Biostatistics_project_2.ipynb

{
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    },
    "kernelspec": {
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      "display_name": "R"
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      "name": "R"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "#Introduction\n",
        "\n"
      ],
      "metadata": {
        "id": "MpVQxE9ACMty"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Ghent University's Laboratory of Microbiology is conducting the Mibirem project, an experimental study, aiming to optimize the preservation of microbial consortia. The preservation methods under evaluation involve lyophilization at room temperature using two distinct techniques (LYO1 and LYO2) and storage at ultra-low temperatures, either -80 °C (CRYO1) or -196 °C (CRYO2). Simultaneously, seven different preservation media labeled as A, B, C (cryopreservationD), and D, E, F, G (lyophilization) are being tested. Fourteen scenarios, combining different preservation methods (lyophilization and cryopreservation) and media types, are being tested. \\\n",
        "\n",
        "To assess the survival rates of microbial consortia under these varied conditions, the researchers collect samples at different time points: 0, 3, 6, 12, 18, 24, and 30 months after initiating storage, with time point 0 representing the moment before storage. The primary focus is on the initial measurement and the 3-month time point, and for each scenario, five tubes containing the microbial consortium are stored for subsequent flow cytometry analysis. \\\n",
        "\n",
        "Flow cytometry, a rapid, reproducible, and cost-effective technique, is employed to quantify total bacterial numbers and assess the live/dead ratio of bacterial cells. The researchers have compiled four distinct datasets, capturing the percentage of live, injured, and dead bacteria in each sample, along with the total number of bacterial cells. Each sample undergoes three measurements for each parameter. \\\n",
        "\n",
        "In this project, the central research question is: Does the CRYO2 preservation method have an effect over time on stored samples, and does this effect vary across different preservation media? \\"
      ],
      "metadata": {
        "id": "bW7cNvCeNLxy"
      }
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    {
      "cell_type": "code",
      "source": [
        "install.packages(\"ggridges\")\n",
        "install.packages(\"grid\")\n",
        "install.packages(\"gridExtra\")\n",
        "library(grid)\n",
        "library(gridExtra)\n",
        "library(ggridges)\n",
        "library(tidyr)\n",
        "library(tidyverse)\n",
        "library(MASS)\n",
        "library(boot)"
      ],
      "metadata": {
        "id": "cfb0pSE1HaUZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7dc241d-619d-4ef4-a7f5-c309ff0904f4"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "Warning message:\n",
            "“package ‘grid’ is a base package, and should not be updated”\n",
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n",
            "\u001b[32m✔\u001b[39m \u001b[34mdplyr    \u001b[39m 1.1.4     \u001b[32m✔\u001b[39m \u001b[34mpurrr    \u001b[39m 1.0.2\n",
            "\u001b[32m✔\u001b[39m \u001b[34mforcats  \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mreadr    \u001b[39m 2.1.4\n",
            "\u001b[32m✔\u001b[39m \u001b[34mggplot2  \u001b[39m 3.4.4     \u001b[32m✔\u001b[39m \u001b[34mstringr  \u001b[39m 1.5.1\n",
            "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.3     \u001b[32m✔\u001b[39m \u001b[34mtibble   \u001b[39m 3.2.1\n",
            "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
            "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mcombine()\u001b[39m masks \u001b[34mgridExtra\u001b[39m::combine()\n",
            "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m  masks \u001b[34mstats\u001b[39m::filter()\n",
            "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m     masks \u001b[34mstats\u001b[39m::lag()\n",
            "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m<http://conflicted.r-lib.org/>\u001b[39m\u001b[23m) to force all conflicts to become errors\n",
            "\n",
            "Attaching package: ‘MASS’\n",
            "\n",
            "\n",
            "The following object is masked from ‘package:dplyr’:\n",
            "\n",
            "    select\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Variables, replicates and hypotheses"
      ],
      "metadata": {
        "id": "WKuS7sm3Lu4d"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this study, the response variable is the percentage of survived bacteria. The explanatory variables are the preservation media and time. The percentage of living cells was measured three times from the same aliquot with the same device, which makes this a pseudoreplication. The measurements were not performed on independent samples. For each scenario, five tubes containing the microbial consortium were used, on which parallel measurements were performed. Thus, these five subsamples are biological replicates.\n",
        "\n",
        "H0_1: On average, there is no difference on the survival of the bacteria between timepoint zero months and after timepoint 3 months using any of the preservation media.\\\n",
        "H1_1: On average, there is a difference on the survival of the bacteria between timepoint zero months and after timepoint 3 months using any of the preservation media. \\\n",
        "\n",
        "If the first null hypothesis can be rejected and the alternative hypothesis is accepted, the following hypothesis can be subsequently investigated.\n",
        "\n",
        "H0_2: On average, there is no difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium A. \\\n",
        "H0_3: On average, there is no difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium B. \\\n",
        "H0_4: On average, there is no difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium C. \\\n",
        "\n",
        "H1_2: On average, there is a difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium A. \\\n",
        "H1_3: On average, there is a difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium B. \\\n",
        "H1_4: On average, there is a difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium C.\n"
      ],
      "metadata": {
        "id": "_PrOYBYFOz7X"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Data Exploration"
      ],
      "metadata": {
        "id": "nblrjwHoL1hM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this study, we encountered pseudoreplication due to the nature of the experimental design. Multiple measurements were taken on the same aliquot using the same device, introducing potential dependencies between observations. To address this, we needed a reliable method to aggregate these repeated measurements and mitigate the risk of inflated significance levels.\n",
        "\n",
        "In our case, the three measurements taken for each sample were averaged, providing a representative value for analysis. This not only addresses the challenge of pseudoreplication but also facilitates a more accurate assessment of differences in bacterial survival between timepoints and preservation media."
      ],
      "metadata": {
        "id": "F6PqjPHJ_DV_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cell_count <- read.csv(\"Cell_Count_v2.txt\", header=TRUE, sep=\"\\t\")\n",
        "cell_count$Medium <- as.factor(cell_count$Medium)\n",
        "cell_count$Method <- as.factor(cell_count$Method)\n",
        "cell_count$Timepoint <- as.factor(cell_count$Timepoint)\n",
        "\n",
        "data <- cell_count %>%\n",
        "  filter(Method %in% c(\"CRYO2\", \"None\"))\n",
        "data <- data[, c(\"sample_name\", \"percent_live_1\", \"percent_live_2\", \"percent_live_3\", \"Medium\", \"Timepoint\")]\n",
        "\n",
        "data <- data  %>%\n",
        "  mutate(\n",
        "    mean_percent_live = rowMeans(across(starts_with(\"percent_live\")), na.rm = TRUE),\n",
        "    std_dev = apply(across(starts_with(\"percent_live\")), 1, sd, na.rm = TRUE),\n",
        "    variance = std_dev^2) %>%\n",
        "  arrange(desc(row_number() %in% (nrow(.) - 4):nrow(.)))\n",
        "data$Medium <- factor(data$Medium, levels = c(\"None\",\"A\", \"B\", \"C\"))\n",
        "data"
      ],
      "metadata": {
        "id": "Xbbl_r61L3nU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 725
        },
        "outputId": "46838e5b-9625-4a02-966b-7736ac952c0e"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 20 × 9</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>sample_name</th><th scope=col>percent_live_1</th><th scope=col>percent_live_2</th><th scope=col>percent_live_3</th><th scope=col>Medium</th><th scope=col>Timepoint</th><th scope=col>mean_percent_live</th><th scope=col>std_dev</th><th scope=col>variance</th></tr>\n",
              "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td>Unpreserved_01</td><td>75.30</td><td>74.00</td><td>74.78</td><td>None</td><td>0</td><td>74.69333</td><td>0.6543190</td><td> 0.4281333</td></tr>\n",
              "\t<tr><td>Unpreserved_02</td><td>75.74</td><td>71.83</td><td>74.42</td><td>None</td><td>0</td><td>73.99667</td><td>1.9890785</td><td> 3.9564333</td></tr>\n",
              "\t<tr><td>Unpreserved_03</td><td>76.77</td><td>74.47</td><td>75.17</td><td>None</td><td>0</td><td>75.47000</td><td>1.1789826</td><td> 1.3900000</td></tr>\n",
              "\t<tr><td>Unpreserved_04</td><td>74.78</td><td>74.22</td><td>74.47</td><td>None</td><td>0</td><td>74.49000</td><td>0.2805352</td><td> 0.0787000</td></tr>\n",
              "\t<tr><td>Unpreserved_05</td><td>73.93</td><td>71.92</td><td>75.39</td><td>None</td><td>0</td><td>73.74667</td><td>1.7422495</td><td> 3.0354333</td></tr>\n",
              "\t<tr><td>CRYO2_A_01    </td><td>63.81</td><td>67.44</td><td>64.40</td><td>A   </td><td>3</td><td>65.21667</td><td>1.9479305</td><td> 3.7944333</td></tr>\n",
              "\t<tr><td>CRYO2_B_01    </td><td>67.28</td><td>64.65</td><td>67.15</td><td>B   </td><td>3</td><td>66.36000</td><td>1.4823292</td><td> 2.1973000</td></tr>\n",
              "\t<tr><td>CRYO2_C_01    </td><td>65.85</td><td>64.02</td><td>65.76</td><td>C   </td><td>3</td><td>65.21000</td><td>1.0315522</td><td> 1.0641000</td></tr>\n",
              "\t<tr><td>CRYO2_A_02    </td><td>75.34</td><td>63.25</td><td>62.61</td><td>A   </td><td>3</td><td>67.06667</td><td>7.1720592</td><td>51.4384333</td></tr>\n",
              "\t<tr><td>CRYO2_B_02    </td><td>70.44</td><td>71.08</td><td>64.76</td><td>B   </td><td>3</td><td>68.76000</td><td>3.4788504</td><td>12.1024000</td></tr>\n",
              "\t<tr><td>CRYO2_C_02    </td><td>74.93</td><td>71.09</td><td>73.92</td><td>C   </td><td>3</td><td>73.31333</td><td>1.9905862</td><td> 3.9624333</td></tr>\n",
              "\t<tr><td>CRYO2_A_03    </td><td>62.11</td><td>62.96</td><td>63.83</td><td>A   </td><td>3</td><td>62.96667</td><td>0.8600194</td><td> 0.7396333</td></tr>\n",
              "\t<tr><td>CRYO2_B_03    </td><td>69.34</td><td>63.61</td><td>65.05</td><td>B   </td><td>3</td><td>66.00000</td><td>2.9807885</td><td> 8.8851000</td></tr>\n",
              "\t<tr><td>CRYO2_C_03    </td><td>70.22</td><td>64.95</td><td>66.98</td><td>C   </td><td>3</td><td>67.38333</td><td>2.6580507</td><td> 7.0652333</td></tr>\n",
              "\t<tr><td>CRYO2_A_04    </td><td>69.51</td><td>69.04</td><td>69.94</td><td>A   </td><td>3</td><td>69.49667</td><td>0.4501481</td><td> 0.2026333</td></tr>\n",
              "\t<tr><td>CRYO2_B_04    </td><td>62.65</td><td>54.25</td><td>61.77</td><td>B   </td><td>3</td><td>59.55667</td><td>4.6167232</td><td>21.3141333</td></tr>\n",
              "\t<tr><td>CRYO2_C_04    </td><td>52.07</td><td>55.81</td><td>57.36</td><td>C   </td><td>3</td><td>55.08000</td><td>2.7195036</td><td> 7.3957000</td></tr>\n",
              "\t<tr><td>CRYO2_A_05    </td><td>64.09</td><td>66.10</td><td>61.61</td><td>A   </td><td>3</td><td>63.93333</td><td>2.2490961</td><td> 5.0584333</td></tr>\n",
              "\t<tr><td>CRYO2_B_05    </td><td>65.98</td><td>63.65</td><td>66.78</td><td>B   </td><td>3</td><td>65.47000</td><td>1.6261304</td><td> 2.6443000</td></tr>\n",
              "\t<tr><td>CRYO2_C_05    </td><td>49.76</td><td>52.14</td><td>58.53</td><td>C   </td><td>3</td><td>53.47667</td><td>4.5352214</td><td>20.5682333</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 20 × 9\n\n| sample_name &lt;chr&gt; | percent_live_1 &lt;dbl&gt; | percent_live_2 &lt;dbl&gt; | percent_live_3 &lt;dbl&gt; | Medium &lt;fct&gt; | Timepoint &lt;fct&gt; | mean_percent_live &lt;dbl&gt; | std_dev &lt;dbl&gt; | variance &lt;dbl&gt; |\n|---|---|---|---|---|---|---|---|---|\n| Unpreserved_01 | 75.30 | 74.00 | 74.78 | None | 0 | 74.69333 | 0.6543190 |  0.4281333 |\n| Unpreserved_02 | 75.74 | 71.83 | 74.42 | None | 0 | 73.99667 | 1.9890785 |  3.9564333 |\n| Unpreserved_03 | 76.77 | 74.47 | 75.17 | None | 0 | 75.47000 | 1.1789826 |  1.3900000 |\n| Unpreserved_04 | 74.78 | 74.22 | 74.47 | None | 0 | 74.49000 | 0.2805352 |  0.0787000 |\n| Unpreserved_05 | 73.93 | 71.92 | 75.39 | None | 0 | 73.74667 | 1.7422495 |  3.0354333 |\n| CRYO2_A_01     | 63.81 | 67.44 | 64.40 | A    | 3 | 65.21667 | 1.9479305 |  3.7944333 |\n| CRYO2_B_01     | 67.28 | 64.65 | 67.15 | B    | 3 | 66.36000 | 1.4823292 |  2.1973000 |\n| CRYO2_C_01     | 65.85 | 64.02 | 65.76 | C    | 3 | 65.21000 | 1.0315522 |  1.0641000 |\n| CRYO2_A_02     | 75.34 | 63.25 | 62.61 | A    | 3 | 67.06667 | 7.1720592 | 51.4384333 |\n| CRYO2_B_02     | 70.44 | 71.08 | 64.76 | B    | 3 | 68.76000 | 3.4788504 | 12.1024000 |\n| CRYO2_C_02     | 74.93 | 71.09 | 73.92 | C    | 3 | 73.31333 | 1.9905862 |  3.9624333 |\n| CRYO2_A_03     | 62.11 | 62.96 | 63.83 | A    | 3 | 62.96667 | 0.8600194 |  0.7396333 |\n| CRYO2_B_03     | 69.34 | 63.61 | 65.05 | B    | 3 | 66.00000 | 2.9807885 |  8.8851000 |\n| CRYO2_C_03     | 70.22 | 64.95 | 66.98 | C    | 3 | 67.38333 | 2.6580507 |  7.0652333 |\n| CRYO2_A_04     | 69.51 | 69.04 | 69.94 | A    | 3 | 69.49667 | 0.4501481 |  0.2026333 |\n| CRYO2_B_04     | 62.65 | 54.25 | 61.77 | B    | 3 | 59.55667 | 4.6167232 | 21.3141333 |\n| CRYO2_C_04     | 52.07 | 55.81 | 57.36 | C    | 3 | 55.08000 | 2.7195036 |  7.3957000 |\n| CRYO2_A_05     | 64.09 | 66.10 | 61.61 | A    | 3 | 63.93333 | 2.2490961 |  5.0584333 |\n| CRYO2_B_05     | 65.98 | 63.65 | 66.78 | B    | 3 | 65.47000 | 1.6261304 |  2.6443000 |\n| CRYO2_C_05     | 49.76 | 52.14 | 58.53 | C    | 3 | 53.47667 | 4.5352214 | 20.5682333 |\n\n",
            "text/latex": "A data.frame: 20 × 9\n\\begin{tabular}{lllllllll}\n sample\\_name & percent\\_live\\_1 & percent\\_live\\_2 & percent\\_live\\_3 & Medium & Timepoint & mean\\_percent\\_live & std\\_dev & variance\\\\\n <chr> & <dbl> & <dbl> & <dbl> & <fct> & <fct> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t Unpreserved\\_01 & 75.30 & 74.00 & 74.78 & None & 0 & 74.69333 & 0.6543190 &  0.4281333\\\\\n\t Unpreserved\\_02 & 75.74 & 71.83 & 74.42 & None & 0 & 73.99667 & 1.9890785 &  3.9564333\\\\\n\t Unpreserved\\_03 & 76.77 & 74.47 & 75.17 & None & 0 & 75.47000 & 1.1789826 &  1.3900000\\\\\n\t Unpreserved\\_04 & 74.78 & 74.22 & 74.47 & None & 0 & 74.49000 & 0.2805352 &  0.0787000\\\\\n\t Unpreserved\\_05 & 73.93 & 71.92 & 75.39 & None & 0 & 73.74667 & 1.7422495 &  3.0354333\\\\\n\t CRYO2\\_A\\_01     & 63.81 & 67.44 & 64.40 & A    & 3 & 65.21667 & 1.9479305 &  3.7944333\\\\\n\t CRYO2\\_B\\_01     & 67.28 & 64.65 & 67.15 & B    & 3 & 66.36000 & 1.4823292 &  2.1973000\\\\\n\t CRYO2\\_C\\_01     & 65.85 & 64.02 & 65.76 & C    & 3 & 65.21000 & 1.0315522 &  1.0641000\\\\\n\t CRYO2\\_A\\_02     & 75.34 & 63.25 & 62.61 & A    & 3 & 67.06667 & 7.1720592 & 51.4384333\\\\\n\t CRYO2\\_B\\_02     & 70.44 & 71.08 & 64.76 & B    & 3 & 68.76000 & 3.4788504 & 12.1024000\\\\\n\t CRYO2\\_C\\_02     & 74.93 & 71.09 & 73.92 & C    & 3 & 73.31333 & 1.9905862 &  3.9624333\\\\\n\t CRYO2\\_A\\_03     & 62.11 & 62.96 & 63.83 & A    & 3 & 62.96667 & 0.8600194 &  0.7396333\\\\\n\t CRYO2\\_B\\_03     & 69.34 & 63.61 & 65.05 & B    & 3 & 66.00000 & 2.9807885 &  8.8851000\\\\\n\t CRYO2\\_C\\_03     & 70.22 & 64.95 & 66.98 & C    & 3 & 67.38333 & 2.6580507 &  7.0652333\\\\\n\t CRYO2\\_A\\_04     & 69.51 & 69.04 & 69.94 & A    & 3 & 69.49667 & 0.4501481 &  0.2026333\\\\\n\t CRYO2\\_B\\_04     & 62.65 & 54.25 & 61.77 & B    & 3 & 59.55667 & 4.6167232 & 21.3141333\\\\\n\t CRYO2\\_C\\_04     & 52.07 & 55.81 & 57.36 & C    & 3 & 55.08000 & 2.7195036 &  7.3957000\\\\\n\t CRYO2\\_A\\_05     & 64.09 & 66.10 & 61.61 & A    & 3 & 63.93333 & 2.2490961 &  5.0584333\\\\\n\t CRYO2\\_B\\_05     & 65.98 & 63.65 & 66.78 & B    & 3 & 65.47000 & 1.6261304 &  2.6443000\\\\\n\t CRYO2\\_C\\_05     & 49.76 & 52.14 & 58.53 & C    & 3 & 53.47667 & 4.5352214 & 20.5682333\\\\\n\\end{tabular}\n",
            "text/plain": [
              "   sample_name    percent_live_1 percent_live_2 percent_live_3 Medium Timepoint\n",
              "1  Unpreserved_01 75.30          74.00          74.78          None   0        \n",
              "2  Unpreserved_02 75.74          71.83          74.42          None   0        \n",
              "3  Unpreserved_03 76.77          74.47          75.17          None   0        \n",
              "4  Unpreserved_04 74.78          74.22          74.47          None   0        \n",
              "5  Unpreserved_05 73.93          71.92          75.39          None   0        \n",
              "6  CRYO2_A_01     63.81          67.44          64.40          A      3        \n",
              "7  CRYO2_B_01     67.28          64.65          67.15          B      3        \n",
              "8  CRYO2_C_01     65.85          64.02          65.76          C      3        \n",
              "9  CRYO2_A_02     75.34          63.25          62.61          A      3        \n",
              "10 CRYO2_B_02     70.44          71.08          64.76          B      3        \n",
              "11 CRYO2_C_02     74.93          71.09          73.92          C      3        \n",
              "12 CRYO2_A_03     62.11          62.96          63.83          A      3        \n",
              "13 CRYO2_B_03     69.34          63.61          65.05          B      3        \n",
              "14 CRYO2_C_03     70.22          64.95          66.98          C      3        \n",
              "15 CRYO2_A_04     69.51          69.04          69.94          A      3        \n",
              "16 CRYO2_B_04     62.65          54.25          61.77          B      3        \n",
              "17 CRYO2_C_04     52.07          55.81          57.36          C      3        \n",
              "18 CRYO2_A_05     64.09          66.10          61.61          A      3        \n",
              "19 CRYO2_B_05     65.98          63.65          66.78          B      3        \n",
              "20 CRYO2_C_05     49.76          52.14          58.53          C      3        \n",
              "   mean_percent_live std_dev   variance  \n",
              "1  74.69333          0.6543190  0.4281333\n",
              "2  73.99667          1.9890785  3.9564333\n",
              "3  75.47000          1.1789826  1.3900000\n",
              "4  74.49000          0.2805352  0.0787000\n",
              "5  73.74667          1.7422495  3.0354333\n",
              "6  65.21667          1.9479305  3.7944333\n",
              "7  66.36000          1.4823292  2.1973000\n",
              "8  65.21000          1.0315522  1.0641000\n",
              "9  67.06667          7.1720592 51.4384333\n",
              "10 68.76000          3.4788504 12.1024000\n",
              "11 73.31333          1.9905862  3.9624333\n",
              "12 62.96667          0.8600194  0.7396333\n",
              "13 66.00000          2.9807885  8.8851000\n",
              "14 67.38333          2.6580507  7.0652333\n",
              "15 69.49667          0.4501481  0.2026333\n",
              "16 59.55667          4.6167232 21.3141333\n",
              "17 55.08000          2.7195036  7.3957000\n",
              "18 63.93333          2.2490961  5.0584333\n",
              "19 65.47000          1.6261304  2.6443000\n",
              "20 53.47667          4.5352214 20.5682333"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the table above, the standard deviation was added as a statistical measure to evaluate the extent of variation among the three replicates. This metric proves valuable in quantifying the dispersion or spread of data points relative to their mean. Overall, most of the standard deviations lie in a range between 0 and 3, which is acceptable given that mean ranges between 55 and 75. However some higher standard deviations are observed at the following samples: CRYO2_A_02, CRYO2_B_02, CRYO2_B_04 and CRYO2_C_05. For these samples, a standard deviation of respectively 7.1720592, 3.4788504, 4.6167232, and 4.5352214 was calculated, indicating a larger spread between each measurement. The variance was added to the table to further look into the variation among the three replicates. For CRYO2_A_02, the calculated variance is 51.4384333, which is very close to the mean (67.06667), although it does not pose a problem as the variance is still lower than the mean. This variation is unwanted as we want reproducible measurements, a higher standard deviation and variance might indicate an error in measurements or handling of the different samples.\n"
      ],
      "metadata": {
        "id": "jmWt3re2l_oE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Group by Medium and Timepoint and calculate mean, variance, and standard deviation\n",
        "mean_var_std <- data %>%\n",
        "  group_by(Timepoint) %>%\n",
        "  summarize(\n",
        "    mean_percent_live = mean(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE),\n",
        "    variance_percent_live = var(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE),\n",
        "    std_dev_percent_live = sd(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE)\n",
        "  )\n",
        "\n",
        "# Print the result\n",
        "print(mean_var_std)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zkxZ0fDTEOqo",
        "outputId": "1da4eed1-c52a-47c0-b8f4-e9157886dce6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[90m# A tibble: 2 × 4\u001b[39m\n",
            "  Timepoint mean_percent_live variance_percent_live std_dev_percent_live\n",
            "  \u001b[3m\u001b[90m<fct>\u001b[39m\u001b[23m                 \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m                 \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m                \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m\n",
            "\u001b[90m1\u001b[39m 0                      74.5                  1.65                 1.29\n",
            "\u001b[90m2\u001b[39m 3                      64.6                 32.7                  5.72\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the table above, the mean percentage of living cells at time point 0 is 74.5% and the variance is 1.65%. The relatively low variance compared to the mean indicates a reasonable fit to a less dispersed distribution. At time point 3, the mean drops to 64.6% and the variance increases to 32.7%."
      ],
      "metadata": {
        "id": "ow5ljTVIBNBK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Group by Medium and Timepoint and calculate mean, variance, and standard deviation\n",
        "mean_var_std <- data %>%\n",
        "  group_by(Medium) %>%\n",
        "  summarize(\n",
        "    mean_percent_live = mean(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE),\n",
        "    variance_percent_live = var(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE),\n",
        "    std_dev_percent_live = sd(c(percent_live_1, percent_live_2, percent_live_3), na.rm = TRUE)\n",
        "  )\n",
        "\n",
        "# Print the result\n",
        "print(mean_var_std)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CtY3gfcsCPpf",
        "outputId": "ab75fcf7-8fc5-4527-c59d-58f7a5204413"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[90m# A tibble: 4 × 4\u001b[39m\n",
            "  Medium mean_percent_live variance_percent_live std_dev_percent_live\n",
            "  \u001b[3m\u001b[90m<fct>\u001b[39m\u001b[23m              \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m                 \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m                \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m\n",
            "\u001b[90m1\u001b[39m None                74.5                  1.65                 1.29\n",
            "\u001b[90m2\u001b[39m A                   65.7                 14.6                  3.82\n",
            "\u001b[90m3\u001b[39m B                   65.2                 16.7                  4.09\n",
            "\u001b[90m4\u001b[39m C                   62.9                 66.5                  8.16\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Upon examining different media categories, we delved into the presence of overdispersion within each medium. The findings reveal that, before storage and after storage in media A and B, there are no signs of overdispersion, as the variance consistently falls short of surpassing the mean. However, upon closer inspection of medium C, post-storage, overdispersion becomes apparent.\n",
        "Interestingly, despite the identification of overdispersion in medium C, the decision to adopt an overdispersion model requires thoughtful consideration. This is due to the relatively subtle discrepancy between the mean and variance.\n"
      ],
      "metadata": {
        "id": "6xlUPxj5CQZL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The data's variability will be further examined through boxplots. First, the original dataset with all the percentages of live bacteria will be used."
      ],
      "metadata": {
        "id": "Nl4dKx1uXyf9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Gather the percent_live columns into a single column\n",
        "data_long <- data %>%\n",
        "  gather(key = \"Replicate\", value = \"percent_live\", percent_live_1:percent_live_3) %>%\n",
        "  mutate(Replicate = gsub(\"percent_live_\", \"\", Replicate))\n",
        "data_long <- data_long[, c(\"Medium\", \"Timepoint\", \"Replicate\", \"percent_live\")]\n",
        "data_long <- data_long %>% arrange(Timepoint)\n",
        "\n",
        "# Boxplot not using the means\n",
        "ggplot(data_long, aes(x = Medium, y = percent_live)) +\n",
        "  geom_boxplot(color= c('#00366C', '#3D1778', '#3D1778', '#3D1778'),  fill = c('#BDD7FB', '#8576B7', '#BFB9DC', '#DFDDF1'), outlier.shape =15) +\n",
        "  geom_point(color = c(rep('#00366C', 15), rep('#3D1778', 45)), alpha=0.7, shape=15) +\n",
        "  labs(title = \"Percentage of Live Bacteria\",\n",
        "       subtitle = 'Grouped by Timepoint and Medium',\n",
        "       y = \"Percentage of Live Bacteria\") +\n",
        "  scale_x_discrete(labels = c(\"Before storage\\nat timepoint 0 months\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium A\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium B\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium C\")) +\n",
        "  geom_vline(xintercept = 1.5, linetype = \"dashed\", color = \"black\") +\n",
        "  theme_minimal() +\n",
        "  theme(axis.title.x=element_blank())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "p2dVDWpsUzYM",
        "outputId": "400205e1-e639-4496-aeff-9ca0ccee74ee"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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EpQ7AAAAFSCYgenlp2dvWHDhmPHjikdBAAAG6DYwamdPHly1KhRa9euVToIAAA2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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Analyzing the boxplots for all the percentages of live bacteria in each medium reveals noticeable variation, indicating unequal dataset variance. The distinct interquartile ranges further support this observation.\n",
        "\n",
        "Although median values across media show little difference, the initial median at timepoint 0 months exceeds those after a 3-month storage in mediums A, B, or C, suggesting a potential decrease in the percentage of living cells over this period."
      ],
      "metadata": {
        "id": "NC51ksilYEDa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "However, as the mean percentages are taken to combat the pseudoreplication issue, the mean percentage of the live bacteria will be used to investigate the data's variability and not the actual percentages."
      ],
      "metadata": {
        "id": "IntQMyTwDUq_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Boxplot using ggplot using the means\n",
        "ggplot(data, aes(x = Medium, y = mean_percent_live, col=Medium)) +\n",
        "  geom_boxplot(color= c('#00366C', '#3D1778', '#3D1778', '#3D1778'),  fill = c('#BDD7FB', '#8576B7', '#BFB9DC', '#DFDDF1'), outlier.shape =15) +\n",
        "  geom_point(color = c(rep('#00366C', 5), rep('#3D1778', 15)), alpha=0.7, shape=15) +\n",
        "  labs(title = \"Mean Percentage of Live Bacteria\",\n",
        "       subtitle = 'Grouped by Timepoint and Medium',\n",
        "       y = \"Mean percentage of Live Bacteria\") +\n",
        "  scale_x_discrete(labels = c(\"Before storage\\nat timepoint 0 months\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium A\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium B\", \"After CRYO2 storage\\nat timepoint 3 months\\nin medium C\")) +\n",
        "  geom_vline(xintercept = 1.5, linetype = \"dashed\", color = \"black\") +\n",
        "  theme_minimal() +\n",
        "  theme(axis.title.x=element_blank())\n",
        "\n",
        "# QQ-plot using ggplot\n",
        "ggplot(data, aes(sample = mean_percent_live)) +\n",
        "  geom_qq(color = c(rep('#00366C', 5), rep('#3D1778', 15)), alpha=0.7, shape=15) +\n",
        "  geom_qq_line(color = c(rep('#00366C', 2), rep('#3D1778', 6))) +\n",
        "  facet_wrap(~Medium, labeller = labeller(Medium = c('None' = 'Before storage\\nat timepoint 0 months', 'A' = 'After CRYO2 storage\\nat timepoint 3 months\\nin medium A', 'B' = 'After CRYO2 storage\\nat timepoint 3 months\\nin medium B', 'C' = 'After CRYO2 storage\\nat timepoint 3 months\\nin medium C'))) +\n",
        "  labs(title = \"QQ Plot of percent_live by Replicate and Medium\",\n",
        "       x = \"Theoretical Quantiles\",\n",
        "       y = \"Sample Quantiles\",\n",
        "       subtitle = \"Grouped by Medium\") +\n",
        "  theme_minimal()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 857
        },
        "id": "BTo4KasdjeYS",
        "outputId": "c7fc0e21-cdfc-43ac-c693-41865a20a356"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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h2HYqHX62fPnt25c+ca2OoAAEANUTuuiq3LLl++fPjw4Y8//vjw4cP79u1TOg4A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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Qvv6LY+Pj705ciRI2fOnHnt2rUtW7Z07tyZnnS0Lz4+fu3atYcOHdq2bVt8fDw3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+ePPNN9u1a3f//fd/8sknrmUeeOCBw/+1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\nRK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Upon exploring the boxplots representing the mean percentages of live bacteria per medium, it becomes evident that there exists unequal variance within the dataset. This observation is substantiated by the obvious distinction in interquartile ranges among the various mean percentages of live bacteria per medium. However, when comparing only the first timepoint and medium B, equal variance is observed.\n",
        "\n",
        "While median values between the media are closely aligned, suggesting no significant differences, the median value at the experiment's onset (Timepoint 0 months) surpasses those observed after a 3-month storage period in mediums A, B, or C. This gives a first indication that the percentage of living cells is decreased after 3 months of storage. With only 5 data points per boxplot, the median can easily be influenced by a single data point that's not quite an outlier but stands out from the others. This can make the boxplot's interquartile range significantly larger. So, the interquartile range of the boxplot might be influenced by individual data points that don't quite fit in with the rest, resulting in unequal variance.\n",
        "\n",
        "Within the data for Medium B, two outliers CRYO2_B_02 (68.76) and CRYO_02_B_04 (59.56) are identified. These outliers, coincidentally associated with higher standard deviations, could pose challenges for the statistical model, complicating the fitting process.\n",
        "\n",
        "The analysis is constrained by a small sample size, comprising only five data points. This limitation affects the reliability of statistical tools such as quantile-quantile (QQ) plots, traditionally more robust with larger datasets. Caution is advised when interpreting results, and findings should be considered preliminary. Supplementing analyses with additional methods and recognizing the impact of small sample variability is crucial for a more nuanced understanding of the data. Considering this, the QQ-plots indicate a normal distribution. The sample quantiles show no big deviations from the theoretical quantiles as the data points on the QQ plot align closely to the straight line."
      ],
      "metadata": {
        "id": "noGoBXSZLQYI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The statistical analysis will be continued with the means of the percentages of live bacteria to combat the pseudoreplication issue."
      ],
      "metadata": {
        "id": "2uqsKh_eDlo2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Model selection and statistical inference"
      ],
      "metadata": {
        "id": "L0NIpyeJL4pc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Model for the timepoint\n",
        "To investigate the first null hypothesis, the percentage of live cells at the first timepoint will be compared to the percentage of live cells after 3 months of storage in either of the media. This will be done to investigate if there is a statistical effect in the percentage of live cells over time when storing the samples by the CRYO2 method.\n",
        "\n",
        "First, a Welch Two Sample t-test is employed to assess whether the percentage of live cells at timepoint 0 differs significantly from the percentage of live cells after three months of storage. This test is chosen due to the comparison between two groups: the initial timepoint before storage and the subsequent timepoint after 3 months, with the Welch correction applied to account for unequal variances. This t-test is used to assess the first null hypothesis."
      ],
      "metadata": {
        "id": "eb7K64tEM70b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t_test <- t.test(data$mean_percent_live~data$Timepoint, var.equal=FALSE)\n",
        "t_test"
      ],
      "metadata": {
        "id": "tikd5PhaYn57",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 216
        },
        "outputId": "64c1125a-2126-434c-b345-32d763794e86"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "\tWelch Two Sample t-test\n",
              "\n",
              "data:  data$mean_percent_live by data$Timepoint\n",
              "t = 7.1498, df = 15.291, p-value = 2.991e-06\n",
              "alternative hypothesis: true difference in means between group 0 and group 3 is not equal to 0\n",
              "95 percent confidence interval:\n",
              "  6.925494 12.794506\n",
              "sample estimates:\n",
              "mean in group 0 mean in group 3 \n",
              "       74.47933        64.61933 \n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The t-test yielded a t-value of 7.1498 with 15.291 degrees of freedom, resulting in an extremely significant p-value of 2.991e-06 (p < 0.001). This p-value leads us to reject the first null hypothesis.\n",
        "\n",
        "Furthermore, a 95 percent confidence interval for the true difference in means was calculated to be between 6.925494 and 12.794506. This interval provides a range within which we can be 95% confident the actual difference in means lies.\n",
        "\n",
        "To further investigate this difference, generalized linear models will be employed."
      ],
      "metadata": {
        "id": "bHhxixU-HknG"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Poisson Generalized Linear Model\n",
        "\n",
        "First, the Poisson model will be used to see if this results in a reliable model suitable for this dataset, since there is count data."
