ml-finance-python
python scripts for finance machine learning
git clone https://9o.is/git/ml-finance-python.git
notebook.ipynb
(191504B)
1 {
2 "cells": [
3 {
4 "cell_type": "markdown",
5 "metadata": {
6 "deletable": true,
7 "editable": true
8 },
9 "source": [
10 "# Exercises: Random Variables - Answer Key\n",
11 "By Christopher van Hoecke, Max Margenot, and Delaney Mackenzie\n",
12 "\n",
13 "## Lecture Link : \n",
14 "https://www.quantopian.com/lectures/random-variables\n",
15 "\n",
16 "### IMPORTANT NOTE: \n",
17 "This lecture corresponds to the Random Variables lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.\n",
18 "\n",
19 "Part of the Quantopian Lecture Series:\n",
20 "\n",
21 "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
22 "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
23 "\n",
24 "----"
25 ]
26 },
27 {
28 "cell_type": "markdown",
29 "metadata": {
30 "deletable": true,
31 "editable": true
32 },
33 "source": [
34 "## Key Concepts"
35 ]
36 },
37 {
38 "cell_type": "code",
39 "execution_count": 1,
40 "metadata": {
41 "collapsed": true,
42 "deletable": true,
43 "editable": true
44 },
45 "outputs": [],
46 "source": [
47 "# Useful Functions\n",
48 "class DiscreteRandomVariable:\n",
49 " def __init__(self, a=0, b=1):\n",
50 " self.variableType = \"\"\n",
51 " self.low = a\n",
52 " self.high = b\n",
53 " return\n",
54 " def draw(self, numberOfSamples):\n",
55 " samples = np.random.randint(self.low, self.high, numberOfSamples)\n",
56 " return samples\n",
57 " \n",
58 "class BinomialRandomVariable(DiscreteRandomVariable):\n",
59 " def __init__(self, numberOfTrials = 10, probabilityOfSuccess = 0.5):\n",
60 " self.variableType = \"Binomial\"\n",
61 " self.numberOfTrials = numberOfTrials\n",
62 " self.probabilityOfSuccess = probabilityOfSuccess\n",
63 " return\n",
64 " def draw(self, numberOfSamples):\n",
65 " samples = np.random.binomial(self.numberOfTrials, self.probabilityOfSuccess, numberOfSamples)\n",
66 " return samples\n",
67 " \n",
68 "def factorial(n):return reduce(lambda x,y:x*y,[1]+range(1,n+1))"
69 ]
70 },
71 {
72 "cell_type": "code",
73 "execution_count": 2,
74 "metadata": {
75 "collapsed": true,
76 "deletable": true,
77 "editable": true
78 },
79 "outputs": [],
80 "source": [
81 "# Useful Libraries\n",
82 "import pandas as pd\n",
83 "import numpy as np\n",
84 "import matplotlib.pyplot as plt\n",
85 "import statsmodels.stats as stats\n",
86 "from statsmodels.stats import stattools\n",
87 "from __future__ import division"
88 ]
89 },
90 {
91 "cell_type": "markdown",
92 "metadata": {
93 "deletable": true,
94 "editable": true
95 },
96 "source": [
97 "---"
98 ]
99 },
100 {
101 "cell_type": "markdown",
102 "metadata": {
103 "collapsed": true,
104 "deletable": true,
105 "editable": true
106 },
107 "source": [
108 "# Exercise 1 : Uniform Distribution\n",
109 "- Plot the histogram of 10 tosses with a fair coin (let 1 be heads and 2 be tails). \n",
110 "- Plot the histogram of 1000000 tosses of a fair coin"
111 ]
112 },
113 {
114 "cell_type": "code",
115 "execution_count": 3,
116 "metadata": {
117 "collapsed": false,
118 "deletable": true,
119 "editable": true
120 },
121 "outputs": [
122 {
123 "data": {
124 "image/png": "iVBORw0KGgoAAAANSUhEUgAAAz4AAAHxCAYAAACs6mmQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
125 "text/plain": [
126 "<matplotlib.figure.Figure at 0x7f20c0f9b210>"
127 ]
128 },
129 "metadata": {},
130 "output_type": "display_data"
131 }
132 ],
133 "source": [
134 "# Histograms with 10 tosses. \n",
135 "cointoss = DiscreteRandomVariable(1, 3)\n",
136 "plt.hist(cointoss.draw(10), align = 'mid')\n",
137 "\n",
138 "plt.xlabel('Value')\n",
139 "plt.ylabel('Occurences')\n",
140 "plt.legend(['Coin Tosses']);"
141 ]
142 },
143 {
144 "cell_type": "code",
145 "execution_count": 4,
146 "metadata": {
147 "collapsed": false,
148 "deletable": true,
149 "editable": true,
150 "scrolled": false
151 },
152 "outputs": [
153 {
154 "data": {
155 "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1oAAAHxCAYAAAB05s2aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAgAAKNj/Bwk0j948AfNcAAAAAElFTkSuQmCC\n",
156 "text/plain": [
157 "<matplotlib.figure.Figure at 0x7f20c11bb0d0>"
158 ]
159 },
160 "metadata": {},
161 "output_type": "display_data"
162 }
163 ],
164 "source": [
165 "# Histograms with 1000000 tosses. \n",
166 "cointoss = DiscreteRandomVariable(1, 3)\n",
167 "plt.hist(cointoss.draw(1000000), align = 'mid')\n",
168 "\n",
169 "plt.xlabel('Value')\n",
170 "plt.ylabel('Occurences')\n",
171 "plt.legend(['Coin Tosses']);"
172 ]
173 },
174 {
175 "cell_type": "markdown",
176 "metadata": {
177 "deletable": true,
178 "editable": true
179 },
180 "source": [
181 "---"
182 ]
183 },
184 {
185 "cell_type": "markdown",
186 "metadata": {
187 "deletable": true,
188 "editable": true
189 },
190 "source": [
191 "# Exercise 2 : Binomial Distributions.\n",
192 "- Graph the histogram of 1000000 samples from a binomial distribution of probability 0.25 and $n = 20$\n",
193 "- Find the value that occurs the most often\n",
194 "- Calculate the probability of the value that occurs the most often occurring. *Use the factorial(x) function to find factorials*"
195 ]
196 },
197 {
198 "cell_type": "code",
199 "execution_count": 5,
200 "metadata": {
201 "collapsed": false,
202 "deletable": true,
203 "editable": true
204 },
205 "outputs": [
206 {
207 "data": {
208 "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAH6CAYAAAAa1O1kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnzsAAAAASUVORK5CYII=\n",
209 "text/plain": [
210 "<matplotlib.figure.Figure at 0x7f20b8132e90>"
211 ]
212 },
213 "metadata": {},
214 "output_type": "display_data"
215 }
216 ],
217 "source": [
218 "# Binomial distribution with p=0.25 and n=20\n",
219 "binomialdistribution = BinomialRandomVariable(20, 0.25)\n",
220 "bins = np.arange(0,21,1)\n",
221 "n, bins, patches = plt.hist(binomialdistribution.draw(1000000), bins=bins)\n",
222 "\n",
