{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "02721582",
   "metadata": {},
   "source": [
    "# Assessing Model 1\n",
    "[credit: cases are from Berkeley Data 8](https://www.data8.org/)\n",
    "\n",
    "A **chance model** describes how a process could generate outcomes at random. It states what stays fixed, what varies, and the probabilities of the possible outcomes. Here, the model fixes the panel size and the eligible population's composition, while the selected panelists vary.\n",
    "\n",
    "You will compare a real jury panel with panels simulated under that model. The question is whether ordinary sampling variability can plausibly account for the observed shortfall. The same reasoning applies when a manager checks whether hiring or promotions follow a stated selection process.\n",
    "\n",
    "Run the demonstration cells in order, beginning with the imports below. Each Interactive Exercise includes its own setup so you can run it independently.\n",
    "\n",
    "```{index} Chance model\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
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    "tags": [
     "hide-input",
     "thebe-init",
     "runnable"
    ]
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6ca8361",
   "metadata": {},
   "source": [
    "```{contents}\n",
    ":local:\n",
    ":depth: 2\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7eb7e417",
   "metadata": {},
   "source": [
    "## Case 1: Swain vs. Alabama\n",
    "\n",
    "In the early 1960s in Talladega County, Alabama, Robert Swain, a Black man, was convicted of raping a white woman and sentenced to death. He appealed, arguing—among other issues—that the jury process was discriminatory. At that time, only men aged 21 and older were eligible for jury service. Although 26% of the county’s eligible jurors were Black, the 100-person jury panel for Swain’s case included only 8 Black men (8%), and none were seated on the trial jury. In 1965, the U.S. Supreme Court denied Swain’s appeal, stating that “the overall percentage disparity has been small.” \n",
    "\n",
    "Because jury panels are intended to be random samples from the eligible population, the key statistical question is whether observing 8% Black on a 100-person panel is a plausible outcome if the true eligible population is 26% Black, or whether the shortfall is unlikely to be due to chance alone."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80fc680d",
   "metadata": {},
   "source": [
    "## Model to Evaluate\n",
    "\n",
    "One way to interpret the data, using a **statistical model**, is that the jury panel was formed by **random selection**, and the low count of Black men arose purely by chance. This view aligns with the Supreme Court’s characterization.\n",
    "\n",
    "To make that model precise, we specify the chance mechanism: treat the panel as a random sample from an eligible population in which 26% of individuals are Black. This is testable **computationally**:\n",
    "\n",
    "- **Simulate** under the model: repeatedly draw panels of 100 from a population with 26% Black.\n",
    "- Characterize expected outcomes: record how many Black panelists appear in each **simulated panel**.\n",
    "- Compared to the **observed** panel, Swain’s panel had 8% Black (8 of 100).\n",
    "- Evaluate **consistency**: if results like “8 of 100” are rare under the model, that is evidence against random selection from a 26% population.\n",
    "\n",
    "We now walk through this assessment step by step.\n",
    "\n",
    "## Choosing a Test Statistic\n",
    "\n",
    "We must select a statistic that helps distinguish the **model** (random selection from the eligible population) from the **alternative** (that the panel included too few Black members to be random). A natural choice is the **count** of Black panelists in the **100**-person panel. Under this choice, smaller counts provide evidence against the random-selection model and in favor of Swain’s claim.\n",
    "\n",
    "## Predicting the Statistic Under the Model\n",
    "\n",
    "If the model were true, how big would the statistic typically be? To answer that, we have to start by working out the details of the simulation.\n",
    "\n",
    "### Generating One Value of the Statistic¶\n",
    "First let’s figure out how to simulate one value of the statistic. For this, we have to sample 100 times at random from the population of eligible jurors and count the number of black men we get.\n",
    "\n",
    "One way is to set up a table representing the eligible population and use a sample as we did in the previous chapter. But there is also a quicker way; we can build a function tailored for sampling at random from categorical distributions. We will use this function, **`sample_proportions`**. The sample_proportions function will take two arguments:\n",
    "\n",
    "- the sample size\n",
    "- the distribution of the categories in the population, as a list or array of proportions that add up to 1\n",
    "\n",
    "As the function uses a numpy ‘method’ an array will be returned containing the distribution of the categories in a random sample of the given size taken from the population. This is an array consisting of the sample proportions in all the different categories.\n",
    "\n",
    "To see how to use this, remember that according to our model, the panel is selected at random from a population of men among whom 26% were black and 74% were not. Thus, the distribution of the two categories can be represented as the list [0.26, 0.74], which we have assigned to the name eligible_population. Now let’s sample at random 100 times from this distribution, and see what proportions of the two categories we get in our sample.\n",
    "\n",
    "**Check your reasoning:** In each repetition, keep the population share at 26% and the panel size at 100. Let the selected count vary. Using 8% as the simulation probability would build the observed shortfall into the model instead of testing the stated 26% model.\n",
    "\n",
    "The multinomial simulation below uses independent draws. It approximates sampling without replacement when the panel is a small share of the eligible population.\n",
    "\n",
    "```{index} Test statistic\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "840e2353",
   "metadata": {},
   "source": [
    ":::{admonition} Multinomial Distribution\n",
    "\n",
    "A **binomial distribution** describes the count in one category across independent trials with a fixed probability. For example, `np.random.binomial(n=100, p=0.26)` returns the number of Black panelists in 100 independent draws under this model.\n",
    "\n",
    "A **multinomial distribution** describes the counts in all categories. It supports two or more categories. The pattern is `np.random.multinomial(sample_size, probabilities)`, where the probabilities sum to one. It returns an array of counts that sum to the sample size.\n",
    "\n",
    "For `np.random.multinomial(100, [0.26, 0.74])`, the first count is for Black panelists and the second is for other panelists. Dividing both counts by 100 converts counts to proportions. The binomial count corresponds to the first count of this two-category multinomial model.\n",
    ":::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "140f05a2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.397911Z",
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     "shell.execute_reply": "2026-08-31T06:01:00.399475Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Binomial count: 25\nMultinomial counts: [33 67]\n"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "result_bi = np.random.binomial(n=100, p=0.26)\n",
    "result_multi = np.random.multinomial(100, [0.26, 0.74])\n",
    "print('Binomial count:', result_bi)\n",
