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Created March 27, 2014 03:59
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AM207: HW#6 and Project Proposal
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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"**AM 207**: Homework 6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"from __future__ import division\n",
"import numpy as np\n",
"import time\n",
"#from prettyplotlib import plt\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_ _ _ _ _\n",
"\n",
"Pavlos Protopapas <br>\n",
"Handed out: Thursday, March 13th, 2014<br>\n",
"Due: 11.59 P.M. Wednesday March 26th, 2014\n",
"\n",
"**Instructions**:\n",
"\n",
"+ Upload your answers in an ipython notebook to the dropbox.\n",
"\n",
"+ Your individual submissions use the following filenames: AM207_YOURNAME_HM7.ipynb\n",
"\n",
"+ Your code should be in code cells as part of your ipython notebook. Do not use a different language (or format) unless you get permission from the TFs. If you use any special libraries you must include them with your code (program should run as is). \n",
"\n",
"+ If you have multiple files (e.g. you've added code files and images) create a tarball for all files in a single file and name it: AM207_YOURNAME_HM7.tar or AM207_YOURNAME_HM7.zip\n",
"\n",
"_ _ _ _ _"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Question 1: Squares beyond compare [10 pts]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider a shape consisting of two squares of equal side and centered at the same point, which \n",
" are rotated by $\\pi/4$ relative to each other. The two squares intersect each other at eight points.\n",
"The squares each have four corners. The intersections and corners lie on eight line \n",
"segments (the sides of the two squares) that contain four points each, two corners and two intersections. \n",
"Use Simulated Annealing to place the sixteen lowest positive integers along these \n",
"line segments so that the sum of the numbers in each line segment is the same \n",
"for all the line segments.\n",
" \n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def permute(starting, L):\n",
" path = starting[:]\n",
" for l in xrange(L):\n",
" x, y = np.random.randint(0, len(path), 2)\n",
" path[x], path[y] = path[y], path[x]\n",
" return path"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def print_subsets(path):\n",
" subsets = []\n",
" # This is a simple way to allow us to reference values off the end, specifically for the last values\n",
" path = path[:] + path[:]\n",
" for i in xrange(8):\n",
" start = 2 * i\n",
" s = path[start:start + 5]\n",
" s[2] = 0\n",
" subsets.append(s)\n",
" return subsets\n",
" \n",
"def get_subsets(path):\n",
" subsets = []\n",
" # This is a simple way to allow us to reference values off the end, specifically for the last values\n",
" path = path[:] + path[:]\n",
" for i in xrange(8):\n",
" start = 2 * i\n",
" s = sum(path[start:start + 5]) - path[start + 2]\n",
" subsets.append(s)\n",
" return np.array(subsets)\n",
"# Test against a known correct solution\n",
"assert (get_subsets([12, 4, 6, 5, 13, 8, 15, 11, 2, 7, 1, 16, 9, 3, 14, 10]) == 34).all()\n",
"\n",
"def distance(path):\n",
" subsets = get_subsets(path)\n",
" d = 0\n",
" for n in subsets:\n",
" d += abs(sum(subsets - n))\n",
" return d"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def A(deltaE, temp):\n",
" return np.exp(-deltaE / temp)\n",
"\n",
"def simulated_annealing(path, MAX_ITER=100, REANNEALING=100, ALPHA=0.9, SCALE=1, TEMP=100, VERBOSE=20, END=lambda d: d == 0):\n",
" dist_trace = []\n",
" accepts = []\n",
" temp = TEMP\n",
" dist = distance(path)\n",
" for it in xrange(MAX_ITER):\n",
" L = int(SCALE * np.sqrt(temp))\n",
" if L < 1:\n",
" L = 1\n",
" if VERBOSE and it % VERBOSE == 0:\n",
" print 'Iteration {} of {} -- L = {} and D = {}'.format(it, MAX_ITER, L, int(dist))\n",
" for sample in xrange(REANNEALING):\n",
" proposed = permute(path, L)\n",
" proposed_dist = distance(proposed)\n",
" if np.random.rand() < A(proposed_dist - dist, temp):\n",
" path = proposed\n",
" dist = proposed_dist\n",
" accepts.append(True)\n",
" else:\n",
" accepts.append(False)\n",
" dist_trace.append(dist)\n",
" if END(dist):\n",
" return path, dist_trace\n",
" temp = ALPHA * temp\n",
" return path, dist_trace"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 124
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"path = range(1, 17)\n",
"better, dist_trace = simulated_annealing(path, ALPHA=0.995, REANNEALING=500, MAX_ITER=2000, VERBOSE=200)\n",
"#\n",
"fig = plt.figure(figsize=(12, 6))\n",
"plt.plot(xrange(len(dist_trace)), dist_trace)\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Distance')\n",
"print 'Solution:', better\n",
"print 'Solution gives distance of {}'.format(distance(better))\n",
"print 'Each of the subsets tallies to:', get_subsets(better)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Iteration 0 of 1000 -- L = 10 and D = 672\n",
"Iteration 200 of 1000 -- L = 6 and D = 304"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Iteration 400 of 1000 -- L = 3 and D = 96"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Iteration 600 of 1000 -- L = 2 and D = 32"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Iteration 800 of 1000 -- L = 1 and D = 16"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Solution:"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" [2, 1, 11, 16, 15, 3, 4, 9, 7, 8, 13, 5, 14, 6, 10, 12]\n",
"Subsets: [34 34 34 34 34 34 34 34]\n"
]
},
{
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"output_type": "display_data",
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T6L4/rD+UsrYOnbRLknbVnEtZmwAAAL0FYTpLMH0FAACg9yFMAwAAAEkiTGcp6k4DAABk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\niML0P2nlsrpEXLaDAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x9210f90>"
]
}
],
"prompt_number": 125
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print 'Solutions to the eight subsets:'\n",
"for s in print_subsets([2, 1, 11, 16, 15, 3, 4, 9, 7, 8, 13, 5, 14, 6, 10, 12]):\n",
" print '|'.join('%2d' % x if x else '_' for x in s)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solutions to the eight subsets:\n",
" 2| 1|_|16|15\n",
"11|16|_| 3| 4\n",
"15| 3|_| 9| 7\n",
" 4| 9|_| 8|13\n",
