{
 "cells": [
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   "id": "f22c0e20",
   "metadata": {
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   "source": [
    "<h1> <center> GEOG 172: INTERMEDIATE GEOGRAPHICAL ANALYSIS </h1>\n",
    "    <h2> <center> Evgeny Noi </h2>\n",
    "        <h3> <center> Lecture 07: Inferential Statistics and Hypothesis Testing </h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a06f555",
   "metadata": {
    "slideshow": {
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    }
   },
   "source": [
    "# Statistical Testing \n",
    "\n",
    "* We are broadly interested in mean of a neighborhood and comparing it to the overall mean of the city\n",
    "* It is expensive to sample / survey entire city, so we would like to develop methdolology that could tell us **how likely** we are to find the values "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d4e5ca9",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Setting up our hypotheses \n",
    "\n",
    "* Null hypothesis: the mean of the neighborhood $\\mu=3.1$. \n",
    "* Alternative \n",
    "    * $\\mu > 3.1$ (one sided test) \n",
    "    * $\\mu \\neq 3.1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "299d737a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Sample Probability \n",
    "\n",
    "* We sample 10 households in the neighborhood and find that $\\mu=11.1$ \n",
    "* How can we relate this value to our 'true' mean? \n",
    "    * Null is **TRUE**, but we have obtained an unusual sample \n",
    "    * Null is **FALSE** \n",
    "    \n",
    "> The role of statistic is to quantify how unusual it would be to obtain our sample if the null hypothesis was true"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d25356a2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Judge Analogy \n",
    "\n",
    "* Think about a judge judging a defendant. \n",
    "* Judge begins by presuming innocence. The judge must decide whether there is sufficient evidence to reject the presumed innocence of the defendant (beyond a reasonable doubt). \n",
    "* A judge can err, however, by convicting a defendant who is innocent, or by failing to convict one who is actually guilty. \n",
    "* In similar fashion, the investigator starts by presuming the null hypothesis, or no association between the predictor and outcome variables in the population. \n",
    "* Based on the data collected in his sample, the investigator uses statistical tests to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis that there is an association in the population. The standard for these tests is shown as the level of statistical significance.\n",
    "\n",
    "Source: [Banerjee A, Chitnis UB, Jadhav SL, Bhawalkar JS, Chaudhury S. Hypothesis testing, type I and type II errors. Ind Psychiatry J. 2009 Jul;18(2):127-31. doi: 10.4103/0972-6748.62274. PMID: 21180491; PMCID: PMC2996198.](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2996198/)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a77b8c9f",
   "metadata": {
    "slideshow": {
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    }
   },
   "source": [
    "# Error Types in Hypothesis Testing \n",
    "\n",
    "* Type I - rejecting a true hypothesis (denoted by $\\alpha$, typically set at 0.01, 0.05, and 0.1). *False positive*\n",
    "* Type II - accepting a false hypothesis *False negative*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95ec5b26",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Errors \n",
    "\n",
    "<img src=\"https://www.simplypsychology.org/type-1-and-2-errors.jpg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62f2769e",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Errors (examples) \n",
    "\n",
    "* Null is **true**, the mean in the urban area is indeed 3.1 (as demonstrated on the sample). \n",
    "    * Reject **true** null (Type I error): $\\alpha$ (**False positive**, i.e. 'falsely rejecting true null') \n",
    "    * Accept **true** null: $1 - \\alpha$ (**True Positive**) \n",
    "* Null is **false**, the mean in the urban area is not 3.1 (biased sample, wrong conjecture in the first place, rare event). \n",
    "    * Reject **false** null: $1 - \\beta$ (**True negative**) \n",
    "    * Accept **false** null (Type II error): $\\beta$ (**False negative**, i.e. 'falsely accepting false null') \n",
    "    \n",
    "> **We can decrease the magnitude of errors by increasing a sample size!**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84d23872",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Inferential Terminology\n",
    "\n",
    "* Random variable (RV) - variable that takes on different values determined by chance. \n",
    "* RVs can be discrete (countable) and continuous (line).\n",
    "* Probability function - mathematical function that provides probabilities for possible outcomes of the RV ($f(x)$) \n",
    "* The probability function for discrete RV is called Probability Mass Function (PMF). $f(x) = P(X=x)$ and $f(x)>0$ and $\\sum f(x)=1$ (sum of probs sum to 1). \n",
    "* The probability function for continuous RV is called Probability Density Function (PDF). $f(x) \\neq P(X=x)$. and $f(x)>0$ with area under curve equal to 1. \n",
    "* Cumulative Density Function ($F(x)$) - probability that RV, $X \\leq x$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb848811",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Expected Value and Variance \n",
    "\n",
    "* Expected value (mean) and variance. $\\mu = E(X) = \\sum x_i f(x_i)$. Multiply each value $x$ in the support by its respective probability ($f(x)$) and add them up. Average value weighted by the likelihood. \n",
    "* Variance: $\\sigma^2 = Var(X) = \\sum(x_i - \\mu)^2 f(x_i) = \\sum x_i^2 f(x_i) - \\mu^2$\n",
    "* Standard deviation: $\\sigma = SD(X) = \\sqrt{VAR}(X) = \\sqrt{\\sigma^2}$\n",
    "\n",
    "> In statistics, we use $\\sigma$ to denote population SD and $s$ to denote sample SD. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b39360ba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Distributions \n",
    "\n",
    "* Each distribution can be defined based on its PMF/PDF. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4edde5c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Binomial Distribution \n",
    "\n",
    "> RV with two outcomes. We have $n$ trials and $p/\\pi$ - success probability.  \n",
    " \n",
    "* $f(x) = \\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x} \\quad for \\quad x = 0,1,2,...,n$\n",
    "* Mean: $\\mu=np$, \n",
    "* Variance: $\\sigma^2=np(1-p)$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b2b5f38c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that all 9 wells fail: 39.0%\n"
     ]
    }
   ],
   "source": [
    "# A company drills 9 wild-cat oil exploration wells, each with an estimated probability \n",
    "# of success of 0.1. All nine wells fail. What is the probability of that happening?\n",
    "import numpy as np\n",
    "\n",
    "n, p, sample = 9, .1, 20000 \n",
    "pct = np.sum(np.random.binomial(n, p, sample) == 0)/20000\n",
    "\n",
    "print(f'The probability that all 9 wells fail: {round(pct,3)*100}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce749fb0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# PMF for Binomial Distribution \n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/Binomial_distribution_pmf.svg/1280px-Binomial_distribution_pmf.svg.png\"> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad3b46e5",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = np.linspace(1,11, num=5) \n",
    "p = np.linspace(0.1, .99, num=5)\n",
    "x = np.arange(0,15)\n",
    "\n",
    "fig, ax = plt.subplots() \n",
    "\n",
    "for nn, pp in zip(n,p):\n",
    "    ax.plot(x, binom(nn,pp).pmf(x), '-*')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d96c18",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Normal Distribution \n",
    "\n",
    "* $N(\\mu, \\sigma^2)$. A standard normal distibution is parameterized by $N(0,1$ and is also known as the $z$ distribution. \n",
    "* $f(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}}e^{-\\frac{1}{2}(\\frac{x-\\mu}{\\sigma})^2}$\n",
    "* Any normal RV can be transformed into a standard normal RV by finding the z-score. Then use [stasndard normal tables](https://online.stat.psu.edu/stat500/sites/stat500/files/Z_Table.pdf). \n",
    "* Z-score can be positive, negative. We can use $z$ to identify outliers (+/-3), max possible $z=\\frac{n-1}{\\sqrt{n}}$\n",
    "\n",
    "$$\n",
    "Z = \\frac{\\text{Observed value - mean}}{SD}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8862535",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Plotted PDF for Normal Distribution \n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Normal_Distribution_PDF.svg/1280px-Normal_Distribution_PDF.svg.png\"> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa6be951",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Exercise 1\n",
    "\n",
    "According to Center for Disease Control, heights for US adult males and females are approximately normal \n",
    "\n",
    "* Females ($\\mu=64$ inches and $SD=2$ inches)\n",
    "* Males ($\\mu=69$ inches and $SD=3$ inches)\n",
    "\n",
    "1. Convert your height to $z$-score \n",
    "2. What is the probability of a randomly selected US adult female being shorted than 65 inches? "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62c59c5",
   "metadata": {},
   "source": [
    "# Answer \n",
    "\n",
    "Find $P(X<65)$\n",
    "\n",
    "$$\n",
    "z = \\frac{65-64}{2} = 0.5\n",
    "$$\n",
    "\n",
    "Equivalently, find $P(Z<0.50)$ from the table (0.6915). So, roughly there this a 69% chance that a randomly selected U.S. adult female would be shorter than 65 inches."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc6423c0",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Sampling Distribution\n",
    "\n",
    "> The sampling distribution of a statistic is a probability distribution based on a large number of samples of size from a given population.\n",
    "\n",
    "---\n",
    "\n",
    "Consider a situation. We need to measure the average length of fish in the hatchery. We a certain number of fish into the tank and sample randomly from the tank, measuring and recording mean at each attempt ($\\bar{x_1}, \\bar{x_2}, \\bar{x_3}, ... \\bar{x_n}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e2439acb",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import default_rng\n",
    "rng = default_rng(12345) # ensure replicability with seed\n",
    "list_of_means, list_of_data = [], []\n",
    "\n",
    "for i in np.arange(0,100):\n",
    "    vals = rng.uniform(low=0.5, high=6.0, size=1000)\n",
    "    list_of_means.append(np.mean(vals))\n",
    "    list_of_data.append(vals)\n",
    "    \n",
    "plt.hist(list_of_means);\n",
    "plt.axvline(np.mean(list_of_means), color='red', lw=3, linestyle='dashed', label='mean of means')\n",
    "plt.title('Sampling Distribution of Means \\n drawn from Uniform Distribution', fontsize=16);\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2d18f1bc",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "\n",
    "dff = pd.DataFrame(list_of_data)\n",
    "dff = dff.T#.to_numpy().flatten()\n",
    "\n",
    "fig, ax=plt.subplots(1,2, figsize=(12,4))\n",
    "\n",
    "dff.plot(kind='hist', color='b', alpha=.1, ax=ax[0], legend=False);\n",
    "sns.histplot(list_of_means,ax=ax[1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ba40d11",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Test Statistic\n",
    "\n",
    "* Test statistic will be **normally distributed** for samples drawn from **normal or near normal distribution** \n",
    "\n",
    "$$\n",
    "z = \\frac{\\bar{x}-\\mu}{\\frac{\\sigma}{\\sqrt{n}}}\n",
    "$$\n",
    "\n",
    "where $SD = \\frac{\\sigma}{\\sqrt{n}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da9a0a60",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Exercise 2 \n",
    "\n",
    "> The engines made by Ford for speedboats have an average power of 220 horsepower (HP) and standard deviation of 15 HP. You can assume the distribution of power follows a normal distribution.\n",
    "\n",
    "> Consumer Reports® is testing the engines and will dispute the company's claim if the sample mean is less than 215 HP. If they take a sample of 4 engines, what is the probability the mean is less than 215?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48a2cb78",
   "metadata": {
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   "source": [
    "# How to solve \n",
    "\n",
    "1. Draw a normal distribution \n",
    "2. Find the mean. Which direction do we need to explore? \n",
    "4. Find the $z$ value, look up area under curve for $z$"
   ]
  },
  {
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   "id": "70c6383b",
   "metadata": {
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    }
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   "source": [
    "# Answer \n",
    "\n",
    "$$\n",
    "SD = \\frac{15}{\\sqrt{4}}=7.5\n",
    "$$\n",
    "\n",
    "$$\n",
    "P(\\bar{X} < 215) = P \\Big( Z < \\frac{215-220}{7.5} \\Big) = P(Z<-0.67) \\approx 0.2514\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adecf662",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "# Central Limit Theorem (CLT) \n",
    "\n",
    "> For a large sample size $\\bar{x}$ is approximately normally distributed, regardless of the distribution of the population one samples from. If the population has mean $\\mu$ and standard deviation $\\sigma$, then $\\bar{x}$ has mean $\\mu$ and standard deviation $\\frac{\\sigma}{\\sqrt{n}}$\n",
    "\n",
    "> he Central Limit Theorem applies to a sample mean from any distribution. We could have a left-skewed or a right-skewed distribution. As long as the sample size is large, the distribution of the sample means will follow an approximate Normal distribution. Samples size of at least 30 is considered **large**. \n",
    "\n",
    "[Clear explanation at StatQuest](https://www.youtube.com/watch?v=YAlJCEDH2uY)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6d469ac",
   "metadata": {
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   "source": [
    "# Types of Statistical Inferences \n",
    "\n",
    "* Estimation - using information from the sample to estimate / predict parameters of interest (estimate median income in urban area) \n",
    "    * point estimates (one value) \n",
    "    * interval estimates (confidence intervals) - An interval of values computed from sample data that is likely to cover the true parameter of interest. Including a measure of confidence with our estimate forms a **margin of error** (the median income in the area is 33,450 $\\pm$ 1,532.\n",
    "* Statistical (Hypothesis) tests - using information from the sample to determine whether a certain statement about the parameter of interest is true (find out if the median income in urban area is above \\$30,000). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "695dd497",
   "metadata": {
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   "source": [
    "## General form of a confidence intervals and MOE\n",
    "\n",
    "$$\n",
    "\\text{sample statistic} \\pm \\text{margin of error}\n",
    "$$\n",
    "\n",
    "$$ \n",
    "\\text{Margin of Error} = M \\times \\hat{SE}\\text{(estimate)}\n",
    "$$\n",
    "\n",
    "where $M$ is a multiplier, based on how confidence we are in our estimate. \n",
    "\n",
    "> The interpretation of a confidence interval has the basic template of: \"We are 'some level of percent confident' that the 'population of interest' is from 'lower bound to upper bound'."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11ade53e",
   "metadata": {
    "slideshow": {
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   "source": [
    "# Inference for the population mean \n",
    "\n",
    "* We would like to derive a point estimate of the population mean $\\mu$. For this, we need to calculate point estimate of the sample mean $\\bar{x}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe137ac3",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Constructing and interpreting CI \n",
    "\n",
    "* When $\\sigma$ is known \n",
    "    * the $(1-\\alpha)$100\\% confidence interval for $\\mu$ is: $\\bar{x} \\pm z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}}$\n",
    "* When $\\sigma$ is unknown: \n",
    "    * Estimate statistic via $t$-distribution $t = \\frac{\\bar{X}-\\mu}{\\frac{s}{\\sqrt{n}}}$. [t-Table](https://online.stat.psu.edu/stat500/sites/stat500/files/t_table.pdf)\n",
    "    * the $(1-\\alpha)$100\\% confidence interval for $\\mu$ is: $\\bar{x} \\pm t_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "641b0aec",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Exercise 3 \n",
    "\n",
    "> You are interested in the average emergency room (ER) wait time at your local hospital. You take a random sample of 50 patients who visit the ER over the past week. From this sample, the mean wait time was 30 minutes and the standard deviation was 20 minutes. Find a 95% confidence interval for the average ER wait time for the hospital.\n",
    "\n",
    "1. Is the data normal and is the sample large enough? \n",
    "2. Locate $t$-value in the table and plug into your formula for CI "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca21000f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Answer \n",
    "\n",
    "Use $\\alpha=0.05/2$ for columns in the table and df=40 for rows. The $t$-value is 2.021.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "    CI &= \\bar{x} \\pm t{\\alpha/2}\\frac{s}{\\sqrt{n}} \\\\\n",
    "        &= 30 \\pm 2.021 \\frac{20}{\\sqrt{50}} \\\\\n",
    "        &= (24.28, 35.72)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "> We are 95% confident that mean emergency room wait time at our local hospital is from 24.28 minutes to 35.72 minutes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eed18ddd",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Checking Normality in Python \n",
    "\n",
    "* Use tips dataset from Seaborn \n",
    "\n",
    "> One waiter recorded information about each tip he received over a period of a few months working in one restaurant. He collected several variables: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2d9c9384",
   "metadata": {
    "slideshow": {
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    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>sex</th>\n",
       "      <th>smoker</th>\n",
       "      <th>day</th>\n",
       "      <th>time</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>239</th>\n",
       "      <td>29.03</td>\n",
       "      <td>5.92</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>27.18</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>22.67</td>\n",
       "      <td>2.00</td>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>17.82</td>\n",
       "      <td>1.75</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sat</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>18.78</td>\n",
       "      <td>3.00</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Thur</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>244 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     total_bill   tip     sex smoker   day    time  size\n",
       "0         16.99  1.01  Female     No   Sun  Dinner     2\n",
       "1         10.34  1.66    Male     No   Sun  Dinner     3\n",
       "2         21.01  3.50    Male     No   Sun  Dinner     3\n",
       "3         23.68  3.31    Male     No   Sun  Dinner     2\n",
       "4         24.59  3.61  Female     No   Sun  Dinner     4\n",
       "..          ...   ...     ...    ...   ...     ...   ...\n",
       "239       29.03  5.92    Male     No   Sat  Dinner     3\n",
       "240       27.18  2.00  Female    Yes   Sat  Dinner     2\n",
       "241       22.67  2.00    Male    Yes   Sat  Dinner     2\n",
       "242       17.82  1.75    Male     No   Sat  Dinner     2\n",
