2022-02-25-logan-release-point-plots.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8c4dea80",
   "metadata": {},
   "source": [
    "## Adding Libraries, Importing Dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "103c36cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "options(warn = -1)\n",
    "library(tidyverse)\n",
    "library(baseballr)\n",
    "library(ggthemes) # Themes for ggplot2.\n",
    "library(ggimage) # Supports images in ggplot2.\n",
    "library(gt) # Create tables.\n",
    "library(readr) # Read in datasets.\n",
    "library(scatterplot3d)\n",
    "library(reshape)\n",
    "library(ExcelFunctionsR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fc93f83e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Custom plot settings.\n",
    "theme_reach <- function() {\n",
    "  theme_fivethirtyeight() +\n",
    "    theme(\n",
    "      legend.position = \"none\",\n",
    "      plot.title = element_text(size = 22, hjust = 0.5, face = \"bold\"),\n",
    "      plot.subtitle = element_text(size = 18, hjust = 0.5),\n",
    "      plot.caption = element_text(size = 16),\n",
    "      axis.title.x = element_text(size=18, margin = margin(t = 20)),\n",
    "      axis.title.y = element_text(size=18, margin = margin(r = 20)),\n",
    "      axis.text = element_text(size = 14),\n",
    "      strip.text = element_text(size = 16, face = \"bold\"),\n",
    "      legend.text = element_text(size = 14)\n",
    "    )\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6739c83c",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_data_2021 <- read.csv(file = \"C:/Users/chris/Documents/Datasets/BaseballR/2021/2021merged.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d23d7da",
   "metadata": {},
   "source": [
    "## Adding Color Code Column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0487e7bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "logan_all <- all_data_2021 %>%\n",
    "  filter(pitcher == 669302) %>%\n",
    "  mutate(color_code = as.factor(pitch_name))\n",
    "\n",
    "colors <- c(\"#000000\", \"#1f78b4\", \"#e41a1c\", \"#33a02c\")\n",
    "colors <- colors[as.numeric(logan_all$color_code)]\n",
    "logan_all$colors <- colors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc5dc157",
   "metadata": {},
   "source": [
    "## 90 deg. (angled top-down) View of Release Points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9a73366a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAPFBMVEUAAAAfeLQzoCxNTU1o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\nfi4hgTxpCiIAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Logan Gilbert Release Points, 2021\n",
       "Grouped by Pitch, All Distances in Ft.\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "logan_release_plot_90 <- with(logan_all, \n",
    "                           scatterplot3d(x = release_pos_x, y = release_pos_y, z = release_pos_z,\n",
    "                                         pch = 16, color = colors, grid = TRUE,\n",
    "                                         main = \"Logan Gilbert Release Points, 2021\\nGrouped by Pitch, All Distances in Ft.\",\n",
    "                                         xlab = \"Distance Left-to-Right, (Catcher's Perspective)\",\n",
    "                                         ylab = \"Distance from Home Plate\",\n",
    "                                         zlab = \"Height off Ground\",\n",
    "                                         angle = 90))\n",
    "legend(\"topleft\", legend = levels(logan_all$color_code),\n",
    "       col =  c(\"#000000\", \"#1f78b4\", \"#e41a1c\", \"#33a02c\"), pch = 19)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc04a6a7",
   "metadata": {},
   "source": [
    "## 60 deg. View of Release Points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a66a1d75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAPFBMVEUAAAAfeLQzoCxNTU1o\naGh8fHyMjIyampqnp6eysrK9vb2+vr7Hx8fQ0NDZ2dnh4eHkGhzp6enw8PD///9G8bVSAAAA\nCXBIWXMAABJ0AAASdAHeZh94AAAgAElEQVR4nO2dCWOrrBKGqVmatidtEv7/fz2RddgUdBTU\nee/9ehJFGJYn7Mg4iUSaLVbbABJpDyKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAi\nkRBEIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQEEUgk\nEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQE7RokxtCj97xd3r6erv/cINx/\nxvQJvzCt63fE6fwoaO9P13vi9riNUT1vp7fRytPX+8vp9orceeuKnw/NadcxxAfpyxT70x0G\nUQLS78lxxKwuoWM8kN66xW+P2xjTHXr6PMlEeQZ31PfJ5m9Fu44hegZeQKlkvyCIEpA8R9DL\nsE5CBUmanBPAeLAvx+iz+nwO7iiuZkaife06htgZ2NdHn31h/PtShcYLaSJI4t/XzfUy6niC\ntA/3d6Ux3l7LDvadApc//voURv++K6M//ncSqDp3+PPKCKStK8jA+2ePgm68P9/fLt/G1b8+\ny8+3p37y/q5/Pv/A08/3Vf3s/fxlHLr/fJ/Z6fMpXcmew1Mb8zyzm/qxjhlpkXKeCq45lr6+\n+mpS99kcZ57/fwYpmArAchNha6PrO9QFVsnvWPVO/onmnHOn/3shkDYuPwN1y+wqvv3KLzqb\nTbPtVz6pijwg6SvSywhAuoBGlOo5mHJ1NreHQPKfCq5BS/UN2b9ynKX8d1PBWm4jbGx0fXd0\nvTL7/FWm01N46tzh/SUCaePyMvCqC6AsQyfztXf1/S4tL/HbeuWwYwFaQxcHKycI+4/SCYZw\nsvf+JUHq68dr7Cn/mmPpp6gLXhfZIXEe9RPhT173UiGw/BOA5Poe06/wRocBIybv8Mt9kdHT\n5rTrGLoZ2Hd6v1/v1goTLbR/cuTt30m6etcWoK3G5M3PaJGPBGH/6R/ruyP/dIl/ydIoaqtX\nxBsG1NckwVP+NcdSJr+8RIfEfdSzWvWRvFTwLP8M4mN9j+osfImBdLbtYAJp43Iz8FP/rt5E\nibqqjP7nujIg9TdfcZBArRL8I/y8yzYOY4qcK7g3AJK4HzwVXIPm9D8DptOXcmb0F6SCZ/nL\njY/je0wX2eqLgHQB7UECaeMKEJEThk9dBD1Xz39itpXx+E9sHkjAqS3AJxh8CqSvl/tdPxVc\ng5aqiS1Z2n1nnn+6BoKp4FvufnV8j+htxOkVTS59JxbjXWrXMQxAgp+YB9I/PReSBOmqe/HF\nILHgnmfW86JnM6NPudccS/UwYP+068z6L3S5eQ3LDJAc3wP1Rp+fkafBnViMd6ldxzAAyfwW\nn4IaqW/hnT+//wZA+oJDDymQQK1z8oOPWaW/mqZQ7Cnnmmspf/2Tw3AX/9FoIvipMAIS9N3X\n62QuX2Vf6k+1KcGdmAm71K5j6GbgdbCPpPvGAyD1HQjTyEmBJLr5po8E2kQjIPGTejb2lHPN\ntVToLgcJ3EejieCnwhhIwHdfFzsb4MwjOXdiJuxSu46hm4GJUTu35TVUI4kuw1WubDilQOpL\nVD9A9iVD+BX/wA65+PCynurrv6pnE3vKueZYejbjCyf/0WgiDIzaQdfKRsd3T58glDtc2eDc\niZmwS+06hqDP0MfTrpQTLbSTf/MmEUiD5K6186Zh3ABFT9uE8Au96q+CH2xzXdcVsafgNcfS\ndxG+PM1csfOo738Qh88wAjC8m+e769Gfk3pwrZ17J2bCHrXrGHogmTIkezpqkbJa2fCrCRCl\nMAESWP19Tqz+VvOddxCCxMZ41TeUYjVGP4z2SjwFr7mW6uGASxCg77+WmwpxkLSN0HfXo08n\naeHqb/dO1IQdatcx9EF6t/ZPYDD3r2