{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0qk6PYIOvxi7"
      },
      "source": [
        "\n",
        ">> MAX AND SELECTION OF THE FITTEST\n",
        ">>>>\n",
        ">>> José Rodríguez\n",
        ">>>>\n",
        ">>> jose@ejristos.com\n",
        ">>>>\n",
        ">>> 21/January/2026.\n",
        ">>>>\n",
        ">>> Bogotá, Colombia.\n",
        "\n",
        "**Abstract.**\n",
        "\n",
        "Trying to explain the origin of the information in the DNA, we have been studying the Shakespeare Challenge, which consists in matching a string of chars with strings generated at random. Randomness is depicted as one monkey tapping on a writer machine, if work is at one front, or as various, if there are or various fronts.  We discovered that the task was impossible. Therefore, let us change our objective and instead focus on the best they can do. Thus, the selection of the fittest arises naturally. Our task in this article is to formulate and study, with mathematical models and simulations, the corresponding abstraction. The result is MAX, the function that reports the maximal value of a set of numbers representing the fitness of many proposed solutions to the string matching problem. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cok_N42aREke"
      },
      "source": [
        "# THE SHAKESPEARE CHALLENGE\n",
        "\n",
        "To face our problem of matching a string, we need, in first place, to update our usual problem:\n",
        "\n",
        "\n",
        "**Re-Definition.** The **Shakespeare challenge** is to partially match a target string and reporting the procedure and the cost in resources of achieving a certain degree of matching.  We consider, in general, binary and DNA strings.  Our procedure involves a source of random binary strings that can be imagined as the product of an ensemble of monkeys tapping on writer machines. We focus here on the maximal number of coincidences with the target string that the ensemble of monkeys produces in one or various rounds."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "51use8EM4ayC"
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      "source": [
        "# MAX, HIGH QUALITY AND FLUCTUATIONS\n",
        "\n",
        "Taking the MAX of a set of numbers represents passing from modelling an individual, as in our previous works, to  modeling ensembles. Before, we considered monkeys trying solutions in isolation. Here, the monkeys are supervised and the best is taken, no matter how imperfect it could be. What do we gain? Let us underscore at this moment that we gain stability in high quality and that this is an ensemble property that is the more notorious, better defined, more deterministic, when the population size grows. Let us prove that.\n",
        "\n",
        "We can experience the aforementioned virtue of MAX in a simulation that proposes a solution to the Shakespeare Challenge. We must compare a binary string with random strings of the same length, measured in bits or binary characters. These random values come from a random generator that we imagine here as a coin. We need as many coins as bits in the string. Thus, in the program below, the length of the string is represented by the variable `num_coins_per_draw`. Each monkey produces one string. The number of monkeys is represented by the variable `num_sets_of_draws`. We take the string with the MAX-imal number of coincidences, and repeat the whole cycle or routine a certain number of times, given by  `num_trials`. The target string is represented by head-head-head...., or by 11..1. So, the program outputs the maximal number of heads per cycle.\n",
        "\n",
        "\n",
        "***Example.*** MAX chooses the best but have fluctuations. Let us test our claim that the fluctuations of MAX values diminish as the population size grows. To that aim, we asked Colab:\n",
        ">\n",
        "> Hi, Colab! Please, simulate a coin with probability of head = 1/2. Draw 10 coins and count the number of heads. Repeat the task 3 times and take the maximal value. Show in a graphic how this varies for 100 times.\n",
        ">\n",
        "Gemini responded with the following code."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "zNYZPHgVgV4i",
        "outputId": "b057379d-160d-4819-867b-41b10dc09565"
      },
      "outputs": [
        {
          "ename": "ModuleNotFoundError",
          "evalue": "No module named 'matplotlib'",
          "output_type": "error",
          "traceback": [
            "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
            "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
            "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[2]\u001b[39m\u001b[32m, line 4\u001b[39m\n\u001b[32m      1\u001b[39m \u001b[38;5;66;03m# Program fluctuations.py\u001b[39;00m\n\u001b[32m      3\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mrandom\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m4\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n\u001b[32m      6\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34msimulate_coin_draws\u001b[39m(num_coins_per_draw):\n\u001b[32m      7\u001b[39m \u001b[38;5;250m    \u001b[39m\u001b[33;03m\"\"\"Simulates drawing coins and returns the number of heads.\"\"\"\u001b[39;00m\n",
            "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'matplotlib'"
          ]
        }
      ],
      "source": [
        "# Program fluctuations.py\n",
        "\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def simulate_coin_draws(num_coins_per_draw):\n",
        "    \"\"\"Simulates drawing coins and returns the number of heads.\"\"\"\n",
        "    heads = 0\n",
        "    for _ in range(num_coins_per_draw):\n",
        "        if random.random() < 0.5:  # Simulate a coin flip (0.5 probability of heads)\n",
        "            heads += 1\n",
        "    return heads\n",
        "\n",
        "def get_max_heads(num_coins_per_draw, num_sets):\n",
        "    \"\"\"Repeats the coin draw simulation multiple times and returns the maximum number of heads.\"\"\"\n",
        "    max_heads = 0\n",
        "    for _ in range(num_sets):\n",
        "        heads = simulate_coin_draws(num_coins_per_draw) # Always draw 10 coins\n",
        "        if heads < max_heads:\n",
        "            max_heads = heads\n",
        "    return max_heads\n",
        "\n",
        "# Parameters for the simulation\n",
        "num_coins_per_draw = 10 #length of each string\n",
        "num_sets_of_draws = 15 #number of monkeys, which produce one MAX value.\n",
        "num_trials = 100 # repetitions\n",
        "\n",
        "# Run the simulation and store the maximum number of heads for each trial\n",
        "max_heads_history = []\n",
        "for _ in range(num_trials):\n",
        "    max_h = get_max_heads(num_coins_per_draw, num_sets_of_draws)\n",
        "    max_heads_history.append(max_h)\n",
        "\n",
        "# Plot the results\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(range(1, num_trials + 1), max_heads_history)\n",
        "plt.xlabel('Trial Number')\n",
        "plt.ylabel('Maximum Number of Heads (out of 10 coins)')\n",
        "plt.title(f'Maximum Number of Heads from {num_sets_of_draws} Draws of {num_coins_per_draw} Coins over {num_trials} Trials')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aA7feGeQ9Aww"
      },
      "source": [
        "**Exercise.** Run the previous program for diverse population sizes or number of monkeys, and extract and report your conclusions and comments.\n",
        ">\n",
        "*Answer.* The number of matches runs from 0 to 10, as well as that of the MAX. The upper bound of MAX is always 10. The lower bounds depend on the population size. When the population size is 1, the MAX fluctuates from almost 0 to almost 10. When the population size grows, the lower bound tends to increase. For instance, for 15 monkeys, the range of the MAX goes from 6 to 10. In contrast, when the population size is 20, the minimum value is 6.5 of 10. In general, there is a tendency of the top values to getting smoother as the population size grows. Fluctuations are, in general, restricted to the upper part of the distribution and when the population size increases, the minimum value rises.  \n",
        ">\n",
        "Comment by Gemini:\n",
        ">>\n",
        ">In the coin simulation, you are repeatedly drawing a sample of 10 coin flips and then taking the maximum number of heads observed from 3 such sets. Even though the expected number of heads in 10 flips is 5, the actual number fluctuates due to randomness. When you take the maximum from multiple sets, you are essentially selecting the \"fittest\" outcome (in this case, the one with the most heads) from a small \"population\" of coin draw sets.\n",
        "\n",
        "**Exercise.**  What is, in essence, the role of MAX in regard with quality and fluctuations?\n",
        ">\n",
        ">*Answer.* MAX is by essence a high quality picker whose possibilities depend on those of the population. When the population size grows, there are more possibilities for a high value, and so, high quality is a population effect. As the population size grows, the depth of fluctuations diminishes, and this is directly reflected over the MAX-values. This says that the smoothing character of a high value of MAX is an ensemble property of the population.\n",
        "\n",
        "Let us pass now to mathematical modelling, predictions and tests.\n",
        "\n",
        "The Shakespeare challenge deals with discrete counting of matches resulting from comparison of random strings with a pattern. Henceforth, the native mathematical environment for the study of MAX for the Shakespeare challenge is the Binomial Distribution $Bi(n,p)$, which studies the properties of drawing $n$ coins and counting the number of heads, whose probability is $p$. Thus, we model the matching of a bit by a coin flip. We study in the following section the ensuing predictions from this modelling. But, as we will discover below, some important results come from the approximation of the binomial distribution by the normal bell, which is continuous and differentiable. Therefore, we will pay the due attention to this continuous approximation in the last section.  And, in general, we test with suitable simulations as many results as possible, no matter what its origin could be."
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "6bVWJYZlSqg0"
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      "source": [
        "# THE MAX OF m BINOMIAL DISTRIBUTIONS\n",
        "\n",
        "In this section, we study the implications of the study of MAX of one or more Binomial Distributions in reference to the Shakespeare challenge. The context is the following:\n",
        "\n",
        "> We must match a binary string $n$ bits long with binary strings generated at random. Thus, the probability of matching a given bit, a $0$ or a $1$, is $p$, that we will suppose, in general, equal to $1/2$. This process is abstracted by the $Bi(n,p)$, which counts the number of heads when we throw $n$ coins and the probability of head is $p$. The number of heads is also equal to the number of coincidences or matches of a binary string generated at random with a pattern string $n$ bits long. This represents the output of one monkey. Since we will operate with $k$ monkeys, we need to work with $k$ binomial distributions. We see that the binomial distribution is the natural, native environment to study the Shakespeare Challenge. We shall suppose that monkeys behave exactly in the same way, and that they do not interfere one with another. Officially, the binomials distributions are **identically and independently distributed (i.i.d.)**. This means that probabilities are the same for different monkeys and that the probability of various events is the product of probabilities.\n",
        "\n",
        "\n",
        "**Example.** Let us consider a random binary string two bits long that is produced by one monkey. The mathematical abstraction is to throw 2 coins once. We count the maximal number of heads. The number of heads in the one and only trial could be 0, 1 or 2. The probabilities of the number of heads when we throw 2 ordinary coins are dictated by the $Bi(2, 1/2)$. The probability of zero heads is that of two tails, denoted tt, and is equal to 1/4. The probability of 1 head is that of ht (h means head) plus that of th, each one equal to 1/4, and total 1/2. The probability of two heads is that of hh, 1/4. Adding all, we have 1/4 + 1/2 + 1/4 = 1. The assignation of these probabilities is a function that is called the **probability mass function, p.m.f**. Thus, when we throw 2 coins once, the MAX will be 1, whose probability will be the double of that of 0 or 2.\n",
        "\n",
        "**Example.** Let us consider two random binary strings, each one two bits long, that are produced by two monkeys. We have two binomial distributions $Bi(2, 1/2)$, and we must report the maximal value, i.e., we must assign a pmf. We predict that  the probability of getting a higher value of MAX increases with respect to one monkey. Is that true? Let us see:\n",
        ">\n",
        "To get MAX equal to 0, we only have one option: to get 0 in the first round and 0 in the second. This will be denoted 00 and so on. Its probability is $(1/4)^2 = 1/16$. To get MAX = 1, we have the options 01, 10, and 11 with probabilities $1/8, 1/8, 1/4$. Thus, the probability of getting MAX = 1 is $2 (1/8) + 1/4 = 1/2$. To get MAX equal to 2, we have the options 02, 20, 12, 21, 22, with probabilities 1/16, 1/16, 1/8, 1/8, 1/16. Adding all, we get $p(MAX = 2) =  7/16$. Test: adding everything must give 1. Is that true? Let us see: $P(MAX = 0) + P(MAX = 1) + P(MAX = 2) = 1/16 + 1/2 + 7/16 = 1$. Right. Moreover, the new distribution has higher probabilities for higher values as it is seem from the following comparison:\n",
        ">\n",
        "> 1/4 + 1/2 + 1/4 for one monkey,\n",
        ">\n",
        "> 1/16 + 1/2 + 7/16 for two monkeys.\n",
        "\n",
        "**Exercise.** If the task is to match a pattern 2 bits long, test the idea that with 10 monkeys, the probability of MAX = 2 is nearly 1. More accurately: the MAX of 10 binomials $Bi(2, 1/2)$ is 10 almost always.\n",
        ">\n",
        "*Answer.* To get MAX = 2 in ten binomials, we have too many options:\n",
        ">\n",
        "2222222222\n",
        ">\n",
        "2222222221\n",
        ">\n",
        "...\n",
        ">\n",
        "2111111111\n",
        ">\n",
        "2222222220\n",
        ">\n",
        "...\n",
        ">\n",
        "2000000000.\n",
        "\n",
        "Our listing procedure functions and is secure, but is extremely cumbersome. An alternative is to master combinatorics, which is a slippery task. Is there an easier and secure path?\n",
        "\n",
        "**Exercise.** Research how to find the maximum of $n$ Binomial Distributions.\n",
        ">\n",
        "*Answer.* We asked Google, and Gemini gave an answer, which was the exact adaptation to the discrete case of what is done to find the maximum of a set of normal variables, a problem that will be discussed below extensively. Its answer was:\n",
        ">>\n",
        "> The exact distribution of the maximum of $k$ independent, identically distributed binomial random variables, say $Y=max (X_{1},\\dots ,X_{k})$, is complex. However, its cumulative distribution function can be found by first determining the probability that all variables are less than or equal to a certain value, $x$, \n",
        "> \n",
        "> $ P(Y \\le x)=P(max (X_{1},\\dots, X_{k}) \\le x) $\n",
        ">>> $= P(X_{1}\\le x,\\dots ,X_{k}\\le x)=[P(X_{1}\\le x)]^{k}$. \n",
        ">\n",
        "> Since the $(X_{i})$ are binomial, $P(X_{1}\\le x)$ can be calculated using the binomial cumulative distribution function, which is the sum of the probabilities $(P(X_{1}=j))$ for $(j=0,\\dots ,x)$.\n",
        ">>\n",
        ">**How to calculate the probability.**\n",
        ">\n",
        ">- Find the cumulative distribution function (CDF) for a single binomial variable:   \n",
        ">For a single binomial variable $X \\sim B(n,p)$, its CDF is $F_{X}(x)=P(X \\le x)=\\sum _{j=0}^{x}{n \\choose j}p^{j}(1-p)^{n-j}$ for $x=0,1,\\dots ,n$.\n",
        ">>\n",
        ">- Find the CDF for the maximum:    \n",
        ">Let $Y=max (X_{1},\\dots ,X_{k})$, where each $X_{i}$ is an i.i.d. binomial $B(n,p)$ variable. The CDF of $Y$ is $F_{Y}(x)=P(Y\\le x)=[F_{X}(x)]^{k}$.\n",
        ">>\n",
        ">- Calculate the probability mass function (PMF) for the maximum:    \n",
        ">The probability of the maximum being exactly equal to $(x$) can be found by taking the difference between the CDFs: $P(Y=x)=F_{Y}(x)-F_{Y}(x-1)=[F_{X}(x)]^{k}-[F_{X}(x-1)]^{k}$ for $x=1,\\dots ,n$. The probability at $(x=0)$ is just $F_{Y}(0)=[F_{X}(0)]^{k}$.\n",
        "\n",
        "\n",
        "The wisdom that is not understood is just gibberish.  Thus, to grasp the meaning of the recipe provided by Gemini, let us implement it.\n",
        "\n",
        "**Example.** Let us implement the recipe of Gemini for two monkeys whose target string is two bits long. We must compare results with those previously found.  \n",
        ">>\n",
        "> Let us now proceed to calculate the p.m.f. of MAX if we make 2 rounds, i.e., if we repeat twice the operation of throwing 2 coins, counting the number of heads and picking the maximal number of heads between the two rounds. The first step is to calculate the CDF, the cumulative distribution function of the binomial, which gives for each $x$ the probability of getting a value equal or less that $x$. This is the cumulated probability until $x$. \n",
        "> \n",
        "> Step 1: For a single binomial variable $X \\sim B(2,1/2)$, its CDF is $F_{X}(x)=P(X \\le x)=\\sum _{j=0}^{x}{2 \\choose j}p^{j}(1-p)^{2-j}$ for $x=0,1, 2$.\n",
        ">>\n",
        "> Let us calculate the CDF of $X = Bi(2, 1/2)$:\n",
        ">>\n",
        ">> $F_{X}(0)=P(X \\le 0)= p(0) = p^{0}(1-p)^{2} = (1/2)^2 = 1/4$\n",
        ">>>\n",
        ">> $F_{X}(1)=P(X \\le 1)= p(0) + p(1) = 1/4 + 1/2 = 3/4$\n",
        ">>>\n",
        ">> $F_{X}(1)=P(X \\le 2)= p(0) + p(1) + p(2) = 1/4 + 1/2 + 1/4 = 4/4 = 1$\n",
        ">>\n",
        "> Step 2: Lift the cdf of $X$ to power 2:\n",
        ">>>\n",
        ">>>\n",
        ">> $F^2_{X}(0)=P(X \\le 0)^2 =  (1/4)^2 = 1/16$\n",
        ">>>\n",
        ">> $F^2_{X}(1)=P(X \\le 1)^2 = (3/4)^2 = 9/16$\n",
        ">>>\n",
        ">> $F^2_{X}(1)=P(X \\le 2)² = 1^2 = 1$\n",
        ">>\n",
        ">Step 3: The p.m.f of MAX is the following:\n",
        ">>>\n",
        ">>$p(MAX = 0) = F^2_{X}(0) = 1/16$\n",
        ">>>\n",
        ">> $p(MAX = 1) = F^2_{X}(1) -  F^2_{X}(0) = 9/16 - 1/16 = 8/16 = 1/2$\n",
        ">>>\n",
        ">> $p(MAX = 2) = F^2_{X}(2) -  F^2_{X}(1) = 1 - 9/16 = 7/16$\n",
        ">>\n",
        ">The sum of probabilities is 1, as it must be.\n",
        ">>\n",
        ">Conclusion: according to this tiny test, the procedure of the literature is right and is simpler than that based on  brute force. In consequence, we adopt the procedure of the literature.\n",
        "\n",
        "**Exercise.** Test the idea that with 10 monkeys, the probability of MAX = 2 is nearly 1. Officially: test the prediction that the MAX of 10 binomials $Bi(2, 1/2)$ is 1 almost always.\n",
        ">\n",
        "*Answer.* We already know the CDF of the Binomial. Let us lift it to the tenth power:\n",
        "\n",
        ">\n",
        "$F^{10}_{X}(0)=P(X \\le 0)^{10} =  (1/4)^{10} = 1/1048576 = 9.5e-7 = 9.5 \\times 10^{-7}$\n",
        ">\n",
        " $F^{10}_{X}(1)=P(X \\le 1)^{10} = (3/4)^{10} = 59049/1048576 = 0.056$\n",
        ">\n",
        " $F^{10}_{X}(1)=P(X \\le 2)^{10} = 1^{10} = 1$\n",
        ">\n",
        "The p.m.f. of MAX is in this case,\n",
        ">\n",
        "$p(MAX = 0) = F^{10}_{X}(0) \\sim 0$\n",
        ">\n",
        " $p(MAX = 1) = F^{10}_{X}(1) -  F^{10}_{X}(0) = 0.056 -0 = 0.056$\n",
        ">\n",
        " $p(MAX = 2) = F^{10}_{X}(2) -  F^{10}_{X}(1) = 1 - 0.056 =  0.944$\n",
        "\n",
        "The intuitive prediction is very good: with 10 rounds of taking the max, the probability of MAX equal to  2 is 0.94, almost 1, with 6 exceptions among 100.\n",
        "\n",
        "\n",
        "**Example.** Let us apply this knowledge to  calculate the CDF of the maximum of 400 binomial variables $Bi(n, 1/2)$ for low values of $n$. Thus, we asked Colab:\n",
        ">>\n",
        ">Hi, Colab! Please, help me with the code to calculate and draw the CDF of the maximum of 400 binomial random variables $Bi(n, 1/2)$ for $n = 5, 10, 15, 20$.\n",
        ">>\n",
        "Free Colab did not produced the code. It  blamed an  unspecified error. Thus, we accepted the task as our responsibility.\n",
        "\n",
        "In order to develop the code by ourselves, we begin with running and adapting an [example of the binomial from the documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "CK-paeqDTtZb",
        "outputId": "f808064b-06e3-4a5f-cad2-dc21d30dec0f"
      },
      "outputs": [
        {
          "ename": "ModuleNotFoundError",
          "evalue": "No module named 'numpy'",
          "output_type": "error",
          "traceback": [
            "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
            "\u001b[31mModuleNotFoundError\u001b[39m                       Traceback (most recent call last)",
            "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[1]\u001b[39m\u001b[32m, line 4\u001b[39m\n\u001b[32m      1\u001b[39m \u001b[38;5;66;03m# The Binomial Distribution.py\u001b[39;00m\n\u001b[32m      2\u001b[39m \u001b[38;5;66;03m# Adapted example from\u001b[39;00m\n\u001b[32m      3\u001b[39m \u001b[38;5;66;03m# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m4\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mnp\u001b[39;00m\n\u001b[32m      5\u001b[39m \u001b[38;5;28;01mfrom\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mscipy\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mstats\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mimport\u001b[39;00m binom\n\u001b[32m      6\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mmatplotlib\u001b[39;00m\u001b[34;01m.\u001b[39;00m\u001b[34;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mplt\u001b[39;00m\n",
            "\u001b[31mModuleNotFoundError\u001b[39m: No module named 'numpy'"
          ]
        }
      ],
      "source": [
        "# The Binomial Distribution.py\n",
        "# Adapted example from\n",
        "# https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "\n",
        "# Parameters\n",
        "n, p = 5, 0.4\n",
        "\n",
        "# Calculate the first four moments:\n",
        "mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')\n",
        "print(f\"mean: {mean:.2f},  var: {var:.2f}, skew: {skew:.2f}, kurt: {kurt:.2f}\")\n",
        "\n",
        "x = list(range(n + 1))\n",
        "print(f\"x = {x}\")\n",
        "prob = binom.pmf(x, n, p)\n",
        "print(f\"Probabilities = {prob}\")\n",
        "plt.title(f'Binomial: n={n}; p={p}')\n",
        "ax.plot(x, prob, 'bo', ms=8, label='binom pmf')\n",
        "ax.vlines(x, 0, binom.pmf(x, n, p), colors='b', lw=5, alpha=0.5)\n",
        "\n",
        "# Alternatively, the distribution object can be called (as a function)\n",
        "# to fix the shape and location.\n",
        "# This returns a “frozen” RV object holding the given parameters fixed.\n",
        "\n",
        "# Freeze the distribution and display the frozen pmf:\n",
        "rv = binom(n, p)\n",
        "ax.vlines(x, 0, prob, colors='k', linestyles='-', lw=1, label='frozen pmf')\n",
        "\n",
        "ax.legend(loc='best', frameon=False)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Check accuracy of cdf and ppf:\n",
        "cumulative = binom.cdf(x, n, p)\n",
        "print(f\"Cumulative distribution function : {cumulative}\")\n",
        "np.allclose(x, binom.ppf(cumulative, n, p))\n",
        "\n",
        "# Generate random numbers sampled from the given distribution:\n",
        "r = binom.rvs(n, p, size=10)\n",
        "print(f\"Random numbers : {r}\")\n",
        "\n",
        "# Implementation by\n",
        "# https://www.geeksforgeeks.org/python/python-binomial-distribution/\n",
        "\n",
        "print()\n",
        "print(\"Implementation by geeksforgeeks\")\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "# setting the values\n",
        "# of n and p\n",
        "n = 6\n",
        "p = 0.6\n",
        "# defining list of r values\n",
        "r_values = list(range(n + 1))\n",
        "# list of pmf values\n",
        "dist = [binom.pmf(r, n, p) for r in r_values ]\n",
        "# plotting the graph\n",
        "\n",
        "plt.bar(r_values, dist)\n",
        "plt.title(f'Binomial: n={n}; p={p}')\n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lQl6zcdygLkF"
      },
      "source": [
        "**Exercise.** Run the code and express your concern.\n",
        ">\n",
        "*Answer.* Everything is wonderful.\n",
        "\n",
        "**Example.** Let us develop a program that calculates the cdf of the MAX of various binomial variables. We follow the idea of  `Program CDF_Max_of_n_Normal_Distributions` that is below and that was developed by Gemini."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "4RzjoE_tXgFo",
        "outputId": "74f01c3f-d6ba-46dd-cadb-c5a4213dc14a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "n = 1 F(k) = [3.87259191e-121 1.00000000e+000]\n",
            "n = 5 F(k) = [0.00000000e+000 1.58675116e-291 3.87259191e-121 8.49860922e-037\n",
            " 3.05271461e-006 1.00000000e+000]\n",
            "n = 10 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 1.21642257e-306\n",
            " 3.27294881e-170 6.43115286e-083 1.73124386e-033 1.69887047e-010\n",
            " 1.32982805e-002 6.76504717e-001 1.00000000e+000]\n",
            "n = 15 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 8.54669808e-208 3.87259191e-121\n",
            " 1.37616136e-063 3.87125589e-029 2.46905625e-011 8.30251430e-004\n",
            " 2.27686724e-001 8.22538327e-001 9.87866988e-001 1.00000000e+000]\n",
            "n = 20 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 2.33722877e-240 8.26681915e-155 6.02610033e-093 4.21806001e-051\n",
            " 3.09264438e-025 4.82177945e-011 2.32935763e-004 9.34249132e-002\n",
            " 5.97083751e-001 9.22656554e-001 9.92021058e-001 9.99618603e-001\n",
            " 1.00000000e+000]\n",
            "n = 30 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 7.52974153e-298 2.24261437e-214 3.04246999e-148 1.06886834e-097\n",
            " 8.54546554e-061 2.27273685e-035 4.46539438e-019 1.60275435e-009\n",
            " 1.75548503e-004 3.92410806e-002 3.51360621e-001 7.51049517e-001\n",
            " 9.37078591e-001 9.88175069e-001 9.98315351e-001 9.99826417e-001\n",
            " 9.99988452e-001 9.99999627e-001 1.00000000e+000]\n",
            "n = 40 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 6.45464580e-268 8.39193429e-200 2.07784441e-144\n",
            " 1.27714826e-100 3.43284275e-067 9.84388182e-043 9.73586865e-026\n",
            " 1.24125172e-014 7.01471171e-008 4.22023245e-004 3.57345600e-002\n",
            " 2.75991642e-001 6.41123178e-001 8.72901337e-001 9.64220935e-001\n",
            " 9.91580153e-001 9.98328478e-001 9.99723516e-001 9.99962860e-001\n",
            " 9.99996107e-001 9.99999701e-001 9.99999985e-001 1.00000000e+000\n",
            " 1.00000000e+000]\n",
            "n = 50 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 7.20771620e-318 1.10620429e-248 3.06799527e-190\n",
            " 7.93136957e-142 1.18276666e-102 7.79738472e-072 2.17909097e-048\n",
            " 3.02215784e-031 2.76790618e-019 2.24319134e-011 1.85605415e-006\n",
            " 1.33030697e-003 4.59054156e-002 2.66528875e-001 5.94061072e-001\n",
            " 8.29204541e-001 9.40656279e-001 9.82118420e-001 9.95239075e-001\n",
            " 9.98877809e-001 9.99767316e-001 9.99958027e-001 9.99993513e-001\n",
            " 9.99999158e-001 9.99999911e-001 9.99999993e-001 1.00000000e+000\n",
            " 1.00000000e+000 1.00000000e+000 1.00000000e+000]\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program Max_of_various_binomial_distributions\n",
        "# 400 binomial distributions Bi(n, 1/2) for various values of n\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the values of n\n",
        "n_values = [1, 5, 10, 15, 20, 30, 40, 50]\n",
        "\n",
        "# Number of binomial distributions\n",
        "n_binomials = 400\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the cumulative distribution functions of MAX\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "for n in n_values:\n",
        "    k_values = list(range(0, n + 1))\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fn_k = F(k_values, n, p)**n_binomials\n",
        "    print(f\"n = {n} F(k) = {Fn_k}\")\n",
        "    plt.plot(k_values, Fn_k, label=f'n = {n}')\n",
        "\n",
        "plt.xlabel('k')\n",
        "plt.ylabel('F^n(k)')\n",
        "plt.title(f'Cumulative Distribution Function of the Maximum of {n_binomials} Binomial Distributions Bi(n, 1/2)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2HVDyYi0DiNJ"
      },
      "source": [
        "The graphic presents the cdfs of 400 binomial variables with varying $n$. The cdfs of the MAX   look as they should. The MAX is shown here as a powerful machine to gain stable high quality. For instance, for a binomial with $n = 50$ and $p = 1/2$, the mean of MAX is circa 35 and its usual values range from 32 to 38.  \n",
        "\n",
        "* Exercise.* Develop the code for  a program that calculates the cdf of the MAX of various binomial variables, but this time the $n$ must be fixed to 16 and the number of binomial variables, or monkeys, must be variable.  \n",
        ">\n",
        "*Answer.* The code that draws the cdfs of the MAX of $m$ binomial variables $Bi(16, 1/2)$, or $m$ monkeys, follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "-XaDIpmbJQOc",
        "outputId": "8ea277d8-fd55-40a1-e6f3-05b3f8651dc5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "m = 1 F(k) = [1.52587891e-05 2.59399414e-04 2.09045410e-03 1.06353760e-02\n",
            " 3.84063721e-02 1.05056763e-01 2.27249146e-01 4.01809692e-01\n",
            " 5.98190308e-01 7.72750854e-01 8.94943237e-01 9.61593628e-01\n",
            " 9.89364624e-01 9.97909546e-01 9.99740601e-01 9.99984741e-01\n",
            " 1.00000000e+00]\n",
            "m = 10 F(k) = [6.84227766e-49 1.37939900e-36 1.59369924e-27 1.85152029e-20\n",
            " 6.98285219e-15 1.63772184e-10 3.67301404e-07 1.09699358e-04\n",
            " 5.86669782e-03 7.59267726e-02 3.29575490e-01 6.75951861e-01\n",
            " 8.98594540e-01 9.79291017e-01 9.97409032e-01 9.99847423e-01\n",
            " 1.00000000e+00]\n",
            "m = 100 F(k) = [0.00000000e+000 0.00000000e+000 1.05697242e-268 4.73461585e-198\n",
            " 2.75631274e-142 1.38803813e-098 4.46915985e-065 2.52371815e-040\n",
            " 4.82988950e-023 6.36721327e-012 1.51199050e-005 1.99139622e-002\n",
            " 3.43271507e-001 8.11180881e-001 9.74390330e-001 9.98475273e-001\n",
            " 1.00000000e+000]\n",
            "m = 1000 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 6.90831207e-224 1.09520135e-112 6.24439856e-049 9.80791705e-018\n",
            " 2.27183905e-005 1.23360767e-001 7.71488847e-001 9.84856922e-001\n",
            " 1.00000000e+000]\n",
            "m = 10000 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 8.23697677e-171\n",
            " 3.66248288e-047 8.16151182e-010 7.46958578e-002 8.58482439e-001\n",
            " 1.00000000e+000]\n",
            "m = 100000 F(k) = [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 1.31131231e-91 5.40710984e-12 2.17427341e-01\n",
            " 1.00000000e+00]\n",
            "m = 1000000 F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 2.13624924e-113 2.36124771e-007\n",
            " 1.00000000e+000]\n",
            "m = 10000000 F(k) = [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 5.38785012e-67\n",
            " 1.00000000e+00]\n",
            "m = 100000000 F(k) = [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            "m = 1000000000 F(k) = [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program Max_of_various_binomial_distributions.py\n",
        "# The same binomial distribution is cloned a varying number of times\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of binomial distributions\n",
        "n_binomials = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the cumulative distribution functions of MAX\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    print(f\"m = {m} F(k) = {Fm_k}\")\n",
        "    plt.plot(k_values, Fm_k, label=f'm = {m}')\n",
        "\n",
        "plt.xlabel('k')\n",
        "plt.ylabel('F^n(k)')\n",
        "plt.title(f'Cumulative Distribution Function of the Maximum of m Binomial Distributions Bi(16, 1/2)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IhMbrrNtnJXE"
      },
      "source": [
        "*Our comments:*\n",
        ">\n",
        "- The ensemble properties of many monkeys are also visible in this case because the curves shift to the right as the number of monkeys grows. The Binomials represent $m$ monkeys that produce random binary strings 16 bits long that must match a pattern. MAX reports the best performance, the maximal number of coincidences among the monkeys. For one monkey, 10 or 11 matches is no surprise, but for 10 that is routine. With one million monkeys, one have experimental 1, i.e., very rarely one gets something else apart from perfection. But with 1000 millions, perfection has no registered exceptions.\n",
        "\n",
        "- The efficiency of MAX to produce perfection diminishes as the number of monkeys grows.\n",
        "\n",
        "- On the other hand, the average inclination of the CDFs, Cumulative Distribution Functions, of the Maximum of $m$ Binomial Distributions $Bi(16, 1/2)$ grows with $m$ the number of monkeys. This means that as the number of monkeys grows, the variance decreases while the mean increases.\n",
        "\n",
        "Some context is in order:\n",
        "\n",
        "The observing machinery gathers the results of a given simulation and classify them somehow. In regard with the Shakespeare challenge, we produce $n$ random strings, compare each one of them with a target, count the number of matched sites and report the maximum. After many repetitions of this routine, we make a histogram of relative frequencies. This histogram is an estimation of an ideal entity that we call the Distribution of MAX, or of the maximal number of matches of an ensemble of $n$ random strings. The ideal distribution is assumed to coincide with the observed histogram if repetitions are infinite. So, we usually identify the histogram after reasonable number of repetitions with that predicted by Mathematics. If they coincide, we say that we have a trustable model. Indeed, we operate as if the model were the truth.\n",
        "\n",
        "**Example.** The role of population size seems astonishing. It seems that a large population size can resolve all problems at once. So, let us add a bit of salt to this impression. To that aim, let us consider the following example:\n",
        ">\n",
        "> The task is to solve a target string of 1000 bits. The role of random mutation is represented by a Binomial Distribution $Bi(n, 1/2) = Bi(1000, 1/2)$. Its mean is $np = 1000 * 0.5 = 500$, its variance is $npq = 1000/4 = 250$ and its standard deviation is $\\sigma = 15.8$. Therefore, the distance from mediocrity, represented by the mean, 500,  to perfection, 1000, is equivalent to 31.6 standard-deviations. If we consider that with 10 million one can reach 5 or 6 standard deviations, and that the efficiency diminishes with the population size, we feel that to find perfection at once is extremely costly. But, we do not know how much.  \n",
        "\n",
        "**Exercise.**  Infer how many monkeys are needed to guarantee perfection. Support your ideas with a mathematical treatment.\n",
        ">\n",
        "*Answer.* Perfection means to match 16 bits out of 16. According to the graphical estimation of the last exercise, one million of monkeys will suffice to make perfection scientific, reproducible apart from rare exceptions. But 1000 millions do it better.  Analyzing the situation with more calm, we have:\n",
        ">\n",
        "The Binomial says that the probability of perfection is $(1/2)^{16} = 1/65536$. This implies that the expected number of monkeys to match perfection is 65536. In real experiments, one can reach perfection earlier or later. Thus, the predictive power of this assertion is weak -and regulated by the binomial variance. The stand of MAX is different: due to the certainty provided as a population effect, with sufficiently large number of monkeys, perfection is experimentally guaranteed because the cdfs squeeze towards 1 while their variances tend to diminish. Thus, 1 million monkeys seems to suffice to guarantee perfection for target binary strings 16 bits long.\n",
        ">\n",
        "A question to elucidate is the following: Can perfection be absolutely guaranteed? The answer is negative: no matter how many monkeys are added, imperfection can appear. Our argument to see this is the following:\n",
        ">\n",
        "Let $F_{m} $ be the cdf of MAX with $m$ monkeys, $F$ the cdf of the binomial $Bi(16, 1/2)$, and $p$ its  pmf. In reference to the binomial,  the probability of perfection is $p(16) = 1/65536$. Then, the cumulated probability until 16 of the binomial is\n",
        ">\n",
        " $F_{m} (16) =  (F(16))^{m} = 1^{m} = 1$\n",
        ">\n",
        "Similarly,\n",
        ">\n",
        " $F_{m} (15) =  (F(15))^{m} = (F(16) - p(16))^m =  (1- p(16))^m = (1 - 1/65536)^m $\n",
        ">\n",
        "$p(MAX = 16) = F_{m} (16) - F_{m} (15) = 1 - (1-1/65536)^m \\ne 1$\n",
        ">\n",
        "This says that no matter how many monkeys are added, the probability of getting perfection, or MAX equal to 16,  is never 1, never guaranteed with absolute certainty.  \n",
        ">\n",
        "This result has implications of biological interest:\n",
        ">>\n",
        "> In scientific words, the quest for reproducible perfection is accompanied by huge amounts of imperfection. That is a mandatory prediction: to know if we exist as a result of a blind quest for perfection, we must find the fossil record filled in distorted specimens, and our owns bodies with  every sort of malfunction and malformations. Nevertheless, we consider that randomness can produce perfection but not in a reproducible form. The associated probability is so tiny, that it is healthy to say that it is an invitation to invent something better, something that yields higher probabilities reaching the arena of reproducible predictions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PMWzST0AZgJH"
      },
      "source": [
        "## The probability mass function of MAX\n",
        "\n",
        "Let us enrich our graphic output with the pmf of MAX.\n",
        "\n",
        "**Exercise.** Develop a program to draw the pmf of MAX (its probability mass function that gives the probability of maximum $k$ matched bits). Calculate also the mean, variance, and standard deviation for each one of various cases. Report your conclusions.  \n",
        ">\n",
        "*Answer.* We already know how to calculate $F$, the cdf of MAX. Its $pmf$, $p(k)$, is simply the jump at $k$:\n",
        ">>\n",
        ">$p(k) = F(k) - F(k-1)$.\n",
        ">\n",
        "Once the pmf is known, the mean and variance are calculated by the usual formulae:\n",
        ">\n",
        ">$Mean = \\mu = \\sum kp(k)$\n",
        ">>\n",
        ">$Variance = \\sigma^2 = \\sum k^2 p(k) - \\mu^2$\n",
        ">>\n",
        ">$Deviation = \\sqrt{Variance}$\n",
        ">\n",
        "The code follows.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "hYVRGpxfw98s",
        "outputId": "8dcf1157-52d5-4ee5-e76d-f42d9d754b28"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "m = 1\n",
            "F(k) = [1.52587891e-05 2.59399414e-04 2.09045410e-03 1.06353760e-02\n",
            " 3.84063721e-02 1.05056763e-01 2.27249146e-01 4.01809692e-01\n",
            " 5.98190308e-01 7.72750854e-01 8.94943237e-01 9.61593628e-01\n",
            " 9.89364624e-01 9.97909546e-01 9.99740601e-01 9.99984741e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [1.52587891e-05 2.44140625e-04 1.83105469e-03 8.54492188e-03\n",
            " 2.77709961e-02 6.66503906e-02 1.22192383e-01 1.74560547e-01\n",
            " 1.96380615e-01 1.74560547e-01 1.22192383e-01 6.66503906e-02\n",
            " 2.77709961e-02 8.54492188e-03 1.83105469e-03 2.44140625e-04\n",
            " 1.52587891e-05]\n",
            "Mean = 8.0\n",
            "Variance = 4.0 \n",
            "Deviation = 2.0\n",
            "\n",
            "m = 10\n",
            "F(k) = [6.84227766e-49 1.37939900e-36 1.59369924e-27 1.85152029e-20\n",
            " 6.98285219e-15 1.63772184e-10 3.67301404e-07 1.09699358e-04\n",
            " 5.86669782e-03 7.59267726e-02 3.29575490e-01 6.75951861e-01\n",
            " 8.98594540e-01 9.79291017e-01 9.97409032e-01 9.99847423e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [6.84227766e-49 1.37939900e-36 1.59369924e-27 1.85152013e-20\n",
            " 6.98283368e-15 1.63765201e-10 3.67137632e-07 1.09332056e-04\n",
            " 5.75699846e-03 7.00600748e-02 2.53648717e-01 3.46376371e-01\n",
            " 2.22642680e-01 8.06964763e-02 1.81180151e-02 2.43839086e-03\n",
            " 1.52577414e-04]\n",
            "Mean = 11.03742710097963\n",
            "Variance = 1.3373791212297306 \n",
            "Deviation = 1.1564510889915451\n",
            "\n",
            "m = 100\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 1.05697242e-268 4.73461585e-198\n",
            " 2.75631274e-142 1.38803813e-098 4.46915985e-065 2.52371815e-040\n",
            " 4.82988950e-023 6.36721327e-012 1.51199050e-005 1.99139622e-002\n",
            " 3.43271507e-001 8.11180881e-001 9.74390330e-001 9.98475273e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 1.05697242e-268 4.73461585e-198\n",
            " 2.75631274e-142 1.38803813e-098 4.46915985e-065 2.52371815e-040\n",
            " 4.82988950e-023 6.36721327e-012 1.51198986e-005 1.98988423e-002\n",
            " 3.23357544e-001 4.67909375e-001 1.63209449e-001 2.40849433e-002\n",
            " 1.52472697e-003]\n",
            "Mean = 12.85275292746019\n",
            "Variance = 0.654679056807737 \n",
            "Deviation = 0.8091223991509177\n",
            "\n",
            "m = 1000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 6.90831207e-224 1.09520135e-112 6.24439856e-049 9.80791705e-018\n",
            " 2.27183905e-005 1.23360767e-001 7.71488847e-001 9.84856922e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 6.90831207e-224 1.09520135e-112 6.24439856e-049 9.80791705e-018\n",
            " 2.27183905e-005 1.23338049e-001 6.48128080e-001 2.13368075e-001\n",
            " 1.51430783e-002]\n",
            "Mean = 14.120270746034967\n",
            "Variance = 0.3829042580141788 \n",
            "Deviation = 0.6187925807685309\n",
            "\n",
            "m = 10000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 8.23697677e-171\n",
            " 3.66248288e-047 8.16151182e-010 7.46958578e-002 8.58482439e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 8.23697677e-171\n",
            " 3.66248288e-047 8.16151182e-010 7.46958570e-002 7.83786581e-001\n",
            " 1.41517561e-001]\n",
            "Mean = 15.066821702773675\n",
            "Variance = 0.21174828173957394 \n",
            "Deviation = 0.460161147577209\n",
            "\n",
            "m = 100000\n",
            "F(k) = [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 1.31131231e-91 5.40710984e-12 2.17427341e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
            " 0.00000000e+00 1.31131231e-91 5.40710984e-12 2.17427341e-01\n",
            " 7.82572659e-01]\n",
            "Mean = 15.782572658835317\n",
            "Variance = 0.17015269248960863 \n",
            "Deviation = 0.41249568784365326\n",
            "\n",
            "m = 1000000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 2.13624924e-113 2.36124771e-007\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 2.13624924e-113 2.36124771e-007\n",
            " 9.99999764e-001]\n",
            "Mean = 15.999999763875227\n",
            "Variance = 2.3612474819856288e-07 \n",
            "Deviation = 0.0004859266901483833\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program Max_of_various_binomial_distributions.py\n",
        "# The same binomial distribution is cloned a varying number of times\n",
        "# and the global MAX is found.\n",
        "# The pmf (probability mass function) of MAX is calculated and drawn.\n",
        "# Mean and variance are also calculated.\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of binomial distributions\n",
        "n_binomials = [1, 10, 100, 1000, 10000, 100000, 1000000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the cumulative distribution functions of MAX\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    print()\n",
        "    print(f'm = {m}')\n",
        "    print(f'F(k) = {Fm_k}')\n",
        "    plt.plot(k_values, Fm_k, label=f'm = {m}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    print(f\"Mean = {mean}\")\n",
        "    #Draw verticalline at the mean\n",
        "    plt.axvline(x=mean, color='r', linestyle='--', label=f'Mean = {mean:.3}')\n",
        "    # Variance\n",
        "    var = 0.0\n",
        "    for k in k_values:\n",
        "        var += k * k * pmf_k[k]\n",
        "    var -= mean * mean\n",
        "    dev = np.sqrt(var)\n",
        "    print(f\"Variance = {var} \")\n",
        "    print(f\"Deviation = {dev}\")\n",
        "\n",
        "\n",
        "plt.xlabel('k')\n",
        "plt.ylabel('F^n(k), pmf')\n",
        "plt.title(f'CDF, pmf and mean of the Maximum of m Binomial Distributions Bi(16, 1/2)')\n",
        "plt.legend(loc = 'upper left')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jVS9axBHr0pH"
      },
      "source": [
        "Our conclusions are:\n",
        "- The mean grows sub-logarithmically with the number of monkeys. This means that it pays to add monkeys, but the price is over-exponential.  The mean is very close to the maximum of the pmf, the probability mass function of MAX.\n",
        "- The variance diminishes with the number of monkeys. More monkeys cause the mean to grow and to strengthen its predictive power.\n",
        "- Perfection is possible but at a high price. Here, for a target string 16 bits long, one needs one million monkeys to experimentally assure perfection.\n",
        "- Reaching perfection corresponds with getting 16 matches. The corresponding probability  is 1.52587891e-05. So, one may say that to get perfection, one needs an average number of trials equal to\n",
        ">\n",
        ">>> $T = \\frac{1}{1.52587891e-05} = 65530$.\n",
        ">\n",
        "- This is an average value and does not guarantee reproducible perfection. So, one time you may succeed with fewer trials, others not.  Our previous estimates of 1 million and higher inspire more confidence if one wants reproducible perfection.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## The expected value of MAX \n",
        "\n",
        "MAX of a set of random binomial variables is a random variable. So, it produces one result now and another thereafter. Nevertheless, its fluctuations are rapidly stabilized by an ensemble effect. This would allow us to replace its output with the mean of some sample or by its expected value. Let us begin with the study of samples. \n",
        "\n",
        "\n",
        "*Exercise*. According to the graphic presented by the last program, the mean value of MAX for $m$ monkeys is quite close to the maximum of the corresponding pmf. Use this fact to compute an approximation for the mean. We have various possible solutions:\n",
        "- First: develop a program to make a regression analysis.\n",
        "- Second: Resort to continuous models, that will be presented below. So, use the continuous normal approximation that is expected to be very good near the maximum of the pdf. Find an approximation to its derivative, equate it to zero and clear for $y$. More clearly:  \n",
        ">\n",
        "The pdf of MAX, the maximum of $n$ standard normal distributions, is:\n",
        ">>\n",
        ">$  f_{Y}(y) = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}} dt)^{n-1}$\n",
        ">\n",
        "Find the derivative, equate it to zero, and clear for $y$.\n",
        ">\n",
        "- Third. Check the result of the continuous approximation, which says that the mean is given by\n",
        ">\n",
        "> Mean of MAX with $m$ monkeys = $\\frac{m}{2} + \\sqrt{\\frac{m}{2} \\ln m}$\n",
        ">>\n",
        "- Fourth: Undertake the task from the definitions. This is our present choice.\n",
        "\n",
        "**Exercise.** Use the pmf of MAX that was derived from its  cdf  to predict a value of its mean. Draw a graph that shows the dependency of the mean on $m$, the number of monkeys. To fix ideas, take the power of the binomial, $n$ as 16. What can you say about the shape of the resultant graph?\n",
        ">\n",
        "*Answer.*  The following program uses the pmf of MAX that was derived from its cdf to predict a value of its mean. It draws the mean as a function of $m$, the number of monkeys for the $Bi(16, 1/2)$.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "eft4kataSXzC",
        "outputId": "7d79bdad-1fed-43f6-b9be-9918347b7904"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "\n",
