functions.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 300,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "' As of day, Dec 2021, the better option is to use methods from \"secrets\" module. You don\\'t need to set such seed anymore.\\nSample Code:\\nimport secrets\\nprint (secrets.randbelow(1_000_000_000)) \\n\\n'"
            ]
          },
          "execution_count": 300,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Imports\n",
        "from time import time\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "\n",
        "# WE WILL ONLY CHOOSE EVEN 'N' FOR THE PLOTS\n",
        "\n",
        "### [IMPORTANT] First run all the cells (Even with erros), to have acces to all the functions,\n",
        "#---------------> they were organized in an interactive way *_*\n",
        "#---------------> then you can test each one of the cell :)\n",
        "\n",
        "''' As of day, Dec 2021, the better option is to use methods from \"secrets\" module. You don't need to set such seed anymore.\n",
        "Sample Code:\n",
        "import secrets\n",
        "print (secrets.randbelow(1_000_000_000)) \n",
        "\n",
        "'''"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "trusted": true
      },
      "outputs": [],
      "source": [
        "def generate_random_number(_range):\n",
        "    '''Generates a number from 0 up to _range(modulo)'''\n",
        "    return (int(time() * 1103515245 + 12345)) % (_range+1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 208,
      "metadata": {
        "trusted": true
      },
      "outputs": [],
      "source": [
        "def generator():\n",
        "    i = 0\n",
        "    while True:\n",
        "        yield i\n",
        "        i +=1\n",
        "\n",
        "def get_list_of_distincts_random_numbers(number_of_elements, _range):\n",
        "    ''' Generates a list of n distincts random numbers'''\n",
        "    if number_of_elements > _range:\n",
        "        # It would run infinitely\n",
        "        raise ValueError(\"Wrong data\")\n",
        "        \n",
        "    lis = set()\n",
        "    for num in generator():\n",
        "        lis.add(generate_random_number(_range))\n",
        "        if len(lis) >= number_of_elements:\n",
        "            break\n",
        "    \n",
        "    return list(lis)\n",
        "\n",
        "def get_list_of_random_numbers(number_of_elements, _range):\n",
        "    ''' Generates a list of n random numbers'''        \n",
        "    lis = []\n",
        "    for num in generator():\n",
        "        n = generate_random_number(_range)\n",
        "        if lis and lis[-1] == n:\n",
        "            continue\n",
        "            \n",
        "        lis.append(n)\n",
        "        if len(lis) >= number_of_elements:\n",
        "            break\n",
        "    \n",
        "    return lis"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 304,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<pyolite.display.Image at 0x3f1ec90>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Effiency: 96%\n",
            "Cycle Length:  173\n",
            "Full period?  Not\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x396d828>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Effiency: 100%\n",
            "Cycle Length:  200\n",
            "Full period?  Yes\n",
            "\n"
          ]
        }
      ],
      "source": [
        "''' Example of use of our built Random number generator '''\n",
        "\n",
        "lis = get_list_of_random_numbers(200, 4000)\n",
        "dlis = get_list_of_distincts_random_numbers(200, 4000)\n",
        "\n",
        "''' Plot and give the info of the first generated list '''\n",
        "plt.plot(lis[::2], lis[1::2], 'go')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(lis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "\n",
        "''' Plot and give the info of the second generated list (with distinct elements)'''\n",
        "plt.plot(dlis[::2], dlis[1::2], 'yo')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(dlis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "\n",
        "print()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 278,
      "metadata": {
        "trusted": true
      },
      "outputs": [],
      "source": [
        "# x = seed number\n",
        "# c = constant\n",
        "# a = previous\n",
        "# m = modulo\n",
        "# n = How many numbers\n",
        "\n",
        "def lcg(X, a, c, m):\n",
        "    return (a*X + c) % m\n",
        "\n",
        "def get_lcg_list_long(x, a, c, m, n):\n",
        "    results = []\n",
        "    for i in range(n):\n",
        "        x = lcg(x, a, c, m)\n",
        "        results.append(x)\n",
        "    return results\n",
        "\n",
        "def get_lcg_list(param: dict(), n: int):\n",
        "    if param == None:\n",
        "        raise ValueError('Wrong data!')\n",
        "        \n",
        "    results = []\n",
        "    x, a, c, m = param['x'], param['a'], param['c'], param['m']\n",
        "    \n",
        "    for i in range(n):\n",
        "        x = lcg(x, a, c, m)\n",
        "        results.append(x)\n",
        "    return results"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 227,
      "metadata": {
        "trusted": true
      },
      "outputs": [],
      "source": [
        "def factor(n):\n",
        "    lis = []\n",
        "    c = 2\n",
        "    while(n > 1):\n",
        "        if(n % c == 0):\n",
        "            lis.append(c)\n",
        "            while n % c == 0:\n",
        "                n = n / c\n",
        "        else:\n",
        "            c = c + 1\n",
        "    return lis\n",
        "\n",
        "def is_multiple_of_all_factor(a, n):\n",
        "    lis = factor(n)\n",
        "    for i in lis:\n",
        "        if a % i != 0:\n",
        "            return False\n",
        "    return True\n",
        "\n",
        "def division_holds(a, m):\n",
        "    return a%4==0 and m%4==0 or a%4!=0 and m%4!=0\n",
        "\n",
        "def get_good_parameters(n:int, lims:dict()):\n",
        "    ''' Generate parameters 'a', 'c', 'm', based on the Hull-Dobell Theorem ''' \n",
        "    \n",
        "    \n",
        "    res = [{'a': 0, 'c': 0, 'm': 0}]\n",
        "    res.pop()\n",
        "    \n",
        "    if lims == None:\n",
        "        m_start, m_end = 99, 100\n",
        "        a_start, a_end = 1, 100\n",
        "        c_start, c_end = 1, 100\n",
        "        m_steps = 1\n",
        "    else:\n",
        "        m_start, m_end = lims['m'][0], lims['m'][1]\n",
        "        a_start, a_end = lims['a'][0], lims['a'][1]\n",
        "        c_start, c_end = lims['c'][0], lims['c'][1]\n",
        "        m_steps = lims.get('steps', 1)\n",
        "            \n",
        "    for m in range(m_start,m_end, m_steps):\n",
        "        for a in range(a_start, a_end):\n",
        "            for c in range(c_start, c_end):\n",
        "                if math.gcd(c, m) == 1 and is_multiple_of_all_factor(a-1, m) and division_holds(a-1, m):\n",
        "                    res.append({'a': a, 'c': c, 'm': m})\n",
        "                    n -= 1\n",
        "                if n == 0:\n",
        "                    return res\n",
        "                           \n",
        "            \n",
        "    return res    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 256,
      "metadata": {
        "trusted": true
      },
      "outputs": [],
      "source": [
        "\n",
        "def get_cycle_length(lis):\n",
        "    ''' Gives the index where the first duplication is encountered \n",
        "    \n",
        "        recall: a sequence start cycling whenever we a repeated number in the progression\n",
        "    '''\n",
        "    \n",
        "    new_lis = []\n",
        "    \n",
