Especificação, suposições e estimação
Especificação do modelo
- De momentos (média e variância) \[
\begin{aligned}
Y|X &= X\beta+\epsilon, \\
\text{E}(\epsilon) &= 0, \\
\text{V}(\epsilon) &= \sigma^2.
\end{aligned}
\]
- Especificação completa (distribuição de probabilidades) \[
\begin{aligned}
Y|X &\sim \text{Normal}(\mu, \sigma^2), \\
\mu &= X\beta.
\end{aligned}
\]
##=============================================================================
## Modelos de Regressão e aplicações no ambiente R
##
## 13 a 17 de Abril de 2015 - Manaus/AM
## Fundação Oswaldo Cruz - FIOCRUZ
##
## Prof. Dr. Walmes M. Zeviani
## LEG/DEST/UFPR
##=============================================================================
##-----------------------------------------------------------------------------
## Definições da sessão.
require(rpanel)
##-----------------------------------------------------------------------------
## Modelo de regressão linear simples.
rls <- function(panel){
with(panel, {
curve(b0+b1*x, xlim[1], xlim[2], ylim=ylim, lwd=2,
ylab=ylab, xlab=xlab, main=main)
ncur <- seq(xlim[1], xlim[2], length=nc)
ncur <- ncur[-length(ncur)]
lapply(ncur,
function(x){
xx <- seq(ylim[1],ylim[2], l=100)
mu <- b0+b1*x
s <- sqrt(s2)
y <- dnorm(xx, mu, s)/scale
ind <- y>0.0001
if(curvas){
lines(y[ind]+x, xx[ind], col="green4")
segments(x, mu, x+dnorm(mu, mu, s)/scale, mu,
col="green4", lty=2)
segments(x, mu-4*s, x, mu+4*s,
col="gray70", lty=2)
}
})
if(simula){
x <- rep(ncur, nr)
y <- rnorm(x, mean=b0+b1*x, sd=s2)
points(x, y)
if(ajusta){
m0 <- lm(y~x)
abline(m0, col=2)
}
}
})
panel
}
panel <- rp.control(xlim=c(0,10), ylim=c(0,10), nc=7, scale=1,
xlab="x", ylab="[Y|x]",
main="Regressão linear simples")
rp.slider(panel, b0, 0, 10, initval=5, showvalue=TRUE,
action=rls, res=0.05, title="b0")
rp.slider(panel, b1, -4, 4, initval=0, showvalue=TRUE,
action=rls, res=0.05, title="b1")
rp.slider(panel, s2, 0, 2, initval=0.1, showvalue=TRUE,
action=rls, res=0.01, title="s²")
rp.doublebutton(panel, variable=nr, initval=2, range=c(1, NA), step=1,
action=rls, showvalue=TRUE,
title="Repetições")
rp.doublebutton(panel, variable=nc, initval=7, range=c(2, NA), step=1,
action=rls, showvalue=TRUE,
title="Valores de x")
rp.checkbox(panel, curvas, labels=c("Modelo teórico"),
initval=FALSE, action=rls)
rp.checkbox(panel, simula, labels=c("Simular do modelo"),
initval=FALSE, action=rls)
rp.checkbox(panel, ajusta, labels=c("Ajustar o modelo"),
initval=FALSE, action=rls)
x11()
rp.do(panel, action=rls)
Estimação
Mínimos quadrados (ordinários)
- Princípio geométrico, projeção de espaços vetoriais.
- Objetivo de Minimizar soma dos desvios ao quadrado \[
\underset{\beta \in \mathbb{R}}{\arg \min}\, S(\beta) = \sum_{i=1}^{n}
(y_{i}-x_{i}^\top\beta)^2 = (y-X\beta)^{\top}(y-X\beta)
\]
- Equações normais \[
X^\top X \beta = X^\top y
\]
- Solução \[
\hat{\beta} = (X^\top X)^{-1} X^\top y
\]
Baseada na função de verossimilhança
- Princípio mais geral.
- Objetivo de Maximizar a verossilhança (log-verossimilhança). Se considerar o modelo tradicional de regressão (distribuição Gaussiana, independência, variância homogênea) \[
\begin{aligned}
\underset{\beta \in \mathbb{R},\, \sigma >0}{\arg \max}\, L(\beta,
\sigma^2) &= \prod_{i=1}^{n} \frac{1}{\sqrt{2\pi\sigma^2}}\cdot
\exp\left\{\frac{(y_{i}-x_{i}^\top\beta)^2}{2\sigma^2}\right\}\\
\underset{\beta \in \mathbb{R},\, \sigma >0}{\arg \max}\, \log
L(\beta, \sigma^2) &= -\frac{n}{2}
\log(2\pi\sigma^2)-\frac{1}{2\sigma^2} \sum_{i=1}^{n}
(y_{i}-x_{i}^\top\beta)^2
\end{aligned}
\]
- Solução (é a mesma em \(\beta\)) \[
\hat{\beta} = (X^\top X)^{-1} X^\top y
\]
Mínimos quadrados generalizados
- Permite acomodar casos onde a suposição de independendia ou variância constante não são verificadas.
Demonstrando a estimação
##-----------------------------------------------------------------------------
## Dados.
## Comprimento da diagonal de aparelhos celulares (cm).
x <- c(12.5, 13.2, 14.4, 11.3, 11.2, 11.2, 11.4, 11.0, 10.6, 12.4, 12.4)
## Peso dos aparelhos (g).
y <- c(136.7, 144.8, 152.6, 120.9, 113.6, 126.9, 91.3, 107.9, 103.6,
116.9, 117.3)
plot(y~x,
xlab="Comprimento diagonal (cm)",
ylab="Peso do aparelho celular (g)")
grid()
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)
##-----------------------------------------------------------------------------
## Gráfico da superfície de mínimos quadrados.
##-----------------------------------------------------------------------------
## Modelo: E(y|x) = b0+b1*x.
y <- matrix(y, ncol=1)
X <- cbind(b0=1, b1=x)
## De forma literal.
XlX <- t(X)%*%X
Xly <- t(X)%*%y
solve(XlX)%*%Xly
## [,1]
## b0 -33.22079
## b1 12.90219
## Equivalente porém numericamente superior.
solve(crossprod(X), crossprod(X, y))
## [,1]
## b0 -33.22079
## b1 12.90219
##-----------------------------------------------------------------------------
## Usando a função lm().
m0 <- lm(y~1+x)
m0 <- lm(y~x)
coef(m0)
## (Intercept) x
## -33.22079 12.90219
summary(m0)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.5642 -5.1349 0.0575 8.0189 15.6162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -33.221 37.878 -0.877 0.40326
## x 12.902 3.153 4.092 0.00271 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.3 on 9 degrees of freedom
## Multiple R-squared: 0.6504, Adjusted R-squared: 0.6115
## F-statistic: 16.74 on 1 and 9 DF, p-value: 0.00271
##-----------------------------------------------------------------------------
## Observados e ajustados.
betas <- coef(m0)
plot(y~x,
xlab="Comprimento diagonal (cm)",
ylab="Peso do aparelho celular (g)")
grid()
abline(a=betas[1], b=betas[2], col=2)
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iWOI7fV3SW4xWgP8CVAbY2Fa0m8zOw1hadr0N5fNsGHiiqUywExvPvTwL2FJhFBajValNAaXJyctnatWsfKjqPpEySJOUQwgRAf3//4lWrVjkTodQh6vX64jRNxwCiKKoMDg46E6HUIarV6rJSqbQTmB4aGlpQdJ5jEeAU4C3A1TT6WT0G3AJ8JILvFBStG3h82wZ9RQdQV/th4NwWrasM8IY3vIGrrrrqNxYuXLh1aGjoc81P2Lp16/MWLFjw40A5iqLHp6enbz377LOf/EWQJEkZuHJ6evrUKIr2hxA+v3r16m3N60iS5Ienp6fPBYii6BuO0TljkBfU+/v7S+0ao1d+Vo7hGHM5xtTU1OWlUrZZjo+PnwTsblq+a16HYzhGL46xe/fuSn9/PwDT09PXxXH82W58HY7hGL04RqlUivL1RnEcX99Nr+P0G2+86xkf/ejrgZ8l72cVBgZ27rrkkq/svOaakf2nn/61oaGh73T66yhyjPHx8VfccsstfOMb3+COO+5ArWEBS8eqBGwmLzy1ynXXXQfwLiAkSXLa4ODgozOP9fX13QD89My/oyiaIqv+AxBCeB3wF1EUzTz+I8Crmx4vJUmyOYqimcyO0VljAOyLoujJPxBd+jocwzF6doyBgYEfBz7c7a/DMRyjV8bo7+9/ZdNj7wUu7sbX4RiO0YtjRFG0J4SwL4RQzrfPjn8di+64g1P/5m9Y9B//EWhcrfVlFix47zfuuOMfKJUuAy7r9NfRCWMsXLiwfN111zE5OcnatV5l2SoWsHSspoG3AS9p0foGgCv/8R//kde+9rWfWLhw4Tebf5EARFG0AXgcYHp6en+5XD6gWh5C+Pcoij4YRdFA/px/esry07Va7W1RFL0kf/69jtE5YwCTU1NTf3P22WePNz2n616HYzhGj45x2vT09HR/f/8B6+jC1+EYjtFrY9wWRdGngP4oih7u4tfhGI7Rc2MMDg6OV6vVH1qwYMFPAEs69XUE6Jt81avOoK/vwf7vf39ZvkAA/ga4KYI7mZqiVip19fsx12NMTk6u/uxnP/uGHTt2IKn3LIMnm9wtKziLJEmSJPWsAEsDXB9gtKkx+3iAmwK8oOh8PcAm7lIPs4AlSZIkSW0U4Ll5kerxpsLVvQGuDbC46Hw9xAKW1MMsYEmSJElSGwR4eYBNAaaaCld3BLg8tLivsQALWFJPs4A1z1Wr1QuTJLmk6BySZqvVahfFcXxx0TkkzRbH8cW1Wu2ionNImi1Jkkuq1eqFRY0fYEGAKwOMNBWt9gfYGOCConLNExaw2qD09E+RpPYrlUqbQwhfGBkZWVJ0FkkNw8PDfcC/RlG0ecuWLScUnUdSw5YtW06Iomgz8C8bN25cUHQeSQ0jIyNLQghfKJVKm+d67AALA1wLfAv4OLAOeAL4ILAqgisiuH2uc0nHy1kIJXWKE4GoUqkMAGNFh5GUWb58+YI0TcsA5XK5DOwtOJKkXL5N9gF9a9as6QOmCo4kKZfv05bI9nHnRIDlwP8AfpFGP6v7gA8BH43gobnKIrWDBSxJnWIK6CuXy+58Sx1kbGxsulKpBCAaGBhw+5Q6yMDAwFQIASCMjY1NF51HUkO5XJ7at28fzEFhOcBLgd8E/guNflYJ8EfA30ewr90ZpLlgAUtSRwghvL1UKi1duXLlw0VnkdSwfv36yTiOf79UKvUPDg6OF51HUsPg4OB4kiTvBvatX79+sug8khpWrlz5cJIk752ent7VjvUHiIBLgeuBVzTu5nPA+7xEUJLaxybukiRJknQYAU4McG2AelNj9icC3BxgddH59CSbuEs9zAKWJEmSJB1EgGcFeG+AB5sKVw8FeGeA04vOp1ksYEk9zAKWJEmSJDUJMBjg1gATTYWruwJcGaBSdD4dkgUsqYdZwJrnkiQpj46ODhSdQ9Js9Xq9Uq/X3UmWOpDbp9S5RkdHB5IkKT/9Mw8UIApwWYDbm4pWIcCmABeHbHZDdTYLWG3gf3xJHSGEUB0fHx91J1zqLCGEKE3Tu9M03T48POzkL1IHGR4e7kvTdHuapneFEKKi80hqqNfrlfHx8dEQwtePdJkAAwGuAr4O/DNZc/ZJ4BPAmggui+CLETjrqOYld0QldYqVQJSm6VJgZ9FhJGW2b99eBp4PsGjRooXAWLGJJM3It8nl8OS2OlFsIkkz8n3aMziC/lQBTgWuAX616fmPAh8CPhLBA+3KKXUTC1iSJEmSJM2xAGcBvw1cQaOf1TeBPwE+GcF4UdmkTuQlhJI6xVeBHRMTE48WHURSw4oVK/YBMbBt3bp1u4vOI6kh3ya3AdV8W5XUIfJ92h1k+7gHyPtb3QYkwM+TFa++BPwY8JIIbrF4JUmdyybukiRJknpSgP585sCvNTVln8xnGFxXdD61nE3cpR5mAUuSJElSTwlwSoB3Bri/qXD1WID3hrzHpHqSBSyph1nAkiRJktQTAqwMcHOA3U2Fq3sCXBtgUdH51HYWsKQeZgFLkiRJUlcL8IoAmwJMNRWuvpz3vbIH9fxhAUvqYRaw5rlarfb+OI5vCSFERWeRdKA4jm+M43hD0TkkzRbH8YY4jm8sOoc0nwXoy/tbjTQVrfbvOeecHfe+5z1/W3Q+FcICVht4oKhOsQzYmX9/OvBggVlUgFqtNgWUJicnl61du/ahovNIyiRJUg4hTAD09/cvXrVqlTMRSh2iXq8vTtN0DCCKosrg4KAzEUpzKMBS4Or8NtPPag/wV49feunf3nvDDXcA00NDQwuKyqjCLKQxk+RJZP8vdJz62rDOk4BB4HnAcrLrexcC+8netMeAe8imFN0GTLchg6TuEwH09/d7arXUQSqVSpSmKQDj4+Nun1IHGRsbiyqVCpBtqwXHkeaNAM8B3gr8IrA4v/t7wB8DH4tgrHbDDafn97ttSi3SigJWBJwP/ATwKrLi1ZFWmHcDdwCfBz4N3NuCPJK602PASVEU+emE1EG2bt26/6yzzhoHFixZsiQtOo+khiVLlqRpVmHev3Xr1v1F55F6XYDzgN8FfpRGP6uvAn8EfDaCJ8+CjKJoTwhhH42zcCQVaAB4I7CdxrWdM7fHgbuALwL/BPwdsBHYBNwOjJJt3M3LTJMVsn5wLl+EOoY9sOa5JEnOqVar5xWdQ9JscRyvS5Lk3KJzSJotSZJzq9Xq2qJzSL0qwIIAlwe4vam/1XTeqP2Cwy1brVbPS5LknLnKqo5iD6wOsYSs6ryTxhvybWAD2VlYzzvC9ZSBNcCvAp8hOxtrZn1fBl7fytDqeBawJEmSJHWEAAsDXBtge1Ph6okANwV4UdH51PEsYHWA1wH3kb0Jk8AngAtbtO6FwJXAnTTe6M1kfbTU+yxgSZIkSSpUgOV5kWpXU+HqvgDXB3hG0fnUNSxgFWgp8HEab8AngRe0cbzXAXfnY+0C/nsbx1JnsIAlSZIkqRABVge4NcBEU+EqCXBlgErR+dR1LGAV6A1kP/hR4KI5GrOf7FLFfWTNnU8//NPV5SxgzXPVavXCJEkuKTqHpNlqtdpFcRxfXHQOSbPFcXxxrVa7qOgcUjcKEAW47BD9rS4OxzmDYJIkl1Sr1VZdsaTuYgGrDY5mg3wr8JfAWJuyHMpLyYpXm+Z4XM2tZWR91SB7vx8sMIsKUKvVxoETJiYmTlm/fv1c/56RdAjDw8N9p5122h6gtHv37sXnn3/+3qIzScps2bLlhEWLFj0OTN19990Lr7jiiqmiM0ndIMAJwFXAm2n0s0qBW4EPR1A93jFGRkaWVCqVR4G9Q0NDJx3v+tR1FtKYgfIkwJnWW6DvKJ77gbalOLyvFDSupLl1IhBVKpUB5r5QLukQli9fviBN0zJAuVwuAxawpA6Rb5N9QN+aNWv6AAtY0mEEeBbwFrIrjGb6WT0C/Bnw51HjA/Xjlu/Tlsj2cSW1wNEUsCSpnaaAvnK57M631EHGxsamK5VKAKKBgQG3T6mDDAwMTIUQAMLY2Nh00XmO0lLgZOABLIyrzQL8AHA9cAWNflbbgBuAjVF29lVLlcvlqX379oGFZallWlnA6gPOO47lA9kpdg8C97ckkaSuEUJ4e6lUWrpy5cqHi84iqWH9+vWTcRz/fqlU6h8cHBx/+iUkzZXBwcHxJEneDexbv379ZNF5jsB64BrgRziw5+k3ydqF3Ah8v4Bc6kF5/6pLyc64ehWN9jlfBD4IfD6CthV+V65c+XCSJO+dnp7e1a4xJB27V9FoUna8t3uB9wGnzekrUJFs4i5JktSbysBHyIoFM/t7+4BHn3LfOHB1QRnVIwIMBLgqwNebGrPvy2cYXFN0Ps0bNnHvcDeQvTl7gV1HeHsiX+YJstOH93BgIes7wIo5fA0qjgUsSZKk3lMGbiPbx5sCPk521cbM2TAV4MeA22nsC75zzlOq6wU4NcA7AzzQVLh6NL/vmUXn07xjAavDzfxh+qmjWOb5ZMWr+8k680M2A90vA/fl6/sKWfM79TYLWJIkSb1nA9n+3S7g1U/z3N8iOyNrGri8zbnUIwKclZ9dtbepcDUa4NoAi4rOp3nLAlaHGyV7c1Ye5XI358td+5T7n012WnEAXnvc6dTpLGDNc0mSlEdHRweKziFptnq9XqnX65Wnf6akudbh2+d6srOu9pO1GzkSf0C2P3gfHvTpMAJcHGBTgKmmwtWXAlwWOuQEiNHR0YEkScpF51AhLGC1QSs37FPzr0fbgP0z+dfXP+X+7wIfyL/3Exipx4UQquPj46MdvBMuzUshhChN07vTNN0+PDzs7MVSBxkeHu5L03R7mqZ3hRCip19izv062fHGx4B/O8Jl/hDYATwL+On2xFK3CtAf4MoAXyO7AuhSsjP2PgGsj+AVEWxqZ3P2I1Wv1yvj4+OjIYSvF51F6hWtLGCdkH892ilIZzbosw7y2Kb869pjSiSpm6wEzkjTdGnRQSQ1bN++vUx2yf/yRYsW+Qmi1EHybXI58IJ8W+0kEfCj+fd/dRTLTZIVvCArTkgEODlkvdHuIeujtgYYI5v468URXBnBnQVGnCXfpz0DWFV0FqlXtPKT1Il8fSeSzSpypMbyr6cc5LFv5l+ffRy5JEmSJM2tU4GTyc6E+epRLrsl//qiliZS1wnwPOA64Jdo9LOauVLnryN4vKBokgrQyjOwHsi/Hu0fmjPyr2MHeWwiv9l8T+p9XwV2TExMPFp0EEkNK1as2AfEwLZ169btLjqPpIZ8m9wGVPNttZPMnFE9TtYD62g89pR1aJ4J8IqQXY2zA3gL2fHgHcAVwAsjuKnTi1f5Pu0Ojr6AK2kOfIysQdkHnuZ5T/WmfLl/P8TjUxz9ZYnqPjZxlyRJ6h2Lyfbrpsmu0Dgar82X7ahLwtReAfry/lYjTU3Z9wfYGOCCovNJR8km7h3uErI3JwXOPsJlTga+ky/3Wwd5/JT8sZ0tyKfOZgFLkiSpt+wg27c72l5Wf5wvdzS9s9SlAiwNcH2AbzcVrvYEuCnAiqLzScfIAlYX+DeyN+gB4JVP89xnk50GGoBdHLwH1svzx7/cwozqTBawJEmSessfcfgrLQ7mVODRfLnXtSGTOkSA5+RFqrGmwtX38mLWaUXnk46TBawucAaNM6oC8K/ArwDnklXPzwH+K/CXwF4apxX/xCHW95v5cz7cztDqCBawJEmSesuZwBNk+3fXHsHzI+Az+fO/Rmv79apDBDgvvyxwX1PhKs4vH+y02TSlY2UBq0s8C/g/NN6sw912Aa8/zLo+QtbE/SfbmFedwQLWPFer1d4fx/EtIYSo6CySDhTH8Y1xHG8oOoek2eI43hDH8Y1F5ziMa8n27/YDb+PQs6AvAT6VP3cv8NI5Sac5EWBBgMsD3N5UtJoOsKlX+1uFEKI4jm+J4/h9RWdRISxgtUE7DxRfB1wF/BDZH6QZAdgK/DPwQRqzjBxKhewsrck2ZFTnWEaj19npwIMFZlEBarXaFFCanJxctnbt2oeKziMpkyRJOYQwAdDf37941apVzkQodYh6vb44TdMxgCiKKoODgzEHt2oAACAASURBVJ02E+GMPyK7sgKyvlgfA24HdpNdwXEJcCXZMcNe4OeB/zXnKdVyIWvg/yvANcAL87v3An8BbIjgW0Vla7dqtbqsVCrtBKaHhoYWFJ1Hc24h2SysACcBewrM0jMO9QlIK3w+v5XIrmE+mewNfJjsrKojdTTPldS9IoD+/n4vF5A6SKVSidI0mwx4fHzc7VPqIGNjY1GlUgGybbXgOIfzP4ARstnKXwi8+xDP+wpwNfD1OcqlNgnZ5aNvA36BxskMDwMbgA9H8+DD6lKpNLNNdvK2KXWVdhawZkyT/YLq+V9Sko7LY8BJURT56YTUQbZu3br/rLPOGgcWLFmyJC06j6SGJUuWpGlWYd6/devW/UXneRqfAjYBP03W//Z5wAlkZ2FV88c3k12toS4VYIisYPlTNPpZ3QW8D/hUNI9OToiiaE8IYR+Ns3AkzZHFZDMBXjzH4/YB7wH+dI7H1dyzB9Y8lyTJOdVq9byic0iaLY7jdUmSnFt0DkmzJUlybrVaXVt0Ds1fAaIAlx2iv9XFYR6fgVStVs9LkuSconOoEPbAKtAv05gxcAOwdA7GXA98lUaz99PnYEwVxwKWJEmS1CUCnBDg2gDfaipc7Q1wc8hmn5fmMwtYBbsUuI/sDXgQeCtZU75WexFZY8epfKx/AZ7dhnHUWSxgSZIkSR0uwDMDvDfAzqbC1SMB3hmypvySLGB1hKXAR8nOxApkjfj+FFjH8Z0aegLZtfCbyKbYDcCjwH8/nrBdZCHwo2SNDv+C7Pr//wDuBL6Wf785f+xtwGtpT/GwSBawJEmSpA4V4AcC3BogbSpcbQtwVchmWZPUYAGrg6wiK2RN0HhT7gf+huzMrNfkz1kMNE8Z2k9WnFgL/CTwh8BtQNq0nu/l65gPvwRfCXyOA1//kd5SsoLfD8556vawgDXPVavVC5MkuaToHJJmq9VqF8VxPNd9MCUdgTiOL67VahcVnUO9qam/1W15X6uZwtVt+f3OTnsYSZJcUq1WLyw6hwphAasNjreh3pnArwM/BzzzMM+bJCtkHe4X3FeAj5AVwSaPM1enOxX4OPC6p9z/PeBbZMXAXTQKWyeQTT/7TODFzL6kchPZFLWPtS9y2y0Ddubfn46zVs47tVptHDhhYmLilPXr148VnUdSZnh4uO+0007bA5R27969+Pzzz99bdCZJmS1btpywaNGix4Gpu+++e+EVV1wxVXQm9YYAA8CVwJuAs/O79wN/B/xplF0losMYGRlZUqlUHgX2Dg0NzYeTM3SghTRmoDwJcKb1Fug7zuXvI5sm9W3A+cAPAy8HVgPPolEg63/KchPAKFmT9i3AF4B7jzNLtzgF+E9gRf7vfycrZn2O7JLMI3EaWU+yXyI7A+sy4A7gZXR3EUvz24lAVKlUBgALWFKHWL58+YI0TcsA5XK5DFjAkjpEvk32AX1r1qzpI+shKx2zkH3Qfg1wNY1+VruAm4GPRPCdgqJ1nXyftkTvtX6RCnO8BawZAfhSfptRITtDaxHZGURTwBNkBZb782Xmo1vIilePkZ25tvkY1vEwWaP7j5EVrz5B1vz+FuDyVoSUCjAF9JXLZXe+pQ4yNjY2XalUAhANDAy4fUodZGBgYCqEABDGxsami86j7hWy9i/XAT9Lo5XLPcCNwEcj2F1Utm5VLpen9u3bBxaWJXWp55M1wJ8C1rdwvec3rfd5LVzvXLIH1jwXx/H1SZLcUHQOSbPFcfyOJEneVXQOSbMlSfKuJEneXnQOdacAFwfYFGCqqb/VFvtbtUaSJDfEcXx90TlUCHtgqev9Atl/4H9uw7o35+v++Tasey5YwJIkSZLaLEBfgCsD3NlUtNqfzzC4ruh8Uo+wgNUGrbqEUEdmptH9tjasexvwI2S9xyRJkiTpSQFOBq4FrqJxXLIH+Cvgpgi+XVQ2SToSFrDm1iP51zPbsO6ZdR5pI3hJkiRJPS7Ac4HfIJsAalF+93eBDwB/HcHjRWWTJHWudWSnED5OY1aPVng22acnAVjTwvXOJS8hnOeSJCmPjo4OFJ1D0mz1er1Sr9crReeQNJvbpw4lwPkH6W91R4DLA5SLzjcfjI6ODiRJ4s96fvISwjawMd/cuhMYIfvk4/O05nK/ZwOfI5ue9T+BrS1YpzTnQgjV8fHxUXfCpc4SQojSNL07TdPtw8PDnrktdZDh4eG+NE23p2l6VwghKjqPitfU32qEbIb4S4GI7HjhwgheFsE/RLCv0KDzQL1er4yPj4+GEL5edBapV7gjOvd+EbgDWEvWt+om4BPAt45yPS8mawr/FrKpbh/P/y11q5VAlKbpUmBn0WEkZbZv314mm0WXRYsWLQTGik0kaUa+TS6HJ7fViWITqSghO8Pjl8mODV6Q3/0E8JfAhyLYXlS2+Srfpz0DOL3oLFKvsIA1974BvArYCDwHeHt+GyU7e6oO3A/sItsJCcAAsISs2eKLyS4TfH7TOr8N/CRHXwSTJEmS1KVCdjXGb5J9SL44v/v7wAeBj0bwUEHRJKnlLGAV4w5gNXAN2ackzyArSD3/cAsdxAPAnwIfBna3MqBUgK8Cp05MTDxadBBJDStWrNiXJEkMlNetW+ffGqmDrFu3bneSJNuAiRUrVnhJ2DwS4GXAW4HXA/353QnwR8Dfe4lg8SYmJh6tVCo7aEzkJamD2E/r2PQBFwB/APwvICb7JZfSaPqWks0uWAX+Efh94OX01s/cJu6SJEnSIQRYkDdgv72pKft03qj9gqLzSTqATdw73CfJLo9bX3SQHrIgv80HFrAkSZKkpwhwYoBrA9SbCld7A9wcsqs6JHUeC1gdbhvZm/PsooOoK1nAkiRJknIBzgzw3gAPNRWuHg7wzmBjcKnTWcDqcLvI3pxeuqxNc8cCliRJkua9AIMBbg0w0VS4uivAlQEqReeTdEQsYHW4/dgscC48j2w2wl5jAWueq9Vq74/j+JYQQlR0FkkHiuP4xjiONxSdQ9JscRxviOP4xqJz6PgEiAJc9pT+ViHAbfn9niTQZUIIURzHt8Rx/L6is6gQFrDaoJUHiruAJWQ9m6ZbuF4dKAB30nu9xpYBO/PvTwceLDCLClCr1aaA0uTk5LK1a9c65bPUIZIkKYcQJgD6+/sXr1q1ypkIpQ5Rr9cXp2k6BhBFUWVwcNAPk7tMgBOAq4A3AS/O754E/h64MYKtRWXT8alWq8tKpdJOYHpoaGi+9DVWw0JgPP/+JGBPgVl6Rl8L17WTrIC1HLi3heuVND9EAP39/X7CKHWQSqUSpWkKwPj4uNun1EHGxsaiSiW7oqxSqXgGcxcJcBrwa8AbaVx98CjwIeAjETxQVDa1RqlUmtkm3TalFmllASsm+9TgImDjcawnbUmaznVxC9ax6DDr+WIL1i8V4THgpCiK/HRC6iBbt27df9ZZZ40DC5YsWdLrf6OlrrJkyZI0zSrM+7du3bq/6Dx6egFeAvwWcAWNflbfAj4AfDJqnLGhLhdF0Z4Qwj58T6WO9CYa13gez63XteJn1Is/P3tgzXNJkpxTrVbPKzqHpNniOF6XJMm5ReeQNFuSJOdWq9W1RefQ4eV9rG4LMN3U3+p2+1v1tmq1el6SJOcUnUOFsAdWG7TydMZnAt8l64F1PHr9FMuZItMe4OFjWP65ZM3y7z/E4887hnV2AntgSZIkqWcE6Ad+BrgOmCli7Af+DrgpyvraSupN9sBqg1ZeQng/8EKyX9Q6tOvIThFeAFwPfOoolw9Ajd5r4i5JkiR1vQCnAG8BrgbOyO/eBdwM3BzBaFHZJKmbtbKABXBPi9fXi/6UrMn9J8g+fVkL/C7ZpzHdpgKc2aJ1nQqwfPly3vzmNz/31a9+9fj69eufaH5CPhXtmVEUlffv37/7YDPVJUlyyvT09NJSqbT/rrvuuu+KK66Yan68Xq9X9u7deybAvn37HnAMx3AMx3AMx3AMx3AMx2jFGAFWTp944m+HvXsvj0I4Mb/7XuBPgL+O4PF6vV6J9+59QSe/DsdwDMc4/jG+/OUvP/93fud3ePDBB9m3zwliW8XrrYvxaeA8YAfwNuD/Ai8qNNHRK5E17t/RottXADZv3syll176lXK5XB8ZGTmxecAkSd5TKpW+G0XRjv7+/geSJPmRpzz+0hDCA1EU7Qgh3LNq1ao/b348hFCamJiIoyjaEUXRDsforDEqlco9SZL8WLe/DsdwjF4do6+vb2cvvA7HcIweHGNnj7yOrh0jwMUBNgF3lZ544heiEE58YvVq7v/d3/1X4AVRdrng453+Ohyj9WNs27btR9I0rXf763CMox9jzZo1tc2bN/PpT38atU6rz8DSkZu5DHAD8HNAFXgHcCMwXWCuIxXIeng9o0XrKwFLHn/8cRYtWrQriqKHTz311AN+DiGEsSiKHsv/uX96enrvU9YxkWcaAIiiaNdTM4cQnszsGJ01BnBKCOEzIyMjp6xfv36sW1+HYzhGj45xchRF0f79+5/696nbXodjOEavjUEIoS+KIoDHuvh1dN0Y0dTU/udce+0PBngP2RUVBJje/cpXpo9ceeXknvXr9wPxs97znqljHaNXflbzdYyRkZElk5OTnyc7bnqsW1+HYxzbGCGEZbt371762GOPodbp9Ybp3eIngI+QbUh3AG8Eth7iuYGs4WOv9cCyifs8V6vVpsl+J50xNDS08+meL2lu1Ov1SpqmKcDExMTSmQKzpOKNjIwsqVQquwAGBgYGXvSiF00UnanXBVhK1tvqV2lMnrQH+Cvgg1F2ZYFErVY7HXgACENDQ175NP/YxL0N2nkG1jOBFcAijvxSxS8Dj7QtUef6NHA7WRHrx4ER4Fay3ljfLzCXNJemgL5yuTz1tM+UNGfGxsamK5VKAKKBgQG3T6mDDAwMTIUQAMLY2Fg3nMHftUI2E/hvAL9EdnwD8D3gj4GPRWBxXwcol8tTee8j/3ZKHexnyS6PC8dwu6qAvJ3mCrJmj4GsSvsu4OSmxwNZgavXLKPx/2BZwVlUgDiOr0+S5Iaic0iaLY7jdyRJ8q6ic0iaLUmSdyVJ8vaic/SqAC8PsCnAVICQ3+IAVwYoF51PnS1JkhviOL6+6BwqxEIax7cLC86iQ3gfBxak9gLfJTurKpBNH/udg9weyB//0Jym7VwnAn9AdsphIPtE5/1kpylbwJIkSZLaJMCCvEA10lS0ms4LWRcUnU9SV7CA1eEupPEGfZjGNeEAH8zvv/wQy67OH//fbczXjc4ga/Kekv18prCAJUmSJLVcgIUBrg2wo6lw9USAm0L3zRguqVgWsDrcJ8nenI8c5LH/lz/2nEMse3L++DfbE63rPYvsDKyZM9ksYEmSJEktEODZeZFqrKlwdV+A64P7pZKOjQWsDncP2Ztz1kEeG80fO9R14hEwzfxs4H40KsCPAj9cdJA2sIA1zyVJUh4dHR0oOoek2er1eqVer1eKziFpNrfPYxfgpQE2BphoKlwl+eWD/kx13EZHRweSJLFX2vxkAasNWjmd5+lkb863DvLYzGyHh5odJQD7yaaX1KFNAF8A/k/RQaRWCyFUx8fHR90JlzpLCCFK0/TuNE23Dw8Pt3P2YklHaXh4uC9N0+1pmt4VQoiKztMNAkQBLgvZDOB3kLU46Qc+B7waGIrg1ijb75aOWb1er4yPj4+GEL5edBapV7RyR3QBWYHqYNOEPp5/XQo8fJDHF5H94fAPhTR/rQSiNE2XAjuLDiMps3379jLwfIBFixYtxKnipY6Rb5PL4clt1X3pQwjZJEm/AvwasCK/OwVuBT4cQbWobOpN+T7tGWQnekhqgVYWsMaAU8lOt33qH89R4CXAIPDvB1n2BfnXh1qYR5IkSdI8FuBM4BrgDcAz8rsfAf4M+PPID80kqWu08hLC0fzrCw/y2Jfyr796iGXfkH+9s4V5JHWXrwI7JiYmHi06iKSGFStW7ANiYNu6det2F51HUkO+TW4Dqvm2qlyAwZCdXfVt4Hqy4tU24GrguRG80+KV2infp91Bto8rqcNsIOtl9aaDPPY8YF/++NtpNEVcQFa8mswf+6m2p1Snsom7JEmSjllzf6umpuwhwG35