43Bs/yMolVwEO8OXIZPYpQKRncOLS/H4aHzQalhl\n62wJTYs8/iTsP4QMQ6RJFRoHF8El5yu0bAAALRB64SXfkXfpYD8wxotL9D2Pynx/tVFPf+o0\n2hJCuXZZL6vQdz+iDdxBbLkUITRN35rEv0ESGKPXrzjumYhZyo1r+tadbpM0BMDk9gDAY6Oe\nPg1kdFhg77KcpyCFPKCQl0+DECgSot033GrMyq0bumHILDfoXR+lFABoT7cvsX5Mr11SS8uM\nzdtTs7Z7g+cVELedYEEBAADn/r++oiydTghCjYcfMzZuTfEKV4TIzmHFpcTVSMMaVi29QpA7\nvWRqUmTnWHWN6eKTlsFBJrFLBfjuoCOrAwAy0I8sU9ClWjdC6ZLVAQC9fsU9Nk+7LsO+/QDA\nC4vC3/4eMIYsK13eFBkZ9giODgMAK68MP/cd/8cf4IlxQIhVVuuPHZDcxRwZhncDQHARMNZ3\nP+L/4O34MCstZ3LPgiTzaRCE8ELvlJQncaSQhGh+kEhUh9nL0BM4Bz0CEid2rLFZcbZhCKux\nGQBc/g0AAPTqRckTO7NzIxlNuDIIQsxN2wFAPXks/s0iZvmOvMvKK1lldapXuSLy8yExsRP5\nBbZMFQoFtVd+H3u/IpAVfvKbrE52P98MbjKJXSqgY6NxSlVRkGngqUm7v5vevqlcPIcX5nlu\nvrFxq/zqYp7FBhQOJVgeESJ1h1MigiYtNgAAa2gKNjRlEcwAIuweW8tTifD7QQuAy7vTHo8w\n128Gzn0nj6FQEDA2V7Xq+74h+YfFKyqFX4vPeAQA+Pysuk5omtWxzpE6WB2dkvuQspZ28bd3\nkZ5wAm6u3ywI9UxVhd//hZPyDxYPSzGErPY1sCTG7gDLXVIF+7g8EcQYmp+F/ALVJecLAMrV\nizIndmhultx2Dvmi2RkyPMSqavzv/jU+i0WhoPbXV4Iv/3chd2dnBjeZxC4VCEpdsp12XAEA\n9ezJmOcgnpygvbci+w9K7kvjOT7JCwqjWR3nyqXzyq0bEA6JknJ9+25PE0mpsJpayITzhMJq\naon/U/j8wDkwqXvRoiBkrF6jXjgTHxN+zeqIymeYG7eaG7ei4KLwayB3SmcjMIFAVvxULLJd\nuTQNACL7D6l+Tbl4HjFLEGqu32Q8tO/BLfZLQe70OrI6WPJpsFZ3sLMnHUdmxq6HIUmPlCSo\np4+DvYWNbWMF0Atnreo6XljstlVMVmqVBcbonT53mPbcYrUN4PLYAHtzKzF4dsY7PjPFCwrd\nwi4oHKK3b5prN9z/pWX4OskkdqnAqmsQhDiOxnhBES8sQgsLvmMfOl7v++h9q7XDvmPJiblu\ng+/UMUcPvrEt6tPgP/yaEpteHB8jN66FX/yh5ENwIs/V+EywuZTYIdNUzpwgw4PYsnyVNcbW\nnTJ/OgAAQtBbztFXME0UCsYfjkteAYqHDvSh6UlHkAzdQYsLIjtHKIq+7wn94f32n5InQDa0\n16ltCQCkvweEEISGv/ld/5F3ae8tEEL4NWPHQ4b0M1X2CAuChG2snUwYW3fSrisocVhE3yW1\nlwYS3D1mBEsqB7ywkIyPOZ7iBXKnqkmMMUQg2+0FZ5MsnkFmMoldKhCqCoriaP3mdfWAEBkZ\ncreEI8siY8NWvbwHssr1K+5LHh4fBeikvbeVRE0KxCzfu38N/fBnKVzgilHPnHSGGFcvf6bv\n2YcsS/vt/7breQhAHRpQblwNfv8fZc7t8PQUXphzBBGzyJ1eu9qKgovq6eNkdFgoqrWqxezc\nJHkyhDyLDULguVmWnRP9E2Mh/WTiMl5NkEgIu59B5OWHv/ldZJoQDomcXMmnR21EIAumnMm3\nLY3E8/LDz7/o++Cw/TsSuXmRR55g1bUPYJVfGkEVz1EDq6IKAIxdD2uv/THh9ZpmbJQ6+WbF\nJayohExNxAdFbh6rrQfOk/lepnCBGb4eMoldKlC7rrq1JEjXVXj0QLLr9T1Kv6cK2t/rFezR\nAUhMij0OMjGGIhGZZ6ywy6EcANDsNACoZ044TmnR/Jzv2IeRJZM0CUGumWUAAIg6ReL5ucBv\nfhEbGqX9PbSnO/z8izJnD97SiQBiydcIT46r507h6SmenWOt6bTklo8GAFZZrVz5zBHk5RXx\nGbZQFFDSJlU116x3//zNdRvtB6yqJvTDn6NQECwrXfJv1rDKkdgJLWDL8lmrWiMHnvYd/Zt9\n/MrKKvTHD4nYHkNKkGli11yOUBRBCFBqbN6hnk6QL2ZlFY52lAxpQSaxSwXIM2nQdRQJs6oa\nQSlKVPUUqsorqlK1unvCM2+wa3jJcgN5cwYAAJGVjVxidfZlmgz2u1/vbhiSCl5YLHx+VwsX\nsju7fX97BxL71mlfD7122YoZWMkHa2hyq7Sw6lqeXwgApK8n8Nof7HoDAVBuXjd27dV3Sn3S\nZzWuAkwSf0rI2LQ8JUoG+pQrF/HCPC8sMjZu48VSD/kCAJ72crFL3M4lS9AlBDFLuXzeGQyH\nyEC/LUpsrllvdnTiuVmhqmnxvshAn1ugGE9NkskJVlKq79oLQqjnT9m/I6txVWT/obRowM3g\nIJPYpQKvTiYhqCp8fiBE3/eE//3D8c9F9h8SPnmLWwDAqmvJ0IAzWFULAFZNvd1DnfBUeaXk\n78hsXxu/bAEAhFjr0rVrWBDCKypJYmGVl5TanY5koM+dZisDfTIndmhxwS3tFjWE5Vx7703H\nKZJ6/GOzpV3mZEg9e9K1QRL02mWzrQMSZ6rI4B169VLkue9YMb0xKVGue2iaKNevsNp6AAAh\naNcVersbGTorqzA375C5mQEA0MwM8nLNIuMjy24TCPF8D9kaOUmq7GjPfBCi733U2L0XTU+L\n7BzJP50Mn0MmsUsF5uq16qdH4xVuAZC1dr29GTI7N/GiEuXieTw3IwoKjQ1bmOTlOlvQ8tRx\nAB5XiEPGpq0AwBqarDWd9OqyFoCgiv6Npx7EMlcATuyDRgAAwhZqZzX17vqc5PJOeHaGuI7L\n8cQ4np3m+YWyn/R7QbtvuO2qaH8PMgw0P4sWFtz/hAz2y5WgWScAACAASURBVJzYuVvvAYBM\njAEAnptVE2eqEGP+t99Y/Pn/lLqC4iW/h/Ro0H/4NaXrqv2Y9vWoly4EX/qJyMtP3fJWShLJ\nwOh2AgAxplw8h4cGAIDV1Jmdm6T+dJI1zCEUHxeECultdTJ8PpnELhWQ8ZHErA4AQMTdXVl1\nreR9xA6UU8dcynxCufKZ/ugBAAh/42laU690d+FImJWUGVt3cpkv3wBI16nLKBYYp7duGNt2\nG1t3ku7r8W12IjdP3/1ISpe4QvCER9IAAHh8nOcXspo62uccybRq6u7/uu4dz9oJCAG6nvTw\nX+781dNDwg6SwX63vjQKBcnEmMzT5bywmIyNJMYEKywGANp9I5bV2aBwyP+3t8PPv5jCBa4M\nnpvHikvIZOKoAVVYYzMAIMvSfvsrsqQ8r3R3qV1XQt/9ocx6kKyyWuTmovmEnhOruS3WGojC\nYeXCGTI+KjTNWtVqrWp9EMvM8FXJJHapIF6gPJYNKd039McOLr9ICBQKCi0g+XCijeNi5wwi\nZK3plPlcz4lpOP3EAAAA6QYACErD33tZPXtSvTsgLMtMB7kToXobfthaJ/pjB8hvfhGfKrHa\nBnPN+hQt7p7wdjzTAiIriwUCQgu4JcQk3yyZzW30tlOSxmxZDQDAvXNSkSQuCWb7WmdiRxRz\n83YAoHe8xq3u9CVImsuGEIg4b5EikMVzcgFAOfkJSfQTwsN31TPH9R17UrfCFULuDjqyOgDA\nE6P2p4Dn5wK/+WXsd6RcuWhu2BJ57EDKl5nhq5JJ7FKCYcQeIneQMd/p48q5k0jXgRCzY52+\n9zHhlztv8Pk9Rg0cQ69CoEhE8gTIRgSy3I35AMBLogd5QlH0nXtIIMA5110DzhLCq2pEIMth\nYS6yc3hVDQDw/ILgD3/uO3UMjwyDz281rjI3bZP3/goAAFbLavHB28hc+tUIAAT6xi32Rijy\nxJPa63+Kf72xeTsrLUv9OleA1xaOVdUAgKd7gfD5hdzvSL160RliFhkesppavMetlrRdUrC2\ne4BMjGFnARLw/CwZHmLVtbTPVeMHIL23QeLEjnpJFuCZGbS4IHJy/e+/5dgdKZ+dNVe1LjcU\nZkgTMoldKuAlpeCypuFL12jf8Y+Xh8wZUy5/hhbmJdeesFpWq255p7ao2SiKhH2fHKHXLiPL\nAi2gb91hbN4hdSUSY6uxRUn0CBJZWWZLe8LLOHf370uK6+gfAHhenlgySRO5eZHHn0ztmr4S\nyrVLy1kdRHdIdHDADlnNbcEXf+Q7dwpPTYicPKNjnSW59S2A+tlZd1C5/BlrWMWLS4ytu9Qz\nCUNIkccOiCSGuTKAImHs8m4BADI0YDW1sKpa5bJT24VVVMl8WXDvXW3wwjyDz1UGSD8QMEZc\nNhsCgPbdziR2aYe8l4m/J8zVa9UTnyQe9iF9y04AQOGwevaE4/W0r4cM3omOksmJ4Wp4wjhq\nzSmE/61Xl7ez4ZDv4yPIYvpOeTeyyDRp93VnMBgk05OspAwA8OyM78P3SH8PMJZVVKzveVTy\n7hPae8tRrgMAcncILSyInDipLbuRS+KuoBj07pA7iO8Oxko+vKomXFWT8nXdO27hCQAgS0F9\nzz5WUqJeuYQW5nhBkbFlh9QXBABASVI0hADAbF+rXL0Yr3InKNX3H/T+J3KQbLCD5eYBAK+s\ncZsQMrm/gVZtvbuvkxcWiZwcZFnurBQt2WxkSC8yiV0qUM+dcrVwCeX2DdbcimamPDd5eGpC\n5uu4ctVlgM05vXaF7X2UDPS7DynUU8eMTVulVTxBE+OepTg8fJeVlCE9ov3pP2MKxnhqUnvt\nj6FvfY81yGsNkswICIcWWU4OAOC7g9rHf8MjdwEhVl2rP/IEk3sUTniUdgRg7Chs216xKVvV\nV0Hk5YNL4ZLFkgmErPZ1Vvu6VC/rXhE+HyuvjHeRt7HqGgEAMA5/60X1zEnS040iEVZeYezc\nyz37JqWBFZfyomKc6KXBS8p4ZTUA6LsfprdvxmfnIjfPkPgcFgB4fgFQGpsutxu+zdbVACAo\nZSWlHn7ZXl0BGSQnPa6A6Q52XewEQLTLOFkvncw9dowhT12D0CIAEJenkP1P8My0tAN9iHqX\nrOwBN+Wzc25fCt/HH4QkTuy8tbUwtosNeHIi8Kf/QlY0lyV3+rQ//t/g9/9RZj8A1tCkOFu4\nkBX3ESg3r6vHj+LpKaH6rOZWfe9jkmvGGmvWaw4ZHYTNTducr+Nc5vPKeERuLiRe64Q/EBth\nEVTRd+4BiSv3DvDcLJp1/vBROBj1fAtkBV/6qe/EUTJ4BwCx2np9117JW4rVSxfAsmIDfNEx\nvutXjd37AEDffyjwu1/Hv57V1svf0pDBTSaxSwmuzhgEwAkFAF5Y5N7mCi0gs1EsEMJz8/C8\n04pUFBQBAE8m/iSxnxgrLhXZOWgxQQtNUGoXTfGU1wjw1KTMfd9Wwyrh1xz5t9XaDloAAHzH\nP4pldTYoHPadPBZ5Qt6uO5aTKxBCiZVv1tJmP1C6u/xv/sV+jPSIcvUSnpwIvfgjmU+ZFVff\nLQi+vP/hXL1wRjl/Gs/Pidw8s3OTvmWHzG8HhYL0VmzIN5o8oEiI9t2WvG8hGWSg3y1ThRYX\nyeSEPZcjcnIiT8iu0BkPnp0BlwcQnp+zNw+sqib00k/U4x/bcifmqjZz2y5pL3EZPodMYpcK\nrKYWD5+GVVEPvsiT39T+/F+xmpDwa+FDz0m+8zNb231nTyaEFMXo3AgArNEjpWAVVbb1k7QI\nVV2+gAkABCIvX+TkAgB4nSALn0/mSx4d6HdXVdFM1PEJj3s1ubumYaRCPX8auSRplMsXzdVr\nQQjfR+87niKjw0rXFZk1XNwK0nbQXL0GAHyfHo3NVKH5OfXYh2hhPiJxUxqen4trOFn+acSu\nbEjX1RMfKzeuoXCIFRaZO/aYre2u/4xMeE0gfV5cengg4A4KvxYrCbPyyvDz/y21i8rw9ZNJ\n7FKBUBRXDEVbTwB4QWHo5f9Obnbh6SmRk2u1tAnN4+cnEUIoN52jBmCaeGqSVdeKQFbk4DP+\nt15FS3ouPDcvcui5VC9yJZDhwQSbSwRgWyhOTbDiUrO1XXENMMZGgOWEDDgH3ACAjI4gwxCq\naqvZOeBJpO8kgXiNKKK5GQBAegS56sfgchORDuHRXGsnr2hhwTESCwDKxXPGxq3S9qVxD+NE\ngCXDZRDC/+ZfYjLgZGKcvPkXceAZmdUueaXHJIRQVb7UjYoW5n2fHKF9PcAZr6jW9+xjZRWp\nXePKsDrWqedPOVQSzbQ1TsyQjExilwrUS+cBHE4NQrn8WUytShBqta99IGu7B9DCvPscFgDo\n0IDdT2M1tQR/8i+0uwsvLrCCItbWIbNMAwC4RTuX48WlrKbO2P2w+unRWJxX1eh7H0vR4u4N\nL73lWNxqbXc5BIDV1nG/F/VVYNk5HtMTdlOgogDG7iGkZCrNksCratxWdVZ1LdjVU69PkIyP\nSpvYiZxcj66SQJbtb0t7b7nNXbSjHyy0r5W2g5AXFnn0MzS1CqoAANIjgd//n1g9kvT3aEMD\noX94mUs8hIRHR4AJx1msiDt5IOOj6idHyMgwUMrqGyMP7YuZUmRII6S+3f7dEG3eQo5gQjJB\nJsfxxDjXAryqxqvClwbE34hEVra5YcsDW8oKSTY0wHNz7Qf6jj3WqlZt6A4PhY2SUqu5TeZz\nWABgtfXgOCsHYGUVdq3O2LKDDA3Q3luxp6yOTlPi2gkAWGvWu5vS7O+YINRqaqG3bsQ9IwBQ\nrANPTnhJuTOxUxSrtR2SuI19TlwGkK6T2RnH/hUxZv/lMGmIEg7h+TnvQR8JoF1X3P0MtP+2\n3ZGmnD3lmKlCluk7+kH4299L4RpXBu3ucnbYASi3bxoP7QMAPDmh/fbXse5bevVSYGgg9P1/\n9CzwZ5CZTGKXCnhuPnG5GoilnjNkWb7Dr8VuWiInJ3zwWVYrr8e8yM3jBYV4ZtoRZ3VxaxaC\njA7juVmel8/KK2VPgyqr3cMTrKKKFy9vvllJGa9r4JxbaeE8UVgkMEZ2EWvpVstaV0efxjj8\n/H+jvbfI0KBAwOoaZdbWsXGb2wIALGn1RfYfDEyM49nYdxLpD+9npeUpWtw9wBi9cgEgMREy\nTXqry1yznpdXitw8x/my0AKsWl4/XzI8BJGwc/+qR/DdQVbfJJT0S1UT2jOWQOEwCgVFdo67\n5g0AZMwpgCAVnqJOsZ4Z39EPHDNVeHZGOXfS2PVwCtaW4Wskk9ilAra6w3EVEBgZSwUt39EP\n4ksRaGEh8OYriz/6uUjSsyIDPJDtSOxEVnasvwTNzQbeegUP37X/ZOWVkWe+zSWW0iBTE46s\nDgBQKBg/94qYBQP9OLiIc/N5gdSDIACgXDiLYkeTS7da0nUVtu2OvcZqbLYam1O+tHuEeCV2\ntPd2tGiXlR368T/R61fw+AhoAau5zVaWlhYUXIzeUBMTITw9DQCCkPCh57RX/4D06C5CKErk\n0HNS106SmLIgywIAq3GV+smHjiFTVlktsySNt68jxuD3g3fnNIDcp/+stIwM9ruC0f2Pd6rq\n0urKID+ZxC4VxKkAREFc4OlJXlSMGKMupx0Ih5Suq8bm7Sla3wrBM1P0rnPIFwUXydAdVtsA\nQgQOvxbL6gCAjA773/xL6MUfSdtM4/bSAQA8N4vnZu1zInJ30H/4NfvkJQvAbOvQDzwjc+Og\nW3gPlsQOYiBdx2PDiHNWWi7z/dUGeel4o7j5A0GIuXY9gLxjsAlomndfYFb0g2DVtcGf/LNy\n9SKeneG5+WbHuuiMtqywMq/6KMb2fo8XFusPP+Y/8m7sGZGVHTn4bMqWdw9Yre3qpx85vnhm\nc5vdY2etanXPkJlyC7tYq1rV82cSu2bAiEkneqWq9pvNkF7Ie2f6uwExCw97uCGRgX6ruQ0i\nYbdUEghwF5DkAc15TE4AAJ6fYwBkbATfHXQ8RUbuktFhT2tzKUjm8Cg4AKBwSHv9T/EOXcqN\naxDIijz6jdSs7h7wKPcKiO+Dptcv+4+8Z7cQCULNnXv07bud/0QmrIoqxTWyY1UkfKNQKIjH\nRkFVeWm55I2qQlGt2gbHPIGgitmyevnPQJaxdVfKl3aPiJxcnpOLE4eXrcqaWD5qbtzKa+ro\njWsouMiLS821G6QuQALgmWn3dgItfa+s9rVWXw+9fjn2FCstt5vVpEU9d8qR1QGAcvO63Ylh\nNjWrF1zj/3Knqhk8ySR2Dxjh14SiJribAwACnsSmUAZErnflgGfnwhc6Z0uJVVXjvsOI7Bye\nVwAA9MY1t+8qvXQe7X1U2u2staZTuXQh4SKOwFy30X5IRof9774V21EgZqrHPuR5eeZqeUez\neXklOAokGFtrl+tz6qdHfWeO2+63Iis78vghqe9JnJNl4eulPjshHFVtND+HpyYhO4cVl0je\nqEr7e7Drt09HhpCuxxI4VlIm+RF5PG7/aACgPcsjR+FDz9K2dtrfC5bJKqvN9nUyK0gDAJ7w\nEADCSwKWxp5HyeCdeFcxs63D6kgbU7sMMTKJ3X1HEMrLK/HIXUc8OmpAiLF5u+/kJwn/JDdP\nZiMXXljMi4rw1HJnsQAQefmspg6SO2dLnaomWijaWI3N9l0WL3hUTxFjEAyCrG+K9Pe6t+ag\n6/b/qp+dTawTIwBQzp2WObFTXVKCwDntumJs2w0AyuUL8T8iFFz0//XV0Es/4cUlqVzkl4dM\njsdtgZb7OMmdXtsfFlmm/73DsYIQKy2LHHxOaimNZF6Cc7O2T0P0ZTNTaG5OFBbJ3HQbxTDc\nMWHo8X9aTS1WU0uqFvRVET4/gMsxaEmAXShq6KWfKlcvkuG7QKnV0CT11ihDciTtefo7g2c5\npYCEqsZmSI2de4yNW2NPsZKy8HPf8e7blQM0P4cc3VoAWNdtbVVWUsZcfmistkFm6U7lykVH\nVgcA9Ha0M5J7VSgFoZAt73RL/BmfcAU9q6qe2oSSgBjzliCejk7wqOdOOf+JZUb1I+XE9X2z\nQUtx34fvxx/zkfEx7fU/OUv7MpHMLIcveQmiudnAH/5v1n/8r8Cf/yvr//t/tDf+hFxaAVLB\nSz2Ki8LRSsg5nhgnQwOSvxcbTwEga3WcgCUhZuemyIGnI/sPZrK69CVTsbvvoHCY9nY7g4ZB\nb9+MFkgw1h/9hrFzL54aF1oWLyiUdsjAhgwNIOZqSouE8fgoq6wGhMKHnvW//UZMn8Kqb4oc\nfEbmgyQ87zFqgEJBZJpCUazWDnHqU0cyZG7cIoi8Px/Bls+9o/+/C4ClIM/JdZ8YSV1SJUT4\n/LER0eX4Uiuhp8S0Zy4oCbyoWBDq7q/l5ZVg291ecc5U4dlpcuuGXc+TEKuxWVCKLMfca01U\nJJJz7a+vkLiDC9p9ww8QfuaFFK/zy8Mam+HYRw6laKNzc+wxHh7S3nkTT08CRM9e9If2yXyh\nQ/Mehw88UYIYMQtPTYIQvLhE5ktchs8h87Hdd3BwwbM33yVSpcksUpXA57oaAIAIZIW/9SKe\nm0UzUyK/UFoB0hiebkjC77fnXoWmhZ99wf/OG3gy2hRlrtugy90lzSurnToFCHhV1CLJ3LiV\ndl1zZBWmrFPYNlZTixJXwQIAwNhsj3YsiJxcNO08CkymOy0DQvWJ/HyUeHwpCgtt7Qm04H3R\nIPPz0tqUotkZ5CpDChrdQZChO8TVjkK7b+DZaWldpJVzp9zXOnr7pi3ljULBwGt/XO6+ZUw9\nfVz4/TLPu3h2DSo3u1hNffTxjWu+I+/ab0poWmTfE9JuJDJ8DpnE7r7DsrIBIfcFIv6ug5hF\nL10gYyOgqFZTs23CIy2x/CAeoao8UQ+W5+VL24LmwFq91nfyU4d3p9neGdt8s/LK4A9+lrU4\nzxfmI7kFIkd2mx1WWu4e6zCWvCVYWYV+4Gn/kXchHAIAQamxc48pt6UYHneJbHEeq40Ym7f5\n3z8c/6Sg1FgaFpEQPDLsbkpD09O2prfIzvYUQ2ES+zspPc5zCQCgQwOIWYLQZAf9aHYWZE3s\niGurAHGjBsqVi+6ZKt+Zk8aWnZIW7YTwPMpHS623+O6g7+03lmeqwmHt8OuhnDy7eTpDGpFJ\n7O4/WoBVVJLhhN2q0LRYBwOKhAO//VVM5Vz57KzZuTHy+JOpXueXRvj9QvWhxCZiVlkdLzCB\nwmHl0nkyPcmzc632NaxY3qZvAKD9vW5HdqQnNs1gLMorRWm5SAfnCeXCGY/g9ct6RZX92Fy9\nxmpqweMjYFm8rDJZg5QkoIV5MjnhjpO+HvurZXZuwvNz6tmT0anYQJa+/6DUowazHq4GAICn\np3hevvBrVvtaevVS/FMiL581S9z25ClQzDmYFhDq7jO2STZiLwPc5/foiVn6pXinquEQMgxJ\nZVwQYkXF8UOvNmzpZ6KeO+XuDVDPHA9nErt0I5PY3XdQOIzHnUPmyNAhooOiAoDvo/cd3jXK\npQtWwyqrWVKnS9rd5cjqAIAO3rE70sBu9P7jb2I2i8q5k/pjB811G1K90C8NudPrDtJEH088\nM4VOf0rmZtXcfHPdBskVffH8rMO1E1wCxUJV0+X031OdGOzZ5CX0h/YZG7eSsVGhUF5emczD\nShY07++PCATsB5FHD/gjkeUJnsKiyJPfjA0wSoingRvPLxB+PwCw2npeUooTswpW38gLi1O0\nvpVjtbTTvh5H0FiaHBdes1PC55PZJI1X1TgTO0JiV+YkquYewQySk0ns7jt4dNjdegKM05Eh\nM2c1AFDPI4zb3dImdt496YyhUFDk5YMQ/sOvxZtnI8Z8R95h9Y3yChx4dg3GJRPKjWu+t1+3\n0wgfgHr2ROj57/HKqpQtcKWIQDZyVRZF4kEeuTtIb3cjPcLKKqw1nUJiCS6ekysCWe6TLyvx\nIxBZ2Vaj1G0MMVhNnfBrDo95XlgcS4+Eqoaf+w6emiRTEzw7h5VVSK6Rxmvq3MfHVvuSgA4h\n4ae/5X/zFbIkpcaqa8NyO0/gKWeRWADA0obB7OhUzp6MnWNGg+u3SHoOCwCM0a5r7iDpvW1/\nTJ4mlvK3nWRwk0ns7j9JfuciVk3xPMKwvI0XZUDkeOVnhNhFLDw3E2tDiYEsi/Te4us3e/xD\nCWDVNe702lo6gEChoO+9v0L8nGkkoh1+NfjyP0s7v2w1t6qnEzuEEDbjes58xz5UT31qP1YA\n+LmToRd/LO+BLMY8N58kJnZCCyRUHIWgt26SuwMAwGrqJBdrwDPTjqwOAEAwx+WCFxXzInlr\nWvEoF864mwJJzy1YspDnhcWh7/+UjA7juVleWMRKy+XNgQAgTvAoBgKgPd3m2vUAwHPzIk9+\n0//Om7H9htW+Tt+1N9Wr/NKgxQX3XDnE5a/m+k2095bjWVPWi3aGzyGT2N13eEWlUBSUmL0J\nSll1dASBl1UQlweXrXogJ1ZzGxx5Jz7RAQCrZbV9DovMLxDokhDbYcJBLDOgd3qRS6oUz86Q\nyXHP4ycZoIN3nCHBY3cgMtgfy+ps8PSU78g7kSe/mZrlrRQ8M0VGnTOVKBwidwejnd2ca6/9\ngfZGFXbg3ClrVWv42RekTR08T//xzAyen4sVthFj9PplMj7GfT62qpVJfE0AADwz7RGcTQxi\nzCqr5bUWTMTzkoXittxWY3Pwp/8D3x3EkTArK5f5WBkAwO/3HOMDLXr6bzW16HseVY9/bHfa\nCULMHXviPe4ypAuZxC4FIKDUUZYTufmxJi193xPa7/5PfNcqLy41N2xJ6RpXAu256cjqAAAt\n9WfwgkKhqu5MSGaBYvWih5KtcuNa1P8jSarqXWqVAGRZbqcTACB3+myVfHrLWYoAANp9A4SQ\nMxNCSRp90Nws1NQBgHr+9HJWBwAA9PZN9cKZZYNz2XA7REfj0V8WCocCv/v1cvftyWPG7kf0\nHQ+lZHH3gmfXqSOIwmHl2iU8O8Nzcs3Va2TWowEAVlZBXZ7dVuJ1TKgqa2iS1iwxHuHzs4pq\nMpxQRBCEWnGpm7Ftl9m+jo4MgRBWRZXkH9CD4pe//KXf73/ppZc+/2VCiH//939/+OGH9+71\nruP++te/5py//PLLX/sKJT1I+nuC9ve4Rcnx9GSsk52VV4a++wNW1yB8PpGTY67bGPrOS7aC\nmpy464sAQEaH7YMYQan+8H7Hs2Zru8wz82jRS952SZGYl3mU5QQhvEhSuyqA5FqDAADgrXrA\nmad2mgyIJDIfsTjt7nI/6xmUBFbppRmUlR2TifZ98LZjpkr99CPs9dOTBNPLBdFaUtgBADI6\nnP2//5fvo/eVz876PjmS9av/17O9WB7ipqqXfk0IWR2d8a/BM9PqqU99R95RLp6T2RcEwLZ3\nc1ZVkRAisZ9E5OSYLavN1vZMVpeMX/ziF7/5zW++8GWc83/7t387evRoshf86le/+o//+I+v\nc2VLyJs9/P0QCrrnEwEAhYKwpNzLK6tCL3xB+i8RXo1lAqFYscfs3ASqTzlzHE9Niuwca02n\nzKKdACBy82HaKT8Ru8WysgpzTaeSqD1h7H5E+CUdURSU8vJyPDrqiLPa+ugDL5U7VlQibXs+\nLykVOXloIWFqh+fkLu8WPO+pXl6fkiDy8gET4Am1HlZXH/1xca64GrwAQLl1Q/dSkZQB6j5c\nFnEfAef+t161dRNtkGn633kj+PK/SNvZqVy5uPRw6eothNLdpW/fbf9Fr132v/dW7LBFnDoW\n+s4PeIGssnwTYyjoHD8CzshA//KMCwC+O0j7e5Fp8Ioqs2W1nCX8B8u//uu/+uRUtFkik9jd\nd0R+oTurA4Tk92NIhlXfpFy64Aiy+qb4S4C5eo3nDl5OrOYW0u/UNYg/Ddcff1LkF6rXLsHc\nLC8sMjZvN9esT+0aV4ZQXNcdSll1rf3QWreBXTrvED7QH30iNWu7B/D0lCOrAwAUDiPO7GFe\nUVoOLoEuLmsHJADQKxcdWR0A0L5oboQ4d3c7AIC7w0EeyJ0+ZwgtB8nEmLsJD4XDdKDP/P/Z\n+9LwOKor7XPvrepN+24tli3L8irL+75iGy+AAbN4wSyOSQIkmSHPTBKYIUOATCbPZDIMSYYv\nIYEACRCwgxcWY2wwtrExtvEuW95ky9r3Xb1V1b3fj5Za1XVvG8m2pGtG76/uo27plrqr6txz\n3vO+w0f1wvK6C6TrqK1VEO/otKCmRseOD80UGtTS4ty6qW3N9e+sXR+IvlEQqhlk37XDdmh/\n8KktfaB7xf1M4beB/6exevXqvl7C16A/setx6BmZYLNZigd65mAz+4TUVtt27SDlpYCQkTnY\nN2ehtNu+cKBJAsPsGwXKGYHTDqksD5a4GCG+6bPJgsWUUq/0AsWorZXwwxO6Ti6cC7TGGFE8\nKx6w79mpXjgLfh9NGeCdOc/IzOqDtXYNpLw0+DhY/Ua6hqurjPSBAOCbdRO5cM489MccTplH\nFHGLoPsPHjfSdaYoTFFoXAJusFaRDZEtvSwQdv+DwXApqaypKlMU5nDwmkFBZ1Xl0gXEsWxx\neRlqbpKziUkTk3kzXwAwUtuHcpRLF8xZHQDgshLb7k99C5b00hJ7DK+//nppaelTTz1lDv76\n17+Oiop65JFHAIBSumfPnoKCAo/Hk52dvXTpUluHHuHrr7/ucrnuvffe999//9SpU08++eQr\nr7xis9mCHLsrvDcAt9u9d+/eU6dOjRgxYs6cORERYTVQCwoKDh48WF9fP3bs2Jtuugldbbm0\nP7HrcSjnC/iLF6muDhLVcVOj861XO/SQGDl3xlVa0rb2EaGqkAxQT5/kg6TwHMy+KfhUKSq0\n79uFqqrA5dRyRvhnzmMOSRsuAIAttqrhgzcEMKf31hHvrEAwV4R3yTIvLJN2YMIMhjtXaF4r\nQ+2sABod41m91rZrByltlzvxzV0o5/01AOHamCsiSK71zV/sfPct80+N5BR9jLwq38bAQaTK\navsW7JXTxCShSRqVOFXVB2WpZ0NomgxjPbfdO5UX7CeGqAAAIABJREFUaQ/Gr8Rv7TswRWFO\nJ2oJGQdh0bG0wxZIuL9Vz57+BiR2xcXFTz/99OLFiydNaldvKSgo+PGPf/zEE08AQFlZ2d13\n333gwIFAg9Xn8w0ePHjv3r3p6ekA8NprryUmJn7xxRcvvPBCbm7uk08++fLLL0dGRgYSuyu/\nFwBqampmzZp19OhRRVF0Xc/Jydm4cWNurrWdpWnaj3/849/+9rcIIUVR/H7/lClTNm/enJp6\nNUOH/cMTPQ5SU8Of58jTFtSesO351KRyiVBAOO2LPb22wu5CoL8FgE1B5dIF54Y3cXkZMnTU\n0mI7csj57t+kJeYDABL1GpDJIQ0YU48fxi/+t/rLpyNe/l/bV1+G62vIABoVI+RB0tgEwaul\nz+oAwMgYxLCV/8ecLmaaazGSkj33rmn94ZOtP3zSc899MvuJAYCWM4Jx/3ltdKfhuj5kqOeu\nVUZyCmDMHA4td6znnjUyi0iDTcA6Mjr0opnT5ZtmHenVR+fJOyxPqVJaaokhSlFr++6IJolm\nqlQbk7XZQkqLcYt1yBc1N+KgWZ8wVfWJ89cbCytWrACATZs2BSMbNmwAgEBy9swzzxw4cOCN\nN97wer0ej2fz5s2XL1/+wx/+EHzx3r17Dx8+fPHixZMnrUWNr33viy++OGTIkIqKipaWlkDh\n8L777qPc3fCFF174zW9+86tf/aq1tbW1tXXDhg2nTp1atWrV1R1vf8Wu52G3C+6cCEFHtZZU\nW0nuAEB4y3NpQOMT+U4fTewcEbV/8pHlp6S8VDl90jwiJxX0zCzlrFWTPaAMEoB9/+e2fbsC\nj3F9vf2z7aipwbdgaa+tsFtgDgdNSMI1IUZ2zOkysnOCT5Gm2fZ/rhScRG2tNDHZP22WLrFg\nlcVSLNCNpbFxgkTnRshTAUA5k4+43qVlDFbPHqZnDwPDkHaoxQxFVMhXCk7pg4YEHvunzwaH\nw3b4AGpqZK4I/9gJGpfqyQPc3ITarGkQAJCy4gBXVR88RM/KtniO+ebMZ0TSuyoSdv8D8cQk\nAGBJycANkjORJsANh+HDh+fl5W3cuPEXv/hFILJhw4ZJkyaNHj0aAMaMGfPzn/98zZo1AIAQ\nuuOOO5KTk4uKioJvr66u3rt3b1aWgKzyte9NSUl54403HA4HADz44IMXL1589tlnt2/fvmRJ\nZx3UMIxf/OIXq1ev/tGPfhSI3HPPPQUFBU8//fTp06dHjeo2CVXSr+A3CdrQYba9uywe8/qg\nIUEvS6GpJVPkNRzUMwerxy3Cb8if294kQj6fxZM0AFJVIW1ih72C3mVwKha522z7TQVUBABg\nO3JIGz9ZTklS3NRoyeoAAHncqLGBBWwMGHO8/25QbIJUVTi3bPDceqc+Kg+khHL+DDKNGgRy\nN1JZjrze4GwyamlxfP4puVQIhk5TM3xz5stbDQIglYKdGxF2/2+ErA4AkEdwEoW4wGHsnzjV\nP3EqMgypS48AEBjzFyJYOUbIu+xu295dasFJ5PHQ2Dj/1JmaxL3ycMwE1nGh80+YquYfR6GO\nsd65C3t8Zb2ClStXPvXUU2fOnBkxYkRBQUF+fv5vf/vbwI/+8R//EQB8Pt/FixcLCws//fTT\nqqqQ62dqamp2drbw137te5csWeIw6SesXLny2WefPX36tDmxu3TpUlNTU1NT07PPPhsMnj17\nFgAKCgr6EzsZQWprLFkdADC18z9v5AznuSlajryGSLaTR7kYU4ou6CNGAQAoipBMA7J6YyPN\nj4u5UQMAcuFcIDPA1ZXCPjKpqpA0seMs3QIgtdUBfyqlqJCXEHPu3N4yfLSkaYTICgkYA58X\nHA4AQD6f6+3XgjsKUlToLC32PPCwkShrQ9Ym6P5b1CtJVYX98524vAwIMQZne+fMZ1HRvbW+\nboPGxvPXMeEQmPxZHQCw6BgaHYubrcrYxuAhna+xO3wLlvgWLAmMvPTuArsNI30gs9st5rY0\neQCNb2doMIfDveIB+64d5NIFRKmRmOybu8CQVV6nu1ixYsVTTz21adOmf/mXf9mwYYOqqsFG\nZ3l5+aOPPrpt2zZd19PT0ydMmBATE5IEp6SEZYJ+7XstJLmMjAwAqAzVoiovLweAy5cvu91u\nc3zevHmRkVdDtZf9u/gNgHLpgiBYXBR87Jsyk1wuIiWdEX3ocJmdJ8TeQR1dJEaIPjhb4Dlo\n6mzKBU0TDvR1yo2KSqoAIK0KALOLBfZoBwuKVAm6/+Bx4+YmOcexmcgvlTkcwURH/epLS50Y\n6Zr9sx3ue9f0xvq6Dz0rRzl3xho0+dvi2mrnW68hXQt0npXTJ1xlxe6Hvhvuw+1z0PQMS2LH\nMDLbEwOAcv6M7cu9uKaaRUToI3P902cL+xVSgFJ+O8dsNqH9oPxZHQSk8jnCHGpqMvf6aWyc\n584VQCliVNqe8tVh6NChEyZMCCZ2t9xyS1JSO31o9uzZlNJ33333pptuCiRSlq4rDu8J/rXv\nragIOSkCOdygQSFy/YGnjz/++He+851rOcbOBV+X39KPK4AZoqEBM/WeEPfKB7zL7tbGTdIm\nTPHcsUJmj0sAoB3egmaYZ3i9i24Llv0DGZN/5lwqq0Ekc7qExgZBwwk6II1FWV/AHE5pvTRo\narpgBtnlogPbdeyYonSK6ZvAVElTVT0tkx8H0YfkBIN8rQgAcJW8c82Whlc7TLtz++5POmxJ\n2y8FuKlRPfhFL6ztasCYctZKz0KUkeJOcTv1zCnn5vWkshwZOm5ush3Y59jy9ytbpPQhcFUF\n5gxpkN9v3oEDpbbDByJefjHy+f+I+PP/U499Je3hAADhhB4BAPk8uNmqEAkYf8OyugBWrFhx\n6NChHTt25OfnP/jgg4Hg2bNnL168+E//9E/Lli0LZGZ+v7+uzqo0JERX3vvxxx+bFbICQxvj\nx4e07AcOHBgfH//BBx+Yg0888cTIkSNbuHmXrqA/setxCBMaaqlvI6SNGO29+RbvgiX6sBEy\nZ3UAYGQN4YPmgT4WFdW27nu++Yu13LHa5OnuNet8M+RVFAOEKN/hUpTg8AQjxHPLcnPSw4ji\nXbJMWgEX1NTYObkcvNGwTnEQfUgOI9YczkhND+fc1edQ84/y5RNS2umvJU5Jpa0GASgXBW5a\nxMTEF1ZVhfmrDEA+n1DOlwTHQSi1f7rN8lPl0gW+tC8J+OJWO0xx++5P7Ds/xg11yNBxXa1j\nx1bbF7t7aX3dR7htGzORZJDPa9/5ceRLv4n8n/+IePPPCifbfkMjMBv73e9+Nz4+/rbbbgsE\nY2NjAWDz5s3Nzc0AUF5efu+997a0tHQlo+rKeysrK9euXVtbW+v3+996661f/vKX8+bNmzFj\nhvn3YIyffPLJ995774knnmhoaGhtbX3llVf+67/+Kzc3N4qrKXQF/Yldj4N2CBGbt3JGprXY\ng5qb1DOn1PzjuL62t5Z2lSAiRhoK1U5jquqfONW79A7fvJsNWWt1AaCWZlJRZo3qOinqtEgy\nMge3PfwDNm8hyxvvmz7bve4xPWdEr66yOwiZWQ7uETxuUtf+1aLxCf5QP1/mdHlvuaN3lncV\nII2C+hZuaQoWSIyhAk6qLgpKAqSLjCVMhXxxd0/WVJWpqpA5Rzs2P6ilGYnkFbFoiEQG0MRk\n4QabdSix48Z621dfWn5q/3Ivar2aEksvQB+SA9h6RDQltbPZQqlz49u2wwdQcxPSdVxe6tzw\nprSZ91UgKytr8uTJRUVFq1atCmoIp6Sk/OQnP9m5c2dCQkJmZmZmZubQoUPvuuuu999/f+XK\nlVf+hV1576pVq7Zv356UlBQVFbVmzZqRI0e+/vrr/K96/PHHH3300V/96leJiYkJCQnf/va3\np02b9sc//vHqjvQbWG6VDerpE4EH5lOKXCyEaXOCT22HD9j2fBrUBNfGT/YuWCJp3Y4x4eye\nUlZi4dOQ2mpcUQaqTc/IlLYUBAAozM4Mh16gWVQUnbuQUuqX3nmCH9bh4/4Jk430DOXMadzW\nYiQma3kTpLW+BQAq0mpnTlenPfHIXOXiBaXjXAMAIynFN2d+L62v+6ApqfwWTjeN8epDh9sO\nH7C8QJM2VSWEpg0MaVMCAMZ60C4sXJdflfQexFwu6nRZtL5ZdIzRoY8oJqpSSqqrdCkvd7iu\nBqi1U2wu16lnTwX0vc2w79iqf/cfJb0ZdR//8R//sW/fPos+3H/+53/edddd+/fvj46OnjFj\nxogRI6qrqxcuXBiYmVi7dq0/1GLg29/+djAvvMJ7McbPPPPMXXfd9b//+7979uy5dOlSXl7e\n7Nmzgz6z69atCwra2Wy23//+94899tihQ4daWlry8vLmz7/6y5ekJ9U3CcJ9qjlISorsOz82\n/1Q9eshISJR0fgIhJjI6YWYKFGOOj98PWmgzRfXddLM2blIvrbCbYNHiSUNqUQdgDF2+iKur\nFNVmDBrCJDaBph2esCFwOGnoiKiRkiqzIIgZ+tARtq/2W2iB2ogQ9XbPrXcqI0YplwpB1420\ndG30WEknfAEAgAqG3ZA+tLMM7J89n5RcNotcaiNz9dGS6tGAYQhmsSkNWqkyVwRNH4jLSsw/\nZ0TRh+RY3yUHlOJLvIMLam7CzU2BK0PYzqasqapiakEEQcpLgdIAVxWLUlXc3IS8XuaUlHbS\nXSxcuHDhQoGAy9SpU6dOnRp8mpyc/NhjjwUeP/TQQ5YXP/xwiB3wFd77s5/9LPBg+fLl/B/9\n1re+ZYnk5eXl5V2Hc1zSr+A3CTQ2nu/00bhODwDbiWP8u9RjhyVN7ACM9IEKZ/htZA0NPrYd\n2h/M6gAA6Zpjx1YjeYCc8xMsMorGxuLQZh9zOo0sk3CRx+3a9E7gtuQEYBGRntuWS2uuyhBm\nCFn0b2lCoqVZhnSdFBWi5iYWn6BnZgnNKiSBcr6AsVAzMQDEcdvbFX1vBKhnQ+ybGAACpl44\nYwwa3B5RVff9D6unT5CyUlAUffAQmTvLuL4OedxcmJHS4uDmwbP0dtdbr5n3tP4586msejSI\nHylojzdCdAwAGOkDwemC0KNmEZE0VcarHAAAFZnlUBrkM4jH/BGCG2Hmtx9m9H9gPQ6aPhAK\nLJrsyDxqIKaehLH7lAE8rZghHBRDAgD1xBH+XbaTR71SJna4tgZzFC7k8aCWFhbbLm3g2P4h\nMRUbUFur871329Y9xlxh7Zz7EOr5M4gxFtr9xxVlSNeC125SXenYvB53zGYaicneu1YFNZll\nA6kstxSJkUjOF7nblOIi8Lhp8gDJ9bcsowbtR2eZPyBEGzNeZs3bToh3Bcgs80vjEtoe/r56\n4gipqaaRkfrwUcaAtF5bYHcRTjKQRXXM+9sdniXLHO+921mVVFTPLXdKK32ipw1Uj1uvzDQ1\nPVjYNoYOg/1WK0tj8BBph+X7EQ6SfgW/STDzfjrAlJLL+ojRgSc0No7vGNFYgVqSDEAej+WG\nygAQo6TwXFAMVtx9bpM0VSVhplVwbXX7p+Bxq+etkmPI41bOn9XGThC8s8/h9QDjWDGUgt8P\nigoASNcdW/6OTYobpLba+cG7bfetk5NMI761hEpeq2dO2bd/ENx16FnZ3jtXSKs1SGPjcJ31\ni8fbjOL6WlJaDAyM9Axpi1sAQOPimSuCP/EtVW3mcPinzIAbAUbGIKYqyK+bt0dG8gDz5kcf\nOtz98PeUk0dJU5MRG6uNGR/O3UEKiCTijQGppsdp/pnzgt6JAMCiojyLbuuFpfXj+qKXErs3\n3nijoKBT5Sg7O3vdunUAwBjbvn370aNHY2Njly5dalHt+2ZA6K+FGzs1fv0TpyqnjiNNM7/A\nP30O9yY5oPktgQ76uh6M0Jg43gBXTuVbAKBhLDGCaibY4xbKU2G3QN9BBtDEJODTs4hI1iFA\nSEoum7+BAeDyMlJbbSSF1VjvQxiDraacEJjy6wBuqLdve898EimXCu27PvEulNTP10hMsSR2\nDCEt1NLN/vlO26H9Qc1L/8SpvvmLe2+J3QEyDEGnT1H5RIeUlZCqSmqzGYOyZDbSUArPIk23\nnEekpSnISAuAxsT6Z93U24u7KihnrHbYAEBMUvkA4JsxRx+UpZw/g91uIzlFGztBXgXpfoRH\nN1g1lNKXX3558eLFo0aNeuGFF+rr63/5y19aVJXD4auvvrLb7cM7MHBge5fkj3/84xtvvJGZ\nmdnU1PTjH//YbJ37jYFwoI+aWng0PsFz54rOjaDT5V1yuz5kKP8uGcAio4T9R2ra+fmnW729\nmd2hTZjSsyu7WtCMQbyKBIuINFLT2x9HxYilHExESalAk1KAy+yMwUM6q3EiyTEAgFZJU1Wh\n2Yl5jFctOGnZGgEw5eQxoRdc38MwlCKrIQ1ijJR26tSo5wpsX+41K5nbDh9Q84/30gq7CVxe\nivhpcV0LITAYhnPj2663XrV/+pHzoy0RL7+onuDNCWUBqq0RRD0eq5qJYSgXztoO7VfPnEJC\n4ztpgEXLQx6PJWKkD/TNu9lzyx3+SdP6s7obFF2t2DHGVq9evX79+rS0tNbW1qamJr/f/9RT\nT73wwgtbt26dOHHild9eVVX10EMPWdSWGxoaPv7446effnrcuHEA8Mwzz2zevPmHP/zh1R2J\ntKDpmbzkt54bsjU3Bme3ffsHuKkR6boRnyDzNB8gBHY7WHouimJkDg4+04eN9N58i/3znYFr\nPY1P8C6+TVr+FqquDJYhg7w0ZHRmCUxVtUnTbQf2mt9lJCbrsvr5KqdO8MYSuLw0+Jhv+bXH\n4yVNVcllwUCfUnLZP3VW4DFy88x9hHQN+f0Syrggj1ugf8tC8ldFlPSoJ45ouWN7dG1Xhw6T\nDA6mAr/t851mh2Kka/ZPPqIDUo3kAT29vKuBcOw9cPXrAG5ucr77Fu5IAZkrwnPHPUaGpH0n\nIz6BcIOxNDHJEkEeDyk8h9taaFyinp0j9c2oH2HQ1Yrd5s2b169f//Of/7y0tHTChAkAMGDA\ngM8++8xut3/3u9+98ntbW1vb2tp4G92DBw9GRESMHdt+nZozZ84XX8hqmHMNINwAKQCgeq4C\ngTGNizeSkiU/kXBdLeLLJ7puOUxt3KTW7/2ze+2jbd/5h7Z135P2YgcAiinj6SxzeX24odMZ\nxjdzrn/StE6WcWaW965V0rruoBbruKglaKRlmL3MA9BH50mbfIsLb6ag2GzeFSGpKo3DKTjN\nUYgvn2jIVByUAeE6+NSkp2Pjyo3I0JVTPAVZCuhDcni+qZGRafbqdXywEZsKe8jd5nzvXUHl\nUg4wEUdTCxVaJ0UXI1950fnRFvuenc4t6yNef0nsfdcPudHVO9OmTZuGDRv205/+1BycO3fu\nj370o8cff7y0tDQjI+zAY1VVFQBs27bt6NGjTqdz6tSpd955JyGkvr4+NTU1qImWlpbm9Xrd\nbrfL1c4EKiwsDNquKYqSnZ0t/P3XCEVRAIAQovbE7I+um/ODINTaGrNiJ/L5yL7d5FwB8vto\nSqo+Zz7t6ANeAYQQjHGPLDs8sG7l2AWg+HzIshJVhbR0ALDcwQgh0HP/8O4Dh+HXK3ZHJ2df\nVemiW2HJbay2xmezQ2QU4Y5LHiDR5A2LjjX/w7U77oWPPyAB2g1CxtgJxs23SPKJBIExDpye\nkD4QuBsMyxzcueBxk9jhA5abkD77JjUMgbJHEbAMV1WVhmsEqypLSkGWISRMIHds5xElJAI3\n9sviE3v0M0IIXWnZV3ijKwJUm4WAy6JjSGJSh708Ba+16wcAis9Lr/mIAjeR6/ufIRVlnTog\nnYV8I/hXUH0dCZXlAwDU1movKTJGjeniXwn8w6/Lgr8WakG+IFhaDMFxFo/b8eEms4ALrqt1\nfbTF/8C3+Tf23MqxxLpLNwq6mtjV19cPGSJwCJ00aRIAVFVVXSGxq6ysBIDm5ub777+/qqrq\n7bffrqys/P73v9/Q0BBpUumMiIgAgIaGhmBi9+qrr27b1m4vGBcXt2PHji6u9ipgt9vtPbG5\nZ8ynKKDrlrAtKsoV00ErplR788+0o+KFW1tsly+p3/0BHtQlmbQeWXZ4MDTYjxA/TODKHIRj\nOonSrL5O3/Y+u1QIAGjIUGXxbSi0zed0Op1yiF6yvHH+HR9agig2PnpwlmBENCpausYeBzpy\ntMa5xSt54x2mDwhiYuBbj4DbzRobUHwCyNevDCBw89AUhc81nDnDOr9yMTFs3WP6u3+jATK4\nzaYsWGyfu7APh3yvZPLo9fhqqiwxRI1IQw8eEbv5Fv+5AjATBxXVsfg2V0zPzl1enTelcfG8\nzo9VNTdFG3rwxPfHJ7I6K3HNlpruvE5HFHNd/zN6dVWQ3og6cjtcVRETHR34UtGmBmH72QmM\ndGcl13fZV4Df3caPgKnu1uA3yrh4TufmmnHJZfOHGARCqIdWrnO3y350F11N7HJzc//617/6\nfD5LGrFnzx6M8fDhVyIb5ebm/s///E+w3hYXF/frX//6gQcesNlsmumyFXhs3gTMmTMn2MB1\nOp0ejuZ5XYAxttvtuq5rVvL19QFKH4i4bqyWM0ILHs6RQ9jyAl3zb3yHPfr4lX8zIQQh1Nun\nASbY6bJy7Fwu34A0CB5Rawv+/QtBhj47dth//ix97IcQGQUAiqKoqqppmiwncFUlv0NkDofH\n0lIpukh27WAVZeB0seEj4aZFwbFZ2YCOHOLTGaOiTOPPIIQgLh4Yg545ua4RNptN13VKKT5z\nmv+p/+QJlmnabcbEwrrHoLUFedwsPtFPCPRRU8xmsxFCvF4vEw1TAwCUlmBDoBbrLy5iwd5l\nbBxa+SD6cBMEmA8xseyWO3xJyT36Sdntdr/fH3bZ4YEaG4QZtK++LjiLDXMX4I1vh/w4Kto/\nbuK1H5HdbscYX98bhOWa0H50hHReFiIiMcY8ScAfFdP1I3I4HN7e+pbi6BjgFHaM6Fi9Y7Wo\nsVH8ITbUd36IAADgcDgAoIdWjhBSZNUCvFHQ1X/fqlWrnn/++XXr1r344ouBCGPsnXfe+dnP\nfrZs2bJIgT1OJ2JiYsypfW5uLmOsoqIiNjY2P7+zONzS0gIAcXGdXaRFixYtWrQo+LS2Vqw3\ndo1QVTVwOXML+NfXDEojawTTVV6Px+jQdXNcvsQnFqiqoq25WTiMGYTD4cAY98iyw4MUX3Lx\nMnVut6ekmCYkti9sx1ZsmbtsazW2b/Uuvg0AHA6Hqqo+n6/XrmhXhv3saZUfIq2qcDc1BbVG\nScll19uvt9/ufD504Auj+LJ79Vo5CZGummp+Way2us0sJciYmn/M9tWXuKGeRkZpYyf4J02X\n7XAwxl6vV/P7o0TcfMPt9vDiiAiDM6KvUroAMMaEELfbHa6niQ1DKGztBdDNR5SaDt/+AW5u\nAsZodAwgBD0sBqmq6hWWfQUokVGCXQ7GbXYnC645e5i6cKl97y7k9QCAkZruW3ybweDaD0pV\nVYxx23X956jpAx1HDlqCemaW+StnHz/Z4udrZA52p6R2/Yjsdvv1XfaV/lZiks2qGYQ8OSOD\ndyIlMjrMh+hgoYt0OByU0h5aud1ud1zvBkJLGEPwa8TVlbd7AV1N7MaNG/e73/3u8ccff+ed\ndxRFyc/P/81vftPQ0DB+/PhXXnnlyu/dunWrz+cLeqU1NjYCQHJy8tChQ998880gqe7MmTOZ\nmZmysXyuEbi5CYnUzkhZsdFh6CnO3jBmUkrFomYBMR8CDjwdiR2usHKDAABXWn3VZAGlgn80\nY+Z2s/2Tjyw/JxVl6qnjWp6MAsWW7XV7MFSkxnboC/vuTwOPcVOjfc9O3NjgXbysN9bXXSBk\nxCUQrotnpIRMUyLNb9v/uXrqBHK30fgE35SZ0jqr0oRE5nJZJnmZohiDBTRiGh0DhiGncHQQ\nRkIScOUrI3mAxWNUGz9ZGzsRNzUwu0NO15YgxAo7oYfjn7sQMFaPHESGAQhpw0f5FiyR9pNS\nCs9bIgwYqSg1hra78OmDsoyMTFJabH6Nf/J0aVsT/QiHbhQ8H3nkkUWLFr388ssFBQWtra1D\nhw6dM2fOypUrRY7wIbDZbC+99NKAAQOmTJnidrtfffXVCRMmxMXFxcbGxsfHr1+/fu3atQ0N\nDdu2bbvzzjuv7XCkQ9jkDHcmc/qQHBu/NRycLad3J4sO47RjKspapygCQWk9ANIHQui2GwCM\npOTg5AQyDD6rAABSWS5nYmdkZCqXrDJpxsjc4GPk9dj37rK8QD1xVBs/WVbtCW4Hj5BuToMY\nc3ywSblwNvAM19Y4t272an5t3KTeWmI3gFuaeX0WxNXJUFOjfdcOpagQGYaRlOKbs8DoGu+2\n96GePc03JXFtDRiGtQyMMYuOlXPXagYpbqfHmK35LNMSjBDfvJt9s+fjpkYWFSW56hsvlY8s\n+SvGnjvutX+6TT1XAJQyRfVPmuqfMbdXV9mP64HudbKzsrJ+8YtfdPdvLFiwoK6u7le/+lWg\nAZeXl/f4448DAELopz/96TPPPPPZZ5+1tLTMmTNn2TIpCwbXABYdQyOicJu1DmzemhtZ2dq4\nSeqxrzrfFRnlvfnWXlpiN0FTUhlRgvaI7cGYOBqfGHyqD8mxcfNi8rqzGwKqH4vvlHdiCAHG\nwJGipLWrUoQKO6aJUVxXyx8OAOCqCgkTO+T1kIrSkBADAKYUFfo7isSkuCiY1QVh3/2JnjtO\nQu9O3uUWAIBSUlWhZ7UrkyOfz/XOX4K2b6Sy3Pnu3zwrH5DTA9cq2xsI6hryec2VOVJWYv9s\nO6mqAISMzMHeeTfL65PWUbBHomAICGERkdKKHwXBIiIQ15E0K+wAAHNFeJfd7dN11NZKo6Ll\nLC7042vR1e/inj17akRcsQDmzp2bmJgY7qcIoZUrVy5fvry0tDQuLs7MosvKynrttdeKi4tj\nY2N7bTioN4E0DfutdB+GMA0tbntvvkUfMlS5cA68HpqSqo2fLKn+FgApPIe4TAi1NiFNC5a4\nfJOnk0sXzCV9IyPTN3l6762yOyBchwIASLnp1gj+AAAgAElEQVQpMcVYz85RzlntYvWhkgoU\n41qrIDYAYLNKdrhcR8pUFfl81htq4GZroqjzFnYAgPx+3FhvyJc6hOPOmuO2o4dwqHoLMnTH\nrh1ta9b17OKuCkKPVGa3m7t4pKbauf6vqGNkilwqdFVWtH3rUUtuIQmM1AxSctka7ODPBKGe\nPGr/Yg9qbmJE0YeP9M27Wc7DAQCalEKsiR0yRgnoCowQUBRpe8r9+Fp0NbH72c9+tmvXrnA/\n3bVr19y5X1OwtdlsQsEUhNA30iI2AFxZHiJYwAAQIEaV8hJt+CjzK/XsYfLWtEwgIr1KZFDU\n0tzpW0CIe+WD6ukTSsllANAHDtJG5Um7+eOsqAAAIJSt7114S0RlBWpuCkb8k6ebzTakArPb\neTt2swGDkZRCY2LNeQMDALtdl7LTRyOjmKryHxMzieazMNxcObtjRtpARgiyFE3tNpraKRqF\nhKlqlSAoA/TUDDungmQMHGQ+6217PkWhg/DI47Z/ude7YEkvrbI7QH7OGgTACNXBVvOPOba9\n3/56Q1dPn8R1te4162QbQgIAoNTsPdMBhuqqITUt+Bzpmm3vLvXoV0jXmKJq4yf5Z82TtjXR\nj3DoamL30ksvmedKGGNVVVVbtmz585///Mwzz8yebfUG7UcHRJUGEJT0cUO9cu40am2lScn6\nqDHSnkvUJdqPIsRcoYR9jLXccVruuN5Z1bWApgwAk9NRRzDV/JRFRLat+56r4CSqKNMURc8Z\nYWTKmAMFYAxI56nf1LyRwNhz63LXu28hn7f9S0mIb9FtkvLZMQZXhEWgmBES7FoCgDEkhymq\nxdjKSB4gp5cGaqi3ZnUADOGQSp5QWlnWQr56Jl9wTQsV1yDiQrJVz08SiF3sSou1qR1PGAuO\nH3W+q6pCKcjX5bN9Q21tvCUGA8B1Ifr59k8+Uk8ea3+LrtkO7ccet2fpHb20yn5cJ3Q1sRs2\nTFBMuvXWW1NTU59++ully5YFncH6YQZNSRNszTHWQ4kySv5xx/YPgy1Otv9z96qH5LwnGQMH\nAcLAQsffUtP4ySly+ZJSdBF0v5GaoY8YLW3FDkTkGCM0sQMApqps2iyDUp8cKi1XgJjCFepG\nRdMHtj38fdvJY7i+zoiK0nPH0jhJjWJxXQ3va4QMg5QUBbvhNDrGt3CpY8eHQe4gc0V4b13e\nqwvtMpSyYj6IvF7cWB/kqurDRwVvsUHooWV+eYC/zsUOAoVk7jWMH4uRA/wsCwCYr+TI3cbX\nxQGA1FbLoc8ZCoedH1tGAMzZ+f/HDXX8V07JP44nz+AtZfshM66V73nfffc999xzp0+f7k/s\nhEA+L1COb0sUMJVGcFOjY8dWM3ENNTc5tm52r17bK2vsHpTzBZasDgAwx8l17NhqGgc5ZBw5\n6Fn1oJxlSBIo15mH37jxNwAAStHRr0jJZTsCY9AQaQl2KIyLHa6qhFCjIxYR6Zs2q5eWdQ0I\nZ5BqGSzVxowz0jKUgnzc1kITkrTccUxWOw3A2PqF64y3Q88a6p80zfbVl8GIkZLqm7ugdxbY\nXVCRlCmLCpmg14ePstVYi3aarKmqkZSscNsJPc1ksGQTpEoAAFKKgzDVRuPizTVUBoAw0od1\n/v8xJ18cAKmv7U/suotLly6VlZXNmhVygaWUfv755zk5OWlpaeHeeF1wrYldQ0MDAPSQi+s3\nALi4CHFpEGh+XF1pdLjBksJziNNfJaXFqLWFRUqnfyiUd0Itzcgwgo0k5VyBecgXAEhFmW3P\nTt/8xb2xxO4iYIVkucn6Q/yRkK45//Y6riwHABsAHDmkjcz13rpcQn4xwxgIEczw8q09j9t+\n7CtUW8NcLn1ErpzjlgBAYwTWtwBA4+OtkYRE/6x5Pb6ga4aROZjP6lhUtOVIfTct0oeNJBfP\nI02jqWnacHnL3nRAOsAhS1DPCrkv+KbMxKUlSlGnRq6WN0Hvsq1qb8MQVOxYcmchn6mqnj1M\nOR8yU8UURcsZ0eNr6z6Qx2O5dCMAoAy1NEOHtXS4jRCVdoMkMfLz82+//faCgoIRIzq/D/v2\n7Zs3b97hw4dlSezOnTvHazdXVlY+9dRTDofDvPR+mIHCmPMw0z4P+60ei+3v9fsYSJfYCWlY\nzOEw04MsF7sA1HMFciZ2LDEZuEICDVX9sO3dZelvqgX5+uBsCck0gLGRmEyqKixhI7Q0gutr\nI956LdiftR055Js93y9nAc/lApsdLGR2u91Is2aipKZaPX4YNTfRmFht3KSgFYpsEO6OqM3G\n7xOM9IHSJtxmKBcEpzyuDz1MQjz33KdcPE/KShjGxqAhxkBZx+YYIwHT4VCQyxe1YZ03O++i\nW131tbiuNlB9ZYT4FiyV81uHG+oExUUAXFcT/BSM1AwaG2eRu6MxsfRG+AZeB7jduOAkampk\ncfFsVN41ClMsWbIkPj5+w4YN//Zv/xYMbtq0KTs7e8KEHlc/7Wpi98gjjwinYjHGzz//fHQY\n0dp+GOkZfJDZVGYSzTeSBHIMzG5nYQoVfQsjPRNgnyWoh86HIkGqyoDzCJcETFQFsXxw4lT1\nwlkJEztkGLhR0IpFvhBqoPOjLRbWnf3znUZ2jpGU0rPr6z5IcZE1qwMAn4/U1ZrPHfXMKcfW\nzcFSpXr8sHfZ3bqU5RPM6WgAAKmrRbpuUd1TzxWQs6ex12skJvknT5ewhB8Aamrig7iZCyJ0\nY4z/MybotIBV85K5ItoeekQ9dxrXVDOnS88ZTmOtVWRJEJbLaG4cE+Jddrdz49soaPPtivDc\ndrf8En3XDnT5kvL3N5HH086Q2P2pvupBOuDq62qqqt59993vvPOOObHbvHnzqlWrrsNyvw5d\n/cD+/d//nbdqJYTk5uYOHjz4Oi/qGwQkcoNmdqeZbaYPyTEGZZFQUVnf7PlXNortKyjcACkA\n4FDTQCM5hVOLRTRJOuXbAIRyvkppsdlVQiiJwjfQZQBqakA+QQ6NqyqhY5IXedy4XODwRgrP\nS5jY8SYN7WhrhY7EDnk99u0fMMMIlryQYTg+fr9t0BBBD7rPgZCAYoeQJeL45CP1aHt/kxQV\nqieOuNesk1PRl0VGAVck5l1qkK6rhw8oxUVADT19oDZ5uqTDExiLXexSuY06IdrIMTCyl9Z1\n1aDxCczusOzuQFH1wSEaZMaAtLaHv6+cL0CNjSwmVh82QtIP6LoCaX518/qALmb7KdjaQja+\nTR/94bWQH+67774//elPp0+fHjVqFAAcO3bs0qVLK1euvC5rvjK6mtjNnDmzR9fxTYVy+SJw\nNGnc0ozcbZ09TYQ8t99j//wzpSAf+bw0JtY/bbaWN74PltsF4Mb29or5oCzVe23iNDX/uHm/\nzojiu+nmXlpidyEsJYYWHY2UVOWiVceYn5yVAeGU20LyG6F0H4hNOPocNE5cBTHHSVkJ8lmr\nesjjweUlQgPWvgUdOIh3sQt4ugSfkpLLwawuAOT3Oz9+v23Nw72xxG6CxifymkGWyhwyDOdb\nrwZJAqS4SD190v3gdyS1IhVx7OgA6ymPWprt+z/HleVgt+tZQ7WJU+XckJOaKmtWBwC6hnw+\ny/+f2e03hEzVdQS6XATcWDeqr0PlpYyTpO465syZk5aWtn79+meeeQYANm3alJOT0ztjpldK\n7A4dOlRfL+CC8JgyZYrZT6IfQTDGQDD8Bha6A3M4vTffAjffEpCF7KXFXRWoKyJw3UKhQfNr\nmMPhWb3WFrC51HVjQJpv7kI50yAAoPGJpMJavrJw7HxzF5LiInOJjsXE+ifP6I31dRMsKppF\nRKDQGipgTE1jvCwqmkVG8TZQ19J66DnQqBh+/JBFxzCzHpDIIQ3CiFb0OVB9LV+wMwtPAAAx\nDRkEgcvLkNcr4bQvuSxabahwnXpov4X6iZsa7Z9/5r35lp5dXPeBWluIiM9Aii6ar2O4qdH1\n+h+DCRMpLlIuXnCvuF/CGZdwE6+4rtaiq0VKi20H9uGGOhYZpY3O03LHSTgidn0hSHk74mKO\nfNeAMV61atU777wTTOx6p1wHV07sfvKTn1zBbcKMrjhP/N+EkS7I92lMjIArQykpL0XNTTQ2\njqamS3su0aQUKMi3BI0sq6cIjY7x3n4PAAClEl7mQiH4V+uhHDuamOS5b61z3y4ouYyIog3O\n9s2ZL+H9FQBQc5M1qwMASpG5MImQd8FS55b15pfo2cP0ITk9v8BuQ7lwhud9o5Zm5PEwZ3ux\nwRCmpISI430NUlZq+s6153i4KkSqN+zclZD71dfgvKoAOOKdUlIkeKNIB7jPEW4/gGjI/sH+\nyUfI6w2RSSopUvOPmVkckiB4plhgMbdUzxU4tmxof9JQT0ouk+oqOa1BriNoYpKgyooQu2Ze\nyurVq59//vn8/Hyn03ny5Mk333zzGn9hF3GlxO6///u/A2omX4t+EbtwwC3Ngq05N1iK62sd\n7/2ddMxm0vSB7mV3W1SgJIFSLDSYF1CnkcejlBSB10uTU+S8vwIA0nVSKWKbFRcZg0LZJymp\n9P6HKaVeuQWKSZitOaquBBOzWx82wnPvGtsXe3BdDXNGaCNztakz5NxOYK+AqAqMIW9nYsei\nY3wz5tq/2G1+iW/mPEm9NIh5q4NEQRAOw9KERHC6+Hifw4iMIpzcoNVAllf0BKs1jySgUdHM\n4UTcF08P5diRksv8rpAUX5YwsaOpGbwKEnO6QprLhmHf/oHljeqRg1ruWGn7LdcFLCXVyB1L\n8o+bg8akaUIH5G5h0qRJOTk577zzTkxMzIgRI8aM6SVxnysldl0ZyjUMY9u2bQ4pSxcyQCm9\nzN8qcXUVMNZ5EzUMx5a/m/12cFmJ84ON7lUPSXijRY2CXJ8ff1POnXFsfz84O6JnD/Pefg8L\n5z3fh9B13goJwk1L1FThoouq308zMiUcMggg3JQ+s1u37PrgbF0+/hmPoBmDGUxVLdx8/4w5\nNCbWfvwwampksXH+CVPkFb8dkKacs85ZGxkh2h969jA9Z4RlHNu76LYeX9xVgUVFgtkcjAEg\npOeEiHgbAwcRblsop+IJMnSgvOcbovGh7iwIeKFpJN9FGwKdfY6ugPxepOtB9i2urxNN+zFS\nWvzNTuwAgN66HCKj8JGDyO9nDgedMtOYMee6/ObVq1e//fbbiYmJvdaHhe4KFNfX11tqeMeP\nH7/77rsPHz7cC9IsNyKYqM1nSddIaTHvokhKi0ltjVAJpW/BIiKBy+1YVEhnGTc1OrZuNvf+\nlMJz9t2fSFjSZw6HkG3Glxjtez7FB/YBQKBor42f7F24tDeW2E0YyQNAUcDitq7a2KDB1pcy\nplwqJFXlzO7QB2dbb1rSgAqlExMSrSoMCOm5YyUUoOFB6gX8LcDWq7Fn2d22IwfVc6fB7aHJ\nKf7ps41kKUfLGSOloU4tCAAYqawwN/f9U2YoZ0+biXcsMkpOLw1cVclrNiHGSGmxWVHZyMzi\nxv9B5080CYBCpRPbs1GDouZGFpyzFnNmkFAQ6hsGpqrGwqXGgiXgccN1LfOvXr36ueeeO3fu\n3J/+9Kfr+GuvjK4mdl6vd9WqVVu2bOF/5HK5cnJkpObIACM1Tc0Pcd9jgSaLKbfjs4rOuISJ\nXXQMcHZb+uCh5qdqQT6yjpoy5cRRuGmRdHw7SoW6nTQ5pCCnniuwHQhR71OPHjKSB0g4vEzK\nSyxZHQAwXWN+P9g6i3lI15x/f4t0CKrZCPHPWeCfNK33Ftpl8PdOAEB1tSFl70DQ71cKTuL6\nOhYZpQ0fde2dlB4CrqoQqJ3UVllfR4h/8nT/5Om9ta6rBNI0kXSl9crGFMW9Zp16YK9aXMQM\nw8jI9E+fzaTsLAur+IEfmJ945y+OKCs2V7mMrGxttIxbCxYRkqy0f/cQYhGdXnA0PoHFxPK+\nzEaHTNI3Hwhd36wOAEaMGHH//fdrmhYQPekddDWx+8tf/rJly5bvfe97WVlZzz333Jo1a6ZO\nnXr48OE//elPx44di4qSVDazz4G5rTkCgNC5VxY6lBQEDRPvWwhMVAFwfSivq41PVREKjNaH\n4fD2FXB9rdjJu7TYLBimnDzKv0Y9eVTCxI7/ygEAMIYb6sHUT7Ht/oSYZHKRYdg/266npkuo\nMs/rmAAA0nWgFEzSEri2xrXhjWAyYdu3y3vrcjkFipmiCvY3qmAcHjfUKadP4tYWGpegjRkv\n2+kTAFNVISONxlqlEpjN5p89X1KlchNoygBGMLIoniBEQ4fhWExs27cesx3YRyrLwWbThwzz\nj50gIX8G2rWZkCUxpfEJIYk1Qp6ltzs3vIlMTVv/7PlyemncQPjrX//ay3+xq4nd7t27c3Nz\nX3zxRQA4ceKEy+Vau3bt2rVr/X7/c8891/vrvlHAOzsBAA7VvTTSMoz0gZaESc8ZIWdrTFhf\nRKEiQEwov+50SThGisLszFEo0VsoNB3OnL6PEWbHyVwhpRGVG20GAPVMvk++xE5oQE7jE8xZ\nHTDm+HCj+cuJNM2x7b229IESzk8IFXYsUrEAoBactH/0XvAuaz/4hXvFA0ayfOROhMDhAK8n\nhHCGkD5kKP9apfCcUnge/H46IFUbO5GJ0tk+B2puRjrlFaT5KxiLiJTTKdECtfC8Katr/5hQ\nW5ul7G0MHOz+1qO2wwdxbQ2NitJG50koA9mPr0VX+2L19fVDhrRfd4YPH372bHtz5Dvf+c5b\nb73Vxssr9CMA/rLFuCDGnmX3mM8fbdhI7+JlPb+4qwEVzeqy0K25NjqP74L5ps2ScC9rxCeA\nSDjQyAjJb1icIMkWkvr7HEZKGmDr/xlFxzDzahlDotleYVBOWFSLcUM9qba2MpHXSy5e6MVF\ndRWY49QCWFWjUWuL/eMPzbUT8LgdH7wbvkvYZ0CtLR0zVWYVF0bKSi2vdGz/wLnxbfX4YbXg\npP2z7a5Xfy+sl/c5cEWZgB1NKa7hvmO6bju037llvWPLBvXIwXB6in2O0L13RyfW6+Htc2hc\ngnfhUveqB723Lu/P6m5QdLVil5WVtXfv3sDjIUOG/P73vw88joiIoJSeOXNm4sSJPbLAGxxG\nQjK5FCrdiUDnxKxZVJT73jW4qTHgXy4tNwgAmMMBlhFYBHpWduhrnJ67Vtm3vU8qywGAKYo2\ndaZ/4tReXGZXgTxugd0CQtQZUubxTZ1BzhWECBQTxT99di+ssLsghWd5XQnmcYcQ7xCi8Qm8\nZilLENTG+hxCO3Yc6nCIeDNZAAAWJt7HsFIXAACANIT00EnRRY6oCriuFtfVCkuYfQi+CdsR\nDylpK4Xn1ONHzBHc1Gj/dJt32d09uLirAgrjHsFwSBxpmuvNV3CHTJV6rsB25lTbygdBPvMJ\nsXiWw8nr4aOmRvvBL3B1JXO69GEjtdF5Em7I+3FldLViN3/+/JMnT95///1VVVWTJ08uKyvb\ntGmTYRivv/46AKSkyNcdkAP8uCtwbb5OaBryebHHLeGmPACk+YNie51gQDjjUSMpxf3At1u/\n+4/uB7/T9g8/9s2YK+fVgVSWA2NWNS3GSFW5OUATkz3LV0JH3kOjY7x33GOkpvfaOrsO3Noi\n+PZomqVx7JsTOo3IgEXH+MfJuD1DnPAEH6Rx8aK7KaJyqtKI/DctejR8VnfleB+CxcRZMp4A\naOg+QSm0mvJBGO/pPoeeliG4XtnsNFT1w/bFbhx6PcRlJfZD+3t6eVcBIWPbSEm1SjTUVke8\n+nv12FekvFQpPOf4aItzq2Bish+So6sVu3vuuWfFihVvvvnmvffee8cdd6xZs+buu++OiYlp\nbGy89dZbMzI4a+R+AEAHnc7qFcvT2z1u54eblI7anpGS6l12FxW1//oYPh8/Q8rCtPCQruOG\nOtTaiimVMwcCAGiXzOBlRq03KmPwEOMH/0wbG30ed7h5FxlAI6MEGbSqMqfLvGHQhw733Lrc\n8flO1NwECBmDs7wLlsjp2mkkJJEiqz+BRViL2R3+6XNsez8zB/Whw41rsHrsORjRsQrHVdWz\nQ7QFqEg5jBGFSllVRQRbhd8QNkLlfJHIiRgZBj/d3OdQ2vd7Idduxu23ySVBo59cugDTZvXs\n+roPASeBAWq2DsA6Pv7AIuGpnD6hjMwV0iX7IS26oWP3zjvvPPXUU4Hi3B/+8Ie8vLwDBw7k\n5uY+8cQTPba8Gx7U7iAtzZaLFuVG25zb3ldMHVtSVeHYvMHz4Hdk85Nmrghms1mkDRCAwY1N\n4fIy5wfv4o7JeSNzsPv2eyQUzTdS0xjGFgchpihGmmiv0tSILl1Q3G1GShpNkzRVpaLJFRQQ\ntwu9ZOujxrSOGoPcbaDa5OSwB0BENCyzTEMAvqkzmaraDu1HrS3M7tByx/pnzpMtYwAAoJTw\nyiYAOFRmwkjL0EaMVs+cMgf9c+YH5WTlAa4os3y1GABilFSU6iaHYj0lVQkV94eAPbF8nxGq\n7ZhvMy0NaX7c2mIufQmdx8J5wfUtBJNeyNpDR7qGuZkeBkCKL/UndjcWuprYHT58OC8vLy8v\nL/A0MjLyJz/5SY+t6psDFh0FXDeWho6/4eYmXqmL1FaTyxel8+5kjCfmMwQ0NA1CPq/r/b8j\nkx0FKS5ybv/Qc8e9vbHI7oBUlPNXZ+H1Wj32Fdm1AzQtcM5ow0Z6b7tLQjKNelHQ8IJG69Y8\nAFJSRMpKAWNjUJa04vKospwPCuYPMPZPmuafNA35/RJmP0Egn1es+sbZt/iW3kHjEmynjqPW\nFhob758yQ5NSfhnxlgaiuD52opF/3CwUwIgioWg5AIBwfh8hZguxdTHSBvJEVV24J+xrsPgE\nKCq0BK3jX4zxLCAEV1D164ek6Gpi96Mf/Sg/P3/16tUPPvjgpEmTenRN3ySQSsHWHEKv4PwF\n/crxPgSpq0FeKxsdMSDlpWZxFlJ4nl+8cv4MamvlCy19C4v0TDsoxY0N5kSHVJQ5dmw1v0Q9\nV0D3f+6fNa+HF9h9iJjszNNmvToz5nj/XfXs6WDAP2ma76ZFPb26q4EwexYFkaErp07imkpw\nReg5I4xE6fS9AYDZHUxREC8izdHbmaL4Z83zz5onYbPSDCNlACDE3/4tBAxGiOfe+21f7FIK\nzyO/z0hJ88+aJ6eLtNDhg8YlWHQEfXPmK4XnzIO9NDrGP03GmSq+jwwB62Hza1SbkZLKS3TJ\nafvWjyugq4ndY4899oc//OHFF1/83e9+N3LkyIceemjNmjX91LqvAaXI3cqHSUuoIHuYGVgW\nLR2Ri+lhhvlDt+a4TXDUwBhuazUkS+xoGFaZhW2mnjrBeUKCLf+ohImdUEQQJaVYMgPbV1+a\ns7pAhKZlSOivSmPicK01/7Y4qwIAam1x/e013OF3Z9v/uW/uQhlnsTFmdgfSLecIsoyWt7+2\nqVE9cQQ1NbLoWC1vnLDP3ufArS18Vscw5l0lmNPpW7DUt0BGLz4zSFGhwBrEZ2USM1dE24Pf\ntX+xi5QUA0ZGZpZv5lwJ1ToBgJRbpWdAxPb2Lb7N+daroOvBY9eGjTT30/txQ6Crid2KFStW\nrFhRVVW1cePGDRs2PPXUU//6r/+6YMGCBx988K677nK5pONOSQGMmcuF3FZygxGaydHoGH3Y\nCLMpOAOgScnGIOmMXFhSMsOEn1Kk6SEpvni2AGMaJZ2MC01OYcgqU8wio6xDZO42fr6C/2Tl\ngGBrjhKsgzjK6ZP8y5TTJyVM7HAj76XBgFnb5Y7tH2Kzi7Fh2HZ/amRmyWa4jBvrRTsfiisr\naGiJUbl0wbF5fbC2p371pff2uyW8y/LELABAlKKaasZRUZXCc+qZ0+Bpo4nJ/olTxTIcfQ2e\nGA0AqK0VKLWYIrKoKGk1R81AhsGnqrzqnpGS6l77iH3/XlRdAc4IbdgIbayMk/L9uDK6Z9yZ\nkpLy2GOP7dy5s7y8/MUXXzQMY+3atSkpKceOHfv6N//fhGrl+jAksN7zLlqmZw8LPqWp6d47\nVsg2OQEAqLVZoD2BEA3dmuvZOXwXTMubIKEhknKpUGA+4fFYhn8tcrgdQfnGlgGsduwAAMA4\nJpBQe0xGLw3GcEMDF0UWU3OkaQpHLkSGrpwv6MnFXQ3CqEAjHFoQQprm2LrF3LFFhu7Y9h5f\nN+p7EHGBAKnWuH33p86NbyunTyiXCm2H9ke88v94WWkZYAhl2KOieKtrpOv2L/e63vlLxJt/\ntn+2XcYzCAAAaGycQHFZ1AencQmeW+5wr33UvfIBbfxk6dy9+9EFdGMqNuRtiuJ0OqOiolRV\nbW1tbWqSjg0mA5C7jTdURoyR6gojM6SRxJxOz12rcEMdrq9jUTFGUrKclBpSVSmIMkaqq/Ss\nzh4rI4p3+QrHR++R0mIAAIS0MePk5G8hUdcYGbrF1labMMV2/Ijlqu2fObfH13cV4EpZAMCL\n1NCEJMzxIKmEpDSEmMPJ+xNYNwm6JqB4MwDRmELfgsbFixlpof98XFHKHzXyeEhZiWwzVcaA\nNM6GFJjDYYQqs5CKMtvBfeYI0vz2rZvdax/phUV2CxZNwQCMBO7sMAzn314jHcM9tvJStSC/\nbe0jErrYCa0gmUPQasMN9bZ9u0hFGVNVI2uof9osJpJd7IfM6F5iV1ZWtnnz5k2bNu3evVvX\n9UGDBv3gBz9YsWLF5MmTe2h9NzQsgkDBsFgNnzHU0owbG5im0ahoCYtbABBOFINxW3MaG+9e\n9RBubkKtLVaraZkg7Bozu53ZQ8bfWESk5577nDs+RJUVEKAKzV6gDRvZS6vsDmhsfHs+bQJO\nt8q5+WfNI8VFZmkx5nD45dPfAgDqdPGKJ8agkNFy5nCyyCjr3QuBIaFAsWEIEjtk1VLmpyuu\nHO9DkNLLgv5/QKDOBIUTIwQAUlMl4UyVUnqZD+IW60bIduQgCR3ZRm2tjl07PLfc2YOLuyoI\np8RQvTWIG+pdf/kj+P2BugKpqSZFhZ77vy1h+6gfV0BXE7tXX331pZdeOnjwIGMsIyPjH/7h\nH1asWDFt2rQeXdyNDhoZxRSVN+PjRz7oQgsAACAASURBVK6Q1+vc+DdS1t5EYw6n95Y7zM1Z\nSUBTUhlCVqEmRaUi/WHk85Kii6i5EdfV6sNHyrntY1yvHALOsFwDwhiQRh95nDY1+ltbaEyc\ntB0K3NzMB5ndepjGgDTP8pWOXdtxbQ0gRFPTvAuWUvm87JDmt3htBRBCpwMAhHw3LXK8/645\nRtPS9RGje3R5VwFSXsoXUIExUllmLsUZyQMAY/6VEqrSYK4vAQBI05DHzSKjghEmUhECEDC9\n+hxCew9+oy40uxMG+x6cjCWAwMrcvvNjixYPqa5Sjxz0T57eo6vrx/VFVxO7v/zlLyUlJYF8\nbsaMGUjKRqFsQLomuIKLuFn2T7aSsmKzN7Pjw81tax+RzTQWFxcJ5DepDppu4dngshLXpneC\nvUv2+U7PXask9J8gJUV8EIWhFqCKMnzqhK21xUhM1seMl1PUF3O7cAAAjmMHAEZWdlvWY8jr\nAUzkFX7j+I4B8JMr2ojREHB5qq9jdrueM9I3d4GEQoPhWRYhcRYZ5Zs22/7FbnPQP3Wm0Buq\nbyHuPGIMoW0Hoeg3i4mVcH6CxsQRKLIEDSk9P7oIFhWNPG7Ld4yfzyMVguFZUl4C0J/Y3Ujo\namL30ksvDR06FMtapZATuLoKUYOXycAVZWYBIaT51bOnLS9CPq96rsA/Sa6aKM/KAgCgDLU2\nm4f8kaG7PtxkZqQhd5vj/XfdD39fupJ+SGOr46Oigm6X7dB+vGsHABAAFYAd2t+2eq1smTcA\nMNUmSByEqi6UqqdOkMuXgBo0faA2biILw4LvQ7CISKHqm3CcRRsxWhsxGhm6hAcShBHwWgjd\nIDFM+G2Pf8YcFhWlHjmIGxpYXJx/3CQtb0IvrrSroKLMjMYnWD4FIytbGz7KIrLjuflWGfnE\nPpEYZFSUJWJkDuZHdvjZuL6HYaD6en4oFnm4w0SCWzwTBfshM7p6+Rs2TLq2oPxggTyYl8lQ\nQv/t4WoS8g1Y0UjrpQ0AAGMWGselJfzUCG5qxOWlsmldstg407P2j4qfISDVVfZdO8zOkai5\nybn9A/c9a3pjld0Bc0UA17vEoWYnAACUut59q9OD9exp9eRR95p1wt50X4IxxJ9CgKio/IPa\nWm0H9pHKcrDZ9CE5/rETJazYkaAPqQkIRBLECGl5E+RM5sxQii/xQX7yAwC8ty6naRnKmVOo\nrZUmpfimzRJ+jn0ObkqMASAcOogNAP4JU5Qzp8w0OxYR6Z23sOcX2D0gn5dnBIFIA9/IGqqc\nstq+Gf1+YleFDRs2nD7dvo1BCGVkZNx8880DBw7shT8t7772GwCWPAAw4b2x9dDkhkVE8gas\nIKeaRoRgBoJFRlnkfHEYRQahxEbfArUJhsX4+pZSGPB8C7n1kqKLyOezjFn0OYStWNZqHf61\nHTtMQsnsuKba9vlnvvmLe3Bx3QeuqQLBPYnhijKLQzFqbor8y5+gYztELhUqhefc96yRrSDE\nq8ICAFCKmxoMh5U/R4qLbAf2kYY6FhHpH52n5U2QkdzpE0yDIVEQCAnYvvX4kq4RihLaaEGB\noPVlhHhWr7V99SW5fBHpmp6e6Z86S8K5N2Z3MKKYJ6Xa41zDwXvToojSy+ZtuZ49TBsto5Gd\n/Fi/fv2ePXsmTJgAAB6PZ//+/YSQjRs3LlnS4zZ6/YldDwKXl1qzOgBgFOl6yIadEP+0WfY9\nO80xmpikj5BOKpZcLuKDvG6nkSgmo0iopoFrBeQz1MyRwYUDzoyBroFUiZ1hCNorANBqnagg\nIktZ5eIF2RI7RsP4VHJFL8fOjyG0yE2KLqonj2l543tobVcHGmZCnI+r5wocWzYEHqOmRkd5\nKamq9C6+rWfX130IR8sNiw8pAAAgw1AP7VdPHMGtLTQuwT9pmpY7VrbMGwBYRCRvAmukijiC\niuKbNgsmT0eaJqfnBAAAxqAQsCR2COkZ1mF55nS2rX3UduQgLi9limIMydFG50n4AfUEDrd5\nXq2tK/H5sxz27yQljHZeh09zxowZmzZtCjxuampavnz5P//zP/cndjc2MJ8fAAAAamqA0Euh\nf8pMZBjqgX0BLpExKMu76DamSMfNFwu4GAaiBjMldjQ+Ucsdp+aHyFZreROEvKg+hmgAgm9H\nUpF3JIuKkk6wihCh2QnieN+8cTsAWC/9MiA5hRGMDG44NMPa0QgzonhJtsROrLATEWktnxiG\nffsHlpepJ474x4yTrX0p1kyOEJwa9h1b1ZNHAyk5rq12bHsPedr8U2b27Pq6D5EmtvjswE2N\n9p0fK5cugGHQmFj/nAWafIPYuLZGUEBljFRXUm7ImtlsvqkzA3RqGh3zfySr+2tt/fcvtw+O\nfNbS+mZdw5+zBi6LvZ4U6piYmLvuuuuHP/yhYRikhyki/YldD4JFiqe9BHGEfDPm+qbOwg11\nNCISZFV9M+Lj+TyIxsbyOajv5qXMFaEePYQ0P7PZtPFT/DPm9M4iuwUmmirgBdm1YSPVjEyL\nPpxv/hLprnqMiRzFANKtaZCelk44apRwbrFvgWqq+KwOQMjyZsBPKskHclnESPN6wDDMjEDc\nUC8svirlpX7JPiZSU80Hef4Wqa5UTx6F0E/IvneXljdBeBr2GRhDpgp38CuFOCEhpPmdG97E\nHZRW3NToeP9dhok+bEQvLbVr4Juw7RBpIiqF5xyffBT4+Fh0jHfhUgmFt64vajT9RyUhtng+\nSr9fVLogL8p1XZkPX331VVJSUk9nddCf2PUohGQLZnPQeAF5DrnbbAe/IFUVzGbXh+RoY8ZJ\nSKbBLSJGmkigjimqb+4C35z5yONmTpd0CVAHcH1Hw8WcEvAVCIw9y1dGHNiHTp0Ar8dISPLP\nmKPnyHX5BgDU3CSeuakohdBsVZsyUy3INyuQMYfTN1c63jcIGWkAuKGOhgy+gJExSCk8Z3mZ\nMXBwD63rqiGubxkG0vyMmK4YJMzpj6UbB2GiJfHz71joW2MYuLbG4HqCfQmEmNMVHP4IXhV4\nRpp64ijmBpXsu3fIltjRxCSGMeLtZ7hBbFJZ7tjy92AiiJqbHFv+7lnzLQnVE68j9re2eSyU\nDwaNhvFVm3tO1DVJZ585c+bZZ58FAI/H8/HHHx87duz555+/ll/YRfQndj0I0dacIb+XV1pH\nzU0Rf/ljcIOuXDirXDzvuXOFbPkQrhVuzQWKuABAii/ZDn6BG+pZZJSWO05OMk1n19LMlBbl\nRszhpEtvp4tv83o8Eh5IAF0XmGR2u/v+h+37dpOii4hRPW2gf9Y8CdVbwCWuXvNNcN+CJaSs\n2OzEagwcpI0Z14NruyqwWAEhgbkiLAreNDaexsTy2r86pz3W52Ciz4iXYRfSHq4U70OINtXG\nAGtyg2sFg0q4sUE2wR3U2MBndQDAkwLVA/ss5T1k6LYv93ruuLcH19fX0HlxVgQAcO3C2fX1\n9V9++WXg8ejRo5966ql77rnnmn/r10OiL983DyIaEwrELd8jxycfWdouyoWz6pl8beSYnlxg\nt8FsgkEBoaWEeuZUpw1AYwMpLcbVlb4FPU4a7S6oK4Jws7rCeWRkGHjPTnz0UGRLM41L8E+e\nrstHK6ZR0aCq/KgHGpzNv5i5Irw33wKGgfx+CUf5AmDR0cAZkTLVxucNNCa2be1j9i8/xxVl\nYLPrQ7K1idMkLHuLtw0urqqNkPfW5c71fzVr+Plmz6cJgqGEvgVqqOeb4JibetEzBzO7HXw+\n8+toTKxstm/I3SZ0ViV1tZbOpXAinimqsITZhyAifXIAwLU1NHSbwRcgGQAKUzX/xmBSpIAP\n6sB43DVfFc3DE72J/sSuB2GIWq5gd/B6nkLaDSm6KFtiJ5wANbg7DTIM+46tlku97chBfcx4\nI1myi7iIfcJEQx6Ojz9AHQpPpLba+dEWn8/rnzi1Z9fXTeCmBvEAr2i/jhvr7Z9sUy5fBErl\n5X1fumi1lwdAmh+1tvKCsSwqyjt/MW5qAISktX0Tlb0ZEpEcjPSB7nXfUw8fIPW1NCJSG50n\no/gtAG5tEYjfuq0KO8wV4Vt0m33r5g4PMcbsDs+ty6X7mMJYnDFO4kAfMdp2aL81OHK0dPu9\nMHaOAmojVwhHIJ6D+SYh06b+S2rKLyuqzMF/z0iNU+RK0LuO/sSuB0EaBaNVTFWspz1jvHYD\nAKAwOg99CHHrQbde73BdLfJ6eBY7LiuWKrFDmiayuWT8DpVUlPG6nbY9n2pjxktlxoVEXzkA\nYPV1EDoYi3