       "243       18.78  3.00  Female     No  Thur  Dinner     2\n",
       "\n",
       "[244 rows x 7 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tips = sns.load_dataset(\"tips\")\n",
    "tips"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "10f2bc04",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "image/png": 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yTpK0Ihw+dNDLp0lasRxplpqbA3T12Dg9M+oWSZKkjjnSLA1wc4DTccRLkqTx40izJEkaqkHmr/trnkbFkWZJkjRUzl/XauRI8xIM8pexZ3pLkiStXo40L8Egfxmfyr+UJUmSVg9HmiVJkqQWhmZJkiSphaFZkiRJamFoliRJkloYmiVJkqQWhmZJkiSphaFZkiRJamFoliRJkloYmiVJkqQWhmZJkiSphaFZkiRJamFoliRJklr0FpqTvDPJsST3z9u2LsneJA81ywv6Or4kSZLUlT5Hmm8Grjxl205gX1VtBvY165IkSdKK1ltorqpPAF8/ZfNVwO7m+W7g6r6OL0mSJHVl2HOa11fVEYBmeeGQjy9JkiQt2Yo9ETDJjiT7k+w/fvz4qMuRpLHnuSiStLBhh+ajSTYANMtjC72xqnZV1WxVzU5NTQ2tQEmaYDfjuSiSdFrDDs17gO3N8+3AHUM+viRpAZ6LIkkL6/OSc7cAnwKem+RQkuuAG4BtSR4CtjXrkqSVy3NRJAlY29eOq+rfLPDSFX0dU1oRzlpLks5298yLpvnqwUc625/UhyQ7gB0AMzMzI65GkrrXW2iWJtYTJ7j2prs7292t12/tbF/SMhxNsqGqjpzpXJSq2gXsApidna1hFihJw7Bir54hSVoRPBdFkjA0S5IanosiSQtzeoYkCfBcFEk6E0eaJUmSpBaGZkmSJKmFoVmSJElqYWiWJEmSWhiapZWuuVlKF4+N0950QpKk5fDqGdJK1+HNUrxRiiRJy+NIsyRJktTC0CxJkiS1MDRLk6TD+dHOkZYkTRLnNEuTpMP50eAcaUnS5HCkWZIkSWphaJYkSZJaGJolSZKkFoZmSZIkqYWhWZIkSWphaJYkSZJaGJolSZKkFoZmSWNr4/SMN3KRJHXCm5tIGluHDx3s7GYu3shFOkVzh9HVdtxnXjTNVw8+sqzPbpye4fChg0M/rlYGQ7MkSVq6Ae4wOtAfoQPe2XSQYw/yh7h/eK9+Ts+QJEmSWhiaJUmSpBaGZkmSJKmFoVmSJElqYWiWJEmSWoz11TMGuTSMpEXo+JJTa87+IR7/3nc6258kSV0Z69Dc5TVawcvFSE8y4KWfTnXr9Vv9zkqSViSnZ0iSJEktDM2SJElSC0OzJEmS1GIkoTnJlUm+lOSvkuwcRQ2SpMWxz9ZYaU5gXs5jlDZOzyy77o3TM6uy7rVPOWfZn+2j3UM/ETDJGuD3gG3AIeAzSfZU1V8OuxZJ0pnZZ2vsDHAC8yhPLh7k4garue5BTg7vut2jGGm+FPirqvpyVX0XeC9w1QjqkCS1s8+WJEYTmjcC8y+efKjZJklaeeyzJQlIVQ33gMk1wE9W1c82668DLq2qXzjlfTuAHc3qc4EvDbXQ4XgG8LVRFzEEtnO82M6l+SdVNdXBfkZigvrsSfl3Pd8kthkms92T2GZYfrtP22+P4uYmh4DpeesXAYdPfVNV7QJ2DauoUUiyv6pmR11H32zneLGdE2ci+uxJ/O89iW2GyWz3JLYZum/3KKZnfAbYnORZSZ4CvAbYM4I6JEnt7LMliRGMNFfViSQ/D/wZsAZ4Z1V9cdh1SJLa2WdL0pxRTM+gqj4EfGgUx15hVu1PmUtkO8eL7ZwwE9JnT+J/70lsM0xmuyexzdBxu4d+IqAkSZK02ngbbUmSJKmFoXlIkrwzybEk98/bti7J3iQPNcsLRlnjoJJMJ/lYkgeSfDHJG5vt49bOc5Lck+S+pp1vb7aPVTtPSrImyeeS3Nmsj107kzyc5AtJ7k2yv9k2du3UP7RQnzUpTv1uj7sk5yd5X5IHm//mPz7qmoYhyZubf9/3J7klyTmjrqlrw8pYhubhuRm48pRtO4F9VbUZ2Nesr2YngF+qqucBLwR+LsmPMn7t/A5weVVdAmwBrkzyQsavnSe9EXhg3vq4tvMlVbVl3uWJxrWd+oGF+qxJcep3e9z9NvDhqvrnwCVMQNuTbAT+MzBbVRczdzLva0ZbVS9uZggZy9A8JFX1CeDrp2y+CtjdPN8NXD3MmrpWVUeq6rPN88eY65A2Mn7trKr6drN6dvMoxqydAEkuAl4OvGPe5rFr5wImpZ0T6wx91thb4Ls9tpL8MPATwB8AVNV3q+qbIy1qeNYC5yZZCzyV01xnfbUbVsYyNI/W+qo6AnOdN3DhiOvpTJJNwPOBTzOG7Wx+1rwXOAbsraqxbCdwI/BW4Il528axnQV8JMmB5s52MJ7t1AJO6bMmwY08+bs9zp4NHAf+ZzMl5R1JnjbqovpWVV8FfhN4BDgC/N+q+shoqxqazvtwQ7M6l+TpwPuBN1XVt0ZdTx+q6vGq2sLc3dEuTXLxiEvqXJJXAMeq6sCoaxmCy6rqx4B/xdxP9D8x6oI0PJPQZ803Yd/tk9YCPwb8flU9H/hbJmDKVTOP9yrgWcAzgaclee1oq1q9DM2jdTTJBoBmeWzE9QwsydnM/c/n3VX1gWbz2LXzpObnvbuYm0s1bu28DHhlkoeB9wKXJ3kX49dOqupwszwG3A5cyhi2U0+2QJ817hb6bo+zQ8Ch5ldBgPcxF6LH3UuBv66q41X1PeADwNYR1zQsnffhhubR2gNsb55vB+4YYS0DSxLm5os9UFW/Ne+lcWvnVJLzm+fnMtcpPciYtbOq3lZVF1XVJuZOHPloVb2WMWtnkqclOe/kc+BlwP2MWTv1ZGfos8baGb7bY6uq/gY4mOS5zaYrgL8cYUnD8gjwwiRPbf69X8EEnADZ6LwP9+YmQ5LkFuDFwDOAo8CvAv8LuA2YYe4f9jVVdepE9lUjyYuAPwe+wA/myf0Kc3MEx6md/4K5kwrWMPeH521V9WtJ/hFj1M75krwY+C9V9Ypxa2eSZzM3ugxzP+G+p6r+27i1U0+2UJ/V3AFxIsz/bo+4lN4l2cLciY9PAb4M/Puq+sZIixqC5rKo1zJ3tZjPAT9bVd8ZbVXdGlbGMjRLkiRJLZyeIUmSJLUwNEuSJEktDM2SJElSC0OzJEmS1MLQLEmSJLUwNEuSpBUnyflJ3tA8f2aS9426Jk02Q7NWlfmd6BnesynJv13EvjYluf8Mr78+ye8u8Nrdp+4jyYuT3Nl2XEnSopwPvAHm7tpZVa8abTmadIZmrTbn03SiZ7AJaA3Ng6iqSbkNqSSNyg3AP01yb5I/njdA8fokdyT5cJIvJfnVEdepCWFo1mozvxP9jeZxf5IvJLl23nv+ZfOeNzejwX+e5LPNYymBd/p0HXOSb3fZKEnSk+wE/k9VbQHecsprlwI/A2wBrkkyO9zSNInWjroAaYl2AhdX1ZYk/xr4T8AlzN068zNJPtG85/u3hU3yVGBbVf19ks3ALcBiO9hLgYuBv2v2/8Gq2t9tkyRJS7S3qh4FSPIB4EWAfbN6ZWjWavYi4Jaqehw4muTjwAuAb53yvrOB302yBXgc+GdLOIYdsyStPNWyLnXO0KzVLIt835uBo8yNSJ8F/P0SjmHHLEmj8Rhw3gKvbUuyDvh/wNXAfxhWUZpczmnWajO/E/0EcG2SNUmmgJ8A7uHJHe2PAEeq6gngdcCaJRxvW5J1Sc5lrmP+iwHrlyQtQvMr3180JwD+xikvfxL4I+Be4P1Om9MwONKsVaWqHk1yshP9U+DzwH3MjQC/tar+JsmjwIkk9wE3A/8deH+Sa4CPAX+7hEOe7JifA7zHjlmShqeqFroS0rGq+vmhFqOJlyp/bZYkSatDktcDs4ZmDZuhWZIkSWrh9AxNvCQ/Cfz6KZv/uqp+ahT1SJKklceRZkmSJKmFV8+QJEmSWhiaJUmSpBaGZkmSJKmFoVmSJElqYWiWJEmSWvx/60VXSDO6xb8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2, figsize=(12,4))\n",
    "sns.histplot(data=tips, x='total_bill', ax=ax[0]);\n",
    "sns.histplot(data=tips, x='tip', ax=ax[1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4c4986f2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import scipy\n",
    "\n",
    "fig, ax = plt.subplots(1,2, figsize=(12,4))\n",
    "\n",
    "sm.qqplot(tips.total_bill, line='45', ax=ax[0], fit=True);\n",
    "sm.qqplot(rng.normal(size=1000), line='45', ax=ax[1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dc20702",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"https://condor.depaul.edu/sjost/it223/documents/nplots.gif\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e1513aa0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The confidence interval for tips is (18.663331704358473, 20.908553541543167)\n"
     ]
    }
   ],
   "source": [
    "# calculating cofnidence intervals \n",
    "import statsmodels.stats.api as sms\n",
    "\n",
    "ci = sms.DescrStatsW(tips.total_bill).tconfint_mean()\n",
    "\n",
    "print(f\"The confidence interval for tips is {ci}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1c38706",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Penguins Data\n",
    "\n",
    "|||\n",
    "|---|---|\n",
    "|<img src=\"https://github.com/allisonhorst/palmerpenguins/raw/main/man/figures/lter_penguins.png\" width=\"300px\">|<img src=\"https://github.com/allisonhorst/palmerpenguins/raw/main/man/figures/culmen_depth.png\" width=\"300px\">|\n",
    "\n",
    "[Source](https://github.com/allisonhorst/palmerpenguins)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e3d514e0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>island</th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "      <th>sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.1</td>\n",
       "      <td>18.7</td>\n",
       "      <td>181.0</td>\n",
       "      <td>3750.0</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.5</td>\n",
       "      <td>17.4</td>\n",
       "      <td>186.0</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>40.3</td>\n",
       "      <td>18.0</td>\n",
       "      <td>195.0</td>\n",
       "      <td>3250.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>36.7</td>\n",
       "      <td>19.3</td>\n",
       "      <td>193.0</td>\n",
       "      <td>3450.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>339</th>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>340</th>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>46.8</td>\n",
       "      <td>14.3</td>\n",
       "      <td>215.0</td>\n",
       "      <td>4850.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>341</th>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>50.4</td>\n",
       "      <td>15.7</td>\n",
       "      <td>222.0</td>\n",
       "      <td>5750.0</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>342</th>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>45.2</td>\n",
       "      <td>14.8</td>\n",
       "      <td>212.0</td>\n",
       "      <td>5200.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>343</th>\n",
       "      <td>Gentoo</td>\n",
       "      <td>Biscoe</td>\n",
       "      <td>49.9</td>\n",
       "      <td>16.1</td>\n",
       "      <td>213.0</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>344 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \\\n",
       "0    Adelie  Torgersen            39.1           18.7              181.0   \n",
       "1    Adelie  Torgersen            39.5           17.4              186.0   \n",
       "2    Adelie  Torgersen            40.3           18.0              195.0   \n",
       "3    Adelie  Torgersen             NaN            NaN                NaN   \n",
       "4    Adelie  Torgersen            36.7           19.3              193.0   \n",
       "..      ...        ...             ...            ...                ...   \n",
       "339  Gentoo     Biscoe             NaN            NaN                NaN   \n",
       "340  Gentoo     Biscoe            46.8           14.3              215.0   \n",
       "341  Gentoo     Biscoe            50.4           15.7              222.0   \n",
       "342  Gentoo     Biscoe            45.2           14.8              212.0   \n",
       "343  Gentoo     Biscoe            49.9           16.1              213.0   \n",
       "\n",
       "     body_mass_g     sex  \n",
       "0         3750.0    Male  \n",
       "1         3800.0  Female  \n",
       "2         3250.0  Female  \n",
       "3            NaN     NaN  \n",
       "4         3450.0  Female  \n",
       "..           ...     ...  \n",
       "339          NaN     NaN  \n",
       "340       4850.0  Female  \n",
       "341       5750.0    Male  \n",
       "342       5200.0  Female  \n",
       "343       5400.0    Male  \n",
       "\n",
       "[344 rows x 7 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pengs = sns.load_dataset(\"penguins\")\n",
    "pengs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "693ba34f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x2b4118cab90>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4kNQYDSq5gQcRERGFCAbFAXamsZ0bd3iREqNBdUsnHA4Z7KUQERERMSgOtPJGK9LiGBQPpFEpERUZgXqLLdhLISIiImJQHEhSSlSYrJgSqw32UkLSlFgNzjayhIKIiIiCj0FxALV09EBKIFoTEeylhKTUWA3K2WxHREREIYBBcQCVN7YjPU4LwXFsXiVHa1De2B7sZRARERExKA4k1hMPLS1Wg9IGBsVEREQUfAyKA6i0gZMnhjIlToty1hQTERFRCGBQHEClDRakx7HJzpfkmEg0Wrpg67EHeylEREQU5hgUB1B5oxVTGBT7FKFQIDVWw53tiIiIKOgYFAdIV68ddW02pHA3uyGlx2lRxrpiIiIiCjIGxQFS3mhFaowGEUr+EQ8lNVaD0npLsJdBREREYY4RW4CUNrQj3cDSieFMNWhRXNcW7GUQERFRmGNQHCCl9RakxXLyxHAyDDqcrmP5BBEREQUXg+IAOVXXxskTI5AWq0Fdm40TKIiIiCioGBQHyOm6dkw16IK9jJAXoVQgPU6LEtYVExERURAxKA6Azu6+yRPczW5kshJ0OHmedcVEREQUPAyKA6CsoR3pcVpEKPjHOxJTDTocqzEHexlEREQUxhi1BcCpujZM5eSJEctO0OE4g2IiIiIKIgbFAXDivBkZrCcesezEKJTUt6PX7gj2UoiIiChMMSgOgGM1bchKYFA8Ujp1BBL0apTUczQbERERBQeDYj+TUuJ0nQXZCVHBXsqEMj1Jj6PVrcFeBhEREYUpBsV+dq65ExqVAjFaVbCXMqFMS4zCgcqWYC+DiIiIwhSDYj87WtOK6Un6YC9jwslLiUYRg2IiIiIKEgbFfna02oxM1hOPWma8DvVtNrRYu4O9FCIiIgpDDIr97PC5VkxjPfGoKRUCM1Ki8XlFc7CXQkRERGGIQbEf2R0SJ86bMT2Z5RMXY0ZqND4+0xTsZRAREVEYYlDsR6UNFsRp1YjRsMnuYsxOi8FHZaZgL4OIiIjCEINiPzpU1YocZokvmjFJj7o2GxrabMFeChEREYUZBsV+9NlZE6YnsZ74YikVAvPSY/FeSWOwl0JERERhhkGxH316tgWz0mKCvYwJLT8jFu+crA/2MoiIiCjMMCj2kzqzDdauXqTHaYO9lAltUaYBH59pQme3PdhLISIiojDCoNhPPj7ThFlpMRBCBHspE1q0RoWcJD3eO90Q7KUQERFRGGFQ7CcflDRidlp0sJcxKVw+LQHbD9YEexlEREQURhgU+4GUEh+VmTB3SmywlzIpXG6Mx/5yE5q5ux0RERGNEwbFflBca4FKKZAaqwn2UiYFnToCBdkGvFx0LthLISIiojDBoNgP9pyqx/ypcawn9qMVM1Pw4scV6LU7gr0UIiIiCgMMiv3greN1WJhpCPYyJpWcZD0MUWr841htsJdCREREYYBB8RhVt3SguqUTszmf2O9unj8Fm94uYbaYiIiIAo5B8Ri9eeQ8Ls02QKlg6YS/zUuPRaxWhZc+rQr2UoiIiGiSY1A8BlJK/O1ANb4wPTHYS5mUhBD4l8VZePrdEjS02YK9HCIiIprEGBSPwaFzrejstiMvlfOJAyUzXodrZiTjB387CillsJdDREREkxSD4jH400cVWD4rGQpOnQio2xamo85sw7N7yoK9FCIiIpqkGBRfpPOtnXjvdAOuyksO9lImvQilAoUrcvHi/kpsP1Ad7OUQERHRJMSg+CI9u6cMV89Ihj4yIthLCQvxUWr85xdn4Mmdxfjzp5XBXg4RERFNMgyKL8KZxnb849h5rMpPC/ZSwkqGQYcf3TgLv957Bj989Sg6u+3BXhIRERFNEmKSNy/5/ZtzOCS+8rv9mJEajS/NZVAcDB3dvfjTxxU422TFw6tm4/rZKcHeTZBF5URERBMcg+JR2vL+Gbx6qAYP3Tibs4mD7Gh1K/76+TmolQqsXTINN+anISo45Sy8EYiIiCY4BsWjsPdUA+5/+TAevXkOkqI1/jw1XSSHlDha3Yo9pxpQXGvBstxE3Jg/BVfNSBrPem8GxURERBMcg+IR2nmsFg++dgz3X5uH3BTOJQ5FbZ09+KyiGQcrW3C63oJLsgz40tw0XDsrGckxAf0hhkExERHRBMegeBgt1m787J+nsOdUAzasyMO0xCh/rIsCrKO7F0fOteLQuVYcqmrFtMQorJybguUzUzAzNdrfNcgMiomIiCY4BsVe2HrsOFjZgh1Ha/Hm0fO4cnoC7rhkarDqVWmMeu0OnKxtw6FzrThyrhW9donFxnhcZkxAfnos8lKioVUrx3IJBsVEREQTXFgGxXVmGwr/eginatvQbXfA1uPw+uLoyAgszUtCQpQ6oIuk8SMlUG+x4eT5NtS0dg55rEalgFqpQIRSgVsWTMGPV832lWFmUExERDTBTeqgWAixC0DiwMdViZmRyXc+lhcRneCKdh3dnXaHzdLbazF19Zrru9Db4/qDkY5ejVBE2MZp2SPCNY3csOtSKKDUJ6iV+ni1UhutEmqdUqGK9Jjh3XmmqKVh+6Pl8P73pUlKudLPyyYiIqJxNKmDYn8RQhRJKQuCvQ53XNPIheq6iIiIKHRwRzsiIiIiCnsMiomIiIgo7DEoHpktwV6AF1zTyIXquoiIiChEsKaYiIiIiMIeM8VEREREFPYYFBMRERFR2JvUW7StXLlS7tq1K9jLoMlvpJt3sFaJxgs3lCEiGqVJnSluamoK9hKIiIiIaAKY1EExEREREdFIMCgmIiIiorDHoJiIiIiIwt6kbrSjkXM4JCpMVtS32ZASo0F2QhQUCvbqEBERUXhgUExwOCR2najD/S8fhq3HAY1KgU13LsDKOakMjImIiCgssHyCUGGyugJiALD1OHD/y4dRYbIGeWVEo9Pe1Yv2rt5gL4OIiCYgZooJ9W02V0DsZOtxoMFigzFJH6RVEY1ca0c3Hnr9OHYXNwAAblkwBY/eMgeREcogr4yIiCYKZooJKTEaaFSet4JGpUBytCZIKyIauRZrN9b878ewOyR+/S+L8OzdC1HW0I7/2n4s2EsjIqIJhEFxCHM4JMob2/HJmSaUN7bD4RjZhmijfV12QhQ23bnAFRg7a4qzE6LG/D0QBVKv3YF/21qE2Wkx+NoV2dColNCpI7B+eQ4+O9uMd0/WB3uJREQ0QbB8IsAudqqDe/ObQafGHQUZyEuOxqy0GExL9DyH+zWSozU4a2rH+pcOjbhpTqEQWDknFTMLl6LB0ncOTp+gieDXe8/A1uvAly/N9Hg8MkKJf7k8Ez99qxjLZybzXiYiomExKA6gsUx1cDa/GXRq3LM4C5v3lHo9h7drbFiRC4NOjVqzzdU0N7Nw6ZD1wQqFgDFJzxpimjBK6y14/qOzeOLWuV7/Pi2YGodXD9Vg7+kGrJiVEoQVEhHRRMLyiQAay1QHZ/Pb6kUZroDY2zm8XeOZ3aVYvSjDdS5n0xzRZCGlxI9eO4bbFqYjQR/p9RghBFbMTMb/7a8c59UREdFExKA4gIaa6jAcZ/ObEBjyHL6uIdwSZ2yao8nmnyfq0GDpwrXDZIAXGxPweUUzmtq7xmllREQ0UTEoDqCxTHVwNr8pBYY8h69rOD9NZtMcTTY9dgee2FmMr1yWCeUwZUgalRILphqw63jdOK2OiIgmKgbFATSWqQ7O5rfbFqbjydvm+TyHr2usXpiOv667HDsLl3JnOppUtn1ehYSoSORnxI3o+IJsA3YcrQ3sooiIaMITUo5szNdEVFBQIIuKioK6BudkiLFMdRjuHP64RjBd7ISOEDLSxU7ev2zjxNZjx7Kf7UXhilxMH2FTaGe3Hfe9dBBFD12LqMiw6S2eUH+BiIhCQdj8HyJY/DHVwXmO7IQoVJis+PSsySN4HHgN55ziUAkyhwp6xzKhg8LPS59WIitBN+KAGAC0aiXyUvT4qKwJ189JDeDqiIhoImNQPEGMNHgMtSBzuPX4mtAx3Ag5Cj+2Hjt+/d4Z3H/djFG/ds6UWHxYyqCYiIh8Y03xBOBwSByraR3ReLexjIELhOHWM5YJHRReXv78HLITojAtcfRNo7OnxODjM00BWBUREU0WDIpDnDPTuvtUw4iCx1ALModbz1gmdFD46LE78Jv3z+Cm+VMu6vXZCVGoa7Oh0cLRbERE5B2D4hDhrAP+5EwTyhvb4XD09WQ5M60OOfRoNqdQCzKHW89YJnRQ+PjH0VrER6mRlxJ9Ua9XKgRmpsbgQGWLn1dGRESTBYPiEODMBt+w+UN85Xef4obNH2LXiTo4HNKVad1+oBqFy3OHDR5DLcgcbj3O0XM7C5dyhBx5JaXE/753BjfMSxvTeXKS9Pi8otlPqyIiosmGjXYhYKhmM2emtdZsw9b9lVi7xAilAlgxMxnz0uMGBY/OIHNm4dKQGNE2kvX4Y0IHTV4flZnQ2WPHgqlxYzpPXooerx8+759FERHRpMNMcQgYqu7WPdNaa7bh+X3lmJka4xEQDyy9AABjkh6LjYkwJumHDYh9lW74g/s4tmAH6DQxbfngDL44JxVCjO2+MSbpUdpgQVev3U8rIyKiyYSZ4hDgzAa7B8bOutvhMq1jHcEWyBFuoTYejiae8sZ2HKsxY+0S45jPpVEpkRarRXGtZcxZZyIimnyYKQ4BI6m79ZX59VV6caymdUQZ30COcAu18XA08bz4SQWuykuGOsI//1RNT4rC4So22xER0WDMFIeAsdQB+yq92H2qATWttmGzskOVboy1xjeQ56bJr6O7F68erMETt83z2zmnJepx6FwrvuG3MxIR0WTBTHGIGCobPJB7DbBOHYGsBK3H8xqVAnYHRpSVDeQIt1AbD0cTy98Pn8fMtBgk6iP9ds5piVE4XmP22/mIiGjyCLlMsRBiKoAXAaQCcADYIqV8RggRD2AbgGwAFQDulFJOus9BHQ6JqmYr6tu6YO3uRZZBB6VSoNZsQ0qMBpkGHd4urveo033itnkwWWxo67LjzSM1uKsgE1v3V44oK+ss3RhY9zvaEW7uDXUpMX2Zbm/nfvbuhZAS+ORMk+s41heTN1v3V2JV/tjGsA001aBFdUsnOrp7oVOH3D9/REQURKH4f4VeAN+TUh4UQkQDOCCEeAfANwDsllL+jxDivwD8F4AHgrhOv3M4JPacrkdpfTue2V3qCiTvvy4Pf/yoAi0d3dhyT8GgOt0fvXYMa5cY8fy+cjy8aja2fVaFWrNtRFlZf4xwG6qhzv3cqTEanKy14MZffcjGOxrS8RozGi1dyE+P8+t5I5QKZMbrUFzbhkuy4v16biIimthCrnxCSlkrpTzY/3sLgGIA6QBuAfBC/2EvALg1KAsMoAqTFUerza6AGOgLeje9U4LVizJg63GgqLLZa52uEH3/fWzHSSzNSx5Vxnc0pRvunGUc75U04HRdGww6tWs9zma/T8+aAACXZSfAIeEKnNNiNVi7xIhTdW04VmP26xg4mvj++lkVluUlBeSHpawEHU7WWvx+XiIimthCMVPsIoTIBrAQwKcAUqSUtUBf4CyESPbxmnUA1gFAZmbmOK3UP+rbbHBI+Ax6Abi2ex44vk3KC8fmp8dgZ+HSgJYmeMsOFy7Pxdb9lag121zNfpt3l7kCdINO5QqI71mchc17+oL/LR+UM2NMLrYeO948WovHb50bkPNPNehwvJp1xURE5CnkMsVOQgg9gO0AviOlbBvp66SUW6SUBVLKgqSkpMAtMADSYjWYmRKNwhU5WL88B2mxfaUP7kHvm0dqsHFNvsf4tsLluXj1YLXr69yU6FFlfC+Gt3Frm/eUYvWiDNc67P1xuzNzrFNHQKNSYPWiDFdA7P78wKbAQG4qQqHr7ZP1mJYY5dcGO3dZCVE4cZ5BMREReQrJTLEQQoW+gPjPUspX+x+uF0Kk9WeJ0wA0BG+F/udwSJysteD7fzvikXndVlSFf7k8C3/8qAIalQIPrJyF62elYF56LOrbbOixSzz8xjFXDfHFNMldDF/j1oSAR9bY/bl6iw0bVuSis8c+7Kg2bvwRvrZ9XoUlOYkBO39mvA5lje2wOySUvJeIiKhfyAXFom8v1+cBFEspN7k99XcAXwfwP/3/fSMIywsYX5nXv35rMeJ0KuRnxHo0wRmT9DAm6eFwSPzxG5eNqEnO24SIiw0wfe3Cd1VuIq7OS8L+chPWXJKB7QeqXQH78RozXimqxoM3zPK5g99Qfx73v3wYMwuXcsbxJFZntuFotRnrlk4P2DW0aiUMOjUqTFZM571ERET9QrF84gsA7gGwXAhxuP/XDegLhq8TQpQCuK7/60nDV+bV1mtHZnwUkqM1qG+zocJk9SgjGGmTnDPzesPmD/GV332KGzZ/iF0n6i66JCHToBtUxvGLOxbAZO3GV5//FE+9XYLff1iOexZnIStBiydvm4dXivoC5Cd3FqNwea7PHfyG+vNosNguar00Mbx+uAaXZcf7bQc7XzLjdTjFZjsiInITcpliKeU+AL7SlyvGcy3jyVfmNUmv8UsZgT8zrw6HxNvF9dj0zmmsXWKEUgEUZMUjUiXw9T98PijbvW3dYsRqVWjp6AYA1Jpt2Lq/EuuWGbFwahyy+mcau38/vv48uPHH5CWlxN+KqnH35YFvkM0waFFc24Yb/TwHmYiIJq5QzBSHhYFNZJkGHTbduWBQ9lSpgNdg1ttOdQ6HREVTOz4tN2HPqXqcabjQnObPzKszwK40deK5vWXYvLsM67YWoaKpY9A1DDo1bD0O1Jpt+N09Ba7d91o6ujEzNQZX5SV7zXA7N/4YKptMk8vJ2jZYunowIzU64NeaatCx2Y6IiDyEXKY4HPhqIrt+Vgp2DthE49OzpmGb0pzn9LbxhzOr7M/Mq68AWx8Z4XGNtFgNvnZFFr7+x89c69m4Jh/pcRrER0UOWdPsj01FaGLZfqAaV05PhEIE/j3OiNfhlQPVAb8OERFNHMwUjxP3zPCxmlav2d8TtWbUt3kGgM5g1p23YLbCZPUIiN3PW2GyDpl5He3oM+dotYFrUikV+O61ea7n7ijIGLSeB7YfRXxU5IhGxl3spiI08fTaHfj7kfP4QgCnTrhLjdGgqb0LHd2943I9IiIKfcwUj4OBmeHCFTleM63um11sXJOPG+emuYLZgVnlgWUEJmsXEvWRQ2aVvWVeAYy6Zrnbbkfh8lzXrGHnCLYeuwNalQLrlhnhkEB6nHZEWW6ij8+YYNCpkR6nHZfrKRUCGQYtSuvbMX9q3Lhck4iIQhuD4nEwsMnN16507ptdPLD9KAw6NZbkJI6ojECtVKC6pWPIEgn3UW5O5Y3to27AS4iKxLaiKqxdYoQQgJTAtqIqPPDFmXjyrVOuc61fnsNmORqRvx2oxpU5CeN6zfQ4LU7XWRgUExERAJZPjIuBNbjbD1QPGknmvisd0Neg1tbZg/dKGlzlD0OVEXR02/Fy0eDz/uKO+ZASPksjLqYBLzshCg+snIXn95Xj2T1leH5fOb58aSaqWjqG/T7ZLEcDWbt6sedUA64wjk/phNOUOC1O13MsGxER9WGmeBwMbHKrNduwragKP7t9PsoaLLg0Kx4P9e9KB1xoUHPf3W64koaUGA1aOrqxdX+lK4MbE6mE3SFx468+9Hmei2nAG9gEl6TXQKkA6i1dXr/Pp26fDwhgVmoMpiWyWY48vXW8DrPSohGrVY3rdTMMOuwvN43rNYmIKHQxUzwOvDW53VWQiZ/uLMbm3WV46I1jWH9N7pANave/fBhnm6yDGuKcTXImaxc2rsmHOqIv4FQIYF5GHP5z+9Ehx7ld7Ogz9ya46cl6ZCfqcWlWPDbduQBZCVrcd00OClfk4L9WzsKWD87g+68cgRBgQEyDvFJ0Dl+YPr5ZYqBvVnFpAzPFRETUJ+CZYiFEPoBs92tJKV8N9HVDiXtmtaTegmM1bdi6v9KVGa40dULCgefuXoQj1a1Ij/XeoFZc14bvv3Ihe/zs3QvR3StdNcEFWbEoXJGHH712zCMQHnge90Y3f44+UygErp+VAluPHQ/2r8FZGtK4v5INdjRIdUsHiuvacN81OeN+7aToSLR19sBi60G0Znyz1EREFHoCGhQLIf4AIB/ACQDO6EwCmLRBscMhUWGyor7NhpSYCwGmM7MKAN/ZdnhQuUJ2vB5f65/n66tBraTe4nrMoFPD1u1ASYMF9y41YvuBalxuTPIIiH019A0sjfDWgHex32t1awcqTFbcu9QIrUoBhRDo7LFj45p56LE7UN7YznnD5PJKUd9sYpVy/D+0UgiBDIMOZQ3tWJhpGPfrExFRaAl0pnixlHJ2gK8RMnxtyuGs4XU4JKQEnrp9PkobLHi5qBotHd3YdOcC2KV0Ba/OBjX3kWcPr5qNbZ9V4fvX52GqQYtuu/SoOX541WzYHQ6PAPiD0w14ZNUcPLrjhOu4x2+di0yDbtDae3sdOFFrRq3ZhrRYLeakxSAiwneg4u17ffbuhWjr7MWWD8pdj21YkYtXiqqx5YNyFC7PxUOvH8cDK2eNeptqmnwcDomXi87h28tzg7aG9P6xbAyKiYgo0EHxJ0KI2VLKkwG+TkgYOHrNfbxZdkLUoCDyydvmYVFmHDLjo3C2yerK6taabdi6vxLrlhkx1aBDhakDdocDq+ZPwaZ3SrB2iRHP7yv3uM5jO07i2bsXIStBi0pTJwBgaV4yfvNBmcfotF/tKcWiTINHVri314HXj9TgodePewTPt85P9xkYe/tej1abXQGx87Fndpdi7RJj33bQe/p+P9zINwoPH5Y1ISoyAtMSgzeNJC1GwwkUREQEIPCNdi+gLzA+LYQ4KoQ4JoQ4GuBrBs1Q4828BZEPvnYMQF+AWdVsxdN39TWpAUBLRze0KiU6+3fcSoiKxKZ3SmDrcUAI77XCR6tb8eNVc1xNc0pFX73yc3vL8OyeMjy3twyVps5B49ZO1JpdAbHzXA+9fhwnas0j/l7TYjU+a6EjIxS475oc3LvUiJmp0TDo1EOOfKPw8OInFbg6Lymoa0g36HC6jkExEREFPlP8BwD3ADiGCzXFk9ZQ4828BcwGnRoHq1o9mtIeXjUbFlsPLDY73jpWi7suy8Tz+8px71LjoPN62/zjTGM7tq1bjM4eO7SqCI/Mrft63NWavQfzdWYb5k8d/ntNi9XgnsVZOG/u9LqunGS9R4Z8w4pcpMZwA49wVtPaic/ONuOrl2cFdR0ZBi3KGtqDugYiIgoNgc4UV0kp/y6lPCulrHT+CvA1g2ao8WbOINLdHQUZroAYuFAGYbHZ8dzeMlw9MxlbPjiDtUuMmBqnxYYVOUiL1fjc/GPH0RrkpURjXnocFhsTMS89dthxaw6HRJI+ctDaNCoFUmN9B67u3+vqRRnYVlQFlVKBx26Z61qnM8jfuKt4UEmFfdL/iERDeeHjCizLTYJGpQzqOpL0kWjp6EZ7V29Q10FERMEX6EzxKSHESwDeBNDlfHCyjmQbaryZM4h0z5jmJUd7zdAK0ReUzk6LgSZC6dFwt2FFLl78pBLbiqrw3N2LUFzbhs4eB7YVVeHby3Nx5bQEVwPbcOPWnM1yG3cVD2rse/zWuZiTFjui77XC1I4otXJQY2BWgg6m9i5XjbP799jYbsP0ZNYUh6P2rl5s+/wcHr15TrCXAoVCIMOgxZmGdm73TEQU5gIdFGvRFwxf7/bYpB7J5mu8mbcAVfaPTDPo1Fi9KMO1C938qXGYnRaDWK0Km/eUejxv67Hj6Tvn4+NyE555twRfmpeGmanRyIzPQVa8DufbOpEZH+URGPsat+Ze5+zcCS9Wo8TCTAN67BJVLR1Djk9zBvvN1m5XQAxcyHj3Tdmw+iwpofD0l08rMWdKDFJCpIQmPU6LUgbFRERhL6BBsZTym4E8/0TjDFCzE6JQYbKiuaMLv/6XhejqkSiua0O8ToUMgw4fnTH1zRiO6AuY71mc5ZGFTYvVYn5GLPRqJaI0Kjz19il8+dJMRKkjUG/pwnlzJ/SREZAS6LY7oFYq0NFt95ibDHg2y9WabXj1YDXuWZyFe/7w2Yi2l3Zmmssb271mvMubrF7Hy41kxzyanGw9dvz2g3J87/oZwV6KS1qsFiWcQEFEFPYCvXnHNADfxuAd7W4O5HVDmft8X4NOjcIVuXj0zRMw6NT42hVZWP+XQ67g8ek7F+COgoxBWdj/fvME1i0zwu4A/vxZFf71ymno6LF7zC3+yS1z8fLnlVg+M3VQQOoMcgc2Bq5eNPhaQ41Pc2aa711q9JoN7nVcGC+3dokRSgWwYmYy5qXHcUZxmPrTxxWY3v+DYahIj9Pi4LmWYC+DiIiCLNCNdq8DqADwKwC/cPsVFhwOifLGdnxypgnlje2uHeCcJQtfuyILteZO3LvUiAdvmIW/fl7lEZD+z65iTEuM8pqFdUhACGBVfjpMHd14ZrdnMPvjN47ja1cavQa5FSYrgMGNgUqF722hvXFmmr01/n332jwk6NTQqBSoNdvw/L5yzEyNYUAcxpqt3fjt+2dwxyU+RpoEyRROoCAiIgS+ptgmpdwc4GuEJF+72xl0KtcYsxityhXMOidIbN1fiVpzXxBaaeqEVqX0moWV/UGxUtG3nbO3YLazu9dnkGtM0g+qcx7pCDcnZ6bZmQ3++e3zcbreAin7MoIAsHaJEfnpMchNieb2zmFu41unsNiYgHSDNthL8ZASE4kGSxdsPfagT8MgIqLgCXSm+BkhxCNCiCuEEIucvwJ8zZDga3c7nTrCNcbssR0nPZ7fvKcUqxdluM6hUSmgUgo8futcjyzshhW5ePVgNbYfqMas1Bgo+6dVuHOOVCtckYP1y/tGpDkfdw9ynXXOvka4PXv3QkgJj2y3k3umudZsQ1mDBb//sBzP7S1DrdnmyhDnpkS7gnAKTx+XNWHPqXrcfknG8AePswiFAmmxGmaLiYjCXKAzxfPQt3nHclzYvEP2fz2p+drdrsdux6Y7F+BUXZvX55X9sW3fWLR5iNOpsHR6EqYadPiwrAmaCAV0KiVaOrph63Hg+X1n8K1lOXjkpjl49M0TF2qKb56LX+0uQVGl2ZWF3lZUhQdWzhqynnN2WjRe+OZl6OjuRXZCFIrrLLjxVx8OqkkG+gL/tNhI/N/ay1HXZoNSIfCjG2bhiZ3FHqPdFKIvc86gODw1tXfhu9sOY+0SI3TqQP+Tc3HS47Q409iOuem+xxASEdHkFuj/Q90GwCil7A7wdUKOr93t4qMisSgzHulxWq+lCrNSY7B+eQ6kBH7x9mm0dHRjZ+FSJEVH4vcflrtKL5yNawVZ8ShrsOCFTyqwdokRQgBSAs+9V4pV+ekoqjS7stDb1i32WdPrrdxjyz0FXrPdM769FKfrLdi4qxh3FWR6NPJ999o8bFiRC2u3HQoBNFq6sPKZD4ecYkGTV2e3Hfe+UIQv5CSG9MiztFgNJ1AQEYW5QAfFRwDEAWgI8HVCTqZBh41r8rHpndNYlZ8OpQK4NCsemQYdFArhKlVwD0KfvG0eGtttmJ0WjY5uOx68YRZqWjvQbO3Cosx4PHv3QhytNsMhAaUAclOisXn3adxxSSYqTZ14bm+ZxxpEf/yZFqvB6kUZqDXbEK2xeq3t9VbuUVTZ7DWbXdXcd+zaJYMb+Z5+twRrlxjx/L5yFC7v22jEoFPjVF0bNCoFshOiWFs8AUkp0djeBSn7doEbyfvXZuvBuheKEKuNwJoQLJtwlx6nQ3GdOdjLICKiIAp0UJyCvl3tPofnjnaTeiSbwyHxdnE9tn5yFuuWTXfVDg8cieZscqtvs6HHLrF592ksn5mKJ3deGK22YUUumtq74XBIdPdKV3ZZo1Lgp7fNw0356Thv7vTZjJcWqxk059hb1tZbuYejf3ORgefVqSNcO+95C5pnpUVj7RIjtu7v29F7JNen0CSlxPaDNXj6nRJYbD1QKgR6HRJfmJ6ImxdMwfKZyV6b0z4ua8IDrx7F3Cmx+OrlWVCI0H6vMwxavHGkJtjLICKiIAp0UPzIaF8ghPgDgFUAGqSUc/sfWwDgNwA0AHoB/D8p5Wd+XKdfObOua5cYBzXTbdxVjPQ4DTq67UiO1kCpADp77DhyrhVXz0gZlHl9Zncp1i0zIi1WMyiT+8PXjmHdMiNeKRq8Qcbjt87Fr/ob97yNZUsfUErhrdzjzSM12LgmHw9sP+oR0KbERHo04w0MmqcatPj+K32B/X3X5Ixq9jGFDiklHv9HMd49WY91y4zITdZDCIGWjm4cqmrFb98/gx/87QgKsuIxPyMWMVoVGi1d+KC0Ea0dPfjKpZm4dFp8sL+NEUmN1aDWbEN3rwPqiED3HxMRUSgK9I527w/1vBDiEynlFQMe/hOAZwG86PbYzwA8KqV8SwhxQ//XV/txqX7lzLoOzKSmxWpwV0Em7tqy3yMT/OInlWjp6MZjt8z1OZO41uy9cc/5nHODDCGAmSnRiNYq8YevX4bSBovX1+0+1YCaVpsrY+ucJOFezvHAylm4flYK5qXHuramdjbpbbpzATbuKva6W92ctAulIb6yyc6xcBS6/vJZFd49WY+HV81GVOSFfyoMOjWWz0zG8pnJsNh6cPJ8G6paOtDZ0A69JgKrF2ZgdlrMhPokQKVUIDk6EmebrJiRGh3s5RARURAEuxV80ABcKeUHQojsgQ8DiOn/fSyA8wFe15g4s65AX+bUoFNj9aIMZBq0OG/uhEGndgW5z+wuxfprcvDU2yWobunwmnmdmRKNDIMWWQlarMpPd9UKv3mkBs64o9Zsw3N7y6BRKVw1vTsLlyIvJdrrOe0OeGRsneUcM769FLXmDqiVSli7e1HZ3IFpiVGDAtiVc1IxMzUazdYubFu3GB3ddujUSnTbHahs7sCs1Gj8+l8WQR8ZgTeP1KDS1OlxfV+zjyk01Jo7sXHXaTx04yyPgHigaI0KlxsTcDkSxnF1gZFh0KK0wcKgmIgoTAU7KJbDHwIA+A6AfwohnkLfbOUrfR0ohFgHYB0AZGZmjnV9F8WZdd24qxg/umEW2rt6PTbp+OHKmbB09cLW2xeoZiXokJ8eA41KiZ/cPAc//vuF0WqFy3Px87dP4YGVM/Hta3Lx0BvHXc89ctMcKCFdQa/7BiDObOxl2QmDMsDOYww6NRotXahvsyElRoNMgw7VrVZ0djtwsrYFDgn895sn8J9fnIUvzfWsAXbONzYm6V2TK775p8+9ZsCdpRyVpk5XNtkf2/w6dwh0rp8NfP7z812nsXxmMjIMumAvZdykxWpRUmcB8oO9EiIiCgYh5Ujj0gBcXIiDUspBm3n0Z4p3uNUUbwbwvpRyuxDiTgDrpJTXDnf+goICWVRU5O9lj4gzYDO1d+GeP3zmytSmxWrwtSuyPILkR26aA3WEwI9eOw6DTo0f3TALJQ0W2B3AqwerUWu2oXBFjtcRbuuvyUFWQhRKBxyvUSmwsz8L7HBIHKtpxe5TDa5jAAxaxy/vWoDWjh7895ueQfm2oir84euXYXqy93KH8sZ23LD5w0FrW7vE6Mpeb1u3GJ09dlcJxliDV187BgapgW+kFwzeX7ZRONfcgRs3f4in71oQsnOFA+GjsiaUNljw23sKgr0Uf+BPh0REoxTsjpKR/sP9dQCv9v/+FQCXBWY5/uPMpJqs3R7B4upFGa5AFOirr330zROoNHXA1uNArdmGU/UWbN5d5toZDvC9lbOt14EndxZDE6HE8/vKXQGxeza2bwRcHGamxriOuaNg8DpO1ra5AmLnY5v39M07rmq2+vxefW1U4izzsPU40Nljx2Jjot92tvO1Y2CFyfc6aWSe33cWV89IDquAGOgrnyip5652REThKtj/17tnhMedB3AVgPfQtxteaaAW5G9psVqPml5fjWeOATnEgXXAzq2cB2Zj47QRqDXbsK2oashsrPsIuAaLDR3ddq8j2HztsjdUgORroxLnhxCBqCH2FYizgW9sbD12vHaoBo/dMifYSxl3abFa1LR0cgIFEVGYCui//EKI1UKIUiGEWQjRJoSwCCHanM9LKY97ec1fAHwCYIYQoloIsRbAtwD8QghxBMCT6K8ZngjmpMXg8VvnuhrvnMGtO41KAffk6QenG/D0nQtQuCIH65fnICtBi+nJejxy0xyPBr4NK3IxNT6q//d5iNWqcFl2gisb63BIlDe245MzTShv7MuAGZP0WGxMRHZC1KB1+FrbrNQYpMRE+vwenTXUA9f26sFqv9YQu3NvZnRfKxv4xuadk/WYlhiFpDD8c1RHKJAc0zeBgoiIwk9Aa4qFEGUAbpJSFgfsIkMIZk2xu95eB07UmlFntiHdoEWlqRPfe+VCLez3r58BtVLgybdOwaBTD6r1fXjVbGz7rApmWw8eWDkLZQ3t6Op14NWD1XjwhlkobbDglaJqtHR0u+pqAQxZc+utJvfZuxeiq0d6rO3hVbORYdBgaU7ykGUPzhrqBosNSfq++ct1bTa/1RB7ux5riv3vX//0OWakRGNZXlKwlxIUm3eX4u7LM3HT/CnBXspYsaaYiGiUAh0UfySl/ELALjCMUAmKnRwOiapmK0zt3bD12tHd40CCXo1uuwOJ+kjYHUBTexe+/sfPBpUiuDetuf9+85cX4ki12WNM2x+/0Vdy7a35bafbphnugWxydN/0icrmDlSarNCoFYhUKpGgVyMz/kJQG0oTHwauP4hrmRRBscXWg8uf3I1ffWVh2NUTO/3twDlMidPie9fPCPZSxopBMRHRKAXk/3xCiNX9vy0SQmwD8Do8t3l+1dvrJjOHQ2LP6XqU1rd7ZIEHZjcbLMM3rYn+Moef3Z6PquYOPL/vwtbPhctz0WztQo9dDltz622s2sDM68JMg0dAHELZWY/109i9d7oRs9NiwjYgBoAMgw4nzpuDvQwiIgqCQNUU39T/KwZAB4Dr3R5bFaBrhrQKkxVHq82DJj4MnJjgq1bWvWnt0mwD/viNS5Edr8NTb58eNC1CpVSMuuZ2JNMcOPFhctt1vA4LpsYFexlBxQkUREThKyApISnlNwFACPEFKeVH7s8JIYJWThFM9W02n9MdKk1W10f/mQYdNq7JxwPbjw7aCMOZCS6ubcMv3y3F//7LIh+TLCQsnT34+e3zIQSw5f0zKGlox6Y7FyDToEN5Y7tH+QMANFq6cO9SIwBg+4Fq1457JfUWAH3NdL4mPjRbu1zfY1qsBnZHX8Y72OUVNHJ2h8S+siY8cevcYC8lqFJjNahrs6Gz2w6tWhns5RAR0TgK9OekvwIwcHMOb49NeikxGp9j1Q6da0VnjwPXz0rB28X12PTOaaxdYkRWvBYmazcAYM0lGZAS2FZUhVX56bD1OKCLjBh0voKsWJQ1WPGw2853P7llLi6fZkB6rA5vF9cPKn9QRwisf+nQoB3vWjq6caymDd/Zdhib7lyAGV62jM5K0KKm1YavPv+Z1ybBYJZX0MgdqW6FQadCgt73lJFwEKFQID1Oi7KGdszLiA32coiIaBwFpHxCCHGFEOJ7AJKEEPe7/fpvAGGVfnGORatvs+EKYwLuvy7PY3TZw6tmQ6dWYuOuYpyoNeP+lw+j0tSJ5/aW4f/2V2JaYhQ6e+wAgE/LG/FfK2chMkKBB780A1qVAk/dPh8bVuQgLbavXOJ71890BcRAXyb3x28cR2tHD6paOryWPxytNg8qwbijIAOFy/vGqjmPUyowaPTaY7fMc2W1vW1MwvKKieHDkkbMTWcQCABTDVqc7v+EhIiIwkegMsVqAPr+80e7Pd4G4PYAXTOkOBwSZ5usKK5tQ2mDBS/3j0z75V0L8OK/Xgprlx0Nli40tXfh5aJzuKsgEy0dF3a/S4vV4Mb8KfjpW8VYlZ8OpQL4f1fn4tfvlaK7V+KuyzJx52/3uzKyT942D4sy43CqzuK1xKHO7H3DDm8bh9h6HJhq0GHTOyWuHfVsPQ7Utdk8NgBJjtZ4lFT42pjEvbyCJRWhaV9ZE5bPTA72MkLClDgtimvbhj+QiIgmlUDVFL8P4H0hxJ+klJVCiJi+h2VYpF+8TWlwliT89K1ibFiRhwdfO+bx3LaiKvz0tnxkJfTNMV69KAMvfVaJuwoysXnPhXKEJ26bC50qAt8dkPF98LVj2Fm4dNAOekBfRjc1VoNojcrrcwPjU41KAX1kxKDHkqM1Xic+uJ9zqPIKllSEJluPHcdr2vAfV+UEeykhYWq8DvtKm4K9DCIiGmeBrilOEkLsQH+2WAhhBvCvUsoDAb5uUHmb0rB5TynWLjFCq1K4AuKBzx2sasHjt8xDca0ZOcnRmDslZlDwW2nqcP0+LVaD1YsyXOPamq1dWJBhwOO3zsVDr1+oKX781rmYkxYLhUJg050LBtUUa1UChSty4JB9u9ol6iPxP7uKcUdBBjbvLhtyVzrnbnb3v3wY2w9UY8OKXI+a4sdumYd1W4sGlVTMdJuX7MvFzkQOpVnKE8GhqlZkJejYWNYvK16HP7B8gogo7AQ6KP4DgP8npfwQAIQQSwD8EUB+gK8bVL6mNERrlEjUR3p9TqkAOnscKK41o9cBPLrjBNZfkzvoWGepQ1aCdlAWOTdZj0WZArfOT0dush51ZhtSYzWYkxaLiIi+OuCB5Q8ZsVq8cfQ8tnxwYdbxf980B7EaFRZOjcNf110+5MYYCoXwOGdqjAbXz05FY3vf+evM3v8s6ttsQwbFFzsTOdRmKU8En501IS8levgDw0R8lBpdvQ40tXchMcwbD4mIwkmg5hQ7WZwBMQBIKfcBmPQpGF8zgjPidDjX3OH1uZmpMdhxtAapcTps3lOKVfnpqG4ZfKxS9O1a98DKWa6AGOgLNB/YfhQVJisiIhSYP9WAL85Nw/ypBldADFzY8GKxMRHGJD2K69sGNeb995snsG7ZdGQlRLmOGyqgdD9ndqIe05MvnD+qf0LGwO9XN0xW8mJnInOW8uh9fMaEGQyKXYQQyE7Q4XTdpP+nioiI3AQ6KP5MCPFbIcTVQoirhBC/BvCeEGKREGLSjmVzlhS4T2l48rZ5iIpU4uWiahQuzx0wwWEu/rDvDO4qyERFk9W1a523Y3OS9bj7siyUN7b73LFuNGp9ZHJl//cxVt12+6DvoXB5LnrsjiFf5yvbPtz3d7GvC1e9dgeO1ZiZKR4gI17HZjsiojAT6PKJBf3/fWTA41cCkACWB/j6QTGwpMBZfnCsxoyWjm5s3V+JtUuMEAJQCCA1JhLfWpaD8sZ2pERHYsOKHGjVSq/HTkuMwlNvn8b3r5/ptWnO1451vvhqzMs0aKFQiBHV5w51TEJUJLYVVbm+B+es5ZVzU4dclzPbPtrv72JfF65O11uQqI+EXhO+Wzt7M9Wgw7EabvdMRBROhJRy+KMmqIKCAllUVBTsZbh8XmHC52dbPOqAC5fnQq9RorPbgaffLXE9fv91eYhUKvDTXadcj21ck4/MeC2qmjux6Z3Tg2qKH791Lm6dnw6FQoy40ay314HXj9QMasxznme4+tzhanjHuzY4SDXFIz1xyP1l2/pJBfaebsC3lk4P9lJCypnGdrzwcQXeuf+qYC/lYrGAnoholAIaFAshUgA8CWCKlPJLQojZAK6QUj4fsIu6CbWguLyxHd/802dYlZ/uypruOFqDH1w/E9//25FB2c0X//UyREYo0NFtR49d4uE3jqHS1ImsBC3+Z3U+jlW3IjVOh4omK7p6HdhxtAYvfPMynKy1jCoo7O114ESteVBjXnljO27Y/OGgde10mxwxkmOcmWT3rPlopkiM1+vGYMIGxRv+cgjJMRrOKB6gu9eBb20twvH//iLUEYGuMgsIBsVERKMU6H/t/wTgnwCm9H9dAuA7Ab5myMpOiMIDK2dhx9EaSAkoFcBPbp4LhcL7phcOKTF/qgEpMRqs21qESlMnAKDS1IlPyk3448eVOF1nQbe9rwa5u1eivq3La6PZ5xXNKG9sh8Ntpw7nbnufVzYjWqPCdbNTXY15DodEo6UL9y41Yv3yvh3znOdzr88dSQ3vwOa+kQao4/26cHToXCtykocejReO1BEKpMZoUMLRbEREYSPQhYSJUsqXhRA/BAApZa8Qwh7ga4YshULg+lkp6LE7XFsja1QKPN3flOerDtZb4KlTK/G1K7I8ZgJvWJGLju5er0Hqh2VN+P2H5a6sMQCfZQbennNuPtLS0e1Rn8sa3omrtaMbTe1dyIjTBnspISk7QYeT59u4/TURUZgIdKbYKoRIQP/HxkKIxQDCunulqqXDFRADfQHr8/vO4LFb5npMaNi4Jh8maxfKG9uRFjt4xJuUcAXEzvM8s7sU8VGRXkegSek5nmyo0WVVzVacqmtzZYkNOjU27ynFHQUZgzbx8DZp49m7F0JK4JMzTYOy0xQ6jlSbMZ2ZdJ+mxrPZjogonAQ6U3w/gL8DmC6E+AhAEoDbA3zNkDYw65sWq8Hymal4dm/frnZKBbBwahye21uKokqzK4P77N0Lsf6lQ67M7VSDzmtGuMduH7RrnTPL6zymwWJzBckDX99s7UJVc6fHZh7O1y+cGoer8pI9gihvm3ecrLXgxl99yM0zQtyRc62Yljj2sXuTVXZCFP5xrDbYyyAionES0KBYSnlQCHEVgBnoa/w4LaXsCeQ1Q93AcoPVizJcEySe21sGoC/bunaJEUWVZlcG9x/fXoqdbiPepITXsoX4qEgsyozHzMKlqDRZcehcK7bur0St2eY6xlnakJWgdTX9AX2bgqiU3reh3rAiF/FRanx61jRoooWzhteYpEd5Y7vXDPRItnWm8XWoqgX5GXHBXkbIyk6MQkm9BXaHhJI/0BERTXoBCYqFEKt9PJUnhICU8tVAXHcicJYbOANHpY8mOyE8v25st7kax4C+JrmBGWFnaYMzSM1OiEJnjwMtHd0A4HGMwyHx7eW5g0axddsdXtczJU6Lwr8ewqr8dCgVwKVZ8bjCmOBqynOOgOvssbtenxarwepFGRACaGzvGo8pEDQKx2vacOuC9GAvI2TpIyMQp1XhbFM7cpK5uQkR0WQXqEzxTf3/TUbfRh17+r++BsB7AMI2KHYvN6hvs0GtVLhKFZycNcDuXw9sXPO1QchQpQ3ux1SYrK6AGOgLfB96/Ti2rVvsNQNdb+4cNBd545p83Dg3DW8X17uC8/9aOQMalQIGnRr3LM5yHe/e5MfAOPga2mzo6rUjKToy2EsJadOS+jbdYVBMRDT5BaTRTkr5TSnlN9HXYDdbSrlGSrkGwJxAXG+icI5A+/SsCQBw+bQELMw0DGpUe/zWudhxtMb19cDmNqeRjB7zdYyvUWod3XavW1R326UrwE2L1WDtEiPONXfg0LkWVDdbce9SI9JiNZAANqzIxR0FF8pCnOd2NvJR8B2rMWN6sh5C8AeUoWTGR+HIOTbbERGFg0A32mVLKd07VeoB5AX4miFpqJ3WBmZzMw06LMo0BHTzCV+j1FJiNLh8WoLHehQCqDBZXQGxewbY2Yj35pEa3LM4Cz12ib98VoXvrMj1Ob+YtcXBd7S6FVnxumAvI+RNT4rCjqNstiMiCgeBHsn2nhDin0KIbwghvg7gHwD2BviaQeHMAvsaQzZwBJpBp8apuja8V9KACpMV2QlRrmxuRIQi4JtPeBulNjAj7SzhyIjT4dKseGhUCo/GQKAv0N1WVIWf3DIXDimxYGos1BEC51o7vY6G4/zi0HCk2uz10wfyNC0xCqfrLOi1O4Y/mIiIJrRAT59YL4S4DcCy/oe2SClfG+o1Qog/AFgFoEFKOdft8W8DWA+gF8A/pJT/GaBlj9pQWWBv5Qresq2b7lyA62eloKqlA/VttkETHvzNV70x4H1Tj2tnJGPjmnyca+4YNFLuroJM/NvWA67jf3LLXLz8eSUKl+cO+h6HC8Tcm/YC/WcQzk6eb8NtbLIblk4dgQS9GiX17Zg9JSbYyyEiogAKdPkE+oNgr4GwEOITKeUVAx7+E4BnAbzodtw1AG4BkC+l7BJCJAdouRfF10YY7mPI3MsVvGVbN+4qHrTTXaAb09xHqTn5Gqm2s3Apbpybho/ONPkcKec8/sdv9DXs9dgd2LZuMTq67SMKcEfywwWNXaOlCx3dbLIbqZwkPQ6fa2VQTEQ0yQW6fGI4gz5Ll1J+AKB5wMP/AeB/pJRd/cc0jMPaRsxX01qDxeb6OtOgw5Z7ClC4IgczU6Nh0Kk9jl+Vnz5op7tgNKYN9b1UtXTgx38/jsLlua7SCF8j5RosXViQYcD8qQZcMX1kZSBD7bJH/nP8vBnGpCg22Y3QtKQoHKxsCfYyiIgowIIdFI90/988AEuFEJ8KId4XQlzq60AhxDohRJEQoqixsdE/qxyGMwvszr1+1uGQeLu4Huu2FmHz7jL84G9H8LUrspAWe+FnAt/BpQ3jaajvpb7NhkpTJ7bur8TPb5/vCvC9HX+uuQOvH6lBb+/IazFH8sMFjd2JGjMy2WQ3YjlJehw6x6CYiGiyC3ZQPFIRAAwAFgP4AYCXhY80l5Ryi5SyQEpZkJSUNC6LG65pzVsG9JndpbijIMN1vLORzV2gG9O8NQdmGnTYuCbf6/fiDJhrzTY8ubMYCTo1IhQKbFiR63H8hhW5SDfo8NDrx3Gi1vs4K2/XHu6HC/KPYzVsshuNzAQdzrfaYO4M6804iYgmvYDXFA9jpJ/fVgN4VUopAXwmhHAASAQwPqngYQy3kYavDOjCqXH467rLXWPYfO1QFwi+6nfVEQKb3jmNtUuMUCqAgqx4XGlMgEIhPHbjA4AuuwPHz5vxSlE11i4xQoi+iRUvflKJ71zbN5KtzmzD/Kkju/b1s1LG9c8gXB2vacN1s1KDvYwJI0KhwPTkKBw+14qr8sbnB20iIhp/QsqRVjAE4OJCzJVSHvfyeDaAHc7pE0KIfwcwRUr5YyFEHoDdADLlMIsvKCiQRUVFAVj56JQ3tuOGzR8Omgm8060RD7gweSGQ84md1zlW04rdpxrgkMD2A9WoNdugUSmwbpkRm3eX+Vxnb68DJ2rNaLP14lsvFuHepUb8/sNy1wzj1YsyoFQAi6fF43iNGVfmJGJuetyI/jxe+OZlSImJhN0BNLYH9s/Az0a6wOD9ZevXZuvB5U+8i99/7dKJ8OcaMrZ9XoXMeB3uv35GsJcyUnxziYhGKSCZYiGEBd4DAAFASilj0PcbbwHxXwBcDSBRCFEN4BEAfwDwByHEcQDdAL4+XEAcStwzrENlQL1Ng/A3b1nawuW52Lq/ErVmG3RqJe67JgfO4pTtB6pdG2709jrwcbkJRZXNSI/VwtbjwPYD1ShcnottRVUe20Bv6S+jqDXbMDtNQqEQrqC/pN7iNXP+YVkTt4MOsJPn25A1MX7QCCm5ydH4oDQkPpgiIqIACUhQLKWMHsNrv+Ljqa9e7DmDbbjyivHkrb55855SrF1ixI6jNYjWqPDLdy/MFt6wIhepMRo4HBL/OF7rmpCxYUWOq7546/5K/PCGWfjPvx0ZVDe9bpkR05P0yE6IcgXj9y41et1NT0rv4+zIf06cb+NOdhchLzUaz71Xhh67AyrlRGnFICKi0QjIv+5CiPihfgXimsEw3C527pxZ4EDuUjcSvuqblQrgsVvm4bEdJz123evssaO80YpjNWZseue067mXi6pdDXa1ZhvKGrxnfx0SaLDYPIJxZ3bZvTmvcHkuXj1Y7XodJ04ExtHqVkxNYFA8WvrICCRHR+Lk+bZgL4WIiAIkUI12B9BXPuEt8pMAjAG67riZqBtNuG8i4qRRKbBiZjI6uu1D7rrnXmZRa7bhxU8q8dTt82Ht6oUuMsLreRUCrnFuzuec2eW1S4yYMyUap+osrvM6X8eJE4Fx4nwbvnFldrCXMSHNSI3Gp2dNmD81LthLISKiAAhIplhKOU1Kaez/78BfEz4gBibuRhPexsc9eds8xGpVSI6+MBLN2051m/eUYvWiDNe5Wjq6oVQI/HJ3KZ56+xQev3XuoNFs+RmxHuPcnGrNNjy/rxwzUmIwMzUGLR3drtdx4kRg2HrsqGruwFQDM8UXY0ZKDD4qMwV7GUREFCCBarSbKaU8JYRY5O15KeXBQFx3PA210UQo18I665tnfHspiuvaUFJvwc//eRotHd149u6F+MUdC/C9Vw5DCO+biTjLKTUqBTauycfsKdH41VcWQKVUwCEl/nzv5WiydEOvUWJKrNbV1OWr2XBaYhSmJUaFRL31ZHe6zoL0OC3UEayJvRiz0qLxx4/Pwu6QUPL+JCKadAJVPnE/gHUAfgHPKRSi/+vlAbruuPFVhjARPvZXKASEAL7/yhGP9a9/6RD+9m9XYN0yI2akRHsvs5iRjCunJ7iCVwA4cd6CjbuKPaZPOIPerP5jhms2DPTUDepvsmM98UWL06lh0Klx4rwZ+RlxwV4OERH5WaDKJ9b1//YGAP8AYAbQCuDv/Y9NeMPtYhdKvDUE+sp0V7V0YPPuMlQ1d3jdqS5Wp8JiYyKyE6JQYbLi84pm3P/yYazKT8e2oiqsXWLE+uU5uHepERt3FXuUk4RKs2G4OlbTyskTYzRnSgw+KmsK9jKIiCgAAr2j3QsA2gBs7v/6KwBeBHBngK8bcKE0Zm0ovhoCZ6d5zwQnRkVCo1LA2m3H9gODd6pbmBmHzHjP8Wq2HgeiNcpBmeLC5blotnYxAxwijlWbseaSjOEPJJ9mp8Xg/ZIm/MfVOcFeChER+VmgiwtnSCnvlVLu7f+1DsCE2RJqOBMh8+mrIdDugNdMd1SkEo/fOhczU6PR0tGN5/aW4dk9ZXj1YDXuKMhAR5cdh6paUN1sxb1LjdCqFNCoFEiP03ltzONM19DQa3egrLEdWfGh90nGRDJ7SgyOVLfC1mMP9lKIiMjPAp0pPiSEWCyl3A8AQojLAXwU4GuSG19lEo3tNo9Md5Jeg7Omdqz5zSew9TiQlaDFozfPwSN/PwGDTo2vXZGFZ3Z7ZoHfPFKDf71yGr57bR4qTVav1+noZvAQCs40WpGoj4RWrQz2UiY0nToC0xKi8OnZZlyVlxTs5RARkR8FavrEMfQ11KkAfE0IUdX/dRaAk4G4Jnk3VEOgM9OdnRCFYzWtOFptxneuzUWvXcLW60CLtRuv/NsV6Oyx42t/+GxQFvi391yC07UWzE6LAYScsI2H4eBYjRnTEpkl9oc56THYe6qBQTER0SQTqM+2VwG4CcBKANMAXAXg6v7f3xiga5IXwzUEOmuO79qyH++dakC0RoVn+0sm/vJ5FU7VWbCvrMlrFvhAZQuefOsUvrW1CE2WbvzgizMGNeadNQ290x+Nj6PVrchkk51fLMiIw97TDcFeBhER+VlAMsVSyspAnJdGb7iGQGfNsUGnxr9fneNRf7wqPx0Pv3Ec9y41es0C2/u/tPU48MPXjuGZLy/EumVGOOSFxryWjm7sLFzKZrsgO1ptxqr8tGAvY1LIToyCxdaLSpPVNXKQiIgmvkDXFFMIcJZJDAxMHQ6JRksX7l3aN5e4utmzLti5gcf2A9UoXJ7rdctnJ1uPA60d3di8u2zQ9UN9Q5PJrtfuwOk6C769nBMT/EEhBBZOjcO7xQ1Yu2RasJdDRER+wqA4THkb1fbIqtnIStCi0tTpOk6jUqDWbMPW/ZX4+e3zUdpgQW5yNJ56+xRqzTaP43TqCNYVh6AzjVbER6mhU/Ovu78syIzDP4/XMigmIppEOC9rkvC2QcdQxx6raR00qu3RHSfxXytnueqC3zxSg0dumuMKjJ96+xTSYrV46u1TuKsg06N++JFVc/DCx+UoXJ7rs36ZguNYjRnGJL4H/jQvPRYnzrehxdod7KUQEZGfCCknbxNUQUGBLCoqCvYyAs7XBh0r56QOmp3sPPZUXZvXUof7r8tDV6/DtWHHhyUN+NGNs9Fm64FGpUSiXgWLzY6DVS2YEqfD+dZOTInTorWjCzNTYiAUgFqpQEe3HSkxobmhSQCM9BsMyl+2h147BglgVf6UYFx+0npmdwnWLMrAHQVTg70Ubyb9XzoiIn/j56mTgK8NOmZ6aXBzHuurea7X4cBze8uQFqvB6kUZuH5OKiIUAnE6FeJ1kVAqgLZOO375bumg17KhLjQdOteK2xdxJzt/uyQrHjuO1oZqUExERKPEoHgS8LVBR4PFhuyEKFSYrKhvsyElRuM61lvz3KM3z0FarAYFWbFYPjN1UGPdtqIqfPnSTLx1rBYPfmkmmqzdcEhAKYB5GbEskwhBXb12lDW0I5sziv1uUWYc/vTRWZg7exCrVQV7OURENEYMiicBXxt0JOk1g8oqfndPgUfz3NolRigVQF5yNJ7YWYyWjm48e/cirH/p4KDNOtYuMeKZ3aVYf00OOnsc2PJBuUe5BoWe4loLpsRpoVFxJzt/06kjMDc9Fv88UYc7mS0mIprw2Gg3CfjaoEOpgGsG8X3X5ODepUYU15rxszX5rsD4+X3l0KqUeGJnMWrNfVnko9WtXjPP0Rol1i4xIsOgQ0d3Lww6teu5+18+jAqTddy/dxra4aoWTGeTXcAsNibgtUM1wV4GERH5ATPFk4CvDTo+PWuCQafGPYuzPEohfnHHfPzxGwWoabFB4xYQOzkkBmWesxK0iNaoXLXE7rOKncE05xGHnqLKFr4nAbQo04Dn9511lScREdHExUzxJOHcoGOxMRHGJD0UCoGUGA3uKMhwBcRAX1b3e68cgVKhwENvHMepegtaOjzHSu0/04hn716EwhU5WL88B1kJWjywchYe23FyUEnF6v4GLo1KAa1KOaKRcDR+DlW1IodBccCoIxS4bJoBrzNbTEQ04TFTPEk5HBIKAeQk6b2WQlSaOrw23GUlaLFmUaarplijUuDJ2+ZBqYDX8wjRFxA/futcFP71ECpNndCoFHj27oWYlqBHg8UWTqPZQkqjpQvmzh6kG7TBXsqktjQnCVv3V2LdMiOE4D1ORDRRMVM8CTlnEa985kM0WrpctcZOGpUC+sgIV13xruO1+N09BShckYPvXT8Tj+444ZERfvC1Y+julV7Pc4UxHtvWLcav9pS6dsIz6NQorW/Hjb/6EF/53ae4YfOH2HWijtnjcXagsgUzUqOhYKAWUDNSo2HrtePwudZgL4WIiMaAQfEk5D63uNvuwIYVnrvMbViRizpzp2v3uaV5yXjojWNI0KnR2d3rNSN8tsk6aLe6h1fNhk6tREe33WNr6NWLMvDMbs+SDTbijb/PK5pZOjEOhBC4Ki8Jf/60KthLISKiMWBQPAm5zy22dtvx4id9o9fWL8/B2iVGvPhJJUwdPa6RbJnxWnT3Sth6HTjf2uk1I9zV63Ad/7M187B2iRFbPjiD8qYOpPaPhHMSwnupRYPFBho/n5abkJcaHexlhIVluUn45/E6tNl6gr0UIiK6SCEXFAsh/iCEaBBCHPfy3PeFEFIIkRiMtU0UKW5Bqj5SiTsKMuD8BP3Vg9Vo6eiGQsA1km1KrBZ3FGTg6XdL8HJRtdeMcLRGiTWXZGDH0RpUNnfiub1lqDR14kevHYPF1uMxEk7ZX2fsTqNSIDma3fnjpb2rF2carcwUj5M4nRrzMmLx6oHqYC+FiIguUig22v0JwLMAXnR/UAgxFcB1APgZ5TCcc4s37iqGgPDYZGPDilzkpuiRk6THldMTkBytQaZBB3NnD2w9Do9NPYQACrIMeOTvx10NdI+smoO/fFbpupbzNe4j4VJjNJiRGuOxacimOxdwx7txdLCyBcakKKgjQu7n3knr2lkpeOHjSnz9ymw23BERTUAhFxRLKT8QQmR7eeppAP8J4I3xXdHE45xbnB6nwV1b9nvU9j6zuxTb1i1GZnwUshP7soi9vQ5MibuwK16t2Ybn9pZBo1JAIYyuemFbjwOP7jiBtUuMOFrTBqAvA5waq3GNhHPOxM2Mjxo0N5nTJ8bPx2eaMJOlE+NqZmo0IIAPS5uwLC8p2MshIqJRCrmg2BshxM0AaqSUR4bLwAgh1gFYBwCZmZnjsLrQpFAIdHTbvdb27j7VgMb2LmTHR6GquQNKhcC5Ziu+e20enn63xGMUW32bDeuX5wAAth+oRq3ZBmV/8tE5im1OWqzX67sHyTS+PixtwuqF6cFeRlgRQuC62Sn43YflDIqJiCagkA+KhRA6AD8CcP1IjpdSbgGwBQAKCgrCegaYs7bYPTDWqBRQKxUob7Ri/UuHPMoqEnQqrL8mB912B67KS0Kjpcs1RcK5g922oiosy03CnLQYpMZqMCctFhH8iD6kmDt7UN5oRW4KM8Xj7QvTE/FK0TmU1lv4509ENMFMhGhmOoBpAI4IISoAZAA4KIRIDeqqQoDDIVHe2O51F7neXgc6unvx2C1zPZrmCpfnQqkQ2PROyaCyimqzDZ09DmzeXYaObjt++laxa2rFvUuN2FZUhcdumYdFmQZ8cW4a5k81MCAOQR+VNWFWWjRUSr43400docB1s1Pwm/fPBHspREQ0SiGfKZZSHgOQ7Py6PzAukFI2BW1RIcC5QcfAZraVc1LhcEi8fqQGD71+HN+5NhdP3T4fJQ0W2B3A1v2VWHNJhteyCoeEa4c6h8OBuwoyXTvdOQNqrVrB2uAQt/dUA+ZMGVzSQuPjulmpuP+Vw6g1dyItlrsJEhFNFCGXShJC/AXAJwBmCCGqhRBrg72mUOS+QQfguUHGiVozHnr9OGw9DrzwcSVM7V3QqpR4fl95X02wj5FpCgEoBPD4rfOgj1S5AmLn+TfvKYWa2ceQJqXE+yWNWDA1LthLCVt6TQSunpGE3zJbTEQ0oYRchCOl/IqUMk1KqZJSZkgpnx/wfHa4Z4kBzw06nJwbZNSaLzxXa7bhNx+UAwB+e88l+NmaeYjTqvCDL84YtMtdVoIOl2QZ4JB2mKxdXs/f0W0fh++OLtaJ821QKRWYEscMZTB9aW4ath+s4YY1REQTSMiXT5B33proshK00KqUUEQJj+dqzTY8s7sU65YZsXl3GQAgLVaDX965AO3dvYjXqdHTX5+8eXcpblmQjuwEvdcmvZQYbsARyv55og4LM+OCvYywZ9CpsSQnEf/73hk8ctOcYC+HiIhGIOQyxTQyzg06nNnerAQtvr08F3dt2Y/Hd5zEIzfN8cgEP3bLXLxSdGG3rVqzDY/uOAmFEPh/Lx3Ev209gGd2l+LLl2YiMUqNx3ecxIYVnjvbcQOO0PePo7W4NDs+2MsgADfNn9I/xrAz2EshIqIRYKZ4gnJu0OHcIEOrUro26jha0wZ8Womnbp8PCAASaGq3oaWj2+McLR3dWJQZh398eymqmq1QRyhwosaM/32/r/a4sb0b65YZsXBqHLISorgBR4grqbegzdaDnGTOhg4FBp0aV89IxtPvlOBnt88P9nKIiGgYzBRPYM4NMhYbEwdt1HG0pg3r/3IIJfUWrP/LIfz2g7MoXJ7rkVneck8Bas02CAFclZcMhRB48q3TqDX31UHWmm3YvLsMWrUSxiQ9A+IQ99rBGlw5PREKbjEcMm7Kn4J/nqhHab0l2EshIqJhMFM8SfjaqMPe/2Wt2Yat+yuxdokRBVmxaLPZsW5rkcc4t9lp0V7PkRzNOuJQZ3dIvHqoGt+9Ni/YSyE3ek0Ebp4/BT/ZcRJb114e7OUQEdEQmCmeJAbWGGtUCmxck48dR2tcx9SabXh+XznioyLxwPajg8a59dolNq7JZx3xBPR+SQNitSpk8b0KOdfPTsHZJivePVkf7KUQEdEQmCmeJAbWGCdHa5ARq4VBp0ZRZTMcEnjzSA0eWDlrUKkF0BcYn6q3YNM7p7F2iRFKBVCQFY8rjQksm5gA/rCvAlfPSB7+QBp3EUoF7lmchR+/cRxX5iRAp+Y/u0REoYj/Ok8izhpjY5Le6453G9fk4/pZKahq6fBaJlFSb0GlqRPP7S1zPbazcCmMSWzcCmUl9RacOG/Gt5Yag70U8iE/Iw45yXr8/J+nOaKNiChEsXxikvK2490D24+iqqXDa6nFk7fN8xjZ5nwNNx8Ifb98twQr56ZCHcG/zqHsq4uz8PfD5/HJGVOwl0JERF4wUzxJDbXjnTFJP6jUQiEwaGQbm+xC37FqM/aXN+MXd3DkV6iL1qhw71IjvrPtEHYWLkWCPjLYSyIiIjdMLU1SzmkU7tyDXPdxbsYkPTLjB2eP2WQX2uwOiYdeP4bbL8mARqUM9nJoBBZMjcMVxkT8x/8dQHevY/gXEBHRuGFQPEl5K5EYKsh1NurtLFyKv667HDsLl2LlnFQ22YWwLR+cQa9D4qq8pGAvhUbhjksyIAF8/5UjcDhksJdDRET9hJST9x/lgoICWVRUFOxlBI3DIVFhsrpKJLgjXcCM9A/Vb3/Z9pU24dt/OYhHb56LpGh+DD/RdPXa8dQ/T2N6sh5P3TEfKqXf8xP8i05ENErMFE9iA0skGBBPDh+XNWH9Swfx7eW5DIgnqMgIJb53/QxUt3Tiq7//lA2tREQhgEEx0QTRY3fgub1luO+lg1i/PAez0mKCvSQaA41KifuvzcNUgw5ffPoD/Hl/JXrsrDMmIgoWlk8QjV1AyydqzZ3YebQWf/y4AknRkfjmldOYIZ5kzjZZse3zKtS12XDnJVPxxbmpmJUWA+XFf7rDj4WIiEaJQTHR2I05KH6/pBG/+6Acth47LLZemKxdaGq/MCJPHaHA8pnJmJkSPda1UgirMHXgw7JGmNzee5VSICVGg1itClHqCESqFNCqlPj+F2cgz/f9wKCYiGiUJnVQLIRoBFDph1MlAmjyw3n8iWsauUCvq0lKuXK4g4QQu/rXMohh+b1TYi69Nc39Memwo9dcb+s1N9j82KPnF9JuVwulsnv4Iye2YH6fisioiIi4NI1SG+11nrzpn8+dbT/8VrOPl4/oniQiogsmdVDsL0KIIillQbDX4Y5rGrlQXddEFi5/puHyfRIRERvtiIiIiIgYFBMRERERMSgemS3BXoAXXNPIheq6JrJw+TMNl++TiCjssaaYiIiIiMIeM8VEREREFPYYFBMRERFR2PM6/3KyWLlypdy1a1ewl0GT34g2SuD9SOMooLssEo0SN5OhCWFSZ4qbmkJxHwkKV7wfiYiIQtekDoqJiIiIiEaCQTERERERhT0GxUREREQU9iZ1ox1NDA6HRIXJivo2G1JiNMhOiIJCwb6MiYjvJRERTVQMiimoHA6JXSfqcP/Lh2HrcUCjUmDTnQuwck4qg6kJhu8lERFNZEEJioUQUwG8CCAVgAPAFinlM0KIxwDc0v9YA4BvSCnP97/mhwDWArADKJRS/jMYaw933jKBDofEiVozas02pMVqMSctBhERCo9jdeoIdNvtSIiK9MgeVpisriAKAAw6NU7VtUGjUiA7IeqiMo3MVgbHwPcyL1nfHyjXIj1OhxlJepxutPi8T0zWLggINFu7kBJz4XkiIqLxEKxMcS+A70kpDwohogEcEEK8A+DnUsqHAUAIUQjgxwD+XQgxG8CXAcwBMAXAu0KIPCmlPUjrD0veMoG/uGMBHNKBH/ztqOuxx2+di5vnTcG7pxs8ji1cnottRVV4YOUsV/awvs3mCqLSYjW4Z3EWNu8pvehMI7OVweP+Xuanx+Arl2Xh+3874noffnLzXDz3XikqTZ2D7pONu4pxV0Gmx3v/+K1zcev8dAbG5BdHq1vxnb8eRmtnDx66cRZWL8oI9pKIKMQE5f82UspaKeXB/t9bABQDSJdStrkdFoULg+VvAfBXKWWXlPIsgDIAl43nmmlwJtDW48D3XjmM0oZ2j8ceev04jp43Dzp2855SrMpPx/0vH0aFyQoASInRQKPquw1XL8pwBUXO17gfe7FrHO056OK4v5f3LpuOR3ec8Hgffvz341iVn+762v0+WZWfPui9f+j14zhRaw7ON0OTSlN7F775x8+xKn8KfvDFGXjiH8X4uIxzw4nIU9BTMEKIbAALAXza//UTQohzAP4FfZliAEgHcM7tZdX9j3k73zohRJEQoqixsTFg6w5H7plAJ1uPA9OTovCrryzE/dflYf3yHBh0atT5OFaIvv82WGwAgOyEKGy6cwE0KoXruYGvcR47ljWO5hz+FE73o/t72d1r9/n+u3/tvE98vfd15uC8bzS5bHzrFK7MScAV0xOQnRCFb3whGw+9cRx2Bzf0I6ILghoUCyH0ALYD+I4zSyyl/JGUciqAPwNY7zzUy8u9/msmpdwipSyQUhYkJSUFYtlhyz0T6JSVoEV7lx0/+NsRbHqnBL//sBxfuyILU2IHH6tRKSBl33+TozUAAIVCYOWcVOwsXIqluYleX+M89mLXONpz+FM43Y/O93LXhqVI1Ef6fP/dv051e7+8HZ8aG5z3jSaPhjYb3jpeh5vzL+RRLsk0QK1U4J8n6oK4MiIKNUELioUQKvQFxH+WUr7q5ZCXAKzp/301gKluz2UAOB/YFdJA7pnAtFgNClfk4JGb5uCxHSc9PvZ+ZncpHBLYuCbfI+B5eNVsxGqUePbuhchOiHKdV6EQMCbpcWlWvOv8ztdsXJMPk7UL5Y3tcIwgq+O+Ruc5Nt25wON6dPEcDonyxnZ8cqbJ63uiUAg4JPDI34+jcHmux/vwk1vmYsfRGtfXT9w2D/lTYrHpzgV480gNfrhyJh5YOQMbV8/Ds3cvxPNfL4BDyhG/90Te/PXzc7hiegL0mgstNEIIXD87BS98XBG8hRFRyAnW9AkB4HkAxVLKTW6P50opS/u/vBnAqf7f/x3AS0KITehrtMsF8Nk4LplwIRM4e8NSFFW24KHXj+PepUavH3u/V9KIN4/U4PdfL0CrtQclDRY8u6cMLR3d2HTngiHPP7NwKerbbOixSzz8xjFXY9ZIGubcz9FgsSE5mtMn/GWkTYz1bTZUmjqxdX8l1i4xQghASsBut2NVfrrr68x4LdRqZd89lRaNQ1Wt+OmuU65zb1iRC51KiT98fNajOZNopKSUePVgDb75hexBz12aHY8/fVKB862dmBKnHf/FEVHICdb0iS8AuAfAMSHE4f7HHgSwVggxA30j2SoB/DsASClPCCFeBnASfZMr7uPkieBwZgIfev24KxjWqBQegbHzY/JKUyc+O9uMLR+Uezx//8uHMbNwKYxJeq/ndz5+w+YPBzXM+Xqdt3MMdxyNjq8mxoHvibOEpdZsw3N7ywD03RNrlxg9vl6zqO/jbOc99cPXjg36xGHdMqOrOXMk7z2Ru1N1FnT29CI3efB9E6FUoCDLgJ3HanHvUmMQVkdEoSZY0yf2SSmFlDJfSrmg/9dOKeUaKeXc/sdvklLWuL3mCSnldCnlDCnlW8FYN/Vxb2bbfqB60Mfkhctz8erBagCAQ15c81yoNczRyN8TbyUsj9/qWToxsKTF17kdEoOaM4lGandxPRZlGiCE908YCrLi8Y9jteO8KiIKVdzRjkbNmQm09ThQa7Zh6/5KrFtmxLwpsTh23oyt+ytR2z81QCm8Z5KHa3xzv8ZoXkeBM9L3xFsJS6ZBh0WZBp8lLb7OrRCA3cH3ni7Ou8UNWDkn1efzc6bE4ld7ymDu6EGsTjWOKyOiUBT0kWw08QzMBLZ0dGNmagyumZGM/IxY3FGQgfXLc7BhRQ4WZcVdVOMbG+ZCz0jeE2cj3qdnTQCAy7ITYEzSIyJCAWOSHouNiTAm6QfVBns794YVuUjQqbHjaA3fexq19q5enK6zYFZajM9j1BEKzJ4Sg32cWUxEAISUk7eru6CgQBYVFQV7GZOSc2te98wfAK+NWNfPSkFVS8eoG9+8XSNEG61GtKjJcD8O9Z6MdTdBh0PibJMVVc1W6NQRiIpUwtZjR/yArcFpREb6hzVp/wew91QDnn63BD/80qwhj/vH0VrYpQM/XZ0/TisLS/zLSxMCyyfoojib2bITolBhsuJAVTMUELj/5cMw6NRYvSgDQgCn69owOy36ohrf2DAXurz9LO2rES/xm5chOSYSmfF9ga0zsK5vsyEl5kJgrVAITE/WY7qXpiii0froTBNmpEYPe9zsKTH47QdnxmFFRBTqGBTTRXNmBjfuKsbdl2XB2t0Lg06NexZnubbs1agUyEqIcgVENHENlwn21Sy370wTtColclP0uDo3GW8X1190NplopD4/24yb5k8Z9risBB2ard2uTz+IKHyxppgumjMzuCo/HU+/WwKHBO4oyHAFxEBfUPTga8dQYbIGebU0Vr4ywc731tdugnYH8MzuUhytNuNErXnIcxD5g63HjtP1FkwfwadMCiEwIyUaBytbxmFlRBTKGBTTRTNZu7B2iRHTEnX4+e3zkR4bielJeo5Sm6QGZoLTYjVYu8SIknoLyhvbkWnQDWqWe+SmOcjPiMX/uzoHucnRHLVH4+J4jRkZBh00KuWIjp+erMfnFQyKicIdyyfoojgcEudbbXh+X7nrY/DC5bmw9To4Sm2Sch+blharGVQm42yqfHndYpQ0tKPR0oXuHjs2/PWQ65jffvUS3h8UcIfPtWJ64sinleQl6/HG4fMBXBERTQTMFIcx5/isT840obyxHQ7HyBvRK0xWPLD9qMfH4M4AacOKXI5Sm4SyE6Lw7N0LUbgiB99ZkYuuXjsMOjWAC2UQVS0diIpU4aHXj6O9y+7attl5zI//fhw/vW0e7w8KqENVrZiWNPJ7ypikR0mDBd29juEPJqJJi5niMDXW8Vm+Pga3dtux/UA1fn77fJQ2WLAw04Cl0xPZRDVJdPdK17bdzk8HnJu1OMsgZP8uhs6d6NxVmjrRaLFh7RIjlIq+HcWuNCbw/iC/OlrdiqvykkZ8vEalRGqMBqfrLJiXERvAlRFRKGOmOEwN1zQ1HF9NVVL2beZxqs6CzbvL8B//dwBVLR1+Xz+NP2/3zOY9pVi9KAPAhTII93vD2z1ittnx3N4ybN5dhnVbi3h/kF+12XrQ1N6F9DjtqF5nTIrC4erWwCyKiCYEBsVhariGJ4dD4kxDO/acqsen5SZUNPWVVzgcEhVN7Whq78LPbs/HhhU5SIvtC4J+uHIm9JFKPHbLXOjUCqTFathENYENLK8xWbu83jNCXCiDyDToICXw1O3zoVcr8cOVM6FR9d0LhStyPO4N5+t5f5A/nTzfhqyL2OwlKyEKR8+1BmZRRDQhsHwiTLk3TTk5M33eSis2rMhFbooeKqXAyfMWPLP7QoPVk7fNw6xUPU7UWlw1pM6P1rcVVbGJagLydg9sXJOPrAQtKk2druM0KgVmpERj3TIjoiIVg2YQP3LTHPzmq4vQ2N6Nh18/PqjsoqWjm/cH+dWJ823IiteN+nXGxCj8+dOqAKyIiCYKZorDVHZC1KDxWZvuXAClAiiqaB70Mfkzu0tRWt8OAeEKiJ3PPfjaMVi7HXioP+hxPr55TykevXmuq4lqLI19NL68lUo8sP0oHr15rsc9U7g8F0/uLMbm3WWobu4c9JpH3zyBNpvdFRA7H9+8pxR3FGSwyY787lh1K6YmjD4ozoyPwtkmK7p67QFYFRFNBMwUhymFQmDlnFTMLFyKBosNSXoNqlut2HmsDp09dq8fkyfpI1FU2eL1OWej1cDHu3sdrq19x9LYR+PLV3nN8Rqzq0luZmoMfvNeGWrNNlyTl4ioSJXX13R293p9fOHUOFyVl8z3n/yquNaCr2bFj/p16oi+sp7S+nbMTWezHVE4YqY4jCkUAsYkPRYbEyEEcKCyFc/sLoVDem+Qqmrp8PlcrDbC6+MpMZEAxt7YR+PLVyNlZ4/D1SR3/8uHsTQvGQDwjSXTcLap3etrdGrv98bF1H0SDaXH7kCFyYoMw+ia7JyyEqJwsrbNz6siookiKEGxEGKqEGKvEKJYCHFCCLGh//GfCyFOCSGOCiFeE0LEub3mh0KIMiHEaSHEF4Ox7onKV9mC8/HPK0w409gOR/8ore0HqlG43HPW8MOrZuOVomqvz/33TXPQ2tGFn9zi+dH6Y7fMRYxGBYdDciezEOZsnvy03IQ9p+pxpsH77nSFy3Px6sFq1+tsPQ7EaiNw3zU5MHf04OWiwffGY7fMxQsfl+PxWz3vjZ/elo+M2IsLXIh8OdtkRVJ05Ih3shsow6DFiRqzn1dFRBNFsMonegF8T0p5UAgRDeCAEOIdAO8A+KGUslcIsRHADwE8IISYDeDLAOYAmALgXSFEnpSSxV/D8FW2cP2sFLxdXI+Nu4pxV0EmunrtUPZPEag127B1f6XrY/Il0xMRpVGipaMbth6Hx3OXZsXjmd2nsWJWKj4rN+GXdy5Al92BM43t2PROCVo6urHpzgWYkRLNncxCkMMhsed0PUrr2z2aJ533yD++vRTFdW2ABH7+9inUmi/8EKNRKZCTpMejO07g8lvmoqWj23VvCAEoBDA9MQo/u30BpkRrkBClxqFzrbA7gF/uPg27dODW+emIiOAHVuQfxbVtmHoRTXZOWQlR+OeJOj+uiIgmkqD830hKWSulPNj/ewuAYgDpUsq3pZS9/YftB5DR//tbAPxVStklpTwLoAzAZeO97onIV9nCwaoW3P/yYazKT8fmPaXYe6oB8zJi8fCq2a7A+Pl95chJ0mNRpgFR6gg8vGo2shK0WL0oA0oFMCs1Bs/sPo3LjUl4ZncpZqfH4dj5Njyw/Sg27y5z1Rnf//JhKBXwyDxmJWix5Z4C1LfZ2HQXRBUmK45Wmwc1Tzp3pxMC+P4rR/DEzmKsWzYdWQla3HdNDgpX5ODpOxfg1++VYlV+Ov647ywevXkOWjq68erB6r6AOEmPaK0K2QlRON1owX/8+SA27y7Dc3vLUGnqxEOvH8eJWu9ZOTZl0sUoqbNgSuzF/6CdFa/D6ToLpOT9RhSOgt5oJ4TIBrAQwKcDnvpXANv6f5+OviDZqbr/MW/nWwdgHQBkZmb6c6kTkq+yhbMmq2vGrEGnxsq5aVj/0iEYdGqsW2bE9CQ9Gi02/OKd04hQKmDQqWB3OLBu2XQ8tuOkx2gtheLCvFrn+Qder67N5mrsa7Z2oabVhnVbiyZ9012o34/1bTZEKBRe37P6Npvr97Vm25Dv/96SJgDAH75RgJoWGx5+47jHe6tRCe/3hdmG+VM918SmTLpYxXUW5I+hSS5Gq4JKKVBrtmHKKDf/IKKJL6ifWwoh9AC2A/iOlLLN7fEfoa/E4s/Oh7y83OuP8lLKLVLKAillQVLSyLf5nKx8NUy5Nz/dUZCBzXtKXcHP5t1leGD7UbR09KLS1DdmS6eOQLwu0hUQARdGa02J07l2s3Oef+D1kqM1rsa++KhIPLD9aFg03YX6/ZgSo4ExKcrHPaL0uH8MQ7z/QF9gvL+82RUQO4+5/+XDiNGovV4j1UtWj02ZdLFK6i3IMFx8+QTQN67ydJ3FTysioolkzJni/ma4rwHIdj+flLJwmNep0BcQ/1lK+arb418HsArACnnhM6xqAO75pAwA58e69nCQnRCFZ+9eiKPVZjgkoBRAvE6N331wxrW5xvprcn3uVJYWq8HqRRmob+uEUuk921dlsmLDily8+Ekl1BECj90yF8/u7ftY3Vl3nOn2P6qhmu6MSfrA/WHQINkJUShraMcPV86EqaMbDgno1UrkpOhxvtWGvOQIPHv3Qqx/6RDONll9vv/AhRpjb8f02B14/Na5rlnWGpUCj986F3PSBmf1eH/QxejstqPB0oWU2MgxnSfdoEVxXRuumZnsp5UR0UThj/KJnegrbTgGwDHMsQAAIYQA8DyAYinlJrfHVwJ4AMBVUsoOt5f8HcBLQohN6Gu0ywXwmR/WHha6eyW2fFDuCka+e20eGtv7mqLuKMjA1Hit1ya4KLUS9yzOcmWRN6zI8XpcQbYB1q5e3FGQAbsDeOfkeRSuyMOPXjvm9ePvoXbTo/GlUAjkJutRYbJ63CPOH3JaOrrxizsWYNeGpWi0dHl93+ZPjcPG1fPQ3NGN7MQor8ekxGhwaVY8cpP1qDPbkBqrwZy0WK9Ndrw/6GKcaWzHlFgNIhRj+wA0w6DDyfMcy0YUjsRYGwqEEAellItG+ZolAD6EZyD9IIDNACIBmPof2y+l/Pf+1/wIfXXGvegrt3hruOsUFBTIoqKi0Sxt0ilvbMcNmz/0CDCyErT43vUzUdZgwaVZ8bg8Ox7vnm7Axl3FuOOSqUiKjnQFJt/44+eu16bFavC1K7I8phT89LZ5iIqMQOFfD7mOu++aHDy/r3xQULOzcCmMSfrJWDM6okWH2v3ocEhUmKxo7ejGeyWNcPaybT9QjZaObqxdYsRze8ugUSmwbd1i9NolPqto9nj/N6zIBQA8s7sUG9fk44szU7C/shkHq1rgkMCbR2rwwMpZo3pvJ+H9EQwj/YOaNB1lrx+qwSsHzmH9NbljOk95Yzv+9HEF3rn/Kj+tjDDy+5EoqPyRKd4qhPgWgB0AupwPSimbfb1ASrkP3v+S7BziNU8AeGIM6wxLAz+KTovV4K6CTPzn3454BBzXzkhGj93hqvV1ziY26NSuMVy1Zhte/KQSL3zzMjikRI9d4uE3juGm+eke1xDCe7Od8+PvgbvpJUdrkM2NHMaVM/DcuKtvqoR7lrhweS627q/0aJzcfaoBDtkXMDtHrkkJvPhJJb5zbS7WLjHCmKjDjhO1HiUST9w2D9fOGN2udbw/6GKU1FuQ5ofZ1+kGLSqbO9Bjd0Cl5LhAonDij6C4G8DPAfwIF7IOEoDRD+emMXI21DmD1NWLLjTVAReamLatWzyo+e2xHSfx1O3zcaq+r+nEmUFM1PfV7P3rC5/hjkumIqu/brnZ2oW2zl4k6SOxYUUOXi6qdgXUAz/+djbdsUY0OKqarThV14bvXz8TP+j/AQm40Dy3bpkR9v6fazQqBeyOvh92Wjq68dzeMlet+R0FGdCpI7DjaA2umZHkCoid5/rRa8eQnaBDd68DKTEjD255f9BoldRbMNtLjfpoRUYokahXo9JkRU5ytB9WRkQThT+C4vsB5Egpm/xwLvKzbrsdhctzXYGwUuE9i+ucKTzw8ZIGC57dU+b6qDxKrcRZUzsiFAJ3X5aFp98tga3HgawELf79qhw8u/eU17rUTXcuQHZC1Hh+6+SDwyFxsKoVWz4ox71LjV7f98x4HX7xdolH5jhJr8Yjq+bgNx+U4a6CTNc95Wyaa7Z2eW/Ea+7Az3addt0HLIOgQChraMd1s1P9cq6pBh1O17UzKCYKM/74bOgEgI5hj6KgSIiKxLaiKqxdYsT65TnITY72OhorUR/p9XFnttDW48Azu0vRZuvF+pcOQSGEKyAGgFX56Xj0zRMeWcJndpfil3ctwM7CpQyEQkiFyYoH+5sgAe8j9KLUEVhzSQZ+fvt8bCuqQq3ZhqV5yfjNB2X43vUzB33a8NDrx5EQ5f0eOttkxepFGRytRgHTY3fgfKsNqTH+acacEqtBST2b7YjCjT+CYjuAw0KI3wohNjt/+eG8NEYOh4RCABtW5OH5feV4dk8Znnr7FB5ZNccVvGhUCvzk5jmIUABP3jYPGpUCabEaFK7IwU9Xz8O89Bjkp8cA6At+bL2O/s04PLOCvuqIJaSrjpjGz1A7wrnXmW8/UI3C5bkeOw0+d/cinGlsBwC88HE57rum73khgEpTJ0rqLV7f6/auHjx2y1yPe+u71+ZBq1Ii06DF+uU5MOjUaLDYQORPVc0dSNSrofbTluHpBh1OcVYxUdjxR/nE6/2/KIS4d/A7d6nLS4nG1DgtHvvHCXz/+jwk6jUob2rH0++WoqWjGz+/fT7+e9UsKBRK/PjvF5qlHlk1B/isEiUN7dBEKKBRKRCt8axVBsAxWiFiuOkNydEXRp7Vmm3Yur8S65YZcUlmHKpbbbjvpYMezZYKOPC//7IIaqUCv3cLeAe+1weqWvFKUTXWLTMi06BDa2c3VAoFfrrLs6TGX9k8Iqeyhna/7kCXYdDiH8dq/XY+IpoYxvxjtZTyBW+//LE4GtpQ2UD3XcGcu9R9/5UjiNWp8O9X5yAvJRrlTe2uMVy2Hgd+8LcjyE6KdgXEzscf3XEC3//iDDz4pZlQKwU2rMhFol6N+6/Lc2UF3zxSg0du8sxAs444OIbbEU4pJJ6+cwEKV+Rg/fIcqCMEtCol4rTqQTvWPbbjJKI1ahw61wpdpBIb18zDm0dqPLLLzmD3lf7Gys27y/DQG8eRHKN1BcTO8z2zu9RVkkPkL2ca273ujnixpsRpUdPaie5e3qxE4cQfO9qtAvAYgKz+8wkAUkoZM9Zzk2/DZQN97QrW1N6F7l6J9S8dGDSCq9Zs8/m6osoWRKkjkBqjwf/sOo0FU+Nw/ewULJwah9bOHsRoVEiNjcQ/vr0Uje0coxVMQ+0IlxGrxeeVra6tmJ3Z4G2fVSHDoPP6uhO1bdi8uwxbPijHAytn4qer56Gtsxd/+MalKD7fhmmJUfjR68ddk0acr3M4pNfzNbbbMD2ZUyXIf8rq2/0yjs1JpVQgOToSFSYr8lLYbEcULvxRgPVLAF8HkCCljJFSRjMgDrzhsoHOzTfcaVQKqJSKQa/bvKcUqxdlQKNSwKBT+Wy4e/rdEgiFAi0d3X3jtRL1uHRaAq6bnYrLjQnIStBjerIei42JrCMOIl/vfXK0BkfPm10BMXAhG3z1zGQI4b3pzr3ZcuOuU/iorBn//n8HcffvPsXP3z6Njh47Wjq6B71OqRA+10HkT2UNfbvZ+VOGQYuSetYVE4UTf9QUnwNwXI51azwalaGygcYkPTINOmy5pwBFlc3QqZWQsm/MkK3H4bEhh/N1SgVQuDwXf9x3Fo+smoNHd5wYlEm29ThQZbLiydvmQSH6G/kUwrUzWn2bbVSzaCkwshOisOnOBa568jsKMpCXHA0pgQaL9/sm06DDlvfP4PFb53psvuF8792PVSr6NoG5oyADmfE66FRK/OiGWXhiZ7FH7fDvPjiDB780E03WbjgkoBTAvIxYltSQX0nZ9+9Pmh9rigEgLVaLkjoLkO/X0xJRCPNHUPyfAHYKId6H5452m/xwbvLBmQ301tjmcEi8XVzvCooGbs3snB/svrHGJVkG/PiN46g0dcJk7cZv77kEBypbYHfAVVqhUSmQnRCFJ3YWu2bOXj8rxXUtbskbGpw7ws3esBQHq1pd49c0KgV++9VLvN43dW02lDS0Y2ZqNNYtM8IhgRkp0Xjq7VMeP0BpVApcPysFmfFReOj1C+d98rZ5+Nu/XwGLrW/zFluvHTNT9TB32vHkW6c87g0if2q2dkMCiNH4439nF6THaTmBgijM+KN84gn0zSnWAIh2+0UB5MwGemtscy+tWL0owxUQAxeane4oyHCNXtu4Jh92uwPfu34GNqzIQWN7N378xnGkxWjx/L5yV0D82C1zsf3AOdSabTDo1DhV14ZPzpqGLOOg4FAoBBwSHvOIbT0O/Pjvx/Hwqtke981jt8xFlFqJ391TgLykaExP0mP/mUbo1AqsvyYXWQla3HdNDgpX5OC3X70EUZERroDYed4HXzsGnToCV0xPRE5KNOamxyErQY//evVoyN8bQzWsUugrb7IiPU4LIfz7Q3iGQYvShna/npOIQps/frSOl1Je74fz0Cg4s4EzC5eiweLZ2OZeWuFrfvDc9FikxGhc0wacH5W/frgG316eA3NnDz4/24Tn7l6EI9WtsDuAZ/eW4t+X5QAALp2WgM17SuGQ3s/vLOOg4PFWYlNp6oTd4cCmOxegvLEdxiQ9Nu4qRqWp0/WDVU5yFO68NAv3vXQIecl6rFs23eM+efK2eV5LcAa+58OV+ISC4RpWKfSVN7Yjzc/1xEBf+URNS98ECn/NPyai0OaPv+nvCiEYFAeBQiFgTBrc2Daw0cpbs1N3f4PVwIa7Vfnp+MmOk2jvsuPqWam476WD2Ly7DM/tLUOlqROP7jiBbyyZ5rGjGZupQpOvhrt4XSTuf/kwOvszt5WmTgAXMrkdXXb8uL8Zb2le8qD75MHXjuGOgoxB5x34ng/V8BcqhmtYpdB3psEakHtKHaFAckwk7wWiMOKPoPg+ALuEEJ1CiDYhhEUIwf0xg8i9tGL7gWpsWOE5U/bJ2+ahvMnqNYvnzCwLAXR293o9prWjx+eOaJxPHDoyDTpsXJM/6L1xf4+9vb/1lq5hP2nIS4ke9j0fqsQnVAyVzaaJoayxHWlxgflBKz2OEyiIwsmYyyeklEPWDwsh5kgpT4z1OjRyA0srUmM0uH52qmt+sEIAlSar14YrKfv+OzMlGknRkV6PSY3xviPavPRYTE/Sc/pECHA2W2565zTWLjFCqQAKsuJxpTEBlc0dHoHqwPc3bUATp7djZqXGYKeX0h13Q5X4hIqhGlZpYihvbMcX56QG5NxT4jiBgiicjEeh1NaBDwghpgoh9gohioUQJ4QQG/ofv6P/a4cQomDAa34ohCgTQpwWQnxxHNY9oTgcEmca2rHnVD0+LTehqtmK7IQoLDYmIjuxb37wZdkJAIDG9i7MSosZlEEuXJ6LHUdr8ORt86BVK9Da0YXHbpk7qClLqZB44rZ5rsdbOrqRGa/DNXnJrkY/96YlNjKNP2dZQKWpE8/tLcN7pxrQ1tmDt4vr0G3vxcbV+V53pnv81nmI0Spc7/sHpxsGNeZtunMBpiVGeS3dGchXiY8/jOa+8nWsr2z6cNls3tOhodfuwPlWW8C2DucECqLw4t8ZNt55+79gL4DvSSkPCiGiARwQQrwD4DiA1QB+63ECIWYD+DKAOQCmoK+OOU9KaQ/s0icGb81CG1bkIjdFj+UzUlyzhN2PKciKxXeuzcNTt8+HrdeOKHUEeh0OfP2KbAgB3PfSIddxf/zGpTB39iBWq8Iv3j6FokozshK0ePrOBeixO6BWKqCN7AsqvDUtqSME1vefj41M48O9LCA/PQZfuSwL3//bEdeIvt3FdXhg5SxUN1ux6Y756Op14KzJihc/PosvzUvD7uI6PHf3QjRbe/Ds3lJXtnlhpgFLpycG/b0bTYOcr2Od4wS9ZdOH+v7YnBc6alo7YYhSBawRLsOgxY6j5wNybiIKPeMRFA9KoUgpawHU9v/eIoQoBpAupXwHgLfROrcA+KuUsgvAWSFEGYDLAHwSyIVPFN6ahZ7ZXYp1y4wwJuphTNIPOuZyYxLuffHAoI+Nf3b7fPzn3464Hi+qNOObf/oc29Ytxl1b9rserzR14rsvH8a6ZUbYHcDz+8qxbd1ir01L65YZBz02s3BpyEwgmIzcywLuXTbd9Z46R/StXWJ0vVf3XZOD5/eVu37vHOF3sMrsevy5vWUA+u6RnSHw3vlqkPN2X/k61v1+Hc33N5prU2CVN1kxxY/bOw80JU6L82YbunrtiIxQBuw6RBQagj5nRgiRDWAhgE+HOCwdfTvnOVX3P+btfOuEEEVCiKLGxka/rTOU+WoWSo/taxI5cq4VFaZ23LvU6Bpd5KuBamBzXVqsBmuXGFFv6cLPb5+P+6/Lw/rlOUiL1cDW44BDXjhXrdn7OgZ+shxOjUzBuh/dm9y6e+2DGufc338hAINOjfuuyUGmQeu6T3zdI83WrqCXDoymQc7Xsb7u1+HuTTbnhY6zjVYkx0QG7PwqpQIpMZEob+QECqJwMB6Z4m5fTwgh9AC2A/iOlHKoiRXePpP0+n9iKeUWAFsAoKCgICwK/Xw1C9WYO/HAq8dc9cJvHqnBPYuzXNv2enuNTh3hejwtVoN7FmdhW1EVotRK1xg25/m2FVVBIQC7o79BK1br9ZwDP1EOp0amYN2P7rvaVZg6BjXOOf9r63FAH6kctOth4fJcSMhB72dWghY1rTZ89fnPglo6MJoGOV/HpsVeXJMdm/NCx5nGdqQEqJ7YaapBh5J6C2alxQT0OkQUfH7JFAsh0oUQVwohljl/OZ+TUi728RoV+gLiP0spXx3mEtUAprp9nQEg7Au9nM0+JmsXfjagWej+6/KgVSnxk1tm47f3XILkmEj8z+p8GJN0eOLWuUiNVuOJ2+Z57Fb29J0L8OaRc3jkpjnQqBRYvSjDNbvYfS6xc6bx47fOQ0asBjuO1mDTnQswJy3G6wiu/IzYkB7LNVk5d7V75O/HUbi8b2e6KLUSj9w0B/vPNOJXX16IZ748H/Mz4tDZY3dliJ3vb05ytJfd7+bhge2+d6kbrwa00Yx789VMNyct9qJGxk2EUXPh4kxjO9ICWD4B9JVQnGazHVFYGHOmWAixEcBdAE4CcDa+SQAfDPEaAeB5AMVSyk0juMzfAbwkhNiEvka7XACfjWXdE93AZp+sBC1+//UC9PTvvlRW3443T9RgzaJM/NvWA66s3iOr5mD7wXKsmJUKY3IU7r92Bh7o34pXo1Lgx6tm4+3jtVi7xIhMg3bIebafVzQjOyEKL3zzMmTGR/kcwQVg2PFdFBj1bTZUmjqx63gt1i2bji0fnMF9V03Hmksy8fjOk7irIBMPbD/mkSHeur8StWYbTpw345WiaqxbZkSmQYfMBB3sDumzdCA7IWrcGtBGOu5tqNF0ERGKixoZNxFGzYWLiqYOfOXSwGaKMwxaHDnXGtBrEFFo8Eem+FYAM6SUN0gpb+r/dfMwr/kCgHsALBdCHO7/dYMQ4jYhRDWAKwD8QwjxTwDon3P8MvoC710A7gv3yRMDm30qTZ2494UiZCVEQR8ZgZ/uOoWvXWnEoztOeGT1Ht1xAl+70ohndpeiub3XFRA7n//JjpOYnR6H5/aW4by50yMb5k6jUsDuAB587RgcEq6AwNsIrkCO5aKhOT/qd+5Mtyo/HdVmGx5984TPTwBWL8pwvb+1Zhs27y7DQ28cR2SEYshd6sZ7d7iR3FcDR9Nt3l2GdVuLUNXSMeJzXOy1KbBsPXY0d3QjUR+4mmKg75OG0/XtAb0GEYUGfwTF5QBUo3mBlHKflFJIKfOllAv6f+2UUr4mpcyQUkZKKVOklF90e80TUsrpUsoZUsq3/LDuCW2oZp+O7r7Gqs4u7zvSOZvprD6eF6Iv0JmX0ffxsrd5toXLc/HqweqANhhxFuzYOT/qVyouvLcOOfSOdkoFXO+v++Md3fYhSwdCsQFtNGvi/TaxVJisSIvRBPwHkpQYDZqtXWjv6g3odYgo+C66fEII8Sv0lUl0ADgshNgNoMv5vJSycOzLI1+Ga/bRqBTQRUZ4PUbb30wXpfH+/NKcRKxemO4qfZiZGo1maxf+b+3l2F9uQmePw/URe6AajDgL1j+cH/Wnx2mx5YNyAIBSDG62c3K+/9//2xHUmm0ejydHa4YsHQjFBrSRron328RT3mhFamzg7y2FQmCqQYfTdRZckmXw67mllNhX1oQj51qRkxyN62anQMn7jShoxpIpLgJwAH31vo8B+Lj/6wP9z1EADZWxcz73wsfleGTVHI9jHlk1By9+XI4NK3LR0dWD716b5/H8xjX5uDQ7flDpQ0F2AhZlGmBM0uP5feWugHi4BqOLzb6N90fxk5lCITAv/ULWP16nxv3X5Xn9BGDTnQuQHBOJL1+a6fH4hhW5UCounM9b6UAoNqANtybn/fl5RTPvtwnmbJMVKQEcx+Yuw+D/Zjtbjx3/tvUAfvTacZTUW/D/2Tvz8Cirs/9/zmSbTPY9ISGBkLAFAsSI2AKtpFpqsW6gra22FV/evlWhtfraWpefa2u1tKK2lYr7awXFlSrVAi1QQQ3IviUEEhKyk30ymWTm/P6YPMNM5pmQkGWynM915UryrGfmuc+ZM/e57++98pOjXP/cDhpa2/v1PgqFouect6dYSvkygBBihZTyKdd9WtlmxcBxrmSfhVmJTE4Mo7HVymtLL6KmuY3Y0CBsdht3fXMK/gbBbX/7EoClc9MRAqSE5Ejvy5G9TTDqi/etu2VvVSCh9zifXafX3xjgx8yxkbRaO3jlx7NpsXaQGh3C+NgQPjtRyys7it3s4pUdxcxKjWRcrPf3figmoHXXJlf7vGVeurK3YUZBVROJ4QOrPKGREmXi4OmGfruelJJfrNtDo6WdR6+ahr+fAbuUvLazmFte/oK//dcc/P36RRxKoVD0gv7QKf4h8FSXbT/S2aboZzSPnd6HtrbPG0XVzdSZrR7VvK7N0a2J0qN7dqUvlb+G4lL8cKenzy4h3Eid2eq0C+j5e98b+xgsvLWpq30qextenKhuYUZy5KDcKy3GxIZ95f12vbd2lXKovIn/d0WWc/JrEIIfzEnjd/84yp//dZzb8zL77X4KhaJnnPdXUSHE94QQHwDjhRDvu/xsAWr7r4mK7jjf8ITBWOr25u0trm3hi5O17D1V57XdQ3EpfrQwnN77viTHudrn+l2lHqEkj1w1nboWKydrVNLdUORkrXlQYooB0qJDOFbZ1C920NDazmMfHua/5qUT6O/+EWwQgqVfHc9ftxVRVt/a53spFIre0RdP8adAORAL/N5lexOwry+NUvSMvoQnDMZStzdv75GKJqTErUJe13YPxaX40cJwee/7mhznap/lDRZe3VnMsvnpTEkM53BFI7//+Ch1Zisr8jLJTAhlwaSEIfcejFbqzVY6bHYignslfHTehBr9CQnyp+SMmXGxffty+Jd/HScnNYrxXq4TFxbEN6Yk8IePj/HkdTP6dC+FQtE7zttTLKUsllL+S0p5sZTy3y4/u6WUSrtmEOhrMtpAa63qeRxXdC4JdtXH1Wu30oL1HcPhve+r/Xe1zzqzlQlxofx242FWbSqkvMHhSX5qUwH7ShtU0t0QoqimheSoYBx1oAaH8bEhHCpv7NM16s1W/u+zYq6c2X2Y2remJ/HxoQrlLVYoBpn+qGjXhEOazZUGHAoUv5BSFvX1Hgp9hnoyWlePo0Dws7V7uPaClCHdbsXwoK/2r+cRr21po7jWfSJiabdjlyj7HEIUVbeQGD648d6p0Sb2ldZz+fSk877GqzuKuSAtiriw7lUzQoP8mT8xjhf/c4J7vz31vO+nUCh6R38k2q0ETgOvAwL4LpAIHAVeAL7eD/dQ6JAQbiQtJphF2cloDpMP9pYNWHKQ3S45WdtCZaOFhHAjqVEmSurMzv+1mNMTNS0Un2khJNCfhPAgxsWEkB4X6kzuA5XUNJTp+pyHYugE9CwZ81yvRfOIj4sJ4WRtC02WDu751iSsNomlw3HdD/aWYRAo+xxCFFU3kzDIk+LxMSH853jNeZ/fbrPz8o6T3PXNyT06/htTEvh/7x/kzssmYQzwO+/7KhSKntMfk+KFUsqLXP5fLYTYKaV8SAhxTz9cX+GF1CgTty/I5N53DzhjKh+5ahqpUaZ+v5de/OYjV03j6c0FFNe2OuM5A/0Ft73+pfMY13hMbbn68Y2HWb4g0yOmeCgmco02hlMRC82eurbVVYO4J6/F9bgoUyA3XZzGM1sKnec8cEUW0SEBA9KvFOfH8epmJiaEDeo9x8WGsHpbEVLK8wrb+MfBChLDjaRG98yOEsKNTIgLZeOBCq6a1X24hUKh6B/6QwjRLoS4Tghh6Py5zmWfStkeQErqzM4JMTiWee999wAldeZ+v5de/Oa97x5gUXay8/871u1hX2mD2zGu8ZjacvWLP5rN7PFRrF02h7/910V8uHzekJx0jUaGU9EUzZ4+XD6PN5Z52lFPX4vrcdfkpPDUJvd49wc/OEhRdcuA9CvF+XG8uoWkiMHRKNaIDgkkwE9w6sz5xfm+uqOYSybH9+qceZmxvP55yXndT6FQ9J7+8BR/H4cm8Z9wTIJ3Aj8QQgQDt/XD9UcU/bk0rcVUJkUYuSYnxRlCcaalzS32sT/u6S1+U7un1obkiGBuW5DB+l2lzkQl13jMoahjqzjLUI9Td8Vul5ScaaG6qQ2z1YaU7rbe2m4jyhTo1jfW7yr1eC2ur1kIdF9/i9U2JN+D0YjdLjl1xkzSIMmxuZIRH8qe0npSY3q3alBc28KRiiZuvSSjV+flpEXxwn9OcLq+lTGRg/slQKEYjfR5UtyZSHeFl93b+3r9kUR/L01rMcXX56a6hSJkxoeSY5ceVbv6ck9v8ZtSOibEN85Jc2vD8gWZvLqzmDqzVcVjDiOGS9EUu12y+WglBZXNTs9u15Cee741iZsuTnPbvyIv0yNBq+tr1nv9yoaHDmX1rYQZ/X0SZzs+NoTdxXV8Z8aYXp237otTfDUjhoBeVqkL8DMwe3w07+0p43++3rsJtUKh6D19Dp8QQsQJIe4RQqwWQryg/fRH40Ya/b00PS4mhIevnM6qzQVEmQK59ZIMbpmXTlF1MyVnWvr1nnryao9cNY0N+8q4JifFQ2Jt1eYCluSm8MAVWUwbE0FzWwdfnKzVLbDQlwIMiv5luBTuOFnbwr7SBo9Qh3vfPcBDV07j8WumM2VMhMf+pzYV0GBud7Ox1CgTj1+bjTHAwPpdpazIcy/isSIvk+yUCI/3QNmtbyiqafGZ1zQzPoz8k2d6dY7NLnlzVynzM+PO654XjY/h/b2nz+tchULRO/ojfOI9YBvwT8DWD9cbsfT30rTBIAjwE0SZAj08tWkxIaRGh/TbPfXkq1KjTOSkRnGsskn3HhMTwnjiH0eciXjLF2SyNr+EuxdOcXqqh1Ni12hguBTuqGy04G8w6NrdruI6Vm0qZHlehu7+TUerKGuwsDArEYCPD1ey8pOjLJ2bjp8BZo6N5IPb5lJaZ8bUqaCSGh3iNTlP2e3gUlTdTNIgK09oTIgL5Xh1C61WG8GBPfNUf3q8hvDgANLO84vllKRwyv9lobi25byvoVAoekZ/JNqZpJR3SynXSSnXaz/9cN0Rh7ZM60pfl6YTwo0syfX01N7zzn5O1rb06z27FnTw9zeQHhfKxIQw3Xscq2xyar5q3uNF2clunurhlNg1WhgOhTsSwo2kx4Xo2p2tcx5sl3jdr9mYZn/Fta08u6WQVZsK+fFLX+BnEFwyOYGL0mMYF+v5Hii79R2FVc0k+CCeGCDQ38C4GBNfnqrr8TlrvzjF3IzY876nn0Fw4bhoPjpQcd7XUCgUPaM/JsUbhBCX9+YEIcRYIcQWIcRhIcRBIcSKzu3RQohPhBAFnb+jXM75lRCiUAhxVAjxzX5o96DTX0vTrsu2UsKkhDBdj1hlo2VAl8O1dtS2tPHY1dPd7nHfoqm8mV/q0SYtkamqyQJ07z1XKLwxLiaEQD/H6oOr3S1fkMnbux12t35Xqdf9mo11Z3/dhUcou/UdhVXNjBlk5QlXJiaGseN4bY+ObWht519Hq/nKhJg+3TM3LYqP9pf36RoKheLc9Ef4xArgHiGEFbDiKOAhpZTh3ZzTgaPa3W4hRBiwSwjxCfAjYJOU8rdCiF8CvwTuFkJMxVEUJAsYA/xTCDFRSjmswjX6Y2lab9n2rzfm6iYHtdscH+IDsRzetR1pMcGs+WEun504g80OTZZ2Z6EO1zZJ6e6pHi6JXYqhhcEgmBAXyqMfHmLp3HSC/A3MGhvJve/tp7zBMTEtb7CwNr+EV2+ezbbCGmx2eHVnMeUNFowBBmJDgpx/d7W/uFBjt+ERym59x4maFr5/ke/e56lJ4Xx0oIJfXDbpnMdu2Hea6cnhhBkD+nzPpzcXUtVoId5HoSMKxWigz55iKWWYlNIgpTRKKcM7/+9uQoyUslxKubvz7ybgMJAMXAm83HnYy8BVnX9fCbwhpWyTUp4ACoHZfW27L/C2NG23S07WNPNZUS2bj1RyvKqZjg67h6dKVy/4vf38poundvmCTO57b79TH/h8l8M1b9kXJ2vZe6rO2ZaSM+7tKK5t5Z539pMQbmTN9iJe/rTYI2Fp+YJMNuwrc/NUD5fELkX/oOd97bpNz+71GB8bwt0Lp7BmexFtHY5+cH1uqrvN5U0kLiyI4AA/1mwvck6CV+RlYumwce97+z28yY9fm42fAd3wiBM1Lc7VES05TztP2e3A09LWQUNrOzGh3ZdJHkgmJYZxtKKJJkv7OY99/bMS5k88vwQ7V/z9DMwcG8mmI1V9vpZCofBOnz3FwlHa5/vAeCnlw0KIsUCSlPLzHp4/DpgFfAYkSCnLwTFxFkJoSufJOPSPNUo7t+ldbxmwDCA1NbX3L8gH9EReSvvQjTIFeCzbFte2Ygr047ZLMrB02JHyrEesL9qqmjf48Y2HPWTfHrt6OlGmQKdXTmtHk6WdpXPTnbqwr948mw67xBToR7vNzsJpiW6e6uGS2HW+DEd7HCi8Jad1rYKoZ/d6CWyutnOssolntxTy6s5ip/1JCeHB/pyut/DKDvftr+woZkJcKMW1rR7nJEcanRrbrlja7RyuaOTON/c6V0dW35hLgJ8Y0uWwRxJF1Q7lCcN5VJTrL4L8/ZicFMa2ghoun57k9biDpxuoarSQnRzZL/edOTaSfxyo4HuzR/c4olAMJP0RU/wn4GLghs7/m4Fne3KiECIUWA/8TErZ2N2hOtt03UdSytVSylwpZW5cXN+/oQ8G3clLda0YZwr0100eOljeiNVm55nNhTy7pdDpEevLcq7mlV6UnaybyLckN8WjHU0WG89uKeSZzYU8tamAmNAgLp4Qy4yxUeSOi9H1VA+HxK7zZTja40DhLTmtaxVEPbv3lsCm2Y6W7FneYHHa35rtRewvbSDI30Cd2erc/uyWQurMVqJDAnXPiQ4J8pqg6qq0UlzbyrJX8zuT/kaW3Q5Vjlc3kzwEiljMTInk44PdJ7690lnBrr/sYsbYSD4/eQZL+7CKGlQohhX9EVN8kZQyRwjxJYCUsk4IEXiuk4QQATgmxP8npXy7c3OlECKp00ucBGhrRaXAWJfTU4BhIdzYk2pylY0W7FK/klZqdDBJEWc9V+02G49dPZ173tnvUSjj3kVTWJ6XgV2Cn4DpOtqqvWmblkzkrcqXNhGJMgXy46+kMTExnJrmNu765kTW5Z/ijksnUdvSBqC8aAqvyWldoyMs7XbCjH7cekmGR5VGbzY7LibEo1/8auFkmto6qGyy8IfrZvLbjYfd5AElktU35pJffAa7hJ3Hq1me57DZID8DTy6eQUFVE+vyS6kzW3ns6uk88Y+jHm3VVmP6s1qlQp/CqmYSwn0XOqGROy6aX729D0u7TbeISL3Zyt/3lfO7xdn9ds/QIH/S40L49HgNCyYn9Nt1FQrFWfpjUtwuhPCj03MrhIgD7N2d0BlysQY4LKVc6bLrfeCHwG87f7/nsv11IcRKHIl2mUCPwjN8SU+1TBPCjYQG+ukm7pxpsXLjnDRndbjokCBiQ4NYNj8du8QZKlFnthIWFMDqrUVu9+pL21y9ZXptm5IYzsYV8zh4upGSM2Z+8tout/CKV3ecIL+4QWm4KgDvSZVdTSItJpgwYwB//Kd7lcaZHXY+Plzp1WZzUiOd/SIk0A9Lh51nthQ6j71v0VSaLO00WWyszS9hWnIEy17Nd4ZC3HaJIw5fL1QoJzUSQDd5ND7MqHSLB4ljVU1MSgjzdTOIDglkXEwIW45U8S2dEIpXPi0md1wUUaZz+od6xYyUSDYdrlKTYoVigOiP8IlVwDtAvBDiURylnR87xzlfBW4EFggh9nT+XI5jMnypEKIAuLTzf6SUB4F1wCFgI3DrcFCe6KmW6biYEGaMjdStpAU4q8NpiTyp0SFMTgzn+W1FzqXgx6/N5r739rtVtjta0UhBVQN7S+rYeKCcvafq6eiwd9u2L06ecSY3aUlwH+wt80hGWnndTMbHhmCXcLSyySP045539nNRuiNcYGK8w4u28UA5u06e4cuSM6oC2ChkXEyIR3Laz78xkdjOMAZt2/+7IouHNxxys6e71+/jYHmDrs2WnHEkv5U3WLgwLZoP9pbR3GbjD/885nbswxsOMT4mlClJYdxz+RQOnW5gYnwot16SwZ2XTeaZLQX84rLJHhUiizv7a2q0Z1LoY1dPxyDwSDxVusUDw/GqZpJ8KMfmyryJcbz06UmP7Y2Wdl74zwmuyO5dKeieMCMlks1HqpBSjZ0KxUDQZ0+xlPL/hBC7gDwcsb9XSSkPn+Oc7ejHCdN5Hb1zHgUe7UtbB5ueVpPTPEl6yUDXXpCCpd3OrLGRfG3i2fi0rslptS1tWDukW2W7tJhgkiODuf/9g25JTFfNSPbatm2FNTy/rcjp5VqYlcjkxDDOtLSxdtkczFab29Jwd6EfQf4GspPD+d7sNO58a6+zDQ8symL97hJunjtBedJGEQaDYEyk0c3GtUnFyz+ejUQSH2akwkuSm17yW5QpkN0l9W5hE49fm01wgH61uyZLO09vKeD63FTW5pfwk/kZ/GVrIWHGVK7PTaWwqqnbCpELsxKZdPs8Dlc0cqyyiSf+cdQZWtE18bQv1SoVnnTY7Jyqa2VM5NCQJJszPpq1X5TwZUkds1Kdkvr88ZNj5KRFDkgp6pSoYGx2SWFVM5lDwGOuUIw0zntSLISIdvm3Cvib6z4pZe8KxI9AeqNlmhBudCYDuR6r6fqmdYlP1BKMXD9wu1a2W5Sd7JwQw9kkpsz4UK9tk/Ksl2vy8nnOe3j7YE8IN+In9MMrxsWGcMv8Cfxv54RYa8ODGw7yu8Uz3O6hGB3EhASxZnuRpy5wWJCbHejZU1KEp80uyU1xTojhrFd57bKLda9RUmd2Jo4unZvOgxsOsnRuOsmRJu56ay+3zEv3WiFy5thI0uNCEQKnAoXGPe/sZ9n8dFZtcu+/Sre4/yg5YyY6JJAg/56VVx5o/P0MLL5gLPe8s593fvpVjAF+/Kewhnf3nOaxq6cPyD2FEMwYG8mWo1VqUqxQDAB9CZ/YBeR3/tb+znf5e9TTGw1evWNddX0NAqdWcFfNYC3UYWL82cp2SRFGUqOCdb1lp+paMQic90uKMLI8L4OHr5yGKdDxf0+rc42LCWFiQphH6McjV00jwCAIMAjdNrRaO1QFsFFId33CtULib6721ACONAXw2NXTSYsJ5tZLMliel0FummfcpqXdTp25jUeu8tTufjO/lNToYG6Zl06Y0Y8oUyCTE8NobbdhabezflcpY6NM3Var87bKMi05guV5Gdy2IIMVeRk8c8MspVvcjxRWNZMyBJQnXJmXGUt0SCDff/4zHv/oCD/9v9389OsTiAjuW7GO7shOiWDTYaVXrFAMBOftKZZSju/JcUKIrM6Y4FFHbzR4XY+tbLQ4dX2/mZXIidpmfvji584l366JQFqow5SkcKcaxI1z0jjd0KrrLbNLWPjUNp65YRYfLZ/HrpJ67n3XXc1ibX5Jj71cMSGBlNWZeWLxDKwdNmJCg3jg/QMU17ayIi9Dtw3BndJyypM2uvDWJwCPCokrr5tJUXUzM1MjsbTb+OYftzExPpRl8yc4Y4612PtXdhQ7QxeMAQbMVjvmtnbdhNSSM62s2V7E/Yum8j9fS3d6iDV5tqom/Sp33VVhTIsJptVq63Giq