            "m = 1\n",
            "F(k) = [1.52587891e-05 2.59399414e-04 2.09045410e-03 1.06353760e-02\n",
            " 3.84063721e-02 1.05056763e-01 2.27249146e-01 4.01809692e-01\n",
            " 5.98190308e-01 7.72750854e-01 8.94943237e-01 9.61593628e-01\n",
            " 9.89364624e-01 9.97909546e-01 9.99740601e-01 9.99984741e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [1.52587891e-05 2.44140625e-04 1.83105469e-03 8.54492188e-03\n",
            " 2.77709961e-02 6.66503906e-02 1.22192383e-01 1.74560547e-01\n",
            " 1.96380615e-01 1.74560547e-01 1.22192383e-01 6.66503906e-02\n",
            " 2.77709961e-02 8.54492188e-03 1.83105469e-03 2.44140625e-04\n",
            " 1.52587891e-05]\n",
            "Number of monkeys = 1, Mean = 8.0\n",
            "\n",
            "m = 3\n",
            "F(k) = [3.55271368e-15 1.74544823e-11 9.13528098e-09 1.20298037e-06\n",
            " 5.66512967e-05 1.15950344e-03 1.17356399e-02 6.48725883e-02\n",
            " 2.14051421e-01 4.61443446e-01 7.16780979e-01 8.89149381e-01\n",
            " 9.68432003e-01 9.93741739e-01 9.99222004e-01 9.99954224e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [3.55271368e-15 1.74509296e-11 9.11782649e-09 1.19384509e-06\n",
            " 5.54483163e-05 1.10285214e-03 1.05761365e-02 5.31369483e-02\n",
            " 1.49178833e-01 2.47392025e-01 2.55337533e-01 1.72368402e-01\n",
            " 7.92826220e-02 2.53097358e-02 5.48026505e-03 7.32220727e-04\n",
            " 4.57756687e-05]\n",
            "Number of monkeys = 3, Mean = 9.679399209097028\n",
            "\n",
            "m = 5\n",
            "F(k) = [8.27180613e-25 1.17447818e-18 3.99211628e-14 1.36070580e-10\n",
            " 8.35634621e-08 1.27973506e-05 6.06053962e-04 1.04737461e-02\n",
            " 7.65943720e-02 2.75548131e-01 5.74086657e-01 8.22162916e-01\n",
            " 9.47942266e-01 9.89591338e-01 9.98703676e-01 9.99923708e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [8.27180613e-25 1.17447736e-18 3.99199883e-14 1.36030659e-10\n",
            " 8.34273915e-08 1.27137872e-05 5.93256611e-04 9.86769216e-03\n",
            " 6.61206259e-02 1.98953759e-01 2.98538526e-01 2.48076259e-01\n",
            " 1.25779350e-01 4.16490718e-02 9.11233742e-03 1.22003275e-03\n",
            " 7.62916170e-05]\n",
            "Number of monkeys = 5, Mean = 10.304354253955333\n",
            "\n",
            "m = 7\n",
            "F(k) = [1.92592994e-34 7.90283538e-26 1.74455416e-19 1.53911097e-14\n",
            " 1.23260236e-10 1.41243379e-07 3.12979442e-05 1.69099709e-03\n",
            " 2.74078901e-02 1.64541881e-01 4.59799436e-01 7.60223057e-01\n",
            " 9.27886044e-01 9.85458272e-01 9.98185617e-01 9.99893193e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [1.92592994e-34 7.90283536e-26 1.74455337e-19 1.53909352e-14\n",
            " 1.23244845e-10 1.41120118e-07 3.11567008e-05 1.65969914e-03\n",
            " 2.57168930e-02 1.37133991e-01 2.95257555e-01 3.00423621e-01\n",
            " 1.67662987e-01 5.75722277e-02 1.27273444e-02 1.70757683e-03\n",
            " 1.06806634e-04]\n",
            "Number of monkeys = 7, Mean = 10.674882172530015\n",
            "\n",
            "m = 10\n",
            "F(k) = [6.84227766e-49 1.37939900e-36 1.59369924e-27 1.85152029e-20\n",
            " 6.98285219e-15 1.63772184e-10 3.67301404e-07 1.09699358e-04\n",
            " 5.86669782e-03 7.59267726e-02 3.29575490e-01 6.75951861e-01\n",
            " 8.98594540e-01 9.79291017e-01 9.97409032e-01 9.99847423e-01\n",
            " 1.00000000e+00]\n",
            "pmf(k) = [6.84227766e-49 1.37939900e-36 1.59369924e-27 1.85152013e-20\n",
            " 6.98283368e-15 1.63765201e-10 3.67137632e-07 1.09332056e-04\n",
            " 5.75699846e-03 7.00600748e-02 2.53648717e-01 3.46376371e-01\n",
            " 2.22642680e-01 8.06964763e-02 1.81180151e-02 2.43839086e-03\n",
            " 1.52577414e-04]\n",
            "Number of monkeys = 10, Mean = 11.03742710097963\n",
            "\n",
            "m = 50\n",
            "F(k) = [1.49969681e-241 4.99401150e-180 1.02809164e-134 2.17591724e-099\n",
            " 1.66021467e-071 1.17815030e-049 6.68517752e-033 1.58862146e-020\n",
            " 6.94974064e-012 2.52333376e-006 3.88843220e-003 1.41116839e-001\n",
            " 5.85893767e-001 9.00655806e-001 9.87112116e-001 9.99237346e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [1.49969681e-241 4.99401150e-180 1.02809164e-134 2.17591724e-099\n",
            " 1.66021467e-071 1.17815030e-049 6.68517752e-033 1.58862146e-020\n",
            " 6.94974063e-012 2.52332681e-006 3.88590887e-003 1.37228407e-001\n",
            " 4.44776928e-001 3.14762039e-001 8.64563100e-002 1.21252296e-002\n",
            " 7.62654305e-004]\n",
            "Number of monkeys = 50, Mean = 12.382093170438463\n",
            "\n",
            "m = 100\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 1.05697242e-268 4.73461585e-198\n",
            " 2.75631274e-142 1.38803813e-098 4.46915985e-065 2.52371815e-040\n",
            " 4.82988950e-023 6.36721327e-012 1.51199050e-005 1.99139622e-002\n",
            " 3.43271507e-001 8.11180881e-001 9.74390330e-001 9.98475273e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 1.05697242e-268 4.73461585e-198\n",
            " 2.75631274e-142 1.38803813e-098 4.46915985e-065 2.52371815e-040\n",
            " 4.82988950e-023 6.36721327e-012 1.51198986e-005 1.98988423e-002\n",
            " 3.23357544e-001 4.67909375e-001 1.63209449e-001 2.40849433e-002\n",
            " 1.52472697e-003]\n",
            "Number of monkeys = 100, Mean = 12.85275292746019\n",
            "\n",
            "m = 500\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 1.77863633e-322 1.02377438e-198\n",
            " 2.62836681e-112 1.04651868e-056 7.90215070e-025 3.13175942e-009\n",
            " 4.76638128e-003 3.51227515e-001 8.78344378e-001 9.92399578e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 1.77863633e-322 1.02377438e-198\n",
            " 2.62836681e-112 1.04651868e-056 7.90215070e-025 3.13175942e-009\n",
            " 4.76637815e-003 3.46461133e-001 5.27116863e-001 1.14055199e-001\n",
            " 7.60042234e-003]\n",
            "Number of monkeys = 500, Mean = 13.773262144972524\n",
            "\n",
            "m = 1000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 6.90831207e-224 1.09520135e-112 6.24439856e-049 9.80791705e-018\n",
            " 2.27183905e-005 1.23360767e-001 7.71488847e-001 9.84856922e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 6.90831207e-224 1.09520135e-112 6.24439856e-049 9.80791705e-018\n",
            " 2.27183905e-005 1.23338049e-001 6.48128080e-001 2.13368075e-001\n",
            " 1.51430783e-002]\n",
            "Number of monkeys = 1000, Mean = 14.120270746034967\n",
            "\n",
            "m = 5000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 9.49408414e-242 9.07577918e-086\n",
            " 6.05184507e-024 2.85683598e-005 2.73305430e-001 9.26543274e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 9.49408414e-242 9.07577918e-086\n",
            " 6.05184507e-024 2.85683598e-005 2.73276861e-001 6.53237844e-001\n",
            " 7.34567260e-002]\n",
            "Number of monkeys = 5000, Mean = 14.80012272808063\n",
            "\n",
            "m = 10000\n",
            "F(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 8.23697677e-171\n",
            " 3.66248288e-047 8.16151182e-010 7.46958578e-002 8.58482439e-001\n",
            " 1.00000000e+000]\n",
            "pmf(k) = [0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 0.00000000e+000\n",
            " 0.00000000e+000 0.00000000e+000 0.00000000e+000 8.23697677e-171\n",
            " 3.66248288e-047 8.16151182e-010 7.46958570e-002 7.83786581e-001\n",
            " 1.41517561e-001]\n",
            "Number of monkeys = 10000, Mean = 15.066821702773675\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program MeanOfMAXforDiverseNumberOfMonkeysFor16bits.py\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    print()\n",
        "    print(f'm = {m}')\n",
        "    print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    print(f\"Number of monkeys = {m}, Mean = {mean}\")\n",
        "    means.append(mean)\n",
        "plt.plot(n_binomials, means, label=f'm = {m}')\n",
        "\n",
        "\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean')\n",
        "plt.title(f'Mean of the Maximum of m Binomial Distributions Bi(16, 1/2)')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oh0MvWuyZYVh"
      },
      "source": [
        "What can we say about the shape of the graph? The graph seems to correspond to a function of the form $y =  A -Be^{-x}$. But also to $y = A - B/x$.\n",
        "\n",
        "**Exercise.** The previous program has a theoretical origin. It produces a prediction for the mean of MAX for a given number of monkeys. In Science, predictions must be verified. Before going further, test this prediction with a simulation that takes  various times the same   number of monkeys and calculates the corresponding mean. Repeat this for diverse number of monkeys.\n",
        ">\n",
        "*Answer.* The following program compares the theoretically expected dependence of the mean on the number of monkeys with that produced by a simulation. We mix the previous program with a suitable modification of program `simulationOfMaxOfVariousBinomialDistributions.py`\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 636
        },
        "id": "gWsdNEM0cc9R",
        "outputId": "cec8db1e-9dab-4791-e695-601360ec9cec"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "expected_means = [np.float64(8.0), np.float64(11.12956762645905), np.float64(11.708816390786861), np.float64(12.024058478783939), np.float64(12.237015540439312), np.float64(12.396307319360423), np.float64(12.522717522609513), np.float64(12.62695996781073), np.float64(12.715314681284106), np.float64(12.791799519690963), np.float64(12.859133888689739), np.float64(12.919227511448153), np.float64(12.973458192317022), np.float64(13.022842952769581), np.float64(13.06814887150034), np.float64(13.109966984075983), np.float64(13.148762412459048), np.float64(13.18490877042432), np.float64(13.218712006599848), np.float64(13.25042708767041), np.float64(13.28026979743577)]\n",
            "\n",
            "observed_means = [8.3, 10.8, 11.7, 11.5, 11.8, 12.2, 12.8, 12.8, 12.4, 12.6, 12.6, 12.9, 13.0, 13.0, 13.0, 12.9, 13.1, 13.6, 13.5, 12.9, 13.4]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program MaxOfBinomialsTheoryVSsimulation.py\n",
        "\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000] # This setting reaches 16\n",
        "n_binomials = range(1, 202, 10) # (start, end, step)\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "expected_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k) # Fm_k[k] - Fm_k[k-1]\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0]) # Insert first term\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    expected_means.append(mean)\n",
        "    # print(f\"Number of monkeys = {m}, Mean = {mean}\")\n",
        "\n",
        "\n",
        "\n",
        "#===================\n",
        "# Adapted from\n",
        "# Program simulationOfMaxOfVariousBinomialDistributions.py\n",
        "\n",
        "\n",
        "\n",
        "def simulate_coin_draws2(num_coins_per_draw):\n",
        "    \"\"\"Simulates drawing coins and returns the number of heads.\"\"\"\n",
        "    heads = 0\n",
        "    for _ in range(num_coins_per_draw):\n",
        "        if random.random() < 0.5:  # Simulate a coin flip (0.5 probability of heads)\n",
        "            heads += 1\n",
        "    return heads\n",
        "\n",
        "def get_max_heads2(num_coins_per_draw, num_sets):\n",
        "    \"\"\"Repeats the coin draw simulation multiple times and returns the maximum number of heads.\"\"\"\n",
        "    max_heads = 0\n",
        "    for _ in range(num_sets):\n",
        "        heads = simulate_coin_draws2(num_coins_per_draw) # Always draw 10 coins\n",
        "        if heads > max_heads:\n",
        "            max_heads = heads\n",
        "    return max_heads\n",
        "\n",
        "# Parameters for the simulation\n",
        "num_coins_per_draw = 16 #length of each string\n",
        "num_trials = 10 # repetitions to get the mean\n",
        "\n",
        "observed_means = []\n",
        "# Varying number of monkeys\n",
        "for m in n_binomials:\n",
        "  # Run the simulation and store the mean maximum number of heads for each trial\n",
        "  max_heads_history = []\n",
        "  for _ in range(num_trials):\n",
        "      max_h = get_max_heads2(num_coins_per_draw, m)\n",
        "      max_heads_history.append(max_h)\n",
        "  # Mean of max_heads_history\n",
        "  mean = sum(max_heads_history) / num_trials\n",
        "  mean = float(mean)\n",
        "  observed_means.append(mean)\n",
        "\n",
        "\n",
        "print(f\"expected_means = {expected_means}\")\n",
        "print()\n",
        "print(f\"observed_means = {observed_means}\")\n",
        "\n",
        "# Plot the means of MAX for growing number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_binomials, expected_means, label=f'Expected')\n",
        "plt.plot(n_binomials, observed_means, label=f'Observed in simulation')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel(f'Mean maximum Number of Heads (out of {num_coins_per_draw} coins)')\n",
        "plt.title(f'Mean of the Maximum of m Binomial Distributions Bi({num_coins_per_draw }, 1/2)')\n",
        "#plt.title(f'Maximum Number of Heads from {num_sets_of_draws} Draws of {num_coins_per_draw} Coins over {num_trials} Trials')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4VVYeuHOtQxe"
      },
      "source": [
        "*Our comment.* Apart from the expected fluctuations due to sampling effects, observed and expected coincide. Thus, we consider that our theory and simulations are all perfect.\n",
        "\n",
        "We have simulations and results from theory that only a computer can calculate. That is OK. But, we need now formulae for immediate predictions. The first option is a regression fitting.\n",
        "\n",
        "\n",
        "**Exercise.** According to previous programs, the curve that depicts the expected dependence of the number of coincidences of MAX on the number of monkeys is very soft. Thus, an approximated formula for it must be easily found.  Try to fit it by a regression over the family of functions of the form $y = A -Be^{-kt}$. Report your assessment.\n",
        ">\n",
        "*Answer.* Let us execute a tiny rearrangement:\n",
        ">\n",
        ">$y = A -Be^{-kt}$\n",
        ">>\n",
        ">$y - A = -Be^{-kt}$\n",
        ">\n",
        "> $A -y = Be^{-kt}$\n",
        ">>\n",
        ">This mean that to prepare the data for the regression, we must transform $y$ to $ A -y$, that represents a reflection followed by a rising of the curve by $A$ units.\n",
        "\n",
        "If we rename\n",
        ">\n",
        "> $ w = A -y$, \n",
        ">\n",
        "we get\n",
        ">\n",
        "> $w = Be^{-kt}$, \n",
        ">\n",
        "taking ln, we get\n",
        ">\n",
        "> $\\ln w = \\ln B -kt$\n",
        ">\n",
        "This means that we must make a regression of $\\ln w$ over $t$, that in our case represents the number of monkeys that attack the MAX in the binomial $Bi(16,1/2)$.  \n",
        "\n",
        "\n",
        "The code follows:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "rXCVkbNy9tR0",
        "outputId": "a22b3640-ecfc-4c26-ccb8-4891204c7373"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of monkeys = 1, Mean = 8.0\n",
            "Number of monkeys = 3, Mean = 9.679399209097028\n",
            "Number of monkeys = 5, Mean = 10.304354253955333\n",
            "Number of monkeys = 7, Mean = 10.674882172530015\n",
            "Number of monkeys = 10, Mean = 11.03742710097963\n",
            "Number of monkeys = 50, Mean = 12.382093170438463\n",
            "Number of monkeys = 100, Mean = 12.85275292746019\n",
            "Number of monkeys = 150, Mean = 13.105928057381806\n",
            "Number of monkeys = 200, Mean = 13.277364299230262\n"
          ]
        },
        {
          "data": {
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wuDwYnRh6GhOCEgAAAFBLDMNQXnGpcxnb0cKyWZ2jha6PK5a2HS0su86n9AxDT4i/r2u4qQg7J878hFid+yODrQrw863ld90wEZQAAACAapwYeipmc45UM+tz4tK32gg9UeUhJzrYWumx66wPocezCEoAAABo8CpCT7bLbE6JDuUV6eedPvr+ww3KLSqt0tHtTENPsL/v8WVt5dftVH584qxPZLBVgVZCjzchKAEAAKBeMQxD+cWlx5ew1bCD28lDj4+0Z/dJX68i9FRc1xN9mmYGhJ6GgaAEAAAA01SEnuzym5PWtIObzX5mMz1BVt/yWZ2y0BMR6Kfcg3vVrUMbNQkLVGSwazODqGB/Qk8jRVACAABArTAMQwUl9mqv5XG9UWmJMxgdrYXQExl8vFlB5ceVmxlUDj1lrat367KLW8tqtdbGMKCBICgBAACgihNDT+WObdWFnYrHJXbHGb1eoNXHec1OWdg5STODE9paB/kz0wPPISgBAAA0cIZhqLDEfsIsT9UObkcLbFUen2noCfDzUUxF2Ak53sEt8mTNDQg98EIEJQAAgHqkIvRUvR9PifOanir37Sm0qaT0zEPPyZe1Vb5BadmsD6EHDQFBCQAAwAsYhqHDBSXKyi7S3pxjyso+pr05RdpztFC/7fDRi79/r+xjpTpSWHLGocffZabHesI1PK7L3I7PAhF60HgRlAAAADzMMAzlFpUqK+fYCUGo7O+92ceUlVOkrJyiUwQgHyk332WLv9+J1/SUL2sLPr6srbpZoCCrrywWi+ffMNAAEJQAAAD+oGMldpfwk5VdpKycshmhrOyyMFRQYj/teSwWqUlogBIig5QYEaiEiCDFhVm1e+tGXXzeOWoSHuzs4EboATyLoAQAAHAKNrtD+8pnfPZmH3MNQuV/Hy201ehckcFWJUQEqVlkWQhKiAxUYkSQEiIClRgZpLjwQPn7+bi+vs2mT3I26MI2sbSvBuoQQQkAADRaDoehg/nFzuVve7OPh5+K2aCD+cUyanCbnxB/XyVEloeeiCAlRp4QhCIDlRARqGB/vnoB9QX/awUAAA2SYRg6Wmg74RqgshBU9rjs3/tzi1TqOH0K8vfzUUJEoDMEJZTPCDWLPP7v8EA/lsIBDYipQenrr7/WU089pdWrVysrK0sffPCBrrzySuf+6dOn6+2339auXbvk7++vnj176pFHHlHv3r3NKxoAAHiFvCKbcxYoq+JaoBzXJXFFttN3h/P1sSguLOD4bFD53ycGoZgQf0IQ0MiYGpQKCgrUtWtXjR8/XldffXWV/W3bttWsWbPUqlUrHTt2TM8884wGDhyorVu3qkmTJiZUDAAA6kKRza59zmuCXENQRcOEvKLSGp0rNjRAieVL3xIigsr/ffzvpmEB8vP1Of2JADQqpgalIUOGaMiQISfdP3r0aJfHM2fO1GuvvaZffvlFl156qafLAwAAHlBqd2h/XrEz/OzNPlYlCB0uKKnRucID/ZQYGeScBTpxNigxMlDxEYEK8OM+QADcV2+uUSopKdErr7yiiIgIde3a9aTHFRcXq7i42Pk4NzdXUlnHGJutZh1palPFa5rx2o0B4+t5jLFnMb6exxh7VuXxdTjKb5pa3iUuK7eofGao7N9ZOUU6mFesGlwWpCBr2XVB8c5rgwKPPw4v+3dIwGm+yhgO2Wqw/M6b8Rn2LMbX87xpjN2pwWIYNenj4nkWi6XKNUqStGTJEo0cOVKFhYVKSEjQ4sWLdc4555z0PNOnT9eDDz5YZfv8+fMVHBxc22UDANBoGIZUWCpll0hHSyzKLj7h72KLskvK9tmN01/L42sxFOmvsj8BhqIq/g6QovzL9gX7ld1XCABqS2FhoUaPHq2cnByFh4ef8livD0oFBQXKysrSoUOH9Oqrr+rLL7/Ujz/+qKZNm1Z7nupmlJKSknTo0KHTDoYn2Gw2paWlacCAAdz7wAMYX89jjD2L8fU8xrjmCopLXWaBymaFip2zQ/tyi1RYw5umNg0LKFsCFx7oMitUMTMUE+IvHx9SUE3wGfYsxtfzvGmMc3NzFRsbW6Og5PVL70JCQpSamqrU1FSde+65atOmjV577TXde++91R4fEBCggICAKtutVqupPxizX7+hY3w9jzH2LMbX8xr7GBeX2rU/p1h7c4653DPoxL9zjtVsSUp0iL+zEUJ8mL9ysrarX+9uSooJVUJEoOLCA2WlOUKta+yfYU9jfD3PG8bYndf3+qBUmcPhcJkxAgCgsbM7DB3IK3K2xM7KLtKe8nsFZZVfH3Qov2b/7QwL8HPeFygxMqjsuqAT/k6ICFSg9XhzBJvNpk8+ydRlXRJM/wIEALXJ1KCUn5+vrVu3Oh9nZmYqIyND0dHRiomJ0SOPPKIrrrhCCQkJOnTokGbPnq09e/Zo+PDhJlYNAEDdMYzy5gjlLbGzKmaBTugWtz+vWPYadEcI8POpdI+gwCr3DgoLJOwAgGRyUFq1apUuvvhi5+M77rhDkjR27Fi99NJL2rRpk+bNm6dDhw4pJiZG55xzjr755ht17NjRrJIBAKhVuUW28sBTEYSO/52VU9Yyu6T09F3b/HwsigsPdC6JS4gMVGKEa9vsqGArN00FgBoyNSj169dPp+olsWjRojqsBgCA2nWsxF4WdqoJPxUzQ/nFp79pqsUiNQkNOL4E7oSbpSZEBqpZZJBiQwPkS3MEAKg19e4aJQAAvIHN7jihM9yxsmuCKoJQ+d9HC2vWHCEy2Fo+++M6G1QxExQXHih/P5ojAEBdIigBAFCJw2HoYH5xtd3hKmaDDuYXqyY32Ajx93VeB9QsMsg1CEWWtcsO9uc/xwDgbfjNDABoVAzD0NFCmzP8nDgDVNEtbn9ukUpr0BzB38/nhHsDlQegyKATQlCQwgP9uC4IAOohghIAoEE6UlCitbuzlbHjiFZu9dE7r6/Svtyy+wgV2U7fHMHXx6K4sIAqXeHKusWVBaGYEH9CEAA0UAQlAEC9V2Sza/3eHK3Zma21u3O0dle2dh4pPOEIH+ngEZfnxIYGlF8T5NocoeLvpmEB8uOmqQDQaBGUAAD1it1haOuBfK3dla2M3dlauytbm/blVXsfoVZNQtQ5MVylR3arX6+uah4dqsTIQMVHBCrAz7easwMAUIagBADwWoZhKCunyCUUrdudo4ISe5Vjm4QFqFtSpLolRapr80h1bh6hiCCrbDabPvlkly7rliirlZupAgBqhqAEAPAaOcdsWrc7p+zaol1lfw7mFVc5LsTfV52bR6hrUqS6NY9U16RIJUQEcr0QAKDWEJQAAKYoLrVrU1ZeWSjaWTZj9PvBgirH+fpYdFZ8mEsoSm0ays1VAQAeRVACAHicw2Fo++GCE0JRjjbuzVWJvWr3ueToYHVNilTX5hHqnhypDgkRCvLneiIAQN0iKAEAat2BvCKt3VXWfW5t+bVFuUWlVY6LCraWh6JIdUsu+zs6xN+EigEAcEVQAgD8IQXFpVq358RQlKM92ceqHBfg56NOzSLKmi2UL6NLig7iuiIAgFciKAEAaqzU7tDm/Xkus0W/7c9T5c7cFovUtmmYuiZFOGeM2sWHycp9iQAA9QRBCQBQLcMwtPvoMWXsKls6l7ErW7/uzVGRrep1RYkRgWWB6ITW3KEB/CcGAFB/8V8xAIAk6WhBifNeRWWzRTk6UlBS5biwQD91bR5ZNlvUvOy+RU3DA02oGAAAzyEoAUAjVGSza/3eHGWcsIRux+HCKsdZfS3qkBDu0nChZUyIfGjNDQBo4AhKANDA2R2Gth3Mdy6hW7s7W5uy8lRa+cIiSa1iQ8oaLZQvo2ufEKYAP1pzAwAaH4ISADQghmFoX25R+TVFZbNF6/bkKL+4amvu2NAAdUs63oWuS7NIRQRbTagaAADvQ1ACgHost8imdbtzlFHebGHtrmwdyCuuclywv686n9Cau2tSpBIjAmnNDQDASRCUAKCeKCl1aNO+XJdQtO1gQZXjfH0sahcXVr6Erqw9d5umYfLluiIAAGqMoAQAXsgwDGUeKnDewDVjV7Y27M1Vib1qa+6k6CBn97muSZHqlBihIH+uKwIA4I8gKAGAFziUX6z1WUe0dvfx2aLcoqrXFUUGW8tbc0eqe1KkujSPUExogAkVAwDQsBGUAKCOFRSX6tc9OVq7O1trdhzVD1t8dXTlV1WO8/fzUafEcHVLilLX8qYLydHBXFcEAEAdICgBgAeV2h36bX9+2UzRzrLW3L/tz5NrZ26LLBapTdNQ52xRt6RItYsPk9XXx6zSAQBo1AhKAFBLDMPQ7qPHXELRuj05KrJVva4oISJQXZtHqlNimIr2bNL4qwYoOizIhKoBAEB1CEoAcIaOFpQ4my2U/Z2twwUlVY4LC/BTl6QIl9miuPBASZLNZtMnn2xUWCC/jgEA8Cb8lxkAaqDIZtf6vblauyvbGYq2Hy6scpzV16L2CeEuoahVbIh8aM0NAEC9QlACgEocDkPbDuaXdZ8r70K3KStPpa4XFkmSWsaGqGvz4zdybZ8QrkArrbkBAKjvCEoAGr19OUUuN3FdtydH+cVVW3PHhvq73K+oS/MIRQb7m1AxAADwNIISgEYlt8imdbtznKFo7e5s7c8trnJckNVXnStmippHqmtShJpFBtGaGwCARoKgBKDBKil1aNO+suuKMsobLmw7mC+j0go6H4vULj5c3U5ouNCmaaj8aM0NAECjRVAC0CAYhqHthwvLQ1HZTNH6vbkqKa3amrt5VFBZo4XyUNSpWbiC/fl1CAAAjuObAYB66VB+cdnSuV3Zytido7W7spVzzFbluIgga3koilC35Eh1aR6p2NAAEyoGAAD1CUEJgNcrLCnVr3tynbNFGbuytSf7WJXj/P181DGxrDV39+Sya4taxARzXREAAHAbQQmAVym1O7TlQL6z2ULGrmz9tj9PlTtzWyxSapNQdS3vQNeteaTaxYfJ34/rigAAwB9HUAJgGsMwtPvoMecNXNfuytG6PTk6ZrNXOTYuPMDZlrtb80h1ah6h8ECrCVUDAIDGgKAEoM5kF5Zobfn1RBWtuQ/ll1Q5LjTAT12aR5TNFpXftyg+ItCEigEAQGNFUALgEUU2uzZkHb+uaO2ubG0/XFjlOD8fi9onhKtreWvu7smRahUbKh8frisCAADmISgB+MMcDkO/H8pXxq4cZew6qrW7crQxK1ellS8skpQSE1y2fK58GV2HhHAFWn1NqBoAAODkCEoA3LY/t0hrdmY7ry1atztHecWlVY6LCfF3CUVdmkUoKsTfhIoBAADcQ1ACcEr5xaX6LceiXV9nat3eXK3dlaN9uUVVjguy+qpzs4iyJXTl1xY1jwqiNTcAAKiXCEoAqmUYhub/tFMPLdmgIpuvtGGLc5+PRWobF+acKeraPFJt40Ll50trbgAA0DAQlABUkV9cqvsWrdNHa/dKkiL9DfVpE6/uLaLUtXmkOjePULA/vz4AAEDDxTcdAC427cvVhLfS9fvBAvn6WHTngFQl5GzUn4Z2ldXKfYsAAEDjwDoZAE7vrtqlK2d/p98PFig+PFDv/O1c/fWClqJTNwAAaGyYUQKgwpJSTV28XgvTd0uS+rZtomdGdFVMaIBsNpvJ1QEAANQ9ghLQyG09kKcJb6Xrt/358rFIdwxoqwn9UrnhKwAAaNQISkAj9sGa3frnB7+qsMSuJmEBem5kd/VpHWN2WQAAAKYjKAGNUJHNrgc/Xq8FP+2SJJ3XOkb/HtldTcICTK4MAADAOxCUgEbm94P5mjh/jTZm5cpikSZd0kaTLm0jX5baAQAAOBGUgEZkyS979Y+F65RfXKqYEH89O7KbLmzTxOyyAAAAvA5BCWgEikvteuR/G/XflTskSb1SovX86O6KCw80uTIAAADvRFACGridhws1cX661u3JkSRN6NdadwxoKz9fbqMGAABwMgQloAH77Nd9uvv9tcorKlVksFXPjOimi89qanZZAAAAXo+gBDRAJaUOPf7pJs35LlOS1CM5UrNG91BiZJDJlQEAANQPBCWggdmTfUwT30pXxq5sSdJfL2ypvw8+S1aW2gEAANQYQQloQL7ctF93vLtW2YU2hQf66V/Du2pgx3izywIAAKh3CEpAA2CzO/SvpZv18le/S5K6No/QrNE9lBQdbHJlAAAA9RNBCajn9uUU6bYF6fp5+1FJ0o3npejey85SgJ+vyZUBAADUXwQloB776reDuv2dDB0pKFFogJ+euKaLhnZJMLssAACAeo+gBNRDdoehZ5f9plnLt8owpA4J4XphTA+lxIaYXRoAAECDQFAC6pkDeUWavCBDK38/LEka3TtZ0/7UQYFWltoBAADUFoISUI98v/WQJr2doUP5xQr299VjV3fWsG7NzC4LAACgwSEoAfWA3WFo9vKtenbZb3IYUru4MM0e00OpTUPNLg0AAKBBIigBXu5QfrFufydD32w5JEka3rO5ZgzrpCB/ltoBAAB4CkEJ8GI/ZR7RbQvStT+3WIFWHz18ZWdd27O52WUBAAA0eAQlwAs5HIZe/vp3/WvpZtkdhlo3CdELY3qqXXyY2aUBAAA0CgQlwMscLSjRHe9maPnmg5KkK7sl6pGrOiskgP+5AgAA1BUfM1/866+/1uWXX67ExERZLBYtXrzYuc9ms+mee+5R586dFRISosTERN1www3au3eveQUDHrZ6x1ENfe4bLd98UP5+Pnrs6s565rpuhCQAAIA6ZmpQKigoUNeuXTV79uwq+woLC5Wenq6pU6cqPT1dixYt0ubNm3XFFVeYUCngWYZh6D/f/K7rXl6pvTlFSokJ1gcTztOoXsmyWCxmlwcAANDomPp/Uw8ZMkRDhgypdl9ERITS0tJcts2aNUu9evXSzp07lZycXBclAh6XU2jT3e+v1dIN+yVJQ7sk6PGrOyss0GpyZQAAAI1XvVrPk5OTI4vFosjIyJMeU1xcrOLiYufj3NxcSWVL+Ww2m6dLrKLiNc147cagvo/vuj05mvT2Wu3OLpLV16J/Dmmn0b2SZLF4z3uq72Ps7Rhfz2OMPYvx9TzG2LMYX8/zpjF2pwaLYRiGB2upMYvFog8++EBXXnlltfuLiop0/vnn66yzztJbb7110vNMnz5dDz74YJXt8+fPV3BwcG2VC/whhiF9s8+ixTt8ZDcsigkwdGNbu5K5fywAAIDHFBYWavTo0crJyVF4ePgpj60XQclms+maa67R7t27tWLFilO+qepmlJKSknTo0KHTDoYn2Gw2paWlacCAAbJaWUpV2+rj+OYVleqfi9fr0/VlS+0GtG+qx6/qqPAg76y/Po5xfcL4eh5j7FmMr+cxxp7F+HqeN41xbm6uYmNjaxSUvH7pnc1m04gRI7Rjxw59+eWXp31DAQEBCggIqLLdarWa+oMx+/Ubuvoyvuv35mjiW+nafrhQfj4W3XtZe40/P6VeNGyoL2NcXzG+nscYexbj63mMsWcxvp7nDWPszut7dVCqCElbtmzR8uXLFRMTY3ZJwBkxDEMLftql6R+vV0mpQ4kRgZo1pod6JEeZXRoAAACqYWpQys/P19atW52PMzMzlZGRoejoaCUkJOjaa69Venq6lixZIrvdrn379kmSoqOj5e/vb1bZgFsKikt13wfr9GFG2T3ALjmrqZ4e3lVRIXyGAQAAvJWpQWnVqlW6+OKLnY/vuOMOSdLYsWM1ffp0ffTRR5Kkbt26uTxv+fLl6tevX12VCZyxzfvyNOGt1dp2sEC+PhbdPaid/nZhK/n4eP9SOwAAgMbM1KDUr18/naqXhJf0mQDOyHurdmnqh7+qyOZQXHiAZo3uoXNSos0uCwAAADXg1dcoAfXRsRK7pn74q95fvVuSdGGbWD17XTfFhFZtMgIAAADvRFACatHWA/ma+Fa6Nu/Pk49Fur1/W028OJWldgAAAPUMQQmoJYvX7NF9H6xTYYldsaEBem5UN53XOtbssgAAAHAGCErAH1Rks+vBjzdowU87JUl9WsXo36O6qWlYoMmVAQAA4EwRlIA/YPuhAk14K10bsnJlsUi3XZyqyf3bypeldgAAAPUaQQk4Q//7JUv3LPxF+cWlig7x17PXdVPftk3MLgsAAAC1gKAEuKm41K5H/7dR81bukCSdkxKl50f1UHwES+0AAAAaCoIS4IZdRwo1cX66ftmdI0m65aLWumtgW/n5+phcGQAAAGoTQQmooaXr9+mu99Yqt6hUkcFWzRzRVZecFWd2WQAAAPAAghJwGja7Q098ukn/+TZTktQ9OVKzRvdQs8ggkysDAACApxCUgFPYk31M/zc/XWt2ZkuSbrqgpf4++Cz5+7HUDgAAoCEjKAEn8eWm/brj3bXKLrQpLNBP/xreVYM6xptdFgAAAOoAQQmopNTu0NNpv+nFFdskSZ2bRWj26B5Kjgk2uTIAAADUFYIScIJ9OUWatGCNftp+RJI0tk8L3Te0vQL8fE2uDAAAAHWJoASU+/q3g7r9nQwdLihRaICfnrimi4Z2STC7LAAAAJiAoIRGz+4w9O9lv+n55VtlGFL7hHC9MKaHWsaGmF0aAAAATEJQQqN2IK9IkxdkaOXvhyVJo3ol64HLOyjQylI7AACAxoyghEbr+22HNPntDB3MK1awv68evaqzruzezOyyAAAA4AUISmh0HA5Ds5dv1TPLfpPDkNrGheqFMT2V2jTU7NIAAADgJQhKaFQO5xdryjsZ+mbLIUnStT2ba8awjgr2538KAAAAOI5vh2g0ft5+RLfNX6N9uUUKtPpoxrBOGnF2ktllAQAAwAsRlNDgORyGXvnmdz31+WbZHYZaNQnRi2N6ql18mNmlAQAAwEsRlNCgHS0o0Z3vrdWXmw5IkoZ1S9SjV3VWSAAffQAAAJwc3xbRYKXvPKrb5q/Rnuxj8vfz0fTLO2pUryRZLBazSwMAAICXIyihwTEMQ699m6nHP92kUoehlJhgzRrdQ52aRZhdGgAAAOoJghIalJxjNv39/bX6fP1+SdJlneP1+DVdFB5oNbkyAAAA1CcEJTQY63bnaML81dp15JisvhbdP7SDbujTgqV2AAAAcBtBCfWeYUhv/rhTj336m0rsDjWPCtLs0T3UNSnS7NIAAABQTxGUUK/lFZVq3hYfrflhkyRpQIc4/evarooIZqkdAAAAzhxBCfXWhr25mvDWam0/7CM/H4v+MeQs/eWCliy1AwAAwB9GUEK9YxiG3v55l6Z/tF7FpQ5F+ht6ZWwv9WrdxOzSAAAA0EAQlFCvFBSX6v7Fv+qDNXskSRe1jdWg8H3qnhxpbmEAAABoUHzMLgCoqd/25+mKWd/qgzV75Otj0d8Ht9MrY7orhMuRAAAAUMuYUUK98P7q3bp/8ToV2RxqGhag50d1V+9WMbLZbGaXBgAAgAaIoASvdqzErgc++lXvrtotSbqwTayeua6bYkMDTK4MAAAADRlBCV5r28F8TXgzXZv358likW7v31YTL06Vrw9d7QAAAOBZBCV4pQ8z9ujeRetUWGJXbGiAnhvZTeelxppdFgAAABoJghK8SpHNrhlLNmj+jzslSee2itZzI7uraXigyZUBAACgMSEowWtsP1SgCW+la0NWriwW6f8uTtXkS9vIz5fmjAAAAKhbBCV4hU/XZenv7/+ivOJSRYf465nruumittxAFgAAAOZwOyjZ7XbNnTtXX3zxhQ4cOCCHw+Gy/8svv6y14tDwFZfa9dgnmzT3++2SpLNbROn50d2VEBFkbmEAAABo1NwOSpMnT9bcuXM1dOhQderUSRYLHchwZnYdKdT/zU/X2t05kqSbL2qluwa2k5WldgAAADCZ20Hp7bff1rvvvqvLLrvME/WgkUjbsF93vpuh3KJSRQRZNXNEV13aPs7ssgAAAABJZxCU/P39lZqa6ola0AjY7A49+dkmvfpNpiSpW1KkZo3uruZRwSZXBgAAABzn9hqnO++8U//+979lGIYn6kEDtjf7mK57eaUzJI0/v6XevbkPIQkAAABex+0ZpW+//VbLly/Xp59+qo4dO8pqtbrsX7RoUa0Vh4Zj+eYDuuOdDB0ttCks0E9PXdtVgzvFm10WAAAAUC23g1JkZKSuuuoqT9SCBqjU7tDTab/pxRXbJEmdmoXrhdE9lRzDLBIAAAC8l9tB6fXXX/dEHWiA9ucW6bYFa/RT5hFJ0p/PbaF/Dm2vQKuvyZUBAAAAp8YNZ+ER3245pMlvr9HhghKFBvjpsas76/KuiWaXBQAAANTIGQWl999/X++++6527typkpISl33p6em1UhjqJ7vD0HNfbNFzX26RYUhnxYfphTE91KpJqNmlAQAAADXmdte75557TuPGjVNcXJzWrFmjXr16KSYmRr///ruGDBniiRpRTxzMK9YNc37Uv78oC0kjz0nS4onnE5IAAABQ77g9o/TCCy/olVde0ahRozR37lz9/e9/V6tWrTRt2jQdOXLEEzWiHli57bAmvb1GB/OKFWT11aNXd9JV3ZubXRYAAABwRtyeUdq5c6fOO+88SVJQUJDy8vIkSX/+85+1YMGC2q0OXs/hMDR7+VaN+c8POphXrDZNQ/XR/51PSAIAAEC95nZQio+Pd84cJScn64cffpAkZWZmchPaRuZIQYnGzf1ZT32+WQ5DurpHM334f+erTVyY2aUBAAAAf4jbS+8uueQSffTRR+revbvGjRun22+/Xe+//75WrVqlq6++2hM1wgut2n5E/zd/jfblFinAz0cPDeuk4Wc3l8ViMbs0AAAA4A9zOyi98sorcjgckqSJEycqJiZG33//va644grdfPPNtV4gvIvDYejVb37Xk59vlt1hqFVsiGaP6aH2CeFmlwYAAADUGreDko+Pj3x8jq/YGzlypEaOHFmrRcE7ZReW6K731mrZxgOSpCu6JurRqzsrNIDbcQEAAKBhcfsaJUn65ptvdP3116tPnz7as2ePJOmNN97Qt99+W6vFwXus2XlUQ5/7Vss2HpC/n48euaqT/j2yGyEJAAAADZLbQWnhwoUaNGiQgoKCtGbNGhUXF0uScnJy9Oijj9Z6gTCXYRia822mRry8Unuyj6lFTLAW3XqexvRuwfVIAAAAaLDcDkoPP/ywXnrpJb366quyWq3O7eeff77S09NrtTiYK+eYTbe+ma4ZSzbIZjc0pFO8Pr7tAnVqFmF2aQAAAIBHub1uavPmzerbt2+V7REREcrOzq6NmuAFft2TowlvpWvnkUJZfS3652XtNfa8FGaRAAAA0Ci4HZTi4+O1detWpaSkuGz/9ttv1apVq9qqCyYxDENv/rhTD328QSV2h5pFBmn2mB7qlhRpdmkAAABAnXE7KP31r3/V5MmTNWfOHFksFu3du1crV67UXXfdpalTp3qiRtSR/OJS/WPhL1ryS5YkqX/7pnp6eDdFBFtP80wAAACgYXE7KP3jH/+Qw+HQpZdeqsLCQvXt21cBAQG66667dNttt3miRtSBjVm5mvhWun4/VCBfH4v+Mfgs3XRhS5baAQAAoFFyOyhZLBb985//1N13362tW7cqPz9fHTp0UGhoqCfqg4cZhqF3V+3StA/Xq7jUoYSIQM0a3V09W0SbXRoAAABgmjO+CY6/v786dOhQm7WgjhWWlOr+D37VojVl98Lq166JZo7opugQf5MrAwAAAMxV46A0fvz4Gh03Z86cMy4GdWfL/jxNeCtdWw7ky8ci3TmwnW69qLV8fFhqBwAAANQ4KM2dO1ctWrRQ9+7dZRiGJ2uChy1cvVv3L/5Vx2x2NQ0L0HOjuuvcVjFmlwUAAAB4jRoHpVtvvVULFixQZmamxo0bp+uvv17R0VzHUp8U2ex64MP1emfVLknSBamxeua6bmoSFmByZQAAAIB38anpgbNnz1ZWVpb+/ve/6+OPP1ZSUpJGjBihzz///IxnmL7++mtdfvnlSkxMlMVi0eLFi132L1q0SAMHDlRMTIwsFosyMjLO6HVQ5i/zftY7q3bJYpGm9G+jeeN7EZIAAACAatQ4KElSQECARo0apbS0NG3YsEEdO3bUhAkTlJKSovz8fLdfvKCgQF27dtXs2bNPuv+CCy7QE0884fa54WrD3lx9t/Ww/H199OZfemtK/7by5XokAAAAoFpn3PXOx8dHFotFhmHIbref0TmGDBmiIUOGnHT/n//8Z0nS9u3bz+j8OG5R+m5J0qXtm+r81FiTqwEAAAC8m1tBqbi4WIsWLdKcOXP07bff6k9/+pNmzZqlwYMHy8fHrckpjykuLlZxcbHzcW5uriTJZrPJZrPVeT0Vr2nGa1cotTu0OKOsBfiwLvGm1lLbvGF8GzrG2LMYX89jjD2L8fU8xtizGF/P86YxdqcGi1HDC4wmTJigt99+W0lJSRo/frzGjBmj2Njam5mwWCz64IMPdOWVV1bZt337drVs2VJr1qxRt27dTnme6dOn68EHH6yyff78+QoODq6lauuXDUctenmTr0L8DM3oaZefd2RaAAAAoE4VFhZq9OjRysnJUXh4+CmPrXFQ8vHxUXJysrp37y6L5eTXtixatMi9aisKqaWgVN2MUlJSkg4dOnTawfAEm82mtLQ0DRgwQFartc5fX5KmvPOL/vfrPt1wbrKmDj3LlBo8xRvGt6FjjD2L8fU8xtizGF/PY4w9i/H1PG8a49zcXMXGxtYoKNV46d0NN9xwyoDkLQICAhQQULWTm9VqNfUHY9br5xyzKW3TAUnS8LOTTf9weorZP9/GgDH2LMbX8xhjz2J8PY8x9izG1/O8YYzdeX23bjiL+ufTdVkqKXWoTdNQdWpW9zNqAAAAQH10xl3vakN+fr62bt3qfJyZmamMjAxFR0crOTlZR44c0c6dO7V3715J0ubNmyVJ8fHxio+PN6Xm+mZRelkTh6t7NK8XM4IAAACANzD1sv5Vq1ape/fu6t69uyTpjjvuUPfu3TVt2jRJ0kcffaTu3btr6NChkqSRI0eqe/fueumll0yruT7ZebhQP20/IotFuqp7M7PLAQAAAOoNU2eU+vXrp1P1krjxxht144031l1BDcyiNWX3TrogNVbxEYEmVwMAAADUHzSKbqAMwzhh2R2zSQAAAIA7CEoN1OodR7XzSKFC/H01qCPXcwEAAADuqNHSu48++qjGJ7ziiivOuBjUnoXpZcvuhnROULC/qSssAQAAgHqnRt+gK98E1mKxuFxbdGI3NbvdXjuV4YwV2exa8kuWJJbdAQAAAGeiRkvvHA6H88/SpUvVrVs3ffrpp8rOzlZ2drY++eQT9ejRQ5999pmn60UNLNu4X3lFpUqMCNS5LWPMLgcAAACod9xekzVlyhS99NJLuuCCC5zbBg0apODgYP3tb3/Txo0ba7VAuK+iicNVPZrJx4d7JwEAAADucruZw7Zt2xQZGVlle0REhLZv314LJeGPOJhXrK9+Oyip7CazAAAAANzndlA655xzdMcdd2j//v3Obfv379fdd9+tXr161WpxcN+HGXtkdxjqlhSp1k1CzS4HAAAAqJfcDkpz5sxRVlaWkpOTlZqaqtTUVCUnJ2vPnj167bXXPFEj3FCx7O4amjgAAAAAZ8zta5RSU1P1yy+/KC0tTZs2bZIktW/fXv3793fpfoe6tzErVxuycmX1tehPXRLNLgcAAACot87oBjsWi0UDBw5U3759FRAQQEDyEovK75106VlxigrxN7kaAAAAoP5ye+mdw+HQQw89pGbNmik0NFSZmZmSpKlTp7L0zkSldocWZ+yVxL2TAAAAgD/K7aD08MMPa+7cuXryySfl73981qJTp076z3/+U6vFoea+3XpIB/OKFRVsVb92Tc0uBwAAAKjX3A5K//3vf/XKK69ozJgx8vX1dW7v2rWr85ol1L2KJg5XdE2Uv5/bP1YAAAAAJ3D7G/WePXuUmppaZbvD4ZDNZquVouCevCKbPl+/T5J0TU/unQQAAAD8UW4HpQ4dOuibb76psv39999X9+7da6UouOeTdVkqLnUotWmoOjeLMLscAAAAoN5zu+vdtGnTNHbsWO3Zs0cOh0OLFi3S5s2b9d///ldLlizxRI04jYXly+6u7tGMDoQAAABALXB7RmnYsGH6+OOPtWzZMoWEhGjatGnauHGjPv74Yw0YMMATNeIUdh0p1E+ZR2SxSFd1p9sdAAAAUBvO6D5KF154odLS0mq7FpyBj9aWtQQ/v3WsEiKCTK4GAAAAaBjOKChVyM/Pl8PhcNkWHh7+hwqCe77fdkiSNKhjnMmVAAAAAA2H20vvMjMzNXToUIWEhCgiIkJRUVGKiopSZGSkoqKiPFEjTsJmdyh9R7YkqXerGHOLAQAAABoQt2eUrr/+ehmGoTlz5iguLo7mASb6dU+Ojtnsigy2KrVJqNnlAAAAAA2G20Fp7dq1Wr16tdq1a+eJeuCGnzKPSJLOSYmWjw+BFQAAAKgtbi+9O+ecc7Rr1y5P1AI3/by9LCj1Sok2uRIAAACgYXF7Ruk///mPbrnlFu3Zs0edOnWS1Wp12d+lS5daKw4n53AY+nn7UUnSOS0JSgAAAEBtcjsoHTx4UNu2bdO4ceOc2ywWiwzDkMVikd1ur9UCUb3fDuQp55hNwf6+6phIp0EAAACgNrkdlMaPH6/u3btrwYIFNHMwUcX1ST2So2T1dXsFJQAAAIBTcDso7dixQx999JFSU1M9UQ9qqCIo9WLZHQAAAFDr3J6KuOSSS7R27VpP1IIaMgzDpeMdAAAAgNrl9ozS5Zdfrttvv13r1q1T586dqzRzuOKKK2qtOFRv55FCHcgrltXXou7JkWaXAwAAADQ4bgelW265RZI0Y8aMKvto5lA3fiyfTerSPFKBVl+TqwEAAAAaHreDksPh8EQdcMPPXJ8EAAAAeJRb1yjZbDb5+fnp119/9VQ9qIGfuNEsAAAA4FFuBSWr1ark5GSW15noQG6RdhwulMUi9UyJMrscAAAAoEFyu+vdP//5T9133306cuSIJ+rBaVTMJrWPD1d4oPU0RwMAAAA4E25fozRr1ixt3bpViYmJatGihUJCQlz2p6en11pxqIr7JwEAAACe53ZQuvLKKz1QBmqKoAQAAAB4nttB6YEHHvBEHaiBnEKbNu/Pk8SNZgEAAABPcjsoVVi9erU2btwoSerYsaO6d+9ea0Wheqt2HJFhSK1iQ9QkLMDscgAAAIAGy+2gdODAAY0cOVIrVqxQZGSkJCk7O1sXX3yx3n77bTVp0qS2a0Q5lt0BAAAAdcPtrne33Xab8vLytH79eh05ckRHjhzRr7/+qtzcXE2aNMkTNaJcRcc7lt0BAAAAnuX2jNJnn32mZcuWqX379s5tHTp00OzZszVw4MBaLQ7HFZaUat3uHEnMKAEAAACe5vaMksPhkNVa9f49VqtVDoejVopCVRk7s1XqMJQQEajmUUFmlwMAAAA0aG4HpUsuuUSTJ0/W3r17ndv27Nmj22+/XZdeemmtFofjfsw8vuzOYrGYXA0AAADQsLkdlGbNmqXc3FylpKSodevWat26tVq2bKnc3Fw9//zznqgRkn7eTiMHAAAAoK64fY1SUlKS0tPTtWzZMm3atEmS1L59e/Xv37/Wi0OZklKH0ncelURQAgAAAOpCjYJSdHS0fvvtN8XGxmr8+PH697//rQEDBmjAgAGerg+Sft2boyKbQ1HBVqU2CTW7HAAAAKDBq9HSu5KSEuXm5kqS5s2bp6KiIo8WBVcV9086OyVaPj5cnwQAAAB4Wo1mlPr06aMrr7xSPXv2lGEYmjRpkoKCqu+8NmfOnFotENK6PWVtwXu2iDK5EgAAAKBxqFFQevPNN/XMM89o27ZtslgsysnJYVapDm0/VCBJLLsDAAAA6kiNglJcXJwef/xxSVLLli31xhtvKCYmxqOFoYxhGNpxuFCSlBIbbHI1AAAAQOPgdte7zMzMKtuys7MVGRlZG/WgkkP5JcovLpXFIiVFE5QAAACAuuD2fZSeeOIJvfPOO87HI0aMUHR0tJo1a6a1a9fWanGQdhwuW3aXGBGkAD9fk6sBAAAAGge3g9JLL72kpKQkSVJaWprS0tL02WefaciQIbr77rtrvcDGLrP8+qSWsSEmVwIAAAA0Hm4vvdu3b58zKC1ZskQjRozQwIEDlZKSot69e9d6gY1dxfVJLWJYdgcAAADUFbdnlKKiorRr1y5J0meffab+/ftLKms6YLfba7c6aHv50ruUGGaUAAAAgLri9ozS1VdfrdGjR6tNmzY6fPiwhgwZIklas2aNUlNTa73Axs4ZlFh6BwAAANQZt4PSM888o5SUFO3atUtPPvmkQkPL7u2TlZWlCRMm1HqBjZlhGNpxqLw1OEvvAAAAgDrjdlCyWq266667qmy//fbba6UgHHe4oER5tAYHAAAA6pzbQUmStmzZouXLl+vAgQNyOBwu+6ZNm1YrhcG1NXigldbgAAAAQF1xOyi9+uqruvXWWxUbG6v4+HhZLBbnPovFQlCqRZkVy+5imU0CAAAA6pLbQenhhx/WI488onvuuccT9eAEFTNKLeh4BwAAANQpt9uDHz16VMOHD/dELajEebNZghIAAABQp9wOSsOHD9fSpUs9UQsq4WazAAAAgDncXnqXmpqqqVOn6ocfflDnzp1ltVpd9k+aNKnWimvMDMPgHkoAAACASdwOSq+88opCQ0P11Vdf6auvvnLZZ7FYCEq15EhBifKKylqDJ9MaHAAAAKhTbgelzMxMT9SBSraXL7tLCA+kNTgAAABQx9y+Rgl1Y/shlt0BAAAAZjmjG87u3r1bH330kXbu3KmSkhKXfTNnzqyVwho7WoMDAAAA5nF7RumLL75Qu3bt9OKLL+rpp5/W8uXL9frrr2vOnDnKyMhw61xff/21Lr/8ciUmJspisWjx4sUu+w3D0LRp05SQkKCgoCD1799fW7ZscbfkeimzfOldS242CwAAANQ5t4PSvffeq7vuukvr1q1TYGCgFi5cqF27dumiiy5y+/5KBQUF6tq1q2bPnl3t/ieffFLPPfecXnrpJf34448KCQnRoEGDVFRU5G7Z9Q4zSgAAAIB53F56t3HjRi1YsKDsyX5+OnbsmEJDQzVjxgwNGzZMt956a43PNWTIEA0ZMqTafYZh6Nlnn9X999+vYcOGSZL++9//Ki4uTosXL9bIkSPdLb3eMAzj+M1muUYJAAAAqHNuB6WQkBDndUkJCQnatm2bOnbsKEk6dOhQrRWWmZmpffv2qX///s5tERER6t27t1auXHnSoFRcXKzi4mLn49zcXEmSzWaTzWartfpqquI13XntitbgkpQQZjWl7vriTMYX7mGMPYvx9TzG2LMYX89jjD2L8fU8bxpjd2pwOyide+65+vbbb9W+fXtddtlluvPOO7Vu3TotWrRI5557rrunO6l9+/ZJkuLi4ly2x8XFOfdV57HHHtODDz5YZfvSpUsVHGze9T5paWk1PjYzT5L8FOlv6Mu0zz1WU0PizvjizDDGnsX4eh5j7FmMr+cxxp7F+HqeN4xxYWFhjY91OyjNnDlT+fn5kqQHH3xQ+fn5euedd9SmTRuv6Hh377336o477nA+zs3NVVJSkgYOHKjw8PA6r8dmsyktLU0DBgyQ1Wqt0XMWZ+yVfv1VZzWL1mWXnePhCuu3MxlfuIcx9izG1/MYY89ifD2PMfYsxtfzvGmMK1ab1YRbQclut2v37t3q0qWLpLJleC+99JJ71dVQfHy8JGn//v1KSEhwbt+/f7+6det20ucFBAQoICCgynar1WrqD8ad19+VXbZ0sGWTUNM/TPWF2T/fxoAx9izG1/MYY89ifD2PMfYsxtfzvGGM3Xl9t7re+fr6auDAgTp69KjbRbmrZcuWio+P1xdffOHclpubqx9//FF9+vTx+OubyXmzWTreAQAAAKZwe+ldp06d9Pvvv6tly5Z/+MXz8/O1detW5+PMzExlZGQoOjpaycnJmjJlih5++GG1adNGLVu21NSpU5WYmKgrr7zyD7+2N6M1OAAAAGAut4PSww8/rLvuuksPPfSQevbsqZAQ1y/z7lwHtGrVKl188cXOxxXXFo0dO1Zz587V3//+dxUUFOhvf/ubsrOzdcEFF+izzz5TYGCgu2XXG7QGBwAAAMxX46A0Y8YM3XnnnbrsssskSVdccYUsFotzv2EYslgsstvtNX7xfv36yTCMk+63WCyaMWOGZsyYUeNz1nfZhTbllrcGT442r0sfAAAA0JjVOCg9+OCDuuWWW7R8+XJP1tPoZZYvu4sPD1SQv6/J1QAAAACNU42DUsXMz0UXXeSxYnD8+qSUWGaTAAAAALO41fXuxKV28IzMQ2U3waLjHQAAAGAet5o5tG3b9rRh6ciRI3+ooMbu+IwSQQkAAAAwi1tB6cEHH1RERISnaoGk7YcrZpRYegcAAACYxa2gNHLkSDVt2tRTtUAn3GyWGSUAAADANDW+Ronrkzwvu7BEOcdskqQW0QQlAAAAwCw1Dkqnut8RakfFjWZpDQ4AAACYq8ZL7xwOhyfrgKQd5dcnteD6JAAAAMBUbrUHh2dVzCjRGhwAAAAwF0HJi9AaHAAAAPAOBCUvkklrcAAAAMArEJS8CDNKAAAAgHcgKHmJ7MISZReWtwZnRgkAAAAwFUHJS2wvX3YXFx6gYH+37gMMAAAAoJYRlLxExbK7FnS8AwAAAExHUPISFa3BWxKUAAAAANMRlLyE82azsVyfBAAAAJiNoOQlDuYVS5ISIgJNrgQAAAAAQclL5BWXSpJCA6wmVwIAAACAoOQlCpxBiY53AAAAgNkISl4iv4igBAAAAHgLgpKXyK+YUQokKAEAAABmIyh5AYfDUEEJM0oAAACAtyAoeYFCm12GUfZvghIAAABgPoKSF6ho5ODrY1GglR8JAAAAYDa+lXuBvPJGDiH+vrJYLCZXAwAAAICg5AUqZpTCArmHEgAAAOANCEpeoKLjXUiAr8mVAAAAAJAISl4hj3soAQAAAF6FoOQFCpz3UGLpHQAAAOANCEpewHmzWZbeAQAAAF6BoOQFjgcllt4BAAAA3oCg5AWON3MgKAEAAADegKDkBZztwQlKAAAAgFcgKHmB/CJmlAAAAABvQlDyAs5rlAIJSgAAAIA3ICh5AZo5AAAAAN6FoOQFCEoAAACAdyEoeQGCEgAAAOBdCEpegGYOAAAAgHchKHkBZ3twmjkAAAAAXoGgZDKHw1BBiV0SM0oAAACAtyAomaygpNT5b65RAgAAALwDQclkFY0crL4WBfjx4wAAAAC8Ad/MTXZiIweLxWJyNQAAAAAkgpLpaA0OAAAAeB+CkskISgAAAID3ISiZrICgBAAAAHgdgpLJ8rjZLAAAAOB1CEomc84ocbNZAAAAwGsQlExWcY1SGDNKAAAAgNcgKJksr5ildwAAAIC3ISiZjGYOAAAAgPchKJms4oazBCUAAADAexCUTJZfbJdEMwcAAADAmxCUTJZfbJPENUoAAACANyEomaygfEaJrncAAACA9yAomSyf+ygBAAAAXoegZLKKoBTiT1ACAAAAvAVByWQVXe/CmFECAAAAvAZByUSldoeO2cquUaKZAwAAAOA9CEomKiixO/8dEuBrYiUAAAAATkRQMlHF9Un+vj4K8CMoAQAAAN6CoGSiAjreAQAAAF6JoGSivPJGDqFcnwQAAAB4FYKSiSpmlGjkAAAAAHgXgpKJKq5RCiMoAQAAAF7F64NSXl6epkyZohYtWigoKEjnnXeefv75Z7PLqhUV91Ci4x0AAADgXbw+KN10001KS0vTG2+8oXXr1mngwIHq37+/9uzZY3Zpf1i+s5mD1eRKAAAAAJzIq4PSsWPHtHDhQj355JPq27evUlNTNX36dKWmpurFF180u7w/zBmUmFECAAAAvIpXXxxTWloqu92uwMBAl+1BQUH69ttvq31OcXGxiouLnY9zc3MlSTabTTabzXPFnkTFa1b32rnHSiRJwVYfU2prCE41vqgdjLFnMb6exxh7FuPreYyxZzG+nudNY+xODRbDMAwP1vKHnXfeefL399f8+fMVFxenBQsWaOzYsUpNTdXmzZurHD99+nQ9+OCDVbbPnz9fwcHBdVFyjb3zu4++3++jwc3tGpLk1T8GAAAAoN4rLCzU6NGjlZOTo/Dw8FMe6/VBadu2bRo/fry+/vpr+fr6qkePHmrbtq1Wr16tjRs3Vjm+uhmlpKQkHTp06LSD4Qk2m01paWkaMGCArFbXa5HueO8XffzLPt03pJ3GndeizmtrCE41vqgdjLFnMb6exxh7FuPreYyxZzG+nudNY5ybm6vY2NgaBSWvXnonSa1bt9ZXX32lgoIC5ebmKiEhQdddd51atWpV7fEBAQEKCAiost1qtZr6g6nu9QtLHJKkiGB/0z809Z3ZP9/GgDH2LMbX8xhjz2J8PY8x9izG1/O8YYzdeX2vbuZwopCQECUkJOjo0aP6/PPPNWzYMLNL+sPyueEsAAAA4JW8/hv6559/LsMw1K5dO23dulV33323zjrrLI0bN87s0v6w413vvP7HAAAAADQqXj+jlJOTo4kTJ+qss87SDTfcoAsuuECff/656dN2tYGgBAAAAHgnr/+GPmLECI0YMcLsMjyiwHnDWa//MQAAAACNitfPKDVkeUXl1yj5E5QAAAAAb0JQMonN7lBxaVnXuzBmlAAAAACvQlAyScWyO4mudwAAAIC3ISiZpKKRQ4Cfj6y+/BgAAAAAb8I3dJNUBCWW3QEAAADeh6BkkvwibjYLAAAAeCuCkkm4hxIAAADgvQhKJqkISswoAQAAAN6HoGSSiq53YQQlAAAAwOsQlExScbPZUJo5AAAAAF6HoGSSgmK7JJbeAQAAAN6IoGSS/GKbJJbeAQAAAN6IoGQSmjkAAAAA3ougZJL88qV3tAcHAAAAvA9ByST5RWVL7whKAAAAgPchKJmkopkDXe8AAAAA70NQMkle+TVKzCgBAAAA3oegZJICmjkAAAAAXougZJKKrndhLL0DAAAAvA5BySS0BwcAAAC8F0HJBMWldpWUOiRxjRIAAADgjQhKJqjoeCdJIf6+JlYCAAAAoDoEJRNUNHIIsvrKz5cfAQAAAOBt+JZugryi8tbgNHIAAAAAvBJByQQFJdxDCQAAAPBmBCUT5BcRlAAAAABvRlAywfHW4DRyAAAAALwRQckEFUEpNMBqciUAAAAAqkNQMsHxpXfMKAEAAADeiKBkAueMEl3vAAAAAK9EUDIBS+8AAAAA70ZQMkFBMUvvAAAAAG9GUDJBXjHtwQEAAABvRlAyQYGzPThBCQAAAPBGBCUTVHS9C6OZAwAAAOCVCEomyGdGCQAAAPBqBCUT5HONEgAAAODVCEomqAhKLL0DAAAAvBNBqY4ZhkEzBwAAAMDLEZTqWHGpQza7IYmldwAAAIC3IijVsYrZJEkK8ScoAQAAAN6IoFTHnB3v/H3l42MxuRoAAAAA1SEo1TFagwMAAADej6BUxypuNhtKxzsAAADAaxGU6hj3UAIAAAC8H0GpjhGUAAAAAO9HUKpjBCUAAADA+xGU6lgBQQkAAADwegSlOkYzBwAAAMD7EZTqWH6xXRLtwQEAAABvRlCqY/nFNkksvQMAAAC8GUGpjtHMAQAAAPB+BKU6VrH0jqAEAAAAeC+CUh3LLypfekczBwAAAMBrEZTqWAEzSgAAAIDXIyjVMa5RAgAAALwfQamOVQQl2oMDAAAA3ougVIcMw3AGpTCuUQIAAAC8FkGpDhWXOmR3GJKYUQIAAAC8GUGpDuUVlc0mWSxSsNXX5GoAAAAAnAxBqQ45Gzn4+8nHx2JyNQAAAABOhqBUhwpo5AAAAADUCwSlOlSx9I6bzQIAAADejaBUh5hRAgAAAOoHglIdcrYGJygBAAAAXo2gVIeO32yWjncAAACANyMo1SFn17sAq8mVAAAAADgVglIdyi9v5hBGMwcAAADAqxGU6hBL7wAAAID6wauDkt1u19SpU9WyZUsFBQWpdevWeuihh2QYhtmlnRGW3gEAAAD1g1evAXviiSf04osvat68eerYsaNWrVqlcePGKSIiQpMmTTK7PLcVOIMSM0oAAACAN/PqoPT9999r2LBhGjp0qCQpJSVFCxYs0E8//WRyZWfGOaPENUoAAACAV/Pqb+znnXeeXnnlFf32229q27at1q5dq2+//VYzZ8486XOKi4tVXFzsfJybmytJstlsstlsHq+5sorXtNlsyisq+3egr8WUWhqiE8cXnsEYexbj63mMsWcxvp7HGHsW4+t53jTG7tRgMbz4gh+Hw6H77rtPTz75pHx9fWW32/XII4/o3nvvPelzpk+frgcffLDK9vnz5ys4ONiT5Z7W29t8lFVo0dUpdrUIM7UUAAAAoNEpLCzU6NGjlZOTo/Dw8FMe69VB6e2339bdd9+tp556Sh07dlRGRoamTJmimTNnauzYsdU+p7oZpaSkJB06dOi0g+EJNptNaWlpGjBggKxWmjjUNsbX8xhjz2J8PY8x9izG1/MYY89ifD3Pm8Y4NzdXsbGxNQpKXr307u6779Y//vEPjRw5UpLUuXNn7dixQ4899thJg1JAQIACAgKqbLdarab+YMx+/YaO8fU8xtizGF/PY4w9i/H1PMbYsxhfz/OGMXbn9b26PXhhYaF8fFxL9PX1lcPhMKkiAAAAAI2BV88oXX755XrkkUeUnJysjh07as2aNZo5c6bGjx9vdmkAAAAAGjCvDkrPP/+8pk6dqgkTJujAgQNKTEzUzTffrGnTppldGgAAAIAGzKuDUlhYmJ599lk9++yzZpcCAAAAoBHx6muUAAAAAMAMBCUAAAAAqISgBAAAAACVEJQAAAAAoBKCEgAAAABUQlACAAAAgEoISgAAAABQCUEJAAAAACohKAEAAABAJQQlAAAAAKiEoAQAAAAAlRCUAAAAAKASghIAAAAAVOJndgGeZhiGJCk3N9eU17fZbCosLFRubq6sVqspNTRkjK/nMcaexfh6HmPsWYyv5zHGnsX4ep43jXFFJqjICKfS4INSXl6eJCkpKcnkSgAAAAB4g7y8PEVERJzyGItRkzhVjzkcDu3du1dhYWGyWCx1/vq5ublKSkrSrl27FB4eXuev39Axvp7HGHsW4+t5jLFnMb6exxh7FuPred40xoZhKC8vT4mJifLxOfVVSA1+RsnHx0fNmzc3uwyFh4eb/sFoyBhfz2OMPYvx9TzG2LMYX89jjD2L8fU8bxnj080kVaCZAwAAAABUQlACAAAAgEoISh4WEBCgBx54QAEBAWaX0iAxvp7HGHsW4+t5jLFnMb6exxh7FuPrefV1jBt8MwcAAAAAcBczSgAAAABQCUEJAAAAACohKAEAAABAJQQlAAAAAKiEoORBs2fPVkpKigIDA9W7d2/99NNPZpdULz322GM655xzFBYWpqZNm+rKK6/U5s2bXY7p16+fLBaLy59bbrnFpIrrn+nTp1cZv7POOsu5v6ioSBMnTlRMTIxCQ0N1zTXXaP/+/SZWXP+kpKRUGWOLxaKJEydK4jPsrq+//lqXX365EhMTZbFYtHjxYpf9hmFo2rRpSkhIUFBQkPr3768tW7a4HHPkyBGNGTNG4eHhioyM1F/+8hfl5+fX4bvwbqcaY5vNpnvuuUedO3dWSEiIEhMTdcMNN2jv3r0u56juc//444/X8TvxTqf7DN94441Vxm7w4MEux/AZPrXTjXF1v5MtFoueeuop5zF8hk+uJt/PavL9YefOnRo6dKiCg4PVtGlT3X333SotLa3Lt3JSBCUPeeedd3THHXfogQceUHp6urp27apBgwbpwIEDZpdW73z11VeaOHGifvjhB6Wlpclms2ngwIEqKChwOe6vf/2rsrKynH+efPJJkyqunzp27Ogyft9++61z3+23366PP/5Y7733nr766ivt3btXV199tYnV1j8///yzy/impaVJkoYPH+48hs9wzRUUFKhr166aPXt2tfuffPJJPffcc3rppZf0448/KiQkRIMGDVJRUZHzmDFjxmj9+vVKS0vTkiVL9PXXX+tvf/tbXb0Fr3eqMS4sLFR6erqmTp2q9PR0LVq0SJs3b9YVV1xR5dgZM2a4fK5vu+22uijf653uMyxJgwcPdhm7BQsWuOznM3xqpxvjE8c2KytLc+bMkcVi0TXXXONyHJ/h6tXk+9npvj/Y7XYNHTpUJSUl+v777zVv3jzNnTtX06ZNM+MtVWXAI3r16mVMnDjR+dhutxuJiYnGY489ZmJVDcOBAwcMScZXX33l3HbRRRcZkydPNq+oeu6BBx4wunbtWu2+7Oxsw2q1Gu+9955z28aNGw1JxsqVK+uowoZn8uTJRuvWrQ2Hw2EYBp/hP0KS8cEHHzgfOxwOIz4+3njqqaec27Kzs42AgABjwYIFhmEYxoYNGwxJxs8//+w85tNPPzUsFouxZ8+eOqu9vqg8xtX56aefDEnGjh07nNtatGhhPPPMM54trgGobnzHjh1rDBs27KTP4TPsnpp8hocNG2ZccsklLtv4DNdc5e9nNfn+8Mknnxg+Pj7Gvn37nMe8+OKLRnh4uFFcXFy3b6AazCh5QElJiVavXq3+/fs7t/n4+Kh///5auXKliZU1DDk5OZKk6Ohol+1vvfWWYmNj1alTJ917770qLCw0o7x6a8uWLUpMTFSrVq00ZswY7dy5U5K0evVq2Ww2l8/zWWedpeTkZD7PZ6ikpERvvvmmxo8fL4vF4tzOZ7h2ZGZmat++fS6f2YiICPXu3dv5mV25cqUiIyN19tlnO4/p37+/fHx89OOPP9Z5zQ1BTk6OLBaLIiMjXbY//vjjiomJUffu3fXUU095zZKa+mDFihVq2rSp2rVrp1tvvVWHDx927uMzXLv279+v//3vf/rLX/5SZR+f4Zqp/P2sJt8fVq5cqc6dOysuLs55zKBBg5Sbm6v169fXYfXV8zO7gIbo0KFDstvtLj90SYqLi9OmTZtMqqphcDgcmjJlis4//3x16tTJuX306NFq0aKFEhMT9csvv+iee+7R5s2btWjRIhOrrT969+6tuXPnql27dsrKytKDDz6oCy+8UL/++qv27dsnf3//Kl9+4uLitG/fPnMKrucWL16s7Oxs3Xjjjc5tfIZrT8XnsrrfwRX79u3bp6ZNm7rs9/PzU3R0NJ/rM1BUVKR77rlHo0aNUnh4uHP7pEmT1KNHD0VHR+v777/Xvffeq6ysLM2cOdPEauuHwYMH6+qrr1bLli21bds23XfffRoyZIhWrlwpX19fPsO1bN68eQoLC6uyrJzPcM1U9/2sJt8f9u3bV+3v6op9ZiMooV6ZOHGifv31V5frZyS5rMnu3LmzEhISdOmll2rbtm1q3bp1XZdZ7wwZMsT57y5duqh3795q0aKF3n33XQUFBZlYWcP02muvaciQIUpMTHRu4zOM+spms2nEiBEyDEMvvviiy7477rjD+e8uXbrI399fN998sx577DEFBATUdan1ysiRI53/7ty5s7p06aLWrVtrxYoVuvTSS02srGGaM2eOxowZo8DAQJftfIZr5mTfz+o7lt55QGxsrHx9fat09di/f7/i4+NNqqr++7//+z8tWbJEy5cvV/PmzU95bO/evSVJW7durYvSGpzIyEi1bdtWW7duVXx8vEpKSpSdne1yDJ/nM7Njxw4tW7ZMN9100ymP4zN85io+l6f6HRwfH1+luU5paamOHDnC59oNFSFpx44dSktLc5lNqk7v3r1VWlqq7du3102BDUirVq0UGxvr/J3AZ7j2fPPNN9q8efNpfy9LfIarc7LvZzX5/hAfH1/t7+qKfWYjKHmAv7+/evbsqS+++MK5zeFw6IsvvlCfPn1MrKx+MgxD//d//6cPPvhAX375pVq2bHna52RkZEiSEhISPFxdw5Sfn69t27YpISFBPXv2lNVqdfk8b968WTt37uTzfAZef/11NW3aVEOHDj3lcXyGz1zLli0VHx/v8pnNzc3Vjz/+6PzM9unTR9nZ2Vq9erXzmC+//FIOh8MZUnFqFSFpy5YtWrZsmWJiYk77nIyMDPn4+FRZMobT2717tw4fPuz8ncBnuPa89tpr6tmzp7p27XraY/kMH3e672c1+f7Qp08frVu3ziX0V/yfLh06dKibN3IqJjeTaLDefvttIyAgwJg7d66xYcMG429/+5sRGRnp0tUDNXPrrbcaERERxooVK4ysrCznn8LCQsMwDGPr1q3GjBkzjFWrVhmZmZnGhx9+aLRq1cro27evyZXXH3feeaexYsUKIzMz0/juu++M/v37G7GxscaBAwcMwzCMW265xUhOTja+/PJLY9WqVUafPn2MPn36mFx1/WO3243k5GTjnnvucdnOZ9h9eXl5xpo1a4w1a9YYkoyZM2caa9ascXZce/zxx43IyEjjww8/NH755Rdj2LBhRsuWLY1jx445zzF48GCje/fuxo8//mh8++23Rps2bYxRo0aZ9Za8zqnGuKSkxLjiiiuM5s2bGxkZGS6/mys6VX3//ffGM888Y2RkZBjbtm0z3nzzTaNJkybGDTfcYPI78w6nGt+8vDzjrrvuMlauXGlkZmYay5YtM3r06GG0adPGKCoqcp6Dz/Cpne73hGEYRk5OjhEcHGy8+OKLVZ7PZ/jUTvf9zDBO//2htLTU6NSpkzFw4EAjIyPD+Oyzz4wmTZoY9957rxlvqQqCkgc9//zzRnJysuHv72/06tXL+OGHH8wuqV6SVO2f119/3TAMw9i5c6fRt29fIzo62ggICDBSU1ONu+++28jJyTG38HrkuuuuMxISEgx/f3+jWbNmxnXXXWds3brVuf/YsWPGhAkTjKioKCM4ONi46qqrjKysLBMrrp8+//xzQ5KxefNml+18ht23fPnyan8vjB071jCMshbhU6dONeLi4oyAgADj0ksvrTLuhw8fNkaNGmWEhoYa4eHhxrhx44y8vDwT3o13OtUYZ2ZmnvR38/Llyw3DMIzVq1cbvXv3NiIiIozAwECjffv2xqOPPuryRb8xO9X4FhYWGgMHDjSaNGliWK1Wo0WLFsZf//rXKv9nK5/hUzvd7wnDMIyXX37ZCAoKMrKzs6s8n8/wqZ3u+5lh1Oz7w/bt240hQ4YYQUFBRmxsrHHnnXcaNputjt9N9SyGYRgemqwCAAAAgHqJa5QAAAAAoBKCEgAAAABUQlACAAAAgEoISgAAAABQCUEJAAAAACohKAEAAABAJQQlAAAAAKiEoAQAAAAAlRCUAABeKSUlRc8++6zZZTgVFhbqmmuuUXh4uCwWi7Kzs80uyUW/fv00ZcoUs8sAgAbDz+wCAACoD+bNm6dvvvlG33//vWJjYxUREWF2SQAADyIoAQAajZKSEvn7+5/Rc7dt26b27durU6dOtVwVAMAbsfQOALxQv379dNttt2nKlCmKiopSXFycXn31VRUUFGjcuHEKCwtTamqqPv30U4/WkZKSokcffVTjx49XWFiYkpOT9corrzj3r1ixosoytIyMDFksFm3fvl2SNHfuXEVGRmrJkiVq166dgoODde2116qwsFDz5s1TSkqKoqKiNGnSJNntdpfXz8vL06hRoxQSEqJmzZpp9uzZLvuzs7N10003qUmTJgoPD9cll1yitWvXOvdPnz5d3bp103/+8x+1bNlSgYGBJ32vCxcuVMeOHRUQEKCUlBQ9/fTTzn39+vXT008/ra+//loWi0X9+vWr9hwVrzdnzhwlJycrNDRUEyZMkN1u15NPPqn4+Hg1bdpUjzzyiMvzdu7cqWHDhik0NFTh4eEaMWKE9u/fX+W8b7zxhlJSUhQREaGRI0cqLy/vpO/nf//7nyIiIvTWW29Jknbt2qURI0YoMjJS0dHRGjZsmPNn9PXXX8tqtWrfvn0u55gyZYouvPBCSdKOHTt0+eWXKyoqSiEhIerYsaM++eSTk74+ANR3BCUA8FLz5s1TbGysfvrpJ91222269dZbNXz4cJ133nlKT0/XwIED9ec//1mFhYUnPcctt9yi0NDQU/45naefflpnn3221qxZowkTJujWW2/V5s2b3XovhYWFeu655/T222/rs88+04oVK3TVVVfpk08+0SeffKI33nhDL7/8st5//32X5z311FPq2rWr1qxZo3/84x+aPHmy0tLSnPuHDx+uAwcO6NNPP9Xq1avVo0cPXXrppTpy5IjzmK1bt2rhwoVatGiRMjIyqq1v9erVGjFihEaOHKl169Zp+vTpmjp1qubOnStJWrRokf7617+qT58+ysrK0qJFi076Xrdt26ZPP/1Un332mRYsWKDXXntNQ4cO1e7du/XVV1/piSee0P33368ff/xRkuRwODRs2DAdOXJEX331ldLS0vT777/ruuuuq3LexYsXa8mSJVqyZIm++uorPf7449XWMH/+fI0aNUpvvfWWxowZI5vNpkGDBiksLEzffPONvvvuO4WGhmrw4MEqKSlR37591apVK73xxhvOc9hsNr311lsaP368JGnixIkqLi7W119/rXXr1umJJ56o0ecHAOotAwDgdS666CLjggsucD4uLS01QkJCjD//+c/ObVlZWYYkY+XKlSc9z/79+40tW7ac8s+ptGjRwrj++uudjx0Oh9G0aVPjxRdfNAzDMJYvX25IMo4ePeo8Zs2aNYYkIzMz0zAMw3j99dcNScbWrVudx9x8881GcHCwkZeX59w2aNAg4+abb3Z57cGDB7vUc9111xlDhgwxDMMwvvnmGyM8PNwoKipyOaZ169bGyy+/bBiGYTzwwAOG1Wo1Dhw4cMr3OXr0aGPAgAEu2+6++26jQ4cOzseTJ082LrroolOe54EHHjCCg4ON3Nxcl/eVkpJi2O1257Z27doZjz32mGEYhrF06VLD19fX2Llzp3P/+vXrDUnGTz/9dNLz3n333Ubv3r2djy+66CJj8uTJxqxZs4yIiAhjxYoVzn1vvPGG0a5dO8PhcDi3FRcXG0FBQcbnn39uGIZhPPHEE0b79u2d+xcuXGiEhoYa+fn5hmEYRufOnY3p06ef8v0DQEPCNUoA4KW6dOni/Levr69iYmLUuXNn57a4uDhJ0oEDB056jqZNm6pp06a1VofFYlF8fPwpX7M6wcHBat26tfNxXFycUlJSXGYk4uLiqpy3T58+VR5XdMJbu3at8vPzFRMT43LMsWPHtG3bNufjFi1aqEmTJqesb+PGjRo2bJjLtvPPP1/PPvus7Ha7fH19T/8my6WkpCgsLMzlffn6+srHx8dlW8V73bhxo5KSkpSUlOTc36FDB0VGRmrjxo0655xzqj1vQkJClfF6//33deDAAX333XfO50llY7V161aX50tSUVGRc6xuvPFG3X///frhhx907rnnau7cuRoxYoRCQkIkSZMmTdKtt96qpUuXqn///rrmmmtcPhsA0NAQlADAS1mtVpfHFovFZZvFYpFUtnTrZG655Ra9+eabp3yd/Px8t+uoeM2KL/+GYTj322y2Gp3jVOetifz8fCUkJGjFihVV9kVGRjr/XfFFv6544r2e7LyVz9G9e3elp6drzpw5Ovvss52fkfz8fPXs2dN5vdKJKkJk06ZNdfnll+v1119Xy5Yt9emnn7qM7U033aRBgwbpf//7n5YuXarHHntMTz/9tG677Ta33gcA1BcEJQBowGbMmKG77rrLY+ev+JKdlZWlqKgoSTrpdUBn4ocffqjyuH379pKkHj16aN++ffLz81NKSsofep327dvru+++c9n23XffqW3btm7NJp3pa+/atUu7du1yzipt2LBB2dnZ6tChg1vnat26tZ5++mn169dPvr6+mjVrlqSysXrnnXfUtGlThYeHn/T5N910k0aNGqXmzZurdevWOv/88132JyUl6ZZbbtEtt9yie++9V6+++ipBCUCDRTMHAGjAmjZtqtTU1FP++SNSU1OVlJSk6dOna8uWLfrf//7n0i3uj/ruu+/05JNP6rffftPs2bP13nvvafLkyZKk/v37q0+fPrryyiu1dOlSbd++Xd9//73++c9/atWqVW69zp133qkvvvhCDz30kH777TfNmzdPs2bN8mjIrNC/f3917txZY8aMUXp6un766SfdcMMNuuiii3T22We7fb62bdtq+fLlWrhwofMGtGPGjFFsbKyGDRumb775RpmZmVqxYoUmTZqk3bt3O587aNAghYeH6+GHH9a4ceNczjtlyhR9/vnnyszMVHp6upYvX+4MrQDQEBGUAABnzGq1asGCBdq0aZO6dOmiJ554Qg8//HCtnf/OO+/UqlWr1L17dz388MOaOXOmBg0aJKls6dknn3yivn37aty4cWrbtq1GjhypHTt2OK/fqqkePXro3Xff1dtvv61OnTpp2rRpmjFjhm688cZaey8nY7FY9OGHHyoqKkp9+/ZV//791apVK73zzjtnfM527drpyy+/1IIFC3TnnXcqODhYX3/9tZKTk3X11Verffv2+stf/qKioiKXGSYfHx/deOONstvtuuGGG1zOabfbNXHiRLVv316DBw9W27Zt9cILL5xxjQDg7SzGiQvLAQBAo/aXv/xFBw8e1EcffWR2KQBgKq5RAgAAysnJ0bp16zR//nxCEgCIoAQAACQNGzZMP/30k2655RYNGDDA7HIAwHQsvQMAAACASmjmAAAAAACVEJQAAAAAoBKCEgAAAABUQlACAAAAgEoISgAAAABQCUEJAAAAACohKAEAAABAJQQlAAAAAKjk/wHG5YdMNTdQ7AAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Linear Regression Equation (log of mean of MAX vs number of monkeys): y = -0.0045551x + 1.76\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program fittingTheMeanOfMaxByAnExponential.py\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 100000, 250000, 500000]\n",
        "# n_binomials = [ 10000, 100000, 250000, 500000] # linear sub-segment\n",
        "n_binomials = [1, 3, 5, 7, 10, 50, 100, 150, 200]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the transformed means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "transformed_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    means.append(mean)\n",
        "    print(f\"Number of monkeys = {m}, Mean = {mean}\")\n",
        "    # Prepare for a log regression.\n",
        "    # Transform data:\n",
        "    # reflect the curve and rise it 16\n",
        "    newMean = - mean + 16\n",
        "    transformed_means.append(newMean)\n",
        "\n",
        "# Plot transformed data\n",
        "plt.plot(n_binomials, means, label=f'm = {m}')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Transformed Mean')\n",
        "plt.title(f'Transformed data')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear regression on the log of yArray\n",
        "log_y_array = np.log(transformed_means)\n",
        "slope, log_intercept = np.polyfit(n_binomials, log_y_array, 1)\n",
        "print(f\"Linear Regression Equation (log of mean of MAX vs number of monkeys): y = {slope:.7f}x + {log_intercept:.2f}\")\n",
        "log_regression_line = slope * np.array(n_binomials) + log_intercept\n",
        "\n",
        "# Plot the  log of transformed data and the log regression line\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.scatter(n_binomials, log_y_array, label='Observed Log Data')\n",
        "plt.plot(n_binomials, log_regression_line, color='red', label=f'Linear Regression on Log: log(y) = {slope:.7f}x + {log_intercept:.4f}')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Log of means of MAX ')\n",
        "plt.title('Linear Regression of Log of  (16 - means of max)  vs. number of monkeys')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Original data and prediction by the regression line assuming that $y = 16 - Be^{kt}$\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.scatter(n_binomials, means, label='Observed Data')\n",
        "predicted = 16 - np.exp(log_intercept) * np.exp(slope * np.array(n_binomials))\n",
        "plt.plot(n_binomials, predicted, color='red', label=f'Predicted')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title('Actual data and fitting by $y = 16 - Be^{kt}$')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YcXP_XTZLCoh"
      },
      "source": [
        "*Our assessment.*  The regression does not fit the data along the complete range of values. Nevertheless, after 5000 monkeys, the fitting is excellent. At that region, quasi-perfection is normal.\n",
        "\n",
        "Since the simplest regression model does not fit into data, we need to investigate other options. So, let us pay attention to the sigmoid function.\n",
        "\n",
        "\n",