/a388F6SDscm7h3uJWTFqJWHePwPaLyBu8mavY813fdvZLMRan6ygCVJkqSjFuCEAFcFqDYVrSYD3BpgbdH5JM1LFrC6XAS8g6xZYmi6TQEfwxkI5zsLWJIkSTpiAU4L8M4ADzQVrh7N73tm0fkkzWsWsHrEUuAysrO1fpxsZgbJApYkSZKeVoCz8rOr0qbC1XcCXBuy2c0lqWgWsNqglbMQHqldwKYCxu0Ut7d5/Re0ef1SW9RqtfeHEJYODQ1dHUVRKDqPpIY4jm8EyqtXr35z0VkkHSiO4w3AvtWrV19XdJZ2C9mH4G8BfphGP6stwHuBz0cwXVQ26alCCFGtVrsZeGz16tXXF51H6gX2nJp7KY0m9u3Qre/pMhozwZwOPFhgFhWgVqtNAaXJyclla9eufajoPJIySZKUQwgTAP39/YtXrVrlTITd78T86xOFptBxq9fri9M0HQOIoqgyODjYczMRBugHfgb4dWBNfvd+4O+AmyJnMVeHqlary0ql0k5gemhoaEHReTTnFgLj+fcnAXsKzNIzijgD61DeDNwH/FPRQdrsNWSv8WSyacn/vNg4UseIAPr7+50hSOoglUolStMUgPHxcbfP7vUa4Mr86zPy+x4C/i9ZIeAzZJc5qIuMjY1FlUr2uWilUunWDzEPKsApZGdbXU2j5cgY8BHglgi+XVQ26UiUSqWZbbKntk2pSJ1SwDoD+DOyCmWvX7f+H8APAf8PWA3sBT5eaCKpMzwGnBRFkZ9OSB1k69at+88666xxYMGSJUvSovPoqD0H+CTwioM89gzgJ/PbFrKzXO6du2g6XkuWLEnTrMK8f+vWrfuLztMKIZvR/DeAn6UxydN3gQ8Afx3B40Vlk45GFEV7Qgj7aJyFI6nLlYDnkp2RFIAvFxtnTr2G7PTnMeDMgrN0Apu4z3NJkpxTrVbPKzqHpNniOF6XJMm5RefQUTsLuJ/sb+vjwP8EXk52qf7p+fc3ALvz59xPVjxQF0mS5Nxqtbq26BzHK8AFATYFmGpqzP6fAS7PLyOUuk61Wj0vSZJzis6hQtjEvUAfo/HDb+ftZ+bo9XSKPyF73R8tOkgHsIAlSVLrLAa+RfZ39U5g+WGe+xzga/lzv0nvnw2vDhGgL8CVAUaailb7A2wMTkwkqbtZwCrQdbS3cPU94Ko5ezWd4yTgAWAKeH7BWYpmAUuSpNb5Q7K/qaPAaUfw/FOB7fkyf9DGXBIBlga4PsC3mwpXewLcFGBF0fkkqQUsYLXBkTaUW0z26VyrTQO7gO+3Yd3d4vfIdhR/m2wK4PnKWQglSWqNAbK/o4uAHwM2HeFyl+bP3UX2t7jnZrRTsUJ2PPFW4JdonOl3H/Ah4K8ieLiobJLUYs5CqJ50KlkPivnOM7DmuWq1emGSJJcUnUPSbLVa7aI4ji8uOoeO2GtpnH11NCLgnnzZ17Q6lNojjuOLa7XaRUXnOJwA5x2kv1Utv3ywXHQ+qV2SJLmkWq1eWHQOFcIzsNrA6bCL9wjzq3m9dFClUmlzCOELIyMjS4rOIqlheHi4D/jXKIo2b9my5YSi8+iInJV/vf0olwtNy7ykdXHULlu2bDkhiqLNwL9s3LhxQdF5mgVYkDdgv51sX/dSsiLp54ALIxiK4NbIM/3Uo0ZGRpaEEL5QKpU2F51F6hV9RQeQpNyJQFSpVAbIZueU1AGWL1++IE3TMkC5XC4DewuOpKd3Sv71kWNYduYSrlNblEVtlG+TfUDfmjVr+sj6qhYqZGca/DJwDfDC/O69wF8AG6JscgGp5+X7tCWyfVxJLWABS1KnmAL6yuVy4TvfkhrGxsamK5VKAP4/e3cfJ1dZ3///dWZ3Zza3GwHDjZHbQBLcjblDIhDFNoq1YFGLVi3Y1hJva7S0xvaLJWp/X25sS0ObtuA9atVgq5WbFKGufhsXlZUw5xwgsgnLPQZCYGEhs7vZ/fz+uM46E5Jsspsze52ZeT8fj3nM7sycOe/d2bNz5nOu87mC1tZWbZ+1YbRw9fIJLDt6Gr96EdWA1tbWYTMDsL6+vhGfWczNdPmXwPuA0dHUO4D1wL8E6m8qDSafzw8PDg5CBgrLIvUizQLWUSk8x3bc8HURaTBmdmkul5s1b948fWgSyZBly5YNhWF4WS6Xa2lvb+8/8BKSAVFy/TrcKVsHu2+VA16ffB2mHUrS197e3h/H8eeAwWXLlg35yGBwGq5w9XuU+1ndC1wJfCeAAR+5RHybN2/ejjiOrxgZGXnWdxYR2ZulcFky6aklK9TEXUREJB0tuFFYBrx9HMtdkCzzFBqlL2MwCAzOM9hU0ZTdkkbtK019dkVE1MQ949IoYH1s0lNLVqiAJSIikp7/g3tPfYiDGyV/NPBIssynqphLapjBVIPVBvdXFK0GDa43WOQ7n4hIhqiAlXGzDuHyUdwL+41JTy1ZoQKWiIhIeqbiTgM0YAswb4zHzgd+lTz2bkCzTcoeDI4xuMLgyYrC1dMGay2dNiIiIvVGBaw69hrcC3un7yDijQpYDS6O43xvb2+r7xwisreenp5CT09PwXcOGbfjgV7ce+sA8K/AW3AFq/nA7wLXJvcZ8ABwnI+gMnHV3D4NXpWMripVFK62GKwymF6NdYrUk97e3tY4jvMHfqTUIRWwqiAr56c/lFxrp0mkQZlZsb+/v1cfkkWyxcyCUql0X6lU2trZ2am+SLXlQeB0YCOuufYHgZuB+5LLTcCq5L5bksc+tK8nkmzq7OxsLpVKW0ul0r1mFqTxnBX9rW7DTQhwIVAAbgfeCpwawHUBaFIHkTH09PQU+vv7e83sbt9ZROpFVnZEn0+uVZkUaVzzgKBUKs3CzUgqIhmwdevWPHACwIwZM6YBfX4TyTg9iRt19VvAu3GzDB6b3Pcw8GPgW0Cnj3ByaJJtcg78Zlud8Ix/Bq3ARcCHgVcnN+/G/X2sC+CXh5ZWpLEk+7RHAUf6ziJSL7JSwBql4ZUiIiIi6ftRchHZg8HhwJ/hRuiNftB+Fnd66b8FbiSfiIiId1k5hfCY5PoZrylExKc7gW0DAwM7fQcRkbK5c+cO4pqBb1m6dOnzB3q8iEyeZJvcAhSTbfWgGSwwuB54DLgMV7x6CPg4cGwAn1LxSmTikn3abajPs0jd+TCuudkdvoOIN2riLiIiIlJlBisNbjQYrmjM3pX0vcrKwW0RkVqnJu516ljckR8D/tpzFvFHBSwRERGRKjBoMbjI4K6KotVugw0GZ/nOJyJSh1TAqiMBcDLwl7jmogb8GpjpM5R4pQKWiIiISIoMXmaw1uDxisJVv8E6gxN95xMRqWMqYFVBmk3c44N4TA6YijvHvrXi9h24GXKeSzGPiIiIiEjDMTgFuAR4DzA9uflR4O+ArwaaTVRERBqcTeDyCPB53Own0tg0AqvBRVF0VRiG15lZ4DuLiOwpDMOrwzBc7zuHiOwtDMP1YRheDWBw5j76W/3c4ALTbN8ik8rMgjAMrwvD8ErfWcQLjcCqgjQ/KP7+QTzGgEHcUZ+twOMprl9q22xge/L1kbhTS6WBRFE0DOSGhoZmL1my5CnfeUTEieM4b2YDAC0tLTPnz5+vmQhFMqKnp2fmwAsv9LXdfDNzLr30LsyWJHcZcDNwZQCbPEYUaVjFYnF2LpfbDox0dHQ0+c4jk24a0J98PR14wWOWupHmKYTfTfG5RKTxBAAtLS2aAUkkQwqFQlAqlQDo7+/X9imSEQazdi9evHqkrY38Y48BLAFeBL4I/HMAPV4DijS4XC43OlhEZxeIpEQ7oiKSFc8Ag0EQ6OiESIZs3rx5N+4I4q62traS7zwijc7gWIN1wEPN/f1r8489xtARR9hILvfXwPEBrFbxSsS/ZJ92ELePKyIidUQ9sBpcHMeLisXict85RGRvYRgujeP4NN85RBqZwXKDDQaDFf2t4heWL7/s3ltu0funSAYVi8XlcRwv8p1DvFAPrDr3EeB83yHEGxWwRERERCoYNCUN2DdVFK1GkkbtZ/nOJyIi+6UCVh07CvfCqjFs41IBS0RERAQwmGaw2mBrReFql8G1Bgt95xMRkQNSAasO5YDjgO/jXtg7/MYRj1TAEhERkYZmMMdgncGzFYWrHQZrzc3SLCIitUEFLI++SvmXX83Luyfp55HsUQGrwRWLxRVxHJ/jO4eI7C2KorPDMFzpO4dIvTLoMLjeYKCicHWvwUUGhbGWDcNwZRRFZ09SVBEZhziOzykWiyt85xAvVMCqgoOdhbBY1RTwGPAB4FtVXo+IZFQul9toZrd0d3e3+c4iImWdnZ3NwK1BEGzs6uqa4juPSL0wCAzOM9gEhMCFQB64HXgr0B7A9QEM7O85urq6pgRBsBH47w0bNjRNSnAROSjd3d1tZnZLLpfb6DuLSL1oPsjHfQm4rQrrHwGeBR6vwnOLSG2ZCgSFQqEV6PMdRkScOXPmNJVKpTxAPp/PA7s8RxKpaQZTgFW4CYxOTm4eAr4NXB3A5oN9rmSbbAaaFy9e3AwMpxxXRCYo2afN4fZxRSQFB1vAeg6IqxlERBreMNCcz+e18y2SIX19fSOFQsGAoLW1VdunyAQZHAN8DPhjyu0SngGuAa4N4InxPmdra+uwmQFYX1/fSFpZReTQ5fP54cHBQVBhWSQ1B1vAEhGpKjO7NJfLzZo3b94O31lEpGzZsmVDYRhelsvlWtrb2/t95xGpNQavAtYA76Tcz+p+4O+Bfw9gwttVe3t7fxzHnwMGly1bNnTIYUUkNfPmzdsRx/EVIyMjz/rOIiIi6VITdxEREakLFf2tbjMYqWjMvim5/WD70IqISG1SE/caNANYAvw28CbPWSTbVMASae1pegAAIABJREFUERGRmmbQarDK4O6KotVQMsPgUt/5RERk0qiAVSOacTMK3oU739cqLmPRkajGpgKWiIiI1CSDww3WGvy6onD1jMEVBif4ziciIpNOBawa8HLgDvYsWu3GzTY4VgHrm7jz/5dVO6BklgpYDS6O43xvb2+r7xwisreenp5CT09P4cCPFGksBvMNrjXoryhcPWSw2mDmZGTQ9imSXb29va1xHOd95xAvVMCqgjRHPeWA7wHLgeeBvwEWAHng4QMsez/uRX1ninlEpIaYWbG/v79XO+Ei2WJmQalUuq9UKm3t7OzU5C8igMFKgxuBe4BVuP3Yn+H2ZecGsC5ws3hXVWdnZ3OpVNpaKpXuNbOg2usTkYPX09NT6O/v7zWzu31nEakXae6Ivgs4E9gBnAX8ahzL3g6sBVakmEdEass8ICiVSrOA7b7DiIizdevWPMkpUDNmzJgG9PlNJOKHuf3m9wCrcT1ewbXLuAG4JoBNk50p2SbnwG+21YHJziAi+5bs0x4FHOk7i0i9SLOA9d7k+lLGV7yi4vGnpBdHREREROTQGLwMV7RaBRyd3Pwi8EVc4Wqbr2wiIiKNJM1TCEf7V31vAsv2J9eT0itARDLpTmDbwMDATt9BRKRs7ty5g0AIbFm6dOnzvvOITBaD4wzWAQ8Bl+GKV48CHweOCWC17+JVsk1uAYrJtioiGZHs027D7eOKSMYM4hq278uDjN3E/eXJ/c+knElqh5q4i4iIiHcGZxjcaDBc0Zg9NLjIXG9XERGRA1ET94x7CvfizNrHfQ8ydgHrzOT+8Z56KPVDBSwRERHxwqA5KVB1VxStRpJC1lm+84mISM1RASvjfoh7cd61j/seZOwC1ueT+69PP5bUCBWwREREZFIZtBmsMXigonD1osE6g5N95xMRkZqlAlbGvR/34mxh7xfoQfZfwFoAvJDc/45qhZPMUwFLREREJoXBK5MiVV9F4erxpJil/RARETlUKmBlXDMQ4V6g24HDKu57kH0XsFYCjyX33U26TeWltqiA1eCiKLoqDMPrzCzwnUVE9hSG4dVhGK73nUPkUBmcbrDBYLCicHVPcvpgwXe+iQjDcH0Yhlf7ziEiezKzIAzD68IwvNJ3FvFCBawqSPuD4gnAT3GztOzETS/8k+T6aKAdOAo3Y+HbgNOT5Z4FVgBxynmkdswGtidfHwk86TGLeBBF0TCQGxoamr1kyZKnfOcRESeO47yZDQC0tLTMnD9/vmYilJpi0AS8HViN67ua3MzNuFkG/ycYu9VFZvX09MwslUp9AEEQFNrb2zUToUhGFIvF2blcbjsw0tHR0eQ7j0y6aUB/8vV03FlncoiaU36+XmAp8FXgTcAnk8uofRWo7gH+cD/3iUjjCABaWlo0ElMkQwqFQlAqlQDo7+/X9ik1w2AqcDHwUWBucnMJ13P1XwIo+sqWlr6+vqBQcAPHCoWCRjCLZEgulxvdJrVtiqSkGjuiTwDnAG8AvgH8eh+P2QlsBN4LLMGdPigije0ZYDAIAh2dEMmQzZs378YdQdzV1tZW8p1H5EAMXmFwBfAQ8I+44tVO4DPACQF8oB6KVwDJNlkC+pNtVUQyItmnHcTt44pIDWkDTsTtQBzhOYtkk3pgNbg4jhcVi8XlvnOIyN7CMFwax/FpvnOIjMWgw+B6g4GK/lb3Gawyd/pGXYrj+LRisbjEdw4R2VuxWFwex/Ei3znEC/XAEqljKmCJiIjIuBgEBucZbKooWpnBbcntOu1VRER8UAEr42Yw8dFV7bjGmoenF0dqjApYIiIiclAMphisNvhVRdFqKBmBpdFIIiLimwpYGfdJYBjXX2C8vox7YT+WaiKpJSpgiYiIyJgMjjBYa7C9onC1M7ntaN/5REREEipgZdytuBfnvAks+zvJsj9INZHUEhWwGlyxWFwRx/E5vnOIyN6iKDo7DMOVvnNI4zI4NRldVaooXD2YjMKa4TufT2EYroyi6GzfOURkb3Ecn1MsFlf4ziFeqIBVBWn2BTguuf7FBJbdnFyrwZ1Ig8rlchvN7Jbu7u4231lEpKyzs7MZuDUIgo1dXV1TfOeRxlHR3+o2IAYuBApAF/BW4MQA1gXwvM+cPnV1dU0JgmAj8N8bNmxo8p1HRMq6u7vbzOyWXC630XcWkXrRnOJzHZlcPz2BZZ9NrjXyRqRxTQWCQqHQCvT5DiMizpw5c5pKpVIeIJ/P54FdniNJnTNoBS4CPkT54OZu4Fu4gtUvfWXLmmSbbAaaFy9e3Ixr5yEiGZDs0+Zw+7gikoI0C1ijR2VbcDsZ4zEzudabrkjjGgaa8/m8/g+IZEhfX99IoVAwIGhtbdX2KVVjcBiuH+oHgKOSm18AvoQrXD3gK1tWtba2DpsZgPX19Y34ziMiZfl8fnhwcBD0GVckNWkWsJ4EXgkcD9w3zmVPSa63p5hHRGqImV2ay+VmzZs3b4fvLCJStmzZsqEwDC/L5XIt7e3t/b7zSP0xmA98AngPMD25+RHg74GvBPCcr2xZ197e3h/H8eeAwWXLlg35ziMiZfPmzdsRx/EVIyMjzx740SJyMIIUn+s/gLcDfwVcMc5lrwY+DnwH+IMUM0l1fQY4I6XnygOv+8IXvsCSJUv+X0tLy10dHR2XBEHwm6OJYRj+ThAEH00e+xzwyY6Ojm2j98dxfJSZ/SNwuJntDoLgqx0dHd+pXEkcx58xszMAzCzWOrQOrUPr0Dq0Dq3DzzrabrvtqMO/9rVjphaLsyn3Zf156YQTvrT1hhveSKHwslr4ObQOrUPr0Dq0Dq3jpevYvXv3ijvvvPMNd999N+vXr5+OG1EshyjNEVjfwRWw/hL4BvDoQS53CvDB5Ov/TDGPVFcO+HPKR0pTsXz5coDXAa+9++67P0O5PxpBEPwB8JbR783sJmBbxffLgHcljyUIAsP9XY7en4vj+DeZgyB4vdahdWgdWofWoXVoHZO3DoPm7V/4wv+ZefvtZ065777RlY5gdgNwTQCboh/84Fzggiz/HFqH1qF1aB1ah9Yx1jqampqmL1++nIULF7J+/XokHWkWsG4A/gI4DejEjaQ6UJPNZbiRW61ACHw3xTxSXSPACuDklJ5vJvDFSy65hI9+9KMXn3TSSdHixYv3GG6bz+cvGRgYuCn5dujpp5++qfL+9vb2m+M4PtfMpgIMDw93Vd4fBMFIHMcrRkZGTgZoamp6WOvQOrQOrUPr0Dq0juqvw+BlwCrgg0f+0z8dj7tz4MWTT7596o4dlwQ7dvyqFn4OrUPr0Dq0Dq1D6ziYdezcubP9b//2b7/+8MMPI9l1LK5ngeGa1d2CG111BjAPN9pqOfB+4L9wzd4NeCq5XxrXbNzfgqHZKBtSHMf53t7eVt85RGRvPT09hZ6enoLvHFJ7DI4zWGfwnIEll0cN1hi83He+eqDtUyS7ent7W+M4zvvOIV5Mo/z5dprnLDKGVwA/pPxiHejyC8pN3KVxqYDV4KIoui+Koie0Ey6SLWYWRFH0QBRFj3R2dqY5clvqmMFrDW40GK4oXEUGF5nrKyIp6OzsbI6i6JEoiraZWZq9bUXkEPX09BSiKHoiiqJ7fWcRL1TAqoJq7Ig+BrwJOBu4GHg9rqhVaQewCfgKcBPudDQRaWzzgKBUKs1CM5KKZMbWrVvzwAkAM2bMmAb0+U0kWWXQBLwX+BiwtHwzNwFXBm7fT1KUbJNz4Dfb6oDfRCIyKtmnPQo40ncWkXpRzSOpP04uAG3A4bjG3zuTi4iIiIjUOHNHlv8UV7g6Mbl5F/B1YH3g+pyKiIiIHJLJOhWgDx2xFZGx3QkcPjAwoAK3SIbMnTt3MI7jEMgvXbr0ed95JDsMXombwOePcJOxgBtlvx74lwCe9BStYSxduvT5OI63AANz584d9J1HRMoGBgZ2FgqFbcDTvrOIiEi61ANLRESkBhi8xmCDwUBFf6t7k/5W6mMoIiKiHlgidU0FLBERkYwyaDK4wGBTRdHKkkbtK821iRARERFHBSyROqYCloiISMYYTDVYbdBTUbQaNLjeYJHvfCIiIhmlApZIHVMBS0REJCMMXmFwhcGTFYWrpw3WmptVS0RERPZPBSyROqYCVoOLouiqMAyvM7PAdxYR2VMYhleHYbjedw6pPoP2ZHRVZX+rLQarDKb7zid7C8NwfRiGV/vOISJ7MrMgDMPrwjC80ncW8UIFrCrQB0XJitnA9uTrI9HMRQ0niqJhIDc0NDR7yZIlT/nOIyJOHMd5MxsAaGlpmTl//nzNRFhnzO0PngusAc6suOunwJXAzQGM+MgmY+vp6ZlZKpX6AIIgKLS3t2smQpGMKBaLs3O53HZgpKOjo8l3Hpl004D+5OvpwAses9SNZt8BREQSAUBLS4saAYtkSKFQCEqlEgD9/f3aPuuIwRTgQuAjwMLk5t3At4B1AfzSVzY5OH19fUGh4CZ+LBQKOjAtkiG5XG50m9S2KZISFbBEJCueAaYHQaCjEyIZsnnz5t0LFizoB5ra2tpKvvPIoTM4Avgo8CHKp+0/C1wL/FsAD3qKJuPU1tZWKrkK8+7Nmzfv9p1HRMqCIHjBzAYpj8IREZE6oR5YDS6O40XFYnG57xwisrcwDJfGcXya7xxyaAwWJP2tShX9rR5KZhmc4TufTEwcx6cVi8UlvnOIyN6KxeLyOI41Y2tjUg+sKqj2cMapwBm4YemHJ+vbAUS4vgovVnn9UjvUA0tq0dHACbj/df3A/cBOr4lERF7C4DzgY8BvAaOngf4M+L+ov5WIiEg1qAdWDTkeNwx9F+Wq40svu4Av4D78iWgEltSKAHgH8L/AMHv+XxsEbsEV7kVEvDFoMbjIYHPFaKvdBhsMzvKdT0REpM5pBFaNeCfwHOUXaxjYAmzCfeC7D9cgdPT+55JlpLGpgCW14DDgf9jz/1sP0A08xJ7FrOuAgp+YItKoDA4zWGvwREXhqt9gncFJvvOJiIg0CBWwasBbKRen7gH+EDdc7qWmAe/BnUpoyTLnTVJGySYVsBpcsVhcEcfxOb5zjGEGEOL+RvuATwIvf8ljTgHWAQPJ436IJsuQOhBF0dlhGK70nUP2z2CewbUGz1cUrh5J+lu1+c4n1ROG4coois72nUNE9hbH8TnFYnGF7xzihQpYGTcLeAr3An0FyB/EMi3Al5NltqMdrEamAlaDi6KoP4qi4e7u7qz+H/g27u/zEeDUAzx2Ba7IZcDlVc4lUlWdnZ3NURQNRFE01NXVNcV3HtmTwUqDGw2GKwpXvzC4wA5uX0xqWFdX15QoioaiKCpt2LChyXceESnr7u5ui6JoOIoizULYmFTAqoLcgR9y0D6Em5b5Z8D7cb1gDmQI+NNkmdnAqhTziEhtmQrkCoVCq+8g+/Ba4F240aLvAO49wOP/F/d/EODjwLHViyZSXXPmzGnCFUKa8/m8CiIZYNCc9LfqBm4DzsX157sJWBHAawK4ITi4fTGpYck22QwUFi9erBG/IhmS7NPmcPu4IpKCNAtYb02ur2B8s9mMJMsAvC3FPCJSW4YB8vn8sO8g+zBaXP8q8IuDXOa7wO1AK/C+KmQSmRR9fX0juKOHtLa2ZnH7bBgGswzW4HrvfQ1YipsU5xpgXgDnBa7nqDSIim3Skm1VRDKiYp9W750iGbQDt4N7+ASWPSJZ9qlUE0kt0SmEDS4MwzVxHGf1dLsncH+b45256w+T5bpSTyQyicIw/HQcx5/1naNRGRybNGF/ruI0wccM1tjevfikwcRx/Nk4ji/1nUNE9hbH8eVhGK7xnUO80CmEGVfCvTgTmXWrkCxbSjWR1BIVsCSrWin/bc4Y57IdyXJPpB1KROqfwWv30d8qTk4f1CynIiIi2aUCVsY9jHtx5k5g2ZOTZR9KNZHUEhWwJKsOw/1djjD+GQVPSpZ9Lu1QIlKfDJqSBuybKopWI0kha6W5XlciIiKSbSpgZdwNuBfnkxNY9pPJst9ONZHUEhWwJKsCyiNMTxznsr+dLPertEOJSH0xmGaw2mBbReFql8G1Bq/2nU9ERETGRQWsjDsf9+I8w/g+5J2QLGO4WXSkMamA1eDiOM739vZmcQZCcLMKGvCxcS73D8ly16eeSGQS9fT0FHp6enTKWhUYzEn6Wz1bUbjaYbDW4Ejf+ST7tH2KZFdvb29rHMeawbcxqYBVBWnOQvh94MfALOAnwOsPYpkVyWNnAT/CTf8sIg3IzIr9/f29Gd0J35BcfwLXE+tgzAb+NPn6htQTiUwSMwtKpdJ9pVJpa2dn53hPo5X9MHiNuf8t23DF8TbgPtyspXMCWBvAdp8ZJfs6OzubS6XS1lKpdK+Z6fRSkQzp6ekp9Pf395rZ3b6ziNSLtHdE3wX8FNcH68fJ5T+BzZRnKTwCWAS8HXgD7vScrcC7U84iIrVlHhCUSqVZZO9D2xeAS4DjgS8CF+F6Yu1PK/AdXNP3O1BxXmrY1q1b87jR0syYMWMa0Oc3Ue1K+ledC6wBzqy463bgGuDmYOz/LSJ7SLbJOfCbbXXAbyIRGZXs0x6FRtOKpCbtAtaTwGtxH/bOB85OLmP5AfB+XIFLRCSLSsAfAv8DvBeYCXwIeGwfj50HfBVYjjs9+o9wxXsRaVAGU4GLgY/gJq4BGML1/rw6cAf6RERERGQM1TgVYAfwNtyHtw8Bv0VyZKjCY7hTBv8N6KpCBhGpPXcChw8MDOz0HWQ/NuFGin4dOA/XoP0/cadB9wEvB96IG13RjPtfeD5wv4+wImmZO3fuYBzHIZBfunTp877z1BKDY3CnB/4J7n8EuML2NcC1ATzhK5vUh6VLlz4fx/EWYGDu3LmDvvOISNnAwMDOQqGwDXjadxYRGZ82XGP3k5KvRV5KTdylViyi3NR9f5fvk5xyJSKNx+BVBtcblCoas/cmswzO8J1PREREqk5N3EXqmApYUmteA6wFvgXchhuZtQZo95hJRDwxCAzOM9hUUbQyg58mt6c5cY6IiIhkmwpYInVMBSwREak5Bq0GqwyKFUWroWQE1lLf+URERMQLFbBE6pgKWCIiUjMMDjdYa/DrisLVMwZXmE4hFhERaXQqYFVBNZq4V5qN24mbARRw00cfiKabF2lAURRdZWazOjo6PhAEgWbtE8mQMAyvBvILFy78iO8svhksAP4KeCdu3wbgEeDvga8E8JyvbNKYwjBcDwwuXLjwE76ziEiZmQVRFF0LPLNw4cI1vvOI1IODKSiN1xHAp4ALgGMnsHw1Mkn2zQa2J18fCTzpMYt4EEXRMJAbGhqavWTJkqd85xERJ47jvJkNALS0tMycP39+Q85EaLASWA28hXI/q5/jClffD2DIVzZpXD09PTNLpVIfQBAEhfb2ds1EKJIRxWJxdi6X2w6MdHR0NPnOI5NuGtCffD0deMFjlrqR9gispcCtwOEVt43gpozeBQynvD4RqR8BQEtLixodi2RIoVAISqUSAP39/Q21fRq0AO8GPg4sTm4eBm4Arglgk69sIgB9fX1BoeAGAhYKBR0EFsmQXC43uk1q2xRJSZoFrJnAzbji1dPA1cAPgF8BOhokIgfyDDA9CAIdnRDJkM2bN+9esGBBP9DU1tZW8p1nMhgcBnwMWAUcndz8IvBFXOFqm69sIpXa2tpKJVdh3r158+bdvvOISFkQBC+Y2SDlUTgikiF/hWtQ9ggTO3VQGpuauDe4OI4XFYvF5b5ziMjewjBcGsfxab5zVJvBKQbXGjxf0Zj9UYPVBm2+84nsSxzHpxWLxSW+c4jI3orF4vI4jhf5ziFeqIl7xv0U9+Jc7DuI1CQVsERExAuDMw1uNBiuKFyFBhcZ5H3nExERkZqjAlbGPYl7cU70HURqkgpYIiIyaQyakwJVd0XRaiQpZJ3lO5+IiIjUNBWwMm4QvTgycSpgiYhI1RnMMlhj8EBF4epFg3UGp/jOJyIiInVBBayM2457cWb6DiI1SQWsBlcsFlfEcXyO7xwisrcois4Ow3Cl7xyHwuDYpEjVV1G4espgrel9R2pYGIYroyg623cOEdlbHMfnFIvFFb5ziBcqYFVBmtNhP55cvzLF5xSRBpHL5Taa2S3d3d1qlCySIZ2dnc3ArUEQbOzq6priO894GSw3uBF4ADez4EzgXuB9wJwA1gauDYJIzenq6poSBMFG4L83bNjQ5DuPiJR1d3e3mdktuVxuo+8sIvUizQLWT5PrxSk+p4g0jqlArlAotPoOIiJlc+bMacI1Mm/O5/M10dDcoMngAoNNwB3Aubh9npuANwLtAVwfwIDPnCKHKtkmm4HC4sWLm33nEZGyZJ82h9vHFZEUHOwbXRPQcoDH/BD4CG7H8LuHkKl0CMuKSO0axn1AHvYdRETK+vr6RgqFggFBa2trprdPc0P0/xT4M+Ck5OYScD3wrwHc7SubSDW0trYOmxmA9fX1jfjOIyJl+Xx+eHBwENw+rohMovdRPn+z2hdpTOqB1eDCMFwTx/HlvnOIyN7CMPx0HMef9Z1jfwzmJP2tnq3ob/V00t/qKN/5RKopjuPPxnF8qe8cIrK3OI4vD8Nwje8c4oV6YHn0alTAkupSAUtERMbFoMPgeoOBisLVfQarDKb7ziciIiINSwWsKjjYUwgj4ORqBhERERE5EIMA19NqDXBmxV23A9cANwegU6lERERERKQqNAJLRET2y2CKwWqD+ytGWw0lI7CW+M4nIiIiUkEjsETqmApYDS6O43xvb69mIBTJoJ6enkJPT0/Bx7oNjjG4wmB7ReFqZ3Lb8T4yiWSJz+1TRMbW29vbGsdxTczgK6lTAasKcr4DiIgAmFmxv7+/VzvhItliZkGpVLqvVCpt7ezsPNjWA4e+XniVudkDH8CdLjgbeAj4OHBcAJ8K4MHJyiOSRZ2dnc2lUmlrqVS618wC33lEpKynp6fQ39/fa2aaAVckJZO2I3oQPgI8BnzfdxAPpgGvB9pxvcbmJLdNw/X66AdeAB4FenA9yX4CvOgjrEiVzAOCUqk0C9juO4yIOFu3bs0DJwDMmDFjGtBXrXVV9Lf6GPDbuO8B7gAuR/2tRPaQbJNz4Dfb6oDfRCIyKtmnPQo40ncWkXqRlQLWUcA/4wo1MzxnmUxvAC4BVgLjHXUyANwGfB74fynnEhERmTQGrcBFwIdxMx8DDAP/DqwL4Je+somIiIhINvguYOWAVwLrku9jj1km0+HA14DffcntjwL3A08AzwIl3DmzU4A24GjgFNzvrIA7Sn0ucCPwPuCZScguUi13AocPDAzs9B1ERMrmzp07GMdxCOSXLl36fJrPbe798M+AD1I+Qv0C8CVc4eqBNNcnUm+WLl36fBzHW4CBuXPnDvrOIyJlAwMDOwuFwjbgad9ZRBrNVyk3IKvm5d2T9PP4dBjuNMDRn7kT+CPgiHE8xxHJMj+peJ77gZelmHOyqYm7iEiDMJifzB64q6Ix+8PJLIMzfecTEREROURq4u7RJ6hu4epRYNWk/TR+fRf3M+8EfieF5zsPN1rLgBtSeD5fVMASEalzBisNbjQYrihc/dzgAgPN0iQiIiL1QgWsKjjY2UpmAsdWYf0juOLL41V47iw6AdiG+yM+HehO6XnPADYlz3sStTkr02zKjbuPBJ70mEVERFJi0IIbYb0aWFK+mZuBKwP3/iUiIiJST6bhenwDTMe1SBCpKe/D7bT/oArPvTF57gur8NyTQSOwRETqiMHLDNYaPF4x2uoFg3UGc33nExEREakijcCqAt9N3BvN0cn1lio89xbgzcAxVXhukaqLougqM5vV0dHxgSAIzHceESkLw/BqIL9w4cKPHOixBsfjWg/8MeWZhR8HrgG+HMBT1cop0ojCMFwPDC5cuPATvrOISJmZBVEUXQs8s3DhwjW+84jUg5zvAA1mdAaKV1ThuUefc0cVnltkMlwSBMHFmzdvHs+EBiJSZXEc54Mg+HgQBB/esmXLjP09zuAMc7PibgM+hitexbjRxycE7nRBFa9EUtTT0zMzCIIPB0Hw8TiO1UdOJEPCMHx5EAQXB0HwF76ziNSLao/AmgGcjJsdrwn4YZXXl3V3JdfnAUcBv07peV8J/O5L1iFSawKAlpYWFdZFMqRQKASlUgmA/v7+PbZPc/sR78EVrJaWb+Ym1N9KpOr6+vqCQqEAuG3VcxwRqZDL5Ua3SW2bIimpxgfFZuADuELKs8AvgduBWz1kyZpf4hq3z8A1r03jdL9X4j4oTAV+BmxO4TlFfHgGGAyCQA0Oy5pxBwBafQeRxrV58+bduCaku9ra2koABm0Ga4D7ga/hile7gOuARQGcp+KVSPUl22QJ6E+2VRHJiGSfdhC3jysiGfRy4A7KzcoM2I2bbXCsnjbfxO0cL6t2wAx4Fe5nNeA54HPAKRN4nlOA/w94Pnmuvgk+T1aoiXuDi+N4UbFYXO47RwbMAj4NROz5v/QJYD0wz180aVRhGC6N4/g0g1cmTdj7Khqz70iatR/pO6dII4rj+LRisbjkwI8UkclWLBaXx3G8yHcO8UJN3DMuhzvaOlqY+TQwP7n9QcYuYF2W3H9VdSNmxunAQ+z54fQB4D+AK3BTjb8P+APgXcnXHwMuTx7zwEuW3QYsntSfIH0qYInAu3F97GyMyyDweTQJh0wig9MNNhgMVhSu7jW4yKDgO5+IiIhIxqiAlXHvxr04T7H3CIEHGbuAdWZy/x1VSZZNbcClwJOM/WF1rMsTuFM49ttUt4aogCWN7tOUt4EIV7g+KrlvBvA7wA8qHnMboIa9UjUGTQYXGGyqKFqZwY0GK60xTv0XERERmQgVsDLuJtyL84F93PcgYxewjkjuf3qMx9SrZuAs4DO40VUh7vdQovwHX8KNyigC38WNWHst9fXhQQUsaWTvoHyq9ZW4SS/25/eBF5LHrq9+NGk0BlMNVhtsrShaDRpcb7U/2ldERERkMqgp12bHAAAgAElEQVSAlXG/Zv/FhwcZu4DVmtw/lH6smtbE2B9k64kKWA2uWCyuiOP4HN85PGgFHsb97f/DQS7zVlzBaxh4dZVySYMxeIXBFQZPVRSunjZY++D69W8Pw3Cl74wisrcwDFdGUXS27xwisrc4js8pFosrfOcQL1TAyrhBXMP2fXmQsQtYL0/u1wwNjUsFrAYXRVF/FEXD3d3dbb6zTLILcX/3vYyvl9DXk+W+Uo1Q0jgMOpLRVQMVhastBqsMpnd2djZHUTQQRdFQV1fXFN95RaSsq6trShRFQ1EUlTZs2NAoBz1FakJ3d3dbFEXDURT1+84iXqiAVQVpnoLWhxstNGsCy47OnvdkenFEpMZMBXKFQqHVd5BJdl5y/RVgYBzL/WtyfS4QpJpI6p5BYHCeuclXQlwhNQ/8FDfC79QArgugf86cOU3Jfc35fF5910QyJNkmm4HC4sWLNbmHSIYk+7Q53D6uiKQgzQLW5uR6IqcAnZ9c/zylLCJSe4YB8vn8sO8gk2y0gN81zuV+gfudHZFcRA7IYIq5mW634CYFOBM3evrrwLIAzgrgxsCdogpAX1/faH82WltbG237FMm0im3Skm1VRDKiYp9W750iGfR+3A7uFvYeIvcg+z+FcAHlhsTvqFY4yTydQtjgwjBcE8fx5b5zePAQ7u9+6QSW3Zks+9KZX0X2YHCEwVqD7RWnCT6T9Lw64UDLh2H46TiOPzsZWUVkfOI4/mwcx5f6ziEie4vj+PIwDNf4ziFe6BTCjGvGTf1uwO3AYRX3Pci+C1grgceS++6mvmbVO1iHAafiPoAeyvDSZxm7z1jWqYAljeqXuL/7N49zuQLuiJ4BL0s7lNQHg1OT/lalisLVQ8ksgzN95xMRERGpUypg1YATgMdxL9LTuOng31Jx26uA3wbWAD+j/II+A7R7yOtLDvggEFP+HRiu/81G4I0TeE4VsERq01dxf/dXjHO5NybLPZJ2IKltFf2tbjMYqShc3ZHc3ogHi0REREQmkwpYNeJo4Fb2LMyMdYmBRV6S+tEC3MKBfy/fY3yjKlTAEqlN5+P+7p8ExjMD4+j/kX+qRiipPQatycyBmyuKVrsNNhic5TufiIiISANRAavGnI1rCvsEexdnnsZ9+HoPbmajRnI55d/DfwJvBxYCHcnX3wSGkvvv5+B726iAJTUtjuN8b29vo81ACG721ntwf/vfOMhl/pjyqM0D9i+S+mZwWNLf6omKwlW/wTqDk9JYR09PT6Gnp6eQxnOJSLq0fYpkV29vb2scx432eVccFbBqWBtwIjCXxp4tawbwPO6PeO0Yj+sA7qN8euWZB/HcKmBJTYui6L4oip5o0J3w1wODuL//69l/b6Ic8HFc4cqAT09KOskkg/kG1xo8X1G4eiTpbzWe0Xxjr8csiKLogSiKHuns7GxO63lF5NB1dnY2R1H0SBRF28ws8J1HRMp6enoKURQ9EUXRvb6ziBcqYFVBmjuiOSqm3X6JvuTS6M4ApgMPA58b43ERcDrwHVxj51uBc4EfVznfeC0DlqT0XDMAfv/3f59Vq1ZdeMwxx/y8vb19U+UD4jg+amRk5M1APpfLPVcoFL538sknD4zev2HDhqZTTz31/JGRkcODINjd1NT0P6eeeupDlc8RRdEyM1sCkMvl7tU6srOOIAjmmVlQKpVmAdtr9eeY4Do23XXXXddu27btQ7t3777wzjvv/N1HH330n3Hb/q+BGeeff/57Zs6c+d4XX3zxFQ888AB33XXXl4G/zdjPoXVMwjrMTYCyGtdjMgcw3Nb2SNPQ0FpefPEbgSuGpvZz3HPPPeeSjPQ77LDDDsOd7loTvyutQ+uo93UUCoWZwByAe+655+J777331lr8ObQOraMe15Hs0x4FHBmG4apa/Tm0jomt47nnnnvt1VdfzX333cc999yDpCPNAtY3gFcD7wO6U3zeejJ6OuCtuNnDxvIc8FZcEettuFMuzwd