6L3FFQ1kxgxtMYLgxD8z9cy2HqsmvKGVu779lSSowZ24j5tTAR/2nKc5rYOQoP6I1deoVBoiIEO2BdC7JZS5gzoTbyQm5sr8/OHjtNak2yqbWkj0M9AS5uNkCB/rDYbMSFBHhNmu12yv6ye61fvZOncdNZsL3L+7vqB/cZ/zcFqs1PRaMEgBE/844hHjLExwMCD38ni/3YWs6+sEWOAgbXL5rD8jS9ZlJ3slL/6YG8Zv702G6TD42yzQ1WTu8yU9lrK6s00W2y0ttsorm1hUkIYd7gsLSdFGLnp4jS3oiQjMKa4Ry9gqNnjYHIuubKi6mZ+/NLnHna4KDsZPwPOyeadl010KkpoGAMM/PG6mbTbJa3WDuLDg/hwXxl5U8dQ09zmNoHW5As1HW8t5CEpwujsK1GmQA+bdVWS0FOaWH1jLve9t9+j/S/+aLavwoN62qmGTcbWir99SUK4kUsmx5/74BHObz46zG2XZHBZVqKvm9JThv0grxgdDMbXTNUZ6L46nOaZvXvhFI8P3iMVjW5awXqawVGmQA6WN+p++LtW68oZG0lpvZl9ZY46KZZ2O7Utbbrt2X+qnhc/LdadHFw2JYGPD1fqvpbfXZvt1r7yBkc1sdU3XoDZaiM2NAh/A/xu8Uyl4zpK6IlcmTc7NBiguc0R2pAUYWRMpH5IUIu1g1+/e8Dty99jHx7C2iFZNj+dCXGhHKtsdk6ItfM0AZTyBouzr6RGB3OmxcqrN8/GJqXHCo+et9tb+zV9ZUXfOVbVxAVpUec+cBQwPTmCzUeqhtOkWKEYFvSHJNu5GDaeiIGku+pwqzYXsCg72U3CSTve3ploB56/NZbkpnhIWK3aXMA1OSnOal3PbytiT2k9lY1ndVaNAQbCjYG67UmMNHFNToqH1Nod6/Y4pbH0XovBIDzaV2e2EhEcwMJpSeSOi2ZmarSqADaK6Ik0oUDo2uGYSJMzkfOanBQC/Q26leaKz5jdzn3g/YMsyk6mvMHCqk2FFFU3s2Z7kZs6RFeN5PIGC2u2F1FyptVZjdFblcWuVRgD/Qy67Q/wG4whduRjt0tO1pgHPDRhuDAjJZJ/H6tW0mwKRT+jRuxB4lzV4YRweHyrm9rYcbyG6qY2okyBrN9VyvIFmU6tYD3N4NRo/cQg7fNYi7vMiA9lw74y57aV183E2mHXPfdkTYvXtmrSWHr7V//7OA99Z5pb+x6+chp2KZU28SilO2lCjTMtbbrHlNS2MD0lgpXXzcTPAKV1Zg/7v2/RVN7ML/U4V7jMY9fll3Lfoqlu5/368ilckBblTI5Liwl2Jrc+dvV0Z6xzR4edvac8tb5dMVttuu0/02J1S4hVnB9l9a2EBvljClQxtHBWmu14dbOvm6JQjCj6NMJ0VqZLkVKe6uYwazf7Rg3nqg5n9Ddw08Vp/PDFzz0SiF7dWcw1OSn4G+ChK6dRVNXMCz+6kN3FdUyICyXAT+hec3JCGL+7djqxoUEUVjUxfUwEL/5otluC04malm6rjHUnjaW3/1hVM7PHR7F22RzKGyxEBAfw+4+PqMp2o5ieSBMmhAfrHjMnPYacTg3Y5MhgNh+p5N09ZW5axy2Wdt1Kc65OtDqzlcbWdpbOTcfPAFljIiiubeG/Xz1bhfHhK6fR2t7BlTOTyUmNxGAQdHTYeXdvGfe6hGZoWt/+/md9Ct5e45en6lm1qVDZfh8pqGoiJVp5iTWc0mxHqsiIV9JsCkV/0SdPsXSs3bx7jmPm9OUewxVNXkrzEqVEBLP6xlzCg/w8PFb3LZrK2OhgLO02Lh4fzarvzeLBK7IYG23i1q+nO5d1I4MDMLfZGBMVjLRL0uNCCA3y5y//LtT1nj3+jyPUNFt5cMNBUqJDSIsJcVvyNRgEfgZ0K+kF+gnW7yr12LfyuplkJUU4K939auFkDxkqcHjO4kKD+OXb+8gvbgBUla/RSk+kCbOSwnnkKvcVhseuno5dSqe9ZCWFM2NsBMvmT2DN9iKe2VzImu1FpMWG8MfrZ7p5fB/6zjS3VRHtC+aa7UUkhBuRdsnKT9wr3t333gFqmq1MTgwnNdrRtoPlDc4JsXbcve8e4GB5wzlf44q8TKcHW9l+3zha0UzyEJNj8zXZyRH8U0mzKRT9Sn+sRe0UQlwopfyiH641IuiaWJQWE8ztCzKdH65pMcH85QcXEGAQWO2S/9cpX5YWE8xPv57hLHZhDDDw0JXTeOenjkIE+8ua+K2XRL2NB8rdvGdJEUGs+u4s2m12Fk5L9JrUpiXCda2kd+dlE7n2ghT8BDz/w1z8hHBTDViYlcjUpDB2l9Tzm41H3LxoP3zxc4prWz2y/UFV+RqN9ESa0N/fwHemjyE2NIgDZQ2kx4Xy+MbDTjtaed1MQoIMnKgx88qOk06Pb25aFEXVLfzWxQb/3xVZfLT/NFfOTCY1ykSjpZ0J8aHcMnc8abEhPLzhINfmjNUNd8gZG8l8l8qRelX0LO12KhoszBjr/TUKBD9bu0dVuOsnDpc3qklxF6YlR/CnfylpNoWiP+mPmOJLcEyMjwsh9gkh9gsh9vXDdYctXROLvnthKiVnzNwyL53bFmRg7ZD85LVdBAX48T+v7aK4tpWkCCO/uGwyD3SpQHf/ewcwCIG1Q3L/ewe8JurNmxjPs1sKz3rPokOZMTaKnFRH4cHPTtTqxjWaAv2dlfSe2VzIs1sKqTNbCQ7wQ0pobLPxxYkzJEUY3RKODAaBXeJRTezedx1tdG3bNTkpzvspbeLRSdfENMC5knK8qpmTNc1sL6rhy5I6AO5Yt4fi2lbgrJe1qdXGE/84SnFtK89uKWTVpkLyi+ucE2Lt2P/3wUGmJkeyalMh9753gNqWdv771V0khBu57fXdFNe2Mj42RDdhL9QY4DZZT4oI1j1OTy/X9TXGhQXphnQo2z8/jlU2kRJl8nUzhhTGAD8mJYbxn8IaXzdFoRgx9MfXy2/1wzVGFK6JRUkRRsKDA9xkzTTvaUXncZpGamFVk1evlMS7JJteUt2J2mbSok18fLiyWyksq83G8gWZHp5nm5ROPWRjgKPMdGq0u3fPWwKVa4JT17Z5q+inGD3oSbRp4Q11ZisPXznNq+xa1+126T1x1fVvS7sdm5TOY8vqzbp232Rxn8hqYR1dY4qzkiK6fY1aOEXXvqdsv/fY7JITNS2kKOUJD6YnR/DPQ5V8U0mzKRT9Qp8nxVLKYiHEXCBTSvmiECIOGNXrg65JN9fk6MulLZufTlLncdfkpLBqc4GzqlbXZB2HV0q4xSt2PWZifBi3Lchwhj/Uma2sXTZHVwpr8vJ5Tm9dTEgQa/NL3MIn1uaXcOXMZLfz7nlnPzPHRrot/XpLLnJNcDIGGMiID2N5XgZ5k+OZnhypEo1GOXoSbU9tKmDp3HSe3VJIaZ1Z165COqsgum7X5Nq82aD2tzHA4JaQ2txm44O9ZR52v+q7s9za6u9v4KoZyWTGh1LRYCExwkhWUoRbkp0evalmqeiek7UtRIcEYgzw83VThhyzUiN57MPDSCkRQtmWQtFX+hw+IYR4ALgb+FXnpgDgtb5edzjjmnTT1bObFGFk6dx0MuPDCA8O4InF2fgZHMdo8muuk99HrpqGzS6pbrbw2NXTdSXZHvpOFqX1ZtbvKuXZLYXOOMhTda3dSmHZ7RIp4a7LJuNvgPW7SlmzvYjbLsnUlbiqarK4JRAaBB7JRY9c5Z7gtHxBJr//+AiTE8PVhFgBOFYYokyB3HqJIzHutgUZRJkCnd5dPfm031w9naAAA8/fdAF3L5zkTOxMjjDy829MdDv2jksn8vbuUqf9bdjn6DMvbC9yJvOt31XKdy9MdUvYu31Bpq4H2GAQhBkDCA8OIKwzvKJrIq0WluQq37a/rIHUKJNXrWNFzzha0URqtAqd0MMR3uPHgc6CTAqFom/0R/jE1cAsYDeAlPK0EGJUa8S4eomqm9t4fluRW5iE65Lt75fM5OsT41i9tcitqpafAeZmxFJW38oNz3/mTNC7f1EWZfWtPLl4BhJJaV0rf/hnAXVmq0cJW81DpieFpbeE/dCV04gJCeB4VbNuPGRcqNHjnGdumMXfb59HdbPDG5YaZSInNYrKRgumQL9zJvopRh96pb9X5GU699eZrcSGBvHk4hn4+wkC/Q08+MFBrB3S47yff2MinxwqZ80PcznT0k51k4W2Djvfm53KuNgQKurNjnCMDjvfzJpJWvRZ+ww3+pObFkV1cxvJEcFkjfH0AOv1k2dumIW1Q3qERnxjUjzv7z99Tvk2Re84Ut7IGJVk55WZYyP55+FKpqd0H9KjUCjOTX+M1NZOaTYJIIToUdCcEOIFIUSVEOKAy7YZQogdncl6Hwghwl32/UoIUSiEOCqE+GY/tHtA0DxIn52oBeCCsVFOb6oWJuG6bPyLN/dgEII7LnV4uzT5tbSYEPyE4ERNCz/7RiZ3XjaRK2Yks6+03pEw9LcvefLjo4yLCeFneZk8sXgG/ga46eI0pyTbX7ce9/Aqa3GNekvY9793gL2lDbz4abHueX4GPM657fUvEQJmj4sB4IviMwBcND6GGWOjyB0Xo7xkCjdsdjwqJT61qQCbXZIWE8wzN+TQZGmn+EwLSPjp/zmS47QKi5qX+ZZ56ZitHaz4xkT+8MlRWtvaCQ7056lNBfzzUAUGIDEimEB/A60WK2da2viy1JHId9H4GLKSI7kgLZrJieGY222U1JmdHl+r1Ub+yTNsL6z2sPl9pQ26YUn7TvdMvk3ROw6VNzJWxRN7ZVZqFB8fqvB1MxSKEUF/eIrXCSGeAyKFEP8F3Az8tQfnvQQ8A7zisu154E4p5b+FEDcDdwH3CSGmAt8FsoAxwD+FEBOllLZ+aH+/oedV0qSkVuRlMiYyWDecYfPRKmJMgdx52URiQoIIDfKnvKGV76/5jChTIDddnMYzWwrPenS/k0V2cjjfzh7Dz7skKyVHBrMiL5MmSzv7yhqpbraydG462cnhZCaEOT223pLk7BI3j7UQMC8jlgvHRfPZiVovVbvaOFLR1G1Cn0KhUdWkb3vjYkNYNn8Ct72+22lHv70m23msVvWx62pLStQ0Hr16GgdPN/PspmM8uGgKwuDHnS7Shg9+J4u/bitk5tgY1uaXcPfCKVw2JUE3EXVBZhzvHyjn/vcOcMu89B4n91V46VNd5dsUveNweRMLpyX5uhlDlkkJYZTVtXK6vlV51BWKPtJnT7GU8kngLWA9MBG4X0r5dA/O2wqc6bJ5ErC18+9PgGs7/74SeENK2SalPAEUArP72vb+Rs/7ese6Pewqrqe5zUZRdbOuvJPNDr/ZeIT48GBO1Law/3QDj310xJmo19Wrdv/7B7ll/gT+8E/34gNPbSqgsLqZ1nYbTRbH9wXN85yZEObmsXWtsOfaFm0OW95g4dkthTy/rcix3SC8nhPgZ9B93apQgUIPU2fCnCvGAANIPJJST9S495kluZ6rLfe9d4CGVhv3vLOf4tpWEqNM3P++u8f2gfcP8v0541m1uYBF2cncsW4PB8v1Pb77yxu4/72z53dtq5bc17X9iV76h558m6JnNFnaqW1pIylcvYfe8DMIZqVG8c/Dlb5uikIx7OmvQLf9wDYcE9r9fbjOAeA7nX8vATT/SjLgWkq6tHObB0KIZUKIfCFEfnV1dR+a0nv0vK9RpkAy48NIjQomONCPOy+b5BaW8PNvTGTbsSqWzk3HbpfYpbsnypsEm0VHnkrz9KbHhrolu+lJQelV4HrgiixiTIGkxQRz6yUZLM/L4A/XzUR2pvJ7q0xmttq6TegbzfjSHocqdmln5XXuFejuWzSV0nqzhx2tyy/loe+cTY5LjTbp2lplY5tze11Lu+4x9WbH9tSoYG6Zl05jaztRpkCP4ypcrqWX/JoaY/JI7nvs6ulkj4nwqMrXE/k2hXeOVjQxNsqkVpzOQU5qFB/uVyEUCkVf6XP4hBDiFuB+YDMggKeFEA9JKV84j8vdDKwSQtwPvA9o2V56I6LU2YaUcjWwGiA3N1f3mIGiq0SZllB0V+cyblpMMD/Lm8iy+enYJRgEmAL9uDYnhd9sPMIt89Lx63ylrtfRS5ZLiNCXQzMIaGptZ1F2Mn4GvMqguSYDFte28OWpehparfzzUAXL5k9weuyMAQYevzab7BTpVWbqZG2L14S+0Y4v7XEoYrdLSs60cvf6fU77un/RVMZGG8k/afGwozqzFUt7B79bPINWa4fTG+vRH8KDnNvjQgN1j4k2ObaXNbTyzOZCnnfRR9Yqzzk8vmevpYUSLZufzpTEcA5XNFLb1MZLn54NLzIIyEmNJDDQ77zk2xTeOVzeqJQnekB2SgSrtx6n3mwlsssXPYVC0XP6Y7S+C5glpfyRlPKHwAU4JNp6jZTyiJTyMinlBcDfgOOdu0o56zUGSAFO96HN/UJXWabUKJObJ3VJrnvow6LsZH71zn5WbXJUj1u1qZBHPzxMrdnqlGSLDQ0iJiSQFXmZTu+Y9jec9S4/vekYj1493W37irxMYkMCabZ2sGZ70Tll0AwGwbiYEMbHhjAuJoS/fV7CzXMneCxh371+nzMUomtlMu0aeh5kVahg9OBNoqwrJ2tbnBNicNjXQxsOEejn72b3gDMWGOB/39rL3ev38+t39zs9x9oxD31nGtMTw502aJN2Hrgiy8NjW2e2sCLvrNygFnK0JDfFedzK62YyPSmCh648e486s5XkyGDe+bKEyYnhpMeHOqtAPr/N0c9Sox227u9vYMbYKL45LYkZY6PUhLiP7C9Tk+KeYAzwY3pKBJ8cUiEUCkVf6I9Eu1KgyeX/JtxDHXqMECJeSlklhDAA9wJ/6dz1PvC6EGIljkS7TODz829y3/GWVHfZlAQ+7PSkdg0r8BYKoc0fyhss/Olfx3nkqixCAv340/dz2HOqHsCZRJcQHsTeU/VclB5Ha1sHt12SQVxoEKYgf0rrzPz530U8+J0sPlw+75wyaK6vIcoUyJLcFKRL1S/XNlY1WdwKd7iiChWMbrz1Bb1ES28JnnVmK3/+dxE3XZzGE4tnYG7roLq5jWZLB89vP8GaH+bSZOkgIjiAz49X8cKPLqS2uY2EMCPTk8IJDg5w2uCh8kY+PlDOMzfksK+0Hpsdnt5cwO0LMvlof7nTK6zdOyspgjeWXeRmt1dljyE9NoSKRgsJYQ7P8YXjop1f9D5Utj4oHDjdwPW5KkuxJ+SmRfPB3tMsUe+XQnHe9MekuAz4TAjxHo6QhiuBz4UQdwBIKVfqnSSE+BvwdSBWCFEKPACECiFu7TzkbeDFzmscFEKsAw4BHcCtvlae8JZU92Fntbj0uFBnYl3XZVy9kAeN8gYL+0obkMDqrUUexy6bn86qTYUAPP29WTzy4WHdpWRvE1hvr6G8wcKqTYWsyMs4r1AIzYPck/sqRhbe+oJr5UQNb1UQY0ODqDNbeXzjUbftv1s8gzqzlaSIYJIi4PJV2xznbj7hPObD5fNIDw5w2mCTpYPpYyOdKhYa9757gGXz09nnUujAkQgXxIyxUW7tDAz0I3dctNfXrGx94Omw2R0rcMpT3CNyUqN44T8naDC3E2EK8HVzFIphSX9Mio9zNswB4L3O390W8JBSfs/Lrqe8HP8o8GivWzdAePN4uXpUtbACbcLwwd4yHr5yGs9sKWDJBWOJCwsiMdxISJAfnxZWk1/cgDHAQE5aJAKBfV464Ej20arUaV7lpAgjpkADf/p+DjVNbVQ3t7Eu/xTX56ZiELD3VB3lDRaSIoKJNPlzut5CQri7V6vra0iKMGIM8OORq6a5FSA431AIu11ysraFykbPeytGDt31BS3mXLMBLcTI1av8yFXTCPAT/GrhZF749AQ3zkljbHQIYUH+NLe189rS2UgpKahq5onFMyirN/Pyp4444ChTINVNbW42lpUUzsnaFqJMgVyTk+KslKcl6mmTcmOAgYevVIlwQ5XC6mZiQ4NQ5Z17RnCgH9OTI/j4UIXyFisU50mfJ8VSygcBOgttSCll0zlOGRF483h19agG+gu3xLogf7j16xnc//5BN33hGy8ex1Uz25kQH8aZlnZ+8ebZSYNWqa7ObMUgHJPXn8xP51hls1t1rweuyOLL4hriwoK4770Dbtv/9lkxx6qa3Za1XV+DVm1PK46wbH46ExPCmJIYzvjY3k9me7OkrhjeeOsLehUQNR3g5268gOqmNkrOmPn9x8eoM1u551uTuePSiaz85BjX56a6aRFrCXF1Zisr8jL5yfx01u8u5VvTk/jhi5972Fj2mHDdqnlxoYHcdkkGlg47BgG5aSrud6iyv7SB8bEqL6E3XDQ+mne+LFOTYoXiPBGa3NZ5X0CIXBxhDppnuAG4WUq5q49t6zO5ubkyPz9/QK7dk0lfUXWzc7k3KcLINTkpTEkMcxYV0NDCIjLiwyisavIaNpESGcyYKCP1LR0c83Lcyz+e7ZwkuG7/3eIZLP/bl2eXm+NC3V7D0rnprNnueb0PdZbAe4Lra++P6w1xejTLH0h79CXe+kJqdDAfH6rELs+udhgDDLy29CK2FlR7tXObHV1bXDo3nWe3FDqPm5IYzm83HmZRdrLTG/zB3jJWfXcWbR12bnrBsx+syMukuc3Gmu1FI/1LWk9f1JBVRLnv3QPYpWRR9hhfN2XYYGm3cfvfdrPlzkuICwvydXNcGZGdTDHy6I/wiReAn0optwEIIebimCRn98O1hyw9SS7TlpU1L+yqzQW6FbK0sIhWa4fXalljo0y0Wju45eVd3NIZVqF3XHVzm+72VmuH828txMP1NRyrbOp1gl139CS8RDEy6NoX4kKNnKhtZvFfdnisdpQ3WKhotHi1c7v0npCqTXy142xSeniUly/I5LOiWhrb9LWzW6w2xsWYePnHs7lwXPRInRCPCPaXNbAoW1Wy6w3GAD9yOhPubp473tfNUSiGHf2xbtikTYgBpJTbcVejGLHoyZO5oi0rX5PjXoXLWyW54EB/r9WyggL8nFXuwHtVrSQvVbWCA/2df7uGeGivYWJCmO5556s17K36ndIuHpm49gUh4LbXv3RLvFu1uYBrclKcNurNfrUupLdPW9TSjgs3+ntUt1u1uYDESJPXaxgEnKozExcWpCbEQ5gOm52jFU0qfOI8+OqEGNbvLvV1MxSKYUl/TIo/F0I8J4T4uhDia0KIPwH/EkLkCCFy+uH6wxK7XSIlPLl4BmnRwd1WyLrj0onkpkVRUd9KTloUj197Vn84LSaYldfNxNph45Z56SRFGFm/q5Rok6em6++XzGS6TlWtB67I4vmtx7tNmtPTGn782mxqW9q61Z31htIuHr14WyXwM8DK62aSlRjOhPhQD/v97TXZTEoI44O9ZR4V41bkZfL27lLn32kxJgoqm3Xvc7KmhfW7Sj2qR95x6URiQwLJTolQdjjEOVbZTGxYIKbA/ljMHF1MGxNBRYOFwqpR4ZtSKPqV/ogp3tLNbimlXNCnG/QBX8Vwdo2xXJGXwXMu8ZNJEUaW5KYwNSmckCB/Glvb+cWbe51LwD//xkQEkpRoEw2tHTz4wUGPZWiAH38ljaljImhttzE+JsTpre7osHOwvMFRVSvcSGRIAOUN59ZUdVWLaLdJ7ntvP8W1reedJKddbxTouY7qmOKueIsnX7tsDllJEXx8uJIXth/nv+ZnEGAQWG12Ikz+nKp1lHkO9BOYjAEUVjVjlxAS6MfkxDBqW6wE+ftRXm/GJh3xk8/pxCUvnZvO27tL+cn8dGrNVmeS66SEMKYlhzM2asTaoSvDOqb4jc9L+OhABT/52gRfN2VY8rfPS0iKMPKry6f4uikaI77DKUYGfZ4UD2V8NQnpOinQyj27ZsIvX5DJFydq+fHc8eQX13kkI912SQZWm103GemJxTMorGpiQnwoM1IidOXW+rP92n1HaJJcf6AmxS50l4R6srZF17aeXDzDmTzqLelT2758QSZr80tYnpdJbbOVlZ8cc5ZRv39RFofLG0mLCeHJj49QXNvqdo1Xb54NAmJCgkiNMlFSZx6pkoHDelL8v2/twxToxzezEn3dlGFJWV0rv914mJ2/ysPfb0ioq4yYjqUY2Zz32pQQ4gdSyte0Ih1d8Va0YzTQdfm4vMHCKzuKee7GC/jiZB1SwhcnarksK4llr+7STUZKDDdyukF/GfpoZRPPbyvikaum8Yt1e5z6xv2VTa+S5BR9obskVG+21WLtwN9gcCbU6R0zJSmM3y2ewel6M4uyk6luauPlT4tZOjedMKMfYcYAbu0s2NG1P2nX2FZYg9Hfj81HKvju7DQPPe4RrEYxrNhdUsePvjLO180YtiRHBRMbGsTWgmoWTE7wdXMUimFDX75CakF5YV5+Ri16SWZ1ZitNrR08v62IZ7cUcvUFY3lww0GvyUgldWbS40K8JhxZ2u3c++4BbvrKWSWKO9bt4WRty4C0XyXJKXqDtyRUb7YVEujvZu96x4yNCuZ/39rLbz86yrNbCmlus1FntvLslkKaLDYe3nBItz+5XsNmh1WbC7jpK+nOCbF2fH/1H0XfaG7roLTOTJqqZNcn5mbG8vpnJb5uhkIxrDjvSbGU8rnO3w/q/fRfE4cf42JCeOzq6W4f8MsXZLJ663Hn9ta2Dq/JSPctmoop0I8AP8Edl070uM7bnZnFrlJr2v9VTZZ+ab9KklP0FbtdUlTdzI7jNc5kTT3b+v2SmQT4C6SULF+QyQd7yzySUVdeN5OspAi3cz/YW+ZMKvXmXdZWjl37jtZvvK2GKHzLvlP1jI8NGSrL/sOWr6TH8tmJM8qmFYpe0JfwiVXd7ZdSLj/faw93DAZBTmqks5KdlDgr0uWkRvLh8nnUNLfpVgGbGB/Gox8eps5s5bGrp/PNrATyJidQVNPM/rIGt+VgV6k17f/+8Ob2RINZoeiO7uKK9WzLbpfsK6vnyY+Psig7GYMBfrd4BiW1LczLjGV6cqSuXaZGmchJjaKisZXnt3n2pznpMQDY7Dj7jjHAgCnQv0cVKRWDzxcnz5AZP6oXG/uF4EA/LhofzZv5p7j1kkxfN0ehGBacd6KdEKIU+DUQBdR13S+lfLlvTes7vkxsOlfFu44OO+/uLXOLadRK2bpOerXkNr3jH/xOFpsOl5OZEImfAXJSo/jK+BgCA/188ppHMSrRrgvnk6zZXZ8BnMooWlKc67bEcCO7Surc+oeWzHpZVpIzVMkYYOC+RVP599EKLssaM5Jjiodtot0Pnv+M2eOjuXBctK+bMuw5Xt3Mn/91nG3/e4mv7XpEdCrFyKcvIpCNwL+A94FL+qU1I4hzeVsNBkFcWCBPLp5Bi7WD+LAg7nnngHNCDO7Jbf7+Bq6akUxmfCin6lqxS/jX4Qq+NinRGUtpDDDwyFXTuGpGMv7+aulR4TvOJ1nTW58BPCbLz9wwC2uH9Ni2btkcSupaOVze5Laq8swNOewrrcdmh9Vbj3PHpZP41tREclKj1GrIEMJml+wtrecHc9J83ZQRQXpsCEH+BrYV1vC1iXG+bo5CMeTpy6T4L8BGIB1wdX8JHN6H9D5ce0SgJRvpTQJO1rZw/3sHWZSdjBBgCvSnzmwFHBJu1+Sk4GeA4AB/TlQ3c6K2hZBAfxLCgwgNCuDbT29j6dx0j+Sie989wOTEMEyB/iNVasqJq67ySH6dwxEtoc5beILes4Oznt+kCCM2O3x2ohZToD+PbzzsLJl+TU4Ktc1WTte3EmUKpLxTpeW217/kw+XzmJoUwJ2dut8AU5Mjua1TlULj7vX7GBdjwmy1KdsZQhypaCTSFEBEcICvmzIiEEJwyeR4Xt1xUk2KFYoecN6TYinlKmCVEOLPUsr/6cc2jQpqW9q4PjfVWaY2LSaYBxZl8ZethW7bV28tcoZV1JmtrMjLZOqYMFZeN5MjFY0e3rgoUyBHKppG8rIwcO7wFIVv0RLquj4fLX64O89vlClQV9d744FyFk5LcvaNrrJrmid69rgYt3v7GfST8DYdqWLVpkJlO0OIL06cYVKCiifuT746IZZ1+accxZwiVMy8QtEdfV5jVxPi8yPQz+D8cAcorm3lL1sL+c012W7bLe12ntrkkJbS/t5VXM/UpDC+lhnnIV21JDdlVEhNnaxtcU56YOS+zuGKFgrx4fJ5vLHsIj5cPs856dR7dvtKG5zbrslJcU6Itf2rNhdwy/wJHn3DVXZN80QbDIKpSWEsm5/ObQsyyIwP05V4s3XOk5XtDB3+c7yWiWpS3K8EB/rxlfQYXv+s2NdNUSiGPD4LPBVCvCCEqBJCHHDZNlMIsVMIsUcIkS+EmO2y71dCiEIhxFEhxDd90+r+w2y1eXivimtbKa1r1fVqpUYHc9uCDKJMgdgl1DS3ER0SyMNXTnOTrpoQFzoqpKa6i1lVDA28aRXrPTu7POvN9SavZvEioybEWdm21CgTRdXNHKloIsjfQEigH3XmNo9+4iptqF1H2Y5vsdsln584Q9aYCF83ZcSxYEoCf/v8FO02+7kPVihGMX2JKe4rLwHPAK+4bPsd8KCU8iMhxOWd/39dCDEV+C6QBYwB/imEmCiltA1ym/sNbzGXwQF+uttLzrSyZrsjlCIsyI+yegs/WPM5UaZAls1PJyMulHGxJposHaNCaupcMauKoYves/PrnNhq2/Se7fjYEN3tF6dHc82sZFKjTHx8uNItLOOOSyci7fDMlgKWzk3HzwAXp8fwy7f3uSW1KtvxPUcqmggz+hMdEujrpow4UqNNxIUFselwJQunJfm6OQrFkMVnnmIp5VbgTNfNQHjn3xHA6c6/rwTekFK2SSlPAIXAbIYxekUMHvxOFg3mNu5bNFXXq6WFT0xICOPu9fuwtNspb7CwalMh/7t+H1LCPe/s9yh88Pi12SOu8IYqMDJ80Xt201POFuZYv6uUFXnuNnzfoqnEhQU5i3Vo2x+5ahoXjYshPS6UkjqzR1jGyk+O0dZhcya02iX8/uMj3HHpJGU7Q4zthdVkJYWf+0DFeXHJ5Hhe/lSFUCgU3eFLT7EePwP+IYR4EseE/Sud25OBnS7HlXZu80AIsQxYBpCamjpgDe0rXeWnDEJwtKKJRz884vT+pseGUlpndpOWsrTbaTC36y4jlzdYKK5t5dWdxSydm44QjsIhyZHGEZdANFwKjAwXexxMupNei/nxbLYV1gBw2yUZWDrsSAlNlnYqGi1OWUItaSgrKcIpP6gXlhFlCiTEGMDKf7on56VFB/PhELed0ca/jlY7i60o+p+Lxkfz+mfFFFU3e5VFVChGO0NtUvw/wM+llOuFENcBa4BvoC/8rSs6L6VcDawGR7GEgWpof+Aq2bb3VB2PfnjYzftrDDCwbH66xzJvUkSw7jKytr28wcKzWwqd26/N0f3+MOzpTvJuqDCc7HEw8fbs4sKCeH5bkYdtL5ufTnyYEX9/AzPGRjFjrOc19cIyluSmeMgWrtpcwFcz5gx52xlNWNpt7DlVz9K5433dlBFLgJ+B+RPjeGVHMf/vO1m+bo5CMSQZahUefgi83fn3m5wNkSgFXD8GUzgbWjEksNslRdXN7DheQ1F1M3Z77+Y/LW2eiXeWdjsT4kI7J7xGludl8OTiGYQG+vHMDbM8ln+zksL7FFLQ19egUHSlO5vS26cXWrEiL5PslAhdO7bbJSdrmvmsqJbi2hb+emMuaTHBznNTo026/cpsHbbpCCOSHUW1jI8NwRQ41Pw0I4sFk+J558syWpX9KxS6DLUR6DTwNRyV8hYABZ3b3wdeF0KsxJFolwl87osG6tFXzVy7XWKzS13vb1ZSOBtXzGN3ST33vLPf7fobV8yjotF9+fd8QwqU7q+ivzlX2WZv+xZmJTLp9nmUnGnB1FmwJjXa047tdsnmo5UUVDa7aRo/fm02yZFGokxBtFj1E08TwlVS3VBi8+EqslOU6sRAEx9uJDMhlPf3lnH9hSqcS6Hoii8l2f4G7AAmCSFKhRBLgf8Cfi+E2As8RmcsppTyILAOOISjit6tQ0l5oq+auSdrW7j3Pf0EufS4UOydCXRdr2+XeMhdeZPBGujXoFB0pTub6m6fwSCYEB/KJZMTuCg9hnGx+nZ8sraFfaUNHprGd6/fR3RIEBPiQ5k2JkIlZA5xpJR8cqiSWWOjfN2UUUHe5Hhe+vQkUqqVQIWiKz7zFEspv+dl1wVejn8UeHTgWnT+dKeZ25OYxcrG7hPk+nr9wXgNCkVXurMpKfW1iHtjb5WNFjd9Y73rDJeEzNHMofJGDAZIiQr2dVNGBdkpkby6o5gvT9WTk6q+iCgUrgy18IlhSV81c7XzvSXIDYYmr9L9VfQ357KpvtpbQrjRQ99Y7zrDISFzNPPR/gouSI1CCPVFZTAwCEHelARe/M8JNSlWKLow1BLthiV91cw91/ld96fFBLP6xlwqGy39lhCndH8V/U13NqW375kbZiElPU70HBcTwvSUCA9NY2W3wwcpJRv2nWb2eCXFNpjMnxjHliPVqoqjQtEFMZLjinJzc2V+fv6g3Mtul5ysbTnvJdpzna/tP9PSRlm9xVm8oz8T4vr6GkYxPXqTBtMehwrd2ZTrvsRwI4fKm3qd6Gm3S0rOtFDZ2IbZ2kFqdAjjY5Xd0kObxIu05WBx8HQDS1/6gpXXzVSe4kFmzfYissZE8PNLJw7G7dTDVQwL1KR4mFFU3czlq7Z5LBd/uHyeWh72HWpS3EeUXfc7w2JS/NAHB6kzt3Ndro7wtGJAOXXGzOMbj/DprxYQ5O830LdTk2LFsECFTwwzukteUiiGK8quRx/tNjvv7jnN3IxYXzdlVDI22sTYaBMf7C33dVMUiiGDmhQPM7TkJVdUQpxiuKPsevSx6XAVieFGxkQq1Qlf8c2sRJ7793Elz6ZQdKImxUOMc1WVUwlxipFIX+1aVWMcfrz86Um+PinO180Y1cxIicBqs/PvY9W+bopCMSRQkmxDiJ5UlVO6q4qRiKrGOLo4VtnEkYpG/ufrE3zdlFGNEIJvT0/imc2FfH1SvK+bo1D4HOUpHkL0tKrc+VatUyiGMqoa4+jhz/86zqVTEwjwUx9BvuYrE2Ipq2/l8xNnfN0UhcLnqBFpCKGSjRSK3qP6zfCiuLaFzUcquXRqoq+bogD8DILvzBjDkx8f9XVTFAqfoybFQwiVbKRQ9B7Vb4YXv//4GJdOSSA0SEXvDRXmZcZRVtfKtgIVW6wY3ahRaQgxLiaEZ26Yxb7SBuwS/ARMT4lQSXQKRTdoSXquMcWu1fESwlXc/VBhz6l6/lNYwxOLZ/i6KQoX/AyCJRek8PCGQ3y0Yj5+qq8oRilqUjzEsHZIVm8tcksYUigU3umapKdVx/v209tU4t0Qot1m55fr93H9hWMJDhzwYhGKXjJ7fDSfHK7k9c+KufHicb5ujkLhE1T4xBBCJQwpFOeHa5KeXaL60RBk1aYCggP9VLGOIYoQgh9ePI7ff3yMigYVj68YnahJ8RBCJQwpFH1H9aOhx7+OVvH6ZyXcMjcdIZS3fqgyNtrEN6Ym8It1e5TWt2JU4rNJsRDiBSFElRDigMu2tUKIPZ0/J4UQe1z2/UoIUSiEOCqE+KZPGj3AqIQhhaLvqH40tDhQ1sDP1u7htgUZRIcE+ro5inNw1cxkzpitPL25wNdNUSgGHV96il8CFrpukFJeL6WcKaWcCawH3gYQQkwFvgtkdZ7zJyHEiAtKU9XqFIq+o/rR0GFX8RluXPMZN39lPJMTw33dHEUP8DMIbl+QyWuflfD27lJfN0ehGFR8lmgnpdwqhBint0841teuAxZ0broSeENK2QacEEIUArOBHYPR1sFCVatTKPqO6ke+x26XvLLjJH/cVMB/z5/AzLGRvm6SohdEmQL5329O4tG/H6a13cb3L0rzdZMUikFhqKpPzAMqpZTa+k0ysNNlf2nnNg+EEMuAZQCpqakD2cYBQUsYSo8L9XVTFP3AcLfH4YrqR75BSslnJ87wm4+OYLHauH/RVJIign3dLMV5kBJl4teXT+H3nxxjd3Ed9y2aSqRJhb8oRjZDdVL8PeBvLv/ruXh0swCklKuB1QC5ubkqU0DhU5Q9KkY6drukoKqZfx2t4u3dZTS1tfOdGcnMy4zFoJLqhjVJkcE8fOU01uaX8PUn/sX3L0rl2gtS1JdNxYhlyE2KhRD+wDXABS6bS4GxLv+nAKcHs10KhUIxWrDZJe/vLaO8wUKHTdJus9PWYaelrYMmSwe1LW2UN1goqTXT0alSMC7GxIXjopmWHIEAjlc1+/ZFKPqNr06IJT02lH8cquTZfx0HICE8iPExISREGIkMDmBCfCg3zE7F30+JWimGL0JK3zmvOmOKN0gpp7lsWwj8Skr5NZdtWcDrOOKIxwCbgEwppe0c168GivuhqbFATT9cpz9Rbeo5A92uGinlwnMd1I/2OBQYqs+6vxmur7OnNrkRx2t0wy8iISDlJ2uye3KjjqZaq93S3HEebew50u6PMAzsPYZ6G3x9f60NBr8O//C4IENgsEeye+mff7zP1ljdrnNmj+xRofA1PpsUCyH+Bnwdx4BcCTwgpVwjhHgJ2Cml/EuX438N3Ax0AD+TUn40iG3Nl1LmDtb9eoJqU88Zqu0azoyW93S0vM7uGArvgWqD7+8/VNqgUAwkvlSf+J6X7T/ysv1R4NGBbJNCoVAoFAqFYnSign8UCoVCoVAoFKMeNSnuGat93QAdVJt6zlBt13BmtLyno+V1dsdQeA9UG3x/fxgabVAoBgyfJtopFAqFQqFQKBRDAeUpVigUCoVCoVCMetSkWKFQKBQKhUIx6lGTYoVCoVAoFArFqGdET4oXLlwocZSDVj/qZyB/eoSyR/UziD89Qtmk+hmkn57i63aqn9Hzo8uInhTX1AzHQlSKkYqyR8VQQ9mkQqFQnGVET4oVCoVCoVAoFIqeoCbFCoVCoVAoFIpRj8/KPCuGN3a75GRtC5WNFhLCjYyLCcFgEL5ulmKQUM9foRhcVJ9TKAYeNSlW9Bq7XbLxYAV3rNuDpd2OMcDAyutmsjArUQ3SowD1/BWKwUX1OYVicFDhE4pec7K2xTk4A1ja7dyxbg8na1t83DLFYKCev0IxuKg+p1AMDmpSrOg1lY0W5+CsYWm3U9Vk8VGLFIOJev4KxeCi+tzw5Z+HKrn8qW1c++dP2Xuq3tfNUZwDNSlW9JqEcCPGAHfTMQYYiA8z+qhFisFEPX+FYnBRfW548p/CGu56ay9XzBjDReOj+eELn3O0osnXzVJ0g5oUK3rNuJgQVl430zlIa/Ft42JCfNwyxWCgnr9CMbioPjf8sLTbuHv9PpbNn8DMsZHMy4zju7PHsuKNL7HZvdaOUPgYlWin6DUGg2BhViKTl8+jqslCfJjKhB5NqOevUAwuqs8NP975soz4MCMzx0Y6t83PjGPrsRre+bKMxRek+K5xCq+oSbHivDAYBOlxoaTHhfq6KQofoJ6/QjG4qD43fJBS8tetRXxvdqrbdiEEV89K5tnNhVwzK1l9qRmCqPAJhUKhUCgUin5if1kDlnYbWWPCPfZljQlHCNhWqEqsD0XUpFihUCgUCoWin3h7dxkXT4hBCE9PsBCCr0+K4/92FvugZYpzoSbFihGH3S4pqm5mx/EaiqqbsaukhmGBem4KxcCg+tbgIaXkk0OVXDgu2usxX82I5T+FNTSY2wexZYqeoGKKFSMKVflpeKKem0IxMKi+NbgUVDXTbrOTGm3yeowp0J/slAg+OlDOd7vEHSt8y4B7ioUQkUKIt4QQR4QQh4UQFwshooUQnwghCjp/R7kc/yshRKEQ4qgQ4psu2y8QQuzv3LdK6K1LKAaFc3kdfOmVUJWfhiZ2u+R4VTObj1TyWVEtJ2vc7UI9N4VCn67jaUeHvVfjq+pbg8vWY9XMHBupGzrhykXjY3h/7+lBapWipwyGp/gpYKOUcrEQIhAwAfcAm6SUvxVC/BL4JXC3EGIq8F0gCxgD/FMIMVFKaQP+DCwDdgIfAguBjwah/QoXzuV18LVXorvKTypr2zfo2cSKvEwyE0JZMCkBg0Go56ZQ6NC176TFBHP7gkzuffdAj8dX1bcGl63HqslJjTrncTPGRrJ6WxEN5nYiTAGD0DJFTxhQT7EQIhyYD6wBkFJapZT1wJXAy52HvQxc1fn3lcAbUso2KeUJoBCYLYRIAsKllDuklBJ4xeUcxXlyPh5db16H/WX17Dhew/6yBh7feNhnXglV+Wlo4Gpb+8vqPWzmqU0FWKx2Ss447EI9N4XCk67j7aLsZOeEGM6Orydq9MdXu11iCvRjeV4Gty3IICnC0Z9U3xoYOmx2dpXUMUVHdaIrxgA/po2JYPPRykFomaKnDHT4RDpQDbwohPhSCPG8ECIESJBSlgN0/o7vPD4ZOOVyfmnntuTOv7tu90AIsUwIkS+EyK+uru7fVzOC0DwQl6/axvf++hmXr9rGxoMV55wYe/M6bDpSxff++hnXr97B9bmpzsFX21/VZBmQ19GVoVb5aTTaY1fb2nSkStdmjlU1sbukHrtdDrnnNpIZjTY5XOk63gqBbl86XNGoG8a28WAF16/eyapNhTy/rYgb56SRFhOs+tYAcai8kdjQIMKNPfP8zhgbyScH1aR4KDHQk2J/IAf4s5RyFtCCI1TCG3rrP7Kb7Z4bpVwtpcyVUubGxcX1tr2jhvONM/Pm0bN1jtOWdjurNhdwTU6K2/7B8kpolZ8+XD6PN5ZdxIfL5/k0oWQ02mNX27JLvNrMPe/s52Rty5B7biOZ0WiTwxVv423X/49VNnmM3Xpj/KrNBaz67izVtwaI/JN1TIzveUjKrNRIthXW0G6zn/tgxaAw0JPiUqBUSvlZ5/9v4ZgkV3aGRND5u8rl+LEu56cApzu3p+hsV5wn3cWZdYeeR2/5gkze3n3WkW9pt+PXaVm+8PhplZ/mpMeSHheqBv9Bpqttrd9VyvIFmbo242pz6rkpFO50HW8/2FvGw1dO8+hLb+aXeozd3sb41nab6lsDxOcnz5ARH9bj46NMgcSHBfFlSf3ANUrRKwY00U5KWSGEOCWEmCSlPArkAYc6f34I/Lbz93udp7wPvC6EWIkj0S4T+FxKaRNCNAkh5gCfATcBTw9k20c6mgfCddA8l0fXbpecrG0hLiyQtcvmYLbaCPAz8Is391DeYHG7Tt7keL4yIYb4MCPjYkJ6PAhr96hstJAQ3rtzFf3L+TwLRwyjP8YAA1GmQK7JSUEI8DfA/y29iH8XVGOzw6s7iylvsKjYRsWopLu+1XXfZVMS+HD5PKqaLMSHGRHAsvnp2CVI6ehLdWarRz9yHeOTIoxck5OCnwGCA/yx26UaVweAvafquWxKQq/OyU6OYMuRKmaP965rrBg8BkN94nbg/zqVJ4qAH+PwUK8TQiwFSoAlAFLKg0KIdTgmzR3ArZ3KEwD/A7wEBONQnVDKE31A80B0VYnw5tH1lgX99OYCrs9NZdXmArfrTE+O7PWg62vlCsVZzudZaOc8vvEwv1o4GXO7zZFQ13n+75fMJDslgtte/7JHNqdQjES661uA132aUoTdLpmcGH7OsVsb4x/feNhtjF69tUiNqwNAdVMbTZYOEiJ69yU/e2wka784xd3fmjxALVP0BuEQcxiZ5Obmyvz8fF83Y8iieSQ0D0R3nsCi6mYuX7XN6f1LjQqmzmx1BHwLSI40UVzbwrzM2POaELveo6v3+sPl84a6dFCPXuxwssfzeRau59x52USe2VLocf4rN88myN+A2WpTKwEDy4izyZFCd30L6FG/6+nY3dFhZ09pPT9Y85mvx9WedvJhOyHZdLiSpzcXcvfC3k1uO+x2fvLaLv591yXEhgYNUOsUOujapCrzPIrpTQxnZaOFKFMgN85JY832Iu5+ez9/3FQAwMufFnPXW3sxCEG7zX7ek5zzjXNW9D/n8yxcz7FL/Sz5nUVnuH71TurM7WpCrBiVdNe3etrvejJ22+2Sjw9XsrOoVvealY1qXO1P9pXWkxbjvYqdN/wNBqaNieA/hTUD0CpFb1GTYkWPSAg3siQ3xbkEB2f1Zq/JScHSbmdtfgkgzruSndKqHTqcz7NICDeSFhPMrZdkMD42hBV5GW7SfMYAA+NiQ1RFLcWopru+1ZN+11N9eU19Ii0mRPeapkC/fnpFCoD9ZY2kRZ9fKNjUpHD+fVTJIw4F1KRY0SPGxYQwMT5M1+MgBCRFGLk+N5UfrPmsV7rHXe+htGqHBufzLFKjTNy+IJM