    "print('Multinomial counts:', result_multi)\n",
    "# These are separate random draws, so their first counts need not match.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "77caef3e",
   "metadata": {
    "execution": {
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   "source": [
    "np.random.seed(42)\n",
    "def sample_proportions(sample_size, probabilities):\n",
    "    \"\"\"Return the proportion of random draws for each outcome in a distribution.\n",
    "    This function is similar to np.random.multinomial, but returns proportions\n",
    "    instead of counts.\n",
    "    Args:\n",
    "        ``sample_size``: The size of the sample to draw from the distribution.\n",
    "        ``probabilities``: An array of probabilities that forms a distribution.\n",
    "    Returns:\n",
    "        An array with the same length as ``probability`` that sums to 1.\n",
    "    \"\"\"\n",
    "    return np.random.multinomial(sample_size, probabilities) / sample_size\n",
    "    # return np.random.multinomial(sample_size, probabilities) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "20e7f3e0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.402862Z",
     "iopub.status.busy": "2026-08-31T06:01:00.402799Z",
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     "shell.execute_reply": "2026-08-31T06:01:00.404880Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "metadata": {},
     "data": {
      "text/plain": "array([0.25, 0.75])"
     },
     "execution_count": 4
    }
   ],
   "source": [
    "eligible_population = [0.26, 0.74]\n",
    "sample_proportions(100, eligible_population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2d407f3",
   "metadata": {},
   "source": [
    "The first entry, accessed with `[0]`, is the proportion of Black men in the random sample. Because the sample contains 100 men, multiplying by 100 converts that proportion to a count.\n",
    "\n",
    "Run the next cell a few times to see the count vary. The model stays the same each time.\n",
    "\n",
    "The exercises use `rng = np.random.default_rng(seed)` to create a random-number generator. A fixed seed makes its sequence reproducible. The call `rng.binomial(n, p)` returns one count for `n` independent trials with probability `p`; `rng.binomial(n, p, size=repetitions)` returns several counts at once. Similarly, `rng.multinomial(n, probabilities)` returns the category counts for one sample. These generator methods use the same model inputs as the NumPy functions above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "73b8cc61",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.405927Z",
     "iopub.status.busy": "2026-08-31T06:01:00.405869Z",
     "iopub.status.idle": "2026-08-31T06:01:00.407066Z",
     "shell.execute_reply": "2026-08-31T06:01:00.406911Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "33.0\n"
    }
   ],
   "source": [
    "print((100 * sample_proportions(100, eligible_population))[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Predict One Panel\n",
    "# A promotion model selects 50 employees independently with a 40% chance\n",
    "# of selecting a woman on each draw. Simulate one count and print it.\n",
    "# Before running, predict the count around which repeated results would cluster.\n",
    "import numpy as np\n",
    "rng = np.random.default_rng(12)\n",
    "### Your code starts here.\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Women selected: 18\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "rng = np.random.default_rng(12)\n",
    "print('Women selected:', rng.binomial(50, 0.4))\n",
    "# Repeated counts should cluster around 50 * 0.4 = 20."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f87941a",
   "metadata": {},
   "source": [
    "## Running the Simulation\n",
    "To get a sense of the variability without running the cell over and over, let’s generate 10,000 simulated values of the count. You can think of that as you did 10,000 times of data collection.\n",
    "\n",
    "The code follows the same steps that we have used in every simulation. First, we define a function to simulate one value of the count, using the code we wrote above.\n",
    "\n",
    "Let's define a function that does this. The function will draw a panel at random and return the number of panelists who are Black."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d4c29949",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.407971Z",
     "iopub.status.busy": "2026-08-31T06:01:00.407914Z",
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     "shell.execute_reply": "2026-08-31T06:01:00.409017Z"
    },
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   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "sample_size = 100\n",
    "\n",
    "def one_simulated_count():\n",
    "    # return sample_size * sample_proportions(sample_size, eligible_population).item(0)\n",
    "    return sample_size * sample_proportions(sample_size, eligible_population)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bc3c943",
   "metadata": {},
   "source": [
    "Next, we create an array of 10,000 simulated counts by using a for loop.\n",
    "\n",
    "**Predict before running:** Should the counts cluster around eight or 26? The model predicts about 26. Eight is the observed count being assessed, not the center of the null distribution.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c4e517ab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.410152Z",
     "iopub.status.busy": "2026-08-31T06:01:00.410106Z",
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     "shell.execute_reply": "2026-08-31T06:01:00.441405Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "counts = np.array([])\n",
    "repetitions = 10000                 ### n\n",
    "for i in np.arange(repetitions):\n",
    "    counts = np.append(counts, one_simulated_count())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "771fe040",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.442519Z",
     "iopub.status.busy": "2026-08-31T06:01:00.442465Z",
     "iopub.status.idle": "2026-08-31T06:01:00.444149Z",
     "shell.execute_reply": "2026-08-31T06:01:00.443937Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "metadata": {},
     "data": {
      "text/plain": "array([25., 33., 29., ..., 33., 25., 23.], shape=(10000,))"
     },
     "execution_count": 10
    }
   ],
   "source": [
    "counts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87801dc1",
   "metadata": {},
   "source": [
    "We can also check the **min** and **max** of the data to get some idea about **bins**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8a5bbf16",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.445052Z",
     "iopub.status.busy": "2026-08-31T06:01:00.445001Z",
     "iopub.status.idle": "2026-08-31T06:01:00.446343Z",
     "shell.execute_reply": "2026-08-31T06:01:00.446175Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "9.0 42.0\n"
    }
   ],
   "source": [
    "print(counts.min(), counts.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62aeced3",
   "metadata": {},
   "source": [
    "## The Prediction\n",
    "To interpret the results of our simulation, we can visualize the results in an **empirical** histogram of the simulated counts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f120523b",
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2026-08-31T06:01:00.502084Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "metadata": {},
     "data": {
      "text/plain": "Text(0, 0.5, 'Percent of Simulated Panels')"
     },
     "execution_count": 12
    },
    {
     "output_type": "display_data",
     "metadata": {},
     "data": {
      "text/plain": "<Figure size 800x400 with 1 Axes>",
