W01_KiK_entropia_wstęp.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mrospond/kik/blob/main/W01_KiK_entropia_wst%C4%99p.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Potrzebne biblioteki...\n",
        "\n",
        "# Obliczenia matematyczne, dla nas głównie logarytm\n",
        "import math\n",
        "\n",
        "# Generowanie liczb losowych\n",
        "import random\n",
        "\n",
        "# Rysowanie standardowych wykresów\n",
        "import matplotlib.pyplot as plt\n",
        "# Obróbka statystyczna przy rysowaniu wykresów i formatowaniu ich wyglądu\n",
        "import seaborn as sns\n",
        "sns.set()\n",
        "# Rysowanie wykresów z interakcją użytkownika (np. obracanie)\n",
        "import plotly.express as px\n",
        "\n",
        "# Pracy z wektorami i macierzami\n",
        "import numpy as np\n",
        "\n",
        "# Tabelaryczneja reprezentacja danych (ramki danych)\n",
        "import pandas as pd\n",
        "\n",
        "# Obliczenia probabilistyczne\n",
        "## Rozkład dwumianowy (Bernoulliego)\n",
        "from scipy.stats import binom\n",
        "## Rozkład normalny (Gaussa)\n",
        "from scipy.stats import norm\n",
        "## Dowolny rozkład dyskretny\n",
        "from scipy.stats import rv_discrete\n",
        "## Entropia różnicowa\n",
        "from scipy.stats import differential_entropy\n",
        "## Entropia Shannona i dywergencja Kullbacka-Leiblera\n",
        "from scipy.stats import entropy\n",
        "## Estymacja rozkładu prawdopodobieństwa z próbek\n",
        "from scipy.stats import gaussian_kde"
      ],
      "metadata": {
        "id": "e9_HTJHJfmD2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Entropia"
      ],
      "metadata": {
        "id": "-7gdGNCstvBp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Entropia źródła dyskretnego\n",
        "\n",
        "Dla rozkładu prawdopodobieństwa:\n",
        "\n",
        "$$ (p_1, p_2, p_3, \\dots, p_N), \\quad \\sum_{i=1}^N{p_i} = 1 $$\n",
        "\n",
        "możemy policzyć entropię jako:\n",
        "\n",
        "$$ H(p_1, p_2, p_3, \\dots, p_N) = -\\sum_{i=1}^N{p_i} \\log{p_i} \\quad \\text{[bit/wiadomość]} $$\n",
        "($\\log = \\log_2$)"
      ],
      "metadata": {
        "id": "h4FB25VxNiUF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Weźmy sobie zmienną losową realizowaną z 4 różnymi wartościami A, B, C, D (możemy powiedzieć, że to są cztery różne wiadomości)\n",
        "\n",
        "#@markdown Prawdopodobieństwa $p_A$, $p_B$, $p_C$ (automatycznie wyliczamy $p_D = 1-p_A-p_B-p_C$):\n",
        "pA = 0  #@param {type: \"slider\", min:0, max:1, step:0.05}\n",
        "pB = 0.25  #@param {type: \"slider\", min:0, max:1, step:0.05}\n",
        "pC = 0.25  #@param {type: \"slider\", min:0, max:1, step:0.05}\n",
        "\n",
        "assert pA+pB+pC <= 1, \"Suma prawdopodobieństw nie może przekracać 1.0!\"\n",
        "\n",
        "#@markdown Jednostka entropii:\n",
        "units = \"bit\" #@param [\"ban/dit/hartley\", \"nat\", \"bit\"]\n",
        "\n",
        "podstawa = {\n",
        "    \"ban/dit/hartley\": 10,\n",
        "    \"nat\": math.e,\n",
        "    \"bit\": 2\n",
        "}\n",
        "\n",
        "pD = 1-pA-pB-pC\n",
        "prawd = [pA, pB, pC, pD]\n",
        "rozklad_prawdopodobienstwa = np.array(prawd)\n",
        "\n",
        "H = entropy(rozklad_prawdopodobienstwa, base = podstawa[units])\n",
        "\n",
        "print(f'Rozkład prawdopodobieństwa: pA = {pA}, pB = {pB}, pC = {pC}, pD = {pD}')\n",
        "print(f'Entropia H({prawd}) = {H} {units}')"
      ],
      "metadata": {
        "id": "iA9qEc8nut4r",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ecc4a7d-77ea-44ec-d308-90614c511e0d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rozkład prawdopodobieństwa: pA = 0, pB = 0.25, pC = 0.25, pD = 0.5\n",
            "Entropia H([0, 0.25, 0.25, 0.5]) = 1.5 bit\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Poeksperymentujmy:\n",
        "*   wartość minimalna?\n",
        "*   co jeśli np. $p_D=0$?\n",
        "*   wartość maksymalna?"
      ],
      "metadata": {
        "id": "IuCakvFOvsxB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Próbkowanie rozkładu { run: \"auto\" }\n",
        "#@markdown Możemy zobaczyć, jak wygląda generowanie zmiennych (wiadomości ze źródła o określonym rozkładzie)\n",
        "\n",
        "#@markdown Ile próbek?\n",
        "ile = 16  #@param {type: \"slider\", min:1, max:30, step:1}\n",
        "\n",
        "#@markdown Prawdopodobieństwa $p_A$, $p_B$, $p_C$\n",
        "pA = 0.6  #@param {type: \"slider\", min:0, max:1, step:0.01}\n",
        "pB = 0.27  #@param {type: \"slider\", min:0, max:1, step:0.01}\n",
        "pC = 0  #@param {type: \"slider\", min:0, max:1, step:0.01}\n",
        "\n",
        "assert pA+pB+pC <= 1, \"Suma prawdopodobieństw nie może przekracać 1.0!\"\n",
        "\n",
        "# Funkcja losuje akurat tylko liczby, a chcemy wiadomości będące literami\n",
        "wartosci_zmiennej_losowej = np.array([0, 1, 2, 3])\n",
        "alfabet = {\n",
        "    0: \"A\",\n",
        "    1: \"B\",\n",
        "    2: \"C\",\n",
        "    3: \"D\"\n",
        "}\n",
        "\n",
        "pD = 1-pA-pB-pC\n",
        "rozklad_prawdopodobienstwa = np.array([pA, pB, pC, pD])\n",
        "custm = rv_discrete(values=(wartosci_zmiennej_losowej, rozklad_prawdopodobienstwa))\n",
        "\n",
        "probka_liczby = custm.rvs(size=ile)\n",
        "probka = [alfabet[key] for key in probka_liczby]\n",
        "\n",
        "# Dla danego rozkładu możemy automatycznie mieć wyliczoną entropię (w natach!)\n",
        "H = custm.entropy()/math.log(2)\n",
        "\n",
        "print(f'Rozkład prawdopodobieństwa: pA = {pA}, pB = {pB}, pC = {pC}, pD = {pD}; z entropią = {H} bit')\n",
        "print(probka)"
      ],
      "metadata": {
        "id": "VCJH09nl130q",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3641e31c-e91a-4ca2-cfdb-3bf530ef91aa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rozkład prawdopodobieństwa: pA = 0.6, pB = 0.27, pC = 0, pD = 0.13; z entropią = 1.3348450434671353 bit\n",
            "['B', 'A', 'A', 'A', 'A', 'D', 'B', 'A', 'A', 'A', 'A', 'A', 'A', 'A', 'B', 'B']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Wiadomo, że:\n",
        "\n",
        "$$ 0 \\leq H(p_1, p_2, p_3, \\dots, p_N) \\leq \\log{N} $$"
      ],
      "metadata": {
        "id": "LLpV72CwuLeQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Jakość generatora liczb losowych { run: \"auto\" }\n",
        "\n",
        "# Pomocnicza funkcja do obrazowania serii wylosowanych danych\n",
        "def licz_entr_cyfry(ser, printing: bool=True) -> None:\n",
        "  if printing:\n",
        "    print(ser)\n",
        "  else:\n",
        "    print(ser[:math.floor(len(ser)/10)])\n",
        "  prawd = []\n",
        "  cyfry = list(range(10))\n",
        "  for c in cyfry:\n",
        "    ile = [num.count(str(c)) for num in ser]\n",
        "    pr = sum(ile)/(2*len(ser))\n",
        "    prawd.append(pr)\n",
        "  H = entropy(prawd, base = podstawa[units])\n",
        "  print(f'Entropia H({prawd}) = {H} {units}, gdy max. H = {math.log2(len(prawd))}')\n",
        "\n",
        "\n",
        "#@markdown Przykład ewidentnie słabego generatora\n",
        "\n",
        "i = 2\n",
        "liczby = []\n",
        "\n",
        "#@markdown Można wybrać modulus do generatora\n",
        "modulus = \"101\" #@param [101, 107, 113, 131, 137, 149, 167, 173, 179, 191]\n",
        "while(len(liczby)<30):\n",
        "  i = (i^3+2*i^2+1) % int(modulus)\n",
        "  liczby.append(i)\n",
        "\n",
        "print(liczby)\n",
        "\n",
        "#@markdown od (w Pythonie lista indeksowana od 0)\n",
        "od = 0 #@param {type: \"slider\", min:0, max:29, step:1}\n",
        "#@markdown do\n",
        "do = 10 #@param {type: \"slider\", min:1, max:30, step:1}\n",
        "assert od < do, \"od-do ma mieć sens!\"\n",
        "\n",
        "seria_gen = [format(num, '0' + str(2) + 'd') for num in liczby[od:do]]\n",
        "licz_entr_cyfry(seria_gen)"
      ],
      "metadata": {
        "id": "gR2BIJIVooJT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a2ef9b79-97e5-40d4-e7d2-6c13a4e56cd5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[6, 10, 30, 34, 1, 7, 21, 59, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98, 65, 98]\n",
            "['06', '10', '30', '34', '01', '07', '21', '59', '65', '98']\n",
            "Entropia H([0.25, 0.15, 0.05, 0.1, 0.05, 0.1, 0.1, 0.05, 0.05, 0.1]) = 3.103701696057348 bit, gdy max. H = 3.321928094887362\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Generator `random` dający rozkład równomierny \n",
        "\n",
        "print(\"Seria liczb takiej samej długości jak poprzednio:\")\n",
        "random_numbers = [random.randint(0, 99) for _ in range(len(seria_gen)+1)]\n",
        "seria = [format(num, '0' + str(2) + 'd') for num in random_numbers]\n",
        "licz_entr_cyfry(seria)\n",
        "\n",
        "#@markdown Długość reprezentacji\n",
        "reprez = 2 #@param {type: \"slider\", min:2, max:5, step:1}\n",
        "\n",
        "print(\"Większa seria liczb:\")\n",
        "dlug = 10**reprez\n",
        "random_numbers = [random.randint(0, dlug-1) for _ in range(dlug)]\n",
        "seria = [format(num, '0' + str(reprez) + 'd') for num in random_numbers]\n",
        "licz_entr_cyfry(seria,False)"
      ],
      "metadata": {
        "id": "Ew0zBODiHHsn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "76fb2a2e-e82f-49c7-c3ae-e2313b42b601"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Seria liczb takiej samej długości jak poprzednio:\n",
            "['86', '21', '00', '93', '46', '78', '59', '60', '74', '08', '38']\n",
            "Entropia H([0.18181818181818182, 0.045454545454545456, 0.045454545454545456, 0.09090909090909091, 0.09090909090909091, 0.045454545454545456, 0.13636363636363635, 0.09090909090909091, 0.18181818181818182, 0.09090909090909091]) = 3.152391277629867 bit, gdy max. H = 3.321928094887362\n",
            "Większa seria liczb:\n",
            "['49', '87', '11', '27', '32', '49', '16', '60', '12', '98']\n",
            "Entropia H([0.155, 0.125, 0.115, 0.085, 0.125, 0.07, 0.1, 0.035, 0.095, 0.095]) = 3.243276443909177 bit, gdy max. H = 3.321928094887362\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Entropia źródła binarnego\n",
        "\n",
        "Dla źródła generującego tylko dwie wiadomości:\n",
        "\n",
        "$$p_A = p \\in [0,1], \\quad p_B = 1-p$$\n",
        "\n",
        "mamy entropię źródła binarnego oznaczaną standardowo $H(p)$:\n",
        "\n",
        "$$ H(p,1-p) = H(p) = -p\\lg{p} - (1-p)\\lg{(1-p)} $$"
      ],
      "metadata": {
        "id": "2l7CNuKjON0u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Nie musimy się męczyć wpisując wzory dla konkretnego rozkładu prawdopodobieństwa (w tym przypadku dwupunktowego)\n",
        "\n",
        "#@markdown Prawdopodobieństwo zajścia zdarzenia:\n",
        "p1 = 0.4  #@param {type: \"slider\", min:0, max:1, step:0.01}\n",
        "\n",
        "prawd = np.array([p1, 1-p1])\n",
        "\n",
        "units = \"bit\"\n",
        "H = entropy(prawd, base = podstawa[units])\n",
        "\n",
        "print(f'Entropia H({p1},{1-p1}) = {H} {units}')"
      ],
      "metadata": {
        "id": "iRTLgtppSDWD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a2e3152f-a9fa-44bd-d90e-e16d3a9235ee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Entropia H(0.4,0.6) = 0.9709505944546688 bit\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8c12HFWpNeoE",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        },
        "outputId": "0544d688-5b4f-4501-8c50-6c653abae233"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#@markdown Narysujemy wykres entropii źródła binarnego (rozkładu dwupunktowego)\n",
        "\n",
        "p = np.linspace(0.01, 0.99, 99)\n",
        "H = -p*np.log2(p) - (1-p)*np.log2(1-p)\n",
        "\n",
        "plt.title('Entropia źródła binarnego')\n",
        "plt.xlabel('$p$')\n",
        "plt.ylabel('$H(p)$')\n",
        "plt.plot(p, H)\n",
        "plt.grid('minor')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Entropia źródła ternarnego\n",
        "\n",
        "Dla źródła generującego trzy wiadomości:\n",
        "\n",
        "$$p_A = p_0, \\quad p_B = p_1, \\quad p_0+p_1 \\in [0,1], \\quad p_C = 1 - p_0 - p_1$$\n",
        "\n",
        "mamy entropię:\n",
        "\n",
        "$$ H(p_1,p_2,1-p_1-p_2) = -p_0\\lg{p_0} - p_1\\lg{p_1} - (1-p_0-p_1)\\lg{(1-p_0-p_1)}$$"
      ],
      "metadata": {
        "id": "uVtng0k6VL1l"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DdcFGNaJVL1m",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 577
        },
        "outputId": "05739ad4-49f4-4461-a767-365864a8ddae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Niedokładność, bo bierzemy prawdopodobieństwa co 0.01:\n",
            "Wartość maksymalna entropii ternarnej = 1.58481870497303, podczas gdy log(3) = 1.584962500721156\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<html>\n",
              "<head><meta charset=\"utf-8\" /></head>\n",
              "<body>\n",
              "    <div>            <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>                <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n",
              "        <script src=\"https://cdn.plot.ly/plotly-2.8.3.min.js\"></script>                <div id=\"f1699b5e-04c3-4cf5-bc32-e02de2201096\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>            <script type=\"text/javascript\">                                    window.PLOTLYENV=window.PLOTLYENV || {};                                    if (document.getElementById(\"f1699b5e-04c3-4cf5-bc32-e02de2201096\")) {                    Plotly.newPlot(                        \"f1699b5e-04c3-4cf5-bc32-e02de2201096\",                        [{\"hovertemplate\":\"p_0=%{x}<br>p_1=%{y}<br>H=%{z}<br>warto\\u015b\\u0107=%{marker.color}<extra></extra>\",\"legendgroup\":\"\",\"marker\":{\"color\":[0.16144054254182066,0.2219407328532109,0.2747433140607801,0.3224933618603243,0.3664462644533775,0.4073407454009861,0.44566434565824065,0.4817630671939111,0.5158951529482093,0.5482606267258944,0.5790188873238004,0.6082998482997923,0.6362113373725785,0.6628442049696137,0.6882759652992883,0.7125734617567773,0.7357948629753384,0.7579911871785623,0.7792074863105536,0.799483779737341,0.8188558002786313,0.8373555973394452,0.8550120296644869,0.8718511717297366,0.8878966517656206,0.9031699350756281,0.9176905631521233,0.9314763567502714,0.9445435893262523,0.9569071359152326,0.9685806015045626,0.9795764321680173,0.9899060116098558,0.9995797452811138,1.0086071338439866,1.016996837450545,1.0247567320521507,1.0318939587528015,1.0384149670533367,1.0443255526962936,1.0496308907073186,1.0543355641337426,1.0584435889005643,1.0619584351357512,1.064883045258098,1.0672198490700031,1.068970776052867,1.070137265023107,1.0707202712709103,1.0707202712709103,1.070137265023107,1.068970776052867,1.0672198490700031,1.064883045258098,1.0619584351357512,1.0584435889005643,1.0543355641337426,1.0496308907073186,1.0443255526962936,1.0384149670533367,1.0318939587528015,1.0247567320521507,1.016996837450545,1.0086071338439866,0.9995797452811138,0.9899060116098558,0.9795764321680173,0.9685806015045626,0.9569071359152326,0.9445435893262523,0.9314763567502714,0.9176905631521233,0.9031699350756281,0.8878966517656206,0.8718511717297366,0.8550120296644868,0.8373555973394452,0.8188558002786314,0.7994837797373409,0.7792074863105535,0.7579911871785623,0.7357948629753386,0.7125734617567773,0.6882759652992884,0.6628442049696138,0.6362113373725785,0.6082998482997923,0.5790188873238004,0.5482606267258944,0.5158951529482093,0.481763067193911,0.44566434565824037,0.4073407454009859,0.3664462644533776,0.3224933618603244,0.27474331406078023,0.22194073285321098,0.16144054254182072,0.2219407328532109,0.2822921890824148,0.3349444868386896,0.38254266919774566,0.4263420906998875,0.46708144015900344,0.5052482226498789,0.5411884030780175,0.5751601860848226,0.6073635558851669,0.6379578703362284,0.6670730006443817,0.6948167306993362,0.7212798655525016,0.7465398724154994,0.7706635459878962,0.793709004425621,0.8157272136052186,0.8367631711605321,0.8568568400846985,0.876043894656111,0.8943563234573944,0.9118229220097013,0.9284696990362244,0.944320214348631,0.9593958620195758,0.9737161093422639,0.987298699737119,1.0001598260107925,1.0123142790419384,1.023775575948086,1.0345560709981456,1.0446670519179397,1.0541188237496093,1.0629207820390392,1.0710814768156298,1.0786086685786527,1.0855093773010513,1.0917899252949617,1.097455974645788,1.1025125598074077,1.1069641158553871,1.1108145028142598,1.1140670264060408,1.1167244555078757,1.1187890365551307,1.1202625050807724,1.1211460945412075,1.1214405425418208,1.1211460945412075,1.1202625050807724,1.1187890365551307,1.1167244555078755,1.1140670264060408,1.1108145028142598,1.1069641158553871,1.1025125598074077,1.097455974645788,1.0917899252949617,1.0855093773010513,1.0786086685786527,1.0710814768156298,1.0629207820390392,1.0541188237496093,1.0446670519179397,1.0345560709981456,1.0237755759480858,1.0123142790419384,1.0001598260107925,0.987298699737119,0.9737161093422639,0.9593958620195758,0.944320214348631,0.9284696990362244,0.911822922009701,0.8943563234573944,0.876043894656111,0.8568568400846984,0.8367631711605321,0.8157272136052186,0.7937090044256209,0.7706635459878962,0.7465398724154995,0.7212798655525017,0.6948167306993362,0.6670730006443817,0.6379578703362284,0.6073635558851668,0.5751601860848224,0.5411884030780174,0.5052482226498787,0.4670814401590033,0.4263420906998871,0.3825426691977458,0.3349444868386897,0.28229218908241493,0.22194073285321095,0.2747433140607801,0.3349444868386896,0.3874449191544763,0.4348896204226209,0.47853391043627,0.5191164421290071,0.5571246835123506,0.5929045611929961,0.6267142402224604,0.6587536638759601,0.6891821476591831,0.7181295189495048,0.7457035162605894,0.7719948976470781,0.7970810816249836,0.8210288124165441,0.8438961558306426,0.8657340234335625,0.8865873564862551,0.9064960594405436,0.9254957457524254,0.943618340780974,0.9608925742945542,0.9773443865976,0.992997266270944,1.0078725331880818,1.021989577307477,1.0353660614000244,1.0480180941158634,1.059960378463827,1.0712063397565794,1.0817682362845948,1.0916572553648005,1.1008835969230273,1.109456546382489,1.117384538320497,1.1246752121052674,1.1313354605210413,1.1373714722228214,1.1427887687242424,1.1475922365074174,1.1517861547474482,1.155374219062915,1.1583595616341835,1.1607447679713685,1.1625318905614013,1.1637224595772382,1.164317490790483,1.164317490790483,1.1637224595772382,1.1625318905614013,1.1607447679713685,1.1583595616341835,1.155374219062915,1.1517861547474482,1.1475922365074174,1.1427887687242424,1.1373714722228214,1.1313354605210413,1.1246752121052674,1.117384538320497,1.109456546382489,1.1008835969230273,1.0916572553648005,1.0817682362845948,1.0712063397565794,1.059960378463827,1.0480180941158634,1.0353660614000244,1.021989577307477,1.0078725331880818,0.992997266270944,0.9773443865976,0.9608925742945542,0.943618340780974,0.9254957457524254,0.9064960594405435,0.8865873564862551,0.8657340234335625,0.8438961558306423,0.8210288124165438,0.7970810816249837,0.7719948976470781,0.7457035162605894,0.7181295189495048,0.6891821476591831,0.6587536638759601,0.6267142402224603,0.5929045611929958,0.5571246835123504,0.5191164421290069,0.4785339104362698,0.4348896204226205,0.3874449191544764,0.3349444868386897,0.2747433140607802,0.3224933618603243,0.38254266919774566,0.4348896204226209,0.48217919020227284,0.5256666624495431,0.5660906530347481,0.6039385916705985,0.6395563653739031,0.673202098256523,0.7050756912421843,0.7353364160075755,0.7641140545540274,0.7915162983984353,0.8176338568998315,0.8425440980969009,0.8663137138648349,0.8890007157022557,0.9106559588025546,0.9313243258853694,0.9510456605801273,0.9698555131192744,0.9877857431090965,1.0048650118991993,1.0211191885631823,1.036571687482719,1.0512437511965642,1.0651546890136516,1.078322079548365,1.0907619435810212,1.1024888923155898,1.113516255086298,1.1238561897747248,1.1335197785814877,1.142517111309747,1.1508573579306258,1.1585488318903812,1.1655990453685268,1.1720147574921704,1.177802016344545,1.1829661954675215,1.1875120254427476,1.1914436210393724,1.1947645043343271,1.197477624140946,1.1995853720209084,1.2010895951011364,1.201991605869783,1.2022921890824148,1.201991605869783,1.2010895951011364,1.1995853720209084,1.197477624140946,1.1947645043343271,1.1914436210393726,1.1875120254427476,1.1829661954675215,1.177802016344545,1.1720147574921704,1.1655990453685268,1.1585488318903812,1.1508573579306258,1.1425171113097465,1.1335197785814877,1.1238561897747248,1.113516255086298,1.1024888923155898,1.0907619435810212,1.0783220795483646,1.0651546890136516,1.0512437511965642,1.036571687482719,1.0211191885631823,1.004865011899199,0.9877857431090965,0.9698555131192744,0.9510456605801273,0.9313243258853694,0.9106559588025546,0.8890007157022556,0.8663137138648348,0.8425440980969007,0.8176338568998315,0.7915162983984353,0.7641140545540274,0.7353364160075755,0.7050756912421842,0.6732020982565229,0.639556365373903,0.6039385916705984,0.5660906530347479,0.5256666624495427,0.48217919020227257,0.4348896204226204,0.38254266919774566,0.32249336186032435,0.3664462644533775,0.4263420906998875,0.47853391043627,0.5256666624495431,0.5689955935892813,0.6092592814269934,0.6469451160855029,0.682398943641963,0.7158788458567442,0.747584679824574,0.7776756718460952,0.8062815569258702,0.8335099778851861,0.8594515936057461,0.884183719779189,0.9077729939704454,0.9302773713052452,0.9517476484356664,0.9722286472589505,0.9917601481809736,1.010377635681394,1.0281129009477386,1.044994534098779,1.061048330008955,1.076297625725199,1.0907635831367362,1.1044654273959895,1.11742064924752,1.1296451776667815,1.1411535278793055,1.1519589288104253,1.1620734332254092,1.1715080132022042,1.1802726430918806,1.1883763717345073,1.195827385387638,1.2026330625736534,1.2088000218478914,1.2143341633218216,1.219240704636849,1.2235242119686693,1.2271886265447818,1.2302372870750866,1.2326729484244832,1.2344977967946407,1.2357134616276786,1.2363210243957121,1.2363210243957121,1.2357134616276786,1.2344977967946407,1.2326729484244832,1.2302372870750866,1.2271886265447818,1.2235242119686693,1.219240704636849,1.2143341633218214,1.2088000218478914,1.2026330625736532,1.195827385387638,1.1883763717345073,1.1802726430918806,1.1715080132022044,1.1620734332254092,1.1519589288104253,1.1411535278793055,1.1296451776667815,1.1174206492475198,1.1044654273959893,1.0907635831367362,1.0762976257251988,1.061048330008955,1.0449945340987787,1.0281129009477388,1.0103776356813943,0.9917601481809734,0.9722286472589503,0.9517476484356664,0.9302773713052451,0.9077729939704452,0.8841837197791889,0.8594515936057457,0.8335099778851861,0.8062815569258703,0.7776756718460952,0.7475846798245738,0.7158788458567442,0.6823989436419629,0.6469451160855026,0.609259281426993,0.5689955935892811,0.5256666624495427,0.47853391043626975,0.42634209069988693,0.3664462644533776,0.4073407454009861,0.46708144015900344,0.5191164421290071,0.5660906530347481,0.6092592814269934,0.6493608652873644,0.6868827537990294,0.7221707506876511,0.7554828938846008,0.7870189951085604,0.8169382336634051,0.8453702958580881,0.8724227740365673,0.898186274733501,0.9227380593302662,0.9461447090189017,0.9684641203838238,0.9897470292547143,1.0100381943052634,1.02937733018856,1.047799852965503,1.065337482592785,1.0820187349900183,1.0978693276969014,1.1129125171108378,1.1271693809645407,1.1406590565406114,1.153398942778747,1.165404872675964,1.1766912610488998,1.1872712317065768,1.1971567272915926,1.206358604429805,1.214886716341229,1.222749984677231,1.2299564620382313,1.2365133863748412,1.2424272282706346,1.2477037319366158,1.2523479506082373,1.2563642769195456,1.259756468731008,1.2625276708040905,1.264680432643682,1.2662167227666499,1.2671379395990745,1.2674449191544763,1.2671379395990745,1.2662167227666496,1.2646804326436822,1.2625276708040905,1.2597564687310083,1.2563642769195456,1.2523479506082373,1.2477037319366158,1.2424272282706346,1.236513386374841,1.229956462038231,1.2227499846772307,1.2148867163412287,1.206358604429805,1.1971567272915926,1.1872712317065768,1.1766912610488998,1.165404872675964,1.1533989427787468,1.1406590565406112,1.1271693809645402,1.1129125171108378,1.0978693276969014,1.082018734990018,1.065337482592785,1.0477998529655033,1.02937733018856,1.0100381943052634,0.989747029254714,0.9684641203838236,0.9461447090189015,0.9227380593302662,0.8981862747335008,0.8724227740365671,0.8453702958580881,0.8169382336634051,0.7870189951085604,0.7554828938846007,0.7221707506876508,0.6868827537990292,0.6493608652873641,0.6092592814269928,0.5660906530347478,0.5191164421290065,0.46708144015900294,0.40734074540098547,0.44566434565824065,0.5052482226498789,0.5571246835123506,0.6039385916705985,0.6469451160855029,0.6868827537990294,0.7242388116428561,0.759359049513646,0.7925014599667256,0.8238658077240087,0.853611223393761,0.8818673428076076,0.9087417059624606,0.9343248650827167,0.9586940251768611,0.9819157088956185,1.0040477520010098,1.0251408270991655,1.0452396271109883,1.0643837982708073,1.0826086854086878,1.099945934282163,1.1164239834761032,1.1320684698806784,1.1469025657367806,1.1609472609073008,1.1742216008699766,1.1867428885860678,1.1985268566436964,1.2095878147431895,1.2199387765708984,1.2295915693173318,1.2385569284772917,1.2468445800820909,1.2544633121259625,1.2614210366375573,1.2677248435957227,1.2733810476835672,1.2783952287061426,1.2827722663572518,1.2865163699039104,1.2896311032581502,1.292119405821428,1.2939836094138297,1.2952254515361838,1.295846085155977,1.295846085155977,1.2952254515361838,1.2939836094138295,1.292119405821428,1.2896311032581504,1.2865163699039102,1.2827722663572523,1.2783952287061426,1.2733810476835674,1.2677248435957227,1.2614210366375573,1.2544633121259623,1.2468445800820906,1.2385569284772917,1.2295915693173318,1.2199387765708984,1.2095878147431895,1.1985268566436964,1.1867428885860678,1.1742216008699766,1.1609472609073008,1.1469025657367804,1.1320684698806784,1.116423983476103,1.0999459342821627,1.0826086854086878,1.0643837982708073,1.0452396271109883,1.0251408270991653,1.0040477520010098,0.9819157088956183,0.9586940251768609,0.9343248650827164,0.9087417059624604,0.8818673428076073,0.853611223393761,0.8238658077240087,0.7925014599667256,0.7593590495136459,0.7242388116428558,0.6868827537990292,0.6469451160855024,0.6039385916705982,0.5571246835123501,0.5052482226498783,0.4456643456582399,0.4817630671939111,0.5411884030780175,0.5929045611929961,0.6395563653739031,0.682398943641963,0.722170750687651,0.7593590495136459,0.7943095546405661,0.827280211626969,0.8584707364991596,0.8880402093880