{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fSPqOh2fAtPI"
   },
   "source": [
    "# Tutorial: Basic PCA approaches\n",
    "\n",
    "This lab focuses on principal component analysis and regression as well as partial least squares regression in R.\n",
    "\n",
    "## Goals:\n",
    "* Understand principal component analysis, and use it for visualization\n",
    "* Implement principal component regression using `pcr()` in the `pls` library\n",
    "* Implement partial least squares using `plsr()` in the `pls` library\n",
    "\n",
    "This lab draws from the practice sets at the end of Chapter 6 in James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). \"An introduction to statistical learning: with applications in r.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mZJs411pW3TN"
   },
   "source": [
    "---\n",
    "# Principal component analysis: the big picture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "buBm3olQW9ep"
   },
   "source": [
    "Principal component analysis (PCA) is a handy way to decrease the dimensionality of your data. PCA helps you identify the dimensions along which your data varies the most, so you can capture the important variance while also simplifying. \n",
    "\n",
    "This can be a bit hard to get a physical intuition for, so if you'd like more discussion about how to think about PCA and dimensionality reduction more generally, I'd recommend checking out [this video from StatQuest](https://www.youtube.com/watch?v=_UVHneBUBW0)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3dwc7bKmeVYi"
   },
   "source": [
    "However, before we move on to PCR and PLS, let's do a quick example of applying PCA in a simple context. In this example, we'll focus on PCA as a tool for visualization using the `iris` dataset. This data set reports petal and sepal lengths for three different subspecies of iris flowers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 283
    },
    "id": "QjW7ByKpe4oY",
    "outputId": "6ac7fe43-9677-4459-c3ee-a12cdfc16208"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sepal.Length</th><th scope=col>Sepal.Width</th><th scope=col>Petal.Length</th><th scope=col>Petal.Width</th><th scope=col>Species</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>5.1</td><td>3.5</td><td>1.4</td><td>0.2</td><td>setosa</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>4.9</td><td>3.0</td><td>1.4</td><td>0.2</td><td>setosa</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>4.7</td><td>3.2</td><td>1.3</td><td>0.2</td><td>setosa</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>4.6</td><td>3.1</td><td>1.5</td><td>0.2</td><td>setosa</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>5.0</td><td>3.6</td><td>1.4</td><td>0.2</td><td>setosa</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>5.4</td><td>3.9</td><td>1.7</td><td>0.4</td><td>setosa</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & Sepal.Length & Sepal.Width & Petal.Length & Petal.Width & Species\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 5.1 & 3.5 & 1.4 & 0.2 & setosa\\\\\n",
       "\t2 & 4.9 & 3.0 & 1.4 & 0.2 & setosa\\\\\n",
       "\t3 & 4.7 & 3.2 & 1.3 & 0.2 & setosa\\\\\n",
       "\t4 & 4.6 & 3.1 & 1.5 & 0.2 & setosa\\\\\n",
       "\t5 & 5.0 & 3.6 & 1.4 & 0.2 & setosa\\\\\n",
       "\t6 & 5.4 & 3.9 & 1.7 & 0.4 & setosa\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | Sepal.Length &lt;dbl&gt; | Sepal.Width &lt;dbl&gt; | Petal.Length &lt;dbl&gt; | Petal.Width &lt;dbl&gt; | Species &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 | 5.1 | 3.5 | 1.4 | 0.2 | setosa |\n",
       "| 2 | 4.9 | 3.0 | 1.4 | 0.2 | setosa |\n",
       "| 3 | 4.7 | 3.2 | 1.3 | 0.2 | setosa |\n",
       "| 4 | 4.6 | 3.1 | 1.5 | 0.2 | setosa |\n",
       "| 5 | 5.0 | 3.6 | 1.4 | 0.2 | setosa |\n",
       "| 6 | 5.4 | 3.9 | 1.7 | 0.4 | setosa |\n",
       "\n"
      ],
      "text/plain": [
       "  Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n",
       "1 5.1          3.5         1.4          0.2         setosa \n",
       "2 4.9          3.0         1.4          0.2         setosa \n",
       "3 4.7          3.2         1.3          0.2         setosa \n",
       "4 4.6          3.1         1.5          0.2         setosa \n",
       "5 5.0          3.6         1.4          0.2         setosa \n",
       "6 5.4          3.9         1.7          0.4         setosa "
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QxEIh4VlfC4E"
   },
   "source": [
    "First, let's convince ourselves that there is some redundant information in this data set. How correlated are the four quantitative variables?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 190
    },
    "id": "NnCVJfYZfBsK",
    "outputId": "89bd1bbf-140f-4323-82f4-39e493ca78df"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 4 × 4 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Sepal.Length</th><th scope=col>Sepal.Width</th><th scope=col>Petal.Length</th><th scope=col>Petal.Width</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sepal.Length</th><td> 1.0000000</td><td>-0.1175698</td><td> 0.8717538</td><td> 0.8179411</td></tr>\n",
       "\t<tr><th scope=row>Sepal.Width</th><td>-0.1175698</td><td> 1.0000000</td><td>-0.4284401</td><td>-0.3661259</td></tr>\n",
       "\t<tr><th scope=row>Petal.Length</th><td> 0.8717538</td><td>-0.4284401</td><td> 1.0000000</td><td> 0.9628654</td></tr>\n",
       "\t<tr><th scope=row>Petal.Width</th><td> 0.8179411</td><td>-0.3661259</td><td> 0.9628654</td><td> 1.0000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 4 of type dbl\n",
       "\\begin{tabular}{r|llll}\n",
       "  & Sepal.Length & Sepal.Width & Petal.Length & Petal.Width\\\\\n",
       "\\hline\n",
       "\tSepal.Length &  1.0000000 & -0.1175698 &  0.8717538 &  0.8179411\\\\\n",
       "\tSepal.Width & -0.1175698 &  1.0000000 & -0.4284401 & -0.3661259\\\\\n",
       "\tPetal.Length &  0.8717538 & -0.4284401 &  1.0000000 &  0.9628654\\\\\n",
       "\tPetal.Width &  0.8179411 & -0.3661259 &  0.9628654 &  1.0000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 4 of type dbl\n",
       "\n",
       "| <!--/--> | Sepal.Length | Sepal.Width | Petal.Length | Petal.Width |\n",
       "|---|---|---|---|---|\n",
       "| Sepal.Length |  1.0000000 | -0.1175698 |  0.8717538 |  0.8179411 |\n",
       "| Sepal.Width | -0.1175698 |  1.0000000 | -0.4284401 | -0.3661259 |\n",
       "| Petal.Length |  0.8717538 | -0.4284401 |  1.0000000 |  0.9628654 |\n",
       "| Petal.Width |  0.8179411 | -0.3661259 |  0.9628654 |  1.0000000 |\n",
       "\n"
      ],
      "text/plain": [
       "             Sepal.Length Sepal.Width Petal.Length Petal.Width\n",
       "Sepal.Length  1.0000000   -0.1175698   0.8717538    0.8179411 \n",
       "Sepal.Width  -0.1175698    1.0000000  -0.4284401   -0.3661259 \n",
       "Petal.Length  0.8717538   -0.4284401   1.0000000    0.9628654 \n",
       "Petal.Width   0.8179411   -0.3661259   0.9628654    1.0000000 "
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor(iris[,1:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D3axc9oefZPK"
   },
   "source": [
    "It looks like `Petal.Width` and `Petal.Length` are highly correlated with each other, and they're also both correlated with `Sepal.Length`.\n",
    "\n",
    "Let's also plot how the three subspecies are distributed with respect to these variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 857
    },
    "id": "SePUqbZUfomg",
    "outputId": "bd3b914a-899f-4eb8-a626-d527c7c5c21e"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e+sMf/uDz+Xr06PHggw9G475fJSFR6dVX7xQAAKBJi9yp5YsXL676eO7cuVUfJyQkzJkzJ2IxAAAAjCrKzg8FAADAuVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAWvQMgLNQDP3o//kgrK1WSUyyjrzB1Ol/vRAAAIOwodgbkW/2R97PVIpqIaCXFnpdetAwfaR71a71zAQCA8OJQrOHYy3xrP/G3uv/QvJ+vlpIS3SIBAICIoNgZjW/zN5p21qgmvi1f6ZAGAABEEMXOcNyuwOOuc4wDAACjoNgZjdK99znGe0Y4CQAAiDCKndGYWrdWOnaqMai072Bq31GPOAAAIHIodgYUc/tdpn6DxGoVEbFaTH0HxtwxW+9QAAAg7LjdiRGZTNbrbpTrbtQ7BwAAiCj22AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIpd6Did2ulToqoNnafCrh74Udzuhs7j9WpFheL1NnQeAKiXSrcUV5hVTe8c/+HxSUGZeBv8Ig00Zha9AxiBdvqU993l6o+7RURiYy3DR5mH/UoUJdh51II8z6uLpKRYREQUpW27mNvvlJiYoAO5XN6V7/m+2SSqKiaTeeCFlrHjJS4u6HkAoF5OlsniL2XXiRiRjPgYGd9XLr9AzzyVbln6tXy5T1RNzCa5tKtcPVBieQOEEbHHrsE8Hs/rL51pdSLicnlXve/buC7oeVTV++Lz/2l1IqJpRw65Fz1fn0TvLPN9tfHMvkNV9X39peftJfWYBwDqweWR51bLrhNnFv2l6vPdtX5NmL26QTbsFf++Q58qn+2Sf3ypZx4gfCh2DeX7botWkFdj0Pvpx+LzBTfPF59pzooag9rxo2phYVDzaCcL1O2bawyq32/T8k8EXB8AQmvTfskvrTn4762i6XRM9sgp2XKo5uCm/VJQpkMYINwodg2lBSxezkqtPLjXDPXE8cDjB/cGl6foZODxwsDjABBaZ7c6EbE7xe6KeBQROUceEckriWwOICIodg2lJCYGGDWZlISEoOYxJdkCj2dkBBcoIVAeEQmYEwBCLSnQCb0Wk8RbIx5FRM6RR0RsnHgMI6LYNZSpZx+Jia3LYO3MQ4eLUvOfQ4mNM3U6P7g8bdopmVk158nINLXrGNQ8AFA/gzpKzFnXJQzuJBazHmlEumRJZnLNwVap0iHIv5qBqECxayglNc167ZTq15ya2razTrw26IlSU83jxv9Xt7OYLbfOCHoes9l6wzQlNe3nhM1SrVOmiVmn11QATUxWstxyscRW2z/XJUtuuFC3PFazzLhMUqsdtMiwyYzLxMQbIIyIq71DwNSzT0yHTuqeXeKwKy2yTed1rce9TkTEMuQyS/c+vi/WqKdOm1q1Nl92eX3udSKitMyOuff/qbt3aKeLlLQMU7ceYq3PPABQPzmdpFtL2XbIW1hS2b2drXsrqc9rYui0z5AnrpbvjkhRuWQmS++2YuVPXRgUxS40lCSbecDgEEyUmmoef20IXnCsVlOvvg2fBgDqJyVBLuqsFhdXZGUFPoE4wmItMogTUtAEsCcaAADAICh2AAAABkGxAwAAMAiKHQAAgEFQ7AAAAAyCYgcAAGAQFDsAAACDoNgBAAAYBMUOAADAIKLsyRM+n6+8vNzr9YqI2+32+XylpaV6hwqO0+nUO0LQfD5fWVmZUq/npOnF7Xa73W5TVD0M0uPxuN1uNukI8Hq95eXl5qh6gLL/dS+6fts+n8/r9bJJR4DH43E4HC6XK4RzVlRU+Hy+EE6IyIiyYmc2m202W2JioojY7XaPx5OSkqJ3qKBFXWa73Z6cnBxdJcnhcMTGxlos0bSFV1ZWShRuHhKFmSsrK202m9Vq/eVVGw2n06koSmxsrN5BguB2u3mVjgy3252YmBgXFxfCOc1mc3T98QO/aHqrBgAAQC0odgAAAAZBsQMAADAIih0AAIBBUOwAAAAMgmIHAABgEBQ7AAAAg6DYAQAAGATFDgAAwCCi6b78jZm69Rtv7kapdCiZLa0TrpXkZH3zaCXF6uavtOLTSmqaaUCO0ixV3zwAACACKHYh4Hn9JXX3Dv/HWmGha9cO64xZpvYd9cqj7tvjWfyyuN1nltd9Zr3pNtP53fTKAwAAIoNDsQ2l/vCdunuHiPbzkKZ6X/+bboE8bu/Sf/zc6vwjy98UdygfDg0AABohil1D+b7+UkRElOqDWmWlFJ/SJY96+JBmL68xqNnL1Z8O6pIHAABEDMWuoTSPO+C46qiMcJIzzpHnnOMAAMAoKHYNZW7bPsCoYjJlZ0c6iv87t2wVeDy7dYSTAACACKPYNZR5zJVKfHyNQcvQS8Wkz+9WaZZqvnREjUHzJcOVtHRd8gAAgIih2DWYyRQz5wGlVRsxKSIi1hjL8MvNV0zQMZFl1K8tV16lZDQXk0lJb24ZN8ky5kod8wAAgMjgdieh0Cw1ZtZcvUNUYzKZhwwzDxmmdw4AABBR7LEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOwAAAIOg2AEAABgExQ4AAMAgKHYAAAAGQbEDAAAwCIodAACAQVDsAAAADIJiBwAAYBAUOxG3W7OXh2Aep1M9fiwE8wAAEAy7y+T26h0CjYNF7wB60goLvP/+l3pwn2iaktLMPOZKc98B9ZhHPXLI84+XpaxMRBRFlB69rVOmiYnSDAAIr037ZcW3UlKRrijSPVumXCgtUvTOBF014fJRWeF5+UX1wF7RNBHRSku8Sxeru34Ieh6n0/PSX/ytTkQ0TdQd33mWLg5tWAAAathySF5eLyUVIiKaJjuPy7MfS4Vb71jQVdMtdr7cjVpJcY1B76r3g53H89G74vHUGFS/2yZedosDAMJoxbc1R4rssm6PHlHQaDTdYqcVFgQaPOnfgRfEPPl5AYfV/BP1ygUAwC9TVTlZFmA8ryTiUdCYNN1iJ/EJgQbjRVGCmkZJCDSPiCm5WT1CAQBQFyaTxFkDjCfFRjwKGpOmW+xMffqfPWjuOzDYecyXDBc5qwumNJPk5PoFAwCgLi7sHGBwUMeI50Bj0oSLXdv2ll9PFItF5MyxV1OnLpYxVwY9T6cuppyL/6vbWa3W2+8KVU4AAAK6ZpCc1+LnRYtZbsiRDs31C4RGoEnf7sQ89DJT1x7q3j3irFRatzWd1zXY47B+1onXqP0H+r5cJ+VlptYdzJePEUuT/sUCACIg1iK/vUJ+OCq7jjhSkmL6dbBmcayoyWvq/UNpnmluntnweUxt25va3tLweQAAqDtFpFcbaRlXYbOZ4wKec4cmpukeigUAADAYih0AAIBBUOwAAAAMgmIHAABgEBQ7AAAAg6DYAQAAGATFDgAAwCAodgAAAAZBsQMAADAIih0AAIBBUOwAAAAMgmIHAABgEBQ7AAAAg6DYAQAAGATFDgAAwCAodgAAAAZBsQMAADAIih0AAIBBUOwAAAAMwhLW2Y8ePfrGG2/s3r1b07QOHTrcdNNNXbt2rbHOrFmzDh06VLUYFxe3fPnysKYCAAAwpDAWO6/X+9BDD/Xu3fupp54ymUzLli175JFHXn311fj4+Oqr2e326dOn5+Tk+BdNpqjciejb+Lnvy/Way6WkZ8Tc+D+SklK/edSDB3xrP9bKy5X0DOu4qyQ1NbQ5dePx+LZ+q+WfUBITTT16Ky2z9Q4EAIABhbHYORyO8ePHjx492t/krrnmmrVr1+bl5XXs2LH6auXl5S1atMjIyAhfknBzP/eUlnfM/7HmcLieeMhy8+3mHj2Dncf3wTvejevOzJN/wrVrh3XKNFPP3iGMqguttNSz6Dnt9Kkzy5+vsYy50nzxpXpmAgDAiMK4eywlJWXixIn+VldeXv7++++3bt26TZs21dfxeDwulys3N3fOnDm33Xbbk08+efz48fBFCgffpvVVra6K961Xg51HzTvu/XKdaNWGNNWzdLGoasMC6s/7zpKfW52IeL3eVR9oeSf0SwQAgDGF9xw7EVFV9ZprrvF4PBdccMFjjz1mtVqrf7aioqJZs2Zer3fmzJkismTJknnz5i1cuDAxMdG/gsfjqaioqD6b2+22WCwi4vV6fT6fy+UK94/wCzZ+EWDQ53MdPSSZLc/+jNfrDZz5yy9EE1FqrO1x/fCddO0eiqD1p2may+Wq51Fyt0t+3F1z0Otxf7dV0tIbnu1cPB6Poig+ny983yLkPB5Po9ikg3TOTboR87+SqFH1V5PH49E7QtA8Ho+qqlG3eUTjJu3z+fwveiGc0+12a5r2y+uhkQl7sTOZTM8//3xxcfFHH330u9/97s9//nNSUlLVZ1NSUhYvXly1eP/990+dOnXTpk0jR470jzgcjgMHDlSt4PF4ysvL/S9wXq9XVVXdX5ptLmfAvmM/nu+LTTh73P/mffZ4Qlmp9exRkYqiIk9pacMyNpTP5ysrK6vfS4ZS4UgO9NLgKi9zhvPn8r80h/ZlLtx8Pp/X6y3V+587WOfapBszr9drt9ujbvNQFKWyslLvIEFQVZVNOjI8Ho/D4Qjt5lFZWRl1vwdIBIqdiLRu3bp169Y9evS44YYb1q9ff8UVV5xrzfj4+ObNmxcVFVWNNGvWrH///lWLubm56enp/v15drvd4/Gk6n15gbdVa9/Ze6RE0gcOFLP57PHS0tKUQJdWeLtd4Ptx19njqf0HSrNmDc/ZEMePH2/evHk999hpmjs5RSur+cqe2Pm85MzMEIQ7B4fDERsb69+5Gy0qKysdDkfUnW96rk26McvPz09LS6txAKGRczqdiqLExsbqHSQIbre7uLg4M5z/08MhGjfpwsJCm80WFxcXwjntdnteXl4IJ0RkhPEcu23btk2fPr1qh7aiKGe/yx4+fHjBggVer9e/6HQ6CwsLW7RoEb5UIWe58TZFqflrNJ93XsBWV9s8F14szWqWVFPXbrq3uoZSFMuvJ9YYM7XrYO7dT5c4AAAYWBiLXZcuXZxO53PPPXf06NH8/PyXX37Z6XT6d7+tWbPmgw8+EJG0tLTc3NwFCxbk5+cfP358/vz5SUlJF110UfhShV5MjPnOe5SEMycFiqKYz+9uue3OeswUe9dcpW178ddEk8nUp5916h2hC6obU+9+1inTlKwWYjJJfIJ58EWWqdMlOu9rAwBAYxbGA1VJSUmPPfbYa6+9du+99yqK0rZt24ceesi/N2779u1lZWXjxo2z2Wz+debMmWO1Ws8///wnn3wyuo41iIi5dVvzw0+KiNjtUu0MwqAlJcX87z0iIk6nhHSPuu5MvfrG9OorXq9E1bFRAACiS3jfZdu1a/eHP/zh7PG5c+dWfdyxY8fHHnssrDEipyGtrjpjtbqf0eoAAAgnDocBAAAYBMUOAADAICh2AAAABkGxAwAAMAiKHQAAgEFQ7AAAAAyCYgcAAGAQFDsAAACDoNgBAAAYBMUOAADAICh2AAAABkGxAwAAMAiKHQAAgEFQ7AAAAAyCYgcAAGAQFDsAAACDoNgBAAAYBMUOAADAICh2AAAABkGxCx27XXZ9F4J5NE0qK0Mwj4gUnwrNPAACKfdWeDSv3imgA4dLtFDMU+kWNSQTAf9h0TuAEbjXr1VXvqv4FxRFrLGxjz1Vn4mcld6PP/Rt+VrcbiXJZr5kuHnoZWIKvnw7K9yv/U07/JNoIooo7TrGTJsucQn1iQQgkHdOrpu3b+HeihoO60YAACAASURBVCMxJuuo9MHPnT+nY3wrvUMh7FRVPv5BPt4hdqfEWmXoeTKxv8Rb6zPVuj3ywTYprpAYswzoINcOkuT4UMdFk8QeuwY7fVqranUiomnidroenhv0PJrmWfoPX+4GcbtFRLOXe1e+51v7ST0Suf/6nHbopzN/TmqiHTroXvBsPeYBENCqotyrvpu3t+KIiLhVzweFG0dumV3mdeidC2H37jZZsVnsThERl0c+3SmvrK/PPOv2yOIvpbhCRMTtk0375S+fiqqGMiqaLIpdQzn/EmDnnOJ0id0e1DzqTwfU3TtqDHrXrpbKiuDmOfCjdjK/xqBWeFL9cVdQ8wA4l/v3LagxcrDy+MJj7+gSBhFjd8nK72sObj0s+wqCm0dV5e3NNQcPnJRvD9U7GvAzil1DKYHOh9NEPF9tCGoerSAvwKjPpxaeDG6e/fvOMb43qHkABKSJtttx6OzxHfaDEc+CiMovCbxT7XhxcPMUV4jDFYJ5gIAodg2lmMwBx63Z7YKbKC7w6RVKfHCnXWiJtsCfSEoOLg+AQBRRbOYAZ6w2syRFPgwiKT4m8HjCOcbPJc4qSqDxxCDnAQKi2DWUqX+/wJ/o3j24ec7rKgk13y2UVm2UjMyg5rEMGBzgeguTyTwwJ6h5AJzL9S0uP3vwuhYjIp8EkZSdKq3Tag4mxUn3IC+bSYyVC1rXHIyxSN8g9wYAAVHsGspy1Y0SF+v/uOqidWXshGDnURKTrNfeKLGxP480S7Vef7MoAf+0O7e4OPOk66p/kaIo5iuvPrs1Aqifp867Myflguojf+w84+JmvfXKg8hQRO64VFKrvZTGW+X2YZIUe+6vOYdpQ6VFys+LVrPcdJFkclgFocDtTkIg9pGnvf9ern77lag+LT4+7q77Je2sP+vqwNTtgpj7HlR/2K6VlijNs8y9+0lMfXbNWwZeKJ3P83z8gVZUpGRkWC8fJ+np9ZgHQEBJ5vgvB/7t3cIvNpftTrEkjc24qGdSJ71DIRJapcoTV8vXByW/VNKSZGAHSanXPUqaJcijk+Tbg3K8WGzx0r+dZJzjJBogWBS70LBMvFYmXtvweZTkFPOQYQ2fR1LTrdffEoJ5AARiUkyTMi+dlHmp3kEQabFWueT8EMxjMcmFnUMwD1ADh2IBAEBEFRUVPfHEE/3798/IyLBarZmZmaNHj/7kk/rcujUoOTk5Xbt2Dfd30Rd77AAAQOScPn164MCBJ0+evPXWW++55x6z2XzgwIFXX3117Nixb7311uTJk8P3rSdPnlwZqod2NlYUOwAAEDlvvPHGoUOHli5det1111UNzpw5s2fPng888MC1115rqsezNOtmzpw5YZq58eBQLAAAiJy8vDwR6d+/f/XB1NTUr776avfu3f5W179//wsvvHDt2rWDBg1KSEhIS0u79dZbS0tLq9Zfv379yJEjk5OTExIS+vXr9+qrr1afbc2aNcOGDbPZbC1atLj22mv379/vH69xKLaWSfLy8m6//fZ27drFxcW1aNHiqquu2rNnTxh+GaFHsQMAAJHTr18/Ebn//vtLSkqqj7du3Tr+P/fkj42NPXDgwG9/+9vnnnvuyJEjL7zwwptvvjlt2jT/Zz/77LNf/epXbrf7n//853vvvTd48ODbbrvtz3/+s/+za9asGTVqVFxc3KJFi5544oktW7Zccskl+fk1H7ZZ+ySTJk368MMPf//7369aterZZ5/dt2/fsGHDKiqCe8inPrSosmnTJrvd7v+4vLz89OnT+uaph5KSEr0jBO3YsWM+n0/vFMGx2+0ej0fvFMGpqKgoLCzUO0XQonGTzsvLc7vdeqcITmVlpdPp1DtFcFwuV35+vt4pghaNm/TJkycrKytDO2d5eXlubm5o5/Tz+XzXXnutiMTGxo4dO/ZPf/rTV199VeNdZsiQISLyxRdfVI3cdtttInLkyBFN0/r27du5c2eHw1H12SuvvNJms/l/CQMGDOjQoUPVW8DXX38dExPz/PPPa5o2ePDg888/3z9eyyT+XYMPPPBA1af279//xBNPHD9+POS/jZCr0x67U6dOTZ06NSsry2w2K2cJZ+0EAACGYjKZli1b9vHHH1911VXbt2//7W9/m5OTk5WVNW/evOq7xBITEy+++OKqxUsuuUREduzYcfLkyW3btl1xxRUmk8n5H2PHji0vL//hhx9OnTq1efPmMWPGWCxnriIYNGiQy+WaNWtW9Qy1TxIfH5+enr5kyZLPPvtMVVUR6dSp07x587KzsyPxC2qYOl08MWPGjLfffvvCCy8cPXq01WoNdyYAAGBso0aNGjVqlIgcPHhw7dq1ixcv/r//+7/169dv3LjRf5pdVlZW9Z1H6enpIlJQUHDixAkRef75559//vkacx47dsx/MDcz8xeexln7JAMHDnzvvfduuummESNGpKenX3rppZMmTbr22murymJjVqeIq1atuu+++5566qlwpwEAAE1Kx44dO3bseNttt/3P//zPq6++unHjRv/OuRq8Xq+IVF0we+utt95+++011uncufPJkydFxL+b7RedaxIRGTJkyL59+9avX79q1aqVK1dOmTJl/vz5X3zxRdVZgI1WnYqdpmnVd4cCAADUg8vlWrFiRWJi4oQJ//VQdUVRhg0b9uqrrx49etQ/kpeX5/P5zGazf7GgoEBEsrKy2rZtKyI+ny8nJ+fs+WNjY0WkahK/w4cPJyQkNG/evGqk9kn8zGbz8OHDhw8f/vTTTy9cuHDmzJnLly+fOnVqvX7uyKnTOXYXXXTRrl27wh0FAAAYW0xMzCOPPDJ9+vSDBw9WH/f5fP/6179EpFevXv6RysrK1atXV62watWq2NjYQYMGpaWlDRo06N13361+Ue3ixYsffPBBr9drs9l69uz54YcflpeX+z+1Z8+e9u3bv/jii9W/Xe2TbNmyZfLkyf6df36XX365iBQWFobq9xA+ddpjt3Dhwquvvrpr167jx4/nagkAAFA/iqK89NJL48aN69Onz+TJky+44ILExMQTJ06sWLHi+++/v+uuu3r27Olfs02bNnPmzDl8+HDnzp0/+eSTd9999+abb05NTRWRp556auTIkcOGDbv33ntbtGixYcOGP/3pT1OmTPGfA/fkk09eeeWVI0eOnD17tt1uf+aZZzIzM++4444aSWqZpFWrVitXrty9e/fs2bPbtm176tSpF154ITk5eeLEiRH+ddVHLVfMtvuPTp06tWvXTkTi4uLanSVC1+9qmsbtTnTC7U4ig9udRAy3O4kMbncSMdF1uxNN03bu3Hnrrbd26tQpNjbWYrFkZWWNGTNmxYoVVSsMGTKka9eumzdvvuSSSxISElJTU2+//fby8vKqFTZs2DBy5EibzWa1Ws8777ynnnqq+mv+Rx99lJOTk5CQkJmZOXHixL179/rHq9/upPZJvvvuu4kTJ2ZmZlqt1uzs7IkTJ27dujVMv43QUjRNO1fnGzFiRF2q4aeffhqymvlLcnNze/XqlZiYKCL+d25/eY8ipaWlKSkpeqcIzvHjx1u2bBm+Z7yEg8Ph8L9e6B0kCJWVlQ6HIyMjQ+8gwYnGTTo/Pz89PT26rvF3Op2KovjPH4oWbre7uLg4KytL7yDBicZNurCw0GazxcXFhXBOu92+Y8eOWk5BC6uLL764qKgoWh720KjU9rYXycYGAACABqrTPpgBAwbs3r377PG33367e/fuoY4EAACA+qhTsduyZYvD4agx6PV6d+7ceeDAgTCkAgAAQNB+4QykqmtgBw4cGHAF/6N8AQAAQmXjxo16R4hWv1Dstm/fvn79+tmzZ48fP77GOd2KomRnZ599y2YAAADo4heKXe/evXv37r1y5cqnn366S5cukckEAACAeqjTzSA+/vjjcOeIdlrhSXXX95rdrrTINvfpL/95BErUc7t92zYn/nRAzW6l9OqrNIuym8sAYeLT1LdPfr6lbE+KJWlMxoV9befpnciwTtnl25+ktFJapkhOJ4mJplsYRYJXlWXfyN4TzZLizJd2k4Ed9A4EvdX2XyQpKekXv97j8bhcrtDliUq+bzZ531shXq9oIor41q62zpil2JL1ztVQWmGB5+9/1UpL4kV82771rVlpve5m0wW99M4F6KzcW/GrLXd+W3bmXgH/b/+iRzvd/lDHW/VNZUjf/iSvfCFu75nF97fJ/WMlM+pfXEPmdIX8brm4fSJiFZHdebKhldwzWu9Y0FVtxe7Xv/511cfbt28/ePDggAEDsrOzfT7foUOHvvvuu379+l144YXhD9moaYUF3vffFq9XREQREdGKTnpXLLFOq/n0kqjjWbJYK/35IXridnv+9VZMu/YG6KxAQ8zd95eqVuf3+wN/H5ba75LUPnpFMqSSCnltw8+tTkROO+SldfLglfplamSe/sjf6n6247h8vlsu66ZTIDQCtRW7pUuX+j9YsWLFzp07Dx8+3LJly6rP/vjjjxMmTPA/FrcpU3d+Lx5PzcEfd4mzUuLidYkUEtqpQu340Zqjzkr1x13mAfrciBxoJJblB7h5+/KCTyl2ofX9UXHWfHGVg4VSVC4ZNj0CNT4F5QEG1/9IsWvS6nQfu0ceeeT3v/999VYnIueff/7s2bMfeuih8ASLGprTGWhU06L9CHXAn6uWcaBpUDW13Fdx9nipt+bNPtFAlWe1Or8Kd2RzNFZer0igZ4Ke3YbRpNSp2O3duzctLe3s8YyMDJ7jZmrRssaIJqIkJkX78UolI1MCPWhVaZkd+TBA42FSTN0TA5yg3jOpU+TDGFvrQBdrxZglK8qe4xouFotYAl2nl81Fbk1bnYpdRkbGa6+9VmNQ07QVK1YELHxNiqlnX1PbdtVHFBHz2CvFVKffbeMVG2sZMabGmKlrD1NH7nqDpu7p8+6qMdI5ofVvWk/SJYyBdW8lF7SuOTihv8RyYex/XHHWxWwWk9xykR5R0GjU6f/H7bff/sgjj3z//feXXXZZ8+bNRSQ/P3/t2rW7d+9+4IEHwpyw0TObLVOn+1a+5/thu7jdSlq6+VejjHEWmvnSEWK1+tZ/ppWVSlycuf8gy+VXyH8eRgI0WaPSB7/b50+/27dot+NQjMkyNuOiZ8+bbbMk6J3LaBSRGZfJO5tl035xeiQ1Qcb0ll9x9lg14/uJyyuf7hKvT0SkWYLMHC7JbIlNm6JpgQ7R/zdN055++unnnnsuLy+vajAjI+M3v/nNww8/bI7gPdtyc3N79eqVmJgoIna73ePxpKY2mp3OmiYet8TE1r5WaWlpSkqUHUg48dNPLdq1M0XVPkiHwxEbG2sJdDS50aqsrHQ4HDUe8dL4ReMmnZ+fn56ebrVaGzhPhc8ZY7JalEi8BjqdTkVRYmN/4RWmUXG73cXFxVlZWQ2fyumRuIb+c9VVNG7Sh4+fSk9NTEqIC+Gcdrt9x44dOTlG2E/RpNTpbU9RlPvvv3/u3LlHjx7Nz8/XNK158+bt27ePrnf6sFOUX2x1UUqLidE7AtAYJZhD+T6KWkSs1UWphBjVwhsyRKSOxc5PUZS2bdu2bds2fGkAAABQb7UVu65du06dOnXevHldu3atZTUujAUAAGgMait2zZo1i4+P938QqTwAAACop9qK3bvvvtuiRQsR+eqrryKVBwAAQDdr165NTk4eMGCA3kHqqbZil52d3bdv3zFjxowZMyYnJyeSV78CAICmSNN8W7/1bfpCO12kNEsz51xsHnRhJO+09eyzz/7617+O3mJX21U0EyZMOHjw4B//+MeLL764efPmkydPfuONNwoKCiIWDgAANCm+9Z96l7+pHTsiFRXaiWPed5Z6P/6ggXO+/vrr3bp1i4+Pb9GixcyZM51Op4jk5+dPnjw5Ozs7MTFx2LBhW7duFZHhw4evXLlyzpw5/fv3F5GCgoLrr78+Ozs7ISFhyJAhX375ZS0T7tix4/LLL09LS2vWrNmoUaP279/fwNj1U1uxe+edd4qKinJzcx999NGePXu+8847t9xyS8uWLfv37//QQw9t2rTJ5/NFLCgAADA2zV7uXb2yxqBv3afaqaJ6z3nw4MFbb711wYIFdrt906ZNubm58+fPF5EJEyaIyA8//FBUVDR06NAxY8ZUVlauXbu2bdu2zz333JYtW0Rk/PjxxcXF27dvLyoqysnJGTt2bFFR0bkmvPrqq1u2bHn06NEjR47YbLapU6fW/xfRAL9w3xuz2ZyTk/PQQw+tX7/+9OnTH3744axZs1wu1+OPPz5kyBD/brzIBAUAAMamnTgugfYZaceO1HvOkpISTdPS0tLMZnPHjh03b948b968rVu3fv311/Pnz09PT4+Pj3/00Ufdbvf7779f/Qu3bdvmXyczMzMhIeHxxx/3+XyrVq0KOKGI5ObmLly4MDExMTk5+YYbbvj222/r8gyIkAviPnZJSUlXXHHFFVdcISIHDx587rnnXnvttWXLli1dujRs8WrSNM3tdvsfJ+D1en0+n8vlith3Dwmv1xt1mTVNc7lc0XU/ao/HoyhKdO1U9ng8bNKRoaqq2+1WVVXvIEHweDx6Rwiax+NRVTXqNo9o3KR9Pp//RS+Ec7rdbh16ybkeF9SA58T07dv3jjvuGDRo0KBBg0aOHDllypQuXbrs3btXRLKzs6uvefDgweqLBw4cMJlMVXd8i4+Pb9eu3aFDh2688cazJxSRbdu2Pf7447t27RIRl8vlf0mP/AOQgvh+Ho/nq6++WrNmzaeffrp582aPx5OVlTVu3LjwhTubpmmqqvpfjlVV9S9GMkDDRWnmqIvtDxzal7lw87+GRtfvWaJzkxaRqleSaOHfnqMrczS+dAibdLUJI1/sTG3aKUk2zV5eNaKJKHHxpvad6j2noiiLFi164IEHVq5c+eGHH/7xj3988803/Xdzq6ysjIsL4vkx/r8JA07Yv3//sWPHPvzwwytXroyLi3vvvff8h3oj75eL3Z49e9asWbNmzZp169aVl5cnJSUNHTr0//7v/0aMGNGzZ88Iv3GaTKa4uDj/v4f/DxT/x1HE7XZHXWb/rz269tipqhp1z4oVETbpyCgtLY2Li2v4s2IjSVGUaHxWbEVFRdRtHtG4Sdvt9tjY2KA6yi/y+Xw6vOxbrZZrp3gWvyLeM7uoFYvFetVkSUio95Rer7e4uLh9+/YzZ86cOXPmnXfe+eKLLy5cuFBEtm/fXvUw3IMHD3bs2LH6F3bp0kVV1V27dvXo0UNEHA7H4cOHu3TpEnDC3/zmN16v97777vO/sOh4n7ja/s1uvfXWNm3adOvW7d577z19+vScOXP8Z9qtXLnynnvu6dWrV3TtDgEAAI2c6fzuMffMMw8bYbqgl3noZTGzf2vq1bchEy5evLhfv35btmxRVTU/P3/nzp1dunTp3r378OHD77333iNHjng8noULF/bs2fPEiRMikpCQsH///pKSkt69e1900UVz5849deqU3W6///77bTbbhAkTAk7Yvn17n8/31VdfuVyuJUuWbNq0SUT8E0ZYbfszXnvtNRHJycmZOXPmyJEj/TcrBgAACB8lPcMy9spQzXbLLbccPXp04sSJBQUF6enpo0ePfuaZZ0Tkrbfemj17dq9evVRV7dmz56pVq/yn3N1xxx3z5s1btmzZ0aNHlyxZMmvWrO7du6uqOmjQoA0bNiQnJwecsFmzZnPnzh0/fryiKBMnTnz33XdHjhzZu3fvbdu2tW/fPlQ/S10otRxB/+ijj/wHYf1nAvbo0WPEiBEjR44cNmxYUlJSBEP+LDc3t1evXomJiSJit9s9Hk9qaqouSeqttLQ0JSVF7xTBOX78eMuWLaPrUKzD4Yi6Q7GVlZUOhyMjI0PvIMGJxk06Pz8/PT09ug7FOp3OaDwUW1xcnJWVpXeQ4ETjJl1YWGiz2UJ7KNZut+/YsaPqSCWiRW1ve1XXwJ44cWLNmjWrV69esmTJ888/b7VaBw8ePHLkyBEjRgwaNCi63jsBAACMqk77YLKzs6dOnfrWW2/l5+dv3779ySefbNas2V/+8pchQ4akp6eHOyIAAADqIridbYqi9OrVS0TMZnN8fPzKlSvLysrCEwwAAADBqWuxy8/PX7NmzSeffPLpp5/6HxebmZk5adKkMWPGhDMeAAAA6qq2Yud0Ojds2LB69erVq1d///33ImIymQYNGjRz5syxY8f279+f250AAAA0HrUVu7S0tMrKShFp3rz5jTfeOHbs2FGjRqWlpUUqWxQqypcMbgoDhItTdceZYho+j0uLvsdz1YXb51NFizM3ogvavKox//4vrZSUKLuHMZqK2v7/9+7de8yYMWPGjBkwYAA752rh+e47bemrmnrmxjFaSrO43z2qbyTASFRN/euxt5859NYRZ0G6NWVa9q8f7nRbkrk+76tv5n382MHX9lUcTbYkXpM1/Mkuv8mwNgt54Mj7/PjRl7+ssNg7KqK4E/ffMMj86w4ddMxTVin/+la2HopxejNbpMiEfjJQzzgh4/bJ4+/LsdNnFlMTZN44ydDn9l9AYLUVu9zc3IjliGIVFdo/X6l+M0CltMT1x4di/99jukUCjOVPh9783f6F/o9PeUqfOfzWT5UnVvR+Ith5/pG36uYdZ/7oKvXaXz7+/m7HoXUDXrQo5lDGjbhdp4teWd0sVm3jX4yzd17+uTM17sSQltm1f2GYeFV5brUcKjqzmFciC9eKDDdCt/v9Cjlp/3mxuEIeXCGLbtEtD3C2Bt1y9sUXX1ywYEGookQpzwtP17zFsyZSVioVFbrkAQym1Gv/w8GXawy+ffLzDcXbg5rHp6n37f1LjcEvS77/V8HaBuVrBOZvOhaj2qqPWLS4Rbmnz7V+uH194OdWV2Xp1xLp58mH2uGi/2p1fm6fvL1ZjzTAOTSo2M2aNeuuu+4KVZQopZaV1BxSREQ8W7ZEPgxgPD86jrjVAKfEfW/fH9Q8Be7TJ93FAeYpD26eRshut5096HXo9giTo4EqZbFDHM6IRwmpbw4EHt+lw+NAgXNq0Dm2y5cvV1U1VFGilGK2aD7f2ePWls0jHwYwHpslIeB4siUxqHkSzXGKKNpZu42CnacRMpkDXQtickU8yBlxZz2qTRMxKxITTY9wCyDlHOfSJUb5zwWDadAeu0mTJl199dWhihKlTH0HBBhVRDp3jXgWwIC6JrbrmdSpxmCKJeny9MFBzZNiSRp11pfEmWLGZw5tUL5GoEfbAB2ubetTkU/i169dzRFFpE9biYnuUxnlV13l7KsIFZEr++sQBjiXaHqse+NkmXSdxNe8Os90xTW6hAGMRxHlrZ6PZMX8fKOlBHPcqz3+X/WROvp793kd41tVLcaarM+eP7t7YtSf0v/A4F5q+vfVR1wpux+7uLdeedqmy+T/rtAtUuTmITqlCR2zWa4aIDVuEdG/vXTO1CkQEEhth2K7dq3TPqc9e/aEKEy0iv3Dn7zvLFO3fqupHolPjP3NLO5mB4RQz6ROPw5Z9o+8j390HG4dlzm5xch2cfX5L9Y6LnPnRf98K++T3ILv2ia3vLrlcAO0OhExifL6hF7/2P3j18cqNFXrnR03vWd3fSNdfoF0y5YtP/mKSl1dWyfkdBJLlO+u8xvbW3q1lb+vl2KH2GLlmkHSp63emYD/Vluxy8jQ7dzbqGOZdJ1Muk7vFIBhpViS7mwTghM/4kwxt7Uad4V5YHp6utVqqHOjbup2/k3d9A5RTZs0yUryFReXZ2UFPksySrVOlUcm6B0COLfait3GjRtr/2K73Z6XlxfSPAAAAKinBp1j9/XXX+fk5IQqCgAAABqirrc7+eijj5YsWXLkyJGq+5v4fL6dO3fGxsaGLRsAAEDj4vV6rVbrmjVrRowYEexXrVq1avTo0eHLJnUsdkuXLr3++ustFkuLFi2OHTuWnZ19+vRpp9N52WWX3XfffWHNBwAAmhq36jnmOtk6NjPG1OjOhTWbzZ9//nnv3rpdeF67Oh2KfeaZZ0aPHn369OmjR4+azeZPPvmkvLz8hRde0DRt6NCovwUUAABoJBy+ytk/zrd9/qtOG69OXHvZ9F3/V+o961FuulIU5dJLL01NTdU7SGB1KnZ79+698847bbYzT63RNM1isdx11119+vSZN29eOOMBAIAm5K49z75wZLn/QYJezff34+/duvOPDZkwJyfnf//3f6sW161bZzabjx8/np+fP3ny5Ozs7MTExGHDhm3dulVEfD6foigvv/xyhw4dpk2bJiKvv/56t27d4uPjW7RoMXPmTKfT6fV6FUX59NNPReTYsWMTJ05MSkryf7aiokJECgoKrr/++uzs7ISEhCFDhnz55Zc1IgVc4exvXT91KnYej8dsPnMPosTExJKSM09Hveqqq/7973/X+3sDAABUOVh5/LUTH9YYfOfkui1l9b9j7g033PDvf/+76gqB5cuXX3bZZa1atZowYYKI/PDDD0VFRUOHDh0zZkxlZaXZbDabzX/729/efvvtF1544eDBg7feeuuCBQvsdvumTZtyc3Pnz59fffJJkyZZrdZ9+/Zt2LDhiy++uP/++0Vk/PjxxcXF27dvLyoqysnJGTt2bFFRUfWvCrhCjW9d75+3TsWuW7dur7zyitvtFpE2bdp88skn/vHTp0+XlpbW+3sDAABU+dFxJPB4ReDxurjuuutOnjxZtVfs7bffvvHGG7du3fr111/Pnz8/PT09Pj7+0Ucfdbvd77//vv9LJkyY0K9fP5vNVlJSomlaWlqa2Wzu2LHj5s2bqx+o3L59+7fffvvkk0+2bNmyS5cu//jHP8aMGbNt2zb/zJmZmQkJCY8//rjP51u1alXVV9W+QtW3rvfPW6eLJ+65556bbrqpuLj4008/nTRp0hNPPHHy5MnWrVu/9NJLjfbkQQAAEF3SrSkBxzPOMV4XWVlZw4cPX7FixdChSLCCcwAAIABJREFUQ9etW1deXn7VVVd99NFHIpKdnV19zYMHD/o/6Ny5s/+Dvn373nHHHYMGDRo0aNDIkSOnTJnSpUuXqvX379+vKEqHDh2qVu7bt++KFStMJlPVs7vi4+PbtWt36NChqq86cOBALStUfet6q9MeuxtvvHHJkiX+y3ofeOCB4cOH//3vf3/44YdNJtPzzz/fwAQAAAAi0j+56wVJHWsMdoxvNTS1T0OmveGGG9555x1N05YtWzZ+/HibzRYfHy8ilZWVWjVVe+OqbuWmKMqiRYv27ds3ZcqUb775pnv37suWLauaVlEUEdE0rfbvrqqq/5hnXVZo+F3k6nqD4smTJz/wwAMikpCQsHr16n379u3atevAgQMDBgxoYAIAAAARMSumpT0fax/fsmqkVWzzpb0eizc1qO5MmjSpqKgoNzf3nXfeuemmm0TEv+Nt+/btVetU7a6rzuv1FhYWtm/ffubMmStXrrzjjjtefPHFqs927txZ07Tdu3f7F7/55psFCxZ06dJFVdVdu3b5Bx0Ox+HDh6vv5/vFFRooiCdPFBQUrFq16vXXX1+8ePGBAwfS0tIM9qRFAACgrx5JHXddtGR5rz/+sfOMf/Z8dM+QZQOTG/oU5OTk5CuuuOL3v/+9yWS6/PLLRaR79+7Dhw+/9957jxw54vF4Fi5c2LNnzxMnTtT4wsWLF/fr12/Lli2qqubn5+/cubN6A+vdu/fgwYPvvffen376ae/evXfccceuXbt69+590UUXzZ0799SpU3a7/f7777fZbP4LNaq+qvYVGqhO59iVlJRMnz793//+t9frrRpUFOWGG27429/+lpiYGKo0AACgiYs3xV6TNTy0c06ZMmXSpEl33XWXxXKm+bz11luzZ8/u1auXqqo9e/ZctWpVjVPuROSWW245evToxIkTCwoK0tPTR48e/cwzz1Rf4YMPPrj99tsvuOCCxMTEiRMnPv300yKyZMmSWbNmde/eXVXVQYMGbdiwITk5uXqDCrhCqH5S5RePDYvItGnT3nrrrZtvvvmSSy5JT0/3er0FBQUrV6587733ZsyYsXDhwlCl+UW5ubm9evXyV0m73e7xeBrtHQLPpbS0NCWl/ieB6uL48eMtW7Y0mRr0ZOEIczgcsbGxVf+Bo0JlZaXD4cjIyNA7SHCicZPOz89PT0+PrmMOTqdTUZToeoqj2+0uLi7OysrSO0hwonGTLiwstNlscXFxIZzTbrfv2LGDJ8JHnTq97b333nsvv/zyzTffXH1w+vTpDzzwwMsvvxzJYgcAAIBzqdM+mIqKCv8x6RpGjRpVWVkZ6kgAAACojzoVux49egS8WmTPnj1cFQsAANBI1KnYPfXUU7Nnz964cWPVCXk+n2/lypV//etfazxbAwAAAHqp0zl2Dz744OHDh4cOHZqYmOg/DTYvL6+ysrJNmzZTpkypfvnFnj31f5obAAAAGqJOxc7tdnfu3Pm8886rGmnZsmUt6wMAACDy6lTstmzZEu4cetFOFqg/7hKXS2ndxnR+d1GU+s3j+2G77/PVWoXD3LKV5fpbJCYmtDmBJq5Sda0oWLuv4lir2OYTM4dlxtTzPkdO1f3g/kVfFn3XOj/r7g7XX5TSM7Q5dXSwUPbkiaZJlyw5r4XeaUKntEK2HZHiCmmZIgPai8Wscx63VzYfkoIySUuQfu3FVt8bjPhU2XpYjhVLSrz0biPpSSFNiSYsiLt8OZ3OH3744dixY0OHDs3IyPB6vdF1k7Cz+dZ/5v3kQ/H5/IumDp2st/1GrEF3MvffXtAO7j8zZ3Gx7/dzLTPnmNt2CGVWoAnbV3H08q2zD1Xm+Rcf2PfXJb0eG50e9O21djl+6v/VLU7VLSLi2LWi8PM7Wk9Y1O23oU2rizc3ydrdPy8O7iTTh9X7D9VGZPsReWmdOD1nFt9NlvvGSIZ+HSivRJ79RE7Zzyyu2CwzLpMerYKep7RSnlklx4vPLC63yC0XS06nkOVEU1bXW87++c9/zszMHDRo0KRJk/b/f/buPDCK+v7/+Hv2yCbZbO4TQoBwXwE88cYDq0VUvEUF0ap8qfpV61G/rfVA23r9PKq1KoXigdV6U69aKx41KJcB5L5JIOQk2d1kd2eP3x/BGDabwGw2mezwfPyV+WR4887kk9nXzrWbN4vIvffeO3PmzLZPUo4vwR3b/B++J4Gf+g9u2+L/8H2tdQIrv2tNdfuFQv7nn+l6hwBaXLH63tZUJyL7/K6rVt9fqzZorXPG8pv2p7ofPV/+3me1y2LQoq6WbDkg1YnIt1vk32t16iZ2Gppl7hc/pToRqWqUFxfr1k9I5PnFP6U6EXF75cUvxO3VXOpvX/+U6kTE55cFX0u1MwZNAocU7F588cXbb7/91FNP/ctf/tI6OGzYsFdeeSV+74oNlrWcXz7gLW1gpeZdfOA//4ow6lelpia6xgC0tbFp59LGdWGDNeq+j2uWaKqzx1O7x1vbbjj0+M5Xu9Bdr1C6OcLgki093kesrdolTb7wwU17D4hWPWnPPtnZbgY1NssPFdrqNPlk1a7wQa9fVmyPujXgJ4cU7J555plZs2a99957M2bMaB2cPn36HXfcMXfu3G7rrZtFfLSyp1kO4TPW2gp5I79ZC9TsjaIpAGHq1cjHMer92o5v7FarO6ivU0yInfbpRySaw0i9TVMHP4JeP1pH/2/E7d+JZl/k1xm3xjpARIcU7DZu3HjhhRe2H584ceK2bdti3VIPUXIjXF2s5OZpvSxFyY78MYjm4iHRtAXgQEOS+1mUCBfMj7Jru4x1lL1YkQh/3WMdg6PsrNfok36og/GlT6Q7ZCxmyY3Zp6VrU5AmpkivD1o3dXqyJEW6lrtv/P/K0BscUrBLTU31eDztxxsaGpKSkmLdUg8xTzhRycgMe9dkOftcrXUSpl3dPgsqhf24MRaIiUxr6l0DrgobPCtrwsTMIzTVSTQlXFpwRthgsjnxkSE3dam/XmDyWEmyHjCSYJbztW2e3mh0Xxne7slaU8ZJojXS2t0vJVHOancX9dgiGaLxHmSzSaYeGT44MEeO4o47xMIhBbuSkpLHHnss7GNh6+rqHnjggQkTNN+Y1lskJVl/Mds8dLiYTCKiZGRap11tGjFac52UFMvV/yPWn/Y0SmG/hJvuiGGnwGHuvkG/mDPo+jRLiojYTNbr+p63cMwDEQ+/de610Q9cknea6cd3YoWJuV8e/VyqJTnG7fa43FS57SwZmLN/ixRmyP+eKUVZOnfVdYois0+TE4aIxSQiYrfJRUfL5LF6tjT1SDnviP3H2yxmmThcrjtF+0QUOX2kTJuw/1EpZpMcUyw3nyHmQ72bEeiMEjqES8oWL158xhlnDBw4cPLkyU899dQ111wTCATeeeed5ubmzz///IQTTuiBRluUlpaWlJTY7XYRcblcqqpmZET5OKuf+NWQ16vYu3wDfXNzoLLCPPAgp3UaGhrS0tK6+n/1rIqKioKCApMpnvY6brfbZrPF1xN5mpub3W53dna23o1o05NTeo+3JichI+KZWU0W7/hubO6wjKR4+kv0eDyKothsts7WUSUYkuRec7bA5/PV19e3fF5RVwSD4vRIWk8l8INO6ZBIY5M4EqXrO8WGZkmxxSDSVVdXOxyOxMRon6oXicvlWrNmTRwfvjlcHdJsmjhx4ieffOJwOJ566ikRmTdv3oIFC4YPH/7pp5/2ZKrrLhZrDFKdiCQlHTTVAeiKAlt211OdiAy3FaXE/4G69hKtvSjVxZDJ1HOp7lAoImnJMUh1IpKWxIE6xNihTqjTTz99xYoVe/fuXbly5cqVK+vq6r799ttTTjmlW5sDAACIOb/fryjKv//971itr7Vg9zl4sAsGg61f5+bmlpSUNDY2fvjhh2vWrOnOxgAAALqF2Wz+/PPPjzyy3W0s0a6vtWD3OUiwe/XVV4uLi1tvm3C73SeccMIpp5xy5ZVXjhkz5pZbbun+DgEAwGEkJLK9RpZuk23VWp8te6gURZk4ceKhX6Z/0PW1Fuw+nQW7Dz/88KqrrgoEAnV1dS0j999//5IlS6699toFCxacc845Tz311HvvvdcjfQIAAOOrb5I//lMeeE+e+4/MeV/mvC9VjV0qOGHChF/+8peti4sXLzabzTt27Gg5cxoIBBRFmTt37sCBA2fOnCkiZWVlY8eOTUpKOvLIIz///HNFUVatWtV6pjUYDCqK8tprr/3sZz8bOXJk//79FyxYIAeeii0vL586dWpKSkp+fv7s2bObmppEZM2aNWeeeWZmZmZ6evrPfvazlk9n7Q6dBbunnnpq0KBBq1ev7tu3r4gEAoF58+addNJJL7744vTp0999990xY8b89a9/7abOAADAYSUk8sLnsqnNJzdtr5G/fC5tLgrTbNq0ae+8807rdWVvvPHGqaee2hJsRMRsNpvN5ueff/6tt956+umng8HglClTxowZs3fv3vnz599xxx0i0vahECaTyWw2P/744y+//PLatWt/97vfzZ492+12t/0fL7jgAqvVumnTpq+++urLL7+88847ReSiiy4qKCjYtWvXzp07HQ5H24/yiq3Ogt2KFSuuueaa9PT9D8NeunRpbW3tjBkzFEUREbPZPHXq1GXL4v7zswEAQG9QXicbKsMHt9fIpqroa1566aVVVVX//e9/RSQQCLz11ltXXnll2Drnn3/+EUcc4XA4lixZsmvXrjlz5qSmppaUlMyePTtizauuuio3N1dETj/99Kampu3bt7d+6/vvv1+6dOkf/vCHgoKCIUOGvPzyy2effbaIlJaWPvfcc3a7PTU1ddq0aUuXLj2U581FobOnfNXX1w8c+NOTsL/88suWn6F1pF+/fjV81D0AAIiFere28UORl5d32mmnvfnmmyeddNLixYudTmf7T0kdPHj/08p27txpNpsHDBjQstjRzRBFRUUtX7Q8O7DtJzhs3rxZUZTW+DR+/Pjx48eLyMqVKx988MG1a9eKiNfrVVU1EAh0x8NWOztil5qa2vaW2C+++KJPnz6tP62IOJ1OszkGz5QCAADI6uCpsh2NH6Jp06a9/fbboVDo9ddfP++88xwOR9gKrY/+DoVCFotF+fHzaToKOUrHHyvf8q2wo3GbN2/++c9/PmnSpO3bt1dWVv7tb3+L9kc5uM6CXb9+/UpLS1u+rqur++yzz0477bS2K6xevbqwsLD7mgMAAIePvhkypl2sGJIng3K7VPaCCy6oqakpLS19++23r7oq/LOn2yooKPB6vbt3725ZXL58udb/a/DgwaFQaN26dS2L33333TPPPLNs2TK/33/77be3HOFbsmSJ9h/iUHUW7C688ML58+f/4x//2Lx58zXXXOP1eq+++urW727atOmNN96YOHFi9zUHAAAOK9eeLCX9floc0UdmnSqmKD6Rt43U1NTJkyf/7ne/M5lMZ555ZidrHn/88dnZ2Q899FBzc/PatWuff/55rf/X2LFjjz322F/96lfbtm3buHHjDTfcsHbt2gEDBgQCgSVLlni93tdee+2bb74Rkdb4GFudndydPXv2/PnzL7nkkpbFyy+/vPUCu3ffffe6665TFOW2227rjrYAAMBhKDVJbjlTqhqlqlGyHZIfo490vuKKKy644IKbbrqp88vaEhIS3nzzzRtvvDEnJ2f8+PFz5sw544wztH5U+qJFi6677rrRo0fb7fapU6c++uijdrv9jjvuOO+88xRFmTp16rvvvjtp0qSxY8euXLmy7RVuMdHZj5ednb18+fIFCxbs2bPnyCOPbE14IuJyuTIyMl544YURI0bEtiEAAHCYy02V3NRYFpw6dWrb694sFkvrot/vb7vmCSecsHz58oSEBBFpuSCtsLCwo/Xz8/Nbx1u/yMnJeffdd8MaeOSRRx555JHWxe57qMhBbsfIzMy89dZb249ffPHFV1xxRScXDwIAAMSXUCg0YsSIE0888Yknnmhubr7//vtPPvnk1NSYZsxupu3oYiubzUaqAwAARqIoyltvvbVz585+/fqVlJTY7fZXXnlF76a0if0DVAAAAOJUSUnJZ599pncX0YvyiB0AAAB6G4IdAACAQRDsAAAADIJgBwAAYBDde/PErl27FixYsG7dulAoNHDgwKuuumr48OFh67hcrhdeeGHVqlWqqg4bNmzWrFm5uV376JAoBIOi8fGDkQUCEpMPzw2FhJuO0QuEJKRIDKZirOoEJWiKxdvRgAS6XkREQhKLnyp220dE/L3snrjQwVc5JAGRmHwweax+ZUGOi6C36sY9gN/vv+eee8aOHfvII4+YTKbXX3/9/vvvnzdvXlJSUtvVnnzySZfLde+999pstoULFz7wwANPP/201qc8Rye4pyLw0l+D9TUSEsWWaJ50lvmk0w7+z9rbs8c792lxuUVERDGPGm2Zfl00dVTV//mnwWVLQs5GJSvbfMrp5qMmkPDQ85oCnoe2/e2lPR/t8dYMTS66Y8AVV/eZHEXyUEP+p3a+/uddb+/wVA5ILLix30U3FV1sUTS/QAclOPOHh/5e+S9f0G9WzMenj3l33MOZlmieLHVe2R2Lqv4bkpCIZCek/+fIZ8ekFEdRZ91ueXu57KiVRIuMLZKLjpK05CjKyLLGdXdt+vOShjVWxXJ65lGPDL1xUFLfKOr883t5d4UEf4xRZ46Wy46Npp9YcXvl7eWybFtCky+vMEPOO0LGFUVTp8Ylv/+n7HOLiCgiw/rInWdHUycQlE/WyOJ1UuuWHIecPlJOHxnNp1QFg/LXL2XpNvEHxWySwXly0xmSnBBNS0A3Md93333dVNrpdNpstssuuywzM9PhcPTr1++dd9458cQTMzIyWtepqal57rnnfvOb3xQXFzscjpKSkgULFowcOTI/Pz9izfLy8ry8vJbnQft8vmAwGBYTNWhy+R7/fcjt2r8Y8Ac3rhd7sqnfAG11fD7fw/eJ19c6EKqukoqdpnFHRVzd6/W2fAZwe+rrLwdLvxKvR0IhaXIH165REpNM/Qdq66cbOJ1Oh8MRX08uVFXVYrH0zDuEWPH7/aqqJidHFRBi6oo19z5f/m6j3x2SUI26773qrzKtqcemjYq4cidT+vaNT8/ZOn+f3xmSUL3f+Untt56gd1LWMVr7Oe/7O/+x97NAKCgiIQnt9FS+XvnvW/pfprXOz1fc9kHNN62LTQHPixXv3dH/SqtJW9bcWCmPfCj1bgmGxBeQXXWypkJOHCJmjdNtnXv7CUtv2Ni0Uw35vUHfOvf2N/f+Z3rBz+3mCNvT7/crihLx05CWbZWXSqXNQ/VlS5UkWmVwnrZ+YiUYlMc+lhU7xOeXUEgamuXbrVKUJQXpmkvd+qo0/bRzlRqnfL9LJoaf+Dm415bIB2XS5JOQSJNX1pRLICgj+0ReuZMp/eS/ZPkOCYYkJBIKSa1Llm2TMyL/ZfSopqYmm83W+YdlaeXz+aqqqgoLC2NYEz2gG1/20tLSpk6d2hK8nE7n+++/X1hY2K9fv7brbNq0yWq1Dhy4P7ukpKQUFhZu2LCh+7pqpf7jNTnwU0REJPDhIq11/K/OCwWD4XXW/SABbed6gju2BctWhBf/+J/i8WhtCeiKr+q//8fe/4QN3r35OVegWVOdrc0VT+58PWzw0e2v7vBUaqqzx1O7qPrrsMEdnsrny8M/sadzvoDvo9rSsEF/KHDR6rs11RGR15aEj1TUy+L1WsvIrzf92X3gVt3trfnj9pe01nnxywinPP+xVHM/sbJkq2ypCh9cuETzadlXvhE1fOcqO2qkTttMlMoG+Wzt/q9b355+uErq3drq1LpkdXl4nSqn/HejtjpAt+r2izGCweDFF1+squro0aPnzJljtVrbfrexsTHsUFBaWlpDQ0PbFbZv39666PP56uvrm5ubRURV1WAwGNCYn1qlVFREOACl+mqqqjRdb2evKI+4dv2yZYFBg9qP+3w+VVXbj1s3bYj0Jl2t27gh2CeaUzMx5Pf7a2tr4+uInd/vd7vd8XXELhAIqKpaU1Ojbxv/rfm+/WBTwPNtRdnY5MHtv9XRlP5qX/gblRZfViw7O23CoffzVl14ymzx0Z6vL0w88dDrfO6M8HOJyIr6DZq2eUhkV312+/FNu71H5DsPvY6IrGiIEAa/q/shYj8t+zpzpKt4/cEI/QRDotdc2lhuFwk/l1Lrkp27a+0JGtLd2vKMiFfWfV7mPmWwhnC3drdNxBE2GArJD9sbh+f52q/f0ZT+dnuiSEr78RXbvMMytf3qY87r9QaDQZfLdfBVD1lzc7O/3eEP9H7dHuxMJtNTTz1VX1//wQcf/N///d/jjz+eknLAH0bnccFms/Xp89Ph8sbGxqSkpJZzVc3NzYFAwG63R9eYkmCNOG53hP/9d85kiVwnKS8v1EFvkXu2R9hfiEhyelpHdXpMc3Oz3W6Pr2Dn8XisVmvEV8Fey+fzSUfTowelOyNfu5Ztz7Qna5jSmb60iCtnJWdo+hnzPJkRxzNt6ZrqDDRFfoOUbLVp3eYJZvG0O5KUZDNrrZNiSZZ2uSLVao9Yx+fzKYoS9t64c3rNJXtyhCZNiqQ7khO0vOYkJUTe52SnWu12De/ZUu2R9wOpKTa7vYMXgkibLiM1ch1HsuZffcz5/f7ExMSW65RiKL7eG6NFT9w+VVhYWFhYOGrUqGnTpn3xxReTJ09u/VZ6enpjY2MoFGoNDQ0NDW0vwrPZbDabrXXRbDYnJia2nN5tObwR9TV2gaOO8X8UfuLVlJVt01gwcOLJ/kXvhI+aTIkDBkRc3+fzRew5NLrE9+F74vO2HVRy8mz9+ut+/4TJZEpMTIyvv/BgMBjzK056QFemdKycU3Di7dueCTtFODqluCRrSMT7Jzqa0qcmHJ27KaPKV992sMCWPTH3yKRI15B1ZGqfiQkbrL7gAUdQFJGbB16iaVsdlTTColj8ofAjEDcWXax1mx/RX77ZHD547GBLUpK2+XZB3sTfb1sQNnhRwWkR+1EURVGUtvvDVpl2qW13pCYlQfSaS0cXy0erwwdHF0qaQ1s/Px8nz7b7YCdF5JSR2uLLqCJxJIrzwKtaMpJlRKHNGimqdTSlJwyW+f+VwIGZXhGZNFrzrz7mXC6XzWbr6NLA6AQCgfja7aNFN/7OVq5cef3113u9+5NKxMt+hwwZoqrqli1bWhYbGxt37do1YsSI7uuqlXniJKWwSNpemmIxW6/7peY6J56q5BWEDVqmXa21juJItV54qbTdRMnJ1sun657qcLgpTMx9bsQdNtNPRzKyrGmvjL5P612xKeakl0bfazcntR15efS9yVpSnYhYTJb5I38b9r/P7nfROMdQTXVE5LXR94eNjLIX31qk+SaMyyeE3wdw1hgZpf2Kid8VX3tCeskBlfMnXd1nckfrd+QPF0b43fz+Ys39xMqAbLnwwJvHslJkhobT5vsdOUCGtrv/43INp/H3S7LKtSdL24OFiVa5bqJETHWdMJnk6hPCd8mTRkvfjA7+AaAHJRSK1WOGwrlcrtmzZ7ccqLNarYsWLfrkk0+eeeaZ/Pz8Tz/91OPxTJkyRUT++Mc/7t279+abb05ISJg7d25jY+Njjz3W0Vm/0tLSkpKSloPeLpdLVdW2h/ei4P/mi+CKZeL1KIVF1qmXSrTHsQOLP/V/86Xi80p6VsKMayUjwiUvLRoaGtLSIp+iEpFQTVVg5TJp2Kfk5JmOnqB0cOarh1VUVBQUFMTXWze32x13R+yam5vdbnd2doeTpyetd+9YWPmvCm/VCPuAa/pMybR2+GyRzqf0Ls/eBbs/3Nq8e1By36v7TO5ry4mun01Nu27d8NSm5p35CVm/GTjjzCztL+8iIrK1efcF39+1rXmPw5L0y6KL7x4wPbo6/qD8d5Nsr5Ekq4wrkqGR7+M/uGAo+Pe9//66vsxmsp6RdfTk7BM6WtPj8XR0xK7F7xfJzloJKtInVX47RXSf+9uq5butgbpG37C+SScOFU0nYdtavF7+WSbNPslMll+cIv2j/fuodck3m6TaJbmpcuIQSe/47vPOp/SeBnl9iVQ5JT1JpoyXER3cWtvDqqurHQ5HbI/YuVyuNWvWTJgQ5d8a9NKNwU5EduzYMX/+/LVr1yqKUlRUdOWVV44dO1ZEHn300cbGxjlz5ohIU1PTCy+8sHLlykAgMGrUqFmzZnWS1WIe7Hpe57uM3olg1zN6VbA7dPE4pSsrK7OysjRdr6a7gwa7Xqjldre8PJ0euxKteJzSBDu06t6Xvf79+0d8Tt4dd9zR+nVycvItt9zSrW0AAAAcDuLpGAwAAAA6QbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQVj0bsAgQo0NwfVrpcml5BWYho8SRdG7I6BXWN64duqq39T46nOs6e+XPDo2bUh0dXxB9f3qrzY27SpMzJ2SfWKG1RFdnWAo+GFNaWn19/19fafknVhgy46uTi+0dJt8t02CATmiv5wwVO9uAOiEYBcDwbIV6puvic/bsqgUFiVcO1uSk/XtCtDdpWX3vFH9bwmJiOwM7B333fQr8372csl9Wutsa9591opbNzbtbFnMtqa/XjLntMyjtNapVRvOWnHrssZ1IiKV8qvNT/911G8uyTtda51e6IH3ZXv1/q9X7pQPVsmDF3FGBjgc8YffVaG6WvXN18Tr/WmkfKf6zus6tgT0BtuaKt+o2p/qWr1S9cketUZrqSvX3Nea6kSkRt03bfW99apTa53/WffI/lQnIiKuQPO1Pzy0rXm31jq9zd+//SnVtahskOc/16kbALoi2HVVcE2Z+LyiRBrAKIpGAAAgAElEQVQEDmPT190XYTQkV3z/O011NjeVf7NvddjgXl/dx7VLNNVxBZrfrlrcfvDNvXGfgEo3RxhctTPCIADDI9h1VcjtjjAaDIaam3u8F6AXqfRGPjJX4avTVKdWbdA03pEGvysQCna9Ti+kBiIM+iP8rACMj2DXVUpOboTRpCTFkdrjvQC9yClpka+B+1nmMZrqDE4uNCsR9lTD7f011clLyEy3pHS9Ti+UmhRh0G7r8T4A9AIEu64yjztCye8TNmg542wxsW1xWJs76tdKu9vDFTE9PeI2TXWyrGm3Fl0eNnh65lGnZRypqY5FMd836Bdhg2NSBl2WP0lTnV7oyuNE2t2If6m2/AzAIAgfXWaxWq++3jRi9P5HnCQlWSafbz7hFL3bAvT31RHPm8XcumhWTEuOnRtFnYcG3/B/A2ckmxNbilxZcNbfS+aYIh3G69zNRZc8OvTGluN2iihTck5cNP6xRFNCFC31KqML5YoJYv1xS5tNMvVIOW6wrj0B0AmPO4kBJSPTevX14vOF3C4lPYOH2AEtTsgc45/09a6mPS/uef9/ii4ssEb50LgEk/WhwbPuH3TdLs/eAlt21FFMEeX2/lfcVnT5ivIfBuX0z0g0zvUSp4+U00fK3gbxBaVfht7dANAPwS52EhKUhEy9mwB6nX7JBQ8MuqHrdSyKeWBS+GUPUTAppkJrToo50oVpcS4vTe8OAOiNU7EAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADMKidwMAeh1vUH1sx6sLdn9Y4a0ebu9/Z/8rL80/I4o6zQHfSUuvX+HcGJKQoihHO0Z+ddSfE8wJWuuEJPRa5aePbX91Q9POQlvuzL6Tbyu6PMFkjaKl+WvX/avMZvUUqOa67Pzd9588PDMxKYo6vU2NU95cJuv3SDAoQ/LloqOkID2aOo3N8vZyWV0uHlUGZsuFR8nAnGjq1LvkT/+WXXUJgVBeklXOGS9nj4mmjhqQj1fJfzdLQ5MUpMvZJXL0wGjqBIPyn/Xy+TqpdUmOQ84YJScPFUWJplSslO2URd9LxT5JTZRjiuWccWLjBRmxYL7vvvv07kGD8vLyvLy8hIQEEfH5fMFgMCkpznbKXq83MTFR7y60cTqdDodD0XcvqJGqqhaLxWSKp2PSfr9fVdXk5GS9G5GZPzz45M7X69RGNeTf4619s+rzAlv2UanDI67cyZQe8PUFG5t2ti5WeKsXVH50a9FlWvt5dtdbv1j7+0pfrRry16oNn9UtK/dWnZ97stY6z636ofTbkVY1wxSyWoMpamPB+9u3nD8i0xQPc9vv9yuKYrFEePF3euSB92VrlXj94gtIZYMs2SLHDpJkjRHa55ff/1PWVIhHFX9Aqp2yZLOM6SfpGqekPyh3vS7VLgn9uLi2QkwmGZavrY6IzP1C/r1W3F4JBGVfkyzbJpkp0j9Lc51/LJV3lovLI4GgOD1StlMURYYXRF65B/bSy7bJM59JfZMEgtLkk417ZWetTBgsUU/EpqYmm80WcXpEzefzVVVVFRYWxrAmekA8vewB6AHf7Fv9yp6PwwZv3/h0U8Cjqc6blf/Z7a0KG9zVvPf96q801XEFmu/a9GzY4N92f/Bdw1pNdQLB4NcrwpNFonP4X1av01SnF1r0vTQ0HTDS5JM3l2mu89la2b3vgBFfQF5bornO35dIkxo++P5KzXU2Vsq3WyMUVwPa6lQ1yserwwcXrZR9TZHW7n6hkLxaesCIIrK6XMp2dvAPAC0IdgAOsNy5vv2gK9C83r1DU52Fez+NOP7Knk801Vnn3h4xUy5r1BbItjTuswUiHOpZX+XVVKcX2lETYXB7teY622NUZ2t4nhcRCQSlujEG/TSrUtmgrc6O2giDwZDsjDTeA+qbpKE5wvi2SD8voBXBDsABkky2yOPmyOMdcVgin8BLs6bEpJ9ks7aTZXZLguw/N3iAhPi/sMlqjjAYxc8V8Z9EUaej84FJGk8Nd/Rfa20pIdL2iaJOrHTUj62DcUATgh2AA0zKOqZ9ZhpmLxpu76+pzm/7z2w3FhKR3wyYrqnOSPuAwcnhV/nYzUlnZB6tqU7flJRm++b24z8bpP2KrV5mXFGEwfHafl2xrHPSsAiDdpukaLxubXTfCBmob4bkpmqrMyRf7O3eHaQmSXGutjqxkpIog/MijJdE2v6AVgQ7AAfon5j/1LBb246kWVJeGX2fovHC7iEphZfmhd1Lq1xVcNaApD6a6pgU0yuj70u12FtHEkzWZ4b/qjBR88vybac6fJYDLiLLGrTyzCLtyaWXOW2kjDkw+g7Ok3PGaq5z5AA5aegBIwXpcskxmuucNESGHng1o0mR/52kuU62Qy6bcMBIcoJcd4rmOwySE2TmSQcc10wwy3WndHjkrAdcc5I4Doy5Fx8thRk6dQNjUUKhCOcmeq3S0tKSkhK73S4iLpdLVdWMjDj7U2hoaEhLS9O7C20qKioKCgri6w5Tt9sd83vEultzc7Pb7c7Ozta7ERGRMuemVys/qfBUD7f3v77w/LyEzI7W7HxKv1r5r19veqbe58ywpj429MZL87W/vIuISKWv9vnydze6dxYm5l5VcPbolOLo6uxpcj+1dGN5jaQkh84eln5ecZR1ep7H41EUxWaLfGI6JPLd1v2POxmaL8cNFlO0N1iu2iWrdonXLwOz5eRhYok2/Xy2Vr5cH3J7g0VZ5uknar61ttXOWlmyRfY1SUG6TBwenocOXVWjfLVx/+NOTh4mWR1fEdAze2m3V75YL+X1kpYkRxdLcVSPlWlVXV3tcDhiezOvy+Vas2bNhAkTDr4qehOCXU8j2PUMgl2PiccpXVlZmZWVZbVG8yQ8vXQe7Honn89XX1+flxfpvGMvFo9TmmCHVvH0Ug0AAIBOEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBxNNz+UUkEAi43e5gMCgiXq83EAg4nU69m9LG6/XGXc/BYNDlcilKtB9RpAev1+v3++Pr0zJUVVVVNe6mRzxOab/f73a7zWb9PitUO1VVFUXx+Xx6N6KB3+/3+/1xNz3icUqrqtrU1KSqagxrNjU1BQKBGBZEz4izYGc2m+12e8tHiimKoqqqw+HQuyltgsFg3PXc2NiYkpISXyHJZDLF40eKxeP0iMee3W633W7nI8W6m8/n8/l8cTc94nFKezye5OTk2H6kmKIo8fXmBy3i6aUaAAAAnSDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAg4in5/IDBrbTs/fjvd/UNTdMtB41IW203u1Ig9/1Se23u701w5KLzsw61qxE+SbQE/R9VFO6w1M5ILHg7OzjbKYoP+zBHwp8UrtkU1N5X1vOWVkTHJbk6OrE0Df7Vq9wbnCYk0/PPKowMVfvdqSyQTZUSigkg/OkMCP6Osu3y6drxOeX0UVywRGx6w9AjyDYAfr7S/k7t214qjnoFREpf/6C3Il/L5ljVXT78/yifuWlq36711fXsjjOMeSf4x/va8vRWmeVa/P539+1rXl3y+Lg5MJ3xz48KqVYa52dnr3nrPzVateWlsUCW/YbJQ+emD5Wa51Y8QbVS1b95v3qr1oWk82JTw279Rd9z9WrHxF5Z7l8tEr8wf2Lp4+UK46Lps5978rO2v1fb6+Vf62Wpy+XhITYNAmgB3AqFtDZ0sZ1t254cn+qExGRt6sW37/lr3r1U686L1t1T2uqE5HvnZtmrHlAax1fUL1s1T2tqU5ENjeVX7r6Hn9I88eKT19zf2uqE5E93ppLV/22we/SWidW7t3yYmuqE5GmgOem9Y+vaNygVz8rdsii739KdSLy2Vr5Uns7by37KdW18Pnlt+90tT0APYlgB+js5d0feYK+sMG/VizSpRkR+ai2tNJXGzb4Wd2yHZ5KTXVKG9asc28PG/zBtfXbhh801dnSXPFF/cqwwd3emo9rlmiqE0Pzdof/djxB38t7PtKlGRH5emOEwa8iDXZu8foIgzW65WcA0SDYATqrVve1H6xR94Uk1PPNiEi1rz7ieFUH4x2pifRzRVPH10EdVVudWAlJqFZtbD8e8ffYM5yeQx3snKr5WCqAXodgB+hsSHK/iIOKKD3fjHTQj0UxD0rq2/U6IjLMXqSpTnFSX1OkWzeGJWurEyuKKBE3xVCd+hGRvNRDHeycPdK1dPrMQgDRItgBOpvd74LchPCbGO8b9AtdmhGRM7OOPa7dbbk3FV2cadWWFEpSBk/NPSVs8OK800baB2qqk5OQ/svCC8MGT8oYd3rm0ZrqxFD7305+Qtaswqm6NCMiZ5dIwoF32ljNMmWc5jrXnBxhcJxueRVANAh2gM7yE7I+GP/4eMfQlsVMa+pfRtx1Sd7pevVjUcxvjv3DeTn7X+StiuVX/af9YfDsKErNG/Xbq/tMbjn0aFJM1/ad8uLIu6Oo88jQG28purT1NuELcie+UfJg1E9g6bpp+Wc+M/xX6ZaUlsWjUkd8eMT/a5/Oe0zfDLnpDMn9MXhn2OX6iTI4T3OdUX3l3HEHHKIblCs3TYpJjwB6iBIK6XMdT3RKS0tLSkrsdruIuFwuVVUzMnTbmUanoaEhLS1N7y60qaioKCgoMJni6W2A2+222WwWSzw90GdbQ/leZ+1RfUdbFLPevYiI7PO7KjxVg5ILE02dPe7ioFPaFWje0bynf1JBijmpK/00B71bmyr6Jua2JqqoVVZWZmVlWa1RPlSvhT8U2NJUkWpJLrBld7GfQ+HxeBRFsdlsnaxT45JQSLIdXT1/+kOF1Lnk2MGS0LWZ6PP56uvr8/K0Z0xdxeNeurq62uFwJCYmxrCmy+Vas2bNhAkTYlgTPSCeXvYAY8tPyHIkJvaSVCci6ZaU9JSuRigRSTEnRfHsuvaSTLaY1IkVi2LWer1gd8uOwa9LRGSUtsspAfQi8XQMBgAAAJ0g2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGYdG7AQBSrzof2PrXRdVfu/zNx6SPfGDQ9eMcQ3TspynouXzV7z6t+84b9KWYk2/qd/GDg2/QsR8RWbFDPl4texskwy4nDJHTR4iJt6XQw/Lt8vFqqWqUDLucNFROHc5URO9CsAN05g2qpy+/caVzY8viouqv/1279JtjXtQx241fMn2je1fL141+90Pb/lbpq5078v/06ueLDbLg6/1fOz2ys1b27JPpJ+jVDg5fn6+Tl7/Z/7XTI6+Wyp4GufI4XXsCDsQbDUBnz5e/05rqWjQHvTdv+H969TO/4oPWVNdqXsU/6/yNuvTj88vfvw0fXLxettfo0Q0OY15VXv8ufPA/a2VXnR7dAB0g2AE6+65xbYTBhh9CEur5ZkTko9rS9oMhCX1cvaTnmxGR3fvEq0YY31bd463g8FZeLz5/hPGtTEX0JgQ7QGc2k1XaZTibKUERRZd+Es3WiOMOa1IPd9LCYtY2DnQTawdTrqNxQBcEO0Bnk7NPkHYZbnL28bo0IyK/6HNu+0GrYj47U58rifqkS3ZK+GCCWUb20aMbHMYKMyTTHj6YYJERBXp0A3SAYAfo7ILciVcVnN12ZEBSwVPDbtOrn5Mzxl+Sd9qBY8qzI+60mPS518qkyHUTJeHA//yyCZLVLu0B3cpkkusmSsKBx+emTZCMdmkP0BF3xQL6e2n0787PPXnR3q9qPQ0n5Yyf3e8Cu1mf854tXi956KyKD57YubBGbRiQVPDU0FuPThupYz9D8uT3F8l/1knlvv2POxmQrWM7OHwNy5eHLpLP18meBsmyy4lDpShL756AAxHsgF7hgtyJZzuOdbvd2dm9IrPM7Dt5Zt/Jenfxk0y7XHSU3k0AIlkpctHRejcBdIxTsQAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBWLq1el1d3bx588rKynw+X3Fx8cyZM4cOHRq2zs0337x9+/bWxcTExDfeeKNbuwIAADCk7g12Dz74YEJCwv3335+UlLRw4cIHHnhg7ty5iYmJbddxuVzXX3/9hAkTWhZNJg4iAtHb4dn77K439/rqTkkfd03fKXq3I2rI/5+65dub9xQn9Tk180iLYta7IyltWPNN3coBocIzco5Os6To3Y7s2Sdbq8ViliF5kmmPvk6NSzbvlWBIBuVKXmr0dRqaZONe8ahSnCN9M6Kv4/bKml2m6vqkUSYZmBN9HQCadGOwczqdOTk5V155Zb9+/URk+vTpX3zxxa5du4YMGRK2Wn5+fnZ2dvd1Ahwm7t0898Ft84MSFJGXdn9416Y//3D8q7kJmXr1s969Y2rZXevdO1oWR6UUvz32D0OTi/Tqx+lvunDV3Z/WficiUiG5CRkLRv/urKwJevUTEnltifz7h/2LVrNccJT8bHQ0pT4ok/dWij8gImIxyxkj5ZJjoqnz1UZZWCpe//7FE4bIzJPEpGiu8/1OmfeluLwWkdS3V0lJP5l9miR075EEACLdeo2dw+G4++67W1KdiNTW1ppMprAAp6qq1+stLS295ZZbrr322j/84Q8VFRXd1xJgYEsafpizbV5LqmtRo+47ZelsvfrxhwKXrPpNa6oTkR9cWy9bdU8gFOzkX3Wr/93wxP5UJyIiVb76aat/V+Gt1qufL9f/lOpERA3I69/K2t2a66zaJW8t25/qRMQfkI9XyzebNdfZXiOvfPNTqhOR/26SD1dprlPjkhcWi8t7QIevf9fxPwAQOz30BsrpdP7pT386//zzMzIOOLLf1NSUnp7u9/tnz54tIq+99trdd9/93HPP2e37T0iEQiG//6fdTCgUCgaDwWCw5euWxZ75EWIlHnsWkbjrue1UiRddnNIPbpsXklDY4PqmHXW+xvTuPOHYUc//rS9b7doSNrjSuXHJvjXHpUV1VKprmgKeV/Z8HDZYrzpf3/PvW4ou7fl+ROSLDRHeWi9eFxqeH/57lE6nx+L1ikj4UbXF62VCsba59NVGRQ2E1/livfx8jLY6325WPGp4na83yqXHBC3xcK1NPO6lu+MFMRgMhkIRpiJ6uZ4IduXl5XPmzBk3btyMGTPCvpWWlvbSSy+1Lt55550zZsz45ptvJk2a1DJSU1OzevXq1hUURdm7d6/NZpMf57Hb7e7+nyCWgsGg0+nUuwttAoHAnj179O5Cm5b9kaJoP4ekn5Yp7fF4ovvn5c6qiONLd5SNTBwQfVsH09GUXu8MT3Ut1u7ZVOTqwqVb0dqj1qohf/vxzXU7Ksz6nCioc/URCb/osKbBV1ER4VfZyZSubcwTSQgv7vRXVGj7s91blyWSHDa4rymk9URKRXW6iCNsUA3I1h177AlxEJjidC/t8Xhiu8fzeDyqqsawIHpGtwe7srKyRx555PLLLz/nnHMOunJSUlJOTk5NTU3rSE5Ozmmnnda6WFpaWlBQ0HI8z+Vyqaoadgiw92toaEhLS9O7C20qKioKCgri674Wt9tts9kslni6qKe5udntdkd9vemIhoFle8JPvyminDLo2ERT+Kt+DHU0pY9xNkukPDChaFy/lH7d109H8oL5jh3JTn9T2Pj4vBH9+urQj4gUpEtjZfhgvxxb6xUsbbW8bLe8rQ3Td4vs2hc+2CfTErFOJwZUytq94YP5aYrWOsVOKd0ZfgjRbpOhxX2juFyv58XjXrq6utrhcITdm9hFLpertrY2hgXRM7r3pXrt2rUPP/zwbbfd1lGq27FjxzPPPNN6stXj8VRXV+fn53drV4AhPTb4JosSHmTPzD6mW1NdJ8Y5hkzOPiFs8Lyck8ekDNKlnwST9c7+V4YNDk4uvCxvki79iMg548JHEizyszGa65w1RhLa3W08eazmOqeOEHu73Ni+yYM6frBktzv5P3lsNDdhANCqG4Odz+d78sknzz333P79+9f8qOU006effrpo0SIRyczMLC0tfeaZZyorKysqKp544omUlJTjjz+++7oCjKpvYs6bJQ+lmJNaR05IL/nn2Mf06kcRZcHoey7NP6N1cVr+mfNH/VavfkTk7oEzfj1gus1kbVk8Pn3M++MedVjCTz72mFF95dqTJeXHgyzZDrnxdOmTrrlOUZbMOu2nR6WkJskNE2WY9jfIWSly8yQp+LGBpASZdpwcW6y5TnKC/O+ZPz3ixGqWc8dHebcvAK2U7rs0sqys7J577gkbvOGGGyZPnvzoo482NjbOmTNHRLZu3Tp//vxNmzZZrdZhw4Zdd911eXl5HdUsLS0tKSnhVGwP41Rsz+jiqdhWSxp+2NpUcUbWUT3zoJODTulatWFLU8Wg5L5Z1l4x812B5tKdKwfn9B+Y0lfvXkREAkHZ0yAWk+SmdnZMq5NTsS2CQalySiAo+Wli7sIfaygk1U7xqNInXSxde+xgZb26p8Y5cmCmLZ7+EONyL91Np2LXrFnT+pRZxItuDHbdgWCnC4Jdz4hVsOth8TilKysrs7KyrFar3o1ocNBg1wv5fL76+vpO3qv3TvE4pQl2aBVPL9UAAADoBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiL3g0AkL2+uvO//3WZc4MaChYkZP5l5K9/nn1cFHW8QfWJna+9uffzWrVhTMqge4qvOTp1RMy7BQD0WgQ7QGdNQc/gry9yBZpbFnd5qyav/NW7Y/94Xu7JmuqEJHTJqt+8X/1Vy+L25j2Lqr/+/KhnJ2YcEeOOAQC9FadiAZ1ds+bB1lT3o+DMtQ9qrbOo+uvWVNfqhrUPd6E1AECcIdgBOvuucV27MaVedQYlqKlO6b417Qc3Nu2s9u2LtjUAQJwh2AE6syjm9oOKiEnjn6fVFPnKio7GAQDGQ7ADdPbzrAj3SfRNzNVa58ysY9qNhSakjU63pETVFwAg/hDsAJ09OfzWwgNjnFkxLRr3qNY6J6aPvaXo0rYjaRbHX0f9X1f7AwDED87RAPrbcdI7N657/J81X3sC3tGOwfNH3dM/MS+KOk8Mu+XUzCPf3Pt5jbqvJGXwLf0vzU/Iinm3AIBei2AH6M8kpj+PuOPx5hvdbnd2dnZXSp2bc9K5OSfFqjEAQHzhVCwAAIBBEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCAIdgAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAg7Do3QAO5PcHt28NNexTcvJM/YpEUfRuCD2kVm1YXLe8tmnfKUlHDbMX6d1OzPiC/ufL313j3lJiL76hcKrFxD4HALoRO9leJFSxS134t1BNdcuiaeAgy5XXKCkOfbtCD3it8tPZ6x7Z53eJiGyX6/qe95cRd5qUuD+g/lntsilltzcHvC2Ld27+84fjHz8l4wh9uwIAA4v7Vw7j8PnUV+a1pjoRCW7b4v/HQh07Qs9Y49p67Q8P7U91IiLyYsV7D29/RceWYsIT9J1bdkdrqhORpoBn8spf+YJ+HbsCAGMj2PUWwQ1rQ3W14YPrfwjV1+nSD3rMvN2LmoPesME/l7+lSzMx9LfdHzQFPGGD7oDnlT0f6dIPABwOCHa9RcjlFAlFGG9s6Plm0JP2eMMDvYjs8daEIs2HOLK5aVfE8Y0djAMAuo5g11soGZki7W6VUBQlM0uPdtBzBiQWtB8sTuqrtJ8PcWWcY2jE8SMdw3q4EwA4fBDsegvTkOFK335hg+Yjj1Ucqbr0gx4zq9/UdEtK2OCvB0zXpZkYmlZwZpY1LWwwJyH9wvxTdekHAA4HBLtew2y2XnmNqXjITwNHHmM570IdO0LP6J+Y/864hwcnF7YsJpsTfz/4f67pe46+XXWdSUxfHv1cfsJPh5z72LK/PPIvJnY7ANBteNxJL6JkZllvuClUVxtq2Kfk5PKgk8PHxIwj1h3/91V1G6tctcf3HZ9qsevdUWyMtA/cc8o/v234YVnD2mPSRh2dNlLvjgDA4Ah2vY6SmcV1dYchi2IekTygKJRjmFTX6ti0UcemjdK7CwA4LHBOBAAAwCAIdgAAAAZBsAMAADAIgh0AAIBBEOwAAAAMgmAHAABgEAQ7AAAAgyDYAQAAGATBDgAAwCDi7JMnAoGA2+0OBoMi4vV6A4GA0+nUuyltvF5v3PUcDAZdLpeiKHo3ooHX6/X7/SZTPL11UVVVVdW4mx7xOKX9fr/b7TabzXo3ooGqqoqi+Hw+vRvRwO/3+/3+uJse8TilVVVtampSVTWGNZuamgKBQAwLomfEWbAzm812u91ut4uIoiiqqjoccfaBqsFgMO56bmxsTElJia+QZDKZbDabxRJPM7y5uTkep0c89ux2u+12u9Vq1bsRDTwej6IoNm/2G8cAABSCSURBVJtN70Y08Pl8Pp8v7qZHPE5pj8eTnJycmJgYw5qKosTXmx+0iKeXagAAAHSCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAwinp7LDxhVc9D7+PaF71d95fI3HZsx+p7imcVJffVuypg+3bnz5eWNqitDrNuH9nP/ZsKYBJ6tD8BACHaAzvyhwJnL//frfWUti+uad7xV9fnSY+YPsxfp25jx/GPT5o++HGxp2fH5ZNd6ua569YLzx+jdFwDEDKdiAZ3Nq1jUmupaOP1NN214XK9+DOydJfawEXPtmJfWrdelGQDoDgQ7QGdf71vVfvCr+u9DEur5ZgxsS+O+RF9B+/FlFU093wwAdBOCHaAzk6K0HzQrZkUijCNq1kjbWUTMbGYABkKwA3Q2KfOYCINZR/d8J8ZW5EhrTtzZfvzEAak93wwAdBOCHaCzaQVnTsk5se1ITkL6n4b9Sq9+DGzmSSG/4m07klCw8sJBg/XqBwBijrtiAZ0porwz9uF5uxct2vtVvc95QtbY2wdMy7am692XAZ1Z1D//vOpnvy1vaLAn2LzHFCs3jhuvd1MAEEsEO0B/ZsV0Xd/zrsw80+12Z2dn692OkZVk5Tz/85zKysqsrCyr1ap3OwAQY5yKBQAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAiCHQAAgEEQ7AAAAAyCYAcAAGAQBDsAAACDINgBAAAYBMEOAADAIAh2AAAABkGwAwAAMAhLt1avq6ubN29eWVmZz+crLi6eOXPm0KFDw9ZxuVwvvPDCqlWrVFUdNmzYrFmzcnNzu7UrAAAAQ+reI3YPPvhgTU3N/fff/+STT2ZnZz/wwAMejydsnSeffLKqquree+999NFHk5OTH3jggWAw2K1dAb2NL6g+tuPVn6+5fdKG2/5n3SPlniq9OwIAxKVuDHZOpzMnJ+eXv/xlcXFxQUHB9OnTGxsbd+3a1XadmpqapUuXXn/99QMHDuzTp8+sWbMqKipWr17dfV0BvU0wFDx75W13bHxm8b4V3zdt+kv5O6NLr9jaXKF3XwCA+NONwc7hcNx99939+vVrWaytrTWZTNnZ2W3X2bRpk9VqHThwYMtiSkpKYWHhhg0buq8roLf52+4P/1O3rO1Ig9914/rH9eoHABC/uvcau1ZOp/NPf/rT+eefn5GR0Xa8sbHR4XAoitI6kpaW1tDQ0LrodrsrKytbF1VVdTqdfr9fRHw+XyAQaLtyXGh/Mrr3CwQCjY2NbX9NvZ/P5/P5fCZTHNwe9OneJe0HP69dHi9zOx6ntN/vdzqdZrNZ70Y0aNnvxdfWDgQCfr8/XmZyq/jayC1UVXW73V6vN4Y1m5qaAoFADAuiZ/TEy155efntt98+evToGTNmtP9ufMUFoGfwdwEAiEK3H7ErKyt75JFHLr/88nPOOaf9d9PT0xsbG0OhUOvLWENDQ9ujena7fdCgQa2LVVVVDofDbreLiMvlUlU1LS2tm3+C2Iu7nl0uV2pqalwc/WrldrttNpvF0kPHpLviZ/nH/b32s7DB07OOiqN5EkettmhubnY4HFarVe9GNPB4PIqi2Gw2vRvRwOfzsZfuGT6fz263JyYmxrCm2WyOr6PaaNG9L9Vr1659+OGHb7vttoipTkSGDBmiquqWLVtaFlvurhgxYkS3dgX0KtMLzj4z69i2I5nW1D8N+5Ve/QAA4lc3Hs/w+XxPPvnkueee279//5qampbBlJSUxMTETz/91OPxTJkyJTMz87jjjnv22WdvvvnmhISEuXPnDho0aOTIkd3XFdDbmBTTP8c/9pfyd97f+1WDz3l81ti7BlxZYMs++L8EAOBA3Rjs1q1bV1lZuXDhwoULF7YO3nDDDZMnT/7+++8bGxunTJkiIjfffPMLL7xw3333BQKBUaNG/fa3v+XqIhxurIrlpn4X/yL7HLfbHXbnOAAAh64bg93YsWPff//9iN+64447Wr9OTk6+5ZZbuq8NAACAw0Q8XQ4PAACAThDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AEAABgEwQ4AAMAgCHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIOw6N2AZjt37kxISBARn88XCATq6ur07kgbj8dTU1OjdxfaNDY2Njc3K4qidyMa+Hw+i8ViMsXTWxdVVX0+X0NDg96NaBOPU9rpdDY2NprNZr0b0cDv94uIxRJPO+1AINDc3OxyufRuRJt4nNJut7uuri6208Pr9cawGnpMPO0jRKS4uLh1qnk8nkAgYLVa9W1JK0VR4mvXLCIejyc9PT2+XgXNZrOiKPEVRlVV9fv9TOkeoKqq2WyOr03d8gcYX+9VQqGQqqrxtZ0lbqe0zWaL7aa2Wq3Z2dkxLIieEWdzNy8vr/Xr8vJyt9tdVFSkYz+HiW3bthUWFsbd3jnuVFdX+3w+pnQP2LNnT15eXkpKit6NGFxjY2NdXR1TugfU1dVlZ2dnZWXp3Qj0F09v/gAAANAJgh0AAIBBEOwAAAAMQgmFQnr3AAAAgBjgiB0AAIBBEOwAAAAMgmAHAABgEHHwHDuXy/XCCy+sWrVKVdVhw4bNmjUrNzc3inVwUIeyGW+++ebt27e3LiYmJr7xxhs92qUhVFRUPPHEE5s3b3733XcjrsCUjpWDbmqmdNfV1dXNmzevrKzM5/MVFxfPnDlz6NChYeswpWPiUDY1U/owFwc3Tzz44IMul+uGG26w2WwLFy7cvn37008/Hfb49UNZBwd1KJvxmmuuueCCCyZMmNCyaDKZMjMz9Wg2jn311Vdz584dP3784sWLO0obTOmYOJRNzZTuuttuuy0hIeH6669PSkpauHDhypUr586dm5iY2HYdpnRMHMqmZkof5nr7H1VNTc3SpUuvv/76gQMH9unTZ9asWRUVFatXr9a6Dg7qEDej0+nMz8/P/hH7iyioqvrYY4+17nbbY0rHykE3tTClu8zpdObk5Pzyl78sLi4uKCiYPn16Y2Pjrl272q7DlI6JQ9nUwpQ+7PX2U7GbNm2yWq0DBw5sWUxJSSksLNywYcPYsWM1rYODOpTNqKqq1+stLS195ZVXnE7n4MGDp0+f3rdvX51ajlennXaaiGzZsqWjFZjSsXLQTc2U7jqHw3H33Xe3LtbW1ppMprDPGGVKx8ShbGqmNHr7EbvGxkaHw9H2o9zT0tIaGhq0roODOpTN2NTUlJ6e7vf7Z8+efdddd/l8vrvvvtvtdvd4swbHlO4xTOnYcjqdf/rTn84///yMjIy240zpmOtoUzOl0duP2IlI231BV9bBQR10M6alpb300kuti3feeeeMGTO++eabSZMmdXNrhx2mdM9gSsdQeXn5nDlzxo0bN2PGjPbfZUrHUCebmimN3h7s0tPTGxsbQ6FQ606hoaEh7A3KoayDg4piMyYlJeXk5NTU1PRIg4cRprRemNJRKysre+SRRy6//PJzzjmn/XeZ0jHU+aYOw5Q+DPX2U7FDhgxRVbX1EpmWC0VHjBihdR0c1KFsxh07djzzzDN+v79l0ePxVFdX5+fn93SvRseU7jFM6ZhYu3btww8/fNttt3UUNZjSsXLQTc2URm8/YpeZmXncccc9++yzN998c0JCwty5cwcNGjRy5EgR+fTTTz0ez5QpUzpZB4fuEDd1aWmp3++/7LLLAoHASy+9lJKScvzxx+vde5ypr68PBAJOp1NEWt5Jp6SkJCYmMqVj7lA2NVO6i3w+35NPPnnuuef279+/9cgQU7o7HOKmZkof5uLgOXZNTU0vvPDCypUrA4HAqFGjZs2a1XIA/9FHH21sbJwzZ04n60CTQ9nUW7dunT9/fss9bsOGDbvuuuvy8vL0bjzO/OIXv6iqqgobOffcc5nSMXcom5op3UVlZWX33HNP2OANN9wwefJkpnRsHeKmZkof5uIg2AEAAOBQ9PZr7AAAAHCICHYAAAAGQbADAAAwCIIdAACAQRDsAAAADIJgBwAAYBAEOwAAAIMg2AFGdt999ykHSk1NPeWUU95+++3u+O9OPPHE4cOHtx+fMGFCcnKyx+NpO/jBBx8oinLNNdeErTx16lSTyVRZWTnh/7d3fyFNvX8cwJ9jOyXallY6EzWLQRe5i5lu2h8XOs1pWTFCV3fZKCMqMErJMZL0or9KYFHgxQqzrJVRUdusmS0NL7KFEdE/NJeFiDXNcm7nd/HwO4zp76u/X138PL5fF+LzOed5zodzIR+eP8e0tElHo4qKiubPnz/pJY1Gk5iY+F9nDwAw8/2//0sxAPhz5eXly5cvJ4T4/f7e3l6z2azT6Wpqag4cODBl366uLoVC8YdfMs/Ly3v+/HlbW1t2djYftNls/E+ez+dzOBwKhSImJqaoqGh0dHQ64/+VJAEABACFHYDwFRQUpKWl8c3Dhw/L5XKj0bh79+7Q0NB/7tvW1vbnCWi1WpPJZLVagwq79PT09vb2N2/e8DNznZ2dQ0NDWq2WEHLw4MFpjv9XkgQAEAAsxQLMOmKxWKfTeTwel8tFI62trdnZ2RKJJCwsLDk5ub6+nsZzc3P3799PCGEYJiUlhQYbGxuVSmVYWJhEIklJSWlsbJzyiSkpKVFRUVarlY+43e7Xr1+XlJSwLBs4aUd/p4Vd4FIsx3GVlZXx8fGhoaFyufzGjRt8l0mTFIlEHz9+1Gq1YrFYLBYXFhYODg7+b68LAGAGQWEHMBuFhYURQrxeLyGkpaUlKytrbGysoaGhublZpVIVFxefPn2aEHLu3LnNmzcTQjo7Oy9fvkwIuXbtml6vj4uLa2pqunr1alRUlF6vv3fv3j8/jmGYDRs2uFyu/v5+GqEFXHZ2dmpqamBhZ7fbIyMjA+cXqZMnT5pMJrVafffuXaPReOzYsa6uLnppYpKEEJ/Pt3Xr1oyMjCtXruzZs6epqam0tPQPXxoAwAzAAYBwmUwmQkh7e3tQfO3atSKRaGhoiOM4hUIhk8lGRkb4qwUFBWKxeHR0lOO44uLiwD8U1dXVmZmZv3//ps3v37+LRKIdO3bQ5po1a1asWDFpJg0NDYQQs9lMm9u3b1+5ciXHcUajUSwWj42NcRzn8XhYli0sLKT3qFQqOprf74+NjU1KSuJHc7vdLMuGh4fTZlCSWVlZhBCLxcJHVq9eHR0dPb13BgAwg2HGDkD4BgcH+/v7+/v7v3z50tnZWVxc/PTpU4PBsGDBgm/fvr148SI/Pz8kJOTXv+Xl5Xk8nlevXk0cqry8vKWlZe7cubQpkUhiYmJ6enqmzCEnJyckJOThw4eEEI7jWlpaNBoNIUSj0Xg8no6ODkJIa2ur1+ul67CBent73W53ZmYmH1myZAm/6jqp0NDQLVu28E2ZTDYwMDBlkgAAMx0OTwAIX35+fmBTJBLt3bv3zJkzhBC3200Iqa2tra2tDer1+fPn1NTUoOCPHz9OnTp169atnp6ekZERQojP51u6dOmUOSxatEipVNrtdo7jXC7X169f6UGK9PT08PBwm822bt06m83GMExubm5QX7qAGxUVFRiMjY3l9whOJJVKGYbhmyzL+v3+KZMEAJjpUNgBCN/Zs2fpKQSGYcLDw5OSkiIiIgJv2Llzp8FgCOolk8kmDrVp0yan03nkyJHc3NyIiAi6eW6aadCzsS6Xy263syyrVqsJISzLZmRk2O32yspKu92uUCikUmlQR26y75j4fL5pPhcAYPZAYQcgfGlpaROPI1AJCQmEEJ/P959uCPTu3bsnT54YDIaqqioaGR8fHxwcXLZs2XTSyMvLM5lMDofD4XCoVCr+88IajaasrOzDhw/d3d0VFRUTO9K5Ov7gBfXp06fpPBQAYFbBHjuAWW3hwoVKpfL27dtDQ0N80Gw2V1RUjI+PE0Logib9nZ6ijYuL4+88f/78r1+/pjl5tmrVqujoaKfT2dHREfhBO41G4/V66VrwxA12hJDExMTFixc/ePCAX059+/bty5cv+RsCkwQAmM1Q2AHMdidOnPj586darTabzVar1Wg07tq1q6+vTyQSEUJiY2MJIdXV1Tdv3pTJZPHx8RcvXrxz547T6Tx06JDFYlm/fn13d/fjx4/pljuexWIRiUR1dXV8hK7b3r9/f2BggJ6coORyuVQqra+vj4yMVKlUEzMMCQkpKSl5//79tm3bLBbLhQsXcnJykpOT+RsCk/zbrwcAYCZBYQcw26nV6kePHkml0n379m3cuPH69etVVVWXLl2iVw0Gg0KhOH78+NGjR1mWtVgsCQkJer1ep9MNDw83NzeXlpbOmzdPp9P19fUFDuv3+30+X9CRBa1WOzIyIpFIlEolH2QYJjMzc3h4OCcnZ86cOZMmaTKZysrKnj17ptfr6+rqampq0tPT6QxiUJJ/89UAAMw0zKS7kgEAAABgxsGMHQAAAIBAoLADAAAAEAgUdgAAAAACgcIOAAAAQCBQ2AEAAAAIBAo7AAAAAIFAYQcAAAAgECjsAAAAAAQChR0AAACAQKCwAwAAABAIFHYAAAAAAvEvYp+m+0TEuKgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "require(ggplot2)\n",
    "ggplot(iris,aes(x=Petal.Length, y = Sepal.Length, col=Species)) + geom_point() + theme_light()\n",
    "ggplot(iris,aes(x=Petal.Width, y = Sepal.Width, col=Species)) + geom_point() + theme_light()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "g46MO3CIh4hV"
   },
   "source": [
    "There are other combinations of variables we could plot, of course, but this is enough to show that all of these variables are providing some information about how these species differ.\n",
    "\n",
    "How can we decrease the dimensionality of this data from 4 variables to 2 without losing too much information? We'll use the `prcomp()` function to do this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "id": "u1TcCIPjirwZ"
   },
   "outputs": [],
   "source": [
    "iris.pca <- prcomp(iris[,1:4],scale. = TRUE) \n",
    "# ^^ \"scale.\" just indicates that all variables should be scaled before PCA is applied, so that units don't matter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Yy4d7ed9lM5P"
   },
   "source": [
    "The first thing we may want to look at is how much variance is explained by each of the components. The `sdev` attribute gives the square root of the eigenvalue for each component - we can turn this into percentages by just dividing by the sum of the vector.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "id": "rnxJipT5k-3o",
    "outputId": "eafda1ef-d32e-4464-d56a-908550f7a916"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data.frame(pc=1:4,var.exp=iris.pca$sdev/sum(iris.pca$sdev)),\n",
    "        aes(x=pc,y=var.exp)) + \n",
    "    geom_point() + \n",
    "    theme_light()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dBO6t3pxmLIt"
   },
   "source": [
    "As you can see, together the first and second components explain over 80% of the variance present with all 4 variables. \n",
    "\n",
    "Let's also look at how much each of the variables contributes to each PC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 190
    },
    "id": "oXPP0V_Amdox",
    "outputId": "12a5faf9-edb0-4b10-b16e-287ac215c8fb"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 4 × 4 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>PC1</th><th scope=col>PC2</th><th scope=col>PC3</th><th scope=col>PC4</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sepal.Length</th><td> 0.5210659</td><td>-0.37741762</td><td> 0.7195664</td><td> 0.2612863</td></tr>\n",
       "\t<tr><th scope=row>Sepal.Width</th><td>-0.2693474</td><td>-0.92329566</td><td>-0.2443818</td><td>-0.1235096</td></tr>\n",
       "\t<tr><th scope=row>Petal.Length</th><td> 0.5804131</td><td>-0.02449161</td><td>-0.1421264</td><td>-0.8014492</td></tr>\n",
