1120 lines
291 KiB
Plaintext
1120 lines
291 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "839f9f95-d3ea-477f-96b6-b23eea60be3c",
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"metadata": {
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"editable": true,
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-94f52a4a45c90a6a",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"source": [
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"# 6. Programmierübung: Monte Carlo Simulationen\n",
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"\n",
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"<div style=\"display:flex;\">\n",
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" <div style=\"text-align: left\">\n",
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" Willkommen zur sechsten Programmierübung Einführung in Python 3.\n",
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" </div>\n",
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" <img style=\"float: right; margin: 0px 15px 15px 0px\" src=\"https://www.python.org/static/img/python-logo-large.c36dccadd999.png?1576869008\" width=\"100\" />\n",
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"</div>\n",
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"\n",
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"Wenn du Fragen oder Verbesserungsvorschläge zum Inhalt oder Struktur der Notebooks hast, dann kannst du mir gerne eine E-Mail an Phil Keier ([p.keier@hbk-bs.de](mailto:p.keier@hbk-bs.de?subject=[SigSys]%20Feedback%20Programmierübung&)) schreiben.\n",
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"\n",
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"Link zu einem Python Spickzettel: [hier](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PythonForDataScience.pdf)\n",
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"\n",
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"Der Großteil des Python-Tutorials stammt aus der Veranstaltung _Deep Learning Lab_ und von [www.python-kurs.eu](https://www.python-kurs.eu/python3_kurs.php) und wurde für _Signale und Systeme_, sowie _Einführung in die Programmierung für Nicht Informatiker_ angepasst.\n",
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"\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"id": "53c75485-1cd4-4ac7-9092-e14b3c400980",
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"metadata": {
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"editable": true,
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-107d356336d8d991",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"source": [
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"## (Continues) Uniform Distribution\n",
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"\n",
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"Die gleichmäßige Verteilung zeigt sich durch ihre charakteristische Form eines Rechtecks mit dem Flächeninhalt 1 = 100%. \n",
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"Technisch gesehen ist diese Art der Verteilung keineswegs exotisch, da PCGs ihr üblicherweise folgen.\n",
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"\n",
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"Eine Uniform Distribution setzt sich aus denselben zwei Parametern zusammen wie die Normalverteilung: \n",
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"$\\mu$ als Mittelwert und $\\sigma$ als Standardabweichung vom Mittelwert. \n",
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"\n",
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"Allerdings interpretieren die Libraries NumPy & SciPy diese Werte etwas anders: \n",
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"$\\mu$ entspricht hier dem kleinsten Wert, während $\\sigma$ den größten Wert markiert.\n",
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"\n",
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"Die folgende Grafik verdeutlicht die Verteilung mit $\\mu = 0$ & $\\sigma = 1$:\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "52d292d3-66ee-4d00-b5eb-e65497839fba",
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"metadata": {
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"editable": true,
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-654d073e308d12e3",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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},
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"outputs": [
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{
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"data": {
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",
|
||
"text/plain": [
|
||
"<Figure size 800x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"from scipy.stats import uniform # Import scipys uniform\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Define the distribution parameters to be plotted\n",
|
||
"sigma = 1\n",
|
||
"mu = 0\n",
|
||
"x = np.linspace(-0.5, 1.5, 1000)\n",
|
||
"\n",
|
||
"\n",
|
||
"# plot the distributions\n",
|
||
"fig, ax = plt.subplots(figsize=(8, 5))\n",
|
||
"\n",
|
||
"dist = uniform(mu, sigma)\n",
|
||
"\n",
|
||
"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
|
||
"\n",
|
||
"plt.xlim(-0.5, 1.5)\n",
|
||
"plt.ylim(0, 1.2)\n",
|
||
"\n",
|
||
"plt.xlabel('$x$')\n",
|
||
"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
|
||
"plt.title('Uniform Distribution')\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "55a561f8-46dc-4a72-a4e3-c7711aede96b",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-0ccc61b247199a19",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"## Random Sampling\n",
|
||
"\n",
|
||
"Wie man aus Verteilungen sampelt, ist bereits aus dem Kapitel zu den PCGs bekannt – schließlich sind diese uniform verteilt.\n",
|
||
"\n",
|
||
"Das folgende Beispiel zieht drei zufällige Zahlen aus einer PCG-uniformen Verteilung mittels NumPy:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "a312483e-058b-4efc-a92a-bc9e370a3559",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-c4c29720ffba7a48",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 800x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Parameters\n",
|
||
"mu = 0\n",
|
||
"sigma = 1\n",
|
||
"\n",
|
||
"# Get a 3 random samples\n",
|
||
"rand = np.random.default_rng(5000)\n",
|
||
"uniform_samples = rand.uniform(mu, sigma, 3)\n",
|
||
"\n",
|
||
"# Linespace\n",
|
||
"x = np.linspace(-0.5, 2, 1000)\n",
|
||
"\n",
|
||
"# Get uniform from linespace\n",
|
||
"dist = uniform(mu, sigma)\n",
|
||
"\n",
|
||
"# Plot Uniform\n",
|
||
"fig, ax = plt.subplots(figsize=(8, 5))\n",
|
||
"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
|
||
"\n",
|
||
"# Plot samples\n",
|
||
"step = 0.1\n",
|
||
"for u in uniform_samples:\n",
|
||
" u = np.round(u, decimals=2)\n",
|
||
" plt.axvline(u, color='r')\n",
|
||
" plt.text(u, .5+step, u, color='g')\n",
|
||
" step += 0.1\n",
|
||
"\n",
|
||
"# Cosmetics\n",
|
||
"plt.xlim(-0.5, 1.5)\n",
|
||
"plt.ylim(0, 1.2)\n",
|
||
"\n",
|
||
"plt.xlabel('$x$')\n",
|
||
"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
|
||
"plt.title('3 Samples from a Uniform Distribution')\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a87b1a90-adff-4eb4-b91b-2de5284f64d3",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-42065ce8f33baff7",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"Random Sampling funktioniert selbstverständlich auch auf Normalverteilungen. Beispiel:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "f1981ddf-87e1-4010-a39c-8a89d172d771",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-d87cc7a18f64858f",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 800x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Import scipys norm\n",
|
||
"from scipy.stats import norm \n",
|
||
"\n",
|
||
"#Parameters\n",
|
||
"mu = 0\n",
|
||
"sigma = 1\n",
|
||
"\n",
|
||
"# Get a 3 random samples\n",
|
||
"rand = np.random.default_rng(5000)\n",
|
||
"uniform_samples = rand.normal(mu, sigma, 3)\n",
|
||
"\n",
|
||
"# Linespace\n",
|
||
"x = np.linspace(-4, 4, 1000)\n",
|
||
"\n",
|
||
"# Get uniform from linespace\n",
|
||
"dist = norm(mu, sigma)\n",
|
||
"\n",
|
||
"# Plot Uniform\n",
|
||
"fig, ax = plt.subplots(figsize=(8, 5))\n",
|
||
"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
|
||
"\n",
|
||
"# Plot samples\n",
|
||
"step = 0.1\n",
|
||
"for u in uniform_samples:\n",
|
||
" u = np.round(u, decimals=2)\n",
|
||
" plt.axvline(u, color='r')\n",
|
||
" plt.text(u, .1+step, u, color='g')\n",
|
||
" step += 0.1\n",
|
||
"\n",
|
||
"# Cosmetics\n",
|
||
"plt.xlim(-4, 4)\n",
|
||
"plt.ylim(0, .5)\n",
|
||
"\n",
|
||
"plt.xlabel('$x$')\n",
|
||
"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
|
||
"plt.title('3 Samples from a Normal Distribution')\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "541dd4a5-8849-43fe-8e8c-305b3b99a350",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-de3ef99af1cebfe1",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"## Monte-Carlo-Simulationen\n",
|
||
"\n",
|
||
"Monte-Carlo-Simulationen werden in vielen wissenschaftlichen und finanziellen (Forschungs-)Feldern angewandt, um stochastisch relevante Probleme auf vergleichsweise elegante Weise zu lösen. Insbesondere lassen sich damit Zufallsereignisse unterschiedlichster Verteilungen miteinander kombinieren. So kann man beispielsweise die Zahl $\\pi$ approximieren.\n",
|
||
"\n",
|
||
"Dazu betrachte folgende Darstellung:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "cd6000b8-cb79-4513-8cae-dc9752e47f93",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-3b11e71ec9f993b5",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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j0b+waKlYjx49gru7OxYtWoQFCxbg+PHjsLa2ljoWERWha9euiI2NhbOzM3r27InZs2dzV3IFoSN1AKqYLl68iL59+yI7OxthYWHo3Lmz1JGI6A3q1KmDQ4cOYcWKFQgICMClS5ewY8cOmJiYSB1No3GLlgoJCgpChw4dUKdOHURHR7NkiSoRLS0tzJw5E0eOHMHZs2fh4uKC+Ph4qWNpNBYtKeTl5SEgIACDBw9Gv379cPr0adSrV0/qWERUBh4eHoiKioJMJoOLiwuOHj0qdSSNpZaiXb16NWxtbWFgYAAXFxdERUUVO9bNzQ0ymazQo3fv3ooxI0aMKPS8p6enOlalypLL5ejbty+WLVuG5cuXY+vWrTA0NJQ6FhG9BTs7O0RGRqJTp07o3bs3li1bxqtJSUDln9Hu2rULU6dOxdq1a+Hi4oLvvvsOHh4eiI+PR506dQqN37t3L7KzsxVfP336FA4ODhgwYIDSOE9PT2zatEnxtb6+vupWoopLSEhA3759kZycjMOHD/OPFqIqxNjYGPv378ecOXPg7++PS5cu4ZdffuEf0mqk8i3alStXYuzYsRg5ciSaN2+OtWvXolq1ati4cWOR483MzGBpaal4HD9+HNWqVStUtPr6+krjatasqepVqZJOnDiBdu3aQQiBqKgolixRFaStrY3FixcjKCgI+/btQ+fOnZGamip1LI2h0qLNzs5GTEwM3N3d//8CtbTg7u6OiIiIEs1jw4YNGDRoEIyMjJSmh4eHo06dOrC3t8f48ePx9OnTYueRlZWFtLQ0pQf9s7fB09MTLi4uiIyMhJ2dndSRiEiFBg4ciLNnz+LBgwdo3749bt68KXUkjaDSon3y5Any8vJgYWGhNN3CwgIpKSlvfH1UVBSuXLmCMWPGKE339PTEr7/+itDQUCxduhQnT55Ez549iz1nLDAwECYmJoqHjY1N2Veqivj+++8xaNAgDBw4EAcPHuTh/0QaonXr1jh37hx0dXXRoUMHREdHSx2pyqvQRx1v2LABrVq1Qrt27ZSmDxo0CN7e3mjVqhV8fHxw6NAhnD9/HuHh4UXOJyAgAHK5XPG4d++eGtJXTEIIzJo1C1OmTMGMGTOwZcsWXkqRSMPY2toqrlXu5uaGY8eOSR2pSlNp0Zqbm0NbW7vQZwGpqamwtLR87WszMjIQFBSE0aNHv3E5jRo1grm5ORITE4t8Xl9fH8bGxkoPTZSTk4MRI0Zg6dKlWLlyJZYtWwYtrQr9txYRqYi5uTlCQ0Ph5uaGPn36YNu2bVJHqrJU+ltWT08PTk5OCA0NVUzLz89HaGgoXF1dX/vaPXv2ICsrC0OHDn3jcu7fv4+nT5/CysrqrTNXVenp6fD29sbOnTuxc+dOfP7551JHIiKJGRkZYd++ffj444/x8ccfY8WKFTz9RwVUfnrP1KlTMXz4cDg7O6Ndu3b47rvvkJGRgZEjRwIAhg0bhrp16yIwMFDpdRs2bICPjw9q1aqlND09PR3z589H//79YWlpiVu3bmHmzJlo0qQJPDw8VL06ldLjx4/Ru3dvXL9+HUeOHFE6OI2INJuuri42bNgAa2trzJgxAw8fPsSKFSu4t6scqbxoBw4ciMePH2Pu3LlISUmBo6MjQkJCFAdI3b17t9AbGh8fjzNnzuD3338vND9tbW3ExcVhy5YteP78OaytrdGjRw8sXLiQ59IWISUlBd27d8eTJ09w6tQptG7dWupIRFTByGQyLFq0CFZWVvjss8/w4sULrFu3jmVbTmRCA/cTpKWlwcTEBHK5vEp/Xvvw4UN069YNL168wIkTJ2Bvby91JCKq4H799VeMHDkSH3/8MTZs2ABtbW2pI6mUOvqAd++pou7du4du3bohKysLJ0+eRJMmTaSORESVwLBhw6Cjo4Nhw4YhJycHW7ZsgY4Oq+Jt8LtXBd27dw9ubm7Iy8vDyZMn0bBhQ6kjEVElMmTIEOjq6mLIkCHIy8vDtm3bWLZvgd+5Kub+/ftwc3NDfn4+Tp48iQYNGkgdiYgqoQEDBkBHRwcfffQRtLS08Ouvv7Jsy4ifdFchDx48QNeuXZGbm4uwsDCWLBG9lQ8++ABBQUHYvXs3RowYUezV9+j1WLRVREpKCrp27YqsrCyEh4fD1tZW6khEVAX0798fO3fuVFxAKD8/X+pIlQ73A1QBcrkcnp6eyMjIwOnTp/mZLBGVqwEDBiAvLw9DhgyBmZkZvvnmG8hkMqljVRos2kru1atX6Nu3L+7cuYPTp0+jUaNGUkcioipo0KBBePbsGSZOnAgLCwv4+/tLHanSYNFWYgV/YUZGRuKPP/5Ay5YtpY5ERFXYhAkT8OjRI8yaNQu1a9fGqFGjpI5UKbBoKykhBMaPH4/g4GDs378fHTp0kDoSEWmAefPmITU1FWPHjoW5uTm8vb2ljlTh8WCoSmru3LlYv349fvnlF/Tp00fqOESkIWQyGX788Uf069cPAwcOxOnTp6WOVOGxaCuhH374AYsWLcKyZcswYsQIqeMQkYbR1tbGtm3b0L59e3h5eSEuLk7qSBUai7aS2bVrFyZPnoxp06ZhxowZUschIg2lr6+Pffv2oXHjxvD09MTt27eljlRhsWgrkaioKAwfPhxDhgzBsmXLpI5DRBrO2NgYR44cgaGhIfr27Yv09HSpI1VILNpK4sGDB/Dx8UHr1q3xyy+/8PZVRFQhWFhYIDg4GElJSfj44495QYsi8Ld1JfDy5Uv4+PhAW1sb+/btg4GBgdSRiIgUWrRogR07duDAgQOYN2+e1HEqHBZtBSeEwOjRo3H16lUcOHAAlpaWUkciIiqkT58+CAwMxKJFixAUFCR1nAqF59FWcEuWLMHOnTuxe/dutGnTRuo4RETFmjlzJq5cuYKRI0eiSZMmcHZ2ljpShcAt2gosODgYX3zxBebOnYsBAwZIHYeI6LVkMhnWr18PBwcH+Pj4IDk5WepIFQKLtoK6fPkyfH190a9fP37mQUSVhoGBAfbt2wcA8PHxwatXryROJD0WbQWUlpaGfv36oXHjxtiyZQuPMCaiSsXKygoHDhxAXFwcJk2aJHUcyfE3eAUjhICfnx8ePXqE//3vfzAyMpI6EhFRqTk5OeHHH3/E+vXrsXPnTqnjSIpFW8GsX78eu3btwvr169G4cWOp4xARldmoUaMwZMgQ+Pn54ebNm1LHkYxMCCGkDqFuaWlpMDExgVwuh7GxsdRxFOLi4uDi4oIRI0ZgzZo1UschInprL168gJOTE4yMjBAREVHhrgOgjj7gFm0FkZ6ejo8++gj29vb49ttvpY5DRFQuatSogd27d+P69euYNm2a1HEkwaKtAAruLXv//n3s3r27wv3FR0T0NhwdHfHtt9/ip59+wm+//SZ1HLVj0VYAmzdvxrZt27Bu3TrY2dlJHYeIqNyNGzcOAwYMwOjRo/HXX39JHUet+BmtxJ/RXrt2Dc7OzhgyZAh++eUXSbMQEamSXC5HmzZtYGZmhrNnz0JPT0/qSPyMtqrLycnBsGHD0KBBA6xatUrqOEREKmViYoKgoCBcvHgRixcvljqO2rBoJbRs2TJcvHgRW7ZsQbVq1aSOQ0Skcm3btsXs2bPx9ddf4+LFi1LHUQvuOpZo1/Hly5fh5OSE6dOna9RfdkRE2dnZaNu2LYQQiI6OlnQXMncdV1E5OTkYPnw47OzseB1jItI4enp62LJlC65fv46FCxdKHUflWLQSCAwMRFxcHLZs2QJ9fX2p4xARqZ2joyPmzJmDwMBAREdHSx1HpbjrWM27jmNjY9G2bVvMmjVLI/6SIyIqTk5ODlxcXJCdnY2YmBhJNjy467iKyc7OxogRI9C8eXPMmTNH6jhERJLS1dXFli1bkJCQgPnz50sdR2VYtGoUGBiIq1evYvPmzRXi/DEiIqm1atUK8+bNw9KlS3H+/Hmp46gEdx2raddxYmIiWrRogenTp+Prr79WyzKJiCqD3NxctG3bFjo6Ovjzzz+hra2ttmVz13EVIYTApEmTYGVlhS+++ELqOEREFYqOjg5Wr16N6OjoKnmFPLUU7erVq2FrawsDAwO4uLggKiqq2LGbN2+GTCZTevz3IvtCCMydOxdWVlYwNDSEu7t7hb7X4YEDB3D06FF8//33vDAFEVER2rdvj5EjRyIgIABPnjyROk65UnnR7tq1C1OnTsW8efNw4cIFODg4wMPDA48ePSr2NcbGxkhOTlY87ty5o/T8smXLsGrVKqxduxaRkZEwMjKCh4cHXr16perVKbWMjAxMnjwZvXr1gre3t9RxiIgqrCVLlkAIgVmzZkkdpXwJFWvXrp2YOHGi4uu8vDxhbW0tAgMDixy/adMmYWJiUuz88vPzhaWlpVi+fLli2vPnz4W+vr7YuXNniTLJ5XIBQMjl8pKtxFuYPXu20NfXF4mJiSpfFhFRZffTTz8JACIiIkIty1NHH6h0i7bg3Ch3d3fFNC0tLbi7uyMiIqLY16Wnp6NBgwawsbFB3759cfXqVcVzSUlJSElJUZqniYkJXFxcXjtPKSQkJGD58uWYNWsWGjduLHUcIqIKz8/PD23atMGECROQl5cndZxyodKiffLkCfLy8mBhYaE03cLCAikpKUW+xt7eHhs3bsSBAwewbds25Ofno3379rh//z4AKF5XmnlmZWUhLS1N6aFqQgh89tlnqFevHvz9/VW+PCKiqkBbWxs//fQTLl68iHXr1kkdp1xUuKOOXV1dMWzYMDg6OqJLly7Yu3cvateu/Vbf8MDAQJiYmCgeNjY25Zi4aHv37sXvv/+OVatWwdDQUOXLIyKqKlxcXDBmzBh88cUXePz4sdRx3ppKi9bc3Bza2tpITU1Vmp6amgpLS8sSzUNXVxetW7dGYmIiACheV5p5BgQEQC6XKx737t0r7aqUSk5ODmbNmoWePXuiT58+Kl0WEVFVFBgYiPz8fCxatEjqKG9NpUWrp6cHJycnhIaGKqbl5+cjNDQUrq6uJZpHXl4eLl++DCsrKwBAw4YNYWlpqTTPtLQ0REZGFjtPfX19GBsbKz1U6ZdffsGtW7ewdOlSlS6HiKiqMjc3h7+/P9asWYOkpCSp47wdlR1m9X+CgoKEvr6+2Lx5s7h27Zrw8/MTpqamIiUlRQghxMcffyxmzZqlGD9//nxx7NgxcevWLRETEyMGDRokDAwMxNWrVxVjlixZIkxNTcWBAwdEXFyc6Nu3r2jYsKF4+fJliTKp8iizFy9eCAsLCzFs2LBynzcRkSZJT08XVlZWwtfXV2XLUMdRxzqqLvKBAwfi8ePHmDt3LlJSUuDo6IiQkBDFwUx3796Fltb/37D++++/MXbsWKSkpKBmzZpwcnLCuXPn0Lx5c8WYmTNnIiMjA35+fnj+/Dk6duyIkJCQQhe2kMJ3332Hv//+GwsWLJA6ChFRpWZkZIR58+Zh/PjxmD59OhwdHaWOVCa81nE57kZ+/PgxGjdujDFjxmDlypXlNl8iIk2Vk5ODFi1aoHHjxjh69Gi5z5/XOq5kvv76a8hkMsyePVvqKEREVYKuri4WL16MkJAQhIWFSR2nTFi05SQpKQk//fQTZs6cCXNzc6njEBFVGf3790fbtm3h7++PyrgTlkVbTubOnYtatWphypQpUkchIqpSZDKZ4n61//vf/6SOU2os2nIQHx+P7du3Y+7cuTAyMpI6DhFRldO1a1f06NEDX331FfLz86WOUyos2nKwdOlSWFpaYtSoUVJHISKqsubMmYOrV6/i4MGDUkcpFRbtW7p79y62bt2K6dOnQ19fX+o4RERVVseOHdGpUycsXry4Un1Wy6J9S9988w2MjY3h5+cndRQioipv9uzZiIqKqlRHILNo38KjR4+wfv16TJo0CdWrV5c6DhFRlefh4YHWrVtj8eLFUkcpMRbtW/j++++hpaWFzz77TOooREQaQSaTISAgAKGhoYiKipI6TomwaMtILpfjxx9/xLhx42BmZiZ1HCIijdGvXz/Y2dkhMDBQ6iglwqItozVr1uDVq1eYOnWq1FGIiDSKtrY2Zs2ahf379+Pq1atSx3kjFm0ZvHr1Ct9++y1GjhwJa2trqeMQEWkcX19f2NjYYNmyZVJHeSMWbRns2bMHjx49wueffy51FCIijaSnp4dJkyYhKCgIjx8/ljrOa7Foy2D16tV4//33YW9vL3UUIiKNNXLkSGhpaWHDhg1SR3ktFm0pxcTEIDIyEhMmTJA6ChGRRqtVqxYGDRqEtWvXIi8vT+o4xWLRltJPP/0EGxsb9OnTR+ooREQab+LEibhz5w4OHz4sdZRisWhL4dmzZ9ixYwfGjRsHHR0dqeMQEWk8Z2dntGvXDqtXr5Y6SrFYtKWwadMm5OXlYfTo0VJHISKi/zNhwgT8/vvvuHnzptRRisSiLaH8/HysWbMGAwYMgIWFhdRxiIjo/wwcOBC1atXCmjVrpI5SJBZtCf3++++4desWJk6cKHUUIiL6FwMDA4wePRqbNm1CZmam1HEKYdGW0M8//4x3330Xrq6uUkchIqL/GDduHORyOfbs2SN1lEJYtCXw7NkzHDp0CCNHjoRMJpM6DhER/UfDhg3RpUsXbN26VeoohbBoS2DPnj3Iy8vDoEGDpI5CRETFGDp0KE6cOIEHDx5IHUUJi7YEtm3bhh49esDS0lLqKEREVIz+/ftDT08PO3fulDqKEhbtGyQlJeHMmTMYOnSo1FGIiOg1TE1N4e3tjW3btkkdRQmL9g22b98OIyMj+Pj4SB2FiIjeYOjQobh06RIuX74sdRQFFu1rCCGwbds29OvXD0ZGRlLHISKiN/D09ISZmVmF2qpl0b5GTEwM4uPjuduYiKiS0NPTw8CBA7F9+3bk5+dLHQcAi/a1tm7dCktLS3Tr1k3qKEREVEIff/wxHjx4gPDwcKmjAGDRFis/Px979uzBoEGDeAMBIqJK5L333kPDhg2xa9cuqaMAYNEWKyYmBsnJyfjggw+kjkJERKUgk8ng4+ODQ4cOVYjdxyzaYhw4cABmZmZo37691FGIiKiUvL298fDhQ8TExEgdhUVbnODgYPTu3Zu7jYmIKqGOHTuiZs2aCA4OljoKi7YoSUlJuHz5Mvr27St1FCIiKgMdHR307t2bRVtRBQcHQ09PDz169JA6ChERlZG3tzfi4uKQlJQkaQ4WbRGCg4PRrVs31KhRQ+ooRERURh4eHtDV1cXBgwclzcGi/Y+///4bJ0+e5G5jIqJKztjYGN26dZN897Fainb16tWwtbWFgYEBXFxcEBUVVezY9evXo1OnTqhZsyZq1qwJd3f3QuNHjBgBmUym9PD09CyXrEePHkVeXh769OlTLvMjIiLpeHt74+TJk3j+/LlkGVRetLt27cLUqVMxb948XLhwAQ4ODvDw8MCjR4+KHB8eHo7BgwcjLCwMERERsLGxQY8ePQrdX9DT0xPJycmKR3ndFuno0aNo3bo16tWrVy7zIyIi6fTp0we5ubn4448/JMug8qJduXIlxo4di5EjR6J58+ZYu3YtqlWrho0bNxY5fvv27ZgwYQIcHR3xzjvv4JdffkF+fj5CQ0OVxunr68PS0lLxqFmz5ltnFUIgLCwM3bt3f+t5ERGR9OrXr48mTZogLCxMsgwqLdrs7GzExMTA3d39/y9QSwvu7u6IiIgo0TwyMzORk5MDMzMzpenh4eGoU6cO7O3tMX78eDx9+vSt8yYmJuLBgwdwc3N763kREVHF0LVr16pbtE+ePEFeXh4sLCyUpltYWCAlJaVE8/D394e1tbVSWXt6euLXX39FaGgoli5dipMnT6Jnz57Iy8srch5ZWVlIS0tTehQlPDwc2tra6NSpUwnXkIiIKjo3Nzdcv34dqampkiy/Ql/2aMmSJQgKCkJ4eDgMDAwU0wcNGqT4/1atWuHdd99F48aNER4eXuRu38DAQMyfP/+NywsLC4OTkxOMjY3LZwWIiEhyXbt2BfDPxtTAgQPVvnyVbtGam5tDW1u70F8RqampsLS0fO1rV6xYgSVLluD333/Hu++++9qxjRo1grm5ORITE4t8PiAgAHK5XPG4d+9eoTEFn88WvCFERFQ1WFlZwd7eXrLdxyotWj09PTg5OSkdyFRwYJOrq2uxr1u2bBkWLlyIkJAQODs7v3E59+/fx9OnT2FlZVXk8/r6+jA2NlZ6/Fd8fDxSUlL4+SwRURUk5ee0Kj/qeOrUqVi/fj22bNmC69evY/z48cjIyMDIkSMBAMOGDUNAQIBi/NKlSzFnzhxs3LgRtra2SElJQUpKCtLT0wEA6enpmDFjBv7880/cvn0boaGh6Nu3L5o0aQIPD48y5wwLC4OOjg46duz4ditMREQVTteuXZGQkICHDx+qfdkqL9qBAwdixYoVmDt3LhwdHREbG4uQkBDFAVJ3795FcnKyYvyaNWuQnZ2NDz/8EFZWVorHihUrAADa2tqIi4uDt7c37OzsMHr0aDg5OeH06dPQ19cvc86wsDC0bdsW1atXf7sVJiKiCqdgb6UUW7UyIYRQ+1IllpaWBhMTE8jlchgbG0MIAWtra4wYMQKBgYFSxyMiIhVo0aIFOnXqhLVr1yqm/bcPVIHXOgbw8OFDpKSkoF27dlJHISIiFWnbti2io6PVvlwWLYCYmBgAKNGBV0REVDk5OzsjLi4OWVlZal0uixZAdHQ0ateuzesbExFVYU5OTsjJycGVK1fUulwWLf7ZonV2doZMJpM6ChERqYiDgwO0tLQUezHVReOLVgiB6OhoODk5SR2FiIhUqFq1amjRooXaP6fV+KJ98OABHj16xM9niYg0gJOTE7do1a3gLxsWLRFR1efs7IzLly+r9YAojS/amJgYWFhYwNraWuooRESkYgUHRF2+fFlty9T4or1w4QKcnJx4IBQRkQZwcHCAtra2Wncfa3zRXr9+HS1atJA6BhERqYGhoSEaNWqEGzduqG2ZGl20WVlZuH37Nuzs7KSOQkREamJvb4+EhAS1LU+ji/avv/6CEAL29vZSRyEiIjWxs7NDfHy82pan0UVbcKN4btESEWkOe3t7JCUlITs7Wy3L0+iivXnzJkxMTFCnTh2poxARkZrY2dkhPz8ft27dUsvyNLpoExMTYWdnxyOOiYg0SMHHher6nJZFy93GREQaxdLSEtWrV2fRqsPNmzd5IBQRkYaRyWSwt7dX2wFRGl20z5494xYtEZEGUueRxxpdtADQsGFDqSMQEZGaNWrUCHfu3FHLsjS+aOvWrSt1BCIiUjNra2ukpKQgPz9f5cvS+KK1sLCQOgIREamZlZUVcnJy8OzZM5UvS6OLtnbt2tDR0ZE6BhERqVnBHdtSUlJUviyNLlpLS0upIxARqdSpU6fg5eUFa2tryGQy7N+/X+pIFYKVlRUAIDk5WeXLYtESEVVQubm5bz2PjIwMODg4YPXq1eWQqOoo+P2fmpqq8mVpdNEW/EVDRCS127dvQyaTYffu3ejUqRP09fURHBz81vPt2bMnFi1ahA8++KAcUlYdenp6qF27NrdoVY1btERUUVy6dAkAsHz5csydOxdXr15F9+7dFc8vXrwY1atXf+3j7t27UsWvlKysrNSyRavRRwKxaImoooiNjYWRkRH27NkDW1vbQs+PGzcOH3300WvnUXCAD5WMtbW1WrZoNbpoedceIqooLl26BG9v7yJLFgDMzMxgZmam3lBVnKWlJa5evary5Wj0rmNjY2OpIxARAfhni9bNza3Y57nruPwZGxvjxYsXKl+ORm/RVq9eXeoIRERIS0vD7du30bp162LHcNdx+atRowbS09NVvhyNLtoaNWpIHYGICJcuXYK2tjZatWpV7Jiy7jpOT09HYmKi4uukpCTExsbCzMwM9evXL1PeqqJGjRrIyMhQ+XI0umi5RUtEFcGlS5dgb28PAwODcp93dHQ0unbtqvh66tSpAIDhw4dj8+bN5b68yqRGjRpq2XUsE0IIlS+lgklLS4OJiQnu3buHevXqSR2HiIgksHXrVgwbNgwAIJfLVXbcjkYfDGVkZCR1BCIikoi69mpqdNFqa2tLHYGIiCSiruN0NLpoiYhIc7FoiYiIVIhFS0REpEL6+vpqWY5ainb16tWwtbWFgYEBXFxcEBUV9drxe/bswTvvvAMDAwO0atUKR44cUXpeCIG5c+fCysoKhoaGcHd3x82bN1W5CkREVMWo6zgdlRftrl27MHXqVMybNw8XLlyAg4MDPDw88OjRoyLHnzt3DoMHD8bo0aNx8eJF+Pj4wMfHB1euXFGMWbZsGVatWoW1a9ciMjISRkZG8PDwwKtXr1S9OkREVEVoaalnp67Kz6N1cXFB27Zt8eOPPwIA8vPzYWNjg88++wyzZs0qNH7gwIHIyMjAoUOHFNPee+89ODo6Yu3atRBCwNraGtOmTcP06dMB/HP+k4WFBTZv3oxBgwa9MVPBebSqPG+KqCITQiAzM1PqGESSevDgAezt7QGo9jxalV4ZKjs7GzExMQgICFBM09LSgru7OyIiIop8TUREhOLKJQU8PDywf/9+AP9cPiwlJQXu7u6K501MTODi4oKIiIgiizYrKwtZWVmKr9PS0t5mtYgqvczMTF4ZjUhNVLrd/OTJE+Tl5cHCwkJpuoWFBVJSUop8TUpKymvHF/y3NPMMDAyEiYmJ4mFjY1Om9SEiIiotjbjWcUBAgNJWclpaGsuWNFq1atXUctcSoors/v37eOedd1S+HJUWrbm5ObS1tZGamqo0PTU1FZaWlkW+xtLS8rXjC/6bmpoKKysrpTGOjo5FzlNfX19th3ETVQYymYyXICWNp4qbOBRFpbuO9fT04OTkhNDQUMW0/Px8hIaGwtXVtcjXuLq6Ko0HgOPHjyvGN2zYEJaWlkpj0tLSEBkZWew8iYiI/is/P18ty1H5ruOpU6di+PDhcHZ2Rrt27fDdd98hIyMDI0eOBAAMGzYMdevWRWBgIABg8uTJ6NKlC7755hv07t0bQUFBiI6Oxs8//wzgn7/Ep0yZgkWLFqFp06Zo2LAh5syZA2tra/j4+Kh6dYiIqIrIzc1Vy3JUXrQDBw7E48ePMXfuXKSkpMDR0REhISGKg5nu3r2rdC5T+/btsWPHDnz55ZeYPXs2mjZtiv3796Nly5aKMTNnzkRGRgb8/Pzw/PlzdOzYESEhIWrbDUBERJWfOm76Dmj4/Wh5Hi0RkeY6ffo0OnfuDID3o1UZDfwbg4iI/s+LFy/UshyNLtrs7GypIxARkUTUdYqbRhctzyMkItJc3KJVA3V9k4mIqOJ58eIFDA0NVb4cjS5abtESEWmuFy9eqOWa3xpdtOo6tJuIiCqe9PR01KhRQ+XL0eii5a5jIiLNxS1aNXj69KnUEYiISCJPnz6Fqampypej0UX735sXEBGR5nj48GGxN7gpTxpdtMXdv5aIiKq+5ORkpbvAqQqLloiINI4Qglu06sCiJSLSTGlpaXj58iWLVtWSk5OljkBERBJ4+PAhALBoVY1btEREmolFqyaZmZk8l5aISAMV7NFk0apBwV81RESkOR4+fAgTExNUq1ZN5cvS+KK9f/++1BGIiEjNHjx4AGtra7UsS6OLVktLCzdv3pQ6BhERqVlCQgKaNm2qlmVpdNHa2toiISFB6hhERKRmCQkJsLOzU8uyNLpomzZtyqIlItIwWVlZuH37Nuzt7dWyPI0u2iZNmiA+Pl7qGEREpEa3bt1Cfn4+t2jVoWnTpkhKSkJ2drbUUYiISE0KNrC4RasGTZo0QV5eHv766y+poxARkZokJCTA2NgYderUUcvyNL5oAfBzWiIiDRIfHw87OzvIZDK1LE+ji9bS0hLVq1fn57RERBokISFBbbuNAQ0vWplMBjs7OxYtEZGGEEIotmjVRaOLFgBatWqFS5cuSR2DiIjU4OHDh3jy5AlatWqltmVqfNE6OzsjLi6ORx4TEWmA6OhoAP/87lcXjS9aJycnZGdn48qVK1JHISIiFYuJiUHt2rVRr149tS1T44vWwcEB2trair9yiIio6oqJiYGzs7PajjgGWLSoVq0amjdvjpiYGKmjEBGRCgkhEB0dDScnJ7UuV+OLFvhnXz23aImIqrYHDx7g0aNHav18FmDRAvjnc9rLly8jKytL6ihERKQiBRtU3KKVgLOzM3JycnD58mWpoxARkYrExMTAwsICdevWVetyWbQA3n33XR4QRURUxRV8PqvOA6EAFi0AwNDQEA4ODjh37pzUUYiISAXy8vLw559/wsXFRe3LZtH+Hzc3N4SFhUEIIXUUIiIqZ5cuXcLz58/h5uam9mWrtGifPXsGX19fGBsbw9TUFKNHj0Z6evprx3/22Wewt7eHoaEh6tevj0mTJkEulyuNk8lkhR5BQUFvlbVr1664f/8+bt269VbzISKiiicsLAwGBgaSbNHqqHLmvr6+SE5OxvHjx5GTk4ORI0fCz88PO3bsKHL8w4cP8fDhQ6xYsQLNmzfHnTt3MG7cODx8+BC//fab0thNmzbB09NT8bWpqelbZe3UqRO0tLQQHh6uuH0eERFVDWFhYejQoQP09fXVvmyZUNG+0uvXr6N58+Y4f/684pylkJAQ9OrVC/fv34e1tXWJ5rNnzx4MHToUGRkZ0NH55+8CmUyGffv2wcfHp0zZ0tLSYGJiArlcDmNjY8X0du3aoWnTpti+fXuZ5ktERBVPbm4uzMzM4O/vjy+++ELpueL6oDypbNdxREQETE1NlU4Mdnd3h5aWFiIjI0s8n4KVLyjZAhMnToS5uTnatWuHjRs3vvaz1aysLKSlpSk9itK1a1d+TktEVMVcuHABL168QNeuXSVZvsqKNiUlBXXq1FGapqOjAzMzM6SkpJRoHk+ePMHChQvh5+enNH3BggXYvXs3jh8/jv79+2PChAn44Ycfip1PYGAgTExMFA8bG5six7m5uSE5ORkJCQklykdERBVfeHg4qlWrpvYrQhUoddHOmjWryIOR/v24cePGWwdLS0tD79690bx5c3z11VdKz82ZMwcdOnRA69at4e/vj5kzZ2L58uXFzisgIAByuVzxuHfvXpHjOnbsCG1tbYSHh791fiIiqhjCwsLQsWNH6OnpSbL8Uh8MNW3aNIwYMeK1Yxo1agRLS0s8evRIaXpubi6ePXsGS0vL177+xYsX8PT0RI0aNbBv3z7o6uq+dryLiwsWLlyIrKysIj/o1tfXL9EH4DVq1EDbtm0RFhaGTz755I3jiYioYsvJycHp06fx5ZdfSpah1EVbu3Zt1K5d+43jXF1d8fz5c8TExCiuK3nixAnk5+e/9vDqtLQ0eHh4QF9fH8HBwTAwMHjjsmJjY1GzZs1yOZqse/fuWLt2LXJzcwt9LkxERJXLuXPnkJGRge7du0uWQWWf0TZr1gyenp4YO3YsoqKicPbsWXz66acYNGiQ4ojjBw8e4J133kFUVBSAf0q2R48eyMjIwIYNG5CWloaUlBSkpKQgLy8PAHDw4EH88ssvuHLlChITE7FmzRosXrwYn332Wbnk9vLywtOnTxEREVEu8yMiIukEBwfDyspK7TcS+DeVbrJt374dn376Kbp37w4tLS30798fq1atUjyfk5OD+Ph4ZGZmAvjnyLCCI5L/ey5rUlISbG1toauri9WrV+Pzzz+HEAJNmjTBypUrMXbs2HLJ3LZtW1haWiI4OBidOnUql3kSEZH6CSFw4MABeHl5QUtLugshquw82orsTedN+fn5ITw8HPHx8Wq/+DQREZWPa9euoUWLFjh06BB69+5d5JhKfR5tZebt7Y2bN28iPj5e6ihERFRGwcHBqFatGrp16yZpDhZtEbp3745q1aohODhY6ihERFRGwcHB8PDwgKGhoaQ5WLRFMDQ0RI8ePXDgwAGpoxARURmkpqbizz//hLe3t9RRWLTF8fb2RkRERKFzgYmIqOI7dOgQABT72aw6sWiLUfDmHD58WOIkRERUWsHBwWjfvn2JrvugaizaYtSpUwcdO3bE7t27pY5CRESlIJfLcezYsTLf4a28sWhfw9fXF8ePH0dqaqrUUYiIqIT+97//ITs7G4MHD5Y6CgAW7WsNGDAAWlpaCAoKkjoKERGV0NatW9GtWzfUrVtX6igAWLSvZWZmht69e2Pbtm1SRyEiohK4e/cuwsPDMXToUKmjKLBo32Do0KGIjo4ul1v/ERGRau3cuRMGBgbo16+f1FEUWLRv0Lt3b5iamnKrloioghNCYOvWrfDx8VHZ5RTLgkX7BgYGBhgwYAC2bduG/Px8qeMQEVExLl26hKtXr1ao3cYAi7ZEhg4dijt37uDs2bNSRyEiomJs27YN5ubm6NGjh9RRlLBoS6Bjx46oX78+tm7dKnUUIiIqQl5eHnbs2IFBgwZBV1dX6jhKWLQloKWlheHDh2Pnzp148eKF1HGIiOg/Dh8+jOTkZAwfPlzqKIWwaEvIz88PL1++5FYtEVEFtHr1arRr1w7Ozs5SRymERVtC9erVg7e3N1avXg0hhNRxiIjo/yQkJOD333/HhAkTpI5SJBZtKUycOBHXrl3DqVOnpI5CRET/Z+3atahVqxYGDhwodZQisWhLoVu3brC3t8fq1auljkJERAAyMzOxadMmjB49GgYGBlLHKRKLthRkMhkmTJiAffv24eHDh1LHISLSeDt27IBcLse4ceOkjlIsFm0pDR8+HPr6+li/fr3UUYiINJoQAqtXr0bv3r3RsGFDqeMUi0VbSiYmJhg6dCjWrVuHnJwcqeMQEWmsP//8E7GxsRX2IKgCLNoymDBhApKTk7F3716poxARaawff/wRjRs3hoeHh9RRXotFWwbvvvsuunfvjqVLl/JUHyIiCfz111/YtWsXJk+eDC2til1lFTtdBTZ79mxcvHgRx44dkzoKEZHGWb58OWrVqoUxY8ZIHeWNWLRl1LVrV7i4uGDx4sVSRyEi0ijJycnYuHEjpkyZAkNDQ6njvBGLtoxkMhkCAgJw+vRpnDlzRuo4REQaY+XKlTAwMKjwB0EVYNG+BS8vL7Ro0QKBgYFSRyEi0gjPnj3DmjVr8Omnn8LExETqOCXCon0LWlpaCAgIwJEjRxAbGyt1HCKiKu+HH35AXl4eJk+eLHWUEmPRvqWBAweiYcOG3KolIlKx9PR0rFq1CmPHjkWdOnWkjlNiLNq3pKOjA39/f+zZswcJCQlSxyEiqrJ+/vlnpKWlYfr06VJHKRUWbTkYPnw4rKysMH/+fKmjEBFVSenp6Vi6dCk+/vhj1K9fX+o4pcKiLQcGBgb46quvsGPHDly8eFHqOEREVc7KlSshl8vx1VdfSR2l1Fi05WTkyJGwt7dHQECA1FGIiKqUR48eYfny5Zg4cWKl25oFWLTlRkdHB4sXL8axY8dw4sQJqeMQEVUZX3/9NbS0tDB79mypo5QJi7YcffDBB3BxcYG/vz+vgUxEVA7++usvrFmzBv7+/qhVq5bUccqERVuOZDIZli5diujoaPz2229SxyEiqvTmzp0Lc3PzSnXe7H+ptGifPXsGX19fGBsbw9TUFKNHj0Z6evprX+Pm5gaZTKb0GDdunNKYu3fvonfv3qhWrRrq1KmDGTNmIDc3V5WrUmJdunRBz5498cUXX/B+tUREbyE2Nhbbt2/HvHnzYGRkJHWcMlNp0fr6+uLq1as4fvw4Dh06hFOnTsHPz++Nrxs7diySk5MVj2XLlimey8vLQ+/evZGdnY1z585hy5Yt2Lx5M+bOnavKVSmVwMBAJCYmYsOGDVJHISKqtAICAmBnZ4dRo0ZJHeXtCBW5du2aACDOnz+vmHb06FEhk8nEgwcPin1dly5dxOTJk4t9/siRI0JLS0ukpKQopq1Zs0YYGxuLrKysEmWTy+UCgJDL5SUaXxYff/yxsLCwEM+fP1fZMoiIqqpjx44JAGLPnj0qXY46+kBlW7QREREwNTWFs7OzYpq7uzu0tLQQGRn52tdu374d5ubmaNmyJQICApCZmak031atWsHCwkIxzcPDA2lpabh69WqR88vKykJaWprSQ9UWL16M9PR0zJs3T+XLIiKqSrKysvDZZ5+hS5cu6N+/v9Rx3prKijYlJaXQtSh1dHRgZmaGlJSUYl83ZMgQbNu2DWFhYQgICMDWrVsxdOhQpfn+u2QBKL4ubr6BgYEwMTFRPGxsbMq6WiVWr149zJs3Dz/88AMuXbqk8uUREVUVK1euxK1bt7B69WrIZDKp47y1UhftrFmzCh2s9N/HjRs3yhzIz88PHh4eaNWqFXx9ffHrr79i3759uHXrVpnnGRAQALlcrnjcu3evzPMqjcmTJ8Pe3h4TJ05Efn6+WpZJRFSZ3blzBwsXLsSUKVPQokULqeOUC53SvmDatGkYMWLEa8c0atQIlpaWePTokdL03NxcPHv2DJaWliVenouLCwAgMTERjRs3hqWlJaKiopTGpKamAkCx89XX14e+vn6Jl1le9PT0sHr1anTr1g1bt27F8OHD1Z6BiKgy+fzzz1GzZs0q9bFbqYu2du3aqF279hvHubq64vnz54iJiYGTkxMA4MSJE8jPz1eUZ0kU3OfVyspKMd+vv/4ajx49UuyaPn78OIyNjdG8efNSro3qde3aFYMHD8aMGTPQt29fmJqaSh2JiKhCOnr0KPbt24egoCDUqFFD6jjlR2WHWQkhPD09RevWrUVkZKQ4c+aMaNq0qRg8eLDi+fv37wt7e3sRGRkphBAiMTFRLFiwQERHR4ukpCRx4MAB0ahRI9G5c2fFa3Jzc0XLli1Fjx49RGxsrAgJCRG1a9cWAQEBJc6ljqPM/u3BgweievXq4tNPP1XL8oiIKpuXL1+Kxo0bi27duon8/Hy1LVcdfaDSon369KkYPHiwqF69ujA2NhYjR44UL168UDyflJQkAIiwsDAhhBB3794VnTt3FmZmZkJfX180adJEzJgxo9A34Pbt26Jnz57C0NBQmJubi2nTpomcnJwS51J30QohxDfffCO0tLTEhQsX1LZMIqLKYuHChUJHR0dcu3ZNrctVRx/IhNC8i/KmpaXBxMQEcrkcxsbGallmTk4OWrdujWrVquHcuXPQ0Sn1Xnsioirp5s2bePfddzFp0iQsXbpUrctWRx/wWsdqoquri19++QUxMTH45ptvpI5DRFQh5OXlYeTIkahbt26FusJfeWLRqtF7772H6dOnY+7cucVeXIOISJN8//33OHfuHDZt2lSpr2f8Otx1rKZdxwVevXqFNm3awMjICBEREdyFTEQa68aNG2jdujXGjx+PlStXSpKBu46rIAMDA2zevBkXLlxQulkCEZEmycvLw4gRI2BjY4NFixZJHUelWLQSaNeuHfz9/fHVV1/h8uXLUschIlK7b775BlFRUdi8eTOqVasmdRyV4q5jNe86LpCVlQUnJyfo6ekhMjISurq6kuQgIlK3a9euoXXr1pg0aRKWL18uaRbuOq7C9PX1sWXLFsTFxSEwMFDqOEREapGbm4vhw4ejUaNGWLBggdRx1IJFKyEnJyfMnj0bCxcuxJ9//il1HCIilVuwYAEuXLiAzZs3w9DQUOo4asGildicOXPQtm1bDBo0CH///bfUcYiIVCY0NBSLFi3C/PnzS3XN+8qORSsxXV1d7Ny5E2lpaRg1ahQ08CNzItIAKSkp8PX1Rffu3REQECB1HLVi0VYADRo0wKZNm7B//3788MMPUschIipXeXl5GDp0KABg27Zt0NbWljiRerFoK4i+fftiypQpmD59OqKjo6WOQ0RUbgIDA3HixAls374dFhYWUsdRO57eI9HpPUXJzs5Ghw4d8OzZM1y4cAEmJiZSRyIieisnT55Et27d8OWXX2L+/PlSxymEp/doGD09PezatQtPnjzBmDFj+HktEVVqjx8/xpAhQ9CpU6cqe8OAkmDRVjCNGjXCxo0b8dtvv+Gnn36SOg4RUZnk5eVh2LBhyMnJwY4dOzTuc9l/Y9FWQP3798ekSZMwZcoUnDx5Uuo4RESl9sUXX+D333/Htm3bYG1tLXUcSbFoK6gVK1agc+fO6N+/P5KSkqSOQ0RUYtu2bcPSpUuxfPly9OjRQ+o4kmPRVlC6urrYs2cPTE1N4e3tjRcvXkgdiYjojSIjIzFmzBiMGDECn3/+udRxKgQWbQVmZmaG4OBg3LlzB0OHDkV+fr7UkYiIinX//n34+PjAyckJa9euhUwmkzpShcCireCaN2+OoKAgHDx4EF9++aXUcYiIipSZmQkfHx/o6upi79690NfXlzpShcGirQR69eqFpUuXIjAwEDt27JA6DhGREiEERo8ejevXr+PAgQMaeVGK19GROgCVzPTp03H58mWMHj0aTZs2Rdu2baWOREQEAFi8eDGCgoLw22+/oXXr1lLHqXC4RVtJyGQy/Pzzz3B0dISXlxdu3boldSQiImzbtg1ffvklvvrqK/Tv31/qOBUSi7YSMTAwQHBwMExMTNCjRw+kpKRIHYmINNjRo0cxcuRIjBo1SqOv/PQmLNpKpnbt2jh27BhevXqFnj17Qi6XSx2JiDTQn3/+iQ8//BC9evXCunXreITxa7BoKyFbW1uEhITg9u3b6Nu3L169eiV1JCLSINevX0fv3r3Rpk0bBAUFQUeHh/u8Dou2kmrVqhUOHjyIyMhI+Pr6Ii8vT+pIRKQB7t27hx49eqBu3bo4ePAgDA0NpY5U4bFoK7GOHTti9+7dOHDgACZMmMC7/RCRSj19+hQeHh7Q0dFBSEgITE1NpY5UKbBoKzkvLy+sX78eP//8M+bNmyd1HCKqojIyMtCnTx88fvwYx44d0/gbBZQGd6xXASNHjsTjx4/h7++P6tWrY+bMmVJHIqIq5OXLl+jbty+uXLmCsLAw2NnZSR2pUmHRVhEzZsxAeno6/P39oaWlhenTp0sdiYiqgIKSjYiIwNGjR+Hs7Cx1pEqHRVtFyGQyzJ8/H/n5+ZgxYwa0tbV55wwieiuvXr2Cj48Pzpw5gyNHjqBz585SR6qUWLRViEwmw8KFC5GXl4epU6cCAMuWiMrk5cuX6NevH06fPo1Dhw7Bzc1N6kiVFou2ipHJZFi8eDEAYOrUqcjJyeFntkRUKpmZmejbty/Onj2LgwcPolu3blJHqtRYtFVQQdnq6urC398f2dnZvMUeEZVIeno6vLy8cP78eRw9ehRdunSROlKlx6KtomQyGRYsWABdXV3MmTMH2dnZmD9/Pi+TRkTFSktLQ+/evREbG4uQkBB07NhR6khVAou2ipszZw709PQwa9YsPH36FKtWrYK2trbUsYiogklOTkbPnj1x+/ZtHD9+HO+9957UkaoMlV6w4tmzZ/D19YWxsTFMTU0xevRopKenFzv+9u3bkMlkRT727NmjGFfU80FBQapclUrN398f69evx9q1a/HRRx/x2shEpCQhIQHt27fH48ePcfr0aZZsOVNp0fr6+uLq1as4fvw4Dh06hFOnTsHPz6/Y8TY2NkhOTlZ6zJ8/H9WrV0fPnj2Vxm7atElpnI+PjypXpdIbM2YM9u3bhyNHjsDDwwPPnz+XOhIRVQBRUVHo0KEDDAwMEBERgVatWkkdqeoRKnLt2jUBQJw/f14x7ejRo0Imk4kHDx6UeD6Ojo5i1KhRStMAiH379pU5m1wuFwCEXC4v8zwqq7NnzwozMzPRsmVLcf/+fanjEJGEjhw5IqpVqyZcXV3FkydPpI4jCXX0gcq2aCMiImBqaqp0FRF3d3doaWkhMjKyRPOIiYlBbGwsRo8eXei5iRMnwtzcHO3atcPGjRtfe0H9rKwspKWlKT00Vfv27XHmzBnI5XK4urri+vXrUkciIgn8+uuv8Pb2Rvfu3fHHH3+gVq1aUkeqslRWtCkpKahTp47SNB0dHZiZmSElJaVE89iwYQOaNWuG9u3bK01fsGABdu/ejePHj6N///6YMGECfvjhh2LnExgYCBMTE8XDxsam9CtUhTRr1gwREREwMTFBhw4dcO7cOakjEZGaCCGwdOlSDB8+HCNGjMDevXtRrVo1qWNVbaXdBPb39xcAXvu4fv26+Prrr4WdnV2h19euXVv89NNPb1xOZmamMDExEStWrHjj2Dlz5oh69eoV+/yrV6+EXC5XPO7du6exu47/7e+//xadO3cWBgYGYseOHVLHISIVy8rKEp988okAIObOnSvy8/OljiQ5dew6LvXpPdOmTcOIESNeO6ZRo0awtLTEo0ePlKbn5ubi2bNnsLS0fONyfvvtN2RmZmLYsGFvHOvi4oKFCxciKysL+vr6hZ7X19cvcrqmMzU1xbFjx+Dn54chQ4YgLi4OixYt4uk/RFXQo0eP0L9/f0RGRmLDhg0YNWqU1JE0RqmLtnbt2qhdu/Ybx7m6uuL58+eIiYmBk5MTAODEiRPIz8+Hi4vLG1+/YcMGeHt7l2hZsbGxqFmzJsu0DAwMDLBlyxY4ODhg5syZiIuLw44dO2BiYiJ1NCIqJxcvXkTfvn2RnZ2N8PDwQh/HkWqp7DPaZs2awdPTE2PHjkVUVBTOnj2LTz/9FIMGDVLcMPjBgwd45513EBUVpfTaxMREnDp1CmPGjCk034MHD+KXX37BlStXkJiYiDVr1mDx4sX47LPPVLUqVZ5MJsO0adNw5MgRnDt3Di4uLoiPj5c6FhGVg6CgIHTo0AEWFhaIjo5myUpBZTulhRBPnz4VgwcPFtWrVxfGxsZi5MiR4sWLF4rnk5KSBAARFham9LqAgABhY2Mj8vLyCs3z6NGjwtHRUVSvXl0YGRkJBwcHsXbt2iLHFkeTT+95k4SEBNGsWTNhYmIijhw5InUcIiqj3NxcMWvWLAFA+Pr6iszMTKkjVUjq6AOZEK85L6aKSktLg4mJCeRyOYyNjaWOU+GkpaXB19cXhw8fxpIlSzBjxgxeI5moEpHL5fD19cXRo0exdOlSTJs2jT/DxVBHH6j0ylBUORkbG+PAgQMICAiAv78/BgwYwCtJEVUSFy9eRNu2bXHmzBkcPnwY06dPZ8lKjEVLRdLS0sLXX3+N//3vfwgNDYWjoyP+/PNPqWMRUTGEEFi1ahXee+89VK9eHefPn4enp6fUsQgsWnqDfv364eLFi7C2tkbHjh2xdOlS5OfnSx2LiP7l6dOn8PHxweTJkzF+/HhERESgadOmUsei/8OipTeytbXFyZMnMXPmTAQEBKBnz55ITU2VOhYRATh9+jQcHR1x5swZHDhwAN999x1PdaxgWLRUIrq6uli8eDGOHTuG2NhYODg44I8//pA6FpHGysvLw8KFC+Hm5oaGDRvi0qVL8Pb2ljoWFYFFS6Xy/vvv49KlS3j33XfRo0cPzJ49G9nZ2VLHItIoDx48wPvvv4958+bhyy+/xIkTJ1CvXj2pY1ExWLRUapaWlggJCUFgYCCWL1+Otm3b4uLFi1LHIqryhBDYtGkTWrRogRs3biA0NBTz58+Hjk6pL/JHasSipTLR0tKCv78/oqKiIJPJ0LZtW8yZMwdZWVlSRyOqku7du4eePXti1KhR6Nu3L65cuYKuXbtKHYtKgEVLb6V169aIiorC3LlzsWTJEjg5OSE6OlrqWERVhhAC69evR4sWLXDlyhUcOnQIW7ZsgZmZmdTRqIRYtPTW9PT0MHfuXERHR0NPTw/vvfceAgIC8OrVK6mjEVVqd+7cgYeHB/z8/DBgwABcuXIFvXv3ljoWlRKLlsqNg4MDIiMjMX/+fHzzzTdo06YNIiMjpY5FVOnk5+dj3bp1aNmyJa5fv46jR49iw4YNMDU1lToalQGLlsqVrq4uvvjiC1y4cAFGRkZwdXXFuHHj8PTpU6mjEVUKFy5cQMeOHTFu3DgMGTIEV69e5RWeKjkWLalEy5YtERERge+++w47d+6EnZ0d1q1bh7y8PKmjEVVIz549w4QJE+Ds7IwXL14gLCwM69at441PqgAWLamMjo4OJk2ahISEBPTt2xfjxo1Du3btEBERIXU0ogojLy8PP//8M+zs7LB9+3Z8++23uHDhAtzc3KSORuWERUsqZ2FhgY0bNyoKtn379hg5ciQv40ga788//4SLiws++eQTeHl5ISEhAZMnT4aurq7U0agcsWhJbd577z1ERUVh7dq1CA4Ohp2dHb7//nteWYo0TkpKCkaPHg1XV1fk5+fj7Nmz2LRpEywsLKSORirAoiW10tbWxieffIKEhAQMGTIEn3/+OZo1a4YdO3bwrkBU5cnlcnz55Zdo3Lgx9u3bhzVr1uD8+fNo37691NFIhVi0JIlatWphzZo1iIuLQ8uWLeHr64vWrVvj8OHDEEJIHY+oXL18+RLLly9Ho0aNsHLlSkyaNAm3bt3CuHHjoK2tLXU8UjEWLUmqZcuWOHDgAM6dOwdTU1P06dMHnTt3xpkzZ6SORvTWcnNzsX79ejRt2hSzZ8/GwIEDcevWLQQGBqJmzZpSxyM1YdFSheDq6orw8HAcPXoU6enp6NSpE7y8vBAXFyd1NKJSy8/Px549e9CiRQv4+fmhc+fOuH79On766SdYWVlJHY/UjEVLFYZMJoOnpydiYmKwc+dO3LhxA46Ojvjoo48QExMjdTyiN8rLy8OuXbvg5OSEjz76CE2aNMHFixexY8cONGnSROp4JBEWLVU4WlpaGDRoEK5du4Z169YhJiYGzs7O6NGjB8LCwvgZLlU4r169wrp162Bvb49Bgwahdu3aOHnyJA4fPgxHR0ep45HEWLRUYenq6mLs2LGIj49HUFAQHj9+jG7duuG9997Dvn37eJQySS4tLQ3Lli1Dw4YNMX78eLRp0wbR0dH4/fff0blzZ6njUQXBoqUKT0dHBwMHDsSFCxcQEhICQ0ND9OvXDy1atMDmzZt5Hi6pXWpqKmbPno369evjyy+/RJ8+fXDjxg3s3r0bTk5OUsejCoZFS5WGTCaDh4cHwsPDce7cOdjb22PkyJFo1KgRFi5ciOTkZKkjUhUXHR2NUaNGwdbWFj/88APGjh2LpKQkrF+/HnZ2dlLHowpKJjTwA6+0tDSYmJhALpfzgt2V3LVr1/Dtt99ix44dyM7OxgcffIDx48fDzc0NMplM6nhUBWRmZiIoKAhr1qxBdHQ06tevj3HjxmHcuHE8RacKUEcfcIuWKrXmzZtj/fr1ePjwIVauXInLly+jW7duaN68OVatWoXnz59LHZEqqYSEBHz++eeoW7cuxowZg9q1ayM4OBh//fUXAgICWLJUYtyi5RZtlSKEwMmTJ7FmzRrs3bsXenp6GDJkCPz8/ODs7MytXHqtrKwsHDp0CGvWrEFoaCjMzc0xatQofPLJJ2jUqJHU8UgF1NEHLFoWbZWVnJyMDRs24Oeff8a9e/dgZ2cHX19f+Pr6onHjxlLHowoiPz8fp0+fxvbt27Fnzx48f/4c7du3x/jx4/Hhhx/CwMBA6oikQixaFWHRapbc3FyEhYVh27Zt2Lt3L9LT0+Hi4gJfX18MHDgQderUkToiSSAuLg7bt2/Hzp07ce/ePdja2mLIkCHw9fVF8+bNpY5HasKiVREWrebKzMzEwYMHsX37dhw9ehRCCLz//vvw9fWFj48PqlevLnVEUqE7d+5g586d2L59O65cuYJatWrho48+gq+vL9q3b8+PFjQQi1ZFWLQEAE+fPsWePXuwfft2nDlzBnp6eujWrRu8vLzg5eUFGxsbqSPSW8rPz0dMTAwOHjyIgwcPIjY2FoaGhvDx8cGQIUPg4eHBm6xrOBatirBo6b/u3LmD/fv34+DBgzh58iRyc3Ph6OioKF0nJydoafEg/cogMzMToaGhOHjwIA4dOoTk5GTUrFkTvXr1gpeXF3r16oUaNWpIHZMqCBatirBo6XXkcjlCQkJw8OBBHDlyBH///TcsLS3Rp08f9OrVC507d0atWrWkjkn/RwiBW7du4cSJEzh06BD++OMPvHz5Ek2bNoW3tze8vLzQoUMH6OjoSB2VKiAWrYqwaKmkcnNzcfbsWRw8eBDBwcG4efMmAODdd9+Fm5sb3NzcWLxqVlCs4eHhiseDBw+gpaWFDh06wMvLC97e3rC3t5c6KlUCLFoVYdFSWd25cwcnT55U/IJPSkoCoFy8nTp1grm5ucRJqw4hBBITE5W+7wXF6uTkpPi+d+jQASYmJlLHpUqGRasiLFoqL8UVb4MGDeDk5AQnJye0adMGTk5OqF27tsRpK778/Hz89ddfiImJUTwuXLiA58+fs1hJJSp10X799dc4fPgwYmNjoaenV6JL4QkhMG/ePKxfvx7Pnz9Hhw4dsGbNGjRt2lQx5tmzZ/jss89w8OBBaGlpoX///vj+++9LdVoGi5ZU5c6dOzh37hwuXLigKAm5XA4AsLGxUSreZs2aoX79+tDW1pY4tTRevnyJxMREXLlyRVGqFy9eLPT9cnJygrOzM1xdXVmsVO4qddHOmzcPpqamuH//PjZs2FCiol26dCkCAwOxZcsWNGzYEHPmzMHly5dx7do1xdVZevbsieTkZKxbtw45OTkYOXIk2rZtix07dpQ4G4uW1OV1W2gAoKenhyZNmsDOzq7Qo06dOpX+vM7c3FzcuXMHCQkJhR53795VjPv3HoCCP0a4B4DUoVIXbYHNmzdjypQpbyxaIQSsra0xbdo0TJ8+HcA/R39aWFhg8+bNGDRoEK5fv47mzZvj/PnzcHZ2BgCEhISgV69euH//PqytrUuUiUVLUhJC4M6dO4iPjy9UPnfu3EHBj6SxsTFsbW1hZWWleFhbWyt9bWVlJcklAoUQSEtLQ3JyMh4+fIjk5GSlx8OHD/Hw4UPcvn0bOTk5AAB9fX00bdq00B8U77zzDg8mI8moow8qzPHuSUlJSElJgbu7u2KaiYkJXFxcEBERgUGDBiEiIgKmpqaKkgUAd3d3aGlpITIyEh988EGR887KykJWVpbi64JdU2lpaSpaG6LXMzMzg6urK1xdXZWmv3r1CklJSUhMTERiYiLu37+PlJQUXLlyBaGhoUhJSVEUVwETExPUqFEDRkZGqF69epEPIyMjGBgYQEtLC9ra2tDS0oJMJoMQAkII5OfnIz8/H3l5ecjMzER6ejrS09ORkZGBFy9eICMjA+np6Yr/f/78OV69eqWUo3r16rCwsICVlRUsLS3RsmVL2NraokmTJmjSpAnq1atX7LnI/FkkqRT821PlNmeFKdqUlBQAgIWFhdJ0CwsLxXMpKSmFrkuro6MDMzMzxZiiBAYGYv78+YWm88o/VBXI5XLFH49SKijnW7duSR2FqNSePn2qsmMASlW0s2bNwtKlS1875vr163jnnXfeKlR5CwgIwNSpUxVfP3/+HA0aNMDdu3cr7cEVaWlpsLGxwb179yrl7m/ml15lX4fKnh+o/OtQ2fMD//yhWr9+fZiZmalsGaUq2mnTpmHEiBGvHVPWezZaWloCAFJTU2FlZaWYnpqaCkdHR8WYR48eKb0uNzcXz549U7y+KPr6+tDX1y803cTEpNL+4yhgbGxcqdeB+aVX2dehsucHKv86VPb8AFR6idVSFW3t2rVVdiRgw4YNYWlpidDQUEWxpqWlITIyEuPHjwcAuLq64vnz54iJiYGTkxMA4MSJE8jPz4eLi4tKchEREb0NlVX43bt3ERsbi7t37yIvLw+xsbGIjY1Fenq6Ysw777yDffv2AQBkMhmmTJmCRYsWITg4GJcvX8awYcNgbW0NHx8fAECzZs3g6emJsWPHIioqCmfPnsWnn36KQYMGlfiIYyIiInVS2cFQc+fOxZYtWxRft27dGgAQFhYGNzc3AEB8fLzSQRwzZ85ERkYG/Pz88Pz5c3Ts2BEhISFKpy9s374dn376Kbp37664YMWqVatKlU1fXx/z5s0rcndyZVHZ14H5pVfZ16Gy5wcq/zpU9vyAetZBIy/BSEREpC68wSYREZEKsWiJiIhUiEVLRESkQixaIiIiFaqSRfv111+jffv2qFatGkxNTUv0GiEE5s6dCysrKxgaGsLd3R03b95UGvPs2TP4+vrC2NgYpqamGD16tNLpSuWptMu6ffs2ZDJZkY89e/YoxhX1fFBQkOT5AcDNza1QtnHjximNuXv3Lnr37o1q1aqhTp06mDFjBnJzc8s9f1nWoeAWjvb29jA0NET9+vUxadKkQpdHVNV7sHr1atja2sLAwAAuLi6Iiop67fg9e/bgnXfegYGBAVq1aoUjR44oPV+Sn4nyVpp1WL9+PTp16oSaNWuiZs2acHd3LzR+xIgRhb7Xnp6eFSL/5s2bC2X77w0iKvp7UNTPrEwmQ+/evRVj1PkenDp1Cl5eXrC2toZMJsP+/fvf+Jrw8HC0adMG+vr6aNKkCTZv3lxoTGl/tgoRVdDcuXPFypUrxdSpU4WJiUmJXrNkyRJhYmIi9u/fLy5duiS8vb1Fw4YNxcuXLxVjPD09hYODg/jzzz/F6dOnRZMmTcTgwYNVsg6lXVZubq5ITk5WesyfP19Ur15dvHjxQjEOgNi0aZPSuH+vo1T5hRCiS5cuYuzYsUrZ5HK50jq2bNlSuLu7i4sXL4ojR44Ic3NzERAQUO75y7IOly9fFv369RPBwcEiMTFRhIaGiqZNm4r+/fsrjVPFexAUFCT09PTExo0bxdWrV8XYsWOFqampSE1NLXL82bNnhba2tli2bJm4du2a+PLLL4Wurq64fPmyYkxJfibKU2nXYciQIWL16tXi4sWL4vr162LEiBHCxMRE3L9/XzFm+PDhwtPTU+l7/ezZswqRf9OmTcLY2FgpW0pKitKYiv4ePH36VCn/lStXhLa2tti0aZNijDrfgyNHjogvvvhC7N27VwAQ+/bte+34v/76S1SrVk1MnTpVXLt2Tfzwww9CW1tbhISEKMaU9ntSlCpZtAU2bdpUoqLNz88XlpaWYvny5Yppz58/F/r6+mLnzp1CCCGuXbsmAIjz588rxhw9elTIZDLx4MGDcs1dXstydHQUo0aNUppWkn98b6us+bt06SImT55c7PNHjhwRWlpaSr+M1qxZI4yNjUVWVla5ZC9QXu/B7t27hZ6ensjJyVFMU8V70K5dOzFx4kTF13l5ecLa2loEBgYWOf6jjz4SvXv3Vprm4uIiPvnkEyFEyX4myltp1+G/cnNzRY0aNcSWLVsU04YPHy769u1b3lGLVNr8b/r9VBnfg2+//VbUqFFDpKenK6ap8z34t5L8nM2cOVO0aNFCadrAgQOFh4eH4uu3/Z4IIUSV3HVcWm+6RR+AN96irzyVx7JiYmIQGxuL0aNHF3pu4sSJMDc3R7t27bBx48Zyvz3U2+Tfvn07zM3N0bJlSwQEBCAzM1Npvq1atVK6w5OHhwfS0tJw9erVCrMO/1Zwj0sdHeVrw5Tne5CdnY2YmBilf79aWlpwd3dX/Pv9r4iICKXxwD/fy4LxJfmZKE9lWYf/yszMRE5OTqGLw4eHh6NOnTqwt7fH+PHj8fTp03LNDpQ9f3p6Oho0aAAbGxv07dtX6d9xZXwPNmzYgEGDBsHIyEhpujreg7J4089BeXxPgAp0mzwpqfIWfWXN87bL2rBhA5o1a4b27dsrTV+wYAG6deuGatWq4ffff8eECROQnp6OSZMmSZ5/yJAhaNCgAaytrREXFwd/f3/Ex8dj7969ivkW9R4VPFeeyuM9ePLkCRYuXAg/Pz+l6eX9Hjx58gR5eXlFfm9u3LhR5GuK+17++997wbTixpSnsqzDf/n7+8Pa2lrpl6Knpyf69euHhg0b4tatW5g9ezZ69uyJiIgIaGtrS5rf3t4eGzduxLvvvgu5XI4VK1agffv2uHr1KurVq1fp3oOoqChcuXIFGzZsUJqurvegLIr7OUhLS8PLly/x999/v/W/S6ASFW1lvUXfv5V0Hd7Wy5cvsWPHDsyZM6fQc/+e1rp1a2RkZGD58uUl+iWv6vz/LqRWrVrBysoK3bt3x61bt9C4ceMyz/ff1PUepKWloXfv3mjevDm++uorpefe5j2goi1ZsgRBQUEIDw9XOqBo0KBBiv9v1aoV3n33XTRu3Bjh4eHo3r27FFEVXF1d4erqqvi6ffv2aNasGdatW4eFCxdKmKxsNmzYgFatWqFdu3ZK0yvye6AulaZoK+st+v6tpOvwtsv67bffkJmZiWHDhr1xrIuLCxYuXIisrKw3XutTXfn/nQ0AEhMT0bhxY1haWhY62i81NRUAKtR78OLFC3h6eqJGjRrYt28fdHV1Xzu+NO9BUczNzaGtra34XhRITU0tNqulpeVrx5fkZ6I8lWUdCqxYsQJLlizBH3/8gXffffe1Yxs1agRzc3MkJiaW6y/5t8lfQFdXF61bt0ZiYiKAyvUeZGRkICgoCAsWLHjjclT1HpRFcT8HxsbGMDQ0hLa29lu/rwCq5lHHBUp7MNSKFSsU0+RyeZEHQ0VHRyvGHDt2TKUHQ5V1WV26dCl0pGtxFi1aJGrWrFnmrEUpr+/VmTNnBABx6dIlIcT/Pxjq30f7rVu3ThgbG4tXr16V3wqIsq+DXC4X7733nujSpYvIyMgo0bLK4z1o166d+PTTTxVf5+Xlibp16772YKg+ffooTXN1dS10MNTrfibKW2nXQQghli5dKoyNjUVERESJlnHv3j0hk8nEgQMH3jrvf5Ul/7/l5uYKe3t78fnnnwshKs97IMQ/v2v19fXFkydP3rgMVb4H/4YSHgzVsmVLpWmDBw8udDDU27yvQlTRo47v3LkjLl68qDi95eLFi+LixYtKp7nY29uLvXv3Kr5esmSJMDU1FQcOHBBxcXGib9++RZ7e07p1axEZGSnOnDkjmjZtqtLTe163rPv37wt7e3sRGRmp9LqbN28KmUwmjh49WmiewcHBYv369eLy5cvi5s2b4qeffhLVqlUTc+fOlTx/YmKiWLBggYiOjhZJSUniwIEDolGjRqJz586K1xSc3tOjRw8RGxsrQkJCRO3atVV6ek9p1kEulwsXFxfRqlUrkZiYqHQ6Q25urhBCde9BUFCQ0NfXF5s3bxbXrl0Tfn5+wtTUVHGE9scffyxmzZqlGH/27Fmho6MjVqxYIa5fvy7mzZtX5Ok9b/qZKE+lXYclS5YIPT098dtvvyl9rwt+zl+8eCGmT58uIiIiRFJSkvjjjz9EmzZtRNOmTcv9D7Oy5J8/f744duyYuHXrloiJiRGDBg0SBgYG4urVq0rrWJHfgwIdO3YUAwcOLDRd3e/BixcvFL/vAYiVK1eKixcvijt37gghhJg1a5b4+OOPFeMLTu+ZMWOGuH79uli9enWRp/e87ntSElWyaIcPHy4AFHqEhYUpxuD/zmUskJ+fL+bMmSMsLCyEvr6+6N69u4iPj1ea79OnT8XgwYNF9erVhbGxsRg5cqRSeZenNy0rKSmp0DoJIURAQICwsbEReXl5heZ59OhR4ejoKKpXry6MjIyEg4ODWLt2bZFj1Z3/7t27onPnzsLMzEzo6+uLJk2aiBkzZiidRyuEELdv3xY9e/YUhoaGwtzcXEybNk3p1Bkp1yEsLKzIf3cARFJSkhBCte/BDz/8IOrXry/09PREu3btxJ9//ql4rkuXLmL48OFK43fv3i3s7OyEnp6eaNGihTh8+LDS8yX5mShvpVmHBg0aFPm9njdvnhBCiMzMTNGjRw9Ru3ZtoaurKxo0aCDGjh1bql+Qqsw/ZcoUxVgLCwvRq1cvceHCBaX5VfT3QAghbty4IQCI33//vdC81P0eFPczWJB5+PDhokuXLoVe4+joKPT09ESjRo2UeqHA674nJcHb5BEREakQz6MlIiJSIRYtERGRCrFoiYiIVIhFS0REpEIsWiIiIhVi0RIREakQi5aIiEiFWLREREQqxKIlIiJSIRYtERGRCrFoiYiIVIhFS0REpEL/D0Rfk0L9argkAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 500x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