+WLV045PDFdRSrSZfdtllAH9nZrs3b9788sWLFz87ep+ZXRUEwYXJ15RKpfcDXx69f8GCBb9jZt8NAncAcmRkZCPuA97o8rk4jn8cBMG05HutI1vr4KVq9OeY0DoWLFjw0dHvN23adNiHPvShvwH+BiCXy/HXf/3XTJkyZfT5RoaHhy9ZvHixjWcd9fK7asR1sHv37sEjjvizlh07Lmb0wEEQ8PzrXsdTf/InvLhkySsBOjo6BtP+OYALR78PguACYH2Wf1dah9bRSOuYOnXqGysee22t/hxah9ZRr+tIBEEQXFvLP4fWMf51zJw5c9pll13Grl27eM1rXoOkI80C1hJcgWZ7is9Zb2Yk10+O+aiyIeCdwLeBdwA/SK5vTj/auI0An8fNLJmGAvDWH/7wh7zuda/7QWtra8+iRYv2GLUXBME3zawV3D+b4eHhH+0RaGTkF7lc7utAa/L9DS9ZfiSKosrMD2sdmVrHCuCFgYGBnTX+cxzSOswseOSRR54AjsNNcDFjZGRk13e/+93h008/fedxxx33YKFQ2Jr1n0PrSGcdLTt2LD7ii188cdbNNx/X9Oyz/5rcvQv4wiOf+Uyx721ve/Mk/RxvAgLcTLmZ/F1pHVpHI66jubn5J2bWBxhwW63+HFqH1lGP6xgYGNhZKBS2mVlrEARdtfpzaB0TW8fu3btf/aMf/ehtW7duRbJptAeTpufev9W439E/j3O5ZlzDd8OdGnLxPh6jHlgiInXC4LikCftzFf2tHjNYY/ofKSIiIpJ100A9sLJsN0nfDdmvlbg/4LsnsGwLbobC0Y3gn4EpFfergCUiUuMMzjC40WC4onAVG1xkbqSqiIiIiGSfClgZpxFYB1YAduJ+T2dN8DnWUt4QHgA+CJyCa5KvApaISI0xaEoKVN0VRauRpJC10typeyIiIiJSO1TAyrhf4V6cY30HybjPUB6FNdGj6ecDj1PeICovtUoFLBFpKAbTDFYbbKsoXO0yuNbcpCgiIiIiUptUwMq4G3AvzkW4hmYTvdS7qcB9uN/VJw/heWYAnwJ6UQFL6kAURVeFYXidmWm0idQ1g1cm/a36KgpXOwzWGhzpO9++hGF4dRiG6w/8SBGZbGEYrg/D8GrfOURkT2YWhGF4XRiGV/rOIl6ogFUFaX5Q/DAVU2sfgkb48Hoi8HvAOtxsfofqZOB4YDrwvRSez4fZlGewPJKDn6lR6kQURcNAbmhoaPaSJUue8p1HJG0GpwOX4EbRtiQ3bwGuBr4ZwAu+so0ljuO8mQ0AtLS0zJw/f/7zvjOJiNPT0zOzVCr1AQRBUGhvb1c/WpGMKBaLs3O53HZgpKOjo8l3Hpl004D+5OvpZHQ/r9Y0p/hc3wOuAbRxHtgDuA8saelJLiK1LABoaWlRHz2pG+beE9+Om4X2zIq7bse9Z94cpHMgo2oKhUJQKpUA6O/v1/YpkiF9fX1BoeA6UhQKhUY4CCxSM3K53Og2qW1TJCVpFrCeAE6ifFRZRGQ8ngGmB0GgoxNS88ydLn4x8FFgbnLzEPBt4B8DuMtXtvHavHnz7gULFvQDTW1tbSXfeUSkrK2trVRyFebdmzdv3u07j4iUBUHwgpkNUh6FIyIidUI9sBpcHMeLisXict85RA6FwSsMrjB4sqK/1c6kv9XRvvNNVBiGS+M4Ps13DhHZWxzHpxWLxSW+c4jI3orF4vI4jhf5ziFeqAeWSB1TAUtEapZBu8H1BgMVhasHk1kGZ/jOJyIiIiKTSgUskTqmApaI1BSDwOA8g00VRSsz+Glyu/pFiYiIiDQmFbBE6pgKWCJSEwymJCOrflVRtBpKRmAt9Z1P6sLLcDMWzwGmeM4iIiIi46cCVhWk2cT9pY7GNa6dwcEfhb4DeLpqiUQks4rF4oqmpqap7e3tt/rOIrIvBkfgmrJ/iHKhvQ/4N+C6wM0wW5eiKDrbzJoXLlx4u+8sdWwGbrbK9wLzK24fBG4D/gW4xUMuybgwDFcGQbC7o6Pjx76ziMie4jg+Z3h4+MVXv/rV/+s7i4js23uAiHK1cTyXVR7ySjZoBFaDi6KoP4qi4e7u7jbfWUQqGZyajK4qVYy4ejgZhTXTd75q6+zsbI6iaCCKoqGuri6NBqqO3wW2s+c+0bPArpfcthF4uaeMkkFdXV1ToigaiqKotGHDhibfeUSkrLu7uy2KouEoijQLYWPSCKwqSLs/x5XAN4H25PsS8CiwM/m+D3hoH5ftyf0dKecRkdoxFcgVCoVW30FEAJI+VrfhDspcCBSAnwPvBE4KYF0Az/nMOBnmzJnTBOSB5nw+n/edpw5dDPwAd/DmV8D7gFnJZQrwKuDvcPtUbwa6gVd4SSqZk2yTzUBh8eLF1TyzQkTGKdmnzeH2cUUkBWm+0a0APpl8/a/AVcCDyffXAH+G20m7YR/LLgSKwLwU82TVpio//1lVfn6RahnGfUAe9h1EGpdBC/Bu4BPA6LTXw7j3rmuC6v8Pz5y+vr6RQqFgQNDa2qrtM12vBdbjPuD8E/BD4Dzgz4FjcEWrbbhC6ltwpxHOB/4TOAP3tykNrLW1ddjMAKyvr2/Edx4RKcvn88ODg4Og/9UimfTvuOFx/7aP+/43ue/Y/Sz7suT+X1UnWqaUmNjplQd7qVU6hbDBhWG4Jo7jy33nkMZkcJjBWoMnKk4TfMFgnbl+jg0tDMNPx3H8Wd856kwA/Az3vncj5X2l/V124YpcO5Pv/3jyI0sWxXH82TiOL/WdQ0T2Fsfx5WEYrvGdQ7zQKYRVEKT4XA/hClSnAve95L5e4Hjc6ReD+8kxDDwDHJ5ipix6HfB9XNEuxI1WS9O+Coi1YDblU0mPBJ70mEVEGoS5kb9/juvfOD25+TFcoeBLAezwlU3q3um4AtaLuINbhyVffxH4L+Bh3H7TElyx6g3Jcvfi9rXuBhZPbmQRERE5SNOA0f5n04EXPGaRfSgBI8C+Gkg+gqs8jnXK4iAwUIVcWdSBa85quF4XohFYIjKJDFYa3GgwXDHiKjS4yFy/J5Fq+xzuPe/F5LqLsXtbXYDbETbcQT8DXlnljCIiIjIxGoGVcUPA7v3cdw/uhTtiP/fPSO4vVSFXVr0J9/vqQ81YQQUsEakyg+akQNVdUbQaSQpZ6h8ok+1blN/37uTgmvz+Fu6A3+hybxj74SIiIuKJClgZtwP34hT2cd9NyX1n72fZVyf3P1KVZNn1D7if+8u+g2SAClgNLo7jfG9vr2YglNQZzDJYY9BbUbh6MelvdYrvfLWgp6en0NPTs6/3d5m4n+De83YDC8ax3Ocpv1++rQq5pMZo+xTJrt7e3tY4jjWyuzGpgFUFuRSfqze5Pmkf9/00uf7gfpb9k+T6lynmqQV/g+v79D7gBM9ZRLwys2J/f3+vdsIlLQbHGazD9RK6AteLcQfwGeD4AFYHcL/HiDXBzIJSqXRfqVTa2tnZmebsxY1udGf2fvbuHTqWdRVfN9LIddmHzs7O5lKptLVUKt1rZmn2thWRQ9TT01Po7+/vNbO7fWcRqRdpFrB+kVyfvY/7voU7xfBdwKWUR2k14YpXH654XCPpx02JncP9bkQa2TzgqFKpNMt3EKltBq81N6vbA8DHcKep34s7WDAngLWBJoo4aFu3bs3jDrLMmTFjho4gpmd05uDx7otVFhFrefZhSUGyTc4BTky2VRHJiGSf9ihgvu8sIvUizQLWeuD9wP/s474HgcuTrz+HOwJ+P24q6C/hdsZ+BGxIMU+tWA+cgRsdICIiE2DQZHCBwSZcM+xzce9xNwFvBDoCuD5onMlCJPtGZyY6BVg0juX+suLrKenFEREREcm2NAtY9+J6Of1qP/evxZ0yN4CbRvJkYCZu5sKvAb9HYx5JfBq4w3cIkQy4E9g2MDCw03cQqR0G0wxW4w6KbADOxI34/TqwOIDzArg9cO81MgFz584dBEJgy9KlS5/3naeOPJ5cB8A3gYMZffpW9mzHoP+XDS7ZJrcAxWRbFZGMSPZpt+H2cUWkRs0CzsOdOvg23LBKETVxF5GDZjAnacL+bEVj9qcN1preV6Q2/A3uPe/F5DrEnUq9LwGwCncQ0IBhXFH26OrHFBERkQlQE3eROqYClogckMFrDDYYDFQUrrYYrDI3ulekVizGveftAp5Kvh4ErgfeAZwGnIXr43YX5ffIe5PrX+z9lCIiIpIRKmCJ1DEVsERknwwCg/MMNlUUrczgtuT2NE+HF5lMnbj3vdtwEw/YGJc+4Crg+eT7P/CQV0RERA6OClhVUO3psGcArwc6gCNwHzJ24s7V/ynl/g8iIiJ7MJgKXAx8FJib3LwbN2PtugB+6SubSEr+HDfpwEpcH9GzcG0WTgeOwZ0yuBW4HXeK4fW4kYY/Br4z+XFFRERE6s9xwBcp92rY12UE+G/cDHwiGoHV4KIouioMw+vMLPCdRfwyOMbgCoMnK0ZbPZPcdrzvfI0oDMOrwzBc7ztHnfoD3KmDhmv2uxr3d57DzTJ4JnAtUEoecx/uoKAIAGEYrg/D8GrfOURkT2YWhGF4XRiGV/rOIl5oBFYVVOOD4rm42Z9GZ9PZjdvZegrXdPRwXJPS0RdxBPgcbpZCaVyzge3J10cCT3rMIh5EUTQM5IaGhmYvWbLkKd95ZPIZtAOfBN4JFJKbHwKuBr4cuFOnZJLFcZw3swGAlpaWmfPnz9frkL4VuBmZTxjjMQZ8GzcL4XOTEUqyr6enZ2apVOoDCIKg0N7erpkIRTKiWCzOzuVy24GRjo6OJt95ZNJNA/qTr6cDL3jMUjfS7huyAvgPXPGqB7gIaAMWAr8NvAlYmtz2BmBjkuEy4C9SziIitSUAaGlpUT+jBlLZ3wqIgAtxxas7gLcCJwbudEEVTTwpFAq/OdjV39+v7bM6/hdYgDtd9g5csWrUc8A3cacXvgcVr6RCX1/fb7bPym1VRPzL5XKj26S2TZGUpLkjmseNvMoDPwSWJN+/uI/HDuP6N7wF+D/JbZ9Dp4aINLJngMEgCHR0ogEYtBqsAu4GfoA7TWoY976xLIAzArgxcKN0xaPNmzfvxh1B3NXW1lbynaeODQDrca0VmoDDcEds24A/xPXKEtlDsk2WgP5kWxWRjEj2aQdx+7gikjF/ijti+Biueft43JQs+3/TDiU1Qz2wGlwcx4uKxeJy3zmkugwON1hr8OuK/lb9BusMTvSdT/YtDMOlcRyf5juHiOwtjuPTisXiEt85RGRvxWJxeRzHi3znEC/UAyvj/gv34vz5BJZ9c7Ls3akmklqiApZIHTNYYHC9QamicPWIwWpzI0xEREREROqFClgZ9zDuxTl1AsuOFi92pppIaokKWCJ1yGClwY0GwxWFq58bXGDulHMRERERkXqjAlbGjU7vPH0CyxaSZdVbo3GpgCVSJwxaDC4yuKuiaDWSFLLO8p1PRERERKTKVMDKuEHci1M40AP34dhk2UdTTSS1RAWsBlcsFlfEcXyO7xwycQaHJf2tnqgoXL2Q9Lea6zufTFwURWeHYbjSdw4R2VsYhiujKDrbdw4R2Vscx+cUi8UVvnOIFypgVUGasxDuSq6nTmDZ1ybXv0gpi4jUmFwut9HMbunu7lY/pBpjMM/gWuAh4DLgKOBx4FPA8QGsDmCrz4wycZ2dnc3ArUEQbOzq6priO4+IlHV1dU0JgmAj8N8bNmxo8p1HRMq6u7vbzOyWXC630XcWkXrRnOJzPQXMBI5h/FOFvie53pBiHhGpLVOBoFAotAJ9vsPIgRmciStSvYXyAZEY+DzwnQAGfGWT9MyZM6epVCrlAfL5fJ7yASsR8SzZJpuB5sWLFzcDw54jiUgi2afNMbEBHiKyD2kWsLYCJwGnAdvGsdxrgPOAnv+fvfuPj6uu8z3+OpNkJiVNU36FIgWptqTVtNAmrFUpP9YKq4K6ruBdd0Wv7uLdH4K666J32SuKroB6EVzcK7v+AF1X6u66ClLxB9ldIegSCHPOESqTEhAUgdJ26BROkma+94/vCTNt2jRJz+R7ZvJ+Ph7zmHTmnPN9p5Pv5OQz5/v9ArcCrQfYTvNjiTS2caA5m83q5DvFjP298XbgYqCn8jC3Ald5cKerbFIbxWKxnMvlDOC1traqf4qkSGtr67gxBsAUi8Wy6zwiUpHNZsdHR0dBhWWRxCRZwLoHOAf4SnybqRXArime92YTSkTqgzHmskwms7irq2ub6yzTlAFegS3cHwaUgJ8DeZehasXAYuC98W1Z/HAE3ARc74HvKpvUVm9v75jv+x/NZDIt3d3dJdd5RKSiu7u7FIbhFcBob2/vmOs8IlLR1dW1LQzDK8vl8k7XWURkstOpTFJWi5s0Nk3iLvUii7366DH2/161BfgDkp1j0BkDJ8STsBerJmbfFk/WfozrfCIiIiIiKaRJ3GsgyauaMsBLEjzevjQBcGPrBJ6Mvz4GeMphFpEDORH4N2Bt/O9ngZ9i5+w6GlhPZRj0D4HfB56Z24jJMPZ7+Wv2nt/qQeBKNL+ViIiIiMhU2rAjNAAWArsdZhGRhOkKLEm7Y4HHsT+jTwJ/zOQ5+9qBS4Dt8XZ57C+sumCgycD5Bu6sutrKGPihgfNMg1xVJiIiIiJSY7oCS6SBqYA1z4VhmB0eHj7QIg5pcAf25zPArrY6lZOAX8fb/2ONcx0yA20GLjEwVFW0GjVwk6lcbSbzWKFQyBUKhZzrHCIymfqnSHoNDw+3hmGYdZ1DnFABqwb0abqIpIIxJl8qlYZTehL+OuAs4Hngd7HFqak8BPwP7C+sdwEvq2W42TKw1MC1wK+Az2EnpN8OfAx4sQcXejDoMqO4Z4zxoih6MIqiob6+viQXfxGRQ9TX19ccRdFQFEUPGGO04JFIihQKhVypVBo2xtzvOotIo1ABS0TSogtYEkXRYtdB9uNd8f31TH8+vv8C/hVoAi6sQaZZM7DG2NUDt2InpO/AFt3eiy1cXe7BEy4zSnoMDQ1lsStPLm1vb9cniCIpEvfJpcBL4r4qIikRn9MuAVa6ziLSKGr5SeqxwHLsnDDTLZTdTZ1OeCwiDW1jfP/PM9zvm8BbgdcCH0400QwZu2jHucClwKurnroLuAr4ngdlF9lEREREREQOphYFrLcDHwG6Z7Hve4Ebko0jInXiHuDIkZGR7a6D7KMNOCL+essM930wvj8huTgzY2ABcBHwZ8CK+OE92GLctR7c6yqb1Ifly5ePhmHoA9menp5drvOISEVPT8+uMAy3ACPLly8fdZ1HRCpGRka253K5regCDZHUuorKRGUGO1/MY9hOa4CdwCP7uf0mfv7zc5pW0kSTuEtaLcb+XJaBmQ7PWEHlvW9OGXiRgSsNPFU1MfuO+LFlc51HRERERGQe0STuKbeBygv0BeDEqueuix8//wD7romf/0EN80m6qYAlabYb+7N50gz3Oyfe7+eJJzoAAy+PVw+MqgpXj8arDC6aqxwiIiIiIvOYClgp9w3si/P/9vPcT+LnDjSM5vD4+V/UJprUARWwJM2+j/3Z/NAM97ueA78vJsaAZ+A8Az80UK4qXN1t4HwDLbVsX0RERERE9qICVso9in1xVu3nueH4uQMNv/Gww3M0Pnj+UgFL0uxd2J/NJ7EF9+lYjh1GbYAzahHKQKuBiwzcX1W02mNgk4HTatGmiIiIiIgclApYKRdhi1BN+3nuMewLN9Wk8aPASA1ySX1QAWueC4Lgat/3bzDGeK6z7EczdgJ3A/wYOOwg2x8FhNRoaLSBIw1cbuA3VYWrkoFrDbw06fZEfN+/xvf9613nEJHJfN+/3vf9a1znEJG9GWM83/dv8H3/KtdZxAkVsFJuDLuy1f78HPvCHXWA59vj56Ma5JL6oALWPBcEwXgQBOa+++472nWWA1hHZS6se4HeA2z3WmBrvN1vSHAFQgMr4/mtnq8qXD0Wz2/VkVQ7ItXCMMwGQWCCIDBbtmxpd51HRCoKhcKiif4ZhuFMFxoRkRrK5/Odcf8cd51FnFABqwamuiJqporAkUCOyVdSDQMvA7qB/9jPvi+J759OMI+I1BcPoKWlJeM6yAHcB5wH3IwtZv03cDfwn9j3v6Oxxas18fYPA78L/PJQGzawEbgEeD0w8f8TAJ8BvunZK1hFaiKXy3lRZD9fKpVKae2fIvNSsVj0crkcYPuq4zgiUiWTyUz0SfVNkYQkeSI6HN/vb/jKXfH9/zrAvu+O7+9NMI+I1JcdwKjnebtdB5nCHcApwE3YT1NeBXwEuBL4C2zxahS4BnuFlj/bhgy0GLjQ2MLZD4FzsSdAtwIbPFjjwU0qXkmtDQ4O7gFKwPMdHR26UlokReI+GQGluK+KSErE57Sj2HNcEUmZidW2/nQ/z52I7bwGuAx7lRbY+bLejR1+aIC31TylpJWGEM5zYRieks/n17vOMQOdwIXAJ4EvAh8DzgcWH8pBDRwez2/166phgs/F81utOPTYIjPn+35PGIanus4hIpOFYXhqPp9f5zqHiEyWz+fXh2F4iusc4oSGEKbcy7DFqK4DPP8xKi/gLuAh7LCbicd+jC6vnM9UwJJ5zcCJcZHq2arC1a8NXGrUJ0RERERE6okKWHXOA/4Ge5mzqbqNA18FFjpLJmmgApbMSwZeZeAWA+NVhaswHj6YO/gRREREREQkZVTAahCLsRMhvxs7wfESt3EkJVTAknnDQHNcoBqoKlqV40LWRqOrUUVERERE6pkKWCINTAWseS6fz28Iw/Ac1zlqycDieEjgw1WFq+cNfNHAya7ziRxIEARn+r6/0XUOEZnM9/2NQRCc6TqHiEwWhuE5+Xx+g+sc4oQKWDWg5bBFJBUymcxmY8xtAwMDHa6zJM3ACQauBR7Frli4DHgGOzfgMg/e60HeZUaRA+nr62sGbvc8b3N/f/8C13lEpKK/v3+B53mbge9v2rSpyXUeEakYGBjoMMbclslkNlIvKCwAACAASURBVLvOItIoml0HEBGJHQZ4uVyuFbvAQ90zsB74IPBmoCV+eAtwDfAND0qusolM19KlS5uiKMoCZLPZLPC840giEov7ZDPQvHbt2mbs3LIikgLxOW0Ge44rIglQAUtE0mIcaM5ms3V98m2gCXgLcAnw6qqnfgRcB3zPg7KLbCKzUSwWy7lczgBea2trXfdPkUbT2to6bowBMMViUb9bRFIkm82Oj46OggrLIolRAUtEUsEYc1kmk1nc1dW1zXWW2TD207U/Bt4HvDR+eA/wz8DnPLjPVTaRQ9Hb2zvm+/5HM5lMS3d3t64aFEmR7u7uUhiGVwCjvb29Y67ziEhFV1fXtjAMryyXyztdZxERkWRpEnepSwaOM3CtgZ1VE7NvN3C5gWNd5xMRERERkTmnSdxFGpgKWFJXDKw2cJOBkarC1SMGLjHQ7jqfiIiIiIg4owKWSANTAUtSz4Bn4DwDd1YVrYyBu+LHtbKriIiIiIiogCXSwFTAmufCMMwODw+3us6xPwYWxFdWPVRVtBqLr8DqcZ1PpNYKhUKuUCjkXOcQkcnUP0XSa3h4uDUMw6zrHOKEClg1oKsFRCQVjDH5Uqk0nKaTcANHGbgceAT4HLAC2I1dTbDLgws9uNddQpHaM8Z4URQ9GEXRUF9fnxZ/EUmRvr6+5iiKhqIoesAY47nOIyIVhUIhVyqVho0x97vOItIoan0iehjwKmANcCTgAduAALgLeK7G7YtI/egCvCiKFgNPugxi4GXAh4ELgImC2mPAZ4GvePCsq2wic21oaCgLLANob29vA4puE4nIhLhPLoUX+uqI20QiMiE+p10CHOM6i0ijqFUB60TgI8CFwIGGBEXA14G/BYZrlENEZFqMLbCfC1wMvAb7b4CfYQtX/+6BligXERERERFxoBZDCC8AfOAibPGqDPwCe8XVncAWYDx+7o+AfLyPiMxv9wBbR0ZGts9lowZajX2/GgS+C2zEvm99C9jgwXoPvqXilcxXy5cvH8X+Xt/S09Ozy3UeEamI++QWIB/3VRFJificdiv2HFdEUuiNwB7sRGU/B/4QWLif7dqAt2OHEpp4n/PmKKOkkyZxlzll4EgDlxt4ompi9t0GrjWw3HU+ERERERGpW5rEPeUWA09jX6CvANNZbaEF+HK8z5NAR83SSdqpgCVzwsBKA180sKuqcPW4gUsNHO06n4iIiIiI1D0VsGogyTmw/gQ4Cvgp8B7sEJyDGcMOI1wFrMcO4/l0gpmk9g5P6DgdAIsWLeLNb37z4htvvPFpz/PMvhvl8/k2z/OyCxYseG7FihWTJioNwzBbLpfbstnsnpUrV+53qIvv+4cDrF69eqfamD9tdL3xjWdkH3nkPcDrqQyfDoFP//JTn7ql+IY3sGDBgudYsWLS/mn6PtSG2lAbakNtqA21oTbUhtpQG+lu4xOf+MTiq6++mmef1dpPSUpyDqw3xvdXMr3i1YRyvA/A7yaYR2rLw84ZtD2h20MAd911Fx/60Id+EYZhYXh4eK8FAIIg+OtMJlPyPG97FEW7giA4s/r5MAxPNsbs8Dxv+9jY2LNBEHyu+nljjBcEwaDneds9z9uuNuZBGz09Lb/63//70eVve9v27COPfBs7SbsH3Iqd32p1GATHP3vuudtT/X2oDbWhNtSG2lAbakNtqA21oTbqpo03velNj991111861vfQpKTZAFr4rKFO2ex7137HEPSzwNyNTx+9plnntnr59MYU/3m4nmet2/7Ofb+md53Bcx9M6uNdLXRuWvXri8YYyZW/5t1GwYON3A599776Iv+9m9PWPDgg5RzOXacf/6u3SedtNaD87z4vapO/6/UhtqY8zY8z2tqhO9DbaiNRmvDGFP9WN1+H2pDbTRaG8YYLwzDG4Dj6/n7UBuH1kY2O52ZlWS6vINvMm0R9oVqBSZdZncQuXj/ESb/AEh6NQGLEjrWUcBD8RDCrosvvni4t7d30qpvAwMDHdlsNjM6OjrS29v73L7P9/f3L1i4cGHr+Pi4Wbt27c59n9+0aVPTypUrFwGMjo6W1EZ62vA8bxuQGRsb61y3bt3Ts2njlLVrO4APAv8TaI832VZub//S9te//suPfuhD+rlSG2pjhm3cd999R7e0tDwF0NLSsmjfS+Xr5ftQG2qjEdsoFAqLoigqApTL5WNOPvnkp+rx+1AbaqMR28jn852ZTOZJoGyMOapevw+1Mbs2HnrooSVXX33146VSiXK5vBDYve92MnNJFrB+ia0urwCGZrjvCuwQsl8CL04wk9SPTuxE/gDHAJNOwKSxBUFQxr4nLVm9evWTB9u+moFXAR9h7/mtHgCuAm72Zl5UF5FYoVDIRVEUAYyMjCzu7e0tus4kItbAwEBHLpfbCdDa2tq6v7laRMSNIAiOAX4DmNWrVyc58knqQxtQir9WASshSXakn8X3b5nFvhNzX92dUBYRqT87gFHP86b15m6g2cCFBgaww5DPxb6n3Qq8FljtwU0qXokcmsHBwT3YE7DnOzo6Itd5RKQi7pMRUIr7qoikRHxOO4o9xxWRlHkzdonIHcBLZrDfsngfg/0DVOanTirLjHY6ziIOhGF4Sj6fX3+w7Qy0GbjEwFYDJr6NGrjJwClzkVVkvvF9vycMw1Nd5xCRycIwPDWfz69znUNEJsvn8+vDMNT56fzURuXv2zbHWeQA+rAv0GPAGdPYfgN22KABflzDXJJ+KmDJlAwcb+BaA8WqwtUzBi43sMR1PhERERERkZgKWHWgEyhQeaH6gPcBpwErgS7g1cCfYQtW5Xi7AipazHcqYMl+GXiFgU3xVVYThastBi4ydjy5iIiIiIhImqiAVSeOAr5N5cU62O078T4yv6mAJS8w0GTgfAN3VhWtjIEfGjjPJDt/n4iIiIiISJJUwKoz64EbscMJ9y1aPQ7chF05TARUwJqvPOz7wOWve93rvv2ON71p8xfh9t3weFXRaiye36rHdViR+SoIgjN939/oOoeITOb7/sYgCM50nUNEJgvD8Jx8Pr/BdQ5xQgWsOtaBndj9pfHXIvtSAWv+eR3wc8AcB+bXF15oxg4//IWrrYowfid8x8CJjnOKzGt9fX3NQRCMBEEw1t/fv8B1HhGp6O/vXxAEwVgQBNGmTZuaXOcRkYqBgYGOIAjGgyAouc4iTqiAVQNzNQynCDwMbI2/FpH5qwm4BritG172TzD2CJSPvekmmnfs4JlM5rkPwXNLIXMavNGDjwE5t5FF5q+lS5c2AVmgOZvNZl3nEZGKuE82A7m1a9c2u84jIhW5XK4V+/f2Ya6ziDQKzSMjInMqA1eeB++/EwiAt0NLM2SeX7PGPPr5z7PzJz9Z9hk4ehd8HBgHLgRucBpaZB4rFosTC67Q2to67jiOiFSp6pMm7qsikhLZbHaif+p3p4hIg9EQwgZnYEEf/N0v9p6UfU+8wuBpvu9fGobhp/bZ7c3AHrs7F8x9ahEB8H3/b8Iw/LjrHCIyWRiGHw/D8DLXOURksjAMP+X7/qWuc4gTGkJYA940t3sF8Pu1DBL7OLB9DtqR9OkEnoy/PgZ4ymEWSZCxq4z+OfAnxMXJURjLwt8D13l2aPFULgc+CvwCWEV8JYiIiIiIiEhKtQET858tBHY7zDLvnM7klQRrcfuDufqGJHV0BVaDMfCyePXAaOKKq8fAvB/2vM8u6DBdhwE77SG1EqGIiIiIiKSersCqgelO9ng/8KVpbPda4ATgTuzVEtO1CngVsAH4pxnsJyIpY+A84GLgt6nMs3fP9fDTD8L7RuEuDn7VVbXngB8Cb8W+R9ybZF4RERERERGZX04ARrBDvxbOcN/XYCuTdyYdSuqGrsCqYwZaDFxoYLBqfquygVsMnBZv9iG7KV/d3zHCMMwODw+3HqCJq+J9P514eBE5qEKhkCsUCloNVCSF1D9F0mt4eLg1DEOt4Ds/6QqsGkhyFcL3YpfZvoHKWM/peii+X5ZgHhGpMQNHGDtH1S+BG4FTsFdMXQd0eXCeVylMj8X3+73y0xiTL5VKwwc4CW/Z5xgiMkeMMV4URQ9GUTTU19c33Su3RWQO9PX1NUdRNBRF0QPGmOnObSsic6BQKORKpdKwMeZ+11lEGkWSJ6LnxPffmcW+T8f3HQllEZEaMtAFfBB4O5UrLn+NLVx92av06WqPxferDnDYLsCLomgxlQn9J0zs88tZhxaRWRkaGsoSf8DU3t7eBhTdJhKRCXGfXAov9NURt4lEZEJ8TrsEu0CViCQgyQLWxKTMhVnsOxrfH2j4kIikgIGNwCXA66lcwflz4GrgZm/qE+c+YA+wFlusmu48eUuAs+KvfzjTzCIiIiIiIlL/khxCODGuM5rFvovj+2cTyiIiCTHQHM9vNYAtIJ0LeMCt2IUbVntw00GKVwDbge/G+17D5Pefe4CtIyMj2/d5/NNADvgJM5v8XUQSsHz58lHAB7b09PTscp1HRCriPrkFyMd9VURSIj6n3Yo9xxWRlPk1doKy5bPY96x43yDRRFJPNIl7yhhYbOBSA8NVE7M/b+CLBk6e5WFfhi10GeDvgKYptvWw82sZYBy7UqmIiIiIiEjaaRL3lNuMfXHeP4t9vxLve12iiaSeqICVEgZebOBaA89WFa62GbjcJDOG/91UXus+4NT9bNMN3FK13YcTaFdERERERGQuqICVcu/BvjhPMrMCxFnYeXEM+/9DVuYHFbAcM/BKA7cYGK8qXD0QDx9Men66PwR2U3nNt2AXgPg29krMicdHgfcl3LaIiIiIiEgtqYCVci3AA9gX6AHg5dPY5y3Y1YwMsKl20aQOqIDlgIGmifmtqopWxsAPDZxnkp0nb18nAl9j70LWxC0C/hVYWcP2RUREREREakEFrDrwMuBp7Iu0B/h34I+AVwInYf8YPQ07zPBuKi+oD7Q7yCvpoQLWHDLQZuASA1urilajBm4ydpXAudQKnH7jjTd+7+abb/6P5ubmjehNXiRVfN+/xvf9613nEJHJfN+/3vf9a1znEJG9GWM83/dv8H3/KtdZxAkVsGrAq8ExTwJuBNZPc/tNwB+jFQjnu07s8FOw8yw95TBLwzJwPPCXwLuARfHDO7Dzz33RgyccRSMIgnEgMzY21rlu3bqnXeUQkb2FYZg1xowAtLS0LFq5cqVWIhRJiUKhsCiKoiKA53m57u5urUQokhL5fL4zk8k8CZRXr1491cJF0pjagFL89ULsqBM5RM01OOZDwKuB12H/SN7A5ImfHwd+DFyPlhUVqTkDv4UtXL0JyMYPPwJ8DviyB2n4g9QDaGlpqeWwRRGZoVwu50VRBECpVFL/FEmRYrHo5XI5wPZVx3FEpEomk5nok+qbIgmpRQELoAx8L74BHA4cgb18bhu62kqk5oz9ZXkucCm2qDzhLuAq4Hue7atpsQNY6HmePp0QSZHBwcE9q1atKgFNHR0dkes8IlLR0dERRbbCvGdwcHCP6zwiUuF53m5jzCiVq3BERKRBaA6shBg4LJ7fqlA1v9VYPL9Vj+t8BxKG4Sn5fH66Q49FZA75vt8ThqFWChZJoTAMT83n8+tc5xCRyfL5/PowDE9xnUOc0BxYIg1MBaxDZOBFBq408FRV4WpH/Ngy1/lERERERETmCRWwRBqYClizZKA7vrpqpKpw9Wh8Fdaigx9BREREREREEqQClkgDUwFrBgx4Bs4zcGdV0coYuNvA+QZaXGcUERERERGZp1TAEmlgKmBNg4EFBi4ykK8qWu0xsMnAaa7zHYp8Pr8hDMNzXOcQkcmCIDjT9/2NrnOIyGS+728MguBM1zlEZLIwDM/J5/MbXOcQJ1TAqgEthy1SBwwcaeByYBj4IrAGeA64Dujy4AIP7nQY8ZBlMpnNxpjbBgYGOlxnEZGKvr6+ZuB2z/M29/f3L3CdR0Qq+vv7F3ietxn4/qZNm5pc5xGRioGBgQ5jzG2ZTGaz6ywijaLZdQAROTADq4CPABcAufjhXwGfBr7qQdFVtho4DPByuVwrjfV9idS1pUuXNkVRlAXIZrNZ4HnHkUQkFvfJZqB57dq1zcC440giEovPaTPYc1wRSYAKWCIpZOA84GLgt6lcKRkAnwG+6cGoq2w1NA40Z7NZnXyLpEixWCzncjkDeK2treqfIinS2to6bowBMMVisew6j4hUZLPZ8dHRUVBhWSQxKmCJpEQ88frvA+8H1lYe5lbgqnofIngwxpjLMpnM4q6urm2us4hIRW9v75jv+x/NZDIt3d3dJdd5RKSiu7u7FIbhFcBob2/vmOs8IlLR1dW1LQzDK8vl8k7XWUREJFnzdhJ3A0cYuNzAE1UTsz9n4FoDJ7nOJyIiIiIiIjOiSdxroNZXYB0GvAo74fSRgAdsww6Fugs7CbXIvGSgC/gg8HZgYfzwNuB64AsePOUqm4iIiIiIiMh8cCJ2pbTnqVQd9709D/wDsMxNREmZeXMFloFXG7jFwHjVFVc/N3ChqUzULiIiIiIiIvVJV2DViQuAZ6m8WOPAFuz8PT8BHgT2VD3/bLyPzG8NXcAy0BwXqAaqilbluJC10dirE+e1MAyzw8PDra5ziMhkhUIhVygUVGAXSSH1T5H0Gh4ebg3DMOs6hzihAlYNZA6+yYy8EfgG0A48ALwD6ABWAqcBG4BV8WN/AITxtt/ArromkhYtwKJDPYiBxQYuBR4CbgR6gAi4AVjnwXke/Mizb2zzmjEmXyqVhnUSLpIuxhgviqIHoyga6uvr0+IvIinS19fXHEXRUBRFDxhj5v2HYSJpUigUcqVSadgYc7/rLCKNIskC1mLgS0AT8FXsKmpfB/a3YtFubNFqHfCVeJ9/xBa2RFzpxQ59fRhbZCpif37vAC4GFkz3QAZOMHAt8EvgSuxQ2e3Ax4BlHrzXA/0y21sXsCSKosWug4hIxdDQUBb7Hra0vb1dnyCKpEjcJ5cCL4n7qoikRHxOuwR7MYeIJCDJAtafAEcBPwXeA4xOY58x4I/ifTqBixLMIzJdrdgC6n9jfwaXUekbbcBZ2GLUL+KvD8jAegO3AMPYolc7dgjte4EXe3C5B7+pxTchIiIiIiIi0qiSLGC9Mb6/EijPYL9yvA/A7yaYR2Q6DgN+hC26GuxVg2cCR8S3E4A/Ax4BjgduZ5852ww0GTjf2Hne7gbOxfatH2H7xcs9uMHb/9WIUnEPsHVkZGS76yAiUrF8+fJRwAe29PT07HKdR0Qq4j65BcjHfVVEUiI+p92KPccVkZTZhi0AHDmLfY+K93060URST1xN4v7PcZvbgDOm2K4VuCne9jlgnYE2A5cYGKqamH3MwE3GDo8VERERERGR+UeTuKdchH1xZjMBcy7eN0o0kdQTFwWs34nbex74rWls7wH/shTMV+EJAzurClfbDVxp4MQa5hUREREREZH0UwEr5X6JfXGWz2LfFfG+jyaaSOqJiwLWj+L2Pj2djQ2cuhu+M1IpWhkDj8RXYbXXNqqIiIiIiIjUCRWwUu5b2Bfnr2ax71/F+34z0URST+a6gNWOXWjAAC850EYGPAPnGbizqmhl+sG8H75tkp1HTkREREREROqfClgp92bsi7ODKQoC+7Es3sdgJ7+W+WmuC1hr47Ye39+TBhbEV1Y9VFW42mPgpj+Cj8f73jIHOeeNIAiu9n3/BmOM5zqLiOzN9/1rfN+/3nUOEZnM9/3rfd+/xnUOEdmbMcbzff8G3/evcp1FnFABqw70YV+gx5h6QuwJG6gMPfxxDXNJ+s11Aes1cVt+9YMGXhTPZfVUVeGqZOBaUynMThRr75qDnPNGEATjQRCY++6772jXWUSkIgzDbBAEJggCs2XLFg2XFkmRQqGwaKJ/hmGYdZ1HRCry+Xxn3D/HXWcRJ1TAqoHmhI/3Nuwf9cuB/4hv/wYMUlml8CjgFOAtwFnYibGHgN9POIvIVCZWvDwawMDLgUuBC6gsRPAY8FngKx48W7Vv5z7HkGR4AC0tLRqWKZIiuVzOiyK7xkqpVFL/FEmRYrHo5XL2tCWXy+kKZpEUyWQyE31SfVMkIUkXsJ4CXgn8A/YqlTPj21S+C7wHW+ASmStbPXj+XFjyT7bo+koqv1z+G/gM8B3PzpO1r4mrC4M5yDmf7AAWep6323UQEakYHBzcs2rVqhLQ1NHRodWCRVKko6MjimyFec/g4OAe13lEpMLzvN3GmFGg5DqLiBzceuBG7FUsZp/b48BNwKucpUuXNuD12Mns/wHYDPwXcC9wX/z15vi5vwJeBxzmJGntzNkQQgOtBi7aCjurhgmWDdxi4LSD7H4i8Hycc10tc843YRieks/n17vOISKT+b7fE4bhqa5ziMhkYRiems/ndU4ikkL5fH59GIanuM4hTmgIYR3rwM4f9NL4a7HOAm4FIiYX+Q52i7CTiJ8+56lro+YFLANHGrjcwG8mCle7wVwH5XfBu6ZxiGbgjjjj7bXIKCIiIiIiInVPBSxpGEdiC1f7FqUew05m/3Xg77DD2D4df/014EdUJr2vvn0XOHxOv4Pk1ayAZWCVgZsMRFVXXD1u4NJl9kpAg53j6o1THGYR8J2qbVclmVFEREREREQahgpY0hCOAApUfpj7sFf/HDWDYxwV7/OfVcd5iPouYiVewDKwMR4WOF5VuAoMXGhgYqWeLHZ45kTb3wP+AOjGLkZwOnA5dn43A+zGDuEUERERERER2R8VsFJuuqsrdALXY4s4vwHuBN5Rq1Ap9C/YH+LtJFMIOQ/YGR/zWwkcz5VEClgGWuIC1X0zmN+qGbiKgw/lDIDe2WaTqeXz+Q1hGJ7jOoeITBYEwZm+7290nUNEJvN9f