223 "plt.title('Binomial Distribution with p=0.25 and n=20')\n",
224 "plt.xlabel('Value')\n",
225 "plt.ylabel('Occurrences')\n",
226 "plt.legend(['Die Rolls']);"
227 ]
228 },
229 {
230 "cell_type": "code",
231 "execution_count": 6,
232 "metadata": {
233 "collapsed": false,
234 "deletable": true,
235 "editable": true,
236 "scrolled": false
237 },
238 "outputs": [
239 {
240 "name": "stdout",
241 "output_type": "stream",
242 "text": [
243 "Maximum occurance for x = 5\n"
244 ]
245 }
246 ],
247 "source": [
248 "# Finding x which occurs most often\n",
249 "elem = np.argmax(n)\n",
250 "print 'Maximum occurance for x =', elem"
251 ]
252 },
253 {
254 "cell_type": "code",
255 "execution_count": 7,
256 "metadata": {
257 "collapsed": false,
258 "deletable": true,
259 "editable": true
260 },
261 "outputs": [
262 {
263 "name": "stdout",
264 "output_type": "stream",
265 "text": [
266 "proabability of x = 5 0.0147857666016\n"
267 ]
268 }
269 ],
270 "source": [
271 "# Calculating the probability of finding x. \n",
272 "n = 20\n",
273 "p = 0.5\n",
274 "x = elem\n",
275 "n_factorial = factorial(n)\n",
276 "x_factorial = factorial(x)\n",
277 "n_x_factorial = factorial(n-x)\n",
278 "fact = n_factorial / (n_x_factorial * x_factorial)\n",
279 "probability = fact * (p**x) * ((1-p)**(n-x))\n",
280 "print 'proabability of x = %d' % x, probability"
281 ]
282 },
283 {
284 "cell_type": "markdown",
285 "metadata": {
286 "deletable": true,
287 "editable": true
288 },
289 "source": [
290 "---"
291 ]
292 },
293 {
294 "cell_type": "markdown",
295 "metadata": {
296 "deletable": true,
297 "editable": true
298 },
299 "source": [
300 "# Exercise 3 : Normal Distributions\n",
301 "## a. Graphing\n",
302 "Graph a normal distribution using the Probability Density Function bellow, with a mean of 0 and standard deviation of 5. \n",
303 "\n",
304 "$$f(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}$$"
305 ]
306 },
307 {
308 "cell_type": "code",
309 "execution_count": 8,
310 "metadata": {
311 "collapsed": false,
312 "deletable": true,
313 "editable": true
314 },
315 "outputs": [
316 {
317 "data": {
318 "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0oAAAH6CAYAAAA5j7yxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAnIWiBAAAAABnoSgBAAAAwFn+PzkfUPKdfILtAAAAAElFTkSuQmCC\n",
319 "text/plain": [
320 "<matplotlib.figure.Figure at 0x7f20a2f90d90>"
321 ]
322 },
323 "metadata": {},
324 "output_type": "display_data"
325 }
326 ],
327 "source": [
328 "# Graphing a normal distribution pdf. \n",
329 "mu = 0\n",
330 "sigma = 5\n",
331 "x = np.linspace(-30, 30, 200)\n",
332 "y = (1/(sigma * np.sqrt(2 * 3.14159))) * np.exp(-(x - mu)*(x - mu) / (2 * sigma * sigma))\n",
333 "plt.plot(x, y)\n",
334 "plt.title('Graph of PDF with mu = 0 and sigma = 5')\n",
335 "plt.xlabel('Value')\n",
336 "plt.ylabel('Probability');"
337 ]
338 },
339 {
340 "cell_type": "markdown",
341 "metadata": {
342 "deletable": true,
343 "editable": true
344 },
345 "source": [
346 "## b. Confidence Intervals. \n",
347 "- Calculate the first, second, and third confidence intervals. \n",
348 "- Plot the PDF and the first, second, and third confidence intervals. "
349 ]
350 },
351 {
352 "cell_type": "code",
353 "execution_count": 9,
354 "metadata": {
355 "collapsed": false,
356 "deletable": true,
357 "editable": true
358 },
359 "outputs": [
360 {
361 "name": "stdout",
362 "output_type": "stream",
363 "text": [
364 "1-sigma -> mu +/- 5\n",
365 "2-sigma -> mu +/- 10\n",
366 "3-sigma -> mu +/- 15\n"
367 ]
368 }
369 ],
370 "source": [
371 "# finding the 1st, 2nd, and third confidence intervals. \n",
372 "first_ci = (-sigma, sigma)\n",
373 "second_ci = (-2*sigma, 2*sigma)\n",
374 "third_ci = (-3*sigma, 3*sigma)\n",
375 "\n",
376 "print '1-sigma -> mu +/-', sigma\n",
377 "print '2-sigma -> mu +/-', second_ci[1]\n",
378 "print '3-sigma -> mu +/-', third_ci[1]"
379 ]
380 },
381 {
382 "cell_type": "code",
383 "execution_count": 10,
384 "metadata": {
385 "collapsed": false,
386 "deletable": true,
387 "editable": true
388 },
389 "outputs": [
390 {
391 "data": {
392 "image/png": "iVBORw0KGgoAAAANSUhEUgAAAzsAAAHrCAYAAADojoMpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
393 "text/plain": [
394 "<matplotlib.figure.Figure at 0x7f20b8184d50>"
395 ]
396 },
397 "metadata": {},
398 "output_type": "display_data"
399 }
400 ],
401 "source": [
402 "plt.axvline(first_ci[0], linestyle='dashdot', label='68% of observations', color = 'blue')\n",
403 "plt.axvline(first_ci[1], linestyle='dashdot', label='68% of observations', color = 'blue')\n",
404 "plt.axvline(second_ci[0], linestyle='dashdot', label='95% of observations', color = 'red')\n",
405 "plt.axvline(second_ci[1],linestyle='dashdot', color = 'red')\n",
406 "plt.axvline(third_ci[0], linestyle='dashdot', label='99% of observations', color = 'green')\n",
407 "plt.axvline(third_ci[1], linestyle='dashdot', color = 'green')\n",
408 "plt.plot(x,y)\n",
409 "plt.title('Graph of PDF with 3 confidence intervals.')\n",
410 "\n",
411 "plt.legend();"
412 ]
413 },
414 {
415 "cell_type": "markdown",
416 "metadata": {
417 "deletable": true,
418 "editable": true
419 },
420 "source": [
421 "---"
422 ]
423 },
424 {
425 "cell_type": "markdown",
426 "metadata": {
427 "deletable": true,
428 "editable": true
429 },
430 "source": [
431 "# Exercise 4: Financial Applications: \n",
432 "Fit the returns of SPY from 2016-01-01 to 2016-05-01 to a normal distribution. \n",
433 "- Fit the returns to a normal distribution by clacluating the values of $\\mu$ and $\\sigma$\n",
434 "- Plot the returns and the distribution, along with 3 confidence intervals. \n",
435 "- Use the Jarque-Bera test to check for normality. "
436 ]
437 },
438 {
439 "cell_type": "code",
440 "execution_count": 11,
441 "metadata": {
442 "collapsed": false,
443 "deletable": true,
444 "editable": true
445 },
446 "outputs": [],
447 "source": [
448 "# Collect prices and returns. \n",
449 "prices = get_pricing('SPY', start_date = '2016-01-01', end_date='2016-05-01', \n",
