{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "630839fb",
   "metadata": {},
   "source": [
    "# Lesson 14: Advanced statistics demonstration\n",
    "\n",
    "This notebook demonstrates key concepts in advanced statistics including hypothesis testing, confidence intervals, and statistical inference.\n",
    "\n",
    "We'll explore:\n",
    "\n",
    "**1. Confidence intervals**\n",
    "\n",
    "- Constructing confidence intervals for sample means\n",
    "- Interpreting confidence interval coverage\n",
    "- Visualizing multiple confidence intervals\n",
    "\n",
    "**2. Hypothesis testing**\n",
    "\n",
    "- Comparing two samples with t-tests\n",
    "- Understanding null and alternative hypotheses\n",
    "- Interpreting p-values and significance levels\n",
    "\n",
    "**3. Type I errors through repeated testing**\n",
    "\n",
    "- Understanding false positive rates\n",
    "- Empirically demonstrating Type I error rates\n",
    "- Visualizing distributions of p-values and t-statistics\n",
    "\n",
    "**4. Multiple testing correction**\n",
    "\n",
    "- Controlling family-wise error rate\n",
    "- Applying Bonferroni correction\n",
    "- Comparing corrected and uncorrected significance levels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86aaf35a",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c784930",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec797e2a",
   "metadata": {},
   "source": [
    "### Population distribution\n",
    "\n",
    "Generate a large sample to represent our population and visualize its characteristics. We'll create 10,000 data points from a normal distribution with mean 100 and standard deviation 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "796bdb87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate population data\n",
    "np.random.seed(42)\n",
    "population = np.random.normal(loc=100, scale=15, size=10000)\n",
    "\n",
    "# Calculate population parameters\n",
    "pop_mean = population.mean()\n",
    "pop_std = population.std()\n",
    "\n",
    "# Plot population distribution\n",
    "plt.title('Population Distribution')\n",
    "plt.hist(population, bins=50, edgecolor='black', color='skyblue')\n",
    "plt.axvline(pop_mean, color='red', linestyle='--', label=f'Mean: {pop_mean:.2f}')\n",
    "plt.axvline(pop_mean - pop_std, color='orange', label=f'±1 SD: {pop_std:.2f}')\n",
    "plt.axvline(pop_mean + pop_std, color='orange')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a22c0f3",
   "metadata": {},
   "source": [
    "## 1. Confidence interval for sample mean\n",
    "\n",
    "Draw a sample of 100 observations from the population and construct a 95% confidence interval around the sample mean. The confidence interval gives us a range of plausible values for the true population mean based on our sample.\n",
    "\n",
    "### 1.1. Construct 95% confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c14d9796",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Draw a sample of 100 data points\n",
    "sample_size = 100\n",
    "sample = np.random.choice(population, size=sample_size, replace=False)\n",
    "\n",
    "# Calculate sample statistics\n",
    "sample_mean = sample.mean()\n",
    "sample_std = sample.std(ddof=1)\n",
    "sample_se = sample_std / np.sqrt(sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c203ae9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct 95% confidence interval\n",
    "confidence_level = 0.95\n",
    "alpha = 1 - confidence_level\n",
    "df = sample_size - 1\n",
    "\n",
    "# Use t-distribution for confidence interval\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "margin_of_error = t_critical * sample_se\n",
    "\n",
    "ci_lower = sample_mean - margin_of_error\n",
    "ci_upper = sample_mean + margin_of_error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "15887ad4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean: 101.75\n",
      "\n",
      "95% Confidence Interval: [98.57, 104.94]\n",
      "Margin of error: ±3.19\n"
     ]
    }
   ],
   "source": [
    "print(f\"Sample mean: {sample_mean:.2f}\")\n",
    "print(f\"\\n95% Confidence Interval: [{ci_lower:.2f}, {ci_upper:.2f}]\")\n",
    "print(f\"Margin of error: ±{margin_of_error:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daad4709",
   "metadata": {},
   "source": [
    "### 1.2. Sample distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ad87f493",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the confidence interval\n",
    "plt.title('Sample distribution with 95% confidence interval')\n",
    "plt.hist(sample, bins=20, edgecolor='black', color='skyblue', label='Sample')\n",
    "plt.axvline(sample_mean, color='blue', label=f'Sample Mean: {sample_mean:.2f}')\n",
    "plt.axvline(ci_lower, color='orange', label=f'95% CI: [{ci_lower:.2f}, {ci_upper:.2f}]')\n",
    "plt.axvline(ci_upper, color='orange')\n",
    "plt.axvline(pop_mean, color='red', linestyle='--', label=f'Population Mean: {pop_mean:.2f}')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a0b67d0",
   "metadata": {},
   "source": [
    "### 1.3. Confidence intervals with reapeated samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b8f5390c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of CIs containing population mean: 96/100\n",
      "Actual coverage: 96.0%\n",
      "Expected coverage: 95%\n",
      "\n",
      "Interpretation: About 95% of confidence intervals should contain the true population mean.\n"
     ]
    }
   ],
   "source": [
    "# Draw 100 samples and calculate confidence intervals\n",
    "num_samples = 100\n",
    "sample_size = 100\n",
    "confidence_level = 0.95\n",
    "alpha = 1 - confidence_level\n",
    "\n",
    "# Store results\n",
    "ci_results = []\n",
    "contains_pop_mean = []\n",
    "\n",
    "for i in range(num_samples):\n",
    "    # Draw sample\n",
    "    sample = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Calculate statistics\n",
    "    sample_mean = sample.mean()\n",
    "    sample_std = sample.std(ddof=1)\n",
    "    sample_se = sample_std / np.sqrt(sample_size)\n",
    "    \n",
    "    # Calculate confidence interval\n",
    "    df = sample_size - 1\n",
    "    t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "    margin_of_error = t_critical * sample_se\n",
    "    \n",
    "    ci_lower = sample_mean - margin_of_error\n",
    "    ci_upper = sample_mean + margin_of_error\n",
    "    \n",
    "    # Check if CI contains population mean\n",
    "    contains = ci_lower <= pop_mean <= ci_upper\n",
    "    \n",
    "    ci_results.append((ci_lower, ci_upper, sample_mean))\n",
    "    contains_pop_mean.append(contains)\n",
    "\n",
    "# Calculate coverage\n",
    "coverage = sum(contains_pop_mean) / num_samples * 100\n",
    "\n",
    "print(f\"Number of CIs containing population mean: {sum(contains_pop_mean)}/{num_samples}\")\n",
    "print(f\"Actual coverage: {coverage:.1f}%\")\n",
    "print(f\"Expected coverage: {confidence_level*100:.0f}%\")\n",
    "print(f\"\\nInterpretation: About 95% of confidence intervals should contain the true population mean.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "78436d9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the confidence intervals\n",
    "plt.figure(figsize=(6, 8))\n",
    "\n",
    "plt.title(f'95% confidence intervals from {num_samples} samples\\n{sum(contains_pop_mean)} intervals contain population mean ({coverage:.1f}%)')\n",
    "\n",
    "for i, (ci_lower, ci_upper, sample_mean) in enumerate(ci_results):\n",
    "\n",
    "    if contains_pop_mean[i]:\n",
    "        color = 'black'\n",
    "        label = 'Pop mean in CI'\n",
    "\n",
    "    else:\n",
    "        color = 'red'\n",
    "        label = 'Pop mean not in CI'\n",
    "\n",
    "    plt.plot([ci_lower, ci_upper], [i, i], color=color, linewidth=1, label=label)\n",
    "    plt.plot(sample_mean, i, 'o', color=color, markersize=2)\n",
    "\n",
    "plt.axvline(pop_mean, color='blue', linestyle='--', linewidth=2, label=f'Population Mean: {pop_mean:.2f}')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Sample Number')\n",
    "\n",
    "ax = plt.gca()\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "unique = [(h, l) for i, (h, l) in enumerate(zip(handles, labels)) if l not in labels[:i]]\n",
    "ax.legend(*zip(*unique), loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b449226",
   "metadata": {},
   "source": [
    "## 2. Comparing two samples with hypothesis testing\n",
    "\n",
    "Draw two random samples from the same population and compare their distributions. We'll use an independent samples t-test to determine if the two samples have significantly different means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "020ea6a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 1 - Mean: 96.97, SD: 15.35\n",
      "Sample 2 - Mean: 101.71, SD: 13.46\n",
      "Difference in means: 4.75\n"
     ]
    }
   ],
   "source": [
    "# Draw two samples of size 50\n",
    "sample_size = 50\n",
    "sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "\n",
    "# Calculate statistics for both samples\n",
    "mean1 = sample1.mean()\n",
    "mean2 = sample2.mean()\n",
    "std1 = sample1.std(ddof=1)\n",
    "std2 = sample2.std(ddof=1)\n",
    "\n",
    "print(f\"Sample 1 - Mean: {mean1:.2f}, SD: {std1:.2f}\")\n",
    "print(f\"Sample 2 - Mean: {mean2:.2f}, SD: {std2:.2f}\")\n",
    "print(f\"Difference in means: {abs(mean1 - mean2):.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "50f1c756",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create boxplot comparison\n",
    "plt.title('Comparison of two samples (n=50 each)')\n",
    "plt.boxplot([sample1, sample2], tick_labels=['Sample 1', 'Sample 2'])\n",
    "plt.ylabel('Value')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4f7b1c4",
   "metadata": {},
   "source": [
    "### 2.1. Hypothesis formulation\n",
    "\n",
    "1. **Null hypothesis (H₀)**: The means of the two samples are equal (μ₁ = μ₂).\n",
    "2. **Alternative hypothesis (H₁)**: The means of the two samples are different (μ₁ ≠ μ₂).\n",
    "\n",
    "This is a two-tailed test because we're checking for any difference, not a specific direction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1c84902",
   "metadata": {},
   "source": [
    "### 2.2. t-test for differences in means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "09aef357",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Independent Samples t-test:\n",
      " - t-statistic: -1.6440\n",
      " - p-value: 0.1034\n"
     ]
    }
   ],
   "source": [
    "# Perform independent samples t-test\n",
    "t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "\n",
    "print(f\"\\nIndependent Samples t-test:\")\n",
    "print(f\" - t-statistic: {t_statistic:.4f}\")\n",
    "print(f\" - p-value: {p_value:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ab712ed",
   "metadata": {},
   "source": [
    "**Result**: The p-value (0.1034) is above the significance level of α = 0.05 so we do not reject the null hypothesis and conclude there is no significant difference between the two sample means."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe8c75b0",
   "metadata": {},
   "source": [
    "### 2.3. Test statistic distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2c853d37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize t-distribution with rejection regions\n",
    "df = 2 * sample_size - 2  # Degrees of freedom for two-sample t-test\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "\n",
    "# Generate t-distribution\n",
    "t_values = np.linspace(-4, 4, 1000)\n",
    "t_pdf = stats.t.pdf(t_values, df)\n",
    "\n",
    "plt.title(f't-distribution (df={df}) with rejection regions (α={alpha:0.2f})')\n",
    "\n",
    "plt.plot(t_values, t_pdf, color='black', label='t-distribution')\n",
    "\n",
    "# Shade rejection regions\n",
    "rejection_left = t_values[t_values <= -t_critical]\n",
    "rejection_right = t_values[t_values >= t_critical]\n",
    "plt.fill_between(rejection_left, stats.t.pdf(rejection_left, df), alpha=0.3, color='red', label='Rejection region')\n",
    "plt.fill_between(rejection_right, stats.t.pdf(rejection_right, df), alpha=0.3, color='red')\n",
    "\n",
    "# Mark critical values\n",
    "plt.axvline(-t_critical, color='red', label=f'Critical values: ±{t_critical:.3f}')\n",
    "plt.axvline(t_critical, color='red')\n",
    "\n",
    "# Mark observed t-statistic\n",
    "plt.axvline(t_statistic, color='green', label=f'Observed t: {t_statistic:.3f}')\n",
    "\n",
    "plt.xlabel('t-value')\n",
    "plt.ylabel('Probability density')\n",
    "plt.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235f8d74",
   "metadata": {},
   "source": [
    "**Decision rules**\n",
    "\n",
    "- **Fail to reject H₀** if p-value ≥ α (evidence is not strong enough to conclude a difference exists)\n",
    "- **Reject H₀** if p-value < α (evidence suggests a significant difference exists)\n",
    "\n",
    "Since both samples are drawn from the same population, any rejection of the null hypothesis would be a Type I error.\n",
    "\n",
    "**Type I error**\n",
    "\n",
    "When using α = 0.05, we will incorrectly reject the null hypothesis (false positive) on average 5% of the time, even when the null hypothesis is true. This is known as a **Type I error** or false positive."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f851e073",
   "metadata": {},
   "source": [
    "## 3. Understanding Type I errors through repeated testing\n",
    "\n",
    "Repeat the sampling and t-test process multiple times to empirically demonstrate the Type I error rate. Since both samples come from the same population, the null hypothesis is always true, so any rejections are Type I errors (false positives)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "caf838f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_tests = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb937a5",
   "metadata": {},
   "source": [
    "### 3.1. T-test with repeated sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c1942101",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from 100 independent t-tests:\n",
      " - Null hypothesis rejected: 6 times (incorrect conclusion)\n",
      " - Null hypothesis accepted: 94 times (correct conclusion)\n",
      " - Errors: 6.0% (expected ~5.0%)\n"
     ]
    }
   ],
   "source": [
    "# Repeat sampling and t-test 100 times\n",
    "sample_size = 50\n",
    "alpha = 0.05\n",
    "\n",
    "rejections = []\n",
    "p_values = []\n",
    "t_statistics = []\n",
    "\n",
    "for i in range(num_tests):\n",
    "\n",
    "    # Draw two samples from the same population\n",
    "    sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Perform t-test\n",