xe5/o3goffzvtWVdmI0uJBbACk+fnzQz1zyr7zY9TWChLzvkXT7ihcO5LGxPon\nTiW11czpoimC0WwZQCMiCCdHLLQ+00aMNlIGKPnHSUsLjU/wjxlnIaXIABYZBTYb8MKiHCPN\nGJDmu2mRfc+nwVzQGJDmu0kuwSAIDGJzZidAFN7sRBsznq8yaGPkmivvCTyZlpLjtP+5pr7I\n5xvqsD+alHhLrHROd11Hf2LXgxAqkaK2NovqGyBEB2Za1GIBQB8oE6EYAMLxvr3W1hILt2GV\nbWuOkcDcCRC/TlxVwb8b6TqqrWFpEhngMqE1CACK4Xjfxw/zSa199yeyZUJM1HlkqsrnDaSs\npLP7H+B9v/d3z33S8b6FamdC1Teg1LFjq3riSPsbY2L/P3vvFSTHdWWL7n3SlGmLhvfeG8IR\nhiQAwhAgKBIk5cdJlEa64pu5EfNiFPFeTPBn9DF/8zUvnu6dpzujO5IoiZToQU+QAAiCMIT3\nAGEbaADtbVVlZeY576Ma1VWZ+2RVFyork4xaHxL7sKu5s6ry5D57r71WcvuOMI6DUCUusuwN\nALy+kU+cAt1dvL6enLsKHNjf587qAEC4BYoB0ivXWNNnqZcvgpHiY8dbs+eFrVwHGSUgd+3A\ntthAP8+n1ZrzF7HWO/qh/dmV9KqHzfmLKhBksECAb49o/PaI0Bkxl4ZqYucjODkVG4m484bU\n5sfjv/lfaA7tJvbkqSHU+xbxWredvHAx0vjIUaK+waF3IBQlbI0koagiGsdkXrEBAdwzejJN\nQdTDxfsWeoQ4mjPGJk9z2AOQtBvW2eE8dQQNsgYpFNXtFaYf+NT5WsvSDu23n/qWX8GVBPKd\nR0HkRvr+vdmsDgCwpzv+xp/7f/gzdw86SHDu9toCAOwhfKVZd1fstT+y9rYMd4s3NKae+S4x\nZhEoWA9d9mZdXfQOpqqAiLaNaQO5HaqxiQwwTbmASNxBjA1bzMVLM9JO9qQpnDxyVFEEvvvd\n73KKA1MBhO4r+LUC1aHn1EwcbxqV+NHz+v49yt3boEfMGbPNB8PI+2aUJ5iodTVTGEtu3xH7\n8+9zj/LpRzaGTaAYEwPoKjcCEBZJ9rQZQtNzM28A4COabJfwb7BQbl4njuac89a7Dk1sknYj\ndOLUESywk0pAU0m0LEcFhVEpIJlzBIyks2spACDpqoULoR895HptQjtzIr3mEb9iKw3us0Rm\n0QEhom+9co/OgZAhALzx58SPnieLYUFBpjouKKqZevZU9P230LIylGK+f2/iez8gNagDBG+i\nBrEVhY8Y4V4HIZT2NuX2LTAttGyzoTGEqepXAt/5TmCjxNUPzEew1rvuRdnhiTc0Go9uZW13\ngCl8zLiQ3kvkY9KlRAoA9pTpiR89rx85xDrbRW19etED9pRpfkc3XLCBAZLdyAZcvO/autRj\nT8Q+2JmV9BTRaOrJb4at7YK5o4i5wysu3rc5d4F+5KBjmNEKX8+Fkq4VQtXdMmkiXuMWvSMf\nxsFC1NRCvqIvUo1LTBsk84H10epCgYExEY27RyXscS6NtLZW5U6L89XdnUrzdWs6MbUdFEQk\nSqSqiNxldoI93dEPdg6OLSMAAOvpjr37RuL7P6xMqEXCWT0VAAioakQjQojozle182cGfzx3\nSjt2OPHXPyalD6oILUKZPXxdgK6pApBZOQHoRw7qn36coYqLWCy1cZu1cIm/8ZUATSMc2SkN\nFADgI0aa8xextrsQi9ujQ+cSCwC8ro4sNpD0IGvhEj59pjj+heju4k2j0kuWhc5PDCBPCyOb\nsDGFTZgE+Xo6fOJkY8OWyL5PhnjfEyYZjz5WmTiHAc29R6FoHOFOqdMPLI/lW4MAgPnACt8i\nKxEsSRzt3N8loUdENJory5cBD5nWIKaS6KpBAgC4m8uu5G8QrnNUsFBv3iDOe0JgextMmpr3\nm1cuuYd7lObrbqXSYKE4DuSZW8dIoZFyZGzqudNDWR0AALDO9siej1JbQ+dQXIUHqomdj+Cx\nmLsXa1OtWPXLC5GP38/+iMlk9P2dicYR3OUEFSyErrtVuNwGXJAx23n9T8q1y5kfI9FY6vGn\nQmfVIEmyuSwNra2F+gZuGFzXKUur4EEWiQEF6bOVXvWQNXOOeuUSpA0+drw1c07YCpAAgKRd\nAcVttxYsSbe1ZnnfQlHMNeusWXN9Da8EYA/FSHMLpyGml6+O7N+TuyZiMTNk5z1MSMrerity\nk3EzCBtDg9QGItcZxVEDADRSoUrsOKm3pyjuip3buwUA1C8vwlZfAqvCJ1QTOx+hUCdRpNQx\n3GJIaFv60UOpMCV2aJqM6rqSgquRjz/IZnUAgKlk9J3XE889T4ogBAXl7h36mdTWarseQqzl\nFnvtD5BIKAIAQXy2J/nMd+3JU90vDxDYR3xAYHPR1wdUcx8TA6y7CxIDAIATJ4vwmRSjSQgN\nyrwvjQ1bzCXLlVvNApFPmhKqL9sQKD4ZKf2dXruOJQa0419kfuQNjaknnpYNPgcFUVsPDMEl\nR2w3OPlbvKHRWrhEPXMyd9GaNpOHzPqWj6KIs4zxMc7xapv6TaHrwnXtAUOlJJkaGt0TSHRD\nSXIAriK0qCZ2PgJJNgyZ7VG/qYSNTGOZmTQoj5YlANysQdt2q75hOq2eOx0q3rebpzW47n70\n2nZs5yuQ8R9DAABMJWNvvzrwt/9dhMkQia4TMIZ1dZBwDr5EPt+r79s9+MPFs/rRQ4m/eI6P\nClfTnLTEICeQAAAtUzt3Wrl+BSzLvtOSXrsuhO1yoWruuign9R0ZSz32hLHmEaWtVcRifMw4\n2Tc2SNiWS0AaAEBQX6TUY09EFFU7dSyzk5jzFhpbnghbnZjUNgIQ7jitmXPsydOU5mu5i+l1\nm8L2MbE2quxNlRv5uAlw6bxj0aZ6MlWEGdXEzkeISITYwakDt6irB5eomO0yqAgWIhoDTQcz\nnXdRCLZrB8e0QZ780KViGizEiCaXWxUIhvYEZ6FUudPiVn3Dvj7l5o1Q8b7ps3VNLWg6QF5i\np7TeHcrqAAAQU6noO28kfvBTXwMcLtgAYckgSJUZ24794b+y9HzlTot2/szAcz8LVVMMbZv1\nujWxAUiFSACl9Y6+d5dyuwU0zZo2w1i3KVSXAwBMUvbG9lZwZatC01PbnjQ2blXu3rZHjiZN\nZgMHI82vucCBfqeHGGLi6W9H9+5Sz51BMy3q6o01j4SQ1pnrSjcE10AVAKRXrFbPnGQ5o+hC\n1YyN1UbsVwzVxM5PkLqdpCD7itWKm/e9fJUvUZUKTCWJyQkAcM0tikhUxGIO91sIH5mG3bzu\nLjYgF5gYcKjIkoJPIFNsDg5KG8Wxo1hQytVLxMvv3g4b7xt6icTO/dUCAP3oIcfQJSYGIp98\nkHrym37FVgIsk6RwkcPyrK019uKvMXPTpZLaqePKzRuJH/43oYXI7CTfMyOnmk8qmAihHzmo\nH/gUk0lQFHPuAmPj1rBVVblbvwkAGKPvi1g8te0pXLOOdXbwMWPDde/cAznTyhsoDRRNS/zF\nDyP7ditXv0QzbU+ckn5kI92briLEqCZ2vkEIUluVZKSZc+bj+s36/j2Zo5WIRI2NW+0wEewg\noxNGMtLcep6MpVc/Etn9Ye4ab2i0FoSM9y1J18A1iuj2wx1cD1njEkj3cUqaTjadjbYdLis7\nkvdNPT6V5uvuRZVaDBAiEhW6jm67KmpeJ7rnQ8w/SrGuTv2LA8ba9T6GOEyIhhEwVPcezOoE\nMouin+pHDkY++WDwB9vWzp5i3V2Jv3guVOqJtH90JOos12V+ub8v+t5b6tUvMz+acxcYW79B\nafQECZYgTkfUvDlAxtJ3/WZl5mxIJsXY8eEUNBgu6kKl6e0/qomdr7i3zeWS0iSEkvTqh83F\nS5U7twUAnzCJ9B0KFnLdTuIpm165Bs20dvCzTKpqT5iU2vYUuTMGCFHvrp4KYEw0OScnRENj\nevmD+tHDuYvm4qWhO8tShD8xosn9rXPbRAKAqK3jISMAAPWUHUaQ4aJvASaTdF9MJ+535Q5B\n9mK3nVJwwUK5ed3JZgBAwZX+Pjt/FgdtO7/7DwCgtNzUvrxgzpnva5DDAstXGcwAU0mwbee0\ngRCxt17JbbZoF86iEMmnA1OmJYH9lKAMpTYPAOrli9F338wWIMw5840nnw2prmoVElQ/Ld+A\nCNEIDFiQ/3DhoymWNABrb4vs/kC5cQ2F4OMmpB59LGwVO6GqbkYaIJ0iAKLx0Ib0g2vV61ft\nmlo+bkLYKNIAgENsp2zujcAUQU0upx/dqtU34MH9kEyIaCy9dIUZpsJJBugiAgIAUOoN1vRZ\n1qy56pcXchdTj4WOyQ6dlDgI1QG3p053izWEzcWO9fXSrVhq3lyoqvvDCNWwDgA1OzW47qxK\nYm+Pw7slA9beBmFK7OjRB0T3raG03HRTaNSL51hXB5douwQCcuZa1BKnI9bbE337tdxWhnbx\nnNhTb2za5mN8VZQb1cTOL6BhYIKyqyKnCgb64y/9JjtbwFpuxl7+bfKv/9aWZIGBQGm5SYy/\nCWCd7aSuhHb8i8inH2cUVvmo0altT9kh0zXImYfI2bItC5MJdxlSKArfsEXMWWA1X+ONTfb4\niW6xgMCB1CkcLeJpCgCpp76lH/5cPX8GB/r4qLHGmkfsaTN8DnD4IPvIVMc5vXSlduEsu9V8\nb0GI2vpUyCSXucQJg5ypsmbOyWqdZGHPmlP+sO4DvN4t7SEAmdtjVNaF4CHrTpD+Zryh0f1V\nJMk2AMC6u0OV2CHJjaa+itrZU26CinbiqPHoY6Fql1fhjWpi5xuMFMlII8ff9IOfOSZG0bL0\nPbuS3/5Ln6IrBbJaDrWuXTwX/fCd7I+svS32yh8GfvjfRJh080kpDWAMqCcNGin2+kt46ULm\nnuEjmlJPfjNsQgDk0Rwkcm5CVdNLV/LaOtbXw0c08UlT/A2uNOi6uyZEW/QqSuJ7P9COHFQz\ncicTJhmrHoKwKfMJQZW9kZQ7MdZvVm7eYO1DnUFz/mJz/mKfQxweCIotICCCa3JZxOL29JnK\n1ct5i5oeNhFppYtK11xCfSBTFwIIm9YgXcgnGcbUEDpaJhoGvVtWEUpUEzu/IGpqhaK4Keru\ngywAKBSrQ2mnJhyDA2/MZUnfA6LbFBIAtHzFfADAVFI/dtjYsMW/CIcLcoBA1NSQhJLIh+/i\npaHGJevqjL3xp4HnfhYqF0VaUEZSEVGar8feeDk7YcrrP05++6+4ZEwkGKQNJHUfJQLFQlHs\nMeNYbw8ahojXoKqGaxAEQLl7myp7C9bZ6VYQFJHIwA9+qp06pty+BYpqzZgVthwIAGj1Fs6h\nv999okhu2xF/+bdZNQ2hacb2HaE67AGA2yUMJF85e/JUPmpMbuYNAPbEyaRwcZCgKtyEUezg\nKIxrMRYLIee7Cg98lRI7xZ/OF2Ms87/l/fs40E9rudXWEv8h6rYRkah3SIhY9rA9oN657WZJ\ngxCKZQrFWdVn1KlX6e5SFMWnN7wEMJdnPABAKkUElkho50871rC3R7t8yV681J/oSgEjE7tk\nElxvOBpGdOerubohrLcntvPV1I+eDw/NDi1LkBpplkl+ebRd72n3TFzUs6AfPZT6wU8rXz5B\nRABQFAVd7ySTKJUwXSevCC1T6etTujpBCIjFYOoMvx+xZNgeQIk4iFJfT5DVGhtTf/t36sVz\n2N4qamrt2fNEXf397wLZN/y+/xIASCaQ6huIv68o6We+q7/+cja3s8dPTD/9HYWUepGgEtsg\nUxwjfAAAo0a7/9P2kmXii8+xL1u3EwBorVlHXpFPkQ/r61cFia9SYufTxHLma6Trujqcu7Eg\nREcr6TgYT6fRdSFi6XJ+8ZxjUVmy3PuSMxlSecP2gABBXlGtqoArTru2FlwEFLVxhF5Xlwk7\nGo3q1IxCJSEiEfcVoaoSb3ui36YyjJhJfJoBwiYVGeobACAej+cmSaL5Gne5ebLWO3WJfghN\nf1lhLK1qbvVEfdLkqPsmunKJ51vzYW9PfNd77K9/7G+ULmQeeDUUh0mMG88dVW8BoGB87jyi\na2wY9q/+H+gYrG+xlpvaxXPK3/+jWzmyXFAUhQzbA1xQxhOxeK1EtFJcuSSOHRa3b2E0Bt1d\nuGU7DvO/6EZmSynXA8KmepRKvIb++3V18A//l7j6pbh1EydOUmbM1oeTlzDGfFfiMNP2QJ8j\nqxMAOkP3TQR1dfCDn9qv/BEykpCqho88Gt28LZp/UZmagk+Rc5lXbxVF46uU2HV3UzX/+4am\naQ0NDalUKkHOOpQKxgW5XQ0gWu4LmTozumSZdvJYdsGeNiOxdCV4XnI0GmWMlTdsD6hMIZ4n\njPUomnDFGVm8TP/0Y8fiwJz5dnd3NBqtra1NJBIpl1xchRFNm+6zOa+p63NdDgqoZcw9z5jQ\nI6Y/X8vSUGMYboZzhrDf399v5vSYtI4OsvLT19pqR8PCS6vjtrBM93MyYdnumyhy4pj7oCAu\nnO3u7Kww77uuri4SifT29rofUdqFs1HXXDlw0Xvrlls6J7LnI72jPW+psyP5zpv+jSg2NjaS\nYXsgdrtFdVeDkonuri5ijPTGtfhLv8n8szBNOPSZdf1q8q9+fJ8eXI2NjaqqlusBUdPb4/66\nWAP9Cervo23pez/Wjx0G2xaI5vxFxqbHi6ejNTU1+fRcG4owlap1HUoRwBgYMMj/dLwW/vJH\n2pVL2NVhT5luj5sAPc6R7ZEjQmoF9wAAIABJREFUR3LOfYo8EokEfub/quOrlNh9xUCyexD4\n2HHkr6e2PWUuWKxcu4K2bU+cbM2aG56OWAZsyLs2Zx9njBwiM1Y9xDra1bODht9C1YxNW2lh\nlODA+iiNCeptF9GYuXiZduJI7iJvGhkuzpMQzFWEA4kOM82lQwwXx663h7oHBJKXSfsmceRc\nhGegj+JvgYTCRUouk4sBQqiqWy1QaCq5fUV2vZe/gMrd2+qpY+bSlb4FOHyQrVjJnERk90fa\n0UODW6IQ2tmTLDGQ+PZfhWf3FtEoaJr7iycotjcAKG2t0Z2vZpvL1ux5qe1Ph02CtApvVBM7\nv0A7SQvAjg6oI8jCONCvnzquXL6EZtpuvg6aZk0LkwlpXmKXLw5iGATvh7HkN55RVqxRrl4C\nTTPnLBD1IVO+lagAyCwZjE1bVcHxXlXVHjch9cQz4RIVQxSMoavcQjpQ2eMnWjPnOITf0stX\nhcsTiZ7nRdKXzx433v1h2KPGkAePoCAoaWXBGJlP07lBaDKGQdhUeY/SSAPbVjra3MvK3dt0\nthsU0kQngZRnx4F+7VhGtDz7oaBy7Ypy87o9eZpf4Q0T2Nebk9UNnck5NSKGZjr6+kssh0Wj\nXjof1fTkN57xPdAqyocQbXlfN8geJ1SRGS0r/vLvsock5U5L7E8vJr77N/bUEMmriiilcqnp\nssOcdvFcZNd7meKKfuRgast2a2a4JLgEUsNiElcDoWr82e+JJSv4l+d5fYM1d2EYJ8UUFVyF\nK0GKgyCmnngmsvcj7fQJsG2haekVq82HNlQiyOLh9t/LVEYo/pa5YIl+8ihruZW7aGzZ7l90\nJYA5WquDEIBETdGaPF3PvxwAsKdMK39Y94GhsnduP5Zs5jImGHMenAR98AgQjPRpIM18ZS6L\nnR3hSezyB6qGTgUsSQxaqZcvMTc3+twp3PhY2Cx9q/BAaDoUXzvQ6Q5DPoZoxWonjzpm5gEg\n8vH7fgRWOpKU7lEsSpYQ2K3myM7Xsi0z7O2JvvlnhaxiBod8Od/BDZq0nQAAsG185Y/q7/6X\nfmBf9IO3a/7j/1WvXPI9xOEAB/pJSwZyEQBENGpseCy1cVt66Qpj/WZzxer7pDqVH60uxR8E\nAMAuwo4CFCXxrb9Mr1jN6xtEJGJPnpb4i+dsyrE0QJBW0cgFKW+ZXrvOUcnjTSPTYUu+szlc\nzjZAq8wgEtQFhHDxGQCA0gEBStVI6gkbJvVELlGT4dTpCIfaMjmQcDyqCC2qFTu/QCcxXMAA\nIe/EWu8Qf6GjjXAnDA4kI81tHJRB5OBnDtoQWpZ28DN7x7f9iK005D9lB59LtEo7QOSz3ez0\n8aHfTgxEd76aeO552b4ZAGScd1IoG0BpvRP78++zQnHis93JHd8JVZFY9oAUsvVozJoxC40U\nDvTzkaND53srM3fSNDJFEJqW+Juf6Ic/V5qvgwBr8lTzwbXSg0dAIL9bMokZY8t25U5LjuML\npFc/HK4apBBCCPdRlTTX4SNH8QmTWMvNvD9QV2dNDZGDC6Pc6kDCGqQ1BRE5RR+qIrSoVux8\nQ660RM4ySZARmkYoxClquFxcKE4GbXUAwLqJmgojCy0BgmLI8RrqmSSE29wJDUM7fcKPuEqD\niNeQXxgxnpIv4Tz61qu58r+YSsV2vior74UIyGyXlm8Gkc/3xv/0onb6hHr1sv7FgZr//B/K\nbWcrM1iwzFnCcbPruvROt2xIpbC/j/V0sfZW7KcKKoGCJYjGpYzXKOI1iR//XWrz49b8xeby\nVYnv/9BYv9nnAIcHTCaQ6rqSiwCQfPKbuZrzoqY2+dS3QzVqQNtO5HGmh2DNmO02Q7MWLqna\nTny1EKa84euFXOLIUDKnamSBx5oz353x2XPnh4sobVKcYlnthCJkiPsWrCozMnorjqcs6Sdm\nmuRsKTmeGRSU9lbaYJ4aF1Xa7mYNAIZ+MzGg3LjmR2wlgp5A4qTbAWtr1fftzl1By4y+87qs\nYBkIBjNpx21NmjsBoG3F/vhf+pGDrLMDe3u0i+fiv/mV+1MLFhKfBnoCCQCU5mv6scPquVPa\nscORvbvCRs+QZtiSzglvaBx47mepbU+ai5em128a+NH/YU+c7GN4wwdpQwwANrUuNC359Hfs\nHIM7c+6C1OZwEVWrKIhqYucX3BRUABCc3u/sydOMNY/krvBRo1Mb/VKrKg3YT7kaSJ6a6SXL\n3IvWkuXlDel+gJaJacOlwCVIlrTQNPLMyhtpG9ZgIGmLCzJvkFTmyPw1MFBFYgCaBaXeuOpe\nZJ0dslZUICBYjAIgRh94tCOHlHzqLZpm2Ki3pJSMLJlgLTejr7086PgihNJyM/6nF2leV1DQ\n6OopH02Y+QIA2nb0g7ej7+/UTh3X934c/8OvlYy0b2jAZBRbiYI0Hz0m+f3n0us3WQuXGJsf\nN554Omzd/yoKosqx8wv0QVYI5JykqKfXbbJmzNbPnWaJAWvK1PTi5eFh12VAVw8leh/WgiXp\n1rt61glAUYxVD5tz5vsV3PAhVE2oqquahYJsxSKmVz0c2fNR3l+I15iLQuQnxhsbATOpdr5M\nPNWK5SNHA6I7L+ej6S5nQKC+c5pGEp5AViWSV48qD8wWiYf0MSSDVgBkH1lxzckGi1xXuixk\nDI3ovk+cin3JhH7oMyM0NSHWdpfmqqaIywQAfe8uLYd6yzraY6+/PPDDn4Wnd0kbJwKw3h6b\n6rcod2/HXnspk22rZ07qhz9PfvP7tiSvrSKcqCZ2voFUVo3VyAYPWWd7dPeHSstNAFC+vICd\nncaGLeHK7SjBKo/9y3j0MWvGHO38SbCFNXeBNWOWn8ENG2imgSqgyoTc0g+u1SyTHdiXSRT4\nqNHJbTtCJQGgtN4FARIapxOipja9co2e78Flzltojx3vS3CloYtqO1om2rabxUW2wERNLW8k\nfM2DAma0JxwfkST1pPeKUO0JnKNJ1ImZZAKJVHtR2sPVXKZBdSbQtrRjLuptX6964Ux4JJe5\nRE2GnNdB246++UpuDTUjaDDw3PPh+uJV4YlqYucbKKcvodL3Bppm7LWXho5Wtq0fOQiqZqzf\n5F+AwwUm+t1O0oJJ73b96CF990eZA7p2+ri5ZFlq65PhYQ1iby9yymBeNj2AKDZts+sbxZcX\nhK5b8xbyCeEy0gCqdgIAQmI6Z6zbBJGofuQgJBMiEjGXLE8//KiP4ZUNSOau9sTJ5qIHHOMs\nqa3fCNcEEhmMRBDRmj5LO3fauRiqAxJjQtPQxQHgpEAxgIjG3LRUHiY9SFFbJxDQtTFw0kB5\nYIC0DGG9IWou044sikKyvVlLs3vujXV2KLdv2ZOm+BFeFX6gmtj5BUaOVkmO5sqFs66CudC+\nOJB+aJ0gRZWCALp6fABSHXzl5nWHfZB28hgfOTq9co1P4Q0Xslojj9PjIGia7MX/xHvSBtqZ\nk+bipanHd/gV3/BBlw8RQdZdVRRr1hzsaGNtrVBXx0Nm0gAAQD01RSwuJNy71Lan7LHj9XOn\nsL/PHjkmveZhe1K4dOzIbUGW2VgLFltfnlcvnh/6zYZG49GtfgU3fKCRIuWBZNrd1vxFbgtp\na+GS8kdWKtjtW9msLm+/I1ux8RqhKO5dndfRFMNAQAoUgG1jKuXeA5nkcEjqL1YRWoRsH/86\ngZoqEJKkgRET6Yi2hX19Mopr5SGQSOJELd241E8ddy9qJ4+GJ7GjD7ISwSoA0D/9GPMFq7RT\nx+1pM815C8sfXElgPcS8DgiBEu6zcuNa/M8vDvYB21uVq5eVlpuprd/wM8ZhgvQAkE+5ouCY\nTGJ3NyYGFCGUllv2hMnhqtglqAkkWfccMbnjO+rZU/qlc8Iw+OQp6QcfDpWLHSYTQJW9ZXO+\nxqqH2J0W9dJQqppe9VCoBIpzHfkwb52ibaiq9cAK7eihvMWaWmveIr/iKwHkaY0h6MQXyXZp\nnWQQLgvpKgqhmtj5BXK6UMYppnVAGJMlgpUHmmmSJQ2yVuwA8QBD+qkWDCTmToBU5ACgfXnB\nvahcPBeixE5yqhYDA+A+HggRfe9NB7tLO3HEXLgkRHoNZPIt7+ZHPnpXu2fmi319kT0fYTJp\nbAiTUhp1v3jInimtd/TD+5W2VgCAW81g2sb6TeHhM4jaOnIEhzTzBQBgLPnMd7XTJ9QvzwOg\nNX+hOTcst08GXGImYY+lWrEAxoYtkExkO+a8cUTyiWfCMzkBAGywUZ5XfxSRGFn25qPHmPMW\naufP5C5aC5fkavVVEX5UEzvfQLZiBe0NYM2ZL/btdpS7zXkLBeVjEwyoY7mHPpgY0QQu9Ynw\nVB8BgMveW9mmTH6g1OxzUOAKVcthDCgyDfb1UnViUJuvhymxo9p8EulE1t6azeqy0A/vTy9f\nJcLTGqOayzKOHSQTsdf+iH33SGm2rR/6TEQi6XxppACBvT10AVWe2eiffhw5sC/zz+ql88rS\n66kt28OTqiodbeQ6mmkyXROqajz+lGhoZDebIRqzFi3h4bl9MhgUIc9/hyXTLQBgbHsKojHt\n1LGM75H5wIpQUb2rKAZhalJ8zeA+xcqPgyJek9zxrdx5THvajFD5lwtVdc/ooVzILb1itVv9\nyFizzpfgSgLa9NbGJa4GnDqyh2qGlKzYCYXJJGlIhEjMF+hxEBkRcLCs5fxtobhcmIMCWuag\n3Inr35C/r589NZTVZRcP75d6x1Uc7vAGIaFqqRfPZbO6DLTjX7jT8SAhy3gkRzhMJuL/+T/0\nA/vUm9fVL89HX385+v5OH8MrAeQtLRmVBQCh6+bsufakKaK2jo8ZZ48aEx6edxVFoprY+QW3\nLCQCQER6kLWnTE8++31rznx7/MT0ogeS254KUbkOgHW2D3GEc3cKSSLAG0ckv/n9IXeaWDz1\n+A5r5hwfQxwmpK1YiZ6t8egWR4bE6xvM0FAGQWYwb1qkmoaoqyddwK0pYfKKJetbkuqOTEY1\nPP5Ogilk8ELylCXNoDCVCpGItESIWEZUJS349NMEHzcokHrLQmEy0ZzIrvcclW/t5FGVom0E\nBUxTZwlJiQEA1LOn4n96Ubl+Ffv72O1b0Q92RvPH4KoIP6qJnW8gOXaSViwAaOdOx//wa/Xi\nOeX2Lf30iZr/+KXSfM3H8IYLid+tWxcgCz5+krVgkT1qjKirtyZN4eNCVNwCAJDmAXQ+bY8e\na//gp2LqDFBViMTMeQsTf/GcbPovENA2xNEoLUCFmNr+tKMKm16xOlwaLhaVkspYUJOmuueC\neX1DeKqqyLmgEjuZT4OoqXGfnISqhSdVlZ2CZPqONA00VNTbvr7MO5634cnnddTLF4tcDAxU\nkZj8HkJGx27Xu45F7djh0Dm/VeGJamLnF8jytWy/w8RA5IOduZUVtMzY26+FRzRfNsZhy6Q0\nhIi99kf9sz1Keyv29aqXzsd++x/hcmQ3CGFVwRhZxxqEbUEqAZYFRlJpb6N1BIKDSFGtWLkd\nkD1xcuK55625C0XTSHviZOOJp41N4XKxox/5ks6yiESSTzyTe70iFks++c3wCKtidxeSZr5k\nYRLAnL9YuGr85gPLwzPnK/NKHrTEdcFtMA8AvImexAwEaFmZlCcv8eGCzu2EIBWskDqQBAWa\n2K3RfAbW0UayBdit5vJGVYWvCMsG8TUDmmlSkF02Fas2X3eLfGJfHwvNOUlmgIjUSAEAaOfP\nKNeu5P2mbUU+fKf8kZUKRjlUIueyZxLraFd+/7/x7p3BH9tbY6/8geZ1BQRGecWSIsyD4Fw/\n/Ll64Qx2dii3mvU9u8JVaQAA6pkkKzYAgD19ZuKvf2LNmstHj7Vmzh747t+Eiskuq7RJ1+sb\nUk99M/c0aM6Znw7TkK+ISMreksalseohx4lXKKqxdn35IysZ5L4djdHMTkSyHmxTJn5Bwf1k\nAQ/eAkpSAplrcxWhRDWx8weGQQ5PkOd1ABAyZq5Eay0ADHNsTcmXfBtcvHs7RFdElj0QZQN9\n+oFPHUU+tCx9/x4/QisR1HvrwdSMHNynnTya/REH+qM7X2XdlBheqCCfuFTa7sb/+F/qlxdY\n21318sWaF38dLrZT5vZ3ZdqiQWp6Zk2fZWzYYo+fyBsarRmzzbXrZOLMgQBJoUFEGUWBjxqd\nfPZ72bqdqG9I7fgWnzDJvwiHC/JADky6+xmbH3d8IvaYceYDK8oeWMmghbdUOrHjI0cJ1xC9\nUFR7apiot1UUQjWx8wUiFheuvQABeB3ttEP71SgKD431smDk4wRl8k50WQXRo9xSaZCNS02X\nMdlZR7ubxcYk4gjBYDhFYgDQjh52rGA6rZ4Ky4giGimaqKpLUlUhojtfzdFKRLTM6LtvhEc0\nf3Bex+3eIjGYB4DI3l3Rd99Qbt9iPd3qlUvx//r/1Ctf+hnj8EC/t0LQmpeZfzmiiY8eLRQV\nEHkkIhXCDAr0GVteJB43IfmXz9lTpouIzmtqzaXLk9/9G5kheCAgK/ZSmWvGkk887UhV0+s3\nhcpwuYqCqCZ2vkDp6iBbYIIS+wYAPmq0uXyVY9FYtyk8QpdKJzlDKpiE+GxPJxwt7anTQ0R4\nop49aJlSYwNSxUo+XFZ5kD0XlBUbbJvUi1YkrKkg4fhAJGcD1t7G2p15NqZS6rXL/oQ1bHBZ\n/0tymyvtrfrBzxyL0ffeDI/cCZ01MCYTDkTDiL30G/XiebQtEEJpa4298nvlxjU/Qxwe3FbR\nQu6QloFyq5ndvoVGmg30axfOK1dDlHkDSEbL5fM39uRpiR89b02fyRtH2OMnJp96Njx2QVUU\niWpi5wuERI/AoxGZ2rjV2LhVNDaBotgjRia3Px2q20lI0gNSHQAArOkzzcXL8pZi8dTWJ8sd\nV+kg2+IiEpHlDen5i92L5sIHyhzWfYC+Ik2ygyuKoIYx7XqJZ0DloaqD7fL8D0TU0S52pII0\ngNTeqvIgjWJBMlIAAKz5unsRB/olp6wAwJy1RgEAApmsX6wdO+yWxY7s/tCX4EqDm+sMXqpv\n6pcXIh+/P9TATSai773FKCJKIMB0mjzveRRKMZmMvv6yevUy6+5Sbt+KvvNWLmGjiq8Eqomd\nP6ihnz0e81+YTKiXzmN3J9i20tWhf3GAdXX4Ft+wIaGeMI8rSj3+lLH5cT56DK9vsKbNHPib\nn8rUrYIB+ZSV7+DWogdEfqptLl5mLlkm+/3KgybTRKVH8/SDa12/HDMXLy1zWKWCdXRISlP0\nriVGjiLrwXzMuLLGVTpIXTqQz5DKIBffqDic2wJCxlZVUlNklFi00t4anktCm4pckT4o9S8O\nuP6CpR85WN6oSoZQVaDmITwUcyIf7MzV9Ebbinz0HvnBVRFaVBM7X8Ba7w73JbF33lBu3sj+\nqLTdjb35Z3KWPhDQLGnOwdW5yEI7fULf/SFra2W9Peq1y/EX/4N1hihVJWdIvSmAfOsTfPmD\nor6e19ZaM+caD60PjxUSCEEbcMmlMdIrVqdXP5xNhnhDY/KZ77ip00FBFrmMwCSisfTadZDf\nHjTnLrDDw82XlEmE7Bw4eSr5y+FxZHc3LiEzryP71pGMT11aJq880CK2BS4/75FKfgo1cR8I\nMG3Q/fKYRHjLstym2Ghb2sXzZY+tCv9QTex8gcwTFsjjIADr7FBcTCDW1hoi9gl5pEZE2ahB\nb0/kw3dyE1Mc6I++/ZpP0ZUAQdYg5Ts42Lbym1+xo4extxf7+9XLF2r+97+TdqvBAJHOhDz8\nSxDtyVN5JpNDhHgN/dwNCpJnvYfQoLH6EWPTNqipAwDQI+bKtcb2p/0JrhS43WgAABBFLZ3Y\n2aPGuG1hU9t3hEjHjr6JpHO75twFxOK8hWUM6X6RJOd15AZcJJ9BojhdebC+PnLrFlxSMjDT\ndLVVPt9TRQgRlg3iawZZX8EeS3eFsJ8+4cnWK497ZJq8KxO6LjXuvHIJXQUk5U6LrBtVeSA1\n/ubRodBPHIWbgyqdgxKmqVQkNGY7mBggGZweV8RabkVfe5l1dQIACMFu34q9/DuZl0DlIfV8\nkxeJkdvKzes40AcAkDbUC2fYnTBpYpOzokJAQvrUNNZtMrZ+gzeNErEYHzM2+e2/sqixpMBg\nUvmBTAsNwJ463chPVe3xE40wKfPR0/wScRAAIE0F3ZNwQYHH47SLXQ1dsRPRmIjXuB9gXCZE\nX0UoUU3sfIGskOPiGg9CSBjrPDxM9sE0KH+PkHeKZcLF9BE/CKBpEgm4fGiX3XQx2RFyu+fh\nhFRxFCD62W6H5wGmkpFD+/0PqjhIrMc9JpEjn3yo5vSMsK839safhstg8xF0r1yR2boAgHL1\nsv7JB6yzHZNJ1no3+sbLytWwDPkCgJuJITwblwCQfmiDufxBXlsn9AgfO97YtE0mMBQAOCfr\nVR4VO3POfGPdpuywiIhEUtuesidN8SvCYQJ7euiKXUzylUM0NmxxbvOjx1oLiNGxKkKLamLn\nD2RcYMmwGG8cYc2Z71i0x0+0KZJNIKATMnnnjmSsC10XHoZdFQa37+1fQx+W1zOGPMvLlUsr\nDaaQvUtZmw8kInxuxZCgQDcuAWRfIbQstwgfJpPahbNljqxUMHI+lzHZcQJNM/bO67mlZfdK\nsGCuVBVB6sKcQWznK9rRw6y/D9MGu3s7/uJ/Kjeu+hjicICpJCkOIlV9AwAAe9Jk0XCPmarp\nECb/aJak5ag8vkLmogdSjz8F8VoAAMbMGXOS3/rLUMliV1EQ1cTOF9DdIsa4nJme2vqkNWde\n9kd70tTkU98KD5lGkBU4+Q5uTZ1hzXD2jIz1m8OyQQiRowIwlBB5CFbZ02a4F62pxGIgYJ3t\n2QQ1J1H1sgzhFP0uPNKJMEwfUkgm3MNGAgD7QqPMRxHzUcZ2AmC3bri1BjExwEJTJxakKaqE\nngEA6pVLqouGH31/Z1imYmVqR/ITLOvujL3yh+xYGPb3Rd/4k0Lp1AQCWUrq5YjNuXrjOiT6\n7/3zVfXKJX+iq8IvhCVv+JqB9FEGzt20syHoep7ht5GUqV4FAjSpg6yH2jBi6slvpZeuyNTA\nRLzG2LLdXPagfxEOD0LQHGH5FZmLloqZs/P+Rk2tsWlb2UMrETkZM+b8k0cNkmyvmJRcXyBA\nkqqKKLNvgXiN+zGGALwhLHO+mKRmSOWdZZnspdc2UlmgTTWX5Ykd6SXPurtIrewAMDAwvMYl\ngH5ov1soLhIap0Emo8zKSwaRQ/vVsyezP6JlRna9p9wOE1e1ikKoJnb+QEamkdCGAEDfu0vL\naSQpba3RV//owROvMMhWrMflAABrva2dP4tmGgRgYkD/bE+odgdBdS6lcr4AgMi//0O+cImI\nxYWu8VFjks9+TyZUEQAk5EUPH9L0g2sdBID0g2tzy8YBQzaIJ5nzFYqSXrHaudjQaM1bVN64\nSgaZkHm0+WQKfJwyng8AQtByJx52LDLBl3C0JpisGCxTOQBgnZ3UYmh0ndxng0ziKqdHqy45\nYrQt7dTx8sZVha8Ixe309QMpFQu6LuuLoWVqx5zGnay3R714ruyxlQZa9U0+cYmmGdv52qAJ\nJgIAYDIRfesVjw2lkmB9vbQkjVzOFwDY6y+zMycxmcC0ydpbY3/4L+VOi18hDhPYKxG/TcvP\nBowZK9dkbQ94Q2N4OssAAGmqLiWE2xtg6BUPbRgcSBQAAPao0clnvuftB1VRuBI7AV5FYl7f\nMCginVNFSq96yIPRUVEgCqSCl6eq9vSZxOK4CSAviVUSsq8KqWmSAaeoCzwclwPkvo0ACB5S\niDhAVE9RwtWrIpyoJna+gOxQ0K2lzL8aGCC1iMMjDkIbDsordsrN6+jiSLGe7pBkQrJukUcN\nUr1yCc+czF1B24q891aZIysZkulXj2cS6+6Kv/L7rMEJ6+mOvfaScve2L+ENH/SzRFW9EjXE\nwTMVAmTS97ZhS4X7CNd5DwG8WafG+s3Gw4+KWAwQRSRiPrjWWLfJzxCHATRNkiDI5Yw0e8Ik\nh1Oi0PXU4zvKH1xJYF1d5LrHFVmUUwu5GAzIsrfIqhwQ4COIGj9vDM3QWxVFoJrY+QNKmIrL\nxZBEPE4e3IWMTlRxCE5lpfJiA12z9BQhqyQo/0QBACJOyzsBgNJMMNaVtrs0n7LiQEnj0qN4\noB/Y5/iY0Lb0fbvLG1jpIDXSmOIxDhI5uE89cyL7IxpG9IOdSmhyO7IVi54FRXbntn5oP6aS\nIAQahnb4c+3EEd8CHCYSNCMN5Rw7AEiv32wtfEDoEUAU8Rpj3SY+arRvIQ4PMvKix4CLNWO2\n8dCG3J3QXPRAOjQ6diQpCBBl+gwAYK5d71gR0Vg6PPToKopANbHzBUjWt+SNS6Hp5iKnnbyo\nqTVdGiiBAE2TljuR62/Zks3aHhUKoUvscR/NCwmXyPKJcAieyDNp6QgOo7zkSQ2UQCCxJ/Z6\nu7UTLnqQZanhoQdRxjPcg6gqROyd1xzvQ2T3h2HxO4nFyC8/9+DYAUQ+2KmeOYFpA4TAxEB0\n13v60UN+RThMCAlRxDv1tKdMG+LaKgoPje0EADBSE1tVPVg05twFqceeyA5d8YbG5De/Hx6n\nwSqKQTWx8wfkDKnnQdbYuC2Xyc7r6hNPfycs1BPG6B3cg/c9aow7VU2vWB2SDUKqAiARZAcA\nawqhKWiPmyA8PLsqCJZKEKuIokGqcU2S3D0GACsMpK7IW/yWVEJxUwKCAl0Qkt9ErKtj0Bck\n749YbvvBQMA6O2h2iS69I5Q7LdrpE45Ffc8uj+NHJSEbnvBQfcO+3tgbLw/5tdh25MA+3UWY\nDgqCdKOROFve+9dCuX41e5xgPd368SNh0aOpojhUEztfwOhig1wcBAAY5k4wYTKpUAWVQIDp\ntGQH9xo1MB77hrlkxWCTQlHNRQ8YG7b4Et/wofRLxt/kxQZ72kyxdEXuilA14/GnyhtY6Rgc\nNcj/nIQQ8sYlKXcSIol5svvvmdhxagTYS7KrgkDbIkYUvSeQJAUk2XqlIQtDXlVlFIMTbQvb\nW8sV1H1Boi/jQb3VTh6RBHINAAAgAElEQVRDV1VMP/RZOaO6D9DnPU8Faf3oIS1/aE89e1I7\n6ZT+riLMqCZ2voCU8+XyxiUA6J9+kqsDiZYZ+fBdpTUU9CDmqHlkhXA95U6Um9fVM8cHd3/b\n0k6fCE/PxU1jH4RkZ89AbHuST581KM2ga+aqtSHpLAMAmJkryn+myrM6ADDnLXTog5gLFoeH\nHkTP83pIJwI4fEgBQMRi5tKVZYyqZAim0OJhHmXvppFk2meNm1jGwEoGSoo43KNILKF2oWeq\nUTHQRFVEjyti1DQ69vWFZPwf09SG5mmkQTq1aOfPlCukKiqAamLnCxAQnMUTQM80SDvtZAKh\nbeUKRQYInisCImDo4jzadrYdfeeN/NKC0D/9mHXTc2cVhsvKdvCzsuUqACAEvvoSu/olZpSN\n06a+f2+IjuYUmUboEe9MiE+cnJc6qFqIei6U3InwLBJbix4w1m/JZg+8pi75zPdCMoHE+npJ\nTWwekRaJhaK6FbDNRUv5hFAkdtAruZflOY09bYZbMZs3jrBHhmJ+gm65CuHRKSYZdSJe433f\nVQ6kgrS3/Q853xaOobcqikQ1sSs/0LaBW+Bi1XsZDnJODleyBFVIrzjyRDhx6P88nrJKR5uL\n8IRo20rztfLHVwKc+9S9q5JX7JTma3jJ6Yakf7YnJPQgOiHzrNix9rbIO6/nxq+dPKof2l/2\n0EoD2pbrcOTl+ZZ5iXrxbHZ0iQ30RQ58SluMVB6yjFnzesqai5am164fTIYYsydNNjZs9iG4\nUoCyN1b+GYnautSW7blJj4hEkt94NiTeiaTCjlAUj3a5tWipO1U1l4dlhpR8rHg5BgGQSTYf\nHZrWRBVFIBS309cNRmqIHpSzmXs9kxgjq/28aWR5QysN9JAveI4oyjb9cDxlKbkTAPBqUijt\nxLgo2nZWBy5YZEyZHLmD97yOdvq4O5HVj4eF941CDHfkWNu/1yGUqFy9HBYmu+SbL6JeDA31\n8kX9872DTHbOlZvNsddfDstNJBH64fXSxiUA2DNm2WMnDP3yyFEeUosVhqCG3tBTYYePaEo9\n+SzklF2thUuM1U5KQGCgrgg8/aDTjzzqqEGISDT90IbyxlWFr6gmdj5A04fsqnI3BE9mg/Gw\n884RtXXpB1aQv1xpSOyqrEapXRUfPYZMZO2Jk8sW1X2AJtMoisdMqKw8GRJjg8wzyfn88XBI\nA0BqggT7+8PQjcV0mtRQ9RhbBgD18sUiFysPlqOwk/v+epdPIrvec6wot5rVc6fLGVmpcPEZ\n7q0bEi84AACIvf260jLkGKu03Iq/9UpIUlVGtmILVROxtwdyLlm5doUk3gUDSoHP+7zHm0Yl\nd3xb1NRkdhMRixvbnvRgGVYRQlQTu/KDdXU4TSYEgLeFIoC1YImxbmNWN1LU1KZ2fEt4Hq0q\nBhwYcDfFAAAtKZlGKKqxZbtjMf3gWh6OaQN6rpBzjweMNX2mW9nEHjs+JJrstJRGxOsswRsI\n6Rle3+DdwK0QZOmOXOUbZF9Iz4GYyiHHGiT3/fXQxMZUipSsC4k7CHkwAEQhr9ixtla3Vgtr\nuam03CxvbKUBk5TCjmcaxDrbI7s/yvsjA/3Rd94oc2SlQQhaoNiT7Y1mOvrxBzgwkNnyMZmI\nvPtmiNxvqygC1cTOB7hToMzRx/t26u/TvziQde7Cgf7Iezs99JMqCWaadFMs7pV3mvMWmQsW\nZ7ME3thkLgqN007f0Jzv0MelaR6nc1FTK3Z8KzexELV1qSe/6VOAwwUp5+uhdQIA5pLl7nJj\nOiRdpFQSqDtJeKaq9vgJ1GIoRg1wgJbTQw97YlUlk2wvtm4lQbotC69vHevrJdeHdOCChaDq\nW55ClerlS26minKrOUONCBZoW3k8yCw/SH6WAAD98AEHvQTNdOSTD8ofXxW+oZrY+QBJ43JI\nnZxCdM8uhx4S62zXwjF0Sc8HIIi41xVFDn6mnT2V7eux7s7Yay9JyW2VBeZ0G7NPIe+jOQBA\nQyPoOc9U26atGAMBNUPKPT8g0dCYfPo72e6zYMxausJ8YLkv4Q0TbGAAyMOEXPwWAIx1mxx1\ncVFX79ZACQaybUHe9xaqak2f6V63Z80tV1D3A5rPwNCj4ivq6QnlkOiWYyr/M8qUrBSvp6Ts\n7B2GM7lgCiCAuJfRZT8Wz+Yyo+y8ldu3yhxcFX6imtiVHzL5cm8iOLtFWJGqN5vdi5WHMNPE\n00dIjAgzsG13Vsq6O9Vzp8obW2mgLWs9VQDQttkrf4CcgzgmE/Gdr0onSyoLpJ6mWEhzQTtx\nNNt+Qs7V40dCMrYsowF58xlEfYOx8TGRFUVTVGPl2pDYt+CAxMzXUz85tfVJUZeX9KQf2RiS\nGiSQE5eqV9nbHjnanjrduTh+oj1hUpljKwlo5Sd2mU6Lp8KOPWase1HEYjwEIjuspyujTuXU\nZ/C8I2jSZ0iKxFUUh2pi5wPyB5GyKVEBPS1qNxThUAFgfb1E1qAwjw0Ckwmyzue2SAoENO/b\nm0zTchPc/k493SwEyTem0xmFnRwIKNRFUq5eduuORt/bGYbhCZneofBUsmWdHZGP3h2qCttW\n9JP31XAYcA0pijneXe/STjzO80eUZH6mlQctd+K9ZSEmv/GsPXZ8dkE0jkg9+c2QyJ0IctTA\nczrKmjnHnuasqqY2bgvFFUm8jrxvInvmHPeiNWN2eUKqoiIIwZfvawc0krmbdzYl8s7S3LsD\nANhUI6byoCMXnjJp0RjJf/fuR1cOJMvesxpEF/kAWBikOy3TxUdDKFTfUm4RKSnr7gwDPUg6\n8eBZOdC/+NzdAtP37y1XUPeDoUJ+7k2D6F1Q1PftcdRQI5/vVa6GIlWlWxOF+AzK7Vu5wx/Y\n3aUf3FfewEqEEGSq6ip4Of41prZsH0q+Ee3JU8PSK6dmQaDQec9cuMSaMy93hY8abawPi3pi\nFcWgmtiVH5hM0W1XbzekdRsdTRl70pSQ+DvRlGfPWRChqqbLdVREoubcBWUMrGSQM6TCcwfn\nEnF8e1QoRPNpeJ4lUPZvQ1BskKXLvNaLjEXW+UJidkIbxSJ6l0+084SyCblYedD1Lc/GJXAe\n/eBtx5p28lgYpmIxlQKbSOwKdFo4j77/1tB3TAil+Xrkw3d8CHDYcJvYZiA8NbEB0R4/aXAT\nyLLzwqFHU0WRCH4H//oBDeqchEg6lGchIlF78rS8lXBonQDQzyTumdgBgLHpcZ6jWidU1Xj8\nqVCwpIUAi5ohrfGqnfARTWIozx7c8MxFS3mT3IWsUsBuWjfLuz5qTZvhXrTHjPWm4FQIVGIn\nANDZcc4Dp8b9yMXKg1HMBATP6QkAcjonJGYn9HyAZ0mV9XS5DGkAAJSbBMO4whCqSp7svIUG\nlZZmpfm6Y1E7d4rUqak0JPM6UOuVqip3WiJ7PhoUwEMAANbe6tZTrCLMqCZ2PoDsIglBClJk\noZ07pZ08mruiXrqgf/F5eUMrDbRup/exDwB7e/DunaEfLUs7+FlIvLFBkCoSBZzI+ZbHxZhx\nADD4RK6rNx9cU/7Yhg+UWIAUINNMmJResTrv91XN2P50OSMrFdhPiIMggvfpyFyyjFgMx5wv\nkA1uTfNWDRSU7qOXo3ElQW0LBXxIJayvUBSJe7opsU7gno1LJjlTYQjIxPTYciFSkHr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w76qxvw9d09kBgNbELrxfGZsfF5FI7onXXLBY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\nxzpttZlarFaFmESrFMtDAu9k9MYsk8lkMpler++oGrt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}, "metadata": { "image/png": { "height": 300, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## Integração com'ode'\n", "out <- ode(y = state, times = time, func = lotkaVolterra, parms = parameters)\n", "\n", "## Plotando\n", "out.df = as.data.frame(out) # exigido pelo ggplot\n", "library(reshape2)\n", "out.m = melt(out.df, id.vars='time') # isso facilita a plotagem colocando todas as variáveis em uma única coluna\n", "\n", "p <- ggplot(out.m, aes(time, value, color = variable)) + geom_point()\n", "print(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Uma coisa interessante a se fazer aqui é dar uma olhada no *espaço de fase*, ou seja, plotar apenas as variáveis dependentes ( nocao número de presas e de predadores em cada momento). Note que no espaço de fase o tempo está implícito. Para torná-lo um pouco mais explícito, usamos um código de cores, para mostrar em que sentido cada para de valores segue-se a outro no tempo:" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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bQ/qbm9jMvDUdhlJUT7TwYgklAUeezavJe+qjjVZPZFchNiHr8uX0RfpC0KAMDl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\nQmcRvWQymUSCs4YFQFEUIUShUAidSCSr76kODJ5r7/X9zet0Ot4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1858JjC2WBOXkCT4HATEVe1m2HK31MP6/lmk5CYVpBkHyAQAAATk9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AwAQdGUoeGkx47RJxevCNgUODSSJyyEIs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\nSUVORK5CYII=" }, "metadata": { "image/png": { "height": 300, "width": 420 } }, "output_type": "display_data" } ], "source": [ "p2 <- ggplot(data = out.df[1:567,], aes(x = P, V, color = time)) + geom_point()\n", "print(p2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "**Parabéns**: agora você tem os elementos básicos para integrar qualquer sistema de equações diferenciais!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mais informações\n", "\n", "* [Introduction to R](cran.r-project.org/doc/manuals/R-intro.html)\n", "* [Crash course in R](http://www.r-bloggers.com/a-crash-course-in-r/)\n", "* [ode package](http://desolve.r-forge.r-project.org/)\n", "* [Some additional example codes](https://github.com/diogro/ode_examples)\n", "* [ggplot2 package](http://ggplot2.org/)\n", "* [A R graph gallery](http://www.sr.bham.ac.uk/~ajrs/R/r-gallery.html)\n", "* [Another tutorial on numerical integration in R](http://www.r-bloggers.com/learning-r-parameter-fitting-for-models-involving-differential-equations/)" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.2.1" } }, "nbformat": 4, "nbformat_minor": 4 }