{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/plain": [ "R version 4.2.2 (2022-10-31)\n", "Platform: x86_64-apple-darwin17.0 (64-bit)\n", "Running under: macOS Catalina 10.15.7\n", "\n", "Matrix products: default\n", "BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib\n", "LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib\n", "\n", "locale:\n", "[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8\n", "\n", "attached base packages:\n", "[1] stats graphics grDevices utils datasets methods base \n", "\n", "loaded via a namespace (and not attached):\n", " [1] fansi_1.0.4 crayon_1.5.2 digest_0.6.31 utf8_1.2.2 \n", " [5] IRdisplay_1.1 repr_1.1.5 lifecycle_1.0.3 jsonlite_1.8.4 \n", " [9] evaluate_0.20 pillar_1.8.1 rlang_1.0.6 cli_3.6.0 \n", "[13] uuid_1.1-0 vctrs_0.5.2 IRkernel_1.3.2 tools_4.2.2 \n", "[17] glue_1.6.2 fastmap_1.1.0 compiler_4.2.2 base64enc_0.1-3\n", "[21] pbdZMQ_0.3-9 htmltools_0.5.4" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sessionInfo()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "library(plot3D)\n", "library(ggplot2)\n", "#library(magick)\n", "library(animation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Random number generation\n", "\n", "## Uniform random number generation\n", "\n", "### Goal\n", "\n", "To generate $U_i \\stackrel{iid}{\\sim} \\text{unif}(0, 1)$.\n", "\n", "* Basis for all other random number generation\n", "* **Fact: NO RANDOM NUMBER IN COMPUTER** --- only look random (PSEUDO-RANDOM)\n", "\n", "### Congruential generator\n", "\n", "\\begin{align*}\n", " x_{i+1} &= a x_i \\mod m, \\quad i=1, 2, \\dotsc \\\\\n", " u_i &= x_i / m.\n", "\\end{align*}\n", "\n", "* Modulus $m$ is a large prime number.\n", "* Multiplier $a$ is a positive integer between 2 and $m-1$.\n", "* Map $f: x \\mapsto ax \\mod m$ maps $\\{1, \\dotsc, m-1\\}$ onto itself and is one-to-one:\n", " - Suppose $x\\in\\{1, \\dotsc, m-1\\}$. Then $f(x) \\neq 0$ since $a$ and $m$ are relatively prime hence $ax$ is not a multiple of $m$. Thus $f$ maps $\\{1, , \\dotsc, m-1\\}$ to $\\{1, , \\dotsc, m-1\\}$.\n", " - If $ay = ax \\mod m$, then $a(y - x) = m k$ for some integer $k$. Since $a$ and $m$ are relatively prime, $y - x = m l$ for some interger $l$. That is, $x = y \\mod m$. Hence map $f$ is one-to-one.\n", " - Since $f$ maps $\\{1, , \\dotsc, m-1\\}$ to $\\{1, , \\dotsc, m-1\\}$ and one-to-one, $f$ is also onto.\n", " \n", "* Note\n", "\\begin{align*}\n", " x_1 &= a x_0 \\mod m \\\\\n", " x_2 &= a x_1 \\mod m = a^2 x_0 \\mod m \\\\\n", " x_3 &= a x_2 \\mod m = a^3 x_0 \\mod m \\\\\n", " & \\vdots \\\\\n", " x_n &= a x_{n-1} \\mod m = a^n x_0 \\mod m\n", "\\end{align*}\n", "Hence if $a^n = 1 \\mod m$ for some $n$, then \n", "$$\n", " x_n = x_0 \\mod m\n", "$$\n", "and the (pseudo)random number generator repeats the sequence. The number $n$ is called the **period** of the RNG, and $x_0$ is called the **seed**.\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 0.646902838954702
  2. 0.394225758267567
  3. 0.618501814315096
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.646902838954702\n", "\\item 0.394225758267567\n", "\\item 0.618501814315096\n", "\\item 0.476891135564074\n", "\\item 0.136097185546532\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.646902838954702\n", "2. 0.394225758267567\n", "3. 0.618501814315096\n", "4. 0.476891135564074\n", "5. 0.136097185546532\n", "\n", "\n" ], "text/plain": [ "[1] 0.6469028 0.3942258 0.6185018 0.4768911 0.1360972" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "
  1. 0.646902838954702
  2. 0.394225758267567
  3. 0.618501814315096
  4. 0.476891135564074
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.646902838954702\n", "\\item 0.394225758267567\n", "\\item 0.618501814315096\n", "\\item 0.476891135564074\n", "\\item 0.136097185546532\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.646902838954702\n", "2. 0.394225758267567\n", "3. 0.618501814315096\n", "4. 0.476891135564074\n", "5. 0.136097185546532\n", "\n", "\n" ], "text/plain": [ "[1] 0.6469028 0.3942258 0.6185018 0.4768911 0.1360972" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "set.seed(2020) # set 2020th seed; does not mean x_0 = 2020\n", "runif(5)\n", "set.seed(2020) # same seed results in same \"random\" sequence\n", "runif(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Primitive root of unity\n", " - Fermat's little theorem: $a^{m} = a \\mod m$.\n", " - Since $a$ is not divisible by $m$, we have $a^{m-1} = 1 \\mod m$.\n", " - Thus the period $n$ satisfies $n \\le m - 1$.\n", " - *Primitive* root of unity: $a$ such that $n = m - 1$\n", " - If $a$ is primitive, then $x_1, x_2, \\dotsc, x_{m-1}$ is a permutation of $\\{1, 2, \\dotsc, m-1\\}$.\n", " - For $m=2^{31} - 1$ (Mersenne prime), $a=7^5 = 16807$ is primitive, leading to the period of $2^{31} - 2$ = `2,147,483,646`. This RNG was used in early versions of MATLAB (up to v4).\n", " \n", "Good RNGs should have long periods, and should give samples which appear to be drawn from a uniform distribution. If the size of the sample is much less than the period of the RNG, then the sample should appear random." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "# returns a congruential generator with fixed $a$ and $m$\n", "congruential_gen <- function(a, m, seed = 1) {\n", " # initial seed for g\n", " if (!hasArg(seed)) seed <- (as.numeric(Sys.time()) * 1000) %% m\n", " g <- function(n) {\n", " u <- vector(length=n)\n", " u[1] <- seed\n", " for (i in seq_len(n-1)) {\n", " u[i+1] <- (a * u[i]) %% m\n", " } \n", " seed <<- (a * seed) %% m # seed update\n", " u / m \n", " }\n", " g\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Autocorrelation\n", "\n", "* Ideally, a pseudorandom number sequence should look i.i.d. If we take the first $p$ values to form an $p$-dimensional vector, the second $p$ values to form a second $p$-dimensional vector, etc, then these vectors should fill the $p$-dimensional hypercube uniformly.\n", "\n", "* However, by construction the sequence generated by congruential generators depends on the previous value, hence tends to be correlated.\n", "\n", "* It is known that congruential generators tend to give $p$-dimensional vectors that concentrate lower-dimensional hyperplanes, for some $p$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "# IBM System/360 RANDU generator\n", "# a = 2^16 + 3 = 65539\n", "# m = 2^31\n", "RANDU <- congruential_gen(65539, 2^31) #, seed=1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 0.273911437810852
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\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.273911437810852\n", "\\item 0.881722685458953\n", "\\item 0.223082294352935\n", "\\item 0.590489596987027\n", "\\item 0.0976969327457482\n", "\\item 0.959275223591249\n", "\\item 0.938878946835757\n", "\\item 0.187296668693307\n", "\\item 0.236369490638026\n", "\\item 0.420046925588395\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.273911437810852\n", "2. 0.881722685458953\n", "3. 0.223082294352935\n", "4. 0.590489596987027\n", "5. 0.0976969327457482\n", "6. 0.959275223591249\n", "7. 0.938878946835757\n", "8. 0.187296668693307\n", "9. 0.236369490638026\n", "10. 0.420046925588395\n", "\n", "\n" ], "text/plain": [ " [1] 0.27391144 0.88172269 0.22308229 0.59048960 0.09769693 0.95927522\n", " [7] 0.93887895 0.18729667 0.23636949 0.42004693" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "RANDU(10)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Output at: RANDU.gif\n", "\n" ] }, { "data": { "text/html": [ "TRUE" ], "text/latex": [ "TRUE" ], "text/markdown": [ "TRUE" ], "text/plain": [ "[1] TRUE" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n <- c(10, 50, 100, 500, 1000, 2000, 5000, 10000, 20000)\n", "\n", "saveGIF({\n", " for (i in 1:length(n)) {\n", " u <- RANDU(n[i])\n", " x <- u[1:(n[i]-2)]\n", " y <- u[2:(n[i]-1)]\n", " z <- u[3:(n[i])]\n", " scatter3D(x, y, z, colvar = NULL, pch=20, cex = 0.5, theta=160, main = paste('n = ', n[i]))\n", " }\n", "}, movie.name = 'RANDU.gif')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [], "source": [ "# Early MATLAB RNG\n", "# a = 7^5\n", "# m = 2^31 - 1\n", "MATLABRNG <- congruential_gen(7^5, 2^31 - 1)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/html": [ "\n", "
  1. 0.273912330320052
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  9. 0.715909354827586
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  1. 'Mersenne-Twister'
  2. 'Inversion'
  3. 'Rejection'
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 'Mersenne-Twister'\n", "\\item 'Inversion'\n", "\\item 'Rejection'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 'Mersenne-Twister'\n", "2. 'Inversion'\n", "3. 'Rejection'\n", "\n", "\n" ], "text/plain": [ "[1] \"Mersenne-Twister\" \"Inversion\" \"Rejection\" " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "RNGkind()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Transformation methods\n", "\n", "From now on, we assume the the problem of generating uniform random numbers has been solved for practical purposes.\n", "\n", "### Inverse CDF method\n", "\n", "For a random variable $X$, let $F$ be its cumulative distribution function (CDF), that is, $F(x) = P(X \\le x)$.\n", "Recall that $F$ is right-continuous and nondecreasing. Also, if $F$ is strictrly increasing, random variable $F(X)$ is uniformly distributed on $[0, 1]$. Below, we generalize this result.\n", "\n", "The inverse CDF of $X$ is defined as\n", "$$\n", " F^{-1}(u) = \\inf\\{x: F(x) \\ge u\\}, \\quad 0 < u < 1\n", " ,\n", "$$\n", "which coincides with the usual inverse of $F$ if $F$ is strictly increasing.\n", "\n", "**Proposition 1**. Let $X$ be a random variable with CDF $F$. Then the following holds.\n", "1. If $F$ is continuous, then $U = F(X)$ is a uniform random variable on $[0, 1]$.\n", "2. If $F$ is not continous, then $P[F(X) \\le y] \\le y$ for all $y \\in [0, 1]$.\n", "3. If $U$ is uniform on $[0, 1]$, then $F^{-1}(U)$ has CDF $F$.\n", " \n", "*Proof*. \n", "* Part 1: We will show that \n", "$$\n", " P[F(X) \\le F(t)] = F(t)\n", " \\tag{*}\n", "$$\n", "for any $t$. Suppose for now this is true. \n", "\\\n", "\\\n", "Let $u \\in (0, 1)$. Then by continuity of $F$, there is $y$ such that $F(y) = u$. By (*), \n", "$$\n", " P[F(X) \\le u] = P[F(X) \\le F(y)] = F(y) = u.\n", "$$\n", "\n", "* Part 3: It suffices to show that $\\{F^{-1}(U) \\le t\\} = \\{U \\le F(t)\\}$. If $F^{-1}(u)=\\inf\\{x: F(x) \\ge u\\} \\le t$, then by the monotonicity and right-continuity of $F$, the set $\\{x: F(x) \\ge u\\}$ is an half-closed interval containing its left endpoint, which is $F^{-1}(u)$. Hence $F(F^{-1}(u)) \\ge u$. Since $F^{-1}(u) \\le t$, again by monotonicity of $F$, it follows that $u \\le F(F^{-1}(u)) \\le F(t)$. Conversely, if $u \\le F(t)$, then by definition $F^{-1}(u) \\le t$.\n", "\n", "* Part 2: by part 3, $X\\stackrel{d}{=}F^{-1}(U)$, where $U$ is uniform on $[0, 1]$. Since $x=F^{-1}(u)$ implies $u \\le F(x)$, it follows from $X\\stackrel{d}{=}F^{-1}(U)$ that $U \\le F(X)$ almost surely. Then,\n", "$\\{F(X) \\leq y \\} \\subset \\{U \\leq y\\}$. Therefore,\n", "$$\n", " P[F(X) \\le y] \\le P(U \\le y) = y.\n", "$$\n", "\n", "* It remains to show (*). Monotonicity of $F$ yields $\\{X > t\\} \\subset \\{F(X) \\ge F(t)\\}$. Hence $\\{X > t \\} \\cap \\{F(X) < F(t) \\} = \\emptyset$. Likewise $\\{X \\le t\\} \\cap \\{F(X) > F(t)\\} = \\emptyset$. Then,\n", "\\begin{align*}\n", " \\{X > t\\} \\cap \\{F(X) \\le F(t)\\} &=\n", " [\\{X > t\\} \\cap \\{F(X) < F(t) \\}] \\cup [\\{X > t\\} \\cap \\{F(X) = F(t)\\}] \\\\\n", " &= \\{X > t\\} \\cap \\{F(X) = F(t)\\}\n", " \\\\\n", " \\{X \\le t\\} \\cap \\{F(X) \\le F(t)\\} &= \\{X \\le t\\} \\cap \\{F(X) > F(t)\\}^c \n", " = \\{X \\le t\\}\n", "\\end{align*}\n", "So,\n", "$$\n", " \\{F(X) \\le F(t) \\} = \\{X \\le t\\} \\cup [\\{X > t\\} \\cap \\{F(X) = F(t)\\}] =: A \\cup B\n", " .\n", "$$\n", "Obviously events $A$ and $B$ are disjoint. However, event $B$ corresponds to the values $x$ of $X$ with which $F(x)$ is constant. Hence $P(B)=\\int_B dF(x) = 0$. Therefore,\n", "$$\n", " P[F(X) \\le F(t)] = P(A) + P(B) = P(A) = P(X \\le t) = F(t).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exponential distribution\n", "\n", "* CDF $F(x) = 1 - e^{-\\lambda x}$ yields $F^{-1}(u) = -\\frac{1}{\\lambda}\\log u$ on $(0, 1)$. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“\u001b[1m\u001b[22mThe dot-dot notation (`..count..`) was deprecated in ggplot2 3.4.0.\n", "\u001b[36mℹ\u001b[39m Please use `after_stat(count)` instead.”\n" ] }, { "data": { "image/png": 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t+INRFAAAEEEEAAAQRcEch6FztXasFBEdBYoNxqQVJT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\n9KrYnqriDdV6/63PV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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# Exp(1)\n", "n <- 1000\n", "u <- runif(n)\n", "x <- -log(u)\n", "expdata <- data.frame(x)\n", "plt <- ggplot(expdata, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Cauchy distribution\n", "\n", "From the density of the Cauchy distribution\n", "$$\n", " f(x) = \\frac{\\beta}{\\pi(\\beta^2 + (x-\\mu)^2)},\n", "$$\n", "its CDF is $F(x) = \\frac{1}{2} + \\frac{1}{\\pi}\\tan^{-1}\\left(\\frac{x-\\mu}{\\beta}\\right)$. Thus\n", "$$\n", " F^{-1}(u) = \\mu + \\beta\\tan(\\pi u - \\pi/2) = \\mu - \\frac{\\beta}{\\tan(\\pi u)}\n", " .\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“\u001b[1m\u001b[22mRemoved 4 rows containing non-finite values (`stat_bin()`).”\n", "Warning message:\n", "“\u001b[1m\u001b[22mRemoved 4 rows containing non-finite values (`stat_density()`).”\n", "Warning message:\n", "“\u001b[1m\u001b[22mRemoved 2 rows containing missing values (`geom_bar()`).”\n" ] }, { "data": { "image/png": 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wEJUr37T+sJECBAYJcCxXC6njlIxcVjd7lPHyNAgACB+gtIkOrfhyIgQIAAgV0I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\nZ3LzZ13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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# standard Cauchy (beta=1, mu=0)\n", "n <- 1000\n", "u <- runif(n)\n", "x <- -1/tan(pi * u)\n", "#hist(x, breaks=40)\n", "cauchydata <- data.frame(x)\n", "plt <- ggplot(cauchydata, aes(x=x)) + \n", " geom_histogram(binwidth=10, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=10 * ..count..), color=\"purple\") + \n", " xlim(-200, 200)\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Discrete uniform distribution \n", "\n", "$X \\sim \\text{unif}(\\{1, 2, \\dotsc, k\\})$. It is easy to verify $F(x) = \\frac{1}{k}\\lfloor x \\rfloor$ for $x \\in [0, n]$ and $F^{-1}(u)=\\lceil ku \\rceil$.\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/plain": [ "x\n", " 1 2 3 4 5 6 7 8 9 10 \n", "108 108 92 93 97 85 94 118 108 97 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k <- 10\n", "n <- 1000\n", "u <- runif(n)\n", "x <- ceiling(k * u)\n", "table(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Geometric distribution \n", "\n", "If $X \\sim \\text{geom}(p)$, then its probability mass functin $p(x) = (1-p)^{x-1}p$.\n", "\n", "For $Y \\sim \\text{Exp}(\\lambda)$, \n", "\\begin{align*}\n", " P(\\lceil Y \\rceil = k) &= P(k-1 < Y \\le k) = F_Y(k) - F_Y(k-1) = (1 - e^{-\\lambda k}) - (1 - e^{-\\lambda(k-1)}) \\\\\n", " &= e^{-\\lambda(k-1)}(1 - e^{-\\lambda}) \\\\\n", " &= (1 - p)^{k-1} p\n", "\\end{align*}\n", "if $\\lambda$ satisfies $p = 1 - e^{-\\lambda}$, or $\\lambda = -\\log(1-p)$.\n", "\n", "For this $\\lambda$, $X = \\lceil Y \\rceil = \\lceil -\\frac{1}{\\lambda}\\log U \\rceil = \\lceil \\frac{\\log U}{\\log(1-p)}\\rceil$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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FTfzpoECBAgQIAAAQIECLRMQEBqWUEN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\nALds2TKuCnFgrlq1atw8dwgQIECAA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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "gengeom <- function(p, nsamp=1) {\n", " u <- runif(nsamp)\n", " y <- log(u) / log(1 - p)\n", " ceiling(y)\n", "} \n", "nsamp <- 1000\n", "p <- 0.3\n", "x <- gengeom(p, nsamp)\n", "geomdata <- data.frame(x)\n", "plt <- ggplot(geomdata, aes(x=x)) + geom_histogram(binwidth=0.25)\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Normal random numbers\n", "\n", "For $X \\sim N(0, 1)$, inverse CDF $\\Phi^{-1}$ does not have a closed form.\n", "\n", "#### Box-Muller\n", "\n", "Generates $X, Y \\stackrel{iid}{\\sim} N(0, 1)$.\n", "\n", "Transforms the random Cartesian coordinates $(X, Y)$ to polar coorinates $(R, \\Theta)$. Since $(X, Y)=(R\\cos\\Theta, R\\sin\\Theta)$,\n", "$$\n", " \\iint_A f_{XY}(x, y)dxdy = \\iint_A \\frac{1}{2\\pi}\\exp\\left(-\\frac{x^2 + y^2}{2}\\right)dxdy\n", " = \\iint_A \\frac{1}{2\\pi}\\exp\\left(-\\frac{r^2}{2}\\right)rdrd\\theta\n", " .\n", "$$\n", "\n", "Hence $R$ has density $f_R(r) = r\\exp(-\\frac{r^2}{2})$ and $\\Theta$ is uninform on $[0, 2\\pi]$. Since\n", "$$\n", " P(R > \\rho) = P(R^2 > \\rho^2) = \\int_\\rho^{\\infty} r\\exp\\left(-\\frac{r^2}{2}\\right)dr = \\exp\\left(-\\frac{1}{2}\\rho^2\\right),\n", "$$\n", "random variable $R^2$ is exponentially distributed with $\\lambda = 1/2$.