    "    t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "    t_statistics.append(t_statistic)\n",
    "    p_values.append(p_value)\n",
    "    \n",
    "    # Check if null hypothesis is rejected\n",
    "    reject = p_value < alpha\n",
    "    rejections.append(reject)\n",
    "\n",
    "# Count results\n",
    "num_rejections = sum(rejections)\n",
    "num_acceptances = num_tests - num_rejections\n",
    "\n",
    "print(f'Results from {num_tests} independent t-tests:')\n",
    "print(f' - Null hypothesis rejected: {num_rejections} times (incorrect conclusion)')\n",
    "print(f' - Null hypothesis accepted: {num_acceptances} times (correct conclusion)')\n",
    "print(f' - Errors: {num_rejections/num_tests*100:.1f}% (expected ~{alpha*100:.1f}%)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0ea131",
   "metadata": {},
   "source": [
    "### 3.2. Distribution of p-values & t-statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4c78b869",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ffFP6bGlpqfadCSHErl27NG6DvPT1zIi+v29t99Pb2NiI0aNH6xxvecJj/et1rC/MMyMPHjwQAMTcuXPzraft95yRkaF2xvnatWtCLpeLadOmSWWF2f5jx44V1tbW4vnz51rjye9+/rzffUxMjAAgFixYoFY390qXLsvURtN3k7sP16xZUzx58kQqz8rKEnZ2dqJ+/foqz2T9+OOPAoCYPHmyVBYSEiIAiFmzZkllDx48EObm5kImk4nNmzdL5RcuXFBrU3WR33G6Xr16ol27dmrluVfYc3/Lud/F4cOH1er27dtXODg45BuDPp8ZmT59urC0tFR7rnHixInC2NhYavuKs4/t2LGjwOOpLtibViFUrFgx355WcjP477//Hjk5OUVahlwuR2hoqM71Bw8eDCsrK+lznz594OjoiN27dxdp+bravXs3jI2N8eGHH6qUjx8/HkII/PTTTyrlAQEBKmekGjZsCGtra1y9erXA5Tg4OKB///5SmYmJidQzxc8//1zkdWjatCl8fX2lzzVq1ECPHj2wd+9eZGdna52uXbt2UCgUiI2NlcoePHiA/fv3Izg4WCozNjaWrpzk5OTg33//lc6Y6NoLU0G2b9+OnJwcvP3221AqldLg4OCA2rVr49ChQwAgXfnYu3cvnjx5opdlA4CbmxsCAwNVynbv3g0/Pz+0aNFCKqtYsSJGjBiB69ev459//lGpP3jwYJX7pP39/SGEwLvvvqtSz9/fHzdv3tTY01VRPH36FMCL31xeZmZm0vjcutrqvTyvklZa33elSpXwxx9/4M6dO3qNv7zgsf4/r8KxXlfm5uYwNTVFfHw8Hjx4UOjp5XK5dPU0Ozsb9+/fR8WKFeHp6VnkY36lSpWQnp6utdemwvruu++gUCjwwQcfqI3L7b5a38vMFRISonIV78SJE7h79y5GjRolHUsBoGvXrvDy8sKuXbvU5jFs2DDp35UqVYKnpycsLS3x9ttvS+Wenp6oVKlSgftcYejaBhSmXSlpW7duRcuWLVG5cmWV9iIgIADZ2dk4fPgwgOJ937nHwh9//BHPnj0rcqxMRgohLS1NpTHIKzg4GM2bN8ewYcNgb2+Pfv36YcuWLYVqrKpVq1aoB85q166t8lkmk6FWrVol3sXfjRs34OTkpLY9ci/f3bhxQ6W8Ro0aavOoXLlygQf8GzduoHbt2mq3x2hbTmHk3XYA4OHhgSdPnuDevXvIyspCcnKyypCdnY0KFSqgd+/e+P7775GZmQngxR+Jz549U0lGAGDdunVo2LAhzMzMULVqVdja2mLXrl149OhRkeN+2aVLlyCEQO3atWFra6synD9/Xnr43M3NDWFhYVi1ahUUCgUCAwOxdOnSYseh6RL4jRs34OnpqVau676R+4e0s7OzWnlOTo7etl1uo5j7Hb4s74P45ubmWuu9PK/CyM7OVtu/srKy8p2mtL7vOXPm4Ny5c3B2doafnx+mTJmi14a9rOOx/j+vwrE+L23HdrlcjtmzZ+Onn36Cvb29dDtQcnKyTvPNycnBwoULUbt2bcjlcigUCtja2uKvv/4q8nFr1KhR8PDwQOfOnVG9enW8++672LNnT5HmBQBXrlyBp6dnvh0y6HuZufK2F7nfqab2wsvLS+07NzMzU7slz8bGBtWrV1d7D5CNjU2REkptdG0DCtOuFEZaWprK/nrv3r0Cp7l06RL27Nmj1lYEBAQA+K9zmuJ8361bt0bv3r0xdepUKBQK9OjRA2vWrNG4/vlhMqKjW7du4dGjR6hVq5bWOubm5jh8+DAOHDiAQYMG4a+//kJwcDA6dOiQ75n2vPPQN20v69I1Jn0wNjbWWC6EKLUYCuvIkSNwdHRUGW7evAkA6NevHx4/fiydFdyyZQu8vLzg7e0tTb9x40bp/RyrV6/Gnj17sH//frRr167AP1p0/c5ycnIgk8mkeecdli9fLtWdP38+/vrrL3z22Wd4+vQpPvzwQ9SrVw+3bt0q0vYB9LO/ats3SnqfcXR0BAAkJSWpjUtKSoKTk5NKXW31AKjU1dXNmzfV9q+Xe2TRpLS+77fffhtXr17F4sWL4eTkhLlz56JevXpqZ8FfRTzWF095ONbnd2wfN24cLl68iMjISJiZmeGLL75AnTp18r3XP9esWbMQFhaGVq1aYePGjdi7dy/279+PevXqFfkKmp2dHc6cOYMffvhBenanc+fOCAkJKdL8DLnM4u7zhmorAN3bgMK0K4Uxb948lf31jTfeKHCanJwcdOjQQWNbsX//fvTu3RtA8b7v3BeyHj16FGPGjMHt27fx7rvvwtfXV6f3quTiA+w62rBhAwCo3ZKSl5GREdq3b4/27dtjwYIFmDVrFiZNmoRDhw4hICBA72/xvXTpkspnIQQuX76s8pBx5cqVNb487caNG6hZs6b0uTCxubi44MCBA3j8+LHKGbMLFy5I4/XBxcUFf/31F3JyclTOmOljOXm3HQBcvHgRFhYWsLW1hVwuV7ts6eDgAABo1aoVHB0dERsbixYtWuDgwYPSw2O5tm3bhpo1a2L79u0q2zYiIqLA2PL7zl7m7u4OIQTc3Nzg4eFR4HwbNGiABg0a4PPPP8eRI0fQvHlzREdHY8aMGQVOqysXFxckJCSolet73yiu3A4ETpw4IT2ECLx46dStW7ekB15z6/7yyy9q++Eff/wBCwuLAre9pt+Wg4OD2v6Vm8xq+y3q+/vO7zfv6OiIUaNGYdSoUbh79y4aN26MmTNnonPnzgUutzzjsV5VeT/Wa1pXb29vrcd24MXvbPz48Rg/fjwuXboEHx8fzJ8/Hxs3btQ6T+DFMb9t27ZYvXq1SvnDhw+ljijym14bU1NTdOvWDd26dUNOTg5GjRqF5cuX44svvkCtWrUKNT93d3f88ccfePbsWb7dCBe0TH3I/U4TEhLQrl07lXEJCQllpq0AXrQBhw4dQmpqqspD7H/88Yc0HgDq16+PChUq4MSJEyq3jmVlZeHMmTMqZZpo+y4HDx6scuvzy4ldfu1FWlqadCUkP8Xdx9588028+eabmDlzJjZt2oQBAwZg8+bNKrfV5YdXRnRw8OBBTJ8+HW5ubhgwYIDWev/++69aWe4OmnvJytLSEgD09mbl9evXq9zbvG3bNiQlJan8weDu7o7ff/9d5RaQH3/8UToTlKswsXXp0gXZ2dlYsmSJSvnChQshk8n09gdLly5dkJycrPJ8xvPnz7F48WJUrFgRrVu3LvK8jx49qnIf782bN/H999+jY8eOMDY2RuXKlREQEKAy5N4famRkhD59+uB///sfNmzYgOfPn6vdopV7tublszN//PEHjh49WmBs7u7uePToEf766y+pLCkpCTt27FCpFxQUBGNjY0ydOlXtLJAQAvfv3wfwomevvM9aNGjQAEZGRoW+nFqQLl264NixYyrrmZ6ejhUrVsDV1bXMvB+gXr168PLywooVK1TOHC9btgwymUx6nwjw4v78lJQUlR5ClEoltm7dim7dumm8P/hllpaWar8rMzMztf2rcuXKUn1A/beo7+9bU1zZ2dlqt5TY2dnByclJ7/tKWcNjvbryfqzXtI9rO7Y/efJEuu0ml7u7O6ysrAr83QAvjvl5f5dbt27F7du31WICdNv+ub/pXEZGRlICWpR9rXfv3lAqlWrfJ/BfW6XLMvWhSZMmsLOzQ3R0tMp8f/rpJ5w/fx5du3bV27KKq0+fPsjOzsaKFSuksszMTKxZswb+/v7SbcU2NjYICAjAxo0bVX6vGzZsQFpaGvr27ZvvcrR9lzVr1lTZX5s3b64yjabv/u2338bRo0exd+9etXEPHz6U2oji7GMPHjxQ2+fzHgt1wSsjefz000+4cOECnj9/jpSUFBw8eBD79++Hi4sLfvjhB5WHrPKaNm0aDh8+jK5du8LFxQV3797F119/jerVq0sZrbu7OypVqoTo6GhYWVnB0tIS/v7+Re5+rkqVKmjRogVCQ0ORkpKCqKgo1KpVS6VLymHDhmHbtm3o1KkT3n77bVy5cgUbN25U6+KwMLF169YNbdu2xaRJk3D9+nV4e3tj3759+P777zFu3LgCu0/U1YgRI7B8+XIMGTIEJ0+ehKurK7Zt24bffvsNUVFR+d7XXZD69esjMDBQpWtfAJg6dapO0wcHB2Px4sWIiIhAgwYN1LpSfOutt7B9+3b06tULXbt2xbVr1xAdHY26desWePmyX79++PTTT9GrVy98+OGHePLkCZYtWwYPDw+VBMrd3R0zZsxAeHg4rl+/jp49e8LKygrXrl3Djh07MGLECEyYMAEHDx7EmDFj0LdvX3h4eOD58+fYsGEDjI2NpUu1+jJx4kR8++236Ny5Mz788ENUqVIF69atw7Vr1/Ddd9+V+EuuHj16hMWLFwOA1NXqkiVLUKlSJVSqVAljxoyR6s6dOxfdu3dHx44d0a9fP5w7dw5LlizBsGHDVL7PPn364M0330RoaCj++ecfKBQKfP3118jOztZpf/H19cWyZcswY8YM1KpVC3Z2dmpnAvPWB4BJkyahX79+MDExQbdu3fT+ffv6+uLAgQNYsGABnJyc4ObmBk9PT1SvXh19+vSBt7c3KlasiAMHDuD48eOYP39+4b6MMozH+tfjWK9pH/f399dY9+LFi2jfvj3efvtt1K1bFxUqVMCOHTuQkpIiddmeO09Nv+e33noL06ZNQ2hoKJo1a4azZ8/im2++UbkqBRRu+w8bNgz//vsv2rVrh+rVq+PGjRtYvHgxfHx8pGOUj48PjI2NMXv2bDx69AhyuRzt2rWDnZ2d2vwGDx6M9evXIywsDMeOHUPLli2Rnp6OAwcOYNSoUejRo4dOy9QHExMTzJ49G6GhoWjdujX69+8vde3r6uqKjz76SG/L0ubw4cPSg9z37t1Denq6dOW4VatWaNWqFYAXHaj07dsX4eHhuHv3LmrVqoV169bh+vXralfCZs6ciWbNmqF169YYMWIEbt26hfnz56Njx47o1KlTvvEU5bihbX/8+OOP8cMPP+Ctt97CkCFD4Ovri/T0dJw9exbbtm3D9evXoVAoirWPbdq0CV9//TV69eoFd3d3PH78GCtXroS1tTW6dOmi+xdRrL64XiF5X+qS+7KjDh06iEWLFql0K5grb3ePcXFxokePHsLJyUmYmpoKJycn0b9/f7Vu1b7//ntRt25dUaFCBZUu3HJfhKWJtu4ev/32WxEeHi7s7OyEubm56Nq1q7hx44ba9PPnzxfVqlUTcrlcNG/eXJw4cULjy5C0xaapq9nHjx+Ljz76SDg5OQkTExNRu3btfF+ElZe2bijzSklJEaGhoUKhUAhTU1PRoEEDjd3eFbZr39yXHua++KlRo0Yau0bUJicnRzg7O2vs9jJ3/KxZs4SLi4s0/x9//FHjtoSGbgj37dsn6tevL0xNTYWnp6fYuHGj1pcefvfdd6JFixbC0tJSWFpaCi8vLzF69GiRkJAghBDi6tWr4t133xXu7u7CzMxMVKlSRbRt21YcOHCgwPXMr2tfbds796WHlSpVEmZmZsLPz0/rSw/zdj+rretVbXHkde3aNY0vaAKgsWvgHTt2CB8fHyGXy0X16tXF559/rtLVcK5///1XDB06VFStWlVYWFiI1q1b69ydYXJysujatauwsrJSeymVNtOnTxfVqlUTRkZGat386uv7vnDhgmjVqpUwNzcX+P8XwmVmZoqPP/5YeHt7CysrK2FpaSm8vb3F119/rdO6lnU81ucf26t2rNe0j2ujVCrF6NGjhZeXl7C0tBQ2NjbC399fbNmyRaWett9zRkaGGD9+vHB0dBTm5uaiefPm4ujRo8Xa/tu2bRMdO3YUdnZ2wtTUVNSoUUO89957IikpSWV+K1euFDVr1hTGxsYqXbBqWvaTJ0/EpEmThJubmzAxMREODg6iT58+4sqVK4Vapib5de2rravx2NhY0ahRIyGXy0WVKlXyfelhXtp+S7ruI9peMqupTX769KmYMGGCcHBwEHK5XLzxxhtau3X/5ZdfRLNmzYSZmZmwtbUVo0eP1nhs0UTbvqFNfu3L48ePRXh4uKhVq5YwNTUVCoVCNGvWTMybN09q54qzj506dUr0799f1KhRQ8jlcmFnZyfeeustldcm6EImRBl6qoyolMhkMowePVrjpWoiIiIiKh18ZoSIiIiIiAyCyQgRERERERkEkxEiIiIiIjII9qZFryU+KkVERERkeLwyQkREREREBsFkhIiIiIiIDILJCJUrrq6uGDJkSKkvd+3atZDJZLh+/XqpL1tXx44dg6mpKW7cuGHoUMqF+/fvw9LSErt37zZ0KESvrDZt2qB+/fqGDqNETZkyBTKZrMSXM2TIELi6uupUt6RjKkws+tSmTRu0adOm1JdLJYvJCBXaqVOn0L17d1SpUgUWFhaoX78+vvrqK0OHpRezZs3Czp07DR1GkUyaNAn9+/eHi4uLoUPR6vz58+jUqRMqVqyIKlWqYNCgQbh3757O0//www9o3LgxzMzMUKNGDUREROD58+cqdXITR01DcnKyVK9q1aoYNmwYvvjiC72tH9Gr6lU+7pdXT548wZQpUxAfH2/oUIiKhQ+wU6Hs27cP3bp1Q6NGjfDFF1+gYsWKuHLlCm7dulUqy09ISICRUcnl0LNmzUKfPn3Qs2dPlfJBgwahX79+kMvlJbbs4jhz5gwOHDiAI0eOGDoUrW7duoVWrVrBxsYGs2bNQlpaGubNm4ezZ89KV3Xy89NPP6Fnz55o06YNFi9ejLNnz2LGjBm4e/culi1bplZ/2rRpcHNzUymrVKmSyuf3338fX331FQ4ePIh27doVex2JXkWGPu7TCytXrkROTo70+cmTJ5g6dSoAqF0t+PzzzzFx4sTSDI+oyJiMkM5SU1MxePBgdO3aFdu2bdNLUvDkyRNYWFjoXN9QyYCxsTGMjY0NsmxdrFmzBjVq1MCbb75Z6svOyMhAYmIiPDw88q03a9YspKen4+TJk6hRowYAwM/PDx06dMDatWsxYsSIfKefMGECGjZsiH379qFChReHLmtra8yaNQtjx46Fl5eXSv3OnTujSZMm+c6zTp06qF+/PtauXctkhEiDkjjuU+Gkp6fD0tISJiYmOk9ToUIF6ThJVNbxqEI627RpE1JSUjBz5kwYGRkhPT1d5SxNQXLvHT558iRatWoFCwsLfPbZZwCAzMxMREREoFatWpDL5XB2dsYnn3yCzMxMlXloembk4cOHGDduHJydnSGXy1GrVi3Mnj1bLbacnBwsWrQIDRo0gJmZGWxtbdGpUyecOHECACCTyZCeno5169ZJt/XkLkvbMyNff/016tWrB7lcDicnJ4wePRoPHz7UuN7//PMP2rZtCwsLC1SrVg1z5sxR20aLFy9GvXr1YGFhgcqVK6NJkybYtGlTgdt2586daNeundo9wq6urnjrrbewb98++Pj4wMzMDHXr1sX27dsLnGdB/vzzT3zwwQdwcnLC119/XWD97777Dm+99ZaUiABAQEAAPDw8sGXLlnyn/eeff/DPP/9gxIgRKg3sqFGjIITAtm3bNE73+PFjZGdn5zvvDh064H//+x+7eybSoLjH/VwnT55Es2bNYG5uDjc3N0RHR6vV0aUdaN26Nby9vTUuw9PTE4GBgdLn9PR0jB8/XmobPD09MW/ePLXfukwmw5gxY7Bz507Ur18fcrkc9erVw549e9SW8euvv+KNN96AmZkZ3N3dsXz58kJthz/++ANdunRB5cqVYWlpiYYNG2LRokXS+CFDhkhXnrp06QIrKysMGDBAGpf7nMb169dha2sLAJg6darUZk2ZMgWA9mdGNm7cCD8/P6mNadWqFfbt2yeN//7779G1a1c4OTlBLpfD3d0d06dPL/A4qslbb72FmjVrahzXtGlTlZNFa9asQbt27WBnZwe5XI66detqvOKdl7a2OT4+HjKZTO0Wtj/++AOdOnWCjY0NLCws0Lp1a/z2228qdR4/foxx48bB1dUVcrkcdnZ26NChA06dOqXbilOhMRkhnR04cADW1ta4ffs2PD09UbFiRVhbW2PkyJHIyMjQaR73799H586d4ePjg6ioKLRt2xY5OTno3r075s2bh27dumHx4sXo2bMnFi5ciODg4Hzn9+TJE7Ru3RobN27E4MGD8dVXX6F58+YIDw9HWFiYSt2hQ4dKScvs2bMxceJEmJmZ4ffffwcAbNiwAXK5HC1btsSGDRuwYcMGvPfee1qXPWXKFIwePRpOTk6YP38+evfujeXLl6Njx4549uyZSt0HDx6gU6dO8Pb2xvz58+Hl5YVPP/0UP/30k1Rn5cqV+PDDD1G3bl1ERUVh6tSp8PHxwR9//JHvNrh9+zYSExPRuHFjjeMvXbqE4OBgdO7cGZGRkahQoQL69u2L/fv35ztfTR49eoRly5ahSZMm8PHxwbp16xAUFIRhw4YVGOPdu3c1Xqnw8/PD6dOn850+d3ze6Z2cnFC9enWN07dt2xbW1tawsLBA9+7dcenSJY3z9vX1xcOHD/H333/nGwPR60gfx/0HDx6gS5cu8PX1xZw5c1C9enWMHDkSMTExUh1d24FBgwbhr7/+wrlz51SWcfz4cVy8eBEDBw4E8OJdUt27d8fChQvRqVMnLFiwAJ6envj444/V2gbgRZIxatQo9OvXD3PmzEFGRgZ69+6N+/fvS3XOnj2Ljh074u7du5gyZQpCQ0MRERGBHTt26LQd9u/fj1atWuGff/7B2LFjMX/+fLRt2xY//vijSr3nz58jMDAQdnZ2mDdvHnr37q02L1tbW+mP9V69ekltVlBQkNblT506FYMGDYKJiQmmTZuGqVOnwtnZGQcPHpTqrF27FhUrVkRYWBgWLVoEX19fTJ48uUi3fAUHB+PatWs4fvy4SvmNGzfw+++/o1+/flLZsmXL4OLigs8++wzz58+Hs7MzRo0ahaVLlxZ6udocPHgQrVq1QmpqKiIiIjBr1iw8fPgQ7dq1w7Fjx6R677//PpYtW4bevXvj66+/xoQJE2Bubo7z58/rLRbKQxDpqGHDhsLCwkJYWFiIDz74QHz33Xfigw8+EABEv379Cpy+devWAoCIjo5WKd+wYYMwMjISv/zyi0p5dHS0ACB+++03qczFxUWEhIRIn6dPny4sLS3FxYsXVaadOHGiMDY2FomJiUIIIQ4ePCgAiA8//FAtrpycHOnflpaWKvPPtWbNGgFAXLt2TQghxN27d4Wpqano2LGjyM7OluotWbJEABAxMTFq671+/XqpLDMzUzg4OIjevXtLZT169BD16tVTW3ZBDhw4IACI//3vf2rjXFxcBADx3XffSWWPHj0Sjo6OolGjRjrNPycnR8THx4tBgwYJc3NzIZPJROvWrcXatWtFenq6TvM4fvy42jbI9fHHHwsAIiMjQ+v0c+fOFQCk7/Nlb7zxhnjzzTelz7GxsWLIkCFi3bp1YseOHeLzzz8XFhYWQqFQaJz+yJEjAoCIjY3VaV2IXif6Ou7Pnz9fKsvMzBQ+Pj7Czs5OZGVlCSF0bwcePnwozMzMxKeffqpS78MPPxSWlpYiLS1NCCHEzp07BQAxY8YMlXp9+vQRMplMXL58WSoDIExNTVXK/vzzTwFALF68WCrr2bOnMDMzEzdu3JDK/vnnH2FsbCwK+nPq+fPnws3NTbi4uIgHDx6ojHu5DQoJCREAxMSJE9XmERISIlxcXKTP9+7dEwBERESEWt2IiAiVmC5duiSMjIxEr169VNqsvMt/8uSJ2rzee+89YWFhoXKMzhuLJo8ePRJyuVyMHz9epXzOnDlCJpOpbEdNyw0MDBQ1a9ZUKWvdurVo3bq19Dlv25zr0KFDAoA4dOiQtI61a9cWgYGBauvr5uYmOnToIJXZ2NiI0aNH57tupF+8MkI6S0tLw5MnT6QrEEFBQfjqq6/w3nvvYfPmzVrPPL9MLpcjNDRUpWzr1q2oU6cOvLy8oFQqpSH3Hv5Dhw5pnd/WrVvRsmVLVK5cWWXagIAAZGdn4/DhwwBe3CIkk8kQERGhNo+idH944MABZGVlYdy4cSr3UA8fPhzW1tbYtWuXSv2KFStKZ+wAwNTUFH5+frh69apUVqlSJdy6dUvtLFJBcs/cVa5cWeN4Jycn9OrVS/psbW2NwYMH4/Tp0yq9S2myaNEieHh4oE2bNoiPj8f48eNx6dIlxMfHIyQkROfnfZ4+fQpA8zM/ZmZmKnWKMv3L07799ttYs2YNBg8ejJ49e2L69OnYu3cv7t+/j5kzZ6pNn7vdlEqlTutC9DrRx3G/QoUKKleZTU1N8d577+Hu3bs4efIkAN3bARsbG/To0QPffvutdLtVdnY2YmNj0bNnT1haWgIAdu/eDWNjY3z44YcqsYwfPx5CCJWr0sCLW0bd3d2lzw0bNoS1tbV0jM7OzsbevXvRs2dPlVtN69Spo3JrmDanT5/GtWvXMG7cOLWONDS1QSNHjixwnoWxc+dO5OTkYPLkyWrP/by8fHNzc+nfjx8/hlKpRMuWLfHkyRNcuHChUMu0trZG586dsWXLFpVb42JjY/Hmm2+qbMeXl/vo0SMolUq0bt0aV69exaNHjwq1XE3OnDmDS5cu4Z133sH9+/el/Ss9PR3t27fH4cOHpdsPK1WqhD/++AN37twp9nJJN0xGSGe5B4v+/furlL/zzjsAgKNHjxY4j2rVqqn1mnTp0iX8/fffsLW1VRlyH4i+e/eu1vldunQJe/bsUZs2ICBAZdorV67AyckJVapU0XFt85f7Lg9PT0+VclNTU9SsWVPtXR/Vq1dXa3AqV66MBw8eSJ8//fRTVKxYEX5+fqhduzZGjx6tdi9rfoSWZx5q1aqltuzcbVvQe1MWLlyIy5cvo0OHDjh69CimT5+u0mDrKnffyfsMEADpVo+XG6PCTp/ftADQokUL+Pv748CBA2rjcrdbabwngKi80cdx38nJSUoScuU9BhWmHRg8eDASExPxyy+/AHhxciglJQWDBg2S6ty4cQNOTk6wsrJSWW6dOnWk8S97+Q/jXC8fo+/du4enT5+idu3aavXytgOaXLlyBQB0eudKhQoVUL169QLrFcaVK1dgZGSEunXr5lvv77//Rq9evWBjYwNra2vY2tpKJ9KKkhQEBwfj5s2b0n5y5coVnDx5Uu0W7N9++w0BAQGwtLREpUqVYGtrKz1Tqo9kJDdpDgkJUdvHVq1ahczMTGk5c+bMwblz5+Ds7Aw/Pz9MmTJF5cQh6R+7WiCdOTk54e+//4a9vb1KuZ2dHQCo/GGtjaY/GnNyctCgQQMsWLBA4zTOzs5a55eTk4MOHTrgk08+0Ti+oB6eSou2nrheTiDq1KmDhIQE/Pjjj9izZw++++47fP3115g8ebLUfaMmVatWBaDb9i+smJgYLF++HDt37oSLiws6d+6M0NBQvPXWWwV2xfsyR0dHAEBSUpLauKSkJFSpUiXfntJenj7v/pCUlAQ/P78CY3B2dkZCQoJaee52UygUBc6D6HWjj+O+LgrTDgQGBsLe3h4bN25Eq1atsHHjRjg4OEgnoYpCl2N0aZHL5Qbptezhw4do3bo1rK2tMW3aNLi7u8PMzAynTp3Cp59+WqSOC7p16wYLCwts2bIFzZo1w5YtW2BkZIS+fftKda5cuYL27dvDy8sLCxYsgLOzM0xNTbF7924sXLgw3+VqO4mU94H73HnMnTsXPj4+GqepWLEigBdX11u2bIkdO3Zg3759mDt3LmbPno3t27ejc+fOhVl90hGTEdKZr68v9u/fLz3ImCv3UmZuzx6F5e7ujj///BPt27cv9Nlpd3d3pKWlFdgIubu7Y+/evfj333/zvTqi6/JzXyyYkJCg0ltIVlYWrl27VuRG0dLSEsHBwQgODkZWVhaCgoIwc+ZMhIeHS7cz5ZXbpe21a9c0jr98+TKEECrrdvHiRQAo8A267dq1Q7t27XD//n2sX78eq1evRu/evaFQKDBgwACEhoZq7dnmZdWqVYOtra3Uc9nLjh07prVxyJU7/sSJEyqJx507d3Dr1q0CuwUGgKtXr2rcR3O3W+4ZUyL6jz6O+3fu3JG6p82V9xhUmHbA2NgY77zzDtauXYvZs2dj586dGD58uEpC4eLiggMHDuDx48cqV0dybzUq7MthbW1tYW5urvG2NE0nOfLKvaJ87ty5YiVNLytMe+nu7o6cnBz8888/Wo+38fHxuH//PrZv345WrVpJ5draFl1YWlrirbfewtatW7FgwQLExsaiZcuWcHJykur873//Q2ZmJn744QeVK1T53aKdK/c227y9WOa98pW7/a2trXXa/o6Ojhg1ahRGjRqFu3fvonHjxpg5cyaTkRLC27RIZ2+//TYAYPXq1Srlq1atQoUKFdReulSY+d6+fRsrV65UG/f06VOkp6fnO+3Ro0exd+9etXEPHz6U3s7du3dvCCE0XmF4+cyXpaWl2kFNk4CAAJiamuKrr75SmX716tV49OgRunbtWuA88nq51xbgxS1fdevWhRBCrXeul1WrVg3Ozs4a/9AHXvwh8HJvL6mpqVi/fj18fHzg4OCgU2xVq1bFRx99hHPnzuHo0aPo0aMHVq9eDR8fHzRu3Fjt/mtNevfujR9//BE3b96UyuLi4nDx4kWVs2TPnj3DhQsXVK6i1KtXD15eXlixYoXKGa9ly5ZBJpOhT58+UpmmN7rv3r0bJ0+eRKdOndTGnTx5EjY2NqhXr17BG4LoNaOP4/7z589VusDNysrC8uXLYWtrC19fX2k5hWkHBg0ahAcPHuC9995DWlqayjN5ANClSxdkZ2djyZIlKuULFy6ETCYr9B+VxsbGCAwMxM6dO5GYmCiVnz9/XmP7k1fjxo3h5uaGqKgotTamqFdfcp/Z06XN6tmzJ4yMjDBt2jS1Kw25y89N5l6OJysrS6eu2/MTHByMO3fuYNWqVfjzzz/VbtHStNxHjx5hzZo1Bc47N8nIfT4UeHFVZMWKFSr1fH194e7ujnnz5iEtLU1tPrntRnZ2ttptYXZ2dnByctJ4mzDpB6+MkM4aNWqEd999FzExMXj+/Dlat26N+Ph4bN26FeHh4SpnOgpj0KBB2LJlC95//30cOnQIzZs3R3Z2Ni5cuIAtW7Zg7969Wl9e9/HHH+OHH37AW2+9hSFDhsDX1xfp6ek4e/Ystm3bhuvXr0OhUKBt27YYNGgQvvrqK1y6dAmdOnVCTk4OfvnlF7Rt2xZjxowB8OKAdeDAASxYsABOTk5wc3ODv7+/2nJtbW0RHh6OqVOnolOnTujevTsSEhLw9ddf44033lBrGHXRsWNHODg4oHnz5rC3t8f58+exZMkSdO3aVe2+57x69OiBHTt2qF0BAV7cqjZ06FAcP34c9vb2iImJQUpKik4Hek3efPNNvPnmm4iKikJsbCxWrVqFffv2Fdi4f/bZZ9i6dSvatm2LsWPHIi0tDXPnzkWDBg1UOjW4ffs26tSpg5CQEKxdu1Yqnzt3Lrp3746OHTuiX79+OHfuHJYsWYJhw4apXNVo1qwZGjVqhCZNmsDGxganTp1CTEwMnJ2dpXuQX7Z//35069aNz4wQaaCP476TkxNmz56N69evw8PDA7GxsThz5gxWrFghvcivsO1Ao0aNUL9+fenB97xdm3fr1g1t27bFpEmTcP36dXh7e2Pfvn34/vvvMW7cuCI9+zZ16lTs2bMHLVu2xKhRo/D8+XPp3VB//fVXvtMaGRlh2bJl6NatG3x8fBAaGgpHR0dcuHABf//9t04JTV7m5uaoW7cuYmNj4eHhgSpVqqB+/foan0upVasWJk2ahOnTp6Nly5YICgqCXC7H8ePH4eTkhMjISDRr1gyVK1dGSEgIPvzwQ8hkMmzYsKHYt6rlvi9lwoQJMDY2VuuquGPHjjA1NUW3bt2k5HLlypWws7PTeGvvy+rVq4c333wT4eHh0p0Pmzdvlk5E5jIyMsKqVavQuXNn1KtXD6GhoahWrRpu376NQ4cOwdraGv/73//w+PFjVK9eHX369IG3tzcqVqyIAwcO4Pjx45g/f36xtgPlo7S776LyLSsrS0yZMkW4uLgIExMTUatWLbFw4UKdpm3durXWrmuzsrLE7NmzRb169YRcLheVK1cWvr6+YurUqeLRo0dSvbxd+wohxOPHj0V4eLioVauWMDU1FQqFQjRr1kzMmzdP6jZSiBddK86dO1d4eXkJU1NTYWtrKzp37ixOnjwp1blw4YJo1aqVMDc3FwCkZWnrPnDJkiXCy8tLmJiYCHt7ezFy5Ei1bhu1rXferhGXL18uWrVqJapWrSrkcrlwd3cXH3/8scr6a3Pq1CkBQK1bTBcXF9G1a1exd+9e0bBhQyGXy4WXl5fYunVrgfMsjNzuNAty7tw50bFjR2FhYSEqVaokBgwYIJKTk1XqXLt2TWXbv2zHjh3Cx8dHyOVyUb16dfH555+rfMdCCDFp0iTh4+MjbGxshImJiahRo4YYOXKk2nKEEOL8+fMCgDhw4IDuK0v0mtHHcf/EiROiadOmwszMTLi4uIglS5ZoXI4u7UCuOXPmCABi1qxZGpf9+PFj8dFHHwknJydhYmIiateuLebOnavStasQL7r21dSVq6b25ueffxa+vr7C1NRU1KxZU0RHR6t1o5ufX3/9VXTo0EFYWVkJS0tL0bBhQ5Xug0NCQoSlpaXGaTV1p3vkyBEpHrzUza+2mGJiYkSjRo2k7du6dWuxf/9+afxvv/0m3nzzTWFubi6cnJzEJ598Ivbu3avSTa62WPIzYMAAAUAEBARoHP/DDz+Ihg0bCjMzM+Hq6ipmz54tYmJi1NrdvF37CiHElStXREBAgJDL5cLe3l589tlnYv/+/WoxCyHE6dOnRVBQkNTOuri4iLffflvExcUJIV50O/3xxx8Lb29v6Tvy9vYWX3/9tc7rSoUnE4KvHabyw9nZGYGBgVi1apWhQylz2rdvDycnJ2zYsEEqc3V1Rf369dVeqkUvjBs3DocPH8bJkyd5ZYSonFm0aBE++ugjXL9+XWNvWERUPvCZESo3nj17hvv377PXIy1mzZqF2NhYtQf3SLP79+9j1apVmDFjBhMRonJGCIHVq1ejdevWTESIyjk+M0Llwt69e7F582Y8ffoU7du3N3Q4ZZK/vz+ysrIMHUa5UbVqVY0PMhJR2ZWeno4ffvgBhw4dwtmzZ/H9998bOiQiKiYmI1QufPnll7h8+TJmzpyJDh06GDocIiIygHv37uGdd95BpUqV8Nlnn6F79+6GDomIionPjBARERERkUHwmREiIiIiIjIIJiNERERERGQQfGZEg5ycHNy5cwdWVlbsZYeIXktCCDx+/BhOTk4wMnp9z1uxPSCi111JtwdMRjS4c+cOnJ2dDR0GEZHB3bx5E9WrVzd0GAbD9oCI6IWSag+YjGhgZWUF4MVGt7a21v8C0tMBJ6cX/75zB7C01P8yiIiKITU1Fc7OztLx8HVVrPaAx3oiegWOAyXdHjAZ0SD3Ury1tXXJJCPGxv/929q6XO6YRPR6eN1vTSpWe8BjPRG9QseBkmoPXt8bgYmIiIiIyKCYjBARERERkUEwGSEiIiIiIoPgMyNEpFcPHz7EjRs3kJ2dbehQSAtjY2O4uLigUqVKhg6FypDMzEwkJCTg+fPnhg6FqFyoUKECPD09IZfLDR1KucZkhIj0IicnB++//z5Wrlxp6FBIR8OHD0d0dPRr/R4ReuHKlSvw8fFBWlqaoUMhKlesrKxw5swZ1KxZ09ChlFtMRohIL95//32sWrUKs2fPRqtWrWBqamrokEiLrKwsHD58GBMnTgQArFixwsARkSHl5ORg6NChUCgU+Omnn2BhYWHokIjKhSdPnmDgwIF49913cfDgQZ7YKSImI0RUbA8ePMDKlSsxe/ZsfPLJJ4YOh3Tw5ptvAgA+/fRTzJkzp9zcsrV06VLMnTsXycnJ8Pb2xuLFi+Hn56e1flRUFJYtW4bExEQoFAr06dMHkZGRMDMzK8Woy7akpCT8/PPP2LRpE1q0aGHocIjKlcjISLzzzjtITk6GU+77RKhQmMIRUbElJiYCAFq1amXgSKgwcr+vGzduGDgS3cTGxiIsLAwRERE4deoUvL29ERgYiLt372qsv2nTJkycOBERERE4f/48Vq9ejdjYWHz22WelHHnZdu/ePQCAu7u7gSMhKn9yfzfajkNUMCYjRFRsuQ+r89as8iX3+yovnQ0sWLAAw4cPR2hoKOrWrYvo6GhYWFggJiZGY/0jR46gefPmeOedd+Dq6oqOHTuif//+OHbsWClHXrbl5OQAePEwLhEVTu7vJvd3RIXHZISIiMq8rKwsnDx5EgEBAVKZkZERAgICcPToUY3TNGvWDCdPnpSSj6tXr2L37t3o0qVLqcRMREQF42kQMojExEQolcpCT6dQKFCjRo0SiOjVwu1LrxqlUons7GzY29urlNvb2+PChQsap3nnnXegVCrRokULCCHw/PlzvP/++/neppWZmYnMzEzpc2pqqn5WgMqU+Ph4tG3bFg8ePMj3eSlXV1eMGzcO48aN08ty27RpAx8fH0RFRellfpoMGTIEDx8+xM6dO0tsGUT6xCsjVOoSExPh5ekFX1/fQg9enl7S8wmkGbdv2ZeYmIiuXbvCwsICdnZ2+Pjjjwt8t8O///6LAQMGwNraGpUqVcLQoUNVumG9fv06ZDKZ2vD777+X9OqUWfHx8Zg1axa+/vprnDp1Ctu3b8euXbswffp0rdNERkbCxsZGGpydnUsxYiqs5ORkfPDBB6hZsybkcjmcnZ3RrVs3xMXF5Ttds2bNkJSUBBsbGwDA2rVrNSYlx48fx4gRI0oidMrH4cOH0a1bNzg5OUEmk+mcWC1duhR16tSBubk5PD09sX79erU6UVFR8PT0hLm5OZydnfHRRx8hIyND4/y+/PJLyGQyvSWjpBmvjFCpUyqVeJrxFEEIggIK3aeDEtsztkOpVPLsfT64fcu27OxsdO3aFQ4ODjhy5AiSkpIwePBgmJiYYNasWVqnGzBgAJKSkrB//348e/YMoaGhGDFiBDZt2qRS78CBA6hXr570uWrVqiW2LqVJoVDA2NgYKSkpKuUpKSlwcHDQOM0XX3yBQYMGYdiwYQCABg0aID09HSNGjMCkSZM0dsMZHh6OsLAw6XNqaioTkjLq+vXraN68OSpVqoS5c+eiQYMGePbsGfbu3YvRo0drvWL27NkzmJqaat1vXmZra6vvsAkvkr+1a9ciPj5e4/j09HR4e3vj3XffRVBQkE7zXLZsGcLDw7Fy5Uq88cYbOHbsGIYPH47KlSujW7duAP7r1CImJgbNmjXDxYsXMWTIEMhkMixYsEBlfsePH8fy5cvRsGHDYq0rFYxXRshgFFDAqRD/FeYPa+L21UVaWhpCQ0NhZWUFe3t7zJ07F7dv34aFhUWJvfxt3759+Oeff7Bx40b4+Pigc+fOmD59OpYuXYqsrCyN05w/fx579uzBqlWr4O/vjxYtWmDx4sXYvHkz7ty5o1K3atWqcHBwkAYTE5MSWY/SZmpqCl9fX5Uz3jk5OYiLi0PTpk01TvPkyRO1hMPY2BgAIITQOI1cLoe1tbXKQGXTqFGjIJPJcOzYMfTu3RseHh6oV68ewsLCVK4IymQyLFu2DN27d4elpSVmzpyJ+Ph4yGQyPHz4EPHx8QgNDcWjR4+kK4pTpkwB8OI2rZdvqXr48CHee+892Nvbw8zMDPXr18ePP/4IALh//z769++PatWqwcLCAg0aNMC3336r8/pcvHgRMplMLYlauHCh1GNTdnY2hg4dCjc3N+ns/6JFi/Kdb951AAAfHx9pHXPXa9iwYbC1tYW1tTXatWuHP//8Uxr/559/om3btrCysoK1tTV8fX1x4sQJndetsDp37owZM2agV69eOk+zYcMGvPfeewgODkbNmjXRr18/jBgxArNnz5bq6NqpRVpaGgYMGICVK1eicuXKelsv0oxXRohI/4QAnjwxzLItLACZTKeqQ4YMwdmzZxEfH4+UlBQEBQXh3LlzCAgIQMWKFbVOl984ABg4cCCio6M1jjt69CgaNGig8uxDYGAgRo4cib///huNGjXSOE2lSpXQpEkTqSwgIABGRkb4448/VBrs7t27IyMjAx4eHvjkk0/QvXv3fGMtT8LCwhASEoImTZrAz88PUVFRSE9PR2hoKABg8ODBqFatGiIjIwEA3bp1w4IFC9CoUSP4+/vj8uXL+OKLL9CtWzcpKSENysHv999//8WePXswc+ZMWFpaqo3Pe8vVlClT8OWXXyIqKgoVKlTA1atXpXHNmjVDVFQUJk+ejISEBACaf+M5OTno3LkzHj9+jI0bN8Ld3R3//POPtC9lZGTA19cXn376KaytrbFr1y4MGjQI7u7u+b4LJ5eHhweaNGmCb775RuVWwm+++QbvvPOOFEP16tWxdetWVK1aFUeOHMGIESPg6OiIt99+u8BlaNO3b1+Ym5vjp59+go2NDZYvX4727dvj4sWLqFKlCgYMGIBGjRph2bJlMDY2xpkzZ1ROdMhkMqxZswZDhgwpcgzFlZmZqfb+IHNzcxw7dgzPnj2DiYkJmjVrho0bN+LYsWPw8/OTOrUYNGiQynSjR49G165dERAQgBkzZpTmaryWmIwQkf49eQIU8Ad7iUlLAzT8cZKXUqnE9u3b8c0338DX1xcA0KtXL6xfvx6rV6/Od9ozZ87kOz6/s+nJyckaH8LOHadtGjs7O5WyChUqoEqVKtI0FStWxPz589G8eXMYGRnhu+++Q8+ePbFz585XJiEJDg7GvXv3MHnyZCQnJ8PHxwd79uyRtl9iYqLKlZDPP/8cMpkMn3/+OW7fvg1bW1t069YNM2fONNQqlA/l4Pd7+fJlCCHg5eWl02zfeecdKWkFoJKMmJqawsbGBjKZLN9btw4cOIBjx47h/Pnz8PDwAADUrFlTGl+tWjVMmDBB+vzBBx9g79692LJli07JCPDidswlS5ZIycjFixdx8uRJbNy4EQBgYmKCqVOnSvXd3Nxw9OhRbNmypcjJyK+//opjx47h7t27kMvlAIB58+Zh586d2LZtG0aMGIHExER8/PHH0vauXbu2yjw8PT2l5280SUxMRN26daXPz58/x7Nnz1SSvs8++6xY7wAKDAzEqlWr0LNnTzRu3BgnT57EqlWr8OzZMyiVSjg6OurUqcXmzZtx6tQpHD9+vMixUOEwGSGi11LuHzMv3+Lj5+eHrVu3FvjHe61atUo6vEJTKBQqzzq88cYbuHPnDubOnfvKJCMAMGbMGIwZM0bjuLz3n1eoUAERERGIiIgohcioNGm7zU6bl68qFtWZM2dQvXp1KRHJKzs7G7NmzcKWLVtw+/ZtZGVlITMzExYWFjovo1+/fpgwYQJ+//13vPnmm/jmm2/QuHFjlaRr6dKliImJQWJiIp4+fYqsrCz4+PgUeb3+/PNPpKWlqT1f9vTpU1y5cgXAi6uSw4YNw4YNGxAQEIC+ffuqvCRT2/M5uZycnFRO4mzfvh3fffcdvvnmG6msSpUqRV4H4MUzYsnJyXjzzTchhIC9vT1CQkIwZ84c6STFy51a5F4tHTt2LKZPn44vvvgCN2/exNixY7F//361qyxUcpiMEJH+WVi8OMNpqGXrIPcM4MsvarS1tYWHhwcUivyfnynObVoODg5q9yfnPpSt7aysg4OD2tt9nz9/jn///TffM7n+/v7Yv39/vrESqSkHv9/atWtrfL5CG023chWWubl5vuPnzp2LRYsWISoqCg0aNIClpSXGjRun9VkwTRwcHNCuXTts2rQJb775JjZt2oSRI0dK4zdv3owJEyZg/vz5aNq0KaysrDB37lz88ccfWudpZGSklrw9e/ZM+ndaWhocHR01Pkyee7vblClT8M4772DXrl346aefEBERgc2bN+v8TEeFChVUTuLY2dnB3Nxcryd2zM3NERMTg+XLlyMlJQWOjo5YsWIFrKyspI4ICurU4uTJk7h79y4aN24szTc7OxuHDx/GkiVLkJmZyVs8SwCTESLSP5lMp1stDMnNzQ1GRka4dOkSnJycAAA//PADEhMTIYSALJ/71otzm1bTpk0xc+ZM3L17V7r1av/+/bC2tla5jSHvNA8fPsTJkyelW8oOHjyInJwc+Pv75xuno6NjvrESqSkHv98qVaogMDAQS5cuxYcffqiWbDx8+DDf94fkZWpqiuzs7HzrNGzYELdu3cLFixc1Xh357bff0KNHDwwcOBDAi+c7Ll68qPV3rc2AAQPwySefoH///rh69Sr69eunsoxmzZph1KhRUlnu1QttbG1tkZSUJH1OTU3FtWvXpM+NGzdGcnIyKlSoAFdXV63z8fDwgIeHBz766CP0798fa9asKdQD5qXFxMQE1atXB/AieXvrrbekKyMFdWrRvn17nD17VmV8aGgovLy88OmnnzIRKSEG7U2rsP1I53a/lnd4uRvLKVOmqI3X9Z5SInp9VKpUCUFBQZg5cyaePn2KP//8E3v27IG5uTkOHjyY77S1atXKd8j7fMfLOnbsiLp162LQoEH4888/sXfvXnz++ecYPXq0dLXm2LFj8PLywu3btwEAderUQadOnTB8+HAcO3YMv/32G8aMGYN+/fpJidS6devw7bff4sKFC7hw4QJmzZqFmJgYfPDBB3raYkRly9KlS5GdnQ0/Pz989913uHTpEs6fP4+vvvpKaw9r2ri6uiItLQ1xcXFQKpV4ouEB/tatW6NVq1bo3bs39u/fj2vXruGnn37Cnj17ALy4WrN//34cOXIE58+fx3vvvafWFbUugoKC8PjxY4wcORJt27aVfuO5yzhx4gT27t2Lixcv4osvvijw2YZ27dphw4YN+OWXX3D27FmEhISo/FEdEBCApk2bomfPnti3bx+uX7+OI0eOYNKkSThx4gSePn2KMWPGID4+Hjdu3MBvv/2G48ePo06dOtI8vLy8sGPHDq0xZGdnIzk5WRo6deqEzZs3q5S93INhWloazpw5I534uXbtGs6cOaPyHqzw8HAMHjxY+nzx4kVs3LgRly5dwrFjx9CvXz+cO3dOpcv0bt26YdmyZdi8eTOuXbuG/fv3q3RqYWVlhfr166sMlpaWqFq1KurXr5/vdqaiM+iVkcL2I71o0SJ8+eWX0ufnz5/D29sbffv2ValXr149HDhwQPpcoQIvABGRuqVLl2LYsGGoVq0ajI2NERUVBblcjgEDBmDmzJkYOnSo3pdpbGyMH3/8ESNHjkTTpk1haWmJkJAQTJs2Tarz5MkTJCQkqNxK8c0332DMmDFo3749jIyM0Lt3b3z11Vcq854+fTpu3LiBChUqwMvLC7GxsejTp4/e14GoLKhZsyZOnTqFmTNnYvz48UhKSoKtrS18fX2xbNmyQs2rWbNmeP/99xEcHIz79+8jIiJCpevbXN999x0mTJiA/v37Iz09HbVq1ZL+Lvn8889x9epVBAYGwsLCAiNGjEDPnj3x6NGjQsViZWWFbt26YcuWLYiJiVEZ99577+H06dMIDg6GTCZD//79MWrUKPz0009a5xceHo5r167hrbfego2NDaZPn65yZUQmk2H37t2YNGkSQkNDce/ePTg4OKBVq1awt7eHsbEx7t+/j8GDByMlJQUKhQJBQUEqD9InJCTku543b96Em5tbvuv98jY/ceIE2rZtK43LfR4uJCQEa9euBQAkJSWpJCfZ2dmYP38+EhISYGJigrZt2+LIkSMqV3vYqUXZJBOFfQqshMhkMuzYsQM9e/bUeZqdO3ciKCgI165dg4uLC4AXV0Z27txZ4G0U+UlNTYWNjQ0ePXpUMn3Mp6f/11OJjj2HvEpOnToFX19fjMAIOMGp4An+3x3cwQqswMmTJ1Xu5yRVhti+ucvkd1O+5Pe9lfhxsJwo1nYoJ8d6/n6Jiq7A3085OQ7kp6Tbg3L90sPVq1cjICBASkRy5d4DXrNmTQwYMEAlcyYiIiIiorKh3N6/dOfOHfz000/YtGmTSrm/vz/Wrl0LT09PJCUlYerUqWjZsiXOnTsHKysrjfPKzMxEZmam9Dk1NbVEYyciIiIionKcjKxbtw6VKlVSu62rc+fO0r8bNmwIf39/uLi4YMuWLVrv/46MjFS595GIiIiIiEpeubxNSwiBmJgYDBo0SOUdAZpUqlQJHh4euHz5stY64eHhePTokTTcvHlT3yETEREREVEe5TIZ+fnnn3H58mWderpJS0vDlStX8u1rXy6Xw9raWmUgIt3ldhNZmJd7keHlfl/sO//1lvvehefPnxs4EqLyJ/d3k/f9JaQ7g265gvqRztuHdK7Vq1fD399fY5/PEyZMwM8//yz1k92rVy8YGxujf//+JbouRK+zGjVqAHjx7iAqP3K/r7ydgNDrJfft1AW9PI+I1OX+bvJ7vxTlz6DPjBTUj3TePqQB4NGjR/juu++waNEijfO8desW+vfvj/v378PW1hYtWrTA77//Lh1siUj/KleujOHDh2PixIkAgFatWhV4CyUZTlZWFg4fPoyJEydi+PDhhXpTNb16HB0d0bp1a3z22WdwdnaGhYWFoUMiKheePHmC8PBwtGnTBg4ODoYOp9wyaDLSpk0b5Peak9wX27zMxsZG45tRc23evFkfoRFRIUVHRwMAPv30UwNHQroaPny49L3R68vIyAgxMTHw9vZGy5YtDR0OUbliZWWFgwcP8jatYii3vWkRUdliZGSEFStWYM6cObhx4ways7MNHdIr4/z58xg4cCCCEAQFFDpPp4QS27EdGzduRJ06daRyY2NjuLi48IoISWrWrAmlUomLFy/i2bNnhg6HSlDu8QRBQYBCy/FEqQS2qx87SJWJiQk8PDwgl8sNHUq5xmSEiPSqUqVK/CO3hCiggBOcCj1dnTp1+GZtKpBcLkeDBg0MHQaVFoUCcMr/eMJjB5UGJiNEREREepaYmAilUplvHYVCIXUAQvS6YjJCREREpEeJiYnw9PJCxtOn+dYzMzdHwoULTEjotcZkhIiIiEiPlErli0SkgOcyMrZvh1KpZDJCrzUmI0REREQlQYfnMohed+yHjIiIiIiIDILJCBERERERGQSTESIiIiIiMggmI0REREREZBB8gJ1IB7r0F68J+5An0q+lS5di7ty5SE5Ohre3NxYvXgw/Pz+Nddu0aYOff/5ZrbxLly7YtWtXSYdKREQ6YDJCVIDExER4eXrhaUb+/cVrYm5mjgsJ7EOeSB9iY2MRFhaG6Oho+Pv7IyoqCoGBgUhISICdnZ1a/e3btyMrK0v6fP/+fXh7e6Nv376lGTYREeWDyQhRAZRKJZ5mPEUQgqCAlv7iNU0HJbZnsA95In1ZsGABhg8fjtDQUABAdHQ0du3ahZiYGEycOFGtfpUqVVQ+b968GRYWFkxGiIjKECYjRDpSQAEnsL94IkPIysrCyZMnER4eLpUZGRkhICAAR48e1Wkeq1evRr9+/WBpaam1TmZmJjIzM6XPqampRQ+aiIgKxAfYiYiozFMqlcjOzoa9vb1Kub29PZKTkwuc/tixYzh37hyGDRuWb73IyEjY2NhIg7Ozc7HiJiKi/DEZISKiV97q1avRoEEDrQ+75woPD8ejR4+k4ebNm6UUIRHR64m3aRERUZmnUChgbGyMlJQUlfKUlBQ4ODjkO216ejo2b96MadOmFbgcuVwOuVxerFiJiEh3vDJCRERlnqmpKXx9fREXFyeV5eTkIC4uDk2bNs132q1btyIzMxMDBw4s6TCJiKiQeGWEiIjKhbCwMISEhKBJkybw8/NDVFQU0tPTpd61Bg8ejGrVqiEyMlJlutWrV6Nnz56oWrWqIcImIqJ8MBkhIqJyITg4GPfu3cPkyZORnJwMHx8f7NmzR3qoPTExEUZGqhf8ExIS8Ouvv2Lfvn2GCJmIiArAZISIiMqNMWPGYMyYMRrHxcfHq5V5enpCCFHCURERUVHxmREiIiIiIjIIJiNERERERGQQTEaIiIiIiMggmIwQEREREZFBMBkhIiIiIiKDMGgycvjwYXTr1g1OTk6QyWTYuXNnvvXj4+Mhk8nUhuTkZJV6S5cuhaurK8zMzODv749jx46V4FoQEREREVFRGDQZSU9Ph7e3N5YuXVqo6RISEpCUlCQNdnZ20rjY2FiEhYUhIiICp06dgre3NwIDA3H37l19h09ERERERMVg0PeMdO7cGZ07dy70dHZ2dqhUqZLGcQsWLMDw4cOlN/JGR0dj165diImJwcSJE4sTLhERERER6VG5fGbEx8cHjo6O6NChA3777TepPCsrCydPnkRAQIBUZmRkhICAABw9elTr/DIzM5GamqoyEBERERFRySpXyYijoyOio6Px3Xff4bvvvoOzszPatGmDU6dOAQCUSiWys7Nhb2+vMp29vb3acyUvi4yMhI2NjTQ4OzuX6HoQEREREZGBb9MqLE9PT3h6ekqfmzVrhitXrmDhwoXYsGFDkecbHh6OsLAw6XNqaioTEiIiIiKiElaukhFN/Pz88OuvvwIAFAoFjI2NkZKSolInJSUFDg4OWuchl8shl8tLNE4iIiIiIlJVrm7T0uTMmTNwdHQEAJiamsLX1xdxcXHS+JycHMTFxaFp06aGCpGIiIiIiDQw6JWRtLQ0XL58Wfp87do1nDlzBlWqVEGNGjUQHh6O27dvY/369QCAqKgouLm5oV69esjIyMCqVatw8OBB7Nu3T5pHWFgYQkJC0KRJE/j5+SEqKgrp6elS71pERERERFQ2GDQZOXHiBNq2bSt9zn1uIyQkBGvXrkVSUhISExOl8VlZWRg/fjxu374NCwsLNGzYEAcOHFCZR3BwMO7du4fJkycjOTkZPj4+2LNnj9pD7UREREREZFgGTUbatGkDIYTW8WvXrlX5/Mknn+CTTz4pcL5jxozBmDFjihseERERERGVoHL/zAgREREREZVPTEaIiIiIiMggmIwQEREREZFBlPv3jJRFiYmJUCqVWscbPX0Kn///95kzZ5Bjbg4AyMzMLPL7ThQKBWrUqFGkaYmIiIiIDIHJiJ4lJibCy9MLTzOeaq1jASD9///dvEULPPn/f8sgg4D2B/rzY25mjgsJF5iQEBEREVG5wWREz5RKJZ5mPEUQgqCAQmMdUzwDsAYA8C5CkQUTXMIlHMKhfKfTukwosT1jO5RKJZMRIiIiIio3mIyUEAUUcIKTxnEmyJL+7QhHPIMplFAWOB0RERER0auED7ATEVG5sXTpUri6usLMzAz+/v44duxYvvUfPnyI0aNHw9HREXK5HB4eHti9e3cpRUtERAXhlREiIioXYmNjERYWhujoaPj7+yMqKgqBgYFISEiAnZ2dWv2srCx06NABdnZ22LZtG6pVq4YbN26gUqVKpR88ERFpxGSEiIjKhQULFmD48OEIDQ0FAERHR2PXrl2IiYnBxIkT1erHxMTg33//xZEjR2BiYgIAcHV1Lc2QiYioALxNi4iIyrysrCycPHkSAQEBUpmRkRECAgJw9OhRjdP88MMPaNq0KUaPHg17e3vUr18fs2bNQnZ2ttblZGZmIjU1VWUgIqKSw2SEiIjKPKVSiezsbNjb26uU29vbIzk5WeM0V69exbZt25CdnY3du3fjiy++wPz58zFjxgyty4mMjISNjY00ODs763U9iIhIFZMRIiJ6JeXk5MDOzg4rVqyAr68vgoODMWnSJERHR2udJjw8HI8ePZKGmzdvlmLERESvHz4zQkREZZ5CoYCxsTFSUlJUylNSUuDg4KBxGkdHR5iYmMDY2Fgqq1OnDpKTk5GVlQVTU1O1aeRyOeRyuX6DJyIirXhlhIiIyjxTU1P4+voiLi5OKsvJyUFcXByaNm2qcZrmzZvj8uXLyMnJkcouXrwIR0dHjYkIERGVPiYjRERULoSFhWHlypVYt24dzp8/j5EjRyI9PV3qXWvw4MEIDw+X6o8cORL//vsvxo4di4sXL2LXrl2YNWsWRo8ebahVICKiPHibFhERlQvBwcG4d+8eJk+ejOTkZPj4+GDPnj3SQ+2JiYkwMvrvHJuzszP27t2Ljz76CA0bNkS1atUwduxYfPrpp4ZaBSIiyoPJCBERlRtjxozBmDFjNI6Lj49XK2vatCl+//33Eo6KiIiKirdpERERERGRQTAZISIiIiIig2AyQkREREREBsFkhIiIiIiIDILJCBERERERGQSTESIiIiIiMggmI0REREREZBBMRoiIiIiIyCAMmowcPnwY3bp1g5OTE2QyGXbu3Jlv/e3bt6NDhw6wtbWFtbU1mjZtir1796rUmTJlCmQymcrg5eVVgmtBRERERERFYdBkJD09Hd7e3li6dKlO9Q8fPowOHTpg9+7dOHnyJNq2bYtu3brh9OnTKvXq1auHpKQkafj1119LInwiIiIiIiqGCoZceOfOndG5c2ed60dFRal8njVrFr7//nv873//Q6NGjaTyChUqwMHBQV9hEhERERFRCSjXz4zk5OTg8ePHqFKlikr5pUuX4OTkhJo1a2LAgAFITEzMdz6ZmZlITU1VGYiIiIiIqGSV62Rk3rx5SEtLw9tvvy2V+fv7Y+3atdizZw+WLVuGa9euoWXLlnj8+LHW+URGRsLGxkYanJ2dSyN8IiIiIqLXWrlNRjZt2oSpU6diy5YtsLOzk8o7d+6Mvn37omHDhggMDMTu3bvx8OFDbNmyReu8wsPD8ejRI2m4efNmaawCEREREdFrzaDPjBTV5s2bMWzYMGzduhUBAQH51q1UqRI8PDxw+fJlrXXkcjnkcrm+wyQiIiIionyUu2Tk22+/xbvvvovNmzeja9euBdZPS0vDlStXMGjQoFKIrnxKTEyEUqks9HQKhQI1atQogYiISh73eyIiIsMzaDKSlpamcsXi2rVrOHPmDKpUqYIaNWogPDwct2/fxvr16wG8uDUrJCQEixYtgr+/P5KTkwEA5ubmsLGxAQBMmDAB3bp1g4uLC+7cuYOIiAgYGxujf//+pb+C5UBiYiK8PL3wNONpoac1NzPHhYQL/MOMyh3u90RERGWDQZOREydOoG3bttLnsLAwAEBISAjWrl2LpKQklZ6wVqxYgefPn2P06NEYPXq0VJ5bHwBu3bqF/v374/79+7C1tUWLFi3w+++/w9bWtnRWqpxRKpV4mvEUQQiCAgrdp4MS2zO2Q6lU8o8yKne43xMREZUNBk1G2rRpAyGE1vG5CUau+Pj4Aue5efPmYkb1elJAASc4GToMolLF/Z6IiMiwym1vWkREREREVL4xGSEiIiIiIoMoUjJy9epVfcdBRESvKLYZRESkTZGSkVq1aqFt27bYuHEjMjIy9B0TERG9QvTZZixduhSurq4wMzODv78/jh07prXu2rVrIZPJVAYzM7NiLZ+IiPSrSMnIqVOn0LBhQ4SFhcHBwQHvvfdevg0CERG9vvTVZsTGxiIsLAwRERE4deoUvL29ERgYiLt372qdxtraGklJSdJw48aN4qwKERHpWZGSER8fHyxatAh37txBTEwMkpKS0KJFC9SvXx8LFizAvXv39B0nERGVU/pqMxYsWIDhw4cjNDQUdevWRXR0NCwsLBATE6N1GplMBgcHB2mwt7fX12oREZEeFOsB9goVKiAoKAhbt27F7NmzcfnyZUyYMAHOzs4YPHgwkpKS9BUnERGVc8VpM7KysnDy5EkEBARIZUZGRggICMDRo0e1TpeWlgYXFxc4OzujR48e+Pvvv/W6TkREVDzFSkZOnDiBUaNGwdHREQsWLMCECRNw5coV7N+/H3fu3EGPHj30FScREZVzxWkzlEolsrOz1a5s2NvbIzk5WeM0np6eiImJwffff4+NGzciJycHzZo1w61bt7QuJzMzE6mpqSoDERGVnCK99HDBggVYs2YNEhIS0KVLF6xfvx5dunSBkdGL3MbNzQ1r166Fq6urPmMlIqJyyFBtRtOmTdG0aVPpc7NmzVCnTh0sX74c06dP1zhNZGQkpk6dqtc4iIhIuyIlI8uWLcO7776LIUOGwNHRUWMdOzs7rF69uljBERFR+aePNkOhUMDY2BgpKSkq5SkpKXBwcNApDhMTEzRq1AiXL1/WWic8PBxhYWHS59TUVDg7O+s0fyIiKrwiJSOXLl0qsI6pqSlCQkKKMnsiInqF6KPNMDU1ha+vL+Li4tCzZ08AQE5ODuLi4jBmzBid4sjOzsbZs2fRpUsXrXXkcjnkcrlO8yMiouIr0jMja9aswdatW9XKt27dinXr1hU7KCIienXoq80ICwvDypUrsW7dOpw/fx4jR45Eeno6QkNDAQCDBw9GeHi4VH/atGnYt28frl69ilOnTmHgwIG4ceMGhg0bVvyVIiIivShSMhIZGQmFQqFWbmdnh1mzZhU7KCIienXoq80IDg7GvHnzMHnyZPj4+ODMmTPYs2eP9FB7YmKiSo9cDx48wPDhw1GnTh106dIFqampOHLkCOrWrVv8lSIiIr0o0m1aiYmJcHNzUyt3cXFBYmJisYMiIqJXhz7bjDFjxmi9LSs+Pl7l88KFC7Fw4cJCzZ+IiEpXka6M2NnZ4a+//lIr//PPP1G1atViB0VERK8OthlERKRNkZKR/v3748MPP8ShQ4eQnZ2N7OxsHDx4EGPHjkW/fv30HSMREZVjbDOIiEibIt2mNX36dFy/fh3t27dHhQovZpGTk4PBgwfzmREiIlLBNoOIiLQpUjJiamqK2NhYTJ8+HX/++SfMzc3RoEEDuLi46Ds+IiIq59hmEBGRNkVKRnJ5eHjAw8NDX7EQEdErjG0GERHlVaRkJDs7G2vXrkVcXBzu3r2LnJwclfEHDx7US3BERFT+sc0gIiJtipSMjB07FmvXrkXXrl1Rv359yGQyfcdFRESvCLYZRESkTZGSkc2bN2PLli3o0qWLvuMhIqJXDNsMIiLSpkhd+5qamqJWrVr6joWIiF5BbDOIiEibIiUj48ePx6JFiyCE0Hc8RET0imGbQURE2hTpNq1ff/0Vhw4dwk8//YR69erBxMREZfz27dv1EhwREZV/bDOIiEibIl0ZqVSpEnr16oXWrVtDoVDAxsZGZdDV4cOH0a1bNzg5OUEmk2Hnzp0FThMfH4/GjRtDLpejVq1aWLt2rVqdpUuXwtXVFWZmZvD398exY8cKsXZERKRP+moziIjo1VOkKyNr1qzRy8LT09Ph7e2Nd999F0FBQQXWv3btGrp27Yr3338f33zzDeLi4jBs2DA4OjoiMDAQABAbG4uwsDBER0fD398fUVFRCAwMREJCAuzs7PQSNxnW+fPnizRdZmYm5HJ5qS2vuNMbKl4ifdNXm0FERK+eIr/08Pnz54iPj8eVK1fwzjvvwMrKCnfu3IG1tTUqVqyo0zw6d+6Mzp0767zM6OhouLm5Yf78+QCAOnXq4Ndff8XChQulZGTBggUYPnw4QkNDpWl27dqFmJgYTJw4sZBrSWVJGtIggwwDBw4s0vQyyCBQevesl7d4iUqSPtoMIiJ69RQpGblx4wY6deqExMREZGZmokOHDrCyssLs2bORmZmJ6OhofccJADh69CgCAgJUygIDAzFu3DgAQFZWFk6ePInw8HBpvJGREQICAnD06NESiYlKTwYyICAQhCAooCjUtJdwCYdwqFjTFlZ5i5eopBiqzSAiorKvyC89bNKkCf78809UrVpVKu/VqxeGDx+ut+DySk5Ohr29vUqZvb09UlNT8fTpUzx48ADZ2dka61y4cEHrfDMzM5GZmSl9Tk1N1W/gpFcKKOAEp0JNo4Sy2NMWVXmLl0jfDNVmEBFR2VekZOSXX37BkSNHYGpqqlLu6uqK27dv6yWw0hQZGYmpU6caOgwiolfSq9ZmEBGR/hSpN62cnBxkZ2erld+6dQtWVlbFDkobBwcHpKSkqJSlpKTA2toa5ubmUCgUMDY21ljHwcFB63zDw8Px6NEjabh582aJxE9E9DoyVJtBRERlX5GSkY4dOyIqKkr6LJPJkJaWhoiICHTp0kVfsalp2rQp4uLiVMr279+Ppk2bAnjxll9fX1+VOjk5OYiLi5PqaCKXy2Ftba0yEBGRfhiqzSAiorKvSLdpzZ8/H4GBgahbty4yMjLwzjvv4NKlS1AoFPj22291nk9aWhouX74sfb527RrOnDmDKlWqoEaNGggPD8ft27exfv16AMD777+PJUuW4JNPPsG7776LgwcPYsuWLdi1a5c0j7CwMISEhKBJkybw8/NDVFQU0tPTpd61iIiodOmrzSAioldPkZKR6tWr488//8TmzZvx119/IS0tDUOHDsWAAQNgbm6u83xOnDiBtm3bSp/DwsIAACEhIVi7di2SkpKQmJgojXdzc8OuXbvw0UcfYdGiRahevTpWrVoldesLAMHBwbh37x4mT56M5ORk+Pj4YM+ePWoPtRMRUenQV5tBRESvniK/Z6RChQpFfn9CrjZt2kAI7e9R0PR29TZt2uD06dP5znfMmDEYM2ZMsWIjIiL90UebQUREr54iJSO5t01pM3jw4CIFQ0RErx62GUREpE2R3zPysmfPnuHJkycwNTWFhYUFGxYiIpLos81YunQp5s6di+TkZHh7e2Px4sXw8/MrcLrNmzejf//+6NGjB3bu3FnYVSAiohJSpN60Hjx4oDKkpaUhISEBLVq04MOIRESkQl9tRmxsLMLCwhAREYFTp07B29sbgYGBuHv3br7TXb9+HRMmTEDLli2LuypERKRnRUpGNKlduza+/PJLtTNgREREeRWlzViwYAGGDx+O0NBQ1K1bF9HR0bCwsEBMTIzWabKzszFgwABMnToVNWvW1EfoRESkR3pLRoAXDyjeuXNHn7MkIqJXVGHajKysLJw8eRIBAQFSmZGREQICAnD06FGt002bNg12dnYYOnRoseMlIiL9K9IzIz/88IPKZyEEkpKSsGTJEjRv3lwvgRER0atBH22GUqlEdna2Wjft9vb2uHDhgsZpfv31V6xevRpnzpzROdbMzExkZmZKn1NTU3WetjgSExOhVCrzraNQKFCjRo1Sied1pMt3APB7yIvbjYqrSMlIz549VT7LZDLY2tqiXbt2mD9/vj7iIiKiV4Qh2ozHjx9j0KBBWLlyJRQKhc7TRUZGYurUqSUSkzaJiYnw9PJCxtOn+dYzMzdHwoUL/IOuBOj6HQD8Hl7G7Ub6UKRkJCcnR99xEBHRK0ofbYZCoYCxsTFSUlJUylNSUuDg4KBW/8qVK7h+/Tq6deumFkeFChWQkJAAd3d3tenCw8OlF/ACL66MODs7Fzv+/CiVyhd/zAUFAdoSJ6USGdu3Q6lU8o+5EqDTd/CiIr+Hl3C7kT4U+aWHREREpcXU1BS+vr6Ii4uTrrTk5OQgLi5O40tuvby8cPbsWZWyzz//HI8fP8aiRYu0JhhyuRxyuVzv8etEoQCcnAyzbHqB30HRcLtRMRQpGXn5rFFBFixYUJRFEBHRK0JfbUZYWBhCQkLQpEkT+Pn5ISoqCunp6QgNDQXw4uWJ1apVQ2RkJMzMzFC/fn2V6StVqgQAauVERGQ4RUpGTp8+jdOnT+PZs2fw9PQEAFy8eBHGxsZo3LixVE8mk+knSiIiKrf01WYEBwfj3r17mDx5MpKTk+Hj44M9e/ZID7UnJibCyEivnUQSEVEJK1Iy0q1bN1hZWWHdunWoXLkygBcvtQoNDUXLli0xfvx4vQZJRETllz7bjDFjxmi8LQsA4uPj85127dq1Oi+HiIhKR5FOIc2fPx+RkZFSowIAlStXxowZM9ibFhERqWCbQURE2hQpGUlNTcW9e/fUyu/du4fHjx8XOygiInp1sM0gIiJtipSM9OrVC6Ghodi+fTtu3bqFW7du4bvvvsPQoUMRFBSk7xiJiKgcY5tBRETaFOmZkejoaEyYMAHvvPMOnj179mJGFSpg6NChmDt3rl4DJCKi8o1tBhERaVOkZMTCwgJff/015s6diytXrgAA3N3dYWlpqdfgiIio/GObQURE2hSrD8SkpCQkJSWhdu3asLS0hBBCX3EREdErhm0GERHlVaRk5P79+2jfvj08PDzQpUsXJCUlAQCGDh3Kbn2JiEgF2wwiItKmSMnIRx99BBMTEyQmJsLCwkIqDw4Oxp49e/QWHBERlX9sM4iISJsiPTOyb98+7N27F9WrV1cpr127Nm7cuKGXwIiofElMTIRSqSz0dAqFAjVq1CiBiMqeom6j8+fPl0A0pYdtBhERaVOkZCQ9PV3l7Fauf//9F3K5vNhBEVH5kpiYCC9PLzzNeFroac3NzHEh4cIrn5AUZxuVd2wziIhImyIlIy1btsT69esxffp0AIBMJkNOTg7mzJmDtm3b6jVAIir7lEolnmY8RRCCoIBC9+mgxPaM7VAqla98MlLUbQQAl3AJh3CohCIreWwziIhImyIlI3PmzEH79u1x4sQJZGVl4ZNPPsHff/+Nf//9F7/99pu+YySickIBBZzgZOgwyrSibCMlCn9rV1nCNoOIiLQp0gPs9evXx8WLF9GiRQv06NED6enpCAoKwunTp+Hu7q7vGImIqBxjm0FERNoU+srIs2fP0KlTJ0RHR2PSpEklERMREb0i2GYQEVF+Cn1lxMTEBH/99Zdeg1i6dClcXV1hZmYGf39/HDt2TGvdNm3aQCaTqQ1du3aV6gwZMkRtfKdOnfQaMxERFawk2gwiInp1FOmZkYEDB2L16tX48ssvix1AbGwswsLCEB0dDX9/f0RFRSEwMBAJCQmws7NTq799+3ZkZWVJn+/fvw9vb2/07dtXpV6nTp2wZs0a6TN7bCEiMgx9thlUvunavXVmZqZO7bYu9V6n7sOJyqMiJSPPnz9HTEwMDhw4AF9fX1haWqqMX7Bggc7zWrBgAYYPH47Q0FAAQHR0NHbt2oWYmBhMnDhRrX6VKlVUPm/evBkWFhZqyYhcLoeDg4POcRARUcnQZ5tB5VdiYiI8vbyQ8VSH7q1lMkAIvdQzMzdHwoVXv/twovKqUMnI1atX4erqinPnzqFx48YAgIsXL6rUkclkOs8vKysLJ0+eRHh4uFRmZGSEgIAAHD16VKd5rF69Gv369VNr3OLj42FnZ4fKlSujXbt2mDFjBqpWrapzbEREVDz6bjOofFMqlS8SkaAgQJFP99aXLgGHDumnnlKJjO2vR/fhROVVoZKR2rVrIykpCYcOvejvPjg4GF999RXs7e2LtHClUons7Gy16e3t7XHhwoUCpz927BjOnTuH1atXq5R36tQJQUFBcHNzw5UrV/DZZ5+hc+fOOHr0KIyNjdXmk5mZiczMTOlzampqkdaHiIj+o+82g14RCgXglE/31rm3cemrHhGVaYVKRkSeS6E//fQT0tPT9RpQYaxevRoNGjSAn5+fSnm/fv2kfzdo0AANGzaEu7s74uPj0b59e7X5REZGYurUqSUeLxHR66SstRlERFT2FOk9I7nyNjSFpVAoYGxsjJSUFJXylJSUAp/3SE9Px+bNmzF06NACl1OzZk0oFApcvnxZ4/jw8HA8evRIGm7evKn7ShARkU6K22YQEdGrp1DJSG43uXnLisrU1BS+vr6Ii4uTynJychAXF4emTZvmO+3WrVuRmZmJgQMHFricW7du4f79+3B0dNQ4Xi6Xw9raWmUgIqLi0XebQUREr55C36Y1ZMgQqRu9jIwMvP/++2oPj2/fvl3neYaFhSEkJARNmjSBn58foqKikJ6eLvWuNXjwYFSrVg2RkZEq061evRo9e/ZUeyg9LS0NU6dORe/eveHg4IArV67gk08+Qa1atRAYGFiY1SUiomIoiTaDiIheLYVKRkJCQlQ+63JVoiDBwcG4d+8eJk+ejOTkZPj4+GDPnj3SA46JiYkwMlK9gJOQkIBff/0V+/btU5ufsbEx/vrrL6xbtw4PHz6Ek5MTOnbsiOnTp/NdI0REpagk2oylS5di7ty5SE5Ohre3NxYvXqz23GCu7du3Y9asWbh8+TKePXuG2rVrY/z48Rg0aFCx4yAiIv0oVDLy8ksE9WnMmDEYM2aMxnHx8fFqZZ6enlrvPTY3N8fevXv1GR4RERWBvtuMwr4kt0qVKpg0aRK8vLxgamqKH3/8EaGhobCzs+OVciKiMqJYD7ATERGVlpdfklu3bl1ER0fDwsICMTExGuu3adMGvXr1Qp06deDu7o6xY8eiYcOG+PXXX0s5ciIi0obJCBERlXm5L8kNCAiQygrzklwhBOLi4pCQkIBWrVpprZeZmYnU1FSVgYiISg6TESIiKvPye0lucnKy1ukePXqEihUrwtTUFF27dsXixYvRoUMHrfUjIyNhY2MjDc7OznpbByIiUsdkhIiIXllWVlY4c+YMjh8/jpkzZyIsLEzjs4i5+N4pIqLSVagH2ImIiAyhqC/JNTIyQq1atQAAPj4+OH/+PCIjI9GmTRuN9eVyOXteJCIqRbwyQkREZV5xXpL7spycHGRmZpZEiEREVAS8MkJEROVCYV+SGxkZiSZNmsDd3R2ZmZnYvXs3NmzYgGXLlhlyNYiI6CVMRoiIqFwo7Ety09PTMWrUKNy6dQvm5ubw8vLCxo0bERwcbKhVICKiPJiMEBFRuVGYl+TOmDEDM2bMKIWoiIioqPjMCBERERERGQSTESIiIiIiMggmI0REREREZBBMRoiIiIiIyCD4ADsRUSGdP3++VKYhKi8SExOhVCrzrWPI30BByy7LsQEvXvpZo0aNUohGVVnebvTqYDJCRKSjNKRBBhkGDhxo6FCIyozExER4enkh4+lTQ4eiLi0NkJXR32whYjMzN0fChQull5CU5e1GrxwmI0REOspABgQEghAEBRSFmvYSLuEQDpVQZESGo1QqXyQiQUGAIp/fxaVLwKFS/g1kZABClO/YlEpkbN8OpVJZeslIWd5u9MphMkJEVEgKKOAEp0JNo0T+t7AQlXsKBeCUz++igNu4SlR5js2QyvJ2o1cGH2AnIiIiIiKDYDJCREREREQGwWSEiIiIiIgMgskIEREREREZBJMRIiIiIiIyCCYjRERERERkEExGiIiIiIjIIJiMEBERERGRQTAZISIiIiIigygTycjSpUvh6uoKMzMz+Pv749ixY1rrrl27FjKZTGUwMzNTqSOEwOTJk+Ho6Ahzc3MEBATg0qVLJb0aRERERERUCAZPRmJjYxEWFoaIiAicOnUK3t7eCAwMxN27d7VOY21tjaSkJGm4ceOGyvg5c+bgq6++QnR0NP744w9YWloiMDAQGRkZJb06RERERESkI4MnIwsWLMDw4cMRGhqKunXrIjo6GhYWFoiJidE6jUwmg4ODgzTY29tL44QQiIqKwueff44ePXqgYcOGWL9+Pe7cuYOdO3eWwhoREREREZEuDJqMZGVl4eTJkwgICJDKjIyMEBAQgKNHj2qdLi0tDS4uLnB2dkaPHj3w999/S+OuXbuG5ORklXna2NjA399f6zwzMzORmpqqMhARERERUckyaDKiVCqRnZ2tcmUDAOzt7ZGcnKxxGk9PT8TExOD777/Hxo0bkZOTg2bNmuHWrVsAIE1XmHlGRkbCxsZGGpydnYu7akREREREVACD36ZVWE2bNsXgwYPh4+OD1q1bY/v27bC1tcXy5cuLPM/w8HA8evRIGm7evKnHiImIiIiISBODJiMKhQLGxsZISUlRKU9JSYGDg4NO8zAxMUGjRo1w+fJlAJCmK8w85XI5rK2tVQYiIip7CtP74sqVK9GyZUtUrlwZlStXRkBAQL71iYio9Bk0GTE1NYWvry/i4uKkspycHMTFxaFp06Y6zSM7Oxtnz56Fo6MjAMDNzQ0ODg4q80xNTcUff/yh8zyJiKjsKWzvi/Hx8ejfvz8OHTqEo0ePwtnZGR07dsTt27dLOXIiItLG4LdphYWFYeXKlVi3bh3Onz+PkSNHIj09HaGhoQCAwYMHIzw8XKo/bdo07Nu3D1evXsWpU6cwcOBA3LhxA8OGDQPwoqetcePGYcaMGfjhhx9w9uxZDB48GE5OTujZs6chVpGIiPSgsL0vfvPNNxg1ahR8fHzg5eWFVatWSSe8iIiobKhg6ACCg4Nx7949TJ48GcnJyfDx8cGePXukB9ATExNhZPRfzvTgwQMMHz4cycnJqFy5Mnx9fXHkyBHUrVtXqvPJJ58gPT0dI0aMwMOHD9GiRQvs2bNH7eWIRERUPuT2vvjyySldel982ZMnT/Ds2TNUqVJFa53MzExkZmZKn/XVu+KZM2eQY26ucdz58+f1soxciYmJUCqVBdZTKBSoUaNGseen7/jLg4LW+XXcJrrQZbvoul+SKl1+92V12xo8GQGAMWPGYMyYMRrHxcfHq3xeuHAhFi5cmO/8ZDIZpk2bhmnTpukrRCIiMqD8el+8cOGCTvP49NNP4eTkpNL1e16RkZGYOnVqsWLNdfPmTeT2zdi8RQs80ctc85eYmAhPLy9kPH1aYF0zc3MkXLiQ7x8nhZnfayEtDZDJMHDgQENHUr4UYrvpsl+SKl1/p2V125aJZISIiKgkffnll9i8eTPi4+PzvUoeHh6OsLAw6XNqamqRu3u/f/++lIwgNBQwMdFc8dIl4NChIi0jL6VS+eIPkqAgQKHIryIytm+HUqnM9w8Tneanx/jLvIwMQIiCt+/rtE10oet203G/JFU6/U7L8LZlMkJERGVecXpfnDdvHr788kscOHAADRs2zLeuXC6HXC4vdrxqHB0BU1PN43S4parQFArAyal05lcS8Zd1BW3f13Gb6ELf+yWpKqfb1+APsBMRERWkqL0vzpkzB9OnT8eePXvQpEmT0giViIgKgVdGiIioXAgLC0NISAiaNGkCPz8/REVFqfW+WK1aNURGRgIAZs+ejcmTJ2PTpk1wdXVFcnIyAKBixYqoWLGiwdaDiIj+w2SEiIjKhcL2vrhs2TJkZWWhT58+KvOJiIjAlClTSjN0IiLSgskIERGVG4XpffH69eslHxARERULk5FXSFH6NS9uX+iGWCZRLl3fp5AX90EiIqKygcnIKyANaZChdPs9N8QyiV6WmJgIL08vPM3g+w+IiIjKKyYjr4AMZEBAIAhBUCCf/rs1uIRLOITC94VuiGUSvUypVOJpxlPug0REROUYk5FXiAIKOKFw/UsrUby+0A2xTKKXcR8kIiIqv/ieESIiIiIiMggmI0REREREZBBMRoiIiIiIyCCYjBARERERkUEwGSEiIiIiIoNgMkJERERERAbBZISIiIiIiAyCyQgRERERERkEkxEiIiIiIjIIJiNERERERGQQTEaIiIiIiMggKhg6ACIiIjKM8+fPF2s8UUkoaL/LzMyEXC4vcD4KhQI1atTQV1hUQpiMEBERvW7S0gCZDAMHDjR0JET/0XW/lMkAIQqcnZm5ORIuXGBCUsYxGSEiInrdZGS8+GMuKAhQKLTXu3QJOHSo9OKi15su+2XuPlnQvqtUImP7diiVSiYjZRyTESIioteVQgE4OWkfr1SWXixEufLbL3P3yYL2XSo3ysQD7EuXLoWrqyvMzMzg7++PY8eOaa27cuVKtGzZEpUrV0blypUREBCgVn/IkCGQyWQqQ6dOnUp6NYiIiIiIqBAMnozExsYiLCwMEREROHXqFLy9vREYGIi7d+9qrB8fH4/+/fvj0KFDOHr0KJydndGxY0fcvn1bpV6nTp2QlJQkDd9++21prA4REREREenI4MnIggULMHz4cISGhqJu3bqIjo6GhYUFYmJiNNb/5ptvMGrUKPj4+MDLywurVq1CTk4O4uLiVOrJ5XI4ODhIQ+XKlUtjdYiIiIiISEcGTUaysrJw8uRJBAQESGVGRkYICAjA0aNHdZrHkydP8OzZM1SpUkWlPD4+HnZ2dvD09MTIkSNx//59vcZORESlrzC39f7999/o3bs3XF1dIZPJEBUVVXqBEhGRTgyajCiVSmRnZ8Pe3l6l3N7eHsnJyTrN49NPP4WTk5NKQtOpUyesX78ecXFxmD17Nn7++Wd07twZ2dnZGueRmZmJ1NRUlYGIiMqWwt7W++TJE9SsWRNffvklHBwcSjlaIiLShcFv0yqOL7/8Eps3b8aOHTtgZmYmlffr1w/du3dHgwYN0LNnT/z44484fvw44uPjNc4nMjISNjY20uDs7FxKa0BERLoq7G29b7zxBubOnYt+/frp9II0IiIqfQZNRhQKBYyNjZGSkqJSnpKSUuBZrHnz5uHLL7/Evn370LBhw3zr1qxZEwqFApcvX9Y4Pjw8HI8ePZKGmzdvFm5FiIioROnjtl4iIip7DJqMmJqawtfXV+Xh89yH0Zs2bap1ujlz5mD69OnYs2cPmjRpUuBybt26hfv378PR0VHjeLlcDmtra5WBiIjKDn3c1qsL3rZLRFS6DH6bVlhYGFauXIl169bh/PnzGDlyJNLT0xEaGgoAGDx4MMLDw6X6s2fPxhdffIGYmBi4uroiOTkZycnJSEtLAwCkpaXh448/xu+//47r168jLi4OPXr0QK1atRAYGGiQdSQiovKBt+0SEZUugycjwcHBmDdvHiZPngwfHx+cOXMGe/bskc5+JSYmIikpSaq/bNkyZGVloU+fPnB0dJSGefPmAQCMjY3x119/oXv37vDw8MDQoUPh6+uLX375hfcMExGVU8W5rbcweNsuEVHpqmDoAABgzJgxGDNmjMZxeR86v379er7zMjc3x969e/UUGRERlQUv39bbs2dPAP/d1qut/SgKuVzOE1dERKWoTCQjRFR2nD9/vlSmMfQyqfwJCwtDSEgImjRpAj8/P0RFRand1lutWjVERkYCePHQ+z///CP9+/bt2zhz5gwqVqyIWrVqGWw9iIjoP0xGiAgAkIY0yCDDwIEDX+llUvkVHByMe/fuYfLkyUhOToaPj4/abb1GRv/dfXznzh00atRI+jxv3jzMmzcPrVu31trVOxERlS4mI0QEAMhABgQEghAEBRSFmvYSLuEQDpWLZVL5Vpjbel1dXSGEKIWoiIioqJiMEJEKBRRwglOhplFCWe6WSURERIZn8N60iIiIiIjo9cRkhIiIiIiIDILJCBERERERGQSfGSEiIiIq43TpzlyhUKBGjRqlEE35oct2y8zM1On9QvrcvomJiVAqC3728XX4TpmMEBEREZVVaWmATLcu0M3MzZFw4cIr/8erTgqx3SCTATr0vKev7ZuYmAhPLy9kPH1aasssy5iMEBEREZVVGRkv/lAOCgIU+XSBrlQiY/t2KJXKV/oPV53put0uXQIOHSrV7atUKl8kIvxOATAZISIiIir7FArAqXBdoBMK3m65t0oZYvvyOwXAB9iJiIiIiMhAmIwQEREREZFBMBkhIiIiIiKDYDJCREREREQGwWSEiIiIiIgMgskIEREREREZBJMRIiIiIiIyCCYjRERERERkEExGiIiIiIjIIJiMEBERERGRQTAZISIiIiIig2AyQkREREREBsFkhIiIiIiIDILJCBERERERGQSTESIiIiIiMogykYwsXboUrq6uMDMzg7+/P44dO5Zv/a1bt8LLywtmZmZo0KABdu/erTJeCIHJkyfD0dER5ubmCAgIwKVLl0pyFYiIqBTou70gIiLDMngyEhsbi7CwMERERODUqVPw9vZGYGAg7t69q7H+kSNH0L9/fwwdOhSnT59Gz5490bNnT5w7d06qM2fOHHz11VeIjo7GH3/8AUtLSwQGBiIjI6O0VouIiPSsJNoLIiIyLIMnIwsWLMDw4cMRGhqKunXrIjo6GhYWFoiJidFYf9GiRejUqRM+/vhj1KlTB9OnT0fjxo2xZMkSAC+uikRFReHzzz9Hjx490LBhQ6xfvx537tzBzp07S3HNiIhIn/TdXhARkeEZNBnJysrCyZMnERAQIJUZGRkhICAAR48e1TjN0aNHVeoDQGBgoFT/2rVrSE5OVqljY2MDf39/rfMkIqKyrSTaCyIiMrwKhly4UqlEdnY27O3tVcrt7e1x4cIFjdMkJydrrJ+cnCyNzy3TVievzMxMZGZmSp8fPXoEAEhNTS3E2ryQlpYGAEhCErKQpbGOKZ4hd843cANZMME93CtwOm0MMe3rssziTMt4y+YyizNteYv3Pu4DeHFcKuzxLLe+EKJQ05WUkmgvNNFre5CeLh3rxY0bgImJ5or3Xny/SEoCsrR8v/dffJcnT56U2hlNEhISCp6XrsvUtZ4+58XYil5Pn/vI67Td9Lx9jYyMkJOT89/njAw0/P9///Xbb8gxM9P9d6rP7/R+GW4PhAHdvn1bABBHjhxRKf/444+Fn5+fxmlMTEzEpk2bVMqWLl0q7OzshBBC/PbbbwKAuHPnjkqdvn37irffflvjPCMiIgQADhw4cOCQZ7h582ZRD/F6VRLthSZsDzhw4MBB81BS7YFBr4woFAoYGxsjJSVFpTwlJQUODg4ap3FwcMi3fu7/U1JS4OjoqFLHx8dH4zzDw8MRFhYmfc7JycG///6LqlWrQiaTaY0/NTUVzs7OuHnzJqytrbWv6CuC6/tqe53W93VaV6Bo6yuEwOPHj+Hk5FTC0emmJNoLTYraHmjyuu1nmnAbcBsA3AZA+d4GJd0eGDQZMTU1ha+vL+Li4tCzZ08ALw78cXFxGDNmjMZpmjZtiri4OIwbN04q279/P5o2bQoAcHNzg4ODA+Li4qTkIzU1FX/88QdGjhypcZ5yuRxyuVylrFKlSjqvh7W1dbnbsYqD6/tqe53W93VaV6Dw62tjY1OC0RROSbQXmhS3PdDkddvPNOE24DYAuA2A8rsNSrI9MGgyAgBhYWEICQlBkyZN4Ofnh6ioKKSnpyM0NBQAMHjwYFSrVg2RkZEAgLFjx6J169aYP38+unbtis2bN+PEiRNYsWIFAEAmk2HcuHGYMWMGateuDTc3N3zxxRdwcnKSGjAiIip/9N1eEBGR4Rk8GQkODsa9e/cwefJkJCcnw8fHB3v27JEeOkxMTISR0X+dfjVr1gybNm3C559/js8++wy1a9fGzp07Ub9+fanOJ598gvT0dIwYMQIPHz5EixYtsGfPHpiZmZX6+hERkX6URHtBREQGViJPorwmMjIyREREhMjIyDB0KKWC6/tqe53W93VaVyFev/UtK7jduQ2E4DYQgttACG6D/MiEKCP9NhIRERER0WvF4G9gJyIiIiKi1xOTESIiIiIiMggmI0REREREZBBMRgqwdOlSuLq6wszMDP7+/jh27Fi+9bdu3QovLy+YmZmhQYMG2L17dylFqh+FWd+VK1eiZcuWqFy5MipXroyAgIACt09ZU9jvN9fmzZshk8nKXXfRhV3fhw8fYvTo0XB0dIRcLoeHh0e52acLu65RUVHw9PSEubk5nJ2d8dFHHyEjI6OUoi2ew4cPo1u3bnBycoJMJsPOnTsLnCY+Ph6NGzeGXC5HrVq1sHbt2hKP83V2/fp1DB06FG5ubjA3N4e7uzsiIiKQlZVl6NBK1cyZM9GsWTNYWFgU+/0t5UVR25lXQVGOTa+ayMhIvPHGG7CysoKdnR169uyJhIQEQ4dVpjAZyUdsbCzCwsIQERGBU6dOwdvbG4GBgbh7967G+keOHEH//v0xdOhQnD59Gj179kTPnj1x7ty5Uo68aAq7vvHx8ejfvz8OHTqEo0ePwtnZGR07dsTt27dLOfKiKez65rp+/TomTJiAli1bllKk+lHY9c3KykKHDh1w/fp1bNu2DQkJCVi5ciWqVatWypEXXmHXddOmTZg4cSIiIiJw/vx5rF69GrGxsfjss89KOfKiSU9Ph7e3N5YuXapT/WvXrqFr165o27Ytzpw5g3HjxmHYsGHYu3dvCUf6+rpw4QJycnKwfPly/P3331i4cCGio6PLzT6mL1lZWejbt6/WlxC/aorazrwqCntsehX9/PPPGD16NH7//Xfs378fz549Q8eOHZGenm7o0MoOQ3fnVZb5+fmJ0aNHS5+zs7OFk5OTiIyM1Fj/7bffFl27dlUp8/f3F++9916JxqkvhV3fvJ4/fy6srKzEunXrSipEvSrK+j5//lw0a9ZMrFq1SoSEhIgePXqUQqT6Udj1XbZsmahZs6bIysoqrRD1prDrOnr0aNGuXTuVsrCwMNG8efMSjbMkABA7duzIt84nn3wi6tWrp1IWHBwsAgMDSzAyymvOnDn/196dx0R1vX0A/w7LKAiDiiBikUUBEbAYiBZxwUpSS9RirbWWsKQKUZnUjVYSoLhS09paJJpW2o6mqU4bhdQA0qqIWhesCBUFUUSYqKDSWgExsp33j1+ct8hiZ1guwveT3IS5nHPu88ww5/Jw7h2Eo6Oj1GFIQqVSCQsLC6nD6HFdPa/2J/9lbhoI7t+/LwCIkydPSh1Kn8GVkQ40NDQgLy8PAQEB2n0GBgYICAjAuXPn2u1z7ty5Vu0B4I033uiwfV+iT77Pq6+vR2NjI4YPH95TYXYbffPdtGkTrK2tsXTp0t4Is9vok+/hw4fh6+uLqKgojBw5Eh4eHkhMTERzc3Nvha0XfXKdOnUq8vLytJdPlJWVITMzE4GBgb0Sc297meeq/uTRo0cvxXxJ+umO8yr1P48ePQIAvvf/RfL/wN5XVVdXo7m5WfuffZ8ZOXIkrl271m6fqqqqdttXVVX1WJzdRZ98n7d+/XrY2tq2+SWnL9In399//x3fffcdCgoKeiHC7qVPvmVlZcjOzkZwcDAyMzNRWlqKlStXorGxEQkJCb0Rtl70yfX9999HdXU1pk2bBiEEmpqasHz58n57CU1Hc1VNTQ2ePHkCExMTiSIbOEpLS5GcnIzt27dLHQr1kO44r1L/0tLSgtWrV8PPzw8eHh5Sh9NncGWEusW2bdugVquRlpaGwYMHSx1Ot6utrUVISAhSUlIwYsQIqcPpFS0tLbC2tsaePXvg7e2NxYsXIzY2Fl9//bXUoXW7nJwcJCYmYvfu3bh06RJSU1ORkZGBzZs3Sx0a9XExMTGQyWSdbs//4nnnzh3MmTMHixYtQkREhESRdx99ngOigSgqKgpXrlyBWq2WOpQ+hSsjHRgxYgQMDQ1x7969Vvvv3bsHGxubdvvY2Njo1L4v0SffZ7Zv345t27bh2LFjmDhxYk+G2W10zffmzZsoLy/HvHnztPtaWloAAEZGRigpKcHYsWN7Nugu0Of1HTVqFIyNjWFoaKjd5+bmhqqqKjQ0NEAul/dozPrSJ9f4+HiEhIRg2bJlAABPT088fvwYkZGRiI2NhYFB//q7TUdzlUKh4KqIjtatW4fw8PBO2zg5OWm/vnv3LmbNmoWpU6diz549PRxd79D1ORgounJepf5HqVQiPT0dp06dwiuvvCJ1OH1K/zrDdiO5XA5vb28cP35cu6+lpQXHjx+Hr69vu318fX1btQeAo0ePdti+L9EnXwD47LPPsHnzZmRlZcHHx6c3Qu0WuuY7fvx4FBYWoqCgQLvNnz9f+2lEdnZ2vRm+zvR5ff38/FBaWqotugDg+vXrGDVqVJ8tRAD9cq2vr29TcDwrwoQQPResRF7muaqvsbKywvjx4zvdnr1f7ty5A39/f3h7e0OlUvWbIleX52Ag0fe8Sv2LEAJKpRJpaWnIzs6Go6Oj1CH1PRLfQN+nqdVqMWjQILF3715RVFQkIiMjxdChQ0VVVZUQQoiQkBARExOjbX/mzBlhZGQktm/fLoqLi0VCQoIwNjYWhYWFUqWgE13z3bZtm5DL5eLgwYOisrJSu9XW1kqVgk50zfd5L9unaemar0ajEebm5kKpVIqSkhKRnp4urK2txZYtW6RK4T/TNdeEhARhbm4uDhw4IMrKysRvv/0mxo4dK959912pUtBJbW2tyM/PF/n5+QKA+PLLL0V+fr6oqKgQQggRExMjQkJCtO3LysqEqamp+Oijj0RxcbHYtWuXMDQ0FFlZWVKl0O/dvn1bjBs3TsyePVvcvn271Zw5kFRUVIj8/HyxceNGYWZmpv25fVnOG7p60VzU371obhoIVqxYISwsLEROTk6r9319fb3UofUZLEZeIDk5WYwZM0bI5XIxefJkcf78ee33Zs6cKcLCwlq1//nnn4WLi4uQy+XC3d1dZGRk9HLEXaNLvvb29gJAmy0hIaH3A9eTrq/vv71sxYgQuud79uxZMWXKFDFo0CDh5OQktm7dKpqamno5av3okmtjY6PYsGGDGDt2rBg8eLCws7MTK1euFA8fPuz9wPVw4sSJdt+Lz3IMCwsTM2fObNPHy8tLyOVy4eTkJFQqVa/HPZCoVKp2X6OB9jfBsLCwdp+DEydOSB1aj+lsLurvXjQ3DQQdve855/4/mRD98BoEIiIiIiLq8/rHBatERERERPTSYTFCRERERESSYDFCRERERESSYDFCRERERESSYDFCRERERESSYDFCRERERESSYDFCRERERESSYDFCRERERESSYDFC9BLZsGEDvLy8pA6DiIgkFh4ejqCgIL37l5eXQyaToaCgoNtiItIHixEiIiKiF/D398fq1av17p+TkwOZTIZ//vlHp34dFQ1JSUnYu3fvfxqjvcLFzs4OlZWV8PDw0Ckeou5mJHUARERERKQbCwuLLvU3NDSEjY1NN0VDpD+ujBDpyd/fH0qlEkqlEhYWFhgxYgTi4+MhhGjTtqamBiYmJjhy5Eir/WlpaTA3N0d9fT0AYP369XBxcYGpqSmcnJwQHx+PxsbGTmN4/i91QUFBCA8P1z5++vQpoqOjMXr0aAwZMgRTpkxBTk6O3nkTEQ004eHhOHnyJJKSkiCTySCTyVBeXt6mXUVFBebNm4dhw4ZhyJAhcHd3R2ZmJsrLyzFr1iwAwLBhwyCTybTzdFZWFqZNm4ahQ4fC0tISc+fOxc2bN7VjOjo6AgAmTZoEmUwGf39/bUz/Xu04ePAgPD09YWJiAktLSwQEBODx48fYsGED9u3bh19++UUbe05OTrsrLlevXsXcuXOhUChgbm6O6dOnt4qFqCdwZYSoC/bt24elS5fiwoULuHjxIiIjIzFmzBhERES0aqdQKDB37lzs378fb775pnb/jz/+iKCgIJiamgIAzM3NsXfvXtja2qKwsBAREREwNzfHxx9/rHeMSqUSRUVFUKvVsLW1RVpaGubMmYPCwkI4OzvrPS4R0UCRlJSE69evw8PDA5s2bQIAWFlZtWkXFRWFhoYGnDp1CkOGDEFRURHMzMxgZ2eHQ4cOYeHChSgpKYFCoYCJiQkA4PHjx1i7di0mTpyIuro6fPLJJ1iwYAEKCgpgYGCACxcuYPLkyTh27Bjc3d0hl8vbHLeyshJLlizBZ599hgULFqC2thanT5+GEALR0dEoLi5GTU0NVCoVAGD48OG4e/duqzHu3LmDGTNmwN/fH9nZ2VAoFDhz5gyampq6++kkaoXFCFEX2NnZYceOHZDJZHB1dUVhYSF27NjRphgBgODgYISEhKC+vh6mpqaoqalBRkYG0tLStG3i4uK0Xzs4OCA6OhpqtVrvYkSj0UClUkGj0cDW1hYAEB0djaysLKhUKiQmJuo1LhHRQGJhYQG5XA5TU9NOL23SaDRYuHAhPD09AQBOTk7a7w0fPhwAYG1tjaFDh2r3L1y4sNUY33//PaysrFBUVAQPDw9t0WNpadnhsSsrK9HU1IS3334b9vb2AKCNAQBMTEzw9OnTTmPftWsXLCwsoFarYWxsDABwcXHpsD1Rd+FlWkRd8Nprr0Emk2kf+/r64saNG9i6dSvMzMy0m0ajQWBgIIyNjXH48GEAwKFDh6BQKBAQEKDt/9NPP8HPzw82NjYwMzNDXFwcNBqN3vEVFhaiubkZLi4ureI5efIkl96JiLrA3d1dO6c+W/H+8MMPsWXLFvj5+SEhIQGXL19+4Tg3btzAkiVL4OTkBIVCAQcHBwDQae5/9dVXMXv2bHh6emLRokVISUnBw4cPdcqnoKAA06dP1xYiRL2FxQhRD1i+fDkKCgq0m62tLeRyOd555x3s378fALB//34sXrwYRkb/W6A8d+4cgoODERgYiPT0dOTn5yM2NhYNDQ0dHsfAwKDNPSr/vsekrq4OhoaGyMvLaxVPcXExkpKSeiBzIqKBITMzUzunfvvttwCAZcuWoaysDCEhISgsLISPjw+Sk5M7HWfevHn4+++/kZKSgtzcXOTm5gJAp3P/8wwNDXH06FEcOXIEEyZMQHJyMlxdXXHr1q3/PMazy8aIehuLEaIueHbSeOb8+fNwdnaGpaUlxo0bp92eFRzBwcHIysrC1atXkZ2djeDgYG3fs2fPwt7eHrGxsfDx8YGzszMqKio6Pb6VlRUqKyu1j5ubm3HlyhXt40mTJqG5uRn3799vFc+4ceP4KSpERDqQy+Vobm7WPra3t9fOp6NHj9but7Ozw/Lly5Gamop169YhJSVF2x9AqzH++usvlJSUIC4uDrNnz4abm1ubFY32+rVHJpPBz88PGzduRH5+PuRyufYy4Odjb8/EiRNx+vTpTj80hagnsBgh6gKNRoO1a9eipKQEBw4cQHJyMlatWtVh+xkzZsDGxgbBwcFwdHTElClTtN9zdnaGRqOBWq3GzZs3sXPnzlb3k7Tn9ddfR0ZGBjIyMnDt2jWsWLGi1WfYu7i4IDg4GKGhoUhNTcWtW7dw4cIFfPrpp8jIyOhy/kREA4WDgwNyc3NRXl6O6upqtLS0tGmzevVq/Prrr7h16xYuXbqEEydOwM3NDcD/iheZTIb09HQ8ePAAdXV1GDZsGCwtLbFnzx6UlpYiOzsba9eubTWmtbU1TExMkJWVhXv37uHRo0dtjpubm4vExERcvHgRGo0GqampePDggfbYDg4OuHz5MkpKSlBdXd1uwaFUKlFTU4P33nsPFy9exI0bN/DDDz+gpKSkO54+og6xGCHqgtDQUDx58gSTJ09GVFQUVq1ahcjIyA7by2QyLFmyBH/++WerVREAmD9/PtasWQOlUgkvLy+cPXsW8fHxnR7/gw8+QFhYGEJDQzFz5kw4OTlpPz7yGZVKhdDQUKxbtw6urq4ICgrCH3/8gTFjxuifOBHRABMdHQ1DQ0NMmDABVlZW7d7T0dzcjKioKLi5uWHOnDlwcXHB7t27AQCjR4/Gxo0bERMTg5EjR0KpVMLAwABqtRp5eXnw8PDAmjVr8Pnnn7ca08jICDt37sQ333wDW1tbvPXWW22Oq1AocOrUKQQGBsLFxQVxcXH44osvtPeyREREwNXVFT4+PrCyssKZM2fajGFpaYns7GzU1dVh5syZ8Pb2RkpKCu8hoR4nE+39UwQieiF/f394eXnhq6++kjoUIiIiopcSV0aIiIiIiEgSLEaIiIiIiEgSvEyLiIiIiIgkwZURIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSBIsRIiIiIiKSxP8BxOHxhfBqXNsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the distribution of p-values and t-statistics\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# Plot p-values distribution\n",
    "ax1.set_title(f'Distribution of p-values from {num_tests} t-tests\\n{num_rejections} rejections (p < {alpha})')\n",
    "ax1.hist(p_values, bins=20, density=True, edgecolor='black', color='purple')\n",
    "ax1.axvline(alpha, color='red', label=f'α = {alpha}')\n",
    "ax1.set_xlabel('p-value')\n",
    "ax1.set_ylabel('Frequency')\n",
    "ax1.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "# Plot t-statistics distribution\n",
    "ax2.set_title(f'Distribution of t-statistics from {num_tests} t-tests\\n{num_rejections} beyond critical values')\n",
    "ax2.hist(t_statistics, bins=30, density=True, edgecolor='black', color='teal')\n",
    "ax2.axvline(-t_critical, color='red', label=f'Critical values: ±{t_critical:.3f}')\n",
    "ax2.axvline(t_critical, color='red')\n",
    "ax2.set_xlabel('t-statistic')\n",
    "ax2.set_ylabel('Frequency')\n",
    "ax2.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52eddd7b",
   "metadata": {},
   "source": [
    "**Interpretation**: When conducting a large number of tests, we will falsely reject the null hypothesis approximately 5% of the time, even when it is true."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2b4e9c0",
   "metadata": {},
   "source": [
    "## 4. Multiple testing correction\n",
    "\n",
    "When performing multiple hypothesis tests, the probability of making at least one Type I error increases. The Bonferroni correction adjusts the significance level to control the family-wise error rate.\n",
    "\n",
    "**Bonferroni correction**: Divide the desired α by the number of tests.\n",
    "\n",
    "- Original α = 0.05\n",
    "- Bonferroni-corrected α = 0.05 / number of tests\n",
    "\n",
    "This ensures the overall probability of making any Type I error across all tests remains at approximately 5%.\n",
    "\n",
    "### 4.1. T-test with repeated sampling and Bonferroni correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ddcc7bd7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from 100 independent t-tests:\n",
      "\n",
      "Bonferroni correction (α = 0.000500):\n",
      " - Null hypothesis rejected: 0 times\n",
      " - Null hypothesis accepted: 100 times\n",
      " - Error rate: 0.00%\n",
      "\n",
      "Uncorrected (α = 0.05):\n",
      " - Expected error rate: ~5.0%\n"
     ]
    }
   ],
   "source": [
    "# Repeat sampling and t-test with Bonferroni correction\n",
    "sample_size = 50\n",
    "alpha = 0.05\n",
    "alpha_bonferroni = alpha / num_tests  # Bonferroni correction\n",
    "\n",
    "rejections_bonferroni = []\n",
    "p_values_bonferroni = []\n",
    "t_statistics_bonferroni = []\n",
    "\n",
    "for i in range(num_tests):\n",
    "\n",
    "    # Draw two samples from the same population\n",
    "    sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Perform t-test\n",
    "    t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "    t_statistics_bonferroni.append(t_statistic)\n",
    "    p_values_bonferroni.append(p_value)\n",
    "    \n",
    "    # Check if null hypothesis is rejected using Bonferroni correction\n",
    "    reject = p_value < alpha_bonferroni\n",
    "    rejections_bonferroni.append(reject)\n",
    "\n",
    "# Count results\n",
    "num_rejections_bonf = sum(rejections_bonferroni)\n",
    "num_acceptances_bonf = num_tests - num_rejections_bonf\n",
    "\n",
    "print(f'Results from {num_tests} independent t-tests:')\n",
    "print(f'\\nBonferroni correction (α = {alpha_bonferroni:.6f}):')\n",
    "print(f' - Null hypothesis rejected: {num_rejections_bonf} times')\n",
    "print(f' - Null hypothesis accepted: {num_acceptances_bonf} times')\n",
    "print(f' - Error rate: {num_rejections_bonf/num_tests*100:.2f}%')\n",
    "print(f'\\nUncorrected (α = {alpha}):')\n",
    "print(f' - Expected error rate: ~{alpha*100:.1f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a81ff9",
   "metadata": {},
   "source": [
    "### 4.2. Distribution of p-values and t-statistics with Bonferroni correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5745b400",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/q2snb25uLoYPH65xvEUB64DPqw7IzjMir1+/FgDEokWLMi2n7neemJiodKX5wYMHQi6Xi1mzZknDsrP9R40aJczMzERKSoraeDJrv59x32/YsEEAEEuXLlUqm36HS5NlqqNq36Qfw2XLlhXv3r2ThicnJwsbGxtRuXJlhWew9u/fLwCIadOmScP69u0rAIi5c+dKw16/fi0MDQ2FTCYTv/76qzT8zp07SnWtJjI7f1eqVEk0adJEaXj6Hff033L6vjh16pRS2a5duwo7O7tMY9DmMyKzZ88WxsbGSs83Tpo0Sejq6kp14qccY7/99luW51NNfFa9ZmnCxMQk055T0jP033//HWlpaTlahlwuR//+/TUu7+/vD1NTU+l7ly5dULJkSRw8eDBHy9fUwYMHoauri5EjRyoMHzt2LIQQ+PPPPxWG+/r6Klxxqlq1KszMzPDvv/9muRw7Ozv07NlTGlasWDGpp4m//vorx+vg7e0NLy8v6Xvp0qXRvn17HD58GKmpqWqna9KkCaysrLB9+3Zp2OvXr3H06FF0795dGqarqyvdMUlLS8OrV6+kKyKa9raUlT179iAtLQ3dunVDdHS09LGzs0O5cuVw4sQJAJDueBw+fBjv3r3TyrIBoEyZMvDz81MYdvDgQdSqVQv169eXhpmYmGDIkCF4+PAhbt++rVDe399fof1z7dq1IYTAgAEDFMrVrl0b//33n8oerXIiISEBwIffXEYGBgbS+PSy6sp9PK/cllf728LCAufPn8fTp0+1Gn9hxzrgf4pCHaApQ0ND6Ovr4+TJk3j9+nW2p5fL5dLd1NTUVLx8+RImJiZwc3PLcV1gYWGB+Ph4tb0zZdfu3bthZWWFESNGKI1L76Ja28tM17dvX4W7d5cuXcLz588xbNgw6RwLAK1bt4a7uzsOHDigNI9BgwZJ/7ewsICbmxuMjY3RrVs3abibmxssLCyyPOayQ9O6ITv1TW7buXMnGjRoAEtLS4V6xNfXF6mpqTh16hSAT9vf6efC/fv34/379zmOlYlIBnFxcQon/Iy6d++OevXqYdCgQbC1tUWPHj2wY8eObFVIDg4O2XqIrFy5cgrfZTIZXF1dc727vkePHsHe3l5pe6Tfmnv06JHC8NKlSyvNw9LSMsuT+qNHj1CuXDmlJjHqlpMdGbcdAJQvXx7v3r3DixcvkJycjMjISIVPamoq9PT00LlzZ/z+++9ISkoC8OEPxPfv3yskIgCwefNmVK1aFQYGBihRogSsra1x4MABxMbG5jjuj4WHh0MIgXLlysHa2lrhExoaKj1oXqZMGYwZMwbr16+HlZUV/Pz8sGrVqk+OQ9Xt7UePHsHNzU1puKbHRvof0Y6OjkrD09LStLbt0iu+9H34sYwP3RsaGqot9/G8siM1NVXp+EpOTs50mrza3wsXLsTNmzfh6OiIWrVqYcaMGVqtvAsr1gH/UxTqgIzUnfPlcjkWLFiAP//8E7a2tlIToMjISI3mm5aWhmXLlqFcuXKQy+WwsrKCtbU1rl+/nuPz2bBhw1C+fHm0bNkSpUqVwoABA3Do0KEczQsA7t+/Dzc3t0w7X9D2MtNlrEfS96mqesTd3V1pnxsYGCg1wzM3N0epUqWU3vNjbm6eo2RSHU3rhuzUN9kRFxencLy+ePEiy2nCw8Nx6NAhpTrE19cXwP86qPmU/e3j44POnTtj5syZsLKyQvv27bFx40aV658ZJiIfefz4MWJjY+Hq6qq2jKGhIU6dOoVjx46hT58+uH79Orp3745mzZpleoU94zy0Td0LtzSNSRt0dXVVDhdC5FkM2XX27FmULFlS4fPff/8BAHr06IG3b99KV/127NgBd3d3eHh4SNNv27ZNev/Gjz/+iEOHDuHo0aNo0qRJln+YaLrP0tLSIJPJpHln/Kxdu1Yqu2TJEly/fh3ffPMNEhISMHLkSFSqVAmPHz/O0fYBtHO8qjs2cvuYKVmyJADg2bNnSuOePXsGe3t7hbLqygFQKKup//77T+n4+riHFVXyan9369YN//77L1asWAF7e3ssWrQIlSpVUrrK/TlhHfBpCkMdkNk5f/To0bh79y7mzZsHAwMDTJ06FRUqVMi0bX+6uXPnYsyYMWjYsCG2bduGw4cP4+jRo6hUqVKO75zZ2NggJCQE+/btk57VadmyJfr27Zuj+eXnMj/1mM+vOgTQvG7ITn2THYsXL1Y4XmvWrJnlNGlpaWjWrJnKOuTo0aPo3LkzgE/b3+kvWz137hwCAgLw5MkTDBgwAF5eXhq9NyUdH1b/yNatWwFAqRlKRjo6OmjatCmaNm2KpUuXYu7cuZgyZQpOnDgBX19frb+FNzw8XOG7EAL37t1TeKDY0tJS5YvRHj16hLJly0rfsxObk5MTjh07hrdv3ypcEbtz5440XhucnJxw/fp1pKWlKVwR08ZyMm47ALh79y6MjIxgbW0NuVyudEvSzs4OANCwYUOULFkS27dvR/369XH8+HHpgbB0u3btQtmyZbFnzx6FbTt9+vQsY8tsn33MxcUFQgiUKVMG5cuXz3K+VapUQZUqVfDtt9/i7NmzqFevHoKCgvDdd99lOa2mnJycEBYWpjRc28fGp0rvLODSpUvSg4XAhxdHPX78WHqINb3s33//rXQcnj9/HkZGRllue1W/LTs7O6XjKz2RVfdb1Pb+zuw3X7JkSQwbNgzDhg3D8+fPUb16dcyZMwctW7bMcrlFEesARYW9DlC1rh4eHmrP+cCH39/YsWMxduxYhIeHw9PTE0uWLMG2bdvUzhP4UBc0btwYP/74o8LwmJgYqTOKzKZXR19fH23btkXbtm2RlpaGYcOGYe3atZg6dSpcXV2zNT8XFxecP38e79+/z7Sr4KyWqQ3p+zQsLAxNmjRRGBcWFlZg6hDgQ91w4sQJvHnzRuGB9fPnz0vjAaBy5crQ09PDpUuXFJqLJScnIyQkRGGYKur2pb+/v0Iz6I+Tuszqkbi4OOkOSGY+9RirU6cO6tSpgzlz5uDnn39Gr1698Ouvvyo0pcsM74j8v+PHj2P27NkoU6YMevXqpbbcq1evlIalH4Tpt6OMjY0BQGtvTN6yZYtCm+Vdu3bh2bNnCn8suLi44J9//lFo9rF//37pSk+67MTWqlUrpKamYuXKlQrDly1bBplMprU/Vlq1aoXIyEiF5zFSUlKwYsUKmJiYwMfHJ8fzPnfunEL73P/++w+///47mjdvDl1dXVhaWsLX11fhk97uU0dHB126dMEff/yBrVu3IiUlRalZVvrVmI+vvpw/fx7nzp3LMjYXFxfExsbi+vXr0rBnz57ht99+UyjXqVMn6OrqYubMmUpXeYQQePnyJYAPPXhlfLaiSpUq0NHRyfat0qy0atUKFy5cUFjP+Ph4rFu3Ds7OzgWmn/9KlSrB3d0d69atU7gyvGbNGshkMul9IcCHdvdRUVEKPX5ER0dj586daNu2rcp2vx8zNjZW+l0ZGBgoHV+WlpZSeUD5t6jt/a0qrtTUVKXmIjY2NrC3t9f6sVJYsA5QVtjrAFXHvrpz/rt376SmNulcXFxgamqa5e8J+FAXZPy97ty5E0+ePFGKCdBs+6f/1tPp6OhIyWdOjrXOnTsjOjpaaX8C/6vDNFmmNtSoUQM2NjYICgpSmO+ff/6J0NBQtG7dWmvL+lRdunRBamoq1q1bJw1LSkrCxo0bUbt2bamJsbm5OXx9fbFt2zaF3+vWrVsRFxeHrl27ZrocdfuybNmyCsdrvXr1FKZRte+7deuGc+fO4fDhw0rjYmJipLrjU46x169fKx3zGc+Fmvgs74j8+eefuHPnDlJSUhAVFYXjx4/j6NGjcHJywr59+xQenMpo1qxZOHXqFFq3bg0nJyc8f/4cq1evRqlSpaSM1cXFBRYWFggKCoKpqSmMjY1Ru3btHHclV7x4cdSvXx/9+/dHVFQUAgMD4erqqtC95KBBg7Br1y60aNEC3bp1w/3797Ft2zal7gqzE1vbtm3RuHFjTJkyBQ8fPoSHhweOHDmC33//HaNHj86yK0RNDRkyBGvXrkW/fv1w+fJlODs7Y9euXThz5gwCAwMzba+dlcqVK8PPz0+h+14AmDlzpkbTd+/eHStWrMD06dNRpUoVpW4R27Rpgz179qBjx45o3bo1Hjx4gKCgIFSsWDHLW5M9evTAxIkT0bFjR4wcORLv3r3DmjVrUL58eYXkycXFBd999x0mT56Mhw8fokOHDjA1NcWDBw/w22+/YciQIRg3bhyOHz+OgIAAdO3aFeXLl0dKSgq2bt0KXV1d6TastkyaNAm//PILWrZsiZEjR6J48eLYvHkzHjx4gN27d+f6i6piY2OxYsUKAJC6TV25ciUsLCxgYWGBgIAAqeyiRYvQrl07NG/eHD169MDNmzexcuVKDBo0SGF/dunSBXXq1EH//v1x+/ZtWFlZYfXq1UhNTdXoePHy8sKaNWvw3XffwdXVFTY2NkpX+jKWB4ApU6agR48eKFasGNq2bav1/e3l5YVjx45h6dKlsLe3R5kyZeDm5oZSpUqhS5cu8PDwgImJCY4dO4aLFy9iyZIl2dsZhRDrgM+jDlB17NeuXVtl2bt376Jp06bo1q0bKlasCD09Pfz222+IioqSumtPn6eq33mbNm0wa9Ys9O/fH3Xr1sWNGzfw008/KdyNArK3/QcNGoRXr16hSZMmKFWqFB49eoQVK1bA09NTOnd5enpCV1cXCxYsQGxsLORyOZo0aQIbGxul+fn7+2PLli0YM2YMLly4gAYNGiA+Ph7Hjh3DsGHD0L59e42WqQ3FihXDggUL0L9/f/j4+KBnz55S973Ozs74+uuvtbYsdU6dOiU9tP3ixQvEx8dLd5IbNmyIhg0bAvjQiUrXrl0xefJkPH/+HK6urti8eTMePnyodAdszpw5qFu3Lnx8fDBkyBA8fvwYS5YsQfPmzdGiRYtM48nJeUPd8Th+/Hjs27cPbdq0Qb9+/eDl5YX4+HjcuHEDu3btwsOHD2FlZfVJx9jPP/+M1atXo2PHjnBxccHbt2/xww8/wMzMDK1atdJ8R3xSn1uFTMYXs6S/sKhZs2Zi+fLlCl0EpsvYdWNwcLBo3769sLe3F/r6+sLe3l707NlTqYu033//XVSsWFHo6ekpdMeW/jIrVdR13fjLL7+IyZMnCxsbG2FoaChat24tHj16pDT9kiVLhIODg5DL5aJevXri0qVLKl9opC42Vd3Jvn37Vnz99dfC3t5eFCtWTJQrVy7Tl1llpK5LyYyioqJE//79hZWVldDX1xdVqlRR2YVddrvvTX+hYfrLm6pVq6aym0N10tLShKOjo8ouLNPHz507Vzg5OUnz379/v8ptCRVdCh45ckRUrlxZ6OvrCzc3N7Ft2za1LzTcvXu3qF+/vjA2NhbGxsbC3d1dDB8+XISFhQkhhPj333/FgAEDhIuLizAwMBDFixcXjRs3FseOHctyPTPrvlfd9k5/oaGFhYUwMDAQtWrVUvtCw4xdzKrrRlVdHBk9ePBA5UuWAKjs/ve3334Tnp6eQi6Xi1KlSolvv/1WoTvhdK9evRIDBw4UJUqUEEZGRsLHx0fjrgkjIyNF69athampqdKLpdSZPXu2cHBwEDo6Okpd+Wprf9+5c0c0bNhQGBoaCvz/S92SkpLE+PHjhYeHhzA1NRXGxsbCw8NDrF69WqN1LaxYB2QeW1GrA1Qd++pER0eL4cOHC3d3d2FsbCzMzc1F7dq1xY4dOxTKqfudJyYmirFjx4qSJUsKQ0NDUa9ePXHu3LlP2v67du0SzZs3FzY2NkJfX1+ULl1afPnll+LZs2cK8/vhhx9E2bJlha6urkI3q6qW/e7dOzFlyhRRpkwZUaxYMWFnZye6dOki7t+/n61lqpJZ973quhnfvn27qFatmpDL5aJ48eKZvtAwI3W/JU2PEXUvllVVVyckJIhx48YJOzs7IZfLRc2aNdV26f7333+LunXrCgMDA2FtbS2GDx+u8tyiirpjQ53M6p23b9+KyZMnC1dXV6Gvry+srKxE3bp1xeLFi6X671OOsStXroiePXuK0qVLC7lcLmxsbESbNm0UXpmgCZkQBegpMiItkslkGD58uMrb0ERERESUv/iMCBERERER5TkmIkRERERElOeYiBARERERUZ77LHvNos8DH38iIiIiKrh4R4SIiIiIiPIcExEiIiIiIspzTETokzg7O6Nfv355vtxNmzZBJpPh4cOHeb5sTV24cAH6+vp49OhRfodCWvTy5UsYGxvj4MGD+R0KUYHVqFEjVK5cOb/DyFUzZsyATCbL9eX069cPzs7OGpXN7ZiyE4s2NWrUCI0aNcrz5VLuYyJSyCUlJWHixImwt7eHoaEhateujaNHj+Z3WFozd+5c7N27N7/DyJEpU6agZ8+ecHJyyu9Q1AoNDUWLFi1gYmKC4sWLo0+fPnjx4oXG0+/btw/Vq1eHgYEBSpcujenTpyMlJUWpXExMDIYMGQJra2sYGxujcePGCm+Pz+480xNRVZ/IyMhcjbNEiRIYNGgQpk6dqvF2IiqMinr9Uli9e/cOM2bMwMmTJ/M7FKJPl63XH1KB06NHD6GnpyfGjRsn1q5dK7y9vYWenp74+++/82T5iYmJKt9QrS3GxsYq34abkpIiEhISlN7uW1BcvXpVABBnz57N71DU+u+//4SVlZVwcXERy5cvF3PmzBGWlpbCw8NDJCUlZTn9wYMHhUwmE40bNxbr1q0TI0aMEDo6OmLo0KEK5VJTU0XdunWFsbGxmDFjhli5cqWoWLGiMDU1VXobtabzTH9D9qxZs8TWrVsVPgkJCbke5+3btwUAERwcnOV2IiqsPqV+yewN8kVF+pu5c1tycrJITEyUvr948ULl27+FEOL9+/dK50Btyvj297yi6i3xVDQwESnEzp8/LwCIRYsWScMSEhKEi4uL8Pb2ztE84+PjtRWeVqhLRAq6kSNHitKlS+dLopSQkCDCwsKyLPfVV18JQ0ND8ejRI2nY0aNHBQCxdu3aLKevWLGi8PDwEO/fv5eGTZkyRchkMhEaGioN2759uwAgdu7cKQ17/vy5sLCwED179szRPNMTkYsXL+ZLnEIIUblyZdGnT58sl09UGH1q/cJE5NPFxcWpHJ5ZIpLbmIiQtrFpViG2a9cu6OrqYsiQIdIwAwMDDBw4EOfOncN///2X6fTpbXgvX76Mhg0bwsjICN988w2AD7fkp0+fDldXV8jlcjg6OmLChAlISkpSmIeqZ0RiYmIwevRoODo6Qi6Xw9XVFQsWLEBaWppCubS0NCxfvhxVqlSBgYEBrK2t0aJFC1y6dAkAIJPJEB8fj82bN0vNbtKXpe4ZkdWrV6NSpUqQy+Wwt7fH8OHDERMTo3K9b9++jcaNG8PIyAgODg5YuHCh0jZasWIFKlWqBCMjI1haWqJGjRr4+eefM92uALB37140adJEqa2us7Mz2rRpgyNHjsDT0xMGBgaoWLEi9uzZk+U8s3Lt2jWMGDEC9vb2WL16dZbld+/ejTZt2qB06dLSMF9fX5QvXx47duzIdNrbt2/j9u3bGDJkCPT0/tcL+LBhwyCEwK5du6Rhu3btgq2tLTp16iQNs7a2Rrdu3fD7779Lx1R25vmxt2/fIjU1Nc/iTNesWTP88ccf7CaaiqRPrV/SXb58GXXr1oWhoSHKlCmDoKAgpTKa1Dc+Pj7w8PBQuQw3Nzf4+flJ3+Pj4zF27FipDnJzc8PixYuVfqsymQwBAQHYu3cvKleuDLlcjkqVKuHQoUNKyzh9+jRq1qwJAwMDuLi4YO3atRqtf7rz58+jVatWsLS0hLGxMapWrYrly5dL4/v16wcTExPcv38frVq1gqmpKXr16iWNS38u4+HDh7C2tgYAzJw5U6obZ8yYAUD9MyLbtm1DrVq1pLqsYcOGOHLkiDT+999/R+vWrWFvbw+5XA4XFxfMnj1b7bk1M23atEHZsmVVjvP29kaNGjWk7xs3bkSTJk1gY2MDuVyOihUrYs2aNVkuQ93fACdPnoRMJlNqtnb+/Hm0aNEC5ubmMDIygo+PD86cOaNQ5u3btxg9ejScnZ0hl8thY2ODZs2aqW1GTNrBRKQQu3r1KsqXLw8zMzOF4bVq1QIAhISEZDmPly9fomXLlvD09ERgYCAaN26MtLQ0tGvXDosXL0bbtm2xYsUKdOjQAcuWLUP37t0znd+7d+/g4+ODbdu2wd/fH99//z3q1auHyZMnY8yYMQplBw4cKCUsCxYswKRJk2BgYIB//vkHALB161bI5XI0aNAAW7duxdatW/Hll1+qXfaMGTMwfPhw2NvbY8mSJejcuTPWrl2L5s2b4/379wplX79+jRYtWsDDwwNLliyBu7s7Jk6ciD///FMq88MPP2DkyJGoWLEiAgMDMXPmTHh6euL8+fOZboMnT54gIiIC1atXVzk+PDwc3bt3R8uWLTFv3jzo6emha9euOWp7HRsbizVr1qBGjRrw9PTE5s2b0alTJwwaNCjLGJ8/f65QIaSrVasWrl69mun06eMzTm9vb49SpUopTH/16lVUr14dOjqKp5tatWrh3bt3uHv3brbnma5x48YwMzODkZER2rVrh/Dw8FyPM52XlxdiYmJw69YtpbiICjtt1C+vX79Gq1at4OXlhYULF6JUqVL46quvsGHDBqmMpvVNnz59cP36ddy8eVNhGRcvXsTdu3fRu3dvAB/eH9WuXTssW7YMLVq0wNKlS+Hm5obx48cr1UHAhwRj2LBh6NGjBxYuXIjExER07twZL1++lMrcuHEDzZs3x/PnzzFjxgz0798f06dPx2+//Zb1hgRw9OhRNGzYELdv38aoUaOwZMkSNG7cGPv371col5KSAj8/P9jY2GDx4sXo3Lmz0rysra2lP9Q7duwo1Y0fX0DJaObMmejTpw+KFSuGWbNmYebMmXB0dMTx48elMps2bYKJiQnGjBmD5cuXw8vLC9OmTcOkSZM0WsePde/eHQ8ePMDFixcVhj969Aj//PMPevToIQ1bs2YNnJyc8M0332DJkiVwdHTEsGHDsGrVqmwvV53jx4+jYcOGePPmDaZPn465c+ciJiYGTZo0wYULF6RyQ4cOxZo1a9C5c2esXr0a48aNg6GhIUJDQ7UWC6mQn7dj6NNUqlRJNGnSRGn4rVu3BAARFBSU6fQ+Pj4qy23dulXo6OgotQMOCgoSAMSZM2ekYU5OTgpNp2bPni2MjY2V2tRPmjRJ6OrqioiICCGEEMePHxcAxMiRI5Xi+rg5k7qmWelNcx48eCCE+NCERl9fXzRv3lykpqZK5VauXCkAiA0bNiit95YtW6RhSUlJws7OTnTu3Fka1r59+xw1LTh27JgAIP744w+lcU5OTgKA2L17tzQsNjZWlCxZUlSrVk2j+aelpYmTJ0+KPn36CENDQyGTyYSPj4/YtGmTxk3rLl68qLQN0o0fP14AUGiTnNGiRYsEAGl/fqxmzZqiTp060ndjY2MxYMAApXIHDhwQAMShQ4eyPc/t27eLfv36ic2bN4vffvtNfPvtt8LIyEhYWVkpTJ8bcaY7e/asACC2b9+uNA1RYaet+mXJkiXSsKSkJOHp6SlsbGykZws1rW9iYmKEgYGBmDhxokK5kSNHCmNjY6kZ0969ewUA8d133ymU69Kli5DJZOLevXvSMABCX19fYdi1a9cEALFixQppWIcOHYSBgYFCM9bbt28LXV3dLJtmpaSkiDJlyggnJyfx+vVrhXEf13V9+/YVAMSkSZOU5pGxOVRmTbMyNhcLDw8XOjo6omPHjgp1Y8blv3v3TmleX375pTAyMlKoCzRpmhUbGyvkcrkYO3aswvCFCxcKmUymsB1VLdfPz0+ULVtWYVjGplkZ/wZId+LECQFAnDhxQlrHcuXKCT8/P6X1LVOmjGjWrJk0zNzcXAwfPjzTdSPt4x2RQiwhIQFyuVxpuIGBgTQ+K3K5HP3791cYtnPnTlSoUAHu7u6Ijo6WPk2aNAEAnDhxQu38du7ciQYNGsDS0lJhWl9fX6SmpuLUqVMAPjQLkslkmD59utI8ctL14LFjx5CcnIzRo0crXNEePHgwzMzMcODAAYXyJiYm0hU0ANDX10etWrXw77//SsMsLCzw+PFjpas6WUm/kmZpaalyvL29PTp27Ch9NzMzg7+/P65evaqyx6ePLV++HOXLl0ejRo1w8uRJjB07FuHh4Th58iT69u0LIyMjjWJMPzZyevxkNf3H02p6nGZnnt26dcPGjRvh7++PDh06YPbs2Th8+DBevnyJOXPm5Gqc6dL3b3R0tNI0RIWdNuoXPT09hbvY+vr6+PLLL/H8+XNcvnwZgOb1jbm5Odq3b49ffvlFamKVmpqK7du3o0OHDjA2NgYAHDx4ELq6uhg5cqRCLGPHjoUQQuGuN/ChOaqLi4v0vWrVqjAzM5PqgtTUVBw+fBgdOnRQaMZaoUIFheZg6ly9ehUPHjzA6NGjYWFhoTBOVV331VdfZTnP7Ni7dy/S0tIwbdo0pbu9Hy/f0NBQ+v/bt28RHR2NBg0a4N27d7hz5062lmlmZoaWLVtix44dCs3htm/fjjp16ihsx4+XGxsbi+joaPj4+ODff/9FbGxstparSkhICMLDw/HFF1/g5cuX0vEVHx+Ppk2b4tSpU1KzcQsLC5w/fx5Pnz795OWS5vSyLkIFlaGhoVK7dQBITEyUxmfFwcEB+vr6CsPCw8MRGhoqtUPN6Pnz52rnFx4ejuvXr2c57f3792Fvb4/ixYtnGaMm0t/V4ebmpjBcX18fZcuWVXqXR6lSpZQqAUtLS1y/fl36PnHiRBw7dgy1atWCq6srmjdvji+++AL16tXTKCah5tkBV1dXpWWXL18ewIf2v3Z2dmrnuWzZMjx69AjNmjXDxo0b4eDgoFEsGaUfGzk9frKa/uNpNT1OszNPVerXr4/atWvj2LFjuRpnuvT9mxfvESDKa9qoX+zt7aUEId3H57o6depkq77x9/fH9u3b8ffff6Nhw4Y4duwYoqKi0KdPH6nMo0ePYG9vD1NTU4X5VKhQQRr/sY//KE5naWmJ169fAwBevHiBhIQElCtXTqmcm5tblu8Tun//PgBo9E4VPT09lCpVKsty2XH//n3o6OigYsWKmZa7desWvv32Wxw/fhxv3rxRGJeThKB79+7Yu3cvzp07h7p16+L+/fu4fPkyAgMDFcqdOXMG06dPx7lz5/Du3Tul5Zqbm2d72R9Lb67bt29ftWViY2NhaWmJhQsXom/fvnB0dISXlxdatWoFf39/tc+7kHYwESnESpYsiSdPnigNf/bsGYAPlUBWVFUmaWlpqFKlCpYuXapyGkdHR7XzS0tLQ7NmzTBhwgSV49Mrofymq6urcvjHyUOFChUQFhaG/fv349ChQ9i9ezdWr16NadOmYebMmWrnXaJECQCQKjJt2rBhA9auXYu9e/fCyckJLVu2RP/+/dGmTRulhDIzJUuWBPC/Y+Vjz549Q/HixVVeDVU1fcbj4dmzZ1I78vSy6pYD/O84zc481XF0dERYWFiuxpkuff9aWVllGRdRYaON+kUT2alv/Pz8YGtri23btqFhw4bYtm0b7Ozs4Ovrm+Pla1IX5BW5XK501yIvxMTEwMfHB2ZmZpg1axZcXFxgYGCAK1euYOLEiUodzWiibdu2MDIywo4dO1C3bl3s2LEDOjo66Nq1q1Tm/v37aNq0Kdzd3bF06VI4OjpCX18fBw8exLJlyzJdrroLQBkfrk+fx6JFi+Dp6alyGhMTEwAf7rQ3aNAAv/32G44cOYJFixZhwYIF2LNnD1q2bJmd1adsYCJSiHl6euLEiRN48+aNwgOF6Q9Tq/vRZcXFxQXXrl1D06ZNs32118XFBXFxcVlWDC4uLjh8+DBevXqV6V0RTZef/tLAsLAwhasXycnJePDgQY4rKmNjY3Tv3h3du3dHcnIyOnXqhDlz5mDy5MlSE4WM3N3dAQAPHjxQOf7evXsQQiisW/qD0Fm9sbZJkyZo0qQJXr58iS1btuDHH39E586dYWVlhV69eqF///5qe5b5mIODA6ytraUeyj524cKFLI+d9PGXLl1S+GP+6dOnePz4sUJPO56envj777+RlpamUMmeP38eRkZGUnKanXmq8++//ypcWc2NONOl79/0K61ERYk26penT58iPj5e4a5IxnNdduobXV1dfPHFF9i0aRMWLFiAvXv3YvDgwQrJhJOTE44dO4a3b98q3BVJb16U3RfMWltbw9DQUKkjDAAKFz3USW/2dfPmzU9KmD6WnXrZxcUFaWlpuH37ttp9dvLkSbx8+RJ79uxBw4YNpeHq6jBNGBsbo02bNti5cyeWLl2K7du3o0GDBgoJ7B9//IGkpCTs27dP4c5UZs2/06U3jc3YK2bGO17p29/MzEyj7V+yZEkMGzYMw4YNw/Pnz1G9enXMmTOHiUgu4jMihViXLl2QmpqKdevWScOSkpKwceNG1K5dO9M7F5np1q0bnjx5gh9++EFpXEJCAuLj4zOd9ty5czh8+LDSuJiYGOlt1p07d4YQQuWdhY+vRBkbGyudaFTx9fWFvr4+vv/+e4Xpf/zxR8TGxqJ169ZZziOjj3tNAT4086pYsSKEEEq9cH3MwcEBjo6OKv/IBz5Uzh/3tvLmzRts2bIFnp6emTbL+liJEiXw9ddf4+bNmzh37hzat2+PH3/8EZ6enqhevbpSO2hVOnfujP379yt0wxkcHIy7d+8qXLV6//497ty5o3C3oFKlSnB3d8e6desUrkCtWbMGMpkMXbp0kYZ16dIFUVFRCl0UR0dHY+fOnWjbtq105yU781T19veDBw/i8uXLaNGiRa7Gme7y5cswNzdHpUqVlGIhKuy0Ub+kpKQodHObnJyMtWvXwtraGl5eXgCyX9/06dMHr1+/xpdffom4uDiFZ/0AoFWrVkhNTcXKlSsVhi9btgwymSzbf1Dq6urCz88Pe/fuRUREhDQ8NDRUZT2XUfXq1VGmTBkEBgYq1WU5veuS/iygJnVjhw4doKOjg1mzZindYUhffnoi93E8ycnJGnUDn5nu3bvj6dOnWL9+Pa5du6bU66aq5cbGxmLjxo1Zzjs9wUh/7hSA0vEKfOjd0MXFBYsXL0ZcXJzSfNLrktTUVKUmaDY2NrC3t1fZRJG0KO+fjydt6tq1q9DT0xPjx48Xa9euFXXr1hV6enrir7/+ynJadS+cSk1NFa1atRIymUz06NFDrFixQgQGBoqhQ4eK4sWLK7xELmOvWfHx8aJ69epCT09PDBo0SKxZs0YsXrxY9O3bVxgbG4sXL15IZfv06SMAiJYtW4rly5eLZcuWiU6dOin0VtKqVSthbGwslixZIn755Rfxzz//CCFU95iR3ltI8+bNxcqVK8WIESOErq6uqFmzpsLb39Wtd8beQKpXry5atWol5syZI9avXy/Gjh0r5HK5aNu2bZbbNiAgQDg4OCi90NDJyUmUL19eWFhYiEmTJolly5aJKlWqCB0dHaVembLr7du3Yv369aJOnTpi9OjRWZaPiIgQJUqUEC4uLuL7778Xc+fOFZaWlqJKlSoKvaQ8ePBAAFDqveyPP/4QMplMNGnSRKxbt06MHDlS6OjoiMGDByuUS0lJEXXq1BEmJiZi5syZYtWqVaJSpUrC1NRU3LlzJ0fzdHV1FV27dhULFiwQQUFBYsiQIUJPT084OjqKyMjIXI9TiA8vNOzdu3eW25mosPrU+sXe3l7Y2NiIESNGiBUrVoj69esLAGLdunVSuezUN+kqV64sAIgKFSoojUtNTRWNGzcWMplMDBkyRKxatUq0b99eAFA6LwJQ2UtSxnrt2rVrwsDAQJQuXVrMnz9ffPfdd8LW1lZUrVpVoxcaHjp0SBQrVkw4OTmJGTNmiLVr14qvv/5aNG/eXCqTXkeqoqqnqooVKwo7OzuxatUq8csvv4gbN24IIVS/ZHHq1KkCgKhbt65YvHixWLFihfD395d66IqOjhaWlpbCyclJLFmyRCxdulRUq1ZNeHh4KPRApS4WdRISEoSpqakwNTUVurq6IioqSmH8nTt3hL6+vqhSpYpYuXKlmD9/vnBxcZGW+3H9ruqFhnXq1BFGRkZi+vTpYvny5cLb21t4eXkpxXzixAlp/02fPl2sW7dOTJ8+XTRs2FC0adNGCCHE69evpV46ly5dKtatWye6deum1PMbaR8TkUIuISFBjBs3TtjZ2Qm5XC5q1qyp8R+0mb35Njk5WSxYsEBUqlRJyOVyYWlpKby8vMTMmTNFbGysVC7jCVuID38QT548Wbi6ugp9fX1hZWUlnQA/TghSUlLEokWLhLu7u9DX1xfW1taiZcuW4vLly1KZO3fuiIYNGwpDQ0OFP4bVdd23cuVK4e7uLooVKyZsbW3FV199pdRloqaJyNq1a0XDhg1FiRIlhFwuFy4uLmL8+PEK66/OlStXBAClLimdnJxE69atxeHDh0XVqlWFXC4X7u7uCm/z1gZ1b+TN6ObNm6J58+bCyMhIWFhYiF69ein9Ia8uERFCiN9++014enoKuVwuSpUqJb799luFfZzu1atXYuDAgaJEiRLCyMhI+Pj4qH0ruibznDJlivD09BTm5uaiWLFionTp0uKrr75Sij234gwNDRUAxLFjx1Quj6go0Eb9cunSJeHt7S0MDAyEk5OTWLlypVJZTeubdAsXLhQAxNy5c1Uu++3bt+Lrr78W9vb2olixYqJcuXJi0aJFSheGNE1EhBDir7/+El5eXkJfX1+ULVtWBAUFZevN6qdPnxbNmjUTpqamwtjYWFStWlXholt2E5GzZ89K8eCjrnzVxbRhwwZRrVo1afv6+PiIo0ePSuPPnDkj6tSpIwwNDYW9vb2YMGGCOHz48CclIkII0atXLwFA+Pr6qhy/b98+UbVqVWFgYCCcnZ3FggULxIYNGzRKRO7fvy98fX2FXC4Xtra24ptvvhFHjx5VilkIIa5evSo6deok1edOTk6iW7duIjg4WAjxoWvp8ePHCw8PD2kfeXh4iNWrV2u8rpQzMiH4WmDKOUdHR/j5+WH9+vX5HUqB07RpU9jb22Pr1q3SMGdnZ1SuXFnpRVZUuIwePRqnTp3C5cuX2WsWUR5bvnw5vv76azx8+FBlr1dEVHjwGRHKsffv3+Ply5fsNUiNuXPnYvv27UoPz1Hh9vLlS6xfvx7fffcdkxCiPCaEwI8//ggfHx8mIURFAHvNohw5fPgwfv31VyQkJKBp06b5HU6BVLt2bSQnJ+d3GKRlJUqUUPnQIxHlnvj4eOzbtw8nTpzAjRs38Pvvv+d3SESkBUxEKEfmz5+Pe/fuYc6cOWjWrFl+h0NEREXYixcv8MUXX8DCwgLffPMN2rVrl98hEZEW8BkRIiIiIiLKc3xGhIiIiIiI8hwTESIiIiIiynOf3TMiaWlpePr0KUxNTdnjDRERPvRE9PbtW9jb20NHh9enWE8QEf1PbtYRn10i8vTpUzg6OuZ3GEREBc5///2HUqVK5XcY+Y71BBGRstyoIz67RMTU1BTAh41pZmam+YTx8YC9/Yf/P30KGBtrPm1KPLDn/6ft9BTQy8a0RES57M2bN3B0dJTOj5+7HNUTn1JHFGWs/6iw4LGq7P/Pa28AOAK5Ukd8dolI+m12MzOz7CUiurr/+7+ZWTYTEV3A6KNpeXATUQHEZkgf5Kie+JQ6oihj/UeFBY9VZR+f15A7dQQbAxMRERERUZ5jIkJERERERHmOiQgREREREeW5z+4ZEfp8JCUlISwsDCkpKfkdClG+0dXVhZOTEywsLPI7FCpiYmJi8OjRI6SmpqovlJIAPPj//18JAfQM8yI0ouz7TI/V/K4jmIhQkXT//n14enoiLi4uv0MhKhAGDx6MoKAgvieEPllaWhqGDh2KH374IXsTfls/dwIi0rbP8FjNrzqCiQgVOWlpaRg4cCCsrKzw559/wsjIKOuJiIqo5ORknDp1CpMmTQIArFu3Lp8josJu6NChWL9+PRYsWICGDRtCX18/v0MiohzK7zqCiQgVOc+ePcNff/2Fn3/+GfXrf35XNYgyqlOnDgBg4sSJWLhwIZtpUY69fv0aP/zwAxYsWIAJEybkdzhEpAX5WUfwHj0VOS9evAAAuLi45HMkRAVHw4YNAQCPHj3K50ioMIuIiADwv+OJiIqG/KojmIhQkZOWlgYA0NPjDT+idOnNZzJ9sJgoC+nHD5tjERUt+VVHMBEhIiIiIqI8x0QkB0JCQnDlyhWNPyEhIfkdMpFW7N27F66urtDV1cXo0aPzOxwiolx38uRJyGQyxMTEZFrO2dkZgYGBWltuo0aNCtR5dsaMGbC1tYVMJsPevXvzOxwqIpiI5EC9+vXh5eWl8afeRw9M//fff/kYORU1Dx8+hEwmkz76+vpwdXXFd999ByGE1pf35ZdfokuXLvjvv/8we/Zsrc8fABITEzF8+HCUKFECJiYm6Ny5M6KiojKdRgiBadOmoWTJkjA0NISvry/Cw8MVyrx69Qq9evWCmZkZLCwsMHDgQKXuna9fv44GDRrAwMAAjo6OWLhwocL4TZs2KWxvmUwGAwODXImFiLQrMjISI0aMQNmyZSGXy+Ho6Ii2bdsiODg40+nq1q2LZ8+ewdzcHMCH84Cqh3kvXryIIUOG5EboKmU8H5mYmMDLywt79uzR+rJCQ0Mxc+ZMrF27Fs+ePUPLli21vozTp0+jXr16KFGiBAwNDeHu7o5ly5ZlOZ0QAosXL0b58uUhl8vh4OCAOXPmKJQ5efIkqlevDrlcDldXV2zatElh/KlTp9C2bVvY29sz0cpjbESfA+3RDqaw07i8Pt4D2AgAePnyJRzL5FJg9Nk6duwYKlWqhKSkJJw+fRqDBg1CyZIlMXDgQK0tIy4uDs+fP4efnx/s7e21Nt+Mvv76axw4cAA7d+6Eubk5AgIC0KlTJ5w5c0btNAsXLsT333+PzZs3o0yZMpg6dSr8/Pxw+/ZtKVHo1asXnj17hqNHj+L9+/fo378/hgwZgp9//hkA8ObNGzRv3hy+vr4ICgrCjRs3MGDAAFhYWCj8cWFmZoawsDDpu0wm03osRKRdDx8+RL169WBhYYFFixahSpUqeP/+PQ4fPozhw4fjzp07Kqd7//499PX1YWeXdZ1vbW2t7bCz9PH56O3bt9i4cSO6deuGW7duwc3NTWvLuX//PgCgffv2Suc8TT18+BBlypRRe5HM2NgYAQEBqFq1KoyNjXH69Gl8+eWXMDY2zjTBGzVqFI4cOYLFixejSpUqePXqFV69eiWNf/DgAVq3bo2hQ4fip59+QnBwsFRH+vn5AQDi4+Ph4eGBAQMGoFOnTjlaP8oh8ZmJjY0VAERsbGz2JoyLEwIQAhAB6C9mYIbGnznyb4T4CUL8BHH14uncWTGSXL58WQAQly9fzu9QsuXt27eiX79+wsTERNjY2IiFCxeKx48fC0NDQ/H27VuV0zx48EAAEFevXlUY3rRpUzFs2DDpe2pqqpg5c6ZwcHAQ+vr6wsPDQ/z5559K89m9e7do1KiRMDQ0FFWrVhVnz54VQghx4sQJAUDhc+LECa1vg5iYGFGsWDGxc+dOaVhoaKgAIM6dO6dymrS0NGFnZycWLVqkMB+5XC5++eUXIYQQt2/fFgDExYsXpTJ//vmnkMlk4smTJ0IIIVavXi0sLS1FUlKSVGbixInCzc1N+r5x40Zhbm6uNn5txZIbMvtd5Pi8WETlaHt8VEeIuLjcCy6fFdbza8uWLYWDg4OIU7FvXr9+Lf0fgFi9erVo27atMDIyEtOnT5fOf69fv1Z5Lpw+fboQQggnJyexbNkyhfkOGTJE2NjYCLlcLipVqiT++OMPIYQQ0dHRokePHsLe3l4YGhqKypUri59//lkhLh8fHzFq1Ci166TqfJSamiqKFSsmduzYIQ179eqV6NOnj7CwsBCGhoaiRYsW4u7du0rzOXTokHB3dxfGxsbCz89PPH36VAghxPTp05XWOSfS65ns6Nixo+jdu7fa8bdv3xZ6enrizp07astMmDBBVKpUSWFY9+7dhZ+fn8ryAMRvv/2WrTiLApW/7f8/r8X+/37PjTqCTbOo6BMCiI/Pn082mkf169cPZ8+excmTJ7Fx40ZMnToV33zzDXx9fWFiYqLxfC5duoTLly+jdu3a0rDly5djyZIlWLx4Ma5fvw4/Pz+0a9dOqcnQlClTMG7cOISEhKB8+fLo2bMnUlJSULduXemq2+7du/Hs2TPUrVtX5fJbtmwJExMTtZ9KlSqpjf3y5ct4//49fH19pWHu7u4oXbo0zp07p3KaBw8eIDIyUmEac3Nz1K5dW5rm3LlzsLCwQI0aNaQyvr6+0NHRwfnz56UyGV/O5ufnh7CwMLx+/VoaFhcXBycnJzg6OqJ9+/a4deuW1mMhKjQKwfn11atXOHToEIYPHw5jY2Ol8RmbWc2YMQMdO3aU7op+rG7duggMDISZmRmePXuGZ8+eYdy4cUrzTEtLQ8uWLXHmzBls27YNt2/fxvz586GrqwvgQxNULy8vHDhwADdv3sSQIUPQp08fXLhwQcMNryw1NRWbN28GAFSvXl0a3q9fP1y6dAn79u3DuXPnIIRAq1at8P79e6nMu3fvsHjxYmzduhWnTp1CRESEtF7jxo3Dxo0fWnWkrzPw4RmWfv365TjerFy9ehVnz56Fj4+P2jJ//PEHypYti/3796NMmTJwdnbGoEGDFO6InDt3TuGcDHw4t6urUyhvsWkWFX3v3gHZ+ENeq+LiABUVX0bR0dHYs2cPfvrpJ3h5eQEAOnbsiC1btuDHH3/Mcvq6detCR0cHycnJeP/+PYYMGQJ/f39p/OLFizFx4kT06NEDALBgwQKcOHECgYGBWLVqlVRu3LhxaN26NQBg5syZqFSpEu7duwd3d3fY2NgAAIoXL55pM4X169cjISFB7fhixYqpHRcZGQl9fX2lPwxsbW0RGRmpdpr0MuqmiYyMlOJPp6enh+LFiyuUKVOmjNI80sdZWlrCzc0NGzZsQNWqVREbG4vFixejbt26uHXrFkqVKqW1WIgKjUJwfr137x6EEHB3d9dotl988QX69+8vff/333+l/+vr68Pc3BwymSzT8+CxY8dw4cIFhIaGonz58gCAsmXLSuMdHBwUEpgRI0bg8OHD2LFjB2rVqqVRnAAQGxsrXahKSEhAsWLFsG7dOuk9WuHh4di3bx/OnDkjXTz66aef4OjoiL1796Jr164APjRBCwoKkqYLCAjArFmzAAAmJibSOfnjdS5dujRKliyZaXyVKlWS3ksh/j9x/PjCWoMGDfDnn38qTFOqVCm8ePECKSkpmDFjBgYNGqR2/v/++y8ePXqEnTt3YsuWLUhNTcXXX3+NLl264Pjx4wA+nHNVnZPfvHmDhIQEGBoaZroOlLuYiBAVAOkVpbe3tzSsVq1a2LlzJ9q1a5fl9Nu3b0eFChXw/v173Lx5EyNGjIClpSXmz5+PN2/e4OnTp6hXr57CNPXq1cO1a9cUhlWtWlX6f3oF8/z5c40rcOBDBVtUeXt7K+yjunXrokKFCli7dm2uPbxPRJ9GZLPjjo/vVuZUSEgISpUqJSUhGaWmpmLu3LnYsWMHnjx5guTkZCQlJcHIyChbyzE1NcWVK1cAfLircezYMQwdOhQlSpRA27ZtERoaCj09PYU75CVKlICbmxtCQ0OlYUZGRgovAS5ZsiSeP3+e6bK3bNmSZXwHDx6U7rw8efIEjRo1UuhJVFUS8PfffyMuLg7//PMPJk2aBFdXV/Ts2VPl/NPS0pCUlIQtW7ZI2/rHH3+El5cXwsLCtPqcDOUOJiJU9BkZfbhyll/L1oBcLgeg+JIwa2trlC9fHlZWVllO7+joCFdXVwBAhQoVcP/+fUydOhUzZszIVrgf361IfyAx/QWRmmrZsiX+/vtvteOdnJwUmjN9zM7ODsnJyYiJiVG4KxIVFaX26mP68KioKIWrc1FRUfD09JTKZKxUU1JS8OrVK2l6Ozs7pd650r+rW3axYsVQrVo13Lt3T6uxEBUaheD8Wq5cOchkMrUPpGekqvlWdmV1lX3RokVYvnw5AgMDUaVKFRgbG2P06NFITk7O1nJ0dHSkcz/w4WLSkSNHsGDBArRt21bj+WS8Uy2TybTS86KTk5P0//SXDH8cryrpd6arVKmCqKgozJgxQ20iUrJkSejp6SkkfBUqVAAAREREwM3NTe253czMjHdDCgAmIlT0yWQa3b7PT2XKlIGOjg7Cw8OlHqn27duHiIgICCGy3UuJrq4uUlJSkJycDDMzM9jb2+PMmTMKbW3PnDmTrSYAmvqUplleXl4oVqwYgoOD0blzZwBAWFgYIiIiFO5EfKxMmTKws7NDcHCw9Mf+mzdvcP78eXz11VcAPtzJiImJweXLl6Wmb8ePH0daWpp0pdDb2xtTpkzB+/fvpRiPHj0KNzc3WFpaqlx2amoqbty4gVatWmk1FqJCoxCcX4sXLw4/Pz+sWrUKI0eOVEo0Ml74yIq+vn6Wb5+uWrUqHj9+jLt376q8K3LmzBm0b98evXv3BvDhgs/du3dRsWJFjeNQR1dXVzoHV6hQASkpKTh//rzUNOvly5cICwvTyrJyW/odD3Xq1auHlJQU3L9/X7qjc/fuXQD/S4K8vb1x8OBBhemOHj2qtk6hvMVEhKgAsLCwQKdOnTBnzhzUqlULd+/exaFDh2BoaIjjx4+jadOmmU7/8uVLREZGIiUlBTdu3MDy5cvRuHFjmJmZAQDGjx+P6dOnw8XFBZ6enti4cSNCQkLw008/aX1dPqVplrm5OQYOHIgxY8agePHiMDMzw4gRI+Dt7Y06depI5dzd3TFv3jx07NgRMpkMo0ePxnfffYdy5cpJXeba29ujQ4cOAD5Uxi1atMDgwYMRFBSE9+/fIyAgAD169JASvy+++AIzZ87EwIEDMXHiRNy8eRPLly9X6Md+1qxZqFOnDlxdXRETE4NFixbh0aNHUhtmbcVCRNq1atUq1KtXD7Vq1cKsWbNQtWpVpKSk4OjRo1izZo1CM6WsODs7Iy4uDsHBwfDw8ICRkZFSkyofHx80bNgQnTt3xtKlS+Hq6oo7d+5AJpOhRYsWKFeuHHbt2oWzZ8/C0tISS5cuRVRUVLaTAyGE9GxZQkICjh49isOHD2PatGkAPtwNat++PQYPHoy1a9fC1NQUkyZNgoODA9q3b5+tZWXk7+8PBwcHzJs3T22ZFy9eSEmbgYEBnj17pvAsnL6+PooXLw7gwz4qXbq01BT41KlTWLx4MUaOHCmVX7lyJX777Tfp3S++vr6oXr06BgwYgMDAQKSlpWH48OFo1qyZlAAOHToUK1euxIQJEzBgwAAcP34cO3bswIEDB6T5xsXFSXe2gQ8dj4SEhKB48eIoXbr0J20nyhwTEaICYtWqVRg0aBAcHBygq6uLwMBAyOVy9OrVC3PmzMn0nSDpPYLo6uqiZMmSaNWqlcILnUaOHInY2FiMHTsWz58/R8WKFbFv3z6UK1cu19cru5YtWwYdHR107twZSUlJ8PPzw+rVqxXKhIWFITY2Vvo+YcIExMfHY8iQIYiJiUH9+vVx6NAhhZcN/vTTTwgICEDTpk2l+X///ffSeHNzcxw5cgTDhw+Hl5cXrKysMG3aNIX+61+/fo3BgwdLD697eXnh7NmzCn88aCMWItKusmXL4sqVK5gzZw7Gjh2LZ8+ewdraGl5eXlizZk225lW3bl0MHToU3bt3x8uXLzF9+nSVzWB3796NcePGoWfPnoiPj4erqyvmz58PAPj222/x77//ws/PD0ZGRhgyZAg6dOigcF7TxJs3b6RmoHK5HE5OTpg1axYmTpwoldm4cSNGjRqFNm3aIDk5GQ0bNsTBgwczvTutiYiICOjoZN75as2aNaWH1VXx8fHByZMnAXy4+zF58mQ8ePAAenp6cHFxwYIFC/Dll19K5aOjo6V3mgAfmqb98ccfGDFiBBo2bAhjY2O0bNkSS5YskcqUKVMGBw4cwNdff43ly5ejVKlSWL9+vfQOEeBDb5ONGzeWvo8ZMwYA0LdvX6WXH5J2yYQ2GgEWIm/evIG5uTliY2Olq8UaiY+XegYZgf6wglMWE/xPMXkyvtkwFwAQUv40PGvUy2IK+hRXrlyBl5cXLl++rNCFIdHnLLPfRY7Pi0VUjrbHR3WEpr05FUY8vxIVTSp/2/9/XnsDwBzIlTqC7xEhIiIiIqI8x0SEiIiIiIjyHBMRIiIiIiLKc0xEiIiIiIgozzERISIiIiKiPMdEhIiIiIiI8hwTESIiIiIiynNMRIiIiIiIKM8xESEiIiIiojzHRISIPlszZsyAp6dnfodBRAXYyZMnIZPJEBMTk2k5Z2dnBAYGam25jRo1wujRo7U2P1LE7VswMBEhokKlsCUPERERaN26NYyMjGBjY4Px48cjJSUl02levXqFXr16wczMDBYWFhg4cCDi4uKk8Q8fPoRMJlP6/PPPP7m9OkSFVmRkJEaMGIGyZctCLpfD0dERbdu2RXBwcKbT1a1bF8+ePYO5uTkAYNOmTbCwsFAqd/HiRQwZMiQ3Qqf/V9iSh5EjR8LLywtyuVzjeuv+/fvo2LEjrK2tYWZmhm7duiEqKkqhzN27d9G+fXtYWVnBzMwM9evXx4kTJ1TO7+XLlyhVqpRGyXR+YCJCRFqXnJyscvj79+/zOJL8lZqaitatWyM5ORlnz57F5s2bsWnTJkybNi3T6Xr16oVbt27h6NGj2L9/P06dOqXyD5xjx47h2bNn0sfLyyu3VoWoUHv48CG8vLxw/PhxLFq0CDdu3MChQ4fQuHFjDB8+XO1079+/h76+Puzs7CCTyTJdhrW1NYyMjLQdeqGj6vyfmpqKtLS0fIgmdzk7O+PkyZOZlhkwYAC6d++u0fzi4+PRvHlzyGQyHD9+HGfOnEFycjLatm2rsP3atGmDlJQUHD9+HJcvX4aHhwfatGmDyMhIpXkOHDgQVatWzdZ65aV8TUTmzZuHmjVrwtTUFDY2NujQoQPCwsKynG7nzp1wd3eHgYEBqlSpgoMHD+ZBtES5Ky4uDv3794epqSlsbW2xaNEiPHnyBEZGRgpXwz+m6src3r17FSrM9DsIW7duhbOzM8zNzdGjRw+8fftWKpOWloaFCxfC1dUVcrkcpUuXxpw5c6TxN27cQJMmTWBoaIgSJUpgyJAhCjH169cPHTp0wJw5c2Bvbw83Nzfpqv327dvh4+MDAwMD/PTTTwCA9evXo0KFCjAwMIC7uztWr16tsA6PHz9Gz549Ubx4cRgbG6NGjRo4f/48Nm3ahJkzZ+LatWvSXYBNmzYBAGJiYjBo0CDpKlKTJk1w7do1hfnOnz8ftra2MDU1xcCBA5GYmKj5DsqBI0eO4Pbt29i2bRs8PT3RsmVLzJ49G6tWrVKbrIWGhuLQoUNYv349ateujfr162PFihX49ddf8fTpU4WyJUqUgJ2dnfQpVqxYrq4PUWE1bNgwyGQyXLhwAZ07d0b58uVRqVIljBkzRuFOokwmw5o1a9CuXTsYGxtjzpw5Ck2zTp48if79+yM2NlY6B82YMQOActOsmJgYfPnll7C1tYWBgQEqV66M/fv3A/hwlbpnz55wcHCAkZERqlSpgl9++SVb65R+3v3Y6NGj0ahRI+l7o0aNMHLkSEyYMAHFixeHnZ2dFK8mcQLA7t27UalSJcjlcjg7O2PJkiUK0zs7O2P27Nnw9/eHmZkZhgwZItVN+/btQ8WKFSGXyxEREYGkpCSMGzcODg4OMDY2Ru3atZX+kD9z5gwaNWoEIyMjWFpaws/PD69fv0a/fv3w119/Yfny5dK2f/jwIQDg5s2baNmyJUxMTGBra4s+ffogOjpammd8fDz8/f1hYmKCkiVLKq1Dbvn+++8xfPhwlC1bVqPyZ86cwcOHD7Fp0yZUqVIFVapUwebNm3Hp0iUcP34cABAdHY3w8HBMmjQJVatWRbly5TB//ny8e/cON2/eVJjfmjVrEBMTg3Hjxml93bQlXxORv/76C8OHD8c///yDo0eP4v3792jevDni4+PVTnP27Fn07NkTAwcOxNWrV9GhQwd06NBBaeMTSYQAUuLz5yOExmH269cPZ8+excmTJ7Fx40ZMnToV33zzDXx9fWFiYvJJm+D+/fvYu3cv9u/fj/379+Ovv/7C/PnzpfGTJ0/G/PnzMXXqVNy+fRs///wzbG1tAXw4gfv5+cHS0hIXL17Ezp07cezYMQQEBCgsIzg4GGFhYdJV/HSTJk3CqFGjEBoaCj8/P/z000+YNm0a5syZg9DQUMydOxdTp07F5s2bAXxIyHx8fPDkyRPs27cP165dw4QJE5CWlobu3btj7NixqFSpknQXIP1KU9euXfH8+XP8+eefuHz5MqpXr46mTZvi1atXAIAdO3ZgxowZmDt3Li5duoSSJUsqJUCqmJiYZPoZOnSo2mnPnTuHKlWqSNsSAPz8/PDmzRvcunVL7TQWFhaoUaOGNMzX1xc6Ojo4f/68Qtl27drBxsYG9evXx759+7JcFyKtKwTn11evXuHQoUMYPnw4jI2NlcZnvJgzY8YMdOzYETdu3MCAAQMUxtWtWxeBgYEwMzOTzkGq/shLS0tDy5YtcebMGWzbtg23b9/G/PnzoaurCwBITEyEl5cXDhw4gJs3b2LIkCHo06cPLly4oOGG19zmzZthbGyM8+fPY+HChZg1axaOHj2qUZyXL19Gt27d0KNHD9y4cQMzZszA1KlTpQtA6RYvXgwPDw9cvXoVU6dOBQC8e/cOCxYswPr163Hr1i3Y2NggICAA586dw6+//orr16+ja9euaNGiBcLDwwEAISEhaNq0KSpWrIhz587h9OnTaNu2LVJTU7F8+XJ4e3tj8ODB0rZ3dHRETEwMmjRpgmrVquHSpUs4dOgQoqKi0K1bNym+8ePH46+//sLvv/+OI0eO4OTJk7hy5YrCOsyYMQPOzs5a3/7ZkZSUBJlMBrlcLg0zMDCAjo4OTp8+DeDDBSg3Nzds2bIF8fHxSElJwdq1a2FjY6NwV/z27duYNWsWtmzZAh2dgtsASi8/F37o0CGF75s2bYKNjQ0uX76Mhg0bqpxm+fLlaNGiBcaPHw8AmD17No4ePYqVK1ciKCgo12OmQij1HbDj0/6Qz7FucYCecsWXUXR0NPbs2YOffvpJOpF07NgRW7ZswY8//vjJYaSlpWHTpk0wNTUFAPTp0wfBwcGYM2cO3r59i+XLl2PlypXo27cvAMDFxQX169cHAPz8889ITEzEli1bpEp85cqVaNu2LRYsWCD9kW1sbIz169dDX18fAKQrVaNHj0anTp2kWKZPn44lS5ZIw8qUKYPbt29j7dq16Nu3L37++We8ePECFy9eRPHixQEArq6u0vQmJibQ09ODnZ2dNOz06dO4cOECnj9/Lp3AFy9ejL1792LXrl0YMmQIAgMDMXDgQAwcOBAA8N133+HYsWNZ3hUJCQnJdLyZmZnacZGRkQpJCADpu6pb6OnDbWxsFIbp6emhePHi0jQmJiZYsmQJ6tWrBx0dHezevRsdOnTA3r170a5du0zjJdKqQnB+vXfvHoQQcHd312i2X3zxBfr37y99//fff6X/6+vrw9zcHDKZTOEclNGxY8dw4cIFhIaGonz58gCgcFXcwcFBIYEZMWIEDh8+jB07dqBWrVoaxampqlWrYvr06QCAcuXKYeXKlQgODkazZs2yjHPp0qVo2rSplFyUL18et2/fxqJFi9CvXz+pXJMmTTB27Fjp+99//433799j9erV8PDwAPDhebmNGzciIiIC9vb2AIBx48bh0KFD2LhxI+bOnYuFCxeiRo0aCheJKlWqJP1fX18fRkZGCtt+5cqVqFatGubOnSsN27BhAxwdHXH37l3Y29vjxx9/xLZt29C0aVMAH5KzUqVKKWwnKysruLi4ZLothw4dim3btknf3717h5YtW0qJGwC1LRg0UadOHRgbG2PixImYO3cuhBCYNGkSUlNT8ezZMwAf7todO3YMHTp0gKmpKXR0dGBjY4NDhw7B0tISwIeEpmfPnli0aBFKly6tcAwXNPmaiGQUGxsLANIfH6qcO3cOY8aMURjm5+eHvXv35mZoRLkqvaL09vaWhtWqVQs7d+7Uyh+Wzs7OUhICACVLlsTz588BfGgKlJSUJJ2gMwoNDYWHh4fClcR69eohLS0NYWFh0h/WVapUkZKQj318ZT8+Ph7379/HwIEDMXjwYGl4SkqK9CBoSEgIqlWrlul5IKNr164hLi4OJUqUUBiekJCA+/fvS+uR8e6Ft7e32gf80n2cBBUUVlZWCufBmjVr4unTp1i0aBETEaIMRDbuTAOK56ycCgkJQalSpaQ/7jNKTU3F3LlzsWPHDjx58gTJyclISkrKlWdMMj4f8PH5P6s4Q0ND0b59e4Vh9erVQ2BgIFJTU6U/wFVtM319fYVl37hxA6mpqUrLSkpKks7dISEh6Nq1a7bW79q1azhx4oTKlgP3799HQkICkpOTUbt2bWl48eLF4ebmplA2ICBA6U5/RrNmzVJIIBs1aoQFCxYozPtTWFtbY+fOnfjqq6/w/fffQ0dHBz179kT16tWluxpCCAwfPhw2Njb4+++/YWhoiPXr16Nt27a4ePEiSpYsicmTJ6NChQro3bu3VuLKTQUmEUlLS8Po0aNRr149VK5cWW05dVcY1V1dTEpKQlJSkvT9zZs32gmYCg9dow9XzvJr2RpIv4r/8R/y1tbWKF++PKysrNROp6Ojo1TJqnogPOOzAzKZTHrwzdDQUKMYs6KqyUPG4elXin744QelE3d6hZaTeOLi4lCyZEmVDw2q6t0mO7JqFte7d2+1d2Pt7OyUmlqk936i7mqqnZ2d9EdCupSUFLx69SrTK7C1a9eWmlsUNatWrcKiRYsQGRkJDw8PrFixQu1V402bNilczQY+/L5y+3mgz1YhOL+WK1cOMpkMd+7c0ai8unNZdmR1Hlu0aBGWL1+OwMBAVKlSBcbGxhg9erTaZ8dUKejnf0NDQ4XnFePi4qCrq4vLly8r3EEA/neezen5P/0OfUYlS5bEvXv3sj1PdWxsbBTuWOvp6cHBwUGrF6yaN2+O+/fvIzo6Gnp6erCwsICdnZ10p+r48ePYv38/Xr9+Ld2RX716NY4ePYrNmzdj0qRJOH78OG7cuIFdu3YB+F8ybmVlhSlTpmDmzJlai/dTFZhEZPjw4bh586bUBk5b5s2bV6A2OOUDmUyj2/f5qUyZMtDR0UF4eLh0y3rfvn2IiIiAEEJtby3W1tZ4+/Yt4uPjpYogq6ZEGZUrVw6GhoYIDg7GoEGDlMZXqFABmzZtUljGmTNnoKOjo3RFKSu2trawt7fHv//+i169eqksU7VqVaxfvx6vXr1SeVdEX18fqampCsOqV6+OyMhI6OnpqW3jW6FCBZw/fx7+/v7SME26u/2Uplne3t6YM2cOnj9/LlVeR48ehZmZGSpWrKh2mpiYGFy+fFlqpnf8+HGkpaVletUtJCQEJUuWzGJtCp/t27djzJgxCAoKQu3atREYGAg/Pz+EhYUpNWFLZ2ZmptDxSVa9HdEnKATn1+LFi8PPzw+rVq3CyJEjlf5ojomJydYFC1XnoIyqVq2Kx48f4+7duyrvNpw5cwbt27eXrlinpaXh7t27as8LqlhbWys9HxsSEpKtTiuyirNChQo4c+aMUuzly5dXSiayUq1aNaSmpuL58+do0KCB2niCg4PV/t2m7vy/e/duODs7Q09P+c9aFxcXFCtWDOfPn0fp0qUBAK9fv8bdu3fh4+OTrXXIS+kXIY8fP47nz59Ld7vfvXsHAErPfejo6EgJ5u7du5GQkCCNu3jxIgYMGIC///47y+Znea1APL0SEBCA/fv348SJE0pt9jKys7NT6k85KipK7ZXCyZMnIzY2Vvr8999/WoubSFssLCzQqVMnzJkzBwkJCbh27RoOHToEQ0NDqacMVWrXrg0jIyN88803uH//Pn7++WelhwizYmBggIkTJ2LChAnYsmUL7t+/j3/++Ud6NqVXr14wMDBA3759cfPmTZw4cQIjRoxAnz59lO5OamLmzJmYN28evv/+e9y9exc3btzAxo0bsXTpUgBAz549YWdnhw4dOuDMmTP4999/sXv3bpw7dw7Ah2ZmDx48QEhICKKjo5GUlARfX194e3ujQ4cOOHLkCB4+fIizZ89iypQpuHTpEgBg1KhR2LBhAzZu3Ii7d+9i+vTpah8Y/5irq2umH3V/DAMfrmxVrFgRffr0wbVr13D48GF8++23GD58uHQX7MKFC3B3d8eTJ08AfKj4W7RogcGDB+PChQs4c+YMAgIC0KNHDylJ3bx5M3755RfcuXMHd+7cwdy5c7FhwwaMGDEi2/ujoFu6dCkGDx6M/v37o2LFiggKCoKRkRE2bNigdpr09vvpn5wcp1S0rFq1CqmpqahVqxZ2796N8PBwhIaG4vvvv1doEqsJZ2dnxMXFITg4GNHR0dIfhh/z8fFBw4YN0blzZxw9ehQPHjzAn3/+KT0bW65cORw9ehRnz55FaGgovvzyS6W/bbLSpEkTXLp0CVu2bEF4eDimT5+e7Y57sopz7NixCA4OxuzZs3H37l1s3rwZK1euzFEvTOXLl0evXr3g7++PPXv24MGDB7hw4QLmzZuHAwcOAPjwN9vFixcxbNgwXL9+HXfu3MGaNWukHrCcnZ1x/vx5PHz4ENHR0UhLS8Pw4cPx6tUr9OzZExcvXsT9+/dx+PBh9O/fH6mpqTAxMcHAgQMxfvx4HD9+HDdv3kS/fv2U/pBfuXKl2ibK6WJjYxEZGSl9/vnnH7i7uysM+9i9e/cQEhKCyMhIJCQkICQkBCEhIdKdrydPnsDd3V3hzvnGjRvxzz//4P79+9i2bRu6du2Kr7/+Wrrw5+3tDUtLS/Tt2xfXrl3D3bt3MX78eDx48ACtW7cG8CH5qly5svQpU6YMgA/1S2Z1Vn7I10RECIGAgAD89ttvOH78uLShMuPt7a308qGjR4+qPZHI5XKYmZkpfIgKolWrVsHAwAAODg7w9fVFYGAgAgMD0atXL7UPrBcvXhzbtm3DwYMHpe4fM3bNqImpU6di7NixmDZtGipUqIDu3btLzYOMjIxw+PBhvHr1CjVr1kSXLl3QtGlTrFy5MkfrOWjQIKxfvx4bN25ElSpV4OPjg02bNkm/f319fRw5cgQ2NjZo1aoVqlSpotCLS+fOndGiRQs0btwY1tbW+OWXXyCTyXDw4EE0bNgQ/fv3R/ny5dGjRw88evRI+iO0e/fumDp1KiZMmAAvLy88evQIX331VY7WQVO6urrYv38/dHV14e3tjd69e8Pf3x+zZs2Syrx79w5hYWEKTSp++uknuLu7o2nTpmjVqhXq16+PdevWKcx79uzZ8PLyQu3atfH7779j+/btSk2SCrvk5GRcvnwZvr6+0jAdHR34+vpKiakqcXFxcHJygqOjI9q3b69RwklFW9myZXHlyhU0btwYY8eOReXKldGsWTMEBwdjzZo12ZpX3bp1MXToUHTv3h3W1tZYuHChynK7d+9GzZo10bNnT1SsWBETJkyQruZ/++23qF69Ovz8/NCoUSPp4kt2+Pn5See0mjVr4u3btwp3fDWVWZzVq1fHjh078Ouvv6Jy5cqYNm0aZs2apfCgenZs3LgR/v7+GDt2LNzc3NChQwdcvHhRulNRvnx5HDlyBNeuXUOtWrXg7e2N33//XbrTMW7cOOjq6qJixYqwtraWHnw/c+YMUlNT0bx5c1SpUgWjR4+GhYWFlGwsWrQIDRo0QNu2beHr64v69esrvXcpOjpaeqZQnVGjRqFkyZKZfj42aNAgVKtWDWvXrsXdu3dRrVo1VKtWTeqK/f379wgLC1NIZsPCwtChQwdUqFABs2bNwpQpU7B48WJpvJWVFQ4dOoS4uDg0adIENWrUwOnTp/H7779LHQMUJjKR3ae4tGjYsGH4+eef8fvvvys08TA3N5faCfr7+8PBwQHz5s0D8KH7Xh8fH8yfPx+tW7fGr7/+irlz5+LKlSuZPluS7s2bNzA3N0dsbGz2kpL4eOD/2zCOQH9YwUnjSYvJk/HNhg+9OYSUPw3PGvU0Xy5l25UrV+Dl5SV14UpEmf8ucnxezGVPnz6Fg4MDzp49q3CxacKECfjrr7+UujMGPnRoEh4ejqpVqyI2NhaLFy/GqVOncOvWLbV33FU9S+jo6Ji97fFRHYG4OEALzxkURDy/EhVNKn/b/39eewPAHMiVOiJf74isWbMGsbGxaNSokUI2uX37dqlMRESE1GUZ8OFKxM8//4x169bBw8MDu3btwt69ezVKQoiIqGjz9vaGv78/PD094ePjgz179sDa2hpr165VO828efNgbm4ufRwdHfMwYiKiz1e+Pqyuyc0YVb3gdO3aNdvduxERUeFiZWUFXV3dbD0XmFGxYsVQrVq1THvOmTx5skJ3yOl3RIiIKHcViIfViYiIMtLX14eXl5fCc4FpaWkIDg7W+AHj1NRU3LhxI9MexfgsIRFR/igw3fcSERFlNGbMGPTt2xc1atRArVq1EBgYiPj4eOnB/IzPEc6aNQt16tSBq6srYmJisGjRIjx69Ehl19RERJS/mIhQkZPeS0ZKSko+R0JUcKR3F5ndvv/zW/fu3fHixQtMmzYNkZGR8PT0xKFDh6Te0CIiIhS64Xz9+jUGDx6MyMhIWFpawsvLC2fPns3W+xlIvfTjJzsv3iOigi+/6ggmIlTkWFtbAwDu37+v9u3LRJ+bU6dOAQCcnDTv8a+gCAgIQEBAgMpxGZ8jXLZsGZYtW5YHUX2e0rtZPXXqFOrUqZPP0RCRtuRXHcFEhIqckiVLwsfHB9988w0cHR1hZGSU3yER5Zvk5GScOnUKkyZNwuDBg7P1BmmijCwtLTF48GBMmjQJANCwYUPo6+vnc1RElFP5XUcwEaEiR0dHBxs2bICHhwcaNGiQ3+EQFQiDBw9GUFBQfodBRUD6cTRx4sR8joSItCW/6ggmIlQklS1bFtHR0bh7967CG6uJPje6urpwcnLinRDSGh0dHaxbtw4LFy7Eo0ePpLdwq5SSAByt/+H/zU4DeoZ5EyRlKjQ0FL179wY6dQKsrJQLREcDe/Zg27ZtqFChQt4HmB8+02M1v+sIJiJUZMnlclSpUiW/wyAiKpIsLCyy/uMlJR5If4VLdU9Ar2i+cb7QsrIC7O3Vjq5QocL/3rJd1PFYzRd8jwgREREREeU5JiJERERERJTnmIgQEREREVGeYyJCRERERER5jokIERERERHlOSYiRERERESU55iIEBERERFRnmMiQkREREREeY6JCBERERER5TkmIkRERERElOeYiBARERERUZ5jIkJERERERHmOiQgREREREeU5JiJERERERJTnmIgQEREREVGeYyJCRERERER5jokIERERERHlOSYiRERERESU55iIEBERERFRnmMiQkREREREeY6JCBERERER5TkmIkRERERElOeYiBARERERUZ5jIkJERERERHmOiQgREREREeU5JiJERERERJTnmIgQEREREVGeYyJCRERERER5jokIERERERHlOSYiRERERESU5/TyOwAquCIiIhAdHZ2jaa2srFC6dGktR0T5jccEEVHuy+pcy/MpFRVMREiliIgIuLu5IyExIUfTGxoY4k7YHZ4oixAeE0REuS8iIgJu7u5ITFB/rjUwNETYHZ5PqfBjIkIqRUdHIyExAZ3QCVawyt60iMaexD2Ijo7mSbII4TFBRJT7oqOjPyQhnToBVirOtdHRSNzD8ykVDUxEKFNWsII97PM7DCpAeExQXlu1ahUWLVqEyMhIeHh4YMWKFahVq1aW0/3666/o2bMn2rdvj7179+Z+oETaZGUF2PNcS0UbH1YnIqICa/v27RgzZgymT5+OK1euwMPDA35+fnj+/Hmm0z18+BDjxo1DgwYN8ihSIiLKLiYiRERUYC1duhSDBw9G//79UbFiRQQFBcHIyAgbNmxQO01qaip69eqFmTNnomzZsnkYLRERZQcTESIiKpCSk5Nx+fJl+Pr6SsN0dHTg6+uLc+fOqZ1u1qxZsLGxwcCBAzVaTlJSEt68eaPwISKi3MdEhIiICqTo6GikpqbC1tZWYbitrS0iIyNVTnP69Gn8+OOP+OGHHzRezrx582Bubi59HB0dPyluIiLSDBMRIiIqEt6+fYs+ffrghx9+gJWq3obUmDx5MmJjY6XPf//9l4tREhFROvaaRUREBZKVlRV0dXURFRWlMDwqKgp2dnZK5e/fv4+HDx+ibdu20rC0tDQAgJ6eHsLCwuDi4qI0nVwuh1wu13L0RESUFd4RISKiAklfXx9eXl4IDg6WhqWlpSE4OBje3t5K5d3d3XHjxg2EhIRIn3bt2qFx48YICQlhkysiogKGd0SIiKjAGjNmDPr27YsaNWqgVq1aCAwMRHx8PPr37w8A8Pf3h4ODA+bNmwcDAwNUrlxZYXoLCwsAUBpORET5L1/viJw6dQpt27aFvb09ZDJZli+cOnnyJGQymdJH3UOLRERUuHXv3h2LFy/GtGnT4OnpiZCQEBw6dEh6gD0iIgLPnj3L5yiJiCgn8vWOSHx8PDw8PDBgwAB06tRJ4+nCwsJgZmYmfbexscmN8IiIqAAICAhAQECAynEnT57MdNpNmzZpPyAiItKKfE1EWrZsiZYtW2Z7OhsbG+l2OxERERERFT6F8mF1T09PlCxZEs2aNcOZM2cyLcsXVRERERERFTyFKhEpWbIkgoKCsHv3buzevRuOjo5o1KgRrly5onYavqiKiIiIiKjgKVS9Zrm5ucHNzU36XrduXdy/fx/Lli3D1q1bVU4zefJkjBkzRvr+5s0bJiNERERERPmsUCUiqtSqVQunT59WO54vqiIiIiIiKngKVdMsVUJCQlCyZMn8DoOIiIiIiLIhX++IxMXF4d69e9L3Bw8eICQkBMWLF0fp0qUxefJkPHnyBFu2bAEABAYGokyZMqhUqRISExOxfv16HD9+HEeOHMmvVSAiIiIiohzI10Tk0qVLaNy4sfQ9/VmOvn37YtOmTXj27BkiIiKk8cnJyRg7diyePHkCIyMjVK1aFceOHVOYBxERERERFXz5mog0atQIQgi14zO+iGrChAmYMGFCLkdFRERERES5LUfPiPz777/ajoOIiIoQ1hNERJSVHCUirq6uaNy4MbZt24bExERtx0RERIUc6wkiIspKjppmXblyBRs3bsSYMWMQEBCA7t27Y+DAgahVq5a246NPFBERgejo6GxPFxoamgvRENHngvUEfa40qXetrKxQunTpPIqIqODKUSLi6emJ5cuXY8mSJdi3bx82bdqE+vXro3z58hgwYAD69OkDa2trbcdK2RQREQF3N3ckJCbkdyhE9JlhPUGfo4iICLi5uyMxIfN618DQEGF37jAZoc/eJz2srqenh06dOqF169ZYvXo1Jk+ejHHjxuGbb75Bt27dsGDBAr7jIx9FR0cjITEBndAJVrDK1rThCMcJnMilyIjoc8F6gj4n0dHRH5KQTp0AKzX1bnQ0EvfsQXR0NBMR+ux9UiJy6dIlbNiwAb/++iuMjY0xbtw4DBw4EI8fP8bMmTPRvn17XLhwQVuxUg5ZwQr2sM/WNNHIfnMuIqKMWE/QZ8nKCrDPXr1L9DnKUSKydOlSbNy4EWFhYWjVqhW2bNmCVq1aQUfnw7PvZcqUwaZNm+Ds7KzNWImIqJBgPUFERFnJUSKyZs0aDBgwAP369VN7S93GxgY//vjjJwVHRESFE+sJIiLKSo4SkfDw8CzL6Ovro2/fvjmZPRERFXKsJ4iIKCs5eo/Ixo0bsXPnTqXhO3fuxObNmz85KCIiKtxYTxARUVZylIjMmzcPVip6g7CxscHcuXM/OSgiIircWE8QEVFWcpSIREREoEyZMkrDnZycEBER8clBERFR4cZ6goiIspKjRMTGxgbXr19XGn7t2jWUKFHik4MiIqLCjfUEERFlJUeJSM+ePTFy5EicOHECqampSE1NxfHjxzFq1Cj06NFD2zESEVEhw3qCiIiykqNes2bPno2HDx+iadOm0NP7MIu0tDT4+/uz7S8REbGeICKiLOUoEdHX18f27dsxe/ZsXLt2DYaGhqhSpQqcnJy0HR8RERVCrCeIiCgrOUpE0pUvXx7ly5fXVixERFTEsJ4gIiJ1cpSIpKamYtOmTQgODsbz58+RlpamMP748eNaCY6IiAon1hNERJSVHCUio0aNwqZNm9C6dWtUrlwZMplM23EREVEhxnqCiIiykqNE5Ndff8WOHTvQqlUrbcdDRERFAOsJIiLKSo6679XX14erq6u2YyEioiKC9QQREWUlR4nI2LFjsXz5cgghtB0PEREVAawniIgoKzlqmnX69GmcOHECf/75JypVqoRixYopjN+zZ49WgiMiosKJ9QQREWUlR4mIhYUFOnbsqO1YiIioiGA9QUREWclRIrJx40Ztx0FEREUI6wkiIspKjp4RAYCUlBQcO3YMa9euxdu3bwEAT58+RVxcnNaCIyKiwov1BBERZSZHd0QePXqEFi1aICIiAklJSWjWrBlMTU2xYMECJCUlISgoSNtx0mckIiIC0dHROZrWysoKpUuX1nJERU9OtnFoaGguRZO7cno88Vj6NKwnqCDS5HyQ1W8/s3kU1vNkftHG/qDCLccvNKxRowauXbuGEiVKSMM7duyIwYMHay04+vxERETA3c0dCYkJOZre0MAQd8Lu8KSViU/dxoXJp6wrj6VPo816YtWqVVi0aBEiIyPh4eGBFStWoFatWirL7tmzB3PnzsW9e/fw/v17lCtXDmPHjkWfPn0+aX2o8IuIiICbuzsSEzI/HxgYGiLsjurfvqbzoKxpY39Q4ZejROTvv//G2bNnoa+vrzDc2dkZT5480Upg9HmKjo5GQmICOqETrGCVvWkRjT2JexAdHc0TViZyuo3DEY4TOJGLkWlfTteVx9Kn01Y9sX37dowZMwZBQUGoXbs2AgMD4efnh7CwMNjY2CiVL168OKZMmQJ3d3fo6+tj//796N+/P2xsbODn5/fJ60WFV3R09Ic/ejt1AqzUnA+io5G4R/1vP8t5hIcDJwrXeTK/aGN/UOGXo0QkLS0NqampSsMfP34MU1PTTw6KyApWsId9fodRpGV3G0cjZ83lCgIeT3lPW/XE0qVLMXjwYPTv3x8AEBQUhAMHDmDDhg2YNGmSUvlGjRopfB81ahQ2b96M06dPMxGhD6ysAPtPPB+om0cOmxV/1rSxP6jQytHD6s2bN0dgYKD0XSaTIS4uDtOnT0erVq20FRsRERVS2qgnkpOTcfnyZfj6+krDdHR04Ovri3PnzmU5vRACwcHBCAsLQ8OGDbO9DkRElLtydEdkyZIl8PPzQ8WKFZGYmIgvvvgC4eHhsLKywi+//KLtGImIqJDRRj0RHR2N1NRU2NraKgy3tbXFnTt31E4XGxsLBwcHJCUlQVdXF6tXr0azZs3Ulk9KSkJSUpL0/c2bNxrFR0REnyZHiUipUqVw7do1/Prrr7h+/Tri4uIwcOBA9OrVC4aGhtqOkYiICpn8rCdMTU0REhKCuLg4BAcHY8yYMShbtqxSs6108+bNw8yZM3M1JiIiUpajRAQA9PT00Lt3b23GQkRERcin1hNWVlbQ1dVFVFSUwvCoqCjY2dmpnU5HRweurq4AAE9PT4SGhmLevHlqE5HJkydjzJgx0vc3b97A0dExx3ETEZFmcpSIbNmyJdPx/v7+OQqGiIiKBm3UE/r6+vDy8kJwcDA6dOgA4MND8MHBwQgICNA4lrS0NIWmVxnJ5XLI5XKN50dERNqR4/eIfOz9+/d49+4d9PX1YWRkxESEiOgzp616YsyYMejbty9q1KiBWrVqITAwEPHx8VIvWv7+/nBwcMC8efMAfGhmVaNGDbi4uCApKQkHDx7E1q1bsWbNGu2uIBERfbIcJSKvX79WGhYeHo6vvvoK48eP/+SgiIiocNNWPdG9e3e8ePEC06ZNQ2RkJDw9PXHo0CHpAfaIiAjo6PyvA8j4+HgMGzYMjx8/hqGhIdzd3bFt2zZ0797901eKiIi0KsfPiGRUrlw5zJ8/H7179860NxMiIvo85bSeCAgIUNsU6+TJkwrfv/vuO3z33XefEiYREeWRHL1HRB09PT08ffpUm7MkIqIihPUEERGly9EdkX379il8F0Lg2bNnWLlyJerVq6eVwIiIqPBiPUFERFnJUSKS3ntJOplMBmtrazRp0gRLlizRRlxERFSIsZ4gIqKs5CgRSUtL03YcRERUhLCeICKirGj1GREiIiIiIiJN5OiOyMdvoM3K0qVLc7IIIiIqxFhPEBFRVnKUiFy9ehVXr17F+/fv4ebmBgC4e/cudHV1Ub16damcTCbTTpRERFSosJ4gIqKs5CgRadu2LUxNTbF582ZYWloC+PDyqv79+6NBgwYYO3asVoMkIqLChfUEERFlJUfPiCxZsgTz5s2TKhcAsLS0xHfffcfeUIiIiPUEERFlKUeJyJs3b/DixQul4S9evMDbt28/OSgiIircWE8QEVFWcpSIdOzYEf3798eePXvw+PFjPH78GLt378bAgQPRqVMnbcdIRESFDOsJIiLKSo4SkaCgILRs2RJffPEFnJyc4OTkhC+++AItWrTA6tWrNZ7PqVOn0LZtW9jb20Mmk2Hv3r1ZTnPy5ElUr14dcrkcrq6u2LRpU05WgYiIcpG26gkiIiq6cpSIGBkZYfXq1Xj58qXUM8qrV6+wevVqGBsbazyf+Ph4eHh4YNWqVRqVf/DgAVq3bo3GjRsjJCQEo0ePxqBBg3D48OGcrAYREeUSbdUTRERUdOWo16x0z549w7Nnz9CwYUMYGhpCCJGtrhhbtmyJli1balw+KCgIZcqUkR50rFChAk6fPo1ly5bBz88v2/Hnhzthd5CmY5jt6aysrFC6dOlciKjoCQ0NzfY03L5UUERERCA6OjpH0xbE4/hT6wmi7Mjs95OdukFd2ZzUL/m5jNyW1fmqIJ6TqGDJUSLy8uVLdOvWDSdOnIBMJkN4eDjKli2LgQMHwtLSMtd6RDl37hx8fX0Vhvn5+WH06NG5srzcMHDgILxLyv50hgaGuBN2hz/oTMQhDjLI0Lt372xPy+1LBUFERATc3dyRkJiQo+kL0nGcX/UEfb4iIiLg5u6OxISc/X4AAHFxgCxn9UiBWkYe0GR7GxgaIuxOwTgnUcGUo0Tk66+/RrFixRAREYEKFSpIw7t3744xY8bkWgUTGRkJW1tbhWG2trZ48+YNEhISYGiofKchKSkJSUn/+8v/zZs3uRKbptqjHUxhl61pohGNPYl7EB0dzR9zJhKRCAGBTugEK1hpPB23LxUU0dHRSEhMyPYxDBS84zi/6gn6fEVHR3/4o7hTJ8BKxe8nPBw4cSLzmSQmAkJ82jyykhfLyANZbu/oaCTuKTjnJCqYcpSIHDlyBIcPH0apUqUUhpcrVw6PHj3SSmDaMm/ePMycOTO/w5CUQAlYwT6/wyjSrGAFe25jKsSKwjFcmOoJKmKsrAB7Fb+f7DR51MY8CsIy8oK69SDSQI4eVo+Pj4eRkZHS8FevXkEul39yUOrY2dkhKipKYVhUVBTMzMxU3g0BgMmTJyM2Nlb6/Pfff7kWHxERfZBf9QQRERUeOUpEGjRogC1btkjfZTIZ0tLSsHDhQjRu3FhrwWXk7e2N4OBghWFHjx6Ft7e32mnkcjnMzMwUPkRElLvyq54gIqLCI0dNsxYuXIimTZvi0qVLSE5OxoQJE3Dr1i28evUKZ86c0Xg+cXFxuHfvnvT9wYMHCAkJQfHixVG6dGlMnjwZT548kSqzoUOHYuXKlZgwYQIGDBiA48ePY8eOHThw4EBOVoOIiHKJtuoJIiIqunJ0R6Ry5cq4e/cu6tevj/bt2yM+Ph6dOnXC1atX4eLiovF8Ll26hGrVqqFatWoAgDFjxqBatWqYNm0agA/dPkZEREjly5QpgwMHDuDo0aPw8PDAkiVLsH79+kLTdS8R0edCW/UEEREVXdm+I/L+/Xu0aNECQUFBmDJlyictvFGjRhBCqB2v6q3pjRo1wtWrVz9puURElHu0WU8QEVHRle07IsWKFcP169dzIxYiIioCWE8QEZEmctQ0q3fv3vjxxx+1HQsRERURrCeIiCgrOXpYPSUlBRs2bMCxY8fg5eUFY2NjhfFLly7VSnBERFQ4sZ4gIqKsZCsR+ffff+Hs7IybN2+ievXqAIC7d+8qlJHJZNqLjoiIChXWE0REpKlsJSLlypXDs2fPcOLECQBA9+7d8f3338PW1jZXgiMiosKF9QQREWkqW8+IZOzh6s8//0R8fLxWAyIiosKL9QQREWkqRw+rp8us610iIiLWE0REpE62EhGZTKbUtpdtfYmIKB3rCSIi0lS2nhERQqBfv36Qy+UAgMTERAwdOlSpN5Q9e/ZoL0IiIio0WE8QEZGmspWI9O3bV+F77969tRoMEREVbqwniIhIU9lKRDZu3JhbcRARURHAeoKIiDT1SQ+rExERERER5QQTESIiIiIiynNMRIiIiIiIKM8xESEiIiIiojzHRISIiAq0VatWwdnZGQYGBqhduzYuXLigtuwPP/yABg0awNLSEpaWlvD19c20PBER5Z9s9ZpFlB2hoaF5Mo225HTZVlZWKF26dI6mjYiIQHR0dI6mTUpKkt7VkB35uY2Jsmv79u0YM2YMgoKCULt2bQQGBsLPzw9hYWGwsbFRKn/y5En07NkTdevWhYGBARYsWIDmzZvj1q1bcHBwyIc1oHT//fcfXrx+p3b8p5xLP0dZncszqyNYD2RPVnU1j92cYyJCWheHOMggKzTvD/jUeA0NDHEn7E62T0IRERFwd3NHQmJCjpYrgwwCIkfTEhUWS5cuxeDBg9G/f38AQFBQEA4cOIANGzZg0qRJSuV/+uknhe/r16/H7t27ERwcDH9//zyJmVTzrFYNr2IT1Y43MDRE2J3sn0s/O3FxgEyDOksmAwTriE8VEREBN3d3JCaor6t57OYcExHSukQkQkCgEzrBClbZmjYc4TiBE7kUmWqfEm80orEncQ+io6OzfQKKjo5GQmLCJ22nwrKNiXIiOTkZly9fxuTJk6VhOjo68PX1xblz5zSax7t37/D+/XsUL148t8IkDSUmJgKdOgFWKs5Z0dFI3JOzc+lnJzHxQ4KhblsCQHg4cOKE+jLp4ylL0dHRH5IQHru5gokI5RorWMEe9tmaJho5a6akDTmJN7+Wm76dCts2JsqO6OhopKamwtbWVmG4ra0t7ty5o9E8Jk6cCHt7e/j6+qotk5SUhKSkJOn7mzdvchYwZc3KCrDP+/NskZTZtkxvRqSuTA6bBH/WeOzmCj6sTkRERdL8+fPx66+/4rfffoOBgYHacvPmzYO5ubn0cXR0zMMoiYg+X0xEiIioQLKysoKuri6ioqIUhkdFRcHOzi7TaRcvXoz58+fjyJEjqFq1aqZlJ0+ejNjYWOnz33//fXLsRESUNSYiRERUIOnr68PLywvBwcHSsLS0NAQHB8Pb21vtdAsXLsTs2bNx6NAh1KhRI8vlyOVymJmZKXyIiCj38RkRIiIqsMaMGYO+ffuiRo0aqFWrFgIDAxEfHy/1ouXv7w8HBwfMmzcPALBgwQJMmzYNP//8M5ydnREZGQkAMDExgYmJSb6tBxERKWMiQkREBVb37t3x4sULTJs2DZGRkfD09MShQ4ekB9gjIiKgo/O/m/tr1qxBcnIyunTpojCf6dOnY8aMGXkZOhERZYGJCBERFWgBAQEICAhQOe7kyZMK3x8+fJj7ARERkVbwGREiIiIiIspzTESIiIiIiCjPMREhIiIiIqI8x0SEiIiIiIjyHBMRIiIiIiLKc0xEiIiIiIgozzERISIiIiKiPMdEhIiIiIiI8hwTESIiIiIiynNMRIiIiIiIKM8xESEiIiIiojzHRISIiIiIiPIcExEiIiIiIspzTESIiIiIiCjP6eV3AKS50NDQXC1POZeTbf057p+crrOVlRVKly6t5WiyltN4k5KSIJfL82x5RJ+LiIgIREdHqxzH34/2ZbZNNd3e6spxfxHARKRQiEMcZJChd+/e+R0KZcB9o5lP3U6GBoa4E3Ynz5KRT41XBhkEhJajIvq8RUREwM3dHYkJCfkdStEXFwfIPrFu08Y8qMhjIlIIJCIRAgKd0AlWsNJ4unCE4wRO5GJklNN9A3xe++dTtlM0orEncQ+io6PzLBHRxn7lMUGkXdHR0R+SkE6dACsVv63wcOAEfz9akZgICKF+WwNZb++s5sH9RWAiUqhYwQr2sNe4fDRU374m7cvuvgE+z/2Tk+2Unz5lv/KYIMolVlaAvYrflpomW/QJ1G1rQPPtzf1FmeDD6kRERERElOeYiBARERERUZ5jIkJERERERHmOiQgREREREeU5JiJERERERJTnmIgQEREREVGeKxCJyKpVq+Ds7AwDAwPUrl0bFy5cUFt206ZNkMlkCh8DA4M8jJaIiIiIiD5Vvici27dvx5gxYzB9+nRcuXIFHh4e8PPzw/Pnz9VOY2ZmhmfPnkmfR48e5WHERERERET0qfI9EVm6dCkGDx6M/v37o2LFiggKCoKRkRE2bNigdhqZTAY7OzvpY2trm4cRExERERHRp8rXRCQ5ORmXL1+Gr6+vNExHRwe+vr44d+6c2uni4uLg5OQER0dHtG/fHrdu3VJbNikpCW/evFH4EBERERFR/srXRCQ6OhqpqalKdzRsbW0RGRmpcho3Nzds2LABv//+O7Zt24a0tDTUrVsXjx8/Vll+3rx5MDc3lz6Ojo5aXw8iIiIiIsqefG+alV3e3t7w9/eHp6cnfHx8sGfPHlhbW2Pt2rUqy0+ePBmxsbHS57///svjiImIiIiIKCO9/Fy4lZUVdHV1ERUVpTA8KioKdnZ2Gs2jWLFiqFatGu7du6dyvFwuh1wu/+RYiYiIiIhIe/L1joi+vj68vLwQHBwsDUtLS0NwcDC8vb01mkdqaipu3LiBkiVL5laYRERERESkZfl6RwQAxowZg759+6JGjRqoVasWAgMDER8fj/79+wMA/P394eDggHnz5gEAZs2ahTp16sDV1RUxMTFYtGgRHj16hEGDBuXnahARERERUTbkeyLSvXt3vHjxAtOmTUNkZCQ8PT1x6NAh6QH2iIgI6Oj878bN69evMXjwYERGRsLS0hJeXl44e/YsKlasmF+rQERERERE2ZTviQgABAQEICAgQOW4kydPKnxftmwZli1blgdRERERERFRbil0vWYREREREVHhx0SEiIiIiIjyHBMRIiIq0FatWgVnZ2cYGBigdu3auHDhgtqyt27dQufOneHs7AyZTIbAwMC8C5SIiLKFiQgRERVY27dvx5gxYzB9+nRcuXIFHh4e8PPzw/Pnz1WWf/fuHcqWLYv58+dr/D4qIiLKHwXiYXUioqyEhobmyTRUsCxduhSDBw+WunQPCgrCgQMHsGHDBkyaNEmpfM2aNVGzZk0AUDmeVIuIiEB0dLTa8VZWVihdunQeRkSkmaJy7Ga1HkDhWZfsYCJCRAVaHOIggwy9e/fO71AojyUnJ+Py5cuYPHmyNExHRwe+vr44d+6c1paTlJSEpKQk6fubN2+0Nu/CICIiAm7u7khMSFBbxsDQEGF37hS5P4KocCsqx64m6wEUjnXJLiYiRFSgJSIRAgKd0AlWsMrWtOEIxwmcyKXIKLdFR0cjNTVVeq9UOltbW9y5c0dry5k3bx5mzpyptfkVNtHR0R/+AOrUCbBS8RuLjkbinj2Ijo4uUn8AUeFXVI7dLNfjQ6FCsS7ZxUSEiAoFK1jBHvbZmiYamd/mJgKAyZMnY8yYMdL3N2/ewNHRMR8jyidWVoB99n5jRAVCUTl2i8p6ZAMTESIiKpCsrKygq6uLqKgoheFRUVFafRBdLpdDLpdrbX5ERKQZ9ppFREQFkr6+Pry8vBAcHCwNS0tLQ3BwMLy9vfMxMiIi0gbeESEiogJrzJgx6Nu3L2rUqIFatWohMDAQ8fHxUi9a/v7+cHBwwLx58wB8eMD99u3b0v+fPHmCkJAQmJiYwNXVNd/Wg4iIlDERISKiAqt79+548eIFpk2bhsjISHh6euLQoUPSA+wRERHQ0fnfzf2nT5+iWrVq0vfFixdj8eLF8PHxwcmTJ/M6fCIiygQTESIiKtACAgIQEBCgclzG5MLZ2RlCiDyIioiIPhWfESEiIiIiojzHRISIiIiIiPIcExEiIiIiIspzTESIiIiIiCjPMREhIiIiIqI8x0SEiIiIiIjyHBMRIiIiIiLKc0xEiIiIiIgozzERISIiIiKiPMdEhIiIiIiI8hwTESIiIiIiynNMRIiIiIj+r727j4qqzOMA/h2Q4UUBkRcRF0UU8AWMkoVFNDA5R5fUKNdcYxFcw7WYsypquYlhWepxrTSWtpVW9OyRpq2gOoK4JqIlpCvChoLkCzhpgNKLiCgIPPuHMTkyvMwwc4eX7+ecew7z8Dz3+f2Gy334ce/MEJHkWIgQEREREZHkWIgQEREREZHkWIgQEREREZHkBpk6ACIiIiKijpSVlenUrmu/xsZGWFu0wv/nx8XFxWg1s9Zpjq6oVCrU1tbqFZ8h5gAAJycnjBo1yiBzGQoLESIiIiLqferrAZkMf/jDH4w7XiaDjVzg1u57D0OmTUNDo35TaqNSqeAzfjzu3L5tuJ3qMYeVtTXKz53rVcUICxEiIiIi6n3u3AGEAJ56CnByav/98+eBI0f0H3//PubNA/DZvbYlS4BWi+7N0Q21tbX3CgR98zDEHLW1uJORgdraWhYiRERERETd4uQEuLm1b+/kNqRujb9/H46Ov7SNGAEIuW5z9CQOKebopfhidSIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIikhwLESIiIiIiklyvKERSUlLg4eEBKysrBAUF4eTJk532//DDDzF+/HhYWVnBz88P2dnZEkVKRERS4xpBRNQ/mbwQ+eCDD5CQkICkpCScPn0aDz30EGbNmoVr165p7Z+fn49FixZh6dKlKCoqQmRkJCIjI3HmzBmJIyciImPjGkFE1H+ZvBB58803ERcXhyVLlmDixIl49913YWNjg927d2vtv3PnTsyePRtr167FhAkTsGnTJjzyyCP429/+JnHkRERkbFwjiIj6L5MWIk1NTSgsLER4eLi6zczMDOHh4SgoKNA6pqCgQKM/AMyaNavD/kRE1DdxjSAi6t8GmXLy2tpatLS0YPjw4Rrtw4cPx7lz57SOqa6u1tq/urpaa//GxkY0NjaqH9+4cQMAUFdXp1uwt279EgOqUQ/R7aFycRd1DT+PFbqNBYDruA4AqEIVmtBk9HEDbWxfi9dUY/tavD0Z29fiBYDv8T0AoL6+XufzW1t/IXQ7NxmbFGsEYKB14r41AnV1QEtL98eaWH19/b0vqqqAJi3H3ff3jq3CwsJf+mphZmaG1tZWzbbWO5j88/onRM/mKC8v7zzO69d79n1D7INz9Nk5RHW1+m81cfky0GrRvX1Icex2Y54u5/hejzXi5/NaW2+jrBHChK5evSoAiPz8fI32tWvXisDAQK1jLCwsRHp6ukZbSkqKcHFx0do/KSlJAODGjRs3bl1s3377rWFO7gYixRohBNcJbty4cevOZow1wqRXRJycnGBubo6amhqN9pqaGri6umod4+rqqlP/v/zlL0hISFA/bm1txQ8//ABHR0fIZDKd4q2rq4O7uzu+/fZb2NnZ6TS2L2K+/Rvz7d90yVcIgZs3b8LNzU2i6LpHijUCMOw6QZoG2u+dVPi8GgefV+2MuUaYtBCRy+WYMmUKDh8+jMjISAD3FoDDhw9DoVBoHRMcHIzDhw9j5cqV6rZDhw4hODhYa39LS0tYWlpqtA0dOrRHcdvZ2Q2oA5T59m/Mt3/rbr729vYSRKMbKdYIwDjrBGkaaL93UuHzahx8Xtsz1hph0kIEABISEhATE4OAgAAEBgZix44duHXrFpYsWQIAWLx4MUaOHIktW7YAAFasWIHQ0FC88cYbePzxx6FUKnHq1Cns2rXLlGkQEZERcI0gIuq/TF6ILFy4ENevX8fLL7+M6upq+Pv7IycnR/1iQ5VKBTOzX97ca+rUqUhPT0diYiJeeukleHl54ZNPPoGvr6+pUiAiIiPhGkFE1H+ZvBABAIVC0eFl9ry8vHZtCxYswIIFC4wcVXuWlpZISkpqdwm/v2K+/Rvz7d/6U759ZY2g9vrTcdib8Hk1Dj6v0pMJ0cver5GIiIiIiPo9k3+yOhERERERDTwsRIiIiIiISHIsRIiIiIiISHIsRB6QkpICDw8PWFlZISgoCCdPnuy0/4cffojx48fDysoKfn5+yM7OlihSw9Al39TUVEyfPh0ODg5wcHBAeHh4l89Pb6Prz7eNUqmETCZTf5ZBX6Frvj/99BPi4+MxYsQIWFpawtvbu08d07rmu2PHDvj4+MDa2hru7u5YtWoV7ty5I1G0PXPs2DHMnTsXbm5ukMlk+OSTT7ock5eXh0ceeQSWlpYYN24c9uzZY/Q4idpUVlZi6dKlGDNmDKytrTF27FgkJSWhqanJ1KH1OfquZaTdli1b8Otf/xq2trZwcXFBZGQkysvLTR3WwGDwz2rvw5RKpZDL5WL37t3i7NmzIi4uTgwdOlTU1NRo7X/8+HFhbm4utm3bJkpLS0ViYqKwsLAQJSUlEkeuH13zfeaZZ0RKSoooKioSZWVlIjY2Vtjb24srV65IHLl+dM23TUVFhRg5cqSYPn26eOKJJ6QJ1gB0zbexsVEEBASIiIgI8eWXX4qKigqRl5cniouLJY5cP7rmu2/fPmFpaSn27dsnKioqxMGDB8WIESPEqlWrJI5cP9nZ2WL9+vUiIyNDABCZmZmd9r906ZKwsbERCQkJorS0VCQnJwtzc3ORk5MjTcA04B04cEDExsaKgwcPiosXL4pPP/1UuLi4iNWrV5s6tD5F37WMOjZr1iyRlpYmzpw5I4qLi0VERIQYNWqUqK+vN3Vo/R4LkfsEBgaK+Ph49eOWlhbh5uYmtmzZorX/008/LR5//HGNtqCgIPGnP/3JqHEaiq75Pqi5uVnY2tqKvXv3GitEg9In3+bmZjF16lTx3nvviZiYmD5ViOia79///nfh6ekpmpqapArRoHTNNz4+Xjz22GMabQkJCSIkJMSocRpDdwqRF154QUyaNEmjbeHChWLWrFlGjIyoc9u2bRNjxowxdRh9Sk/XburatWvXBABx9OhRU4fS7/HWrJ81NTWhsLAQ4eHh6jYzMzOEh4ejoKBA65iCggKN/gAwa9asDvv3Jvrk+6CGhgbcvXsXw4YNM1aYBqNvvq+++ipcXFywdOlSKcI0GH3y/eyzzxAcHIz4+HgMHz4cvr6+2Lx5M1paWqQKW2/65Dt16lQUFhaqb2m4dOkSsrOzERERIUnMUuvL5yvqv27cuNEn1pDewhBrN3Xtxo0bAMBjUwK94gMNe4Pa2lq0tLSoP623zfDhw3Hu3DmtY6qrq7X2r66uNlqchqJPvg968cUX4ebm1u6Pm95In3y//PJL/POf/0RxcbEEERqWPvleunQJubm5iIqKQnZ2Ni5cuIDnn38ed+/eRVJSkhRh602ffJ955hnU1tZi2rRpEEKgubkZy5cvx0svvSRFyJLr6HxVV1eH27dvw9ra2kSR0UB14cIFJCcnY/v27aYOpc8wxNpNnWttbcXKlSsREhICX19fU4fT7/GKCOll69atUCqVyMzMhJWVlanDMbibN28iOjoaqampcHJyMnU4kmhtbYWLiwt27dqFKVOmYOHChVi/fj3effddU4dmFHl5edi8eTPeeecdnD59GhkZGcjKysKmTZtMHRpRn7Ju3TrIZLJOtwf/SL569Spmz56NBQsWIC4uzkSRE7UXHx+PM2fOQKlUmjqUAYFXRH7m5OQEc3Nz1NTUaLTX1NTA1dVV6xhXV1ed+vcm+uTbZvv27di6dSs+//xzTJ482ZhhGoyu+V68eBGVlZWYO3euuq21tRUAMGjQIJSXl2Ps2LHGDboH9Pn5jhgxAhYWFjA3N1e3TZgwAdXV1WhqaoJcLjdqzD2hT74bNmxAdHQ0nn32WQCAn58fbt26hWXLlmH9+vUwM+tf/6fp6HxlZ2fHqyHUI6tXr0ZsbGynfTw9PdVff/fdd5gxYwamTp2KXbt2GTm6/qUnazd1TaFQYP/+/Th27Bh+9atfmTqcAaF/rbQ9IJfLMWXKFBw+fFjd1traisOHDyM4OFjrmODgYI3+AHDo0KEO+/cm+uQLANu2bcOmTZuQk5ODgIAAKUI1CF3zHT9+PEpKSlBcXKze5s2bhxkzZqC4uBju7u5Shq8zfX6+ISEhuHDhgrrgAoBvvvkGI0aM6NVFCKBfvg0NDe2KjbYiTAhhvGBNpC+fr6h3c3Z2xvjx4zvd2s4hV69eRVhYGKZMmYK0tLR+V/Abm75rN3VOCAGFQoHMzEzk5uZizJgxpg5p4DDxi+V7FaVSKSwtLcWePXtEaWmpWLZsmRg6dKiorq4WQggRHR0t1q1bp+5//PhxMWjQILF9+3ZRVlYmkpKS+tzb9+qS79atW4VcLhcfffSRqKqqUm83b940VQo60TXfB/W1d83SNV+VSiVsbW2FQqEQ5eXlYv/+/cLFxUW89tprpkpBJ7rmm5SUJGxtbcX7778vLl26JP7zn/+IsWPHiqefftpUKejk5s2boqioSBQVFQkA4s033xRFRUXi8uXLQggh1q1bJ6Kjo9X9296+d+3ataKsrEykpKTw7XtJUleuXBHjxo0TM2fOFFeuXNFYR6j7ujrXke6ee+45YW9vL/Ly8jSOy4aGBlOH1u+xEHlAcnKyGDVqlJDL5SIwMFB89dVX6u+FhoaKmJgYjf7//ve/hbe3t5DL5WLSpEkiKytL4oh7Rpd8R48eLQC025KSkqQPXE+6/nzv19cKESF0zzc/P18EBQUJS0tL4enpKV5//XXR3NwscdT60yXfu3fvio0bN4qxY8cKKysr4e7uLp5//nnx448/Sh+4Ho4cOaL197Etx5iYGBEaGtpujL+/v5DL5cLT01OkpaVJHjcNXGlpaVqPWf5PVHednetIdx0dlzxHGp9MiH54DwIREREREfVqvDmTiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEiIiIiIgkx0KEqJfZuHEj/P39TR0GERH1QrGxsYiMjNR7fGVlJWQyGYqLiw0WE5G+WIgQERERdSAsLAwrV67Ue3xeXh5kMhl++uknncZ1VDDs3LkTe/bs6dY+tBUt7u7uqKqqgq+vr07xEBnDIFMHQERERETdY29v36Px5ubmcHV1NVA0RD3DKyJEnQgLC4NCoYBCoYC9vT2cnJywYcMGCCHa9a2rq4O1tTUOHDig0Z6ZmQlbW1s0NDQAAF588UV4e3vDxsYGnp6e2LBhA+7evdtpDA/+Ny4yMhKxsbHqx42NjVizZg1GjhyJwYMHIygoCHl5eXrnTURE964oHD16FDt37oRMJoNMJkNlZWW7fpcvX8bcuXPh4OCAwYMHY9KkScjOzkZlZSVmzJgBAHBwcIBMJlOfu3NycjBt2jQMHToUjo6OmDNnDi5evKje55gxYwAADz/8MGQyGcLCwtQx3X+V46OPPoKfnx+sra3h6OiI8PBw3Lp1Cxs3bsTevXvx6aefqmPPy8vTeqXl7NmzmDNnDuzs7GBra4vp06drxEJkLLwiQtSFvXv3YunSpTh58iROnTqFZcuWYdSoUYiLi9PoZ2dnhzlz5iA9PR2//e1v1e379u1DZGQkbGxsAAC2trbYs2cP3NzcUFJSgri4ONja2uKFF17QO0aFQoHS0lIolUq4ubkhMzMTs2fPRklJCby8vPTeLxHRQLZz505888038PX1xauvvgoAcHZ2btcvPj4eTU1NOHbsGAYPHozS0lIMGTIE7u7u+PjjjzF//nyUl5fDzs4O1tbWAIBbt24hISEBkydPRn19PV5++WU8+eSTKC4uhpmZGU6ePInAwEB8/vnnmDRpEuRyebt5q6qqsGjRImzbtg1PPvkkbt68iS+++AJCCKxZswZlZWWoq6tDWloaAGDYsGH47rvvNPZx9epVPProowgLC0Nubi7s7Oxw/PhxNDc3G/rpJGqHhQhRF9zd3fHWW29BJpPBx8cHJSUleOutt9oVIgAQFRWF6OhoNDQ0wMbGBnV1dcjKykJmZqa6T2JiovprDw8PrFmzBkqlUu9CRKVSIS0tDSqVCm5ubgCANWvWICcnB2lpadi8ebNe+yUiGujs7e0hl8thY2PT6e1MKpUK8+fPh5+fHwDA09NT/b1hw4YBAFxcXDB06FB1+/z58zX2sXv3bjg7O6O0tBS+vr7qgsfR0bHDuauqqtDc3IynnnoKo0ePBgB1DABgbW2NxsbGTmNPSUmBvb09lEolLCwsAADe3t4d9icyJN6aRdSF3/zmN5DJZOrHwcHBOH/+PF5//XUMGTJEvalUKkRERMDCwgKfffYZAODjjz+GnZ0dwsPD1eM/+OADhISEwNXVFUOGDEFiYiJUKpXe8ZWUlKClpQXe3t4a8Rw9epSX1omIDGzSpEnq82zb1e8///nPeO211xASEoKkpCR8/fXXXe7n/PnzWLRoETw9PWFnZwcPDw8A0Gk9eOihhzBz5kz4+flhwYIFSE1NxY8//qhTPsXFxZg+fbq6CCGSEgsRIj0tX74cxcXF6s3NzQ1yuRy/+93vkJ6eDgBIT0/HwoULMWjQvYuPBQUFiIqKQkREBPbv34+ioiKsX78eTU1NHc5jZmbW7jUp97+mpL6+Hubm5igsLNSIp6ysDDt37jRC5kREA1d2drb6PPvee+8BAJ599llcunQJ0dHRKCkpQUBAAJKTkzvdz9y5c/HDDz8gNTUVJ06cwIkTJwCg0/XgQebm5jh06BAOHDiAiRMnIjk5GT4+PqioqOj2PtpuFSMyBRYiRF1oWxzafPXVV/Dy8oKjoyPGjRun3tqKjaioKOTk5ODs2bPIzc1FVFSUemx+fj5Gjx6N9evXIyAgAF5eXrh8+XKn8zs7O6Oqqkr9uKWlBWfOnFE/fvjhh9HS0oJr165pxDNu3Di+MwoRUQ/J5XK0tLSoH48ePVp9jh05cqS63d3dHcuXL0dGRgZWr16N1NRU9XgAGvv4/vvvUV5ejsTERMycORMTJkxodyVD2zhtZDIZQkJC8Morr6CoqAhyuVx9O/CDsWszefJkfPHFF52+aQqRsbAQIeqCSqVCQkICysvL8f777yM5ORkrVqzosP+jjz4KV1dXREVFYcyYMQgKClJ/z8vLCyqVCkqlEhcvXsTbb7+t8foRbR577DFkZWUhKysL586dw3PPPafxfvTe3t6IiorC4sWLkZGRgYqKCpw8eRJbtmxBVlZWj/MnIhrIPDw8cOLECVRWVqK2thatra3t+qxcuRIHDx5ERUUFTp8+jSNHjmDChAkA7hUuMpkM+/fvx/Xr11FfXw8HBwc4Ojpi165duHDhAnJzc5GQkKCxTxcXF1hbWyMnJwc1NTW4ceNGu3lPnDiBzZs349SpU1CpVMjIyMD169fVc3t4eODrr79GeXk5amtrtRYbCoUCdXV1+P3vf49Tp07h/Pnz+Ne//oXy8nJDPH1EnWIhQtSFxYsX4/bt2wgMDER8fDxWrFiBZcuWddhfJpNh0aJF+N///qdxNQQA5s2bh1WrVkGhUMDf3x/5+fnYsGFDp/P/8Y9/RExMDBYvXozQ0FB4enqq3w6yTVpaGhYvXozVq1fDx8cHkZGR+O9//4tRo0bpnzgREWHNmjUwNzfHxIkT4ezsrPU1HC0tLYiPj8eECRMwe/ZseHt745133gEAjBw5Eq+88grWrVuH4cOHQ6FQwMzMDEqlEoWFhfD19cWqVavw17/+VWOfgwYNwttvv41//OMfcHNzwxNPPNFuXjs7Oxw7dgwRERHw9vZGYmIi3njjDfVrV+Li4uDj44OAgAA4Ozvj+PHj7fbh6OiI3Nxc1NfXIzQ0FFOmTEFqaipfM0KSkAltH4hARADufYaHv78/duzYYepQiIiIiPoVXhEhIiIiIiLJsRAhIiIiIiLJ8dYsIiIiIiKSHK+IEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5FiIEBERERGR5P4P9yoWUIP4cJMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the distribution of p-values and t-statistics with Bonferroni correction\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# Plot p-values distribution\n",
    "ax1.set_title(f'Distribution of p-values from {num_tests} t-tests\\n{num_rejections_bonf} rejections (p < {alpha_bonferroni:.6f})')\n",
    "ax1.hist(p_values_bonferroni, bins=20, density=True, edgecolor='black', color='purple')\n",
    "ax1.axvline(alpha_bonferroni, color='red', label=f'α Bonf = {alpha_bonferroni:.6f}')\n",
    "ax1.axvline(alpha, color='orange', label=f'α uncorrected = {alpha}')\n",
    "ax1.set_xlabel('p-value')\n",
    "ax1.set_ylabel('Frequency')\n",
    "ax1.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "# Plot t-statistics distribution\n",
    "df = 2 * sample_size - 2\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "\n",
    "df = 2 * sample_size - 2\n",
    "t_critical_bonferroni = stats.t.ppf(1 - alpha_bonferroni/2, df)\n",
    "\n",
    "ax2.set_title(f'Distribution of t-statistics from {num_tests} t-tests\\n{num_rejections_bonf} beyond critical values')\n",
    "ax2.hist(t_statistics_bonferroni, bins=30, density=True, edgecolor='black', color='teal')\n",
    "ax2.axvline(-t_critical_bonferroni, color='red', label=f'Critical Bonf: ±{t_critical_bonferroni:.3f}')\n",
    "ax2.axvline(t_critical_bonferroni, color='red')\n",
    "ax2.axvline(-t_critical, color='orange', label=f'Critical uncorrected: ±{t_critical:.3f}')\n",
    "ax2.axvline(t_critical, color='orange')\n",
    "ax2.set_xlabel('t-statistic')\n",
    "ax2.set_ylabel('Frequency')\n",
    "ax2.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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