      "image/png": 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S/ggGHdH7zo9yK7ANUsPbd2gpLSk66Ig+t2Vr2nq9d19fpmtxMOjwdt5558g5SW0BjfjF44+7YNDh6Vj1I86xvhvIHAIPlDq6CAUL1dSIUI+HeshFjXydfOJdHNWDGysQ8NTQFI0UxAs6RBcPfyGKvpgpvcY3KJTykKhBEZZ6AH0+fnFO+6rhdi9Rz5wuEL7HVxdn9arFos9GPXLxqMdUNBKQTIF+PD5YVK+sRsCi+QXA/DoMsfgLlY69VNJ3gmmA6n0L1lUUB30u8QIcpax4akTGS/sI3i/RBASFUYMrXs6/jg0/sqhe+yClfPk6Gj1HrAaoqJGkXtJMUqPTn4/UENP/1chXepcCaI2KJjsKpGNBgalG/nwevW4+PaWwmdbC7j+lNPm0MD1HvEaxgif1+BfV+UApVuqljvccfjuVNqMUmliChcvR7ztZ+lx1bdAIS3Raqj/mNbqjc5casdGjnOJTJ9VTX1i6kUYkfCAXrEcojH8NdWrF+w5Ev0b09ctfS9VATzcdOB3+WFINikZv4lEnkb+mB4+/aBrVidcBp2u9H/UOe4wgOaRaoczQBV7D4RpmVk5yPIlmz9AMKb6gWQFOcHaORHzPt+gC6nPMY12gggr7eyIq6PMNZ/W4Fxc/o4hO3IW9H6UlKF9d+0gNKzUWoqlhlCjgC87QtHr16lCr46pxp149UcpDrNEVBTjqyVRjVkFKrBE01aKod0yjJ7q/GuZqTCnYjJfP71M3NNKhxyoVQnnzCnS1LdpH8XrGsyWYJhgtuH8T3U8NxODnEla8xmP09kS/RnBmm2DaXKLgtSioUyRRoynYkaD6A43kRRcEB8Vq0GZi/ym48dI5b2X6fKDOG53jEh132l9FcWxqhEa1TbopONSIqUY+FBwoLcrXi+mz1LlAtQPBwm2fXqnvfbLnLY2+q5NFo3iFUfG1pgEXnbOSnZUveP0S1RP5zoREnXTZ5o8lbUeiCQg0qqM6HM00GTyOM/XdQGYReKDUr1yuE5J6o5I9kQcvQtGCsyilwk9VK+qF9z3YheUSp5P+5HvY1eMXb1aSouBrELQdhc1OE5yRJ17tQmHD9sGgJOyUk7pA+Wk4o9OsgtRzqYkD1COohlF040a59OrpVHG10hs0eqGbKPjV6JoCllh5zkqJ0N/U26u6It2UuqHGjRrGKuxUj3G8nudMSrTPg42+RPfLxOdS2GsEXyf6NYKjX4V978LOFJTMyuU6F+hY0eernHIFExr5UK1QrAa0zhWqJSusbsJTOkk29l/w+5jOeauozwd+nxbFsRm97Ro586NnCn6U6qcidwUgagArrUeLRmby+pKI9mEqoyPxjim/ncW92KU/JpL5vvptVZqnvlOxvmthvxvILAIPlImVy1ORaKrP4AlH84PHSsGJJV4ebaKeurKmNL3XYE+gRsh0K4wajn6msyCtaKwAQbPEqEhTQYp6zFRorSJmFTxrNWMV/wepoarUDU0PrLx9BUPq4VPDQQ1W3ZSjrTzn4Po0KPkrl+vzUkCrGYt0XKgHXCNbsaahVcDhgw6NxipFS49XCqlSZfz5ShMQaJSuKNLyMvFdLk3ng0xQoKUAUj917RAVbgcDD399UcpPcIKGwiQ7C1Tw+qVOE9WclAW5diyVdQQeQIAWEvR0wQ8T4ARHVApbtCp6iDsVvmBZPW0qwCuuUQ9fG6Aef/X0JerlDBZVF0XRdCzaV5rdJlUKPDTDSqyLoFK1dJHXTRd/pV9ovQT1dmu/KGVP6T+xZu7RrDt+Bjb12isQUbChPGvtL6V1KEUjuF99z1xhi7kl21NaFgRHPAvrWQ7b85wKfUYaCVNAqc9Rx4BS86KPe18Mq8JZzdoTr1c2nXqmVPdfOuet0nY+yDSNgmrmNHUgRC/WqOuLapGUWpZO51mia4LOTwpOdQv7GtpOjdJFr99R1HRMqPYomcUf/bbq+kugUrJRXA4EqNfS57Qmmp0kEV1o/Sw1Pqc3HuUGh6VpEUUXGD87UyoydXLWVLS+EVzY+/WLHKpoMVFOdjYpIPA5vGog+Dnn4938tIqa5SWZVa4VsGpaT83CovnyvWQWi/QryivI0doFonn3oz9fXwNSWGM0etHCskzrFETXP8VT2HGaKTqX+B5vNcQ1c1g0X9CtouR4QYe+44W9p3QFG6mFnZcS/b20nQ8yTaPfvlMo+hzr6wv1WWajU0ATP/j9r3NG2NExXyOlehEdt8V9bdGECvEmHxBNT+zrUrIR0CGzCDyAqEaj8vJFRZ5+TvtU+dlalOudaPrGVKdKjJ5y0Z/gg/PtJyvYExm9OnsqggtpRU/LGKRaCD/jiObgjzWlYVGmWSklQo1CrSmQ6KbgxE/7mWyxpqfZa/zMMqkuWhecVz/6sZrNxzdg4jUu1Euo1K9cUb9+/UjjVSNa8Rp26oX301AXBaXh+el7FchG1zL4nPxEDVFNE66e32zSNvri22BwHmvEMFEQXdrOB8lIpQGvFEvfQx+9mrefClw1FX7q50zzo6qqYSts6uV4/DVQ1wU/xXLYa0uigKEw/ljSMefXTIpFx6MPkMIu7IiiQ+ABRFF+rhqautio+DfR1Hq6j/L0o6e4VG+1Dwouv/zymLPUjB8/3qVWhKVRFT/Xu2aGSTQDly4g0cPVwcLBn376KfR2aOYa9fD7hnms96SLj/LbfSNLK+kWh+CohQK3ZBo76r3UbFO+QebnlReNTGjWmXg0auYblMFGiHrnCuvB1iq7XnQDxq/9ocaotiHW/tYUy36WnVzhR4l0rMeqxxEtMqZRpKKiY8zXEOk8oFqPIL82gVLrYhVY67up4Lco+KlTNXOW1m+IRemGiVJfStP5IFmanUrHVmEdUQoolG7pA5XoNUw0RbefcVGTVmg2u0Q04uCnd0+WFiz1o/ZayLGwbVYHm9IBg1QfokBedF0Jnoui6ViJLk7P1LVFaWs+hVgjyLGm6dbv/MrmGjFMZbFFFA9qPIAYw7uamUQFwTppqtGp9Ta0iJJOqGrEK09Xxb/qWVXPkhp/wXUMNKSulV9VXKygRL0wuiDp9+qZ0eOU/6/Zi9JJ+9BCYVqsS/m4KlbU+iE6WSvtRMGTfq8hdxW4qsGgv3m6AOriovtobnoVMDZt2jRSzKrpG5OdUUkpJJprXw0K5bFr1jH17ukCqIJpPb+f5lCzNcVbpTjbVJzr6yJ80JYMzVyjfateYH12frE8XeR10dN71ZTGakSqt08jFLqg+xWy9Vn4hfh8g0INL6XLqXdRqQ0qNte2KThSUOp7K3Uf35ALNgzUINAMLmpc6DjVvP367HS8DR8+3KXwaJ0ZHae5Qg1YzSqmY03fL3031Xmg41zfWa2zoEJv7U+f5lMU+eBqtGohUdWWaAV4rULua8F0LPlgSJ+hzhNKF1HQ+NFHH7nRTJ1zdIxkO91K31uNwiow1miFzg36nWqY9G/tUzWWCztvlZbzQbL0vVSvum76bDRFsgIsjRIpsFTjW+dhHV8a8RBNpx09aYXSsHQfvV99vpq8ROch3TSKqWNRQZ0+ZwWiOkZ1rCRa1yjW5Cs6ZlQbpvOQtlUTHaijRed81aCpw0Kfn0bS9HlosUjfuSJ6T1rgUOc9baemg9ZNaaB6Dl+/ohErnQ91rgt2jgSnd9fkG1ohXec3/13Tvkm04Gqw1uT222935zjVcOg6qn9rhEx0bVMdlZ9iWsFcthbKReYQeABxGjDqaVHwocamGnK6xSsijbVQk4IXneDVS66Uq+iLkE7UGm73tRph6CKjHjEFFGrMqoc9ldoUjcbooqBeIzUQgrToWTBQSURB17hx41zjWnUHalzpFk0X2Hj7sSj4VCl9tqmsGq+eS6Vl6aKt5/CBh6ihMHLkSHeLRb1waojFWltCvZGJeiTVyNGMR9GNY12QtZKyGtVq3KnhEFxpWhd1BSZq6OZS4KGGnYJLHWcKxjQSqFuQOhA0GuTX1ihsytdM0PlBDUj12qrjQY06P4qh4FUNOPUqxzpP6PjRd0YBU7YDDx03fv/NnTvXbVf0gmzaf3ovWrSttJ8PkqXaK50zNNrpF3RMRAG/grRYHTcKWHTO1r5RYOwDmnjCTKetIE/7XzOhKfhQEJko7S3Wa2hUVR1WGgXTc+j5dEuGOmC0yKQWXtVxHT1iouM4ehQ3UdCu78zNN9/sAowbbrhhi/uow0UjnOrsQ8lH4AHEoUa3eqMVHOjEqUJdXUTVuFGvikYV2rdv7y6esRagU6GfGo26kKtROmvWLNdTpB4jNWTVwAiz+F009R4pl18XCZ3o1ZBVg1MBkXrkFNiohy1WD796IjWyoe1T4BJ2Hnhfk6CiUzUklF6hHjH1lik40vSgGjVS71txUQNcDTtR0FHYnO5B2kda5VdpWrqpV1Ofo4I8pWHop1LyNNuPRiHU0FQqnGp9dOGOXtBSjV6NnqlRp32m3m4FMErbUmqXRsbUu6gAJ95K4fq7GtVDhw51PY767LSv1Ruo0RT16qcyZWdZoX2t1BEFZqrlUACi76wWg1Sqi4I1v7qzFNUCafquKQDV56QeaU1aoEkC9PmqQadceo2caj0Xperou6vjR4GJtl2BR1HQ62qkRR0PyquPtf+0AF5pPx+kQguC6tyh86yOLZ1j9X7UENb5Up+jrgE612qU4Mgjj0w4kqYRI42Q6NqgY1EjTH6mNX3/Vauk11QAEbZjStugBr6uQdr/GtnQ9uq6oM9A9TwKLnQe0Uh3vM9Q71XXQI3A6NjU+U3Buq47GtlQgBEriFBwrfep76CCWHXgFTYLXzyaplgjNgpedWxq9NIfq7oGq6PQF6Kj5Cu3fPny7E8KDgBACXH33Xe7FA718Cu1rShGPQAAFJcDAHKIRhM0MuhTggg6AKDoEHgAAMoM5c0nShfUSIfP0VfqEACg6FDjAQAoM5Q3r5mDtAaL8uSVB65ARDVamhjAT6esmgU//S4AoGgQeAAAyhTVbaiQO9ZK4aLiXRV0k2YFAEWLwAMAUGZoWmhNfaqZ6DTzkGYL0gJnmkFONR2aUU4zKpXklbIBoKxiVisAAAAAWUdxOQAAAICsI/AAAAAAUHIDD+XNahVPvxJwkFa51IqYTZo0sU6dOrlVKwEAAADkrtCBx/Dhw+3UU0+1adOmFfj9yJEj7YorrnDzpP/555/2zjvvWMeOHW3ZsmWZ2F4g49avX++KUPUTyBaOMxQVjjUUBY4zFGngobnQy5cv74KKoHvvvdf9vOSSS2z06NF24IEH2u+//27Dhg0L+1JA1v3999/FvQnIARxnKCocaygKHGcossBjwYIFtsMOO1j16tUjv/vmm2/c7/fff3+75ZZb7IQTTnBpVwpQ3nzzzbAvBQAAACBXAw+lTtWtW7fA76ZMmeJ+Hn/88ZHfKThRrce8efPS2U4AAAAAuRh45OXl2erVqwv8burUqVauXDk74IADCvy+Zs2a9tdff4XfSgAAAAC5GXg0atTIFRWpgFzy8/PdSrFVq1a1vffeu8B9ly5darVr105/awEAAADkVuDRoUMHF2x0797dXn/9dVdMrvSrI444wipUqBC534oVK1yaVf369TO1zQAAAABKmf9FCCnq27evTZgwwd5//3374IMPbPPmzValShXr379/gfu98cYb7m+a3QoAAABAbgodeGy//fYuteqBBx5wiwg2bNjQevXqZc2aNStwv88++8z22GMPO+aYYzKxvQAAAAByKfCQevXq2aBBgxLeZ+jQoem8BAAAAIBcrvEAAAAAgGQReAAAAAAoGalWffr0SfuFtL7HQw89lPbzAAAAACijgcezzz7rAgfNThUWgQcAIJZVVtlW5oe7vtSsWM5q2IaMbxMAoJgCj+gpcgEAyBQFHS1H/xTqsbO6NrYaFTO+SQCA4go8BgwYkI3XBgAAAJAjKC4HAAAAkHUEHgAAAABKfuDx448/2lVXXWVt27a1+vXrW+3atQv8/emnn7bBgwfb6tWr030pAAAAALm4cvmLL77optpdv359ZMYrzV4VtHz5chd4NGvWzE455ZT0thYAAABAbo14zJw503r27GkbNmywHj162KRJk6x169Zb3O+kk05yQclrr72W7rYCAFBA5Qp5tjC/UuibpvIFAJTwEY8HHnjANm7caHfccYf16tXL/a5KlSpb3G/nnXe27bbbzr744ov0thQAgChr8jdbqzHhpuIVpuMFgFIw4jF58mSrXr16JOhIRLUfv/32W9iXAgAAAJCrgceSJUusSZMmSd23fPnybnQEAAAAQG4KHXjUqFHD/vjjj6Tuu2DBgi1muwIAAACQO0IHHi1btrRff/3Vvvvuu4T3mzJligtQ2rRpE/alAAAAAORq4NG5c2c3W9Xll19uq1atipuO1bdvXzfFru4PAAAAIDeFntXqnHPOsTFjxtinn35qBx98sJ1++umR1Ktnn33WZs2aZc8995wtW7bMDj/8cDetLgAAAIDcFDrwyMvLs7Fjx7o1PN555x0bOnRo5G8XX3yx+6kRkQ4dOtiTTz6Zma0FAAAAkHsrl9eqVcvGjx9vH374oU2YMMEtKqiVyrfaaitr0aKFnXrqqXbMMcdkbmsBAAAA5F7g4R166KHuBgAAAAAZLS4HAAAAgGQReAAAAAAo2alWmzZtcjNXvfHGG/bjjz/a6tWrXUF5LJpSd/r06em8HAAAAIBcCzy0dscZZ5xh06ZNixtsRAceAACUJJUr5NnC/EqhHluzYjmrYRsyvk0AUFaFDjwGDx5sU6dOtWrVqlnXrl2tbdu2VqdOHTfNLgAApcGa/M3WasxPoR47q2tjq1Ex45sEAGVW6MBj4sSJkbU82rdvn9mtAgAAAFCmhB6eWLx4sTVs2JCgAwAAAED2Ao/atWvbNttsE/bhAAAAAHJI6MCjQ4cONnv2bFdkDgAAAABZCTwGDBhglStXtv79+9vff/8d9mkAAAAA5IDQxeU///yzXXPNNXb99dfbV199Zeedd57tuuuubpareNq1axf25QAAAADkYuBx4oknRtbmUMrVwIEDE95f9126dGnYlwMAAACQi4FHgwYNWBQQAAAAQHYDj2+++SbsQwEAAADkGJYZBwAAAJB1BB4AAAAAso7AAwAAAEDJrfHwvvjiCxs7dqx9/fXXtmzZMsvPz495PxWiT58+Pd2XAwCUMKussq3M3xz68ZuMiUoAIBekFXjceuutdt9999nmzYVfcJgBCwDKJgUdLUf/FPrxM7o0yej2AADKWKrVG2+8Yffee69tt912dv/991vz5s1dcPHyyy/byJEjrU+fPrbNNttY1apV7Z577rGJEydmdssBAAAAlP3A46mnnnKBxmOPPeZWLd96663d79u3b28nn3yy3XbbbTZ16lQXkOjfO+20Uya3GwAAAEAuBB5fffWVG+049NBD495Hf3/iiSds5cqVdvfdd4d9KZfKpRETrZberFkz23HHHW3fffe1vn372rx585J+nk2bNtmjjz5qBx10kNWtW9d22WUX6969e8zn+Pvvv23IkCHWqlUra9SokZ1yyiluhfZYNMKjbfrpp/CpBgAAAEBZFjrwWL58udWvXz/y/woV/lsusmbNmgL323nnnW333Xe3999/P/RGXnfddW5U5fvvv7cTTjjBLrzwQjeCMmrUKDvkkEPs22+/Tep5FKj079/fBTI9e/a0I444wl555RU7/PDD7Ycffihw32HDhrkaFgU6Xbp0cQsmnnbaabZ69eoC9/vtt9/shhtusAEDBljjxo1Dv0cAAACgLAtdXL7tttvahg0bIv9XPYf8/PPP1qJFiy1GGn7//fdQr7N48WJ75JFHrGHDhjZ58uRISpc8/PDDNnDgQPdTt0Q++ugje/rpp91ox0svvWSVKlVyv+/UqZO7XXXVVTZhwoTI/RXUHHbYYTZu3Dj3/44dO9rxxx9vb775pp1++umR+1155ZUuuFJNCwAAAIAMj3hotENBgdeyZUv3c9KkSQXup5EEjVQEA4ZUzJ8/3wUuBxxwwBbPceyxx7qfS5YsKfR5FHSIAhUfdMhRRx1lBx98sL333nu2YMGCyO8XLlxorVu3jvx/7733dj9/+eWXyO+U/vX666/bAw88EBnxAQDkhsoV8mxhfqVQN01BDAC5JnRrWSMHqvPQCIfSnlQDMXjwYLvrrrts7dq1duCBB7rARHUSqpdQOlMYqsNQoDBlyhRXK1KzZs0CM2tJojoTT6MlW221lQtgoinlSn//5JNP7KyzzooEVlqbxJsxY4b72aBBA/dzxYoVdvXVV1vv3r0LBCipWL9+fajHIbP++uuvAj+BbCjLx9nmvHQ7XjYX02PTe/ya/E3Waky42r6ZXXayipuycw0oy8caSg6OM3hVqlSxZIW+Wijt6Nlnn3UpTOeee66rhbj00kvd1LoaAdBNVE+hQu7rr78+dErXjTfe6Oo82rZt6163Ro0aNnPmTPfaF1xwgav5SER1J6rFUApY+fLlt/h7kyb/nUM+WOehmhLVbpx55pku+FHKlQrIjznmGPd3/U07+tprr7WwFi1a5IIylAzBETwgW8ricVaxXtO0Hp/EUlBZeWxxvvbG/I22YNH/RtmzoSweayh5OM5yW/ny5SPt6KwGHhrRiC7Ivummm2zPPfd0K5lrJERreLRr184uu+wyF3yEpfqJevXqucDmySefLLANZ5xxRqFpThopkeBoSZD/vb+ff03VsDzzzDP22WefuVQrjehUr17djY4odevFF1+0ihUruvStMWPG2Lp169zoiYKvOnXqFPq+9J5Q/NRboxPnDjvsUCAND8iksnycLUlzxCOd9WXTXZu2uF67QsUKVrdhQ8uGsnysoeTgOEMYGS9MUOF1sPg6E9Tg1yKEGl3o3Lmzq/XQLFP6v6bYVRCgkZBMR3AqONctOj1Ks2MpJUvF51pE8fHHH7c77rjDBRK6v9Kvxo8fn9GhKWSfTpx8Jsi2sniclcvPS/cZiumxxffa5crlZf04KIvHGkoejjOkIqWrhYq8NcOUGtyqddBN9RXDhw93f8uGDz74wO68807r0aOH9evXz9VeaNRBox3PPfecG3FQGlYisUY0UhkRCVINi+o7FGiI3ruCEK0Hctxxx7kUrLffftvmzp0b4t0CAAAAZVNKIx6qe3jttddc3YanAmyNPqgwW2lJmaZGvGi9jmga3mvatKnbBq2voYAkFhWVK9VL6V+qqYiu8/jxxx/dT9VyJKK6EtWuaBFCTR+sAETTBCu9zNtrr73czzlz5rhtAwAAAJDCiMe//vUve/XVV13QceSRR9ott9zibvq3fqe/BdfByBQ/W0K8KXOXLl1qeXl5buQjEdWaqMhcs2NFe/fddyMzdcWjgEU1JqrhiE4lC65n4v9dLt3EYwAAACAXA4/nn3/eNaa18rfqFy655BJ3079V16DgQ6lPmeanv9VK4hphCFKhudbb0GxXlStXjgQiGm3Qz6Bu3bq5n7fffnuBqd80oqJi8Q4dOlijRo3ibodSzPS8mh7YU62JRlL8qIx/PtEsXwAAAABSTLVSOpNSlq644oot/qbAQw3z4LoXmaL1QZ544gn79NNPbd9993V1FGrwa10NTaermbMUTHgjRoxwxegKkK655prI79u3b+9SxVSIrrqUo48+2k2xq5mplDal2o14lKKlOhPVb/h1PLxevXq52bxU9K7i8tGjR7spdwtL2wIAAABySdKBx7Jly6x58+YxU5r0u8aNG9vs2bMzvX2uHkPBgUY89POFF15wIxbbb7+9a+wrEEp2dGHo0KFuLY9Ro0a5onAFUpoVS2uMaPvjUVG7HqcC92ga9dG+0XS6H3/8sQuM9DoAAAAAQgQe+fn5Vq1atbh/VyN+48aNlg1Ko1LjX7fCaJQjONIRpFoQjVDolopEtSsKjHy9CwAAAIDY0p18HQAAAAAyO52u1rvQtLmx+MJv1WIEp9uNnlkKAAAAQO5JKfD4z3/+Yx07dkx4H9VMxKIZsaJnmgIAAACQG1IKPOKNZGT7sQAAAAByJPD4888/s7slAIBis8oq28r8cB1Em4wFUwEAGR7xAACUTQo6Wo7+KdRjZ3RpkvHtAQCUPcxqBQAAACDrCDwAAAAAZB2BBwAAAICsI/AAAAAAkHUEHgAAAACyjsADAAAAQNYReAAAAADIOgIPAAAAAFlH4AEAAACgZKxc/sknn2Tkxdq1a5eR5wEAAABQBgOPE0880cqVK5fWC+nxS5cuTes5AAAAAJThwKNBgwZxA49ff/3VNm7c+N8nq1DBtt12W1u2bFnkdxUrVrS6detmcpsBAAAAlMUaj2+++ca+/vrrLW4aCdm8ebN169bNpkyZYosXL7bvvvvO/dT/9ftNmzZZx44d3f0BAAAA5KakRjxiGT16tA0fPtyGDh1q5513XoG/5eXlWbNmzdzf2rRpY3379rUWLVpYly5dMrHNAAAAAHJlVqsnn3zSpVBFBx3R9HfdT/cHAAAAkJtCBx5z5861HXfcMan76n5z5swJ+1IAAAAAcjXwUDrVDz/8YPn5+Qnvp7/rfunOigUAAAAgBwMP1W6sXLnSbrzxxoT3u+mmm2zFihW27777hn0pAAAAALlaXH755Zfbhx9+6ArMP/vsM+vRo4c1b97c6tSpY3/88YfNnj3bRowYYTNmzHCjI/369cvslgMAAAAo+4HHIYcc4matuuqqq2z69Ol28cUXb3EfTbWrdTzuuusud38AAAAAuSl0qpWfserjjz920+Ruv/32LtDwN/1fv//oo4/s/PPPz9wWAwAAAMidEQ9vt912s4ceesj9WzUfq1evturVq1vNmjUzsX0AAAAAyoC0A48gBRsEHAAAAACyEnhs3LjR1XksXLjQ1q5da2effXYmnhYAAABAGZFW4KFajiFDhtjDDz/spsz1goHHpZde6ma/eumll6xx48bpbS0AAACA3CouV9Ch4vI77rjDBR0NGzZ0tR3RjjjiCJs/f75NmjQp3W0FAAAAkGuBx9ixY10woVGM999/363X0bJlyy3ud+SRR7p1PN5+++10txUAAABArgUeo0ePtnLlytkTTzxhrVq1inu/rbbaynbaaSebM2dO2JcCAAAAkKuBx6xZs6xevXrWunXrQu9bu3ZtW7ZsWdiXAgAAAJCrgceGDRts2223Teq+69evt8qVK4d9KQAAAAC5GnhoZfJ58+YlFXR8//331qBBg7AvBQAAACBXA4+DDjrIrVI+bty4hPd76qmnXPBxyCGHhH0pAAAAALkaeFx00UXuZ//+/e21116LeZ+nn37abr75ZqtYsaJdeOGF4bcSAAAAQG4uIKiZrG666Sa78cYbrWvXrrbDDjvYunXr3N9OPPFEmz17tiso13ofgwYNsl133TWT2w0AAAAgF0Y8/Krkmk63fv369ttvv7mFBBVofPLJJ7Z06VKrW7euPfbYY9azZ8/MbTEAAACA3Bnx8E477TQ7+eST7fPPP7eZM2fa8uXL3dodLVq0sAMPPNClWQEAAADIbWkHHlK+fHnbf//93Q0AAAAAMhZ4dOzY0Vq2bOnqNwpzzTXXuAUHJ06cGPblAAAoMypXyLOF+ZVCP75mxXJWwzZkdJsAoMQGHpMnT7aNGzcmdd9vvvnGPv3007AvBQAoxCqrbCvzN4d+/CYrl9HtQWJr8jdbqzE/hX78rK6NrQaZzAByMdWqMH///bfl5aVVxw4ASEBBR8vR4RuyM7o0yej2AAAQLevRgGa5mj9/vtWoUSPbLwUAAACgtI94aMYqpUwFLVmyxMaOHRv3MVrX4+OPP7Zff/3VDj744PS2FAAAAEDZDzwmTZpkd911V4Hf/fDDD9anT59CRzyUZlXY/QAAAACUXUkHHo0aNbKDDjoo8n8tEqj0qT333DPm/cuVK2fVqlWzxo0bW+fOna1NmzaZ2WIAAAAAZTfwOOecc9zN22abbdwigRoJAQAAAICsFJe/8sorNnjw4LAPD/2ap5xyihtF2WGHHWyvvfay7t272y+//JLU4zdt2mSPPvqoG7mpW7eu7bLLLu7x8+bNizkT15AhQ6xVq1ZutEevO3v27JjPO3LkSNtxxx3tp5/CzygDAAAAlGWhp9MtymJx1Yn069fPNfAVdJx++ulWvXp1V7SulK8FCxZYgwYNCn2evn372tNPP23Nmze3nj17use/9NJL9t5779k777zjAhFv2LBhduutt9rRRx/tfj9u3Dg77bTTbOrUqe61vd9++81uuOEGGzBggNs2AAAAAMW0jke6hg8f7oKOCy64wI2ylC9fvsDfk1nI8KOPPnJBh0Y7FGxUqvTfFWM7derkbldddZVNmDAhcv9Ro0bZYYcd5gIOv1L78ccfb2+++aYLfLwrr7zSdt55Z4rnAQAAgGwGHi+++KKbUvfrr7+2ZcuWxQ0CVGy+dOnSlJ9fU/Iq2FDjftCgQVsEHVKhQuFvQ0GHDBw4MBJ0yFFHHeVGbzTqoZGThg0but8vXLjQTjzxxMj99t57b/czmNY1ceJEe/311+3dd99NahsAAACAXJVWa/nCCy+0F154waVCFSaZ+8SigGD58uXWpUsXV3fx2muvuWl8t956azci0aRJcqvtTp482bbaais74IADtvjbEUcc4f6utK2zzjrL/a5+/foumPJmzJjhfvqUrhUrVtjVV19tvXv3ttatW4d6b+vXrw/1OGTWX3/9VeAnUBqPs8156XZ+bC6mx+bqa6e33Zs3b4p7DeGchqLAcQavSpUqlqzQV6rnnnvOxo8fb7vuuqvdc889dvPNN9v06dPtyy+/tD///NOmTZtmI0aMsEWLFrn1P9q3bx/qdfScopGOdu3a2ffffx/5m9YHUcP/tttuS/gca9ascbUYmoUr1oiJD14U0HjnnXeeq90488wzIzUeKiA/5phj3N/1N+3oa6+91sLSvlEwhZJh8eLFxb0JyAHZOs4q1mua1uND9g2l/dhcfe10t3tj/kZbsGhBwvtwTkNR4DjLbeXLl096ECCtwOPZZ5916VOPPfaY6/GvXLmy+71SonRTalK3bt1cA171Exq5CEOro8vDDz/sZpjS8+y2225uNELF4g899JAr6tbsVPGsXLnS/axZs2bMv/vf+/uJajY2bNhgzzzzjH322Wfu/SjlS4XlGh1R6pbSzCpWrOjSt8aMGePSwjR6cv/991udOnUKfW/16tVLeX8g89RboxOnZkoLpuEBpek4W5LmiEe5csXz2Fx97XS3u0LFClb3/1ODo3FOQ1HgOEMYoa9UM2fOdCMA0WlGSqlSQCIKRhQYtGzZ0k1N+/jjj6f8OpoCV3RQq3Gv1xQViavgXPUZeo1EgUfYCE4Bk25BGtpWwKOULKV63Xvvve593XHHHS6Q0P01CqPRoEwOTSH7dIzxmaC0Hmfl8vPSfYZiemyuvnZ6212uXF6hxxHnNBQFjjMUSeCxevXqAtPH+mh31apVBUYW1POv6WtVPxGGfy4FOD7o8JQ6pdGVH3/80dWB1KpVK+kRjVRGRIKUNqb6DgUafsYtBSE+8NH7V+3L3LlzrWnT9FIfAACIpXKFPFuYXyluvY9S7zQKFisgrVmxnNWwDUWwlQCQocBDAYVqJ7zatWu7nwoCokdB1q5d62a8CsM33lVMHov/faJCbRWVa8HAn3/+2dVURNd5aJsluI5HvFGeBx54wC1CqJXbFYD8/vvvtueee0buo0UNZc6cOQQeAICsWJO/2VqNCbdo7ayuja1GxYxvEgAUKvTYvKadVcG2p/oLpVlpat2gr776yhVtb7fddqFe55BDDok05KPl5+e7oEGBRWHPr8J0BUpTpkzZ4m+aDtenb8WjgOXSSy91NRzBdTxEtSDR//bpZgAAAADSCDwUEChFafbs2e7/WtVb6VYqNv/nP//pfmq2qVNPPdX9XYvvhaF0rg4dOrgAw6/F4d13331u1OGEE06IrKOhtUIUpESvGaJCd7n99tsLTP329ttvu2JxvUajRo3ibscjjzzinle1KsHRFo2k6DmCzyfNmjUL9X4BAACAsih0qpVW8n7nnXds1qxZtvvuu7sREE2pe80117jZnrQ6uGgURI1wzfwUlhr7Rx99tBtxePXVV10Kk2a10mrket1bb701cl9N4avZp/r37++2xdN0vpphS8HLoYce6p5PIzbaVqVNqXYjHqVo3XnnnW4KXb+Oh9erVy+76aabrHPnzq64fPTo0W7K3cLStgAAAIBcEjrwUC3D+++/v0UjfJ999nHpVmqsV61a1aU4abShWrVqoTdSox56LRV0Ky1KU+pq+rYePXq4RfySmbpWhg4d6grSR40a5YrClaKl1cmvv/76AoXy0fr16+cep9eLdskll7j6Fc249fHHH9txxx3nXgcAAADA/6S71O0W9ttvP3fLNI00DBs2rND7aZQjONIRpAUHFRzplooJEybE/ZsK1W+55RZ3AwAAABBbuhO/AwAAAEChCDwAAAAAlIxUqz59+qT9QppeViuMAwAAAMg9SQUezz77rAscNENVWAQeAAAAQO5KKvDQ1LQAAAAAkNXAY8CAAaFfAAAAAAAoLgcAAACQdQQeAAAAAEruAoILFixI+TENGzYM+3IAAAAAcjHwaNWqVcqzWi1dujTsywEAAADIxcAj1al105mKFwAAAECO1nj8+eefcW8LFy60Dz/80M4991yrUqWKDRs2zP0eAAAAQG4KPeKRSLVq1WyvvfayBx54wFq2bGmXXHKJ7bzzznbggQdm4+UAAAAA5PqsVj169LCaNWvafffdl+2XAgAAAJCrgUdeXp4b7Zg2bVq2XwoAAABALq/joal3169fXxQvBQAAACAXA48HH3zQlixZYrvuumu2XwoAAABAWSsuHzx4cMKpc//44w+XXjVz5ky3hsf5558f9qUAAAAA5GrgMWjQIBdQFLZuh+7Tu3dv6969e9iXAgAAAJCrgcdZZ50VN/DQ7zWl7i677GLHHnusKy4HAAAAkLtCBx6PPPJIZrcEAAAAQJlVJLNaAQAAAMhtBB4AAAAASm6qVdCsWbPsxx9/tDVr1kSKymM5++yzM/FyAAAAAHIp8Hj55Zftuuuus4ULFyZ1fwIPAIhvlVW2lfnxO28S2WTxZxkEAKBUBx6vvPKK/fOf/7RNmzZZ5cqVbaeddrLtttsu4RS7AID4FHS0HP1TqMfO6NIk49sDAECJCDyGDBni0qo0inH77bfbNttsk9ENAwAAAFB2hA48vvvuO6tVq5Y99NBDlpdHjToAAACALAQeNWrUsAYNGhB0AAAAAChU6Kihbdu2Nm/ePFfjAQAAAABZCTyuvPJKW7t2rd13331hnwIAAABAjgidatW6dWt74oknrE+fPjZt2jTr1q2bNWnSxKpVqxb3MQ0bNgz7cgAAAABydR2PFi1auADkrbfecrdENM3u0qVL03k5AAAAALk4q9Xxxx9vf/75Z8LVyr1k7gMAAACgbAodeNxyyy22bNkya9WqlQ0cONCNfNSpUyezWwcAAAAgtwOPKVOmWNWqVW3ChAm27bbbZnarAAAAAJQpoWe1ys/Pt6ZNmxJ0AAAAAMhe4NGsWTNX3wEAAAAAWQs8LrzwQluwYEGhs1kBAAAAQOjAo1OnTnb55ZfbBRdcYA899JCtWrUqs1sGAAAAoMwIXVyu2axk3bp1dsMNN7hb7dq14y4gqHU8pk+fHn5LAQAAAORe4DF//vwtfrdkyZK491fgAQAAACA3hQ48XnnllcxuCQAAAIAyK3TgcfDBB2d2SwAAAACUWaGLywEAAAAg6yMeAACg9KlcIc8W5lcK/fiaFctZDduQ0W0CkBuSCjzGjh3rftasWdNOOOGEAr9Lxdlnn53yYwAAQOasyd9srcb8FPrxs7o2thoVM7pJAHJEUoFH79693axUTZs2jQQe/nepIPAAAAAAclNSgcdBBx3kgowGDRps8TsAAAAAyEjg8eqrryb1OwAAAACIhVmtAAAAAGRdqQw8hg4darVq1XK3adOmJf24TZs22aOPPurSxOrWrWu77LKLde/e3ebNm7fFff/++28bMmSItWrVyho1amSnnHKKzZ49O+bzjhw50nbccUf76afwxXoAAABAWZbR6XRXrFjhGuEKBvLz813D/txzz7XmzZtn7DW+/fZbu/POO22rrbayNWvWpPTYvn372tNPP+22p2fPnvbrr7/aSy+9ZO+995698847bnu9YcOG2a233mpHH320+/24cePstNNOs6lTp1r16tUj9/vtt9/shhtusAEDBljjxo0z9j4BAACAnAw8pk+fbjfffLNrXN97771b/F2jBh07drSFCxe6/2/evNkVnz/++OP24IMP2plnnpn2xiqYueiii2zPPfe0Jk2auGAgWR999JELOjTaoWCjUqX/zmHeqVMnd7vqqqtswoQJkfuPGjXKDjvssMhr6L0df/zx9uabb9rpp58eud+VV15pO++8s/Xp0yft9wcAAABYrqdavfvuu/bhhx/G7dXXCMIvv/ziAo699trLjQ40bNjQBQsaaZg/f37aG3vPPfe4dKeHHnrIypcvn9JjFXTIwIEDI0GHHHXUUXbwwQe7UY8FCxZEfq8AqnXr1pH/77333u6n3qM3ceJEe/311+2BBx6wChVYixEAAACIJ+nW8pQpUyI9/7H+phQkjXBcf/311q9fP/d7BR1du3a1t99+240g6G9hacRFNRfXXnut7b777ik/fvLkyS4964ADDtjib0cccYT7+yeffGJnnXWW+139+vXt66+/jtxnxowZ7qefUlhpZVdffbVbzyQYoKRi/fr1oR6HzPrrr78K/ASK6zjbnJdOB8bmNB6b7uN57aJ9bPG+9ubNm7h+gWsnIqpUqWLJSvoqp8LpOnXquLSiaOr1F42GaHTDq1ixot1444321ltvudGSsIHHhg0bIilWl112WcqPVy2IajFatGgRc6REaVvyww8/RH533nnnudoNpYj5Gg8VkB9zzDHu7/qbdrQCobAWLVrkithRMixevLi4NwE5fpxVrNc09PNuTrMdm87jee2ifWxxv/bG/I22YNH/MgSQ27h25rby5ctH2tEZDTyWLFkS94n9aIca5dGLCqqxrxmkfvzxRwvrjjvucEHBBx98kHKKlaxcudL9rFmzZsy/+9/7+4lqNhTwPPPMM/bZZ5+5VKvBgwe7wnKNjih168UXX3TBldK3xowZY+vWrXOjJ/fff78L0gpTr169lN8LMk+9NTpx7rDDDgXS8ICiPs6WpDHike56ruk8ntcu2scW92tXqFjB6jZsmN6ToNTj2okwkr7KrV27NuZwmmo6Zs6c6f69//77x3ysAg9/n1QpqFFxumaNUhBTVBTgqOBctyANL2tURylZKj5Xob0K6BUcKZDQ/ZV+NX78+IwOTSH7dOLkM0G6VlllW5m/ZZfy5iqbrGK9mrayYgUrVy52ed1mS6dFmGZrktcuRY8t3tfW8cu5Eh7XTmQl8Nh6660jxePBUY3//Oc/tnr1ave7eLUOqvXQyECqNm7c6FKsWrZsGakbCSPWiEYqIyJBd911l6vvUKAhw4cPd0GI1gORVatW2YUXXmhz5861pk3Dp00AKJ0UdLQcHW5Nnxldkh+uBgCgzM5qtccee7gGuq/nCM7sJOrt32mnnWI+VjNaaSguVQpolGL1zTffuNQlv2igbmPHjo3MSqX/T5o0Ke7zqKhcoy4///xzzJoKnwYWXMcjFo3aaAarQYMG2TbbbOMCkN9//93Vnnia0UvmzJmT8vsFAAAAyqqkRzxOPvlkV2Nx+eWXu5EIpT2p9kFT22q0Q9PnxjJr1iw3CqD1M1JVuXJltwBhLJ9++qkLSo477jjbbrvt3OriibRr187+9a9/uRm49O/oqYIl0TYqYLn00ktdDUdwHQ9RLUj0v6NrXQAAAIBclnTgoWlxn3zySTf6cP7550d+r9QrjTjEW0BPi/KpEX7ooYemvHFVq1Z19R2xKAVLgYcCof322y/y+6VLl7pb7dq13c3r1q2bCzxuv/32AgsIaqpfFYt36NAhYfDyyCOPuFEMvx6ITz/TSIqew79//VuaNWuW8vsFAAAALNdTrbRAnoIIP52sAg7dNL3uc889FzOVSgXpI0eOdP9Ww74ojBgxwtq2bet+BrVv395NkauREgVBmuZXix526dLFpU2pdiMepWjdeeedbjpgv46H16tXLzcS1LlzZ1d0rjQs7aPC0rYAAACAXJLS3I1KaVKQoboGNcZr1KhR6GJ+qr3QiEdJGAEYOnSoSxHTYoYqClftx4knnugCingrsosK2/W4Hj16bPG3Sy65xJYtW+am0/34449d6pdeBwAAAMD/hJo0fvvtt3e3wlSrVs2aN29u2aDUJ92iXXPNNe4WS15enhuh0C0VGulJNO3uLbfc4m4AAAAA0ky1AgAAAICwCDwAAAAAZB2BBwAAAICsI/AAAAAAkHUEHgAAAACyjsADAAAAQMkIPD755BO3YjkAAAAAZC3w0CJ7/fv3L/C7jh072oABA0K9KAAAAIDckvQCgps3by7w/8mTJ9vGjRuzsU0AAAAAcnHEo0aNGrZo0aLsbw0AAACA3B3x2GOPPWzKlCl29dVX29FHH21Vq1Z1v1+5cqWr/0hWu3btwm8pAAAAgLIdeFx22WUu8Hj88cfdzfvPf/7jaj2SUa5cOVu6dGn4LQUAAABQtgOPY445xl588UV78skn7bvvvrN169bZ/PnzrVKlSrb99ttnfysBAAAA5EZx+aGHHupu3jbbbGN77723vf7669naNgAAAAC5voBggwYNrG7dupndGgAAAAC5PeIRjQUFAQAAAGQ98Ii2cOFCmzt3rq1atcpNv7vbbrtZvXr1MvX0AAAAAHI58Jg4caINHjzYzXAVrWXLlm4K3mRnvgIAAABQNoWu8ZA77rjDzj//fPv222/dyuZ5eXlWp04d91P/nzlzpnXr1s3dDwAAAEDuCh14fPTRR3b33Xe7f3fu3NkmT55sixcvdtPt6qf+f+aZZ7q/33PPPfbxxx9nbqsBAAAA5Eaq1aOPPuoWBbztttusd+/eBf5Wvnx5l2Y1fPhwa9WqlV177bU2YsQIO+SQQzKxzQAAoJhUrpBnC/MrhXpszYrlrIZtyPg2ASjjgcfnn39utWvXtosuuijh/Xr16mX33nuvTZ06NexLAQCAEmJN/mZrNeanUI+d1bWx1aiY8U0CUNZTrf7880/baaed3KhHIvp7o0aN3P0BAAAA5KbQgUetWrVswYIFSd33l19+cfcHAAAAkJtCBx5t2rSxP/74w0aNGpXwfiNHjrTff//d9tlnn7AvBQAAACBXA48LLrjATZl75ZVXurU65s2bV+Dv+v9VV13lbkq30v0BAAAA5KbQxeVHHnmk9ezZ081u9fjjj7tb1apV3ToeGglZt26du5+CExWgH3HEEZncbgAAAAC5soDgoEGD7OGHH3ZF5gow1q5daz///LP7qf83btzYhg0bxgKCAAAAQI4LPeLhnXPOOe42d+5cd1u9erVVr17ddtttN9t1110zs5UAACCn1wAR1gEBcjzw8Jo2bepuAAAAmV4DRFgHBMjhVCsAAAAASAaBBwAAAICsI/AAAAAAkHUEHgAAAABKT3E5AJQFq6yyrczfHPrxm6xcRrcHAICygsADAAIUdLQcHX7WnRldmmR0ewAAKCtItQIAAABQcgOPwYMH25gxY5K679ixY939AQAAAOSm0IHHoEGDbPTo0UndVwEKgQcAAACQu4ok1Wrz5vCFmgAAAABKvyIJPJYsWWLVqlUripcCAAAAUJpntVq5cqWtWLGiwO/++usvW7BgQdzHrFu3zj744AObM2eO7bnnnultKQAAAICyH3gMGzbM7rrrrgK/++qrr6xVq1ZJPf7MM89MfesAAAAA5FbgoTqNYK1GuXLlCq3dUHpV48aN7ayzzrLevXunt6UAAAAAyn7gcc0117ibt80229gBBxxgr7/+era2DQAAAECur1zev39/a9CgQWa3BgAAAECZFDrwGDBgQGa3BAAAAECZVSTT6QIAAADIbaFHPGTTpk323HPP2RtvvGE//vijrV69Om7BuYrRp0+fns7LAQAAAMi1wGPVqlV2xhln2LRp05JamVyBBwAAAIDcFDrwGDx4sE2dOtVNmdu1a1dr27at1alTx/LyyN4CAAAAkKHAY+LEiS7IGDt2rLVv396yZdGiRfbSSy/Z22+/bXPnzrXFixe7qXz3339/u+yyy2zfffdNKTXsscces1GjRrnUsK222soOO+wwu/76623nnXcucN+///7bhg4dak8//bT9+eef1qZNGxs0aJDtvvvuWzzvyJEj3VTDn376qVu3BAAAAEBBoYcnFAA0bNgwq0GHjBgxwq699lqbN2+eHX744XbxxRe79UNee+01O/roo23ChAlJP1ffvn3dNMBKDevZs6cdccQR9sorr7jn/eGHH7ZYqf3WW2+1Zs2aWZcuXeybb76x0047zdWxBP322292ww03uFm+CDoAAACADI941K5d2408ZJtGGiZNmmQHH3xwgd9rdOHkk0+2yy+/3E444QSrXLlywuf56KOP3OjFQQcd5EZQKlWq5H7fqVMnd7vqqqsKBDEaFdFoyLhx49z/O3bsaMcff7y9+eabdvrpp0fud+WVV7rRkj59+mT4nQMAAABlR+gRjw4dOtjs2bNdkXk2nXTSSVsEHaIA4pBDDrHly5fbt99+W+jzKOiQgQMHRoIOOeqoo9zzv/fee7ZgwYLI7xcuXGitW7eO/H/vvfd2P3/55ZcC6WZauf2BBx6wChXSmiAMAAAAKNNCBx5KLdIog1KXVA9RHCpWrOh+li9fvtD7Tp482dV0KE0rmlKu5JNPPon8rn79+vb1119H/j9jxgz306/WvmLFCrv66qutd+/eBQIUAAAAAFsK3U3/888/u4JqFWZ/9dVXdt5559muu+7qZrmKp127dpYpGp344IMPrG7dutayZcuE912zZo2rxWjRokXMIKVJkybuZ7DOQ+9HtRtnnnmm7bLLLi7lascdd7RjjjnG/V1/q1Kliqs/CWv9+vWhH4vM+euvvwr8RG7bnJfu6OXmUvhYXrt0PTZ3X3vz5k1cO0sIrp3w1B5OVugr7IknnhhZm0MpV0phSkT3Xbp0qWVCfn6+Kw7fsGGD3XTTTYWOeKxcudL9rFmzZsy/+9/7+4lqNvT8zzzzjH322Wcu1UpTCFevXt2Nnih168UXX3SjLnrvY8aMsXXr1rnRk/vvv99NLZzMjF3FNVqE2BMmABXrNU3r8Uksa1TiHstrl67H5vJrb8zfaAsW/S8tGsWPa2duK1++fKQDP6uBh1KOimNRQE2Jq/QmFZd369bNzjrrrKztSBWc6xaknhbNjqXXVfH5vffea48//rjdcccdVq9ePXd/bd/48eMLfQ3dH8VPvTU6ce6www4F6n+Qm5akOeKRzmmxuB7La5eux+bya1eoWMHqNmyY3pMgI7h2IozQV1hNL1scQYdGItSo79y5s913331JPS7WiEYqIyJBd911l6vvUKAhw4cPd0FI9+7d3f9VbH/hhRe6NUeaNm2asaEpZJ9OnHwmKJef7iKo5UrhY3nt0vXY3H3tcuXyOE+XMFw7kYpSs8y4H+nQgoVnnHGGPfLII0mvkq6ictWCqC4lVmqTFhMU1XIkMnPmTDeDlRYS1FTCCkB+//1323PPPSP32WuvvdzPOXPmpPgOAQAAgLIrrzQFHc8995xbxO/RRx9Naiar6MJ2FZlPmTJli7+9++67kSl641HAcumll7oajuA6HqJakOh/F0caGgAAAFBmAw8FBS+//LJbyE8zQGndjaDp06e7aWp1v3TSqxR0nHLKKW4l80RBhwrYNdoQXciuehC5/fbbC8zA8Pbbb7tica1L0qhRo7jPqxEWPe+QIUMiv9t6663dSIqeI/h8ohXPAQAAAPxXWlWUms1KDXrVM2z+/6kqonv6n3/+eTdCoRmgDj300JRfQzNJKb1Ks0lput677757i/to5XKf4qTARI/R+iKa7tdr3769myJXs1FpO44++mg3xa62S2lTqt2IRylad955p5tC16/j4fXq1cvNrKWaExWLjx492k25W1jaFgAASE3lCnm2MD9cIXPNiuWshv0vQwFAKQo8lixZYqeeeqprvKvRf/zxx7u1Ln766acC9+vUqZMrwH7ttddCBR7z5893P1evXm333HNPzPtopMIHHokMHTrUreUxatQot02q/dC0wFqLpHHjxnEf169fP/e4Hj16bPG3Sy65xJYtW+am0/3444/tuOOOc68DAAAya03+Zms1pmA7I1mzuja2Gv9ddxhAaQs8tFaFgo6zzz7bHn74YTfSoQX9ogOPNm3auAa+pr8NQylOuiVLoxzBkY4gFaNrhEK3VEyYMCHu35T2dcstt7gbAAAAgAzXeLzxxhtWuXJll9ZUWCH1Tjvt5NKVAAAAAOSm0CMeCxYscHUMNWrUKPS+1apVc6t6A0BRWGWVbWV+uCWSN6W9xgEAAMho4KEFY7SKd7L1IMkszgcAmaCgo+XocHngM7o0yfj2AACANFKtmjRp4kY9VFidyLx589ytefPmYV8KAAAAQK4GHpq9KT8/32677ba499EUuwMHDnQ1IJo9CgAAAEBuCh14aGaoHXfc0UaOHGnnnnuuvffee5FVuzUS8vrrr1vHjh3dNLoqLvcL+AEAAADIPaFrPLRqtxYHPOuss2zSpEn26quvRv7WqlWryIiHgpNnn33WqlatmpktBgAAAJA7Ix6y55572ieffGJXXHGFW4BPgYa/aRXviy++2C2qR30HAAAAkNtCj3h4tWrVsuuuu87d1q5daytWrHALBjKLFQAAAICMBR7R63XoBgAAAAAZSbXSjFbJTKerv+t+GzduDPtSAAAAAHI18Bg9erQrIh8zZkzC++nvut/YsWPDvhQAAACAXA08XnnlFbc+xznnnJPwfpr1SiZOnBj2pQAAAADkauAxZ84cq1u3rtWuXTvh/erUqeOm1P3uu+/CvhQAAACAXA08/vjjDxdQJEMBiu4PAAAAIDeFDjw0Ze7vv/+e1H0VdFSuXDnsSwEAAADI1cBDiwL+8ssv9vXXXye8n/6uWa123333sC8FAAAAIFcDj44dO7oVyvv06RN3St0///zT/V1F6Lo/AAAAgNwUegHB888/35588kmbNWuW7b///tatWzdr27atbb311m718qlTp9rTTz/t0qx222036969e2a3HAAAAEDZDzyqVKli48aNszPPPNPNcHXvvfducR+NiCjFSmt46P4AAAAAclPowEN23nln+/DDD23UqFFuXY9vv/3WVq1aZTVq1LCWLVvaySefbOeeey6F5QAAAECOCx14qGBc6tevbz179nQ3AAAAAMho4LHXXnu5xQFnz54d9ikAIKZVVtlW5m8O/fhNVi6j2wMAAIox8FA6VaNGjSwvL/TEWAAQk4KOlqN/Cv34GV2aZHR7AJR+lSvk2cL8SqEfX7NiOathGzK6TUCuCR14NG3a1BYvXpzZrQEAAMiCNfmbrdWY8B0as7o2thoVM7pJQM4JPVxx9tlnuwUEVVwOAAAAAFkJPLQuhxYF/Mc//mETJkywTZs2hX0qAAAAAGVc6FSrk046ya3TsXLlSrvgggusb9++Lv2qWrVqMe+v1csnTpyYzrYCAAAAyLXAY/LkyQX+r/U7vvzyy7j3V+ABAAAAIDeFDjwefvjhzG4JAAAAgDIrdOBxzjnnZHZLAAAAAJRZLMIBAAAAoOSOeET7/fffbeHChbZ27Vpr165dpp4WAAAAQBmQduAxbtw4u+++++y7776LFJEvXbo08vcbbrjBvvrqKxsxYoTtuOOO6b4cgFJilVV2K5CHscmYjAIAgLImrcCjf//+9thjj7lpdStWrOiCjvz8/AL3ad68uT344IP22muvubU/AOQGBR0tR4dbJXhGlyYZ3x4AAFBKazwUSGgUY7vttrNnnnnGFi1aZG3atNnifscdd5wLSN588810txUAAKBYVK6QZwvzK4W6aQQYQBojHk888YQLKB599FE7/PDD496vVq1a1qBBA5s1a1bYlwIAAChWa/I3W6sx4UZxZ3VtbDUqZnyTgNwZ8VDdxvbbb58w6PB0vyVLloR9KQAAAAC5GnisXr3a6tatm9R9N27caOXLlw/7UgAAAAByNfBQbcf8+fMLvd/ff/9tP/zwAzNaAQAAADksdOCx33772fLly+3tt99OeL/x48e70ZGDDjoo7EsBAAAAyNXAQ1Pjahrdfv362YwZM2Le58MPP3RT7qoInal0AQAAgNwVelar9u3bW48ePdw6HkceeaTtvffeNm/ePPe33r17u1msvvnmGxecXHbZZda6detMbjcAAACAXFlA8K677rL69evbPffcY9OmTYv8fuzYse5n1apV7corr7TLL788/S0FAAAAkJuBh2g0o1u3bq7WY+bMma7uY6uttrIWLVrYscce64rQAQAAAOS2UIHHihUr7Kef/ruITuPGjd0igZ06dXI3AAAAbLnqeRg1K5azGrYh49sElPjAY/HixS5t6s0337RNmza53+Xl5bmRjSFDhtgOO+yQre0EAAAolVj1HEgx8Fi7dq2dcMIJ9uOPP7qC8eA6Ha+99prNmTPHzWKlug4AAAAU72iJMGKCUhl4PP74424hQNVvXHXVVXbooYe6AETBhorLv//+e3efSy65JLtbDKBIrLLKtjL/f50Mqdpk5TK6PQCQi9IZLRFGTFAqA49XX33VrcfxyCOPWMeOHSO/1zS6qvM4//zz3X0IPICyQUFHy9HhL3YzujTJ6PYAAIAcWUBQqVS1a9cuEHR4J598svvbd999l+ntAwAAAJBLgcfKlStt5513jvt3/W3VqlWWLV9++aWbNatRo0ZWr149t2jhiy++mNJzbNiwwQYPHmxt2rRxhfC77767mw74jz/+2OK+69evt2uvvdZatmzpRnS6du1qCxcujPm8t9xyi+22225uKmEAAAAAaaRaaRarChXi371ixYqRma4y7aOPPrLTTz/dqlSpYqeddppVr17dJk6caP/4xz/sl19+SSq9S9t2zjnn2Lvvvmv77befnXTSSa5m5emnn3Z1Ku+8806BNUeuv/56V7Ny6qmnutGcMWPG2Nlnn23vv/++lS9fPnI/rV3ywAMPuBXcNa0wAAAAgCwsIJhtGzdudKMSmrZXNSR77bWX+/3VV19tRxxxhN16660u1UsjIYk8++yzLug444wzXJCgehV58skn3RTBt912mw0dOjQSpDzzzDN27rnnuqBC9tlnH+vVq5cbeVHg4mf0uvTSS93oiwIUAACAkoQ1RFBqAw+NLihVKZYFCxa4n/H+Lv379w812qHFCrt06RIJOmTrrbd2AUPv3r1t7NixhT63RjbkhhtuiAQdolETBRfjx4+3O++8000HvHTpUpdq1bp16wJF9H4f+MBDhfZz5851QQpKt+AoVkmz2irZqpCzS1WrmGdr88OPRNaunHQ25hbybHPox6fz2Fx97dK63bn62qV1u3nt0nesrMvfZIe98HOox07u1CjhjFgl+dqJkqnc8uXLk2rRbLPNNgUa7NH82h6J7rNs2bKUN1D1E/fee6898cQTLt0qekHDZs2aWfv27V3qVTwKIlQXsssuu9i0adO2+Hu/fv3sqaeecuuRHHTQQW7EQ/c/66yzIqMg48aNswsvvNDefvttF3j8/PPP7r433XST9ejRI+X3BQAAAOSSpEc81MhOFFRki+owREFDNBWIq95DixomohETBRNNmsSe3tP/Xq+l96m0LhWTK9hZvXq1C7o0qqIRFxWm+2Bljz32sAsuuCAD7xIAAAAo21Jax6M4aDYtqVmzZsy/16hRI3Kfwp5D6Vmx+OcOPo9qR1RM//LLL9u6devssMMOc2lkGlZUEDJ58mSXBrZmzRq3oKIfcVHRuhZU1EKLAAAAAEpJcXlxUa3HoEGD3C1oyZIlNnDgQDfioel4+/bt61K0lJKlEaErrrjCqlWrZkOGDCm2bQcAAABKmvDVSkUk1mhEkNYOiTcaEv0cK1asCDWqEjRgwADbfvvtXYCh1x49erSb2UprjGjGLE3tq0J2pWgBAAAAKCWBh6/t8LUe0cXlauDHq90ILm6ouo14tSD+97HqSILeeustmzBhgt1///1WqVIlmzdvnpvud88994zcR3Ug+fn5rq4EAAAAQCkJPNq1a+d+vvfee1v8TetyBO+TKG1K63Bo6tv58+dvMRuXFgVUTYafMjcWBTiavrd79+62//77b7EievS/i6MQHwAAACipSnzgceihh7oRixdeeMG+/vrryO+VNqVpdjXyoGlvvd9++83mzJmzRVpVt27dItPz+ql/RdPoauRCqVIKUOLxj9M6IF7jxo3diu2aYtfTv7VN+hsAAACAUhJ4aGYpLfCn6XBPOOEEt4q5irsPPvhg+/777+3666+3nXbaKXL/m2++2dq2bWuTJk0q8DznnHOOW+lcAczRRx/t1t8477zzXK2GHn/dddfF3Qat/fH444+72ao0i5anqXy1urlqOrSWh276t4IcZrUqGZ5//nk3AYBmJVNtTq1atWzMmDFx7696n2uvvdZNlaz7K41Oxxg1O4hn0aJFNmzYMDv11FPdcVOnTh3bbbfd3Lnh888/j/kYjjOEoTWpdNwcd9xxbnITTSmvY+2YY45x9YZK843GsYZM0SQ6uobqFmtNNI41ZHQBweL2xRdfuJXFp06d6k6uLVq0sD59+thpp51W4H4XXXSRm+724YcfdqudBykN6r777nON0YULF7r1OXTCVtChL0ksei2NumihQo2ORNN0ulo13U+ne/LJJ9tdd92VcPQERUcnvgULFljt2rXdbGP6d6xjw3+Wxx57rH3zzTfWoUMHV6+jUTal+Wn9Fs1eVqVKlWJ5Hyi51ImhC7JGOdUhst1227maNE1BrlFSdVoEz1McZwhr6dKl1rJlS3ec7Lrrru5YW758uRtp17lNx5M611TTKBxryJRvv/3WDj/8cNcZrOPKL6bscayhzAUeQBgffPCBm3ygUaNGLujUiFi8wOOOO+5wQaNGSNSYjG5YKs1OdT5AkDodtt12Wxd0BH366aeuI0Kjn999951VrlzZ/Z7jDGFp5F8TmiidN0i/O+WUU9z6UupYU4eacKwhE9QBe+SRR7rUcl1Px40bt0XgwbGGMpNqBaRDKVYKOgqjnulnnnnGpc9pQcgg/V+/VxodEE2LhkYHHXLQQQfZIYcc4nqk1VsoHGdIh0YyooMOUS/0iSeeWGCWRo41ZIrSzGfPnm0PPfSQW0Q5GscaUkHgAfz/dM2//vqrm7Esuj5H/9fvNQnBL7/8UmzbiNJHPYTiL9YcZ8jWSIif5VFpyMKxhkyYPn26WxBZKeWqK4qFYw2pIPAAAuvExFsTxv8+1noyQCzKuVeqX926dV1evnCcIRP++usvV/Oo9Bb1KB9wwAEu9UUppKpJFI41pEt1saqbVa2kJvaJh2MNqaiQ0r2BMsqvXr/11lvH/Ltf1d7fDygsJ7pnz57uwq0cZz/iwXGGTAUegwcPjvxf60ZdcsklduONN0Z+x7GGdCmwVbCgDpRYKVYexxpSwYgHAGQ47aV3796uuFxTawfXGQIyQTnzqh1atmyZzZo1y+XgK4dedR407pAJmkH0wQcftCuvvDKSvgdkAoEHEOiRiV540vMXc38/IF7QoWm+x48fb507d3YzqQVxnCHTxeb169e37t272/33329Tpkxx+fjCsYawNEuaUqyUItqvX79C78+xhlSQagWY2S677FJgRpho/vf+fkC8kY7nnnvOzjjjDHvkkUci6yl4HGfIFq2xIJpSVzjWEJYW/PP1GFoQNZajjjrK/dTClb7onGMNySDwAP7/hLjjjjvav//9b7cQUnBmDv1fv9cK9w0aNCjW7UTJDzq0WOCjjz4aMyea4wzZ8ttvvxWYSY1jDWFpzaFzzz035t+UQqqg5LjjjnMLWGq6eo41pIJUK+D/izN1olVPz913313gb/q/fq98fSBeepWCDi3iNmLEiLiFmBxnSIfWUli7du0Wv9fvBg4cWKAnmmMNYVWtWtXVd8S6tW3b1t1HiwHq/1qhnGMNqWDlcpRpKrj87LPP3L+1iNuMGTPc1JONGzd2vzvwwAPtvPPOi/TMaMXfmTNnWocOHaxVq1bu/u+99561adPGXn31VXdCBoI0ralmGFLBb69evWIGHSeccIK7QAvHGdI51oYNG+bOYepprlGjhi1atMjeeecdV2iu89mECRMixw/HGjJNtR9jx47dYuVyjjUki1QrlGkKOnSSDFIBpm6eDzw0PKyT46BBg+yVV16xjz/+2HbYYQe7+OKL3eJJnDQRy/z5891P9eppdqFY1Ej0gQfHGcI69thjXUqVZhzSTY09FeyqCPj000+3rl27ulXMPY41FBWONSSLEQ8AAAAAWUeNBwAAAICsI/AAAAAAkHUEHgAAAACyjsADAAAAQNYReAAAAADIOgIPAAAAAFlH4AEAAAAg6wg8AAAAAGQdgQcAAACArCPwAMqQPffc02rVqmUff/yx5ZI333zTjj/+eGvYsKF7/0W1Dy666CL3WnfeeacVJ/+ef/7552LdjtJEn5n2mT7DsvQ90jZr2/UeULIV12c1depUO/30023nnXe2bbbZxm3DmDFjinQbkLsIPJBzTjjhhEhDrV+/fnHvt3jxYhp0pcCHH35oZ511ln366afus9p///3tgAMOsJo1aybd+Iy+bbvttta4cWM77rjj7NFHH7W//vrLck2s/VKnTh1r1qyZderUyV544QXbvHlzcW9mibZ8+XJ3jBV3YFoWztXB76YazEcffbTdf//9tmbNmuLezFJlzpw5dtJJJ9m7775rVapUsf3228+dL7fffvtCH7tp0yZ7++237a677rKzzz7bmjdvnnJHz6JFi+zyyy93wdYOO+xgTZs2tXPPPdemTZuWVMCk++oxeuxee+1lV1xxhXtOlB4VinsDgOL0zDPP2CWXXGJNmjQp7k1BSE888YRrAF9wwQV2zz33hHoOBSktWrSI/H/t2rW2YMEC++yzz9xt7NixNnHixKSCmbJG+8W/bzXyfvzxR9f40G3ChAn29NNPW4UKZetSoqBTjbJq1aql9TwrVqywwYMHu39fc801VhS0zWqY7bjjjlZWNGjQwN0kPz/f5s2b5xqhuun4mzRpUpl6v9mk/bV+/Xo79thj3ShH+fLlk37sypUrXadDWDNmzHBBj74XOk533313+/333+2VV16x1157zQWSXbt2jbvdffv2dcFP7dq1XdCjc5HO///617/cczDKVzow4oGcpRPuxo0b7bbbbivuTUEavvvuO/dTPaBh6YL1xhtvRG4fffSRff/99/bAAw9YXl6eTZ8+3YYOHWq5SA1nv1/Uq6mL/dVXX+3+psaCRoTKGgWZ6oHdZ599rLTRNmvb9R7Kii5dukSOQfXU//DDDzZq1Cjbaqut3L/Vg47UzpdHHnlkSkGH6Fyoc+V5551n9957r73//vtWuXLlpB6rYEefo4KOww47zGbNmuVGq7/99lt3jvn7779dYDF79uwtHqv7KjtBQYe/zwcffOB+du7c2Y0sKmDZsGFDSu8HxYPAAzlLPTc68b744ouuYYnSad26de5n1apVM/q8OjZ0gT3xxBPd/9XggbmGxrXXXusaLvL8888X9yYhB5188sl21VVXRWq81PhEds+XGvlU54M6ZP75z3/a3nvvnfRjNWLxyy+/WI0aNezJJ590tSVSrlw569mzp51xxhmuI1BpXNF8YKKUsJtuuskqVqzofq9RkwcffNB22mknlw5NnUrpQOCBnKVcddUGKE3nlltuyXhRcbz6kOBjNXR93XXXWatWraxu3bouZ1UjML7nRtv21FNP2aGHHmr169d3uc3/+Mc/bP78+YVuo3qSzj//fNttt91cPqxyeXVSV89TPDq5jx492g2HK/1MOf0a0u7Ro4d98803he4L9WbdeOONtu+++7r3k+rQ9zvvvOM+E6WK6LW17eecc47rGYtXAOz3RceOHSP7XLnhmdKoUaNIikcqVHNy/fXXW4cOHdyxpvej96Ueutdffz3hY/W5K31EedRKR1D+tR6rxr4+w99++y3p7VCqmI4b7Zdbb73VMkXHpGhkKN33HCzmVorbxRdf7I47vW/9beDAge67ksnjNpFExeU6FtVzq89lu+22c8dH69at3e+Uuhn8Xuh77UXXKgQbSaonUzCn+iSlDOn7qu3XKJ7OB0pHyUTBsq+Z0Gv/+eefNmDAAHc/7We93qWXXuq2JVWrV692AWj37t2tbdu2bp/o+9+mTRuXg6/UqGzwx6B6wjUS54/H++67z3UY7LHHHm5fanu0L4cPHx63Xit4HlPj/I477nDnMT1+l112ceddja4kopHSbt26uX2pY1Ape6eddpq9+uqrWXj35ka2tF3+u6JjX6/38ssvx/3sJ0+e7P7fp0+fyLFYFClK6uCTU045xdXpRNP7EI1qKdXVU3rnW2+9VeA+0R0hukaIUq5Q8pWtxFwgRcq7VpHse++95y4a7du3L7LXVkPqqKOOchdKXTjU86MgRXUKM2fOdHUFqlvQyVQXFPXqzJ07153AldusC4jvNYr2xRdfuAaqGmRqIFWvXt09VhdTNe71HEpTCFKPoRq6aqiKGkDKq/7pp59s/Pjx9tJLL7kLt2ZDiWXZsmV2+OGHu/srYFDDM1GQE02NID2/6KKti6H2h9J5dLvyyitdkOapUaNg7KuvvnKBWrAWIVivkS7tS9F+TIWG/rVP9BmpEabbwoUL3UVUN6UOKEiLpkaPGnB6z6KLdMuWLd3noxzpzz//3L1vNXQLo7xnNb7V2NJxpeMpU2IVlod9z8GUCj2Hjhvtb/VsKhB5+OGH3TGv4CW6niTd4zYV6rVV41y23nprt43aD3qPalzqWFTxq+y6666uR1i/E/XWBvliXj32iCOOcMGk3pu+6/q+KgDQsaf3ffDBBydV/JssFeMecsgh7jX1XVXjTQ13vT+dB3VLpZ5J5yL1Wmv7fQPY10kpB1+fg845mU5di3UMqhNJaWbah9oWfXf++OOPSE2IvhPalkqVKsV8zlWrVrnzso5F7Ru9F3/eVdCpFB/fGRHcjv79+9uIESPc/9WY1zld+1fXFt30Pbz77rsz9t71ndD5UK+t19P7DL6eOnCGDRvm0qP8OVHXA3VI6dqjYErnWVFwlU163S+//NL9+6CDDop5H3WM6TPRcaPOAgXh8vXXX0euI/Ee265dO/dT3xcFof49o2Ti00FOUwPFN8ZuvvnmIn3txx9/3F0wdGLVhVvpXgqCdPFWr496zvR7pRHopK3eZF04tc1qrOjCE8/tt9/uGhbKgdXFUo9Xo01FeXqOWI0/XRjVeDvwwAPda/3nP/9xDRA1/hWw6OKhXrJgD3eQhs819K2G8b///e/IRToZzz77rGscKr1JucPKQ9bFUzOwqMdXQZkazsGePOV4az/5BlmwFiHdC7wa/3r/l112mdsnel/6dyqUEqDPVA1gPYf2h/adGsK64KtXNtZMLspXV9Chhq3eox6jXGo1YDW6o/2UzGQIavDpGJKRI0dmNOgQHRuiBky679nTaImKXvW567H6buix2v963HPPPZfx4zZZeh69P3+sqfdb389PPvkkUuzsgxJRT7/2uxesIdJNjVtRqogajOq91/dVz6NjXw1f7Ud9z+vVq2eZpE4JNarVwaF9pu+sjjF9l/ReHnrooZSeT8eAjlU9Vg1bfe/1PvQ5Kh1KDd3evXtnfBY0fwyqoem/E2eeeaZLi1TQo/Oe9qUastoeNW71eSU6dz722GPuPKRGrM5jOra0fzRyp6Bax1Q0pR4p6FCHgI5R7Qdtm96/Oo507Ot5Yx2/Yd+3DzpUb6XASJ+fjn29jhrweq3g+9Q5UcedH93QecYfi/rsskmfhR/Fj3fu0jZr/4nej+e/t/q7n2AgmkaWRAFKMtkAKF4EHsh5aiCod08XmlhD1Nmii5sah/5kK+r59DUF6rVTA8f3/PgTrG8AKyCJR719eu7giIgaZoMGDXL/1oUmmL6hhoJmKdKJXSMtwREDXdTVaFDDVSf2Rx55JO77UQpHsCGabB6xDxQ0lK7cYd9jpedU2o2fScXPEJRpaowE02DUa679pf2knnLtm2DaTDJUH6IUp2gqrFQDW7Svg/xIl6j3WXnswd477U/1ZGrbElGw5o9rzTylFKRM0eiJHzkTbU867zlIx7cavQq6PDXI/Uw3aiQFZeK4TdaSJUtcw1Pb5nv3g9SQ79WrV8rP6xtZF154oUvdCtLnp5EtPXcm6XnVUaARKU/Htw+covdzYdQo17Gq806Q8vmVJqfRHnUm+NHDTNC52p83jjnmGPe99SlFGllRZ0WQ9qGfCCHRMajjRgFjsIGsY9ofv9H7RiNu2g6dq5Tup8A5SOf0IUOGuH8r8M4EdcIo6FD6mFL0fM2D6FzpP0dNiFESCq6V1ufFG6UP/i1Yr+P/rc83+jON9ZzU+pR8pFoh5ymVRVPqapRANzX8U53tIwxdkGL14ChfXL28OtEqHzaaL+hTb2g8SveIbgSI8n/VU6Y0Dj8cL2qcigr8/AU8mhqv6tWLVW/hG4hKB0uVegX9e1HPdCy6kI4bN871pqr3TAsFZlL0dLoqclQ6yq+//uoaGmqgaUQs1Wlj1YOtz1K917r46nnF1yuoRz9IaSCiPHmfv54K37uvAFABrUbQlPKRDqWQBKfT1WelnH7Roo1qhKfznoM0QhNsRHnaHzr2fB6/l4njNlnqtVbgp/ehtLF0ZlEL8seyGtIaBYmXApRJ8faX9nNh55ZEx56+KwoGNdqklCU/wuFrI/TZq24iVTqe/efnp9NdunSp+786OjRKGqTUKo00aMRDHSxqfAdHWxTsaVQzVseI6pN8D3qsfaOGrY5r39jVsaDvg95XvGJrrQek41rBl0a3ggFfqvQdVEdJovOlfq8gR/tIozU+Fam4C9ol0fHtZ8gK3t//O9HjNPV1rNdCyUTgAZi5nlENUasRrIucem6zLd6Qs+/1jHXxC/7dN/5iidfYVECl3kkFHnqvwZ523/CdMmVKzMf6PFulecWSag1EdI+vGgHx3rOeW9uuxo3un+nAQ+kHsQpAlaKhXmylLOgi7mtQkqG0HM1Lnyi9RD3oQQqsgo2cVKl3X40tff4KOoKjaWH5bRIFXgrU1YOtlBY1YIO9kGHec5DqImLxuejRx3wmjttkqSdco2/q3VaxvAJVBYf6rJR7HjZPXseX0mIUWGsUSQ1fPaf2sY7LeL286Yi3n33aooKGVKgxrX2SKKgs7LNPRLMh6eY/B42kaB9pdEPHfLBeTQGcGt6Jzo86PhU8xAo8Cts3fv/4wMMfgwq2okc7gvznqOMwncBDwbfOg4nO89o2jdpqn+l8WdyBR3A/J1qM1Y/OBO/v/53occFawkzPbojMI/AAzNyFS7nIuimdRxfRbIu3OJm/QBX290QSFaLGalz44Wn1TBY2c0u8HqWwi635BoJvXMaiBq/qU9R7mWqjKB1q+ClFR5MOaNYejYypiLMw6m1VmoMaScrB1oxbGg3ScabfqfdWqSnRM2X59xZMNUqFz4dW8Wui/ZkKNepVL5St95zMMeTTzaIDmkwct6lQWouCXo2gqMGpoEzHh76TCkI0a1iqMwQpqFa6mM47qk1QwKib6LWUix9rNp90pHNuiUUNfQUdPiVJQYHOM74HW6Ni+v6kOjNccNQtmQUY1fhXypoasKeeeqp7XaVYacRO5xAVHvsZleJtS2HHYPRx6I9BjbLoVpjgjE3pnC+1PYm+4wpuFHgU5fkynuDoWqLg06dkBe/vz4Xaz9rvsY7RYCpXvJFPlBzUeAD/T1PP6sKpHimNfiTiT37xenY1HF6cEk2/6f+mXkPP9xgqv14n+MJumeRTwhJdtJWu41MrgttdFDTFsV5Tn3WyOeoqlvcNMjWYNK2nnsM3XoIXyiD/3jQtcRiazlWNVdX/qDagKPO7w77ndBT1cavvvUZDVVSuIE85/ZqGVaMdSjFSWpdS9FKlYEXPpYazPjul9WnEQ2mFmglM9VollUZP/Ro3qp1QTZSOweDCctn47GNR6p2OedV4aJ9pHyrQ8CmSYUdckjkGlbaazDGYTBCfzPlSQVSic6afcruoz5exqCPEHw/R6ZKeRjT8qKRG5T3/b/1d34dYfGqgUq6iZxxDyUPgAfw/5eCqEFKUM5xo3QB/sYl34k93Bp10xVr9VTRE77ctWLDq6xuUl1/U/HaoRzpebrnej08vyHShbWEUcPgAM9mGi1+7Jd70j/FmdvKjKZqBJwwFzkoZ00/1oqsxVFQ5z2HfczqK87hVyqPqwbTug96bRnfUwA6uJZDqCILy2DWZhCaQUL2ERtikJAce/nNXek+s1B91GvgphYtqWxRwxJpStSwcg0rR9YGUZrGKRQGO6tOK43wZi9JkNf25aBa1WPTZKLhQqlRw1FAdP76GI95jfc2LXoOpdEs+PiEgQDnr6qlVA0K56oXVZ8S7kBV3Q0EzIsUaddFc9OoJU5ClNTc8pSWIcs1TWawsE9Sj5fdnvGku/fSeusjHm1IxW7R2hk9viFeDEs3nGcdajE2zI/nRgWjqMVdjVYFHrMXrkqEePwUfKrrVFJtKG0w3vSOb7zkdxXncBqlX2QeNvsEXnbYT5jPwM9qFGUUpKv5zV0pPrPeoUZBkUpCyfQyq80BTF2ea6jr0uqoH0/ct29Tp5Ws24p0vtX6HOmqUnprptVPC8hOlqAYnVgeOFsr1M5QFvzd6v37q6eD01J5GuPy5RZOnoOQj8AAC1Ojza1wkmnJRFxvdV3nemsPd08leUzaqULQ4qaGsostgeonmpPd50pr1KlgMq/ejolYFXMrN94uxBWkmGQVjCmoyTYsD+ouPbn6EQekEyqFXfrjP9S5KylvXxAOi/aWVw5PhGwaaRjM4+qV9qKLseKMQCqz8KrxK6VF9RTCdT0WU2hexPp8gFZUr+NAijgpgFFAnKrbNhLDvOR1Fedxq1E3F5XoNHZdBanD6NSV8z66o4ednBIu3po1GNxQ4RaeCqfGsBmT0c5Y0GuXQ+9TIhmrkgoW+amTqOxucdagojkHNqhacblxBkUaP/CJ2maQ6C3/+0qxsum74mdw8HZ/6vZ+SN12aKlvXH82opRG3YL2K0s18p1nfvn0LpLwVJ53PdF7SZ6Ep0336nc5vumb6NaxUHxZNv9OoiSaQ0AQW/v0q0NXnqpEupff5xTtRslFcDkRR74rSReIN6/qebzVI1eN0ww03uOBDJz41cpSfr561eFMdFgWljGmRMBWu6qaTvS++1bSPsRZL1Lz+qnNRA0nTP+qCqvekYEq5t+q1zlbjX41tNfI1a5Ry2nUx1ciGFoPyr6uLu4qTs0G9lcEZaYLT6erCqMajAqLo1d7jUWNSo0vKSVbah2bKUQqAGq/qHVcRshpp8eboV4+gFnzUhVQ56kqdUsNUz6eLro67wtbyUHHppEmT3D7Tsazce60gncqK1KlI5z2no6iOW6WBqA5DN/XI6hygRp2OET/KoemFg72uahwq6FLNmNYi0XfRz4ak41yBrOqGtF6M7qvPWY14pXkqF17Hod6Pvg8llRqLagyqAagZARUsawRTI1D6DmnacL2nouiM0f7XKu+qwdF+V/qb9rdm8FNApEAuzForhdEEADrv6zqgmh8d5xpx1L7RflCRt84jmZpdSpNd6PukQEaTEqjhrn2u0Ww/Oqb3n41r0Nlnn+06sTxfR6aasuB04wrEg6PTGhXSd0fnI31XNUKo0W7tH31/dK5QinNwWnNPqVc6Lyrg0gQWvpZN3xF9V1SArucuKUEWEmPEA4jBr1Bc2CJtmlpTJ1A17HUSVM+kFv7TSbg4aXhdU3Nq2FqNLzUG1RAcMGCAaxjEKjjUbCDqLVMjSBdw9TCpQa6Ltu6vXnOlkGUroNLihmoYa5vVo6xARI0xbYt6TrX+SLbo4qXeNH9TY1CfqS54aiAq9Sle7UIsmspSNRZKc9J+VdCn19BFWxfkRFMP6wKt1AGlFSgI9p+DRiy0xov2Q7IjL2q06vPW+1BjQY3isIXr2XzP6Siq41bfH3UoaIE2Naj0vdIxqoBECyQqaFbjJzrHXA1EBc16vM4RykfXzacDKajQSIrOHRoVUmqfnlujVTr2NMKif5dkCpD13jWblQJjTeGqgFnvXSN0RbEukmjf6xyi/aagQ41wNfpV0K3zcnCxy0zSeeqWW25xayPp3K/vndbs0PGh4FHBlzqCNBtapuiY0YiHUpg0oqRjXsePUmj1XVAwko16B32n1THib/F+72vygrTOiTpBNEubjg/VqOh40bTIqmlKNI29HqPOGN1X+1szyqkTRaMnes5UF3hF8Sm3fPny+BOuAwAAAEAGMOIBAAAAIOsIPAAAAABkHYEHAAAAgKwj8AAAAACQdQQeAAAAALKOwAMAAABA1hF4AAAAAMg6Ag8AAAAAWUfgAQAAACDrCDwAAAAAZB2BBwAAAICsI/AAAAAAkHUEHgAAAAAs2/4PHEjANggA0FIAAAAASUVORK5CYII="
     }
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.hist(counts, bins=np.arange(5.5, 46.6, 1),\n",
    "        weights=np.ones(len(counts)) / len(counts), edgecolor='white')\n",
    "from matplotlib.ticker import PercentFormatter\n",
    "ax.yaxis.set_major_formatter(PercentFormatter(xmax=1))\n",
    "ax.set_title('Prediction Assuming Random Selection')\n",
    "ax.set_xlabel('Number of Black Panelists in a Panel of 100')\n",
    "ax.set_ylabel('Percent of Simulated Panels')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00137510",
   "metadata": {},
   "source": [
    "The histogram shows us what the model of random selection predicts about our statistic, the number of Black panelists in the sample.\n",
    "\n",
    "To generate each simulated count, we drew 100 times at random from a population in which 26% were Black. So, as you would expect, most of the simulated counts are around **26**. They are not exactly 26: there is some variation. The counts look like they range from about **12** to about **42**. Although we know that the minimum is **9**, from the graph, we can't really tell, although we have a good guess. We also know that if we did not set the random seed, the `min()` and `max()` will vary a little every time. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37e97132",
   "metadata": {},
   "source": [
    "## Comparing the Prediction and the Data ##\n",
    "In the panel selected for the trial, there were eight Black panelists. The histogram of simulated counts is redrawn below with value **eight** shown as a **red dashed line**, with the region for eight or fewer shaded. The dot is very far out in the left hand tail of the histogram. Very few of the 10,000 counts simulated by random selection came out to be eight or less. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "df1679a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.503406Z",
     "iopub.status.busy": "2026-08-31T06:01:00.503338Z",
     "iopub.status.idle": "2026-08-31T06:01:00.549455Z",
     "shell.execute_reply": "2026-08-31T06:01:00.549252Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "metadata": {},
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x1117c1a90>"
     },
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "metadata": {},
     "data": {