        "    for i in lis:\n",
        "        if i in new_lis:\n",
        "            break\n",
        "        new_lis.append(i)\n",
        "    return len(new_lis)\n",
        "    \n",
        "def get_info(lis, lcg:None):\n",
        "    ''' Generates a dictionary with basic information about our given list '''\n",
        "    \n",
        "    slis = set(lis)\n",
        "    lis_len = len(lis)\n",
        "    set_len = len(slis)\n",
        "    efficiency = int(set_len / lis_len * 100)\n",
        "    \n",
        "    if efficiency == 100:\n",
        "        cycle_length = lis_len\n",
        "    else:\n",
        "        cycle_length = get_cycle_length(lis)\n",
        "    \n",
        "    info = {'lcg': lcg,\n",
        "            'list': lis,\n",
        "            'efficiency': efficiency,\n",
        "            'cycle_length': cycle_length,\n",
        "            'full_period':'Yes' if efficiency == 100 else 'Not'\n",
        "           }\n",
        "    \n",
        "    return info\n",
        "    \n",
        "def print_info(info:dict):\n",
        "    if info['lcg'] != None:\n",
        "        a = info['lcg']['a']\n",
        "        c = info['lcg']['c']\n",
        "        m = info['lcg']['m']\n",
        "        print('a = ', a, '\\nc = ', c, '\\nm = ', m)\n",
        "        \n",
        "    print('Effiency: ', info['efficiency'], '%', sep='')\n",
        "    print('Cycle Length: ', info['cycle_length'])\n",
        "    print('Full period? ', info['full_period'], end='')\n",
        "\n",
        "    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 307,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[{'a': 7, 'c': 1, 'm': 54}, {'a': 7, 'c': 5, 'm': 54}]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x46d8b90>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "a =  7 \n",
            "c =  1 \n",
            "m =  54\n",
            "Effiency: 100%\n",
            "Cycle Length:  54\n",
            "Full period?  Yes\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x49c4c28>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "a =  7 \n",
            "c =  5 \n",
            "m =  54\n",
            "Effiency: 100%\n",
            "Cycle Length:  54\n",
            "Full period?  Yes\n"
          ]
        }
      ],
      "source": [
        "# Example of use\n",
        "\n",
        "lims = {\n",
        "        'a': [5, 10],\n",
        "        'c': [1, 10],\n",
        "        'm': [50, 100],\n",
        "        'steps': 2\n",
        "}\n",
        "\n",
        "''' Getting a list of 'n' good parameters '''\n",
        "# params = get_good_parameters(3, None)\n",
        "params = get_good_parameters(2, lims)\n",
        "print(params)\n",
        "\n",
        "for i in params:\n",
        "    p = i\n",
        "    p['x'] = 0\n",
        "    lis = get_lcg_list(p, p['m'])\n",
        "    \n",
        "    ''' ploting the graph '''\n",
        "    \n",
        "    # the length of the list cannot be odd\n",
        "    if not len(lis) & 1:\n",
        "        plt.plot(lis[::2],lis[1::2], 'bo')\n",
        "        plt.show()\n",
        "        \n",
        "        ''' Generating information '''\n",
        "        info = get_info(lis, p)\n",
        "        print_info(info)\n",
        "        print()\n",
        "   \n",
        "    \n",
        "    \n",