      ],
      "metadata": {
        "id": "2ixpn6ZyPr5U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Perform Poisson Generalized Linear Model\n",
        "model_poisson <- glm(mean_percent_live~Timepoint, data=data, family=poisson)\n",
        "# Make diagnostic plots\n",
        "glm.diag.plots(model_poisson)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "_bTMVb7mnhyt",
        "outputId": "084a2887-c86f-418b-faab-486379969520"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.216667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 66.360000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.210000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.066667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 68.760000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.313333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 62.966667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.383333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 69.496667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 59.556667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 55.080000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 63.933333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 53.476667”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Q3p66KlW9UNGarb+p5WR7NIJBtK5TRk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              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The upper left plot validates the homoscedasticity between the groups. The distribution of residuals deviates from the ideal scenario of equal scattering around zero between the two groups, indicating the presence of heteroscedasticity. Specifically, there is a notable increase in variability among the samples at timepoint 3 months, while the samples at timepoint zero months exhibit less variability, as evidenced by their closer proximity. It's important to note that the group at timepoint zero months comprises fewer data points compared to the group at timepoint 3 months. This difference in sample size could potentially influence the observed variability in the spreading of residuals.\n",
        "\n",
        "The upper right plot functions as a diagnostic tool to evaluate whether the data points follow a Poisson distribution. In an optimal scenario, the ordered deviance residuals would closely follow the theoretical Poisson distribution line, indicating a Poisson-distributed dataset. However, the deviations observed from the expected Poisson distribution line imply a divergence from an ideal Poisson distribution within the dataset.\n",
        "\n",
        "The lower left  plot represents the Cook's distance plot which is a valuable diagnostic tool used to assess the influence of individual observations on a statistical model. In this plot, each point represents an observation, and its vertical position indicates the Cook's distance, a measure of the impact of that observation on the model's fitted values.\n",
        "The dashed vertical line on the plot corresponds to the threshold calculated as h/(h-1), where h is the number of model parameters. Points falling close to or to the left of this line suggest that the observations exert a typical or expected influence on the model and do not stand out as influential outliers. In this plot some data points are situated on the line, but the majority is located left to the threshold line, indicating that there are no outliers present.\n",
        "\n",
        "The lower right plot is quite similar to the lower left plot. The y-axis indicates the Cook's distance, a measure of the impact of that observation on the model's fitted values. The x-axis corresponds to the case or observation number, with each point on the plot indicating a specific data point in your dataset. There is no dashed horizontal line, indicating the threshold value, visible in the plot, as the data points are located below it and there are no outliers present.\n"
      ],
      "metadata": {
        "id": "isS6CqLTVL5d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_poisson)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "2zIWBbz2MErv",
        "outputId": "7cdc2a1b-aa33-4fca-fb0c-b064aec3a632"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = poisson, \n",
              "    data = data)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182  83.183   <2e-16 ***\n",
              "Timepoint3  -0.14201    0.06097  -2.329   0.0198 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for poisson family taken to be 1)\n",
              "\n",
              "    Null deviance: 11.3620  on 19  degrees of freedom\n",
              "Residual deviance:  6.0525  on 18  degrees of freedom\n",
              "AIC: Inf\n",
              "\n",
              "Number of Fisher Scoring iterations: 3\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The observed deviations from ideal scenarios, such as the heteroscedasticity in the upper left plot and the departure from a Poisson distribution in the upper right plot, suggest limitations in the fit of the Poisson model to the data. Adding to this, the infinite AIC (Akaike Information Criterion) value reinforces the notion that the Poisson model is not a suitable fit for the dataset. The AIC serves as a measure of model goodness-of-fit, with lower values indicating a better fit. An infinite AIC suggests that the Poisson model does not effectively capture the complexity of the data, emphasizing the need for alternative modeling approaches to better represent the underlying structure of the dataset.\n",
        "\n",
        "It is important to note that the Poisson model could have performed better if multiple timepoints were included in the dataset. The current analysis, with measurements taken only at 0 and 3 months, may not fully capture the temporal dynamics of the underlying processes. Considering the inclusion of additional timepoints at 6, 12, 18, 24, and 30 months could provide a more comprehensive understanding of the data. A more extensive dataset could potentially reveal patterns and trends over time, enhancing the suitability of the Poisson model for capturing the observed variability.\n",
        "\n",
        "Given these considerations, we plan to investigate other models that may better accommodate the characteristics of the data and provide a more accurate representation of the underlying processes."
      ],
      "metadata": {
        "id": "MVYE-s7lEien"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Negative Binomial Generalized Linear Model"
      ],
      "metadata": {
        "id": "ZoUcgBZlkRUa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In our quest for a better model following the limitations of the Poisson model, we are considering various alternatives to achieve a more optimal fit for our dataset. An alternative that is often explored in such situations is the negative binomial model. This model is designed to address overdispersion, where the variability in the data exceeds what the Poisson model can account for. Overdispersion occurs when the variance of the data is greater than the mean. The negative binomial model is specifically tailored to handle such overdispersion and can perform effectively in this scenario. However, in our data set, the variance is lower than the mean value of the percentage of living bacteria, indicating that the negative binomial model is also not appropriate. Given this, the negative binomial model is not suitable for our dataset so we are continuing our exploration of alternative models that may be more appropriate for our dataset."
      ],
      "metadata": {
        "id": "Sm9AWQwQIzkt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_negative_binomial <- glm.nb(mean_percent_live~Timepoint, data=data)\n",
        "glm.diag.plots(model_negative_binomial)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "NTtx7LTiGcQG",
        "outputId": "48c3dc91-a856-4e73-9cb9-ccbe53a39e7c"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.216667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 66.360000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.210000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.066667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 68.760000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.313333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 62.966667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.383333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 69.496667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 59.556667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 55.080000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 63.933333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 53.476667”\n",
            "Warning message in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace > :\n",
            "“iteration limit reached”\n",
            "Warning message in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace > :\n",
            "“iteration limit reached”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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K+Llm5VN2Sobut7Wh3NIpFsKJXTkJFF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hLVx7mdS/YFqHMs2E2krtT19fsfOqG2807p/p6nJZHS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\nSAAIACIBIACIBIAAIBIAAoBIAAjg/wGFdCSYfztulQAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similar to the 2 previous models, the upper left plot indicates that there is heteroscedasticity, since the two groups scatter differently around zero.\n",
        "\n",
        "However, the upper right plot indicates that the data does not follow a negative binomial distribution, since the ordered deviance residuals are not aligning with the theoretical negative binomial distribution line.\n",
        "\n",
        "The two lower plots are again very similar to the previous models, as the data points do not cross the thresholds, indicating that there are no outliers present.\n"
      ],
      "metadata": {
        "id": "IgQkPYG3kpJ-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_negative_binomial)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 488
        },
        "id": "2GQAqUaPMf_g",
        "outputId": "76b509a7-d0fb-417d-a115-8ad774deda8e"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm.nb(formula = mean_percent_live ~ Timepoint, data = data, \n",
              "    init.theta = 4038620.625, link = log)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182  83.182   <2e-16 ***\n",
              "Timepoint3  -0.14201    0.06097  -2.329   0.0198 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for Negative Binomial(4038621) family taken to be 1)\n",
              "\n",
              "    Null deviance: 11.3618  on 19  degrees of freedom\n",
              "Residual deviance:  6.0524  on 18  degrees of freedom\n",
              "AIC: 132.89\n",
              "\n",
              "Number of Fisher Scoring iterations: 1\n",
              "\n",
              "\n",
              "              Theta:  4038621 \n",
              "          Std. Err.:  142623950 \n",
              "Warning while fitting theta: iteration limit reached \n",
              "\n",
              " 2 x log-likelihood:  -126.893 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The AIC value is 132.89, which is lower than the Poisson model. Although this provides a better fit than the previous model, we continue looking for a model that performs better because of the lack of overdispersion of the data."
      ],
      "metadata": {
        "id": "mt5V5wS1MkK9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Gaussian Generalized Linear Model\n"
      ],
      "metadata": {
        "id": "zYXjTXjepWzQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We opted for a Gaussian Generalized Linear Model (GLM) for our analysis due to the normal distribution observed in the dataset. This choice allows us to effectively model the relationship between variables while accommodating the data's inherent distribution characteristics."
      ],
      "metadata": {
        "id": "WxIq5LDuBox2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_gaussian <- glm(mean_percent_live~Timepoint, data=data, family=gaussian)\n",
        "glm.diag.plots(model_gaussian)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "ylc5pKDzclUL",
        "outputId": "412aa41f-2ae1-40e2-de77-bca04631aa57"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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AVn3cbH6OFS9r3onQeTSDmDYgghsa/wPsAIkbTBcrGhgTWfkPXBrqAY0ZDxPtL5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\nAoBIAAgAIgEgAIgEgAAgEgAC+H/yklr7jWrWXwAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similar to the last model, the upper left plot indicates that there is heteroscedasticity, since the two groups scatter differently around zero.\n",
        "\n",
        "However, the upper right plot indicates that the data follows a normal distribution, since the ordered deviance residuals follow the theoretical normal distribution line.\n",
        "\n",
        "The two lower plots are again very similar to the previous model, as the data points do not cross the thresholds, indicating that there are no outliers present.\n"
      ],
      "metadata": {
        "id": "KdOawbQUjVao"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_gaussian)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "TxUROrntNm1G",
        "outputId": "e84126e4-b56b-478b-ba5f-678eec3cbed6"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = gaussian, \n",
              "    data = data)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept)   74.479      2.061  36.137  < 2e-16 ***\n",
              "Timepoint3    -9.860      2.380  -4.143 0.000611 ***\n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for gaussian family taken to be 21.23896)\n",
              "\n",
              "    Null deviance: 746.87  on 19  degrees of freedom\n",
              "Residual deviance: 382.30  on 18  degrees of freedom\n",
              "AIC: 121.77\n",
              "\n",
              "Number of Fisher Scoring iterations: 2\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The AIC of the Gaussian Generalized Linear Model is 121.77, which is lower than the Poisson and Negative Binomial model. This model provides a better fit to the data than the previous two models."
      ],
      "metadata": {
        "id": "2LwLbspYNr9c"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### The Best Model\n",
        "\n",
        "After testing several models, the Gaussian Generalized Linear Model emerged as the most effective performer. It demonstrated superior ability in fitting the data and capturing variances compared to the other two models. This is evident in the diagnostic plots, particularly the upper right plot, where the data distribution closely aligns with a normal distribution. This alignment is observed through the ordered deviance residuals, which closely follow the theoretical normal distribution line.\n",
        "\n",
        "Furthermore, the AIC value serves as a valuable tool for model comparison. The model with the lowest AIC is considered the most favorable. In this case, the Gaussian Generalized Linear Model achieved the lowest AIC score (121.77), affirming its superiority in performance on the provided dataset."
      ],
      "metadata": {
        "id": "5-9B2N_dlNIZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "FORMULEEEE"
      ],
      "metadata": {
        "id": "XtakImadp0d5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_gaussian)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "Y2e7ZMQMn4CF",
        "outputId": "0ab34986-22de-4369-f818-a98ac45d6789"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = gaussian, \n",
              "    data = data)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept)   74.479      2.061  36.137  < 2e-16 ***\n",
              "Timepoint3    -9.860      2.380  -4.143 0.000611 ***\n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for gaussian family taken to be 21.23896)\n",
              "\n",
              "    Null deviance: 746.87  on 19  degrees of freedom\n",
              "Residual deviance: 382.30  on 18  degrees of freedom\n",
              "AIC: 121.77\n",
              "\n",
              "Number of Fisher Scoring iterations: 2\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "conf_intervals <- confint(model_gaussian)\n",
        "conf_intervals"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "6TpBA_lFp8-A",
        "outputId": "cb2ad7b8-d115-48ec-adbb-3984c5adab9a"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Waiting for profiling to be done...\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>(Intercept)</th><td> 70.43981</td><td>78.518853</td></tr>\n",
              "\t<tr><th scope=row>Timepoint3</th><td>-14.52444</td><td>-5.195565</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA matrix: 2 × 2 of type dbl\n\n| <!--/--> | 2.5 % | 97.5 % |\n|---|---|---|\n| (Intercept) |  70.43981 | 78.518853 |\n| Timepoint3 | -14.52444 | -5.195565 |\n\n",
            "text/latex": "A matrix: 2 × 2 of type dbl\n\\begin{tabular}{r|ll}\n  & 2.5 \\% & 97.5 \\%\\\\\n\\hline\n\t(Intercept) &  70.43981 & 78.518853\\\\\n\tTimepoint3 & -14.52444 & -5.195565\\\\\n\\end{tabular}\n",
            "text/plain": [
              "            2.5 %     97.5 %   \n",
              "(Intercept)  70.43981 78.518853\n",
              "Timepoint3  -14.52444 -5.195565"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* The estimated intercept (β0) is 74.479 (95% CI [70.43981, 78.518853]). This is the predicted percentage of living cells for Timepoint 0 months.\n",
        "* The coefficient for Timepoint 3 months (β1) is -9.860 (95% CI [-14.52444, -5.195565]). This is the predicted difference in percentage of living cells for Timepoint 3 months compared to Timepoint 0 months. Thus the predicted percentage of living cells is 64.619 at Timepoint 3 months.\n",
        "* Both intercept and coefficient have extremely significant p-values (p < 0.001), providing reason to reject the first null hypothesis. This suggest that storing over 3 months using the CRYO2 method in any of the media has a significant effect on the percentage of living cells in the samples.\n",
        "* The dispersion parameter for the Gaussian family is provided (21.23896). It characterizes the variability of the residuals around the fitted values.\n",
        "* The null deviance (746.87) represents the deviance of the null model (i.e., a model with no predictors). The residual deviance (382.30) represents the deviance of the fitted model. As the value gets lower, the fitted model performs better than the null model.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "VXjWyVWnn8uS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Models on Medium level\n",
        "\n",
        "\n",
        "To investigate the 2nd, 3rd and 4th null hypothesis, the amount of live cells before storage and after storage in respectively medium A, B or C will be  compared. Therefore, the dataset was split in three dataframes, one for each medium and the datapoints of the first timepoint. This will be done to see if the statistical effect is different for either one of the preservation media."
      ],
      "metadata": {
        "id": "8V-tXAXKdpli"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data_none_a <- data %>%\n",
        "  filter(Medium == 'None' | Medium == \"A\")\n",
        "\n",
        "data_none_b <- data %>%\n",
        "  filter(Medium == 'None' | Medium == \"B\")\n",
        "\n",
        "data_none_c <- data %>%\n",
        "  filter(Medium == 'None' | Medium == \"C\")"
      ],
      "metadata": {
        "id": "-F_EUnKi-ljF"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Both Poisson and Gaussian generalized linear models will be checked again, as the Gaussian model may not necessarily be the most appropriate choice for our analysis when looking on a medium level. The Negative Binomial generalized linear model will only be re-evaluated on the dataframe for medium C, as the data for medium C show signs of overdispersion."
      ],
      "metadata": {
        "id": "ZvUfOQ7vCJSf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Poisson Generalizd Linear Model\n"
      ],
      "metadata": {
        "id": "QDDLKR8ePHUL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_poisson_a <- glm(mean_percent_live~Timepoint, data=data_none_a, family=poisson)\n",
        "glm.diag.plots(model_poisson_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 799
        },
        "id": "FgndJxWkQcSc",
        "outputId": "a3214832-c547-486a-eef4-d4150e46cf72"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.216667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.066667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 62.966667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 69.496667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 63.933333”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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UTamEauOaXMcc0NvwNtSE89pm0+K0/d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\nWoEDAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_poisson_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "xAYrsEC0Qs-t",
        "outputId": "105ba167-a1c3-4cad-e482-079c4943ca7b"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = poisson, \n",
              "    data = data_none_a)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182   83.18   <2e-16 ***\n",
              "Timepoint3  -0.12487    0.07568   -1.65   0.0989 .  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for poisson family taken to be 1)\n",
              "\n",
              "    Null deviance: 3.16214  on 9  degrees of freedom\n",
              "Residual deviance: 0.43436  on 8  degrees of freedom\n",
              "AIC: Inf\n",
              "\n",
              "Number of Fisher Scoring iterations: 3\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model_poisson_b <- glm(mean_percent_live~Timepoint, data=data_none_b, family=poisson)\n",
        "glm.diag.plots(model_poisson_b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 763
        },
        "id": "3hNWITJTQnYx",
        "outputId": "f83f8b54-899b-4bab-f3dc-75e9e6258657"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 66.360000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 68.760000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 59.556667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.470000”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Ta1L3YQ6eeIqcp/BN8n/EN4AyEC3wnZ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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_poisson_b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "rmUZytVvQ0x1",
        "outputId": "417e3f08-765c-4bc1-9121-68d2f5a2792b"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = poisson, \n",
              "    data = data_none_b)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182  83.183   <2e-16 ***\n",
              "Timepoint3  -0.13261    0.07584  -1.749   0.0804 .  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for poisson family taken to be 1)\n",
              "\n",
              "    Null deviance: 3.81399  on 9  degrees of freedom\n",
              "Residual deviance: 0.74957  on 8  degrees of freedom\n",
              "AIC: Inf\n",
              "\n",
              "Number of Fisher Scoring iterations: 3\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The diagnostic plots for the poisson model for medium A and B does not show a good fit of the model to the data. On top of this, the AIC value reaches infinity, indicating that the poisson model does not capture the variance in the data."
      ],
      "metadata": {
        "id": "YMH2x0BnUUx-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_poisson_c <- glm(mean_percent_live~Timepoint, data=data_none_c, family=poisson)\n",
        "glm.diag.plots(model_poisson_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 799
        },
        "id": "vLYw1TubQnzn",