      "text/plain": "<Figure size 800x400 with 1 Axes>",
      "image/png": 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"
     }
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.hist(counts, bins=np.arange(5.5, 46.6, 1),\n",
    "        weights=np.ones(len(counts)) / len(counts), edgecolor='white')\n",
    "from matplotlib.ticker import PercentFormatter\n",
    "ax.yaxis.set_major_formatter(PercentFormatter(xmax=1))\n",
    "ax.set_title('Prediction Assuming Random Selection')\n",
    "ax.set_xlabel('Number of Black Panelists in a Panel of 100')\n",
    "ax.set_ylabel('Percent of Simulated Panels')\n",
    "ax.axvspan(5.5, 8.5, color='red', alpha=0.15, label='Eight or fewer')\n",
    "ax.axvline(8, color='red', linestyle='--', label='Observed: 8')\n",
    "ax.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "990f1df6",
   "metadata": {},
   "source": [
    "## Conclusion of the Data Analysis\n",
    "\n",
    "The graph above shows a strong mismatch between the observed panel and the stated random-selection model. It shows that if we select a panel of size 100 at random from the eligible population, we are very unlikely to get counts of Black panelists that are as low as the eight that were observed on the panel in the trial. \n",
    "\n",
    "This is evidence that the model of random selection of the jurors in the panel is not consistent with the data from the panel. While it is *possible* that the panel could have been generated by chance, our simulation demonstrates that it is hugely unlikely. \n",
    "\n",
    "The reality of the trial panel is very much at odds with the model's assumption of random selection from the eligible population. When the data and a model are inconsistent, the model is hard to justify. After all, the data are real. The model is just a set of assumptions. When assumptions are at odds with reality, we must question those assumptions. \n",
    "\n",
    "Therefore the most reasonable conclusion is that **the assumption of random selection is unjustified for this jury panel**. In other words, the most reasonable conclusion is that the **jury panel was *not* selected by random sampling from the population of eligible jurors**. Notwithstanding the opinion of the Supreme Court, the difference between 26% and 8% is not so small as to be explained well by chance alone.\n",
    "\n",
    "In this seeded run, none of the 10,000 simulated panels had eight or fewer Black panelists. This does **not** mean the probability is zero. A finite simulation can miss very rare outcomes. Report that no such outcomes occurred in 10,000 repetitions, rather than claiming the outcome is impossible.\n",
    "\n",
    "The analysis challenges the specified chance model. By itself, it does not identify which stage of the selection process caused the mismatch or establish an individual's intent.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "739f6ff8",
   "metadata": {},
   "source": [
    "### Statistical Bias\n",
    "\n",
    "The analysis above provides **quantitative evidence of unfairness** in Robert Swain's trial. The data support his position that he was denied the impartial jury to which he was entitled by the U.S. Constitution. \n",
    "\n",
    "Additional data show that the exclusion of Black panelists was pervasive. The Supreme Court judgment, written in 1965, includes evidence provided by Robert Swain that \"only 10 to 15% of ... jury panels drawn from the jury box since 1953 have been [Black], there having been only one case in which the percentage was as high as 23%.\" Look at where 10% and 15% lie on the horizontal axis of the histogram above. Values like that are also highly unlikely under random selection from the eligible population.\n",
    "\n",
    "When a process produces errors that are systematically in one direction – such as the percentage of Black panelists always being lower than expected – then data scientists say the process is *biased*. Quantification of such bias is an important responsibility of data science. \n",
    "\n",
    "Arguments such as the one in this section are now more frequently presented in courts of law. In the 1960s, the Supreme Court looked at the data but drew the wrong conclusion that \"the overall percentage disparity has been small.\" For the meaning of \"small,\" it was wrong to rely on what simply seemed reasonable to the majority of the Court. Views on what was reasonable were not only purely subjective, they were also vulnerable to the influence of pervasive racial prejudice. If arguments in the case had included the quantitative analysis of this section, the Court might not have concluded that the percentage disparity was small.\n",
    "\n",
    "```{index} Statistical bias\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Limit the Conclusion\n",
    "# A simulation gives counts far above the observed number of promotions.\n",
    "# Which conclusion follows from this comparison alone?\n",
    "# A: The stated random-selection model fits poorly.\n",
    "# B: A particular manager deliberately discriminated.\n",
    "# Print A or B and explain your choice in a comment.\n",
    "### Your code starts here.\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "A\n"
    }
   ],
   "source": [
    "### Solution\n",
    "print('A')\n",
    "# The comparison challenges the model. It does not identify intent or the\n",
    "# stage in the promotion process responsible for the discrepancy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "acd82219",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cell-fab19417",
   "metadata": {},
   "source": [
    "\n",
    "## Section Practice\n",
    "\n",
    "Use this short exercise to check the main workflow from this section.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cell-8c23f542",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.550653Z",
     "iopub.status.busy": "2026-08-31T06:01:00.550595Z",
     "iopub.status.idle": "2026-08-31T06:01:00.552064Z",
     "shell.execute_reply": "2026-08-31T06:01:00.551891Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Practice Assessing a Model\n",
    "# A company says promotions go to eligible employees at random. 40% of eligible\n",
    "# employees are women, but only 12 of the last 50 promotions went to women.\n",
    "#   1. Simulate 10,000 rounds of 50 random promotions under the company's model:\n",
    "#      rng.binomial(50, 0.4, size=10000) gives the number of women each time.\n",
    "#   2. Compute the proportion of simulated rounds with 12 or fewer women.\n",
    "#   3. Print that proportion. Is 12 consistent with random selection?\n",
    "import numpy as np\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "observed_women = 12\n",
    "### Your code starts here\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cell-d2891057",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:01:00.552991Z",
     "iopub.status.busy": "2026-08-31T06:01:00.552925Z",
     "iopub.status.idle": "2026-08-31T06:01:00.554458Z",
     "shell.execute_reply": "2026-08-31T06:01:00.554286Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Simulated average: 20.0\nProportion with 12 or fewer: 0.0131\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "\n",
    "rng = np.random.default_rng(42)\n",
    "observed_women = 12\n",
    "\n",
    "simulated_women = rng.binomial(50, 0.4, size=10000)\n",
    "proportion = np.mean(simulated_women <= observed_women)\n",
    "\n",
    "print('Simulated average:', round(np.mean(simulated_women), 1))\n",
    "print('Proportion with 12 or fewer:', proportion)\n",
    "# Random selection usually gives about 20 women; 12 or fewer is rare,\n",
    "# so the data are not consistent with the model of random selection.\n"
   ]
  }
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