{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "46e329ab",
   "metadata": {},
   "source": [
    "# Multiple testing inflates the chances of false positives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12c2f106",
   "metadata": {},
   "source": [
    "In neuroimaging, it is very common to test many variables simultaneously (e.g. the brain activity in different voxels), which results in a multiple testing problem.\n",
    "\n",
    "Let's say that we have one variable, \"var1\", whose mean we know is not significantly different from zero because we are simulating it as such. Assuming $\\alpha=0.05$, we would expect to observe, on average, 5% false positives if we tested its mean multiple times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8357e495",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.04"
      ],
      "text/latex": [
       "0.04"
      ],
      "text/markdown": [
       "0.04"
      ],
      "text/plain": [
       "[1] 0.04"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1234)\n",
    "\n",
    "n.trials<-100\n",
    "alpha<-0.05\n",
    "\n",
    "is.sig<-c()\n",
    "for(itrial in c(1:n.trials)){\n",
    "    var1<-rnorm(20)\n",
    "    pv<-t.test(var1)$p.value\n",
    "    is.sig<-c(is.sig, pv<alpha)\n",
    "}\n",
    "\n",
    "fp.prop <- sum(is.sig)/n.trials\n",
    "fp.prop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b09085",
   "metadata": {},
   "source": [
    "Let's say we don't have one variable but two, i.e. \"var1\" and \"var2\", both with means that are not significantly different from zero because we are simulating them in that way. If we test them simultaneously and assuming $\\alpha=0.05$, let's see how many false positives we expect on average:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b0498ee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.07"
      ],
      "text/latex": [
       "0.07"
      ],
      "text/markdown": [
       "0.07"
      ],
      "text/plain": [
       "[1] 0.07"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1234)\n",
    "\n",
    "n.trials<-100\n",
    "alpha<-0.05\n",
    "\n",
    "is.sig<-c()\n",
    "for(itrial in c(1:n.trials)){\n",
    "    var1<-rnorm(20)\n",
    "    var2<-rnorm(20)\n",
    "    \n",
    "    pv.1<-t.test(var1)$p.value\n",
    "    pv.2<-t.test(var2)$p.value\n",
    "    is.sig<-c(is.sig, (pv.1<alpha | pv.2<alpha))\n",
    "}\n",
    "\n",
    "fp.prop <- sum(is.sig)/n.trials\n",
    "fp.prop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb140008",
   "metadata": {},
   "source": [
    "**Our likelihood of getting a false positive is now above the threshold $\\alpha=0.05$!**\n",
    "\n",
    "Let's see what happens if we have even more variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c16b158f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.15"
      ],
      "text/latex": [
       "0.15"
      ],
      "text/markdown": [
       "0.15"
      ],
      "text/plain": [
       "[1] 0.15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Three variables\n",
    "set.seed(1234)\n",
    "\n",
    "n.trials<-100\n",
    "alpha<-0.05\n",
    "\n",
    "is.sig<-c()\n",
    "for(itrial in c(1:n.trials)){\n",
    "    var1<-rnorm(20)\n",
    "    var2<-rnorm(20)\n",
    "    var3<-rnorm(20)\n",
    "\n",
    "    pv.1<-t.test(var1)$p.value\n",
    "    pv.2<-t.test(var2)$p.value\n",
    "    pv.3<-t.test(var3)$p.value\n",
    "\n",
    "    is.sig<-c(is.sig, (pv.1<alpha | pv.2<alpha | pv.3<alpha))\n",
    "}\n",
    "\n",
    "fp.prop <- sum(is.sig)/n.trials\n",
    "fp.prop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "37a0a66e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.17"
      ],
      "text/latex": [
       "0.17"
      ],
      "text/markdown": [
       "0.17"
      ],
      "text/plain": [
       "[1] 0.17"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Four variables\n",
    "\n",
    "set.seed(1234)\n",
    "\n",
    "n.trials<-100\n",
    "alpha<-0.05\n",
    "\n",
    "is.sig<-c()\n",
    "for(itrial in c(1:n.trials)){\n",
    "    var1<-rnorm(20)\n",
    "    var2<-rnorm(20)\n",
    "    var3<-rnorm(20)\n",
    "    var4<-rnorm(20)\n",
    "\n",
    "    \n",
    "    pv.1<-t.test(var1)$p.value\n",
    "    pv.2<-t.test(var2)$p.value\n",
    "    pv.3<-t.test(var3)$p.value\n",
    "    pv.4<-t.test(var4)$p.value\n",
    "\n",
    "    is.sig<-c(is.sig, (pv.1<alpha | pv.2<alpha | pv.3<alpha | pv.4<alpha))\n",
    "}\n",
    "\n",
    "fp.prop <- sum(is.sig)/n.trials\n",
    "fp.prop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9ae0546",
   "metadata": {},
   "source": [
    "**Takeway**: If we increase the number of hypothesis tests, we increase the chances of getting false positives!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87f95da4",
   "metadata": {},
   "source": [
    "# We need to choose an appropriate significance threshold\n",
    "\n",
    "If we perform $m$ indepndent tests, the probability of claiming at least **one** false positive is the following\n",
    "\n",
    "$$P(\\mbox{at least one test is False} | H_0) = 1- (1-\\alpha)^m , $$\n",
    "\n",
    "where $\\alpha$ is the type I error rate used to reject or not the null hypothesis in one particular test, and $m$ is the number of statistical tests performed.\n",
    "\n",
    "$P(\\mbox{at least one test is False} | H_0)$ is also known as the **family-wise error rate** (FWER)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0286da53",
   "metadata": {},
   "outputs": [],
   "source": [
    "compute.fwer<-function(alpha, m)\n",
    "    return(1 - (1-alpha)^m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f2b3193",
   "metadata": {},
   "source": [
    "Let's see what happens when we increase the number of tests $m$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aa80ff2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.2 ──\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.4.0      \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 1.0.1 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.1.8      \u001b[32m✔\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.10\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtidyr  \u001b[39m 1.2.1      \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.5.0 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mreadr  \u001b[39m 2.1.3      \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.5.2 \n",