"ax.add_patch(circle)\n",
|
||
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
"\n",
|
||
"plt.xlim(-1, 1)\n",
|
||
"plt.ylim(-1, 1)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ad96fd0a-3e95-4670-966b-6defe5dbade4",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-c67a16c39ab32478",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"source": [
|
||
"Vorliegend ist der Einheitskreis mit Radius = 1, dessen Flächeninhalt sich zu \n",
|
||
"$$A_{circle} = \\pi$$ ergibt.\n",
|
||
"\n",
|
||
"Das umgebende Rechteck besitzt die Seitenlänge \n",
|
||
"$a = r \\cdot 2 = 2$, woraus ein Flächeninhalt von \n",
|
||
"$A_{square} = 2 \\cdot 2 = 4$ folgt.\n",
|
||
"\n",
|
||
"Damit ergibt sich das Verhältnis\n",
|
||
"$$\n",
|
||
"\\frac{A_{circle}}{A_{square}} = \\frac{\\pi}{4}\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Jeder Punkt $(x, y)$ in diesem Diagramm ist gleichwahrscheinlich, also uniform verteilt. \n",
|
||
"Mittels Monte-Carlo-Methodik können wir nun den Wert von $\\pi\\$ approximieren. \n",
|
||
"Nach einfachem Umstellen erhalten wir:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\pi = 4 \\cdot \\frac{A_{circle}}{A_{square}}\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Nacheinander werden dafür zufällig gleichverteilte $x$- und $y$-Werte gezogen.\n",
|
||
"\n",
|
||
"Für das folgende Beispiel nutzen wir bewusst nur wenige Werte, um die Darstellung nicht zu überladen:\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "082ce292-4b01-4b93-abaa-c810232f0d0a",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-1c33d4a20d47764c",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 500x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Get Uniform x, y samples\n",
|
||
"rand = np.random.default_rng(42) # Set fixed Value\n",
|
||
"x_rand = rand.uniform(-1, 1, 100)\n",
|
||
"y_rand = rand.uniform(-1, 1, 100)\n",
|
||
"\n",
|
||
"# Plot \n",
|
||
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
"ax.add_patch(circle)\n",
|
||
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
"plt.xlim(-1, 1)\n",
|
||
"plt.ylim(-1, 1)\n",
|
||
"\n",
|
||
"# Plot samples as small circles\n",
|
||
"for x, y in zip(x_rand, y_rand):\n",
|
||
" c = plt.Circle((x,y), 0.01, color='green')\n",
|
||
" ax.add_patch(c)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "162d35ab-bd1d-4304-8302-cf96b493740d",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-102b588af1bbdfe3",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"source": [
|
||
"Um zu bestimmen, ob einer der Werte im Kreis liegt, nutzen wir die parametrisierte Kreisgleichung:\n",
|
||
"\n",
|
||
"$$\n",
|
||
"x^2 + y^2 = r,\\quad r = 1\n",
|
||
"$$\n",
|
||
"\n",
|
||
"Mittels dieser lassen sich die Werte elegant in zwei Kategorien einordnen: \n",
|
||
"„im Kreis (`circle`)\" und „im Rechteck (`square`)\".\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "400c3fb5-6e2b-48c1-9b0b-9b4aa4504da2",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-856462e1221faa4c",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# reserve two arrays\n",
|
||
"circle_coords = []\n",
|
||
"square_coords = []\n",
|
||
"\n",
|
||
"for x,y in zip(x_rand, y_rand):\n",
|
||
" # calculate distance from origin\n",
|
||
" dist_from_origin = x**2 + y**2\n",
|
||
"\n",
|
||
" # if distance smaller or equal than 1, the point is in the circle\n",
|
||
" if dist_from_origin <= 1:\n",
|
||
" circle_coords.append((x,y))\n",
|
||
"\n",
|
||
" # by definition is every point in the square\n",
|
||
" square_coords.append((x,y))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fcdc0830-f68f-4b28-b5d8-3c15271900ad",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-19f6113a9887beef",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"Mittels der Länge der beiden Listen lässt sich dementsprechend $\\pi$ approximieren:\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "86d96bbb-9877-4fcc-af03-8b5b1898dda5",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-f8c1f8a2e8c65aae",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Pi = 3.12\n",
|
||
"Difference to real Value 0.02159265358979301\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"pi = 4 * len(circle_coords) / len(square_coords)\n",
|
||
"print(f\"Pi = {pi}\")\n",
|
||
"print(f\"Difference to real Value {np.pi - pi}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f83c18b-189b-4090-9080-c3bb74207418",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-204384254c42936a",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"Plotten wir im Folgenden die 100 zufällig gleichverteilten Werte:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "18862b4a-cdb5-4799-9c32-68b411da3d58",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-cb4b3ecde6b0ab70",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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mwdWrSqfJTo4MlQdHhnpaQmTN7pOeDhUrZg10YUn798PWrVCkCLz00jU+/ng4K1asoEGDBnz//ffUrFnTsoEkycoIIViyZAkjRowgJSWFMWPGMHz4cPmL5zO6dAnq1IE7d7Jeu7rCoUNPdxVPjgwlvRCVCvz8sqbQU2L883r14MMPM0hOnkzNmv7s2rWLX3/9ld27d8siK0mASqUiNDSUs2fPMnjwYMaPH0/VqlX5448/lI6Wp8yYAcnJWX1RjEa4exe++07pVP+QhVYym+3bt1O1alXGjh3LoEGDOHv2LG+88Ybs6GRGwljgLlDlCy4uLkybNo2oqChKlSpFu3bt6NSpE9euXVM6Wp6Q04Qq1jTJiiy0Uq5LSUlh0KBBNG/eHB8fH44dO8ZXX32Vry/TKy3+aCzHXBuj19hyQ+vL0W/ClI4kPYdKlSqxdetWVq5cyaFDh6hSpQpz586lAN7heyY9emTdKlOrsxajMWudtZD3aOUP/1y1detW+vfvz+3bt5k6dSqDBg1CrZa/z5nbUbcQqiTvxQY9BtTcx4H7Jy5StEoxpaNJz+nOnTsMGzaMBQsW0LJlS+bMmUPJkiWVjmW1wsJg5sysIvvWW9Cs2dPtJ+/RSnlGcnIyAwYMoGXLlpQvX57jx48zePBgWWQtpGLyfmzIep5LgxEn7nF96ymFU0kvonDhwsybO4/fZ67kxpFrVKlchZ9++kme3T5CSAgsXw4rVz59kbUU+VNQemGbN2+matWqLFu2jNmzZ/PXX39RpkwZpWMVKLE2JdH/69vZiIrC1X0VTCS9KF2ajvDS3Xnlrdc4fvMUS0UQQ/43mJdeekmOnZzHyEIrPbeUlBT69u1LmzZtqFSpEidOnGDgwIGys5MC0mYv4q7KFQADanZ3+ZZSzcopnEp6EXt7fE+9qytMr9umbWdJ0HCio6OpWrUqM2fOlGe3eYQstNJzOXToELVq1eK3337j559/ZsuWLZQqVUrpWPlWalwquyr9jwt2lThQrB1XwrJPBl+lT13Ul2I4tfAgCQcu0+S3dxRKKuUW9dnT6PlnpDQ9Grzu3ObEiROEhoYyePBgXn75ZRITExVMKT0NWWilZ2I0Gpk+fTr169enSJEiHD16lH79+smzWDM7UbsX9c/MpVzmGWrd/BNtiyakxqVm28a1pCuVe9XBO7CEQiml3CSq1TDddwfQYsBYtTouLi7Mnj2bNWvWmJ5J37Nnj4JJpScp0IU2ORnWrIH167NGT5Ie7+bNm3To0IHhw4fz3nvvsWfPHspacgDlAkoYBQGxG9BiAMAGPT6Ga1zacELhZJI5NVw0iN3+/U2v9/j1peHSIabXnTp14ujRo5QqVYomTZrw2WefYTAYlIgqPUGBfrzH1zeZq1ezunNXrw579oCzs8LhrFRYWBihoaFkZmaycOFC2rZtq3SkPOXankvE/nWSwrXLUL5j5WfeP1HtgZu4ne0344t/nKFsG//cCylZpbRbaQAU8iiU4/t6vZ5PP/2Uzz77jKZNm7Jo0SK8vb0tGTFPk4/3mNmNG//8/cQJ+P575bJYK71ez/jx42nWrBn+/v4cO3ZMFtlntH/kaoo18iNwQnvKdqrKzpe/eeZjnB06E+O/7teF1X7fKovsibkR7Ko6mJ3V3+HChtNKx3mka3svEzn5z4fudVujQh6FHllkAbRaLZ9++inbtm3j9OnT1KhRg82bN1swofREZpvp1oo9mOhXpUo2zeOs1QoxbJjSyaxLfHy8aNKkiVCr1WLixIlCr9crHSnPMRqMIhlnYUBlmjBcj1rEH4t95mOdW3tS7B6wUBz5JswMSV9c1Ky9IhOtaUmlkLjwxxmlYz1k7ztLRSZaIUDo0Ijd/RcoHSnXxMfHizZt2ghAjB49Wn7PPgVLTPxeoAst/FNoQYitW5VOZj0OHz4sfH19haenp9i5c6fScfKs+3fui2z/yf5eolcdVzparttdtpfQoTF9xky0Ykf9j5SOlU3G3QxxHzth+DujEUQGNuJu7F2lo+Uag8EgpkyZItRqtWjbtq1ISkpSOpJVs0ShLdCXjqdMyZo+rmpVWLIEWrRQOpF1WLZsGQ0aNKBYsWIcOnSIxo0bKx0pz7J3s+eEUz3ThOE6NMSqi1OiST58xjWnnudW1hs9+XIS9mSY7pmpAFt0JMfkn0dk1Go1H374IX/88Qd79+4lKCiIs2fPKh2rQCvQhXbQIDh9Go4fh+7dlU6jPIPBwOjRo+nevTuvvPIKu3fvpkQJ+ajIi/IMX8ORoi25pSrKaecg7m/YhoO7g9Kxcp372CEYUaNDiw4t6ThQ5tM+SsfKxqNSUS7a+KP7+363Dg1XtGXwrOWjcLLc16pVKw4cOIBKpSIoKIhNmzYpHangMtu58r98//33olSpUsLOzk7UrVtXREREPHLbJk2a/H1ZN/vStm1b0za9e/d+6P1WrVo9dR5LXCrIa5KSkkS7du2EWq0W06ZNE0ajUelIUh50ZtkRsSNgmNhR90Nxadt5pePk6OqeS+KIaxORqCosjjnXt9qcuSU5OVm0b99eqFQqMWXKFPm9/R/54h7tsmXLhK2trZg3b544efKkGDBggHBzcxPx8fE5bn/79m0RGxtrWk6cOCE0Go2YP3++aZvevXuL1q1bZ9suMTHxqTNZS6HV64XQ6RSNIIQQ4uzZs6JixYrC1dVVbNq0Sek4kiTlMr1eL0aPHi0A0aNHD5GWlqZ0JKuRL+7RTp8+nQEDBtCnTx8qV67MrFmzKFSoEPPmzctxe3d3d7y8vEzL1q1bKVSoEK+99lq27ezs7LJtV7hwYXN/lFwjBIwbBw4OYGcH/fuDXv/k/cxh+/bt1K1bFyEEBw4coHXr1soEkSTJbDQaDZMmTWLZsmWsXr2axo0bEx8fr3SsAsOshTYzM5PIyEha/KuXkVqtpkWLFoSHhz/VMebOnUu3bt1wdHTMtj4sLIxixYrh7+/PW2+9xe3btx95jIyMDFJSUrItSlq+HCZOBJ0ua+7EefPgq6+UyLGc1q1bExQUREREBH5+fpYPIUmSxXTt2pW9e/dy/fp16tevz7lz55SOVCCYtdDeunULg8GAp6dntvWenp7ExcU9cf8DBw5w4sQJ+vfvn21969at+eWXX9i2bRtTpkxh586dtGnT5pHDj02ePBlXV1fT4uur7PRhhw6Bjc0/r1WqrHWW9O2339KtWze6du3K+vXrcXV1tWwASZIUUatWLfbt24eNjQ0NGjTgkKV/+BRAVt3reO7cuVSrVo26detmW9+tWzc6duxItWrV6Ny5Mxs2bODgwYOEhYXleJzRo0eTnJxsWq5evWqB9I9WoUL2S8UqVdY6SxBCMGrUKIYOHcoHH3zAwoULsbW1tUzjkiRZhdKlS5vGKg8JCWHLli1KR8rXzFpoPTw80Gg0D90LiI+Px8vL67H73rt3j2XLltGvX78ntlO2bFk8PDw4f/58ju/b2dnh4uKSbVFS//7Qtes/rxs2hDFjzN+uTqfjzTffZMqUKUyfPp2pU6eiVlv171qSJJmJh4cH27ZtIyQkhPbt27No0SKlI+VbZv0pa2trS0BAANu2bTOtMxqNbNu2jeDg4Mfuu3LlSjIyMnjjjTee2M61a9e4fft2nhlIW6PJGiDj0iU4fx62bYP/3ILOdampqXTs2JGlS5eydOlS3n//ffM2KEmS1XN0dGT16tX07NmTnj178uWXX8rJ5M3BbP2Z/7Zs2TJhZ2cnFixYIE6dOiUGDhwo3NzcRFxcnBBCiJ49e4pRo0Y9tF/Dhg1F165dH1p/9+5dMWLECBEeHi5iYmLEX3/9JWrXri0qVKgg0tPTnyqTtTzeYykJCQkiMDBQODk5ia0WGGcy6dIdEXfkhjDoDGZvS5KkF2c0GsWYMWMEIN5//31hMBSc711L1AOtuQt5165duXnzJuPGjSMuLo6aNWuyefNmUwepK1euPHT58uzZs+zZs4c///zzoeNpNBqioqJYuHAhSUlJ+Pj40LJlSyZOnIidnZ25P06eExcXR/Pmzbl16xa7du2iVq1aZmtLGAU7G31MyL5JuAJRzvUpdXwjrqXczNamJEkvTqVS8dlnn+Ht7c0777zD3bt3mT17try1lEsK9Hy05px/0BrcuHGDZs2acffuXbZv346/v3mnVTv4yUYCJ7Q3vdajYV+l/jQ+Ncus7UqSlHt++eUX+vTpQ8+ePZk7dy4ajebJO+VhlqgHZj+jlZRx9epVmjVrRkZGBjt37qR8+fJmb/PeodPo0aAl6zErLQbcrh03e7uSJOWeXr16odVq6dWrFzqdjoULF6LVylLxIuRXLx+6evUqISEhGAwGdu7cSZkyZSzSrlNwNbQb/3mWWY+GO6XNd6lakiTz6NGjBzY2NvTo0QODwcCiRYtksX0B8gJ8PnPt2jVCQkIwGo0WLbIAdca0IqzFZxj+/m91rHBTam+ebLH2JUnKPa+99horVqzg999/p1evXuiVGic2H5D3aPPRPdrr168TEhJCZmYmO3fupHTp0orkyEjJID0pHdeScrQpScrrfv/9d7p27Uq3bt1YuHBhvrtnK+/RSk8tLi6Opk2bmu7JKlVkAexc7LBzkT3AJSk/6NKlC0uXLqV79+5otVrmzZsneyM/I1lo84Hk5GRat27NvXv32L17t0UvF0uSlP+99tprGAwGevTogbu7O1999RUqlUrpWHmGLLR5XHp6Op06deLy5cvs3r2bsmXLKh1JkqR8qFu3biQmJjJkyBA8PT0ZOXKk0pHyDFlo87AHv2FGRETw119/UbVqVaUjFTg3TyZw6bdDOJQoQpU+dVGp5W/5Uv41ePBgEhISGDVqFEWLFqVv375KR8oTZKHNo4QQvPXWW6xbt441a9bQoEEDpSMVOKcXH8b7jeYEkgTArmkDaHRqdoEutka9kV3tp1Js9++kObjj+M0kKr0RoHQsKReNHz+e+Ph4BgwYgIeHBx07dlQ6kvUz2+COViw/jHX88ccfC0DMnz/fIu0d+SZMhHX+WkSMXS+MBqNF2rR2xx2DhA6NEGBajny9Q+lYitrR4jNh/PtroUMj7uIkru6OUTqWlMv0er149dVXhb29vdi1a5fScV6IJeqB7DqWB82YMYPPPvuMqVOn8uabb5q9vZ0vf0PNoSE0XDOcuhM7sDNAzvwDUDg91jQK1gNpF+MUSmMdfHYv48H5vBYDTqQSM3e7opmk3KfRaFi0aBH169enQ4cOREVFKR3JqslCm8csX76c9957j+HDh/PBBx+YvT19up7gNR8CoMEIQMjRb4k9dN3sbVu7CxVamwbnMKDmPg6UfL2ewqmUdd/ODf1/fqxo3fPPs+rSP+zs7Fi9ejXlypWjdevWXLp0SelIVksW2jzkwIED9O7dmx49ejB16lSLtKlL02GL7qH16bfvWaR9axa49xv2+vUlQe3JRbvKRH+3mRINSysdS1HqaVPR8c8z1EdcQ6gzsZOCiSRzcnFx4Y8//sDBwYFOnTqRmpqqdCSrJEeGyiMjQ12/fp3AwEBKlSrFjh07sLe3t1jbEV4dqRO/EQ1G9Gg471Cd8okH0NrLvnTSwy5vv8CVhTvQFnGlzmedsSlko3QkycxOnjxJcHAwzZs35/fff89TA1pYoh7IQpsHCu39+/dp3LgxcXFxHDx4EC8vL4u2n3YrjQOtPqbw+YMke1ek6vovcK9QxKIZJEmybhs2bKBjx46MGTOGiRMnKh3nqckhGCWEEPTr14+TJ0+yZ88eixdZgEIehQiJnG7xdiVJyjvat2/P5MmTGTVqFFWqVKFbt25KR7IastBauS+++IKlS5eyYsUKateurXQcq3V+3Smufb8GCjlQ46veFC7nrnQkSSpwPvzwQ06cOEGfPn0oX748derUUTqSVZCXjq340vG6devo3LkzY8eOZcKECUrHsVon5x+gXN/GaNGjQnBDWxKnM5Gy2EqSAtLT0wkJCeHatWscPHgQb29vpSM9liXqQd65Y13AHD9+nNDQUF555RXGjx+vdByrdnfMZLTo0GJAgxEf/RWiPvhV6ViSVCDZ29uzevVqADp37kx6errCiZQnC60VSklJ4ZVXXqFcuXIsXLgwT/XgU4JGl4Gafy7MCFSI9AwFE0lSwebt7c3atWuJiori3XffVTqO4uRPcCsjhGDgwIEkJCTw+++/4+joqHQkq6d7403UCAyo0KMhAztKv/+y0rEkqUALCAjg+++/Z86cOSxdulTpOIqSnaGszJw5c1i+fDnLly+nXLlySsfJE+p//TrhWg2qJUsw2DpQdNqH+L1UQelYklTg9e3bl+3btzNw4EDq1KlDhQoF8/tSdoayos5QUVFRBAUF8eabbzJz5kyl40iSJL2wu3fvEhAQgKOjI+Hh4RYdbOdpyM5QBUhqaiqvv/46/v7+fP3110rHkSRJyhXOzs6sWLGC06dPM3z4cKXjKEIWWisg/p5b9tq1a6xYscLqfuOTJEl6ETVr1uTrr7/mxx9/5LffflM6jsXJQmsFFixYwKJFi5g9ezZ+fn5Kx5EkScp1gwYN4rXXXqNfv35cvHhR6TgWJQutwk6dOsWQIUPo168foaGhSsd5YSfmRrCnXC/2lO3JsRm7lI4jSZKVUKlUzJkzBw8PD7p27UpmZqbSkSxGFloF6XQ6evXqRdniZfmwy/ukxuXtKaZOL4rEv38j6l1cQr2YpVR9tynHvt+tdCxJkqyEq6sry5Yt48iRI0yaNEnpOBYjC62Cpk6diiryPmEX4vFrWxWNd1H2f7hK6VjPLWH6IkCgxYAWA0bUJH//i9KxJEmyIoGBgXz00Ud8/vnnHDlyROk4FiELrUKOHz/OhAkT+F2Vgpu4A4A96dSa1p1bp28qnO75CG0O847mtE6SpALt448/pnLlyvTu3btAXEKWhTYHR4/CmDEwYQLExub+8XU6Hb1796ZS+UqUFNfQYgBABdiRyc3IK7nfqAWU+/ItUlXO6NGgR0M69pSYKodfkyQpO1tbWxYuXMjp06fz1Ny1z0uODPUf+/ZBSAgIkbX8+GNW4c3NCSgmT55MVFQUERERXAwOpaTuPFoMGFBxn0J4NyibbfsbEVdJ2H8Rzwbl8a5TPPeC5DLfxmW4vvcox8b9CkYjZcb0oGwzObqVJEkPq1mzJmPHjuXTTz+lU6dO+XtKPVEAJScnC0AkJyc/9N6rrwqhVj8os1l//+KL3Gv7yJEjQqvVio8//lgIIcSFjadFjE15IUAkqgqLyKl/Zdt+z1uLRCZaIUBkYCPCP1yVe2EkSZIUlJmZKWrVqiWqVKki0tPTFcnwuHqQW+Sl4/8wGLK/VqkeXve8MjMzefPNN6lcuTJjx44FoGzbipRKj+bu9RTc9Lep/UFz0/apcakEzuyLFj0AWnRUnxqKLk2XO4EkSZIUZGNjw8KFC4mOjs7Xc27LQvsf/ftnnctqNKDVgoMDvP567hx78uTJnDx5kgULFmBra2tar1KrcPZxRqVWZds+6fwtbMnkwVo1UIj7JF9Oyp1AkiRJCqtWrRrjx49nypQpHDx4UOk4ZiEnFchhEOmtW2HxYrCzg6FDoVKlF2/z/PnzVKlShREjRvD5558/1T66NB0JLuXwNNxAiwEdGq7ZlKV0+tmHirIkKS01LpWT3/4FQJX3WuDk5aRwIimv0Ov1BAYGotVq2b9/PxqNxmJtW2JSAVloLTB7jxCCdu3acerUKU6dOkWhQoWeet+Lf5wh/bU3KJV2hhjHqrhsWELJkLJP3lGSLCjx3G2SqwRTRncOgBibCrieDMe9QhGFk0l5xb59+2jQoAGzZs3if//7n8XazTez9/zwww+ULl0ae3t7goKCOHDgwCO3XbBgASqVKtvy30H2hRCMGzcOb29vHBwcaNGiBefOnTP3x3hua9euZdOmTXz77bfPVGQh6x5u5XuHcBSpVE3dL4usZJWien2Jr+6f8Wt9dReJenO6gomkvKZ+/fr06dOH0aNHc+vWLaXj5CqzF9rly5czbNgwxo8fz+HDh6lRowatWrUiISHhkfu4uLgQGxtrWi5fvpzt/alTp/Ldd98xa9YsIiIicHR0pFWrVqSnp5v74zyze/fu8d5779G2bVs6duyodBxJMgt10m0E/9zOEKhQ37mtYCIpL/riiy8QQjBq1Cilo+Qus/Vn/lvdunXFkCFDTK8NBoPw8fERkydPznH7+fPnC1dX10cez2g0Ci8vLzFt2jTTuqSkJGFnZyeWLl36VJks0Z37gY8++kjY2dmJ8+fPm70tSVLK/tFrhABh/HsRIPZ/tFbpWPnOqV8PiR0NxogdL30ubp25qXQcs/jxxx8FIMLDwy3SXp5/vCczM5PIyEhatGhhWqdWq2nRogXh4eGP3C81NZVSpUrh6+tLp06dOHnypOm9mJgY4uLish3T1dWVoKCgxx5TCdHR0UybNo1Ro0ZRrpyyAzckX0lmd/k3uWTrx4Fi7bi255KieaT8JWhSJ3b3mcd5u6qct6vK7j7zCPpcXsHJTUe/CaN8z3o02DuFhlvHkV6lNonn8t9Vg4EDB1K7dm0GDx6MIbeerVSYWQvtrVu3MBgMeHp6Zlvv6elJXFxcjvv4+/szb9481q5dy6JFizAajdSvX59r164BmPZ7lmNmZGSQkpKSbTE3IQTvvPMOJUqUYOTIkWZv70nO1X6d4AuLKK07R62bWxBNm3I/8b7SsaR8pNG8PlRIP06F9OM0mtdH6Tj5ju7zqagxYoMeLQa8Ddc4PmaZ0rFynUaj4ccff+TIkSPMnj1b6Ti5wuqeow0ODqZXr17UrFmTJk2asGrVKooWLfpCX/DJkyfj6upqWnx9fXMxcc5WrVrFn3/+yXfffYeDg4PZ23scXZqO2re3msZUtsGAr/4SV7aeVTSXJElPT23UocJoei1QgS5/Dl4TFBRE//79GTNmDDdv5s1JVv7NrIXWw8MDjUZDfHx8tvXx8fF4eXk91TFsbGyoVasW58+fBzDt9yzHHD16NMnJyabl6tWrz/pRnolOp2PUqFG0adOG9u3bm7Wtp6G113IPx399i2ZxLFFYkTySJD27zN4DUQN6NOjQkooz5T98RelYZjN58mSMRiOfffaZ0lFemFkLra2tLQEBAWzbts20zmg0sm3bNoKDg5/qGAaDgePHj+P996j+ZcqUwcvLK9sxU1JSiIiIeOQx7ezscHFxybaY088//8yFCxeYMmWKWdt5Wiq1iuNv/4T41z93WKOxlGhQSsFUkiQ9i+Dpr3Hg43XsL9Od8Ip9uPPnQYoHl1Q6ltl4eHgwcuRIZs6cSUxMjNJxXozZuln9bdmyZcLOzk4sWLBAnDp1SgwcOFC4ubmJuLg4IYQQPXv2FKNGjTJtP2HCBLFlyxZx4cIFERkZKbp16ybs7e3FyZMnTdt88cUXws3NTaxdu1ZERUWJTp06iTJlyoj79+8/VSZz9jK7e/eu8PT0FL169cr1Y7+oc2tOiD1vLRJRs/YqHUWSJOmJUlNThbe3twgNDTVbG5bodWz2afK6du3KzZs3GTduHHFxcdSsWZPNmzebOjNduXIFtfqfM607d+4wYMAA4uLiKFy4MAEBAezbt4/KlSubtvnwww+5d+8eAwcOJCkpiYYNG7J58+aHBrZQwjfffMOdO3f49NNPlY7ykPKdqlC+UxWlY0iSJD0VR0dHxo8fz1tvvcWIESOoWbOm0pGeixyCMRcvI9+8eZNy5crRv39/pk+3/Kg4V3fFcPfSbUq2rCjHmZUkKV/Q6XRUqVKFcuXKsWnTplw/fr4ZgrGg+Pzzz1GpVHz00UcWbzusyXh8m5Slcu9AUov7cfGPMxbPIEmSlNtsbGyYNGkSmzdvZseOHUrHeS6y0OaSmJgYfvzxRz788EM8PDws2vaJuRGE7PrnUrWHMYG73QdaNIMkSZK5dOnShcDAQEaOHElevAgrC20uGTduHEWKFGHo0KEknrvNwU82cvTbnRj1/32oJvelRF3K9lqLgWKpF3PeWJIkKY9RqVSm+Wp///13peM8M3mPNheuyZ89e5ZKlSrxww8/0Kp0M5zbNaKoyHrIOqJYe+pcXYPG1nzzK17aeo7iLSujwYAagR4NB3xfpf6V/DdqjCRJBVerVq24fv06UVFR2TrR/pfBAGFhcO8eNGgARR4zW6O8R5tHTJkyBS8vL/r27cvNPh9SWCSa3gtK2EDEB7+Ztf3SL1XgyMeruKUuRiY2HC7Whiq7Z5m1TUmSJEsbO3YsJ0+eZP369Y/cRqeDNm2gRQvo1AkqV4a/xztSjCy0L+jKlSv8+uuvjBgxAjs7O5zv3jANdQhgRIXu+qOnBMwtdSd2oJghDhtDBnXj1+Nays3sbUqSJFlSw4YNadSoEZMmTXrkvdqlS2Hr1n9e374NSs+6JwvtC/rqq69wcXFh4MCszkcJddpi/HteTgMqDGjw7tbEYnlUatWTN5IkScqjPvroIw4cOPDIHsg3b8K/ryobDPCfEXstThbaF5CQkMCcOXN49913cXLKem614Zax7AocwQ2NLzG2lTj6yVr8Xq2ucFJJkqT8oVWrVtSqVYtJkybl+H7TpqBSZS0PtG1roXCPIDtDvcDN7zFjxvDtt99y5coV3N3dczGhJEmS9CgrV67k9ddfJyIigrp16z70/oYNMHo0pKZCaChMmACaR/RHtURnKFlon/MLm5ycTMmSJRkwYABffvllLieUJEmSHsVgMFC5cmUqV67M6tWrX+hYstexFZs5cybp6ekMGzZM6ShSPnR+7Un2lg4lwqsTewcvVjqOJFkVjUbDqFGjWLNmDSdPnlQ6zhPJM9rn+A0mPT2dUqVK8fLLLzNrlnyMRspd1/ZcwrVRdRxIQ40RNYLdb86l0fy+SkeTJKuRmZlJ+fLladq0KQsXLnzu48gzWiu1cuVKEhISeP/995WOIuVDF75ZjyOpaP8egEQALqsWKB1LkqyKra0t7777LsuWLePmzZtKx3ksWWifww8//MBLL72Ev7+/0lGkfEhVKPt0j0bU6LTKTwEpSdamT58+qNVq5s6dq3SUx5KF9hlFRkYSERHB4MGDlY4i5VO1vujGJRs/jKjQo8GABpsJY5WOJUlWp0iRInTr1o1Zs2ZhMBievINCZKF9Rj/++CO+vr60b99e6ShSPuXs44zHxQPs7vIte1p9xuVVh6nxdiOlY0mSVRoyZAiXL19m48aNSkd5JNkZ6hluficmJlK8eHHGjh2ryJyzkiRJ0sOCgoJwc3Njy5Ytz7yv7AxlZebPn4/BYKBfv35KR5EkSZL+NnjwYP7880/OnTundJQcyUL7lIxGIzNnzuS1117D09NT6TiSJEnS37p27UqRIkWYOXOm0lFyJAvtU/rzzz+5cOECQ4YMUTqKJEmS9C/29vb069eP+fPnk5aWpnSch8hC+5R++uknqlevTnBwsNJRJEkqgDJTM7m6K4bUuFSlo1ilQYMGkZyczMqVK5WO8hBZaJ9CYmIiGzZsoE+fPqhUcho6SZIsK/r34yS6lsa3SVlsvIuw752lSkeyOmXKlKFJkyb8+uuvSkd5iCy0T2HlypUYDAa6deumdBRJkgogTY+ueBgTALAlk8DvexN76LrCqazPG2+8wfbt27l+3bq+NrLQPoVFixbRsmVLvLy8lI4iSVIBI4yCkpnn0JI1IIMKsEHHzQMxygazQl26dMHW1palS63rjF8W2ieIiYlhz549vPHGG2Y5fnpSOulJ6WY5tiRJeZ9KreK8QzV0ZE2oakTFfezxalhe4WTWx83NjY4dO7Jo0SKlo2QjC+0TLF68GEdHRzp37pyrxzVkGthVcQD2hR2wLVyInVXewqg35mobkmQNEs/d5vTiw9y5kKh0lDyr0PoVXLMpB0AqTpwY/xvFqssrbDl54403OHbsGMePH1c6iokstI8hhGDRokW88sorODo65uqx93T/gYZnswbCViNofGoWe3r9lKttSJLSIkavoZBfcSq9EYBdeV8OTvhD6Uh5Uqnm5SmdfoaUq8k46ZII/KSd0pGsVuvWrXF3d7eqs1pZaB8jMjKSs2fPmuWysfr4UQx/XwoC0KGFo0dzvR1JUkrarTSqf9EdWzIAsOc+lT7pii5Np3CyvEmlVuFSwgW1Vv7YfhxbW1u6du3K4sWLMRqt4yqh/Bd7jF9//RUvLy+aNWuW68c2lK+Imn/+E2gxYPST0+5J+Ufi2Zs4kG76IaNG4EQqSTF3FM0l5X89e/bk+vXrhIWFKR0FkIX2kYxGIytXrqRbt25otdpcP379FUM56N3R9DqixKs0WPJ2rrcjPTthFOwdsoSwxuMIH7YSYSxw827kimI1vIlXe6H/+8qNHg3XNb4U8fdQOJmU39WrV48yZcqwfPlypaMAkPsVJJ+IjIwkNjaWl19+2SzHt3WyJejaKuKOxqLWqqlX1ROVWg6GYQ12VR9Ck5Mz0aHFZreesL0fEhIxRelYeY6tky3Jy7eQ1uM1SurOc9nWD7HyN3npUzI7lUpF586dWb58OUajEbVa2f9zcpq8R0yL9PHHHzNz5kzi4+PNckYrWaebJxMoWvXhSSPuxafiWCx3O8QVJEa9URZYyaLCwsJo2rQpBw4cIDAw8JHbyWnyFLRu3TratWsni2wBo0/LzHl9ut7CSfIXWWQlS2vYsCGFCxdm3bp1SkeRhTYnMTExHD9+nE6dOikdRbIwz1o+RBZugQE1RlQYUBPh1QnXkq5KR5Mk6RlotVratWsnC621WrduHba2trRs2VLpKJKFqbVqKkWvZXfwSA54d2Z3k7HUPGsdHSokSXo2HTt2JCoqipgYZYerlNdFc7Bu3TqaNWuGs7Oz0lEkBRTyKETIvklKx5Ak6QW1atUKGxsb1q9fz7vvvqtYDnlG+x937txh586d8rKxJElSHufi4kKzZs0Uv3xskUL7ww8/ULp0aezt7QkKCuLAgQOP3HbOnDk0atSIwoULU7hwYVq0aPHQ9m+++SYqlSrb0rp161zJumnTJgwGA+3bt8+V40mSJEnK6dixIzt37iQpKUmxDGYvtMuXL2fYsGGMHz+ew4cPU6NGDVq1akVCQkKO24eFhdG9e3d27NhBeHg4vr6+tGzZ8qH5BVu3bk1sbKxpya1pkTZt2kStWrUoUaJErhxPkiTzEUZBWJspnLerwknHuhz6fIvSkSQr0759e/R6PX/99ZdyIYSZ1a1bVwwZMsT02mAwCB8fHzF58uSn2l+v1wtnZ2excOFC07revXuLTp06PXem5ORkAYjk5ORs641GoyhevLgYMWLEcx9bkiTLCXv5GyFACBB6VCITrTi95LDSsSQrU758eTF48OAc33tUPchNZj2jzczMJDIykhYtWpjWqdVqWrRoQXh4+FMdIy0tDZ1Oh7u7e7b1YWFhFCtWDH9/f9566y1u3779wnnPnz/P9evXCQkJeeFjSZJkfs47/rn3pkGgQhD3y58KJpKsUdOmTdmxY4di7Zu10N66dQuDwYCnZ/aRdjw9PYmLi3uqY4wcORIfH59sxbp169b88ssvbNu2jSlTprBz507atGmDwWDI8RgZGRmkpKRkW3ISFhaGRqOhUaNGT/kJJUlSUoZTEdNYygBqjKiLuj9mD6kgCgkJ4fTp08THxyvSvlX3Ov7iiy9YtmwZq1evxt7e3rS+W7dudOzYkWrVqtG5c2c2bNjAwYMHHzlTw+TJk3F1dTUtvr6+OW63Y8cOAgICzDYMlyRJucvr589IVrmZXp9wDqbudz2VCyRZpaZNmwIoNpuPWQuth4cHGo3mod8i4uPj8fLyeuy+X375JV988QV//vkn1atXf+y2ZcuWxcPDg/Pnz+f4/ujRo0lOTjYtV69efWgbIQQ7duww/YNIkmT9yrTyw3j8FPveXUbER2upeGMH9m72T95RKlC8vb3x9/dX7PKxWQessLW1JSAggG3bttG5c2cga/q5bdu28fbbj54SburUqXz++eds2bKFOnXqPLGda9eucfv2bby9vXN8387ODjs7u8ce4+zZs8TFxcn7s5KUxxStUoyi33ZVOoZk5Zo2bcr27dsVadvsl46HDRvGnDlzWLhwIadPn+att97i3r179OnTB4BevXoxevRo0/ZTpkxh7NixzJs3j9KlSxMXF0dcXBypqakApKam8sEHH7B//34uXbrEtm3b6NSpE+XLl6dVq1bPnXPHjh1otVoaNmz4Yh9YkiRJsjpNmzYlOjqaGzduWLxtsxfarl278uWXXzJu3Dhq1qzJ0aNH2bx5s6mD1JUrV4iNjTVtP3PmTDIzM3n11Vfx9vY2LV9++SUAGo2GqKgoOnbsiJ+fH/369SMgIIDdu3c/8az1cXbs2EFgYCBOTk4v9oElSZIkq/PgaqUSl4/lfLQuLggh8PHx4c0332Ty5MlKx5MkSZLMoEqVKjRq1IhZs2aZ1sn5aC3kxo0bxMXFUbduXaWjSFZIl6Yj8dxthLHA/U4qSflKYGAghw4dsni7stACkZGRAE/V8UoqWPYM+hWjoxPufh6cL1SNGxEP91iXJClvqFOnDlFRUWRkZFi0XVlogUOHDlG0aFE5vrGUTcyWaIJnv4ktmQCUzjhLXOs3lQ0lSdJzCwgIQKfTceLECYu2KwstWWe0derUQaVSKR1FsiIJO0+jwciD/xU26CmdfFTJSJIkvYAaNWqgVqtNVzEtpcAXWiEEhw4dIiAgQOkokpUp2tD/X2UWdGi54lxVwUSPtv/DVZxyrMOZQrXY1WuO0nEkySoVKlSIKlWqWPw+bYEvtNevXychIUHen5UeUrZtRfb2noPu73FdrtmUwWPjQoVTPezI9B3UnfYqFdMO43//KI1/Hci+d5cpHSvPOvLVdsLqDCesxWckxdxROo6UywICAuQZraU9+M1GFlopJ40W9EN3M5m4yOuUTD1NiYallY70kOQlGzGgQY1ABehRI9atVzpWnrTv/RXUGNGCBpHf0XDbJ9zxD+LujbtmbzczNZPo36K4vP2C2dsq6OrUqcPx48ct2iGqwBfayMhIPD098fHxUTqKZGbCKMhMzXzm/Qp5FMKrtg8aW82TN1aCmxsq/nn0SKBG7+ymXJ48zH32F4DABj1aDJTRneP4FxvN2ubNkwlc9qiN32s1KNW8PLsqDpCPkpnRgw5Rx48ft1ibBb7QHj58mICAANkRKp879PkW7miLYutsx+lCtfPVYzq15r7NJVs/0+tbak/85n+kYKK8Sy0M/PcngdDnPP1mbjnTeSSlM86YXjc++zP7R/yW6+0kX0nm4CcbiZz853P9wplf1KhRA41GY9HLxwW+0J4+fZoqVaooHUMyo/ijsVT5uDNuIhGA8vePc6tF/hmE3rWUG95XDxI+bCX73l2GfXQU3nWKKx0rT4rv+i4qQIcGHVpi1cWpPLyNWdt0STiPDf8Ucz0aMs7E5GobcYdvcLdsDQIntCfgo1ac9Q7hfuL9XG0jr3BwcKBs2bKcOXPmyRvnErPO3mPtMjIyuHTpEn5+fk/eWMqzbmw/gyfpptc26PFLPaxgotznWMyR4K9eVTpGntdoQT/2FyuMbs0GDM5uVJr7AYXLmXci+TsV62M4sA8NRgC0GHBrmbuj1EWHfkKw4brpdeXUCPb0/4kmq97L1XbyCn9/f6Kjoy3WXoEutBcvXkQIgb+/v9JRpFx0L+Eeh0etwJh2n7KD2+BRpzQG1KYfZHo0XLMtR3mFc0rWqd7UV2DqK5Zrb8sEwmvdIOjSctKx40j3aTQeGpKrbdgm30Tzr7NmI2pEws1cbSMv8fPzY+3atRZrr0BfOn4wUbw8o80/UuNSuV6yHo3m96XR8rcp3KQaabHJ7Ov9E3qyOjMlqj0w/LpE4aSSlMXezZ6GMb+i0aXjZEih8ZJBud5GZkgr1H93mDMCGgy4vdoi19vJK/z9/YmJiSEz0zL3qgv0Ge25c+dwdXWlWLFiSkeRcsnhYYtomHESADUCe9K5M/QTGsWuIXFMZ+6cTcCnfmmKuTsonFSSslNrzXfe02jR/wi7fYey2+egV9kS97/x1M/ls+a8xM/PD6PRyIULFyhe3Pz9GQp0oT1//jx+fn6yx3E+YkxJ/ftp0qzf3jUYsM1IBcC9QhHcKxRRMJ0kKUOlVhGyZTQwGoCyysZR3IPbhdHR0RYptAX+0rG8bJy/+A5qRya2GP6+UKYC7nXopnQsSZKsiJeXF05OThbrEFWgC+25c+dkR6h8plz7Slz4OYzIom046hrC7l5zaDi/n9KxJEmyIiqVCn9/f86ePWuR9gr0pePExER5RpsPVe0XBP02KB1DkiQr5ufnZ7FCW6DPaAHKlCmjdARJkl7Qzi7fcVPtSaLag7BGY584hOG+d5ex268vYUEjSTx320IpJWtStmxZLl++bJG2CvQZLWCRG+GSJJlPxOg12QZeCNnzGbtCfWi89K0ct9/Z5TuarHoPHVpUCK5WWY3NpUicfZwtFVmyAj4+PsTFxWE0Gs3eVoE/o/X09FQ6giRJL+D+1t1kYmN6rUeNdt+uR25fZt03ANkmDjg9M8zMKSVr4+3tjU6nIzEx0extFehCW7RoUbTaAn9SL0l5m7dPtlGPQEVm0UdfqRLZ5jr6ew9Ngf5RWCA9mLEtLi7O7G0V6P9dXl5eSkeQJOkF1ft1CFGujUyvL9pVpubKMY/c/kqP0aiATGwwoCbarhpV321mgaTK2LVrFx06dMDHxweVSsWaNWuUjmQVvL29AYiNjTV7WwX6dE4WWknK++zd7KkW9xcnFkci9AYqdK2NvZv9I7dvtLA/B8v6kLZ2K8KjKLXnvY2DlY4UptfrX/iq271796hRowZ9+/bllVcsN4aztXvw8z8+Pt7sbRXoQvvgNxpJkvI2rb0267GupxQ4vi2Mb2vGRM/u0qVLlClThuXLlzNjxgwOHDjA0qVLX7g4tmnThjZtzDvVX15ka2tL0aJFLXJGKy8dS5IkWYFjx44BMG3aNMaNG8fJkydp3ry56f1Jkybh5OT02OXKlStKxc+TvL295RmtuclCK0mStTh69CiOjo6sXLmS0qVLP/T+oEGDeP311x97jAcdfKSn4+PjI+/RmpuctUeSJGtx7NgxOnbsmGORBXB3d8fd3byT0Bc0Xl5enDx50uztFOhLxy4uLkpHkCRJArLOaENCQh75vrx0nPtcXFy4e/eu2dsp0Ge0Tk5OSkeQJEkiJSWFS5cuUatWrUduIy8d5z5nZ2dSU1PN3k6BLrTOznLINUmSlHfs2DE0Gg3VqlV75DbPe+k4NTWV8+fPm17HxMRw9OhR3N3dKVmy5HPlzS+cnZ25d++e2dsp0JeO5Rlt3iKMgp0vf8Nx5/oc8mjNyfkHlI4kSbni2LFj+Pv7Y2//6Od/n4dRb2Tbqm3UqlXLdLY8bNgwatWqxbhx43K1rbzI2dnZIpeOVUKIx09zkQ+lpKTg6urK1atXKVGihNJxpKcU1vlrQtYOA7LGs83Ejpt/RVGqeXmFk0mS9Tn1yyE8+nSgmDGORJU7V79bQ423Gz15xwLk119/pVevXgAkJyebrd9OgT6jdXR0VDqC9Aw8/lpm+rsWI/akc2nOnwomenr3E+8T1uIzdvv1Y1fobIx6888YIhVcRr0Rjzfb425MAMBVJFH6nQ7cT7yvcDLrYqmrmgX6Hq1Go1E6gvQMMuxc0d9ToyWrSKkRaNys/z67IdPAmbJtaJS8GyNqbM7NI+zMWUIipysdTcqn7lxIpJj4ZyAGDUZcSeby0RuUalZOwWTWxVL9dAr0Ga2UtzhM/5wM7E0zr5xwqkedL15TNNPTuLjxNLWSd6LBiA16AOof/l6e1UpmU7icO7dVHhj+/hFvQMVdnChaXQ47+2+y0ErSf1TuHUjizhPsDp3NvreXUOF62GMHj7cWKrXqoXWCh9dJUm5Ra9XcmLWOZFVhAO7hzLmpayjkUUjhZNbFUoW2QHeGMufNb0l6wKg3ctirDbVu/4UBDbboCAseTci+SUpHk/I5XZqOWyfjKVKpGLZOtkrHsToXLlygfPmszpR5vjPUDz/8QOnSpbG3tycoKIgDBx7/WMbKlSupWLEi9vb2VKtWjT/++CPb+0IIxo0bh7e3Nw4ODrRo0YJz586Z8yNI0nNTa9VUu7iO3R2nEV59EHv+9wtN9nyudCypALApZIN3YAlZZB/BUv10zF5oly9fzrBhwxg/fjyHDx+mRo0atGrVioSEhBy337dvH927d6dfv34cOXKEzp0707lzZ06cOGHaZurUqXz33XfMmjWLiIgIHB0dadWqFenp6eb+OJL0XOxc7AhZO4wmx76j4ayeOV5OliTJstRqy9w9Nful46CgIAIDA/n+++8BMBqN+Pr68s477zBq1KiHtu/atSv37t1jw4YNpnX16tWjZs2azJo1CyEEPj4+DB8+nBEjRgBZp/yenp4sWLCAbt26PTGTvHQsFXRCCNLS0pSOIUmKun79Ov7+/oB5Lx2b9fGezMxMIiMjGT16tGmdWq2mRYsWhIeH57hPeHg4w4YNy7auVatWrFmzBsgaPiwuLo4WLVqY3nd1dSUoKIjw8PAcC21GRgYZGRmm1ykpKS/ysQoMYRTsH7mKjANR2NaoRPA3XeWZWD6RlpYmR0aTJAsxa6G9desWBoMBT0/PbOs9PT05c+ZMjvvExcXluH1cXJzp/QfrHrXNf02ePJkJEyY812coyHYGjyLkwFR0aLHZpWdn2B6aRH2vdCxJkqQ8pUAMWDF69OhsZ8kpKSn4+voqmMj63Uu4R8iBqQCmZz+bHP+B22c/oYi/h5LRpFxQqFAhi8xaIlmnmC1nKfRqGzxFVl+ZXVXfotG+qQXuitW1a9eoWLGi2dsxa6H18PBAo9EQHx+fbX18fDxeXl457uPl5fXY7R/8GR8fj7e3d7ZtatasmeMx7ezssLOze96PUSDp7mU+03op99xPvE9Ex8+xv3iK9HJVqLd+TK4/L6xSqeQQpAWYrt8ISorbpgLQ5sRMjs59nZpDQ5SMZXG5PYnDo5i1y5WtrS0BAQFs27bNtM5oNLJt2zaCg4Nz3Cc4ODjb9gBbt241bV+mTBm8vLyybZOSkkJERMQjjyk9O7cyhYnw7IABNUZU6NEQ6d4Cz5pyZBlzEkbBCf9XaLR3MnVj19BozySi/F5FGJ+tz6Ih02CmhFJ+UCT1Mlqy/x9JPXNVoTTKMRotNDqbMLNly5YJOzs7sWDBAnHq1CkxcOBA4ebmJuLi4oQQQvTs2VOMGjXKtP3evXuFVqsVX375pTh9+rQYP368sLGxEcePHzdt88UXXwg3Nzexdu1aERUVJTp16iTKlCkj7t+//1SZkpOTBSCSk5Nz98PmM/fv3Bc7Go0V4d6dxY7g0eLezXtKR8r3Eo7HCQEPLbfO3Hyq/Y//vF9c1ZQUAsRZu2ri0l/nzJxYyot2VegrdGiEAGFAJTLRigsbTysdy+Kio6MFYPZ6YPZCK4QQM2bMECVLlhS2traibt26Yv/+/ab3mjRpInr37p1t+xUrVgg/Pz9ha2srqlSpIjZu3JjtfaPRKMaOHSs8PT2FnZ2daN68uTh79uxT55GFVrJWdy4m5lhok68++f/q3di7IlFVWOhQCwFCh0ZcsPG3QGopr7kbe1fs9X1dpOIormtKiIiP1ykdSRFHjhyxSKGVQzDK52glKxNW/R1Cjn9PJjZZwzXWfv+pZvqJ/v04fq9Wf2h92s17coxbScrB7t27ady4MZCHn6O1dgXwdwwpD2hy9Dv2DW1A5tFT2AZUpclXTzdDkUd1HzKxwQYdKsCAmiSVO+7uDuYNLOU5Rr2RPW/+jOrgAQwlyxC0fBgOBfD/yd27dy3SToEutJmZsgetZH1UahX1v3vyCGf/5V6hCPve+YU6M3phi457OHH1698oUsAe2ZCebFe9DwiJnI4OLepoI1Hl/qJ6/F9obAvWHN2WesStQE+TJ58jlPKb+t914+6ZG5xdfhSuXqXme02UjiRZGaPeSP3IGUDWM/IajNRKCuPixtMKJ7M8eUZrAZb6IkuSJRXx95CDikjPTKUpeOddd+/excHBgfv375u1nYL3lf0XeUYrSVJBo9aq2RecNSFLJjYYUHOoSCvKtjX/CEnW5u7duxYZ87tAn9Heu3dP6QiSJEkW12TP5+wZVBHD/oOIUqUJXvw2am3BO+9KTU3F2dmZmzdvmrWdAl1o5aVjSZIKIpVaRcOfegG9lI6iKEud0Ra8X2H+5fbt20pHkPIQQ6aBsJc+55RjHSKLtOT04sNKR5Ik6QXcvn0bNzc3s7dToM9o/zt5gSQ9zu5Wn9Ek7BNUgD5NQ/obTbhW+gQlGpRSOpokSc/hxo0b+Pj4mL2dAn1G+6j5ayUpJyX2reDBE6laDDiRyqX5OxTNJOUf6UnpHPpsMwc/2UhqnOyoaQmxsbHZZoEzlwJ9RisLrfQs0uzcMGSq0fDPjB/aIq4KJpLyi7s37nK9XCPqpB8D4PLn5UiPCsejUlGFk+VfQghu3LjxyClbc5M8o5Wkp6SaNo1M/pnX+HDh5tSZ0EHBRFJ+Edn7OyqkHze9Lq6/xIk3JiuYKP9LSUnh/v37Fim0BfqMNjY2VukIUh5S7X/1uVzhOFd+CUNb1I3AiZ3Q2hfobyEpl6hu3cSAJvvVkjvmfeSkoLtx4waALLTmJs9opWdVqlk5SjUrp3QMyYyu7ooh9q+TuNcpS/mOlS3SZqHOLbE9+i0CUJHVB0DVqpVF2i6oLFloC/Sl47S0NPksrSRJJuHDf8OriR91J3agbKeq7HzlW4u0Gzi+LXv6zSfGxo/L2nLs7Pw19X8ItUjbBdWDK5qy0FrAg99qpLxDGAVhbaZw3q4KJ53qcujzLUpHkvIBo95Itel90KAHQI2g4eph3DyZYJH2G/78JmUzz1JKd54mq4eikrMumdWNGzdwdXWlUCHzz9Vc4AvttWvXlI4gPaNdr35HyOZRlM88RcV7h6jxcXvOLD2idCwpj0tPSseJ1Gw/FDUYSb5wS7FM5rDvnaXsK9mVXRUHcCXsotJxFHP9+nWLPEMLBbzQqtVqzp07p3QM6Rm57Fhr+rsGgQpB3K9bFUwk5QeFPApxwjEI3d9dV3RouK7xpUTjsgonyz27e/9M/e97EHT1N4LPLsCxWV3ijxbMTqHR0dFUqFDBIm0V6EJbunRpoqOjlY4hPaN0Jw/0/DNBtRojmqLuCiaS8oti+9ZwpGhLbqqKcco5mMyNf2HvZq90rFxT5LfZCLLO1G3Q4y5uE/3NH0rHUkR0dDR+fn4WaatA9zquUKGCLLR5kOdPE0lptx13kTVW9QnnYAK/fUPhVFJ+UKy6F8USNgKQH4eK0GtsEahQIYCsHs4qWxtlQykgIyODS5cu4e/vb5H2CvQZbfny5Tl79qzSMaRnVLaNP4aok+x7dxkRH62l4o0d+eqsQ5LMJWPExxhRo0OLATUXbCtS89NXlI5lcRcuXMBoNMozWkuoUKECs2bNIjMzE1tbW6XjSM+gaFVPin7bVekYkpSnBI5rw0nffdxcsBFcXKg9cwBOXuafJs7aPDjBstQZbYEutOXLl8dgMHDx4kUqVqyodBxJkiSzq9KnLvSpa9Y2MlMzOTRmNYaku5Tu1xzfxmXM2t6zio6OxsXFhWLFillkLIUCX2gh64suC60kSdKLy0jJ4GyJZtS/uw+Ae78U4tTCnVTuVUfhZP84e/Ysfn5+qFSWeVa5QN+j9fLywsnJSd6nlSRJyiWHRq6k+t9FFsCOdO6//5GCiR4WHR1tscvGUMALrUqlws/PTxZaSZKkXKK/k4KRf84UtRixz0hSLtB/CCFMZ7SWUqALLUC1atU4duyY0jEkSZLyhdIDWpKBPfp/lZebIa8rmCi7GzducOvWLapVq2axNgt8oa1Tpw5RUVFkZmYqHUWSJCnPK9W8PBd+3sEx9+accKxLWLtpNF4zTOlYJocOHQKyfvZbSoHuDAUQEBBAZmYmJ06coHbt2krHkSRJyvOq9guCfn8qHSNHkZGRFC1alBIlSliszQJ/RlujRg00Go3ptxxJkiQp/4qMjKROnToW63EMstBSqFAhKleuTGRkpNJRJEmSJDMSQnDo0CECAgIs2m6BL7SQda1entFKkiTlb9evXychIcGi92dBFlog6z7t8ePHycjIUDqKJEmSZCYPTqjkGa0C6tSpg06n4/jx40pHkSRJkswkMjIST09PihcvbtF2ZaEFqlevLjtESZIk5XMP7s9asiMUyEILgIODAzVq1GDfvn1P3liSJEnKcwwGA/v37ycoKMjibctC+7eQkBB27NiBEELpKJIkSVIuO3bsGElJSYSEhFi8bbMW2sTEREJDQ3FxccHNzY1+/fqRmpr62O3feecd/P39cXBwoGTJkrz77rskJydn206lUj20LFu27IWyNm3alGvXrnHhwoUXOo4kSZJkfXbs2IG9vb0iZ7RmHRkqNDSU2NhYtm7dik6no0+fPgwcOJAlS5bkuP2NGze4ceMGX375JZUrV+by5csMGjSIGzdu8Ntvv2Xbdv78+bRu3dr02s3N7YWyNmrUCLVaTVhYmGn6PEmSpGdh1Bu5uvMiwigo2bQcaq28aGgtduzYQYMGDbCzs7N848JMTp06JQBx8OBB07pNmzYJlUolrl+//tTHWbFihbC1tRU6nc60DhCrV69+7mzJyckCEMnJydnWBwYGih49ejz3cSWpIMu8lymu7rkk7t28p3QURaQnp4uIou2EACFAHCzSUty/c1/pWJIQQqfTCWdnZ/HZZ5899N6j6kFuMtuvW+Hh4bi5uWV7MLhFixao1WoiIiKe+jjJycm4uLig1WY/+R4yZAgeHh7UrVuXefPmPfbeakZGBikpKdmWnDRt2lTep5Wk53B2xTESnUtSomFp1EXdCR/+25N3ymfCu39HwM1Npte1bv/F/te+UjCR9MDhw4e5e/cuTZs2VaR9sxXauLg4ihUrlm2dVqvF3d2duLi4pzrGrVu3mDhxIgMHDsy2/tNPP2XFihVs3bqVLl26MHjwYGbMmPHI40yePBlXV1fT4uvrm+N2ISEhxMbGEh0d/VT5JEnKYvfGqxQx3sz6OxkETO/BzRPxCqeyLHXMBQxoTK+NqNFcln0+rEFYWBiFChWy+IhQDzxzoR01alSOnZH+vZw5c+aFg6WkpNCuXTsqV67MJ598ku29sWPH0qBBA2rVqsXIkSP58MMPmTZt2iOPNXr0aJKTk03L1atXc9yuYcOGaDQawsLCXji/JBUURr2RkroLaDEAoAJs0REfcUnRXJamCqyDLTrTaxv0iIBABRNJD+zYsYOGDRtia2urSPvPXGiHDx/O6dOnH7uULVsWLy8vEhISsu2r1+tJTEzEy8vrsW3cvXuX1q1b4+zszOrVq7GxsXns9kFBQVy7du2RQyja2dnh4uKSbcmJs7MzgYGB7Nix47HtSZL0D7VWzUXbSuj/PpszouI+DnjVL6twMstqOL8fYYEfkIkNmdiws9ZQGv76P6VjFXg6nY7du3crdtkYnqPXcdGiRSlatOgTtwsODiYpKYnIyEjTuJLbt2/HaDQ+tnt1SkoKrVq1ws7OjnXr1mFvb//Eto4ePUrhwoVzpTdZ8+bNmTVrFnq9/qH7wpIk5Uy9ZhXXO7allP4iqThxdsJyAis9+edEfqJSqwg5MBWj/guEUdDEVvPknSSz27dvH/fu3aN58+aKZTDbPdpKlSrRunVrBgwYwIEDB9i7dy9vv/023bp1w8fHB8iaSaFixYocOHAAyCqyLVu25N69e8ydO5eUlBTi4uKIi4vDYMi6LLV+/Xp+/vlnTpw4wfnz55k5cyaTJk3inXfeyZXcHTp04Pbt24SHh+fK8SSpICjbxp+SGedJvnQHJ10SgePaKB1JMWqtGo0sslZj3bp1eHt7W3wigX8z6ynb4sWLefvtt2nevDlqtZouXbrw3Xffmd7X6XScPXuWtLQ0IKtn2IMeyf99ljUmJobSpUtjY2PDDz/8wPvvv48QgvLlyzN9+nQGDBiQK5kDAwPx8vJi3bp1NGrUKFeOKUkFgUqtwrWUm9IxJMlECMHatWvp0KEDarVyzzSrRAF8liUlJQVXV1fTo0P/NXDgQMLCwjh79qzFB5+WJEmScsepU6eoUqUKGzZsoF27djlu86R6kBvksCU56NixI+fOnePs2bNKR5EkSZKe07p16yhUqBDNmjVTNIcstDlo3rw5hQoVYt26dUpHkazI3Rt32V2uN9e1pTjm0ohzq08oHUmSpMdYt24drVq1wsHBQdEcstDmwMHBgZYtW7J27Vqlo0hW5GTgmwRfXExxwxWq3A2ncJemJMXcUTqWJEk5iI+PZ//+/XTs2FHpKLLQPkrHjh0JDw9/6FlgqeCqfmOTaVAGLQY8xC0urT2mcCpJknKyYcMGgEfem7UkWWgf4cE/zsaNGxVOIlmLOxoPDGTvHOdUpmA9KypJecW6deuoX7/+U437YG6y0D5CsWLFaNiwIStWrFA6imQlYj/5CR3/DOEWVmcE5TtVUTCRJEk5SU5OZsuWLXTu3FnpKICZn6PN60JDQxkyZAjx8fF4enoqHUdSWJ2PW3O18WmurT+Mc8UShPSz/ATSkiQ92e+//05mZibdu3dXOgogz2gf67XXXkOtVrNs2TKlo0hWwrdxGYKndaHqf4psxOg1JGi8SFfZs9/nZVKu5TwVozmkxqVy8NNNRE7+k4yUnMf7lqSC5Ndff6VZs2YUL15c6SiALLSP5e7uTrt27Vi0aJHSUSQrdmHDaWp/8RoexgTsyaBO7HqONcmdIUGf5ObJBG771iRwfFsCPmrFBa/6pMalWqRtSbJGV65cISwsjDfeeEPpKCay0D7BG2+8waFDh3Jl6j8pf4rbGIkNetRkDbKmxUDpK7st0vap0M/x0V82vfa/f5RDfX6wSNuSZI2WLl2Kvb09r7zyitJRTGShfYJ27drh5uYmz2qlR3KqUirbax0abjqXsUjb2qSbqDCaXhtQw035SJpUMAkh+PXXX+ncubPZhlN8HrLQPoG9vT2vvfYaixYtwmg0PnkHqcCp8XYjdgR+YHp9S+1F4aUzLdK2aNES7d+FVgC26HF6uaVF2pYka3Ps2DFOnjxpVZeNQfY6fqI7d6BIkeFcvmxg/foDdOpUT+lIkhVqemAql7cNJPVKIqXaVMbby8ki7Tb4qTdhcbcou+VHjCoN13qNoeGYVhZpW5KszaJFi/Dw8KBlS+v6ZVPO3vOYyws3b0JgIFy+DCCwt7/L2bMulCxpsai57n7ifSLr/I+aMatJVTsTM/Q7gr96VelYkiRJL8RgMODr60uXLl2YMWPGU+8nZ+9R2Pffw7VrD16pSE934LPPMpWM9MIiQj4kOGYxTqRSzBhH3eldObtCDiMoSVLetnHjRmJjY+ndu7fSUR4iC+1j3L0L2aejVREVdVGpOLnCJzoMzd/39NQI1BiJX7tf4VSSJEnPThgFYR2+4pRjIG5dPqN7qfbUqVNH6VgPkYX2MV5+GQyGfxdbLTdufE9evtqe5FoaPRrTaxXg4OerXCBJMgN9up7Yg9dIT0pXOopkRjtf/pqQDSOonHaIBvpI5l7+i4ubrG8ecVloH6NRI1i/HkJCsv4+ZswJrl79gV27dikd7bl5Lf+WBI236fUu/wHUGdtGwUSSlLvOrjjGbUdfvOv6YixchIgxcl7p/KrI9t9Mf9dgxI4Mrv68RcFEOZOdoZ7h5rcQgkqVKlG9evU8PdlAalwqMWujcPBylYPiS/nOZZtyFNdfRosBI5CJHffOXKOIv4fS0aRcdrBoG2rd2mqavhJgT/8FNJzz9PdpZWcoK6NSqRg8eDCrV6/mxo0bSsd5bk5eTlT7X31ZZKV8R5+up5T+oukHrxqwJ4P4iEuK5pLMw/m7SdzHwfT6uFMwgV91UzBRzmShfUa9e/fGzs6OOXPmKB1FkqT/0NpribHxM/VDMKIijUJ4BVtmpC7Jsvy71eTlCgGML9GNfUOX4x8bhp2LndKxHiIL7TNydXXljTfeYPbs2eh0OqXjSJL0H4aVq4jTZM3acg8nTk38HfcKRRROJZnD/v372XZuJ/V+6kX9r1/H1sn2yTspQN6jfY5r8lFRUdSoUYNly5bRtWtXMyTMG4RREPXDbtJvJFK6axCeNb2fvJMkWYAwCu5cSMS1lBsaW82Td5DypNDQUCIiIoiOjkatfr7zRkvco5WF9jm/sC1atCAxMZHIyEhU2R+2LRCEUbC3fC8axmRNtpCCC9cWbqNyL+t7hk2SpPzn4sWL+Pn58fXXX/POO88/LaXsDGXFPvroI44cOcKWLdbXldwSDk/9y1RkAQpxD+MQy8zBKkmSNG3aNIoUKUL//v2VjvJEstA+p6ZNmxIUFMSkSZOUjqKI9Ks3s73WYsA1PV6hNJIkFSSxsbHMmzePoUOH4uDg8OQdFCYL7XNSqVSMHj2a3bt3s2fPHqXjWFyp7vVJwyFr/lOy5kG9ULm9wqkKjpPzD7Cz5nuE1RnB5e0XlI4jSRY1ffp07O3tGTx4sNJRnoq8R/sC1+SNRiPVq1enVKlSbNy4MRcT5g1RP+7BZsR7uGTe4lzljgTv+dIqu9bnN1Ez91JpcIjp9X0KkbTjCCVDyioXSpIsJDExkZIlS/Lee+/x+eefv/Dx5D1aK6dWqxk9ejR//PEHR48eVTqOxVUf3JBKaZEU118mJGqGLLIWcnfKj6gQ2KDHBj2FuMfFCb8qHUuSLGLGjBkYDAbee+89paM8NVloX1DXrl0pU6YMkydPVjqKVGDkcBGq4F2YKrB0aTqu7blEyrUUpaNYXGpqKt999x0DBgygWLFiSsd5arLQviCtVsvIkSNZuXIl0dHRSseRCgDnDwcjUKFDiw4taThS9pNeSseSLODytvPEuvpTolEZCvm6syt0ttKRLOqnn34iJSWFESNGKB3lmch7tLlwTT49PZ1y5coREhLC4sWLcyGhJD3eibkR3P52EcLGhjJTB1OqeXmlI0kWEOXSkEp3I7BBD2QNMRmz/iTl2lcCsp5vTzx3G629FtdSbgomzX2pqamUK1eOdu3aMW/evFw7rrxHm0fY29vzySefsGTJEo4cOaJ0HKkAqNoviCZRMwiJnC6LbAHim3raVGQB1AhuR5wHICMlgwM+nSlSsSiupQuzs9L/MOqNL9zm3iFLCPd9nd3+/bkSdvGFj/e8pk+fTnJyMp988oliGZ6XLLS5pE+fPvj7+zN69Gilo0jSExn1Rg59tpm9gxdzbc8lpeNITynGrRY6tAAYAR1aPEOyzmbDO31BnfgNpm2bnPmJvQMXvlB7u3rNocGPodS99jv1ohfi1Kwu8UdjX+iYzyMhIYFp06YxZMgQSpYsafH2X5QstLlEq9UyadIktmzZwvbt25WOI0mPZNQbOVDyVeqMbUODmW/g3qgyUTP3Kh1LegreWxZwwT5rest0HDj4zq+mKxp2509m2zYTGwxRJx86xrPw+H02gqxJ1W3QU1jcJvqbP17omM/j888/R61W89FHH1m87dwgC20uevnllwkKCmLkyJEUwFvfUh5xeMpW6sWuNr22JQPNiKHKBZKemndgCSreP0rK1WTsMu5S/7t/5l7N8KuWbVtbdGhrVn2h9vQaO4z8M5a7ClDZW3aGnIsXLzJz5kxGjhxJkSJ5cxYmWWhzkUqlYsqUKRw6dIjffvtN6TiSlKPMuMRsr7UYccm8rVAa6Xm4lHB5aFai4NUfcsCns+n1zmpDaPBT7+c6vi5NR1idEXinnkeNQI86a/Q324rU/OTlF4n+zMaNG4eHh0eeem72v8xaaBMTEwkNDcXFxQU3Nzf69etHamrqY/cJCQlBpVJlWwYNGpRtmytXrtCuXTsKFSpEsWLF+OCDD9Dr9Y84omU1adKENm3aMGbMGDlfrWSVyvRqxF2csk2OfqHGKwqnkl6UnYsdwdd/J/lyEqmxd2kS9T0q9fPNLLa32VgaR06nqEj4+4xWxe56H1L0QgROXk65G/wxjh49yuLFixk/fjyOjo4Waze3mbXQhoaGcvLkSbZu3cqGDRvYtWsXAwcOfOJ+AwYMIDY21rRMnTrV9J7BYKBdu3ZkZmayb98+Fi5cyIIFCxg3bpw5P8ozmTx5MufPn2fu3LlKR5Gkh3gHluDqwh2ccG3ABdtK7Ar6kAa75IAr+YVrSdcXLobFj25A/ffAKBoEWgxo/MrhUsI8j788yujRo/Hz86Nv374WbTfXCTM5deqUAMTBgwdN6zZt2iRUKpW4fv36I/dr0qSJeO+99x75/h9//CHUarWIi4szrZs5c6ZwcXERGRkZT5UtOTlZACI5Ofmptn8ePXv2FJ6eniIpKclsbUiSJJlDZOFmQodGiKwxx4QAsX/0Gotm2LJliwDEypUrzdqOJeqB2c5ow8PDcXNzo06dfyYCb9GiBWq1moiIiMfuu3jxYjw8PKhatSqjR48mLS0t23GrVauGp6enaV2rVq1ISUnh5Mmce9hlZGSQkpKSbTG3SZMmkZqayvjx483eliRJUm5y+ulr7qr+OXvd7/0ygZ92sFj7GRkZvPPOOzRp0oQuXbpYrF1z0ZrrwHFxcQ+NRanVanF3dycuLu6R+/Xo0YNSpUrh4+NDVFQUI0eO5OzZs6xatcp03H8XWcD0+lHHnTx5MhMmTHiRj/PMSpQowfjx4xk1ahR9+vShRo0aFm1fkqTclRRzB42dFmcfZ6WjmJ3fq9W5GXWaiMXh2BZ1pe67TVBrLdd3dvr06Vy4cIFVq1ahUj3ffWZr8sxfuVGjRj3UWem/y5kzZ5470MCBA2nVqhXVqlUjNDSUX375hdWrV3PhwvPPuTl69GiSk5NNy9WrV5/7WM/ivffew9/fnyFDhmA0vvgILZIkWV56UjoRXh1xK+uOc3EXwmq+hzDm/8f3ilb1JGhyZ2oNa2rRInv58mUmTpzI0KFDqVKlisXaNadnPqMdPnw4b7755mO3KVu2LF5eXiQkJGRbr9frSUxMxMvL66nbCwoKAuD8+fOUK1cOLy8vDhw4kG2b+Ph4gEce187ODjs7y0/hZmtryw8//ECzZs349ddf6d37+braS5KknP3tP6NR/D/zTYcc+469b9elwY+hCqbKv95//30KFy6cr267PXOhLVq0KEWLFn3idsHBwSQlJREZGUlAQAAA27dvx2g0morn03gwz6u3t7fpuJ9//jkJCQmmS9Nbt27FxcWFypUrP+OnMb+mTZvSvXt3PvjgAzp16oSbm5vSkSRJegYOF06g+tfUhJnYoDtyQsFE+demTZtYvXo1y5Ytw9k5/1yiN9v1gEqVKtG6dWsGDBjAgQMH2Lt3L2+//TbdunXDx8cHgOvXr1OxYkXTGeqFCxeYOHEikZGRXLp0iXXr1tGrVy8aN25M9erVAWjZsiWVK1emZ8+eHDt2jC1btvDxxx8zZMgQRc5an8aXX37J/fv3GTt2rNJRJEl6RvfLVUX8a3QkW3TY1MwflzStSXp6Ou+88w7NmjXj9ddfVzpO7jJbf2YhxO3bt0X37t2Fk5OTcHFxEX369BF37941vR8TEyMAsWPHDiGEEFeuXBGNGzcW7u7uws7OTpQvX1588MEHD3W7vnTpkmjTpo1wcHAQHh4eYvjw4UKn0z11Lkt05/6vr776SqjVanH48GGLtSlJStr15lxxU1VUpOAswqoOFrr7T/89ak3SbqeJiKLtTI+57Kj+jjAajErHyncmTpwotFqtOHXqlEXbtUQ9kPPRmmn+wf/S6XTUqlWLQoUKsW/fPrRas3X4liTFHf12JzWHhiDIGh/XiIpdTT8hZLv1DCzzLIRRcOdCIloHG4sP2lAQnDt3jurVq/Puu+8yZcoUi7Yt56PNR2xsbPj555+JjIzkq6++UjqOJJlV0sa96NGYLriqEbgc3alophehUqtwr1BEFlkzMBgM9OnTh+LFi1vVCH+5SRZaC6pXrx4jRoxg3LhxjxxcQ5LyA21ZXzQYTK91aLjnUUrBRJK1+vbbb9m3bx/z58/P0+MZP468dGyhS8cPpKenU7t2bRwdHQkPD5eXkKV8yZBp4EDZrgRf/x2AGBs/HA/tpFj1p3+0T8r/zpw5Q61atXjrrbeYPn26IhksUQ9kobVwoQU4cOAAwcHBTJw4Mc9OZCxJTyKMgujfotCl3KfcKzVwcHdQOpJkRQwGAw0aNCAxMZGjR49SqFAhRXJYoh7I0ykF1K1bl5EjR/LJJ5/QoUMHqlWr9uSdJCmPUalV+L8uhx6VcvbVV19x4MAB9uzZo1iRtRR5RqvAGS1kDZodEBCAra0tERER2NjYKJJDkiTJ0k6dOkWtWrV49913mTZtmqJZZK/jfMzOzo6FCxcSFRXF5MlyLlBJkgoGvV5P7969KVu2LJ9++qnScSxCFloFBQQE8NFHHzFx4kT279+vdBxJkiSz+/TTTzl8+DALFizAwaFg3LeXhVZhY8eOJTAwkG7dunHnzh2l40iSJJnNtm3b+Oyzz5gwYUKOY96fOQP790NqqgLhzEgWWoXZ2NiwdOlSUlJS6Nu3LwXwlrkkSQVAXFwcoaGhNG/enNGjR2d7Twh45x2oVAmCg7P+fIGZUa2OLLRWoFSpUsyfP581a9YwY8YMpeNIkiTlKoPBwBtvvAHAokWL0Gg02d7/6y/4/vt/XsfGwttvWzKheclCayU6derE0KFDGTFiBIcOHcr2XkZKBrv8+5OiciFOU5x97y1XKKUkSdKzmzx5Mtu3b2fx4sV4eno+9P6VK9lfGwxw6ZJlslmCLLRWZMqUKdSoUYOuXbuSnJxsWh/eYiwNoufjwl2KGW9Q77vunPrl0GOOJEmSZB127tzJ+PHjGTt2LM2bN89xm7p1QaMB1d+DY6vV0KSJBUOamSy0VsTW1pbly5dz69Yt+vfvb7pfW+zkDjQYgX/+wW6uC1copSRJ0tO5efMmPXr0oFGjRo+dMKBaNVi+HDw9wcEBXnsN8tPcK7LQWpmyZcsyb948fvvtN3788UcAUtxKouefexpqBHblSigVUZIk6YkMBgO9evVCp9OxZMmSh+7L/leXLln3ZtPSYNkyyE/zC8hCa4W6dOnCu+++y9ChQ9m5cyclVkwnTvNPYd1Ttid1P++kYEJJkqTHGzNmDH/++SeLFi3Cx8dH6TiKkkMwKjQE45PodDpat27NsWPHOHjwIEUdinJx9THsizpT4ZVqqNSqJx9EkiRJAYsWLaJnz5589dVXDBs2TOk4jyVn7zGTvFBoARITE6lbty4ODg7s27cPZ2dnpSNJklURRsHx2fu4d+4GJTrXwbdxGaUjFXgRERE0adKE7t27M2/ePFQq6z4pkGMdF3Du7u6sW7eOy5cv88Ybb2A0GpWOJFnY7bO32DtkCeHDf+N+4n2l41idXbXeo/rghgR//TpFm1Qi8outSkcq0K5du0bnzp0JCAhg1qxZVl9kLUWe0VrxGe0Df/zxB+3bt2fUqFFMmjRJ6TiShVzbcwnbxkEUEwkARNtVw/viXpx95JUNgDNLj1CxR23TawNqbmhL4au7qGCqgistLY3GjRuTkJDAwYMHc3xe1hrJM1oJgLZt2zJlyhQmT57MkiVLlI4jWUhM34kUFomm1+UyThL5v58UTGRd0q7ezvZagxFX/S2F0jwboz5/XZ0SQtCvXz9Onz7N2rVr80yRtRRZaPOIESNG0LNnT/r168fBgweVjiNZgM29JDQYTK+NqEFOPGFS+uVaJKrcTY++6dFwvGQ7hVM93q3TNzni1hRhY8NNtScHJ/yhdKRcMWnSJJYtW8Yvv/xCrVq1lI5jdWShzSNUKhU//fQTNWvWpEOHDlzITyNuSznSt+2IGoEAjKhQY6RIL+suJJbkXqEIt1aGcdKlPle1Zdjn14eaB39WOtZjxTTuTdXk3Wgw4i5uUu2TV7i297LSsV7IokWL+Pjjj/nkk0/o0qWL0nGskrxHm0vX5I3GrEGxt28HLy/45JOsP3PbzZs3adiwIXq9nr179+JljkYkqyCMgt2hsyi2dg56tS1pwz6m7qftlY4lvYA7ancKi+xXJQ6MXZ9n/103bdpEx44d6dWrFz///HOe7PwkH+8xE3N8YceMgUmTssbqVKuhZEk4dgzM8UTOpUuXaNCgAcWKFSMsLAxXV9fcb0SSpFx3ulAAFe4fQ/uvWwLnVh2nwstVFUz1fPbv30/z5s1p0aIFv//+O1qtVulIz0V2hspD5szJ+lOIrJknYmIg3EzDEZcuXZrNmzdz6dIlOnXqRHp6unkakiQpV2kXLyRR7QFk3Q4IazctTxbZ06dP065dO2rXrs2yZcvybJG1FFloc4md3dOtyy3VqlVj/fr1REREEBoaisFgePJOkiQpqsLLVXGMvcDZZUeIP3iVkA0jlI70zK5evUrLli0pXrw469evx8HBQelIVk8W2lzy2WdZf2q1WZePmzWDBg3M22bDhg1ZsWIFa9euZfDgwRTAuwAAJF9JJmLMOg5O+IOMlAyl40jSYzkWc8S/a0286xRXOsozu337Nq1atUKr1bJ582bc3NyUjpQnyPP9XNK7N5QuDTt3ZnWCevPNrKJrbh06dGDOnDn07dsXT09PPv30U/M3akXiDt9AXzeYIEPWzNGnptSm1KVdOBbLR1N/SJIVuHfvHu3bt+fmzZvs3bu3wE8U8Cxkoc1FTZooM1lxnz59uHnzJiNHjsTJyYkPP/zQ8iEUEt1zIsGGG6bX/vePsrvvzDx5SU6SrNX9+/fp1KkTJ06cYMeOHfj5+SkdKU+RhTaf+OCDD0hNTWXkyJGo1WpGjCgYhcYm+RZq/hllx4gabuWN0YEkKS94UGTDw8PZtGkTderUUTpSniPv0T6Hb74Bd3dwcYHhw7OeoVWaSqViwoQJjBkzhg8++ICvv/5a6UgWoX+pDZq/C60R0GDA9bWWyoaSpHwiPT2dzp07s2fPHjZu3Ejjxo2VjpQnyTPaZ7R+Pbz//j+vp0+HEiWyr1OKSqVi4sSJGAwG0xyQ71tDMDNqOLcPYYlJlNo0C73alpsDP6b+8GZKx5Iks0lPSufEDzsRBiOVBzU2W3+E+/fv88orr7B79242bNhASEiIWdopCGShfUZ794KNDeh0Wa9VKtizxzoKLWQV2wcz/AwbNgydTpev79mq1CpC1g4Dsn6xqKBsHEkyq7s37nK9XCPqpB8DIOYzP1xP7sO9QpFcbSctLY1OnTqxd+9e1q9fT7Nm8pfXFyEL7TPy9QW9/p/XD0aBsiYPiq2NjQ0jR44kMzOTjz/+WOlYkiS9oMhe39Iw/YTpta/uAnt6fEHIwWm51kZqaiodOnTg4MGDbNq0iSZK9PDMZ2ShfUYDBsDGjbBpU9brqlVh3DhlM+VEpVLx6aefYmNjw9ixY8nMzGTChAl5cixSSZKyqG4mYCT797A2MSHXjp+SkkK7du04evQomzdvpmHDhrl27IJMFtpnZGsLGzZAVFTW5ePq1c07AtSLGjt2LLa2towaNYrbt2/z3XffodFolI4lSdJzcOjUEtuoGQhABWgxoGqVO53/YmNjadOmDZcuXWLr1q3Uq1cvV44rmbnXcWJiIqGhobi4uODm5ka/fv1ITU195PaXLl1CpVLluKxcudK0XU7vL1u2zJwfJRu1GmrWhMBA6y6yD4wcOZI5c+Ywa9YsXn/9dTk2siTlUXU/bc/uXnO4bFOey9qy7Oz8NQ1+DH3h40ZHR1O/fn1u3rzJ7t27ZZHNZWadvadNmzbExsYye/ZsdDodffr0ITAwkCVLluS4vcFg4ObNm9nW/fTTT0ybNo3Y2FicnJyyQqtUzJ8/n9atW5u2c3Nzw97e/qlyWWK2Bmu0bt06unbtSt26dVm7dq0cPk2SJA4cOEC7du3w8PBgy5YtlLS2TidmZpF6IMzk1KlTAhAHDx40rdu0aZNQqVTi+vXrT32cmjVrir59+2ZbB4jVq1c/d7bk5GQBiOTk5Oc+Rl61d+9e4e7uLqpWrSquXbumdBzpKZz9LUrsCBgudtQZIS5sPK10HCkf+eOPP0ShQoVEcHCwuHXrltJxFGGJemC2Qjt37lzh5uaWbZ1OpxMajUasWrXqqY5x6NAhAYi9e/dmWw8IHx8fUaRIEREYGCjmzp0rjEbjI4+Tnp4ukpOTTcvVq1cLbKEVIuuXIF9fX+Hr6ytOnTqldBzpMc4sPyrSsBeZaEUmWpFKIXF+vfw3k17cwoULhVarFR06dBD37t1TOo5iLFFozXaPNi4ujmLFimVbp9VqcXd3Jy4u7qmOMXfuXCpVqkT9+vWzrf/0009ZsWIFW7dupUuXLgwePJgZM2Y88jiTJ0/G1dXVtPj6+j77B8pHKlWqRHh4OK6urjRo0IB9+/YpHUl6hPgJs9Cix+bvxZZMrn7ys9KxpDxMCMGUKVPo3bs3b775JqtWraJQoUJKx8rXnrnQjho16pEdlh4sZ86ceeFg9+/fZ8mSJfTr1++h98aOHUuDBg2oVasWI0eO5MMPP2TatEc/RzZ69GiSk5NNy9WrV184X15XvHhxdu/eTbVq1WjevDlLly5VOpKUk5y6UBTQ6RClF5eZmclbb73FqFGjGDduHD/99JOctN0CnvkrPHz4cN58883HblO2bFm8vLxISMj+fJderycxMREvL68ntvPbb7+RlpZGr169nrhtUFAQEydOJCMjA7scugHb2dnluL6gc3NzY8uWLQwcOJAePXoQFRXFZ599Jh//sSJFPxqA6DkP3d/fqnq0+HzUR+FUUl6UkJBAly5diIiIYO7cufTt21fpSAXGMxfaokWLUrRo0SduFxwcTFJSEpGRkQQEBACwfft2jEYjQUFBT9x/7ty5dOzY8anaOnr0KIULF5bF9DnY29uzcOFCatSowYcffkhUVBRLlizB1dVV6WgSUOmNAE6r9pMwZR6o1HiPG4Bfl2pKxyrw7iXcIzkmkWI1vNHaW/8Z4ZEjR+jUqROZmZmEhYU9dDtOMjOz3f0VQrRu3VrUqlVLREREiD179ogKFSqI7t27m96/du2a8Pf3FxEREdn2O3funFCpVGLTpk0PHXPdunVizpw54vjx4+LcuXPixx9/FIUKFRLjxo176lwFudfx42zevFm4ubkJf39/cebMGaXjSJJZHZr8pzjq0lCcLFRHhHX9QRgNj+5Q+W973lokMrAVAsRVTUmr7wm+dOlS4eDgIOrUqSOuXr2qdByrk6d7HQshxO3bt0X37t2Fk5OTcHFxEX369BF37941vR8TEyMAsWPHjmz7jR49Wvj6+gqDwfDQMTdt2iRq1qwpnJychKOjo6hRo4aYNWtWjts+SkEqtAaDEFevCnHz5tNtHx0dLSpVqiRcXV3FH3/8Yd5wkqSQU78eEjo0Qo9KiKy73mLXm3OfuN/VPZdEJlph/HsfHRpx2qGmBRI/O71eL0aNGiUAERoaKtLS0pSOZJXyfKG1VgWl0CYnC9GokenniHj3XSEe8xTUv/ZLFu3btxcqlUpMmTLlsY9OSVJetKPpBKFDY/rmMKASEcXaPXG/w19u++cb6u8lDXsLJH42SUlJol27dkKtVotp06bJ7+HHyNOP90jKGzsW/v3kznffwW+/PXk/FxcX1q5dy+jRoxk5ciSvvfYaSUlJZsspSZamcnNFxT+9t42oyXQs/MT9vBr7kYkNxr9f69Bw0dG67pkfOXKEwMBA02TtI0aMkJOJKEwW2jzq5En44QdYtiz7tH3/dvo0GAz/vNZq4WmfvFKr1Xz++ef8/vvvbNu2jZo1a7J///4XDy5JViDgx35csKtiep2icqXE7CdPw+UdWILDHy7nPlnPnV61KYfzBsuNs/44Qgi+++476tWrh5OTEwcPHsw2TK2kHFlo86AtW7ImNXjnHejeHdq2zV5QH6hVK2sChAf0eqhR49naeuWVVzhy5Ag+Pj40bNiQKVOmYDQan7yjZHanF0Wyt3Qo4b6vc/DTTUrHyVOcvJwocW0/+95dxp4BC9EfPUnplyo81b71pryMfUYKSRcTKZN+hpIhZc2c9slu375N586dee+993jrrbcIDw+nQoWn+zySBZjtorQVy+v3aKtVE0Klyn6rKKd+S2lpQnTsmPW+Wi3E+PHP32ZmZqYYPXq0UKlUomXLliIuLu75Dya9sLO/RYn72P3doUctBIgDn2xUOpakgF27dokSJUoId3d3sXbtWqXj5DnyHq2Uo7t3Hx4cKKfZBx0cYO3arO3v34dPPnn+Nm1sbJg0aRJbtmzh6NGj1KhRg7/++uv5Dyi9kBvfrECDAS0GNBgxoEY3d6HSsSQLMhgMTJw4kZCQEMqUKcOxY8fo2LGj0rGkHMhCmweF/mv6SY0G3N2hceNHb+/klDVhfW546aWXOHbsGNWrV6dly5Z89NFHZGZm5s7BpadnZ5etM49AhdFGDthSUFy/fp2XXnqJ8ePH8/HHH7N9+3ZKlCihdCzpEWShzYMmTIBJk6BBA+jQAfbuBU9Py7Xv5eXF5s2bmTx5MtOmTSMwMJAjR45YLoBEpS/7cVtdFANq9GjIxI6ik4crHSvPSbuVxvl1p7h99pbSUZ6KEIL58+dTpUoVzpw5w7Zt25gwYYIcr/hvBw9Co0ZQqRKMGgU6ndKJ/ma2i9JWLK/fo7Umhw8fFjVq1BAajUZ8/PHHIj09XelIBUbC8Tixo+1UseOlz8XFzWeVjpPnnFl+VCSoipkGntjZ8yelIz3WlStXRKtWrQQgevXqJW7fvq10JKty+bIQjo5Z/VEgqx/LBx88eT9L1AOVEAVvKpCUlBRcXV1JTk7GxcVF6Th5XmZmJl988QUTJ07E39+fBQsWUKdOHaVjSdJjnberQunMs2jJ6rJvQM31Heesohfxvwkh+Pnnnxk+fDguLi7Mnj2bdu3aKR3L6ixeDG+8kX1duXJw/vzj97NEPZCXjqUXZmtry7hx4zh06BC2trbUq1eP0aNHk56ernQ0SXqkEpkXTUUWQIOR24cvK5joYZcvX6ZVq1YMHDiQ1157jRMnTsgi+wiF/zPeiFoNHh7KZPkvWWilXFOjRg0iIiKYMGECX331FbVr1yYiIkLpWJKUo7POdUzTDxpRcR8HfJpVVDhVFqPRyOzZs6latSqnT59m06ZNzJ07Fzc3N6WjWa3WraFz539e29vD118rFicbWWilXGVjY8OYMWM4fPgwjo6OBAcHM2jQIG7fvq10NEnKpujWJZwrlDWCS5LKnZMTV+FZ01vhVHD48GEaNmzIoEGD6NGjBydPnpQjPD0FtRp+/x02bcq6jHzqFAQHK50qi7xHK+/Rmo1er+fHH39k7NixaLVaJk2aRP/+/eXE8pJV0aXp0NprUamVHQ84MTGRjz/+mFmzZlGlShVmzJhBSEiIopkKAnmPVsrTtFot7777LtHR0XTq1IlBgwZRt25dwsPDlY4mSSY2hWwULbIGg4GffvoJPz8/Fi9ezNdff83hw4dlkc1HZKGVzM7T05N58+aZCmz9+vXp06cP8fHxCieTJGXt37+foKAg/ve//9GhQweio6N57733sLGxUTqalItkoZUspl69ehw4cIBZs2axbt06/Pz8+Pbbb+XIUlKBExcXR79+/QgODsZoNLJ3717mz5+PpyVHnpEsRhZayaI0Gg3/+9//iI6OpkePHrz//vtUqlSJJUuWyFmBpHwvOTmZjz/+mHLlyrF69WpmzpzJwYMHqV+/vtLRJDOShVZSRJEiRZg5cyZRUVFUrVqV0NBQatWqxcaNGymA/fOkfO7+/ftMmzaNsmXLMn36dN59910uXLjAoEGDZOfAAkAWWklRVatWZe3atezbtw83Nzfat29P48aN2bNnj9LRJOmF6fV65syZQ4UKFfjoo4/o2rUrFy5cYPLkyRT+7wgLUr4lC61kFYKDgwkLC2PTpk2kpqbSqFEjOnToQFRUlNLRJOmZGY1GVq5cSZUqVRg4cCCNGzfm9OnT/Pjjj3h7K/+srmRZstBKVkOlUtG6dWsiIyNZunQpZ86coWbNmrz++utERkYqHU+SnshgMLB8+XICAgJ4/fXXKV++PEeOHGHJkiWUL19e6XiSQmShlayOWq2mW7dunDp1itmzZ7N/fyx16oTh67ue6dOPyHu4ktVJT09n9uzZ+Pv7061bN4oWLcrOnTvZuHEjNWvWVDqepDA5MpQcGcqqXb8O1asLkpLE372S1fj5DeeLLxrTqVMn1Gr5u6KknJSUFGbNmsXXX39NfHw8r776KiNHjiQgICBX27lyBSIioGhRaNIEVMoOYpWvyJGhpAJvxQpISlJhNKoBLSqVilu3uvLKK69QpUoVFixYIJ/DlSwuPj6ejz76iJIlS/Lxxx/Tvn17zpw5w4oVK3K9yO7ZAxUrwuuvQ9Om8OabUPBOj/I2WWglq/bwb+4q6tWrx759+/D396dPnz6ULVuWiRMnEhsbq0REqQA5dOgQffv2pXTp0syYMYMBAwYQExPDnDlz8PPze+Hjp6XByJHQqhW89x6kpMCQIZCR8c82v/wCu3e/cFOSJZltSnkrlpycLACRnJysdBTpCW7cEKJoUSG02qxFrRZiy5Z/3j958qTo37+/KFSokNBqteK1114T27dvF0ajUbnQUr5y7949MXfuXFGnTh0BiJIlS4pJkyaJxMTEXG+rXbus/+MghEYjRP36Qnh5Zb3+9/L777nedIFliXog79HKe7RW7/p1+P57uH8fXnsNGjR4eJvk5GR++eUXfvzxR86cOUPFihV566236NWrl5zDU3ou0dHRzJw5kwULFpCcnEzr1q156623aNu2rVkGmUhJAVfXh9d37w7Ll4PRCBoNODrC6dPg45PrEQokS9QDWWhloc1XhBDs3LmTmTNnsmrVKmxtbenRowcDBw6kTp06qGQvEukxMjIy2LBhAzNnzmTbtm14eHjQt29f/ve//1G2bFmztp2eDoUKPXz/9fJlmDYN/vgDvLzg22+hTh2zRilQZKE1E1loC4bY2Fjmzp3LTz/9xNWrV/Hz8yM0NJTQ0FDKlSundDzJShiNRnbv3s3ixYtZuXIlSUlJ1K9fn7feeotXX30Ve3t7i2WZOBHGjcs6czUYYOhQ+PprizVfIMlCayay0D6ZXg83b2Y9TqDVKp3mxej1enbs2MGiRYtYtWoVqampBAUFERoaSteuXSlWrJjSESUFREVFsXjxYpYuXcrVq1cpXbo0PXr0IDQ0lMqVKyuWa9MmOHYsq6dxp07yUR5zk4XWTPJjoY2PhylT4PZtaNMGunV7/mOFh0PHjnDrFri5wZo1Wc/u5QdpaWmsX7+exYsXs2nTJoQQvPTSS4SGhtK5c2ecnJyUjiiZ0eXLl1m6dCmLFy/mxIkTFClShNdff53Q0FDq168vby0UQLLQmkl+K7TJyVCjRlanISGyLjnNmAFvv/3sxzIYwNMT7tzJ6nyhVoOzM8TFgQWvoFnE7du3WblyJYsXL2bPnj3Y2trSrFkzOnToQIcOHfD19VU6ovSCjEYjkZGRrF+/nvXr13P06FEcHBzo3LkzPXr0oFWrVnKS9QJOFlozyW+F9rffsnrj/pufH5w9++zHio/P6nDxX5cuQalSzxUvT7h8+TJr1qxh/fr17Ny5E71eT82aNU1FNyAgQI5ClUekpaWxbds21q9fz4YNG4iNjaVw4cK0bduWDh060LZtW5ydnZWOKVkJWWjNJL8V2tWr4ZVXsq+rXBlOnnz2YxkMWYU2MTH7GW18PNjZ5U5ea5ecnMzmzZtZv349f/zxB3fu3MHLy4v27dvTtm1bGjduTJEiRZSOKf1NCMGFCxfYvn07GzZs4K+//uL+/ftUqFCBjh070qFDBxo0aIA2r3c2kMxCFlozyW+FNi0NgoLg1KmswqjXw6JFEBr6fMfbvx86dMi6R1u4cNY92saNczVynqHX69m7dy/r169n3bp1nDt3DoDq1asTEhJCSEiILLwW9qCwhoWFmZbr16+jVqtp0KABHTp0oGPHjvj7+ysdVcoDZKE1k/xWaCHrYfcff8zqDNWqFbRo8WLHMxiyeh17eOT9Xse56fLly+zcudP0Az4mJgbIXngbNWqEh4eHwknzDyEE58+fz/Z1f1BYAwICTF/3Bg0a4JrTiA+S9Biy0JpJfiy0kjIeVXhLlSpFQEAAAQEB1K5dm4CAAIoWLapwWutnNBq5ePEikZGRpuXw4cMkJSXJwiqZRZ4utJ9//jkbN27k6NGj2NrakpSU9MR9hBCMHz+eOXPmkJSURIMGDZg5cyYVKlQwbZOYmMg777zD+vXrUavVdOnShW+//faZHsuQhVYyl8uXL7Nv3z4OHz5sKhLJyckA+Pr6Ziu8lSpVomTJkmYZzi8vuH//PufPn+fEiROmonrkyJGHvl4BAQHUqVOH4OBgWVilXJenC+348eNxc3Pj2rVrzJ0796kK7ZQpU5g8eTILFy6kTJkyjB07luPHj3Pq1CnT6Cxt2rQhNjaW2bNno9Pp6NOnD4GBgSxZsuSps8lCK1nK487QAGxtbSlfvjx+fn4PLcWKFcvzz3Xq9XouX75MdHT0Q8uVK1dM2/37CsCDX0bkFQDJEvJ0oX1gwYIFDB069ImFVgiBj48Pw4cPZ8SIEUBW709PT08WLFhAt27dOH36NJUrV+bgwYPU+Xuwz82bN9O2bVuuXbuGz1OOsi0LraQkIQSXL1/m7NmzDxWfy5cv8+Bb0sXFhdKlS+Pt7W1afHx8sr329va26BCB//4MKSkpxMbGcuPGDWJjY7MtN27c4MaNG1y6dAmdTgeAnZ0dFSpUeOgXiooVK8rOZJJiLFEPrKabS0xMDHFxcbT4Vy8eV1dXgoKCCA8Pp1u3boSHh+Pm5mYqsgAtWrRArVYTERHByy+/nOOxMzIyyPjXhI4PLk2lpKSY6dNI0uO5u7sTHBxMcHBwtvXp6enExMRw/vx5zp8/z7Vr14iLi+PEiRNs27aNuLg4U+F6wNXVFWdnZxwdHXFycspxcXR0xN7eHrVajUajQa1Wo1KpEEIghMBoNGI0GjEYDKSlpZGamkpqair37t3j7t273Lt3j9TUVNPfk5KSSE9Pz5bDyckJT09PvL298fLyomrVqpQuXZry5ctTvnx5SpQo8chnkeX3oqSUB//3zHnOaTWFNi4uDgBPT89s6z09PU3vxcXFPTQurVarxd3d3bRNTiZPnsyECRMeWi9H/pHyg+TkZNMvj0p6UJwvXLigdBRJema3b982Wx+AZyq0o0aNYsqUKY/d5vTp01SsWPGFQuW20aNHM2zYMNPrpKQkSpUqxZUrV/Js54qUlBR8fX25evVqnrz8LfMrL69/hryeH/L+Z8jr+SHrF9WSJUvi7u5utjaeqdAOHz6cN99887HbPO+cjV5/j/sXHx+Pt7e3aX18fDw1a9Y0bZOQkJBtP71eT2Jiomn/nNjZ2WGXw7BGrq6uefY/xwMuLi55+jPI/MrL658hr+eHvP8Z8np+wKxDrD5ToS1atKjZegKWKVMGLy8vtm3bZiqsKSkpRERE8NZbbwEQHBxMUlISkZGRBAQEALB9+3aMRiNBQUFmySVJkiRJL8JsJfzKlSscPXqUK1euYDAYOHr0KEePHiU1NdW0TcWKFVm9ejUAKpWKoUOH8tlnn7Fu3TqOHz9Or1698PHxoXPnzv9v72xjori6OH7WlV1AWKBZFWmVyku3VBbBD1CIdU0hupa2JDapYGOxNdAXiW1tUWkrVGhTWolNamhrDC9+sN2oQTEpoLGBtBKUSldFQMJS1Nq0JGDlvVbw/3zos/Mw7gK7ywwvPueXbOKcOTP3f+6ZO8eQe+cSEVFYWBgZjUZKS0uj+vp6qq2tpYyMDEpOTnZ4xjHDMAzDTCWyTYbKzs6mQ4cOCcdRUVFERFRdXU2rV68mIqLW1lbRJI4dO3bQwMAApaen0+3bt2nlypVUVVUlWr5w+PBhysjIoPj4eOGDFV9++aVT2tRqNeXk5Nj9c/JsYbbHwPqnn9kew2zXTzT7Y5jt+ommJob/y08wMgzDMMxUwRtsMgzDMIyMcKFlGIZhGBnhQsswDMMwMsKFlmEYhmFk5IEstJ988gnFxcWRp6cn+fr6OnQNAMrOzqZFixaRh4cHJSQkUFtbm8jn1q1b9NJLL5FGoyFfX1/asmWLaLmSlDjb1rVr10ihUNj9HT16VPCzd95kMk27fiKi1atX22h7/fXXRT43btygxMRE8vT0pAULFlBmZiYNDw9Lrt+VGKxbOOp0OvLw8KAlS5bQtm3bbD6PKFcOCgsL6dFHHyV3d3eKiYmh+vr6cf2PHj1Kjz/+OLm7u5Ner6eKigrReUfGhNQ4E8PBgwfpqaeeIj8/P/Lz86OEhAQb/82bN9v0tdFonBH6S0tLbbTdv0HETM+BvTGrUCgoMTFR8JnKHPz444/03HPPUUBAACkUCjpx4sSE19TU1NCKFStIrVZTSEgIlZaW2vg4O7ZswANIdnY29u3bh+3bt8PHx8eha/Lz8+Hj44MTJ07g0qVLeP7557F06VIMDQ0JPkajEcuXL8e5c+fw008/ISQkBCkpKbLE4Gxbw8PD+OOPP0S/PXv2wMvLC319fYIfEaGkpETkNzrG6dIPAAaDAWlpaSJtPT09ohjDw8ORkJAAs9mMiooKaLVaZGVlSa7flRgaGxuxfv16nDx5EhaLBT/88ANCQ0PxwgsviPzkyIHJZIJKpUJxcTGampqQlpYGX19fdHZ22vWvra2FUqnE559/jubmZnz44Ydwc3NDY2Oj4OPImJASZ2PYuHEjCgsLYTab0dLSgs2bN8PHxwc3b94UfFJTU2E0GkV9fevWrRmhv6SkBBqNRqTtzz//FPnM9Bx0d3eL9F+5cgVKpRIlJSWCz1TmoKKiAh988AHKyspARDh+/Pi4/r/++is8PT2xfft2NDc3Y//+/VAqlaiqqhJ8nO0TezyQhdZKSUmJQ4X23r178Pf3x969ewXb7du3oVar8d133wEAmpubQUT4+eefBZ/KykooFAr8/vvvkuqWqq3IyEi8+uqrIpsjD99kcVW/wWDAW2+9Neb5iooKzJkzR/Qy+vrrr6HRaHDnzh1JtFuRKgdHjhyBSqXC3bt3BZscOYiOjsbWrVuF45GREQQEBODTTz+16//iiy8iMTFRZIuJicFrr70GwLExITXOxnA/w8PD8Pb2xqFDhwRbamoqkpKSpJZqF2f1T/R+mo05+OKLL+Dt7Y3+/n7BNpU5GI0j42zHjh1YtmyZyLZhwwasXbtWOJ5snwDAA/mnY2eZaIs+Ippwiz4pkaKthoYGunjxIm3ZssXm3NatW0mr1VJ0dDQVFxdLvj3UZPQfPnyYtFothYeHU1ZWFg0ODoruq9frRTs8rV27lnp7e6mpqWnGxDAa6x6Xc+eKvw0jZQ7++ecfamhoED2/c+bMoYSEBOH5vZ+6ujqRP9G/fWn1d2RMSIkrMdzP4OAg3b171+bj8DU1NbRgwQLS6XT0xhtvUHd3t6TaiVzX39/fT4GBgbR48WJKSkoSPcezMQdFRUWUnJxM8+bNE9mnIgeuMNE4kKJPiGbQNnnTiZxb9LmqZ7JtFRUVUVhYGMXFxYnsubm59PTTT5OnpyedPn2a3nzzTerv76dt27ZNu/6NGzdSYGAgBQQE0OXLl2nnzp3U2tpKZWVlwn3t5ch6TkqkyEFXVxfl5eVRenq6yC51Drq6umhkZMRu31y9etXuNWP15ejn3Woby0dKXInhfnbu3EkBAQGil6LRaKT169fT0qVLqb29nd5//31at24d1dXVkVKpnFb9Op2OiouLKSIignp6eqigoIDi4uKoqamJHnnkkVmXg/r6erpy5QoVFRWJ7FOVA1cYaxz09vbS0NAQ/fXXX5N+LolmUaGdrVv0jcbRGCbL0NAQffvtt7R7926bc6NtUVFRNDAwQHv37nXoJS+3/tEFSa/X06JFiyg+Pp7a29spODjY5fuOZqpy0NvbS4mJifTEE0/QRx99JDo3mRww9snPzyeTyUQ1NTWiCUXJycnCv/V6PUVERFBwcDDV1NRQfHz8dEgViI2NpdjYWOE4Li6OwsLC6MCBA5SXlzeNylyjqKiI9Ho9RUdHi+wzOQdTxawptLN1i77ROBrDZNs6duwYDQ4O0ssvvzyhb0xMDOXl5dGdO3cm/NbnVOkfrY2IyGKxUHBwMPn7+9vM9uvs7CQimlE56OvrI6PRSN7e3nT8+HFyc3Mb19+ZHNhDq9WSUqkU+sJKZ2fnmFr9/f3H9XdkTEiJKzFYKSgooPz8fDpz5gxFRESM6xsUFERarZYsFoukL/nJ6Lfi5uZGUVFRZLFYiGh25WBgYIBMJhPl5uZO2I5cOXCFscaBRqMhDw8PUiqVk84rET2Ys46tODsZqqCgQLD19PTYnQx14cIFwefUqVOyToZytS2DwWAz03UsPv74Y/j5+bms1R5S9dXZs2dBRLh06RKA/02GGj3b78CBA9BoNPj777+lCwCux9DT04Mnn3wSBoMBAwMDDrUlRQ6io6ORkZEhHI+MjODhhx8edzLUs88+K7LFxsbaTIYab0xIjbMxAMBnn30GjUaDuro6h9r47bffoFAoUF5ePmm99+OK/tEMDw9Dp9PhnXfeATB7cgD8+65Vq9Xo6uqasA05czAacnAyVHh4uMiWkpJiMxlqMnkFHtBZx9evX4fZbBaWt5jNZpjNZtEyF51Oh7KyMuE4Pz8fvr6+KC8vx+XLl5GUlGR3eU9UVBTOnz+Ps2fPIjQ0VNblPeO1dfPmTeh0Opw/f150XVtbGxQKBSorK23uefLkSRw8eBCNjY1oa2vDV199BU9PT2RnZ0+7fovFgtzcXFy4cAEdHR0oLy9HUFAQVq1aJVxjXd6zZs0aXLx4EVVVVZg/f76sy3uciaGnpwcxMTHQ6/WwWCyi5QzDw8MA5MuByWSCWq1GaWkpmpubkZ6eDl9fX2GG9qZNm7Br1y7Bv7a2FnPnzkVBQQFaWlqQk5Njd3nPRGNCSpyNIT8/HyqVCseOHRP1tXWc9/X14b333kNdXR06Ojpw5swZrFixAqGhoZL/x8wV/Xv27MGpU6fQ3t6OhoYGJCcnw93dHU1NTaIYZ3IOrKxcuRIbNmywsU91Dvr6+oT3PRFh3759MJvNuH79OgBg165d2LRpk+BvXd6TmZmJlpYWFBYW2l3eM16fOMIDWWhTU1NBRDa/6upqwYf+u5bRyr1797B7924sXLgQarUa8fHxaG1tFd23u7sbKSkp8PLygkajwSuvvCIq3lIyUVsdHR02MQFAVlYWFi9ejJGREZt7VlZWIjIyEl5eXpg3bx6WL1+Ob775xq7vVOu/ceMGVq1ahYceeghqtRohISHIzMwUraMFgGvXrmHdunXw8PCAVqvFu+++K1o6M50xVFdX233uiAgdHR0A5M3B/v37sWTJEqhUKkRHR+PcuXPCOYPBgNTUVJH/kSNH8Nhjj0GlUmHZsmX4/vvvRecdGRNS40wMgYGBdvs6JycHADA4OIg1a9Zg/vz5cHNzQ2BgINLS0px6Qcqp/+233xZ8Fy5ciGeeeQa//PKL6H4zPQcAcPXqVRARTp8+bXOvqc7BWGPQqjk1NRUGg8HmmsjISKhUKgQFBYnqgpXx+sQReJs8hmEYhpERXkfLMAzDMDLChZZhGIZhZIQLLcMwDMPICBdahmEYhpERLrQMwzAMIyNcaBmGYRhGRrjQMgzDMIyMcKFlGIZhGBnhQsswDMMwMsKFlmEYhmFkhAstwzAMw8gIF1qGYRiGkZH/AMv0R08/67UCAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 500x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Plot \n",
|
||
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
"ax.add_patch(circle)\n",
|
||
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
"plt.xlim(-1, 1)\n",
|
||
"plt.ylim(-1, 1)\n",
|
||
"\n",
|
||
"# Plot samples not in the circle\n",
|
||
"for coord in square_coords:\n",
|
||
" c = plt.Circle(coord, 0.01, color='blue')\n",
|
||
" ax.add_patch(c)\n",
|
||
"\n",
|
||
"# Plot samples in the circle\n",
|
||
"for coord in circle_coords:\n",
|
||
" c = plt.Circle(coord, 0.01, color='red')\n",
