{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding 3D vectors "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](images/1.Adding3DVectors.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Subtracting 3D vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](images/2.Subtracting3Dvectors.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "displacement: \n",
    "\n",
    "the occupation by a submerged body or part of a body of a volume which would otherwise be occupied by a fluid.\n",
    "\n",
    "> So for 3D vectors, it's more related to volume operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing lengths and distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](images/3.FindDistanceOf3DVector.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pythagorean theorem:\n",
    "\n",
    "$\n",
    "length = \\sqrt{(\\sqrt{x^2 + y^2})^2 + z^2} = \\sqrt{x^2 + y^2 + z^2}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing angles and directions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in 2D, you can think of a 3D vector as an arrow or a displacement of a certain length in a certain direction. In 2D, this means that two numbers—a length and an angle making a pair of polar coordinates—are sufficient to specify any 2D vector. In 3D, one angle is not sufficient to specify a direction but two angles are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](images/4.sphericalCoordinates.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Polar coordinates were useful because they allowed us to perform any rotation of a collection of plane vectors by simply adding or subtracting from the angle.  We were also able to read the angle between two vectors by taking the difference of their angles in polar coordinates. \n",
    "\n",
    "In three dimensions, neither of the angles $\\phi$ and $\\theta$ lets us immediately decide the angle between two vectors. And while we could rotate vectors easily around the z-axis by adding or subtracting from the angle $\\phi$ , it’s not convenient to rotate about any other axis in spherical coordinates. We need some more general tools to handle angles and trigonometry in 3D. We’ll cover two such tools, called vector products, in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3.3\n",
    "\n",
    "Draw (4, 0, 3) and (–1, 0, 1) as Arrow3D objects, such that they are placed tip-to-tail in both orders in 3D. What is their vector sum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from draw3d import *\n",
    "from vectors import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 0, 4)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = (4,0,3)\n",
    "b = (-1,0,1)\n",
    "c = add(a, b)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NPZup0tPTBfFxEFKDwDAMEhISkJCQwIqU6FQtGg35M3qZKKACJ8/3YTQaMTQ0hLa2NpjNZpbwjEajoPfPMIwUwAEAvYSQ1YJdOAAmNDHQo0NLSwuKi4uDlhZtNhsaGxsRFxeHRYsWuS3EUIiByoinT5/O5gBCqRRwTWKp0xN1bOKDYK/leTb23JGp6jE5OTkqcy75wB+5MAyDpKQkJCUlsdEQ1+jF5XIhJSVFsIlaQsBX8pErtqKVG4PBgP7+ftx+++3o6urCTTfdhNWrV2PNmjWR3sKdAJoBJAd7oFCYsMTA7XaTSqVBFzVdzNOmTWPPiFxIJBLWZ9EfCCHo7OyEUqnEvHnz3MJcvt2VTqeTzWsEMokVMsz0NHM9cuQIHA4HW1rk2yNBIVRFgc81PI1eaElRo9HAZDLh4MGDbv4N43Fs4tuIRQnvn//8J2666SZs3LgRvb29Eb02wzCFAC4E8DiATRFdLARMOGLwpU2QSqV+FzXNA6hUKq/FzEWwhW2329HQ0ID4+HhUV1f7bNUNRk5GoxH19fUoKipCYWFhkHfqH5HoGBiGYedEZGdn++yRoNLn8VpogUBLisnJyTAajSgtLcXQ0BBbKfCcgRGIfIQK50MtV1L/jSVLlgjx8s8DuBfAmIoiJhQx+JM1+zsGWK1WNDQ0ICkpyedi5iJQ1EETlVOnTvUZbQS6B4qBgQG0tbWhvLzcbTQdX7hcLlitVkEqDtzF4qtHgluSk8vl7O/DnSERDdByn0wmc/OgoMcm6kERKAEoVOQTDjHwNQoOBIZhVgNQEkJ+ZBjmrIgvGAImBDEEs1zzFTFQ9eGMGTN4aRN8HSUIIejq6kJ/fz+qqqoC/jH97eIulwtHjhyByWTCwoULw17YbW1tmD9/Pl555RUsW7Ysask3T7MXs9kMrVbrJn2eCJOg/DVyeR6bPK3tqXQ7PT0dEolEkIgoVB2DgHLo0wFczDDMBQDiACQzDPNPQsi1Qlw8EMadGPhYrnGJweVyoa2tDUNDQ5g/fz7v5Jrnjm+329HU1MQOjAn2h/cVMVgsFlbFOHPmzIgWE319uiDGKisfHx+PgoICNtOu1+vR3d2N4eFhDA0NsUrAtLQ0wVuzA4GPQMiz25I2Uel0OjQ1NbFmK2q1OiIz3XAiBiGIgRByP4D7AeB4xHD3WJACMM7EwFebQImBLsT09PSQ1YfciIHOmpw8eTLy8vJ4Pd9zsUbaL6HX62E0GtmEIFd+O16g0uesrCwkJiaiqKjIzchVKpWyu7GvYbhCIpzWb24T1aRJk2A0GtHc3IyhoaGIzHTDIYbxtP8XAuNCDKH6JkgkEtbua/bs2WG5NUskEthsNnR1daG3t9dN48D3+S6Xyy3ZGUrEAvyUDKOlzOTkZBw7dgwSiYSdsjTWEUMgeJrR2mw2aLVa9PX1YWRkBPHx8Wx+gu/oOr4QQlLMMKNTtaZNmwbA20w3NjaWtY1LSkrye/+hHiUMBoPgnZWEkC8BfCnoRQNgzIkhVFmzy+XCwMAADAYDFi9eHNBMJdjr9vf3IyUlhdesSU8wDMO28SYkJARNdvp6Pi0hAsD8+fPZL5zNZkNTUxOA0VxDV1cXYmNjYbFYxkWH4C9pJ5PJ2GG4hBA2P8E939OFFimEMIvxXND+zHR7enqg1+uRkJDARkS+lIx8caK3XANjTAx8x8FR0D76xMREZGdnh00KdIiLQqFAWVlZWNcwmUxQq9UoKyvjNa/SE4QQHDhwAAUFBex5mOYsqEYfAIqLi5GTkwOVSuWmQ0hPTx+zoTN8svlcRWNhYaGXSYrRaERrays7LCdUIhbSOt4ffJnp6nQ6LyVjqMc7k8kU1vFyImFMiCGccXC0/FdaWgqXy4XBwcGwXrunpwfd3d2YPHkyTCZT2Nc4duwYUlJSwiIFtVoNo9GIefPm+f3CcB2A4uLikJKSgilTprA6BK1Wi87OTkgkEjZ8DxT+jjU8TVL27duH1NRUtuLBtY7jc99CRAyhGqxQM12uB4VWq4XVasX+/fuRnJzMEnSg6pNQ5crxRNSJIdRxcHS+o81mY8t/w8PDIbO20+nEoUOHQAhBdXU1RkZGYDAYQr5Gc3MzXC4Xqqqq2GMAX3CbsJKSktz0DZ6fg7+qhKcOgZ7zafhLh+Kmp6e7HTvGO0fBMIxbxyXXOo7eNzds90Q0vBpDvX/qQUHFcyMjI2xrPCHELZHJjUwMBsMJbdICRJEYaJTQ1dWF/Px8Xn8gg8GAhoYGNtymi4ePJNrXdbgKxFCbqEwmE+rq6th7odUTvnA4HKyScsGCBfjxxx8DPp9vVcLznG80GqHVat2OHQ6HI+xjFxAdv0ZuWzl3Bga3kYrmJ2JjYwW5ByHIhUvQnh4UOp3Oy0zX6XQKknxkGCYOwNcA5Bhdp1sJIQ9HdNEQEBVi4GoTurq6eMmDe3t7cezYMZSVlXkpB/n0OVBQP8fy8nI31g6FGGjWuqysjG3cCuX5BoMB9fX1buXQYJWGcHQM3Dp+cXExe+zo7OxEZ2cnBgYGQgrfhUKwe+eG7TTfQndj6ghFW7cjWdzRjDpiYmK8zHR1Oh1efvll7NmzBx0dHVi7di2uu+66cBvCrADOIYQYGIaJBfBfhmE+IoTsjeDt8IbgxOCpTQgGh8OBQ4cOAYBfH8ZAvRIUNOx3Op0+r8NnYRNCcPToUXYALXfX5btYBwYG0N7e7kVMoRBDuKDHDr1ej7i4ONY/INixwxNjbcvGbaQCRr8THR0dGBkZwY8//uhWVgxlRqcQxMA3TyGXy5Gbm4tHHnkER44cwV133YXW1tawdSlk9MtCz76xx/+N2flQMGIIJ8Go1+vR0NCA4uJiFBQUBBU4+QNtXvI8gnARjBisVivq6+uRlpbmdxJVoOfTKVRGoxHV1dVeyalgxEDPqELqGOiX1d+xg5q9hFM1CIRIiSUmJgYKhQJxcXEoKiqCxWJhz/Y0TKeRUCCCEypiCMcItqysDOeee25Er33ch+FHANMAvEgI+SGiC4YAQSMGvpOkuX4FFRUVQc9jgRYl3aF9HUG4CJSnoC3bgfouAi1Wm82Guro6pKenY+7cuX59CKIdMQSCv2OHZ9UgIyMj4oqAkEYvwGhZMT8/360/ghKczWZjy7mebeXUYCUShGMEazQaBUk+EkKcAKoYhkkF8B7DMGWEkMaIL8wDghEDbY/2/GLTBUH/yLRHITY2lrfQyFfLNJ0iZbVafe7Qvq7heW/U7WlwcDBgyzZ9H75AXZqCNXPxJQZKrtGuKnhWO3yZ0dLSaKhu2NFMHHoSHLW902q1bm3lNBEYSRI20H0EgsViEXSIMCFkiGGYLwCsBHBiEYM/0GNATEwMu4imTJnCu0fBF6jwKS8vj9cUKcA7gelwONDY2AiZTBayipGiu7sbPT09rEtTMHAXu91uh16vR3JyMkuqgDD1+3DArRp0d3ezDUh0IG4oxw6hI4ZA8GV7R2XPKpUKcrkcNpstbCPacCIGel+RgGGYLAD246QQD2A5gKcjumgIGBNisNvt6O7uxuDgIO9F5A90AC0dMc8X3IiB5jaoUWyocLlcOHToEFwuV1hRz8jICFvKpA039L3QexxPHQLtMcjPz2ePHUNDQ27HDhpt+EoGCqVaDOcaXNlzTEwM4uPjWWcuGuLT/ASfXT1UYhDw75YH4I3jeQYJgP8QQnYIdfFgiDoxMAzDmqnwaW/2B0IIWlpawvY9oF9ef+VMvjCbzairq0NeXh6Ki4tD3oH6+/vR0dGBiooKxMbGgmEYGAwGaDQaAD9FIQ6HQ5DkWTjw3K09m6m4xw6aDKREIZfLBYsYhCCX+Ph4pKWluRnRarVaNhIKJjcP52/AJ88WDISQegBzI7pIBBCUGDw/DK1WC51Oh6lTp2LSpElhX9dsNsNkMiE/Pz9s3wOXywWz2QylUhnyeDoKh8OBgwcP+p1qHQgMw6Cjo4Mtp9KReQzHK5BhGGRnZyMpKQn9/f04cOAA67BE52JMBAm0p1jJc7EpFApWxxJutSMaTVTcz7qkpMSn3NyzrTzU9xCt5PFYI2oCp/b2dmg0GmRnZ4dldUZBxUZyuRyTJk0K68tCd3mJRILKysqQr0FDUavViqVLl4acWLLZbFCr1cjOzkZ5eblf/0j6JaYW5LNnz4bZbIZGo2E7GP1l4IVEKDu+52KzabVQajQYOj50JtixI9A9CKFBCLSofcnN6UBfqgWRSCRITEzk/ZmYzeYTvk8CiAIxUD1ASkoKFixYELbIg+oCDAYDqqurUVNTwyYxQwF3LFxzc3PIpEClzXFxcUhISAiZFGg+Izk5OaBWA/BdOYmPj2eHy3pm4Mezocql18Pe3gFHRztsh4/A1tICR0cHiNGImEULkXzLLSgtLQ167PB7/ShEDMHAnURF28rb2tqgVquhUqnc8hP+qh0ng0kLIDAxaLVaNDY2YubMmWzzDB/VoieoU1NGRgbmzZvHCqZCCdMIIWhra4toAC2VNtMk5XfffRfS87n5BNp4Ewi03OuvXOmZgacNVd3d3W6LznP8Xajwtzs6h4aguftu2NvaQSwWMHI54HSCHDeZOf4mkPCb30BzvJM12LHDX7VjPBOYwE9t5UlJScjJyUFWVhbbbdnY2Ain0+nz3kVi8AG5XO61CGNiYkL6otId3tOpKRSCsdlsqK+vR3JyctgDaOncxXCSlHS2g9FoZPMZfLQJofSEAN4NVTSJOTg4CKVSCb1ej4yMDMHG2EkSEuDUaECMRoAQEM+/a0wMEtdeCklWFpiuLq/n+zrj+6t2UD1HJBBSEs3ttpw0aZLXvUulUshkMtTW1kZ8lGAYpgjAmwByMCqD/hshZHNEFw0RghKDQqHwIgG+C5oQgtbWVgwNDfnc4flehzsWjjr1eL5OoC8c7ZfQ6/VewilPsZYvUFJKTU11U0F6EoOvawSLGALBM4kZGxuL2NhYNkcTFxfnZhMfCP7eIyOTIfO556Dc8DP3KIH+XipF8k03wcTzPB6o2qHRaGCz2ZCdnR2WyAqIriTa1703NTVh27ZtqKurw2WXXYYbb7wRK1euDOdlHQB+Qwg5yDBMEoAfGYb5hBByKJL3EgqiWpUARj9Am80W8HncPgV/O3ywowRXZu1PKxFsYXMXNT3CeD4/kHae5hOmTZvmRUp8IwahstpSqdSt+4+2OUeaxIydMgXJd9yB4T/9CeBuAjIZEq+6EtLUVJCRkbAWJPfY0djYiOzsbJjN5rBEVoBwEQOf15LL5Zg3bx5uu+02/Pe//8VNN90U8qxTCkJIP4D+4/9fzzBMM4ACACcmMfh8gZiYgDs9X7flQBED7dAMNhaOLjxfX5ZgkQYQeHHTng1/vR98iIE57isZDUm0pw0bHQPHTWJmZGRAoVAEJE/H4CDMn30GJiEBxGRiyYGJkSL5Zz8DIJzyMSkpCdnZ2UGPHf6qHePh6UD9HmfNmhXR61IwDDMJo3qGMWugAsZI+egrx8AtafJxW/ZHDL5MWfzB345M7d+CqTL99Vv4O3pwwWexh2pI4w/BFoNnEtOzcgCANX3hZt/NX30F3RNPQnHlFch48gkMXnkVXENDYOLikLRhAyTHCVGIioJn8jFUkRXfzyIYQtUxCOkQzTCMAsA2AHcRQkYEuShPjMlRwnNBeyYH+TCyr0UZ6lg4z4XncrnQ3NwMh8OB6urqoCG1ZzOX3W5n34evowcXnsRAd0BuYpBefyyaqLjwrBy0tLSwvSQulwtpiYlI3LIV5MABZPzxGcgrKgAAGc88DdXtdwAxMVCsX89eT6idOtA1+FQ7HA5HRCIrYPyGzRw3Z9kG4C1CyLsRX3D0mr8E8Mvj/5kCoJMQcravx45ZExUFnxbnYNdxuVw4fPgwzGZzSPJobtbfYrGgrq4OOTk5KCkp4fVF5gqTaD4h0LxLz+fSxW42m1FbW4u4uDg2MZiRkcEeJcYTDDM6FDc5ORmZmZkwHz4M7QMPwpKXB9VvNkEFIL2nZ1SJOXcukm/5JaQZGZBwOlPHWhLtr9oxMDAQkcgKCP0oYTKZeH0fAoEZvcFXATQTQv5fRBfjgBDyMoCXj5PO5wD8XntMcgzUMp7PVGp/4E6jqqurQ1ZWFmbNmhXSH5lGHTSvEerwGrqjB8sn+AIlBkqMc+bMYY8tVN1ICMHg4CCrsox0t+OLXbt2YeHChaz2hBKYYctWjPztb0j91a+QsPpClHDulXo1pi5cOBq+OxxsxDUWEUMg0GNHXFwcqqurwxZZAeM2hep0ANcBaGAYpvb4z35HCNkV6YWPYzOAzwkhH/p7wJgcJex2Ow4ePIjExMSwW5wlEgn0ej2OHTsW9lg4hmHQ09ODkZGRkKdIUXR0dMBisfDygPB8bWojP3/+fLYdmAppqKqSVgp0Oh1+/PFHyOVyZGRk8CozhgpCCP70pz/hkUcewS9+8Qv88Y9/HP2FXg/b5j/DqdMh65X/Q2xJCfsceq/Uq5EmBDs6Otid2Zd/Rjj3JlQDma9jh0ajYY8dNN/ir9oRCkEJcZQghPwXQFRkrAzD/AxACYDbAz0u6hGDXq/HyMgIqqqq/Gb7g4EQAo1Gg+HhYSxatCisBU1dfZOSksIiJ7vdjqGhIWRmZgbNJ3iCOxejuroaUqnUr7LR5XKx3gGVlZVevRK0ZBfpkFm73Y5f//rXePPNN3HZZZfhscceAwBYfvwRst89AMnZZyP72T+CCWB0wpVkAz8lBPv6+mAymWC1Wtnfh2qYEmnU4Y+YuMcOX0KlmJgYlojD2fkn8hQqhmHmA7gbwJmEkIBZbsGJgYbMXHekhISEsEnBbrejoaEBAJCfnx8WKVBPyISEBBQXF4dMClQaTV2NQ/nCUts3mUyGrKysgIuZEgP3+p69EkNDQ9BoNOjo6GBNUjMyMpCQkMD7voaGhnDdddfhq6++wr333osHHngAcDox/NJLMG7/EPabbkLiOWcHJAVfoDuzVCqF0WhERkYGNBrNT0nM49ZxycnJUW8n50ssntUO6i9J/RusViv6+/t5i6wmuCT6dgDpAL44/tkcIITc6OuBUYkY7HY7Ghsb2TPe3r3hOV5TQ5OpU6dCKpVCp9OFfA2q/CsvL8fAwEDI5UCuNLq7uzuk5+v1etTX12PGjBkwm81BH89NjvqLKLg7tMVigUajQXt7O8xmMytaCnSPnZ2duPzyy9He3o6XX34ZV199NRy9vdD+z/+ASVQg55//QEcYnzMXVARGJcSTJ09mI7aBgQEcOXLEayCu0AhX3OTpL/nDDz/AarW6HTvS09O9hsxQCOX3GA0QQn7O97GCEwPXvi2ccW4UVFtQVVWFxMREaLXakDL2VGI9PDzMWsErlUreC5s+n1rJU1MVvmdnSiiVlZVQKBTsvIRACFUSHRcXh4KCAhQUFLh1Xg4MDEAqlcJisSAjI4O1NPvhhx+wfv16OBwOfPDBBzjjjDNg2rMHQ8/9PyRtuB6K9evBSCQgWm3EYbzn87lzGIiPgTNCHZEownF39gWpVIpJkyaxxw7ukBkasdFjB8MwghwlGIb5O4DVAJSEkPCGrUYIwYmhr68PVVVVYSfKPEfL0Ux3OE1UKSkpblbwfCXHVJ+QlJTklk/gk1SjXZ1DQ0NuCUp/HgxcRJK044qWKIlJpVI2JN63bx9+//vfo6CgAFu3bsXUggJof/8obPV1yPzzZsgEUuoBgcN4YrVi+IUXEDN5MnJmzkLhrFlwHfcD5SYxbTYbDAZDWD6NQGhzK/3BM+qQSqVuY/c8jx0ffPABayoUIV4H8AJGG6nGBYITw5w5c3w6RfMJ7TzHwnG/EHwXNT1++JI287kGzSf4iniCLW7uWDrP2RShdFcKIXCKjY1Fbm4u8vLy8Oyzz+Kxxx7D3Llz8dBDD8Hc1ITe39wNWWUlst58E1KPM7EQiT+/z2cYGLZuAyQSMLGxIBYLpDk5kM2Zg5y5VSiaNQukpAQHm5rcfBppQpBvJWgsZl96HjucTic+/fRT/PznP4fdbseXX34ZVtRCCPn6uBR63DAm067pbh/oQ/Y1Fs7XNQKht7cXXV1d7PHDE8GIQalUorW11W+rdaAdnZIaHZ7jibGURFPYbDbcdddd+Oc//4nLL78cL77wAuzb3sXIG2+AuelGqEtL0dnY6HPhRUoM/v7WjEwG2Zw5sNXXgxxvrnP29cHc1wfzV1+NFulsdmSVl2P6318FIaNTpzUaDXp6egCAPecHSmKOZQMVMPp5nXbaaZDL5fjss89gs9nGRIMSLUSlKuEJuqh9sb2nU5O/slagRUNnTNhstoDSZn9+B9zwf8GCBX7vwV/EoNVq0dzcHNC5OpTuSiEihuHhYdx44434+uuv8dvf/hb33nwzdPfeB2I0IOf11xBTUIB8wOfCc7lcUCgUrLV9qAgWccSfey5sLS2AZ9et3Q5IJJBkZkJ/2ToA7lOnJ0+ezNrDeyYxqaCJYizH01Fw37eQcyXGA2MaMXiC224dTBvgb1Fzpc3BZkxQA1YuHA4HW4r0NZrO8/mexNDV1YX+/v6gginPxe5wONDX14fU1FS21BiqUYs/dHd347bbbkN3dzdefvllrJ00GcrrrkfixRch+aabwHCI09fCa2xshEqlQnd3NxQKBRtNhKJF8NntaLfDWl8Pe3v7KAl4Qi6HbPp0ZPx5M3pbWnxel2sPz01icqd909LjeIynE0L1OREwJsTgy8WJSoO5NnCB4Itc6E7NVwnpGXX4mkodCNzFTRuwnE4nFixY4PYF6r50LWSzZyFt40bIpk3zeq7JZEJtbS3S0tLcSo0ulyviHMMPP/yAa665Bk6nE+9v3Yry2jro3nob6X94DHHz5wd9fmxsLOLj45Gfn4+kpCRWJUi1CHR3DhRN0HsnhMDR3Q3r3r2wfL8X1poaxJSUQL5o4WjbttH405Pi4hC3cCEynnwC5LjjVTAwjPvUbK5YSa1WgxDCqknHYtiMEAnPiYIxjxi4wqdQeia453vuNUKRNnN3/GD5hEDPt9lsqK2tZb0CvAxd4uJg3LkLpk8+hTQ7G8nr1oEsXgQSG8uSGe2VoMeT4eFh9n/r6+ths9lgMplCqu5s27YNv/zlL5GTk4O/PfYYpr76dzhyc5D91j8hDWMUu6dKkIbxfX19aGlpQWJiIhtN0NDZZTCAfL8XrqZGDNTVgdgdiFu8GAmrViLt4YfY+3D298O8ew/7eSVceCFS770HjEQCV5i2blyxUmpqKoaGhhATE4POzk6YTCYkJSWx5UU+ScxwGqiEEDcxDPMvAGcByGQYpgfAw4SQVyO+cAgY0xwDzdrL5fKweyYcDgeampoQExMT8jUkEgkcDoebhVyo4bHZbMb+/fsDdoemXn8dlA89DGKzwdHTA93LL4P85S8gBQXoWroUczdsQHxqKutsRUuNCQkJSExMxIwZM1BTU8PKoKliMDU11ef7JYTgueeew6OPPoolS5bgmYsuQsYLLyLxll8icd26kBeZv3DYM4w3Go3QKJU4smMnYpoakXjkKCRdXWCmTwezcCEyr9+AmKlTfF4rftkyWL74EgCQ9POfIennP2cfJ1RFQSaTuVUNRkZGoNVq3ZKYGRkZ7AwJT4xTAxUIIeuDPyq6GLOjhMFgwNGjR8MeCweM/rH379/Py5TFFwghUCqVyM3Nxbx580L+8un1eiiVSlRXVwf8AsSffjrAOQqQ4xZfMZ2dSBkcxMDbbyPricchO+sst+fRo058fDxkMhkqKirY8FitVqO1tZVt0aaKQZvNhjvvvBNvvfUWrli7Fo/m5ML5+ReQPvE4FIsWhfT++MIxOAjr3r2w7t2L2P37kZWRCdmihbBfdy10eXlQDQ+PjoZLiEe61eozootbuBCQMEi95x4kXnSR2++i4RDNMAxSUlKQkpLilsTs6+vDyMgIEhIS2M+V3u94EcNEwJgQAzXRWLBgQdiqMKVSCZPJhEWLFvksZwaD0WhEc3Mz4uPjMXPmzJCeS1WQOp0OhYWFQf/40uRkyGbOhK3RezAxsdsRk5WFuKoqOI/3lHCNWjzdkT21/CaTCRqNBocPH4ZWq8Uf/vAHHDhwAPf8/Oe4oaMD8bPnQP/0U2AikOV6RgwuiwW2gzWw7P0elr0/wKXVQr5wIeKWnIbUX/8aUo5eJAdATGsr4uPj4XA4WCMcWmKkUY8kORn5n3/ulghlX28MZkr4in64SUxaXQqluiCke9N4I6pHCZqgMxgMKC4uDutD45YSExISwiIFlUqFI0eOYNq0aVCpVD4fo1Qq8dxzz2HVqlU4/fTT2TMot2oxZcoU3qq2pAsvgOboUYBjCEqkUsTm5yP/9dfApKbCbrWywhi+VQna9my323HDDTfgWGcnHr/4Ylzc0IiRDdcDy5fDYbEgouHvhMDZ3g59XT0se/fC1tiI2JkzELdoEdIffhixs2aCCbKT0jIiHYqr0+mgUqm8ox4fxCBUxMDX5JZhGCgUCigUCrchvseOHYNKpYJWq+XVrEaVmicDohYx0LFwubm5SE9P59VE5AmuNHn+/Pn4/vvvQyoHUV9JrVaL6upq2O12tv3ZE3V1dXjppZewefNmJCcnY/ny5TjnnHOQl5eHqqoq5OfnY3BwkHe1wD53LojT+VNTvUQCSCTIfekvYFJT2TMwJQb6vpxOJ2w2Gwghfne9vXv3Yv369XA5nXhj6TIsVCQh7e1nYU1KYudK0F2QbzejU6eDdd8+WL7fC8W338KYkID4JUuguPwyyJ9+ivVz5APPv5GnlJhGPbRPghtNcPtFIoHT6QxbS0CjNL1ej4SEBCQnJ7Nt2WazmRWEUfk5hclkEiOGQKA7NB3+qlKpQp6O5Ms6jX5p+Jz7POXJdDf2J5Javnw5+vr68MUXX2DXrl3YtWsXtm3bBoZhUF1djZUrV2LJkiW88iPd3d3oHR5GXm4OnD29YORySCZNgrW4CMrf3o+sF/4X0uMWYzRSAEZzMWazGX19fYiPj2cTthKJhP23ZcsW3HrrrSjIyMBfsnNQdtFqJG3YAEYqRQzA7lh0AMrAwAAOHz7MVhAyMjJGCcluh62+AZYf9sKydy8cXd2Qz5+PuMWLYVy2FMULF4a9+wUjb67Zi6cfgkwmQ2JiYsQKUCEl0Vzps8vlYgVh3d3dAMCa6Oj1eqH8Hldi1GVJCuAVQshTEV80RAhODCaTCZ2dnW5DY0IdU0dH1Xtap/GdPkz9F0pKStwWcjBJtEKhwOrVq1FRUYENGzaAYRh89tln2L17Nx577DEQQpCVlYXVq1fjggsuwNlnn+12f9SL0mq1orq6GsMXXIChV16FvLQUCU89iUOtrSj8cAfUm36D7P/9MxiPpJxUKmUNTiqOG65SMnM4HHjuuefw5JNPYmFREf5cXIKpTz/FGrN6gjtXgq0gNDai7e1/IfbQIciPHoW0qAgJp52G1Lvugqy8HMzx3c/Z2Bi9Xgkf98nNoZjNZvT29kKv12Pfvn1hd11GSxItkUjYJCYwGtVqtVp8/PHHeOqpp5Ceno7CwkKsXr06LA8ShmGkAF4EsBxAD4D9DMNsH8thM0AUiCExMdFraAxfYuAuLF+j6vlch0YrvpyjgxGDy+XCoUOjnz8dVb9o0SL87ne/g1KpxLvvvosdO3Zg27ZteO211