\n", "\n", "Thus for independent $U, V \\sim \\text{unif}(0, 1)$, set\n", "$$\n", " R = (-2\\log U)^{1/2}, \\quad \\Theta = 2\\pi V\n", " .\n", "$$\n", "Then $(X, Y) = (R\\cos\\Theta, R\\sin\\Theta)$ are independently $N(0, 1)$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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RIxacGdYYUKbI25PJ639WyrYr3HR9RrQlirXqpV5bZg9qK1ZcTrCCCAQBAFSJCC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\nER31dEjHv1mv4d8NK+TclzTvz349d0BQ078f0IZ3mE+pERlPdxEgQNoFhJe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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "boxmuller <- function(nsamp) {\n", " n <- ceiling(nsamp / 2)\n", " u <- runif(n)\n", " v <- runif(n)\n", " r <- sqrt(-2 * log(u))\n", " theta <- 2 * pi * v\n", " x <- r * cos(theta)\n", " y <- r * sin(theta)\n", " samp <- c(x, y)\n", " samp[seq_len(nsamp)]\n", "}\n", "#hist(c(x, y))\n", "n <- 1000\n", "normdata1 <- data.frame(x = boxmuller(n))\n", "plt <- ggplot(normdata1, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Marsaglia\n", "\n", "* From the Box-Muller transformation, we learned that if $R^2 \\sim \\text{Exp}(1/2)$ and $\\Theta\\sim\\text{unif}(0, 2\\pi)$ and they are independent, $(R\\cos\\Theta, R\\sin\\Theta)$ are i.i.d. standard normal. \n", "\n", "* On the other hand, if a random point $(U, V)$ is uniformly distributed on the unit disk, and let $(U, V) = (T\\cos\\Phi, T\\sin\\Phi)$, then\n", "$$\n", " P(T^2 \\le t^2, 0 \\le \\Phi \\le \\phi) = \n", " \\frac{t^2\\phi}{2\\pi}, \\quad t^2 \\le 1, ~ \\phi \\in (0, 2\\pi) \\\\\n", "$$\n", "which means that $T^2 = U^2 + V^2 \\sim \\text{unif}(0, 1)$, $\\Phi \\sim \\text{unif}(0, 2\\pi)$, and they are independent.\n", "\n", "* Therefore, if we sample $(U, V)$ uniformly from the unit disk, and set $T = \\sqrt{U^2 + V^2}$, $\\cos\\Phi = U/T$, $\\sin\\Phi=V/T$, then $T^2\\sim\\text{unif}(0,1)$ and $-2\\log T^2$ is identically distributed to $R^2$, i.e., $\\text{Exp}(1/2)$, and $\\Phi$ is identically distributed to $\\Theta$, i.e., uniform on $(0, 2\\pi)$. Therefore, if we set $(X, Y)$ such that\n", "$$\n", " X = \\sqrt{-2\\log T^2}\\frac{U}{T},\n", " \\quad\n", " Y = \\sqrt{-2\\log T^2}\\frac{V}{T},\n", "$$\n", "then $X, Y$ are i.i.d. standard normal.\n", "\n", "* One way to sample from the unit disk is to sample $(U, V)$ from $\\text{unif}[-1, 1]\\times\\text{unif}[-1, 1]$, and discard the sample if $U^2 + V^2 > 1$ and resample (see acceptance-rejection sampling below).\n", "\n", "* Algorithm:\n", " 1. $U, V \\stackrel{iid}{\\sim} \\text{unif}[-1, 1]$;\n", " 2. If $T = \\sqrt{U^2 + V^2} > 1$, go to 1;\n", " 3. Set $X = \\sqrt{-2\\log T^2}\\frac{U}{T}$ and $Y = \\sqrt{-2\\log T^2}\\frac{V}{T}$.\n", " \n", "* This method avoids the trigonometric function evaluations of the Box-Muller, but uses $4/\\pi$ as many random pairs on average." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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+8ch8TzkHq48AYBBBAIigABUlBamnoigAACnQIjVaPIiiM0ekZIh7+Tu0e9T4zh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\n6fAHwwp2ymKFODQCrQiQILUCxMvtEwgEAjr++OO323nufzbrhV9uVMSZGuG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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "marsaglia <- function(nsamp) {\n", " n <- ceiling(nsamp / 2)\n", " it <- 0\n", " x <- numeric(n)\n", " y <- numeric(n)\n", " while (it < n) {\n", " u <- 2 * runif(1) - 1\n", " v <- 2 * runif(1) - 1\n", " tau <- sqrt(u^2 + v^2)\n", " if (tau > 1) next\n", " x[it] <- sqrt(-4 * log(tau)) * u / tau\n", " y[it] <- sqrt(-4 * log(tau)) * v / tau\n", " it <- it + 1\n", " }\n", " samp <- c(x, y)\n", " samp[seq_len(nsamp)] \n", "}\n", "n <- 1000\n", "normdata2 <- data.frame(x = marsaglia(n))\n", "plt <- ggplot(normdata2, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Random numbers by definition\n", "\n", "### Bernoulli\n", "\n", "1. Set the success probability $p$\n", "2. Generate $U \\sim \\text{unif}(0, 1)$.\n", "3. Let $X = \\mathbb{I}_{\\{U \\le p\\}}$.\n", "4. Then $X \\sim \\text{Ber}(p)$.\n", "\n", "### Binomial\n", "\n", "1. Set the success probability $p$\n", "2. Generate $n$ independent $X_i \\sim \\text{Ber}(p)$.\n", "3. Let $X_n = \\sum_{i=1}^n X_i$.\n", "4. Then $X_n \\sim B(n, p)$.\n", "\n", "### Negative binomial\n", "\n", "1. Set the success probability $p$\n", "2. Generate $r$ independent $X_i \\sim \\text{Geom}(p)$.\n", "3. Let $X_r = \\sum_{i=1}^r X_i$.\n", "4. Then $X_r \\sim \\text{NegBin}(r, p)$.\n", "\n", "### Poisson\n", "\n", "1. Generate $U_i \\stackrel{iid}{\\sim} \\text{unif}(0, 1)$.\n", "2. Find $N$ such that $\\prod_{i=1}^N U_i \\ge e^{-\\lambda} > \\prod_{i=1}^{N+1} U_i$.\n", "3. Then $N \\sim \\text{Poi}(\\lambda)$.\n", "\n", "- This is because $T_i = -\\frac{1}{\\lambda}\\log U_i \\stackrel{iid}{\\sim} \\text{Exp}(\\lambda)$,\n", "and is the waiting time between the $i-1$st and the $i$th event of the Poisson counting process $N(t) \\sim \\text{Poi}(\\lambda t)$.\n", "- That is, $N \\sim \\text{Poi}(\\lambda) \\iff T_1 + \\dotsb + T_N \\le 1 < T_1 + \\dotsb + T_N + T_{N+1}$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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66xd3k/8YH6nDlzuDdcxBiOhgJSk09EvJxpxmOlyisaWn8Dysc//vHiY70/97nP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\nCRAgQIAAAQIECBBIS0BASqseRkOAA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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## Binomial random number generation\n", "genbin <- function(n, p) {\n", " u <- runif(n)\n", " x <- sum(u < p)\n", "}\n", "n <- 10; p <- 0.6\n", "nsamp <- 1000\n", "x <- numeric(nsamp)\n", "for (i in seq_len(nsamp)) {\n", " x[i] <- genbin(n, p)\n", "}\n", "bindata <- data.frame(x)\n", "plt <- ggplot(bindata, aes(x=x)) + geom_histogram(binwidth=0.25)\n", "print(plt)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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w2wewIECBAgQIAAAQIE0hEQkNLphZEQIECAAAECBAgQINBnAQGpzw2wewIECBAg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\nYcGCBeH6668PV199dbjxxhsb1ztBc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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# Negative binomial random number generation\n", "gengeom <- function(p, nsamp=1) {\n", " u <- runif(nsamp)\n", " y <- log(u) / log(1 - p)\n", " ceiling(y)\n", "} \n", "nsamp <- 1000\n", "p <- 0.6\n", "r <- 5\n", "x <- numeric(nsamp)\n", "for (i in seq_len(r)) {\n", " x <- x + gengeom(p, nsamp)\n", "}\n", "negbindata <- data.frame(x)\n", "plt <- ggplot(negbindata, aes(x=x)) + geom_histogram(binwidth=0.25)\n", "print(plt)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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BwgqwkQIECAAAECBAgQSEdAQEqn1yolQIAAAQIECBAgQCBHQEDKAbKaAAECBAgQ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\nBAgQIECAAAECpRBwFbtStMkgCRAgQ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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# Poisson random number generation\n", "genpoi <- function(lam, maxiter=1000) {\n", " u_cum <- 1.0\n", " k <- 0\n", " while (u_cum > exp(-lam) && k < maxiter ) {\n", " u <- runif(1)\n", " u_cum <- u_cum * u\n", " k <- k + 1\n", " }\n", " k - 1\n", "}\n", "lam <- 3 # Poisson rate\n", "nsamp <- 1000\n", "x <- numeric(nsamp)\n", "for (i in seq_len(nsamp)) {\n", " x[i] <- genpoi(lam)\n", "}\n", "poidata <- data.frame(x)\n", "plt <- ggplot(poidata, aes(x=x)) + geom_histogram(binwidth=0.25)\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Chi-square\n", "\n", "1. Generate $Z_1, \\dotsc, Z_{\\nu} \\stackrel{iid}{\\sim} N(0, 1)$.\n", "2. Let $X_{\\nu} = \\sum_{i=1}^{\\nu} Z_i^2$.\n", "3. Then $X_{\\nu} \\sim \\chi^2(\\nu)$.\n", "\n", "Alternatively, for even $\\nu$:\n", "\n", "1. Generate $U_i \\stackrel{iid}{\\sim} \\text{unif}(0, 1)$.\n", "2. Let $X_{\\nu} = -2\\log(\\prod_{i=1}^{\\nu/2} U_i) = \\sum_{i=1}^{\\nu/2}(-2\\log U_i)$.\n", "3. Then $X_{\\nu} \\sim \\chi^2(\\nu)$.\n", "\n", "This is because $\\chi^2(\\nu) = \\text{Gamma}(\\nu/2, 2)$, where 2 is the scale parameter.\n", "\n", "### Student's $t$\n", "\n", "1. Generate $Z \\sim N(0, 1)$ and $X \\sim \\chi^2(\\nu)$ independently.\n", "2. Let $T = Z / \\sqrt{X/\\nu}$.\n", "3. Then $T \\sim t(\\nu)$.\n", "\n", "### $F$\n", "\n", "1. Generate $X_1 \\sim \\chi^2(\\nu_1)$ and $X_2 \\sim \\chi^2(\\nu_2)$ independently.\n", "2. Let $$F = \\frac{X_1/\\nu_1}{X_2/\\nu_2}.$$\n", "3. The $F \\sim F(\\nu_1, \\nu_2)$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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6NVo3Rt332iItr21yuPTc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\ndeV3tbP3q678rprvV4H2aR1rV95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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## chi-square random number generation\n", "genchisq1 <- function(nsamp, nu) {\n", " z <- matrix(rnorm(nsamp * nu), nrow=nsamp)\n", " rowSums(z^2)\n", "}\n", "nu <- 6\n", "n <- 1000\n", "chisqdata1 <- data.frame(x = genchisq1(n, nu))\n", "plt <- ggplot(chisqdata1, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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dphfXRB165dddFFF0VftvidzDFgyhSvPsXF1rWRCU47c22dhNfrbXG8tl7P69QE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Dt99+e9wyBx54YOc7oQQCCCCAAAJfC9CD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\nsMMO67RMZ9swy6+77rre+hreZr9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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## chi-square random number generation 2\n", "genchisq2 <- function(nsamp, nu) {\n", " u <- matrix(runif(nsamp * nu / 2), nrow=nsamp)\n", " -2 * log(apply(u, 1, prod) )\n", "}\n", "nu <- 6\n", "n <- 1000\n", "chisqdata2 <- data.frame(x = genchisq2(n, nu))\n", "plt <- ggplot(chisqdata2, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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TISqK2tJQYZyVlzkPpiXlhYKKFQSDo6OqwplFLSFlAxUO9HXV1daR/rxQM2/Umd\nshaQhtP6jfeHPrOLqX4AZtujt7d32HtW5TJVY1C2PdMt1SfypX6i/pWVlebvQTgcnmhRHJ+h\nAN+PMoSz+DC+H6UOqr7LqD9eJVt8nyCl80Gazr7J4NmevoD6KyExSN/N6iOIg9Wi6ZUXjUbN\nv5jzuxBz2/Wk8TGm6TLp1LDx/hBb55QRBRWroXGqPUa1LyiNr8mw9bFW8/90BVScRxqnWwb7\nT0wg/rs29HU+sRI5OhMBPpczUUt8DNcgJfZhKwIIIICAQwV6m0Va12hSd6wuhcnPlra9F6qN\n5Yfp0rJak2hqZ3nY3mYagAACCPhRgATJj1GnzwgggIAHBPY8oz7CNJl6pnNnrxvJXHuMMarU\no8mBDcxmN9KG5wgggIBTBEiQnBIJ2oEAAgggkJbA3mdjScbUM9xzPU/d8lhbm1eRIKUVbHZG\nAAEEcihAgpRDbKpCAAEEELBGQDcGjfY9Z0wcUqtL9VEuSpCOGUiQ3iRBsuaVQCkIIICA9QIk\nSNabUiICCCCAQJYFWtdq0teqyZTTosa051muzMLiqxbpEizWpflNPn4tZKUoBBBAwFIB3qEt\n5aQwBBBAAIFcCOx5JpYVTXHR6XXKJWDcVq/WuGFs5/tGgteWCynqQAABBBBIV4AEKV0x9kcA\nAQQQsF1AnV4nosuU090zQUMcrXbgNDs1mx0LAggggIDzBEiQnBcTWoQAAgggkEAgdFCMU9Q0\nqT5Sl6LaBDs6dFPt0bGkjgTJoQGiWQgg4HsBEiTfvwQAQAABBNwlsP9FTfSIJpNPdc/kDEOF\na5fF2t2yio/goS48RgABBJwiwLuzUyJBOxBAAAEEUhLY97fYR5eaoMGNS+k0kaJ644axb3GK\nnRvjR5sRQMD7AiRI3o8xPUQAAQQ8JbDXuP4oWKRL/XHuHEFSwVDXIalZ+A7u9FRo6AwCCCDg\nCQESJE+EkU4ggAAC/hDo2i3mDHD1K4zpsovc2+faZQPXIb3Fx7B7o0jLEUDAqwK8M3s1svQL\nAQQQ8KDA/hdiH1uTT3Hn6XXxkAxeh8RMdnESfiKAAAKOEchzTEtoCAIIIIAAAobA+vXrx3XY\n/uhMY1uNdE/bYuzXM+Z+vb29Y6530kp1LyS1tJIgOSkstAUBBBAwBUiQeCEggAACCDhGIBwO\ny4c+9KFx2/P/5G3Jl3ZZ+aVTjLsgjX8NUiDg7BMkCqpEymbp0vq2MSOfMRimObu548aDDQgg\ngIAXBUiQvBhV+oQAAgi4XGDy5MmycuXKYb3Ib6uXyt9PkYOHvSOXn335sG1Dn/ziF7+QaNT5\np+Cp65C2PxKUji0ilXOH9oDHCCCAAAJ2CpAg2alP3QgggAACYwrMmTNHfvaznw3b9tbtvfL0\n77tk5b8dL8u+dOqwbUOf/OpXvxI3nGZXY5xmt/0R4zS7NQEjQXJ+QjfUmMcIIICAlwUY1Pdy\ndOkbAggg4CGBnc+EzN7MOMMbf9tjogYPvTjpCgIIeEqABMlT4aQzCCCAgDcFdF2XXc+FpGSS\nJrULvZEgVR9lXEOlGdchreWGsd581dIrBBBwqwAJklsjR7sRQAABHwk0r4tIT7MuM87I90yv\n80tFKo4QaXtHk2jEM92iIwgggIDrBUiQXB9COoAAAgh4XyB+et1MDyVIKmo1S6IS6dGkYzOj\nSN5/FdNDBBBwiwAJklsiRTsRQAABHwvEE6Tpp3tnBEmFs2bJwP2QOM3Ox69uuo4AAk4TIEFy\nWkRoDwIIIIDAMAHz+qPnw1I6RZOaecFh29z+hATJ7RGk/Qgg4EUBEiQvRpU+IYAAAh4SaHkn\nIr0tukw/zVujRypE1UcyUYOHXqp0BQEEPCJAguSRQNINBBBAwKsCO58Lm12b4cEEKb+MiRq8\n+rqlXwgg4F4BEiT3xo6WI4AAAr4QUNN7q2X6qd6Y3ntk0KqPik3U0Lll5BaeI4AAAgjYIUCC\nZIc6dSKAAAIIpCyw628hKa437n+0yJsJUo26H5KxtL7NR3LKLwp2RAABBLIowLtxFnEpGgEE\nEEBgYgKt70ake78u0z7gveuP4jKDCRIz2cVJ+IkAAgjYKkCCZCs/lSOAAAIIJBLY/fzA6XUf\n8Obokeq7OVGD8bPtbe6FlOi1wDYEEEAgVwIkSLmSph4EEEAAgbQFdhnTe6tluodHkAoqRcpm\n6tL2jiZ67Gy7tJ04AAEEEEDAOgESJOssKQkBBBBAwGKB3S+ERM30Vr/MW/c/GsmkRpFCnZoc\n3D5yC88RQAABBHItQIKUa3HqQwABBBBISeDg3qgc2BKVqSfmSyDo7dPP1Ex2amljooaUXhvs\nhAACCGRTgAQpm7qUjQACCCCQsYAaPVLLNA9ffxTHGZyoYZ23E8F4f/mJAAIIOFmABMnJ0aFt\nCCCAgI8F9rwYu/5o2snencEuHl4maohL8BMBBBCwX4AEyf4Y0AIEEEAAgTEEdr8YEs249GjK\nCu/OYBfvdnGDSFF9bKKG+Dp+IoAAAgjYI0CCZI87tSKAAAIIJBAIRgqkcXVEGozJGfJL/XHa\nmRpF6m3SpKcxAQybEEAAAQSyLkCClHViKkAAAQQQSFegunOe6MYZdlNP8v7pdXGbwdPsuA4p\nTsJPBBBAwBYBEiRb2KkUAQQQQCCRQE3nAnPz1JO9f3pd3KHGGEFSSys3jI2T8BMBBBCwRYAE\nyRZ2KkUAAQQQSCRQ27HQ3DzNRwlS9ZGxqb7b3+GjOdFrg20IIIBAtgV4F862MOUjgAACCKQt\noE6xK5sekPLp3r5B7FCYstkieaW6tHKK3VAWHiOAAAI5FyBByjk5FSKAAAIIJBKolzlSEC43\nbhDrn9PrlIdmzEVRtUiXg9tEQl2JhNiGAAIIIJBNARKkbOpSNgIIIIBA2gKzZLl5jN8SJNXp\n6sXqOiRN2tf7Y+Y+M9D8DwEEEHCYAAmSwwJCcxBAAAG/C8yW40yCKT4bQVKdjiVIIm3vkCD5\n/feA/iOAgH0CJEj22VMzAggggMAYArOMBCmihWTSMf46xU5RDE71TYI0xiuDVQgggEBuBEiQ\ncuNMLQgggAACKQiEDopMkgVyoGyLBAv8N4pSNV8XLaBLGxM1pPBqYRcEEEAgOwIkSNlxpVQE\nEEAAgQwEWtcERP3XWv5uBke7/5BgkUj5ESIHNmkSjbi/P/QAAQQQcKMACZIbo0abEUAAAY8K\ntKyKfSy1+TRBUmFV90OK9GrS+b5Hg0y3EEAAAYcL+O8Eb4cHhOYhgAACfhZoXe3+BKm7u9sM\n4b59+2TDhg1phzNUV28cM1Xef75djp5blfbxHIAAAgggMDEBEqSJ+XE0AggggICFAi1vBaVT\nGqW7qNHCUnNb1OrVq80Kb7/9dlH/0l3myelyuTwkT973phx92ZnpHs7+CCCAAAITFCBBmiAg\nhyOAAAIIWCNwcKdIX7MmO+RNawq0uZSTTjpJjjzyyLRb0aNyw4dFSg9MT/tYDkAAAQQQmLgA\nCdLEDSkBAQQQQMACgfj1R9s9kiB95jOfkS9/+ctpy2zbtk3ufbjRSJBmpH0sByCAAAIITFyA\nSRombkgJCCCAAAIWCLS8FZvWe4essqA0dxexR96Rgr4q6W1xdz9oPQIIIOBGARIkN0aNNiOA\nAAIeFGhZrRIkXXbJWx7sXXpd2iPrzAPauWFsenDsjQACCFggQIJkASJFIIAAAghMTEDd86f1\nbc24B5AuvcY0DX5f1AiSWtrW++9muX6PPf1HAAH7BbgGyf4Y0AIEEEDA9wIHNmoS6dGkZqmR\nKW3xN0dXV5fsHRhBWv3YDllb/WJGIKWlpXL++edndCwHIYAAAn4WIEHyc/TpOwIIIOAQgfj1\nRzXLoiJ/dEijbGpGW1ubMdH5ZglLnzS+0SO3vnFNRi2ZPn06CVJGchyEAAJ+FyBB8vsrgP4j\ngAACDhCIXX8kYiZIDmiP3U2ISkQ6S3bK1L6F8rOf/Fy0oJ5Wk/7t3/4trf3ZGQEEEEDgkAAJ\n0iELHiGAAAII2CSgEqRAvi5Vi4wRJBZTIDKpWWTrHPnYyZdK/ZL0Pq5vuOEGFBFAAAEEMhRg\nkoYM4TgMAQQQQMAagUivyIFNmlQt1CVYYE2ZXiilp2qP2Y2mNcZ1WSwIIIAAAjkTIEHKGTUV\nIYAAAgiMJdBmTGWtR9QEDemdRjZWWV5a11O12+xO45qwl7pFXxBAAAHHC5AgOT5ENBABBBDw\ntkD8+qNaEqRhge6u3mU+ZwRpGAtPEEAAgawLkCBlnZgKEEAAAQQSCbSuid3rp2YZI0hDnSKF\n3VI2LSBNaxlBGurCYwQQQCDbAiRI2RamfAQQQACBhAItqwMSLNKlch4J0kiouiVB6WnUpWsf\nk1eMtOE5AgggkC0BEqRsyVIuAggggEBSgVCXSIdxY9jqxboE0puoLWnZXtih3kiQ1MIokhei\nSR8QQMAtAiRIbokU7UQAAQQ8KND2tnF6nc4EDeOFtn5pLGvkOqTxhFiPAAIIWC9AgmS9KSUi\ngAACCKQo0Lp24PqjJZxeNxYZI0hjqbAOAQQQyK4ACVJ2fSkdAQQQQCCBAAlSAhxjU838oAQL\n1Sl23AspsRRbEUAAAesESJCss6QkBBBAAIE0BVrXGhM0FOtSMZcRpLHoAnma1C4KSuuGiERC\nGI1lxDoEEEDAagESJKtFKQ8BBBBAICWBwQkaFhkTNMTmIkjpOL/tVLckT6IhMZMkv/Wd/iKA\nAAJ2CJAg2aFOnQgggAAC0rZuYIIGrj9K+GpoWBqfyY7T7BJCsREBBBCwSIAEySJIikEAAQQQ\nSE+A649S81IjSGphqu/UvNgLAQQQmKgACdJEBTkeAQQQQCAjAXOKb+PI6qO4tiYR4OBMdmsY\nQUrkxDYEEEDAKgESJKskKQcBBBBAIC2BVuMUu0CBLpXzSJASwZXUB6RkssYIUiIktiGAAAIW\nCpAgWYhJUQgggAACqQlEekU6NmtStcCYoCF2BllqB/p0r3rjNLvufbp0N0V9KkC3EUAAgdwJ\nkCDlzpqaEEAAAQQGBNo3aqJHNKlhgoaUXhP1TNSQkhM7IYAAAlYIkCBZoUgZCCCAAAJpCbS+\nbcxgZyzVR3J6XSpwagRJLU1rwqnszj4IIIAAAhMQIEGaAB6HIoAAAghkJsAEDem5DU7UsJaJ\nGtKTY28EEEAgfQFHn/nd2Ngob7311pi9mjNnjhxxxBHS2dkpL7/88qh9zjjjDMnPzx+1nhUI\nIIAAAvYLqBEkLaBL9UJGkFKJRs3CoASMj7TmtYwgpeLFPggggMBEBBydIO3YsUPuuuuuYf0L\nh8PS0tIiV111lZkgrVmzRr73ve9JXV3dsP1OPPFEEqRhIjxBAAEEnCEQNQZB1DVIFXN0CRY5\no01Ob0Uw37hea0FQWtZHJBpWE1vETlF0ertpHwIIIOBGAUcnSMuXL5eHHnpomOutt94qb7zx\nhqxcudJcv3nzZlm8eLHcfvvtw/bjCQIIIICAMwU63tMk2qcZ1x8xI1s6EVKn2TW/HZG2dyNS\nu8jRH9/pdIt9EUAAAccJuOoaJJUY/fnPf5YbbrhBiopif3ZUCdL8+fMdB0uDEEAAAQTGFmgz\n7n+kFiZoGNtnvLV18YkauA5pPCLWI4AAApYIuOZPUH19fXLzzTfLZz7zGVmwYMFg51WCVFhY\nKNddd51s3LhRFi5caJ5+N23atMF94g/efffd+EPzZ01NjeTlpU6Qzr7DKuKJZQLEwDLKtAsK\nBGJ/T9E0La3fm7Qr4oCEAioO6p9Tfxe6u7tl+/btCfuw44VJxvY66a7aJZs3dw3bV51GzTK2\nwNCJGhZ8Zux9hq71+u+q6l8wGBRd5zq2oXHP5WMVA7U49f0olxZ210UMUotA/DWbbO/Us4Nk\nJWV5+7PPPivNzc3yiU98YrAmNUHDvn37ZPLkyXLxxRfLKaecYp6Sd+WVV8qvf/1rKSsrG9w3\nFArJBRdcMPhcPbjsssvk2muvHbYu0ZP6+vpEm9mWAwFikAPkJFWo0dv4CG6SXdmcRYGSkpIs\nlp550c8//7ycdtppCQv4J/mDzJXT5FNf/ZD0SHvCfdl4SKB+aewjuymFiRriyYPX3zPVH0hZ\n7Bfw+uvMfuHkLSAGyY3UHv39/Snt6JoESZ1apz50a2trBzumEqAHH3xQ1EhQQUGBuX7RokVy\nySWXyFNPPTV4nZLaoP7i+slPfnLwWPVg2bJlov7amWxRXwbVh01PT0+yXdmeRQEVh97e3izW\nQNGJBNTvQHFxsai/8Kf6BpOoPLZlJqD+Yq7ez9QffZy4xH9HlyxZIitWrBiziYffv1xCee3y\nD383/D1Z7axeX/fcc8+Yx/l9ZdmUgBTXacZMdsmn+lajKtFoNKXPOLe6qs999XpR/WSxR0Al\nqOr9iO9H9vjHa+X7UVwi+c9IJDKYMyTa2xUJkprNTs1W99Of/nRYX9QXNjV6NHQ5/PDDRWXR\ne/fuHbraHIb/zne+M2ydejJyv1E7GCvUdOFq6PLAgQNjbWZdjgTUhyExyBH2GNWoL+YqQVJf\nzInDGEA5WqU+CNV7khpBd+Jy8OBBs1nnnHOO3HLLLaOa2LEzYsxO2i7zzsmX637+81HbVYJF\ngjSKZXBFnTFRw86nw9LbFpWi6sSXEavEwcu/q9XV1aJeb079Y8Fg0Dz8QP3RWiVIXn6duSF8\nfD9KPUrqu0x5eXnSAxK/uyY9PDc7vPrqq1JVVSVLly4dVuG2bdvM0aKdO3cOrlcJT1NTk4x1\nDdLgTjxAAAEEELBFoGlNbPQjfrqYLY1wcaX1TNTg4ujRdAQQcIuAKxIkdcHvYYcdNsp09uzZ\n5rUQP/vZz6Strc0cDbrjjjtE/VXpzDPPHLU/KxBAAAEE7BVoWh2bhKFhWdDehri09kMTNTCZ\nhUtDSLMRQMAFAq5IkNRIkTp1bqzlmmuuka1bt8pHP/pRc6KG3bt3m6fiOfUC5rH6wDoEEEDA\nLwKNjCBNKNTxEaRUrkOaUEUcjAACCPhYwBXXII289mhovNSU3w888IA5w506L7+ysnLoZh4j\ngAACCDhIoGlNWPKN078rD3fF3+ccJBdrSu3ioGjG4FtTChM1OK7xNAgBBBBwiYArEqRULOvq\n6lLZjX0QQAABBGwS6D+oS/t7UZl6Up45M6hNzXB1tXlFmlTPC0rzurDoUV20QOw+NK7uFI1H\nAAEEHCbAn/AcFhCagwACCHhVoPlt47oZ456e9Uu5/mgiMVbXIYWNO1S0b2F664k4ciwCCCAw\nngAJ0ngyrEcAAQQQsFSgcXVsBruGZZ45ecFSn1QLU1N9q0WdrsiCAAIIIGC9AAmS9aaUiAAC\nCCAwhkDT2tgXekaQxsBJY1V8ogauQ0oDjV0RQACBNARIkNLAYlcEEEAAgcwFzHsgGZ86dUcy\ngpS54qFTFOMJ50TK4lgEEEAAgdECJEijTViDAAIIIGCxgK7roq5Bqp4TkPwSJhaYCG/FjKAU\nVmnGKXaxUxYnUhbHIoAAAgiMFiBBGm3CGgQQQAABiwUOvB+V0EFj9GgJo0dW0KrrkDq2R6Wv\ng4karPCkDAQQQGCoAAnSUA0eI4AAAghkRSB+OpiagY1l4gINS41E05gRsPltRpEmrkkJCCCA\nwHABEqThHjxDAAEEEMiCQPx0sHr1xZ5lwgKHZrIjQZowJgUggAACIwRIkEaA8BQBBBBAwHqB\n+IxrjCBZY2uOIBlFxUfmrCmVUhBAAAEElAAJEq8DBBBAAIGsC6gv8gUVmlTO5hQ7K7BrFxuO\nxid4fGTOijIpAwEEEEAgJkCCxCsBAQQQQCCrAqEuXdQkDXVHkRxZBa1mAqyeG5AmY2ZANUMg\nCwIIIICAdQIkSNZZUhICCCCAwBgCzeuMG8Qa3+E5vW4MnAmsUjeMDXeJtG9hJrsJMHIoAggg\nMEqABGkUCSsQQAABBKwUiF9/VHcUEzRY6Vq/NDYi17TGSEBZEEAAAQQsEyBBsoySghBAAAEE\nxhKIT0XNCNJYOpmvUyNIaoknoJmXxJEIIIAAAkMFSJCGavAYAQQQQMBygfhMa1yDZC0tI0jW\nelIaAgggEBcgQYpL8BMBBBBAICsCagSpfFZACiv4yLESuGJmUAqrNGaysxKVshBAAAFDgE8r\nXgYIIIAAAlkT6Nwdkd5WnQkasiSsRpE6tkWl7wATNWSJmGIRQMCHAiRIPgw6XUYAAQRyJTB4\n/RETNGSFvH4p1yFlBZZCEUDA1wIkSL4OP51HAAEEsisQT5Bqj+QeSNmQ5jqkbKhSJgII+F2A\nBMnvrwD6jwACCGRRoHldxCy9npvEZkW5gRGkrLhSKAII+FuABMnf8af3CCCAQFYFmt8OSyBf\npHo+I0jZgK5dHBTNoG1aE0tEs1EHZSKAAAJ+EyBB8lvE6S8CCCCQI4FoRJeWDRGpWRCUYL6W\no1r9VU1ekWYmnyoR1aO6vzpPbxFAAIEsCZAgZQmWYhFAAAG/C7RtjkqkV6SO64+y+lJoMGay\nC/eItL7LTHZZhaZwBBDwjQAJkm9CTUcRQACB3Aq0rAubFXKD2Oy6D85ktybmnd3aKB0BBBDw\nvgAJkvdjTA8RQAABWwSajBvEqqWOKb6z6n9oJjuuQ8oqNIUjgIBvBEiQfBNqOooAAgjkViA+\ngx2n2GXXvWFZ7F5IjasZQcquNKUjgIBfBEiQ/BJp+okAAgjkWECdYpdfJlIxi4+abNKXTg5I\ncYNmzGRHgpRNZ8pGAAH/CPCp5Z9Y01MEEEAgdwLhoLRviUrt4jzRNGawyza8GkXq2qNLdxMT\nNWTbmvIRQMD7AiRI3o8xPUQAAQRyLpDXUiu6cUlMnXGfHpbsCxy6DolRpOxrUwMCCHhdgATJ\n6xGmfwgggIANAnnNdWatXH+UG/xD1yExUUNuxKkFAQS8LECC5OXo0jcEEEDAJoG85nqz5lru\ngZSTCDQsi43UNTFRQ068qQQBBLwtQILk7fjSOwQQQMAWgXiCVHdkbIY1Wxrho0qr5wclWCTS\nuJoRJB+Fna4igECWBEiQsgRLsQgggICfBdQpdkU1mpRN4WMmF6+DQFAz7jcVlNZNEQn36rmo\nkjoQQAABzwrwyeXZ0NIxBBBAwB6BAimVQEeFMYMdEzTkMgLqOiTdmKMhfv+pXNZNXQgggICX\nBEiQvBRN+oIAAgg4QGCSzBPN+I8EKbfBODRRAzPZ5Vae2hBAwGsCJEheiyj9QQABBGwWmCwL\nzBZw/VFuA1HPRA25Bac2BBDwrAAJkmdDS8cQQAABewQmy0KzYu6BlFv/+iXGhBjGPXmZqCG3\n7tSGAALeEyBB8l5M6RECCCBgq0B8BIlT7HIbhoIyTarmBKRpjXGKHfM05Baf2hBAwFMCJEie\nCiedQQABBOwXmGScYhct7paSej5ich2NhqPzJHRQpDoyK9dVUx8CCCDgGQE+vTwTSjqCAAII\n2C8Q7QpKlUyVcF2T/Y3xYQtUgqSWhnDsNEcfEtBlBBBAYMICJEgTJqQABBBAAIG4QP+uEvNh\nuK45voqfORRoODo2tXpDKDZRRg6rpioEEEDAMwIkSJ4JJR1BAAEE7Bfo31FqNoIEyZ5YTBoY\nQZrECJI9AaBWBBDwhAAJkifCSCcQQAABZwj07xwYQaplBMmOiJQ0BKR0qiYNIU6xs8OfOhFA\nwBsCJEjeiCO9QAABBBwhENrJCJLdgVA3jC3Va6U0Um93U6gfAQQQcKUACZIrw0ajEUAAAWcK\nqBGkTmkUvbjXmQ30QasajhmYqKGf65B8EG66iAACWRAgQcoCKkUigAACfhTo7xCJtBbKftnk\nx+47ps+TjolN1FDPRA2OiQkNQQABdwmQILkrXrQWAQQQcKzAgXc1s237SJBsjdHgVN/9XIdk\nayCoHAEEXCtAguTa0NFwBBBAwFkCBzbFEqT9stFZDfNZaypnB6VHa2eiBp/Fne4igIB1AiRI\n1llSEgIIIOBrgfgIEqfY2f8yaMzfKBWRKdLXan9baAECCCDgNgESJLdFjPYigAACDhWIJ0ic\nYmd/gPbnrTcb0bYuNqpnf4toAQIIIOAeARIk98SKliKAAAKOFlAJUqCyX7qFYQu7A7U/b4PZ\nhNa3SZDsjgX1I4CA+wRIkNwXM1qMAAIIOE4g1CnSs1eTgundjmubHxu0P/8ds9uta0mQ/Bh/\n+owAAhMTIEGamB9HI4AAAggYAgc2x76IF8wgQXLCC6ItuF36tS5pXcvHvBPiQRsQQMBdArxz\nuitetBYBBBBwpEB8Brt8RpCcER8jX1UTNRzcLqLuT8WCAAIIIJC6AAlS6lbsiQACCCAwjkB8\ngoaCGV3j7MHqXAs0FqiJGjRp4zqkXNNTHwIIuFyABMnlAaT5CCCAgBMEDiVInGLnhHioNqgR\nJLVwHZLJwP8QQACBlAVIkFKmYkcEEEAAgfEEVIJUUK1LsCo03i6sz7FAbATJSJAYQcqxPNUh\ngIDbBUiQ3B5B2o8AAgjYLBA2Bo26d4tUztNtbgnVDxVozdsmwWJdWtfwUT/UhccIIIBAMgHe\nNZMJsR0BBBBAIKFAbAY7TSrnkiAlhMr1Rk2XmiW6dG5looZc01MfAgi4W4AEyd3xo/UIIICA\n7QIdA1N8V5Ag2R6LkQ1QCRITNYxU4TkCCCCQWIAEKbEPWxFAAAEEkgjEJ2jgFLskUDZsjiVI\nIi1ruGGsDfxUiQACLhUgQXJp4Gg2Aggg4BQBEiSnRGJ0O2qXRs2VzGQ32oY1CCCAwHgCJEjj\nybAeAQQQQCAlAZUg5ZXpUjIlpd3ZKYcC5UeI5JUyUUMOyakKAQQ8IECC5IEg0gUEEEDALoFI\nn0jXDmMGO64/sisECevVjDPrao7S5eB2TfrbE+7KRgQQQACBAQESJF4KCCCAAAIZC3Rs0USP\nGjPYMcV3xobZPrBmaWx2QU6zy7Y05SOAgFcESJC8Ekn6gQACCNggwAx2NqCnWWXtsliC1LKa\niRrSpGN3BBDwqQAJkk8DT7cRQAABKwSYoMEKxeyWUbssNlFDCzeMzS40pSOAgGcESJA8E0o6\nggACCOReID6CxDVIubdPtcayWSIF1bowgpSqGPshgIDfBUiQ/P4KoP8IIIDABAQOvCsSLNKl\ndMYECuHQrAvUGtch9ezVpKcx61VRAQIIIOB6ARIk14eQDiCAAAL2CEQjIp1bNSk/QheNTxN7\ngpBirfGJGhhFShGM3RBAwNcCfKT5Ovx0HgEEEMhc4OA2kWjImMGOKb4zR8zRkfHrkFpX87Gf\nI3KqQQABFwvwTuni4NF0BBBAwE6B+AQNFSRIdoYhpbprj2Ymu5Sg2AkBBBAwBEiQeBkggAAC\nCGQkMDhBA/dAysgvlwcVN4iUTGWihlyaUxcCCLhXgATJvbGj5QgggICtAgc2x+6rwyl2toYh\n5crV/ZD62zXjurGUD2FHBBBAwJcCJEi+DDudRgABBCYuoEaQtKAu5YdNvCxKyL5A7dED90N6\ni4/+7GtTAwIIuFmAd0k3R4+2I4AAAjYJ6MYlLR3vaVI22zhXO9+mRlBtWgJch5QWFzsjgICP\nBUiQfBx8uo4AAghkKtC9RyTczQx2mfrZcVzNEiOr1XRpXhU7NdKONlAnAggg4AaBPDc0Mptt\nrKmpSVp8MBg090ll36SFsUPGAioOxCBjPssOLCgoIA6WaaZfUCAQEE3TJD/f3mGbg2+Gjcb3\nyqSjCo3XQ8VgRyoqDj0eXMkDWwRGvWcaH3c1C7ulbV1UKsuqJVjg7kQpLy9P1OtNV8OZLLYI\nqBiohc9mW/gHKx31uz64hQcjBcJh9dmVfPF9gtTR0ZFUqaqqStSbQCr7Ji2MHTIWUG/AxCBj\nvgkfqL6YFxYWSigUks7OzgmXRwGZCagYqPejrq6uzAqw6Ki9a1RBASma1Wf8XvYNltrd3T34\nmAf2CkSj0VHvmTXLNGldr8n2lzul7mh72zfR2lVypF5vqX7hmWh9HD9agO9Ho03sWMP3o9TV\n1R8YS0tLkx7g+wQpnTfWdPZNKs8OaQuovxISg7TZLDsgPpJKHCwjzagglRypZNXu34W2jbGR\n9bIjIkZbDv0F3+52ZYTq0YPG+l2tOdo4s/6BPNn/WlSqjopN2uDW7qv+RSLq9ZfaX4Td2k8n\nt1vFQC3EwN4ojfW7bm+LnFt7/LtMshb6PkFKBsR2BBBAwE8Cf/zjH+W+++5L2uUzNtwi9XKk\nXP6NT0k42Du4P6OLgxSOfFB3TOwLbctb7j69zpG4NAoBBDwjQILkmVDSEQQQQGDiAnv37pXX\nX389aUHnyRQ5IHvk5VXPJ92XHZwjUDlfl7xSY6KGN9UcTRHnNIyWIIAAAg4SYBY7BwWDpiCA\nAAJOEXjooYfM02bUqTMj/3Xu75cyqZMlZ80ate22225zShdoxxgCmvGpX7NUl4PbNeltGWMH\nViGAAAIIGFfYsiCAAAIIIDBCQF3npM7VHutf+7uxnesW5Y3ari6AZXG2QP3ygdPsmO7b2YGi\ndQggYJsACZJt9FSMAAIIuFOgdWPs1KyaBbGJGtzZC/+2uu7Y2OQMsdPs/OtAzxFAAIHxBEiQ\nxpNhPQIIIIDAmAKtGwYSpIUkSGMCOXxl7cBEDU1vMNrn8FDRPAQQsEmABMkmeKpFAAEE3CrQ\nMpAg1ZIguTKERbUi5YfpomayizJPgytjSKMRQCC7AiRI2fWldAQQQMBzAmoEqahGk5IGPkLc\nGlx1ml2kR5N246axLAgggAACwwX4dBvuwTMEEEAAgQQCoR5dOrZHheuPEiC5YFPdwEQNzW+S\nILkgXDQRAQRyLECClGNwqkMAAQTcLNC2yTgny5gErYbT69wcRhlMkLgOydVxpPEIIJAdARKk\n7LhSKgIIIOBJAa4/8kZYqxYYN4wt06XpNb4GeCOi9AIBBKwU4J3RSk3KQgABBDwuwBTf3giw\numFs3bG6dO3SpGe/N/pELxBAAAGrBEiQrJKkHAQQQMAHAkzx7Z0g1x8Xux9S0+tch+SdqNIT\nBBCwQoAEyQpFykAAAQR8IqBGkIJFIpWz+fhwe8jrByZqaHqdWLo9lrQfAQSsFeBd0VpPSkMA\nAQQ8KxCN6NL2bkSq5wVFCzDq4PZA1xqn2GkBXZoZQXJ7KGk/AghYLECCZDEoxSGAAAJeFejY\nZtw7p8+YwW5B0Ktd9FW/8ktFqhbp0vq2JuFuX3WdziKAAAIJBUiQEvKwEQEEEEAgLsAMdnEJ\n7/ysX6GLHtGk5S1GBL0TVXqCAAITFSBBmqggxyOAAAI+EWCCBu8FuuF446ZWxtL4GgmS96JL\njxBAIFMBEqRM5TgOAQQQ8JkAU3x7L+D1xw/MZPcqXwe8F116hAACmQrwjpipHMchgAACPhMw\nT7EzPjXUJA0s3hAoniRSNtOYqOFNTaIRb/SJXiCAAAITFSBBmqggxyOAAAI+EVAjSBWzApJf\nzOlYXgq5GkUKd2nS/g5x9VJc6QsCCGQukHaCdP/998vXvva1cWt8+OGHZdasWdLT0zPuPmxA\nAAEEEHCXQHdjVPradKldyOiRuyKXvLUNJwxch/QKCVJyLfZAAAE/COSl0smmpibp7+83d33r\nrbfktddek927d486VO3z2GOPyY4dO6S3t1eKi4tH7cMKBBBAAAH3CcRnsGOKb/fFLlmL61fE\nrkNqNK5DWnB57HGyY9iOAAIIeFkgpQTpnnvukWuvvXaYw/Tp04c9H/pk2bJlUl1dPXQVjxFA\nAAEEXLBDksIAAEAASURBVCzABA0uDl6SplccIVJUp0vTq4wgJaFiMwII+EQgpQTpmmuukXA4\nLKFQSJ555hnZvn27fO5znxtFlJeXZyZGn/zkJ0dtYwUCCCCAgHsFmOLbvbFLpeXqNLsdjwbk\nwGaRyrmpHME+CCCAgHcFUkqQ8vPz5frrrzcVFixYIOvXr5dvfetb3lWhZwgggAACwwQYQRrG\n4bkn6jQ7lSA1vhIwEiROs/NcgOkQAgikJZBSgjS0xE9/+tNDn/IYAQQQQMAHAuoapOI6TUrq\n0p7bxwc67u/i0Ika5v6j+/tDDxBAAIGJCKSdIKnK/vCHP8h//dd/mafaqdnqdD02A87QhrS1\ntQ19ymMEEEAAAZcKhLp16dwZlWknZ/SR4dJeu7vZBw8eFE3T5IYbbkitI8bH+NzCG+S9/wvJ\n/91w0+AxatbasrKywec8QAABBPwgkPan3UsvvSRqFEnNULd06VJpaGgw34T9gEUfEUAAAT8K\ntG4y7iBqfIFmBjv3RF/98TIajcrdd9+dcqM/J6fKkfIR+dPdT0mLbDWPu+qqq0iQUhZkRwQQ\n8IpA2gnSgw8+KEVFRbJq1SqZO5crOb3yQqAfCCCAwHgCg9cfcQ+k8YgcuX7KlCnypz/9KeW2\n7f5tpWz9scgvrn9Ufvjil+S5555L+Vh2RAABBLwkkHaCtHfvXlm+fDnJkZdeBfQFAQQQSCAw\nOIPdAm4Sm4DJcZsKCwtlxYoVKbdrf0HYSJAOSP6OGVJTU5PyceyIAAIIeE0g7attVXKkRo+6\nu7u9ZkF/EEAAAQTGEBgcQSJBGkPHO6salgalsEqTXc+FvdMpeoIAAghkIJB2gqTufzR16lS5\n8cYbpb+/P4MqOQQBBBBAwE0CKkEKFhn3x5md9keGm7rp+7ZqAU2mn5pnTshRdLDe9x4AIICA\nfwXSPsVO3Si2vr5evv/978ttt90m06dPl9LS0lGCa9asGbWOFQgggAAC7hLQo7q0vRuR6vlB\nUV+gWbwtMOP0fNnyPyGpbJ7v7Y7SOwQQQCCBQNoJkpq+u6+vT4477rgExbIJAQQQQMALAge2\nRiXSxwx2XohlKn2YcUa+uVtl04JUdmcfBBBAwJMCaSdIl19+uah/LAgggAAC3hdQN4hVSy0z\n2Hk/2EYP643rkIpqNKlgBMkX8aaTCCAwtgAnlI/twloEEEAAAUOACRr89TJQN5edflq+FPZW\nSb3M8Vfn6S0CCCAwIJD2CNKtt94qP/6xcaOEJMv27duT7MFmBBBAAAGnC5AgOT1C1rdv5gfz\n5L0/9ctc48axLAgggIAfBdJOkOrq6mTevHnDrCKRiOzYsUNUUlRdXS1///d/P2w7TxBAAAEE\n3ClgJkjG3AxqkgYWfwjMPDN2HdIc+YA/OkwvEUAAgRECaSdIn/3sZ0X9G2t5//335ZxzzhF1\n924WBBBAAAH3C6ibxFbMCkh+MTPYuT+aqfWgdmGe9Be2y5y+U0SPdqV2EHshgAACHhKw9Bqk\nww8/XL7xjW/Id77zHVGjSiwIIIAAAu4V6G6KSm+rLjXcINa9Qcyw5e31G6VEqqVzU2w0KcNi\nOAwBBBBwpYClCZISmDFjhnR2dsrmzZtdCUKjEUAAAQRiAlx/5N9XwoGGDWbnW18t9C8CPUcA\nAd8KWJogdXd3yx133CHBYFBmzpzpW1Q6jgACCHhBQJ1epxam+PZCNNPrgxpBUkvrq0XpHcje\nCCCAgAcE0r4G6a677pJf/OIXo7oeCoXMSRpaWlrkc5/7nJSUlIzahxUIIIAAAu4RaNkYS5A4\nxc49MbOqpf0lrdIk70lg1RHGjYJDEmQgySpaykEAARcIpJ0g9ff3S1fX6Is21ajRkUceaU7S\ncPXVV7ug6zQRAQQQQCCRAKfYJdLx/rZ35Tmp75sjzW9oMulk3fsdpocIIIDAgEDaCdKVV14p\n6h8LAggggIC3BdQpdkU1mpQ0WHo2trfRPNS7zUaCdLJ8XvY9HzASJCZe8lBo6QoCCCQRSDtB\nipcXDofl2WeflU2bNok6vW7ZsmXmv6qqqvgu/EQAAQQQcKlAtC8gHdujMvXEjD8mXNpzmh0X\neE9eEAnosvc5TZZeF1/LTwQQQMD7Ahl98r355pvmdUbr1q0bJfS9731Pvv71r49azwoEEEAA\nAfcIhPYUixhnVXH9kXtiZnVLe6VDKhb1S+vaAulrEymstroGykMAAQScKZB2gtTe3i4rV64U\nNYJ06623yooVK6SsrEy2bdsmv/zlL+X666+XoqIiueaaa5zZY1qFAAIIIJBUILQrNtFOzcJg\n0n3ZwbsCtSf2Sce6Qtn/QkBmXhD1bkfpGQIIIDBEIO0ESc1ip5KkVatWybx58waLWrJkiVx4\n4YXyT//0T3LnnXeSIA3K8AABBBBwn0D/7oEEiZvEui94Fra49qRe2XpXhXma3cwLLCyYohBA\nAAEHC6R95e2aNWvk9NNPH5YcDe3f5Zdfbt4kds+ePUNX8xgBBBBAwEUCod3GKXbGwil2Lgpa\nFppacVS/5JWq65DS/rqQhdZQJAIIIJAbgbTf8dR03mqq7/GW+LZIhBlvxjNiPQIIIOB0AXWK\nnbr3TeVhaX9MOL1rtC8NgYBxnoma4rt7tyYdW9I4kF0RQAABFwuk/cm3fPlyee655+S1114b\n1W1d1+WWW26Ruro6mTFjxqjtrEAAAQQQcL6AJpqE9pRI1dygBIKa8xtMC7MqMOW02LVHe59N\n+ytDVttF4QgggEC2BNK+BukLX/iCOTmDOs3ui1/8ohx//PFSUVFhTtJw7733mtcmqckaWBBA\nAAEE3ClQLTNFDwWklgka3BlAi1s95fRDCdL8zzNRg8W8FIcAAg4USDtBKi4ulhdffFE+//nP\ny2233TasS9XV1XL77bfLpZdeOmw9TxBAAAEE3CPQIHPNxnL9kXtils2Wlh8mUjZTl/0vaRIx\nzrAPFmSzNspGAAEE7BdIO0FSTZ46dar85S9/kV27dsmGDRukpaVFjjjiCFm4cKE55bf93aIF\nCCCAAAKZCkyS2AylTPGdqaD3jlOjSJvvD0rTa5pMPsW4QRYLAggg4GGBjBKkuMf06dNF/WNB\nAAEEEPCOACNI3omlVT2JJ0jqOqTJpzAJk1WulIMAAs4UyOiKy2g0Kup+SE888cRgr/7whz+Y\n03+rkSUWBBBAAAH3CsQSJF1q5nOTWPdG0dqWTzJGjbQ8Y7rvZ5i0w1pZSkMAAScKpJ0ghUIh\nOeaYY0Td7+i9994b7JOa/vv111+X8847Tx544IHB9TxAAAEEEHCXQINxil1efZ/kl/Bl2F2R\ny15r88tE6o/TpX1DQLr3Za8eSkYAAQScIJB2gvTss8/K22+/LY8++qh86UtfGuzDRRddJDt3\n7pSzzjpLvvrVr4oaZWJBAAEEEHCXgNZdJKVSI/nTut3VcFqbdYGpHxyYze6ZtL86ZL1tVIAA\nAghYKZD2u9wjjzwip512mjlSNLIhNTU18pWvfEX2798vW7duHbmZ5wgggAACDhcINteaLcyf\nToLk8FDlvHlTzohNzrCXBCnn9lSIAAK5FUg7QVLNy8/PH7eVKklSS0EB84COi8QGBBBAwKEC\ngeaB93ASJIdGyL5mVS/SpXiScR3S3zSJMk+DfYGgZgQQyLpA2gnSGWecIc8884x5L6SRrVOn\n1X3/+9+XhoYGmTFjxsjNPEcAAQQQcLhAsKXabGH+tB6Ht5Tm2SEw5YyohDo0aX6D69Ps8KdO\nBBDIjUDa03yfc845smLFCnPGuk996lOybNkyKS8vl927d8tDDz0kGzdulN/85je5aT21IIAA\nAghYKhA/xa6AESRLXb1SmLoO6f3fBY3Z7ALSsIJhJK/ElX4ggMBwgbQTpLKyMnnyySfNWezU\n9UhDZ6xTo0bq+cUXXzy8Fp4hgAACCLhCQJ1i1yWtEqwMuaK9NDK3ApNPNab7Duqy52lNll6X\n27qpDQEEEMiVQNoJkmpYUVGR3H///aLrujkZgxo9Ouyww2TatGmiaQy75yp41IMAAghYKRA2\n5mUIdJRLo7xmZbGU5SGBggqRuuW6NL2qSU+jSHGDhzpHVxBAAIEBgbSvQRoqp5Khww8/XD7w\ngQ/I9OnTSY6G4vAYAQQQcJlAxxZN1H+N8q7LWk5zcykQm+5bM0aRJvQVIpdNpi4EEEAgLQHe\n3dLiYmcEEEDAuwId78XOAGiUzd7tJD2bsMC0D8Wm+97zFF8hJoxJAQgg4EgB3t0cGRYahQAC\nCOReoGNzLEHazwhS7vFdVGPVQmO67ynGdN/PGdN9c6maiyJHUxFAIFUBEqRUpdgPAQQQ8LjA\ngYEEiVPsPB5oC7o37cyohA9q0vQ61x1bwEkRCCDgMAESJIcFhOYggAACdgl0GGfW6XlhaZOd\ndjWBel0iELsOSYTT7FwSMJqJAAJpCaScIL344ouyadOmtApnZwQQQAABdwhEjVvadG7VJFLb\nKrrxHwsCiQTUdN+BAl12/zXlrxGJimMbAggg4CiBlN/ZvvGNb5j3OGptbZVvfetbjuoEjUEA\nAQQQmJjAwW1iXE9iXFNiJEgsCCQTyCsRaThBF3Xd2kEGHJNxsR0BBFwmkDRB6uzslP3798sX\nv/hFefTRR+WUU06RF154QTo6OlzWVZqLAAIIIDCeQHyChkgdCdJ4RqwfLjDVuA5JLXsYRRoO\nwzMEEHC9QNIE6X//939l8uTJcumll8qqVavMG8I++eSTUlFh3C2OBQEEEEDAEwLxCRpIkDwR\nzpx0YtqHYgkSp9nlhJtKEEAghwJJE6QLL7xQWlpa5N5775XjjjtOtm/fbo4iMYKUwyhRFQII\nIJBlAUaQsgzsweLLDxMpP1yX/S9pEu7xYAfpEgII+FYgaYJUUlIiNTU1cvvtt8t5550narKG\nT3/604wg+fYlQ8cRQMCLAuomsVpAl2hNmxe7R5+yJKBOs4v2abL/Bab7zhIxxSKAgA0CeanW\n+d///d9SWloqlZWVcvXVV6d62IT3U9dAvfzyy6PKOeOMMyQ/P99cr/ZRiZv6uWLFCpk5c+ao\n/VmBAAIIIDC+gDrFrmyWSGswdtrU+HuyBYFDAtPOisqmu4LmbHbTzjKmQmRBAAEEPCCQcoJ0\n5JFH2tLdNWvWyPe+9z2pq6sbVv+JJ55oJkhbt26Vz3/+83L44YfLtGnTRCVy3/nOd+SEE04Y\ntj9PEEAAAQTGFujeIxLu0qRiHsnR2EKsHU+gYYUueaX6wP2QSJDGc2I9Agi4SyDlBMmubm3e\nvFkWL15snuI3VhtuuukmUddJqVEtTdPkvvvukx/+8Ifyu9/9znw+1jGsQwABBBA4JBCfoKFy\nLvc/OqTCo1QEAsaJHFNO02XnYwFp36BJ1UJeQ6m4sQ8CCDhbIOk1SHY3XyVI8+fPH7MZavKI\nDRs2yMqVKweTofPPP1/27Nkj69evH/MYViKAAAIIDBeIT9BQQYI0HIZnKQlMjc9m9yTXIaUE\nxk4IIOB4AVeMIBUWFsp1110nGzdulIULF8pVV11lnk63b98+E3jq1KmD0LW1tVJQUCCNjY3m\nyNPgBuPBli1bhj6V6upqCQaDw9YlepLOvonKYVvmAsQgc7uJHhkIxP6eokZqicNENTM/XsXB\n6hioCRrUUj1fk0Cz4/9uljkeR6YtoH7Xk/2+zzhL5FVRp9kFZck1uUuS4r8H0SinhqYdWIsO\nUDFQS7LXiEXVUUwCAWKQAGfIpvh3mSGrxnzo6ARJTbqgkiB1H6aLL77YnF78oYcekiuvvFJ+\n/etfy969e0UlT+rf0KW8vFza2obPxBQKheQjH/nI0N3ksssuk2uvvXbYukRPGhoaEm1mWw4E\niEEOkJNUUVRUJOofi70CatIcq5bubQeMosIy5+R6KVtTZlWxlOMBAXX9b9L3XeOjcdJx7dK4\nKiLleXVSXJO7JHvk578HyF3ZhaSvEVf2yl2NJgapxau/vz+lHSeUIB08eNCcPe69994zR3RO\nPvlkqa+vT6niVHYqKyuTBx980JxmXI0KqWXRokVyySWXyFNPPSVVVVUSDodHFRWJRERNTz50\nURnjxz72saGr5KijjpLu7u5h68Z6or4Mqr+S9PRwo4exfHK1TsWht7c3V9VRzwgB9TtQXFxs\n/s6l+gYzogieWiCg/kqo3s/UH32sWlrWh6V0mnEvm0CPEFurVL1RjvqMTOVzcsZZxlTfr4ts\nevigzPvMhL5apAynvheo7wCMIKVMZvmOKkFV70d8P7KcNq0C+X6UOpd6v4jnFImOSuldbPny\n5aKu7bnxxhsHy3rmmWfMRGXnzp2D61RC8+1vf1u++tWvDq6byAP1hUyNHg1d1Gx1KglTo0dz\n5swRlQypN++hCZG6ie2UKVOGHmYO/6oJHUYuqpxki5pOPC8vTw4cUH9lZbFLQL2giYFd+rFT\nKFSCpL6YEwf74qA+CNV7khpht2LpaxXpbS6QyadFzLjyRwgrVL1Thnqdqd/7ZEvtB9SpVvny\n3p97ZdKHczObnTpNXv2h1so/FiTrJ9uHC6jLGlSCxGfCcJdcP+P7Ueri6o+MKl9JtqQ0Dq4m\nSohf76MK3L17tzka09TUJB//+MfNGePuvfdeOe644+Rf//Vf5f77709Wb0rbt23bNioJUwmN\nqldN6T19+nQzcXnnnXcGy1OTNqjscOh1SYMbeYAAAgggMEzgwLuxawgq5zH72DAYnqQlULNE\nl6J6XfY+G5BobvKjtNrHzggggEA6AiklSCML/OUvfynt7e3yq1/9StQ1QZ/+9KfNRObpp582\nrxX693//95GHZPR89uzZ5rUOP/vZz8xrilRydMcdd5iTK5x55pnmTWvPPvtsueeee8y/Iqm/\nfN59991y7rnnWnqqX0aN5yAEEEDABQLxCRqY4tsFwXJwE40TPmTqmVHpb9ek+Y1Y0u3g5tI0\nBBBAIKFARgmSmkJbneamptceuVxzzTXmDHI7duwYuSmj56o8dTPYj370o2bypUavfvrTnw6e\nUnfFFVeY5xJecMEFctFFF5kjSl/+8pczqouDEEAAAb8JxEeQmOLbb5G3vr/TBqb73vNURl8t\nrG8QJSKAAAIZCqR0DdLIstX1PWpmG3Ue/MiltdU4od1YrDqPfcGCBfLAAw9Ic3OzWV9lZeWw\nKtU5yD/60Y9EXXekziu0cmanYRXxBAEEEPCgQDxB4hQ7DwY3x12afKouWp4uu/+qybLrc1w5\n1SGAAAIWCqT8Z54XX3xRfvKTn8jLL78sn/jEJ2TTpk2yevXqYU1RkyXcdttt5sVPajIFKxeV\nkI1MjoaWX1FRQXI0FITHCCCAQAoCKkEqrNWlsDqFndkFgQQC+cZ1zw0n6HJgY0C6diXYkU0I\nIICAwwVSSpBWrFgh27dvl3/5l3+Rk046SU499VSzW0NPsVPTcc+aNUsee+wx+frXv26e6ubw\nvtM8BBBAwNcCIWMivJ59mjB65OuXgaWdHzzN7umUvl5YWjeFIYAAAlYJpHSK3RNPPCG6rsuW\nLVvMUSM1cvTWW2+ZEyPEG6JmklMjSGqa7+uuuy6+mp8IIIAAAg4VOLCZGewcGhrXNmvqB6Oy\n6kZjttu/BmTuZ6Ou7QcNRwABfwuklCApInVPInXfIfVPnWI3crnqqqvk+uuvT+nmSyOP5TkC\nCCCAQO4F4tcfMUFD7u29WmPFHJGyWbrsf1GTiHFf72CRV3tKvxBAwMsCaY2Bqzslq/sMjXWn\ndXWNkLpRlbp30UsvveRlM/qGAAIIeEIgniBxip0nwumYTkw1ZrOL9Giy/2Wm+3ZMUGgIAgik\nJZBSgqQSInUD2PLyclm0aJGoCRG+8pWvmKfUjaxNTcF98sknj1zNcwQQQAABhwl0cJNYh0XE\nG82ZZtwPSS1M9+2NeNILBPwokNIpdjfddJPceuutZnL0kY98RB5++GH58Y9/LE8++aQ89dRT\nMnnyZD/a0WcEEEDA1QJqBKmgUpfiBld3g8ZnQUBNzKSWH/zgB1JcXJxWDVokKEcE/p+88etm\nue/A/yc1NTVpHT90Z/UHV3VDeBYEEEAglwJJEyQ1OYN6g7zwwgvlkUceMdv2/e9/X37729/K\npZdeKmeeeaa88MILou5HxIIAAggg4A6BcLeYUzHXH6+7o8G0MqcCe/fuNev79a9/nVG9l8op\nsrj/XHnuD6ulWbZkVIY6KC8vjwQpYz0ORACBTAWSJki7du0yZ6tTydDQ5eKLL5ba2lo5//zz\n5aMf/aiome7UNUgsCCCAAALOF+h4T10foqb4ZqYx50fLvhY++uij5md9ui34yd89KbJV5N/P\n+5Gc+s26dA+XNWvWyBVXXJH2cRyAAAIIWCGQNEEqLCw062lvbx9Vnxr2vvvuu+WSSy6Ryy67\nTH71q1+N2ocVCCCAAALOE4hP0MAMds6LjZNadOyxx2Z0Gv33Z99hJkhluxbICSfMSbtL4XA4\n7WM4AAEEELBKIGmC1NDQIFOmTJG77rpLPvWpT0lJScmwuj/72c/Kvn375Nprr5WqqirJz88f\ntp0nCCCAAALOEziwKTbDGDPYOS82XmhRb3GL7JNNMvmduRLq1iW/JPZ680Lf6AMCCHhfIKVZ\n7G688UZz6m41GcO3vvWtUSpf+9rXzHsg3X777XLnnXeO2s4KBBBAAAFnCcRHkEiQnBUXL7Vm\no/xVJByQHU+HvNQt+oIAAj4QSClBuvzyy+Wee+4RNZq0du3aMVm++93vyh133JH2bDdjFsZK\nBBBAAIGsCqgEKb9cl5IpWa2Gwn0ssEmeMnu/9S/9Plag6wgg4EaBlBIk1bHPfe5z8t5778lv\nfvObcfv5z//8z/Luu+9yLdK4QmxAAAEE7BcI94gc3CFSOZ8Z7OyPhndb8L68LFphRLb+hREk\n70aZniHgTYGUE6R490degxRfH/9ZX18v//AP/xB/yk8EEEAAAYcJdGw2rgfR1Qx2JEgOC42n\nmhORkBQf1S4dW6PS+m7EU32jMwgg4G2BtBOkZBzqNDt1zRILAggggIAzBbj+yJlx8WKrio9u\nNbu17XFOs/NifOkTAl4VsDxBUhM1fPvb3/aqF/1CAAEEXC8wOIMdp9i5PpZO70DJ0W1mE7c+\nzml2To8V7UMAgUMCSaf5PrRrao9uvfVW6ejoSG1n9kIAAQQQyLlAe3yKbxKknNv7rcL8yb1S\nNTcgu54LSbhPl7xCpvv222uA/iLgRgHLR5DOOecc+eQnP+lGC9qMAAII+EJAjSDlVxgz2E32\nRXfppM0Cs88pkHC3yK6/MYpkcyioHgEEUhSwPEFKsV52QwABBBCwQUB9Ue3ayQx2NtD7tsrD\nzo3dQH7b/5Eg+fZFQMcRcJlA2qfYdXd3y8aNG6W5uVl6e3ultLRUqqurZdGiRVJUVOSy7tNc\nBBBAwF8CB9QMdqJJ1fyovzpOb20TmHF6vgQKRLY/QYJkWxCoGAEE0hJIOUFas2aN/OAHP5AH\nH3xQ+vr6RlWSn58vF154odx2220yderUUdtZgQACCCBgv8CBjbFrQLgHkv2x8EsL8ks1mXZy\nnux8JiwH90albAonr/gl9vQTAbcKpJQgvfTSS3LWWWeJpmny8Y9/XBYvXiw1NTVSUVEhnZ2d\n0traKhs2bJBHHnnEHEn67W9/Kx/+8IfdakK7EUAAAc8KMEGDZ0Pr6I7NOrvATJC2P9Eviy/h\nbBNHB4vGIYCApJQgfeELXzCToieffFIqKyvHZevq6pLzzjtPbrnlFhKkcZXYgAACCNgnEB9B\nqlrATWLti4L/ap59dr688HWRbcZpdiRI/os/PUbAbQJJE6SWlhZzdOjxxx9PmBypjqvrkW6+\n+WY55ZRTpLGxURoaGtzmQXsRQAABTwuoEaTCGl2K6jzdTTrnMIGGo4NSXK/J9r+GRNd184wU\nhzWR5iCAAAKDAklPBC4uLpaSkpLBA5I96O/vl0gkMuZ1SsmOZTsCCCCAQPYE+o1b1PXs1aSS\n0aPsIVPymALqFP2ZZ+ZLT6MuTWsiY+7DSgQQQMApAkkTJJUcnXvuuXLdddfJzp3G3LAJFjVq\ndM0118isWbNkxowZCfZkEwIIIIBArgXU/Y/UUsUNYnNNT32GwKyzYtN9b3+S2ex4QSCAgLMF\nkp5ip5qvkiN189fZs2fL6aefbl6PVFdXZ55yF5+kQU39/de//tUcNn/qqaec3WtahwACCPhQ\nIJ4gMYLkw+A7oMtDE6Tj/r3YAS2iCQgggMDYAiklSMcdd5ysW7dOvvGNb4iaoe7pp58eVZpK\nmK666iq5+uqrzRGkUTuwAgEEEEDAVoH2gSm+GUGyNQy+rbxiRlCq5wdk1/MhCffqklcUG9H0\nLQgdRwABxwqklCCp1peVlcmPf/xj89/u3btFTd6gbhpbX18vU6ZMSes6Jcdq0DAEEEDAwwLt\nGwbugcQ1SB6OsrO7NutD+bL69j7Z81JYZn4wdsqds1tM6xBAwI8CKSdIQ3GmTZsm6h8LAggg\ngIB7BNQpdiVTdSmocE+baam3BGZ+qMBMkNRsdiRI3ootvUHASwJJJ2nwUmfpCwIIIOBXgZ5G\nkb5WTbj/kV9fAc7o94zT80QLiux4iokanBERWoEAAmMJkCCNpcI6BBBAwGMC8dPrqhZyg1iP\nhdZV3SmqCsikY/Nk/5th6W2PuqrtNBYBBPwjkNEpdv7hoacIIICAuwReeeUV2bNnz6hGh5+e\nb6w7WjZ3vibv/3H7qO3xFWpCHhYEsimg7oe077Ww7Hw2LHMvKshmVZSNAAIIZCRAgpQRGwch\ngAACzhT4+c9/Lo8//vioxn1KbpPjjQTp5vuvk733vzNqOysQyJWASpBeu6lHdj4dIkHKFTr1\nIIBAWgIkSGlxsTMCCCDgDoHvfve7UlFxaDaG/lvOFn13VL7+gy+Jlj/+qU133nmnrF+/3h2d\npJWuFJh2cp4EC43rkIwEiQUBBBBwogAJkhOjQpsQQACBCQpcdtllMnnyZLMUParLbV9rlYoF\nQbn0mi8lLPmxxx4jQUooxMaJCqj7H005MU92GafYde2PSukkLoeeqCnHI4CAtQK8K1nrSWkI\nIICA4wTa3otKuEek/ihj+jAWBBwgEJ/ie+czjCI5IBw0AQEERgiQII0A4SkCCCDgNYHmtWGz\nS3VLSJC8Flu39ieeIHGanVsjSLsR8LYACZK340vvEEAAAWl6O2Iq1C/hrGpeDs4QmHx8nuSV\nijCC5Ix40AoEEBguQII03INnCCCAgOcE/n/27gNAjrL+//hndvf65ZJceieNBBICISS0UEIT\n6U1+CooKqKggov7Fgqj4ExQL6g8UROGHItIRy48qJRDpSYCQhJBeSL0kl7tc3d35P89uNrlL\nru3d1pn36HK7szPPPM/rmczOd55nnkm0INHFznNVm7cFChY4GnZUgbab7p816+IBfN4Whowj\ngIDnBAiQPFelFAgBBBBoLWBbkAp7O6oYRRe71jJ8yqbA8OPjLZr2eUhMCCCAQC4JECDlUm2Q\nFwQQQCDFAk21rqqXRxmgIcWuJNdzgRHHF8QSWfsCAzX0XJMUEEAglQIESKnUJC0EEEAgxwS2\nLDBX512pPyPY5VjNkJ3B03fdh0SAxM6AAAI5JkCAlGMVQnYQQACBVApsfnvXAA0HM0BDKl1J\nq+cCLe9Dqv2w/YcX93xLpIAAAggkJ0CAlJwXSyOAAAJ5JbB51xDfAw7m/qO8qjifZHb4cbvu\nQ3qRbnY+qXKKiUBeCBAg5UU1kUkEEECgewKxFiTHdLGbTAtS9wRZK50Cw4/ddR/SbAKkdDqT\nNgIIJCdAgJScF0sjgAACeSPguq5sC1KfsQEVlpsoiQmBHBOwz0MKFktrZzOSXY5VDdlBwNcC\nBEi+rn4KjwACXhaoXhFVc400gPuPvFzNeV22UJGjIYeHtHVhRHWbuQ8pryuTzCPgIQECJA9V\nJkVBAAEEWgpsfjt+VZ77j1qq8D7XBIYfF+9mt+4lutnlWt2QHwT8KkCA5Neap9wIIOB5AUaw\n83wVe6KAw4+J3x9HNztPVCeFQMATAgRInqhGCoEAAgjsK7BpfrwFaSAj2O2Lw5ycERh6ZIEc\nEyOtpQUpZ+qEjCDgdwECJL/vAZQfAQQ8K7BpfkRFfR1VjGKIb89WsgcKVlDmaODUoGyLZ1ON\neaoxEwIIIJBlAQKkLFcAm0cAAQTSIdBULdWsipoBGgiO0uFLmqkVGH5MgVzzTOMPX+E+pNTK\nkhoCCHRHgACpO2qsgwACCOS4wLb34sN6DzyE5x/leFWRPSMwzARIdlr7EsN9xyD4DwIIZFWA\nACmr/GwcAQQQSI/AtgWJAIkWpPQIk2oqBYbNjAfyjGSXSlXSQgCB7goQIHVXjvUQQACBHBbY\nmmhBmkoLUg5XE1nbJVDaP6DKiQFteD2sSDP3IbFjIIBAdgUIkLLrz9YRQACBtAjYFqRAoVR5\nAC1IaQEm0ZQLDJtZoHC9tGku3exSjkuCCCCQlAABUlJcLIwAAgjkvkBQBapeIvWfFFSwIN7V\nLvdzTQ79LjD06F3d7F4mQPL7vkD5Eci2AAFStmuA7SOAAAIpFhiiA+WGzdDJh9K9LsW0JJdG\nAduCZKd1cwiQ0shM0ggg0AUBAqQuILEIAgggkE8CQ3VQLLuDCJDyqdp8n9e+44IqHeSYAImh\nvn2/MwCAQJYFCJCyXAFsHgEEEEi1wHBNiSVpH77JhEA+CQw9ukD1m1w1rIm3JuVT3skrAgh4\nR4AAyTt1SUkQQACBmMAwHSwn4JqHxNLFjl0ivwSGHRXfZ2sWlOZXxsktAgh4SoAAyVPVSWEQ\nQMD3Aq6joeYepF7jpIJSBmjw/f6QZwCJgRpqF5TkWc7JLgIIeEmAAMlLtUlZEEDA9wJltUPN\nGHYlqjyIZ8n4fmfIQwB731ywSKp5hxakPKw+soyAZwQIkDxTlRQEAQQQkCp2jI4xECCxN+Sj\nQLDQ0aDDQqpfWahiVeRjEcgzAgh4QIAAyQOVSBEQQACBhECv6l0B0hRakBIm/M0vgaGx+5Ac\njdJh+ZVxcosAAp4RIEDyTFVSEAQQQCDeghRVVJUESOwOeSowzIxkZ6f9NCNPS0C2EUAg3wUI\nkPK9Bsk/AgggsEsgGpF67RilLVqqgjJYEMhPgSFHxEeyG6Xp+VkAco0AAnkvQICU91VIARBA\nAIG4wI4PHAWjRVqj+ZAgkLcCZYMCKhrapJE6VDKjMjIhgAACmRYgQMq0ONtDAAEE0iSw9e34\nyeRavZ2mLZAsApkRKJ9UbwZp6KXCrQMzs0G2ggACCLQQIEBqgcFbBBBAIJ8FqnYFSLQg5XMt\nkncrUD65PgZRvGEEIAgggEDGBQiQMk7OBhFAAIH0CGyd78g1AzR8qHfTswFSRSBDAr1MC5Kd\nijaOzNAW2QwCCCCwR4AAaY8F7xBAAIG8FYg2S9sWOtpZvk5NqsvbcpBxBKxA6diG2H5cvHE4\nIAgggEDGBQiQMk7OBhFAAIHUC2xf5Cja5Ki697LUJ06KCGRYwDED2dmuogXb+6tpe4Y3zuYQ\nQMD3AgRIvt8FAEAAAS8IVJnudXba0Xu5F4pDGRDQar0px/xvyzxGsmN3QACBzAoQIGXWm60h\ngAACaRGo2nUSSYCUFl4SzYLAKhMg2WnLW5yqZIGfTSLgawGOOr6ufgqPAAJeEbAtSIFCV7W9\n1nilSJTD5wKr9FZMoGouLUg+3xUoPgIZF4g/rjrjm82dDfbt27fTzASDwdgyXVm208RYoNsC\ngUBA1EG3+Xq8ouPET1IKCwuphx5rdj8B++/AvkKhPYfvplpX1UvqNGi6mV/Eda/u67JmLgnU\naKPCvapVNa+3+vTpo8QxKJHHgoIC9erVS67rJmbxN8MCieMQv80Zht9rc/Y8lTrYC6Wdj5FI\npJ1vWs/e8wvber5vPtXU1HRaVntgtgeBrizbaWIs0G2ByspK6qDbej1f0Z6UFxUVqbm5mXro\nOWe3U7B1YI9HO3fu3J3GhjnmrWsuIBwcUXhtePd83iCQ7wINg9YotLS31s2rVe/xrUtTUVGh\nuro6hcPs861lMveJ86PMWXe0JXuxgHPUjoT2fGfPZcrKyvbMaOed7wOkZA6sySzbjjezeyBg\nrxJSBz0A7OGqiZZU6qGHkD1c3QZH9gDf8t/Cpjdsq1FAlYdE5K7hanoPiVk9hwQaBq5R+dLJ\n2vhGVGWjo61yZo9F9mpwy38LrRbgQ9oFEq131EHaqTvcAL/LHfK0+jJxLtNqZhsf6IvRBgqz\nEEAAgXwS2DIvfijvf2jrE8h8KgN5RaAtgcaBa2OzuQ+pLR3mIYBAugQIkNIlS7oIIIBAhgTs\nyWNRpavyURnaIJtBIEMCjQM+lBNyGeo7Q95sBgEE4gIESOwJCCCAQB4L7Fwn1W901G8qXevy\nuBrJejsCbiisvge62r7QUbi+nYWYjQACCKRYgAApxaAkhwACCGRSoGpu/DDej+51mWRnWxkU\nsMG/G3G09R2G+84gO5tCwNcCBEi+rn4KjwAC+S6w+c34SeOAabQg5Xtdkv+2BfodGt+3Ew9D\nbnsp5iKAAAKpEyBASp0lKSGAAAIZF9jylgmQHFeJk8iMZ4ANIpBmgf5T44OPECClGZrkEUBg\ntwAB0m4K3iCAAAL5JRBplLYtcNR7gquC8vzKO7lFoKsCvcZKBRVmoIZd3Um7uh7LIYAAAt0V\nIEDqrhzrIYAAAlkW2Pquo2iTowGH0b0uy1XB5tMo4JhG0n6HuKpb56hhSxo3RNIIIIDALgEC\nJHYFBBBAIE8FYt3rTN77c/9RntYg2e6qgA2Q7LTFDGnPhAACCKRbgAAp3cKkjwACCKRJYMsb\n8UN4/8N4QGyaiEk2RwQSozRW7Xooco5ki2wggIBHBQiQPFqxFAsBBLwvsPmN+ANiK8w9GkwI\neFkg8ZwvBmrwci1TNgRyR4AAKXfqgpwggAACXRaoXSU1bHbUfzr3H3UZjQXzVqBkgFQ6zFXV\nfEcuu3ze1iMZRyBfBAiQ8qWmyCcCCCDQQmDzru51A6bTva4FC289LNDfPDC2eYejmuUeLiRF\nQwCBnBAgQMqJaiATCCCAQHICm1+P36w+gBak5OBYOm8F+iWehzSfU5e8rUQyjkCeCHCUyZOK\nIpsIIIBASwF7/1Gg0FXlFPobtXThvXcFuA/Ju3VLyRDINQECpFyrEfKDAAIIdCLQuM1V9ftO\n7NkwwaJOFuZrBDwiYC8GOAFzH9I8hvr2SJVSDARyVoAAKWerhowhgAACbQusf8Xed2QeEHs4\nrUdtCzHXiwKhUqlif1fb3nMUafJiCSkTAgjkigABUq7UBPlAAAEEuiiw4T/xwGjg4QzQ0EUy\nFvOIgO1mF21ytH0RrUgeqVKKgUBOChAg5WS1kCkEEECgfYH1c0xg5LhigIb2jfjGmwL9Dolf\nHKCbnTfrl1IhkCsCBEi5UhPkAwEEEOiCQLjO1Zb5rvpOclXQqwsrsAgCHhLYHSCZ5yExIYAA\nAukSIEBKlyzpIoAAAmkQ2PSGFA2L+4/SYEuSuS/Q5wBXwWI7UAOnL7lfW+QQgfwV4AiTv3VH\nzhFAwIcCG+bEuxgNOpL7j3xY/b4vciAk9Z3sasdSqamGQUp8v0MAgECaBAiQ0gRLsggggEA6\nBNa/HE+VEezSoUua+SAQ62bnOto0l4sE+VBf5BGBfBQgQMrHWiPPCCDgS4FwvbT5LanyQEfF\n/XxJQKERiD3/yzJsejOCBgIIIJAWAQKktLCSKAIIIJB6gS1vOYo2S0NmcoN66nVJMV8E+k2N\ntxxtfJMWpHypM/KJQL4JECDlW42RXwQQ8K3Aplfih+yhx3Do9u1OQMHVa7RU2Ns1LUgESOwO\nCCCQHgF+ZdPjSqoIIIBAygU2zom3HA2ZyaE75bgkmFcCleZ5SLVrXdVvyqtsk1kEEMgTAX5l\n86SiyCYCCPhbIFwnbZnrqHKSVNKfLnb+3hsofeJ5SFvmYYEAAgikXoAAKfWmpIgAAgikXGDT\na47csKMhx6Q8aRJEIO8E+h0S7163ZW7eZZ0MI4BAHggQIOVBJZFFBBBAYOOc+OF6yLG0HrE3\nINBvavwZSLQgsS8ggEA6BAiQ0qFKmggggECKBez9R07A1eCjUpwwySGQhwIlA6Xy4Y4IkPKw\n8sgyAnkgQICUB5VEFhFAwN8CTdXS1nfM/UdTXBVW0ILk772B0icEBh4WUNN2RzUrEnP4iwAC\nCKRGgAApNY6kggACCKRNIDZ6neto8LHxbkVp2xAJI5BHAoOmxU9hquZzKpNH1UZWEcgLAY4q\neVFNZBIBBPwssOGl+KF68DE898XP+wFlby0wcHowNqNqPq2qrWX4hAACPRUgQOqpIOsjgAAC\naRawAVKw2FX/w2hBSjM1yeeRwMBDzSmM46pqHgFSHlUbWUUgLwQIkPKimsgkAgj4VWDnOqlm\nuaMBh7sKFvlVgXIjsK9AYS9HvcdJ2xY4iob3/Z45CCCAQHcFCJC6K8d6CCCAQAYENsyOH6bp\nXpcBbDaRdwL9D5UiDY62L6IVKe8qjwwjkMMCBEg5XDlkDQEEENgwO37iN+Q4utexNyCwt4AN\nkOzEfUhxB/6LAAKpESBASo0jqSCAAAIpF3BNTGTvPyru76rPgQRIKQcmwbwXGDAtXgTuQ8r7\nqqQACOSUAAFSTlUHmUEAAQT2CGx711HjVju8d1QOPYj2wPAOgV0CfQ+UAoUM1MAOgQACqRUg\nQEqtJ6khgAACKRNY/0I8KhpM97qUmZKQtwQCBVLfya6qlzhq3umtslEaBBDInkAoe5tmywgg\ngAACHQmsfyF+DWuIaUFiQsBPAgsWLIgV9w9/+IP+9Kc/tVl0Z1ez6qkN1+sI91J99KBPalXw\ntVbLTp8+Xffdd1+reXxAAAEEOhMgQOpMiO8RQACBLAg010qb33TMvUdRlQzKQgbYJAJZFIhG\n4xcFKioqNGhQx/8AGqrNWPjm/5MrZkn9N+zO9cKFC1VXV7f7M28QQACBrgoQIHVViuUQQACB\nDApsfNmRG3Y05HhajzLIzqZyTODSSy/VzTff3GGuti2N6K7x23XxMVfrrIeviy0biUQUCnGK\n0yEcXyKAQLsC3IPULg1fIIAAAtkT+PD5+OF56CwCpOzVAlvOB4G+44IqrnS0/jWeFpsP9UUe\nEcgHAQKkfKgl8ogAAr4TsPcfhUpd9Z/O8N6+q3wKnLTA4Bkh1a6NqnY9FxSSxmMFBBDYR4AA\naR8SZiCAAALZFdixVNq5xtGgma6ChdnNC1tHIB8EbIBkJ1qR8qG2yCMCuS9AB93cryNyiAAC\nPhJYvXq11jzUy5R4kAqnbNLy5dtblb6oqCh2b8XOnW2Padze/FaJ8AEBjwkMOTx+OrPhtWaN\nP4erCh6rXoqDQMYFCJAyTs4GEUAAgfYFzjjjDJ235XbtbwKky39+qrb9fG37C/MNAgjEBGhB\nYkdAAIFUChAgpVKTtBBAAIEeCoTcYo3RkWqo2KgzzjbDFic5Pfzww6qvr09yLRZHIL8FSvsH\n1HtsQBveDMuNct9eftcmuUcg+wIESNmvA3KAAAII7BbYr+lIhVSkwz83St/9+Z92z+/qm2ef\nfZYAqatYLOcpgaFHhLToL02qWhhR3wMcT5WNwiCAQGYFGKQhs95sDQEEEOhQYGzzsbHvx5zG\nfRQdQvElAnsJDN51H9KHrzLc9140fEQAgSQFCJCSBGNxBBBAIJ0CY5uOV5NTq2HH0MCfTmfS\n9p7AnoEaCJC8V7uUCIHMChAgZdabrSGAAALtCmxf5KgiOkSrS15TsIAuQu1C8QUCbQgMPCSk\nYJFEC1IbOMxCAIGkBLhEmRQXCyOAAALtC9TV1enpp59uf4FOvml+aqJZYopWlbxs/l7YydJ8\njQACLQWChY4GTg1p/ethNdUwUENLG94jgEByAgRIyXmxNAIIINCuwJYtW/SlL32p3e87++LL\n+pf2k2sCpP90tijfI4BAGwJDzEAN6809SBvfoJtdGzzMQgCBLgoQIHURisUQQACBrgoceuih\nuuSSS7q6eGw5d2ehItdN1xp3vupCVUmty8IIIBAXsAGSnT58NRKfwX8RQACBbggQIHUDjVUQ\nQACBtgQcJ37f0IQJE3T11Ve3tUi78xbe26gn3FotcrrfRa/dxPkCAZ8IDD0yflqz4TVakHxS\n5RQTgbQIMEhDWlhJFAEEEEhOYPk/m2IrLBIBUnJyLI3AHoGKkUGVDXFMNztakPao8A4BBJIV\nIEBKVozlEUAAgRQLRMOuVjzZrPJhAa1z3k1x6iSHgL8EhhxZoIYqV/002l8Fp7QIIJAyAQKk\nlFGSEAIIINA9gbWzzahb1a7GnF7QvQRYCwEEdgsM3XUf0igdtnsebxBAAIFkBAiQktFiWQQQ\nQCANAsv+Ee9eN/aswjSkTpII+EtgyK77kPbTdH8VnNIigEDKBAiQUkZJQggggED3BGyAFCqV\nRpxAC1L3BFkLgT0Cgw8LKWDGahhFgLQHhXcIIJCUAAFSUlwsjAACCKRWoGpRWNXLohp1UoEK\nSuKj4KV2C6SGgL8EQsWOBkwNaogOVChS7K/CU1oEEEiJAAFSShhJBAEEEOiewLK/N8dWHHMm\n3eu6J8haCOwrYIf7DiioytoJ+37JHAQQQKATAQKkToD4GgEEEEinwLK/m/uPTMPR2DMIkNLp\nTNr+EhhyVDBW4H61B/ir4JQWAQRSIkCAlBJGEkEAAQSSF6jbFNWHr4Y1eEZIZYM5HCcvyBoI\ntC0wZNdIdv0JkNoGYi4CCHQowC9yhzx8iQACCKRPYPm/TOtR1LQencXgDOlTJmU/CvQaHtB2\nrZNtQXJdPwpQZgQQ6IkAAVJP9FgXAQQQ6IHA0sfjw3uPY3jvHiiyKgJtC6zQqyqMlKv6fQY/\naVuIuQgg0J4AAVJ7MsxHAAEE0ijQXO9q1TPN6j0moP6TzZjETAggkFKBFXo9lt7mNwiQUgpL\nYgj4QIAAyQeVTBERQCD3BFY/26xwneledzaDM+Re7ZAjLwis1GuxYmx+nQDJC/VJGRDIpAAB\nUia12RYCCCCwS2B39zoCJPYJBNIisF4L1Ryo05Y3ONVJCzCJIuBhAY4aHq5cioYAArkp4EZd\nLftHk4orHQ2bSfe63KwlcpXvAq4ZAaWqfLFqVzuq35jvpSH/CCCQSQECpExqsy0EEEDACNih\nves3uRpjnn0UCNL9h50CgXQJbOn1XizpTa9xupMuY9JFwIsCHDG8WKuUCQEEclpg6d92jV53\nNsN753RFkbm8F9jca0GsDJtf40JE3lcmBUAggwIESBnEZlMIIICAFVhmhvcOFkv7fYQBGtgj\nEEinwNby9xUocLXpVQKkdDqTNgJeEyBA8lqNUh4EEMhpgapFYW1bEtWokwpUUMZJW05XFpnL\ne4FIoEmVB7vavthRU3XeF4cCIIBAhgTy4u7guro6/ec//9GHH36oyZMn69BDD93NU1NTo1de\neWX358SbWbNmqaCA7isJD/4igEBuCOzuXncOrUe5USPkwusCAw93teXNgOzzkIad5Hq9uJQP\nAQRSIJDzAdKTTz6pn/3sZzrooINUWlqqu+66S2eccYa+8Y1vxIr/9ttv68Ybb1T//v1bcRx5\n5JEESK1E+IAAArkgsPRvzZJpux97JgFSLtQHefC+wIAjotJtQW16JWACpIj3C0wJEUCgxwI5\nHSBFo1Hdc889uuKKK/Sxj30sVtjZs2fru9/9rs455xyNGzdOH3zwgSZNmqTbbrutxxgkgAAC\nCKRToGZdRBveCGvY0SGVDqSHczqtSRuBhMDAGa6cgLkP6RW6tCZM+IsAAh0L5PQv9NatWzV9\n+nSdfPLJu0sxderU2Hvb3c5ONkCaMGFC7D3/QQABBHJZYNnjpvXI9PAZdy6tR7lcT+TNWwIF\nvaS+k11tfddRc623ykZpEEAgPQI53YJku8197Wtfa1Xyf//73woGg7uDIhsgFRUV6Vvf+pYW\nL16sAw44QFdeeaWGDRvWaj37YdWqVa3mVVRUxNJqNbODD3a7TNkVoA6y5x8IxK+nOI6T1L+b\n7OU481tOGLW3Ze4/ak+G+QikT8D+bgw6Wtr6jqOqt4IadkL6tuW3lO3vgZ34bc5+zVMHXauD\nzn6nE6nkdICUyGTi77Jly3THHXfo4osv1qBBg2QHaNiwYYMGDx6sT3ziE5o5c6YefvhhffnL\nX9a9996r8vLyxKpqbm7WKaecsvuzfXPppZfq2muvbTWvow8DBw7s6Gu+y4AAdZAB5E42UVxc\nLPti2lfADijT3tSwPao1LzSr/5Sg+ozhYkt7TsxHIJUChYWFsr8bE05r0qLf1ahmfpkGfrws\nlZsgLSPAb3P2dwPqoGt10NQUfw5hZ0vnTYD0zjvvxFqJTjjhBF122WWxctkA6KGHHlJlZaXs\nQdBOBx54oD796U/LtjSdffbZsXn2PzZibPnZzrMj4nV0QmOXsZM9GbRXSerr6+Mz+G9WBGw9\nNDQ0ZGXbbFSxfwMlJSUKh8Pq6gHGb24dHSOW/7NZUdPDbjzd6/y2W1DeLApEIpHY73zlNNO3\n1TR2rPp3o/nMvUipqhLbg8eeX3V07EvVtkinfQHOj9q32fsbO75BImbY+7uWn/MiQHr55Zf1\n/e9/XxdeeKG+8IUv7M6/DVps61HLacyYMRowYIDWr1/fcnas+ffmm29uNc9+2Hu5fRYwM+xw\n4aFQSNXVPEShLZ9MzbM7NHWQKe19t2Ob722AZFtjqYd9fewc26rd3vTBY/GrVtx/1J4Q8xFI\nvYANkBLHq8qDQto819GWtdWy9yUx9VygX79+sQApYdzzFEmhOwKcH3VdzZ7LtOxh1t6aOT1I\ng830888/r+uvv15f+cpXWgVH9ruVK1fGWovWrFljP8YmG/Bs3ry5zXuQEsvwFwEEEMikQHO9\nq5VPNqlidEADD86L61KZ5GFbCGREYNBMV27U0aZXaUHKCDgbQSCPBXI6QKqqqtJPfvITHX/8\n8dpvv/1kn3mUeNkR7uw826x4++23a9u2bbHWoN/+9rfq27evTjzxxDyuFrKOAAJeElj5VLPC\n5vYkutd5qVYpS74JDDraPA/JTBtezulTn3xjJb8IeFIgpy9lPvHEE7G+w88884zsq+VkR607\n/fTTdc011+iGG27QueeeG/vadrG79dZbYw+Vbbk87xFAAIFsCXzwaGNs0+PPY3jvbNUB20Vg\n4OHmeUghVxvn0ILE3oAAAh0L5HSA9MlPflL21dE0ceJE3XfffdqyZUvsXqHevXt3tDjfIYAA\nAhkViDS7Wv6PZpUOdjT0yJw+5GbUhY0hkE4B1zWDMpjJ9kR5/PHHd2/KGTVL2xf209/+8oSc\n8s5Hs7L3Op911lm71+cNAgj4Q8Azv9b2mUlMCCCAQK4JrHm+WY3bXU25okhOgCvXuVY/5Meb\nAnakKjvZx4N88Ytf3F3IU/RN2dcd/+8felt/2z2/vTd2hDYCpPZ0mI+AdwU8EyB5t4ooGQII\n5LPAB4/Er1LTvS6fa5G856uA7XZvB3lKTO7yAYr8Rrrk8G8p+InjE7Pb/PuLX/xC69ata/M7\nZiKAgLcFCJC8Xb+UDgEEsijgRl198LcmFVc6GjmrIIs5YdMI+FNg6NChuvrqq3cXPhp2ddv/\nblPRhv31+asP3z2/rTd/+ctfCJDagmEeAj4QYCgXH1QyRUQAgewIrHs5rPpNrsaeVahAiO51\n2akFtorAHgH773DE8SHVrIpq2weRPV/wDgEEEGghQIDUAoO3CCCAQCoFliS6153P6HWpdCUt\nBHoiMOrkeGvuyqebe5IM6yKAgIcFCJA8XLkUDQEEsidgR9H64NEmFfSSEidk2csNW0YAgYTA\nqFPiFyxWPtX5KHaJdfiLAAL+EiBA8ld9U1oEEMiQwPpXw6pdG9XYMwsVKqJ7XYbY2QwCnQpU\n7h9U7zEBrX6uWZGm+HDgna7EAggg4CsBAiRfVTeFRQCBTAkkuteclmf/AABAAElEQVTtT/e6\nTJGzHQS6LLDfqQUK75TWvhTu8josiAAC/hEgQPJPXVNSBBDIoMCSh5sUKpP2+yj3H2WQnU0h\n0CWB0afu6mb3JN3sugTGQgj4TIAAyWcVTnERQCD9AqVVI2OjZI05rVAFJXSvS784W0AgOYGR\nJxQoYGKkFU8wUENyciyNgD8ECJD8Uc+UEgEEMijQd/XU2Nb2/xitRxlkZ1MIdFmgoMwM931c\ngarei6h6JcN9dxmOBRHwiQABkk8qmmIigEDmBPquOUShUmnM6QRImVNnSwgkJzDmjPhw38v/\nSTe75ORYGgHvCxAgeb+OKSECCGRQYLgOUdHO/hptu9eV0r0ug/RsCoGkBMacEb+AsfyfdLNL\nCo6FEfCBAAGSDyqZIiKAQOYEDtbZsY1NuJDWo8ypsyUEkhfoMyaoygOCWvNCs5p3Mtx38oKs\ngYB3BQiQvFu3lAwBBLIgcLDOUSTYSPe6LNizSQSSFRh7ZoEijWawBkazS5aO5RHwtAABkqer\nl8IhgEAmBXa8W6RKjVD1sAV0r8skPNtCoJsC486Nt/QufYz7kLpJyGoIeFKAAMmT1UqhEEAg\nGwJb/l0e2+y2kXOzsXm2iQACSQoMOTyksiGOlpn7kCLNdLNLko/FEfCsAAGSZ6uWgiGAQCYF\n3Ki0+dlyNahG1UMXZnLTbAsBBLop4DiOxp1TqKZqV2ueZ7CGbjKyGgKeEyBA8lyVUiAEEMiG\nwKbXHDVtDmmB/k9uMJyNLLBNBBDohkCim92Sh+lm1w0+VkHAkwIESJ6sVgqFAAKZFlj1WPxw\nOl+PZnrTbA8BBHogMHJWgUr6O/rg0SZFw3Sz6wElqyLgGQECJM9UJQVBAIFsCURNz5zV/woo\n1DuiJXohW9lguwgg0A2BQMjR+PMK1VDlavVzdLPrBiGrIOA5AQIkz1UpBUIAgUwLrH/RdK/b\n5qj/CbWKKpLpzbM9BBDoocD+FxbFUnj/QbrZ9ZCS1RHwhAABkieqkUIggEA2BVY+Gj+UDjy1\nNpvZYNsIINBNgRHHh1QyMN7NLtJEN7tuMrIaAp4RIEDyTFVSEAQQyIZA805p7VMBlQ5zVXFw\nQzaywDYRQKCHAoGgo4kfL1LjNlfL/0UrUg85WR2BvBcgQMr7KqQACCCQTYG1TwYUqXe033lR\nmRGDmRBAIE8FDrg4/tDYhfcSIOVpFZJtBFImQICUMkoSQgABPwqseDh+GB19Pvce+bH+KbN3\nBIbMKFCf8QGtMC1IDdvNg82YEEDAtwIESL6tegqOAAI9FajfKG2Y7ajvQVH13r+nqbE+Aghk\nW+DATxUp0igt/iutSNmuC7aPQDYFCJCyqc+2EUAgrwVigzO4jkafz9XmvK5IMo/ALoFJnzaj\n2ZkzowV3cT8hOwUCfhYgQPJz7VN2BBDokcDyhwJygq5GnUuA1CNIVkYgRwQqRgY16qQCbXwz\not51++VIrsgGAghkWoAAKdPibA8BBDwhsPUdR9WLAxoyy1XJAE8UiUIggIARmPzZ+DORxmw+\nFQ8EEPCpAAGSTyueYiOAQM8EbOuRncZcyOAMPZNkbQRyS2D8eYXmoocZmbLqRBW4JbmVOXKD\nAAIZESBAyggzG0EAAS8JRMz926seC6iwj6thp/BQSS/VLWVBIFjoaPKlRSqMlOsQnQsIAgj4\nUIAAyYeVTpERQKBnAuuedtS41VxhNvceBeOPTulZgqyNAAI5JTDl88Vyzf+OdD+bU/kiMwgg\nkBkBAqTMOLMVBBDwkMCyvwZjpRnzcQZn8FC1UhQEdgv0GRPU+t5vaLgO1qbXeAL0bhjeIOAT\nAQIkn1Q0xUQAgdQI1H0orX/BPPtoclSVB9G9LjWqpIJA7gksGfRYLFPv3xm/IJJ7OSRHCCCQ\nLgECpHTJki4CCHhSYNkD5rBpnn009hO0HnmygikUArsENvaerw1apLVPOqpdDQsCCPhJgADJ\nT7VNWRFAoEcCromJlt0XVLDY1X7nESD1CJOVEcgDgRed38mNOlr0W1qR8qC6yCICKRMgQEoZ\nJQkhgIDXBda/6KhunaORZ0RV2NvrpaV8CCAwTw+rdKgr23JcvwkPBBDwiwABkl9qmnIigECP\nBZbeG7+KPO6TtB71GJMEEMgDgagT1gFXRBRtNK1It9OKlAdVRhYRSIkAAVJKGEkEAQS8LmAH\nZ1j3lKPe+0c1YAaDM3i9vikfAgmBsRdHVTzA1Qf/SytSwoS/CHhdgADJ6zVM+RBAICUCtvXI\n3osw/jO0HqUElEQQyBOBUIk06SsRRRocvfcbWpHypNrIJgI9EiBA6hEfKyOAgB8Eos3S0r8E\nFCpzNfoCAiQ/1DllRKClgO1Wa+9FWvrngGpXtfyG9wgg4EUBAiQv1iplQgCBlAqs/ldADZud\nWHBUUJ7SpEkMAQTyQCBYJE251tyL1Oxo/k20IuVBlZFFBHokQIDUIz5WRgABPwgs+WP8ULn/\npRE/FJcyIoBAGwKjz4+qz6SoVv89qM1vOm0swSwEEPCKAAGSV2qSciCAQFoEqt52tOWtgAYf\nE1Xv8WnZBIkigEAeCDjmjGnaD+IXSd66zt6TmAeZJosIINAtAQKkbrGxEgII+EXg/Tt3tR5d\nRuuRX+qcciLQnsCgo12NOD2qre8EzEOjOYVqz4n5COS7AP+6870GyT8CCKRNoG6DtOrvAfUa\n7WrYSQztnTZoEkYgjwQO/X5YwRJX838cVMOWPMo4WUUAgS4LECB1mYoFEUDAbwJL7jbdaMKO\nJlweke1ew4QAAgiUDTcDNnwjoqZqR299nwEb2CMQ8KIAP/lerFXKhAACPRYI15mhvf8UUGFv\nV2P+i5sNegxKAgh4SGDC5+IDNqx6LKh1zzBgg4eqlqIgEBMgQGJHQAABBNoQsM89sleIx386\nqlBpGwswCwEEfCsQCElH3mJaloOuXv9myBwrfEtBwRHwpAABkierlUIhgEBPBKJhafHvgwoU\numJo755Isi4C3hXoO9nVpK9EVb/R0Rvfpqudd2uakvlRgADJj7VOmRFAoEOBVY8HVLcu/mDY\nkoEdLsqXCCDgY4HJX42ockpUq/4W1MrHOKXy8a5A0T0mwL9mj1UoxUEAgZ4JuGawuoW3mkOj\n4+qALzG0d880WRsBbwsECkxXu/8xo9oVm6521wZVu9rb5aV0CPhFgADJLzVNORFAoEsC9obr\n6vcDGnm6q4oxXVqFhRBAwMcC9gHS026IKFzraM4XQ4o2+xiDoiPgEQFzmyETAggggEBC4L1f\nx+8lOPAqWo8SJvxFwI8CixcvVjQa1cSJE7tU/AtCt+rAeafp6vF/0jPFN+5e58EHH9SUKVN2\nf+YNAgjkvgABUu7XETlEAIEMCax/0VHVvICGnhBV5UE8GDZD7GwGgZwUsMGRnYYOHdql/L0R\n+ZWGrzxYRzZdrpoBH+iNuke1bdu2WJDVpQRYCAEEckaAAClnqoKMIIBAtgUW/CreejT5GlqP\nsl0XbB+BXBAIBAJatGhRl7OycW5Yfz2qWmfuvFmTzh6mW+65ocvrsiACCOSOAPcg5U5dkBME\nEMiiwIaXHW1+LaDBx0TVfxqtR1msCjaNQN4KDDo0pFm/KlPjdlcDnrhAQRXmbVnIOAJ+FiBA\n8nPtU3YEENgt8O4v4q1HB32D1qPdKLxBAIGkBQ6+olgTLypU4aahOls/Tnp9VkAAgewLECBl\nvw7IAQIIZFlgw+xdrUfHRjVgOq1HWa4ONo9A3guc8vtyNVdu1lH6rKqf75f35aEACPhNgHuQ\n/FbjlBcBBPYRePvmeOvR+CtrtWrVxn2+7+qM9evXd3VRlkMAAQ8LFJSZiy6nPaR+935aH/5m\nP1WfEZEdDpwJAQTyQ4AAKT/qiVwigECaBNY9a0aum2tGrjsxqjc3P6EvX/jlNG2JZBFAwE8C\n4cotelhf08WNd+ilywM69YlmhUr9JEBZEchfAQKk/K07co4AAj0UcE1vurd/YluPXE35ZkQv\nLo0neNhhh2nChAlJp75p0yY988wzSa/HCggg4E2BeXpEXz71R9r+5EC98e2gjvw19zh6s6Yp\nldcECJC8VqOUBwEEuiyw6vGAti8MaOSZkfhzj3YFSJdccomuuuqqLqeTWPDll18mQEpg8BcB\nBGICg69YJa3urxUPBc0oma5GXxB/vhI8CCCQuwIM0pC7dUPOEEAgjQLRsPTuz4JyAqb16P9x\nVTeN1CSNgK8FAoWuZt4eVrDE1RvfCqpmha85KDwCeSFAgJQX1UQmEUAg1QLL7guYExVHYz4e\nVcW4VKdOeggggMAeAXuMmX5jROE6R3O+GFK0ec93vEMAgdwTIEDKvTohRwggkGaBcJ1pPfpl\nUMFiVwd9ndajNHOTPAIIGIEx/xXVqLMj2vpOQO/8PD5yJjAIIJCbAtyDlJv1Qq4QQKAbAu++\n+65WrlzZ6ZqN/5qopk2TVHjK+/r3mwt2Lz937tzd73mDAAII9ERg8+bNsdVfeuklrVmzJvbe\nnRWSM/tkLby1RCuKX1JoXFWnm5g8ebJGjx7d6XIsgAACqRMgQEqdJSkhgECWBR544AHddddd\nHeaiTP30bb2pqLbpuqc/qoand3S4PF8igAAC3RFYuHBhbLWbbrqp1epjdbS+oMe09mf76Rf6\ntJq0s9X3e3+44YYbdPnll+89m88IIJBGAQKkNOKSNAIIZEfgmmuu0YgRI9rcePTRGdLLveSc\n+aZunPWDVss88sgjmjNnTqt5fEAAAQR6IvDVr35VI0eObJVE9G+L1W/2gbrxyGcU+Nirrb5L\nfJg3b57+/Oc/Jz7yFwEEMihAgJRBbDaFAAKZEbjoootkn2W097Ttg4j+99rtKt8voM8+dIpC\nRR9ptcjy5csJkFqJ8AEBBHoqYI9H06dPb5VM+Iuu/jx1u7a+sr/Ou2GaRp1U2Op7++H+++8n\nQNpHhRkIZEaAQRoy48xWEEAgBwRmf6suNnrUzB+XmuDIyYEckQUEEPCjQKjY0an/Wy7HjNXw\n1OU71VRjnlrNhAACOSNAgJQzVUFGEEAgnQJrX27W0kebNOiwoCZ+Yt+rtencNmkjgAACewsM\nObxA075WrJpVUb307Y7vQ9p7XT4jgEB6BQiQ0utL6gggkAMCruvqxa+bsb3NdPwvyuQ4tB7l\nQLWQBQR8L3D0DaXqMz6g+b9t1Lo5PBzJ9zsEADkjQICUM1VBRhBAIF0Ci+9v0obXwxp7