|
||
" ax.add_patch(c)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "704b68d6-4210-4f90-a1ae-9a0078fc8796",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-b0626976cd84b809",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"Um einen genaueren Wert für $\\pi$ zu erhalten, muss lediglich die Anzahl der Samples erhöht werden (hier: 1 Million).\n",
|
||
"\n",
|
||
"Da im Folgenden auf eine grafische Darstellung verzichtet wird, lässt sich die Berechnung darauf vereinfachen, lediglich zu zählen, wie viele Punkte im Kreis liegen – die konkreten Koordinaten sind dabei nicht mehr von praktischem Nutzen:\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "38ca2a0d-3198-48c2-8af0-26516a01c9d9",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-0512fe6559228e5c",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Pi = 3.14178\n",
|
||
"Difference to real Value -0.00018734641020667908\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Get Uniform x, y samples\n",
|
||
"sample_size = 1_000_000\n",
|
||
"rand = np.random.default_rng(42) # Set fixed Value\n",
|
||
"x_rand = rand.uniform(-1, 1, sample_size)\n",
|
||
"y_rand = rand.uniform(-1, 1, sample_size)\n",
|
||
"\n",
|
||
"# reserve two arrays\n",
|
||
"in_circle = 0\n",
|
||
"in_square = 0\n",
|
||
"\n",
|
||
"for x,y in zip(x_rand, y_rand):\n",
|
||
" # calculate distance from origin\n",
|
||
" dist_from_origin = x**2 + y**2\n",
|
||
"\n",
|
||
" # if distance smaller or equal than 1, the point is in the circle\n",
|
||
" if dist_from_origin <= 1:\n",
|
||
" in_circle += 1\n",
|
||
"\n",
|
||
" # by definition is every point in the square\n",
|
||
" in_square += 1\n",
|
||
"\n",
|
||
"pi = 4 * in_circle / in_square\n",
|
||
"print(f\"Pi = {pi}\")\n",
|
||
"print(f\"Difference to real Value {np.pi - pi}\")"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "167e5e63-254b-4158-9e14-f3c9ddf0259f",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-95ca10cecf8fe36e",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"### Aufgabe – Arbeitszeit abschätzen\n",
|
||
"\n",
|
||
"*15 Punkte*\n",
|
||
"\n",
|
||
"Du befindest dich erneut in der Situation, dass dein Chef dich beauftragt, zwei wichtige Aufgaben bis zum Ende des Arbeitstages zu bearbeiten. Gleichzeitig bist du abends auf einem Grillfest mit deinen Freunden verabredet, das um 18 Uhr beginnt. \n",
|
||
"\n",
|
||
"Da du nun im Zwiespalt stehst, sowohl deinen beruflichen Aufgaben nachzukommen als auch das Grillfest pünktlich zu erreichen, fragst du dich, wie hoch die Wahrscheinlichkeit ist, dass du es in den nächsten 9 Stunden schaffst, beides unter einen Hut zu bringen.\n",
|
||
"\n",
|
||
"Nach einigen Überlegungen stellst du Folgendes fest:\n",
|
||
"\n",
|
||
"- Für die erste Aufgabe benötigst du zwischen 1–5 Stunden. \n",
|
||
"- Für die zweite Aufgabe benötigst du zwischen 2–6 Stunden. \n",
|
||
"- Egal wie schnell du eine Aufgabe erledigst, es gibt keine Auswirkungen auf die andere Aufgabe (die Aufgaben sind unabhängig voneinander).\n",
|
||
"\n",
|
||
"Nun sollst du die Wahrscheinlichkeit berechnen, dass du pünktlich beim Grillfest ankommst.\n",
|
||
"\n",
|
||
"Gehe dazu wie folgt vor:\n",
|
||
"\n",
|
||
"1. Nimm an, dass beide Aufgaben gleichmäßig verteilt sind, und speichere die Verteilungen in den Variablen `exc1` & `exc2`.\n",
|
||
"2. Verwende eine geeignete Anzahl an Samples und speichere diese in der Variablen `sims`.\n",
|
||
"3. Speichere die Wahrscheinlichkeit, dass du pünktlich zum Grillfest kommst, in der Variablen `chance` mit einer Genauigkeit von zwei Nachkommastellen.\n",
|
||
"4. Plotte die Verteilungen der Aufgabenzeiten und beziehe dabei die Variable `chance` ein, z.B. als Annotation oder Beschriftung.\n",
|
||
"\n",
|
||
"In der Markdownzelle (Keine Antwort = 0 Punkte):\n",
|
||
"- Stelle dein Ergebnis begründet dar.\n",
|
||
"- Interpretiere deinen Plot.\n",
|
||
"- Erkläre in eigenen Worten, warum dein Ergebnis aussagekräftig ist."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "cb2bda83-a3f7-4c46-a2be-f809ec55558c",
|
||
"metadata": {
|
||
"editable": true,
|
||
"nbgrader": {
|
||
"grade": true,
|
||
"grade_id": "cell-65cc1054d6bb7253",
|
||
"locked": false,
|
||
"points": 2,
|
||
"schema_version": 3,
|
||
"solution": true,
|
||
"task": false
|
||
},
|
||
"slideshow": {
|
||
"slide_type": ""
|
||
},
|
||
"tags": []
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 900x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"rand = np.random.default_rng(42) # Use this rng!\n",
|
||
"# BEGIN SOLUTION\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"sims = 1_000 # 1 Punkt\n",
|
||
"\n",
|
||
"# 2 Punkte\n",
|
||
"exc1 = rand.uniform(1,5,sims) \n",
|
||
"exc2 = rand.uniform(2,6,sims)\n",
|
||
"\n",
|
||
"duration = exc1 + exc2 # 1 Punkt\n",
|
||
"chance = float(np.round((duration > 9).sum()/sims, decimals=2)) # 1 Punkt\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots(figsize=(9,6))\n",
|
||
"ax.hist(duration, density=True) # 1 Punkt\n",
|
||
"ax.axvline(9, color='r') # 1 Punkt\n",
|
||
"ax.text(0.5,0.25,\n",
|
||
" f\"Chance to attend the Party {(1-chance)*100:.0f}%\",\n",
|
||
" ha='center', va='center', transform=ax.transAxes,\n",
|
||
" bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
|
||
" color='#de2e0b'\n",
|
||
" )\n",
|
||
"plt.show()\n",
|
||
"# END SOLUTION"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a12f9c24-2068-4ea9-8a73-83738cf654aa",
|
||
"metadata": {},
|
||
"source": [
|
||
"# BEGIN SOLUTION\n",
|
||
"# END SOLUTION"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "0910695e-4c60-4608-9152-519db84687d9",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": true,
|
||
"grade_id": "cell-9fd6737ce69879f1",
|
||
"locked": true,
|
||
"points": 5,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Hier werden ihre Lösungen getestet...\n",
|
||
"import math\n",
|
||
"assert math.isclose(chance, 0.13, rel_tol=0.1)\n",
|
||
"\n",
|
||
"### BEGIN HIDDEN TESTS\n",
|
||
"assert sims > 999\n",
|
||
"assert sims < 10_000_000\n",
|
||
"\n",
|
||
"trand = np.random.default_rng(42)\n",
|
||
"\n",
|
||
"texc1 = trand.uniform(1,5,sims) \n",
|
||
"texc2 = trand.uniform(2,6,sims)\n",
|
||
"\n",
|
||
"assert np.array_equal(exc1, texc1)\n",
|
||
"assert np.array_equal(exc2, texc2)\n",
|
||
"### END HIDDEN TESTS"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "aaaf624d-63ed-4645-a793-0ef2aebcb44d",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-8eb45ec252910d85",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"### Aufgabe – Simulation einer Körpergewichtszunahme\n",
|
||
"\n",
|
||
"*25 Punkte*\n",
|
||
"\n",
|
||
"Gegeben sind die nach Altersgruppen aufgeschlüsselten Durchschnittskörpergewichte (in kg) von Männern in Deutschland. \n",
|
||
"Quelle: [Statistisches Bundesamt](https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Gesundheit/Gesundheitszustand-Relevantes-Verhalten/Tabellen/koerpermasse-maenner.html)\n",
|
||
"\n",
|
||
"Ziel ist es, mittels Monte-Carlo-Simulation den mittleren wöchentlichen Gewichtszuwachs zu bestimmen und die Wahrscheinlichkeit zu finden, dass ein Durchschnittsmann innerhalb einer Woche 3 kg abnimmt.\n",
|
||
"\n",
|
||
"**Vorgehensweise:**\n",
|
||
"\n",
|
||
"1. Bestimme das arithmetische Mittel der Durchschnittsgewichte über die Altersgruppen und speichere diesen Wert in `avg_weight` mit einer Genauigkeit von 1 Dezimalstelle.\n",
|
||
"2. Wähle eine geeignete Anzahl an Samples (`sims`) für die Simulation.\n",
|
||
"3. Nimm an, dass das Durchschnittsgewicht normalverteilt ist, mit einer Standardabweichung von 5% des Durchschnittsgewichts, und speichere die simulierten Werte in `men_normal`.\n",
|
||
"4. Nimm an, dass die tägliche Gewichtsschwankung eines Mannes gleichverteilt zwischen ±2.5 kg ist.\n",
|
||
"5. Simuliere die Gewichtszunahmen/-abnahmen für eine Woche (7 Tage) und speichere die Ergebnisse in `gain_week`.\n",
|
||
"6. Berechne die durchschnittliche wöchentliche Gewichtszunahme/-abnahme und speichere das Ergebnis in `duration`.\n",
|
||
"7. Bestimme die Wahrscheinlichkeit, dass ein Mann 3 kg oder mehr abnimmt, und speichere sie in `gain_percent`.\n",
|
||
"8. Plotte die Verteilung der simulierten Werte und markiere die relevanten Kennzahlen (Durchschnitt, Schwankungsbereich, Wahrscheinlichkeit).\n",
|
||
"\n",
|
||
"In der Markdownzelle (Keine Antwort = 0 Punkte):\n",
|
||
"- Bewerte & Beurteile die gegebenen Daten, sowie Quelle.\n",
|
||
"- Erkläre & Interpretiere deinen Plot.\n",
|
||
"- Bewerte die angewandte Methodik im Zusammenhang mit der Aufgabe, beziehe dein Ergebnis anschaulich mit ein.\n",
|
||
"- Beurteile anhand deiner Simulation den [Bild Artikel](https://www.bild.de/leben-wissen/psychologie-liebe/gewichtszunahme-in-der-ehe-das-stimmt-vor-allem-fuer-maenner-67d2e348aae7056ac7dd201d) - *\"Ehe macht dick – vor allem die Männer\"*"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "b8b21830-be8e-43f2-ae68-7e1867aa46e4",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": false,
|
||
"grade_id": "cell-a9d02e6e26d7f2eb",
|
||
"locked": true,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Given\n",
|
||
"avg_weight_per_men = {\n",
|
||
" \"18 - 20\": 77.9,\n",
|
||
" \"20 - 25\": 80.5,\n",
|
||
" \"25 - 30\": 83.3,\n",
|
||
" \"30 - 35\": 85.6,\n",
|
||
" \"35 - 40\": 86.7,\n",
|
||
" \"40 - 45\": 88.1,\n",
|
||
" \"45 - 50\": 89.8,\n",
|
||
" \"50 - 55\": 89.0,\n",
|
||
" \"55 - 60\": 88.8,\n",
|
||
" \"60 - 65\": 87.9,\n",
|
||
" \"65 - 70\": 86.7,\n",
|
||
" \"70 - 75\": 85.3,\n",
|
||
" \"75+\": 81.0\n",
|
||
"}"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 88,
|
||
"id": "926897fc-25a8-470c-b06b-946f7370a048",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": true,
|
||
"grade_id": "cell-ef59ae554f2f4540",
|
||
"locked": false,
|
||
"points": 2,
|
||
"schema_version": 3,
|
||
"solution": true,
|
||
"task": false
|
||
}
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x500 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"0.31\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"rand = np.random.default_rng(420) # Use this rng!\n",
|
||
"\n",
|
||
"# BEGIN SOLUTION\n",
|
||
"avg_weight = np.round(np.mean(list(avg_weight_per_men.values())), decimals=1) # 1 Punkt\n",
|
||
"\n",
|
||
"sims = 1_000 # 1 Punkt\n",
|
||
"\n",
|
||
"# 3 Punkte\n",
|
||
"sigma = np.round(avg_weight * 0.05, decimals=1)\n",
|
||
"men_normal = rand.normal(avg_weight, sigma, sims)\n",
|
||
"gain_week = [\n",
|
||
" rand.uniform(-2.5, 2.5, sims)\n",
|
||
" for _ in range(7)\n",
|
||
"]\n",
|
||
"\n",
|
||
"# Sum up 2 Punkte\n",
|
||
"duration = np.zeros(sims)\n",
|
||
"for gain in gain_week:\n",
|
||
" duration += gain\n",
|
||
"duration += men\n",
|
||
"\n",
|
||
"gain_percent = float(np.round((duration < avg_weight-3).sum()/sims, decimals=2)) # 1 Punkt\n",
|
||
"\n",
|
||
"plt.figure(figsize=(10,5))\n",
|
||
"plt.hist(duration, density=True) # 1 Punkt\n",
|
||
"plt.axvline(avg_weight-3, color='r') # 1 Punkt\n",
|
||
"plt.show()\n",
|
||
"print(gain_percent)\n",
|
||
"# END SOLUTION"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "01d0d2ee-af6a-46b4-8cdf-652024bb468d",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": true,
|
||
"grade_id": "cell-089ff54f3c3db43b",
|
||
"locked": false,
|
||
"points": 3,
|
||
"schema_version": 3,
|
||
"solution": true,
|
||
"task": false
|
||
}
|
||
},
|
||
"source": [
|
||
"# BEGIN SOLUTION\n",
|
||
"# END SOLUTION"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 94,
|
||
"id": "dfe81dfc-5096-4c5b-8e84-81267e212cfa",
|
||
"metadata": {
|
||
"nbgrader": {
|
||
"grade": true,
|
||
"grade_id": "cell-87149b330de46548",
|
||
"locked": true,
|
||
"points": 8,
|
||
"schema_version": 3,
|
||
"solution": false,
|
||
"task": false
|
||
}
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Hier werden ihre Lösungen getestet...\n",
|
||
"import math\n",
|
||
"assert math.isclose(float(gain_percent), 0.3, rel_tol=0.1)\n",
|
||
"\n",
|
||
"### BEGIN HIDDEN TESTS\n",
|
||
"assert sims > 499\n",
|
||
"assert sims < 2_001\n",
|
||
"\n",
|
||
"trand = np.random.default_rng(420)\n",
|
||
"\n",
|
||
"t_sigma = np.round(avg_weight * 0.05, decimals=1)\n",
|
||
"t_men = trand.normal(avg_weight, sigma, sims)\n",
|
||
"t_gain_week = [\n",
|
||
" trand.uniform(-2.5, 2.5, sims)\n",
|
||
" for _ in range(7)\n",
|
||
"]\n",
|
||
"\n",
|
||
"assert math.isclose(sigma, t_sigma, rel_tol=0.1)\n",
|
||
"\n",
|
||
"for el1, el2 in zip(gain_week, t_gain_week):\n",
|
||
" assert np.array_equal(el1, el2)\n",
|
||
"\n",
|
||
"assert np.array_equal(t_men, men)\n",
|
||
"\n",
|
||
"t_duration = np.zeros(sims)\n",
|
||
"for gain in t_gain_week:\n",
|
||
" t_duration += gain\n",
|
||
"t_duration += t_men\n",
|
||
"\n",
|
||
"assert np.array_equal(t_duration, duration)\n",
|
||
"### END HIDDEN TESTS"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (ipykernel)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.11.6"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|