" 7| 8|_| 5|14\n",
"13| 5|_| 6|10\n",
"14| 6|_|12| 2\n",
"10|12|_| 1|11\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Overview of Method:**\n",
"\n",
"To begin with, I wrote a generic simulated annealing solver to be used for the task.\n",
"\n",
"The distance that we attempt to optimize for in this task is the difference each subset has compared to all other subsets.\n",
"The function `get_subsets` picks out the eight line segments that must be equal to each other and sums each individual line segment together.\n",
"Deriving a distance measure from this is simple -- calculate the difference between each individual subset to all the other subsets.\n",
"\n",
"To propose new potential solutions, the numbers were permuted at random.\n",
"The number of elements to be permuted at each step was determined by the value of $L$, described fully next paragraph, but related to the temperature that the simulated annealing system was at during the current iteration.\n",
"\n",
"The simulated annealing solver is generic and could be used for other tasks.\n",
"For the value of $L$, we take $\\sqrt{T}$ where $T$ is the current temperature.\n",
"The solver has a number of option including a user specifiable end function.\n",
"In this case, the end function is triggered when the solution is 0 as we know a solution with no error exists.\n",
"\n",
"The simulated annealing solution proceeds as we would expect.\n",
"As time progress and our temperature begins to cool, we can see the variance in the proposed solutions (i.e. the distances) decrease.\n",
"A long time is spent in the tail of the function, between samples 300k and 500k, as we need a very specific permutation to be triggered to reach zero error.\n",
"Eventually this is reached however and we arrive at our optimal solution."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Question 2: A tired salesman [10 pts]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the traveling salesman problem, the quality of the solution can be measured in \n",
"different ways, beyond the shortest path. For example, the total time of travel may also \n",
"be important, and may depend on the means of transportation that connect pairs of \n",
"cities. Consider a random distribution of $N$ points on a plane representing the cities \n",
"that must be visited by the traveling salesman. Assign a value $s_i, i=1,\\dots,N$\n",
"to each city that represents its size, as measured by its population (take $1 \\leq s_i \\leq 10$).\n",
"For cities that are farther than a certain \n",
"distance and are larger than a certain size, assume that there are airplane connections \n",
"between them. For the rest of the cities there is only a car connection. Assume that \n",
"air travel is faster by a factor of 10 than car travel. \n",
"\n",
"a) Use Simulated Annealing to find solutions to the traveling salesman problem for \n",
"$N=100$, optimizing the path by the total distance travelled while keeping track \n",
"of the time of travel. \n",
"\n",
"b) Now redo the problem by optimizing the the path by the total \n",
"time of travel, while keeping track of the distance traveled. Are the two solutions \n",
"similar or different? \n",
"\n",
"c) How do your results change if the thresholds (population/distance) for having a flight between two cities are altered?\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"FLIGHT_DISTANCE = 200\n",
"FLIGHT_POPULATION = 7\n",
"def l2norm(a, b, ALLOW_FLIGHT=False):\n",
" d = np.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2)\n",
" if ALLOW_FLIGHT and d > FLIGHT_DISTANCE:\n",
" ka, kb = tuple(a), tuple(b)\n",
" if city_sizes[ka] > FLIGHT_POPULATION and city_sizes[kb] > FLIGHT_POPULATION:\n",
" return d / 10\n",
" return d\n",
"assert l2norm([3, 4], [0,0]) == 5\n",
"\n",
"def distance(path, ALLOW_FLIGHT=False):\n",
" return sum(l2norm(path[i - 1], path[i], ALLOW_FLIGHT) for i in xrange(len(path)))\n",
"# Test the total distance travelled along the edges of a square\n",
"assert distance(np.array([[0, 0], [1, 0], [1, 1], [0, 1]])) == 4\n",
"# Test the total distance travelled along the edges of a triangle (hyptoenuse = 5)\n",
"assert distance(np.array([[0, 0], [4, 0], [4, 3]])) == 5 + 4 + 3\n",
"\n",
"def nearest_neighbours_path(cities, ALLOW_FLIGHT=False):\n",
" path = [cities[0]]\n",
" to_add = set(tuple(x) for x in cities[1:])\n",
" while to_add:\n",
" # Find next closest point\n",
" d, best = sorted([(l2norm(path[-1], pt, ALLOW_FLIGHT), pt) for pt in to_add])[0]\n",
" to_add.remove(best)\n",
" path.append(best)\n",
" return path\n",
"\n",
"def getXY(path):\n",
" return [x for x, y in path], [y for x, y in path]\n",
"\n",
"def plot_map(path, title):\n",
" fig = plt.figure(figsize=(6, 6))\n",
" #\n",
" small_cities = [c for c, s in city_sizes.items() if s <= FLIGHT_POPULATION]\n",
" big_cities = [c for c, s in city_sizes.items() if s > FLIGHT_POPULATION]\n",
" #\n",
" plt.plot(*getXY(small_cities), color='#004466', ls='', marker='.', ms=20)\n",
" plt.plot(*getXY(big_cities), color='#006699', ls='', marker='.', ms=40)\n",
" plt.plot(*getXY(path), color='r', ls='--')\n",
" plt.title(title)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 176
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def A(deltaE, temp):\n",
" return np.exp(-deltaE / temp)\n",
"\n",
"def flight_sa(path, MAX_ITER=100, REANNEALING=100, ALPHA=0.9, SCALE=1, TEMP=100, ALLOW_FLIGHT=False):\n",
" flight_trace = []\n",
" ground_trace = []\n",
" temp = TEMP\n",
" dist = distance(path, ALLOW_FLIGHT)\n",
" for it in xrange(MAX_ITER):\n",
" L = int(SCALE * np.sqrt(temp))\n",
" if L < 1:\n",
" L = 1\n",
" if it % 25 == 0:\n",
" print 'Iteration {} of {} -- L = {} and D = {}'.format(it, MAX_ITER, L, int(dist))\n",
" for sample in xrange(REANNEALING):\n",
" proposed = permute(path, L)\n",
" proposed_dist = distance(proposed, ALLOW_FLIGHT)\n",
" if np.random.rand() < A(proposed_dist - dist, temp):\n",
" path = proposed\n",
" dist = proposed_dist\n",
" if ALLOW_FLIGHT:\n",
" flight_trace.append(dist)\n",
" ground_trace.append(distance(path, False))\n",
" else:\n",
" ground_trace.append(dist)\n",
" flight_trace.append(distance(path, True))\n",
" temp = ALPHA * temp\n",
" return path, ground_trace, flight_trace"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 177