759,0.9161182137782962,0.9428122353564714,0.9682127699741065,0.9923969640983729,1.0154312795576,1.0373734888902564,1.0582741989496858,1.078178034238031,1.0971245697587875,1.1151490761428609,1.1322831218130427,1.1485550647046752,1.1639904575514164,1.178612384724336,1.1924417442814617,1.205497485722093,1.2177968115985958,1.2293553493827813,1.2401872986523066,1.2503055576414326,1.2597218324096136,1.2684467312629486,1.2764898465756176,1.2838598257700837,1.290564432903234,1.2966106020534505,1.3020044834978894,1.3067514834999523,1.3108562983864118,1.3143229434758479,1.317154777320283,1.3193545216363707,1.320924277228159,1.3218655361378815,1.322179190202273,1.3218655361378815,1.320924277228159,1.3193545216363705,1.317154777320283,1.3143229434758479,1.3108562983864118,1.3067514834999523,1.3020044834978894,1.2966106020534507,1.290564432903234,1.2838598257700837,1.2764898465756178,1.2684467312629488,1.2597218324096136,1.2503055576414328,1.2401872986523066,1.2293553493827813,1.2177968115985955,1.2054974857220928,1.1924417442814614,1.178612384724336,1.1639904575514164,1.1485550647046752,1.1322831218130431,1.1151490761428609,1.0971245697587875,1.078178034238031,1.0582741989496858,1.0373734888902564,1.0154312795575997,0.9923969640983731,0.9682127699741065,0.9428122353564714,0.916118213778296,0.8880402093880759,0.8584707364991602,0.8272802116269692,0.7943095546405663,0.7593590495136462,0.7221707506876514,0.6823989436419632,0.6395563653739031,0.5929045611929962,0.5411884030780175,0.4817630671939111,0.5158951529482093,0.5751601860848226,0.6267142402224604,0.673202098256523,0.7158788458567442,0.7554828938846007,0.7925014599667256,0.827280211626969,0.8600770457282798,0.8910916278196342,0.9204829856849239,0.9483806484984665,0.9748920455740209,1.0001076142217782,1.0241044400865138,1.0469489217730061,1.068698766066936,1.0894045114028876,1.1091107110521705,1.12785686581912,1.1456781689999003,1.1626061083677746,1.178668957701573,1.1938921818651316,1.208298773424656,1.2219095344597373,1.23474331406078,1.2468172096638401,1.258146738618058,1.2687459850490004,1.278627726059874,1.2878035405214303,1.2962839030826354,1.3040782655458985,1.31119512736192,1.3176420966871214,1.3234259431939321,1.3285526436178587,1.333027420855272,1.336854777284509,1.34003852286414,1.3425817984613853,1.3444870947768595,1.3457562671560164,1.346390546510337,1.346390546510337,1.3457562671560164,1.3444870947768595,1.3425817984613853,1.34003852286414,1.336854777284509,1.333027420855272,1.3285526436178587,1.3234259431939321,1.3176420966871216,1.31119512736192,1.3040782655458987,1.2962839030826354,1.2878035405214303,1.2786277260598742,1.2687459850490004,1.258146738618058,1.2468172096638401,1.23474331406078,1.2219095344597373,1.208298773424656,1.1938921818651316,1.178668957701573,1.1626061083677748,1.1456781689999007,1.1278568658191201,1.1091107110521705,1.0894045114028879,1.068698766066936,1.0469489217730061,1.0241044400865138,1.000107614221778,0.9748920455740209,0.9483806484984665,0.9204829856849239,0.8910916278196342,0.8600770457282801,0.8272802116269693,0.7925014599667257,0.755482893884601,0.7158788458567444,0.6732020982565231,0.6267142402224604,0.5751601860848226,0.5158951529482094,0.5482606267258944,0.6073635558851669,0.6587536638759601,0.7050756912421843,0.747584679824574,0.7870189951085604,0.8238658077240086,0.8584707364991596,0.8910916278196342,0.9219280948873624,0.9511391111759744,0.9788541494868961,1.0051805805925724,1.0302087809807992,1.0540157730728,1.0766678897205657,1.098222769291018,1.1187308789879074,1.1382366978833829,1.1567796494470395,1.1743948463255123,1.1911136921355523,1.2069643727861679,1.2219722613363317,1.2361602543738117,1.2495490535693046,1.2621574028969047,1.2740022896699967,1.285099115785632,1.2954618442383217,1.3051031249425709,1.3140344031119968,1.322266012823796,1.3298072579086146,1.3366664819166876,1.342851128598483,1.3483677940847816,1.353222271744058,1.357419590524249,1.3609640474436813,1.363859234776122,1.3661080623727542,1.3677127754755969,1.3686749682993518,1.3689955935892812,1.3686749682993518,1.3677127754755967,1.3661080623727542,1.3638592347761223,1.3609640474436813,1.357419590524249,1.353222271744058,1.3483677940847816,1.342851128598483,1.3366664819166876,1.3298072579086149,1.322266012823796,1.3140344031119968,1.3051031249425709,1.295461844238322,1.285099115785632,1.2740022896699967,1.2621574028969045,1.2495490535693046,1.2361602543738117,1.2219722613363317,1.2069643727861679,1.1911136921355523,1.1743948463255123,1.1567796494470397,1.138236697883383,1.1187308789879076,1.0982227692910183,1.0766678897205657,1.0540157730728,1.030208780980799,1.0051805805925724,0.9788541494868961,0.9511391111759744,0.9219280948873623,0.8910916278196342,0.8584707364991602,0.8238658077240087,0.7870189951085607,0.747584679824574,0.7050756912421844,0.6587536638759603,0.6073635558851669,0.5482606267258945,0.5790188873238004,0.6379578703362284,0.6891821476591831,0.7353364160075755,0.7776756718460952,0.8169382336634051,0.853611223393761,0.8880402093880759,0.9204829856849239,0.9511391111759744,0.9801675029619655,1.007697575303009,1.0338366381491553,1.0586750047646467,1.0822896318179214,1.1047467837422096,1.1261040276735996,1.1464117566166816,1.1657143723088643,1.1840512175702131,1.2014573208908514,1.2179639980177093,1.2335993430549297,1.2483886330830491,1.262354664280941,1.2755180332029905,1.2878973737006227,1.2995095576351323,1.310369865772515,1.32049213391858,1.3298888783306988,1.3385714036507192,1.346549895984074,1.3538335032609439,1.3604304046256108,1.366347870286894,1.3715923130085426,1.3761693322105968,1.380083751480983,1.383339650153225,1.3859403894850528,1.387888633869053,1.389186367416494,1.3898349061758577,1.3898349061758577,1.389186367416494,1.3878886338690533,1.3859403894850528,1.3833396501532251,1.380083751480983,1.3761693322105968,1.3715923130085426,1.366347870286894,1.360430404625611,1.3538335032609439,1.346549895984074,1.3385714036507192,1.3298888783306988,1.32049213391858,1.310369865772515,1.2995095576351323,1.287897373700623,1.2755180332029907,1.262354664280941,1.2483886330830491,1.2335993430549297,1.217963998017709,1.2014573208908517,1.1840512175702131,1.1657143723088643,1.1464117566166816,1.1261040276735996,1.1047467837422096,1.0822896318179214,1.0586750047646467,1.033836638149155,1.007697575303009,0.9801675029619655,0.9511391111759744,0.9204829856849239,0.8880402093880759,0.8536112233937613,0.8169382336634052,0.7776756718460954,0.7353364160075756,0.6891821476591833,0.6379578703362285,0.5790188873238005,0.6082998482997923,0.6670730006443817,0.7181295189495048,0.7641140545540274,0.8062815569258702,0.8453702958580878,0.8818673428076076,0.9161182137782962,0.9483806484984665,0.9788541494868961,1.007697575303009,1.0350402793845224,1.0609895084579333,1.0856355100346986,1.1090551723644957,1.1313146886497212,1.152471551827304,1.1725760775670933,1.191672586956968,1.2098003386604825,1.2269942732979389,1.2432856148114013,1.2587023613265775,1.2732696895151085,1.2870102904395573,1.2999446505316392,1.312091288190689,1.3234669541469457,1.3340868019777037,1.3439645338316386,1.353112525394352,1.3615419333359278,1.3692627878613335,1.3762840724947976,1.3826137928389521,1.3882590357355857,1.3932260200000117,1.3975201396922612,1.401146000715457,1.404107451387086,1.4064076075062821,1.4080488723348807,1.40903295181793,1.4093608652873644,1.4090329518179303,1.4080488723348807,1.4064076075062821,1.404107451387086,1.401146000715457,1.397520139692261,1.393226020000012,1.3882590357355855,1.3826137928389521,1.3762840724947976,1.3692627878613335,1.3615419333359278,1.353112525394352,1.3439645338316386,1.3340868019777037,1.323466954146946,1.3120912881906888,1.2999446505316394,1.2870102904395573,1.2732696895151085,1.2587023613265775,1.2432856148114013,1.2269942732979386,1.2098003386604825,1.1916725869569682,1.1725760775670933,1.152471551827304,1.1313146886497212,1.1090551723644957,1.0856355100346986,1.0609895084579333,1.0350402793845224,1.0076975753030093,0.9788541494868959,0.9483806484984665,0.9161182137782958,0.8818673428076075,0.8453702958580881,0.8062815569258706,0.7641140545540274,0.7181295189495049,0.6670730006443818,0.6082998482997923,0.6362113373725785,0.6948167306993362,0.7457035162605894,0.7915162983984353,0.8335099778851861,0.8724227740365672,0.9087417059624605,0.9428122353564714,0.9748920455740209,1.0051805805925724,1.0338366381491553,1.0609895084579333,1.086746372492618,1.1111974093459056,1.13441943603664,1.1564785715680586,1.1774322315423484,1.1973306509798298,1.2162180668118707,1.2341336498322029,1.2511122488562638,1.2671849918476819,1.2823797765232696,1.2967216744383578,1.310233266532839,1.3229349237863381,1.3348450434671353,1.3459802491167672,1.3563555606553948,1.3659845396599244,1.3748794138441929,1.38305118397782,1.39050971585982,1.3972638194727718,1.4033213170522767,1.4086891014916876,1.413373186246309,1.4173787476913684,1.420710160713951,1.4233710281729481,1.4253642047367425,1.4266918155009498,1.42735526969407,1.42735526969407,1.4266918155009498,1.4253642047367425,1.4233710281729481,1.420710160713951,1.4173787476913682,1.413373186246309,1.4086891014916876,1.4033213170522765,1.3972638194727718,1.39050971585982,1.38305118397782,1.3748794138441929,1.3659845396599244,1.3563555606553952,1.3459802491167672,1.334845043467135,1.3229349237863381,1.310233266532839,1.2967216744383578,1.2823797765232696,1.2671849918476819,1.2511122488562638,1.2341336498322026,1.2162180668118705,1.1973306509798298,1.1774322315423487,1.1564785715680586,1.1344194360366402,1.1111974093459056,1.086746372492618,1.0609895084579333,1.033836638149155,1.0051805805925724,0.9748920455740208,0.9428122353564714,0.9087417059624604,0.8724227740365671,0.8335099778851861,0.7915162983984353,0.7457035162605896,0.6948167306993364,0.6362113373725785,0.6628442049696137,0.7212798655525016,0.7719948976470781,0.8176338568998315,0.8594515936057461,0.8981862747335008,0.9343248650827166,0.9682127699741065,1.0001076142217782,1.0302087809807992,1.0586750047646467,1.0856355100346986,1.1111974093459056,1.1354508105601309,1.1584724564970583,1.1803283888251839,1.201075942497166,1.2207652683768133,1.2394405155256714,1.2571407629326086,1.273900763434625,1.289751544586455,1.3047208989886,1.3188337880737202,1.3321126773296184,1.3445778166048652,1.3562474759790373,1.3671381453365394,1.3772647040257617,1.3866405656518463,1.3952778020281662,1.4031872495183872,1.410378600379875,1.4168604812281769,1.4226405203504593,1.4277254052800656,1.4321209317874966,1.4358320452319429,1.438862875041894,1.4412167629454893,1.4428962854448923,1.4439032709191701,1.4442388116428562,1.4439032709191701,1.4428962854448923,1.4412167629454893,1.438862875041894,1.4358320452319429,1.4321209317874968,1.4277254052800652,1.4226405203504593,1.4168604812281769,1.410378600379875,1.4031872495183872,1.3952778020281662,1.3866405656518463,1.3772647040257617,1.3671381453365394,1.3562474759790373,1.3445778166048652,1.3321126773296184,1.3188337880737202,1.3047208989885999,1.289751544586455,1.2739007634346253,1.2571407629326086,1.2394405155256711,1.2207652683768133,1.201075942497166,1.1803283888251839,1.1584724564970583,1.1354508105601309,1.1111974093459056,1.0856355100346986,1.058675004764647,1.030208780980799,1.000107614221778,0.9682127699741063,0.9343248650827164,0.8981862747335008,0.8594515936057457,0.8176338568998317,0.7719948976470782,0.7212798655525017,0.6628442049696138,0.6882759652992883,0.7465398724154994,0.7970810816249836,0.8425440980969009,0.884183719779189,0.9227380593302662,0.9586940251768609,0.9923969640983729,1.0241044400865138,1.0540157730728,1.0822896318179214,1.1090551723644957,1.13441943603664,1.1584724564970583,1.1812908992306925,1.2029407252565103,1.2234791853706584,1.2429563425671233,1.2614162541025862,1.2788979029874792,1.2954359416499073,1.311061292528294,1.3258016381004714,1.3396818243470088,1.3527241956246545,1.3649488745932767,1.3763739976753187,1.387015914183415,1.3968893554941928,1.4060075793123286,1.4143824930452427,1.4220247595149513,1.4289438876117893,1.4351483100028688,1.4406454496153465,1.4454417762977625,1.4495428548045806,1.452953385036395,1.4556772352909442,1.4577174691301484,1.4590763663396218,1.4597554383444657,1.4597554383444657,1.4590763663396218,1.4577174691301484,1.4556772352909442,1.4529533850363947,1.4495428548045806,1.4454417762977625,1.4406454496153465,1.4351483100028688,1.4289438876117895,1.422024759514951,1.4143824930452424,1.4060075793123286,1.3968893554941928,1.387015914183415,1.3763739976753187,1.3649488745932767,1.3527241956246545,1.3396818243470088,1.3258016381004714,1.311061292528294,1.2954359416499073,1.278897902987479,1.2614162541025862,1.242956342567123,1.2234791853706584,1.2029407252565103,1.1812908992306927,1.1584724564970583,1.13441943603664,1.1090551723644957,1.0822896318179214,1.0540157730728,1.0241044400865136,0.9923969640983727,0.9586940251768608,0.922738059330266,0.8841837197791886,0.8425440980969006,0.7970810816249837,0.7465398724154995,0.6882759652992884,0.7125734617567773,0.7706635459878962,0.8210288124165441,0.8663137138648349,0.9077729939704454,0.9461447090189017,0.9819157088956184,1.0154312795576,1.0469489217730061,1.0766678897205657,1.1047467837422096,1.1313146886497212,1.1564785715680586,1.1803283888251839,1.2029407252565103,1.224381457724494,1.2447077491554597,1.2639695707385294,1.2822108837519481,1.2994705707972523,1.3157831791862378,1.3311795212346567,1.3456871639682513,1.359330832236536,1.3721327432075574,1.384112885884049,1.3952892561166856,1.4056780552463375,1.4152938587491661,1.4241497599238961,1.4322574926362979,1.4396275363413569,1.4462692059809723,1.452190728862247,1.4573993102275347,1.4619011889093374,1.465701684203524,1.4688052348799365,1.4712154310700942,1.4729350396193692,1.4739660233594083,1.4743095546405662,1.4739660233594083,1.4729350396193692,1.4712154310700942,1.4688052348799365,1.465701684203524,1.4619011889093374,1.4573993102275347,1.452190728862247,1.4462692059809723,1.4396275363413569,1.4322574926362979,1.4241497599238961,1.4152938587491661,1.405678055246337,1.3952892561166856,1.384112885884049,1.3721327432075572,1.359330832236536,1.3456871639682513,1.3311795212346567,1.3157831791862378,1.299470570797252,1.282210883751948,1.263969570738529,1.2447077491554597,1.2243814577244938,1.2029407252565103,1.1803283888251839,1.1564785715680586,1.1313146886497212,1.1047467837422094,1.0766678897205657,1.046948921773006,1.0154312795575997,0.9819157088956184,0.9461447090189015,0.9077729939704452,0.8663137138648346,0.8210288124165438,0.7706635459878962,0.7125734617567773,0.7357948629753384,0.793709004425621,0.8438961558306426,0.8890007157022557,0.9302773713052452,0.9684641203838236,1.0040477520010098,1.0373734888902564,1.068698766066936,1.098222769291018,1.1261040276735996,1.152471551827304,1.1774322315423484,1.201075942497166,1.2234791853706584,1.2447077491554597,1.2648187049730302,1.2838619280340555,1.3018812792078858,1.3189155359797473,1.3349991355387647,1.3501627747486011,1.364433899503943,1.377837107465603,1.3903944821444942,1.4021258719715803,1.4130491248257724,1.4231802861474752,1.432533767006898,1.441122487161116,1.4489579971088675,1.4560505823567045,1.4624093524865152,1.4680423171205994,1.472956450485274,1.477157745954445,1.4806512616932297,1.4834411583052511,1.4855307292054793,1.48692242428532,1.4876178673016733,1.4876178673016733,1.48692242428532,1.4855307292054793,1.4834411583052507,1.4806512616932297,1.477157745954445,1.472956450485274,1.4680423171205994,1.4624093524865152,1.4560505823567045,1.4489579971088677,1.441122487161116,1.432533767006898,1.423180286147475,1.4130491248257722,1.4021258719715803,1.390394482144494,1.3778371074656033,1.364433899503943,1.3501627747486011,1.3349991355387647,1.318915535979747,1.3018812792078855,1.283861928034055,1.26481870497303,1.2447077491554595,1.2234791853706584,1.2010759424971658,1.1774322315423484,1.152471551827304,1.1261040276735996,1.098222769291018,1.068698766066936,1.0373734888902564,1.0040477520010098,0.9684641203838235,0.9302773713052449,0.8890007157022554,0.8438961558306421,0.7937090044256205,0.7357948629753386,0.7579911871785623,0.8157272136052186,0.8657340234335625,0.9106559588025546,0.9517476484356664,0.9897470292547143,1.0251408270991655,1.0582741989496856,1.0894045114028876,1.1187308789879071,1.1464117566166814,1.172576077567093,1.1973306509798298,1.2207652683768133,1.242956342567123,1.263969570738529,1.283861928034055,1.302683189255492,1.3204771101558799,1.3372823580977733,1.3531332548182082,1.3680603760497918,1.3820910404985092,1.3952497121680392,1.4075583339975246,1.4190366064461661,1.4297022214924093,1.4395710601707064,1.448657360009617,1.4569738573991848,1.4645319088897144,1.4713415946277462,1.4774118065103667,1.482750323143838,1.4873638732958807,1.4912581892096501,1.4944380508840434,1.4969073222061353,1.4986689796369295,1.4997251339930844,1.50007704572828,1.4997251339930844,1.4986689796369295,1.496907322206135,1.4944380508840434,1.4912581892096501,1.4873638732958805,1.482750323143838,1.477411806510367,1.4713415946277462,1.4645319088897144,1.456973857399185,1.4486573600096169,1.4395710601707064,1.429702221492409,1.4190366064461661,1.4075583339975246,1.3952497121680394,1.3820910404985092,1.3680603760497922,1.3531332548182082,1.3372823580977735,1.3204771101558799,1.3026831892554922,1.2838619280340555,1.2639695707385292,1.242956342567123,1.220765268376813,1.19733065097983,1.1725760775670935,1.1464117566166816,1.1187308789879076,1.089404511402888,1.0582741989496858,1.0251408270991655,0.9897470292547143,0.9517476484356664,0.9106559588025548,0.8657340234335625,0.8157272136052186,0.7579911871785625,0.7792074863105536,0.8367631711605321,0.8865873564862551,0.9313243258853694,0.9722286472589505,1.0100381943052634,1.0452396271109883,1.078178034238031,1.1091107110521703,1.1382366978833829,1.165714372308864,1.191672586956968,1.2162180668118707,1.2394405155256714,1.2614162541025862,1.2822108837519481,1.3018812792078858,1.3204771101558799,1.3380420222262994,1.3546145673296104,1.3702289460717927,1.3849156069967516,1.3987017351533386,1.4116116539734633,1.423667158424504,1.4348877930651966,1.4452910854680339,1.4548927431258187,1.4637068202000798,1.471745859132425,1.4790210111131499,1.4855421386039913,1.491317902485999,1.4963558359068385,1.5006624065034793,1.5042430683528574,1.5071023047373213,1.509243662589979,1.5106697792970871,1.511382402372084,1.511382402372084,1.5106697792970871,1.509243662589979,1.5071023047373213,1.5042430683528574,1.5006624065034793,1.4963558359068385,1.491317902485999,1.4855421386039913,1.4790210111131499,1.471745859132425,1.4637068202000796,1.454892743125819,1.4452910854680343,1.4348877930651969,1.423667158424504,1.4116116539734636,1.3987017351533386,1.3849156069967516,1.370228946071793,1.3546145673296104,1.3380420222262996,1.3204771101558799,1.3018812792078858,1.2822108837519481,1.2614162541025864,1.2394405155256714,1.2162180668118707,1.1916725869569682,1.1657143723088643,1.138236697883383,1.1091107110521707,1.0781780342380312,1.0452396271109885,1.0100381943052634,0.9722286472589505,0.9313243258853695,0.8865873564862552,0.8367631711605322,0.7792074863105536,0.799483779737341,0.8568568400846985,0.9064960594405436,0.9510456605801273,0.9917601481809736,1.02937733018856,1.0643837982708073,1.0971245697587872,1.1278568658191197,1.1567796494470395,1.1840512175702127,1.2098003386604825,1.2341336498322029,1.2571407629326083,1.278897902987479,1.2994705707972523,1.3189155359797473,1.3372823580977733,1.3546145673296104,1.3709505944546685,1.386324512890226,1.400766637523055,1.4143040128302367,1.4269608142719166,1.4387586809150084,1.4497169929122953,1.4598531042946201,1.469182539187755,1.4777191578047935,1.4854752972273346,1.492461890960869,1.4986885704510973,1.5041637511204733,1.5088947049859112,1.5128876215181606,1.516147658077609,1.5186789809926386,1.5204847981216105,1.5215673835475612,1.5219280948873626,1.5215673835475612,1.5204847981216105,1.5186789809926386,1.516147658077609,1.5128876215181606,1.508894704985911,1.5041637511204733,1.4986885704510973,1.492461890960869,1.4854752972273346,1.4777191578047935,1.469182539187755,1.4598531042946206,1.4497169929122953,1.4387586809150086,1.4269608142719166,1.4143040128302367,1.400766637523055,1.3863245128902264,1.370950594454669,1.3546145673296104,1.3372823580977735,1.3189155359797473,1.2994705707972523,1.2788979029874792,1.2571407629326086,1.2341336498322026,1.2098003386604828,1.1840512175702131,1.1567796494470397,1.1278568658191201,1.0971245697587877,1.0643837982708075,1.0293773301885603,0.9917601481809736,0.9510456605801274,0.9064960594405436,0.8568568400846988,0.799483779737341,0.8188558002786313,0.876043894656111,0.9254957457524254,0.9698555131192744,1.010377635681394,1.047799852965503,1.0826086854086878,1.1151490761428609,1.1456781689999003,1.1743948463255123,1.2014573208908514,1.2269942732979389,1.2511122488562638,1.273900763434625,1.2954359416499073,1.3157831791862378,1.3349991355387647,1.3531332548182082,1.3702289460717927,1.386324512890226,1.4014538950336535,1.4156472668170768,1.4289315247458139,1.441330688379545,1.4528662323792307,1.4635573633560055,1.4734212519736805,1.4824732284095934,1.490726947516827,1.4981945286921776,1.5048866744250988,1.5108127707026957,1.5159809718166695,1.5203982716177162,1.524070562860036,1.5270026859500505,1.5291984681413944,1.5306607539892083,1.5313914276799632,1.5313914276799632,1.5306607539892083,1.5291984681413944,1.5270026859500505,1.524070562860036,1.5203982716177162,1.5159809718166695,1.5108127707026957,1.5048866744250988,1.4981945286921776,1.4907269475168268,1.4824732284095934,1.4734212519736805,1.4635573633560055,1.4528662323792307,1.441330688379545,1.4289315247458139,1.4156472668170772,1.401453895033654,1.3863245128902264,1.370228946071793,1.3531332548182082,1.3349991355387647,1.3157831791862378,1.2954359416499073,1.2739007634346253,1.2511122488562638,1.2269942732979386,1.2014573208908514,1.1743948463255125,1.1456781689999007,1.115149076142861,1.082608685408688,1.0477998529655033,1.0103776356813943,0.9698555131192745,0.9254957457524255,0.8760438946561112,0.8188558002786314,0.8373555973394452,0.8943563234573944,0.943618340780974,0.9877857431090965,1.0281129009477386,1.065337482592785,1.099945934282163,1.1322831218130427,1.1626061083677746,1.1911136921355523,1.2179639980177093,1.2432856148114013,1.2671849918476819,1.289751544586455,1.311061292528294,1.3311795212346567,1.3501627747486011,1.3680603760497918,1.3849156069967516,1.400766637523055,1.4156472668170768,1.4295875212220555,1.4426141413428435,1.4547509823331688,1.4660193453123427,1.4764382535244673,1.48602468368492,1.4947937606110278,1.5027589214710713,1.5099320546458088,1.5163236171660983,1.5219427338882936,1.526797280937876,1.530893955448993,1.5342383332218792,1.5368349155882077,1.5386871664983937,1.539797540611012,1.5401675029619655,1.539797540611012,1.5386871664983937,1.5368349155882077,1.534238333221879,1.530893955448993,1.526797280937876,1.5219427338882936,1.5163236171660983,1.5099320546458088,1.5027589214710713,1.4947937606110278,1.48602468368492,1.4764382535244673,1.4660193453123427,1.4547509823331688,1.4426141413428435,1.4295875212220555,1.4156472668170772,1.4007666375230552,1.3849156069967519,1.368060376049792,1.3501627747486011,1.3311795212346567,1.3110612925282943,1.2897515445864547,1.2671849918476819,1.243285614811401,1.2179639980177093,1.1911136921355523,1.1626061083677748,1.1322831218130431,1.099945934282163,1.0653374825927853,1.0281129009477388,0.9877857431090967,0.9436183407809741,0.8943563234573946,0.8373555973394453,0.8550120296644869,0.9118229220097013,0.9608925742945542,1.0048650118991993,1.044994534098779,1.0820187349900183,1.1164239834761032,1.1485550647046752,1.178668957701573,1.2069643727861679,1.2335993430549297,1.2587023613265775,1.2823797765232696,1.3047208989886,1.3258016381004714,1.3456871639682513,1.364433899503943,1.3820910404985092,1.3987017351533386,1.4143040128302367,1.4289315247458139,1.4426141413428435,1.4553784388202258,1.467248098790039,1.4782442390045625,1.4883856887594653,1.4976892194101132,1.5061697380890307,1.5138404509484609,1.5207130009105667,1.5267975838754546,1.5321030465332584,1.5366369682929113,1.5404057293345943,1.5434145663837942,1.5456676174689654,1.5471679566439553,1.5479176194167725,1.5479176194167725,1.5471679566439556,1.545667617468965,1.5434145663837942,1.5404057293345943,1.5366369682929113,1.5321030465332584,1.5267975838754546,1.5207130009105667,1.5138404509484609,1.5061697380890307,1.4976892194101132,1.4883856887594653,1.478244239004563,1.4672480987900387,1.4553784388202258,1.4426141413428435,1.4289315247458139,1.4143040128302367,1.398701735153339,1.3820910404985094,1.3644338995039431,1.3456871639682513,1.3258016381004714,1.3047208989885999,1.2823797765232698,1.2587023613265775,1.2335993430549297,1.2069643727861679,1.1786689577015728,1.1485550647046754,1.1164239834761032,1.0820187349900185,1.044994534098779,1.0048650118991995,0.9608925742945544,0.9118229220097013,0.8550120296644869,0.8718511717297366,0.9284696990362244,0.9773443865976,1.0211191885631823,1.061048330008955,1.0978693276969014,1.1320684698806784,1.1639904575514164,1.1938921818651316,1.2219722613363317,1.2483886330830491,1.2732696895151085,1.2967216744383578,1.3188337880737202,1.3396818243470088,1.359330832236536,1.377837107465603,1.3952497121680392,1.4116116539734633,1.4269608142719166,1.441330688379545,1.4547509823331688,1.467248098790039,1.478845535995202,1.4895642177525033,1.499422767997601,1.5084377404010587,1.5166238110793633,1.5239939407261618,1.5305595111328656,1.5363304400333624,1.5413152774012366,1.5455212856914553,1.5489545060094523,1.5516198117774949,1.55352095112747,1.554660578962659,1.5550402793845226,1.554660578962659,1.55352095112747,1.5516198117774949,1.5489545060094527,1.5455212856914557,1.5413152774012364,1.5363304400333624,1.5305595111328658,1.5239939407261618,1.5166238110793628,1.5084377404010587,1.499422767997601,1.4895642177525035,1.478845535995202,1.4672480987900387,1.4547509823331688,1.4413306883795447,1.4269608142719166,1.4116116539734633,1.3952497121680394,1.3778371074656033,1.3593308322365363,1.339681824347009,1.3188337880737202,1.2967216744383578,1.2732696895151085,1.2483886330830491,1.2219722613363317,1.1938921818651316,1.1639904575514164,1.1320684698806784,1.0978693276969016,1.061048330008955,1.0211191885631825,0.9773443865976001,0.9284696990362246,0.8718511717297366,0.8878966517656206,0.944320214348631,0.992997266270944,1.036571687482719,1.076297625725199,1.1129125171108378,1.1469025657367806,1.178612384724336,1.208298773424656,1.2361602543738117,1.262354664280941,1.2870102904395573,1.310233266532839,1.3321126773296184,1.3527241956246545,1.3721327432075574,1.3903944821444942,1.4075583339975246,1.423667158424504,1.4387586809150084,1.4528662323792307,1.4660193453123427,1.4782442390045625,1.4895642177525033,1.5,1.5095699919979073,1.518290516400752,1.5261760038664247,1.5332391539578216,1.5394910703001343,1.5449413739107014,1.5495982978091416,1.5534687653756745,1.556558454412514,1.5588718484453603,1.5604122764555344,1.5611819