Ch1_Exercises.ipynb

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    "language_info": {
      "name": "python"
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  "cells": [
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        "<a href=\"https://colab.research.google.com/github/macquarrielucas/Notes/blob/main/Ch1_Exercises.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# 1.1\n",
        "\n",
        " R can generate numbers from all known distributions. We now know how to generate random discrete data using the specialized R functions tailored for each type of distribution. We use the functions that start with an r as in rXXXX, where XXXX could be pois, binom, multinom. If we need a theoretical computation of a probability under one of these models, we use the functions dXXXX, such as dbinom, which computes the probabilities of events in the discrete binomial distribution, and dnorm, which computes the probability density function for the continuous normal distribution. When computing tail probabilities such as it is convenient to use the cumulative distribution functions, which are called pXXXX. Find two other discrete distributions that could replace the XXXX above.\n",
        "\n",
        " **find all the functions that have to do with distributions in python**"
      ],
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      "source": [
        "## d-functions\n",
        "\n",
        "In R, the dXXXX functions return the value of the pdf for the distribution XXXX at a given input (and some parameters for the distirbution). For example, the PDF for the gaussian is\n",
        "$$f(x \\mid \\mu, \\sigma) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp\\left(-\\frac{(x - \\mu)^2}{2 \\sigma^2}\\right)\n",
        "$$\n",
        "\n",
        "so running\n",
        "```\n",
        "dnorm(x,\\mu ,\\sigma )\n",
        "```\n",
        "will return $f(x,\\mu ,\\sigma )$.\n",
        "\n",
        "## p-functions\n",
        "The pXXXX functions return the cumulative distribution function. For example, if we want the cdf of the gaussian distribution\n",
        "$$F(q) = \\int_{-∞}^q f(x|\\mu, \\sigma)dx $$\n",
        "\n",
        "We can run\n",
        "```\n",
        "pnorm(q,\\mu,\\sigma)\n",
        "```\n",
        "To calculate from the other side, i. e\n",
        "$$\\int^{∞}_q f(x|\\mu, \\sigma)dx $$\n",
        "we do\n",
        "```\n",
        "pnorm(q,\\mu,\\sigma, lower.tail=FALSE)\n",
        "```\n",
        "\n",
        "## q-functions\n",
        "The qXXXX functions return the *inverse of the cumulative distribution function*. Returning to the example of the Gaussian, if\n",
        "$$F(q) = \\int_{-∞}^q f(x|\\mu, \\sigma)dx $$\n",
        "we are interested in calculating\n",
        "$$F^{-1}(p).$$\n",
        "\n",
        "Note that the inverse is well defined because the CDF is monotonic. It answers the question \"which value of $q$ in $F(q)$ will give an area of $p$?\" i.e it returns the $p$'th percentile. Some people refer to this distribution as the ppf - Percent Point Function.\n",
        "\n",
        "## r-functions\n",
        "\n",
        "Instead of calculating data related to the distributions, *the rXXXX functions sample from a given distribution*. In particular, we can get a vector of $n$ samples from the Gaussia distribution by running\n",
        "```\n",
        "rnorm(n,\\mu,\\sigma)\n",
        "```\n",
        "\n",
        "## Python Scipy equivalents\n",
        "\n",
        "Scipy takes a different approach to calculating statistics. Rather than have a different function for each statitic and each distribution, we should first create an instance of a distribution object and then call its methods to get the relevant information. A list of supported distributions can be found at:\n",
        "https://docs.scipy.org/doc/scipy/reference/stats.html. By default, the distribution objects are standardized so calling\n",
        "```\n",
        "from scipy.stats import norm\n",
        "rv1 = norm()\n",
        "```\n",
        "instantiates an object describing a normal distribution with mean $0$ and standard deviation $1$. To define one with mean $\\mu$ and standard deviation $\\sigma$ we need to use the loc and scale parameters like so\n",
        "```\n",
        "rv2 = norm(loc = \\mu, scale = \\sigma)\n",
        "```\n",
        "Scipy parameterizes their distributions with a generalized concept of location and scale rather than the typical parameters mathematiciations may be used to. To make sure, check the Scipy documentation to see how to define the distribution you want. Once you have instantiated your distribution object with your parameters of choice, getting the Scipy equaivalents of dXXXX, qXXXX, pXXXX, rXXXX is just method calls:\n",
        "\n",
        "```\n",
        "from scipy.stats import norm\n",
        "rv = norm()\n",
        "#Scipy             # R equivalent\n",
        "rv.rvs(size=10)     #rnorm(size=10)\n",
        "rv.pdf(x=0.5)       #dnorm(x=0.5)\n",
        "rv.cdf(q=0.5)       #qnorm(q=0.5)\n",
        "rv.ppf(p=0.5)       #pnorm(p=0.5)\n",
        "\n",
        "```\n",
        "where size,x,q,p values were chosen just for example."
      ],
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        "id": "IWs7GjiXr85o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1.2\n",
        "\n",
        "Calculate the probability mass at $x=2$ for the binomial distribution $B(10,0.3)$. Then use the PMF to calculate the CMF at $x=2$ and compare with the value calculated with R (Python).\n"
      ],
      "metadata": {
        "id": "5GBM6Kgy7zAM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import binom\n",
        "\n",
        "rv = binom(n=10, p=0.3)\n",
        "print(rv.pmf(2))\n",
        "print(rv.pmf(0)+rv.pmf(1)+rv.pmf(2))\n",
        "print(rv.cdf(2))"
      ],
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      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.2334744405000001\n",
            "0.38278278639999996\n",
            "0.3827827863999998\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1.3 / 1.4\n",
        "Whenever we note that we keep needing a certain sequence of commands, it's good to put them into a function. The function body contains the instructions that we want to do over and over again, the function arguments take those things that we may want to vary. Write a function to compute the probability of having a maximum as big as m when looking across n Poisson variables with rate lambda.\n",
        "\n",
        "Rewrite the function to have default values for its arguments (i.e., values that are used by it if the argument is not specified in a call to the function).\n"
      ],
      "metadata": {
        "id": "bKb0lRDT9WJE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sol: Let $X_i, i=1, \\dots, n$ be independent samples from $Pois(\\lambda)$. Whats the probability that $max(X_1, \\dots, X_n)> m$?"
      ],
      "metadata": {
        "id": "YOaPIqsU9tt2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as sp\n",
        "import numpy as np\n",
        "\n",
        "def func(m=7,n=100,lam=0.5):\n",
        "    pois = sp.poisson(lam)\n",
        "    epsilon = 1 - pois.cdf(m-1) #1 - P(X < M)\n",
        "    print(epsilon)\n",
        "    return 1-np.exp(-n*epsilon)\n",
        "\n",
        "func()"
      ],
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      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0023796028768572e-06\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.00010023293663119492"
            ]
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          "metadata": {},
          "execution_count": 15
        }
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1.5\n",
        "\n",
        "In the epitope example, use a simulation to find the probability of having a maximum of 9 or larger in 100 trials. How many simulations do you need if you would like to prove that “the probability is smaller than 0.000001”?\n",
        "\n"
      ],
      "metadata": {
        "id": "oOaPDiL9A8s6"
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    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "def trial():\n",
        "    n,p= 100, 0.01\n",
        "    lam = n*p\n",
        "    pois = sp.poisson(lam)\n",
        "    simulation = pois.rvs(size=100)\n",
        "    if simulation.max() >= 9:\n",
        "        return 1\n",
        "    else:\n",
        "        return 0\n",
        "\n",
        "count = 0\n",
        "for i in range(100000):\n",
        "    count += trial()\n",
        "print(count/100000)"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "apSup1fEA-2I",
        "outputId": "89506631-20da-4f93-c2cd-7c009e440948"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "8e-05\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1.6\n",
        "Use ?Distributions in R to get a list of available distributions17. Make plots of the probability mass or density functions for various distributions (using the functions named dXXXX), and list five distributions that are not discrete."