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.random.seed(28)\n",
"N = 100\n",
"#\n",
"# Generate random positions for each of the N cities and create an initial random path\n",
"cities = np.random.randint(0, 300, (N, 2))\n",
"cities = [list(x) for x in cities]\n",
"path = cities[:]\n",
"#\n",
"# Generate random populations for each of the cities\n",
"city_sizes = {}\n",
"for city in cities:\n",
" city_sizes[tuple(city)] = np.random.randint(0, 11)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 191
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print 'With no flight allowed:'\n",
"ALLOW_FLIGHT = False\n",
"plot_map(nearest_neighbours_path(path, ALLOW_FLIGHT), 'Plot of cities and nearest neighbour method')\n",
"print 'Distance given by nearest neighbour method:', distance(nearest_neighbours_path(path, ALLOW_FLIGHT), ALLOW_FLIGHT)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"With no flight allowed:\n",
"Distance given by nearest neighbour method:"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 2944.01674053\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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dbiO6o1+ZXjpt0xJx0mk5Xt90zJzoIL9KyVIWssIvhp+jkhYXTjIw4SwDr50l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I7RSMisN8gf/yDGuHqejkbGSYjVq3s6BKfhkOCrVCq+/fbbCq//8ccfdh2nS0LDks1ZgPiuY0yO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\nh+Hjn6ugb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"text": [
"<matplotlib.figure.Figure at 0x597d050>"
]
}
],
"prompt_number": 192
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ARGS = dict(TEMP=50, ALPHA=0.98, REANNEALING=2000, MAX_ITER=200)\n",
"ALLOW_FLIGHT = False\n",
"#\n",
"#better, ground_trace, flight_trace = flight_sa(path, ALLOW_FLIGHT=ALLOW_FLIGHT, **ARGS)\n",
"#\n",
"print 'With no flight allowed:'\n",
"print 'Initial path (random) =', distance(path, ALLOW_FLIGHT)\n",
"print 'Improved path using SA =', distance(better, ALLOW_FLIGHT)\n",
"#\n",
"plot_map(better, 'Plot of cities and path via simulated annealing')\n",
"#\n",
"fig = plt.figure(figsize=(12, 6))\n",
"plt.plot(xrange(len(ground_trace)), ground_trace, label='Ground distance', lw=2)\n",
"plt.plot(xrange(len(flight_trace)), flight_trace, label='Flight distance', lw=2)\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Distance')\n",
"plt.title('Distance via simulated annealing (no flight allowed)')\n",
"plt.legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"With no flight allowed:\n",
"Initial path (random) = 15782.1638221\n",
"Improved path using SA = 3325.09707623\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 211,
"text": [
"<matplotlib.legend.Legend at 0x16792850>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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TX6egU2dEf3+9NHKZjKk9IivlWkEQYFbfaIdU9o5IQbcepP7+F+o2bfEDznXr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\n",
"text": [
"<matplotlib.figure.Figure at 0xeb5dbd0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Fv3/lfGvHDcOgfv1beOON1/jyyyXYbDaef34MAKGhrRk+/BE++uhT3nprCjEx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\nvjRg8Fo+GvuaHC1IPaTGpRDn9YOBPaX7aRyXQmUkSGUkSMR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f5l//+heDBw+OzmHv2LEj\nhw4d4r333gPgz3/+MzfffLP7b1BE5AKlKTEiIg3EgAEDeOSRR/jWt75FKBTCGMOQIUOYOXMmY8aM\noVOnTjRr1owbbriBd95556TnH5vPfuL9Y+Lj48nJySEQCPCzn/2Mjh078uGHH2JZFn6/nxkzZjBh\nwgQqKipITU3lpZdeqpP3LCJyIbDMiaf5i4iI/JtHH32U+Ph4HnzwwfruiojIBUlTYkRE5GtpzXUR\nkfqjEXYRERERkRimEXYRERERkRimgl1EREREJIapYBcRERERiWEq2EVEREREYpgKdhERERGRGKaC\nXUREREQkhv1/YwBnI+20GQQAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1675d9d0>"
]
}
],
"prompt_number": 211
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ALLOW_FLIGHT = True\n",
"print 'With flight allowed between cities with population > {} and distance > {}:'.format(FLIGHT_POPULATION, FLIGHT_DISTANCE)\n",
"plot_map(nearest_neighbours_path(path, ALLOW_FLIGHT), 'Plot of cities and nearest neighbour method')\n",
"print 'Distance given by nearest neighbour method:', distance(nearest_neighbours_path(path, ALLOW_FLIGHT), ALLOW_FLIGHT)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"With flight allowed between cities with population > 7 and distance > 200:\n",
"Distance given by nearest neighbour method:"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 2790.55721884\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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iVqs5cuQImzdvpkOHDowdO5bk5GQOHjxI27ZtUavVeHl5Ubt2bU6e\nPFkiFSgOwsMTQ8NG9lZDpowh3NwgzXZjyJkZ2XLj+7qtmdJ6IKPP7aVaSpzZ/jlPNi+RvA1zaoYy\nsX5bElVq7jhZf4JYpvDk2cJ3dzct/U5KSmLAgAHMmTOH9PR0xo0bR2hoKHPnzuXtt9+mSZMmaDSa\nrOM8PT1JSMg7WqVKpcyaYClrqFSmAFNy/UqIf/8FPz/w8bFKccWtn8LXG0Vaqk2vz/ReTXFxUfNG\n5CGL+xcEP8aqwOaU0ybzyvGtfNikO5IE8/q04OVuIWRkmC/GKi4dQ+qyfMeBrN9JKicWVwticbWg\nbDJZ1+XuXZRffoGxTx9EcON8o4UWBId7Nq1MZv2KSr59upiYGDp37szw4cMZPHgwffv2JTQ0FIC+\nffty7NgxvLy8SEr6b0wxKSkJHyu9fHbh6lV7ayBTUPR61BG9UD09GPR6e2tjorwflK9gMWm1NZnW\nJZhVYzpTu7yXxf133LxodjeaDw6uo5eIY+XozrzczfpeaZmEB9cplIx0+jSKBZ+hbh6GukF9lK+/\nhrR/X6FzUMsUnDzdMm/fvk3Hjh354osv6NSpEwCtW7dmwYIFNG/enIULF3L9+nVefPFFunbtyqFD\nh0hPT6dVq1acOHEizzF8e7ll5od69040Tz9F0ueL0fbtX6QyHgXXMHCc+ql370QzqC/pQ4aTPP/T\nYrcUHa1++WEwGnPNyNa0ggcrPxiPslNnkhctsWndcnOnfRgzt0ytFqc9u3DabEquooiNJXXCJFIK\nGCcpZxhthUIiPLgOzWsH2N3n3RYU1y0zT4M/ZcoU1qxZQ7169bK2zZs3j2nTpqFWq6lcuTJLlizB\nw8ODb775hiVLlmA0Gpk+fTp9+/bN88SOavDJyMBz0nicN/xM0qeL0A4uvHtdaTMYhcUR6+fy/TI8\nX55C8uy5pE2YVKyyHLF+xcF14ae4z3uH+0f+xrOcF/j52XQNRZEXHWVkoD64H2M5Pwz16pvvFyLb\nx7xIH5hSjk0Nvi1xWIMPYDDgMW0yrj8uJ2n+Z6QPH1Wow8uawciJo9bPfeYbuC5eROL3q4oV5tdR\n61dUpIR4fJsEYaxaFeWtm2Rs+YX4uoVPc2hvvIYORLi4ousZga5LN1YePcfkfHLJLhg/qEy5gRbX\n4D9aoRUKilJJ8scLwckJz5enABTa6MuUPCmz3kEZE40i9p5VyjMYjaw/GU3k39GcyjFUElzFh96N\n/Onb2PGT1wuNN+lDh+OyYjmibh1UT0agXL+ldIUWEQJ985Y4b9yA1/jRCCcn2gbUY5TShx8q18nK\nnZsT2e8/O3ILPy+EwO39d9H26oOhUcFbRGWthZgTh65fjm5/UdBoXFl//ApvbDhkcYHTw9Qq58n0\nbiEl4uZYHKR790AIvHw9UHXpjLgXS3zUVowBNe2tWqFRXLmM85ZN/PP5F1RJjKN6+yEYJcsf3ep+\nPhxZML2ENbQd8pCOA+LQBtEKlPX6fXPoQq7ujrkxs3sTJrVvYPqRkYHi+jWMfuXhgWuzo6DRuMLN\nmyg7mGLoxG/aZpOYPyVBs8lziL19h1Rl7vl9ZYOfHcfui8rIlDCf/3m20MYeYPbW43z+51kAFLdu\nUq55Y5z2/2Vt9axD5crEr92I0dML6e5de2tTZNoEBeZp7DNlZP5DNvgyZZ6CGrWo0zHM3nq8yOeZ\nvfU4UadjEK5upg02iqdjDYw1Aojf8WehhiodjdxCZLdMuI17hj5PmUcV2eAXAZeli/H4v5flBSKl\nAOWlC/i2CMF59Y95yhmMRuZsO1Hs88397QQZLi