450 " fields = 'price')\n",
451 "returns = prices.pct_change()[1:]"
452 ]
453 },
454 {
455 "cell_type": "code",
456 "execution_count": 12,
457 "metadata": {
458 "collapsed": false,
459 "deletable": true,
460 "editable": true
461 },
462 "outputs": [],
463 "source": [
464 "# Calculating the mean and standard deviation. \n",
465 "sample_mean = np.mean(returns)\n",
466 "sample_std_dev = np.std(returns)\n",
467 "\n",
468 "x = np.linspace(-(sample_mean + 4 * sample_std_dev), (sample_mean + 4 * sample_std_dev), len(returns))\n",
469 "sample_distribution = ((1/(sample_std_dev * 2 * np.pi)) * \n",
470 " np.exp(-(x - sample_mean)*(x - sample_mean) / (2 * sample_std_dev * sample_std_dev)))"
471 ]
472 },
473 {
474 "cell_type": "code",
475 "execution_count": 13,
476 "metadata": {
477 "collapsed": false,
478 "deletable": true,
479 "editable": true
480 },
481 "outputs": [
482 {
483 "data": {
484 "image/png": "iVBORw0KGgoAAAANSUhEUgAAAy0AAAHiCAYAAADlMSNOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xt0VPW9///XXBPIhUBCEhISNqZELhGhIMq3ZSkVKV7K\nKrqUKOjiKHJaLR7qXejyaAOoKE04P7wGWO1CDliPij3gMkU9R4vcNNB6ggoYmEBAINwJuUwys39/\nRFIxhFwmmb2HPB9rZRF2Zva8+eSTz4dXPns+22GapikAAAAAsCmn1QUAAAAAwIUQWgAAAADYGqEF\nAAAAgK0RWgAAAADYGqEFAAAAgK0RWgAAAADYmrs1D/rLX/6ipUuXyu1264EHHtCll16qRx55RKZp\nqnfv3lqwYIE8Hk9n1woAAACgC3K0dJ+WEydOaPLkyVq9erXOnDmj//iP/1BdXZ3Gjh2r8ePHKz8/\nX3369FFubm64agYAAADQhbR4ediGDRv0k5/8RN26dVNSUpJ+//vfa8uWLRo7dqwkaezYsdqwYUOn\nFwoAAACga2rx8rD9+/erurpav/71r3X69Gndf//9qqmpabwcLDExURUVFZ1eKAAAAICuqcXQYpqm\nTpw4oRdffFH79+/XXXfdpe9fUdbC1WWSpOLi4tCqBAAAANAljBgxosmxFkNLUlKShg8fLqfTqYyM\nDMXExMjtdsvv98vr9erQoUNKTk5u14ujZcXFxbTd9xgFhiTJN8tnaR2RzDAMSZLP52vyNfpbK33X\nhjpPG6L16G8hoh+2yfn624XGQ7QO83LzGOPap7nFjhbf0/KTn/xEmzdvlmmaOn78uKqqqjR69Gi9\n//77kqSioiKNGTOmY6sFAAAAgO+0uNKSkpKin//857rtttvkcDj05JNPKicnR48++qj+/Oc/Ky0t\nTZMmTQpHrQC/yekA/EaxA9CGsAP6YcgYD0PHvIxwadV9Wm677Tbddttt5xxbtmxZpxQEAACAyGSa\npmpra60uwzZqamqsLsHWoqKi5HA4WvXYFi8PAwAAAFqjtraW0PKdIUOGWF2CrbW1r7RqpQUAAABo\njaioKEVHR1tdBi4yrLQAAAAAsDVCCwAAAABbI7QgohgFRuOe8GgfwzAa702AdjKMf94jA7AK/TBk\njIehY15GuBBaAAAAcFHZuXOnrrvuOq1YseKCj9uxY4fKysqaHK+urtaTTz6pm2++Wbfffrt+9atf\n6eDBg22uY82aNbr++utVXFys+++/v8nXV6xYocWLF7f5vO2xePHiC7ZHZWWlPv300w5/3S1btuiB\nBx4I+TyEFgAAAFw0qqurNXfuXI0ePbrFx65bt0579uxpcvyZZ55R37599fbbb2vlypX65S9/qQcf\nfLDNtWzYsEEPP/ywRowYoRdffLHNzw+n7du3a/369Z1y7tZua3wh7B4GAACAi0ZUVJSWLFmi1157\n7Zzjq1ev1ooVK+T1ejVw4EBNnjxZq1atUq9evZSYmKjLLrtMknTmzBmtX79eH374YeNzJ0yYoJ/+\n9KeSpM2bNys/P18ej0epqamaN2+e1q5dq+LiYh07dkw+n09333230tLS9Mknn6ikpETx8fGaOXOm\nNm3apI0bN2r+/PlKTk5WUlKSMjIyJEn5+fnaunWrAoGApk6dqhtuuEFPPPGEkpOTVVJSooMHD+qF\nF17QoEGDVFhYqL/+9a9yuVx68MEHNWrUKK1YsUJr1qyRy+XSuHHjNG3atGbbaPz48Ro3bpy2bt2q\n+Ph4vfrqq8rLy9OZM2d0ySWX6Oqrr9acOXNUX18vp9OpefPmKTU1VePHj1dOTo6GDRumDz/8UH/6\n058kNaziJCQkKCsrS4sWLZLH41GPHj1UUFDQYd9XQgsAAAA6T3PvG/L5OubxP+B0OuX1epscX7Zs\nmQoLC5WSkqJ33nlH/fr105gxYzRhwoTGwCJJ+/btU//+/ZusDsTGxkqSnnrqKf3xj39USkqK5s6d\nqzVr1sjhcGjXrl164403tHv3bj300EN65513Gs9/xRVXNJ7vD3/4gxYuXKjs7GzNmDFDGRkZ+vzz\nz3XgwAEtX75cfr9fN998s8aNGydJ8vv9Wrp0qVatWqXVq1ere/fuWrdund58803t3btXhYWFSktL\nU1FRkVauXClJys3N1YQJE5SamnreNtq3b58mTZqkRx99VLm5udqxY4fuuece7dq1S7feeqvmzJmj\nu+++W6NHj9bHH3+sF198UXl5eSovL9fLL7+srKwsrVq1SpWVlYqNjdVHH32kV155Rdu2bdPChQuV\nnp6uxx57TOvXr1f37t1b9X1rCaEFAAAAF72bbrpJ9913nyZOnKibbrpJUVFRzT42EAic9/jJkyfl\ndDqVkpIiSRo1apS2bNmiIUOGaNiwYZKk1NRUnT59utlz79+/X9nZ2ZKkK664QrW1tdq2bZu++OIL\n3XXXXTJNU5J0+PBhSdLIkSMbz/vFF1/oyy+/1NChQyVJmZmZysvL03vvvaeysrLG51dVVam8vLzZ\n0BIXF6cBAwZIkpKTk1VZWXnO17dt2yafz6eXXnpJpmmqV69ekqRu3bopKytLkjR27Fh98sknGj58\nuKKjo5WcnKyePXtqzpw5CgQCKi8v1+jRowkt6Jp8s3xWlxDxfK38TRUugDaEHdAPQ8Z4GLpWzctt\nbedO+r7MmDFDEydO1Pvvv69p06Zp+fLl531cRkaG9uzZo7q6Onk8nsbjJSUlyszMVDAYbDxWV1cn\nl8slSY1/SmoMHufjdDqbPM7r9eqWW27RjBkzmjze7Xaf83i3231ODWeff8011+jpp59u9nWbq+F8\n9Xo8Hi1atEhJSUlNXues6667Tq+//rqOHz+u8ePHS5Jmz56twsJC9e/fX3l5ea2qpbUILQCAsAkE\nAiotLZUklZWVKS4uzuKKzpWVlXXOfzwAXBxM01RBQYFmzpypadOmqbS0VN9++60cDofq6urOeWxM\nTIyuvfZaLVq0SA8//LAkqaioSK+//rqWL18up9OpgwcPKjU1VVu2bNHIkSNVX1/fqhokKSUlRT6f\nT/369dPmzZs1fPhwDR06VM8995zuvfde+f1+Pf/88/rd73533vMMHjxYL730koLBoI4dO6annnpK\nv/vd7/T888+rpqZGUVFRmj9/vh555JHzXibXHIfD0fjvuPzyy7Vu3Trdfvvt2rhxo44dO6Ybb7zx\nnHAzbNgwPf300zp16pR+//vfS2rYgaxPnz46deqUNm/erIEDB7b69VtCaAEAhE1paanufOI/1b1H\ncsOBNW3fQrSzVJ08rOXP3NF42QaAyLR9+3Y9++yzOnDggNxut4qKirR48WLFxMRo8uTJio+PV0ZG\nhgYNGqSRI0dq/vz5io2N1VVXXdV4jtmzZ2vBggX6xS9+oYSEBKWmpjbu/pWXl6cHH3xQbrdbmZmZ\nuvHGG/Xuu++2WNfZ97TMmjVLM2fOVHp6utLS0iRJw4cP15VXXqnJkydLku64445mz5Oenq6JEyc2\nPuahhx5Samqqpk2bpilTpsjtduvaa6+9YGD5/vt1zn4+ZMgQLVy4UH369NHMmTP1+OOPa+3atXI4\nHHr22WebPO9s3V999VXjZWhTpkxRbm6u+vfvr+nTp2vx4sXt2nXtvDWbF1q/6iDFxcUaMWJEZ7/M\nRYm2QzjR39DZdu7cqX999gPF9ky3upQmKo/v16uPjyO0XKQY38KjpqZGkhQdHW1xJbC75vpKcz+r\n3KcFAAAAgK0RWgAAAADYGqEFEcUoMGQUGFaXEdEMw5DR3B74aB3DaP4+AkC40A9DxngYOuZlhAuh\nBQAAAICtEVoAAAAA2BqhBQAAAICtEVoAAABwUVmwYIFyc3N16623at26dc0+bseOHSorK2tyvLq6\nWk8++aRuvvlm3X777frVr36lgwfbfl+pNWvW6Prrr1dxcbHuv//+Jl9fsWKFFi9e3ObztsfixYu1\nYsWKZr9eWVmpTz/9tMNfd8uWLXrggQdCPg+hBQAAABeNzZs3q7S0VKtWrVJhYaHmz5/f7GPXrVun\nPXv2NDn+zDPPqG/fvnr77be1cuVK/fKXv2zXTRI3bNighx9+WCNGjGi8OaVdbd++XevXr++Uc//w\nppTt4e6AOoCw8c3yWV1CxPP5fFaXEPloQ9gB/TBkjIehs+O8PGrUKF1++eWSpPj4eFVXV8s0Tb37\n7rtasWKFvF6vBg4cqMmTJ2vVqlXq1auXEhMTddlll0mSzpw5o/Xr1+vDDz9sPOeECRP005/+VFJD\nKMrPz5fH41FqaqrmzZuntWvXqri4WMeOHZPP59Pdd9+ttLQ0ffLJJyopKVF8fLxmzpypTZs2aePG\njZo/f76Sk5OVlJSkjIwMSVJ+fr62bt2qQCCgqVOn6oYbbtATTzyh5ORklZSU6ODBg3rhhRc0aNAg\nFRYW6q9//atcLpcefPBBjRo1SitWrNCaNWvkcrk0btw4TZs2rdk2Gj9+vMaNG6etW7cqPj5er776\nqvLy8nTmzBldcskluvrqqzVnzhzV19fL6XRq3rx5Sk1N1fjx45WTk6Nhw4bpww8/1J/+9CdJDas4\nCQkJysrK0qJFi+TxeNSjRw8VFBR02PeV0AIAAIBO09y20s2FxrY+/occDkfjXdbffPNNXXPNNXI4\nHFq2bJkKCwuVkpKid955R/369dOYMWM0YcKExsAiSfv27VP//v2brA7ExsZKkp566in98Y9/VEpK\niubOnas1a9bI4XBo165deuONN7R792499NBDeueddxrPf8UVVzSe7w9/+IMWLlyo7OxszZgxQxkZ\nGfr888914MABLV++XH6/XzfffLPGjRsnSfL7/Vq6dKlWrVql1atXq3v37lq3bp3efPNN7d27V4WF\nhUpLS1NRUZFWrlwpScrNzdWECROUmpp63jbat2+fJk2apEcffVS5ubnasWOH7rnnHu3atUu33nqr\n5syZo7vvvlujR4/Wxx9/rBdffFF5eXkqLy/Xyy+/rKysLK1atUqVlZWKjY3VRx99pFdeeUXbtm3T\nwoULlZ6erscee0zr169X9+7dW/V9awmhBQAAABedDz74QG+//baWLl0qSbrpppt03333aeLEibrp\nppsUFRXV7HMDgcB5j588eVJOp1MpKSmSGlZ1tmzZoiFDhmjYsGGSpNTUVJ0+fbrZc+/fv1/Z2dmS\npCuuuEK1tbXatm2bvvjiC911110yTVOSdPjwYUnSyJEjG8/7xRdf6Msvv9TQoUMlSZmZmcrLy9N7\n772nsrKyxudXVVWpvLy82dASFxenAQMGSJKSk5NVWVl5zte3bdsmn8+nl156SaZpqlevXpKkbt26\nKSsrS5I0duxYffLJJxo+fLiio6OVnJysnj17as6cOQoEAiovL9fo0aMJLQAAALC/tl6G1xGX7f3t\nb3/Ta6+9pqVLlzaukMyYMUMTJ07U+++/r2nTpmn58uXnfW5GRob27Nmjuro6eTyexuMlJSXKzMxU\nMBhsPFZXVyeXyyVJjX9Kagwe5+N0Ops8zuv16pZbbtGMGTOaPN7tdp/zeLfbfU4NZ59/zTXX6Omn\nn272dZur4Xz1ejweLVq0SElJSU1e56zrrrtOr7/+uo4fP67x48dLkmbPnq3CwkL1799feXl5raql\ntXgjPgAAAC4alZWVev755/XKK68oLi5OUsN/yvPz85WUlKRp06Zp2LBh+vbbb+VwOFRXV3fO82Ni\nYnTttddq0aJFjceKior03HPPKT4+Xk6ns3EnsS1btignJ6dVdZ0NBikpKfL5fDJNU5s3b5YkDR06\nVB999JFM01Rtba3mzp3b7HkGDx6sbdu2KRgM6siRI/rNb36jnJwcbdq0STU1NTJNU/PmzZPf7299\no6nhsrr6+npJ0uWXX96469rGjRu1du3ac/4NkjRs2DCVlpbq448/1oQJEyQ1tH2fPn106tQpbd68\nuUnbhoKVFgAAAFw03nvvPZ04cUKzZs2SaZpyOBxasGCBYmJiNHnyZMXHxysjI0ODBg3SyJEjNX/+\nfMXGxuqqq65qPMfs2bO1YMEC/eIXv1BCQoJSU1Mbd//Ky8vTgw8+KLfbrczMTN1444169913W6zr\n7HtaZs2apZkzZyo9PV1paWmSpOHDh+vKK6/U5MmTJUl33HFHs+dJT0/XxIkTGx/z0EMPKTU1VdOm\nTdOUKVPkdrt17bXXnrMq0lwt3/98yJAhWrhwofr06aOZM2fq8ccf19q1a+VwOPTss882ed7Zur/6\n6qvGy9CmTJmi3Nxc9e/fX9OnT9fixYvbtevaeWs2L7R+1UGKi4s1YsSIzn6ZixJtdy6jwJBkz91K\nIsXZNzieb/md/tZKZ98kys5DbbZz507967MfKLZnutWlNFF5fL9efXxc47Xmtkc/bJPzjW8XGg/R\nOj+cl2tqaiSp8Y3wQHOa6yvN/V+Ey8MAAAAA2BqhBQAAAICtEVoAAAAA2BqhBQAAAICtEVoAAAAA\n2BpbHiOisGtY6NglpwPQhrAD+mHIGA9Dx7yMcGGlBQAAABeNmpoazZo1S3feeacmT56s//3f/232\nsTt27FBZWVmT49XV1XryySd188036/bbb9evfvWrxhtKtsWaNWt0/fXXq7i4WPfff3+Tr69YsUKL\nFy9u83nbY/HixVqxYkWzX6+srNSnn37a4a+7ZcsWPfDAAyGfh9ACAACAi8ZHH32kyy67TMuXL1d+\nfr6eeeaZZh+7bt067dmzp8nxZ555Rn379tXbb7+tlStX6pe//GW7bpK4YcMGPfzwwxoxYkTjzSnt\navv27Vq/fn2nnPuHN6VsDy4PAwAAwEXjhhtuaPz8wIED6tOnjyRp9erVWrFihbxerwYOHKjJkydr\n1apV6tWrlxITE3XZZZdJks6cOaP169frww8/bDzPhAkT9NOf/lSStHnzZuXn58vj8Sg1NVXz5s3T\n2rVrVVxcrGPHjsnn8+nuu+9WWlqaPvnkE5WUlCg+Pl4zZ87Upk2btHHjRs2fP1/JyclKSkpSRkaG\nJCk/P19bt25VIBDQ1KlTdcMNN+iJJ55QcnKySkpKdPDgQb3wwgsaNGiQCgsL9de//lUul0sPPvig\nRo0apRUrVmjNmjVyuVwaN26cpk2b1mwbjR8/XuPGjdPWrVsVHx+vV199VXl5eTpz5owuueQSXX31\n1ZozZ47q6+vldDo1b948paamavz48crJydGwYcP04Ycf6k9/+pOkhlWchIQEZWVladGiRfJ4POrR\no4cKCgo67PtKaAEAAECnMQqM8x5v7v0wbX18c3Jzc3X48GG98sorkqRly5apsLBQKSkpeuedd9Sv\nXz+NGTNGEyZMaAwskrRv3z7179+/yepAbGysJOmpp57SH//4R6WkpGju3Llas2aNHA6Hdu3apTfe\neEO7d+/WQw89pHfeeafx/FdccUXj+f7whz9o4cKFys7O1owZM5SRkaHPP/9cBw4c0PLly+X3+3Xz\nzTdr3LhxkiS/36+lS5dq1apVWr16tbp3765169bpzTff1N69e1VYWKi0tDQVFRVp5cqVjf/2CRMm\nKDU19bxts2/fPk2aNEmPPvqocnNztWPHDt1zzz3atWuXbr31Vs2ZM0d33323Ro8erY8//lgvvvii\n8vLyVF5erpdffllZWVlatWqVKisrFRsbq48++kivvPKKtm3bpoULFyo9PV2PPfaY1q9fr+7du7fp\n+9YcQgsAAAAuOqtWrdLXX3+thx9+WH/5y19000036b777tPEiRN10003KSoqqtnnBgKB8x4/efKk\nnE6nUlJSJEmjRo3Sli1bNGTIEA0bNkySlJqaqtOnTzd77v379ys7O1uSdMUVV6i2tlbbtm3TF198\nobvuukumaUqSDh8+LEkaOXJk43m/+OILffnllxo6dKgkKTMzU3l5eXrvvfdUVlbW+PyqqiqVl5c3\nG1ri4uI0YMAASVJycrIqKyvP+fq2bdvk8/n00ksvyTRN9erVS5LUrVs3ZWVlSZLGjh2rTz75RMOH\nD1d0dLSSk5PVs2dPzZkzR4FAQOXl5Ro9ejShBV3T2d++sFtJ+xmGIYldc0LyXRuyexMsRT8MGeNh\n6FozL7d1zg51jt++fbsSExOVmpqqgQMHKhAI6NixY5oxY4YmTpyo999/X9OmTdPy5cvP+/yMjAzt\n2bNHdXV18ng8jcdLSkqUmZmpYDDYeKyurk4ul0uSGv+U1Bg8zsfpdDZ5nNfr1S233KIZM2Y0ebzb\n7T7n8W63+5wazj7/mmuu0dNPP93s6zZXw/nq9Xg8WrRokZKSkpq8zlnXXXedXn/9dR0/flzjx4+X\nJM2ePVuFhYXq37+/8vLyWlVLa/FGfAAAAFw0PvvsMy1btkySdOTIEVVXV6tXr17Kz89XUlKSpk2b\npmHDhunbb7+Vw+FQXV3dOc+PiYnRtddeq0WLFjUeKyoq0nPPPaf4+Hg5nc7GncS2bNminJycVtV1\nNhikpKTI5/PJNE1t3rxZkjR06FB99NFHMk1TtbW1mjt3brPnGTx4sLZt26ZgMKgjR47oN7/5jXJy\ncrRp0ybV1NTINE3NmzdPfr+/9Y2mhjfL19fXS5Iuv/xyrVu3TpK0ceNGrV279px/gyQNGzZMpaWl\n+vjjjzVhwgRJDTuQ9enTR6dOndLmzZubtG0oWGkBAADAReP222/X7NmzNWXKFNXW1urf//3fJTWE\nkcmTJys+Pl4ZGRkaNGiQRo4cqfnz5ys2NlZXXXVV4zlmz56tBQsW6Be/+IUSEhKUmprauPtXXl6e\nHnzwQbndbmVmZurGG2/Uu+++22JdZ9/TMmvWLM2cOVPp6elKS0uTJA0fPlxXXnmlJk+eLEm64447\nmj1Penq6Jk6c2PiYhx56SKmpqZo2bZqmTJkit9uta6+99pxVkeZq+f7nQ4YM0cKFC9WnTx/NnDlT\njz/+uNauXSuHw6Fnn322yfPO1v3VV181XoY2ZcoU5ebmqn///po+fboWL17crl3XzluzeaH1qw5S\nXFysESNGdPbLXJRou3NxeVjoLnQ5BP2tlbgsp9127typf332A8X2TLe6lCYqj+/Xq4+Pa7zW3Pbo\nh21yvvGNy8NC98N5uaamRpIUHR1tUUWIFM31leb+L8LlYQAAAABsjdACAAAAwNZ4TwsiCpeFhY7L\nIDoAbQg7oB+GjPEwdMzLCBdCCwAAADpMbW2t1SUgAtTW1l7wXjk/xOVhAAAA6BBRUVFt+o/oxWz7\n9u1Wl2Brbe0rrLQAAACgQzgcDnYO+x7aouOw0gIAAADA1ggtAAAAAGyN0IKIYhQYjTeyQvsYhtF4\nQzW0k2H888Z+gFXohyFjPAwd8zLChdACAAAAwNYILQAAAABsjdACAAAAwNYILQAAAABsjdACAAAA\nwNa4uSQiim+Wz+oSIp7P57O6hMhHG8IO6IchYzwMHfMywoWVFgAAAAC2RmgBAAAAYGuEFgAAAAC2\nRmgBAAAAYGuEFgAAAAC2RmhBRDEKDBkFhtVlRDTDMGQYhtVlRDbDaPgArEQ/DBnjYeiYlxEuhBYA\nAAAAttbifVq2bNmif/u3f9OAAQNkmqYuvfRSTZ8+XY888ohM01Tv3r21YMECeTyecNQLAAAAoItp\n1c0lR40apUWLFjX+/YknntCdd96p8ePHKz8/X2+99ZZyc3M7rUgAAAAAXVerLg8zTfOcv2/ZskVj\nx46VJI0dO1YbNmzo+MoAAAAAQK1caSktLdV9992nkydP6v7771dNTU3j5WCJiYmqqKjo1CIBAAAA\ndF0O84fLKD9w6NAhbd26Vddff7327dunu+66S1VVVdq8ebMkae/evXrssce0cuXKZs9RXFzcsVUD\nACJSWVmZ/r81BxXbM93qUpqoPL5fM29KVb9+/awuBQC6tBEjRjQ51uJKS0pKiq6//npJUkZGhpKS\nklRSUiK/3y+v16tDhw4pOTm5XS+OlhUXF9N2CBv6GzpbXFyctOag1WU0KycnR9nZ2VaXgU7A+IZw\no8+1T3OLHS2+p+W///u/tWzZMklSRUWFjh49qptvvlnvv/++JKmoqEhjxozpwFIBAAAA4J9aXGn5\n2c9+poceekgffvih6uvr9fTTT2vgwIF67LHH9Oc//1lpaWmaNGlSOGoFAAAA0AW1GFpiYmL0yiuv\nNDl+dvUFAAAAADpTq7Y8BgAAAACrEFoQUYwCQ0aBYXUZEc0wDBmGYXUZkc0wGj4AK9EPQ8Z4GDrm\nZYQLoQUAAACArRFaAAAAANgaoQUAAACArRFaAAAAANgaoQUAAACArbV4nxbATnyzfFaXEPF8Pp/V\nJUQ+2hB2QD8MGeNh6JiXES6stAAAAACwNUILAAAAAFsjtAAAAACwNUILAAAAAFsjtAAAAACwNUIL\nIopRYMgoMKwuI6IZhiHDMKwuI7IZRsMHYCX6YcgYD0PHvIxwIbQAAAAAsDVCCwAAAABbI7QAAAAA\nsDVCCwAAAABbI7QAAAAAsDW31QUAbeGb5bO6hIjn8/msLiHy0YawA/phyBgPQ8e8jHBhpQUAAACA\nrRFaAAAAANgaoQUAAACArRFaAAAAANgaoQUAAACArRFaEFGMAkNGgWF1GRHNMAwZhmF1GZHNMBo+\nACvRD0PGeBg65mWEC6EFAAAAgK0RWgAAAADYGqEFAAAAgK0RWgAAAADYGqEFAAAAgK25rS4AaAvf\nLJ/VJUQ8n89ndQmRjzaEHdAPQ8Z4GDrmZYQLKy0AAAAAbI3QAgAAAMDWCC0AAAAAbI3QAgAAAMDW\nCC0AAAAAbI3QgohiFBgyCgyry4hohmHIMAyry4hshtHwAViJfhgyxsPQMS8jXAgtAAAAAGyN0AIA\nAADA1ggtAAAAAGyN0AIAAADA1ggtAAAAAGzNbXUBQFv4ZvmsLiHi+Xw+q0uIfLQh7IB+GDLGw9Ax\nLyNcWGkBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFkQUo8CQUWBYXUZEMwxD\nhmFYXUZkM4yGD8BK9MOQMR6GjnkZ4UJoAQAAAGBrhBYAAAAAtkZoAQAAAGBrhBYAAAAAtkZoAQAA\nAGBrbqueDkVZAAAgAElEQVQLANrCN8tndQkRz+fzWV1C5KMNYQf0w5AxHoaOeRnhwkoLAAAAAFsj\ntAAAAACwNUILAAAAAFsjtAAAAACwNUILAAAAAFsjtCCiGAWGjALD6jIimmEYMgzD6jIim2E0fABW\noh+GjPEwdMzLCBdCCwAAAABbI7QAAAAAsDVCCwAAAABba1Voqa2t1XXXXafVq1fr4MGDuvPOOzV1\n6lT99re/VV1dXWfXCAAAAKALa1Voeemll5SQkCBJWrRoke688069/vrryszM1FtvvdWpBQIAAADo\n2twtPWD37t3avXu3rr76apmmqc8++0y///3vJUljx47VsmXLlJub2+mFApLkm+WzuoSI5/P5rC4h\n8tGGsAP6YcgYD0PHvIxwaXGl5bnnntPjjz/e+Pfq6mp5PB5JUmJioioqKjqvOgAAAABd3gVXWlav\nXq3hw4crPT39vF83TbPVL1RcXNy2ytCItkM40d/QmcrKyqwu4YJKSkp0+vRpq8tAJ2F8Q7jR5zrO\nBUPLxx9/rPLycv3P//yPDh06JI/Ho+7du8vv98vr9erQoUNKTk5u1QuNGDGiQwruaoqLi2k7hA39\nDZ0tLi5OWnPQ6jKalZOTo+zsbKvLQCdgfEO40efap7mgd8HQkp+f3/j54sWL1bdvX23dulXvv/++\nJk6cqKKiIo0ZM6ZjKwUAAACA72nzfVoeeOABrV69WlOnTtWpU6c0adKkzqgLAAAAACS1Yvews37z\nm980fr5s2bJOKQZoiVFgSGK3klAYhiGJXXNC8l0bsnsTLEU/DBnjYeiYlxEubV5pAQAAAIBwIrQA\nAAAAsDVCCwAAAABbI7QAAAAAsDVCCwAAAABba/XuYYAdsDtJ6NglpwPQhrAD+mHIGA9Dx7yMcGGl\nBQAAAICtEVoAAAAA2BqhBQAAAICtEVoAAAAA2BqhBQAAAICtEVoQUYwCQ0aBYXUZEc0wDBmGYXUZ\nkc0wGj4AK9EPQ8Z4GDrmZYQLoQUAAACArRFaAAAAANgaoQUAAACArRFaAAAAANgaoQUAAACArbmt\nLgBoC98sn9UlRDyfz2d1CZGPNoQd0A9DxngYOuZlhAsrLQAAAABsjdACAAAAwNYILQAAAABsjdAC\nAAAAwNYILQAAAABsjdCCiGIUGDIKDKvLiGiGYcgwDKvLiGyG0fABWIl+GDLGw9AxLyNcCC0AAAAA\nbI3QAgAAAMDWCC0AAAAAbI3QAgAAAMDWCC0AAAAAbM1tdQFAW/hm+awuIeL5fD6rS4h8tCHsgH4Y\nMsbD0DEvI1xYaQEAAABga4QWAAAAALZGaAEAAABga4QWAAAAALZGaAEAAABga4QWRBSjwJBRYFhd\nRkQzDEOGYVhdRmQzjIYPwEr0w5AxHoaOeRnhQmgBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFgAAAAC2\nRmgBAAAAYGtuqwsA2sI3y2d1CRHP5/NZXULkow1hB/TDkDEeho55GeHCSgsAAAAAWyO0AAAAALA1\nQgsAAAAAWyO0AAAAALA1QgsAAAAAWyO0IKIYBYaMAsPqMiKaYRgyDMPqMiKbYTR8AFaiH4aM8TB0\nzMsIF0ILAAAAAFvjPi0AcBEKBAIqLS21uowm9uzZY3UJAIAIRGgBgItQaWmp7nziP9W9R7LVpZzj\naPlXSuw7yOoyAAARhtACABep7j2SFdsz3eoyzlF18pDVJQAAIhDvaQEAAABga6y0IKL4ZvmsLiHi\n+Xw+q0uIfLQh7IB+GDLGw9AxLyNcWGkBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFgAAAAC2RmgBAAAA\nYGuEFkQUo8CQUWBYXUZEMwxDhmFYXUZkM4yGD8BK9MOQMR6GjnkZ4UJoAQAAAGBrhBYAAAAAtkZo\nAQAAAGBrhBYAAAAAtkZoAQAAAGBr7pYeUFNTo8cff1xHjx6V3+/Xr3/9aw0cOFCPPPKITNNU7969\ntWDBAnk8nnDUiy7ON8tndQkRz+fzWV1C5KMNYQf0w5AxHoaOeRnh0mJo+eijj3TZZZfpnnvu0YED\nB/Qv//Iv+vGPf6ypU6fq5z//ufLz8/XWW28pNzc3HPUCAAAA6GJavDzshhtu0D333CNJOnDggPr0\n6aPPPvtMP/vZzyRJY8eO1YYNGzq3SgAAAABdVosrLWfl5ubq8OHDevnll3X33Xc3Xg6WmJioioqK\nTisQAAAAQNfW6tCyatUqff3113r44Ydlmmbj8e9/DgAAAAAdrcXQsn37diUmJio1NVUDBw5UMBhU\nTEyM/H6/vF6vDh06pOTk5BZfqLi4uEMK7opoO4QT/e3iUFZWZnUJEamkpESnT5+2ugx0EsY3hBt9\nruO0GFo+++wzHThwQLNnz9aRI0dUVVWlMWPG6P3339fEiRNVVFSkMWPGtPhCI0aM6JCCu5ri4mLa\n7nuMAkMSu5WEwjAMSeffNYf+1krftaGdd2+Ki4uT1hy0uoyIk5OTo+zsbKvLaJ0I6Id2cr7x7ULj\nIVqHebl5zKnt01zQazG03H777Zo9e7amTJmi2tpaPfXUUxoyZIgeffRR/fnPf1ZaWpomTZrU4QUD\nAAAAgNSK0BIVFaWFCxc2Ob5s2bJOKQgAAAAAvq/FLY8BAAAAwEqEFgAAAAC2RmgBAAAAYGutvk8L\nYAfsThI6dsnpALQh7IB+GDLGw9AxLyNcWGkBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFgAAAAC2RmgB\nAAAAYGuEFkQUo8CQUWBYXUZEMwxDhmFYXUZkM4yGD8BK9MOQMR6GjnkZ4UJoAQAAAGBrhBYAAAAA\ntkZoAQAAAGBrhBYAAAAAtkZoAQAAAGBrbqsLANrCN8tndQkRz+fzWV1C5KMNYQf0w5AxHoaOeRnh\nwkoLAAAAAFsjtAAAAACwNUILAAAAAFsjtAAAAACwNUILAAAAAFsjtCCiGAWGjALD6jIimmEYMgzD\n6jIim2E0fABWoh+GjPEwdMzLCBdCCwAAAABbI7QAAAAAsDVCCwAAAABbI7QAAAAAsDVCCwAAAABb\nc1tdANAWvlk+q0uIeD6fz+oSIh9tCDugH4aM8TB0zMsIF1ZaAAAAANgaoQUAAACArRFaAAAAANga\n72kBYHuBQEClpaVWl3FeWVlZcrlcVpeBDmAGg9qzZ4/VZZwX/QxAV0doAWB7paWluvOJ/1T3HslW\nl3KOqpOHtfyZO5SdnW11KegA1acr9ORrR9S9h70CMv0MAAgtiDBGgSGJ3UpCYRiGpMjbNad7j2TF\n9ky3ugxJ0pIl90qScm95ytpC0OHs1M9a9N3PMruItV+kjod2wryMcOE9LQAAAABsjdACAAAAwNYI\nLQAAAABsjdACAAAAwNYILQAAAABsjd3DEFHYnSR07JITuunTCxs+Ob7f2kLQtfGzHDLGw9AxLyNc\nWGkBAAAAYGuEFgAAAAC2RmgBAAAAYGuEFgAAAAC2RmgBAAAAYGvsHoaIYhQYktitJBSGYUhi15xQ\nLFlyryQp95anrC0EXdt3P8vsItZ+jIehY15GuLDSAgAAAMDWCC0AAAAAbI3QAgAAAMDWCC0AAAAA\nbI3QAgAAAMDW2D0MEYXdSULHLjmhmz69sOGT4/utLQRdGz/LIWM8DB3zMsKFlRYAAAAAtkZoAQAA\nAGBrhBYAAAAAtkZoAQAAAGBrhBYAAAAAtsbuYYgoRoEhid1KQmEYhiR2zQnFkiX3SpJyb3nK2kLQ\ntX33s8wuYu3HeBg65mWECystAAAAAGyN0AIAAADA1ggtAAAAAGyN0AIAAADA1ggtAAAAAGyN3cMQ\nUdidJHTskhO66dMLGz45vt/aQtC18bMcMsbD0DEvI1xYaQEAAABga4QWAAAAALbWqsvDFixYoK1b\ntyoQCGjGjBm67LLL9Mgjj8g0TfXu3VsLFiyQx+Pp7FoBAAAAdEEthpbNmzertLRUq1at0okTJzRp\n0iRdddVVmjp1qn7+858rPz9fb731lnJzc8NRLwAAAIAupsXLw0aNGqVFixZJkuLj41VVVaXPPvtM\nP/vZzyRJY8eO1YYNGzq3SgAAAABdVouhxeFwKDo6WpL0X//1X7rmmmtUXV3deDlYYmKiKioqOrdK\n4DtGgSGjwLC6jIhmGIYMw7C6jIi2ZMm9WrLkXqvLQFdnGA0faDfGw9AxLyNcWr3l8QcffKC33npL\nS5cu1fjx4xuPm6bZqucXFxe3vTpIou2+z+/3S6JNQtFSG9qxbcvKyqwuoVklJSU6ffq01WU0Yec2\nQ9udr5/lfPezXGLDn1m7+uH4xpwSOtrwwmiXjtOq0PK3v/1Nr732mpYuXarY2FjFxMTI7/fL6/Xq\n0KFDSk5ObvEcI0aMCLnYrqi4uJi2+x7v37yS6E+h8Hqbb0O79re4uDhpzUGryzivnJwcZWdnW11G\nE3ZuM7TdefvZBX6W0dT5xrcLjYdoHebl5tl1TrW75oJei5eHVVZW6vnnn9crr7zSMAlKGj16tIqK\niiRJRUVFGjNmTAeWCgAAAAD/1OJKy3vvvacTJ05o1qxZMk1TDodDzz33nObMmaM33nhDaWlpmjRp\nUjhqBQAAANAFtRhabrvtNt12221Nji9btqxTCgIAAACA72v1G/EBO/DN8lldQsTz+XxWlxDxpk8v\nbPjk+H5rC0HXxs9yyBgPQ8e8jHBp8T0tAAAAAGAlQgsAAAAAWyO0AAAAALA1QgsAAAAAWyO0AAAA\nALA1dg9DRDEKDEnsVhIKwzAksWtOKJYsuVeSlHvLU9YWgq7tu59ldhFrP8bD0DEvI1xYaQEAAABg\na4QWAAAAALZGaAEAAABga4QWAAAAALZGaAEAAABga+wehojC7iShY5ec0E2fXtjwyfH91haCro2f\n5ZAxHoaOeRnhwkoLAAAAAFsjtAAAAACwNUILAAAAAFsjtAAAAACwNUILAAAAAFtj9zBEFKPAkMRu\nJaEwDEMSu+aEYsmSeyVJubc8ZW0h6Nq++1lmF7H2YzwMHfMywoWVFgAAAAC2RmgBAAAAYGuEFgAA\nAAC2RmgBAAAAYGuEFgAAAAC2xu5hiCjsThI6dskJ3fTphQ2fHN9vbSHo2vhZDhnjYeiYlxEurLQA\nAAAAsDVCCwAAAABbI7QAAAAAsDXe0wIACDNT8tTK4aqTTIckh2Q6ZJqO77783bGASzJdVhYKALAJ\nQgsAoOM56+WIqpIjqlrO6IY/HVHV6nPpMXliK+Rwma06TbA2WmZNjMyaGAVrYmRWN3xu+qMlOTr3\n3wAAsA1CCyKKUWBIYreSUBiGIYldc0KxZMm9kqTcW56ythBbCcoZe1LO+KMNH7En5HCeJ5j4Haqv\njJIz0ENmvafhmMNs+NDZPyWHw5RcdXJEV8nV46jU4+g5pzEDTpk1sQqc6qXgid4KVvaUzC52xfN3\nP8vsItZ+jIehY15GuBBaAKCdzGBQe/bssbqM8+r8ukw5oqvkjD8iV/xROeOPyeGub/iKKZlneihw\nJl5mbXcFa7vJrO0us7abDpf+n7r3SFFsz/TWv5SzvuG1os/IEX1Gjm5nGj7vVilPzCmpj09mwKXg\nySQFTvRW4GSSVBfdSf/u8Guun/Wvb2jvPTt3hrukRllZWXK5uIQPQOcjtABAO1WfrtCTrx1R9x6l\nVpfSxNHyr5TYd1CHn9fhrZYrab9cvffLGVXdeDxY012Bo30UOJWo4KlEKeDpuBcNumVWxStQFf+D\nYgJyxh+Tq0eFnAkVcvU6JFevQw1POROnwMneChxJk1kT23G1WKC5frbyZEP7/+uzH1hRlqpOHtby\nZ+5Qdna2Ja8PoGshtABACLr3SG7bqkGYVJ081IFnC8qZcETu3vvkTKiQwyGZAZfqj6YqeCpRwZOJ\nMv3dO/D1Wsl0KXiyt4Ine0t7v1v56VEhV0KFnHHH5Ik5LU/abgVOJqr+cKaCx3srUjfNPF8/czgb\nVjjs2P8AoKMRWgAA5+XwVsvVu1zu3uVyeGslScHKHqo7nKHAsVQpaKcpxCGzJkaBmhgFDhmSs16u\nhAq5kvfJ1eOoXD2OKlgbrcDhDNVX9JXqo6wuGADQBnaacQAANuCMOyZ3n91y9jjSsKpS71b9oUzV\nV/SV+cNLtOwq6FbgWB8FjvWRo9tpuZP3yZW0X56MXXKnf6PA8VQFDmUqWJkgdiEDAPsjtCCisDtJ\n6NglJ3TTpxc2fOLbam0hHcwRc0KevrsaduuSFDidoEBFXxuuqrSNWR2nurLBqtuXLVfSfrlT9sqd\n+K3cid8qcDpB9eXZCp7uZXWZbdbYD9FujIehY15GuETuLAQA6BCObqfk6fuNXD0PS5ICJxNVVz5A\n5pkEiyvrYEG3Aof7KXA4s2E1KbVMrp6H5Rq0RYETveU5HrC6QgBAMwgtANBFOaIr5U7/Ru7Eg5Kk\nwOmeqi8fEJGrDm3jUPB0ovynExtWlzJ2ypVQoT7jpdpvg1JFT5m1FmwsAABoFqEFALoYh7da7r67\n5Eo8IIdDClbGq27/AAVPJqmrvb/DPJMg/9dXyNnjiJT8D0WnnZCZ+jcFKjJUtz+LN+wDgE0QWgCg\nq3AE5U4pkzv9GzlcAQWrYuUvH6DgiWR1tbByLoeCJ3vr8D96quel0Yq99KjcKXvlStqv+m/7q/7b\nSyQzMrdKBoCLBaEFALoAZ+xxeYztcnavlFnnlb9ssAJH0tS1w8oPOVR7MEEe/yC5ksrlSS9teK9P\n4req8w3pApfNAYB9EVoQUYwCQxK7lYTCMAxJ7JoTiiVL7pUkTRz3a4sraQWXX56MnXInl0uS6g/3\nVd2+bCngtbgwGzOdClRkKnA0rWE3tZQyRQ3a8l3bXSoFPFZXKOmf/ZBdxNqP8TB0zMsIF0ILAFyU\nTEX1Oa7oQTvk8PgVrIptWC2o7Gl1YZEj6Fbd3kGqP9pH3v4lcieXy5VwWHV7BzVsA80qFQCEDaEF\nAC4yjugzSrn6hKJT6mQGnKrbm636Qwbvy2gn80yCarf/P7lTfXKnfyPvj/6hwPEDqisbLNPfzery\nAKBLILQAwEXDlCt5nzwZX8vhCqr2cJzMA8Nl+tm+N2SmU/XfXqLAsRR5jC/l6lkhZ/x61ZUPUOBQ\nP7HqAgCdi9ACABcDd628l5TIlVAhs96jig2x0ulMxfYksHQkszZG/h0j5Uo6IE/m1/L2+1qBhAr5\nd18m1UVbXR4AXLS4VgAAIpwz4bCiL/tUroQKBU4mqub/fqKq8mjx2//O4lDgSLpqvvipAid6y9Xj\nqKJzPpUz4bDVhQHARYuVFkQUdicJHbvkhK5xtybfVmsLcdbLk7lD7uR9MoNO+csGcqlSONVHyb/z\nx3Il75Unc4eisreq/lCm6vZeKpmuTn95dg0LHeNh6JiXES6EFgCIQI6Yk/Je8g85u1UpWBUnf+lQ\nmdVxVpfVBTkUONxPwdO95M36h9wpe+WMOyZ/6eV8PwCgA3F5GABEFFPuPqWKGrRJzm5VqvvWUO32\n0fwH2WJmdZxqt49W/aFMObtXKmrIRrlSfJJMq0sDgIsCKy0AECncfnkv+UKuhCMy/VGq3T1UwVOJ\nVleFs0yX6soGK3AiSd5LShrepN/jiPy7h0r13MwTAELBSgsARABHzElFDdkgV8IRBU4kqabkJwQW\nmwqeTFZNyU8UOJEkV8IRRQ3ZIEfMCavLAoCIRmgBAFsz5eq9V1GDNsnhrVFd+Y/k3zmC39zbXV2U\n/DtHqG7fADm8NYoatFmu3nvF5WIA0D5cHoaIYhQYktitJBSGYUhi15xQLFlyryRp4rhfd+4LOQPy\nGNvlTjogs94jf+lQBU/27tzXRAdyqP7bLAXP9JA36x/y9v9S9bEnVecb3CG7i53th+wi1n6Mh6Fj\nXka4EFoAwIYcUWfkHbBNzu6VClb2kP+bYTL93awuC+0QPJWk2u3/T94fbZO79345u5+S/5vhMmu5\n8ScAtBaXhwGAzTh7HlTUkI1ydq9U/aFM1X51JYElwpn+bqr96krVH+4rZ8xpRQ3ZIGePCqvLAoCI\nQWgBANsw5U7fqagBf5ccpvylQ1VXNlgyGaovCqZLdb4c+XfnSM6goi4tljt9l3ifCwC0jMvDAMAO\nnPXyZn0hV8/DCtZ0k3/Xj7n3ykUqcKSvglVx8g74uzzppQ2Xi5VeLgWZkgGgOfz6DgAs5oiqUtTg\nTXL1PKzAyV6q/ZKbRV7szKoeqi0ZrcDJRLl6Vihq8CY5oqqsLgsAbItf6yCisDtJ6NglJ3SNuzX5\ntoZ8Lmf8UXl/9Hc53HWqP9hPdXsvFb9P6iICXvl3jJAnc4fcqWWKGrJR/l3DFDzduvvvsGtY6BgP\nQ8e8jHBhZgQAS5hypZTJe+nnkrNe/t05qts7SAzLXY1TdXsHyb9nSMMlgpd+LlfyXquLAgDbYaUF\nAMLNEZSn35dyJ5fLrPPKv2u4gpU9ra4KFgpUZMisjpF3wN/lNb5UfbfTDSGWTRgAQBK/0gOA8HLX\nyjvwM7mTyxU8E6/a7aMJLJAkBSt7NfSHqji5U/Y1rMK5/VaXBQC2QGgBgDBxdDutqCGb5Io7rvqj\nqdx/BU2Y/m6q/fJKBY6lyBV/TFGDN8oTX291WQBguVaFlp07d+q6667TihUrJEkHDx7UnXfeqalT\np+q3v/2t6urqOrVIAIh0zh4Vihq0Wc6oatWV/0h1pZdLQZfVZcGOgm75vxmmuv1ZckZXK/Vnx+VJ\nPG11VQBgqRZDS3V1tebOnavRo0c3Hlu0aJHuvPNOvf7668rMzNRbb73VqUUCZxkFhowCw+oyIpph\nGDIMw+oyItqSJfdqyZJ7W/14V3KZvNnFkjMo/zeXq/7AjyQ5Oq9AXAQcqt8/QP5vLpfDZarHj31N\n3qDf1n6IphgPQ8e8jHBpMbRERUVpyZIlSk5Objy2ZcsWjR07VpI0duxYbdiwofMqBICI1fCGe6/x\nlVTvVe1XoxQ41sfqohBBAsf66OD/9pRZ55LX+FKezK8kmVaXBQBh1+LuYU6nU16v95xj1dXV8ng8\nkqTExERVVFR0TnUAEKmc9fL+6O9yJRxRsCpW/p0jeP8K2sV/1KPjm36knlfslzu1TI7oKvm/udzq\nsmQGg9qzZ4/VZZxXIBCQJLlc/7wEs6ysTHFx5960tb6+4f1CO3fuDFttWVlZ59QFoHVC3vLYNFv3\nG5/i4uJQX6rLou3+ye9v2EmHNmm/ltrQjm1bVlZmdQlt4vBWyZu9Vc7ulQqcSJL/m2FSkB3m0X7B\nGq9qv7pS3qx/yJVQoajBm9Ww4mLdZYbVpyv05GtH1L1HqWU1NOdo+VfqFpeo7j2Sz/3CmoPn/PXI\nyWpJ0r8++0FY6qo6eViPTRmqfv36heX1woF5+cJol47Trlk0JiZGfr9fXq9Xhw4dOufSseaMGDGi\nPS/V5RUXF9N23+P9W8OqH23SfmdXTs/Xhnbtb3FxcU3+s2FXztjj8g7YJofHzx3u0bECHvl3/lie\nfl/LnbJXDm+tzDpvy8/rRN17JCu2Z7qlNZxP1clDrarN6WxY8QjnvyEnJ0fZ2dlhe73OxrzcPLvO\nqXbXXNBr10w6evRoFRUVSZKKioo0ZsyY9lcGABcJV69v5R34meSuk983mDvcoxM4VVc2WP6yQZJM\nOTx+OXtGRqAHgFC0uNKyfft2Pfvsszpw4IDcbreKior0wgsv6PHHH9cbb7yhtLQ0TZo0KRy1AvLN\n8lldQsTz+XxWlxDxpk8vbPjEt/W7I6bcfXbLk7FLZsDVcIf7k70tqw8Xv8Chfrp3Zr68P/q7olx/\nV92+bNV/21/sStc21579WUa7MS8jXFoMLUOGDNHy5cubHF+2bFmnFAQAEcURlKf//8nd+4CCtdEN\nb7ivjmv5eUCIgid7q/bLq+TNLpYnY6cc0WdU5xsimazuAbj4MLIBQDs5vUH1GOlrCCyVPVT75WgC\nC8LKrI5T7ZdXKXgmXu7e++W99HPJxQ2fAVx8CC0A0A6OqDNKvfa4vL3OKHAsRbVfj5LqoqwuC11R\nXfR39wBKkSv+mKIGb5IjqsrqqgCgQxFaAKCNnLHH9P+3d++xcdV3n8ff5zZjj2d8v8VOYgfnQkgg\nBFp4gGrh6ZOqEmKpVJGSRur+UYlWdLcSvaiirQRqtSsqqkWwahFLQ6VKLQuFNmy1f5RtadlySR4o\nCRACIRcnjhPHl/HdY3tmzjm//WNsh1xJnGQu9ucljc6cOeeMvzP55Zz5nt/vfE903U68RMBkZ8NM\nSWPdd0EKKHTJHLye7IkV2OUpotfswI4PFzoqEZHLRkmLiMhFcOp6chXCbJ/BtxOkDjSji5+lOFj4\n3WvIHF4Hrk/k6rdw6noKHZSIyGWhu51JSWl/vB1QtZJL0d7eDqiK2MUzuK0H8VoP8Yv/8jtMNsLd\n//afiVUVOi5ZrLZtuw/4RDW7GcHAMky6nMjKd4l0vE82Oonf04GS6zO9MvMdqorY/Om4LPminhYR\nkU9jBXgd7+G1HiKcLsdko6rQJEUtHKvPXaCfLsdbehDvqvfBCgodlojIvOmoKyJyPl6a6Nq3cOt6\nCcZrSH94CxidsZbiZ6bjpPf+C8F4NW797I1P04UOS0RkXpS0iIicg1U+PnNB8yh+soXMvs+CHyl0\nWCIXzo+S2fdZ/OQSnMQI0XU7sMrHCx2ViMhFU9IiInIWdlU/0Wt2YkenyXavItt5rYaESWkyDtnO\n68geW4Udnc6166qBQkclInJRdAQWETmFwWk6QmT1LsCQPnA9/gldxCylzsLv6SBzcANYhsjqd3Ca\njgCm0IGJiFwQVQ+TkqLqJJdOVcPOwwrxln+E29SNyURJH7gBkzqzPNhctaYju/IcoMhJp1cNuxDB\n0BLCdDnRVbuJtO3DL0uRPbp20fYiqmrYpdNxWfJlce6lRERO52aIrHkbt6mbMJUg/eG/nDVhESl1\nJlWdqyyWSuA2dRNZ/Q44mUKHJSJyXkpaRGTRs8rHia7bgVM5TDDURPqjmzGZ8kKHJXLFmEw56Y9u\nJpc3/JoAABkzSURBVBhuxKkaJLpuJ1bZRKHDEhE5Jw0PEymA3zy7nf6hsUKHcYahgV5uvPHGQoeR\nV3Z1H5GO97GcgOzxDvzjK9H1K7IohC6ZAxtxlx7Aa+kkum4HmUMbCEcaCx2ZiMgZlLSIFMDr73