+D3E1T6f3t9Pn3TE7VC72+elIut18bhPfPd79izay1\nO5uNOdarq7Newl6/6b565Cl4zbFU9mAu32GAgf9aTirEQTI2At9dj9z6HO5H8u5ETdif9h/D\nMb1iHQBSRAfAYbqOmzZMjjT9XZx1AKSkXpROAzouSGDgYGgRDEnrO7YvkKR0XJDMFoHoDmxS\noCtxNKDjgqTGDU6DizJJpDwdGCQSCU8EEomEIAKJREIQgUQiIYhAIpEQRCCRSAgikEgkBO0O\nJP+Ue0S5ay8zVmLqGd+Tv241cuLpqHc3OHXsLTV1g7voEyLjfmYft5qpQcuDdcPYobeivYEU\nnHKPqMkgMXdPRPSE+lHv4HLqYZBY4rwingx8lkpAwg+9Fe0sXuEp94iaAxLcpRd9csw7ebJk\n/G0yieCifmaYXagSkPBDb0X7ilf6lHsMTQFJ/OudXz8JpIs4U/jiuo5a9LqfB3aGrFyUveAI\npE0occp9f3a9uBQ5PN7ZkneGW/LAafTPzxM7f0eKrTkw35ZceJKPeQCeBGF/nuU2vItthv2C\nPYFh1E7mjNVhkLg5H0UHY0/CB4EPvTMAGuYkRexQfWBL8N4B10IQ+u60q1glTrk/y1/y6OHx\nwSZxeYKbcxq9d9q+9dgemP+pCb5DE+wDUZB0ILr/dAMG+Lr1x6nY+I2AdIcnBMGT8G3gQ+8M\ncAyDSRE9VN/aEr53gEDapBKn3DPRt4gfHg+KgZJoEDqn0Yd7p90nTubEeHCIJAxDn1/vgWT8\nvTveRce1Tv15DnYz7whI6rBueQGehG8CH3xngGMYTIroofpBCn5GbeIE0mYUyySmzq5PHEMF\nikF/klXfm7l7p9H/syfje8UWHJivWl1Pp2emH9B9JLf4f4szrPpSebYG3OLdm7usBK7eeFwK\nJFgDisYt9+AafGeAY5iTFCx2qD5IweC9A3CwIZVD+9Cu4mWyyc06UfYSh8eDYqCPdvz0TqO/\ngjOB3MDAgfmq1XXzf6uN/rhf/JW/L9mZY7Fj+42U23v4VqNY9F2Q3JPwPf+NQxC4Y5iTFNFD\n9d2EfgU2EUibUwKkF/zXOzw+KJLix9bm/sn1NRGYOULlpEOBZjDmno06SEG0qJk23cnGZsAi\nFyT3JHzrKPnOAMdXJymih+p7thBI29fAKffxjj8PiyQD/Rimv3DPi/AJ+TN+DzoIQur8+ukg\nfQODvke98Jtxzkn42tHAOwMSIDHfKzfYJEg8/XVH2lW8Bk65d2qkEw/ynaWPv0+DBPEQvZiL\ne5CKX2wmg2QKPVO9kxGQ7m7zFZ6Er64NvTPA8dU7mD9yqD6B1GtX8Ro45T52eHzPwa91Jm5H\njr9Pv5EMHJgvStzdGykYBuni95Giz3Buz1aVSq6RsN8u7oCKMPPToWTonQEXr4/kd4ru0RcZ\nEkg7UvqU+2DU7iRGB36BM338/bd3Gv23+45MLfDEV/9dtnq+uOuER773/7wio3bRZ5TXegr0\nWw5qDIL0e3VeQOuehK8CV26jNZJjmJMU0UP1S0F68T1qXyClT7kPDo/3Tqi239ypo1+eMY8k\nisZTfHZKSQIkfYq+8feb++UwCEr7+3LupyxyqpvwnP3byDsDHMNgUrheubHKAkmFHvu12Lj2\nFqHUKffcPzxelnsxGa+cwYUFzmn0qmV1DYoIPDBfdmTcs0gTIOkT6n+9lQ3AjfPkP9j1u+oJ\nnTAAnyN/sOECAh98Z4BjmJMUjldurLJAUqETSO0rccp9r8gR+v9gMfh31ufAe6fRPz/FQfJh\nEYEH5os+lNudSIBkTqjvV7H5p+VHQHKGMO6wJMZB0oOEtlkLz9lXgQ++MwAa5iaF45UTShZI\nKnQCabdCyNpvzNP491fSdi7KL6n5IP2dEA8/pgPrtyYCSWouSLJRFSyZnSo6sH5rIpCkUED6\nGneXKTqwfmsikKTmgnQWIxekw4pAIpEQRCCRSAgikEgkBBFIJBKCCCQSCUEEEomEIAKJREIQ\ngUQiIYhAIpEQRCCRSAgikEgkBBFIJBKCCCQSCUEEEomEIAKJREIQgUQiIYhAIpEQRCCRSAgi\nkEgkBBFIJBKCEEFiuxNe2pD2LkyQ8LxqQ7uLEGk5EUhp7S5CpOVEIKW1uwiRlhOBlNbuIkRa\nTgRSWruLEGk5EUhp7S5CpOVEIKW1uwiRlhOBlNbuIkRaTgRSWruLEGk5EUhp7S5CpOVEIKW1\nuwiRlhOBlNbuIkRaTgRSWruLEGk5EUhp7S5CpOVEIKW1uwiRlhOBlNbuIkRaTgRSWruLEGk5\nEUhp7S5CpOVEIKW1uwiRllMlkH5dx6/bmbHLd3mQY6cr3KWr+LOpO8ZFsT2kw6oOSK8T874K\nnV6lQY6AdGbSVfxZAomEpkVBSpbwq3vjk12enD8v7FYa5Ij5jEAiraMFQUpXFv+8y4yJquhV\nfADWwiCRNqDCIrOUaoD0ZBcfJPjt+8xOsrt0f9dcp5ty8cVOX5zfGKy24IPWMb+//b/clQXC\n1c3cgl5SjbR5HQCk9E/GhT3dqzf2+TRfruKhy/vTl3z+JjwTX3pCIEnAG+D4W378tiBdo14S\nSNvXkUH6Yv/8+L/5ON9+xcc7u7z468JEhfJPNAOFZ++r3+rvKQiDO45P7K//eLZNu9Mf/zv1\nDhwvCaTNizWTSeuD9MeuYQm+f74dnvrB6qvoL716R9of8edX/H1y59kgCOX4Dr+q7/fASwJp\n62LtZNL6faRzP8gdKcG/X6eeFoe/5/3rYkp9ZOzA8cY4fvejrn9/wQMRLwmkTYvxdjJpdZA+\nRfWgirJ7/0+2xuxzF9Bw43wEJOuYf/XzUqdnDCTXSwJp0zoISPF5JDBuqcu0ceWV7U92/r4/\nM0ECjt+6386wj2Qce14SSFsWM38a0KIgRV2Ffacrk6Pdr34Y4Wo6OLKY54IEHNsL+oG+g3U3\nfTMCaRdi4G99rQ6Scgsd/zL2/e43/V56oP71Q2z8W5b6X/6X20cCjs9yaO5sRyfkqN098JJA\n2q6Y8091tQBSPzpgJo9UL6bv4ejLvzkgAcf/zKcz6ys5xvoxQTFo53lJIG1XBJJw6zr++zy9\nMfonv3y/i7+coH2X/8uvbZINDzZYx3JlQ9+c+z1LkPqVDV889JJA2qyY929tVQJpE9pdhHYk\nFnyoLAIprd1FaD9ikU91RSCltbsI7UcE0pa0uwjtRiz6saoIpLR2F6G9iCU+1xSBlNbuIrQT\nseSXiiKQ0tpdhHYiAmlj2l2E9iE28K2eCKS0dhehXYgNfq0mAimt3UVoFyKQrPoVQZ9ykXcz\ne+4jati048rPlFYyqQZIauXo2ds33pwaNu2wCvKklUxaFKSPj4+Iuy9xOMPrC+xhbVMNm3ZU\nhVnSSiYtCNKHlO/sKQDi/ULsTwKJVCQCyerG5IYG/rp+O1sc4NmNz6ve93A7sZvCzZwcabdT\nwLMf0dVKHpG0IjnSSiYtB9LHR5ykC/uDD8nDG7+9sxvFqfpfXG3z+xTk2JMjIUhfZkcgulrJ\nI5JSLENayaT1QXIbc+rMR7Et3D8O8twftCB3iTPv5EjtETj7EV+t5BFJKpofrWRSfZB+nWvO\ncZD6KJS7/GhOjoQgeWc/YqqVPCJJHRSkVB/JB8n+jRwHCU7SAqcPRe/jq5U8IgnFs6OVTFof\npKvpI91fDkix4yAJJJJSIjdayaT155G+9Kjdr3uEY/Q4SAckGxKBdDilMqOVTFp/ZYOZRxLH\n2HlM+CA5fST35Mhf+ZA8+/ETLxpWreQRiRNIEX2KlQ39TBF3QYocBwlG7cDJkec3gq8LHLW7\nDwW4dIRIyyuZF61kUgWQdGcIrLXr/8aPg7z4R+r31Zl4k9hVgnTRZz/iq5U8Ig1kRSuZVAMk\n/u9qjoMEzMSPg7yd3lfNygZ1cuTX6d2YU+3B67tvhRcJqFbyiDSQE61kUhWQyr1OLV1YdKle\nK3lEIpBm+9mvWXhdWWo1HYF0BA1lRCuZ1DhIagHeKXWfQDqABvOhlUxqHCT+Ld7TnA6TQNq9\nhrOhlUxqHaSa2l2EtikCaevaXYQ2qZFcaCWTCKS0dhehLWosE1rJJAIprd1FaIsikLav3UVo\ngxrNg1YyiUBKa3cR2p7Gs6CVTCKQ0tpdhDanjBxoJZMqgCTnfu4suVzBc+l+cgXObMVXK3l0\nXBFIg+56h69TxtE/oyDBM1vx1UoeHVY5GdBKJi0K0uPxiLmTeyKSy348l94nKOfMVny1kkdH\nVVb6t5JJC4L0kArdMbGjKKPsj4DkntmKr1by6KDKS/5WMqkOSH+M6ZdR6DNV/T1IdtdffzSr\nd9SqVHBmq3qEsdeZXfsTIXi/m/YVPDgxQqRVRSBJPR4Jkt5l/awHGuyZqv6u2JM+YujWd6a8\no1al/DNb9V+xe/Z2EXXes3fvPzgtQqRVlZn6rWRSFZA+mTjsUXy2B63K7/3hDO9rnz1qcge6\nPqQYHLWqH3a91X+Fp29v+vrq6+08eHBahEhrKnvoalEr8lUFJHvKgj1TFZ4c9NufqHoS3yRH\n3DtqVT/sesuNV7/iY9+2O8cenBYh0orKTvtWMqlKH+n0xZh/ZENwVp34dtFQMA5PiOTgYfcb\n8ODz3bZ7yorNe3BihEjriUCySoN07w86ecrP+m8cpHcX6myvezykzmxVLn7fbbubPJSIQNqY\n8pO+lUyqNY90tk22IZB+/2Td5R21KpU6s1U7PJ37/6cmoaZEiLSOClK+lUyqtbLhKV9/5JV+\nce7WBfaR+klXrvtI3mhB5MzWXwjSjX2LQIIHkSNEQlZJwreSSbVA6t+E9AdBsqenfveDbDc9\nave+8aVH88xRq0rOma3w+FV5+w2rGGYIH8SNEAlZBFKeOz0W4LTH7Omp3jzSX0+Dd9SqFjyz\nFR6/qm6r9mPkQdQIkXBVlO6tZFI9kN7F/BNOw5rTU8Va1Ktd2fD1rkr8o1a1wJmtzvGr6q5u\n04UPYkaIhKqyZG8lkyqAtBntLkLbEIGE51Ub2l2ENqHCVG8lkwiktHYXoS1oq5N9BFJau4vQ\nBlSc5q1kEoGU1u4ixFNz5O2IQGonSmjaXYSSq7aaUXmSt5JJBFJau4tQ8yBNSPFWMolASmt3\nEUrubGlEUxK8lUwikNLaXYQIpOVEIKW1uwg1DtKk9G4lkwiktHYXobb7SNOSu5VMqgHS63Zm\n7CJO9fH2GS36Ar5iNWUMiloGaeObxiqA9DqpF8O+CKTV1SpGBNKQV13XRdx9ikPrnhez4wh4\n0UqyCDVlDJZ2xlEzmbQgSJ1U6E6exfWKbB8nkBZXoyBNTutWMqkKSO5nc7rqzT9QVR6Zimdh\noVrJI1S1CdL0pG4lk5YDqesSJN3AHjsD0sVukLXnosojU/EsLFQreYQqAmkZVQCph+Z8+5XP\nKJDEsQp/J+9AVXlkajW1kkeoahKkGSndSibVAInfP/tBu34buAZJnK7av3zMORdVnQ5ZS63k\nEapaBGlOQreSSRX6SEK/Xyd5dqMzBO6dA1l57KGVPEJVgyDNSudWMqkWSP3pQGcCaX0RSMto\n/XkkQweEyAEpdFpHreQRqtoDaV4yt5JJ669suDL5yi9zlqo9RfXXO1CVQMJXcyDNTOVWMml9\nkN60fL/e/5hzhuVQnRm1A+eiEkj4IpCWUYW1dupV5OYFYnby6NM7UJVAwldrIM1N5FYyqcbq\n77/Pkz4f1XaKvpyVDXLOlkDCV2MgzU7jVjKpBkhb0e4i1KstkOYncSuZRCCltbsI9SKQlhGB\nlNbuItSrKZAQUriVTCKQ0tpdhHq1BBJGAreSSQRSWruLUK+GQEJJ31YyiUBKa3cR6kUgLSMC\nKa3dRahXOyDhJG8rmUQgpbW7CPVqBiSk1G0lkwiktHYXoV6tgISVuK1kEoGU1u4i1ItAWkYE\nUlq7i1CvRkBCS9tWMolASmt3EerVBkh4SdtKJhFIae0uQr2aAGmHpW6HUULT7iLUi0BaRjuM\nEpp2F6FeLYCEmbCtZBKBlNbuItSrAZBQ07WVTMIEaXfCS5t2RCAto1bsmChk8zeeGjmqDxJu\nIreSZa3YMVEEUqmqg7TTLGvFjmnCtn7bqZGl2iDtNctasWOS0I3fdGrkiUBaRq3YMUX4tm85\nNTJVGaTd/va1YscUEUgTVBek/WZZK3ZM0AKmbzg1clUVpB1nWSt2lGsJy7ebGtkikJZRK3YU\naxHDN5sa+aoJ0p5/+1qxo1gE0jRVBGnXWdaKHaVaxu6tpkaB6oG07yxrxY5CLWT2RlOjRATS\nMmrFjjItZfU2U6NI1UDa+W9fK3aUiUCarFog7T3LWrGjSIsZvcnUKFMlkHafZa3YUaLlbN5i\nahSKQFpGrdhRoAVN3mBqlKoOSPv/7WvFjgIRSHNUBaQDZFkrduRrSYu3lxrFqgHSEbKsFTuy\ntajBm0uNchFIy6gVO3K1rL1bS40JqgDSIX77WrEjVwTSTK0P0jGyrBU7MrWwuRtLjSkikJZR\nK3bkaWlrt5Uak7Q6SAf57WvFjiwtbuymUmOa1gbpKL99rdiRJQJpvlYG6TBZ1oodOVre1i2l\nxkQRSMuoFTsytIKpG0qNqVoXpOP89rViR4YIJAytCtKBsqwVO8a1hqXbSY3JWhOkI2VZK3aM\nahVDN5Ma00UgLaNW7BjTOnZuJTVmaEWQDvXb14odYyKQkLQeSMfKslbsGNFKZm4kNeZoNZAO\nlmWt2DGstazcRmrMEoG0jFqxY1CrGbmJ1JintUA62m9fK3YMikDC00ogHS7LWrFjSOvZuIXU\nmKl1QDpelrVix4BWNHEDqTFXBNIyasWOtNa0sP3UmK1VQDrgb18rdqRFIKFqDZCOmGWt2JHU\nqgY2nxrzRSAto1bsSGld+1pPDa2u66Y+ugJIh/zta8WOhFY2r/HUUOqkpj28PEjH/O1rxY6E\nCKSI2gbpoFnWih1xrW1d26mh1HVzSCKQllErdkS1unFNp4ZW2yAd9bevFTtiWt+2llPDqGmQ\nDvvb14odMRFIcTXcRzpulrViR0QVTGs4NYAIpKohxtWKHaFqWNZuarhqdR7pwL99rdgRqIph\nzaaGr8kcLQrSkX/7WrEjEIE0pCZBOnSWtWKHrzp2tZoagQikqoFG1IodniqZ1WhqhGoRpGP/\n9rVih6taVrWZGhE1CNLBf/tascMVgTSi9kA6epa1YoejakY1mRoxEUi1w/XVih1Q9WxqMTWi\nag6kw//2tWIHFIE0qtZAoixrxQ6giiY1mBpxNQYSZVkzdljVtKi91EiIQGogaEet2GFU1aDm\nUiOltkCi37527DAikAI9HkHpbwokyjLejh1ade1pLTV6PaTciwRSE4EDtWKHUmVzGksNIRck\n9aklkOi3r1crdkjVtqZ2+BE9HoAk87EhkOi3T6gVO6RqW1M7/IhaB6l2ktUOX6sVO4SqG1Pd\ngFAQJPuZQGolfK1W7OhV35b6FoQKK6SWQKqeYtUNUGrFDt6EKQ2YEKhpkOonWH0LpFqxgzdh\nSgMmROSM2TXVR2ogvRowQagVO9qwpAUbIjKFn0Bq0QShVuxow5AmjPDlnL3V1DxSC8nVgg29\nyA6oNqxw5J8GKUFoAqQmUqsJIzjZ4aoNKxy1C1IbidWGFc3YQWYkFJyYTyC5asOKVuxow4p2\n7LCqCtLgychszsHJeGoly5qwowkjejVjiFFFkIbP6mezjvLHUytZ1oQdTRjRqxlDrOr1kQZJ\nYfPeiYGnVrKsBTtasEGqHUuMqoE0/D4zNnx7PbWSZQ3Y0YAJWg2ZYuUWVg0SY9bYyBbapHBA\nYjPfG4inVrKsvh31LbBqyZZespx2sPDLz0xKXoltoU2qHKQIK2zuCzjx1EqW1bejvgVWLdli\nW3V1QOLDIFEfyVV1O6obAFXbGLdgpkFizJLk7Pwb1xSQfFoYtK6yameZVm07aofvqq41XtG0\n5bgOSMnmG7O3CzxbSK0UINpxD9UKSOKvA5IBpT5INpEa4KiZEkQgQVU1p0vKObZBGrpCH4kn\nmm8EUkx0lhJUUyDpC4+2QAJpRCBZ0eF+UE2B5NdH6gAU6Xb5eSQZzEB9RCBB1bSjlTSwaqKP\nBHomLkYOSI6tBXQUgqRgMTwx73Z1tVKICCSo1kB6eOLrgaTD77jTwmOw+iOQrCra0UoSANU2\nqevcchtytBJIsE0JDWJOh4xAsqpnRyspAFXdJlE0GwMJVJGME0gJEUhQ1W1SRdN0SUy5deeR\nlgbJGeSwIDFv0opAsqpmRysJ4Ki6UZ33r983qgAS6LQx2N7jBBJULTtaib+r6lb5IHWiv++B\nJNt9C4FkO0VhhQSG4x0ra6p6lilVsqOV6HuqblYI0rvkuyDZ/ooVGki6vrHEBBx11EeKiUCC\nqm6WXmjXIEh2TyyBFFEdO1qJva/qdnV2yO6hjib2QAI9fysskMBYgrYhBpK1tr6qZ5lSFTta\niXyg6obZBXaqgyKrIL4+SFztzbXBmZCBtfVVPcuUatjRStxDVbcMNp8kSLrwVgYJ7Im1LBFI\nVgQSVGXLbEG1Jdp0ifRa71X6SNyCJMxiYMWFRYlAsqpgRytRj6iZ1d8GJFsB6X1864PEFUhB\nnUQgWa1vRysxj2kLIK0xjyTM4RYkBpZcAJIIJKvV7Wgl4lHVNG6Yo07v5JPdlxCkR+aepFFX\npjPGDUisI5DGRCBB1TTOYvN4JCqkNEhw4c5IMOGlLnICpQeSdkIgpbS2Ha3EO66FrRso6hAc\ndzZnaZBAn8dxYEFiEB0CKa6V7Wgl2gktat5gYQcgOWPQsT5SGqQMkspBguflE0gprWtHK7FO\nqRpIsC23Lkiwa+Y40CCxznUCPxbFfxm1UqQIJKgl7Rss7OMgdXoeiS8HkruEov/v0XkgdQRS\nXKva0Uqkk2oCpC4BknGJ2kcaA8njiEBKaE07WolzWtVAig02OKVWgaS9wB9sMHQ4IAUcuTYV\nJsESaqVQodkhWh7wsLXlglpO9QcbzAYG+7Mv9RgEacY80iBIIUcEUlxYdrD+/2zQw1aiPKB6\nIHHJRxcWbAiSbQGGKxsyVzfE55FKQIKnodRXK6UKyQ5m/Ur52EqMh1RtHsm05nyQVLl9u1gK\nJNCmDPpIzEIDNj5svuoAACAASURBVEoRSBGtBlIrER7U0kaOz8fGQeJLgxSvkVjnnH1CIA1o\nLZBaie+waoEEAZENOVtHQJAG+kjlIHXg6LwoSMzZIWurLAIporX6SK3Ed1iNgASG8PQOWdW9\nwgMJcuqDpFpyrAtrJE4gxbXSqF0r0R1RfZB0fSS/9Mx4c7SP6DzSgN8JE1w+HhFOmHMndCC7\nUbmjhUuplZK1jh2txHZMlUDyzpB7uPJBUoV3HkheRRMBibl34iAZs6qplaK1ih2tRHZUjYIE\nvtjKCxUkeTgDvGMGvt3WHXxULmElkITw7Yj42EpkR1UNJDi84IP0wATJw8UBhMM7AKSH586C\nZFxMTZD5WiLL7te+i3J91rbD8Z+0TXXHBenSx//t86mEpDUqi81USNUGG/x2ltemC+oov2OS\nVyNBGsLFqrpGevgVEugmcaePBOydkSYzhZ9l3+zy6kH6Zp9V7agTBo6qTciKzoYdk9bVACZI\nATdRkPQFd22QGPDoeBKkWYkyT/hZdmIvPQZdww41+h3zj0DSGihx3cMFyXl/bNhvKu8j+dzo\n04jMd2dVhQeSMMIFie8VJNGsqwaSmYvd8lhDGyBxARKokFBACiogSy33QQq3TzzU7JUBiYPe\n0pwUmS38LDurGumPnde3A6xpCH0kkLRihf2hjlOVIHELEoDGQmVnbmaAFFyR38GV/sATuITh\nSCCpPtL9xL7Xt4NAGvVaHwHk6mEHxRyQYH0kGlVudVS+siFVIelLmmcLklMjdTwGkura1dQC\nWXZVA5eXCnYQSCMeSw2CpCjSID08kPQLxftFQ1NWf3v1kb9GyDEkAMlMdXEXJN7lTgQvpaXm\nkdj1XxU7qI807HECJLf4dgakzukguTXSTJD87xGSeACStecIIE0R4qJVqSXDWFxLWcpSqROA\n1C0GklrVEHaQYiBFtsYSSIOieSSoGiAFJVbP0KCDpAu/+BjnRC0hioAEg983SCaXTqeqdtQJ\nA0erg8TzQZrbR+IQpJAjFaCeF2bOnc6tII8B0rPOhGzlMHBUY7AhCZIuvOrDsiDZAOWnYBPF\nMUC6O+sNK8wjVQ8DRwtZ2ulD8COFLkqSW7IfrqaBBAo/zwfJu+eMR+wRJH6GHP3Ws6NaGDha\nxFJV9OLzSMMgiQnYcFVDOUi6+MM+Uixgg4oA6RHc2z1IvHBlkH0K24xKYeBovqWPcCW0Bokn\nQHp4xyb4IMU0H6RHNEQDS+RAO+eRHYM0TQQS1FxLdeMLypY9t7Ard84Kb11iNVdYIAEb9DzS\nEEiP8MhvCQ/8zHcP0u+1wDGBBLUeSLbHEQWp07u4lwIJNtNCjlIgOdvMdwvSLT3IuqodVcLA\n0UxLTTmEF0dAgh+6h23mcVs7IILUdbNAOkSNZDm6V7WjThg4WgIk3Yhy+khhhQSaVd7MDZwL\nnQhSuInCBguuW++jIHm1015BOrF//MKezwujUbupWgAkWzS5D5JbB8AJWO+OnkfKBslUPOBC\np+o6ZZ7xyA9OYZ9m6AgrG77etdFf0fJvAglqgT6SuRQFCZZepyDDcl1aI4GKx4TGXT8BSM7C\nPtNT0xOyqcH5nYN07/ciUR9psvBBskXXgKTLsctLej+sA5IcLi8CKfDmYeqkTu0Yd8ODIB2w\naXd9N+2e7Mx/CaTJwp9HCkByCmz8S2xjOQBpbGWDLeyeCR5Jqo02BFJ6tnjHIN17gMSRXHSK\n0FQhWOqVqxRInAcgBadw4YCU8CoDJB4HSbjZMUjvDtL7zydjt8p2VAkDR/gguSejPuB4BCSG\npUByOEAHSXwI2pcZIMm9sjsFaZIIJKi1QdJluD/YVH0FRE0EyesjpTiymNjuUxokPUfcgVEK\nAgmIQIJaEiRZ2CFItjJ4t8qdfv0skBQKo4MNYWj6W+f3kdRDzgZDvkeQvHObq9lRLwwcLQ8S\nd768C6zAyJ+1mQESqDC4f0VvaVLX4yBJwVE7e59AWsmOemHgaG2QuNyn9Aj6IqYSmQqSb0Nf\n5JkLUkgtgTRdBBLUAiCZkmfnkWQNJEGSdZJXis1uBm8/UgZIsJyr7+pexxWz+oc2BOkRgOTV\nWD065jOBBEUgQa0Bkmo1dGp3kL8yCBZdBZJxUgySeY5rkEzIBSCZA4S6bvcgPW8ndrq9qttR\nLQwcLQGSfo9yHKRoKdZlFwOk3i8FEme2N8YtSOzhGhGutXPtM3XTDkF6nkTmFL0ZaQk76oWB\no+X6SAYk05EVpXkYpIcCCSxaLeoj2QWwPAMkdWxxdNEqNG/Pi1Y/2eXFX5eiNQ1L2FEvDByt\nDJK3hCFGEipI3cPyoVc2qNEOeenRJUBy3oa0Y5D6dyP1B3GVnGi3hB31wsDRCkuElgZJrfWW\nnwA2EiR4RRBhbenE+yf0fNZBQVIDMRPOPyGQoFYAiSc5CscbnD5SNkhigkp+KgSpI5AIJBSt\nBtLDW/wdgPSwIClhgNQ5F+QkEZwOJpAIJBSt0EfidoFBDCRdgOXXuSCZ7a/coagDL670AE72\nkQDjBNKSdjDO6R2yfAykDszEBPslRAEW9YPELDiOqxgkgyVPHq4aeU9SCqTeNrP7Yq8g1V4i\nxLRfEQ8PDZKczJF+g8Iaq5LEHaYX8qCAJLCURyWnq5gApehrXXTZIpCWtMNwFPPx4CDxJEgK\nGbVyJ+g1zQbJKRKFIAUkHQKk6SKQoJYFCRRVTZAGyQ6dJUGa0EeaBJKcfE2CxAikqAgkqCVA\n6usbFyS7C4kBjhiD98Km3zyQWClIctcuXH1HIA2J+khQxZY+HsHggvGL6fEX9Yl3HiyyWHog\nJQ9smDJqx3QnaRwksATowcCQh88RgRQX3qhdun/WSlzHVWip7ro415RPKjUASF694xRbTJB0\nMRdhGgzMPFJ8YBsYJEwJTxGiPtKgaB4JagZI5l/lU1KWFV2C3V2yLj7FfSTli7ZCUyBLvUOs\n4WMIpKBKIpDiIpCgyiy1pd3b9zrEkWzOWZA6AEqkQpoJksHArP52WXLh7my7LjqP1Nm1rgSS\nJ3w7jjPYMBUk81ykBvJVChIgx/sKQep8kADDaZB0lUUgRbS0Hbb4LBwQiqaCBJGSHiGCpI7L\nmgdSFwXJraA4gTRd1LSDmtpHckHq/20EJHedamcMcCskByTYRzooSPdr/7t/LdomSyBBYYBk\nS+MYSd0CIME+Uue9G0yBBC65IAHTj7r6W+giG1BlG85p0SrU5Hkkw5FhaqBOciqkEZLyQVJp\nb6kJUOhXdts2HSTJNQRuST8gSN/s8urT8rvKIfoHnZANN3hbBFiKJf3DjwmS8rr/Iot5eGo3\nYMvgE6mQHnYb7zFB6rebq5m/9e047BIhZ4O3+jcBEuf6ZDnZfMqqkyaAJA+fCziKgmTrphGQ\nrLG7B0k06wikWZoOUhe8/IEzZ8xSLRN66OpIfXCKcISoTJAgrRkgdQEoygzBt3uuBDCwO8Q8\n0lnVSH/svL4dBwdJF1XQAeIuSKpGkijJ+kj/GdyfNA2kxySQzOKFY4Ok+kj3U//6y9XtOHYf\nCRZECJJB6SFPWu1BenOgTg4WNwB7HkbzQBrsIxWCBNA+AEj8qmJf8i5mWrTqaCJIbknU3SUL\nEmBLgGTad2ggeX2kFEjugoYER5Akb6rrGCCJeSR2/Vfdjhph4CjX0odZ8h0BienVDfLvMEgQ\nNDyQuG6JuSBZdvy2G4E0VwQSVJ6lhgueB5IthxIkI0SQzDwStyCJPeMuSAFKWSAdq480TQQS\n1ESQuFsSXZA4AEnsZwhBCkjqJoD0MBc61brjHURcv41ioE4y1Zq1i0DKFIEElWWpZkCUoAhI\n3AXJfSMe4wAb5grURfNBUscj+5UN86lhEgu3lvJBkvNI/CAg3U6maq5qR5UwcJQLkk1nOI9k\nrnogufuPLDEOQguAFKl/hkEy07NMrcpz30FxEJBuNrGq2lEnDBxNB4l3qp8C9iSJP27LSJZf\nAxLE6qFmlBgSSAAUWO1FQeqCMT6/RjoQSKxo/mg5O+qEgaPMPhL4xXJBUsN5Lkjyp/3hlVB9\nwkgHuEKtkVhcPkcatShI4IkjgTTpKWwzKoWBo5kgKRAckPyKwO0a6UsPhYoCqUdtJkgwkKEK\nKQ5SCN9xQLqxCW++JJAcZVqaA9JDrlnz13+GowzhmlV1Aw8kf+ORjwpcuhrh6GAg8cul/M2X\nBJKjPEsBRw5IFgUejsnJAhoMM4hbC4Okh+FsxROA4kLm32fHAukOM7iiHVXCwBESSEELTpVS\n6CINEngEqY+k0JBNOB8S534Uo4OB9GXjXdWOOmHgKMtSJ5kjIKWaR4wlQPLel7QYSHGKtHHM\nbQP6Do4DUtmq7+XsqBMGjsYsZXDaPwBJNejSILEESExShApSDJSk9HLb/m3NCSfHAYlG7eZr\n2FK/bPXXQpCiHQ3Dh2KlC1Y1dLpF2CH0kSKoDIPECCSjLxq1m60skPS/Hx88nEeKjos5nR/V\nh4Jl1IIEnysAqbfKgpSLj3WmWnYCJPlW2fDhw4DEvy6/TdhRJQwcJS1lLDzKJAYSywBJ3/Yq\npYf3XN48kmMY/xA2BYRkSoPEjw0SiHNVO+qEgaOEpV6B4x8CI1FqQ5BYAIo3HqcmbdhDbTf3\nQIJkjYEUsNAb5ZT+FDMaDo8UAolAwlAuSFohSLHBhnBgW5TLB3MvLgFSWp2ehYURk2sqoiAd\np480TQQSVNxSn6MRkIJh5ARIcmwBbEoqBinCRyZInVX8vvgP9uQIpGERSFCZIHHDUQhS7LBi\nyxEouJ0aEIdFtbCPFAlKVEnp+aAQpMR9BdKj0+uHjgTSv/7QYjqzYYZGQHow1WweAokDxx5I\nTtntPHcPr0aaDJKHR4iKgSMNnANSd6yVDfLsb1brFKHKYeBouI/0UGdq9cVVltlBkMKde6Mg\nydcgy5oqZ9QuxtGHR4ffzISsJjA6Nkjf7HR//1PpXLvaYeBoDCTuDoIPguQPb3sD48HKBwDS\nIwukWHdIVkh+oJYisarCwSWto4J0Zn/i3yonrVYPA0dD80h9GfRB6tRBxWLgQLgbep/LIEiP\nQpBU69LxQ8wj6dlVJ1Bm1yjlztIeFiQz6k3D35OVtrQvgjxoS3WyTJnCyge7+QCk7hG4M4vw\nBkB6g+KBZA/mFM3OD25ACjYZFU3OHhgkWyOdqtpRJwwcDYDEzYRrAJIsdczrA8Ehug44tyeM\nxFAaAkmz018xI/ABSNxumRjYP04gJUV9pPmaApLPVRdQw3SPfwQkORRQCpKw6UOtTP/ger+r\nb1R0m1FwATb8jgoSjdrN1zhI3s5Tp3y6RdYFSQ7aMfdmGUiGnWiNNMBIsjbyRiW81d+HBYn/\no7O/Z2oCSH6B1dc8qtQl12VYtLNBCvpIQ0o36uwYfKdBAoPjRwVpipDtiHrXSlzHZS1l3pBN\npGnHfRgGQNL3QfmNt+1yQPpIjdrNkWwQEkhThWQHzJKlwlhBduDTjwkTh3C5K4ODWiXSsovN\n6Qx0+nP6SAIlOY8UXdwwT3L1N9NmEkiZwrKDDXjXSlzHFQeJRTYjydsDIMWab6kGnbO6IRsk\n5ux7x5LdRmGNPg5IXmLUsIOlvdscSE5CDpU67m8ZB5xEqUn0+rUy5pG8vhE6SQQSUBU71EtS\nFw1jaU0AaeD+CDWxMjy2smEApKC/NsECFgGJHQkk5ecETzHtYHsEaaTYPT50YUNQAUj2Ia4M\ncCvAyFhHpg0EEhpIXtKWeLYPkGAfaazoizI9ocDGfRsBiakt7h8gOB59fQuBNMfP2iAlLNgM\nSCayIOYjxa4v2gzUSLOAGgFJuYqBFHIT52gcLAIJuWl3FQuOfk+fMwwaC6MtmYKpvriXdamK\nkZX5u/+Ibp+F/mSC1M8jaWsHQfLNHDPUOfzEPkYgZTyTuH4zS2Bvs33cE0jTFTm3ISzHQyBZ\nn3JACtub4+08TiBJPxFBmrYpI+aPyaXGBQ11TR4pfpnNuShI3jRTAUhcmxrvI40YGndoQXKs\nIpBynklcP03alFEWRluyxcl+cm/Mkj1KyHnRmFtk4yCJXUgeSH1Zln24ApBASInrRwfJSw8E\nO27s1J/bej+xr/nWzfZhDcUKVvJG+Thd9Ewu10UcJL1SFQ42KGyEddrAkiE6AinlmysMO/Sm\njGuBR4mwtwFSDJjU9QlDy2MgdXNBKpnMSjk8PEjTlbZDbsq4F/ijmxr5YTSlSMFKNeumzNGA\nw+2iXiZAslOwch7pYTkSJAmQSheBJyynPtJ0Ya3+tl5tdtQuvzc0abZzpGWXBdJDHpccgIQk\nAmm6CCSozAKXDZLLzeDg93SQMuz1/o0YKu4SSNNFIEE5JShdQgtAGpuDNeU4o49kQHL7SDkB\nKKudr64BXdfF55EIpCwl7fg665TM9mfjfSTugjRUP+W27MbnYPsy/CgASR+makDK7h75BhNI\nqErZUfxq5wHXrcR1XPbnfbjvkd1FQgDJzCM9wLBdj9IHE4eQjxthbHa/u0aEIPX/0VbzXKUn\nZKe82rksjPbkgFRULBMaA6nLAcms/lYPmV5TEUj+6DiBhKrRJUILhtGOxPEH3JkMw9p7igiS\neUphpDpM1rOiUcTdgyRjBj9w/8sKdlwnvdq5LIxWpDed6l6eSuuSUjlVBSDBld3v5l4XglRG\n0v5BijrJKIy3k04WBDuepymvdi4LoxUZkNyShkfS4LlyeSA5XTIXpIlHcmlWhM/+uXZHBulm\n0wjBDjbJt7IwGlG4extdyfGyIpDMaY54IOlREwuS62DDIE2ukNik4YFjgqT7RPrLQHlEqZeS\n3fxMkD66JEgsskAoayQEgtSxHYLUy/kQfEk9iGoHoloDCfSJwKuVY4WtT1T8mqoUJLCWQT2l\nQErAPz40D5t14yAJh9sDSf9xpjdTc51At0nDA0cGSRWYWQ2kKSoBibkgmcU+4tSGIZDSJHW+\nSwMSi4Gk9Og67UY8oFjsBl+ttpqSeT2lgXe5PMsL1QFB+vDacsMgLTB4pwqnWgg+WiPBRUHa\nSlUjJfzPnS6GTpM1khJyjfSDlJljZWsKSHeTBAiGgAQt8K0sjEoK+kSqz5RT8FA0AyTjh+wj\nxb0fAik8GTYTJHYYkIoX9Qx6ySb5VhZGJUVA4qrD5GsZuHJAkvvJe4j0Yru+PgJzshNBirk2\n/64H0gocMf2XQZfOl7imLeoZKeS/l9wdstPDWF2tg6ScgbeJST0+nPoEc9ehBSmYR7IO8EBa\npT5yBhpYcDX93CKjdi82/2C7bYAUlq2lWntIICW9nwmS3sQb9JF+sEBaqV3H/LPVmHM1pa9l\nRu320rTzp44gJXGQ+BIg6RJqFYBk9BEoc4RsAKP0Dt39gTRVX1MW9YzZ8r2P47js1JH63v8x\nhUi+xNjXIhXSKiANqBwk/HmkxjkCiYJgjPVsF8dxxUCCxejD73Es0qp7zAQpO6Dcdp23fy8E\nSd1AXdnQOEcLgXRG2JZUHyRTFM0FvuJwtyyPLBckb7vEFJByjPEsSYKEfWRx6xxN1DEmZPcB\nEr5BBBKajgsSbrHM0kSQHouBZP59REACLhFB2gJH//rTUa//ip5J2zPFt9IwVlOkj4RbLLOU\nCZJdUJcAqXRoe1DrgrQFjvQhw5eSh5IGTfKtMIx11AMUgoRZFnPlgpRe2aCcm3pUrHCwK0of\ns0Hq/M9rgbQFjr6ZeDXYvWyFQ8qiab6VhbGKNEIQo1ZB6pnRS4TEWzUNSP2ZDRak2YZkgbRE\nH2kLIJ3Ni1jOBU+lLJrmW1kYq8jURR/O1QZB0g04s9bOA8l6Ml0KxlogbYGjia8GSw9/T/Gt\nLIw1ZIcZPJDq95FGQTJ9pC51qFfx+EMnTSgBCXEeaRMcgTqkZC3CeI207ZUN2wHJWFoAUrGK\nQcLcar4NjqiPFFUapAoklYIkt1Gw/DPER0UgZYhG7WJK9ZG2AdJDN94iIPW3Sld5A5BG55Gw\nQdoKR/rVYGjzSBN8Kw1jBSVBsoWrqCjOUWkfaRCkfkC8eMOEB5KxZgWQtsPRJB1gZYMa+P7w\nLoHSVYbDLBWCZEcTHp6lHxsDCYuj5UvT9TblqZRZ03wrC2MtfYC/4pMssFWUPY+kBhvMgw+v\nHfcRHi2UE3wIkr6zEZCWL0y4O2SLfWNmO2J2GGspCtIkDOYra2VDDCTGmMfRpkDaDkf8jLpD\nttQ3uZ807mNLIL3LQD2McpcIwQlZ8KgDEmNsAkjaBCVn9G5JkDbEEX9dMXfIFvoGaqOWQVIF\nb4MgsdgIXTlHlUDaTgeJL7dDNss3Zv/dAkglRW+uHs7HYpAESmLMLmTGBSkXqA2DtEpJAmlS\n8hSOb+C0o3ZBCoreKpoOEljZIB6I2J0Tl6Aei39cEKRlOZL2ww/6cnkIt8kHK2AVcmD/YmFM\nlXPSidfHXlX4IE3R6iAtXB+x6P3x8+uifjHsUbvpHjUJUm7JWlalIMklQt38/UeBCUqrzCMt\n3UGKljwWXMkLgj1xQfr+VYVv/pLVmiCJnK+0QjWicpAeHw8CSam4QppQ8j7d1Jpr3fPEbrrw\nzT9otRpIqkNUafNRRHkgqbuLgFRhZcPSAw0iXs4H67q45L2uTnLNNe/EPp+yrfjq67oytdO0\n2yRIxi0ECW2YcX2QFh+wM5OXzizmRJDEQ2hNu292NR7eZh4QafNwljdTZOYr1wVpoPpoHaSf\nYZD6I4t/fiRIP+9P/X/dz+NncVn7k5ntN/CaAOnKfo2Hvwj7KCrVSACkRqqkDJCsWwjSQ74r\n9mN2I2/1GqnWe5BmgDRNsaD02f0MfMEOYwVZkOy4ca2Bb6k5IKmB8JkWrA3SajOx+wFJz4hl\nhrGGOigmZ2OrrVaVxXUqSOK9fWxzIK3BkUHGYaclkNSXvAHwoLc3EsYa6kKxvoG08tIGq6I+\nkjw9aJkayXxl2wfJLXosuLqSBvpIQr8s65V9wOx2Ru3kPJKLkSgcAUndOusdCkDS5LggzbZg\nXZDafqEYruKjdnby6MqyNps3CpLIai2eBokxh7SlVDCPBECyDG0MpE0tVZ2rmJGvE7urj/fS\nll3LIDnlxy9h7YDUr2z48DQnVBirNUE6FEdxK++MXfvW3e8nY5m7klrsI3Eus1tBMnzcyRIg\n+f7VAcmxiEDK0P3aNwuvRUsR4lbeTyqlT/fo/ZhHStlhrKI4SNEitsIIxGSQSgNKRmVFkLbL\nkTiJrh9mKyEpZSbeYVzVQeIfXh8pStQaA3kFi1YNQIUgdeBv7PZqIG2Xo292efUgfRetM13D\nziogiUxXIJlKSSoG0ioj4oUgqacWAGn5eaRNbS53dWIvrjYKFjy1O5DkKXZmoE5cclp3H+tA\nw1hYnou2UUCQskjqbJBdcF1/3hpIFX6Ezea+I4Ok+hQeSHAqqdsKSPbhmSA5blYCacMciQO0\neoZw3o+EqfVBsuCIix3UxxoD3arYet+ng5TduhuJ2KzV3/kgbZkj3UdCehsFptZLjo8GQZp8\n+Il5rLyPlL69Ckgb7iD10pv7cN5Ggai6IIGWnige3VZA0g9iLrNdp2m36QqJy3kkjLdRTD+T\nKD+MZfThkcQ7+F0XzFkgFR0QLMuo0bIg5Ri2Ckhb52iSUqu/MVf81RxsgBd0wdxEjTQxtDE3\nK4B0SI4SIE09kyg/jIWkuTEHCIEayZSm99dJJbW82MoyarQCSLP6SCggbbyD9Nbr1i8wPd2K\nTr+PWTv9TKL8MBaTxIjruVgCyXWzHZCqcfQ8qVmk2UuEpp9JlB/GctKvb/FBshGaz1FftnKc\nyTJqlAnSVKPMnwE3i4O0eY74hX32ddHrlrcVTyll70abdtwDCfSRbGGa30PK7GVNA2meZSO3\nlwZp+xzZoj97ZUM/arc7kGBp6mIfi4prZZCmVlqLg7T9DpJca9frNRukDY/acR8kueW44/E9\nFBN//nOnoqaAlGXA7kGqOWJ3Y+LVYL8XVvL6152N2nEfJFWAFgApx50so0a7B2kPHKn9SAxh\nZcOmR+1SIOHNHOWvjagGUtKXZUHaB0dqM96lZKXdrkbtOrWyTn8VQZtI4IGUvyu9Wh+pDkgL\nd5BkDHwnztWK2s2onV7LcAiQsgKO3tgCSInyAi/7r52or6OAhKrcAfQZ80h2W98kA5M3FgRp\n8fe3wI+bAWlrYXRa8T4SYn3E5KD5csPfop804eCgzvypAtJqL+bj9nziZcrW11knV8FDabf/\n+sELlONP6oEUliicltPyIDF99EnU42gfqS5Ii88gCfuNExZexdKXTa6Cp5JuJ40BFoaBqChI\nP6wTL9dZYrH3ZJDMbtdRkNI7YxcCqfb7kYyZyVJk/rDgKprKdsZqpWz4lkfaFe63LQsDVZ1F\nSV3oA9YnrY6W+bQST08ECeAxDNKDDZDUXo204nuQIuygljDct5qf2Z/4t+wEiLIwUNVBiQt9\nuAqkouIfLaCZVyNupoJUfDhkTZBWWxqkhxkWBOnKivZPjJgwbeVeWRjI8lBSILkV0moHCMnQ\nZBk1AieosmyQys492ThIo0XFHkpY9FiJnqdL5jndOSbYGinvFP0pYWDLA6kPVoJki6IP0rJc\nzQOJjXSUoqHVAWnVF4pF/kVu2hmVPJW4vrk+EverJNW+8yokt8ezcAU1BySl/uVij9bPtVun\nPoJjDO4H3AIGkqvkqdSNjY3a9XJAYnobRQDSzC5TwaNz+khKAqQCi2qAtFYHiYGSDcbwWlgg\nNDiPVHYmkc6qojBw5b6dT4EU4WhLIPX74o8CUhNATBWW8UNLNmqAxFTTLmzZwZecF6uMwQhI\n2fNIWvmjDbVA2i1HvxhbzQvFoh9xwxiWHGGAdZK+GoA0471dCCCZR4tAyqiVao7aIagdjm4m\nuQoe2glIdqxONOY+PpxjinUp0hzlg5RYptMtBVJvm9dHkvY+tDUjoa0O0s/uQLIcZb9lj+8P\nJPds1dkg9YU34n4hkLTpMHg4Ar5nkJrhiJ/YP35hz+cl97WvQvvoI4Hm3EcEJHjod3nLLv7A\n0iCpzRRARtCweAAAHb9JREFU7YHE8Zp27XAkliB8vWujv6IRa7QI6KxaMoykQpC6tEYLY3Ax\n9gweSG9rJUhO7fMAY3wBSI2steP8BwmkhjgSIN376dMDvmhswyBpSjpvUVAI0scISMCstUD6\nwaqRWgLp+m7aPdmZ/x4QpLCPNIsj70zjeiBBlNhYjQTM2hpILXH0ro2YWo+A8TJmQ+OpdK1d\nW4MNIVIZAHgDdUuCZDgBfaQPOUynBuoeprXneDQU5Fog/SD1kZriqO8gcXGUVsmxdqMgPWcu\nwLB5OMubcSmO+rUMH+DVYmFLb6TcRy7XAEl2nARIkXHGNkDqZ2IxQGqMo2mKReLupP1G9iPx\nTm0uf0MD3msezCmlSBpALHpnCZAASbY194iMMzYB0o9MdQJJKBqJM0j684S9GTlhoCsFUlYn\nSQA3XDhzLsbc5PeR5IRsCNIjGPfeFUitcTStVzPaRyrxqE/5gjBwJVfa8XGQQpSmLL5bAqQP\nXxokXy2A9KNSfS5IrXE0sVeDOSGbOohi8aSSGaybcuMgDTTjsrXAPNK2QFJJvy+QpvdqEJcI\nsZSPCyeVh8iHXG7XdSFLtrMUGQkrFGKNpFc2OE26xkH6wQKpKY5m9GqS8fguOiWvIZCMghsf\nLkiwfJXXUDggKXIckJRj2Efy0dkPSI1x1Av3FKHCU/IqgpRsvXl3RNlMVEjDVESrroODhNS0\na5CjiUrFpPSshnp9pCRIPkaiXFim8kEaKLEZboZAAo0500eCrgmkGvp+942e58LxarxRO6WC\nMHBUBNLHB/joF78iEUgy9WeB1CRHYonQqY88Rh/pNumUvLIwkFTAEVxGB4psl+4jlU0uxdwU\ngNQ9YHD7ByleMKSlgRO21iEnF/ZPnIv6D2cbxXXKKXmFYeBIwzKwmAGCBD7qzwMgjZTYDDf5\nfSTPit2DlCgX8LL7HqR1SOrD/OsX2iG8jNnRfMtm+zCsACTRRhoHSd2wf0pEIMm0XxQk+x4k\nNvQErvoSf+23mR8NpEhLLgDJtuf8dd3uOMRQISxX4TySE/IjAlJz2yhmgZTDUQ2QLuzv3p8v\njNS0Q1RbILm9Hg8kp/aarRyQ4FZz+OzuQUoPc7HYe5AGn0GVWN3w1RtS4fCTmmGMc/ShBusi\nJ5+ALXz4JO0RpB8kkJKFgjl/KoDEv09iK9K56CV7g78LUpeiDU4FYWApSpKLlbkQrA1yxu5C\nkGatJCoFCYZcA6TSF439THvRmDVnsMw405JrgjRJGSCxuS+kqAjSRxQkuJV8ECR3rUGxtgZS\nRo30g9S0GysT/nuQNgsS/9Rvo/jl17JNt/lhICkEyQDVgc1ynV7S4KDxEZDE4M11QXoIZtRj\nTYKE1EcaLRL+e5BWAqkPDiRXyZOJ6zfzfqQLf83cJVtvQtYFSaWOuzhoCCQwXzpJE0DqDgHS\nUImI1UQbBsl5Y9/ccxtmPT3qexqjj3GQ3E5QF3SQkiDlDEkQSKk8G7vpzMOGVxtUetEqeGPf\nJkEyDTrdQcoo+Z7qgKTv7hekkQLBWn4PUkrppp3uI90KZ6byw0ARSzXtAEhB3ydXAy07VJA+\n1OEnbYP0gwRS00Dw+2e/E+9yK1whl4wUeGMfm/n6yyUTjqX6SHCMIQ3SyArwdUAygTQOElaN\n1DJIz4tJq8uz5MF0pO7ijX19tdRP887RggnXe50Lki5dFikHki5cu7pS0w6E8ABu9wpSyxy9\nTux87/c9PP+dy2Z9Nr6yQXg9FSSXkUi9tQ5IH8cCqWWO3j0a24u5FFUg2wZJ+jxYJTnXmOaF\nma3cYCtFRZDCZ/cKUtMc8TOz7bnn7EWr0wfT88NAkfE4FySAVOcVXr/eElqlj+Q1MI1bAml9\nOaUdYRvFNkCy/g7USQmQOgOS7OY7tZbRaoMNobc7BaltjpBBwtbiICVhibyMwudIbfCLgzSw\naHWhwYadg9Q4R8cEaaxCErgkAXO2nAOXQ2CEJTbDTd48knbR6Qd2CVLrHC0CUj/8zfm1aDC9\nNAwcXw0emScKhSCBNuAIG16JzXCTtbJBjXw8CKS68pKr5MnUjYv0iJ3mk7RI8gFPfZAej8c4\nR/AgRotSsoAmSmyGm1yQeu0cpOY5WgCkb3Z59R59F73/rywMLE9LQJI1TxykZH8oXWIz3GQu\nEVIk7Rmk9jmaofSi1ZdsIzY6agcHGvwDuR6PJEqq5rHYfMjhhGKOCCSV/Pkg7ZqjwW0UDYOk\nvXQxMV8tSB/B6Q0fzq5ZVcCoRiKQ5ikVu7Oqkf6afPVlYuCbW2welhuLku0N+SCVo0R9JJkB\n2SDtm6OxPtK99DD9kjDm+xhruH2oOsm74IKkqypQxgikRUHaOUfp+F1V0s/bijQcxmwPE10g\nD5wAJOvCFrHS8QZckNRs1n5B2jtHo9soss/2Uh2q6JKjCXYNBmU+RUEKwEmDBIpYbZD64k0g\nbVdYEezHJlL76pETEXqXBdKH9/XDjEGAIkYgLQnS7jnCiqHdWh/xcTWQADSPCFkfntziVrWP\ntHOQ9s/RBkHyfOvAG81BZWTmkeDogiSlYwQSWxWkA3CU2EbhKNubVUASmelc4Aokp1UnSkO8\nGrKXvIgWYEQgdTb1RxUvANIi9SlydVtCAmmtPpLCxLnELUiGI11uQpIGQCoSgWRSf0yJ/Gfw\nAwuubkxpuwt/FtYZtRsCCW6a0OXGgtQRSKwOSMnFM/BfAmlWGKUyoMBr9jr3OBIk2fGGHp0e\npA6BIwLJpv607GfRb1vlaGcgBZuKTJUkKywCaX2Q0qs5GXhDLItd3ZLwQVpwsIEVg6RqIv3Y\nh95XLtt6wxgMazWQ+LZBSmY+HJ9y37m8yWpp6RrJ5iGGZz8KCPjaqk5ffF82xKgw/SMbPpi3\ngGiQg0GtBtLPeiBlvmhM/GteNDb7hWLOv7Fvm9CWmnYsMdhg66kQJJekLYLUXo3EC2qksbyP\nDzIQSIVhTPAmbNpZcdiIU1OsECPdRzIczSDpuCDxApBGs37XIHmJn+9NwjUqSEGllADJzBvt\nCCQOPBo0a2GQeC5IQzlvpu+defzUpH7zQl/ZsNiErPYlD6TIQatMD3/bQXH/FecFYBFIMvVz\nsix9V04+cq9m2iBHmLWF85uCHobHkSXJ6SPFN/E5ZMlCEuGobFD8UCDxJUCyg3X6Q7BeaEPa\nCkjGj1yQApQIJLYySJsEYqr2ABIH7HRdiJKLlS4kkXZdCUmLgMRbBIkPgZSTZYcQFkiMpfuJ\nCGEAL4I+UhIkUCV9fIQgeWWMQMIF6VgcIUaXuZ1G1DCgD1NA+iCQ1G0CaSGtEd3ZYTgedB5K\nzhKhcZC6FEgt9JGqgsSHQeJlIB2Mo0OA5FRIBFIhSNwDSaT5KEhH42gTILnPW1DUd3ONA5Ae\nYN8RAIkNgNTAPFIIEo+C5E/1+WYtAhIvAOlwHG0BJO/xEpC6D3cn3whIJZoPEmcE0n7UPkj+\n06U1EtiAtE2Q+GogRVd/TwHpeBxtEaRkH8kD6YNACm+XgsRTIC2X4dtU8yAFD4+A9CFhsiB9\ntArSjyinbYDEU007AilTrYMUPqvmjeB309wzwwtvkOBIXZMgyVnsTJC4foI5HxJmTQLpxwGJ\nD4K0WH5vVo2DFHlUTGU4i7+3BpI+u43FQeLK7dogcSSQDsnR1kHqXFl0HJAaG7XLBInrgtwQ\nSDYPlsjtLattkGJP5oLE4iDJk4q7wnNVUyU2w83mQJKDIDGQOIGUVNMgRR+EIHWlICmcotso\nylQEkir47YPEZ4N0UI6aBin+XA5I7sqGj85ft9oWSHxFkHgcpB8BUTZI+Hm9eR0IJFBFFb8N\nKVViM9w0A5IAJAskngJpsazevhoGKfGYBcnHqBPnm5h5JHUKpJxH2gRIb2Z4HZC4CxIPQVo0\nq3egdkFKPTUCkjxJn1uQuuZA+rEFe22Q+FSQlszpXahZkJIPGZAMPXBn3xBIvIU+Ek/USDwb\nJD4EEk8a1ydpDkj63AALEs8F6cAc7QQk+Mq+rYMkj0Pjk0FSrIR3FgcpnmU6dO98IOfLDtQq\nSOlnRkHiAyBVmkeaABLnE0DimSBpN5wNgqSzITMDEyDBD/Eve1CjIA08EvSRzEe5+vtDrRpK\ngWRWNqz4WhcA0g8EifsgcRyQYvcXBynhisF/nS+7IqlNkIaeSILENUh8ACReGyTugsRFG05W\nRFGQ1IflQeIGJGlGKUgjHLnfCKR1wsgDidvT3DueBRLfOEgaJwcUDj8OgcQ9kDgmSCk3Jmz5\nxXFNIC0cxuAD7lo77oLEDUhcgNSj9S4f7+tNgKRaTrrUeyDpuJtiz+Ig8TRI3ILEPQfG8067\nEf7wpUGyNxkgKtvfrahFkNjAy6vEq63Ma67kF/W2sfc/H+9/Pn7kZ/bzBumnB+nnfa0H6X37\n/V8NkNTM0ePn3Ud62yC/vv/2pj/eHx7ionw7l7yrX9Sl39ilvqi/PzAU8EU9b58ADoznnfyn\n96W/olY2iLudeXPY+3sHbRqSDX+0CFCNtGYYw+6HayRuayTeXo30o/ryqjYarZHAT7m8qP46\nIIU1Eg9qJA5qJFNrvf/XLw1iOnCY7tarrAwcc+FVRQTSGmGMOB8CiUOQfgxIvBWQhLUaEluc\n0iDpJGH6CZbTtIuBZD03bt5JxHFAyndAIK0WRobrGEjm0of8GgOJS5B4RZB0BLNAsmkCQHr/\n/eG6dmIMdrngA2BMIgnSDzcgxXIBBSQbMHRJIC0eRo7jPJB4TZA4BInjgvTDcUD64UggDd7X\nEQUxBld3o32C9NZP35LTIIkWHwSJNwUSByBxW4ABF/oPk/WI4Q2080BLUPofAYkvAtLYbW2Y\n/sCcqzsRWmxsC35WGFlunSOExkDiZSCl5jqxQbKRXRgkngTJsyPIBySQjiGsRDA/sIlMQTUn\nA6S+G50AibcIEox7AiSlH+NGg8QngfSDBRJx1AspFUCTN/QxP4xMl1GQtARIohvdf9oHSEA/\nwM0ISDwKEtftunQYwBkfcjR+8zjaJ0g/xq8P1dJDBIlngqQaXQokjgPSD0wpDyQnJZlubHsg\n6QB++KCczBzKFuJIqimQyo2JHGuTBEmG0P8rCpYGiQcEAP2w8O4YSLwcpCAZkinhlH8NUowV\nCJLv3VAA1smAhaHDw6ulPtIEW+Ig6e64+iocBCDxHJD8+gmAlKy6IiD9xEFKRHsgHdx6ZAAk\njUACpJ9MkEYNIo6U0BLCFKPJYUwxJQqS6Y7Lr9IBBIk7IA2hkwcSD+87IP0kaqRi+e0xAJLv\npQOS/9hIu863L20scaS1RkqsDJLtjouvysEkkHhbIAXl38zQlIEUehQoDyTiyKgdkGZZMgqS\n+VfdUyBxH5bIN+6Cojo8EZC4dq8dOn0k7oA0SWH5DwYogjsxkMY5IpBKhZ8UEwcb0AzRxGSA\nxNFA0gPNUZA4EkiR8s8SnwdByuAoDyTiyGrptICFchU7fhIgeaFNAYkDkHhnZm9GQPrRIM2N\n41j5zwUph6MskIgjoFaadlh2/KRqpDC8EKQ4VnNBEsHNB2m0/C8H0mQnB1IjIOFVSClywgA/\nbJuLl4HUezAGkhpTYLrTPzuShSDZq971LI4IpFIhpYYZI4r5Nx4GIkfTQDLAAKyiIPE0SHxR\nkAoH2sBV93oeR2vm2T6ECZL9UxgGJkeZYpq4JEjc1jAxkPTPRgCSavrp1GAmvFnRLB1oA1ed\n67kptF6e7USIIIEiUxgGXgcpW6MgARKKQeIhSDOjWRAzTwuBRBx5agGkChVSAiReCBIHIPEI\nSD/R6dBlYxYIWpDtD4FUqAZAqsFRCBJ3QOIuSDwNEh8A6Sfs6i8fs0DAgqKm74zbBxQWSEwX\nmeI+UhWOBkH64QmQtHvlBYN1FvBYO/kJGlYTNYsjYEFZjT357iGFlyQsOTK1K5B4IUgYIpDa\n1xpJMhhGHY6iIHnf9AVuWnD2WfkPaMxGQPrhSLGbx5G1obDpO/HmQVUbpEocuQU/DpLrthgk\nuClqlmZyZGworbEL7zFTazu1t1OX71iVQarFUQiKvvJjBuzc+2FxiA9ta5B+3MvTNZcjE7Ep\nDxXccn5n/B+d/euoIIVGmPJGIPE5ILHItwOoLkhNcORk/Q/HAWl28dea75GJWPlDBXdY9Oth\nOKoLUhscQZDUAEHMsHyQeDMxEzIRK36o5IbXF2LRqztWTZBGXruzmsKXAMUsY/5FBp2x4EMz\nmmRRPAXsYt54JgddI/fqnlUVJKwAUNpResR66H76gnu3oYbdeMSSD5Vc925H2sY7V0WQ2uLI\njFgP3B+44HxpiqPRiKUeKrjs3493mHateiA1xpEZaEvfH7oAv7TF0WjEEg/lXw0chL3J/Wv7\nIGEV28xDfBMXlgBppV+IxEO5F517fp8IeeilYVUDqbUKCQ+kxiqkaf6U55mZhw3S5QgcVQOp\nOY4KD+nxL9gvu+BoSp6BBUJgATMNfy8axvY4ygVpHxwtmme71MZBWrHYrgxSZSDDDCKOBlUH\npA1WSJkg7aRCIpBKVQWkLXKUB9JeOFowz3aqGiBtkqMskHbD0SGngmZpyyCtW2zXBKk+kAdc\nmzBPFUDaZoU0YjbL9idH9YEkkAq1Pkgb5SgDpB1xdMBVpzO1Okhb5Wjc8D1xtFCe7VgEUhPl\ndhGPCKQVtTZIxNFqHmEdz0oc5WhlkIij1TzCOlWSOMrSuiARR6t5hHWqJHGUJwKpLX9aMYhA\nKtSqIBFHq3mEdTwrcZSpNUEijlbzCOtUSeIoV8gJNbSxkjhazSOsUyWJo2whpRRjA4eeEUhr\ne0QgrS6slBpKeIYa0h6LLbJHWMezEkf5QkuqgZRnqAHtsdjieoR1qiRxVCC8tEq+sI8nb0zR\nLostqkdYp0om8iz+HqTDHHKSEmbsGYHUgkdLgxR1gprHWxRq5BOvHk4BNkX7LLaYHuH4k84z\nd2CcRb4cUrhxj1fvOK/2Fh7VPHx0QX9aNGiEI/crgbTKhCza0CDWrzaWRzs2KJVnifcgwS+H\nFH7cI/NIBNJaHq0AkvkDPxBIS8edkbar8WJDIGmtvkN2Vx4d1iB//p1AIpBa8GdzBvngEEho\n42nib7w50Fxx21y5Xd2ftEcAmWDMgUDC8Sa1rKS54rahclvJnwGPzNQri149qhBB8tvNpH2K\nHfo9SCkRSCQSgggkEglBWCAxRh1O0oGFV+5Zeh8FibR3UcEnkRBEIJFICCKQSCQEEUgkEoII\nJBIJQQQSiYQgAolEQhCBRCIhiEAikRC0LEjMPUFw+gph58k5C42hDXMsYgztcESkJOJ4KYRk\n0KG0aCo5a4bmljUW/VLJIjSDnGNGZmWG50/tFDqalkwqd/vXzGKLcs6G++yMwg+fn7dYFx4g\nN++3xkvpuil0OC2eVGh5ggGS4xOWRbMMYnh1Nj5IxFG+lk4r0+CY29pm+CDNbf+j1EgQgHkG\nLQAS9ZCytdpgg9vOm+vR7IbibIvwqkikJFqqRiKSsrRa0252cGg1EpZF6CBFv07wB6+PNM+g\nQ2n5VELLFOyWVPTrBH92ZRCBNFHLpBILmmITg4t4NK2YGI/8Bws9ivgz06CZIEX8mWMQgTRR\nS6ZSZAQIbShpqt3M/zh9tA3FHz4bAFx/EJP6WFoUJMa97J1aarE8Cn9q53M0zyDn0Xke4fiD\nltQH07LJ5LSDMNatzPQI61BD1MMRkZIIyx+0PDuWKJ1IJAQRSCQSgggkEglBBBKJhCACiURC\nEIFEIiGIQCKREEQgkUgIIpBIJAQRSCQSgggkEglBBBKJhCACiURCEIFEIiGIQCKREEQgkUgI\nIpBIJAQRSCQSgggkEglBBBKJhCACiURCEIFEIiGIQCKREEQgkUgIIpBIJAQRSCQSgggkEglB\nBBKJhCACiURCEIFEIiGIQCKREEQgkUgIIpBIJARVAEm+7e58e8kvzr37RB9jV1+fjN1cH1Pe\nqzfwXX4jvoGvscfvV/HP3+eJfYb3vStD77+L3pN2nT6f6efydB8K/jot2UlA1UB6F48n9/P2\nPPENwtHHru8wvhwfk95rk9hv6Jv9Gnv8ycTvwU39OngF3n9iIkgqrWbozIaCf7HZoB5eVUDq\n/z4v7JK4NdHH8OrTu5X0Xt24RUwCD8Uev9z6v1/s9P5Rf335Bd5/YgJI/d/Xhd3SD+ZoJGFv\nkXiTilQNpP5XMmhRIIPk3xoDKepgEKR/okJ6aoA+2eegYUPxu17Thr3YKf1gjkYS9sX+zfOf\nVBGke1/qxJf75d0/uauGTP/93So73aTb55WdvoT724ldZHn9PrPTd8RHeI9ZWWfqy9vNGT7v\ngiS/vEO7iY/v/27CBMcvpbP4Kb8xaSF/Xb+h+eYJbbrxC0aCsdeZXfntBlIialjwiHUuPb65\nSWADVoa8H2NnaXf/AwDcXc6cNEsVQRKZ2n/5luX9W+f3l/wui+Kp/9gXvYvoK/QVwFWODIQ+\nwnsDIF38592mnXXzKUvf1bEO6peJgnhhf+CiNd8JsDfd+AUjIS5KBkxKeIbJGil4xDp/J5GJ\nE0geHbAB6X2lB/rZ34bJ+C16h6TpqgiS/r3np74c/tNY9X//9d9l7XB5vXP53H9/f/rsC9y9\n//TuNtxDH517qabdP3b6438n2JoxzP0pV3flhkETwvbRTRLk3nDMlwFq061fwFBxUcqmhGPx\n8+LFWz0CE87ECTiDASvf/okfpa/3XScZ/+Z2wg6vFkBihglYIlVJ1ONo1/6T+GW+in7Ji11D\nH517KZCuIri7W6XJX2eDhXbDoAkhSBcWG8OH5ssAtekwOsZQZmsD5ncbzajdK/YITDhp79Vx\nBgM2Cd5TemZeMr5iwyykArUA0u3dUvlzftqf968LKIluKQ6abIl7KZDUpQDa8+numOV8jIMU\n8Sphvm8AMBQ8bVPCiY+cRwofCRIu6bMN+PPdtnuadqdJxonDPCStiiA9ZVfm/emr7wid7GD1\nxYVhNkhuwbJFx3X6y+R0SjlIV9NHur8S5kP3aZBsSgQxiz7iJ1wGSL/vtt2tr6kIJFRVBOmf\nbbzz++1seyGf7Px