yCTybBs2TKsWrUK5513HvR6PVJSUlgvyqQ1a+AcHkHar++CSyrF1GnToL7mapDNf4bhF79A3O9/j6y8PMjlctjtduj1ejAM46bglEgksNls+NWvfoW3334bF+fn46kLVyPr/t9ColC45Se83o/BAOuBA7Ds3QvL3h8Qa7UiZ/FixKxdC/OM6dA6HOgeGYFCLkeGRoOMjIyQ7OoCIVxiiY+PR1ZWFlwuF6ZNm+ZlHUdJJJgxzVg0UQGjScycnBxcd911MBqN7HzLI0eOhGtOtBBAKyGkHQAYhvk3gDUYw2EzQJSOEr568YMdJegg20Amr4GSc9RsVqPR+O25CEQMVqsVtbW1yM3NRXFxsdfrZ2dn48orr8TSpUsxbdo0fPfdd/joo4/w0UcfYdOmTQCAadOm4aKLLsKqVauwZMkSxBQUIP2+e0e/YAzDnrNdL/wvBu++B9ZnnkHjz34Gu8sFq9UKuVwOs9ns9tparRbr16/Hf//7X9xRUIgH/vgMW96j0QRVTBKnE67WVmDPx3A01KO/oxOy8nLELV6MzGcvQ8zUqey1k3F8MOJxD0S1Wo36+noAo7ug0WhEfHx8WAs80hwBfT5fYxpf07TGuokKGI2WZ86ciWuuuSaSly0A0M357x4A0ak7B8CYCpz8gcqj+Uyj8rWw6QwEuVzO5hN8wR8xUHOZYK9Pny+TyXDWWWfhrLPOwr333ovPPvsMx44dwxdffIEXXngBf/rTn5CSkoLly5fj/PPPx/nnn+8mhpLExiL3j89Auek3yNuyFZ1rLkZJSQm7SBsbG5GVlYWhoSFccdll6OrsxP+bPx8b//EPN2NWiUQCh1IJ03ffwfL997Ds2w9Jehqcs2ZBctllyDn7bEji4wMuEK66kdb3a2tr0d/fj/b2diQlJSEzM9Mr0RYIkfYL+FvU/oxpjh07BqlUylYOaI5irIlhIvs9hopxbaIihLBNSHzk0b6uQ9udPfMJvuDry9rf34/Ozs6gU6jo87lVia6uLvT19eHiiy9GXFwc7rnnHuj1enz66af46KOPsHv3bmzduhUMw2DhwoVYuXIlVq5cifLycjAyGRy/2QTT/b/DtE8/Q9bDDyE1NRUajQZFRUX4+OOPcedtt4GxWvHKlVfh/GeeRkxaGlwWC6w1NTB//z0s3++FU61G3MKFSFhyGtJ+/Wt0m0wYGRrC7NmzQY5XObjHDT6hsVwux4wZMyCXyzEyMgKNRoOuri5IJBI2lA/UexBVP4fj8DdNi3o4OJ1OJCUlIS4uLqTZnFyEO54uQvQCKOL8d+Hxn40ponaU4C4gXwva6XSiqakJEomEdU4OBs8dn+YT/Hk4BAIdLUfbvfl8eejr0zZvu93ude80gbl69WoAQG1tLXbv3o2PPvoIv//971kXpSVLlmDhwoW49vk/wXTfb9H+2B8AjH4ZP9qxA7/85S9RIJPhrZdeQuakSeh95RUwdXWQd3RCOm0qFKefgYyHH4Js9mwwxyOpluMdiVVVVewXmj1mHC+L0r8DHe0eLJqgibYpU6bAZrNBo9Gwi492MnqG8tGKGAKBaxHvcrlQU1PDDvbxnM3J997GKWLYD2A6wzCTMUoIVwG4OtKLhooxiRg8DU7oLl9YWIiioqIAz3QHJRiaT1Cr1W7VD75wOByoq6tDcnKy26j6YKA6g4MHDyItLc2rzZue+WkZEgDmzZuHefPm4Xe/+x0GBgawe/dubNmyBbt27cLWrVvx0EMPYUl1NWo/3I7k7GzojUbccPPNkEskeP2yy5H55j/AxMYia8liyDduhHX6DKjNJvTqdJDb7cjs60NaWhqOHj2KtLQ0r6YubpTgcrlYgqAE6y+a8PWZyGQyt8VHowkaytNoItIcQ6QCJ4lEwno1ymQy2Gw2t4EzfB2hQu2WFEISTQhxMAxzO4A9GC1X/p0Q0hTRRcPAmBADF5Hs8lKplLVjl8vlvOdecuF0OrFv376wzGqpx195ebnbGDIqRvIkBU+kpaWhtLQUy5cvR2ZmJr799ls2mtBZrdB1/5RzOqu4GFOXLkXSmWcghmNzpwBAsyAmkwn9/f3Yv38/YmNjoVAovOZhckF/RndBX9EE970EgkQiQWpqKisdtlqtbGJQp9Oho6MD2dnZYZm7Ci2JlslkyM3NRW5urk9jGhpNJCUleb1uqMQghEP08YlTQk2dCgtjcpQAfpI2UxViqANIgNGdvru7G9OmTfNpnxYMarUaZrMZixcv5jUElws6uSgpKSksUtDr9WhqasKMGTPYLPs555yDc845B/fddx8uueQSHDx4kH38ns5OVNx3L8477zysXLkSy5cv90qMOp1OqFQqVFVVISkpCVqtFv39/WhpaYFCoUBmZiYraPIFX9HEyMgILBYLGIaBzWZzE1cFglwuZ0VAtbW1yMzMxNDQEDv/gltmDIZoNFFR+DKmoR2XVKBEo4lQISofQ4TdbofZbIbD4QhYNQgEtVqNvr4+5OXlhUwK1L9BqVSyEtdQQBOkVVVV7DmeXpcrZ/ZHCiqVip1N4Rlqtra2Yu3atejo6HD7+cqVK5GRkYGPP/4YW7ZsYTUVNIGZm5vL+knQa3KbggwGA1QqFerq6gCALZX6O2NLJBK2/l5VVcUqL2lUEUpuAgBSU1PZOj4tM3KnadE2cl/RhBAVBb7kQnUIOTk5buPrGhsbYTQa0d7eHtSYhkKsSoQAKm2WyWSYPn16yH9wQgg6OzuhUqkwefLkkKWyLpeLTXIuWLAAe/fu5Z0cowk9h8OBBQsWsBO26H1RbYa/90QIQXd3NzvI13Pn/vbbb3HVVVeBEIKcnBykpKTAYDBgzZo12LVrF77++mu8/PLLOHjwIHvkePjhh/Hwww8jJycHF154IS688EIsW7bMraLDLUF6Jg0NBgNSUlLYaIIuzMHBQRw7dgxz585lczbcaIL7j35+/kjC8/PllhmdTieGh4eh0WjQ1tbGzubMyMhg34MQEUM48DSm2bdvHxQKRUBjGi7sdntYkfBEBBOkKSgsfzGHwwGn04n+/n50dHSgoqIChw4dwty5c0NS1jmdTjQ2NiI2NhazZs2CUqmE0WjE1KlTeT2f+kHm5eWhuLgYwGgDEp8qCK3nZ2RkYPLkyWzicf/+/aiurg56dKAqTpfLhdmzZ3t90f/1r3/h1ltvRUlJCbZt24a0tDT87ne/w+eff47Dhw9Dp9N5hbOEEHz//ff47LPP0NjYiC+++IIVIlEF5sqVKwN6VdD6v1qthlarRWxsLKRSKaxWK+bNmxe0OsNNWlKSoEQglUohkUhw8OBBVFRU8Kr0UM9GjUYDm82G1NRUOBwOpKam8rLb8wf6dwoXhBAcOHCAvQYrK9do2OFH3KlUEokEZ555JmpqasLJj/h8AsMwlwN4BMBsAAsJIQfCfkMhIioRA223tlgsrLQ5kFO0L9DKBdeUJZSeC3+iJVpyDEQM1AuS28BFQcNqulv6Ap23mZaWhkmTJrk9jhCCJ554Ak888QSWLl2Kt956iyUAbmehJylQuXZGRgYefPBBMAwDq9WKb775Brt372b/AUBpaSlLEgsXLnR7r9z6PyEELS0tGBkZgUwmw4EDB5CWloasrCy/blFc7wh6X9zjBv1Hfx5s56cNVYWFhWx7dkdHBzvxiUYTY+267Bn1cFuzS0pK2JF7SqUSR44cwQsvvABgdIRBOCZCftAIYC2Avwp1Qb6ICjHQEJErbeYji6bQaDRoaWnxsmPnSwx9fX1sWOyZ7ArWL6FWq3H48GFUVFS4ZZjpzpiUlIR9+/YhJSUFWVlZSE9Pd1t4ZrMZ9fX1mDRpkhepWK1W3Hrrrfj3v/+Na665Bi+88IJb6OlP8k3bz7OystjIBxhN+J133nk477zz8Mc//hFHjhzBRx99hD179uD555/Hs88+i4yMDLcEJhUEUaKRyWRYuHAhGxHRL/vhw4eRkJDA5ib8LUyamIyJiYHT6UR7e7ubA1Io4iranj0yMoKkpCQkJCS4javnGtFG+6gRTMPAHbnncrmwadMm3HDDDbjhhhuQlpaGf//73xHfAyGkGYhsxke4iAoxTJ8+3esLzmdRc/MJvvQJwQayEEJw5MgRmEwmv6Ilf8RAVZgDAwNer81NMs6ZMweEEAwPD7NJRblcjqysLMhkMrS1tWHOnDlepViNRoP169fj22+/xcMPP4x77rnH6w/u6/1Ropk8eXLAphyGYTBz5kzMnDkTd911F4aGhtjO0I8//hjvvPMOpFIpFi9ejPPPPx+TJ0/G/PnzMWnSJLfXp0RAQ2e1Wo2Ghga4XC5kZGQgMzPTZyKOfvYAUFlZyZrc+iqHSqXSgAlMGtFRB+ji4mKvobhcK7ZoRBOhWMdLJBKUlZUhOTkZe/bsEXRo0HhhTJqogODEwM0n+NMnBGqiortqSkoKqqqq/LKsL2LgWsF7Gsz6qjwwDOMmxzWZTGhvb2erHmq1GgDYBdTa2op169ahu7sbr7/+Oi6//HK/98bN+YyMjKCpqckn0QRDamoq1q1bh3Xr1sHpdOLHH39km74efvhhAEBxcTFWrVqFFStWYNmyZW7ejNzQmTpEUw8CvV6PpKQkt4ipsbGRdbnidoaGI67ylRz2HIpLz/tNTU1etvZCIBJxUyjPO++88/DZZ595ewACDxBCPuB9IYExZgInGmr6AnV7KiwsDHg+80cugeZNesKTGKhgKjMz0ysfwFUyBqo89Pf3w263Y+nSpSCEuC2gtrY23HfffZBKpdi1axcWL14c8N7o+6PRSGVlZdgDgimkUikWLlyI0tJSrFixAklJSfjhhx+we/du/OMf/8Bf//pXJCQk4KyzzmJzE559J3QWJhUJjYyMQK1Ws9bsaWlpXkcnz/dG7wX4SVzlqxwaLDfh67yv1WrdqgcOhwM2my3sKsFYyaE//fRTABiXidaBMGbEIJVKfeYY/OUTfMHXbk+VlJ45AT7XoIQybdo0tzCdr2iJTuaWyWRuUQpdQG+//TZuv/12FBQU4LHHHoNcLkdPTw8yMzN9OifTe+vu7mZnZgjljzA8PIxDhw6hrKwMSUlJKC0txcaNG2GxWPD111+zyctdu0YFdxUVFVi5ciVWrVqF+fPnuy0S2kMRHx8PrVaLqVOnQiqVoq2tjSUJ2pHpb3H5iyacTidMJpNXfiIQYmJi3DQcQ0NDaG5uRkNDA4DAykZ/CKeB6mTxewTG8SjBHRrDt9/Bc3BNZ2cn1Gp1SEpKuvj8EQpfUrDZbKivr0dOTo5Xv4dn5eHtt99GWloaTCYTVCoVmpqa4HQ6vc7sEsnoCL2hoaGw7O39gVrPU+ESF3FxcWxr+HPPPYfm5mbs3r0be/bswXPPPYdnnnkGmZmZWL58OVatWoVzzz0XqampbCl4ypQpbEs5bYemFYXW1lY2/+KPDIGfogmGYXD06FEkJycjJSWF/VvQvzklmWDRBJ3PUVlZ6aVsDKVPIpSIIRoO0QzDXArgfwFkAdjJMEwtIWSFoC/iB2MaMdA/MO2slEqlIQ2Nodegz4+JiQlZSSmRSNDX1wej0ehFKHyVjNQzYfr06V4yZavViltuuQXvvPMOrrvuOvz5z39mXyMhIQElJSUoKSnxOrMnJydDqVSCEIKysjLBMtF9fX3o7e31KbDyBMMwmDNnDubMmYNNmzZBp9OxLeR79uzBv/71LzaBWVZWhvXr13uNF+S2ZgOj+Re1Wo1Dhw7BbrcjPT0dmZmZXv0cLpcLDQ0NrFSZ+3M3M5og4ir6HPpzT2Ujt0+CloV9dV1OhJkShJD3ALwn6EV5YkxzDFarlc0nFBQUhNRZCfzU3bh///6wnu9yuaDRaCCTybwSnHxJQaPR4OjRoygrK/PaIdRqNdavX4/vvvsOjzzyCO6++26/1+Ge2a1WKw4ePMjmYWpra4PussFAO1BHRkYwb968sEayp6Wl4fLLL8fll1/Ofu7vv/8+du7ciW+//RZ//etfMXnyZFamfeaZZ3pFfgkJCSguLmYrC776OdLS0tDc3IyMjAy3cizg+8jhSRaeCUy+fRJUEXrs2DEYjUYkJyez9yMeJaIAf0cJg8GAgwcPsu7RoWJ4eBgmkwkLFiwIucmFzpuUy+UoLCx0+6NzM+WBvgzd3d0YGBjwufsePXoUa9euRW9vL9544w1cdtllvO7LZDKhvr4e06dPR15eHgghmDlzJnvkcDgcbAmR71h6KlwihKCiokKQI4lUKsWMGTNwySWX4OGHH4ZarcaePXuwe/duvPbaa3jppZeQmJiIc845BytXrsSKFSu8lIueuQCDwYDBwUG0tLRAJpMhNTWVbWTy189B7wXwn8C02+283rNnG7ler4darcaxY8fgcDiQkJAAo9EY1F8SOLn6JIAxihgIIezgjiVLloS1C/b29qKrqwsJCQkhkwJNMk6fPh0Gg4ElAb75BFqjt9lsPnffb775BuvXr+dVeeCCJsloQpDqGAIdOXz1OXBBy77Uqk2oI4lnL0VRURFuvPFG3HjjjTCbzfjqq6/YBOaHH34IYNQwhiYwPXMmDMNALpdDp9OxG4VGo0FHRwdrAhPofQL+owmNRoPY2FjY7Xbe4iqJxN39uaOjA2az2c1fkprS+LofkRhCBM0HOJ3OsEJjT0v2ffv2hfR8zySjyWTyCkkDkQKdT5GcnIwZM2Z4Pe6tt97CbbfdhilTpmDbtm1u5+NAGBwcZC3l6Gfiq+rCPXJw+xza29u9Ent2u50d8iOgLBc9PT0YHBz02+sSHx/PHicIIWhqamITmM888wyeeuopZGVl4fzzz2cTmHK5HLW1tZg6dSqbp+Du3vR90rZtGjX5K93Shd/V1QWLxcIK0egRkVbEgomruNfLyMhATk4Oez+UuHy1kRuNxrBatf2BYZg/ArgIgA1AG4CfE0KGBHuBIIjqUcJisaC2thb5+fnIyMjA0aNHQ7oO/aKnpaX5dY72B26rNTfJyLVnC0YK1Lm6uLjYSx9BCMEf/vAHPPXUU1i2bBneeustXscjqrDUaDSYN2+e20ILdkbm9jlMnz7drcpht9thtVoxadKksLwq/N1rZ2cnhoeHUVVVxStPwTAMysrKUFZWhrvvvhsajYZNYO7atQtvvfUWYmJiUF5ejtWrV7PJSH/vExjVuVCpOp1c5aufo729HUajEWVlZV6JTU9xlecgH09wk4+e9+PZRt7X14ejR4/ijDPOCPETDohPANx/3NHpaQD3A7hPyBcIhKh0VwKjJqvNzc1smGixWNDU1IT58+fzer4/jcF3332HJUuWBCQJ2gcAAHPmzHH7w/f09MBgMGDKlCkBG6Fo3X/27Nle+gqLxYJf/vKX2LJlC66//nps3ryZV7mUEILDhw/D6XT67Lh8+umn8eijj2J4eDgkA1Pa2p6bmwuTycTryMHnXo8ePQq73e7zXsOBw+HAV199hbfeegt1dXWst8XUqVOxYsUKrFq1CmeccUbAz5L2c6jVauh0Orafw2AwwOFwYM6cOUE3EG5ugvv951Y6Wltb3azrA13r+++/x9NPP43u7m7MmjULzz//PKZNmxbCJ+O7u5L95WjZ8jJCSES+9KEgat2VPT09mD9/PhsmB1I+ekKpVLImJJ6ipWDdkTTJmJ2d7eV/SAhBSkoKNBoN9u3bh+TkZGRnZ3s1QtEw31fdX6VSYf369fj++++DVh64cDqdbuW4QMm1ULT21FylsrKSzYoHO3IEA7fBis9C4wuz2YyEhARs3rwZSUlJ6OrqYn0mXn31VfzlL3+BQqHAueeeixUrVmDFihVekZpnP4fBYEBLSwtMJhPi4+PR3t4eNFHLR6rtcDh4vW+JRILTTz8ds2bNwkMPPYSSkpJwB80EwkYA7wh90UCICjFIJBJUVlYGdYr2BHdozIIFC3zuHPQ6vohBr9ejvr4eM2bMcJvjwM0nxMfHo6ysjG2EUiqVaGtrQ1xcHLKysmA2m9kSn+d5+siRI1i7di36+vrw5ptvYt26dbw+D6vVykq+A1nc0y8iXwL1Za4CBD5y+BJWcUEJLDU11a3BKlIMDQ2hpaUFFRUVLIEVFxfj5ptvxs033wyTyYSvvvqKtd3/4IPRNoF58+axCUyu+zVFX18fkpKSsGDBAjgcDi9tSGZmZkAxk69Kh9FoxPDwMIqKimC3291+7y9yorZuU6ZM4f2ZnHfeeRgYGEBTU5NnrwTbJ8EwzAMAHADe4n1hATBmOgZfPpBc0Gy6TCYLKFry12FJo4zKykq37LC/JCPDMG5mptST0Wq1IiEhAb29vcjKymK/xF9//TWuvvpqSKVS7N69GwsXLuT1vqkYiuv16A/cL2cwdHV1Qa1W8zJX4VvlcLlcrLGNUHkKAG6Wcf4iloSEBKxatQqrVq0CIQQNDQ3Ys2cPPvroIzz55JN44oknkJ2djRUrVuDWW29FeXk5WlpaIJFIMHPmTDAM47OfQ6VS4dixY5BIJGykEWgmhtVqRVNTE0pLS6FQKNz0EsBPzVWeCUyDwRCyjuF4nwTgp1eCYZifAVgN4FwS5MwvNKJGDMGIgAu+TVSAd4clVxrtGWWEIm8+cuQI8vPzUVRUBJvNBrVajaNHj8JiseDbb7/FY489hilTpuDdd9/lvZPSBeFLDOXvvQGBIwZCCJv08rWDBoO/KkdbWxssFgtycnICTuMKFSqVCh0dHV5RTSAwDIOKigpUVFTgnnvugUqlwieffII9e/Zg+/btuOKKK9ijzrRp03z+XWk/By0/Wq1W9n366+eg38PZs2ezz+MrrhLKIZpz/ysB3AtgGSHEJNiFeWLM7eM9QcfT8RU9cY8kXD9HzyiDr5LRaDSioaEBU6dOZY8fcrkcBQUFyMvLw+9//3s8++yzqK6uxgMPPACj0QiVSuWVl/BEf38/uru7Q1oQwXIM9P3K5XJBZNP0yCGXy6HRaDBr1izYbDZeRw4+GBgYYD+DSJrBsrKycPXVV+Pqq6+G1WpFS0sL4uLi3Fq8g4H+Tf31c6SmpqK/vx+lpaU+W9z9iasIIbBarWhoaBDaUOUFAHIAnxy/7l5CyC+FfIFAGFdi6Onp8UpSBgMlhkBDaPkYtQI/7eilpaVebG+xWPCLX/wCW7duxYYNG7B582bExMS4GbTQvAQ1aaGv3dHRgeHhYV5hvud7A3wTg8PhQH19PTIzM71kw5FAr9ejsbERpaWlrJdBOMIqT/T29mJgYABz584Ne0ScJ6imxbOfIlR49nPodDo0NDRALpejpaUF6enpyMrKQkpKStAEpsPhwG233YZrr702Io9KTxBCQiprCI2oHiV8/Yx+6f2NeAsGiUQCg8GAQ4cOYebMmW41cL5HB2D0i9vX1+dzR1epVLjyyivxww8/4NFHH8WmTZvYa9G8xPTp09nogWvRTv0TKysrQw7z/R0laPLSl54iEvhKCFJ4nteHhobcqhyZmZnIysrySejHjh2DVqvlrX3gA9pklZKSImhS1GKxsFZ+1IiWejs0Nzez/RyZmZleUY/T6cQtt9yC0tJSPPzww+NiwRYtRE3HQJ2iudi3bx/KysrQ1NTk5r4cCmprazE8PIz58+fzSjJ6gp7RTSYTysrKvL64hw8fxrp