        "outputId": "439ae35c-791a-4e62-904a-057e31076cae"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.210000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.313333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.383333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 55.080000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 53.476667”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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gaVSKvcaCCSDeA7jmT1GUOeT5gsq2oTgEg2ICqvkC25cpGkmk0BItkAzSIN8ENn\n28iIDYhkAzSLVMsPnW0jIzYgkg2Iup92OxvOkVCrqUAkGxBtIm285Bb9YylbDIhkAzSL9Mg6\n+ogXnW1LyOijcj0vCK/UbCCSDdAsUrXZtJoXnW2Lz+jDBL1TzVgRiGQDouun3Zao2u3tBSLZ\nAB6R5rrnJT34us62kREbEMkG8IhECpTFNyk62xab0Z8rRNZmJSCSDdAuUvv2pHV7J+2q5+ps\nW2hGhy6/SmBtlgIi2QDtIr03kLRq46LLFzrbFpnR/2r+9Q9xtVkLiGQDeH7a3XBcTNsCM1qf\nfecZYZVZDZkiFcwfM3jw2EUnVAtAJDb49toV/LjDRYRCxmVUWjGKrpq4CHkiFQ1KIMlZWYkk\n9Rm1a2IgEhs8Iq2v6xnNNlwhYzM6IqwmCyJPpKEZk1zDWpTsHJc6XqUIRGKDR6Qr2sxYrBCu\nEDIShjyRcqZ6702srVIEIbHBI1I5llGADcvobL/PRFRjYeSJlLjGey8/SaUIRGKDR6Sa5xgK\nGZXRkZY19Q5UaXXkiVT/Ke+9YU1VikAkNnhEeoblhDaDMtrbsGl0DF4XBnkiTXV0X7Bl187N\n8zo75qoUgUhs8Ig0Mqdp914uwhUyJqPtVdv+qbsSqyNx9/eseu7dRs1U/9+FSGxw/bSr18BN\n2FKGZPThoPO667A8Ug/I7lk2b/6KferrIRIbOs7+Pr8lQgFkJAac2WADdIj0XQWdbevNKKoP\nHvlhhEiFv6msgEhs8Ih0ol+djIyMdAfjkMWSMirqrffCQrtghEjN1V4JkdjgEWlATv/Uvt3S\nex5gKy4no1O3ZX2p4+V2wgiRpo9VWQGR2OARqfoqmnWAFlzNeAGQlIwOX10n2g8f+cD/SDaA\nR6SEvbTybko3Nudq8YPxXsgwrgoU6rf4nf/FNsMIkQ4GjvHcoY4X0p+3ytiCR6RLVtHGiyg9\nkMpWPCije5t7cegYqeQT+09WzowRIuUHvvLLBV6S5vFWGVvwiNSr6u5BNRau6Rr+OJKPfLV0\nyy/R3nYsYoJIZSAkNnhEOtpx36GGhJT/iK248Izm/4/vdXZFnkg9fLSFSPrgPY5UvGH10bAF\npGVUOjQx2k/3DkKeSCnZTTzkQSR98IhU4OHXcIVkZXS+e/mlHC+zM/JEmlTNO9AFw8+Gkv1n\ntdUeU3ANx0UYrpDVlBE7x2/M3eq8XbP8oPbX2hWJ/yN1aOe5RD9iSMcGpZL4tt9rrD924BHp\nHRevP5AXfn8Oe0ZaePOyfbT0hfIJKXG9BA3BYn0kilQwxfOFtLWNSglPSOevavDB7rV3lodJ\nKug41+79B8KuZs5IM2MzZp4v+aJhO75X2w9TD8h6QpqWVei8Lb3tLuENRAk6RCrO0dk2p0hn\nK7zrWuyMW6+zfbtgBZH+eZ+yeD9DeANRgg6R9qXrbFurSHOuUxbfEvdp381e0dm+XZAt0sm/\nbFNf6Qmp00Bl8ZnasAExD49IQxQeyL0lclGWjFgZH/+qstxCjinLyyDSRXCJdIysVV/pCWmE\ne0DokVfwNBAL8IiU5SL70h4MZ3+zZMRG8YBkzyXrZ9JmuxZ74nH290VIE2lP6rBzlH6UNp2n\ngVhA8vxI4kTqnOmr6elK84rpxqZt1AaejDasIBJdmlOldcMknAquBpdIJUeOMI4QLE6kJ8oG\nSC4Zk5pSyfHPWLlAVrpIRSvDHEnwhXRi9og3dvJUHxtwiPR5h/KEVLgjjCFlsGWkmYLPFu/h\nfa39sMJeOxAB7SI9S9L/+fSwe6o6xlH6U9gRuSLBnNHeY3qasT0QyQZoFimf9HQdmqMXhpKV\ndJOuvaGsGX2S9raeZmwPRLIBmkW661rv//i33UL75ulpmzGjGYnDYmW3Qmggkg3QLFKVN7z3\n5pe/nvxHT9tMGZU+nTBFTyNRAESyAZpFSvzYe28dqavvqAJTRtPTPtXVSBQAkWyAZpGyp3nv\nLUzT+YuLKaM/9+prJAqASDZAs0i33uy9d1cLnW0jIzYgkg3QLNIS8swF1/L8M0Tv6SIRM/rh\nMZ0tRAcQyQZoP470MKk95LW3h9UgPfTuS4uU0drMzjpbiA6sIdJPT3TsH2sX+WuA48yGOZcr\ns7XM0L1POkJGi1J7F+ltIiqwhEivJl0/qFNSxxiYRYcPrnPtCrduLRTQdviMXo1/QUAb0YAV\nRNoc5zrlfkdVteGnYx7JZ3+HJXxGN8wxvkfWxAoi/ds9XsDL9YQ3ECVYQCRkFAEriHTXIGWx\nMkF4A1GCBUQKkVFsnxIUjPZj4sIAACAASURBVBVE6tVVWcyqLLyBKMECIl2c0b5mr5nSIYti\nBZEWpf7ovD13ja7T/aMZC4h0UUbf5t4YM2PWsWAFkUrvyhj9yZuNa4YdXTeWsYBIwRmtyuiM\nsXH9sYJItGTqVWmXPhp+vPdYxgIiBWW0MnEo/kUKwBIigfBYQaRAdiwwuh9WByLZAOuJBIKB\nSDbAWiKdYpy7LLYwV6SJm0IzZbZgJs0UXOEbbwuucNoClW3h5BEzRQrMaPY7r9etOovtLc2Y\nrOH9v6yhrJaNP+sVDRVPZHxnLqYu4s1IvEh5BDDBMO6wLPLMfu92gT0j8SKpcZxsEVxjrXcF\nV3j7EMEVPnWT4Arl0ETDUVgtv0j/IBom9emg4RKo97PZy2r6X+Nh7stHIJIfECkyECk0EMkP\niBQZiBQaiOQHRIoMRAoNRPIDIkUGIoUGIvkBkSIDkUIDkfyASJGBSKGBSH5ApMhApNBAJD8g\nUmQgUmiME+lc7l7BNV6/THCFfV4SXOFr9wquUA7tPmAvO/tO9rKncg6yF35Qw7QAX1zJXpY2\n/oq97LiBGioOwDiRAIhiIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKA\nSAAIACIBIACIBIAApIt0M9npuz85pYdrcY8yZFgt3RWWTr0iLW/AEee96Q2Tqj3JO39wiApF\n9fDCsw2SK/cr1NtDiXgiUYj4rv0LR3hHAWvDVRxYTYTNxFyrxt5q3A6hkC3SzETfp6qgQ7Vs\npbe3tsx3skF3hc87nlw9JeNmSueQ4aunpP9bXIWienh/+UlfTM28QWcP5eGLRCHCuw4sHP4d\nBa4NU3FgwQibiblWjb3Vth1CI1mkw5kDfJ+qKTf90UTpbcseYV7BXmFJVk/n7QTyB61/j/PO\npASu+b5DViiohyezXBc4TSSHdPVQIr5IFCK868DC4d9R4NowFQcWjLCZmGvV2Ftt2yE0kkXq\n1G6tT6QDJdTd28seElJh6a4/nLeLyI49ZL7zzn7lVkiFonroZhL5TVcPJeKLRCHCuw4oHP4d\nBa1VrziwYITNxFyrxt5q3A6hkSvSB2l7Az5V7t7mabioOEKFlPbKKV7mvog9eYyoCgX28Fzh\nh1V6Uz09lIzfByjyuy4rHP4dBa1VrziwYITNxFyrxt4GFeZLX6pIR6tMpCFEyrzt7+nVeuwT\nUSF93zGbzie7XHezBouqUGAP7yMJT5bq6aFs/D5Akd91WeHw7yhorXrFgQUjbCbmWjX2Nqgw\nX/pSRbq3RUkokXKumLVheo3aJwRUOCPhGd9myuT4mIauUGAPf141IfOuUh09lEPRsWPHTir3\n/D5Aau86VGG1d+QuG7RWfXMGFoywmZhr9RC5tyEL86UvU6TlKd/TUCIpbCBv6q9wdPwk5+0K\nstl5W5I4VlSFAnvoZA35mL+HklhJCPmLcs8vEoUQ7zpUYbV35C4bam3IzRlYMMJmYq7VQ+Te\nhiwcueJQyBSppyPeCYlv7XvGr7dnyCjdFY5OXexa7CPznLc7yUJRFYrq4a+zC5y3J8jz/D2U\nxPG1a9duU+4Ff4BCvOtQhdXekbtsqLUhN2dgwQibiblWD5F7G7Jw5IpDIVOkg9udzCJL9/ie\nUXq7u9M66vqSmKO3wsXxn7jvNHWNRjYu9U9RFYrq4XYy0Xn7X2c93D2UTtkHiOFd+33awr+j\ngLXhKg6sJsJmYq5VY28DC/OlL/3MBuV3zvTmhZRuzc/Pa5uff7CoSfVZG6blNDyns8JztW90\nHTjL/5Uudgxb/UrqaL099FUoqof0zrQJa2bWbHBWZw+l4Y1E6W2kdx1QOMI78q2NVHFAwUib\niblWjb3Vth1CY4xIY8lvlLZxzyY4mR56oEZiTu/f9Va43TM94duUzmmUWHNcqbgKBfWQnh1Z\nM7HmfQeozh5KwxeJ0tsI7zqwcIR35F0bseKAgpE2E3OtGnuraTuEBietAiAAiASAACASAAKA\nSAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKASAAI\nACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKASAAIwF4i\n9ajiuVPtESH1zSUHRFUV7Sy5NTuxyl2rg551bcCwBBYIWVxAAL4qQven1gDdLUTEpiLNXiek\nPtd2969qdnsh1UYhD5Obp338xrXk2cCnRYgkIEtfFRCJDZ9Iggje7oMgUmhmk3GuRWkv8t+A\n50WIJBKIxEbAT7uaI8fWTrt6A6Ul45um5g4+Tenxh6ok1Bh4ktIao+5P/cJdsvITj+Wm/GWT\n9zlf2cLOaRXvn+r5aVc8rnZKk3foDYSQubR4TJ3ES/75a0Atsc5lTdxzC53Jus27XXwb0LdJ\n1bawwkXFW17nenpsYqErAF9yvlA9kZRVpxDUxFdtMlObTXd/HHwNZA1xFnyHFJRV6hLJW1QW\nNhapXs6oM6durEvpU3GTf/k0925KO1VdtWdF1f6U1m3We/1xd8maFZ+7UHBjbpHnOV/ZOzOX\n7Jlc3SPSsPLvbnuBLDjeqnXBefpIubf3rqrbrNi/lhingAzx3PtXWolnu/g2oG+Tqm1hhYuK\nv+FwrWn2DyUAX3K+UD2RlFWnENjE+cy7t+2c6FiuVOFrwCeSr1KnSL6isrCxSA0aO78lZ5CC\n0+X6Op+ZSX6mv+x23ulfx7mqhm9ytloNnDdfkqXu53xlC+NGOu/c4xbpVLmnnA8ee5m2cf60\nO5E8nLqmEF3pX0uMs5W87rn3NCl0bxffBizb/Gpb2MXFxQsTX6F0B/lAybIsOU+o3kjKalcI\nbGKPMrvyxsOuKsqa84nkq9Qpkq+oLOwsUnfnncXkx/XkI+ed/WQe/W3IZVWyUjOcqzr7XlLL\nNcnucTLR/Zyv7FqnWpS+6Rbpa/Kxu7BLpHXkE+UVL/jXEuNsc80vqjCUHHVvF98GLNv8aluY\nhi5+a0tKR1c8p2RZlpwnVG8kZcUVApsobXbJyHXFVPk4lDXnE8lXqVMkX1FZ2FmkXtS1zXcs\nI4nJTsjE4obVF+060DfDs8pNrX7OmyIyyv2cr+xSssb58D23SJ+RfHdhl0jLlDXFZIR/LTHO\nMcfjnnt3Z5S6t4tvA/o2qeoWpqGLz3Ecoo37KFkGJecM1RtJWXGFwCbokVFNSfaoYlcVZc15\nRSqr1PU/kreoLKJApI3krR0uCjc4fydQ2i1IJNdfpCPkVfdzvrJrlC+w19wibVX+7lO3SOuV\n78Kj5CWIVMbVuWeV5blLOnu2rm8D+jap6hamoYufSpv0PVmrZBmUnDNUbyRlxRUCm3A9c+jZ\n+BddVZQ1l+0S6XVSUFapZ6+dUlQWUSDS6XJPO++c201Xu76UjmSkB4pUo9j1HfaZ+zlf2d8d\nrju3u0U6nTHI+aBPX9qmnet/pCecD5Y464JIPt4nTyjLh+M2eraubwP6NqnqFqahi9Nu7UbW\nLlWyDErOFaonEr/iLgKb2LvA9VyLbq4qypq71FWmFykoq9Qpkq+oLGwmUqVlLr4NEIkOT5u6\na1On7GNH0roe/LrFfY7t5/1Fyn3op41NahV7tPCWpe0zF24fV9uz125k4qRN4x3zaecamw7S\nweVm7vus9nWlEMmPweSmd5ZObemYRL1fU74N6NukaluYhi5Ol6Q0cu0gcAYQlJwrVG8kZcWp\nr2nvc+sdI7bvnpXytpKhr4Hu1faXfJhHCsoqdYrkKyoLm4lEFDoFilQ6oV5ixl0/OB/US7l8\n+YG6aVv8RRo4Ojf5r7u8GfjK/nZHuYx73yd73MeRRtdMbjzD+QMkJ/k154O8hCp9jlGI5M/S\nW7MTq3bZ4Lrr3i6+DejbpGpbmIYuTi9kkZ+o+9dFYHKuUL2RlBUva9r33PvXlC/XdKK7Cl8D\nB9pVqNxzHvm1rFLXTztvUVnYSyQOjDiqDQBEAkAAEAkAAUS9SAAYAUQCQAAQCQABQCQABACR\nABAARAJAABAJAAFAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAA\nRAJAABAJAAFAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJA\nABAJAAFAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJ\nAAFAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFA\nJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAE\nAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAEAJEA\nEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAEAJEAEABE\nAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAEIF6kqyoBJu4R\nvumRkWjYMxIvUvmxKwEDfa4RvumRkWA0ZCRBpCXCq4xKXjRTJGTEhIaMIJJZQCTrA5FsAESy\nPhApgG1d6zXrvd/sXgQDkfj5sF1ei9Gn5bcDkfx5N6Hj1MnXp31pdj+CgEjc9El++N3n8+r9\nLr0hiOTHkQqvOG9LH2xQanZPAoFIvKxK/Mp5e+qKB6W3BJH8WFCp2LXYT743uyeBQCReHu6g\nLN7Llt4SRPLjtSbKojT+c5M7EgRE4qVrP2XxhaNYdksQyY8PK5x1LX4iO83uSSAQiZchbZTF\n1GrSW4JIfpyqPKSE0rN3tDC7I0FAJF6+iVvkvD1U+3HpLUEkf1akXzX8sdrVd5jdjyAgEjfP\nxd82pk/6305KbwgiBfDb0Js6jJO/1TUCkfjZ0ueGru+WyG8HItkAiGR9IJINgEjWByLZAIhk\nfSCSDYBI1gci2QCIZH0gkg2ASNYHItkAiGR9IJINgEjWByLZAIhkfSCSDYBI1scEkY7t9lIO\nITFhvEjISCsmiNSM+BggqMoox3iRkJFWTBDpiO/bzjFKUJVRjvEiISOtmPo/EkJiw8z/kZAR\nGxDJBkAk6wORbABEsj4QyQZAJOsDkWwARLI+EMkGQCTrA5FsAESyPhDJBkAk6wORbABEsj4Q\nyQZAJOsDkWwARLI+EMkGQCTrA5FsAESyPhDJBkAk6wORbABEsj4QyQZAJOsDkWwARLI+EMkG\nQCTrA5ECODnx/j4ziszuRTAQyZKUzu//r/GFngcQyZ+vqtW6/56sZvvN7kcQEMmKHLm+Qpde\nDbKWux9BJD/O1ex51rmBWrU2uyNBQCQr8s9mhygteqzSEeURRPJjaeoJ12Ir+cXsngQCkSzI\nqeRlrkVRznTlIUTy4/UmyqIk7nOTOxIERLIgP5NDyvKmp5SFTJEK5o8ZPHjsohOqBawW0pzK\npa7F72Sr2T0JRKJItsvIMvxBvlWWzV5SFvJEKhqUQJKzshJJ6jOlKkWsFtLhlNmuxbCaBsyC\nrQVpItkwI+twzb2u28/i/qc8kifS0IxJrr1fJTvHpY5XKWK5kP6T0P+TDzonfGp2P4KQJpId\nM7IMG8vdNH/Z0JTH3Y/kiZQz1XtvYm2VItYLaWXL8pkdtpndi2CkiWTLjCzDrq6VU6/5wPNA\nnkiJa7z38pNUiiAkNqSJhIyEIU+k+k957w1rqlIEIbEhTSRkJAx5Ik11dF+wZdfOzfM6O+aq\nFEFIbEgTCRkJQ+Lu71n13BPsNFusVgIhsSFv9zcyEoXUA7J7ls2bv2Kf+nqExIbMA7LISAwy\nRfpjR7Gy/PVtlQIIiQ2JIiEjQcgTqbAdIbn/57qXr/ZKhMSGNJGQkTDkifRQxZcW3U/GUoSk\nG2kiISNhyBOpxpvOm3nxbyAk3UgTCRkJQ55I5ZSDfVPjP0ZIepEmEjIShjyRmrkP9o1IXYqQ\ndCJNJGQkDHkiTXH0/MO1HBXfOvCVc8d7IY9rqzJWkSYSMhKGPJFKx2XuVu4srh34yn5tvZCH\ntVUZq0gTCRkJQ+ZxpBLPNS7ntqsUwM8GNiQeR0JGgsCl5jYAl5pbHyNEKvxNZQVCYsMAkZCR\nTvhEmjfRefPQB6pFA2mOPUL64BIJGRkKl0gzyGPO2z6OWWwvnD5WZQVCYoNHJGRkLFwiNXlB\nWYxvprNxhMQGj0jIyFi4REpxj2qwKSX8CzDUkyB4REJGxsIlUt5MZTGxVrjiGOpJGDwiISNj\n4RJpTIWRH+cvHJQ4OlxxDPUkDB6RkJGxcIlU9Hg5QkjFkcXhimOoJ2HwiISMjIXzONKprz/b\ndiZ8cQz1JAy+40jIyEgwHJcNwHBc1ke7SI+so494CVccQz0JQ7NIyMhwtItUbTat5iVseQz1\nJArNIiEjw8FwXDYAw3FZHy6R5p5XFgdf19k4QmKDRyRkZCxcIpECZfFNhKPmEUFIbPCIhIyM\nhUOk9u1J6/ZO2lXP1dk4QmJDu0jIyGg4RHpvIGnVxkWXL3Q2jpDY0C4SMjIarp92NxwX0zhC\nYoPnpx0yMha+vXbLD9Oi8d2m6W0cIbHBtdcOGRkKl0hT476iw+NbpEzS2ThCYoNHJGRkLHwX\n9k2mRRXH0Rm4aMwYuC7sQ0aGwndh3076JTlEf07T2ThCYoPrwj5kZChcIlX6jo5wftNtz9DZ\nOEJig0ckZGQsXCK1uXth1mhKR/xVZ+MIiQ0ekZCRsXCJ9FUmuewYXeBgHetJDYTEBo9IyMhY\n+HZ/n99TSuneDXobR0hscO3+RkaGgiGLbQCGLLY+8i7sYwAhsSHtwj4GkBEbEi/siwxCYkPe\nhX2RQUZs4KedDcBPO+uDC/tsAC7ssz64sM8G4MI+64ML+wLY0qlOowfCjGBgDriwzyQWta3e\n/KmTTEVxYZ8/M+K7THujVTm970s0uLDPHB5MGTT7xbp11OZgC0DPhX3nt2jsWDBWC+lIeeWi\ng7711UaUNwkdF/ZFXUYG8t+Er5y3Z5o/wFJYz1677yqwdyokVgtpfqYyUvYB8r3ZPQlEx167\nqMvIQAbepiz+rxJLYS6RTvSrk5GRke6or7FnwVgtpNeaKIvS+M9N7kgQPCJFa0YG0q2vsviS\nXGAozCXSgJz+qX27pfc8oLVrCnfW8UL6cVUgjY/KK4PO/0h2md2TQHhEitaMDOTxvyuLaTks\nhblEqr6KZh2gBVev0NgzN5+95YU8yVWBNE5VebTE+aO4g95LD0TDI1K0ZmQgW+IWOG8P1n6c\npTCXSAl7aeXdlG5srrlvgVjuZ8PKjCuG/btWjR/N7kcQPCJFbUYGMiGh/ajeFVqdYinLJdIl\nq2jjRc5/ylO19y0A64V0eHj7O8czbTgj4REpejMykG39W3ebVcJUlEukXlV3D6qxcE3XBpp7\nFkhMh6QBHpGQkbFwiXS0475DDQkp/5HOxhESGzwiISNj4T6OVLxh9VG9jSMkNniPIyEj48DZ\n3zYAZ39bH5z9bQNw9rf1wdnfNgBnf1sfnP1tA3D2t/XBtC42ANO6WB9M62IDMK2L9cG0LjYA\n07pYH0zrYgMwrYv1wbQuNgDTulgfTOtiAzCti/XBtC42ANO6WB9M62IDMK2L9cG0LjYA07pY\nH4z9bQMw9rf1gUg2ACJZH4hkAyCS9YFINgAiWR8ukbzDQRzR2ThCYoNHJGRkLFwidXZffbmm\nevgXFMwfM3jw2EUnVAsgJDZ4REJGxsIlUk7bk5QWj46/MVzxokEJJDkrK5GkPqM2Jj1CYoNH\nJGRkLFwi7Wt8TcGBVgnPhR3xa2jGpP3ORcnOcanjVYogJDZ4REJGxsK3s+Foq0uz6mwMXzxn\nqvfexNoqRRASG1w7G5CRoXDutTt3d9z/IhRPXOO9l5+kUgQhscG31w4ZGYl2kQYo9E9v5LwN\nV7z+U957w5qqFEFIbGgWCRkZjnaRavkRrvhUR/cFW3bt3Dyvs2OuShGExIZmkZCR4Ug8IDur\nHlFotlitBEJiQ94BWWQkCj6Rile+MOKlLyLOtLpn2bz5K8LMEY6Q2OASCRkZCpdIh5oqX2Mt\nGUd8OjhZZQVCYoNHJGRkLFwidau/4njxkY9rPcT2wny1H4UIiQ0ekZCRsXCJlLVaWSxlmlwT\nIemGRyRkZCx8U1/+oix+SQxXvIePtghJH1xTXyIjQ+ESKW+6spieF654SnYTD3kISR88IiEj\nY+ESaXTa8E/WfDy03JhwxSdV+8NzDz8bdMIjEjIyFi6Rih9JJoSkDC4OW75DO88Jk0Eh/bTS\nCxnJ3tFYhkckZGQsnAdkT6xbtv5khPIFUw6672xtE/D8VcTHg8yNxzR8B2SRkZFIPSAbCfxs\nYEPmAdlIICM2jDggqwpCYsOAA7KqICM2jDggW/ibygqExIYBB2SRkU6MOCDbHHuE9GHAAVlk\npBN5B2TLmD5WZQVCYkPaAdkykJFO5B2QZQAhsSHtgCwDyIgNeQdkMdSTMKQdkEVGwpB3QBZD\nPQlD2gFZZCQMeQdkMdSTMKQdkEVGwuAR6Zhye6IwfHEM9SQMDpGQkcFwiDS/4i7XYnT26rDF\nMdSTMLSLhIyMRrtIXyf+/YBreejG9N3himOoJ2FoFgkZGY52kbo1Ouu+c6Zev3DFMdSTMDSL\nhIwMR7tINf7jfeLl+mHLY6gnUWgWCRkZjnaRkj70PrE4JcIrMNSTGDSLhIwMR7tIWdO8T7x2\nic7GERIbmkVCRoajXaRb2noelzTvoLNxhMSGZpGQkeFoF+kT8vhp1/LIveQznY0jJDY0i4SM\nDIfjONKjpGqvcRMezNB/NT9CYkP7cSRkZDQ8ZzZ8cG08IUk3LtXdOEJig+PMBmRkMHzn2p3Z\n+8s5AY0jJDa4zrVDRoYicVqXyCAkNuRN6xIZZMQGRLIBEMn6QCQbAJGsD0SyARDJ+kAkGwCR\nrA9EsgEQyfpAJBsAkawPRLIBEMn6QCQbAJGsD0SyARDJ+kAkGwCRrA9EsgEQyfpAJBsAkawP\nRLIBEMn6QKRAtr+3YI/ZfbgIiCSNgwtnbhJSEUTyp6AjqZGd8PB5s/sRBESSRMmI5Eq1HDft\nF1AVRPKj9O9XfEfpqmoDzO5IEBBJEs9UWkzprlbNivRXBZH82Bin/Kz7JPGo2T0JBCLJ4UIl\nZTa2wnIf6a/LBJFe7OOFPCqoSkG85R6W9HzcFyZ3JAjjRbJuRiLZSdw/6lpFmI2NBRNEGtPF\nC/m3oCoFMc09t8lpx3qTOxKE8SJZNyOR7CXuKQaufVZ/Xfhp58f3ZLNrMSvttNk9CQQ/7eRQ\nkvuia7En8XP9dUEkf7pVX3Tm+JsVxpndjyAgkiSmJb945Pzy+m3V5v3UAETy5+ywpDhS8VUB\n21UoEEkWM6uQuPh+fwqoCSIF8ufGzWfN7sNFQCRpnN/2pZhdtBDJBkAk6wORbABEsj4QyQZA\nJOsDkWwARLI+EMkGQCTrA5FsAESyPhDJBkAk6wORbABEsj4QyQZAJOsDkWwARLI+EMkGQCTr\nA5FsAESyPhDJBkAk6wORbABEsj4QyQZAJOsDkWwARLI+EMkGQCTrA5FsAESyPhDJBkAk6wOR\nbABEsj4yRSqYP2bw4LGLTqgWsF5IJR89M3612Z24CIki2TCjYL6aMPr9C2Z3QqJIRYMSSHJW\nViJJfUZteCvLhbSrefkbWiTdetzsfgQhTSQ7ZhTEmW7xV9+Y0Wib2f2QJ9LQjEmukZVLdo5L\nHa9SxGohFTdr/zulPzXpYnZHgpAmkg0zCqZ/3reUHutS64zJ/ZAnUs5U772JtVWKWC2kzxN/\ndy3Wxv1mdk8CkSaSDTMK4kzqQtfiVMZ8kzsiT6TENd57+UkqRawW0huNlEVxnMX+TZImkg0z\nCmIHcX/p3TDa5I7IE6n+U957w5qqFLFaSO9WUxbHydcmdyQIaSLZMKMg9pGflOUVL5rcEXki\nTXV0X7Bl187N8zo75qoUsVpIe+NXuBYvZ1ls7ktpItkwo2DqPuG63RS32eR+SNz9PaseUWi2\nWK2E5UIanP7SD1uGJs4wux9ByNv9bcOMgvgood83P76Rfa/Z/ZB6QHbPsnnzV+xTX2+5kEre\nyiWk8RKzuxGMzAOytssomPyrHCT7JdMPJOGAbCC7ps87ZHYfLsL+B2RLNv3ff0+KqCgUJ6yw\nkxUHZP05eo8jJSnhcdO/3oKwxQHZ88fU121vQXKTKs/W2j0Ph1/uP3oj52sNAwdk/bk23kGI\nI6Gv2f0IwhIHZL/u3arrTNUp2L68NoHUnFIcemVh5Y6H6PkJCWq/mYvf6dVl7B9qVc/NqH93\nq/gHVeq2Cjgg68cGQhIa1nEQh8XOEbLCAdmn4+8c07fCDadCl/o4offab/9T8aHQa1+oq/yN\nH3ht6NWHr6r0r/5NKi0LvfanxBdKKN2YOUGlgxYBB2T96E5qnaf091SywOyeBGKBA7Jfxi11\n3h6sNTxkodK6w5RCju0hV9/t/hO/LDn0H7SO1xQ4/yo9nhl66rzhLZTFi/VVOmgRcEDWj2qk\n0LWYSe4xuyeBWOCA7MO3KIvX80IW2kN2Kcsmr4Rc3a23svg0NeTaYwn5rsWFyjNDru7aX1nk\nx5Wo9NAamHBA9hrio5+2KmWTS7a6FlPIXWb3JBDjD8helNFdjyiLVQkh69nu/gaiLceGXP1K\nDWVe3t5/V3lxgbJUOcun193K4v0M9bdhBUw4IPu/lV5SVA8DmsPNJHvZhbPvJpK3ze5JIMYf\nkL0ooz7u75bpuSGrOZn8qWtxKv39kKtP1Gy9nRY+4f7LcxGHiPsHYf3JIVfPL+86ylXSpmvY\nN2I6ph6QLW+xQ58/EBKXGJdAHBbbQ2TmAVlPRsuSNjlvTzR5OHSpB+rtcK69R+1iht3tSSqp\n/YlKE1fd57r9MGFX5KDCHAAACW1JREFUyLUlbXJe37i4VeZO9T5aAVMvNbeaSPQfzi9nByHP\nmd2PIMy81Nyb0QMpD7/7bPXGR0KXOnlH4t9uya63RbWaPcu+VT06tzGt9azFDyeOUVl97rka\nJOOeMK5bAiNEKlQ78mw5kej0DEdc1XyzexGMASJFzmhRu7y/Pqt++Vz+M4+/d46z8T3da2S0\nWhqmwGnOig3ECJGaq73SeiJZEwNEQkY6MUKk6aH35SAkVgwQCRnpBP8j2QAr/I8EwmPq2d/l\nJ25i4LPXZ/Pw1ptcL3vjba6XTZ7B9bJJ61m2wCMmnv3NlpGT/Ne4toCbGZNNe/EkPS+ew5OR\n+LO/8whg4hZtmx4ZmQB7RuLP/mbjqZu4XtbrX1wv6/AY18uu5junsjrvpQViEJaRk+f/quPF\nL7TQ8eIJV+t48X+u0vHiiVfwvEr82d9sQCRpCMuIQiR2xJ/9zQZEkoawjChEYkf82d9sQCRp\nCMuIQiR2xA/HxQZEkoawjChEYkf8cFxsQCR5iMqIQiR2xJ/9zQZEkomYjChEYkf8mQ1sQCRb\nAJFYgUhhgEgQiRWzRHqNbzjaEUO5Xvbgf7he9o/3uF7218+4XmZF3u2o48Wz7tTx4vf+oePF\n/3e7jhfPvY3nVWaJBEBUAZEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAA\nRAJAABAJAAFAJAAEYJBI0xsmVXuyyPOgdOoVaXkDPFMg3Ex2Unrhhcbl6vQrlNrYPcpVo7WC\n18tuLeDN2gzdfVfC5WLX7eUrdfyV77X8n6bJKT2UJccnxBiR5pDhq6ek/9vz6HnHk6unZNys\n3J+Z6NrWj6XP37Oy7t+kNnZry3wnG4LXy27N/83aDb19d4fLQ0G1dp8vadSc78W8n6aCDtWy\nFZF4PiHGiFTfNX/rpAT3l0RJVk/n7QTimjr+cOYA17bOGui8P43skdlYyx6h1stuzf/N2g29\nffeEy8PwvLOU/jBdfcKZcPB+mqbc9EcTJTaeT4ghIu0h8523+5Vb5w+GXa5kFpEdzttO7da6\ntnXFIdT1PSBEJLXGLnso1HrZrfm/Wbuht++ecHlo8CRnmy54P00HSqgiEtcnxBCRlhFl1rdk\n/+nbeuUUU/pB2l5lWz95ybqSg1e3ldpY3mPq6+W1VvaMXeHuuzdcDk473hqQk9XzKF/DOj5N\nikhcnxBDRJrvnmg+a3DZU+87ZlN6tMpEqmzr0kEkgbQ+LrWxzNv+nl6tx75Q6yW2VvaMTeHu\nuy9cDn4h1Z78Zl7uX9QmAQiPjk+TIhLXJ8RIkTLLejYj4Rnn7b0tStzbemzGlG8XNWpbIrOx\nnCtmbZheo/aJi9fLbK3sGXvC33dfuBzsJK751peQlVyv1vFp8hdJ2yfEEJFWkM3O25JE3wRy\no+MnOW+Xp3xPlW39W/xE58PNRP+AhuqNudlA3rxovdTWgp6xG/x994XLwx9knPP2JHmF58V6\nPk2KSFyfEENE2kfmUdfXzELP49Gpypvs6Yh3QuJbf6F89ZwlL0pszM0ZMip4vdzWgp6xGTr6\n7guX69WVHnXe/Emm8LxWz6dJEYnrE2LM7u+mnZ0341L/dD9aHP+Jsjy43ckssnTPPuL63ttM\nFkhsbHenddT1ZTMnaL3s1rzP2BE9ffeFy/Xq7rUuuPYXbuB5rZ5Pk3v3N88nxBiRFjuGrX4l\ndTSl05sX0nO1b3QdrMx3H7dW/vrfecn83WuurK4+V6P+xoqaVJ+1YVpOw3Nl641oLfDN2gv9\nfefe/f19uQ75c6pw7sbl/TRtzc/Pa5uff5DrE2LQKUJzGiXWHFfq/D+Q/Ea3e6YVfFtZo2zr\nU09WT8jsLOZ4rFpjhx6okZjT+3e/9Ua0Fvhm7YX+vnOLRNe3TMnsc5LvtbyfpjbutzuZ6xOC\nk1YBEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAEAJEA\nEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAEAJEAEABE\nAkAAEAkAAUAkAAQQZSI16OW7e/nzzpvp2fudt5NTelxc5MmGgiZ2AXx8emt2Uq0em83uhiCi\nVqTfHM6INicvp7SgQ7XsECIV33Cn0b0DfjxG2k5b/FL9JDGTYplO1Io085JSSlvd5rw35aY/\nmoQQiX7r+MzYzgE/FpGhrsWZv1U8ZnZXhBBtIvWdUiux2Ubnve7dKV1D1jvvHSihASL5itze\nyqReAkqvq1mkLPfvovT4Q1USagw8SelXbTJTm02ntGR809TcwadN7qImok2khvd8s6ZRnVJa\nesm7lA6+xDNZVIBI3iL07bgCc3oJ6JmEsv9maaeqq/asqNqfns+8e9vOiY7l9Km4yb98mnu3\ned3TTrSJVNv5PTeF/EY3kV8pvaaj5+kAkbxF6E9kkSmdBJTuVeYt9/DLbudN/zp0jzL/8cbD\np8v1dS5nkp9N6hwP0SZSN+r6+f0jHdfMeaf6AM/TikhFx44dO+lXhJ4gr5vW0VjnFzKh7MFv\nQy6rkpWaQUubXTJyXTGl68lHzmf3K5OL24VoE8n1g2Ex2UFbDXHeKT/c87Qi0kpCyF/8ilAa\nP06tHiCZc0kP+u4XN6y+aNeBvhmUHhnVlGSPKl5GEpOdkIkmdlArUSrSiUTXHrnAv0jH165d\nu81fJPxFMpEbM44oy0NjTmwgHzjvdMtwP342/sWN5K0dLgpN7J9WolSkD1POOu9cc5fn6Yt2\nfysi4X8kE/mU3FviXJxpk124mqxx/jHKSKd7lWNKLbqdLve0c3lut6kd1EiUitSvneuRe6/d\n1vz8vLb5+QeDilA6FXvtTGQ4aTHlw5frpefTI2ldD37d4j7H9tWOEdt3z0p5mw5Pm7prU6ds\nOx1hilKR6rzkeuQ+jtSGKEwOKkLp7X8zq5vAyYrbspPrPOj6s7O4Xsrlyw/UTdvy/jXlyzV1\n/mdUOqFeYsZdP5jdQy1EmUhBtLw9zMptjhWGdQREO9Et0jfJ6mcBlbS+w8CegCgnukWi0y7Z\nr7bqqQY4+xsII8pFAsAYIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKA\nSAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKASAAI\n4P8BKCY4i2NqyJkAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_poisson_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "vEDUoMQVQ4N4",
        "outputId": "dc2f2824-5d81-4815-e520-389001364b22"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = poisson, \n",
              "    data = data_none_c)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182  83.183   <2e-16 ***\n",
              "Timepoint3  -0.16909    0.07659  -2.208   0.0273 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for poisson family taken to be 1)\n",
              "\n",
              "    Null deviance: 9.4516  on 9  degrees of freedom\n",
              "Residual deviance: 4.5594  on 8  degrees of freedom\n",
              "AIC: Inf\n",
              "\n",
              "Number of Fisher Scoring iterations: 4\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Although the AIC value for the poisson model for medium C is also infinity, indicating a bad fit of the model to the data, the diagnostic plots show the opposite. The upper right plot indicates that the data is close to following a poisson distribution, since the ordered deviance residuals are aligning with the theoretical poisson distribution line."
      ],
      "metadata": {
        "id": "PpyPSyGfU6VZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The Poisson model for all cases (A, B, and C) was tested to investigate the impact of time on each medium when storing the bacteria for 3 months using the CRYO2 method. However, the Poisson model did not provide a satisfactory fit due to reasons mentioned earlier."
      ],
      "metadata": {
        "id": "KXdIyncnPoes"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Negative Binomial"
      ],
      "metadata": {
        "id": "OeC7D32mSfr_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Despite the subtle difference between the mean (62.9) and variance (66.5) in the dataframe related to medium C, a negative binomial model will be tested since there is overdispersion in the data related to medium C."
      ],
      "metadata": {
        "id": "xzkf8N3aSykr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_negative_binomial_c <- glm.nb(mean_percent_live~Timepoint, data=data_none_c)\n",
        "glm.diag.plots(model_negative_binomial_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 871
        },
        "id": "t_u9EHQWRIcU",
        "outputId": "298f7cb0-97e6-4296-be1c-2d3c1370784e"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.693333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.996667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 75.470000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 74.490000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.746667”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 65.210000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 73.313333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 67.383333”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 55.080000”\n",
            "Warning message in dpois(y, mu, log = TRUE):\n",
            "“non-integer x = 53.476667”\n",
            "Warning message in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace > :\n",
            "“iteration limit reached”\n",
            "Warning message in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace = control$trace > :\n",
            "“iteration limit reached”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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/iOI1l9xpDx8Xov8bASEMkGROUVsiUXL5BUsylAJBugWaQBfuhsGxmxAZFsgGaR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\nX6VfAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_negative_binomial_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 488
        },
        "id": "C7NtO9gGRKRs",
        "outputId": "f11a9da3-ca8c-43ed-ade9-1117e77fd538"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm.nb(formula = mean_percent_live ~ Timepoint, data = data_none_c, \n",
              "    init.theta = 2601815.288, link = log)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  4.31052    0.05182  83.181   <2e-16 ***\n",
              "Timepoint3  -0.16909    0.07659  -2.208   0.0273 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for Negative Binomial(2601815) family taken to be 1)\n",
              "\n",
              "    Null deviance: 9.4514  on 9  degrees of freedom\n",
              "Residual deviance: 4.5593  on 8  degrees of freedom\n",
              "AIC: 71.186\n",
              "\n",
              "Number of Fisher Scoring iterations: 1\n",
              "\n",
              "\n",
              "              Theta:  2601815 \n",
              "          Std. Err.:  114052314 \n",
              "Warning while fitting theta: iteration limit reached \n",
              "\n",
              " 2 x log-likelihood:  -65.186 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The AIC value for the negative binomial model for medium C is 71.186, indicating a reasonable fit of the model to the data. The upper right plot indicates that the data is close to following a negative binomial distribution, since the ordered deviance residuals are aligning with the theoretical negative binomial distribution line."
      ],
      "metadata": {
        "id": "yVEGga3gWlMS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Gaussian Generalized Linear Model\n",
        "Now, we aim to scrutinize the suitability of the Gaussian GLM model for each medium (A, B, and C). Despite our initial findings suggesting its effectiveness in capturing the temporal effects when storing bacteria, it remains crucial to confirm whether the Gaussian model is the best fit for each specific medium."
      ],
      "metadata": {
        "id": "o6a8iMGUOzt6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_gaussian_a <- glm(mean_percent_live~Timepoint, data=data_none_a, family=gaussian)\n",
        "glm.diag.plots(model_gaussian_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "GOO6K4FyVMiN",
        "outputId": "965e5b51-091b-4d50-95d8-12e56c4c8d19"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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zU5qsxUj9TLJoIxWqQzZJ36Qk9I7fspk5VxPA0UBnhEOvdk1ZSUlGIuhiGLWTLS\nxP774vuR88rsza9rX92R2EGk4Tcqw4EOv4GngcIAj0h9M/ok9upcrBvDBUCCRcp7p+idv52N\nXS7Pn0pYrnV1h2IHkfYlPn+Z0qVJs3kaKAzwiFT+K5p2iGbdwnDnIcEizSg6NZfSJ66Tvi/+\neV+dyD85yI3RImWvCnEWsjekFWVL3VMjbhRP/YUCHpFi9tFSeyjddHP4okwZsXPltPx4oWP0\nTXcWuekPrWs7FTvstZO+0H8w8u3dwquPGHhEKvkVrbOE0kOJOtvWJtLW/fnz3/3npc8iZoz8\nsNhDJBASHpG6l9nTv8LiNR35jiPloyWjc/2i3tHZnGOBSA6AR6TT7Q4cqUVIkU90tq0howgc\niJgdiOQAeI8j5WxcfVpv2+wZ9Y1+OuIGImYHIjkAHpGyPBzV2TZ7Rm99p7MpRwORHADXcFxE\n0xWyqiAjNiCSA+AR6V2ZN5+orHcoOZaMcidXOqWzGccDkRyAjnPtPnxCZ9sMGf16R1G947k6\nH4jkAHSIlJOhs+2wGWW/GPdAhA6MrwWI5AB0iHSgmM62w2a0uTznFUuRBURyADwiPavwRNn7\ndLaNjNiASA6AR6Q0mfTruuq9/UPIjFaEHOyrUAGRHICV90cKkdGJrtGF5Wqj8EAkB8AlUu6p\nUyJOGVXPaFHJehsFNBAhQCQHwCHSN62LEFL0HyEuNGJENaPn4sdc0V175ACRHIB2kV4ixR55\ncXCnMq5xlO4MPSJXGFQz2rJTT7URB0RyAJpFyiTdTsrTq4PIKvqDrrEwCszodJ6eKiMSiOQA\nNIvU9g7vO/2B+2ivynraLiCjK6Pi9H9ljDQgkgPQLFJp3yBYC4vcRf6jp+1rM9pQt0ShvXxP\nHYjkADSLFPupd249qTZLV9vBGeUOiHo0S1eNkQlEcgCaRUqf6Z1bnKzz50xwRufvLSwDbGkD\nIjkAzSLdf693rm1DnW0jIzYgkgPQLNJnZIwyntyVMUTfF7vAjN7vr7OyCAYiOQDtx5GeIlWe\nnTpjcAXSVe+O6vyMDtwXjzOCVLGHSDtfaNdnmfDqIwaOMxs+uF6+zLz+bN0HfLwZ5Y2JS+uM\njFSxhUj/jburf/u4djjjRAWuc+1O/vTTSQFtezNqQ6r2Q0bq2EGkLVHzpMcdZcYKbyBCsMHZ\n31ui5ENTyEgVO4j0tPu2i29UF95AhGC1SD+fQEbhsINIbd07g1bFCG8gQrBWpPP9o+cio3DY\nQaTuHZXJ3FLCG4gQLBVpVKWyS5FRWOwg0pLE36XHy7fqOt0/krFSpNio/vK995BRGOwgUl7b\nlFGfv12not7RdSMWK0WKcx87QkZhsININHf6TcnXPaN7vPeIxeqdDTLIKDS2EAmExg4igdBA\nJAcAkewPRHIAEMn+WCvSxB+CWTJjnh4mz9G1+hu61p47UdfqsxdeszU8DLBSpMCM5r2r4Q+a\nouGv17Lp39LwJpk7SUPFE+eyl52+hDcj8SJVJoAJveMOIyPjYc9IvEgF0HaArtUrztGz9p/k\nNz2rf5GkZ2065v90rW4Odaeyl9XyjfQE+ZW9cOvn2Mt+mM5eVtP32Kc6aKg4AIgUBogUCEQq\nGIgUBogUCEQqGIgUBogUCEQqGIgUBogUCEQqGIgUBogUCEQqGIgUBogUCEQqGIgUBogUCEQq\nGIgUBogUCEQqGFNE6jNe1+p3rtCz9vmMI3pW31xLz9p0xsO6VjeHlh+xl53Xhr3shYzD7IV7\naLgtwNob2cvSOt+xlx3XT0PFAZgiEgCRDkQCQAAQCQABQCQABACRABAARAJAABAJAAFAJAAE\nAJEAEABEAkAAEAkAAUAkAAQAkQAQgMEi7X6wSIl2R/1nuFa/OqFOUtUnNd49dYdnbLIZlM6q\nFVduSDbn2nnTb0iu3PcUd+MS95Jd2lY3jSkJXX3znZQeV2IrHGabBiwNVXFgNWGCYq5VY281\nboeCMFakrHItv/ms9s1+M3yrP1ds4d5V1TRe2nMxU+a/rh/oB2To6mnFnuZc+xXXkNXTUu7l\nbVxiTqxNRcpqXS49/w10fyO5zxvZCofepoFLQ1QcWDBMUMy1auyttu1QMMaKNLTy35Run3Up\nf4Zv9TT5MpGZZK/2HuQ1eoLSGp2kuckx2u8HLq+dm9ZNmnuNnOBsnNLjqX1tKtK0Fifq5r+B\nGnUNUTS4cOhtGrg0RMWBBcMExVyrxt5q2w4FY6xINYcEz/CtXvxZKn+qcIj0XsoJupcslOYO\nKo/a187bLSu0hOzga1yifSLfHrQAACAASURBVMt1NhXpUC71ewM16M1eOPQ2DVqqXnFgwTBB\nMdeqsbcat0PBGCrSRdc7fTPSup3On+FbnQ4puT738C3NtffgaqWRlC4nW+X5+NFca7vpnpHD\n1zilHyXvs6tIEn5voMphL/bOLxx6mwYtVa84sGCYoJhr1djboMIM26EADBVpPyk3ZPOCsrfl\n+Wb4Vqd5/UkMaXpWew9mFjlF6UKyW55PG8i1tsKHrnmcjdPTpSdSZ4iU+sA9xcp1PcBUOPQ2\nDVqqXnFgwTBBMdeqsbdBhRm2QwEYKtIu0lZ6/Iys8s3wrU7Hpkz7cUnt5rmae1DzKerbjKma\nRVLWlpkdM0Zz097VH2uYaz+Rss+cOXNemfN7A2XcMHfjrApVzrEUVtum7rJBS9UqDq4mTFDM\ntXoI39sCC4evuCAMFekEGSc9nieTfDN8qx+LnijNbCFLtXbgR/KN9LiSbJEec2PHcq0tMSp6\nstaWfauvSPiV2k+kVYSQ25S5ukG/rDeSt1kKq21Td9mClhZQcXA1YYJirtVD+N4WWDh8xQVh\n7M6GEs9ID3+RafkzXKuvVf6V/U1e1dr+yBLyoYMDZAGV/78t5lpb8ihRs8H5q3dzRUuQ6KY8\nVRjG2XXr1v2szAW/gS6RkSyF1bapu2xBSwuoOLiaMEEx1+ohfG8LLBy+4oIwVqQula7KO7w2\n5s9wrX6AyP8RtpBFWtu/4wFlUk8erWxc4l98ay+N/lxru36rH94mMZcs49jjaAr5b6A97ddT\n+cP7A5bCYbZpwNJQFQdWEyYo5lo19jawMMN2KABjRfo1qXXmB6Wb+83wrd6m5MI9a24sr+1b\nq0Sx/spkqWvw6kmJo/jWvlyliXJwVfNpGZ7GZWz31c7DT5mZlZtnZh6ms24+SbPrlp+7cWZG\nrcsshcNsU9/ScBUHFAwXFHOtGnurbTsUjMGnCG1olJDa87z/DNfqF4aUj0ntoPlDPZuMcM98\nUDu24jhtuwx9a28LONmHo3FqX5Gauf+0KXQsOUbpkScqxGb8+0+2wmG2qXdp2IoDCoYLirlW\njb3VtB0KBietAiAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgAC\ngEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgA\nCAAiASAAiASAACASAAKASAAIwFkidS3tmSk3QEh988khUVVFOp/dnx5buu3qoFflDRiSwAIF\nFhcQgK+KgvtTqa/uFsLiUJHmrRdSn7zd/aua10pItRHIU+TemZ++dQd5KfBlESIJyNJXBURi\nwyeSIIK3e3+IVDDzlLuQ0rzu5OuA10WIJBKIxEbAV7uKI8ZWSb5lI6W54+sllh14kdKzvUvH\nVOh3ntIKIx9PXOsuWeqF58om3PaD9zVf2ZMdkos/Pt3z1S5nXJWEuu/Suwkh82nO6KqxJR85\nGlBLYadBXfe9hS6lPeDdLr4N6NukaltY4Zrije6UXx4be1IOwJecL1RPJPnVKQQ18V2z1MT6\ns9xvB18Dac9KBd8lWfmVyiJ5ixqFg0WqnjHy0oUm1SgdFjVl/xdlH6a0fZmv9q4s04fSavX/\nveGsu2TF4i9fzWpSNtvzmq9sm9TP9k4p7xFpcJH3fp5AFp1t3DTrCh2QNGPfV9Xq5/jXUsjJ\nIs965h5NzvVsF98G9G1StS2scE3xt1zykvr/VALwJecL1RNJfnUKgU1cSX34510TXSuUKnwN\n+ETyVSqJ5CtqFA4WqWYd6VNyNsm6mNRLemUO+YPu3yPN9KkqLarguzlbpZrSw7dkmfs1X9mT\nUfL99Dq5RbqQNEx68twbtJn01e5c/FAq30J0lX8thZyfyJueuRfJSfd28W3A/M2vtoVlri1+\nMnYSpTvIR0qW+cl5QvVGkl+7QmATe5W7K286LleR35xPJF+lkki+okbhZJG6SDNLye