9fw6AlPIx2jbkuSC9ebh6oWWC9KVH7X77SETNh+49v1xvVUqk4uN/dBIu\n7TMw5HTu/+8HSyDNVEWQzvJ3EV4G+e2XxAvoI/nzT9aTqz8EEWnaXW1/wr3xZwcbnD6Sax2U\n6iOZeaSLHEHzzL9EuirA0MDbBGSpR6Rpv1xNKABnsYDf1dG34N5JRuojzVU1kNTKhv7LWQ5z\niR9W2Rn45X9+J+O7H2S69ZWYGHV7f48NNsB7yoMnDPnJE6N24p+rec4ZtdMuWLCS5qbGCT7F\nyoZ+yss3v3/Cmm79AoYCKmxKBDGLPQITTtp7d5zBgM16rDfiAn8nGX9p1G6mqoCkutA6b//J\n7799yeiLolq4Ziss8dfOI13s466P7j3xXfqopL4k55FeokoC/rggqcdB4f7VbTrlXKy1A+bD\nAOU8khsd2L/pZVPCNQwGAh6xzt/R6T9dXWc2YGmIfOysog6T8YvmkWaqGkiXL/WFqwn6Pid/\nz6LgffZf7/anV/7tx6jMygb2+fR9lK7sPfFd+Silv3yfEisbbjbMfk3ArwuSehwW7rPG8d/1\nbbOq46z5OkBtOoyOMRT6Z1LCM4zz6CPG+fvC1cQJJI8OWBoiH/un23TAHa1smCvqYw4p3nOA\nBb+RddMzxwqe4bJHUpkIpKjE6oTXNdpz+AcXpl7a6FvMBIlWf88WgRSVWi8XXXPtrNJW+5Fq\nax5ItB9pvgikuL4v/SbeDIf3z3E3y2seSJGtvaRCEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIh\niEAikRBEIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQE\nEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQg\nAolEQhCBRCIhiEAikRBEIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBE\nIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQEEUgkEoII\nJBIJQQQSiYQgAolEQhCBRCIhiEAikRBEIJFICCKQSCQEEUgkEoIIJBIJQQQSiYQgAolEQhCB\nRCIhiEAikRBEIJFICPoPY1kSj3CfgrcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Logan Gilbert Release Points, 2021\n",
       "Grouped by Pitch, All Distances in Ft.\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "logan_release_plot_60 <- with(logan_all, \n",
    "                           scatterplot3d(x = release_pos_x, y = release_pos_y, z = release_pos_z,\n",
    "                                         pch = 16, type = \"h\", color = colors, grid = TRUE,\n",
    "                                         main = \"Logan Gilbert Release Points, 2021\\nGrouped by Pitch, All Distances in Ft.\",\n",
    "                                         xlab = \"Distance Left-to-Right, (Catcher's Perspective)\",\n",
    "                                         ylab = \"Distance from Home Plate\",\n",
    "                                         zlab = \"Height off Ground\",\n",
    "                                         angle = 60))\n",
    "legend(\"topleft\", legend = levels(logan_all$color_code),\n",
    "       col =  c(\"#000000\", \"#1f78b4\", \"#e41a1c\", \"#33a02c\"), pch = 19)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "540fae5b",
   "metadata": {},
   "source": [
    "## 2-Dimensional (X, Z) View of Release Points (Catcher's Perspective)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d5f277ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAY1BMVEUAAAAfeLQzoCw8PDxJ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\nqwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data = logan_all,\n",
    "       aes(x = release_pos_x, y = release_pos_z, color = pitch_name)) +\n",
    "  geom_point(size = 2.5) +\n",
    "  guides(color = guide_legend(override.aes = list(size = 6))) +\n",
    "  geom_abline(slope = 0.80,\n",
    "              intercept = 7.48,\n",
    "              size = 2) +\n",
    "  xlim(-3.5, -0.5) +\n",
    "  ylim(5.4, 6.6) +\n",
    "  theme_reach() +\n",
    "  theme(panel.grid.major = element_blank(),\n",
    "        panel.grid.minor = element_blank()) +\n",
    "  theme(legend.position = \"bottom\") +\n",
    "  theme(legend.key.size = unit(2, 'cm')) +\n",
    "  labs(x = \"Horizontal Position (ft)\",\n",
    "       y = \"Height off Ground (ft)\",\n",
    "       title = \"Logan Gilbert Release Points, 2021\",\n",
    "       subtitle = \"Catcher's Perspective\",\n",
    "       color = \"\") +\n",
    "  annotate(\"text\", x = -1.0, y = 5.6, label = \"Avg. Horizontal Pos.\\n-2.46\", size = 5, fontface = 2) +\n",
    "  annotate(\"text\", x = -3.0, y = 6.3, label = \"Avg. Horizontal Pos.\\n-1.25\", size = 5, fontface = 2) +\n",
    "  scale_color_manual(values = setNames(logan_all$colors, logan_all$pitch_name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ae27fca2",
   "metadata": {},
   "outputs": [],
   "source": [
    "ggsave(\"logan-gilbert-release-points.png\", width=15, height=10, dpi=\"retina\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6cf53e95",
   "metadata": {},
   "source": [
    "## Classify Pitches as 'LEFT' or 'RIGHT' According to their Relation to Line Shown Above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2881b10e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = -9.35\n",
    "x2 = 0\n",
    "y1 = 0\n",
    "y2 = 7.48\n",
    "left_or_right = function(x, y, output){\n",
    "  d = (x - x1)*(y2 - y1) - (y - y1)*(x2 - x1)\n",
    "  return (ifelse((d > 0), \"RIGHT\", \"LEFT\"))\n",
    "}\n",
    "logan_all <- logan_all %>%\n",
    "  mutate(grp_left_or_right = left_or_right(release_pos_x, release_pos_z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac04362c",
   "metadata": {},
   "source": [
    "## Find Clear Shift in Release Point X after 8-21-2021."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2236edca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 24 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>game_date.y</th><th scope=col>left_count</th><th scope=col>right_count</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>2021-05-13</td><td> 71</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-05-19</td><td> 74</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-05-25</td><td> 78</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-05-31</td><td> 80</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-06-06</td><td>105</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-06-13</td><td> 91</td><td>  1</td></tr>\n",
       "\t<tr><td>2021-06-19</td><td>100</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-06-26</td><td> 28</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-07-02</td><td>101</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-07-08</td><td>103</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-07-18</td><td> 94</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-07-24</td><td> 75</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-07-30</td><td> 89</td><td>  1</td></tr>\n",