169Df349XXnkFl156Ka/7MplMqK2tBfDTjhRs1/FEc3Mz9u3bhyuuuIItk9KjDp/kZShQqVRob29HZWVlyGpUWuVQq9VuR46kpCRW0uwpMooETqcT9fX1PpusIgEV4M2aNcunFwjtxlSr1dBoNABGyT8+Ph4ZGRm46667kJubiyeeeCJSUphwjDLmxGCz2TBjxoyQa700RO/p6cGUKVPckpShGKtQC7KpU6d6Pe7LL7/ENddcg9jYWGzZsoW3/Tj1JigpKUFubi6cTic0Gg1UKhVGRkaQnJyMrKyskMVGnuYqQqG/vx89PT2oqqqK2AiGHjlUKhXbo0Db0YWIFpxOJ+rq6pCdnS2ozDsYKfgC7cZ89dVX8eabbyI9PR2PPvooVqxYEXRSexBMOGIYs6PE4OAgRkZGUFFRETIpcP0bijhzHAH+SUYqbw6kJfjrX/+KvLw8bNu2DSUlJbzujZ7RuQpJqVTq1kVI8xLUQdkzL+EL9PG+RFaRgFvmFGLhUr8DrVaL3Nxc5OTk8D5yBANtQc/NzRW0fBoOKQCj3Zg5OTkYGRnBxRdfjCuuuAIfffQR5s2bJ2gkMxEQtYiBqscIIeygU5lMhpKSkpCMTWmSkQ6N6e7uBiEExcXFvJOMdPHOmjUrYOWDymr5flloVtvX6Dl/oHkJlUoFACxJcJ/f29uL/v5+VFZWCmbtRo7PDjWbzSgtLRUszKeVkoSEBK8qATVpUalUIVc5HA4Hamtr2eqQUAiXFIDR9/rQQw/BaDTipZdeEtLCfsJFDFElBovFgsbGRsTFxWHmzJloaWlBTk4O77PyyMgIGhoa3JKMfX19sNlsKCoq4pVkpBWEioqKiE1VuaDJy8rKyrANR202G0sSFosF6enpcDgcsFqtqKioECxxRwhBc3OzmxhICISikqRHDrVaHbTKQaeAFRUVCZpsjYQUCCF47LHHMDg4iFdeeUWwv81xnDrEYDAYcODAARQXF7Nh4NGjR5GSksLrKDE4OMi6JHN30/7+fhgMBtbROVCSkYbNFRUVgu+8NMEm1BeEliPNZjMrzgknL+EJl8vl09pdiPutq6tDTk5OyGd/bpVDo9G4HTmkUilqamowadIkQXsOKCnMnDkzZJMgQgiefvpptLW14c033xSaFIBTiRhGRkZgNpvdmLm9vR3x8fEBQ0Pu0cMzlKbndZqhzs7O9jlKzeVysQ5GQnUG0utSgdH06dMF33m59Xmal9BoNLzzEp6gZJOVlRWyDV4g0B29sLBQkDCfHjkGBweh1+uRmZmJkpKSsIVVnrBaraipqQmbFJ5//nnU1dXh7bffFkyT4YFThxhcLhfbgEJx7NgxSKVSvzuM5xBbf0pGuuMolUoMDQ0hKSkJ2dnZrN6/oaEB6enpXt2VkYAOtMnOzhZ8kQXrT+CTl/AEnZchdDhOu1eF3tFpLolONOdz5OB73UhI4S9/+Qu+++47vPPOO9GcZH1qE0Nvby/sdrvP86hnktHtJjik4Ln7c7P+KpUKVqsVeXl5mDp1qmDHB6qh58qmhbouHZTD97qeeQlfegkaNk+bNs3LBCUS0Ov6cseO9Lp1dXWYPn26W/4p0JGDT5UjUlJ45ZVX8Mknn2Dbtm3RHqp76hADIQQ2m83tZwMDAz7H2NMko+dkasB9GlSg3X9oaAiHDh3ClClT2NCUlg3DLZcBP2kJwhkTFwi0UhLJdZ1OJ7RaLZRKJauXSE5ORnd3N+bMmRNygi0QqGltOIm7QAjl7M+tcjgcDpYUfR056EbjSTZ8QAjBG2+8ge3bt+P9998P+7sTAk5tYlCpVNDpdJgxYwb7s4GBAVaBxw2NQ5E304aliooKtz+i2Wxmd1en04msrCxkZ2fzLi0qlUp0dHSgoqJCUC0B7dEIpcwZDIQQ9Pb2orW1FTKZDAkJCWHlJXzBYDCgoaHBrZ9CCNBILByyCVTloKXOcEgBAP75z3/iP//5D7Zv3y5oJSsATm1ioNOKZ8+eHTTJyFfe3NbWBoPBgLKysoCJIdpKrVQqYbFY2JDUX4Krq6sLKpVK0IoGMEqEXV1dqKysFDQ8pfMuKisrER8fH1ZewhfoYN3y8nJBXZBpBDJnzpyIyYZ75FCr1bBYLMjPz0dJSUnIu/1//vMfvP7669i5c+dYzok4dYgBGA3nuBgZGUFXVxdmz57NmrLMnDkzrHZpqoaMi4sLuULgdDrZkFSv1yMtLY2tcDAMw1rFCykEAkaTrxqNBhUVFYJmt6mTU1VVlc/owJdeIjs7O2gfh06nw+HDh1myEQpGoxH19fWCS73p8aG4uBh2u53XkYOL9957D3/961+xY8cOQSMjHji1iMFms7mZtRiNRrar0tckKb6kYLVaUV9fj7y8vIj187Q3X6lUQqfTwel0Ijk5GaWlpYItXmqsarPZvMxpIwW1dq+srOR1v77yEr70EtQFOZwmq0CgxxKhIxCbzYaamhqv4wOdXUk3AX/vd8eOHXj++eexc+fOsIYhRYhTmxhUKhVqa2sxb968sJOMgeZGRnqvtbW17JeC6gdo8jLc4wTVPsTFxfl1GwoH1LlqZGQkbKEVt6JDs/60BNnb2+s3AgkXNOHqq807ElBSmDZtWsDvhK8qR11dHWJjY/Hqq69i586dgn6nQsCpSww0ycgwDJYsWfLTC4SQZAynN4EPaGszl2wIIW7n9HAqHNEyV6GTsRwOh6ACLqPRiLa2Nmg0GiQmJoacrA2EkZERHDp0SHBpOl9S8AWTyYQHH3wQH3zwAfLz87F27Vo88MADgt0bMDrW8Prrr8fg4CAYhsHNN9+MO++80/NhE44YourgRI1Z2traMDw8jAULFuDAgQPs70Mhhe7ubgwODvKa2hwKPMfEce9doVBAoVBg8uTJsFgsUCqVrO1ZsEVDzVVKSkqQk5Mj2P1Sa3e5XC6otTswWi1xOBxYunQpm4ehvpfU1YjmYULB8PAwmpubBc9VREIKAHDgwAHs378fNTU1SEhIQE1NjWD3RhETE4PnnnsO8+bNg16vx/z587F8+XLMmTNH8NcSElGNGKhwhTZRMQyD7777DqeddhrvfILL5WJ3R6HP5zRp51nmDAbPCgeVZ9PkVrTMVahhSVpamqAuRgDYiVPl5eVenzHNS6hUKgwPD4fkLxGtBGakpPD999/j7rvvxo4dOwRt6Q6GNWvW4Pbbb8fy5cu5P55wEUNUieHAgQNIS0tzSxDSSVJ8SIHOjUxJSRF0QCsdX6fVaiOuEFBTFqVSCb1ej4SEBNZ3QkhBFJVO5+fnB5xNESpoyZfOewxGvP7yEpmZmV7lVz628eEgUlLYv38/7rzzTmzfvn1MfRQ6OzuxdOlSNDY2elY9Ti1i8CxXAsC3337LzmQI9CWkcmHqiiQUqKGoy+US9HwOjAqiaAepXq936+GIpCOPHkuE7k+gI/MIISHPBqXw1EtkZmYiOzsbFosFra2tqKqqElSvQZPEU6dODYsUampqcOutt+L999+PyFA2VBgMBixbtgwPPPAA1q5d6/nrU4sYuPZuNJ/Q0tKCoaEhZGZmIicnBwqFwusLGS0ZcrQiEGC0bDgwMMCKtejAE6VSGVGFgwqBhD6WEEKCzmYIFfSI1dPTA71ej/z8fOTm5oaVl/B3/draWkyZMiWsHpCGhgbcdNNN2LZtG6ZPnx7x/fCF3W7H6tWrsWLFCmzatMnXQ05NYvBMMtLEllKphNFoZMeNJycnQ6lUorOzU3AZMt11i4qKhLb5Rnt7O6u+9BcZGAwGtwoHTV4GCrF9WbsLAerRkJSUxPpaCAXu30+v14eVl/CFSEnh0KFD2LhxI9555x3Mnj075OeHC0IINmzYgPT0dDz//PP+HnbqEYPD4QhYeaBn9MHBQWi1WkgkEsyePRsZGRmCfWGpqGbmzJmC7ro0AmIYJqRQnFY4uD0cWVlZboIfmrQTurwXLcdlYDSZ29XV5WUy6ysvQd8zn2NGpKRw+PBhbNiwAW+99RbKy8tDfn4k+O9//4szzzzTLan7xBNP4IILLuA+7NQiBovFwrvycOjQIXaSMd1lUlJSkJOTg7S0tLBzAaGOieMLaq5C5xyES2JUusutcMTGxmJgYEDwpB11XRLaXBUYbWSjoqhgyVyal1Cr1SCEsH0rvmZK2u121NTUhE0K7e3tuPrqq/Hmm2+iqqoq5OePEU4tYrj66quh0+mwZs0aXHjhhT6TRTabDfX19cjJyXGTSLtcLtaMRafTsSPrMzIyeJNEX18fenp6BG9YoiYoBQUFglYInE4njh49isHBQcTGxrI9HJEQIwW95+LiYkF1FcDo59zf3x/WgBmal1CpVDCbzW56CYfDgZqaGkyePDksH4xjx47hqquuwquvvooFCxaE/PwxxKlFDIQQtLS0YOvWrWxjysUXX4yLLroIWVlZGBgYwLFjx4IainBH1ms0GigUCrZE5uuLSM/9er0e5eXlgnr00WrJ1KlTBTVBAeBWQmUYBjqdjm1VT0pKQlZWlt/3HAi0uSgUQxi+6OnpgVKpRGVlZcSfM1cvMTQ0BJvNhoKCAkyZMiXka/f09OCKK67Ayy+/jMWLF0d0X2OAU4sY3C50vF6+bds2fPDBB7DZbNBqtXjnnXdCUvDR6UBKpRJqtRrx8fFstj8mJgYulwvNzc2QSqWCOiIDwpir+AJ3grWvjk5/FY7MzMygKlDqeSB0VQMYbU2n3aJCkq/dbsfBgweRk5PD+i6Ekpfo7+/H5Zdfjueffx5Lly4V7L6iiFOXGLh4/fXX8dJLL+GCCy7Ap59+CkIILrroIlxyySUoLCwMiSSMRiMGBwehVqsRExMDq9WK3NxcwcuRNFchdDIwHGt3o9HIJi8DVThoe7PQRAaMRjdDQ0M+lZKRgOYUPI8PfPMSg4ODWLduHZ599lmcc845gt1XlCESAwAcPHgQs2fPRnx8PAgh6O/vx7Zt2/Dee+/BZDJh9erVWLNmTUh25xaLBTU1NVAoFDCbzW7ToCLNL0TLXIWa3yYlJYVNZBaLhU1eOp1OVmBEuzqF9jwAgI6ODuj1ekHnUwI/uU9PmjQp4JHHV17CZrMhMzMTV1xxBR5//HGsWLFCsPsaA4jEEPDFCIFSqcR7772Hd999FzqdDhdccAEuueQSzJgxw+/CoS5D3DFxZrOZ3VUBsMeNULUR0TJXoRUCIV2naYWjr68Pw8PDyMvLQ35+fkiDdQOB5m7MZrPgfSuUFEpKSkJSd9K8xB/+8Ad88MEHqKiowO23344LL7xQUOctio0bN2LHjh3Izs5GY2OjUJcViSEUaDQavP/++3j33XcxMDCAFStW4NJLL3WTMtNW7EAhvtVqhVKpZHfVrKws5OTkBDwS0NZmu90u+CKgdXmhx9oD7uVZk8nE9nCkpqZGVOGgOSKr1Sp4V2e4pEAxPDyMdevW4Te/+Q0KCgqwY8cOPPTQQ1Gxe//666+hUChw/fXXi8QwETA0NITt27fj3XffRWdnJ5YvXw6n04mUlBTceeedvL8E1OZMqVSy4WdOTo7bWTVa5irAT8lAoY1mAPdBuNwjj2fpN1hVxxPUgYr6P0wkUtDr9bjssstwxx134IorrhDsvgKhs7MTq1evFolhomF4eBgbNmxAY2MjFAoFzj77bKxZswYLFiwIaTe02+2sNNtsNrMuw+3t7cjKyhJcGUgVmNFIBg4MDKC7uzvoaHta4aCJvGBTrmijFQDBqzyRkoLRaMTll1+OG2+8Eddee61g9xUMpwIxRNWoJVpQqVQoKyvDu+++C4vFgo8++gh/+9vfcMcdd2DZsmVYs2YNFi9eHHQ3jI2NRV5eHvLy8uB0OtHf34+6ujpIpVJYLBYMDQ0Jdj6njWFCex0CozZsAwMDmDt3btA8CJ2LmZKSgmnTprEVjtraWrbCQXMxtGISExMj6Eg+4Kdp1sXFxWGRgslkwlVXXYUNGzaMKSmcKjghIwZ/sFgs+OSTT7B161b8+OOPOO2003DppZfi9NNP5yXTpf0UycnJboapXAViOIvD09pdSHBFUZFqCbgVDofDAUIIkpOTvcYFRgqqaAxXhWmxWLB+/XqsXbsWN998s6CExQenQsRwUhEDFzabDZ9//jm2bduG7777DosWLcIll1yCpUuXeoXMQ0NDaGlp8dlPQV2kBwcH2f6N7OxspKen81osNMSvrKwUNBlGCEFHRwfb1SnkwqXzP2mPi9ls9jkKLxxESgpWqxXXXnstVq5cidtvv33MSQEQiQE4gYmBC4fDga+++gpbt27FN998g7lz5+KSSy7B2WefjW+++QYKhQJz584N2rBEXYYHBwdZmXIgI5bu7m52aI2QpU6aDKQVEyEXB7clmxqZeLpUhVvhiJQU7HY7NmzYgDPPPBObNm0aF1JYv349vvzyS6jVauTk5OD3v/89brjhhkgvKxLDeMPpdOLbb7/F1q1b2bmE999/Py666KKQFI00iTc4OMi6KnMz/VQEJLQykJ77pVJpQG1HOHC5XKynZElJid/H+KpwZGRkBCQ/mlMoKioKixQcDgc2btyI+fPn47e//e24kEIUMeHezClHDBQvvfQSPv30U/zqV7/C9u3b8cknn2D69Om45JJLsGLFipAShIQQGAwGVprtcDgQFxeHiooKQY8PtIwaHx+PqVOnCro4qE9DZmYmb8GVZ4WD+j96VjgoKRQWFoal23A6nfjFL36BmTNn4qGHHjrZSAEQiWHiQKVSIT09nT0CuFwu1NTUYMuWLdizZw+Ki4tx8cUX44ILLuBdWqQLVyqVIi4uju3foNLsSEiC+j+kpqYK7hDtdDpZFWYkk71ohUOtVoNhGDYX09LSEhEp3HHHHcjPz8fjjz9+MpICIBLDiQF6zt6yZQt27dqF7OxsrFmzBqtXr/bboUh33PT0dLcwnKoPVSoVJBJJyENr6LXr6uqQlZUlmHyae+3a2lpWPi0ULBYLBgcH0d7ejtjYWOTn57NzOPgubpfLhbvuugupqal45plnBD2STTCIxHCigZ7pqadESkoK1qxZg4suugiZmZlgGIYV6gQzbqGWbkqlEoQQNpIIVMKktvEFBQWCelUCP4X40bx2YWEhMjIy3IRkfIbqulwu3HfffZBIJNi8efPJTAqASAwnNqhvwrZt27B9+3bI5XKcddZZ+PTTT/Haa6+FtOPabDaWJBwOh8/JVrSnQmjbeOAn1WE0HJ0CEQ6tcKhUKoyMjPgs/7pcLvzP//wPzGYz/vKXv5zspACcisRwzz334MMPP4RMJsPUqVPx2muvsR2QJzIIIfjyyy9x7bXXYurUqW6eEgUFBSGdhWlX5ODgINu/kZqaiiNHjmDGjBmC91RQz4NoEA49muTn5weNQjwrHAzDoLm5Ge3t7dBqtXjllVcENYDxxO7du3HnnXfC6XTixhtvxG9/+9uovVYQnHrE8PHHH+Occ85BTEwM7rvvPgDA008/HellJwSeffZZnH/++SgvL0dfXx/rKWGxWFhPiVB9FhwOB3p7e9He3g6ZTMYeN+j4u0gRqeNyIIRCCp6g07vvueceHDhwAAsXLsRNN92ENWvWCHqP3HudMWMGPvnkExQWFqK6uhr/+te/xmum5IQjhqj3Spx//vns/1+8eDG2bt0a7ZccM9x9993s/y8oKMCvfvUr3HHHHVAqlXj33Xfx61//GsPDw7jggguwZs0aXroDi8WCvr4+zJ8/H4mJidBoNOju7oZer2fP5uEOcKHej+GOdguESEiB4r333kNSUhL6+vrQ0dGB/v5+Qe+Ri3379mHatGmYMmUKAOCqq67CBx98MOGHzY4VxrSJ6u9//zuuvPLKsXzJMQfDMMjJycEtt9yCW265BWq1Gh988AEeeOABDA4OYuXKlaynhOfipoYz3EYrGjG4XC5otVr09fWhpaUlZPWhxWJBbW1tVLwfIyUFQghefPFF/Pjjj/jPf/7DNm1Fc1pUb2+vW4WnsLAQP/zwQ9Re70SDIMRw3nnnYWBgwOvnjz/+OBsKPv7444iJicE111wjxEueMMjMzMQNN9yAG264ATqdDh9++CEee+wxdHV1Yfny5bj00ktRXl6Ouro6WCwWVFZW+lRgSiQSZGZmIjMzkz2bDw4O4siRI0Gt9akHxKxZswTP73DLneGSwv/93//hm2++wdatW6PiuiQidAhCDJ9++mnA37/++uvYsWMHPvvss5NVoMILaWlpuP7663H99ddjZGQEO3fuxHPPPYe6ujo4HA78+c9/5qVvkEgkSE9PR3p6OmutPzg4iNbWVigUCuTk5LD9G5QUZs+eLbgHRKQaCEIIXn/9dezevRvvv/++oH6awVBQUIDu7m72v3t6egQfwnMiI+rJx927d2PTpk346quvwp5psGXLFjzyyCNobm7Gvn37JvrwkJCwa9cuPProo7jpppvw6aeforGxEWeddRbWrFmDRYsWhZSV97SZl8lkMBgMKC8vR1pamqD3LYQw6h//+Ae2bNmC7du3C+q8zQcOhwMzZszAZ599hoKCAlRXV+Ptt99GaWnpmN7HcUy43TLqxDBt2jRYrVY22bV48WK8/PLLIV2D2qv/4he/wLPPPntSEUNbWxsyMzPZ3dxiseDjjz/G1q1bcfDgQZx++um49NJLcdppp4XUoWkwGFBbW4v09HTo9XrIZDLk5OSEPG3bF6gSMycnJ+xd9p133sEbb7yBnTt3umk3xhK7du3CXXfdBafTiY0bN+KBBx4Yl/vAqUgMQuKss8466YghEGw2Gz777DNs27YN33//PRYvXoxLLrkEZ555ZsC+C2ohx01icmdRRNK/IQQpvPvuu/jb3/6GnTt3Cm5tf4JCJIZIcKoRAxd2ux1ff/01tmzZgm+++Qbz589nPSW4Z3M6LauiosLvTkyt9ZVKJdvs5GtgjSeEIIUdO3Zg8+bN2Llz50khdBMIIjH4A5/KxqlMDFw4nU7897//xdatW/HFF1+gvLwcl1xyCeLj49HS0oKNGzfyPrNzrfVdLhdrre/ZvyEEKezZswdPP/00du7cKbiO4gTHhCOGCWMGG6yyEQ4mkORVUEilUixbtgzLli2Dy+XC3r178b//+7/Ys2cPzj77bOTn5+P888/n5Skhl8tRVFSEoqIi1lq/ubkZDoeDnWoVHx/PtmWHSwqff/45nnzySZEUThBMGGIQGk6nE7fddpub5PXiiy8+6ZRtEokEs2fPRnt7O2pqaqBSqbBlyxY8++yzmDRpEi6++GKsWrWKV6lSJpOhoKAABQUFrLX+0aNHodPpkJqaipSUFNYHMhR8/fXXeOSRR7Bjxw7Bp22PNR566CGkp6fjrrvuAgA88MADyM7Oxp133jm+NyYwJsxRIhDee+893HHHHVCpVEhNTUVVVRX27NkT8Dnff/89HnnkEfZxTz75JADg/vvvj/r9jgdsNptbIpEaum7duhW7du1CTk4O1qxZgwsvvJC38pEeHzIzMyGXyzE4OAiTyYT09HTk5OTw6t/47rvvcO+992LHjh2C+j2MFzo7O7F27VocPHgQLpcL06dPx759+yKNgsSjRDi49NJLcemll4b0nFNN8upZXZBIJKisrERlZSUeffRR1lNi7dq1SE1NZY1n/O3g1P+R6+qUk5PDtk3T/o20tDTk5OT47N/Yt28f7rnnHmzfvv2kIAUAmDRpEjIyMlBTU4PBwUHMnTv3pDwanfSN7iJG+zfmzJmDhx56CD/88ANefPFFjIyM4KqrrsLq1avxt7/9DQMDA6DRo8vlYiMFT6s3OkW8rKwMixYtQmZmJvr7+7F3714cOnQIKpUKVqsVBw8exJ133on33ntPcNcpf9iyZQtKS0shkUhw4MCBqL3OjTfeiNdffx2vvfYaNm7cGLXXGU+ctMQgSl59g2EYTJ8+Hffffz++++47vPrqq3A4HLj++uuxatUqbN68GZdccgmkUmnQBU37N+bMmYPFixcjNzcX9fX1mDdvHq688krceuutgg/tDQQ6nWzp0qVRfZ1LL70Uu3fvxv79+7FixYqovtZ44aQlhurqahw9ehQdHR2w2Wz497//jYsvvjika2zcuJHdHU9GMAyDyZMn4+6778Y333yD1157DW+99RaGh4exadMmPP/88+jo6ECQPBR7rfT0dOTl5SEpKQnPPfccWltb8eCDD47BOxnF7NmzMXPmzKi/jkwmw9lnn40rrrgiqkYy4wpCSKB/JzR27txJpk+fTqZMmUL+8Ic/hPz8r776ivz444+ktLQ0Cnc38fDee++RF154gbhcLtLf309efPFFcu6555Lq6mryyCOPkJqaGmIwGIjRaPT57+DBg6S8vJw0NDSM6/tYtmwZ2b9/f9Su73Q6SWVlJTly5IhQlwy2Dsf830lNDEKgo6PjlCEGf1CpVOT//u//yMqVK8n8+fPJgw8+SPbv3+9GEvX19aS8vJzU1NRE9V7OPfdcUlpa6vXv/fffZx8TTWJoamoikydPJps2bRLysuNOBJ7/Tohy5XgiCnMKT2jodDps374d27ZtQ3d3N84//3wsXrwYjzzyCF599dUJoUo9ARWyYrlSxImNtLQ0bNiwARs2bMDIyAh27NiBBx98EI8//viJtBBFBIEYMQSBGDGcOAhHCDdBMOEihpO2KjFR0N3djbPPPhtz5sxBaWkpNm/ePN63dNLi0ksvRU9PD6xWKwYHB08UUpiQEIkhANavX48lS5bg8OHDKCwsxKuvvhryNWJiYvDcc8/h0KFD2Lt3L1588UUcOnQoCncrQoRwEI8SY4w1a9bg9ttvx/Lly8f7VkRMHIhHiVMZnZ2dqKmpwaJFi8b7VkSICAiRGMYIBoMB69atw/PPP4/k5OTxvh0RIgJCJIYxgN1ux7p163DNNddg7dq1YV3DYrFg4cKFqKysRGlpKR5++GGB71KEiJ8g5hiiDEIINmzYgPT0dDz//PMRXcdoNEKhUMBut+OMM87A5s2bsXjxYuFuVsR4QcwxnGr49ttv8Y9//AOff/45qqqqUFVVhV27doV8HYZhWKs2u90Ou91+Sg/vERFdiMrHKOOMM87g1Z3IB06nE/Pnz0draytuu+22kzKJec899+DDDz+ETCbD1KlT8dprr4lu0uMAMWI4gSCVSlFbW4uenh7s27fvpFRjLl++HI2Njaivr8eMGTNYSz4RYwuRGE5ApKam4uyzz8bu3bvH+1YEx/nnn89O3Fq8eDF6enrG+Y5OTZzyxLB//35UVFTAYrHAaDSitLR0Qu7EKpUKQ0NDAEYHxnzyySeYNWtWWNdyOp2YO3cuVq9eLeAdCo+///3vWLVq1XjfximJYFWJUwIMw/wBQByAeAA9hJAJF78yDFMB4A0AUowS+n8IIY+Gea1NABYASCaEjDk7MAzzKQBfnm8PEEI+OP6YBzB6j2uJ+CUdc4jEAIBhGBmA/QAsAE4jhDjH+ZaiBoZhCjFKMI8D2DQexBAMDMP8DMAvAJxLCDGN8+2ckhCrEqPIAKAAEIvRyME4vrcTVTwP4F4AE3KaLMMwKzF6f8tEUhg/nPI5huP4K4D/AfAWgKfH+V6iBoZhVgNQEkJ+HO97CYAXMEpanzAMU8swzMvjfUOnIk75iIFhmOsB2AkhbzMMIwXwHcMw5xBCPh/ve4sCTgdwMcMwF2A0MkpmGOafhJBrx/m+WBBCpo33PYgQcwynLBiGOQvA3RMxxyBi/CEeJUSIEOEFMWIQIUKEF8SIQYQIEV4QiUGECBFeEIlBhAgRXhCJQYQIEV4QiUGECBFeEIlBhAgRXhCJQYQIEV4QiUGECBFe+P8H6MrG7Rp78AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Arrow3D(a),\n",
    "    Arrow3D(b),\n",
    "    Arrow3D(c),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Arrow3D(b, color=red),\n",
    "    Arrow3D(a, color=blue),\n",
    "    Arrow3D(c, color=purple),\n",
    "    Arrow3D(b, c, color=blue),\n",
    "    Arrow3D(a, c, color=red),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3.5—Mini Project\n",
    "\n",
    "The following comprehension creates a list of 24 Python vectors:\n",
    "\n",
    "```python\n",
    "from math import sin, cos, pi\n",
    "vs = [(sin(pi*t/6), cos(pi*t/6), 1.0/3) for t in range(0,24)]\n",
    "```\n",
    "\n",
    "What is the sum of the 24 vectors? Draw all 24 of them tip-to-tail as Arrow3D objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sin, cos, pi\n",
    "vs = [(sin(pi*t/6), cos(pi*t/6), 1.0/3) for t in range(0,24)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.440892098500626e-16, -7.771561172376096e-16, 7.9999999999999964)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theSum = add(*vs)\n",
    "theSum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
      "[(0, 1), (2, 3), (4, 5), (6, 7), (8, 9)]\n"
     ]
    }
   ],
   "source": [
    "vs2 = list(range(10))\n",
    "print(vs2)\n",
    "arr = [(vs2[i-1], v) for i, v in enumerate(vs2) if i%2 == 1]\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "arrowList = [Arrow3D(vs[i-1], v) for i, v in enumerate(vs) if i%2 == 1]\n",
    "draw3d(\n",
    "    *arrowList\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-4.440892098500626e-16, -7.771561172376096e-16, 7.9999999999999964)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "current_sum = (0,0,0)\n",
    "arrows = []\n",
    "for v in vs:\n",
    "    next_sum = add(current_sum, v)\n",
    "    arrows.append(Arrow3D(next_sum, current_sum))\n",
    "    current_sum = next_sum\n",
    "print(current_sum)\n",
    "draw3d(*arrows)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3.10\n",
    "\n",
    "Find a vector in the same direction as (–1, –1, 2) but which has length 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.449489742783178"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = (-1,-1,2)\n",
    "theLength = length(v)\n",
    "theLength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.4082482904638631, -0.4082482904638631, 0.8164965809277261)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar = 1/theLength\n",
    "v = scale(scalar, v)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
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