8byCfS\nzEGygB57tkHptMQUaVEH3yqV5JvsniUT3a/5yq6T1KL0bbdI35NP3YVlkdaTz5U1JvjXUsj5\n2Xfjz0HktHu7+DZg/uZX28K04OL3N6J0VPHLSpb5yXlC9UaSX1whsIm8+iVHrM+hytshvzmf\nSL5KJZF8RY3CySJ1p/I237GcxMZLkIk5tcov2X2oV4pnkZtKT1L5fq4j3a/5yi4ja6Sn77tF\n+pJkugvLIi1XluSQ4f61FHLOuJ73zD2ckufeLr4N6NukqluYFlz8A9cRWqenkmVQclKo3kjy\niysENkFPjaxH0kfmyFXkN+cVKb9S+TeSt6hRRIBIm8g7O2RObpS+J1DaOUgk+T/SKfJf92u+\nsmuUD7CpbpF+Uv7vU7dIG5TPwtPkdYiUzy1l/1aml0t28Gxd3wb0bVLVLUwLLn4hefKvZJ2S\nZVByUqjeSPKLKwQ2Ib9y5KXoV+Uq8ptLl0V6k2TlV+rZa6cUNYoIEOli0ovSzOU9dLX8oXQq\npVigSBVy5M+wL92v+cr+6ZJnHnSLdDGlv/SkZy/arKX8G+kF6clnUl0QyceH5AVl+lTUJs/W\n9W1A3yZV3cK04OK0c8sRVfKULIOSk0P1ROJXXCawiX2L5NcadparyG/uOrlMd5KVX6kkkq+o\nUThMpBLLZX4MEIkOTZ6++4f26WdOJXc8/H3Df7m2XfEXqWzvnZvqVsrxaOEtS1ulLt42ropn\nr92I2Mk/jHctpB0q/HCYDkyac+DLKnfmQSQ/BpIW7y6b3sg1mXo/pnwb0LdJ1bYwLbg4/Syh\ntryDQAogKDk5VG8k+cWpr2nvaxtcw7ftmZswQ8nQ10CXcgdzP65MsvIrlUTyFTUKh4lEFNoH\nipT3WvXYlLbbpSfVE65fcaha8lZ/kfqNKht/+25vBr6yx/6RlPLYh2Sv+zjSqIrxdWZLX0Ay\n4qdKTyrHlO55hkIkf5bdnx5b5qGN8qx7u/g2oG+Tqm1hWnBxejWN7KTubxeBycmheiPJL57f\ntO+1D28tklRvorsKXwOHWhYt1W0BOZpfqfzVzlvUKJwlEgdmHNUGACIBIACIBIAAIl4kAMwA\nIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEg\nAIgEgAAgEgACgEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgE\ngAAgEgACgEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAg\nEgACgEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgAC\ngEgACAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgA\nCAAiASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAi\nASAAiASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAA\niASAACASAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASA\nACASAAIQL9JNJQATnYRvemQkGvaMxItUZOwqwEDPW4VvemQkGA0ZaRbpEqV5qyZN26Qe0mda\nqyycvGqcSMhIEBoy0ijSkRtn05O3EomWF1WKICQ2DBMJGQnDOJHa1N5OHyn72fm/Fpfqq1IE\nIbFhmEjISBjGiVRUSiBtgTz3fppKEfuF9HPH6vX/fdDqXgRjmEiOzMhEPmlZueGLF5iKGidS\ncialZTbLc+sTVYrYLqT3YtpNn3JX8rdW9yMIw0RyYkYm0ju+73uvVLnuOEtZ40S6/97LtM8Q\naebq/Y1UitgtpFNFJ0mPeT1q5lndk0AME8mBGZnINzEbpceLN3VnKWycSH9kVB76Trm2456p\nlLRRpYjdQlpUIkeeHCS/Wt2TQAwTyYEZmUj/+5XJ/1JZChsnEj0xpKaLEJLadbtaCbuFNLWu\nMsmL/sbijgRh3O5v52VkIp16KZNvyVWGwgaKJHFx/64TIRbbLaSPi/4tT3aSXVb3JBADjyM5\nLiMTeb6JMpmZwVLYWJHCYLeQLpR6NpfSv//R0OqOBGGoSGGwW0Ym8kPUYunxaLVnWQqbIdLJ\nYyoLbBfSymI3DX2uSvkdVvcjCBNEck5GJjI++v7RvYo1Os9S1gyRbg5cUzmS7mYgb5VGcWxQ\ni9bjmDacmZggkoMyMpEfe93d8d1cpqJmiDRrbMDT33wn+pHhvFUWLkwQCRnpxNLfSK6RwquM\nSKz8jYSM2DBSpKyFowcOHLvknGoBhMSGgSIhI0EYJ1J2/xgSn5YWSxLHqJ0ogJDYMEwkZCQM\n40QalDJZPvszd9e4xPEqRRASG4aJhIyEYZxIGdO9cxOrqBRBSGwYJhIyEoZxIsWu8c5lxqkU\nQUhsGCYSMhKGcSLVGOadG1xPpQhCYsMwkZCRMIwTabqry6Ktu3dtWdDBNV+lCEJiwzCRkJEw\nDNz9Pbe6+9B4/aVqJRASG8bt/kZGojD0gOze5QsWrjygvhwhsWHkAVlkJAac2eAAcGaD/YFI\nDgAi2R+I5AAgkv2BSA4AItkfiOQAIJL9gUgOACLZH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4A\nItkfiOQAIJL9gUgOACLZH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4AItkfiOQAIJL9gUgOACLZ\nH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4AItkfiOQAIJL9sUCkk3u8EITEhPkiISOtWCBS/fz7\nk/5bUJURjvkiISOtWCDSX75PO3xtYMN8kZCRVvAbyQHgN5L9gUgOACLZH4jkACCS/YFIDgAi\n2R+I5AAgkv2BSA4AItkfiOQAIJL9gUgOACLZH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4AItkf\niOQAIJL9gUgOACLZH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4AItkfiOQAIJL94RNpwUTpofdH\nehtHSGxwiYSMTIVLpNnkOemxp2uuzsYREhs8IiEjc+ESqe4EZTK+vs7GERIbPCIhI3PhEinh\nZ2XyQ4LOxhESGzwiISNz4RKp8hxlMrESy2pN96ouQkhs8IiEjMyFS6TRRUd8mrm4f+yoUMV3\neYhetmuXShGExAaPSMjIXLhEyn4+iRBSfEROyOJ+qBRBSGzwiISMzIXzONKF77/8+VLo4vfG\nPrVOJnruunUqRRASG3zHkZCRmRh4QHZOast90iR6m2oJhMSGcQdkkZEotIs0YD0d4CX0Csfb\nJ0/MRUj60SwSMjId7SKVm0fLeQm3ykelG/6KkHSjWSRkZDoGn2t36rFEF0LSi7Hn2iEjEXCJ\nNP+KMjn8JsNay7sdVl2GkNjgEQkZmQuXSCRLmWzGUXNz4BEJGZkLh0itWpGmrSRali/LtuLJ\nYwFPv1vkhQxjbrxQo10kZGQ2HCK93480bibz0Fq2FW8O/HXVpIQX0ou58UKNdpGQkdlwfbW7\n+6ymNmaNVVmArw1s8Hy1Q0bmwrfXbsVxmj2+80y9jSMkNrj22iEjU+ESaXrUd3RodMOEyaFX\nyFo4euDAsUvOqRZASGzwiISMzIXvwr4pNLv4ODo75EVj2f1jSHxaWixJHJOnUgQhscF1YR8y\nMhW+C/t20W/JEfpHcqjig1ImH5QmubvGJY5XKYKQ2OC6sA8ZmQqXSCV+ocOlT7ptKaGKZ0z3\nzk2solIEIbHBIxIyMhcukZo9vDhtFKXDbw9VPHaNdy4zTqUIQmKDRyRkZC5cIn2XShqcoYtc\nIcd6quE7kje4nkoRhMQGj0jIyFz4dn9f2Sv9Nt23MWTx6a4ui7bu3rVlQQfXfJUiCIkNrt3f\nyMhUDDz7e2519zXM9ZeqlUBIbBh39jcyEoWRF/bRvcsXLFx5QH05QmLDwAv7kJEgjL2wLwwI\niQ1DL+wLAzJiA4PoOwAMom9/DL+wLxQIiQ2jL+wLBTJiAxf2OQBc2Gd/zLiwTxWExIYJF/ap\ngozYMOPCPlUQEhsmXNinCjJiQ8+FfVe26mwcIbGh48I+ZGQSevba/VJUZ+MIiQ0de+2QkUlw\niXTuyaopKSnFXDV0Nm6/kLI/HDp6pdWduAYekSI3I6Gse3nw+5dFVMQlUt+MPom9Ohfrdkhn\n47YL6ff6xVvcHd/8lNX9CIJHpIjNSCQX28fceW96tc0CquISqfxXNO0QzbpF72e33ULKrtNa\ncmjP9W2t7kgQPCJFakZC6V31V0rPP1Lugv6quESK2UdL7aF00806G7dbSF/HKQdfNriOWt2T\nQHhEitSMRHIpcYkySf2f/rq4RCr5Fa0jdeFQos7G7RbSW3WUSU7Uaos7EgSPSJGakUh2Evcn\nZhMBfyOXSN3L7OlfYfGajjV1Nm63kOa4j16eJiK+NAuER6RIzUgkh8l2ZXrjBP11cYl0ut2B\nI7UIKfKJzsbtFtKB6C/kyYSSV63uSSA8IkVqRkKpNVB+/C5qi/6quI8j5WxcfVpv47YL6YUi\n47Zu6h8zz+p+BMF7HCkiMxLJ8pjH1/0yKfUJAVXh7G9/8t6rSqJu+NLqbgSDs7+NYsOd0aTc\n5GwBNeHs7yDOXLS6B9eCs7+N4/JJMfXg7G8HgLO/7Q/O/nYAOPvb/phxWxdVEBIbJtzWRRVk\nxAZu6+IAcFsX+2PkbV3CgpDYMPC2LmFBRmwYd1sXVRaM90IGcVVQ6DDsti6qICOtGHdbF1We\nbO6FPMVVQaHDsNu6qIKMtGLcbV0YwNcGNgy7rQsDyIgN427rwgBCYsOw27owgIzYMO62Lgwg\nJDYMu60LA8iIDeNu68IAQmLDsNu6MICM2MDY3w4AY3/bH4jkACCS/YFIDgAi2R+I5AAgkv3h\nEinXM9U7/htCYoNHJGRkLlwidXBffbmmvM7GERIbPCIhI3PhEimj+XlKc0ZFN9HZOEJig0ck\nZGQuXCIdqHNr1qHGMS/nhijNAkJig0ckZGQufDsbTje+Lq3qJt2NIyQ2uHY2ICNT4dxrd/nh\nqN/0N46Q2ODba4eMzES7SH0V+hSrLT3qbBwhsaFZJGRkOtpFquSHzsYREhuaRUJGpoMDsg4A\nB2TtD59IOasmDH99bZ7exhESG1wiISNT4RLpSD0i00jviE8IiQ0ekZCRuXCJ1LnGyrM5pz6t\n1Ftn4wiJDR6RkJG5cImU5r4R17IMnY0jJDZ4REJG5sJ368v9ymR/rM7GERIbXLe+REamwiVS\n5VnKZFZlnY0jJDZ4REJG5sIl0qjkoZ+v+XRQ0ujQK5zYkaNMj85QKYCQ2OARCRmZC5dIOQPi\nCSEJA3NCFT/ZkpCyyu2iM9WOQCEkNnhEQkbmwnlA9tz65RvOhy7eu/jrSx4nYylC0g3fAVlk\nZCbGHZCt8Lb0sCD6LYSkG8MOyCIjYRh3QDZpjfw4PfpThKQXww7IIiNhGHdAtv4wZTI8cRlC\n0olhB2SRkTCMOyA7zdXthDwdGd0UIenDsAOyyEgYxh2QzRuXukeZWVoFIenDsAOyyEgYRh6Q\nzfX80r28TaUAQmLDwAOyyEgQRh6QDQtCYsPAA7JhQUZsGHdANp+Tx1QWICQ2DDsgmw8y0olx\nB2TzuTnw+/eLD3khTzM3Xqgx7IBsPshIJzwinVEez51kXXHW2ICnr/X0QgYyN16o4RAJGZkM\nh0gLi++WJ6PSV+ttHF8b2NAuEjIyG+0ifR97zyF5eqRJsT2hV8haOHrgwLFLzqkWQEhsaBYJ\nGZmOdpE61/7bPXOp+pOhimf3jyHxaWmxJHGM2glfCIkNzSIhI9PRLlKF/3hfeKNGqOKDUiYf\nlCa5u8YljlcpgpDY0CwSMjId7SLFfex9YWlCqOIZ071zE6uoFEFIbGgWCRmZjnaR0mZ6X5ha\nMlTx2DXeucw4lSIIiQ3NIiEj09Eu0n3NPc9zb24dqniNYd65wfVUiiAkNjSLhIxMR7tIn5Pn\nL8rTU4+RL0MVn+7qsmjr7l1bFnRwzVcpgpDY0CwSMjIdjuNIz5Ay3ce91iOFjAhdfm515dIy\nUn+pWgmExIb240jIyGx4zmz46I5oQuKaLAu7xt7lCxauPKC+HCGxwXFmAzIyGb5z7S7t239Z\nQOMIiQ2uc+2Qkangti4OALd1sT8QyQFAJPsDkRwARLI/EMkBQCT7A5GCuJxtdQ+uBSLZlJxL\nvlmIFMDCOtFxd661uhfBQCRb8mPzBFe16bnuJxDJn5GJw7/9umf0Qqv7EQREsiNfxz785cbx\nKT3dzyCSH4dilQP8Y8vY7OsdRLIj9fvIjxuitirPIJIfc8sol7edJFus7kkgEMmGHCO/KNMb\nJygTiOTHm3WUSW50prX9CAYi2ZA/yGFl2tx9Bj1E8uPL+NPy5HvXYat7EghEsiGXEpWrJy+X\nnKM8hUh+XK3R7i/pl9ItD1rdkSAgkh3pcd1OSacepf9SnkEkf36tkd6mVfJdJ6zuRxAQyY6c\nbx3XvH3Z8uvdzyBSAFfee2bwx6HvcmcBEMmefDms//QLnnmI5AAgkv2BSA4AItkfiOQAIJL9\ngUgOACLZH4jkACCS/YFIDgAi2R+I5AAgkv2BSA4AItkfiOQAIJL9sUCkR272QvoIqjLCMV8k\nZKQVC0RaOt4LGSyoygjHfJGQkVbw1c4B4Kud/YFIDgAi2R+IFMTx01b34Fogkg5yD14KX0g/\nEMmf3LfKEFLj4/AFzQUicfPXwCQS1eRn4xuCSP4MSJn4+09DYmdY3Y8gIBIv2Q2rL9qzvn3S\nT4a3BJH82Bu1Sp5MTL1idU8CgUi8zC3+pzxp+4DhLUEkP94rr0zOku8t7kgQEImXJzork0+S\nDG8JIvnxVm1lkhO12uKOBAGReOncS5msjsoxuiWI5Edm7HF5sjbquNU9CQQi8TKmvjIAx9g6\nhrcEkfzIub7FMUq31+5kdUeCgEi8HEwe+DelXxSdZnhLEMmfvbcm33VL7D/+srofQUAkbr4s\nV7JJrdghxg8MBZECyP183KvfWt2Ja4BI/Jz/YMRbO01oByI5AIhkfyCSA4BI9gciOQCIZH8g\nUgBb21et/cQBq3sRjPNFWtSs/C0jL4Qv51wgkj+zox+a+VbjJLvdRNbxIv0r8Zl5E6pUt9vN\nCUQCkfw4VWSyPOlVw2bD6DtdpOVx8u0hL1zfW39VtgUi+bEwVTmT5BD51eqeBOJ0kXq1VSZz\nSuuvyrZAJD+m1lUmedHfWNyRIJwuUvt+yuSbKJv9pxcJRPLjkyLKxZS/k91W9yQQp4s0oKUy\neauS/qpsC0Ty40LpZ3Jz6aXWt1vdkSCcLtKmqKXS48GKw3gryNXfB6OBSP6sSk6KiUso/bvV\n/QjC6SLRl6PvG9m9SNOLXCtnT6oZU+bxowK6YSRGipS1cPTAgWOXnFMtYDuRxsc2vOX2G2I+\nsbofQRgokkkZbe3dtMsHfL+Q8u5Lfz3zfw1L7RXRD+MwTqTs/jEkPi0tliSOUduCdhPpaNx8\neTKsnOGXgWnDMJGckNHiJPkXa3bjzhb3IwzGiTQoZfJBaZK7a1zieJUilocUxPullLfTCfKj\n1T0JxDCRnJDRvx9SJguLW9yPMBgnUsZ079zEKipFLA8piDfr/Na+co3uh6IKy+5vgRmd37Dy\niIAeXctD7sHHM6NU9jicHHhr7Yc2G9K0FowTKXaNdy4zTqWI3URaHhfliomKiiUHre5JIIaJ\nJC6j/xaPSoh63IjBNV+4U5m8cV3Bi38t2eDVtztGTzagZU0YJ1IN387OwfVUithNpGOu+M+z\nL78ZFWuzA4eGiSQso/8kT7+Us65OEwM23G8xk6Vafyz5SsGLG/8jW3p8L97qM42NE2m6q8ui\nrbt3bVnQwTVfpYjdRHqNZJS+8/Zi5Yn13xQCMEwkLRllr5297JRKoexUZVCEfbGZonso8V5y\ng8dbxTySXeDCEy53VlXfNKBlLRi4+3tudaJQf6laCbuJ1CX2fhIT7epJpljdk0CM2/3NntEP\nDWKqJqfOLLjQDuL+fXTLBK5e5Lzb/aGx6qeGHxr36CC1AdJ+I8oIkLSJ1W8lQw/I7l2+YOHK\nEP9z7SZSbxJTsVe34tFE7ePZIow8IMuY0Z+pXU/SnCkxBQu3nRxTprepfP8KzfGbSjzap26J\n5Tzrno5aL09yK0wPV9JgcGaDH1NJtSvSt4Ukst/qngRigzMbXqqpHFsbcEeBha6kzJInh+NW\n8TTR7tYs6b/S86lcuyruu0c+X+K1ZKuHIjRDpJPHVBbYTaSnSFTdkS+UjSKLrO5JICaIFC4j\nz07oZQkFlxqXMj+X/njTnTwnxZ2JyZQnV0vN4ViZ7q9a4fnRd8d/wLOuSMwQ6ebANW8lPp7k\nrdIYusZ2kH4jxfQjU63uSSAmiBQuo049lMknyQWvnvdSUmI66fAnT9PbSJYyvXsUz9r00oQH\nGve1/nR9M0SaNTbg6W+rvCSo/sS1hlfJ5r2Lvzg2hXxndU8CMUGkcBn9t5xyxumjLdQqyFrx\n4R98TR8h25RpDZvt4tGGpb+RinwmvEpd/BldYvHFM9PiStjstH0rfyN5MjpftdHm7IP9Ytcb\n0MRN/5IfP46x/t+KDiw9+9tuItE3XNEuEhu90up+BGHl2d/ejA60IS5S62sj+rApuencpU/F\njjaibtOw9Oxv24lE1zQplt5mu9W9CMbKs7/zMzq+ZpdBZ8Xv7VIhpfEyY+o2C0vP/rafSPbE\nyrO/kREblp79jZDYsPLsb2TEhqVnfyMkNqw8+xsZsWHp2d9FJv7AwJdvzuPhnbe5VntrBtdq\nU2ZzrTZ5A8sWGGDh2d9sGUlkTuXaAm5mT7Fs5cl6Vv6AJyPxZ39XJoCJ+7RtemRkAewZiT/7\nm41hqgcBQ9L9Ua7V8NVpTgAACDFJREFUWj/Htdotr3GtVn4e12rCEJWRxCt6BjGb0FDHyq/d\nomPl/9ykY+WJN/CsJf7sbzYgkpGIyYhCJHbEn9nABkRyBBCJFYgUAogEkViBSCGASBCJFYgU\nAogEkViBSCGASBCJFYgUAogEkViBSCGASBCJFatEmvoY12rDB3Gt1uM/XKv9832u1W7/kms1\nO/JeOx0rz22jY+X3/6lj5f89qGPl+Q/wrGWVSABEFBAJAAFAJAAEAJEAEABEAkAAEAkAAUAk\nAAQAkQAQAEQCQAAQCQABQCQABACRABAARAJAACaJNKtWXLkh3ltY502/IblyX8/NtO8luyi9\nOqFOUtUnTxraWCdliKpKwcuNbi3gj3UYuvuuhMvF7geLlGh3lG9d/nfTlISuypTjHWKOSB+Q\noaunFXva8+wV15DV01LuVebnxMrb+rliC/euqvZ/hjZ2f6NMiY3By41uzf+PdRp6++4Ol4es\nci2/+az2zXwr876bslqXS1dE4nmHmCNSjU7Sw+QY94dEblo36fE1It86/nhqX3lbp/WT5meS\nvUY21qhrQcuNbs3/j3UaevvuCZeHoZX/pnT7rEtcK/O+m6a1OFFXiY3nHWKKSHvJQunxoPIo\nfWHYLSezhOyQHtu3XCdv6+LPUvlzQIhIao016F3QcqNb8/9jnYbevnvC5aHmEM42ZXjfTYdy\nqSIS1zvEFJGWk63yJN7/9m3dM3Io/Sh5n7Kth5Rcn3v4luaGNlb5OfXlxrWW/4pT4e67N1wO\nLrre6ZuR1u00X8M63k2KSFzvEFNEWkiUO4mmDcx/6UPXPEpPl55IlW2d15/EkKZnDW0s9YF7\nipXreqCg5Qa2lv+KQ+Huuy9cDvaTckM2Lyh7m9odB0Oj492kiMT1DjFTpNT8ns2OGSM9PtYw\n172tx6ZM+3FJ7eZCbpes1ljGDXM3zqpQ5dy1y41sLf8VZ8Lfd1+4HOwibaXHz8gqrrV1vJv8\nRdL2DjFFpJVki/SYG+u7W/2o6MnS44qEX6myrY9FT5SebiH6756g3pibjeTta5Yb2lrQK06D\nv+++cHk4QcZJj+fJJJ6V9bybFJG43iGmiHSALKDyx8xiz/NRicof2c0VLUGim65VPnr+Jq8a\n2JibS2Rk8HJjWwt6xWHo6LsvXK61SzwjPfxFpvGsq+fdpIjE9Q4xZ/d3vQ7Sw7jEv9zPlkZ/\nrkwPb5OYS5btPUDkz70tZJGBje1pv57KHzYfBC03ujXvK05ET9994XKt3aXSVXl/4UaedfW8\nm9y7v3neIeaItNQ1ePWkxFGUzrr5JL1cpYl8sDLTfdxa+e/fpuTCPWtuLH/OwMay65afu3Fm\nRq3L+cvNaC3wj3UW+vvOvfv716TWmR+U5tyNy/tu+ikzs3LzzMzDXO8Qk04R+qB2bMVxedLv\nQHKMbvPcVnCGskTZ1heGlI9J7SDmeKxaY0eeqBCb8e8//Zab0VrgH+ss9PedWyS6oVFCas/z\nfOvyvpuauf/cKVzvEJy0CoAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACAS\nAAKASAAIACIBIACIBIAAIBIAAoBIAAgAIgEgAIgEgAAgEgACgEgACAAiASAAiASAACASAAKA\nSAAIACIBIACIBIAAIBIAAoBIAAgAIgEggAgTqWZ33+z1r0gPs9IPSo9TErpeW2RILUE3dgF8\nfHF/elylrlus7oYgIlakYy4poi3xKyjNal0uvQCRcu5uY3bvgB/PkeYzl75eI07MTbEsJ2JF\nmlMyj9LGD0hz01qcqFuASPRH15fmdg74sYQMkieX/q/4Gau7IoRIE6nXtEqx9TdJc126ULqG\nbJDmDuXSAJF8RR5sbFEvAaV3VsxWpgd3U3q2d+mYCv3OU/pds9TE+rMozR1fL7HswIsWd1ET\nkSZSrU6b19SumkfzSr5H6cCSnptFBYjkLUJnRGVZ00tAL8Xk/5ql7ct8tXdlmT70SurDP++a\n6FpBh0VN2f9F2Yet6552Ik2kKtLn3DRyjP5AjlJ6azvPywEieYvQnWSJJZ0ElO5T7lvuYf8e\n6aFPVbpXuf/xpuMXk3pJ0znkD4s6x0OkidSZyl+/f6fj6ksz5ft6XlZEyj5z5sx5vyL0HHnT\nso4WdvaT1/KfHHu2Qem0xBSaV7/kiPU5lG4gn0ivHlRuLu4UIk0k+QvDUrKDNn5Wmiky1POy\nItIqQshtfkUojR6nVg8wmMtxPXzzObXKL9l9qFcKpadG1iPpI3OWk9h4CTLRwg5qJUJFOhcr\n75EL/I90dt26dT/7i4T/SBbSJOWUMj0y+txG8pE00znF/fyl6Fc3kXd2yJy0sH9aiVCRPk74\nW5q5ta3n5Wt2fysi4TeShXxBHsuVJpeapZ9cTdZI/4xSitF9yjGlhp0vJr0oTS/vsbSDGolQ\nkZ5sKT9z77X7KTOzcvPMzMNBRSidjr12FjKUNJz28RvVi2XSU8kdD3/f8F+ubatdw7ftmZsw\ngw5Nnr77h/bpTjrCFKEiVX1dfuY+jtSMKEwJKkLpg/9nVTeBxMoH0uOr9pD/7SytnnD9ikPV\nkrd+eGuRpHrSL6O816rHprTdbnUPtRBhIgXR6MEQC392rTStIyDSiWyRNsernwWU2/QfJvYE\nRDiRLRKdWfKg2qJhNXH2NxBGhIsEgDlAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQ\nCQABQCQABACRABAARAJAABAJAAFAJAAEAJEAEABEAkAAEAkAAUAkAAQAkQAQAEQCQAAQCQAB\nQCQABACRABDA/wOweo3votOlCAAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Similar to the plots of the entire dataset, the upper left plot indicates that there is heteroscedasticity, since the two groups scatter differently around zero. The upper right plot indicates that the data follows a normal distribution, since the ordered deviance residuals follow the theoretical normal distribution line. The data points in the two lower plots do not cross the thresholds, indicating that there are no outliers present.\n",
        "\n",
        "The theoretical normal distribution line is almost a perfect fit for the data points, indicating that this model is a very good representation of the data."
      ],
      "metadata": {
        "id": "rqY0hJ_4tr-c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_gaussian_a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "ZkYzxhlHvVl_",
        "outputId": "9fbf12d2-9970-4c2f-c373-b364ee7cb17e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = gaussian, \n",
              "    data = data_none_a)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept)   74.479      0.850  87.624 3.21e-13 ***\n",
              "Timepoint3    -8.743      1.202  -7.274 8.61e-05 ***\n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for gaussian family taken to be 3.612363)\n",
              "\n",
              "    Null deviance: 220.014  on 9  degrees of freedom\n",
              "Residual deviance:  28.899  on 8  degrees of freedom\n",
              "AIC: 44.991\n",
              "\n",
              "Number of Fisher Scoring iterations: 2\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "conf_intervals_a <- confint(model_gaussian_a)\n",
        "conf_intervals_a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "66j0wIpMEVmx",
        "outputId": "032ee03a-6b4e-40bf-8dfc-063e901760ec"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Waiting for profiling to be done...\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>(Intercept)</th><td> 72.81340</td><td>76.145271</td></tr>\n",
              "\t<tr><th scope=row>Timepoint3</th><td>-11.09933</td><td>-6.387341</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA matrix: 2 × 2 of type dbl\n\n| <!--/--> | 2.5 % | 97.5 % |\n|---|---|---|\n| (Intercept) |  72.81340 | 76.145271 |\n| Timepoint3 | -11.09933 | -6.387341 |\n\n",
            "text/latex": "A matrix: 2 × 2 of type dbl\n\\begin{tabular}{r|ll}\n  & 2.5 \\% & 97.5 \\%\\\\\n\\hline\n\t(Intercept) &  72.81340 & 76.145271\\\\\n\tTimepoint3 & -11.09933 & -6.387341\\\\\n\\end{tabular}\n",
            "text/plain": [
              "            2.5 %     97.5 %   \n",
              "(Intercept)  72.81340 76.145271\n",
              "Timepoint3  -11.09933 -6.387341"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* The estimated intercept (β0​) is 74.479 (95% CI [72.81340, 76.145273]). This is the predicted percentage of living cells for Timepoint 0 months.\n",
        "* The coefficient for Timepoint 3 months (β1) is -8.743 (95% CI [-11.09933, -6.387341]). This is the predicted difference in the percentage of living cells in Medium A for Timepoint 3 months compared to Timepoint 0 months. Thus, on average, the predicted percentage of living cells in Medium A is 65.736 at Timepoint 3 months.\n",
        "* Both the intercept and coefficient have extremely significant p-values (p < 0.001), providing a reason to reject the second null hypothesis. This suggests that storing over 3 months using the CRYO2 method in Medium A has a significant effect on the percentage of living cells in the samples.\n",
        "* The dispersion parameter for the Gaussian family is provided (3.612363). It characterizes the variability of the residuals around the fitted values.\n",
        "* The null deviance (220.014) represents the deviance of the null model (a model with no predictors). The residual deviance (28.899) represents the deviance of the fitted model. As the value gets lower, the fitted model performs better than the null model."
      ],
      "metadata": {
        "id": "qpCmiGmEvWFO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_gaussian_b <- glm(mean_percent_live~Timepoint, data=data_none_b, family=gaussian)\n",
        "glm.diag.plots(model_gaussian_b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "TEJnBXXhHfK_",
        "outputId": "b954c99e-5ad2-4514-aa15-92039ef610e7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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AHmjWoeHEky+rVbiM/UhEgSYOAyityf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\nIBIAAoBIAAgAIgEgAIgEgAD+H4SHW9TaQUShAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The upper left plot indicates that there is heteroscedasticity, since the two groups scatter differently around zero.\n",
        "\n",
        "The upper right plot indicates that the data follows a normal distribution, since the ordered deviance residuals follow the theoretical normal distribution line. However, the ordered deviance residuals follow the line with less precision, suggesting that this may not be the ideal fit. Nevertheless, an alternative poisson model was analyzed and it was found that this particular model still provided the best fit.\n",
        "\n",
        "The data points in the two lower plots do not cross the thresholds, indicating that there are no outliers present."
      ],
      "metadata": {
        "id": "K6BEcJ5jw2ZD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_gaussian_b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "baZSLjJKw1az",
        "outputId": "5b571e5a-3c05-43fb-93d2-874321eaba05"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = gaussian, \n",
              "    data = data_none_b)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept)   74.479      1.100  67.728 2.51e-12 ***\n",
              "Timepoint3    -9.250      1.555  -5.948 0.000343 ***\n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for gaussian family taken to be 6.046513)\n",
              "\n",
              "    Null deviance: 262.278  on 9  degrees of freedom\n",
              "Residual deviance:  48.372  on 8  degrees of freedom\n",
              "AIC: 50.142\n",
              "\n",
              "Number of Fisher Scoring iterations: 2\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "conf_intervals_b <- confint(model_gaussian_b)\n",
        "conf_intervals_b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "sIsn4QXIEsSt",
        "outputId": "a29e5a0f-4207-4ad8-dae0-cdb81bd6efa5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Waiting for profiling to be done...\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>(Intercept)</th><td> 72.32399</td><td>76.63467</td></tr>\n",
              "\t<tr><th scope=row>Timepoint3</th><td>-12.29811</td><td>-6.20189</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA matrix: 2 × 2 of type dbl\n\n| <!--/--> | 2.5 % | 97.5 % |\n|---|---|---|\n| (Intercept) |  72.32399 | 76.63467 |\n| Timepoint3 | -12.29811 | -6.20189 |\n\n",
            "text/latex": "A matrix: 2 × 2 of type dbl\n\\begin{tabular}{r|ll}\n  & 2.5 \\% & 97.5 \\%\\\\\n\\hline\n\t(Intercept) &  72.32399 & 76.63467\\\\\n\tTimepoint3 & -12.29811 & -6.20189\\\\\n\\end{tabular}\n",
            "text/plain": [
              "            2.5 %     97.5 %  \n",
              "(Intercept)  72.32399 76.63467\n",
              "Timepoint3  -12.29811 -6.20189"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* The estimated intercept (β0) is 74.479 (95% CI [72.32399, 76.63467]). This is the predicted percentage of living cells for Timepoint 0 months.\n",
        "* The coefficient for Timepoint 3 months (β1) is -9.250 (95% CI [-12.29811, -6.20189]). This is the predicted difference in the percentage of living cells in Medium B for Timepoint 3 months compared to Timepoint 0 months. Thus, on average, the predicted percentage of living cells stored in Medium B is 65.229 at Timepoint 3 months.\n",
        "* Both the intercept and coefficient have extremely significant p-values (p < 0.001), providing a reason to reject the third null hypothesis. This suggests that storing over 3 months using the CRYO2 method in Medium B has a significant effect on the percentage of living cells in the samples.\n",
        "* The dispersion parameter for the Gaussian family is provided (6.046513). It characterizes the variability of the residuals around the fitted values.\n",
        "* The null deviance (262.278) represents the deviance of the null model (a model with no predictors). The residual deviance (48.372) represents the deviance of the fitted model. As the value gets lower, the fitted model performs better than the null model."
      ],
      "metadata": {
        "id": "TEWTZerPw28g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model_gaussian_c <- glm(mean_percent_live~Timepoint, data=data_none_c, family=gaussian)\n",
        "glm.diag.plots(model_gaussian_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "YLKCvwmCHn7f",
        "outputId": "a454f40f-5da1-4fcd-b38d-b1af3f8f47a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Mfa7TlQn5Dkb3W2HSEZHcs2+E4GOCBr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\nJhMWp/T2+AAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Again, the upper left plot indicates that there is heteroscedasticity, since the two groups scatter differently around zero.\n",
        "\n",
        "The upper right plot indicates that the data follows a normal distribution, since the ordered deviance residuals follow the theoretical normal distribution line. However, the ordered deviance residuals follow the line with less precision, suggesting that this may not be the ideal fit. Nevertheless, alternative models (poisson and negative binomial) were analyzed and it was found that this particular model still provided the best fit.\n",
        "\n",
        "The data points in the two lower plots do not cross the thresholds, indicating that there are no outliers present."
      ],
      "metadata": {
        "id": "LRwX6dZ9w7tX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(model_gaussian_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        },
        "id": "AiKCBi2hw47Y",
        "outputId": "5db313ea-42bb-40cc-9dd4-41a09ab89b2b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = mean_percent_live ~ Timepoint, family = gaussian, \n",
              "    data = data_none_c)\n",
              "\n",
              "Coefficients:\n",
              "            Estimate Std. Error t value Pr(>|t|)    \n",
              "(Intercept)   74.479      2.672  27.872 2.96e-09 ***\n",
              "Timepoint3   -11.587      3.779  -3.066   0.0154 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for gaussian family taken to be 35.70279)\n",
              "\n",
              "    Null deviance: 621.25  on 9  degrees of freedom\n",
              "Residual deviance: 285.62  on 8  degrees of freedom\n",
              "AIC: 67.9\n",
              "\n",
              "Number of Fisher Scoring iterations: 2\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "conf_intervals_c <- confint(model_gaussian_c)\n",
        "conf_intervals_c"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        },
        "id": "LOUuYgpiFfbs",
        "outputId": "e96a7efe-ef38-464b-fa1b-31dfabd5b674"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Waiting for profiling to be done...\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
              "<thead>\n",
              "\t<tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><th scope=row>(Intercept)</th><td> 69.24195</td><td>79.716714</td></tr>\n",
              "\t<tr><th scope=row>Timepoint3</th><td>-18.99344</td><td>-4.179891</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA matrix: 2 × 2 of type dbl\n\n| <!--/--> | 2.5 % | 97.5 % |\n|---|---|---|\n| (Intercept) |  69.24195 | 79.716714 |\n| Timepoint3 | -18.99344 | -4.179891 |\n\n",
            "text/latex": "A matrix: 2 × 2 of type dbl\n\\begin{tabular}{r|ll}\n  & 2.5 \\% & 97.5 \\%\\\\\n\\hline\n\t(Intercept) &  69.24195 & 79.716714\\\\\n\tTimepoint3 & -18.99344 & -4.179891\\\\\n\\end{tabular}\n",
            "text/plain": [
              "            2.5 %     97.5 %   \n",
              "(Intercept)  69.24195 79.716714\n",
              "Timepoint3  -18.99344 -4.179891"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* The estimated intercept (β0) is 74.479 (95% CI [69.24195, 79.716714]). This is the predicted percentage of living cells for Timepoint 0 months.\n",
        "* The coefficient for Timepoint 3 months (β1) is -11.587 (95% CI [-18.99344, -4.179891]). This is the predicted difference in the percentage of living cells in Medium C for Timepoint 3 months compared to Timepoint 0 months. Thus, on average, the predicted percentage of living cells in Medium C is 62.892 at Timepoint 3 months.\n",
        "* Both the intercept and coefficient have extremely significant and significant p-values (p < 0.001 and p = 0.0154, respectively), providing a reason to reject the first null hypothesis. This suggests that storing over 3 months using the CRYO2 method in Medium C has a significant effect on the percentage of living cells in the samples.\n",
        "* The dispersion parameter for the Gaussian family is provided (35.70279). It characterizes the variability of the residuals around the fitted values.\n",
        "* The null deviance (621.25) represents the deviance of the null model (i.e., a model with no predictors). The residual deviance (285.62) represents the deviance of the fitted model. As the value gets lower, the fitted model performs better than the null model."
      ],
      "metadata": {
        "id": "s11r8av5ck-q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Both diagnostic plots and AIC values indicate that the Gaussian generalized linear models perform the best out of the models tested on the data on medium level."