doGG\nH1uQrs2QLgIIIJCUgO1qd8qd5bF1nv7cTkWa6GqXFCALI5AmAQKkNMGSLAII5IZAuMHVS+be\no4CJi477WVluZIpcIIAAArsERhxXoIMuK9LWRRG9/pN6XBBAIAcECJByoBLIAgIIpE/gzV/W\nq2Z1VId8qVh9x/P0+vRJkzICCHRX4NibS1Uy0NFrN9bLjrbJhAAC2RUgQMquP1tHAIE0Cuzc\nENXrN9WruNLREdeXpHFLJI0AAgh0X6C4b0DH/7JMkUbp319mwIbuS7ImAqkR8P1zkPr27dup\nZDAYv+rclWU7TYwFui0QCAREHXSbr8crJgY2KCwszNl6KCoqalXOl6+rU3OtdPSvSlRSyfWg\nVjh8QACBnBI48OIiLbirQaueadbi+02ktGsqLS3N2WNuKBQ/jeS3OVFb2flrz1Opg67ZRyJd\na6H1fYBUW2vOnjqZ+vTpI7vzdWXZTpLi6x4I2H/81EEPAHu4qg1QbQDS3Nycs/Vg85aYNs0P\na8Hdjeo7IRDrXpeYz18EEEAgVwVO+m257pmyXS98facq/jt+cbaxsTFnj7m9e/eWDZL4bc7u\nHlVQUEAddLEK7MXesrLO70f2fYDU8oSqPVs7RLCdurJse2kwv+cCth6og547djeFREtqLtdD\nNBrdXbznrzHdVMzH435epmABw3rvhuENAgjkrEDlhKCmf6Mkdi+SHh4by6e94p2rv32cH+XG\nrpTLv8u5IbQnF4lzmT1z2n5Hn5O2XZiLAAJ5LLD5uVKtfSGsUScXaOwZPBQ2j6uSrCPgO4HD\nv1uiXqMC2vnkCA3WRN+VnwIjkAsCBEi5UAvkAQEEUiYQVKGW/6ZSjumdcvwtpSlLl4QQQACB\nTAgUlDqaZY9d0YDO1U8zsUm2gQACewkQIO0FwkcEEMhvgWN1hRrWFWjKF4rUf5LvexHnd2WS\newR8KjD+3CIVTdmisTpawXfG+1SBYiOQPQECpOzZs2UEEEixQLCuXCfqGoV6RXT0DbQepZiX\n5BBAIIMCvT/zvsJqUsFTR6mZkb8zKM+mEJAIkNgLEEDAMwKD3vqoitVLoz6/XSX9OLx5pmIp\nCAI+FCgYUqfZ+q0CNWVa8Mv4iHY+ZKDICGRFgDOIrLCzUQQQSLVA1duOen9wmDZqiYZdsCPV\nyZMeAgggkHGBZ/VLRStqtfjOgKo/yPjm2SACvhUgQPJt1VNwBLwl8NZ1QTnmf4/ru3K49chb\nlUtpEPCpQJPMw65PnSM37Oit73Fg8+luQLGzIECAlAV0NokAAqkVWPFIQFveCqhmxELTfvR8\nahMnNQQQQCCLApHJyzTwqKg2zA5o9b94plsWq4JN+0iAAMlHlU1REfCigL15eb554nygwNWG\nw//hxSJSJgQQ8LnA9BvD5tEFrub+IKRwnc8xKD4CGRAgQMoAMptAAIH0Cbz366DqNzqa+Pmo\nmiuq0rchUkYAAQSyJNB7f2nC5VHVrXO0wBzzmBBAIL0CBEjp9SV1BBBIo0DNCmnxHQGVDHI1\n6auRNG6JpBFAAIHsChz09UjsWLf49oB2LM1uXtg6Al4XIEDyeg1TPgQ8LGBvWo42OzrkuogK\nyjxcUIqGAAK+Fygol6Z+PxI75r3xHQZs8P0OAUBaBQiQ0spL4gggkC6Bdc84+vC5gAbMiGr0\n+dF0bYZ0EUAAgZwR2O+cqAYfE9XGlwNa+RincDlTMWTEcwL86/JclVIgBLwvEGlUbMhbJ+Dq\nsB/Ttc77NU4JEUAgIXCYGbDBDkoz9wdBNfHItwQLfxFIqQABUko5SQwBBDIhsPC3AdWudjTu\nkqj6TnIzsUm2gQACCOSEQMVY6cAro2rY7Gj+jxmwIScqhUx4ToAAyXNVSoEQ8LZA7Rpp4f8E\nVVTp6uBraT3ydm1TOgQQaEtg0lci6jXa1dI/B7T5DZ6N1JYR8xDoiQABUk/0WBcBBDIuYAdm\niDTEB2Yo7J3xzbNBBBBAIOsCwSJpxs1hkw9Hr33DHBObsp4lMoCApwQIkDxVnRQGAW8LrH3a\n0bqnA+o/Laox/8XADN6ubUqHAAIdCQw62tWYj0e04wPHtKpzOteRFd8hkKwA/6KSFWN5BBDI\nikC43gzMcF1IdmCG6T+JyKFXSVbqgY0igEDuCBx6fUTFA9zYw2O3L+KgmDs1Q07yXYAAKd9r\nkPwj4BOB98zT43eudbT/pQzM4JMqp5gIINCJQGEfafpNYblhR69eE1TU9rpjQgCBHgsQIPWY\nkAQQQCDdAtUfmIEZzMh1JYNcTfkmAzOk25v0EUAgfwRGnOZq5FkRbX0noIW3clqXPzVHTnNZ\ngH9JuVw75A0BBOSaUbxf/2YodoV02g0R2afJMyGAAAII7BGYfqPpatff1bu/DGrru3S12yPD\nOwS6J0CA1D031kIAgQwJLL/fDGP7WkBDZkU18kwGZsgQO5tBAIE8EiiqNKPa/Tze1e4/V9qR\nPvMo82QVgRwUIEDKwUohSwggEBdo2CLN+1FQwRI7MAOd69kvEEAAgfYEhp/iauzF8VHt7HGT\nCQEEui9AgNR9O9ZEAIE0C7x1fVBN2x1N+UZE5SPSvDGSRwABBPJcYNoPzQNkx7hacndQ9rEI\nTAgg0D0BAqTuubEWAgikWWDdvx2t+ltQfSdHNeHzdK1LMzfJI4CABwRCpdLRvw0rUODq1a+G\ntHOdBwpFERDIggABUhbQ2SQCCHQs0LxTeuNb8WceHf7ziAL0FukYjG8RQACBXQKVU1xN/V4k\n1vo+54qQos3QIIBAsgKhZFdgeQQQQCBdAnfddZc2bNigyhdOU8W6Gaqe+rJu/+ez0j+7tsU3\n33yzawuyFAIIIOBhgQmXR7XupUZteKZIvz9rrrYe82S3S1tRUaErr7yy2+uzIgL5KECAlI+1\nRp4R8KjAgw8+qNp3yvRFfV+btUy/mPdxhecxHJNHq5tiIYBAGgXGfPtDvftMVAPePkJ/f/su\nzdej3drasGHDCJC6JcdK+SxAgJTPtUfeEfCYQDBapAv1a9lbi2f+xtFHpyR31fOyyy7TsmXL\nPKZCcRBAAIHkBULlru7Rp/XVwLP6VOh23XjbN1U6PrkLTueee27yG2YNBDwgQIDkgUqkCAh4\nReDQDZerv8Zo6lXFOuGq6UkXq6ysLOl1WAEBBBDwqsAGLdaqI+/V2DmXa82P9tfFr/dW2aCu\n335eVFTkVRrKhUCHAl3/V9JhMnyJAAII9Exg06uOJm45T1VaqWNuMkMxMSGAAAII9Fhg24j5\nOuJ7JapZHdXj59Yo3OD2OE0SQMDrAgRIXq9hyodAHgiE6xQbklZy9VDgahWU8fyOPKg2sogA\nAnkicNQPSzT+gkKtfyWsJz5dK9clSMqTqiObWRIgQMoSPJtFAIE9AnN/EFTtakeL+j+iFc6r\ne77gHQIIIIBAjwUcx9zT+adyDT48pCUPNmn2teaqFBMCCLQrwD1I7dLwBQIIJCMQiUR08cUX\nJ7NKbNmBWw/VEQuuU03JWj1af13S67MCAggg4EWBhQsXxop1zz336NlnzeMOkpwaGloPyFBQ\n4ujcv/fSfUdV682fNah8WEDTri5JMlUWR8AfAgRI/qhnSolA2gVsl43Zs2cntZ0y9dM3dLsi\nCuuP9Z/WdnMHUjDIU2GTQmRhBBDwpMD27dtj5bIjc6ZqdM7SgQGd/2SF/mqCpBeuqVPpgIAO\nuIiBGDy5A1GoHgnQxa5HfKyMAAJ7Cxx11FGqqanp0ut/T/tAvTTQ3EBcpEU1L6ukhKuZe3vy\nGQEE/C1w8803d+l4uvdx95lnnmkTru+4oM5/okIF5dKTn6nV8v9ranM5ZiLgZwFakPxc+5Qd\ngTQI2Bag8nLzy9vJNP93DVr1f40aNjOkmd+vUCDoyPaTZ0IAAQQQ2CNgh9ruyjF1zxrxdx1d\ncBo0LaRz/lahR0/boX9cUKPzTMA04riCvZPgMwK+FaAFybdVT8ERyJ7AlvfCevHrO1XUx9Fp\n95bHgqPs5YYtI4AAAv4TGHlCgc54sJcizdJjZ+7Q+tfMGyYEEIgJECCxIyCAQEYFmutd/fO/\nahWul06+o0wVo7jnKKMVwMYQQACBXQLjziqMjW7XvFN65NQabZwXxgYBBIwAARK7AQIIZFTg\n+at3quq9iA66vEgTLuTm4IziszEEEEBgL4EDPlGkU+4sU2O1q4dP3qHN7xIk7UXERx8KECD5\nsNIpMgLZElh0X6PevbNR/SYFNes3ZdnKBttFAAEEEGghcNClxTrxtjI1VJmHdZ+4Q7YbNBMC\nfhYgQPJz7VN2BDIoULU4ome+UKuQiYvOfKhc9pkcTAgggAACuSFwyBeLzYWrUtVvdvXgCTtU\ntZAgKTdqhlxkQ4AAKRvqbBMBnwk073T19/Nr1Fxr7ju6vVz9DmAATZ/tAhQXAQTyQODQq0p0\n/C0mSNoUD5L6hcfkQa7JIgKpFyBASr0pKSKAwF4CT11Wq60LI5ryhSId+EnuO9qLh48IIIBA\nzghM+6oJkn5ZqrqNri7cepcqmwmScqZyyEjGBAiQMkbNhhDwp8Cbv6jX+w80afCMkGb9mvuO\n/LkXUGoEEMgngWnXxIOksmh/XbDlD6pekk+5J68I9FyAAKnnhqSAAALtCKx8ukmzr61TyUBH\nZz1SrlAR9x21Q8VsBBBAIKcEbJD0fK+fqizaT8+eX6Dt73P8zqkKIjNpFSBASisviSPgX4Gt\nSyL658dr5ZijzFkP91Kv4TzvyL97AyVHAIF8FHir7M96offNaqxy9O8LQtq+mCApH+uRPCcv\nQICUvBlrIIBAJwIN26J67IwdatzmxoaOHX5MQSdr8DUCCCCAQC4KzCv/iw79YXhPkLSIICkX\n64k8pVaAACm1nqSGgO8FnGhIj59bo+0fRHXoV4s15XPFvjcBAAEEEMhngYmfi2raj0yQtNW0\nJH0spG0LCZLyuT7Je+cCBEidG7EEAggkIXDokqu09sWwxpxZoON/UZrEmiyKAAIIIJCrAhMu\ni+qwH7cIkt4jSMrVuiJfPRcgQOq5ISkggMAugTP0Aw3ffKwGHRbUGX/tZe4/4geUnQMBBBDw\nisD+nzVB0k1hNW1TrCVp8/yIV4pGORBoJUCA1IqDDwgg0F2BxbeHdLyu1M7i9TrvXxUqKCM4\n6q4l6yGAAAK5KrD/p6Oa/tOImrZLj32kThveDOdqVskXAt0WIEDqNh0rIoBAQmDpvQG9c2Oh\ndmij/jP5hyodyKElYcNfBBBAwGsC4z8V1YyfRdRogqSHT6rRlrlcEPNaHfu9PJzF+H0PoPwI\n9FBg+YMBvf7NoAp7u/q9LlBdycYepsjqCCCAAAK5LjDu4qhOvLNYTTWunvuvkDa/TpCU63VG\n/rouQIDUdSuWRACBvQSWPxDQq9cEVdBLOvbeRm3Qor2W4CMCCCCAgFcFDrykQB/9U5ki9dJz\nnwhp4xyCJK/Wtd/KRYDktxqnvAikSGDJPbuCo3Jp1v1hVR4cTVHKJIMAAgggkC8CB1xcpKN/\nF1G0WXrhUyF9+BxBUr7UHflsX4AAqX0bvkEAgXYEFvw6oDe/HVJhX+nEh8LqP9VtZ0lmI4AA\nAgh4XWDkmVEdc2dYrrlONvuzIa3+F0GS1+vc6+UjQPJ6DVM+BFIoEI24evHqJr3z05BKBrs6\n+bFmVU4hOEohMUkhgAACeSkw/COujrsnLCckzflCSLYLNhMC+SrA3puvNUe+EciwQFONGdL1\nzBq9Z64SVox3dcrfm9V7/wxngs0hgAACCOSswJDjXJ3w17BCZYrdn7rodk4zc7ayyFiHAuy5\nHfLwJQIIWIEdy6QnTg1o5RPNGnZcIBYclQ3HBgEEEEAAgdYCA2a4OunRsIr7S/NuCGnej4Jy\n6WjQGolPOS9gGkKZEEDACwKvvvqqnnvuuR4X5cgjj9SsWbN2p2P7kr/61ZDCOx0d/KUiHfmT\ngHbUNuz+njcIIIAAAt4UqK2tjRXsxhtvbLOAJSUlCgQC2rlz5z7fhz7aV4Me/5QW/a5SO9aE\nNfNWR8HCfRZjBgI5KUCAlJPVQqYQSF7grbfe0q233pr8inutEY1GYwFS2AzbOu+HQX3wp6AC\nRa6O/HVUR32lXPX15gsmBBBAAAHPC9TV1cn+JnT3t6Vcv9Nl+qv0z6l6fosZyOGPYRWZwX2Y\nEMh1AQKkXK8h8odAkgI/+tGPNHPmzCTXkt555x1dffXVsfXsU9FfuTqkmmWOKsa5Ovp2M1Ld\nQfTITRqVFRBAAIE8Fxg0aJDuv//+bpXi+uuv1+9eOlu/P/Z9bZpdoqfPKNBxf2pWxdhuJcdK\nCGRMgAApY9RsCIHMCEyePFnHH3980hsLBs0DX1Wiyv+comduD5nhWh2NvySiqddHFCpNOjlW\nQAABBBDwgEBxcXG3flNs0QcMGKAm1WnKLVu07vahev/OoJ46vUBH/zasoSdwY5IHdg/PFoFL\nwp6tWgqGQHIC2/5Trv+nOeozf6ZKhpiHv/61WdN/QnCUnCJLI4AAAgjsLeCYs81pP4xoxs/C\niphe2vaBsu/eEog9N2nvZfmMQC4IECDlQi2QBwSyKLB1SUSPnrFDH3xrpPpomKqn/Eenv9As\nO1wrEwIIIIAAAqkSGHdxVCc+ElbJQOndn4X0/EUh1W9OVeqkg0DqBAiQUmdJSgjklUCduWH2\nuat36p7J27XiX80qn1ynX+lEVc18UgXmGRZMCCCAAAIIpFpgwGGuPvpMswYfG9WG2QH936wC\nrX3KSfVmSA+BHglwD1KP+Fg5VQJ33323nnrqqQ6TKygoUHNzc4fLfOYzn9Gpp57a4TJ+/7Kp\nxtVbt9TrzV80qGmHq16jAjrmplJtGb5QHx67wPAc63ciyo8AAgggkAKBRYsWxVL54he/qMLC\nvcb4dh2NG322Jq68SLM/W6A1A5/XgrF3q7kgPrR4y81/7Wtf04wZM1rOysh7O4LfRRdd1ONt\n2aHQ77vvvh6nQwKZEyBAypw1W+pAYOnSpZo9e3YHS3Ttq1NOOaVrC/pwqaZaV/Nva9AbP6tX\nQ5Wr4kpHx/6sVFOvLFao2NFLL/kQhSIjgAACCKRNoLq6Opa2fU5fW9Nsvaihuksf120asWmW\n+m46SP/U9/WmHmi1+CWXXNLqc6Y+uOYJt6k4N3EcWsgyVWep2g4BUqokSSclAi+++KKmTp2a\ndFoPPfSQLrvssqTX88MKjTuimndrg+be0qD6La4KeklHfK9Eh329WEW96WXrh32AMiKAAALZ\nFFiyZIkGDx7cbhaizeYC3q/Mb9XN/fXxxtv0lcN+qyNuDOqB1/5H3/ve99pdL1NfHHHEEXr6\n6ae7tTn74PW5c+d2a11Wyp4AAVL27NlyGwJlZWXq1cucwSc52WFImVoL7NwY1dxfN2j+b01X\nuup4YHT4d0o0zQRGJZUERq21+IQAAgggkC6B8vLyTn/bj7tBOvgzEb3wtZ1a9niz/n5KWMUT\nztAo/T1d2epyuvYxGN05N7EbsN3rmPJPgAAp/+qMHCPQoUDjqlI9dXmtFt3bqEijVNzP0VE/\nLNHUq4pV3JcDdYd4fIkAAgggkDWBPmOCOudvFVrzYrNe/k6dPvzPCF2lJ1RzU5VWNgU04rSo\ngnvdypS1zLJhTwsQIHm6eimcXwSiEalg8Vh9QY9q7Venaa0aY4MvTLumWFMuLzaj0tH/2S/7\nAuVEAAEE8l1gxHEF+sSc3vrZ5+/V0jtLtP+y4/WfL0mFfV2NOiuqUWdHNWCGK/t8JSYE0iFA\ngJQOVdJMm0Dth1FtM8/t2b48opo1Ue00n+s2u6paPF1f1bMq/M1I/ePuAtn7IZ2Aq6DpeRcs\nMcGD6bVXWOGqqFIq6ufGnsFQMthVqXkgaulQ13yXtiynNeGaFdLyB4LmFVD5xrM03myteGK1\nTrphmMafV6hAkMAorRVA4ggggAAC6RMYv16/1zd1xw8f0JDVx2vlIwF9cE8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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "## Student's t random number generation\n", "gent <- function(nsamp, nu) {\n", " z <- rnorm(nsamp)\n", " chisq <- genchisq1(nsamp, nu)\n", " trv <- z / sqrt(chisq / nu)\n", "}\n", "nu <- 6\n", "n <- 1000\n", "tdata <- data.frame(x = gent(n, nu))\n", "plt <- ggplot(tdata, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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QQAABBKoRIEGqRsvAY3Ua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\nyfv166cRI0Y0G1GfPn2afZ0XEfCiQI8ePVrc9+Ndr2WapYxr3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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# F random number generation\n", "genF <- function(nsamp, nu1, nu2) {\n", " chisq1 <- genchisq1(nsamp, nu1)\n", " chisq2 <- genchisq1(nsamp, nu2)\n", " Frv <- chisq1 / nu1 / chisq2 * nu2\n", "}\n", "nu1 <- 10; nu2 <- 6\n", "n <- 1000\n", "Fdata <- data.frame(x = genF(n, nu1, nu2))\n", "plt <- ggplot(Fdata, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Acceptance-rejection sampling\n", "\n", "Suppose we want to sample from a distribution with complicated density $f(x)$. It is not easy to use the above method since neither the cdf nor its inverse is analytically available.\n", "\n", "John von Neumann, while working on the Mahanttan Project, suggested the following:\n", "\n", "1. Find the \"envelope\" of $f$, i.e., a simple density $g(x)$ such that \n", "$$\n", " f(x) \\le c g(x) =: h(x)\n", "$$\n", "for all $x$, for some constant $c > 0$.\n", "\n", "2. Sample a random variable $X$ distributed according to $g$. \n", "\n", "3. Accept $X$ as a representative of $f$ if\n", " - $U \\le \\displaystyle\\frac{f(X)}{h(X)}$,\n", " - where $U$ is a uniform random variable on $[0, 1]$ drawn independently.\n", " \n", "4. Reject $X$ otherwise. Go to Line 2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why AR sampling works?\n", "\n", "**Definition** (Body of a function). For a nonnegative, integrable function $f$, its body is defined and denoted by\n", "$$\n", " B_f = \\{(x, y): 0 \\le y \\le f(x) \\}.\n", "$$\n", "\n", "- Thus the volume $B_f$ is $|B_f| = \\int_{-\\infty}^{\\infty}f(x)dx = \\int_{-\\infty}^{\\infty}\\int_0^{f(x)}1dydx$.\n", "\n", "**Theorem 1**. Supose random variable $X$ has density $g$, $U\\sim\\text{unif}[0, 1]$ is independent of $X$, and there exists $c > 0$ such that $f(x) \\le c g(x)$ for all $x$. Then, the random vector $(X, cg(X)U)$ is uniformly distributed over the body $B_{cg}$ of $cg$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Theorem 1 states that the AR sampling scheme uniformly samples from $B_{cg}=B_h$.\n", "- The sample is accepted if and only if $0 \\le h(X)U = cg(X)U = Y \\le f(X)$, i.e., $(X, Y) \\in B_f$. The conditional density of $(X, Y)$ given $\\{(X, Y) \\in B_f\\}$ is merely\n", "$$\n", " \\frac{|B_{cg}|^{-1}\\mathbb{I}_{B_{cg}}(x,y)}{P(B_f)}\\mathbb{I}_{B_f}(x,y)\n", " = \\frac{|B_{cg}|^{-1}\\mathbb{I}_{B_{cg}}(x,y)}{|B_f|/|B_{cg}|}\\mathbb{I}_{B_f}(x,y)\n", " = \\frac{1}{|B_f|}\\mathbb{I}_{B_f}(x,y)\n", " .\n", "$$\n", "That is, $(X,Y)|\\{(X, Y)\\in B_f\\} \\sim \\text{unif}(B_f)$.\n", " + This means the accepted sample $(X, Y)$ is drawn according to $\\text{unif}(B_f)$.\n", "- Now the marginal density of $X$ is $f$. To see this, note when $(X, Y) \\sim \\text{unif}(B_f)$,\n", "\\begin{align*}\n", " P(X \\in A) &= \\frac{|\\bar{A}|}{|B_f|},\n", " \\quad\n", " \\bar{A} = B_f \\cap \\{(x, y): x\\in A\\} = \\{(x, y): x \\in A, ~ 0 \\le y \\le f(x)\\}.\n", " \\\\\n", " &= \\frac{\\int_A f(x)dx}{1}, \\quad \\because |B_f| = \\int_{-\\infty}^{\\infty}f(x)dx = 1\n", " \\\\\n", " &= \\int_A f(x)dx.\n", "\\end{align*}\n", "\n", "- Thus sample $X$ is drawn according to $f$!\n", "\n", "- The total acceptance ratio is\n", "\\begin{align*}\n", " P\\left(U \\le \\frac{f(X)}{cg(X)}\\right) \n", " &= \\int_{-\\infty}^{\\infty}\\int_{0}^{f(x)/[cg(x)]} 1\\cdot g(x) du dx \\\\\n", " &= \\int_{-\\infty}^{\\infty} g(x) \\int_{0}^{f(x)/[cg(x)]} 1 du dx \\\\\n", " &= \\int_{-\\infty}^{\\infty} g(x) \\frac{f(x)}{cg(x)} dx \\\\\n", " &= \\int_{-\\infty}^{\\infty} \\frac{f(x)}{c}dx \\\\\n", " &= \\frac{1}{c} \\int_{-\\infty}^{\\infty} f(x) dx \\\\\n", " &= \\frac{1}{c}\n", " .\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Proof of Theorem 1\n", "\n", "We want to show that the joint density of $(X, cg(X)U)$ is \n", "$$\\frac{1}{|B_{cg}|}\\mathbb{I}_{B_{cg}}(x, y).$$\n", "\n", "Let $Y = cg(X)U$. Then $Y|\\{X=x\\} \\stackrel{d}{=} cg(x) U \\sim \\text{unif}[0, cg(x)]$. That is, the conditional density of $Y$ given $X$ is\n", "$$\n", " p_{Y|X}(y|x) = \\frac{1}{cg(x)}\\mathbb{I}_{[0, cg(x)]}(y).\n", "$$\n", "By construction, the marginal density of $X$ is given by $p_X(x) = g(x)$. Therefore the joint density of $(X, Y)$ is\n", "\\begin{align*}\n", " p_{XY}(x, y) &= p_X(x)p_{Y|X}(y|x) = \\frac{1}{c}\\mathbb{I}_{[0, cg(x)]}(y) \\\\\n", " &= \\begin{cases} 1/c, & \\text{if } 0 \\le y \\le c g(x), \\\\\n", " 0, & \\text{otherwise}. \\end{cases}\n", " \\\\\n", " &= \\frac{1}{c}\\mathbb{I}_{B_{cg}}(x,y).\n", "\\end{align*}\n", "Now since\n", "$$\n", " 1 = \\int_{-\\infty}^{\\infty}\\int_0^{cg(x)}\\frac{1}{c}dydx = \\frac{1}{c}|B_{cg}|,\n", "$$\n", "we have\n", "$\\frac{1}{|B_{cg}|}\\mathbb{I}_{B_{cg}}(x, y)$\n", "as desired." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Marsaglia\n", "\n", "> One way to sample from the unit disk is to sample $(U, V)$ from $\\text{unif}[-1, 1]\\times\\text{unif}[-1, 1]$, and discard the sample if $U^2 + V^2 > 1$ and resample.\n", "\n", "We have $X=(U, V)$.\n", "\n", "* Target density: $f(u, v) = \\frac{1}{\\pi}\\mathbb{I}_{\\{u^2+v^2<1\\}}(u, v)$ (uniform from unit disc)\n", "* Sampling density: $g(u, v) = \\frac{1}{4}\\mathbb{I}_{\\{|u|<1, |v|<1\\}}(u, v)$ (uniform from $[-1, 1]^2$)\n", "* Envelope: $h(u, v) = \\frac{1}{\\pi}\\mathbb{I}_{|u|<1, |v|<1}(u, v) = \\frac{4}{\\pi}g(u, v)$, hence $c=4/\\pi$.\n", "* Accptance criterion\n", "$$\n", "\\frac{f(U,V)}{h(U,V)} = \\frac{\\mathbb{I}_{\\{U^2+V^2 < 1\\}}}{\\mathbb{I}_{\\{|U| < 1, |V| < 1\\}}}\n", "= \\begin{cases} 1, & \\text{if } U^2 + V^2 < 1 \\\\ 0, & \\text{otherwise} \\end{cases}\n", "$$\n", "* Thus we accept the sample from $g$ iff $U^2 + V^2 < 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: gamma random numbers\n", "\n", "Recall that the Gamma distribution with shape parameter $\\alpha$ and scale parameter $\\beta$ has density\n", "$$\n", " f_{\\Gamma}(x; \\alpha, \\beta) = \\frac{1}{\\Gamma(\\alpha)\\beta^{\\alpha}}x^{\\alpha-1}e^{-x/\\beta}\n", "$$\n", "for $x \\ge 0$. If $X \\sim \\text{Gamma}(\\alpha, \\beta)$, then $cX \\sim \\text{Gamma}(\\alpha, c\\beta)$.\n", "Hence it suffices to sample from $\\text{Gamma}(\\alpha, 1)$. Furthermore, $X\\sim \\text{Gamma}(\\alpha, 1)$ and $\\alpha > 1$, then $X \\stackrel{d}{=} Y + Z$ where $Y \\sim \\text{Gamma}(\\lfloor \\alpha \\rfloor, 1)$, $Z \\sim \\text{Gamma}(\\alpha - \\lfloor \\alpha \\rfloor, 1)$ and independent of $Y$. \n", "The $Y$ can be generated by summing $\\lfloor \\alpha \\rfloor$ independent $\\text{Exp}(1)$ random variables.\n", "Therefore we only need to sample from \n", "$\\text{Gamma}(\\alpha, 1)$, $\\alpha \\in (0, 1)$.\n", "\n", "If $0 < \\alpha < 1$, we see that\n", "$$\n", " x^{\\alpha - 1}e^{-x} \\le \\begin{cases} x^{\\alpha - 1}, & \\text{if } 0 \\le x \\le 1, \\\\ e^{-x}, & \\text{otherwise}. \\end{cases}\n", "$$\n", "Thus we choose \n", "$$\n", " h(x) = \\begin{cases} x^{\\alpha - 1}/\\Gamma(\\alpha), & \\text{if } 0 \\le x \\le 1, \\\\ e^{-x}/\\Gamma(\\alpha), & \\text{otherwise}. \\end{cases}\n", "$$\n", "leading to\n", "$$\n", " g(x) = \\begin{cases} x^{\\alpha - 1}/(1/\\alpha + 1/e), & \\text{if } 0 \\le x \\le 1, \\\\ e^{-x}/(1/\\alpha + 1/e), & \\text{otherwise}. \\end{cases} \n", "$$\n", "and\n", "$$\n", " c = \\frac{1}{\\Gamma(\\alpha)}\\left(\\frac{1}{\\alpha} + \\frac{1}{e}\\right).