{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "In this brief tutorial, we are going to see how to make use of the different probability distributions in R.\n", "\n", "There is one simple rule here, that no matter what distribution we’re talking about, there will ALWAYS be a *d* function, a *p* function, a *q* function and a *r* function, each representing the following:\n", "\n", "- *d*: **probability density**, i.e. the probability of obtaining a particular outcome under that distribution.\n", "- *p*: **cumulative probability function**. Here one specifies a particular quantile, and it tells you the probability of obtaining an outcome smaller than or equal to that quantile.\n", "- *r*: **random number generation**. It generates n random outcomes from the distribution.\n", "- *q*: **quantile**. One specifies a probability value, and gives the value of the variable for which there’s a probability of obtaining an outcome lower than that value.\n", "\n", "We'll understand all these better now with several examples, which you guys will complete in class." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Binomial Distribution\n", "\n", "The binomial distribution models the distribution of the number of sucesses of a given outcome after a certain number of trials.\n", "\n", "In R, for this distribution we will have:\n", "\n", "- `dbinom` \n", "- `pbinom`\n", "- `rbinom`\n", "- `qbinom`" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
function (x, size, prob, log = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (x, size, prob, log = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (x, size, prob, log = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (x, size, prob, log = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (q, size, prob, lower.tail = TRUE, log.p = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (q, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (q, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (q, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (n, size, prob) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (n, size, prob) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (n, size, prob) \n", "NULL\n", "```" ], "text/plain": [ "function (n, size, prob) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (p, size, prob, lower.tail = TRUE, log.p = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (p, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (p, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (p, size, prob, lower.tail = TRUE, log.p = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "args(dbinom)\n", "args(pbinom)\n", "args(rbinom)\n", "args(qbinom)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, *size* and *prob* are the parameters of the binomial distribution. Let's see documentation to see the meaning of the rest of arguments." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "?dbinom" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, say that we have a coin that we toss three times. Then, the probability of getting two heads in these tosses would be:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.375" ], "text/latex": [ "0.375" ], "text/markdown": [ "0.375" ], "text/plain": [ "[1] 0.375" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the same as using `dbinom` as follows:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.375" ], "text/latex": [ "0.375" ], "text/markdown": [ "0.375" ], "text/plain": [ "[1] 0.375" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# i.e. 0.5 * 0.5, as expected\n", "dbinom(2, size=3, prob=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, say we want to calculate the probability of getting two heads or lower. For this, instead of the previous probability, we should be summing the probabilities of getting no heads and one head." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.875" ], "text/latex": [ "0.875" ], "text/markdown": [ "0.875" ], "text/plain": [ "[1] 0.875" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p.0<- (0.5 * 0.5 * 0.5) # prbability of no heads\n", "p.1<- (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) # prability of one head\n", "p.2<- (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) + (0.5 * 0.5 * 0.5) # probability of two heads\n", "p.0 + p.1 + p.2 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But the above is the same as computing the cumulative probability, so we should be able to get it with `pbinom`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.875" ], "text/latex": [ "0.875" ], "text/markdown": [ "0.875" ], "text/plain": [ "[1] 0.875" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pbinom(2, size=3, prob=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the following, we are going to put into practice all this considering a dice instead of a coin, and later a gaussian distribution, but the logic behind the use of the above functions will be always the same." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: If you roll a dice 20 times, compute the probability of getting x = 4 sixes.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: If you roll a dice 20 times, compute the probability of getting x = 4 sixes or lower.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: At a probability 0.6, which value is more likely?
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: Simulate 100 random numbers with the same setting as above 20 times.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: See what happens when the different parameters in the binomial distribution change. For example, generate 1000 random numbers, with the same probability as before, but now for sizes 20, 50 and 100. In each case, plot the histogram.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: Now, do the same but varying the probabilities of success (e.g. consider 1/6, 3/6 and 5/6). Keep the number of trials, i.e. the parameter size, fixed to 20, for example.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- `dnorm`\n", "- `pnorm`\n", "- `rnorm`\n", "- `qnorm`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
function (x, mean = 0, sd = 1, log = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (x, mean = 0, sd = 1, log = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (x, mean = 0, sd = 1, log = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (x, mean = 0, sd = 1, log = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (n, mean = 0, sd = 1) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (n, mean = 0, sd = 1) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (n, mean = 0, sd = 1) \n", "NULL\n", "```" ], "text/plain": [ "function (n, mean = 0, sd = 1) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "
function (p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n",
       "NULL
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL\n", "```" ], "text/plain": [ "function (p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) \n", "NULL" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "args(dnorm)\n", "args(pnorm)\n", "args(rnorm)\n", "args(qnorm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: In the week 2 about descriptive statistcs, we mentioned that, for gaussian distributions, 68% of the points lie within 1 standard deviation around the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. Let's demonstrate this using pnorm. Since this function gives the cumulative probability function up to a certain value (the area under the curve), we can just use a difference of pnorms to get the areas that we desire. Let's suppose the mean is zero and the standard deviation 5
" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "m<-0 # mean\n", "s<-5 # standard deviation" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAYAAAD958/bAAAEDmlDQ1BrQ0dDb2xvclNwYWNl\nR2VuZXJpY1JHQgAAOI2NVV1oHFUUPpu5syskzoPUpqaSDv41lLRsUtGE2uj+ZbNt3CyTbLRB\nkMns3Z1pJjPj/KRpKT4UQRDBqOCT4P9bwSchaqvtiy2itFCiBIMo+ND6R6HSFwnruTOzu5O4\na73L3PnmnO9+595z7t4LkLgsW5beJQIsGq4t5dPis8fmxMQ6dMF90A190C0rjpUqlSYBG+PC\nv9rt7yDG3tf2t/f/Z+uuUEcBiN2F2Kw4yiLiZQD+FcWyXYAEQfvICddi+AnEO2ycIOISw7UA\nVxieD/Cyz5mRMohfRSwoqoz+xNuIB+cj9loEB3Pw2448NaitKSLLRck2q5pOI9O9g/t/tkXd\na8Tbg0+PszB9FN8DuPaXKnKW4YcQn1Xk3HSIry5ps8UQ/2W5aQnxIwBdu7yFcgrxPsRjVXu8\nHOh0qao30cArp9SZZxDfg3h1wTzKxu5E/LUxX5wKdX5SnAzmDx4A4OIqLbB69yMesE1pKojL\njVdoNsfyiPi45hZmAn3uLWdpOtfQOaVmikEs7ovj8hFWpz7EV6mel0L9Xy23FMYlPYZenAx0\nyDB1/PX6dledmQjikjkXCxqMJS9WtfFCyH9XtSekEF+2dH+P4tzITduTygGfv58a5VCTH5Pt\nXD7EFZiNyUDBhHnsFTBgE0SQIA9pfFtgo6cKGuhooeilaKH41eDs38Ip+f4At1Rq/sjr6NEw\nQqb/I/DQqsLvaFUjvAx+eWirddAJZnAj1DFJL0mSg/gcIpPkMBkhoyCSJ8lTZIxk0TpKDjXH\nliJzZPO50dR5ASNSnzeLvIvod0HG/mdkmOC0z8VKnzcQ2M/Yz2vKldduXjp9bleLu0ZWn7vW\nc+l0JGcaai10yNrUnXLP/8Jf59ewX+c3Wgz+B34Df+vbVrc16zTMVgp9um9bxEfzPU5kPqUt\nVWxhs6OiWTVW+gIfywB9uXi7CGcGW/zk98k/kmvJ95IfJn/j3uQ+4c5zn3Kfcd+AyF3gLnJf\ncl9xH3OfR2rUee80a+6vo7EK5mmXUdyfQlrYLTwoZIU9wsPCZEtP6BWGhAlhL3p2N6sTjRdd\nuwbHsG9kq32sgBepc+xurLPW4T9URpYGJ3ym4+8zA05u44QjST8ZIoVtu3qE7fWmdn5LPdqv\ngcZz8Ww8BWJ8X3w0PhQ/wnCDGd+LvlHs8dRy6bLLDuKMaZ20tZrqisPJ5ONiCq8yKhYM5cCg\nKOu66Lsc0aYOtZdo5QCwezI4wm9J/v0X23mlZXOfBjj8Jzv3WrY5D+CsA9D7aMs2gGfjve8A\nrD6mePZSeCfEYt8CONWDw8FXTxrPqx/r9Vt4biXeANh8vV7/+/16ffMD1N8AuKD/A/8leAvF\nY9bLAAAAOGVYSWZNTQAqAAAACAABh2kABAAAAAEAAAAaAAAAAAACoAIABAAAAAEAAANIoAMA\nBAAAAAEAAANIAAAAAN/ryxkAAEAASURBVHgB7N0JvG11XTd+ZhCJQQUFFJzjUSEJEYdAHMIp\nEyMzrLRS0cw05d/jPywMA5tEcmigzCAFG8TADEnFAQVLDRU1wWK+gKnM8yTP53vZS9fe7HPu\n2ueee885a71/r9fnrnGvvdb7t885+3vX2mtvsIFGgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECAwTWDDaTPNIzBQgYfmuLcaHfv1GV44h8P2mb/jaNldGX6t\ntV49vrbTtHOaEcPeCmyTI3t8sltySXJe8t/JnYm2MIHn52GPSurn51/n2cSPZ9nWyR3J5+ZZ\nr1l074z8aFI/21c3MzsM62d6i+Tc5Psd1q9VFvKYjpu2GoFFEdglW9l2tKX6ebh0Uba67jdS\nP/O/Pnqav8xwlp/ldb93noEAAQI9Ezg9x1MFT+Xf5jm2326tN/km+IDWstrOxvNsZ5ZFm2bl\n1ycPn+VB1l3nAi/IM9yeNK+bZrjDOn/m/j7B/XNoN4xMy3eu9sgsaOyvm2ul0fzHZPilpH5e\nmz6qIvYZyVxtoyw4MrkqaR5T+/W3yZbJtLaQx0zbjnkE1ofAB/IkzWv779bHEy7ic3xltO9v\nXcRt2hQBAgQITBFYrgXSs7Kv30zqD9keU/bbrKURuF+e9rakeYPRDC9bmt3pzbO+c2Ra/5s9\n138w1JmgOmPUmM9XIO2b9ZqCq1m/GdaZp5cm09opmdmsNzmsN2e1D5NtIY+Z3IZpAutLYCUX\nSK8MUv1c1s92XdWhESBAgMA6EliMAqnejJ3fylxv8LoeQl0C0X5zpkDqKrfu13vyRN/8cqZ3\nSuoSLm1hAg/Ow25N6jV/eDKtPSQz28VRrTtfgfTpLG9+hqroqgLs6615VdBulrTb/ploHlPD\nk5Pjk1ta81+T8XbbPxOzPqb9eOME1rfASi6Q6j8o6ue+fuaOXt9wno8AAQJDEliMAmmxvXbN\nBttvunZf7CewvQUL/FKrb+oPdV1epa2dwHF5ePN6r0vo2u1HMvGHSbtIadadq0DaK+s369Rn\nh34sqVZn/+pzhs2yl9TMVvuXjDfLTmrN/4PW/P/JeLvPF/KY1qaNEljvAiu5QCqsE5P6Ob0p\nqf+c0ggsmsAmi7YlGyJAoAR2TQ5qURyT8foF3rR6k/fSpM4yPCipN3vfTj6dfCSpS36aVpfW\n1VmKdqs3clckn0zqMp92qz8QL07q8xb1IdZzk3OSDyf1B2SuVkXX85J683hx8pmkPhj/uGS/\npNo3kvbnsl6V6eZzGO/N+KOTX0xq/z+afGw0XmfQatv7J7V/WyT1gdqvJf+YXJK0Wx3vPqMZ\n/57hWcn+yTOSesNcnyOpN6J1yWG18j4weUJS2zojqf1sO2ayU+vq94BsrZyb/Ww2/pujkTr+\nZv+aZZPDLn4vyoPuP3rgP2W4Knl28hPJI5Lqk3rNlMlcbaMs+MmkHrdLUvb1mqg+nnz9ZNbq\n18DTayStjqHW+7WkXgufT+q1VM7NsWZ0g3qN3y+pfqh9uz6pMzwfTKofNkx+KnlqUsdzZnJa\nckHSbrV/VXRWq9fut1aP/fCfP85ouTWtPB7YTMwxrJ+1ptXzfnU08b0M358026v1/m607L4Z\nPnc0XoM/b43/acb//9H0wzKs1+tnk4U8ZrSZmQfVp+vCv9mR+jmr498z+X5SZp9KvpLM1ep3\nWfVdmdTn725Ovp18Iqmf17uSdvuFTKzta7u9vRpv99PksmnTv56Zk/vVXm9dO7efq+t4/Xw9\nK6mflW2T7yT1c3RCcnEyV6vf7fUzWMP6uan+rH5ZSFts52YfZvnb2DymLmk9OLlXcljymkQj\nQIAAgUUWOD3bqz+YlXYxMPk0v91a786JhQe0ltV2Nm4tf07Gr5xY3jxfDb+YbJo0rd6wtZe3\nx3+jWWk0rDcc9Wa0vU4zXm806w/rtPaGzLwtadZthsdlXvs4/zbT7VZ/mJt16w307a3p/834\nJkm9aa43V816k8P68Pt+SbsdlYlmvbdm/B2t6Wb+9Zn3xOTpSb3hb+Y3w7/KvFnbLH77ZOPN\nc00b/mKHJ+/i96XW89Qb1pNa083zVp8fmkxrVST/e9Ks2x7W67YKm3pj0W6vzkSz3okZ/2Rr\nuubX665eo806Nazi6dKJeTX/H5KtRsP2+jVe/faopN1emYlmvbe1F4zGjx0tr9drHfPBo+l6\nzLXJtHZyZjbbnHxd1JupZtn/tB782Nb8Wr5Ta1mNfi9pHtf09UIeM7HZzpPryr92oIqGKm6a\n42uG9Xp5S9L+fZbJ1a1+/ut12Kw7OTwhyzZbveYP//lSa/2FvLZ/uKUfjk0+75qmq3Cfr61L\n5/med9qy2pcqBuY6puqfg6Y8sI7xjUn793Ozjfr5/pekma6/N11as37X4Zqc6zmfk8zyt7HZ\nz/od9/2k9qUeX0WtRoAAAQKLLHB6ttf80v9mxuvNwrS0/1DVH6Z2OyATzTZq2LyhqLMO17SW\nXZbxOktzdlLbaB7z1ow3rWuB9HN5wOQblPY2a9s1/bRmw6Phz2bYPG8N649o/c998wbputby\nv814u7Xf4N+UBe3tvGu04kcn5l+S6W8lzR+0eswNyRZJ047KSLOtZru3Zt6Frfm1vPat+aNf\nlu1t1vJfSbq2Wf32yYabfZw2bN40z/f8XfzabyKb9atvJouRcth14sm2yvRZSXv/Jl8TtawK\noPYbmFe3HtP4N9uo19gOSb1Za+bVsFmv9qv6s72siuCarj5sjqFZfmHmtd/QfGi0bi2vYmmy\n/Wlm/EXyiNGCn8+w2dZcBdIXWuvUa6vdXpSJ5vE3thY8pzW/ltfxtts3M9E87v+OFizkMe1t\nzjK+rvxf0TquOr4qRNvFYM17W9JuT8xE+2fvlkx/LWn6vXH63faDMr42r+2JTf1gsnmursP2\n6/4HG2mNrCvn1lN0Hv2jrNkcV/0slV/9/Wj3T43vmLRb+2ekHl8/w+cl9Xuk2V4zrL83XVqz\nftfhmpwfkCed9W9jez/riopmX/ZsLzBOgAABAosjcHo20/yi7TqsN53tNleB9OKs1Gzz4+0H\nZPyZo2V16UNdwrR1Uu1BSV1O0TyuhvW/hLsn902q1RuUplCo5aclj0zqj/u+SRUkzePPz/iW\nSbXNkppuln014w9Mqm2V/HPSLKvhcUm7fScT7eX/mOnnJ29LfjypfW8KrHoDVcfYtFqv/dgn\nNAsyPGpi2cmZ/pHR8ipW24+7M9PPGy0rk4tby/9pNH9Ng4X4VUH38OSwpNmf8qh5lWZ/Mzpn\nW5NfPfBLSbP9Gv5xcu+k2q8m7WWvWD33h/98pLX8+oz/clL9un3yB0n7Te2rMt20V2ekvd3v\nZrrm/XLy+0m1em2116k30k+vBWl17Bck7eX1et8m2Typ524ve3Smm3Z1Rpplz25mtobtYqpm\nt9/8zVUg1c9Us83faW2rRidfh7WP1V6eNI+pN5ST7cuZ0Sw/ZrRwIY+Z3G7X6XXhX8fefk0e\nn+mdk+qz9rFVMdx+E/6OTDevpdMzfq+kWu3jfySNU/1eare1eW23t9Mef10mZkn7sdPG14Xz\ntOfpMq/9e/zJrQfUz8Rnk1uSMv3lpGn1O779s/j1TO86Wli/R05Jmv6p4ftGy9Y0mMW41l1T\ne3FWaPajfle02zMzUcvq57j9t7G9zhdH69R6r28vME6AAAECiyNQf+CbX9Rdh/Umvd3mKpDa\nb2jrDevhyR5J879r27Q30hrfNePtfalCoN1OyESz/KKM1xuadvs/mag3ec06h4wW7tOaV8v2\nHc1vBvfJSFPg1PLjmgWjYfvNVBUm7bNAzap1bA9LJrdd+1j/Y9/s03My3rSjMtLMvz3jtR9N\nu19GmmU1/KtmwWhY083yT08sm2tyoX61vZclzfNdPtcTzDG/i1/7TeTZ2c5kgXBJ6/kPaz3P\nI1vza//aBVCz2omtddr7/urW/HpsTU+2TTOjOe4aHj2xwrtby+vNc1N412o7tZbVY/dPqtUb\ntvY2H7N67vz/dCmQ2v9T/lsTm6vXXfs567Va7Y1JM79ep5PtC5nRLG/eVC7kMZPb7Tq9Lvzb\nr+X6nfaAiZ1pvwl9y8SyKoqflFTftlsVpI1TmbXbQl/b7W2s6/F14bzQfW7/rH8qG/mZZNvR\nxupnZ5PReHsw+Tt+v/bCjN8/uTlp+qh5LU+sts4nf7W1D7P8bWx27EOtx7+zmWlIYG0Fpv1Q\nre02PZ5AHwTOz0EcN8eBPCXznzHHsrlmfyYLqlCpn7mtkiNG+V6G9b9m9T/+lSpKZmlPba38\ndxm/tTVdo99MzkyaP44/VjPTHnr3YPW/9ZjPtaZr9Kqk3hQ9rSbW0P4ly+t/MCdb/eEtx0uS\nJyR1tqb+aJfdlknTJou6Zn49tvajaZNnCc5qFoyG7XXn2ubEQ1bfOKCZN4tf85jFGM7l1972\n5zNRxUa7XZGJB41mNG+WanL/0bwa3Jm8tzXdjP51Rg4eTeyYYZ1Z+u5ouj34x/bEHOP1Omm3\ndj9V369qLWz3Uc1u+qnerLXbpe2JtRi/Oo+t46u22d2DH/w7OX3laEk9pmmT69T89ry1eUzz\nHGs7XAz/R7Z24qKM/3hruka/lTxuNO/ho2EzqDe1ZyVVIL0wqZ/xfZO9k6Y1/dxMt4ezvLbb\nj5scf8XkjDVM18/ALG0xnGd5vva6p2fil0cz9s+wUr8Pzk7+NamzQV9O2u2hrYn6/fzZ1nSN\n/m/y1aT6a5a22M5r+7ex/buiLgHWCCyKwCaLshUbIdA/gfNzSEfOcVj1pvMZcyyba3Zt7+XJ\n3yQbt1a6X8brjWqliqU3JtPe0Gb2PVptp/0/vRfeY427Z1yQwX6jZY8aDR88Gtag3hhXMTPZ\n6g14l3bxHCtVIfinyYuSGp+r1R/6aa39RruW1xmldrumPZHx2yam1zS5Nn5r2vYsy+fya29j\n8lhr2bSitOa3z9hclulpLvWaaLd6XdQblXary6nqNbmmNl8/Te73tH2p7VeB1rR6wz25zWbZ\nrMNv5wFNgTR5lrM9fXPWa/a1HtO0+htZr5P6mW9a+3HNz8hCHtNsb22Hk1btn5PmmJrnmMv/\nEc0KGdYb63rTPVfbeWLBT2W6flc2//kysXj15Fw/47Vwch9r3lyv7Vo2V/uruRbMMf89mT/t\n994cq9/jNbkQ57m2vab5r8sKeyTtwnWjTFfRWnlzUn12SHJ5Uu3Bq/+9+596fU471mbd1qpr\nHF1s57X923hpa4+3bY0bJbBWAvXLXyNAYP0IHJ+n+XTyquTAZLek3apYqj/aFyafai+YY7ze\ntN2Q1CUu1Zrh3VM//HebH47+4A1v+01VPe+01n7TOm15M6/eSE+2rTOjjqH5g177+bHRvE9n\n+Mmk2f5cb57ab0Cy+j3aXG/27rHiHDPWxm+OTS5o9jS/yQ3dOjkj03O5td9wdnlN1KanFUJd\n9qseO9lP7TdiXfuo/YZ4Mf8u1f+SN+2+zcho2H7dN4VOLWo/pqbrcd+pkVFrP655g7mQxzTb\nW9vhYvi3+6mO9avz7FT7DelLs97fJFVEVvtaUj/nn04ek/xBUm2u12otm+W1XesvVVsM54Xu\ne11Z8Pjk+cmvJk9Jtkra7bmZODHZfzTz6tGwBvX7eFq797SZSzBvsf42Nj+PS3AInrJvAov5\nh6hvNo6HwLoQuDgbfVPy28lOyVOTn0nqD1+9ydhwNF3FxbRW/2vYbhdlYvfRjL3bC0bjtc09\nW/PrDUy1i1b/e/c/W2Tw2OQrrXn1x3ev1vR8o9Pe4NQf66Y4qv+df3RySWsj7aKtCpWlahfl\niRfit5j7O81vcvvtomNy2eT0Ra0Z22X8Ycn5rXk1+rjWdL05/lZruhntsl/Nums7bBcg98rG\n6g1dvSlc27aqtYE6S9Zu7f+guLS1oP2Yml2Pa/aviqMqmJrWPG4hj2m2sRyGF7R2oi4FflYy\nX1HTrH5YRup3TLU/S16zeuzuf5qfq5qa72d8ltd2a/P3GH3/Peb0a0YZnpx8KNkkqYLpgOSl\nyYOTak9J6vV5ZdL+ma/fA3W1wbeTptXfkvbPQDN/TcN15bzQv43tvyXTfo+t6XgsJzBVoH7I\nNAIE1r3A7+cpnpb8aHJmUgVR/W/XCaP8W4b1x67apncPVv9bb1babbP2RMbrj2XzRuTgjP95\n8vmkab+ZkQePJuqNSD1Ptc8l9Qa0+Z/Ft2f8p5Mbknr+dybtN4KZnLNN7mOt+OTW2udkvF0c\nPSHT7eNYyt9DC/VrHd5aj07zW5uNVh/fmDT/O3x0xl+YNP8Dvn3Gfydp2icy0ixr5tVwsfer\nve3J8e+Nnq95Ldw/04tRIH0g23n56Mn2y3CPpF6P9aaqfl6a9r5mJMPLks8m+47m1Zv+T4/G\nXzUa1qDe0NV61RbymHrcTknzHxjVBx+rmUvQzmw9Z+1TvdH+1GjexhnWcdYb6m8kJyWnJlUs\nPjJp2keakdGwvJvW9GszvS6Gv7QuNroOtjlrn/9Y9uEtSf3teHBSv1v/MzlrlPp5r/GmbTYa\n+VqG9Zqq3+cbJr+VHJo07RcyskszMcNwsZ1/P8+9kL+NzS7X67Bp32pGDAmsrcD6+KW1tvvo\n8QT6IHB9DuJJowOpQqTetJ6S1KVF9WZk/6Rpn2lGMqzHtdsfZKLO9Px78sHkL5J6o1dvVOqN\nTL2pOS6p/z2s5zswaVqt+x+jiXrz+ZfJ/x1NPzXD/06+nDwmeVDStd01ZcV6w9i0fTJShVod\n79OT9pvzTN7jUpGat77aQv0Wc/+m+a3N9m/Mg383eftoI1WM1+vln5MqmuoNzs5JtVr311eP\n3fOfxd6vez7DD+fUG7kvJVU8V3tAUq/HtW2fzAa+ntRrut4kVkH8T8kzkvsk1ers0PtXj/3w\nn3dmdN/R5M9keEJybfLS0bwavCO5szW9kMfUz13z3FdnvNmn1mbXy2gVPPWGevfRsx2XYf2c\nXp7UMT8xqVY/y8evHrv7y35vznid8av25uSa1WMbbPCKDJ81Gq/BVq3xoY/O2uf1c/Dk5L4j\nuPKvvx/1M12v60OSplWBcMVo4tsZ1u+3146m35DhTsnHk0cnzfyMLmlb6N/GZqfbZ4br+DUC\nBAgQWGSB07O9elNYqf+Vm6v9dhY067XfINX6B7SW1TpVtFTbIjktaR431/DkrLNh0m5fycTk\n+s2b31rv/km9uZlcpz1dbxR/JGm3zTJRbxbb6zXjH838etPUTP9txtut3lQ2y17aXjAar/+Z\nrDdLzTrtYZlVAdXMOyrjTavxZv7nmpmtYbOshs9pza/R+l/WZvnnJ5bNN7lQv5e1nq/eSM7S\n1uRX26qCoTme352y8U+1lv/xlOWvybzvt9ZpttUMb8iyF0087tWt9S+cWNZMbtpap7ZVxUa7\nvTkTzXN8ob0g4xu1ltU6z2wt/6PWsnozt6b281mheZ4qXuZq9RxVCDbrtofl86opD6yf2/od\n0F63PX5elk3+PC3kMb/Qeo6rMt6lrSv/x+bJL0naxzk5fszEDtbvocl1mun2tm7Jeu0iaW1f\n2xO7sU4m15XzQvr8WTnCMmxspw1vzfInTEhUUXX+HI+rn5n27//3TTx2fU2uzd/G2sf6j4Xy\nqL8rTbGeUY3A2gnUHyuNAIF1L1B/3J6fVHF12ZSn+27mHZr8fFK/7Nut3ug2/ytY8+vSp/bP\n7v9mev/kL5L/StqPr+eq/yl8elL/U9dut2Wi3iDXWaQqoKqg+ffk95KfTupNZdNubkY6DuvN\n0XOTb06s/41M75u0zyLVPixlW6jfUu5zl+d+d1aq19NHk3YBUW+k/i3ZI/mHZLm0j7V2pP6X\nfbFaHeuTknOS9s/GtzP9guQvk8lWb7aek/xJ0v65qZ+9k5LHT8zP5Oo3aLM+ph7XtCpYl7LV\nf8TslZyctF8vtU8XJ7+evL4mWq1+n1XRVC5Nq98Vf5r8aFKPq7Z5cuDqMf+0Bbr2+Wl5UP3e\n/HBSRf1k+9fM2Cep39/tdmUmqk/rNdv0Uf0MfDWp7X06aVr7Z6OZtz6Gt+RJFvq38RF57Laj\nnfxUhvXa0wgQIEBghQpUcbNz8oRRHpDh5FmjzBprm2Tq0Un9sav/cZuv3ScL6w3h/eZZqf63\nu/ahXWhNrn56ZtQfzcofTi7sOF3bf0jyE8l8+9Nxc+tltS5+62VHFvFJqh9+LKnXUL2WlmOr\nn4ELknq91Rv0eo0udqs3U/XG8IEzbLjsym3vZE0/e81mZ3lMHXf9B8hZzYOXybB+bsuqhmvq\ni62zzuOS3ZPl+vrKri2btjZ9XmfiHpXsn+yWdD1rsmXWrSJq+2S5tvq5meVvY/3nX/M36heX\n60HZLwIECBBYOQL1x7L+R7HOIp2fvD9pt/oj+t2k+ePzS+2FxgmsI4E6I9G85uo/EIbQ6n/P\n65j/ZAgH6xhXC+jzxXkhnJbN1M/OdUn9TdMIECBAgMBaC3wxW2jejNbw9OStyYnJpUmzrC5B\n2ybRCKxrgSrM681Ovfb+bF0/2TLY/stHx1pnzn5kGeyPXVj3Avp8cYx3zGZuT+p3xZGLs0lb\nIUCAAAECd3/30Y2BaAqhacP6A3QwLALrUeCNea56LdZldn0vGh6ZY6wzR30/zhyiNhLQ54vz\nUjg8m6nfE3V5avsGIIuzdVshQIAAgUEL1Gcx6g3a15Irk/qDc/1oui67qw9aawTWp0B9oL8u\n+6zX4m+uzyf2XAQIrAiB+ixgXdlQvyPqjJxGYNEF6oOCGgECBBqBurVtnTXSCCylQBVJ9Vqs\nz8ndspQ74rkJEFh2AnUzh+YzR81VEMtuJ+0QAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIDA\nihPYcMXt8drv8HbZxDbJ5skNyTXJjYlGgAABAgQIECBAgACBQQjsmaN8T/Kd5K4pOT/zjk22\nTzQCBAgQIECAAAECBAj0VuDwHFlTFF2c8bOSjyR/n3w0+Y/kiqTW+V7y4kQjQIAAAQIECBAg\nQIBA7wRemCOqwqcKoR+f5+jqUsP9ki8mtf6TEo0AAQIECBAgQIAAAQK9EjghR1OXz9Xnjbq0\n+nzSdclfdlnZOgQIECBAgAABAgQI9Etgo34dzj2OZo/M+Xxy6z2WTJ9xdWafk+w8fbG5BAgQ\nIECAAAECBAj0WaDvBVJ9tmivZNOOnVhnkKqoOrfj+lYjQIAAAQIECBAgQIDAihH4hexpfabo\nw8k+8+x1fQZp36Ru2HBH8uREI0CAAAECBAgQIECAQK8EqvB5fVLfc1SF0qrk35N/TT4wGtYl\neJcntfz25HWJRoAAAQIECBAgQIAAgd4KPDRHVgXRZUkVQu1U8fTfyduSByUaAQIECBAgQIAA\nAQIDFagzLENrW+eAt0m2SOqLY69NNAIECBAgQIAAAQIECGwwxAKp3e27ZuJHkyqUzktuTjQC\nBAgQIECAAAECBAj0UuCVOaoTk3tNHN3umW6+FLa53O6azHtjsvHEuiYJECBAgAABAgQIECDQ\nC4H35iiqAKpL6ppWnzOqYqjmV5FUXwpbRVTdwKHmvT3RCBAgQIAAAQIECBAg0DuBaQXSCTnK\nKoReM3G0W2a6WfaMiWUmCRAgQIAAAQIECBAgsOIFphVIF+ao6vuOprW6FO97yVunLZxh3oOz\nbt0x77sdc2XWq88/9f2Le3OIGgECBAgQIECAAIHlK7DJ8t21dbZndRe70+fYehUp5yaPmWN5\n19mXZsVfSzbr+IBHZr2jkuqP2zo+xmoECBAgQIAAAQIECCyywBALpP+MYd2kYVq7b2bunRw3\nbeEM8+7Muh+eYf0nzrCuVQkQIECAAAECBAgQWEcCQ7mk6wvxq88XvSE5K3lc8tNJu+2SiXcn\nddbnM+0FxgkQIECAAAECBAgQINAHgZ/NQXwouSCpGzO0c0mmm/bcjNye1PIzk/X9/VB1Bqme\nu+sleVlVI0CAAAECBAgQIEBgsQX6fondBwNWqVa3+n5sK+0iqL77qD5/9IHk9UkVKxoBAgQI\nECBAgAABAgMTaBcJAzv0scOtu9fdkdRZpKVodQapLv3bPHGThqXoAc9JYPkL7JRdrP/k0RYu\n8JU89PKFP9wjCRAgQGAIAn0/g9SlD6soqS+PPb/LytYhQIDAEgm8ZaONNvqVjTfe+PtL9Pwr\n+mnvuOOOje+666766oeXr+gDsfMECBAgsM4FhlIgPSSSz0z+N/l4ckOyY/KupOZvldyU/Gny\ne8lSnUnKU2sECBCYKrDJs571rI3e/OY3D+XmOlMRFjrziCOO2ODUU08dyt+8hTJ5HAECBAhE\nYAh/LOozRW9v9fZFGX98UsXQQck1yUeTxyaHJQ9PXpRoBAgQIECAAAECBAgMTKDv/xP5rPTn\n0ck3ktclhyb1RbGfS34ueWNS1/U/J3lo8r6