419397697,1.5611819419397697,1.5604122764555344,1.5588718484453603,1.556558454412514,1.5534687653756745,1.5495982978091414,1.5449413739107014,1.5394910703001343,1.5332391539578216,1.5261760038664252,1.518290516400752,1.5095699919979078,1.5,1.4895642177525033,1.4782442390045625,1.4660193453123427,1.4528662323792307,1.4387586809150084,1.423667158424504,1.4075583339975246,1.390394482144494,1.3721327432075572,1.3527241956246547,1.3321126773296184,1.310233266532839,1.2870102904395575,1.262354664280941,1.2361602543738117,1.208298773424656,1.178612384724336,1.1469025657367804,1.1129125171108378,1.076297625725199,1.0365716874827193,0.9929972662709442,0.9443202143486311,0.8878966517656207,0.9031699350756281,0.9593958620195758,1.0078725331880818,1.0512437511965642,1.0907635831367362,1.1271693809645407,1.1609472609073008,1.1924417442814617,1.2219095344597373,1.2495490535693046,1.2755180332029905,1.2999446505316392,1.3229349237863381,1.3445778166048652,1.3649488745932767,1.384112885884049,1.4021258719715803,1.4190366064461661,1.4348877930651966,1.4497169929122953,1.4635573633560055,1.4764382535244673,1.4883856887594653,1.499422767997601,1.5095699919979073,1.5188455359952018,1.5272654771854148,1.5348439850956859,1.5415934811226912,1.5475247721750747,1.5526471623162075,1.5569685454909616,1.5604954817763368,1.5632332590779805,1.5651859417710257,1.566356407430246,1.5667463724926178,1.5663564074302458,1.5651859417710259,1.5632332590779805,1.5604954817763368,1.5569685454909614,1.5526471623162073,1.5475247721750747,1.5415934811226912,1.5348439850956859,1.5272654771854148,1.5188455359952018,1.5095699919979078,1.4994227679976009,1.488385688759465,1.4764382535244673,1.4635573633560055,1.4497169929122953,1.4348877930651966,1.4190366064461661,1.4021258719715806,1.384112885884049,1.3649488745932767,1.3445778166048652,1.3229349237863381,1.2999446505316394,1.2755180332029905,1.2495490535693046,1.2219095344597373,1.1924417442814614,1.1609472609073008,1.1271693809645404,1.0907635831367364,1.0512437511965644,1.007872533188082,0.959395862019576,0.9031699350756281,0.9176905631521233,0.9737161093422639,1.021989577307477,1.0651546890136516,1.1044654273959895,1.1406590565406114,1.1742216008699766,1.205497485722093,1.23474331406078,1.2621574028969047,1.2878973737006227,1.312091288190689,1.3348450434671353,1.3562474759790373,1.3763739976753187,1.3952892561166856,1.4130491248257724,1.4297022214924093,1.4452910854680339,1.4598531042946201,1.4734212519736805,1.48602468368492,1.4976892194101132,1.5084377404010587,1.518290516400752,1.5272654771854148,1.5353784388202256,1.5426432926661053,1.5490721634031817,1.5546755409861306,1.5594623904035776,1.563440242297174,1.5666152668473536,1.5689923328091961,1.5705750531512876,1.5713658183886445,1.5713658183886443,1.5705750531512876,1.5689923328091961,1.5666152668473536,1.563440242297174,1.5594623904035776,1.5546755409861306,1.5490721634031817,1.5426432926661053,1.5353784388202256,1.5272654771854148,1.518290516400752,1.5084377404010587,1.4976892194101128,1.48602468368492,1.4734212519736805,1.4598531042946201,1.4452910854680339,1.4297022214924093,1.4130491248257724,1.3952892561166856,1.3763739976753187,1.3562474759790373,1.3348450434671353,1.3120912881906888,1.287897373700623,1.2621574028969045,1.23474331406078,1.2054974857220928,1.1742216008699766,1.140659056540611,1.104465427395989,1.0651546890136518,1.0219895773074772,0.9737161093422642,0.9176905631521234,0.9314763567502714,0.987298699737119,1.0353660614000244,1.078322079548365,1.11742064924752,1.153398942778747,1.1867428885860678,1.2177968115985958,1.2468172096638401,1.2740022896699967,1.2995095576351323,1.3234669541469457,1.3459802491167672,1.3671381453365394,1.387015914183415,1.4056780552463375,1.4231802861474752,1.4395710601707064,1.4548927431258187,1.469182539187755,1.4824732284095934,1.4947937606110278,1.5061697380890307,1.5166238110793633,1.5261760038664247,1.5348439850956859,1.5426432926661053,1.5495875212220558,1.5556884784896978,1.5609563153489607,1.56539963348525,1.5690255736436507,1.5718398868540293,1.5738469904649177,1.575050010385146,1.5754508105601308,1.575050010385146,1.5738469904649177,1.5718398868540293,1.5690255736436507,1.56539963348525,1.5609563153489607,1.5556884784896976,1.5495875212220558,1.5426432926661053,1.5348439850956856,1.5261760038664247,1.5166238110793633,1.5061697380890307,1.4947937606110278,1.4824732284095934,1.469182539187755,1.4548927431258187,1.4395710601707064,1.423180286147475,1.4056780552463373,1.387015914183415,1.3671381453365394,1.3459802491167672,1.323466954146946,1.2995095576351323,1.2740022896699967,1.24681720966384,1.2177968115985955,1.1867428885860678,1.1533989427787468,1.1174206492475196,1.0783220795483646,1.0353660614000246,0.9872986997371193,0.9314763567502714,0.9445435893262523,1.0001598260107925,1.0480180941158634,1.0907619435810212,1.1296451776667815,1.165404872675964,1.1985268566436964,1.2293553493827813,1.258146738618058,1.285099115785632,1.310369865772515,1.334086801977704,1.356355560655395,1.3772647040257617,1.3968893554941928,1.4152938587491661,1.4325337670068983,1.448657360009617,1.4637068202000798,1.4777191578047935,1.490726947516827,1.5027589214710713,1.5138404509484609,1.5239939407261618,1.5332391539578216,1.5415934811226912,1.5490721634031817,1.5556884784896978,1.5614538950336536,1.566378200611759,1.5704696070128525,1.5737348358314522,1.5761791866908765,1.577806589879902,1.578619644737758,1.5786196447377578,1.577806589879902,1.576179186690877,1.5737348358314518,1.5704696070128525,1.566378200611759,1.5614538950336536,1.5556884784896978,1.5490721634031812,1.5415934811226912,1.5332391539578218,1.5239939407261618,1.5138404509484609,1.5027589214710715,1.490726947516827,1.4777191578047935,1.4637068202000798,1.4486573600096169,1.432533767006898,1.415293858749166,1.3968893554941926,1.3772647040257615,1.356355560655395,1.3340868019777037,1.310369865772515,1.285099115785632,1.2581467386180578,1.2293553493827813,1.1985268566436962,1.1654048726759636,1.129645177666781,1.0907619435810212,1.048018094115863,1.0001598260107925,0.9445435893262525,0.9569071359152326,1.0123142790419384,1.059960378463827,1.1024888923155898,1.1411535278793055,1.1766912610488998,1.2095878147431895,1.2401872986523066,1.2687459850490004,1.2954618442383217,1.3204921339185802,1.3439645338316386,1.3659845396599244,1.3866405656518463,1.4060075793123288,1.4241497599238961,1.441122487161116,1.4569738573991848,1.471745859132425,1.4854752972273346,1.4981945286921776,1.5099320546458088,1.5207130009105667,1.5305595111328656,1.5394910703001343,1.5475247721750747,1.5546755409861306,1.5609563153489607,1.566378200611759,1.570950594454669,1.574681289515961,1.5775765559836066,1.5796412064211682,1.5808786445478213,1.5812908992306927,1.5808786445478213,1.5796412064211682,1.5775765559836068,1.574681289515961,1.570950594454669,1.566378200611759,1.5609563153489607,1.5546755409861306,1.5475247721750742,1.5394910703001343,1.5305595111328656,1.5207130009105667,1.5099320546458088,1.4981945286921776,1.4854752972273346,1.471745859132425,1.456973857399185,1.441122487161116,1.4241497599238961,1.4060075793123286,1.3866405656518461,1.3659845396599244,1.3439645338316386,1.32049213391858,1.295461844238322,1.2687459850490004,1.2401872986523064,1.2095878147431895,1.1766912610488995,1.1411535278793055,1.1024888923155896,1.0599603784638267,1.012314279041938,0.9569071359152326,0.9685806015045626,1.023775575948086,1.0712063397565794,1.113516255086298,1.1519589288104253,1.1872712317065768,1.2199387765708984,1.2503055576414328,1.2786277260598742,1.3051031249425709,1.329888878330699,1.353112525394352,1.374879413844193,1.3952778020281662,1.4143824930452427,1.4322574926362979,1.4489579971088677,1.4645319088897144,1.4790210111131499,1.4924618909608691,1.5048866744250988,1.5163236171660983,1.5267975838754546,1.5363304400333624,1.5449413739107014,1.5526471623162075,1.5594623904035778,1.56539963348525,1.5704696070128525,1.574681289515961,1.5780420222262996,1.580557588272082,1.5822322736472711,1.5830689115989394,1.5830689115989398,1.5822322736472711,1.580557588272082,1.5780420222262996,1.574681289515961,1.5704696070128525,1.5653996334852498,1.5594623904035776,1.5526471623162073,1.5449413739107014,1.5363304400333624,1.5267975838754546,1.5163236171660983,1.5048866744250986,1.492461890960869,1.4790210111131494,1.4645319088897144,1.4489579971088677,1.4322574926362976,1.4143824930452424,1.3952778020281658,1.3748794138441929,1.353112525394352,1.3298888783306988,1.3051031249425709,1.278627726059874,1.2503055576414326,1.2199387765708982,1.1872712317065763,1.1519589288104248,1.1135162550862976,1.071206339756579,1.0237755759480855,0.9685806015045619,0.9795764321680173,1.0345560709981456,1.0817682362845948,1.1238561897747248,1.1620734332254092,1.1971567272915926,1.2295915693173318,1.2597218324096136,1.2878035405214303,1.3140344031119968,1.3385714036507192,1.3615419333359278,1.38305118397782,1.4031872495183872,1.4220247595149516,1.4396275363413569,1.4560505823567045,1.4713415946277462,1.4855421386039918,1.4986885704510973,1.5108127707026957,1.5219427338882936,1.5321030465332584,1.5413152774012366,1.5495982978091416,1.5569685454909616,1.563440242297174,1.569025573643651,1.5737348358314522,1.5775765559836066,1.580557588272082,1.5826831892554925,1.5839570744556966,1.584381457724494,1.583957074455697,1.5826831892554922,1.580557588272082,1.5775765559836068,1.5737348358314518,1.5690255736436507,1.5634402422971738,1.5569685454909614,1.5495982978091416,1.5413152774012364,1.532103046533258,1.5219427338882936,1.5108127707026957,1.498688570451097,1.4855421386039913,1.4713415946277462,1.4560505823567045,1.4396275363413569,1.422024759514951,1.403187249518387,1.3830511839778197,1.3615419333359275,1.3385714036507192,1.3140344031119968,1.2878035405214303,1.2597218324096136,1.2295915693173318,1.1971567272915924,1.162073433225409,1.1238561897747243,1.0817682362845942,1.034556070998145,0.9795764321680166,0.9899060116098558,1.0446670519179397,1.0916572553648005,1.1335197785814877,1.1715080132022042,1.206358604429805,1.2385569284772917,1.2684467312629488,1.2962839030826354,1.322266012823796,1.3465498959840743,1.3692627878613335,1.39050971585982,1.4103786003798753,1.4289438876117895,1.4462692059809723,1.4624093524865152,1.477411806510367,1.491317902485999,1.5041637511204733,1.5159809718166695,1.526797280937876,1.5366369682929113,1.5455212856914553,1.553468765375675,1.5604954817763368,1.5666152668473536,1.5718398868540293,1.5761791866908765,1.5796412064211682,1.5822322736472711,1.5839570744556966,1.58481870497303,1.58481870497303,1.583957074455697,1.5822322736472711,1.5796412064211682,1.576179186690877,1.5718398868540293,1.5666152668473536,1.5604954817763368,1.5534687653756745,1.5455212856914553,1.5366369682929113,1.526797280937876,1.5159809718166695,1.5041637511204728,1.491317902485999,1.4774118065103667,1.4624093524865152,1.4462692059809723,1.4289438876117893,1.4103786003798748,1.3905097158598199,1.3692627878613335,1.3465498959840738,1.3222660128237962,1.296283903082635,1.2684467312629486,1.2385569284772917,1.206358604429805,1.171508013202204,1.1335197785814874,1.0916572553648,1.0446670519179393,0.9899060116098551,0.9995797452811138,1.0541188237496093,1.1008835969230273,1.142517111309747,1.1802726430918806,1.214886716341229,1.2468445800820909,1.2764898465756176,1.3040782655458985,1.3298072579086149,1.3538335032609439,1.3762840724947978,1.3972638194727718,1.4168604812281769,1.435148310002869,1.452190728862247,1.4680423171205998,1.482750323143838,1.4963558359068385,1.5088947049859112,1.5203982716177162,1.530893955448993,1.5404057293345943,1.5489545060094527,1.556558454412514,1.5632332590779805,1.5689923328091961,1.5738469904649177,1.577806589879902,1.5808786445478213,1.5830689115989394,1.584381457724494,1.58481870497303,1.584381457724494,1.5830689115989398,1.5808786445478213,1.577806589879902,1.5738469904649182,1.5689923328091961,1.5632332590779805,1.556558454412514,1.5489545060094523,1.540405729334594,1.530893955448993,1.5203982716177158,1.508894704985911,1.4963558359068383,1.482750323143838,1.4680423171205994,1.452190728862247,1.4351483100028688,1.4168604812281766,1.3972638194727716,1.3762840724947973,1.3538335032609436,1.3298072579086144,1.3040782655458985,1.2764898465756176,1.2468445800820906,1.2148867163412287,1.1802726430918804,1.1425171113097463,1.100883596923027,1.0541188237496089,0.9995797452811133,1.0086071338439866,1.0629207820390392,1.109456546382489,1.1508573579306258,1.1883763717345073,1.222749984677231,1.2544633121259625,1.2838598257700837,1.31119512736192,1.3366664819166876,1.3604304046256108,1.3826137928389521,1.4033213170522767,1.4226405203504593,1.4406454496153465,1.4573993102275347,1.472956450485274,1.4873638732958807,1.5006624065034793,1.5128876215181606,1.524070562860036,1.5342383332218792,1.5434145663837942,1.5516198117774949,1.5588718484453603,1.5651859417710257,1.5705750531512876,1.575050010385146,1.578619644737758,1.5812908992306927,1.5830689115989398,1.583957074455697,1.583957074455697,1.5830689115989398,1.5812908992306927,1.578619644737758,1.575050010385146,1.5705750531512876,1.5651859417710259,1.5588718484453603,1.5516198117774949,1.5434145663837942,1.534238333221879,1.5240705628600364,1.5128876215181606,1.5006624065034793,1.4873638732958812,1.472956450485274,1.4573993102275347,1.4406454496153465,1.4226405203504593,1.4033213170522765,1.3826137928389524,1.360430404625611,1.3366664819166876,1.31119512736192,1.2838598257700842,1.2544633121259625,1.222749984677231,1.1883763717345075,1.150857357930626,1.1094565463824893,1.0629207820390394,1.0086071338439866,1.016996837450545,1.0710814768156298,1.117384538320497,1.1585488318903812,1.195827385387638,1.229956462038231,1.2614210366375573,1.290564432903234,1.3176420966871214,1.342851128598483,1.366347870286894,1.3882590357355857,1.4086891014916876,1.4277254052800656,1.4454417762977625,1.4619011889093374,1.477157745954445,1.4912581892096501,1.5042430683528574,1.516147658077609,1.5270026859500505,1.5368349155882077,1.5456676174689654,1.55352095112747,1.5604122764555344,1.566356407430246,1.5713658183886445,1.5754508105601308,1.578619644737758,1.5808786445478213,1.5822322736472716,1.5826831892554925,1.5822322736472711,1.5808786445478213,1.578619644737758,1.5754508105601308,1.5713658183886443,1.566356407430246,1.5604122764555344,1.55352095112747,1.545667617468965,1.5368349155882077,1.5270026859500505,1.516147658077609,1.5042430683528574,1.4912581892096501,1.477157745954445,1.4619011889093374,1.4454417762977625,1.4277254052800654,1.4086891014916876,1.3882590357355857,1.366347870286894,1.342851128598483,1.3176420966871212,1.290564432903234,1.2614210366375573,1.2299564620382315,1.195827385387638,1.1585488318903814,1.117384538320497,1.0710814768156298,1.016996837450545,1.0247567320521507,1.0786086685786527,1.1246752121052674,1.1655990453685268,1.2026330625736534,1.236513386374841,1.2677248435957227,1.2966106020534505,1.3234259431939321,1.3483677940847816,1.3715923130085426,1.3932260200000117,1.413373186246309,1.4321209317874966,1.4495428548045806,1.465701684203524,1.4806512616932297,1.4944380508840434,1.5071023047373213,1.5186789809926386,1.5291984681413944,1.5386871664983937,1.5471679566439553,1.554660578962659,1.5611819419397697,1.5667463724926178,1.5713658183886443,1.575050010385146,1.577806589879902,1.5796412064211682,1.580557588272082,1.580557588272082,1.5796412064211682,1.577806589879902,1.575050010385146,1.5713658183886443,1.5667463724926178,1.5611819419397697,1.554660578962659,1.5471679566439553,1.5386871664983937,1.5291984681413944,1.5186789809926386,1.5071023047373213,1.4944380508840434,1.4806512616932297,1.465701684203524,1.4495428548045806,1.4321209317874968,1.413373186246309,1.3932260200000117,1.3715923130085426,1.3483677940847816,1.3234259431939321,1.2966106020534505,1.2677248435957227,1.2365133863748414,1.2026330625736534,1.165599045368527,1.1246752121052677,1.0786086685786527,1.0247567320521507,1.0318939587528015,1.0855093773010513,1.1313354605210413,1.1720147574921704,1.2088000218478914,1.2424272282706346,1.2733810476835672,1.3020044834978894,1.3285526436178587,1.353222271744058,1.3761693322105968,1.3975201396922612,1.4173787476913684,1.4358320452319429,1.452953385036395,1.4688052348799365,1.4834411583052511,1.4969073222061353,1.509243662589979,1.5204847981216105,1.5306607539892083,1.539797540611012,1.5479176194167725,1.5550402793845226,1.5611819419397697,1.5663564074302458,1.5705750531512876,1.5738469904649177,1.576179186690877,1.5775765559836068,1.5780420222262996,1.5775765559836068,1.576179186690877,1.5738469904649177,1.5705750531512876,1.566356407430246,1.5611819419397697,1.5550402793845224,1.5479176194167725,1.539797540611012,1.5306607539892083,1.5204847981216105,1.509243662589979,1.4969073222061353,1.4834411583052511,1.4688052348799365,1.452953385036395,1.4358320452319429,1.4173787476913684,1.397520139692261,1.376169332210597,1.353222271744058,1.3285526436178585,1.3020044834978892,1.2733810476835672,1.2424272282706346,1.2088000218478916,1.1720147574921707,1.1313354605210413,1.0855093773010513,1.0318939587528015,1.0384149670533367,1.0917899252949617,1.1373714722228214,1.177802016344545,1.2143341633218216,1.2477037319366158,1.2783952287061426,1.3067514834999523,1.333027420855272,1.357419590524249,1.380083751480983,1.401146000715457,1.420710160713951,1.438862875041894,1.4556772352909442,1.4712154310700942,1.4855307292054793,1.4986689796369295,1.5106697792970871,1.5215673835475612,1.5313914276799632,1.5401675029619655,1.5479176194167725,1.554660578962659,1.5604122764555344,1.5651859417710259,1.5689923328091961,1.5718398868540293,1.5737348358314522,1.574681289515961,1.5746812895159612,1.5737348358314522,1.5718398868540293,1.5689923328091961,1.5651859417710259,1.5604122764555344,1.554660578962659,1.5479176194167725,1.5401675029619655,1.5313914276799632,1.5215673835475612,1.5106697792970876,1.4986689796369295,1.4855307292054793,1.4712154310700942,1.4556772352909442,1.4388628750418937,1.420710160713951,1.401146000715457,1.380083751480983,1.357419590524249,1.333027420855272,1.3067514834999523,1.2783952287061424,1.2477037319366155,1.2143341633218212,1.1778020163445453,1.1373714722228216,1.0917899252949619,1.038414967053337,1.0443255526962936,1.097455974645788,1.1427887687242424,1.1829661954675215,1.219240704636849,1.2523479506082373,1.2827722663572518,1.3108562983864118,1.336854777284509,1.3609640474436813,1.383339650153225,1.404107451387086,1.4233710281729481,1.4412167629454893,1.4577174691301484,1.4729350396193692,1.48692242428532,1.4997251339930844,1.511382402372084,1.5219280948873626,1.5313914276799632,1.539797540611012,1.5471679566439556,1.55352095112747,1.5588718484453603,1.5632332590779805,1.5666152668473536,1.5690255736436507,1.5704696070128525,1.570950594454669,1.5704696070128525,1.5690255736436507,1.5666152668473536,1.5632332590779805,1.5588718484453603,1.55352095112747,1.5471679566439553,1.539797540611012,1.5313914276799632,1.5219280948873626,1.511382402372084,1.4997251339930842,1.48692242428532,1.472935039619369,1.4577174691301484,1.4412167629454893,1.4233710281729481,1.404107451387086,1.3833396501532251,1.360964047443681,1.3368547772845087,1.3108562983864118,1.2827722663572518,1.2523479506082371,1.2192407046368487,1.1829661954675215,1.1427887687242424,1.0974559746457881,1.0443255526962936,1.0496308907073186,1.1025125598074077,1.1475922365074174,1.1875120254427476,1.2235242119686693,1.2563642769195456,1.2865163699039104,1.3143229434758477,1.34003852286414,1.363859234776122,1.3859403894850528,1.406407607506282,1.4253642047367423,1.4428962854448923,1.4590763663396218,1.4739660233594083,1.4876178673016733,1.50007704572828,1.511382402372084,1.5215673835475612,1.5306607539892083,1.5386871664983937,1.545667617468965,1.5516198117774949,1.556558454412514,1.5604954817763368,1.563440242297174,1.56539963348525,1.566378200611759,1.566378200611759,1.5653996334852498,1.5634402422971738,1.5604954817763368,1.556558454412514,1.5516198117774949,1.545667617468965,1.5386871664983937,1.5306607539892083,1.5215673835475612,1.511382402372084,1.5000770457282802,1.4876178673016736,1.4739660233594083,1.459076366339622,1.4428962854448923,1.4253642047367427,1.4064076075062824,1.3859403894850528,1.3638592347761223,1.3400385228641403,1.3143229434758479,1.2865163699039104,1.2563642769195456,1.2235242119686693,1.1875120254427478,1.1475922365074174,1.1025125598074084,1.0496308907073193,1.0543355641337426,1.1069641158553871,1.1517861547474482,1.1914436210393724,1.2271886265447818,1.259756468731008,1.2896311032581502,1.317154777320283,1.3425817984613853,1.3661080623727542,1.387888633869053,1.4080488723348805,1.4266918155009498,1.4439032709191701,1.4597554383444657,1.4743095546405662,1.4876178673016733,1.4997251339930844,1.5106697792970871,1.5204847981216105,1.5291984681413944,1.5368349155882077,1.5434145663837942,1.5489545060094527,1.5534687653756745,1.5569685454909614,1.5594623904035776,1.5609563153489607,1.5614538950336536,1.5609563153489607,1.5594623904035776,1.5569685454909616,1.5534687653756745,1.5489545060094527,1.5434145663837942,1.5368349155882077,1.5291984681413944,1.5204847981216105,1.5106697792970876,1.4997251339930844,1.4876178673016736,1.4743095546405662,1.4597554383444657,1.4439032709191701,1.4266918155009498,1.408048872334881,1.3878886338690535,1.3661080623727544,1.3425817984613855,1.3171547773202832,1.2896311032581504,1.2597564687310083,1.2271886265447818,1.1914436210393726,1.1517861547474482,1.1069641158553873,1.0543355641337433,1.0584435889005643,1.1108145028142598,1.155374219062915,1.1947645043343271,1.2302372870750866,1.2625276708040905,1.292119405821428,1.3193545216363707,1.3444870947768595,1.3677127754755969,1.3891863674164937,1.40903295181793,1.42735526969407,1.4442388116428562,1.4597554383444657,1.4739660233594083,1.48692242428532,1.4986689796369295,1.509243662589979,1.5186789809926386,1.5270026859500505,1.534238333221879,1.5404057293345943,1.5455212856914557,1.5495982978091414,1.5526471623162073,1.5546755409861306,1.5556884784896976,1.5556884784896978,1.5546755409861306,1.5526471623162075,1.5495982978091416,1.5455212856914557,1.5404057293345943,1.534238333221879,1.5270026859500507,1.5186789809926386,1.509243662589979,1.4986689796369295,1.48692242428532,1.4739660233594083,1.4597554383444657,1.4442388116428562,1.42735526969407,1.4090329518179305,1.3891863674164942,1.367712775475597,1.3444870947768595,1.319354521636371,1.292119405821428,1.2625276708040907,1.2302372870750866,1.1947645043343271,1.155374219062915,1.11081450281426,1.0584435889005643,1.0619584351357512,1.1140670264060408,1.1583595616341835,1.197477624140946,1.2326729484244832,1.264680432643682,1.2939836094138295,1.320924277228159,1.3457562671560162,1.3686749682993515,1.3898349061758577,1.4093608652873644,1.42735526969407,1.4439032709191701,1.4590763663396218,1.4729350396193692,1.4855307292054793,1.496907322206135,1.5071023047373213,1.516147658077609,1.524070562860036,1.530893955448993,1.5366369682929113,1.5413152774012364,1.5449413739107014,1.5475247721750747,1.5490721634031817,1.5495875212220558,1.5490721634031812,1.5475247721750747,1.5449413739107014,1.5413152774012364,1.5366369682929113,1.530893955448993,1.5240705628600364,1.516147658077609,1.5071023047373213,1.4969073222061353,1.4855307292054793,1.4729350396193692,1.459076366339622,1.4439032709191701,1.42735526969407,1.4093608652873646,1.3898349061758577,1.3686749682993518,1.3457562671560166,1.320924277228159,1.2939836094138295,1.2646804326436825,1.2326729484244832,1.1974776241409462,1.1583595616341837,1.114067026406041,1.0619584351357512,1.064883045258098,1.1167244555078757,1.1607447679713685,1.1995853720209084,1.2344977967946407,1.2662167227666496,1.2952254515361838,1.3218655361378815,1.346390546510337,1.3689955935892812,1.3898349061758577,1.4090329518179303,1.4266918155009498,1.4428962854448923,1.4577174691301484,1.4712154310700942,1.4834411583052511,1.4944380508840434,1.5042430683528574,1.5128876215181606,1.5203982716177162,1.526797280937876,1.5321030465332584,1.5363304400333624,1.5394910703001343,1.5415934811226912,1.5426432926661053,1.5426432926661053,1.5415934811226912,1.5394910703001343,1.5363304400333624,1.532103046533258,1.526797280937876,1.5203982716177158,1.5128876215181606,1.5042430683528574,1.4944380508840436,1.4834411583052511,1.4712154310700942,1.4577174691301487,1.4428962854448923,1.4266918155009498,1.4090329518179305,1.3898349061758577,1.3689955935892812,1.3463905465103372,1.3218655361378817,1.2952254515361838,1.2662167227666499,1.2344977967946407,1.1995853720209086,1.1607447679713687,1.1167244555078757,1.064883045258098,1.0672198490700031,1.1187890365551307,1.1625318905614013,1.2010895951011364,1.2357134616276786,1.2671379395990745,1.295846085155977,1.322179190202273,1.346390546510337,1.3686749682993518,1.389186367416494,1.4080488723348807,1.4253642047367425,1.4412167629454893,1.4556772352909442,1.4688052348799365,1.4806512616932297,1.4912581892096501,1.5006624065034793,1.508894704985911,1.5159809718166695,1.5219427338882936,1.5267975838754546,1.5305595111328658,1.5332391539578216,1.5348439850956859,1.5353784388202256,1.5348439850956859,1.5332391539578218,1.5305595111328658,1.5267975838754546,1.5219427338882936,1.5159809718166695,1.508894704985911,1.5006624065034793,1.4912581892096501,1.4806512616932297,1.4688052348799365,1.4556772352909442,1.4412167629454893,1.4253642047367427,1.408048872334881,1.3891863674164942,1.3686749682993518,1.3463905465103372,1.322179190202273,1.295846085155977,1.2671379395990745,1.2357134616276788,1.2010895951011364,1.1625318905614015,1.118789036555131,1.0672198490700033,1.068970776052867,1.1202625050807724,1.1637224595772382,1.201991605869783,1.2363210243957121,1.2674449191544763,1.295846085155977,1.3218655361378815,1.3457562671560164,1.3677127754755967,1.3878886338690533,1.4064076075062821,1.4233710281729481,1.438862875041894,1.4529533850363947,1.465701684203524,1.477157745954445,1.4873638732958805,1.4963558359068385,1.5041637511204733,1.5108127707026957,1.5163236171660983,1.5207130009105667,1.5239939407261618,1.5261760038664252,1.5272654771854148,1.5272654771854148,1.5261760038664247,1.5239939407261618,1.5207130009105667,1.5163236171660983,1.5108127707026957,1.5041637511204733,1.4963558359068385,1.4873638732958812,1.477157745954445,1.465701684203524,1.452953385036395,1.4388628750418937,1.4233710281729481,1.4064076075062824,1.3878886338690533,1.3677127754755969,1.3457562671560164,1.3218655361378815,1.295846085155977,1.2674449191544763,1.2363210243957121,1.2019916058697833,1.1637224595772384,1.1202625050807726,1.0689707760528673,1.070137265023107,1.1211460945412075,1.164317490790483,1.2022921890824148,1.2363210243957121,1.2671379395990745,1.2952254515361838,1.320924277228159,1.3444870947768595,1.3661080623727542,1.3859403894850528,1.404107451387086,1.420710160713951,1.4358320452319429,1.4495428548045806,1.4619011889093374,1.472956450485274,1.482750323143838,1.491317902485999,1.4986885704510973,1.5048866744250988,1.5099320546458088,1.5138404509484609,1.5166238110793628,1.518290516400752,1.5188455359952018,1.518290516400752,1.5166238110793633,1.5138404509484609,1.5099320546458088,1.5048866744250986,1.4986885704510973,1.491317902485999,1.482750323143838,1.472956450485274,1.4619011889093374,1.4495428548045806,1.4358320452319429,1.420710160713951,1.404107451387086,1.3859403894850528,1.3661080623727542,1.3444870947768595,1.320924277228159,1.2952254515361838,1.2671379395990745,1.2363210243957121,1.202292189082415,1.164317490790483,1.1211460945412075,1.0701372650231071,1.0707202712709103,1.1214405425418208,1.164317490790483,1.201991605869783,1.2357134616276786,1.2662167227666496,1.2939836094138295,1.3193545216363705,1.3425817984613853,1.3638592347761223,1.3833396501532251,1.401146000715457,1.4173787476913682,1.4321209317874968,1.4454417762977625,1.4573993102275347,1.4680423171205994,1.477411806510367,1.4855421386039913,1.492461890960869,1.4981945286921776,1.5027589214710713,1.5061697380890307,1.5084377404010587,1.5095699919979078,1.5095699919979078,1.5084377404010587,1.5061697380890307,1.5027589214710715,1.4981945286921776,1.492461890960869,1.4855421386039913,1.4774118065103667,1.4680423171205994,1.4573993102275347,1.4454417762977625,1.4321209317874968,1.4173787476913684,1.401146000715457,1.3833396501532251,1.3638592347761223,1.3425817984613855,1.3193545216363707,1.2939836094138295,1.2662167227666496,1.2357134616276786,1.2019916058697833,1.164317490790483,1.1214405425418208,1.0707202712709103,1.0707202712709103,1.1211460945412075,1.1637224595772382,1.2010895951011364,1.2344977967946407,1.2646804326436822,1.292119405821428,1.317154777320283,1.34003852286414,1.3609640474436813,1.380083751480983,1.397520139692261,1.413373186246309,1.4277254052800652,1.4406454496153465,1.452190728862247,1.4624093524865152,1.4713415946277462,1.4790210111131499,1.4854752972273346,1.4907269475168268,1.4947937606110278,1.4976892194101132,1.499422767997601,1.5,1.4994227679976009,1.4976892194101128,1.4947937606110278,1.490726947516827,1.4854752972273346,1.4790210111131499,1.4713415946277462,1.4624093524865152,1.452190728862247,1.4406454496153465,1.4277254052800654,1.413373186246309,1.397520139692261,1.380083751480983,1.360964047443681,1.34003852286414,1.317154777320283,1.292119405821428,1.2646804326436822,1.2344977967946407,1.2010895951011364,1.1637224595772384,1.1211460945412075,1.0707202712709103,1.070137265023107,1.1202625050807724,1.1625318905614013,1.1995853720209084,1.2326729484244832,1.2625276708040905,1.2896311032581502,1.3143229434758479,1.336854777284509,1.357419590524249,1.3761693322105968,1.393226020000012,1.4086891014916876,1.4226405203504593,1.4351483100028688,1.4462692059809723,1.4560505823567045,1.4645319088897144,1.471745859132425,1.4777191578047935,1.4824732284095934,1.48602468368492,1.4883856887594653,1.4895642177525035,1.4895642177525033,1.488385688759465,1.48602468368492,1.4824732284095934,1.477719157804794,1.471745859132425,1.4645319088897144,1.4560505823567045,1.4462692059809723,1.4351483100028688,1.4226405203504593,1.4086891014916876,1.3932260200000117,1.376169332210597,1.357419590524249,1.3368547772845087,1.3143229434758479,1.2896311032581504,1.2625276708040905,1.2326729484244832,1.1995853720209084,1.1625318905614013,1.1202625050807726,1.0701372650231071,1.068970776052867,1.1187890365551307,1.1607447679713685,1.197477624140946,1.2302372870750866,1.259756468731008,1.2865163699039102,1.3108562983864118,1.333027420855272,1.353222271744058,1.3715923130085426,1.3882590357355855,1.4033213170522765,1.4168604812281769,1.4289438876117895,1.4396275363413569,1.4489579971088677,1.456973857399185,1.4637068202000796,1.469182539187755,1.4734212519736805,1.4764382535244673,1.478244239004563,1.478845535995202,1.4782442390045625,1.4764382535244673,1.4734212519736805,1.469182539187755,1.4637068202000798,1.456973857399185,1.4489579971088677,1.4396275363413569,1.4289438876117895,1.4168604812281766,1.4033213170522765,1.3882590357355857,1.3715923130085426,1.353222271744058,1.333027420855272,1.3108562983864118,1.2865163699039102,1.259756468731008,1.2302372870750866,1.197477624140946,1.1607447679713685,1.1187890365551307,1.0689707760528673,1.0672198490700031,1.1167244555078755,1.1583595616341835,1.1947645043343271,1.2271886265447818,1.2563642769195456,1.282772266357252,1.3067514834999523,1.3285526436178587,1.3483677940847816,1.366347870286894,1.3826137928389521,1.3972638194727718,1.410378600379875,1.422024759514951,1.4322574926362979,1.441122487161116,1.4486573600096169,1.454892743125819,1.4598531042946206,1.4635573633560055,1.4660193453123427,1.4672480987900387,1.4672480987900387,1.4660193453123427,1.4635573633560055,1.4598531042946201,1.4548927431258187,1.4486573600096169,1.441122487161116,1.4322574926362979,1.422024759514951,1.4103786003798748,1.3972638194727718,1.3826137928389524,1.366347870286894,1.3483677940847816,1.3285526436178585,1.3067514834999523,1.2827722663572518,1.2563642769195456,1.2271886265447818,1.1947645043343271,1.1583595616341835,1.1167244555078752,1.067219849070003,1.064883045258098,1.1140670264060408,1.155374219062915,1.1914436210393724,1.2235242119686693,1.2523479506082373,1.2783952287061426,1.3020044834978892,1.3234259431939321,1.342851128598483,1.360430404625611,1.3762840724947976,1.39050971585982,1.4031872495183872,1.4143824930452424,1.4241497599238961,1.432533767006898,1.4395710601707064,1.4452910854680343,1.4497169929122953,1.4528662323792307,1.4547509823331688,1.4553784388202258,1.4547509823331688,1.4528662323792307,1.4497169929122953,1.4452910854680339,1.4395710601707064,1.432533767006898,1.4241497599238961,1.4143824930452424,1.403187249518387,1.39050971585982,1.3762840724947973,1.360430404625611,1.342851128598483,1.3234259431939321,1.3020044834978892,1.2783952287061424,1.2523479506082371,1.2235242119686693,1.1914436210393724,1.1553742190629148,1.1140670264060408,1.0648830452580977,1.0619584351357512,1.1108145028142598,1.1517861547474482,1.1875120254427476,1.219240704636849,1.2477037319366158,1.2733810476835672,1.2966106020534507,1.3176420966871216,1.3366664819166876,1.3538335032609439,1.3692627878613335,1.38305118397782,1.3952778020281662,1.4060075793123286,1.4152938587491661,1.423180286147475,1.429702221492409,1.4348877930651966,1.4387586809150086,1.4413306883795447,1.4426141413428435,1.4426141413428435,1.4413306883795447,1.4387586809150084,1.4348877930651966,1.4297022214924093,1.423180286147475,1.4152938587491661,1.4060075793123286,1.3952778020281658,1.38305118397782,1.3692627878613335,1.3538335032609439,1.3366664819166876,1.3176420966871212,1.2966106020534505,1.2733810476835672,1.2477037319366155,1.2192407046368487,1.1875120254427476,1.151786154747448,1.1108145028142598,1.061958435135751,1.0584435889005643,1.1069641158553871,1.1475922365074174,1.1829661954675215,1.2143341633218214,1.2424272282706346,1.2677248435957227,1.290564432903234,1.31119512736192,1.3298072579086149,1.346549895984074,1.3615419333359278,1.3748794138441929,1.3866405656518463,1.3968893554941928,1.405678055246337,1.4130491248257722,1.4190366064461661,1.423667158424504,1.4269608142719166,1.4289315247458139,1.4295875212220555,1.4289315247458139,1.4269608142719166,1.423667158424504,1.4190366064461661,1.4130491248257724,1.4056780552463373,1.3968893554941928,1.3866405656518461,1.3748794138441929,1.3615419333359278,1.346549895984074,1.3298072579086146,1.31119512736192,1.290564432903234,1.2677248435957227,1.2424272282706346,1.2143341633218212,1.1829661954675215,1.1475922365074174,1.106964115855387,1.0584435889005641,1.0543355641337426,1.1025125598074077,1.1427887687242424,1.177802016344545,1.2088000218478914,1.236513386374841,1.2614210366375573,1.2838598257700837,1.3040782655458987,1.322266012823796,1.3385714036507192,1.353112525394352,1.3659845396599244,1.3772647040257617,1.387015914183415,1.3952892561166856,1.4021258719715803,1.4075583339975246,1.4116116539734633,1.4143040128302367,1.4156472668170772,1.415647266817077,1.4143040128302367,1.4116116539734633,1.4075583339975246,1.4021258719715806,1.3952892561166856,1.387015914183415,1.3772647040257617,1.3659845396599244,1.353112525394352,1.3385714036507192,1.3222660128237962,1.3040782655458985,1.2838598257700842,1.2614210366375573,1.2365133863748414,1.2088000218478916,1.1778020163445453,1.1427887687242424,1.102512559807408,1.054335564133743,1.0496308907073186,1.097455974645788,1.1373714722228214,1.1720147574921704,1.2026330625736532,1.229956462038231,1.2544633121259623,1.2764898465756176,1.2962839030826354,1.3140344031119968,1.3298888783306988,1.3439645338316386,1.3563555606553952,1.3671381453365394,1.3763739976753187,1.384112885884049,1.390394482144494,1.3952497121680392,1.3987017351533386,1.400766637523055,1.4014538950336537,1.4007666375230552,1.398701735153339,1.3952497121680394,1.390394482144494,1.384112885884049,1.3763739976753187,1.3671381453365394,1.3563555606553952,1.3439645338316386,1.329888878330699,1.3140344031119968,1.2962839030826354,1.2764898465756176,1.2544633121259625,1.2299564620382315,1.2026330625736534,1.1720147574921707,1.1373714722228216,1.0974559746457881,1.049630890707319,1.0443255526962936,1.0917899252949617,1.1313354605210413,1.1655990453685268,1.1958273853876378,1.2227499846772307,1.2468445800820906,1.2684467312629488,1.2878035405214303,1.3051031249425709,1.32049213391858,1.3340868019777037,1.3459802491167672,1.3562474759790373,1.3649488745932767,1.3721327432075572,1.377837107465603,1.3820910404985092,1.3849156069967516,1.3863245128902262,1.3863245128902264,1.3849156069967516,1.3820910404985094,1.3778371074656033,1.3721327432075572,1.3649488745932767,1.3562474759790373,1.3459802491167672,1.334086801977704,1.3204921339185802,1.3051031249425709,1.2878035405214305,1.2684467312629488,1.2468445800820906,1.222749984677231,1.195827385387638,1.165599045368527,1.1313354605210413,1.0917899252949619,1.0443255526962936,1.0384149670533367,1.0855093773010513,1.1246752121052674,1.1585488318903812,1.1883763717345073,1.214886716341229,1.2385569284772917,1.2597218324096136,1.2786277260598742,1.295461844238322,1.310369865772515,1.323466954146946,1.334845043467135,1.3445778166048652,1.3527241956246545,1.359330832236536,1.364433899503943,1.368060376049792,1.3702289460717927,1.370950594454669,1.370228946071793,1.368060376049792,1.3644338995039431,1.3593308322365363,1.3527241956246547,1.3445778166048652,1.3348450434671353,1.323466954146946,1.3103698657725151,1.295461844238322,1.2786277260598742,1.2597218324096138,1.2385569284772917,1.2148867163412287,1.1883763717345075,1.1585488318903814,1.1246752121052677,1.0855093773010513,1.038414967053337,1.0318939587528015,1.0786086685786527,1.117384538320497,1.1508573579306256,1.1802726430918806,1.2063586044298051,1.2295915693173318,1.2503055576414328,1.2687459850490004,1.285099115785632,1.2995095576351323,1.3120912881906888,1.3229349237863381,1.3321126773296184,1.3396818243470088,1.3456871639682513,1.3501627747486011,1.3531332548182082,1.3546145673296104,1.3546145673296104,1.3531332548182082,1.3501627747486011,1.3456871639682513,1.339681824347009,1.3321126773296184,1.3229349237863381,1.3120912881906888,1.2995095576351323,1.285099115785632,1.2687459850490006,1.2503055576414328,1.2295915693173318,1.2063586044298051,1.1802726430918806,1.150857357930626,1.117384538320497,1.0786086685786527,1.0318939587528015,1.0247567320521507,1.0710814768156298,1.109456546382489,1.1425171113097465,1.1715080132022044,1.1971567272915926,1.2199387765708984,1.2401872986523066,1.258146738618058,1.2740022896699967,1.287897373700623,1.2999446505316394,1.310233266532839,1.3188337880737202,1.3258016381004714,1.3311795212346567,1.3349991355387647,1.3372823580977733,1.3380420222262996,1.3372823580977733,1.3349991355387647,1.3311795212346567,1.3258016381004714,1.3188337880737202,1.310233266532839,1.2999446505316394,1.287897373700623,1.2740022896699967,1.258146738618058,1.2401872986523066,1.2199387765708984,1.1971567272915926,1.1715080132022042,1.1425171113097465,1.1094565463824893,1.0710814768156298,1.0247567320521507,1.016996837450545,1.0629207820390392,1.1008835969230273,1.1335197785814877,1.1620734332254092,1.1872712317065768,1.2095878147431895,1.2293553493827813,1.2468172096638401,1.2621574028969045,1.2755180332029907,1.2870102904395573,1.2967216744383578,1.3047208989885999,1.311061292528294,1.3157831791862378,1.3189155359797473,1.3204771101558799,1.3204771101558799,1.3189155359797473,1.3157831791862378,1.311061292528294,1.3047208989885997,1.2967216744383578,1.2870102904395575,1.2755180332029905,1.2621574028969045,1.24681720966384,1.2293553493827813,1.2095878147431895,1.1872712317065766,1.1620734332254092,1.1335197785814877,1.1008835969230273,1.0629207820390394,1.016996837450545,1.0086071338439866,1.0541188237496093,1.0916572553648005,1.1238561897747248,1.1519589288104253,1.1766912610488998,1.1985268566436964,1.2177968115985955,1.23474331406078,1.2495490535693046,1.262354664280941,1.2732696895151085,1.2823797765232696,1.289751544586455,1.2954359416499073,1.2994705707972523,1.3018812792078858,1.3026831892554922,1.3018812792078858,1.2994705707972523,1.2954359416499073,1.2897515445864545,1.2823797765232696,1.2732696895151085,1.262354664280941,1.2495490535693046,1.23474331406078,1.2177968115985955,1.1985268566436964,1.1766912610488998,1.1519589288104253,1.1238561897747248,1.0916572553648003,1.054118823749609,1.0086071338439866,0.9995797452811138,1.0446670519179397,1.0817682362845948,1.113516255086298,1.1411535278793057,1.165404872675964,1.1867428885860678,1.2054974857220928,1.2219095344597373,1.2361602543738117,1.2483886330830491,1.2587023613265775,1.2671849918476819,1.2739007634346253,1.278897902987479,1.2822108837519481,1.283861928034055,1.2838619280340553,1.2822108837519481,1.278897902987479,1.273900763434625,1.2671849918476819,1.2587023613265775,1.2483886330830491,1.2361602543738117,1.2219095344597373,1.2054974857220928,1.1867428885860678,1.165404872675964,1.1411535278793055,1.113516255086298,1.0817682362845946,1.0446670519179395,0.9995797452811136,0.9899060116098558,1.0345560709981456,1.0712063397565794,1.1024888923155898,1.1296451776667815,1.153398942778747,1.1742216008699766,1.1924417442814612,1.208298773424656,1.2219722613363317,1.2335993430549297,1.2432856148114013,1.2511122488562638,1.2571407629326086,1.2614162541025862,1.263969570738529,1.26481870497303,1.263969570738529,1.2614162541025862,1.2571407629326083,1.2511122488562638,1.243285614811401,1.2335993430549297,1.2219722613363317,1.208298773424656,1.1924417442814614,1.1742216008699766,1.1533989427787468,1.1296451776667813,1.1024888923155898,1.0712063397565794,1.0345560709981452,0.9899060116098555,0.9795764321680173,1.0237755759480858,1.059960378463827,1.0907619435810212,1.11742064924752,1.1406590565406114,1.1609472609073008,1.178612384724336,1.1938921818651316,1.2069643727861679,1.217963998017709,1.2269942732979386,1.2341336498322026,1.2394405155256711,1.242956342567123,1.2447077491554597,1.2447077491554595,1.242956342567123,1.2394405155256711,1.2341336498322026,1.2269942732979386,1.217963998017709,1.2069643727861679,1.1938921818651316,1.178612384724336,1.1609472609073008,1.140659056540611,1.1174206492475196,1.0907619435810212,1.059960378463827,1.0237755759480855,0.9795764321680169,0.9685806015045626,1.0123142790419384,1.0480180941158634,1.0783220795483648,1.1044654273959893,1.1271693809645407,1.1469025657367804,1.1639904575514164,1.178668957701573,1.1911136921355523,1.2014573208908517,1.2098003386604825,1.2162180668118705,1.2207652683768133,1.2234791853706584,1.2243814577244938,1.2234791853706584,1.2207652683768129,1.2162180668118707,1.2098003386604825,1.2014573208908514,1.1911136921355523,1.1786689577015728,1.1639904575514164,1.1469025657367804,1.1271693809645404,1.104465427395989,1.0783220795483646,1.0480180941158632,1.0123142790419382,0.9685806015045623,0.9569071359152326,1.0001598260107925,1.0353660614000244,1.0651546890136516,1.0907635831367362,1.1129125171108378,1.1320684698806784,1.1485550647046752,1.1626061083677748,1.1743948463255123,1.1840512175702131,1.1916725869569682,1.1973306509798298,1.201075942497166,1.2029407252565103,1.2029407252565105,1.2010759424971658,1.19733065097983,1.1916725869569682,1.1840512175702131,1.1743948463255125,1.1626061083677746,1.1485550647046754,1.1320684698806784,1.1129125171108378,1.0907635831367364,1.0651546890136518,1.0353660614000246,1.0001598260107925,0.9569071359152329,0.9445435893262523,0.987298699737119,1.021989577307477,1.0512437511965642,1.0762976257251988,1.0978693276969014,1.116423983476103,1.132283121813043,1.1456781689999005,1.1567796494470397,1.1657143723088643,1.1725760775670933,1.1774322315423487,1.1803283888251839,1.181290899230693,1.1803283888251839,1.1774322315423484,1.1725760775670935,1.1657143723088643,1.1567796494470395,1.1456781689999005,1.132283121813043,1.1164239834761032,1.0978693276969016,1.076297625725199,1.0512437511965644,1.0219895773074772,0.9872986997371193,0.9445435893262528,0.9314763567502714,0.9737161093422639,1.0078725331880818,1.036571687482719,1.061048330008955,1.082018734990018,1.0999459342821627,1.1151490761428609,1.1278568658191201,1.1382366978833829,1.1464117566166816,1.152471551827304,1.1564785715680586,1.1584724564970583,1.1584724564970583,1.1564785715680586,1.152471551827304,1.1464117566166816,1.1382366978833829,1.12785686581912,1.1151490761428609,1.099945934282163,1.0820187349900185,1.061048330008955,1.0365716874827193,1.007872533188082,0.9737161093422642,0.9314763567502714,0.9176905631521233,0.9593958620195758,0.992997266270944,1.0211191885631823,1.0449945340987787,1.065337482592785,1.0826086854086878,1.0971245697587875,1.1091107110521705,1.1187308789879076,1.1261040276735996,1.1313146886497212,1.1344194360366402,1.1354508105601309,1.13441943603664,1.1313146886497214,1.1261040276735996,1.1187308789879074,1.1091107110521705,1.0971245697587875,1.082608685408688,1.0653374825927853,1.044994534098779,1.0211191885631825,0.9929972662709442,0.959395862019576,0.9176905631521234,0.9031699350756281,0.944320214348631,0.9773443865976,1.0048650118991993,1.0281129009477388,1.0477998529655033,1.0643837982708073,1.078178034238031,1.0894045114028879,1.0982227692910183,1.1047467837422096,1.1090551723644957,1.1111974093459056,1.1111974093459056,1.1090551723644957,1.1047467837422096,1.0982227692910183,1.0894045114028879,1.078178034238031,1.0643837982708073,1.0477998529655033,1.0281129009477388,1.0048650118991993,0.9773443865976001,0.9443202143486311,0.9031699350756281,0.8878966517656206,0.9284696990362244,0.9608925742945542,0.9877857431090965,1.0103776356813943,1.02937733018856,1.0452396271109883,1.0582741989496858,1.068698766066936,1.0766678897205657,1.0822896318179214,1.0856355100346986,1.086746372492618,1.0856355100346986,1.0822896318179214,1.0766678897205657,1.0686987660669363,1.0582741989496858,1.0452396271109883,1.02937733018856,1.0103776356813943,0.9877857431090965,0.9608925742945542,0.9284696990362246,0.8878966517656207,0.8718511717297366,0.9118229220097013,0.943618340780974,0.9698555131192744,0.9917601481809734,1.0100381943052634,1.0251408270991653,1.0373734888902564,1.0469489217730061,1.0540157730728,1.0586750047646467,1.0609895084579333,1.0609895084579333,1.058675004764647,1.0540157730728,1.0469489217730061,1.0373734888902564,1.0251408270991653,1.0100381943052634,0.9917601481809734,0.9698555131192744,0.943618340780974,0.911822922009701,0.8718511717297366,0.8550120296644868,0.8943563234573944,0.9254957457524254,0.9510456605801273,0.9722286472589503,0.989747029254714,1.0040477520010098,1.0154312795575997,1.0241044400865138,1.030208780980799,1.033836638149155,1.0350402793845224,1.033836638149155,1.030208780980799,1.0241044400865138,1.0154312795575997,1.0040477520010098,0.989747029254714,0.9722286472589503,0.9510456605801273,0.9254957457524254,0.8943563234573944,0.8550120296644868,0.8373555973394452,0.876043894656111,0.9064960594405435,0.9313243258853694,0.9517476484356664,0.9684641203838236,0.9819157088956184,0.9923969640983729,1.000107614221778,1.0051805805925722,1.007697575303009,1.0076975753030093,1.0051805805925724,1.000107614221778,0.9923969640983727,0.9819157088956184,0.9684641203838236,0.9517476484356662,0.9313243258853694,0.9064960594405435,0.876043894656111,0.8373555973394452,0.8188558002786314,0.8568568400846985,0.8865873564862551,0.9106559588025546,0.9302773713052451,0.9461447090189015,0.9586940251768609,0.9682127699741063,0.9748920455740208,0.9788541494868961,0.9801675029619655,0.9788541494868959,0.9748920455740208,0.9682127699741063,0.9586940251768609,0.9461447090189017,0.9302773713052451,0.9106559588025546,0.8865873564862551,0.8568568400846984,0.8188558002786313,0.7994837797373409,0.8367631711605321,0.8657340234335625,0.8890007157022556,0.9077729939704452,0.9227380593302662,0.9343248650827164,0.9428122353564714,0.9483806484984665,0.9511391111759744,0.9511391111759744,0.9483806484984665,0.9428122353564714,0.9343248650827164,0.9227380593302662,0.9077729939704452,0.8890007157022556,0.8657340234335624,0.8367631711605319,0.7994837797373406,0.7792074863105535,0.8157272136052186,0.8438961558306425,0.8663137138648348,0.884183719779189,0.8981862747335008,0.9087417059624605,0.916118213778296,0.9204829856849239,0.9219280948873623,0.9204829856849239,0.9161182137782958,0.9087417059624604,0.8981862747335008,0.8841837197791886,0.8663137138648348,0.8438961558306423,0.8157272136052184,0.7792074863105533,0.7579911871785623,0.7937090044256209,0.8210288124165438,0.8425440980969009,0.8594515936057457,0.8724227740365672,0.8818673428076075,0.8880402093880759,0.8910916278196342,0.8910916278196342,0.8880402093880757,0.8818673428076075,0.8724227740365671,0.8594515936057457,0.8425440980969007,0.8210288124165438,0.7937090044256206,0.7579911871785622,0.7357948629753386,0.7706635459878962,0.7970810816249839,0.8176338568998315,0.8335099778851861,0.8453702958580881,0.8536112233937613,0.85847073649916,0.8600770457282799,0.85847073649916,0.8536112233937613,0.8453702958580881,0.8335099778851861,0.8176338568998317,0.7970810816249839,0.7706635459878964,0.7357948629753386,0.7125734617567773,0.7465398724154995,0.7719948976470781,0.7915162983984353,0.8062815569258706,0.8169382336634052,0.8238658077240087,0.8272802116269692,0.8272802116269692,0.8238658077240087,0.8169382336634052,0.8062815569258706,0.7915162983984353,0.7719948976470782,0.7465398724154997,0.7125734617567775,0.6882759652992884,0.7212798655525017,0.7457035162605894,0.7641140545540274,0.7776756718460954,0.7870189951085607,0.7925014599667257,0.7943095546405662,0.7925014599667257,0.7870189951085604,0.7776756718460954,0.7641140545540274,0.7457035162605896,0.7212798655525017,0.6882759652992885,0.6628442049696138,0.6948167306993362,0.7181295189495049,0.7353364160075756,0.747584679824574,0.7554828938846008,0.759359049513646,0.7593590495136462,0.755482893884601,0.747584679824574,0.7353364160075756,0.7181295189495049,0.6948167306993364,0.6628442049696138,0.6362113373725785,0.6670730006443818,0.6891821476591831,0.7050756912421842,0.7158788458567442,0.7221707506876511,0.7242388116428559,0.7221707506876511,0.7158788458567444,0.7050756912421843,0.6891821476591832,0.6670730006443818,0.6362113373725785,0.6082998482997924,0.6379578703362284,0.6587536638759601,0.673202098256523,0.682398943641963,0.6868827537990294,0.6868827537990294,0.682398943641963,0.673202098256523,0.6587536638759602,0.6379578703362285,0.6082998482997923,0.5790188873238004,0.6073635558851669,0.6267142402224604,0.6395563653739031,0.6469451160855026,0.6493608652873644,0.6469451160855026,0.6395563653739031,0.6267142402224604,0.6073635558851669,0.5790188873238004,0.5482606267258944,0.5751601860848226,0.5929045611929961,0.6039385916705984,0.6092592814269931,0.6092592814269931,0.6039385916705984,0.592904561192996,0.5751601860848226,0.5482606267258944,0.5158951529482093,0.5411884030780174,0.5571246835123504,0.5660906530347479,0.5689955935892812,0.5660906530347481,0.5571246835123504,0.5411884030780174,0.5158951529482093,0.481763067193911,0.5052482226498787,0.519116442129007,0.5256666624495429,0.5256666624495429,0.519116442129007,0.5052482226498787,0.4817630671939109,0.44566434565824037,0.4670814401590033,0.47853391043626986,0.4821791902022727,0.47853391043626986,0.4670814401590033,0.4456643456582403,0.4073407454009859,0.42634209069988727,0.4348896204226207,0.4348896204226205,0.4263420906998871,0.40734074540098586,0.3664462644533777,0.3825426691977458,0.3874449191544765,0.3825426691977458,0.36644626445337786,0.32249336186032446,0.33494448683868977,0.3349444868386898,0.3224933618603245,0.27474331406078023,0.28229218908241493,0.2747433140607803,0.221940732853211,0.221940732853211,0.16144054254182078],\"coloraxis\":\"coloraxis\",\"symbol\":\"circle\"},\"mode\":\"markers\",\"name\":\"\",\"scene\":\"scene\",\"showlegend\":false,\"x\":[0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.01,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.02,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.03,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.04,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.06,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.07,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.08,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.09,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.11,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.12,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.13,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.14,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.15,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.16,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.17,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.18,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.19,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.21,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.22,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.23,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.24,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.25,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.26,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.27,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.28,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.29,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.3,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.31,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.32,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.33,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.34,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.35,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.36,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.37,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.38,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.39,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.4,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.42,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.43,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.44,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.45,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