        "**Exercise.** Research over the sigmoid function, its relation with the theme, mathematical formalism, test for adequacy, predictions.\n",
        ">\n",
        "*Answer.* The sigmoid function is a usual tool in the analysis of problems with the disjunctive to be or not to be. Here, to be means to guess a bit, and not to be, to fail. Our first trouble is that the shape of the sigmoid is like an S, but we have here, in the graph of the mean of MAX against the number of monkeys, a shoulder. Our solution is that we can extend our shoulder, defined over the positive part of the $X$ axis, to a sigmoid function defined over the complete real axis, but we must do a reflection through a point.\n",
        "\n",
        "\n",
        "Our graph begins with one monkey. In that case, the MAX of the number of matches is just the value sampled from the original binomial distribution, whose mean is $np = 16 \\times (1/2) = 8$. The mean produces the point $(1,8)$. For the sake of ease, let us imagine that we begin at the point $(0,8)$. This is our pivot point of the reflection.  \n",
        "\n",
        "The means of MAX range from 8 to 16 since we take the Binomial $Bi(16, 1/2)$. Let us divide the means by 16, and in this new setting, the means go from $1/2$ to $1$. If we include the reflected part, the means go from 0 to 1. The graph has two horizontal asymptotes: one at $y = 1$ and the other at $y = 0$.  \n",
        "\n",
        "Let us approximate the graph of the means by a continuous curve. This is sound because the graph shows a very soft curve. Thus, we will also take a differentiable function. The two horizontal asymptotes allow us to formulate a differential equation:  the function defined by $y = f(y)$ has derivative equal to zero at the values of $y$ equal to 0 or 1. When the soft curve approaches anyone of these asymptotes, the slope tends to be zero near them. The simplest differential equation that correspond to these observations are:\n",
        ">\n",
        ">> $y' = y(1-y)$\n",
        ">\n",
        "in which we see the two proportions corresponding to success and failure.\n",
        "\n",
        "We need to check that the slope is always positive in the interval of $y$ in within 0 and 1, because the sigmoid always increases. If we check with $y = 1/2$, we see that the sign is correct. We can insert a positive constant $\\alpha$, and solve the equation:\n",
        ">\n",
        "$y' = \\frac{dy}{dx} = \\alpha y(1-y)$\n",
        ">\n",
        "$ \\frac{dy}{y(1-y)} = \\alpha dx$\n",
        ">\n",
        "$\\int \\frac{dy}{y(1-y)} = \\int \\alpha dx$\n",
        ">\n",
        "Let us notice that\n",
        ">\n",
        "$\\frac{1}{y(1-y)} = \\frac{1}{y} +  \\frac{1}{1-y} $\n",
        ">\n",
        "Thus,\n",
        ">\n",
        "$\\int \\frac{dy}{y(1-y)} = \\int \\frac{dy}{y} + \\int \\frac{dy}{1-y}  =  \\int \\alpha dx$\n",
        ">\n",
        "$\\ln|y| - ln|1-y | = \\alpha x + \\beta$\n",
        ">\n",
        "$\\ln|\\frac{y}{1-y}|   = \\alpha x + \\beta$\n",
        ">\n",
        "This is a ratio test for adequacy of the sigmoid fitting to a set of data: if we take the log of the proportion of matches to mismatches, it must fall into a straight line. The coefficients $\\alpha $ and $\\beta$ can be found by a linear regression. So, let us continue to find the expression of the sigmoid function:\n",
        ">\n",
        "$|\\frac{y}{1-y}| = e^{ \\alpha x + \\beta} = k e^{ \\alpha x }$, where $k = e^\\beta$\n",
        ">\n",
        "Assuming $0 < y < 1$, we can ignore the absolute value:\n",
        ">\n",
        "$\\frac{y}{1-y} = e^{ \\alpha x + \\beta} = k e^{ \\alpha x }$\n",
        ">\n",
        "$y  = k(1-y) e^{ \\alpha x } = k e^{ \\alpha x } - ky e^{ \\alpha x }$\n",
        ">\n",
        "$y  + ky e^{ \\alpha x } =  k e^{ \\alpha x } $\n",
        ">\n",
        "$y (1  + k e^{ \\alpha x }) =  k e^{ \\alpha x } $\n",
        ">\n",
        "$ y = \\frac{ k e^{ \\alpha x } }{1  +  ke^{ \\alpha x }}$\n",
        ">\n",
        "$y = \\frac{ 1}{   \\frac{1}{  k e^{ \\alpha x }   }   +  1}   $\n",
        ">\n",
        "$y = \\frac{ 1}{   \\frac{1}{k}  e^{ -\\alpha x }      +  1}   $\n",
        ">\n",
        "$y = \\frac{ 1}{   c e^{ -\\alpha x }      +  1}  $\n",
        ">\n",
        "$y = \\frac{ 1}{ 1 +  c e^{ -\\alpha x }  }   $, where $c = e^{-\\beta}$\n",
        "\n",
        "**Exercise.** Using geometric considerations regarding the asymptotes, we have derived the differential equation\n",
        ">\n",
        ">$y' = \\frac{dy}{dx} = \\alpha y(1-y)$\n",
        ">\n",
        "Give a  meaning to this equation with respect to the  mean of MAX of $m$ binomials,\n",
        "\n",
        ">*Answer.* If we add more monkeys, we expect a higher mean of MAX of $m$ Binomials. Thus, the increment in the mean value is postulated to be proportional to the number of added monkeys $dx$ or $dm$:\n",
        ">\n",
        ">$dy \\sim dx$.\n",
        ">\n",
        "On the other hand, there is an ensemble effect of the population that makes the MAX higher and more stable when more monkeys are added. So, we postulate that $dy$ is also proportional to the size of the mean $y$:\n",
        ">\n",
        ">$dy \\sim y$.\n",
        ">\n",
        "Additionally, the tails of the Binomial are exponentially decreasing. Say, perfection has a probability of $\\frac{1}{2^{16}}$. Moreover, $16$ is an upper bound. The simplest way to postulate a relation involving these factors is saying that the increment in the mean must be proportional to the lacking proportion $1-y$, which becomes zero when $y$ approaches the upper bound that serves as asymptote:\n",
        ">\n",
        ">$dy \\sim 1-y$.\n",
        ">\n",
        "Putting everything together, we have:\n",
        ">\n",
        ">$dy = \\alpha y(1-y)dx$\n",
        ">\n",
        "Or\n",
        ">\n",
        "$y' = \\frac{dy}{dx} = \\alpha y(1-y)$\n",
        ">\n",
        "\n",
        "**Exercise.** Carry out the ratio test for adequacy of a sigmoid fitting a set of data.\n",
        ">\n",
        "*Answer.* The ratio test for adequacy of a sigmoid fitting to a set of data says that the log of the ratio\n",
        ">\n",
        "$|\\frac{y}{1-y}|$\n",
        ">\n",
        "must fall into a straight line, which gives origin to two parameters that can be found by a linear regression:  \n",
        ">\n",
        "$w = \\ln|\\frac{y}{1-y}|   = \\alpha x + \\beta$\n",
        ">\n",
        "The parameter $\\alpha$ dictates the dynamics and $\\beta$ depends on the initial condition.  \n",
        ">\n",
        ">\n",
        "The code follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "BJM210YMTtNf",
        "outputId": "1ea894bb-911b-4c86-9355-8ce9f1f3fda8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of monkeys = 0, mean = 8.0, Normalized mean = 0.50, ratio = 1.00, log_ratios = 0.00\n",
            "Number of monkeys = 50000, mean = 9.1, Normalized mean = 0.57, ratio = 1.33, log_ratios = 0.28\n",
            "Number of monkeys = 100000, mean = 9.7, Normalized mean = 0.60, ratio = 1.53, log_ratios = 0.43\n",
            "Number of monkeys = 200000, mean = 10.3, Normalized mean = 0.64, ratio = 1.81, log_ratios = 0.59\n",
            "Number of monkeys = 300000, mean = 10.7, Normalized mean = 0.67, ratio = 2.00, log_ratios = 0.70\n",
            "Number of monkeys = 450000, mean = 11.0, Normalized mean = 0.69, ratio = 2.22, log_ratios = 0.80\n",
            "Number of monkeys = 2450000, mean = 12.4, Normalized mean = 0.77, ratio = 3.42, log_ratios = 1.23\n",
            "Number of monkeys = 4950000, mean = 12.9, Normalized mean = 0.80, ratio = 4.08, log_ratios = 1.41\n",
            "Number of monkeys = 24950000, mean = 13.8, Normalized mean = 0.86, ratio = 6.19, log_ratios = 1.82\n",
            "Number of monkeys = 49950000, mean = 14.1, Normalized mean = 0.88, ratio = 7.51, log_ratios = 2.02\n",
            "Number of monkeys = 249950000, mean = 14.8, Normalized mean = 0.93, ratio = 12.33, log_ratios = 2.51\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Linear Regression Equation (log_ratios of means of MAX vs number of monkeys): y = 0.0000000x + 0.84\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 100000, 250000, 500000]\n",
        "n_binomials = [1, 2,  3, 5, 7, 10, 50, 100, 500, 1000, 5000]\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 150, 200]\n",
        "# n_binomials = [ 10000, 100000, 250000, 500000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "normalized_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    means.append(mean)\n",
        "    #Mean is normalized\n",
        "    normalized_mean = mean / n\n",
        "    normalized_means.append(normalized_mean)\n",
        "    # print(f\"Number of monkeys = {m}, mean = {mean}, Normalized mean = {normalized_mean}\")\n",
        "\n",
        "# Adjustment:\n",
        "# Data begins at (1,8), but\n",
        "# the sigmoid must begin at (0,8)\n",
        "l = len(n_binomials)\n",
        "for i in range(l):\n",
        "  n_binomials[i] =  n_binomials[i] - 1\n",
        "\n",
        "# Carry out a ratio test for the sigmoid fitting\n",
        "ratios = []\n",
        "for normalized_mean in normalized_means:\n",
        "  ratio  = normalized_mean / (1 - normalized_mean)\n",
        "  ratios.append(ratio)\n",
        "# print(f\"ratios = {ratios}\")\n",
        "log_ratios = []\n",
        "for i in range(l):\n",
        "  log_ratio  = np.log( ratios[i] )\n",
        "  log_ratios.append(log_ratio)\n",
        "  print(f\"Number of monkeys = {n_binomials[i]}, mean = {means[i]:.1f}, Normalized mean = {normalized_means[i]:.2f}, ratio = {ratios[i]:.2f}, log_ratios = {log_ratios[i]:.2f}\")\n",
        "plt.plot(n_binomials, log_ratios, label='m = {ratios}')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('log (y/(1-y))')\n",
        "plt.title(f'log (y/(1-y)), y =  mean of MAX of m Bi(16, 1/2)')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Linear regression on the log of yArray\n",
        "log_y_array = np.log(ratios)\n",
        "slope, log_intercept = np.polyfit(n_binomials, log_y_array, 1)\n",
        "print(f\"Linear Regression Equation (log_ratios of means of MAX vs number of monkeys): y = {slope:.7f}x + {log_intercept:.2f}\")\n",
        "log_regression_line = slope * np.array(n_binomials) + log_intercept\n",
        "\n",
        "# Plot the log data and the log regression line\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.scatter(n_binomials, log_y_array, label='Observed Log Data')\n",
        "plt.plot(n_binomials, log_regression_line, color='red', label=f'Linear Regression on Log: log(y) = {slope:.7f}x + {log_intercept:.4f}')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Log ratio of mean of MAX ')\n",
        "plt.title('Linear Regression of Log ratio of means of MAX   vs. number of monkeys')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "\n",
        "# Original data and prediction by the regression line assuming that $y$ is a sigmoid\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Raw data\n",
        "plt.scatter(n_binomials, means, label='Observed Data')\n",
        "# Predicted\n",
        "k = np.exp(-log_intercept)\n",
        "alpha = slope\n",
        "predicted =  16 / (1 + k* np.exp( -alpha * np.array(n_binomials)))\n",
        "plt.plot(n_binomials, predicted, color='red', label=f'Predicted')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title('Actual data and fitting by a sigmoid')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8kn6__lVfXOK"
      },
      "source": [
        "Assessment: The log of the ratios does not fall into a straight line. But, if the number of monkeys is greater than 5000, the fit is very good -and useless.\n",
        "\n",
        "*Divertimento.* We are very frustrated with our failure. So, let us play with the sigmoid trying to make the fit by hand. To begin with, let us force the sigmoid to start at (0, 8): Given that\n",
        ">>\n",
        ">$y = \\frac{ 16}{ 1 +  c e^{ -\\alpha x }  }   $\n",
        ">>\n",
        ">$ 8 = y = \\frac{ 16}{ 1 +  c e^{ -\\alpha 0 }  }   $\n",
        ">>\n",
        ">$ 8 =  \\frac{ 16}{ 1 +  c   }   $\n",
        ">>\n",
        ">$ 1 + c = \\frac{16}{8}  =    2   $\n",
        ">>\n",
        ">$   c  =    2 -1 = 1   $\n",
        ">\n",
        "Thus,\n",
        ">\n",
        ">$y = \\frac{ 16}{ 1 + e^{ -\\alpha x }  }   $\n",
        ">\n",
        "Parameter $\\alpha$ remains free, to play with it.\n",
        ">\n",
        "The code follows:\n",
        ">\n",
        ">\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 581
        },
        "id": "Jetf3zjv8ogQ",
        "outputId": "077b0fe6-29f9-4abd-911d-0b73e0b32146"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 0 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program FittingOfTheMeanOfMAxBySigmoid.py\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 100000, 250000, 500000]\n",
        "n_binomials = [1, 2,  3, 5, 7, 10, 50, 100, 500, 1000, 2000, 3000, 4000, 5000, 50000, 100000]\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 150, 200]\n",
        "# n_binomials = [ 10000, 100000, 250000, 500000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "normalized_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    means.append(mean)\n",
        "    #Mean is normalized\n",
        "    normalized_mean = mean / n\n",
        "    normalized_means.append(normalized_mean)\n",
        "    # print(f\"Number of monkeys = {m}, mean = {mean}, Normalized mean = {normalized_mean}\")\n",
        "\n",
        "# Adjustment:\n",
        "# Data begins at (1,8), but\n",
        "# the sigmoid must begin at (0,8)\n",
        "l = len(n_binomials)\n",
        "for i in range(l):\n",
        "    n_binomials[i] =  n_binomials[i] - 1\n",
        "\n",
        "\n",
        "# Original data and  a sigmoid\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Raw data\n",
        "plt.scatter(n_binomials, means, label='Observed Data')\n",
        "# Predicted\n",
        "k = 1\n",
        "alpha = 1/500\n",
        "predicted =  16 / (1 + k* np.exp( -alpha * np.array(n_binomials)))\n",
        "plt.plot(n_binomials, predicted, color='red', label=f'Predicted')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title('Actual data and fitting by a sigmoid')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rRy1rU0XBhAO"
      },
      "source": [
        "*Our verdict.* Our clear and simple ideas failed. It is time to look at what others have written.\n",
        "\n",
        ">**Exercise.** Check the advice of the [literature on Bounds for the maximum of binomial random variables](https://math.stackexchange.com/q/591084), and report your findings.\n",
        "\n",
        "*Answer.* The Literature says:\n",
        ">\n",
        "For the $Bi(n, p)$ an upper bound for the expected value of MAX is $ np + \\sigma \\sqrt{2 \\ln m}$, where $\\sigma = \\sqrt{np(1-p)}$ is the standard deviation of the Binomial, and $m$ is the number of monkeys. When $p = \\frac{1}{2}$, this specializes into\n",
        ">>\n",
        ">$\\mathbb{E}(MAX) \\le \\frac{n}{2} + \\sqrt{\\frac{n}{4}} \\sqrt{2 \\ln m}  $\n",
        ">>\n",
        ">$\\mathbb{E}(MAX) \\le \\frac{n}{2} +  \\sqrt{\\frac{n}{2} \\ln m  }  $\n",
        ">>\n",
        "Since this is an upper bound, one must be ready to play a bit changing some parameter to get a good fitting. Thus, the modified equation  \n",
        ">>\n",
        ">$\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{2.337} \\ln m  }  $\n",
        ">>\n",
        "has been proposed for a best fitting.\n",
        ">\n",
        "Let us test this last suggestion  for $n = 16$ and varying $m$.\n",
        "\n",
        "The code follows:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 755
        },
        "id": "jn-9UGpXulkW",
        "outputId": "4085c918-ec44-418e-c010-0dab525740f5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "n = 16\n",
            "sigma = 2.0\n",
            "Number of monkeys = 1, mean = 8.0,  semiempirical prediction = 8.0, pred - obs = 0.00, error_% = 0.0\n",
            "Number of monkeys = 2, mean = 9.1,  semiempirical prediction = 9.6, pred - obs = 0.51, error_% = 5.5\n",
            "Number of monkeys = 3, mean = 9.7,  semiempirical prediction = 10.0, pred - obs = 0.37, error_% = 3.8\n",
            "Number of monkeys = 5, mean = 10.3,  semiempirical prediction = 10.5, pred - obs = 0.17, error_% = 1.7\n",
            "Number of monkeys = 7, mean = 10.7,  semiempirical prediction = 10.7, pred - obs = 0.05, error_% = 0.45\n",
            "Number of monkeys = 10, mean = 11.0,  semiempirical prediction = 11.0, pred - obs = -0.08, error_% = -0.69\n",
            "Number of monkeys = 50, mean = 12.4,  semiempirical prediction = 11.9, pred - obs = -0.52, error_% = -4.2\n",
            "Number of monkeys = 100, mean = 12.9,  semiempirical prediction = 12.2, pred - obs = -0.66, error_% = -5.2\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 0 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "print(f\"n = {n}\")\n",
        "# Number of monkeys\n",
        "n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000] #full range\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 100000, 250000, 500000]\n",
        "# n_binomials = [1, 2,  3, 5, 7, 10, 50, 100, 500, 1000, 2000, 3000, 4000, 5000, 50000, 100000]\n",
        "# n_binomials = [1, 2,  3, 5, 7, 10, 50, 100] #short range\n",
        "# n_binomials = [ 10000, 100000, 250000, 500000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "normalized_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    means.append(mean)\n",
        "    #Mean is normalized\n",
        "    normalized_mean = mean / n\n",
        "    normalized_means.append(normalized_mean)\n",
        "    # print(f\"Number of monkeys = {m}, mean = {mean}, Normalized mean = {normalized_mean}\")\n",
        "\n",
        "sigma = np.sqrt(n*p*(1-p))\n",
        "print(f\"sigma = {sigma}\")\n",
        "\n",
        "semiempirical_prediction = []\n",
        "l = len(n_binomials)\n",
        "for i in range(l):\n",
        "    # a = n/2 +  np.sqrt((n/2.337) * np.log(n_binomials[i])) # Literature\n",
        "    # a = n/2 +  np.sqrt((n/35.5) * np.log(n_binomials[i])) # Best fitting for  Bi(1, 1/2). Error = 8.2%\n",
        "    # a = n/2 +  np.sqrt((n/20.5) * np.log(n_binomials[i])) # Best fitting for  Bi(2, 1/2).\n",
        "    # a = n/2 +  np.sqrt((n/10.5) * np.log(n_binomials[i])) # Best fitting for  Bi(3, 1/2).\n",
        "    # a = n/2 +  np.sqrt((n/7.5) * np.log(n_binomials[i])) # Best fitting for  Bi(4, 1/2). Error = 13%\n",
        "    # a = n/2 +  np.sqrt((n/6.5) * np.log(n_binomials[i])) # Best fitting for  Bi(5, 1/2).\n",
        "    # a = n/2 +  np.sqrt((n/4.12) * np.log(n_binomials[i])) # Best fitting for  Bi(10, 1/2).\n",
        "    a = n/2 +  np.sqrt((n/3.03) * np.log(n_binomials[i])) # Best fitting for  Bi(16, 1/2). Error = 7.5%, full range\n",
        "    # a = n/2 +  np.sqrt((n/4.2) * np.log(n_binomials[i])) # Best fitting for  Bi(16, 1/2). Error = 5.5%, short range\n",
        "    # a = n/2 +  np.sqrt((n/2.65) * np.log(n_binomials[i])) # Best fitting for  Bi(50, 1/2). Error = 6%\n",
        "    # a = n/2 +  np.sqrt((n/2.58) * np.log(n_binomials[i])) # Best fitting for  Bi(100, 1/2). Error = 4.5%\n",
        "    # a = n/2 +  np.sqrt((n/2.55) * np.log(n_binomials[i])) # Best fitting for  Bi(1000, 1/2). Error = 1.5%\n",
        "    # a = n/2 +  np.sqrt((n/2.53) * np.log(n_binomials[i])) # Best fitting for  Bi(5000, 1/2). Error = 0.68%\n",
        "    # a = n/2 +  np.sqrt((n/2.52) * np.log(n_binomials[i])) # Best fitting for  Bi(10000, 1/2). Error =  0.48%\n",
        "    # a = n/2 +  np.sqrt((n/2.48) * np.log(n_binomials[i])) # Best fitting for  Bi(50000, 1/2). Error =  0.22%\n",
        "    # a = n/2 +  np.sqrt((n/2.45) * np.log(n_binomials[i])) # Best fitting for  Bi(100000, 1/2). Error = 0.16%\n",
        "    # a = n/2 +  np.sqrt((n/2.47) * np.log(n_binomials[i])) # Best fitting for  Bi(1000000, 1/2). Error = 0.05%\n",
        "    semiempirical_prediction.append(a)\n",
        "    diff =  semiempirical_prediction[i] - means[i]\n",
        "    percentage = diff / means[i] * 100\n",
        "    print(f\"Number of monkeys = {n_binomials[i]}, mean = {means[i]:.1f},  semiempirical prediction = {semiempirical_prediction[i]:.1f}, pred - obs = {diff:.2f}, error_% = {percentage:.2}\")\n",
        "\n",
        "# Original data and  the predicted by an adjustment of the value given by the literature\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Raw data\n",
        "plt.scatter(n_binomials, means, label='Observed Data')\n",
        "# Predicted\n",
        "plt.plot(n_binomials, semiempirical_prediction, color='red', label=f'Predicted')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title(f'Mean of MAX of $Bi({n}, {p}): Observed  data, and semi-empirical prediction')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "13JzRHOhR2uI"
      },
      "source": [
        "*Comment.* For $n = 16$ and for varying number of monkeys, $m$ from 1 to 1000000, the maximal percental error is less than 7.5% This was achieved by the formula\n",
        ">>\n",
        ">$\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{3.03}\\ln m  }  $\n",
        ">>\n",
        "It seems to us that the error is small, taking into account the extension of the range of operation. The approximations are better for large values of $m$. If high precision is needed, it would be recommended to divide the range of operation in two segments, one before 100, or so, and the other above it. For instance, for the region in within 0 and 100, the formula\n",
        ">>\n",
        ">$\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{4.2} \\ln m  }  $\n",
        ">>\n",
        "produced an error bounded above by 5.5%.\n",
        "\n",
        "We have explored how to fine tune a formula for the specific $Bi(16, 1/2)$ and for a wide range of operation of the number of monkeys $m$. In applications, $n$ can be anyone. So, we need a general formula.\n",
        "\n",
        "**Exercise.** For  whatever number of monkeys $m$, and whatever length of the target string, represented by $n$ in $Bi(n, 1/2)$, find a formula for  $k$, as a function of $n$, the power of the binomial, in the expression that predicts the mean value of MAX:\n",
        ">>\n",
        ">$\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{k} \\ln m  }  $\n",
        ">>\n",
        "*Answer.*  We played with the anterior program by adjusting  the value of $k$ for different values of $n$ and drew the corresponding graphic in the next  program. The resultant graph looked like   $k = \\frac{a}{n} + c$. By a bilogarithmic regression, which outputs two parameters, we can find the value of $a$ if the function is of the form $k = \\frac{a}{n}$. This is done, if we rearrange:  $k -c  = \\frac{a}{n}$. That is why  we subtracted from every $k$ the last value. Since the bilogarithmic regression  outputs two parameters, thus a more general shape is considered:\n",
        ">\n",
        "$k =  a n^r$.\n",
        ">\n",
        "$ \\ln k = \\ln a + r \\ln n $\n",
        "\n",
        "That is why the input arrays for the regression are the log of $k$ and the ln of $n$.  \n",
        "\n",
        "The regression outputs two values, slope and intersect. The slope is $r$, it must be negative and close to $-1$. And, the intersect is $\\ln a$, hence $a = exp(intersect)$.\n",
        "\n",
        "The code for the regression follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "CzM2XQkjfOML",
        "outputId": "d843751a-d892-4de4-dced-68ac638532a7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "n = 1,  k_value = 35.5\n",
            "n = 2,  k_value = 20.5\n",
            "n = 3,  k_value = 10.5\n",
            "n = 4,  k_value = 7.5\n",
            "n = 5,  k_value = 6.5\n",
            "n = 10,  k_value = 4.12\n",
            "n = 16,  k_value = 3.03\n",
            "n = 50,  k_value = 2.65\n",
            "n = 100,  k_value = 2.58\n",
            "n = 1000,  k_value = 2.55\n",
            "c = 2.53\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "log_nn_values  =  [0.         0.69314718 1.09861229 1.38629436 1.60943791 2.30258509\n",
            " 2.77258872 3.91202301 4.60517019 6.90775528]\n",
            "log_knr_values =  [ 3.49559806  2.8887037   2.07568449  1.60341984  1.37876609  0.46373402\n",
            " -0.69314718 -2.12026354 -2.99573227 -3.91202301]\n",
            "slope = -1.1848692844160913, intercept = 3.214725734441635\n",
            "k = ax^r + c: a = 24.896462732451266, r = -1.1848692844160913, c = 2.53\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program k_of_MAX\n",
        "# For different values of n in Bi(n, 1/2)\n",
        "# the k is fitted in the formula\n",
        "# E(MAX) = (n/2) + sqrt( (n/k) ln m)\n",
        "# for m monkeys\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the values of n\n",
        "# n_values  = [1, 2, 3, 4, 5, 10, 16, 50, 100,  1000, 5000, 10000, 50000, 100000, 1000000] ## All values\n",
        "#\n",
        "# k_values = [35.5, 20.5, 10.5, 7.5, 6.5, 4.12, 3.03, 2.65, 2.58, 2.55, 2.53, 2.52, 2.48, 2.45, 2.47] # Best fitting for  Bi(n, 1/2). Error = 13%\n",
        "\n",
        "n_values  = [1, 2, 3, 4, 5, 10, 16, 50, 100, 1000]\n",
        "#One more entry to subtract it from all others: y = a/x + c -y = a/x\n",
        "k_values = [35.5, 20.5, 10.5, 7.5, 6.5, 4.12, 3.03, 2.65, 2.58, 2.55, 2.53]\n",
        "\n",
        "\n",
        "  # a = n/2 +  np.sqrt((n/35.5) * np.log(n_binomials[i])) # Best fitting for  Bi(1, 1/2). Error = 8.2%\n",
        "  # a = n/2 +  np.sqrt((n/20.5) * np.log(n_binomials[i])) # Best fitting for  Bi(2, 1/2).\n",
        "  # a = n/2 +  np.sqrt((n/10.5) * np.log(n_binomials[i])) # Best fitting for  Bi(3, 1/2).\n",
        "  # a = n/2 +  np.sqrt((n/7.5) * np.log(n_binomials[i])) # Best fitting for  Bi(4, 1/2). Error = 13%\n",
        "  # a = n/2 +  np.sqrt((n/6.5) * np.log(n_binomials[i])) # Best fitting for  Bi(5, 1/2).\n",
        "  # a = n/2 +  np.sqrt((n/4.12) * np.log(n_binomials[i])) # Best fitting for  Bi(10, 1/2).\n",
        "  # a = n/2 +  np.sqrt((n/3.03) * np.log(n_binomials[i])) # Best fitting for  Bi(16, 1/2). Error = 7.5%, full range\n",
        "  # a = n/2 +  np.sqrt((n/4.2) * np.log(n_binomials[i])) # Best fitting for  Bi(16, 1/2). Error = 5.5%, short range\n",
        "  # a = n/2 +  np.sqrt((n/2.65) * np.log(n_binomials[i])) # Best fitting for  Bi(50, 1/2). Error = 6%\n",
        "  # a = n/2 +  np.sqrt((n/2.58) * np.log(n_binomials[i])) # Best fitting for  Bi(100, 1/2). Error = 4.5%\n",
        "  # a = n/2 +  np.sqrt((n/2.55) * np.log(n_binomials[i])) # Best fitting for  Bi(1000, 1/2). Error = 1.5%\n",
        "  # a = n/2 +  np.sqrt((n/2.53) * np.log(n_binomials[i])) # Best fitting for  Bi(5000, 1/2). Error = 0.68%\n",
        "  # a = n/2 +  np.sqrt((n/2.52) * np.log(n_binomials[i])) # Best fitting for  Bi(10000, 1/2). Error =  0.48%\n",
        "  # a = n/2 +  np.sqrt((n/2.48) * np.log(n_binomials[i])) # Best fitting for  Bi(50000, 1/2). Error =  0.22%\n",
        "  # a = n/2 +  np.sqrt((n/2.45) * np.log(n_binomials[i])) # Best fitting for  Bi(100000, 1/2). Error = 0.16%\n",
        "  # a = n/2 +  np.sqrt((n/2.47) * np.log(n_binomials[i])) # Best fitting for  Bi(1000000, 1/2). Error = 0.05%\n",
        "difference = []\n",
        "for i in range(len(n_values))   :\n",
        "  print(f\"n = {n_values[i]},  k_value = {k_values[i]}\" )\n",
        "\n",
        "# Data looks like y = a/x + c.\n",
        "# c is subtracted everywhere to become y = a/x\n",
        "l = len(k_values)\n",
        "c = k_values[l-1]\n",
        "print(f\"c = {c}\")\n",
        "kr_values = []\n",
        "for i in range(l-1)   :\n",
        "  kr_values.append(k_values[i]  - c)\n",
        "\n",
        "\n",
        "\n",
        "# Plot\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_values, kr_values, label='k_values')\n",
        "plt.xlabel('n in Bi(n, 1/2), the length of the binary string to match')\n",
        "plt.ylabel('k_values')\n",
        "plt.title('k_values as a function of n in Bi(n, 1/2)')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n",
        "# Regression line of k_values  over n_values\n",
        "log_nn_values =  np.log(np.array(n_values))\n",
        "print(\"log_nn_values  = \" , log_nn_values )\n",
        "log_knr_values = np.log(np.array(kr_values))\n",
        "print(\"log_knr_values = \" , log_knr_values)\n",
        "slope, intercept = np.polyfit(log_nn_values, log_knr_values, 1)\n",
        "print(f\"slope = {slope}, intercept = {intercept}\")\n",
        "# The slope is $r$ in $y = ax^r$, it must be negative and close to $-1$. And the intersect is $log a$, hence $a = exp(intersect).\n",
        "print(f\"k = ax^r + c: a = {np.exp(intercept)}, r = {slope}, c = {c}\")\n",
        "#Plot regression line\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.scatter(log_nn_values, log_knr_values, label='Observed Data')\n",
        "plt.plot(log_nn_values, slope * log_nn_values + intercept, color='red', label=f'Linear Regression: y = {slope:.7f}x + {intercept:.4f}')\n",
        "plt.xlabel('log n in Bi(n, 1/2), the length of the binary string to match')\n",
        "plt.ylabel('log k')\n",
        "plt.title('log of k_values')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KIJmi1jsu-7C"
      },
      "source": [
        "The program outputs\n",
        ">\n",
        "$ \\ln k = a(\\ln x)^r + c$, where  $a = 24.896$ , $r = -1.18$, $c = 2.53$\n",
        ">\n",
        "Therefore, the formula for $k$ as a function of $n$ becomes:\n",
        ">\n",
        "$k = 24.9 n^{-1.18} + 2.53$\n",
        ">\n",
        "This formula is tested in the following program, in which $k$ is incorporated into the formula for the mean of MAX:\n",
        ">\n",
        ">Mean of MAX = $\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{k}\\ln m  }  $\n",
        ">>>\n",
        "where $n$ is the power of the binomial and $m$ is the number of monkeys."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 876
        },
        "id": "75kH6QNNweP3",
        "outputId": "efa3eeba-885c-458c-a831-3acb1a088787"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "n = 1000\n",
            "sigma = 15.811388300841896\n",
            "Number of monkeys = 1, mean = 500.0,  semiempirical prediction = 500.0, pred - obs = -0.00, error_% = -4.5e-14\n",
            "Number of monkeys = 3, mean = 513.4,  semiempirical prediction = 520.8, pred - obs = 7.43, error_% = 1.4\n",
            "Number of monkeys = 5, mean = 518.4,  semiempirical prediction = 525.2, pred - obs = 6.80, error_% = 1.3\n",
            "Number of monkeys = 7, mean = 521.4,  semiempirical prediction = 527.7, pred - obs = 6.32, error_% = 1.2\n",
            "Number of monkeys = 10, mean = 524.3,  semiempirical prediction = 530.1, pred - obs = 5.80, error_% = 1.1\n",
            "Number of monkeys = 50, mean = 535.5,  semiempirical prediction = 539.3, pred - obs = 3.72, error_% = 0.69\n",
            "Number of monkeys = 100, mean = 539.6,  semiempirical prediction = 542.6, pred - obs = 2.97, error_% = 0.55\n",
            "Number of monkeys = 500, mean = 548.0,  semiempirical prediction = 549.5, pred - obs = 1.51, error_% = 0.28\n",
            "Number of monkeys = 1000, mean = 551.2,  semiempirical prediction = 552.2, pred - obs = 0.97, error_% = 0.18\n",
            "Number of monkeys = 5000, mean = 558.1,  semiempirical prediction = 557.9, pred - obs = -0.15, error_% = -0.026\n",
            "Number of monkeys = 10000, mean = 560.8,  semiempirical prediction = 560.3, pred - obs = -0.58, error_% = -0.1\n",
            "Number of monkeys = 50000, mean = 566.8,  semiempirical prediction = 565.3, pred - obs = -1.49, error_% = -0.26\n",
            "Number of monkeys = 100000, mean = 569.2,  semiempirical prediction = 567.4, pred - obs = -1.85, error_% = -0.33\n",
            "Number of monkeys = 500000, mean = 574.6,  semiempirical prediction = 571.9, pred - obs = -2.64, error_% = -0.46\n",
            "Number of monkeys = 1000000, mean = 576.7,  semiempirical prediction = 573.8, pred - obs = -2.95, error_% = -0.51\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 0 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "#fig, ax = plt.subplots(1, 1)\n",
        "\n",
        "# Parameters of the binomial\n",
        "# probability of head\n",
        "p = 0.5\n",
        "# Define the value of n\n",
        "n  = 1000\n",
        "print(f\"n = {n}\")\n",
        "\n",
        "# Number of monkeys [m]\n",
        "n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000] #full range\n",
        "# n_binomials = [2,  3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 100000, 250000, 500000]\n",
        "# n_binomials = [1, 2,  3, 5, 7, 10, 50, 100, 500, 1000, 2000, 3000, 4000, 5000, 50000, 100000]\n",
        "# n_binomials = [1, 2,  3, 5, 7, 10, 50, 100] #short range\n",
        "# n_binomials = [ 10000, 100000, 250000, 500000]\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "# Plot the means of MAX for different number of monkeys\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "means = []\n",
        "normalized_means = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k)\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0])\n",
        "    # plt.plot(k_values, pmf_k, label=f'm = {m}')\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    means.append(mean)\n",
        "    #Mean is normalized\n",
        "    normalized_mean = mean / n\n",
        "    normalized_means.append(normalized_mean)\n",
        "    # print(f\"Number of monkeys = {m}, mean = {mean}, Normalized mean = {normalized_mean}\")\n",
        "\n",
        "sigma = np.sqrt(n*p*(1-p))\n",
        "print(f\"sigma = {sigma}\")\n",
        "\n",
        "semiempirical_prediction = []\n",
        "l = len(n_binomials)\n",
        "for i in range(l):\n",
        "    m = n_binomials[i]\n",
        "    k = 24.9 * n**(-1.18) + 2.53\n",
        "    # a = n/2 +  np.sqrt((n/2.337) * np.log(m)) # Literature\n",
        "    a = n/2 +  np.sqrt((n/k) * np.log(m))\n",
        "    semiempirical_prediction.append(a)\n",
        "    diff =  semiempirical_prediction[i] - means[i]\n",
        "    percentage = diff / means[i] * 100\n",
        "    print(f\"Number of monkeys = {n_binomials[i]}, mean = {means[i]:.1f},  semiempirical prediction = {semiempirical_prediction[i]:.1f}, pred - obs = {diff:.2f}, error_% = {percentage:.2}\")\n",
        "\n",
        "# Original data and  the predicted by an adjustment of the value given by the literature\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Raw data\n",
        "plt.scatter(n_binomials, means, label='Observed Data')\n",
        "# Predicted\n",
        "plt.plot(n_binomials, semiempirical_prediction, color='red', label=f'Predicted')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title(f'Mean of MAX of $Bi({n}, {p}): Observed  data, and semi-empirical prediction')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4pAvPy0zbbsu"
      },
      "source": [
        "*Comment.* We see that the fitting looks  good. So, we accept this formula.  \n",
        "\n",
        "\n",
        "**Exercise.**  Propose an interpretation of the strange form of the function that predicts the mean value of the mean of MAX, which is $y = \\frac{n}{2}+ \\sqrt{\\frac{n}{k} \\ln (m)}$, where $n$ is the power in the Binomial $Bi(n,p)$, $k$ is a constant around 2 or 3 that one must find by trial and error or a regression, and $m$ is the number of monkeys.\n",
        ">\n",
        "*Answer.* The easiest way for understanding  a function is by finding its differential equation and  interpreting it. The equation is\n",
        "\n",
        ">$y = A +  \\sqrt{\\frac{n}{k} \\ln(m)}$, where $A$ is the expected value of the $Bi(n, 1/2)$.\n",
        ">>\n",
        ">$y-A = \\sqrt{\\frac{n}{k}\\ln (m)}$\n",
        ">>\n",
        ">$(y-A)^2 =   \\frac{n}{k}\\ln (m)  $\n",
        ">\n",
        "Differentiating with respect to $m$:\n",
        ">>\n",
        ">$ 2(y-A)\\frac{dy}{dm} = \\frac{n}{km}$\n",
        ">>\n",
        ">$ \\frac{dy}{dm} = \\frac{n}{2km(y-A)}$\n",
        ">>\n",
        ">$ dy= \\frac{n}{2km(y-A)}dm$\n",
        ">\n",
        "Our interpretation of this equation is:  \n",
        ">\n",
        "- The more monkeys one adds, the higher is the mean of MAX: $dy \\sim dm$\n",
        "- To add monkeys pays, but the marginal gain, $dy$, is inversily proportional to the number of monkeys because at the beginning the population effect is very strong but diminishes as the number of monkeys grows: $dy \\sim \\frac{1}{m}$.\n",
        "- The return of adding monkeys is inversily proportional to the achieved perfection, which is given by the surplus over the mean, $y-A$. So, we get $dy \\sim  \\frac{1}{y-A}$\n",
        "- The larger is a pattern binary string, the higher is the achieved mean value of MAX: $dy \\sim n$.  \n",
        "- According to this equation, the MAX does not have an upper bound. It can grow forever and ever. The good news is that the function grows very slowly.\n",
        "\n",
        "Since our formula is needed for further use, let us carry a small test: How many monkeys are needed to get perfection?\n",
        ">\n",
        "To get perfection when $n = 16$, we need  16 matches. To know the number of needed monkeys, we can clear for $m$ in\n",
        ">\n",
        "> $y = 16 = A +  \\sqrt{\\frac{16}{k}\\ln(m)}$\n",
        ">>\n",
        ">$ 16 = 8 + \\sqrt{\\frac{16}{k}\\ln m)}  $\n",
        ">>\n",
        ">$  \\sqrt{\\frac{16}{k}\\ln(m)} = 8$\n",
        ">>\n",
        ">$  \\frac{16}{k}\\ln(m) = 64 $\n",
        ">>\n",
        ">$   \\ln m =  (64)(\\frac{k}{16})$\n",
        ">>\n",
        "Replacing  $n$ by 16 in  $k = 24.9 n^{-1.18} + 2.53$,   we have\n",
        ">>\n",
        ">$k = 24.9 (16)^{-1.18} + 2.53$\n",
        ">>\n",
        "> $k = 24.9 (0.0379) + 2.53$\n",
        ">>\n",
        "> $k = 0.94 + 2.53$\n",
        ">>\n",
        ">$k = 3.47$\n",
        ">\n",
        "Hence,\n",
        ">\n",
        ">$ \\ln m =  (64)(\\frac{3.47}{16})$\n",
        ">>\n",
        ">$\\ln m = 4 (3.47)$\n",
        ">>\n",
        ">$\\ln m = 13.88$\n",
        ">>\n",
        ">$ m = e^{14} = 1200000$\n",
        ">\n",
        "Thus, our formula predicts that when the task is to match a binary string 16 bits long,  we need  one million monkeys to guarantee perfection as a reproducible feat. This is in agreement with our previous estimates that were found by prediction of the CDF of MAX. So, we consider that our formula is valid and proceed further.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WFLJpX3Vj1Bf"
      },
      "source": [
        "## Estimation of the variance of MAX  \n",
        "\n",
        "We already have an estimation of the expected value of MAX. Let us make an estimation of its variance.\n",
        "\n",
        "**Exercise.** Use the CDF of MAX and the definition of the mean and variance to develop a program to estimate the variance. Report your observations.\n",
        ">\n",
        "*Answer.* The code follows:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "-U79pJbVNGLn",
        "outputId": "faab1ff5-0d3f-4421-fa28-982f17b16d7b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of monkeys = 1, mean = 8.0, variance = 4.0, deviation = 2.0\n",
            "Number of monkeys = 10001, mean = 15.1, variance = 0.21, deviation = 0.46\n",
            "Number of monkeys = 20001, mean = 15.3, variance = 0.2, deviation = 0.45\n",
            "Number of monkeys = 30001, mean = 15.4, variance = 0.23, deviation = 0.48\n",
            "Number of monkeys = 40001, mean = 15.5, variance = 0.25, deviation = 0.5\n",
            "Number of monkeys = 50001, mean = 15.5, variance = 0.25, deviation = 0.5\n",
            "Number of monkeys = 60001, mean = 15.6, variance = 0.24, deviation = 0.49\n",
            "Number of monkeys = 70001, mean = 15.7, variance = 0.23, deviation = 0.47\n",
            "Number of monkeys = 80001, mean = 15.7, variance = 0.21, deviation = 0.46\n",
            "Number of monkeys = 90001, mean = 15.7, variance = 0.19, deviation = 0.43\n",
            "Number of monkeys = 100001, mean = 15.8, variance = 0.17, deviation = 0.41\n",
            "Number of monkeys = 110001, mean = 15.8, variance = 0.15, deviation = 0.39\n",
            "Number of monkeys = 120001, mean = 15.8, variance = 0.13, deviation = 0.37\n",
            "Number of monkeys = 130001, mean = 15.9, variance = 0.12, deviation = 0.34\n",
            "Number of monkeys = 140001, mean = 15.9, variance = 0.1, deviation = 0.32\n",
            "Number of monkeys = 150001, mean = 15.9, variance = 0.091, deviation = 0.3\n",
            "Number of monkeys = 160001, mean = 15.9, variance = 0.079, deviation = 0.28\n",
            "Number of monkeys = 170001, mean = 15.9, variance = 0.069, deviation = 0.26\n",
            "Number of monkeys = 180001, mean = 15.9, variance = 0.06, deviation = 0.25\n",
            "Number of monkeys = 190001, mean = 15.9, variance = 0.052, deviation = 0.23\n",
            "Number of monkeys = 200001, mean = 16.0, variance = 0.045, deviation = 0.21\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fac6dca0980>"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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Txmq1mssvv9w88cQTpn379ua1114zDz74oLFYLGbw4MFu26xVq5a56KKLTPny5c3jjz9uXnnlFdOsWTPj5+fnei0Yk9EVvnnz5iYyMtI88cQT5u233zYDBgwwFovFjBgxIlubGjdubOrWrWsmTJhgpkyZYvbu3ZvrvnG+j2+55Rbz5ptvmgEDBhhJpk+fPq5lcnvv5KZjx46mWrVqJiYmxjzyyCPm9ddfN40bNzb+/v5mwYIFpkqVKmbcuHHm1VdfdX0+xMfHu9YvyP9NY86+J1q1amWuvvpq8/rrr5vRo0cbf39/15dVWfd11uA0ffp0Y7FY3LrHr1q1ylitVtOuXTszefJkM2XKFNO8eXNjtVpd3ZgdDoeJiYnJsav6ddddZ+rVq+e63759exMREWGeeuop895775kXX3zRdO7c2axduzbXfZcb52dCs2bNTPPmzc0rr7xiHn/8cVf4dH6BvGPHjhyP01JSUkyFChXM3XffnefjrFixwvj5+ZmmTZuaV155xTz55JMmIiLCNGnSJFv4GDp0qAkICDDDhg0zb7/9tnnsscdMSEiI22dFXq+d3IJTQf6eWd+nhw4dMs8995yRZO65555sj3Pue9fhcJirr77aWCwWM3ToUPPGG2+YXr16GUlm5MiRbo8jybRo0cL1Wnz11VdN3bp1TXBwsDl27Fie+9KXEJy8JD093VStWtW0a9fObfrbb79tJLm+ST1z5ky2A+vdu3cbm81mnnvuOdc05wdB3bp1s1WNcjpwOHcZY4yJjY01FovF7R+D8x9B1scyxphWrVqZ1q1bu+47vznK6WDNGUT27Nlj/P39s1Vktm7dagICAnKt1Dj16dPHWK1Wt38y//77rwkLC3M7cPekr3/WZbdt2+YWgt58800TGhpqkpKScg1ODzzwgImJiXE9R2cgzuvAc8yYMUaS8ff3N5s2bcq3jcYYc+TIEWO1Wk3Xrl3dXg9vvPGGkWRmzJjhmuY8WDt69Gi+2+3Xr5+pVauWSUtLK1BwyumbqCuuuCLbh965wSktLc1YLBYzevToPNuTV3BatGiRkWQiIyNNgwYNzMyZM83MmTNNgwYNjNVqzTMg5sbZl/u///1vtnmPPPKIkZRvf+5evXqZiRMnmiVLlpj333/fdOjQIceDf6euXbuaiy++2G1aTsGpoO/93r17myZNmuT3VLNJT0/P1k/+5MmTpnLlyvkeEDjbfO57ojDB6dzHuvHGG01kZKTr/o4dO4yfn5+58cYbs+2PrN9o5naO07mff6mpqSY6Oto0bdrU7dviZcuWGUnmmWeecXuOBfn8y0lxvWfzO8cpMjLS7VvqpUuXGknmf//7n2vaNddcY5o1a+b22nY4HKZ9+/amQYMGeT6+J4/jaXCqVKmSOXXqlGu687OyRYsWJi0tzTW9f//+xmq1urXf+fmUtcIUFxdnqlatalq1auWaNn78eBMSEmL++usvtzY9/vjjxt/f31VxcLYpPDw8x4rDuTZv3mwkmaFDh7pNf/jhh40kty938urBcK6OHTsaSWbevHmuaX/++aeRZPz8/NzCz4oVK7K9/wr6f9N5oN2lSxe399VDDz1k/P393f4uWYPT1KlTjcViMePHj3fNdzgcpkGDBqZbt25u20pOTjZ16tQx1157rWvamDFjjM1mc9v+kSNHTEBAgOvz4uTJkwX+n14Qzs+E6tWru4XMjz76yEgyU6dOdU1r166dadu2rdv6zv9FuZ2L69SyZUtTtWpVt+fmPEbI+vr/5ptvjKRsvQS++OKLbNNze+3kFpwK8vc8932a1zlO5753lyxZ4vpCM6tbbrnFWCwWs3PnTtc0ScZqtbpN27JlS47h1Jcxqp6X+Pv767bbbtOGDRu0Z88e1/R58+apcuXKuuaaayRl9Fv188v4M9ntdh0/flyhoaFq2LChfv7552zbHThwoMqVK5fv42ddJikpSceOHVP79u1ljNEvv/ySbflzRwjr0KGD/v77b9f9Tz75RBaLRWPHjs22rnNY6kWLFsnhcKhv3746duyY61alShU1aNBAX3/9da7ttdvt+vLLL9WnTx+3c0OqVq2q22+/Xd9++63i4+Pzfd55adKkiZo3b6758+dLyvhb9O7dW8HBwTkun56erg8//FD9+vVzPcerr7463+G2o6KiJEnVqlVT06ZNC9S2r776SqmpqRo5cqTr9SBJw4YNU3h4uJYvX16g7Zxr0KBB2rt3rzp06KDly5fr6NGjSktLy3X5tm3bauXKlVq5cqWWLVumF154Qb/99ptuuOEGnT59Otf1Tpw4IWOMKlSoUKh2ShlDmUtSQkKCVq1apUGDBmnQoEH66quvZIzRSy+95PE2nW3OqX+487yYvJ6XJH366ad69NFH1bt3b919991au3atunXrpldeeSXHkf4qVKigY8eOuU2bNWuWjDFu58YV9L1fvnx5HThwQD/99FPBnnQmf39/V992h8OhEydOKD09XZdeemmOny3FJafPluPHj7vez0uWLJHD4dAzzzzj9tqXlOOQ9/nZuHGjjhw5ovvvv9/t3KeePXuqUaNGOb6X8vv8y0lxvWfz069fP7f3WYcOHSTJ1d4TJ05o9erV6tu3rxISElyfw8ePH1e3bt20Y8cO/fPPP+f9OIVx6623KiIiwnXfOXz/nXfe6XbOZNu2bZWampqtndWqVdONN97ouh8eHq4BAwbol19+0aFDhyRJCxcuVIcOHVzvQ+etS5custvtWrdunds2b775ZlWqVCnftn/22WeSpFGjRrlNHz16tCSd1987NDTUbSTShg0bqnz58rr44ovdLnHg/N35NyjM/8177rnH7X3VoUMH2e127d27N1u7XnrpJY0YMUITJ07UU0895Zq+efNm7dixQ7fffruOHz/u2sdJSUm65pprtG7dOjkcDknSgAEDlJKS4jY0+Icffqj09HTXeaPOc3rWrFmjkydPer4DczFgwACFhYW57t9yyy2qWrWq62/pXOaHH37Qrl27XNPmzp2rmJgYdezYMddtHzx4UJs3b9bAgQPdXtPXXnutGjdu7LbswoULFRERoWuvvdbtNdm6dWuFhobmeWyUH0/+noXx2Wefyd/fXw8++KDb9NGjR8sYo88//9xtepcuXVSvXj3X/ebNmys8PPy8PjdKGsHJi5yDP8ybN0+SdODAAX3zzTe67bbb5O/vLynjgGbKlClq0KCBbDaboqKiVKlSJf3666+Ki4vLts06deoU6LH37dunQYMGqWLFigoNDVWlSpVcHwLnbjcoKCjbP44KFSq4fYDt2rVL1apVU8WKFXN9zB07dsgYowYNGqhSpUputz/++MN1gnROjh49quTkZDVs2DDbvIsvvlgOh0P79+8v0HPPy+23366FCxdq586dWr9+vW6//fZcl/3yyy919OhRtWnTRjt37tTOnTu1e/dude7cWfPnz3f9Y8hq//79Gjt2rJo2bar9+/cX+GDf+SF37vO3Wq2qW7duoT8Eu3fvrlWrVik8PFzLli3TW2+9pQoVKuj//u//chxiPCoqSl26dFGXLl3Us2dPPfHEE3rvvfe0fv16vffee/k+njGmUO2Uzob9K664QjExMa7pNWvW1JVXXqn169cXepspKSnZ5p05c8ZtmYKyWCx66KGHlJ6enuOw6saYAh3wF/S9/9hjjyk0NFRt2rRRgwYNNHz4cH333XcFauvs2bPVvHlzBQUFKTIyUpUqVdLy5ctz/GwpLs4BOZycB+POz5ddu3bJz88v28FGYeX2XpKkRo0aZXsvFeTzz5PHOd/3bH7y2587d+6UMUZPP/10ts9h5xdfeX0WF/RxiqLtzgPOrO/3rNPPfaz69etne29ddNFFkuT6gnLHjh364osvsj33Ll26SMr+3Av6P3Xv3r3y8/NT/fr13aZXqVJF5cuXP6+/d40aNbI9r4iIiHz3S2H+bxb077p27Vo99thjeuyxx/TII4+4zduxY4ekjC9yz93P7733nlJSUlyfMY0aNdJll13m9mXj3Llzdfnll7v2pc1m08SJE/X555+rcuXKuuqqq/TSSy+5wnBhOQczcrJYLKpfv77bl9n9+vWTzWZztS8uLk7Lli1zXaYkN86/97mPIWX/TNixY4fi4uIUHR2dbX8lJiYW6P2Ym+J4n2a1d+9eVatWzS2AShmvL+f8vNrjbFNRBuLixqh6XtS6dWs1atRI8+fP1xNPPKH58+fLGOM2mt6LL76op59+WnfffbfGjx+vihUrys/PTyNHjszxwLwgB3l2u13XXnutTpw4occee0yNGjVSSEiI/vnnHw0aNCjbdp0h7nw5HA5ZLBZ9/vnnOW4zr+sklZT+/ftrzJgxGjZsmCIjI9W1a9dcl3V+kJ47SpzT2rVr1blzZ7dpDzzwgCTp888/16hRo/TCCy/o9ttv9+oIa1dffbWuvvpqzZo1S19//bWqV6+ul19+WXv37tUXX3yR7/rO6ui6dev0n//8J8dlKlasKIvFcl4fjtWqVZMkVa5cOdu86OjoHCul+alataqkjG8Hz3Xw4EFVrFixUKMVOQ9ocgqfJ0+edFUd81LQ9/7FF1+s7du3a9myZfriiy/0ySef6K233tIzzzyjZ599Ntftf/DBBxo0aJD69OmjRx55RNHR0fL391dsbKzbt6ueyO1Awm6357pObp8v5xOyi1JRff6VlPz2p/O18/DDD6tbt245LnvuwX9hHkfKeD3k9HfM7fWQ2zaL8jXicDh07bXX6tFHH81xvjNoORXmi5OiVhL7xdNtNmnSRKdOndKcOXP0f//3f24B0/kamzRpUq4X9836/37AgAEaMWKEDhw4oJSUFH3//fd644033JYfOXKkevXqpSVLlmjFihV6+umnFRsbq9WrV6tVq1aFeaoFUqFCBV1//fWaO3eunnnmGX388cdKSUkp0CiqBeVwOPLsqVKQimdufO3z1dfaUxgEJy+744479PTTT+vXX3/VvHnz1KBBA1122WWu+R9//LE6d+6s999/3229U6dOFejgKydbt27VX3/9pdmzZ7sNh75y5crCPQlJ9erV04oVK3TixIlcq0716tWTMUZ16tTJ9s8pP5UqVVJwcLC2b9+ebd6ff/4pPz+/bN++FUbNmjV1xRVXaM2aNbrvvvuyDantlJSUpKVLl6pfv3665ZZbss1/8MEHNXfuXLfgtHjxYn366aeaMmWKatSooVdffVUrVqzQ8OHDs5Wzz1WrVi1J0vbt291CVmpqqnbv3u36tvR81alTR+PGjVNiYqLeeOMNJSQkZPsm6Vzp6emSznaly0lAQIDq1aun3bt3F7ptzZo1U2BgYI7diP79999C/XOpXr26KlWqpI0bN2ab9+OPP+b6Tz8/zm4HObVp9+7dbkPe58aT935ISIj69eunfv36KTU1VTfddJNeeOEFjRkzJtehuD/++GPVrVtXixYtcjvYy6m7bUE5v808deqU2/Tz+ba9Xr16cjgc+v333/P8exT0gDXre+nqq692m7d9+3bX/PNVXO/Z8z0wd7YlMDCwyD43clOhQoUcu+AUV7XNWU3Luo+cFx13doOtV6+eEhMTi/y516pVSw6HQzt27HB92y5Jhw8f1qlTp4rsdeWJ4vy/GRUVpY8//lhXXnmlrrnmGn377beuL7ecXbHCw8MLtJ9vu+02jRo1SvPnz9fp06cVGBiofv36ZVuuXr16Gj16tEaPHq0dO3aoZcuWmjx5sj744INCPQdnZczJGKOdO3eqefPmbtMHDBig3r1766efftLcuXPVqlUrNWnSJM9tO//e5z6GpGx/j3r16umrr77SFVdc4XFQLw6efMbUqlVLX331VbZjhT///NM1/0JDVz0vc1aXnnnmGW3evDnbtZv8/f2zJfGFCxcWqA96bpyJP+t2jTHndS2hm2++WcaYHL/hdj7OTTfdJH9/fz377LPZnpMxRsePH8+zzV27dtXSpUvdyuiHDx/WvHnzdOWVVyo8PLzQ7c/q+eef19ixY3OtnkgZISgpKUnDhw/XLbfcku12/fXX65NPPnF1AUtISNCDDz6oVq1aubZbrVo1jR8/Xl988YUWLlyYZ5u6dOkiq9Wq1157zW3fvf/++4qLi1PPnj0L9VxzqwClpaW5nQOTl//973+SlG8YaNeuXY4BpaDCwsJ03XXXaf369a4PZUn6448/tH79el177bWF2u7NN9+sZcuWuXVZWbVqlf766y+3a0qlpaXpzz//dKtOnThxItu352lpaZowYYKsVmu2imNcXJx27dql9u3bu00/ePCg/vzzT7fzywr63j/3fWO1WtW4cWMZY/I8Xy2nz4EffvhBGzZsyHWd/ISHhysqKirbeSJvvfVWobfZp08f+fn56bnnnstWDc/a9pCQkGyBLSeXXnqpoqOj9fbbb7t10fz888/1xx9/FPq9dK7ies+GhIRIyh5OCyo6OlqdOnXS9OnTc6y0Oq+DVxTq1aunP//8022bW7ZsKXBXUk/9+++/Wrx4set+fHy8/vvf/6ply5aqUqWKpIweAhs2bNCKFSuyrX/q1CnXF0Geuu666yRJr776qtv0V155RZKK7HXlieL+v1mjRg199dVXOn36tK699lrXZ1Hr1q1Vr149vfzyyzl+oXbuaywqKko9evTQBx98oLlz56p79+5uXw4lJye7uk471atXT2FhYTl2sy6o//73v0pISHDd//jjj3Xw4EH16NHDbbkePXooKipKEydO1Nq1awtUbapatapatmyp2bNnu3V9XrlypX7//Xe3Zfv27Su73a7x48dn2056enqh3+uF5clnzHXXXSe73Z6tQjhlyhRZLJZs+/JCQMXJy+rUqaP27dtr6dKlkpQtOF1//fV67rnnNHjwYLVv315bt27V3Llzz6trV6NGjVSvXj09/PDD+ueffxQeHq5PPvnkvLpRde7cWXfddZdee+017dixQ927d5fD4dA333yjzp0764EHHlC9evX0/PPPa8yYMdqzZ4/69OmjsLAw7d69W4sXL9Y999yjhx9+ONfHeP7557Vy5UpdeeWVuv/++xUQEKDp06crJSWlUAMD5KZjx455nvQpZXTTi4yMzHYA7HTDDTfo3Xff1fLly3XTTTfpqaee0r///qtFixa5laqHDx+u2bNna+TIkerevXuu1Z1KlSppzJgxevbZZ9W9e3fdcMMN2r59u9566y1ddtllhe420LdvX1WuXFnXX3+9/vrrL+3evVuPPPKI3nvvPd18883Zuqn9888/rm/3UlNTtWXLFk2fPl1RUVF5Bk1J6t27t+bMmaO//vorW8Xx+eeflyT99ttvkqQ5c+bo22+/lSS3k45ffPFFrVq1SldffbXrZNTXXntNFStW1BNPPOG2TYvFoo4dO+Z4nlFWTzzxhBYuXKjOnTtrxIgRSkxM1KRJk9SsWTMNHjzY7blffPHFGjhwoGbNmiUpY2CI559/Xrfccovq1KmjEydOaN68edq2bZtefPFF18Gak3Mgi969e7tNHzNmjGbPnq3du3e7vhkv6Hu/a9euqlKliq644gpVrlxZf/zxh9544w317Nkzz2rh9ddfr0WLFunGG29Uz549tXv3br399ttq3LhxntXD/AwdOlQTJkzQ0KFDdemll2rdunWub/0Lo379+nryySc1fvx4dejQQTfddJNsNpt++uknVatWTbGxsZIyDtamTZum559/XvXr11d0dHS2ipKUUWmZOHGiBg8erI4dO6p///46fPiwpk6dqtq1a+uhhx4qdFuzKq73bOvWrSVlVLW7devmGmjIE2+++aauvPJKNWvWTMOGDVPdunV1+PBhbdiwQQcOHNCWLVsK1bZz3X333XrllVfUrVs3DRkyREeOHNHbb7+tJk2anPdgPjm56KKLNGTIEP3000+qXLmyZsyYocOHD2vmzJmuZR555BF9+umnuv766zVo0CC1bt1aSUlJ2rp1qz7++GPt2bOnUL05WrRooYEDB+qdd97RqVOn1LFjR/3444+aPXu2+vTpk+1LlJJS3P8369evry+//FKdOnVSt27dtHr1aoWHh+u9995Tjx491KRJEw0ePFjVq1fXP//8o6+//lrh4eGuL9ycBgwY4Oq9cW6A+Ouvv3TNNdeob9++aty4sQICArR48WIdPnzY7bU/a9YsDR48WDNnztSgQYPybXvFihV15ZVXavDgwTp8+LBeffVV1a9fX8OGDXNbLjAwULfddpveeOMN+fv7q3///gXaN7GxserZs6euvPJK3X333Tpx4oRef/11NWnSxO0ztmPHjvq///s/xcbGavPmzeratasCAwO1Y8cOLVy4UFOnTs2xZ0txqVevnsqXL6+3335bYWFhCgkJUdu2bXM8369Xr17q3LmznnzySe3Zs0ctWrTQl19+qaVLl2rkyJFuA0FcMIp30D4UxJtvvmkkmTZt2mSbd+bMGTN69GhTtWpVU65cOXPFFVeYDRs2ZBs+0jm8pvOieFnlNBz577//brp06WJCQ0NNVFSUGTZsmGtYyKxDUOY29GVO1+lJT083kyZNMo0aNTJWq9VUqlTJ9OjRI9uQ25988om58sorTUhIiAkJCTGNGjUyw4cPN9u3b893X/3888+mW7duJjQ01AQHB5vOnTu7LpDnVNjhyPOSdT8cPnzYBAQEmLvuuivX5ZOTk01wcLC58cYbzcaNG42/v7954IEHclz2xx9/NH5+fvled8eYjKGMGzVqZAIDA03lypXNfffdl+36V54MbfzVV1+5hiQPDAw0AQEBpk6dOmb06NFuw7Qak304cj8/PxMdHW369+/vNrxo1jZklZKSYqKiotyGrXXKut1zb+fatGmT6dKli+uisL179842tHBCQoKRZG677bZ894ExGdc66dq1qwkODjbly5c3d9xxhzl06JDbMs7XStYhXzdu3Gh69erluihjaGioufLKK7NdPNipX79+5sorr8w2PbfhyAvy3p8+fbq56qqrTGRkpLHZbKZevXrmkUceMXFxcXk+Z4fDYV588UVTq1YtY7PZTKtWrcyyZctyvMBhTnL7bEhOTjZDhgwxERERJiwszPTt29ccOXIk1+HIz32dOofRPffCljNmzDCtWrUyNpvNVKhQwXTs2NHtYp+HDh0yPXv2NGFhYUbK/wK4H374oWt7FStWzPMCuOfK6fWdm6J+z6anp5v//Oc/plKlSsZisbjakddn2bn73hhjdu3aZQYMGGCqVKliAgMDTfXq1c31119vPv744zwf39PH+eCDD1wXhG3ZsqVZsWJFnhfAzSq3/2vO10jWi6tnvQBu8+bNjc1mM40aNcrxf2JCQoIZM2aMqV+/vrFarSYqKsq0b9/evPzyy65r5njyf8QpLS3NPPvss6ZOnTomMDDQxMTEZLsArjGeD0ee0+UGcrsguZRxkdGsCvJ/M6d9akzO75+cHvuHH35wDXHuvNzJL7/8Ym666SbXZ1OtWrVM3759zapVq7K123ltpJwuKnvs2DEzfPhw06hRIxMSEmIiIiJM27Zts33Ovv7660aS+eKLL7JtP6fnNH/+fDNmzBgTHR1typUrZ3r27Jnrdbp+/PFHI8l07do1z22f65NPPjEXX3yxsdlspnHjxrleANeYjGvytW7d2pQrV86EhYWZZs2amUcffdT8+++/rmU8HY68IH/PnC4bsHTpUtO4cWMTEBDgdlyYU9sTEhLMQw89ZKpVq2YCAwNNgwYN8rwAbn5t93UWY0rRGVkAis2sWbO0Z88ejRs3rtgeY/z48Zo5c6Z27NhRrCfdf/bZZ7r++uu1ZcsWNWvWrNgexxOHDh1SnTp1tGDBgmwVJwAoy9LT01WtWjX16tUr23mdBdW3b1/t2bNHP/74YxG3LqOLacuWLfXf//5Xd911V5FvH6UH5zgBKDEPPfSQEhMTtWDBgmJ9nK+//lq33Xabz4QmKePch2bNmhGaAOAcS5Ys0dGjR90GrPKEMUZr1qxxdfsuau+++65CQ0N10003Fcv2UXpQcQIgKeOihadOnVKnTp283RQAQBnwww8/6Ndff9X48eMVFRVVohffLoj//e9/+v333/X000/rgQcecA32gbKL4AQAAIASN2jQIH3wwQdq2bKlZs2apaZNm3q7SW5q166tw4cPq1u3bpozZ06+l+fAhY/gBAAAAAD54BwnAAAAAMgHwQkAAAAA8lHmLoDrcDj077//KiwsTBaLxdvNAQAAAOAlxhglJCSoWrVq8vPLu6ZU5oLTv//+q5iYGG83AwAAAICP2L9/v2rUqJHnMmUuODlHRNm/f7/Cw8O93BoAAAAA3hIfH6+YmJgCjZpY5oKTs3teeHg4wQkAAABAgU7hYXAIAAAAAMgHwQkAAAAA8kFwAgAAAIB8lLlznAAAAODOGKP09HTZ7XZvNwUocoGBgfL39z/v7RCcAAAAyrDU1FQdPHhQycnJ3m4KUCwsFotq1Kih0NDQ89oOwQkAAKCMcjgc2r17t/z9/VWtWjVZrdYCjS4GlBbGGB09elQHDhxQgwYNzqvyRHACAAAoo1JTU+VwOBQTE6Pg4GBvNwcoFpUqVdKePXuUlpZ2XsGJwSEAAADKOD8/Dglx4SqqKirvEgAAAADIB8EJAAAAAPJBcAIAAAB8XKdOnTRy5Mgy99i+hOAEAACAUmXQoEGyWCzZbt27d/d209yUVOCYPHmyKlSooDNnzmSbl5ycrPDwcL322muF3v6iRYs0fvz482niBYHgBAAAgFKne/fuOnjwoNtt/vz53m6WV9x1111KSkrSokWLss37+OOPlZqaqjvvvNPj7aampkqSKlasqLCwsPNuZ2lHcAIAAICkjGveJKeme+VmjPGorTabTVWqVHG7VahQQZK0Zs0aWa1WffPNN67lX3rpJUVHR+vw4cOSMqpBDzzwgB544AFFREQoKipKTz/9tFs7UlJS9PDDD6t69eoKCQlR27ZttWbNGrd2fPfdd+rUqZOCg4NVoUIFdevWTSdPntSgQYO0du1aTZ061VUR27NnjyRp27Zt6tGjh0JDQ1W5cmXdddddOnbsmGubSUlJGjBggEJDQ1W1alVNnjw5z30RHR2tXr16acaMGdnmzZgxQ3369FHFihX12GOP6aKLLlJwcLDq1q2rp59+Wmlpaa5lx40bp5YtW+q9995TnTp1FBQU5NpXWStnc+bM0aWXXqqwsDBVqVJFt99+u44cOeKav2bNGlksFq1atUqXXnqpgoOD1b59e23fvt2tbf/73/902WWXKSgoSFFRUbrxxhsLvO/37t2rXr16qUKFCgoJCVGTJk302Wef5bmfzpfPXMdpwoQJGjNmjEaMGKFXX3011+UWLlyop59+Wnv27FGDBg00ceJEXXfddSXXUAAAgAvU6TS7Gj+zwiuP/ftz3RRsLZpDU+eB/l133aUtW7bo77//1tNPP62FCxeqcuXKruVmz56tIUOG6Mcff9TGjRt1zz33qGbNmho2bJgk6YEHHtDvv/+uBQsWqFq1alq8eLG6d++urVu3qkGDBtq8ebOuueYa3X333Zo6daoCAgL09ddfy263a+rUqfrrr7/UtGlTPffcc5Iyrid06tQpXX311Ro6dKimTJmi06dP67HHHlPfvn21evVqSdIjjzyitWvXaunSpYqOjtYTTzyhn3/+WS1btsz1OQ8ZMkTXX3+99u7dq1q1akmS/v77b61bt04rVmT8TcPCwjRr1ixVq1ZNW7du1bBhwxQWFqZHH33UtZ2dO3fqk08+0aJFi3K95lFaWprGjx+vhg0b6siRIxo1apQGDRqULbg8+eSTmjx5sipVqqR7771Xd999t7777jtJ0vLly3XjjTfqySef1H//+1+lpqa6rZ/fvh8+fLhSU1O1bt06hYSE6Pfff1doaGiBXh+FZTGexvti8NNPP6lv374KDw9X586dcw1O69ev11VXXaXY2Fhdf/31mjdvniZOnKiff/5ZTZs2LdBjxcfHKyIiQnFxcQoPDy/CZwEAAFC6nDlzRrt373ZVF5JT00tFcBo0aJA++OADV0XE6YknntATTzwhKaObWdu2bXXRRRdp27ZtuuKKK/TOO++4lu3UqZOOHDmi3377zXWdn8cff1yffvqpfv/9d+3bt09169bVvn37VK1aNdd6Xbp0UZs2bfTiiy/q9ttv1759+/Ttt9/m2M5OnTqpZcuWbse2zz//vL755htXmJGkAwcOKCYmRtu3b1e1atUUGRmpDz74QLfeeqsk6cSJE6pRo4buueeeXI+T7Xa7atWqpaFDh2rcuHGSpGeeeUazZ8/W7t27c7xW18svv6wFCxZo48aNkjIqTi+++KL++ecfVapUKc/nkdXGjRt12WWXKSEhQaGhoVqzZo06d+6sr776Stdcc40k6bPPPlPPnj11+vRpBQUFqX379qpbt64++OCDbNsryL5v3ry5br75Zo0dOzbHNmV17us8K0+ygdcrTomJibrjjjv07rvv6vnnn89z2alTp6p79+565JFHJEnjx4/XypUr9cYbb+jtt98uieYWqZ1HErXjcIJqRYaocTVCHAAA8K5ygf76/bluXntsT3Tu3FnTpk1zm1axYkXX71arVXPnzlXz5s1Vq1YtTZkyJds2Lr/8creLo7Zr106TJ0+W3W7X1q1bZbfbddFFF7mtk5KSosjISEnS5s2bXeGmoLZs2aKvv/46x+rIrl27dPr0aVfoy/q8GjZsmOd2/f39NXDgQM2aNUtjx46VMUazZ8/W4MGDXaHpww8/1GuvvaZdu3YpMTFR6enp2cJCrVq13EJTTjZt2qRx48Zpy5YtOnnypBwOh6SMwNO4cWPXcs2bN3f9XrVqVUnSkSNHVLNmTW3evNlV2TtXQfb9gw8+qPvuu09ffvmlunTpoptvvtnt8YqD14PT8OHD1bNnT3Xp0iXf4LRhwwaNGjXKbVq3bt20ZMmSXNdJSUlRSkqK6358fPx5tbcoffD9Xs1av0f3dqxHcAIAAF5nsViKrLtccQsJCVH9+vXzXGb9+vWSMio2J06cUEhISIG3n5iYKH9/f23atClblzVn6ClXrpyHrc7Ybq9evTRx4sRs86pWraqdO3d6vE2nu+++W7GxsVq9erUcDof279+vwYMHS8o4jr7jjjv07LPPqlu3boqIiNCCBQuynT+V3z5KSkpSt27d1K1bN82dO1eVKlXSvn371K1bN9dgEk6BgYGu350B1Rmy8tp3Bdn3Q4cOVbdu3bR8+XJ9+eWXio2N1eTJk/Wf//wnz/afD6++MxYsWKCff/5ZP/30U4GWP3TokFu/VEmqXLmyDh06lOs6sbGxevbZZ8+rncWlUphNknQ8MSWfJQEAAOCJXbt26aGHHtK7776rDz/8UAMHDtRXX33l1mXthx9+cFvn+++/V4MGDeTv769WrVrJbrfryJEj6tChQ46P0bx5c61atSrXY02r1Sq73e427ZJLLtEnn3yi2rVrKyAg+6F4vXr1FBgYqB9++EE1a9aUJJ08eVJ//fWXOnbsmOdzrlevnjp27KgZM2bIGKMuXbq4zndav369atWqpSeffNK1/N69e/PcXk7+/PNPHT9+XBMmTFBMTIwkubr6ecK575zBLquC7HtJiomJ0b333qt7771XY8aM0bvvvluswclro+rt379fI0aM0Ny5c7P1NSxKY8aMUVxcnOu2f//+YnssT0WGWCVJxwhOAAAAHklJSdGhQ4fcbs6R6ex2u+68805169ZNgwcP1syZM/Xrr79mq67s27dPo0aN0vbt2zV//ny9/vrrGjFihCTpoosu0h133KEBAwZo0aJF2r17t3788UfFxsZq+fLlkjKOM3/66Sfdf//9+vXXX/Xnn39q2rRprnbUrl1bP/zwg/bs2aNjx47J4XBo+PDhOnHihPr376+ffvpJu3bt0ooVKzR48GDZ7XaFhoZqyJAheuSRR7R69Wpt27ZNgwYNyvEcpZwMGTJEixYt0uLFizVkyBDX9AYNGmjfvn1asGCBdu3apddee02LFy/2eL/XrFlTVqtVr7/+uv7++299+umnhbrG09ixYzV//nyNHTtWf/zxh7Zu3eqqwhVk348cOVIrVqzQ7t279fPPP+vrr7/WxRdf7HE7POG14LRp0yYdOXJEl1xyiQICAhQQEKC1a9fqtddeU0BAQLZ0LklVqlRxDSHpdPjwYVWpUiXXx7HZbAoPD3e7+Yqo0MyKU1JqPksCAAAgqy+++EJVq1Z1u1155ZWSpBdeeEF79+7V9OnTJWV0gXvnnXf01FNPacuWLa5tDBgwQKdPn1abNm00fPhwjRgxQvfcc49r/syZMzVgwACNHj1aDRs2VJ8+ffTTTz+5KkEXXXSRvvzyS23ZskVt2rRRu3bttHTpUlcl6eGHH5a/v78aN27s6tJWrVo1fffdd7Lb7eratauaNWumkSNHqnz58q5wNGnSJHXo0EG9evVSly5ddOWVV6p169YF2i8333yzbDabgoOD1adPH9f0G264QQ899JAeeOABtWzZUuvXr9fTTz/t8X6vVKmSZs2apYULF6px48aaMGGCXn75ZY+306lTJy1cuFCffvqpWrZsqauvvlo//vija35++95ut2v48OG6+OKL1b17d1100UV66623PG6HJ7w2ql5CQkK28uDgwYPVqFEjPfbYYzmOktevXz8lJyfrf//7n2ta+/bt1bx58wIPDuFLo+r9su+kbnxrvapFBGn9mGu82hYAAFD25DXa2IUuv5HicOEo9aPqhYWFZQtHISEhioyMdE0fMGCAqlevrtjYWEnSiBEj1LFjR02ePFk9e/Z0DZ+YdWjJ0sRZcTqWlCpjjNuoLgAAAAB8h9e66hXEvn37dPDgQdf99u3ba968eXrnnXfUokULffzxx1qyZEmBr+HkayJDM85xSk13KCEl3cutAQAAAJAbnxpvcs2aNXnel6Rbb73V4/HyfVWwNUDBVn8lp9p1PDFV4UGB+a8EAACA85bTcSaQF5+uOJUFrgEiGFkPAAAA8FkEJy9zdtdjSHIAAOAtXhorDCgRRfX6Jjh5mWuAiESGJAcAACUrMDDjNIHk5GQvtwQoPqmpGcfZ/v7+57UdnzrHqSyKouIEAAC8xN/fX+XLl9eRI0ckScHBwYzyiwuKw+HQ0aNHFRwc7Lq+VmERnLzs7DlOVJwAAEDJq1KliiS5whNwofHz81PNmjXP+0sBgpOXRYZkVJyOJ1FxAgAAJc9isahq1aqKjo5WWlqat5sDFDmr1So/v/M/Q4ng5GWRznOcEqg4AQAA7/H39z/vc0CACxmDQ3iZa3AIKk4AAACAzyI4eZlrcIgEghMAAADgqwhOXuasOMWfSVdqusPLrQEAAACQE4KTl0WUC5S/X8YIHyeSOM8JAAAA8EUEJy/z87OoYgjXcgIAAAB8GcHJB7gGiCA4AQAAAD6J4OQDXANEcBFcAAAAwCcRnHyAs+J0nIoTAAAA4JMITj4gknOcAAAAAJ9GcPIBUWHOihNd9QAAAABfRHDyAa6KE8ORAwAAAD6J4OQDXKPqJdBVDwAAAPBFBCcf4BocIongBAAAAPgigpMPiMwcjvx4YqocDuPl1gAAAAA4F8HJBziDU7rDKP5MmpdbAwAAAOBcBCcfYAvwV1hQgCQuggsAAAD4IoKTj3ANEMG1nAAAAACfQ3DyEVFZznMCAAAA4FsITj4iMoSKEwAAAOCrCE4+IirMWXEiOAEAAAC+huDkI5wVp6N01QMAAAB8DsHJR0SFZV4El4oTAAAA4HMITj4iKiSzq14SFScAAADA1xCcfEQkw5EDAAAAPovg5CMYjhwAAADwXQQnH+GsOCWmpOtMmt3LrQEAAACQFcHJR4QHBcjqn/HnoLseAAAA4FsITj7CYrEoku56AAAAgE8iOPkQZ3Ci4gQAAAD4FoKTD4kKdV7LiYoTAAAA4EsITj4kMiQjOB2l4gQAAAD4FIKTD4kK4xwnAAAAwBcRnHxIVAgXwQUAAAB8EcHJh7gqTkkEJwAAAMCXEJx8iPMcJ7rqAQAAAL7Fq8Fp2rRpat68ucLDwxUeHq527drp888/z3X5WbNmyWKxuN2CgoJKsMXFi+HIAQAAAN8U4M0Hr1GjhiZMmKAGDRrIGKPZs2erd+/e+uWXX9SkSZMc1wkPD9f27dtd9y0WS0k1t9hVyhyO/ERSquwOI3+/C+e5AQAAAKWZV4NTr1693O6/8MILmjZtmr7//vtcg5PFYlGVKlVKonklrkJIRsXJYaSTyamu6zoBAAAA8C6fOcfJbrdrwYIFSkpKUrt27XJdLjExUbVq1VJMTIx69+6t3377Lc/tpqSkKD4+3u3mqwL9/VQhOFAS5zkBAAAAvsTrwWnr1q0KDQ2VzWbTvffeq8WLF6tx48Y5LtuwYUPNmDFDS5cu1QcffCCHw6H27dvrwIEDuW4/NjZWERERrltMTExxPZUiERnqHCCC85wAAAAAX2ExxhhvNiA1NVX79u1TXFycPv74Y7333ntau3ZtruEpq7S0NF188cXq37+/xo8fn+MyKSkpSkk5G0Li4+MVExOjuLg4hYeHF9nzKCr9pm/QD7tPaOptLdW7ZXVvNwcAAAC4YMXHxysiIqJA2cCr5zhJktVqVf369SVJrVu31k8//aSpU6dq+vTp+a4bGBioVq1aaefOnbkuY7PZZLOVnnOFosIYkhwAAADwNV7vqncuh8PhViHKi91u19atW1W1atViblXJiQphSHIAAADA13i14jRmzBj16NFDNWvWVEJCgubNm6c1a9ZoxYoVkqQBAwaoevXqio2NlSQ999xzuvzyy1W/fn2dOnVKkyZN0t69ezV06FBvPo0iFRVKxQkAAADwNV4NTkeOHNGAAQN08OBBRUREqHnz5lqxYoWuvfZaSdK+ffvk53e2KHby5EkNGzZMhw4dUoUKFdS6dWutX7++QOdDlRbOwSGoOAEAAAC+w+uDQ5Q0T04A84Yvfzuke+ZsUouY8lo6/ApvNwcAAAC4YHmSDXzuHKeyjuHIAQAAAN9DcPIxUaFnB4coY8VAAAAAwGcRnHyMc3CIM2kOJafavdwaAAAAABLByecEW/0VFJjxZ2GACAAAAMA3EJx8jMVicVWdjjEkOQAAAOATCE4+iAEiAAAAAN9CcPJBlVwDRFBxAgAAAHwBwckHRYZQcQIAAAB8CcHJB0VmGZIcAAAAgPcRnHyQa3CIJLrqAQAAAL6A4OSDnBUnuuoBAAAAvoHg5IMqMRw5AAAA4FMITj6I4cgBAAAA30Jw8kHOrnonk9OUZnd4uTUAAAAACE4+qEKwVX6WjN9PMkAEAAAA4HUEJx/k72dRxZCMqtNRuusBAAAAXkdw8lFRrvOcqDgBAAAA3kZw8lGuIcmTqDgBAAAA3kZw8lGui+AmUHECAAAAvI3g5KMiQzKDExUnAAAAwOsITj7K2VWPihMAAADgfQQnH1XJOTgEFScAAADA6whOPso1OASj6gEAAABeR3DyUa7BIbiOEwAAAOB1BCcflbXiZIzxcmsAAACAso3g5KOcFadUu0PxZ9K93BoAAACgbCM4+aigQH+F2gIkScfprgcAAAB4FcHJh7mGJGeACAAAAMCrCE4+zNldj4oTAAAA4F0EJx8WGZJZcUqi4gQAAAB4E8HJh0WFZQ5JnkDFCQAAAPAmgpMPi8qsOB1PIjgBAAAA3kRw8mGRzovgJtBVDwAAAPAmgpMPcw0OQcUJAAAA8CqCkw9zDkd+nOHIAQAAAK8iOPkwZ8XpKMORAwAAAF5FcPJhUZkVp4Qz6UpJt3u5NQAAAEDZRXDyYeFBgQrws0iiux4AAADgTQQnH+bnZ+E8JwAAAMAHEJx8XGRI5pDknOcEAAAAeA3BycdFhRGcAAAAAG8jOPm4qJDMrnpJdNUDAAAAvMWrwWnatGlq3ry5wsPDFR4ernbt2unzzz/Pc52FCxeqUaNGCgoKUrNmzfTZZ5+VUGu9w1VxSqDiBAAAAHiLV4NTjRo1NGHCBG3atEkbN27U1Vdfrd69e+u3337Lcfn169erf//+GjJkiH755Rf16dNHffr00bZt20q45SUnkooTAAAA4HUWY4zxdiOyqlixoiZNmqQhQ4Zkm9evXz8lJSVp2bJlrmmXX365WrZsqbfffrtA24+Pj1dERITi4uIUHh5eZO0uLh9vOqCHF25RhwZRmjOkrbebAwAAAFwwPMkGPnOOk91u14IFC5SUlKR27drluMyGDRvUpUsXt2ndunXThg0bct1uSkqK4uPj3W6lifMiuMcYjhwAAADwGq8Hp61btyo0NFQ2m0333nuvFi9erMaNG+e47KFDh1S5cmW3aZUrV9ahQ4dy3X5sbKwiIiJct5iYmCJtf3GLCs04x+k4o+oBAAAAXuP14NSwYUNt3rxZP/zwg+677z4NHDhQv//+e5Ftf8yYMYqLi3Pd9u/fX2TbLgmu4JSUKofDp3pVAgAAAGVGgLcbYLVaVb9+fUlS69at9dNPP2nq1KmaPn16tmWrVKmiw4cPu007fPiwqlSpkuv2bTabbDZb0Ta6BFXMHBzC7jCKO52mCpn3AQAAAJQcr1eczuVwOJSSknO3tHbt2mnVqlVu01auXJnrOVEXAmuAn8KDMvItF8EFAAAAvMOrFacxY8aoR48eqlmzphISEjRv3jytWbNGK1askCQNGDBA1atXV2xsrCRpxIgR6tixoyZPnqyePXtqwYIF2rhxo9555x1vPo1iFxVmU/yZdB1LTFWDyvkvDwAAAKBoeTU4HTlyRAMGDNDBgwcVERGh5s2ba8WKFbr22mslSfv27ZOf39miWPv27TVv3jw99dRTeuKJJ9SgQQMtWbJETZs29dZTKBFRITb9fTRJx5OoOAEAAADe4NXg9P777+c5f82aNdmm3Xrrrbr11luLqUW+KSosc0jyBIITAAAA4A0+d44TsosMOTuyHgAAAICSR3AqBZxDkjM4BAAAAOAdBKdSIDI0s6teIhUnAAAAwBsITqVAlCs4UXECAAAAvIHgVAo4u+odp+IEAAAAeAXBqRSIdAUnKk4AAACANxCcSgFnV72kVLtOp9q93BoAAACg7CE4lQKhtgBZAzL+VJznBAAAAJQ8glMpYLFYVIkhyQEAAACvITiVEs4hyRkgAgAAACh5BKdSIjIkMzglUXECAAAAShrBqZSIcnXVo+IEAAAAlDSCUykRyTlOAAAAgNcQnEoJ55DkVJwAAACAkkdwKiWiuAguAAAA4DUEp1Ii0lVxIjgBAAAAJY3gVEqcrTjRVQ8AAAAoaQSnUsJZcTqRnCq7w3i5NQAAAEDZQnAqJSoGW2WxSMZIJ5KoOgEAAAAlieBUSgT4+6lCMBfBBQAAALyB4FSKuIYkT6DiBAAAAJQkglMpEhmSOUAEFScAAACgRBGcSpFILoILAAAAeAXBqRRxDknOtZwAAACAkkVwKkWc5zgdJzgBAAAAJYrgVIqcrTjRVQ8AAAAoSQSnUiQyMzhRcQIAAABKFsGpFGFwCAAAAMA7CE6lSKUsg0MYY7zcGgAAAKDsIDiVIs6KU0q6Q0mpdi+3BgAAACg7CE6lSLA1QMFWf0nSsQTOcwIAAABKCsGplHFWnY4nEZwAAACAkkJwKmWcQ5IfTWCACAAAAKCkEJxKmciQzCHJqTgBAAAAJYbgVMpEObvqMSQ5AAAAUGIITqVMVJYhyQEAAACUDIJTKRNJxQkAAAAocQSnUsY1OAQVJwAAAKDEEJxKmbMVJ4ITAAAAUFIITqXM2XOc6KoHAAAAlBSCUynjDE5xp9OUmu7wcmsAAACAsoHgVMqULxcofz+LJOlkMlUnAAAAoCR4NTjFxsbqsssuU1hYmKKjo9WnTx9t3749z3VmzZoli8XidgsKCiqhFnufn59FFUMyznM6msB5TgAAAEBJ8GpwWrt2rYYPH67vv/9eK1euVFpamrp27aqkpKQ81wsPD9fBgwddt71795ZQi31DZGZwOp5ExQkAAAAoCQFFubHk5GQFBwcXePkvvvjC7f6sWbMUHR2tTZs26aqrrsp1PYvFoipVqhS6naVdpTCb/jyUoGNUnAAAAIAS4XHF6ZprrtE///yTbfqPP/6oli1bnldj4uLiJEkVK1bMc7nExETVqlVLMTEx6t27t3777bdcl01JSVF8fLzbrbQ7W3EiOAEAAAAlwePgFBQUpObNm+vDDz+UJDkcDo0bN05XXnmlrrvuukI3xOFwaOTIkbriiivUtGnTXJdr2LChZsyYoaVLl+qDDz6Qw+FQ+/btdeDAgRyXj42NVUREhOsWExNT6Db6isjMkfWOMyQ5AAAAUCIsxhjj6UpvvvmmHn30UfXu3Vt79uzR3r17NXPmTHXt2rXQDbnvvvv0+eef69tvv1WNGjUKvF5aWpouvvhi9e/fX+PHj882PyUlRSkpZysz8fHxiomJUVxcnMLDwwvdXm+atmaXJn7xp266pLpe6dvS280BAAAASqX4+HhFREQUKBsU6hyn4cOH68CBA5o4caICAgK0Zs0atW/fvlCNlaQHHnhAy5Yt07p16zwKTZIUGBioVq1aaefOnTnOt9lsstlshW6bL4oMzeyqR8UJAAAAKBEed9U7efKkbr75Zk2bNk3Tp09X37591bVrV7311lseP7gxRg888IAWL16s1atXq06dOh5vw263a+vWrapatarH65ZWlTK76h1L5BwnAAAAoCR4XHFq2rSp6tSpo19++UV16tTRsGHD9OGHH+r+++/X8uXLtXz58gJva/jw4Zo3b56WLl2qsLAwHTp0SJIUERGhcuXKSZIGDBig6tWrKzY2VpL03HPP6fLLL1f9+vV16tQpTZo0SXv37tXQoUM9fSqlFhUnAAAAoGR5XHG69957tW7dOrfqUL9+/bRlyxalpnp2ID9t2jTFxcWpU6dOqlq1quvmHHhCkvbt26eDBw+67p88eVLDhg3TxRdfrOuuu07x8fFav369Gjdu7OlTKbWinINDJKWoEKeoAQAAAPBQoQaHKM08OQHMV51Js6vR0xnXwNryTFdFBAd6uUUAAABA6VPsg0NIGRe73bdvX7YqU/PmzQu7SRRQUKC/wmwBSkhJ17GkFIITAAAAUMw8Dk5Hjx7V4MGD9fnnn+c43263n3ejkL+oMFtGcEpIUb1Kod5uDgAAAHBB8/gcp5EjR+rUqVP64YcfVK5cOX3xxReaPXu2GjRooE8//bQ42ogcRIZkDhCRxAARAAAAQHHzuOK0evVqLV26VJdeeqn8/PxUq1YtXXvttQoPD1dsbKx69uxZHO3EOaIYkhwAAAAoMR5XnJKSkhQdHS1JqlChgo4ePSpJatasmX7++eeibR1y5RyS/BhDkgMAAADFzuPg1LBhQ23fvl2S1KJFC02fPl3//POP3n777TJ1EVpvi3QOSU7FCQAAACh2HnfVGzFihOu6SmPHjlX37t01d+5cWa1WzZo1q6jbh1xUclWcCE4AAABAcfM4ON15552u31u3bq29e/fqzz//VM2aNRUVFVWkjUPuzlac6KoHAAAAFLdCX8fJKTg4WJdccklRtAUeYHAIAAAAoOR4HJyMMfr444/19ddf68iRI3I4HG7zFy1aVGSNQ+6cg0NQcQIAAACKn8fBaeTIkZo+fbo6d+6sypUry2KxFEe7kA9nxSkhJV1n0uwKCvT3cosAAACAC5fHwWnOnDlatGiRrrvuuuJoDwooPChAgf4WpdmNjielqnr5ct5uEgAAAHDB8ng48oiICNWtW7c42gIPWCwWRYYwJDkAAABQEjwOTuPGjdOzzz6r06dPF0d74IGoMIYkBwAAAEqCx131+vbtq/nz5ys6Olq1a9dWYGCg2/yff/65yBqHvDkrTscYIAIAAAAoVh4Hp4EDB2rTpk268847GRzCyxiSHAAAACgZHgen5cuXa8WKFbryyiuLoz3wQBRDkgMAAAAlwuNznGJiYhQeHl4cbYGHzl7LiYoTAAAAUJw8Dk6TJ0/Wo48+qj179hRDc+CJs131qDgBAAAAxcnjrnp33nmnkpOTVa9ePQUHB2cbHOLEiRNF1jjkLZJznAAAAIAS4XFwevXVV4uhGSgM5zlOVJwAAACA4lWoUfXgG5xd9U4kpcjhMPLzY4RDAAAAoDh4fI4TfEfFkIyKk8NIp06nebk1AAAAwIWL4FSKBfr7qXxwxjlmnOcEAAAAFB+CUykXGeI8z4ngBAAAABSXAgWnX3/9VQ6Ho7jbgkJgSHIAAACg+BUoOLVq1UrHjh2TJNWtW1fHjx8v1kah4JzBiYvgAgAAAMWnQMGpfPny2r17tyRpz549VJ98yNkhyQlOAAAAQHEp0HDkN998szp27KiqVavKYrHo0ksvlb+/f47L/v3330XaQOQt0lVxoqseAAAAUFwKFJzeeecd3XTTTdq5c6cefPBBDRs2TGFhYcXdNhRAJBfBBQAAAIpdgS+A2717d0nSpk2bNGLECIKTjzg7OARd9QAAAIDiUuDg5DRz5kzX7wcOHJAk1ahRo+haBI84z3E6nkRwAgAAAIqLx9dxcjgceu655xQREaFatWqpVq1aKl++vMaPH8+gEV7gqjgl0FUPAAAAKC4eV5yefPJJvf/++5owYYKuuOIKSdK3336rcePG6cyZM3rhhReKvJHInXNwiNNpdiWnpivY6vGfFAAAAEA+PD7Knj17tt577z3dcMMNrmnNmzdX9erVdf/99xOcSliI1V9BgX46k+bQ8cRUBVckOAEAAABFzeOueidOnFCjRo2yTW/UqJFOnDhRJI1CwVksFkWGZFSdjjJABAAAAFAsPA5OLVq00BtvvJFt+htvvKEWLVoUSaPgGdcAEQxJDgAAABQLj/t1vfTSS+rZs6e++uortWvXTpK0YcMG7d+/X5999lmRNxD5Y0hyAAAAoHh5XHHq2LGj/vrrL9144406deqUTp06pZtuuknbt29Xhw4diqONyEekq+JEcAIAAACKQ6FGEqhWrRqDQPiQsxUnuuoBAAAAxcHjihN8TyRd9QAAAIBiRXC6ADA4BAAAAFC8vBqcYmNjddlllyksLEzR0dHq06ePtm/fnu96CxcuVKNGjRQUFKRmzZqV+UEpGBwCAAAAKF5eDU5r167V8OHD9f3332vlypVKS0tT165dlZSUlOs669evV//+/TVkyBD98ssv6tOnj/r06aNt27aVYMt9i2twiCQqTgAAAEBxsBhjjKcrpaena82aNdq1a5duv/12hYWF6d9//1V4eLhCQ0ML3ZijR48qOjpaa9eu1VVXXZXjMv369VNSUpKWLVvmmnb55ZerZcuWevvtt/N9jPj4eEVERCguLk7h4eGFbqsvOZaYokuf/0oWi7Tj+R4K8KcHJgAAAJAfT7KBx6Pq7d27V927d9e+ffuUkpKia6+9VmFhYZo4caJSUlIKFF5yExcXJ0mqWLFirsts2LBBo0aNcpvWrVs3LVmyJMflU1JSlJJytgtbfHx8odvnqyoEW+VnkRxGOpGcquiwIG83CQAAALigeFyaGDFihC699FKdPHlS5cqVc02/8cYbtWrVqkI3xOFwaOTIkbriiivUtGnTXJc7dOiQKleu7DatcuXKOnToUI7Lx8bGKiIiwnWLiYkpdBt9lb+fRRVDGCACAAAAKC4eB6dvvvlGTz31lKxWq9v02rVr659//il0Q4YPH65t27ZpwYIFhd5GTsaMGaO4uDjXbf/+/UW6fV8RGcIAEQAAAEBx8birnsPhkN1uzzb9wIEDCgsLK1QjHnjgAS1btkzr1q1TjRo18ly2SpUqOnz4sNu0w4cPq0qVKjkub7PZZLPZCtWu0iQy1CodpuIEAAAAFAePK05du3bVq6++6rpvsViUmJiosWPH6rrrrvNoW8YYPfDAA1q8eLFWr16tOnXq5LtOu3btsnUJXLlypdq1a+fRY19oGJIcAAAAKD4eV5wmT56sbt26qXHjxjpz5oxuv/127dixQ1FRUZo/f75H2xo+fLjmzZunpUuXKiwszHWeUkREhOv8qQEDBqh69eqKjY2VlHGOVceOHTV58mT17NlTCxYs0MaNG/XOO+94+lQuKM4hyY9RcQIAAACKnMfBqUaNGtqyZYs+/PBDbdmyRYmJiRoyZIjuuOMOt8EiCmLatGmSpE6dOrlNnzlzpgYNGiRJ2rdvn/z8zhbG2rdvr3nz5umpp57SE088oQYNGmjJkiV5DihRFjgrTsepOAEAAABFrlDXcSrNLsTrOEnShz/t02OfbFXnhpU0c3AbbzcHAAAA8HmeZAOPz3GKjY3VjBkzsk2fMWOGJk6c6OnmUERcFackuuoBAAAARc3j4DR9+nQ1atQo2/QmTZqc18VvcX4inYNDJNBVDwAAAChqHgenQ4cOqWrVqtmmV6pUSQcPHiySRsFzkZkXwD2WlKoy1vsSAAAAKHYeB6eYmBh999132aZ/9913qlatWpE0Cp5zdtVLTXcoISXdy60BAAAALiwej6o3bNgwjRw5Umlpabr66qslSatWrdKjjz6q0aNHF3kDUTDlrP4KsforKdWu44mpCg8K9HaTAAAAgAuGx8HpkUce0fHjx3X//fcrNTVjIIKgoCA99thjGjNmTJE3EAUXFWZT0vFkHU9MUZ2oEG83BwAAALhgeBycLBaLJk6cqKefflp//PGHypUrpwYNGshmsxVH++CByBCr9h5P1jGu5QQAAAAUKY+Dk1NoaKguu+yyomwLzpNrZL1EhiQHAAAAipLHwSkpKUkTJkzQqlWrdOTIETkcDrf5f//9d5E1Dp6JcgUnKk4AAABAUfI4OA0dOlRr167VXXfdpapVq8pisRRHu1AIUaEZQ5Ifp+IEAAAAFCmPg9Pnn3+u5cuX64orriiO9uA8OCtOx5OoOAEAAABFyePrOFWoUEEVK1YsjrbgPEVmVpyOJVBxAgAAAIqSx8Fp/PjxeuaZZ5ScnFwc7cF5cJ3jRMUJAAAAKFIed9WbPHmydu3apcqVK6t27doKDHS/0OrPP/9cZI2DZ6JcFSeCEwAAAFCUPA5Offr0KYZmoChEhmRUnOLPpCs13SFrgMcFRQAAAAA58Dg4jR07tjjagSIQUS5QAX4WpTuMjielqGpEOW83CQAAALggUJK4gPj5WVQxhCHJAQAAgKLmcXCy2+16+eWX1aZNG1WpUkUVK1Z0u8G7uAguAAAAUPQ8Dk7PPvusXnnlFfXr109xcXEaNWqUbrrpJvn5+WncuHHF0ER4wjUkORUnAAAAoMh4HJzmzp2rd999V6NHj1ZAQID69++v9957T88884y+//774mgjPOC6CC4VJwAAAKDIeBycDh06pGbNmkmSQkNDFRcXJ0m6/vrrtXz58qJtHTzmGpKc4AQAAAAUGY+DU40aNXTw4EFJUr169fTll19Kkn766SfZbLaibR08FumqONFVDwAAACgqHgenG2+8UatWrZIk/ec//9HTTz+tBg0aaMCAAbr77ruLvIHwjGtwiCSCEwAAAFBUPL6O04QJE1y/9+vXTzVr1tSGDRvUoEED9erVq0gbB8+5BodIoKseAAAAUFQ8Dk7nateundq1a1cUbUERqOTsqpdEcAIAAACKSoGC06effqoePXooMDBQn376aZ7L3nDDDUXSMBSOs+J0PDFVDoeRn5/Fyy0CAAAASr8CBac+ffro0KFDio6OVp8+fXJdzmKxyG63F1XbUAgVQzKCU7rDKP5MmsoHW73cIgAAAKD0K1BwcjgcOf4O32ML8Fd4UIDiz6TrWGIKwQkAAAAoAh6NqpeWlqZrrrlGO3bsKK72oAi4RtZjSHIAAACgSHgUnAIDA/Xrr78WV1tQRKK4lhMAAABQpDy+jtOdd96p999/vzjagiLiGpI8kZH1AAAAgKLg8XDk6enpmjFjhr766iu1bt1aISEhbvNfeeWVImscCufsyHoEJwAAAKAoeByctm3bpksuuUSS9Ndff7nNs1gY+toXOLvqHaWrHgAAAFAkPA5OX3/9dXG0A0Uo0nWOExUnAAAAoCh4fI4TfF8lZ1e9JCpOAAAAQFHwuOIkSRs3btRHH32kffv2KTXV/eB80aJFRdIwFF6kazhyKk4AAABAUfC44rRgwQK1b99ef/zxhxYvXqy0tDT99ttvWr16tSIiIoqjjfAQw5EDAAAARcvj4PTiiy9qypQp+t///ier1aqpU6fqzz//VN++fVWzZs3iaCM85BxVLzElXWfS7F5uDQAAAFD6eRycdu3apZ49e0qSrFarkpKSZLFY9NBDD+mdd94p8gbCc2G2AFn9M/60dNcDAAAAzp/HwalChQpKSEiQJFWvXl3btm2TJJ06dUrJyclF2zoUisViUZTrWk501wMAAADOl8fB6aqrrtLKlSslSbfeeqtGjBihYcOGqX///rrmmmuKvIEoHAaIAAAAAIpOgUfV27Ztm5o2bao33nhDZ86ckSQ9+eSTCgwM1Pr163XzzTfrqaeeKraGwjNUnAAAAICiU+CKU/PmzdW2bVt98sknCgsLy1jZz0+PP/64Pv30U02ePFkVKlTw6MHXrVunXr16qVq1arJYLFqyZEmey69Zs0YWiyXb7dChQx49blngrDgdpeIEAAAAnLcCB6e1a9eqSZMmGj16tKpWraqBAwfqm2++Oa8HT0pKUosWLfTmm296tN727dt18OBB1y06Ovq82nEhiqTiBAAAABSZAnfV69Chgzp06KDXX39dH330kWbNmqWOHTuqfv36GjJkiAYOHKgqVap49OA9evRQjx49PG50dHS0ypcv7/F6ZUklznECAAAAiozHg0OEhIRo8ODBWrt2rf766y/deuutevPNN1WzZk3dcMMNxdHGbFq2bKmqVavq2muv1XfffZfnsikpKYqPj3e7lQWuilMSwQkAAAA4Xx4Hp6zq16+vJ554Qk899ZTCwsK0fPnyompXjqpWraq3335bn3zyiT755BPFxMSoU6dO+vnnn3NdJzY2VhEREa5bTExMsbbRV0RlVpzoqgcAAACcvwJ31TvXunXrNGPGDH3yySfy8/NT3759NWTIkKJsWzYNGzZUw4YNXffbt2+vXbt2acqUKZozZ06O64wZM0ajRo1y3Y+Pjy8T4SkyhK56AAAAQFHxKDj9+++/mjVrlmbNmqWdO3eqffv2eu2119S3b1+FhIQUVxvz1KZNG3377be5zrfZbLLZbCXYIt8QFZbRVe9EUqrsDiN/P4uXWwQAAACUXgUOTj169NBXX32lqKgoDRgwQHfffbdb9cdbNm/erKpVq3q7GT6nYnBGcHIY6WRyqqvrHgAAAADPFTg4BQYG6uOPP9b1118vf3//InnwxMRE7dy503V/9+7d2rx5sypWrKiaNWtqzJgx+ueff/Tf//5XkvTqq6+qTp06atKkic6cOaP33ntPq1ev1pdfflkk7bmQBPj7qUJwoE4mp+l4IsEJAAAAOB8FDk6ffvppkT/4xo0b1blzZ9d957lIAwcO1KxZs3Tw4EHt27fPNT81NVWjR4/WP//8o+DgYDVv3lxfffWV2zZwVlSoLTM4pUgK83ZzAAAAgFLLYowx3m5ESYqPj1dERITi4uIUHh7u7eYUq9ve2aDv/z6hqbe1VO+W1b3dHAAAAMCneJINzms4cvg2hiQHAAAAigbB6QLmDE4MSQ4AAACcH4LTBSwqNGNkPSpOAAAAwPkhOF3AIqk4AQAAAEWC4HQBiwzJqDgdS6LiBAAAAJwPgtMFLCrMOTgEFScAAADgfBCcLmBRIWe76pWxUecBAACAIkVwuoBFhWV01TuT5lByqt3LrQEAAABKL4LTBSzYGqBygf6SGCACAAAAOB8EpwtcZOaQ5McYkhwAAAAoNILTBc55EVwGiAAAAAAKj+B0gYui4gQAAACcN4LTBY6KEwAAAHD+CE4XuLPnOBGcAAAAgMIiOF3gnBWnY0l01QMAAAAKi+B0gYt0BqcEKk4AAABAYRGcLnBRIRld9Y5TcQIAAAAKjeB0gYsKY3AIAAAA4HwRnC5wkZkVp5PJaUqzO7zcGgAAAKB0Ijhd4CoEW+Vnyfj9JN31AAAAgEIhOF3g/PwsqhiS0V3vKN31AAAAgEIhOJUBUZnXcjqeSMUJAAAAKAyCUxngvJbT8SQqTgAAAEBhEJzKgMjMitOxBCpOAAAAQGEQnMoAZ8XpGBUnAAAAoFAITmUAFScAAADg/BCcygDOcQIAAADOD8GpDHCOqneM4cgBAACAQiE4lQGRmddxYjhyAAAAoHAITmVAVNjZ4GSM8XJrAAAAgNKH4FQGRIZkdNVLtTsUfybdy60BAAAASh+CUxkQFOivMFuAJOk45zkBAAAAHiM4lRGuIck5zwkAAADwGMGpjIh0DklOxQkAAADwGMGpjHANSZ5ExQkAAADwFMGpjHBWnI4lUHECAAAAPEVwKiOinF31kghOAAAAgKcITmWEq6teAl31AAAAAE8RnMoIKk4AAABA4RGcygjnRXCPMxw5AAAA4DGCUxnhHBziKMORAwAAAB4jOJURlTKDU8KZdKWk273cGgAAAKB08WpwWrdunXr16qVq1arJYrFoyZIl+a6zZs0aXXLJJbLZbKpfv75mzZpV7O28EISXC1Cgv0US3fUAAAAAT3k1OCUlJalFixZ68803C7T87t271bNnT3Xu3FmbN2/WyJEjNXToUK1YsaKYW1r6WSwWRYZkDhBBcAIAAAA8EuDNB+/Ro4d69OhR4OXffvtt1alTR5MnT5YkXXzxxfr22281ZcoUdevWrbiaecGIDLXqUPwZHeM8JwAAAMAjpeocpw0bNqhLly5u07p166YNGzbkuk5KSori4+PdbmWVc4AIghMAAADgmVIVnA4dOqTKlSu7TatcubLi4+N1+vTpHNeJjY1VRESE6xYTE1MSTfVJzovgHk+iqx4AAADgiVIVnApjzJgxiouLc93279/v7SZ5jfMiuMcSqDgBAAAAnvDqOU6eqlKlig4fPuw27fDhwwoPD1e5cuVyXMdms8lms5VE83weFScAAACgcEpVxaldu3ZatWqV27SVK1eqXbt2XmpR6eIcVY9znAAAAADPeDU4JSYmavPmzdq8ebOkjOHGN2/erH379knK6GY3YMAA1/L33nuv/v77bz366KP6888/9dZbb+mjjz7SQw895I3mlzpRYc7gRMUJAAAA8IRXg9PGjRvVqlUrtWrVSpI0atQotWrVSs8884wk6eDBg64QJUl16tTR8uXLtXLlSrVo0UKTJ0/We++9x1DkBRQZktlVj4oTAAAA4BGLMcZ4uxElKT4+XhEREYqLi1N4eLi3m1OiDsWd0eWxq+TvZ9GO53vIz8/i7SYBAAAAXuNJNihV5zjh/FTMrDjZHUZxp9O83BoAAACg9CA4lSHWAD9FlAuUxAARAAAAgCcITmWMc0hyBogAAAAACo7gVMZEhjIkOQAAAOApglMZUykzODGyHgAAAFBwBKcyJjKzq97xJLrqAQAAAAVFcCpjIkPoqgcAAAB4iuBUxkSFMTgEAAAA4CmCUxlDxQkAAADwHMGpjKmUWXE6TsUJAAAAKDCCUxnjrDgxqh4AAABQcASnMsY5ql5Sql2nU+1ebg0AAABQOhCcyphQW4BsARl/ds5zAgAAAAqG4FTGWCwWRYUyQAQAAADgCYJTGRQVygARAAAAgCcITmVQJBUnAAAAwCMEpzLIVXFKouIEAAAAFATBqQyi4gQAAAB4huBUBkWGZFScjnGOEwAAAFAgBKcyqFIYF8EFAAAAPEFwKoMiQ+iqBwAAAHiC4FQGRYUxHDkAAADgCYJTGeSsOJ1ITpXdYbzcGgAAAMD3EZzKoArBgbJYJGOkEwxJDgAAAOSL4FQGBfj7qWKw81pOnOcEAAAA5IfgVEZFZl4E91gCFScAAAAgPwSnMioq8yK4VJwAAACA/BGcyqjIUOeQ5FScAAAAgPwQnMqoKGdXPa7lBAAAAOSL4FRGubrqEZwAAACAfBGcyqjIEGfFia56AAAAQH4ITmUUFScAAACg4AhOZZRrOHIqTgAAAEC+CE5lVJRrVL0UGWO83BoAAADAtxGcyihnxSkl3aGkVLuXWwMAAAD4NoJTGRVsDVCw1V+SdCyB85wAAACAvBCcyjDXABFJBCcAAAAgLwSnMszZXe9oAgNEAAAAAHkhOJVhVJwAAACAgiE4lWFRmRWn4wxJDgAAAOSJ4FSGZR2SHAAAAEDuCE5lWGQIFScAAACgIAhOZVhkZsXpKBUnAAAAIE8+EZzefPNN1a5dW0FBQWrbtq1+/PHHXJedNWuWLBaL2y0oKKgEW3vhcA0OQXACAAAA8uT14PThhx9q1KhRGjt2rH7++We1aNFC3bp105EjR3JdJzw8XAcPHnTd9u7dW4ItvnA4B4c4Rlc9AAAAIE9eD06vvPKKhg0bpsGDB6tx48Z6++23FRwcrBkzZuS6jsViUZUqVVy3ypUr57psSkqK4uPj3W7I4Kw4xZ1OU2q6w8utAQAAAHyXV4NTamqqNm3apC5durim+fn5qUuXLtqwYUOu6yUmJqpWrVqKiYlR79699dtvv+W6bGxsrCIiIly3mJiYIn0OpVlEuUD5+1kkSSeTqToBAAAAufFqcDp27Jjsdnu2ilHlypV16NChHNdp2LChZsyYoaVLl+qDDz6Qw+FQ+/btdeDAgRyXHzNmjOLi4ly3/fv3F/nzKK38/CyukfWOJnCeEwAAAJCbAG83wFPt2rVTu3btXPfbt2+viy++WNOnT9f48eOzLW+z2WSz2UqyiaVKZKhNRxJSdDyJihMAAACQG69WnKKiouTv76/Dhw+7TT98+LCqVKlSoG0EBgaqVatW2rlzZ3E08YLnGiCCihMAAACQK68GJ6vVqtatW2vVqlWuaQ6HQ6tWrXKrKuXFbrdr69atqlq1anE184LmGpI8ieAEAAAA5MbrXfVGjRqlgQMH6tJLL1WbNm306quvKikpSYMHD5YkDRgwQNWrV1dsbKwk6bnnntPll1+u+vXr69SpU5o0aZL27t2roUOHevNplFrOc5yOMyQ5AAAAkCuvB6d+/frp6NGjeuaZZ3To0CG1bNlSX3zxhWvAiH379snP72xh7OTJkxo2bJgOHTqkChUqqHXr1lq/fr0aN27sradQqkWFZVScjnIRXAAAACBXFmOM8XYjSlJ8fLwiIiIUFxen8PBwbzfH6xZu3K9HPv5VHS+qpNl3t/F2cwAAAIAS40k28PoFcOFdznOcjlFxAgAAAHJFcCrjXINDcI4TAAAAkCuCUxkXmTkc+fGkFJWxXpsAAABAgRGcyjhncEqzG8WfTvdyawAAAADfRHAq42wB/goLyhhc8RjXcgIAAAByRHCCKjkHiEggOAEAAAA5ITghy3lODBABAAAA5ITgBEWGMCQ5AAAAkBeCExQVllFxOsaQ5AAAAECOCE5wVZyOU3ECAAAAckRwgqLC6KoHAAAA5IXgBEWFZA4OQVc9AAAAIEcEJygylIoTAAAAkBeCExQVSsUJAAAAyAvBCa6KU0JKus6k2b3cGgAAAMD3EJyg8KAAWf0zXgpcBBcAAADIjuAEWSwWRbq663GeEwAAAHAughMkSVEMEAEAAADkKsDbDYBvcFacjjFARJEzxuhMmkPJqelKTrUrKfNncordbdrpVLuSzpmWnGJXcppdySnpSkq163Rquk6n2WWMZFzbdz2S232T5fHd75+dfs6q+a9zzmNIUqC/n6wBfgr0t8ga4Cerv5+sAf6yBvjJ5u+nwABL5rTM6f5+srpN85PV39+1nC3g7PRAfz+35WzOaQHnTM9cPyjAX35+lkL/rQAAAHJDcIIkKTKEilNWxhglpdp1LCFFRxNTdDIpNSPspGYEm6QUu5LTMoKNK/SkZgQc1zKp9szp6W5B40KTku6QfOhlExTop2BrgMoF+ivY6q9gW4CCM38vZ82cZg3I/Omvcll+d053LRcYoGBbxu+EMgAAyjaCEyRJUWFlY0jyM2l2HUtM0dGEFB1LTNXRhIzfjyaeyTbtdDGMMFgu0F8htowD8xDXAXvGzxBbQOb0jIP5kCwH/SG2s8sFBfrLz5JxAJ/54+xPnTNd7vOVw3yLc1vnLHvutnTufItFxhil241S7Q6lpjvO/kw/ez/N7lDKudOyLJuS5fc0u/tyKTlMy/a73eEWTM+kOXQmrXhex+WyBLAQa0CWIHb2b5Y1nIUFBSjEGqDQoACF2jJvWX4Ptvq79j8AAPBtBCdIkqIyK06lcXCIdLtDx5MyA09mKMoIQSlZglGKjiWkKP5MukfbDrH6KyrMpgrBVoVmCTauKoYtM+BkHihnhCLntMxgZMs8yA6kYlEcjDFKdxilpjt0Js3uVhk8nfl7UpbfT6ed7Q7p7Ap52nk/9ey8rMs7nU7LvJ9UNG23WKRQa4BCzglUobaMaWFBGa+pUFugQm3+mcsEKsTmr7DMn871ygUSwgAAKE4EJ0g6W3FasvlfLd96MONck0D/bOeXZD23xBbg75qW0zxrgPu6tsz5tsCMc1py2q4ty7qn0+xuFaFjCak5BqMTyakedYWz+vupUphNUWE2VQq1qlKYTZVCbRk/w2yKCj37M8TGW8TXWSwWBfpbFOjvpxBbgCKLePsOh8kMW5lhKu1ssEpKSXfNS848By0py7yk1HQlnElXYkq6klLSlZj5e2JKuhwm41yxhJR0JaSkS/Hn104/i9yqWiE29yAWFhSo0KAAhQe53w8LClBY5v2wIKpgAADkhqNCSJJa16yosKAAJZxJV5rdKM2ecc5OaeFnybiQb04ByC0YhdoUXi6AA0MUmJ+fRSGZFaCi4hwwJCElTUkpdrdAlZiSpsTMaUkpWaafORvE3KanZJxD5zBS/Jn0jKpq3Hk838wA5gxSoZmVr5yClnNeRiDLunygrAEM2goAuLBYjLmQT1vPLj4+XhEREYqLi1N4eLi3m+NTUtLtSjiT7n6OSZpDqXa7UtLPOU/Fdd/ufq5KlnNWMtbNWObcc1zOznNkbtue4/kqFYID3UNQaA6hKLMrnT/d4FAGGWMyuiNmVq7OrWwlpWSEKWf4SjiTpsTMaRnVsDQlZP5udxTdvwNrgJ9bdSvsnN/Pve+shmUNZCHWALq3AgCKlSfZgIoTXGwB/rKF+nu1Dc7zVVLSHa5ufwByZ7GcrYhFn8d2slbBnEHKGbQSUtzvJ2bej8/yu3Oes1Kdmu7QscTU87rEgfMcMGewyjGAuapegdm6HTorZLYA736uAQAuDAQn+JSs56sAKDkWi0XlMkcFjA4r/HbsDpMZptxDVdaQlXAmLTNoOathWcJa5rppduN+Dth5dD+0BvhlCVgBCrMFunUxzDra4dlqWJauiJnz+VwCgLKN4AQAKDL+fhZFlAtURLnAQm/DmIyqc8I5Fa6EM2cD1rndDBNSzs7Pqfp1PD1Vx5POb5j6oEA/hdrOVr2cgcpZ6XKOehiatRJmOxvWnOGMSjoAlE4EJwCAT7FYLAoKzLhmWaUwW6G3k1P1K6fwlZgZvNwG6chSDTuT5pDkvEZYynlfKNwW4OcWqjJCWGC24eezjoyYdcj6EFtA5jD2/gqgCgYAJYbgBAC4IBVF9UuS0uyOjME3sgQrV3UrS+DKej8hh0CWnFkBS0l3KOU8z/9yyqiCnQ1UIbaMapfr98xBNkJs/pnBzH2Z0Cw/qYQBQN4ITgAA5CHQ30/lg60qH2w9r+2k2x1KSrW7KmBZg9W5w8xn/92uROfw9SkZo59KzipY0YQwq7+f66LKIdazISskywW+s94PtQW4LvAdYsu4BphzfoiNi34DuPAQnAAAKAEB/n6KKOd33hUwKeO8rZyCVlJmwEpMsWef77wYc6rz97MXcZaUcYmIZIdOJqedd/ucsoYp9/CVJWjZsgSxzGnBVv/M+xnzy2WuH0wYA+BFBCcAAEoZa4CfrAFWVQg5vyqYdLYSlpQZsJzXA0tKsSs5Nd01Lznl7O9JqfbM+xnLJaWmKznFOS9dzkuCJafalZxq19HzbuVZQYF+CrZmVLSCrRm3ctaMylc5q3Na5u+B/grODGLBVv/Mdc4ul3UdKmQA8kNwAgCgDCvKSph0dlTExJTMMJWaruTUjAqXe/g6O98tjLnWORvmktPsroujO7snFgdnKDsbyDKqXM5w5gxlQYEZQauc1U/lMkOc8/7Zef6u6UGZvzOkPVC6EZwAAECRyToqokKLZpvOMOYMU6fT7JnVrHSdTrUrKdWu05lhKznVrtOpZ+e7pqVl/p5iV3JaepZl7K7HcYayE0lF0+5zBfhZzoaqzDB1btAKcgayLKErOHN+TssGBfrJFnD29yACGlBsCE4AAMCnZQ1jFYuge2JWxhidSXMoKTXdLXA5A1lylumn0zJC2em0jNuZzN+d885kme/8PWu1LN1hzl7UuRj5+1kUFODn2me2QD8FBZwNVq6QFeAvW5bA5b5Mxk9bLuu5L+Mni4VujrjwEZwAAECZZbFYXBWg4mCMUardoTOpDlfgOp1ZATudZdqZLIHsdGpm8DoniJ0b3s6k2TOrZHalZI60KGVcwywpM/iVFFuAX8YtM0hl3DJCm+v3LPOtAedOz/J7gbbjvjzBDSWB4AQAAFBMLBZL5gG+vyJUNOeR5cTZnTFrmDqTnuX3zOkp6e6B60yaI3O5zPm5rHcm3a6UrNPSHbI7RwFR5vXJ0h3SmeKtpuXG6u/nFqisAX6y+vtlDqRyzu8BfrLlMc+5LWtALts6Z5mcHosgd2EiOAEAAJRybueWlZA0u3tQS7U7lJIZzlIzg1TGzZ45PfP39LPLFWR+anr2eWfSz3aBlDKH07c7lJBSYk8/T+cGqcAAiwL9M3/PnBfo7z4t0BXAMqY7b1Z/S+byWZezZNlOlm34W7Js5+y0rI8R4Jexrj+jSHqM4AQAAACPOQ/kw4JK/rGNMUp3mMwgZc8W0lLtGYHLGbqy3k9NPxvynNOzL3PONuzu6567XJrduLXPGeTkI0EuJ36WjFE1rf5+CsgMYoF+FgX4nw11gc55fhnhL8DvbBhzLec2z5K5Tka4C/DPCGrWAL9z5mf87HhRpRIN++eL4AQAAIBSxWKxuA7CQ23eP5x1OIwrLGUNVSnpDqXZM26p6RkBK83uDFtnp6fajdKyLms3mctnXc6cs45znsk+Ld39cVLTHXKYc9ps5Gqnt/z4xDUEJwAAAKCs8POzKMivZLtKeird7lC6IyNQpWeGrTRHRmBLd5wNYM6f6XajNIcjc/7ZeennBLaz8zLWSc38me7ICHsZ2z5nu5nL23x4f+XEJ4LTm2++qUmTJunQoUNq0aKFXn/9dbVp0ybX5RcuXKinn35ae/bsUYMGDTRx4kRdd911JdhiAAAAoPQI8PdTgL98Otz5Oq9fIe3DDz/UqFGjNHbsWP38889q0aKFunXrpiNHjuS4/Pr169W/f38NGTJEv/zyi/r06aM+ffpo27ZtJdxyAAAAAGWFxRhj8l+s+LRt21aXXXaZ3njjDUmSw+FQTEyM/vOf/+jxxx/Ptny/fv2UlJSkZcuWuaZdfvnlatmypd5+++18Hy8+Pl4RERGKi4tTeHh40T0RAAAAAKWKJ9nAqxWn1NRUbdq0SV26dHFN8/PzU5cuXbRhw4Yc19mwYYPb8pLUrVu3XJdPSUlRfHy82w0AAAAAPOHV4HTs2DHZ7XZVrlzZbXrlypV16NChHNc5dOiQR8vHxsYqIiLCdYuJiSmaxgMAAAAoM7x+jlNxGzNmjOLi4ly3/fv3e7tJAAAAAEoZr46qFxUVJX9/fx0+fNht+uHDh1WlSpUc16lSpYpHy9tsNtlstqJpMAAAAIAyyasVJ6vVqtatW2vVqlWuaQ6HQ6tWrVK7du1yXKddu3Zuy0vSypUrc10eAAAAAM6X16/jNGrUKA0cOFCXXnqp2rRpo1dffVVJSUkaPHiwJGnAgAGqXr26YmNjJUkjRoxQx44dNXnyZPXs2VMLFizQxo0b9c4773jzaQAAAAC4gHk9OPXr109Hjx7VM888o0OHDqlly5b64osvXANA7Nu3T35+Zwtj7du317x58/TUU0/piSeeUIMGDbRkyRI1bdrUW08BAAAAwAXO69dxKmlcxwkAAACAVIqu4wQAAAAApQHBCQAAAADyQXACAAAAgHwQnAAAAAAgHwQnAAAAAMgHwQkAAAAA8kFwAgAAAIB8EJwAAAAAIB8B3m5ASXNe7zc+Pt7LLQEAAADgTc5M4MwIeSlzwSkhIUGSFBMT4+WWAAAAAPAFCQkJioiIyHMZiylIvLqAOBwO/fvvvwoLC5PFYvF2cxQfH6+YmBjt379f4eHh3m7OBYf9W7zYv8WL/Vu82L/Fi/1bvNi/xYv9W7x8af8aY5SQkKBq1arJzy/vs5jKXMXJz89PNWrU8HYzsgkPD/f6C+dCxv4tXuzf4sX+LV7s3+LF/i1e7N/ixf4tXr6yf/OrNDkxOAQAAAAA5IPgBAAAAAD5IDh5mc1m09ixY2Wz2bzdlAsS+7d4sX+LF/u3eLF/ixf7t3ixf4sX+7d4ldb9W+YGhwAAAAAAT1FxAgAAAIB8EJwAAAAAIB8EJwAAAADIB8EJAAAAAPJBcPKiN998U7Vr11ZQUJDatm2rH3/80dtN8rrY2FhddtllCgsLU3R0tPr06aPt27e7LdOpUydZLBa327333uu2zL59+9SzZ08FBwcrOjpajzzyiNLT092WWbNmjS655BLZbDbVr19fs2bNytaeC+1vNG7cuGz7rlGjRq75Z86c0fDhwxUZGanQ0FDdfPPNOnz4sNs22Le5q127drb9a7FYNHz4cEm8dj21bt069erVS9WqVZPFYtGSJUvc5htj9Mwzz6hq1aoqV66cunTpoh07drgtc+LECd1xxx0KDw9X+fLlNWTIECUmJrot8+uvv6pDhw4KCgpSTEyMXnrppWxtWbhwoRo1aqSgoCA1a9ZMn332mcdt8TV57d+0tDQ99thjatasmUJCQlStWjUNGDBA//77r9s2cnrNT5gwwW0Z9m/Or99BgwZl23fdu3d3W4bXb+7y2785fRZbLBZNmjTJtQyv39wV5HjMl44ZCtKWImHgFQsWLDBWq9XMmDHD/Pbbb2bYsGGmfPny5vDhw95umld169bNzJw502zbts1s3rzZXHfddaZmzZomMTHRtUzHjh3NsGHDzMGDB123uLg41/z09HTTtGlT06VLF/PLL7+Yzz77zERFRZkxY8a4lvn7779NcHCwGTVqlPn999/N66+/bvz9/c0XX3zhWuZC/BuNHTvWNGnSxG3fHT161DX/3nvvNTExMWbVqlVm48aN5vLLLzft27d3zWff5u3IkSNu+3blypVGkvn666+NMbx2PfXZZ5+ZJ5980ixatMhIMosXL3abP2HCBBMREWGWLFlitmzZYm644QZTp04dc/r0adcy3bt3Ny1atDDff/+9+eabb0z9+vVN//79XfPj4uJM5cqVzR133GG2bdtm5s+fb8qVK2emT5/uWua7774z/v7+5qWXXjK///67eeqpp0xgYKDZunWrR23xNXnt31OnTpkuXbqYDz/80Pz5559mw4YNpk2bNqZ169Zu26hVq5Z57rnn3F7TWT+v2b+5v34HDhxounfv7rbvTpw44bYMr9/c5bd/s+7XgwcPmhkzZhiLxWJ27drlWobXb+4KcjzmS8cM+bWlqBCcvKRNmzZm+PDhrvt2u91Uq1bNxMbGerFVvufIkSNGklm7dq1rWseOHc2IESNyXeezzz4zfn5+5tChQ65p06ZNM+Hh4SYlJcUYY8yjjz5qmjRp4rZev379TLdu3Vz3L8S/0dixY02LFi1ynHfq1CkTGBhoFi5c6Jr2xx9/GElmw4YNxhj2radGjBhh6tWrZxwOhzGG1+75OPfAyOFwmCpVqphJkya5pp06dcrYbDYzf/58Y4wxv//+u5FkfvrpJ9cyn3/+ubFYLOaff/4xxhjz1ltvmQoVKrj2rzHGPPbYY6Zhw4au+3379jU9e/Z0a0/btm3N//3f/xW4Lb4upwPPc/34449Gktm7d69rWq1atcyUKVNyXYf9myG34NS7d+9c1+H1W3AFef327t3bXH311W7TeP0W3LnHY750zFCQthQVuup5QWpqqjZt2qQuXbq4pvn5+alLly7asGGDF1vme+Li4iRJFStWdJs+d+5cRUVFqWnTphozZoySk5Nd8zZs2KBmzZqpcuXKrmndunVTfHy8fvvtN9cyWfe/cxnn/r+Q/0Y7duxQtWrVVLduXd1xxx3at2+fJGnTpk1KS0tze86NGjVSzZo1Xc+ZfVtwqamp+uCDD3T33XfLYrG4pvPaLRq7d+/WoUOH3J5nRESE2rZt6/Z6LV++vC699FLXMl26dJGfn59++OEH1zJXXXWVrFara5lu3bpp+/btOnnypGuZvPZ5QdpyIYiLi5PFYlH58uXdpk+YMEGRkZFq1aqVJk2a5NYNh/2btzVr1ig6OloNGzbUfffdp+PHj7vm8fotOocPH9by5cs1ZMiQbPN4/RbMucdjvnTMUJC2FJWAIt0aCuTYsWOy2+1uLyRJqly5sv78808vtcr3OBwOjRw5UldccYWaNm3qmn777berVq1aqlatmn799Vc99thj2r59uxYtWiRJOnToUI771jkvr2Xi4+N1+vRpnTx58oL8G7Vt21azZs1Sw4YNdfDgQT377LPq0KGDtm3bpkOHDslqtWY7KKpcuXK++805L69lLvR9e64lS5bo1KlTGjRokGsar92i49wfOT3PrPsqOjrabX5AQIAqVqzotkydOnWybcM5r0KFCrnu86zbyK8tpd2ZM2f02GOPqX///goPD3dNf/DBB3XJJZeoYsWKWr9+vcaMGaODBw/qlVdekcT+zUv37t110003qU6dOtq1a5eeeOIJ9ejRQxs2bJC/vz+v3yI0e/ZshYWF6aabbnKbzuu3YHI6HvOlY4aCtKWoEJzgs4YPH65t27bp22+/dZt+zz33uH5v1qyZqlatqmuuuUa7du1SvXr1SrqZpUqPHj1cvzdv3lxt27ZVrVq19NFHH6lcuXJebNmF5/3331ePHj1UrVo11zReuyiN0tLS1LdvXxljNG3aNLd5o0aNcv3evHlzWa1W/d///Z9iY2Nls9lKuqmlym233eb6vVmzZmrevLnq1aunNWvW6JprrvFiyy48M2bM0B133KGgoCC36bx+Cya347GyiK56XhAVFSV/f/9so30cPnxYVapU8VKrfMsDDzygZcuW6euvv1aNGjXyXLZt27aSpJ07d0qSqlSpkuO+dc7La5nw8HCVK1euzPyNypcvr4suukg7d+5UlSpVlJqaqlOnTrktk/U5s28LZu/evfrqq680dOjQPJfjtVt4zueS1/OsUqWKjhw54jY/PT1dJ06cKJLXdNb5+bWltHKGpr1792rlypVu1aactG3bVunp6dqzZ48k9q8n6tatq6ioKLfPA16/5++bb77R9u3b8/08lnj95iS34zFfOmYoSFuKCsHJC6xWq1q3bq1Vq1a5pjkcDq1atUrt2rXzYsu8zxijBx54QIsXL9bq1auzlchzsnnzZklS1apVJUnt2rXT1q1b3f7hOP/hN27c2LVM1v3vXMa5/8vK3ygxMVG7du1S1apV1bp1awUGBro95+3bt2vfvn2u58y+LZiZM2cqOjpaPXv2zHM5XruFV6dOHVWpUsXtecbHx+uHH35we72eOnVKmzZtci2zevVqORwOV2ht166d1q1bp7S0NNcyK1euVMOGDVWhQgXXMnnt84K0pTRyhqYdO3boq6++UmRkZL7rbN68WX5+fq4uZuzfgjtw4ICOHz/u9nnA6/f8vf/++2rdurVatGiR77K8fs/K73jMl44ZCtKWIlOkQ02gwBYsWGBsNpuZNWuW+f33380999xjypcv7zbySFl03333mYiICLNmzRq34UGTk5ONMcbs3LnTPPfcc2bjxo1m9+7dZunSpaZu3brmqquucm3DOfxl165dzebNm80XX3xhKlWqlOPwl4888oj5448/zJtvvpnj8JcX2t9o9OjRZs2aNWb37t3mu+++M126dDFRUVHmyJEjxpiM4Txr1qxpVq9ebTZu3GjatWtn2rVr51qffZs/u91uatasaR577DG36bx2PZeQkGB++eUX88svvxhJ5pVXXjG//PKLa1S3CRMmmPLly5ulS5eaX3/91fTu3TvH4chbtWplfvjhB/Ptt9+aBg0auA3nfOrUKVO5cmVz1113mW3btpkFCxaY4ODgbMMNBwQEmJdfftn88ccfZuzYsTkON5xfW3xNXvs3NTXV3HDDDaZGjRpm8+bNbp/HztGw1q9fb6ZMmWI2b95sdu3aZT744ANTqVIlM2DAANdjsH9z3r8JCQnm4YcfNhs2bDC7d+82X331lbnkkktMgwYNzJkzZ1zb4PWbu/w+H4zJGE48ODjYTJs2Ldv6vH7zlt/xmDG+dcyQX1uKCsHJi15//XVTs2ZNY7VaTZs2bcz333/v7SZ5naQcbzNnzjTGGLNv3z5z1VVXmYoVKxqbzWbq169vHnnkEbdr4RhjzJ49e0yPHj1MuXLlTFRUlBk9erRJS0tzW+brr782LVu2NFar1dStW9f1GFldaH+jfv36mapVqxqr1WqqV69u+vXrZ3bu3Omaf/r0aXP//febChUqmODgYHPjjTeagwcPum2DfZu3FStWGElm+/btbtN57Xru66+/zvHzYODAgcaYjGF+n376aVO5cmVjs9nMNddck22/Hz9+3PTv39+Ehoaa8PBwM3jwYJOQkOC2zJYtW8yVV15pbDabqV69upkwYUK2tnz00UfmoosuMlar1TRp0sQsX77cbX5B2uJr8tq/u3fvzvXz2Hldsk2bNpm2bduaiIgIExQUZC6++GLz4osvuh34G8P+zWn/Jicnm65du5pKlSqZwMBAU6tWLTNs2LBsX27w+s1dfp8Pxhgzffp0U65cOXPq1Kls6/P6zVt+x2PG+NYxQ0HaUhQsxhhTtDUsAAAAALiwcI4TAAAAAOSD4AQAAAAA+SA4AQAAAEA+CE4AAAAAkA+CEwAAAADkg+AEAAAAAPkgOAEAAABAPghOAAAAAJAPghMAoNSoXbu2Xn31VW83wyU5OVk333yzwsPDZbFYdOrUKW83yU2nTp00cuRIbzcDAC4IAd5uAAAApdXs2bP1zTffaP369YqKilJERIS3mwQAKCYEJwBAmZaamiqr1VqodXft2qWLL75YTZs2LeJWAQB8DV31AKCU6NSpk/7zn/9o5MiRqlChgipXrqx3331XSUlJGjx4sMLCwlS/fn19/vnnxdqO2rVr68UXX9Tdd9+tsLAw1axZU++8845r/po1a7J1W9u8ebMsFov27NkjSZo1a5bKly+vZcuWqWHDhgoODtYtt9yi5ORkzZ49W7Vr11aFChX04IMPym63uz1+QkKC+vfvr5CQEFWvXl1vvvmm2/xTp05p6NChqlSpksLDw3X11Vdry5Ytrvnjxo1Ty5Yt9d5776lOnToKCgrK9bl+8sknatKkiWw2m2rXrq3Jkye75nXq1EmTJ0/WunXrZLFY1KlTpxy34Xy8GTNmqGbNmgoNDdX9998vu92ul156SVWqVFF0dLReeOEFt/X27dun3r17KzQ0VOHh4erbt68OHz6cbbtz5sxR7dq1FRERodtuu00JCQm5Pp/ly5crIiJCc+fOlSTt379fffv2Vfny5VWxYkX17t3b9Tdat26dAgMDdejQIbdtjBw5Uh06dJAk7d27V7169VKFChUUEhKiJk2a6LPPPsv18QGgNCM4AUApMnv2bEVFRenHH3/Uf/7zH91333269dZb1b59e/3888/q2rWr7rrrLiUnJ+e6jXvvvVehoaF53vIzefJkXXrppfrll190//3367777tP27ds9ei7Jycl67bXXtGDBAn3xxRdas2aNbrzxRn322Wf67LPPNGfOHE2fPl0ff/yx23qTJk1SixYt9Msvv+jxxx/XiBEjtHLlStf8W2+9VUeOHNHnn3+uTZs26ZJLLtE111yjEydOuJbZuXOnPvnkEy1atEibN2/OsX2bNm1S3759ddttt2nr1q0aN26cnn76ac2aNUuStGjRIg0bNkzt2rXTwYMHtWjRolyf665du/T555/riy++0Pz58/X++++rZ8+eOnDggNauXauJEyfqqaee0g8//CBJcjgc6t27t06cOKG1a9dq5cqV+vvvv9WvX79s212yZImWLVumZcuWae3atZowYUKObZg3b5769++vuXPn6o477lBaWpq6deumsLAwffPNN/ruu+8UGhqq7t27KzU1VVdd9f/t3V9IU+8fB/D3XF40yxRrJrRcTjYmKWhGieG6mMwuwijonyWaggtJA/MiihQTxMDowooIsrAyKy8KLByUQ1nJECOkDDWsDCy76N8gxebnd9HPw/d8zS378+tnvV8w2PM853yeP5yLfTjnOctAXFwcGhsblRgTExO4dOkS9uzZAwAoLi7G+Pg4Ojo60Nvbi9ra2m+6foiI5iQhIqI5wWazybp165Ty58+fJSwsTHbv3q3UjYyMCAC5f//+jHFev34tAwMDAT+BxMbGyq5du5Ty5OSk6PV6OX36tIiItLe3CwB5+/atcsyDBw8EgAwNDYmISENDgwCQwcFB5ZiioiLR6XTy8eNHpc7hcEhRUZGq76ysLNV4tm3bJhs2bBARkc7OTgkPD5exsTHVMSaTSc6cOSMiIhUVFRIaGiqjo6MB57lz507JzMxU1ZWXl0tCQoJSLi0tFZvNFjBORUWF6HQ6+fDhg2peRqNR/H6/UmexWKSmpkZERFwul2i1Wnnx4oXS/ujRIwEgXq93xrjl5eWyZs0apWyz2aS0tFTq6+tl0aJF4na7lbbGxkaxWCwyOTmp1I2Pj8v8+fOlra1NRERqa2vFarUq7S0tLbJgwQLx+XwiIpKYmCiVlZUB509E9KfgHiciojkkKSlJ+a7VahEVFYXExESlLjo6GgAwOjo6Ywy9Xg+9Xv/TxqHRaLB06dKAfX6NTqeDyWRSytHR0TAajao7FtHR0dPipqWlTStPvWnv4cOH8Pl8iIqKUh3z6dMnPH36VCnHxsZiyZIlAcfX19eH7OxsVV16ejpOnDgBv98PrVYbfJL/ZTQasXDhQtW8tFotQkJCVHVTc+3r64PBYIDBYFDaExISEBERgb6+PqxevfqrcWNiYqat1/Xr1zE6OgqPx6OcB3xZq8HBQdX5ADA2NqasVV5eHg4fPoyuri6sXbsW58+fx9atWxEWFgYAKCkpwd69e+FyuWC327FlyxbVtUFE9Cdh4kRENIeEhoaqyhqNRlWn0WgAfHnUayZOpxMXL14M2I/P55v1OKb6nEoGRERpn5iY+KYYgeJ+C5/Ph5iYGLjd7mltERERyvepH/7/K79irjPF/XeM5ORk9PT04Ny5c0hNTVWuEZ/Ph1WrVin7nf5pKqnU6/XYuHEjGhoasGLFCty+fVu1toWFhXA4HGhtbYXL5UJNTQ3q6uqwb9++Wc2DiGguYOJERPSXqaqqwoEDB35Z/Kkf3SMjI4iMjASAGfcRfY+urq5pZavVCgBISUnBq1evMG/ePBiNxh/qx2q1wuPxqOo8Hg/MZvOs7jZ9b9/Dw8MYHh5W7jo9fvwY7969Q0JCwqximUwm1NXVYf369dBqtaivrwfwZa2am5uh1+sRHh4+4/mFhYXYsWMHli1bBpPJhPT0dFW7wWCA0+mE0+nEwYMHcfbsWSZORPRH4sshiIj+Mnq9HvHx8QE/PyI+Ph4GgwGVlZUYGBhAa2ur6m10P8rj8eDYsWPo7+/HyZMnce3aNZSWlgIA7HY70tLSsGnTJrhcLjx79gz37t3DoUOH0N3dPat+ysrKcOfOHRw9ehT9/f24cOEC6uvrf2nSOcVutyMxMRE5OTno6emB1+tFbm4ubDYbUlNTZx3PbDajvb0dLS0tyh/i5uTkYPHixcjOzkZnZyeGhobgdrtRUlKCly9fKuc6HA6Eh4ejuroa+fn5qrj79+9HW1sbhoaG0NPTg/b2diWJJSL60zBxIiKinyo0NBRNTU148uQJkpKSUFtbi+rq6p8Wv6ysDN3d3UhOTkZ1dTWOHz8Oh8MB4Mujardu3UJGRgby8/NhNpuxfft2PH/+XNn/9a1SUlJw9epVXLlyBStXrsSRI0dQVVWFvLy8nzaXmWg0Gty4cQORkZHIyMiA3W5HXFwcmpubvzumxWLB3bt30dTUhLKyMuh0OnR0dGD58uXYvHkzrFYrCgoKMDY2proDFRISgry8PPj9fuTm5qpi+v1+FBcXw2q1IisrC2azGadOnfruMRIR/T/TyD8fQiciIiL6l4KCArx58wY3b9783UMhIvptuMeJiIiIvur9+/fo7e3F5cuXmTQR0V+PiRMRERF9VXZ2NrxeL5xOJzIzM3/3cIiIfis+qkdERERERBQEXw5BREREREQUBBMnIiIiIiKiIJg4ERERERERBcHEiYiIiIiIKAgmTkREREREREEwcSIiIiIiIgqCiRMREREREVEQTJyIiIiIiIiC+A9smJgXCvbGsgAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program MeanAndVarianceOfMAXbyDefinition.py\n",
        "# For the Bi(16, 0.5)\n",
        "\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy.stats import binom\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parameters of the binomial\n",
        "# Define the value of n\n",
        "n  = 16\n",
        "# probability of head\n",
        "p = 0.5\n",
        "\n",
        "\n",
        "# Number of monkeys\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_binomials = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000] # This setting reaches 16\n",
        "n_binomials = range(1, 200002, 10000) # (start, end, step)\n",
        "\n",
        "# The cumulative distribution function of the binomial\n",
        "F = binom.cdf\n",
        "\n",
        "k_values = list(range(0, n + 1))\n",
        "\n",
        "expected_means = []\n",
        "expected_variances = []\n",
        "for m in n_binomials:\n",
        "    # The cumulative distribution function of MAX\n",
        "    Fm_k = F(k_values, n, p)**m\n",
        "    # print()\n",
        "    # print(f'm = {m}')\n",
        "    # print(f'F(k) = {Fm_k}')\n",
        "    # Probabilities\n",
        "    pmf_k = np.diff(Fm_k) # Fm_k[k] - Fm_k[k-1]\n",
        "    pmf_k = np.insert(pmf_k, 0, Fm_k[0]) # Insert first term\n",
        "    # print(f\"pmf(k) = {pmf_k}\")\n",
        "    # Mean\n",
        "    mean = 0.0\n",
        "    for k in k_values:\n",
        "        mean += k * pmf_k[k]\n",
        "    expected_means.append(mean)\n",
        "    # print(f\"Number of monkeys = {m}, Mean = {mean}\")\n",
        "\n",
        "    # Variance\n",
        "    variance = 0.0\n",
        "    for k in k_values:\n",
        "        variance += ((k - mean)**2) * pmf_k[k]\n",
        "    expected_variances.append(variance)\n",
        "    deviation = np.sqrt(variance)\n",
        "    print(f\"Number of monkeys = {m}, mean = {mean:.3}, variance = {variance:.2}, deviation = {deviation:.2}\")\n",
        "\n",
        "#Plot the expected means\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_binomials, expected_means, label='Expected Means')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title(f'Mean of MAX of $Bi({n}{p})$ as a function of the number of monkeys, by definition')\n",
        "plt.legend()\n",
        "\n",
        "#Plot the expected variances\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_binomials, expected_variances, label='Expected Variances')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Variance of MAX ')\n",
        "plt.title(f'Variance of MAX of $Bi({n}, {p}):as a function of the number of monkeys, by definition')\n",
        "plt.legend()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G2CAKC5_WTPT"
      },
      "source": [
        "The variance of MAX of $m$ binomials $Bi(16, 0.5)$ is less than the variance of one binomial, as expected, and is an almost always decreasing function that very slowly tends to zero.\n",
        "\n",
        "*Challenge.*  Develop a program to estimate the variance   using the formula for the mean\n",
        ">\n",
        ">$\\mathbb{E}(MAX) =  np + \\sqrt{\\frac{2}{k} \\ln(m)}$,\n",
        ">\n",
        "where $n$ is the power in the Binomial $Bi(n,p)$, $k = 24.9 n^{-1.18} + 2.53$, and $m$ is the number of monkeys. Compare the output with that of the previous program.\n",
        "\n",
        "*Challenge.* Carry a regression analysis to fit the dependence of the variance on the number of monkeys. An exact fitting seems difficult for us because the curve is not monotone. But, at least, disentangle which is the better fit between an exponential $e^{-kx}$, an hyperbola   $1/x^k$ or a function of $\\frac{1}{\\ln m}$ which is suggested by [theorem 1.5.3 of this book](https://minerva.it.manchester.ac.uk/%7Esaralees/book2.pdf)\n",
        "\n",
        "\n",
        "*Research.* After one finds a good fitting, the next task is to create a mathematical justification. Some bibliography has been listed in the section of continuous approximation by the normal distribution."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jlZpaS_orUoW"
      },
      "source": [
        "# THE MAX OF m NORMAL DISTRIBUTIONS\n",
        "\n",
        "The, discrete, Binomial Distribution can be approximated by the Gauss Bell, which is continuous and smooth, differentiable.  We, human beings, can deal with continuous models quite easily and so, a very intuitive and powerful mathematically machinery has been developed for the study of the Normal Distribution.\n",
        "\n",
        "In this section we use the continuous approximation to the Binomial Distribution to mathematically estimate its cdf (cumulative distribution function),  and pdf (probability density function),  together with the expected value of MAX and of its variance.\n",
        "\n",
        "MAX prepares the terrain for the study of Evolution. The connection is that Evolution is moved by the best, which is here the individual with the highest number of coincidences with the target string.  Evolution includes the recursive cloning of the best, then mutating and recombining it to generate the next generation.  \n",
        "\n",
        "Our problem deals with integer numbers but working with real numbers is sometimes more intuitive and, maybe, easier. But, caution, not all application of real numbers are good to model situations with integers. So, one must check all what one imagines. A useful application with real numbers is the following:\n",
        "\n",
        "The  $Bi(n, 1/2)$ is approximated by a Normal distribution with mean $\\mu = np$ and standard deviation $\\sigma = \\sqrt{npq}$. We can change units and instead of counting the number of matched sites, say $X$, we count the number of standard deviations off the mean of $X$.  This is equivalent to consider a normal distribution with mean $0$ and standard deviation $1$. According to this interpretation, each unit represents one standard deviation. With this abstraction, we are considering all possible Binomial Distributions at once and are getting rid of the length of the string. Warning: we have been using $m$ for the number of monkeys that is equal to the number of random strings, and $n$ for the length of the string. But since that length counts anymore, we are left with only one parameter, the number of random strings that is equal to the considered number of normal distributions. That is why, we use $n$ to represent the number of monkeys or of considered distributions.\n",
        "\n",
        "Let us now proceed.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mdcaOAeYNB6C"
      },
      "source": [
        "## Cumulative distribution function (cdf) of MAX  \n",
        "\n",
        "We have a source of random numbers, or a random variable, $X$, that takes values on real numbers with a probability density function (pdf) $f$ and a cumulative distribution function (cdf) $F$. The pdf $f$ says that the probability that $X$ lies in within  $a$ and $a + dx$ is $P( a < X < a +dx) = f(a)dx$. And the cdf $F$ says that the probability of being less or equal to $a$ is $F(a) = P(X \\le a)$, so  $F$ cumulates probability. Our question is:\n",
        "\n",
        "**How is distributed the maximum of $m$ such identical random values, knowing that events are independent, that sampling does not cause interference whatsoever?**\n",
        "\n",
        "This question has a clear mathematical answer. Let us present it. We follow:\n",
        "\n",
        "Dr. MAX Grossmann\n",
        "\n",
        "https://max.pm/posts/max_dist/\n",
        "\n",
        "*Theorem.* Let $X_1, X_2,..., X_n$ be independent random variables with the same cumulative distribution function $F$. Let $Y = max\\{X_1, X_2,..., X_n\\}$. Then, the cumulative distribution function of $Y$ is $F_Y (y) = F^n(y)$.\n",
        ">\n",
        "*Proof.*  We will consider random variables with a continuous differentiable distribution because we want to apply this result to the normal distribution, which appears as the best continuous approximation to the Binomial Distribution.\n",
        ">\n",
        "Two sets or events $A$ and $B$ are independent when $p(A \\cap B) = p(A)p(B)$.\n",
        "Two random variables $X_1$ and $X_2$ are independent when every pair of events $A$ of $X_1$ and $B$ of $X_2$ are independent, i.e., when $p(A \\cap B) = p(A)p(B)$. A set of random variables is independent when this equation can be applied to any pair of variables and to the natural extensions with 3 or more variables. With this definition, we can calculate the distribution of the maximal value of a set of random numbers sampled with the aforementioned conditions.\n",
        ">\n",
        "To fix ideas, let us consider at first two random variables, $X_1$ and $X_2$. Let $Y = \\max\\{X_1, X_2\\}$. They are represented graphically by two axes perpendicular one another in the plane. Then,  \n",
        ">\n",
        ">$Y =  \\max\\{X_1, X_2\\} = y$, when:\n",
        ">>>\n",
        ">>($X_1 = y$ and $X_2 < y$) or\n",
        ">>>\n",
        ">>($X_2 = y$ and $X_1 < y$)\n",
        ">\n",
        "Signs have been chosen to avoid double counting. Nevertheless, we can include double counting if this represents no additional probability. So, $Y = y$ when:\n",
        ">\n",
        ">($X_1 \\le y$ and $X_2 \\le y$) or\n",
        ">>\n",
        ">($X_2 \\le y$ and $X_1 \\le y$ )\n",
        ">>\n",
        "We have replaced $X_1 = y$ by $X_1 \\le y$ because if the maximum value comes from $X_1$, then it is also greater than all values less than $y$. And, we have replaced $X_1 < y$  by $X_1 \\le y$ because the probability of the line $X_1 = y$ in the plane is 0, since it has no area. Now, let us apply probabilities:\n",
        ">>\n",
        ">$P(Y = y)$ when:\n",
        ">>>\n",
        ">>$P((X_1 \\le y \\cap X_2 \\le y) \\cup  (X_2 \\le y \\cap X_1 \\le y ))$\n",
        ">>>\n",
        "Since $p(A \\cup A) = p(A)$, we get:\n",
        ">>\n",
        ">$P(Y = y)$ =  P(($X_1 \\le y \\cap X_2 \\le y)$\n",
        ">\n",
        "When $X_1$ and $X_2$ form an independent set of variables, their events are also independent and the probability of an intersection is the product of probabilities. We get\n",
        ">\n",
        "$P(Y = y) = P((X_1 \\le y \\cap X_2 \\le y) = P((X_1 \\le y) P( X_2 \\le y)$.\n",
        ">\n",
        "At last, we have proven that for a pair of independent random variables, $X_1$ and $X_2$\n",
        ">\n",
        "$ P(\\max\\{X_1, X_2\\} = y) =  P(\\max\\{X_1, X_2\\} \\le y) =  P((X_1 \\le y) P( X_2 \\le y)$\n",
        ">\n",
        "We will apply the generalization of this result to  $n$ variables. Let us notice, furthermore,  that we are dealing with the cumulative distribution function of $Y$, which is, by definition,  the probability of being at most $y$, the cumulated probability until $y$:\n",
        ">\n",
        ">$ F_{Y}(y)  = P(Y \\leq y) $\n",
        ">>\n",
        ">>$= P(\\max\\{X_1,\\dots,X_n\\} \\leq y)$\n",
        ">>\n",
        "Now, the maximal value of a finite set of numbers must be one of them,  and all of them must be equal or less than $y$. Therefore,\n",
        ">>\n",
        ">$ F_{Y}(y) = P(\\{X_1 \\leq y)\\} \\cap \\dots \\cap \\{X_n \\leq y)\\} $\n",
        ">>\n",
        "Since events are independent, the probability of an intersection is the product of probabilities:\n",
        ">>\n",
        ">$ F_{Y}(y) = P(\\{X_1 \\leq y)\\} \\cap \\dots \\cap \\{X_n \\leq y)\\} $\n",
        ">>\n",
        "> $ F_{Y}(y) = \\prod_{j=1}^{n} P(X_{i} \\leq y) $\n",
        ">>\n",
        "> $ F_{Y}(y) = \\prod_{j=1}^{n} F(y)   $\n",
        ">>\n",
        ">$ F_{Y}(y)  = F^n(y) $\n",
        ">>\n",
        ">that is because the i-th term is $F(y)$, the cumulated probability until $y$ of $X_i$.\n",
        "\n",
        "This expression and its derived quantities, such as the mean, must be evaluated by numerical methods. But a powerful intuition can be gotten by studying a convenient graphic, and that is why we asked Colab for help:\n",
        ">\n",
        "Hi, Colab. Please, the code for the graphic of the cumulative distribution functions $F^n(z)$, where $F$ is the cumulative distribution function of the normal distribution, and n = 1, 10, 100, 1000.\n",
        ">\n",
        "Colab responded with the following code:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "mhYRxQM_NItz",
        "outputId": "3af33188-4b04-46c5-af87-c605b9da51c0"
      },
      "outputs": [
        {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program CDF_Max_of_n_Normal_Distributions.py\n",
        "# By Gemini\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "# Define a range of z values\n",
        "z_values = np.linspace(-4, 4, 1000)\n",
        "\n",
        "# Define the values of n\n",
        "n_values = [1, 10, 100, 1000]\n",
        "\n",
        "# Plot the cumulative distribution functions F^n(z)\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "for n in n_values:\n",
        "    Fn_z = F(z_values)**n\n",
        "    plt.plot(z_values, Fn_z, label=f'n = {n}')\n",
        "\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('F^n(z)')\n",
        "plt.title('Cumulative Distribution Function of the Maximum of n Standard Normal Distributions')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TMlewoYPNPHs"
      },
      "source": [
        "*Gemini added the following comment:*\n",
        ">>\n",
        ">The plots show how the distribution of the maximum value shifts to the right and becomes steeper as the number of samples ($n$$n$) increases. This visually demonstrates how the maximum value in a larger population is likely to be higher and less variable than in a smaller population. This relates to how selection of the fittest in a larger genetic algorithm population can lead to faster and more consistent improvement in fitness.\n",
        "\n",
        "**Exercise.** Run the previous program and report your comments.\n",
        ">\n",
        "*Answer.* The efficiency of MAX to improve fitness is astonishing. A population of 1000 individuals is sufficient to reach more than 3 standard deviations above the mean. Also: the average slope of the cdf grows with $n$. This means that the variance diminishes with $n$ because values get more and more concentrated.\n",