bR\nG6wodBhnMIOHCx1CHhnclk68pQcwgUP6wPWEw82FDkokzyz8Y6sxkwm8FXuIrNqFf2wV/omrUPIu\nIsVESYuILD52gLdiD25dL2G6jMyBGzCTlYWOSqRggqElhNMxIqt24y07gBUbJ3v4WgidQocmIgIo\naZES0/54O6BqJZfilW33AYu3ao4VmSKyajd2xRjBeDWZAxvBj17Ue2yb+Q7v3nT/lQhR5ILMtsP5\nVBE7GzNZRXrvLURW7cat68UumyRzYOOCvr5rse8PLwcdlyVfdCG+iCwadmKI6Lod2BVj+P1Lyey7\n6aITFpEFzY+S2XcTfv9S7Iqx3P+X+FChoxIRUdIiIouBwW0+TOTqt8HJkulaS/bIukV7bwqR8zI2\n2SPryBxZC26WyNVv4zR2oRtRikghaXiYiCxsto+34gPcul5MJkrm4AbCidpCRyVS5CyC/jbMVJzI\nyneJtH+EHx8le+QaCPXTQUTyT3seEVmwrLIJIivfxY5N5K5fOXg9ZMsKHZZIyQjH60jvvZXIyndx\n63uwY2O561zSFYUOTUQWGY2NEJEFya7uy43Hj03g97blrl9RwiJy0WZvROn3LceOTeT+X1X3FTos\nEVlk1NMiJUXVSS7dwq+SY+ZulmcCm8yh6wgGWy7rX5ir1nRk12V9X5GLcbmqhl0QY5PtuoZwogqv\nfS/R1bupDmJkukv7RpQLf3945em4LPmipEVEFg43TaTjfZyqQcLpWG4Yy1Si0FGJLBjBYCvhZCWR\nVbupWjtJpvEwQVeDqvCJyBWn4WEisiDYiUHK1r+JUzVIMNxAeu8tSlhErgAzlSC99xYmj0eI1KUo\nW/8mdny40GGJyAKnpEVESlyI23ogV87YzZA9uobMgRsg8AodmMjCFXgMvFHFxP4m8NJE1r6Fu+QQ\nKossIleKhoeJSOnypol0vIdTOUyYLidzcAMmVV3oqEQWCYupw414QRveVe/jLTuAXTVI5tB1Knoh\nIpedelpEpCTZ1f2UXfsGTuUwwVAT6Q9uVcIiUgDheC3pvbcSDDfiVA5Rtv4N7Or+QoclIguMelqk\npLQ/3g6oWsmleGXbfUAJV82xQrxlH+M2d2FCm8zhawgGlgFW3kLYNvMd3r3p/rz9TZHTzbbDvFYR\nOxc/QubARpzGbrzl+4iu3oXf20a2ezUYp9DRnVPJ7w+LgI7Lki9KWkSkZFhlKSId72FXjBFOVZA5\neL0uthcpGhZB/3LC8ZrczSibu7ATQ2QObcBMxwsdnIiUOA0PE5GiFxpD+fIk0XVvYFeM4Q+0qjqY\nSJGarS7m9y/Frhgnum4HTkM3ukhfRC6FelpEZI4JQ/bv31/oME4xnBnj2Y//N/G1SUzWI915HeFw\nc6HDEpHzCV2yR9YTjNYTWfEBkRV7CWr6yBxer4v0RWRelLSIyJzU+DBf++GzxKqK4S7XhrLWYSqu\nPoHthqT7E4THPqOb2ImUkHC4mXSqCm/FBzjVScqufZ3s0bUEyRbyeR2aiJQ+JS0icopYVSPxmtbC\nBuFNE2nfi1MzgPFdkv9egRlpI16jhEWk1JhMOZmPP4PTcAxv+T4iV+0hqOklc2Sdel1E5IIpaZGS\nouokl67Yq+Q4tSfw2j/EcrMEo3VkD68n1fURsariOSs7V63pyK7CBiKLWlFUDbtgFsHAMsLRerwV\ne3BqBihLvEG2ay3B4BIK1etS7PvDUqDjsuSLkhYRKQ7eNJG2j3Bq+zCBQ+bIWoL+5WgIicjCket1\n+WyuNPKyj4l0vH+y10VDP0XkPJS0iEiBGZymLrylB7CcgGC8hmzneky6otCBicgVMVMaebbXpbaf\nssphst2rCQaWohMVInI2SlpEpGCs2CiRFXuxK8Ywvkemcy1BshX9aBFZ+Ew6RmbfTTiNR/GW7Sey\nYi9hwzEyR9ZhJisLHZ6IFBklLSKSf7aPt/QATlMXlgV+soXs0TUaHiKy6FgE/W0Ew014y/fh1vUS\nXfcmQV8b2WOrINTPFBHJ0d5ARPLIYNf0EWn7CCuSJpyKkTmyjnC8rtCBiUghZcvIHrqeYCCJ1/4h\nbnMXTm0v2aNXEww1o95XEVHSIiWl/fF2QNVKLsUr2+4D8l81xyqbwFu+D6c6iQktssdW4p9YAcbJ\naxyXw7aZ7/DuTfcXOBJZzGbbYWlVETu/cKye9J7bcJccxm3pJLLyPYLRY2S7rsFMX/7r3Aq1P1xI\ndFyWfFHSIiJXlpvGaz2I03gMyzK5MsZdazHT8UJHJiLFyDj4PSsJBlvw2j7EqU5ir3+doH852Z4O\n8COFjlBECkBJi4hcGVaA23wEt6UTywkIpyrIdK8hHGlAQz1E5NOYdIzM/huxa/rwln2cGzJWfxy/\n5yr8vraS7KUVkflT0iIil5nBqTuBu3Q/dnQak/XIdK/JlTI1dqGDE5GSYhEON5MeacxVGWs9hLd8\nP07TUfxjqwgGW9BJEJHFQUmLiFw2dmIIb9k+7PgYJrTJ9qzAP3EVBF6hQxORUmZsgr52gmQr7pJO\n3OYuIh17CJuPkO1eQzhWX+gIReQKU9IiIpfMTgzith7CqRwCwB9sxu9ejcnEChyZiCwogYd/bA1B\n/3LcpQdw63uIXv1PgpF6ssdXYlLVhY5QRK4QJS1SUlSd5NJdvio5BjsxhNt6EKdyGGDR/HCYq9Z0\nZFdhA5FFbSFVDbtYJlNOtvM6/N52vGUf41QncaqTBKN1+D0dF/w+qhp26XRclnxR0iIiF8lgV870\nrCRmk5UGssc7FnyyIiLFxUxWkvn4M7kTKC2dOFWDOFWDNNV7THfFIDTomheRhUFJi4hcIINdlcRt\nOYSTGAEgGG4g27MSk6oqcGwisnhZhON1ZD6uw44P47Z0UtYwQFnDEcKJYbI9HapaKLIAKGkRkfOz\nA5y6HtymLuzYBADBcGOuZ2VSyYqIFI9woobM/hsZGfl3ajcERJtGia7eRZhK4Pe2EwwtURVDkRKl\npEVEzsqKTOE0HsVtPIblZjGhhZ9cgt+7AjNZWejwRETOKTPiMfbuUhItlbhLOnHqThDp2INZ/jF+\n/1L8/uWQLSt0mCJyEZS0iMgnGNzqFF7Huzi1fViWwWQ9ssc78PuX6SAvIiXFTCXIdm7AP7YKp6kb\nt+EYXmsnbsthwuFG/L42wvEaNHRMpPgpaZGS0v54O6BqJZfilW33AadVzXGyOLUnqFkZ4NV2AhCm\nEmT72ggGl+jO06fZNvMd3r3p/gJHIovZbDtczFXELpTJxPC71+AfX4lTewK3qQunto8/P/Tfwdh8\n4fv/LbevC/Wz6GLpuCz5ov+dIotW7sJ6p/44Tk0/lh1iQkj3VcLQ1Tr7KCILT+gQJJcSJFux4yMQ\n/i+wQyIr9mKW7yMYbiJIthCO1aH9n0hxUdIisthYBuyAsutfxYqkAQinKvCTrYzuOoQpayNeU1vg\nIEVEriSLcKIG40cAQ/bYSpz647j1Pbj1PZhMFD/ZQjDYgplKFDpYEUFJi8iiYEWmsGv6cOtOYHnT\nuRftAL9vGX6ydaZksUU41Ymly1ZEZFGx8HtW4vd0YMdHcr3Ptb14LYfxWg4TpipzCcxQs67rEykg\nJS0iC5LBKkvh1Pbh1PRhV4zlXjVA6GBCh+nd/6prVURE5uR6X8KJGrJda7GrB3Dre7CrBoi07YO2\nfYQTVbkhZMONmOl4oQMWWVSUtIgsGAarYgynphenph+7PJV7NbQIRupPHmj9P8ysroRFROSsjEM4\n3ExmuBncDE7tCZzaPuzEMF58FG/ZfsKpGMFwE+FII+FENboGRuTKUtIiJUXVSU7jTeNUDWJXJnEq\nB7EiGQBM4BAMNeUSlZEGCLy5Tf5NlYYu2Vy1piO7ChuILGqqGnbpLmh/6EcI+tsI+ttyCUzVQO7E\nUFUSr+UwtBzGZCIEow2Eo3UEY3XgR6988EVCx2XJFyUtIqXE9rETQzOJyuDcHeoBTCYyM+66iXCs\nHkL1pIiIXFZ+hGCwlWCwFawAu2oQp7ofp6Yft+E4NBwHIJyME47lEphwvOaUE0ciMj9KWkSKmTeN\nHR85+agYxbINACawCUbqcwfG0XrMVBwNTxARyRPj5IaGjTSSPTIzPLdy5oRSfBi3eQK3uQtjLEyq\nkmCsjogbMJGdLHTkIiVJSYtIsbBCrNj4TIIynJtGp+cWGwMmVYU/Vkc4Wkc4UQPGLmDAIiKSY+X2\nz6kqOHEVWGFuHz6bxFSM4sVHqWqBn33wP2k8XMequhVzj/bqpXiOemNEzkdJi0gBGCfAjg3mkpSZ\nh1U+gWWHJ9fJegTDDYQT1blHqkp3axYRKQXGJhyvJRyvheOrZob2DuM73Wy8oYKe6X7eOPpP3jj6\nTwBc26W9eint1UtZXt3K8qpWlle3EI9UFPiDiBQP/QISuYJSmUlOjPfTM97H8bFeukaP0zVyjLHr\nh/nkZZomtDFTcYJUFeF4Lkkx6Rga7iUisgCELuFoA5PDGf7T5k2sWrWKvokB9g8e5sDgYQ4OHuHw\n8FEODh05ZbO68hqWV7fkkpiqVlorm2hONBLzygvzOUQKSEmLlJT2x9uB4qlWYowhlZlkYHKIgdQg\nPeN99Iz3cWK8nxPjfYylJ87YpqasCne0gqlUI2YyQThZiZmOAfkZ6vXKtvsAVRG7FNtmvsO7N91f\n4EhkMZtth6oiNn+F2h9alkVzopHmRCP/of1mALJBluNjfRwdPc7R0eN0jeSmu0/sZfeJvadsXxVN\n0JxoZEm8keZEA0sSjTTHG2mqqCcWyW9CU2zHZVm4lLSInIMxhqnsNCPTo4xMjzE0NcJAaoiBySEG\nJ4cYSA2RnBxi2k+fsa1t2TRW1NFR286SRCMtiSZaEo0sr2qlsizBfT94nPFgRQE+lYiIFCPP8Wiv\nWUp7zdJTXh9PT3B0tIejI8dzJ8Qm+ukd72f/YCcfJw+d8T7lXhn15TXUV9RSd9q0trya6rJKytwo\nlqWefCkt805aHnnkEd577z0sy+JHP/oR11577eWMS+SyM8Yw7acZz6QYT08wnk4xkclNxzMpxqbH\nGZkem3nkEpVMkD3n+1VEYjTFG2iI1VIfq6W+opaWRCNLEk00VdTjOjonICIilyYRjbOucTXrGlef\n8rof+PSnkpyYGODEeC6RGZjMnUwbnByme+zEOd8z4nhUl1VSNfOoLqukuixBZTRBIlpBIhInHokR\nj1QQj1ZQ7pYpyZGCm9evqrfffpuuri6ee+45Dh06xI9//GOee+65yx2bLHLGGPzQJxv4ZIIM00EG\nPwwwGN7v/YhpPz33SPsZpvwpJjNTTGanmfSnmMpOMZnJPZ/MTjORSRGEwaf+XceyqSqrZGnlEqrL\nq2Z25pXUlldRH6ujPpY7Y6UxxSIiUiiu49JS2UxLZfNZl09mpxicHJ5LYpKTQwxNjjKazp2cG50e\np3Ooi8CEZ93+k2zLnktiYl455V4Z5V4ZMa+cicwklmXxp31/IeaVUeZGiTgRytwoUTdC1JmZuhHK\nnCgRx8OxHSVBctHmlbTs2LGDTZs2AdDR0cHY2BipVIqKClW5ON1kZoppP41h5t4aM9OTE/PJWTDm\nlNeGM6P0jvdjZtc15hPPT76HmdnOmJPzYAhNbqVwZqcUGoMhnFkfjAlnXjOEs89npnPzhARhODOf\ne8zOB3PzAcHcNMhNwwDfBIRhiB8GuQQk9PHnHgHZwJ97PRNkyQbZU6bm5DcDwPDUCAD/9f/9jwv6\n/j3HI+aVE/PKaIzVEo/GScycOUpEKkhEK4hH4iSiFVRG49SUVRGPVmBbKiUsIiKlK+aVE6sqZ1lV\nyznXCU1IKjM5k8SMMZoeZyI9yUQmNwJhIpNiIjNJKn1yfiA1SDb0595jKjsFwG/f++MFx2ZZFhHb\nw3M8PMclYntEnJl528V1XFzbwbHd3Lzt4Nouru3i2Dau5eDYM4/Z55Z9ytS2LGzLxrY++dzGsW0s\nZuctrNkp9sx6udesmTgtbCyLuW1yrwFYc89zU2vus1lYYMFgZoSesV745PLcSrntZovtWCeXWVhE\n3AiV0fgFf5+LxbySlmQyyfr16+fma2pqSCaTSlpO0zVyjAf/7yMXdBbjvI6+cHkCKkKOZed2RI5L\nxPGI2B4VXjmec3IHFnE8Ik7uLM3ful7EsizuXf8fibpRytwoZW6EqBul3M2d9YlFynNTt6xoh2gF\nk0NY0wW6wViYG/Jmje49Y1F2oh/frst3RJ9qanyIYqqkZmZ67Iotrk8q1tiKNS4o3tjOFddsO5wY\nPp7niHKK9fuCC48tzPN3ODnan5e/c6FsyyYRjZOIxs+b3JwuG2SZ8tNMZad48+n/g8Hwg8/dz1R2\nmnSQZtrPkPbTpIPM3GiItJ9mOsiQnTkxOTuKIhP6ZIMsk9mpuefhpf5uKiZHX5zXZj++/dtsaL7m\nMgdT2ixjjPn01U710EMPcccdd/D5z38egK1bt/LII4/Q1tZ21vXfeeedS4tSREREREQWhRtvvPGM\n1+Z1GrqxsZFkMjk339/fT0NDw0X9YRERERERkQsxr4H7t912Gy+//DIAe/fupampiVgsdlkDExER\nERERgXn2tGzcuJF169axZcsWHMfhoYceutxxiYiIiIiIAPO8pkVERERERCRfVNdVRERERESKmpIW\nEREREREpakpaRERERESkqClpKTDf9/n+97/P1q1b+drXvsaxY8fOWOdPf/oT99xzD/feey8vvnjq\nTYqSySQ33XQTb7/9dr5ClhI33zYXBAEPPvggW7duZcuWLezatSvfoUuJeeSRR9iyZQtf/epX2bNn\nzynL3nzzTTZv3syWLVt48sknL2gbkfOZT3t79NFH2bJlC5s3b+Yvf/lLvkOWEjaf9gaQTqf5whe+\nwEsvvZTPcBcGIwW1fft289Of/tQYY8zrr79uHnjggVOWT05Omi9+8YtmYmLCTE9Pm7vuusuMjo7O\nLf/BD35gvvzlL5u33norr3FL6Zpvm/vDH/5gfvKTnxhjjDlw4IC555578h67lI633nrLfPOb3zTG\nGHPw4EFz7733nrL8zjvvNL29vSYMQ7N161Zz8ODBT91G5Fzm09527txpvvGNbxhjjBkeHjZ33HFH\n3uOW0jSf9jbrscceM/fcc4/Zvn17XmNeCNTTUmA7duxg06ZNANx6661nnL1+7733uO6666ioqCAa\njXLDDTfMrbNz507i8TirV6/Oe9xSuubb5r70pS/x4IMPAlBbW8vo6GjeY5fS8cl21tHRwdjYGKlU\nCoDu7m6qq6tpamrCsixuv/12duzYcd5tRM7nYtvbzp07uemmm3jiiScAqKysZGpqCqOCqnIB5tPe\nAA4dOkRnZye33357wWIvZUpaCiyZTFJbWwuAZVnYto3v+2ddDrkfiwMDA2SzWX75y1/yne98J+8x\nS2mbb5tzHIdIJALAb37zG+666678Bi4l5fR2VFNTQzKZPOuy2TZ2vm1Ezudi21t/fz+WZVFWVgbA\nCy+8wO23345lWfkNXErSfNob5IYjzp78k4s3r5tLyvy88MILvPjii3M7RWMM77///inrhGF43veY\nPQv09NNP85WvfIV4PH7K6yKfdDnb3Kzf/e53fPjhhzz11FOXN1hZ0M63jzrXMu3XZL4upr399a9/\n5Y9//CPPPPPMlQ5LFqgLaW8vvfQSGzdupLW19VO3kbNT0pJHmzdvZvPmzae89sMf/pBkMsmaNWvm\nzna77sl/lsbGRgYGBubm+/r62LhxI9u3b+e1117jt7/9LUePHmXPnj088cQTdHR05OfDSEm4nG0O\ncknQq6++ypNPPonjOHn4BFKqGhsbT+kl6e/vp6GhYW7Z6W2ssbERz/POuY3I+cynvQG89tprPP30\n0zzzzDNzJwFFPs182ts//vEPuru7+fvf/05vby/RaJTm5mZuueWWvMdfqjQ8rMBuu+02/vznPwPw\nt7/9jZtvvvmU5Rs2bOCDDz5gYmKCVCrF7t27ufHGG3n22Wd57rnneP7557njjjt4+OGHlbDIBZlv\nm+vu7ub555/nF7/4BZ7nFSJ0KSG33XYbL7/8MgB79+6lqamJWCwGQGtrK6lUip6eHnzf59VXX+Vz\nn/vcebcROZ/5tLeJiQl+/vOf89RTT5FIJAoZvpSY+bS3xx57jBdeeIHnn3+ezZs3861vfUsJy0VS\nT0uB3Xnnnbzxxhts3bqVaDTKz372MyA3/Ovmm29mw4YNfO973+PrX/86tm3z7W9/W2eD5JLMt839\n6le/YnR0lPvuuw9jDJZl8etf//qUXhqRWRs3bmTdunVs2bIFx3F46KGH2L59O4lEgk2bNvHwww/z\n3e9+F4C77rqLtrY22trazthG5ELMp739/ve/Z2RkhAceeGBun/boo4/S3Nxc4E8jxW4+7U0unWU0\nqE5ERERERIqYhoeJiIiIiEhRU9IiIiIiIiJFTUmLiIiIiIgUNSUtIiIiIiJS1JS0iIiIiIhIUVPS\nIiIiIiIiRU1Ji4iIiIiIFLX/D3hFGlI8qkdtAAAAAElFTkSuQmCC\n",
485 "text/plain": [
486 "<matplotlib.figure.Figure at 0x7f20a2ad7610>"
487 ]
488 },
489 "metadata": {},
490 "output_type": "display_data"
491 }
492 ],
493 "source": [
494 "# Plotting histograms and confidence intervals. \n",
495 "plt.hist(returns, range=(returns.min(), returns.max()), normed = True);\n",
496 "plt.plot(x, sample_distribution)\n",
497 "\n",
498 "plt.axvline(sample_std_dev, linestyle='dashed', color='red', label='1st Confidence Interval')\n",
499 "plt.axvline(-sample_std_dev, linestyle='dashed', color='red')\n",
500 "plt.axvline(2*sample_std_dev, linestyle='dashed', color='k', label='2st Confidence Interval')\n",
501 "plt.axvline(-2*sample_std_dev, linestyle='dashed', color='k')\n",
502 "plt.axvline(3*sample_std_dev, linestyle='dashed', color='green', label='3st Confidence Interval')\n",
503 "plt.axvline(-3*sample_std_dev, linestyle='dashed', color='green')\n",
504 "\n",
505 "plt.legend();"
506 ]
507 },
508 {
509 "cell_type": "code",
510 "execution_count": 14,
511 "metadata": {
512 "collapsed": false,
513 "deletable": true,
514 "editable": true
515 },
516 "outputs": [
517 {
518 "name": "stdout",
519 "output_type": "stream",
520 "text": [
521 "The JB test p-value is: 0.923015693884\n",
522 "We reject the hypothesis that the data are normally distributed False\n",
523 "The skewness of the returns is: -0.102081900914\n",
524 "The kurtosis of the returns is: 3.07608657316\n"
525 ]
526 }
527 ],
528 "source": [
529 "# Run the JB test for normality. \n",
530 "cutoff = 0.01\n",
531 "_, p_value, skewness, kurtosis = stattools.jarque_bera(returns)\n",
532 "print \"The JB test p-value is: \", p_value\n",
533 "print \"We reject the hypothesis that the data are normally distributed \", p_value < cutoff\n",
534 "print \"The skewness of the returns is: \", skewness\n",
535 "print \"The kurtosis of the returns is: \", kurtosis"
536 ]
537 },
538 {
539 "cell_type": "markdown",
540 "metadata": {
541 "deletable": true,
542 "editable": true
543 },
544 "source": [
545 "---\n",
546 "\n",
547 "Congratulations on completing the Random Variables answer key!\n",
548 "\n",
549 "As you learn more about writing trading models and the Quantopian platform, enter a daily [Quantopian Contest](https://www.quantopian.com/contest). Your strategy will be evaluated for a cash prize every day.\n",
550 "\n",
551 "Start by going through the [Writing a Contest Algorithm](https://www.quantopian.com/tutorials/contest) tutorial."
552 ]
553 },
554 {
555 "cell_type": "markdown",
556 "metadata": {
557 "collapsed": true,
558 "deletable": true,
559 "editable": true
560 },
561 "source": [
562 "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
563 ]
564 }
565 ],
566 "metadata": {
567 "kernelspec": {
568 "display_name": "Python 2",
569 "language": "python",
570 "name": "python2"
571 },
572 "language_info": {
573 "codemirror_mode": {
574 "name": "ipython",
575 "version": 2
576 },
577 "file_extension": ".py",
578 "mimetype": "text/x-python",
579 "name": "python",
580 "nbconvert_exporter": "python",
581 "pygments_lexer": "ipython2",
582 "version": "2.7.12"
583 }
584 },
585 "nbformat": 4,
586 "nbformat_minor": 2
587 }