.46,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.47,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.48,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.49,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.51,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.52,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.53,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.54,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.55,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.56,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.57,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.58,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.59,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.6,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.61,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.62,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.63,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.64,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.65,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.66,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.67,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.68,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.69,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.7,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.71,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.72,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.73,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.74,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.76,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.77,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.78,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.79,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.8,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.81,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.82,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.83,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.84,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.85,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.86,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.87,0.88,0.88,0.88,0.88,0.88,0.88,0.88,0.88,0.88,0.88,0.88,0.89,0.89,0.89,0.89,0.89,0.89,0.89,0.89,0.89,0.89,0.9,0.9,0.9,0.9,0.9,0.9,0.9,0.9,0.9,0.91,0.91,0.91,0.91,0.91,0.91,0.91,0.91,0.92,0.92,0.92,0.92,0.92,0.92,0.92,0.93,0.93,0.93,0.93,0.93,0.93,0.94,0.94,0.94,0.94,0.94,0.95,0.95,0.95,0.95,0.96,0.96,0.96,0.97,0.97,0.98],\"y\":[0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.95,0.96,0.97,0.98,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.95,0.96,0.97,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.95,0.96,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.95,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.01,0.02,0.03,0.04,0.05,0.06,0.01,0.02,0.03,0.04,0.05,0.01,0.02,0.03,0.04,0.01,0.02,0.03,0.01,0.02,0.01],\"z\":[0.16144054254182066,0.2219407328532109,0.2747433140607801,0.3224933618603243,0.3664462644533775,0.4073407454009861,0.44566434565824065,0.4817630671939111,0.5158951529482093,0.5482606267258944,0.5790188873238004,0.6082998482997923,0.6362113373725785,0.6628442049696137,0.6882759652992883,0.7125734617567773,0.7357948629753384,0.7579911871785623,0.7792074863105536,0.799483779737341,0.8188558002786313,0.8373555973394452,0.8550120296644869,0.8718511717297366,0.8878966517656206,0.9031699350756281,0.9176905631521233,0.9314763567502714,0.9445435893262523,0.9569071359152326,0.9685806015045626,0.9795764321680173,0.9899060116098558,0.9995797452811138,1.0086071338439866,1.016996837450545,1.0247567320521507,1.0318939587528015,1.0384149670533367,1.0443255526962936,1.0496308907073186,1.0543355641337426,1.0584435889005643,1.0619584351357512,1.064883045258098,1.0672198490700031,1.068970776052867,1.070137265023107,1.0707202712709103,1.0707202712709103,1.070137265023107,1.068970776052867,1.0672198490700031,1.064883045258098,1.0619584351357512,1.0584435889005643,1.0543355641337426,1.0496308907073186,1.0443255526962936,1.0384149670533367,1.0318939587528015,1.0247567320521507,1.016996837450545,1.0086071338439866,0.9995797452811138,0.9899060116098558,0.9795764321680173,0.9685806015045626,0.9569071359152326,0.9445435893262523,0.9314763567502714,0.9176905631521233,0.9031699350756281,0.8878966517656206,0.8718511717297366,0.8550120296644868,0.8373555973394452,0.8188558002786314,0.7994837797373409,0.7792074863105535,0.7579911871785623,0.7357948629753386,0.7125734617567773,0.6882759652992884,0.6628442049696138,0.6362113373725785,0.6082998482997923,0.5790188873238004,0.5482606267258944,0.5158951529482093,0.481763067193911,0.44566434565824037,0.4073407454009859,0.3664462644533776,0.3224933618603244,0.27474331406078023,0.22194073285321098,0.16144054254182072,0.2219407328532109,0.2822921890824148,0.3349444868386896,0.38254266919774566,0.4263420906998875,0.46708144015900344,0.5052482226498789,0.5411884030780175,0.5751601860848226,0.6073635558851669,0.6379578703362284,0.6670730006443817,0.6948167306993362,0.7212798655525016,0.7465398724154994,0.7706635459878962,0.793709004425621,0.8157272136052186,0.8367631711605321,0.8568568400846985,0.876043894656111,0.8943563234573944,0.9118229220097013,0.9284696990362244,0.944320214348631,0.9593958620195758,0.9737161093422639,0.987298699737119,1.0001598260107925,1.0123142790419384,1.023775575948086,1.0345560709981456,1.0446670519179397,1.0541188237496093,1.0629207820390392,1.0710814768156298,1.0786086685786527,1.0855093773010513,1.0917899252949617,1.097455974645788,1.1025125598074077,1.1069641158553871,1.1108145028142598,1.1140670264060408,1.1167244555078757,1.1187890365551307,1.1202625050807724,1.1211460945412075,1.1214405425418208,1.1211460945412075,1.1202625050807724,1.1187890365551307,1.1167244555078755,1.1140670264060408,1.1108145028142598,1.1069641158553871,1.1025125598074077,1.097455974645788,1.0917899252949617,1.0855093773010513,1.0786086685786527,1.0710814768156298,1.0629207820390392,1.0541188237496093,1.0446670519179397,1.0345560709981456,1.0237755759480858,1.0123142790419384,1.0001598260107925,0.987298699737119,0.9737161093422639,0.9593958620195758,0.944320214348631,0.9284696990362244,0.911822922009701,0.8943563234573944,0.876043894656111,0.8568568400846984,0.8367631711605321,0.8157272136052186,0.7937090044256209,0.7706635459878962,0.7465398724154995,0.7212798655525017,0.6948167306993362,0.6670730006443817,0.6379578703362284,0.6073635558851668,0.5751601860848224,0.5411884030780174,0.5052482226498787,0.4670814401590033,0.4263420906998871,0.3825426691977458,0.3349444868386897,0.28229218908241493,0.22194073285321095,0.2747433140607801,0.3349444868386896,0.3874449191544763,0.4348896204226209,0.47853391043627,0.5191164421290071,0.5571246835123506,0.5929045611929961,0.6267142402224604,0.6587536638759601,0.6891821476591831,0.7181295189495048,0.7457035162605894,0.7719948976470781,0.7970810816249836,0.8210288124165441,0.8438961558306426,0.8657340234335625,0.8865873564862551,0.9064960594405436,0.9254957457524254,0.943618340780974,0.9608925742945542,0.9773443865976,0.992997266270944,1.0078725331880818,1.021989577307477,1.0353660614000244,1.0480180941158634,1.059960378463827,1.0712063397565794,1.0817682362845948,1.0916572553648005,1.1008835969230273,1.109456546382489,1.117384538320497,1.1246752121052674,1.1313354605210413,1.1373714722228214,1.1427887687242424,1.1475922365074174,1.1517861547474482,1.155374219062915,1.1583595616341835,1.1607447679713685,1.1625318905614013,1.1637224595772382,1.164317490790483,1.164317490790483,1.1637224595772382,1.1625318905614013,1.1607447679713685,1.1583595616341835,1.155374219062915,1.1517861547474482,1.1475922365074174,1.1427887687242424,1.1373714722228214,1.1313354605210413,1.1246752121052674,1.117384538320497,1.109456546382489,1.1008835969230273,1.0916572553648005,1.0817682362845948,1.0712063397565794,1.059960378463827,1.0480180941158634,1.0353660614000244,1.021989577307477,1.0078725331880818,0.992997266270944,0.9773443865976,0.9608925742945542,0.943618340780974,0.9254957457524254,0.9064960594405435,0.8865873564862551,0.8657340234335625,0.8438961558306423,0.8210288124165438,0.7970810816249837,0.7719948976470781,0.7457035162605894,0.7181295189495048,0.6891821476591831,0.6587536638759601,0.6267142402224603,0.5929045611929958,0.5571246835123504,0.5191164421290069,0.4785339104362698,0.4348896204226205,0.3874449191544764,0.3349444868386897,0.2747433140607802,0.3224933618603243,0.38254266919774566,0.4348896204226209,0.48217919020227284,0.5256666624495431,0.5660906530347481,0.6039385916705985,0.6395563653739031,0.673202098256523,0.7050756912421843,0.7353364160075755,0.7641140545540274,0.7915162983984353,0.8176338568998315,0.8425440980969009,0.8663137138648349,0.8890007157022557,0.9106559588025546,0.9313243258853694,0.9510456605801273,0.9698555131192744,0.9877857431090965,1.0048650118991993,1.0211191885631823,1.036571687482719,1.0512437511965642,1.0651546890136516,1.078322079548365,1.0907619435810212,1.1024888923155898,1.113516255086298,1.1238561897747248,1.1335197785814877,1.142517111309747,1.1508573579306258,1.1585488318903812,1.1655990453685268,1.1720147574921704,1.177802016344545,1.1829661954675215,1.1875120254427476,1.1914436210393724,1.1947645043343271,1.197477624140946,1.1995853720209084,1.2010895951011364,1.201991605869783,1.2022921890824148,1.201991605869783,1.2010895951011364,1.1995853720209084,1.197477624140946,1.1947645043343271,1.1914436210393726,1.1875120254427476,1.1829661954675215,1.177802016344545,1.1720147574921704,1.1655990453685268,1.1585488318903812,1.1508573579306258,1.1425171113097465,1.1335197785814877,1.1238561897747248,1.113516255086298,1.1024888923155898,1.0907619435810212,1.0783220795483646,1.0651546890136516,1.0512437511965642,1.036571687482719,1.0211191885631823,1.004865011899199,0.9877857431090965,0.9698555131192744,0.9510456605801273,0.9313243258853694,0.9106559588025546,0.8890007157022556,0.8663137138648348,0.8425440980969007,0.8176338568998315,0.7915162983984353,0.7641140545540274,0.7353364160075755,0.7050756912421842,0.6732020982565229,0.639556365373903,0.6039385916705984,0.5660906530347479,0.5256666624495427,0.48217919020227257,0.4348896204226204,0.38254266919774566,0.32249336186032435,0.3664462644533775,0.4263420906998875,0.47853391043627,0.5256666624495431,0.5689955935892813,0.6092592814269934,0.6469451160855029,0.682398943641963,0.7158788458567442,0.747584679824574,0.7776756718460952,0.8062815569258702,0.8335099778851861,0.8594515936057461,0.884183719779189,0.9077729939704454,0.9302773713052452,0.9517476484356664,0.9722286472589505,0.9917601481809736,1.010377635681394,1.0281129009477386,1.044994534098779,1.061048330008955,1.076297625725199,1.0907635831367362,1.1044654273959895,1.11742064924752,1.1296451776667815,1.1411535278793055,1.1519589288104253,1.1620734332254092,1.1715080132022042,1.1802726430918806,1.1883763717345073,1.195827385387638,1.2026330625736534,1.2088000218478914,1.2143341633218216,1.219240704636849,1.2235242119686693,1.2271886265447818,1.2302372870750866,1.2326729484244832,1.2344977967946407,1.2357134616276786,1.2363210243957121,1.2363210243957121,1.2357134616276786,1.2344977967946407,1.2326729484244832,1.2302372870750866,1.2271886265447818,1.2235242119686693,1.219240704636849,1.2143341633218214,1.2088000218478914,1.2026330625736532,1.195827385387638,1.1883763717345073,1.1802726430918806,1.1715080132022044,1.1620734332254092,1.1519589288104253,1.1411535278793055,1.1296451776667815,1.1174206492475198,1.1044654273959893,1.0907635831367362,1.0762976257251988,1.061048330008955,1.0449945340987787,1.0281129009477388,1.0103776356813943,0.9917601481809734,0.9722286472589503,0.9517476484356664,0.9302773713052451,0.9077729939704452,0.8841837197791889,0.8594515936057457,0.8335099778851861,0.8062815569258703,0.7776756718460952,0.7475846798245738,0.7158788458567442,0.6823989436419629,0.6469451160855026,0.609259281426993,0.5689955935892811,0.5256666624495427,0.47853391043626975,0.42634209069988693,0.3664462644533776,0.4073407454009861,0.46708144015900344,0.5191164421290071,0.5660906530347481,0.6092592814269934,0.6493608652873644,0.6868827537990294,0.7221707506876511,0.7554828938846008,0.7870189951085604,0.8169382336634051,0.8453702958580881,0.8724227740365673,0.898186274733501,0.9227380593302662,0.9461447090189017,0.9684641203838238,0.9897470292547143,1.0100381943052634,1.02937733018856,1.047799852965503,1.065337482592785,1.0820187349900183,1.0978693276969014,1.1129125171108378,1.1271693809645407,1.1406590565406114,1.153398942778747,1.165404872675964,1.1766912610488998,1.1872712317065768,1.1971567272915926,1.206358604429805,1.214886716341229,1.222749984677231,1.2299564620382313,1.2365133863748412,1.2424272282706346,1.2477037319366158,1.2523479506082373,1.2563642769195456,1.259756468731008,1.2625276708040905,1.264680432643682,1.2662167227666499,1.2671379395990745,1.2674449191544763,1.2671379395990745,1.2662167227666496,1.2646804326436822,1.2625276708040905,1.2597564687310083,1.2563642769195456,1.2523479506082373,1.2477037319366158,1.2424272282706346,1.236513386374841,1.229956462038231,1.2227499846772307,1.2148867163412287,1.206358604429805,1.1971567272915926,1.1872712317065768,1.1766912610488998,1.165404872675964,1.1533989427787468,1.1406590565406112,1.1271693809645402,1.1129125171108378,1.0978693276969014,1.082018734990018,1.065337482592785,1.0477998529655033,1.02937733018856,1.0100381943052634,0.989747029254714,0.9684641203838236,0.9461447090189015,0.9227380593302662,0.8981862747335008,0.8724227740365671,0.8453702958580881,0.8169382336634051,0.7870189951085604,0.7554828938846007,0.7221707506876508,0.6868827537990292,0.6493608652873641,0.6092592814269928,0.5660906530347478,0.5191164421290065,0.46708144015900294,0.40734074540098547,0.44566434565824065,0.5052482226498789,0.5571246835123506,0.6039385916705985,0.6469451160855029,0.6868827537990294,0.7242388116428561,0.759359049513646,0.7925014599667256,0.8238658077240087,0.853611223393761,0.8818673428076076,0.9087417059624606,0.9343248650827167,0.9586940251768611,0.9819157088956185,1.0040477520010098,1.0251408270991655,1.0452396271109883,1.0643837982708073,1.0826086854086878,1.099945934282163,1.1164239834761032,1.1320684698806784,1.1469025657367806,1.1609472609073008,1.1742216008699766,1.1867428885860678,1.1985268566436964,1.2095878147431895,1.2199387765708984,1.2295915693173318,1.2385569284772917,1.2468445800820909,1.2544633121259625,1.2614210366375573,1.2677248435957227,1.2733810476835672,1.2783952287061426,1.2827722663572518,1.2865163699039104,1.2896311032581502,1.292119405821428,1.2939836094138297,1.2952254515361838,1.295846085155977,1.295846085155977,1.2952254515361838,1.2939836094138295,1.292119405821428,1.2896311032581504,1.2865163699039102,1.2827722663572523,1.2783952287061426,1.2733810476835674,1.2677248435957227,1.2614210366375573,1.2544633121259623,1.2468445800820906,1.2385569284772917,1.2295915693173318,1.2199387765708984,1.2095878147431895,1.1985268566436964,1.1867428885860678,1.1742216008699766,1.1609472609073008,1.1469025657367804,1.1320684698806784,1.116423983476103,1.0999459342821627,1.0826086854086878,1.0643837982708073,1.0452396271109883,1.0251408270991653,1.0040477520010098,0.9819157088956183,0.9586940251768609,0.9343248650827164,0.9087417059624604,0.8818673428076073,0.853611223393761,0.8238658077240087,0.7925014599667256,0.7593590495136459,0.7242388116428558,0.6868827537990292,0.6469451160855024,0.6039385916705982,0.5571246835123501,0.5052482226498783,0.4456643456582399,0.4817630671939111,0.5411884030780175,0.5929045611929961,0.6395563653739031,0.682398943641963,0.722170750687651,0.7593590495136459,0.7943095546405661,0.827280211626969,0.8584707364991596,0.8880402093880759,0.9161182137782962,0.9428122353564714,0.9682127699741065,0.9923969640983729,1.0154312795576,1.0373734888902564,1.0582741989496858,1.078178034238031,1.0971245697587875,1.1151490761428609,1.1322831218130427,1.1485550647046752,1.1639904575514164,1.178612384724336,1.1924417442814617,1.205497485722093,1.2177968115985958,1.2293553493827813,1.2401872986523066,1.2503055576414326,1.2597218324096136,1.2684467312629486,1.2764898465756176,1.2838598257700837,1.290564432903234,1.2966106020534505,1.3020044834978894,1.3067514834999523,1.3108562983864118,1.3143229434758479,1.317154777320283,1.3193545216363707,1.320924277228159,1.3218655361378815,1.322179190202273,1.3218655361378815,1.320924277228159,1.3193545216363705,1.317154777320283,1.3143229434758479,1.3108562983864118,1.3067514834999523,1.3020044834978894,1.2966106020534507,1.290564432903234,1.2838598257700837,1.2764898465756178,1.2684467312629488,1.2597218324096136,1.2503055576414328,1.2401872986523066,1.2293553493827813,1.2177968115985955,1.2054974857220928,1.1924417442814614,1.178612384724336,1.1639904575514164,1.1485550647046752,1.1322831218130431,1.1151490761428609,1.0971245697587875,1.078178034238031,1.0582741989496858,1.0373734888902564,1.0154312795575997,0.9923969640983731,0.9682127699741065,0.9428122353564714,0.916118213778296,0.8880402093880759,0.8584707364991602,0.8272802116269692,0.7943095546405663,0.7593590495136462,0.7221707506876514,0.6823989436419632,0.6395563653739031,0.5929045611929962,0.5411884030780175,0.4817630671939111,0.5158951529482093,0.5751601860848226,0.6267142402224604,0.673202098256523,0.7158788458567442,0.7554828938846007,0.7925014599667256,0.827280211626969,0.8600770457282798,0.8910916278196342,0.9204829856849239,0.9483806484984665,0.9748920455740209,1.0001076142217782,1.0241044400865138,1.0469489217730061,1.068698766066936,1.0894045114028876,1.1091107110521705,1.12785686581912,1.1456781689999003,1.1626061083677746,1.178668957701573,1.1938921818651316,1.208298773424656,1.2219095344597373,1.23474331406078,1.2468172096638401,1.258146738618058,1.2687459850490004,1.278627726059874,1.2878035405214303,1.2962839030826354,1.3040782655458985,1.31119512736192,1.3176420966871214,1.3234259431939321,1.3285526436178587,1.333027420855272,1.336854777284509,1.34003852286414,1.3425817984613853,1.3444870947768595,1.3457562671560164,1.346390546510337,1.346390546510337,1.3457562671560164,1.3444870947768595,1.3425817984613853,1.34003852286414,1.336854777284509,1.333027420855272,1.3285526436178587,1.3234259431939321,1.3176420966871216,1.31119512736192,1.3040782655458987,1.2962839030826354,1.2878035405214303,1.2786277260598742,1.2687459850490004,1.258146738618058,1.2468172096638401,1.23474331406078,1.2219095344597373,1.208298773424656,1.1938921818651316,1.178668957701573,1.1626061083677748,1.1456781689999007,1.1278568658191201,1.1091107110521705,1.0894045114028879,1.068698766066936,1.0469489217730061,1.0241044400865138,1.000107614221778,0.9748920455740209,0.9483806484984665,0.9204829856849239,0.8910916278196342,0.8600770457282801,0.8272802116269693,0.7925014599667257,0.755482893884601,0.7158788458567444,0.6732020982565231,0.6267142402224604,0.5751601860848226,0.5158951529482094,0.5482606267258944,0.6073635558851669,0.6587536638759601,0.7050756912421843,0.747584679824574,0.7870189951085604,0.8238658077240086,0.8584707364991596,0.8910916278196342,0.9219280948873624,0.9511391111759744,0.9788541494868961,1.0051805805925724,1.0302087809807992,1.0540157730728,1.0766678897205657,1.098222769291018,1.1187308789879074,1.1382366978833829,1.1567796494470395,1.1743948463255123,1.1911136921355523,1.2069643727861679,1.2219722613363317,1.2361602543738117,1.2495490535693046,1.2621574028969047,1.2740022896699967,1.285099115785632,1.2954618442383217,1.3051031249425709,1.3140344031119968,1.322266012823796,1.3298072579086146,1.3366664819166876,1.342851128598483,1.3483677940847816,1.353222271744058,1.357419590524249,1.3609640474436813,1.363859234776122,1.3661080623727542,1.3677127754755969,1.3686749682993518,1.3689955935892812,1.3686749682993518,1.3677127754755967,1.3661080623727542,1.3638592347761223,1.3609640474436813,1.357419590524249,1.353222271744058,1.3483677940847816,1.342851128598483,1.3366664819166876,1.3298072579086149,1.322266012823796,1.3140344031119968,1.3051031249425709,1.295461844238322,1.285099115785632,1.2740022896699967,1.2621574028969045,1.2495490535693046,1.2361602543738117,1.2219722613363317,1.2069643727861679,1.1911136921355523,1.1743948463255123,1.1567796494470397,1.138236697883383,1.1187308789879076,1.0982227692910183,1.0766678897205657,1.0540157730728,1.030208780980799,1.0051805805925724,0.9788541494868961,0.9511391111759744,0.9219280948873623,0.8910916278196342,0.8584707364991602,0.8238658077240087,0.7870189951085607,0.747584679824574,0.7050756912421844,0.6587536638759603,0.6073635558851669,0.5482606267258945,0.5790188873238004,0.6379578703362284,0.6891821476591831,0.7353364160075755,0.7776756718460952,0.8169382336634051,0.853611223393761,0.8880402093880759,0.9204829856849239,0.9511391111759744,0.9801675029619655,1.007697575303009,1.0338366381491553,1.0586750047646467,1.0822896318179214,1.1047467837422096,1.1261040276735996,1.1464117566166816,1.1657143723088643,1.1840512175702131,1.2014573208908514,1.2179639980177093,1.2335993430549297,1.2483886330830491,1.262354664280941,1.2755180332029905,1.2878973737006227,1.2995095576351323,1.310369865772515,1.32049213391858,1.3298888783306988,1.3385714036507192,1.346549895984074,1.3538335032609439,1.3604304046256108,1.366347870286894,1.3715923130085426,1.3761693322105968,1.380083751480983,1.383339650153225,1.3859403894850528,1.387888633869053,1.389186367416494,1.3898349061758577,1.3898349061758577,1.389186367416494,1.3878886338690533,1.3859403894850528,1.3833396501532251,1.380083751480983,1.3761693322105968,1.3715923130085426,1.366347870286894,1.360430404625611,1.3538335032609439,1.346549895984074,1.3385714036507192,1.3298888783306988,1.32049213391858,1.310369865772515,1.2995095576351323,1.287897373700623,1.2755180332029907,1.262354664280941,1.2483886330830491,1.2335993430549297,1.217963998017709,1.2014573208908517,1.1840512175702131,1.1657143723088643,1.1464117566166816,1.1261040276735996,1.1047467837422096,1.0822896318179214,1.0586750047646467,1.033836638149155,1.007697575303009,0.9801675029619655,0.9511391111759744,0.9204829856849239,0.8880402093880759,0.8536112233937613,0.8169382336634052,0.7776756718460954,0.7353364160075756,0.6891821476591833,0.6379578703362285,0.5790188873238005,0.6082998482997923,0.6670730006443817,0.7181295189495048,0.7641140545540274,0.8062815569258702,0.8453702958580878,0.8818673428076076,0.9161182137782962,0.9483806484984665,0.9788541494868961,1.007697575303009,1.0350402793845224,1.0609895084579333,1.0856355100346986,1.1090551723644957,1.1313146886497212,1.152471551827304,1.1725760775670933,1.191672586956968,1.2098003386604825,1.2269942732979389,1.2432856148114013,1.2587023613265775,1.2732696895151085,1.2870102904395573,1.2999446505316392,1.312091288190689,1.3234669541469457,1.3340868019777037,1.3439645338316386,1.353112525394352,1.3615419333359278,1.3692627878613335,1.3762840724947976,1.3826137928389521,1.3882590357355857,1.3932260200000117,1.3975201396922612,1.401146000715457,1.404107451387086,1.4064076075062821,1.4080488723348807,1.40903295181793,1.4093608652873644,1.4090329518179303,1.4080488723348807,1.4064076075062821,1.404107451387086,1.401146000715457,1.397520139692261,1.393226020000012,1.3882590357355855,1.3826137928389521,1.3762840724947976,1.3692627878613335,1.3615419333359278,1.353112525394352,1.3439645338316386,1.3340868019777037,1.323466954146946,1.3120912881906888,1.2999446505316394,1.2870102904395573,1.2732696895151085,1.2587023613265775,1.2432856148114013,1.2269942732979386,1.2098003386604825,1.1916725869569682,1.1725760775670933,1.152471551827304,1.1313146886497212,1.1090551723644957,1.0856355100346986,1.0609895084579333,1.0350402793845224,1.0076975753030093,0.9788541494868959,0.9483806484984665,0.9161182137782958,0.8818673428076075,0.8453702958580881,0.8062815569258706,0.7641140545540274,0.7181295189495049,0.6670730006443818,0.6082998482997923,0.6362113373725785,0.6948167306993362,0.7457035162605894,0.7915162983984353,0.8335099778851861,0.8724227740365672,0.9087417059624605,0.9428122353564714,0.9748920455740209,1.0051805805925724,1.0338366381491553,1.0609895084579333,1.086746372492618,1.1111974093459056,1.13441943603664,1.1564785715680586,1.1774322315423484,1.1973306509798298,1.2162180668118707,1.2341336498322029,1.2511122488562638,1.2671849918476819,1.2823797765232696,1.2967216744383578,1.310233266532839,1.3229349237863381,1.3348450434671353,1.3459802491167672,1.3563555606553948,1.3659845396599244,1.3748794138441929,1.38305118397782,1.39050971585982,1.3972638194727718,1.4033213170522767,1.4086891014916876,1.413373186246309,1.4173787476913684,1.420710160713951,1.4233710281729481,1.4253642047367425,1.4266918155009498,1.42735526969407,1.42735526969407,1.4266918155009498,1.4253642047367425,1.4233710281729481,1.420710160713951,1.4173787476913682,1.413373186246309,1.4086891014916876,1.4033213170522765,1.3972638194727718,1.39050971585982,1.38305118397782,1.3748794138441929,1.3659845396599244,1.3563555606553952,1.3459802491167672,1.334845043467135,1.3229349237863381,1.310233266532839,1.2967216744383578,1.2823797765232696,1.2671849918476819,1.2511122488562638,1.2341336498322026,1.2162180668118705,1.1973306509798298,1.1774322315423487,1.1564785715680586,1.1344194360366402,1.1111974093459056,1.086746372492618,1.0609895084579333,1.033836638149155,1.0051805805925724,0.9748920455740208,0.9428122353564714,0.9087417059624604,0.8724227740365671,0.8335099778851861,0.7915162983984353,0.7457035162605896,0.6948167306993364,0.6362113373725785,0.6628442049696137,0.7212798655525016,0.7719948976470781,0.8176338568998315,0.8594515936057461,0.8981862747335008,0.9343248650827166,0.9682127699741065,1.0001076142217782,1.0302087809807992,1.0586750047646467,1.0856355100346986,1.1111974093459056,1.1354508105601309,1.1584724564970583,1.1803283888251839,1.201075942497166,1.2207652683768133,1.2394405155256714,1.2571407629326086,1.273900763434625,1.289751544586455,1.3047208989886,1.3188337880737202,1.3321126773296184,1.3445778166048652,1.3562474759790373,1.3671381453365394,1.3772647040257617,1.3866405656518463,1.3952778020281662,1.4031872495183872,1.410378600379875,1.4168604812281769,1.4226405203504593,1.4277254052800656,1.4321209317874966,1.4358320452319429,1.438862875041894,1.4412167629454893,1.4428962854448923,1.4439032709191701,1.4442388116428562,1.4439032709191701,1.4428962854448923,1.4412167629454893,1.438862875041894,1.4358320452319429,1.4321209317874968,1.4277254052800652,1.4226405203504593,1.4168604812281769,1.410378600379875,1.4031872495183872,1.3952778020281662,1.3866405656518463,1.3772647040257617,1.3671381453365394,1.3562474759790373,1.3445778166048652,1.3321126773296184,1.3188337880737202,1.3047208989885999,1.289751544586455,1.2739007634346253,1.2571407629326086,1.2394405155256711,1.2207652683768133,1.201075942497166,1.1803283888251839,1.1584724564970583,1.1354508105601309,1.1111974093459056,1.0856355100346986,1.058675004764647,1.030208780980799,1.000107614221778