\n", "$$\n", "Density $g$ has cdf\n", "$$\n", " G(x) = \\begin{cases} x^{\\alpha}/(1 + \\alpha/e), & \\text{if } 0 \\le x \\le 1, \\\\ \n", " \\frac{1 + \\alpha/e - \\alpha e^{-x}}{1 + \\alpha/e}, & \\text{otherwise}. \\end{cases} \n", "$$\n", "whose inverse is\n", "$$\n", " G^{-1}(u) = \\begin{cases} [(1 + \\alpha/e)u]^{1/\\alpha}, & \\text{if } 0 \\le u \\le 1/[1+\\alpha/e], \\\\ \n", " -\\log(1/\\alpha + 1/e) - \\log(1 - u), & 1/[1+\\alpha/e] \\le u < 1. \\end{cases} \n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/html": [ "1501" ], "text/latex": [ "1501" ], "text/markdown": [ "1501" ], "text/plain": [ "[1] 1501" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "0.7505" ], "text/latex": [ "0.7505" ], "text/markdown": [ "0.7505" ], "text/plain": [ "[1] 0.7505" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gengamma_ar <- function(nsamp, alph) {\n", " # sample X from g\n", " v <- runif(nsamp) # unif rv for inverse method\n", " idx <- v > 1 / (1 + alph * exp(-1))\n", " x <- numeric(nsamp)\n", " x[idx] = -log(1 / alph + exp(-1)) - log(1 - v[idx])\n", " x[!idx] = ((1 + alph * exp(-1)) * v[!idx])^(1 / alph)\n", " \n", " # test acceptance\n", " u <- runif(nsamp)\n", " idx2 <- (x > 1)\n", " accept <- logical(nsamp)\n", " accept[idx2] <- (u[idx2] < x[idx2]^(alph - 1))\n", " accept[!idx2] <- (u[!idx2] < exp(-x[!idx2]))\n", " \n", " x[accept]\n", "}\n", "\n", "n <- 2000\n", "alph <- 0.5\n", "x <- gengamma_ar(n, alph) \n", "length(x)\n", "length(x) / n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "text/html": [ "0.748540580270693" ], "text/latex": [ "0.748540580270693" ], "text/markdown": [ "0.748540580270693" ], "text/plain": [ "[1] 0.7485406" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma(0.5) / (1 / alph + exp(-1) ) # acceptance ratio" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true } }, "outputs": [ { "data": { "image/png": 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UmClNOTQFgECBAgQIAAAQJNC0iQmibL\nxgbza0GqJUiHDNSQjUpVSgIECBAgQIAAgZYLSJBaTtyZA6QWpJ6BcvSvOPbxh6vPQoo4sNVQ\n38dWsoQAAQIECBAgQKBIAhKknNZ2akE63gh2Kezhk7Qg5bT6hUWAAAECBAgQILBAAQnSAuG6\nfbP0HKSh44xgl8o/tKEWhXuQur02lY8AAQIECBAgQKBdAhKkdkm38TiH90WMH567BalvOKJ/\nVXpYrC52bawehyJAgAABAgQIEOhiAQlSF1fOQot2aHtty7lakNJa6T6kg1sXeiTbESBAgAAB\nAgQIEMiXgAQpX/VZjWZkZ61FaK57kNLKQxvKceRAKY4czCGEkAgQIECAAAECBAg0KSBBahIs\nC6vXn4E0uK42CMPxyjy0vrZOumfJRIAAAQIECBAgQKDoAhKkHJ4B9WcgDZ0wd3D1VqZDlVHv\nTAQIECBAgAABAgSKLiBByuEZMLq3FtTA6rmD04I0t5E1CBAgQIAAAQIEiiMgQcphXY/urrUG\nDayeu4vdRAvSdi1IOTwVhESAAAECBAgQINCkgASpSbAsrH74aAtS/3xakI4+K8k9SFmoWWUk\nQIAAAQIECBBotYAEqdXCHdj/6J7aQQcqzziaaxpaX1vjkBakuagsJ0CAAAECBAgQKICABCmH\nlTy6p97Fbu7gBo+2INVHvpt7C2sQIECAAAECBAgQyK+ABCmHdVsfpKF/1dzB1Ue6G9GCNDeW\nNQgQIECAAAECBHIvIEHKYRUfrnSx61tWjp6+uYMbWBtR6imHFqS5raxBgAABAgQIECCQfwEJ\nUg7rOHWxm88ADSn0UqU33uC6CPcg5fBEEBIBAgQIECBAgEDTAhKkpsm6f4PUxW4+Q3zXI0n3\nIY3srL/zmwABAgQIECBAgEBxBSRIOav7scPlGDtYqiRI8w8sjWSXtjlyYP7bWJMAAQIECBAg\nQIBAHgUkSDmr1ZFdtaG9B+YxQEM9dCPZ1SX8JkCAAAECBAgQKLqABClnZ8BI/RlIq+d+BlI9\n9ImR7HbUhgevz/ebAAECBAgQIECAQNEEJEg5q/HR3bXEaL6DNKTwB9fXtjm0PWcYwiFAgAAB\nAgQIECDQpIAEqUmwbl995GiC1FQXu8oodmka2aUFqSbh/wQIECBAgAABAkUVkCDlrOYnEqQm\nutgNVp6FlKbRXbXf/k+AAAECBAgQIECgqAISpJzV/MjuWkDNjGI3uLbWxW5kpxaknJ0OwiFA\ngAABAgQIEGhSQILUJFi3rz6y5+g9SKtqv+dT3noLkmchzUfLOgQIECBAgAABAnkWkCDlrHYn\nhvleM//ABuotSO5Bmj+aNQkQIECAAAECBHIpIEHKWbXWW5AWNkhDzjCEQ4AAAQIECBAgQKBJ\nAQlSk2DdvvrkPUjz72LXNxzRO1Q2SEO3V67yESBAgAABAgQItFxAgtRy4vYeYHTiHqTmjjtQ\nGcnOIA3NmVmbAAECBAgQIEAgfwISpJzV6ejeo4M0rGgusDSS3YhhvptDszYBAgQIECBAgEDu\nBCRIOavS0X2V7nLD5Sg1WbNpJLvx0VIcOZAzEOEQIECAAAECBAgQaEKgyY/RTezZqh0ROPxY\nOfpXNn/owXW1lidDfTdvZwsCBAgQIECAAIH8CEiQ8lOX1UhSF7v+JrvXpQ0nnoVkqO+cnRHC\nIUCAAAECBAgQaEZAgtSMVgbWTV3s+lfMfwS7ekhpkIY0jboPqQbh/wQIECBAgAABAoUUkCDl\nqNoPHyxHeSyib0EtSLWk6tDOUo5EhEKAAAECBAgQIECgOQEJUnNeXb324X0LG8EuBTW4rhaa\nFqSurmKFI0CAAAECBAgQaLGABKnFwO3c/cjEEN/Nd7GbGKRBF7t2VpljESBAgAABAgQIdJmA\nBKnLKmQxxRldRAtS/R6kEYM0LKYKbEuAAAECBAgQIJBxAQlSxiuwsfgTXewWMsx35UGxaTLM\nd6Oo1wQIECBAgAABAkUTkCDlqMbrXez6FjCK3eCaGsSoFqQcnRFCIUCAAAECBAgQaFagr9kN\nWrH+j370o/jud78bq1evjp//+Z+P5cuXTznMvn374oYbboj0+9xzz41TTz21qeVTVs7xm8V0\nsetfVYEplWN0T46BhEaAAAECBAgQIEBgDoGOtyD97d/+bbz+9a+PH/7wh/G5z30uLrroorjz\nzjsnin333XfHxRdfHJ/97Gfj5ptvjle96lVx4403znv5xIoFeJEeEpumhTwotlQ5EwZWV56D\ntNsw3wU4VYRIgAABAgQIECBwDIGOtiDt2rUrrrzyynj7298ez3ve86pFfP/73x9XXXVVvO99\n75t4n5KmSy+9NEqlUlx99dXxwQ9+MD7zmc9U36f1j7f8GHHncna9BWkhXewSyEClm93I7lzS\nCIoAAQIECBAgQIDAvAQ62oL0hS98IU4++eSJ5CiV+I1vfGO85S1vqRZ+x44dcdttt1VbkFJy\nlKYXvOAF8dBDD8Wtt94acy2vblCg/y2mBSkxDawux+FKF7ty86OEF0hZqAQIECBAgAABAnkW\n6GgL0v333x+nnXZa9f6ilCwdOnQofvmXfzl+9Vd/tWq+devW6u/NmzdP1MEJJ5wQAwMDsW3b\ntol5x1p+1llnTawzNjYWr33tayfepxfnn39+vPCFL5wyL8tvRveNVYu/btPKWLu2t+lQlm84\nFDvHx2J5z5oYXJOfrna9vb0Vj7WVxE/mVz8p+vpqf/orV66M8fHx+uzC/+7p6Yn0k84X01SB\ndM5wmWqSri1r1qxxbWlgSSZpWrFiRSxbtqxhSbFfputK/d+iYkvMjJ7LTJN0vXVtmeqyVNeW\nlA/MZ+pogvToo4/Gww8/HHfccUe1Zeiee+6Jyy67LFLXu9/8zd+sLhscHIz00zilD3VpnRTk\n8ZY3bpM+BH79619vnBVPfOITY2hoaMq8LL8Z3ftYtfgrNwxW4mq+apdvOFzZvnLiHByIoZOa\nT7C62W76OdTNZW1n2dKXDaaZAvUEcuaS4s5JH/DydL1cqpp0bZld0rVldpf6h7zZlxZzbuoh\n5Noys+5dW2aapDmLvbaMjo7OvuNpc5v/FD1tB4t5mxKcBx54IK655po48cQTq7tKyU+6z+il\nL31p9Pf3x5EjR2YcIm2Xvpmaa3njhmnd73znO42zqsj1VqopCzL6ZnRfbfS/3Qe3x+Fa41tT\nkYwPph6XvfHAHdvj4HB+WltSq+POnTt9y9twNqRvd9NPcpnvxaJh89y+TP8gpYtvGjHTNClw\n0kknVc+TdL6YJgXStSV9WacVdtIkjUKb/h13bZk0Sa/StSX97N27d+qCgr9Ln/3S57x0y4Rp\nUmDdunWxe/du15ZJkuoI1/UGkpGRkYYlzb1MX/Zt3Lhxzo06miBt2LAhnvKUp0wkR6m0z372\ns6sj1qWL6/r166utRAcOHJjSVJ8uMJs2bYr0LW9Klo61fHr0CXb6lKduV42DNCykN1kapCFN\nI7vKuUsmUj3nqa5rNbXw/9ctuEw1bHSZusS7JFD3oTEp4G9o0mL6K+fLpEjdov57colXSYDL\nzPMgmXCZdKlbtMulo4M0nHHGGfHII49MOQHuuuuu6rdP6Zu5NIBDSoJuueWWCaE0aEP6ti7d\ndzTX8omNCvKiPkhD39THSM07+oE1tVYjQ33Pm8yKBAgQIECAAAECORPoaIKURqQ7ePBg/I//\n8T+q3TfSvUh///d/H8997nOrQ3inB8eed9551WG/H3vsseogDh//+MfjggsuiNT6NNfynNXV\nnOGkFqS+4YieBd4+NNGCZKjvOa2tQIAAAQIECBAgkE+BjiZIqcvb5ZdfHl/72tfi+c9/frzu\nda+Lxz/+8fGmN71pQjvNS/cEpNHmLrnkkmqL0hve8IZ5L59YsQAvRioPih1YtfDR5yZbkAqA\nJUQCBAgQIECAAAECswh09B6kVJ40FHd66Ov27durXeumj9qRhpX90Ic+VL2xMY3+km4AbZzm\nWt64bt5fH660IA0uYnTiwaP3IOlil/czRXwECBAgQIAAAQLHEuh4glQvWBqQ4XjTqlWrjrc4\n5lp+3I1zsjB1sVt52sIbBQfW1u9BygmIMAgQIECAAAECBAg0KdA1CVKT5bb6NIE0at15H1se\npeH0AKxD05bO7+3kPUgL76Y3vyNZiwABAgQIECBAgEB3CkiQurNemi5V5TlrcdbLhyKNDb/Q\nR5UMrK4ddtQgDU3724AAAQIECBAgQCAfAgvvj5WP+EXRINA7UHlMbOUBsaO7GmZ6SYAAAQIE\nCBAgQKBAAhKkAlX2fEJNgzyM7tHFbj5W1iFAgAABAgQIEMifgAQpf3W6qIjSUN8jutgtytDG\nBAgQIECAAAEC2RWQIGW37lpS8nQf0vhIKcYWNs5DS8pkpwQIECBAgAABAgTaJSBBapd0Ro4z\nOZJdRgqsmAQIECBAgAABAgSWUECCtISYedjVwOqjz0JyH1IeqlMMBAgQIECAAAECTQpIkJoE\ny/vqhvrOew2LjwABAgQIECBA4HgCEqTj6RRwWRqkIU2jewoYvJAJECBAgAABAgQKLyBBKvwp\nMBWgfg+Sob6nunhHgAABAgQIECBQDAEJUjHqed5R6mI3byorEiBAgAABAgQI5FBAgpTDSl1M\nSAZpWIyebQkQIECAAAECBLIuIEHKeg0ucfknu9gt8Y7tjgABAgQIECBAgEAGBCRIGaikdhZx\nogVpdzuP6lgECBAgQIAAAQIEukNAgtQd9dA1pZi4B8lzkLqmThSEAAECBAgQIECgfQISpPZZ\nZ+JIkwlSJoqrkAQIECBAgAABAgSWVECCtKSc2d9ZT19E3/JyjO4uZT8YERAgQIAAAQIECBBo\nUkCC1CRYEVZPAzV4UGwRalqMBAgQIECAAAEC0wUkSNNFvI80UIMEyYlAgAABAgQIECBQRIFK\nhypTpwV2794dO3bsWHQx9u3bF6Ojo5H2t5hpbODUGB9ZHmOHInqHFrMn2xIgQIAAAQIECBDI\nloAEqQvq61Of+lS8733v64KS1Irw8rg6nhoXVluRhiVIXVMvCkKAAAECBAgQINB6AQlS643n\nfYTnPve5ceqpp857/VaseOONN8bB22stUCOVgRqGTyy34jD2SYAAAQIECBAgQKArBSRIXVQt\nb3zjG+OSSy7paIle//rXx/1HE6TRxfXU62gcDk6AAAECBAgQIEBgIQIGaViIWs63ORC7qhFK\nkHJe0cIjQIAAAQIECBCYISBBmkFixsHYU0UY3etZSM4GAgQIECBAgACBYglIkIpV3/OK9mDU\n+tZpQZoXl5UIECBAgAABAgRyJCBBylFlLlUoEy1Ie7QgLZWp/RAgQIAAAQIECGRDQIKUjXpq\naynrLUiH97b1sA5GgAABAgQIECBAoOMCEqSOV0H3FeBA/R4ko9h1X+UoEQECBAgQIECAQEsF\nJEgt5c3mzg/VEyRd7LJZgUpNgAABAgQIECCwYAEJ0oLp8rvhgfogDbrY5beSRUaAAAECBAgQ\nIDCrgARpVpZizxyPI1EaGguj2BX7PBA9AQIECBAgQKCIAhKkItb6PGLuW1FJkHSxm4eUVQgQ\nIECAAAECBPIkIEHKU20uYSw91QRpCXdoVwQIECBAgAABAgQyICBBykAldaKIqQVp7GApxg93\n4uiOSYAAAQIECBAgQKAzAhKkzrh3/VF7VxyplnF0T9cXVQEJECBAgAABAgQILJmABGnJKPO1\no9TFLk0SpHzVq2gIECBAgAABAgSOLyBBOr5PYZemLnZpMlBDYU8BgRMgQIAAAQIECikgQSpk\ntc8ddO9KXezmVrIGAQIECBAgQIBA3gQkSHmr0SWKZ6KL3e7SEu3RbggQIECAAAECBAh0v4AE\nqfvrqCMlnOhit7cjh3dQAgQIECBAgAABAh0RkCB1hL37D9pbvwdpd/eXVQkJECBAgAABAgQI\nLJWABGmpJHO2n56JYb51sctZ1QqHAAECBAgQIEDgOAISpOPgFHnRRBc7z0Eq8mkgdgIECBAg\nQIBA4QQkSIWr8vkF3Lvy6DDfBmmYH5i1CBAgQIAAAQIEciEgQcpFNS59EL1Hu9gdNkjD0uPa\nIwECBAgQIECAQNcKSJC6tmo6W7CeoXL09JcrD4rtbDkcnQABAgQIECBAgEA7BSRI7dTO2LEG\nVkeM6mKXsVpTXAIECBAgQIAAgcUISJAWo5fzbftTgqQFKee1LDwCBAgQIECAAIFGAQlSo4bX\nUwQGVpfj8L6I8viU2d4QIECAAAECBAgQyK2ABCm3Vbv4wFIXu4hSGKhh8Zb2QIAAAQIECBAg\nkA0BCVI26qkjpRxYU64eVze7jvA7KAECBAgQIECAQAcEJEgdQM/KIQdW1Uo6uqeUlSIrJwEC\nBAgQIECAAIFFCUiQFsWX741rXewM1JDvWhYdAQIECBAgQIBAo4AEqVHD6ykCuthN4fCGAAEC\nBAgQIECgAAISpAJU8kJDnGhB8iykhRLajgABAgQIECBAIGMCEqSMVVg7i5uG+U6TQRraqe5Y\nBAgQIECAAAECnRSQIHVSv8uPPdGCtNcgDV1eVYpHgAABAgQIECCwRAISpCWCzONuJhKk3XmM\nTkwECBAgQIAAAQIEZgpIkGaamHNUwCANTgUCBAgQIECAAIGiCUiQilbjTcTb7zlITWhZlQAB\nAgQIECBAIA8CEqQ81GKLYuhfGVHqKcfhPS06gN0SIECAAAECBAgQ6DIBCVKXVUg3FadUGZsh\ntSKN7jFIQzfVi7IQIECAAAECBAi0TkCC1DrbXOw5DdQwYpCGXNSlIAgQIECAAAECBOYWkCDN\nbVToNdJADbrYFfoUEDwBAgQIECBAoFACEqRCVXfzwQ6siSiPl+Lwvua3tQUBAgQIECBAgACB\nrAlIkLJWY20u78DqcvWIowZqaLO8wxEgQIAAAQIECHRCQILUCfUMHXPyYbEGashQtSkqAQIE\nCBAgQIDAAgUkSAuEK8pmqYtdmrQg1Rz8nwABAgQIECBAIN8CEqR81++io9PFbtGEdkCAAAEC\nBAgQIJAhAQlShiqrE0XVxa4T6o5JgAABAgQIECDQKQEJUqfkM3LcNMx3mnSxy0iFKSYBAgQI\nECBAgMCiBCRIi+LL/8b1FqSR3QZpyH9ti5AAAQIECBAgQECC5Bw4rkA9QRrdfdzVLCRAgAAB\nAgQIECCQCwEJUi6qsXVB6GLXOlt7JkCAAAECBAgQ6D4BCVL31UlXlWiiBWmPLnZdVTEKQ4AA\nAQIECBAg0BIBCVJLWPOz0/6VEaWecuhil586FQkBAgQIECBAgMCxBSRIx7axpCJQqjQc9a9O\no9hpQXJCECBAgAABAgQI5F9AgpT/Ol50hKmbnWG+F81oBwQIECBAgAABAhkQkCBloJI6XcSB\n1eU4vCeiXHskUqeL4/gECBAgQIAAAQIEWiYgQWoZbX52PLCmkhyNl+LIY/mJSSQECBAgQIAA\nAQIEZhOQIM2mYt4UgdSClCbd7KaweEOAAAECBAgQIJBDAQlSDit1qUOaGOp7t4EaltrW/ggQ\nIECAAAECBLpLQILUXfXRlaVJXezSNLK79tv/CRAgQIAAAQIECORVQIKU15pdwrgG1xztYidB\nWkJVuyJAgAABAgQIEOhGAQlSN9ZKl5Wp3oI0qotdl9WM4hAgQIAAAQIECCy1gARpqUVzuL+J\nQRq0IOWwdoVEgAABAgQIECDQKCBBatTwelaBgbW12aN7DNIwK5CZBAgQIECAAAECuRGQIOWm\nKlsXyKBBGlqHa88ECBAgQIAAAQJdJSBB6qrq6M7CTHSx26UFqTtrSKkIECBAgAABAgSWSkCC\ntFSSOd7PxCANe3IcpNAIECBAgAABAgQIVAQkSE6DOQX6llVOlIGy5yDNKWUFAgQIECBAgACB\nrAtIkLJeg20q/8DqCMN8twnbYQgQIECAAAECBDomIEHqGH22Dpy62Y0a5jtblaa0BAgQIECA\nAAECTQtIkJomK+YGA2vKcWR/KcaPFDN+URMgQIAAAQIECBRDQIJUjHpedJT1ob5HDdSwaEs7\nIECAAAECBAgQ6F6Bvu4tWntKtmbN0Yf8tOdwsx5leHh41vmdnLly5cpotFmxcaRSnLEYHFtV\nmZ+tvLq3tzdWr67cRGWaEOjrq/3pr1ixIsbHxyfmF/1FT09PpPOl8dwvukk9/nTOcKlr1H6n\nc2XVqlVTZxb8Xf3asnz58ujGf9s6VT2uLceWd82daVP/3FIul2cuLOicpbq2zPczT+ETpP37\n93f8VBsdHe14GaYX4ODBg9Fo07MirVGK3Q8djIEt09fu7vf9/f1x4MCBcKGZrKdly5ZFcjl0\n6FAcPnx4ckHBXw0MDFRdGs/9gpNUw08fdMfGxqZcE7hE9VxxbZl6JqRzxbVlqkl6l0wGBwf9\nDU2jGRoaqn5J55o7FSYlA+naMt8P81O3zue7+rVlZGQkFvO5uVQqRfoCZ66p8AlSN3w4TB88\num06cuTIlA/OfatSq1HlD3ZHmp+tbzRSYpTqWYI0eZbVz7np9Ty5RjFf1b/l7YbrQrfVQP3v\nqNvK1cnyJJP0N+RDzGQtpCQgTeka4+9o0iVdW9J5wmTSpP7KtaUuMfm7buLaMmmSvsBM02I/\nt6TWuflM2eorNZ+IrNMSgYl7kHaXWrJ/OyVAgAABAgQIECDQDQISpG6ohQyUIT0HKU2ju2q/\n/Z8AAQIECBAgQIBAHgUkSHms1RbENLC21q3OKHYtwLVLAgQIECBAgACBrhGQIHVNVXR3Qeot\nSCO7dLHr7ppSOgIECBAgQIAAgcUISJAWo1egbQfrLUi7CxS0UAkQIECAAAECBAonIEEqXJUv\nLOCBo4+LGtmpBWlhgrYiQIAAAQIECBDIgoAEKQu11AVlrHaxK5VjVAtSF9SGIhAgQIAAAQIE\nCLRKQILUKtmc7bdUOVNSkjRimO+c1axwCBAgQIAAAQIEGgUkSI0aXh9XIHWzM8z3cYksJECA\nAAECBAgQyLiABCnjFdjO4qeBGkb3RpTH23lUxyJAgAABAgQIECDQPgEJUvusM3+k6kAN5VJ4\nFlLmq1IABAgQIECAAAECxxCQIB0DxuyZAvWhvkd2zVxmDgECBAgQIECAAIE8CEiQ8lCLbYph\nYG3tQKMGamiTuMMQIECAAAECBAi0W0CC1G7xDB9vcE25WnpDfWe4EhWdAAECBAgQIEDguAIS\npOPyWNgoUG9BGtnlYbGNLl4TIECAAAECBAjkR0CClJ+6bHkkg5VhvtNkqO+ag/8TIECAAAEC\nBAjkT0CClL86bVlEA5VhvtPkYbEtI7ZjAgQIECBAgACBDgtIkDpcAVk6/ODEIA1ZKrWyEiBA\ngAABAgQIEJi/gARp/laFX3Pg6CANhvku/KkAgAABAgQIECCQWwEJUm6rdukDm7wHySANS69r\njwQIECBAgAABAt0gIEHqhlrISBn6V0eUesphmO+MVJhiEiBAgAABAgQINC0gQWqarLgblCoN\nRylJMsx3cc8BkRMgQIAAAQIE8i4gQcp7DS9xfGmgBvcgLTGq3REgQIAAAQIECHSNgASpa6oi\nGwUZXFeOw3sjxseyUV6lJECAAAECBAgQINCMgASpGS3rRm2o75KHxToXCBAgQIAAAQIEcikg\nQcpltbYuqImHxe5q3THsmQABAgQIECBAgECnBCRInZLP6HHrD4sd2Wmo74xWoWITIECAAAEC\nBAgcR0CCdBwci2YKpHuQ0jSqBWkmjjkECBAgQIAAAQKZF5AgZb4K2xuAFqT2ejsaAQIECBAg\nQIBAewUkSO31zvzR6i1IhvrOfFUKgAABAgQIECBAYBYBCdIsKGYdW2Cg8hykNHlYbM3B/wkQ\nIECAAAECBPIlIEHKV322PJrBdbVDaEFqObUDECBAgAABAgQIdEBAgtQB9CwfcnBtbZAGo9hl\nuRaVnQABAgQIECBA4FgCEqRjyZg/q0B9kAaj2M3KYyYBAgQIECBAgEDGBSRIGa/Adhe/pz+i\nb3k5tCC1W97xCBAgQIAAAQIE2iEgQWqHcs6Oke5Dcg9SzipVOAQIECBAgAABAlUBCZIToWmB\ndB/S6O6Icu12pKa3twEBAgQIECBAgACBbhWQIHVrzXRxuVILUnmsFIf3dnEhFY0AAQIECBAg\nQIDAAgQkSAtAK/omA/WR7HYVXUL8BAgQIECAAAECeROQIOWtRtsQz8SzkHaW2nA0hyBAgAAB\nAgQIECDQPgEJUvusc3OkwXX1ZyHlJiSBECBAgAABAgQIEKgKSJCcCE0LDJ1Q28RQ303T2YAA\nAQIECBAgQKDLBSRIXV5B3Vi8iRakHd1YOmUiQIAAAQIECBAgsHABCdLC7Qq7pXuQClv1AidA\ngAABAgQI5F5AgpT7Kl76AAePdrE7tHPp922PBAgQIECAAAECBDopIEHqpH5Gjz3Zxc4odhmt\nQsUmQIAAAQIECBA4hoAE6RgwZh9bYHBtWlaOES1Ix0ayhAABAgQIECBAIJMCEqRMVltnC93T\nFzGwOioJkhakztaEoxMgQIAAAQIECCy1gARpqUULsr80UMOIUewKUtvCJECAAAECBAgUR0CC\nVJy6XtJI031Io3sixseWdLd2RoAAAQIECBAgQKCjAhKkjvJn9+C1ob5LMboruzEoOQECBAgQ\nIECAAIHpAhKk6SLez0tg8IRydT0DNcyLy0oECBAgQIAAAQIZEZAgZaSiuq2Y9YfFHtphoIZu\nqxvlIUCAAAECBAgQWLiABGnhdoXecuJZSIb6LvR5IHgCBAgQIECAQN4EJEh5q9E2xTN0Qu1A\nhvpuE7jDECBAgAABAgQItEVAgtQW5vwdZKIFyVDf+atcEREgQIAAAQIECiwgQSpw5S8m9MGj\nLUjuQVqMom0JECBAgAABAgS6TUCC1G01kpHyDK0/OoqdFqSM1JhiEiBAgAABAgQIzEdAgjQf\nJevMEJhoQdpuFLsZOGYQIECAAAECBAhkVkCClNmq62zB+5dH9A6VY0QLUmcrwtEJECBAgAAB\nAgSWVECCtKScxdpZakU6pAWpWJUuWgIECBAgQIBAzgUkSDmv4FaGN3RCpQWp8hykcu12pFYe\nyr4JECBAgAABAgQItEVAgtQW5nweJLUglcdKMbo7n/GJigABAgQIECBAoHgCEqTi1fmSRWwk\nuyWjtCMCBAgQIECAAIEuEZAgdUlFZLEYRrLLYq0pMwECBAgQIECAwPEEJEjH07HsuAITLUiV\n+5BMBAgQIECAAAECBPIgIEHKQy12KIahyj1IaTKSXc3B/wkQIECAAAECBLIvIEHKfh12LILB\n9bXh6w55FlLH6sCBCRAgQIAAAQIEllZAgrS0noXaW70FacSzkApV74IlQIAAAQIECORZQIKU\n59ptcWz1e5C0ILUY2u4JECBAgAABAgTaJiBBaht1/g40uK4Wk3uQ8le3IiJAgAABAgQIFFVA\nglTUml+CuPuWRfQOl2Nk+xLszC4IECBAgAABAgQIdIGABKkLKiHLRRhabxS7LNefshMgQIAA\nAQIECEwVkCBN9fCuSYGhDZUWpF0R42NNbmh1AgQIECBAgAABAl0oIEHqwkrJUpGGNlRKWy7F\niKG+s1RtykqAAAECBAgQIHAMAQnSMWDMnp/AcKUFKU2HHi3NbwNrESBAgAABAgQIEOhiAQlS\nF1dOFoqW7kFK06FHa7/9nwABAgQIECBAgECWBSRIWa69Lih7ugcpTYb67oLKUAQCBAgQIECA\nAIFFC0iQFk1Y7B1MJEhakIp9IoieAAECBAgQIJATAQlSTiqyU2HUu9gddA9Sp6rAcQkQIECA\nAAECBJZQQIK0hJhF3NXQ+loXOw+LLWLti5kAAQIECBAgkD8BCVL+6rStEVWH+a4c0T1IbWV3\nMAIECBAgQIAAgRYJSJBaBFuU3Q6sjugZKMdB9yAVpcrFSYAAAQIECBDItYAEKdfV257g0n1I\nnoPUHmtHIUCAAAECBAgQaK2ABKm1voXYe7oPaWRHRLl2O1IhYhYkAQIECBAgQIBAPgUkSPms\n17ZGle5DKo+VYmRnWw/rYAQIECBAgAABAgSWXECCtOSkxdvhxLOQtpeKF7yICRAgQIAAAQIE\nciUgQcpVdXYmmOGNteMe2taZ4zsqAQIECBAgQIAAgaUSkCAtlWSB91NvQTq4TQtSgU8DoRMg\nQIAAAQIEciEgQcpFNXY2iOETa6MzaEHqbD04OgECBAgQIECAwOIFJEiLNyz8HuoPi9WCVPhT\nAQABAgQIECBAIPMCEqTMV2HnA6i3IB10D1LnK0MJCBAgQIAAAQIEFiUgQVoUn42TwOQgDe5B\nckYQIECAAAECBAhkW0CClO3664rS9y2L6FtWjoOPSJC6okIUggABAgQIECBAYMECEqQF09mw\nUWD4xIhDjzbO8ZoAAQIECBAgQIBA9gQkSNmrs64s8dDGcozuKcXYSFcWT6EIECBAgAABAgQI\nzEtAgjQvJivNJTBcSZDSpBVpLinLCRAgQIAAAQIEullAgtTNtZOhsg1trBXWfUgZqjRFJUCA\nAAECBAgQmCHQN2NOB2d85zvfid27d8ev/MqvTCnFvn374oYbboj0+9xzz41TTz21qeVTVvam\nJQL1FiRDfbeE104JECBAgAABAgTaJNA1LUiPPPJI/Kf/9J/iuuuumxL63XffHRdffHF89rOf\njZtvvjle9apXxY033jixzlzLJ1b0oqUCE0N9P2oku5ZC2zkBAgQIECBAgEBLBbqiBWl8fDze\n8573RKk088P1+9///rjooovi0ksvrS6/+uqr44Mf/GB85jOfqb6fa3lL9ex8QiAN0pCmg1tn\n1uHESl4QIECAAAECBAgQ6HKBrmhB+uu//utqsvNLv/RLU7h27NgRt912W7UFqZ48veAFL4iH\nHnoobr311phr+ZSdedNSgWUn1Xavi11Lme2cAAECBAgQIECgxQIdb0G6/fbbIyVIH//4x+NT\nn/rUlHC3bt1afb958+aJ+SeccEIMDAzEtm3bJuYda/lZZ501sU5qpfrQhz408T69eOYznxnP\neMYzpszrxJvBwcFOHPa4x1y+fHmsXLnyuOs0Lux/fGpBGo3R7f2V7SpPju2iqaenJ1asWNFF\nJep8UdLfUJqWLVsW3Xj+dUqot7c30k8z536nytru43KZKZ6uLelaaZoU6O/vr74ZHh6u/ls9\nuaTYr9LfT19fn2vLLKdB+jtyzZ0Kk84X15apJkt1bUn5wHymjiZIIyMj1a51v/M7vxMnnXS0\nCaKh1A8//HD1w9v0D3DpD2nXrl0xNjZ23OUNu6qu+9GPfrRxVhw+fDh+4Rd+Ycq8TryZHl8n\nyjD9mOmDczNJRco/egZ2xKFtpaa2m37cVr1vJpZWlaEb95s+xJhmCtQTyJlLijsn/YPt72hm\n/TOZaZLmuLbM7lL/kDf70mLOdW2Zvd5dW2Z3Wey1ZXR0dPYdT5vb0QTpyiuvjNNOOy2e//zn\nTytW7W26kBw5cmTGspQYpQ/wcy1v3DB9c/PJT36ycVZs2bKl2k1vyswOvNm/f38Hjnr8Q6bR\nBFMXxmamNFDDvgfGmt6umWMsZN3Vq1fH3r17o1yu3Se1kH3kbZt0gUl/Q3v27Jn1byxv8c43\nnnRNST8HDhyY7yaFWC+13KcvlNLfkWlSwLVl0qL+qn5tSedKOmdMNYF0XUlfvHTjv/edrKN1\n69ZVv8BO/xaZJgVWrVpVHbnZ55ZJk6GhoWqrWhrRer5JzuTWk6/SLTvpvJtr6liClEat+7u/\n+7t46lOfGm9729uq5bzrrruqQaf3f/iHfxjr16+v/uGkDyvpw1x9ShfeTZs2VZurU7J0rOX1\n9dPvBPKsZz2rcVb1dWql6vSUYui2Kf3D1uwJOHxiX2z/bikOHTgcPR07s2ZKpgtMisWFZtKm\n3kKSvoBotp4n95K/V+k6kb7NZDKzbut/RzOXFHdOMknXyvl22SiClGvL7LWcri3pi1rXlpk+\nri2zm7i2THVJXzKkaSGfTxv3lP6Nn8/UsY+x6Vum17zmNVPKuHPnzuq3K2eeeWb1W9yTTz65\nekG55ZZb4pxzzqmumwZtSP8YpfuO0oU4XXCOtXzKzr1pucDwiekQpTj4SMTyLS0/nAMQIECA\nAAECBAgQWHKBjiVIqfnw5S9/+ZSAHn300Ug/jfPPO++8uOqqq+IpT3lKNRlKgzlccMEFsWHD\nhuq2cy2fcgBvWiowfNLRob4r9yEt36I7W0ux7ZwAAQIECBAgQKAlAl0xzPfxInvd615XbSl6\n4QtfGJdcckk1SXrDG94wsclcyydW9KLlAsMnHk2QaoMPtvx4DkCAAAECBAgQIEBgqQU61oI0\nWyC///u/P2P22rVrq8Nzp/uOUr/B6cMezrV8xg7NaJlArYtd5WGxj6SHxWpBahm0HRMgQIAA\nAQIECLRMoKsSpONFmbrkHW+aa/nxtrVsaQQmW5BSgmQiQIAAAQIECBAgkD2Bru9ilz3S4pZ4\n+OijrNIgDSYCBAgQIECAAAECWRSQIGWx1rq0zMvq9yBVu9h1aSEViwABAgQIECBAgMBxBCRI\nx8GxqDmBgTURPYPlOGCQhubgrE2AAAECBAgQINA1AhKkrqmKfBRkWaWb3cGt7kHKR22KggAB\nAgQIECBQPAEJUvHqvKURp2chje4uxZGDLT2MnRMgQIAAAQIECBBoiYAEqSWsxd3pss2ehVTc\n2hc5AQIECBAgQCD7AhKk7NdhV0WQutil6YBudjUI/ydAgAABAgQIEMiUgAQpU9XV/YVNXezS\ndPBh9yF1f20pIQECBAgQIECAwHQBCdJ0Ee8XJbBsUy1BMpLdohhtTIAAAQIECBAg0CEBCVKH\n4PN62GWbapEd0IKU1yoWFwECBAgQIEAg1wISpFxXb/uD08Wu/eaOSIAAAQIECBAgsHQCEqSl\ns7SnisDwiZX/lTws1slAgAABAgQIECCQTQEJUjbrrWtL3dMXMbTew2K7toIUjAABAgQIECBA\n4LgCTSdIf/EXfxFvfetbj7nT//2//3ecdtppcfCgJ4UeEynnC9JADQcfiSiP5zxQ4REgQIAA\nAQIECOROoPJ9/9zTo48+GqOjo9UVv/e978W3v/3tePDBB2dsmNb5whe+EPfdd18cOnQohoeH\nZ6xjRv4FhisDNez8fikOPXq0y13+QxYhAQIECBAgQIBATgTmlSBdddVV8ba3vW1KyCeffPKU\n941vnv70p8fatWsbZ3ldIIGJob4rI9kNn1gb9rtA4QuVAAECBAgQIEAgwwLzSpDe/OY3x5Ej\nR+Lw4cNx/fXXx7333huveMUrZoTd19dXTYxe9KIXzVhmRnEElm8++iykhyJOeHpx4hYpAQIE\nCBAgQIBA9gXmlSD19/fHO97xjmq0P/ETPxG33nprvOtd78p+9CJoicCyzbXd7n+wVHmhBakl\nyHZKgAABAgQIECDQEoF5JUiNR37JS17S+NZrAjMEltVbkDwsdoaNGQQIECBAgAABAt0t0HSC\nlML5m7/5m/iTP/mTale7NFpduTyzlWDXrl3dHbnStUxgIkGqdLEzESBAgAABAgQIEMiSQNMJ\n0je+8Y1IrUhphLqnPe1psXHjxiiVUlcqE4GawPBJ6XflYbEPOS+cEwQIECBAgAABAtkSaDpB\nuuaaa2JoaCj+5V/+JZ74xCdmK1qlbYtA70DtYbEHdLFri7eDECBAgAABAgQILJ1A0w+Kffjh\nh+OZz3ym5Gjp6iCXe0rd7A5u9bDYXFauoAgQIECAAAECORZoOkFKyVFqPTpw4ECOWYS2WIFl\nWyrJ0VgpDj6y2D3ZngABAgQIECBAgED7BJpOkNLzjzZv3hzvfve7Y3R0tH0ldaRMCTQ+LDZT\nBVdYAgQIECBAgACBQgs0fQ9SelDshg0b4rLLLosrrrgiTj755Fi+fPkMxJtuumnGPDOKIzBl\nJLtnFCdukRIgQIAAAQIECGRboOkEKQ3fPTIyEuecc062I1f6lgrUHxZbG8lu5jDwLT24nRMg\nQIAAAQIECBBYoEDTCdJv//ZvR/oxETiewPIttaRo/4OG+j6ek2UECBAgQIAAAQLdJdD0PUjd\nVXyl6VaBiQTpAQlSt9aRchEgQIAAAQIECMwUaLoF6fLLL48Pf/jDM/c0bc699947bY63RRIY\nOjGi1Ft5WOyDRYparAQIECBAgAABAlkXaDpBWr9+fTzpSU+aEvfY2Fjcd999kZKitWvXxm/+\n5m9OWe5N8QR6eiOGT4rYrwWpeJUvYgIECBAgQIBAhgWaTpBe9rKXRfqZbfrxj38c559/fmza\ntGm2xeYVTGD5yeV49Fs9MXYooneoYMELlwABAgQIECBAIJMCS3oP0hlnnBHvfOc747/+1/8a\nqVXJVGyBifuQdLMr9okgegIECBAgQIBAhgSWNEFKcZ9yyimxb9++uPPOOzPEoKitEFi2pbbX\nA0ayawWvfRIgQIAAAQIECLRAYEkTpAMHDsSf/dmfRW9vb5x66qktKK5dZklgsgXJSHZZqjdl\nJUCAAAECBAgUWaDpe5A+9rGPxZ//+Z/PMDt8+HB1kIYdO3bEK17xili2bNmMdczofoH9+/dX\nC3nPPfdEf3//ogq8p7yysv3pcd/3d8SRZ2xb8L6e+MQnRk/PkubyCy6LDQkQIECAAAECBPIt\n0HSCNDo6GvUP0Y00qdXo7LPPrg7ScOmllzYu8jpDAt/97nerpV2KhwGfFD8Rvx//FJ+7+svx\nv65+44IVbr311lizZs2Ct7chAQIECBAgQIAAgfkKNJ0g/c7v/E6kH1O+BS655JI44YQTFhVk\nz+hgxF9GnLX5p+PVz3910/u69tpr4/777296OxsQIECAAAECBAgQWKhA0wlS/UBHjhyJr371\nq3H77bdH6l739Kc/vfrjm/66ULZ/v+td76rW52Kj+NPP74w1y54U/+XjH296VxdeeKEEqWk1\nGxAgQIAAAQIECCxGYEEJUuqGle4zuvnmm2cc+33ve1/84R/+4Yz5ZhRTYNVpPbHj1rEol8tR\nKhmsoZhngagJECBAgAABAtkRaDpB2r17d1x88cWRWpAuv/zyOPfcc2PFihWRbur/xCc+Ee94\nxztiaGgo3vzmN2dHQUlbJrD69J549F/HYv/D5VixWYLUMmg7JkCAAAECBAgQWBKBphOkNIpd\nSpL+5V/+JZ70pCdNFOInf/In46KLLorXvva18ZGPfESCNCFT7BerTuutAByOPfeMVRIkI9EV\n+2wQPQECBAgQIECg+wWa/sR60003xXOe85wpyVFjmGn0s/SQ2IceeqhxttcFFVhVaUFK0957\nxwsqIGwCBAgQIECAAIEsCTSdIKXhvNNQ38ea6svGxsaOtYr5BRJI9yClaW+lBclEgAABAgQI\nECBAoNsFmk6QnvnMZ8bXvva1+Pa3vz0jtnQj/h//8R/H+vXr45RTTpmx3IziCdS62GlBKl7N\ni5gAAQIECBAgkE2Bpu9Bes1rXlMdnCF1s/ut3/qt+Omf/ulYtWpVdZCGT37yk9V7k9JgDSYC\nSUAXO+cBAQIECBAgQIBAlgSaTpCGh4fjhhtuiFe/+tVxxRVXTIl17dq1ceWVV8YrX/nKKfO9\nKa7A8Lqe6F+hi11xzwCREyBAgAABAgSyJdB0gpTC27x5c3zxi1+MBx54IG677bbYsWNHPP7x\nj4+nPOUp1SG/s0WgtK0WWHV6b+y5yz1IrXa2fwIECBAgQIAAgcULLChBqh/25JNPjvRjInA8\ngerDYm8eiwPbxmPZxqZvezveri0jQIAAAQIECBAgsKQCC/q0Oj4+Hul5SNdee+1EYf7mb/6m\nOvx3alkyEWgUWP249CykiD13a0VqdPGaAAECBAgQIECg+wSaTpAOHz4cz3jGMyI97+hHP/rR\nRERp+O9//ud/jgsvvDD+6q/+amK+FwRWP652mu2527OQnA0ECBAgQIAAAQLdLdB0gvTVr341\nfvCDH8TnP//5eP3rXz8R3SWXXBL3339/PO95z4u3vOUtkVqZTASSwOqjD4vdc49zwhlBgAAB\nAgQIECDQ3QJNJ0if+9zn4hd/8RerLUXTQ1u3bl286U1vikceeSTuvvvu6Yu9L6jAqqNd7Pbq\nYlfQM0DYBAgQIECAAIHsCDSdIKXQ+vv7jxlhSpLSNDAwcMx1LCiWgC52xapv0RIgQIAAAQIE\nsizQdIL03Oc+N66//vrqs5CmB5661V122WWxcePGOOWUU6Yv9r6gAkNremJwTckgDQWtf2ET\nIECAAAECBLIk0PQw3+eff36ce+651RHrXvziF8fTn/70WLlyZTz44IPx2c9+Nn74wx/Gpz/9\n6SwZKGsbBFIr0vZbxqI8Xo5ST6kNR3QIAgQIECBAgAABAs0LNJ0grVixIq677rrqKHbpfqTG\nEetSq1F6/9KXvrT5ktgi1wLpPqRt3xuLfQ+Ox6pTasN+5zpgwREgQIAAAQIECGRSoOkEKUU5\nNDQUf/EXfxHlcrk6GENqPXrc4x4XW7ZsiVJJ60Amz4QWF7o+kt3eykh2EqQWY9s9AQIECBAg\nQIDAggUWlCDVj5aSoTPOOKP6U5/nN4HZBCYHahiLk3/+2IN8zLateQQIECBAgAABAgTaJdD0\nIA3tKsznXykAAEAASURBVJjj5Etg9Rm1bnV7fuxZSPmqWdEQIECAAAECBPIlIEHKV312bTT1\nBGn3XWNdW0YFI0CAAAECBAgQICBBcg60RaDaxa5ye5oWpLZwOwgBAgQIECBAgMACBSRIC4Sz\nWXMCfYOlWLGlJ3b/WAtSc3LWJkCAAAECBAgQaKfAvBOkG264IW6//fZ2ls2xciaw+oyeOLC1\nHIcPlHMWmXAIECBAgAABAgTyIjDvBOmd73xn9RlHO3fujHe96115iV8cbRRYMzFQg1akNrI7\nFAECBAgQIECAQBMCcyZI+/bti0ceeSR+67d+Kz7/+c/Hs5/97Pinf/qn2Lt3bxOHsSqBiDWP\nr51uu41k53QgQIAAAQIECBDoUoE5n4P0D//wD/HSl740+vv74/Dhw/Grv/qr8X/+z/+Jnp45\nc6suDVmxOiVQH8luj/uQOlUFjkuAAAECBAgQIDCHwJxZzkUXXRQ7duyIT37yk3HOOefEvffe\nW21F0oI0h6zFMwTSPUhpMpLdDBozCBAgQIAAAQIEukRgzgRp2bJlsW7durjyyivjwgsvjDRY\nw0te8pJYtWpVl4SgGFkRqN+D5FlIWakx5SRAgAABAgQIFE9gzi52dZKPfvSjsXz58li9enVc\neuml9dl+E5i3wLKNPdG/MkKCNG8yKxIgQIAAAQIECLRZYN4J0tlnn93mojlcHgXWPL43dtw6\nFuXxcpR6Kk+ONREgQIAAAQIECBDoIoE5u9h1UVkVJQcCa57QG+OjEXvvG89BNEIgQIAAAQIE\nCBDIm4AEKW812uXxrH1C7ZTbfZcEqcurSvEIECBAgAABAoUUkCAVsto7F3RqQUrT7h95WGzn\nasGRCRAgQIAAAQIEjiUgQTqWjPktEUj3IKVJgtQSXjslQIAAAQIECBBYpMC8B2mY7TiPPfZY\nddjvH/3oR7Fly5b4uZ/7udiwYcNsq5pHoCqwpt7FTguSM4IAAQIECBAgQKALBebVgvTMZz4z\n3v3ud08p/vXXXx9nnnlmXHDBBfG7v/u78Wu/9mtxxhlnxOWXXz5lPW8INAqs2NITvUNpqG/3\nIDW6eE2AAAECBAgQINAdAvNqQbrzzjtj69atEyV+8MEH49d//dfj0KFD8Ru/8Rvxohe9qPr6\n6quvjt/7vd+L9evXx8te9rKJ9b0gUBcolUqRutmlZyGVy5WhvivvTQQIECBAgAABAgS6RWBe\nCdL0wn7iE5+I3bt3xzXXXBP/9t/+24nFL3/5y+Pf/bt/F3/wB38gQZpQ8WK6QOpmt+OWsXjs\nofFYuaV2T9L0dbwnQIAAAQIECBAg0AmBeXWxm16wW2+9tXqv0cUXXzx9Ubz5zW+Obdu2xX33\n3TdjmRkEksDaJx4dqOFO3eycEQQIECBAgAABAt0lsKAEadOmTdVudP39/TOi2blzZ3Ve6n5n\nIjCbQD1B2nWnob5n8zGPAAECBAgQIECgcwLzTpBuuOGG+O///b/HN7/5zWq3uttvvz3+9V//\ndUrJDxw4EFdccUWsWLGiOmDDlIXeEDgqsOZoC5IEySlBgAABAgQIECDQbQLzugfp3HPPjRtv\nvDHe+MY3Vsvf21vrIpW62N17773Veel+pNe//vWxffv2eO973xt9ffPadbd5KE8bBNY+sZaX\n79aC1AZthyBAgAABAgQIEGhGYF5ZzLXXXlsdceyuu+6qthqllqPvfe97kZ6DVJ9uueWWSC1I\nf/RHfxRvf/vb67P9JjBDIA313bcsYucd7kGagWMGAQIECBAgQIBARwXmlSClEqbhmJ/whCdU\nfxpHrquXPj0L6R3veEcMDAzUZ/lNYFaB6lDfT+iNXXdUhvoerwz13WOo71mhzCRAgAABAgQI\nEGi7wLzvQUolO3jwYNx2220xOjo6o6Dp2UcpObrnnnviG9/4xozlZhBoFEgDNYxVxvHYd79W\npEYXrwkQIECAAAECBDorMK8EKSVE6QGwK1eujDPPPDNWrVoVb3rTm6pd6qYX/0//9E/j537u\n56bP9p7AFIH6fUgGapjC4g0BAgQIECBAgECHBeaVIL3//e+Pyy+/PJ785CfH7//+78cpp5wS\nH/7wh+Occ86JrVu3djgEh8+iwORIdlqQslh/ykyAAAECBAgQyKvAnAlSuVyOD3zgA3HRRRdF\nGojhsssuizvvvDP+6q/+KtKgDb/8y78cu3btyquPuFoksO7JtZEQd93uWUgtIrZbAgQIECBA\ngACBBQjMmSA98MAD1dHqXvnKV07Z/Utf+tL4+7//+2qy9Gu/9muz3pc0ZQNvCDQIrH1SLUHa\nKUFqUPGSAAECBAgQIECg0wJzJkiDg4PVMu7evXtGWc8777z4+Mc/Hl/72tfiVa96VXUo8Bkr\nmUFgFoFlG3picG2pOpLdLIvNIkCAAAECBAgQINARgTmH+d64cWNs2rQpPvaxj8WLX/ziWLas\n8gCbhullL3tZ9T6kt73tbbFmzZro7+9vWOolgWMLpG52D3/7SBwZKUffoKG+jy1lCQECBAgQ\nIECAQLsE5mxBSgV597vfXR26+6STTop3vetdM8r21re+tfoMpCuvvDI+8pGPzFhuBoHZBKrd\n7CpjNOz+kfuQZvMxjwABAgQIECBAoP0C80qQfvu3fzuuuuqqSK1J3//+92ct5Xvf+974sz/7\nsxgeHp51uZkEpgusfXLt9DNQw3QZ7wkQIECAAAECBDolMK8EKRXuFa94RfzoRz+KT3/608cs\n63/8j/8x7rjjjvjLv/zLY65jAYG6QH0ku513GOq7buI3AQIECBAgQIBAZwXmnSDVizn9HqT6\n/PrvDRs2xL//9/++/tZvAscUqI9kpwXpmEQWECBAgAABAgQItFmg6QRprvKlbnbpniUTgbkE\n1j6xMtR35Qzc+UP3IM1lZTkBAgQIECBAgEB7BOYcxa7ZYqSBGm699dbMJEnLly9vNsQlX39g\nYGDJ95mFHfYNlWL16T1zJkip1XIx9dTT0zNj9MUs+LSyjPVzbmhoyMiTDdB9fX2RfhZzvjXs\nLlcv098Rl6lVWr+2pAeqm2oC9ZFs07Ul/S2ZagKuLcc+E1xbZtq4tsw0afzcsphry3yv10t+\n9br88stj7969MyPr0jnzherS4me+WOt+ojfu/sLh2P/IeCw/8dgNmoutp8Vun3noaQHUPdLv\n+utpqxTybd2DyezVz2WmS/2cmbmk2HO4TK3/+t9O/ffUpd5xmXkO+BuaalI/RxbrUt/P1L3P\nfLfkCdL5558/8yhdPOfAgQMdL93o6GjHy9CpAqx7Si1BSt3sjpUgpTqqf3OwkHKmFqiDBw9K\nBBrw0rdT6RvekZGRKPL510BSfVl/MHY3XBeml62T71evXh3j4+PBZWot1K8tycZUE2i8tqTr\ni6kmkK4tpVLJ39C0E2LVqlWuLdNM0ts0InT63OLaMomT/n6SS7quLOba0ttbub1jHtOxv7Kf\nx8ZWIbBYgdSClKadt7kPabGWtidAgAABAgQIEFi8QNMtSOkbxB/+8Iexffv2OHToULVP+tq1\na+PMM8+sfiO9+CLZQ5EEJhIkAzUUqdrFSoAAAQIECBDoWoF5J0g33XRTfOADH4hrrrlm1qat\ndGPmRRddFFdccUVs3ry5awNWsO4SOKHSxS5NRrLrrnpRGgIECBAgQIBAUQXmlSB94xvfiOc9\n73nV/rO/8Ru/EWeddVasW7cuUt/Rffv2xc6dO+O2226Lz33uc9WWpL/+67+O5z//+UU1FXcT\nAsMn9MTw+lLs0MWuCTWrEiBAgAABAgQItEpgXgnSa17zmmpSdN1110W6WfdY0/79++PCCy+M\nP/7jP5YgHQvJ/BkCqZvdgzccicP7y9G/vDRjuRkECBAgQIAAAQIE2iUw5yANO3bsqLYOvec9\n7zlucpQKnJ6R8d/+23+Lr3/967Ft27Z2xeA4GRc44cxKN7vKY0R0s8t4RSo+AQIECBAgQCAH\nAnMmSGlIvTSU6XynNGTw2NjYrPcpzXcf1iuWwLqUIFWm7bccKVbgoiVAgAABAgQIEOg6gTkT\npJQcXXDBBfH2t7897r///uMGkFqN3vzmN8dpp50Wp5xyynHXtZBAXaDaglR5s+NWQ33XTfwm\nQIAAAQIECBDojMC87kFKydGLXvSiOP300+M5z3lO9X6k9evXV7vc1QdpSEN/f+lLX6oO5PDl\nL3+5M9E4aiYFJEiZrDaFJkCAAAECBAjkUmBeCdI555wTN998c7zzne+MNELdV77ylRkYKWH6\n3d/93bj00kurLUgzVjCDwDEEVm7pjYHVlZHstCAdQ8hsAgQIECBAgACBdgnMK0FKhVmxYkV8\n+MMfrv48+OCDkQZvSA+N3bBhQ2zatKmp+5TaFZzjZEcgtSI9/K3KSHYHKyPZDRvJLjs1p6QE\nCBAgQIAAgXwJzDtBagx7y5YtkX5MBJZKoJogffNI7Lp9LDY+fUGn5VIVxX4IECBAgAABAgQK\nLDDnIA0FthF6GwXq9yFtv8VADW1kdygCBAgQIECAAIFpAhKkaSDedkZg/dm1ob533Gyo787U\ngKMSIECAAAECBAgkAQmS86ArBNafXetWt/1mLUhdUSEKQYAAAQIECBAoqIAEqaAV321hr9jc\nE4NrSyFB6raaUR4CBAgQIECAQLEEJEjFqu+ujjZ1s9t773iMPlbu6nIqHAECBAgQIECAQH4F\nJEj5rdvMRVa9D6mSG+24xX1Imas8BSZAgAABAgQI5ERAgpSTisxDGO5DykMtioEAAQIECBAg\nkG0BCVK26y9Xpa+PZLf9BwZqyFXFCoYAAQIECBAgkCEBCVKGKivvRV3/1NpQ34/+QBe7vNe1\n+AgQIECAAAEC3SogQerWmilguYbW9sTKU3pi+/e1IBWw+oVMgAABAgQIEOgKAQlSV1SDQtQF\n1v9kbxzcXo7HHh6vz/KbAAECBAgQIECAQNsEJEhto3ag+Qhs+MnaA2MfvUk3u/l4WYcAAQIE\nCBAgQGBpBSRIS+tpb4sU2FBpQUrTo7rZLVLS5gQIECBAgAABAgsRkCAtRM02LRPY8LRagrT9\n+1qQWoZsxwQIECBAgAABAscUkCAdk8aCTgisfVJv9A5FbLvJQA2d8HdMAgQIECBAgEDRBSRI\nRT8Duiz+nt5SnHBmb+y6fSxKY7X7kbqsiIpDgAABAgQIECCQYwEJUo4rN6uhbfypvhg/HLHi\nsZOzGoJyEyBAgAABAgQIZFRAgpTRistzsVOClKYVe07Lc5hiI0CAAAECBAgQ6EIBCVIXVkrR\ni7Txp2oDNazcK0Eq+rkgfgIECBAgQIBAuwUkSO0Wd7w5BTY+rdKCVDkzJUhzUlmBAAECBAgQ\nIEBgiQUkSEsManeLF+hfXop1T+qJFXtPjVLlPxMBAgQIECBAgACBdglIkNol7ThNCaT7kHrH\nB2NDPKGp7axMgAABAgQIECBAYDECEqTF6Nm2ZQL1gRq2xNNadgw7JkCAAAECBAgQIDBdQII0\nXcT7rhA48Zm1kexOiad3RXkUggABAgQIECBAoBgCEqRi1HPmojzx3/RGufKfBClzVafABAgQ\nIECAAIFMC0iQMl19+S384KqeOLh8a2yOp0Z5PL9xiowAAQIECBAgQKC7BCRI3VUfStMgsHf1\n3TEYy+Oxu2rPRWpY5CUBAgQIECBAgACBlghIkFrCaqdLIbCvkiClac8t/UuxO/sgQIAAAQIE\nCBAgMKeABGlOIit0SiC1IKVpz821ARs6VQ7HJUCAAAECBAgQKI6ABKk4dZ25SPetuifGYyx2\n/0ALUuYqT4EJECBAgAABAhkVkCBltOKKUOzxvtHYGj+MvT/si7GRIkQsRgIECBAgQIAAgU4L\nSJA6XQOOf1yB++K7UT5cil23lI67noUECBAgQIAAAQIElkJAgrQUivbRMoGUIKVpx79IkFqG\nbMcECBAgQIAAAQITAhKkCQovulGgniBt/54EqRvrR5kIECBAgAABAnkTkCDlrUZzFs8jcXv0\nLhuvtCA5VXNWtcIhQIAAAQIECHSlgE+dXVktClUXKEc51jz1SDx2bykO7ajP9ZsAAQIECBAg\nQIBAawQkSK1xtdclFFjzU4ere9v+z7rZLSGrXREgQIAAAQIECMwiIEGaBcWs7hJY+/RagvTo\nd5yu3VUzSkOAAAECBAgQyJ+AT5z5q9PcRVRLkMqx/TtakHJXuQIiQIAAAQIECHSZgASpyypE\ncWYK9K8qx+onlWPHTaUYG5253BwCBAgQIECAAAECSyUgQVoqSftpqcD6c8oxPlJ5YOwPtCK1\nFNrOCRAgQIAAAQIFF5AgFfwEyEr4G366XC3qtm9JkLJSZ8pJgAABAgQIEMiigAQpi7VWwDJv\nPHe8GvWj33LKFrD6hUyAAAECBAgQaJuAT5tto3agxQisODVi+KRyPPrtUpRrjUmL2Z1tCRAg\nQIAAAQIECMwqIEGalcXMbhTY+DPjMbqnFHt+qJtdN9aPMhEgQIAAAQIE8iAgQcpDLRYkhg3n\nHr0P6UYJUkGqXJgECBAgQIAAgbYLSJDaTu6ACxXY+DMSpIXa2Y4AAQIECBAgQGB+AhKk+TlZ\nqwsE0rOQBteV45FvOG27oDoUgQABAgQIECCQSwGfNHNZrfkMqlTpWXfiz5ZjZEcpdt+um10+\na1lUBAgQIECAAIHOCkiQOuvv6E0KbPy52nDf274hQWqSzuoECBAgQIAAAQLzEJAgzQPJKt0j\ncOLP1hKkR25w6nZPrSgJAQIECBAgQCA/Aj5l5qcuCxHJ6idGDG2o3If0Tc9DKkSFC5IAAQIE\nCBAg0GYBCVKbwR1u8QInPrvyPKRdpdj1A93sFq9pDwQIECBAgAABAo0CEqRGDa8zIXDSz9eG\n+976dQlSJipMIQkQIECAAAECGRKQIGWoshS1JnDSz9fuQ9r6daevc4IAAQIECBAgQGBpBXzC\nXFpPe2uDwPItESsfX45Hv12KsZE2HNAhCBAgQIAAAQIECiMgQSpMVecr0NSKNHaoVE2S8hWZ\naAgQIECAAAECBDopIEHqpL5jL1hg0y/Wutk9/FWn8IIRbUiAAAECBAgQIDBDwKfLGSRmZEHg\nxGeXo9RXjoe/aqCGLNSXMhIgQIAAAQIEsiIgQcpKTSnnFIH+5REbzinH7tt64uAjUxZ5Q4AA\nAQIECBAgQGDBAhKkBdPZsNMCm55ztJvd15zGna4LxydAgAABAgQI5EXAJ8u81GQB49j0nNrz\nkB76im52Bax+IRMgQIAAAQIEWiIgQWoJq522Q2Dt2eUY2liOrZUWpPGxdhzRMQgQIECAAAEC\nBPIuIEHKew3nOL5SpeFo8y+Nx+ieUmz/jlakHFe10AgQIECAAAECbROQILWN2oFaIbD5l2v3\nIT30FadyK3ztkwABAgQIECBQNAGfKotW4zmLd9Mv1Ib7fuhLWpByVrXCIUCAAAECBAh0RECC\n1BF2B10qgf6VERvPrQ33vf/Bpdqr/RAgQIAAAQIECBRVQIJU1JrPUdxbnlfrZvfgl5zOOapW\noRAgQIAAAQIEOiLgE2VH2B10KQU2/8rR+5Cuczovpat9ESBAgAABAgSKKOATZRFrPWcxrzoj\nYuUZleG+byjFkQM5C044BAgQIECAAAECbRWQILWV28FaJZC62Y2PlGLr1w3W0Cpj+yVAgAAB\nAgQIFEFAglSEWi5AjFvOq3Wze+Bap3QBqluIBAgQIECAAIGWCfg02TJaO26nwIafLsfAmnI8\nVLkPqVxu55EdiwABAgQIECBAIE8CEqQ81WaBY+npjdj8S+NxaHspdnxPN7sCnwpCJ0CAAAEC\nBAgsSkCCtCg+G3eTwJbzak1HD+pm103VoiwECBAgQIAAgUwJSJAyVV0KezyBzc8dj57+cjzw\nj1qQjudkGQECBAgQIECAwLEFJEjHtrEkYwL9KyM2Pqsce27vicfuzVjhFZcAAQIECBAgQKAr\nBCRIXVENCrFUAieff3Q0u390ai+Vqf0QIECAAAECBIok4FNkkWq7ALEa7rsAlSxEAgQIECBA\ngEALBSRILcS16/YLLN8Ssfbs8Xj0W6UY3d3+4zsiAQIECBAgQIBAtgUkSNmuP6WfRSCNZlce\nK8WDX3Z6z8JjFgECBAgQIECAwHEEfII8Do5F2RSo34f0oPuQslmBSk2AAAECBAgQ6KCABKmD\n+A7dGoF1Ty3Hss3leOj6UoyNtuYY9kqAAAECBAgQIJBPAQlSPuu18FGlwRqO7C/FIzd4JlLh\nTwYABAgQIECAAIEmBCRITWBZNTsCJ1cSpDQ9eK1TPDu1pqQECBAgQIAAgc4L+PTY+TpQghYI\nbPzZcvQtL8eD1znFW8BrlwQIECBAgACB3Ar0dUNkDz30UHz961+P3t7e+Nmf/dnYvHnzlGLt\n27cvbrjhhki/zz333Dj11FObWj5lZW8KIdA7ELH5ueW47/M9se17Y9E79ZQphIEgCRAgQIAA\nAQIEmhfo+Nfr//k//+d4xSteEXfccUd84QtfiP/wH/5DfPOb35yI5O67746LL744PvvZz8bN\nN98cr3rVq+LGG2+c9/KJFb0onMCW82vd7O7+/JHCxS5gAgQIECBAgACBhQl0tAXp9ttvj//7\nf/9vXHPNNbFx48ZqBH/0R38UV1xxRTzrWc+qvn//+98fF110UVx66aVRKpXi6quvjg9+8IPx\nmc98pvp+ruULY7FVHgQ2/9J4lHrK8ePPH44nvD4PEYmBAAECBAgQIECg1QIdbUHatWtXvPrV\nr55IjlKwP/VTPxVbt26NcrkcO3bsiNtuu63agpSSozS94AUviNQl79Zbb51zeXUD/yuswODa\niPXnlOPR743HgYcLyyBwAgQIECBAgACBJgQ62oL0Mz/zM5F+Gqcvf/nL8ZSnPKXaOpQSpTQ1\n3pN0wgknxMDAQGzbtm1is2MtP+ussybWSQnXddddN/E+vTj99NNjw4YNU+Z14k1fX0eroRMh\nN3XMoaGhSD8LmU6/sJIgfascj1w/ED/xSkN+1w3r51z6W+rp6ej3JPUidcXv5JLuhVzo+dYV\nQbSoEOk84TIVN31xNzg4WP1Cb+qS4r6rX1v6+/ur/44XV2Jq5K4tUz0a36W/I9eWRpGo/u24\ntkw1qV9b0ueWeqPJ1DWW9l1XfTL/n//zf8ZNN90UH/3oR6tRPvzww9V/fNJJ0jitXLkyUuvT\n2NjYcZc3bnPkyJF4wxve0Direj/T2972tinzOvFm2bJlnThsZo65Zs2aWLu20hy0gOnsl4zF\nP/+X3fHwV/riWW9ZtYA95HuT9LdkmingH+uZJukfp4X+Hc7cW37mpOuTaaaAa8tMkzRn+ueZ\n2dcq1lzXltnr27VldpcVK1bMvmCec0dHR+e1ZtckSJ/4xCfi05/+dLz3ve+NJz/5ydXCp2+g\nUmIzfUqJUUoq5lreuF36Vvitb31r46x46lOfGnv37p0yrxNvDh061InDdv0xH3vssWoZ031q\ni/nHduiUp8Q9147Hl75wffQMlRccdzqHUhfQPEzpH+n0s3///uoXDXmIaSliSP9Qpx9/k1M1\nV61aVb0WHzhwYOqCgr9bvnx5JJPUQ8FUE0jf7qYvGJLLbP9+F9XJtWX2mk//to+Pj1f/LZp9\njWLOTZ9xDx486NrSUP1LdW1J1+u0r7mmjidI6Q/jT/7kT+JLX/pSfOADH5jyAXT9+vXVD2/p\nQtvYypKSmk2bNlU/yKRk6VjLG4NP3UPS/U7Tp9RK1elpvtlsp8vZ7uOn+8/SdMkllyzq0C+M\n/yd+MV4fl174/8at8Y8L3lf6MHTnnXcuePtu2rDeNSglAs6/yZppTBwn53qVEiQfYmaeB8PD\nw9V/f5KNqSZQ7y6Vri0jIyNYjgqka0tKHNOXUqZJAQnSpEXjq/qXDK4tjSpR/Rta7LUlfdk9\nn6njCdJ73vOeare6j3zkI3HGGWdMKfPJJ59cTYJuueWWOOecc6rL0ofmdMKk+45SBpi+lTnW\n8ik78yazAq997WsX1S1h8P5Kc+zfRbz47LfEzl+qtU42i/GpT33KP/bNolmfAAECBAgQIJBB\ngY4mSF/84herLUd/8Ad/UH0IbLr/qD6dffbZsXr16jjvvPPiqquuqg7ckJKhj3/843HBBRdM\nDK4w1/L6/vzOrkAayn0x9z6MHynHlet3xUm7zol3ffi8BUGkwUPuueeeBW1rIwIECBAgQIAA\ngewIdDRBSg9/TdNll102Q+wf//Efq93qXve610V6NtILX/jCaivC0572tCmDLcy1fMaOzSic\nQE9fKU4/vz/u+F+j8cj3jsSJP9XR075w/gImQIAAAQIECGRJoKOfFP/8z/98TqvUcvChD32o\nOphC6jeY7gNpnOZa3riu18UVOOPCWoJ09xdGJUjFPQ1EToAAAQIECBCYUyAzD0BJNwlPT44a\no5treeO6XhdP4HHPr4xYUjnbf/wPh4sXvIgJECBAgAABAgTmLZCZBGneEVmRwCwCyzb0xEnP\n7IuHv3UkDu4w4tQsRGYRIECAAAECBAhUBCRIToPCCKRudlHJje7+/7QiFabSBUqAAAECBAgQ\naFJAgtQkmNWzK/C4X609GOyeL87vKcrZjVTJCRAgQIAAAQIEFiogQVqonO0yJ3Div+mN4Y2l\nuOcfD0d53JPvM1eBCkyAAAECBAgQaIOABKkNyA7RHQLpCe9puO+D28ux9Z+PdEehlIIAAQIE\nCBAgQKCrBCRIXVUdCtNqgTOOdrO7+4vuQ2q1tf0TIECAAAECBLIoIEHKYq0p84IFTjuvMlBD\n5ayXIC2Y0IYECBAgQIAAgVwLSJByXb2Cmy4wvK4nNv10X2z9zpE4sN1w39N9vCdAgAABAgQI\nFF1AglT0M6CA8Z9+QW2473uv082ugNUvZAIECBAgQIDAcQUkSMflsTCPAo9LCVJlusfzkPJY\nvWIiQIAAAQIECCxKQIK0KD4bZ1HgpHP6YuiENNz3aJTLhvvOYh0qMwECBAgQIECgVQISpFbJ\n2m/XCpR6SnHa8/rjwCPl2PavY11bTgUjQIAAAQIECBBov4AEqf3mjtgFAul5SGlKD401ESBA\ngAABAgQIEKgLSJDqEn4XSuD08weq8aZudiYCBAgQIECAAAECdQEJUl3C70IJrNjUE+uf2hsP\nfeNIjD7mPqRCVb5gCRAgQIAAAQLHEZAgHQfHonwLpG5245UGpPuv180u3zUtOgIECBAgQIDA\n/AUkSPO3smbOBCbuQ7pWgpSzqhUOAQIECBAgQGDBAhKkBdPZMOsCW36+P/qGI+691n1IWa9L\n5SdAgAABAgQILJWABGmpJO0ncwJ9g6U4+Rf6Y9cd47H3XsN9Z64CFZgAAQIECBAg0AIBCVIL\nUO0yOwIT3ewM952dSlNSAgQIECBAgEALBSRILcS16+4XOO28o89Dch9S91eWEhIgQIAAAQIE\n2iAgQWoDskN0r8D6s/pi+eZS3PeVwzE+Zrjv7q0pJSNAgAABAgQItEdAgtQeZ0fpYoHTnjcQ\nI7vK8ch3jnRxKRWNAAECBAgQIECgHQISpHYoO0ZXC5yum11X14/CESBAgAABAgTaKSBBaqe2\nY3WlwGm/UrkPqZSG+/Y8pK6sIIUiQIAAAQIECLRRQILURmyH6k6BZRt7YsPTeuOhG4/E6D73\nIXVnLSkVAQIECBAgQKA9AhKk9jg7SpcLpG525cotSPddrxWpy6tK8QgQIECAAAECLRWQILWU\n186zInDaeQPVot577WhWiqycBAgQIECAAAECLRCQILUA1S6zJ7Dl2X3RN1y5D+k6LUjZqz0l\nJkCAAAECBAgsnYAEaeks7SnDAn2DpTj5F/pj1x3jsffesQxHougECBAgQIAAAQKLEZAgLUbP\ntrkSOO15ldHsKtM9WpFyVa+CIUCAAAECBAg0IyBBakbLurkWOO3o85AM953rahYcAQIECBAg\nQOC4AhKk4/JYWCSBDU/ti+WbSnHflw9Hedxw30Wqe7ESIECAAAECBOoCEqS6hN8EKgKnPW8g\nDu0sx9bvVMb8NhEgQIAAAQIECBROQIJUuCoX8PEEdLM7no5lBAgQIECAAIH8C0iQ8l/HImxC\n4PQ0UEOpMlDDtYb7boLNqgQIECBAgACB3AhIkHJTlQJZCoFlG3ti49N746FvHomRveNLsUv7\nIECAAAECBAgQyJCABClDlaWo7RFI3ezKlVuQ7vuK+5DaI+4oBAj8/+3dB5xcZb3/8e+Zsn2z\nmy1JSO8htBACJCGUG8AQIk0QLIBwQf3jxXsBL14V9F5EpclLiqKiIHpBBL3Se5feI6GEhIQ0\n0rNJtpdp/+c5k012k91ktszMmZnP4XWYmTPnPOX9zJ7Mb57nPAcBBBBAAAHvCBAgeactKIlH\nBEYfl+eWZMVTbR4pEcVAAAEEEEAAAQQQSJUAAVKqpMknYwSGzQooUGyuQ3qS65AyptEoKAII\nIIAAAggg0E8CBEj9BEky2SPgz3M0cnZQtZ9GteWTSPZUjJoggAACCCCAAAII7FGAAGmPROyQ\niwKj58aH2S17gmF2udj+1BkBBBBAAAEEcleAACl3256a70ZgzFwz3bdZlj/BMLvdMPEWAggg\ngAACCCCQdQIESFnXpFSoPwTKx/lVPt6nVS+EFG6N9UeSpIEAAggggAACCCCQAQIESBnQSBQx\nPQJ2mF24SfrsRXqR0tMC5IoAAggggAACCKRegAAp9ebkmCECY46PD7Nb9hgBUoY0GcVEAAEE\nEEAAAQT6LECA1GdCEshWgRFmJrtAobTsMSZqyNY2pl4IIIAAAggggMDOAgRIO4vwGoFtAsFC\nR8P/Jagti6MqbRuKCwIIIIAAAggggEAOCBAg5UAjU8XeC4ydFx9mN7x+Ru8T4UgEEEAAAQQQ\nQACBjBEgQMqYpqKg6RAYMy9+P6Th9TPTkT15IoAAAggggAACCKRYgAApxeBkl1kC5WP9qpjs\n115NByoYMxcksSCAAAIIIIAAAghktQABUlY3L5XrD4GxJwTlj+VpXOSI/kiONBBAAAEEEEAA\nAQQ8LECA5OHGoWjeEBh3YnyY3aTIsd4oEKVAAAEEEEAAAQQQSJoAAVLSaEk4WwSGHhZQq79O\nE8NHKxbLllpRDwQQQAABBBBAAIGuBAiQulJhGwIdBHx+R5+VvKESVavmXafDOzxFAAEEEEAA\nAQQQyDYBAqRsa1HqkxSBFaUvuel+9gR/MkkBJlEEEEAAAQQQQMAjAnzb80hDUAxvC6wueVNh\nteqzJ/mT8XZLUToEEEAAAQQQQKBvAnzb65sfR+eIQNjfrE/9r6huiWPWHKk01UQAAQQQQAAB\nBHJQgAApBxudKvdO4GP/U+6Bqx7nz6Z3ghyFAAIIIIAAAgh4X4Bvet5vI0roEYGFgSfl+GJa\n9Sh/Nh5pEoqBAAIIIIAAAgj0uwDf9PqdlASzVaDJ2azq6TFtXuBT42fZWkvqhQACCCCAAAII\n5LYAAVJutz+176HAiM9H3SNW0ovUQzl2RwABBBBAAAEEMkOAACkz2olSekRgxDwbIMW08mH+\ndDzSJBQDAQQQQAABBBDoVwG+5fUrJ4llu0DRELnD7Gre9alhVbbXlvohgAACCCCAAAK5J0CA\nlHttTo37KDDqlG3D7B7kz6ePlByOAAIIIIAAAgh4ToBveJ5rEgrkdYGRJ0Td2eyWEyB5vako\nHwIIIIAAAggg0GMBAqQek3FArgsUVEqDj4hp64c+bV3k5DoH9UcAAQQQQAABBLJKgAApq5qT\nyqRKYMwX48Pslv2NP6FUmZMPAggggAACCCCQCgG+3aVCmTyyTmDE8VEFimNafp9PsXislHV1\npEIIIIAAAggggEAuChAg5WKrU+c+CwSKJHtPpOZ1jta9yDC7PoOSAAIIIIAAAggg4BEBAiSP\nNATFyDyBcV+Odx0tvdufeYWnxAgggAACCCCAAAJdChAgdcnCRgT2LDBoRkyl42Ja9YSjlpo9\n788eCCCAAAIIIIAAAt4XIEDyfhtRQg8LjP9qRLGwo2V/5U/Jw81E0RBAAAEEEEAAgYQF+FaX\nMBU7IrCrwJgzovIFY/rkf/1M1rArD1sQQAABBBBAAIGMEyBAyrgmo8BeErD3RBp5UlQNKxyt\neY7JGrzUNpQFAQQQQAABBBDojQABUm/UOAaBDgITz4tP1rD4D0zW0IGFpwgggAACCCCAQEYK\nECBlZLNRaC8JVE2NqfLAqNa+4GjrInqRvNQ2lAUBBBBAAAEEEOipAAFST8XYH4EuBCZ/y/Yi\nOVr4G/6kuuBhEwIIIIAAAgggkDECfJvLmKaioF4WGD4vqpKRMa