4ANgugZjWssLLVnlhqvZfXpbHrcBQvRp/KVeZR\nRjb4RUGpwnXpEjxeniIbfQfHUDMQXa8n8XzpBdT79+Yqt/5kdL4TtAXh4r0kNvx7ByFJDmvwpb/2\n4PbxB/ZWo9hYCqPtVq0qO1t35s0bpzk+89ky5YNvDWS3zCKQPnIMODnh8eIkJK2WpM++kBOmOyqS\nRNL8z1BcvYLXyCHE/fI7xpq1zMQi/4622ikj/45hvKvtQiQXF+n0adzen4O2Tz8MtWpn26fesxt9\nm3bg4K6mmeQMo63RuMLdu6jq16Pu/5aQ/N58O2voWJSOu+qApA8ZRtKiJTj//BOez491nDguMuY4\nO5O4bAXCS4Nm6ECkhHgzkVM3zKNKFpWTN+LIqF0H8WBox9EwDh2G8PXF9atF2bYrz/2D5qkI3N98\n3eZxgGxK+fKkvTAVl/99i+KSHI75YWSDXwy0/QeRuGQZ6gP7Udy8YW91ZPJAlCtHwoo1SAkJqI4d\nNdufuagqL6qkxNHl2pl85W4npxG/fTfpY54tkq42x82NtFHjcFn9I9L92KzNhnr1SZ77AW5ff4Xb\nh+/ZUcHik/rs8xjL+eG24GN7q+JQyAa/mOie7Mv9/ccw+tewtyoy+WCoU5f7B0+g79i50Mc2uRfN\nv6ve5Lctn/H24Y2luwUMpI0aB0Yjrt8tzbY9fcx4Ul6fgfv8ebgu+cJO2lkBd3cS//djgYOwPSrI\nA8/WwLVsxt4uk7iZXCbNgnx5+IMi99fhpG81ZoVF4K7X8dbRTWh0abzYegDCwgrPih6O/zyI8uVJ\nHzgE5/VrSX3xlWweO6kvvoIUH4/HjNcx+viiHTDYjpoWnYymYfZWweGQDb7MI4fFKItKX3D3zvUY\no0LB/JDuANxz8eDzvatw12sZFz7MzL2xcZXSkQsi5Y2ZCFdXc/dMSSLl7TmgVpMREmof5WRsgmzw\nbYRi5Y9I7TojvDT5C8uUKDnzqqqMRjJS4sDdm8axMdRIuk9UQO6JQhY16kSikwuuGXqLvuy9rZwc\n3FaIcuVy3ylJpLz5dskpI1MiyAbfFty5g3LKZDQ1a5Gwej3CR/YFdiT+OvufwX/8XjSfnt/HkEad\nmfj3H4y8cJADFQKIqpF3yr3ldVtb3B7o50mfYH+k2FiktFSM1Rw7qJrMo4U8aWsLKlQg49etKK9e\nQfPUk6ZIhTIOw8Mt/FMevnhm6DlycD29r55gapuBdIh4uUirUCUJ3ugaglKhwP2dmXiNGWZNtWWK\ngerYEbyeGQDp6fZWxa7IBt9GiKbNiF+3GeWtG3j364l0+7a9VZKxwHUXD7o3fYI3ApsT2GYQCyvX\nRa8sWsf3zW5NiAiqZvrh6uqwC6+Kg8u3X5dK33bh5o7Tjt9w/fZre6tiV2SDb0MMDRsRv+EXpLg4\nvJ4fa291ZB6QM77K3x6+vFczlAS1MyTchthrhSpPkkzhkad46/Hu2RXFzRsIN/dSZfCdftmM2/tz\n8hZKScF1yRd4D+xT6tadGOrVJ33IMNw+/RApPvsiO4PRyNrjVxj2w26afBBJ5ZmrqDxzFU0+iGTY\nD7tZe/wKhjISQkU2+DbGULceCZFbSP5AXgDiKOQbQTHhNhPCqlKrnGe+ZQX6efLN4HamWPguLihu\nXMc7ojuKO7eRUlOspLHtUV65jNun81Fcz+Nj5+5OwppI0OvRDOiNFBubu6wDkvrqG0haLW4LP83a\nFnU6hrafbeH5tfvY+s91biSmYjAKDEbBjcRUtv5znefX7qPtZ1uIOh1jR+2tg5wAxQaU9QQhpb1+\nBUl+fe7b2Xg5ubDhVDSRp6I5mSPFYeMqPvQO9qdPcPYUh4qYaDT9n0R1+RIAd+8k2q4iRSC3eycl\nJeLbJIj0oSNMLpl5oDx/Du/ej2Oo7k/Cz1EITy+b6VtY8ns23ebOxu2rz7m/7ygLLiUVOhx2tkQ3\ndkDOeOWAlHaDmB9loX5mC68wDfW0bRBI95YNCahYrsj1k27fxi+4DgBxv/7uUAuA8rp37m/NwGX5\nd9w/fiZfI646cQxN317ounYjafEym+haFPJ7NqXEBDR9evL9oOcZG1O08ND2NPqywXdACmoQpbt3\nEeXLl4RKVqUsGPy8sEb9pLj7aIYMIG3seLRPDbSWasUmr7oprl/Dt3ljUt6cTdpzk/ItS3VgP8aK\nFR0qL25B7l3U39GMWVW8bGRLn25nlzzGcorDUorLD//Dt31zVKeKn3RDxvEQPr7Eb9rmUMY+P4xV\nq6Ht3Q+n334tkHxGy1YOZewLgsFoZM5vJ4tdztzfTpTKiVzZ4NsJ7RO9MFTzR9MvAtXRw/ZWR8YW\nKJX21qDQJM+bb5qYLaNYNdHNKevlUCgpZINvJ4RvORJ+3oihdm00/XujOrDf3irJyCA03qXyQ1VQ\nrJrophQafDm0gh0RGm8S1kSiebo/3oP6krDqZ/St2pjJ5TXB2CYoUE7jVopQHTyA+vgR0p593t6q\nWB8hcPvwPYSnV4HmAOxBzkQ3akMG/sn3uaipUOiyTloxaU5JIRt8OyM8PIlftQ7PV1/EULmK2f7c\nXAhX7z7M6t2moaDDn70hG31HIyMD5dXLGCpWBg+PrM1Ou37H/cP3kO7fJ/W16aU+kXhOpLQ03OfP\nQ3h5kf7McHurY0bORDeL//yBtrcv0nDAW2QoCtezKUjSHEdDHtJxBNzdSVq0BGONALNdOSM7WqIg\nMjIli+LuHXxbN8Np75/Ztqe+/Dopb8zE/eMPcJ/xGpTCib9ckSRSZs4mbdhIPKZNxilqg701ypeF\njTpTN+EOY//ZQ+i9aPyTStdissIiG3wH5+HIjsWRkSlZxIOkOGbhFSSJ1Kkvk/Teh7h9/RWeUydC\nRoYdNMwfl+Xf4TbvncIdJEkkf/AJ2og+eE0Yg/r37bZRrojkTE5zzM+fFbVb8P6BdRxc/x6vndhq\ndkz15PsMvnAQSWT/OJeGRDc5kQ2+gyO38Esnws3d9Eea5W5/+pjxJC74Eud1a1AdO1KCmhUcxZ3b\nuC1agHT3buEOVCpJWrQEXXhHPGa9AQaDbRQsAsEWktPMCOvNPRcP5oT2YGprczfafpePsvL3pRz7\neQ69rp7ISm9ZWhLdPIxs8B0Yt/fn0P/SqWzbmiXeLfX5VB8JnJwQKlWe8XS0g5/h/sETZDRvWYKK\nFZy0kWNBocD12yWFP9jJicSly00ung7k9dO7kXlymitefgQ+PYe3wp60GCn1s+AutI94mUQnF6K2\nfsHeyPfpeONcqUl08zCywXdAFJcv4bJ0Ce4fvc/HB7cw7tpZAFrH3+LAwQ08c+tCNvmc0R9lHAPh\n6oaUknfETGOVqiWkTeER5cqRPvgZXL/7JteeSp64uWGsVNn6ihWDvo39CxQULyd7KtchPOJlejz+\nAs6GDLZt+Yx+fqXP56X0aVxGUR0+iMva1aj/2IHq8iWEUom+eUsSb95iyT9/4qdPZ8yNfzjs5cfq\nitkNfL7RH2XsgqFefYS7u73VKBap4yfi8t1SXH5aSfqI0fZWp9goFQqmdwthzMo9hT9YkvjVvxHb\n/INY17QcbapWs76CNkY2+A6C+uABnH7biq7jY6S8ORt9+3CExpvoO7F83yOCuRcPAfB46BNkKLJ3\nzEpLC/9RW08Qv6VoE5bq/Xsx+NdwiNa/sVYguh69UO/fax2DLwSkpoIdP4QRDaszs3uTQkfKzGRG\n96a0yS14mhAO7WorB0+zAZYCOEl37+K063cknY70IRZS3+n1oFJZfFgSVq2k9uTxADR4aiopame7\nGsqiBBcrSEhiR1lPYNfgcAYDPuEtkdLTiV8TibGWdT/mRapbaiq4uVnl/G4fvofT1l9IWBeF8NJY\npcyHKUz9Pv/zbKGMviSZsprlFSnTc9xIhK8vqS+9irFiJcC6DR05WqYDotG4gl5P6vadOP2xA/Uf\nO1CfND1Yus5dSFi1rnDlDeyDcHIiadES09J3O1MUo7Fq1yEmL16dp8yC8YMY3KF5sXSzBvaOBpoZ\nU19KSSFhTSSGBkFWK9vedVOdOoGmT08yGgWb3gNX67o2FrZ+UadjmLPtRL7xdQL9PHmja0jeETKF\nwHXhJ7gt/BRJpyVtzHjOPz2C0Flf5ll2YRo6ssF3QDQaV7h3D3W1Kghvb3QdOqHr1AV9x84YLaym\nzRedDik1BeHtGG5gRTEaL3y1KmtlcG4MCg9j4YTBxdLNGtjbKIIppr73wN4obt0kYdU6MkKbWaVc\nR6ibav8+vAf1QdcunMTvfgS12mplF6V+BqOx0Ilu8kKKj8P1i4W4LfkCnZCYXq0RH9UIyVW+MA0d\n2eBbgSJ3uZKTcfrrT3QdO4Ozc9bmzIcued9hDPXqF8gtzV7j2wajkfUno4n8O5pTOR724Co+9G7k\nT9/G2R/2orxUzSbPIeZe3rFHqvv5cGTB9CLUwro4glGEBzH1n34K5ZXL3D98CuFReO+SnDhK3Zx2\nbMNr2GC0Eb1J+uIbq7luOkr9AKQ7dzg09ln230lgdq3cP9iFaegU1+A/8pO2hYpVIwTKv0/h9Md2\n01DNwf1Iej3xG7agb9POrAxDUEPr6/AwQuAUtQFdr95QwNbHw+TVnb2RmJqV03P+H38zvVs+3dlC\nMPDWReqnxjO7ZlOHnuAqLtKdO0gpyRhr1irS8cLHl4S1G1EdP2YVY+9I6B7rRtKX3+A2fx5SXBzC\nz8/eKlkdUaEC4wOaE+ORd0OnJBdOlimDX5RWckFXsvp38MVz4rO4rF2NcHVF16YdKbPeQdepC4ba\ndYqld2F0eBjViWN4jRuJtv8gkj77wjTpW0AKM2F1KTaJMSv3FCu1W5ugQFbvPowkBLMuH+Gyi6eZ\nsS8t3kYFxf39d1GdOE789t1FLkN4eKJvF25FrYqH20fvm+anXp9R7LK0vfuhfSLCqkM6MnlTZhZe\nZbaSJy9ezerdh4m5F0fMvThW7z7M5MWrCZsyl+i7982OyxmHxj1Dj58uzaJM2ogxxK+J5N65qySu\n/Jm0Z5/HUKdusVupOXXod/sS3nptnjIAGU2akvT5Ypx//gnP58eaPH0KQGG9EzKZvfU4n/95ttDH\nwX9rBR6PjSEoJZ4PLYxpXr51j1W7Dlm8T6UR4eaW50rb0oiUlobbV4uQ4q0UGriMG/ucjZictsWS\njC0pMy38orSSFdFXqbvhJz6/c4N6qQnUS4mnujaF5ZVqM7xRZ7OyM1q2sr7iZNfdyWhg1d87+Kli\nIEMt6JAT7YDBCGdnvCaMQdLqSFyyLNt8Qk6iTscU2f8YTEY/qJovfZsEFOq4zIf65asnOezpxy4f\n8xWYB89f4eD5K4DjuGgWB5PBz3ulbVG5dfQ4O5P0JT7nkzZ2PK5fLsTl++9Im/yiTc5RlmjbIDBr\nWNZHn86NP39geMNOrKpUO5tMSVFmDL6lFrB7hp66qQm4GDPY512Jv85ezDYbrvr3HG8e+50Lrl78\n4+7Nikq1+cfdm2Oe9htP1CmUvBcQyszLR9nk55/twcj1mCf7kqh2wmvcCDzemk7ye/MtyhmMRuZs\nK0fWJTgAACAASURBVH4O3TejDvNk48LFEfEv78uZZyNoMHAJ07sOBpF3r8jSEFapw9U2LfxbR45R\np2dn1tcIYXWtZlk9zILmSLhyO5atB04X6WNhrFQZbb8BuH7zFWkTJoKTk3Ur92CezBDc2Lrl2omH\nW+8970WjFoI/vSvlKmNryozBz9kC/v1IFJ3ibgJwxNOPsJb9zGR04Z14fubn/PhX3i1eW9+QzPHt\nTGbVakZgWiLLzuziqosH+7wr5auDrkdPEn5ci6FuvVxlrJXP8987iaw5epkedQrnYup//BAG/xpc\nbtMB/joGQPu4m3zw7wEea9aTVOV/3fucH+fSiK1a+DuT9Kys2ZS5Fw+hydDxYt3WiBzDirl9MK/c\njqXe6Jlm2wuTUCd1wiR8V/+I84af0Q58upi1yY7zqhV4TptM4vJV6B7rZtWy7YF/eV8Of/YGe89c\npMWsVzjhWwlFteoMstPCyTIzhp+T+inxbChfg9Zhvena9AnLQmo1rRrlbiAzsXWXy6x8SWJMg3AO\ne/oReWIbtVITC6SDPrxjnsGqrJnPc83Ry4U+JnXqy8Tt+JM9565kbbvm7E5Y0l0+Ob8PF8N/ceHL\nQshnY8VKGGrWsnp44L/+ucR7NUOZVK8NU2L+5pszu1DkiNWeW46E3SfP51t+ftfe0LARuk6PoTp7\npuBKFxBt/0HoOj2G1+hhqPfvtXr59sC/vC+DWzSixZVz1B4/jiMLprNwwmAGd2he4sOWZcbg52wB\n33Jy47aTK/u9KxKndrEok9u2osgUB0vla5Uq+oR0J8rPn/sPQikUl5z5PIvD8ZiiZQbKuVL4spsX\n0+q0YuSN85zav5bO969bQz2HQNu7H3F/HrR6eOBMg7yoeiOGB3VkxM1/mXvhkEUZKe4+iuirkJwM\nQrD71L/5ll+QhDoJP/xEyqxCJkcpCGo1id98jz60GV7PDER1sujzTY6E0587kVJT0D7e0656lJkh\nnYcnRwC2lavGXScXM5mcPNzlsldQr7x0SHlhBNuLo4MQSCnJCA/PfHNwOmfoGfvPHtbXbMIN97xX\n9d5MLPpQRc4hrAX+wfzmW40lZ3ez4+hm3qrZlH/CJxS5/EeJ5VXqEqd2prLW8v1wWf0jHjPfAEA4\nOfGB0olpSieWVqnPQv9GFo8pUO/Klt41rq4kLl+Fpl8EmsH9iN+4tdiuz/ZGSktDF94JQ/2iuTVb\nizwNvl6vZ/To0Vy9ehWtVsuMGTNo0KABI0eORKFQ0KhRIxYtWoQkSXz99dcsWbIElUrFjBkz6Nmz\nZL9kOVvAr9cxTyqRWyvZv7wv/h187TpmbCsd3Oa9g9Nv20j4KY/8okIw6OJh5h1cT7SHD18F2dbv\nO+fHGeCshw/hYU/y7PWznHb3YaAc8jlXcn4wN5WvYVEGQBvRh4y69VDExqKIu89PKzeiSojnprN1\ngqHZCuHpRcKqdXj83zSMNgiyVtJoe/dD27ufvdXI2+CvWLGC8uXLs3z5cuLi4ggJCSE0NJS5c+cS\nHh7Oc889R2RkJK1atWLhwoUcOXKEtLQ02rVrR9euXXGy9gx+HjhCS90R0T7ZD9fl3+Hd9wkadZ7I\nCbLfk1a3L/LxvjW0vnOZKP9gXmnVH4Mi/yGIyl5FNxi5fXiFJLG4milQ2KdlbBGWNbH0wbQkA2Cs\nWg3jQ3HbDyvLs3zHgTyPdZQFcKJcOZKWfGdvNcoUeRr8AQMG0L9/fwCMRiNqtZqjR48SHm5qAfbo\n0YNt27ahVCpp27YtarUatVpN7dq1OXnyJGFhYbavwUM4Qkvd5uh0qE4cK3BaPEPDRsRv+AXNUxFs\nWjuPVl1f4LqHabjmxZO/8fH+tZzwrUaXJ6ayo1rBu5tNqpcrkJzz2tWoD+43uYo+GMsu0sc5Pd00\njOBA6fLsRXHmncKD6+Rr8OWEOmWXPA2++4MkBUlJSQwYMIB3332Xl19+OWu/p6cnCQkJJCYmotFo\nzLbLWB/XLxfiPn8e8WujCrwQzFC3HvGRv6CJ6MHuqPl06vUS0Z7l2OTfmEQnV5bVbYOxkLF4BjSt\nmb+Q0YjbZx9h8K9hZqgL+3F2f3cW6kMHSPpoIYZGwYXS1W7o9SgvXsBYpYpVY78Xpzcb3rguAI2S\n71NJm8oO36pmLp2FbeF7vPIixgoVSH3l/4pQG5mSJN9J25iYGPr168fEiRN5+umnefXVV7P2JSYm\n4u3tjZeXF0lJ//l3JyUl4eOT96SfSqXMimxX1lCpTMbNJvV79WXEH7/hPWoI+t17IPD/2Tvr8KbO\nL45/bpKmbeoChRaKFae4SxlSYDAchssGQzacKbb92MY2psA2GIwJMtyH22C4u2txq0sauff3R2lX\nSdMkTdJS8nmePYPkve99L0nOPfe853yPiT/OGlUQ/93D7dd6kqhICetc9Q7gqneA0cNCYh4x/fBq\nBr4ykFhlyvWUK+xFr7ohSKJxoVVh82YUly8hzfox1/8WQs/XUezZjU94GOK48egnTspWS10viiw/\nfpMVJ25w+m5k2gZzUU8V1Yr50r1maV6vVSpbuVurfX4PY1CG1UO7YhVShw65mysToV5BhIYEMbSD\nefstfn7uXP/zM3T9++N9+Rh1KwwCQSAstGzKf1XLUTLAtKe3VORuLsh+nYPTRx/YvpOVKCKb+wvi\nm4MMFn3Z9LeXD0i9PksxKo/86NEjXnnlFX7++WeaNWsGQIcOHRg/fjxNmzZl2LBhtGjRgrCwMMLD\nwzl69ChqtZr69etz+vRpozF8UZTQ6aybn5wBtRphy2ak2nWgmH17T6Z+KDa7vqdPcWrSGK0gsOyz\nH9h+61Faul2WH64kIWzdihQSAiEhrDl1i57zd5l8qqrP7rBnw7ec8Q2iddvRJDspWTa4JV1rlsrx\n+hStwyEuDt3+g9ZRxUxORvb1dORffgHFg9H99DNS8+YZhqw5dYtJ649x7Ums0alCCnnyWYfaBiUi\nrPb5xcWh9PdF9+cCxJ7WLVCyFIVCDgkJCEWLII4dh35y1iIss7lxA6fKFdF/9z3i8LdzP58RhNOn\nUDRqiNihI/qFi7I8Odr8t2cmssWL4OlTxNFjrDKfQiFHJrP8t2TU4I8ePZoVK1ZQvvx/xUkzZsxg\n1KhRaDQaKlWqxLx58xAEgV9//ZW5c+ciiiITJ06kc+fORk9saz18ITYG/5DixM6ZT3KX7jY7jyHs\nocn96MhRAju15bSHL61rtEVrYKP13DtdKDtjOsp/dpEw9l0SP0r5cZsrntbo4TW2bfyBXUEVOP71\nHD7qVBe9KPLHv5ez1dEfpIyn+4iexM79neROXa1yzanIr1zGY9xI9MWKEzdnftrrlojCGVIAtdrn\np9dTqKgPcd/ORN1vYO7mshJeXq7I/lqM4o2BPDt8ymLp5sx4DuqP4swpIg+dtPk+i3LDOjzfGoC6\ndz/iv52ZwZnIT3r4AN5tmiEGFCX2z7+sMp9N9fBnzJjBjBkzsrz+zz//ZHlt8ODBDB482OKFWBvJ\nwxPJxQXZ40d5vRSbsDsJVlUNZ+SdczhJIlr++5EVTk5k6o1jVOzyK1JwMDHzF6J57b+QQqqBM9U4\n7i8SQrdWw9iw7WdaLvuBNcGfMenvEwa96FQd/dLn/6GOTwC7S9fktVxea2b05coTvX4LJP33o86N\nAihgseyzUeRyJGdnhCTbCKhZimzRIrT1GljN2AMkDh+BT9uWKDdvzPBdswWa9h2J/24WHmPeQfL0\nSikAy4d9FWQP7uN04jixM423OLQnBabwKguCgFg4ANnjx3m9Epuw/+J19vgGssc3o56Ni17HmcOr\ncBb1LG7VhTa/zjaonjmiSUVK+LozbetJ3t74O0vL1OFoYcMbsWX8PejWaxgJnWrgPmwQfyYGcC3Y\n+Mbp7MqvML9CIzTLDzElRm19gyqTpcWLraEAWsLX3WoNXtJjS8VMi7h7F2HXTtTfZHXkcoOudl00\nYc2Q37WefIcx1L37IcTE4P7xBPSly6Du/4ZdzmsOyi2bkGQyNK3a5PVS0ii4Bh8QCxUusB5+dtWQ\narmCwRXDOOgVgMqnKG2MSCW3r1ycdsFesPYrhm2eQa8u77LRK8XoGern+W1kPKu7Tuacb5BJa9Q8\nF0OzpRedWQE09Nldmt+/xKzKzc3KPJq2/TRtKwaZ3LfUVHSVQxE9PK06Z67w9kb/82ySW2ajL5UL\nYlastaunnTR8BJKHB8nt2tvtnObgvGUj2gaNkHzN2wS3JQXb4BcOKLAG3xiplZemlEbJPDwRNm1B\n0bs7a9d9R8yiZQY7LKV50SYa+8zYyovOrADa4t4lvj+0gt7XjvJWWF/O+Jl2vutP41h7NoKu1Upa\ndX0xq/+26ny5xt0d8c1BSLaIcedBWEXdd4Ddz2kKQlwsTvv2kjBlal4vJQMFRjzNEJqwV9DWrpvX\ny7AJ1hR9k9w9iFmyCm2t2nj17obT7p0Z3reWjv607afRi2LOA80gswLoD1Vb0qjDe7hrkzm2ehrT\njqzBRacxba6z9glH2BK9KLLy1C36LdpL9enrKDplKUWnLKX69HX0W7SXJUevW/0zcJAVyd2DqC27\nUXd5Pa+XkoECbfDVg4aQ+P6EvF6GTTClGtKsikk3N2IWLUfbsDFu06dBuuStnHT0ndLJGhsj1Yu2\nJoYUQA8UCaFG14l8VrMt489s59/1XyNIORu5M1ZUE80LNpy/Q6MZm3h75UG2XrrH/dhE9KKEXpTS\nGtIPXLCHqp+tZsP5O3m93IKNIKAPrYpUqFBeryQDBdrgF2RsIuvs6krMn0uI+WtFhsdzYzr6pWOf\ncGn5x7xy/zL9rxxk5bY5KMTsc6Ct7UVnpwCqkTsxtVZ7qnWdzGc12yEJOX/Vc1ITzc/8+O9FBi3Z\nZ1KDm2tPYhm0ZJ/F/YlNJi+eJLRa5CPeQXHqhP3P/QJQoGP4BRmbicU5OyNl2ug1pqN/T+XNDU9/\n1m/9iWfO7pzzDURnRHzN3l70JZ+iXDLQPze/E/Ek0uTP1pSU1CKJMUQ6q9I20sGGm+mShGe/Hmjr\n1CNp9Hjrzp0TyckIJ0/gtWol0eu2oC9fwb7nz+cYLbyyJbYuvMpL8lvxR24pOmUpeiMyCu4aNTs2\nfk+9J7d45bVx7AnMvouYXCbwYGpPq62t+vR13M+FNn96Aj1VnHq/o1U/P9nDBwjx8WbpuUc8iaT2\n6GlGx6S2Idxw/g6DluzLcc6V2+bgnxzPK+3fzfLe/F6Nrb6Z7j52BMrtW4k8fs5gWrCt8PJyhWfP\nkDV7BSE2lugNWxGDs8pHv6jktvDKEdJxkCMyUaT5vewf/+OVLrRpO4qOrYazp2g5O64MQgONazaZ\nQ1UrzpWK6tvpeA42L5PElAYkBy5cN3kz3UedQPuIM6wvUc3g+7bYTE8aNgL540c4r15h1XlNws8v\npf+DkxPe3TogPLJjpp4oIr+ec1exvKJgG3xJwnnFUuQXzuf1Sl5ohtw9xc6NPzDyXPYaPNHObqwv\nWT3H1LwAd+uKWnWsEmy9uUKtN1cqkkoFZlbamtJicP/F6yY3pe95/ShySWRxiOGMNVtspuvLVyC5\nZStUs2dlSACwF2LRQKJXrIPERNw//8Ru51WcPolvg1r5th9vwY7hCwLuE94nccRokipVzuvVvLBc\na9GO7yOuMvPAMpz1Wr6p1triuaztRXeuGsw3u8+ZZPhKxD1lyc5feSusH+cz1ROU8fegkxkGXy+K\nrDkTka2WUMcqwXSuGmxRpW2OHr4kcejcVaLdA42Pe07/q4fYWqwyj1TZSzSvs0ENQtLwkXh3bY/T\n7h1om4dbdW5TEEuVJmbtJsQiRex2TuXmjYhe3mhr5c+eHAXb4ANi4YJbbWsvOoaW4O0G3VErnPj6\n8Gpc9Do+q2lZC0tre9FymYyJraqZFMd+oPIiJPYJb13ax5iGPdJeFwSYEF7N5CrbDefv8Pm20wZv\nMqlaQlsv3eOb3edYGqellpWlFUonxXF+1e/c2LWU8x6FuORdhMveAZzzCeK0f8ZYfLnoh9R/fJOe\nzY3rXNliM13bOAzNK82RPbOs4b01sHcvXOctG9GEt7Ztz99cULBDOlCg9XTsReeqwZT292RCnU58\nXOs1Pj22niEX9po9j7letKm0r1ycKa2r5zhOI3fij3IN6H/lUIZirMmtqpu8aWlO+uONZ3H8cf4+\nUkKCWWGNnNJp4xROLG/ZmX2FSlJYHcdbl/axaPfvzNm3OMtYZ72OlaVqsq6k4fh9KjZJSRUEYpav\nJbm79Tbp8zPyG9dQXLpI8qv27edtDi+Hh//wYV4v44UmvRc9tVZ77rj5srpUDbPmMNeLNhdTFUDn\nVWjCe2e20/3GcRaVb8DkVlnlkbPDEkXOByovzvgEsv6fc7zdzLROXZl71nrqNHR6fIutfsV45Kzi\nidKVmMEDGbvzelr2lFdyIr7JCVnmOutXjO7hQ81ac4FHp0uRcLayFIRy8yYkZ2e0zVpYdV5r8pJ4\n+I6QTm5J70X/XqERMc7mNTE3x4u2lBFNKjK/V2NK+3lkO+aqdwC7Assz6toBfu3Z2GRjb6ki55pS\nNanZdRKf7DxncnVrZg+/sCaJPy/8Q+WEqAxj0m+AxziruOlpeVWntTfT8y2ShOdbA3GbMsHqm8mi\nry9J/d9Acs/++5fXFHgPX9uwCSjtlwdckDFXRx9SnChzvOjc0r5ycdpWDGLt2QjWnY3gTKYN1aqB\nPuj936TGgh8pWcwDU37y1tQSMkWRM3NR3fXjKf/ebSqUoFPnrmmFV6GBPlarQbBFSmq+RBDQNmyE\n+8QPkLy9SRz/gdWmTu7Vl2SrzWYbHIVXNqCgFV5lZtfNR1naCMqfyyno01XZlvH3YEJ4NZt79maj\n06XcibLpzJT581t56hZvrzxolVPP7t7A7GyY7Lq35fW6zEaSQK8Hhe38TFN/e6qvv8Dt6y+ImzYd\n9eBhNluPtXEUXjmwO52rl+TMpC7M7t6ANhWCCPRU8fveBSze/RvBbkraVAhidvcG7BvVNv8Ze0gx\nOGa04TOmJWQulmgJSaqURi+Z0zs7Vw02Gr4yFVttpmdAq8U7vCmu83+x7XlMJPHdD0kcMhyPCe/j\nvHxJXi/HbhT4kI4D2yCXyeharWSaV6isIOI5bBCdLq0idtzvdi2ntwRjefQ1gv3oXrM0rUOKIJfJ\njGoJmYtF6Y8KBZJSiZCYcVPWnJTU7LD1ZnoaTk7oy5TBde5skgYNtamXbxKCQMLUL5DFxuKybElK\nJlE+bJNobRwG34FV0HToTKzSGc/B/fF8ow+xvy0CF5e8XpZBcsyjP5fIxnN3KO3nwcRW1UxKWex2\n4zgySWR5mYwFNwpRT+XI+9z28CXa2c3i9Ed1jz7oy4RkeT11M93SFo/22ExPJWn4SFxavYLzxvUk\nd+xil3MaRSYj7rtZoNW+FMYeCnAM3xy1QWtT0GP4xq7Padd2vAb2QVu3ATELloDKvGweW2NJaqUg\n5JzQMezCHmbv+4vyr/+PK97/VXb6J8XxZOG7dG05lNWla1pdPC4Vc6/L3pvpqXh1aouQlEj0lt02\nMbJ58dtTffkZYqHCqAcNsfm5chvDL5Aefma1wd4PrnLf2Y1lT6PS8ptT1QYdWBdt83BiFi1HNet7\nBFFvUhaMvTBkFN+6uBfv5CS+rp69XIQpLtGCsvV59/Q2ft27kKbtx6fp7yc4pYS2VM8LvWyV/pja\nlD67J5f0lC3syYctqubJ/krS8JF49euB0+GDaOs3tPv5rY5Oh+tvc1EPGGTxFKbKdFgj7FYgN20z\na5G8e/sMPR9dMzrGgfXQhr1CzPK1+SofObs8+rIxj/no1BaT2iD6qBP437H1BMVnjcMnOjnzVlg/\nmjy8xtvn96S9nvRcf95Nl5KwZ8v0x/aVi7N/dNsMm+lymYBcJhDoqaJNhSD+HNCU0xO75Nlmuia8\nNcmt2kBi1iKxfENyMrIH900a6nToALLoaJLbWNYU3pQuZW+vPEijGZus0qWsQHr4mdUGHzqrKJKc\nlGVMz6b5U+CoQJCPYqLG8uhTK2+73TjBonL1DY7xUScw5txORp/diVLUc8qvGGvcsxru3UEVmFuh\nMV8eWcPfJUK57eGfsjmoUOL2/IZiC0XO9GTeTM9Masgjz5DJiF203OrTpoZwj167xd6zVxFFyeIQ\nrvuE91Hu3Z2ipV/EePMc5ZaN6AOKoKtRy+w1mxOGu/EsjkFL9vEoMZmP2ppX5Z6eAmnwM3vv1109\n6P/gKm2eRrDFP9jgGAcFF2MywqmVt0Mv7s1i8L2TExh79j9DP7tSGNOrtTaqOvle/W688uAKNZ9G\npBh8IEHhjEqnsU/640tIdg1jlu09ZlEIN3HUWJTbt+D1eiei125C8vUzPFCScN68EU3rtmBmuMWS\nvSSACeuOopDLeK+1cW2k7CiQBj8zk8vUoUxSHBtPbWFCSF2+Kpmz0JYDK6PV4jZ1Cld7DWDvkzi7\nbqbnlEc/t0ITlu76lUqR97ng+5/ksL86nrFndzCvQuMcDX0qsUpXKnf/JEObx+OFgol0cctV+qPT\noQMIsTFoWr1q0fEFGVMbxgQ3Ne27JZYoSczytXh3bINX727ErFxvMDwpv3IZ+Z0IktuaJ5ZmqUxH\nKu+vPuww+OlpWCmj+FS0kzOvVW/NxzdOEKlwThvjwH7IHtxHsXoFLgsX8VXNdtxzcU97z1JPzFRy\nyqNfU6o6T1zc6XD7dAaDf80rgMA+04lXmpdemrmnb9tXRzGlde7SH13+Woj86mWHwTeAqQ1jzAnh\n6itUJGbpary6tMdzQG9iFq/IkmasL1+ByEMn0AeZ/rlaS6bDUgrkpm2jilmNuSjI+LhMbeYVq5jt\nGAe2QwwuwdLJX6PS69h7fAMlkgyHWGwRassp910jd6Ja18l8Wb1NlvcyG3tztyYEAaa0zn36oyWN\nVF4INJqU/3JB5u9Ms8h7HDyylq+uHuKVyPs4iXqLvle6GrWIXbgUycMTsmkBqS8dYlaRoaldymxF\ngTT4pnjveenhRzyJZOmeo4ycs5Raoz6n1qjPGTlnKUv3HCXiSWSercvWbIpOJqx2ewQJ9h5bT5nE\nmCxjTPHWbMEDN2+TrLlMEHJU5EyljL+HWYqcxpBUbggJBczgx8fjW686Lsv+st6cksS3Vw4RlJzA\nwPtX2H3ib0bdOWfxdNrGYcT+sdhq9STWlOmwhAIZ0smsNphTrFh+9gz6ipXsUu5t7Q2mF4kDF65z\nx9WTsNrt2XX8b6ZeP0af0BZZxlibAHdXq6lKBri7mqTI2TE0mE6hwcgFAed1q9E0CkPy97f4vCke\nfrxVriHf4O6OLrQqrnN+RN2nv9kbn6mkD+F2eHKbGvHPaFbzNfb4FKVW7BPuubgRZsDBk9+4hr5Y\nMCiVuboMc7CmTIclFEiDDylGP7ipb45xOyEmGu/O7dBVq07sL7/n6kdpCtbeYHoRueviTpPaHYiX\n26cNnC1khHNKf0xFiIrE/b0xaJq1IO6X3y0+r6RyK5AhnaThI/Hu+CrKHVst3p9I3zDmiFdhRpdr\nwD8+RUEQOOZVOG1MBiQJr+6dECIj0Ya9gqZFOJoW4YhBxQyew1qV+zbpLGYGBdbgm4rk5U3s74vw\nHDIQn1ZNif1tIbrqNbOMs1Y1nC02mF4U0ntij7JpoGKLUFvHKsFsvXTPOnOZmVYp+fiSNHwkbl98\nSnLn7mgsLNDRVQlF3fX1lLLffFTjkFu09RuirVET19k/Wmzw039nHjqrmBmctbOYoe9V7K9/oty5\nHeXO7bi/NwZBktBVrEzU1t0ZNmgzP5UHJCcy4s55Jj+pbdWncledhkknNrK/SAibDFyDNXjpDT6A\ntklTorbvxfPNvni3b03c9O9J7tU37X1zmlZPbFWNvg3LZXuuzB5+IU0S7jotN1We2Y4pKGRu3Zfd\nGGvTuWow3+w+l+vNMkvz6GWPUlpsur83hqgGDZG8vE0+9j/P8iEHtAEweprdNKHsgiCQNHwknkPe\nQHH6JLpq5hcVpQ/hmlx4JQjoatRCV6MWie9+iBD5DOU/u5BfuZQlGyfz73HNmW00iHmMWibn89I1\n08aY8lSeXXjx1Yiz/LR/CYEJMdxXmf79MBeHwX+OWKw40eu34v7BODzeH4u2SVPEYsUtroYb3zLn\nO/QrkffZcnIToiDQp0pz1hQuldvLyJ9IEq4/zqBZ/cY5DrWFh5/XMsKSyg1JJkOIj8ftk0nEf/+j\nSce9LPs9ya91JLl9pxTVSgtJDeEO7RAGmC+eJvn6ZWguk579F6/TNPI+P17ezyb/4mif6yT978Zx\nLrj7sKZwKZOfyjOHF4Pio/jh4HK63TzBzsDytHl1VAbxPWtTILN0LMbFhfgffiLqnwNmG/v0TFh3\nlG93nDX4XnqDdsSrEJPL1GajfzArz2xnVMTZLGNeeJKT8XhnCO6fTqHEmeMcmzGBmUN70COsNsX9\nfSju70OPsNrMHNrDpsYrfU9eS8iNjLCkUiH5+pIwZSpORw9DvGmbr6bu97zwKBTEzl+ArnbdvF6J\nQQ5cuE6MQslJDz8G3r9CWPRDJpapzerCJVlydictnt01+XPoWCXdE6IksXHLjzR5eJU+zd6kZbux\nNjX24PDwsyII6MuUzXU13IR1RwlQOdO+cnGE+DgkpTMolRnCGolyJ74uWR1Bkvjm6iFmXDlICXU8\nTkNet9bV5CnC06d4DeyN4tQJYn+eR3K3HgSDSZvptiCvevKmbLgmoR7wJure/UzO236Z93vMQXEo\npc2jrn4Dm53jlKc//as0R5AkKiZEcVXlhQCsP7WVtWe20SUgwKR5MoQXBYH+zQYS4e5L6dinLN41\nn7cb9yYmm/0ta+Aw+AawVjXcwuXb6KG/guuSxcR/9S3J3XoY9N4lQWB8uQZEuLjjpdPQoXLWRhcv\nGvIrl/Hq0x0hPo7oVX+jq2dYmMzemCMjbK2evJJKBUmJKXcPM4p0DHmNMklEFGRGxxRksmTLbjxi\nAAAAIABJREFUSBJ79ixB6ePNw5UbCPUKsvo50ycbSILABff/nkK7VAvnvVunKVy3tsFjDSV7pG9B\ncsavODJRZM6+xbjqtGly2sbIzZ69w+AbwFA1XK9rR2gXcZa3wvqRpDCStytJhD24yphzO+l46zRa\nd3fUAwehbdAIMF4jUKZij4KxEQc4HTmE5OJC9Ip1iCXz195ETnn0NUv4071mKVqVKWIVDXKxaCC6\n6jVSKkpz0fqxZFIsG09tYXDFMA7a+NE/P2JoT6PD41uUeniH5oFV2T16Gpd/m0rJgGzEzizEWLJB\notyJ/5WpzczQClneS0v2eBpLl5sniQyugt6A7Rh6cS91ntymSft3s8hyGOKrzvXMv4jnOAy+AQxV\nw4kIdL55kiqR9+ncahg3PQsZPLbV3Qts3TyTS14BvNO4Fw/adWHeoFYZxphaI/Aio+47AHW3Hvm2\nzaGxPHprd03StH4VTWvzUw4za0I9VroSqXBm06ktNKv5Gqc8/QvWfs9zhNgYJFcVOGWs08jyNCNJ\nfHLjOHu9i7DbJ0UDae+ZK5QMt25ox5LK/dT9v5CYR2zbt4Twexfp2+wNFpfN+KQbkBjDF0fW8Fu5\nhuwrWtboOQQBPu9Qx2LhNHBs2hrEUDXcspA6NOj0AR5aNcdXT6NNhOFy7R1BFWnVdjSVXv+EOZWa\ncvSZFYyGTpf7OfKCfGrs8wtCfBzKzRuzfT9zimqi3Il2NV7luqsn205uokJCVIHThBIeP8a3eiWc\n163O8l7mPY3UqtpPStdKi3PsPXvV6mtKfSo3Ndngx38v8tXGo3x8bAPnVkylbMxj2rd+O4uxB/j2\n0Ep0Mjnv1+9qdA2pMh2mZP8Zw+HhGyC7argzfsWp3XkCi3fPT9ld7/AuB4pkjLeLMhnbi1XKcS5T\nkd2JwKtbB+K/+Bpt8/BczWUzClgxkL1wWfAHbp9OIXrLLoP55waLhRRKWtdoy57jG9hxYiORnqPs\nsVS7IRUujK5GLVxn/0hy19czfK8ye/ij7pzL4N2DbQw+mP5UvuH8Hf5cuQP1kokAfFmtNZ/WbEei\ngdi8IIk8UHkxvn43nqVTj5UJIAhCVpkOR4tD+xPl4sZrrUfwac22lIi3vdCZ6OOLvnQZvPq8jsvi\nBTY/n7nI7t3Fu0Mb5OctF6h6WUkaPBR9uQp4jH7HoGJkdp5ly5aNOfzdHPwL+1Py5JE8WLltSXp7\nBE5nT+O0/1+j4zpVa8XASq/kG2cjNdnDU6MG4ImLO/+r9ZpBYw8gCTLeq9+NP8tn7O1bys+Du5+8\nzqn3O7Kgbxhdq5W0irEHh4dvkJzEtkSZjE9qdzB5rlzh7k7swmW4vz8Wj7EjkN27S+J7H+WLL7ni\n5HE8+/XMEmt1YCJKJXEzfsK7TXNUs74ncfwHWYYY8yzjwhvnq77B1kLTPBxd+Qq4/jwTbeOwtNcz\n72nEK5TEZ9oEDQs1Hge3JWnJHn7FaPraeLZsnsmyHfPo2mqYSZuxqVx/GsfasxE56jRZgsPDN0Co\nFRtNW6VptUJB/LczSfhwEm7ffIn72BEpYZQ8RFi9Cu9ObRGDgojesgt95Sp5up58jVaL4sQxhMhn\nWd7SVa9J0jujUX03HfnFC2ZNWxCNPZAmt+C8YxvyK5fTXjZlv8LeBl949t9nmj7ZY29gObqFD+XV\nO+f47Z8/ESTDevrZse6sbWSUHQbfABmq4XI7l7V6mAoCiePeJ3bm7BQp5zz08GXffYdTr55oWrYm\nes0mxICXL0XQHIT4OHzaNEf57x6D7ye8+yH6EiVRbtts55XlX9RdX0fdo3eG77kp2TJhVbPXsbIm\nQnwcbpM/wq9WZeQ3rgFZkz02BYfSv9kb9Ll2hDcvHzBr/jM2klF2hHQMkNdiW8ZI7tnHqvNZRNEi\n6D/4kNixH1qsYf4yIancUv6QlM0Gvqsr0Vt3p3RWyiWyiNuIhQNe/AwpZ2fiZs3J8JIpfS6snYOf\nBUlCuXED7hPfRxYVScL4D1I09TGcoLE0pC6PXD3Z+zzlskLUA4LjIzntV8xoj2RbySg7DL4B8lps\nK78j9uqd8gcr5akXeJRKJLkcISEh2yHWMPZoNHh3eQ1dpSrEzl9QIPdWsuxpqNXIHtxHLFXa5ueW\n3buL+/tjcd6+leQW4cR/8Y1JRYW7g/4rynrs6sGhtV+yoFx9RjXqZcvlGqTgWSMrkVuxrc871Ml1\nSb5ZFMDmGAUGQUBytUNPWqWS+M+no9yxFY+Rw7Ltw1qQcJ/wHl4De9vnZHo98uvXiJm/kNi/VmYx\n9qYkaES6uPN1tVYMvfgvJWOfZjtOkqDfor2sPHULvRU/R5MM/uHDh2nWrBkAJ0+epFixYjRr1oxm\nzZqxYsUKAObNm0edOnVo0KABGzdmX0zyIjGiSUWzjb4gwLSOdXJdIGEOsps38K1bDec1K60+txBV\ncHvs2hNJpUJIsv1NWdP6VeJ+movzmpW4vz8uzzf3bY22bn0UFy8Y3BC3NmJwCaIOHEfTvqPBPTRT\nkz1+CG1BtFLF/45vyP5cksTWS/d4e+VBGs3YxIbzdyxed3pyDOlMnz6dRYsW4e6eUhhw/Phxxo0b\nx7hx49LGPHz4kFmzZnH8+HGSkpJo3Lgx4eHhKO3YK9JWWCK2ZawBii0QA4PQNg7Dc+ibxN+7R9I7\no6yyqeuy6E/cpkwg+u9t6CtVtsJKX150teog+huW4zCE4uxpRF+/bFvuGSO5czeExEQ8xo5AcnMj\n4X+fmz1HfkN2/x5ikaJZ9oy09VJkFJyOHLaom5jZneyMhGhN7azmJOoprI6j/9VDfF2tFed8jQu+\npfbZmNK6OhNfy9qNzxxy9PBDQkJYvXp1msLb8ePH2bhxI02bNmXw4MHEx8dz5MgRGjVqhJOTE56e\nnoSEhHDmzJlcLSw/0b5ycfaPbsvs7g1oUyGIQE8VcpmAXCYQ6KmiTYUgZndvwL5Rbe0bxknF2Zm4\nn+eROGoc7lMn4z7hPdDrLZ9Pr8ftk0l4jBtJcueu6Mva9wZWEIn98y/Ub75l2mCtFs8BvfEYP8pi\nD13dpz/xn36BGGR99Uh7I7txHd/aoSi3Zs1iEkuWQl+kKE4H95s974bzd2g0YxNvrzzI1kv3uB+b\niKjX0+/iPqavncXWi3fN8rA7Vw2mtF/OqbIJCmd2BpYHYPa/i01e79Stp7Lts2EqgiTl/I26desW\nvXr14uDBg/zxxx9Uq1aNGjVqMG3aNKKioqhevTpnz57lyy+/BGDAgAH079+fFi1aZDunKErodLkw\nSvkYhSKlyCIvrk82ZzbysWOQOnVG99cS8z39hAQUA/oj/L0B/RdfIY4Zk2WOvLw+e5Afrk/YsAGn\nbl3Q/TofsV9/q82bH67NEhRhjUGhQLfrnyzvyfv2Qbh1E92+A0avTy+KLD9+kxUnbrDv2kNi1Bk7\nbFWKvM/sfYsJe3iNv8rUYVDT/qjTFXaZEqpdc+oWPefvyvF6XHUazq/4BJ/kRJq2H88ZP9MdxZVD\nW9K1pmWb1GZv2nbu3JkaNWqk/fnkyZN4enoSF/dfuCMuLg4fH+sVLzkwHXHYcHTLViC2amW+sZck\nFO3bIezaiW7FKsSxY/NFRe/LiNS+PfrXeyB/7114+DCvl5Pn6MeOQ7Z/P8LRrFISUps2UKy40U3q\nNaduUfWz1QxcsIeN5+5kMPYqbTJfHF7NqVWfUiQplpZtx9CnxeAMxh6Md7JLpXP1kkzrmLMKbpJC\nSY0uk7jp4c+2TTMoG/0ox2PS1rH2qMljM2O2h9+gQQNmzpxJnTp1mDVrFvfu3WPs2LGEh4dz9OhR\n1Go19evX5/Tp00Zj+BqNzmrys/kNa8vr2hPl9i2IRYqiC81egvVFvj5TyC/XJzx9im+TOmjrNST2\n90VWuflGqRPZe+YKO05cMpjHnm97Mej1+NavgbZ6TeLm/ZHtMEOfXU6tSsec2cGXR9bwRfU2fFm9\nDckK4+ms83s1zjF0a2p71EJJsfy7/hvWl6jK+/W75Tg+FemXISaPTY/JBr93794cOHCA06dP8847\n7+Dk5ETRokWZO3cu7u7u/Prrr8ydOxdRFJk4cSKdO3c2OqfD4L+4OK7PfjivWYn7u2NS+iwXz10R\nX8STSAYMepdgdTyb/Q3PlZ+borvM/wX3iR8QefgUYomSBsdk/uxMMbxKvZbg+EiueZnWprCMvwf7\nRrXNscYmrQFKDskefup4Ip1VSILpARebGnxb4DD49keIikTyyf2POb9en7WwxfXJ7kQgi44y+uRk\nEElCiIxE8st9BenSPUdxGzWc3o+u0656G3YZyA6ZObRH/m3Mk5CA2xdTSXpnNGLRQIND0n92G87f\nyVXxpDFmd29gkriZXhTTOqttu3wf0Zi5NUNm3FKD7yi8ekmQ37iGb51quPz+a8oLGk1a82cHtsf1\nl5/wGDbI/AMFwSrGHlIaiAyv2IS93kVYf2orDaKz7g2Y0jg9z3BzI+Gzr7I19ukx1Je67uObtLh7\n0SpLMVXcLLWz2oK+YUZt+evXj3J47ZcoRNtupjsM/kuCvkQpkrt2x+ODcbiPH43X653w7tkF4Wn2\n1X4OrIg9Km1z4MCF62hkcjpXa8UJT382ndpCcFJcljEFgfR9qb2TE/j538UcXPsVo8/ttMr81hY3\nu+oVQN0ntxhopsiauTgM/suCXE78l9+S1HcArgt/R3lgHzG/L0Ly98/rlb0USCoVQmL2Wjr2JFHu\nRJ8qzfHWaagZV3Bu+M6rVyBsTsnVX3cuAiSJ3lcPc2n5x/S9dphxDbrRudXwbI8Pio9i5bY5VIh6\nkOO5LBE3Mya9cNI/mGWlazHv30VUfWadqlpDOAz+S4TTgX04/70u7e+uc38u8KX3+YUUg28FD18U\nc+wElR3p5YWjFErmBVbgtotHtmNeNFwWL0Q+ZzaQIlX8y7+LWLz7N/4tUpaK3f/HjNCW6LNpRFLt\n6R3u/vUhXW+dpES8bWQacpJe+KRWewA2bf7RJucHh8F/eUhIwPOtAegqVeHp5VtEr9mIuldfR569\nnZBUbgjJybmrgAaUf6/Du3M7nLLR1jdG+gYi8QolQyqFcdLTP9sx+R35pYsZHBZt/QYIBw+AXs+j\n+CQWla1HuzYj6B4+lHvuho2tTBT54NQWjqz9gkhnFS3bjmFr8Zyb+VjSyS6nPhu651k/QYnReCXb\nJvznMPgvC25uRK9YT8zytUg+vmgbNUHTwXjqrAProQ8KQlu3vsHeteagea0j2noN8Bg7EozILRvC\nFO/9RfHwFSeP4xtWD6c9u9Ne0zZohBATg3AupTjq36Ll2BRsvDK2sDqO905vY2aV5gT2mc7OYhVN\nOr8lnexykl6o/DyUdNw/GC9N9iGjcgHZ6+jnhCMt0wY40hZfbPL79cmvXcWnWUOSBg4i4dMvzTr2\nhS28yowk4dOsEWLhwsTO+gXJ3R0EAf+yxdF/NZ0S9/2N9qVOj486gd7XjiAKAnMqhZmUD29qWmZm\njKWKfnRyEx+c2or3wB+yffIWBFgxxHJpBUcDFAcZkN2/hxj44gtuFWT0IWVJeH8ibp99THKHzujq\n1DP52JIBfpQMb0DHupb3esgXCAKJw97Bc9Rw/EPLkjDuPRI/nIxUsyayffsIbfyGyQY/ysWN8jEP\nGXn+HzRyBfMrNDY6Pjed7FL7bBgqBiuWEI2bTkOxhCjuuhu+8X7eoY7Fxh4cIZ0CifzsGZyXLDL/\nuGtX8W1QE9UP3zg2c/M5ScNHoKtaHdff5uX1UvIExZlTqH75Oe3vV7v0Yumeo/xQvh4DohQcPXEy\nyzFN71/Otpn4qEa92FqsUo5pkdboZJddn43JtTswrEkfw8ZekvBSP8t1nw2Hh1/AUG7ZhOewQejK\nliO5Ww+z2tzpy4SQOHwkbtOmIrtzh/ivvgWF4yuSL1EoiFm03KyiLL0osuTodVacuMHF6w9oefIf\ndhSriDqwuGHt9/yIXo/bxxNw/fUX9OXKkxzeGqfdu2j70bc8cH7eO1juBQ/vQDFPULrgqUlixoFl\nDLxykM7hw1hbqobBqReH1GXBP39QIu4ptz0MpytPblXdKhLoI5pUZMfRUxx4qAZlSv/hSBd3w08X\nGjVE3cPTNfcJFvn4k3VgFpKE68+z8BzQC01YU6LXbDS/p6kgkPjhJOK+m4XLXwvwHNDL7I1BB/ZD\nCggw+Yacqv2eqhYZGxnFL3sXUvVJBPdjE23SXckmyOXIYmJImPAxUTv+Je7neRzp0pskmYF/h6h7\nNL1/mTMrp9L15gkGh/VjbcnsQ1lrS1YnSe5Ez+vHsrwnCDCldXVGNDFtU9cUetYKgbvn4dENSIgG\nnSblyVqSUv6cEJ3y3t3zkBBtlQ11h/tWENBqcf/wXVwX/k7i8JEkTJkKcsP5xqag7jsAsUgRPAcP\nxKtPd2LWbHSkb+YWrRbFiePoy4TYvdjNVOVGyNhdyZrGzZrEzZqT9mdJqeSHKo2IjsxopJ1EPdNO\nbmFcxBkOBJSh2WvjuOlpvONYnNKVJWXq4KFRZ3g9tZOdtZsbpRnwhKiU/3LAGimzDoNfAJA9eohy\n22bivp2Jut9Aq8ypadma6HWbkD194jD2VkBQJ+HTvhWxc+aT3KW73c5rjrFPT+oxeWr0TRQTMyQH\nISJQK+4JH4XU5Zuq4Yg5GPtUBr0yAAAXuYy6JfzoVSuETqG2CXMFF/Ll2IwJHLhwnW0nL/D3EeNa\n+w4P3wEAYrHiRB46CW5uVp1XV81wrNOB+UiuKgCb6ukIT58iJMSnSQdvOH/HImOfytStpyjh654n\nbTudDuzDfeIHxM6Zj758BbOP18tktKj5GpIgQOwT/FTOeBUPMbkvtb2uObiQL8FNfenZtA4RTyI5\ncOE6+y9et1nKrMPgFxSsbOyzI+JJJCePRLD37FX+OX0FeEHzuO2NQoGkVCIk2c7gew3oBaKY0nRe\nELKoRVrCtO2naVsxyG4bucLTp7j/bxIuy/5CW7OWScc0rFSGZXuzxt2ldE8HLcsV4YchbdOkis9k\nalheNdCHjqHBNvPmTSG98bcVDoPvwGQinkRSe/Q0yidEc9nNO+31ZXuPpf3g8nMDjbxGUqnAhh5+\nwqRP8O74Kq6/zmFhvXZGvVm13Il5FRpz28N4ls/1p3GsPRthUZGRWYgiLn8txG3qZBAl4qZ/nxKe\nNGEvqlHF5wZfkmgY84gD3kUMjkmVKk5/Lem96mnz/2UaBduBcRj8FwlRRPXVZ+CqInHMu3Y//YEL\n1ymXEM3ZQyuYWbwK75Wtn8GLSh0T3LRg/UisheRqW8VMbYNGJL0xGLdpUzky1vjGcLzShSFh/Uya\nd50dDL7syWPcJn+Epk1b4v83DalwYZOPTY1tt4q8y9aTm2lYuwMHMxl9Q/HvVAcmMwXZgXGkZb4o\nJCXhMeQN3L7/JouRtRf7L17nips375Wtz9iIsyw9uxNnvS7LGAeG0datjxhQ1KbnSJj8P0Q/fwYv\n/M5qxXPW1n43hBhQhKiDx4mb/atZxh7+2/xs/8FYHvoFMOXhJYr7+9AjrDYzh/bI1mgb0/6vHvuU\nv87u5NDpS2ZfS37G4eG/AAiPHuE1oCeKC+eJmb8ATftOebKO1B/IjOBQ7jq7sej8bmZdPsCQSmFZ\nxjjIirHm29ZCcvcg7psZ1O/VlQaPbnCwSO4zOyzRfrcEsYjlN8PgQr4EN6+Pz8eTaD16FCfH9EQs\nbfzac3JOej26zlcb/4aWDS1eV37D4eHnc+SXLuLzanNkd+8SvW5znhn7zKwKKM0fRctRP+ZRXi/F\nQSa0zVtSqeenVjH21kZ29w6q6dNsJt0h9usPvr6o5v6c41hjzskpDz8uqrwp/691OmTlFxwGP58j\neXqiK1+B6C270NUwLWvBVmSOg57w8Oeei5vRMQ7yhvigEiaPddEZl2y2RPs9C1otrj/PwrdxXVz/\n/A3ZXRtV86pUiEOH4bJkEUKk+Y1M3rh3iT4ProIgsLhICK3uXYP4eBssNG9wGPx8jhgYROySVYjF\n7J8LnZnMlX7zilXk1RptjY5xkDfk1F0plcYPrnL7rwmUjn2S7RhLtN/Tozh6GJ/wprj9bxLqHr2I\nPHAMsbhlapOmoB82nPhPPk+rfciOLM6JJNE4+iELzu+mz4OrLCkSgkqvxXnLRput1d44DL4DkylI\nDTQKOjl1V0rlpH9xkuUKZu1fmm2YpaOFUsAATrt24NMuHEkmI3rzTuK/+g7