,0.9682127699741063,0.9343248650827164,0.8981862747335008,0.8594515936057457,0.8176338568998317,0.7719948976470782,0.7212798655525017,0.6628442049696138,0.6882759652992883,0.7465398724154994,0.7970810816249836,0.8425440980969009,0.884183719779189,0.9227380593302662,0.9586940251768609,0.9923969640983729,1.0241044400865138,1.0540157730728,1.0822896318179214,1.1090551723644957,1.13441943603664,1.1584724564970583,1.1812908992306925,1.2029407252565103,1.2234791853706584,1.2429563425671233,1.2614162541025862,1.2788979029874792,1.2954359416499073,1.311061292528294,1.3258016381004714,1.3396818243470088,1.3527241956246545,1.3649488745932767,1.3763739976753187,1.387015914183415,1.3968893554941928,1.4060075793123286,1.4143824930452427,1.4220247595149513,1.4289438876117893,1.4351483100028688,1.4406454496153465,1.4454417762977625,1.4495428548045806,1.452953385036395,1.4556772352909442,1.4577174691301484,1.4590763663396218,1.4597554383444657,1.4597554383444657,1.4590763663396218,1.4577174691301484,1.4556772352909442,1.4529533850363947,1.4495428548045806,1.4454417762977625,1.4406454496153465,1.4351483100028688,1.4289438876117895,1.422024759514951,1.4143824930452424,1.4060075793123286,1.3968893554941928,1.387015914183415,1.3763739976753187,1.3649488745932767,1.3527241956246545,1.3396818243470088,1.3258016381004714,1.311061292528294,1.2954359416499073,1.278897902987479,1.2614162541025862,1.242956342567123,1.2234791853706584,1.2029407252565103,1.1812908992306927,1.1584724564970583,1.13441943603664,1.1090551723644957,1.0822896318179214,1.0540157730728,1.0241044400865136,0.9923969640983727,0.9586940251768608,0.922738059330266,0.8841837197791886,0.8425440980969006,0.7970810816249837,0.7465398724154995,0.6882759652992884,0.7125734617567773,0.7706635459878962,0.8210288124165441,0.8663137138648349,0.9077729939704454,0.9461447090189017,0.9819157088956184,1.0154312795576,1.0469489217730061,1.0766678897205657,1.1047467837422096,1.1313146886497212,1.1564785715680586,1.1803283888251839,1.2029407252565103,1.224381457724494,1.2447077491554597,1.2639695707385294,1.2822108837519481,1.2994705707972523,1.3157831791862378,1.3311795212346567,1.3456871639682513,1.359330832236536,1.3721327432075574,1.384112885884049,1.3952892561166856,1.4056780552463375,1.4152938587491661,1.4241497599238961,1.4322574926362979,1.4396275363413569,1.4462692059809723,1.452190728862247,1.4573993102275347,1.4619011889093374,1.465701684203524,1.4688052348799365,1.4712154310700942,1.4729350396193692,1.4739660233594083,1.4743095546405662,1.4739660233594083,1.4729350396193692,1.4712154310700942,1.4688052348799365,1.465701684203524,1.4619011889093374,1.4573993102275347,1.452190728862247,1.4462692059809723,1.4396275363413569,1.4322574926362979,1.4241497599238961,1.4152938587491661,1.405678055246337,1.3952892561166856,1.384112885884049,1.3721327432075572,1.359330832236536,1.3456871639682513,1.3311795212346567,1.3157831791862378,1.299470570797252,1.282210883751948,1.263969570738529,1.2447077491554597,1.2243814577244938,1.2029407252565103,1.1803283888251839,1.1564785715680586,1.1313146886497212,1.1047467837422094,1.0766678897205657,1.046948921773006,1.0154312795575997,0.9819157088956184,0.9461447090189015,0.9077729939704452,0.8663137138648346,0.8210288124165438,0.7706635459878962,0.7125734617567773,0.7357948629753384,0.793709004425621,0.8438961558306426,0.8890007157022557,0.9302773713052452,0.9684641203838236,1.0040477520010098,1.0373734888902564,1.068698766066936,1.098222769291018,1.1261040276735996,1.152471551827304,1.1774322315423484,1.201075942497166,1.2234791853706584,1.2447077491554597,1.2648187049730302,1.2838619280340555,1.3018812792078858,1.3189155359797473,1.3349991355387647,1.3501627747486011,1.364433899503943,1.377837107465603,1.3903944821444942,1.4021258719715803,1.4130491248257724,1.4231802861474752,1.432533767006898,1.441122487161116,1.4489579971088675,1.4560505823567045,1.4624093524865152,1.4680423171205994,1.472956450485274,1.477157745954445,1.4806512616932297,1.4834411583052511,1.4855307292054793,1.48692242428532,1.4876178673016733,1.4876178673016733,1.48692242428532,1.4855307292054793,1.4834411583052507,1.4806512616932297,1.477157745954445,1.472956450485274,1.4680423171205994,1.4624093524865152,1.4560505823567045,1.4489579971088677,1.441122487161116,1.432533767006898,1.423180286147475,1.4130491248257722,1.4021258719715803,1.390394482144494,1.3778371074656033,1.364433899503943,1.3501627747486011,1.3349991355387647,1.318915535979747,1.3018812792078855,1.283861928034055,1.26481870497303,1.2447077491554595,1.2234791853706584,1.2010759424971658,1.1774322315423484,1.152471551827304,1.1261040276735996,1.098222769291018,1.068698766066936,1.0373734888902564,1.0040477520010098,0.9684641203838235,0.9302773713052449,0.8890007157022554,0.8438961558306421,0.7937090044256205,0.7357948629753386,0.7579911871785623,0.8157272136052186,0.8657340234335625,0.9106559588025546,0.9517476484356664,0.9897470292547143,1.0251408270991655,1.0582741989496856,1.0894045114028876,1.1187308789879071,1.1464117566166814,1.172576077567093,1.1973306509798298,1.2207652683768133,1.242956342567123,1.263969570738529,1.283861928034055,1.302683189255492,1.3204771101558799,1.3372823580977733,1.3531332548182082,1.3680603760497918,1.3820910404985092,1.3952497121680392,1.4075583339975246,1.4190366064461661,1.4297022214924093,1.4395710601707064,1.448657360009617,1.4569738573991848,1.4645319088897144,1.4713415946277462,1.4774118065103667,1.482750323143838,1.4873638732958807,1.4912581892096501,1.4944380508840434,1.4969073222061353,1.4986689796369295,1.4997251339930844,1.50007704572828,1.4997251339930844,1.4986689796369295,1.496907322206135,1.4944380508840434,1.4912581892096501,1.4873638732958805,1.482750323143838,1.477411806510367,1.4713415946277462,1.4645319088897144,1.456973857399185,1.4486573600096169,1.4395710601707064,1.429702221492409,1.4190366064461661,1.4075583339975246,1.3952497121680394,1.3820910404985092,1.3680603760497922,1.3531332548182082,1.3372823580977735,1.3204771101558799,1.3026831892554922,1.2838619280340555,1.2639695707385292,1.242956342567123,1.220765268376813,1.19733065097983,1.1725760775670935,1.1464117566166816,1.1187308789879076,1.089404511402888,1.0582741989496858,1.0251408270991655,0.9897470292547143,0.9517476484356664,0.9106559588025548,0.8657340234335625,0.8157272136052186,0.7579911871785625,0.7792074863105536,0.8367631711605321,0.8865873564862551,0.9313243258853694,0.9722286472589505,1.0100381943052634,1.0452396271109883,1.078178034238031,1.1091107110521703,1.1382366978833829,1.165714372308864,1.191672586956968,1.2162180668118707,1.2394405155256714,1.2614162541025862,1.2822108837519481,1.3018812792078858,1.3204771101558799,1.3380420222262994,1.3546145673296104,1.3702289460717927,1.3849156069967516,1.3987017351533386,1.4116116539734633,1.423667158424504,1.4348877930651966,1.4452910854680339,1.4548927431258187,1.4637068202000798,1.471745859132425,1.4790210111131499,1.4855421386039913,1.491317902485999,1.4963558359068385,1.5006624065034793,1.5042430683528574,1.5071023047373213,1.509243662589979,1.5106697792970871,1.511382402372084,1.511382402372084,1.5106697792970871,1.509243662589979,1.5071023047373213,1.5042430683528574,1.5006624065034793,1.4963558359068385,1.491317902485999,1.4855421386039913,1.4790210111131499,1.471745859132425,1.4637068202000796,1.454892743125819,1.4452910854680343,1.4348877930651969,1.423667158424504,1.4116116539734636,1.3987017351533386,1.3849156069967516,1.370228946071793,1.3546145673296104,1.3380420222262996,1.3204771101558799,1.3018812792078858,1.2822108837519481,1.2614162541025864,1.2394405155256714,1.2162180668118707,1.1916725869569682,1.1657143723088643,1.138236697883383,1.1091107110521707,1.0781780342380312,1.0452396271109885,1.0100381943052634,0.9722286472589505,0.9313243258853695,0.8865873564862552,0.8367631711605322,0.7792074863105536,0.799483779737341,0.8568568400846985,0.9064960594405436,0.9510456605801273,0.9917601481809736,1.02937733018856,1.0643837982708073,1.0971245697587872,1.1278568658191197,1.1567796494470395,1.1840512175702127,1.2098003386604825,1.2341336498322029,1.2571407629326083,1.278897902987479,1.2994705707972523,1.3189155359797473,1.3372823580977733,1.3546145673296104,1.3709505944546685,1.386324512890226,1.400766637523055,1.4143040128302367,1.4269608142719166,1.4387586809150084,1.4497169929122953,1.4598531042946201,1.469182539187755,1.4777191578047935,1.4854752972273346,1.492461890960869,1.4986885704510973,1.5041637511204733,1.5088947049859112,1.5128876215181606,1.516147658077609,1.5186789809926386,1.5204847981216105,1.5215673835475612,1.5219280948873626,1.5215673835475612,1.5204847981216105,1.5186789809926386,1.516147658077609,1.5128876215181606,1.508894704985911,1.5041637511204733,1.4986885704510973,1.492461890960869,1.4854752972273346,1.4777191578047935,1.469182539187755,1.4598531042946206,1.4497169929122953,1.4387586809150086,1.4269608142719166,1.4143040128302367,1.400766637523055,1.3863245128902264,1.370950594454669,1.3546145673296104,1.3372823580977735,1.3189155359797473,1.2994705707972523,1.2788979029874792,1.2571407629326086,1.2341336498322026,1.2098003386604828,1.1840512175702131,1.1567796494470397,1.1278568658191201,1.0971245697587877,1.0643837982708075,1.0293773301885603,0.9917601481809736,0.9510456605801274,0.9064960594405436,0.8568568400846988,0.799483779737341,0.8188558002786313,0.876043894656111,0.9254957457524254,0.9698555131192744,1.010377635681394,1.047799852965503,1.0826086854086878,1.1151490761428609,1.1456781689999003,1.1743948463255123,1.2014573208908514,1.2269942732979389,1.2511122488562638,1.273900763434625,1.2954359416499073,1.3157831791862378,1.3349991355387647,1.3531332548182082,1.3702289460717927,1.386324512890226,1.4014538950336535,1.4156472668170768,1.4289315247458139,1.441330688379545,1.4528662323792307,1.4635573633560055,1.4734212519736805,1.4824732284095934,1.490726947516827,1.4981945286921776,1.5048866744250988,1.5108127707026957,1.5159809718166695,1.5203982716177162,1.524070562860036,1.5270026859500505,1.5291984681413944,1.5306607539892083,1.5313914276799632,1.5313914276799632,1.5306607539892083,1.5291984681413944,1.5270026859500505,1.524070562860036,1.5203982716177162,1.5159809718166695,1.5108127707026957,1.5048866744250988,1.4981945286921776,1.4907269475168268,1.4824732284095934,1.4734212519736805,1.4635573633560055,1.4528662323792307,1.441330688379545,1.4289315247458139,1.4156472668170772,1.401453895033654,1.3863245128902264,1.370228946071793,1.3531332548182082,1.3349991355387647,1.3157831791862378,1.2954359416499073,1.2739007634346253,1.2511122488562638,1.2269942732979386,1.2014573208908514,1.1743948463255125,1.1456781689999007,1.115149076142861,1.082608685408688,1.0477998529655033,1.0103776356813943,0.9698555131192745,0.9254957457524255,0.8760438946561112,0.8188558002786314,0.8373555973394452,0.8943563234573944,0.943618340780974,0.9877857431090965,1.0281129009477386,1.065337482592785,1.099945934282163,1.1322831218130427,1.1626061083677746,1.1911136921355523,1.2179639980177093,1.2432856148114013,1.2671849918476819,1.289751544586455,1.311061292528294,1.3311795212346567,1.3501627747486011,1.3680603760497918,1.3849156069967516,1.400766637523055,1.4156472668170768,1.4295875212220555,1.4426141413428435,1.4547509823331688,1.4660193453123427,1.4764382535244673,1.48602468368492,1.4947937606110278,1.5027589214710713,1.5099320546458088,1.5163236171660983,1.5219427338882936,1.526797280937876,1.530893955448993,1.5342383332218792,1.5368349155882077,1.5386871664983937,1.539797540611012,1.5401675029619655,1.539797540611012,1.5386871664983937,1.5368349155882077,1.534238333221879,1.530893955448993,1.526797280937876,1.5219427338882936,1.5163236171660983,1.5099320546458088,1.5027589214710713,1.4947937606110278,1.48602468368492,1.4764382535244673,1.4660193453123427,1.4547509823331688,1.4426141413428435,1.4295875212220555,1.4156472668170772,1.4007666375230552,1.3849156069967519,1.368060376049792,1.3501627747486011,1.3311795212346567,1.3110612925282943,1.2897515445864547,1.2671849918476819,1.243285614811401,1.2179639980177093,1.1911136921355523,1.1626061083677748,1.1322831218130431,1.099945934282163,1.0653374825927853,1.0281129009477388,0.9877857431090967,0.9436183407809741,0.8943563234573946,0.8373555973394453,0.8550120296644869,0.9118229220097013,0.9608925742945542,1.0048650118991993,1.044994534098779,1.0820187349900183,1.1164239834761032,1.1485550647046752,1.178668957701573,1.2069643727861679,1.2335993430549297,1.2587023613265775,1.2823797765232696,1.3047208989886,1.3258016381004714,1.3456871639682513,1.364433899503943,1.3820910404985092,1.3987017351533386,1.4143040128302367,1.4289315247458139,1.4426141413428435,1.4553784388202258,1.467248098790039,1.4782442390045625,1.4883856887594653,1.4976892194101132,1.5061697380890307,1.5138404509484609,1.5207130009105667,1.5267975838754546,1.5321030465332584,1.5366369682929113,1.5404057293345943,1.5434145663837942,1.5456676174689654,1.5471679566439553,1.5479176194167725,1.5479176194167725,1.5471679566439556,1.545667617468965,1.5434145663837942,1.5404057293345943,1.5366369682929113,1.5321030465332584,1.5267975838754546,1.5207130009105667,1.5138404509484609,1.5061697380890307,1.4976892194101132,1.4883856887594653,1.478244239004563,1.4672480987900387,1.4553784388202258,1.4426141413428435,1.4289315247458139,1.4143040128302367,1.398701735153339,1.3820910404985094,1.3644338995039431,1.3456871639682513,1.3258016381004714,1.3047208989885999,1.2823797765232698,1.2587023613265775,1.2335993430549297,1.2069643727861679,1.1786689577015728,1.1485550647046754,1.1164239834761032,1.0820187349900185,1.044994534098779,1.0048650118991995,0.9608925742945544,0.9118229220097013,0.8550120296644869,0.8718511717297366,0.9284696990362244,0.9773443865976,1.0211191885631823,1.061048330008955,1.0978693276969014,1.1320684698806784,1.1639904575514164,1.1938921818651316,1.2219722613363317,1.2483886330830491,1.2732696895151085,1.2967216744383578,1.3188337880737202,1.3396818243470088,1.359330832236536,1.377837107465603,1.3952497121680392,1.4116116539734633,1.4269608142719166,1.441330688379545,1.4547509823331688,1.467248098790039,1.478845535995202,1.4895642177525033,1.499422767997601,1.5084377404010587,1.5166238110793633,1.5239939407261618,1.5305595111328656,1.5363304400333624,1.5413152774012366,1.5455212856914553,1.5489545060094523,1.5516198117774949,1.55352095112747,1.554660578962659,1.5550402793845226,1.554660578962659,1.55352095112747,1.5516198117774949,1.5489545060094527,1.5455212856914557,1.5413152774012364,1.5363304400333624,1.5305595111328658,1.5239939407261618,1.5166238110793628,1.5084377404010587,1.499422767997601,1.4895642177525035,1.478845535995202,1.4672480987900387,1.4547509823331688,1.4413306883795447,1.4269608142719166,1.4116116539734633,1.3952497121680394,1.3778371074656033,1.3593308322365363,1.339681824347009,1.3188337880737202,1.2967216744383578,1.2732696895151085,1.2483886330830491,1.2219722613363317,1.1938921818651316,1.1639904575514164,1.1320684698806784,1.0978693276969016,1.061048330008955,1.0211191885631825,0.9773443865976001,0.9284696990362246,0.8718511717297366,0.8878966517656206,0.944320214348631,0.992997266270944,1.036571687482719,1.076297625725199,1.1129125171108378,1.1469025657367806,1.178612384724336,1.208298773424656,1.2361602543738117,1.262354664280941,1.2870102904395573,1.310233266532839,1.3321126773296184,1.3527241956246545,1.3721327432075574,1.3903944821444942,1.4075583339975246,1.423667158424504,1.4387586809150084,1.4528662323792307,1.4660193453123427,1.4782442390045625,1.4895642177525033,1.5,1.5095699919979073,1.518290516400752,1.5261760038664247,1.5332391539578216,1.5394910703001343,1.5449413739107014,1.5495982978091416,1.5534687653756745,1.556558454412514,1.5588718484453603,1.5604122764555344,1.5611819419397697,1.5611819419397697,1.5604122764555344,1.5588718484453603,1.556558454412514,1.5534687653756745,1.5495982978091414,1.5449413739107014,1.5394910703001343,1.5332391539578216,1.5261760038664252,1.518290516400752,1.5095699919979078,1.5,1.4895642177525033,1.4782442390045625,1.4660193453123427,1.4528662323792307,1.4387586809150084,1.423667158424504,1.4075583339975246,1.390394482144494,1.3721327432075572,1.3527241956246547,1.3321126773296184,1.310233266532839,1.2870102904395575,1.262354664280941,1.2361602543738117,1.208298773424656,1.178612384724336,1.1469025657367804,1.1129125171108378,1.076297625725199,1.0365716874827193,0.9929972662709442,0.9443202143486311,0.8878966517656207,0.9031699350756281,0.9593958620195758,1.0078725331880818,1.0512437511965642,1.0907635831367362,1.1271693809645407,1.1609472609073008,1.1924417442814617,1.2219095344597373,1.2495490535693046,1.2755180332029905,1.2999446505316392,1.3229349237863381,1.3445778166048652,1.3649488745932767,1.384112885884049,1.4021258719715803,1.4190366064461661,1.4348877930651966,1.4497169929122953,1.4635573633560055,1.4764382535244673,1.4883856887594653,1.499422767997601,1.5095699919979073,1.5188455359952018,1.5272654771854148,1.5348439850956859,1.5415934811226912,1.5475247721750747,1.5526471623162075,1.5569685454909616,1.5604954817763368,1.5632332590779805,1.5651859417710257,1.566356407430246,1.5667463724926178,1.5663564074302458,1.5651859417710259,1.5632332590779805,1.5604954817763368,1.5569685454909614,1.5526471623162073,1.5475247721750747,1.5415934811226912,1.5348439850956859,1.5272654771854148,1.5188455359952018,1.5095699919979078,1.4994227679976009,1.488385688759465,1.4764382535244673,1.4635573633560055,1.4497169929122953,1.4348877930651966,1.4190366064461661,1.4021258719715806,1.384112885884049,1.3649488745932767,1.3445778166048652,1.3229349237863381,1.2999446505316394,1.2755180332029905,1.2495490535693046,1.2219095344597373,1.1924417442814614,1.1609472609073008,1.1271693809645404,1.0907635831367364,1.0512437511965644,1.007872533188082,0.959395862019576,0.9031699350756281,0.9176905631521233,0.9737161093422639,1.021989577307477,1.0651546890136516,1.1044654273959895,1.1406590565406114,1.1742216008699766,1.205497485722093,1.23474331406078,1.2621574028969047,1.2878973737006227,1.312091288190689,1.3348450434671353,1.3562474759790373,1.3763739976753187,1.3952892561166856,1.4130491248257724,1.4297022214924093,1.4452910854680339,1.4598531042946201,1.4734212519736805,1.48602468368492,1.4976892194101132,1.5084377404010587,1.518290516400752,1.5272654771854148,1.5353784388202256,1.5426432926661053,1.5490721634031817,1.5546755409861306,1.5594623904035776,1.563440242297174,1.5666152668473536,1.5689923328091961,1.5705750531512876,1.5713658183886445,1.5713658183886443,1.5705750531512876,1.5689923328091961,1.5666152668473536,1.563440242297174,1.5594623904035776,1.5546755409861306,1.5490721634031817,1.5426432926661053,1.5353784388202256,1.5272654771854148,1.518290516400752,1.5084377404010587,1.4976892194101128,1.48602468368492,1.4734212519736805,1.4598531042946201,1.4452910854680339,1.4297022214924093,1.4130491248257724,1.3952892561166856,1.3763739976753187,1.3562474759790373,1.3348450434671353,1.3120912881906888,1.287897373700623,1.2621574028969045,1.23474331406078,1.2054974857220928,1.1742216008699766,1.140659056540611,1.104465427395989,1.0651546890136518,1.0219895773074772,0.9737161093422642,0.9176905631521234,0.9314763567502714,0.987298699737119,1.0353660614000244,1.078322079548365,1.11742064924752,1.153398942778747,1.1867428885860678,1.2177968115985958,1.2468172096638401,1.2740022896699967,1.2995095576351323,1.3234669541469457,1.3459802491167672,1.3671381453365394,1.387015914183415,1.4056780552463375,1.4231802861474752,1.4395710601707064,1.4548927431258187,1.469182539187755,1.4824732284095934,1.4947937606110278,1.5061697380890307,1.5166238110793633,1.5261760038664247,1.5348439850956859,1.5426432926661053,1.5495875212220558,1.5556884784896978,1.5609563153489607,1.56539963348525,1.5690255736436507,1.5718398868540293,1.5738469904649177,1.575050010385146,1.5754508105601308,1.575050010385146,1.5738469904649177,1.5718398868540293,1.5690255736436507,1.56539963348525,1.5609563153489607,1.5556884784896976,1.5495875212220558,1.5426432926661053,1.5348439850956856,1.5261760038664247,1.5166238110793633,1.5061697380890307,1.4947937606110278,1.4824732284095934,1.469182539187755,1.4548927431258187,1.4395710601707064,1.423180286147475,1.4056780552463373,1.387015914183415,1.3671381453365394,1.3459802491167672,1.323466954146946,1.2995095576351323,1.2740022896699967,1.24681720966384,1.2177968115985955,1.1867428885860678,1.1533989427787468,1.1174206492475196,1.0783220795483646,1.0353660614000246,0.9872986997371193,0.9314763567502714,0.9445435893262523,1.0001598260107925,1.0480180941158634,1.0907619435810212,1.1296451776667815,1.165404872675964,1.1985268566436964,1.2293553493827813,1.258146738618058,1.285099115785632,1.310369865772515,1.334086801977704,1.356355560655395,1.3772647040257617,1.3968893554941928,1.4152938587491661,1.4325337670068983,1.448657360009617,1.4637068202000798,1.4777191578047935,1.490726947516827,1.5027589214710713,1.5138404509484609,1.5239939407261618,1.5332391539578216,1.5415934811226912,1.5490721634031817,1.5556884784896978,1.5614538950336536,1.566378200611759,1.5704696070128525,1.5737348358314522,1.5761791866908765,1.577806589879902,1.578619644737758,1.5786196447377578,1.577806589879902,1.576179186690877,1.5737348358314518,1.5704696070128525,1.566378200611759,1.5614538950336536,1.5556884784896978,1.5490721634031812,1.5415934811226912,1.5332391539578218,1.5239939407261618,1.5138404509484609,1.5027589214710715,1.490726947516827,1.4777191578047935,1.4637068202000798,1.4486573600096169,1.432533767006898,1.415293858749166,1.3968893554941926,1.3772647040257615,1.356355560655395,1.3340868019777037,1.310369865772515,1.285099115785632,1.2581467386180578,1.2293553493827813,1.1985268566436962,1.1654048726759636,1.129645177666781,1.0907619435810212,1.048018094115863,1.0001598260107925,0.9445435893262525,0.9569071359152326,1.0123142790419384,1.059960378463827,1.1024888923155898,1.1411535278793055,1.1766912610488998,1.2095878147431895,1.2401872986523066,1.2687459850490004,1.2954618442383217,1.3204921339185802,1.3439645338316386,1.3659845396599244,1.3866405656518463,1.4060075793123288,1.4241497599238961,1.441122487161116,1.4569738573991848,1.471745859132425,1.4854752972273346,1.4981945286921776,1.5099320546458088,1.5207130009105667,1.5305595111328656,1.5394910703001343,1.5475247721750747,1.5546755409861306,1.5609563153489607,1.566378200611759,1.570950594454669,1.574681289515961,1.5775765559836066,1.5796412064211682,1.5808786445478213,1.5812908992306927,1.5808786445478213,1.5796412064211682,1.5775765559836068,1.574681289515961,1.570950594454669,1.566378200611759,1.5609563153489607,1.5546755409861306,1.5475247721750742,1.5394910703001343,1.5305595111328656,1.5207130009105667,1.5099320546458088,1.4981945286921776,1.4854752972273346,1.471745859132425,1.456973857399185,1.441122487161116,1.4241497599238961,1.4060075793123286,1.3866405656518461,1.3659845396599244,1.3439645338316386,1.32049213391858,1.295461844238322,1.2687459850490004,1.2401872986523064,1.2095878147431895,1.1766912610488995,1.1411535278793055,1.1024888923155896,1.0599603784638267,1.012314279041938,0.9569071359152326,0.9685806015045626,1.023775575948086,1.0712063397565794,1.113516255086298,1.1519589288104253,1.1872712317065768,1.2199387765708984,1.2503055576414328,1.2786277260598742,1.3051031249425709,1.329888878330699,1.353112525394352,1.374879413844193,1.3952778020281662,1.4143824930452427,1.4322574926362979,1.4489579971088677,1.4645319088897144,1.4790210111131499,1.4924618909608691,1.5048866744250988,1.5163236171660983,1.5267975838754546,1.5363304400333624,1.5449413739107014,1.5526471623162075,1.5594623904035778,1.56539963348525,1.5704696070128525,1.574681289515961,1.5780420222262996,1.580557588272082,1.5822322736472711,1.5830689115989394,1.5830689115989398,1.5822322736472711,1.580557588272082,1.5780420222262996,1.574681289515961,1.5704696070128525,1.5653996334852498,1.5594623904035776,1.5526471623162073,1.5449413739107014,1.5363304400333624,1.5267975838754546,1.5163236171660983,1.5048866744250986,1.492461890960869,1.4790210111131494,1.4645319088897144,1.4489579971088677,1.4322574926362976,1.4143824930452424,1.3952778020281658,1.3748794138441929,1.353112525394352,1.3298888783306988,1.3051031249425709,1.278627726059874,1.2503055576414326,1.2199387765708982,1.1872712317065763,1.1519589288104248,1.1135162550862976,1.071206339756579,1.0237755759480855,0.9685806015045619,0.9795764321680173,1.0345560709981456,1.0817682362845948,1.1238561897747248,1.1620734332254092,1.1971567272915926,1.2295915693173318,1.2597218324096136,1.2878035405214303,1.3140344031119968,1.3385714036507192,1.3615419333359278,1.38305118397782,1.4031872495183872,1.4220247595149516,1.4396275363413569,1.4560505823567045,1.4713415946277462,1.4855421386039918,1.4986885704510973,1.5108127707026957,1.5219427338882936,1.5321030465332584,1.5413152774012366,1.5495982978091416,1.5569685454909616,1.563440242297174,1.569025573643651,1.5737348358314522,1.5775765559836066,1.580557588272082,1.5826831892554925,1.5839570744556966,1.584381457724494,1.583957074455697,1.5826831892554922,1.580557588272082,1.5775765559836068,1.5737348358314518,1.5690255736436507,1.5634402422971738,1.5569685454909614,1.5495982978091416,1.5413152774012364,1.532103046533258,1.5219427338882936,1.5108127707026957,1.498688570451097,1.4855421386039913,1.4713415946277462,1.4560505823567045,1.4396275363413569,1.422024759514951,1.403187249518387,1.3830511839778197,1.3615419333359275,1.3385714036507192,1.3140344031119968,1.2878035405214303,1.2597218324096136,1.2295915693173318,1.1971567272915924,1.162073433225409,1.1238561897747243,1.0817682362845942,1.034556070998145,0.9795764321680166,0.9899060116098558,1.0446670519179397,1.0916572553648005,1.1335197785814877,1.1715080132022042,1.206358604429805,1.2385569284772917,1.2684467312629488,1.2962839030826354,1.322266012823796,1.3465498959840743,1.3692627878613335,1.39050971585982,1.4103786003798753,1.4289438876117895,1.4462692059809723,1.4624093524865152,1.477411806510367,1.491317902485999,1.5041637511204733,1.5159809718166695,1.526797280937876,1.5366369682929113,1.5455212856914553,1.553468765375675,1.5604954817763368,1.5666152668473536,1.5718398868540293,1.5761791866908765,1.5796412064211682,1.5822322736472711,1.5839570744556966,1.58481870497303,1.58481870497303,1.583957074455697,1.5822322736472711,1.5796412064211682,1.576179186690877,1.5718398868540293,1.5666152668473536,1.5604954817763368,1.5534687653756745,1.5455212856914553,1.5366369682929113,1.526797280937876,1.5159809718166695,1.5041637511204728,1.491317902485999,1.4774118065103667,1.4624093524865152,1.4462692059809723,1.4289438876117893,1.4103786003798748,1.3905097158598199,1.3692627878613335,1.3465498959840738,1.3222660128237962,1.296283903082635,1.2684467312629486,1.2385569284772917,1.206358604429805,1.171508013202204,1.1335197785814874,1.0916572553648,1.0446670519179393,0.9899060116098551,0.9995797452811138,1.0541188237496093,1.1008835969230273,1.142517111309