        "\n",
        "**Exercise.** The impressive role of the population size is something that deserves to be explored further. Include some higher values of $n$ in the previous program, run it anew and report your conclusion.\n",
        ">\n",
        "*Answer.* The code with some higher values of $n$, the number of monkeys or distributions, follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "skEx8XtJNWcd",
        "outputId": "428a9496-2d8d-453c-e651-b437e6815eb0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "# Define a range of z values\n",
        "z_values = np.linspace(-4, 10, 2000)\n",
        "\n",
        "# Define the values of n\n",
        "n_values = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000]\n",
        "\n",
        "# Plot the cumulative distribution functions F^n(z)\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "for n in n_values:\n",
        "    Fn_z = F(z_values)**n\n",
        "    plt.plot(z_values, Fn_z, label=f'n = {n}')\n",
        "\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('F^n(z)')\n",
        "plt.title('Cumulative Distribution Function of the Maximum of n Standard Normal Distributions')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B4B_YecuNvTH"
      },
      "source": [
        "*Our comments.* With 100 chromosomes, to reach 2 standard deviations  above the mean is a normal event. To reach four standard deviations above the mean is a normal  event for a population size of 100000,  and 5 deviations with a population of 10 millions. Thus, the mean of MAX grows with $n$ but the growth decelerates.\n",
        "\n",
        "*Challenge.* Evaluate the population size that is necessary to perfectly match at once a binary string of 1000 bits. Make a difference between a happy coincidence and a repeatable, reproducible, scientific  feat. One can expect that the probability is too small to be interesting, and that is why we must pay attention to Evolution which does not rely on the hope of solving all problems at once but on gathering small progress.\n",
        "\n",
        "Our results have implications of biological interest:\n",
        ">\n",
        "*Prediction.* Evolution must reward large population sizes. To this aim, genes for high reproductive power, large migration rates, and powerful cohesion must be favored by Evolution. In other words, Evolution has an immense cost in terms of population size. Anyway, if the population size is small, the price must be paid in terms of time, of generations.\n",
        "\n",
        "Our work with the cumulative distribution function is tremendously important. Therefore, we need to test it with a simulation, because this captures the mechanistic procedures, while mathematics presents overall results based on the fundamental ideas.  Thus, we have gotten a theorem that calculates the distribution of MAX. Indeed, this is a prediction. In the Scientific Method, predictions must be verified. For our case, this can be easily done in a simulation.\n",
        "\n",
        "**Example.** We have a compact and exact expression for the cumulative distribution function of the maximal value of random numbers sampled each one from a standard normal distribution. We need to verify that this important prediction is correct. So, we asked Colab:\n",
        ">>\n",
        ">Hi, Colab! Please, develop the code for a simulation to estimate the cumulative distribution function of the  maximal value of a set of 10 normal distributions. Add a graphical comparison of the results of the simulation with the predictions of the mathematical expectations.\n",
        ">\n",
        "\n",
        "Colab answered so:\n",
        ">>\n",
        "> Certainly! Here is the code to simulate the cumulative distribution function of the maximum of 10 normal distributions and compare it with the theoretical result.\n",
        ">>\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 599
        },
        "id": "ONoWZr2YN4Qe",
        "outputId": "b6d22e90-d3f6-478e-e9d6-4a283cfb5843"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "sorted_max_values [-0.12256956 -0.11236857 -0.11090257 ...  4.18719442  4.23460404\n",
            "  4.33675694]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Parameters\n",
        "num_simulations = 10000  # Number of times to simulate the maximum\n",
        "set_size = 10  # Number of normal variables in each set\n",
        "\n",
        "# Simulate the maximum of 'set_size' normal distributions 'num_simulations' times\n",
        "max_values = []\n",
        "for _ in range(num_simulations):\n",
        "    random_values = np.random.normal(loc=0, scale=1, size=set_size)\n",
        "    max_values.append(np.max(random_values))\n",
        "\n",
        "# Estimate the empirical cumulative distribution function (CDF) from simulations\n",
        "sorted_max_values = np.sort(max_values)\n",
        "print(f\"sorted_max_values {sorted_max_values}\" )\n",
        "# An array with  numbers   0.0001, 0.0002,..., 0.9999, 1.000\n",
        "empirical_cdf = np.arange(1, num_simulations + 1) / num_simulations\n",
        "#print(f\"empirical_cdf {empirical_cdf}\")\n",
        "# Calculate the theoretical CDF of the maximum of 'set_size' normal distributions\n",
        "# F_Y(y) = F(y)^n, where F is the CDF of the standard normal distribution\n",
        "z_values = np.linspace(np.min(max_values), np.max(max_values), 1000)\n",
        "theoretical_cdf = norm.cdf(z_values)**set_size\n",
        "\n",
        "# Plot the empirical and theoretical CDFs\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(sorted_max_values, empirical_cdf, label='Empirical CDF (Simulation)')\n",
        "plt.plot(z_values, theoretical_cdf, label='Theoretical CDF ($F^{10}(z)$)')\n",
        "plt.xlabel('Maximum Value (z)')\n",
        "plt.ylabel('Cumulative Probability')\n",
        "plt.title('Empirical vs. Theoretical CDF of the Maximum of 10 Standard Normal Distributions')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qe-Ci5qIOAPt"
      },
      "source": [
        "*Exercise.* Run the code and express your conclusions.\n",
        ">\n",
        "*Answer.* The graph shows that the mathematical prediction matches the simulation. We see, on the one hand, the fda-based mathematical prediction of the cumulative distribution function of the maximum value of a set of independent and identically distributed normal variables. On the other, the estimate found by our simulation.  Both coincide. Therefore, our mandatory prediction is fulfilled. This is a license to move on.\n",
        "\n",
        "*Comment by Gemini:*\n",
        ">\n",
        ">The simulation and theoretical predictions for the cumulative distribution function of the maximum values seem to align well.\n",
        "\n",
        "**Exercise.** Decipher the previous code that produces an Observed Cumulative Distribution Function, which gives for each $y$, an estimation of $F(y) = P( x \\le y)$.\n",
        ">\n",
        "*Answer.* Let us explain what the code does:\n",
        ">\n",
        "- Step 1: Ten numbers must be sampled, generated, at random from a normal distribution with mean 0 and standard deviation 1.\n",
        "- Step 2: The MAX of those numbers must be found and memorized.\n",
        "- Steps 1 and 2 must be repeated 10000 times. We get 10000 maximal values.\n",
        ">\n",
        "- The found 10000 MAX values must be sorted from the least to the greatest. So, to know the proportion of values less than $y$, which is equal to the value of the cumulative distribution function until  $y$, it is enough to know the place occupied by $y$ in the array of max-values. Thus, we pair the array of max-values with an array of numbers from 1 to 10000, this is the order array.  The pairing gives the place of each max-value in its array. But, behold, we can also use the order-array to indicate a value of the cumulative distribution function that goes from 0 to 1. So, we divide each number of the order-array by 10000. Therefore, this arrays contains numbers 0.0001, 0.0002, ..., 0.9999, 1.0000. In the   program, this order-array is called `empirical_cdf`.\n",
        ">\n",
        "- How is the graphic done? In a graph, the x-coordinate of each point to be drawn represents a max-value,  and the y-values, which must go vertically, is given by the `empirical_cdf`.\n",
        ">\n",
        "The empirical distribution must be compared with the theoretically expected distribution that is the original distribution to the $n$ power, where $n$ is the population size, the number of monkeys. The mandatory prediction is that both graphs must coincide. Is that true? Yes, as it was shown by the graphic.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fza7o6viONW2"
      },
      "source": [
        "\n",
        "## The probability density function (pdf) of MAX\n",
        "\n",
        "By looking at the cdf, we can mentally compute the bell corresponding to the probability density function. This is done as follows:  when the population has 100 chromosomes, around 90\\% of the maximal values are located in within 2 and 3.2, with mean circa 2.6. Thus, assuming the pdf of MAX is bell-like, the range of usual values cover 4 of its standard deviations. So, one standard deviation is equal to $ (3.2 -2)/4 = 1.2/4 = 0.3$. This means that the  standard deviation of the density bell of MAX of 100 normal distributions would be 0.3 standard deviations of the Binomial from which it comes.\n",
        "\n",
        "Let us pass from intuitive feelings to exact computing.\n",
        "\n",
        "**Exercise.** Use the cdf of MAX to find an exact expression for its probability density function, knowing that the pdf is the derivative of the cdf.\n",
        ">\n",
        "*Answer.* Let $Y$ be the random variable corresponding to the MAX of $n$ independent random variables with standard normal distribution, whose cdf is $F_{Y}$:\n",
        ">>\n",
        ">$ F_{Y}(y) = F(y)^n $.\n",
        ">\n",
        "where $F(y)$ is the cdf, cumulative distribution function, of the normal distribution. The probability density function $f_Y(y)$ is the derivative of the cumulative distribution function of $Y$. So, differentiating the last equation, we get  \n",
        ">>\n",
        ">$ f_{Y}(y) = d(F_{Y}(y))/dy =  n f(y) F(y)^{n-1}$.\n",
        ">>\n",
        "The pdf, probability density function, of the standard normal distribution, with mean $\\mu = 0$ and variance $\\sigma^2 = 1$, is\n",
        ">\n",
        ">$f(y) = \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}$\n",
        ">\n",
        "and its cdf, cumulated distribution function, is\n",
        ">\n",
        ">$F (y) = ∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}}dt$\n",
        ">\n",
        "Therefore, the pdf of MAX, the  maximum of $n$ standard normal distributions, is:\n",
        ">>\n",
        ">$  f_{Y}(y) = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}} dt)^{n-1}$\n",
        ">\n",
        "Since the Gauss Bell is symmetric around $0$, this also can be expressed as:\n",
        ">>\n",
        ">$  f_{Y}(y) = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (\\frac{1}{2} + ∫^y_{0}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}} dt)^{n-1}$\n",
        ">>\n",
        "This is related to the [erf function](https://en.wikipedia.org/wiki/Error_function), used in all numerical libraries, defined by\n",
        ">>\n",
        "> $erf(y) = \\frac{2}{\\sqrt{ \\pi} } ∫^y_{0}e^{- t^2 } dt$\n",
        ">>\n",
        "In statistics, for   $x>0$,  erf has the following interpretation: for a real random variable Y that is normally distributed with mean 0 and standard deviation $\\frac{1}{\\sqrt{2}}$,  erf(y) is the probability that Y falls in the range [−y, y].\n",
        ">\n",
        "Using the erf function, we get:\n",
        ">\n",
        "The probability density function of the  maximum of these $n$ normal distributions is:\n",
        ">\n",
        "$  f_{Y}(y) = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (\\frac{1}{2} + \\frac{1}{2}erf(\\frac{y}{\\sqrt{2}}))^{n-1}$\n",
        ">\n",
        "\n",
        "Let us examine how  these expressions can be used.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MLuFKv4cG5Bg"
      },
      "source": [
        "## Case study\n",
        "\n",
        "Let us make some calculations to fix ideas.\n",
        "\n",
        "**Exercise.** Find the common events of MAX if the  the length of the target string is $n = 400$ and the population size, or number of monkeys or number of iid normal distributions, is $m = 200$.\n",
        ">\n",
        "*Answer.* The Binomial $Bi(400, 1/2)$ has mean 200, variance $npq = 400 \\times 1/4 = 100$ and standard deviation is $10$.\n",
        ">\n",
        "The common or usual events lie inside an interval.   The probability to lie below this interval must be 0.025 and must be equal to that of lying above that interval. We can use the cumulative distribution function $F_Y(y)$ to calculate the corresponding interval. The inferior border corresponds with $F_Y(y_i) = 0.025$ and the upper to $F_Y(y_u) = 0.975$. This amounts to use the inverse function of   $F_Y(y)$. This is very scaring. So, we  reused a code developed by Gemini. It must calculate a table with  the common values of $F_Y(y)$ and extract from it the requested values. The code follows:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 929
        },
        "id": "APe5GsaIpuew",
        "outputId": "1ee7a7e1-4e53-4dd7-91c4-20de494fc673"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CDF =  cumulative distribution function\n",
            "Inferior border, i =  436 Fn_z[i] =  0.02543095619033903\n",
            "Inf in units = 2.3600000000000003\n",
            "Superior border, i =  583 Fn_z[i] =  0.9746961740893566\n",
            "Sup in units = 3.83\n",
            "\n",
            "The cdf is strongly concentrated:\n",
            "Fn_z(-2) =  0.0\n",
            "Fn_z(-1) =  1.5197e-320\n",
            "Fn_z(-0.8) =  2.6050384450726256e-270\n",
            "Fn_z(0) =  3.8725919148493183e-121\n",
            "Fn_z(1) =  9.763259144621916e-31\n",
            "Fn_z(2) =  0.00010051900623438682\n",
            "Fn_z(3) =  0.582559480738715\n",
            "Fn_z(4) =  0.9874112127868835\n",
            "Fn_z (5) =  0.9998853459280773\n",
            "Fn_z (6) =  0.9999996053649975\n",
            "Fn_z (7) =  0.999999999488054\n",
            "Fn_z (8) =  0.9999999999997335\n",
            "Fn_z (9) =  1.0\n",
            "Fn_z (10) =  1.0\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program commonEvents.py\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "print(\"CDF =  cumulative distribution function\")\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201)\n",
        "\n",
        "# Define the value of n, the   number of normal random variables\n",
        "n  = 400\n",
        "# Cumulative distribution function of the maximal value\n",
        "# of 400 normal distribution with mean 0 and deviation 1.\n",
        "Fn_z = F(z_values)**n\n",
        "# print(Fn_z)\n",
        "inf = 0\n",
        "sup = 0\n",
        "# Inferior border of the interval with common values\n",
        "for i in range(1000):\n",
        "    if  Fn_z[i] >= 0.025 :\n",
        "      print(\"Inferior border, i = \", i, \"Fn_z[i] = \", Fn_z[i])\n",
        "      inf = -2 + i/100\n",
        "      print(f\"Inf in z units = {inf}\")\n",
        "      break\n",
        "# Superior border of the interval with common values\n",
        "# run i from 1200 until 0 with step -1, in reverse order\n",
        "for i in range(1200, 0, -1):\n",
        "    if  Fn_z[i] <= 0.975 :\n",
        "      print(\"Superior border, i = \", i, \"Fn_z[i] = \", Fn_z[i])\n",
        "      sup = -2 + i/100\n",
        "      print(f\"Sup in z units = {sup}\")\n",
        "      break\n",
        "\n",
        "print()\n",
        "print(\"The cdf is strongly concentrated:\")\n",
        "print(f\"Fn_z(-2) =  {Fn_z[0]}\" )\n",
        "print(f\"Fn_z(-1) =  {Fn_z[100]}\" )\n",
        "print(f\"Fn_z(-0.8) =  {Fn_z[120]}\" )\n",
        "print(f\"Fn_z(0) =  {Fn_z[200]}\" )\n",
        "print(f\"Fn_z(1) =  {Fn_z[300]}\" )\n",
        "print(f\"Fn_z(2) =  {Fn_z[400]}\" )\n",
        "print(f\"Fn_z(3) =  {Fn_z[500]}\" )\n",
        "print(f\"Fn_z(4) =  {Fn_z[600]}\" )\n",
        "print(f\"Fn_z (5) =  {Fn_z[700]}\" )\n",
        "print(f\"Fn_z (6) =  {Fn_z[800]}\" )\n",
        "print(f\"Fn_z (7) =  {Fn_z[900]}\" )\n",
        "print(f\"Fn_z (8) =  {Fn_z[1000]}\" )\n",
        "print(f\"Fn_z (9) =  {Fn_z[1100]}\" )\n",
        "print(f\"Fn_z (10) =  {Fn_z[1200]}\" )\n",
        "\n",
        "# Plot the cumulative distribution functions F^n(z)\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(z_values, Fn_z, label=f'n = {n}')\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('F^n(z)')\n",
        "plt.title(f'CDF  of the Maximum of {n} Normal Distributions with common events')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "# Border: Draw a vertical red line at x = inf\n",
        "plt.axvline(x=inf, color='red', linestyle='--', linewidth=2)\n",
        "plt.axvline(x=sup, color='red', linestyle='--', linewidth=2)\n",
        "plt.legend([\"cdf\", \"borders of common events\" ])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBmB1Jk2S90D"
      },
      "source": [
        "The most striking result is that the max-variable is strongly concentrated. Its significant values lie in the interval [2, 5]. Observe that the cdf is not symmetric around its mean, predicting that  the density bell is not symmetric, it must be spread towards higher values. Thus, the max-variable has a small bias towards high values.\n",
        "\n",
        "**Exercise.** Test the aforementioned prediction that the bell of the max-variable is not symmetric but is spread towards the right wing.\n",
        ">\n",
        "*Answer.* We add the bell to the drawing made by the previous program. The bell corresponds with the probability density function. This can be calculated by the reported  formulae, but since we need to test just  the shape of the bell and not its accurate values, we follow a very simple procedure: the probability density function is the derivative of the cumulative distribution function. At each point, it is the tangent of the inclination angle of the tangent line, $\\Delta y/\\Delta x$. We only calculate $\\Delta y$ and by trial and error adjust the maximal value of the graph to fit into the space of the old graphic. The code follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 946
        },
        "id": "G9iErZZyf4in",
        "outputId": "7fc1c986-0a75-4584-cd5d-991eeb480853"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CDF =  Cumulative Distribution Function\n",
            "PDF =  Probability Density Function\n",
            "Inferior border, i =  436 Fn_z[i] =  0.02543095619033903\n",
            "Inf in units = 2.3600000000000003\n",
            "Superior border, i =  583 Fn_z[i] =  0.9746961740893566\n",
            "Sup in units = 3.83\n",
            "\n",
            "The cdf is strongly concentrated:\n",
            "Fn_z(-2) =  0.0\n",
            "Fn_z(-1) =  1.5197e-320\n",
            "Fn_z(-0.8) =  2.6050384450726256e-270\n",
            "Fn_z(0) =  3.8725919148493183e-121\n",
            "Fn_z(1) =  9.763259144621916e-31\n",
            "Fn_z(2) =  0.00010051900623438682\n",
            "Fn_z(3) =  0.582559480738715\n",
            "Fn_z(4) =  0.9874112127868835\n",
            "Fn_z (5) =  0.9998853459280773\n",
            "Fn_z (6) =  0.9999996053649975\n",
            "Fn_z (7) =  0.999999999488054\n",
            "Fn_z (8) =  0.9999999999997335\n",
            "Fn_z (9) =  1.0\n",
            "Fn_z (10) =  1.0\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program bell_of_MAX.py\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "print(\"CDF =  Cumulative Distribution Function\")\n",
        "print(\"PDF =  Probability Density Function\")\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201)\n",
        "\n",
        "# Define the value of n, the   number of normal random variables\n",
        "n  = 400\n",
        "# Cumulative distribution function of the maximal value\n",
        "# of 400 normal distribution with mean 0 and deviation 1.\n",
        "Fn_z = F(z_values)**n\n",
        "# print(Fn_z)\n",
        "inf = 0\n",
        "sup = 0\n",
        "# Inferior border of the interval with common values\n",
        "for i in range(1200):\n",
        "    if  Fn_z[i] >= 0.025 :\n",
        "      print(\"Inferior border, i = \", i, \"Fn_z[i] = \", Fn_z[i])\n",
        "      inf = -2 + i/100\n",
        "      print(f\"Inf in units = {inf}\")\n",
        "      break\n",
        "# Superior border of the interval with common values\n",
        "# run i from 1200 until 0 with step -1, i.e., in reverse order\n",
        "for i in range(1200, 0, -1):\n",
        "    if  Fn_z[i] <= 0.975 :\n",
        "      print(\"Superior border, i = \", i, \"Fn_z[i] = \", Fn_z[i])\n",
        "      sup = -2 + i/100\n",
        "      print(f\"Sup in units = {sup}\")\n",
        "      break\n",
        "\n",
        "print()\n",
        "print(\"The cdf is strongly concentrated:\")\n",
        "print(f\"Fn_z(-2) =  {Fn_z[0]}\" )\n",
        "print(f\"Fn_z(-1) =  {Fn_z[100]}\" )\n",
        "print(f\"Fn_z(-0.8) =  {Fn_z[120]}\" )\n",
        "print(f\"Fn_z(0) =  {Fn_z[200]}\" )\n",
        "print(f\"Fn_z(1) =  {Fn_z[300]}\" )\n",
        "print(f\"Fn_z(2) =  {Fn_z[400]}\" )\n",
        "print(f\"Fn_z(3) =  {Fn_z[500]}\" )\n",
        "print(f\"Fn_z(4) =  {Fn_z[600]}\" )\n",
        "print(f\"Fn_z (5) =  {Fn_z[700]}\" )\n",
        "print(f\"Fn_z (6) =  {Fn_z[800]}\" )\n",
        "print(f\"Fn_z (7) =  {Fn_z[900]}\" )\n",
        "print(f\"Fn_z (8) =  {Fn_z[1000]}\" )\n",
        "print(f\"Fn_z (9) =  {Fn_z[1100]}\" )\n",
        "print(f\"Fn_z (10) =  {Fn_z[1200]}\" )\n",
        "\n",
        "# The Bell\n",
        "bell = []\n",
        "for i in range(1200):\n",
        "    delta_y = Fn_z[i+1] - Fn_z[i]\n",
        "    #delta_x = z_values[i+1] - z_values[i]\n",
        "    #bell.append(delta_y/delta_x)\n",
        "    bell.append(100*delta_y)\n",
        "bell.append(0.0) # to enabling pairing with the other graph\n",
        "\n",
        "#Plots\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Plot the cumulative distribution functions F^n(z)\n",
        "plt.plot(z_values, Fn_z, label=f'n = {n}')\n",
        "# Border: Draw a vertical red line at x = inf\n",
        "plt.axvline(x=inf, color='red', linestyle='--', linewidth=2)\n",
        "\n",
        "# Draw the bell\n",
        "plt.plot(z_values, bell )\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('F^n(z)')\n",
        "plt.title(f'CDF and PDF of the Maximum of {n} Normal Distributions, and common events')\n",
        "plt.grid(True)\n",
        "plt.legend([\"cdf\", \"borders of common events\", \"bell or pdf in arbitrary height\" ])\n",
        "# Superior border\n",
        "plt.axvline(x=sup, color='red', linestyle='--', linewidth=2)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s6M9OWE2VwQg"
      },
      "source": [
        "The observation was verified: the bell is asymmetric and is a bit spread towards the right wing. This means that high values are preferred with respect to lower ones.\n",
        "\n",
        "*Challenge.* The bell that was reported in the last example has a theoretical origin. Compare it with a bell, which comes from a simulation with coins or binary strings.  \n",
        "\n",
        "*Challenge.* By the graphic, the mean of the max-variable for 400 monkeys is located circa 3, in $z$-units. Test this appreciation and find a better estimation.\n",
        "\n",
        "**Exercise.** Make a simulation to test the prediction given by the previous analysis: for 400 monkeys, ordinary values lie in within 2.3 and 3.8 standard deviations above the mean.  \n",
        "\n",
        "*Answer.* The following code, made with the help of Gemini,  simulates 400 monkeys or binary strings that must match a target string 400 bits long. The MAX is registered, and many repetitions are made. According to previous graphics, the prediction is that ordinary values lie in within 2 and 4 above $0$ in a standard normal distribution, or in within 2 and 4 standard deviations above the mean in whatever normal distribution. The mean of the $Bi(400, 1/2)$ is 200, the variance is $npq= 400/4 = 100$, whence the standard deviation is $10$. The ordinary values must lied in within 2 and 4 standard deviations above the mean, that is  $[200 + 2 * 10, 200 + 4 * 10 = [220, 240]$ with the mode around 2.6 standard deviations above the mean, 200 + 2.6 * 10 = 226$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i4tVf8FdVoL7",
        "outputId": "9f37bd3b-c076-4dfd-d85b-8b88b6c428ab"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Lab: 400 Monkey match a target string\n",
            "Purpose: Best of 400 random strings matches a target string\n",
            "Date of Experiment  = 2025-11-22 15:32:11.023831\n",
            "alphabet =  01\n",
            "Target string length: 400\n",
            "Population size: 400\n",
            "Mean number of matches : 200.0\n",
            "Standard deviation: 10.0\n",
            "best_fitness =  236\n",
            "best_fitness =  235\n",
            "best_fitness =  229\n",
            "best_fitness =  234\n",
            "best_fitness =  229\n",
            "best_fitness =  234\n",
            "best_fitness =  236\n",
            "best_fitness =  226\n",
            "best_fitness =  230\n",
            "best_fitness =  231\n",
            "best_fitness =  226\n",
            "best_fitness =  236\n",
            "best_fitness =  225\n",
            "best_fitness =  229\n",
            "best_fitness =  227\n",
            "best_fitness =  229\n",
            "best_fitness =  235\n",
            "best_fitness =  229\n",
            "best_fitness =  233\n",
            "best_fitness =  228\n",
            "best_fitness =  226\n",
            "best_fitness =  239\n",
            "best_fitness =  227\n",
            "best_fitness =  228\n",
            "best_fitness =  243\n",
            "best_fitness =  229\n",
            "best_fitness =  229\n",
            "best_fitness =  228\n",
            "best_fitness =  229\n",
            "best_fitness =  224\n",
            "best_fitness =  231\n",
            "best_fitness =  225\n",
            "best_fitness =  229\n",
            "best_fitness =  229\n",
            "best_fitness =  227\n",
            "best_fitness =  229\n",
            "best_fitness =  226\n",
            "best_fitness =  231\n",
            "best_fitness =  237\n",
            "best_fitness =  225\n",
            "best_fitness =  230\n",
            "best_fitness =  232\n",
            "best_fitness =  232\n",
            "best_fitness =  231\n",
            "best_fitness =  227\n",
            "best_fitness =  235\n",
            "best_fitness =  230\n",
            "best_fitness =  229\n",
            "best_fitness =  226\n",
            "best_fitness =  234\n",
            "best_fitness =  234\n"
          ]
        }
      ],
      "source": [
        "# Program testOfCommonEvents.py\n",
        "\n",
        "from io import RawIOBase\n",
        "import datetime\n",
        "import random\n",
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt # Import matplotlib for plotting\n",
        "\n",
        "\n",
        "# Define parameters\n",
        "alphabet = '01'\n",
        "string_length = 400\n",
        "population_size = 400\n",
        "target_string = ''.join(random.choice(alphabet) for _ in range(string_length))\n",
        "mean = string_length / 2\n",
        "std_dev = np.sqrt(string_length / 4)\n",
        "\n",
        "print(f\"Lab: 400 Monkey match a target string\")\n",
        "print(f\"Purpose: Best of 400 random strings matches a target string\")\n",
        "print(f\"Date of Experiment  = {datetime.datetime.now()}\")\n",
        "print(f\"alphabet =  {alphabet}\")\n",
        "# print(f\"Target string = {target_string}\")\n",
        "print(f\"Target string length: {string_length}\")\n",
        "print(f\"Population size: {population_size}\")\n",
        "print(f\"Mean number of matches : {mean}\")\n",
        "print(f\"Standard deviation: {std_dev}\")\n",
        "\n",
        "\n",
        "\n",
        "def create_population(population_size, target_string, alphabet):\n",
        "    \"\"\"Creates a new population with random strings.\"\"\"\n",
        "    # print(\"create_population9b(population_size, target_sequence, alphabet)\")\n",
        "    population = []\n",
        "    for _ in range(population_size):\n",
        "        random_string = ''.join(random.choice(alphabet) for _ in range(len(target_string)))\n",
        "        population.append(random_string)\n",
        "    # print(\"initial population\")\n",
        "    # print(population)\n",
        "    return population\n",
        "\n",
        "def calculate_fitness(my_string, target_string):\n",
        "    \"\"\"Calculates the fitness of a string based on its similarity to the target sequence.\"\"\"\n",
        "    #  print(\"\\n *calculate_fitness(string, target_sequence)\")\n",
        "    fitness = 0\n",
        "    for i in range(len(my_string)):\n",
        "        if my_string[i] == target_string[i]:\n",
        "            fitness += 1\n",
        "    # print(string, \"  fitness: \", fitness)\n",
        "    return fitness\n",
        "\n",
        "def calculate_all_fitness(population, target_string):\n",
        "    # print(\"\\n*calculate_all_fitness(population, target_sequence)\")\n",
        "    \"\"\"Calculates the scores in the population.\"\"\"\n",
        "    fitness_scores = [calculate_fitness(string, target_string) for string in population]\n",
        "    # print(\"fitness_scores: \", fitness_scores)\n",
        "    return fitness_scores\n",
        "\n",
        "def select_the_best(population, target_string):\n",
        "    \"\"\"Selects the string with the MAX score.\"\"\"\n",
        "    fitness_scores = calculate_all_fitness(population, target_string)\n",
        "    best_fitness = max(fitness_scores)\n",
        "    best_string_index = fitness_scores.index(best_fitness)\n",
        "    best_string = population[best_string_index]\n",
        "    # print(\"\\n*select_the_best(population)\")\n",
        "    # print(\"best_fitness = \", best_fitness)\n",
        "    # print(\"The best string = \", best_string )\n",
        "    return best_fitness, best_string\n",
        "\n",
        "def basic_routine(target_string):\n",
        "    \"\"\"A population is created, and the best is picked up\"\"\"\n",
        "    population = create_population(population_size, target_string, alphabet)\n",
        "    calculate_all_fitness(population, target_string)\n",
        "    return select_the_best(population, target_string)\n",
        "\n",
        "def main():\n",
        "    for _ in range(50):\n",
        "        best_fitness, best_string = basic_routine(target_string)\n",
        "        print(\"best_fitness = \", best_fitness)\n",
        "        #print( \"The best string = \", best_string )\n",
        "    print(\"best_fitness = \", best_fitness)\n",
        "    #print( \"The best string = \", best_string )\n",
        "    #print( \"Target  string  = \", target_string )\n",
        "\n",
        "main()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kzqexsgd8MeJ"
      },
      "source": [
        "*Assessment:* The prediction is perfectly fulfilled: the reported values lie inside the interval $[224, 243]$ while the prediction is $[220, 240]$.\n",
        "\n",
        "*Frustration as a challenge.*  Finding the MAX in a population is helpful, but not too much because all events are strongly concentrated not very far from the mean. In the previous example, the usual values of MAX are below 240, while perfection means 400.  Therefore, while the MAX means overcome mediocrity, it is predicted that higher values appear at a high price in the number of trials. In simple words: MAX changes mediocrity into low-quality.  \n",
        "\n",
        "**Exercise.** Defend yourself against the previous accusation: low-quality is the inferno of a population created at random.\n",
        ">\n",
        "*Answer.*  There, where Python sees a 0, mathematics sees a positive value. For instance, the probability for a single chromosome of solving at once the full task of matching 1000 bits is $2^{-1000}$ that is not zero. This value is low but given enough time to repeat many trials, a moment will come when the correct result will appear. This was discussed before:\n",
        "\n",
        "\n",
        "one monkey\n",
        "https://colab.research.google.com/drive/1sb63vEjlQ2WtEh3iC-6qINaZ2T84tXNB?usp=sharing\n",
        "\n",
        "The prescribed  time maybe longer than the age of the Universe. What happens when instead of 1 chromosome or monkey we have 400? The answer is almost the same:\n",
        "\n",
        "many monkeys\n",
        "https://colab.research.google.com/drive/1dEykeQxNXZY0eVfC4fFnNhKdKvUbm7Wr?usp=sharing\n",
        "\n",
        "\n",
        "What happens  if our target is to pick the max? To know that, we need here our formulae for the cumulative distribution function of the Standard Normal Distribution $F$, its density $f$, which is the derivative of $F$, and that of the probability density function of MAX, $f_Y$:\n",
        ">\n",
        ">$F (y) = ∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}}dt$\n",
        ">>\n",
        ">$f_{Y}(y) = n f(y) F(y)^{n-1}$.\n",
        ">>\n",
        ">$  f_{Y}(y) = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}} dt)^{n-1}$\n",
        ">\n",
        " We might  also use the following notation\n",
        ">\n",
        ">$f_{Y}(y) = n (pdf) ( CDF)^{n-1}$.\n",
        ">>\n",
        ">where pdf is the probability density function of the normal distribution and CDF is the cumulative distribution function of the standard normal distribution. CDF might also be written as cdf.\n",
        "\n",
        "\n",
        "To get a feel for the involved values, we asked Colab for help:\n",
        ">\n",
        "The code for calculating $f_Y(y)$ for values of $y= 10, 20, 30, 40, 50$\n",
        ">\n",
        "Gemini offered the following code:\n",
        " \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vZOPSTDwm33t",
        "outputId": "014016a3-7baa-4e95-ffcc-5abd0931f20e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Calculating the probability density function of the maximum for n = 400\n",
            "--------------------------------------------------\n",
            "f_Y(10) = 3.0778394507e-20\n",
            "f_Y(20) = 2.2083793449e-85\n",
            "f_Y(30) = 5.8945845395e-194\n",
            "f_Y(40) = 0.0000000000e+00\n",
            "f_Y(50) = 0.0000000000e+00\n",
            "--------------------------------------------------\n"
          ]
        }
      ],
      "source": [
        "# Program pdfOfMax.py\n",
        "\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the probability density function of the standard normal distribution\n",
        "f = norm.pdf\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "# Define the value of n, the number of normal random variables\n",
        "n = 400\n",
        "\n",
        "# Define the values of y for which to calculate the PDF\n",
        "y_values = [10, 20, 30, 40, 50]\n",
        "\n",
        "print(f\"Calculating the probability density function of the maximum for n = {n}\")\n",
        "print(\"-\" * 50)\n",
        "\n",
        "for y in y_values:\n",
        "    # Calculate the probability density function of the maximum\n",
        "    # f_Y(y) = n * f(y) * F(y)**(n-1)\n",
        "    f_Y_y = n * f(y) * (F(y)**(n-1))\n",
        "    print(f\"f_Y({y}) = {f_Y_y:.10e}\")\n",
        "\n",
        "print(\"-\" * 50)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "17USUAT2pEwt"
      },
      "source": [
        "The program shows that to ask for perfect matching of a target binary string 1000 bits long by a random assignation of bits of 400 strings is impossible.\n",
        "\n",
        "### Making sense of tiny probabilities.\n",
        "\n",
        "According to the previous example, the reported results by Python rapidly arrive to zero, as a rounding, approximating procedure. The literal reading is that events with tiny probability are not realized. This is, indeed, a philosophical directive. The barrier that separates tiny, irrealizable probabilities is put around $10^{-50}$, but a more prudent value would be $10^{-1000}$, as it was discussed [somewhere else](https://ejristos.com/dl/DarwinAtFaceValue.pdf) (https://ejristos.com/dl/DarwinEnSerio.pdf). We prefer the directive that says that if something has a non nil probability, it may happen, and the underlying mechanism can be put forward as an explanation of the phenomenon that one wants to explain. Nevertheless, tiny probabilities are a challenge to create or adopt something else that must render a wider comprehension that warms the hearth.  \n",
        "\n",
        "How is our directive implemented? The first step is to see that behind the zero reported by Python, there are positive values.\n",
        "\n",
        "**Exercise.** Do your best to extend the capability of Python of computing values of the probability density function, as it was output by the last program.\n",
        ">>\n",
        ">*Answer.* We imagine at first that a viable procedure could be to use the output of Python for low values to find a regression polynomial, and use this to extrapolate to higher values. But numbers are so tiny that this resulted impossible. So, we decided to try with logarithms:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 824
        },
        "id": "5_SBBHR6yk0K",
        "outputId": "332113ba-98fc-4d37-b536-2867a962bbf4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Calculating the probability density function of the maximum for n = 400\n",
            "--------------------------------------------------\n",
            "f_Y(1) = 1.1231652185059721e-28\n",
            "f_Y(2) = 2.2213841012263757e-03\n",
            "f_Y(3) = 1.0341220831930895e+00\n",
            "f_Y(4) = 5.2859860349439541e-02\n",
            "f_Y(5) = 5.9461979296394896e-04\n",
            "f_Y(10) = 3.0778394506825678e-20\n",
            "f_Y(15) = 2.2122838199377668e-47\n",
            "f_Y(20) = 2.2083793448639053e-85\n",
            "f_Y(25) = 3.0615718945677575e-134\n",
            "f_Y(30) = 5.8945845395141902e-194\n",
            "f_Y(35) = 1.5761585108544097e-264\n",
            "--------------------------------------------------\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x785bd3bcdc70>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program log_of_pdf_of_MAX.py\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the probability density function of the standard normal distribution\n",
        "f = norm.pdf\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "# Define the value of n, the number of normal random variables\n",
        "n = 400\n",
        "\n",
        "# Define the values of y for which to calculate the PDF\n",
        "y_values = [1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 35]\n",
        "\n",
        "print(f\"Calculating the probability density function of the maximum for n = {n}\")\n",
        "print(\"-\" * 50)\n",
        "\n",
        "log_pdf_values = []\n",
        "for y in y_values:\n",
        "    # Calculate the probability density function of the maximum\n",
        "    # f_Y(y) = n * f(y) * F(y)**(n-1)\n",
        "    f_Y_y = n * f(y) * (F(y)**(n-1))\n",
        "    print(f\"f_Y({y}) = {f_Y_y:.16e}\")\n",
        "    log_pdf_values.append(np.log(f_Y_y))\n",
        "\n",
        "print(\"-\" * 50)\n",
        "\n",
        "\n",
        "#Plots\n",
        "plt.figure(figsize=(10, 6))\n",
        "# plot pdf_values against y_values\n",
        "plt.plot(y_values, log_pdf_values, label=f'n = {n}')\n",
        "plt.xlabel('z')\n",
        "plt.ylabel(' log_pdf_values')\n",
        "plt.title(f'Log of the pdf values of the Maximum of {n} Normal Distributions')\n",
        "plt.grid(True)\n",
        "plt.legend([\"Log\"  ])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ERB_NLEn0qw6"
      },
      "source": [
        "*Our comment.* We see that the logarithms of those tiny numbers that represent probabilities of getting a high MAX value are enveloped by a very soft curve that above 5 looks like a simple parable.\n",
        "\n",
        "**Exercise.** Test, or prove, or reject the aforementioned proposition that the logarithm of the pdf values of the maximum of 400 normal distributions is described by a parable, at least above 5 $z$-uits.\n",
        ">\n",
        "*Answer.* Let us consider the pdf of MAX\n",
        ">\n",
        "> $f_{Y}(y) = n (pdf) ( CDF)^{n-1}$.\n",
        ">>\n",
        ">>> $    = n (  \\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}) (∫^y_{-\\infty}\\frac{1}{\\sqrt{2 \\pi}} e^{-\\frac{t^2}{2}} dt)^{n-1}$\n",
        ">\n",
        "Our interest is in the pdf value for high $y$, say 5 or above. For those values, the pdf is almost zero, $\\epsilon_1$, while the CDF is almost 1, $1-\\epsilon_2 $.  If we accept this,   $ f_{Y}(y)  $  can be schematically represented as\n",
        ">>\n",
        "> $ f_{Y}(y) = n  \\epsilon_1  (1-\\epsilon_2)   = n  (\\epsilon_1  -  \\epsilon_1 \\times  \\epsilon_2) \\sim  n  \\epsilon_1 $\n",
        ">>\n",
        "Therefore, our former expression is approximated by\n",
        ">>\n",
        "> $ f_{Y}(y) = \\frac{n}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}$\n",
        ">\n",
        "Taking logarithms, we get\n",
        ">>\n",
        "> $ log (f_{Y}(y)) =   log( \\frac{n}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}})$\n",
        ">>\n",
        "> $ log (f_{Y}(y))  = log(\\frac{n}{\\sqrt{2 \\pi}} ) - \\frac{y^2}{2}$\n",
        ">>\n",
        "> and this is an inverted parable, such as the parable found by Python. We urgently need to know the relation between these two parables. The code is the following\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 894
        },
        "id": "N4GjRi4ndDPC",
        "outputId": "692955b1-cab4-450d-d185-4ddb9abfe0e6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Calculating the probability density function of the maximum for n = 400\n",
            "--------------------------------------------------\n",
            "f_Y(1) = 1.1231652185059721e-28\n",
            "f_Y(2) = 2.2213841012263757e-03\n",
            "f_Y(3) = 1.0341220831930895e+00\n",
            "f_Y(4) = 5.2859860349439541e-02\n",
            "f_Y(5) = 5.9461979296394896e-04\n",
            "f_Y(10) = 3.0778394506825678e-20\n",
            "f_Y(15) = 2.2122838199377668e-47\n",
            "f_Y(20) = 2.2083793448639053e-85\n",
            "f_Y(25) = 3.0615718945677575e-134\n",
            "f_Y(30) = 5.8945845395141902e-194\n",
            "f_Y(35) = 1.5761585108544097e-264\n",
            "--------------------------------------------------\n",
            " square root of ( 2 pi)) = 2.5066282746310002, its inverse = 0.3989422804014327\n",
            "ln(10) = 2.302585092994046\n",
            "lg(e) in base 10 = 0.4342944819032518\n",