k5tdZJY0AAQIECBAgQIAAgYEJ9P0M0gvSnzcm\n+4yG1b11y+9/TlYlVTzVl7pWuyV5ZfLsUf4tQ40AAQIEeiBw880311HskvxMDw5nqQ7hS3ni\n9ldkLNV+eF4CBAisU4G+F0hVGJ2WVJHUtI9lpIqhjyRNcdQsq7+g5yaPaGYYEiBAgMDKF/jv\n//7vDXKDi/0322yzJ6/8o1n/R3Dbbbdtcueddx6XZ37Z+n92z0iAAIH1K9D3AunqcFaRVJcS\nNnd+qpsx/E4y7UYM22b+3kldaqcRIECAQE8Ecge7DZ75zGdumJtc+ELuBfTp6CYX9Z2BGgEC\nBHov0PfPINVlcnUL77pJwwNavVmX1r2zNV2jmyZvTTZPPploBAgQIECAAAECBAgMTKDvBVLd\nqe7spG7QcFGyXTKt1d3s6jNJv5Z8Kvn7RCNAgAABAgQIECBAYGACfS+Q6rNGP5EclZyT1CV3\n09q9M7Muu6izSnVHu7sSjQABAgQIECBAgACBgQn0vUCq7qwbL9Rnjuq7j+Zq/5QF90vqTFMV\nVRoBAgQIECBAgAABAgMU6PtNGrp2aRVRGgECBAgQIECAAAECAxcYwhmkgXexwydAgAABAgQI\nECBAoKuAAqmrlPUIECBAgAABAgQIEOi9gAKp913sAAkQIECAAAECBAgQ6CqgQOoqZT0CBAgQ\nIECAAAECBHovoEDqfRc7QAIECBAgQIAAAQIEugookLpKWY8AAQIECBAgQIAAgd4LKJB638UO\nkAABAgQIECBAgACBrgIKpK5S1iNAgAABAgQIECBAoPcCCqTed7EDJECAAAECBAgQIECgq4AC\nqauU9QgQIECAAAECBAgQ6L2AAqn3XewACRAgQIAAAQIECBDoKqBA6iplPQIECBAgQIAAAQIE\nei+gQOp9FztAAgQIECBAgAABAgS6CiiQukpZjwABAgQIECBAgACB3gsokHrfxQ6QAAECBAgQ\nIECAAIGuAgqkrlLWI0CAAAECBAgQIECg9wIKpN53sQMkQIAAAQIECBAgQKCrgAKpq5T1CBAg\nQIAAAQIECBDovYACqfdd7AAJECBAgAABAgQIEOgqoEDqKmU9AgQIECBAgAABAgR6L6BA6n0X\nO0ACBAgQIECAAAECBLoKKJC6SlmPAAECBAgQIECAAIHeCyiQet/FDpAAAQIECBAgQIAAga4C\nCqSuUtYjQIAAAQIECBAgQKD3Agqk3nexAyRAgAABAgQIECBAoKuAAqmrlPUIECBAgAABAgQI\nEOi9gAKp913sAAkQIECAAAECBAgQ6CqgQOoqZT0CBAgQIECAAAECBHovoEDqfRc7QAIECBAg\nQIAAAQIEugookLpKWY8AAQIECBAgQIAAgd4LKJB638UOkAABAgQIECBAgACBrgIKpK5S1iNA\ngAABAgQIECBAoPcCCqTed7EDJECAAAECBAgQIECgq4ACqauU9QgQIECAAAECBAgQ6L2AAqn3\nXewACRAgQIAAAQIECBDoKqBA6iplPQIECBAgQIAAAQIEei+gQOp9FztAAgQIECBAgAABAgS6\nCiiQukpZjwABAgQIECBAgACB3gsokHrfxQ6QAAECBAgQIECAAIGuAgqkrlLWI0CAAAECBAgQ\nIECg9wIKpN53sQMkQIAAAQIECBAgQKCrgAKpq5T1CBAgQIAAAQIECBDovYACqfdd7AAJECBA\ngAABAgQIEOgqoEDqKmU9AgQIECBAgAABAgR6L6BA6n0XO0ACBAgQIECAAAECBLoKKJC6SlmP\nAAECBAgQIECAAIHeCyiQet/FDpAAAQIECBAgQIAAga4CCqSuUtYjQIAAAQIECBAgQKD3Apv0\n/gjveYDbZdY2yebJDck1yY2JRoAAAQIECBAgQIDAwAWGcgZpz/Tze5LvJFclFybnJquSKpLO\nT45Ntk80AgQIECBAgAABAgQGKjCEM0iHp2+PGPXvJRl+PqkiqQqjOpN0n2SX5JDkoOS1yYmJ\nRoAAAQIECBAgQIDAwAT6XiC9MP1ZxdFpyZuSs5NpbcPM3Dc5OjkhuSg5K9EIECBAgAABAgQI\nEBiQQN8vsTswfXlBUsO5iqPq7ruSM5IDkuuTlyQaAQIECBAgQIAAAQIDE+h7gbRH+rMuqbu1\nY79enfXOSXbuuL7VCBAgQIAAAQIECBDokUDfC6Qr0ld7JZt27LO6w10VVXUDB40AAQIECBAg\nQIAAgYEJ9L1AOj79uVtyUrLPPH3bfAapPqu0ZXLyPOtaRIAAAQIECBAgQIBATwX6fpOGuhvd\nDsmRyfOSy5JVyZXJdcnWSd3Fbtdkx+SO5NDkzEQjQIAAAQIECBAgQGBgAn0vkOrmC8ckpyRH\nJfslk2eSbsq8y5O6g907kksTjQABAgQIECBAgACBAQr0vUBqurTuZHfwaKLOGtX3H22R1BfH\nXptoBAgQIECAAAECBAgQ2GAoBVK7q+vSuopGgAABAgQIECBAgACBMYEhFkh1p7o6g7R5ckNy\nTXJjohEgQIAAAQIECBAgMHCBvt/FrunePTPynqQuqbsquTCpW3mvSqpIOj85Ntk+0QgQIECA\nAAECBAgQGKjAEM4gHZ6+PWLUv5dkWF8cW0VSFUZ1JqnuYrdLckhyUPLapO5+pxEgQIAAAQIE\nCBAgMDCBvhdIL0x/VnFU32/0puTsZFprvgep7mR3QnJRclayNu1H8uCuvrWuRoAAAQIECBAg\nQIDAEgt0fQO/xLu54Kc/MI+sO9jV8NZ5tlK3Az8jOSC5OHlJsjYF0sPz+G8lVXhpBAgQIECA\nAAECBAisEIG+F0h7pB/qkrr5iqN2V12diXOSndszFzD+P3nMo5LNOj629vN9Hde1GgECBAgQ\nIECAAAEC60ig7wXSFXHbK9k0ub2DYd3hroqVumHD2ra6CUTXdu+uK1qPAAECBAgQIECAAIF1\nJ9D3u9gdH7rdkpOSfeZhbD6DVJ9V2jI5eZ51LSJAgAABAgQIECBAoKcCfT+DdGL6bYfkyOR5\nyWXJquTKpL4sduuk7mK3a7JjckdyaHJmohEgQIAAAQIECBAgMDCBvhdIdfOFY5JTkqOS/ZLJ\nM0k3Zd7lydHJO5JLE40AAQIECBAgQIAAgQEK9L1Aarq07mR38GiizhrV9x9tkdQXx16baAQI\nECBAgAABAgQIEOj8PT19oqpL6ypN2zwjdYnd+cmdzUxDAgQIECBAgAABAgSGJ9D3mzQ0PfqQ\njLwqeUGy1Whmfebog8n3kvOSKprqMrxNE40AAQIECBAgQIAAgQEKDOESu9enX9/e6tuLMv74\n5E+Tg5Jrko8mj00OSx6evCjRCBAgQIAAAQIECBAYmEDfzyA9K/1ZN1/4RvK6pO5QV59B+lzy\nc8kbk52S5yQPTerLWmv+MxONAAECBAgQIECAAIGBCfT9DFJdUndjUneuq2G1umHDPyerkiqe\nms8d3ZLxVybPHuXfMtQIECBAgAABAgQIEBiQQN/PIFVhVF/+2hRH1bUfS6oY+kjSFEcZXd1u\nzr/nJo+4e9K/BAgQIECAAAECBAgMSaDvBdLV6cwqktrHWd979DvJN5PJtm1m7J3U9yJpBAgQ\nIECAAAECBAgMTKBdOPTx0OsyuQcldZOGB7QOsC6te2drukbr7nVvTeq2359MNAIECBAgQIAA\nAQIEBibQ9wKp7lR3dlI3aLgo2S6Z1upudvWZpF9LPpX8faIRIECAAAECBAgQIDAwgb4XSPVZ\no59I6vuNzknqkrtp7d6ZuVlSZ5XqjnZ3JRoBAgQIECBAgAABAgMT6HuBVN1ZN16ozxzVdx/N\n1f4pC+6X1JmmKqo0AgQIECBAgAABAgQGKND323x37dIqojQCBAgQIECAAAECBAYuMIQzSAPv\nYodPgAABAgQIECBAgEBXAQVSVynrESBAgAABAgQIECDQewEFUu+72AESIECAAAECBAgQINBV\nQIHUVcp6BAgQIECAAAECBAj0XkCB1PsudoAECBAgQIAAAQIECHQVUCB1lbIeAQIECBAgQIAA\nAQK9F1Ag9b6LHSABAgQIECBAgAABAl0FFEhdpaxHgAABAgQIECBAgEDvBRRIve9iB0iAAAEC\nBAgQIECAQFcBBVJXKesRIECAAAECBAgQINB7AQVS77vYARIgQIAAAQIECBAg0FVAgdRVynoE\nCBAgQIAAAQIECPReQIHU+y52gAQIECBAgAABAgQIdBVQIHWVsh4BAgQIECBAgAABAr0XUCD1\nvosdIAECBAgQIECAAAECXQUUSF2lrEeAAAECBAgQIECAQO8FFEi972IHSIAAAQIECBAgQIBA\nVwEFUlcp6xEgQIAAAQIECBAg0HsBBVLvu9gBEiBAgAABAgQIECDQVUCB1FXKegQIECBAgAAB\nAgQI9F5AgdT7LnaABAgQIECAAAECBAh0FVAgdZWyHgECBAgQIECAAAECvRdQIPW+ix0gAQIE\nCBAgQIAAAQJdBRRIXaWsR4AAAQIECBAgQIBA7wUUSL3vYgdIgAABAgQIECBAgEBXAQVSVynr\nESBAgAABAgQIECDQewEFUu+72AESIECAAAECBAgQINBVQIHUVcp6BAgQIECAAAECBAj0XkCB\n1PsudoAECBAgQIAAAQIECHQVUCB1lbIeAQIECBAgQIAAAQK9F1Ag9b6LHSABAgQIECBAgAAB\nAl0FFEhdpaxHgAABAgQIECBAgEDvBRRIve9iB0iAAAECBAgQIECAQFcBBVJXKesRIECAAAEC\nBAgQINB7AQVS77vYARIgQIAAAQIECBAg0FVAgdRVynoECBAgQIAAAQIECPReQIHU+y52gAQI\nECBAgAABAgQIdBVQIHWVsh4BAgQIECBAgAABAr0XUCD1vosdIAECBAgQIECAAAECXQUUSF2l\nrEeAAAECBAgQIECAQO8FFEi972IHSIAAAQIECBAgQIBAVwEFUlcp6xEgQIAAAQIECBAg0HsB\nBVLvu9gBEiBAgAABAgQIECDQVUCB1FXKegQIECBAgAABAgQI9F5AgdT7LnaABAgQIECAAAEC\nBAh0FVAgdZWyHgECBAgQIECAAAECvRdQIPW+ix0gAQIECBAgQIAAAQJdBRRIXaWsR4AAAQIE\nCBAgQIBA7wU26f0R3vMAt8usbZLNkxuSa5IbE40AAQIECBAgQIAAgYELDOUM0p7p5/ck30mu\nSi5Mzk1WJVUknZ8cm2yfaAQIECBAgAABAgQIDFRgCGeQDk/fHjHq30sy/HxSRVIVRnUm6T7J\nLskhyUHJa5MTE40AAQIECBAgQIAAgYEJ9L1AemH6s4qj05I3JWcn09qGmblvcnRyQnJRclai\nESBAgAABAgQIECAwIIG+X2J3YPrygqSGcxVH1d13JWckByTXJy9JNAIECBAgQIAAAQIEBibQ\n9wJpj/RnXVJ3a8d+vTrrnZPs3HF9qxEgQIAAAQIECBAg0COBvhdIV6Sv9ko27dhndYe7Kqrq\nBg4aAQIECBAgQIAAAQIDE+h7gXR8+nO35KRkn3n6tvkMUn1Wacvk5HnWtYgAAQIECBAgQIAA\ngZ4K9P0mDXU3uh2SI5PnJZclq5Irk+uSrZO6i92uyY7JHcmhyZmJRoAAAQIECBAgQIDAwAT6\nXiDVzReOSU5Jjkr2SybPJN2UeZcndQe7dySXJhoBAgQIECBAgAABAgMU6HuB1HRp3cnu4NFE\nnTWq7z/aIqkvjr020QgQIECAAAECBAgQILDBUAqkdlfXpXWVanVpXZ1RqkLpvOTmRCNAgAAB\nAgQIECBAYKACfb9JwyvTr/U5pHtN9O/umf5iclHyb8mXk7rj3RuTjRONAAECBAgQIECAAIEB\nCvS9QKqzQ3Vp3Watvn1Qxj+bPC75UnJs8oHkhuQPkz9JNAIECBAgQIAAAQIEBigwxEvsqgiq\nzyD9RvLuVp/X7b3/Onl9cmryiUQjQIAAAQIECBAgQGBAAkMskJ6U/v1C0i6OqsvrbnYvT56Z\nPC1Z2wJpz2yjfeYqk3O2R825xAICBAgQIECAAAECBNabwBALpLqL3elzCNdNGs5NHjPH8q6z\nH5YV6/K9vl/C2NXDegQIECBAgAABAgRWhMAQ38D/Z3qmbtIwrd03M/dO6oYNa9POz4PrNuJ1\nc4gu2T/raQQIECBAgAABAgQILLHAUM4g1SV1dUaniqOzkt9Nfjr5cNK0XTLyR0ldFveZZuZa\nDG/PYytd2m1dVrIOAQIECBAgQIAAAQLrVqDvBVLdbGHb5LHJi0fJYHWrzyA1BdJzM35yUh5V\nQNVd7TQCBAgQIECAAAECBAYm0PcC6YPpz0q1unNdFUpNNqyZo1bffVSfP6rCqO5id1eiESBA\ngAABAgQIECAwMIG+F0jt7rw2E3Xp3LTL5z6e+fX5o66XxGVVjQABAgQIECBAgACBvgkMqUCa\nr+/q7JFGgAABAgQIECBAgMDABYZ2F7s1HW9darddUneg0wgQIECAAAECBAgQGJjAmgqGPnDc\nPwfxD8lVyXXJp5InJ9Na3f671nvjtIXmESBAgAABAgQIECDQb4G+F