       "\t<tr><td>2021-08-04</td><td> 86</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-08-10</td><td> 97</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-08-15</td><td> 88</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-08-21</td><td> 94</td><td>  0</td></tr>\n",
       "\t<tr><td>2021-08-27</td><td>  0</td><td> 91</td></tr>\n",
       "\t<tr><td>2021-09-01</td><td>  0</td><td> 94</td></tr>\n",
       "\t<tr><td>2021-09-07</td><td>  0</td><td> 84</td></tr>\n",
       "\t<tr><td>2021-09-13</td><td>  0</td><td> 99</td></tr>\n",
       "\t<tr><td>2021-09-19</td><td>  0</td><td> 99</td></tr>\n",
       "\t<tr><td>2021-09-24</td><td>  0</td><td>110</td></tr>\n",
       "\t<tr><td>2021-09-29</td><td>  0</td><td> 92</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 24 × 3\n",
       "\\begin{tabular}{lll}\n",
       " game\\_date.y & left\\_count & right\\_count\\\\\n",
       " <chr> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 2021-05-13 &  71 &   0\\\\\n",
       "\t 2021-05-19 &  74 &   0\\\\\n",
       "\t 2021-05-25 &  78 &   0\\\\\n",
       "\t 2021-05-31 &  80 &   0\\\\\n",
       "\t 2021-06-06 & 105 &   0\\\\\n",
       "\t 2021-06-13 &  91 &   1\\\\\n",
       "\t 2021-06-19 & 100 &   0\\\\\n",
       "\t 2021-06-26 &  28 &   0\\\\\n",
       "\t 2021-07-02 & 101 &   0\\\\\n",
       "\t 2021-07-08 & 103 &   0\\\\\n",
       "\t 2021-07-18 &  94 &   0\\\\\n",
       "\t 2021-07-24 &  75 &   0\\\\\n",
       "\t 2021-07-30 &  89 &   1\\\\\n",
       "\t 2021-08-04 &  86 &   0\\\\\n",
       "\t 2021-08-10 &  97 &   0\\\\\n",
       "\t 2021-08-15 &  88 &   0\\\\\n",
       "\t 2021-08-21 &  94 &   0\\\\\n",
       "\t 2021-08-27 &   0 &  91\\\\\n",
       "\t 2021-09-01 &   0 &  94\\\\\n",
       "\t 2021-09-07 &   0 &  84\\\\\n",
       "\t 2021-09-13 &   0 &  99\\\\\n",
       "\t 2021-09-19 &   0 &  99\\\\\n",
       "\t 2021-09-24 &   0 & 110\\\\\n",
       "\t 2021-09-29 &   0 &  92\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 24 × 3\n",
       "\n",
       "| game_date.y &lt;chr&gt; | left_count &lt;int&gt; | right_count &lt;int&gt; |\n",
       "|---|---|---|\n",
       "| 2021-05-13 |  71 |   0 |\n",
       "| 2021-05-19 |  74 |   0 |\n",
       "| 2021-05-25 |  78 |   0 |\n",
       "| 2021-05-31 |  80 |   0 |\n",
       "| 2021-06-06 | 105 |   0 |\n",
       "| 2021-06-13 |  91 |   1 |\n",
       "| 2021-06-19 | 100 |   0 |\n",
       "| 2021-06-26 |  28 |   0 |\n",
       "| 2021-07-02 | 101 |   0 |\n",
       "| 2021-07-08 | 103 |   0 |\n",
       "| 2021-07-18 |  94 |   0 |\n",
       "| 2021-07-24 |  75 |   0 |\n",
       "| 2021-07-30 |  89 |   1 |\n",
       "| 2021-08-04 |  86 |   0 |\n",
       "| 2021-08-10 |  97 |   0 |\n",
       "| 2021-08-15 |  88 |   0 |\n",
       "| 2021-08-21 |  94 |   0 |\n",
       "| 2021-08-27 |   0 |  91 |\n",
       "| 2021-09-01 |   0 |  94 |\n",
       "| 2021-09-07 |   0 |  84 |\n",
       "| 2021-09-13 |   0 |  99 |\n",
       "| 2021-09-19 |   0 |  99 |\n",
       "| 2021-09-24 |   0 | 110 |\n",
       "| 2021-09-29 |   0 |  92 |\n",
       "\n"
      ],
      "text/plain": [
       "   game_date.y left_count right_count\n",
       "1  2021-05-13   71          0        \n",
       "2  2021-05-19   74          0        \n",
       "3  2021-05-25   78          0        \n",
       "4  2021-05-31   80          0        \n",
       "5  2021-06-06  105          0        \n",
       "6  2021-06-13   91          1        \n",
       "7  2021-06-19  100          0        \n",
       "8  2021-06-26   28          0        \n",
       "9  2021-07-02  101          0        \n",
       "10 2021-07-08  103          0        \n",
       "11 2021-07-18   94          0        \n",
       "12 2021-07-24   75          0        \n",
       "13 2021-07-30   89          1        \n",
       "14 2021-08-04   86          0        \n",
       "15 2021-08-10   97          0        \n",
       "16 2021-08-15   88          0        \n",
       "17 2021-08-21   94          0        \n",
       "18 2021-08-27    0         91        \n",
       "19 2021-09-01    0         94        \n",
       "20 2021-09-07    0         84        \n",
       "21 2021-09-13    0         99        \n",
       "22 2021-09-19    0         99        \n",
       "23 2021-09-24    0        110        \n",
       "24 2021-09-29    0         92        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logan_all_LR <- logan_all %>%\n",
    "  group_by(game_date.y) %>%\n",
    "  summarize(left_count = sum(grp_left_or_right == \"LEFT\"),\n",
    "            right_count = sum(grp_left_or_right == \"RIGHT\"))\n",
    "logan_all_LR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29562d7c",
   "metadata": {},
   "source": [
    "## Compute Average Release Point X Values used in Annotations Above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "50bd8df4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-2.45471840659341"
      ],
      "text/latex": [
       "-2.45471840659341"
      ],
      "text/markdown": [
       "-2.45471840659341"
      ],
      "text/plain": [
       "[1] -2.454718"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "-1.25339312406577"
      ],
      "text/latex": [
       "-1.25339312406577"
      ],
      "text/markdown": [
       "-1.25339312406577"
      ],
      "text/plain": [
       "[1] -1.253393"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logan_pre <- logan_all %>%\n",
    "  filter(game_date.y <= \"2021-08-21\")\n",
    "logan_post <- logan_all %>%\n",
    "  filter(game_date.y > \"2021-08-21\")\n",
    "\n",
    "mean(logan_pre$release_pos_x)\n",
    "mean(logan_post$release_pos_x)"
   ]
  }
 ],
 "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": "4.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}