124u4/W9f8tzWIm66OI2kCKMzS/50vRlQKwCK0Ut3fetc/a43+vKa17ms3qyr/qJkwPqXQ6cbGRfbe08xwPTkCLYX1jCSw1mHC4ORaKcYARgMgilJ4bqKFVLCNTmeXuQ71u1hci/i1jSt2skumdZqiX1wcc18n5QQxsYV86ho9HwWetnzJXVmj2pbT20q4InFMzhS0cTa/BIWZTtq7hgDDMSFGr1eSz1zxUjlXOPcwqxEpiyfx+mGVposHYyJDHaqRXjTl590+zyEwK0PaV7n5jYbH+wtY+ncdIRwKFaszS9h4bREX74NI4p6s5VGSzsJ4ee3qpnYuaJ2vLq5V5Juiv5HTYoVPWZ8rKdixYq8TF7ZUcyS3BSvsXC9SebQYuWGeGLdiKSnihPejosyBejawNHKJtZsL3LaimY3J2qbSYs28fHhSqU4ohhVdDfO2e2SXSV1zi+YxgADj1w1jatmJHuNOT5c0cidb+5160OXTUnQVZ8wBhh46MpppEQED9bLHfEcLm8iLSYEgzi/MUsI4fAWF9SoSbGPUZNixTlx9eRNTQrj77fPo7rZQliQP3Xmdn72jUznEnlvdI/1rq88hb7DmxfK1dtvt0v2l9VzpKKRW+als35XKeUNFu5Yt4e1yy7WtYELx0WRFj2NMKM/v1w4iWNVLbyyw6GtunbZnHPeU6EYyXQd/8zWDo8Vl3vfPUBmfKhXfXkkHv1RqwoZHxbE7uIz/G7xDE7WtNDWYefZLQWkx4aQkxqlxtp+4GhFI2Oj+vYlY+qYcP59rJoffXV8P7VKcT6oSbGiW7x5BS+bksD7+05zzzv7nbrFDyzK4sENB53HPXb19HPGAytt4qFDd5nv6XGhus9q+YJMZyEOKe08ctU0Nw/Xg9/J4v73DlBc24oxwMB9i6by9u5SZ7GX8obu76lQjGT0+tQjV00jyhToVhDJ0m6nosHC9ORI3dW6Rz88TJ3Z6tYftT5U09zGYx8d9bj31oJqqpra1FjbDxw83UhyHyfFWWMiePE/J+mw2fH3U+levkK984pu8eY9PFje4JwQAxTXtvKXrYWsXDKD3107nT/dkMPEhHNParxd/2RtS4+zrBX9w7ky3/We1arNDvURY4ABIQRPby5g6dx0bluQwe8Wz+BP/yqkuLbVefzDGw5xTU6K89pJEcHOeyZFGLn1kgyW52VgCvTnZI169oqRjV6fuvfdAyzJTXE7zhhgIDHC6IxH/nD5PF78US7L5qfzyo5i55dL1/6YFGFk76k6bHbJMzfMIjs53O16NjtKBaafOFLRRGrU+SXZaUQEBxAfFsTe0oZ+apXifFCeYkW3ePMe6nn4imtbMbfbuP/9gz32+nq7/pmWNo5UNCkP8iByriqH3p6VnwFWXjcTs9VGcW0rz24pBOC2BRnOCbHr8UKczarPSgr3WnVLi0GuM1vVs1eMSLz1qQlxoc4wCc17nJUUAZyNR65stLBqU6HHuX4GeO7GHL446R6X/MAVWfBZMceqmp0eZbUq03eklByvbiYlum+TYoCsMeFsL6jmgrSofmiZ4nxQk2JFt3iLYdM8fF23l5wxe3h9p66Yh12iGzPs7foBfgYVazrInCsrXtMhXpSdjBAQFRzA2GgT7TY7yZHBhAb66T7Lrv/Py4jlmlnJzmsvzEokOdLI9at3eihXLJ2bzrNbCtWzV4xIvI1/42JMrFs2h/IGC8lRwRj9/fii+AwJ4UZSo0yU1pvxMwjdc/Mmx4OE/351t1t/evCDgzx34wU0tnbw163HKW+wKB34fuB0g4XgAD9Cg/o+nZqWHMHGgxWs+MbEfmiZ4nxQ4ROKbvGmm1nf2saKPHfty4evnMab+aVu50eZAtldUu9VV9Pb9c1Wm6pu5wO6q5TlqkP8zOZCnvj4KMerm3nk74e5fvUODlU08vslZ5/lB3vLeGBRltuzfeSqaVyQGuV2bYNBeH3eQf4G59/q2StGGnrj3/IFmSx/40tK6y3kTU6g5Ewri57Zzvf++hk/fulzPjpYzkcHKrjrrb0e+sOaR7nciwf6i5N13PXWXhZOSyItJljpwPcDBZVNjO0HLzHA5MRwjpQ30WRp75frKXqP8hQrPOiaDX3ZlAQ2rphHZWMbLdYOYkODeOiDA3x9UgJPLJ6BEBAdEkBzm406s9V5naQII7++fArHqpo8MqNdvcd6ergna1vOW81CMTCU1Jl5enMBK/IySYkyYW7roM5s5aaL03h841Huemsfb/3kYt76ycWcrDHT0tZBu83OU9+dRb3ZytjoYI6UN7G1sNpZqECbGJsC/fU9ZrEhzr/Vs1cMJ3qiqmMwCC6bksBrSy/ieHUzpkB//rr1OMW1rdyxbg9v/eRip9ILQEigHwVVzazeWoSl3c6rO4tZOjcdPwNkxIfx+4+PkJMaRVJEsNuqTmiQH1JCtCmQW+alsza/hFXfncX05EgVktRHCiqb3Sp39oVAfwOTEsPYcbyWy7KUjrQvUJNihRt62dDP3DALa4d02/bAoiz+srXQqSrw0HeysHTYWL4gk1WbC4gyBXLTxWnc+dZZ7Uwtjg1gd0m9M1FPL174XPGtisGntqWNm78yHnO7jbtcnusDV2SRFGGkvMFCdZOFOnOH27NdkZfJR/vL+db0JJ7aVKD7zK22s7bjai+n683q2SuGHb3R/O6q0718QSbVzQ7nwpGKJucEWFNvEQLnl8fyBotHDH9Vk4WclChuvSST+9874ByLXfueVtFOTYj7zpGKRsZE9p/mc9aYcP51tFpNin2ECp9QuKGXDb2vtMFj24MbDjqrk1na7dz//kGiTUGszS9h6dx07rl8inMQ1o7RMqOX5Ka4KVe4Kk5ouGZZv7HsIqfmphrEfUegn4Fas9XjuT74wUGuyUkhLSaY0KAAj2f71KYCbpk/weM812ceE3LWdm5bkMHSuQ5v1qyxUerZK4Yd3anqnOs413Gyq17xwxsOMTE+jBV5GW7eSa2yqLaiUtrQyv3vOc69JidFdywOULJf/cLxqhaS+3FSnJ0Syb+PVauSzz5C9QqFG3rZ0HaJxzZNRcD1f7uUfPfCVNZsL+JoZZNXpYKxUaYexQt3F9+qGHzMVptXWwgOMHDrJZlsK6zR3d/a1tHtMx8XE8LdC6c445XXbC/i7oVTuHBctHr2imFHd5rfPTnOzwAT48N09+0+Vc9zW4u46eI0Z9Gk5Qsy2bCvzLmi4npdV8+y63XMVlt/vdxRi5SSoprmfvUUj40Kpq3DxokaJZXnC1T4hMINvWxoP6GvIqB9kU2KMLIkNwVjgB8XjovixR/lYrPD8zrnXJAWRWFls4oXHuLoxUMmhBu92sJF46O58YXPuWVeutt+zTZMQf6syMtgXf7Zwh2uz1xbGZjqErueFq3CJRTDE2+qEpq9a/2rtd2m2y/yJscTGhTgddzVVmDW/DCX0EB/rHY7X82IwWqzc7K2hfgw9/vrXSchXI23faW2xRHmEm7sv6mUEIKZYyP519FqpbbjA5SnWOGGXjZ0TEggd142yW3bA1dksWFfGUkRRm66OI3VW4tY9uoufrDmc74saeCP/zzKI1dN88iqvv+9A/gbBD//xkQPxQkVMzo00OIhuyqGpEaZmJ4S4aE6svK6mdDpjVq/q9SZEe9qG7f/7UsP79YjV03zELw/VN7ED1/8nJtfyufbT7srlSgUwwVvqjrjYkLc+tfNL+Xr9ouspAjGx+orU7y926Hw4/AoC6anRFLdZOX61TtZ8pedXL5qG6X1Lc7xd/2uUt0+q8bbvnO8qpnkyGCE6N+VrOzkSD45XNmv11T0DDGS41Zyc3Nlfn6+r5sx7NC8GMW1LXx5qp4380u56eI0Wttt+BscigD15jaiTUFEhQSw9OV8Dy/E0rnpbNhXxu+XzGRrQTU2O87yvlryVWu7jVljI0nrokQwDOlRw4eLPRZVN3P5qm0ez/TD5fMYFxNCcW0LpxtaabbYSIoIYmpSBCV1Zuc5SRFGvn9RKlOTwvnp67s9rvPE4hkcqWhiw74yXvzRbKc3pLv7Ko9JrxlRNjncsNslJWdaqGxsw2ztIDU6hPGxjjHOm53r9YuTNc28/WUZyZHBlNW38mYXj/JbP7kYm02y6WgVdolT4Wd5Xgbv7Slzqk+EBPoBMDkxzFfjbU9vNqwmJK9/VsI/D1fyX53qIP2Fpd3Gra/v5rN78ggzBvTrtRVOdG1ShU8oPNCrmNRitbF+Vyk3zknjf12UB55YnO1VX7a4tpWa5jbdqkut7TYmJ4bztYnxw3kyPCLpLh5yXEwIh3UqDV42JcGpFgLgZxDsKa3Xvc7RyiZnxrxrNa3u7qsmxYrhgjflifGx3VeG1OsX5Q2OMTgpwsiNc9KckpfGAAO/WjiZT4/XsvKTYx4KP3aJW3VJjTeWXaT6Uj9yvLqZhLCgfr+uMcCPyYlhbD1Ww7ezk/r9+grvqEnxKKZr3GhqlImSOrPzf205TxvAl+SmOBUCtNUifz+DbrxaZnwoy/MyCA/W15/NmxyvNDKHCK5eLU2HOi0m2K1EszHAQGK4kf1l9U7dVFfd6Q+Xz2NqUhjL5qcza2wk//N/uz3ii7XraItTXePIzxWHqVAMB7wpT2gVGb3Z+aSEMG5bkMEHe8tIDDdSVN1Ma7uNXy6chARCgvx47sYLqGpsIz48iILKJueEWLvPqs2OKpDeYv9VX+pfCquaB6wk88yxkXx0oFxNigcZFVM8SukaN/rjlz7n3b1lbnGkh8qbeOaGWc64tMmJYVyfm+pUCHh+WxHtNrtHVaWff2Mi5vYOVm8t4hfr9unGs6kJ8dDAbpdsPlrJRwcqnLG81z23g9sXZJIW48io1rSqD5U3cf3qnaza5Hj2N85xxEFq3tzyBgtv5pdS22L1iC/WrrMizxETqRfX2F0cpkIxXDiX8oSena/Iy+SxDw/z/LYi7rxsEgdPNzljjv+4qQA/g0Da4b9f3cVdb+3jv1/dRURwoFfliukpEaovDQInaloYE9F/yhOuXJAWzb+PVWPtsJ/7YEW/oTzFowzNO1zd1ObmzViUneyhiXnHuj2s/a85/On7OYQE+eMn4I51e92OOV7VzLt7ypzeYykhJNBAca3ZWYXpo/3lTg/iCIgfHlGcrG1hX2mDs0AAOJ7rve8eYO2yObS224gPMyIlfPvpbR5eqd8tnkFhVRPBAf6EBvmzJDeFU2ccBTfKGyxuFbfyJsUTYQrgwnFRBPgZMFttnKxtcdqDpkAxefk8KhstmAL9nNn0ymYUw4VzrXi42rmWt/HKjmJnrLBrxTpw9LWVnxxj2fx0t22ldWbnfZIijFyTk4KfAb6WGceMFIfTYfLyeVQ1na0UqvpQ/9Fus1PRYCE+vP/DJwCiQwJJiQrmP4U1XDI5fkDuofBEeYpHEa7e4a56st60LDcdreLml/L54QufU9nY5nHMuvxSVuRNdHqPN+wrIyjAn9Vbz3qTF05L4s38UoID/ZTm7BCjstHiVXu4td3m1IiuatL3fhVWNbFqUyHXr97BidpmJsaHsS7/rIe4vMHCmu1FjIsJYXpKJKnRIVR1Zsq7KltoChMGg2BcTAh15na3bHqlQqEYLvRkxUPL2zAG+LFqU6FzQgzedeG7mv+6/FLuWzSVtJhgbpyTxprtRazaVMj313zGx53KBUrnfeA4dcZMTGjggBZBuXBcNO/vLRuw6ys8UZ7iUUTXWLe0mGBndvKkhDDSYoKxdkiuyUlBCE2f2JG1bGm3c6yyycMDUme2kpMayYedHglTgB/Xrd7p4VFcNj9dxbMNQbrTHtaeV0eHnQA/A49fOx1ToD9/3XqcfWWNGAMM2DpPsbTbue31L1n/PxezJDeFDrvkicUzKKs3Y7bayEmNdGbedxdvCeeOyVQohjKunuCuXtqueRxd8zYAQgP9dPtj1zltndlKY2s7d102mTvf2uvRXybdPo8J8aq/DBQna1vcqgoOBBeNj+GXb+/D0m5zfhYrBpYeT4qFEDk6mxuAYillR/81STFQuMa6bT1axU/mZ/DghoPOzOWHr5xGq7WDxz464tz2829MJCnCSHmDhXX5pTx29XRnGV/NA5IaHeL08H24v1zXyzExIUzFsw1BHB5ch/awVgrW1bPV0WHn3b1lztAaY4CBBxZlEbi7hAWTE3l1Z7HzWlGmQI5WnF361WIls1MiSI3uPvNeqVAoRhKaJ9jVXr2pUjxzwyxue/1LLO120mKCSY4K9uiPd31zEv5COCfLmtLEKzuKufaCFN3+crii0SkDp+h/iqpbiB/gAijRIYGkx4bwz8OVLMoeM6D3Ujjojaf4T0AOsA+Hvtu0zr9jhBA/kVJ+PADtU/QjrrFu8ybGOyfE4BhE73vvgEfc2h/+eYylc9N5dkuhm1dYL+bzZG0LBVWe3mRjgIEpieFqcB6CGAyCBZMSyIgLJSc1ykNTdX9ZvUes+YMbDvLKzbO56629bsu+S3JTnF+YtGOf2lTA32+f53z2PVGYUCoUipGItxWQDbfNZe2yOZQ3WIgNDeIHaz4jyhTozNMwCEiJMnGippknF8+g3WansLqFV3c64pC9rfQcq2xialK4+iI5QDjk2AZ+TPpqRixrvzilJsWDRG+CYU4Cs6SUuVLKC4BZwAHgG8DvBqBtin7GNdbNWwxx17g1S7sdIXDzCnuL+axstLjFk4LjvMeunu7U6FQMPQwGwbjYUC5Kj+GSyQlMiD8bf1jeoO+1rW5q44bZaW7POTXapH9s89mJc0/iLZUKhWIk4m0F5EilQ9XlJ6/tZmtBNZZ2O+UNFp7dUsgzmwtZtamQ/WUN/PGfBZyqM+PnJ9iwr8xZCGl6SgSPXT3do/Ldm/mlTsULRf9TVN1C4gCHTwDMHh/NnlP1lNW3nvtgRZ/pjad4spTyoPaPlPKQEGKWlLKov0scKgYG11i32uY2nt9W5OFd6OrMNQYYmJwQxmtLL2JmSiQna1s4WdvC0YpGokyBzknTHev2sHbZxdSZrU7FAc3LocWTKgafrjGMvc1AjwsN0vVCxYUF0WG38+TiGRTVtNDWYafB3H5OD2938Za9OUahGG54WwHxE4IVeZm0WG1kxod51TBekZeJzS4prGpm5ZKZSCTRIUGMiwmh5EwLy+anY5cOBaBXdxZTZ7aq1ZUBpOSMecBjigGC/P2YmxHLazuLuXvh5AG/32inN57io0KIPwshvtb58yfgmBAiCGgfoPYp+hkt9rfB0u6hH/zo1dOJDQn00Bx+9MPDSCQfH650amc+t/WsTi04PB7tNhsrr5tJndnKs1scyhOTE8Od8aSKwaWrFvX5qDgYDPDAoiw3m3hgURbHKhpZ8cZe7nxrL/4GwbZjVfgbhK4mdVcPrxZv2V1WfE+OUSiGE3orIMsXZPLbjYcBR4nmJz8+4tHfli/I5K9bjyMlPLOl0KkwUdVkdX5ZTI0OYXJiOM9vK3KGuqnVlYGjrcNGbbOV2NCBkWPrSt6UBN74vARLu21Q7jea6Y2n+EfAT4Gf4Ygp3g7ciWNCfEl/N0wxcJysbeG2179kYnwov1s8g1ZrByGB/pit7fz530VuXt5AP0Gd2Uqgn8EjHk6rnvTslkKMAQaiQ4LISY1WHr4hQl9UHDQPs7VDsn53idNOggP9eeXTIi5KjwMcyXWWDhs/+8ZEfvr6bo9YyNTogRG2VyiGIt2tzGgrIMnL5rDpSBU2O8644Kc2nR1L/7K1kNeWXkSH3U6wvx8P//0gt8yfwP/qKExofVmtrgwup86YiQsLwm+Q3t/kyGAy4kN5M/8UN148blDuOVrp8aRYStkK/L7zpyvNQoj1Uspr+61ligGjstFClCmQhdOSnAOtMcDAQ9+ZRlxoIM9uKXQe++SSbJ65YRZmq003Hs413lgbhLtmXSt8w/mqOLhmyUeZArnp4jQ3O1m+IJNXdxaTFGHkxjlprNpcwC3z0t1iIV0pOdPKwqxE9QGtGNF4U5dwtX2DQWC22li1yb2PaGMpQHFtK+02OxdPiKWjw853Z6dRWNV0zr6sxt7B42TN4IROuHJF9hie3XKc6y4cS5C/kmcbKPpTpzhdb6MQ4iTQBNiADillrhAiGlgLjMORwHedlLKu8/hfAUs7j18upfxH5/YLgJeAYOBDYIWUUqn5d4M3r0VCuJEluSms2lzgVg2ptN7MLy+fzO7ieiwddvwEnGluY9bYKOfkt2us27yMWK6ZlUxqlImSMy1UNrbRYu0gzUXBQDH42O0SU6D/eak4uHqYyxssvLKj2FmRMDEiiJM1rfxy4STiw43sKq7jlnnphAbpa6va7CiNYcWooKcrM95ii0MC/bj1kgz8DBDoZ8Bul5TUmXl6cwF3Xja5277c19wBRe84WdtCXNjghE5oZCaEkRwVzGs7ilk6T3e6pegH+rMUS3cT1EuklDOllLmd//8S2CSlzAQ2df6PEGIq8F0gC1gI/EkIoX0l+jOwDMjs/FnYj20fcXQXTzouJoSMuFDnhFirhvRmfil7TzXwTGfW87t7yhgbHcLx6iZHPNsNszziRS8cF824mBD+VVDFRwcq+OGLn3PzS/l8+2lVhcxXaM9++Ru7PZRAehJn2NXDXN5gYdWmQiJNARw83cRvNx6mrN7Cj1/6gic/Psbz24oI8vdj9Y0XsDwvg9sWZJAWE8wDi7LYdqzK6dFSKEYy3a3MuNI1tjgtJphnb5hFRHCAW1W6jQcraGi1cn1uKi9/WuQRa/zIVdNIjTL1S+6AonecqGnxSRLj9bljeWZLIbXNbYN+79GCryraXQl8vfPvl4F/AXd3bn9DStkGnBBCFAKzO73N4VLKHQBCiFeAq4CPBrXVw4iSMy0cqWjkls5vlOt3lbp5LVKigjEGGLgm56zH+JqcFKdgfFKEketzU/m5y1Lg49dm84+fzaO8wT1mrai6mX2lDc6iDaCqkPkSV4+VpgTiZ4C8yfFMT44EoKi62atXyZuHucMmeXpzAb+4bLJHfOPjG4+wbH46qzY54svvWzSV9btLmDcxnmNVzSoLXjHi6am+tsEguGxKAmuXzaGqqY2G1nb2ehk/n78pl7YOG3lTEvnL1kJnvL6U8PTmAnJSowBUBchB5kRNC/MyYwf9vmOjTXw1I5b/98FBnv6eXj01RV/pT0+xt7UaCXwshNglhFjWuS1BSlkO0Pk7vnN7MnDK5dzSzm3JnX933e7ZCCGWCSHyhRD51dXV5/dKhjl2u2R3ST2rtxbxzGaHCsSNc9KIMgU6vRZCOFQF/Axn9YpdtYuvyUlhbX4JS+emc9uCDG6Zl87KT45SXNvK7HExzsG2qLqZY5VNJEcE98hLMtrwhT26eqy0GN9Vmwpp7cxc3ny0knf3lPGf47W8t6eMzUcr3bxKVpvNw8O8fEEm9a3tXJ+b6jW+UbuEpd3OwxsO8cOvpDMlKYxnbpilsuCHEGqMHBh6qq9ttzuUfK5fvZPCqmZKzphJjgjmlnnpbnGqlnY7O0+c4bmtRYQHB2DtkE7t4me3FFJc20pVk6XHHmpF/1FcayZhgKvZeePanBR2F9fz/t7TPrn/SOe8PMVCiChgrJRyn8vmu70c/lUp5WkhRDzwiRDiSHeX1tkmu9nuuVHK1cBqgNzc3FG5fnSytsWtsthZhYBMggP8sdslEcGBrN9dwu15E928G9rfYUY/rs9NdXqRtYnRkfIGUqKCGRcT4pZUsiIvQ1Uh08EX9tidx6rkTAsFle6lmO9bNJVD5Q1MTYrAYBDEhQYhBDx4RRamIH9K68y88UUJTy6e4Uyq07u+a4S/pd3O0comnt9WxMrrZg7Gy1b0EDVGDgw9VYDQVnKiTIGEBwe4lXPWkli1whxGf4PzS6a2EqPhOr6qsXfwaLc5vnDEDZIcW1eMAY7Y8/vfPUBGXChTx4T7pB0jlR57ioUQ/xJChHcmye0FXhRCrNT2eyvzLKU83fm7CngHmA1UCiGSOq+bBFR1Hl4KjHU5PQU43bk9RWe7QgdXz4EWM7x6axF3r9/P9at3OD2DP/pKOodPN/KrhY4kjvW7Sp06s6nRJueEGM5KsCVGmqhqsngklazLL+2RRq1i4OnOY1XZ2Ob8EIazXt2TNWb+U1iD1WrjUHkTT20q4I+bCiioaiIuLIjHrp6OlI7j1+/yrFq4Ii+Tt3eXkhRh5NZLMliel8GkhDCiTIHcsW4PJ2tbfPZ+KBSDxbn0te12SXVTG7fMS+eey6fw8IZDHmPs9y9KZXleBo9cNY0J8aEkRRixtNtJjTJhDDCQFGFkeV4GTy6egZSQGmVSFSAHkdK6VmJCAvH368+F9t4xPjaEmy5O48cvfk5Jrdln7RiJ9MZTHCGlbBRC3AK8KKV8QAixr7sThBAhgEFK2dT592XAQ8D7wA+B33b+fq/zlPeB1zsn22NwJNR9LqW0CSGahBBzgM+Am4Cne9H2UYWrp9A1ZhgcXuOiaodOsead+M3V03nrJxdT3dRGQWUTDy6aginQ3y0eWatcV9HQSlpUMMcqm7hlXrpzn6ZS8Nebcumw2UlV6hM+ozuPVYu1w2up2ee3FfHkkhmcOmPmp1/PIDM+lN9uPExxbWunnWRz2dRYMhMiMRjgicUzKK5tYX5mLFXNbQT6C93VhVd3Fp9TBk6hGKloyhC1LW2crrdw9/p9WNrtLM/LcFP/0STZMuJD+dnaPW4rOS2WdlJjTLzz04s5XN7sXAnUJsCXTUngQ6VRPCicrG0hKcL3+usXT4jFbLWx5LlP+b9b5pARr8bX/qA3k2L/Tq/udcCve3hOAvBOZxlof+B1KeVGIcQXwDohxFKgBFgCIKU8KIRYBxwCOoBbpZRaCZf/4awk20eoJDuvaJ7CO9btcYsTBvj+Rams/OSYm3fiV+/s5++3z8MY0MGLnxZz24IMfvLaLo+JTZ3ZyoS4UK7/607d5b46s5XkyGA1+RkCeNMsTYsO8Rr6EGUK5NQZs9fl3D9uOsrtCyZy77tnP5AfuWoaU5MimNYZdnH96p0enq9l89PVUq5iVOKqXbx0bjprtp9NpgvyN5AWE+zxRfK+RVOJMgU6HREPbzjE0rnp3PTC5zx+bTZPbXIfkCbwcQAAd7NJREFUv+9Yt4cPO5Pq1Ng78BTXDL4cmzfypiQQ4G/guud28NebLuCCtGhfN2nY0xv//0PAP4BCKeUXQoh0oKC7E6SURVLKGZ0/WVLKRzu310op86SUmZ2/z7ic86iUcoKUcpKU8iOX7flSymmd+25TGsXe0TyFHy6fx7zMWOeyGkBcaJCup7CwqpmQIH+W5KboLuktyU3hkaum89CGgx77rslJ6XbJzm6XFFU3s+N4DUXVzUoqyIeMj9UvNfv27lI39RFwf74Ai7KTnRNibf+97x6gpM7sLEqgZ1sTE8JG3FKusmnFubDbJfvL6p1hZl0dFAYh+OXCKR5hag9vOOTsc9o27dy71+9jUbZ7jrlKqhtcfKFR3B3zM+P4r3njufmlfDYeKPd1c4Y9valo9ybwpsv/RYCqYDdE0TyFqVEmHr8227lkF2L0Irdlt7OnpI7xsSG6E5uUyGACDI5qS133ZSeH8+HyebpLdj2p8qQYPLQvTJNun8exyiYOVzQ6PcFdP7TBvdKWq1KJ634tNMJbgt+UxHCfP+v+LG6gbHrk0l92otnIkYpGj/6g/d9itVFQ1dxtn9POkS7KLl1DWVVS3eBSVGPmwrQoXzfDjZljo7h74WR+/c4BGlrbuf7CVF83adjSm0S733Um2gUIITYJIWqEED8YyMYp+oYm/bPyk6MsnZvO8rwMEsKDPBLiVuRlEh8eRKOlg9jQIDfPsnZMqDHAmRHddV9ihJHKRkfyXVePmbcqTyrxyncYDIK0aBNjo4JJjTZRZ7YC4NdZtdAV7QNZm9zq7dc+kL0l+I2P9a2XuL+LGyibHpn0p51oNmKXZ/vU+l2l/PryKc4CN5MTw7DZ7bp9SpuHu67kaP/npkWrpDofUlzb4jM5tu4YHxvCry+fwpP/OMpbu06d+wSFLr2JKb5MSvm/QoircahBLAG2AK8NSMsUPaI7z4brh/ezWxxSPu/tKeOeb01h2fx07BIMAhIjjNz55l6Ka1tJiwnmwe9k8cD7B93iRiOD/QlOCuOub07iiX8cddu3/I0vnclYXT1m3Wloqvg339DRYeejg+UUVDXjbzDw5JIZ+BsE9S1t/PwbE/nDP4+5Pd8zzW2d8ZDHeeg707j//QPO/Q9dOY2UzqSTnkpSDTY9Lb/rSnf9Stn0yKSndtITb7JmI5pSy6rNBcSFBhLob3DKIabFBPOLSyexIi/TLY7/4SunER0SwLM3zCLMGMB97+13OiRWXjeTr6THqKQ6H2GzS8rrLcSHD53wCVeSIoO5+1tTePTvh0gMD2auDwqMDHd6MykO6Px9OfA3KeUZIVRH9CWuy7hRpkCW5KYwMT6MKUnhpEWbnNI/oUF+dNgklg7HYB8fFsTBztCjjPgwfv/xEWdYRHFtK3/6VyEv/uhCqpraOF7dzO8/Pkad2cqKvExiTAGsyMtkcmIY0SGBzgkx6H+I9LTKk2LwOFLZSGldq5tW8Yq8TC4aH011s5VXbp7N9sIabHb4+97TXH3BWCKsHczLnMI/D5bxu8UzaLV2YAr05+VPi5iUEMqMsY7lRG8Jfn2lL8vavZ3Enis8Qtn0yEOzr3PZSU9DZxLCjaTFBLMoO5lQox/P3XgB5jYbRyoanUl0xbWt/P6Tozx+TTZ/uG4mlg4bJ2paWPmJY7y949KJzM808fR3Z1He0Eao0Y8xEcED1scU56ai0UJYsD9B/n6+bopXkiODue2SDG7/2242LJ9HcqTvlTKGE72ZFH/QWXijFfipECIOUNH9g4C3CYGrCPyNc9LcMpgfuWoaT28uwNohueniNJ7ZUujcNzEh1CkCf9uCDI844eLaVmqarc44ZI2nNjmUBGx2CA70w2y16cYYu36IuCphuH6IqOU+31FnbvdIqHtqUwF/uiGH/351F8vzMli1qdCpca2VdNbsSvsSpS3tnmlpG9D29jWG91yT2K79S8ruy+Yqmx452O2SkjMt7C6pp7i25ZxfdnrqTU6NMnH7gkye3lzA9bmp/Pernmo+2sS4srGNY1XNbsoUACs/OcbUpFz2lzW4eZJV/LrvKK5pIWkIhk50ZeqYCBZOS+Rnb3zJ2mUXK1vpBb1JtPulEOJxoLFTN7gFuHLgmqaA7r3BZ8yOZe3JiWHc1TlxgbOqAEvnOnSG3/jCUa5Zc+xX1LfqVrHTMAYYMLfp69napSPhqqeVlIbqkvpoxtKurxLRYnWoH2pxkF01rl3tSlOrsHTYCA0KwG6XA/ZMzyf8wRW9Sezj12aTGmXSnXA/uXhGtx5DZdO+pz8S4lyT4VZvLSLKFOgMdfD2Zaenqw4ldWZnX9ErgrQiL5PmNptjLA0PoryxVfe6TZYOjy+wvbF9Rf9SfMZM/DCYFAMsmj6Gh/9+iNd2FnPTV8b5ujnDht6WeU4GLhVCuFrFK/3YHkUXvHmD02KCWZ43kTXbi7hlXrrXDObQIM9yzT//xkR+v2QGv3hzr7OKXVdt2pqWNt0J7+SEMPwMAtk5CXpy8QwKqppYl19Kndmq6zFTy31Dh44OO8EBfrrPtrLR4fXferSKZ2/Ioaa5Tdeuwox+bra4emvRgHqv+hrDazAILpuSwOobc8kvPoPNDis/OUqAn4GpSWEeE+6CqqYefdlTNu0b+kv9QxtbtfGzvMHCqzuLnQ6EeRmxXDgu2mtYhOZk+GBvmUfojGazeoouXcs7r95axP2LppIWE+y28mYMMHjYIaj4dV9ysqaFWB+Vd+4tBoNg6dzxPPr3w1yenTRs2u1rejwpFkI8AHwdmAp8CHwL2I6aFA8o2uB6TU4Ka/PPenwnJbh7h70VZEiONHl4kf/wz2OsWzaHv98+j6KaZoz+Bp6/KZfKRgvFZ8y8urMYwCPp6oErsnjCZel8RV4mr+xwFPV47Orp5KRGkhqtPGZDmYPlDfz63f3cedkknvz4bMLkLxdOprXdxi+/NYkoUyC3vr6bW+al69rVmEiTM6QCBt571ZcYXs2jeLK2hb2n6nkz31GBERwhEi//eLbHpGNdfimPXT3dWTUsLSaYh6+cTmWj4zzlFfYtvVk5cK0mF+hnwGy1OT3Lrl+2NPsqb7Dw7JZCx0rJrGSP56yFRdz77tlk00eumkZqlMntOG3yPCkhzMN29bTgH9pwiGduyOG213c7r3vfoqlYbZIVeRmsc7FbFb/uO07UtDA5MczXzegxKVEmvpoZyxP/OMrj12b7ujnDgt4U71gM5AEVUsofAzMA9dVjgNEmBGFGh8d3zfYintlcSEFVk3NQ1TKcXWV6HrlqGhv2lVHlxcvWYrUxIT6U0CB//ne9I7v5yY+PYfT3o85spbzBwieHynnuxgv43bXTee7GC/jLvwvdkuqe2uQo7GBpt3PPO/sdahZqsjCk0eIY12w/wdK56fzyW5P40w05xIQGYmm3EeRncCqPeLOrkm4SkgYCb1Jv54rhdZXYuvmlfJ7bWsSNc9JIijA622y2dnhIYtWZreSkRvLh8nm89ZM53HHpJJa9mt8vcm6KvtPdyoEr2vP/8Uuf88WJOq5fvdPtGSZFOMZWPTv3Zl9aWETXkKKSOrPbcSkRwfy/K7Iorm3hD9fNJC0m2Hltb1rwja3tLJufzh2XTuQP181k9dbj/Peru3huaxE3XZzmbK+KX/cdxbXmISnH1h1XzUxm44EKCquafd2UYUFvwidapZR2IUSHECIcqALSB6hdik60CYHdLrnTxTunxX26Lvstm5/OrLGRpMWEkBpl4oLUKIrPmHW9bKZAR/asKdCfOrOVqiZHmWbX5cPJCWHOBBG9hDxteVD7uydLev1ZREHRc7T3PTokEGOAgfIGC2/vLuXGOWn81MU79dB3spzZ8a7LyRPjQ0mMMHJBahQHyxudiZsaA+m9Ot8YXj2P4qrNBSydm+70BqZG6yfNpUSaKKkz02jpoKi62a3srorp9C09XTnQnr9eXO8d6/bw99vnOZ+9Nn5OTAhjSmI442P17cvbhLzYZUxLjTLx0aEKZ6Ky5vUNC/LjaGULp7vkdGjtP13vGF9zUiO55ZV8j0TYNT/MJTE82GvbFAOLlJJTdcNvUhwa5M/l0xNZ+clR/vT9C3zdnCFPbzzF+UKISOCvwC5gN/D5QDRKcRZtQhAS5Oc2iHb1btSZrUxODOdrE+NJjwvF39+ABB54/4CHF+S+RVNptzmuZbXZWL4gk3X5p1i+IJM6s5VntxTy/LYiLB02j4HbFddKSz2ZFPV3EQVFz3B93x/ZcIgHrsjymkh3//sHWZJ7tsRseYOFNduL8DMI4sKC8Pc3MD054rw8t31Bi+Gdkx7rTHY7F94mMEK4FxbRSqK/sewiPlw+j8umJPDx4cpuPcyqrK7v6OnKQXdxvZZ2O9XNFuez/8P1M7hqZjKXT0tiQrx3+9Im5K4YAwx8eareOaZ9WlTrptxjaXeUbhbCwJrtRby2s8RjTF6+IJM3d50iJcqEAaHbXj+D6LZtioGlptmKv0EQEtTbVCzfc9nURHYcr6WgssnXTRny9EZ94qedf/5FCLERCJdS7huYZilcMRgEaTEhbt6F8gYLa/NLWLtsDq3tNjfvmeYVPFbZRHFtq5v3V0posbQTHeKIfIkJCWJtfgmLspNJiQ7mycUzKKppoa3DTmWjxXlPVxF6zfuhxRT3dFLk6rlLijByTU4KRyoaSY4MZnpyhBrs+xnNDqqb2pzv+76yRvismCcXzwD0Jwup0Sbnc9eec0xooPP5Dhf1BW8exXkZsVwzK9mtza5JcydrmjlS0cgt8xwLYet3lXp4mONCjRRVN6sVDx/QU/tzncB68yx3TZi022W3z1VPyeSOSydis0tuW5ABwL7Seq/e5PsWTeXhDYfOeqbjw0iMMFJntvL7JTPJHhNBaYO+J1nFEfuWkjMtJEYMz2dgDPDjm1mJrNpcwNPfy/F1c4Y0vfrKI4TIBsZp5wkhMqSUbw9Au0Yl3YUW6A3Gdy+cwvTkSLdB2zUzW0uU0pJHwDG4rr4x1znBGRcTwt0Lp/D4xsOMi8nkrrfOfs9JijA6J8LaJPwP182koKqZAD/BzLGRzBwb2eNJgea50fRvB0u9YDTS1Q5cP2D3lTVy29++ZO1/z9H98I0wBrhVPBwfG8KFae5Z+ENVfcG1D8WHGXnmhlnc9vqXbqERXRUFup6/u6TerbCJpivr6mE+UdvscV1lv4NHT+xPGzMf33j4nFJr4KlqoSVYBvgJtzHOdUJuEILDpxv5zSdHnNf+Q6cXu2u/So8L5YXtx1l53UxarR3EhRn5SnoM/v4G3XYrHeyhxckaM4nDLHTClUunJvDztXs4dcbM2GjTuU8YpQgpe7Z0LYR4AcgGDgJab5dSypsHqG19Jjc3V+bn5/u6GT2iJzJDHR12DpY3UN5gISkimKykcLcB1W6X7C+rZ9ORKuzSIa317ewxbgoSj1+bzbenJemet/lIFc9tdReQT4sJZtV3Z9HabiMu1IhBODy+pkB/EsKDPNQmupvYF1U3c/mqbZ0lg4s8PjQ+HL5xmj2aCQ2mPWrvtRYP/vw2z/d744p5HCpvcrO5R66aTlZSKC1WG3XmdsKNAbrPeajgam9JEUYKq5vZV9rg0NMWMD0lgoy4UCoaPT2KerZ6srbF+b5pGAMMLJufzlcnxBIXFoRBwMKnPI8ZYvY75GxyoOhuzNH2nWlpI6CL+kRXe9b6TJQpkJsuTiM8OMCpEuFtgrz3lCOBr+uY+fNvTOKXb+9z6VfTMFs7qGy0smFfGYuyk1mzvcirzWjtHsorMb2kp40fsrF0v//4KKfrW1l8wVhfN+W8+dvnJUQEB/DwVdN83ZShgK5N9sZTPEdKObWfGqPowrlkhux2yceHK71OmvUm1b9aOBmDQbh5/UKC/DwGV4NBYLbaWJevFyIx0emNPtfE/Vz7NQ/IkYpGpb05wLjG0+qFvqy8biap0SGkRJrc9Huf3nzMIQXVIfusAzvQdLW3e741CZvEo3x1Rmcscnfnaq8xyhSga5sTE8KcHuYdx2uU/Q4RzjXm9GZFo7LR4tSDb223OXWEkyKMXJ+byrJX8z3uYbZ6FsKxdkgC/NzHXXNbB3/+dxF1ZisPLMrib58Xd2szQ3UlZjRTVN1CWszw9rB+MyuRX769jzsunUhUSKCvmzMk6c2keIcQYqqU8tCAtWYE0lO1hXMVKOhu0jwuJoT9ZfUe+2vNVucEQcMYYODlH88mLiyI1ChHhn1tpxfl+xelEuRv4KnvzqK+xUqI0Z/pyeHO9nprQ/KyOUxPjjznxF5bekyODNZtl4qZ6z+6xtPapeTB72QxNjqYMRHBpEY7lmIPljeQX3wGu4S3dzu0UAsqm4dFFS3XwjbX5KSQER/mVNKAs1n7OalRjIsN1T2362t85ebZukvfUxLP9gNvscoJYUb2nqrzupKj6H/6Wu3QdfUtJiSQR6/K4qevf+kWcqSXkKrdQ88WluSm8Is393rYx5+/n0Nzm42XPy3iW9OT+PrkeNptdvaequvWg60YGpysbWH2+GhfN6NPRIcEkpsWxWs7i7k9L9PXzRmS9GbEfhnHxPioEGKfEGK/EEIl2nVDb9QWvGU1axNFb5PmykYLGw9WsOlIlcd+f4N+NaTPTpzhxy99zrt7y5wanj9Y8xn/91kJDZZ2mizt1LS08cQ/jnDwdJOzvd7asOlIFRsPVvRIP9RgED5RLxhtaF75tJhgbpyTxjNbCrl7/X5ufimfQ+VNTtu8fvVO3swvxSDgjksnct+3p5ASFezV1oYSrp69NduL2H1KP8HJbO3QPVfv2N0ldazI89SsHR971jb11A+euWEWu0ocS+k/eW0316/ewbt7y+jocL+Hon/pqWaxHh0ddt7dW+Z8Zje+8Dk1ze1EmRweNO35elOvqGqy6NrCxPgw3eN3ldRz11t7uXRqEvHhQby3p4z9pY0e+skdHXaKqpvZcbyGoupmpc4zRDh1ZvjJsemxcFoSL316krYOm6+bMiTpjaf4BeBGYD9nY4oV3dAbL8a5kitcPRKacoOfAQL9DDy+8TBXzEj28Fikx4XoerSmjQlnfOxk7nprr1PDs2sZaS3B6PGNh5mcGEZ6XKhXD5nN7qgOtnbZxT3Kmh4u6gXDmbNeeaMz5tFV8SM+LEi3fLgxwOC15KymbT1USAg3siTX3YunZ3+aV7zruXrHNllsvL271E3zu6tt6tlvs6XdmXgHZ4s6ZMaHMmNs1EC9BaOevlQ7PFje4FGI4/73D/Dk4hms3nrcGXKkXdObekVXW5BS/3gpz1YUXTY/nUXZyR4e6Mc3HqbdZnfTOB6KoUujjXqzFZtdEm4cfnJsXUmNNpEaY+K9L09z3YXDNz56oOiNp7hESvm+lPKElLJY+xmwlo0AeuPF0AZXV71U14Gwq+dvzfYiVm0q5PtrPuP63FS2Hq3y0L4M9DN4bFuRl8mv3z3grIineUH0lghXbS5gUXays716XpHlCzJ5e3cplnY77TZbjz3A56M7q+gdWqy4NiF2tZutBdVen/tDGw5x98IpXrWthwrjYkLcvHLeKvCl6WRad2fL5Q0WVm0qJDjQz6ttdrXf0w36fb2iYWh510ca51vtEHAWY3HF0m7nWFUT35qexMYD5Sybn86khFAeu3q613t0tYW0aBMPXTlN17a0e9ilvgd6UXayh8bxHev2cLK2pQ/vkqKvnKhpYUxkMEKMjM+pb01L4i9bj6tVCB1687XniBDideADoE3bqCTZvNNbL0Z3yRVOz1+Ekev/utNj8vrCj3Jptth45KppGAP8GBdjIjjAn0c/PMTSuemMjzVh9PejtN7MtRekYAr0cxu0vS0R+hlwttfZhmVz2FZQQ2pMCKc7r/fB3jKiQ4LISY3utQdYVbkbODQbdJ38JkUYyYwP6/a5F1Y1O7WtDcJd23qoYDAIpiSGOfuYa2XHsVEmTtaaeXpzATNTImmxdnjE+moevtP1ZurNHRTVtHDtBSms31VKndnao2I0mt3GhQbpeteHq67pcEHPU5saZerReJIUEex15eupTQX86YYcdpXU8+THR3nl5tmsXTan04aMZCWd1VXvOn5JCeu+KOZ3i2cg7RI/g2D11uOUd35BMgYYMAj3qqQafgbvoRpDKZ5/tDEcyzt3x7Qx4SDhX8eqWDA5wdfNGVL0ZlIcjGMyfJnLNgmoSbEXBkJv8lRdq8egGWUK5ESN2SkfZAww8NjV07kgLdKpQbxs/gTnUqExwMDPvzGRX18+hee3F7F8QSZtHTbdD4jctGi39hoMgqykCAqqmvnfzrLTmkcuNcrU66zpnkjRKc6froofmsf45U+LeGBRFhWN+oUCOux2Z6GKFXmZpMeHDrmYb7tdcuJMC3dcOpGVnzhkB+vMVoID/DC3dTi9vgfLG92Wox+5ahpXzUjG399AapSJ/WUNbvtX5GWSmdD969Wz24eunMazWwoorm113icrKWIQ35HRieuY05vxZEpCGA9dOY373zs7Lj5wRRbtHTZumZdOa7uNDfvKuG/RVA6ebtK9JuBxv6e/N4sFkxPdxscVeZlUN1sd6hNXZOGH5Nl/H/dQhbkwLfq8w0EUA8fJmhbiwoaWU6AvCCH4dnYSz2wuVJPiLvRYp/icFxLiV1LK3/TLxfqJoaDB2Vu9ST2vKTjik4trW/AzCI6UN9LYZmP9LseH/vK8DF01B8fSXxiJ4Ua+v+Yzj/1/vG4mhyoaMQX6MT42lNrmNh5ymVjraRqDuwau6/XOR6e1P6/lQ4a0JqxDh7qB61fvcGpEL52bzoZ9ZXz3wlQ3PVbtA39KYli3etS+ROsjJ2tb2HuqnpiQQGparNilo2Lj27tLCfQX/OKyyRRWNTExIYxH/37YzVO3tlMxZXthjVNqS8MYYGDDbXMxGASVjRZMgf5YbTZiQoKc/deb3b629CJqm9tI7PQm+lB9Ykjb5EDR9blkJ4ezbP4EEJAUbmT6GMcz0eynsLIJq01i6bAjJWzYV8aVM5NZtanQOQZmJYWz6JntumMU4GEHr9x8Icte3eVx/BOLZ3CkookN+8pYcsFYWtvtRBj9yEmLpt1mJyHc4eXuTnpzGDOsdYpvf303yVEmvjYxztdN6Tdsdsldb+3lj9fP5KL0GF83xxf0Waf4XCwBhtSkeCjQG8+pnpfjmRtmeWjGLl+QyQd7y7hxThpr80sYG2XSXXKzS/jFm3t58DtZuvvb7ZJVmwqd25IijCydm052cjiZCWHnLR/XG/rzWgp9XBU/NI+xEFBc28rjG486n7sQMC8j1qnHO34Ivv96feS+RVN5M7/UOenVdGVdPXVaVTotjrSiwUKYsYX84jO69neksok733Q/f21+CXcvnMLCrESvdttht/PNaUmD9n4o3HF9LtnJ4Xxvdhp3utjBw1dOI9IUwO1/+9Lt2WoOBnCENYDjed69fh9/+n6O1zFKS55zpaqpTff4o5VNzsqilg678+83ll3ExRPO6mirJOShx4maFnLHDW85tq74GQRXZI9h5SfHWPvfF/u6OUOG/nRjqF7bDXa7PKfMjp5axb7SBo9tWgLcqs0F/OKyyVQ1WXTl3LQB2xTor7s/NSqYtJhg7rxsIo9fM517Lp9ChNHP6bHwNhCfSz6uN/TntRTe0WIv8yYnYAwwEBrkx/K8DG5bkMG1F6Tw9u5Snt9W5KjY5hIrOdSkofT6yMMbDrEkN8V5jLek0WtyHMdosb6VjRZnXKcrxgADxyqbdPuclvTUE7sdiu/fSMf1udwyfwIPbjjo9hzve+8A+8saurUN18VTS7udkCD98TM+zOjFDvxIiwnm1ksc/eu2BRmkxQQzKSHM+bd2D2/qPCoJeeggpaT4zPAu8eyNeRNjKTljZsfxWl83ZcjQn5NiNeJ7oad6xXreJ7uOJ8JVNaKwqonXdpZ4aKtq2c7GAAOldWaPrHzHEnk4ty/IdGjYvr2fu97ai03CgdMNfHSw3KvGal8yvgfyWoru0TzGz9wwiwA/A6u3FvHM5kKe31bETRen8cTibFKjHEoNvdHYHky8eWhTo0xOG/KWrCTEWUWKKQnhdNgkH+wt8+gbj109nTfzS3XP1zyE57Lbofr+jXRcn0trW4fXFbSu2zTbWJF3ViUCtKIsQV6ftZ4dRIf4c+slmazZfrZ//eRrGfx163Ge31bET7+ewaGyejXWDRPqzO3YpSRsBMixdcXfYODqWcn85qPD9Fco7XCnP5+y+jrrhZ7qFeupVfgJ75qXxgADCybFM2tsJKYgP577QQ526Vi+q2luI9BfsHxBJq/sKCbQX7B22Rxa223OJbmTtS0eOp1PbSpg2fx0qpraSI1u0NVY7a3OcHfqEkqzeHBwfQbxoUEemrpPbSpgRV4mJXXmc1ZQ9GVYizdFl7QYE68tvYidRbWkxbjrcydFGPnxV9KYkhRBdnI442NCOd3Yyr3v7ef63FTW5pewdG46fgbISY1ifKyJOrPV7b6ufc6bPm1qlImSMy1UNrbRaGmnpLaFKFOgM2RjKLx/I52uz0XPVlyHlqQIh9b15IQwVl43gw6bjSW5KdilY+ydnhJBanQIqdEhXscoPZ3im1/a5dZ3HvzgIEvnprOvrJEH3j/IKz+ezX1XBKmxbhhwoqaFMREjR46tK1/NiOUfByt4f+9prpyZ7Ovm+JweT4qFENFSyjPdHPJmP7RnRNLTuFk9tYrpKRE8ctU0N+UILb5x5XUzyU6JxGAQzupMrsfdt2gqaz8voc5sZeV1M5meHOk2AHtrl+ZJqWpswxs9jZXuSTZ4bxUrFL2j6zNYnpeh+9xbrDanTQ7VWG9vii4XpDni/aqa2nh842FnVn+UKZD/+Vo6LVYb/9WZUKd5g60dkld3FnNNTgpCgM0OoUF+jI3yvIdrn+uqT6upHmw+WulWIltTeXnp05POibGv37/RgPZcUiKCPdQlHrpyGm3tDqWdKFMgN12c5nxeaTHB3Pr1TGfSsraqYLdL/P0N3cpluu7bcbzG60qF9nd9azuzR2dy07DjZE3LiJZWNAjBD+ak8ejfD7NgcjxhxgBfN8mn9MZT/JkQYg/wIvCR7OJrl1I+1p8NG0n0VK9Yz/tkEPDDFz9n6dx0gvwNjIsNoaLezKrvzmJ6ciTgyLiubmrz8Po+vOEQf7huJja7JDjAkXHtqmZhEKJbT0qkqfedw26XnKhpofhMCyGB/oQE+fH4xsNDzuM4mujq9dXTR9Wee1yokaLqZlrbbazIy2CdSwLbUIj1PtfKwmVTEkiONFLb0sZrSy/CLu1UNVqxtJt5YvEMTtS0YLXZeWrTMUc1vE2FzoQnY4CBa3OS3e7hUJ/wo91mZ+G0RK+evZO1LewrbXBTgbG0O6qXLZ2b7pS38/X7NxpwXRWZPS6KV2+ezYmaFkKD/AkO8qOgooknFs/AIByJyNrzWpSdzP3vu4+helUJz6Wr7m28d40jjg4J7LbdSq996FBU3TyiNIr1mJwYTnZKBI/+/TC/vTbb183xKb2ZFE8EvgHcDDwthFgLvCSlPDYgLRtB9EavWM/rUFzb6vzg1nhj2UXAWY3MW+al///2zjw8qup8/J8zk0kmk30hISQkEBK2sBsRLVAN1qJFUcStVlvFUtsiVH+2Lq1at9atWim2arWtS6vgrhQRBSz6FdTIvicEAokhCQGyT7Y5vz/uvcNM5k4WSJgs5/M8eTJz5i7vvfe95577nncxtU40trgoKK9hWa5WkMAzm0WMI9grx6vhUxcWbEVKqG5o6tRxmlmFF83I5MZzhvLsugL34EpZzE4vra2+b31TxK3nD+epT7yve2ZiOPsratyuFUb7y+sL3bMNPcH/0WxmwXgZ21VSRV5ZNctytbRsC87LZMnaPK7KTuXXrbJReJZBb31Pdnb2wgjaa8uXuaecv76MWR/0h8vG8uqGQmaOSfLKCfzg7DFe18tfIZvDlU7GD/a//dYzX2b9vXEfGbonW4XgqHztPZd95bVkJPT9Z9U1k1O5+51tfLKzlPNH99/cxR0eFOuW4Y+Bj4UQ5wGvAr8QQmwB7pRSru8mGXs9p+I325aVubUF0Gy5vaU1vKgX6HhlQ6GXNauk0sk//+8Ai2ZkMjjWgcNmpUmPmH/964Msvnpim7K1tmy4XNLHD9XwUZ4zKcXLIqcsZqeP1jpUUunkP18Vsmz+FCpqG925iAFmPv2Zz/V76YbJDIjomf6PRoaHnYer2Fd24uVvYU4mLim5573tzJuabpqN4qkrJ7D0p1OobmjCYQuivrmFT/eUMTQ+TPfN77jFLjHS7tf/f1pGPHMmJvfI89fXMPOFv/udbTwxd7w7NZvRXnSszvR6tf4+MNJOYUUNpZUNOJtb+Mfn+3hs7njqG5pxhATxj8/3MXJghPsFyrO/31deQ35ZDQCXn5GClLA09yDfyfB2neipPvwKKDhSw7TM+PYX7OU4goP4xbkZ/PrNLbz183P6rd51xqc4DvgRcB1QCtwCvA9MQPMnHtoN8vUZTtZvti0r85f7K9yd6FvfFPlURzIGwsYgYN7UdB9rVkmlk0dX7uHpqyfwi/9s9PKla6sal5ll49HLx5laWoIsFuDEwN2ofqc4PZjp0B0zRzGmlY+5P19IieyRHaSZDho6v3hNHvdfnOWVNcITZ5OLvLIarFbB4eP11Da28PTqPB8/045a7IbEhTE2JYpFMzJ91jXyPiu6H3++8BJfHViWW8QfLhvL3e9sw9nk4oMtxdw3K8udxs3oqxpczXyxr5r7P9jB3ReN5PJJ3jmw75uVRVW9d2Cm0d9X1DYgJT79clOLtyw91Ye/vyOl5ODRuj7tU+zJ8MQIrsgezPX/+Iq3f34OCX3cbcSMzrhPrAdeAS6VUnrmK8oVQjzb1opCCCuQCxRLKWcJIWKBpcAQ4ABwpZTymL7sXcA8oAVYKKX8SG8/A/gXWrnpFcCi1n7NfRF/VmYAm9XCwhkZuCSs21OGEPDkFeMRQrCvvMZdrAC0DjbCbiVFT13V2hqSlRTJ0vlTOFzp7FA1LjPLRkF5jem20+PDcAELcjKQEv6yJo9JqTEdCtJTPnanTkdnKjrq+95T2H/EVwcXr8njsbnj2VtaTVL0iRyyZsdlswoam1wcqW3k+XUFxDiCueuiUeSXVXPTtHR3QYeOWOwsFkHOiEQyBoQzKTWGusZmUmPDGBqvdPZ04k+HB0X5th+ra2REYjgv/jib9QVHkRJe+6rQXcjmO8PiiLQHUVHbyP0f7NCD8cL42SutMkss38Gr8zR3ttZ9VqwjxJ3dRAjcluKZYwZ2SO6eeu/1F0oqtYqWjuC+l47NH+eNSKCqvokrn1vPa/OnkBQVGmiRTiududIj/A1CpZSPtrPuImAXEKl/vxNYLaV8RAhxp/79DiHEaOBqIAsYBHwihBgupWwB/gbMBzagDYpnAh92Qv5eS2src3Oziy8KKsgtPIpLwoZ95VwzOc3LwrFoRqbXNtLiQomw23j8o90+FuUnr5zgThJv+M61h5llY1luEffMGu1VMtjwn/vjit3uATrQrgVE+dh1LR2ZqeiM73ugcbkku0qqTK1r+WXVLFmTT1qcln3gmbV5Pjp/38VZxIbZ2F9eh0tCjCOY66ak+a2CV6gHqbalexaLYEh8OEPilWUvUPjTYYsFHx249fzhHKioY29pNS98diJAcmtxFWlxoWQmhHPDv77moUtP+B6XVplXqztS0+C3IuktOZleWYHMZsp6073XnygoryU5un8NCgFmT0jGahHM+esXvHzjZDITIwIt0mmj3UGxEOID9MIcZnn6pJSXtLN+CvAD4GHgNr15NnCu/vkl4FPgDr39dSllA7BfCJEPTBZCHAAiDb9lIcTLwKX00UGxyyXd+U7rGpuJDQuhsaWFuLAQUmMc/Hd7CXe8tdWr82xtMXv964P89qJR7C6txirgzKGx3PSSlpLqlQ2aNSTUZmFKehwS6c5M0dEBZ0KEueWl1tnkZRVZs/swC2cM51czMjlS28CrG7QUce1ZQJSPXffhzwLfG3JGG7IfqKgFPz68xsy0FqCax5+umMDukkqeu+4MyqoasNusvPRFAT85J52s5HCkFIxMjPDxOTVcjl78vIBNh45T3+RSL2WnmfZmi8x+n5k1kNGLplFa1UBtQzPxESE0NbtYs/uw5gvc2IwjOIhjtQ38vze2EOMI9howp8WF8siccawvqOCWnAxS9Mqfs8YlMzAyxFTnUmJC2VZ83N1nJUXZmTMpha1FlYxLjuLpqydyvE7z33/piwKfmbLecO/1R/aV15DUT1wnWjNr3CCiQm1c+dx6nrl2EucM6/t+1dAxS/ET+v85wEC0ADuAa9BcH9rjz8BvAM9XjUQpZQmAlLJECJGgtyejWYINivS2Jv1z63YfhBDz0SzKpKamdkC8noW/fKdGntQHZ491D4hBe3jvPuxtMUuKsnNVdqr7Ia8VNwhzFxIoqXTy9sYirpuSxo9e/LLTlliXS7K/osbHf/Lhy8ZS62ziyU9OPFxu/m4G8/XpRrvNwm3fG076gLB2LSB9xceup+ljexb4npwzurXsaXGhPj6ghnXXoLCinoraRqqcLe5pb2M5Z1MTdcdbuPf97X6zt1h1C+MrG7QMHH3hpayn6aQ/2tNVf79fMCqRnSXVXu23XzCCa6cM8ZoJMGIgSiqdbkNBhN1KQoSdG/71tXu5xddM4BfnZnDf+zv4bG84912c5XansNssPD53HIUV9ewprXIPiK+bkuZllfbM4rIwJ5OjtQ0+etST773+Sn5Z30/H1hbTMgcQGxbML17dyMOXjeUH45ICLVK3026ZZynl/6SU/wMmSimvklJ+oP/9EJja1rpCiFlAmZTymw7KYzYak220m8n7vJQyW0qZPWDAgA7uNvA0N7vYcugYK3eUEBZspb6phZumpbMgJ4MYRzCL1+Txk7OHUFnf5PPwNvLOGsyZlOITbX/3O9u4IjulzWVuW7ZZs8B5bluP7l+/7wgF5TVuy8yC/2zi5fXag2RBTgbzp6czNM7BpLQYXrphMn+//gx+fcFI98PD2MeTH+9laFx4h6L5PY8JeqePXU/TR38W+NbX/XRipmNmv3994KiX7IUV9Ty7Lp/H5o5nQU4GT8wdz9Lcg15uOnabBYfNapp9YlBMmFdeWjN9y0iIcLtQGC9lHZG5J9PTdNITz/O6rbjSNMf5gYpamptdbDx4jGpnE4/PHc+45Ej37ztKKt16Mi45ksfmjifaYWNQVCh3XzjK3acaMRCepEQ73IF3SVF25k1Np7FJct/7Wj+2tbiK174s5Im543nmhxNZOn8KowZG8v/e2Ozuh8361qdX5zFnUopb92zWdh+9ih5Afln/tRQbZA2K4s4LR3LPe9tZvvXbQIvT7XTmzhwghEg3vgghhgLt9ajfAS7R3R9eB3KEEK8CpUKIJH07SUCZvnwR4OnVmgJ8q7enmLT3CYxqdFc9v4EHl++i4Egdz68rYMmafF74rIDrpqQxPCGcsBAb+WXVPh35B1uKuWfWaHe71WIebT88MaLdZYyHPpyw1Fy0+DOu+fuXXLT4M1buOOy24pZUOnlmbT5L1uSzeHU+a/aUM/fZ9VTUNhIeEsTu0mrTfZTXOGkPw8fOM1BK+didOm1Z4AOBPx0zBpmev3+W75sdo7Ci3u0T2tTi4vqzh3jpzCNzxnG01twPtLz6RLuRvcVz3UUzMvnjil0+xUvak1lxcrQ+r1c9v56rslO9BiXOJhdV9Y28u6WYH734JXe8tY1fv7mFayanuQfGxgvMuORIrpms+Ynf/sZWfvzPr6hpaOaDLcVcNyWNtbvLeHD2GNLiQrluShovfl7g7rMMa69nm8HW4ioWvLYJR7CVscnRlNdoemTokL++1bOiXV1jy2k5p4pTY195Tb/0KW5NWlwYd8wcyT3vbueLfUcCLU630plB8a3Ap0KIT4UQnwJr0QLo/CKlvEtKmSKlHIIWQLdGSvkjtFRuP9YX+zHwnv75feBqIUSIPujOBL7SXS2qhRBThObYfL3HOr2eHSWV7kCMOZNS3IFqcMKqNX/6MO59fzvLcn0f3ldlp7L0Ky3CeeGMDM4ZFmdq9Ro1MJIVC6fx+vyzmDEysV1L7IGKWh5ducttDb5pWjqPrtyFIzjIdF0pT1hzHMFB7rytbe3DH4aPnSHvioXTlD9nF9DTLPDtWa7NcnF7YrdZGJEYwdNXT+RYXSMxjmCeuGI8d144gvnT07FZBSWVTj/HHOJuN6bQ509P5/nrzmDRjEwcNivH6hrdy//xsrEMiQvrkdb2voDZeV28RrOwGthtFppd+FTvvH/5Dm6aPgy7zUJSVCh2m4Wbpg9zu9Z4bm/WuGQWr8nj3JEJNDQ188DsMTibtZm58BCrqbXXTH82HTrOyh2H3fEVhg5lJkT47R+Nz/15Sr63UNPQTGV9E/ERIYEWpUeQGuvgF+dmsOA/myg+Xh9ocbqNDg+KpZQr0Qapi/S/EVLKVSe530eA7wkh8oDv6d+RUu4AlgE7gZXAL/XMEwA/B14A8oF99KEgO8OyAVpVpRhHML88L4MFORnuqT6XlD7+b49ePpZ5U9O1ohzFVTyzVrPYbj10nIcvG+tjZR0aH0b6gHCmpMczNjmqXUtsRW0DV2Wn8uLnJ6zWV2WnIqXLZ92FOZm8vVFz+3Y2uWhqaXHnbT1Za6/hYzclPd6dHUNxavQEC7znFPmBito2Ldeelm1/1ty/r9vHkZoGHvtoD7ct28Ltb2zB5YI3cov4f29sQYLPegtzMik+Vst9s7Lc7cfqGkmKDCU0WPDoyj08u67A/UI4b2o6KbGhWCyix1nb+wr+zqvhaWDo6pEac8u/s7GZJ6+cQFZSJE9eOYH6xma/Fltnk4uspEhqG1387JVvWLxa698EgrtmjvSy9prp3cKcTN7ILeK2ZZuxWnDfUyWVTp5YtZuHLh3jo6dvbyxSM169iP165gmLSYKB/sqY5Ci+n5XIr17f1GdnxjpTvMMG/AyYrjd9KoR4TkrZoVrAUspP0bJMIKWsAGb4We5htEwVrdtzgTEdlbcn4hkpHWEPoq6xhdqGZuLCgrn7whFUNbQQH2bzKR6waEYmSR55Ng23hUUzMnjx8wKvjt9us1DpbGFiWigr2ohkbiva2ZBTujD1xfxOxhRmZg1kxC3TKDhSQ0OTi6N1DVx7ViouCekDwqhvaiFjQDjD4lXe1p5EoKPcWwdHLZqRYRrNH2qzsn7fEfeshKH3K7eX8MTc8VgskBhhZ1dJJT+dPsxdwhm8M0e8vbGI0YMiqa5v5l83TOZIdQORoUFYLVDb6KKssp7nrjuD43VN2CyCf/xfAffoA2XjPjNkunySFtvbVk5ZlVv75PF3XqdnDmB0UiRJev70HSVVpstlJIQjJXyyu5TU2FDqG4PNr1N4MEuumUhosNVd6hw0vXnqk70sOC/D7WrmaYiYPz2drEFRtLS4yC+v5fIzUnjrmyIOVzl97qnUGAeTUmMoq3YyINyO1QITU6NVVoleRH55NYOU64QPs8YO4qH/7uQ/XxXyoylDAi1OlyM6Wv9CCPECYENLoQZaZbsWKeVN3STbKZOdnS1zc3MDLQbgPRgwq5p118yR1DW1kBrrYG9pNctyi7x8Ge+dNQohLF5Rz3+cM5aGJhe//8A7+n5p7kH++ZPJJxXF7CnnL87N4MmP9/os89pPz+KsoXGs3HGYR1fu4oozBpMW50AgKDhSS4vLRawjmH98sZ87Zo5idFIEJZV9epDQoQPqSfoYKArKa7ho8YlS0klRdp974aFLx/CXNXkUVtS7M5jc/8EO0/vmoUvHUF3fxJHaJrfPplF044HZoxkQbmfX4SpcUvO9vyo7VSum8J2hRDts/OatbV4vnykxoXx/1EA+2VPmleXiwdljsVkFCRF2LAJ2fFtFXlm1u6y0kfVg1a7SnpJbu9fppFk2CU9dMM7n+SMSeH/bt165f/84ZyxNzS7uff9EX/jXaydypLrRq+2Bi0djs1nZf6SW5KhQDh2vd+uLwd0XjmBofDhVzmYOHq11X+O7Zo6koUULFvbUmQvHDFS5qdunozdAjzE/PrZyN2XVDVw+KaX9hfsZh47W8YcVu1hz+7nEhgUHWpyTxVQnO1O840wp5XiP72uEEFtOTab+g6e/3JxJKe4HO2juEnVNJ8rMXpGdwm3fG05ZtZNXN2jR9FaLhZXbNCuZkY7j+XX7AG3qbvfhKlpcWrWkO2aOOunpOU85G1tcppaWxEi729/YGGRclZ3qk4Lo6jNTuW3ZZuZPT2fx6vxADxIUPYDWU+QllU5eXl/ISzdMRiIJtVl5cPkOZo1L9hjkHuSxueMR4GMR/suaPBbNGM6jH+3xejFcs/swobYgbm1VAnpp7kFmjUvmDx/uZv70dK9tPb06j0UzMimqrHdb/o7WNlB83Mn8V3JN02v94bKxTEqNJjXWv69xX0jjdjpoPYsRarOy8PVNFFZo/ovG+fzvLdO4dHwymQnhFB+vx+WCkCALt7y9yevcbz5UyRf55Tw2dzyNzS0MiAjBHmRh48HjPL+uwEsvjAwjaXGhxEXYueX1Te7f75k1mqr6JqobmlmyNt9HZy4YPdDvMSl6L7sPVzMuOSrQYvRIBsc6OHtYHE9/spf7Z/fqCXwfOhNo1yKEGGZ80TNRqBDaDuByScqrG9wp1iLsVq+BgTFINqpqPb+ugF+/uZW/rMnnuilppMWFUny8njOHxvHwil3UNTSz4LVNlNc0Mm14AvllNWQmRJCdFsU/fzL5lAad7flwGv5wpVVOd8CK8b/1wyIlxoGzyYXhemQ81L4+cLTXpbFSdA1mgX7H6hoZEBHC5CFxNDS7uOrMNIIsmv698FkBOSMH8u3xOvaYZDOZNS7ZnUILTrhO3Po9LYWQWZCV4VPaWv2cTdoMx97Sancxm9iwEJ+84J7pte5+ZxsuifI17iI84wjqGlvcA2IDZ5OLXYer9OqbMcQ4glnw2iaO1jb6nHuXhOLjDew5XM2Bijq2F1e6r59ZMJ/dZuH3F4/ht6306cHlO6lpaMHZ7DrpbDqK3kd+WQ3JMcp9wh+XjB/E25uK+1zQXWcsxb8G1gohCvTvQ4AbulyiPobZlOBjc8dxx8wR1OppecJDrG4LspkP75NXTuDB5Ts5VtfI/OnpOEKCSIsL5YeT09w+cUZ0/NBTLDqTFGVn4YwMgiwWhsaHcayugSfmjicsxEpaXJjb/SEx0u4ORjEGGZ44m1zUNTR7RV0b7Z/lH+GFzwpO2Wqs/Dd7H/7K2Vot8O7mYp5evZdZ45KJslt57PJx7Pi2ivqmZqakx3KkponstCiuPyed+oZmHCFBlByvN9W943W+gyQjaKvFpb3gtVYVu81CcWU9f16dxxXZKQxPiMARbDXdjmd6LaOgTFu+xorOY5zPGEcwcyalIARYBXx7rI4DFbWkDwhnULSdJddMxGoR3DlzBBLc/erAiGBu+M4Qnvx4r3sGrrrBPPhueEI486amU+EnfZ9xvdX17R84m1o4XOlkoMoS4pdoRzDnjUjg2U/38eClfcda3BlL8f8BzwEu/e85YH13CNWXaD2lGuMIpvhYPU+vznNndIi020iLC/U7uMwvq3FnqEiNdfDSFwU8MHuMT5DIXe9s48Pth086Z6rLJdlZUs3z6wp48uO9/PrNLdQ4W3h81W7qm1xeg84hcWGcmRbrZUX2xG6zEBVq46mrJvDZ3jKvds/UbSebxkrliu2dtE61999bphEcJHhrozYgvio7leVbiwkJsvJ14VFqGpsB+LbSydpdh7kyO5U/rdrNwWP15JVVMyY50lT3YsKCTdtHDoxk+dZibj1/OAPCQ7z0d9GMTD7dXeaerVnw2ia2FB1vN72WMSjqCZk9+hKpMQ4emzuO689Oc2fAeW5dARaLhaO1DTQ3u/j6wDFuf3MLP//3Rv68Og84McMQGmLj318Wes3A7T7sm+fdbrNQXuPEaoE4P3pjEdp2TyWbjqL3UFBey8AoO0GqyEqbXDhmIO9sKqaipiHQonQZnQm0WwZUAf/Wm64BYqSUV3STbKdMTwgiWb/vCNf8/Uv391+eZ54x4q/XTmLLoeM8t873t8fmjmdvaTVWAWcPi2ProeMMHRDOT1/2LRT46Jyx3PfBDlZ0wo/RsLgWVtRS29jC0doGYhwh7NeD5uw2K0+vzvPZZnOzixXbS/jTx3t8fIp//f0RvPDZfo7VNfqUODX89wBen38WU9I7b95uHbBlnKvOHHcX0uuCmgKJp4XfERzEwtc3cvH4ZHclx9RYB2EhQTzy4S53gNU9s0aTGBlCQVkNEuF+IUyLC+WX52a6K9MZg9uIECu1jS6vmZQ/XDaWZpcLuy2Ib4/XYQGmpMdRUdtIkNXCb97cypxJKV73p1kgoKc+P3r5OH4wJomgIIvXsQUis0crer1OFpTX8NGOw17uDqDd50vnTwHgquc3eF2rK7JTSI4K5Vh9I1JCrCMYR0gQT6zaTWFFvWkJ5t9fnEVYiJX8shq2HjrOBWOSvAKa77s4i6SoEI7UNDJqYAR2WxDlNQG/vr2NXhVo997mYpZ+fYhbcjIDLUqP54XPChiXEsWi84cHWpTOcsqBdiNaBdqtVYF27dN6StWfNXhvaQ1jU6J44JIsr2jp+y7O4k96h263WYgMtZEUHUqE3WY6lecICfKa0m0PM/eO+2ZluR8ixoAkxhHss82gIAvjUqKYPSEZiwUemzueA0dqaXa5aGx2uQe+T6/O4/G547EKePC/vhXCToa2/DdVUFPPxUzfFuZkEm63YrVYvAafni9QDy7fybyp6VgtuIOkQKto98yneTwxdzy7S6uxCEiJCeXv6wq4fFIK86enaz6/AsJCrBRWNPDkxyfuryevDGNm1kAOVNRyrK7R5/5sHQgYHxZCeU0D9U0ttLjgyY/3YLNa3G5Ahk+s0sFTp7TKSW1ji7lrVmML1c4mrwGxMdg1y1LiqUtGnvf0+DCiHDYeXL7Dq6976xutEJIQICU8+7987puVRbTDxqikKCwWwbAEdX37MrtLqlUluw7y/ayBPP7RHn5xXkafKF/emUHxJiHEFCnlBgAhxFloLhUKD1r7uabGOLx8KI0qb60Hs9XOZpZ9XcjPpme6H+SjB0bw6Ee7vaKvH/9oD4tmZDI0PoxFMzJ9LFhFx+pIiwt153ltz9fWLGL+/uU7mDc1nWf0SOsHl+9k/vR00wFsSaWTxavzfdoX5GS4PzubXOSVVTMpNcarQtipTD0q/83eib+qZU9eMZ7b3vDNNfz43PHsKa3mrW+KEEILnmo9SCqsqMdmtXCGngWivqmZWeOSqKhrdAfTvZFbBNkpXgNqz+wQhuvDnsO+OXCNQMD0AeEUlNdww7++9vpdZZjoHhIj7YQHW0mLC/XKRvLBlmISIuwEWy3ua+UZj9E6u4+hS0afBlqZ+xiHjV/8Z6NPUJ3ncgYtUjJjZKKyCvcTdh2uYuLgmECL0SsYHOsgMTKEj3eWctHYpECLc8q0OygWQmxDm9KwAdcLIQ7q39PQKs8pdMysYEb+0v/eMo1dh6v49lgdt54/3Gtad2FOJpsPVXD+6EHc9sZmtyvCTdPSTaOvB0SE4GxqITMx3MsS5rBZ+WBrMbfkZLqnFdtLg+bP4upZxMfZ5GJ4YoTPANblkjS3SNPBqadXjuHLGR0a1GZBkc7gL2BL+ff1bPzpm78AqD2l1bzwWQGLZmjTmLWNLab6lpl4wjrb2NjCrpJqnvxku9c9ZrGYz9IYswszswYyOimCtLgwd0aL1nqlZihOH6kxDoYOCHPnqfZ0dwiyagPVhTmZLF6T52Xh9zcbZ7V4u8PcNC3d73Ke2G0W0uNVRc3+xN7D1VwyblCgxeg1nDsigVc3FPaPQTEwq9ul6CP4y1O6YuE0hiWEMzQ+jINHa6moaeTFH2dT19hCeEgQwUEWzhkWx9V/1wayxvTepMHRfqyhIQghGJ4YTkSIjaaWFuy2II7WNnDnhaP50YtfmlrDzB7anhXDPPfRelA7amCkz0PhQEUtv3tvm/vBZDy0Hpw9hiVr89zr3ndxFv/4fB+PzZ3QZVPLga7MpugYrWdOEiLMLfzp8WF+9dBIo7XgvAx3sFPrAh4WgTvIcldplWk6tsVXT2ThjAy39fitb7SiDMbsgsUiGBIfTmpsGBMGR3tVJ/P0gU6LC/V6WVUzFN3DwWN1FJTX+lh9f//BDl65cTKg5WWfNzWdER4V6MB8Nm54QgR/nDOWm1/9ps3lRg2MdLcbL0VD47WXIpXxpu9T7WziaF0jiSrzRIc5c0gsr2wo5NDROgbHOgItzinR7qBYSll4OgTpC3TEirSzpNrHn3Jp7kFuyckkxhFMSaXTXV72zgtH+Aw4F83I5I63tnGsrpH7Ls5i1fYSJqfHuR8cC2dkdMqS1djS4mO5vu/iLJ7934nytp4PhdbHW1hR7x7ECwH2IAvRDhuzJyS7LdhNzS3cfG5Gl1txlf9mz8Zs5mTJDyeaWviDrIJ7Zo3mweU7ffxAQdNhZ7OLY3WNDIy089sLRxEabOXgsTr+tGqvu6pccJBga1Glzz0Q4wimsr7Jq2jD3ReOJD0hnNIqzcfdGOB46lVHq6ypGYqup6K2gfjwENP+rPBoHX9Zk+eeVYtxBLtflsxenBbmZPLwil1ckZ3i3t66PWU+OnfPrNFU1Dh57rozCLZavAa+/mYCVTGivsWew9WkxjrUNe0EwUEWzh4Wxxu5h7jtghGBFueU6IxPsaId2vNzNbMkL809yB3fH0l1QzOPzBmLs9nFnsPVNLa4sACv6ZaQ1JhQiivreXn9icwN93+wg+euO4OfvXLC8uGS5tYPgaCgvMbLsuFySVpaJKE2i5cbhlVIHrp0LLUNzWQmRDA03twaYhyvMYgHWDgjg1te2+Sz///eMk11Mv0MM31f8J9NrFw0zceN5kBFLdLl4rG54wmyaNWkPLOU2G0WJg2OZt7UdP795QFuu2AkGwoqfArD3HZ+JpkJET73wBXZKV7W4xhHMLWNLdz0Uq7XAKd1SXKzY/jdu9tZOn8K9U0taoaiGwm2Wig6Vmfanx08Wuf1Qm61wLAB4dx+wXCiQ4M5WtvAU1dOYEdJFVLi1iWjf4xxBDNzTBLPr9vnXn9cSjTfHq+jrLqRv3++n0cvH+eVy1pVLOwf7DpczeCY3m3tDATTMwewZE0evzp/eK/uD9WguAsx83P9w2Vj3VO7rS3J45IjufncDHYfrsIl4a+f5nP1mam89tVBjtU18uDsMdw0NZ2HV+zipmnpLFlzIvgjKcrOnEkpVNY3cdO0dN76poiSSqe7Cl1r6/Kvlm52W9MMy8aBilp2llTxmF4i18Bus/Cb74/geH0TLompldjf8Q5PiDC17JTXOFXEdj/D38zJ4SonU9LjvQYSqTEONoXY+M2bW9zZAzyDMu+/JIs/f7KX8ppGrpuSxo16sJunRXlAeDDpCREUlFXz4Owx7kGw3WZhsF5d0cAsGMusJPmAiGDTY6hvajmpVIKKjlPX2MKyXN/+7IFLsnh1QyG/PC/DHfvwRm4RjnOsDIp28Bu9FPiCnAxe+Mw7xeUHW4q5Z9ZoSquc7m0aL/R2m4V5U9N58fMCFuZksvXQcTZJyEwMJ2dEovIn7yfsKK4kRVWy6zRD4hzYgizkFh5j8tDYQItz0qhBcRdi+LmO0IPq9pZW8/hHewgOEjw4eywhQRa3leLas1JJjgllz+Eq3sgtcufwff3rg8yZlMIza/O5573tLJqR6eNfPC45kqsmp5pONZdUOlmae5DH5o6nvqHZx7rsadkorXISFhxk2tEPjLJT39TCoyt3MXJghGmnb+bXK00s1Z3JhqHoO3QmQ8jBY3Xu8rpGGrT509MZOTCCSLuNb4/XsbW4itsvGG5a9XHBeRnEhAWzQM8m8NDs0Tw2dzxSuoh2BHOkupFFMzJYlqu9PPoLxmpteV46f4rKctLN+PPTTYy0c6yu0cs9yyIgITKEC8cmeblH3Pa94cSFB5NfdqIU+FvfFHHXzJHuLCRWoeUtXvrVQa49K830+ocEaQNjZ3MLZ6TFcO9725k9IZn0eFWxsL+w49sq5kxMDrQYvQ4hBOcMi+Otb4p69aC49yeV62FYLAIh4PY3trhTlV2Vncr8V3L51dLN3H3hSK4/O40la/O5dekWnltXwHVT0ohxBLN4TR6zxiUTYbfyy/MyuGmaNihYvrWYP3+yl/suziItLpSbz81wD4jhxMBgzqQU7DYLV5+Zyh9X7KK4sp7Fq/PdA2Jj2bJq7XtipJ0we5BpBacWF/xlTT5XZadytNZ/tRrD/9Kw/A2N967qlRYX6s6GoSrP9S86U+GttRXOSPWXX1bLTS/nUtPQwh0zR5AcE2o6mEmICHHfE0lRdoTFwp9W7ab4mJOfvfIN/+8N7V67/uw0kqLs7tSInrQOMHU2aflwVZW67qOtypSG/hyra+SZtfl8sKWY7LRYgjzyWYN2nZ78eC+FFXVu9wgDZ7OL59edqIbnbHZRXtPIoeP1ptc/IyGcFz8vYPHqfH72yjdclZ2KI9hKWbVTVSzsB7S4JPllNaTGKfeJk+GcYfGs3HGYxmZX+wv3UJSluBsorXIS4whmzqQUUmNC+bay3h1EV+VsZome/xd8c2gOjXcgBPzZI53UPbNGEx5ipbq+iQdnjzENJHI2uUiLDeX567JJiwtlYmo0obYgnl9X4JZFCM1aYtRzHxIXRlmV02++Y0M2o3oU+LfquFyS/UdqKTxaS3x4MG/efDbVzmYcwVavqlPKD6//4C9DCGjVyjx1yF8WlIZmFzGOYIYNCOdwlROb1UJ2WhRnpQ9ACAgPsSIlRNht3JKTgUUIYh3BfFtZzxVnDPaxKhuFZIpMUiMaleo8958YaeesoXEqy0kXY/Qj5dUNbfrpGvpztLaB4uNO5r+S6zeVmkvi5T42Z1IK//lKszKHBFkYGh9GyfE67r5oFH9ft8+n37tn1mgeXbnLp2/+85UTCLVZ+XJ/BaMGRrBs/hS+rXSSFBVKVpJvVh5F72X/kVpiHDYcwWpodDLEh4cwOCaU/+0t53ujEwMtzkmhrnw3YFYa1nBvcDa7TDt0IU4EkITarO5BtLNJSyi/4Dztgb+7pIphA8JNBxCFR+u5932txPOU9HhcLsmSH04kr7TGS5YRAyNJjdUe7NlpsRyvb/LJd/zsugK3bHWNLUDbeZhX7Sr1al80I5PMxHD3Nlofr/LD6x+0zhDiT4eSokJM83ev3F7C9Wen8TM9jVZaXCi/ODeD+97fYVq5bNGMTP68Os/tk2+me3ll1SxenU9aXChPXjmB/LIaLAJSYx2mxWVUlpOuxVMH/A1wjf7BOPcAP3rxK/eyZv2fReBVsW54YphP+fmFOZk8sWo3V5+ZyuDYUBacp6Xoy0gIp+horWle+IYWF1c9v8FU31T2ib7Fjm8rGeInhkbRMSYPjeOdTUW9dlCs3Ce6gRYXphWVrj0rlaxBkabTdhYBC3MyeSO3iKdXa1YOAyMd1dLcg0xMjeGRlbtYmJPpNY334OwxvL2xCGeTi6r6RrYcOsaqnYeJDg02DSg6UFELaKWaLxg9kEsnJHNGajQAz64r8Ir6N/I1+ou+3lFS6dP+9Oo8thZVui2ArY9X+eH1L1wuSUF5DV8fOOrWlaQoO/OmpmuBpi4IC9YGtU/MHcdt52fikpJrp6ThbGohxhEMwKxxydynl0E3C5Yz7h1nk8uducATbYo8ggU5Gdw3K4sHl+/kyY/3smRtPlmDIlmxcBqvzz+LFQunqcFON9G6H+lI/+DpXmNYgz37v1vPH05GvIMl10zkVzMyGZUUwcAou6n/+axxyTy9Og+rsLBkbT5PfryXB5fvJCnaYSrLvvIav/rm2Zcqej9bDh0ntZfn2Q00Z6XHsm7vEeoamwMtykmhBsXdQFm1eZRyWpyDct1dwbNDv2fWaEJtVnegnGE5NrDbLIQFW7lj5iiaWqRXKqIFORnMm5qO3Wbh8jNSuGB0PHlltVz1/AZufnUj6/LK/VpiDAxrzHeHJzByYKSptczlkpRXN3DTNG2fSVF297YMmVvvwyWhqUX5ZPZ3PP1GNx06xryp6dz2veHcO2s0y7cWs3h1Pte++CUhtiBeXl/Iy+sPEGa3sWRtPne8tc3td58UZe9Q5TLj3lmWW8Q9s0Z76d7CnEz+uGIXL3xWwJ7SakoqnW6dTI0N8/KPVwPi7qG9Aa5Z/2AEucEJa/BffzjJ3f9t2HeE2ibJ7W9u4Y63t3H7G1sorKh3v0wZGPqhzRjUuPddUunkiVW7eeCSMV6y/OGysTiCrSzIySAkyNJuX6ro3WwpqvSbbUnRMSLtNoYnhrN6V1mgRTkplPtEN+AvSlkg+MOHu4lxBLujqUcmRvD4qt0+FbKM57ExJTw0PozzRyZyULd+eeYG9kwl9OKPs5mn514F/3mLzSy1bfmAtp7yNtxBjtU1khQV6nc6MzYshEmpsconsx9jWAZjHMFE2G38+RNft6KSSif3vLed+dPTaXFhGkg6b2o64K3PZnpnBMsdq2skPjyEJ+aORyIpOqZlYjlW18ifrphA1qAIJqZGK508zXj2j8YAd/70dCYOjiYtLsz0WrRO/3isrhFbkMWdcm3xNRPdqdhA05l7dX0yAp7hhH4Y/uqvbSxi/vR0kqNCOXisnmW5hSz96RTqmlpoapHc8942d5GWp/SXe5V9om/S4pLsKqniZ9PTAy1Kr2fy0Dje3VTMxeN7X6lsZSnuBobEhfHo5eN8rMEFR2rdD4Jn1uazZE0+D6/YxYLzvC0l912cRbhunZg3NZ2X1xfyq6Wam0JFbYPPthfmZLpdJ4qO1Xt12h21xBhYLIIhcWEkRNgprXJyoKKW/Ud83SYWr8njiuwUnrxyAllJkfzpCm9r8KIZmYxLifLyyVQWuP6JYRmcMynFb9YU43tqjAOrxb8F+IMtxTwwW7PmGZXLWuvd2xuL3PfF79/fwYLXNvHrN7dyzrA4nrpqPCsWTuP7oxNxSbyyTXhiuHus33eEgvIalS2lC2mdxeFYXSMjB0by3eEJpv2DEZQ3ICKYpfOn8M+fZDN/ejr/+KyA+2ZlYbdZqG9oNtWZoXr5cDjRVy7fWuzWk+AgwciBkZRWNyAENDZLahqbsQjB/Fdy3cYKZ5OLR1bu8pl5ULNefYeC8hqiQ21E2G2BFqXXc+aQGDYUVFDlbAq0KJ1GWYq7AYtFMCja7rYGS6nVU29xuXwsDcfqGjmmV1/KK6uhodlFZX0jj3y4x2e7ew5X89QneQQHCZ6/Lpu6xma2FVd5Vf5qHcVv5C1+dd5ZNLtc7VrFzAKhnpg73vSBM3FwNN8dngBAiE2waEYmsY5gwkKCiAsP5sy0WDUAVrgtg+25O9htFg5XOU0r0tltFqYMjeWsITEcqKhzB4ZaBfzl6ok0uVwItBLNd84cyd6yGq/7wtl0ouBGe+V6VTnf7sXfjJTZuTW7Fn+4bCxv6PmmK2obeWzueOLDbaY6Yw+yurNPDIkP49vjddx/yRgOVtTyx8vGUFzp9Nr2fRdncfc727h4fLKPrhZW1JMWG8p/b5lGeY2a9eprbD50XBWY6iIcwUFkDYpi1Y5S5p6R0v4KPQg1KO4m4sJCePHzE9WUkqLs/Py76T5pgBbmZPLPL7Qp3fnTtbRsi2ZkmHbwRcfruW5Kmjbd+EouL9842WsfAC99UeBTzeuWnEwmpEQTFOQ9MdA6vVpqjMM0aC6vrNpUnjT9gVBQXsOC//iWdl65aBouiU/6NkX/wrAM7jlc5dYjoyKj1QKZCRFa/u3vZvDs//JpbJY+98l9F2fx23e3cfsFI3l4xS4fXXv5xsl8nn8El9TStL34uZaK0Kh65pmKsL1yvaqcb/fjL6NHc7OLHSWVlOgpzyLtQT7X4u53trndIrYWV7HwtU08NHs091+S5Q7CtNssPDB7DC9+vo/cwkovfatpaCYmLJjY8GBu/vdGr23f/8EOUzcd4/ugaAfpA8LV4KkPsungcWX170ImD43lvc3FalCs0DDzgRsUE8qw+HDGJEfx5f6jSImXNSs5KpQFORnYbVbT9FSGD6+R03hbUaXP4OHGqcM4f0QCwxPDOVzpZGCUnaykKNMBcWsLzEOXjuFoTYOPhWRZbhF/uGwsd+sVx1pPG5qVP41xBLPx4HGfdZS1rf9hWAZHJ0WQFhfG06v3+qTKuu/iLAZGBTN7QjLJ0aEcrW1kwXkZOJtdDE+M4E+63/1+3QXJE2eTi8/zj7jLM996/nAeuGQ0FbVNpqkI2yvXq8r5BobmZhfvbinmd++eeKF/cPYYd3pKA2eTphPGoNVusxDpCKayzju1ZEtLCxePS6a8ptFH3xbNyCQ61OZ35sIz37FZn6foe2w8eIxrJqcGWow+wxlpMfzz//ZzrLaRmLDg9lfoIahBcTfhHggsmkZpVQO1jc2kxYaRFheGBHeAiIHdZqG4sp4la7SgkKQoO0/MHc/u0mqfwXNqbCiLZmQwdnAkx2qaeerKCYTbg4hx2BiZGElQkIXxg2MYP9i/fGbWsN+9u53H5443dfGYlBrNCj/TnWaBhVdkp7gHxMb2lbWt/2KxCIbEh5MaG8awAWE+BV3u/2AHi2ZkMjwhgiCrcFv8ABbkZLh9OxtbfF2Q7DatAqOxrac+2cu/553Fve9/aap/7ZXrVeV8A8OOkkr3gBi0a3aPn2C51BjNjeHg0Vo2HTpOkEWYziD8/fps/jhnHDf+62uv7T69Oo9//uRMv4GaHQ0AVPQNahuaOVBRqzJPdCF2m5Xxg6P5cPthfnhW73nZUIF23czOkmp+/M+vuPFfufzgL5+xZk8pLpfkibnjWTRDS21mWCHGpURht1lIirJzRXYKYSFWXvisgGfW5nvlDT54tJ53Nxezv7yORUs38fN/b+SnL+fyxb4KPs0r61BQkD9r2P4jtaaBeW2lqzIrfzo8IUKlL1L4YLEI6hpb/FjoBNEOG3WNLTx11QTS4kIBiAyxsnBGBgtyMggP0WZRzAJNPbdVbjLjYehfe+V6VTnfwOAvtePwhAj39V80I4O7Zo7kltc3sae0mmkZA7RAOT/r7vi2iqKjdaa/FR+v9wnUvG9WFsu3FgPtBwAq+g5bijTXCZtVDYm6kil6IY/ehLIUdyOtrbExjmDySk/43xouC+nxYcSFB5Mc5WDFLVPZeOg4v3t3OzGOYFMf5Fc2FDJnUoqXNc3Z5OLJj/cyf3o66fHtV9/yZw0z0hTNm5qO1QIzRiYwNjm6zQeCWeCM7EQqOEX/wl9J5zHJkdz0Ui4xjmCuyE7hV+cPJyo0iPLqRp785ISv6N0XjuQvV09kT2k1Z6TFcOfbW72m17UXS/M0gQkR9nYDvToTCKboGP7Kw3vi75pF2LVy9cb1v3fWaK6ZnMqjK3cxOimCEYkRxIaZB