      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n"
     ]
    },
    {
     "data": {
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/zypk2bWrZsecUVV+Tk5OzGiyQmJlZc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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 900
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "alpha<-0.05\n",
    "m<-c(1:100)\n",
    "fwer<-sapply(m, function(x) compute.fwer(alpha, x))\n",
    "fwer.m05.df<-data.frame(fwer=fwer, alpha=alpha, m=m)\n",
    "\n",
    "options(repr.plot.width=15, repr.plot.height=10)\n",
    "\n",
    "ggplot(data = fwer.m05.df, mapping = aes(y=fwer, x=m)) + geom_point() + \n",
    "                geom_line() + \n",
    "            geom_hline(yintercept=0.05, color='darkgrey', linetype='dashed', linewidth=1.5) + \n",
    "            scale_x_log10() + theme_bw(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f416d7bf",
   "metadata": {},
   "source": [
    "As we increase the number of test, so clearly does fwer.\n",
    "\n",
    "Let's see what happens when we consider a different value of $\\alpha$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cdfaebb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0qSwtPVZjmHbjlPPCZ/9PIMFW2mBEwe\nxSgAAABwVEaK2dKT1sZ8/Nps6d4zWC7veXCwVrSjJcvnpLEhpy/OZaeloS4N9ZMQFmAPxSgA\nAABwhEZK+catufa+MeyntNvM1vzhlVk+d2JiARwGxSgAAABwhL5xa35wzxjmv/TM1NflmM6c\nf3xaGycsFsBhUIwCAAAAY/DIlnz91jz6VBrr0zd0uGc11ed15+eKMyYyGcBYKEYBAACAw/X4\ntnzoexkqJsngyKHnP/fYPOfYNNTn5GMyu32i0wGMgWIUAAAAeDalcm5cnQefTLmcddv2tKKH\n46ylefulabFkHpiSFKMAAADAQZVK+fAP8uCThzt/Rmt+5/kZHM6yOfZWAqY0xSgAAACwv6Fi\nNmzPUDGrN42hFe1szTsvy6mLJjIZwDhRjAIAAAD7uPPxfPGmdPUnSaFw6PmvPCcdLZndnjOX\npLVpotMBjA/FKAAAALDXxq586qcZenpjpXL5EPMvOTmvPW+iQwGMP8UoAAAA1Lrd2yvdtyHD\nxXTv2tuKHsyJC7JkdpoacubSnLV0UiICjDfFKAAAANS0cjkf/VHueeJw53c059++OLPbJzIT\nwMRTjAIAAECNKpZSTm5++NCtaFtz2hpTKufkhXnNuVpRYDpQjAIAAEDNeXxb/vnnWbMl5aTt\nMLZLev15edGpEx8LYBIpRgEAAKC2bOvN//pe+odSTgpJ78AocwqFPdsuNdTlijO1osA0pBgF\nAACAmjA4nI1daWnM9+9O/1CSFA4++cwleemZGRzJinkWzgPTk2IUAAAApr8f3JNv3Z7BkSRp\nqD/E5NbGvOV5WdA5CbkAKkYxCgAAANPczWvy1V/ufTpSHGXOzLbMaMnQSE5YkN94jlYUmP4U\nowAAADA9bevNlu7M6ch37zr05JedlSvPnPhMAFOGYhQAAACmm/6hfO6G3PbYnqeFZ7mZaJLk\nucfmpWdMcCaAKUYxCgAAANPNF27c24ome/aX389zj83i2SmXc/LCnLV0spIBTBmKUQAAAJgm\n+oeyayil5FePHmJmY31e9ZwsnzspsQCmJMUoAAAAVL2NXfniTVm9KUlamw4xubUpb3meVhSo\ndYpRAAAAqG59g/nrH2Zb756nu4ZGn/a7F6elMU0NOfmYdLRMWjqAKUoxCgAAANVt1UN7W9GD\nWTwrF5+UxvpJCQRQDRSjAAAAUH3Wb89378r67ZnRkpHiISYvnZ13vlgrCrAPxSgAAABUmTWb\n87++v6cPffIgc1oa80dXZXNX5nTkhPmpq5vEfADVQDEKAAAAVeYLNx36KtGLT8pxc3OcHZYA\nDkIxCgAAAFWgZyCrN2VwJMd0ZsOOUSbUF1Is73l8+uL85vmTmQ6g+ihGAQAAYKq7eU2+dHN2\nDT/bnEtPzbK52TWU4+bl1EWTlQygailGAQAAYEpbvz1fuDHDh1o7f94KfSjAGLj3MgAAAExp\nN67e24o+vVY+hX3nvOhUrSjA2LhiFAAAAKacR7bk+geztScLOrO9f+/4M31ooS4vOS3rt2VG\na847LucfX4mUANVMMQoAAABTyw2r87kb9jx+aNPocxbMyG9dNGmJAKYhS+kBAABgCukZyJdu\nOfS0V66c+CgA05piFAAAAKaQNZszNDLK+Oz2PQ+aG/PGC/L8EyczFMA0ZCk9AAAAVNgDG/Pd\nu/LEjsxqy5JZo8/5vYuzoDMDw1k8K00+zQMcNf8rBQAAgEq68/F87Md7HnfvyuPbRpnTWJ/j\n56ejZTJzAUxzltIDAABAxZTL+eJNh572mxdoRQHGmStGAQAAoGK296Wrf5TxC45P70C29mb+\njFx+es5ZPunJAKY7xSgAAABMqvXbc80dWb897c05ffHoc5bPzSvOntxYADVGMQoAAACT59Gn\n8j++m5Hi3qcpJOX9p521dJJzAdQc9xgFAACAyfPFm/a2onuUU1/YZ+A1z82yOZOYCaAmuWIU\nAAAAJslQMetG23T+eSdlVmue2JGZbbnw+Jy6aNKTAdQexSgAAABMoMHhrFqd9dszoyXnLE+h\nkPIBC+dbG/Pa8yoRDqCGKUYBAABgomzvy3/7dnb07Xn6/bvTUH/AUvrkTHcUBZh07jEKAAAA\nE+ULN+5tRXcbKaZ+38/il5xsqyWACnDFKAAAAEyIoZHcu2GU8Zecnoa6rNuW9uace1zOWzHp\nyQBQjAIAAMD4GinmqZ7Mac9waZTbiSYpJK8/f9JjAbAvxSgAAACMj6Fivv6rXPdAiqUUkvOO\nT0tjBob3n3bsvEqEA2BfilEAAAAYH1/5RX76wJ7H5eRXa0eZc/LCXHD8ZIYCYHSKUQAAABgH\nO/tz/YOjjL/6ObnriazfnhnNOXdFXv3c1BUmPRwAB1CMAgAAwDjY3D36HUU72/Knr5r0NAAc\nimIUAAAAjlD3rty/MT0DWTYnna2jzznYOACVpRgFAACAI3H7uvzDqvQP7Xm6cFYKhf0vGp3T\nntMXT340AA6trtIBAAAAoPps7c1nfra3FU2yqSt1yay2vSOz2vLOy9LSOPnpADg0V4wCAADA\nmN36aAaG9x8sF/KXr8vqTdm8M3M6ctZSrSjA1KUYBQAAgDHrGRhlsFTK4HBWLp/0NACMnWIU\nAAAADsv9G/PYU2lpzGmLM69jlAmtTZlpqyWAKqEYBQAAgEMYKebj1+aeJ/Y8rS+ks22UaVev\nTJ29PACqhGIUAAAADuGbd+xtRZMUy9nRl5OOSaGQ1ZuSpLkhrzgnV55ZqYAAjJliFAAAAA7h\nlodHGVw8O793cXoH07MrCzpT71pRgKqiGAUAAIBD6BscZbB3IEk6mtPRPMlxABgH/p4FAAAA\n+yuV8vi2PLAxO3clyZzRtlpaPGuSQwEwnlwxCgAAAPt49Kl8ZlWe7EqSukJOXZStvfvPmdmW\nl5w++dEAGDeuGAUAAIC9egfz8Wv3tKJJSuXcvzHl5IozMqd9z+DJC/P+l6WztVIZARgHrhgF\nAACAvX7+SLr69x+sT37zgrz5ouzclaaGtDZWIhkA48oVowAAALDX9gNWzScZKu7Zamlmq1YU\nYJpQjAIAAMBes9pGGWyqt/U8wHRjKT0AAAA17dGn8uP78lRP5nbkhaeMso4+yaWnpqF+0pMB\nMJEUowAAANSuX67Np3665/EjW/LLtUkyoyV1hezctWf8whPy+vMrEw+AiaMYBQAAoEYNDucL\nN+0/WEje//IsnJm1W9I7kKVzsnBmJcIBMMEUowAAANSox7Zl19D+g+Xkya4sn5NTF1UiEwCT\nxeZLAAAA1Khy+WAHJjUGABWhGAUAAKC2PFN7LpubhgM+FjfU5cRjJjcQAJVgKT0AAAC14ueP\n5Lt35cmd6WzJeSuyZWdGSvvPefVzM7ejEuEAmFyKUQAAAGrCqofy+Rv3PO7qz7X3Jcnpi3PF\nmVn1ULZ0Z25HXnRqVi6vYEYAJo9iFAAAgOlvpJSv/nKU8cvPyDnLcs6ySQ8EQKW5xygAAADT\n39ae9B+wAX2SJ7ZPehQApgbFKAAAANNfc+PYxgGY9hSjAAAATH8zWtLRvP9gU71F9AC1yz1G\nAQAAmIbufDzfvzubuzOrLResyD1PpHcwdXUpPb0NfUNd3nxRFnRWNCUAlaMYBQAAYLq5YXU+\nd8Oex9278vi2JDlzaX7/Bbn10WzsyszWXHB8lsyuYEYAKkwxCgAAwLQyVMw//3yU8Vc/J3Pa\n89IzJz0QAFOSe4wCAAAwrTzZlYHhUcYf2zrpUQCYwhSjAAAATCsNB/mk21A/uTkAmNoUowAA\nAEwrC2elrWn/wcb6nL6kEmkAmKrcY3RSDQ8PJ9mxY0dzc3Ols4yD/v7+/v7+SqcAJsPAwMDA\nwEClUwCTp6enp6enp9IpgMnQ19fX19dX6RRHq3ew7t4nm7oH6uZ3FM9YNPT1Ozv6h5pTSMp7\n51x1em8GBrb6jYaat2PHjkpHOCpDQ0OlUqnSKZgmFKOTqq6uLklzc3NLS0ulsxy54eHhYrGY\npKGhoaHBPyGY/gYGBurr6xsbGysdBJhwg4OD5XI5SWNjY329FacwzZVKpaGhoWnwW/19G+u/\n8POWgeHC7qdNDeWhkcKxc0tveO7A7esbNnfXzW4rX7hiZPmcJFX8QQyORrlcHhwc3P24ubm5\nUChUNs/RqK+vr+r8TCnV/fOv6uz+gNHW1tbR0VHpLEeuu7t7dzHa1NTU1tZW6TjAhBsYGGhs\nbKzq/3EBh2loaGh3MdrS0jI9FrgAz2JkZGRoaKi5ubm1tbXSWY5cz0D+6Zf7bLU0NFJoa8of\nX1XX0th22vJnhv2Jl5pWKpWeKUbb2tqq+s+filHGkXuMAgAAUK3ueSJ9g/sP9g+le1cl0gBQ\nVRSjAAAAVKsDW9Hd+ocmNwcAVUgxCgAAQLVaPGuUwfq6HNM56VEAqDaKUQAAAKrVzv4ceLPB\nq85Ja1Ml0gBQVWy+BAAAQHUYHM4P783Dm5PktMWpK+Rff5XGhpx8TB7cmJFS2prysrPzirMq\nHRSAaqAYBQAAoAoMDOf/+1Y27dzz9L4NSdLZmvddmeVzUyqleyCz2ioYEIAqYyk9AAAAVeBb\nt+9tRZ9x/oosn5skdXVaUQDGRjEKAABAFbh/4yiD67ZNeg4ApgvFKAAAAFWgXD7cQQA4HIpR\nAAAAqsCK+aMMnrxw0nMAMF0oRgEAAJjqdvZnzZb9B4/pzNUrK5EGgGnBrvQAAABMOY9tzS1r\n0tWfhbOycmk+/bNs6c4lp6SlPqs3p1DIqYty1Tlpaax0UACqlmIUAACAqeW6B/JPN+99+p07\nUk5ecXZef37lMgEw7VhKDwAAwBTyVE+++ot9RsrJjJa8TisKwLhSjAIAADCF3LchQ8X9B3sG\nsqmrEmkAmL4UowAAAEwhIwe0orsNH2QcAI6MYhQAAIApZMX8UQZbG7No1qRHAWBaU4wCAAAw\nhWzpTgr7D775ojTWVyINANOXXekBAACopL7BPNWTuR2Z0ZLrH8w/3py2xlx0Qh7alB19WTQr\nLz87zz220ikBmHYUowAAAFTG4HC+/PPc+HDK5SRZPCsbu9LZmvddmeVzKx0OgOlOMQoAAEBl\n/NMtuenhvU83dqWhLu9/WZbNqVwmAGqGe4wCAABQAdv79mlFdxsppW+wEmkAqD2KUQAAACrg\nqZ7Rxzd3T24OAGqVYhQAAIAK6GwZfXxm6+TmAKBWKUYBAACogIUz03lAB7qgM6cvrkQaAGqP\nYhQAAIDJVirnH25I9640/dqWwPNn5N++eJ8RAJg4fuAAAAAw4crJuq15qidzO7J8bj53Q25Z\nk+Vz876X5Ynt2bwzczty2uI01lc6KAA1QzEKAADAxNrZn0/+NKs37Xna3py+wRw3L+9/Wdqb\nc/piy+cBqABL6QEAAJhYf/+zva1okr7BNNXnD16a9ubKZQKg5ilGAQAAmEAbu3L/xv0Hh4rZ\nsKMSaQDgaYpRAAAAJtCOvrGNA8DkUIwCAAAwgeZ2jG0cACaHYhQAAIAJNG9GZrbtP3jCgpx8\nTCXSAMDTFKMAAABMlJFSPnlddvbvs8/SqYvyzstS5/MoABXVUOkAAAAATCvlcoZG0tyYYimf\nui53rMtJx+R9V6ZnIJu7M7cjC2dWOiIAKEYBAAAYLz0D+eov86tHMzSSuR1pb87j23LSMfnD\nK9PcmObGzJtR6YgA8DTFKAAAAOOgVMrHr82azXuebuvNtt4s6MwfXpmWxoomA4DRuKcLAAAA\n4+C2dXtb0Wf0DqSxvhJpAOBQFKMAAACMgw07RhnsH8qOvkmPAgCHQTEKAADAOGhtGmWwcJBx\nAKg4xSgAAADjYOXy1Bf2HzxjadqbK5EGAA5FMQoAAMDRKic/vCfFcn69Gl3QmbdeUrFIAPDs\n7EoPAADAUSknX7ol1z+YpbPztkvy4KZ078rSOblgRRrsvATAVKUYBQAAYMy2dOfxbWltyvHz\n8927ct39WTgz7395ZrbmuPmVDgcAh0ExCgAAwBiUy/nHm3P9g3ueNtVnqJgFnfmjV2Rma0WT\nAcBYuMcoAAAAY/D9u/e2okmGiikU8rsXZ1Zb5TIBwNgpRgEAABiDn9y//0i5nHufqEQUADgK\nilEAAAAOVznp2jXK+I7+SY8CAEdHMQoAAMDhKiRz20cZn98x6VEA4OgoRgEAAN6xLQcAACAA\nSURBVBiD05fsP9LWlEtPrUQUADgKdqUHAADgcN2xLjc9nIa6lAspFpNk3oy89QWZ64pRAKqN\nYhQAAIDDcv/GfOqnqS/k31+ZZXPyxI60NmbJ7NRbiwhAFVKMAgAAcFDbejNSyvwZefSpfPza\nlMt51+U5dVGSnLKw0uEA4CgoRgEAABjFQ5vyhRuzaWeStDdnpJThkbzjspy9rNLJAGA8KEYB\nAADY35bufPRHGRje87RvMEmuPDPnr6hgKAAYT+4EAwAAwP5+dO/eVvQZa5+qRBQAmBiKUQAA\nAPa3uftwBwGgSilGAQAA2N+MlsMdBIAqpRgFAABgf+cfP8rgC0+Z9BwAMGEUowAAAOxjqJgf\n3pMkdYW9g5ecnMtPr1QiABh/dqUHAABgr2Ipf/uTrN6UlcvzpguyenNGSjlhQZbNqXQyABhX\nilEAAAD2KJfzmVW5e31OW5x/++I01mfBzEpnAoCJoRgFAACoaY9tzf0bUyzlhAW56/H84pGs\nmJ/3XJ7G+konA4CJpBgFAACoXd+4o/EnD+wzsmR2/vDKtDRWKBAATBabLwEAANSoe59s+skD\n+18uc/aydDRXJA4ATCrFKAAAQI2684lRGtA7H5/8IABQAYpRAACAGjUwMspHwv7ByQ8CABWg\nGAUAAKhRCzpGDhxcMnvygwBABShGAQAAatSpC4cK+4401uc151YmDABMMsUoAABALXqqp/CV\n22YkWTgzhUKSLJmd91yeExZUOBgATI799x8EAABg2uvqz0d+VNczWHjtc4df+ZzGoZGMlNLW\nVOlYADCJFKMAAAC1ZddQ/uZH2dZbePFJ/S85tZA0NjVEKQpArVGMAgAATH9PduXx7WlvyrK5\n+eR1eXxbnndC+crT+5P2SkcDgMpQjAIAAExnpVI+d2NuenjP04b6jBSzcnl+7/nF7u6KJgOA\nirL5EgAAwHT2rTv3tqJJRoqpK+T156XOx0EAapufhAAAANPZT+/ff6RUzi/WViIKAEwlilEA\nAIBpa6SY3sFRxnf0T3oUAJhiFKMAAADTVkN9ZraNMj5/xqRHAYApRjEKAAAwnZ173P4jHS25\n5OQKJAGAKcWu9AAAANPWEzvy8zUpFFJXSLGUJAtn5q2XZFZbRkYqHQ4AKkoxCgAAMD1t78tf\n/zC7hvK2F2bl8mzsSmtTFs+0Hz0AJIpRAACAaal3MP/7B9nRlzdckItPSpKTjql0JgCYSvyh\nEAAAYLoZKuZjP86TXXnxaXnZWZVOAwBTkitGAQAApoN7nsidj2fXUJbPy+ons2ZzLjg+b3le\npWMBwFSlGAUAAKh6X7olP7l/z+OfP5IkJx6Tt78whUIFQwHAlGYpPQAAQHW794m9regzOprT\nUF+JNABQJRSjAAAA1e2u9aMM3rsh5fKkRwGA6qEYBQAAqG7DxVEGi6WUFKMAcHCKUQAAgOp2\n3LxRBpfPSb0PfABwcH5OAgAAVLdTF43SgdqPHgCenV3pAQAAqljvQD724xRLOWVRtvWkbygr\n5uXVz82Jx1Q6GQBMbYpRAACAajVUzMeuzaadufKsvPGCSqcBgKpiKT0AAEBVKpfzdz/Nms05\nf0XecH6l0wBAtVGMAgAAVKV//nluX5eTF+btl6ZQqHQaAKg2ltIDAABUh/6hPPhk+gazdHYe\n2Jhr78+iWXnP5Wmsr3QyAKhCilEAAIAqcPf6fHZVegb2jnS25Q+vTHtz5TIBQDVTjAIAAEx1\n2/vy6euza2ifwRPmZ15HhQIBQPVzj1EAAICp7ldr929Fk9yzPsPFSqQBgGlBMQoAADDV7dw1\nyuBIKX2Dkx4FAKYLxSgAAMBUt6BzlMHWxnS2THoUAJguFKMAAABT3QXHp/mAHSJefk7qfKQD\ngCPlpygAAMBU983bMjiSlsY9Txvq88pzctXZFc0EAFXOrvQAAABT2o/uzbX3Z9Gs/JdXZmA4\nPQNZNDPNjYc+EQB4FopRAACAqeuux/PVX6ajJX9wRdqb096cuR2VzgQA04Kl9AAAAFPUY1vz\nqZ+moS5/cMXo+y8BAEdMMQoAADAVbe3N3/woQ8X8mxflhAWVTgMA046l9AAAAFPFAxuzelPK\nyXHz8vVb070rb7ww5x5X6VgAMB0pRgEAACqvnPz99fn5I/sMXnpqrjyzQoEAYLqzlB4AAKDy\nfvbg/q1okqWzKhEFAGqDYhQAAKDyfrl2tMFHJz0HANQMxSgAAEDl9Q8d7iAAMC4UowAAAJW3\ndPZog3MmPQcA1AzFKAAAQOW94OQU9h1pbsxvPKcyYQCgFlTjrvTDm2695qvfXnXnwxt2DNbP\nmLP4pHMvvfp1V6+cX3+oE/u+/6dv/uRdh5jU8uI//eq/P//pZ/0//MCb/88d5dGnLnzd3/zd\n7x0/puwAAAAH6BvMF29KOZk/I9t6k2TF/LzpwiycWelkADB9VV0xOrj6X/7kT7780ECSQmNL\n89DOzY/86nuP/Or6VW/80798yxltR/8GdfW/XrA+unbtQVpRAACA8VAs5ZPXZdPOXHFG3nxR\nhospJ02HvPADADg6VVaM7rzxo3/+5YcGMuPMN7z33a+9YHFbqefRG7/88U9+d82ar/z3jx33\nyf90ceeznN160dv/6ti+UQ/13/mPH/qX+3Zl1gXvfOOvLVbZtnbtziQLXvof/uMVxxxwUuPc\nJUf35QAAAPzTLbl/Y85amjdemCSNKlEAmBRVVYyW137zSzf2JHMuf9+f/fa5LUlSP2PFpe/4\ni45d7/7z67bd/IWvPfT8t51SOOj5dbOPPX20G5pn26q/+v59u1JY+Mr/+L4XLdj7AuW1jzyW\npOmU8y8+5RS/nQAAAOPtO3fmZw9myey887LUHfzDDAAw7qpp86XiHd/9wYYkx73y9btb0ae1\nn/umq09Ksun66+4b+8L38qbvffgTN+9MYdlr3v/Ws/ZZjP/E2rWDSY4/6SStKAAAMN5ufTT/\n9/bMbMsfXpnWpkqnAYAaU03F6Nq77+lLsuA5Kxfvf2jhypULk3Tdeuuasb7qzp/+/RfvG0hh\n0dXv+a1TGvc5NLx27fokc046ac6RZgYAAPh15XL6h5Lksa35zKo01uW9l2dOe6VjAUDtqaKl\n9IOPP745SZYvW3bgwSVLliSb8tS6df05aQxbMPXf+oUv/Ko/mXnZ23/r1P3/Qrtu7SPFpO7E\nxfWr/vlvfnTTXWue7Bpp6jxmxVnPu+K1r37R8R3WuQAAAIetbzBfuzW3rMnQSGa0ZLiY4WLe\n9ZKsmF/pZABQk6qoGN2xbXs5Sef8+c0HHmyeO7c96cv2bduTwy5Gy49943M/2ZHUn/abbzn/\ngLP61q7dkiS3f/Y//XKktGdweMf6e1etv/eGn9zw9j/746tXjBIlSR577LFdu3YdON7b25uk\nWCyOjIwcbsipp1zec8OCUqlU1V8IcPh8v0OtqfZfV2AKKpfzyevq79+45/KKnoEkOWtp+ewl\nxUp9txWLxfgpD7WhVCo987hYLD7zub4aVXV4ppoqKkb7+/uTpKW5ZbSjzc3NSV/6d/Uf/isO\n/PIb31tfTjove8OVo/yNdu3atUlSKrae/LI3vfGl5594THup6/F7Vn39n75265Ztt/79n398\n3sf+w/M6R3vlD37wg/fee++B4ytXrkzS3d3d1jaGy1qnrIGBgYGBgUqnACbD0NDQ0NBQpVMA\nk6e/v3/P717AOFm9pen+jft/enhgY7Zs3dnUUMkP+bt27Rr1qg5guuru7q50hKMyPDz86z0v\nHI0qusdosVRMkoaGUcvcxsbGJCkWD/97Y+uPvnFDb1I4/jdef+4oV37uKs485cwTlx37/Hd9\n+H/+u6vPP3Hh7Bkz5i4740Vv+dP//ceXzU+yfdVnv/6Qb0UAAODQNvWMsqPrSKmwtc9OrwBQ\nGVV0xWhTU1OSHGSVx/DwcHLQ2nQ0a7/3nQeKSdOFr37FAZs5JUnryjf/2co3j3KgMPOit73p\nnFUfv6u45aabHn7rKacc7jsCAAC1qrVx9MtCW5usCQWAyqiiYrS1tTVJBkdfyzk4OJgk7e2H\nu0R9zQ03bUrSfN6lF419A8iZZ59zXO56JFueeGIop+y/aVPy+c9/ftTzPvvZz955552zZ8+e\nN2/emN90yuju7t69oratrW163BMAeHZbt25taWnp6OiodBBgwm3fvn332rQZM2Y0Nx/kZurA\nEXl+W751d4aK+wyesCAnLZtdoUQZGRnp6upqb2/f81kLmL5KpdL27dt3P549e3Z9fRVfq97U\n1FRXV0ULoJnSquhf0px58+uTdG/bNsolo4PbtvUlKcydM+fwXm3tTTc/maT1gheeP+o9Sw+h\nvX13mzo8NHwEZwMAADWmfyiFwj4j8zryby6tUBoAoKquGG04dvni3LK+/MQTG5Jj9zu4YcOG\nJFmw/