      ],
      "metadata": {
        "id": "RnPRwsQYICsM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy.stats as sp\n",
        "\n",
        "# Define the distributions\n",
        "binom = sp.binom(10, 0.2)\n",
        "norm = sp.norm()\n",
        "planck = sp.planck(2)\n",
        "wald = sp.wald()\n",
        "poisson = sp.poisson(50)\n",
        "\n",
        "cont_dists = [norm, wald]\n",
        "dis_dists = [binom, planck, poisson]\n",
        "\n",
        "# Plot continuous distributions individually\n",
        "for dist in cont_dists:\n",
        "    x = np.linspace(dist.ppf(0.001), dist.ppf(0.999), 100)\n",
        "    plt.figure()\n",
        "    plt.plot(x, dist.pdf(x), label=f'{dist.dist.name} PDF')\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('PDF')\n",
        "    plt.title(f'{dist.dist.name.capitalize()} Distribution')\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "# Plot discrete distributions individually\n",
        "for dist in dis_dists:\n",
        "    x = np.arange(dist.ppf(0.01), dist.ppf(0.99))\n",
        "    plt.figure()\n",
        "    plt.plot(x, dist.pmf(x), label=f'{dist.dist.name} PMF', marker='o', linestyle='None')\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('PMF')\n",
        "    plt.title(f'{dist.dist.name.capitalize()} Distribution')\n",
        "    plt.legend()\n",
        "    plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "OoZVkf3dPIaS",
        "outputId": "04cd0d34-a8f8-49d2-9cb2-783147ad6f9c"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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HoVDgqaeeQm5uLrKyspz+DFfhsJSMvj9dhvyL1QCAo4V6mashIvIv1SYL+i/8yuOfe/SFCQjUtK15DQsLQ3JyMjIzM5GSkoLMzEzMmTMHzz//PCorK1FeXo7Tp09j7NixAID4+Hj87//+r3T9E088ga+++gqbN2/GiBEjGr3/yZMn8eWXX2L//v24+uqrAQDvvfce+vXr59TPlJWVhQ8//BA33HBDq+f27dsXgG1ejr2m8vJyBAcHS+cEBwejqKjIqRqcwXAjow9/zJW+/+1CFapqzQjS8k9CRNSRjB07FpmZmXj66afx/fffY8mSJdi8eTN2796NixcvIi4uDr179wZg29xu8eLF2Lx5MwoKCmA0GlFbW9vs5oXHjh2DSqXC8OHDpWN9+/ZFeHh4q3UdOnQIwcHBsFgsMBqNmDRpElauXNnqdfaeq4Z71oSEhCA7O1t67oqbY7aELalMivU1+OaYrVswQK1EtcmC40V6DO/eWebKiIj8Q4BaiaMvTJDlc50xbtw4rFu3Dr/88gvUajX69u2LcePGITMzE5cuXZJ6bQDgtddewxtvvIEVK1Zg0KBBCAoKwuzZs1sdLmqPPn36YMuWLVCpVIiLi2vzzSyPHTsGAEhKSpKOKRQK9OrVy+U1NofhRiabDuTDYhUxIrEzgrRK7DpRiqOFDDdERK4iCEKbh4fkZJ93s3z5cinIjBs3Dq+88gouXbqEp59+Wjp3z549uP3226UJxlarFSdPnkT//v2bfO++ffvCbDYjKytLGpY6ceJEm+6crtFonA4kVqsVb775JpKSkjB06FCnrnUlTiiWgcUq4qP9eQCAP6d2Q/+4UADA0fOcd0NE1NF06tQJgwcPxsaNG6WJw9dddx2ys7Nx8uRJh56b3r17Y8eOHdi7dy+OHTuGRx55BMXFxc2+d58+fXDzzTfjkUcewY8//oisrCw89NBDLlupdOHCBRQVFeHs2bPYsmUL0tLSsH//frz33ntQKp3rwXIlhhsZZJ4oQWF5DToFqnHzwBgMiLOt9T/CScVERB3S2LFjYbFYpHDTuXNn9O/fHzExMejTp4903nPPPYdhw4ZhwoQJGDduHGJiYnDHHXe0+N7r169HXFwcxo4diz/84Q94+OGHERUV5ZK609LSEBsbi0GDBmHu3Lno168ffv31V1x//fUuef/2EkRn1qz5Ab1ej7CwMJSXlyM0NFSWGh54/wB2Hi/Bw9f1wPxb+iGnrArjXs+ERqXA0ecnQKVk5iQickZNTQ1+++03JCUlQafTyV0OtVNLf0dn2m+2oh527pIBu07YJhJPHdENANCtcyCCtSoYzVacKa2SszwiIiKfx3DjYZsO5EMUgdG9IpAUGQQAUCgE9IsNAQAcPV8uZ3lEREQ+j+HGg8wWKz46kA8A+POI7g6vSfNuCjjvhoiI6Eow3HjQ+fIalFbUQqNU4Mb+0Q6v9Y/liikiIiJXYLjxIIPRdhOxEJ2q0V3A7cvBjxTqnbovCRER1eN/P32bq/5+DDceVGU0AwACNI3X/veODoZKIaC82oTC8hpPl0ZE5NPUajUAwGAwyFwJXQn7TstXukeO92/d6Eeq63puApsIN1qVEr2ignG8qAJHCsoRH+6+W8ETEfkbpVKJ8PBw6W7XgYGBDvc2Iu9ntVpRWlqKwMBAqFRXFk8YbjyoqtbWc9PcduAD4sJwvKgCR8/rcdOAGE+WRkTk82JibP/dtAcc8j0KhQLdunW74mAqa7j57rvv8NprryErKwvnz5/Hp59+2upOi5mZmUhPT8eRI0eQkJCA5557Dvfff79H6r1S1abme24A27yb/2QDR7lTMRGR0wRBQGxsLKKiomAymeQuh9pBo9G45I7hsoabqqoqDBkyBA888AD+8Ic/tHr+b7/9hkmTJuHRRx/Fxo0bkZGRgYceegixsbGYMMHzd351lkEalmqu56Z+UjEREbWPUqmU9b5GJD9Zw83EiRMxceLENp+/Zs0aJCUlYenSpQCAfv36Yffu3Vi+fLlPhJv6Yamm/6XrV7ccvOByNcoNJoQFqj1WGxERkb/wqdVS+/btQ1pamsOxCRMmYN++fTJV5JyWJhQDQFiAGl072SYSH+FOxURERO3iU+GmqKgI0dGOm99FR0dDr9ejurq6yWtqa2uh1+sdHnIxmFoelgLqh6Y474aIiKh9fCrctMeSJUsQFhYmPRISEmSrxdDKsBQA9I+13YaB4YaIiKh9