2MQBGe6ziEik4VheE4+n9/gOoc4oQJWyr0TOzn7h6bY5jjgUfZfHPhErQOmwDKgDIyTbCHkVVXHPTHB486lQypgGTg8nt/q11WFq+cMfNHAmmke5njgb4AB7DDBPdhhnd8E3gRo+fgaCoKgFATB+MDAgObJE0mRvr6+5iAIRoIgGOvv71/gOo+IVPT39y8IgmAsCIJo06ZNTa7ziEjFwMBARxAE40EQaBXC+UkFrBpoTvBY52ELVE9Nsc0XgBOw8zh9HlvMOhv4I+AjwM3Yq1wa1enYK9VuxRZJktKPnVT8d4ANwCMJHjvVDJwE/AXwdmBh/PA27FV+f+/BkzM43GPAFfFN5t5hgJfL5VqBouswImItXbq0KYqiLEA2m81iV2IVkRSI+2Qz0Lx27dpm7IeZIpIC8TlthsZbPV7EmSQLWGvj+zsO8PxZ2Emyd2ELOY/Gj38L26nfji1kXZJgprQ5Nr7fUoNjb8EWsF5Ug2OnjoFXAx8GXk/lyqgHgSuBmz0YcZVNZm0caM5mszr5FkmRYrFYzuVyBvBaW1vVP0VSpLW1ddwYA2CKxWLZdR4Rqchms+Ojo6OgwrJIYpIsYC3Bds7HDvD8n8f311EpXk34EraA1ejjg5+J74+rwbEnjrmtBsdOBWN/Xt8OXAz0VD11K3AtcIdnh1JKHTLGXJbJZBZ3dXU17M+wSD3q7e0d833/o5lMpqW7u1vDIERSpLu7uxSG4RXAaG9v75jrPCJS0dXVtS0MwyvL5fJO11lEZLI9wIFObJcCY9irYpbs5/kjsGNDd9QmWmr0YL/PZ9n//8NsHY9dHc9QuRKu3hxwDiwDiw1cauDhqvmtRg3cZOr3+xUREREREZHGpDmwUm4H9sVp3c9zn4yfu2mK/ffEt0Z3D/b/4l6SGe53PJCPj3l3AsdzZVIBy8AJBq41UKwqXD0TT9aeZAFQREREREREJCkqYKXcXdgX57x9Hu/ETsg81dVBTfHz82Heopdjr1SbuBLrCuxE5DN1ErYwuCs+VnGWx0mLFwpYd8LrDGyKr7KaKFxtMXCRqUzULiIiIiIiIpJGKmCl3F9iX5xfULmyaCFwW/z496fY96XxNk/UMmCKvAI7D5ipuj0M/Ct2EvJLgHcC/wN4W/z1xcCn4m0e3mffrdT/ULpOwNxmi1XlqsLVoIF3GMi6Dii1FYZhdnh4eH9XcIqIY4VCIVcoFHKuc4jIZOqfIuk1PDzcGoah/o6Zn1TASrmFVAorzwE+9gojg11ye8UU+74j3q6vxhnTpAO4DHiKvYtRM7k9AVwKtM9x9lropFK0Khu41cBvuw4lcycIggeDIHhCJ+Ei6WKM8YIgeDgIgsf6+vqSXPxFRA5RX19fcxAEjwVBsNUY47nOIyIVhUIhFwTBE0EQPOA6izihAlYNJHkiWgJeC/wbsAZYHT++HVugKkyx7/nx/eYE86RdEfgE9oqr9dj/u25soe847A/5xB/yI9j/319h/x8D4AfAz2iwVfc+DxwHG37PDkmV+aUL8KIoWgw86TqMiFhDQ0NZYBlAe3t7G/b3l4ikQNwnl8ILfXU+TMchUhfic9olwDGus4g0iqQ/SZ0YyvYqbCFmO3AHdp6mqVwJhMDXE85TD/YAd8a3fTXF9+NzF8eti+3dVMVOEREREREREZlnajEUoMyBCzIH0h/fZG/zpnAlgl2h88iRkZHtroOISMXy5ctHwzD0gWxPT8/BPpASkTnU09OzKwzDLcDI8uXLR13nEZGKkZGR7blcbivwjOssIiKSrBdWIYy/FhEREREREalHmgOrBmo9GWs7dijh4djhcD+ocXsiIiIiIiIiItJgalHAagbeA7wXOBnIVD031eooGRpsQvIZaAPOoDKJ+9L4sTbs/1kJ2A08TmUS9//ErvYoIiIiIiIiIiIzcDRwN5VL5Qx2kvJy/PWB/BO2SNNb64ApcxZwKxCx9//ZdG4RcAtw+pynrg0NIRQREREREZFGoCGENZDkFVgZ4NvAeuyqg58GvgU8BDwMvHiKfR/CvqgXAAMJZkqrI4EbgTfs8/jj2P+LJ4CdVApbC4AO4FjgJOB4IAecG99uAd4J7JiD7CI1EQTB1caYYcMwmAAAIABJREFUxatXr36v53lTFbxFZI75vn8NkF2zZs2fuc4iInvzff96YHTNmjUfcJ1FRCqMMV4QBF8EdqxZs+ZS13lEGsFUQ/pm6veBbwDbgNOAX1Q99wi2gHWg9l6NXbXwp8ArE8yURkcAPwOWx//+D2wx61bs/910HIUtXP1PKldgFYBXUL9FrE7gyfjrY4CnHGYRB4IgGAcyY2NjnevWrXvadR4RscIwzBpjRgBaWloWrVy5UisRiqREoVBYFEVREcDzvFx3d7dWIhRJiXw+35nJZJ4EyqtXr25ynUfmXBt2lBnAQuyUQHKIMgffZNr+IL6/jL2LV9Mxsf1JycVJrRuwxasdwOuxwwi/yvSLV8TbfhU7b9YbgSJ27qwbEswpMtc8gJaWliTfl0TkEOVyuRc+fCqVSuqfIilSLBZf6J/VfVVE3MtkMhN9Un1TJCFJnohOzF/17VnsO1GZXJRQlrRaBrwFOyfY2cDmBI55C7YQZuJjn5jAMUVc2AGMep6nTydEUmRwcHAP9vf08x0dHZHrPCJSEffJCCjFfVVEUiI+px2lfkfIiKROknNgHQGMM7uhX+3xfWnKrerf6dgK/K0kO9dXP3A78DvABuyQzbnwAZIb8pkD+OxnP8vpp5/+D7lc7t7Vq1dfUT0Xku/7p3uedxGQBZ4tl8uXn3zyyY9PPP/ggw8euWfPnk8ARxpj9gBfX7NmzW3Vjfi+/wHP814JYIwJ1UZ62gBuNsZ8bfXq1aVatdEo/1dqQ204aOOnxpjnnnvuuaOx8zXW6/ehNtRGQ7WxZ8+ehcBtwKKVK1d+zff9uvw+1IbaaMQ2uru7S/l8/gzgrUEQbKrX70NtzK6N8fHxDXfccQf3338/X/va15BkJFnAKmLnZlqMnYB8JiaGDjb6vEfHxvdbanDsLdgC1otqcOz9yQB/C7QmedCzzz4b7LDIc4Mg+DxVn1jEbyQTQ1Vpamr6KfCPE/8eGxs7zfO8/xVvC3ay/BfeTIwxmTAMX8jsed7vqY30tIG9MvGvqVKP34faUBuN2obneWQymVvq/ftQG2qjAdt4S4N8H2pDbTRcG2vWrPnvMAz76v37UBszb6O5ubn17LPP5owzzlABK0FJFrAGgdcC5wA3z3DfN8f3P0swTxo9E98fV4NjTxxzJnNpHYoy9rVemdDx2oHPfOxjH+Oiiy76y2OPPTZYs2bNXpfblsvlD3ue91/xP8daW1u/Uf38li1bbl21atU7jDGHAWQymTuqn/c8r+z7/guZPc97RG2oDbWhNtSG2lAbakNtqA21oTbUhtpIso1du3adfM0111z38MMPI+n0Huw8TFuwM+5XeyR+bn9WYWfkN8Dv1SpcSvRgv89ngSUJHvd4Kv+HaxM87lzqxOY38dciIiIiIiIi9aiNyt+3+9ZHJAWagQD7Av0IOyfWhEfYfwFrI/Cr+Ln7SXZS+bS6B/v93ksyw/2OB/LxMe9O4HiuqIA1z+Xz+Q1hGJ7jOoeITBYEwZm+7290nUNEJvN9f2MQBGe6ziEik4VheE4+n9/gOoc4oQJWDSRZMNqDnbvoCeA1QAG4CrtCXjbe5uXxc5cCPwV+iC3i7AT+EDssrdG9C3u11Drs1WpXUJkDbCZOAj4JPACswV7V9c5kIorMvUwms9kYc9vAwECH6ywiUtHX19cM3O553ub+/v4FrvOISEV/f/8Cz/M2A9/ftGlTk+s8IlIxMDDQYYy5LZPJJLHyvIiQ7BxYAMPYYXJfBc4G/iq+TQj3s8/PscWr/T3XiH6OLeJtAk4ALotvw9h5xArYIuBOYARbsW0FOrCTwJ+EHSa4rOqYDwNvBR6ak+9ApDYOA7xcLteKXRRCRFJg6dKlTVEUZQGy2WwWeN5xJBGJxX2yGWheu3ZtM3ZFcBFJgficNoM9xxWRBCRdwAJbfDkHOBM7L9ZGJs/3tB07YfvXgX8BRmuQI81+hr1q6n3AxcDR2ILUsql22o/fAJ8DvgDsSjKgiAPjQHM2m9XJt0iKFIvFci6XM4DX2tqq/imSIq2trePGGABTLBbnw0gGkbqRzWbHR0dHQYVlkcTUooA14T/iG9irh47EVqB3Mncr5aVZEfgEcCWwHruCYzewAruiYBuQi7cdAUrY+cIK2LnGfoAthOlkRRqCMeayTCazuKurS+8PIinS29s75vv+RzOZTEt3d3fJdR4Rqeju7i6FYXgFMNrb2zvmOo+IVHR1dW0Lw/DKcrm803UWEZG50BTf5gNN4i4iIiIiIiKNQJO410ASV2C1AmcBXcDh2OGBW7ErEUYJHH8+0+WmIiIiIiIiIiKHoAn4EHYonNnPbRfw19R2mKI0Dl2BJSIiIiIiIo1AV2ClSBNwM3sXrLZjV8F7Zp/Hv8P8GQYns6cC1jwXhmF2eHi41XUOEZmsUCjkCoVC7uBbishcU/8USa/h4eHWMAyzrnOIEypg1UBmlvt9ELgg/vpfsZOPHwGchJ2sfRXw5fj5NwKXHkJGEZkHjDH5Uqk0rJNwkXQxxnhRFD0YRdFQX1+frqoWSZG+vr7mKIqGoih6wBjjuc4jIhWFQiFXKpWGjTH3u84i0ihmU8BaCPyf+OsvAG8Ffr7PNluA91Rt91fAotkEFJF5owtYEkXRYtdBRKRiaGgoCywDlra3t+sTRJEUifvkUuAlcV8VkZSIz2mXACtdZxFpFLMpYP0etoj1OPCBg2z7SaAAdAC/M4u2RERERERERERknptNAeus+P5LwOhBti0DX4u/3jiLtkRk/rgH2DoyMrLddRARqVi+fPko4ANbenp6drnOIyIVcZ/cAuTjvioiKRGf027FnuOKiCOD2InIzjrYhrHfjre/s2aJpBFoEncRERERERFpBJrEvQZmMxnrcfH9r6e5/XB8v2wWbTWiWhfyTqvx8UVERERERERE5tRsCljt8f2T09z+6fhek7hbvYBWWRMRERERERERmabZFLAm9tk9ze2fj+8Pm0Vbjehs4N+Bw7Fzivy92zgiIiIiIiIiIo1nB3YcZ8cM9pkY+ynWamAn9v/knY6zpIXmwJrngiC42vf9G4wxnussIrI33/ev8X3/etc5RGQy3/ev933/Gtc5RGRvxhjP9/0bfN+/ynUWcUJzYNXAbP5QfBQ4AViOXVVhOiaKV/rDtOJs4DbslWwvA37lNo5znVSGpR4DPOUwizgQBME4kBkbG+tct27d0wfdQUTmRBiGWWPMCEBLS8uilStXaiVCkZQoFAqLoigqAniel+vu7tZKhCIpkc/nOzOZzJNAefXq1U2u88icawNK8dcLmf4INpnCbIYQPo0tYL0BeGCG+26cxjY/mnGi+vQD4DrgA8AVwLvdxhFxzgNoaWnJuA4iIhW5XM6LogiAUqmk/imSIsVi0cvl7NSquVxOHxSLpEgmk5nok+qbIgmZTQFrK9ADXDuLfX84jW3mUwf/P8DbscMIr6CyYqPIfLQDWOh5nj6dEEmRwcHBPatWrSoBTR0dHZHrPCJS0dHREUW2wrxncHBwj+s8IlLhed5uY8wolatwROQQzeaT1IHEU8xfJeAL2NfhbY6ziDjled5ryuXyGd3d3folL5IiF1xwwbgx5kzP885YsWLFiOs8IlKxYsWKEc/zTi+Xy2dccMEF467ziEhFd3d3qVwun+F53mtcZxERScqRwCtdh0gBTeIuIiIiIiIijUCTuIs0MBWwREREREREpBGogFUDmoxVRERERERERERSTQUsEUmFfD6/IQzDc1znEJHJgiA40/f96awkLCJzzPf9jUEQnOk6h4hMFobhOfl8foPrHCKNQgUsEUmFTCaz2Rhz28DAQIfrLCJS0dfX1wzc7nne5v7+/gWu84hIRX9//wLP8zYD39+0aVOT6zwiUjEwMNBhjLktk8lsdp1FpFGogCUiaXEYkMnlcq2ug4hIxdKlS5uALNCczWazrvOISEXcJ5uB3Nq1a5td5xGRivicNoM9xxWRBKiAJSJpMQ6QzWa1DLhIihSLxTJ2AlJaW1vVP0VSpKpPmrivikhKVJ3T6nenSEL0SY2IpIIx5rJMJrO4q6trm+ssIlLR29s75vv+RzOZTEt3d3fJdR4Rqeju7i6FYXgFMNrb2zvmOo+IVHR1dW0Lw/DKcrm803UWERFJVieVZUY7HWcRERERERERma02Kn/ftjnO0jA0hFBERERERERERFJNBSwREREREREREUk1FbBEJBXCMMwODw9rBUKRFCoUCrlCoZBznUNEJlP/FEmv4eHh1jAMtYKvSEJUwBKRVDDG5Eul0rBOwkXSxRjjRVH0YBRFQ319fVr8RSRF+vr6mqMoGoqi6AFjjOc6j4hUFAqFXKlUGjbG3O86i0ij0ImoiKRFF+BFUbQYeNJ1GBGxhoaGssAygPb29jag6DaRiEyI++RSeKGvjrhNJCIT4nPaJcAxrrOINApdgSUiIiIiIiIiIqmmApaIpMU9wNaRkZHtroOISMXy5ctHAR/Y0tPTs8t1HhGpiPvkFiAf91URSYn4nHYr9hxXREQaSCdg4lun4ywiIiIiIiIis9VG5e/bNsdZGoauwBIRERERERERkVRTAUtERERERERERFJNBSwREREREREREUk1FbBEJBWCILja9/0bjDGe6ywisjff96/xff961zlEZDLf96/3ff8a1zlEZG/GGM/3/Rt837/KdRaRRqE/FCUtOoEn46+PAZ5ymEUcCIJgHMiMjY11rlu37mnXeUTECsMwa4wZAWhpaVm0cuVKrUQokhKFQmFRFEVFAM/zct3d3VqJUCQl8vl8ZyaTeRIor169usl1HplzbUAp/nohsNthloahK7BEJC08gJaWFr0viaRILpd74cOuUqmk/imSIsVi8YX+Wd1XRcS9TCYz0SfVN0USohNREUmLHcCo53n6dEIkRQYHB/dgP0F8vqOjI3KdR0Qq4j4ZAaW4r4pISsTntKPYc1wREWkgnYCJb52Os4gDYRieks/n17vOISKT+b7fE4bhqa5ziMhkYRiems/n17nOISKT5fP59WEYnuI6hzjRRuXv2zbHWUQkYSpgiYiIiIiISCNQAasGNIRQRERERERERERSTQUsERERERERERFJNRWwRCQV8vn8hjAMz3GdQ0QmC4LgTN/3N7rOISKT+b6/MQiCM13nEJHJwjA8J5/Pb3CdQ6RRqIAlIqmQyWQ2G2NuGxgY6HCdRUQq+vr6moHbPc/b3N/fv8B1HhGp6O/vX+B53mbg+5s2bWpynUdEKgYGBjqMMbdlMpnNrrOINAoVsEQkLQ4DMrlcrtV1EBGpWLp0aROQBZqz2WzWdR4RqYj7ZDOQW7t2bbPrPCJSEZ/TZrDnuCKSABWwRCQtxgGy2ey46yAiUlEsFsvYFXRobW1V/xRJkao+aeK+KiIpUXVOq9+dIgnRJzUikgrGmMsymczirq6uba6ziEhFb2/vmO/7H81kMi3d3d0l13lEpKK7u7sUhuEVwGhvb++Y6zwiUtHV1bUtDMMry+XyTtdZREQkWZ3YT/hN/LWIiIiIiIhIPWqj8vdtm+MsDUNDCEVEREREREREJNVUwBIRERERERERkVRTAUtEUiEMw+zw8LBWIJwbGWAZ0AOsQcN25SAKhUKuUCjkXOcQkcnUP0XSa3h4uDUMQ63gK5IQFbBEJBWMMflSqTSsk/CaOhK4GngUeBgYAPLAb4CfAu9EvxdkH8YYL4qiB6MoGurr69PiLyIp0tfX1xxF0VAURQ8YYzzXeUSkolAo5Eql0rAx5n7XWUQahU5ERSQtugAviqLFwJOuwzSg84EbgMXxvyPs/3MWOAZ4RXz7c+ACYNhBRkmhoaGhLPaKPdrb29uAottEIjIh7pNL4YW+OuI2kYhMiM9pl2DPs0QkASpgpUMbcAbQDazAnoi0xTcPKAG7gceBAhAA/wk85yKsiNSdPweuw76fDAJXALdR+UNnCXAh8GGgF7gHeDXwizlPKiIiIiIiIqlzFnAr9koIM8NbBNwCnD7nqWujk8r3pvl45qEgCH4WBMHQwMBAi+ssDeY0YAzbt64EmqbY9kXYoYQG2AJoTjLBGOMFQZAPguBBY4yGmIqkiDEmEwTBg0EQ3K8hhCLpMjAw0BIEwVAQBD9znUWcaKPy922b4ywNQ7/o3DgSuBF4wz6PPw48BDwB7KRS2FoAdADHAicBx++z3y3YuWt21C5yzXVSGTZ2DPCUwywijcLDFqR+C/g68I5p7NOJvUrrRcBfAP+3ZulERERERBpTG3YkFcBC7IgqkbpzBHYY4EQ1tg94F3DUDI5xVLzPf1Yd5yHg8ARzzjVdgSWSvFOxfepZ4OgZ7PfOeL+hWoQSEREREWlwugJLGsK/YH+ItwOvS+B452Gv1jLAtxI4nisqYIkk76PYPvWNGe7XCuyK912ZdCgRERERkQanApbUvWVAGRjHTpSclFdVHffEBI87l1TAEknejdg+9Rez2Pdn8b77DnUWEREREZGpqYBVA5qMdW6djp2T5nvAQILH7Qdux76eGxI8rsicCYLgat/3b9AktIlaGN+Xptxq/3bF94sSyiJ1zPf9a3zfv951DhGZzPf9633fv8Z1DhHZmzHG833/Bt/3r3KdRaRRqIA1t46N77fU4NgTx3xRDY4tMhf+wvO8Px4cHJzJfHAytYmFEWbzvnBcfP9EQlmkToVhmPU87/2e5/3pli1b2l3nEZGKQqGwyPO8P/U87/1hGGZd5xGRCt/3j/Y87489z/tL11lEGoUKWHPrmfj+uCm3mp2JY26rwbFF5oIH0