        "#print(lis)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 314,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "image/png": 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MAOkK0mpJsBJdwGkIVBNy7GZy4ccZ5JmRYSwzAKQrlikhUcL8VDMl0IuSskDV31lCC6AJgrb0WjLCWGYA8IKXqyXRi4J+IgA0QdCWXktGGMsMAF7warUkupGRBiaBmCCIS6/1JYxlBpA9JnVzerGkYV+9KJGI24sydWo4z5NJn3dA0QJogiCvj5pIGMsMIDtM6+acONEd43dhovyYSMTNmTpxYuLfYXIvimmfd0ARAJrAi5uJ38JYZgD+M7Gb04vVkkztRTHx8w4oAkAThHHptTCWGYC/TJ4slu6Shib2opj8eQcQAaApwrg+ahjLDMA/JndzSu497sABaetWqa7OfW1pSe7eZ2Iviumfd8AwCcQkVVXugN8wDZwNY5kB+COo3ZxeTlBIZrWkRO977jm3WzQS6dlqFtZelKB+3oYiADRNf28m2RTGMsMezEbMniB2cwZp+bZYL0q88qxcGb5elCB+3gZjJZA0kEkcMFyQKnsb9bVihuR2cya7Yka6grp6kSkPKbHPu7U1/jjAVFdI6QX1N2MAASA+ZiNmX26uNH167/v8+Mf+BDtBnqAQ60WZPt19DWPwJzE50GcEgABwoSBX9jaJRqX6+t73Wb/en88hWxMUolGpqck9D01N5l9zTA70jVEBYG1trUpKSjRo0CCVlpZqx44dve6/bt06jRkzRkOGDNGIESN0//3364svvvCptAACi9mIwdDX5yD59zlkY4KCrQmR05kdjaQZEwC++uqrqqmp0eLFi/X+++9rzJgxqqys1Oeffx53//fee08zZ87U3/3d3+nDDz/Uxo0btWPHDs2ZM8fnksNKtj3Vhw2zEYMh1c8hk98rvyco2D4EwZRu7QAzJgBcsWKF5syZo9mzZ+u6667TCy+8oCFDhuill16Ku39zc7NKSkr005/+VN/4xjd022236R/+4R/6bDUE0mbrU32YMBsxGFL5HDL9vfIz7x5DEOADIwLAs2fPaufOnaqoqOjelpOTo4qKCjU3N8d9T1lZmQ4dOqQ33nhDjuOovb1dmzZt0p133ulXsSHZ1xJm+1N9WJiYZDeMkv0cjh3L/PfKzwkKDEGAD4wIAI8fP65oNKrCwsIe2wsLC9XW1hb3PbfeeqvWrVun6upqDRw4UMOHD1dBQYFqa2sT/p3Ozk51dHT0+AmloARdtrWE8VQfHsxGDIZkPocVK6SaGn++V35NUGAIAnxgRADYH3v37tW8efO0aNEi7dy5U1u2bNGBAwc0d+7chO9ZunSpCgoKun+Ki4t9LLFHghJ02dgSxlN9uDAbMRj6+hyGDvX3e+XHBAWGIMAHRiSCPnv2rIYMGaJNmzbprrvu6t4+a9YsnThxQq+//vpF77n33nv19ddfa+PGjd3btm/frokTJ+rIkSMaEeeL1dnZqc7Ozu5/d3R0qLi4ODyJJIOSxLSv5K4eJvsMlPp6N+juS11d37nP4B9TkuyGXaLPwcTvlY8JkW1FImhDloIbOHCgxo0bp8bGxu4AsKurS42NjXr44YfjvufLL7/UgAE9Dz/3/3+REsXEeXl5ysvL867gfuqr+zEScbtJpk7N/A0llZYwk5aI46k+nExcqjCMQW2iz8HE75WJ6/wicIzpAq6pqdGLL76ol19+Wfv27dODDz6oM2fOaPbs2ZKkhQsXaubMmd37T5kyRQ0NDfrXf/1X7d+/X++9955++tOfasKECRo5cmS2DiNzgtT9aOv4FiYWIAiCMgzEK6Z+r7weghCUsd8IDCNaACWpurpax44d06JFi9TW1qaxY8dqy5Yt3RNDjh49qoMHD3bvf9999+nUqVNatWqV/vEf/1GXXXaZbr/9di1btixbh5BZQQq6THxiTwZP9ci2RMNAYmNvwzi20eTvVVWV2yuTbmsta1ojDiPGAGZLqMYQNDW5T/p92bo1891dto9viXczLi52KyluxsgU08fe8r2KLyhjvwMmVPV3hhAApiFUF1DQgq7YTUmK/8Ru+k0pjGOwEG6ZeAgM2nUctPJkm+lBfxpCVX9niDFdwOhD0LpJYuNb4nVL2PDEbuLEAgSb18NAgtityPeqJ1sn3CEpxkwCQRKClteMBb8B/3g59tbGPJ5hFKSx3wgcuoDTENomZLpJAPt4NQyEbsXwCNLY74AJbf3tIVoAbRTrJpk+3X3lJg2Yz6vl7YKUUgq9MzVFDjxBAAgAtvBiGAjdiuHBmtboBQEgANgk3bG3tubxDKugjf1GYDAGMA2MIQBgnaCllEJyGPvdA/U3aWAAIPNMqnyDllIKySFFDi5AFzAAZJJpa+9KdCsCBqALOA00IQPolenLcJnUsgmrUH8TAKaFCwhAQuTLAwKL+psuYADIDPLlAQgwAkAAyATy5QEIMAJAAMgE8uUBCDDSwABAJsSW4eorXx7LcCEImNBjHVoAASATUl2GKxqVmpqk+nr3NRr1qaCwnompitAnAkAAyJRk8+VRAfuDIPtisVRFF05Yam11t3MNGos0MGlgGjmApPTWvWZ6rsCgaGiQ5s3rGegUFbmttLaeX4tTFVF/EwCmhQsIQFosroB9RZAdX1OT29rcl61bjVtGjvqbLmAAyB5yBWZeNOq2/MVr64htmz/fzu5gUhVZjQAQALKFCjjzCLITI1WR1QgAASBbqIAzjyA7sViqogtnqcdEIlJxMamKDEUACADZQgWceQTZiaWaqghGIQAEgGyhAs48guzeJZuqCMYhAASAbKICziyC7L5VVUkHDrizfevq3NeWFq49w5EGJg1MI4cRWAIqGPgcMiteHsDiYjf4I9CxDvU3AWBauIAQeiTHhU0IsvH/UX8TAKaFCwihRnJcAJai/mYMIGAnkuMCgNUIAAEbkRwXAKw2INsFAALDpvFBJMcF7GHTvQ1JIwAEJPsmQ5AcF7CDbfc2JI0uYCA2GeLCLtHWVnd7Q0N2ypVJJMcFzGfjvQ1JIwCE3WydDEFyXMBstt7bkDQCQNjN5skQrEABmMvmexuSwhhA2M32yRBVVdLUqf4MEGcgOuAf2+9t6BMBIOzGZAg3CJs0KbN/g4HogL+4t6EPrASSBjKJGyAalUpK3EHR8b4KkYgbqLS00FrVl0QtfKw4AviPe1uvqL8ZAwjbMRnCGw0NbmVTXi7NmOG+lpRIGzcyEB3IBu5t6AMBIMBkiPT0lmri7rsZiA5kC/c29IIu4DSErgmZQfi94/ykLtbN1FuQl4y6Omn6dE+KBOAC3NsuErr6OwOYBGILBuH3zY/JEKbpK9VEshiIDmQO9zbEQRewDcgGj0xJN4UEK44AQFYQAJqObPDIpFRa7hiIDgCBQQBoOrLBI5OSXVN440YGogNAgDAG0HRkg0cmxVJNTJvmBnvntzSf38JXVSX98IcMRAeAgCAANB3Z4JFpsVQT8SYZxYI/iYHoABAgpIFJQyimkWciGzwpBRAP1wWAkAhF/Z1htACaLtkuumQratLJIBFa+AAgNJgEYgOvssGTTgYAACPQBZyG0DUhp9NF19eKD5YvLA4ACI/Q1d8ZQBewTdLpokslnQzdgAAABJpRXcC1tbUqKSnRoEGDVFpaqh07dvS6f2dnp5588kldddVVysvLU0lJiV566SWfShsypJMBAMAYxrQAvvrqq6qpqdELL7yg0tJSrVy5UpWVlfrDH/6gK6+8Mu577r77brW3t+s//uM/dM011+jo0aPq6uryueQhQToZAACMYcwYwNLSUt1yyy1atWqVJKmrq0vFxcV65JFHtGDBgov237Jli3784x9r//79uvzyy/v1N60aQ5CJdDIAAGSBVfV3AkZ0AZ89e1Y7d+5URUVF97acnBxVVFSoubk57nt+85vfaPz48Xr66ac1atQojR49Wo899pi++uqrhH+ns7NTHR0dPX6sEUsnI7GmKwAAIWdEAHj8+HFFo1EVFhb22F5YWKi2tra479m/f7+2b9+uDz74QJs3b9bKlSu1adMmPfTQQwn/ztKlS1VQUND9U1xc7OlxBJ5X6WQAAOaJRqWmJqm+3n2NRrNdIvTCmDGAqerq6lIkEtG6detUUFAgSVqxYoWmTZum1atXa/DgwRe9Z+HChaqpqen+d0dHh51B4NSprPgAAPg/LBIQOkYEgEOHDlVubq7a29t7bG9vb9fw4cPjvmfEiBEaNWpUd/AnSd/+9rflOI4OHz6sa6+99qL35OXlKS8vz9vChxErPgAAYmKLBFw4Pjy2SAA9RIFkRBfwwIEDNW7cODU2NnZv6+rqUmNjo8rKyuK+59Zbb9WRI0d0+vTp7m0ff/yxcnJyVFRUlPEyAwB8RPdkZkSjbstfvMmBsW3z53O+A8iIAFCSampq9OKLL+rll1/Wvn379OCDD+rMmTOaPXu2JLf7dubMmd37z5gxQ1dccYVmz56tvXv3atu2bXr88cd1//33x+3+BQCEVEODm8WgvFyaMcN9LSlh+UovpLJIAALFiC5gSaqurtaxY8e0aNEitbW1aezYsdqyZUv3xJCjR4/q4MGD3ftfcsklevvtt/XII49o/PjxuuKKK3T33XfrqaeeytYhAAC8RvdkZrFIQGgZkwcwG8gjBAABxhrmmdfU5Lao9mXr1kCNHaf+NqgLGACAHuiezLyJE90g+sL8sDGRiFRc7O6HQCEABACYie7JzGORgNAiAAQAmIk1zP3BIgGhxBjANDCGAAACjDXM/RWNhmaRAOpvg2YBAwDQQ6x7cto0N9g7Pwike9J7LBIQKnQBw3skXAUQFHRPAnHRAghvsR4kgKBhDXPgIowBTANjCC6QKOFqrKuFp20AQABQf9MFDK+wHiQAAKFBAAhvkHAVAIDQIACEN0i4CgBAaDAJBN4g4SoQfCHK0wYgs2gBhDdYDxIItoYGNylyebk0Y4b7WlLibgdgHQJAeIP1IIHgis3Qv3Ccbmuru50gELAOASC8Q8JVIHiYoU9yeiAOxgDCWyRcBYIllRn6Ji7jRXJ6IC4CQHjPz/UgGdQO9M7mGfqJktPHur7pmYDF6AJGeDGoHeibrTP06foGekUAiHBiUDuQnIkTpSuu6H2fK64wb4Y+yemBXhEAInx4sgfQF5u7voEkEAAifHiyBy6WaKbru+9KX3zR+3u/+MK874utXd9AkpgEgvDhyR7oqbeZrp2dyf0O074vseT0ra3xewsiEff/Tev6BpJECyDChyd74P/0NR72k0+S+z2mfV9ITg/0igAQ4cOyc4ArmfGwL75o7/eF5PRAQgSACB+vn+xZJQBhlcx42MOHpTlz3H/b2BJWVSUdOCBt3SrV1bmvLS0Ef7AeASDCyasne3IJIsySHbd37bV2t4TFktNPn+6+mhrsAimIOE68vgMko6OjQwUFBTp58qTy8/OzXRw7pbMSSKJVAmKtIjZUjAi3pib3oaUvW7e6gQ8r5wCSqL8lAsC0cAElEIZKJhp1W/oSdZ/FZgi2tASv7EBM7Drua6Yr1zHQA/U3XcDwWli6VMklCBMw0xVAPxEAwjthWp6NXIIwBTNdAfQDiaDhjb7SUUQi7vJsU6cGozWCXIIwSVWV+90K+tALAIFBAAhvpNKlOmmSb8VKiFUCYJrYTFcASAJdwPBG2LpUGTsFALAYASC8EcYuVcZOAQAsRRqYNDCN/DxhTkcRhrQ1AADPUH8zBhBeiXWpTpvmBnvnB4FB71Jl7BQAwDJ0AcM7dKkCABAKtADCW6SjAAAg8AgA4T26VAEACDQCQAAA/MKkMwQEASAAAH5oaHBXTDo/aX5RkTuBjjHS8BmTQACYIxqVmpqk+nr3NRrNdokAV5jWSocVyAOYBl/yCJnYXWDiMSH7aF3xB9/f1MXypCZaLjPIeVINRR5AWgCDraHBvWmUl0szZrivJSXhflI08ZiQfbSu+IPvb/+kslY64BMCwKAysUIz8ZiQfdGo2/IXrzMjtm3+fLqD08X3t//CtlY6rEAAGEQmVmgmHhOCgdaVzOP7m54wrpUO4xEABpGJFZqJx5QJTGJIHa0rmcf3Nz0TJ7pj/GLLYl4oEpGKi939AJ8QAAaRiRVaqsdkYyDE+Kr+oXUl80y8J/kptla6dHEQGPS10mEsAsAgMrFCS+WYbAyEGF/Vf7SuZJ6J9yS/sVY6AoY0MGnI2DTyWMqA1tb4Y27CmDIg2WNavlyqrr54n1jlbuKNkhQR6YsF0FLPa8fk68ZPJt6TsoU0OoFAGhhaAIPJxO6CZI5pxQqppsa+geaMr0ofrSuZZeI9KVtia6VPn+6+cs6QJQSAQWVihdbXMQ0damcgxPgqb1RVSQcOSFu3SnV17mtLSzi/K0Fk4j0JsJhRAWBtba1KSko0aNAglZaWaseOHUm977333tOAAQM0duzYzBYwVSZWaL0dk62BEOOrvEPrSmaZeE8CLDUg2wXwyquvvqqamhq98MILKi0t1cqVK1VZWak//OEPuvLKKxO+78SJE5o5c6b+6q/+Su3t7T6WOEmxCs0kiY7J1kAoNomhr/FVTGJAEJh4TwIsZEwL4IoVKzRnzhzNnj1b1113nV544QUNGTJEL730Uq/vmzt3rmbMmKGysjKfSoqEbJ3NyfgqAIDPjAgAz549q507d6qioqJ7W05OjioqKtTc3JzwfWvWrNH+/fu1ePFiP4qJvtgcCDG+CgDgIyO6gI8fP65oNKrCwsIe2wsLC/XRRx/Ffc8nn3yiBQsW6N1339WAAcmdhs7OTnV2dnb/u6Ojo/+FRnyxQGjevJ4TQoqK3ODP5ECoqkqaOpUUEQCAjDMiAExVNBrVjBkztGTJEo0ePTrp9y1dulRLlizJYMkgye5AiPFVAGxFjkRfGZEI+uzZsxoyZIg2bdqku+66q3v7rFmzdOLECb3++us99j9x4oT+4i/+QrnnXVhdXV1yHEe5ubn63e9+p9tvv/2ivxOvBbC4uNjqRJIAAKStoSF+z89zz2Wk54dE0IaMARw4cKDGjRunxsbG7m1dXV1qbGyMO7kjPz9fe/bs0e7du7t/5s6dq29961vavXu3SktL4/6dvLw85efn9/gBAABpYCnMrDCmC7impkazZs3S+PHjNWHCBK1cuVJnzpzR7NmzJUkLFy5Ua2urXnnlFeXk5OiGG27o8f4rr7xSgwYNumg7AADIkGjUbflLtAJUJOKuADV1Kt3BHjMmAKyurtaxY8e0aNEitbW1aezYsdqyZUv3xJCjR4/q4MGDWS4lAADolspSmIyP9pQRYwCzhTEEAACkob5emjGj7/3q6twVfjxC/W3IGEAAABBCtq4AFQDGdAGjF0ytBwAEEUthZg0tgKZraJBKSqTycreZvbzc/TezqgAA2WbzClBZRgBoMqbWAwCCjqUws4JJIGkI9CDSaNRt6Us0uyrWrN7SwpMVACD7fByuFOj62yeMATQVU+sBAGHCUpi+ogvYVEePersfAAAwBgGgqZhaDwAAEiAANFVsav2Fs6piIhGpuJip9QAAWIgA0FSxqfWJ5vg4DlPrAQCwFAEgAACAZQgATRWNSvPmJf7/SESaP9/dD4gnGpWamty1OpuauFYAwCAEgKZKJQ0McCFWkAEAoxEAmoo0MOgvVpABAOMRAJqKNDDoj9jQgXiTh2LbGDoAAKFHAGgq0sCgPxg6kBzGRwIIOQJAU8XSwEgXB4Gxf5MGBhdi6EDfGB8JwAAEgCarqpI2bZJGjeq5vajI3V5VlZ1yIbgYOtA7xkcCMETEcRJlCkZfOjo6VFBQoJMnTyo/Pz/bxUksGnW77I4edSvuiRNp+UN80ajbmtXaGn8cYCTiPkC0tJh7DSX6vsTOTaIuchvODWCI0NTfGTQg2wWAD3JzpUmTsl0KhEFs6MC0aW5Ac34QaMPQgYYGdxLM+UFeUZF7Ti6/PPnxkXzfAAQcXcCwW9gG8/tRXluHDvTVvfv668n9HpvHRwIIDVoAYa/eWnuCGOT4Wd6qKmnqVHuGDvSV/iYSkdatS+532To+EkCoMAYwDYwhCLFYa8+Fl3+smzPVlq5Mj7NMVF7JLbPJLXN+aGpyZ/P2ZehQ6Ysv7B0fCRiC+psuYNjI62THmU4L0lt5JXc7yZnTk2y37d/+rftKaqXMC9vwDCBkCABhHy+THfuRFqSv8kokZ05Xst22U6faOT7Sb+RaBDKOMYCwT6rJjntLC9LXuLH5892gIZ1WodZWb/fDxWIr5/SV/ib22ds0PtJviYY7xB6qCLQBTxAAwj6pJDsOQlqQY8e83Q8XSzX9DamVMsOvhyoAdAHDQsmuk3z8eDDSggwb5u1+iM/W9DdBwlrUgG9oAYR9kmntWb5cevTRYKQFuTAgSXc/JGZb+pugYS1qwDe0AMJOfbX2DBvWd0vEsWNuWpC+WhInTkyvrLEWy9548XfginXvTp/uvhL8+Ye1qAHfEADCXlVV0oED0tatUl2d+9rS4m4PUlqQWItlJBL/70QipB+BGZIdnsHDDpA2AkD4K2i5vRK19gQtLQjj02CD2MOORK5FIMNYCSQNZBJPUZiWXotG3bxjfaUFia36kOmVQM4vF+PTYLp494riYjf4C9q9AqFE/U0AmBYuoBR4vfSaH2JlluJPFAlimQFT8LCDDKL+JgBMCxdQkmKtaYkmVQR5DVVaIgDAONTfpIGBH1LJ7RW05LqkBQEAGIgAEJkX9txerPoAADAMs4CReeT2AgAgUAgAkXnk9gIAIFAIAJF55PYCACBQCADhDxIZAwAQGEwCgX+YUQsAQCAQAMJfzKgFACDrCAABAPADq5sgQAgAAQDItDCthQ4rMAkEAIBMiq0rfuGKSK2t7vaGhuyUC1YjAAQAIFOiUbflz3Eu/r/Ytvnz3f0AHxEAAgCQKamshQ74iAAQAIBMCfta6DAWk0BgJmbbAQgC1kJHQNECCPM0NEglJVJ5uTRjhvtaUsJAawD+Yy10BBQBIMzCbDsAQcJa6AgoowLA2tpalZSUaNCgQSotLdWOHTsS7tvQ0KA77rhDw4YNU35+vsrKyvTWW2/5WFp4jtl2AIKItdARQMYEgK+++qpqamq0ePFivf/++xozZowqKyv1+eefx91/27ZtuuOOO/TGG29o586dKi8v15QpU7Rr1y6fSw7PMNsOQFBVVUkHDkhbt0p1de5rSwvBH7Im4jjxmkvCp7S0VLfccotWrVolSerq6lJxcbEeeeQRLViwIKnfcf3116u6ulqLFi1Kav+Ojg4VFBTo5MmTys/P73fZ4ZH6enfMX1/q6qTp0zNfHgBAIFF/G9ICePbsWe3cuVMVFRXd23JyclRRUaHm5uakfkdXV5dOnTqlyy+/PFPFRKYx2w7InGhUampyH7SamhhKAYScEWlgjh8/rmg0qsLCwh7bCwsL9dFHHyX1O5599lmdPn1ad999d8J9Ojs71dnZ2f3vjo6O/hUYmRGbbdfaGn8cYCTi/j+z7YDUsI4tYBwjWgDTVVdXpyVLlmjDhg268sorE+63dOlSFRQUdP8UFxf7WEr0idl26A0tWP3DzHrASEYEgEOHDlVubq7a29t7bG9vb9fw4cN7fe/69ev1wAMPaMOGDT26kONZuHChTp482f1z6NChtMsOjzHbDvGQG7J/mFkPGMuIAHDgwIEaN26cGhsbu7d1dXWpsbFRZWVlCd9XX1+v2bNnq76+XpMnT+7z7+Tl5Sk/P7/HDwKI2Xb+CEuLGi1Y/cfMesBYRowBlKSamhrNmjVL48eP14QJE7Ry5UqdOXNGs2fPluS23rW2tuqVV16R5Hb7zpo1S88995xKS0vV1tYmSRo8eLAKCgqydhzwSG6uNGlStkthrrCMCeurBSsScVuwpk5laEA8rGMLGMuIFkBJqq6u1rPPPqtFixZp7Nix2r17t7Zs2dI9MeTo0aM6ePBg9/7/9m//pj/96U/6yU9+ohEjRnT/zJs3L1uHAIRDmFrUaMFKDzPrAWMZkwcwG8gjBOtEo+7YuURBVWymdUtLMFrUyA2Zntjn3dfM+qB83kCSqL8NagEE4IOwtajRgpUeZtYDxiIABJC8sI0Ji+WGvDB4iYlEpOJickP2hpn1gJGMmQQCwAdha1GLtWBNm+YGe+d3Y9KClbyqKneizLvvusH9iBFu0Bz28xaNmndMQJIYA5gGxhDAOmEdExZv1nJxsRv8pdqCRdBghrDMZEdGUH8TAKaFCwhWis0CluK3qAW1W9CLwC3ZoIEgMdhi1/CF1V/Qr2F4hvqbMYAAUmXrmLBk09+w6kiwsboJIIkWwLTwBAGrhamVK93uvmTT3yxfLlVX07IUZE1NblDel61bSSZvMOpvJoEA6K+wrLaSqLsv1nKXTFCWbPqbhx5i1ZGgC9tMdiBD6AIGkLqwrAPsVXdfssHA8eOJ/y9oORJtFbaZ7ECGEAACSE2Yxrh5lbjay2CAlqXsIjckIIkAEEAqwrQOsORdd18yQcOwYcn9LVqWsovVTQBJBIAAkhXG2ZNedfclEzSsXk3LUljYOpMdOA8BIIDkhG0dYMnb7r6+goZp02hZCpOqKunAAXe2b12d+9rSQvAHazALGEBywjh70uul4PpaEi0WJMZLOdOfVUeQWWGZyQ5kAAEggOSEdfak10FZX0GDqevmwi5hyvOJfiERdBpIJAmrhHUd4BgqNCA5FqyTTP1NCyCAZHndneo3uvvSQwBtBy8SpyMUmAQCIHnMnrRTmHI/ov/CONMf/UYXcBpoQoa1aA2yR6IWIdY3No9F6yRTf9MFDKA/6E61Q18tQqxvbJYwzvRHv9EFDACIL4y5H9F/YZ3pj34hAAQAxEeLkF1YJ9kqBIAAgPhSaRGKRt0xZPX17isTBcKHdZKtQgAIAIgv2Rah48eZJWwKZvpbg1nAaWAWEQDjxWYBS/FzPz72mPTss8wSNo3hM/2pv2kBBAD0prcWoVdfdbt8yRtnnthM/+nT3VeDgj+4CABtx7gdAH2pqpIOHHDzv9XVua8tLdKwYcwSBkKKPIA2s2C9RwAeiZf7kVnCQGjRAmir2LieC5/eY+s9MngbQF/IGweEFgGgjVjvEYAXyBsHhBYBoI3I7g/AC+SNA0KLANBGjNsB4JVs5I1j8hqQNiaB2IhxOwC8VFUlTZ3qT944Jq8BniARdBpCm0gyGnWz9Le2xh8HGIm4N9SWFrpuAARHbPIaSaeRptDW3x6iC9hGjNsBEDZMXgM8RQBoK9Z7BBAmTF4DPMUYQJv5OW4HANLB5DXAUwSAtouX3R8AgobJa4Cn6AIGAAQfSacBTxEAwh/k7QKQDiavAZ4iAETmNTS4aWfKy6UZM9zXkhLWGwaQGiavAZ4hD2AayCOUBPJ2AfBaNMrkNaSF+psAMC1cQH2IJZxOlLqBhNMA4CKo9RX1N13AwWTKeDnydgFA3xgmgywgAAwak24E5O0CgN7Fhslc+LDc2upuD+O9H6FAABgkpt0IyNsFAImxvB2yiAAwKEy8EZC3CwASY5gMsogAMChMvBGQtwsAEmOYDLKIADAoTL0RkLcLAOJjmAyyiLWAg8LkG0FVlTR1KikOAOB8sWEyra3xh//EUmUxTAYZQAAYFKbfCHJzpUmTsl0KAAiO2DCZadPce/z5936GySDD6AIOCsbLAYB9GCaDLGElkDRkJJN4Q4M7G/j8CSFFRW5wyI0AAMzESiC+YiUQw1oAa2trVVJSokGDBqm0tFQ7duzodf+mpibdfPPNysvL0zXXXKO1a9f6U9C+XBiTE6MDgNliw2SmT3dfCf6QYcYEgK+++qpqamq0ePFivf/++xozZowqKyv1+eefx92/paVFkydPVnl5uXbv3q358+frgQce0FtvveVzyc8TSwTd2tpz+5Ej4UwEDQAAAsmYLuDS0lLdcsstWrVqlSSpq6tLxcXFeuSRR7RgwYKL9v+nf/on/fa3v9UHH3zQve3HP/6xTpw4oS1btiT1Nz1tQo5G3SXfEuUCjE0CaWnhyRAAgDTQBWxIC+DZs2e1c+dOVVRUdG/LyclRRUWFmpub476nubm5x/6SVFlZmXB/Sers7FRHR0ePH8+YmAgaAAAEkhEB4PHjxxWNRlVYWNhje2Fhodra2uK+p62tLe7+HR0d+uqrr+K+Z+nSpSooKOj+KS4u9uYAJHMTQQMAgMAxIgD0y8KFC3Xy5Mnun0OHDnn3y01OBA0AAALFiETQQ4cOVW5urtrb23tsb29v1/Dhw+O+Z/jw4XH3z8/P1+DBg+O+Jy8vT3l5ed4U+kKmJ4IGAACBYUQL4MCBAzVu3Dg1NjZ2b+vq6lJjY6PKysrivqesrKzH/pL09ttvJ9w/40gEDQAAfGJEAChJNTU1evHFF/Xyyy9r3759evDBB3XmzBnNnj1bktt9O3PmzO79586dq/379+uJJ57QRx99pNWrV2vDhg169NFHs3UIZIQHAAC+MKILWJKqq6t17NgxLVq0SG1tbRo7dqy2bNnSPdHj6NGjOnjwYPf+3/jGN/Tb3/5Wjz76qJ577jkVFRXp3//931VZWZmtQ3BVVUlTp5IRHgAAZIwxeQCzgTxCAACED/W3QV3AAAAASA4BIAAAgGUIAAEAACxDAAgAAGAZAkAAAADLEAACAABYhgAQAADAMgSAAAAAliEABAAAsIwxS8FlQ2wRlY6OjiyXBAAAJCtWb9u8GBoBYBpOnTolSSouLs5ySQAAQKpOnTqlgoKCbBcjK1gLOA1dXV06cuSILr30UkUiEU9/d0dHh4qLi3Xo0CFr1yn0AufRG5xHb3AevcF59IbN59FxHJ06dUojR45UTo6do+FoAUxDTk6OioqKMvo38vPzrftiZgLn0RucR29wHr3BefSGrefR1pa/GDvDXgAAAIsRAAIAAFiGADCg8vLytHjxYuXl5WW7KKHGefQG59EbnEdvcB69wXm0G5NAAAAALEMLIAAAgGUIAAEAACxDAAgAAGAZAkAAAADLEABmSW1trUpKSjRo0CCVlpZqx44dve7f1NSkm2++WXl5ebrmmmu0du1afwoacKmcx4aGBt1xxx0aNmyY8vPzVVZWprfeesvH0gZbqtdkzHvvvacBAwZo7NixmS1gSKR6Hjs7O/Xkk0/qqquuUl5enkpKSvTSSy/5VNrgSvU8rlu3TmPGjNGQIUM0YsQI3X///friiy98Km0wbdu2TVOmTNHIkSMViUT02muv9fke6hqLOPDd+vXrnYEDBzovvfSS8+GHHzpz5sxxLrvsMqe9vT3u/vv373eGDBni1NTUOHv37nWef/55Jzc319myZYvPJQ+WVM/jvHnznGXLljk7duxwPv74Y2fhwoXOn/3Znznvv/++zyUPnlTPZcz//u//OldffbXz13/9186YMWP8KWyA9ec8/s3f/I1TWlrqvP32205LS4vzX//1X8727dt9LHXwpHoet2/f7uTk5DjPPfecs3//fufdd991rr/+eueHP/yhzyUPljfeeMN58sknnYaGBkeSs3nz5l73p66xCwFgFkyYMMH5yU9+0v3vaDTqjBw50lm6dGnc/Z944gnn+uuv77GturraqayszGg5gy7V8xjPdddd5yxZsiQTxQuV/p7L6upq55//+Z+dxYsXEwA6qZ/HN9980ykoKHC++OILv4oYCqmex2eeeca5+uqre2z71a9+5YwaNSqj5QyTZAJA6hq70AXss7Nnz2rnzp2qqKjo3paTk6OKigo1NzfHfU9zc3OP/SWpsrIy4f426M95vFBXV5dOnTqlyy+/PFPFDIX+nss1a9Zo//79Wrx4sR/FDLz+nMff/OY3Gj9+vJ5++mmNGjVKo0eP1mOPPaavvvrKr2IHTn/OY1lZmQ4dOqQ33nhDjuOovb1dmzZt0p133ulXsY1AXWMXAkCfHT9+XNFoVIWFhT22FxYWqq2tLe572tra4u7f0dFhbUXRn/N4oWeffVanT5/W3XffnYkihkZ/zuUnn3yiBQsW6D//8z81YMAAP4oZeP05j/v379f27dv1wQcfaPPmzVq5cqU2bdqkhx56yI8iB1J/zuOtt96qdevWqbq6WgMHDtTw4cNVUFCg2tpaP4psDOoauxAAwkp1dXVasmSJNmzYoCuvvDLbxQmVaDSqGTNmaMmSJRo9enS2ixNqXV1dikQiWrdunSZMmKA777xTK1as0Msvv0yFm4K9e/dq3rx5WrRokXbu3KktW7bowIEDmjt3braLBgQWj+4+Gzp0qHJzc9Xe3t5je3t7u4YPHx73PcOHD4+7f35+vgYPHpyxsgZZf85jzPr16/XAAw9o48aNF3V32CjVc3nq1Cn9z//8j3bt2qWHH35YkhvIOI6jAQMG6He/+51uv/12X8oeJP25JkeMGKFRo0apoKCge9u3v/1tOY6jw4cP69prr81omYOoP+dx6dKluvXWW/X4449Lkm688Ub9+Z//uSZOnKinnnpKI0aMyHi5TUBdYxdaAH02cOBAjRs3To2Njd3burq61NjYqLKysrjvKSsr67G/JL399tsJ97dBf86jJNXX12v27Nmqr6/X5MmT/Shq4KV6LvPz87Vnzx7t3r27+2fu3Ln61re+pd27d6u0tNTP4gdGf67JW2+9VUeOHNHp06e7t3388cfKyclRUVFRxsscRP05j19++aVycnpWZ7m5uZIkh+Xuk0ZdY5nszkGx0/r16528vDxn7dq1zt69e52///u/dy677DKnra3NcRzHWbBggXPvvfd27x+bmv/44487+/btc2pra5ma76R+HtetW+cMGDDAqa2tdY4ePdr9c+LEiWwdQmCkei4vxCxgV6rn8dSpU05RUZEzbdo058MPP3Teeecd59prr3UeeOCBbB1CIKR6HtesWeMMGDDAWb16tfPpp58627dvd8aPH+9MmDAhW4cQCKdOnXJ27drl7Nq1y5HkrFixwtm1a5fz2WefOY5DXWM7AsAsef75552//Mu/dAYOHOhMmDDB+e///u/u/5s1a5bzve99r8f+W7dudcaOHesMHDjQufrqq501a9b4W+CASuU8fu9733MkXfQza9Ys/wseQKlek+cjAPw/qZ7Hffv2ORUVFc7gwYOdoqIip6amxvnyyy99LnXwpHoef/WrXznXXXedM3jwYGfEiBHOPffc4xw+fNjnUgfL1q1be73nUdfYLeI4tI8DAADYhDGAAAAAliEABAAAsAwBIAAAgGUIAAEAACxDAAgAAGAZAkAAAADLEAACAABYhgAQAAAEyrZt2zRlyhSNHDlSkUhEr732Wsq/Y8OGDRo7dqyGDBmiq666Ss8884z3BQ0xAkAAABAoZ86c0ZgxY1RbW9uv97/55pu65557NHfuXH3wwQdavXq1fvnLX2rVqlUelzS8WAkEAAAEViQS0ebNm3XXXXd1b+vs7NSTTz6p+vp6nThxQjfccIOWLVumSZMmSZJmzJihc+fOaePGjd3vef755/X000/r4MGDikQiPh9F8NACCAAAQuXhhx9Wc3Oz1q9fr9///vf60Y9+pO9///v65JNPJLkB4qBBg3q8Z/DgwTp8+LA+++yzbBQ5cAgAAQBAaBw8eFBr1qzRxo0bNXHiRH3zm9/UY489pttuu01r1qyRJFVWVqqhoUGNjY3q6urSxx9/rOXLl0uSjh49ms3iB8aAbBcAAAAgWXv27FE0GtXo0aN7bO/s7NQVV1whSZozZ44+/fRT/eAHP9C5c+eUn5+vefPm6Wc/+5lycmj7kggAAQBAiJw+fVq5ubnauXOncnNze/zfJZdcIskdN7hs2TL94he/UFtbm4YNG6bGxkZJ0tVXX+17mYOIABAAAITGTTfdpGg0qs8//1wTJ07sdd/c3FyNGjVKklRfX6+ysjINGzbMj2IGHgEgAAAIlNOnT+uPf/xj979bWlq0e/duXX755Ro9erTuuecezZw5U8uXL9dNN92kY8eOqbGxUTfeeKMmT56s48ePa9OmTZo0aZK+/vrr7jGD77zzThaPKlhIAwMAAAKlqalJ5eXlF22fNWuW1q5dq3Pnzumpp57SK6+8otbWVg0dOlTf/e53tWTJEn3nO9/R8ePHNWXKFO3Zs0eO46isrEw///nPVVpamoWjCSYCQAAAAMswFQYAAMAyBIAAAACWIQAEAACwDAEgAACAZQgAAQAALEMACAAAYBkCQAAAAMsQAAIAAFiGABAAAMAyBIAAAACWIQAEAACwDAEgAACAZQgAAQAALPP/AHwB8SbkPCEGAAAAAElFTkSuQmCC",
            "text/plain": [
              "<pyolite.display.Image at 0x4721420>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Effiency: 100%\n",
            "Cycle Length:  200\n",