NjDqznX/eLnTyZpufCF5x14vWeSpPeRm2+6f1NX34LnvekFyw842tXVlSTNc+a6YBIA\nAHh2vYP56I8zOJI3nJ/6+nT1Z/GsnH98mqr4mi0AqHpVVIxm+Tlnz/rK+q4Nd9619beP3Xcl\n+qY77tiUZMbZ56w4rJfqeeD+DUkKp5191kF60ZRXf+9v//7uchbuuuAFv3/8fgefuv229Unq\nTj/9lMJoJwMAAOxWLOVvf5It3bnqnLzs7EqnAQCeVkVL6VN3xosumZdk9TVfuaP/1w/03fYv\n31mTZNnLrzr7sL6g8kOrH06S5aeedtALPmecf9HpdUk2XfuVVTv2PXvHzz77tdXlZMYLrrp0\n5li/CgAAoKb848158Mmce1xee26lowAAv6aaitEUTnnD7z+vI9nyw//5gc/esK6nlJR61t3w\nd3/2oeu2JZ0X/9arjv/16zfXX/fpj3zkIx/5yFfu7N/vhZ58ZE1/kpYTTlhy8Heb99LfuWpR\nXdJ9yyf+7KPfv++pXcWk1L/h9m/8jz/+m5u7kpnPf8fbLjiS+5MCAAC14rt3ZdVDWT43b790\n/3uMAgCVVU1L6ZPMfOG7/3jN5r/85tqHvvWh91zz1y3NGRwYKSdpOfktH/iDizv3mdz18E3X\nX9+VnHbKW9+4cp8rQ7dt3ZYk8+bPf7Y3azr9bR94744P/p8bN637ySf/808+1bD37ernnP//\nfPB9LzzMjZ4AAIBadNtj+cZtmdmW916R5ir77AUA01/V/XCecc7bPvSJs7/9r99ZdcfDG7f3\nF9vmHXfSyhde/YZXnb/wYHcLPUCxq6s3SebNm/fsE+sXv/iPPnrKC7/3rR/dfOfD67f1Fhs6\nFyw/4ZyLLn/Vq15wrF2XAACAg3p8Wz7zszTW5b2XZ057pdMAAAeoumI0SeMx57323ee99pDz\nznrHF695x2gH6i/5r9+65HDfrXXJRa/7dxe9bgz5AACAGjRczA/uzs/XpmdXFszIU70ZGsn/\ne1lWPOtCNQCgUqqxGAUAAJhyPv3T3L5uz+PewSS58IRceHwFEwEAz6aqNl8CAACYku7bsLcV\nfcYDG1MqVyINAHAYFKMAAABH69GnRhns3pWtPZMeBQA4PIpRAACAo9VQP/p4k7uXAcBUpRgF\nAAA4Wmct3fv4mdXzx87NrLZKpAEADoNiFAAA4Gh1NKe1cc/jQpKkrSlvv7RygQCAQ7GuAwAA\n4KgMFfOxa7NrOJedlrpCdu7Kktl58WmZ0VLpZADAwSlGAQAAjlw5+dyqPPpUnn9ifuf5lU4D\nABw2S+kBAACO3DW35xdrc9y8/O4LKh0FABgLxSgAAMARuu2xXHNHZrXlPVek6SAb0wMAU5Ni\nFAAA4Eg8vi2f+Vka6/PeKzLb7vMAUG0UowAAAGO2c1c+9uMMjeRtL8xx8yqdBgAYO5svAQAA\nHK7uXWluSF1dPv7jbO/La87NBcdXOhMAcEQUowAAAIf2i0fyr7/K9r4Ukhkt6R7IeSvyypWV\njgUAHCnFKAAAwCHcvT6fvn7P43LSPZD6urzpghQqGQoAOCruMQoAAHAIX791/5FiKT9bXYko\nAMA4UYwCAAAcwpM7RxvsmvQcAMD4UYwCAAAcQnvTKIMdzZOeAwAYP4pRAACAQ7johMMdBACq\nhc2XAAAADmHX8D5PG+rymnNz8sIKpQEAxoNiFAAA4Nlce39WPZRFs/K687KxKy2NOWNxFs2q\ndCwA4OgoRgEAAA5q9aZ89Rdpb84fXJEFnXnusZUOBACME/cYBQAAGN3W3nziJykn73pJFnRW\nOg0AMK4UowAAAKMYGM5Hf5TegfzWRTl1UaXTAADjTTEKAACwv3I5f3d9NuzIJSfnstMqnQYA\nmACKUQAAgP19/bbc+XhOOia/c3GlowAAE0MxCgAAsI9bH83378rcjrz78jT4zAQA05Rd6QEA\ngFpXTu5Yl7Vb0tiQee35x1vS1Jj3XpEZLZVOBgBMGMUoAABQ00aK+cgP8+CTe0cKyTtfnGVz\nKpcJAJh4loUAAAA17Zo79mlFk5STeh+VAGC689MeAACoab98dLTBtZOeAwCYXIpRAACgpu0a\nOtxBAGA6UYwCAAA1belo9xIddRAAmE4UowAAQE27/PT9R2a25WVnVSIKADCJ7EoPAADUroHh\nfOO2JJnbke19qS/ktMV504WZ0VLpZADABFOMAgAANapczt9dnw078oKT87ZLMlxMXcF+9ABQ\nKxSjAABAjfq/t+fOx3PSMfndi5Oksb7SgQCASeSPoQAAQC267bF8987M7ci7XpIGH4wAoPb4\n+Q8AANSc9dvzmZ+lsT7vekk6WyudBgCoBMUoAABQW3oH84lrMzSSt16S4+ZVOg0AUCGKUQAA\noIaUSvnbn+SpnrzinFx4QqXTAACVoxgFAABqyJd/ngefzJlL85pzKx0FAKgou9IDAADT3Nbe\nbO/Ngs7ctyHXPZCFM/POy1JXqHQsAKCiFKMAAMC0taM//7Aq923Y87RQSEtj3n152poqGgsA\nmAIUowAAwPRUKudT1+XhzXtHyuUsm5PFsyqXCQCYMtxjFAAAmJ4e3rxPK/rM4JbuSqQBAKYY\nxSgAADA9be0Zffypg4z//+zdZ3hUZcLG8XvSeyGhJZRQQu8QQOm9iyKyorgiFnRBcHVdfXXt\numtvIBasKAoINgQpoSPSE3oRQg0tvdeZeT+ACmSAlEnOTPL/XX6YPOfM89zDLhfDzTnnAQAA\nVQrFKAAAAIDKKdDb9niQT8XmAAAADoliFAAAAEDl1Ky2QvxsDIYHG5EGAAA4GIpRAAAAAJVT\nao5yCi4ZaVRD9/Y2JgwAAHA07EoPAAAAoBLKK9C7y5Sdp9uuU51gJWephr8a1ZTJ6GAAAMBB\nUIwCAAAAqGys0qfrdDJF3SLVv4XRaQAAgEPiVnoAAAAAlc2iWG05okY1dGc3o6MAAABHRTEK\nAAAAoFLZfVI/bFegt/7RT26uRqcBAACOimIUAAAAQOVxJk0frJLJpH/0U7CP0WkAAIADoxgF\nAAAAUEnkFmh6tLLzdcf1iqxpdBoAAODYKEYBAAAAVAZWqz5crVOp6t9CPZsanQYAADg8ilEA\nAAAAlcH327XjuCJrakwXo6MAAABnQDEKAAAAwFmZLUrJksWq7ce0KFYhfprUT278LQcAABSD\nm9EBAAAAAKDEsvP17Wat/11mi9xdZbXKzVWT+inA2+hkAADASVCMAgAAAHAyVunjNYo9fuHH\nArMktQpXRKiBoQAAgJPhJhMAAAAATibu3F+t6HlWaU+8UrINCgQAAJwQxSgAAAAAJ3M69fIR\nk2SVzhQZBwAAuBKKUQAAAABOxtfT9rifV8XmAAAAzoxiFAAAAICTaR6mgCIdaL0Q1Qk2Ig0A\nAHBOFKMAAAAAnIzZIpdL/yoT6q+JvWUyGRQIAAA4IXalBwAAAOBMLFZ9uFqp2RrUSnWqKTFT\ntQLUPkIerkYnAwAAToViFAAAAIAzmbtJu0+qZbhu6SwXLhEFAAClxa30AAAAAJzGxsNavkeh\n/prYh1YUAACUCcUoAAAAAOdwPEmfr5enu6YOkN8VNqYHAAAoJopRAAAAAE4gM0/TV6igUBN6\nKJzd5wEAQJlRjAIAAABwdBaLZqxQYoaGt1NUA6PTAACASoFiFAAAAICjm7NZ+0+rVR2N7GB0\nFAAAUFlQjAIAAABwaL8dUvQe1QrU/Wy4BAAA7IdiFAAAAIDjOp6kL36Vp7sm9ZOPh9FpAABA\nJeJmdAAAAAAAuIRVSsqUt7vMFr27XAWFeqAvGy4BAAA7oxgFAAAA4EDWHtD8rcrMlSRvd+UU\naGR7dWLDJQAAYG8UowAAAAAcxZYj+nz9Xz/mFMjdVX2aGxcIAABUXjxjFAAAAICj+GH75SMF\nZq3eb0QUAABQ2VGMAgAAAHAIVulsmo3xM7YGAQAAyohiFAAAAIBDMEm+njbG/bwqPAoAAKgC\nKEYBAAAAOIrrG18+4u6q6xoZEQUAAFR2FKMAAAAAHEWe+ZIf3V31ty5qUN2gNAAAoFJjV3oA\nAAAADmHDIa3ep1qBGttFp1Ll5aFW4QrxMzoWAACopChGAQAAABjveJJmrZeXuyb3V1iQWtc1\nOhAAAKjsuJUeAAAAgMHSc/TuchWYdXdPhQUZnQYAAFQNFKMAAAAAjGSx6P2VSs7SDe3VMcLo\nNAAAoMqgGAUAAABgpG826cAZtaunG9obHQUAAFQlFKMAAAAADPPbIa3Yq1qBureXTCaj0wAA\ngKqEYhQAAACAMY4n6Ytf5eWuSf3k7WF0GgAAUMVQjAIAAAAwQGaepq9QQaEm9FB4sNFpAABA\n1UMxCgAAAKCiWSyasUKJGRrRXp0aGJ0GAABUSRSjAAAAACranE3af1qt6rDhEgAAMIyb0QEA\nAAAAVAnn0nUuXaH+OpKg6L2qFaj7+8iFDZcAAIBBKEYBAAAAlK/MXH2yTjuOX/jRZJKHmyb1\nkw8bLgEAAONwKz0AAACA8nVxKyrJalU1H9UONC4QAAAAxSgAAACAcnUm7ZJW9MJgug6eNSIN\nAADAHyhGAQAAAJSjpMySjQMAAFQMilEAAAAA5SjIx/Z4sG/F5gAAALgUxSgAAACAchQerIbV\nLx+sF6KmtYxIAwAA8Ad2pQcAAABQjrLylJojk2T9YyQiVBP7yJWLNAAAgKEoRgEAAACUF4tV\nH65WcqaGt1OnCJ1NV6ifIkJlMhmdDAAAVHkUowAAAADKy7zN2n1SLcN1Ywe5mFQvxOhAAAAA\nf+D2FQAAAADlYuNhLdutUD9N7CMXLhEFAAAOhmIUAAAAgP2dSNbn6+XprqkD5edpdBoAAIAi\nKEYBAAAA2FlWnqZHq6BQE3ooPNjoNAAAALZQjAIAAACwJ4tVH61WQoaGtlVUA6PTAAAAXAHF\nKAAAAAB7mr9Fu06qZbhu6mh0FAAAgCujGAUAAABgN9uOaukuhfppYm82XAIAAA6NYhQAAACA\nfZxI1sdr5O6qSf3l52V0GgAAgKuiGAUAAABgB1l5em+F8gs1oafqhxidBgAA4FooRgEAAACU\nldWqj1brXLqGtFHnhkanAQAAKAY3owMAAAAAcEoFZsUeV0KGQv0Ul6BdJ9UiTKM6GR0LAACg\neChGK1RhYaGk9PR0X19fo7OUntlsPv8iNzc3Pz/f2DAAKkZ+fn5qaqrRKQCUO4vFcv5FVlZW\nTk6OsWHg4M5muH78q29S1l+3oPl7WcZ2yEhPsxqYCiVitVol5eTk5OXlGZ0FQPk6//v9vPT0\ndJPJiXfHKygouPjjAGXBrfQAAAAASsZi1ayNPhe3opJcTPJwNyoRAABAiXHFaIVyc3OTFBAQ\nEBQUZHSW0ktPTz9/oaiXl5ePj4/RcQCUu8TERA8PDz8/P6ODACh3ycnJ5y8a9fX19fT0NDoO\nHNeRBJ1Ov3wwLcflbHZgqzpGBEKpFBYWpqament7e3t7G50FQPmyWCzJycnnXwcEBLi6uhqb\npyzc3d2d+opXOBSuGAUAAABQMpm2bry2XmEcAADAMVGMAgAAACiZWoE2Bk1XGAcAAHBMFKMA\nAAAASqa6v5qHXT7Yob4iQo1IAwAAUCo8YxQAAABAyZxO1dEEuZgkyWKVi0ndIvW3LkbHAgAA\nKAmKUQAAAAAlkJWnd5Yrp0B391SXRkrMUIif3J14Gw8AAFBFUYwCAAAAKC6rVTPX6Fy6BrVW\nt0iJ54oCAACnxTNGAQAAABTXd9u084Sah+mWTkZHAQAAKBuKUQAAAADFsv2YFu9QiJ/u7yMX\n/iYBAACcHF9nAAAAAFzb6VR9skZurprUT/5eRqcBAAAoM4pRAAAAANfw54ZLf++miFCj0wAA\nANgDxSgAAACAq/lrw6VWFzZcAgAAqAQoRgEAAABczfd/brgUZXQUAAAA+6EYBQAAAHBFMce0\niA2XAABAZcRXGwAAAAC2nU7Vx2y4BAAAKimKUQAAAAA25BRo+grlFOiO69lwCQAAVEIUowAA\nAAAuZ7Xqw1U6naqBrdS9idFpAAAAyoGb0QEAAAAAOISsPK3cq/hU+XkpN187TyiyJhsuAQCA\nSotiFAAAAIDOpuulhcrM/WvEx0OT+8uVe8wAAEAlxdccAAAAAPp07SWtqKTsfCVlGpQGAACg\n/FGMAgAAAFVddr5+P2tjfOeJCo8CAABQUShGAQAAgKquwFyycQAAgEqAYhQAAACo6gK8FeJn\nY7xB9QqPAgAAUFEoRgEAAICqziRd1/jywdZ11L6+EWkAAAAqBLvSAwAAAFXd6VSt2CM3F4UH\nKzFT/l6KaqihbWQyOhgAAED5oRgFAAAAqrSsPL2zXDkFurunukUanQYAAKCicCs9AAAAUHVZ\nrZq5RufSNag1rSgAAKhaKEYBAACAqmvBVu08oRZhuqWT0VEAAAAqFsUoAAAAUEVtO6pfdirE\nTxP7yIW/GQAAgCqGrz8AAABAVXQiWR+vkburJvWTv5fRaQAAACocxSgAAABQ5WTl6b0Vyi/U\nXT0VEWp0GgAAACNQjAIAAABVi8Wqj1brXLqGtFGXhkanAQAAMAjFKAAADEEGRAAAIABJREFU\nAFC1fLtFu06qRZhGseESAACowihGAQAAgCpk42Et3aVQP93fRy4mo9MAAAAYh2IUAAAAqCpO\nJOvz9fJ015SB8mPDJQAAULVRjAIAAABVQlaepkeroFATeqhOsNFpAAAAjEYxCgAAAFR+Fqs+\nXK2EDA1rq6gGRqcBAABwABSjAAAAQOU3d5N2n1TLcN3Y0egoAAAAjsHN6AAAAAAA7C8rTwtj\ndfCMTCYFeGnHCdUM0AN92XAJAADgAopRAAAAoLLJytNzPygx868Rk0n39paPh3GZAAAAHAy3\n0gMAAACVzY8xl7SikqxWbT1iUBoAAACHRDEKAAAAVDYHz9gYPGBrEAAAoMqiGAUAAAAqG5vP\nEeXhogAAABejGAUAAAAqm+ZhNgZbhFd4DgAAAAdGMQoAAABUNm3qXHKBqFUKD9bwtsYFAgAA\ncDzsSg8AAABUKmk5mrlGJqlrI6XlSFKzMA1sKQ+++wMAAFyEL0cAAABA5VFg1rTlSsnW6E4a\nyiWiAAAAV8at9AAAAEDl8dUGxSWoY4SG0IoCAABcFcUoAAAAUEks36N1B1W3mu7pxR70AAAA\n10AxCgAAAFQGB89o3mb5empyf3nyxCwAAIBroRgFAAAAnF5Spt5bIas0qZ+q+xudBgAAwBlQ\njAIAAADOLd+s91YoI1e3dlGz2kanAQAAcBIUowAAAIATs0qfrtXRRF3fWP1bGJ0GAADAeVCM\nAgAAAE5s0Q5tjlOjGhrf3egoAAAAToViFAAAAHBWu0/qh20K9NY/+snN1eg0AAAAToViFAAA\nAHBKZ9L0wSqZTHqgr4J9jE4DAADgbChGAQAAAOeTW6Dp0crO1x3Xq0kto9MAAAA4IYpRAAAA\nwMlYrfpwtU6lqn8L9WxqdBoAAADnRDEKAAAAOJnvt2nHcUXW1JguRkcBAABwWhSjAAAAgDPZ\nfkyLdijET5P7y42v8wAAAKXlZnQAAAAAAFeTb9YvOxVzTJm5CvXX0QS5u2pSP/l7GZ0MAADA\nmVGMAgAAAI7LatW05doTf+HH5CxJGtlBEaEGhgIAAKgMuPcGAAAAcFxbj/7Viv41eMSIKAAA\nAJULxSgAAADguA6dtTEYn6KcggqPAgAAytHWf0WYTCaTydT/49Syz3b05U7nZ+v0+tGyz1Zp\nUYwCAAAAjsvN1cagSXI1VXgUAACAyoViFAAAAHBcrevYGGxaWx5sFgAAAFA2FKMAAACA46oV\nKM9LO1A/T43vblAaAACASoR/aAYAAAAcVIFZ06KVV6hukZKUmad61TSgpfy8jE4GAADg/ChG\nAQAAAEdklT5bpyMJuq6x7u5pdBoAAIBKh1vpAQAAAEe0eIc2Hlb9EN3ZzegoAACgpCzJMfPf\nemzCiOtaRISF+Hu6e/pVq1mvWdcRE/7vgxXH8oo7yx+byzd+PFayJm/74snbe7aoF+rn6ekX\n2qD9wPHPfLk10XLtacznNnzyxB1929Sv7u/lHVi7Yes+tz/58doTBeWe39FxxSgAAADgcHaf\n1PfbFOitKQPYZwkAACeTveuju8f8a87+jIsH81POZaWcO3Fg08+fvfHqLe//8tXdTT1KMGfe\n7g9HDn1w4V9lZtLR2OVHY5fPmv7hMz8tfKZb8JXeaD296KHRd7y7LcX6x8iZI7vPHNm9+usZ\nHz/89Q9vDKlVIfkdE1+yAAAAAMdyOlXvr5Kriyb3V7Cv0WkAAECJHJk5sufE6FRJ8qjZfuCQ\nnq0jQn1MucnH9/y6ZMnm+Fyp4Mi3E8e06BjzbLvi3sqdvmzSsB3bTlhcQtuPmXBb3+ahhadj\nF8/69Of9GdbkX58d0Ct/+caXuvnYeufh10belJBQIFNAkx79Ojer5Z1x5Lfl0bsTC6XUTW+O\nvbvV7kV31Sn3/I6KYhQAAABwIFl5ene5cvJ1Vw81qmF0GgAAUDKpc//92PlWsfYNH6ycM7GZ\n90UHC04ufGjo6Bm78mXe+cFH65+e0bOYzWJCzDbJL+rfP/38vz41LrzngUf+OW/igHGf/16Q\ns+uVB16+Neb51q428iQkyLf1fTPnvn5rc3/T+bHMne/c0v+hJQlS2uKXpsfe9XK78s7vqJw8\nPgAAAFCJWKz6aLXOpmtQa/VoYnQaAABQUmk/ffFjiiT5jXj9s0tbRUnudUa8+b8xgZKks9u2\nxZdk5tBRny565c9WVJI86o/5+IenO3pIMu96/ek5qVd44+gvVn449s9WVJJfm6mfv9TXXZJ0\neN260xWS3yFRjAIAAACOYu4m7TqpluG6pZPRUQAAQCnkNR376ouPT75r7BP/HF3N1gme7do1\nP/8qIyPD1glX0OGRl2+pXmTUtcVDj9/kK0k5S7/7JdvWG5vd/5+bQ4uM1hwypMP5V8eOHauI\n/I6JW+kBAAAAh7DhkJbvUa1A3d9HLlzAAACAM6rR5Y6HulzleN65I6eyzr8sKLjarvCXaXvL\n6EibB/wGD+lhmrvEqpxlS9daxw42XXY8sGfPNrbeFxYebpKsl/eb5ZXfQVGMAgAAAMY7fE6f\nr5eXuyb1k6+n0WkAAIAdWHOTjh06+Pvvh+Pi4g4d2Lt7V+y2mIMJeRe2h7darVd/+0X82rVr\ndKVDLVrU1ZLjUuaxY8lSyGWHa9SseXlXKklycXd3kcyS2Wwu//yOimIUAAAAMFhatmaskNmi\nSX0VHmx0GgAAUDbmxK1fvvXmx3MWb4pLK7TLjCGhoTbrTUkKCgqSjks6e/Zs0WLU39+/xKvZ\nP7+johgFAAAAjFRg1rvRSsnWmM5qW8/oNAAAoGyS1z83cuRz65MvvpzSzT+sccs2HaKu695n\nUKf9j3R+4tcSTurqamPD+Qv+vKXdw8Oj6FGT6YqNqm3lkt9RUYwCAAAAhrFKn63TkQR1baTB\nrY1OAwAAyujMN3fd+Oz6ZEnybTL8vvvGDLi+Y+uWkXUC3P844+jLuSWfNjX1ClvOS0pOTj7/\nolatWiWf+TLllN9RUYwCAAAAhvllhzYeVv0Qje9udBQAAFBmu95/8ackSXJr/+T6X19s5130\nlMTExPMvSvKMzuR9+86pTw1bhxJ27TorSarRqJFfSfNerrzyOyp2uwQAAACMsfukvtumQG9N\nGSAPrlgAAMDppW/YsPf8q94T/2mrVZROrl9/7Pwri8VS/Jk3LV6cbPPAuR9++E2SFDJixPXF\nn8+28svvoChGAQAAAAOcSdP7q+Tqosn9FexrdBoAAGAHuXl5F17l5OTYOiHlpyde33Th9Z/P\nBi2O/CWvvrwlr8hw1ppn/7e8QJJCR43pe+XnkBZT+eV3UBSjAAAAQAXZHKe3l+n5HzVjhd74\nRTn5Gne9Gtm8LQ4AADif6m3aXHjM58YZ/1uVdunBvMPfTh5wx5fxf/ycnZ1dgqnN+16/8ZZ3\nY9P/GrEk/vbSDaPfP2KVFDj01ecG2th6qYTKMb9j4o4dAAAAoCLM3ayluy68PpooSZ0i1KOJ\ngYkAAIB9mXo+8GDbD5/cUSjz7zMGNYsdd8+ozo1reeecO7Z3/fdzFsYmFEhyd3crKCiU0pKS\nCotdzbm7uxecWjg1qvFnI0YP6VDHK+Polp/nL96bYpHkGnbjezPuqu3Q+R2Uc6cHAAAAnMLx\nJC3dJatkumjw8FlZrHIxXfFdAADAubi0fGz+Jzv73zv3WL4Kzmz47MUNn1182BTS9cEP3mn0\nYZep0ZJl27ZY3dKpeBO3eezzG1dNefrXhNjv34/9/qID/u0nf73w7eHhDp7fQXErPQAAAFDu\nDpyRLm1FJaXk6GyarbMBAICzcm389zk7ty946b7hnZvUCvR2d3X3Dgit27zroLFTX/tu56EN\n74zuPGJQR5MkHf5m1obC4s4beP1/1uxZ9/7DN3dpXNPf0907qG6bfnf857MNv2+eNjy8zA8X\nLf/8jokrRgEAAAAAAAC7CWg56okPRz1xpcMN/rXV8q8io51eP2p9/arTutbsdv8b3e5/ozgR\nIh7fan38qmeMnlNonWP7UKnyOyWuGAUAAADKXdNaNgaDfVUzsMKjAAAAQBLFKAAAAFABagbI\nz+vywQk9eMAoAACAYbiVHgAAAChfVqs+WqPMXDWtLW93pWYrLEiDWqtuNaOTAQAAVGEUowAA\nAED5WrBNMccUWVOPDJKbHXdHAAAAQBlwKz0AAABQjrYc0S87FOqnSf1oRQEAABwIxSgAAABQ\nXo4m6pM18nTXlIEK8DY6DQAAAC5in2I09bc5X0TvTym0y2QAAABAZZCarWnLVWDRfb1VJ9jo\nNAAAwPlEPL7VarVardat/4owOktlZJdiNHPhy+PHD2hes1bLmz/YY48JAQAAAOeWb9a0aKVk\n65YotatndBoAAAAUYZdidOeWLXmSCpJOB0dE2mNCAAAAwIlZpU/X6kiCrm+swa2NTgMAAABb\n7FKMpqSknH/RuEULD3tMCAAAADixH7Zpc5wa19T47kZHAQAAwBXYpRht2br1+XmOHjyYb48J\nAQAAAGe19Yh+jlWInyazDT0AAIADs0sxGjHxf5Mj3SUlfP7o/61LtseUAAAAgBM6lqSP18rD\nXVMGsA09AACAQ3OzyyyB/d7esLr+/eOfWhD7Zt9ma0bfOaZ/t85tG9UOCQrwdjdd4U1etWoF\n2WV1AAAAwBGkZevd5Sowa3I/1a1mdBoAAABclV2K0ZWPdfr3Ckle1XyVnZWwbc7r2+a8fs13\n3Wy1zrfH6gAAAIDx8s16N1opWRrdSe3rG50GAAAA12KXYjT58LZt2+wxEQAAAOCMrNJn63Qk\nQVENNKSt0WkAAABQDHYpRgPrtWzZssTvqmePpQEAAADj/RSjTYcVEaq7e+pKT5ICAACAQ7FL\nMTrgzd277TEPAAAA4Hy2HdVP2xXkowcHyMM+z/AHAABAubPLrvQAAABAFXU8SR+vkburHuyv\nYB+j0wAAAKDYKEYBAACAUkrL0bvLlV+oCT3VoLrRaQAAAFAS5Xarj7UgKzU5OSVd1RrUDeKG\nIgAAAFQSp1O1J165BQqvpsU7lJylmzqoc0OjYwEAAKCE7F1ZFiZsnTtjxuxFq36NOZpeKKnL\na0c2/itCOvjfniNWNrn74ccnDW3sa+dFAQAAgAqxZJe+26pCy18jHSI0vL1xgQAAAFBa9ryV\nPnvvrPFtG0SNe/azX7acb0UvcuT3mIMrPnlsWKu2t87clWPHVQEAAIAKceis5m2+pBWVFOTN\nNvQAAABOyW7FaP7ed4def+cXe7P+mNjlkqkTjxzJlCTlHZ57X7+/fXHEXusCAAAAFWNTnI3B\nzbYGAQAA4PjsVIwWbnv65ofXpElyC+s19aOl24+lzL7p4hNCx3+1buaU7rVcJClh4YP/+OKM\nfVYGAAAAKkZWno3B7HxZKzwJAAAAys4+xWjCV8+8s98suTa5b+HO1W/fO7B9vYDLnl7qVaf7\nPe+s2f7dXY1dJGUseeOjvXZZGgAAAKgYtYNsD3IrPQAAcEh5hxe9cvegdvWq+Xh4