NLSovel5NwX3792hvudAHQBewA/0URSd3K53AtXRZZKJfVPkRQpFosv9M/qvioi7mUymYk+qb4pkhCdiM6tiT8mzwOWJHjc46nMU3PfVBuKpNgOYNTzPC0xm5zvAqPAK4EzZ7DfR7AnWz/GLjgh89jg4OAe7DDU5zs6OiLXeUSkIu6TEVCK+6qIpER8TjuKPccVEalL92AncruXZIb7HQ/k42PencDxXNEk7vNcGIan5PP59a5zNKDPYvvVL5nee8752AUhysAraphL6ojv+z1hGJ7qOoeITBaG4an5fH6d6xwiMlk+n18fhuEprnOIE5rEXRrCy7GfZBvgWeAK4KRZHOck4JNUlrovzvI4aaEClkhttAMPYPvWI9irsfanGfgAMBZv+5m5CCciIiIi0oBUwKoBjcd14xXAJuw8MxOGgUGggJ00eScwgv2BbwU6sJPAnwSsBZZV7fsw8NZ4/3rVSWXC6WOApxxmEWk0JwG3AS/FvqfcDvwb9qqsLHAK8IdUiuDfBN6BnQNLRERERERmpo3KSuALAU2TInWtA7gMW6gxs7w9AVyKvcKi3ukKLJHaOhz4R2xR6kDvKU8D73UVUERERESkQegKrBrQFVjuNQPrsauEdQMrsCsKtgG5eJsRbPX2V9grtALgB8DPsPPUNAJdgTXP5fP5DU1NTYd1d3ff7jpLg1sBvAk7lPA47OSiW4H/3979h1tW1/UCf++ZYQbQYQaEAEuQREUByQJFSi+pUf7IH5gp9WBWZFZUpnalq3bJi/mkD8bNMk1K0zQD9SlFxfyBphfll8nMwZBRhgBDEgeGGYb5wcy+f3zXdu8Zz9l7n3PW2WuffV6v59nP2jPru7/fz15nrb3P+pzvj88k+VjK0GbYy/r1609vt9srHve4x32m6ViAva1bt+7prVbrgRNPPPHzTccC7G1qaupnd+/eve2kk076YtOxMHJ6YC0ACazxtrza7m40ipkdmzKcsQ4HJbn4jDPOyLnnnvsbj3jEI758/PHH39Bb4MYbb1y9c+fOpyZZ2Wq1Np9wwgmfbrVa7d4y1U3WYa1W64EVK1b822Me85jv9e6fmpo6ds+ePY9PkuXLl39dG+PTRqvV+vskq3bs2HHIySefvHmxvg9taGPS2ti+ffvPLFu27J9arVZrx44dB5188snbFuP70IY2JrGNK6+88oDVq1dvSbJnz549Z61cufLzi/F9aEMbk9jGtddeu2bVqlWb2u32jiS/sljfhzbm1samTZtOveCCC95344035tZbb5XAqsmKpgOgr3FNXCXJspQVFdfWWemFF16YJO/as2fP9muvvfaITiIjSXbt2nVRq9X6tc6/p6amXpLkfT3//tl2u315q9XqlP9oSk+TJEm73V42NTV1TavVWpsk2hivNjpWrVq1f8qiBIvyfWhDG5PWxvLly7/fxsqVK89O8s7F+D60oY1JbGP16tXPSPmD5/Jly5Z9aLG+D21oYxLbqH6nXdZqtQ5Imf94Ub4PbcytjYMPPnjthRdemC1btuS0004L9ZDAYq72pFzIj6mpvuVJfvorX/lKTjnllCuWL19+y80337y1t0Cr1fpku90+Kkna7fYDrVbr2t797Xb760kuS5n0Pq1W66P7vH7P+vXre2O+TRvj00ar1Xpqu91etnLlyt09ZRbd+9CGNiatjSRHt9vtp1X/tWjfhza0MaltdG6iWq3WZ5Ms2vehDW1MWhsrV67cvXPnzrRarT3tdvtzi/V9aGNubezevfuEa6655qdvvvnmAJPHJHdL3Lp1614zNTX1pqbjAH7QunXrXj81NfWGpuMAftDU1NQbpqamXtd0HMAPmpqaetO6dete03QcNML97QIwB9b4ODhlcuW1SQ5MmfDtniR3pyx1v6u50EbCJHcAAABMAve3TJwfT/K2JP+ZmZe1bye5P8mVSf48yRMaiXThyVADAAAwCdzfMjFWp8wftSf9E1czPa5O8pyRR72wXOAAAABMAve3TISDklyXciLvSfKJJC9LckqSY6r9y6rtXUm2JTknyVuTfC17J7Lelcm5GFzgS9zU1NTKjRs37t90HMAP2rBhw6oNGzasajoO4Ae5PmF8bdy4cf+pqamVTcdBI9zfLoBlTQewBL05ZejgbUlOS/LMJH+T5JokG5Pcm5LYujfJB5IcUD1/ZZIfqx4frOo6J8knk/hQZNFrt9vXb926daNfwmG8tNvt1vbt2/9j+/bt37ziiiusXgxj5Iorrlixffv2b27fvv3r7Xbb3LYwRjZs2LBq69atG9vt9teajgUmhV9ER+uQJL+WMiH7M5LcMKD8pUl+N8nzklxS/d/1Sc5K8u5q/5OTXJzkJQsQb1PWRlJuKXp0ktb555//uJTeh8AYOO6441Z+6EMfOiZJLrjggscm2dJwSEDlggsuWH3RRRf9SJIcd9xxj0qys+GQgMr5559/6HnnnXdEksNTFuxiaTmw6QAmkQTWaD0tyX5JPpLByask+Wq1nW7i9n+t6vtCkrOT/EP1f5Pg9qYDYPTa7XZarVYuv/zyq5uOBejauHHj959fddVV1zcYCrCPq6666vvPN27ceGODoQD7uPzyy3Peeeel6h25qel4YBJIYI3Ww6rtsDcA96WsQHjkDPuvTXJekr9I8idZ3AmsbSlJveObDoRmTE1NZe3atdm8eXPToQA9du3alZtuuin77bdftm3b1nQ4QI9t27Zl48aN2blzZ3bt2tV0OECPzZs357bbbss999zTdCg064aUe11YdF6dMonba2fxmp3pf8IvS5k7q50yPxYsVp1VOQ9vOhBgL6vSnYR0TcOxAHtbk+71aQ5JGC+Hp7twF1ADk7iP1m3VdthE06NShhz+d58ye5L8bfX8aXOMCwAAAGBsSWCN1mdSJnD/+SSPHaL8y6vtl4aoN0lOn1tYAAAAAND1lyldSW9LWUFwOq0k56Y7pOqpA+pclZIYW19TjNAEQwhhPBlCCOPLEEIYX4YQQs1M4j5656WsKnhKkn9Lcl21vSPl53F0kp9J8qNV+fck+dyAOnckuTvJofWHCwAAAMBSdFCS96b7F7PpHnuSvD3DJxkvzeJehRD0wILxpAcWjC89sGB86YEFTJQTkrw5ZY6rjUluTvLF6v9OaDAuaIIEFownCSwYXxJYML4ksABgQklgwXiSwILxJYEF40sCC2pmFUIAAAAAxpoEFgAAAABjTQILAAAAgLEmgQUAAADAWJPAAgAAAGCsSWABAAAAMNYksAAAAAAYaxJYAAAAAIw1CSwAAAAAxpoEFgAAAABjTQILAAAAgLG2oukAACrXJHlIkk1NBwLsZWeSdUlWJtnScCzA3rYkuTHJjpRrFRgfm5J8K8n3mg4EAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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)
##-----------------------------------------------------------------------------
## Visualização.
rp.regression(x=x, y=y)
Métodos numéricos considerados na estimação
##-----------------------------------------------------------------------------
## Usando decomposição QR de X.
QR <- qr(X, LAPACK=TRUE)
Q <- qr.Q(QR, complete=TRUE)
## Q é ortonormal.
round(t(Q)%*%Q, 3)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
## [1,] 1 0 0 0 0 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0 0 0 0
## [3,] 0 0 1 0 0 0 0 0 0 0 0
## [4,] 0 0 0 1 0 0 0 0 0 0 0
## [5,] 0 0 0 0 1 0 0 0 0 0 0
## [6,] 0 0 0 0 0 1 0 0 0 0 0
## [7,] 0 0 0 0 0 0 1 0 0 0 0
## [8,] 0 0 0 0 0 0 0 1 0 0 0
## [9,] 0 0 0 0 0 0 0 0 1 0 0
## [10,] 0 0 0 0 0 0 0 0 0 1 0
## [11,] 0 0 0 0 0 0 0 0 0 0 1
## R é triangular superior.
R <- qr.R(QR, complete=TRUE); R
## b1 b0
## [1,] -39.84043 -3.3031771
## [2,] 0.00000 0.2983644
## [3,] 0.00000 0.0000000
## [4,] 0.00000 0.0000000
## [5,] 0.00000 0.0000000
## [6,] 0.00000 0.0000000
## [7,] 0.00000 0.0000000
## [8,] 0.00000 0.0000000
## [9,] 0.00000 0.0000000
## [10,] 0.00000 0.0000000
## [11,] 0.00000 0.0000000
## Estimação.
z <- t(Q)%*%y; z
## [,1]
## [1,] -404.294816
## [2,] -9.911903
## [3,] -5.000805
## [4,] 7.483397
## [5,] 1.608694
## [6,] 14.908694
## [7,] -23.541900
## [8,] -1.240712
## [9,] 0.160475
## [10,] -12.194868
## [11,] -11.794868
betas <- backsolve(R, z); betas
## [,1]
## [1,] 12.90219
## [2,] -33.22079
##-----------------------------------------------------------------------------
## Usando decomposição de Cholesky.
XlX <- t(X)%*%X
XlX <- crossprod(X); XlX
## b0 b1
## b0 11.0 131.60
## b1 131.6 1587.26
## U é a triangular superior (upper), L é a inferior (lower).
U <- chol(XlX)
L <- t(U)
## LU = XlX.
L%*%U
## b0 b1
## b0 11.0 131.60
## b1 131.6 1587.26
## Estimação.
d <- t(X)%*%y
z <- forwardsolve(L, d); z
## [,1]
## [1,] 401.76387
## [2,] 46.24218
betas <- backsolve(U, z); betas
## [,1]
## [1,] -33.22079
## [2,] 12.90219
str(m0)
## List of 12
## $ coefficients : Named num [1:2] -33.2 12.9
## ..- attr(*, "names")= chr [1:2] "(Intercept)" "x"
## $ residuals : Named num [1:11] 8.6434 7.7118 0.0292 8.326 2.3162 ...
## ..- attr(*, "names")= chr [1:11] "1" "2" "3" "4" ...
## $ effects : Named num [1:11] -401.76 -46.24 -4.78 7.28 1.39 ...
## ..- attr(*, "names")= chr [1:11] "(Intercept)" "x" "" "" ...
## $ rank : int 2
## $ fitted.values: Named num [1:11] 128 137 153 113 111 ...
## ..- attr(*, "names")= chr [1:11] "1" "2" "3" "4" ...
## $ assign : int [1:2] 0 1
## $ qr :List of 5
## ..$ qr : num [1:11, 1:2] -3.317 0.302 0.302 0.302 0.302 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:11] "1" "2" "3" "4" ...
## .. .. ..$ : chr [1:2] "(Intercept)" "x"
## .. ..- attr(*, "assign")= int [1:2] 0 1
## ..$ qraux: num [1:2] 1.3 1.31
## ..$ pivot: int [1:2] 1 2
## ..$ tol : num 1e-07
## ..$ rank : int 2
## ..- attr(*, "class")= chr "qr"
## $ df.residual : int 9
## $ xlevels : Named list()
## $ call : language lm(formula = y ~ x)
## $ terms :Classes 'terms', 'formula' length 3 y ~ x
## .. ..- attr(*, "variables")= language list(y, x)
## .. ..- attr(*, "factors")= int [1:2, 1] 0 1
## .. .. ..- attr(*, "dimnames")=List of 2
## .. .. .. ..$ : chr [1:2] "y" "x"
## .. .. .. ..$ : chr "x"
## .. ..- attr(*, "term.labels")= chr "x"
## .. ..- attr(*, "order")= int 1
## .. ..- attr(*, "intercept")= int 1
## .. ..- attr(*, "response")= int 1
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## .. ..- attr(*, "predvars")= language list(y, x)
## .. ..- attr(*, "dataClasses")= Named chr [1:2] "nmatrix.1" "numeric"
## .. .. ..- attr(*, "names")= chr [1:2] "y" "x"
## $ model :'data.frame': 11 obs. of 2 variables:
## ..$ y: num [1:11, 1] 137 145 153 121 114 ...
## ..$ x: num [1:11] 12.5 13.2 14.4 11.3 11.2 11.2 11.4 11 10.6 12.4 ...
## ..- attr(*, "terms")=Classes 'terms', 'formula' length 3 y ~ x
## .. .. ..- attr(*, "variables")= language list(y, x)
## .. .. ..- attr(*, "factors")= int [1:2, 1] 0 1
## .. .. .. ..- attr(*, "dimnames")=List of 2
## .. .. .. .. ..$ : chr [1:2] "y" "x"
## .. .. .. .. ..$ : chr "x"
## .. .. ..- attr(*, "term.labels")= chr "x"
## .. .. ..- attr(*, "order")= int 1
## .. .. ..- attr(*, "intercept")= int 1
## .. .. ..- attr(*, "response")= int 1
## .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## .. .. ..- attr(*, "predvars")= language list(y, x)
## .. .. ..- attr(*, "dataClasses")= Named chr [1:2] "nmatrix.1" "numeric"
## .. .. .. ..- attr(*, "names")= chr [1:2] "y" "x"
## - attr(*, "class")= chr "lm"
##-----------------------------------------------------------------------------
## Usando decomposição espectral.
##-----------------------------------------------------------------------------
## Informações da sessão.
Sys.time()
## [1] "2015-04-13 14:22:17 BRT"
sessionInfo()
## R version 3.1.2 (2014-10-31)
## Platform: i686-pc-linux-gnu (32-bit)
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=pt_BR.UTF-8
## [4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=pt_BR.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=pt_BR.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=pt_BR.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets base
##
## other attached packages:
## [1] rmarkdown_0.3.3 knitr_1.8
##
## loaded via a namespace (and not attached):
## [1] digest_0.6.4 evaluate_0.5.5 formatR_1.0 htmltools_0.2.6 stringr_0.6.2
## [6] tools_3.1.2 yaml_2.1.13