0hbpfu+mPxcUmeHViVP\nSc5Ijko0AgQIECBAgAABAgQI/ECg7wXSb+VIH5QckTww2S2pL4L9enJY8vZEI0CAAAECBAgQ\nIECAwGqBvhdIT8pRfic5Mrl+9RHf/WWx+2X8s0nd0ruKKI0AAQIECBAgQIAAAQIb9L1A2jl9\nXIXQHRN9Xbf8/qnknOSPkroETyNAgAABAgQIECBAYOACfS+QLk7/PiOZdle6umHDc5L6XNLx\nyVw3bsgijQABAgQIECBAgACBIQj0vUA6PZ24TfLWZKcpHXpZ5v1kUpffnZo8N9EIECBAgAAB\nAgQIEBioQN8LpHenX/8rqc8aXZr8fDLZzsuMA5LvJ/VZpWob3j3wLwECBAgQIECAAAECQxLo\ne4F0Szpzn+SdySXJbcm09pXMfFxy2rSF5hEgQIAAAQIECBAgMAyBTQZwmDfkGF83ynwF4flZ\n59lJ3Qa8CiuNAAECBAgQIECAAIGBCQyhQGp3aV1Gt6ZWXyyrESBAgAABAgQIECAwQIH5zqgM\nkMMhEyBAgAABAgQIECAwZAEF0pB737ETIECAAAECBAgQIDAmoEAa4zBBgAABAgQIECBAgMCQ\nBRRIQ+59x06AAAECBAgQIECAwJiAAmmMwwQBAgQIECBAgAABAkMWUCANufcdOwECBAgQIECA\nAAECYwIKpDEOEwQIECBAgAABAgQIDFlAgTTk3nfsBAgQIECAAAECBAiMCSiQxjhMECBAgAAB\nAgQIECAwZAEF0pB737ETIECAAAECBAgQIDAmoEAa4zBBgAABAgQIECBAgMCQBRRIQ+59x06A\nAAECBAgQIECAwJiAAmmMwwQBAgQIECBAgAABAkMWUCANufcdOwECBAgQIECAAAECYwIKpDEO\nEwQIECBAgAABAgQIDFlAgTTk3nfsBAgQIECAAAECBAiMCSiQxjhMECBAgAABAgQIECAwZAEF\n0pB737ETIECAAAECBAgQIDAmoEAa4zBBgAABAgQIECBAgMCQBRRIQ+59x06AAAECBAgQIECA\nwJiAAmmMwwQBAgQIECBAgAABAkMWUCANufcdOwECBAgQIECAAAECYwIKpDEOEwQIECBAgAAB\nAgQIDFlAgTTk3nfsBAgQIECAAAECBAiMCSiQxjhMECBAgAABAgQIECAwZAEF0pB737ETIECA\nAAECBAgQIDAmoEAa4zBBgAABAgQIECBAgMCQBRRIQ+59x06AAAECBAgQIECAwJiAAmmMwwQB\nAgQIECBAgAABAkMWUCANufcdOwECBAgQIECAAAECYwIKpDEOEwQIECBAgAABAgQIDFlAgTTk\n3nfsBAgQIECAAAECBAiMCSiQxjhMECBAgAABAgQIECAwZAEF0pB737ETIECAAAECBAgQIDAm\noEAa4zBBgAABAgQIECBAgMCQBRRIQ+59x06AAAECBAgQIECAwJiAAmmMwwQBAgQIECBAgAAB\nAkMWUCANufcdOwECBAgQIECAAAECYwIKpDEOEwQIECBAgAABAgQIDFlAgTTk3nfsBAgQIECA\nAAECBAiMCSiQxjhMECBAgAABAgQIECAwZAEF0pB737ETIECAAAECBAgQIDAmoEAa4zBBgAAB\nAgQIECBAgMCQBRRIQ+59x06AAAECBAgQIECAwJiAAmmMwwQBAgQIECBAgAABAkMWUCANufcd\nOwECBAgQIECAAAECYwIKpDEOEwQIECBAgAABAgQIDFlAgTTk3nfsBAgQIECAAAECBAiMCWwy\nNjWMie1ymNskmyc3JNckNyYaAQIECBAgQIAAAQIDFxjKGaQ908/vSb6TXJVcmJybrEqqSDo/\nOTbZPtEIECBAgAABAgQIEBiowBDOIB2evj1i1L+XZPj5pIqkKozqTNJ9kl2SQ5KDktcmJyYa\nAQIECBAgQIAAAQIDE+h7gfTC9GcVR6clb0rOTqa1DTNz3+To5ITkouSsRCNAgAABAgQIECBA\nYEACfb/E7sD05QVJDecqjqq770rOSA5Irk9ekmgECBAgQIAAAQIECAxMoO8F0h7pz7qk7taO\n/Xp11jsn2bnj+lYjQIAAAQIECBAgQKBHAn0vkK5IX+2VbNqxz+oOd1VU1Q0cNAIECBAgQIAA\nAQIEBibQ9wLp+PTnbslJyT7z9G3zGaT6rNKWycnzrGsRAQIECBAgQIAAAQI9Fej7TRrqbnQ7\nJEcmz0suS1YlVybXJVsndRe7XZMdkzuSQ5MzE40AAQIECBAgQIAAgYEJ9L1AqpsvHJOckhyV\n7JdMnkm6KfMuT+oOdu9ILk00AgQIECBAgAABAgQGKND3Aqnp0rqT3cGjiTprVN9/tEVSXxx7\nbaIRIECAAAECBAgQIEBgg75/BmlaF2+cmZU69q2SeycaAQIECBAgQIAAAQIEBlMg7Zm+fk9S\nZ4yuSi5M6k519XmkG5Lzk2OT7RONAAECBAgQIECAAIGBCgzhErvD07dHjPr3kgzre5GqSKrC\nqC61q5s07JIckhyUvDapmztoBAgQIECAAAECBAgMTGDWAuld8flEcmpy+wqwemH2sYqjun33\nm5Kzk2mtuc133ajhhOSi5KxEI0CAAAECBAgQIEBgQAKzFkjPic1rku8mdZbluOQryXJtB2bH\n6gYNNbx1np2su92dkRyQXJy8JFmbAqlc62zUZkmX9vAuK1mHAAECBAgQIECAAIF1KzBrgfTE\n7E7dDa4KiNeN8tUMj0uqYKrP+Cyntkd2pi6pm684au/v1Zk4J9m5PXMB4/X4uq141wKp63oL\n2BUPIUCAAAECBAgQIECgq8Csd7GrAqi+K2iv5DHJHyf3S45JLktOSV6QbJosh3ZFdqL2tev+\nbJd1q6iqGzisTauzUHVWqD7b1CVlphEgQIAAAQIECBAgsMQCsxZI7d39RibemFQBsH9Sn096\nQvKh5PLk7ckjkqVsx+fJd0tOSia/ILa9X81nkOqzSlsmJ7cXGidAgAABAgQIECBAYBgCs15i\nN03lYZm5X/KUZIekPs9TZ5p+M6nL8I5I3pIsRavL/mqfjkyel9RZrlXJlcl1ydZJ3cVu12TH\n5I7k0OTMRCNAgAABAgQIECBAYGACCy2Q6vuCfj75xeTxI7O6rKwKoTprc0HykKQuvasC6ZLk\nuGR9tyrWah/q0r+jkirkJs8k3ZR5dcar7mD3juTSRCNAgAABAgQIECBAYIACsxZIB8XoV5MD\nknrszckJyd8mn0yqIGnahRl5ZfL85OnJcclStSrY6uYS1eqs0TbJFkmd6bo20QgQIECAAAEC\nBAgQILC6yJmF4U+ycp0Z+vekiqJ/SOYrMOqStYuTs5Pl0DbKTtSldZVpbePMrAKqCr9bpq1g\nHgECBAgQIECAAAEC/RWogmGW9u6s/H+SJyZ/lcxXHGXx6s/6PDjDusxtqdr988RVyF2VVGH0\nqeTJybS2e2bWem+cttA8AgQIECBAgAABAgT6LTBrgfT2cJyb1CVzD2vR7JTxvxvNb81e8tGt\nsgdfTH4uqbNDdYOGpyRnJPWZJI0AAQIECBAgQIAAAQI/EJi1QKpC6MPJJ5J9frCVDTZ4aMZ/\naTT/La35Sz36W9mBByV1o4gHJnXL772TryeHJVXwaQQIECBAgAABAgQIEFgtMGtT0QZ/AABA\nAElEQVSBVHd6e3ZSl9p9bPUW7v7ncxnUjRs+m/xu8qRkObTaj7oRw5HJ9aMd+s8M6252ta+v\nT6qI0ggQIECAAAECBAgQILDBLAXShvGqO9L9c/IbyfeSdvt4Jl6U3JnULcCXQ9s5O1GFUN0s\not3qs1M/lZyT/FFSl+BpBAgQIECAAAECBAgMXGCWAulHYnWv5PR5zK7Isi8lu8yzzvpcVHfQ\ne0ZSt/SebHXDhuck9bmk45O5btyQRRoBAgQIECBAgAABAkMQmKVAqoLiW8lj54HZNMsempw/\nzzrrc1EVc/WdR29NdpryxJdl3k8mdfndqclzE40AAQIECBAgQIAAgYEKzFIgFVHdIvsVSfOl\nqzWvaXXHuGOT7ZO6icNyaPVZqf9K6rNGlybTLv07L/Pr81PfT+qzStXqckKNAAECBAgQIECA\nAIGBCcxaIB0eny8nJyZ1u+8PJe9NTksuSX4leV/y0WQ5tFuyE3W3vXcmtX+3JdPaVzLzcUkd\nh0aAAAECBAgQIECAwEAFNpnxuOuOcE9NquDYPzkwac621Gd5Dkv+OllO7YbszOtGma8grMsC\n6w59dRvwKqw0AgQIECBAgAABAgQGJjBrgVQ8VXD86sipPt9TN2S4OKnPKC33VpfRranVF8tq\nBAgQIECAAAECBAgMUGAhBVKbqW6X/bX2DOMECBAgQIAAAQIECBBYqQILKZCeloP9pWSHpG77\n3Vxil9EftOMydvwPpowQIECAAAECBAgQIEBgBQjMWiDVF6r+Q4fj+kyHdaxCgAABAgQIECBA\ngACBZSUwa4H0+9n7G5NDkrrld920YVrr8lmfaY8zjwABAgQIECBAgAABAksmMEuBdO/s5SOS\n+q6jus23RoAAAQIECBAgQIAAgV4JzHfb68kDvTkz6k51dQZJI0CAAAECBAgQIECAQO8EZimQ\n6rK5+mzRwcksj+sdmgMiQIAAAQIECBAgQKCfArMWOq8Iw03JB5P9kl2S+05J3d1OI0CAAAEC\nBAgQIECAwIoSmLVA+nCOrm7v/YKkziZdnHxvSt6YeRoBAgQIECBAgAABAgRWlMAsN2moA/ty\ncnmHI/xmh3WsQoAAAQIECBAgQIAAgWUlMGuB9GvLau/tDAECBAgQIECAAAECBBZRYNZL7NpP\nXZ8z2j3ZZzSzbgOuESBAgAABAgQIECBAYMUKLKRAqhsz/GNSt/s+J3lbUu39yZHJ5jWhESBA\ngAABAgQIECBAYKUJzHqJ3Y45wLOTunNdfc5oy6RpG2bkTcmByeOSWxKNAAECBAgQIECAAAEC\nK0Zg1jNI78yR1aV1+yaPSqpYatpBGTkqeXTy0mamIQECBAgQIECAAAECBFaKwKwF0tNzYH+W\nfG7KAd6ZeUck1yZPmLLcLAIECBAgQIAAAQIECCxrgVkKpK1zJNsl581zRLdn2TdG682zmkUE\nCBAgQIAAAQIECBBYfgKzFEjXZfe/new9z2FUEVWX2J07zzoWESBAgAABAgQIECBAYFkKzFIg\n1QF8NHl58ppkq6Tdts3E3yXbJB9vLzBOgAABAgQIECBAgACBlSAwa4H0hhzU5cm7ksuSJyUP\nTU5Ozk+enxyXnJ5oBAgQIECAAAECBAgQWFECsxZI1+Tofjw5NtkiuX+yU1KFUbXXJnWGSSNA\ngAABAgQIECBAgMCKE5j1e5DqAL+XvCr59WTX5AHJRUmdWdIIECBAgAABAgQIECCwYgUWUiA1\nB1u39b5glGaeIQECBAgQIECAAAECBFaswKyX2K3YA7XjBAgQIECAAAECBAgQWJPArGeQ6rNH\n9bmjNbW/zwoVjQABAgQIECBAgAABAitGYNYC6SdzZA9Zw9GtyvLPrGEdiwkQIECAAAECBAgQ\nILDsBGYtkPbMEUxellfTD0wekxyT1JmjGmoECBAgQIAAAQIECBBYUQKzFkjXznF0V2b+V5Nv\nJF9OPpt8ONEIECBAgAABAgQIECCwYgQmzwat7Y5/JRu4OKlL8TQCBAgQIECAAAECBAisKIHF\nLpA2z9HfN9lhRSnYWQIECBAgQIAAAQIECERg1kvstshjNpwiV9vZPjky2Sr5UqIRIECAAAEC\nBAgQIEBgRQnMWiD9V45uTXexqy+P/asVpWBnCRAgQIAAAQIECBAgEIFZC6Qz8phvTZH7fuZd\nl5yTvCeZ62YOWaQRIECAAAECBAgQIEBgeQrMWiD98vI8DHtFgAABAgQIECBAgACBtRdY7Js0\nrP0e2QIBAgQIECBAgAABAgSWSGDWM0jHZj/vv4B9fV8ec9ICHuchBAgQIECAAAECBAgQWG8C\nsxZIe2TPHpPUneqq3Zlck9wnmXZ3u8xe3f6jGTEkQIAAAQIECBAgQIDAchWY9RK7X8qB3Jh8\nONkrqdt+3280fHaG30yqGKqzTPV9SE2OybhGgAABAgQIECBAgACBZS0w6xmkv8nRfDl5QVJ3\nrmvabRk5Lfl6cl7yM8lfJhoBAgQIECBAgAABAgRWjMAsZ5A2z1E9IXl/0i6O2ge7KhNfSZ7S\nnmmcAAECBAgQIECAAAECK0FglgLpjhzQDcnO8xzYpln2sOTKedaxiAABAgQIECBAgAABAstS\nYJYCqW7I8PHksOTxU45my8xr7nJXl9tpBAgQIECAAAECBAgQWFECs34G6a05up9I6kYMZyR1\nU4brkwcmT0t2SOpzSh9JNAIECBAgQIAAAQIECKwogVkLpHNydHsn7032TfZLmva/GXll8p5m\nhiEBAgQIECBAgAABAgRWksCsBVId2xVJ3dK7Ls97ZFK39D4/uSy5K9EIECBAgAABAgQIECCw\nIgVm+QzS5AHWXe3qpgy3JHX3uvoMkkaAAAECBAgQIECAAIEVK7CQAmmXHO0/JvWFsXXJ3duS\nau9PjkyqcNIIECBAgAABAgQIECCw4gRmvcRuxxzh2cl9k7pBQ/us0YaZflNyYPK4pM4saQQI\nECBAgAABAgQIEFgxArOeQXpnjuxeSd2g4VFJFUtNOygjRyWPTl7azDQkQIAAAQIECBAgQIDA\nShGYtUB6eg7sz5LPTTnAOzPviOTa5AlTli+XWdtlRx6c/GhSX3p770QjQIAAAQIECBAgQIDA\n6jvRdWXYOitWcXHePA+4Pcu+MVpvntXW+6I984x1+/HvJFclFybnJquSG5K6C199ye32iUaA\nAAECBAgQIECAwEAFZjmDdF2Mvp3sPY9VFVF1iV0VH8ulHZ4dqUsBX5bcnHw++dfkH5LTki8k\n9VmqQ5L6XNWLE40AAQIECBAgQIAAgQEKzHqTho/G6OXJ15PjknbbNhPHJdskH0+WQ3thdqIu\n+6tCqG4gUYXStFY3mKjPVR2dnJBclJyVaAQIECBAgAABAgQIDEhgljNIxfKG5PLkXcllyZOS\nhyYnJ3WZ2vOT45LTk+XQ6o56FyQ1nKs4qv2sL7g9IzkguT55SaIRIECAAAECBAgQIDAwgVkL\npGvi8+NJfV5ni+T+yU5JFUbVXpvUGabl0vbIjtQldbd23KGrs945Sd28QSNAgAABAgQIECBA\nYGACsxZIxfO95FVJfW7nYcmTkyoo6ruR6szSnclyaVdkR/ZKNu24Q3UTiiqqltNnqDruutUI\nECBAgAABAgQIEFhbgVkLpD/LE74tqc8uVSFUl6/VZ3Xqsrvl2I7PTu2WnJTsM88ONp9Bqs8q\nVeFXlwxqBAgQIECAAAECBAgMTGCWmzRsHpv6AthVyf+3QpxOzH7ukByZPC+pz03V/l+Z1F35\ntk7uk+ya7JjckRyanJloBAgQIECAAAECBAgMTGCWAum22Fyf1BmWOuNSNzZY7q328ZjklOSo\nZL9k8kzSTZlXZ8DqDnbvSC5NNAIECBAgQIAAAQIEBigwS4FUxcYLkn9MPpy8O/mf5LvJZKub\nInS9McLkY9fFdF0KePBow3XWaJukbjLxneTaRCNAgAABAgQIECBAgMDqzxLNwlCfP6ozSD81\nylyPPSILfm+uhUs8vy6tq1SrS+vqjFIVSuclNycaAQIECBAgQIAAAQIDFZjlDFIR1d3d6lbY\na2pVbCyH9srsxFOSlyXt4mf3TL83eVzStDqT9AdJFYHL6U58zf4ZEiBAgAABAgQIECCwjgVm\nLZBevo73Z7E3X2eH6tK6X0uaAulBGf9sUpfZfSn5z6Quu6vPJ/1hcv/kDYlGgAABAgQIECBA\ngMDABNZUIFXRUOt8skcuVQRVcfQbSX2Oqml16eBfJ69PTk0+kWgECBAgQIAAAQIECAxIYE0F\n0jtjUcXEQyZM6hK1+yafnpi/EiaflJ38QtIujmq/6252dYbsmcnTkrUpkLbK46vQ2izp0uqL\ndjUCBAgQIECAAAECBJZYYE0F0ly7d2QW/HRSt/teaa0upzt9jp2uy/Dqc1aPmWN519lVIFUh\ntmnHB9Q+aQQIECBAgAABAgQILLHAQgukJd7ttXr6+sxRnQGb1uqs2N7JcdMWzjDv21n32TOs\n/8Sse9YM61uVAAECBAgQIECAAIF1ILDROtjmctxkXVJ3QlI3X6hCpO5eV2fA2m2XTNRld3VZ\n3GfaC4wTIECAAAECBAgQIDAMgb6fQaqbLWybPDZ58SgZrG5VDH14NP7cDE9OyqMKqA8kGgEC\nBAgQIECAAAECAxPoe4H0wfRnpVrdbKIKpSbtz09tnPn1+aMqjOrmCnclGgECBAgQIECAAAEC\nAxPoe4HU7s76Iti6dG7a5XMfz/z6/NHtiUaAAAECBAgQIECAwEAFuhRI28XmjyZ8HjWanpzf\nrFYFx9rcJrvZzvoaNl8iu76ez/MQIECAAAECBAgQILAMBboUSHVp2v+dY9/nml/fKbSSCqQ5\nDs9sAgQIECBAgAABAgSGJLCmAulNwdh2ASDnLOAxHkKAAAECBAgQIECAAIElFVhTgfSvS7p3\na//kr8gmFvIlrHUnu8+v/dPbAgECBAgQIECAAAECK0lgTQXSSjqWafv66sysu9bN2n4vD1Ag\nzapmfQIECBAgQIAAAQIrXKDvBdKz0z8fSp6YnJK8N+nSzuuyknUIEJhJ4LBNNtlkrs8tzrSh\nIa5855133muIx+2YCRAgQIDA+hboe4H07YA+Nalbe1exdETy5UQjQGD9Czxy99133+Znf/Zn\n1/8z9+AZjz766B4chUMgQIAAAQLLX6DvBVL1wK3Jy5Kzk3clP5FoBAgsgcCOO+64wTOe8Ywl\neOaV/5R//ud/vvIPwhEQIECAAIEVILDRCtjHxdjFb2QjhyV1w4bdF2ODtkGAAAECBAgQIECA\nQP8EhlIgVc/V9Sl7JF+rCY0AAQIECBAgQIAAAQKTAkMqkCaP3TQBAgQIECBAgAABAgTGBBRI\nYxwmCBAgQIAAAQIECBAYsoACaci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDI\nAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBA\ngACBMQEF0hiHCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAA\nAQIECBAYsoACaci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydA\ngAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiH\nCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoAC\naci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBA\nYExgk7EpEwQIECBAgACBCYHrr7++5jwyOWRikcnuAp/Lqv/VfXVrEiCwVAIKpKWS97wECBAg\nQGCFCFx44YUbbLHFFvtsu+22j10hu7ysdvOaa67Z9JZbbnlfdupXl9WO2RkCBKYKKJCmsphJ\ngAABAgQINAJ33XXXBk972tM2evOb33yvZp5hd4Ejjjhig1NPPdXHGrqTWZPAkgr4YV1Sfk9O\ngAABAgQIECBAgMByElAgLafesC8ECBAgQIAAAQIECCypgAJpSfk9OQECBAgQIECAAAECy0lA\ngbScesO+ECBAgAABAgQIECCwpAIKpCXl9+QECBAgQIAAAQIECCwnAQXScuoN+0KAAAECBAgQ\nIECAwJIKKJCWlN+TEyBAgAABAgQIECCwnAQUSMupN+wLAQIECBAgQIAAAQJLKqBAWlJ+T06A\nAAECBAgQIECAwHISUCAtp96wLwQIECBAgAABAgQILKmAAmlJ+T05AQIECBAgQIAAAQLLSUCB\ntJx6w74QIECAAAECBAgQILCkAgqkJeX35AQIECBAgAABAgQILCcBBdJy6g37QoAAAQIECBAg\nQIDAkgookJaU35MTIECAAAECBAgQILCcBBRIy6k37AsBAgQIECBAgAABAksqoEBaUn5PToAA\nAQIECBAgQIDAchJQIC2n3rAvBAgQIECAAAECBAgsqYACaUn5PTkBAgQIECBAgAABAstJQIG0\nnHrDvhAgQIAAAQIECBAgsKQCCqQl5ffkBAgQIECAAAECBAgsJwEF0nLqDftCgAABAgQIECBA\ngMCSCiiQlpTfkxMgQIAAAQIECBAgsJwEFEjLqTfsCwECBAgQIECAAAECSyqgQFpSfk9OgAAB\nAgQIECBAgMByElAgLafesC8ECBAgQIAAAQIECCypgAJpSfk9OQECBAgQIECAAAECy0lgk+W0\nM+tpX7bL82yTbJ7ckFyT3JhoBAgQIECAAAECBAgMXGAoZ5D2TD+/J/lOclVyYXJusiqpIun8\n5Nhk+0QjQIAAAQIECBAgQGCgAkM4g3R4+vaIUf9ekuHnkyqSqjCqM0n3SXZJDkkOSl6bnJho\nBAgQIECAAAECBAgMTKDvBdIL059VHJ2WvCk5O5nWNszMfZOjkxOSi5KzEo0AAQIECBAgQIAA\ngQEJ9P0SuwPTlxckNZyrOKruvis5IzkguT55SaIRIECAAAECBAgQIDAwgb4XSHukP+uSuls7\n9uvVWe+cZOeO61uNAAECBAgQIECAAIEeCfS9QLoifbVXsmnHPqs73FVRVTdw0AgQIECAAAEC\nBAgQGJhA3wuk49OfuyUnJfvM07fNZ5Dqs0pbJifPs65FBAgQIECAAAECBAj0VKDvN2mou9Ht\nkByZPC+5LFmVXJlcl2yd1F3sdk12TO5IDk3OTDQCBAgQIECAAAECBAYm0PcCqW6+cExySnJU\nsl8yeSbppsy7PKk72L0juTTRCBAgQIAAAQIECBAYoEDfC6SmS+tOdgePJuqsUX3/0RZJfXHs\ntYlGgAABAgQIECBAgACBDfr+GaRpXbxxZlbq2LdK7p1oBAgQIECAAAECBAgQGEyBtGf6+j1J\nnTG6KrkwqTvV1eeRbkjOT45Ntk80AgQIECBAgAABAgQGKjCES+wOT98eMerfSzKs70WqIqkK\no7rUrm7SsEtySHJQ8tqkbu6gESBAgAABAgQIECAwMIG+F0gvTH9WcVS3735TcnYyrTW3+a4b\nNZyQXJSclWgECBAgQIAAAQIECAxIoO8F0oHpy7pBQw1vnadf6253ZyQHJBcnL0nWpkC6Xx5f\nd8/bLOnS7ttlJesQIECAAAECBAgQILBuBfpeIO0Rvrqkbr7iqC18dSbOSXZuz1zAeH2fUl3G\nt2nHx/a9HzoyWI0AAQIECBAgQIDA0gr0/Y35FeHdK6lC5fYO1NtlnSqq6oYNa9OuyYNfN8MG\nnph1f2aG9a1KgAABAgQIECBAgMA6EOj7bb6Pj9luyUnJ5BfEtjmbzyDVZ5W2TE5uLzROgAAB\nAgQIECBAgMAwBPp+BunEdOMOyZHJ85LLklXJlcl1ydZJ3cVu12THpC6NOzQ5M9EIECBAgAAB\nAgQIEBiYQN8LpLr5Qt0s4ZTkqGS/ZPJM0k2Zd3lSd7B7R3JpohEgQIAAAQIECBAgMECBvhdI\nTZfWnewOHk3UWaNtki2S+uLYaxONAAECBAgQIECAAAECGwylQGp3dV1aV9EIECBAgAABAgQI\nECAwJtD3mzSMHawJAgQIECBAgAABAgQIzCegQJpPxzICBAgQIECAAAECBAYl0PdL7F6R3qzP\nHM3azsoD6gtmNQIECBAgQIAAAQIEBiTQ9wLp1enLxy6gP38vj1EgLQDOQwgQIECAAAECBAis\nZIG+F0jPTud8KHliUrf6fm/SpZ3XZSXrECBAgAABAgQIECDQL4G+F0jfTnc9NflMUsXSEcmX\nE40AAQIECBAgQIAAAQL3EBjCTRpuzVG/bHTk77qHgBkECBAgQIAAAQIECBAYCQyhQKpD/UZy\nWFI3bNg90QgQIECAAAECBAgQIHAPgaEUSHXgRyd7JF+rCY0AAQIECBAgQIAAAQKTAkMqkCaP\n3TQBAgQIECBAgAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoACaci979gJECBAgAABAgQIEBgT\nUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAA\ngSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiHCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBA\ngAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoACaci979gJECBAgAABAgQIEBgTUCCNcZggQIAA\nAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuO\nnQABAgQIECBAgACBMQEF0hiHCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRI\nYxwmCBAgQIAAAQIECBAYsoACaci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDI\nAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBA\ngACBMQEF0hiHCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAA\nAQIECBAYsoACaci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydA\ngAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiH\nCQIECBAgQIAAAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoAC\naci979gJECBAgAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBA\nYExAgTTGYYIAAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiHCQIECBAgQIAA\nAQIEhiygQBpy7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoACaci979gJECBA\ngAABAgQIEBgTUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIA\nAQIECBAgQIAAgSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiHCQIECBAgQIAAAQIEhiygQBpy\n7zt2AgQIECBAgAABAgTGBBRIYxwmCBAgQIAAAQIECBAYsoACaci979gJECBAgAABAgQIEBgT\nUCCNcZggQIAAAQIECBAgQGDIAgqkIfe+YydAgAABAgQIECBAYExAgTTGYYIAAQIECBAgQIAA\ngSELKJCG3PuOnQABAgQIECBAgACBMQEF0hiHCQIECBAgQIAAAQIEhiywyQAPfrsc8zbJ5skN\nyTXJjYlGgAABAgQIECBAgMDABYZyBmnP9PN7ku8kVyUXJucmq5Iqks5Pjk22TzQCBAgQIECA\nAAECBAYqMIQzSIenb48Y9e8lGX4+qSKpCqM6k3SfZJfkkOSg5LXJiYlGgAABAgQIECBAgMDA\nBPpeIL0w/VnF0WnJm5Kzk2ltw8zcNzk6OSG5KDkr0QgQIECAAAECBAgQGJBA3y+xOzB9eUFS\nw7mKo+ruu5IzkgOS65OXJBoBAgQIECBAgAABAgMT6HuBtEf6sy6pu7Vjv16d9c5Jdu64vtUI\nECBAgAABAgQIEOiRQN8LpCvSV3slm3bss7rDXRVVdQMHjQABAgQIECBAgACBgQn0vUA6Pv25\nW3JSss88fdt8Bqk+q7RlcvI861pEgAABAgQIECBAgEBPBfp+k4a6G90OyZHJ85LLklXJlcl1\nydZJ3cVu12TH5I7k0OTMRCNAgAABAgQIECBAYGACfS+Q6uYLxySnJEcl+yWTZ5JuyrzLk7qD\n3TuSSxONAAECBAgQIECAAIEBCvS9QGq6tO5kd/Boos4a1fcfbZHUF8demyx2e2A2WJf1bdZx\nw3VZn0aAAAECBAgQIECAwBILDKVAajPXpXWVanVpXZ1RqkLpvOTmZDHa97KRv0u63hyi9uOR\ni/HEtkGAAAECBAgQIECAwMIF+l4gvTI0T0lelrSLn90z/d7kcUnT6kzSHyRvS+5sZi5weEse\n92czPPaJWfc3Z1jfqgQIECBAgAABAgQIrAOBvt/Frs4O1aV17UvdHpTpzyZVHH0pOTb5QHJD\n8ofJnyQaAQIECBAgQIAAAQIDFOj7GaRpXVpFUH0G6TeSd7dWqM8B/XXy+uTU5BOJRoAAAQIE\nCBAgQIDAgAT6fgZpWlc+KTO/kLSLo1qv7mb38uTK5GmJRoAAAQIECBAgQIDAwASGWCDVXey+\nNkc/1+eUzk0eM8dyswkQIECAAAECBAgQ6LHAEAuk/0x/1k0aprX7ZubeyRXTFppHgAABAgQI\nECBAgEC/BYZSINUldSckb0jOSuoGDT+dtNsumajL7uqGDp9pLzBOgAABAv+vvTuBtq2u7wP+\neAzBgYcKGqIxsRG0ElERo6I4RYMaKkSD1iTGqSilbbBC2sY0BjFkWMumzWDTlart0qCJRolx\nQMUBQyuIJhqDBhUrkPCQQRkeDhFQ+v3xzo6bnXPO3Xc495x79ue/1vftff77v6fP/t/39v/s\nc+4jQIAAAQIEhiGw7L+koX7Zwt2ShyU/O0omt5caDL1rNH9Mpu9MyqMGUPVb7RQCBAgQIECA\nAAECBAYmsOwDpLfnelaq1G+uq4FSkz2qclT2zLS+f1QDo/otdrclCgECBAgQIECAAAECAxNY\n9gFS+3LWfwRbH50b9/G5D6a+vn90S6IQIECAAAECBAgQIDBQgSENkKZd4np6pBAgQIAAAQIE\nCBAgMHCBofyShoFfZqdPgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJ\ngAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOk\nPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAw\nCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQI\nECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBA\ngAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFc\nZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAf\nAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQI\nECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAAB\nAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkra\nECBAgAABAgQIECAwCAEDpEFcZidJgAABAgQIECBAgEAfAQOkPkraECBAgAABAgQIECAwCAED\npEFcZidJgAABAgQIECBAgEAfgb36NNKGAIHbBeoNhf1ZrFlgnzWvaUUCBAgQIECAwCYJGCBt\nErTdLIXAf8tZnLwUZ+IkCBAgQIAAAQIExgoYII1lUUlgrMD+j3vc47adeOKJYxeqnC5wyimn\nTG9gKQECBAgQIEBgAQQMkBbgIjiErSOw3377bTvkkEO2zgEv0JHuvffeC3Q0DoUAAQIECBAg\nMF7AL2kY76KWAAECBAgQIECAAIEBChggDfCiO2UCBAgQIECAAAECBMYLGCCNd1FLgAABAgQI\nECBAgMAABQyQBnjRnTIBAgQIECBAgAABAuMFDJDGu6glQIAAAQIECBAgQGCAAgZIA7zoTpkA\nAQIECBAgQIAAgfECBkjjXdQSIECAAAECBAgQIDBAAQOkAV50p0yAAAECBAgQIECAwHgB/1Hs\neBe1BAgQIECAAIENEbjhhhtqOw9OfmlDNjjMjXwop/2Xwzx1Z73ZAgZImy1ufwQIECBAgMCg\nBC6//PJtO3bsOPyggw46dFAnvkEne9VVV+29a9euB2ZzL9qgTdoMgakCBkhTeSwkQIAAAQIE\nCKxf4Kijjtp+2mmn3Wn9WxreFk4//fRtZ5999h7DO3NnPC8B30Gal7z9EiBAgAABAgQIECCw\ncAIGSAt3SRwQAQIECBAgQIAAAQLzEjBAmpe8/RIgQIAAAQIECBAgsHACBkgLd0kcEAECBAgQ\nIECAAAEC8xIwQJqXvP0SIECAAAECBAgQILBwAgZIC3dJHBABAgQIECBAgAABAvMSMECal7z9\nEiBAgAABAgQIECCwcAIGSAt3SRwQAQIECBAgQIAAAQLzEjBAmpe8/RIgQIAAAQIECBAgsHAC\nBkgLd0kcEAECBAgQIECAAAEC8xIwQJqXvP0SIECAAAECBAgQILBwAgZIC3dJHBABAgQIECBA\ngAABAvMSMECal7z9EiBAgAABAgQIECCwcAIGSAt3SRwQAQIECBAgQIAAAQLzEjBAmpe8/RIg\nQIAAAQIECBAgsHACBkgLd0kcEAECBAgQIECAAAEC8xIwQJqXvP0SIECAAAECBAgQILBwAgZI\nC3dJHBABAgQIECBAgAABAvMSMECal7z9EiBAgAABAgQIECCwcAIGSAt3SRwQAQIECBAgQIAA\nAQLzEthrXjue437vnn3vn3xf8vXkhuQbiUKAAAECBAgQIECAwMAFhvIE6fBc59cn1yTXJZcm\nn0+uSGqQ9P+SP0zumSgECBAgQIAAAQIECAxUYAhPkH411/b00fX9u0wvSGqQVAOjepJ0j+SH\nkpcmP52cnLwlWcZyTE7qWct4Ypt0To/ZpP3YDQECBAgQIDASuOaaen97W/0b/IZRlcnqBc7K\nKu9d/WrDXGPZB0jPzmWtwdH7k/+cfCoZV/ZI5eOS307enFyWnJ8sW3n2fe5zn+cfdthhy3Ze\nm3I+55133qbsx04IECBAgACB7wl85Stf2Zb7l4Nz/3Lw92rN9RW46KKLtu3cubM+NWaA1BOt\nBgbLXGqw8+jk0OTbPU60vp90eVJPkP51j/aTmvxIFvxVss+kBp366rT1nahqf2tn2Ua+fP32\n7dtftOeee353Izc6lG3dcsste8ZvW/y+M5Rz3sjz5Lc+TX781iewvrX1P37rE1jf2vrf+vxu\nvfXWPW+77bb/la2csL4tDWftZR8gXZRL+Znkeau4pP83ba9PnrGKdbpNa8Dz5GTv7oIJr+s6\nHJi8ccLyjaq+dzb0sI3a2AC3Ux/HrFIf0VRWL8Bv9WbtNfi1NVY/z2/1Zu01+LU1Vj/Pb/Vm\n7TX4tTXWNv/XWe3Kta1qrWUTOCcndHHSd6BST5B2Ja9JFAIECBAgQIAAAQIECCyVwM/lbG5L\n3pU8asqZ1ROc+g7ShUl9xO2xiUKAAAECBAgQIECAAIGlEqiBz8uTbyQ1ULoi+XhSX1L749G0\nfqtdPXKs5bckL0sUAgQIECBAgAABAgQILK1A/dKEGhDtTGog1E4Nni5J/kty30QhQIAAAQIE\nCBAgQGCgAvWEZWhlR064/v+jfZP6xfo3JgoBAgQIECBAgAABAgQIECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECCweQJ7bN6u7GlBBPZZ\nkONwGAQIECBAgAABApsjcPPm7GY59mKAtBzXse9ZfDwNH9W3sXYECBAgQIAAAQJLIXBhzuLR\nS3Emm3ASe23CPuxicQS+nEP5WnLG4hySIxmQwK+MzlX/G9BFX6BT1f8W6GIM8FD0vwFe9AU6\n5ep/Ny7Q8Sz8oRggLfwl2tADrMer1yYXbOhWbYxAP4Hqe1X0v90O/txcAf1vc73t7Y4C+t8d\nPbzaXIGm/23uXrfw3rZv4WN36AQIECBAgAABAgQIENhQAQOkDeW0MQIECBAgQIAAAQIEtrKA\nAdJWvnqOnQABAgQIECBAgACBDRUwQNpQThsjQIAAAQIECBAgQGArCxggbeWr59gJECBAgAAB\nAgQIENhQAQOkDeW0MQIECBAgQIAAAQIEtrKAAdJWvnqOnQABAgQIECBAgACBDRUwQNpQThsj\nQIAAAQIECBAgQGArCxggbeWr59gJECBAgAABAgQIENhQgb02dGs2tugCNy/6ATq+pRbQ/5b6\n8i78yel/C3+JlvoA9b+lvrwLf3L638JfIgc4T4F7ZOcVhcA8BPS/eajbZyOg/zUSpvMQ0P/m\noW6fjYD+10iYEiBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECCwaAJ7LtoBOZ4NFbhztvbw5LHJ3ZJdybeTcaX6wpHJI5Nbk+sShcBGCfxU\nNlR97NoJG9T/JsCoXreAvrVuQhtYpcD90v6Y5KIp6+mXU3AsWpPAj2Stuo87dLT216ZsRf+b\ngmPRcgs8P6d3dXJbKzVAOjnplkNScXHSbvu5vL5vt6HXBNYg8JKsU33r1Anr6n8TYFSvW0Df\nWjehDaxSYEfa/21y05T19MspOBatWuCgrPHOpH0PV/MfSWrQ1C36X1fE68EI/ETO9LvJpckr\nkgcnNTD6fFI/ND+fNGWPzJyX1ODpecnByUuSbyaXJ3dJFAJrFTguK96cVL8bN0DS/9Yqa72V\nBPStlYQs32iBu2eD70/q77tJAyT9cqPVh7297Tn9jybV596aPD15QvKGpO4DP5vsmzRF/2sk\nTAcpcG7Oun5Yju6c/Y+N6uvpUFNOyky1PbGpGE1rkDSuvtPMSwJjBQ5I7ZlJ9aF/GE3HDZD0\nv+AoMxHQt2bCaqMTBJ6Z+iuT+juvPso+aYCkXwZH2TCBJ2RL1efOH7PF946WPbu1TP9rYZgd\nlkC9m/CJpAZB9RnTbqmnSPUdo2bZhZmvG9j6jlK71McEvpV8sl1pnkBPgepX9Zf225L6uGfN\njxsg6X+BUWYioG/NhNVGxwg8PXX1d9xXk2OTTyWTBkj6ZXCUDRN4QbZ0aXLCmC0+N3XVL09r\nLdP/WhhmCTQC9Zj1xuRLo4q9M613uv5m9Lo7+XQq6uNR1U4hsBqBP0jjp4xWqBuG+ku6O0DS\n/0ZAJhsuoG9tOKkNThH4iSz7teQeozaTBkj65RREizZc4Jezxfq3t74+UUX/2+3Q68962qAM\nR+A/5VR3JO8YnXJ9XnqfZNJvOrkuy+oH6p6JQmA1Av8mjT+0wgr63wpAFq9ZQN9aM50V1yDw\nwazzyqT+zZxW9MtpOpZtpMCB2djLk/p+efNvsf63CuG9VtFW060t8Jwc/q8mlySvSqrUYKlK\nfSxgXGn+sveLGsbpqFuvgP63XkHrTxLQtybJqJ+ngH45T/3h7Lvu2d6T1CCpPnp3VVJF/9vt\n0OtPA6ReTAvZqDp69wlgfZeo0i0vTMX/TK5N6reK1XeLqjRtu9vZvfR731P6TlNhSmAksJr+\nNwlN/5sko369AvrWegWtPwsB/XIWqrbZFqhB0buSRyW/l9Rvs2uK/tdI9JhOujHusaomcxao\n7wdd38mrxhxTPTX638kVyeOTi5Om1LsK9fnU5nPTTX0zbepvbCpMCYwE+va/aWD63zQdy9Yj\noG+tR8+6sxLQL2cla7slcP/kgqT+s9hfT16WtIv+19ZYYd4TpBWAFnjxR3Js9Z/RtcvnWy/q\nd93/TnJyUr+J7hnJ1Um73JoX1yTNQKi9rOarvv4/pBvqhUKgJbBS/2s1nTir/02ksWCdAvrW\nOgGtPhMB/XImrDYagfr/Ls9J6jvjL01el3SL/tcV8XpwAvVksJ4a1dOhP0vunEwq52bBLUk9\nlm2X+iGr+vPaleYJrEHg2KxTfbH7W+xqU/pfKSizENC3ZqFqm30EPpVGk37Nt37ZR1Cb1Qg8\nIo3rl23tSo5eYUX9bwUgi5db4KSc3m3JWUnz/x1NOuNnjdr+x06DXxrVH9+p95LAagWmDZD0\nv9Vqat9XQN/qK6XdRgtMGyDplxutPezt3Smnf2lS3y+qj9atVPS/lYQsX1qBA3Jm9d2kGiB9\nOHnnhNw19VXqaVN9VK9+EUP9Pw5PSc4Yva4BlkJgvQLTBkj633p1rT9JQN+aJKN+1gLTBkj6\n5az1h7X9V+d0635vZzLpfu+EFon+18IwOyyB43K69cOyUur34TelPl73vuS7SbPeBzJ/UKIQ\nWK/AtAFSbVv/W6+w9ScJ6FuTZNTPUmDaAKn2q1/OUn9Y2/50Tre5b5s0/d0Oif7XAfGSwEoC\n+6XBEYmB0UpSls9CQP+bhaptloC+pR8sooB+uYhXZTjHpP8N51o7UwIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIDAPxHY85/UqCBAgACBRRN4Wg7omOTCKQf2U1lWf6dfO6FN\nLTsyeWRya3JdMqnMqu2k/alfboG9c3rHJTuSnQt0qj+bY3lY8jcLdEwOhQABAgQIECBAYAWB\ne2X5V5PnTGn3kiy7LTl1QptDUn/xqE21q3wuuW/SLbNq292P18MRuHtOtfrcOxbslI/I8fxD\n8pAFOy6HQ4AAAQIECBAgMEXgrVn2ySnL6535m5NJA6Q9suy8ZFfyvOTgpAZU30wuT+6SNGVW\nbZvtmw5TYFEHSHU13pLUz5dP1JSGQoAAAQIECBBYcIHDc3w18Dl+zHEekLozR8vrXfBJA6ST\nRstOzLRdmqdO7fpZtW3v1/zwBBZ5gPTQXI762fmXw7sszpgAgUkC9W6hQoAAgWUQ+PGcRN2I\nvTt5cVIDiD9PdibHJhckVyVPTX4suTr5YDLu+wf7pP5ZyWFJlc8k70nqqUu7rLTP89O4Ph5X\n+3x4Uvv6QFLfE9o3OTo5Krk+qSdFX07a5c15UcdeH7P7VntB5i9MHpn8aVLH9sbkF5PfTtql\n2tVN4EHJDa0F9X2QMvhsUh5VZtV299b7/VnXsM55vXa1t0OSukYPTC5LPpqMu96p3vbYpL6P\nUk/Yrku+mFT/qcFnU5pjuyAVfftSs24z3S8z25sXE6bfTn17v91mT0zFgcnbk7p2T072Ss5N\nPpZUqXOu767Vxyj/MnlrUgOBtZYfyIrHJ/dPrknqI5rvTer7bN3ygFT8ZHK35CPJRUmZnpX8\ndDKp7J0Fd560sFV/Y2t+0uxqjvfz2chNSfNzMGmb6gkQIECAAAECW0rg3Tna+sjYa5O6EazU\nAOgho/lXZ1o3dVXffCTtlsy/NGmXw/PikqTa7UrqZqzmq64GJO2y0j7PSOMvJbV+7aumdeN9\nn+Tc0evmWL6R17XvpuyfmVrnj5uKzvQP8vopo7pjM61tnzp63UzqhrNuticNCj6dZbX/ajer\nttn0qkpzvdZjVzssizr37yZ/n9SN/HeSX0/abw6W89uS8qu2NXit+coXknsnTWmOrW9fatZr\nT/8uL5rtT5r+TnuFMfNnpa7O6ZVJbaPpQzV/UvLMpM69XT+pH6XZiqX6WQ3Yavs14K9t13x9\nNK36crv897xojqmxfP2obqXvIL141K7Wn5YaeE0rqzne2s6vJbW/GiArBAgQIECAAIGlEajB\nSt0EX5+ckPxM8vikuamtm9+6ET4y2Ss5LqkbveuS5l3rO2W+3k3+evLcZHtSN9PPSmqwtDPZ\nkTSlzz7PTOO6yf7+5E1J3YjVYOjs5DHJPskvJlVf7/I3pZZVXXcA1yxvT48dte0OkO41qj+3\n3bg1/+HR8jq+WbVt7a7XbPt6rdXuGaPz+otM69yq1JObtyRl+oKkKa/KTNXVoOTApMqDknoy\nV/U1oGpK+9hW6kvNOt3pGamoQfy0HN9dqfP6rLyu/nxT8tSkBrdHJzWYb/r0L2S+BhL3S76Y\n1LnUea2lfDkr1WDn0NHKd820XGqbvzWqq8kJSdX9UdL8TD05818b1b8j02mlfjanuTTL6ud0\nWul7vM02npSZOu4XNhWmBAgQIECAAIFlEKjBSt3k/LvOyTQ3tZelvgYj7VI3ubVOtany8qRe\n1zvz3XJKKmrZaa0FK+3z79P2+1rtH5H52kbd2O5o1dcg7ObkM626GhhV2/qY1Erl2DSotqd2\nGh48qq+b/XGlGQQckoWzajtuv9Pqmuu1Hrsa5JbHEZ0d3SWvv5lcmZR5lRoYnZM0N/RVV6XW\nrW28vV6MSnNsl+X1Sn2pWWcW07Oy0Tq2f9vZ+HtG9a/u1P/KqL6eLK227JsV6snbR5PGLLO3\n9+tXZPr0ejEqdc2uSroDmJNTV8e70gApTdZdVnO8zc7un5k6vtc0FaYECAxboN4dVQgQILBM\nAhdOOJm/Sn0NQtrlstGLHaPpQ0fTN4+m7cmZoxc1yOmWSfusj/TVO/pNuWg084VM64lUU+rm\n7Opkv6Yi0x8dzddN51pLfSyqyqS/6/fcvfj2G+BZtR3tYtWTtdrVU5MHJpck9RHFGtQ0qRvh\nTyY/kNw7qfLvk6OTGjhVOTA5KjmmXqR0B05V16cvVbtZlzqOdmn61yfalZn/yuh1u391mkx8\nWf3iY8kTkvOTehPhQUn1699M3pdUOSD5waQGm93vy701dZtV+h5v+3iuyIv6GXxwu9I8AQLD\nFdhruKfuzAkQWFKBSyecV72z3S3dQUHdWNeN0rhByTWprxu/etLSLZP2eXmnYb0TX+WG3ZM7\n/NksayoPHc3UzdtaS51znc89Jmygqb8xyyuzaDth1ytWr9WunoZVqelnbp8b/0ddx51JDR5/\nPnlhclhSN/pV6qOaVdpPTXbX7H5K0sw3025fauq70zem4p7dys7rP8/rP+zUjXvZ16jbt8Zt\na1rd8Vn4J8mTkkcn/zWpPv+m5DeSeuOh7KqUabfUz04NqFYqNVCtAetK5Tlp8PUpjfocb3v1\nOrZrk+Znrr3MPAECAxQwQBrgRXfKBJZcoPuUqDnd+s7GSqW+G1Q3xHdK6ulDu+yTF/XxneZG\nuL1s0j4n1bfXnTTfHG89EanBy1pKfSerbk6bgVB3G1VfT05qwFY30bNom82uqazVrrk+H8he\nXzNlz58dLXttpicl9b2VtyX1hKkGVlcmzZOXzN6hNNfmDpU9Xxyedt1fbNBd9a+7FRNer9Vo\nwuYmVle/+PHkAcnTk6clT0xOS45Mnpp8Lalyl92TO/xZP1M1EF2p1MDxUSs1yvLmyeekpn2O\nt71uHVs9Ra6ff4UAAQK3f1EZAwECBAjsFqiPZT05OTT5+O6qf/zzn2eubvQu/8ea2c40N+e1\n3/Xs8+KsXx8ZOzD5atKUuhl9UHJB0jxhmFXbZp+bMf1SdlJPwup8Pzxmh3UDXud7U3KvpAZH\nf5s8IvlW0pTHjmZWuhlv2ved1sf9tlKpAU8N6q5NvpB8MfndpJ601UCynvrcOynD8qv+2i0/\nnIq9u5VjXr85dZX1lL7HWwPgptTx7Zs0P3NNvSkBAgMV6POOzkBpnDYBAgMUeOfonF+RaQ2G\n2uWXRy/+rF05w/l6olHlgbsna/7z97NmfVrgxZ0t/KtR/e+16mfVtrWLmc/WTfo5yRHJT3b2\n9qN5fV7yhqQGUf8sqXJ10h4c1bWvgVOVPjf2u1su55/1UcT/k5zZOb16YlQD9xps1lO7mn4s\neUry8KRdTm6/mPF83+NtH0YzqGt+5trLzBMgMECBvQZ4zk6ZAAECkwTqY1k1AHpm8u6kbqTr\n41QvSKrudcmbks0o78tOTk+am7e17rMGfRcnv5nsl/xF8sSkBoF1ru3f0jarttnNtvcnT02e\nlpTzLMvLsvH6mNo7kt9Kzk8OT16a1BOhGhzeklyU1JORJyVnJO9Nfih5blJPRurGf9LHE7No\nS5dH5+gvSD6eHDnlTOop0blJGVX/qD5Tg8l/kTwmOSu5LqlSg/BPJB9MXpnU07zjkhclNYDa\njLKa422Op3kTon7mFAIECBAgQIDA0gjUgKaeCuzonNFDRvW/36mvl68eLXt8a1k9Maj6r4+W\n1TbrRu83kj2SdlntPutNqdreh9obGc1flmn7Heza15VJ3cSuVI5Ng9ruqRMa1sfN6uavBnvV\nrlKDlIOSbplV2/dnR7XfGiRNK5Ou12rsavs1sDwvqRvz5pyvyPwLknY5Ki8uSZo2t2a+ruv9\nRtNavz5CVmXSsdWycX2p6mdRzspG63gP6Gy8BnlVX+fULi/Mi6p/fquyBkhV16d/1X7ekpRN\nrVPZlbw26T5he0TqPpzcnFS7q5InJDclNWDdjLKa463jeWNSA+a71wuFAAECBAgQIEBgvEAN\nUO6f3Hf84k2pPSV7qZvMuunciFJPkI5Ixg2MygfMjwAAAoZJREFUutufRdvPZSf1MbfNLHfO\nzh6W/HBST4/Gle2pvF9SA6B9k6GUZ+dE/3QVJ3vXtK3rd0hSPx/Tyv5ZWO3mWfoc7/fnAOuJ\n2P+Y54HaNwECBAgQIECAQD+Benf+i0n7Y3D91ly8VvWUrr7rU4MRZf4C++QQzk5+Yf6HMtcj\nqCfDNyT15FQhQIAAAQIECBDYAgLPyDHWx7wesAWOddoh/ocs3OynR9OOZ+jLfjAA9bHAlZ4E\nLbNTPSW9PqkntQoBAgQIECBAgMAWEjgnx/q6LXS8DpXAVhCoQXs9oe1+j2orHLtjJECAAAEC\nBAgMWqA+/vPQQQs4eQIbL1C/va6epCkECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQGAJBP4/lKfBNOyGMToAAAAASUVORK5CYII=", "text/plain": [ "Plot with title “Histogram of rnorm(1000, mean = m, sd = s)”" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "# Just to visualize what we are saying\n", "hist(rnorm(1000, mean = m, sd = s))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: Now, generate 1000 random numbers from a gaussian distribution with mean = 1 and sd = 0.1. And plot the distribution of these numbers using ggplot, using geom_histogram and overlaying a density curve using the function geom_density (You may visit this page to see how to do this ). Do you guys see anything weird in your plot?
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we said in the lectures that the student´s t-distribution looks like a gaussian distribution but heavier tails. Let's see this by generating 1000 random numbers under both distributions and plotting their density curves together, using the geom_density function we´ve just learned." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Practice: Generate 1000 random numbers from a gaussian distribution with mean = 0 and sd = 1. Then generate 1000 random numbers from a t-distribution using the function rt with df = 15
" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.2.2" } }, "nbformat": 4, "nbformat_minor": 5 }