fCrcxMTEoLi42OFYcXExQkNDERDQ9L4w8+bNQ3l5ufTIz8/3RKlNkiYUa5sPN1LPDW/DQERE1C4+tc/NyJEjsW3bNodjO3bswMiRI5u9RqvVQqvVuru0NpHCjbqFnpu6cHOqpBI1Jgt0LZxLREREjcnac1NZWYmDBw/i4MGDAGxLvQ8ePIi8vDwAtl6XadOmSec/+uijOHv2LP7v//4Px48fx9tvv43Nmzdjzpw5cpTvNIOx5U38ACA2TIcQrQoWq4hzl7iNOBERkbNkDTc//fQThg4diqFDhwIA0tPTMXToUCxcuBAAcP78eSnoAEBSUhK++OIL7NixA0OGDMHSpUvx7rvv+sQycKBtw1KCICChcyAAIPcCww0REZGzZB2WGjduXIt3AH3//febvObnn392Y1XuY2hlKbhdt86BOHpej7yLDDdERETO8qkJxb7OPiwVoG45U3aPYM8NERFRezHceJC95yaohWEpANKwVD57boiIiJzGcONBbR2WknpuGG6IiIicxnDjQdWt3DjTrluDnhurtfk5SURERNQYw42HmCxWGC1WAK333MSFB0CpEFBrtqKkotYT5REREfkNhhsPsQ9JAUBAK+FGrVQgLlwHAFwxRURE5CSGGw+xD0mpFAI0ytZ/7d07BwEAci9UubUuIiIif8Nw4yFV9mXgGiUEQWj1fK6YIiIiah+GGw+x99wEtTKZ2I4rpoiIiNqH4cZDqmrt95Vq240w7SumOOeGiIjIOQw3HmIw2XpuWptMbCeFG+5STERE5BSGGw9xdliqW92w1IUqIyrren2IiIiodQw3HmIflmprz02oTo1OgWoA7L0hIiJyBsONh1Sb2nZfqYY474aIiMh5DDceUlVbN+emlTuCN9QtwrbXTd5F7nVDRETUVgw3HlJtdG61FAB06xwAgD03REREzmC48RDpjuBODEvV71LMcENERNRWDDceUmUPN04MS3GXYiIiIucx3HhIe4al7LsUn7tUDXPdHcWJiIioZQw3HtKeYanoUB00SgXMVhHny2vcVRoREZFfYbjxECncONFzo1QI6MpJxURERE5huPEQgzQs1fY5NwD3uiEiInIWw42HtKfnBmC4ISIichbDjYdccbjhcnAiIqI2YbjxkPpww2EpIiIid2K48RBDO5aCA0D3CPtGfrwFAxERUVsw3HiA1SpKN850tucmoW61lL7GjHKDyeW1ERER+RuGGw+oMVsgirbvne25CdSo0CVECwDI5Q00iYiIWsVw4wH2+TYAEKB2LtwAnHdDRETkDIYbD6iuCzcBaiUUCsHp67vXhRveQJOIiKh1DDceUNXOycR2CVwOTkRE1GYMNx7QnvtKNWS/gSaHpYiIiFrHcOMBhtq6cKN2bqWUHefcEBERtR3DjQfY97gJaOewlD3cnC+vhtFsdVldRERE/ojhxgPse9wEtXNYqkuIFjq1AlYRKLhc7crSiIiI/A7DjQdU1dpXS7VvWEoQBA5NERERtRHDjQe099YLDXXrbLsNA8MNERFRyxhuPMC+z017h6WAhncH5y7FRERELWG48YAq45UNSwFAt7p7TLHnhoiIqGUMNx5QXTcsdSU9N/a7g+dd5IRiIiKiljDceIDUc3MFc24SGgxLifa7cBIREVEjDDceYJ9zE9iOm2bade0UAEGwBaWLVUZXlUZEROR3GG48QFotpW3/nBudWomYUB0AzrshIiJqCcONB9iHpa5kKTjQYGiK4YaIiKhZDDceIC0F17S/5wZouByc4YaIiKg5DDceUHWF95ay686eGyIiolYx3HhAtYuGpbpF2MJNLsMNERFRsxhuPMAghZsrG5ayz7nJZ7ghIiJqFsONB7ji3lJA/bBUkb4GNXV3GiciIiJHDDduZrJYYbLYNt270gnFnYM0CNIoIYrAuUvcqZiIiKgpDDduZh+SAq58QrEgCByaIiIiagXDjZvZh6RUCgEa1ZX/urtHcMUUERFRSxhu3MzgopVSdva9bnK51w0REVGTZA83q1atQmJiInQ6HVJTU7F///4Wz1+xYgX69OmDgIAAJCQkYM6cOaipqfFQtc4z1LpmpZRdN+nu4Aw3RERETZE13GzatAnp6elYtGgRsrOzMWTIEEyYMAElJSVNnv/hhx9i7ty5WLRoEY4dO4b33nsPmzZtwvz58z1cedu5aqWUXTfOuSEiImqRrOFm2bJlmDlzJmbMmIH+/ftjzZo1CAwMxLp165o8f+/evRg9ejT+/Oc/IzExETfddBOmTp3aam+PnAx1S7YDta4NN3kXDRBF0SXvSURE5E9kCzdGoxFZWVlIS0urL0ahQFpaGvbt29fkNaNGjUJWVpYUZs6ePYtt27bhlltuafZzamtrodfrHR6eJA1LqV0zLBUfHgCFAFSbLCitrHXJexIREfkT17S47VBWVgaLxYLo6GiH49HR0Th+/HiT1/z5z39GWVkZxowZA1EUYTab8eijj7Y4LLVkyRI8//zzLq3dGdKwlIt6bjQqBWLDAlBwuRr5Fw2ICtG55H2JiIj8hewTip2RmZmJxYsX4+2330Z2djY++eQTfPHFF3jxxRebvWbevHkoLy+XHvn5+R6s2PWrpQCumCIiImqJbD03kZGRUCqVKC4udjheXFyMmJiYJq9ZsGAB7rvvPjz00EMAgEGDBqGqqgoPP/ww/vrXv0KhaJzVtFottFqt63+ANrKHmwAXDUsBtr1u9p29wBVTRERETZCt50aj0WD48OHIyMiQjlmtVmRkZGDkyJFNXmMwGBoFGKXS1iPirZNrq+uGpYJcNCwF1N9Ak+GGiIioMdl6bgAgPT0d06dPR0pKCkaMGIEVK1agqqoKM2bMAABMmzYN8fHxWLJkCQBg8uTJWLZsGYYOHYrU1FScPn0aCxYswOTJk6WQ422q7D03bhiWyuOwFBERUSOyhpspU6agtLQUCxcuRFFREZKTk7F9+3ZpknFeXp5DT81zzz0HQRDw3HPPoaCgAF26dMHkyZPx8ssvy/UjtMo+LHWlN81siLdgICIiap4geut4jpvo9XqEhYWhvLwcoaGhbv+82R/9jM8OFuK5Sf3w0LU9XPKelw1GJL+wAwBw7IWbXdorRERE5I2cab99arWUL3LHsFRYgBohOltPUP4l9t4QERE1xHDjZtVuGJYSBAFJkbZ7TP1WVuWy9yUiIvIHDDduVlW3WsrVQ0eJEQw3RERETWG4cTN39NwAkHpuchhuiIiIHDDcuJnBDXNuAKBHF1u4OctwQ0RE5IDhxs2ke0u5ONxwzg0REVHTGG7czB373ABAYl24Ka2oRUWNyaXvTURE5MsYbtzIahXdNiwVqlMjMlgDgDfQJCIiaojhxo1qzBbpe1feW8rOPjTFeTdERET1GG7cyN5rAwA6levDjbQcvJThhoiIyI7hxo0MtXVDUmolFArB5e+fVLdiKucCww0REZEdw40bGUy2lVLuGJICgB4cliIiImqE4caNqmrdM5nYLikyGADwW2klOtj9T4mIiJrFcONG9t2JA9WuXQZu1z0iEACgrzHjYpXRLZ9BRETkaxhu3EjawM9Nw1I6tRLx4QEAOO+GiIjIjuHGjeyrpVy9O3FD0nJwrpgiIiICwHDjVvXhxj3DUgCQGGkbmuJtGIiIiGwYbtzIXfeVakiaVMxwQ0REBIDhxq08MSzVgzfQJCIicsBw40aeGJayz7nJuVAFq5XLwYmIiBhu3MgTw1JdOwVApRBQY7KiSF/jts8hIiLyFQw3buSJnhuVUoFunTmpmIiIyI7hxo3sm/gFqN37a07ivBsiIiIJw40bGS1WAIBW7b5hKQBIZLghIiKSMNy4kaku3KiV7LkhIiLyFIYbN6oPN4JbP8e+HDyH4YaIiIjhxp1MZtvSbI27e2662MJN3kWDFKiIiIg6KoYbNzJ6aFgqOkQHnVoBs1XEuUvVbv0sIiIib8dw40bSsJTKvb9mhUJAYoR93k2lWz+LiIjI2zHcuJGn5twAQI8u9nBjcPtnEREReTOGGzcyWWxzbtw9LAWAPTdERER1GG7cyGj2zJwboH45+NlSrpgiIqKOjeHGjTw5LNUrKhgAcKqEPTdERNSxMdy4kT3cuHspOAD0jg4BAJRW1OKywej2zyMiIvJWDDdu5Mk5N8FaFeLDAwAAJ4vZe0NERB0Xw40bGT20FNzuqmjb0NSJ4gqPfB4REZE3YrhxE1EUPTrnBgCuqhuaOsVwQ0REHRjDjZtYrCJE26iUR+bcAPXzbk4y3BARUQfGcOMm9vk2gGfm3AD1w1KnOOeGiIg6MIYbNzE2uIGlp8KNfTn4hSojLlTWeuQziYiIvA3DjZuYHcKNZ+bcBGpUSOjMFVNERNSxMdy4Sf0ycAGC4JlwAwBXRdVNKi7hvBsiIuqYGG7cpH6llGd/xZxUTEREHR3DjZsYZQo39knFJ4s4LEVERB0Tw42byNVzY9/r5mRJBURRbOVsIiIi/8Nw4yYmsy1YaDw0mdiuV1QwFAJw2WBCKVdMERFRB8Rw4yaevvWCnU6tRLfOgQC43w0REXVMDDduItewFMBJxURE1LEx3LiJnOFGmlTMnhsiIuqAGG7cxB5uPD3nBuANNImIqGNjuHETo9m+iZ8Mw1JR9cNSXDFFREQdDcONm8g5LNWjSxAUAqCvMaOkgiumiIioY5E93KxatQqJiYnQ6XRITU3F/v37Wzz/8uXLmDVrFmJjY6HVanHVVVdh27ZtHqq27ezhRiXDsJROrURiZBAA4EQRh6aIiKhjkTXcbNq0Cenp6Vi0aBGys7MxZMgQTJgwASUlJU2ebzQaceONNyInJwcff/wxTpw4gbVr1yI+Pt7Dlbeufs6NPL/iq6K4YoqIiDomlZwfvmzZMsycORMzZswAAKxZswZffPEF1q1bh7lz5zY6f926dbh48SL27t0LtVoNAEhMTPRkyW1mtMg35wawrZjafoR73RARUccjW8+N0WhEVlYW0tLS6otRKJCWloZ9+/Y1ec2WLVswcuRIzJo1C9HR0Rg4cCAWL14Mi8XS7OfU1tZCr9c7PDzBZJZnEz+73g1uw0BERNSRyBZuysrKYLFYEB0d7XA8OjoaRUVFTV5z9uxZfPzxx7BYLNi2bRsWLFiApUuX4qWXXmr2c5YsWYKwsDDpkZCQ4NKfozn1E4o9P+cGqF8Ofrq4kiumiIioQ5F9QrEzrFYroqKi8M4772D48OGYMmUK/vrXv2LNmjXNXjNv3jyUl5dLj/z8fI/UKvecm6TIIKgUAipqzThfXiNLDURERHKQbc5NZGQklEoliouLHY4XFxcjJiamyWtiY2OhVquhVCqlY/369UNRURGMRiM0Gk2ja7RaLbRarWuLbwO559xoVAokRgbhdEklThRXIC48QJY6iIiIPE22nhuNRoPhw4cjIyNDOma1WpGRkYGRI0c2ec3o0aNx+vRpWK1W6djJkycRGxvbZLCRk5z73Nj1jw0FABwt9Mw8IyIiIm8g67BUeno61q5diw8++ADHjh3DY489hqqqKmn11LRp0zBv3jzp/MceewwXL17EU089hZMnT+KLL77A4sWLMWvWLLl+hGbVTyiWZ84NAAyMt4WbwwXlstVARETkabIuBZ8yZQpKS0uxcOFCFBUVITk5Gdu3b5cmGefl5UGhqM9fCQkJ+OqrrzBnzhwMHjwY8fHxeOqpp/Dss8/K9SM0y2y1DUvJNecGAAbGhQEADhcy3BARUccha7gBgMcffxyPP/54k69lZmY2OjZy5Ej88MMPbq7qyhm9YFhqQF24yb9YjXKDCWGBatlqISIi8hSfWi3lS6RhKRnDTVigGgmdbROJj7D3hoiIOgiGGzeRe58bOw5NERFRR8Nw4yamuqXgGpl2KLYbGF8Xbgq4YoqIiDoGhhs38YY5NwAwIK5uxRR7boiIqINwquXduXMnzGazu2rxK96wzw1Q33PzW1kVKmv5tyMiIv/nVMt744034uLFi9Lza665BgUFBS4vyh94y5ybyGAtYsN0EEXg2HkOTRERkf9zKtz8/gaMR44cQW1trUsL8hcms/z73NjZl4RzMz8iIuoI5G95/ZS3zLkBGu5UzJ4bIiLyf061vIIgQBCEZp9TPWlYSubVUkD9cnDudUNERB2BUzsUi6KI8ePHQ6WyXWYwGDB58uRGN63Mzs52XYU+ylvm3AD1k4pPlVSixmSBTq1s5QoiIiLf5VS4WbRokcPz22+/3aXF+BNpnxsvGJaKDtUiMliDskojjp3XY2i3TnKXRERE5DZXFG6oeca62y+ovCDcCIKAAXFh+PZkKQ4XMtwQEZF/a3fLW1ZWhp9++glZWVm4cOGCK2vyC940LAXUTyo+whVTRETk55wON0eOHMF1112H6OhopKamYsSIEYiKisINN9yAEydOuKNGn2QPN94wLAXwHlNERNRxODUsVVRUhLFjx6JLly5YtmwZ+vbtC1EUcfToUaxduxbXXnstDh8+jKioKHfV6zPsc268YSk4UD+p+ERRBYxmq+z3vCIiInIXp8LN8uXL0b17d+zZswc6nU46fvPNN+Oxxx7DmDFjsHz5cixZssTlhfoaoxctBQeArp0CEKpTQV9jxsniCinsEBER+RunWt4dO3bg2WefdQg2dgEBAXjmmWfw1Vdfuaw4XyWKotfNuREEQQo03O+GiIj8mVPh5uzZsxg2bFizr6ekpODs2bNXXJSvs1hF2O9U4S1zboD6oSnuVExERP7MqZa3oqICoaGhzb4eEhKCysrKKy7K19nn2wDeM+cGAAbE2f52h7hiioiI/JhTc24AW8BpalgKAPR6faOba3ZE9vk2gHeFmyFdwwEARwv1qDVboFVxp2IiIvI/Tt9+4aqrrmrxdd5rCjA7hBvv+X10jwhERJAGF6qMOFxQjuHdO8tdEhERkcs5FW527drlrjr8Sv0ycO+6saggCBjevRO+PlqMrNxLDDdEROSXnAo3Y8aMweuvv44tW7bAaDRi/PjxWLRoEQICAtxVn0+qXynlPUNSdg3DDRERkT9yqvVdvHgx5s+fj+DgYMTHx+ONN97ArFmz3FWbzzJ6ebgBgKzcS5wfRUREfsmp1vef//wn3n77bXz11Vf47LPP8N///hcbN26E1Wpt/eIOxJt7bgbGh0GjVKCs0oi8iwa5yyEiInI5p1rfvLw83HLLLdLztLQ0CIKAwsJClxfmy0xmW4+IxosmE9vp1ErpJpo/5XBoioiI/I9T4cZsNjdaBq5Wq2EymVxalK/ztlsv/F5Kom0icVYeww0REfkfp5eC33///dBqtdKxmpoaPProowgKCpKOffLJJ66r0Ad587AUAAzrZpt3k81JxURE5IecCjfTp09vdOzee+91WTH+wtvDjX1S8YniCpRXmxAWoJa5IiIiItdxKtysX7/eXXX4FXu48cY5NwDQJUSL7hGByL1gwMH8yxh7VRe5SyIiInIZ7+xa8HFGs30TP+/99Q6vG5rKyrkocyVERESu5b2trw/z9mEpABieWBduOKmYiIj8jPe2vj7M5OWrpYD6eTcH8y473AuLiIjI13lv6+vDpHCj8M45NwDQOyoEIVoVqowWHC+qkLscIiIil2G4cQOjxfvn3CgVAobW9d5kc2iKiIj8iPe2vj7MZPb+YSmgflIxdyomIiJ/4t2tr4+qn1DsvcNSAJCSWH8TTSIiIn/BcOMG9fvcePevd0hCOBQCUHC5GkXlNXKXQ0RE5BLe3fr6KF+YcwMAwVoV+sbU3UQzl/vdEBGRf/Du1tdH+cI+N3Yjkmw30dx35oLMlRAREbmG97e+Pqh+QrF3z7kBgDG9IgEAe06XyVwJERGRazDcuIGvzLkBgNQenaFUCMi5YED+RYPc5RAREV0x7299fZDJ6htzbgAgRKdGckI4AGDvGfbeEBGR7/P+1tcHScNSPhBuAGB03dDU96cYboiIyPf5RuvrY3xlnxs7+7ybvWcuwFrX60REROSrGG7cwFS3FFzj5TsU2w3tFo4gjRIXq4w4VqSXuxwiIqIr4hutr48x+tBScMBWZ2qPCABcNUVERL7PN1pfH+NL+9zY2efd7D7N/W6IiMi3+U7r60N8bc4NUD/vZv9vF1BrtshcDRERUfsx3LiByVw358aHem6uig5GZLAWNSYrb6RJREQ+zXdaXx/ia3NuAEAQBIzpxXk3RETk+3yn9fUh0rCUj6yWshvTuwsAzrshIiLf5hWt76pVq5CYmAidTofU1FTs37+/Tdd99NFHEAQBd9xxh3sLdJIvzrkBgNF1PTeHzl1GucEkczVERETtI3u42bRpE9LT07Fo0SJkZ2djyJAhmDBhAkpKSlq8LicnB//7v/+La6+91kOVtp20z40PDUsBQGxYAHp2CYJVBPadZe8NERH5Jtlb32XLlmHmzJmYMWMG+vfvjzVr1iAwMBDr1q1r9hqLxYJ77rkHzz//PHr06OHBatvG6GO3X2hojLQkvFTmSoiIiNpH1tbXaDQiKysLaWlp0jGFQoG0tDTs27ev2eteeOEFREVF4cEHH2z1M2pra6HX6x0e7mYfllL52LAU0GC/G95nioiIfJSs4aasrAwWiwXR0dEOx6Ojo1FUVNTkNbt378Z7772HtWvXtukzlixZgrCwMOmRkJBwxXW3xh5ufG1YCgBG9oyAWikg54IBZ0or5S6HiIjIaT7V+lZUVOC+++7D2rVrERkZ2aZr5s2bh/LycumRn5/v5irr59z44rBUiE6Na+puxbDjaLHM1RARETlPJeeHR0ZGQqlUorjYsREtLi5GTExMo/PPnDmDnJwcTJ48WTpmtdYNAalUOHHiBHr27OlwjVarhVardUP1zTP66FJwu5v6R+P7U2XYcbQYj47t2foFREREXkTW1lej0WD48OHIyMiQjlmtVmRkZGDkyJGNzu/bty8OHTqEgwcPSo/bbrsN119/PQ4ePOiRIafWiKLos0vB7dL624YJs/MuobSiVuZqiIiInCNrzw0ApKenY/r06UhJScGIESOwYsUKVFVVYcaMGQCAadOmIT4+HkuWLIFOp8PAgQMdrg8PDweARsflYrGKEG2jUj455wawLQkf3DUMv54rR8axYtw9opvcJREREbWZ7OFmypQpKC0txcKFC1FUVITk5GRs375dmmScl5cHhcJ3QoJ9vg3gm3Nu7G7qH41fz5Vjx1GGGyIi8i2CKIpi66f5D71ej7CwMJSXlyM0NNTl719ebcKQ578GAJx8aSI0Pjrv5kRRBSas+A4alQI/L7gRQVrZczAREXVgzrTfvtnyejH7fBvAd+fcALa7hHePCITRbMX3p7ihHxER+Q6GGxczS8vABQiC74YbQRBwYz/b0ODXR7gknIiIfAfDjYvVr5Ty/V/tTQNsy/EzjpfA3KBHioiIyJv5fgvsZYx+FG6Gd++EzkEalFebsD/notzlEBERtYnvt8Bexp96bpQKAeP7RgHgbsVEROQ7fL8F9jIms23OjcaHJxM3dGP/+nk3HWxhHRER+SiGGxfz9Vsv/N61vbtAp1ag4HI1jp2vkLscIiKiVvlHC+xF/GlYCgACNEpc17sLAGD7kabv1E5ERORN/KMF9iL+Fm4AYNLgWADA5wcLODRFRERez39aYC9hDzf+MucGsM27CdQokXvBgOy8y3KXQ0RE1CKGGxczmu2b+PnPrzZQo8LNdXvefPZzgczVEBERtcx/WmAv4Y/DUgDwP8PiAQBbfy2E0cwN/YiIyHv5VwvsBUx+tlrKblTPSHQJ0eKSwYRvT/JeU0RE5L38qwX2Av445wawbeh3+5A4AByaIiIi78Zw42LGuhtnqhT+96u1D03tOFaM8mqTzNUQERE1zf9aYJmZzP45LAUA/WNDcVV0MIxmK7YfPi93OURERE3yvxZYZvUTiv1rWAoABEHAHUNtvTefcmiKiIi8FMONi9XPufHPX+0dybZw88PZiyi4XC1zNURERI35ZwssI/ucG39bCm4XFx6Aa3p0BmDbsZiIiMjb+GcLLCN/3eemof+xD01l83YMRETkffy3BZZJ/YRi/5tzYzdxUCy0KgVOlVTydgxEROR1GG5czN/n3ABAqE6NyXV73mzYlyNvMURERL/jvy2wTExW/55zYzdtZHcAwLZDRSirrJW5GiIionr+3QLLQBqW8vNwM7hrOIYkhMNosWLTgXy5yyEiIpL4dwssA3/e5+b3pl1j673Z+EMuzBbeTJOIiLwDw42LmeqWgmv8cIfi35s0OBadAtUoLK9BxvESucshIiICwHDjcsYOsBTcTqdW4q6rEwAAG/blylwNERGRjf+3wB7WEfa5aeje1O4QBGD36TKcKa2UuxwiIiKGG1frSHNuACChcyBu6BMFgL03RETkHRhuXMxkrptz00F6bgDgvrpl4f/JOoeqWrPM1RARUUfXcVpgD+lIc27sruvdBYkRgaioNeMz3m+KiIhk1nFaYA+RhqU6wGopO4VCwL11y8Lf/f43WKy83xQREcmn47TAHtLR5tzY3T2iG8IC1PitrApfHDovdzlERNSBMdy4mLTPTQcalgKAYK0KD4xOAgC8ves0rOy9ISIimXSsFtgDjB3k9gtNuX9UIoK1KhwvquCmfkREJJuO1wK7WUfb56ahsEC1tHJq5c5TEEX23hARked1vBbYzTrqnBu7B8ckQadW4Jdz5dh9ukzucoiIqANiuHEx+5ybjthzAwCRwVpMHdENALBy52mZqyEioo6oY7bAbmTsgEvBf+/h63pArRTw428XcSDnotzlEBFRB9NxW2A3EEWxww9LAUBsWADuHN4VAHtviIjI8xhuXMhiFWGfQ9vRloL/3mNje0GpEPDtyVJk5V6SuxwiIupAOnYL7GL2+TZAx51zY9ctIhB/HBYPAFi87RhXThERkcd07BbYxezzbQCGGwBIv7EPAtRKZOVewldHiuQuh4iIOgi2wC5kcgg3HXfOjV1MmA4zr7XtWvzKl8elDQ6JiIjcieHGhczSMnABgsBwAwAPj+2JyGAtci4YsPHHXLnLISKiDoDhxoU68u7EzQnWqjDnxt4AgDczTqG82iRzRURE5O/YCruQkeGmSVNSEtArKhiXDCa8ncml4URE5F5shV2IPTdNUykVmDexLwBg/Z4cnLtkkLkiIiLyZ2yFXchkts250XAycSM39I3CyB4RMJqteOXL43KXQ0REfozhxoV464XmCYKAv07qB4UAbP31PDJPlMhdEhER+Sm2wi7EYamWDYwPw4zRtqXhz312GAajWeaKiIjIH7EVdiGGm9al33gV4sMDcO5SNZbvOCl3OURE5Ie8ohVetWoVEhMTodPpkJqaiv379zd77tq1a3HttdeiU6dO6NSpE9LS0lo835Ps4YZzbpoXpFXhpTsGAgDe2/0bDheUy1wRERH5G9nDzaZNm5Ceno5FixYhOzsbQ4YMwYQJE1BS0vScjMzMTEydOhW7du3Cvn37kJCQgJtuugkFBQUerrwxo9m+iZ/sv1avdn3fKEweEgerCMz95FeYLdy5mIiIXEf2VnjZsmWYOXMmZsyYgf79+2PNmjUIDAzEunXrmjx/48aN+Mtf/oLk5GT07dsX7777LqxWKzIyMjxceWMclmq7hbf2R6hOhcMFery/N0fucoiIyI/I2gobjUZkZWUhLS1NOqZQKJCWloZ9+/a16T0MBgNMJhM6d+7c5Ou1tbXQ6/UOD3cxcbVUm3UJ0eKvk/oBAJZ+fRJ5F7j3DRERuYasrXBZWRksFguio6MdjkdHR6OoqG13kX722WcRFxfnEJAaWrJkCcLCwqRHQkLCFdfdHM65cc5dKQm4pkdnVJssePKjnx1uPEpERNRePt3F8Morr+Cjjz7Cp59+Cp1O1+Q58+bNQ3l5ufTIz893Wz1GC+fcOEMQBCy9KxmhOhUO5l/Gim+4eoqIiK6crK1wZGQklEoliouLHY4XFxcjJiamxWtff/11vPLKK/j6668xePDgZs/TarUIDQ11eLiLyWzreVAx3LRZfHgAXvmj7e/3duYZ7D1TJnNFRETk62RthTUaDYYPH+4wGdg+OXjkyJHNXvf3v/8dL774IrZv346UlBRPlNom9ROKOSzljFsGxWJKSgJEEUjf9AsuVRnlLomIiHyY7F0M6enpWLt2LT744AMcO3YMjz32GKqqqjBjxgwAwLRp0zBv3jzp/FdffRULFizAunXrkJiYiKKiIhQVFaGyslKuH0FSP+dG9l+rz1l0W3/06BKEIn0N/u8/v0IURblLIiIiHyV7KzxlyhS8/vrrWLhwIZKTk3Hw4EFs375dmmScl5eH8+fPS+evXr0aRqMRd955J2JjY6XH66+/LtePIOGcm/YL1Kjw5t1DoVEqsONoMf71Q67cJRERkY9SyV0AADz++ON4/PHHm3wtMzPT4XlOTo77C2on7nNzZQbGh+H/bu6Dl744hhe2HkW/2FCkJDa9xJ+IiKg5bIVdyD6hWK3inJv2emB0Em4eEAOTRcSj/8pC4eVquUsiIiIfw3DjQpxzc+UUCgFL7xqCvjEhKKs04uENP6HaaJG7LCIi8iFshV2Ic25cI0irwrvTUxARpMHhAj2e+fgXTjAmIqI2YyvsQmbOuXGZrp0Csfre4VApBGz99Tzezjwjd0lEROQj2Aq7EPe5ca0RSZ3x4h0DAQCvfXUCX/x6vpUriIiIGG5cylQ3LKXhjTNdZuqIbrh/VCIAYPamn/HdyVJ5CyIiIq/HVtiFjByWcosFt/bHrYNjYbKIeGRDFrJyL8ldEhEReTG2wi7EfW7cQ6kQsOyuZIy9qguqTRY88P4BHC/Sy10WERF5KbbCLsQ5N+6jUSmw+t5hGN69E8qrTbjvvf3Iu2CQuywiIvJCDDcuZDLXzblhz41bBGpUWDf9avSNCUFpRS3+/O4PDDhERNQIW2EX4pwb9wsLVOOfD45AUmQQzl2qxp/+sRenS+S/aSoREXkPtsIuJA1LcbWUW0WF6LDp4WtwVXQwivW1mPKPfThayDk4RERkw1bYhTjnxnOiQnX46OGRGBgfigtVRtz9zj78nMdVVERExHDjUtI+NxyW8ojOQRp8OPMaDO/eCfoaM+5990fsPlUmd1lERCQztsIuZDRzzo2nherU2PDgCIzuFYEqowXT1+/Hhz/myV0WERHJiK2wC3GfG3kEalRYd//VuCM5DhariPmfHsJLW4/CYuXNNomIOiK2wi5kDzcaFefceJpWpcTyKclIv/EqAMC7u3/DIxuyUFVrlrkyIiLyNIYbF7LPuVEp+GuVgyAIeHJ8b7w5dSg0KgW+OVaMO9fsQ05ZldylERGRB7EVdiEjl4J7hduGxOGjh69BZLAGx87rcetbu7HtEO8oTkTUUbAVdhFRFLkU3IsM69YJW5+4FlcndkJlrRl/2ZiNv205glqzRe7SiIjIzRhuXMRiFSHWzV/lUnDvEBOmw4czr8EjY3sAAN7fm4O71uzjLRuIiPwcW2EXsc+3AbhaypuolQrMm9gP701PQViAGr+cK8fNb3yHDT/kQhS5moqIyB+xFXYR+3wbgOHGG43vF40vnhyDEUmdYTBasOCzw7jvvf0ouFwtd2lERORibIVdxOQQbjjnxht17RSIj2Zeg4W39odOrcDu02W4efl32HQgj704RER+hOHGRcx1w1JqpQBBYLjxVgqFgAfGJGHbk9diWLdwVNSa8ex/DuGuf+zD8SLefJOIyB8w3LgIdyf2LT26BOP/PToK82/piwC1EgdyLmHSm7vx4tajqKgxyV0eERFdAbbELmJkuPE5SoWAh6/riYynx2LiwBhYrCLe2/0bxi/9Fp9kn4OVt28gIvJJbIldhD03visuPACr7x2ODx4YgaTIIJRU1CJ98y+Y9NZufHuylPNxiIh8DFtiFzGZbQ2ghpOJfdbYq7pg++xr8ezNfRGiU+HYeT2mr9uPe979EYfOlctdHhERtRHDjYvw1gv+QatS4rFxPfHdM9fjoTFJ0CgV2HvmAiav3I2HPvgJv567LHeJRETUCkHsYH3uer0eYWFhKC8vR2hoqMvet6SiBt8cLUGARoH/GdrVZe9L8sq/aMCyHSfx2cECaQfqsVd1wZPje2F4987yFkdE1IE4034z3BC1wZnSSqzadRqfHyyEpW6icWpSZzw4Jgnj+0VDqeBwJBGROzHctIDhhq5E7oUqvL3rDP6TfQ7mupDTPSIQM0Yl4k8pCQjSqmSukIjIPzHctIDhhlzhfHk1Ptibi3/vz0N5tW1fnBCdCv8zNB5TR3RDv1j+s0VE5EoMNy1guCFXMhjN+E92Adbv/g1ny6qk48kJ4Zg6IgG3Do5jbw4RkQsw3LSA4YbcwWoVsffMBfx7fx6+OlIkDVkFapSYMCAG/zM0HqN6RkDFfZCIiNqF4aYFDDfkbqUVtfhP9jl8tD8PORcM0vEuIVpMHhyHW4fEIrlrOBSchExE1GYMNy1guCFPEUURP+dfxqfZBdj6ayEuGervWRUbpsOEATG4ZVAshnfvxNVWREStYLhpAcMNycFotuK7k6X4/JdC7DxWjCqjRXotMliD6/tEYXy/KIzp3QXBnKNDRNQIw00LGG5IbjUmC3afKsO2w+ex42gxKmrM0mtqpYDUpAiMvaoLxvSORN+YEAgCe3WIiBhuWsBwQ97EaLbip5yLyDhegoxjxQ5zdAAgMliLMb0iMLpXJK7pEYGunQIYdoioQ2K4aQHDDXmzs6WV2Hm8BLtPl+HHsxdRbbI4vB4XpkNqjwikJnVGSmJn9IgM4sRkIuoQGG5awHBDvqLWbEF27mV8f6oU+85ewKFz5dISc7uwADWGdQvHsG6dMKx7JwzqGoZQnVqmiomI3IfhpgUMN+SrDEYzsnIv4cezF7H/t4v45dxl1Jqtjc7rERmEQV3DMCje9ugXF8rAQ0Q+j+GmBQw35C+MZiuOndcjO+8SsvMu4+e8Szh3qbrJcxM6B6B/bCj6xYaib0wIrooOQfeIIC5BJyKfwXDTAoYb8mcXq4w4VFCOX/Mv49eCchwt1KPgctOBR6tSoGeXYFwVHYyeXYLRKyoYPaOCkRgRBI2KOykTkXdhuGkBww11NJcNRhw9r8fRQj2Ona/AqZIKnCyuQI2p8ZAWACgVAuLDA5AYGYSkiEAkRgYhMSIICZ0D0bVTAHRqpYd/AiIihpsWMdwQARariHOXDDheVIHTJZU4U1qJM6VVOFNSicpac4vXxoTq0K1zIOI7BaBrpwDEhwcgvu5rbFgAAjQMP0Tkegw3LWC4IWqeKIooqahFTlkVci5U4bcyA3LKqpB70YC8C1UOOys3JzxQjdiwAMSF6RAdpkNMqA7RoVpEh+oQHapDVIgWnQI1XMJORE5xpv3mPu9EJBEEQQohqT0iHF4TRRGXDCbkXTQg76IBBZeqce6SAQWXq3HuUjUKL1fDYLTgssGEywYTjp3XN/s5KoWAyGAtuoRoERmsQWSwFpEhWkQEadAlRIvOQRp0CtQgIliDzkEaaFXsDSKitmO4IaI2EQQBnYNsYSM5IbzR66IoQl9jxvnyapy/XIPC8moUl9egWF+LIn0NivU1KKmoxcUqI8xWEUX6GhTpa9r02UEaJTrVBZ7wQDU6B2kQHqBGWKDta3igGmEBtkeo/atODZ1awR2diToghhsicglBEKSA0Tem+S5jo9mKC1W1KNHXoqSiFhcqa1FWWYuySiPKKmtxodKIi1VGXKgy4pLBCItVRJXRgipjdbNL3ZujVgoI0akRqlMhRKdGiE6FYK3j90FaFYJ1KgRrlQjS2I4Fam3PAzUqBGlUCNQqoVZyBRmRr/CKcLNq1Sq89tprKCoqwpAhQ/DWW29hxIgRzZ7///7f/8OCBQuQk5OD3r1749VXX8Utt9ziwYqJqL00KgViw2yTj1tjtYrQ15hwyWDCJYMRl6qMuGQw4bLBaBv+qjZKw2D6GhPKq03QV5ugrzHDYhVhsoi4WGULS1dKrRQQoLYFnkCNEgEaZd1XFQLVtuc6tRIBaiUCNAroVLbnOrUCWnXd9yoFdGoltHVf7d9r1QpoVXXfqxRQMUgRXRHZw82mTZuQnp6ONWvWIDU1FStWrMCECRNw4sQJREVFNTp/7969mDp1KpYsWYJbb70VH374Ie644w5kZ2dj4MCBMvwEROQuCoWA8EANwgM1SEJQm68TRVtvT0WNCfpqMypqTKioMUNfY0JlrRkVNWZU1tiOV9ZaUFVrRpXRjMpas+37WgsMRttXo8W2ZN5kEWGymKGvaXk1mSsoBFsI1KqU0KgU0ChtoUdjfygVUCtt39u+CtIxtfS6ALXSFpQ0SgEqpQIqhQCNSgGVQgGVUoBaKUClUEhfVfZrFPXnqxq8plIIUCpsz21f619XKGD7KoBDgSQ72VdLpaam4uqrr8bKlSsBAFarFQkJCXjiiScwd+7cRudPmTIFVVVV2Lp1q3TsmmuuQXJyMtasWdPq53G1FBE5w2i2otpogcFkhsFogaEu+BhMFlQbLXWvWVBjtKDaVPcwWlBjsj+sqDHbvq81W1FjsqJW+t72tdZsgcniPwtXVQoBirrwoxQEKJV1X+vCkUIQpHCkqDtHoRCgVKD+e8F2nkIBh2vsrysE1L1e91rdc0Gwvc/vv7c9h/Q+9u8VDa5TNDgm2D9fgHSu/RwBtuAtwHae9DogfY7wu2uBBsdgvwYAHK8X6q4RYPsgoYnr6i5zeF5fR/172iOm0PC9615D3fO6sx0+t/497X/RBtegPrwKTbyHnVatQFSIzmX/TAE+tFrKaDQiKysL8+bNk44pFAqkpaVh3759TV6zb98+pKenOxybMGECPvvssybPr62tRW1trfRcr29+BQcR0e/Ze0vC4N77c1msIox1Qcf21fYwmq0wWuq+mq0wWix1X0WYGrxmslhhsojS90aL7avZIkrP7d+bLCLM1vrnZqsIc91xi1WEyWqFxSpKr1usonSOue57i7X5MGa2ioBVxJUPBpKvGtYtHJ/8ZbRsny9ruCkrK4PFYkF0dLTD8ejoaBw/frzJa4qKipo8v6ioqMnzlyxZgueff941BRMRuYlSISCgbi6PLxBFEVYRUkiyiCIs9q91AcjaIAg5PETH51ax/rjV4RikY/ZzrHWfa7GKEKXr7PXYXrNK1zQ4TxQh2jKXdK7FCoiwH7e9l2j/2ax1x0QRsP3P4RzUXWO/1n6dKEL6rIbHrNIxW134/XVA3XFR+ixRRKP3sdfb8Dr87rnDeWL93+v3r9VdKn2P3713w9cbflb98fpz0OC9Aci+fYPsc27cbd68eQ49PXq9HgkJCTJWRETk+4S6oSClQgmt37ck5Gtk/UcyMjISSqUSxcXFDseLi4sRExPT5DUxMTFOna/VaqHVal1TMBEREXk9WdcbajQaDB8+HBkZGdIxq9WKjIwMjBw5sslrRo4c6XA+AOzYsaPZ84mIiKhjkb0zMT09HdOnT0dKSgpGjBiBFStWoKqqCjNmzAAATJs2DfHx8ViyZAkA4KmnnsLYsWOxdOlSTJo0CR999BF++uknvPPOO3L+GEREROQlZA83U6ZMQWlpKRYuXIiioiIkJydj+/bt0qThvLw8KBT1HUyjRo3Chx9+iOeeew7z589H79698dlnn3GPGyIiIgLgBfvceBr3uSEiIvI9zrTf3OObiIiI/ArDDREREfkVhhsiIiLyKww3RERE5FcYboiIiMivMNwQERGRX2G4ISIiIr/CcENERER+heGGiIiI/Irst1/wNPuGzHq9XuZKiIiIqK3s7XZbbqzQ4cJNRUUFACAhIUHmSoiIiMhZFRUVCAsLa/GcDndvKavVisLCQoSEhEAQhCt6L71ej4SEBOTn5/M+VT6Afy/fw7+Z7+HfzPf4yt9MFEVUVFQgLi7O4YbaTelwPTcKhQJdu3Z16XuGhoZ69T8Q5Ih/L9/Dv5nv4d/M9/jC36y1Hhs7TigmIiIiv8JwQ0RERH6F4eYKaLVaLFq0CFqtVu5SqA349/I9/Jv5Hv7NfI8//s063IRiIiIi8m/suSEiIiK/wnBDREREfoXhhoiIiPwKww0RERH5FYabdlq1ahUSExOh0+mQmpqK/fv3y10SNWPJkiW4+uqrERISgqioKNxxxx04ceKE3GWRE1555RUIgoDZs2fLXQq1oKCgAPfeey8iIiIQEBCAQYMG4aeffpK7LGqGxWLBggULkJSUhICAAPTs2RMvvvhim+7d5O0Ybtph06ZNSE9Px6JFi5CdnY0hQ4ZgwoQJKCkpkbs0asK3336LWbNm4YcffsCOHTtgMplw0003oaqqSu7SqA0OHDiAf/zjHxg8eLDcpVALLl26hNGjR0OtVuPLL7/E0aNHsXTpUnTq1Enu0qgZr776KlavXo2VK1fi2LFjePXVV/H3v/8db731ltylXTEuBW+H1NRUXH311Vi5ciUA2/2qEhIS8MQTT2Du3LkyV0etKS0tRVRUFL799ltcd911cpdDLaisrMSwYcPw9ttv46WXXkJycjJWrFghd1nUhLlz52LPnj34/vvv5S6F2ujWW29FdHQ03nvvPenYH//4RwQEBOBf//qXjJVdOfbcOMloNCIrKwtpaWnSMYVCgbS0NOzbt0/GyqitysvLAQCdO3eWuRJqzaxZszBp0iSHf9/IO23ZsgUpKSn405/+hKioKAwdOhRr166VuyxqwahRo5CRkYGTJ08CAH755Rfs3r0bEydOlLmyK9fhbpx5pcrKymCxWBAdHe1wPDo6GsePH5epKmorq9WK2bNnY/To0Rg4cKDc5VALPvroI2RnZ+PAgQNyl0JtcPbsWaxevRrp6emYP38+Dhw4gCeffBIajQbTp0+Xuzxqwty5c6HX69G3b18olUpYLBa8/PLLuOeee+Qu7Yox3FCHMmvWLBw+fBi7d++WuxRqQX5+Pp566ins2LEDOp1O7nKoDaxWK1JSUrB48WIAwNChQ3H48GGsWbOG4cZLbd68GRs3bsSHH36IAQMG4ODBg5g9ezbi4uJ8/m/GcOOkyMhIKJVKFBcXOxwvLi5GTEyMTFVRWzz++OPYunUrvvvuO3Tt2lXucqgFWVlZKCkpwbBhw6RjFosF3333HVauXIna2loolUoZK6Tfi42NRf/+/R2O9evXD//5z39kqoha88wzz2Du3Lm4++67AQCDBg1Cbm4ulixZ4vPhhnNunKTRaDB8+HBkZGRIx6xWKzIyMjBy5EgZK6PmiKKIxx9/HJ9++il27tyJpKQkuUuiVowfPx6HDh3CwYMHpUdKSgruueceHDx4kMHGC40ePbrRFgsnT55E9+7dZaqIWmMwGKBQOMYApVIJq9UqU0Wuw56bdkhPT8f06dORkpKCESNGYMWKFaiqqsKMGTPkLo2aMGvWLHz44Yf4/PPPERISgqKiIgBAWFgYAgICZK6OmhISEtJoTlRQUBAiIiI4V8pLzZkzB6NGjcLixYtx1113Yf/+/XjnnXfwzjvvyF0aNWPy5Ml4+eWX0a1bNwwYMAA///wzli1bhgceeEDu0q4Yl4K308qVK/Haa6+hqKgIycnJePPNN5Gamip3WdQEQRCaPL5+/Xrcf//9ni2G2m3cuHFcCu7ltm7dinnz5uHUqVNISkpCeno6Zs6cKXdZ1IyKigosWLAAn376KUpKShAXF4epU6di4cKF0Gg0cpd3RRhuiIiIyK9wzg0RERH5FYYbIiIi8isMN0RERORXGG6IiIjIrzDcEBERkV9huCEiIiK/wnBDREREfoXhhoiIiPwKww0RERH5FYYbIiIi8isMN0Tk80pLSxETE4PFixdLx/bu3QuNRoOMjAwZKyMiOfDeUkTkF7Zt24Y77rgDe/fuRZ8+fZCcnIzbb78dy5Ytk7s0IvIwhhsi8huzZs3CN998g5SUFBw6dAgHDhyAVquVuywi8jCGGyLyG9XV1Rg4cCDy8/ORlZWFQYMGyV0SEcmAc26IyG+cOXMGhYWFsFqtyMnJkbscIpIJe26IyC8YjUaMGDECycnJ6NOnD1asWIFDhw4hKipK7tKIyMMYbojILzzzzDP4+OOP8csvvyA4OBhjx45FWFgYtm7dKndpRORhHJYiIp+XmZmJFStWYMOGDQgNDYVCocCGDRvw/fffY/Xq1XKXR0Qexp4bIiIi8ivsuSEiIiK/wnBDREREfoXhhoiIiPwKww0RERH5FYYbIiIi8isMN0RERORXGG6IiIjIrzDcEBERkV9huCEiIiK/wnBDREREfoXhhoiIiPwKww0RERH5lf8PxsHj1yPlGEYAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install genomicranges"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WFdYYPUuQ9uH",
        "outputId": "095bbc77-9716-4443-b4e9-c8accee525b2"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting genomicranges\n",
            "  Downloading GenomicRanges-0.4.28-py3-none-any.whl.metadata (10 kB)\n",
            "Collecting biocframe>=0.5.11 (from genomicranges)\n",
            "  Downloading BiocFrame-0.5.11-py3-none-any.whl.metadata (12 kB)\n",
            "Collecting iranges>=0.2.11 (from iranges[optional]>=0.2.11->genomicranges)\n",
            "  Downloading IRanges-0.2.11-py3-none-any.whl.metadata (6.0 kB)\n",
            "Collecting biocutils>=0.1.3 (from genomicranges)\n",
            "  Downloading biocutils-0.1.5-py3-none-any.whl.metadata (3.5 kB)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from genomicranges) (1.26.4)\n",
            "Collecting ncls==0.0.68 (from iranges>=0.2.11->iranges[optional]>=0.2.11->genomicranges)\n",
            "  Downloading ncls-0.0.68-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (4.6 kB)\n",
            "Requirement already satisfied: polars in /usr/local/lib/python3.10/dist-packages (from iranges[optional]>=0.2.11->genomicranges) (0.20.2)\n",
            "Requirement already satisfied: pandas in /usr/local/lib/python3.10/dist-packages (from iranges[optional]>=0.2.11->genomicranges) (2.1.4)\n",
            "Requirement already satisfied: python-dateutil>=2.8.2 in /usr/local/lib/python3.10/dist-packages (from pandas->iranges[optional]>=0.2.11->genomicranges) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas->iranges[optional]>=0.2.11->genomicranges) (2024.1)\n",
            "Requirement already satisfied: tzdata>=2022.1 in /usr/local/lib/python3.10/dist-packages (from pandas->iranges[optional]>=0.2.11->genomicranges) (2024.1)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.2->pandas->iranges[optional]>=0.2.11->genomicranges) (1.16.0)\n",
            "Downloading GenomicRanges-0.4.28-py3-none-any.whl (37 kB)\n",
            "Downloading BiocFrame-0.5.11-py3-none-any.whl (18 kB)\n",
            "Downloading biocutils-0.1.5-py3-none-any.whl (45 kB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m45.1/45.1 kB\u001b[0m \u001b[31m2.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading IRanges-0.2.11-py3-none-any.whl (19 kB)\n",
            "Downloading ncls-0.0.68-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (2.4 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.4/2.4 MB\u001b[0m \u001b[31m40.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: ncls, biocutils, biocframe, iranges, genomicranges\n",
            "Successfully installed biocframe-0.5.11 biocutils-0.1.5 genomicranges-0.4.28 iranges-0.2.11 ncls-0.0.68\n"
          ]
        }
      ]
    }
  ]
}