2436emdV4uKWVDAAEEEEAA\nAQQQ2J0AAdLudHgPgQQFfObyo72/FVE0ZHqRfs21SAmysRsCCCCAAAIIIOA5AQIkzzUJBcpU\ngXFfjqpwiJny+06fmjdkai0oNwIIIIAAAgggkNsCBEi53f7Uvh8F/PnSPheaXqRWRx/9il6k\nfqQlKQQQQAABBBBAIGUCBEgpoyajXBAYf2ZURUNNL9KffGpYlQs1po4IIIAAAggggEB2CRAg\nZVd7Ups0C/gLpP0vjV+LtOBaepHS3BxkjwACCCCAAAII9FiAAKnHZByAwO4FxpweVdnEqJbf\n59Om+dwXafdavIsAAggggAACCHhLgADJW+1BabJAwM5oN+3KiKmJo3d+6FcslgWVogoIIIAA\nAggggECOCBAg5UhDU83UCgw5Mqbhc6Oqme/T0rv5M0utPrkhgAACCCCAAAK9F+CbW+/tOBKB\n3QpMuzIsf2FM//ypX80bd7srbyKAAAIIIIAAAgh4RIAAySMNQTGyT6B4uHTAf0XUVuvo7R8E\nsq+C1AgBBBBAAAEEEMhCAQKkLGxUquQdgUlfj6pyalSrHvNp2d/5c/NOy1ASBBBAAAEEEECg\nawF+1u7aha0IdBKIRCJmsoWY6urqOm1P5MX+P/PrxS+U663LfCrcp05Fw6KJHLbbffx+v4qL\ni3e7D28igAACCCCAAAII9FyAAKnnZhyRgwLLli1Ta2ur9t57717Vfqb+Vae1/ly3H/OJfq0T\nFVPfgqRJkybp+eef71VZOAgBBBBAAAEEEECgewECpO5teAeBTgI+n09z5szptC3xF2u14d23\nNWbDdF045nYtmXRv4ofutOdTTz210xZeIoAAAggggAACCPSXAAFSf0mSTtYLFBUV6fHHH+91\nPVu2RHXnQbUavfxEXXzTVzXuxLxepVVSUtKr4zgIAQQQQAABBBBAYM8CXDW+ZyP2QKBfBAoG\n+nTi30rlN3HR419r0JYl9mayLAgggAACCCCAAAJeEiBA8lJrUJasFxhycEBH/7JYrVtjevAL\n9WpriGV9nakgAggggAACCCCQSQIESJnUWpQ1KwQO+EaB9v9Gvmo+iOjxcxrc2fGyomJUAgEE\nEEAAAQQQyAKBnL8GKS+vd9eB9Gfb2ymbWXJL4JhfFavmw4iW3Nem13/SrJn/XdQjAMdx1JfP\nbvtnLhDI+VNAJ3frYSfj6IttpwSz6EVfP3NZRLG9KtYkGAzyI8d2EanjucXeGoElLsC5pftP\nAueWXW3aTaLRvs14u2vKmbul/dzS13OutU1kyflvR4WFhYk4JXUf29gsuSXgz3N00t9Lddch\ntXr1imZV7e/XhC/kJ4xgv8T35bPb/pnLz893v+AlnHGW72hPwH21zVYiXHZtWWtSUFCw6xs5\nvKX9Rxf7I0P78xzm2F51+1mxHn05b29PLMuecG7ZtUHbzy38yLDDpv18Ys8t7cHSjncTf5Zo\n0JnzAVJtbW3iqknas6WlJUkpk6yXBYqH+HTKA6W654haPXZ2g776ql/VByT2J2lvXNuXz66d\nCc8GSY2NjWpra/MyU0rLZgNGu/bmhsApLWiKM7MzOPb1M5fiIqckO/s3VF9fr0T/wU1JodKc\niT232C8wTU1N7r3j0lwcz2Rvzys2mO7LedszlenHgtiAkXPLrqCVlZXuv0OcW3bYFBcXu+cW\n+73F3peyt4sNrhKZDZhrkHorzHEI9IPA4GkBzbm9ROFG6YGT69W0ie70fmAlCQQQQAABBBBA\noNcCBEi9puNABPpHYPJX8nXo9wtUtzyqh083v0aHGbffP7KkggACCCCAAAII9FyAAKnnZhyB\nQL8LHP6zIo09IajPXgjr+YtNdxILAggggAACCCCAQFoECJDSwk6mCHQWcHyO5v25RBV7+/TP\nW1r1/h+4Lq2zEK8QQAABBBBAAIHUCBAgpcaZXBDYo0D+AJ9OfmCA8socPftvjVr7ZmiPx7AD\nAggggAACCCCAQP8KECD1ryepIdAngYpJfs27q0QRM7HcQ6c2qHE9kzb0CZSDEUAAAQQQQACB\nHgoQIPUQjN0RSLbAuBPydNgVhWpYbSZtOINJG5LtTfoIIIAAAggggEBHAQKkjho8R8AjAjN+\nVKixJwa1+sWwXvjPJo+UimIggAACCCCAAALZL0CAlP1tTA0zUMBxzKQNd5Zo4ESf5t/coo/u\n6v1N0TKw+hQZAQQQQAABBBBImwABUtroyRiB3Qvkl5lJG+4vVbBEevqbDdrwz/DuD+BdBBBA\nAAEEEEAAgT4LECD1mZAEEEieQOU+Ac39Y4nCzdKDX6hXcw2TNiRPm5QRQAABBBBAAAGJAIlP\nAQIeF5h4Wr4O/X6B6pZH9ciX6uXE+LP1eJNRPAQQQAABBBDIYAG+aWVw41H03BE4/GdFGj03\nqJXPhjW37Ue5U3FqigACCCCAAAIIpFiAACnF4GSHQG8EHJ+jz/8lPmnDjPB5mrT1hN4kwzEI\nIIAAAggggAACexAgQNoDEG8j4BWBgnKfTnlogJpVq8PXf1frX3W8UjTKgQACCCCAAAIIZI0A\nAVLWNCUVyQWBikl+/bXg39yqvnheQLWLc6HW1BEBBBBAAAEEEEidAAFS6qzJCYF+EfjU/7Je\nHny9QnWOnj8zqKa1/ZIsiSCAAAIIIIAAAggYAQIkPgYIZKDAovKHtd8lETWtdvTcl4Nq3ZyB\nlaDICCCAAAIIIICABwUIkDzYKBQJgUQEDvhuRBO+FlHdJzZICqhtayJHsQ8CCCCAAAIIIIDA\n7gQIkHanw3sIeFzg4KsiGnN6RFs+8OnZLwXoSfJ4e1E8BBBAAAEEEPC+AAGS99uIEiLQrYBj\n/oJn3BDR6NNMkPS+T8+cGuCapG61eAMBBBBAAAEEENizAAHSno3YAwFPC9ggaebNEY0/O2Jm\ntfPpqROD2rqQKcA93WgUDgEEEEAAAQQ8K0CA5NmmoWAIJC7gmHjo0Gsj2v/SsJrWOCZICmjV\nYwRJiQuyJwIIIIAAAgggEBcgQOKTgEAWCez/nagO+1VY0Yj00teDevfHfkXasqiCVAUBBBBA\nAAEEEEiyAAFSkoFJHoFUC4w+Nao5D4VVMjKmj2/166kTAgy5S3UjkB8CCCCAAAIIZKwAAVLG\nNh0FR6B7gYr9Yzr+6ZBGnxqf4e7x4wJacJ3pTWrp/hjeQQABBBBAAAEEEOBGsXwGEMhagWCp\nzHC7iI64PaT8CumDG/16dHZQnz3FtUlZ2+hUDAEEEEAAAQT6LEAPUp8JSQABbwuMOD6mE14M\nacK5ETWukl48N6hHTw5p4/thbxec0iGAAAIIIIAAAmkQIEBKAzpZIpBqgbwB0iHmprJznwxr\n0MyoVj8f0/8eWKuX/0PcNynVjUF+CCCAAAIIIOBpAQIkTzcPhUOgfwUG7hvTsX8Pa85fAho4\nwacld0sPzwrqvWv8CtX3b16khgACCCCAAAIIZKIAAVImthplRqCPAqM/79O5H5RrxnVSsET6\n8Ga/HpoZ1OI7fIoy8q6PuhyOAAIIIIAAApksEMjkwlN2BHJRoKmpSUuWLNHkyZN7XX3H3FnW\nrtFoVMFYkQ7L/4Zmbv6G3r68UI//aImeLviZlgZfTCj9o446Sr/97W8T2pedEEAAAQQQQAAB\nrwsQIHm9hSgfAl0I+P1+DRkypIt3erdpke7VqvCzOnjjNzWx7nh9tekOrSx+Va8NulF1eau7\nTDQSibiBWmNjY5fvsxEBBBBAAAEEEMhEAQKkTGw1ypzzAhMnTtT777+fFIf174T13EUm6Hnl\nMI1Zc5gOvrRQ003PUrCw8/TgNTU1qqqqSkoZSBQBBBBAAAEEEEiXANcgpUuefBHwqMDgaQF9\n5eUyHX9XiQoqHL3xs2b9cZ+tWvpIm0dLTLEQQAABBBBAAIH+EyBA6j9LUkIgqwT2OTNf5y0a\nqIMuLlD9qqgeOLFeD55Wr/rVkayqJ5VBAAEEEEAAAQQ6ChAgddTgOQIIdBLIK3U0+4ZinfV2\nmYZMD2jJfW26Y/JWzb+lRbFop115gQACCCCAAAIIZIUAAVJWNCOVQCC5AoMODOirrw7Q0b8q\ndme/e+7bjXrseGmwJiU3Y1JHAAEEEEAAAQRSLECAlGJwskMgUwUcn6OpFxbo3I/KNP6UoDa+\nI31HL2jC0jMUac3UWlFuBBBAAAEEEECgswABUmcPXiGAwB4ESof5dfL9AzT7j1KjajR++Wl6\n/HMmYHqz8yx3e0iGtxFAAAEEEEAAAU8KECB5slkoFALeFxh1gnSdZmrV0GdVt0R6+pSA3vqB\nX6EG75edEiKAAAIIIIAAAt0JECB1J8N2BBDYo0CL6vXB5N/pmL+HVTpG+uRPfj1yVFCrn6Y3\naY947IAAAggggAACnhQgQPJks1AoBDJLYPDMmOY9G9I+346oZYP0j3OCevkCv5o3ZlY9KC0C\nCCCAAAIIIECAxGcAAQT6RcBfIB14WURzHw+r4oCoVj7k16NHBrX0L5xm+gWYRBBAAAEEEEAg\nJQJ8c0kJM5kgkDsCA/eLac6jYU3977AibdIb/xnQM6cFVLc0dwyoKQIIIIAAAghkrgABUua2\nHSVHwLMCPr80+YKoPv98SHv9S1QbXvPpsWOCWnC9nynBPdtqFAwBBBBAAAEErAABEp8DBBBI\nmkDJSGn23WEddktYeQOkD37h12NHB7XmeSZxSBo6CSOAAAIIIIBAnwQCfTqagxFAIOcFIpGI\nmpubd+sweK50zGHSR9cXaNndeXrhzKD2+lxI+1/WouKR0d0e25M3A4GAgsFgTw5hXwQQQAAB\nBBBAoJMAAVInDl4ggECiAps3b3Z3feGFFzRu3LhED9NwHagv6Fpz46RpWvV0VC/pVj2rG9Wi\nuoTT6G7Hc845R1dffXV3b7MdAQQQQAABBBDYowAB0h6J2AEBBHYnUFlZqSlTpuxul13e+zB2\nrbauO0qTln5Fs9v+Q7MC5+nTUQ9qxfAnFPG37rL/njbU19frrbfe2tNuvI8AAggggAACCOxR\ngABpj0TsgAACuxOYMWOGHnnkkd3t0u17ocaY3v5Fs96+3tHeS8/U1NqzdNBFBZrybwUqrEj8\nEsl3331X06ZN6zYf3kAAAQQQQAABBBIVSPwbSKIpsh8CCCCQoECw2NHMHxXp68vKdegPCt1p\nwV/5UbN+N2KLnvx6g9a+GUowJXZDAAEEEEAAAQT6R4AAqX8cSQUBBPogYHuLjriqSN9YUa4j\nrilSYaVPH9zeqrun1+mOyVv0yv80af27YcVisT7kwqEIIIAAAggggMCeBRhit2cj9kAAgRQJ\nFJT7dOj3CnXwpQX69NGQPryjRZ8+FtLrVza7a2GVo2FHmBnwpgdUfaBflZP9Kh3B7zwpah6y\nQQABBBBAICcECJByopmpJAKZJeDzOxp/Up67ttZGtfSRkJY92qaVz4W05P42d22vkS9Pyqse\nqgv1qCqfK9brl/gVLJUCRWYtjilYIvd1cEBM+RVS4aCYCodIfnMcCwIIIIAAAgggsLMAAdLO\nIrxGAAFPCeSX+bTPmfnuagu2dWlE694Ka+OCiDYviqj204i2LItotA6Vs8rRp/cmUHwnpqKh\nUvmkmCqmxDRoelTVh5rhe/kJHMsuCCCAAAIIIJDVAgRIWd28VA6B7BMoH+eXXff+8o662Vns\nDpk2Xf96xgW69MLLFKp3FG6Uu4YaHfNaaquVWjc7al4vNa12VL/M0ZrnfGa16fjlL4hp+LEx\nTfxSRBVH0MO0Q5dnCCCAAAII5JYAAVJutTe1RSBrBaIKK1xYr7IJtoodJ3Po+Lxz9W2wtOkd\nR+tfNYHSMz6tMLOVrzDD+fIrg5pwdlQTz4+ooLLzMbxCAAEEEEAAgewWIEDK7valdgjkhEBN\nTY1bzwULFuimm27qeZ2rzSFfMSPsNg5Vwfv7Kfre3vrgxny9f0tEzQfNV9OMNxQr6NkNbA8/\n/HDuzdTzluAIBBBAAAEE0i5AgJT2JqAACCDQV4ENGza4ScyfP1927euSrxLN0Nf0L6Fvq/SN\n6dIbE/WErtZr+qPpm4omlHwwGCRASkiKnRBAAAEEEPCWAAGSt9qD0iCAQB8E5s2bpwsuuKAP\nKXQ+NNr6qbY82Czn/4br1Jbr9JVx/63B316qgnHmAqdultdee01XX311N++yGQEEEEAAAQS8\nLkCA5PUWonwIIJCwwOjRo3XiiScmvH9CO35Rarg2qucvadTiv5Zo1Xen6BBzn6aZVxQpkO/s\nkkQ4HN5lGxsQQAABBBBAIHMEuMNi5rQVJUUAgTQJlAz16cR7S/WFR0tVPMSnN69p0V3TarX+\nHYKhNDUJ2SKAAAIIIJA0AQKkpNGSMAIIZJvA2Hl5OvfDMu13fr5qPozozzNq9eqPmxQNdz9T\nXrYZUB8EEEAAAQSyXYAAKdtbmPohgEC/CuQP8Om420rc3qSiakevXdGsu2fWquYjepP6FZrE\nEEAAAQQQSJMAAVKa4MkWAQQyW8D2Jp3zQbkmfSlP69+O6M6DavXmdc2KRTK7XpQeAQQQQACB\nXBcgQMr1TwD1RwCBXgsUVvh0wj2lOuHeEuWVOnrpe01a/f2pGqr9ep0mByKAAAIIIIBAegUI\nkNLrT+4IIJAFApPOyDfXJpVr4hl5altaqov1rAqfPEpttVlQOaqAAAIIIIBAjgkQIOVYg1Nd\nBBBIjkDRoPhMd4Mv+0BbtVr5b03Vw7OC+vj3PkVak5MnqSKAAAIIIIBA/wsQIPW/KSkigEAO\nCxQfvFnX6TA1H/Wqws3Su/8T0EMzTaD0O59C9TkMQ9URQAABBBDIEAECpAxpKIqJAAKZIxBW\ni1qPeFMnvR7SxPMjattqAqUrArr/oKDeuNSv9a85ikUzpz6UFAEEEEAAgVwSCORSZakrAggg\nkEqBwmrp4J9EtN9FES3+o19L7vJp6d1+d82viGnwrKiqpsU0cL+YBoyLqWCQ5DjdlzBqZhK3\n1zXZNVTvKNwgt5cq2hY/xjFn9GCxlDdQKhxs0qvsPi3eQQABBBBAAIGuBQiQunZhKwIIINAr\ngYULF7rH3XnnnXr22Wc7pzHWpyEVUzWs5nAN2TpNrQ8P1MqHd+wSdcJqC9Qr5DfThTsh84Yj\nXywgf6RAwUiRAtGCHTsn8Czka1J90WcaObNE+80bpEGHRVUyIoED2QUBBBBAAIEcFiBAyuHG\np+oIIND/ArW18anrVqxYIbvuurxiNv3K3TxYEzVCB2mIJqtaY1UWG6qiUIXyQ8Xyq9TdxwzQ\nMwP2mszED+vNY52azTP7qkX1ajVrm3kVUUgx859fAeWb44pVoTIz2XhVdLQqG8ap4Wm/Xn86\nXpLSsTENmxPVyBNM79VBsfhG/o8AAggggAAC2wUIkLZT8AQBBBDoP4GrrrpK3/nOd/ovwV6k\n9Mtf/lI/+O5Ruum/7tTe+Udq3Us+bXjd0ce/9btryciYRn8xqrFfitCz1AtfDkEAAQQQyE4B\nAqTsbFdqhQACaRYIBExvTn5+WkthyxA2/Uz+sZs1+aSoJn8rqnCTtPYFRyse8Gv1M44++IXf\nrGbo3xExjT8rquFzo/IF01psMkcAAQQQQCCtAgRIaeUncwQQQCC1AoEiacS8mFnN9U510sqH\n7MQRPrd3yfYwFVTFNPYrUY0/0/QqjUxt2cgNAQQQQAABLwgQIHkh54ZDAAAi/ElEQVShFSgD\nAgggkASBlStXuqk+8cQT3VwPtS3T4yX/tCoVzJ+i6AeT9dEv8/XhL819m8asUOuU91UwbYPp\niTJXOzWZ7qc+LqeffrqGDBnSx1Q4HAEEEEAAgeQJECAlz5aUEUAAgbQKLFu2zM3/gQcekF0T\nWfJUpAN1qmbqHI1YNlV5y0ar6YEtmq/79K4e0gq9lUgy3e4za9YsAqRudXgDAQQQQMALAgRI\nXmgFyoAAAggkUeDSSy/V4Ycf3sMcGtW6bL7qnhks34vVmlV/vmbpfAWqWlQ8s0Yl02tUMLlO\njj+xZG+//XY9/HCHOc0TO4y9EEAAAQQQSLkAAVLKyckQAQQQSK3AIYccopNPPrl3mV4sRUIx\nLXs8pI//0qqlJsapfXiYu+aXOxr1uaBGHRvUiNlBDZzQfbT0wgsv9C5/jkIAAQQQQCDFAgRI\nKQYnOwQQQCDTBPxBR+NPynPXcEtMy58KaelDbSZoatPiv8VXW6eiIY6GHhbU0JkB7TU9oMHT\nAgoWOZlWXcqLAAIIIJDjAgRIOf4BoPoIIIBATwQCBTuCJXvcpg/CWvFsSJ/9I6zVL4e05L42\nd7Xv2eF3lfv6NeSQgIqXTzW3rt1PsYh9hwUBBBBAAAHvChAgebdtKBkCCCDgeYGq/QKy67SL\n4kXd8klEa18Pa+0bIa17K6KN74W1aUFEA/V5fcesi8+IaMs0R4OmxzRoZlTVB8fkL/B8NSkg\nAggggEAOCRAg5VBjU1UEEEAg2QL2OiS77nN2/Ca5kbaYNpoA6Vf/dY+WPl+nmZUnacOrhWY1\nJbnBL19eTNWHxjR0dlRDj42qbEKyS0j6CCCAAAII7F6AAGn3PryLAAIIINAHAX+eoyEHB9Q4\n5R3d8/yNOut3o7TPyIO08U1H61+J36B2/cs+2XX+T6SS0eYmtsdHNeLzUVUdFOtDzhyKAAII\nIIBA7wQIkHrnxlEIIIAAAr0UKKiSRswzgdA8e0FSRE1rpDXP+bT6aRswOVr4G7+7Fg2LafQp\nUY0y68B9CZZ6yc1hCCCAAAI9FCBA6iEYuyOAAAII9K9A0VBp/FlRdw03mWDpeUcrHzIB0zM+\nfXSL313LJkY1+lQTLH0hqpIR/Zs/qSGAAAIIINBRgACpowbPEUAAAQSSIvDqq/aiI+mss85S\nIJDYPz3BokKNDxytfVtO0JjFh6v2mqD+eU1MqwPz9VH+o/o4/wk1+Wp6Xd7nnntOVVWmO4sF\nAQQQQACBDgKJ/SvV4QCeIoAAAggg0FOBUCjkHlJUVKT8/PgEDomk8ZlelF3zI2Wa0HisJjTM\n1bDWqRoePkifa7xcawrma1nRP8z6ouqCqxNJUuvXr1dTU5Oi0WhC+7MTAggggEBuCRAg5VZ7\nU1sEEEAgrQL33Xefpk+f3qcy1K2MaNG9bVr0t1Y5b03TsJZpOnzzd1Q+wadRxwY1/Kj4zWoH\njDQ3YupiOfXUU3X//fd38Q6bEEAAAQQQkAiQ+BQggAACCGSUgA18DvluobvWrYpo6UMhffpo\nm7lZbUjv/abVXW2FCgeZ+y1NCahisl/l43wqNccVD3a0+r0GlWqw/u1fL1Yg32f2tBNA+OSL\nBuSP5pk1X4FIoYJmDUSKFAgXbXtuXxe677v7OEFz41vHHB1VzIkq4mtV2N+sUKBRrcFaNefV\nqDl/o5rMGvN1f4fcYDCou+++2xaZBQEEEEDAAwIESB5oBIqAAAIIINA7gQEj/Jp6oV0LFG6N\nad0bYX32Usi9We36d8Na8XTIXTumfob+En85v+PW5D2PKKwaLdNaLdQavW+GDL6nVZqvJm1x\nM7UBEgsCCCCAgHcECJC80xaUBAEEEECgDwKBfEfDjzRD7MzavjRvjmrzxxHVfhpV/WdRNa2P\n6s5b/6pos1/HHnmcgv48xUwHkmM6ksxT+QscBQqlYImjvFIpb0D8MWgfS8z2UvN+kRl+Yfaz\n+ztmFJ89PmousYo0x9TWILVujal5Q0wNq2OqXxlT7VKf8hdN0KDGCZqik9qLprJxjuZvflLv\n1T6jrR87KpsYc8uxfQeeIIAAAgikRYAAKS3sZIoAAgggkAqBwgqfhh1m1x25nXnv5VrbvFbX\n3LtWQ4YM3PFGEp/FTBRVuyyqDaZXa93bZn3TrG+FNbZhjsZqjh472gRdJTFVTY2p0qwVB8Tv\n/VQ80gRhThILRtIIIIAAArsIECDtQsIGBBBAAAEE+lfAMVFO+VhzLZRZJ34xPotfNBLTIcPm\nqHDDaM2ZcKby144wN8otN6vNOz7BRDQQUri8RuGyzQqX1ilSXK9oUaOiea1mbVPMb7qu/PFr\noDqW2JGJquylVe6DeeKPuNdBxUx6sWDIPV4+u0PnpaKiQt/85jc7b+QVAgggkGMCBEg51uBU\nFwEEEEDAGwI+v6OFda+oOfaMXll8m1uoElVphKZqmA7QXtpXg8OTVLVpjIo2Den3Qreo3r0O\nqkGb1KCN5tUGrS9v0+I8n5ngIqb8Sqmg0jxWmKGFZWYai64nBez3cpEgAgggkG4BAqR0twD5\nI4AAAgjktIDf79dTTz3VjUGLYtGFCm0Mqs2soZqgIrUBhRv95joqn2JtZha9sFmj23qMbCp2\nSJ5d27uQzAR67mx7IUfRNp97XKTBr/yGoErq9lJF3QhzEZV7gLRVevsye+yui+15Ul7YjAU0\nCZpeKzcP2wkVM8dGzUVcYZ+cqLkIK9xkLsgyZYsGzS6mbE68B8tMBSjlmzQKW6WSZsUGmP0G\nmv0r6xSrrpUGm8xt+tuWvfbaS8cee2z7Sx4RQACBlAkQIKWMmowQQAABBBDYVcDn8+noo81F\nSGlaYlEzqURNTOMH7W+mPx/kToFuH21vll2LNNCs5Sa2KVVeyEx1rnwzKXrAToxuQjD7n5ni\n3MzUF1HIrG3bH6N2+nPzn2MCKH84aGKfQuU3l6ho60BzdGU8hutQZ7tvjZabmf4+dGf7c4Z9\nrLqVYTkDmzvs1fensTa/YptKzFqsWI1ZtxYpVlugWEO+Yo1m5o1WM8lHyOxjpnC3i+OPKVjg\nU3GFmf692E7cYdaymPLKtz2a3jXbw5ZXavYzE3v43Uk8TI9bXsys8Z63SIFRKjTOJh50rykz\nSdseOcd8C/OZ7PyJ3zu57wCkkBMC//jHP7R58+ak1dVOTqNW8wE2fyv2BxF38ZkfToJmNT+E\n2IlvOi72JuHHHXdcx02efp4VAVJ9fb1eeeUV2Ud7A8KRI81VrSwIIIAAAgggsEcBx+eoqNrR\nOmehooNqdNm15+50TJt5vWHbutNbvXwZbQoouqVA0Y1FimwoVmRNicKrS1W9ariqWsaYAYYn\nSKullh9KjdqsdWaK9PVaZAYCLjWvVqrWhFB2SGCz6kxY1uQGY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"text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "gamdata <- data.frame(x = x)\n", "plt <- ggplot(gamdata, aes(x=x)) + \n", " geom_histogram(binwidth=0.25, fill=\"white\", color=\"black\") + \n", " geom_density(aes(y=0.25 * ..count..), color=\"purple\")\n", "print(plt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate random numbers\n", "\n", "### Batch methods\n", "\n", "#### Multinomial\n", "\n", "Suppose we want to sample $(X_1, \\dotsc, X_k) \\sim \\text{mult}(n, p_1, \\dotsc, p_k)$, where $\\sum_{i=1}^k p_i = 1$, $\\sum_{i=1}^n X_i = n$.\n", "\n", "* Method 1: draw $n$ independent realization from pmf $(p_1, \\dotsc, p_k)$. \n", " + An easy way is to declare category $j$, $j \\in \\{1, \\dotsc, k\\}$ if \n", "$$\n", " U \\in \\left[\\sum_{k=0}^{j-1} p_k, \\sum_{k=0}^{j} p_k \\right),\n", "$$\n", " where $U \\sim \\text{unif}[0, 1]$. Take $p_0 = 0$.\n", " \n", "* Method 2: sample $k$ independent Poisson random variables $(X_1, \\dotsc, X_k)$ with means $\\lambda p_1, \\dotsc, \\lambda p_k$. If the total number of successes $\\sum_{i=1}^k X_i$ is equal to $n$, then the conditional distribution of $(X_1, \\dotsc, X_k)$ is the desired multinomial.\n", " + We must be fortunate for the sum to be exactly $n$.\n", " \n", "#### Multivariate normal\n", "\n", "Suppose we want to sample $\\mathbf{X} = (X_1, \\dotsc, X_p)$ from MVN $N(\\boldsymbol{\\mu}, \\boldsymbol{\\Sigma})$. If we can find $\\mathbf{L} \\in \\mathbb{R}^{p \\times p}$ such that $\\mathbf{L}^T\\mathbf{L} = \\boldsymbol{\\Sigma}$, then \n", "$$\n", " \\mathbf{L}^T\\mathbf{Z} + \\boldsymbol{\\mu}, \\quad \\mathbf{Z} \\sim N(0, \\mathbf{I}_p)\n", "$$\n", "follows the desired distribution.\n", "\n", "* Random vector $\\mathbf{Z}$ consists of $p$ independent standard normal random numbers.\n", "\n", "* Possible choices of $\\mathbf{L}$ are:\n", "\n", " + Cholesky decomposition of $\\boldsymbol{\\Sigma}$: $\\mathbf{L}$ is lower triangular.\n", " + Matrix square root: if $\\mathbf{Q}\\boldsymbol{\\Lambda}\\mathbf{Q}^T$ is a eigenvalue decomposition of $\\boldsymbol{\\Sigma}$, where $\\boldsymbol{\\Lambda} = \\text{diag}(\\lambda_1, \\dotsc, \\lambda_p)$ with $\\lambda_i \\ge 0$, then\n", "$$\n", " \\mathbf{L} = \\mathbf{Q}\\boldsymbol{\\Lambda}^{1/2}\\mathbf{Q}^T,\n", " \\quad\n", " \\boldsymbol{\\Lambda}^{1/2} = \\text{diag}(\\lambda_1^{1/2}, \\dotsc, \\lambda_p^{1/2})\n", " .\n", "$$\n", "such a matrix is symmetric and positive semidefinite, and is often denoted by $\\boldsymbol{\\Sigma}^{1/2}$.\n", "\n", "* For large $p$, finding such a decomposition is challenging.\n", "\n", "#### Multivariate $t$\n", "\n", "A multivariate $t$ distribution with degrees of freedom $\\nu$, scale matrix $\\boldsymbol{\\Sigma}$, and location vector $\\boldsymbol{\\mu}$ is the distribution of the random vector\n", "$$\n", " \\mathbf{T} = \\frac{1}{\\sqrt{\\chi^2_{\\nu}/\\nu}}\\mathbf{X} + \\boldsymbol{\\mu},\n", "$$\n", "where $\\mathbf{X} \\sim N(0, \\boldsymbol{\\Sigma})$, and $\\chi^2_{\\nu}$ is the chi-square random variable with $\\nu$ degrees of freedom, independent of $\\mathbf{X}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sequential sampling\n", "\n", "In many cases we can sample a random vector by sampling each component in turn and conditioning:\n", "\\begin{align*}\n", " p_{X_1, \\dotsc, X_p}(x_1, \\dotsc, x_p) \n", " &= p_{X_1}(x_1)\\prod_{j=2}^p p_{X_j|X_1, \\dotsc, X_{j-1}}(x_j | x_1, \\dotsc, x_{j-1}) \\\\\n", " &= p_{X_1}(x_1)p_{X_2|X_1}(x_2|x_1) \\prod_{j=3}^p p_{X_j|X_2, \\dotsc, X_{j-1}}(x_j | x_1, \\dotsc, x_{j-1}) \\\\\n", " &= \\dotsb\n", "\\end{align*}\n", "\n", "#### Multinomial\n", "\n", "For $(X_1, \\dotsc, X_k) \\sim \\text{mult}(n, p_1, \\dotsc, p_k)$, it is immediate to see that $X_1 \\sim B(n, p_1)$. Given $X_1 = x_1$, $(X_2, \\dotsc, X_k) \\sim \\text{mult}(n - x_1, p_2 / (1 - p_1), \\dotsc, p_k / (1 - p_1) )$. Hence $X_2 | \\{X_1 = x_1\\} \\sim B(n - x_1, p_2 / (1 - p_1) )$ and so on.\n", "\n", "#### Multivariate normal\n", "\n", "If we want to sample $\\mathbf{X} = (X_1, \\dotsc, X_p)$ from MVN with mean $\\boldsymbol{\\mu}=(\\mu_1, \\dotsc, \\mu_p)^T$ and covariance matrix $\\boldsymbol{\\Sigma} = (\\sigma_{ij})$, then note that the first component $X_1 \\sim N(\\mu_1, \\sigma_{11})$. From the conditional distribution formula for multivariate normal, we see that\n", "$$\n", " (X_2, \\dotsc, X_p) | \\{X_1 = x_1\\}\n", " \\sim N(\\bar{\\boldsymbol{\\mu}}, \\bar{\\boldsymbol{\\Sigma}}),\n", " \\quad\n", " \\bar{\\boldsymbol{\\mu}} = \\boldsymbol{\\mu}_2 + \\boldsymbol{\\Sigma}_{12}^T(x_1 - \\mu_1)/\\sigma_{11},\n", " ~\n", " \\bar{\\boldsymbol{\\Sigma}} = \\boldsymbol{\\Sigma}_{22} - \\boldsymbol{\\Sigma}_{12}^T\\boldsymbol{\\Sigma}_{12}/\\sigma_{11}\n", "$$\n", "if we partition\n", "\\begin{align*}\n", " \\boldsymbol{\\mu} &= (\\mu_1, \\boldsymbol{\\mu}_2)^T \\\\\n", " \\boldsymbol{\\Sigma} &= \\begin{bmatrix}\n", " \\sigma_{11} & \\boldsymbol{\\Sigma}_{12} \\\\\n", " \\boldsymbol{\\Sigma}_{12}^T & \\boldsymbol{\\Sigma}_{22}\n", " \\end{bmatrix} \n", " .\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "jupyter": { "outputs_hidden": true }, "tags": [] }, "outputs": [], "source": [] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "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": "4.2.2" }, "toc": { "colors": { "hover_highlight": "#DAA520", "running_highlight": "#FF0000", "selected_highlight": "#FFD700" }, "moveMenuLeft": true, "nav_menu": { "height": "153px", "width": "252px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, "skip_h1_title": true, "threshold": 4, "toc_cell": true, "toc_position": { "height": "441.3333435058594px", "left": "0px", "right": "903.3333129882813px", "top": "140.6666717529297px", "width": "166px" }, "toc_section_display": "block", "toc_window_display": true, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 4 }