747,1.1802726430918806,1.214886716341229,1.2468445800820909,1.2764898465756176,1.3040782655458985,1.3298072579086149,1.3538335032609439,1.3762840724947978,1.3972638194727718,1.4168604812281769,1.435148310002869,1.452190728862247,1.4680423171205998,1.482750323143838,1.4963558359068385,1.5088947049859112,1.5203982716177162,1.530893955448993,1.5404057293345943,1.5489545060094527,1.556558454412514,1.5632332590779805,1.5689923328091961,1.5738469904649177,1.577806589879902,1.5808786445478213,1.5830689115989394,1.584381457724494,1.58481870497303,1.584381457724494,1.5830689115989398,1.5808786445478213,1.577806589879902,1.5738469904649182,1.5689923328091961,1.5632332590779805,1.556558454412514,1.5489545060094523,1.540405729334594,1.530893955448993,1.5203982716177158,1.508894704985911,1.4963558359068383,1.482750323143838,1.4680423171205994,1.452190728862247,1.4351483100028688,1.4168604812281766,1.3972638194727716,1.3762840724947973,1.3538335032609436,1.3298072579086144,1.3040782655458985,1.2764898465756176,1.2468445800820906,1.2148867163412287,1.1802726430918804,1.1425171113097463,1.100883596923027,1.0541188237496089,0.9995797452811133,1.0086071338439866,1.0629207820390392,1.109456546382489,1.1508573579306258,1.1883763717345073,1.222749984677231,1.2544633121259625,1.2838598257700837,1.31119512736192,1.3366664819166876,1.3604304046256108,1.3826137928389521,1.4033213170522767,1.4226405203504593,1.4406454496153465,1.4573993102275347,1.472956450485274,1.4873638732958807,1.5006624065034793,1.5128876215181606,1.524070562860036,1.5342383332218792,1.5434145663837942,1.5516198117774949,1.5588718484453603,1.5651859417710257,1.5705750531512876,1.575050010385146,1.578619644737758,1.5812908992306927,1.5830689115989398,1.583957074455697,1.583957074455697,1.5830689115989398,1.5812908992306927,1.578619644737758,1.575050010385146,1.5705750531512876,1.5651859417710259,1.5588718484453603,1.5516198117774949,1.5434145663837942,1.534238333221879,1.5240705628600364,1.5128876215181606,1.5006624065034793,1.4873638732958812,1.472956450485274,1.4573993102275347,1.4406454496153465,1.4226405203504593,1.4033213170522765,1.3826137928389524,1.360430404625611,1.3366664819166876,1.31119512736192,1.2838598257700842,1.2544633121259625,1.222749984677231,1.1883763717345075,1.150857357930626,1.1094565463824893,1.0629207820390394,1.0086071338439866,1.016996837450545,1.0710814768156298,1.117384538320497,1.1585488318903812,1.195827385387638,1.229956462038231,1.2614210366375573,1.290564432903234,1.3176420966871214,1.342851128598483,1.366347870286894,1.3882590357355857,1.4086891014916876,1.4277254052800656,1.4454417762977625,1.4619011889093374,1.477157745954445,1.4912581892096501,1.5042430683528574,1.516147658077609,1.5270026859500505,1.5368349155882077,1.5456676174689654,1.55352095112747,1.5604122764555344,1.566356407430246,1.5713658183886445,1.5754508105601308,1.578619644737758,1.5808786445478213,1.5822322736472716,1.5826831892554925,1.5822322736472711,1.5808786445478213,1.578619644737758,1.5754508105601308,1.5713658183886443,1.566356407430246,1.5604122764555344,1.55352095112747,1.545667617468965,1.5368349155882077,1.5270026859500505,1.516147658077609,1.5042430683528574,1.4912581892096501,1.477157745954445,1.4619011889093374,1.4454417762977625,1.4277254052800654,1.4086891014916876,1.3882590357355857,1.366347870286894,1.342851128598483,1.3176420966871212,1.290564432903234,1.2614210366375573,1.2299564620382315,1.195827385387638,1.1585488318903814,1.117384538320497,1.0710814768156298,1.016996837450545,1.0247567320521507,1.0786086685786527,1.1246752121052674,1.1655990453685268,1.2026330625736534,1.236513386374841,1.2677248435957227,1.2966106020534505,1.3234259431939321,1.3483677940847816,1.3715923130085426,1.3932260200000117,1.413373186246309,1.4321209317874966,1.4495428548045806,1.465701684203524,1.4806512616932297,1.4944380508840434,1.5071023047373213,1.5186789809926386,1.5291984681413944,1.5386871664983937,1.5471679566439553,1.554660578962659,1.5611819419397697,1.5667463724926178,1.5713658183886443,1.575050010385146,1.577806589879902,1.5796412064211682,1.580557588272082,1.580557588272082,1.5796412064211682,1.577806589879902,1.575050010385146,1.5713658183886443,1.5667463724926178,1.5611819419397697,1.554660578962659,1.5471679566439553,1.5386871664983937,1.5291984681413944,1.5186789809926386,1.5071023047373213,1.4944380508840434,1.4806512616932297,1.465701684203524,1.4495428548045806,1.4321209317874968,1.413373186246309,1.3932260200000117,1.3715923130085426,1.3483677940847816,1.3234259431939321,1.2966106020534505,1.2677248435957227,1.2365133863748414,1.2026330625736534,1.165599045368527,1.1246752121052677,1.0786086685786527,1.0247567320521507,1.0318939587528015,1.0855093773010513,1.1313354605210413,1.1720147574921704,1.2088000218478914,1.2424272282706346,1.2733810476835672,1.3020044834978894,1.3285526436178587,1.353222271744058,1.3761693322105968,1.3975201396922612,1.4173787476913684,1.4358320452319429,1.452953385036395,1.4688052348799365,1.4834411583052511,1.4969073222061353,1.509243662589979,1.5204847981216105,1.5306607539892083,1.539797540611012,1.5479176194167725,1.5550402793845226,1.5611819419397697,1.5663564074302458,1.5705750531512876,1.5738469904649177,1.576179186690877,1.5775765559836068,1.5780420222262996,1.5775765559836068,1.576179186690877,1.5738469904649177,1.5705750531512876,1.566356407430246,1.5611819419397697,1.5550402793845224,1.5479176194167725,1.539797540611012,1.5306607539892083,1.5204847981216105,1.509243662589979,1.4969073222061353,1.4834411583052511,1.4688052348799365,1.452953385036395,1.4358320452319429,1.4173787476913684,1.397520139692261,1.376169332210597,1.353222271744058,1.3285526436178585,1.3020044834978892,1.2733810476835672,1.2424272282706346,1.2088000218478916,1.1720147574921707,1.1313354605210413,1.0855093773010513,1.0318939587528015,1.0384149670533367,1.0917899252949617,1.1373714722228214,1.177802016344545,1.2143341633218216,1.2477037319366158,1.2783952287061426,1.3067514834999523,1.333027420855272,1.357419590524249,1.380083751480983,1.401146000715457,1.420710160713951,1.438862875041894,1.4556772352909442,1.4712154310700942,1.4855307292054793,1.4986689796369295,1.5106697792970871,1.5215673835475612,1.5313914276799632,1.5401675029619655,1.5479176194167725,1.554660578962659,1.5604122764555344,1.5651859417710259,1.5689923328091961,1.5718398868540293,1.5737348358314522,1.574681289515961,1.5746812895159612,1.5737348358314522,1.5718398868540293,1.5689923328091961,1.5651859417710259,1.5604122764555344,1.554660578962659,1.5479176194167725,1.5401675029619655,1.5313914276799632,1.5215673835475612,1.5106697792970876,1.4986689796369295,1.4855307292054793,1.4712154310700942,1.4556772352909442,1.4388628750418937,1.420710160713951,1.401146000715457,1.380083751480983,1.357419590524249,1.333027420855272,1.3067514834999523,1.2783952287061424,1.2477037319366155,1.2143341633218212,1.1778020163445453,1.1373714722228216,1.0917899252949619,1.038414967053337,1.0443255526962936,1.097455974645788,1.1427887687242424,1.1829661954675215,1.219240704636849,1.2523479506082373,1.2827722663572518,1.3108562983864118,1.336854777284509,1.3609640474436813,1.383339650153225,1.404107451387086,1.4233710281729481,1.4412167629454893,1.4577174691301484,1.4729350396193692,1.48692242428532,1.4997251339930844,1.511382402372084,1.5219280948873626,1.5313914276799632,1.539797540611012,1.5471679566439556,1.55352095112747,1.5588718484453603,1.5632332590779805,1.5666152668473536,1.5690255736436507,1.5704696070128525,1.570950594454669,1.5704696070128525,1.5690255736436507,1.5666152668473536,1.5632332590779805,1.5588718484453603,1.55352095112747,1.5471679566439553,1.539797540611012,1.5313914276799632,1.5219280948873626,1.511382402372084,1.4997251339930842,1.48692242428532,1.472935039619369,1.4577174691301484,1.4412167629454893,1.4233710281729481,1.404107451387086,1.3833396501532251,1.360964047443681,1.3368547772845087,1.3108562983864118,1.2827722663572518,1.2523479506082371,1.2192407046368487,1.1829661954675215,1.1427887687242424,1.0974559746457881,1.0443255526962936,1.0496308907073186,1.1025125598074077,1.1475922365074174,1.1875120254427476,1.2235242119686693,1.2563642769195456,1.2865163699039104,1.3143229434758477,1.34003852286414,1.363859234776122,1.3859403894850528,1.406407607506282,1.4253642047367423,1.4428962854448923,1.4590763663396218,1.4739660233594083,1.4876178673016733,1.50007704572828,1.511382402372084,1.5215673835475612,1.5306607539892083,1.5386871664983937,1.545667617468965,1.5516198117774949,1.556558454412514,1.5604954817763368,1.563440242297174,1.56539963348525,1.566378200611759,1.566378200611759,1.5653996334852498,1.5634402422971738,1.5604954817763368,1.556558454412514,1.5516198117774949,1.545667617468965,1.5386871664983937,1.5306607539892083,1.5215673835475612,1.511382402372084,1.5000770457282802,1.4876178673016736,1.4739660233594083,1.459076366339622,1.4428962854448923,1.4253642047367427,1.4064076075062824,1.3859403894850528,1.3638592347761223,1.3400385228641403,1.3143229434758479,1.2865163699039104,1.2563642769195456,1.2235242119686693,1.1875120254427478,1.1475922365074174,1.1025125598074084,1.0496308907073193,1.0543355641337426,1.1069641158553871,1.1517861547474482,1.1914436210393724,1.2271886265447818,1.259756468731008,1.2896311032581502,1.317154777320283,1.3425817984613853,1.3661080623727542,1.387888633869053,1.4080488723348805,1.4266918155009498,1.4439032709191701,1.4597554383444657,1.4743095546405662,1.4876178673016733,1.4997251339930844,1.5106697792970871,1.5204847981216105,1.5291984681413944,1.5368349155882077,1.5434145663837942,1.5489545060094527,1.5534687653756745,1.5569685454909614,1.5594623904035776,1.5609563153489607,1.5614538950336536,1.5609563153489607,1.5594623904035776,1.5569685454909616,1.5534687653756745,1.5489545060094527,1.5434145663837942,1.5368349155882077,1.5291984681413944,1.5204847981216105,1.5106697792970876,1.4997251339930844,1.4876178673016736,1.4743095546405662,1.4597554383444657,1.4439032709191701,1.4266918155009498,1.408048872334881,1.3878886338690535,1.3661080623727544,1.3425817984613855,1.3171547773202832,1.2896311032581504,1.2597564687310083,1.2271886265447818,1.1914436210393726,1.1517861547474482,1.1069641158553873,1.0543355641337433,1.0584435889005643,1.1108145028142598,1.155374219062915,1.1947645043343271,1.2302372870750866,1.2625276708040905,1.292119405821428,1.3193545216363707,1.3444870947768595,1.3677127754755969,1.3891863674164937,1.40903295181793,1.42735526969407,1.4442388116428562,1.4597554383444657,1.4739660233594083,1.48692242428532,1.4986689796369295,1.509243662589979,1.5186789809926386,1.5270026859500505,1.534238333221879,1.5404057293345943,1.5455212856914557,1.5495982978091414,1.5526471623162073,1.5546755409861306,1.5556884784896976,1.5556884784896978,1.5546755409861306,1.5526471623162075,1.5495982978091416,1.5455212856914557,1.5404057293345943,1.534238333221879,1.5270026859500507,1.5186789809926386,1.509243662589979,1.4986689796369295,1.48692242428532,1.4739660233594083,1.4597554383444657,1.4442388116428562,1.42735526969407,1.4090329518179305,1.3891863674164942,1.367712775475597,1.3444870947768595,1.319354521636371,1.292119405821428,1.2625276708040907,1.2302372870750866,1.1947645043343271,1.155374219062915,1.11081450281426,1.0584435889005643,1.0619584351357512,1.1140670264060408,1.1583595616341835,1.197477624140946,1.2326729484244832,1.264680432643682,1.2939836094138295,1.320924277228159,1.3457562671560162,1.3686749682993515,1.3898349061758577,1.4093608652873644,1.42735526969407,1.4439032709191701,1.4590763663396218,1.4729350396193692,1.4855307292054793,1.496907322206135,1.5071023047373213,1.516147658077609,1.524070562860036,1.530893955448993,1.5366369682929113,1.5413152774012364,1.5449413739107014,1.5475247721750747,1.5490721634031817,1.5495875212220558,1.5490721634031812,1.5475247721750747,1.5449413739107014,1.5413152774012364,1.5366369682929113,1.530893955448993,1.5240705628600364,1.516147658077609,1.5071023047373213,1.4969073222061353,1.4855307292054793,1.4729350396193692,1.459076366339622,1.4439032709191701,1.42735526969407,1.4093608652873646,1.3898349061758577,1.3686749682993518,1.3457562671560166,1.320924277228159,1.2939836094138295,1.2646804326436825,1.2326729484244832,1.1974776241409462,1.1583595616341837,1.114067026406041,1.0619584351357512,1.064883045258098,1.1167244555078757,1.1607447679713685,1.1995853720209084,1.2344977967946407,1.2662167227666496,1.2952254515361838,1.3218655361378815,1.346390546510337,1.3689955935892812,1.3898349061758577,1.4090329518179303,1.4266918155009498,1.4428962854448923,1.4577174691301484,1.4712154310700942,1.4834411583052511,1.4944380508840434,1.5042430683528574,1.5128876215181606,1.5203982716177162,1.526797280937876,1.5321030465332584,1.5363304400333624,1.5394910703001343,1.5415934811226912,1.5426432926661053,1.5426432926661053,1.5415934811226912,1.5394910703001343,1.5363304400333624,1.532103046533258,1.526797280937876,1.5203982716177158,1.5128876215181606,1.5042430683528574,1.4944380508840436,1.4834411583052511,1.4712154310700942,1.4577174691301487,1.4428962854448923,1.4266918155009498,1.4090329518179305,1.3898349061758577,1.3689955935892812,1.3463905465103372,1.3218655361378817,1.2952254515361838,1.2662167227666499,1.2344977967946407,1.1995853720209086,1.1607447679713687,1.1167244555078757,1.064883045258098,1.0672198490700031,1.1187890365551307,1.1625318905614013,1.2010895951011364,1.2357134616276786,1.2671379395990745,1.295846085155977,1.322179190202273,1.346390546510337,1.3686749682993518,1.389186367416494,1.4080488723348807,1.4253642047367425,1.4412167629454893,1.4556772352909442,1.4688052348799365,1.4806512616932297,1.4912581892096501,1.5006624065034793,1.508894704985911,1.5159809718166695,1.5219427338882936,1.5267975838754546,1.5305595111328658,1.5332391539578216,1.5348439850956859,1.5353784388202256,1.5348439850956859,1.5332391539578218,1.5305595111328658,1.5267975838754546,1.5219427338882936,1.5159809718166695,1.508894704985911,1.5006624065034793,1.4912581892096501,1.4806512616932297,1.4688052348799365,1.4556772352909442,1.4412167629454893,1.4253642047367427,1.408048872334881,1.3891863674164942,1.3686749682993518,1.3463905465103372,1.322179190202273,1.295846085155977,1.2671379395990745,1.2357134616276788,1.2010895951011364,1.1625318905614015,1.118789036555131,1.0672198490700033,1.068970776052867,1.1202625050807724,1.1637224595772382,1.201991605869783,1.2363210243957121,1.2674449191544763,1.295846085155977,1.3218655361378815,1.3457562671560164,1.3677127754755967,1.3878886338690533,1.4064076075062821,1.4233710281729481,1.438862875041894,1.4529533850363947,1.465701684203524,1.477157745954445,1.4873638732958805,1.4963558359068385,1.5041637511204733,1.5108127707026957,1.5163236171660983,1.5207130009105667,1.5239939407261618,1.5261760038664252,1.5272654771854148,1.5272654771854148,1.5261760038664247,1.5239939407261618,1.5207130009105667,1.5163236171660983,1.5108127707026957,1.5041637511204733,1.4963558359068385,1.4873638732958812,1.477157745954445,1.465701684203524,1.452953385036395,1.4388628750418937,1.4233710281729481,1.4064076075062824,1.3878886338690533,1.3677127754755969,1.3457562671560164,1.3218655361378815,1.295846085155977,1.2674449191544763,1.2363210243957121,1.2019916058697833,1.1637224595772384,1.1202625050807726,1.0689707760528673,1.070137265023107,1.1211460945412075,1.164317490790483,1.2022921890824148,1.2363210243957121,1.2671379395990745,1.2952254515361838,1.320924277228159,1.3444870947768595,1.3661080623727542,1.3859403894850528,1.404107451387086,1.420710160713951,1.4358320452319429,1.4495428548045806,1.4619011889093374,1.472956450485274,1.482750323143838,1.491317902485999,1.4986885704510973,1.5048866744250988,1.5099320546458088,1.5138404509484609,1.5166238110793628,1.518290516400752,1.5188455359952018,1.518290516400752,1.5166238110793633,1.5138404509484609,1.5099320546458088,1.5048866744250986,1.4986885704510973,1.491317902485999,1.482750323143838,1.472956450485274,1.4619011889093374,1.4495428548045806,1.4358320452319429,1.420710160713951,1.404107451387086,1.3859403894850528,1.3661080623727542,1.3444870947768595,1.320924277228159,1.2952254515361838,1.2671379395990745,1.2363210243957121,1.202292189082415,1.164317490790483,1.1211460945412075,1.0701372650231071,1.0707202712709103,1.1214405425418208,1.164317490790483,1.201991605869783,1.2357134616276786,1.2662167227666496,1.2939836094138295,1.3193545216363705,1.3425817984613853,1.3638592347761223,1.3833396501532251,1.401146000715457,1.4173787476913682,1.4321209317874968,1.4454417762977625,1.4573993102275347,1.4680423171205994,1.477411806510367,1.4855421386039913,1.492461890960869,1.4981945286921776,1.5027589214710713,1.5061697380890307,1.5084377404010587,1.5095699919979078,1.5095699919979078,1.5084377404010587,1.5061697380890307,1.5027589214710715,1.4981945286921776,1.492461890960869,1.4855421386039913,1.4774118065103667,1.4680423171205994,1.4573993102275347,1.4454417762977625,1.4321209317874968,1.4173787476913684,1.401146000715457,1.3833396501532251,1.3638592347761223,1.3425817984613855,1.3193545216363707,1.2939836094138295,1.2662167227666496,1.2357134616276786,1.2019916058697833,1.164317490790483,1.1214405425418208,1.0707202712709103,1.0707202712709103,1.1211460945412075,1.1637224595772382,1.2010895951011364,1.2344977967946407,1.2646804326436822,1.292119405821428,1.317154777320283,1.34003852286414,1.3609640474436813,1.380083751480983,1.397520139692261,1.413373186246309,1.4277254052800652,1.4406454496153465,1.452190728862247,1.4624093524865152,1.4713415946277462,1.4790210111131499,1.4854752972273346,1.4907269475168268,1.4947937606110278,1.4976892194101132,1.499422767997601,1.5,1.4994227679976009,1.4976892194101128,1.4947937606110278,1.490726947516827,1.4854752972273346,1.4790210111131499,1.4713415946277462,1.4624093524865152,1.452190728862247,1.4406454496153465,1.4277254052800654,1.413373186246309,1.397520139692261,1.380083751480983,1.360964047443681,1.34003852286414,1.317154777320283,1.292119405821428,1.2646804326436822,1.2344977967946407,1.2010895951011364,1.1637224595772384,1.1211460945412075,1.0707202712709103,1.070137265023107,1.1202625050807724,1.1625318905614013,1.1995853720209084,1.2326729484244832,1.2625276708040905,1.2896311032581502,1.3143229434758479,1.336854777284509,1.357419590524249,1.3761693322105968,1.393226020000012,1.4086891014916876,1.4226405203504593,1.4351483100028688,1.4462692059809723,1.4560505823567045,1.4645319088897144,1.471745859132425,1.4777191578047935,1.4824732284095934,1.48602468368492,1.4883856887594653,1.4895642177525035,1.4895642177525033,1.488385688759465,1.48602468368492,1.4824732284095934,1.477719157804794,1.471745859132425,1.4645319088897144,1.4560505823567045,1.4462692059809723,1.4351483100028688,1.4226405203504593,1.4086891014916876,1.3932260200000117,1.376169332210597,1.357419590524249,1.3368547772845087,1.3143229434758479,1.2896311032581504,1.2625276708040905,1.2326729484244832,1.1995853720209084,1.1625318905614013,1.1202625050807726,1.0701372650231071,1.068970776052867,1.1187890365551307,1.1607447679713685,1.197477624140946,1.2302372870750866,1.259756468731008,1.2865163699039102,1.3108562983864118,1.333027420855272,1.353222271744058,1.3715923130085426,1.3882590357355855,1.4033213170522765,1.4168604812281769,1.4289438876117895,1.4396275363413569,1.4489579971088677,1.456973857399185,1.4637068202000796,1.469182539187755,1.4734212519736805,1.4764382535244673,1.478244239004563,1.478845535995202,1.4782442390045625,1.4764382535244673,1.4734212519736805,1.469182539187755,1.4637068202000798,1.456973857399185,1.4489579971088677,1.4396275363413569,1.4289438876117895,1.4168604812281766,1.4033213170522765,1.3882590357355857,1.3715923130085426,1.353222271744058,1.333027420855272,1.3108562983864118,1.2865163699039102,1.259756468731008,1.2302372870750866,1.197477624140946,1.1607447679713685,1.1187890365551307,1.0689707760528673,1.0672198490700031,1.1167244555078755,1.1583595616341835,1.1947645043343271,1.2271886265447818,1.2563642769195456,1.282772266357252,1.3067514834999523,1.3285526436178587,1.3483677940847816,1.366347870286894,1.3826137928389521,1.3972638194727718,1.410378600379875,1.422024759514951,1.4322574926362979,1.441122487161116,1.4486573600096169,1.454892743125819,1.4598531042946206,1.4635573633560055,1.4660193453123427,1.4672480987900387,1.4672480987900387,1.4660193453123427,1.4635573633560055,1.4598531042946201,1.4548927431258187,1.4486573600096169,1.441122487161116,1.4322574926362979,1.422024759514951,1.4103786003798748,1.3972638194727718,1.3826137928389524,1.366347870286894,1.3483677940847816,1.3285526436178585,1.3067514834999523,1.2827722663572518,1.2563642769195456,1.2271886265447818,1.1947645043343271,1.1583595616341835,1.1167244555078752,1.067219849070003,1.064883045258098,1.1140670264060408,1.155374219062915,1.1914436210393724,1.2235242119686693,1.2523479506082373,1.2783952287061426,1.3020044834978892,1.3234259431939321,1.342851128598483,1.360430404625611,1.3762840724947976,1.39050971585982,1.4031872495183872,1.4143824930452424,1.4241497599238961,1.432533767006898,1.4395710601707064,1.4452910854680343,1.4497169929122953,1.4528662323792307,1.4547509823331688,1.4553784388202258,1.4547509823331688,1.4528662323792307,1.4497169929122953,1.4452910854680339,1.4395710601707064,1.432533767006898,1.4241497599238961,1.4143824930452424,1.403187249518387,1.39050971585982,1.3762840724947973,1.360430404625611,1.342851128598483,1.3234259431939321,1.3020044834978892,1.2783952287061424,1.2523479506082371,1.2235242119686693,1.1914436210393724,1.1553742190629148,1.1140670264060408,1.0648830452580977,1.0619584351357512,1.1108145028142598,1.1517861547474482,1.1875120254427476,1.219240704636849,1.2477037319366158,1.2733810476835672,1.2966106020534507,1.3176420966871216,1.3366664819166876,1.3538335032609439,1.3692627878613335,1.38305118397782,1.3952778020281662,1.4060075793123286,1.4152938587491661,1.423180286147475,1.429702221492409,1.4348877930651966,1.4387586809150086,1.4413306883795447,1.4426141413428435,1.4426141413428435,1.4413306883795447,1.4387586809150084,1.4348877930651966,1.4297022214924093,1.423180286147475,1.4152938587491661,1.4060075793123286,1.3952778020281658,1.38305118397782,1.3692627878613335,1.3538335032609439,1.3366664819166876,1.3176420966871212,1.2966106020534505,1.2733810476835672,1.2477037319366155,1.2192407046368487,1.1875120254427476,1.151786154747448,1.1108145028142598,1.061958435135751,1.0584435889005643,1.1069641158553871,1.1475922365074174,1.1829661954675215,1.2143341633218214,1.2424272282706346,1.2677248435957227,1.290564432903234,1.31119512736192,1.3298072579086149,1.346549895984074,1.3615419333359278,1.3748794138441929,1.3866405656518463,1.3968893554941928,1.405678055246337,1.4130491248257722,1.4190366064461661,1.423667158424504,1.4269608142719166,1.4289315247458139,1.4295875212220555,1.4289315247458139,1.4269608142719166,1.423667158424504,1.4190366064461661,1.4130491248257724,1.4056780552463373,1.3968893554941928,1.3866405656518461,1.3748794138441929,1.3615419333359278,1.346549895984074,1.3298072579086146,1.31119512736192,1.290564432903234,1.2677248435957227,1.2424272282706346,1.2143341633218212,1.1829661954675215,1.1475922365074174,1.106964115855387,1.0584435889005641,1.0543355641337426,1.1025125598074077,1.1427887687242424,1.177802016344545,1.2088000218478914,1.236513386374841,1.2614210366375573,1.2838598257700837,1.3040782655458987,1.322266012823796,1.3385714036507192,1.353112525394352,1.3659845396599244,1.3772647040257617,1.387015914183415,1.3952892561166856,1.4021258719715803,1.4075583339975246,1.4116116539734633,1.4143040128302367,1.4156472668170772,1.415647266817077,1.4143040128302367,1.4116116539734633,1.4075583339975246,1.4021258719715806,1.3952892561166856,1.387015914183415,1.3772647040257617,1.3659845396599244,1.353112525394352,1.3385714036507192,1.3222660128237962,1.3040782655458985,1.2838598257700842,1.2614210366375573,1.2365133863748414,1.2088000218478916,1.1778020163445453,1.1427887687242424,1.102512559807408,1.054335564133743,1.0496308907073186,1.097455974645788,1.1373714722228214,1.1720147574921704,1.2026330625736532,1.229956462038231,1.2544633121259623,1.2764898465756176,1.2962839030826354,1.3140344031119968,1.3298888783306988,1.3439645338316386,1.3563555606553952,1.3671381453365394,1.3763739976753187,1.384112885884049,1.390394482144494,1.3952497121680392,1.3987017351533386,1.400766637523055,1.4014538950336537,1.4007666375230552,1.398701735153339,1.3952497121680394,1.390394482144494,1.384112885884049,1.3763739976753187,1.3671381453365394,1.3563555606553952,1.3439645338316386,1.329888878330699,1.3140344031119968,1.2962839030826354,1.2764898465756176,1.2544633121259625,1.2299564620382315,1.2026330625736534,1.1720147574921707,1.1373714722228216,1.0974559746457881,1.049630890707319,1.0443255526962936,1.0917899252949617,1.1313354605210413,1.1655990453685268,1.1958273853876378,1.2227499846772307,1.2468445800820906,1.2684467312629488,1.2878035405214303,1.3051031249425709,1.32049213391858,1.3340868019777037,1.3459802491167672,1.3562474759790373,1.3649488745932767,1.3721327432075572,1.377837107465603,1.3820910404985092,1.3849156069967516,1.3863245128902262,1.3863245128902264,1.3849156069967516,1.3820910404985094,1.3778371074656033,1.3721327432075572,1.3649488745932767,1.3562474759790373,1.3459802491167672,1.334086801977704,1.3204921339185802,1.3051031249425709,1.2878035405214305,1.2684467312629488,1.2468445800820906,1.222749984677231,1.195827385387638,1.165599045368527,1.1313354605210413,1.0917899252949619,1.0443255526962936,1.0384149670533367,1.0855093773010513,1.1246752121052674,1.1585488318903812,1.1883763717345073,1.214886716341229,1.2385569284772917,1.2597218324096136,1.2786277260598742,1.295461844238322,1.310369865772515,1.323466954146946,1.334845043467135,1.3445778166048652,1.3527241956246545,1.359330832236536,1.364433899503943,1.368060376049792,1.3702289460717927,1.370950594454669,1.370228946071793,1.368060376049792,1.3644338995039431,1.3593308322365363,1.3527241956246547,1.3445778166048652,1.3348450434671353,1.323466954146946,1.3103698657725151,1.295461844238322,1.2786277260598742,1.2597218324096138,1.2385569284772917,1.2148867163412287,1.1883763717345075,1.1585488318903814,1.1246752121052677,1.0855093773010513,1.038414967053337,1.0318939587528015,1.0786086685786527,1.117384538320497,1.1508573579306256,1.1802726430918806,1.2063586044298051,1.2295915693173318,1.2503055576414328,1.2687459850490004,1.285099115785632,1.2995095576351323,1.3120912881906888,1.3229349237863381,1.3321126773296184,1.3396818243470088,1.3456871639682513,1.3501627747486011,1.3531332548182082,1.3546145673296104,1.3546145673296104,1.3531332548182082,1.3501627747486011,1.3456871639682513,1.339681824347009,1.3321126773296184,1.3229349237863381,1.3120912881906888,1.2995095576351323,1.285099115785632,1.2687459850490006,1.2503055576414328,1.2295915693173318,1.2063586044298051,1.1802726430918806,1.150857357930626,1.117384538320497,1.0786086685786527,1.0318939587528015,1.0