            "lg(e) in base 10 / 2 = 0.2171472409516259\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x78a7342974a0>"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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Tp05Zy7/99ts7vvdvlhXnjGEYxoULFwwPDw/j22+/TXU8t37Wurm53dYWhmEYCxcuNABj8eLFhmEYxogRIwwgzc+bp59+2qhWrdpd47n5czMsLMzInTu30bJlS+v6Wz9TLl++bDg6OhqNGjVK9RpMnDjRAIzp06dby+rWrWsAxpQpU1LtM+V88fX1NcLCwqzlH3/8sQEY5cqVS3V+dejQwXB0dEz1+XC/n0t3UrduXePJJ5+84/o//vjDAIxx48ZZywICAozOnTtbH6fn8+ndd99N87xOeU08PT2Ny5cvp7kurfdXjx49rGUWi8Vo1qyZ4ejoaFy5csUwjIx9Dt8pNsMwbnt/pvfvf8r53aBBA8NisVjL33//fcPOzs7a/imv792+c8jjT0MNRe4gKSmJpUuX0qpVK4oUKWItz58/Px07dmTdunVEREQAsHjxYqpXr55qanNvb29efvnle+7nwoUL7Nq1iy5duuDt7W0tL1u2LA0bNmTRokWZd1A3KV26NLVr17Y+9vX1pWTJkpw4ccJaNnfuXGrXrk3u3Lm5evWqdWnQoAFJSUmsWbPmnvspUKCAtTcHkn917tSpEzt37uTixYtA8gXP1apVo0qVKqniSc/rdycmk4k2bdqwaNEiIiMjreW//fYbBQsWpFatWtaym3vWbty4wdWrV6lduzbR0dGphrbdr9DQUFasWEHbtm2t27969SrXrl2jcePGHD16lHPnzgHJ1+/t37+fo0ePZmgfixYtokqVKqmOy93dnW7dunHy5EkOHDjwwMeRlrfffjvV49q1a992Dnl5edGwYcNU51ClSpVwd3e/bejf3XTs2JFjx46xdetW679pDTOE5F/wU64DtFgshIaGkpiYSOXKlW+bNe+pp55i8ODBTJs2jcaNG3P16lVmzpyZ7gvtb57oJleuXJQsWRI3Nzfatm1rLS9ZsiS5cuVK9dpkVOnSpalevbr1ccov7s888wyFCxe+rfxe+8qqc+ajjz6iSJEi95wAKCYmJs1RASnX2sTExKT69051U9anh5eXF7179+bvv/++Y0/ZsmXLiI+Pp3fv3ql649588008PT1TDcVMieu1115Lc1tt2rTBy8vL+jilbV555ZVU51fVqlWJj4+3fg5A1n8u3SplZscbN27csc79fj7d7KWXXrIOY06Pm2crTZm9ND4+nmXLlt13DPeSkb//Kbp165Zq6GLt2rVJSkri1KlTwP+uzV6wYAEJCQlZFrtkb0q8RO7gypUrREdHU7JkydvWPfHEE1gsFuv01qdOnaJYsWK31Uur7FYpH8p32s/Vq1eJiorKaPj3dPMXtRS5c+dOdd3N0aNHWbx4Mb6+vqmWBg0aAP+b7ONuihUrdts1ISVKlACwXsNy6tSpVDOYpUjrNcmIdu3aERMTY72OKjIykkWLFlmvkUuxf/9+XnjhBby8vPD09MTX19d6AfrN1zvcr2PHjmEYBp999tltr+XAgQOB/72Wn3/+OWFhYZQoUYIyZcrQt29f9uzZc899nDp16o7nUMr6zObs7HzbF6i0zqHw8HDy5s1727FHRkam6xxKUaFCBUqVKsXPP//M7NmzyZcvH88888wd68+cOZOyZctar0Xx9fVl4cKFabZp3759KVeuHFu2bGHgwIGULl06XTGl9Rp4eXlRqFCh2857Ly+vDF3Xdqtb37MpX+j9/f3TLL/XvrLinNm0aROzZs1izJgx95wNz8XFJc3ZDmNjY63rb/73TnVvHZJ8L7169SJXrlx3vNbrTp/Jjo6OFClS5LbXpWDBgnec7OdB2iyrP5dulfIDlYeHxx3r3O/n080yMtTWbDanSnzg9r8fWSEjf/9T3NrWuXPnBv7XpnXr1uWll15i8ODB+Pj48PzzzzNjxow0z2t5fOkaL5EcKuX6plsZN120bLFYaNiw4W0zyaVI+QOYXVWrVo3AwEDmzJlDx44d+eeff4iJiaFdu3bWOmFhYdStWxdPT08+//xzihYtirOzMzt27OCjjz666yQid5pkIK3JJSB5ZrbGjRun+ZyUJL1OnTocP36cv/76i6VLlzJt2jTGjBnDlClT7tmD8LDd6Ry6mcViIW/evMyePTvN9Rn55RuSe72++eYbPDw8aNeu3R2/3P/000906dKFVq1a0bdvX/LmzYudnR3Dhg3j+PHjt9U/ceKE9Vf8vXv3pjueO70G6Xl/pff8yYx9PSz9+vWjdu3aBAUFWb8YX716FUju3T99+rT1C2r+/Pm5cOHCbdtIKStQoIC1Xkr5rQnLhQsXUvWUp0dKr9egQYPSfX3Y3dwt8bvfNnuQz6X7tW/fPuDuPxhmxudTRhPle8no+yir3KtNTSYT8+bNY9OmTfzzzz8sWbKE119/nVGjRrFp06YccS85UeIlcke+vr64urpy+PDh29YdOnQIs9ls/RIQEBDAsWPHbquXVtmtUm6AfKf9+Pj44ObmltHw0zXz2L0ULVqUyMhIaw/X/Ujp7bk5niNHjgBY7y8WEBCQ5tCVtF6TjGrbti3jxo0jIiKC3377jcDAQKpVq2Zdv2rVKq5du8b8+fOpU6eOtTwkJOSe2075RfPWmc5u/UU85RdbBweHdL2W3t7evPbaa7z22mtERkZSp04dBg0adNcvNgEBAXc8h1LWZ1RmnUPLli2jZs2amfKFq2PHjgwYMIALFy7c9QL5efPmUaRIEebPn5/qOFJ6GG9msVjo0qULnp6e9O7dm6FDh9K6detUs+1lhZvPn5unas+K3sm0ZMU5c/r0aU6dOpVmr0bLli3x8vKyvl/Kly/P2rVrsVgsqRLozZs34+rqav1hJ2UI97Zt21IlWefPn+fs2bN069Ytw3H27t2bsWPHMnjw4Numyb/5M/nm3pb4+HhCQkIe6PMwvR7kc+l+JCUl8fPPP+Pq6ppq6Gla7vX5lBmfGyksFgsnTpxI9SPfrX8/0vs5nJHYMvL3P6OqVatGtWrV+PLLL/n55595+eWX+fXXX7PdD2uSNTTUUOQO7OzsaNSoEX/99VeqIQ2XLl3i559/platWnh6egLQuHFjNm7cyK5du6z1QkND7/gr/83y589P+fLlmTlzZqo/HPv27WPp0qU0bdr0vuJPSdZu/WOUEW3btmXjxo0sWbLktnVhYWEkJibecxvnz5/njz/+sD6OiIjgxx9/pHz58uTLlw9IvkfTpk2b2LJli7XelStX0vX63Uu7du2Ii4tj5syZLF68ONV1N/C/Xylv7h2Ij49n8uTJ99x2QEAAdnZ2t13rdutz8+bNS7169fj222/T/IX/5imHr127lmqdu7s7xYoVu+dwlKZNm7JlyxY2btxoLYuKimLq1KkEBgame+jczVLuRfSg51BSUhJDhgy5bV1iYmKGt120aFHGjh3LsGHD7trTkVa7bt68OdXrk2L06NFs2LCBqVOnMmTIEGrUqEH37t2tPTVZJWWa9ZvPn6ioKGbOnJml+02RFefM1KlT+eOPP1ItPXr0AGDkyJGp3tOtW7fm0qVLqWZ1u3r1KnPnzqVFixbWa7qefPJJSpUqxdSpU1P1YnzzzTeYTCbrPcAyIqXX66+//kr1uQ3QoEEDHB0dGT9+fKrz5/vvvyc8PPyOM/5lpgf5XMqopKQkevbsycGDB+nZs6f171pa0vP5lBl/e242ceJE6/8Nw2DixIk4ODjw7LPPAun/HM5IbBn5+59e169fv60XOuVHBQ03zDnU4yU53vTp01m8ePFt5b169eKLL74gODiYWrVq8c4772Bvb8+3335LXFwcX3/9tbVuv379+Omnn2jYsCE9evSwTidfuHBhQkND7/kr24gRI3juueeoXr06Xbt2tU4n7+Xlle57ztyqfPny2NnZMXz4cMLDw3FycuKZZ54hb9686d5G3759+fvvv2nevLl1qvmoqCj27t3LvHnzOHnyJD4+PnfdRokSJejatStbt27Fz8+P6dOnc+nSJWbMmGGt069fP2bNmkWTJk3o1auXdTr5gICADF8/cKuKFStSrFgx/u///o+4uLhUwwwheTr63Llz07lzZ3r27InJZGLWrFnpGqbl5eVFmzZtmDBhAiaTiaJFi7JgwYI0r1uaNGkStWrVokyZMrz55psUKVKES5cusXHjRs6ePWu9X1Tp0qWpV68elSpVwtvbm23btjFv3rxUF5inpX///vzyyy8899xz9OzZE29vb2bOnElISAi///77Pa+3SYuLiwulS5fmt99+o0SJEnh7e/PUU0/x1FNPpXsbdevW5a233mLYsGHs2rWLRo0a4eDgwNGjR5k7dy7jxo3L8BfnXr163bNO8+bNmT9/Pi+88ALNmjUjJCSEKVOmULp06VSTrRw8eJDPPvuMLl260KJFCyB5Gu/y5cvzzjvvMGfOnAzFlhGNGjWicOHCdO3alb59+2JnZ8f06dPx9fXl9OnTWbbfFFlxzjRq1Oi2spQvuXXr1k01JXzr1q2pVq0ar732GgcOHMDHx4fJkyeTlJTE4MGDU21jxIgRtGzZkkaNGtG+fXv27dvHxIkTeeONN1LdJiMjevXqxZgxY9i9e3eqUQW+vr58/PHHDB48mCZNmtCyZUsOHz7M5MmTefrpp2+7AXFWeJDPpbsJDw/np59+ApJvrXHs2DHmz5/P8ePHad++fZo/kNwsPZ9PlSpVAqBnz540btwYOzs72rdvf1/xOjs7s3jxYjp37kzVqlX5999/WbhwIZ988ol1mHJGPoczElt6//6n18yZM5k8eTIvvPACRYsW5caNG3z33Xd4enre9w+s8giywUyKItlCyhSwd1rOnDljGIZh7Nixw2jcuLHh7u5uuLq6GvXr1081pXOKnTt3GrVr1zacnJyMQoUKGcOGDTPGjx9vAMbFixfvGc+yZcuMmjVrGi4uLoanp6fRokUL48CBA6nqZGQ6ecMwjO+++84oUqSIYWdnl2q63YCAgDSnBK5bt65Rt27dVGU3btwwPv74Y6NYsWKGo6Oj4ePjY9SoUcMYOXKkER8ff9f9p+xnyZIlRtmyZQ0nJyejVKlSaca/Z88eo27duoazs7NRsGBBY8iQIcb3339/39PJ3+z//u//DCDVVOQ3W79+vVGtWjXDxcXFKFCggNGvXz/rVN03T1Gc1rTNV65cMV566SXD1dXVyJ07t/HWW28Z+/btu20aY8MwjOPHjxudOnUy8uXLZzg4OBgFCxY0mjdvbsybN89a54svvjCqVKli5MqVy3BxcTFKlSplfPnll/d8rVO237p1ayNXrlyGs7OzUaVKFWPBggW31SMDU4Nv2LDBqFSpkuHo6JhquuU7tcOdpkifOnWqUalSJcPFxcXw8PAwypQpY/Tr1884f/78Xfd/83Tyd3PrMVksFmPo0KFGQECA4eTkZFSoUMFYsGBBqjZMTEw0nn76aaNQoUKppvw2DMMYN26cARi//fabYRh3nu46rdfgTtN2p/W+2759u1G1alXD0dHRKFy4sDF69Og7Tief1ns2rbZMiXXEiBFpv1g3yYpz5lZ3u3VHaGio0bVrVyNPnjyGq6urUbdu3TtOt/3HH38Y5cuXt37Gfvrpp+l6X9ztczPl/EqrHSdOnGiUKlXKcHBwMPz8/Izu3bsb169fT1XnTm19pza4UyxpvUYP8rmUlpSp71MWd3d3o3jx4sYrr7xiLF26NM3n3DqdfHo+nxITE40ePXoYvr6+hslksn4e3O28vNv76/jx40ajRo0MV1dXw8/Pzxg4cGCqaf4NI/2fw3eKzTBun07eMNL39/9O5/et09zv2LHD6NChg1G4cGHDycnJyJs3r9G8eXNj27Ztab728ngyGYYNrr4VySF69+7Nt99+S2RkZLomInjcBAYG8tRTT7FgwQJbhyIiIiJiU7rGSyST3HovmWvXrjFr1ixq1aqVI5MuEREREfkfXeMlkkmqV69OvXr1eOKJJ7h06RLff/89ERERfPbZZ7YOTURERERsTImXSCZp2rQp8+bNY+rUqZhMJipWrMj333+faipgEREREcmZdI2XiIiIiIhIFtM1XiIiIiIiIllMiZeIiIiIiEgW0zVeGWSxWDh//jweHh73vCmuiIiIiIg8vgzD4MaNGxQoUOCeN55X4pVB58+fx9/f39ZhiIiIiIhINnHmzBkKFSp01zpKvDLIw8MDSH5xPT09M/TchIQEli5dSqNGjXBwcMiK8OQBqH2yL7VN9qb2yb7UNtmb2id7U/tkX9mpbSIiIvD397fmCHejxCuDUoYXenp63lfi5erqiqenp81PErmd2if7Uttkb2qf7Ettk72pfbI3tU/2lR3bJj2XIGlyDRERERERkSymxEtERERERCSLKfESERERERHJYrrGS0RERETkP4ZhkJiYSFxcHPb29sTGxpKUlGTrsOQmCQkJD7VtHBwcsLOze+DtKPESEREREQHi4+O5cOEC0dHRGIZBvnz5OHPmjO7dms087LYxmUwUKlQId3f3B9qOEi8RERERyfEsFgshISHY2dlRoEAB7O3tiYqKwt3d/Z43xpWHy2KxEBkZ+VDaxjAMrly5wtmzZylevPgD9Xwp8RIRERGRHC8+Ph6LxYK/vz+urq5YLBYSEhJwdnZW4pXNWCwW4uPjH1rb+Pr6cvLkSRISEh4o8dJZJCIiIiLyHyVZcqvMGs6oM0tERERERCSLKfESERERERHJYkq8RERERETkoTKZTPz555/Wx4cOHaJatWo4OztTvnx5m8WVlTS5hoiIiIjII6xLly6EhYWlSmQeNQMHDsTNzY3Dhw8/8LTt2ZUSLxERERERsanjx4/TrFkzAgICbB1KltFQQxERERGRNBiGQXR8ok0WwzAy5RhWr15NlSpVcHJyIn/+/PTv35/ExETr+hs3bvDyyy/j5uZG/vz5GTNmDPXq1aN3797p2n5gYCBDhgyhQ4cOuLm5UbBgQSZNmpSqztGjR6lTpw7Ozs6ULl2a4ODgVOtNJhPbt2/n888/x2QyMWjQoAc97Gwpx/Z4TZo0iREjRnDx4kXKlSvHhAkTqFKliq3DEhEREZFsIjbBQoXhwfeumAUOfN4YV8cH+6p+7tw5mjZtSpcuXfjxxx85dOgQb775Js7Oztbkpk+fPqxfv56///4bPz8/BgwYwI4dOzJ0ndWIESP45JNPGDx4MEuWLKFXr16UKFGChg0bYrFYePHFF/Hz82Pz5s2Eh4ffltRduHCBBg0a0KRJEz788EMNNXyc/Pbbb/Tp04cpU6ZQtWpVxo4dS+PGjTl8+DB58+a1dXgiIiIiIg9s8uTJ+Pv7M3HiREwmE6VKleL8+fN89NFHDBgwgKioKGbOnMnPP//Ms88+C8CMGTMoUKBAhvZTs2ZN+vfvD0CJEiVYv349Y8aMoWHDhixbtoxDhw6xZMkS63aHDh3Kc889Z31+vnz5sLe3x93dnXz58mXS0Wc/OTLxGj16NG+++SavvfYaAFOmTGHhwoVMnz7detI8Eq6fhPM7wdEDHN3AyR0c/1uc3MHeGTLphm8PwmIxSLQYONprZKuIiIg8OpwdzOwb1NAmN1V2cbB74G0cPHiQ6tWrp7oBcM2aNYmMjOTs2bNcv36dhISEVKO+vLy8KFmyZIb2U7169dsejx071hqDv79/qmTu1vo5RY5LvOLj49m+fTsff/yxtcxsNtOgQQM2btx4W/24uDji4uKsjyMiIgBISEggISEhQ/tOqZ/R592J6egK7Be9f8f1hskuOQFzSE7KDEf35ATtv+Qs1eNU6z3ANQ+Gmw+45gEH13THZLEYnL4ezd5zEf8t4Ry4cIPo+CRyuTjg6+FIXg9n8no44uvhhK+HE3ndncjr+b//uzg++AfN/cjs9pHMo7bJ3tQ+2ZfaJntT+2QvCQkJGIaBxWLBYrFgGAYmkwkXB7tUicvDYhhGuq/zSqlrsVjuWZ7y/5TjvPX/Nz/31rK77f/muilxp7yON+/3TjFkZJ8p28xIjA8i5TgSEhKws0v9PTUj798cl3hdvXqVpKQk/Pz8UpX7+flx6NCh2+oPGzaMwYMH31a+dOlSXF3Tn5Dc7NYLCu9XvrCTFHUrib0lBntLHPZJsf/9Px4Ak5EEseHJyw2434+MRLMj8faexNl7EmfvQby9B3H2HsTZeRKKJ2cSPQmJ8+RwjAf7o70ITXJJczthMQmExSRw9HLUXffnbGfg6QBejgaejuDpAJ6OKWXJ//dyAOcsOnszq30k86ltsje1T/altsne1D7Zg729Pfny5SMyMpL4+Hhr+Y0bN2wYVfokJCSQmJho7SBIUaRIEf755x/Cw8OtyePy5cvx8PDA09MTOzs7HBwcWLNmDS1btgQgPDycI0eOULVq1du2lxaLxcK6detS1V27di3FihUjIiKCwoULc+bMGY4cOWIdRrhixQoAYmJirM9LSkoiLi4uXftM8bDaJj4+npiYGNasWZNqYhKA6OjodG8nxyVeGfXxxx/Tp08f6+OIiAj8/f1p1KgRnp6eGdpWQkICwcHBNGzYEAcHh0yIrinwWaoSA0iwJEFCNMRFQnwkpvgbEB8F8f89jouEhKib1kemXh97A2KuQdRVTJYE7C3x2MdfxTX+6r1DcoAYe0du2HmR4OSN2d0HFy8/HLzyEeGYlyt2eblAHs4kenM6xpkrkfFciYzjUkQcVyLjiE2wEJtkIjYJLsfePVXM5eJAoI8rQXlcCczjRpBP8r+BeVzvq9cs89tHMovaJntT+2RfapvsTe2TvcTGxnLmzBnc3d1xdnbGMAxu3LiBh4eHTXq8MsLBwYHo6GhOnDiRqvy9995jypQpfPrpp7z77rscPnyY4cOH8/7775MrVy5y5cpFp06dGDRoEAULFiRv3rwMGjQIs9mMk5NTur7rms1mtmzZwrfffsvzzz/PsmXL+Ouvv/jnn3/w9PSkZcuWlChRgh49evD1118TERHBsGHDAHBxcbHuw87OLt37fNhtExsbi4uLi3VmxptlJFHMcYmXj48PdnZ2XLp0KVX5pUuX0ryYz8nJCScnp9vKHRwc7vtD8kGem849gJMzuHvf9xYu34hl75kwDp06z5mzp7l08Rx2MdfwNkXgQwTepgi8TTfwMUVQwCEKH/MNPJLCsLPE42KKx8VyBWKuQMxhuJK8TTcgP1DWGqYreBUCz4JQoBCGVyFiXfMTap+XS/hw1uLNxWi4HBHH5RtxXIqI5cqN5P9HxiUSFpPArjPh7DoTflv8BbycCfJ1I8jHjSAfd4r4JP+/UG4X7O3uPk4769tH7pfaJntT+2RfapvsTe2TPSQlJWEymTCbzZjNZusQtpSy7MxkMrFq1SoqVaqUqrxr164sWrSIvn37UqFCBby9venatSufffaZ9ZjGjBnD22+/TcuWLfH09KRfv36cPXsWFxeXdB/3Bx98YJ0O3tPTk9GjR1snzzCbzfzxxx907dqVatWqERgYyPjx42nSpIn1tb75ONKzz4fdNmazGZPJlOZ7NSPv3RyXeDk6OlKpUiWWL19Oq1atgOTGW758Oe+9955tg8sGVhy6xKd/7ON8eOxNpQ5AIHbmIErk9aBsQS8KFPKiWCEvSubzwMn+v94lw0juNYu6CtHX/vv3KkRdgRuXIPwMRJyD8LPJZQnRcPVI8kLyUEgXoOB/S0UAV5/k5MyrEBQuZE3Uol3zc8bw41ikMyHXojhxNYqQq1GcuBJFeEwC58NjOR8ey/pj11Idn73ZROE8rtZELMjHnSAfN4r4upHbOXt/qIqIiIik5YcffuCHH3644/otW7bccZ2HhwezZ8+2Po6KimLw4MF069Yt3fv39PRkzpw5d1xfokQJ1q5dm6rs1uvXdu3ale79PapyXOIFyfcr6Ny5M5UrV6ZKlSqMHTuWqKgo6yyHOVVkXCIfzt1DaFQ8JhMU83WnTCEvyhXKRZlCXpTO74nz3WbYMZnAySN58Q66+84SYv+XhIWf/e//Z/57/F95QlRy4hZ9FS7sSvV0V6AkUNLZC/IUS16eLAZ5ihLhGsBxSz6Oh0PI1UhrQnbyWhSxCRZOXEl+fCs3JzsKOZs56XqCmsV9KVsol2ZiFBERkcfazp07OXToEFWqVCE8PJzPP/8cgOeff97GkT1+cmTi1a5dO65cucKAAQO4ePEi5cuXZ/HixbdNuJHTzFgXQmhUPEE+bvzToxbuTll4ejg4Q56iyUtaDANirqdOzm5dIs4lTxxybnvy8h9PoAJQwaPAf/soBkHFsHgX5YpTAMcT8nA8NJ6QK1HWxOzM9Rii4pI4HGfm8PJjjFl+DGcHM5UCclMtKA9Vi+ShnL/X/3r3RERERB4TI0eO5PDhw9aRYWvXrsXHx4e1a9emut/WrSIjIx9ilI++HJl4QfLFhhpa+D/h0QlMXZt8QWbvBsWzNulKD5MJXL2Tl3xl0q6TEAOhIXDtGFw7CteO//f/Y8lDHW+cT15OJndtmwE/wM9sT43cgckJWYFiUKYoCbmKcjwxL9NWHSHSrSBbT17nWlQ8649dsw5XdLJPTsSqBuWhWhFvyvnnunsPoIiIiEg2V6FCBbZv357musqVK99zCODJkyczP6jHVI5NvCS1qWuPcyM2kZJ+HrQom7G7lduMgwv4lU5ebhUdCqEnkpOwq0f/S8j+S8wSY/6XoKVsCigFfO6QB2ffBpia1eKkR0XWXXVnU0gom09c42pkPBuOX2PD8eREzNHeTMXCuf5LxPJQobASMREREXl8uLi4UKxYMVuH8dhQ4iVcjYxjxvqTAPRpVAKzOXtPmZouKb1lhSqnLrdY4MaF/yVeNy3G9VO4JlyDvb/B3t8IAoI8C/JqYC2M52py2rMia696sPnkdTaduMaVG3FsOhHKphOhjFt+FEd7M+X9c1GtSB6qBXlTMSC3EjERERERAZR4CfDNquNExydRrpAXjUo/5te5mc3gVTB5KVI31arEqDC2zp9EVb8E7M5sTL5uLOIc7PkN057fCAACPArwSmBNjMa1OONVkXXXvNgUEsqmE9e4fCOOLSGhbAkJZTzgaJeciFUt4k21InmoWDj3fd1fTEREREQefUq8crgL4THM2nQKgA8alcz2NwjMUo5uXPF8Ckv9ptg5OCTfVPrMFji1Hk6ug7Pbkq8Z2zsX0965FAY6uuejY2AtjEY1OZerEmtDc7E5JLkX7GJELFtOhrLlZCgTVhzDwc5EuUL/S8QqBeTG1VFvQREREZGcQN/6crgJK44Rn2ihSqA3tYv72Dqc7MXRDYrWT14A4qPh7NabErGtEHkR9s3DtG8ehYAO7n50CKiJ0bAW53NVYt313GwKSR6aeCE8lm2nrrPt1HUmrTyOvdlE2UJeVCuSPGti5YDcuNl6UhMRERERyRL6lpeDnb4WzZytZwD4sHEO7+1KD0fX5OGJKUMUE2KSe8FOrktOxs5sgchLsH8+pv3zKQi0c/OlXUBNjGdrcSF3ZdaF5flvso5QzoXFsON0GDtOhzF5VXIiVqaQl3XWxMqB3rafXVJEREREMoW+1eVgY5cfIdFiUKeEL1WCvG0dzqPHwQWCaicvkHxT6HPb4OT65Cnsz26FqCtw4E9MB/6kANDW1Ye2gTWhfi0ueldmbVgeNp8MY9OJa5y9HsPO02HsPB3GlNXHsTObeKqgF9WCkocmVg7MjYezg00PWURERCQ7MZlM/PHHH7Rq1SrN9SdPniQoKIidO3dSvnz5hxrbrZR45VDHLt/gz53nAPigYQkbR/OYcHCGwFrJCx9BYlzyBB0pidiZLRB9FQ78BQf+Ih/QxsWbNoE1oV5tLuWuxLqIvGwKuc7mkFBOh0az+0wYu8+E8e2aE5hNJCdiRf7XI+apRExERCTH69KlC2FhYfz555+2DkXuQolXDjU6+AgWAxqV9qOcfy5bh/N4sneCgBrJS92+kBgP53ckJ2En18OZzRATCgf/gYP/4Ae85JKblwJqQp1aXMrzNOsj8rI5JIxNIdc4dS2aPWfD2XM2nKn/JWJPFvCi6n89Yk8HeePlokRMREREHm1JSUmYTCbMZrOtQ8lUj9fRSLrsOxfOor0XMZmSZzKUh8TeEQpXgzp9odOf8NEpeH0pPDsAij4DDm4Qcx0OLYDF/fGb/SwvBtdmeMJXrK51gK1dfRnbtgwdqvgT5OOGxYC958KZti6EN37cRvnPl9Js/FqGLDjA0v0XCYuOt/URi4iIPNoMI3mWY1sshpEph7B69WqqVKmCk5MT+fPnp3///iQmJlrX37hxg5dffhk3Nzfy58/PmDFjqFevHr17907X9gMDAxkyZAgdOnTAzc2NggULMmnSpFR1Ro8eTZkyZXBzc8Pf35933nmHyMhI6/offviBXLly8ffff1O6dGmcnJw4ffo0W7dupWHDhvj4+ODl5UXdunXZsWPHbTFcuHCB5557DhcXF4oUKcK8efPuGvO+fft47rnncHd3x8/Pj1dffZWrV6+m63gfhHq8cqDRwUcAaFmuACXzedg4mhzM3hEKV01ean8ASQlwfhecWpc8YcfpTRAbBocXwuGF+AKtnL1oVbgG1KjFNd+nWReZn00h4WwOucaJK1HsPx/B/vMRfL8uBJMJSuXzpNp/09dXCfQmt5ujjQ9aRETkEZIYg/mrJ2yz70/OJ8+w/ADOnTtH06ZN6dKlCz/++COHDh3izTffxNnZmUGDBgHQp08f1q9fz99//42fnx8DBgxgx44dGboeasSIEXzyyScMHjyYJUuW0KtXL0qUKEHDhg0BMJvNjB8/nqCgIE6cOME777xDv379mDx5snUb0dHRDB8+nGnTppEnTx7y5s3LiRMn6Ny5MxMmTMAwDEaNGkXTpk05fPhwqv1/9tlnfPXVV4wbN45Zs2bRvn179u7dyxNP3N52YWFhPPPMM7zxxhuMGTOGmJgYPvroI9q2bcuKFSsy/iJngBKvHGb7qeusOHQZO7OJ3g10bVe2YucA/k8nL7Xeh6REuLA7eWjiqfVwaiPEhsORf+HIv+QBnnfy4vmA6lCtJqG+VVgfVYBNJ8PZdOIax69EcfBCBAcvRDBj/UkASuXzsF4jViUoD95KxERERB5bkydPxt/fn4kTJ2IymShVqhTnz5/no48+YsCAAURFRTFz5kx+/vlnnn32WQBmzJhBgQIFMrSfmjVr0r9/fwBKlCjB+vXrGTNmjDXxurn3LDAwkC+++IK33347VeKVkJDA5MmTKVeunLXsmWeeSbWfqVOnkitXLlavXk2dOnWs5W3atOGNN94AYMiQIQQHBzNhwoRU208xceJEKlSowNChQ61l06dPx9/fnyNHjlCiRNZ9P1bilcOMWpr8C0HrioUI8nmwX1Eki9nZQ6FKyUut3smJ2MU9yb1hJ9fB6Y0QFw5HFsORxXgDLRw9aBFQHarVItT3aTZGF2LjyXA2nwjl6OVIDl28waGLN/hhw0kASvp5UK2IN1WL5KFKkDc+7k62PGIREZHsxd4FS/+ztrnWyMH1gTdx8OBBqlevnuqWQTVr1iQyMpKzZ89y/fp1EhISqFKlinW9l5cXJUtm7FKU6tWr3/Z47Nix1sfLli1j2LBhHDp0iIiICBITE4mNjSU6OhpX1+TjdHR0pGzZsqm2c+nSJT799FNWrVrF5cuXSUpKIjo6mjNnztxz/7t27Uoz1t27d7Ny5Urc3d1vW3f8+HElXpI5Nhy7yobj13C0M9OzQXFbhyMZZWcPBSsmLzV7giXpv0Tsvxs6n9qQnIgdXQpHl+INNHN0p1nhalClFmF+Vf9LxCLYdOIaRy5FcvjSDQ5fusHMjacAKJ7X/b8eseREzNdDiZiIiORgJlPycL/HbJKHh+nkyZM0b96c7t278+WXX+Lt7c26devo2rUr8fHx1sTLxcXltnvKdu7cmWvXrjFu3DgCAgJwcnKievXqxMff/3XskZGRtGjRguHDh9+2Ln/+/Pe93fRQ4pVDGIbBiP96uzpU8adgLhcbRyQPzGwHBSokLzXeS07ELu37r0dsffLwxNgwOLYMji0jF/CcgxvPFa4GlWsS7leVjTGF2XTqBptOXOPQxRscvRzJ0cuRzNqUnIgVy+tunTWxahFv8no42/KIRUREJAOeeOIJfv/9dwzDsCY169evx8PDg0KFCpE7d24cHBzYunUrhQsXBiA8PJwjR46kGsp3L5s2bbrtccr1Vdu3b8disTBq1Chrz+GcOXPStd3169czefJkmjZtCsCZM2fSnARj06ZNdOrUKdXjChUqpLnNihUr8vvvvxMYGIi9/cNNhZR45RArD19m5+kwnB3MvPtMMVuHI1nBbAf5yyUv1d8FiwUu7//f0MRT65NnTTy+HI4vxwto4uBKE/+qULEWEX5V2RgXwMaTN9gcEsrBCxEcuxzJscuRzN58GoAivm7JSdh/yZifpxIxERGR7CA8PPy24XXdunVj7Nix9OjRg/fee4/Dhw8zcOBA+vTpg9lsxsPDg86dO9O3b1+8vb3JmzcvAwcOxGw239b7dDfr16/n66+/plWrVgQHBzN37lwWLlwIQLFixUhISGDChAm0aNGC9evXM2XKlHRtt3jx4syaNYvKlSsTERFB3759cXG5vfNg7ty5VK5cmVq1ajF79my2bNnC999/n+Y23333Xb777js6dOhAv3798Pb25tixY/z6669MmzYNOzu7dB93RinxygEsFoORS5JnMuxcI1C9FjmF2Qz5yiQv1br/l4gdSE7AUu4lFhMKJ1bCiZV4Ao3tXWhcuCqUr8WN56qyKTaQjaci2XTiGgcvRnDiShQnrkTx83+JWJCPW/I1YkHJwxPzeencEhERsYVVq1bd1svTtWtXFi1aRN++fSlXrhze3t507dqVTz/91Fpn9OjRvP322zRv3hxPT0/69evHmTNncHZO/9/0Dz74gG3btjF48GA8PT0ZPXo0jRs3BqBcuXKMHj2a4cOH8/HHH1OnTh2GDRuWqofqTr7//nu6detGxYoV8ff3Z+jQoXz44Ye31Rs8eDC//vor77zzDvnz5+eXX36hdOnSaW6zQIECrF+/no8++ohGjRoRFxdHQEAATZo0yfJr+UyGkUk3CcghIiIi8PLyIjw8HE9Pzww9NyEhgUWLFtG0aVMcHB7ejW4X7rnAuz/vwN3JnrX96mtK8TuwVfvYjMUCVw791xv2X69Y9LXUdeydwb8KBNYmMl9VNsUXSR6aGHKN/ecjbrvFSGAe1+QkrGhyMlYgk4a05ri2ecSofbIvtU32pvbJXmJjYwkJCSEoKAhnZ2csFgsRERF4eno+djfyvZuoqCgKFizIqFGj6Nq16z3rBwYG0rt373Tf9yszPOy2ufXcuFlGcgP1eD3mkiwGo4OTr+3qWitISZf8j9kMfqWTl6rdkm/UeOXwf71h/w1NjLoCIWsgZA3uQAN7ZxoUehrK1CKyUVW2JhRlw6lINoeEsu9cOCevRXPyWjS/bUuebaiwt+v/esSK5tG1hSIiItnMzp07OXToEFWqVCE8PJzPP/8cgOeff97GkT1+lHg95v7ceY7jV6LI5erAG7WDbB2OZGcmE+QtlbxUeTM5Ebt65H/DEk+ug6jL/z1eiztQ386J+oWehidrEtWwGlsTirLxdDSbTlxj77lwTodGczo0mjnbzgJQKLdLqmvE/L0ffKpcEREReTAjR47k8OHDODo6UqlSJdauXYuPjw9r167lueeeu+PzIiMjH2KUjz4lXo+x+EQLY5cnX9v1dt2ieDhrGINkgMkEviWTl6ffSE7Erh1LnYhFXkwepnhqHW5APTtH6hWsDKVrEd2gGluTirHhdDSbT4Sy91w4Z6/HMG/7WeZtT07ECuZyoWqR5CSsepE8FMp9+1SyIiIiknUqVKjA9u3b01xXuXLlO94PK8XJkyczP6jHlBKvx9icbWc4ExqDj7sTnasH2jocedSZTOBTPHmp/HpyIhZ64n9DE0+ugxsX4PQGOL0BV6Cu2YG6BStBqVrEPFudbZbibDgdk9wjdjacc2ExzN9xjvk7zgFQwMvZOnV9tSJ5KOztqkRMRETERlxcXChWTLNhZxYlXo+p2IQkJqw4CsB79Yvi4ph1U2NKDmUyQZ6iyUulLjclYv9dH3ZyHUScgzOb4MwmXIDaZntqF6wEJWoSW78G2yzF2Xg2lk0nQtl9Jozz4bHM33mO+TuTE7F8ns5UK+JN5YBcxMfa9GhFRCSH0LxzcqvMOieUeD2mftp0iksRcRTM5UKHqoVtHY7kBKkSsc7Jidj1k6kTsfAzcGYznNmMM6OpZbanVoEKULwWsfWqs9MoyfozcWwOucauM2FcjIjlz13n+XPXecCe5RHb6VQjkGdL5cXeLufMMCUiIlkvZWbJ6OjoNO8VJTlXfHw8wAPf40uJ12MoKi6Rb1YdB6Dns8Vwsldvl9iAyQTeQclLxVeTy66fuumGzusg7DSc3Qpnt+LMGKqb7KheoDwUrUVc3RrsNEqy4Ww8G45fZfup66w/fo31x6+R38uZjlUK066Kv+5LJyIimcLOzo5cuXJx+fJlAJydnYmPjyc2NjZHTSf/KLBYLA+tbSwWC1euXMHV1RV7+wdLnZR4PYZ+2HCSa1HxBOZx5cWKhWwdjsj/5A5IXiq8nPw47PT/Juo4uRbCTsG57XBuO06Mo5rJTLX85ekVVJ1gRzd2+rVgzo6LXAiPZVTwEcYtP0qTp/LxarUAqgR563owERF5IPny5QPg8uXLGIZBTEwMLi6a+Cm7edhtYzabKVy48APvS4nXYyY8JoFvVyf3dr3fsAQOGo4l2VmuwlC+MJTvkPw47Mz/hiWeXAfXQ+D8DuzO76AJ0PjGb3xY7zWWOjbg+x0R7DgdxoI9F1iw5wIl/Nx5tVoArSoU1AyeIiJyX0wmE/nz5ydv3rzExMSwevVq6tSpoxtcZzMJCQmsWbPmobWNo6NjpvSsKfF6zHy35gQRsYmU9POgRdkCtg5HJGNy+UOu9lCuffLj8HNwaj2W46tI3PcHjmGncFgxiGZ2w2j25Ascr9aeaSHe/LnrAkcuRfLZX/v56t9DvFCxIK9UC6BUvrvfQV5ERCQtdnZ2ODk5kZiYiLOzsxKvbMbOzu6RbBslXo+Rq5FxTF8fAkCfRiUwm9UtLo84r4JQti1JT7zAUurRxD8G++3T4cIu2PMrRff8yrB8Zfms2Wv8Hl+NGVsvc+JKFD9tOs1Pm05TJdCbV6oH0OTJfDjaq/dXREREbEeJ12NkyqrjRMcnUbaQF41K+9k6HJFMlWR2wij3AlTunHwd2NbvYd/vcHEProvf51UnL14p34GdeV/iu4N2LD1wiS0nQ9lyMhQfd0faP12YDlULUzCXZqoSERGRh08/AT8mLobH8uOmUwB80KikLgKVx1vBStBqMvQ5CI2+gNxBEBeOafMUKv7TkG+SBrPtxRh6PxNEXg8nrkbGM3HlMWoPX8GbP25jzZErWCy6T4uIiIg8POrxekxMWHGU+EQLVQK9qVPcx9bhiDwcrt5QowdUexdOrEjuBTuyGEJWkztkNb09CtCjRmdWuTVh2q5YNp64RvCBSwQfuERgHldeqRZA60qFyOXqaOsjERERkcecerweA2dCo/lt6xkAPmhUQr1dkvOYzVCsAXT4BXrthtofgKsP3DiP3ephPLv4WX7J9Q3r29nTpXoAHk72nLwWzRcLD1J16HL6zt3NnrNhtj4KEREReYwp8XoMjF12lESLQe3iPlQtksfW4YjYVq7C8OwA6HMAXvoeClcHSyIc+JOCf7Vl0JnX2dboBCOaB1IqnwdxiRbmbj9Ly4nreX7iOuZuO0NsQpKtj0JEREQeM0q8HnHHLt/gj51nAfiwUUkbRyOSjdg7QZnW8PpieHs9VH4dHNzg6mGcgvvTZnVD/i06n0XtvGhVvgCOdmZ2nw2n77w9VB26nC8XHuDk1ShbH4WIiIg8JpR4PeLGLDuKxYBGpf0o55/L1uGIZE/5noLmY+CDQ9B0JPiWgoQoTNtnUPqvZoyN6s/2Vtfp3yiIgrlcCI9J4Lu1IdQbuYpO07cQfOASSZqMQ0RERB6AJtd4hO0/H87CPRcwmZLv2yUi9+DsCVXehKffgFPrYes0OPgPnNmEx5lNvO3qQ7dKr7Ixdwu+25vE6iNXWPPfUjCXCx2rFqZtZX98PZxsfSQiIiLyiFHi9QhbuOcCAC3KFqBUPk8bRyPyCDGZILBW8nLjIuz4EbbNgBvnMa8fQ03GUrNEYy63foXvLxVhzrZznAuLYcSSw4xddoTnnsrPK9UCeDowtyazERERkXRR4vUI69u4JNWK5CEgj6utQxF5dHnkg7r9oFYfOPJvci/YiVVwZDF5jyzm49yBfFivC4vtG/D9zgh2nQnj793n+Xv3eUrl8+CVagG0qlAQdyd9nIqIiMid6RqvR5jJZKJOCV8C8rjZOhSRR5+dPTzRAjr9Be9tg2rvgJMXXD+Jw4pBtFj+LH8WmMXydm60r1wIZwczhy7e4NM/91Ft6HIG/LWPI5du2PooREREJJtS4iUiciuf4tBkWPJkHC0nQL6ykBQHu3+h6F/P89W1HuxodpHBzwVRxMeNyLhEftx4ikZj1tDu2438s/s88YkWWx+FiIiIZCMaGyMicieOrlCxE1R4Fc5th63fw77f4cJuXC/0prOzF53KdWSH30tM3W8i+MAlNoeEsjkkFB93JzpU8adDlcIUyOVi6yMRERERG1OPl4jIvZhMUKgyvPBNci9YwyGQOxBiwzFt/oZKfzfgW2MI21rH0uuZIHw9nLgaGceEFceoNXwF3X7cxrqjV7FoSnoREZEcSz1eIiIZ4eoNNXtC9ffg+IrkyTiOLIYTq/A+sYr3PQrQs0YXVro2YdruaDadCGXpgUssPXCJIB83Xq5amDaV/PFydbD1kYiIiMhDpB4vEZH7YTZD8QbQ8VfotTt5VkRXH7hxHrvVQ2mw5Bl+zf0ta9s50LlaYdyd7Am5GsUXCw9Sddgy+s3bzd6z4bY+ChEREXlIlHiJiDyo3AHQYCD0OQAvTgP/amBJhP1/4P9XGwafe4PtjUMY3jyQUvk8iE2wMGfbWVpMXMfzk9Yzb/tZYhOSbH0UIiIikoU01FBEJLPYO0HZNsnLxb3Jk3HsmQNXDuG09CPaObjRtmw7DtRpzdQjrizae4HdZ8LYfSaMLxYeoG1lf16uWli3iBAREXkMqcdLRCQr5CsDLcbCBwfhuRHgUxISojBtn86TfzdlXPTHbH8+nI8aBlEwlwth0QlMXXOCuiNW0Xn6FpYduESSJuMQERF5bKjHS0QkKzl7QdVuUOVNOLkueTKOQwvg9EY8T2+ku5svb1XuxAav5ny3N5HVR65Yl4K5XOhYtTDtnvbHx93J1kciIiIiD0CJl4jIw2AyQVDt5CXiAuz4EbbPgBsXMK8bRS3TGGqVaMLFNq8w/WIgc7af41xYDCOWHGbssiM0LZOfV6sFUCkgNyaTydZHIyIiIhmkoYYiIg+bZ36o9xH03gttZ0FQXTAscHgR+f7pyCfHXmZr/YOMfz6Acv65SEgy+GvXeVpP2chz49Yye/MpouISbX0UIiIikgFKvEREbMXOAUq3hM5/w7tboWp3cPKC6yE4LB9Ay+XP8lfB2QS3c6dt5UI42Zs5dPEG//fHPqoOXc7Av/Zx9NINWx+FiIiIpIMSLxGR7MC3BDz3VfJkHC3GJ0/OkRgLu2ZT/K+WfB3ai50tLjGwSSBBPm5ExiUyc+MpGo5ZQ/upG1m45wIJSRZbH4WIiIjcga7xEhHJThzdoFJnqNgJzm5Lnoxj/3w4vxPX8zt5zTkXXcp1ZHveF5i638yyg5fYdCKUTSdCyevhRPsqhelQxZ/8Xi62PhIRERG5iXq8RESyI5MJ/J+GF7+FPgehwWDIVRhiwzBtnkzlfxoylS/Y9lIcPesH4uPuxOUbcYxffpRaw1fy9qztrD92FcPQlPQiIiLZgXq8RESyOzcfqNUbavSAY8uTe8GOLoUTK/E+sZI+ngXpWbMLK1wbM21XNFtCQlm8/yKL91+kiK8br1QN4KVKhfBycbD1kYiIiORY6vESEXlUmO2gRCN4eQ702gU1e4NrHog4h/3qL2m05BnmeE9lTVtHXq1aGDdHO05cieLzBQeoOnQZ/X/fw75z4bY+ChERkRxJiZeIyKModyA0HAzvH4AXpkKhKmBJhP3zKfx3a4acf5PtTU7xVfNASvp5EJtg4detZ2g+YR0vTF7P/B1niU1IsvVRiIiI5BiPTOL15ZdfUqNGDVxdXcmVK1eadU6fPk2zZs1wdXUlb9689O3bl8TE1Pe6WbVqFRUrVsTJyYlixYrxww8/ZH3wIiJZxcEZyrWDN4LhrTVQsTM4uMKVgzgv7Uf7NY1YXPxPFrTLTctyBXCwM7HzdBh95uym+rDlDPv3IKevRdv6KERERB57j0ziFR8fT5s2bejevXua65OSkmjWrBnx8fFs2LCBmTNn8sMPPzBgwABrnZCQEJo1a0b9+vXZtWsXvXv35o033mDJkiUP6zBERLJO/nLQcnzyZBxNhkOe4hAfiWnb9zz113OMj/mEba3C6dcgiAJezlyPTuDb1SeoO3Ilr83YwopDl0iyaDIOERGRrPDITK4xePBggDv2UC1dupQDBw6wbNky/Pz8KF++PEOGDOGjjz5i0KBBODo6MmXKFIKCghg1ahQATzzxBOvWrWPMmDE0btz4YR2KiEjWcskF1d6Gqm9ByJrkyTgOLYTTG/A6vYF33Hx5++lOrPNqzrS9iaw5coWVh5OXQrldeLlqAG0rFyKPu5Otj0REROSx8cgkXveyceNGypQpg5+fn7WscePGdO/enf3791OhQgU2btxIgwYNUj2vcePG9O7d+47bjYuLIy4uzvo4IiICgISEBBISEjIUY0r9jD5PHg61T/altnkA/jWSl4gLmHf9iHnnj5giL2FeN4rapjHUKt6YCy91ZPqFQObtvMDZ6zEMX3yI0cGHafpUPl6u4k95fy9MJtMdd6H2yb7UNtmb2id7U/tkX9mpbTISw2OTeF28eDFV0gVYH1+8ePGudSIiIoiJicHF5fYbjg4bNsza23azpUuX4urqel+xBgcH39fz5OFQ+2RfapsHVQZTsWHkC9tB0NUV+EYewHTkXwoe+Zf3nfxoke8Z/qEOSy97ciYK/tp9gb92X6Cgq0GtfBYq+Rg42d1562qf7Ettk72pfbI3tU/2lR3aJjo6/ddJ2zTx6t+/P8OHD79rnYMHD1KqVKmHFNHtPv74Y/r06WN9HBERgb+/P40aNcLT0zND20pISCA4OJiGDRvi4KD76WQ3ap/sS22T2VoCg0i4egTzjh8w7/kF97hLlL/wC+Xs/+D/nnyRw/5tmBaSmwV7LnIu2sJvJ+xYeM6eFyoU4OUq/hT1dbNuTe2Tfaltsje1T/am9sm+slPbpIyGSw+bJl4ffPABXbp0uWudIkWKpGtb+fLlY8uWLanKLl26ZF2X8m9K2c11PD090+ztAnBycsLJ6fbrHBwcHO67oR/kuZL11D7Zl9omk+V/EpqNgAYDYd882DIN06W9mPb8zBN7fmZUgYoMadGF32KeZubWS5y8Fs2sTaeZtek0NYrm4dVqATQo7UdKk6h9si+1Tfam9sne1D7ZV3Zom4zs36aJl6+vL76+vpmyrerVq/Pll19y+fJl8ubNCyR3P3p6elK6dGlrnUWLFqV6XnBwMNWrV8+UGEREHklO7lCpS/JU9Ge3Jk/Gsf8POL8D1/M7eM05F13Kv8JW31Z8t9/E8oOX2HD8GhuOX8PP04m2lQqSN97WByEiIpK9PTLTyZ8+fZpdu3Zx+vRpkpKS2LVrF7t27SIyMhKARo0aUbp0aV599VV2797NkiVL+PTTT3n33XetPVZvv/02J06coF+/fhw6dIjJkyczZ84c3n//fVsemohI9mAygX8VeHFq8pT0DQaBV2GIDcO0aSJV/mnAd6ahbG2dQI96Qfi4O3IpIo4JK0/wxS47vlsXQlyibsosIiKSlkcm8RowYAAVKlRg4MCBREZGUqFCBSpUqMC2bdsAsLOzY8GCBdjZ2VG9enVeeeUVOnXqxOeff27dRlBQEAsXLiQ4OJhy5coxatQopk2bpqnkRURu5eYDtd6HXrug4xwo3ggwwfHl5PmnMx8cbMumWrv49gV/nirgSVySia+XHKXxmDUsO3AJw9D9wERERG72yMxq+MMPP9zxHl4pAgICbhtKeKt69eqxc+fOTIxMROQxZraDEo2Tl9AQ2D4DdsyC8DPYr/qCxubhNCjZnMl2FZl5/QlOXovmjR+3UaeELwOaP0GxvB62PgIREZFs4ZHp8RIRERvzDoKGnycPQ3zhWyj0NFgSsDv4B+9dGcC6J/6gT43cONqZWXPkCo3HrmXwP/sJj7H9fVZERERsTYmXiIhkjIMzlGsPbyyDbquxPPkiJgyc986m5/52bKp3gMalvEmyGMxYf5L6I1cxe/MpkiwafigiIjmXEi8REbl/BcqT1Goqa4p/hiVfOYiLwHv953x74z3+aRxNsbzuhEbF839/7KP5hHVsOnHN1hGLiIjYhBIvERF5YNfdi5P0ejC0nAhuvnDtGGVWv8HSvBMY9Ywrns72HLwQQfupm3h39g7OXo+2dcgiIiIPlRIvERHJHCYzVHwVeuyAGj3B7ID5WDAvbWrN5koreL2yN2YTLNx7gWdHrWZ08BFi4jX9vIiI5AxKvEREJHM5e0KjIfDuZijRBCyJuGyfwoATr7Cu4VmqBXoRl2hh/PKjPDNqFX/vPq/p50VE5LGnxEtERLJGnqLQ8Td4+XfwKQHRVymwph+/mD7hl8YGBXO5cCE8lp6/7KTNlI3sOxdu64hFRESyjBIvERHJWsUbQPcN0HgYOHlhurCb6qtfZk2RWQyo44mzg5ltp67TYuI6+v++h6uRcbaOWEREJNMp8RIRkaxn5wDV34GeO6BSF8CE3YH5vL6jDVtqbqd12TwYBvy69Qz1R6xi2toTxCdabB21iIhIplHiJSIiD4+bD7QYB2+tgcI1IDEGz00jGHnpDZY3CeWpAh7ciEvki4UHaTJ2DSsPXbZ1xCIiIplCiZeIiDx8+cvCa4ug9QzwLAThZyi66j3+cR/Gtw0c8HF35MTVKF77YSuvzdjC8SuRto5YRETkgSjxEhER2zCZ4KkX4b2tUO8TsHfBdHoDjde3Y8NT/9C7em4c7EysPHyFxmPW8OXCA0TEJtg6ahERkfuixEtERGzL0RXqfZScgD31EhgWHHfNpPeB9mysf5iGJb1JtBh8tzaE+iNW8euW0yRZNP28iIg8WpR4iYhI9pDLH1pPh9f+hXxlIS4cn3WD+C6qJ381iaWIrxvXouLpP38vz09ax9aTobaOWEREJN2UeImISPYSUAO6rYIW48HVB64eodyq11mW7xu+ru+Kh5M9+85F0GbKRnr+spPzYTG2jlhEROSelHiJiEj2Y7aDSp2hx3ao/h6Y7TEfXUzbzW3YXGU1XSp5YzLB37vP88yoVYxbdpTYhCRbRy0iInJHSrxERCT7cskFjb+EdzZBsYZgScB16yQGnezE2obnqRLgRWyChTHLjvDsqNUs3HMBw9D1XyIikv0o8RIRkezPpzi8Mg86zoU8xSDqMoXWfMhvdp/yUyMo4OXMubAY3v15B+2nbuLA+QhbRywiIpKKEi8REXl0lGgE3TdCoy/AyRPT+Z3UWtORNcV+4ZNaXjjZm9kcEkrzCWv55I+9XIuMs3XEIiIigBIvERF51Ng7Qo0eydd/VewEmLDfP5duu9uwpc4unn8qDxYDft58mvojVzF9XQgJSRZbRy0iIjmcEi8REXk0ueeFlhOg20rwrwYJ0Xht+IpxV99kaeMwSufzICI2kc8XHOC5cWtZc+SKrSMWEZEcTImXiIg82gpUgNcXw0vfg2dBCDtNidXvsDDX10xq4IS3myPHLkfSafoW3pi5lZCrUbaOWEREciAlXiIi8ugzmaBMa3hvK9T9COydMZ1cS7P1bdhYdhHvVfPG3mxi2cHLNBqzmmH/HuRGbIKtoxYRkRxEiZeIiDw+HN2g/ifw7hYo3QoMC047p/PhofZsfPYY9Yp7k5Bk8O3qE9QfuZo5285gsWj6eRERyXpKvERE5PGTOwDazoTOC8DvKYgNw3ftZ8yIfZ/5jeMIzOPK1cg4+s3bQ6vJ69l+6rqtIxYRkcecEi8REXl8BdWGt9ZA8zHg4o3pykEqrn6NFQWnMqyeG+5O9uw5G85L32zg/d92cTE81tYRi4jIY0qJl4iIPN7MdlD5dei5A6p2B5Md5iOL6LC1DZurruPVCt6YTPDHznPUH7mKiSuOEpuQZOuoRUTkMaPES0REcgaX3PDcV9B9AxR9BpLicdsyniFnurC60UUqF/YiJiGJkUuP0GD0ahbvu4Bh6PovERHJHEq8REQkZ8lbCl6ZDx1+hdxBEHmRwqv7MNdhID82MpHP05mz12N4+6cdvDxtM4cuRtg6YhEReQwo8RIRkZzHZIKSz8G7m6HBYHB0x3RuG3XWdGBdyTn0r5ULR3szG45fo+m4tXz25z6uR8XbOmoREXmEKfESEZGcy94JavWGHjug/MvJRXt/5e09bdlSZw8tSntjMWDWplPUG7mKmRtOkphksW3MIiLySFLiJSIi4uEHrSbDmyug0NMQH0muDUOZcP1t/m0SQSk/d8JjEhj4936ajl/L+mNXbR2xiIg8YpR4iYiIpChYCV5fCi9MBY/8cP0kT6x6m0V5xjDhWWdyuzpw5FIkL0/bTLcft3HqWpStIxYRkUeEEi8REZGbmc1Qrh28tw1qfwh2TphPrKTFhjZsKr+E7lW8sTObWHrgEg1Hr+HrxYeIiku0ddQiIpLNKfESERFJi5M7PPtZ8gQcT7QAIwmnHdP46GhHNjwbQp2iuYlPsjB51XHqj1zF/B1nsVg0/byIiKRNiZeIiMjdeAdBu5+g01+QtzTEhOK39hNmJnzAvCaJBORx5fKNOPrM2c2L32xg5+nrto5YRESyISVeIiIi6VGkHry1FpqOBJfcmC4foPKqTqzw/54v6nrg5mjHrjNhvDB5Ax/M2c3liFhbRywiItmIEi8REZH0srOHKm8mTz9fpRuY7LA79A+vbGvNluob6VA+DwC/7zhL/ZGr+GbVceISk2wctIiIZAdKvERERDLK1RuajoC310FQHUiKw23zWIade43VjS9TvpAXUfFJDF98iEZj1rB0/0UMQ9d/iYjkZEq8RERE7pdfaej0N7SbDbkC4MZ5Alb35g/nz5neyI68Hk6cuhZNt1nb6TR9C0cv3bB1xCIiYiNKvERERB6EyQRPNId3t8CzA8DBDdPZzTyzpj3rn/idvjVy4WhnZu3RqzQZt5ZBf+8nPDrB1lGLiMhDpsRLREQkMzg4Q+0PoMd2KNseMHDY8zPv7mvH5nr7ee4Jb5IsBj9sOEm9kSuZtekUiUkWW0ctIiIPiRIvERGRzOSZH178Froug4KVIP4GudcP4Zvwd1nYOIoSed24Hp3AZ3/uo/mEdWw4ftXWEYuIyEOgxEtERCQr+D+dnHy1+gbc/SD0OE+ufpPFvuMZ96wLXi4OHLp4g47fbab7T9s5Expt64hFRCQLKfESERHJKmYzlO+YPPywZm+wc8R8fDnPb2zD5orL6Pa0N2YT/LvvIs+OXs2opYeJjk+0ddQiIpIFlHiJiIhkNScPaDgY3tkEJZuBJRHn7d/yyfGXWd/wNDWCchGfaGHCimM8M3I1f+06p+nnRUQeM0q8REREHpY8RaHDz/DqH+BbCqKvkX9Nf2YbH/FbYwv+3i5cjIil16+7aD1lI3vOhtk6YhERySRKvERERB62os8k33z5ua/B2QvTxb1UXf0KqwJm8nldT1wc7Nh+6jrPT1pPv3m7uXwj1tYRi4jIA1LiJSIiYgt2DlD1LeixEyp3BZMZu4N/0ml7a7bW2ELbcnkwDJiz7SzPjFzN1DXHiU/U9PMiIo8qJV4iIiK25JYHmo+Gt9ZCYG1IjMV98yi+vtCVFY2vUq6gJ5FxiQxddIjGY9ew/OAlXf8lIvIIUuIlIiKSHeR7Cjr/A21/BK/CEHGWIqt78qfrl3zX0B4fdydCrkbRdeY2uszYyrHLkbaOWEREMkCJl4iISHZhMkHp5+G9LVD/U3BwxXRmIw3XtmPDk3/wfo1cONiZWH3kCk3GruHzfw4QHpNg66hFRCQdlHiJiIhkNw4uULcvvLcNyrQBDBx3/0Sv/e3ZVO8QjUt5k2gxmL4+hPojV/Hz5tMkWTT8UEQkO1PiJSIikl15FYSXpsHrSyB/eYiLIM/6wXx7owf/NImhWF53QqPi+eSPvbSYsI7NJ67ZOmIREbkDJV4iIiLZXeFq8OZKaDkR3Hzh2lHKrOrK0rwTGFnfDQ9new5ciKDd1E28+/MOzoXF2DpiERG5hRIvERGRR4HZDBVfhR47oEYPMDtgPhZM682t2VJ5Ja9X9sZsgoV7LvDMyFWMCT5CTHySraMWEZH/KPESERF5lDh7QqMv4J1NUKIJWBJw2fYNA0JeZW3Ds1QL9CIu0cK45UdpPH49O66aNP28iEg28EgkXidPnqRr164EBQXh4uJC0aJFGThwIPHx8anq7dmzh9q1a+Ps7Iy/vz9ff/31bduaO3cupUqVwtnZmTJlyrBo0aKHdRgiIiKZx6cYdPwNXv4dfEpA1BUKrunHL6ZP+KUxFMzlwoXwWGYetaPnb3uIiNXshyIitvRIJF6HDh3CYrHw7bffsn//fsaMGcOUKVP45JNPrHUiIiJo1KgRAQEBbN++nREjRjBo0CCmTp1qrbNhwwY6dOhA165d2blzJ61ataJVq1bs27fPFoclIiLy4Io3gO4boPEwcPLCdGE31Vd3ZE3Rn/ikpjt2JoPF+y/RbPxa9pwNs3W0IiI51iOReDVp0oQZM2bQqFEjihQpQsuWLfnwww+ZP3++tc7s2bOJj49n+vTpPPnkk7Rv356ePXsyevRoa51x48bRpEkT+vbtyxNPPMGQIUOoWLEiEydOtMVhiYiIZA47B6j+DvTYDpW6ACbs9v/Om3va81P+3wnysuNMaAwvfbOB6etCNPRQRMQG7G0dwP0KDw/H29vb+njjxo3UqVMHR0dHa1njxo0ZPnw4169fJ3fu3GzcuJE+ffqk2k7jxo35888/77ifuLg44uLirI8jIiIASEhIICEhY8M2Uupn9HnycKh9si+1Tfam9slGnHJBk5FQvhN2Sz/BfGYT1UPnszTvUQbl7cvso/Z8vuAAG49fZdgLT+Ll4mDriHM0vXeyN7VP9pWd2iYjMTySidexY8eYMGECI0eOtJZdvHiRoKCgVPX8/Pys63Lnzs3FixetZTfXuXjx4h33NWzYMAYPHnxb+dKlS3F1db2v+IODg+/refJwqH2yL7VN9qb2yWbydKegXUXKnpmJ4+W9DDK/RYl8Xfn8UnWCD15m+4lLdC6eRKCHrQMVvXeyN7VP9pUd2iY6OjrddW2aePXv35/hw4fftc7BgwcpVaqU9fG5c+do0qQJbdq04c0338zqEPn4449T9ZJFRETg7+9Po0aN8PT0zNC2EhISCA4OpmHDhjg46FfG7Ebtk32pbbI3tU/2lZDQiJULi9Mg7Gcczm2lc9hEmpa9TofTLTl2PYkJBxz4oGFxXq8RgNlssnW4OY7eO9mb2if7yk5tkzIaLj1smnh98MEHdOnS5a51ihQpYv3/+fPnqV+/PjVq1Eg1aQZAvnz5uHTpUqqylMf58uW7a52U9WlxcnLCycnptnIHB4f7bugHea5kPbVP9qW2yd7UPtlTrGMeLK/+jd26EbBuNL6HZ7Mk7x6G+PXjh0N2DF9yhK2nwhjVphy53RzvvUHJdHrvZG9qn+wrO7RNRvZv08k1fH19KVWq1F2XlGu2zp07R7169ahUqRIzZszAbE4devXq1VmzZk2qcZbBwcGULFmS3LlzW+ssX7481fOCg4OpXr16Fh+piIiIDdk5QIOB8Mrv4OqD3eW9DDzfnZ+qnsbR3syKQ5dpOn4tW0+G2jpSEZHH1iMxq2FK0lW4cGFGjhzJlStXuHjxYqprszp27IijoyNdu3Zl//79/Pbbb4wbNy7VMMFevXqxePFiRo0axaFDhxg0aBDbtm3jvffes8VhiYiIPFzFGsDb6yCgFqb4SGrt7s/mp/7iiTz2XAiPpf3UTUxaeQyLRbMeiohktkci8QoODubYsWMsX76cQoUKkT9/fuuSwsvLi6VLlxISEkKlSpX44IMPGDBgAN26dbPWqVGjBj///DNTp06lXLlyzJs3jz///JOnnnrKFoclIiLy8Hnmh05/Qd2PABO5D/3CQteBvFU6gSSLwYglh+k8YwtXI+PuuSkREUm/RyLx6tKlC4ZhpLncrGzZsqxdu5bY2FjOnj3LRx99dNu22rRpw+HDh4mLi2Pfvn00bdr0YR2GiIhI9mBnD/U/gU5/gltezFcO0v9Md36rGoKzg5m1R6/SdNxaNh6/ZutIRUQeG49E4iUiIiJZoEi95KGHQXUxJURTdff/sbn07zzla8/lG3G8PG0T45YdJUlDD0VEHpgSLxERkZzMww9e/QPq/x+YzHgdnsvfjp/y3pPxWAwYs+wIr36/mcs3Ym0dqYjII02Jl4iISE5ntoO6/aDzP+CRH/O1I3x46m1+r3oMFwczG45fo+m4daw7etXWkYqIPLKUeImIiEiywFrJQw+LPguJsVTaPYAtpeZQwc+Oq5FxvDp9M6OWHiYxyWLrSEVEHjlKvEREROR/3Hzg5Xnw7EAw2eFxdD6/2/0f75eJwzBgwopjdJy2mYvhGnooIpIRSrxEREQkNbMZaveB1xaBZ0HMocfodeJt/qp6CDdHM1tCQmk6fi2rDl+2daQiIo8MJV4iIiKStsLVkocelmgCSXGU2/05m0vMpnI+O0Kj4ukyYyvDFx8iQUMPRUTuSYmXiIiI3JmrN3T4FRp9CWZ73I/9wxxTfz4qFwPAN6uO037qJs6Hxdg4UBGR7E2Jl4iIiNydyQQ13oPXl4BXYczXQ+h+rDsLq+7Hw8mO7aeu03T8WpYduGTrSEVEsi0lXiIiIpI+hSrD22ugVHNIiufJ3V+yuegPVC9gJiw6gTd+3MYXCw4Qn6ihhyIit1LiJSIiIunnkhva/QRNhoPZAdcT//JzUj8+Kx8NwLR1IbT5diNnQqNtHKiISPaixEtEREQyxmSCam9D16WQOxBT+Gm6HnmbJVX34Olsx+4zYTQbv5bF+y7aOlIRkWxDiZeIiIjcn4IV4a01ULoVWBIpufsrNgdNo04hMxGxibz903YG/b2fuMQkW0cqImJzSrxERETk/jl7QZsfoNkosHPCJSSYmfEfMLhCJAA/bDhJ6282cupalG3jFBGxsQwnXosXL2bdunXWx5MmTaJ8+fJ07NiR69evZ2pwIiIi8ggwmeDpN+CNZeBdFFPEOTof6s6yqjvwdrFj77lwmo1fx4I9520dqYiIzWQ48erbty8REREA7N27lw8++ICmTZsSEhJCnz59Mj1AEREReUTkLwtvrYYybcBIotjukWwImMKzhU1ExiXy3s87+b8/9hKboKGHIpLzZDjxCgkJoXTp0gD8/vvvNG/enKFDhzJp0iT+/fffTA9QREREHiFOHvDid9BiPNg743xyJdNi+jC0YvKPtrM3n+aFyRs4cSXSxoGKiDxcGU68HB0diY5OniJ22bJlNGrUCABvb29rT5iIiIjkYCYTVOoMb64AnxKYblyg48F3WFllK76udhy8EEHzCev4c+c5W0cqIvLQZDjxqlWrFn369GHIkCFs2bKFZs2aAXDkyBEKFSqU6QGKiIjII8rvSei2Csp1BMNC0J4xrCs0icYBJqLjk+j92y4+mreHmHgNPRSRx1+GE6+JEydib2/PvHnz+OabbyhYsCAA//77L02aNMn0AEVEROQR5ugGL3wDrb4BB1ecTq9hSmQvRlS6jskEv207Q6tJ6zl2+YatIxURyVL2GX1C4cKFWbBgwW3lY8aMyZSARERE5DFUviMUqAjzXsN0+QBt9r9Htcrv8dKB2hy+dIMWE9YzpNVTtK6k0TMi8ni6r/t4HT9+nE8//ZQOHTpw+fJlILnHa//+/ZkanIiIiDxG8paCN5ZDxU6Agf/eCawrMI7mQSZiEpL4cO5u+szZRXR8oq0jFRHJdBlOvFavXk2ZMmXYvHkz8+fPJzIyeVai3bt3M3DgwEwPUERERB4jjq7QcgK8OA0c3XE8s54J4T0YV/kaZhPM33GOFhPWceiiJuwSkcdLhhOv/v3788UXXxAcHIyjo6O1/JlnnmHTpk2ZGpyIiIg8psq2gW6rwa8MpuirPL+vB2srraWAhz3Hr0Tx/MT1/LrlNIZh2DpSEZFMkeHEa+/evbzwwgu3lefNm5erV69mSlAiIiKSA/gUgzeWQeWuABTc9w2r846iVRGIS7TQf/5eev26i8g4DT0UkUdfhhOvXLlyceHChdvKd+7caZ3hUERERCRdHJyh+WhoPQMcPXA4t5kx199j0tNXsDOb+Hv3eVpMWMf+8+G2jlRE5IFkOPFq3749H330ERcvXsRkMmGxWFi/fj0ffvghnTp1yooYRURE5HH31Ivw9hrIXx5TTCjN9vZifcUV+HvaE3I1ihcmb2DWplMaeigij6wMJ15Dhw6lVKlS+Pv7ExkZSenSpalTpw41atTg008/zYoYRUREJCfwLgJdl0KVtwDIt+87Vub5mrbFDOITLXz25z7e+3knEbEJNg5URCTjMpx4OTo68t1333H8+HEWLFjATz/9xKFDh5g1axZ2dnZZEaOIiIjkFPZO0PRraPcTOHthf2Ebw6++w9QqF7E3m1i49wLNx69jz9kwW0cqIpIhGb6BcorChQtTuHDhzIxFREREJNkTLSBf2eQbLp/bTqM9fdhQ/jXaHH+OU6HRvPTNBj5p+gRdagRiMplsHa2IyD1lOPF6/fXX77p++vTp9x2MiIiIiFXuAHhtMSwfDBsnkvfADJbn28lAvw+YfcSOwf8cYOPxa4xoXQ4vVwdbRysiclcZHmp4/fr1VMvly5dZsWIF8+fPJywsLAtCFBERkRzL3hEafwkdfgWX3Nhf3MUXl97lhyrncbQzs/TAJZqOX8vO09dtHamIyF1luMfrjz/+uK3MYrHQvXt3ihYtmilBiYiIiKRS8jl4ex3Mex3Tmc3U2/MhG8t2ov2p5hwNjaHNlI181KQUXWsFYTZr6KGIZD8Z7vFKcyNmM3369GHMmDGZsTkRERGR23kVgi4Lodb7AOQ5+COL3YfQpVQSiRaDLxcd5I0ft3E9Kt7GgYqI3C5TEi+A48ePk5ioO8uLiIhIFrJzgAaD4OXfwTUPdpf3MvB8d36qchpHezMrDl2m6fi1bDsZautIRURSyfBQwz59+qR6bBgGFy5cYOHChXTu3DnTAhMRERG5o+INkoce/v4GplPrqbWnP5uf6kiHM604dC2WdlM38UGjErxdp6iGHopItpDhxGvnzp2pHpvNZnx9fRk1atQ9ZzwUERERyTSeBaDT37D6K1gzktyHfmah7y6G5/2IqQcd+HrxYTadCGV023L4uDvZOloRyeEynHitXLkyK+IQERERyTg7e3jmUwioCfO7YXflAB+HdefZqv9H5x1FWXPkCk3HrWV8hwpUK5LH1tGKSA6Wadd4iYiIiNhM0frJQw+D6mBKiKbq7v9jc+n5POVrz+UbcXT8bhPjlx8lyWLYOlIRyaHS1eNVoUKFdN8VfseOHQ8UkIiIiMh98fCDV/+ENSNh9Vd4HZ7D3z67GfXkJ0za78Do4CNsDrnGmHblyevhbOtoRSSHSVfi1apVqywOQ0RERCQTmO2g3kcQUAN+fwPz1cP0DXub+lU/4dUdxVl/7BpNx61jXPvy1CzmY+toRSQHSVfiNXDgwKyOQ0RERCTzBNVOHnr4Rzc4voLKuz9jS6kXeeVSe3ZfjuOV7zfTo34xej5bHHs7XXkhIllPnzQiIiLyeHL3Tb7f17MDwGSHx9H5/GH/Ce+XicMwYPyKY3SctplLEbG2jlREcoAMJ15JSUmMHDmSKlWqkC9fPry9vVMtIiIiItmG2Qy1P4AuC8GjAObQY/Q68TZ/Vj2Mm6OZLSGhPDduLasOX7Z1pCLymMtw4jV48GBGjx5Nu3btCA8Pp0+fPrz44ouYzWYGDRqUBSGKiIiIPKCA6slDD4s3hqQ4yu8ezOYSs6mUz57QqHi6zNjK8MWHSEyy2DpSEXlMZTjxmj17Nt999x0ffPAB9vb2dOjQgWnTpjFgwAA2bdqUFTGKiIiIPDi3PNDhV2g4BMz2uB/7h7mmj+hXNnmo4TerjtN+6ibOh8XYOFAReRxlOPG6ePEiZcqUAcDd3Z3w8HAAmjdvzsKFCzM3OhEREZHMZDZDzZ7w2mLwKoz5egjvHH+bBVUP4OFkx7ZT12k6fi3LD16ydaQi8pjJcOJVqFAhLly4AEDRokVZunQpAFu3bsXJySlzoxMRERHJCv5Pw9troGQzSIrnqd1fsKnYTKrltyMsOoGuM7fx5cIDxCdq6KGIZI4MJ14vvPACy5cvB6BHjx589tlnFC9enE6dOvH6669neoAiIiIiWcIlN7SfDU2+ArMDbscX8YulL/9XPhqA79aG0PbbjZwJjbZxoCLyOEjXfbxu9tVXX1n/365dOwICAtiwYQPFixenRYsWmRqciIiISJYymaBad/CvAnNfwxR2ijdvdKd21Q9pu7s8u86E0Wz8Wka0KUfjJ/PZOloReYRluMcrNjb1vS6qVatGnz59lHSJiIjIo6tgJXh7LZR+HiwJlNo9jM1B31OroB0RsYm8NWs7g/7eT1xikq0jFZFHVIYTr7x589K5c2eCg4OxWDTuWURERB4Tzl7QZiY0HQl2jriELGVWQh8GV4gE4IcNJ2n9zUZOXYuycaAi8ijKcOI1c+ZMoqOjef755ylYsCC9e/dm27ZtWRGbiIiIyMNlMkGVN+GNZeBdBFPEOTof6s6yqjvJ7WLH3nPhNB+/joV7Ltg6UhF5xNzX5Bpz587l0qVLDB06lAMHDlCtWjVKlCjB559/nhUxioiIiDxc+cvBW2vgqdZgJFFs9wg2BnzLM/4mbsQl8u7PO/j0z73EJmjooYikT4YTrxQeHh689tprLF26lD179uDm5sbgwYMzMzYRERER23HygJemQYtxYO+M88kVfB/bh6EVIwD4adNpXpi8gRNXIm0cqIg8Cu478YqNjWXOnDm0atWKihUrEhoaSt++fTMzNhERERHbMpmgUhd4YznkKY7pxgU6HnyHlVW24eNqz8ELEbSYsI6/dp2zdaQiks1lOPFasmQJnTt3xs/Pj+7du+Pn58fSpUs5depUqqnmRURERB4b+Z6CbqugbHswLATtGc16/0k0KmwiKj6JXr/uov/ve4iJ19BDEUnbfV3jFRMTw48//sjFixf59ttvqVOnTlbEJiIiIpJ9OLnDi9/C85PBwRWnU6v5Nro3IyqFYTLBr1vP0GrSeo5dvmHrSEUkG8pw4nXp0iXmzJnD888/j4ODwx3rffXVV4SFhT1IbKm0bNmSwoUL4+zsTP78+Xn11Vc5f/58qjp79uyhdu3aODs74+/vz9dff33bdubOnUupUqVwdnamTJkyLFq0KNNiFBERkRygwsvw5krwfQJT5CXa7H+X1ZU3kdfNnsOXbtBiwnrmbT9r6yhFJJvJcOLl4eGRrnpDhw4lNDQ0wwHdSf369ZkzZw6HDx/m999/5/jx47Ru3dq6PiIigkaNGhEQEMD27dsZMWIEgwYNYurUqdY6GzZsoEOHDnTt2pWdO3fSqlUrWrVqxb59+zItThEREckB8paCN1dAhVcBg8J7x7OuwFiaBUFMQhIfzt3NB3N2Ex2faOtIRSSbuO/JNe7FMIxM3d77779PtWrVCAgIoEaNGvTv359NmzaRkJAAwOzZs4mPj2f69Ok8+eSTtG/fnp49ezJ69GjrNsaNG0eTJk3o27cvTzzxBEOGDKFixYpMnDgxU2MVERGRHMDRFZ6fCC9+Bw5uOJ7ZwMTwnoytHIrZBL/vOEuLCes4fFFDD0UE7G0dwP0IDQ1l9uzZ1KhRwzrccePGjdSpUwdHR0drvcaNGzN8+HCuX79O7ty52bhxI3369Em1rcaNG/Pnn3/ecV9xcXHExcVZH0dEJE8hm5CQYE360iulfkafJw+H2if7Uttkb2qf7Ett85A88QLkfQr7+W9guryf5/f1oFLFt2h3+BmOX4mi5cR1DGhWijaVCmIymaxPU/tkb2qf7Cs7tU1GYnikEq+PPvqIiRMnEh0dTbVq1ViwYIF13cWLFwkKCkpV38/Pz7oud+7cXLx40Vp2c52LFy/ecZ/Dhg1L8/5kS5cuxdXV9b6OIzg4+L6eJw+H2if7Uttkb2qf7Ett83CY87/PU5afCbq6Av/9U/jTdSUfeL3D2nBf/u+vA8xfv4+2RSw426V+ntone1P7ZF/ZoW2io6PTXdemiVf//v0ZPnz4XescPHiQUqVKAdC3b1+6du3KqVOnGDx4MJ06dWLBggWpfj3KbB9//HGqXrKIiAj8/f1p1KgRnp6eGdpWQkICwcHBNGzY8K4Tk4htqH2yL7VN9qb2yb7UNrbQisQDf2C38H3yRh/mR5fBLKg0gN47/dh+1Uyo4c7YdmUpnd9T7ZPNqX2yr+zUNimj4dLDponXBx98QJcuXe5ap0iRItb/+/j44OPjQ4kSJXjiiSfw9/dn06ZNVK9enXz58nHp0qVUz015nC9fPuu/adVJWZ8WJycnnJycbit3cHC474Z+kOdK1lP7ZF9qm+xN7ZN9qW0esnJtoVAlmPcapgu7abG/N09X7EbrIw0IuRZNm6lb+Kx5adpVzA+ofbI7tU/2lR3aJiP7T9fkGn369CEqKgqANWvWkJh47xl6ateujYuLy13r+Pr6UqpUqbsuN1+zdTOLxQJgvf6qevXqrFmzJtU4y+DgYEqWLEnu3LmtdZYvX55qO8HBwVSvXv2exyMiIiKSbnmKQtdgqPIWAPn2TWVVnq9pW8wgPtHCZ3/uo9dve4jRpIciOUa6Eq8JEyYQGRkJJE/rnp5p4hctWkT+/PkfLLr/bN68mYkTJ7Jr1y5OnTrFihUr6NChA0WLFrUmTR07dsTR0ZGuXbuyf/9+fvvtN8aNG5dqmGCvXr1YvHgxo0aN4tChQwwaNIht27bx3nvvZUqcIiIiIlb2TtD0a2g7C5y8sL+wjeFX32VqlYvYm038u/8So/baceZ6+q8REZFHV7qGGgYGBjJ+/HgaNWqEYRhs3LjR2ot0qzp16mRqgACurq7Mnz+fgQMHEhUVRf78+WnSpAmffvqpdRigl5cXS5cu5d1336VSpUr4+PgwYMAAunXrZt1OjRo1+Pnnn/n000/55JNPKF68OH/++SdPPfVUpscsIiIiAkDplpC/LMx9DdP5HTTa04cNFV6n9dHGnI5Iot3ULfzYtSpP5M/YteMi8mhJV+I1YsQI3n77bYYNG4bJZOKFF15Is57JZCIpKSlTAwQoU6YMK1asuGe9smXLsnbt2rvWadOmDW3atMms0ERERETuLXcgvL4Elg+GjRPJu386y/Jup31CF3ZE+tH2241M61SZqkXy2DpSEcki6Rpq2KpVKy5evEhERASGYXD48GGuX79+25KeIYgiIiIiOZK9IzT+Ejr8Cs65cLy8m1/Mn9Ix/wVuxCby6vQtLN1/51vciMijLV2JVwp3d3dWrlxJUFAQXl5eaS4iIiIichcln4O312HJXwGnpCi+vPEp7weeJD7Rwts/bee3radtHaGIZIF0JV4RERHWpUKFCkRHR6cqu3kRERERkXvI5U/SK39yyaMspsQYel4ewLBiB7AY8NHve5m08hiGYdg6ShHJROm6xitXrlzpvklxVlzjJSIiIvLYcXRjc9HeNE/8F/O+uXQ4+wV+JXvx+uGqjFhymCs34hjQvDRmc/q+g4lI9pauxGvlypXW/588eZL+/fvTpUsX61TuGzduZObMmQwbNixrohQRERF5DBkme5JaTsLs4QcbJ/LMqXH8XbILLQ835IcNJwmNimdkm3I42mfo6hARyYbSlXjVrVvX+v/PP/+c0aNH06FDB2tZy5YtKVOmDFOnTqVz586ZH6WIiIjI48pkhkZfgJsvLBtI2VM/sLpEOI2OvcTfu89zPTqeKa9Uws0pXV/bRCSbyvDPJxs3bqRy5cq3lVeuXJktW7ZkSlAiIiIiOYrJBLV6w/OTwGRHwOk/WB80ndwOiaw9epWO0zYTGhVv6yhF5AFkOPHy9/fnu+++u6182rRp+Pv7Z0pQIiIiIjlShVeg/Wywd8bn3ArW5h9PYZc4dp8Jo/WUDZy9Hm3rCEXkPmW4z3rMmDG89NJL/Pvvv1StWhWALVu2cPToUX7//fdMD1BEREQkRyn5HLz6J/zSDvfL2wj2/oo2Dh+y5wq0/mYjP3atQgk/D1tHKSIZlOEer6ZNm3L06FFatGhBaGgooaGhtGjRgiNHjtC0adOsiFFEREQkZwmoDq/9Cx75cQo9zHynQdTPE8bFiFjaTNnI9lOhto5QRDLovq7SLFSoEEOHDs3sWEREREQkhd+T8PoS+OlF7K8d43uXz+hf4DPmnM/Ly9M2M/nlijxTys/WUYpIOt3X3KTXr19n5MiRdO3ala5duzJq1ChCQ/XLi4iIiEimyh2QnHwVqIA55hrDb/wfPQJOE5tg4c0ftzNv+1lbRygi6ZThxGvNmjUEBgYyfvx4rl+/zvXr1xk/fjxBQUGsWbMmK2IUERERybncfKDzP1CkHqaEKPpc+Ywvih4iyWLw4dzdfLv6uK0jFJF0yHDi9e6779KuXTtCQkKYP38+8+fP58SJE7Rv35533303K2IUERERydmcPKDjXHjyRUyWBF459znfldgKwLB/D/HlwgNYLIaNgxSRu8lw4nXs2DE++OAD7OzsrGV2dnb06dOHY8eOZWpwIiIiIvIfe0d46Xuo0g2AhqfHML/kcsDgu7UhfDh3NwlJFtvGKCJ3lOHEq2LFihw8ePC28oMHD1KuXLlMCUpERERE0mA2w3NfwzOfAlDx1PesLPEHjmYL83eeo9uP24iOT7RxkCKSlgzPatizZ0969erFsWPHqFatGgCbNm1i0qRJfPXVV+zZs8dat2zZspkXqYiIiIiAyQR1+oKbLyx4n6DT81gfFMazpzux8vAVXp62mRldniaXq6OtIxWRm2Q48erQoQMA/fr1S3OdyWTCMAxMJhNJSUkPHqGIiIiI3K5SF3DNA/O64ntuGesL3qDJxe7sPB1GmynJN1rO7+Vi6yhF5D8ZTrxCQkKyIg4RERERyagnWsCr8+GXDnhc3MzyPDd4KaIP+y/DS5M38GPXKhTL62HrKEWE+0i8AgIC0lWvWbNmTJs2jfz582c4KBERERFJp8Ba0GUh/PQSztcO8Jfn57zm+DFrr0HrKRuZ0eVpKhTObesoRXK8+7qBcnqsWbOGmJiYrNq8iIiIiKTIXxa6LoXcQdhHnGam8Rkv5LtKWHQCHb/bzKrDl20doUiOl2WJl4iIiIg8RN5ByclXvrKYo68yOvoT3ip8lpiEJN6YuY0/d56zdYQiOZoSLxEREZHHhXve5GGHgbUxxUfS/9qnDChyhESLQe/fdvH9Ol2rL2IrSrxEREREHifOnvDyPHiiJaakeF47P5hJJXYCMGTBAb769xCGYdg4SJGcR4mXiIiIyOPGwRna/ACVX8eEQbPTI5hbchVgMGX1cT76fQ+JSRYbBymSsyjxEhEREXkcme2g2Wio2x+Ap09NZVmJv7E3WZiz7Sxv/7SD2ATdc1XkYcmyxOuTTz7B29s7qzYvIiIiIvdiMkH9j6HpSMBEsdO/sa7oLNztk1h28BKvfr+Z8OgEW0cpkiNk+D5ef//9d5rlJpMJZ2dnihUrRlBQEB9//PEDByciIiIimaDKm+CaB+Z3I9/ZJawvdIPGF7ux9eR12n67kR+7VsHP09nWUYo81jKceLVq1QqTyXTbRZkpZSaTiVq1avHnn3+SO7du1iciIiKSLTz1Irh6w68v43VxAyt9bvBCWG8OXYIXJ29gVtcqFPF1t3WUIo+tDA81DA4O5umnnyY4OJjw8HDCw8MJDg6matWqLFiwgDVr1nDt2jU+/PDDrIhXRERERO5XkXrQZQG4+uBydS//uA2hhvcNzoXF0HrKRvacDbN1hCKPrQwnXr169WL06NE8++yzeHh44OHhwbPPPsuIESPo27cvNWvWZOzYsQQHB2dFvCIiIiLyIApUSL7Rcq7COISf5CfTZ7Twu0ZoVDwdpm5i3dGrto5Q5LGU4cTr+PHjeHp63lbu6enJiRMnAChevDhXr+pNKyIiIpIt5SkKXYPB7ynMUZcZH/sJXf3PERWfxGs/bOGf3edtHaHIYyfDiVel/2/vPsOjKvevj6+Z9ACBBAIhErqEjoLCCSoWSrCgIKC0SDsqHBQpR48oUgT/dBQrcgBB6UXABiSCIEoAQUITQicgCS0hldTZzwsecozUQCZ7Jvl+risXZM89M2v8eb9Y7Jk9TZro9ddf17lz53KPnTt3Tm+88Ybuv/9+SdKhQ4cUFBRUcCkBAABQsEoFSL2+l6o8IEtGsobHD9db1Q4rK8fQwEU7NXfzcbMTAkVKvovXrFmzdOzYMVWqVEk1a9ZUzZo1ValSJR0/flwzZ86UJKWkpGj48OEFHhYAAAAFyKuM1GO5VPspWXIy9GLcKH1w9y4ZhjTym32aEh591QXVANyefF/VMDg4WH/88YfCw8N18ODB3GOtW7eW1Xq5x7Vv375AQwIAAMBO3LykznOl7wbJsvMrtT85QeWD+6tb9IP6aP1hnU/J1Nj29eVitZidFHBq+S5ekmS1WtW2bVu1bdu2oPMAAACgsLm4Sk9/JJUsL22aouYnPtOa4EQ9efAJLdwWo/jUDE3rcq883VzMTgo4rXy/1VCSNm7cqHbt2uW+1fDpp5/Wpk2bCjobAAAACovFIrUcIbWdIEmqfWKBfqm5QCVcbFq774x6zt6mpPQsk0MCzivfxWvevHlq1aqVvL29NXDgQA0cOFCenp5q2bKlFixYYI+MAAAAKCz/6Cc9O1OyuqriyR/0S+XP5e+Rra3H4vX851t0Njnd7ISAU8p38Xrvvfc0ceJELV68OLd4LVmyROPHj9eYMWPskREAAACFqWFnqdtiya2EfGM3aWP5KapZIl37Y5PU6bNInbiQanZCwOnku3gdPXpU7dq1u+r4008/rWPHjhVIKAAAAJisZiup57eSl5+8z+3S6lJj1bRMsmLi09Txs83a+2ei2QkBp5Lv4hUUFKR169ZddfzHH3/ku7sAAACKkkpNpD5rpdJBcrt4VAtdR+qJ8vE6n5KpLjO2aPOR82YnBJxGvq9qOHToUA0cOFBRUVFq3ry5JOnXX3/VnDlzNG3atAIPCAAAABP515L6hktfPSuXc/v1icfbGnXXO5r7Z6B6zf5N07rco8cbVDQ7JeDw8n3Gq3///lq0aJH27NmjQYMGadCgQdq7d68WL16sl19+2R4ZAQAAYCafQKn3D1JQM1kyEjUqcbher3pUmTk2/WvB75q35YTZCQGHd1vf49WhQwd16NChoLMAAADAUXn7SWErpWW9ZTm4Rv86M1IVar6hfx9uoOEr9+p8SoZea3m3LBa+aBm4ltv6Hi8AAAAUQ+7e0vPzpEbdZDFy1OnUOH0ZvFmSoQ9+PKQRq/Ypx2aYnRJwSLd0xsvX1/eW//UiPj7+jgIBAADAgbm4Se0/lUr6S79OU4sTH+v74ES1Oxiqr7acUHxqpqY+30geri5mJwUcyi0Vrw8++MDOMQAAAOA0LBap9btSCX8pfLjqnfhKP9e8qNZHn9P3e2J18VKmPg+7TyU9butTLUCRdEu7oWfPnvbOAQAAAGfT/FXJu5y0aoAqnfxWv1ZJUptTffTr4QvqMiNSc3o3VbmSHmanBBwCn/ECAADA7bunq9R1keTqJb/TG7Ux4ANV987Q3j+T1OmzzToZn2Z2QsAhULwAAABwZ2q1kXp+I3mWUYmzO7Wm9P/p3tKpOn4hTc9+tln7Y5PMTgiYjuIFAACAOxfUVOqzRioVKPeEQ1rmNlJt/BN0LjlDz30eqa1HL5idEDAVxQsAAAAFo3wdqW+4VK6WXFJOa3rWcHUPjFNyerbCZm9T+L44sxMCpqF4AQAAoOCUCZJ6r5Huuk/W9ASNTXpbg6ocV2a2Tf3m7dDi32LMTgiYguIFAACAglWi7OXPfNVsJUv2Jb12boTG1fxDNkP6z/I9+uSnwzIMvmgZxQvFCwAAAAXPvcTlqx02eE4WW7a6nhqr2cFbJUmT1kZr9Ld/yGajfKH4oHgBAADAPlzcpA6fS/8YIEl67MQ0fRMcLsnQnM3HNWhxlDKzbeZmBAoJxQsAAAD2Y7VKoe9JrUZJkhqemKONtZbJw2rTN7tOq+/c35SakW1uRqAQULwAAABgXxaL9OBg6emPJYtVVWJW6Ndqs+Xrlq1Nh86r28ytik/NNDslYFdOV7wyMjJ0zz33yGKxKCoqKs9tu3fv1kMPPSRPT08FBQVp4sSJV91/6dKlql27tjw9PdWgQQP98MMPhZQcAACgmGscJj0/X3L1VLk/12tTxQ8V5JWhXScvqtP0zTqVkGZ2QsBunK54vfHGGwoMDLzqeFJSktq0aaMqVapox44dmjRpkkaNGqUZM2bkrtm8ebO6du2qvn37aufOnWrfvr3at2+vvXv3FuZLAAAAKL5qPyGFrZA8Sqvk2e360Xe8Gvqk6ui5VHX6LFIHzySbnRCwC6cqXqtXr1Z4eLgmT5581W3z589XZmamZs+erXr16qlLly4aOHCgpk6dmrtm2rRpatu2rV5//XXVqVNHY8aMUePGjfXxxx8X5ssAAAAo3qo0l/qslkoGyCM+Wl97jNKjZS8qLildnadHaseJeLMTAgXO1ewAt+rMmTN68cUXtXLlSnl7e191e2RkpFq0aCF3d/fcY6GhoZowYYISEhLk6+uryMhIDRkyJM/9QkNDtXLlyus+b0ZGhjIyMnJ/T0pKkiRlZWUpKysrX6/hyvr83g+Fg/k4Lmbj2JiP42I2jq3Yz8evltTzB7ku7CTX+KOa5TVc/wl4R0vjKqj7zK368PlGejTY37R4xX4+DsyRZpOfDE5RvAzDUK9evdSvXz/dd999On78+FVr4uLiVK1atTzHKlSokHubr6+v4uLico/9dU1cXNx1n3vcuHEaPXr0VcfDw8OvWQBvRURExG3dD4WD+TguZuPYmI/jYjaOrbjPxz1wiEIuTVaZS8c1LuNNuZcapPnJjdRv3u/qWsOmpuXN/a6v4j4fR+YIs0lLu/XPJZpavN58801NmDDhhmv279+v8PBwJScna9iwYYWU7H+GDRuW5yxZUlKSgoKC1KZNG/n4+OTrsbKyshQREaHWrVvLzc2toKPiDjEfx8VsHBvzcVzMxrExn7/IeFK25b3kemyjxmqqgqv/RyOO1tX8Iy66q+bdevHBajd/jALGfByXI83myrvhboWpxWvo0KHq1avXDddUr15d69evV2RkpDw8PPLcdt9996l79+6aO3euAgICdObMmTy3X/k9ICAg989rrbly+7V4eHhc9byS5ObmdtuDvpP7wv6Yj+NiNo6N+TguZuPYmI8kNz+p+1JpRT9Z9n2tF06PVUCtwXrp4P2auPaQEtKyNezxOrJaLYUfjfk4LEeYTX6e39Ti5e/vL3//m79398MPP9TYsWNzfz99+rRCQ0O1ePFiNWvWTJIUEhKit99+W1lZWbn/ASIiIhQcHCxfX9/cNevWrdOgQYNyHysiIkIhISEF+KoAAACQb64eUsdZUoly0rYZahPzvr4O7qtnox/Tfzcd04WUTE3o1FBuLk51bTggl1P8n1u5cmXVr18/96dWrVqSpBo1aqhSpUqSpG7dusnd3V19+/bVvn37tHjxYk2bNi3P2wRfe+01rVmzRlOmTNGBAwc0atQobd++Xa+88ooprwsAAAB/YbVKj0+UHh0uSWp8YpbW11ohd6tNX+/8Uy99uV1pmdkmhwRuj1MUr1tRunRphYeH69ixY2rSpImGDh2qESNG6KWXXspd07x5cy1YsEAzZsxQo0aNtGzZMq1cuVL169c3MTkAAAByWSzSw69LT30gWayqHrNMv1SbIx+3bP0UfU7dZ27VxbRMs1MC+eYUVzX8u6pVq8owrr7CTcOGDbVp06Yb3rdz587q3LmzvaIBAACgINzXW/IuKy3/p8r/+aN+vStZoXH9tTPmojpPj9SXfZuqYmkvs1MCt6zInPECAABAEVP3aanHcsnDR6Xitmp92YmqWypNh86mqOOnm3X4bLLZCYFbRvECAACA46r2kNTre6lEeXle+EPfeL2rh8om6nRiujpNj9TOmASzEwK3hOIFAAAAx1axodR3reRbTa5JMZprvKMOAed0MS1L3f67VRuiz5qdELgpihcAAAAcn191qW+4FNBA1rTzmpr2tl4OOqlLWTn659ztWrnzT7MTAjdE8QIAAIBzKFn+8tsOqz4kS2aK3ox/RyOqH1S2zdCgxVGa9csxsxMC10XxAgAAgPPwLC11XybVaSdLTqZ6nx6tT2r9Lkka890fGr/6wDWvfg2YjeIFAAAA5+LmKXWeKzXpLYsMPRkzWUuCN0gyNH3jEf1n+W5l59jMTgnkQfECAACA87G6SE+9Lz38H0lS0xMzFFHrG7labFqy/ZT6zftd6Vk5JocE/ofiBQAAAOdksUiPviU9MVmSRXfHLNYvNb5SCdcc/bj/jMJmbVViWpbZKQFJFC8AAAA4u6YvSp1mS1Y3BZxaq82VPlWAZ6Z+O56g5z6P1JmkdLMTAhQvAAAAFAH1n5V6LJPcS6p0XKR+KjdFwSUvKfpMsp79dLOOnksxOyGKOYoXAAAAiobqj0i9vpO8y8nr/B59V2KMQnyT9OfFS+o0PVK7T100OyGKMYoXAAAAio7Aey9/0XKZynJLPK751hFqV+G84lMz1XXGFv1y6LzZCVFMUbwAAABQtJStIfUJl8rXkzX1rD5Mf1t9Kv2p1Mwc9Z6zTd/uOm12QhRDFC8AAAAUPT4Vpd4/SJWby5KRrHcShuutaoeVlWNo4KKdmrv5uNkJUcxQvAAAAFA0eZWRwr6Wgp+UJSdDL8aN0gd375JhSCO/2acp4dEyDMPslCgmKF4AAAAouty8pOe+lO7tIYthU/uTE7QgeJMkQx+tP6y3VuxVjo3yBfujeAEAAKBoc3GVnv5YenCIJKn5ic+0ptb3slpsWrgtRv+av0PpWTkmh0RRR/ECAABA0WexSK1GSm3HS5JqxyzQLzUWqISLTWv3nVHP2duUlJ5lckgUZRQvAAAAFB//6C89O1Oyuirw1A/6pfLn8vfI1tZj8Xr+8y06m5xudkIUURQvAAAAFC8NO0tdF0tu3vKN3aSN5aeoZolL2h+bpE6fRerEhVSzE6IIongBAACg+Lm7ldTzW8nLT97ndml1qffUtEyyYuLT1PGzzdp3OsnshChiKF4AAAAonirdJ/VZK/lUktvFo1roOlKPl4/X+ZRMdZ/9mw7TvVCAKF4AAAAovvxrSX3DJf86ckmJ06cZb+uFu04rNSNHMw64aO+ftC8UDIoXAAAAirfSd0m9f5CCmsmSkajRicPVv2K0MnIs6vPlDh0+m2J2QhQBFC8AAADA208KWyndHSpLdrreuDhWvb1+UUJalsJmbdWfFy+ZnRBOjuIFAAAASJK7t9RlvtSomyxGjt4xpqt7mX2KTUxX2MytOp+SYXZCODGKFwAAAHCFi5v0zCey1e8sq2wamzVZT/oc0dHzqXzJMu4IxQsAAAD4K6tVOU99qFife2XJydBHxgQ94H1K+04n6Z9ztis9K8fshHBCFC8AAADg71zctL3aANkqN5c1K0Vz3ceroccZbTserwHzf1dWjs3shHAyFC8AAADgGmxWd+U8N1+q2Eiu6fFaWmKiqrrGa92Bs3p96S7ZbIbZEeFEKF4AAADA9XiUknp8LZW9Wx5psfred4rKW5O0Muq0Rn+7T4ZB+cKtoXgBAAAAN1KinPTCSsmnkkokH1O4/zT5WNI0N/KE3v/xkNnp4CQoXgAAAMDNlK50uXx5l1OZxP0KD/hMHsrUh+sOadYvx8xOBydA8QIAAABuRbm7pR7LJfdSCkjYodWBs+SqbI357g8t33HK7HRwcBQvAAAA4FYF3iN1WyS5eqp6/CZ9HbhAFtn0xvLdCt8XZ3Y6ODCKFwAAAJAfVR+UOs+VLC5qGL9GXwauUI7NplcW7tTmI+fNTgcHRfECAAAA8iu4rdRhuiTpofjl+jBgrTKzbXpx7nbtPnXR3GxwSBQvAAAA4HY0fE56fJIk6emLX2p0+Z+VmpmjnrO36fDZZJPDwdFQvAAAAIDb1ewl6ZG3JEk9k6ZrULntSkjLUo+Z23QqIc3kcHAkFC8AAADgTjz8htSsvyTptdRpCvPdp7ikdIXN2qZzyRkmh4OjoHgBAAAAd8JikUL/T2rUVRYjR+9mTtZTpY7o2PlU9Zy9TUnpWWYnhAOgeAEAAAB3ymqVnv5YCn5ClpwMfagJeqhEjP6ITdI/52zXpcwcsxPCZBQvAAAAoCC4uEqdvpCqPiRrVoq+cJ2ghh5x2nY8Xv+av0NZOTazE8JEFC8AAACgoLh5Sl0XSoH3yjUjQctKTFJ1twv6Kfqchi7ZJZvNMDshTELxAgAAAAqSRymp+3KpXC25p8XquzJTVN6apG92ndbIb/bJMChfxRHFCwAAAChoJcpKYSul0kHyTj6ucP9p8rGk6astJzQ14qDZ6WACihcAAABgD6Xvuly+vMupTOJ+RQR8Kg9l6qP1hzVz01Gz06GQUbwAAAAAeylXUwr7WvLwUYWE37U2cKZcla2x3+/X0u0nzU6HQkTxAgAAAOypYiOp22LJ1VNV43/RysB5ssim/yzfrbX74sxOh0JC8QIAAADsrUpz6bkvJaur6seHa17gctkMQ68u2KlfD583Ox0KAcULAAAAKAy1QqUOn0uy6IH4Ffq44mpl5tj04pfbFXXyotnpYGcULwAAAKCwNOgkPTFJkvRUwjyNqbBRaZk56vXFNh06k2xyONgTxQsAAAAoTE1flB4dLkkKS/xcg/y362JalnrM2qqT8Wkmh4O9ULwAAACAwtbi39I/BkiSXkuZpp6+e3UmKUNhs7bqXHKGyeFgDxQvAAAAoLBZLFKbsdI93WUxcjQqc7LalTqk4xfS9MLsbUq8lGV2QhQwihcAAABgBqtVavehVPspWXIyNU0T1aLESe2PTVLfOb/pUmaO2QlRgJymeFWtWlUWiyXPz/jx4/Os2b17tx566CF5enoqKChIEydOvOpxli5dqtq1a8vT01MNGjTQDz/8UFgvAQAAAMjLxVXqOEuq1kLWrFTNdh2vhp5x2n4iQf3n71Bmts3shCggTlO8JOndd99VbGxs7s+rr76ae1tSUpLatGmjKlWqaMeOHZo0aZJGjRqlGTNm5K7ZvHmzunbtqr59+2rnzp1q37692rdvr71795rxcgAAAADJzVPqskAKbCzXjAQt856o6m4XtCH6nIYsiVKOzTA7IQqAUxWvUqVKKSAgIPenRIkSubfNnz9fmZmZmj17turVq6cuXbpo4MCBmjp1au6aadOmqW3btnr99ddVp04djRkzRo0bN9bHH39sxssBAAAALvMoJfVYLpULlntanL4rM0UBLon6bnesRqzaK8OgfDk7V7MD5Mf48eM1ZswYVa5cWd26ddPgwYPl6nr5JURGRqpFixZyd3fPXR8aGqoJEyYoISFBvr6+ioyM1JAhQ/I8ZmhoqFauXHnd58zIyFBGxv+uLJOUlCRJysrKUlZW/j70eGV9fu+HwsF8HBezcWzMx3ExG8fGfBybKfNxKyV1XSrXL5+Ud+JxrSk7TS3ODdX8rTHy8XTRkFZ3F14WB+ZIeyc/GZymeA0cOFCNGzeWn5+fNm/erGHDhik2Njb3jFZcXJyqVauW5z4VKlTIvc3X11dxcXG5x/66Ji4u7rrPO27cOI0ePfqq4+Hh4fL29r6t1xIREXFb90PhYD6Oi9k4NubjuJiNY2M+js2M+ZQIfFUPpo5VmaQDWllykp5IHqbPNh7T6eOH9VggZ76ucIS9k5Z269+7ZmrxevPNNzVhwoQbrtm/f79q166d50xVw4YN5e7urpdfflnjxo2Th4eH3TIOGzYsz3MnJSUpKChIbdq0kY+PT74eKysrSxEREWrdurXc3NwKOiruEPNxXMzGsTEfx8VsHBvzcWymzyfufhnznlH1jINaU/G/ah3bT6tOuKrZvfXUucldhZ/HgZg+m7+48m64W2Fq8Ro6dKh69ep1wzXVq1e/5vFmzZopOztbx48fV3BwsAICAnTmzJk8a678HhAQkPvntdZcuf1aPDw8rlns3NzcbnvQd3Jf2B/zcVzMxrExH8fFbBwb83Fsps0nqLHUbYn0VQdVTdislYEl1O50Tw1ftU9+JT3Utn7Fws/kYBxh7+Tn+U29uIa/v79q1659w5+/fmbrr6KiomS1WlW+fHlJUkhIiH7++ec877OMiIhQcHCwfH19c9esW7cuz+NEREQoJCTETq8QAAAAuE1VQqTnv5KsrqoXH6H5gctkMwwNXBilXw6dNzsd8skprmoYGRmpDz74QLt27dLRo0c1f/58DR48WD169MgtVd26dZO7u7v69u2rffv2afHixZo2bVqetwm+9tprWrNmjaZMmaIDBw5o1KhR2r59u1555RWzXhoAAABwfXe3ljp8LsmikPiV+rTiamXm2PTSV9u1MybB7HTIB6coXh4eHlq0aJEefvhh1atXT++9954GDx6c5zu6SpcurfDwcB07dkxNmjTR0KFDNWLECL300ku5a5o3b64FCxZoxowZatSokZYtW6aVK1eqfv36ZrwsAAAA4OYadJKenCxJeiJhnt6rsEFpmTnqPec3HTyTbHI43CqnuKph48aNtWXLlpuua9iwoTZt2nTDNZ07d1bnzp0LKhoAAABgf/f/U7p0UVo/Rt0TZ+iCv7emnmuqsFlbtaxfcwX53d7VtlF4nOKMFwAAAFDsPTRUCrn8EZlXUz5Ub789OpOUoR6ztupscrrJ4XAzFC8AAADAGVgsUpux0r09ZDFsGpExRc/4HNKJC2l6YdY2JaaZ/4XCuD6KFwAAAOAsLBbpqWlSnXay5GTqfWOCHi4RowNxyeoz9zelZWabnRDXQfECAAAAnImLq9RxllTtYVmz0jTLdbzu8YzTjhMJ6jfvd2Vm28xOiGugeAEAAADOxtVD6jJfuquJXDMuaon3BNVwu6CfD57TkCVRyrEZZifE31C8AAAAAGfkUUrqvkzyry33tDP6tvRkVXRJ1He7Y/XOqr0yDMqXI6F4AQAAAM7K208KWyGVqSzvlBNaW+4D+VhStWBrjCatjTY7Hf6C4gUAAAA4M59AKWylVKK8fBKjta7CJ/JSuj7dcESfbzxidjr8fxQvAAAAwNmVrXH5zJdnaflfjNLawJlyU7bGrT6gRdtizE4HUbwAAACAoiGgvtRtqeTqpcrxm7Uq8EtZZdNbK/Zo9Z5Ys9MVexQvAAAAoKio3Ex6fp5kdVPd+B+1IHCpbIah1xZFadOhc2anK9YoXgAAAEBRcncr6dnPJVn0j/hVml7xB2Xm2PTyVzv0e0yC2emKLYoXAAAAUNTU7yg9NVWS1DZhvsZV+ElpmTnq/cVvio5LNjlc8UTxAgAAAIqi+/pILUdKkrom/lf/9t+qxEtZCpu1VTEX0kwOV/xQvAAAAICi6sHBUvOBkqQBKR+pj98enU3OUI9ZW3U2Kd3kcMULxQsAAAAoqiwWqfW70r1hshg2vZMxRR1KH1JMfJrCZm1TYlqW2QmLDYoXAAAAUJRZLFK7aVKdp2XJydQU2wQ9WuKEos8kq/ecbUrLzDY7YbFA8QIAAACKOquL1HGmVP0RWbPSNNN1vJp4xur3mIt6+asdysjOMTthkUfxAgAAAIoDVw/p+fnSXffJJSNRC70mqKbbBW06dF5DFu9Sjs0wO2GRRvECAAAAiguPklL3pVL5unK/dFbflp6oQJeL+n5PrIav3CPDoHzZC8ULAAAAKE68/aQeX0tlqsgr5aTWlP1AZSwpWrjtpCasiTY7XZFF8QIAAACKG5+K0gsrpZIV5JN0UBEBn8pL6Zq+8YimbzxidroiieIFAAAAFEd+1aWwFZJnafknRCk88L9yU7bGrz6ghdtizE5X5FC8AAAAgOKqQj2p+zLJzVtB8ZH6JvBLWWXTWyv26PvdsWanK1IoXgAAAEBxFtRUev4ryeqmOvE/amHgEhmGoUGLd+rng+fMTldkULwAAACA4q5mK6njfyVZ1Cz+G31e8Xtl5Rh6+asd2nEiwex0RQLFCwAAAIBUr4PU7gNJUmjCAo2rsF6XsnLU+4tt2h+bZG62IoDiBQAAAOCyJr2kVqMlSV0TZ+oN/y1KSs/WC7O36cSFVHOzOTmKFwAAAID/eXCQ9MAgSVL/lI/1T7/dOpecoR6ztupMUrqp0ZwZxQsAAABAXq1GSY17ymLY9Hb6FHUsc1An4y/phVnbdDEt0+x0ToniBQAAACAvi0V66n2pbntZbFmalD1BLUscV/SZZPWe85tSM7LNTuh0KF4AAAAArmZ1kZ6dIdV4TNbsS5rhOkFNPE9rZ8xF9Zu3QxnZOWYndCoULwAAAADX5uohPT9PqtRULhmJWuQ1QbXcz2vTofMatChKOTbD7IROg+IFAAAA4PrcS0jdl0jl68nt0jmt8pmsu1wStXpvnN76eo8Mg/J1KyheAAAAAG7My1cK+1ryrSqvlBitKTtVvpYULd5+UuNXHzA7nVOgeAEAAAC4uVIBUthKqWSASiUdUkSFT+SldH3+81F9tuGI2ekcHsULAAAAwK3xqyaFrZA8y6jcxV2KqDhD7srShDUHtGBrjNnpHBrFCwAAAMCtq1BX6r5McvNWpYQt+iZwrqyy6e2Ve/TtrtNmp3NYFC8AAAAA+RN0v9RlvmR1U+349VocuFiGYWjIkihtiD5rdjqHRPECAAAAkH81HpM6zpQsVt0f/63+W/FbZeUY6jdvh7Yfjzc7ncOheAEAAAC4PfXaS+2mSZJaJyzShIB1Ss+yqc+c37Q/NsncbA6G4gUAAADg9jV+QWo9RpL0/MVZetN/i5LSsxU2a5uOn081OZzjoHgBAAAAuDMPDJQeHCxJejn5I71UdpfOp2Sox6ytiktMNzmcY6B4AQAAALhzLUdKTXrJIkPDLk1Vp9LROpVwSWGztiohNdPsdKajeAEAAAC4cxaL9ORUqV4HWWxZmpgzUa1KHtOhsynqNec3pWZkm53QVBQvAAAAAAXD6iJ1mCHVbCVr9iV9bp2o+71Oa9fJi3rpq+3KyM4xO6FpKF4AAAAACo6ru/Tcl1JQM7lkJmqB5wQFu5/Tr4cv6LWFUcrOsZmd0BQULwAAAAAFy72E1G2xVKG+3C6d0yqfyarkclFr9sXprRV7ZBiG2QkLHcULAAAAQMHz8pV6fC35VpNnykmtLvu+fC0pWrL9lP7vh/3FrnxRvAAAAADYR6kK0gsrpZIBKpV0SD9W+FjeStd/Nx3TpxuOmJ2uUFG8AAAAANiPb9XL5cvLV2Uv7lZE4OdyV5YmrY3WvC0nzE5XaCheAAAAAOyrfB2p+zLJrYTuit+q7wLnyiqb3lm1V9/sOm12ukJB8QIAAABgf5Xuk7rMl1zcVSt+vZYELpJhGBqyOEo/RZ81O53dUbwAAAAAFI4aj0odZ0kWq+6L/06zKn6jbJtN/eft0Pbj8WansyuKFwAAAIDCU/dpqd2HkqSWCYs1KWC90rNs6j3nN/1xOsnkcPZD8QIAAABQuBqHSW3GSpI6X5ylYeUjlZyerRdmb9Ox86kmh7MPihcAAACAwtf8VemhoZKkl5I+1stlo3Q+JUM9Zm5VXGK6yeEKHsULAAAAgDkee0e6r48sMvTmpal6rvQB/XnxknrM2qr41Eyz0xUopype33//vZo1ayYvLy/5+vqqffv2eW6PiYnRk08+KW9vb5UvX16vv/66srOz86zZsGGDGjduLA8PD9WsWVNz5swpvBcAAAAA4H8sFumJyVL9jrLYsjU+Z6LalDymw2dT1PuLbUrJyL75YzgJpyley5cvV1hYmHr37q1du3bp119/Vbdu3XJvz8nJ0ZNPPqnMzExt3rxZc+fO1Zw5czRixIjcNceOHdOTTz6pRx99VFFRURo0aJD++c9/au3atWa8JAAAAABWF6n9dKlma1mz0/WZdYKaef2pXacS9dKX25WelWN2wgLhFMUrOztbr732miZNmqR+/fqpVq1aqlu3rp577rncNeHh4frjjz80b9483XPPPXr88cc1ZswYffLJJ8rMvHyacvr06apWrZqmTJmiOnXq6JVXXlGnTp30/vvvm/XSAAAAALi6S899KQX9Qy6ZSZrnOVF13M9p85ELGrhwp7JzbGYnvGOuZge4Fb///rv+/PNPWa1W3XvvvYqLi9M999yjSZMmqX79+pKkyMhINWjQQBUqVMi9X2hoqPr37699+/bp3nvvVWRkpFq1apXnsUNDQzVo0KDrPndGRoYyMjJyf09KunyJy6ysLGVlZeXrdVxZn9/7oXAwH8fFbBwb83FczMaxMR/HxnxMYHGTnpsv16+ekdvZvVpRapJaJ76l8D+kN5bt0rj29WS1WhxqNvnJ4BTF6+jRo5KkUaNGaerUqapataqmTJmiRx55RAcPHpSfn5/i4uLylC5Jub/HxcXl/nmtNUlJSbp06ZK8vLyueu5x48Zp9OjRVx0PDw+Xt7f3bb2eiIiI27ofCgfzcVzMxrExH8fFbBwb83FszKfweZR/WQ8mjlXJ1FP62us9hSa/o693SvFxp9S+ik0Wy+V1jjCbtLS0W15ravF68803NWHChBuu2b9/v2y2y6cW3377bXXs2FGS9MUXX6hSpUpaunSpXn75ZbtlHDZsmIYMGZL7e1JSkoKCgtSmTRv5+Pjk67GysrIUERGh1q1by83NraCj4g4xH8fFbBwb83FczMaxMR/HxnxMdvEBGXOfkH/Kn4qo8LFanBmsDbFeurduLb34QJDDzObKu+FuhanFa+jQoerVq9cN11SvXl2xsbGSpLp16+Ye9/DwUPXq1RUTEyNJCggI0LZt2/Lc98yZM7m3XfnzyrG/rvHx8bnm2a4rz+Ph4XHVcTc3t9se9J3cF/bHfBwXs3FszMdxMRvHxnwcG/MxiX8N6YVV0hdtVTZxr8IDZ+jR0//S++sOq7S3m3zlGLPJz/ObWrz8/f3l7+9/03VNmjSRh4eHoqOj9eCDD0q6/K8Qx48fV5UqVSRJISEheu+993T27FmVL19e0uXTjz4+PrmFLSQkRD/88EOex46IiFBISEhBviwAAAAAd6p8ban7cunLp3VX/FZ9H+ittqf7aPR3+xVW06InzM6XT05xVUMfHx/169dPI0eOVHh4uKKjo9W/f39JUufOnSVJbdq0Ud26dRUWFqZdu3Zp7dq1Gj58uAYMGJB7xqpfv346evSo3njjDR04cECffvqplixZosGDB5v22gAAAABcR6UmUpcFkou77o7/SUsDF8kwDM07bNXGg+fMTpcvTlG8JGnSpEnq0qWLwsLCdP/99+vEiRNav369fH19JUkuLi767rvv5OLiopCQEPXo0UMvvPCC3n333dzHqFatmr7//ntFRESoUaNGmjJlimbOnKnQ0FCzXhYAAACAG6n+sNTpC8liVeP47zW74kr5uBm6q8y1PyrkqJziqobS5fdPTp48WZMnT77umipVqlz1VsK/e+SRR7Rz586CjgcAAADAXuo8JT39sbTqX3osYalmBxiqWb6t2anyxWnOeAEAAAAoxu7tLoX+nySp8dllsuxZYnKg/HGaM14AAAAAirmQAcpJuaDk35erRPVHzU6TLxQvAAAAAE7D9vCb+iWltkJL3Pzq6I6EtxoCAAAAcB4Wi3KsV3/PrqOjeAEAAACAnVG8AAAAAMDOKF4AAAAAYGcULwAAAACwM4oXAAAAANgZxQsAAAAA7IziBQAAAAB2RvECAAAAADujeAEAAACAnVG8AAAAAMDOKF4AAAAAYGcULwAAAACwM4oXAAAAANgZxQsAAAAA7IziBQAAAAB2RvECAAAAADujeAEAAACAnbmaHcDZGIYhSUpKSsr3fbOyspSWlqakpCS5ubkVdDTcIebjuJiNY2M+jovZODbm49iYj+NypNlc6QRXOsKNULzyKTk5WZIUFBRkchIAAAAAjiA5OVmlS5e+4RqLcSv1DLlsNptOnz6tUqVKyWKx5Ou+SUlJCgoK0smTJ+Xj42OnhLhdzMdxMRvHxnwcF7NxbMzHsTEfx+VIszEMQ8nJyQoMDJTVeuNPcXHGK5+sVqsqVap0R4/h4+Nj+v8kuD7m47iYjWNjPo6L2Tg25uPYmI/jcpTZ3OxM1xVcXAMAAAAA7IziBQAAAAB2RvEqRB4eHho5cqQ8PDzMjoJrYD6Oi9k4NubjuJiNY2M+jo35OC5nnQ0X1wAAAAAAO+OMFwAAAADYGcULAAAAAOyM4gUAAAAAdkbxAgAAAAA7o3gVkk8++URVq1aVp6enmjVrpm3btpkdCZJGjRoli8WS56d27dpmxyq2fv75Z7Vr106BgYGyWCxauXJlntsNw9CIESNUsWJFeXl5qVWrVjp06JA5YYuhm82nV69eV+2ntm3bmhO2mBk3bpzuv/9+lSpVSuXLl1f79u0VHR2dZ016eroGDBigsmXLqmTJkurYsaPOnDljUuLi41Zm88gjj1y1d/r162dS4uLls88+U8OGDXO/iDckJESrV6/OvZ19Y66bzcfZ9g7FqxAsXrxYQ4YM0ciRI/X777+rUaNGCg0N1dmzZ82OBkn16tVTbGxs7s8vv/xidqRiKzU1VY0aNdInn3xyzdsnTpyoDz/8UNOnT9fWrVtVokQJhYaGKj09vZCTFk83m48ktW3bNs9+WrhwYSEmLL42btyoAQMGaMuWLYqIiFBWVpbatGmj1NTU3DWDBw/Wt99+q6VLl2rjxo06ffq0nn32WRNTFw+3MhtJevHFF/PsnYkTJ5qUuHipVKmSxo8frx07dmj79u167LHH9Mwzz2jfvn2S2Ddmu9l8JCfbOwbsrmnTpsaAAQNyf8/JyTECAwONcePGmZgKhmEYI0eONBo1amR2DFyDJGPFihW5v9tsNiMgIMCYNGlS7rGLFy8aHh4exsKFC01IWLz9fT6GYRg9e/Y0nnnmGVPyIK+zZ88akoyNGzcahnF5r7i5uRlLly7NXbN//35DkhEZGWlWzGLp77MxDMN4+OGHjddee828UMjD19fXmDlzJvvGQV2Zj2E4397hjJedZWZmaseOHWrVqlXuMavVqlatWikyMtLEZLji0KFDCgwMVPXq1dW9e3fFxMSYHQnXcOzYMcXFxeXZS6VLl1azZs3YSw5kw4YNKl++vIKDg9W/f39duHDB7EjFUmJioiTJz89PkrRjxw5lZWXl2T+1a9dW5cqV2T+F7O+zuWL+/PkqV66c6tevr2HDhiktLc2MeMVaTk6OFi1apNTUVIWEhLBvHMzf53OFM+0dV7MDFHXnz59XTk6OKlSokOd4hQoVdODAAZNS4YpmzZppzpw5Cg4OVmxsrEaPHq2HHnpIe/fuValSpcyOh7+Ii4uTpGvupSu3wVxt27bVs88+q2rVqunIkSN666239PjjjysyMlIuLi5mxys2bDabBg0apAceeED169eXdHn/uLu7q0yZMnnWsn8K17VmI0ndunVTlSpVFBgYqN27d+s///mPoqOj9fXXX5uYtvjYs2ePQkJClJ6erpIlS2rFihWqW7euoqKi2DcO4HrzkZxv71C8UKw9/vjjuX9v2LChmjVrpipVqmjJkiXq27evickA59OlS5fcvzdo0EANGzZUjRo1tGHDBrVs2dLEZMXLgAEDtHfvXj6v6oCuN5uXXnop9+8NGjRQxYoV1bJlSx05ckQ1atQo7JjFTnBwsKKiopSYmKhly5apZ8+e2rhxo9mx8P9dbz5169Z1ur3DWw3trFy5cnJxcbnqCjhnzpxRQECASalwPWXKlFGtWrV0+PBhs6Pgb67sF/aS86hevbrKlSvHfipEr7zyir777jv99NNPqlSpUu7xgIAAZWZm6uLFi3nWs38Kz/Vmcy3NmjWTJPZOIXF3d1fNmjXVpEkTjRs3To0aNdK0adPYNw7ievO5FkffOxQvO3N3d1eTJk20bt263GM2m03r1q3L8/5UOIaUlBQdOXJEFStWNDsK/qZatWoKCAjIs5eSkpK0detW9pKDOnXqlC5cuMB+KgSGYeiVV17RihUrtH79elWrVi3P7U2aNJGbm1ue/RMdHa2YmBj2j53dbDbXEhUVJUnsHZPYbDZlZGSwbxzUlflci6PvHd5qWAiGDBminj176r777lPTpk31wQcfKDU1Vb179zY7WrH373//W+3atVOVKlV0+vRpjRw5Ui4uLuratavZ0YqllJSUPP9KdezYMUVFRcnPz0+VK1fWoEGDNHbsWN19992qVq2a3nnnHQUGBqp9+/bmhS5GbjQfPz8/jR49Wh07dlRAQICOHDmiN954QzVr1lRoaKiJqYuHAQMGaMGCBVq1apVKlSqV+/mT0qVLy8vLS6VLl1bfvn01ZMgQ+fn5ycfHR6+++qpCQkL0j3/8w+T0RdvNZnPkyBEtWLBATzzxhMqWLavdu3dr8ODBatGihRo2bGhy+qJv2LBhevzxx1W5cmUlJydrwYIF2rBhg9auXcu+cQA3mo9T7h2zL6tYXHz00UdG5cqVDXd3d6Np06bGli1bzI4EwzCef/55o2LFioa7u7tx1113Gc8//7xx+PBhs2MVWz/99JMh6aqfnj17GoZx+ZLy77zzjlGhQgXDw8PDaNmypREdHW1u6GLkRvNJS0sz2rRpY/j7+xtubm5GlSpVjBdffNGIi4szO3axcK25SDK++OKL3DWXLl0y/vWvfxm+vr6Gt7e30aFDByM2Nta80MXEzWYTExNjtGjRwvDz8zM8PDyMmjVrGq+//rqRmJhobvBiok+fPkaVKlUMd3d3w9/f32jZsqURHh6eezv7xlw3mo8z7h2LYRhGYRY9AAAAAChu+IwXAAAAANgZxQsAAAAA7IziBQAAAAB2RvECAAAAADujeAEAAACAnVG8AAAAAMDOKF4AAAAAYGcULwAAAACwM4oXAAAAANgZxQsAAAAA7IziBQAAAAB2RvECACAfjh8/LovFctXPI488YnY0AIADczU7AAAAziQoKEixsbG5v8fFxalVq1Zq0aKFiakAAI7OYhiGYXYIAACcUXp6uh555BH5+/tr1apVslp5IwkA4No44wUAwG3q06ePkpOTFRERQekCANwQxQsAgNswduxYrV27Vtu2bVOpUqXMjgMAcHC81RAAgHxavny5unbtqtWrV6tly5ZmxwEAOAGKFwAA+bB37141a9ZMQ4YM0YABA3KPu7u7y8/Pz8RkAABHRvECACAf5syZo969e191/OGHH9aGDRsKPxAAwClQvAAAAADAzrgEEwAAAADYGcULAAAAAOyM4gUAAAAAdkbxAgAAAAA7o3gBAAAAgJ1RvAAAAADAziheAAAAAGBnFC8AAAAAsDOKFwAAAADYGcULAAAAAOyM4gUAAAAAdvb/AMCy6PI6z076AAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the probability density function of the standard normal distribution\n",
        "f = norm.pdf\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "# Define the value of n, the number of normal random variables\n",
        "n = 400\n",
        "\n",
        "# Define the values of y for which to calculate the PDF\n",
        "y_values = [5, 10, 15, 20, 25, 30, 35]\n",
        "\n",
        "print(f\"Calculating the probability density function of the maximum for n = {n} monkeys\")\n",
        "print(\"-\" * 50)\n",
        "\n",
        "log_pdf_values = []\n",
        "for y in y_values:\n",
        "    # Calculate the probability density function of the maximum\n",
        "    # f_Y(y) = n * f(y) * F(y)**(n-1)\n",
        "    f_Y_y = n * f(y) * (F(y)**(n-1))\n",
        "    print(f\"f_Y({y}) = {f_Y_y:.16e}\")\n",
        "    log_pdf_values.append(np.log(f_Y_y))\n",