9oNig6lvMpp+tvxukZeXl/olZLtrY0HWXz1ROqbWtR170d8vf8omcpPvMsZPziav39e4Hbl7A2o16JupLU11qwi0u/e3c6ne8tZse0wn+aV8W2V0z2FWFLpdHfaS344kXlT091uFP4i+V2SDlljzaxhD106huVbiympdPLi5wWMHBjZ7oDYoHXataHxytqmMKexpcVnNmJhTiY7iyuJcQRz3ZQ0nl9XwK1Lt7D5UKXPy98fPtzNntJqnli1l21Fx7kqO9VHz47XN/hYAT31r700gSqNYNfhWbzlmr9/yUWLP2PljsM+M1pZSZE8dKl38YyHLxvLve97u1Q8sHwndY0t3HjOUDYePM4P/vIZO4qrTHWqvMpJY4vLNHVfU4ukpNLJ4tX5HDpez4ufF3Dj1GGMTY5W172fsaHgKMMHRgRajD5HcJCFM4fE8MGW4kCL0mGUpbgbaW2NbWsg+/TqPM1iER3qtYzRaS+dP4XbP9/iY+1o/d0i6JA11swalhrjYFJqTJdYx5S1TeGPuLAQluYe9EpZuDT3ILPGJTNnUopXaV6XNL9nnM2a1bDS2cLbHjMb549MwGIRrNpZqlUi04P1LAJGJ0Uo/QsAHc3mERRk4dLxyWQmnAgSbmxxeRU2MtZ3Saioa+SPK3fjbHKREGnniVW7fXTq/10wkr2l1bz1TZHXby+vL+RyPSrebrMwLSOeOROTVR/VD2lucbGl6Dg3fmdooEXpk5ydHs/bm4r46fRhgRalQ6hBcTfSOgOFVfivwOVschFksbh9jFsvkxgZ4rWtD7YUc9/FWdz/wYlp5du+N5z0AWEdtsaapUUyS5N0svhLu6ToH/ibMh8SF8YdM0d5ZT65Z9Zonl+3zzQ/rL+XP89qeM+szScpStuHZ8aThTmZvPWNltP2nGFxDIlXuni66Uw2j9ZBwgXlNabXf3hiBPUNzdw0LZ23vimi+HidT4aJhTmZfHu8DqvQ/IONCqDGNgwXryevnMCZQ1RO9f7K1uJKEiJDCLer4VB3MDopkmf/10BeaTWZiT3fGq+04BRoz0/O01p6tLaBIIuFxEg7D+hVvTx9hO02C5kJ4dzz3navVEBpcaHcf8kYSiqdjEiMYOWiaRyucjIg3E6QFV66YTJVziaiQ20MiAghNVZZOhSnn9b3QkpUKBsOHCW38CguqVWiu2PmKHdKvgtGJbJ0/hRKKp3Eh4fw/Lo8rspOJcgCC2dkYMysr9tT5uNX/9ClY8kYEMaipZu8fInNMp4Y5aFf/LxA+bMHiFPJ5tHasGAEwxkp+uw2C3fNHMmAyBCKjtbx+NzxFB+vZ1B0KIeP1zEhNYYIu5UhcWHc5fGy9Njl4xgUbefySco63N/5Iv8IWUlRgRajz2KxCL6TEc9bG4u488JRgRanXdSg+CTpaNUrwzK2+3A1ty3bTIwj2B0MV1JZz8vrtdzDD106hkdW7qKwop5XNhQyb2o6UXYr8RF2bn71G7/7SItTli9FYDG7Fx6cPYYla/PcA5eFOZk8unIXIwdGMCQujFW7Sn1yZK/a8S3njUzyCqpbNCOT0YMifKqIAT7WZn8ZT6wWlD97ADEb2Hb0ehiGhRG3TGPX4SqQ8Lg+IAYteLmuqYXblm1xGxFunp7Bb97c4jWDFm0P8sph7AixMilVWYcV8FneEaZmxgdajD7N1Ix4nli1h19/fyTWHn7PdWugnRDCLoT4SgixRQixQwhxv94eK4T4WAiRp/+P8VjnLiFEvhBijxDi+x7tZwghtum/LRZCBPTM+vOTO1BR2+ayho/wnW9vJTnGweVnpDB/ejpJUcHMGpfMgpwMLj8jhbc3FlHpbDHN9Wu2D4UiUJjdC/e8t51Z45Ld3xevyWPWuGTKqp2mWVkOHq1j7hmpHK6sJ8YR7F7v6dV5pESHMSzBO+jNGCytWDiN1+efxYqF0xiVFOkOpjKw2yzMGJmgisYEELNr1ZnrYbEIhiWEc9GYJBwhVi8f49bBy7PGJXP/ct+sPEWVTt7ILUJKzU99W1ElB4+qfrS/U9/YwtbiSkYnRQZalD7N4FgHUaE2PssrD7Qo7dLdluIGIEdKWSOEsAGfCyE+BOYAq6WUjwgh7gTuBO4QQowGrgaygEHAJ0KI4VLKFuBvwHxgA7ACmAl82M3y+6UzfnL+lt1bWs2SNZov5OAYh7tks2FZC7KYBxmpylqKnoQ//fZ8bTUstgkRdq/lk6LsXDclzccX1PAV1nIOO03L6rb2WXe5pKlFMispqt10YIrupbPxBW35o7cVvOwvmNkRbPXRs7S4MOVu1s/ZsL+C9PgwHMFq0ry7mZYZz2tfHeTcEQmBFqVNutVSLDVq9K82/U8Cs4GX9PaXgEv1z7OB16WUDVLK/UA+MFkIkQRESinXSykl8LLHOgHB8JPzxJ+fnL9lpe43eUV2Cve85512aPGaPLKSozq8D4UiULSn38b37LRYhsSFeS3fOtuEoftzJp3IDNBRfTezSF4wKpFVu0rbTQem6Dm0lcKtdSpJI3jZE7PvKdEOHz27+51tatatn7N2dxljkpU/8engOxnx/F9+BeXVDYEWpU26PU+xEMIqhNgMlAEfSym/BBKllCUA+n/j1SEZOOSxepHelqx/bt1utr/5QohcIURueXn3meo7U/XKbNlFM7QqXHabhcExDnOLcFUDj10+TuX67cWcLn0MJG3lvDa+P3r5OM5Jj3Nb+4zl/Vn2hDg5fTcskpOHxAGwLr+cPYervFwy+rsLUk/XybZc0zxffJ790STsNu8Khx9sKeaB2d65jm/73nAaW1ymelZYUatekPopUko+2VnKpNSY9hdWnDKO4CAmD43hjdxD7S8cQLp9zkB3fZgghIgG3hFCjGljcbN5LNlGu9n+ngeeB8jOzu623q51Ht4B4XasFvhyf4XXdJ8xDTggIpil86dQ16hVSrJaYGJqNKE2K+v3VZhGZx+ucjI2JYqXbphMXWMzqbFhDI3v3HRfRypJKbqP06WPgaStnNelVU4cwVYaW1wcPFbn1j939okqJ4tmZLAst8irlPmkwdEsmz+FMe0UjzHTb8An8K+1S0Z/dkHqyTrpcknKqxu4aVo6gDudnuc1M158AH61VAtenjc1nViHjczEcJxNLbxy42SqG5qIc4QQHWajrKrBtI/ddOg49U0u5XPeD9lbWkOLlAyOCQ20KP2GnJGJPLM2n599d1iPDbg7bY40UsrjQohP0XyBS4UQSVLKEt01okxfrAgY7LFaCvCt3p5i0h5QjM55SFyYaSYKY+q2dftZQ3WLWXy49hCoaeDeWaO9UrXdev5w7EEWbnop12vdofEdt5p1NEOGQnGqmPmMGllXbvjX1+3eF4tmZLozsSzMyeT+5Tu4Y+YoxpjOB2n40+8RiRE+lkYjNdsza/OVC1IPxex6Gi8zx+oafa6ZZ1aLz/aWcc1Zacx/5RuvdZfm7uSOmaO4YFSij7+557ZbFxJR9H1WbCshe0gsAY7Z71cMGxBOVKiNj3eWMnPMwECLY0p3Z58YoFuIEUKEAucDu4H3gR/ri/0YeE///D5wtRAiRAgxFMgEvtJdLKqFEFP0rBPXe6wTcPxN9+0oqWwzQ0Vzs4ttxcdpbpFkDYrk+evOYEFOBvOmpuOS0l2tyWzdU5GrP08dK04fnbkvnl6dx28vGuUuZV5YUc9tyzaz/4h/XfW3/cKjtV3qkqE4PZhdz8Vr8rj+7DSevy6b0ionBeU1uFzSPUMQ47CxdP7Z3DNrtLuQkee6s8Ylc9uyzRw8VsfMrIG8dMNkdx/beuZA0b/479YSzkyLDbQY/Y4LRg/kuf/tC7QYfuluS3ES8JIQwoo2AF8mpVwuhFgPLBNCzAMOAlcASCl3CCGWATuBZuCXuvsFwM+BfwGhaFknApZ5ojX+ou+NDrd1e1m1k9QYB+9uKeZ37253Wy7+du0kXvhMy0CxICfjlDNPdCZDhkLR1XT2vthdWu1VdczZ5GLX4Sq/LkP+th8WEmQ6Va5K+fZs/F3PlJhQ5r9yYsZsyQ8n0tgsvay+j10+zu+LkGefNyAixN3HGqiZg/7HrpIqqpxNZCaq5+DpZvLQWJblHuKbwqOc0QNfSro7+8RWKeVEKeU4KeUYKeUDenuFlHKGlDJT/3/UY52HpZTDpJQjpJQferTn6tsYJqVcoGeh6BH4i743Sja3bk+IsLOjpNI9IAat4/79Bzv442VjvYJEzNY9VbnUA0BxOvCnfwPCQ0zbW49T7TYLe0ur/c5s+Nt+YkSIaRDsmUNi3T6pip6Hv+uZV1bj1U9uLfKdadinl4Nuva5Rytno8zoTIK3ou7y9sZhzhsVhUa4Tpx2rRfCDcUn8+ZO8QItiSrdnn+gP+Otos5Ki/HbAZtaywop6oh1BrFg4jXOHx/PoKWaeUA8ARSDxp38WCyzMyfRqv/X84WQmhHu1LczJ5I3cIr9T2/62nxobdkrFIhSBwex6/uGysbyRW+S1nEv6ZixZllvEg62yTizMyWT51mKvPu9UC4koej9NLS7e3ljEtMwBgRal3/Ld4QPYfbiabwqPBVoUH1TG6i7ALPremKL1154UFWo6xRsbFuIOWJrkkoxNjvJZtyvkUii6G3/6d6CilqW5B5k3NR0hQEr4z1eFPPPDSe5SvFLiN8Cqve0b+t2ZYhGKwGN2PS0CjtU1ei1n5Cb27DuP1TWSnRbD0vlTKK1qIDYsGIlk5piBPn1eZwuJKPoWH+8sJSnKzqBolXUiUNisFi6dkMwjH+5i2c/O7lHBjmpQ3EX462j9tWclRfLQpWO8fIofunQMWUlR7a7bFXIpFKcDf1kp7pg5yidrxMjESA4erfdpb2tmQ+l336IjVQrHpkSZVi5MUy/8ig7wwmcFnD8qMdBi9Hu+O3wAq3Ye5qMdPSsThRoUB4igIAuXjk8mMyGcw5VOBkbZyUqKIiioZ3i0qPzGiu7CK09xpZOkqFCykiIJCrKomQ2FF/5mA4BO64nq0xS5B45SfLye7CE9L8Crv2G1CK6bksbv39/BtMx4wkJ6xnC0Z0jRTwkKsjB+cAzjB7e/7OlE5TdWdCculzTN323ol7L8KjzxpxOd0RPVpykAnvx4LxePG9RjC0f0N7IGRTEyKYI/rtjFQ5eNDbQ4gAq0U5ig8hsruhOlX4rTjdI5xbq95RyoqOW7I1SAXU/i2rPSWLWzlNW7SgMtCqAGxQoT2spvrFCcKkq/FKcbpXP9G2dTC/e8t51rJqcSZFHDnp5EeEgQvzg3g9vf2EJBeU2gxVGDYoUvKr+xojtR+qU43Sid69888uFuBkWHkt0Di0UoYMTACK7MHsx1L35FSWV9QGVRg2KFDyq/saI7UfqlON0oneu/vLe5mA+3l3DDOUMCLYqiDc4dkcB5IwZwxbPr2X8kcG5NogcVhutysrOzZW5ubqDF6JUYkdoqC0CH6NCJUfp4AqVf3Y7SyVYonQsoHT3RXTog+WjHYe58ayt3zBxJmnoB6hWs3VPGG7mHePiysVw0Nqk7d2Wqkyr7hMIUlQVA0Z0o/VKcbpTO9R+aWlwsWZPPqxsKuf2CEWpA3Is4b0QCg2NCefi/u3jzmyLumDmSEQMjTtv+1aBYoVAoFApFr6e2oZn/bi3hr5/mExsWzAOzxxAbFhxosRSdJCMhgj9cNpZVOw9z9fPrGTEwgjmTUjh3xIBujwNQg2KFQqFQKBQ9mmpnE9uLq2h2uXA2uahrbKayvomyqgb2H6lle3ElhUfrGBofxswxAxkzSKsOe7S2sZ0tK3oq5wyL58whseQeOMaLn+3nN29uJSTIwvDECIYNCCMpOpS4sGAiQ22EhwRht1mwWS0EWSxYLYKMhPBOvxT1aZ9iIUQ5UNgFm4oHjnTBdroSJVPH6W65jkgpZ7a3UBfqY0+gp17rrqa3HmdX6mRPOAdKhsDv/1Rk6Kg+rtT34UPMeTcmRU6eM6it9V1NDS7Z1OBqa5kejXQJhKVvDsq64tiEwBoa0WFjbl3el0fL335wv5+fTXWyTw+KuwohRK6UMjvQcniiZOo4PVWu3kx/Oaf95TjboiecAyVD4PevZOh+1LEFHpWSTaFQKBQKhULR71GDYoVCoVAoFApFv0cNijvG84EWwAQlU8fpqXL1ZvrLOe0vx9kWPeEcKBkCv39QMnQ36tgCjPIpVigUCoVCoVD0e5SlWKFQKBQKhULR71GDYoVCoVAoFApFv0cNij0QQtiFEF8JIbYIIXYIIe7X22OFEB8LIfL0/zEBkM0qhNgkhFjeg2Q6IITYJoTYLITI7QlyCSGihRBvCiF2CyF2CSHODrRMvRkhxD+EEGVCiO0ebb8XQhTr132zEOKiQMrYFQghBgsh1uo6s0MIsUhv79O6Y3Z99fZbhBB79HPxmEf7XUKIfP2373eXDEKICUKIDUbfIoSY3M0ydPr6d7UcbcjwuN6fbRVCvCOEiD7dMnj8frsQQgoh4j3aTkmGrjz3Qogz9GdSvhBisRBCnNyZ6Do68+zuTccFnX/e9orjk1KqP/0PEEC4/tkGfAlMAR4D7tTb7wQeDYBstwH/AZbr33uCTAeA+FZtAZULeAm4Sf8cDEQHWqbe/AdMByYB2z3afg/cHmjZuvg4k4BJ+ucIYC8wuq/rjp/rex7wCRCif0/Q/48GtgAhwFBgH2DtJhlWARfqny8CPu1mGTp1/btDjjZkuAAI0tsfDYQM+vfBwEdoxV7iu0qGrjz3wFfA2WjP8g8NHQrwPdahZ3dvOy5drg4/b3vL8SlLsQdSo0b/atP/JDAb7eKj/7/0dMolhEgBfgC84NEcUJnaIGByCSEi0R6wLwJIKRullMcDKVNvR0q5DjgaaDm6GylliZRyo/65GtgFJNPHdcfP9f058IiUskFfpkxvnw28LqVskFLuB/KByZwifmSQQKT+OQr4tptl6Oz173I5/MkgpVwlpWzWF9sApJxuGfSfnwJ+g3ZtDE5Zhq4690KIJCBSSrleaiOtlwnw/drJZ3evOS44qedtrzg+NShuhT7VsRkoAz6WUn4JJEopS0C7gYGE0yzWn9E6I8/ylYGWCbTOcZUQ4hshxPweIFc6UA78U5+uekEIERZgmfoqC/Tp3H+IvudSMASYiDZT1B91ZzgwTQjxpRDif0KIM/X2ZOCQx3JFnBgwdTW/Ah4XQhwCngDuOl0ydPD6d6scrWTw5EY0S9pplUEIcQlQLKXc0mqxLpXhFM99sv65S2TpIv5Mx5/dvem4oPPP215xfGpQ3AopZYuUcgLa2/hkIcSYQMojhJgFlEkpvwmkHH74jpRyEnAh8EshxPQAyxOENg37NynlRKAWbfpG0bX8DRgGTABKgD8FVJouRAgRDrwF/EpKWRVoeQJEEBCD5jr2a2CZ7uNn5ufXXTk9fw7cKqUcDNyKbo3qbhk6cf27TQ5/Mgghfgs0A/8+nTLo+/wtcK/Zol0lQxec+9Opn+1yEs/uXnFcHnT2edsrjk8Niv2gTwN8CswESnUTP/r/Mv9rdjnfAS4RQhwAXgdyhBCvBlgmAKSU3+r/y4B30KbNAilXEVCkW/cB3kS7aQN+rvoSUspS/eXRBfydLpi+7gkIIWxoD+V/Synf1pv7o+4UAW/r7mRfoVm54vX2wR7LpXDCraGr+TFgXIM3OKFj3SZDJ69/t8jhRwaEED8GZgHX6lPMp1OGYWg+oFv051AKsFEIMbCrZOiic1/ECdeSk5alC+nss7u3HJdBZ5+3veL41KDYAyHEAKFH9gohQoHzgd3A+2idNPr/906XTFLKu6SUKVLKIcDVwBop5Y8CKROAECJMCBFhfEYLBtkeSLmklIeBQ0KIEXrTDGBnIGXqixgdns5laNe9V6NbQl8Edkkpn/T4qT/qzrtADoAQYjhaAM0RtHNxtRAiRAgxFMhEC5DpDr4Fvqt/zgHy9M/dIsNJXP8ul8OfDEKImcAdwCVSyrpWsnW7DFLKbVLKBCnlEP05VIQWGHe4K2ToqnOvT9VXCyGm6Nu8ngDeryfx7O4Vx2VwEs/b3nF8sgdEMPaUP2AcsAnYivagv1dvjwNWo3XMq4HYAMl3LiciWAMqE5o/0Rb9bwfw2x4i1wQgV7+G76JNA/eI69cb/4DX0FwkmtAehvOAV4Bt+jl+H0gKtJxdcJxT0abstgKb9b+L+rru+Lm+wcCreh+4EcjxWP63aFHje+iiCHE/MkwFvtH7ly+BM7pZhk5f/66Wow0Z8tF8MY22Z0+3DK2WOYBH1qFTlaErzz2QrevtPmAJetXeQP/RwWd3LzyuCXTiedsbjk+VeVYoFAqFQqFQ9HuU+4RCoVAoFAqFot+jBsUKhUKhUCgUin6PGhQrFAqFQqFQKPo9alCsUCgUCoVCoej3qEGxQqFQKBQKhaLfowbFCoVCoVAoFIp+jxoUBxAhxBAhhE/hA72G+Gj98wEhRLz+uaaz2+oCGc8VQpzj8f1fQoi5Xb0fRc+hK/XSZBsnrT9KF/seQoiFQohdQohiIcQSve1mIcT1AZLHrddduM0hQogfenz/iXGsit7PqTx79T5teVfLpDh5ggItgMIXKeVNgZbBg3OBGuCLAMuhCDA9QC/PReliX+MXwIVo1euyAaSUz3bnDvWqWUJqZcpPB0OAHwL/OU37UygUJ4myFAeeICHES0KIrUKIN4UQDiHEp0KI7JPdoBDCKoR4XAjxtb7dn+nt5+rbflMIsVsI8W/9AYEQ4iK97XMhxGIhxHIhxBDgZuBWIcRmIcQ0fRfThRBfCCEK2rLU6fv7nxBimRBirxDiESHEtUKIr4QQ24QQw/Tl/iWE+JsQYq2+ze8KIf6hW5D+dbLnQXFKdIleCo0lQoidQoj/Agkev52h68c3QoiPhF4+Wt/Pn3Ud2y6EmKx0se8hhHgWrTLm+2iVsIz23wshbtc/++iCxzKvCCHWCCHyhBA/9Vj/1x593/162xD9Gv4VrUrf4A7I9yNdPzYLIZ4TQlj19hohxMNCiC1CiA1CiES9fZj+/WshxAPixAzKI8A0fTu36m2DhBArddkfa0eOGiHEo/p98ol+P3yq6+cl+jI/EUK8K4T4QAixXwixQAhxmxBiky5TbPtXRHEKmPWXM/Tzv03vQ0JAK9st9GctMEdvs+i6MMDje77wM2vR0X5KXyZXCLHDuBf09kf0PnmrEOIJve0K/R7bIoRY5+9A9WNbpq+7VAjxpTiF8UqPI9BlAvvzH5oFQQLf0b//A7gd+BTI1tsOoJfUBGra2dZ2/fN84Hf65xC0MoxD0SxtlUAK2gvRerQSm3a0MqJD9XVe40RJyt8Dt3vs51/AG/r6o4H8NmQ6FzgOJOlyFAP3678tAv7ssc3XAQHMBqqAsfo+vgEmBPpa9ae/LtbLOcDHgBUYpOvDXMCGZvEdoC93FfAP/fOnwN/1z9M99FrpYh/7M/QI+AmwpPV1bkcXtgCh+vqHdP26AHhev34WYLm+3hDABUzpoDyjgA8Am97+V+B6/bMELtY/P8aJvnY5cI3++WbjvsCjxK/+/SdAARCF1vcWAoPbkEmil8QF3gFW6ffPeGCzxzbzgQhgAFo/f7P+21PArwJ9rfvqH+b95e90nRyut70M/IoTz9pMXUeXceJZe59xnXQ9fquNfXaon0IvsYzW/34KjANi0cosGxWNo/X/24BkzzY/+74deE7/PAZoRn8u9IU/ZSkOPIeklP+nf34VbZB6qlwAXC+E2Ax8iVaLPFP/7SspZZHUpg43o93QI4ECKeV+fZnX2tn+u1JKl5RyJ5DYzrJfSylLpJQNaHXNV+nt2/R9G3wgtbtsG1Aqpdymy7ij1XKK00NX6eV04DUpZYuU8ltgjd4+Aq1D/VjX09+hvawZvAYgpVwHRAohov1sX+li38efLrwnpayXUh4B1gKT0fq+C4BNaBbhkZzo+wqllBs6uM8ZwBnA17p+zkCzagM0og2AQRuADNE/n432kgbtu0qsllJWSimdwE4grY1lG4GV+udtwP+klE346u1aKWW1lLIcbVD8gcc6nsspup7W/eUMYL+Ucq/e9hJaXzhSb8/T+5hXPbbxD8Dwpb8R+Gc7++xIP3WlEGIj2v2QhWY8qAKcwAtCiDlAnb7s/wH/0mddrG3sdyragBwp5XZgazty9iqUT3Hgke18PxkEcIuU8iOvRiHOBRo8mlrQdEB0cvue22hvXc9lXR7fXXjrX4PJMmbLKU4PXamXZusKYIeU8uxT3L/Sxb6PP10waxfAH6WUz3n+IDT3m9pO7FMAL0kp7zL5rUkfjMCJPrSzmPXD/vDcn1snpZQuIYSZ3noth9Lb00Fn+kfTZaWUh4QQpUKIHOAs4Np2ttNmPyWEGIpm1T1TSnlMd6uwSymbdTekGcDVwAIgR0p5sxDiLOAHwGYhxAQpZYXJfjs7XuhVKEtx4EkVQhgDg2uAz7tgmx8BPxdC2ACEEMOFEGFtLL8bSNcfHKBNZRtUo03JKfoXXaWX64CrhebnngScp7fvAQYY+xBC2IQQWR7rXaW3TwUqpZSVKF3sr5jpAsBsIYRdCBGH5qLwNVrfd6MQIlxfJ1kIkWCyzfZYDcw11hVCxAoh2rLmAmwALtc/X+3RrvS279O6v/wEGCKEyNDbrgP+h/asHSr0GAZ9WU9eQLMeL5NStpyiTJFoL4KVut/7hQD6vRElpVyB5tIxQW8fJqX8Ukp5L3AE/373nwNX6uuMRnPb6DOoQXHg2QX8WAixFc3X529dsM0X0KbkNgotVcxztGEpkFLWo0WBr9Sd/0vRpt9Am4K7THgHNyn6Pl2ll+8AeWhTfH9DezAgpWxE8y1+VAixBc2V5xyP9Y4JIb4AngXm6W1KF/snZroA8BXwX7TB6INSym+llKvQXBfWCyG2AW9yEgNS3R3nd8Aq/R74GM0fvS1+BdwmhPhKX9boQ7cCzXoA063+Vlb0alr3l08BNwBv6HroAp7V3WXmA//Vn7WFrbbzPhBO+64T7SKl3ILmNrEDzTXDcO+IAJbrsv4PMHTycT0ocDuaMWOLn03/Fc2gsRW4A02/K/0s2+sQJ2ZlFP0ZIUS4lLJGCCGAZ4A8KeVTgZZL0f8QQnyKFmiVG2hZFIHFny4IIX6PFsj2RCDkMkMI4QDqpZRSCHE1WtDd7EDLpeg96FkcnpJS9tiXfqFlYbFJKZ26xXs1WkBhY4BF6xKUn5HC4KdCiB8DwWhvl8+1s7xCoVAoTnAGsEQ3LBxHC5ZSKDqEEOJO4Oe070scaBzAWt09UwA/7ysDYlCW4l6HEGIs8Eqr5gYp5VmBkAd6pkyK00tP0YGeIoeiZyOE+BItNZ8n10kptwVCHuiZMikCixDit8AVrZrfkFI+fBr2/X3g0VbN+6WUl3X3vgOJGhQrFAqFQqFQKPo9KtBOoVAoFAqFQtHvUYNihUKhUCgUCkW/Rw2KFQqFQqFQKBT9HjUoVigUCoVCoVD0e/4/ZtLfu7IHLMIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 14 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(pengs, corner=True, diag_kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8d83d670",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x2b40f3a7610>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "def quantile_plot(x, **kwargs):\n",
    "    quantiles, xr = stats.probplot(x, fit=False)\n",
    "    plt.scatter(xr, quantiles, **kwargs)\n",
    "\n",
    "g = sns.FacetGrid(pengs, height=4)\n",
    "g.map(quantile_plot, \"body_mass_g\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7c3db841",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4201.754385964912"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pengs.body_mass_g.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6f054e1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Hypothesis Testing (Continued) \n",
    "\n",
    "1. Check normality and sample size for tips (good on both) \n",
    "2. Set up hypotheses\n",
    "3. Decide on significance level $\\alpha$ \n",
    "4. Calculate test statistic and/or $p$-value\n",
    "5. Make decision about null hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb454c0a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# P-value\n",
    "\n",
    "> $p$-value is defined to be the smallest Type I error rate ($\\alpha$) that you have to be willing to tolerate if you want to reject the null hypothesis.\n",
    "\n",
    "> $p$-value (or probability value) is the probability that the test statistic equals the observed value or a more extreme value under the assumption that the null hypothesis is true. \n",
    "\n",
    "If our p-value is less than or equal to $\\alpha$, then there is enough evidence to reject the null hypothesis.\n",
    "If our p-value is greater than $\\alpha$, there is not enough evidence to reject the null hypothesis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a66010f0",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Demo\n",
    "\n",
    "* Check Normality\n",
    "* Set-up hypotheses: $H_0$: $\\mu = 4201$ AND $H_a$: $\\mu \\neq 4201$ (two-tailed test)\n",
    "* $\\alpha=0.05$\n",
    "\n",
    "<img src=\"https://ethanweed.github.io/pythonbook/_images/04.04-hypothesis-testing_15_1.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "577f5e1d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ttest_1sampResult(statistic=0.01739630065824133, pvalue=0.9861306342800811)\n",
      "Our p-value is not below alpha, thus we cannot reject the null hypothesis.\n",
      "We are 95% confident, that the population mean body weight of penguins is indeed 4201 grams\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "print(stats.ttest_1samp(pengs.body_mass_g.dropna(), popmean=4201))\n",
    "print('Our p-value is not below alpha, thus we cannot reject the null hypothesis.')\n",
    "print(f'We are 95% confident, that the population mean body weight of penguins is indeed 4201 grams')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e0b57f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Demo 2 \n",
    "\n",
    "* $H_0$: $\\mu \\leq 1000$ AND $H_a$: $\\mu > 1000$ (one-tailed test) \n",
    "* $\\alpha=0.05$\n",
    "\n",
    "<img src=\"https://ethanweed.github.io/pythonbook/_images/04.04-hypothesis-testing_20_1.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5e804cc4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ttest_1sampResult(statistic=73.83313651463514, pvalue=4.1249540274922355e-212)\n",
      "Our p-value is below **alpha**, thus we cannot accept the null hypothesis.\n",
      "We are 95% confident, that the population mean body weight of penguins is greater than 1000 grams\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "print(stats.ttest_1samp(pengs.body_mass_g.dropna(), popmean=1000, alternative='greater'))\n",
    "print('Our p-value is below **alpha**, thus we cannot accept the null hypothesis.')\n",
    "print('We are 95% confident, that the population mean body weight of penguins is greater than 1000 grams')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d0cec90",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Independent Samples $t$-test\n",
    "\n",
    "> Use for comparing the mean of two groups\n",
    "\n",
    "#### Does flipper length vary depending on the sex of the penguin? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d29c8c7d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='flipper_length_mm', ylabel='Count'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data=pengs, x=\"flipper_length_mm\", hue=\"sex\", element='step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "70cfa238",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pingouin as pg\n",
    "\n",
    "ax = pg.qqplot(pengs.flipper_length_mm, dist='norm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8c785b7f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9517050385475159, pvalue=5.392858604125195e-09)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "\n",
    "shapiro(pengs.flipper_length_mm.dropna()) # p-val<0.05 - departure from normality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2c26cc38",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pointplot(x = 'sex', y = 'flipper_length_mm', data = pengs)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7c451044",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>dof</th>\n",
       "      <th>alternative</th>\n",
       "      <th>p-val</th>\n",
       "      <th>CI95%</th>\n",
       "      <th>cohen-d</th>\n",
       "      <th>BF10</th>\n",
       "      <th>power</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>T-test</th>\n",
       "      <td>4.807866</td>\n",
       "      <td>325.278352</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>0.000002</td>\n",
       "      <td>[4.22, 10.06]</td>\n",
       "      <td>0.526244</td>\n",
       "      <td>5880.711</td>\n",
       "      <td>0.997654</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               T         dof alternative     p-val          CI95%   cohen-d  \\\n",
       "T-test  4.807866  325.278352   two-sided  0.000002  [4.22, 10.06]  0.526244   \n",
       "\n",
       "            BF10     power  \n",
       "T-test  5880.711  0.997654  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pingouin import ttest\n",
    "pengs.dropna(inplace=True)\n",
    "\n",
    "ttest(pengs.loc[pengs.sex=='Male', 'flipper_length_mm'], pengs.loc[pengs.sex=='Female', 'flipper_length_mm']) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dab6806b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>U-val</th>\n",
       "      <th>alternative</th>\n",
       "      <th>p-val</th>\n",
       "      <th>RBC</th>\n",
       "      <th>CLES</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>MWU</th>\n",
       "      <td>18173.0</td>\n",
       "      <td>two-sided</td>\n",
       "      <td>9.011341e-07</td>\n",
       "      <td>-0.311183</td>\n",
       "      <td>0.655592</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       U-val alternative         p-val       RBC      CLES\n",
       "MWU  18173.0   two-sided  9.011341e-07 -0.311183  0.655592"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# amend for normality via Wilcoxon\n",
    "pg.mwu(pengs.loc[pengs.sex=='Male', 'flipper_length_mm'], pengs.loc[pengs.sex=='Female', 'flipper_length_mm'], alternative='two-sided')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1cfc0f6",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Potential Problems\n",
    "\n",
    "* Non-normality of data (bi-modal) \n",
    "* Homogeneity of variance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54073633",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "References: \n",
    "\n",
    "[Banerjee, A., Chitnis, U. B., Jadhav, S. L., Bhawalkar, J. S., & Chaudhury, S. (2009). Hypothesis testing, type I and type II errors. Industrial psychiatry journal, 18(2), 127.](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2996198/)\n",
    "\n",
    "\n",
    "[Rogerson, P. A. (2019). Statistical methods for geography: a student’s guide. Sage.](https://search.library.ucsb.edu/permalink/01UCSB_INST/1aqck9j/alma990022376840203776) \n",
    "\n",
    "[Penn State STAT 500: Applied Statistics Course Materials](https://online.stat.psu.edu/stat500/)\n",
    "\n",
    "[Learning Statistics with Python](https://ethanweed.github.io/pythonbook/landingpage.html)"
   ]
  }
 ],
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  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python (geo_env)",
   "language": "python",
   "name": "geo_env"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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