            "Full period?  Yes\n"
          ]
        }
      ],
      "source": [
        "''' Long numbers for the value of 'm', are more likely to have full Cycle, when few numbers 'n' are needed '''\n",
        "\n",
        "params = {\n",
        "        'x': 3,\n",
        "        'a': 51,\n",
        "        'c': 70,\n",
        "        'm': 1103515245,\n",
        "}\n",
        "\n",
        "# n -> how many numbers (chosen)\n",
        "n = 200\n",
        "lis = get_lcg_list(params, n)\n",
        "\n",
        "\n",
        "plt.plot(lis[::2], lis[1::2], 'ro')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(lis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "   \n",
        "    "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 296,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x49f93e0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Effiency: 100%\n",
            "Cycle Length:  8\n",
            "Full period?  Yes\n",
            "[0, 3, 2, 5, 4, 7, 6, 1]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "''' Example : (LCG Full Period Conditions)  \n",
        "\n",
        "    m = 8 , a = 5 , c= 1\n",
        "'''\n",
        "\n",
        "lis = get_lcg_list_long(1, 5, 3, 8, 8)\n",
        "plt.plot(lis[::2], lis[1::2], 'ro')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(lis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "print(lis)\n",
        "print()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 318,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<pyolite.display.Image at 0x494d670>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Effiency: 100%\n",
            "Cycle Length:  2000\n",
            "Full period?  Yes\n"
          ]
        }
      ],
      "source": [
        "''' Example : glibc (used by GCC)\n",
        "\n",
        "    m = 2^31, a = 1103515245 , c = 12345\n",
        "    \n",
        "    seed = 3 (chosen)\n",
        "    n = 2000 (chosen)\n",
        "'''\n",
        "\n",
        "params = {\n",
        "        'x': 3,\n",
        "        'a': 1103515245,\n",
        "        'c': 12345,\n",
        "        'm': 2**31,\n",
        "}\n",
        "\n",
        "# n -> how many numbers (chosen)\n",
        "n = 2000\n",
        "lis = get_lcg_list(params, n)\n",
        "\n",
        "\n",
        "plt.plot(lis[::2], lis[1::2], 'ro')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(lis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "trusted": true
      },
      "outputs": [
        {
          "ename": "NameError",
          "evalue": "name 'get_lcg_list' is not defined",
          "output_type": "error",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m/var/folders/c8/cftlqtps3pqc1zqh25116mpc0000gn/T/ipykernel_80835/1424661819.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;31m# n -> how many numbers (chosen)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m \u001b[0mlis\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_lcg_list\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'get_lcg_list' is not defined"
          ]
        }
      ],
      "source": [
        "''' Example : Java's java.util.Random\n",
        "\n",
        "    m = 2^48, a = 25214903917 , c = 11\n",
        "    seed = 3 (chosen)\n",
        "    n = 20000 (chosen)\n",
        "'''\n",
        "\n",
        "\n",
        "params = {\n",
        "        'x': 3,\n",
        "        'a': 25214903917,\n",
        "        'c': 11,\n",
        "        'm': 2**48,\n",
        "}\n",
        "\n",
        "# n -> how many numbers (chosen)\n",
        "n = 2000\n",
        "lis = get_lcg_list(params, n)\n",
        "\n",
        "\n",
        "plt.plot(lis[::2], lis[1::2], 'go')\n",
        "plt.show()\n",
        "\n",
        "''' Generating information '''\n",
        "info = get_info(lis, None)\n",
        "print_info(info)\n",
        "print()\n",
        "   "
      ]
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