      ],
      "metadata": {
        "id": "NU_UdVZQXcX0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Conclusion"
      ],
      "metadata": {
        "id": "AGvVfSgWL9lC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The gaussian generalized linear model revealed that there is an extremely significant (p < 0.001) difference of the survival of the bacteria between timepoint zero months and after timepoint 3 months using any of the preservation media.\n",
        "\n",
        "The percentage of bacteria after three months of storage using the CRYO2 method in any of the preservation media decreases on average for 9.860% (95% CI [14.52444, 5.195565], p = 0.000611 < 0.001). On average, the predicted percentage of living bacteria before storage is 74.479% (95% CI [70.43981, 78.518853], p = 2e-16 < 0.001) and after 3 months of storage 64.619% of living bacteria are expected.\n",
        "\n",
        "Furthermore, three other gaussian generalized linear model revealed that there is also an extremely significant (p < 0.001) difference on the survival of the bacteria between timepoint zero months and timepoint 3 months when stored in medium A and B. While there is only a significant (p < 0.05) difference when stored in medium C.\n",
        "\n",
        "When the bacteria are stored for three months using the CRYO2 method in preservation medium A, B and C, there is on average a decrease of 8.743% (95% CI [11.09933, 6.387341], p = 8.61e-05 < 0.001), 9.250% (95% CI [12.29811, 6.20189], p = 0.000343 < 0.001) and 11.587% (95% CI [18.99344, 4.179891], p = 0.0154 < 0.05) of living bacteria respectively. For all the preservation media, the predicted percentage of living bacteria before storage is on average 74.479% (A: 95% CI [72.81340, 76.145273], p = 3.21e-13 < 0.001; B: 95% CI [72.32399, 76.63467], p = 2.51e-12 < 0.001; C: 95% CI [69.24195, 79.716714], 2.96e-09 < 0.001). For preservation medium A, B and C, on average, the expected percentage of living bacteria after three months of storage is 65.736%, 65.229% and 62.892%.\n",
        "\n",
        "The results derived from the Gaussian Generalized Linear Models suggest that, on average, preservation medium A performs better than medium B and C, as it exhibits a higher percentage of bacterial survival. However, to make this statement, additional information from the later time points is essential.\n",
        "\n",
        "The plot below visually emphasizes the observed differences in bacterial survival percentages before and after three months of storage using the CRYO2 method in various preservation media. It provides a clear representation of the trends across different conditions and supports the statistical findings derived from the Gaussian Generalized Linear Models."
      ],
      "metadata": {
        "id": "QFHGeOfXDsoC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Combine the values into a data frame\n",
        "data_none <- data %>% filter(Medium == 'None')\n",
        "data_a <- data %>% filter(Medium == 'A')\n",
        "data_b <- data %>% filter(Medium == 'B')\n",
        "data_c <- data %>% filter(Medium == 'C')\n",
        "\n",
        "ridgeline_data <- data.frame(DataTimepoint0 = data_none$mean_percent_live, DataTimepoint3_A = data_a$mean_percent_live, DataTimepoint3_B = data_b$mean_percent_live, DataTimepoint3_C = data_c$mean_percent_live)\n",
        "\n",
        "# Melt the data for plotting\n",
        "melted_data <- gather(ridgeline_data, key = \"medium\", value = \"mean_percent_live\")\n",
        "melted_data$medium <- factor(melted_data$medium, levels = rev(c(\"DataTimepoint0\", \"DataTimepoint3_A\", \"DataTimepoint3_B\", \"DataTimepoint3_C\")))\n",
        "\n",
        "# Create ridgeline plot\n",
        "ridgeline_plot <- ggplot(melted_data, aes(x = mean_percent_live , y = medium)) +\n",
        "  geom_density_ridges(alpha = 0.7, color = c(rep('#3D1778', 1536), rep('#00366C', 512)), fill = rev(c(rep('#BDD7FB', 512), rep('#8576B7', 512), rep('#BFB9DC', 512) , rep('#DFDDF1', 512)))) +\n",
        "  labs(x = \"Percentage of Live Bacteria\") +\n",
        "  scale_y_discrete(labels = rev(c(\n",
        "  \"Before storage\n",
        "  at timepoint 0 months\",\n",
        "  \"After CRYO2 storage\n",
        "  at timepoint 3 months\n",
        "  in medium A\",\n",
        "  \"After CRYO2 storage\n",
        "  at timepoint 3 months\n",
        "  in medium B\",\n",
        "  \"After CRYO2 storage\n",
        "  at timepoint 3 months\n",
        "  in medium C\")))+\n",
        "  theme_ridges() +\n",
        "  theme(axis.title.y=element_blank())\n",
        "\n",
        "title <- textGrob(\"Ridgeline Plot of Percentage of Live Bacteria\", gp = gpar(fontsize = 14, fontface = \"bold\"), just = \"center\")\n",
        "caption <- textGrob(\"When the bacteria are stored for three months using the CRYO2 method,\n",
        "  on average, the mean percentage of living bacteria\n",
        "  decreases with 8.743% in medium A (95% CI [11.09933, 6.387341], p = 8.61e-05),\n",
        "  decreases with 9.250% in medium B (95% CI [12.29811, 6.20189], p = 0.000343 < 0.001)\n",
        "  and decreases with 11.587% in medium C (95% CI [18.99344, 4.179891], p = 0.0154 < 0.05).\", gp = gpar(fontsize = 12), just = \"center\")\n",
        "\n",
        "grid.arrange(\n",
        "  ridgeline_plot,\n",
        "  title,\n",
        "  caption,\n",
        "  nrow = 3,\n",
        "  heights = c(0.7, 0.05, 0.15)\n",
        ")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "nE5DXR7yrSsA",
        "outputId": "73180148-036a-4355-d6e9-7c1be526d308"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "Warning message:\n",
            "“package ‘grid’ is a base package, and should not be updated”\n",
            "Picking joint bandwidth of 1.95\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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uz83XA2toWg2AEAALCAaTkBbrZsB2kJ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U6FgAEAJI7AAAoO+7E5GW8/bTCFtdFQ1Z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NSlDt9e/tfOWVgc5vqxl4uMTjy7m07r4uZZ\nJDkWTOxYBo/HAwAcHBwaGhru37//+vVrdXV1Ly+vwMDA/g9xdHQkk8lRUVH+/v7v3793dHR0\ncnLi4eF58uTJzZs3c3JyZs2a1dn5b7/UqqqqiRMn3rlzZ8GCBQEBAV5eXhkZGSYmJnFxccgO\niYmJ1tbW5eXlPj4+hw4dam9vt7a2RqMH+UEPIsLebt26BQDYuXNnnyPLduzYERMTY2hoOLgI\nR4Ss5KLdSx5c8Ilube5YtM78yO0VsmO5tnqS8ylqSPndX7lgzdTW5g6/zaErp59Li81nd1D/\ng06jRz945zL5xIW9z2g02uKNFseD/1LVlmF3XBDUHzQGPd1R7/zTNdZLJ9VVNx/1erTU7PSL\nh++4e5JwDgSHcLMMkrUICwv7+/sjW/z9/RUVFUNDQ11dXfs5RFlZ2cfHBwCgo6MTGRkZEhJi\nYGBw5MgRAICenl58fPyZM2fS0tKMjIwAAHv27CktLU1KStLX10cKcXFx0dDQ2Lx5M1Jvd/Dg\nQRqNFh4ePmHCBACAm5ubp6dnfHz871zUL0XYW0pKSvdawD/K5+yyG34xiS9yAAAG5irLNk0X\nJwuxOygIYLGYeW7GZnPG3Tr1KunFp03OAVoT5ZZuNJ8wRZm9gXV2dEU/eHfnfFxpYQ0Wh5kx\nX3++u6mgMFxcDhoxSPw8SzZaWjkbPLgUF/cs+8CakBsnXi1YbTrDUWfkzng3ssDEjsWWLl3K\nfK2goEAkEr9//97/Ifb29szXysrKAAAbGxvmFhUVFQAAhUIBADAYjAcPHmhpaUlLSzPnK8Hh\ncEZGRtHR0U1NTUQiMTY2VlFREcnqECtXrrx48eLvXNTAI+xTRUWFoKCggMBQTQ/Lmd4nF949\n/yb5VR6DwVAeR3byNFHXlUVqQCEOISop6HXU/sviifcvxmX+U7DJOUBZc7TDysnTbMfjCcP9\nv7GilPrsbvrjWyl1VU1YLGaq9fh5K40lZYSHOQwIYgmx0YKr91nbrzAOvZ7w5tmH41vCrh15\nYb3YYO5iAwn4cDvEYGLHYmPGjOn+Iw6H66eNEkEm/zfADakh674Fh8MBAJBCKisrq6urq6ur\n++zs+e3bN0FBwdbWVgUFhe7bVVVVf/kyBhthn9BoNDLJ55+gtbkjJux9+M3k/OwyAMBYLel5\nK431TJTb2trYHRrUNyVN8q6LC/OzS8MCEtPjPh9e//C8zzPLedrTHXTUdKSHuh9kc2P7Py9y\nXjx6lxb3hU6j8/LhZy2aONdl4kgZVwhB/ZAcI7x6n/X81VMi76bEhL67dfr17bOxBlPGWjnr\nTp6hPvyPT38IeFtZDMlyfvOQHxXS2NgIANDW1j58+HDvd6WkpKqqqgAAPDw83bfz8PD85pfT\nwCPsk5SUVF5eXnV1dZ8LanEHWhf9bULBy9DMuGcfWps70GiUvtnYOYsmahrIsTs0aECUx5G3\nnppfXlIb/SAj9klWaEBSaECSpLSQ8Ux1QwtVrUlyrG1FKi2qSY/7kvgiJyO+oLOjCwCgoCo5\nzV7HdLYWLx+s1oW4iqiEwJKNlvNXmb15lv3y0dvkv/OS/87jE+AxmaluNltT30wJNtGyFkzs\nRhLmyiczZ87sc4empiYAQI/KoaampoFPatPR0fEbAfbNyMgoLy8vIiKiz76GDAYjOztbS0uL\n5ecdBg11LRnxX5Ji8v55mdtQ1wIAEBHnt1pgYGGnA/vSjUSSMsJLvSwXrTPPeJOfGPUpIz7/\n4bV/Hl77B0/AqmpLj5sgq6ItraQuKSUrjMb82oCkhrqWgpzy/Oyy3MzvWSlFlWX1yHayrMgk\nSzXjmZoySsO31CwEDT8eIn66o950R73CvIrYJ+//efExKuRtVMhbHl6cnqmSwRRlPVOlMYrw\nr4AFYGI3kkhISIiKiubm5lKpVCGh//KGqqoqZBoRSUlJPB5fWFjY/aisrKwfFdi7FbXHsSzh\n6up648YNX19fBweH3qvyXbx4cc2aNefPn/f09GT5qYdCZVn9p7cl2alFWclF+R/KkMkyBIX5\nLOfpTp6hoa4vC1cGG+mwWMxEc9WJ5qqdHV3ZaUXvEwuyUguzU4uzUoqQHXB4rJSs8GiZUSKS\n/MJi/HRUJ0mAh5+fn8iHb2nuAAB0tHU21rc11LVUVzRUfKeWFdcieT+Cj5+gbzZ23ER57cmK\nZFkRtlwjBLGLvIqE/JbpSzdZ5mWWJL/KzXiTnxidkxidAwAQkeDXMpDTnCCrpiOtpCnF+TPh\ncSaY2I0wjo6O/v7+fn5+Bw8eRLZUVVVpaWnp6+tHRERgsVgjI6PY2Ni0tDTm+IkLFy78qDSk\nr15OTg5zejlkahLWMjExcXJyCg4OtrS0vHPnjqKiIrK9q6vr4sWLXl5eo0ePXrhwIcvPyxLV\n5Q2lRTUlBdVFnyu/5lbkZ5fV1zYjb2GwaCVNstYked3JSkrjyDCf4z44PFZ3spLuZCUAQFND\n6+fs0qKc8qL8yrKiasq3uuL8yoEUgsGiRSQE5FUlxyiJy46VUFQfTZYXhb8t0B8OjUap6Y5R\n0x3jumV6WXHN+6Sv2SmFn95+ex2R/ToiGwCAxqDJcsKKapJjlMXllMXI8iKjxwgLicAR4j8H\nE7sRZu/evc+ePTt06BCFQjEzMysrK7t06VJNTc26deuQHbZu3RoXFzdnzpzly5eLiIjExcW1\ntLQICvbdEXvJkiX+/v5eXl5+fn5EIvHx48dJSUm9K9V+X0BAQHt7e3h4uKqqqomJydixY6lU\nanJycnFxsYKCQlRU1KhRo1h+0p9qa+loaWpvamxrpLY2Ulvra1vqa5trKxtrq5qqyxsqS+vL\nv9d1tHd1P0REnF/PVFlZkzxWS1p5HBl2h/pzkAR4mUkeoqm+tbaysb62pa62oaO1k8H4L1fj\nE+DhJRL4BXmExPhHiZAwWDhjKAT9kJSsiJSsiJXzBAaDUVZU8zm7tOBD2de88m/5lSUF1d33\n5OHFScqMEh0tKCrBP0qUJCzOLyhMFBQmCggR+QR4+Ph5iCQCH/+fvkwITOxGGHFx8ZSUFF9f\n36dPnwYFBZFIJFNT0wcPHhgYGCA7WFlZ3bt37+DBgydPnhQUFJw7d+6JEye0tLT67Dw3adKk\nwMDAY8eOzZ49W0BAwMbGJiIiQl1dHVlFh4WIRGJYWFhERERgYGBycnJCQgIPD4+6urq3t/ey\nZct4eXuuZd7R0dGjpyAajabTWTbLZbD/P3fOvOl/yQFeEkFCepQ4WUhSZtToMcJSciJjlMRI\ngv8TaldX148O7w7p48hgMAa4PzQi8PDhpOSFpeSFkfVaMBhMn7sxAL0Lzr8/ksG/3OEkISMk\nISNkMksDAMBgMCrL6suKayhFteUldZVl1Oqy+vLvdUWff1JZzkPE4fBYPn4CBovmJeIBAER+\nAhqNAigUiZn2oVA8RAz4/6keEBgM+pce17Uny2sbyf3aFf4YBoPh42NBlSRcKxbiRC0tLT1W\nQsPj8Swc2PHmaW70/SwiP56XhOfhxfEJ8JAECCRBHoFRvIIiREFhXhEJfh4i7N4BQRDEcVqa\nOuqqmuprWxvqWhvqWv+PvfuMi+Jq/wZ+hi0svfcm2LETO5AYxY4IVuyiaOya+FcssSZiokns\nYkkUy22PqJHYWxQLdqNY0IgVpChIr25VASEAACAASURBVPu8OM89n7m3DltANr/vq+Xs2TnX\nnHNm9mLa5mUX5ecWFeSWFOQVF+SVFBWUlpaUFeaXFheVlhaXlxSXlZbo63lbdZs4f7etv66W\nJhaLdfLsCCR28CkqLy83pH+RpVLp+/fvhUKhsnPiUKO9f/9eIBBgcA3Shw8fCCHVcq0I6FBF\nhTQ/t4gQQqQk7+P/Px308ePHkuJSY7Gpwo8U5pWUq/sxNK+6DnZOOrt4ycjISIMnpsnDqVj4\nFAkEAmUntmoi+u+TkZGRsfG//eIPQ8UwDAbXINGHgGJwDYCJyf9/wqu90/8vSU83Ki8vV/jA\n/xoNl/QCAAAAGAgkdgAAAAAGAokdAAAAgIFAYgcAAABgIJDYAQAAABgIJHYAAAAABgKJHQAA\nAICBQGIHAAAAYCCQ2AEAAAAYCCR2AAAAAAYCiR0AAACAgUBiBwAAAGAgkNgBAAAAGAgkdgAA\nAAAGAokdAAAAgIFAYgcAAABgIJDYAQAAABgIJHYAAAAABgKJHQAAAICBQGIHAAAAYCCQ2AEA\nAAAYCCR2AAAAAAYCiR0AAACAgUBiBwAAAGAgkNgBAAAAGAgkdgAAAAAGAokdAAAAgIFAYgcA\nAABgIJDYAQAAABgIJHYAAAAABgKJHQAAAICBQGIHAAAAYCCQ2AEAAAAYCCR2AAAAAAYCiR0A\nAACAgUBiBwAAAGAgkNgBAAAAGAgkdgAAAAAGAokdAAAAgIFAYgcAAABgIJDYAQAAABgIJHYA\nAAAABgKJHQAAAICBQGIHAAAAYCCQ2AEAAAAYCCR2AAAAAAYCiR0AAACAgUBiBwAAAGAgkNgB\nAAAAGAgkdgAAAAAGAokdAAAAgIFAYgcAAABgIJDYAQAAABgIJHYAAAAABgKJHQAAAICBQGIH\nAAAAYCCQ2AEAAAAYCCR2AAAAAAYCiR0AAACAgUBiBwAAAGAgkNgBAAAAGAgkdgAAAAAGAokd\nAAAAgIFAYgcAAABgIJDYAQAAABgIYXUHAPCvIBKJhEJsboZJJBIJBILqjgL0QigUMgxT3VGA\nXohEIiMjAzy8xUil0uqOAQAAAAB0wABzVQAAAIB/JyR2AAAAAAYCiR0AAACAgUBiBwAAAGAg\nkNgB6ExsbCyjyPfff8/Wyc7OnjZtWq1atcRisaura2RkZGpqajXGDJVy7NixL774wsLCwtra\numPHjufPn+e+i8GtoSQSicItl2GYlJQUWgeDW3M9evRo2LBhLi4uIpHIwcEhLCwsMTGRW8HA\nBhfPXwDQmezsbELIoEGDPD09ueX+/v70RUlJSadOnW7dutW3b18/P79nz55t37797NmzN2/e\ntLGxqYaIoTK2bt06atSo2rVrT5s2raioaNu2bV27dj137lz79u0JBrcmmzFjRmlpqUzh3r17\n09LSLC0tCQa3Jnvw4EG7du1EItGkSZPq1Knz4sWLdevW+fv7nzhxomPHjsQgB1cKADqyYMEC\nQsj169eVVfjll18IIT/++CNbsnfvXkLI9OnTqyRA0Ny7d+/Mzc1btGiRl5dHS5KTk83NzSdM\nmED/xOAakhs3bggEgu+//57+icGtuQYPHkwIOXv2LFty9+5dQkiHDh3on4Y3uHiOHYDOTJs2\nbdWqVcnJyXXq1FFYoUWLFs+ePcvIyDA2NmYL69at+/Hjx7S0NDwH9VP2008/zZgx4/jx4127\ndmULpVIpO2oYXINRXl7eqlWroqKiO3fuiMVigsGtydq2bXvt2rWSkhKRSMQWWllZ2draPn/+\nnBji4OIaOwCdoadira2ty8vLX79+nZmZyX23qKjo77//bt26NXf3QQgJCAhIT0+nuxj4ZJ0+\nfdrExISeuykuLv748SMhhN3pY3ANyZo1a27fvr1+/Xqa1WFwa7QGDRoQQh4/fsyWZGZm5uXl\nNWzYkBjo4CKxA9CZnJwcQsjKlSsdHBw8PDwcHBzq16+/a9cu+u6rV6/Ky8s9PDxkPuXl5UUI\n+eeff6o4WqiUR48eeXt7379/PyAgwMTExMrKqk6dOrGxsfRdDK7ByM/Pj46O7tSpU4cOHWgJ\nBrdGi4qKsrGxGTp06KVLl9LS0m7fvh0eHi6RSOiVMwY5uEjsAHSGHrHbvXv3zJkzt2/fPnv2\n7LS0tCFDhmzcuJEQkpubSwgxMzOT+ZS5uTn7Lnyy3r9/n5+f37Nnz7Zt2+7fv3/VqlWlpaUR\nERE0ccfgGoy1a9dmZGTQb30Kg1ujNWzY8MqVK6WlpYGBgS4uLn5+fsnJyadPn27Tpg0x0MHF\nXbEAOjNv3rxJkyZ169aN3U0MHTrUz89vzpw5ERERtET+ig16nWtNvJLjX6WkpOTFixfbtm0b\nPnw4Lenfv3+9evWmT58+cOBAWoLBrekKCwt/+umnzz//PDAwUOYtDG4N9fDhw549e5aVlf38\n88/16tVLT0//5ZdfunfvfuDAgaCgIFrHwAYXiR2AztALsLh8fX179OgRFxd39+5deue8/L+A\n9GotCwuLqgkSNGNubl5WVtavXz+2xMXFpXv37vv3709KSqIPxcDg1nQHDx7MzMwcPXo0txCD\nW6ONGjXq3bt3T548cXNzoyXh4eH16tUbOXLk8+fPDXJwcSoWQL8cHR0JIXl5eZ6enkKh8MWL\nFzIVnj17RgipW7duNQQHvNWqVYsQwr2xjhDi4OBACMnNzcXgGoa9e/cKBIKQkBBuIQa35srL\ny7t27VqbNm3YrI4QYmpq2qlTpzdv3jx58sQgBxeJHYBu5OXlxcTE7N69W6b8wYMHhBAvLy+x\nWPzZZ58lJiYWFBSw71ZUVFy4cMHDw0PmmcbwqWnXrl15efmtW7e4hU+fPiWEeHh4YHANQElJ\nydmzZ1u0aGFtbc0tx+DWXIWFhVKptKioSKaclhQVFRnk4CKxA9ANU1PTJUuWjB079tGjR2zh\n4cOHL1261KJFCx8fH0LI6NGjCwoKli9fzlbYtGnT27dvIyMjqyFiqIyRI0cyDDNnzpzi4mJa\ncuPGjdOnTzdt2pTeUofBremSkpLy8/ObNWsm/xYGt4ZycHDw9va+cePGkydP2MLs7OzTp09b\nWlo2btyYGOTgVuPDkQEMzOHDhxmGMTMzGz169Lx588LCwhiGsbS0vHnzJq1QVlZGL8ru3bv3\nokWLwsPDGYZp0qRJfn5+9UYOfEybNo0Q0rx580WLFo0ZM8bExEQsFp87d46+i8Gt6fbs2UMI\nYX9tgguDW3MdPHjQyMjIzs5u7ty5W7ZsWbJkibe3NyFk3bp1tILhDS4SOwBdunz5cvfu3a2t\nrYVCoaur6/Dhw5OTk7kVcnNz/+///s/Ly0skErm5uU2cODErK6u6ooVKqaio2LBhQ7NmzSQS\niZWVVY8ePRITE7kVMLg1WkxMDCFk1apVCt/F4NZcly9fDg0NdXBwEAqFNjY2QUFB8fHx3AoG\nNrj4STEAAAAAA4Fr7AAAAAAMBBI7AAAAAAOBxA4AAADAQCCxAwAAADAQSOwAAAAADAQSOwAA\nAAADgcQOAAAAwEAgsQMAAAAwEEjsAAAAAAwEEjsAAAAAA4HEDgAAAMBAILEDAAAAMBBI7AAA\nAAAMBBI7AAAAAAOBxA4AAADAQCCxAwAAMEC5ubnDhw+3tLQUi8XLli3TeDkrV65kGCYyMlKH\nsf0bVFe/IbEDAIBKS0tLY+QYGRnZ2Ni0b99+1apVRUVF1R3jv9233367Y8cOqVTapUsXR0dH\n+QrsIKalpVV9eAopnFcmJia1a9ceMmRIQkJCdQdYAzBSqbS6YwAAgBomLS3NxcWFENKsWTOh\nUEgLS0pKUlJScnNzCSHNmzc/c+aMra1tdUapncGDB9+7d+/+/fvVHYiGGjRo8Pjx47i4uNDQ\nUIUV2EFMTU11dnZWtpzy8vLS0lKhUMgOtP4onFeZmZlv3rwpKysjhKxevXry5Ml6al23I16V\n/caFxA4AACpNRU7w559/RkZGpqamDho0aNeuXdUUoA40aNBAKBTW3MTOzs7u/fv3z58/r1Wr\nlsIKPBO7qqQspIyMjOnTp+/YsUMsFr98+dLJyUkfrdf0EadwKhYAAHSpR48emzZtIoTs3bv3\n/fv31R2OhvLy8pKTk6s7Cq2Ul5cTQqr4cJGeODg4bNmyxdzcvKSk5NKlS/powgBGnEJiBwAA\nOta9e3exWFxRUXHnzh1ueUJCQt++fZ2dncVisbOzc9++fS9fvsytsGLFCoZhFixYcOPGDT8/\nP4lEwj3md/r06V69ejk6OhobG9euXXvhwoUFBQUyTattYs2aNbSJgoKCWbNm1a5d29jY2MnJ\nafjw4e/evaN1hg4damFhUVFR8eDBA3qZ1+vXrwkhpaWlq1evbtu2rZWVlUgkcnBw6Nmz57lz\n52RiKCwsnDNnjo+Pj0Qi8fLymjlzZkFBwcyZMxmGWbVqVaWiVebkyZPBwcGOjo5isdjBwaFb\nt26HDh1i3+3Xrx/DMDk5OYQQDw8PhmG+/fZbPotViHsTQIcOHRiGWbt2rXy1wMBAhmFoTq/l\n2ikkFArd3d0JIRUVFdxynoNCVM4fZSPOZy2UTVr5myf4h6oVKQAAQCWlpqbSL5HU1FSFFegJ\ntcOHD7MlGzduNDIyMjIy6tixY2RkJE0RGIb57bff2DoxMTGEkMmTJ3t4ePj4+HTp0uWPP/6g\nb61evZphGLFY/OWXXwYHB9OTcc2bN8/Pz69UEzTzmDZt2hdffOHg4BAWFtalSxdTU1NCSIsW\nLSoqKqRS6a5duwYPHkwIsbOzmz59+vTp07Ozs6VS6bBhwwghZmZmvXr1Gjp0aOvWrQkhDMPs\n37+fXX55eXnHjh0JIVZWVuHh4cOGDbO1tQ0ICBg7diwhZP369ZWKVqGlS5cSQoRCYadOnSIj\nIzt37iwWiwkhs2fPphW2bds2ffp0Y2NjQshXX301ffr0Y8eOaTCI1IoVKwgho0ePZgeoQ4cO\n8osyMjISiURZWVnarJ2KkD5+/GhiYsIwzOPHj7nlfAZFqm7+KBtxbSYtt98qFaqWkNgBAECl\nqc4JCgsLGYYhhCQmJtKSR48eiUQisVh86tQpttqxY8dEIpFEInnx4gUt+e233wghbm5uoaGh\n5eXlbM2///5bJBJZW1vfu3ePluTl5X3xxReEkKioqEo1sWXLFkKIra1tp06dPnz4QAsfPHhA\nT1leuXKFlly5coUQ0qhRI3ZRtMTc3PzZs2dsIT0C5+3tzZbs3r2bEOLg4JCSkkJLMjIyGjdu\nbGlpSQiJiYmpVLTybt68aWRkJJFIrl27xhbeunVLIpEwDHP58mW20MrKihDy6tUrZYvSILHL\nyMgQCoUCgSA9PZ1bhx7DCwkJ0XLtlIX04cOHgQMHEkJGjBjBLec5KHzmj/yIazlpZRI7nqFq\nD6diAQBAxzZv3iyVSu3s7Jo3b05L1q1bV1paOnbs2KCgILZat27dRowYUVRUtHXrVlpiZGRE\nCElLS6NHStiav/32W2lp6cSJE5s0aUJLzMzMFi9eXKtWrSdPnlSqCZpx5ubm/vrrr9bW1rTQ\n19e3Q4cOhBAVF867urru3r17x44dPj4+bOG4ceOMjIyeP3/OPjFk7969hJCJEyd6eXnREnt7\n+w0bNnz8+JG7NJ7RytuwYUNFRcXo0aPp8R6qRYsWERER0v+mrfpjb28fFBRUXl5++PBhbvmB\nAwcIIfSgF9Fi7Vi9e/cO+K9mzZo5OTmdPHly1qxZv/76K7caz0HhM3/kaTlpZfAMVXuGcE0l\nAAB8CsrKylJSUg4cOLB48WJCyOzZs0UiEX3r7NmzhJDg4GCZj3Tv3v3XX3/966+/uIWNGjWS\nee7a8ePHCSE092J9/vnnz58/Z/+sbBMy94rS67dk0i8uT09PT09P+jonJycrK4te7GVpaZmd\nnZ2Tk0Pv4qSXFX755Zfcz/r7+3t4eLx69UqzaLnorQPdunWTKe/UqVNMTAw9LKRX4eHhx48f\nP3jwIHv1WHp6+sWLFy0sLEJCQmiJxmvHSkxMlCmxtLR88eLFvXv3/Pz82EKeg8Jn/sjTctLK\n4Bmq9pDYAQCA5ui1dPKmTJnyzTffsH+mpKQQQtatW0fPVLIyMzMJIf/88w+3UP5hFvQLmOZe\nylSqCfYrliUQCIjchfky7t69u3DhwtOnT+fl5cm8Jf3vs8Pevn2rMNQmTZpwE7tKRctFP+jt\n7S1TTvPUly9fqohfJ8LCwr766qszZ87k5OTQs70HDx4sLy8PDQ01MTHhBqnB2rG4jzspLCx8\n/fr1gQMHli1bduDAgdjYWPbQIOE3KHzmjzwtJ608PqFqD4kdAABozs/Pjz0sxzCMhYVFo0aN\nhgwZ0rJlS7aOVCrNz88nhPzxxx8KF0Kfacyil6NxP15cXEwIYRuSV9kmVCxKmWvXrn355ZeF\nhYX+/v6hoaEuLi707oRRo0axC5dKpSUlJYQQNsVhWVhYaBwt94OFhYUKly+RSAgh8rcJ65yl\npWWPHj3i4uKOHj06ZMgQ8t/zsPQ10WLtlDExMalbt+7s2bNbtWrVuXPniRMnhoaG0vtdeA6K\n2vkjT8tJK49PqDqBxA4AADQXHx+v9hQSwzBmZmb5+fk3b97knkfjif6oVGFh4fv372vXrq2P\nJviYPXt2YWHhxIkTZR72ERERwQ1DKBSWlZXRTIKLZglaRsswjKmpaUFBgXwCR0vMzc35L01j\n4eHhcXFxBw8eHDJkSFZW1oULFxwdHdkL0fQ3FkFBQTY2Nh8+fEhMTKTnVXkOitr5I0/na8En\nVJ3AzRMAAKB39ILxFy9eaPZxeuZR/uN5eXnsWS0tm1Dr2rVrhJBx48ZxC58/fy5zWs3BwYEQ\nIn8tfFJSEvdPjaOlp1zlz2bSEmU/MqFbvXr1Mjc3P378eFFRUVxcXFlZ2cCBA+m5bEp/Y0Fv\nXmazZJ6Dwmf+yNPtWvAMVXtI7AAAQO/ozQT79u2TKX/8+PGxY8fo6UUV6JMpZO7EvH37toWF\nRcOGDXXShELyVz7RM56slStXytT09fUlhMg8wzYxMVEmFdM42s8//5wQcvToUZnyEydOsO/q\nm4mJSUhISEFBwV9//fX7778Tzv2wlD7GghBy586djIwMQkjdunW55WoHhc/8kfmIntZCbaja\nQ2IHAAB6N27cOJFIdODAgT179rCF6enp4eHhPXr0oMmBCuPHjzcyMtq7d++pU6doSX5+/qxZ\nswgh4eHhOmlCBr0k7u3bt/SaOUIIzQC4GVVMTMwff/xBjwbReyYIIb179yaErF69ml5iTwh5\n//792LFjbW1tddIhEyZMEAgEsbGxCQkJbOGlS5d27twpEolkDgjpD+32I0eOnD9/3sfHp23b\nttx3dTsWVEJCQr9+/QghAQEB9erVo4U8B4XP/JEfcd2uBc9QdUCHz8QDAIB/CZ7PtuXasGED\nfWr/559/HhERERwcTK9/HzJkCPtYV/pssL59+8p/fPny5YQQhmHatm3brVs3e3t7QkiTJk0K\nCgp00sTo0aMJIcuXL6d/FhQU0KfcNWzYsEuXLmfOnKG3RhoZGYWFhU2YMKF169YmJiZnzpyh\nPydQv379r7/+WiqV5ufn069wBweHfv36jRw50t7ePjQ0lN5bwD6gmGe0Cv3yyy+EEKFQ2Llz\n5zFjxnTq1EkgEDAMs27dOm41/g8orlOnTn1F7t+/L1X0CwpSqbS4uNjGxoZe/v/tt9/KL1yz\ntWNDatSoUbP/8vX1tbOzo+U+Pj7//PMPW5/noEh5zB/5Eee5FspmlEy/8Q9VS0jsAACg0jRI\n7KRSaUJCQp8+fZycnIRCoaWlpb+//+bNm7lf8yoSO6lUeuLEia5du9ra2opEIh8fn5kzZ+bk\n5OiqCZnETiqVxsXFeXt7i8ViDw+PixcvSqXS9evX169fXyQSOTk59e7d++bNm1KpNDk52c/P\nTywWN2vWjH4wLS0tIiLC0dFRIpE0bNhw6dKlJSUl9GTlxo0bKxWtMqdOnerZs6e9vb1IJHJ0\ndAwLC6MRcvFP7JS5fv26VElix/YYISQpKUnh8jVYO4UhGRkZ2draBgYG/vzzz3l5eTIf4Tko\nUh7zR37E+awFz8SuUqFqg5Hq7rQuAAAAKBQcHBwfH79nzx7601gAeoLHnQAAAOjMmzdvEhIS\nTExMevXqxRYWFRXRn1Kgt1YA6A8SOwAAAJ35559/Bg4caGVllZCQ0KhRI0JIRUXFt99+m5GR\n0bBhQ/a3SgH0BKdiAQAAdGnkyJHbtm0TiUSdOnWytra+c+fOo0ePTE1NT5w4ERAQUN3RgYFD\nYgcAAKBL5eXl27Zt+/XXX5OTk3NycpycnDp06DBr1ix6AA9Ar5DYAQAAABgIPKAYAAAAwEAg\nsQMAAAAwEEjsAAAAAAwEEjsAAAAAA4HEDgAAAMBAILEDAAAAMBBI7AAAAAAMBBI7AAAAAAOB\nxA4AAADAQCCxAwAAADAQSOwAAAAADAQSOwAAAAADgcQOAAAAwEAgsQMAAAAwEEjsAAAAAAwE\nEjsAAAAAA4HEDgAAAMBAILEDAAAAMBBI7AAAAAAMBBI7AAAAAAOBxA4AAADAQCCxAwAAADAQ\nSOwAAAAADAQSOwAAAAADgcQOAAAAwEAgsQMAAAAwEEjsAAAAAAwEEjvQVmxsLMMwDMM0btxY\ndc1JkybRmiNHjqyyYPiHV40+zSA3b97s6+trbGxsaWkZGhpa3eGAjul2fD/NOVxDoTNBG0js\n4H+sXLmSUcTIyMja2rpVq1bz589PT0+v7jA/dcq60dLSskmTJt98882LFy+qO0Y1jh8/Pnbs\n2IcPH5aUlOTm5qakpCisZgBr+u9U2fG1t7ev2gDVUzb3JBKJh4dHr169du7cWVFRUd1hAlQ1\nYXUHADWDVCrNycm5cePGjRs3YmJi4uPjW7duTd9q3br1ihUrCCGf4K6ffGLh5ebm3r9///79\n+5s3b963b1/37t11stikpKRGjRoRQkpLS4VC3WzUsbGx9IW3t/ecOXMcHR0r9XE9rWn10kc/\nVxctx1fep7OhFRcXv379+vXr10ePHo2NjY2Pjzc2NtZTW3qaEp9OZ0JNVLP3TaA/IpGoS5cu\n7J8FBQWPHj1KTU0lhGRmZvbt2zc5OVkikRBCfH19fX19qy1Qdao3PG43lpSUPH369Pnz54SQ\nvLy8AQMGJCcnOzs7a9/Kvn37tF+IjJcvX9IXU6ZMiYyMVFu/ata0eumjn6tLZcdXrWrc0CQS\nyejRo9k/MzMzT58+nZWVRQg5c+bMypUro6Ki9NS0nqbEJ75ThU8cEjtQzNLS8ujRo9ySsrKy\nBQsWREdHE0Jev3595MiRAQMGVFN0NYZ8N27atOmrr74ihOTl5W3ZsmXOnDnat7J//37tFyKj\npKSEvjA3N+dTv2rWtHrpo5+rS2XH91NmZma2du1absnHjx8/++yzp0+fEkL++OMP/SV2hjQl\nwGDgGjvgSygUfv/995aWlvTPu3fv0hcKr/OtqKhYtWpVo0aNJBKJs7PziBEj0tLSGIaRX2xF\nRcXKlSsbNWpkYmLi4uIyatSod+/excTE0GXK5I63bt0aNmyYp6ensbGxvb19t27djh8/rjps\n+fBWr15NSyIiIgghe/bsadmypZmZmb29/dChQ9+8eSOzBA0aVWHs2LGtWrWirxMTE1VXzsjI\nmDNnTrNmzSwtLSUSiZeX1+DBgxMSEtgK3bp1YxgmKSmJ/ikSiRiG2bNnjzbLHDduHMMwN2/e\npH+OGTOGYZjmzZvrcE3Vdil3jHJycvr3729paTlo0CC2QnJy8tixY318fCQSiaWlZfv27Tds\n2FBeXi4TQ6UaIsong+p+Li8v37x58xdffGFraysUCu3t7bt3737ixAmZYPQ91akqG18ZMhta\np06d6J/cY2nU0KFD6VshISHar69ClpaW7Nn/jx8/ct/iOVhE3RxTu+lpM8kV7lT5Rw7/dlIA\nDnphByHEzs5OYYXatWvTCtOnT6clW7dupSWNGjViq8nvzb28vNibYUeMGMHWlL9D1tvbe/bs\n2fT10KFD2ZpbtmxReBXL0qVL2TrywciX/Prrr7QkNDR03bp1MkurXbt2Xl5epRqtbDf279+f\nvvvll1+q6MOLFy/a2NjIN00I+fbbb2mdrl27yr+7e/duZYHxWSY9zCajWbNmOllTnl26adMm\nWtinT5+xY8fS1127dqXvxsXF0csAZHTv3r2srKxSDfGcDCr6uby8PDg4WP5dQkhMTAy3N3Q7\n1T+F8eWSmcMbN26kfzo7O1dUVLDVysrKbG1t6Vu7du3SZn1VxxYeHk7f7du3L1vIf7DUzjHV\nm56Wk1x+h8A/cgAkdvA/VO8r37x5w+6tNmzYQAvl90Hnzp1jdzoDBgz4888/9+zZ06BBA/az\nbGJ35swZtmanTp22bdu2evVqd3d39vQQW/P+/fsikYgQIhAIVq5c+c8//xw/ftzLy4sQwjBM\nYmKismBUlDRu3Njc3Lxz584zZ87k/me8du3aSjVa2W5s1qwZfXfIkCHKgnz79i37/ffZZ59t\n375979693IM6+/btoxH+5z//YQvPnz9/8eLFjIwMhVHxXObTp08vXrxYv359WhgVFXXx4sXb\nt2/rZE0rO44tW7Y0Nja2s7Nr3br1yJEjpVLpP//8Y2ZmRt/t16/f4cOH169fz17AN2/ePM0a\nUj0ZVPTzzp07aaGpqen+/fvv3r07c+ZMWmJubp6dnU0b0vlU/xTGl0tmDmdmZrLb+40bN9hq\n7M7BzMyMJs0638oyMjI2bdokEAjoEs6fP8++xXOw+MwxFVNC+0kuv0PgGTmAFIkdyFC2ryws\nLExMTGzbti1918rK6v379/Qt+X3Q0KFDaUmzZs3Ky8tp4bNnz+QTu8GDB9OSOnXqFBcX08J7\n9+6xJ23ZmuzRjsjISDYq9tSGigxJRQkhZPjw4fRwQm5uro+PDy0cNmxYpRrl341SqXT9+vVs\n61u2bFEW5PTp02mJt7d3fn4+5wNCewAAIABJREFU+/Hhw4fT8saNG9OShw8fsgssLS1VFlKl\nlimVSj/77DNauHnzZhXLrOyaVnYcCSFdunQpKChgK0+aNImWN23alJ1d8fHxtNDc3LywsFCz\nhlRPBmX9vGzZsp49e/bs2ZM9GFNeXu7g4EBrHjlyhBbqfKrLq+LxlSE/h9ljWgsXLmSrff31\n17Rw0KBBWq4vG5sy7u7ue/fu5X6E52DxnGPKpoT2k1y+M3lGDiCVSnHzBCiWlZWl8JI4QgjD\nML/88ouyMz6EkEuXLtEX/fv3NzL6/9dx+vj4+Pv7X7hwgVuTvfQnPDxcLBbT102aNGnXrt3l\ny5e5NU+ePElftG3btqioiL5u166dUCgsKytj362s7777jq6mubl5v379li1bRgh59eqVrhrN\nzc3t168ffV1aWvr48ePHjx/TP2vVqsW9aEzGoUOH6IuRI0eampqy5WPHjt2+fTsh5P79+69e\nvfLw8OC/svpYJovnmmrQpUuXLjUxMWH/ZL9fBw4cyM6uzp07Hzt2jL6mV0Fp0JDqyaDMjBkz\nZsyYwS0xMjJyd3fPyMgghKSlpdHCKpjqeh1fDQwYMIBeARYfH79gwQJa+Mcff9AXbKarp01b\nIBD4+/vLPMeO52DxnGPKaD/J5fGMHIDgrliorMaNGy9atKhPnz7KKkilUvZJCnXq1OG+1ahR\nI25iJ5VK2W/Nhg0bcms2bdqU+21XUlLy9u1b+joyMlL+6QwZGRlZWVl2dnaVWhdHR0dPT0/2\nT/Z1bm6urhotKSn5/fff5cudnZ0PHTqk8CIe+qlnz57R1zKPnud21MOHD/l/SetjmTLLV7um\nGnSphYWFn58ftxX6FBVCCHu5JyFEJBJ169aNW62yDameDKr98ccfMTExSUlJb968KSsr475F\nM4AqmOr6Hl8NhIWFjRs3rrS09MaNG+/evXNyckpKSqJ3qtra2tLjeTrZyiQSCffCwaKiouTk\n5PPnz+/du3fv3r07d+48ePAgm0yrHSyec0wZ7Se5MmojB6CQ2IFi3MeSlZWVsfdeqc7qCCFF\nRUXsf8ky/4NyjyLI1JR55oLMnzL3tSn0/v37yiZ27IkMSuYppvpo1MzMzNvbOyQk5JtvvlHx\nQW4yIdMV7KU/hF/OoddlqqBwTTXoUpmn33HDs7a2VrYQDRpSPRlU+OWXX9hzoDY2Nm5ubgKB\n4MmTJ4WFhWydKpjqVTy+fNjY2HTp0iU+Pl4qlf75558RERFHjhyhb/Xr149ehaaTrczMzGzl\nypUyhdevX+/YsWNeXl58fPyGDRumTJlC+A0WzzmmjPaTXCE+kQNQeNwJKEYfS0YdP36cPcs2\nZcoU1d8NEomEPXmRn5/PfSsnJ0emJnu2t6CggPuWTBMWFhbs60OHDim8qqBu3bqVW0N1dNKo\nzJVJeXl5f//995IlS1R/UXGblukKbpdaWVlptjq6WiYXnzXVoEvZAy0UN0eRmTNcVTZhcnJy\n2OfzzZ07NyMj4++//75z547Mwqtgqut7fDUzcOBA+oKe3GQTO/bUvP5GqlWrVuy/pvT/Up6D\nxXOOKaP9JJfHM3IACokd8PLzzz/T421v3rz59ttvVdRkGMbd3Z2+Zq+you7cuSNT083Njb5+\n9OgR9y32IXmUsbExu0xlP2qpc9XSKCUWi9ldtkxX3L9/n33dtGnT6l1mZWnfpRKJhF0Cd85I\npdKlS5d+//3333///cuXL6ts7G7evFlcXExfz5gxg96JWV5ezp4Vpapgqn8K4yuvd+/e9Njn\nqVOn3rx5c+3aNUKIm5vb559/TivodaRKS0vpC5qf8RwsnnNMWaP6WCOekQNQSOyAF09PT/aB\nW2vXrr1x44aKyuzNs3v37mWvBbl58+b169dlarZp04a+2LNnD7sXvnv3Lv0C4AoKCqIvdu3a\nxZ7Vevr0aVhY2Pjx49XeH6eZammUCg0NpS+2b9/OPWzA3mravn17+vue3HtcMjMzdbJM/dG+\nS9nrnHbv3s1eWvTXX3/NmTNn3rx53333HT1kovOxU9jP3EL2q3f79u3sQTJ2VlfBVP8UxleG\npaUlHa+PHz9GRUXR1eHekUD0tpXdvn377Nmz9DVNefkPFs85pmzT0+vcUx05ACF4QDH8LxVP\nNygqKmIvJfbz82OfBCt/Zz73p6V69OgRFxe3Zs0aV1dX9hzH8OHDaU32Pj5CSFBQ0J49e1au\nXMmtyT4D4t69e/SiHEJIv379Tp8+/fvvv7OHH+bPn68sGD4l1ObNm2n5Z599VqlGK9WNCsmH\nlJaWxv7+d7t27bZu3bpr1y72matGRkZnz56lNbOzs9k+7Nev34EDB7iPDePiv0ypHh6HQWk8\njqxHjx6xF8CFhIQcOnRo/fr1Li4utGTChAk6aUh+Mijs57dv37JfumPGjElKStq4caNEIqlX\nrx4t7NKlS1JSUnFxsc6nujy9jq9YLO6txPbt21X05K5du8j/kpmf2m9lEolkIsfYsWO7du3K\nPlzJyMjo2rVrUqmU/2DxnGPKNj3tJ7nMW/wjVzGU8O+BxA7+h+rvafZRBYSQFStW0EKFu6ew\nsDCZvbmvr+/UqVPpa/YRVlKplPuzQlS9evXGjRtHX3N/o4J96KiMsLAwFVmmNokdz0Yr243y\nFIaUkJDAPm+WSygUbtq0iftx9mgQ9d133ylriP8y9ZTYSTUdR66dO3cqfKx/p06duM9v06Yh\nhZNBYT/L/56Ev7+/zFUHz58/l+p6qiukv/FVISoqSkVP5ubmcm+iqlevnnwrWm5lKgiFQu4P\nM/AfLJ5zTNmmp+Ukl3+Lf+QAOBULlRAcHNyzZ0/6et68ea9fv1ZWc8+ePfPnz/fy8hKLxR4e\nHuPHj7948SL7CAnueaL9+/d/++23tWrVEovF7u7u48aNu3z5Mns1MXffOmbMmCtXrgwcONDV\n1VUkEllaWvr7+//2228HDhxQuA/ViWpplGrfvv3Dhw9nzpzZqFEjMzMziURSu3btMWPG3Lt3\nb8yYMdyaO3fu7Ny5s7m5uZmZma+vb6NGjbRfpv5o36VDhgy5ffv28OHDPT09xWKxhYVFu3bt\nNm7ceOLECe6d1zofO4X9vGHDhvnz59erV08ikfj4+MydO/fUqVPNmjWLjo52cHAwNjb28/Oj\nZ+6qYKp/CuMrw9zcnN1pEM5tE1y6HSmGYczNzZs2bTplypT79++zqTOpzGDxnGPKNj2dzz3+\nkQMwUqm0umMAkDV06FD6cz0zZsygz4kFMEiY6gCgW3iOHVSnu3fvHj58+OXLlyKRKCYmhhbm\n5eWxD2dv1apV9UUHoDOY6gBQNZDYQXViGIb9raGKiophw4bl5+cvW7aM/k6Ou7u7/GVJADUR\npjoAVA2cioVqNnPmzOXLl8uXW1tb//nnn+3atav6kAD0AVMdAKqAYOHChdUdA/yrde7cuVWr\nVnl5eTk5OUVFRSYmJvXr1x82bNj27dtV3AQAUONgqgNAFcAROwAAAAADgcedAAAAABgIJHYA\nAAAABgKJHQAAAICBQGIHAAAAYCCQ2AEAAAAYCCR2AAAAAAYCiR0AAACAgUBiBwAAAGAgkNgB\nAAAAGAgkdgAAAAAGAokdAAAAgIFAYgcAAABgIJDYAQAAABgIJHY6ExkZyTDM06dPDS+M8PBw\nhmFev36tw2XqA40zLS2tugOpwYRCYdu2bVVU2LVrl7u7u1AonDFjhl4j+UQ2qE/Hp9YhVb+5\nfWo9AJSexkXtvgiUQWL3PwICAhiGefDggUz5pEmTGIZZvHixTPmJEycYhhkwYEBVBajADz/8\nYAB7Op2sRfPmzbt27WpsbKyTkKrRJzumOTk5kZGReXl53333XdeuXXW78E92ravLJ94hVbC5\nVVkPSKXSAwcOhIaGurq6GhsbOzo6tmzZcsmSJe/evWPr7Ny5k5FjbGzs4+MzZsyY58+f02oX\nLlwwMjJq06ZNRUWFwjViGGbSpEkyTYeFhbm7uxsbG1tbWzdv3nzmzJmvXr2S//iHDx/+7//+\nz8vLy9jY2NvbOzQ09OrVq7ruDPU+8ZkJRAocS5YsIYT8/PPPMuV169YlhLRv316m/JtvviGE\nbN26VSqVjh49mhCSnJxcNaFSb9++JYQcO3aMLdFHGAMHDiSEvHr1SofL5JJfi3+z6u0NgUDQ\npk0bZe9ev36dEDJhwgSdt1s1M7kGQYdUWQ98+PAhKCiIEGJqatqrV69JkyYNGjSodu3ahBAH\nB4e//vqLVtuxYwchxN/fP4pj7NixLVq0IIRYWVn9/ffftOZXX31FCFm9erVMQ//884+JiYmH\nh8fHjx9pSUZGxueff04IMTc3p02PHj26adOmhBBjY2P6zcLKysqqVasWIaRnz57z5s0bMmSI\nUCiUSCT37t3TbYeoVmXjonpfBCoIqyh/rCF69Ogxd+7cEydO0IyNevHiRXJycqNGjRITE3Ny\ncqysrNi3Tp48yTBM9+7dqyNYQgihX7Q1nWGsha58yr1RVFRECLGwsND5kj/lta4W6JAq64Eh\nQ4acPn26d+/emzdvdnBwoIUVFRWbNm2aNGlS7969Hz165OjoSMuDgoIWLlwos4SffvppxowZ\nc+bMOXLkCCFk2bJlR48enTt3Lj0Ox1abOHFiYWHhxo0b6RZUXl7et2/fv/76a9CgQWvXrrW1\ntWVrnjx5cvDgwaNGjbK3tw8ODqaF8+fPT0lJWbNmDXvAr0+fPn379p01a1Z8fLw+ekYhzMwa\noLozy0+Om5ubRCIpKChgSzZu3EgI2bx5MyHk4MGDbHlqaiohpGXLlvRP+l/Ls2fPfvjhB29v\nb7FY7OHhsXjx4oqKCvYjaWlpEyZM8PT0FIlE9vb2vXv3TkxMZN8dNGgQISQ3N3fmzJleXl5i\nsdjd3f2XX37hLoGrZ8+e3KG8ePGiTsKQR4/YPXv27JtvvnF1dRWLxfXr11+3bh23zrVr10JD\nQ+3s7EQikZeX19ChQ58/f86tkJqaOnr0aFdXV1NT06ZNm65cubK0tFTZWqgNkob07t27oKAg\niURy+PBhtjA1NZVnSPJUf0Rhoxr0Z1FR0bJly5o2bWppaWlubt6kSZNly5aVl5er6I2UlJSR\nI0e6urqKRCI7O7tevXpdu3ZN+8Di4+P9/PwkEomDg8Po0aM/fPig4r9kmXOvX331lTaxcWk2\nkzVe68qOF90wP3z4MHbsWEdHRxMTkzZt2ly7di0/P3/q1Kmurq5mZmbt2rW7efMm91Oqu0X1\nxq5Zh6iYVwrRVj58+MCWlJaWEkI6derEZ4HczY3Pvuvo0aOtWrUyMTFxcnKaMmVKQUGBu7t7\nixYtVMRWBTu3Y8eOEUL8/Pzo7kjGkiVLOnXqdPnyZel/j9gtWLBAvlpxcbFYLLa1tWVLaIYX\nGhrKluzdu5cQMnToULZk9+7dhJAOHToo3MNfuHCBYZjatWuzHT5t2rROnTqVlJSwdSoqKkxM\nTLy8vJStnWZTV0UfajwuqjcHaSX3RaAaEjtZdI4eP36cLenTp4+Tk1NBQYFYLGa/zKRS6bZt\n2wgh8+fP534wIiKiRYsWS5cuXbZsmYeHByFk165dtEJ6erqXl5eVlVVUVNSOHTuio6PpRRXn\nz5+nFUaMGEEI6dq167hx465cuZKQkNClSxdCyJYtWxSGeuXKlWHDhtEY4uLisrKydBKGPLoH\n79mzZ2BgYHR09Pz58318fGiySyvcuHFDIpG4urouXrx406ZNs2bNsrCwcHR0zMzMZBt1c3Oz\nsrKaPHnyTz/9RP8HHT16tLK1UBsk/cjgwYO7d+8eHR1NT4Jwv2nUhiRP7UcUNqpBf0ZERNDl\nxMTEbNiwISwsjBAyceJEZb3x8uVLR0dHc3PzGTNmxMbGLlmyxM3NzdjYmE37NAvs0qVLAoHA\n1dU1Ojp68+bNQ4cODQwMFIlEynamly9fjo6OJoT06dMnLi7uzp07GscmQ7OZrNlaazBedMMM\nCgpatGjRrVu3YmNjJRKJp6dncHBwVFTUjRs3Dhw4YG1t7eTkxH7pqu0W1Ru7Zh2iYl4ppDax\nU71A7uamdt914cIFgUDg7Oy8aNGidevWdejQISQkxMrKStlkq7KdG019fv/9d2UVWCoSu6Ki\nIqFQ6OHhwS2k/UOPBWRnZ7u4uDg4OHD3P/RUj4rY6AniCxcuKKtQVFQkEon8/f2VVdBg6qru\nQ83GRe3mUNl9EaiGxE7W77//Tgj5+uuv6Z9lZWXW1tbh4eFSqfSLL77w9vZmaw4ZMoQQcvXq\nVfonndwBAQHsFnLz5k1CSEhICP1z/PjxQqHw+vXr7BJevnxpYWEhc8xv0KBBbIVnz54RQoKD\ng5VFu3TpUqLocgdtwpBH91CBgYHs/44pKSlisZjtjfXr1/v5+Z07d479yJo1awgha9asYRsl\nhJw4cYKtQL9U7t+/r3At1AY5atQoQkiXLl24ByS43zRqQ5Kn9iMKG9WgP01NTdu1a8ct+frr\nr/v27VtWVqawN+jemXu0OCkpSSAQtG3bVpvA6PcK93jGhAkTCCEqdqYXL14khERFRWkZmzwN\nZrJma63BeNFIxo8fz5bQ+6X69evHlkydOpUQkpCQwLNb1G7sGnSI6nklT21ip3qB3M1N7ep0\n7tyZEMJ2e1lZ2Zdffql6slXNzs3Hx4dhmJycHGUVWCoSu0WLFhFCRo0axS189+6dra2tm5tb\nTk4O3bJ2797NrWBra2tiYqLwSCH1008/EUJ++OEHZRVWrVqlep+mwdRV24cajIvazUGDfRGo\ngGvsZHXu3FkkEp04cYL+mZiYmJ2dTf9zCgoKmjdv3tOnT+vUqSOVSk+fPu3g4NCqVSvux6dP\nny4SiejrFi1aCAQCeqmpVCrdv39/06ZN3d3d2QcEiESi9u3bnzhxIi8vz9zcnBbSbYDy8fEx\nNTXV4Dkj2ochb9y4cUZG//82ai8vL39//3Pnzr169crDw2P8+PE0dSOElJaWlpeX+/r6EkJS\nUlJoo/v27fPw8KA7d2r16tXTp093cnKSb4hPkAzD0L5iQ5KhOiTNPiLfqGb9KRKJXrx4kZ6e\nzl6488svvyiLSiqVHjp0yMnJKTQ0lC1s2LBhu3btLl26lJWVZWdnp0Fgpqam58+fr127NncC\njxkzZv369coi0VVslaJsJhONhsPMzEzj+d+nTx/2Nb2bqnfv3mxJ/fr1CSH08gw+3UILNdjY\nVXRIpeYVH5VdoIrVuXjxYoMGDVq2bEn/FAgEUVFR586d0yAq3e7c3r17Z2VlZWlpybP18+fP\nc6+xy87Ovnbt2tWrV+vUqSPz2ARHR8cVK1aMGDGif//+p0+f7tWrV3h4OPtuWVnZ+/fva9Wq\nJRQq/Rb28vIihCh7oMyFCxdmzJgREBAwbtw41TFXaupqvIGoGBfVm4ONjY32+yLgQmIny8LC\nIiAggE1ZaIZHM5LOnTvPmzfvxIkTderUuXfv3rt374YNGybzdUU3G4phGHNz88LCQkJIenp6\nZmZmZmami4uLfKMvX76kOQQhxNPTk/uWSCSi/0ZXivZhyKP3arF8fHzOnTv34sULetR9x44d\nv/76671797Kzs9k6ZWVlhJDU1NSsrCw/Pz/6Tcx+nJ7Plcc/SLpLUkZFSNp8hNuoZv25ePHi\nqVOn1q1bt3fv3l9++WWXLl3c3NyUhZSWlpaTk/PZZ59xe4+GcenSpSdPnrRr106DwKysrAoL\nC2WGoEGDBsrC0GFslaJsJnPbYl+rXWs7OzuN5z93jOiXMbeEfqXRTZV/t2iwsavokErNKz4q\nu0Blq5OdnV1UVFSnTh3uu+3bt9csKt3u3IyMjMrLy/m3fuHChQsXLnBLHB0d58yZM336dO7d\nD9Tw4cN37dp14sQJS0vLmJgY7lv0aSkKH4nCou8KBAL5t3bv3h0REdG4cePDhw+rSA0p/lNX\nmy8IZeOidnPw9PTUfl8EXEjsFOjRo8e5c+dOnjw5evToU6dO1atXj+6wWrZsaW1tffLkyYkT\nJ546dYrWlPmssqc65ebmEkKaN29Oj2PLcHV1ZV+z//RoQ/sw5Mn8U2tqakr+e5vknDlzli5d\n2rJlyxUrVnh7exsbGz948CAyMpLWpJs3/+dd8Q+Se4eyDNUhafMRbqOa9eeUKVMaN268Zs2a\ngwcP7tixg95YvX79evoPuoz8/HxCiJmZmUy5iYkJ+64GgWVkZBBCJBIJt1wikcjsfFXTLLZK\nUTttKrXWmZmZqiuoaEh+w1S2qfLvFg02dhUdUql5xUdlF6hsdbKyssh/9xgsCwsLhSmLWrrd\nubm6uj5+/DgzM9Pe3p5P6wsWLGCP2BUWFvr6+mZlZY0fP14+q6O+/vrrEydODBgwQCYnFggE\njo6OqampRUVFMpsh68WLF/KRS6XShQsXLl68uFu3bvv27eNzizr/qavNF4SycVG7ORQUFBCt\n90XAhcROgR49esyYMePMmTMDBgy4du0ae6BbIBB07Njx7NmzFRUVp06dEggE/J/Rym5+3bp1\n00vQ+g9D5kgJ3RpNTU2LiopWrlzp4eFx7tw59kB9Tk4OW9PZ2ZkQwj0Gpr8gKbUh6eQj2oTa\nsWPHjh07FhcXX7x4cefOndu3bw8KCnrw4IFYLJapSYPhZgMULVG2W1cbWF5eHvlvXs4tlEql\n/NdCs9j0R+1aFxcXq66gE9XYLfznlUIlJSW6XSBF0wiZyVZQUFCpQ2VqabYxtm/f/vHjx3/8\n8Qe9U0SGVCr9+++/ZU5WsExMTFauXBkaGjp58uS4uDiFdWjyqjCFbd++fVxc3OnTp9kHmsg4\nefIkISQwMJAbT2Rk5JYtWyZPnrxixQrNMmMV9PE9pXZzoBmelvsi4MIvTyjg6+tbq1at8+fP\nX758uby8nF5gRwUFBWVnZ9+6dSshIaFdu3Y2NjY8l+nk5GRvb//o0SOZ/IYeOKky2oTx8OFD\n7p/04mgfH5+0tLTCwsKWLVtyL7/gnq0wMzNzcHB4+PAh9zTT48eP165dK/8jH1oGSakNSScf\n0T5UY2PjoKCg2NjYcePGPX369M6dO/J1nJ2dbW1tHz58KLObS0pKYhhG2SlOtYE5OzuLxWL2\ncfnUvXv3+IStZWz6o3atq2YzrPZu4TOvyP+eg6Nk5kNlF6iMs7OzkZERPf7EunbtWqUWopZm\ng0vzucWLF9ODVTLWr1/frFmzdevWKft47969u3fvfujQoUOHDlU2YHr3z4IFCxSef7906dKZ\nM2eaNm3KvfLs66+/3rJlS3R09OrVq3We1RH9bCBqNwed7IuAC4mdYt27d09NTd2xY4dAIKB3\nb1H0Yrt169bl5+fLn4dVrX///kVFRcuXL2dLMjIymjZt2qtXL43jpNu2zLE0PYWxZcsW9vXr\n168vX77s6+vr7Ozs5OTEMAz3poQ7d+5s376dcP4J6927d1ZWFn1ADLVw4cLJkyfTIyjya6Fl\nX/EJSfuPaBbq1atX3dzc6JJZ9EpN+kUr3xt9+vRJTU09fPgwN7bExMSOHTtaW1trFphQKGzf\nvv3Tp0+5jxtV8QWmjGaxydNgJiukdjj0sRnK075bKtshaueVPHodFfcfNu7HNVigMmKxuGXL\nlvfu3Xv06BEtKS8v//HHH1V/qmp2boGBgQMHDkxJSencuTP9Z5UqKytbvXr11KlTXVxcBg8e\nrKLRVatWGRsbT548WWFqqEJwcHBwcPCtW7fCwsLS09O5b505cyY0NFQgEKxdu5YtPHjw4KpV\nq6ZOnTp79uxKNVQpavtQg3FRvTnw2ReVlJTcuXMHv2PGE07FKtajR4+YmJh9+/a1bt2aexFP\nnTp1atWqtWvXLqLoAjvVFi5cGB8fHx0dnZqa+sUXX7x9+3bDhg1ZWVlTpkzROE56wekPP/zw\n/PnzwMBAmVt0dRtGcXFxWFhY9+7dCwoKNm3aVFJSMm/ePEKIiYlJz549jx49Om7cuA4dOiQl\nJa1du/Y///lPSEhIfHz87t27Q0JCFixYcPTo0fHjx9+9e9fLy+vChQtHjx4dPny4n5+fwrXQ\nsq/4hCRzzQefj+ikP1u2bGlraztmzJhLly41b96cYZgbN27ExsYGBAQ0b95cYW8sWrTo6NGj\nw4YNmzJlSv369VNSUtatW2dubq76FkW1gc2cOfPChQvBwcGjRo2ys7O7cOFCQUFBZS+G0yw2\neRrMZIXUrrU+NkN52ndLZTtE7bySN3z48JiYmG+++Wb58uWmpqaHDx++cuUKezJOgwWqMGPG\njP79+/fo0WPChAmWlpY7d+708fFRfQFlle3ctmzZUlxcfOjQoQYNGgQGBtarVy87O/vq1asv\nXrzw8fE5fvy46jMzdevWnT59enR09Ny5c1evXq02SK5du3YNHDgwPj7e29u7Y8eOtWrVKioq\nunnz5u3bt83Nzfft28c9Dztz5kxCSEVFxaxZs2SWExUVxf/0kWpq+1CDcVG7OajdF718+bJF\nixb+/v6XLl3SyWoauCp8tEpNkp+fT6/lnDdvnsxbY8aMIYS4ubnJlCv8vTwrK6tGjRqxf6am\npo4fP97Dw0MoFFpbW4eEhHCfvs1nCTJKSkr69u1rYmJiY2Ozf/9+nYQhj94b//79+2nTprm4\nuIjF4oYNG3J/xzA9PX3w4MEODg5WVlYdO3akj51ctGiRubm5s7MzfdJVSkrK0KFDHR0dRSKR\nj4/Pzz//zD5eS34tNOsr7oO1+IQkQ+1HlP0kYmX7Mysra9q0abVr1zY1NbWysmrWrFl0dHRu\nbq6K3nj58mVERISLi4tQKHR0dAwPD09KSlLdG3wC27NnT5MmTcRisYODw6hRoz58+ODh4aHs\nxwCkip5jp3FsMjSYyRqvdWXHS76hBQsWEM7vgkilUvrLNNwHlWnQLdy106BDVM8rhWJjY319\nfemvQYwdOzY7O9vV1TUgIIDPAuWfY6d6t/Pbb7/Vr19fLBZ7eXnNnTu3pKRELBbL/wA3q2p2\nbqwjR4706dOH/jSChYXLJbEDAAAgAElEQVRFmzZt1q9fz/0JIhXPscvPz/fw8DAyMpJvi95m\nx32yvby4uLg+ffq4ubmJxWJLS8vmzZvPnj07LS1NppqK73Flv6mj2dRV3YeajYvqzUGqbl+U\nnJxMCAkMDFTRjcBipLg+EQAAqtbHjx+trKxCQkK4Z+gAlNmyZcuRI0c0uJbxXwjX2AEAgH5t\n3bq1Q4cO9AcJqNjYWEJIQEBAtcUENcqff/7p7+9f3VHUDLjGDgAA9MvX1/fq1avBwcHjx493\ndXW9ffv2pk2bPD096ZUtAKoVFhY2bdoUs4UnnIoFAAC9S0hIWLJkyc2bNz98+ODo6Ni1a9fv\nvvtO9TNvAUADSOwAAAAADASusQMAAAAwEEjsAAAAAAwEEjsAAAAAA4HEDgAAAMBAILEDAAAA\nMBBI7AAAAAAMBBI7AAAAAAOBxA4AAADAQCCxAwAAADAQSOwAaqrIyEiGYZ4+fVrdgYAB2rVr\nl7u7u1AonDFjhsIK4eHhDMO8fv2afZ2WlqZ2sfxraoYb1adM3/0A/2ZI7ABqjB9++AFpXE1X\nIwYxJycnMjIyLy/vu+++69q1q9r6zZs379q1q7GxsQ5rfrJ0MoIG0A/wyUJiB1AzpKamzp49\n+9PPCUCFmjKIycnJhYWFQ4YMmT17dlBQkNr6s2bNOn78uI2NjQ5rfpp0NYI1vR/gU4bEDqBm\