BdRq2HHE\npDeXHy8otxlKu1z22kmNXExB90SXJJld2KUYzVg0f1mupFp3Tn97cMjVVqs98t23b6suSbuW\nLbPH0gAAAEAF6d5Ebq6XD97cyYgoAAAA15C9+fne7YY//umyHSfSLB5uueeObP95xiMD21z/\n9Lr0cpihtMtZTn57753vxxlzB45ddqXfHRNTICl05Nj+3tc612/YuJFBX32cqn37SrtcwZmt\nP81buDb29/iUPFf/amGRHXuNuHlEu+pFvqXalr30mbHvxVzhl7vWzW9/dGdDey4HAACAysBq\n1ewNKjQr0FvpubJaFeKn0Z3Urp7RyQAAAIpImHfX0Gc2Ziqk15OfzPz3iMgAS9KOec/e84/p\nW7e+cNOENvvnjw615wylXC7v8Nf3Drnz66NGPZjILsVoYmKiJNWtV684txHVr19fSlV6Mcvp\ny+QdnPOf/3x9IFeSyd3LMz/t7OEtiw9vWb32b0+9eHtLn2LMcCSuBCV02ZcDAABAZTBvi7Yf\nU2RNPTpEZqvyChRwzWsCAAAADGGJfeOpeUlS2IQvf35xiJ8kuYS0vW3a8uD0VkNnxS947OWN\no17verUbyUs0Q6mWyzow99+3TZyxPa0cPn9x2aUY9fHxkfKVkZFRnLMTEhIkKcjWI5quJW39\nO899fSBX/q3GTJk8qnOYjyXjyPqvp72/6NChuf99N+L9x7sFXGuKpLi4NEk1Bv7r0QE1ixx1\nDwm373IAAABwfusOaukuhfprcn+5ucpN8rTL92gAAIByULhs+ocHJbWZ/Pj5mvIPQUOemRI1\n67EtcV99se7Vrr2u3IyWaIYSL5d/4JtH7nvkw7WnC6TAzvcOyps5b0fZP3Up2OUZoxEREZJ0\neM2ak9c817z1x0WnJKl+/RKvY437Yfb6DKla/4efHtclzMckufo36DXxhUf7hkgZG76Yf+Ca\n14Ja4w4fleTRNKpbUxsahnradTkAAAA4u4Nn9OWv8nbX1AHy9zI6DQAAcGbWlGTz9i3mTb9a\nT8WX3yoxq1alSooYODDy8kMNBwxoKOns4sXb7DZDiZdLXv7e9LWnCzwjhj69eOe6//a51l39\n5cYuxWijQYMaSbL+9tazS1KvembejpcffO+wJDXo16+ky5hjFi2JlxQxfHTHS76R+na8dUSk\npDOrV+65VlV5Mi4uT1LDyMhrPSPULssBAADAqZ1J07RoWaVJ/RUebHQaAADgzMzrV+e//lLh\n3C8Lv5ub/84rhfO+krU8qqXsPXuOSFKLFs2LHmzatKkkHd+16ypPuSzRDCVfzuTToM99b0cf\n3L/ouSH1PIrxicqLXYpRdZr44HUekk5+MnbYU9GnC22elHdi8VODBzy1MVeSW8cH7inx/p1x\nO3dlSarRvl3Y5YdqtWtXS1Lq1q2Hrj5HQVzcCUnVIiOrVcRyAAAAcGKZeXpnmbLydPt1alHk\nOyEAAEDxWY4cLlz4nQoL/hwxb9tsXruiHJY6HR9vlRRar56N7XF8wsODJOnUqVN2mqHky9Wc\n8OXKD6f2q+dZ9PyKZadnIzV4YPpTs7s/tSUndcOLAyK/7jtqVF+d7wzTD6ycPyt77+bVPy34\naduZ8//bu7d46O3JkcXZqOliecePn5WkenXrFj0YHh4unVHCsWPZirzKnkjH4g6bJZfGYa5r\nv3l72a87Dp1OLfQIqNmg9XUDRt3Yu6HfX6HsshwAAACcldmiGSt0Nl2DW6t3M6PTAAAAJ2E9\nccy828YTMy0H9hYdLFwVbc3OLjruElbHpW2H0kZIP7/lua+vr62jPj4+57dFv8oVoyWaoezL\nGcZeD4336PCfhXPPDBj73q4sZcWt/PL1lRcO7Pv47ls+vvhM94hbZi58uXvJ9/BMSUq2Sgqo\nXt1GnewZEuIrZSk5KVm6clOZFRd3TpK2f/L45kLLhcGClBO7157YvW7FunuefmxEA0/7LQcA\nAACn9dUG7T+tNnU1OsroKAAAwHlYTsWbV0cX9+ycbNsnt48qQzFaWFgoSR4eNu9S9/T0vOgk\nO8xQ9uUMY8fdNGuOmL5pa/enH3rqg6WHMm2e4V4j6vYn331zStdSPZ0p+3yB7uVp84n3np6e\nUpayc2y07H+Ji4uTJIvZu8ngW/82MKpxTV9L6vFdaxd8NX/ruaStM5+bFvruv64LKPNy48eP\n3717d9Hxdu3aSUpJSbnwfwonl52dnW3rnzUAVD65ubm5ublGpwBQcTIyMjIyMoxOYaSVB33W\nHPAJCywc0yYtOYnnyqMyy8rKysrKMjoFgIqTkpJidIQyyc/Pt1gs1z7POC7NWrrfM6nouHnj\nekuRK0lNoTXcbryl6Mkm/4AyRPD29pak/Px8W0fz8vKkK/aYpZih7MsZxo7FqCTvZre+tmTM\nk/tX/7JszYate48nJKdkFnr4B4fUbti2a89+Qwd3CS/9Pp5mi1mS3NxsZnZ3d5cks/lqvzdy\nzIFNWzU+m1Fj5BOPDqx9Yfcl/5a9b2/RvtHbD/93VULy2k8WjOhyV1MXuywHAAAAZ7T7tOfS\n/T7+XpbxXdI93GhFAQBACZgCA02BgTbGQ6vnHzqo3JzzP1olk+Q2/EaXyKb2juDv7y9JOTk5\nto5euMgt0FbIUs1Q9uUMY99iVJLkEtSs79hmfcfae94LzfIVrrwtKCiQrthjXuDdbuzT7WwF\nMwV2nXBr27XTdpjP/frr73c1bWqX5QAAAOB0Tqa6fbPNz81kHd85PcibfwUHAAD2YQqu5n7X\nxMIF31jPnZXk4uvrOnSkS/NW5bBU7bp13bS1MCE+Pl+6/ELN7Pj4VEmm8PCr7CxZohnKvpxh\n7NLrrfnv335wHzFixNAezaq522NCmy5cl5t31etyfX1L+8TPwDZtI7TjsM6dPJmvph5lW+7Z\nZ5+1WZMvW7YsNjY2ICAgKCiolDkdQFZW1vli2MvLy8ur9NcAA3AWqampHh4ePj48Uhmo/NLT\n08/fm+bj4+OYtzuVt5RsfbnFrdCi+3ubW9fzMzoOUL7MZnNGRoa3t3fleNIXgKuwWCx/bn0T\nEBDg4uJibJ6ycHd3d978LhENPR550pqSrMJCU0ioyuuDeLRqFanv91n37z8oXd68HjhwQJIi\nWrWyuVdSKWYo+3KGsUsxmrB93tsL5r39b9eAxtcPHjHiQkVq72spq4VWd9Uhc3pSUmHR3HlJ\nSVmSTCHVqpV2/j/2zirIL5A8yrZcRESEzfENGzZIcnV1depLTU0m0/kXLi4uTv1BABQfv9+B\nqsbZv66UTm6Bpq9QSrbGdFZUQ1ej4wAVhD/lgarg4odyurq6uro68R9zf5YSzssUXOryqrha\n9utX84V9Zw9ER594sVXdSw7FLVsWJ6la375t7TZD2Zczil2baXP6oXXz3vr3HX2b1wiN7Hnr\nw6/NXrU/2W5bTrnVrxcmyXryZHzRg/Hx8ZJUo179q1zAmHl4w9KF382ds/64raOpqamS5Fkt\nxMc+ywEAAMBpWK36aLVOJKt7Ew1ubXQaAACAMnDtcfutdSVtevuFZekXH0j95blpWyU1f2BS\n36vW4yWaoezLGcUuxeiI6TG/fPrfKbf0iAy68A+N5rRD6+a+9e9xfZvXCI3sdevDr89eeSC5\noIzL1GvbJkhSfOyOxMsPnYmJOSPJv03bBleZwHpw8YyZn8/+etbKuKIHE7ZvOyHJpUWLpib7\nLAcAAACn8c0mxR5Xk1r6ezejowAAAJSRS9cnXhkVLB2bOWbQw3N2J5slc/KuOVMGjp0VL4WO\nfv6h9hd3gvtmTR43bty4cS8sTyvVDCVcznHYJZVnrXaD7/q/d+atPZiYeHj9/OlP3j2sQx3f\n8/WiOe3Q2rlvPTquX7Ma1Zv0uvWR12evOlDKq0hdWvbuESrp4E9zY7IvPpC1bc7PhyTVHTKs\nzdU+kH9U1xYuks5Ez12bcskRa8qaT+YftEr+3Yf1CrTTcgAAAHAOaw8oeo9qBGhyP7nxBQ8A\nADi/GmM/mvdwex+lbXxrbOtQHz8/n9A2Y6dtSZNf5+cXfz469JKTz26eP3v27Nmzlx7IKeUM\nJTrZcdj5e59rYMNuN0968eOft51IOrNz2Rev/PPWPs1Dzm/IZE77fe3cNx8d17dZjepNeo19\nZG6JZzc1HTP+Oj/p3NJXnvlk3bEMi2TJOLbuo6dfW5kkBXS77YaGFz9n4sTKD998880335wb\n+0evGTrwjmG1XaT036Y//c4vexJyzJIlO377d/977O0NqVLg9RMndPYq5XIAAABwRnviNWuD\nfD310ED58ZwkAABQSYT0f+O33YtevWdw+3rV3PPzTIF12gyY8N+FsWueiirmPkglmqHsyxnA\nZLVay3sNS8axTdGLFy9evPiXlTHx2X+sd7PVOr/kk2Xs+PSpF3+Iy5NkcvPyVF5uoVWSV5Pb\nX3rxb5GXfJPd9eHfn1yUKjWf+MUrw4IvDJpPrXzj2ffWnynQZTO4Vou6+9nHhkd4lHa54vjk\nk0/ef//9H3/8MTw8vOSf3VGkp6fn5+dL8vHxYZdqoCpITEz08vLy82N3ZqDyS05OPr85g7+/\nfxXZpfp0ql5aqLxCPTxIzcOMTgNUrMLCwtTUVF9fX29vb6OzAChfFoslOTn5/Ovg4GCn3nxp\n6tSp+/fvX7p0qdFBUBlUwOaD+cmnTpw+l5SWmVNgLnsJ6992wmvT2yz89ue1Mb+fSs42+4RG\nRLbrOWLMDVG1PK79bsk1rO+/32nac/GPyzbE/n4iKdPsFlCjXqO2XfvfcEP3+kU7vrIuBwAA\nAIeVmat3lis7X3d2oxUFAACocsqnGLXmntu3ac2aNWtWr1mz5rc9Z3MuL0TdgyOj2pV2dvea\nnUZN7jTqmue1njjrp4m2DniHd735H11vtvNyAAAAcHBWacPvWrlPSZkK8VV2gc6la1hb9Wpm\ndDIAAABUOPsVo9ac07t/u1CGrt24LyHv8hNc/SM69OjTp2+fvn36dm8X7stj7QEAAFChftyu\nn2IuvE7PkaTwYI3qaGAiAAAAGMYuxej2d2+a+t7azQeT8y8/YvIJb9utT5++ffr06durU0SA\nEz/DAgAAAE4tKfOvVvRPZ9KUnqtAnq8IAABQ9dilGI1b+8P6g3/8YPKq3rRDl65dr7u+e89e\nvbo0qeZujyUAAACAMjmaaGPQbNGxRLWpW+FpAAAAYDS7389u8g9r0rxV2w5RXbpe1zGSVhQA\nAACOwe0K33zduKkJAACgSrJLMdpy5D9G92ga4i5J1vS4X7//6KUpY/u3qR1Uo3nP0Q88PX3u\nqj1nc+2xEAAAAFBKjWvKs8i/2vt5qlF1I9IAAADAaHa5lb75He99e4esWfGx61asWLFixYqV\n62JPZlmVn7h/3YL96xZ88ILkWb15l959+vTu3bt37+taVPe0x7oAAABAcVmt8nJTXsFfI26u\nuquHjbYUAAAAVYH9dqWXyTe8/eC/tx/8939JBUkHNq5auXLlihX9yO11AAAgAElEQVQrVm08\nmFwg5SXsW/vtvrXfznhOJq+aLbr26nP33Gnj7Lc6AAAAcEX5Zr2zXGk56tlUHm5KzFB1f/Vp\nrlqBRicDAACAQez+jNHz3EOa9hj9wDMz5q89kJByYvvSL9968r5RPZufv1DUmnt2z+p5038o\nn6UBAACAS1it+miVDp9TVAPd2U23ddWUARrblVYUAABUbnmHF71y96B29ar5eHgF1GrYccSk\nN5cfL7j2+0o5Q/FPTp85yMV0JY0fjy3xJy0lO14xegUuvnXa9xro4eYqS0FeasKSnYnmcl8T\nAAAA+NM3m7T9mJrU0r29ZDIZnQYAAKAiZG9+vl+/ZzZmSnLx9PXOPXdk+88ztv88+5unFq54\nvkeAvWco0cmxMbFW+3zKsimnK0YlWbNObv/li1cfuWNQ27DgWq363fbP/3226I9W1DUoskfH\nclsaAAAAuGD5HkXvUY0ATerHBvQAAKCqSJh319BnNmYqpNeTPxxMyc7MzE6InT25U6DStr5w\n04T5iXaeoWTLxcfEnJMUcc/Xv9kwf1IT+/06XJ2drxgtTD28efWK6Ojo6OiVGw8kXXaxrHtI\n8x6Dhw0fNmzY4O5Ngsv/YlUAAABUbTuOa+4m+Xnpn4Pk72V0GgAAgIphiX3jqXlJUtiEL39+\ncYifJLmEtL1t2vLg9FZDZ8UveOzljaNe73q16yVLNEMJl7PExOyU5NV1+C1duxpaENrlitH0\nQ6vmvvPkvSO6NKgW2rjbTROfee/bdX+1op412wwa/3/vzl9/OOnc3hVfvfbPsb1pRQEAAFDe\njibqg1Vyc9HUAapZnNvFAAAAKoXCZdM/PCipzeTHz9eUfwga8syUKElxX32xzmK3GUq63IGY\nmGxJ7aOijC4I7bL+ssf73rrg0iGTT3iHvkOHDRs2fFj/TnV9eZQTAAAAKlJiht5epnyz/tFX\njWoYnQYAAECStDhxw7Kkzdnm3C6BLf8eNsTdVC7VYMyqVamSIgYOjLz8UMMBAxo+tiXu7OLF\n29Qryj4zlHC5vJiYfZLCoqLCSvn57KY0v/r7oxecDGzdpmXjGj6XXXDq4l8/qv+w4cOGDRvW\nt30tblYCAACAEbLy9OZSpedobFd1jDA6DQAAgCTprj0vfn5qkSTJOjP+x/dOzF8b9YGfq7e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tsqtiWcW1ILZ1i7uWddtjFxsqumLvhVUR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\nsbNqX0JE7ITMMeenDws4mRyR0Ca6+Y2tLjA5IQDATBSjAABIks+vL9fq4+X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dMXhkw75/vyFtzdt9uz2KTy/qvIpv5PkWTdxnbNfHolIi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\nY1PSLC6vO/DwE8++4OyZVX1f26hfNQy8OWDwpffhEZFWr8PTnhZpdtpEJ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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 900
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m<-c(1:100)\n",
    "\n",
    "alpha<-0.05\n",
    "fwer<-sapply(m, function(x) compute.fwer(alpha, x))\n",
    "fwer.m05.df<-data.frame(fwer=fwer, alpha=alpha, m=m)\n",
    "\n",
    "alpha<-0.005\n",
    "fwer<-sapply(m, function(x) compute.fwer(alpha, x))\n",
    "fwer.m005.df<-data.frame(fwer=fwer, alpha=alpha, m=m)\n",
    "\n",
    "alpha<-0.001\n",
    "fwer<-sapply(m, function(x) compute.fwer(alpha, x))\n",
    "fwer.m001.df<-data.frame(fwer=fwer, alpha=alpha, m=m)\n",
    "\n",
    "fwer.m.alphas.df<-rbind(fwer.m05.df, fwer.m005.df, fwer.m001.df)\n",
    "fwer.m.alphas.df$alpha<-as.character(fwer.m.alphas.df$alpha)\n",
    "\n",
    "options(repr.plot.width=15, repr.plot.height=10)\n",
    "\n",
    "ggplot(data = fwer.m.alphas.df, mapping = aes(y=fwer, x=m, color=alpha)) + geom_point() + \n",
    "                geom_line() + geom_hline(yintercept=0.05, color='darkgrey', linetype='dashed', linewidth=1.5) +  \n",
    "            scale_x_log10() + theme_bw(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b424763c",
   "metadata": {},
   "source": [
    "We can see that if we decrease our initial $\\alpha$ we can keep FWER more under control. This makes sense, because we are being more strict with respect to when to claim something to be significant or not."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f98b0162",
   "metadata": {},
   "source": [
    "# Controlling the FWER: Bonferroni Correction\n",
    "\n",
    "Let's see what happens in our first example with 4 variables, but using but $\\alpha' = \\frac{\\alpha}{m}$ instead of $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "79471175",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.06"
      ],
      "text/latex": [
       "0.06"
      ],
      "text/markdown": [
       "0.06"
      ],
      "text/plain": [
       "[1] 0.06"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1234)\n",
    "\n",
    "n.trials<-100\n",
    "alpha<-0.05\n",
    "alphap<-alpha/4\n",
    "is.sig<-c()\n",
    "for(itrial in c(1:n.trials)){\n",
    "    var1<-rnorm(20)\n",
    "    var2<-rnorm(20)\n",
    "    var3<-rnorm(20)\n",
    "    var4<-rnorm(20)\n",
    "\n",
    "    \n",
    "    pv.1<-t.test(var1)$p.value\n",
    "    pv.2<-t.test(var2)$p.value\n",
    "    pv.3<-t.test(var3)$p.value\n",
    "    pv.4<-t.test(var4)$p.value\n",
    "\n",
    "    is.sig<-c(is.sig, (pv.1<alphap | pv.2<alphap | pv.3<alphap | pv.4<alphap))\n",
    "}\n",
    "\n",
    "fp.prop <- sum(is.sig)/n.trials\n",
    "fp.prop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9271c31",
   "metadata": {},
   "source": [
    "As we can see, now the FWER is around the error that we aimed for (~0.05)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7b3b573",
   "metadata": {},
   "source": [
    "# Controlling the FWER decrease the statistical power"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eb94439",
   "metadata": {},
   "source": [
    "Let's assume we have generated 1000 statistics, and we are going to test whether their means are greater than zero or not. The first 100 should be significant, because they are sampled from a gaussian distributions with mean=3, whereas the rest (900) should not:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "51dc7cda",
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1234)\n",
    "z.sigs<- rnorm(100, mean=3)\n",
    "z.no.sigs <- rnorm(900)\n",
    "\n",
    "m.sig<- length(z.sigs)\n",
    "m.no.sig<- length(z.no.sigs)\n",
    "m<- m.sig + m.no.sig\n",
    "\n",
    "pvs<-c(pnorm(c(z.sigs, z.no.sigs), lower.tail = FALSE))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72af3c7c",
   "metadata": {},
   "source": [
    "Let's have a look at both type I and II errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1100ea8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of true tests claimed significant =  93 \n",
      "Number of false positives =  44 \n",
      "Type I error =  0.04888889 \n",
      "Type II error =  0.07"
     ]
    }
   ],
   "source": [
    "alpha <-0.05\n",
    "\n",
    "cat(\"Number of true tests claimed significant = \", sum(pvs[1:m.sig]<alpha), \"\\n\")\n",
    "\n",
    "cat(\"Number of false positives = \", sum(pvs[(m.sig+1):m]<alpha), \"\\n\")\n",
    "\n",
    "type.I.error<-sum(pvs[(m.sig+1):m]<alpha)/m.no.sig\n",
    "cat(\"Type I error = \", type.I.error, \"\\n\")\n",
    "\n",
    "type.II.error<-sum(pvs[1:m.sig]>alpha)/m.sig\n",
    "cat(\"Type II error = \", type.II.error)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "338d4129",
   "metadata": {},
   "source": [
    "Let's correct for Bonferroni by taking $\\alpha' = 0.05/1000$, instead of $\\alpha$=0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3e64068c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of tests claimed significant using bonferroni =  16 \n",
      "Number of true tests claimed significant =  16 \n",
      "Number of false positives =  0 \n",