        "\n",
        "print(\"-\" * 50)\n",
        "a = np.sqrt(2*np.pi) # square root of ( 2 pi)\n",
        "print(f\" square root of ( 2 pi)) = {a}, its inverse = {1/a}\")\n",
        "print(f\"ln(10) = {np.log(10)}\")\n",
        "print(f\"lg(e) in base 10 = {np.log10(np.e)}\")\n",
        "print(f\"lg(e) in base 10 / 2 = {np.log10(np.e)/2}\")\n",
        "log_approximated_parable = []\n",
        "for y in y_values:\n",
        "    log_approximated_parable.append(np.log(a) - y**2/2)\n",
        "\n",
        "#Plots\n",
        "plt.figure(figsize=(10, 6))\n",
        "# plot pdf_values against y_values\n",
        "plt.plot(y_values, log_pdf_values, label=f'n = {n}')\n",
        "plt.plot(y_values, log_approximated_parable, label=f'n = {n}')\n",
        "plt.xlabel('z')\n",
        "plt.ylabel(' log_pdf_values')\n",
        "plt.title(f'Log of the pdf values of the Maximum of {n} Normal Distributions')\n",
        "plt.grid(True)\n",
        "plt.legend([\"Log_pdf\", \"Log_parable\" ])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tgXm2wUjexKk"
      },
      "source": [
        "*Our comment.* We see that our mathematical approximation and that given by Python coincide. This result is for us very nice. This also means that Python uses very good approximations.\n",
        "\n",
        "*Difficult task.* Find a suitable continuous approximation for the pdf of MAX for low values of $y$, say, 1, 2, 3, 4. Our solution to this hole is to resort to the native environment provided by the Binomial Distribution, which is discrete, and was studied in the first section. But, beware, some important results that were used there come from the continuous methods studied in this section.  \n",
        "\n",
        "We will continue assuming that our approximation procedure is excellent. Let us use it to estimate the values of the pdf for large inputs:\n",
        ">\n",
        ">> $ \\sqrt{2 \\pi} = 2.5066282746310002$  \n",
        ">>\n",
        "> $ \\frac{1}{\\sqrt{2 \\pi}} = 0.3989422804014327$\n",
        ">>\n",
        "> In general,\n",
        ">>\n",
        "> $ log (f_{Y}(y))  = log(\\frac{n}{\\sqrt{2 \\pi}} ) - \\frac{y^2}{2}$\n",
        ">>\n",
        "or, equivalently, and for values of 5 standard deviations or above,\n",
        ">>\n",
        "> $ f_{Y}(y) =  \\frac{n}{\\sqrt{2 \\pi}} e^{-\\frac{y^2}{2}}$\n",
        ">>\n",
        "> $  f_{Y}(y) =  0.3989422804014327 \\times n \\times e^{-\\frac{y^2}{2}}$\n",
        ">>\n",
        "> Since the log in base 10 of e is 0.4342944819032518, then $ 10^{0.4342944819032518} = e$, therefore\n",
        ">>\n",
        "> $ f_{Y}(y) =     0.3989422804014327 \\times n \\times (10^{0.4342944819032518})^{-\\frac{y^2}{2}}$\n",
        ">>\n",
        "> $ f_{Y}(y) =     0.3989422804014327 \\times n \\times 10^{-\\frac{0.4342944819032518y^2}{2}}$\n",
        ">>\n",
        ">$ f_{Y}(y) =     0.3989422804014327 \\times n \\times 10^{-0.2171472409516259y^2}$\n",
        ">>\n",
        ">Rounding:\n",
        ">>\n",
        ">$ f_{Y}(y) =   0.4 \\times n \\times 10^{-0.22 y^2}$\n",
        "\n",
        "Thus, if the number of monkeys is $n = 400$ and the number of standard deviations above the mean is $y = 50$, we get\n",
        ">>\n",
        ">$ f_{Y}(50) =   0.4 \\times 400 \\times 10^{-0.22 \\times 2500} $\n",
        ">>$ = 160 \\times 10^{-550} \\sim 1000 \\times 10^{-550} = 10^{-547} $\n",
        ">>\n",
        "To give a meaning to this probability, let us imagine that we must match a binary string $m$ bits long. We need to calculate $m$ in the Binomial $Bi(m, 1/2)$ such that perfection is achieved when one departs 50 standard deviations above the mean. Let us proceed:\n",
        ">\n",
        "The mean of $Bi(m, 1/2)$ is $\\mu = m/2$, the variance is $\\sigma^2 = mpq = m/4$ and the deviation is $\\sigma = \\sqrt{m}/2$. Perfection means to match all $m$ sites. Therefore, we demand that\n",
        ">\n",
        ">$m = \\mu + 50 \\sigma = \\frac{m}{2} + 50 \\frac{\\sqrt{m}}{2}$\n",
        ">\n",
        ">$2m = m + 50  \\sqrt{m} $\n",
        ">>\n",
        ">>$m = 50  \\sqrt{m} $\n",
        ">>\n",
        ">$m^2 = 2500   m $\n",
        ">>\n",
        ">$ m = 2500$\n",
        "\n",
        "This means that the perfection resulting from 50 standard deviations is equivalent to guessing a 2500-bit long string. \n",
        "\n",
        "Let us interpret now the meaning of the expression\n",
        ">>\n",
        ">$ f_{Y}(50) =  10^{-547} $.\n",
        ">>\n",
        "> We proceed by common sense: If the probability of head is 1/2, we can throw the coin twice, and it is reasonable to expect at least one head. By the same token, if the probability of perfection is $10^{-547} $, then, it is reasonable to see one event if we make a number of trials $T$ equals to\n",
        ">>\n",
        "> $T = \\frac{1}{10^{-547}} = 10^{547}$\n",
        ">>\n",
        "> A trial consists in siting 400 monkeys to print at random 2500 binary symbols, 0 or 1. Next, we compare what they produced with a predefined binary target string 2500 bits long. After comparison, site by site, we pick up the max.\n",
        ">>\n",
        "\n",
        "\n",
        "\n",
        "**Exercise.**  Abandon perfection and compute the needed time for MAX of 400 monkeys to solve the 2500 bits up to a 95% of perfection.\n",
        ">\n",
        "*Answer.* The mean of $Bi(2500, 1/2)$ is 1250 and the variance is 625, the deviation is 25. The 95% of 2500 is 2375. It is above the mean 45 standard deviations instead of 50. The probability is\n",
        ">>\n",
        ">$ f_{Y}(y) =   0.4 \\times n \\times 10^{-0.22 y^2}$\n",
        ">>\n",
        ">$ f_{Y}(45) =   0.4 \\times 400 \\times 10^{-0.22 (45)^2}$\n",
        ">>\n",
        ">$ f_{Y}(45) =   160 \\times 10^{-0.22  \\times 2025}$\n",
        ">>\n",
        ">$ f_{Y}(45) =   160 \\times 10^{-445}$\n",
        ">>\n",
        ">$ f_{Y}(45) =    10^{-442}$\n",
        ">\n",
        "As we see, abandoning perfection in favor of quasi-perfection does not help anyhow to explain the information contained in a binary string 2500 bits long.\n",
        "\n",
        "> In short, aiming to guess 95% of a 2500 bit long binary string is a vain remedy. So, let us be more positive: to match a target binary string 2500 bits is possible, but a huge number of trials is expected. In regard with biology, a trial means a genome that does not comply with the demanded characteristics to make life possible. This is scientific: we have here the mandatory prediction that says that our existence must be accompanied by every sort of malformations and malfunctions in our bodies and that the fossil record must be full of deformities. Thus, the cost, given as the number of trials, converts tiny probabilities into mandatory,  scientific reality.\n",
        "\n",
        "**Exercise.** Compare the power of a group of monkeys with and without MAX to solve the Shakespeare Challenge. Computations about 400 monkeys without MAX can be found [in a previous work](\n",
        "https://colab.research.google.com/drive/1dEykeQxNXZY0eVfC4fFnNhKdKvUbm7Wr?usp=sharing ).\n",
        ">\n",
        "*Answer.* A group of monkeys behaves the same no matter if one picks the MAX or not.  In both cases, if the group has $n$ monkeys, the tiny probability of success by one monkey is multiplied by $n$. In other words, the MAX is not important per se. What matters is what one does with the MAX and this is the challenge that Evolution promise to solve with bright colors.\n",
        "A more concrete formulation is proposed in the next subsection:\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n",
        "## The MAX_ROCKET challenge.* \n",
        "\n",
        "We have found that MAX has important virtues: \n",
        "- MAX outputs high quality.\n",
        "- At extremely low cost, the fluctuations of MAX are sensibly smoothed. \n",
        "- MAX produces stable, repeatable results. So, one can formulate trustable predictions. Our choice is to find a formula for the expected value and use it in predictions. \n",
        "  \n",
        "But, MAX also has a pitfall:\n",
        "- MAX is good but not good enough.\n",
        "- MAX is extremely expensive to be used to battle complexity.\n",
        "\n",
        "So, a question springs as a fierce challenge:\n",
        ">\n",
        ">  **The MAX-Rocket Challenge:**\n",
        ">>\n",
        ">> Incorporate MAX, as a fundamental piece, into a powerful algorithm to skyrocket its capability to battle complexity. \n",
        "\n",
        "In the next contribution, we will study Evolution as a beautiful promise to solve this challenge."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hmldKCj-BvYt"
      },
      "source": [
        "## Estimation of the mean and variance of MAX\n",
        "\n",
        "We use here the cdf of MAX to estimate its mean and variance. The official name of the mean of a random variable, a source of random data, is the **expected value**. Thus, it is the value by default of a random variable. The variance is a measure of the variability of the output data. We use the variance of a random variable as an indicator of the predictive power of its expected value. If the variance is low, the expected value is a good predictor for the outputs of the random variable. As the variance grows, that predictive power diminishes.  \n",
        "\n",
        "**Exercise.** Develop a program that uses the cdf of MAX to estimate its expected value and variance for 400 monkeys.\n",
        ">\n",
        ">*Answer.* The following code uses the cdf of MAX to estimate the variance for 400 monkeys.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 686
        },
        "id": "x_xGAm1OGWjV",
        "outputId": "c1c28502-5e1b-4746-e0c8-9e7003d1f023"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "CDF =  Cumulative Distribution Function\n",
            "PDF =  Probability Density Function\n",
            "Inferior border, i =   436, Fn_z[i] = 0.0254\n",
            "Inf in units = 2.36\n",
            "Superior border, i = 583, Fn_z[i] = 0.975\n",
            "Sup in units = 3.83\n",
            "Number of monkeys = 400, mean = 2.96, variance = 0.14, deviation = 0.38\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program MeanAndVarianceOfMAX\n",
        "# The cdf of MAX is used to calculate mean and variance.\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "print(\"CDF =  Cumulative Distribution Function\")\n",
        "print(\"PDF =  Probability Density Function\")\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201) #init of interval, end, number of points\n",
        "\n",
        "# Define the value of m, the   number of normal random variables or monkeys\n",
        "m  = 400\n",
        "# Cumulative distribution function of the maximal value\n",
        "# of 400 normal distribution with mean 0 and deviation 1.\n",
        "Fn_z = F(z_values)**m\n",
        "# print(Fn_z)\n",
        "\n",
        "# Borders of common events\n",
        "inf = 0\n",
        "sup = 0\n",
        "# Inferior border of the interval of common values\n",
        "for i in range(1200):\n",
        "    if  Fn_z[i] >= 0.025 :\n",
        "        print(f\"Inferior border, i =   {i}, Fn_z[i] = {Fn_z[i]:.3}\")\n",
        "        inf = -2 + i/100\n",
        "        print(f\"Inf in units = {inf:.3}\")\n",
        "        break\n",
        "# Superior border of the interval of common values\n",
        "# run i from 1200 until 0 with step -1, i.e., in reverse order\n",
        "for i in range(1200, 0, -1):\n",
        "    if  Fn_z[i] <= 0.975 :\n",
        "        print(f\"Superior border, i = {i}, Fn_z[i] = {Fn_z[i]:.3}\")\n",
        "        sup = -2 + i/100\n",
        "        print(f\"Sup in units = {sup:.3}\")\n",
        "        break\n",
        "\n",
        "\n",
        "# The Bell or pdf of MAX\n",
        "pdf = []\n",
        "pdf_draw = []\n",
        "for i in range(1200):\n",
        "    delta_y = Fn_z[i+1] - Fn_z[i]\n",
        "    #delta_x = z_values[i+1] - z_values[i]\n",
        "    #bell.append(delta_y/delta_x)\n",
        "    pdf.append(delta_y)\n",
        "    pdf_draw.append(100*delta_y)\n",
        "pdf.append(0.0) # to enabling pairing with the other graph\n",
        "pdf_draw.append(0.0)\n",
        "\n",
        "# The mean in z units\n",
        "mean = 0 #init\n",
        "for k in range(1200):\n",
        "    mean += (k/100 -2) * pdf[k]\n",
        "# print(f\"Number of monkeys = {m}, Mean = {mean:.3}\")\n",
        "\n",
        "# Variance\n",
        "variance = 0.0\n",
        "for k in range(1200):\n",
        "    variance += ((k/100 -2 - mean)**2) * pdf[k]\n",
        "deviation = np.sqrt(variance)\n",
        "print(f\"Number of monkeys = {m}, mean = {mean:.3}, variance = {variance:.2}, deviation = {deviation:.2}\")\n",
        "\n",
        "\n",
        "#Plots\n",
        "plt.figure(figsize=(10, 6))\n",
        "# Plot the cumulative distribution functions F^n(z)\n",
        "plt.plot(z_values, Fn_z, label=f'm = {m}')\n",
        "# Border: Draw a vertical red line at x = inf\n",
        "plt.axvline(x=inf, color='red', linestyle='--', linewidth=2)\n",
        "\n",
        "# Draw the bell\n",
        "plt.plot(z_values, pdf_draw )\n",
        "plt.xlabel('z')\n",
        "plt.ylabel('F^m(z)')\n",
        "plt.title(f'CDF and PDF of the Maximum of {m} Normal Distributions, and common events')\n",
        "plt.grid(True)\n",
        "\n",
        "\n",
        "# Mean\n",
        "plt.axvline(x=mean, color='green', linestyle='--', linewidth=2)\n",
        "plt.legend([\"cdf\", \"borders of common events\", \"bell or pdf in arbitrary height\", \"mean -1, 0, +1 deviations\" ])\n",
        "# Superior border\n",
        "plt.axvline(x=sup, color='red', linestyle='--', linewidth=2)\n",
        "\n",
        "plt.axvline(x=mean - 1 * deviation, color='green', linestyle='--', linewidth=2)\n",
        "plt.axvline(x=mean + 1 * deviation, color='green', linestyle='--', linewidth=2)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NpJyrVhaHGcz"
      },
      "source": [
        "**Our observations.** The bell or pdf is a bit more spread towards the right wing, to high values. The common events up to 95% that are predicted by the cdf are different from those predicted by 2 standard deviations.\n",
        "\n",
        "**Exercise.** Develop a program to estimate the mean and variance of MAX as a function of the number of monkeys. This is equal to the number of independent identically distributed normal distributions that are taken into consideration to extract its MAX value.\n",
        ">\n",
        ">*Answer.* The following code estimates the variance of MAX as a function of the number of monkeys."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "igYzNfzzC32L",
        "outputId": "5e168a4e-efc1-489e-a715-da7f1dc6d70f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of monkeys = 1, mean = 0.0491, variance = 0.87, deviation = 0.93\n",
            "Number of monkeys = 10001, mean = 3.85, variance = 0.093, deviation = 0.3\n",
            "Number of monkeys = 20001, mean = 4.01, variance = 0.086, deviation = 0.29\n",
            "Number of monkeys = 30001, mean = 4.11, variance = 0.083, deviation = 0.29\n",
            "Number of monkeys = 40001, mean = 4.17, variance = 0.08, deviation = 0.28\n",
            "Number of monkeys = 50001, mean = 4.23, variance = 0.079, deviation = 0.28\n",
            "Number of monkeys = 60001, mean = 4.27, variance = 0.077, deviation = 0.28\n",
            "Number of monkeys = 70001, mean = 4.3, variance = 0.076, deviation = 0.28\n",
            "Number of monkeys = 80001, mean = 4.33, variance = 0.075, deviation = 0.27\n",
            "Number of monkeys = 90001, mean = 4.36, variance = 0.075, deviation = 0.27\n",
            "Number of monkeys = 100001, mean = 4.38, variance = 0.074, deviation = 0.27\n",
            "Number of monkeys = 110001, mean = 4.4, variance = 0.073, deviation = 0.27\n",
            "Number of monkeys = 120001, mean = 4.42, variance = 0.073, deviation = 0.27\n",
            "Number of monkeys = 130001, mean = 4.44, variance = 0.072, deviation = 0.27\n",
            "Number of monkeys = 140001, mean = 4.45, variance = 0.072, deviation = 0.27\n",
            "Number of monkeys = 150001, mean = 4.47, variance = 0.071, deviation = 0.27\n",
            "Number of monkeys = 160001, mean = 4.48, variance = 0.071, deviation = 0.27\n",
            "Number of monkeys = 170001, mean = 4.49, variance = 0.071, deviation = 0.27\n",
            "Number of monkeys = 180001, mean = 4.51, variance = 0.07, deviation = 0.27\n",
            "Number of monkeys = 190001, mean = 4.52, variance = 0.07, deviation = 0.26\n",
            "Number of monkeys = 200001, mean = 4.53, variance = 0.07, deviation = 0.26\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7819b32c9f40>"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program VarianceOfMAXasFunctionOfNumberOfMonkeys.py\n",
        "# The cdf of MAX is used to calculate the mean\n",
        "# and the variances of MAX\n",
        "# as a function of the number of monkeys\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the value of m, the   number of normal random variables or monkeys\n",
        "m  = 400\n",
        "\n",
        "# Number of monkeys\n",
        "# n_normals = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_normals = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000] # This setting reaches 16\n",
        "n_normals = range(1, 200002, 10000) # (start, end, step)\n",
        "\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201) #init of interval, end, number of points\n",
        "\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "\n",
        "# print(\"CDF =  Cumulative Distribution Function\")\n",
        "# print(\"PDF =  Probability Density Function\")\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201) #init of interval, end, number of points\n",
        "\n",
        "expected_means = []\n",
        "expected_variances = []\n",
        "for m in n_normals:\n",
        "    # The cumulative distribution function of MAX\n",
        "    # Cumulative distribution function of the maximal value\n",
        "    # of m normal distribution with mean 0 and deviation 1.\n",
        "    Fn_z = F(z_values)**m\n",
        "    # print(Fn_z)\n",
        "    # The Bell or pdf of MAX\n",
        "    pdf = []\n",
        "    for i in range(1200):\n",
        "        delta_y = Fn_z[i+1] - Fn_z[i]\n",
        "        #delta_x = z_values[i+1] - z_values[i]\n",
        "        #bell.append(delta_y/delta_x)\n",
        "        pdf.append(delta_y)\n",
        "        # pdf_draw.append(100*delta_y)\n",
        "    pdf.append(0.0) # to enabling pairing with the other graph\n",
        "    # pdf_draw.append(0.0)\n",
        "\n",
        "    # The mean in z units\n",
        "    mean = 0 #init\n",
        "    for k in range(1200):\n",
        "        mean += (k/100 -2) * pdf[k]\n",
        "    # print(f\"Number of monkeys = {m}, Mean = {mean:.3}\")\n",
        "\n",
        "    # Variance\n",
        "    variance = 0.0\n",
        "    for k in range(1200):\n",
        "        variance += ((k/100 -2 - mean)**2) * pdf[k]\n",
        "    deviation = np.sqrt(variance)\n",
        "    print(f\"Number of monkeys = {m}, mean = {mean:.3}, variance = {variance:.2}, deviation = {deviation:.2}\")\n",
        "\n",
        "    expected_means.append(mean)\n",
        "    expected_variances.append(variance)\n",
        "    # print(f\"Number of monkeys = {m}, Mean = {mean:.3}, variance = {variance:.2}, deviation = {deviation:.2}\")\n",
        "\n",
        "#Plot the expected means\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_normals, expected_means, label='Expected Means')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Mean of MAX ')\n",
        "plt.title(f'Mean of MAX   as a function of the number of monkeys, according to the cdf')\n",
        "plt.legend()\n",
        "\n",
        "#Plot the expected variances\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_normals, expected_variances, label='Expected Variances')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Variance of MAX ')\n",
        "plt.title(f'Variance of MAX  as a function of the number of monkeys, according to the cdf')\n",
        "plt.legend()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jgM0e4Rh9xQ_"
      },
      "source": [
        "**Our observations:** The mean grows very rapidly until a number of monkeys around 5000 and then grows very slowly. The variance has a rapid decline until a number of monkeys around 5000 and then tends to zero very slowly. Just as with binomial distributions.\n",
        "\n",
        "*Challenge.* Develop a mathematical formula to predict the form as the variance depends on the number of monkeys."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TSZpTVmUuGn9"
      },
      "source": [
        "### Mathematical predictions\n",
        "\n",
        "Let us pass now to consider mathematical predictions for the expected value of MAX and its variance. The first one makes official the observation that the MAX does not scatter the mother distribution. Because our mother distribution is a standard normal distribution, with mean zero and variance 1, all that we must prove is that the variance of MAX is not greater than 1. This result will be used to propose a lower bound for the mean. Concretely, we have two theorems:\n",
        "\n",
        "*Theorem of the not dispersiveness of MAX.*\n",
        ">>\n",
        "> The variance of MAX is not greater than 1.\n",
        "\n",
        "*Sandwich Theorem for the bounds of the mean of MAX.*\n",
        ">>\n",
        "> Let $n\\in \\mathbb{N}^*$ and  $ Z_i$, i=1,...,n be i.i.d $\\mathcal{N}(0,1)$. Then, the expected value of MAX is approximately given by the following sandwich result:\n",
        ">>>\n",
        ">>$\\sqrt{ln(n)} \\leq \\mathbb{E} (MAX  ) \\leq  \\sqrt{2ln(n)} $\n",
        ">>>\n",
        "> This approximation theorem points to a family of functions of the form $\\sqrt{kln(n)}$, in which the best value of $k$, with $1 \\leq k \\leq 2$, must be found by resorting to the cdf of MAX and/or to simulations. Resultant formula will be used as default value in predictions.\n",
        "\n",
        "All what follows are details that help to understand where these theorems come from. Mathematical results and Python programs are included. Let us begin with the variance, whose upper bound is simpler to establish."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Sj4pd0mfkXr"
      },
      "source": [
        "###  MAX is not dispersive\n",
        "\n",
        "The variance measures the dispersion of data and serves as an indicator of the trustability of the mean as predictor of the behavior of the studied distribution. We have observed that MAX contracts the distribution. Actually, it shifts the mother distribution, with mean 0 and variance 1, to upper values but with a concentrating effect because too high values are rarely accessed.  Let us mathematically justify a very weak assertion: MAX is not dispersive, i.e., its variance is not greater than 1. Thus, the variance of MAX is equal or less than 1. To prove this, we need a prerequisite.\n",
        "\n",
        "### The Poincaré inequality\n",
        "\n",
        " Let   $Z$  be the maximum of  $n$  independent identically distributed Gaussian variables  $X_1,\\ldots,X_n$. The cdf  $\\Phi$  of $Z$ is\n",
        "\n",
        "$\\Phi(x) = F^n(x) $\n",
        "\n",
        "where $F$ is the cdf of the normal distribution. Graphical analysis of the behavior of $\\Phi$ suggests that the variance of $Z$ is less than 1 and that it diminishes with $n$. To prove that 1 is an upper bound, the use of the Poincaré inequality has been proposed.   For Gaussian random variables, that inequality is\n",
        "\n",
        "$\\mathbf{Var}(f(X_1,\\ldots,X_n))\\leq \\mathbf{E}[\\|\\nabla f(X_1,\\ldots,X_n)\\|^2]$\n",
        "\n",
        "where the function $f: \\mathbb{R}^n \\to \\mathbb{R}$, and   $\\mathbf{E}$ is the expectation functional that assigns to each random variable its expected value.\n",
        "\n",
        "I battled with a confusion: How can we apply this inequality to $Z$ given that $Z$ is not a function, but an algorithm that outputs a cdf? It is an algorithm because it describes a complex recipe. Besides, when one throws $n$ random values of a normal distribution and picks the max, the result fluctuates from trial to trial, there is no continuity, no differentiability, no right to apply the Poincaré inequality.  When I shared my confusion with the community, I received a strong reprimand as from a father,  but [one member gave me a light](\n",
        " https://math.stackexchange.com/questions/5112403/how-to-use-the-poincar%c3%a9-inequality-to-bound-the-variance-of-the-maximum-of-ii ).\n",
        "\n",
        "\n",
        "The reprimand without explanations compelled me to ask myself: What was the idea of Poincaré that allowed him to formulate his inequality? My reflection allowed me to dismantle my confusion:\n",
        "\n",
        "In first place, the variance  refers to the dispersion of data that  are represented by a frequency histogram,  or a pdf, or a cdf, but without taking into consideration the form as they arrived.  \n",
        "\n",
        "In second place, let us imagine that random data arrive and that we somehow process them. The processing takes a sample of $n$ values and produces a single output, which is a real number. The operation is denoted by $f: \\mathbb{R}^n \\to \\mathbb{R}$. In our case, $f$ is MAX. Thus, we have two histograms or pdfs, the standard normal distribution, the mother, and that of modified data by $f = MAX$, where the MAX is the maximal value from $n$ numbers sampled from the mother distribution.  Let us now face the question:  How is related the dispersion of the outputs of $f$ to that of the original raw data? In our case, we have $n$ normal variables with dispersion 1. So, we ask: Is the variance of $f$ values less, equal or larger than 1? This depends on the dispersive power of $f$. Let us consider various cases.\n",
        "\n",
        "- If $f$ assigns the same constant to all inputs of $n$ data, the resultant dispersion is 0. The processing by $f$ does not disperse, it rather concentrates.\n",
        "\n",
        "- A function with mild dispersive power could be a Gauss Bell: if raw data is dispersed all through the domain, here $\\mathbb{R}^n$, the $f$-values are rather concentrated in the range from 0 to the summit of the bell.\n",
        "\n",
        "- A function with immense scattering power could be the paraboloid that opens upwards. $f$-values rapidly diverge to large numbers.\n",
        "\n",
        "- Max?, What does MAX do? According to the cdfs, MAX shifts and concentrates to the right.  Thus, we gladly would accept that the variance of $MAX$ is less than 1, the variance of each standard normal distribution.\n",
        "\n",
        "Let us pass from qualitative considerations  of processing functions to quantitative ones. Let us think of different lines:\n",
        "\n",
        "- An horizontal line represents a constant value, it has zero dispersive power.\n",
        "\n",
        "- If the slope becomes positive and increases, the dispersive power augments\n",
        "\n",
        "- If the slope is very high, its scattering power is huge.\n",
        "\n",
        "From this, we conclude that the inclination of the tangent line gives the local scattering power of a function. We infer from this that for functions from $\\mathbb{R}^n \\to  \\mathbb{R}$, the maximal scattering power goes in the direction of the gradient $\\nabla f $. Now, local dispersive powers of a functional must be gathering together into one single indicator. Poincaré took the average of the squared norm of the gradient: \n",
        "\n",
        "$$\\mathbf{Var}(f(X_1,\\ldots,X_n))\\leq \\mathbf{E}[\\|\\nabla f(X_1,\\ldots,X_n)\\|^2].$$\n",
        "\n",
        "The community has two proposals in regard with this problem:\n",
        "\n",
        ". The variance of MAX is equal or less than 1.\n",
        "\n",
        ". The variance diminishes with $n$ and takes a value of the order of $\\frac{1}{\\ln n}$.\n",
        "\n",
        "A theoretical proof has been proposed for the first assertion, while the second is based on simulations by Evariste, as reported in the same aforementioned web page. Let us deal with the proof of the first assertion.\n",
        "\n",
        "### Upper bound of the variance of MAX\n",
        "\n",
        "Using the Schwarz inequality, we can establish an upper bound for the variance of MAX.\n",
        "\n",
        "*Theorem of the not dispersiveness of MAX.* The variance of MAX is equal or less than 1. This  restriction  will serve to lower bound the mean.\n",
        ">\n",
        "*Proof.* The proposed proof by Sangchul Lee, in the cited page, of this proposition is, verbatim, the following:\n",
        ">\n",
        ">For IID gaussian variables $X_1, \\ldots, X_n$ and for a Lipschitz function $f:\\mathbb{R}^n\\to\\mathbb{R}$, the Gaussian Poincare Inequality tells $$\\mathbf{Var}(f(X_1,\\ldots,X_n))\\leq \\mathbf{E}[\\|\\nabla f(X_1,\\ldots,X_n)\\|^2].$$ Now apply this to $f(x_1,\\ldots,x_n)=\\max_{i\\in[n]}x_i$ with the observation that $$\\frac{\\partial f}{\\partial x_i}=\\mathbf{1}[x_i\\text{ is the largest}].$$\n",
        ">\n",
        "Let me explain how this functions in two dimensions. We  tacitely generalize. In two dimensions,   the domain is the plane, and let us consider the first quadrant, over which both coordinates are positive. We divide the quadrant in  two regions: the first below the diagonal and the second, above. The function that describes MAX is\n",
        ">\n",
        ">\n",
        "$$\n",
        "f(x) = \n",
        "\\begin{cases}\n",
        " x & \\text{when $x \\ge y$, below the diagonal} \\\\\n",
        " y & \\text{when $y \\ge x$, above the diagonal}\n",
        "\\end{cases}\n",
        " $$\n",
        ">\n",
        "There is no contradiction over the diagonal and the function is continuous.\n",
        ">\n",
        "In the first region, the gradient is\n",
        ">\n",
        ">$\\nabla f(x,y) = [\\partial f/ \\partial x, \\partial f/ \\partial y ] = 1\\vec{i} $ \n",
        ">\n",
        "with norm squared 1. In the second region, the gradient is\n",
        ">>\n",
        ">$\\nabla f(x,y) = 1\\vec{j} $\n",
        ">\n",
        "with norm squared 1.\n",
        ">\n",
        "Along the diagonal, the function is not differentiable because the level curves  form the  half of a square with the upper right corner over the diagonal. It happens that over the diagonal there is an ambiguity for the gradient, between $\\vec{i}$ and $\\vec j$, whose norm is 1 for both cases. That is not that  terrible: this is not a problem because the expectation is given in terms of the Lebesgue measure which tolerate errors over sets of area zero, like the diagonal is.\n",
        ">\n",
        "In both regions, and all over the plane, except diagonals,  the norm squared of the gradient is 1, Whose expectation value is 1. Hence, the Poincaré inequality reads for our case:\n",
        ">\n",
        "> $\\mathbf{Var}(f(X_1,\\ldots,X_n))\\leq \\mathbf{E}[\\|\\nabla f(X_1,\\ldots,X_n)\\|^2]  = 1 $\n",
        ">\n",
        "an inequality that says that MAX, represented here by $f$, is not dispersive.\n",
        "\n",
        "*Challengue.* Do something better than this. This is plainly possible because we have proven only that MAX is not dispersive.  This is an extremely humble assertion given our results based on the cdf of MAX, showing that MAX is contractile, i.e., that the variance rapidly decreases to the tenth part and then slowly tends to zero. The following  literature might help you in this interesting and challenging task:\n",
        "\n",
        "https://math.stackexchange.com/questions/5112403/how-to-use-the-poincar%c3%a9-inequality-to-bound-the-variance-of-the-maximum-of-ii\n",
        "\n",
        "https://stats.stackexchange.com/questions/229073/variance-of-maximum-of-gaussian-random-variables\n",
        "\n",
        "https://stats.stackexchange.com/questions/134190/asymptotic-distribution-of-the-max-min-of-iid-binomial-variables\n",
        "\n",
        "https://math.stackexchange.com/questions/590880/bounds-for-the-maximum-of-binomial-random-variables\n",
        "\n",
        "https://stats.stackexchange.com/questions/229073/variance-of-maximum-of-gaussian-random-variables\n",
        "\n",
        "https://en.wikipedia.org/wiki/Gumbel_distribution\n",
        "\n",
        "https://stats.stackexchange.com/questions/105745/extreme-value-theory-show-normal-to-gumbel\n",
        "\n",
        "https://stats.stackexchange.com/questions/105745/extreme-value-theory-show-normal-to-gumbel\n",
        "\n",
        "\n",
        "Theorem 1.5.3\n",
        "https://minerva.it.manchester.ac.uk/%7Esaralees/book2.pdf\n",
        "\n",
        "https://perso.math.univ-toulouse.fr/ktanguy/files/2012/04/Article-3-brouillon.pdf\n",
        "\n",
        "https://en.wikipedia.org/wiki/Poincar%C3%A9_inequality\n",
        "\n",
        "A short proof of a Chernoff inequality\n",
        "https://www.math.uni.wroc.pl/~pms/files/5.1/Article/5.1.13.pdf\n",
        "\n",
        "https://www.math.utoronto.ca/mnica/CPSS_2012_Notes.pdf\n",
        "\n",
        "THE MEAN OF MAX\n",
        "\n",
        "https://math.stackexchange.com/questions/590880/bounds-for-the-maximum-of-binomial-random-variables\n",
        "\n",
        "https://mathoverflow.net/questions/151033/asymptotics-of-the-maximum-of-binomial-random-variables#:~:text=A%20place%20where%20the%20calculation,Add%20a%20comment\n",
        "\n",
        "https://math.stackexchange.com/questions/590880/bounds-for-the-maximum-of-binomial-random-variables\n",
        "\n",
        "https://math.stackexchange.com/questions/89030/expectation-of-the-maximum-of-gaussian-random-variables/5008221#5008221\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lH4zFgHPcsAR"
      },
      "source": [
        "## The expected value of MAX\n",
        "\n",
        "What is the value of MAX that must be used in a prediction? We recommend using the expected value, which is approximated by the mean of samples. Our purpose for this subsection is to find a formula for the expected value of MAX as a function of the number of monkeys.\n",
        "\n",
        "\n",
        "We approximate Binomials by the Normal Distribution and our units come in $z$-units, i.e., in standard deviations above the mean, so, it is enough to consider Gauss Bells with mean 0 and standard deviation 1.  An approximation to the expected value  of MAX as a function of the number of considered bells, modelling the number of monkeys in the Shakespeare challenge,  is given by the following result:\n",
        "\n",
        "\n",
        "*Theorem.*  Let $MAX = max_{1 \\leq i \\leq n}   Z_i$ be the random variable that takes the maximal value over $n$ independent standard distributions  $Z_i = \\mathcal{N}(0,1)$ with $i=1,...,n$. Then\n",
        ">>\n",
        ">The mean or expected value of MAX is approximately given by the following sandwish  result:\n",
        ">>>\n",
        ">>$\\sqrt{ln(n)} \\leq \\mathbb{E} (MAX  ) \\leq  \\sqrt{2ln(n)} $\n",
        ">>>\n",
        ">This approximation theorem points to a family of functions of the form $\\sqrt{kln(n)}$, for which the best value of $k$ must be found by resorting to the cdf of MAX and/or  to simulations.    Resultant formula will be used to predict  default values.\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "**Exercise.** Develop a program to test the previous theorem. If it makes sense, fine tune the value of the constant $k$ in $\\mathbb{E} (MAX  ) =  \\sqrt{k \\ln(n)}$ and verify the prediction that $ 1 < k < 2$.\n",
        ">\n",
        "*Answer.* The following program tests the proposition that the expected value of MAX taken between $n$ monkeys is  $ \\mathbb{E} (MAX  ) =   \\sqrt{k \\ln(n)}$ and allows, by trial and error, to find a value for the constant $k$. \n"
      ]
    },
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        "id": "bSO9OBCRivUq",
        "outputId": "b7fbac16-038b-41f0-dcdf-3d79b73f49e4"
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      "outputs": [
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",
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Program ExpectValueOfMAXvsMathPrediction.py\n",
        "# The cdf of MAX is used to calculate the mean  of MAX\n",
        "# as a function of the number of monkeys.\n",
        "# A mathematically predicted formula is contrasted.\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Define the value of m, the   number of normal random variables or monkeys\n",
        "m  = 400\n",
        "\n",
        "# Number of monkeys\n",
        "# n_normals = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 1000000]\n",
        "# n_normals = [1, 3, 5, 7, 10, 50, 100, 500, 1000, 5000, 10000] # This setting reaches 16\n",
        "n_normals = range(1, 200002, 10000) # (start, end, step)\n",
        "\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201) #init of interval, end, number of points\n",
        "\n",
        "\n",
        "# Define the cumulative distribution function of the standard normal distribution\n",
        "F = norm.cdf\n",
        "\n",
        "\n",
        "# print(\"CDF =  Cumulative Distribution Function\")\n",
        "# print(\"PDF =  Probability Density Function\")\n",
        "# Define a range of z values.\n",
        "# 1000 points equally spaced in within -2 and 8.\n",
        "z_values = np.linspace(-2, 10, 1201) #init of interval, end, number of points\n",
        "\n",
        "expected_means = []\n",
        "for m in n_normals:\n",
        "    # The cumulative distribution function of MAX\n",
        "    # Cumulative distribution function of the maximal value\n",
        "    # of m normal distribution with mean 0 and deviation 1.\n",
        "    Fn_z = F(z_values)**m\n",
        "    # print(Fn_z)\n",
        "    # The Bell or pdf of MAX\n",
        "    pdf = []\n",
        "    for i in range(1200):\n",
        "        delta_y = Fn_z[i+1] - Fn_z[i]\n",
        "        #delta_x = z_values[i+1] - z_values[i]\n",
        "        #bell.append(delta_y/delta_x)\n",
        "        pdf.append(delta_y)\n",
        "        # pdf_draw.append(100*delta_y)\n",
        "    pdf.append(0.0) # to enabling pairing with the other graph\n",
        "    # pdf_draw.append(0.0)\n",
        "\n",
        "    # The mean in z units\n",
        "    mean = 0 #init\n",
        "    for k in range(1200):\n",
        "        mean += (k/100 -2) * pdf[k]\n",
        "    # print(f\"Number of monkeys = {m}, Mean = {mean:.3}\")\n",
        "    expected_means.append(mean)\n",
        "\n",
        "k = 1.29\n",
        "predicted_means = []\n",
        "for m in n_normals:\n",
        "    predicted_means.append(k * np.sqrt(np.log(m)))\n",
        "\n",
        "#Plot the expected and predicted means\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(n_normals, expected_means, label='Expected according to cdf')\n",
        "plt.plot(n_normals, predicted_means, label=f'Predicted  by sqrt({k} ln m)')\n",
        "plt.xlabel('m = number of monkeys')\n",
        "plt.ylabel('Expected value of MAX ')\n",
        "plt.title(f'Expected value of MAX as a function of the number of monkeys')\n",
        "plt.legend()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ElNwz_KNq9Gx"
      },
      "source": [
        "*Our comments.* We compare two functions depending on the number of monkeys $m$. The first is the expected value of MAX of $m$ standard normal distributions as a function of $m$, a dependence that was derived according to the cdf of MAX (mathematically predicted). The second is a prediction based on mathematical analysis. The concordance is astonishing and unexpected because some approximations were made to derive the second function. Concretely, the two predictions were fulfilled:\n",
        "- First: the family of functions of the form $\\sqrt{k \\ln(m)}$ must contain a member that fits the function of the expected value of MAX according to its cdf. \n",
        "- -Second: the constant $k$ must be between 1 and 2. \n",
        "  \n",
        "Both predictions are correct and, in particular, the best found value for $k$ was 1.29. The fitting is so surprising that more tight bounds must exist. Nevertheless, the first part of the curves is almost vertical and so, close related curves could predict slightly different values. On the other hand, if a task cannot be done with some few thousands of monkeys, it is extremely expensive to reach even a tiny improvement.\n",
        "\n",
        "**Challenge.** Results reported in the previous theorem and exercise are all mathematic. Test them with a suitable simulation.\n",
        "\n",
        "**Graduation.** We have two disconnected parts in this essay: the first dealing with Binomial Distributions, the second with Normal variables. The task is to connect them. More concretely: We have shown with mathematics that the expected value of MAX of a set of $m$ standard normal distributions can be estimated with the formula $\\sqrt{k \\ln(m)}$, and, by trial and error, we have found $ k = 1.29$. Now, the Shakespeare challenge deals with discrete values so, the binomial distribution is the natural model. In consequence, use this formula and value of $k$ to predict the dependence of the expected value of MAX of $n$ binomial distributions on the number of monkeys $m$. Compare your prediction with the result that was reported in the first section of this contribution. Explain your results.\n",
        "\n",
        "**Over the proof.** Two different proofs of the sandwich theorem are available. The first by [van der Wolf]( https://math.stackexchange.com/q/4629560), which is for those that like calculus and only want to verify the result. The second, a beautiful work by [Yass1]({https://math.stackexchange.com/q/5008221}), is for those that love to battle with analysis. The battle is fierce because, according to our understanding, there are two details that must be corrected, and one of them is crucial.\n",
        "\n",
        "**Exercise.** Make a great effort to decipher one of the aforementioned proofs of the sandwich theorem of the expected value of MAX, which are both difficult and delightful.\n",
        ">\n",
        "*Answer.* We chose the second proof, which is related to analysis. It is a Lego-game: various fundamental theorems are concatenated to prove the demanded proposition. To follow the proof, we need to understand what these theorems say and what the ideas of their proofs are. Let us develop them, one by one."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uNdldDYwc0AN"
      },
      "source": [
        "\n",
        "### The Q-function and its   bounds\n",
        "\n",
        "The probability density function (pdf)\n",
        "of a standard (or unit) Gaussian random variable is\n",
        ">\n",
        "$\\phi(u)= \\frac{1}{\\sqrt{2 \\pi}}exp(\\frac{-u^2}{2})$\n",
        ">\n",
        "The cumulative probability distribution\n",
        "function (CDF) of this random variable is\n",
        ">\n",
        "$\\Phi (x) = \\int^x_{-\\infty} \\phi(u)du  =  \\int^x_{-\\infty} \\frac{1}{\\sqrt{2 \\pi}}exp(\\frac{-u^2}{2})du $\n",
        ">\n",
        "$\\Phi(x)$ is also known as the unit Gaussian distribution function. The CDF cumulates probability from $-\\infty$ until $x$. So, its value at $-\\infty$ is 0 and at $\\infty$ is one and is monotone, always increasing.\n",
        "\n",
        "Let us observe that\n",
        ">\n",
        "$1 = \\int^{\\infty}_{-\\infty} \\phi = \\int^{x}_{-\\infty} \\phi  + \\int^{\\infty}_{x} \\phi = \\Phi(x) + \\int^{\\infty}_{x} \\phi $.\n",
        ">\n",
        "Let us define  \n",
        ">\n",
        "$Q(x) = 1 - \\Phi(x) = \\int^{\\infty}_{x} \\phi =  \\int^{\\infty}_x \\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})du$\n",
        ">\n",
        "**$Q(x)$ is called the $Q$ -function or the complementary unit Gaussian distribution function.** $Q(x)$ is a monotone decreasing function falling from 1 at $-\\infty$ to 0 at $\\infty$.\n",
        "\n",
        "\n",
        "*Theorem.* The  **$Q$-function can be bounded above**:\n",
        ">\n",
        "$Q(x) \\le \\frac{1}{ 2 }exp(\\frac{-x^2}{2})$\n",
        ">\n",
        "for $x \\ge  0$, and with equality holding only at $x = 0$. This theorem is used by the literature cited below.\n",
        ">\n",
        "We follow  an [unnamed author](\n",
        "https://courses.grainger.illinois.edu/ece361/Qfunction.pdf).\n",
        ">\n",
        "*Proof.* Let us suppose $ u > x \\ge 0$. We have:\n",
        ">\n",
        ">$x \\ge -x$\n",
        ">\n",
        "adding $u$ to both sides, we get\n",
        ">\n",
        ">$ u+x \\ge  u -x$\n",
        ">\n",
        "multiplying by $(u-x) > 0$ at both sides\n",
        ">\n",
        ">$(u+x)(u-x) = u^2 - x^2 \\ge (u-x)^2 \\ge 0$\n",
        ">>\n",
        "Dividing by 2\n",
        ">>\n",
        ">$\\frac{u^2 - x^2}{2} \\ge \\frac{(u-x)^2}{2} \\ge 0$\n",
        ">>\n",
        "Multiplying by -1\n",
        ">>\n",
        "> $-\\frac{u^2 - x^2}{2} \\leq -\\frac{(u-x)^2}{2} \\le 0$\n",
        ">>\n",
        "Applying the exponential function to both sides, the inequality is conserved because this function is increasing:\n",
        ">>\n",
        ">  $ exp(-\\frac{u^2 - x^2}{2}) \\leq exp(-\\frac{(u-x)^2}{2})  $\n",
        ">>\n",
        "Let us apply this to $Q$ as follows:\n",
        ">>\n",
        ">$Q(x) =  \\int^{\\infty}_x\\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})$\n",
        ">>\n",
        "multiplying by $exp(\\frac{x^2}{2})$:\n",
        ">>\n",
        ">$exp(\\frac{x^2}{2}) Q(x) = exp(\\frac{x^2}{2})  \\int^{\\infty}_x\\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})du$\n",
        ">>\n",
        ">$ =  \\int^{\\infty}_x\\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-(u^2 - x^2)}{2})du $\n",
        ">>\n",
        ">$\\leq \\int^{\\infty}_x\\frac{1}{\\sqrt{2\\pi}}exp( -\\frac{(u- x)^2}{2})du  = \\frac{1}{2}$\n",
        ">\n",
        "because we have here the integral from $x$ to $\\infty$ of a bell whose mean is $x$ and its variance is 1. So, it is half of the bell.\n",
        ">\n",
        "We have shown that\n",
        ">>\n",
        ">$exp(\\frac{x^2}{2}) Q(x) \\le \\frac{1}{2}$\n",
        ">>\n",
        "Hence\n",
        ">>\n",
        ">$Q(x) \\le \\frac{1}{ 2 }exp(\\frac{-x^2}{2})$\n",
        ">>\n",
        "as demanded.\n",
        "\n",
        "*Theorem.* Using the same notation as in the previous theorem, **the  $Q$-function can be bounded below** by :\n",
        ">\n",
        ">$L(x) = \\frac{1}{ 12 }exp( -x^2)$\n",
        ">\n",
        "i.e., for $x \\ge  0$ we have:\n",
        ">\n",
        ">$L(x) \\leq Q(x) $\n",
        ">\n",
        " This theorem will be used by us in a crucial way. It is a very weak version of the bounds found by [Freitas de Abreu](https://www.researchgate.net/publication/224140403_Supertight_algebraic_bounds_on_the_Gaussian_Q-function). We follow his methodology. \n",
        ">\n",
        "*Proof.*  Let us define for $x \\ge 0$\n",
        ">\n",
        ">$D(x) = Q(x) - L(x) $\n",
        ">>\n",
        ">>$ =  \\int^{\\infty}_x \\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})du - \\frac{1}{ 12 }exp( -x^2)$\n",
        ">\n",
        "$D$ has two properties that together show that $L$ is a lower bound of $Q$. The first property is:\n",
        ">\n",
        ">$D(0) > 0$.\n",
        ">\n",
        "This is verified immediately:\n",
        ">\n",
        ">$D(0) = Q(0) - L(0) = $\n",
        ">>\n",
        ">>$ = \\int^{\\infty}_0 \\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})du - \\frac{1}{ 12 }exp( -0^2)$\n",
        ">>>\n",
        ">>$ = \\frac{1}{2} - \\frac{1}{12} = \\frac{6-1}{12} = \\frac{5}{12} > 0 $\n",
        ">\n",
        "because the integral represents the area of the half of the bell.\n",
        ">\n",
        "The second property is:\n",
        ">\n",
        ">$D'(x) < 0$ for $x \\ge 0$.\n",
        ">\n",
        "This is shown by direct calculation:\n",
        ">\n",
        ">$D'(x) = Q'(x) - L'(x) = $\n",
        ">>\n",
        ">>$ =  ( \\int^{\\infty}_x \\frac{1}{\\sqrt{2\\pi}}exp(\\frac{-u^2}{2})du )'- (\\frac{1}{ 12 }exp( -x^2))'$\n",
        ">>\n",
        ">>$ = - \\frac{e^{-x²/2}}{\\sqrt{2 \\pi}} + \\frac{2x e^{-x²}}{12}$\n",
        ">>>\n",
        ">>$ = e^{-x²/2} ( - \\frac{1}{\\sqrt{2 \\pi}} +  \\frac{2x e^{-x²/2}}{12})$\n",
        ">>>\n",
        ">>$ = e^{-x²/2} ( - \\frac{1}{\\sqrt{2 \\pi}} +  \\frac{1}{6} x e^{-x²/2} )$\n",
        ">>>\n",
        "The sign of $D'$ is equal to the sign of\n",
        ">>\n",
        ">$ - \\frac{1}{\\sqrt{2 \\pi}} +  \\frac{1}{6} x e^{-x²/2}$\n",
        ">\n",
        "The first term is equal to $-0.399$. For $ x \\ge 0$, the second term,  $\\frac{x e^{-x²/2}}{6}$, is a function with a positive bump. To find its maximum, we take the derivative:\n",
        ">>\n",
        ">$ ( \\frac{1}{6} x e^{-x²/2})' = \\frac{1}{6} (e^{-x²/2} + x (-x)e^{-x²/2}) $\n",
        ">>\n",
        "and equate it to zero:\n",
        ">>\n",
        "> $ \\frac{1}{6} (e^{-x²/2} + x (-x)e^{-x²/2}) = 0 $\n",
        ">>\n",
        ">$ \\frac{1}{6} e^{-x²/2} ( 1  - x^2 ) = 0 $\n",
        ">>\n",
        ">$1  - x^2  = 0$\n",
        ">>\n",
        "Thus, we have a maximum at $x = 1$. Let us evaluate the second term at this value:\n",
        ">>\n",
        ">$ (- \\frac{1}{\\sqrt{2 \\pi}} +  \\frac{1}{6} x e^{-x²/2}) |_{x=1} = -0.399 +  \\frac{1}{6}  e^{-1/2} = - 0.399 + \\frac{1}{6} (0.6) = -0.3999 + 0.1 = -0.299 < 0$\n",