nuH79enWHANqqKYNYVFRECLGwsKjuQD45NWUE4d8MiR3o0YsXLyIiItzc3MRisb29fUhISGJi\nIvvu4MGDGYbJy8uLioqqVauWsbGxh4fHihUrpFKpimUmJiaGhYXZ29uLxeJatWoNGzYsJSWF\nvhUQEGBkZPT27Vtu/devXxsZGX3xxRf0z3fv3k2cONHLy0ssFjs4OISGhnL31PTCl/T09M6d\nO5uYmBw5ckRto1R8fHzr1q1NTU2dnZ2nTp1aWFjo4eHh5+fHVlDdrlrBwcG9e/cmhHTv3p1h\nmEuXLrFvGRkZ/fjjjz4+PsbGxp6ent999x23AyvbLh2U7Ozsr776ysnJydTUtG3btomJiQUF\nBdOmTXNzczM3N2/fvv2tW7e4n1LbiuoO1GAmhIWFMQyTmpoaGRnp5ORkbGzcoEGDmJgY/lEp\nG+u0tLTIyEg3NzczM7NmzZqtWrWqrKyM5zJVr4iyQayW2aVi2+zWrVtgYCAh5Mcff2QYZty4\ncaoXRThXjKndBrnXlvEZd7XrrlBJScn06dPd3NzoxFi/fj33XbUdrmwOKBtBDWaazDV2akMC\nqAQpgH68fPnS0dHR3Nx8xowZsbGxS5YsofvZixcv0gojRowghHTt2nXcuHFXrlxJSEjo0qUL\nIWTLli3Klnnjxg2JROLq6rp48eJNmzbNmjXLwsLC0dExMzNTKpWuW7eOELJmzRruR1asWEEI\n2bRpk1QqTU9P9/LysrKyioqK2rFjR3R0tLu7u7Gx8fnz52nlYcOGEUIGDx7cvXv36Ojov//+\nW22jUqn0woULAoHA2dl50aJF69at69ChQ0hIiJWVVZs2bWgFte2qdeXKFRrb/Pnz4+LisrKy\npFLp6NGjCSEREREtWrRYunTpsmXLPDw8CCG7du3SuF06KEFBQYsWLbp161ZsbKxEIvH09AwO\nDo6Kirpx48aBAwesra2dnJxKSkp4tqK2AzWYCQMHDiSEtG7dOioqKiEh4eLFi507dyaEbN68\nmWdUCsc6PT3dzc3Nyspq8uTJP/30U3BwMCFk9OjRPJepekUUDmK1zC7V2+bly5ejo6MJIX36\n9ImLi7tz546KIXj16hX7OjU1Ve02yNbkM+5q111ZVD179gwMDIyOjp4/f76Pjw93YqjtcBVz\nQOEIajbTuP2gNiSASkFiB/pC99oHDx5kS5KSkgQCQdu2bemfNC8ZNGgQW+HZs2eEkODgYGXL\nXL9+vZ+f37lz59iSNWvWsF8k6enpQqGwQ4cO3I+0a9fO2Nj4w4cPUql0/PjxQqHw+vXr7Lsv\nX760sLBo2bIl/XPUqFGEkC5dupSXl/NsVCqV0pSCXWxZWdmXX35JCGG/ftS2y8fSpUsJIceO\nHWNLaAcGBASwOdbNmzcJISEhIRq3S5c5fvx4tmTAgAGEkH79+rElU6dOJYQkJCTwbEVtB2ow\nE+j3Ivcj2dnZxsbGtWrV4hmVwrEeP348IeTEiRNsSc+ePQkh9+/f57NMtSsiP4jVMrvUbpsX\nL14khERFRSlbglRJYqd2G+QmNGq7S+26K4sqMDCQHdaUlBSxWOzt7U3/VNvhqueA/AhqNtO4\n/aA2JIBKQWIHelFRUWFlZeXk5FRRUcEtDwgIIITQ/0Tpbv348ePcCqamps2bN+fTRElJSWFh\n4ZkzZwgh06dPp4XdunUTCATv3r2jf7569YphmD59+tCQ7O3t/fz8Uv8XvekvNzeXDek///lP\npRqVSCQNGjTgVjt+/Dj79cOnXT6UJXZxcXFsSUVFhUAgoN8omrVLl3nq1Cm2ZO7cuYSQHTt2\nsCX0xNaBAwc0aEVhB2owE+j34uHDh7mF9DL/t2/fajbWFRUVdnZ2Hh4e3En77Nmzs2fPZmRk\n8F+mihWRH0S1naPz2cVn29Q4sZOq3AalihI7Fd2let1VRCWzCdN08OXLlzKV5Ttc9RyQyo2g\nxnsVbj+oDgmgsoQEQA/S0tJycnI+++wzhmG45fXr17906dKTJ0/atWtHSzw9PbkVRCJRaWmp\niiXv2LHj119/vXfvXnZ2NlvIXgU1aNCg48ePHzp0aOzYseS/ycfQoUMJIenp6ZmZmZmZmS4u\nLvKLffnypa+vLxsk/0azs7OLiorq1KnDrd++fXv2Nf92NVO3bl32NcMw5ubmhYWFWrbr5ubG\nvhYKhTIlIpGIEEKHiWcrqkeNquxMIITUq1dPPuy0tDQjIyMNxjo1NTUrK8vPz487aX18fOi5\nvHfv3vFcpg6ntD5mF/9tUzMqtkGFlHWX2nVXoWnTptw/fXx8zp079+LFC3qtgooOVz0H5Gmz\nV+His4EA8ITEDvQiPz+fEGJmZiZTbmJiwr5L0SyBpzlz5ixdurRly5YrVqzw9vY2NjZ+8OBB\nZGQkWyEsLGzcuHG///47/VLZt2+fjY0NPZOSm5tLCGnevDn9n1uGq6sr+9rKyop/o1lZWYQQ\nU1NT7kcsLCwEAgF9zb9dzSh7FJY27coPirJh4tOK2lFT3YQKMt1O51t2dja9nbOyY00TYu37\nU4dTWh+zi/+2qRkV26BCyrpL7bqrYGlpyf2TLoTe6qu6w1XPAXka71W4eG4gADwhsQO9MDc3\nJ4q+JGiJZo9RKCoqWrlypYeHx7lz5+jyCSE5OTncOhYWFj179jx06NCHDx/y8/OvXr06ZswY\nsVjMbbRbt246bJR+LdHvDFZBQUF5eTkbkgbtaq9q2lXbCp9R05jMBKOLtbOz02zdnZ2dCSHc\nQyZc+ujPapld+tg2uVRsg5Widt1VoPkZ91OEEFNTU7UdrnoOyNN+Vuh1A4F/JzzuBPTC2dnZ\n1tb24cOH0v99YkVSUhLDMKrPSiiTlpZWWFjYsmVLdvdHCLlw4YJMtcGDB5eVlcXHx8ucA3Jy\ncrK3t3/06JHMXjsjI0ObRp2dnY2MjF68eMH91LVr19jXmrWrvappV20rPEdNMw8fPuT+mZyc\nTAhxcXHRbN3NzMwcHBwePnzIPXP6+PHjtWvXPnjwQB/9WS2zSx/bpgxl22ClqF13FWQmBr0n\nw8fHR22Hq54D8g1pPyv0uoHAvxMSO9CXPn36pKamHj58mC25c+dOYmJix44dra2tNVigk5MT\nwzDcxzvduXNn+/bt5H//re/Ro4eVldWxY8cOHTrk5eVFLwmn+vfvX1RUtHz5crYkIyOjadOm\nvXr10rhRsVjcsmXLe/fuPXr0iFYoLy//8ccfuQtR225JScmdO3dUP86enoGSORShmgbrqwHV\nrfAcNc1s2bKFff3kyZPr16/Xr1/fwcFBbVTK9O7dOysra9u2bWzJwoULJ0+eXFxcrPEyuWQG\nsWpmlzydb5syVGyD/PFZd2W4E+P169eXL1/29fV1dnbmMxtVzwH5zVDLWaHXDQT+parzzg0w\naG/evHF2djY3N58zZ862bdsWLVrk6OhoYWFx9+5dWoHeLJacnMz9lJWVVaNGjZQtkz5T6quv\nvtq9e/e8efNsbGz+/PNPoVDo7u6+a9euvLw8Wi0iIsLW1lYoFM6ZM4f78Xfv3tErtSMiImJj\nY6Ojoz09PUUi0cmTJ1WEpLbR/fv3E0K8vb2XL1++cePGwMDAESNGGBsbs/fuqW2XHmry9/dX\n0Z8HDhwghLRu3frnn39OTEzk04Fq25Unv8wFCxYQQtinD0ql0s2bNxNCdu/ezbMVtR2owUyg\nNxUGBQUFBwdv2LBh/fr1tWrVIpx7DzUb61evXjk7OwuFwkmTJi1fvpxGPnz4cG2WyV0R+UGs\ngtklT+22qc1dsZSybVD+rlgV3aV23ZVF1aVLl9DQ0I0bN65YsaJhw4bc6aq2w1XPAfkR1GxW\ncPuB524NgCckdqBHL1++jIiIcHFxEQqFjo6O4eHhSUlJ7LsafJ2np6cPHjzYwcHBysqqY8eO\nNNtYtGiRubm5s7Mz+71y8uRJ+n8LtzkqNTV1/PjxHh4eQqHQ2to6JCTk2rVrqkPi0+hvv/1W\nv359sVjs5eU1d+7ckpISsVjcvn17nu3SxC4wMFBFZ5aUlPTt29fExMTGxmb//v08O1B1u/I0\nSOzUtqK2AzVO7JKTk6dNm+bq6ioWi319fWNjY7l1NBhrqVSakpIydOhQR0dHkUjk4+Pz888/\nl5WVabNM7orID2IVzC6FVG+b2id2yrbBSiV2fNZdBv1liPfv30+bNs3FxUUsFjds2HDr1q1s\nBT4drmIOyI+gVKNZwe0Hnrs1AJ4YqcqfbwIADXz8+NHKyiokJIR7tku1LVu2HDly5NChQ3oN\nzGCEh4fv3bv31atX7u7u1R1LVdNgdhmMf/O6A/CEa+wAtLV169YOHTrQX32gYmNjCSGVurTo\nzz//9Pf313lsUNPpZHbVUP/mdQfQGB53AqAtX1/fq1evBgcHjx8/3tXV9fbt25s2bfL09Bwz\nZgzPJRQWFjb9f+ydd1wUx9vAZ7nGwR29Hh5HC1EMVYwNFCkSlAjWWLBQgg2DBgU1lqARiTUG\nBRKjIWAEI7YYo8kvUmxYEKJGBSl2KUoOQhW42/ePed3PZu9udzlQlOz3r9u5Z2Znnpl55tnZ\nmVknJ/ryDP8dut+63l7+y2VnYFAb5lUsA0MPcOHChY0bN167dk0qlZqYmPj7+2/YsKH7hw8z\nqOI/9Sr2v9y6/stlZ2BQD8axY2BgYGBgYGDoIzBr7BgYGBgYGBgY+giMY8fAwMDAwMDA0Edg\nHDsGBgYGBgYGhj4C49gxMDAwMDAwMPQRGMeOgYGBgYGBgaGPwDh2DAwMDAwMDAx9BMaxY2Bg\nYGBgYGDoIzCOHQMDAwMDAwNDH4Fx7BgYGBgYGBgY+gh9x7Fjs9lDhw7t7Vy8lUybNg1BkOrq\naqX/RkREIAhSXl7+mnP1xkKurjcHfI94W/IMAIiKiuLxePjvvvc9oqKikJekpqb2dnYY3kT6\n9++PNZL79+/3dnb+06xdu5bL5ebn5/d2RujSdxw7BrVxcXHx9/fn8XjwMjExsftuXElJyaxZ\ns8zNzTkcjrGx8YQJE65cuUIir6mpiahAqVH79NNPEQSJiIjAB1ZWVkZGRtra2vJ4PGNj4+Dg\nYPxNKysr/fz89PT0LCwsYmNj5XI5Ic2JEyc6Ojp2dHSQF42grreC3srzsmXLEATR09NrbW2l\nI5+Zmbl79+6tW7cOGjQIhjx48CA8PNzCwoLL5UokkpiYmMbGRkw+LS1NaZv54osvoEBPVToE\nRdHs7Ozg4GCRSMTj8UxMTNzd3Tdu3FhTU4PJlJSUIAjywQcfUKa2d+/eEydOjB07Fgvp6OhY\nuXIli8Vyd3dXGoVSgEB9ff2SJUusrKy4XK5IJIqIiKiqqsILkKuXjgB5p6MjQJNTp06NGjVK\nKBTq6el5e3vn5eWRy1Pel9xG0bFIXSqaUpMFVNdpamrqiRMnxo8fT62a3qOrdh5CWZVdbed0\nIO8L5JZk3bp1w4YNmzp16rNnz3oqP68WtK/AYrGGDBnS27l463n69CkA4NSpU1hIeHg4AKCs\nrIx+In/99ZdQKDQwMFi7dm16evqGDRvMzMzYbPaZM2dURVm9enWcAlZWVpqamnV1dQThq1ev\nslgsAEB4eDgWWFJSYmhoyOVyQ0JC1q1bN3PmTA6Hw+FwLl68CAUGDx7s5+fX0NBQXFysra39\nzTff4NPMzs7W0NC4fPky/WK+4fR6j3jx4oWRkZGGhgYA4IcffqCUb2xsNDQ0HDp0KBZSWVlp\nZGSEIMiUKVPWr18PvaWhQ4e2t7dDgR07dgAApk+fTmg5OTk5UKAHK10qlfr6+gIAtLS0Pvzw\nw6ioqOnTp9va2gIAjI2Nz549C8Xu3LkDAPD39ydJatGiRQCAe/fu4QNv377t5uYmFAo1NDQG\nDRqkGItSgMCLFy/c3NwAAJMmTdq4cWNYWBiHw7G2tv7777+hAKV6KQUoOx2lAE327dsHALC1\ntV29evWyZcuMjY25XO6FCxdUyVPel9JGUVqkLhVNqclCadRpdHS0YlN5Q1DDzqM0qrKr7ZwO\nlH2B0pKUlZWxWKywsLAeyc+rhnHsGP7F8ePHu+/YzZgxAwCAdQkURa9fvw4A8PLyop9IYWEh\ni8X64osvCOEdHR0uLi7Ozs4EK+nn54cgSH5+PhZy5MgRAMDUqVNRFK2srAQAnDx5Ev41ceLE\n0aNHY5JSqdTMzGzp0qX0s/fm0+s94sCBAwCAhQsXIgji4eFBKZ+YmIivIxRFp02bBgDYs2cP\nFgLHud27d8PLdevWAQCuXr2qNMGerXQ4tRYUFFRbW4sFymSylJQUFoulr69fU1ODquvYNTQ0\n8Pl8d3f3srIyHo+nOJ5RCiiyfft2AMCXX36JhRw8eBAAEBMTAy8p1UspQN7p6AjQoaamRiAQ\nuLq6NjU1wZCysjKBQLBw4UJVUSjvq4aNIlgk+kVTZbLo1Omb7NipoUPKqlSjndOBsi+QWxLI\njBkz2Gx2ZWVlj2TplfK2OnYnT550c3PT1NQ0NjYODw+XSqWEYay6unrhwoWWlpYcDsfIyCgo\nKOjKlSv4FKqqqsLDw0UikZaWlpOT01dffdXR0QH/+uijjwAANTU1vr6+mpqax48fp5nm5cuX\ng4ODDQ0NORyORCIJCQnBd8i2trbNmzc7OTnp6OgIBAJHR8fNmzfLZDKaeaaMjkckEjk6OuJD\nHBwcCKMmHHczMjJgeauqqsaNG4efzT137hz60rGrqKhITEy0trbmcrlisXj9+vVyuVxV7QwZ\nMgQAgD3WQ3R0dKysrFRFIdDZ2enq6jpgwIAXL14Q/kpMTEQQ5NSpUwQruXr16pUrVxIS4XA4\nzs7OKIrm5OQAAG7evAn/iomJwWcmPDzc2toaszXkYOpCUXT69OkAgMbGxtjYWIlEwuVy+/Xr\nt337dhLlwChSqTQyMtLExITP5w8ZMuTy5cvNzc3R0dEikUhbW3vYsGHXrl3Dx6Jse+Q9Ap9n\nWMtSqRSLC19E+vj4dCeHinh5eQEA7t696+npCQC4ffs2ibBMJjMzM+vfvz8+UEdHRyQS4ZUp\nlUr5fD42qweHPVVPHT1Y6bC9ubm5YVYCz8aNG318fOBUjXqOXV1dXUxMDOwySsczSgFFXFxc\nhEJhW1sbPtDOzs7ExASqlFK9lALknY6OAB22bNkCADh9+jQ+kKSL0blvV22UokWiXzRVJotO\nnarh2AUHBwMAnj59Gh4ebmJiwuVy33333eTkZJIoZaqBRkMpath5yqqkoxNKY6gIZV8gtySQ\nwsJCAMAnn3xCfq83gbfSsTt//jyLxRKJRAkJCXv27AkJCfH09ORwONgwVltbK5FIdHV14+Li\nMjIyEhIS+vXrx+Px8vLyMAELCwtdXd3Fixdv3bo1MDAQ3+VmzZoFAJgxY0ZAQEBCQgIcGCjT\nLCws1NTUFIlE69ev//bbb1esWCEUCk1MTJ4/fw4FQkNDYbIpKSmpqakTJkwAACxatIhmnsmj\nE5gzZw6CINg8M1wDJBAIYmNjMZnIyEi4oB4b9QsKCmDZ165de/ToUfjGATp2oaGhrq6umzZt\n2rx5s1gsBgAcOHBAVQXNmTMHP6CiKPrs2TMNDY2AgACaVQwnxnNzcwnh5eXlfD5/wYIFUqlU\n8b0GgcePHwMAgoOD0ZdjfFFREfxr0aJFEokE/s7JyUEQ5Pfff6eZN7yTBEvq7+8/f/78goKC\nCxcujBkzBgCwb98+VdFhFF9f3/j4+KKiorS0NE1NTUtLy8DAwLi4uMLCwuzsbD09PVNTU8xi\nUrYNyh7RJcdOjRwqUlpaCgAYPnw4iqJ79uwBAHz66ackWr169SrBaDY1NQEARo4cSZB0cnLi\ncrmdnZ1YVp89e9bZ2fno0aNnz57hJXuw0qGze/jwYUpJtV/FYlD6bXQcu9bWVhaLhdUpxty5\nc+FzGqV66ehfEXynU09AEX9/fz6fDxtbW1tbQ0MD/biq7ttVG6XKIpHcAkLTZPWgYwc7+/vv\nvx8XF3fhwoVz5875+fkRZl7xkC8wDQoKUnUjNex8l6pSqU4ojaEilH0BpbIkELlcbmxsbGdn\nR5LnN4S30rELCAgAAOCd9IULFwIAsGFswYIFbDYbP6368OFDoVDo7u6OCQAAfvvtN0wAjnZ/\n/fUXiqJhYWEAgDFjxuDnwyjTTE5OdnNzw/f8pKQkAEBSUhK81NLSGjZsGL4gS5cunTRpEjSR\nlOmTRyewf/9+AMDPP/8ML7OysthsdmhoKH4Bk729vYuLC/rvUX/Tpk1A2atYDw8PbBSHOxbH\njx+veF/I7du39fX1nZ2dz507V1VVVVRU5OPjo6WldenSJVVR8DQ1NRkbGyv2QxRFfXx8zM3N\n6+vrya1kc3Nzbm6uk5OTUCiEKi0rKwMAHDt2DAqMGzfO09MTRdGWlhY7O7u5c+e2tLRERkZa\nWVnZ2NgsXbpU6cQMBK8uqJzp06dj/1ZUVAAAAgMDVUWHURYsWICFTJ06FQAwefJkLARac2zd\nCWXboOwRXXLs1MihIjExMdhY8s8//2hpaRkZGSnOv2LAhodVEIqiMpmMzWY7ODgQJOFW30eP\nHqEvJyc+++wzfX19OA7Z29v/+OOPULIHK93GxgZBEDouxRvi2N29excAMHfuXEI4fOX0v//9\nj1K9dPSPR7HTdVVAFRKJxMHBoaioaMSIEQiCAABsbW2///57mtGV3rdLNorEIlEWjabJ6nHH\nDm+U6uvreTyeqok0uVx+SDUkqyHVsPNdqkqlOqE0hopQ9gWUypJgQN2+mW/G8bx9jp1MJuPz\n+ba2tvjA4uJibBiTy+VGRkZubm5V/8bf3x8A0NjYKJfLDQ0NxWIxfga4oqIiJycH+ulwYMNX\nKmWahEy2t7e3traeOXMG4N7i6+rqikQiuBCHAJ30SaIrUl1djSDIsmXL4OW8efNcXV3T09PZ\nbDZ89wQ3ScTFxaH0HLujR4/icwv3K5FkoKSkBL78hVhaWtJfLg3XWmGr0TG+//57AEB2djaK\noiRWUldXF940JCQEPo1BHBwcfH19GxoaLl26xOPxduzYgaLo8uXLTU1N4fy/oaHhqVOnfv75\nZ6FQmJiYqCp7io4d4c2ClpYW9JiVAqNAawL57LPPAAAZGRlYSHJyMlZSyrZB2SNQtRw7+jlU\npK2tzcjIiM/nY54QnAnOyspSpRb4NAWfrDA8PT0RBLlx4wYWUlJSwuFwAAB37txBX77ttbGx\n2bRpU3p6+sqVK3V0dAAAqampUL6nKl1bW1tPT0/Vv3jeEMcOPn0pzujDd2FHjhxBaaiXUgBD\nVaejL0CCUCiUSCTm5uYxMTHZ2dk7d+60tLQkmGhVkNyXvo1SZZEob0HTZKGvwLHDVhBB4L6f\np0+f0k+HDl21812qSkWddHUghtDpC5SWBLJ69WqCbXwzefscOzjd7efnhw+EhynAYYz8sK5b\nt249efJEMQU8cGArLCzEQijThGLp6ekjR47U09PD/xsdHQ3/3blzJwBAR0dn1qxZ+/bte/z4\ncZfSJ4muFCcnJ2xct7e3j46Ohrv0YaP88ccfAQBw+xIdx44w4urq6g4cOFDVrW/fvm1tbS0W\ni7dt23bixIm9e/cOHDhQV1eXTn9oaWkxMjJSfAFUU1NjYGCAzYSRWMkVK1ZERkYOHz5cQ0PD\nw8MDM7VXr161tLSEm9inTJnS3t5+7do1Fot16NAhFEXNzMzWrFkDJRcuXEhY7IVH0bEjrB4j\nV45iFPjgiF+DDN9dZmZmojTaBmWPQNVy7OjnUBHYukJCQrAQ+FbU19dXlVrgsQ7V1dX4QBjL\nysrq6NGjJSUlWVlZNjY2cCMqXMJ85syZ7Oxs/Dq5W7du8Xg8AwMDODvYU5UuFAqFQqGqf/G8\nUY5dVFQUIXzz5s3g5XMapXopBTBUdTr6AuTlBf/eWP306VOBQGBmZqbqjTDlfenbKFUWifIW\n9E0W+gocO4LnDV81YssSegQ17HyXqlJRJ5TGUCqVzsOxZcsWlF5foLQkkK+//prE7r05sEnU\n9GbS0tICANDU1MQHwjOH4G94zJKLiwv0UQiIRKK6ujoAAOWZXthzGJ00AQCrVq3atGmTu7v7\njh07rK2teTzerVu38KcWffLJJ++9915SUtKRI0cyMjIQBAkICEhOTpZIJHTSJ4muNP9+fn47\nd+5sbm5uaGi4e/duYmKiRCIRi8X5+fm+vr55eXna2toeHh7kSsDo0hFoYWFhNTU1d+/etbCw\ngCHTpk2zt7efO3fuvXv34BO/Ko4cOfL8+XPoW+CJjo5ub2/fvXs35d0xHebl5QUGBk6YMKG4\nuFhDQ8Pd3f3Bg3UyUSsAACAASURBVAdVVVU6Ojra2tqdnZ0RERGBgYGTJ0+WSqXV1dX9+/eH\nEQcMGJCSktLR0UGeVQyaYuRRVCVC2Tbg0UokPUI96OdQkW+//RYA4OXlhR2I2K9fP1NT0zNn\nzlRWVtrY2ChG+eeff8C/Ox0AYPTo0UlJSXFxcXBFqUAg2LBhQ2FhYUVFBXxj4u3tTUjHwcFh\n7NixR48evX79+uDBg3uq0kUiUWlp6fPnz42MjGgqoXeB8w2EM+fASz0LhUJAQ72UAhiqOh19\nARIEAkFnZ+fkyZOxEHNz84CAgEOHDt2+fdvR0ZEkrqr70rdRqiwS5S3om6xXgZaWFv5SW1sb\nAFBfX69UmOTgUuh1Kf1LDTvfnaoENIxhU1PTN998g4WMGDFi2bJldPoCpSWBgXDWpqGhgTyf\nvc7b59jx+XwAQFtbGz4QOtrwN6wnAICqM0Jhg1PVxJVCmWZbW9tXX30lFotzc3MFAgEMVKx+\nb29vb2/vFy9enDt3bv/+/enp6b6+vrdu3aJMnzw6l8tVFPbz89u2bVtBQUFNTQ2CIHBnooeH\nx9mzZwEAeXl5o0aNUhqxmzQ1NV2+fNnLywvr7QAALS0tHx+f9PT0u3fvDhw4kCT6wYMHWSwW\n4VjOU6dOZWVlrVmzRkNDA05QwT7Z0tLy+PFjHR0d2HUJeHl5BQUFHThwoLS0dMCAATDQ3Nwc\n/ti6dWtlZeUvv/wC8wxeNi2YWxRFm5ubCZOvvQJl24CZJ+kRlLS3t3cjg0RKS0vhEe2KZ7EC\nAPbu3btx40bFcFiDDQ0NBA81Kipqzpw5RUVFGhoacGvboEGDzM3NSarGxMQEvFQLpPuVPnz4\n8NLS0hMnTsA9TARQFL1586aTk5OqLL1+LC0t2Wz2gwcPCOFwDeg777wDLynV21X9K+10XRJQ\nxMrK6s8//yQ4CsbGxkDZaK0K/H3FYjF9G6XUIlHe4v79+2qYrB6kubkZfwkHI0NDQ0XJzs5O\nrD0oEhQUdOzYMcVw9ex8N6uS0hjC9RKEQJp9QRFFSwLdBsLz5xvI2/flCTMzMy6Xe+/ePXzg\njRs3sN+mpqZGRkYlJSUE1w07M1pbW9vY2PjOnTv43UClpaW7du26deuW0ptSplldXd3a2uru\n7o55dQAAVV8g4fF4vr6+aWlp8+fPLy8v//PPPynTJ4+u9C4jR47k8Xjnz5/Pzc0dOHAgnGnw\n9PS8fPnyvXv3ysrK4LqEHqe1tRVFUYKfAV56HorheNrb23NyclxdXQnDBlytuGHDBvFLoNXI\nzMwUi8UJCQlPnjxxdnaePXu20psSbBwAoKysLD4+fsuWLXA2FD7OYl9HaG5uRhCE8MjbW1C2\nDcoeQQBaVXzjJ8TtJnC6LiIigrAKOyMjg8Viff/9952dnYqxYPuEs+l4ZDKZUCgcNWqUp6en\nUCh8+PBhcXEx3OXX1NSUkpKSmZlJiAJ7seJMdncqHfpz69evVzr8JCcnOzs799bcjFK4XO6g\nQYOuXLkCX3FA5HJ5fn6+WCyGC5sAqXopBSg7XVd7pSqGDRsmk8mKiorwgXCSCe7QJ0B5X/o2\nSpVForwFpcmiWXa1gUsCMOBGIuwJBw9cmaCKuLg4pemrZ+e7WpUEujRQYlD2BfqWBN7oLZi2\n77WXwN0ArnPE7wGEJyXid8UCAFatWoUJ1NbWmpmZYcsd4FwCfvs3PIoTHs2l9Ehe8jRbWloQ\nBHF1dcX+LS4uho8y8+bNQ1G0oKBAJBIRzt+HS23gugfy9CmjK8Xb29vf39/GxgZbN3rz5k0A\nwOLFiwFuEQZ+ARZcdgDXk0KUaoN8GZm1tTWHwyktLcVCpFKpgYGBjo4OPEmotbW1uLi4vLyc\nEBEu+VdchnL79u0T/yYrKwsAMGbMmBMnTsCC9OvXj8vl4jdklZaWCgQCgUAAbRCGXC738vLy\n8vLC754xNTWFW0lQFA0NDX333XdVlU5xjV2XlKMYBa5gg6cGQggr2CjbM2WPwOcZpoY/WDU2\nNhYorLHrUg4x2traDA0NeTwe/hRfjEmTJoF/b33FgO9WCCu+Y2NjORwOVi6ZTDZx4kQAQEFB\nAby0sLAQCAT45URwdgHfEyHdrHT0pQ6HDBmCb7cdHR07d+5ksVjm5ubwdKHeWmOn2Kegh/35\n559jISkpKQCA+Ph4eEmuXjoClJ2OUuDFixfFxcWU54chCOLt7Y2dQ3b16lUNDQ0nJydVZae8\nL6WNgqiySJS3oGOy8NBcY0dHXbChjhs3Dp8xBEHIm7caqGHnKasSj6pdseTGUCnkfYG+JYF+\nQpeqo1d4Kx27X3/9FUEQExOTFStWbNmyJTAw0NvbW1dXFxvGampq4CNpaGhoWlpaQkICPMwQ\nO7bq0aNH8OMnUVFRMAUAwOzZs+G/SkdryjRhIvPmzcvMzFyzZo2+vv6vv/7KZrP79et34MCB\n+vr69957j8vlfvzxx7t3705OTg4LC4OLbeFIQ55+R0cHeXSlbNq0Cc4g/vTTTzBELpcbGBgI\nBAJLS0tMDD/qZ2dnAwDef//9bdu2QYOuhu9y5MgRDQ0NQ0PDzz77bN++fRs3brS2tga4A+uh\nf6l4fAC0fYpfm1BEcSXy0aNHWSwWh8OZNm3aZ599NnfuXDgls2vXLkLcb7/9ls/nE0oUExNj\nYmJy9uzZ06dPCwSCzZs3q7r163fsKNseZY/A57mgoAAAMGjQoJycnEuXLq1cuRJOxvSIYwe3\nTYSGhiotO/woJH7IwYCfmMR2GkGuX7+upaWlp6cXHR0dHx8PPxy5fPlyTOD48eMIgmhra4eH\nh69Zs2bChAkIgujo6CgentzNSkdRtLm5GZ6JwGazR48ePW/evI8++gg+zdvY2Ny9exeKqefY\n5eXlYV8xYrFYZmZm2CU8CJNSQLFPdXZ2wgUYQUFB8fHx06ZNQxDE0dGxubmZpnopBSg7HaUA\nnEkaMWIEibpQFF2yZAkAwMXFJT4+/uOPP+bz+VwuFztbSrHslPeltFEQEotE3+BAFE0WZZ2i\nCo4dHXXBzu7r6xsYGJiampqcnGxlZQXobSLuEurZefKqpNQJpTFUCmVfoGNJ5HK5iYkJ/hw7\nmq339fNWOnYoimZlZTk6OnK5XGNj47CwMKlUKhaL8c51VVXVggULxGIxm83W09MbP3484YuQ\n9+/fDwkJMTEx4XA4NjY227Ztw3blqPqIFnmatbW1M2bMMDY21tXV9fb2hqNgfHw8XHxaVVVV\nV1e3ZMkSW1tbLS0tXV1dZ2fnhIQE/A5t8vQpoysCT8oG/95s+OGHHwIAIiIisBD8qN/e3j5p\n0iQ+n6+vrw93Dqrhu6AoevHixeDgYGNjYzabra+v7+vri//ohSrHDj5F7dy5kyRliNItZpcu\nXYI3ZbFYenp6vr6+2El+GE+fPtXV1cV/WwbS0tIyd+5cIyMjMzOzJUuWkOy2e/2OHUqjPZP3\nCHyeURRNS0tzcHDg8/mmpqaRkZH19fUikQj76ld3HLuRI0cCAP78809VxXd0dGSxWIqnoMlk\nMlNT0wEDBhDCCwoK/P39DQwMNDU13dzcFE9+vnjxYkBAgJ6eHpvNFolEs2fPVuy53a90jJ9/\n/nnixIkikYjD4QiFwiFDhiQnJ7e0tGAC6jl2SheDQ2BxKAWU9qnGxsZly5ZJJBIOh2NhYbFo\n0SLCl5cp1UspQNnpyAXg0AjPFyRBLpenpqY6Oztramrq6uqOHTsWPz+ttOyUGSO3URByi0TH\n4GAomizKOkVVOHbk6oKdvaysbMmSJSKRiMvlOjg4pKWlkURRGzXsPHlV0tEJpTFUCmVfoLQk\ncHft4sWLsRCarff187Y6dgwMDH0MaNN//fXX3s7IK4f8Vex/jb1795J83uA/juJxJ5Tqgo6d\n4rMTQzeZOXMmm80mnNTzZrbet2/zBAMDQ58kKirK0NBww4YNvZ0RhtfKr7/+OmLEiN7OxVsD\no65eoaKiIisra/bs2YTTmt7M6mAcOwYGhjcCgUCQlJRUUFAAv8XX58nPzz99+vSjR496OyO9\nSWtrq5OT08cff9zbGXnjOH/+/OnTpwmHdDDq6hVkMllYWJihoSH8BgnGG1sdb985dgwMDH2V\n6dOnX7x4cdmyZcOHDx80aFBvZ+fVAr9BnpKSMn/+/N7OS6/B5/PXrl3b27l4E4mIiCgtLSUE\nMurqFeLj4wsKCn7//Xd45B7GG1sdCEr7FFMGBgYGBgYGBoY3GeZVLAMDAwMDAwNDH4Fx7BgY\nGBgYGBgY+giMY8fAwMDAwMDA0EdgHDsGBgYGBgYGhj4C49gxMDAwMDAwMPQRGMeOgYGBgYGB\ngaGPwDh2DAwMDAwMDAx9BMaxY2BgYGBgYGDoIzCOHQMDAwMDAwNDH+H1OXZsNnvo0KGv7XZ9\niWnTpiEIUl1drfTfiIgIBEHKy8tfc67eWMjV9eaA7xFvS57xREVF8Xi8a9eu9XZGXiFRUVHI\nS1JTU3s7Owy9QP/+/bE2cP/+/d7ODsN/grVr13K53Pz8fPWiMzN2bwEuLi7+/v48Hg9eJiYm\ndt+Ne/DgQXh4uIWFBZfLlUgkMTExjY2N5FGkUumyZcskEgmPx7O2tg4ODr506RL2b1paGqKM\nL774ApOpr69fsmSJlZUVl8sViUQRERFVVVXYv5WVlX5+fnp6ehYWFrGxsXK5nJCBiRMnOjo6\ndnR0kOeToK63gtef5/379+OrSUNDw9jY2MXFJTY2tq6ujjJ6Zmbm7t27t27din3RlbxFUTaP\nnqp9CIqi2dnZwcHBIpGIx+OZmJi4u7tv3LixpqYGkykpKUEQ5IMPPqBMbe/evSdOnBg7diwW\n0tHRsXLlShaL5e7urihP3lOUQhmFssOWlJTMmjXL3Nycw+EYGxtPmDDhypUrhLuQZ5uOAB1O\nnTo1atQooVCop6fn7e2dl5dHLk9ZdnK7QSfnlMohUW9qauqJEyfGjx/fVT28TuioqKtRui9Q\nWVkZGRlpa2vL4/GMjY2Dg4MV2yTGp59+iiBIRESE2il0h15RIFDdbtetWzds2LCpU6c+e/ZM\nnfKgrwsWizVkyJDXdru+ytOnTwEAp06dwkLCw8MBAGVlZfQTqaysNDIyQhBkypQp69evh2Pb\n0KFD29vbVUWpq6uzsrICAIwbN27NmjUzZ85ks9mampo3btyAAjt27AAATJ8+Pe7f5OTkQIEX\nL164ubkBACZNmrRx48awsDAOh2Ntbf33339DgcGDB/v5+TU0NBQXF2tra3/zzTf4DGRnZ2to\naFy+fJl+Md9werdHZGRkAABGjBgBqyk2NjY8PNzGxgYAYG9v39TURBK3sbHR0NBw6NChWAhl\ni6JsHj1Y+1Kp1NfXFwCgpaX14YcfRkVFTZ8+3dbWFgBgbGx89uxZKHbnzh0AgL+/P0lSixYt\nAgDcu3cPH3j79m03NzehUKihoTFo0CBCFMqeoghlFEr1/vXXX0Kh0MDAYO3atenp6Rs2bDAz\nM2Oz2WfOnKGZbToCdNi3bx8AwNbWdvXq1cuWLTM2NuZyuRcuXFC77JR2gzLnlMqhYw+jo6MV\nW8IbAh0VdTVK9wVKSkoMDQ25XG5ISMi6detmzpzJ4XA4HM7FixcV83P16lUWiwUACA8PxwK7\nlEJ36BUFolTttqysjMVihYWFqVEixrF7yzh+/Hj3Hbtp06YBAPbs2YOFQLO1e/duVVHgCJeU\nlISFHD58GAAwduxYeLlu3ToAwNWrV1WlsH37dgDAl19+iYUcPHgQABATE4OiaGVlJQDg5MmT\n8K+JEyeOHj0ak5RKpWZmZkuXLqVfxjefN8GxW7duHT6ws7PTx8cHAJCRkUESNzExEV9ZKI0W\nRd48erb24dRaUFBQbW0tFiiTyVJSUlgslr6+fk