247567320521507,1.0710814768156298,1.109456546382489,1.1425171113097465,1.1715080132022044,1.1971567272915926,1.2199387765708984,1.2401872986523066,1.258146738618058,1.2740022896699967,1.287897373700623,1.2999446505316394,1.310233266532839,1.3188337880737202,1.3258016381004714,1.3311795212346567,1.3349991355387647,1.3372823580977733,1.3380420222262996,1.3372823580977733,1.3349991355387647,1.3311795212346567,1.3258016381004714,1.3188337880737202,1.310233266532839,1.2999446505316394,1.287897373700623,1.2740022896699967,1.258146738618058,1.2401872986523066,1.2199387765708984,1.1971567272915926,1.1715080132022042,1.1425171113097465,1.1094565463824893,1.0710814768156298,1.0247567320521507,1.016996837450545,1.0629207820390392,1.1008835969230273,1.1335197785814877,1.1620734332254092,1.1872712317065768,1.2095878147431895,1.2293553493827813,1.2468172096638401,1.2621574028969045,1.2755180332029907,1.2870102904395573,1.2967216744383578,1.3047208989885999,1.311061292528294,1.3157831791862378,1.3189155359797473,1.3204771101558799,1.3204771101558799,1.3189155359797473,1.3157831791862378,1.311061292528294,1.3047208989885997,1.2967216744383578,1.2870102904395575,1.2755180332029905,1.2621574028969045,1.24681720966384,1.2293553493827813,1.2095878147431895,1.1872712317065766,1.1620734332254092,1.1335197785814877,1.1008835969230273,1.0629207820390394,1.016996837450545,1.0086071338439866,1.0541188237496093,1.0916572553648005,1.1238561897747248,1.1519589288104253,1.1766912610488998,1.1985268566436964,1.2177968115985955,1.23474331406078,1.2495490535693046,1.262354664280941,1.2732696895151085,1.2823797765232696,1.289751544586455,1.2954359416499073,1.2994705707972523,1.3018812792078858,1.3026831892554922,1.3018812792078858,1.2994705707972523,1.2954359416499073,1.2897515445864545,1.2823797765232696,1.2732696895151085,1.262354664280941,1.2495490535693046,1.23474331406078,1.2177968115985955,1.1985268566436964,1.1766912610488998,1.1519589288104253,1.1238561897747248,1.0916572553648003,1.054118823749609,1.0086071338439866,0.9995797452811138,1.0446670519179397,1.0817682362845948,1.113516255086298,1.1411535278793057,1.165404872675964,1.1867428885860678,1.2054974857220928,1.2219095344597373,1.2361602543738117,1.2483886330830491,1.2587023613265775,1.2671849918476819,1.2739007634346253,1.278897902987479,1.2822108837519481,1.283861928034055,1.2838619280340553,1.2822108837519481,1.278897902987479,1.273900763434625,1.2671849918476819,1.2587023613265775,1.2483886330830491,1.2361602543738117,1.2219095344597373,1.2054974857220928,1.1867428885860678,1.165404872675964,1.1411535278793055,1.113516255086298,1.0817682362845946,1.0446670519179395,0.9995797452811136,0.9899060116098558,1.0345560709981456,1.0712063397565794,1.1024888923155898,1.1296451776667815,1.153398942778747,1.1742216008699766,1.1924417442814612,1.208298773424656,1.2219722613363317,1.2335993430549297,1.2432856148114013,1.2511122488562638,1.2571407629326086,1.2614162541025862,1.263969570738529,1.26481870497303,1.263969570738529,1.2614162541025862,1.2571407629326083,1.2511122488562638,1.243285614811401,1.2335993430549297,1.2219722613363317,1.208298773424656,1.1924417442814614,1.1742216008699766,1.1533989427787468,1.1296451776667813,1.1024888923155898,1.0712063397565794,1.0345560709981452,0.9899060116098555,0.9795764321680173,1.0237755759480858,1.059960378463827,1.0907619435810212,1.11742064924752,1.1406590565406114,1.1609472609073008,1.178612384724336,1.1938921818651316,1.2069643727861679,1.217963998017709,1.2269942732979386,1.2341336498322026,1.2394405155256711,1.242956342567123,1.2447077491554597,1.2447077491554595,1.242956342567123,1.2394405155256711,1.2341336498322026,1.2269942732979386,1.217963998017709,1.2069643727861679,1.1938921818651316,1.178612384724336,1.1609472609073008,1.140659056540611,1.1174206492475196,1.0907619435810212,1.059960378463827,1.0237755759480855,0.9795764321680169,0.9685806015045626,1.0123142790419384,1.0480180941158634,1.0783220795483648,1.1044654273959893,1.1271693809645407,1.1469025657367804,1.1639904575514164,1.178668957701573,1.1911136921355523,1.2014573208908517,1.2098003386604825,1.2162180668118705,1.2207652683768133,1.2234791853706584,1.2243814577244938,1.2234791853706584,1.2207652683768129,1.2162180668118707,1.2098003386604825,1.2014573208908514,1.1911136921355523,1.1786689577015728,1.1639904575514164,1.1469025657367804,1.1271693809645404,1.104465427395989,1.0783220795483646,1.0480180941158632,1.0123142790419382,0.9685806015045623,0.9569071359152326,1.0001598260107925,1.0353660614000244,1.0651546890136516,1.0907635831367362,1.1129125171108378,1.1320684698806784,1.1485550647046752,1.1626061083677748,1.1743948463255123,1.1840512175702131,1.1916725869569682,1.1973306509798298,1.201075942497166,1.2029407252565103,1.2029407252565105,1.2010759424971658,1.19733065097983,1.1916725869569682,1.1840512175702131,1.1743948463255125,1.1626061083677746,1.1485550647046754,1.1320684698806784,1.1129125171108378,1.0907635831367364,1.0651546890136518,1.0353660614000246,1.0001598260107925,0.9569071359152329,0.9445435893262523,0.987298699737119,1.021989577307477,1.0512437511965642,1.0762976257251988,1.0978693276969014,1.116423983476103,1.132283121813043,1.1456781689999005,1.1567796494470397,1.1657143723088643,1.1725760775670933,1.1774322315423487,1.1803283888251839,1.181290899230693,1.1803283888251839,1.1774322315423484,1.1725760775670935,1.1657143723088643,1.1567796494470395,1.1456781689999005,1.132283121813043,1.1164239834761032,1.0978693276969016,1.076297625725199,1.0512437511965644,1.0219895773074772,0.9872986997371193,0.9445435893262528,0.9314763567502714,0.9737161093422639,1.0078725331880818,1.036571687482719,1.061048330008955,1.082018734990018,1.0999459342821627,1.1151490761428609,1.1278568658191201,1.1382366978833829,1.1464117566166816,1.152471551827304,1.1564785715680586,1.1584724564970583,1.1584724564970583,1.1564785715680586,1.152471551827304,1.1464117566166816,1.1382366978833829,1.12785686581912,1.1151490761428609,1.099945934282163,1.0820187349900185,1.061048330008955,1.0365716874827193,1.007872533188082,0.9737161093422642,0.9314763567502714,0.9176905631521233,0.9593958620195758,0.992997266270944,1.0211191885631823,1.0449945340987787,1.065337482592785,1.0826086854086878,1.0971245697587875,1.1091107110521705,1.1187308789879076,1.1261040276735996,1.1313146886497212,1.1344194360366402,1.1354508105601309,1.13441943603664,1.1313146886497214,1.1261040276735996,1.1187308789879074,1.1091107110521705,1.0971245697587875,1.082608685408688,1.0653374825927853,1.044994534098779,1.0211191885631825,0.9929972662709442,0.959395862019576,0.9176905631521234,0.9031699350756281,0.944320214348631,0.9773443865976,1.0048650118991993,1.0281129009477388,1.0477998529655033,1.0643837982708073,1.078178034238031,1.0894045114028879,1.0982227692910183,1.1047467837422096,1.1090551723644957,1.1111974093459056,1.1111974093459056,1.1090551723644957,1.1047467837422096,1.0982227692910183,1.0894045114028879,1.078178034238031,1.0643837982708073,1.0477998529655033,1.0281129009477388,1.0048650118991993,0.9773443865976001,0.9443202143486311,0.9031699350756281,0.8878966517656206,0.9284696990362244,0.9608925742945542,0.9877857431090965,1.0103776356813943,1.02937733018856,1.0452396271109883,1.0582741989496858,1.068698766066936,1.0766678897205657,1.0822896318179214,1.0856355100346986,1.086746372492618,1.0856355100346986,1.0822896318179214,1.0766678897205657,1.0686987660669363,1.0582741989496858,1.0452396271109883,1.02937733018856,1.0103776356813943,0.9877857431090965,0.9608925742945542,0.9284696990362246,0.8878966517656207,0.8718511717297366,0.9118229220097013,0.943618340780974,0.9698555131192744,0.9917601481809734,1.0100381943052634,1.0251408270991653,1.0373734888902564,1.0469489217730061,1.0540157730728,1.0586750047646467,1.0609895084579333,1.0609895084579333,1.058675004764647,1.0540157730728,1.0469489217730061,1.0373734888902564,1.0251408270991653,1.0100381943052634,0.9917601481809734,0.9698555131192744,0.943618340780974,0.911822922009701,0.8718511717297366,0.8550120296644868,0.8943563234573944,0.9254957457524254,0.9510456605801273,0.9722286472589503,0.989747029254714,1.0040477520010098,1.0154312795575997,1.0241044400865138,1.030208780980799,1.033836638149155,1.0350402793845224,1.033836638149155,1.030208780980799,1.0241044400865138,1.0154312795575997,1.0040477520010098,0.989747029254714,0.9722286472589503,0.9510456605801273,0.9254957457524254,0.8943563234573944,0.8550120296644868,0.8373555973394452,0.876043894656111,0.9064960594405435,0.9313243258853694,0.9517476484356664,0.9684641203838236,0.9819157088956184,0.9923969640983729,1.000107614221778,1.0051805805925722,1.007697575303009,1.0076975753030093,1.0051805805925724,1.000107614221778,0.9923969640983727,0.9819157088956184,0.9684641203838236,0.9517476484356662,0.9313243258853694,0.9064960594405435,0.876043894656111,0.8373555973394452,0.8188558002786314,0.8568568400846985,0.8865873564862551,0.9106559588025546,0.9302773713052451,0.9461447090189015,0.9586940251768609,0.9682127699741063,0.9748920455740208,0.9788541494868961,0.9801675029619655,0.9788541494868959,0.9748920455740208,0.9682127699741063,0.9586940251768609,0.9461447090189017,0.9302773713052451,0.9106559588025546,0.8865873564862551,0.8568568400846984,0.8188558002786313,0.7994837797373409,0.8367631711605321,0.8657340234335625,0.8890007157022556,0.9077729939704452,0.9227380593302662,0.9343248650827164,0.9428122353564714,0.9483806484984665,0.9511391111759744,0.9511391111759744,0.9483806484984665,0.9428122353564714,0.9343248650827164,0.9227380593302662,0.9077729939704452,0.8890007157022556,0.8657340234335624,0.8367631711605319,0.7994837797373406,0.7792074863105535,0.8157272136052186,0.8438961558306425,0.8663137138648348,0.884183719779189,0.8981862747335008,0.9087417059624605,0.916118213778296,0.9204829856849239,0.9219280948873623,0.9204829856849239,0.9161182137782958,0.9087417059624604,0.8981862747335008,0.8841837197791886,0.8663137138648348,0.8438961558306423,0.8157272136052184,0.7792074863105533,0.7579911871785623,0.7937090044256209,0.8210288124165438,0.8425440980969009,0.8594515936057457,0.8724227740365672,0.8818673428076075,0.8880402093880759,0.8910916278196342,0.8910916278196342,0.8880402093880757,0.8818673428076075,0.8724227740365671,0.8594515936057457,0.8425440980969007,0.8210288124165438,0.7937090044256206,0.7579911871785622,0.7357948629753386,0.7706635459878962,0.7970810816249839,0.8176338568998315,0.8335099778851861,0.8453702958580881,0.8536112233937613,0.85847073649916,0.8600770457282799,0.85847073649916,0.8536112233937613,0.8453702958580881,0.8335099778851861,0.8176338568998317,0.7970810816249839,0.7706635459878964,0.7357948629753386,0.7125734617567773,0.7465398724154995,0.7719948976470781,0.7915162983984353,0.8062815569258706,0.8169382336634052,0.8238658077240087,0.8272802116269692,0.8272802116269692,0.8238658077240087,0.8169382336634052,0.8062815569258706,0.7915162983984353,0.7719948976470782,0.7465398724154997,0.7125734617567775,0.6882759652992884,0.7212798655525017,0.7457035162605894,0.7641140545540274,0.7776756718460954,0.7870189951085607,0.7925014599667257,0.7943095546405662,0.7925014599667257,0.7870189951085604,0.7776756718460954,0.7641140545540274,0.7457035162605896,0.7212798655525017,0.6882759652992885,0.6628442049696138,0.6948167306993362,0.7181295189495049,0.7353364160075756,0.747584679824574,0.7554828938846008,0.759359049513646,0.7593590495136462,0.755482893884601,0.747584679824574,0.7353364160075756,0.7181295189495049,0.6948167306993364,0.6628442049696138,0.6362113373725785,0.6670730006443818,0.6891821476591831,0.7050756912421842,0.7158788458567442,0.7221707506876511,0.7242388116428559,0.7221707506876511,0.7158788458567444,0.7050756912421843,0.6891821476591832,0.6670730006443818,0.6362113373725785,0.6082998482997924,0.6379578703362284,0.6587536638759601,0.673202098256523,0.682398943641963,0.6868827537990294,0.6868827537990294,0.682398943641963,0.673202098256523,0.6587536638759602,0.6379578703362285,0.6082998482997923,0.5790188873238004,0.6073635558851669,0.6267142402224604,0.6395563653739031,0.6469451160855026,0.6493608652873644,0.6469451160855026,0.6395563653739031,0.6267142402224604,0.6073635558851669,0.5790188873238004,0.5482606267258944,0.5751601860848226,0.5929045611929961,0.6039385916705984,0.6092592814269931,0.6092592814269931,0.6039385916705984,0.592904561192996,0.5751601860848226,0.5482606267258944,0.5158951529482093,0.5411884030780174,0.5571246835123504,0.5660906530347479,0.5689955935892812,0.5660906530347481,0.5571246835123504,0.5411884030780174,0.5158951529482093,0.481763067193911,0.5052482226498787,0.519116442129007,0.5256666624495429,0.5256666624495429,0.519116442129007,0.5052482226498787,0.4817630671939109,0.44566434565824037,0.4670814401590033,0.47853391043626986,0.4821791902022727,0.47853391043626986,0.4670814401590033,0.4456643456582403,0.4073407454009859,0.42634209069988727,0.4348896204226207,0.4348896204226205,0.4263420906998871,0.40734074540098586,0.3664462644533777,0.3825426691977458,0.3874449191544765,0.3825426691977458,0.36644626445337786,0.32249336186032446,0.33494448683868977,0.3349444868386898,0.3224933618603245,0.27474331406078023,0.28229218908241493,0.2747433140607803,0.221940732853211,0.221940732853211,0.16144054254182078],\"type\":\"scatter3d\"}],                        {\"template\":{\"data\":{\"bar\":[{\"error_x\":{\"color\":\"#2a3f5f\"},\"error_y\":{\"color\":\"#2a3f5f\"},\"marker\":{\"line\":{\"color\":\"#E5ECF6\",\"width\":0.5},\"pattern\":{\"fillmode\":\"overlay\",\"size\":10,\"solidity\":0.2}},\"type\":\"bar\"}],\"barpolar\":[{\"marker\":{\"line\":{\"color\":\"#E5ECF6\",\"width\":0.5},\"pattern\":{\"fillmode\":\"overlay\",\"size\":10,\"solidity\":0.2}},\"type\":\"barpolar\"}],\"carpet\":[{\"aaxis\":{\"endlinecolor\":\"#2a3f5f\",\"gridcolor\":\"white\",\"linecolor\":\"white\",\"minorgridcolor\":\"white\",\"startlinecolor\":\"#2a3f5f\"},\"baxis\":{\"endlinecolor\":\"#2a3f5f\",\"gridcolor\":\"white\",\"linecolor\":\"white\",\"minorgridcolor\":\"white\",\"startlinecolor\":\"#2a3f5f\"},\"type\":\"carpet\"}],\"choropleth\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"type\":\"choropleth\"}],\"contour\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"contour\"}],\"contourcarpet\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"type\":\"contourcarpet\"}],\"heatmap\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"heatmap\"}],\"heatmapgl\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"heatmapgl\"}],\"histogram\":[{\"marker\":{\"pattern\":{\"fillmode\":\"overlay\",\"size\":10,\"solidity\":0.2}},\"type\":\"histogram\"}],\"histogram2d\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"histogram2d\"}],\"histogram2dcontour\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"histogram2dcontour\"}],\"mesh3d\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"type\":\"mesh3d\"}],\"parcoords\":[{\"line\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"parcoords\"}],\"pie\":[{\"automargin\":true,\"type\":\"pie\"}],\"scatter\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scatter\"}],\"scatter3d\":[{\"line\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scatter3d\"}],\"scattercarpet\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scattercarpet\"}],\"scattergeo\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scattergeo\"}],\"scattergl\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scattergl\"}],\"scattermapbox\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scattermapbox\"}],\"scatterpolar\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scatterpolar\"}],\"scatterpolargl\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scatterpolargl\"}],\"scatterternary\":[{\"marker\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"type\":\"scatterternary\"}],\"surface\":[{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"},\"colorscale\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"type\":\"surface\"}],\"table\":[{\"cells\":{\"fill\":{\"color\":\"#EBF0F8\"},\"line\":{\"color\":\"white\"}},\"header\":{\"fill\":{\"color\":\"#C8D4E3\"},\"line\":{\"color\":\"white\"}},\"type\":\"table\"}]},\"layout\":{\"annotationdefaults\":{\"arrowcolor\":\"#2a3f5f\",\"arrowhead\":0,\"arrowwidth\":1},\"autotypenumbers\":\"strict\",\"coloraxis\":{\"colorbar\":{\"outlinewidth\":0,\"ticks\":\"\"}},\"colorscale\":{\"diverging\":[[0,\"#8e0152\"],[0.1,\"#c51b7d\"],[0.2,\"#de77ae\"],[0.3,\"#f1b6da\"],[0.4,\"#fde0ef\"],[0.5,\"#f7f7f7\"],[0.6,\"#e6f5d0\"],[0.7,\"#b8e186\"],[0.8,\"#7fbc41\"],[0.9,\"#4d9221\"],[1,\"#276419\"]],\"sequential\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]],\"sequentialminus\":[[0.0,\"#0d0887\"],[0.1111111111111111,\"#46039f\"],[0.2222222222222222,\"#7201a8\"],[0.3333333333333333,\"#9c179e\"],[0.4444444444444444,\"#bd3786\"],[0.5555555555555556,\"#d8576b\"],[0.6666666666666666,\"#ed7953\"],[0.7777777777777778,\"#fb9f3a\"],[0.8888888888888888,\"#fdca26\"],[1.0,\"#f0f921\"]]},\"colorway\":[\"#636efa\",\"#EF553B\",\"#00cc96\",\"#ab63fa\",\"#FFA15A\",\"#19d3f3\",\"#FF6692\",\"#B6E880\",\"#FF97FF\",\"#FECB52\"],\"font\":{\"color\":\"#2a3f5f\"},\"geo\":{\"bgcolor\":\"white\",\"lakecolor\":\"white\",\"landcolor\":\"#E5ECF6\",\"showlakes\":true,\"showland\":true,\"subunitcolor\":\"white\"},\"hoverlabel\":{\"align\":\"left\"},\"hovermode\":\"closest\",\"mapbox\":{\"style\":\"light\"},\"paper_bgcolor\":\"white\",\"plot_bgcolor\":\"#E5ECF6\",\"polar\":{\"angularaxis\":{\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\"},\"bgcolor\":\"#E5ECF6\",\"radialaxis\":{\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\"}},\"scene\":{\"xaxis\":{\"backgroundcolor\":\"#E5ECF6\",\"gridcolor\":\"white\",\"gridwidth\":2,\"linecolor\":\"white\",\"showbackground\":true,\"ticks\":\"\",\"zerolinecolor\":\"white\"},\"yaxis\":{\"backgroundcolor\":\"#E5ECF6\",\"gridcolor\":\"white\",\"gridwidth\":2,\"linecolor\":\"white\",\"showbackground\":true,\"ticks\":\"\",\"zerolinecolor\":\"white\"},\"zaxis\":{\"backgroundcolor\":\"#E5ECF6\",\"gridcolor\":\"white\",\"gridwidth\":2,\"linecolor\":\"white\",\"showbackground\":true,\"ticks\":\"\",\"zerolinecolor\":\"white\"}},\"shapedefaults\":{\"line\":{\"color\":\"#2a3f5f\"}},\"ternary\":{\"aaxis\":{\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\"},\"baxis\":{\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\"},\"bgcolor\":\"#E5ECF6\",\"caxis\":{\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\"}},\"title\":{\"x\":0.05},\"xaxis\":{\"automargin\":true,\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\",\"title\":{\"standoff\":15},\"zerolinecolor\":\"white\",\"zerolinewidth\":2},\"yaxis\":{\"automargin\":true,\"gridcolor\":\"white\",\"linecolor\":\"white\",\"ticks\":\"\",\"title\":{\"standoff\":15},\"zerolinecolor\":\"white\",\"zerolinewidth\":2}}},\"scene\":{\"domain\":{\"x\":[0.0,1.0],\"y\":[0.0,1.0]},\"xaxis\":{\"title\":{\"text\":\"p_0\"}},\"yaxis\":{\"title\":{\"text\":\"p_1\"}},\"zaxis\":{\"title\":{\"text\":\"entropia\"}}},\"coloraxis\":{\"colorbar\":{\"title\":{\"text\":\"warto\\u015b\\u0107\"}},\"colorscale\":[[0.0,\"#440154\"],[0.1111111111111111,\"#482878\"],[0.2222222222222222,\"#3e4989\"],[0.3333333333333333,\"#31688e\"],[0.4444444444444444,\"#26828e\"],[0.5555555555555556,\"#1f9e89\"],[0.6666666666666666,\"#35b779\"],[0.7777777777777778,\"#6ece58\"],[0.8888888888888888,\"#b5de2b\"],[1.0,\"#fde725\"]]},\"legend\":{\"tracegroupgap\":0},\"title\":{\"text\":\"Entropia \\u017ar\\u00f3d\\u0142a ternarnego\"}},                        {\"responsive\": true}                    ).then(function(){\n",
              "                            \n",
              "var gd = document.getElementById('f1699b5e-04c3-4cf5-bc32-e02de2201096');\n",
              "var x = new MutationObserver(function (mutations, observer) {{\n",
              "        var display = window.getComputedStyle(gd).display;\n",
              "        if (!display || display === 'none') {{\n",
              "            console.log([gd, 'removed!']);\n",
              "            Plotly.purge(gd);\n",
              "            observer.disconnect();\n",
              "        }}\n",
              "}});\n",
              "\n",
              "// Listen for the removal of the full notebook cells\n",
              "var notebookContainer = gd.closest('#notebook-container');\n",
              "if (notebookContainer) {{\n",
              "    x.observe(notebookContainer, {childList: true});\n",
              "}}\n",
              "\n",
              "// Listen for the clearing of the current output cell\n",
              "var outputEl = gd.closest('.output');\n",
              "if (outputEl) {{\n",
              "    x.observe(outputEl, {childList: true});\n",
              "}}\n",
              "\n",
              "                        })                };                            </script>        </div>\n",
              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "#@markdown Narysujemy wykres entropii źródła ternarnego\n",
        "\n",
        "zakres = [x/100 for x in range(1,100)] # 0.01-0.99\n",
        "p0 = []\n",
        "p1 = []\n",
        "H = []\n",
        "\n",
        "for p0a in zakres:\n",
        "  for p1a in zakres:\n",
        "    if (p0a+p1a < 1):\n",
        "      p0.append(p0a)\n",
        "      p1.append(p1a)\n",
        "      H.append(entropy([p0a,p1a,1-p0a-p1a], base=2))\n",
        "\n",
        "print(\"Niedokładność, bo bierzemy prawdopodobieństwa co 0.01:\")\n",
        "print(f\"Wartość maksymalna entropii ternarnej = {max(H)}, podczas gdy log(3) = {math.log2(3)}\")\n",
        "\n",
        "df = pd.DataFrame(\n",
        "    {\n",
        "    'wartość':H, 'p_0':p0, 'p_1':p1, 'H':H\n",
        "  }\n",
        ")\n",
        "fig = px.scatter_3d(df, x='p_0', y='p_1', z='H',\n",
        "                    color='wartość',\n",
        "                    title=\"Entropia źródła ternarnego\",\n",
        "                    color_continuous_scale=px.colors.sequential.Viridis)\n",
        "fig.update_layout(scene = dict(\n",
        "    xaxis_title='p_0',\n",
        "    yaxis_title='p_1',\n",
        "    zaxis_title='entropia')\n",
        ")\n",
        "fig.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Wcześniej mieliśmy zadany rozkład, ale oczywiście możemy sobie obejrzeć dla różnych typowych rozkładów, np. dwumianowego..."
      ],
      "metadata": {
        "id": "lkl35h3s48zi"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown A teraz dla całego rozkładu dwumianowego $B(N,\\theta)$: $\\Pr\\{k\\} = \\binom{N}{k}\\theta^k(1-\\theta)^{N-k}$\n",
        "\n",
        "N = 20  #@param\n",
        "theta = 0.26  #@param {type: \"slider\", min:0, max:1, step:0.01}\n",
        "\n",
        "assert isinstance(N, int) and N>1, \"N musi być wartością całkowitą większą od 1!\"\n",
        "\n",
        "xmin=0\n",
        "xmax=N\n",
        "k = range(xmin,xmax+1)\n",
        "binom_dist = binom(n=N, p=theta)\n",
        "entropy_bin = binom_dist.entropy()/math.log(2)\n",
        "B = binom_dist.pmf(k)\n",
        "\n",
        "plt.vlines(k,0,B,linewidth=100/N)\n",
        "plt.title(f'$H(X) = {entropy_bin:.2f}$')\n",
        "plt.xlim(xmin-0.5,xmax+0.5)\n",
        "plt.xlabel(f'$k$')\n",
        "plt.ylabel(f'$\\Pr(k)$')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "lQsHUGDqUB8z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "outputId": "022f7a46-8e1f-44d4-b383-bfd89c56fba0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title { run: \"auto\" }\n",
        "#@markdown Tutaj po prostu próbkujemy z rozkładu (tj. generujemy wyniki na podstawie danego rozkładu)...\n",
        "\n",
        "ile = 1200  #@param\n",
        "\n",
        "assert ile>1, \"musimy losować więcej razy niż 1!\"\n",
        "\n",
        "wynik = binom_dist.rvs(ile)\n",
        "print(wynik)\n",
        "\n",
        "wartosci = np.arange(N+2)\n",
        "\n",
        "ile_razy, _ = np.histogram(wynik, bins=wartosci)\n",
        "prawd = ile_razy / len(wynik)\n",
        "\n",
        "h = entropy(prawd, base = 2)\n",
        "\n",
        "plt.vlines(wartosci[:-1],ymin=0,ymax=prawd,linewidth=100/N)\n",
        "plt.title(f'$H(X) = {h:.2f}$ (dla rozkładu z próbkowania)')\n",
        "plt.xlim(xmin-0.5,xmax+0.5)\n",
        "plt.xlabel(f'$k$')\n",
        "plt.ylabel(f'$\\Pr(k)$ (z próbkowania)')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "XSm6jxkd5yWa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 322
        },
        "outputId": "2b99d109-7ae6-4381-c698-d061978fb953"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[6 4 2 ... 6 7 4]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Entropia ciągłego rozkładu prawdopodobieństwa (entropia różnicowa)\n",
        "\n",
        "Dla funkcji gęstości prawdopodobieństwa:\n",
        "\n",
        "$$ f: X \\rightarrow [0,+\\infty), \\quad \\int_{-\\infty}^{+\\infty}{f(x)dx} = 1 $$\n",
        "\n",
        "możemy policzyć entropię różnicową jako uogólnienie dla rozkładu dyskretnego:\n",
        "\n",
        "$$ h(X) = E[-\\log{f(X)}] = -\\int_{X}{f(x)\\log{f(x)}dx} \\quad \\text{[bit]} $$\n",
        "\n",
        "Entropia źródła ciągłego to tak naprawdę:\n",
        "\n",
        "$$ H(X) = h(X) - \\lim_{\\Delta{x} \\rightarrow 0} \\log{\\Delta{x}} $$"
      ],
      "metadata": {
        "id": "nJxlq6CCEhzK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Entropia różnicowa dla rozkładu normalnego (Gaussa) { run: \"auto\" }\n",
        "#@markdown Można zobaczyć, jak to się zmienia...\n",
        "\n",
        "x_min = -10 #@param\n",
        "x_max = 10 #@param\n",
        "\n",
        "assert x_min < x_max, \"Zakres musi być zdefiniowany prawidłowo!\"\n",
        "\n",
        "loc = 0  #@param {type: \"slider\", min:-10, max:10, step:0.5}\n",
        "scale = 0.13 #@param {type: \"slider\", min:0.01, max:10, step:0.01}\n",
        "\n",
        "if x_min > loc-3*scale:\n",
        "  x_min = loc-3*scale\n",
        "\n",
        "if x_max < loc+3*scale:\n",
        "  x_max = loc+3*scale\n",
        "\n",
        "x_axis = np.arange(x_min, x_max, 0.01)\n",
        "\n",
        "normal_dist = norm(loc=loc, scale=scale)\n",
        "entropy_n = normal_dist.entropy()/math.log(2)\n",
        "y_axis = normal_dist.pdf(x_axis)\n",
        "plt.plot(x_axis, y_axis)\n",
        "plt.title(f'$H(X) = {entropy_n:.2f}$')\n",
        "plt.xlabel(f'$X$')\n",
        "plt.ylabel(f'$N({loc},{scale})$')\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "4G0MId23PqSx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "outputId": "dd980623-c1bc-409d-b50c-2cbef3906d05"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Jak widać, entropia różnicowa może być ujemna!\n",
        "\n",
        "Z wszystkich rozkładów o tej samej wariancji rozkład Gaussa daje największą entropię różnicową."
      ],
      "metadata": {
        "id": "jN61gRmC-FBu"
      }
    }
  ]
}