       "\t<tr><th scope=row>Petal.Width</th><td> 0.5648565</td><td>-0.06694199</td><td>-0.6342727</td><td> 0.5235971</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 4 of type dbl\n",
       "\\begin{tabular}{r|llll}\n",
       "  & PC1 & PC2 & PC3 & PC4\\\\\n",
       "\\hline\n",
       "\tSepal.Length &  0.5210659 & -0.37741762 &  0.7195664 &  0.2612863\\\\\n",
       "\tSepal.Width & -0.2693474 & -0.92329566 & -0.2443818 & -0.1235096\\\\\n",
       "\tPetal.Length &  0.5804131 & -0.02449161 & -0.1421264 & -0.8014492\\\\\n",
       "\tPetal.Width &  0.5648565 & -0.06694199 & -0.6342727 &  0.5235971\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 4 of type dbl\n",
       "\n",
       "| <!--/--> | PC1 | PC2 | PC3 | PC4 |\n",
       "|---|---|---|---|---|\n",
       "| Sepal.Length |  0.5210659 | -0.37741762 |  0.7195664 |  0.2612863 |\n",
       "| Sepal.Width | -0.2693474 | -0.92329566 | -0.2443818 | -0.1235096 |\n",
       "| Petal.Length |  0.5804131 | -0.02449161 | -0.1421264 | -0.8014492 |\n",
       "| Petal.Width |  0.5648565 | -0.06694199 | -0.6342727 |  0.5235971 |\n",
       "\n"
      ],
      "text/plain": [
       "             PC1        PC2         PC3        PC4       \n",
       "Sepal.Length  0.5210659 -0.37741762  0.7195664  0.2612863\n",
       "Sepal.Width  -0.2693474 -0.92329566 -0.2443818 -0.1235096\n",
       "Petal.Length  0.5804131 -0.02449161 -0.1421264 -0.8014492\n",
       "Petal.Width   0.5648565 -0.06694199 -0.6342727  0.5235971"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "iris.pca$rotation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hsnOUcGfkZ03"
   },
   "source": [
    "PC1 seems to be drawing almost evenly from `Sepal.Length`, `Petal.Length`, and `Petal.Width` - remember that these were quite correlated in the original data. PC1 seems to be picking up on the common variability across those three variables. PC2, on the other hand, is drawing most heavily from `Sepal.Width`. Let's also look at the coordinates of each observation in `iris` in the new coordinate system we've generated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 252
    },
    "id": "HjsQ2aTbnzgt",
    "outputId": "19bfe7be-0d92-4bda-8d28-7f1728be7247"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 6 × 4 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>PC1</th><th scope=col>PC2</th><th scope=col>PC3</th><th scope=col>PC4</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>-2.257141</td><td>-0.4784238</td><td> 0.12727962</td><td> 0.024087508</td></tr>\n",
       "\t<tr><td>-2.074013</td><td> 0.6718827</td><td> 0.23382552</td><td> 0.102662845</td></tr>\n",
       "\t<tr><td>-2.356335</td><td> 0.3407664</td><td>-0.04405390</td><td> 0.028282305</td></tr>\n",
       "\t<tr><td>-2.291707</td><td> 0.5953999</td><td>-0.09098530</td><td>-0.065735340</td></tr>\n",
       "\t<tr><td>-2.381863</td><td>-0.6446757</td><td>-0.01568565</td><td>-0.035802870</td></tr>\n",
       "\t<tr><td>-2.068701</td><td>-1.4842053</td><td>-0.02687825</td><td> 0.006586116</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 4 of type dbl\n",
       "\\begin{tabular}{llll}\n",
       " PC1 & PC2 & PC3 & PC4\\\\\n",
       "\\hline\n",
       "\t -2.257141 & -0.4784238 &  0.12727962 &  0.024087508\\\\\n",
       "\t -2.074013 &  0.6718827 &  0.23382552 &  0.102662845\\\\\n",
       "\t -2.356335 &  0.3407664 & -0.04405390 &  0.028282305\\\\\n",
       "\t -2.291707 &  0.5953999 & -0.09098530 & -0.065735340\\\\\n",
       "\t -2.381863 & -0.6446757 & -0.01568565 & -0.035802870\\\\\n",
       "\t -2.068701 & -1.4842053 & -0.02687825 &  0.006586116\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 4 of type dbl\n",
       "\n",
       "| PC1 | PC2 | PC3 | PC4 |\n",
       "|---|---|---|---|\n",
       "| -2.257141 | -0.4784238 |  0.12727962 |  0.024087508 |\n",
       "| -2.074013 |  0.6718827 |  0.23382552 |  0.102662845 |\n",
       "| -2.356335 |  0.3407664 | -0.04405390 |  0.028282305 |\n",
       "| -2.291707 |  0.5953999 | -0.09098530 | -0.065735340 |\n",
       "| -2.381863 | -0.6446757 | -0.01568565 | -0.035802870 |\n",
       "| -2.068701 | -1.4842053 | -0.02687825 |  0.006586116 |\n",
       "\n"
      ],
      "text/plain": [
       "     PC1       PC2        PC3         PC4         \n",
       "[1,] -2.257141 -0.4784238  0.12727962  0.024087508\n",
       "[2,] -2.074013  0.6718827  0.23382552  0.102662845\n",
       "[3,] -2.356335  0.3407664 -0.04405390  0.028282305\n",
       "[4,] -2.291707  0.5953999 -0.09098530 -0.065735340\n",
       "[5,] -2.381863 -0.6446757 -0.01568565 -0.035802870\n",
       "[6,] -2.068701 -1.4842053 -0.02687825  0.006586116"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(iris.pca$x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2C5I8UzJn-5i"
   },
   "source": [
    "This matrix gives us the coordinates of every observation (i.e., each flower measured) with respect to each principal component. Instead of \"How long is the sepal of flower A?\" or \"How wide is the petal of flower B?\", we're now asking things like \"Where does flower A fall along principal component 1?\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yR_lMMORnxnB"
   },
   "source": [
    "Finally, let's look at how well we can visualize the species clusters using PC1 and PC2, instead of our original variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "id": "yDfHXE-Nnffx",
    "outputId": "d6cf2031-9223-4013-d2e6-896f879bc923"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data.frame(PC1=iris.pca$x[,1],PC2=iris.pca$x[,2],Species=iris$Species),\n",
    "        aes(x=PC1,y=PC2,col=Species)) + \n",
    "    geom_point() + \n",
    "    theme_light()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4awTXYfWpgNL"
   },
   "source": [
    "We can see that the first two PCs do a pretty good job of capturing the variance across the four original variables. Compare this plot to the two original scatter plots. Reason about why it looks the way it does, given how the first two PCs drew from the original variables. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FRT6EvxAd4qn"
   },
   "source": [
    "---\n",
    "# Principal component regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HV2ThgzPdrev"
   },
   "source": [
    "Now that we've got a firmer grasp on what PCA is doing generally, let's try out principal component regression using the `pcr()` function from the `pls` library. We'll use the `Hitters` dataset for this example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "id": "4vxQ0LJNcCSH"
   },
   "outputs": [],
   "source": [
    "install.packages(\"pls\") # Uncomment if not installed\n",
    "library(pls) # load for the pcr function\n",
    "install.packages(\"ISLR\") # Uncomment if not installed\n",
    "library(ISLR) # For Hitters dataset\n",
    "library(tidyverse)\n",
    "hit.dat <- Hitters %>% drop_na() # get rid of missing values in Hitters dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1cfNDLjwrImB"
   },
   "source": [
    "Let's apply PCR to the `Hitters` dataset, trying to predict `Salary`. The `scale` input just indicates that we want to scale the variables prior to dimensionality reduction, and setting `validation` to \"CV\" triggers the use of 10-fold cross validation to evaluate the number of PCs to use. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "GidxAwCBAx_r",
    "outputId": "687694d0-5c2c-417d-ff13-4db04b8fe9a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: \tX dimension: 263 19 \n",
      "\tY dimension: 263 1\n",
      "Fit method: svdpc\n",
      "Number of components considered: 19\n",
      "\n",
      "VALIDATION: RMSEP\n",
      "Cross-validated using 10 random segments.\n",
      "       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps\n",
      "CV             452    351.9    353.2    355.0    352.8    348.4    343.6\n",
      "adjCV          452    351.6    352.7    354.4    352.1    347.6    342.7\n",
      "       7 comps  8 comps  9 comps  10 comps  11 comps  12 comps  13 comps\n",
      "CV       345.5    347.7    349.6     351.4     352.1     353.5     358.2\n",
      "adjCV    344.7    346.7    348.5     350.1     350.7     352.0     356.5\n",
      "       14 comps  15 comps  16 comps  17 comps  18 comps  19 comps\n",
      "CV        349.7     349.4     339.9     341.6     339.2     339.6\n",
      "adjCV     348.0     347.7     338.2     339.7     337.2     337.6\n",
      "\n",
      "TRAINING: % variance explained\n",
      "        1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps\n",
      "X         38.31    60.16    70.84    79.03    84.29    88.63    92.26    94.96\n",
      "Salary    40.63    41.58    42.17    43.22    44.90    46.48    46.69    46.75\n",
      "        9 comps  10 comps  11 comps  12 comps  13 comps  14 comps  15 comps\n",
      "X         96.28     97.26     97.98     98.65     99.15     99.47     99.75\n",
      "Salary    46.86     47.76     47.82     47.85     48.10     50.40     50.55\n",
      "        16 comps  17 comps  18 comps  19 comps\n",
      "X          99.89     99.97     99.99    100.00\n",
      "Salary     53.01     53.85     54.61     54.61\n"
     ]
    }
   ],
   "source": [
    "set.seed(2)\n",
    "pcr.fit=pcr(Salary~., data=hit.dat ,scale=TRUE, validation =\"CV\")\n",
    "summary(pcr.fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DPhgbSEftTT3"
   },
   "source": [
    "The `% variance explained` section of the output above shows us the cumulative variance explained by each additional PC, reaching 100% after 19 PCs. Since there were 19 variables to start with (not counting `Salary`, since that's our dependent variable), this makes sense since unless some variables contribute no information at all, you'll need the same number of PCs to explain all variance as the number of variables you originally put in. The first 5 PCs explain 84% of the variance in the data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lSIgQ8SOr6Fh"
   },
   "source": [
    "The `VALIDATION` section of the output above shows us the cross-validated root mean squared-error for each number of components used (we can just square this to get the normally used mean squared-error). We can also visualize this using the `validationplot()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "id": "GpToD_6xuF8f",
    "outputId": "d9ec4c7d-bd68-4d66-911c-4f33d3331811"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title “Salary”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "validationplot(pcr.fit,val.type=\"MSEP\") # MSEP shows cross-validated mean-squared error as error metric. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7ZJG9Li4uTOA"
   },
   "source": [
    "The best performance is around 16 PCs, but it looks like that doesn't do much better than 6 PCs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LTwXJ0evvGtx"
   },
   "source": [
    "Let's try this again, fitting and cross-validating PCR with a training subset and then testing it on the remaining data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "id": "8Fq7TKmyvNsN"
   },
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "train=sample(1:nrow(hit.dat), nrow(hit.dat)/2) # Identify train observations\n",
    "test=(-train) # Identify test observations\n",
    "y.test=hit.dat$Salary[test] # Identify test dependent variable values\n",
    "x.test=select(hit.dat,-Salary)[test,] # Identify test independent variable values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "id": "YPsppG2Kxdxi",
    "outputId": "ba2d2dd0-5d04-43f4-d72d-260229e5c9f8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title “Salary”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcr.fit=pcr(Salary~., data=hit.dat,subset=train,scale=TRUE, validation =\"CV\") # Run cross-validated PCR fit on training set\n",
    "validationplot(pcr.fit,val.type=\"MSEP\") # plot CV MSE for num of PCs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "B8zNaGj4wb7L"
   },
   "source": [
    "It looks like, for the training set, the best number of PCs is 5. How does that look on the test set? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "id": "q_pWqrCBwax4",
    "outputId": "ef0f86ef-9e5e-4992-cfc6-b81517c24e47"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "142811.810376319"
      ],
      "text/latex": [
       "142811.810376319"
      ],
      "text/markdown": [
       "142811.810376319"
      ],
      "text/plain": [
       "[1] 142811.8"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate prediction error on test set \n",
    "pcr.pred=predict(pcr.fit,x.test,ncomp=5)\n",
    "mean((pcr.pred-y.test)^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3DZXquuuv_0B"
   },
   "source": [
    "Now that we've got a good model selected (with M = 7 principal components), let's fit it to the whole dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vUt3bU6HwIIz",
    "outputId": "8d55cc5b-8350-4cc0-f8d4-841b2a8a576a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: \tX dimension: 263 19 \n",
      "\tY dimension: 263 1\n",
      "Fit method: svdpc\n",
      "Number of components considered: 5\n",
      "TRAINING: % variance explained\n",
      "        1 comps  2 comps  3 comps  4 comps  5 comps\n",
      "X         38.31    60.16    70.84    79.03    84.29\n",
      "Salary    40.63    41.58    42.17    43.22    44.90\n"
     ]
    }
   ],
   "source": [
    "pcr.fit = pcr(Salary~., data=hit.dat, scale=TRUE, ncomp=5) # fit PCR to the full data set using our selected number of PCs, M = 5\n",
    "summary(pcr.fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-CbTJ__c0UM1"
   },
   "source": [
    "---\n",
    "# Partial least squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zpd5JH-40YpC"
   },
   "source": [
    "The function for performing partial least squares is `plsr()`, also in the `pls` package. Let's apply cross-validated PLS to the `Hitters` training dataset, again trying to predict `Salary`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "y4CbCCom0qEv",
    "outputId": "8d4dfc13-47f2-434d-fd1b-3c4e6fe5dc58"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: \tX dimension: 131 19 \n",
      "\tY dimension: 131 1\n",
      "Fit method: kernelpls\n",
      "Number of components considered: 19\n",
      "\n",
      "VALIDATION: RMSEP\n",
      "Cross-validated using 10 random segments.\n",
      "       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps\n",
      "CV           428.3    325.5    329.9    328.8    339.0    338.9    340.1\n",
      "adjCV        428.3    325.0    328.2    327.2    336.6    336.1    336.6\n",
      "       7 comps  8 comps  9 comps  10 comps  11 comps  12 comps  13 comps\n",
      "CV       339.0    347.1    346.4     343.4     341.5     345.4     356.4\n",
      "adjCV    336.2    343.4    342.8     340.2     338.3     341.8     351.1\n",
      "       14 comps  15 comps  16 comps  17 comps  18 comps  19 comps\n",
      "CV        348.4     349.1     350.0     344.2     344.5     345.0\n",
      "adjCV     344.2     345.0     345.9     340.4     340.6     341.1\n",
      "\n",
      "TRAINING: % variance explained\n",
      "        1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps\n",
      "X         39.13    48.80    60.09    75.07    78.58    81.12    88.21    90.71\n",
      "Salary    46.36    50.72    52.23    53.03    54.07    54.77    55.05    55.66\n",
      "        9 comps  10 comps  11 comps  12 comps  13 comps  14 comps  15 comps\n",
      "X         93.17     96.05     97.08     97.61     97.97     98.70     99.12\n",
      "Salary    55.95     56.12     56.47     56.68     57.37     57.76     58.08\n",
      "        16 comps  17 comps  18 comps  19 comps\n",
      "X          99.61     99.70     99.95    100.00\n",
      "Salary     58.17     58.49     58.56     58.62\n"
     ]
    }
   ],
   "source": [
    "set.seed(1)\n",
    "pls.fit <- plsr(Salary~.,data = hit.dat, subset=train, scale=TRUE, validation=\"CV\")\n",
    "summary(pls.fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LfyjKx3n1R0I"
   },
   "source": [
    "Interestingly, the lowest RMSE is when only one partial least squares direction is used. Let's look at how a model with only one PLS direction performs on the test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "id": "6yka2bYI1q0v",
    "outputId": "883d36df-a6f8-47c8-fa39-a34fe0ae6143"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "151995.259555806"
      ],
      "text/latex": [
       "151995.259555806"
      ],
      "text/markdown": [
       "151995.259555806"
      ],
      "text/plain": [
       "[1] 151995.3"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pls.pred = predict(pls.fit,x.test,ncomp=1)\n",
    "mean((pls.pred - y.test)^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CDK0LNkO13at"
   },
   "source": [
    "This is higher than the test error we got using 5 principal components in the PCR example above, but still comparable. Now let's look at PLS for the full data set, using M = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "V-n1_rWF2L9J",
    "outputId": "30b20844-e91f-4a01-ffef-308f9db52a67"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: \tX dimension: 263 19 \n",
      "\tY dimension: 263 1\n",
      "Fit method: kernelpls\n",
      "Number of components considered: 1\n",
      "TRAINING: % variance explained\n",
      "        1 comps\n",
      "X         38.08\n",
      "Salary    43.05\n"
     ]
    }
   ],
   "source": [
    "pls.fit = plsr(Salary~.,data=hit.dat,scale=TRUE,ncomp=1)\n",
    "summary(pls.fit)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Note that the amount of variance in `Salary` explained by the one-component PLS fit, 43.05%, is similar to that explained by four principal components, 43.22%, in the PCR example. This is because, while PCR is only trying to maximize variance explained in the predictor variables, PLS is trying to maximize variance explained in both the predictors and the response. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LkHGqR5BbkOX"
   },
   "source": [
    "*Notebook authored by Patience Stevens and edited by Amy Sentis.*"
   ]
  }
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