1NDaquY9fQ0MDn893d3cvKyng8nqI5puwp\nqu5CEoVSvTNmzAAAYF4yiqLXr18HAHh5edHMNqUAHWpqagQCgaurK/ZgUFZWJhAIFi5cqHbZ\nye0GnZxTKoeOPXyTHTtKFakRpfsCfn5+CILk5+djAkeOHAEATJ06lZCZjo4OFxcXZ2dngmNH\nPwVympubU1NTly9frkqgVxRIp8fNmDGDzWZXVlbSLuv/86ocu5MnT7q5uWlqahobG4eHh0ul\nUsIwVl1dvXDhQktLSw6HY2RkFBQUdOXKFXwKVVVV4eHhIpFIS0vLycnpq6++6ujogH999NFH\nAICamhpfX19NTc3jx4/TTPPy5cvBwcGGhoYcDkcikYSEhOA7altb2+bNm52cnHR0dAQCgaOj\n4+bNm2UyGc08U0bHIxKJHB0d8SEODg6EwfLAgQNwiIXlraqqGjduHH629dy5c+hLx66ioiIx\nMdHa2prL5YrF4vXr18vlclW1o6OjIxKJ8AJSqZTP5+PnYAgsWbLEx8cH/wgrl8v5fL5EIoGX\n0PCR+JcuLi5CobCtrQ0faGdnZ2JiIpfLc3JyAAA3b96E4TExMVZWVphYeHi4tbU1+TQSBqYu\nFEWnT58OAGhsbIyNjZVIJFwut1+/ftu3bydRDowilUojIyNNTEz4fP6QIUMuX77c3NwcHR0t\nEom0tbWHDRt27do1fCzKtkfeI/B5hrUslUqxuPD9o4+PT3dySECpY4e+nFrbvn27qogymczM\nzKx///74QMoWRd48erD2T506BQBwc3PDzAWejRs3+vj4wCd+9Ry7urq6mJgY2BGUmmPKnqII\nZRRK9Q4ZMgQAQJhx19HRwdRImW1KATps2bIFAHD69Gl8IElfQ2mUndxu0Mk5pXLo2EM1HLvg\n4GAAwNOnT8PDw01MTLhc7rvvvpucnEwSpUw10DgohVJFakTpvsDq1atXrlyJ/7ezs5PD4Tg7\nOxMyk5iYiCAI7Ll4x45+CqqorKxctmyZvr4+giAkXlqvKJBOjyssLAQAfPLJJzTLi/FKHLvz\n58+zWCyRSJSQkLBnz56QkBBPT08Oh4MNY7W1tRKJRFdXNy4uLiMjIyEhoV+/fjweLy8vDxOw\nsLDQ1dVdvHjx1q1bAwMD8VU+a9YsAMCMGTMCAgISEhLgeECZZmFhoaampkgkWr9+/bfffrti\nxQqhUGhiYvL8+XMoEBoaCpNNSUlJTU2dMGECAGDRokU080wencCcOXMQBMFmZeHSH4FAEBsb\ni8lERkbCBfXYqF9QUADLvnbt2qNHj9bV1aEvHbvQ0FBXV9dNmzZt3rxZLBYDAA4cOKD01k1N\nTQCAkSNHEsKdnJy4XG5nZye9Skbb2to4HM6IESOwEgEAnj171tnZ+ejRo2fPnuGFW1tbWSwW\n5ppgzJ07F3qlcGgvKiqC4YsWLcIse05ODoIgv//+O82M4Z0kmCt/f//58+cXFBRcuHBhzJgx\nAIB9+/apig6j+Pr6xsfHFxUVpaWlaWpqWlpaBgYGxsXFFRYWZmdn6+npmZqaYkMFZdug7BFd\ncuzUyKEiqhy7jz/+GACAf0omcPXqVYKtodOiyJtHD9Y+9HoPHz5MKan2q1gMmg4QoafQAR+F\nvnoxzxhF0WfPnmloaAQEBKiRbbUdO39/fz6fD1tdW1tbQ0ODGongy05pN+jknFw5NO2hGo4d\n7NTvv/9+XFzchQsXzp075+fnR5gaxEO+fjQoKEhprK6qiE6U7gsozerjx48BAMHBwfjA8vJy\nPp+/YMECqVRKcOxopqCUM2fOBAUFaWhoaGtrz58//86dO6oke0WBhHBVPU4ulxsbG9vZ2anK\nvCpeiWMXEBAAAMDPWCxcuBAAgA1jCxYsYLPZ+PcyDx8+FAqF7u7umAAA4LfffsME4Gj3119/\noSgaFhYGABgzZgx+PowyzeTkZDc3t9zcXEwgKSkJ4N4CaGlpDRs2DF+QpUuXTpo0CfZtyvTJ\noxPYv38/AODnn3+Gl1lZWWw2OzQ0FP+MaG9v7+Ligv571N+0aRNQ9irWw8MDG8XhRsXx48cr\n3hdFUZlMxmazHRwcCOFwh+ajR4+UxlJk586deO3Bx9PPPvtMX18fWiJ7e/sff/wR/nv37l0A\nwNy5cwmJwDd0//vf/8rKygAAx44dg+Hjxo3z9PREUbSlpcXOzm7u3LktLS2RkZFWVlY2NjZL\nly5VOh8DwasLKmf69OnYvxUVFQCAwMBAVdFhlAULFmAhU6dOBQBMnjwZC4FWHls5RNk2KHtE\nlxw7NXKoCHTsFi9ejE0JXLlyJS4uTkNDQ7Ga8MAWiNUUSq9FkTePHqx9GxsbBEHouBSvzbEj\n9BQ64KPQUe/t27f19fWdnZ3PnTtXVVVVVFTk4+OjpaV16dIlNbKttmMnkUgcHByKiopGjBiB\nIAgAwNbW9vvvv+9SIviyU9oNOjknVw5Ne6i2Y4c3PvX19TweDz8bjUculx9SjaqFZV1VEZ0o\n3RcghDc3N+fm5jo5OQmFQsJ6DB8fH3Nz8/r6enLHjiQFgtg333zz3nvvAQAsLS2//PJLknVy\nkF5RICGcpMfBVtTVNQBskkcE9ZDL5Xl5eba2toMHD8YCP/744+TkZPgbRdFDhw45OTn169cP\nO9+Bw+EMHz78t99+a2pq0tbW/umnn8RiMXy+gXz99dcxMTGmpqYAAGgy5syZo6GhQTNNgUCw\nYMEC6C8CADo6OmQyGXz7ie1g53A4Dx48qK2tNTExgSHwNTnN9EmiK+Lr64sgyNmzZz/88EMA\nQG5urqOj4+jRozMyMpqbm7W1tauqqu7evRsXF0dT7TExMRwOB/52dXVlsVhwm4UiGhoaw4YN\nO3/+/M2bNx0dHWFgaWkpdAfh8ysl+fn5y5cv9/DwmD9/Pgypr68HAGRmZsbGxlpYWNy5c2f3\n7t0zZ85sbGycN28e3GKmra1NSEcgEAAAGhsb7ezsHBwcdu3aNXr06Dt37vzxxx9wIde6desa\nGxu3bdu2Zs2aw4cP79+/v6OjY+bMmaampvSVAx/ZITY2NlpaWvDJj4SJEydiv9955x0AQFBQ\nEBby7rvvAgDgFifKtqGlpUXeI9SDfg5JSEpKgo83EARB5s+fDzWvCuiE2dnZYSF0WhR58+jB\n2q+pqdHV1dXR0SEv+GtDsad0NQod9Q4YMKCgoGDixImenp5QwNLS8o8//oBvIV8bf//9NwBg\n3LhxM2bMWLp06ZMnT7Zt2xYaGsrlcuFCN0oIZae0G3TSJFdOj9hDEuACPoiurq6np+cff/xR\nVVVlbm5OkEQQZPLkyV1NXw0VUUbpvgA+UE9Pr6GhAQAQEhJy9OhRuEMLkpaWdubMmezsbF1d\nXWgilEKSAh6ZTNavXz+pVDp8+PCDBw9OmjQJbsggp1cUSJkrDGjby8vL4R4jmvS8Y1dVVdXa\n2kpQff/+/bHftbW1z58/f/78uWLLBgA8fPhQT0+vrq7Ozc0NOnAQGxsbQppw6KKZJvThMjIy\nvvvuuxs3buDbUGdnJ/yxfv366Ojod955JygoaPTo0WPGjLGwsKCfPkl0RUxNTR0dHc+dOwcv\nc3NzAwICRo4c2dnZWVBQ4Ovrm5ubCwCA7w3pAKsfgiCIQCBobW1VJRwfH+/t7T1+/PgdO3YM\nGDDgzz//XLVqlaWlZUVFBZ0TNzIzM0NDQ997773jx4+z2f/fhNasWRMVFfXBBx9grTkkJMTN\nzW3VqlXwJTV46ZHjQVEUC//hhx8mTZqkp6cHAJg8efKiRYuKioq2b9+elZVlYGDw448/Lly4\nEG5YmzVrVlpaGn3HztLSEn/J4XAoT83A1x0sIz4E+tAwEcq2oaurS94j1IN+DkmYMmUKnO0D\nAPzzzz8lJSVpaWlHjx796aefsFGQwPPnzwEARkZG+EDKFkXePLhcbk/VvoaGhkwmIy/1a0Np\nT1EjCqV679y5M27cuM7Ozm3bttnb29fW1m7fvj0gICA7OxtuEH49tLe3P3jw4Icffpg9ezYM\nmTJlir29fUxMzEcffUQ5yqpSF7ndoIRSOd20h+TY29vjL2Enra6uVmou1EYNFVFG6b4AZMGC\nBX///fdff/114MCB+/fv//DDD9AY1tbWxsTEBAYGTpo0ibx0qlJQvLtUKnVzc9u5c2dXz+vp\nFQXSAc4TQatLn5537FpaWgAAmpqa+EBNTU2sMNBddXFxge90CIhEIniMFmWP0tXVxX5TpgkA\nWLVq1aZNm9zd3Xfs2GFtbc3j8W7duoU/NeeTTz557733kpKSjhw5kpGRgSBIQEBAcnKyRCKh\nkz5JdKX59/Pz27lzZ3Nzc0NDw927dxMTEyUSiVgszs/P9/X1zcvL09bW9vDwIFcCRpcM0OjR\no5OSkuLi4uBCQIFAsGHDhsLCwoqKCuxNmVJQFP3888/hiQA//fSTUCjE/vL29iYIOzg4jB07\n9ujRo9evX4fJKj6p/PPPPwAAmI67u/uDBw+qqqp0dHS0tbU7OzsjIiICAwMnT54slUqrq6sx\nZ2jAgAEpKSkdHR3YJCU5NMXIo6hKhLJtwIOISHqEetDPIQkODg6ESYJFixa5urrOnDkT7tVS\njAKrDN/7AI0WRd48Bg8e3FO1LxKJSktLnz9/TnA9XzMkPUWNKJTqDQsLq6mpuXv3LubcT5s2\nzd7efu7cuffu3VOjYaiHQCDo7OzEtyhzc/OAgIBDhw7dvn0bmw9TRFXZ4cwrud2ghFI5attD\nOmhpaeEv4YONqtkpkgNKBQKBmZmZYrgaKqKM0n0BfCBmGPPy8gIDAydMmFBcXKyhoREdHd3e\n3r57925VRaZMgSDGYrFWrVq1Z8+ewYMHDx8+fMmSJRMnTqR8nOgVBZJnCQ981oUTlvTpeceO\nz+cDANra2vCBcEcb/I2VStXRoNAMkUzMKkKZZltb21dffSUWi3Nzc+F0KFCmLG9vb29v7xcv\nXpw7d27//v3p6em+vr63bt2iTJ88OpfLVRT28/Pbtm1bQUFBTU0NgiBwgsTDw+Ps2bMAgLy8\nvFGjRimN2CNERUXNmTOnqKhIQ0MD7t8ZNGiQubk5bEZKQVE0IiJi3759ixcv3rFjB51Zbvi0\n0dTU5OzslckzbwAAIABJREFUzGazHzx4QBCAK97w043Yg+zWrVsrKyt/+eUX8PKFCGxaAAAt\nLS0URZubm0ly+9qgbBsw8yQ9gpL29vZuZLBrSCQSb2/vw4cP37p1C57DRADarIaGBoKrqkaL\nwpoHFtL92h8+fHhpaemJEyeweWI8KIrevHnTycmJQgvdQ42eQhmFRL1NTU2XL1/28vLCT9lq\naWn5+Pikp6ffvXt34MCBPVxCFVhZWf35558EP9LY2BiQvn4iKbulpSVNu6EKmspRo/XSpLm5\nGX8JBx1DQ0NFyc7OTpISBQUFHTt2TDFcDRVRRoHn/HVHQGkRvLy8goKCDhw4UFpaev/+/ays\nrDVr1mhoaMCFMdDpaWlpefz4sY6OjtLVFPgUBgwYQPgXQZCNGzeuXbv2wIEDSUlJU6dOtbS0\njIqKioiIIHHQe0WBqjKjCHSECA/SlPT8lyfMzMy4XO69e/fwgTdu3MB+m5qaGhkZlZSUEFw3\n7IRlbW1tY2PjO3fu4F8klZaW7tq169atW0pvSplmdXV1a2uru7s75tUBAFR9r4PH4/n6+qal\npc2fP7+8vPzPP/+kTJ88utK7jBw5ksfjnT9/Pjc3d+DAgXCCwdPT8/Lly/fu3SsrK/P391ca\nsUeQyWRCoXDUqFGenp5CofDhw4fFxcX4RY2KLF26dN++fQkJCV9//TVh4GlqakpJScnMzCRE\ngfUFzxkZNGjQlStX4IQuRC6X5+fni8ViwqtSAEBZWVl8fPyWLVvgbCh8zMVeLjc3NyMIQngU\n7i0o2wZljyCg+BaVEPdVA8dggieKARuq4tcpSFoUZfMghHen9qE/t379eqWeRHJysrOzM51J\ngu5A0lPUjkKi3tbWVhRFFesLhqiqx1fBsGHDZDJZUVERPhDOQsGt+kohKXtX7YYiNJWjhj2k\nCdyjgwGXqCp9D8tisUg2T6hae6CGiiijdF/gyZMnzs7O2Bt5DKjw5ubmM2fOAAA2bNggfgn0\nsDMzM8VicUJCAmUKSrUBAODxeKGhoUVFRWfPnn3//fdXrVolFosXLlwINzS8IQpUlXlF4DjS\n5fcPXdpqQRMvLy/w7z2AcOUsflcsAGDVqlWYQG1trZmZGbZXEb4hxW8Lh0tQ4dFcSo/kJU+z\npaUFQRBXV1fs3+LiYvgMN2/ePBRFCwoKRCLRDz/8gE8T7omDpzCQp08ZXSne3t7+/v42NjbY\nqSg3b94EACxevBgAgO3Qxm+Z3Lx5MwDgyJEjWCJKtaGrqztw4EBV942NjeVwOFgFyWQyuBK/\noKAAhrS2thYXF5eXl2NR4Kmh0dHRShOUyWQWFhYCgQC/qxw+X2I6//bbbwEAn3/+OSaQkpIC\nAIiPjyekJpfLvby8vLy88GcIwfXy8HdoaOi7776rqnSKu2K7pBzFKHArEzw1ELJnzx4AQGZm\nJrykbM+UPQKfZ5ga/sCR2NhYoLArtks5VETVcSdXr17l8/kCgUDVuXHwtQh2eCSWQ5IWRad5\nYHSz9tGXyhwyZAi+AXd0dOzcuZPFYpmbm8ONcq9oVyx5T0G73rlQGh3W2tqaw+GUlpZiUaRS\nqYGBgY6ODuEkLVXZphR48eJFcXEx+UHohYWFCIJ4e3tjN7169aqGhoaTk5PaZadvN1TlnFI5\nlOpFFXbF0tEGbIfjxo3DQkpLSxEEIW+9akCpIkW1U0bpvkC/fv24XC5+X3ZpaalAIIDrv2/f\nvn3i32RlZQEAxowZc+LECWgoyFOgqZxHjx6tXLnSyMgIXxFvggLxkHRJ6Pn0/q5YAEBsbGx+\nfn5gYGBYWJihoWF+fn5LSwt+LvHzzz8/efJkQkJCVVXVqFGjnj59mpqaWldX98knn0CBdevW\n/fLLLwsWLLh+/bpEIsnPz//ll19mz56t9N0QnTT5fP64ceN++eWX+fPne3l53b59e9euXT/+\n+OP48eNPnjyZmZk5duxYAwODjz/++Pz58y4uLgiCFBYWpqWleXh4uLi4UKbv7u5OHl0pfn5+\nGzdubGpqGjVqFAwZOHCggYHB999/b2lpqXR9PVw0mpiYeO/ePU9PT/xGS/rMnDlz165dY8aM\nmTNnjoGBwYkTJwoLC5cvX459k768vNzV1dXHx+ePP/6AIdC3kMvlK1asIKQWFxenr6+fnJwc\nHBzs7u4+bdo0kUj0119/HTt2TEdH57vvvoNiYWFhGRkZn3/+eXFxsZub2507dw4ePOjo6Lhs\n2TJCgt99993ly5dv3LiBX4UWEhLy/fffjxs3rqWl5dChQ2vXrlWj4K8IyvZM2SPwzJ49OyUl\n5dNPP92yZYuWltbx48cLCgq6tCyDPn/88Qc2afHixYuKiorTp0/LZLJ9+/YpbumCwE9T5OTk\n4L+eSd6iNDQ0KJsHRvdrf9++fS9evDh27Fj//v09PT3t7e3r6+svXbr04MEDGxub06dPd2fh\nVH5+PjxJFQDQ2dn55MkTrEcsX77c0NCQsqeo0bkoO+y2bdsmT548fPjw+fPn29raVlVVfffd\nd3///ffu3bvhQknKbFMKPHz40NXVdcSIEefPn1elnEGDBkVHR3/11VdDhw6dMGHC48eP9+/f\nz2az4QkmQC3DQmk3KHNOqRxK9SpCRxuQFy9efPjhh4GBgXK5fPPmzSiK9rjtolSRotopo3Rf\nICkpafLkyZ6enpMmTbK1tX3y5MmhQ4eam5t37dqlqak5YMAAwrtU+MZDLBbDY2spU6CpnH79\n+iUkJKxdu7a4uPiNUiBluwUAoCiak5NjZ2fXpS2xALyyb8VmZWU5OjpyuVxjY+OwsDCpVCoW\ni/FP51VVVQsWLBCLxWw2W09Pb/z48YQPQd6/fz8kJMTExITD4djY2Gzbtg07EE7VR7TI06yt\nrZ0xY4axsbGurq63tzec3oiPj4eLUquqqurq6pYsWWJra6ulpaWrq+vs7JyQkNDY2Egzfcro\nisBzpQEA1dXVWCA8ACUiIgILwU/ntLe3T5o0ic/n6+vrHzp0SJU2yCelUBQtKCjw9/c3MDDQ\n1NR0c3MjHNgLJw7x5yuSNCHsYeLixYsBAQF6enpsNlskEs2ePZuQq8bGRvi1bw6HY2FhsWjR\nInjGMp6nT5/q6uriv8QCaWlpmTt3rpGRkZmZ2ZIlS0gOUn79M3YojfZM3iPweUZRNC0tzcHB\ngc/nm5qaRkZG1tfXi0QiDw+P7uSQAJyxw6OpqWlnZzdlyhSS0+9QFJXJZKampgMGDCCEk7co\nlEbzQHui9jF+/vnniRMnikQiDocjFAqHDBmSnJzc0tKCCag3Y6d0iwwEFoeyp6jXueioNzg4\n2NjYmM1m6+vr+/r64j9jQ5ltSgH4DhGeL0iCXC5PTU11dnbW1NTU1dUdO3YsfqJavbKT2w3K\nnFMqh456CTN2dLQBO3VZWdmSJUtEIhGXy3VwcEhLSyNXoHqQq0hR7ZRRekTg0qVLUO0sFktP\nT8/X1xc7ulURpefYdSmF7vD6FUin3cIzdxYvXtzV4ry+b8UyMDD0DaBJ+vXXX3s7I68c8lex\n/zX27t2r6vsHfR7FA4optQEdO/pHvjMwEJg5cyabzVb1JQ8Sen7zBAMDQ98mKirK0NBww4YN\nvZ0RhtfKr7/+OmLEiN7OxZsCow2GV0pFRUVWVtbs2bNVHchMAuPYMTAwdA2BQJCUlFRQUID/\nakUfJj8///Tp048ePertjPQmra2tTk5O8FPC/ynOnz9/+vRpwtEV/1ltMLweZDIZXJBN/h0g\nVbySzRMMDAx9m+nTp1+8eHHZsmXDhw8fNGhQb2fn1QI/3Z2SkkL/s2B9Dz6f/0btWHptRERE\nlJaWEgL/s9pgeD3Ex8cXFBT8/vvv8BjIroKgtE9JZWBgYGBgYGBgeJNhXsUyMDAwMDAwMPQR\nGMeOgYGBgYGBgaGPwDh2DAwMDAwMDAx9BMaxY2BgYGBgYGDoIzCOHQMDAwMDAwNDH4Fx7BgY\nGBgYGBgY+giMY8fAwMDAwMDA0EdgHDsGBgYGBgYGhj4C49gxMDAwMDAwMPQResexY7PZQ4cO\nfdVRGCDTpk1DEKS6ulrpvxEREQiClJeXv+Zcvb2Q6/PNAd9l3pY8E4iKiuLxeNeuXevtjLxC\noqKikJekpqb2dnYY3kT69++PNZL79+/3dnYYep+1a9dyudz8/Hyl/zIzdn0fFxcXf39/Ho8H\nLxMTE3vEjevo6Fi5ciWLxXJ3d1dPAE9aWhqijC+++AKTKSkpmTVrlrm5OYfDMTY2njBhwpUr\nV7B/NTU1laaAmcLKyko/Pz89PT0LC4vY2Fi5XE7Iw8SJEx0dHTs6OsizStDnW0Fv5RlF0ezs\n7ODgYJFIxOPxTExM3N3dN27cWFNTQxk3MzNz9+7dW7duxb5F++DBg/DwcAsLCy6XK5FIYmJi\nGhsbMXnKJtRTDYB+0UpKShAE+eCDDyhT27t374kTJ8aOHYuFkHcf8r6gFHLt0RGorKyMjIy0\ntbXl8XjGxsbBwcEkN/30008RBImIiFBbgA70EyHRJ6XpADSUQ1kjlCmQZDI1NfXEiRPjx4+n\np5Xeob6+fsmSJVZWVlwuVyQSRUREVFVVdT8KScXRGTXw9EiT605ZuhSFvHTr1q0bNmzY1KlT\nnz17ppgyu2fLxvAGsmLFihUrVsDfVVVVK1eudHFxsbOz606ad+7cCQkJKSsrU1uAQH19PQBg\n+vTplpaW+PARI0bAH7du3Ro2bBiHw4mKirKzs3vw4MHu3btHjBjx22+/eXt7AwCWL1+uOCQf\nPHiwurpaR0cHADBt2jQ9Pb2HDx9WVlZ6eHjY2dlFRkZikocPHz5+/HhBQQGHwyHPKl6fbwu9\nkuf6+vopU6b88ccfWlpaPj4+Eomkrq7uypUrq1ev3rlz5+HDhz09PVXFbWpqWrx48dChQxcv\nXgxD7t279/7779fV1U2ePNnR0fHixYvbt2+/ePHi2bNnYZVRNqGeagDdLJpSvL29rayssEvy\n7kPZFxSh1B6lQGlp6YgRIxobG6dOnWpra1teXv7TTz/9+uuv+fn5w4YNI9yusLDw66+/Jikv\npQAd6CdCrk9K00GpHMoaoUyBPJNeXl4AgD/++IOmZl4/7e3tPj4+RUVFkyZNcnNzq6ioSE9P\nz8nJuXbtmr6+vtpRyCuOssvj6ZEmp4pXUXzy0rFYrL179/bv33/FihV79+4lpo72BiwWa8iQ\nIa86CoMix48fBwCcOnUKCwkPDwcAlJWV0U+koaGBz+e7u7uXlZXxeLxBgwZ1VUCRdevWAQCu\nXr2qSmDGjBkAgJycHCzk+vXrAAAvLy9VUQoLC1ks1hdffIGiaGVlJQDg5MmT8K+JEyeOHj0a\nk5RKpWZmZkuXLqXM51tEr3cZOP8UFBRUW1uLBcpkspSUFBaLpa+vX1NToypuYmIivr5QFJ02\nbRoAYM+ePVhIdHQ0AGD37t3wkrwJ9WwDoFm0O3fuAAD8/f1Jklq0aBEA4N69e1gIZfdRoy9Q\nao9SwM/PD0GQ/Px8TODIkSMAgKlTpxLu1dHR4eLi4uzsDAAIDw9XzAylAB3oJ6KGOcKbDpSG\ncihrhDIFOpmEUfBN5c1h+/btAIAvv/wSCzl48CAAICYmRu0olDqhHDUwutnkmpubU1NTly9f\nrnZZ1IhCp3QzZsxgs9mVlZWEcGrH7vLly8HBwYaGhhwORyKRhISE4BvW9OnTAQCNjY2xsbES\niYTL5fbr12/79u1yuRyTOXnypJubm6amprGxcXh4uFQqpRxyKKNUV1cvXLjQ0tKSw+EYGRkF\nBQVduXIFn0JVVVV4eLhIJNLS0nJycvrqq686OjrgXx999BEAoKamxtfXV1NT8/jx4zTTJFdF\nW1vb5s2bnZycdHR0BAKBo6Pj5s2bZTIZzTxTRscjEokcHR3xIQ4ODoSB8MCBAwCAjIwMWN6q\nqqpx48bhffpz586hLx27ioqKxMREa2trLpcrFovXr1+Pr0ECdXV1MTEx7e3tKIoq7W+UAopA\nm0XiXw4ZMgQ+5eADdXR0rKyslMp3dna6uroOGDDgxYsXKIrm5OQAAG7evAn/jYmJwUcMDw+3\ntrZuamqizCf6sv1UVVWh9No/ARhFKpVGRkaamJjw+fwhQ4Zcvny5ubk5OjpaJBJpa2sPGzbs\n2rVr+FiUjZO8y+DzDJuBVCrF4sLpCh8fn+7kkMCpU6cAAG5ubli/w7Nx40YfH5+LFy8qjSuT\nyczMzPr3748P1NHREYlEeMVKpVI+nz906FB4Sd6EerAB0C+aeo4dZffpal9AaWiPUmD16tUr\nV67Ep9nZ2cnhcJydnQn3SkxMRBAEaknpIEopQAf6iXTVHBFMB0pDOZQ1QpkCnUyq4dgFBwcD\nAJ4+fRoeHm5iYsLlct99993k5GSSKGWqgQZEKS4uLkKhsK2tDR9oZ2dnYmKiyhhSRqHUCeWo\ngaF2k6usrFy2bJm+vj6CICRe2qsoPp3SFRYWAgA++eQTQjiFY1dYWKipqSkSidavX//tt9+u\nWLFCKBSamJg8f/4cCsyZMwdarvnz5xcUFFy4cGHMmDEAgH379kGB8+fPs1gskUiUkJCwZ8+e\nkJAQT09PDodD4thRRqmtrZVIJLq6unFxcRkZGQkJCf369ePxeHl5eZiAhYWFrq7u4sWLt27d\nGhgYiK/OWbNmAQBmzJgREBCQkJAAbT1lmpSqCA0NhcmmpKSkpqZOmDABALBo0SKaeSaPTmDO\nnDkIgvz999/wEi7rEQgEsbGxmExkZCSCINXV1digXlBQAMu+du3ao0eP1tXVoS8du9DQUFdX\n102bNm3evFksFgMADhw4QN42IJSGkqZjBxvSs2fPOjs7Hz169OzZM6UC2MCMouizZ880NDQC\nAgKUJrhjxw4AQG5uLryE43pRURG8XLRokUQiwf5CEOT333+nzCQE7yRRtn9VJfX19Y2Pjy8q\nKkpLS9PU1LS0tAwMDIyLiyssLMzOztbT0zM1NcXGCcrGQ9lluuTYqZFDRaB3ePjwYZpaxXP1\n6lWCtWpqagIAjBw5kiDp5OTE5XI7OztRqibUgw2AftHUc+zwKO0+Xe0LlNqjo15FHj9+DAAI\nDg7GB5aXl/P5/AULFkilUqWDKKUAHdROhI45IpgO+m1PVY10Vb096NjBjv/+++/HxcVduHDh\n3Llzfn5+hLlDPOQLTIOCgpTGam1tZbFYmAHBmDt3Lpw16H4Uko5AMmpA1GstZ86cCQoK0tDQ\n0NbWnj9//p07d1RJvqLi0ymdXC43Nja2s7MjhFM4dsnJyW5ublgTR1E0KSkJAJCUlAQvoVsw\nffp0TKCiogIAEBgYCC8DAgIAAPjZhYULFwIASBw7yigLFixgs9n4KcqHDx8KhUJ3d3dMAADw\n22+/YQJwMPvrr79QFA0LCwMAjBkzBj8fRpkmpSq0tLSGDRuGL8jSpUsnTZoE+y1l+uTRCezf\nvx8A8PPPP8PLrKwsNpsdGhqKPf+hKGpvb+/i4oL+e1DftGkTUPYq1sPDAxuk4SbE8ePHK95X\nkZ5y7OCT5WeffYatSLC3t//xxx8xgdu3b+vr6zs7O587d66qqqqoqMjHx0dLS+vSpUuKqTU1\nNRkbG+O7DVylcezYMXg5btw4T09PFEVbWlrs7Ozmzp3b0tISGRlpZWVlY2OzdOlSpZMxELw+\nKdu/IjDKggULsJCpU6cCACZPnoyFQAt+4cIFeEnZeCi7TJccOzVyqIiNjQ2CIA0NDaoESICt\nFKssFEVlMhmbzXZwcCBIwm2/jx49QqmaUA82APpFe0WOXZf6AkpDe3TUi6e5uTk3N9fJyUko\nFBJeFfn4+Jibm9fX16saRCkF6KB2IpTmSNF00FEOeY10Vb097tjhDVR9fT2Px1M1uSuXyw+p\nRtUU+927dwEAc+fOJYTDl4n/+9//uh9FqU4oRw1Il1pLc3PzN99889577wEALC0tv/zyS2wC\nRRWvqPg0SwermNAqurDGrr29vbW19cyZMwD3GhiOAadPn8ZLamlpQZdCJpPx+XxbW1v8v8XF\nxSSOHWUUuVxuZGTk5uZW9W/8/f0BAI2NjXK53NDQUCwW46dAKyoqcnJyoM8L84xXEGWadFSh\nq6srEomULhuikz5JdEWqq6sRBFm2bBm8nDdvnqura3p6OpvNhq+Tnj59CgCIi4tD6Tl2R48e\nxecWbkGik5Oecuzg6mAbG5tNmzalp6evXLkSLltOTU3FZEpKSuAbZ4ilpaUqQwNXaJ09exYf\n6ODg4Ovr29DQcOnSJR6Pt2PHDhRFly9fbmpqCuf8DQ0NT5069fPPPwuFwsTERFVZVXTsVLV/\npcAo+N7+2WefAQAyMjKwkOTkZABAdnY2SqPx0Ollajh29HOoFG1tbT09PVX/kgMfveBjGIan\npyeCIDdu3MBCSkpK4MJz+DBN2YR6qgHQL9orcuzQrvQFCKX2KAUwdHV14U1DQkIIsxHff/89\n1iqUDqKUAnToTiKU5kip6aCjHPIaoa9ekkyq7dhhy40gvr6+AICnT5/ST4ccOBeg+H5py5Yt\nAIAjR450P4pSndAZNbrUWjo7O6EXNXz48IMHD6qaq+5mWWhGoVM6FEVXr16t6D5SO3bp6ekj\nR47U09MDOKKjo+G/cAy4ffs2Poquru7AgQPRl3P1fn5++H9bW1tJHDvKKORncd26devJkyeK\nKeCBeS4sLMRCKNOko4qdO3cCAHR0dGbNmrVv377Hjx93KX2S6EpxcnLCdGhvbx8dHQ135sMK\n/vHHHwEAZ86cQek5doRBFKtBSnrKsTtz5kx2djZ+kdOtW7d4PJ6BgQFc6XL79m1ra2uxWLxt\n27YTJ07s3bt34MCBurq6is9DLS0tRkZGii8+rl69amlpCXeMT5kypb29/dq1aywW69ChQyiK\nmpmZrVmzBkouXLiQsMALj6Jjp6r9K0UxCnxKw6+83rNnDwAgMzMTpdF46PQyNRw7+jlUilAo\nFAqFqv4lBx7rUF1djQ+E71KtrKyOHj1aUlKSlZVlY2Nja2sLAIBrhymbUE81APpFe3UzdjT7\nAgal9igFMFasWBEZGTl8+HANDQ0PDw/Mt6upqTEwMMDmqhUHUUoBOnQzEXJzpMp0UCqHskbo\nq5ckk2o7dgTfEb7jw5YldB/opkRFRRHCN2/eDP49a6B2FKU6oezyXW0t0BK6ubnR2ZChdllo\nRqEsHQRu9SWYYorjTlatWrVp0yZ3d/cdO3ZYW1vzeLxbt24pHgOj6oCAlpYWAICmpiY+EB4a\npOqOlFHg2T8uLi7QRyEgEonq6uoAAJRHdmHPnXTSBDRU8cknn7z33ntJSUlHjhzJyMhAECQg\nICA5OVkikdBJnyS60vz7+fnt3Lmzubm5oaHh7t27iYmJEolELBbn5+f7+vrm5eVpa2t7eHiQ\nKwGj109lUzymwcHBYezYsUePHr1+/frgwYPDwsJqamru3r1rYWEBBaZNm2Zvbz937tx79+7h\nW+CRI0eeP38OvRM87u7uDx48qKqq0tHR0dbW7uzsjIiICAwMnDx5slQqra6u7t+/P5QcMGBA\nSkpKR0cHnZMvgOr236UoqhKhbDzwHKMu9bKezaFSRCJRaWnp8+fPjYyMunrrf/75B/y7hwIA\nRo8enZSUFBcXB5efCgSCDRs2FBYWVlRUwIdsyibUUw2gO0XrEej3BQxK7VEKYGDtMC8vLzAw\ncMKECcXFxRoaGtHR0e3t7bt371aVbUoBOvRIIqpQZToolUNZI/TV+yrQ0tLCX2pra4OXp2ko\nQnLKqUAgMDMzUwyHM0mKx/LBjiwUCnskiiKUXb6rrYXFYq1atWrPnj2DBw8ePnz4kiVLJk6c\nyGKxyGO9ouJTlg4GwpmmhoYGvCSZY9fW1vbVV1+JxeLc3FyBQAADCfHJ4fP5MB18IPRA1Y6C\nqUnVsZ/4Q61oQpkmTVV4e3t7e3u/ePHi3Llz+/fvT09P9/X1vXXrFmX65NG5XK6isJ+f37Zt\n2woKCmpqahAEgedmeXh4nD17FgCQl5c3atQopRHfIkxMTAAATU1NTU1Nly9f9vLywuwmAAAe\nIZaenn737t2BAwdi4QcPHmSxWKoO8zQ3N4c/tm7dWllZ+csvv8BbgJdtD6aMomhzczNhdrZX\noGw8MPNd6mUE2tvbu5FB5QwfPry0tPTEiRNwVxABFEVv3rzp5OSkNC60eg0NDQRvNSoqas6c\nOUVFRRoaGnBP2aBBg8zNzUmqCWtCWEj3G0B3itZ9utQX8FBqr6vq9fLyCgoKOnDgQGlp6f37\n97OystasWaOhoQGnkOEQ1dLS8vjxYx0dnQsXLpALwEon59SpU91PhAQS00GiHJo1okbr7Sma\nm5vxl3DkMjQ0VJTs7Ox85513VKUTFBR07NgxxXBLS0s2m/3gwQNCOFxwrDRBNaLQBOvyarQW\nBEE2bty4du3aAwcOJCUlTZ061dLSMioqKiIigsT/fp3FVzRo0NUhPAaTfXmiurq6tbXV3d0d\nc2UAAKo+YaEUMzMzLpd77949fOCNGze6E8XU1NTIyKikpITgumHnL2traxsbG9+5cwe/wae0\ntHTXrl23bt1SelPKNLukCh6P5+vrm5aWNn/+/PLy8j///JMyffLoSu8ycuRIHo93/vz53Nzc\ngQMHwskDT0/Py5cv37t3r6ysDK7BeitoampKSUnJzMwkhMP6kkgkra2tKIoSfBfw0pvBh7e3\nt+fk5Li6upKby7Kysvj4+C1btsDpUvgIC19fAgCam5sRBCE85vYWlI2nq70MPvngewchbo8A\nnZ7169crPpUCAJKTk52dnVU9ScPGDKfe8chkMqFQOGrUKE9PT6FQ+PDhw+LiYrjLj7IJEcK7\n0wC6U7TuQ78vECDRHqXAkydPnJ2dZ8+erfSmzc3NcMHxhg0bxC+B3kxmZqZYLE5ISKAUoFP2\nHklEFeSmg0Q5NGuEUv+vDrgkAANuJMKecPDAlQmqiIuLU5o+l8sdNGjQlStX4As3iFwuz8/P\nF4ul/ZqkAAAHqUlEQVTFhPN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}