      "Type I error =  0 \n",
      "Type II error =  0.84"
     ]
    }
   ],
   "source": [
    "alphap <- alpha/m\n",
    "\n",
    "cat(\"number of tests claimed significant using bonferroni = \", sum(pvs<alphap), \"\\n\")\n",
    "\n",
    "cat(\"Number of true tests claimed significant = \", sum(pvs[1:m.sig]<alphap), \"\\n\")\n",
    "\n",
    "cat(\"Number of false positives = \", sum(pvs[(m.sig+1):m]<alphap), \"\\n\")\n",
    "\n",
    "type.I.error.bonf<-sum(pvs[(m.sig+1):m]<alphap)/m.no.sig\n",
    "cat(\"Type I error = \", type.I.error.bonf, \"\\n\")\n",
    "\n",
    "\n",
    "type.II.error.bonf<-sum(pvs[1:m.sig]>alphap)/m.sig\n",
    "cat(\"Type II error = \", type.II.error.bonf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "599be408",
   "metadata": {},
   "source": [
    "By controlling for the false positives using Bonferroni, we have reduced our the number of true effects being claimed significant!!! This means that our statistical power is reduced (or our Type II error rate increased)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd2a2119",
   "metadata": {},
   "source": [
    "# Controlling the FDR: BH Correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "463a9aa0",
   "metadata": {},
   "outputs": [],
   "source": [
    "q<-0.05\n",
    "\n",
    "# Sort p-values in decreasing order\n",
    "o <- order(pvs, decreasing = TRUE)\n",
    "# reverse order\n",
    "ro <- order(o)\n",
    "# Adjust p-values multiplying with the number of tests and dividing by each test rank\n",
    "p.adj.sorted<-m/c(m:1) * pvs[o]\n",
    "# Fine tune p-values \n",
    "p.adj<-pmin(1, cummin(p.adj.sorted))[ro]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0eccae17",
   "metadata": {},
   "outputs": [
    {
     "data": {
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opRAAAAAPLXAw88cMMNN6T2nMXFxX/6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\ndfd+XPzpwbu5QhbSbdSoAa3CvF20ipSbf/741aa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Gjw8ssvGzW+9NJLLVu2fLZ6AQAAUFYQjAIAAKAsys7OfvjwYd4WjUaz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\nu6AD5QAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 900
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "\n",
    "p.adjust.df<-data.frame(p.adj=sort(p.adj), ix=c(1:m))\n",
    "\n",
    "ggplot(p.adjust.df, mapping = aes(x=ix, y=p.adj)) + geom_point() + \n",
    "geom_hline(yintercept=0.05, color='red') + scale_x_log10() + theme_bw(20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c8ade0dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of tests claimed significant using FDR =  48 \n",
      "Number of true tests claimed significant =  45 \n",
      "Number of false positives =  3 \n",
      "Type I error =  0.003333333 \n",
      "Type II error =  0.55"
     ]
    }
   ],
   "source": [
    "q<-0.05\n",
    "cat(\"number of tests claimed significant using FDR = \", sum(p.adj<q), \"\\n\")\n",
    "\n",
    "cat(\"Number of true tests claimed significant = \", sum(p.adj[1:m.sig]<q), \"\\n\")\n",
    "\n",
    "cat(\"Number of false positives = \", sum(p.adj[(m.sig+1):m]<q), \"\\n\")\n",
    "\n",
    "type.I.error.bonf<-sum(p.adj[(m.sig+1):m]<q)/m.no.sig\n",
    "cat(\"Type I error = \", type.I.error.bonf, \"\\n\")\n",
    "\n",
    "type.II.error.bonf<-sum(p.adj[1:m.sig]>q)/m.sig\n",
    "cat(\"Type II error = \", type.II.error.bonf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01ebbb95",
   "metadata": {},
   "source": [
    "As we can see, correcting for FDR can increases the number of true positive effects that are detected, which can increase the statistical power and potentially reduce the Type II error rate.\n",
    "\n",
    "It's important to keep in mind that this also comes at the cost of potentially increasing the number of false positives, since FDR control is a trade-off between the proportion of true positives and false positives among all rejected null hypotheses. Choosing an appropriate FDR threshold is important to balance the trade-off between statistical power and Type I error rate (false positives)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3b3e951",
   "metadata": {},
   "source": [
    "# Multiple testing correction in R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df574072",
   "metadata": {},
   "source": [
    "We can use the `p.adjust` R built-in function to adjust p-values for multiple testing. It takes as input a vector of p-values, and a method argument that specifies the method to use for adjusting the p-values.\n",
    "\n",
    "The available methods are:\n",
    "\n",
    "- *bonferroni*: The Bonferroni correction, which is a simple method that controls the FWER at a strict level by multiplying each p-value by the number of tests.\n",
    "\n",
    "- *holm*: Holm's step-down procedure, which is a more powerful version of the Bonferroni correction that controls the FWER.\n",
    "\n",
    "- *hochberg*: Hochberg's step-up procedure, which controls the FWER at a slightly weaker level than Holm's method.\n",
    "\n",
    "- *BH*: The Benjamini-Hochberg procedure, which is a widely used method for controlling the FDR.\n",
    "\n",
    "- *BY*: The Benjamini-Yekutieli procedure, which is a modified version of the Benjamini-Hochberg procedure that controls the FDR under weaker assumptions.\n",
    "\n",
    "- *fdr*: the same as *BH*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07b8c356",
   "metadata": {},
   "source": [
    "Let's see how tow apply this function to correct our generated p-values for bonferroni and FDR:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c67922b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of tests claimed significant using bonferroni =  16 \n",
      "number of tests claimed significant using FDR =  48 \n"
     ]
    }
   ],
   "source": [
    "cat(\"number of tests claimed significant using bonferroni = \", sum(p.adjust(pvs, method = \"bonferroni\")< 0.05), \"\\n\")\n",
    "cat(\"number of tests claimed significant using FDR = \", sum(p.adjust(pvs, method = \"BH\")< 0.05), \"\\n\")"
   ]
  }
 ],
 "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
}