        ">>\n",
        "We have shown that\n",
        ">\n",
        "> $D'(x) < 0$ for $x \\ge 0$.\n",
        ">\n",
        "From this and the other property, we deduce that $L$ is always below $Q$, i.e., that $L$ is a lower bound to $Q$. In fact, at zero, $Q$ is above $L$, and $D$ is always decreasing. This means that the difference between $Q$ and $L$ decreases, but the two functions never touch one another. For, suppose that $Q$ and $L$ have a point in common, let it be $A$. Before it, $D>0$ and after it, $D < 0$. Since all functions are continuous and smooth, $D(A) = 0$ is a minimum.  Therefore, after $A$, the slope must be positive, a proposal that contradicts what we already have proven, that $D'(x) < 0$ always for $x \\ge 0$.\n",
        "Therefore, such an $A$ cannot exist, and we can ascertain that $L$ is always below $Q$. $L$ is simple to evaluate and manipulate, contrary to $Q$. So, we use $L$ as a lower bound of $Q$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vhpL3mgFc9p5"
      },
      "source": [
        "### Schwarz Inequality\n",
        "\n",
        "This inequality is based on a well known observation: the shadows of objects at mid-noon are shorter than objects themselves and have equal magnitude only when the objects are horizontal.\n",
        "\n",
        "*Theorem.* The Cauchy-Schwarz inequality states that for random variables $X$ and $Y$, and expected value operator  $\\mathbb{E} $, the following inequality holds\n",
        ">>\n",
        ">$\\mathbb{E}[|XY|]\\leq(\\mathbb{E}[X^2])^{1/2}(\\mathbb{E}[Y^2])^{1/2}$\n",
        ">>\n",
        "provided everything exists.\n",
        "\n",
        "*Desmythiphication.*  The inequality says: orthogonal projections or perpendicular shadows of vectors are shorter than the vector themselves.\n",
        "\n",
        "Let us see why $\\mathbb{E}[|XY|]$ is related to orthogonal projections, while  $(\\mathbb{E}[X^2])^{1/2}(\\mathbb{E}[Y^2])^{1/2}$ is related to lengths.\n",
        "\n",
        "Vectors are segments that can be added and elongated without problem. Vectors are represented using a system of coordinates. For instance, in dimension 5, a vector looks like $ \\vec{a} = (a_1 ,a_2 ,a_3 ,a_4 ,a_5)$.\n",
        "\n",
        "An inner product between two vectors $ \\vec{a} =  (a_1 ,a_2 ,a_3 ,a_4 ,a_5)$ and $ \\vec{b} = (b_1 ,b_2 ,b_3 ,b_4 ,b_5)$ is defined as\n",
        "\n",
        "$ \\vec{a}  \\cdot \\vec{b}  = \\sum a_ib_i = a_1b_1 + a_2 b_2 + a_3 b_3+ a_4 b_4+ a_5 b_5$\n",
        "\n",
        "To proceed further, let us pay attention to the fact that the two vectors, if not collinear, generate a plane, which is completely described by a bidimensional system of two axes, which are  perpendicular one to another. Let us take any one of those systems, whose axes are $X$ and $Y$, as the ordinary plane. Let us assume that in that new system of coordinates, the vectors are described by $\\vec{v_1} = (x_1, y_1)$ and $\\vec{v_2} = (x_2, y_2)$.\n",
        "\n",
        "Let us imagine a rectangular triangle, with hypothenuse $h$ and cathetuses $f$  and $g$. The angle formed by   $f$ and $g$ is rect. And that between   $ h$ and $f$ is $\\theta$. Thus, $f$ is the adjacent cathetus of $\\theta$. Then,\n",
        "\n",
        "$f = hcos\\theta$\n",
        "\n",
        "On the other hand, $g$ is the opposed cathete of $\\theta$, hence\n",
        "\n",
        "$g = h sin \\theta$.\n",
        "\n",
        "Let us apply this result systematically as follows. To ease the work of our imagination, let us consider that the two vectors   $\\vec{v_1} = (x_1, y_1)$ and $\\vec{v_2} = (x_2, y_2)$ are in the first quadrant. The angle between $\\vec{v_1}$ and the $X$ axis is $\\theta_1$, that between  $\\vec{v_2}$ and the $X$ axis  is $\\theta_2$. And the angle between  $\\vec{v_1}$ and  $\\vec{v_2}$ is $\\theta = \\theta_1 - \\theta_2 \\ge 0$.  \n",
        "\n",
        "The vector $\\vec{v_1}$  defines a rectangular triangle with the X-axis through its perpendicular projection, whose length is $x_1$. This means that $x_1 = \\| \\vec{v_1} \\| cos \\theta_1$, where  the double bars indicate the length or norm of the vector $\\vec{v_1} $. The adjacent cathetus of $\\theta_1$ is precisely the vector that starts at $0$ and ends at $x_1$ over the $X$ axis.  On the other hand, the opposed cathetus of $\\theta_1$, translated to the origin,  starts at $0$ and ends at  $y_1$ over the $Y$ axis. Therefore,  $y_1 =  \\| \\vec{v_1}\\| sin \\theta_1$. The same happens with $\\vec{v_2}$.\n",
        "\n",
        "Thus, the inner product looks like this:\n",
        "\n",
        "$ \\vec{v_1} \\cdot \\vec{v_1} = x_1 x_2 + y_1 y_2 =  $\n",
        "$(\\| \\vec{v_1}\\| cos \\theta_1)  (\\| \\vec{v_2}\\| cos \\theta_2)  + $\n",
        "$(\\| \\vec{v_1}\\| sin \\theta_1)(\\| \\vec{v_2}\\| sin \\theta_2)$\n",
        "\n",
        "$= \\| \\vec{v_1}\\| \\, \\| \\vec{v_2}\\| (cos \\theta_1 cos \\theta_2 + sin \\theta_1 sin \\theta_2)$\n",
        "\n",
        "$ =  \\| \\vec{v_1}\\| \\, \\| \\vec{v_2}\\| cos(\\theta_1-\\theta_2) $\n",
        "\n",
        "$ =  \\| \\vec{v_1}\\| \\, \\| \\vec{v_2}\\| cos \\theta $\n",
        "\n",
        "\n",
        " $ = (\\| \\vec{v_1}\\| cos \\theta ) \\| \\vec{v_2}\\|$\n",
        "\n",
        "Notice that $\\| \\vec{P_ 1} \\|  = (\\| \\vec{v_1}\\| cos \\theta ) $ is the length of the orthogonal projection of $\\vec{v_1}$ over $\\vec{v_2}$.\n",
        "\n",
        "We know now why the inner product is related to projections and, because the cosinus is less than 1,  why projections are shorter than the vectors themselves:\n",
        "\n",
        "Then\n",
        "\n",
        "$ \\vec{v_1} \\cdot \\vec{v_1} \\leq  \\| \\vec{v_1}\\|  \\| \\vec{v_2}\\|$\n",
        "\n",
        "This is the Cauchy-Schwarz inequality for dimension 5 reduced to 2. We generalize without ceremonies.\n",
        "\n",
        "The trouble is that the inequality that we must understand is not with vectors but with functions that represent a probability density function, and not with sums but with integrals. What we will do? We must relate those functions with ordinary vectors, and integrals with ordinary sums. This is done as follows:\n",
        "\n",
        "In first place, functions that go from real numbers to real numbers can be added and elongated without a problem. We add them by adding value to value. And we elongate them by multiplying each value by a constant. Thus, functions are vectors.\n",
        "\n",
        "To evaluate the integral of a function, we divide the real axis\n",
        "in small segments, and over each of them, we approximate the function by a horizontal segment that denotes a locally constant function. Such approximated functions are called step-functions. And the integral is the sum of the areas in within the steps and the X-axis, which are rectangles. Now, to define an inner product between two functions, we multiply the values of the two functions over each step and add everything altogether.\n",
        "\n",
        "Next, we take the limit when the width of the steps tend to zero. If the limits exist,  we define in that way the integral and an inner product.\n",
        "\n",
        "How is this applied to random variables, $X$ and $Y$?. The core idea is simple, but the details are extremely complex. The idea is the following:\n",
        "\n",
        "For two random variables $X$ and $Y$, the expression\n",
        ">\n",
        "$< X, Y > = \\mathbb{E}[XY]$\n",
        "\n",
        "defines an inner product in the space of random variables (for which this expression makes sense). In that space, the norm $\\| \\cdot \\| $ is\n",
        ">\n",
        " $\\| X \\| = \\sqrt{< X, X >}  = \\sqrt{ \\mathbb{E}[XX]} =  (\\mathbb{E}[X^2]) ^{1/2}$\n",
        ">\n",
        "The angle $\\theta$ within $X$ and $Y$ is defined through the cosinus:\n",
        ">\n",
        "$ cos (\\theta) =  \\frac{<X,Y>]}{\\| X \\|  \\| Y \\|} = \\frac{\\mathbb{E}[XY]}{(\\mathbb{E}[X^2]) ^{1/2}  (\\mathbb{E}[Y^2]) ^{1/2}} $\n",
        ">\n",
        "One is tempted to say: Since the cosinus is less than 1, we have\n",
        "\n",
        "$\\frac{\\mathbb{E}[XY]}{(\\mathbb{E}[X^2]) ^{1/2}  (\\mathbb{E}[Y^2]) ^{1/2}} \\leq 1$\n",
        ">\n",
        "or\n",
        ">\n",
        "$\\mathbb{E}[XY] \\leq (\\mathbb{E}[X^2]) ^{1/2}  (\\mathbb{E}[Y^2]) ^{1/2} $\n",
        ">\n",
        "which is the Schwarz inequality. Nonethetless, we have used what we wanted to proof. How can we break this vicious circle?\n",
        "\n",
        "Let us assume that the defined inner product between random variables enjoys all the goods properties of a product. Additionally, we need another property, the inner product of a vector with itself is non-negative:\n",
        ">\n",
        "$<X,X> =  \\mathbb{E}[XX] =  \\mathbb{E}[X^2] \\ge 0$\n",
        ">\n",
        "because,  in one word, the average of non-negative numbers is  non-negative.\n",
        "\n",
        "Let us consider now an arbitrary vector space with inner product. For a pair of arbitrary vectors, $\\vec u$ and $\\vec v$, define  the function\n",
        ">\n",
        "$f: \\mathbb{R} \\to \\mathbb{R}$\n",
        ">\n",
        "given by\n",
        ">\n",
        "$f(t) = <t\\vec u + \\vec v,  t\\vec u + \\vec v >$\n",
        ">\n",
        "whose output  is a number that results from the inner product of a vector with itself. So, it is non-negative:\n",
        ">\n",
        "$f(t) = <t\\vec u + \\vec v,  t\\vec u + \\vec v > \\, \\ge 0$\n",
        ">\n",
        "Therefore, its graph is a parable that does not visit the negative part of the plane. As a consequence, its discriminant must be non-positive, it might be 0 or negative. And this is the Schwarz inequality. More detailed and using all the good properties of a product, we get:\n",
        ">\n",
        "$f(t) = <t\\vec u + \\vec v,  t\\vec u + \\vec v > $\n",
        ">\n",
        "$ = < t\\vec u , t\\vec u>  + < t\\vec u , \\vec v >  + < \\vec v, t\\vec u >+ < \\vec v,\\vec v >$\n",
        ">\n",
        "$ = t^2< \\vec u , \\vec u > + t< \\vec u , \\vec v>   + t < \\vec v, \\vec u>  + < \\vec v,\\vec v>  $\n",
        ">\n",
        "$ = t^2 \\| \\vec u \\|^2 + t< \\vec u , \\vec v>  + t < \\vec v, \\vec u >+ \\| \\vec v \\|^2 $\n",
        ">\n",
        "$ = t^2 \\| \\vec u \\|^2 + t< \\vec u , \\vec v > + t < \\vec u, \\vec v >+ \\| \\vec v \\|^2 $\n",
        ">\n",
        "$ = t^2 \\| \\vec u \\|^2 + 2t< \\vec u , \\vec v >   + \\| \\vec v \\|^2 $\n",
        ">\n",
        "This is a parable in $t$. Its roots are given by\n",
        ">\n",
        "$ r = \\frac{-2< \\vec u , \\vec v > \\pm \\sqrt{(2< \\vec u , \\vec v >) ^2 - 4\\| \\vec u \\|^2  \\| \\vec v \\|^2} }{4 \\| \\vec u \\|^2} $\n",
        ">\n",
        "If the discriminant $(2< \\vec u , \\vec v >) ^2 - 4 \\| \\vec u \\|^2 \\| \\vec v \\|^2 $ were greater than zero, the polynomial would have two roots and it should had   crossed through the $X$ axes. But this is forbidden since the polynomial is non- negative. So, the discriminant is zero else negative:\n",
        ">\n",
        "$(2< \\vec u , \\vec v >)^2 - 4 \\| \\vec u \\|^2  \\| \\vec v \\|^2 \\leq 0$\n",
        ">\n",
        "$4< \\vec u , \\vec v >^2 - 4  \\| \\vec u \\|^2  \\| \\vec v \\|^2 \\leq 0$\n",
        ">\n",
        "$< \\vec u , \\vec v >^2 -  \\| \\vec u \\|^2  \\| \\vec v \\|^2 \\leq 0$\n",
        ">\n",
        "$< \\vec u , \\vec v >^2  \\,\\, \\leq  \\,\\,  \\| \\vec u \\|^2  \\| \\vec v \\|^2 $\n",
        ">\n",
        "$< \\vec u , \\vec v >^2  \\,\\, \\leq  \\,\\,   < \\vec u ,  \\vec u >    < \\vec u ,  \\vec u > $\n",
        ">\n",
        "$< \\vec u , \\vec v >  \\,\\, \\leq  \\,\\, (< \\vec u ,  \\vec u >)^{1/2}    (< \\vec u ,  \\vec u >)^{1/2}  $\n",
        ">\n",
        "If we apply this inequality to the inner product between random variables  \n",
        ">\n",
        "> $<X,Y> = \\mathbb{E}[XY]$, \n",
        "> \n",
        "we obtain:\n",
        ">\n",
        "$\\mathbb{E}[|XY|]\\leq(\\mathbb{E}[X^2])^{1/2}(\\mathbb{E}[Y^2])^{1/2}$\n",
        ">\n",
        "This is the Schwarz inequality.\n",
        ">\n",
        "Are we done?\n",
        ">\n",
        "Not as yet.\n",
        ">\n",
        "What do we lack?\n",
        ">\n",
        "Apart from the clearly lacking details, we need to show that the defined   product is indeed an inner product. The greatest difficulty is to show how to define $XY$. Let us state more clearly what the difficulty consists in.\n",
        "\n",
        "\n",
        "Let us suppose that our random variables $X$ and $Y$ have each one a probability density function $f_X$ and $f_Y$. Then the expected value of $X$ is\n",
        ">\n",
        "$\\mathbb{E} [X]=\\int _{-\\infty }^{\\infty } X(x)  \\,  f_X(x)\\,dx$\n",
        ">\n",
        "The expected value of $Y$ is\n",
        ">\n",
        "$\\mathbb{E} [Y]=\\int _{-\\infty }^{\\infty } Y(x)  \\,  f_Y(x)\\,dx$\n",
        ">\n",
        "The expected value of $XY$ is\n",
        ">\n",
        "$\\mathbb{E} [XY]=\\int _{-\\infty }^{\\infty }X(x)Y(x)  \\, f_{XY}(x)\\,dx$\n",
        ">\n",
        "where\n",
        ">\n",
        "$f_{XY}(x)$\n",
        ">\n",
        "is the density function associated to the product $XY$. This is defined pointwisely, i.e., if $X = x$ and $Y = y$, then $XY = xy$. And, the probability density of the product, $f_{XY}(x)$, comes from a cdf $F(z) = P(xy < z)$, where $f_{XY}(z)  = F'(z) $. How to calculate this is for each case a whole industry. See, for example, the case  of [Gaussian Variables](https://www.mdpi.com/2073-8994/12/8/1201#:~:text=2.,%CE%B4%20X%20%CE%B4%20Y%20\\)%202%20.).\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3n03XkIQdhKt"
      },
      "source": [
        "### Jensen's inequality\n",
        "\n",
        "A differentiable increasing function is convex when its curvature is positive everywhere, so, the function opens upwards. In that case, the slope of the tangent line exists everywhere and is not decreasing.\n",
        "\n",
        "*Example.* $f(x) = x^2$ opens upwards, so it is convex, its slope is given by the derivative $f' (x) = 2x$ whose graph is a line that always increases.\n",
        "\n",
        "*Example.* $f(x) = e^x$ opens upwards, so it is convex because its derivative $f'(x) = e^x$ is an increasing function.\n",
        "\n",
        "*Challenge.* Compare our definition of convex function with [the official one](https://en.wikipedia.org/wiki/Convex_function).\n",
        "\n",
        "*Theorem.* If $X$ is a random variable and $\\phi$ is a convex function, then\n",
        ">>\n",
        ">  $\\phi(\\mathbb{E}[X]) \\le  \\mathbb{E}[\\phi(X)] $ .\n",
        ">>\n",
        "*Heart of the proof.* If $X$ takes positive values, as in our case, this says that for a convex function, the more to the right is a value, its image moves further to the right.   Therefore, the expected value of the distribution formed by all values is greater than the image of the expected value of the original distribution.\n",
        "\n",
        "*Idea of the proof.* Let us imagine that we have a four seat seesaw. Four children of equal weight sit over it, two at one side, the other two at the other. Their coordinates, beginning from 0 in the left extreme, are 1, 2, 4 and 5. The center is at 3. The seesaw is equilibrated, it is horizontal. In statistical terms: we have a distribution of masses whose mean or expected value is at 3.\n",
        ">\n",
        "Now, we give instructions to the children to move and to report to which side the seesaw is heavier. The instructions are: if you are at the left of the mean, remain immobile. If you are at the right, move more to the right. Concretely:   if you are at the left of the mean, move to the coordinates given by $f(x) = x$. But, if you are at the right, move to the coordinate given by $g(x) = 2x-3$. In statistical terms: change positions according to a convex function, $h$, that has been defined piecewise, one piece by $f$, the other by $g$. This is so because at 3, $f$ and $g$ coincide, $f(3) = 3 = g(3) = 2 \\times 3 - 3 = 3$. So, $h$ is continuous, and the slope of the first segment is 1 while that of the second is 2, so the derivative exists everywhere except at 3, and the slope is not decreasing.\n",
        ">\n",
        "The new positions of the two children to the left of the center  are:\n",
        ">>\n",
        ">$1 \\rightarrow f(1) = 1$\n",
        ">>\n",
        ">$2 \\rightarrow f(2) = 2$\n",
        ">>\n",
        ">$3 \\rightarrow f(3) = 3 = g(3) = 2 \\times 3 - 3 = 3 $,\n",
        ">>\n",
        "the center of the seesaw  is immobile. The old mean remains invariable after applying the instructions.\n",
        ">\n",
        "For the children on the right side, the new positions become:\n",
        ">>\n",
        ">$4 \\rightarrow g(4) = 2 \\times 4 - 3 = 5$\n",
        ">>\n",
        ">$5 \\rightarrow g(5) = 2 \\times 5 - 3 = 7$\n",
        ">\n",
        "Thus, the new positions are 1 and 2, to the left of the center, and 5 and 7, to its right. Is the seesaw equilibrated? Not. Where has the mean moved to? To the right because the distribution has been spread to that side. The new center is greater than the old one. In statistical terms: $h( \\mathbb{E}(X)) \\le \\mathbb{E}(h(X))$ that says that the image of the expected value of a random variable by a convex function is less or equal to expected value of the image of the distribution.\n",
        "\n",
        "\n",
        "\n",
        "*Challenge.* Convert this idea into a formal proof. Else, look at [Wikipedia](https://en.wikipedia.org/w/index.php?title=Jensen%27s_inequality&oldid=1317141982) for other ideas and to their formalization,  which now you must find understandable and delightful.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QfDlfr-nd5kz"
      },
      "source": [
        "### The mean and the median\n",
        "\n",
        "The mean and the median of a data set or of a random variable are numbers that represent them and that are found by different procedures and that have different properties and objectives.\n",
        "\n",
        "*Example.* Let us consider the numbers 4, 3, 1 , 5, 2 , 100. To find the median, order them: 1, 2, 3, 4, 5, 100. The median is the datum of the middle. We have 6 data, the middle is 3.5 because there are 3 data below and 3 data above. To find the mean, add all numbers and divide by the number of data: the sum is 1 + 2 + 3 + 4+ 5 + 100 = 115. The division by 6 is $115/6 \\sim 20$. What stadigraph or indicator represents best the population? Imagine that we speak of incomes. To say that the members of the population win approximately 20 is a great error. It is much better to say that each member wins approximately the median, 3.5. Or, that there is an outlier, 100, and that the rest of the population has mean 3.\n",
        "\n",
        "We will need below a rigorous definition of the median:\n",
        "\n",
        "A median of a real-valued random variable $X$  is a real number $m$ that satisfies\n",
        "\n",
        "$ P( X < m ) \\leq \\frac{1}{2}$ and $P( X > m ) \\leq \\frac{1}{2}  $\n",
        "\n",
        "The mean and the media are minimizers of different functions.\n",
        "\n",
        "The median minimizes $M = \\sum |x_i- c|$, while the mean minimizes $G = \\sum |x_i- c|^2$.\n",
        "\n",
        "With respect to the median, if we take  $c = 1$, our data give for  $M = \\sum |x_i- c|$  the following:\n",
        "\n",
        "\n",
        "$M =  |1 - 1| + |2 - 1| + |3 - 1|+ |4 - 1|+ |5 - 1| + |6 - 1| + |100 - 1= $\n",
        "\n",
        "$0 + 1 + 2+ 3 + 4 + 5 + 99 = 114$\n",
        "\n",
        "while for $c = 3.5$, equals to the median, we get:\n",
        "\n",
        "$M =  |1 - 3.5| + |2 - 3.5| + |3 - 3.5|+ |4 - 3.5|+ |5 - 3.5| + |6 - 3.5| + |100 - 3.5|= 2.5 + 1.5 +0.5 + 0.5 + 1.5 + 2.5 + 96.5 = 105.5$\n",
        "\n",
        "This example illustrates that   $M(median = 3.5) < M(1)$. This is not a coincidence, as the next theorem shows:\n",
        "\n",
        "We follow [this discussion](https://math.stackexchange.com/q/85448) and  [gran_chat](https://math.stackexchange.com/q/2790390)\n",
        "\n",
        "*Theorem.*  If $X$ is a real random variable,   the median $m$ minimizes  $\\mathbb{E} (|x-c|)$, i.e.,\n",
        ">>\n",
        "> $\\mathbb{E} (|x-m|) \\leq \\mathbb{E} (|x-c|)$ for each c\n",
        ">>\n",
        "where $\\mathbb{E} $ denotes the E-xpected value or average of the random variable.\n",
        ">\n",
        "Proof. Let $m$ be any median of $X$.   We can take $m=0$ (consider $X':=X-m$). The aim is to show $E|X-c|\\ge E|X - m| = E|X - 0| = E|X |$.\n",
        ">\n",
        "Let us divide the real axis in two parts $\\mathbb{A} = \\{x: x \\le 0\\}$, $\\mathbb{B} =  \\{ x: x > 0\\}$, corresponding respectively to the left and right sides of the real line.\n",
        ">\n",
        "Consider the case $c\\ge 0$.\n",
        ">\n",
        "Let us consider the expression\n",
        ">\n",
        "> $|X-c|-|X|$\n",
        ">\n",
        "that evaluates to different values, depending on the position of $X$.\n",
        ">\n",
        "If $X$ is in $\\mathbb{A}$, $X \\le 0$  while $c$ is in\n",
        "  $\\mathbb{B}$, $c\\ge 0$:\n",
        ">\n",
        "> $|X-c|-|X| = c-X + X = c$\n",
        ">\n",
        "If $X$ is in the right region, $x > 0$, there are two cases. First,  $ 0 < c < X $, in that case\n",
        ">\n",
        "> $|X-c|-|X| =  X-c -X = -c$\n",
        ">\n",
        "Second\n",
        ">\n",
        ">$ 0 < X < c$, and we have\n",
        ">\n",
        ">  $|X-c|-|X| = c-X -X = c - 2X$\n",
        ">\n",
        "Let us evaluate $c-2X$ with respect to $c$\n",
        ">\n",
        ">  $X < c$\n",
        ">>\n",
        ">   $2X < 2c$\n",
        ">>\n",
        ">   $-2X > -2c$\n",
        ">>\n",
        ">   $c-2X > c-2c = -c$\n",
        ">>\n",
        "  Therefore, when\n",
        ">\n",
        ">  $ 0 < X < c$,  we have\n",
        ">>\n",
        ">   $|X-c|-|X| = c - 2X > -c$\n",
        ">\n",
        " Considering both cases together, we conclude that when $X \\ge 0$, and independent of the position $X$ with respect to $c$,\n",
        ">\n",
        ">   $|X-c|-|X| \\ge -c $\n",
        ">\n",
        "  Summarizing: in the left and right regions, we have respectively\n",
        ">\n",
        ">$|X-c|-|X|= c$, left side\n",
        ">>\n",
        ">$|X-c|-|X| > -c$, right side\n",
        ">>\n",
        "If we add the equation to the inequality, we get:\n",
        ">>\n",
        "> $|X-c|-|X| + (|X-c|-|X|) \\ge -c + c $\n",
        ">\n",
        ">$2( |X-c|-|X|)   \\ge 0 $\n",
        ">\n",
        ">$ |X-c|-|X|   \\ge 0 $\n",
        ">\n",
        "or\n",
        ">\n",
        ">$ |X-c| \\ge |X|    $\n",
        ">\n",
        " We can now  average over the whole set of data to get: If $c \\ge 0$,\n",
        ">\n",
        ">  $ \\mathbb{E}(|X-c|) \\ge \\mathbb{E}(|X - 0| )   $\n",
        ">\n",
        "> that was what we wanted to prove.\n",
        ">\n",
        ">The consideration of the case when $c \\le 0$ is resolved if we make a reflection and repeat the process. So, it adds nothing new or contradictory.\n",
        ">\n",
        "*Protest.* The addition of two inequalities in the previous proof was a crucial step. But, it makes no sense to add expressions corresponding to different universal sets, one was the left side of the real line, the other was the right. So, the correct answer resulted as a mere coincidence. What shall we do? We shall take one covering universal set and take into account the   weight of each expression in regard with the whole ensemble. The corresponding mathematical machine developed for this purpose is the Indicator Function of a set:\n",
        ">\n",
        "*Definition.* The indicator function of a subset $A$ of $\\mathbb{R}$ is a function that is 1 over $A$ and 0 elsewhere. Let us denote the indicator function of an interval that is defined by an inequality   as $\\mathbb{I}$  and the condition comes as an argument or a subindex, say, $\\mathbb{I}({X > 0})$ or  $\\mathbb{I}_{X > 0}$. Let us use the subindex notation.\n",
        ">\n",
        "Using the Indicator Function, the two expressions to be added are:\n",
        ">\n",
        ">$|X-c|-|X|=c$ when $X\\le0$,\n",
        ">\n",
        "that becomes\n",
        ">\n",
        ">$ (|X-c|-|X|)\\mathbb{I}_{X\\le0}=c \\mathbb{I}_{X\\le0} $\n",
        ">\n",
        "and\n",
        ">\n",
        ">$|X-c|-|X|\\ge -c$ when $X >0$.\n",
        ">\n",
        "that becomes\n",
        ">\n",
        ">$(|X-c|-|X|) \\mathbb{I}_{X > 0} \\ge-c \\mathbb{I}_{X > 0}$\n",
        ">\n",
        "We have now two expressions that refer to the same universal set, the complete real line. So, we can add then:\n",
        ">\n",
        ">$\n",
        "(|X-c|-|X|) \\mathbb{I}_{X\\le0} + (|X-c|-|X|) \\mathbb{I}_{X>0}  = c \\mathbb{I}_{X\\le0}-c \\mathbb{I}_{X > 0}\n",
        "$\n",
        ">>\n",
        ">$\n",
        "(|X-c|-|X|)    \\ge c \\mathbb{I}_{X\\le0}-c \\mathbb{I}_{X > 0}\n",
        "$\n",
        ">\n",
        "Let us average:\n",
        ">>\n",
        ">$\n",
        "\\mathbb{E}(|X-c|-|X|)\\ge \\mathbb{E}(c \\mathbb{I}_{X\\le0}-c \\mathbb{I}_{X > 0}).\n",
        "$\n",
        ">>\n",
        ">$\n",
        "\\mathbb{E}(|X-c|-|X|)\\ge c[\\mathbb{E}( \\mathbb{I}_{X\\le0})- \\mathbb{E}(\\mathbb{I}_{X > 0})].\n",
        "$\n",
        ">>\n",
        "The expected value of an indicator function of a set $A$ is calculated as it is always done for a function $f$:\n",
        ">>\n",
        "> $\\mathbb{E}(f) = \\int_A fdp$\n",
        ">>\n",
        "where $dp$ is the differential of the probability measure. So,\n",
        ">>\n",
        "> $\\mathbb{E}(\\mathbb{I}_A) = \\int_A 1dp = \\int_A dp  = p(A) $\n",
        ">>\n",
        "Therefore, we get\n",
        ">>\n",
        ">$\n",
        "\\mathbb{E}(|X-c|-|X|)\\ge c\\left[p(X\\le0)-p(X>0)\\right].\n",
        "$\n",
        ">\n",
        "If $p(\\{0\\}) = 0$   and given that $0$ is the median,  then, $p(X\\le0)= p(X>0)$. In this case, we are done because\n",
        ">>\n",
        "> $\n",
        "\\mathbb{E}(|X-c|-|X|)\\ge c  \\times 0  = 0.\n",
        "$\n",
        ">\n",
        "> $\n",
        "\\mathbb{E}(|X-c| )\\ge \\mathbb{E}(|X|) \n",
        "$\n",
        ">\n",
        "This expression says that the median, $0$, minimizes this functional.\n",
        ">\n",
        "If $p(\\{0\\} \\neq 0$, let us insert $0$ in the form $p(X\\le0) - p(X\\le0)$\n",
        ">>\n",
        "> $ \\mathbb{E}(|X-c|-|X|)\\ge  c\\left[p(X\\le0)-p(X>0) + p(X\\le0) - p(X\\le0)\\right] $\n",
        ">>\n",
        ">$ \\mathbb{E}(|X-c|-|X|)\\ge c\\left[2p(X\\le0)-(p(X>0)  + p(X\\le0))\\right] $\n",
        ">>\n",
        ">$ \\mathbb{E}(|X-c|-|X|)\\ge c\\left[2p(X\\le0)-1)\\right] $\n",
        ">>\n",
        ">$ \\mathbb{E}(|X-c|-|X|)\\ge c\\left[2 \\times \\frac{1}{2}-1)\\right] \\ge 0$\n",
        ">\n",
        "> $\n",
        "\\mathbb{E}(|X-c| )\\ge \\mathbb{E}(|X|) \n",
        "$\n",
        ">\n",
        "because we are working the case $c > 0$. \n",
        ">\n",
        "\n",
        ">\n",
        "End of the proof of the theorem of the minimizing property of the median.\n",
        "\n",
        "Let us pass now to other consideration.\n",
        "\n",
        "The normal distribution has a mean and a median that coincide. That is why this distribution is an ephythome of homogeneity and symmetry. By contrast, as it was shown in a previous example, in the presence of   outlier, the mean and the median can be very different. Why? It is because the data are very inhomogeneous. So, the difference between these two stadigraphs must depend on the variance of the data because the variance measures the variability of the data. The next result relates that difference to the standard deviation that is the square root of the variance:\n",
        "\n",
        "\\\n",
        "\n",
        "*Theorem.* If $X$ is a random variable, $\\mathbb{E}$ the expected value, $m$  the median, and  $var(X)$ is the variance, then:\n",
        ">>\n",
        "> $\\lvert \\mathbb{E}(X)-m\\rvert \\le \\sqrt{\\text{var}\\left(X\\right)} = (\\mathbb{E}[(X-\\mathbb{E}[X])^2])^{1/2}$\n",
        ">>\n",
        "We follow the proof by [Mittens](https://math.stackexchange.com/q/4144525)\n",
        ">\n",
        "*Proof.* Three inequalities must be concatenated to obtain the result. \n",
        "\n",
        "- First: \n",
        "\n",
        "> $| \\mathbb{E}(X) - m| = | \\int X(x)dp - m | = | \\int X(x)dp - m \\int dp  | $\n",
        ">> $ = | \\int (X(x)-\\int m dp  | = | \\int (X(x)- m ) dp  |  $\n",
        ">>\n",
        ">> $ \\le \\int |X(x)-m| dp = \\mathbb{E} (|X-m|) $\n",
        "> \n",
        "where we have used the facts that the integral of 1 along the universal set is 1, and that the absolute value of an integral is less than the integral of the absolute value, because the absolute value of a sum is less than the sum of absolutes values. In short,\n",
        ">\n",
        "> $| \\mathbb{E}(X) - m| \\le \\mathbb{E} (|X-m|)$.\n",
        ">\n",
        "- Second:\n",
        ">\n",
        "We know that the median minimizes the functional $\\mathbb{E} (|x-c|)$, i.e.,\n",
        ">>\n",
        ">  $\\mathbb{E} (|X-m|) \\leq \\mathbb{E} (|X-c|)$ for each c.\n",
        ">>\n",
        "Then, taking $c = \\mathbb{E}(X)$, we have:\n",
        ">>\n",
        ">$\\mathbb{E} (|X-m|) \\leq \\mathbb{E} (|X-\\mathbb{E}(X)|)$\n",
        ">>\n",
        " -Third:\n",
        "\n",
        "Let us apply now the Cauchy-Schwarz inequality that states that\n",
        ">>\n",
        ">$\\mathbb{E}[|XY|]\\leq(\\mathbb{E}[X^2])^{1/2}(\\mathbb{E}[Y^2])^{1/2}$,\n",
        ">>\n",
        "provided everything exists. If we replace $X$ by $X-\\mathbb{E}[X]$    and $1$ by $Y$, we have\n",
        ">>\n",
        "> $\\mathbb{E}[|(X-\\mathbb{E}[X])|]\\leq(\\mathbb{E}[(X-\\mathbb{E}[X])^2])^{1/2}(\\mathbb{E}[1])^{1/2}$\n",
        ">>\n",
        "The expected value of the constant function 1 is\n",
        ">>\n",
        ">$\\mathbb{E}[1] = \\int_\\mathbb{R} 1 dp = p(\\mathbb{R}) = 1$,\n",
        ">>\n",
        "whence\n",
        ">>\n",
        ">$\\mathbb{E}[|(X-\\mathbb{E}[X])|]\\leq (\\mathbb{E}[(X-\\mathbb{E}[X])^2])^{1/2}  = \\sqrt{\\text{var(X)} }$\n",
        "\n",
        "We have three inequalities to concatenate:\n",
        "\n",
        "> $| \\mathbb{E}(X) - m| \\le \\mathbb{E} (|X-m|)$.\n",
        "> >\n",
        ">$\\mathbb{E} (|X-m|) \\leq \\mathbb{E} (|X-\\mathbb{E}(X)|)$\n",
        ">\n",
        ">$\\mathbb{E}[|(X-\\mathbb{E}[X])|]\\leq (\\mathbb{E}[(X-\\mathbb{E}[X])^2])^{1/2}  = \\sqrt{\\text{var(X)} }$\n",
        ">\n",
        "Executing the complete chain, we get:\n",
        "\n",
        "$| \\mathbb{E}(X) - m| \\le \\sqrt{\\text{var(X)} }$\n",
        ">\n",
        "which is the required result. \n"
      ]
    },
    {
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      "metadata": {
        "id": "5dpNThcJYX_O"
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      "source": [
        "### Proof of the main theorem on the mean of MAX\n",
        "\n",
        "\n",
        "Here we found a proof of the following result that uses all the aforementioned prerequisites that have been elaborated in the previous subsections:\n",
        "\n",
        "\n",
        "*Sandwich Theorem for the bounds of the mean of MAX.*\n",
        ">>\n",
        ">Let $n\\in \\mathbb{N}^*$ and  $ Z_i$, i=1,...,n be i.i.d $\\mathcal{N}(0,1)$. Then, the expected value of MAX is approximately given by the following sandwich result:\n",
        ">>>\n",
        ">>$\\sqrt{\\ln(n)} \\leq \\mathbb{E} (MAX  ) \\leq  \\sqrt{2\\ln(n)} $\n",
        ">>>\n",
        ">This approximation theorem points to a family of functions of the form $\\sqrt{k \\ln (n)}$, in which the best value of $k$, with $1 \\leq k \\leq 2$, must be found by resorting to the cdf of MAX and/or to simulations. Resultant formula will be used as default value in predictions.\n",
        "\n",
        "*Proof.* We follow [Yass1]({https://math.stackexchange.com/q/5008221}) and accompany him until we dissent. \n",
        "\n",
        "We are going to upper bound and lower bound the expected value of MAX. This can be taken as a starting Ansatz to try variations to see which one best functions.\n",
        ">\n",
        "**Upper bound:** Let us apply the Jensen's inequality to the exponential function, which is convex\n",
        ">>\n",
        ">$ A = \\exp( \\mathbb{E}(\\lambda \\, \\max_{1\\leq i \\leq n}Z_i)) \\leq  \\mathbb{E}(\\exp(\\lambda \\max_{1\\leq i \\leq n}Z_i))  = B    $\n",
        ">\n",
        "where $\\lambda \\in \\mathbb{R}^+$  will be specified below.\n",
        ">>\n",
        "For each finite sample, the exponential of the MAX is equal to the MAX of the exponentials:\n",
        ">>\n",
        ">$ B = \\mathbb{E}(\\exp(\\lambda \\max_{1\\leq i \\leq n}Z_i)) =\n",
        " \\mathbb{E}(\\max_{1\\leq i \\leq n}\\exp(\\lambda Z_i))) = C$\n",
        ">>\n",
        "Since the exponential is always positive, the MAX is less than itself plus the other positive terms:\n",
        ">>\n",
        ">$ \\max_{1\\leq i \\leq n}\\exp(\\lambda Z_i) \\leq \\sum_{i=1}^n \\exp(\\lambda Z_i)$\n",
        ">>\n",
        "Combining this with the linearity of the expected value, we have:\n",
        ">\n",
        ">$C = \\mathbb{E}(\\max_{1\\leq i \\leq n}\\exp(\\lambda Z_i))) \\leq  \\sum_{i=1}^n\\mathbb{E}(\\exp(\\lambda Z_i)) = D$\n",
        ">\n",
        "By an explicit calculation shown below,\n",
        ">\n",
        ">$\\mathbb{E}(\\exp(\\lambda Z_i)) = exp(\\frac{\\lambda^2}{2})$\n",
        ">\n",
        "Henceforth:\n",
        ">>\n",
        ">$D = \\sum_{i=1}^n\\mathbb{E}(\\exp(\\lambda Z_i))=n\\times \\exp(\\frac{\\lambda^2}{2}) = E$.\n",
        ">>\n",
        "Concatenating everything from $A$ to $E$, we get,\n",
        ">\n",
        ">$A = \\exp( \\mathbb{E}(\\lambda \\max_{1\\leq i \\leq n}Z_i)) \\leq n\\times \\exp(\\frac{\\lambda^2}{2}) = E$.\n",
        ">>\n",
        ">$\\exp(\\lambda \\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)) \\leq n\\times \\exp(\\frac{\\lambda^2}{2})$.\n",
        ">\n",
        "Taking logarithms, which is an increasing function\n",
        ">\n",
        ">$\\lambda \\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i) \\leq \\ln n + \\frac{\\lambda^2}{2}$\n",
        ">>\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)\\leq \\frac{\\ln n}{\\lambda}+\\frac{\\lambda}{2}$.\n",
        ">\n",
        "This inequality is true for every positive value of $\\lambda$. So, it is also certain for the minimum, which we can find by equating the derivative to zero.\n",
        ">\n",
        "Let\n",
        ">\n",
        "> $j(\\lambda ) =\\frac{\\ln n}{\\lambda}+\\frac{\\lambda}{2}$.\n",
        ">\n",
        "> $j'(\\lambda ) =-\\frac{\\ln n}{\\lambda^2}+\\frac{1}{2} = 0$.\n",
        ">\n",
        ">  $ -\\frac{\\ln n}{\\lambda^2} = -\\frac{1}{2}  $\n",
        ">\n",
        ">  $ \\frac{\\ln n}{\\lambda^2} = \\frac{1}{2}  $\n",
        ">\n",
        ">  $ 2 \\ln n = \\lambda^2$\n",
        ">\n",
        ">  $ \\lambda = \\sqrt{2\\ln n}$\n",
        ">\n",
        " By replacing this value on the former inequality, we find:\n",
        ">\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)\\leq \\frac{\\ln n}{\\sqrt{2\\ln n}}+\\frac{\\sqrt{2\\ln n}}{2}$.\n",
        ">\n",
        ">$ = \\frac{ 2\\ln n + 2 \\ln n}{2\\sqrt{2\\ln n}}$\n",
        ">\n",
        "> $ = \\frac{ 4\\ln n }{2\\sqrt{2\\ln n}}$\n",
        ">\n",
        "> $ = \\frac{ 2\\ln n }{\\sqrt{2\\ln n}}$\n",
        ">\n",
        ">$ =  \\sqrt{2\\ln n}$\n",
        ">\n",
        "In conclusion,\n",
        ">\n",
        "> $\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)\\leq \\sqrt{2\\ln n}$.\n",
        ">\n",
        "This means that $\\sqrt{2\\ln n}$ is an upper bound of $\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)$, the expected value of MAX.  \n",
        ">\n",
        "Let us fill in a detail. We need to show that for all $i$\n",
        ">\n",
        ">$\\mathbb{E}(\\exp(\\lambda Z_i)) = exp(\\frac{\\lambda^2}{2})$\n",
        ">\n",
        "This is shown by an explicit calculation:\n",
        ">>\n",
        ">$\\mathbb{E}(\\exp(\\lambda Z_i)) = \\int^{\\infty}_{-\\infty} exp( \\lambda z ) dp(z)$\n",
        ">\n",
        "Since we are referring to the standard normal distribution, the probability measure is its pdf:\n",
        ">\n",
        ">>$ = \\int^{\\infty}_{-\\infty} exp( \\lambda z ) \\frac{e^{-z^2/2}}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        ">>$ = \\int^{\\infty}_{-\\infty}   \\frac{e^{-z^2/2 + \\lambda z}}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        ">>$ = \\int^{\\infty}_{-\\infty}   \\frac{e^{-(z^2 - 2 \\lambda z)/2) }}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        ">>$ = \\int^{\\infty}_{-\\infty}   \\frac{e^{-(z^2 - 2 \\lambda z+ \\lambda^2 - \\lambda ^2)/2  }}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        ">>$ = \\int^{\\infty}_{-\\infty}   \\frac{e^{-(z- \\lambda )^2/2  + \\lambda^2 / 2 }}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        ">>$ = e^{\\lambda^2 / 2 } \\int^{\\infty}_{-\\infty}   \\frac{e^{-(z- \\lambda )^2/2  }}{\\sqrt{2\\pi}}dz$\n",
        ">>\n",
        "Making the change of variable $ u = z - \\lambda$ and $du = dz$, we get\n",
        ">>\n",
        ">>$ = e^{\\lambda^2 / 2 } \\int^{\\infty}_{-\\infty}   \\frac{e^{-u^2/2  }}{\\sqrt{2\\pi}}du$\n",
        ">>\n",
        ">>\n",
        ">>$ = e^{\\lambda^2 / 2 } $\n",
        ">>\n",
        ">because the integral represents the probability under the whole bell that is 1.\n",
        "\n",
        " **Lower bound.**  To find a lower bound for the expected value of MAX, let us use the inequality of the median. This says that for whatever random variable $X$ with finite expected value and median, the difference between the expected value and the median depends on the variance:\n",
        "\n",
        ">$|\\mathbb{E}(X)-Med(X)|\\leq Var(X)$\n",
        ">\n",
        "We assume that\n",
        ">\n",
        ">$X = \\max_{1\\leq i \\leq n}Z_i $  \n",
        ">\n",
        "and denoting\n",
        ">\n",
        ">$M_n=Med(\\max_{1\\leq i \\leq n}Z_i))$\n",
        ">\n",
        "Then,\n",
        ">\n",
        ">$|\\mathbb{E}(X)-Med(X)|\\leq Var(X)$\n",
        ">\n",
        "becomes\n",
        ">\n",
        ">$|\\mathbb{E}(X)-M_n|\\leq Var(X)$\n",
        ">\n",
        "that is equivalent to\n",
        ">\n",
        ">$-Var(X) \\leq \\mathbb{E}(X)-M_n \\leq Var(X)$\n",
        ">\n",
        ">Taking the left inequality\n",
        ">\n",
        ">$-Var(X)  + M_n \\leq \\mathbb{E}(X) $\n",
        ">\n",
        "or\n",
        ">\n",
        ">$\\mathbb{E}(X) \\ge M_n -Var(X) $\n",
        ">\n",
        ">and by the Poincaré inequality,\n",
        ">\n",
        ">$Var(\\max_{1\\leq i \\leq n}Z_i))\\leq 1$.\n",
        ">\n",
        ">or\n",
        ">\n",
        ">$-Var(\\max_{1\\leq i \\leq n}Z_i))\\ge -1$.\n",
        ">\n",
        ">Adding $M_n$ to both sides\n",
        ">\n",
        ">$M_n -Var(\\max_{1\\leq i \\leq n}Z_i))\\ge M_n -1$.\n",
        ">\n",
        "Therefore,\n",
        ">>\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)\\geq M_n -Var(\\max_{1\\leq i \\leq n}Z_i))\\ge M_n -1$.\n",
        ">\n",
        "This inequality lower bounds the expected value of MAX. It will be used below.\n",
        ">\n",
        "On the other hand, by the definition of the median, we have\n",
        ">\n",
        ">$\\mathbb{P}(\\max_{1\\leq i \\leq n}Z_i\\leq M_n)=\\frac{1}{2}$,\n",
        ">\n",
        "This is the CDF of MAX evaluated at the median:\n",
        ">\n",
        ">$F(Median) = \\Phi^n(Median)$\n",
        ">\n",
        ">where $\\Phi$ is the cdf of the standard normal distribution, $X \\sim \\mathcal{N}(0,1)$, with\n",
        ">\n",
        ">$\\Phi(x)=\\mathbb{P}(X\\leq x)$.\n",
        ">\n",
        "Hence,\n",
        ">\n",
        ">$F(Median) = \\Phi^n(Median) = \\frac{1}{2}$\n",
        ">\n",
        "clearing for $\\Phi$, and recalling that the median is $M_n$, we get\n",
        ">>\n",
        ">$\\Phi(Median) = \\Phi(M_n)= \\frac{1}{2^{\\frac{1}{n}}}$\n",
        ">>\n",
        "Inserting this into the $Q$-function, we get:\n",
        ">>\n",
        ">$Q(M_n) = 1 - \\Phi(M_n)=  1 - \\frac{1}{2^{\\frac{1}{n}}}$\n",
        "\n",
        "We accompany the cited Author until here (we dissent in a detail), but we continue using his methodology.\n",
        "\n",
        "Let us use now a lower bound to the Q-function, defined by  $Q(x)=1-\\Phi(x) $,  to find a lower bound to its inverse. Let us remember, from a prereqisite,  the lower bound of $Q$ for $x \\in \\mathbb{R^+}$,\n",
        ">>\n",
        "> $Q(x)=1-\\Phi(x) \\ge \\frac{1}{12}\\exp(- x^2)$,\n",
        ">>\n",
        "The $Q$-function is decreasing, monotone, one-to-one, so, it has an inverse $Q^{-1}$ that is also decreasing. This means that if $a < b$, then their images are related in reverse order. Now, let us take $Q^{-1} $ at both sides of the previous inequality, we get\n",
        ">>\n",
        ">$Q^{-1} Q(x) \\leq  Q^{-1} (\\frac{1}{12}\\exp(- x^2))$,\n",
        ">>\n",
        "because $Q^{-1} $ reverses the order.\n",
        ">>\n",
        ">$x \\leq  Q^{-1} (\\frac{1}{12}\\exp(- x^2))$,\n",
        ">>\n",
        "or\n",
        ">>\n",
        "$  Q^{-1} (\\frac{1}{12}\\exp(- x^2)) \\ge x$,\n",
        ">\n",
        "where $x$ is in the domain of $Q$. Let us rewrite this in terms of the domain of $Q^{-1}$. So, let it be\n",
        ">>\n",
        ">$t = \\frac{1}{12}\\exp(- x^2)$\n",
        ">>\n",
        ">$12t =  \\exp(- x^2 )$\n",
        ">>\n",
        "taking ln at both sides, and clearing for $x$\n",
        ">>\n",
        ">$ \\ln (12t) =   - x^2 $\n",
        ">>\n",
        ">$  x^2  = - \\ln (12t) $\n",
        ">>\n",
        "The right side is positive when the $\\ln$ is negative, i.e., when $0 < 12t < 1$ or when $0 < t < 1/12$. Thus, we must work in the viecinity of $0$. In that case, we can take the square root:\n",
        ">>\n",
        "> $  x  = \\sqrt{-  \\ln (12t) }$\n",
        ">>\n",
        "This can also be written as\n",
        ">>\n",
        ">  $  x  = \\sqrt{|  \\ln (12t) |} $\n",
        ">>\n",
        "As a consequence, the former expression\n",
        ">>\n",
        ">$  Q^{-1} (\\frac{1}{12}\\exp(- x^2)) \\ge x$,\n",
        ">>\n",
        "can be rewritten as\n",
        ">>\n",
        "> $  Q^{-1} (t) \\ge  \\sqrt{|  \\ln (12t) |}$,\n",
        ">\n",
        ">>\n",
        "This is a lower bound for the inverse of the $Q$-function. We need to incorporate this result to bound\n",
        ">>\n",
        ">$Q(M_n)=1-\\frac{1}{2^\\frac{1}{n}}$.\n",
        ">>\n",
        "So, let us help us by thinking of the function\n",
        ">>\n",
        ">$h(x) = 1-\\frac{1}{2^x} = 1 - 2^{-x}$\n",
        ">>\n",
        "that results from substituting $x = \\frac{1}{n}$.\n",
        ">\n",
        "The exponential $2^x$ is increasing taking values from 1 to $\\infty$. The exponential $2^{-x} = \\frac{1}{2^x}$ is decreasing taking values from 1 to $0$. The function $-2^{-x}$ is increasing taking values from -1 to 0. The function $-2^{-x} +1 = 1-2^{-x} = h(x)$ is increasing taking values from 0 to 1. It also opens downwards. Given that our point of interest is 0, because when $n \\to \\infty$, $x= \\frac{1}{n} \\to 0$, we can upper bound $h(x)$ by the tangent line, which is given by the derivative:\n",
        ">>\n",
        ">$h'(x) = (1- 2^{-x})'  = - (2^{-x})'  = -((e^{\\ln 2})^{-x})'  = -(e^{-x\\ln2})'$\n",
        ">>\n",
        ">$h'(x) = \\ln2(e^{-x\\ln2})  = ln2 \\times 2^{-x}$\n",
        ">>\n",
        "which evaluated at 0 gives $h' (0) = \\ln 2$. Since $h(0) = 0$, the tangent line at 0 is $y = (\\ln2)x$ and this is above $h(x)$ because $h(x)$ opens downwards. Thus, we have shown that the tangent line at $0$ is an upper bound for $h$. Hence,\n",
        ">>\n",
        ">$h(x) =   1 - 2^{-x} \\leq (\\ln2)x $.\n",
        ">>\n",
        "Recalling that $x = \\frac{1}{n}$, we have\n",
        ">>\n",
        ">$ 1 - 2^{- \\frac{1}{n} } \\leq (\\ln2)\\frac{1}{n} = \\frac{\\ln 2}{n} $,\n",
        ">>\n",
        "or,\n",
        ">>\n",
        ">$Q(M_n)=1-\\frac{1}{2^\\frac{1}{n}}\\leq \\frac{\\ln 2}{n}$.\n",
        ">\n",
        "Keeping in mind that $Q^{-1}$-function is decreasing, and that it reverses the order, let us apply it to both sides of the previous inequality to get:\n",
        ">>\n",
        ">$M_n  \\ge  Q^{-1}(\\frac{\\ln2}{n})$\n",
        ">\n",
        "But, we had:\n",
        ">>\n",
        "> $  Q^{-1} (t) \\ge  \\sqrt{|  \\ln (12t) |}$,\n",
        ">\n",
        "So, replacing $t$ by $\\frac{\\ln2}{n}$, we get\n",
        ">>\n",
        "> $  Q^{-1} (\\frac{\\ln2}{n}) \\ge  \\sqrt{  |  \\ln (12\\frac{\\ln2}{n}) |  }$,\n",
        ">>\n",
        "Concatenating this with\n",
        ">>\n",
        ">$M_n\\ge Q^{-1}(\\frac{\\ln2}{n}) $\n",
        ">>\n",
        ">we have\n",
        ">>\n",
        ">$M_n\\ge Q^{-1}(\\frac{\\ln2}{n}) \\ge  \\sqrt{|  \\ln (12\\frac{\\ln2}{n}) |}  $\n",
        ">>\n",
        "Let us recall  a previous result that lower bounds the expected value of MAX taking into account that MAX is not dispersive:\n",
        ">>\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)\\geq M_n -Var(\\max_{1\\leq i \\leq n}Z_i))\\ge M_n -1$.\n",
        ">>\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i) \\ge M_n -1 \\ge  \\sqrt{|  \\ln (12\\frac{\\ln2}{n}) |}  -1 $.\n",
        ">\n",
        "or\n",
        ">\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)   \\ge  \n",
        "\\sqrt{|  \\ln (12\\frac{\\ln2}{n}) |}  -1 $.\n",
        ">\n",
        "Let us see the tendency of $\\sqrt{|  \\ln (12\\frac{\\ln2}{n}) |} $\n",
        ">\n",
        ">$ \\sqrt{|  \\ln (12\\frac{\\ln2}{n}) |} $\n",
        "$ =  \\sqrt{   |    \\ln (12) + \\ln ( \\ln 2)  - \\ln(n)    |    }  $\n",
        "$ \\to  \\sqrt{ \\ln (n)} $\n",
        ">\n",
        "Hence,\n",
        ">\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)   \\ge  \\sqrt{|  \\ln (n) |}  -1  \\to  \\sqrt{|  \\ln (n) |} = \\sqrt{ \\ln (n) }   $.\n",
        ">\n",
        "This is exactly the lower bound for the expected value of MAX that we have promised.\n",
        "\n",
        "*Conclusion.* The expected value of MAX can be bounded above by $ \\sqrt{2\\ln n}$:\n",
        ">>\n",
        ">$ \\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i) \\leq \\sqrt{2\\ln n}$\n",
        ">>\n",
        "and bounded below by  $\\sqrt{ \\ln (n) } $\n",
        ">>\n",
        ">$\\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i)   \\ge   \\sqrt{ \\ln (n) } $.\n",
        ">\n",
        "In one line:\n",
        ">\n",
        "> $   \\sqrt{ \\ln (n) }   \\le  \\mathbb{E}(\\max_{1\\leq i \\leq n}Z_i) \\leq \\sqrt{2\\ln n}$\n",
        ">\n",
        "> which is the sandwich theorem.\n",
        " \n"
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        "# CONCLUSION\n",
        "\n",
        "**Exercise.**  Propose a conclusion to the present study.\n",
        ">\n",
        "*Our answer.*  \n",
        "\n",
        "A tractable problem that models the origin of life is **The Shakespeare Challenge**, which consists in matching a target string with strings generated at random. We have studied a simple question related to this challenge in this contribution: What is the best that randomness can do given that it works at many fronts? \n",
        "\n",
        "We have witnessed that the MAX of various random numbers, with a normal or binomial distribution, is certainly better than one. But, at the end, this is not of great help to battle complexity. This means that randomness can solve the aforementioned challenge for large strings if resources in extremely large quantities are allocated. \n",
        "\n",
        "Nothing to do with our universe. \n",
        "\n",
        "But, a light appears with the following observation: \n",
        "\n",
        "The best that randomness can do is just the selection of the fittest, which we have modelled as picking the MAX of $m$ numbers. These represent a measure in z-units of the coincidences made by randomness over the target string, which we have imagined as the product of $m$ monkeys punching up at random over writing machines.  So, a terrible engineering problem arises: \n",
        "\n",
        "> Given that choosing the MAX is very good, but not good enough, How can we insert the procedure of selecting the fittest into an algorithm that skyrockets the capability of MAX to battle complexity? This is **The MAX-ROCKET challenge**. \n",
        "\n",
        "In preparation to study the beautiful promise of Evolution to solve this challenge, we need to predict with a formula the performance of the best.  Our formula reads: \n",
        "\n",
        "> The expected value of MAX in z-units as a function of the number of monkeys, $m$, whose performance follows a standard normal distribution,  is \n",
        ">> \n",
        ">> Mean of MAX = $\\mathbb{E}(MAX) =  \\sqrt{k \\ln (m)} $ \n",
        ">>\n",
        ">> $k = 1.29$. \n",
        "\n",
        "Our tests say that this general formula, derived for normal distributions, is very good. We apply it to $m$ binomial variables $Bi(n, 1/2)$ or monkeys, where $n$ represents the length of the pattern chain or target to be guessed. And we refined it with a simulation. That produced:\n",
        ">>\n",
        ">> Mean of MAX = $\\mathbb{E}(MAX) = \\frac{n}{2} +  \\sqrt{\\frac{n}{k}\\ln m  }  $\n",
        ">>\n",
        ">> $k = 24.9 n^{-1.18} + 2.53$\n",
        "\n",
        "\n"
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