JyzvnA3NDQADqNwaD\nq/EnkyzOiSDwVqUwFhQtx4Lzu2kQ84izAcXZN+1rao36nJFzlrJ0z1EinkTacPG2xdEAxQZY2kBD\niI9DUrlBPlYrjHgSycmbBbvwylYNUGS3biJ79hRdLdsV1qSiF0UazdiUlotfMeo+F30CDY7teuM4\nK3fMpWOr4azPJC5Wxt+DfaPaWl6MpNXivHIZyd172kV51ZzPLuJJJB/0fZvdvoGI6ZqeyCSR+Rf2\n0v/BFT4uXZvpJauhydQLN6/SNb28XFEqLf93dGTp5BNkt2/h1fd1ktt3IvH9CXm9nGwJLuRLaEgQ\n/cMbFNgbtq1w/W0eym2biTqUVavd2shlMia2qsagJfuo/fgWR9d+QZfwoawpVTPL2FWlarK1WCVm\nHFjO9mKVSFIoAetov+PkRHKvvpYfb0PKXDjNjpOb2DJmIn/4lkjbxC3q68Wg52NG3jnHjOAqWQz+\ni1pv4jD4+QDFkcN4DeyFpHInuWOXvF6OAxshqVQ21dLJTFp3pS0SfweH8vO+JfxTtDxRmTbaEQRG\nNuzJuZX/Y8LJTUyuk5IJZpb2e1IS8hvX0VfOuQG4vTGkUdO8TBAz535OXO261PrwPWqlu6mNnLOU\nI1duMahSGMHqeOKe3wDTs//idZtKINgKh8HPY5xXLcdjzDvoqtUg5o+/7C6dm1tkt24iv38PbUPj\nbeEcgKRys6vBh//ULocl9OH8ik/47tAK3nhlYJZxV70DGNqkD0cLlUQQUoy9qUqZTrt34vHBONDp\niDx8yvw+DDbkzr2HTHxjNFv9M9646v+7HvmzZ1Qt24zlz6IzhGdSbwqiIOOWq6fBeV/UepP8Gyx+\nCXBeuhjP4YNJbt+J6JXrXzhjD+C64Hc8Rg7L62W8EEgqV5tKK2THiCYVmfpWe75q2ZeBVw7S+s45\ng+P+KN8IdbkK/NqzsUnGXvboIR5DBuLdozP6ooHELFmVr4w9wKMFC9lyajPV4p6mvdbi2V2G3bvI\nhyF1uaHyfGGNtyU4DH4eomnZmvjPviTup7ng4pLXy7EIfYmSyO7dBY3xXG4HgMoNQafLk3+r9pWL\nM+q3r3lQqz4zz28l0MMVuUxALhMI9FTRpkIQs7s3YN+otiaFcZzXrsKnYW2Ue/8hduZsYtZuskjG\n2NYs8ixKhLMb42+fSXvtzfuX2eNdlJ+KVwayVtwW5Gy0fB/SsYdGdF4h+fuTNOTtvF5GrtAHl0AQ\nRWR37+RYyv6yow8qhqZRE9BqQZk1Lmxr5HI5XsuX4OfqyimF8Rz1nBADipDcviMJU6Yi+ZreV9fe\n/Hv5NjOCQ/ny2mE+CqnLPRd3+lVphrdWk6ZJldnDT1PfNMKLWm+Srw3+y6hm96Khf95sQx5x22Hw\nc0DbtBkxTZvl7SKKFUv5fy4zrLQNGqFt0MgKC7I9vwZV4OMbxxl15xwflK2PKMiIVGb/RF2QPfx8\nHdIxJbb2osTfFMePgk6X88AXDLFYcSRBQH77Vl4vxYEVESKf4TFsEPKrV1KeSF5QGlYqQ6xCydyg\nigy9exEPAzISmY13qvrmzKE96BFWm+L+Piapb74I5GsP3xSp3RchPcrlt3m4T3yf+Glfp1QAFiSU\nSpI7d0XMx4/1DsxHcnHFZfUKXFavIPGtYSR8Pj2vl2QRqeGZH4KrsN87gAR5VpNnKDxjj+5TeUG+\nNviZvfeiyQn4apO56OadVhmXrz18nQ63jyegmjeHpEFDrNZgPL8RN+e3vF6CA0vRapE9foQYVOy/\n15KTUf3yU9pfZc/MFyHLL6R670+UrqwtXMromJeBfG3wM9P3wVWmXztCrNyJI16FWVW4FBv982kc\nMTYWz349Ue7eSdwXX6MeNDSvV+TAQRY8xo1EceoEUTv+BWdnnPb/i/v7Y5HfuE7i8JEozpzC6eD+\nFMVId/e8Xq7ZBBfy5cwH/Qnp0o6vug/ht8QUR7GgJH6YS742+JmbE88pVonjnoWoH/OIejGPCVbH\nG747x8eDs3Oe5gTLJ01EOHyImL9WoG0enmfrcJCP0OlwOnwQXUg5pICAvF4NAIlD3san9Suovv+a\nxA8n4bJ4AZKnF1Hb96KvEors1k18m9TF7bvpJEyZmtfLtYiQBfNxdpIzYtIY3nH3yOvl5Cn52uBn\nTo+KUyjZ5RvELt+gtNdmGoi/qeb+jOqHb9BVrY62Vh20teugq1UHMTAoy1hboZ/6KfF93kBfwbRq\nRQcvAcnJeHduR+xPc1PExPIB+tCqJI4ai2rmdyS/1pG46d+DSpUm4CeWLEXi+A8QEuxfMGYNZHci\ncFmykIQPJyG95MYe8rnBtzQ9KrlteyQXV5yOH8V53WpUs2cBEPflt6jffMvi9ZhVE+Dt7TD2DjLy\nXK7X3vIKOZE49n2cN27AY8w7RG/ZlUWtNXHMu3m0styj+uFbJE/PDL97ISYap7170LTvaNNz58ca\nonwvj2yNfzTZ/Xsojh9DF1oVsWTWjRvnpYtBLkdbqw5iqdIpMoEG1mGoJiA9qelatpLXzS9kuT69\nHud1q9FVqYq+XPk8XJl1sOXn518igIQPJ5M0fITV5zYFLy9XSEhAN/lj1F1fR18lFADFsSN4twsn\n7sdf8s3ThyWk/+xkdyLwrVedhA8nkTRqXNoYl0V/4jFuJJEHjqMPKWuTdZhjL8yhwMsjWyM9SgwM\nQmMknOOyajnKPbtTxvr6oq2VEgJKGjAIyS8l3TC7bCClqGfc7TN8V6LqCyuZmmtkMjy2Zlf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Ln50Um+fin/uaoQLNDTyRWiiOzuHQg1v/F4bntBOC9djMvyJcSsXJ9tr2h7YGyzv7mTjgpvv4m6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\nVWp8JzQSX62aj68WXbvNbWMuc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"text": [
"<matplotlib.figure.Figure at 0x95931d0>"
]
}
],
"prompt_number": 213
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ALLOW_FLIGHT = True\n",
"#\n",
"better2, ground_trace2, flight_trace2 = flight_sa(path, ALLOW_FLIGHT=ALLOW_FLIGHT, **ARGS)\n",
"#\n",
"print 'With flight allowed between cities with population > {} and distance > {}:'.format(FLIGHT_POPULATION, FLIGHT_DISTANCE)\n",
"print 'Initial path (random) =', distance(path, ALLOW_FLIGHT)\n",
"print 'Improved path using SA =', distance(better2, ALLOW_FLIGHT)\n",
"#\n",
"plot_map(better2, 'Plot of cities and path via simulated annealing')\n",
"#\n",
"fig = plt.figure(figsize=(12, 6))\n",
"plt.plot(xrange(len(ground_trace2)), ground_trace2, label='Ground distance', lw=2)\n",
"plt.plot(xrange(len(flight_trace2)), flight_trace2, label='Flight distance', lw=2)\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Distance')\n",
"plt.title('Distance via simulated annealing (flight allowed)')\n",
"plt.legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"With flight allowed between cities with population > 7 and distance > 200:\n",
"Initial path (random) = 15529.3006575\n",
"Improved path using SA = 3340.35195453\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 218,
"text": [
"<matplotlib.legend.Legend at 0x1562a210>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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FTlVnB0J8PYgM9qNfcOnG0ajwPfzucTf489gf/By1nbE3zplNQ1oaQkJ8gZGL\nsjKxYyBv9SzcNEyKyoE9H3+H0K8fimeexv6HZaBQoHnyKRL+PUTSkh8QkpNxHxyJ4ujhQpVto5iI\nIu59HsNt9DBEDw8S128maf1mdO06lLVkFZ6s79vPVf1JkysZE3s+dxqZjMQNW1APG1HaIpqQXY3B\n8cP3cX+8u1kvn3tibhmVfT7sO3sJNBoUx46YPf/3sU0s+G+/8UdaAty5hG/qNeKbybnfvSonXovk\nh2GdGNi0TqkHTapwPfycdEy8TbeEm+xxr0Y1rXlzSvsN63CZMgFJJkNyd0f08ETy8EQT0Y+MFybm\nSi/cvYvs3l0m1feknnNL5uw8X+Ccvr+3CzPCjQFQDJE/Qs2aGAIaPEwgk6GN6Ie2byTKA/vKfezT\nSodMhnrIM6TNesfoodEKKKJOIrt9q8yDn5SniGypCjvWVqnLoDtXeMs/xzMuCBiCGpe4DDkRUlOw\n27gB+9WrsNu3B8nRCU1EJEJKMpKnV7a0ec4gSBKN0hPpEXeD9jP24X3zMkJ6OvfPXqZdkL+p9w+w\ny706r109yfT6rUhQ2gPGtSGHrz5H37QZus5lt2Bd4RR+zot7184BAege2hfpwRRJzkU1bYdOJC9e\nhhAfjywxASEhHll8PJKTeTMq1e/rcJnxGgAjgGcdHElzdmVd2GPMaNwz2wsV4uvBcA+JXop0yLiF\ndFkDtWtgeH8+uhRN7sIFwfxqP0BqKqhUoCx4c4aNwmNtu2/V6lXY/f1XmSr8wkZkG9augZlSikfO\nd3JdlTrUUqfipNeR9mAaoywXul2eH43qr61GPbDwazR9I8HZ2WzavNb/dh/dSMfE22gFGUd8apL2\n8qvounRD8vQ0WXZlsqhmEDNiTjDm5gU+qmNcD2wf6I+g1SCpVNZvYCGocAo/58W9a+eAQpLw0GmI\nt7M3pcmK6FcbjV9ti+vQ9BuEPqQ5soR408dBnhBPv+Yt6N27b670Dgs/wfnd2dmOSTIZjpNfIX36\nW7nSK44fRXHqJKKncaQhengieXri8NVCVJs3kj5xCuqnnwV7e4tltoFpjt5uzy5S5y+wfvE+Puib\nhZp+y2/eRLTAh05JmREXJkhPZkS2O+kapj4WXKT68iLnO7nRpw4bferkSlNWpM2YTer7HyEWQgfk\n5IuajZlfpxm73KvjWa0KRydPNZ3L+TG7rXLk16r1mHDjDB/XDkYUZGw7fpZnE5JQGyTkOQsvRSqc\nws95cY8/fNr7AAAgAElEQVS6ePNKQBt0WYarxe1NSN7e6AvhGyVj3AtoBgwyfiDi43HWpEJ8PNo6\nZnpTWi12O//B6f25uU5pevVG16IlztOn4fjxB2S88BIZI0ajPHQA5cF9xo+DpxeSp/EjYahd95H2\n4WLCzGIsaWmQxwiusMhib6L8dxeaAYPRPtE/y/EbGBrmb11RUmbERY3INmODce3ouZb1C503Lyx5\n30qyhy8kJ6HasB4hKQlmvpHrvKFxE4vLyjlayeSXag/l75ujLX4+nhz5bAb7zl5i2/GzbDoUxcJa\nTXjmdjQR966xoUodNh2KIiUxieU7D9P7XnyZWXpVOIWf9eJm9pjW+NWmt5U2XhUJe3vEmrUQaxo3\nTYhuRpcK+qTsztPsNm7Aaf5cklatIX3SKwiJiaaPhCwhHkOduhgaNiL99Zk4LvwYp3lv4/jFJ2QM\nH4X9TyuNaTUPp4lSZ84mI0tPIxPVmtXY7dphGjmIHp6Inp7og5si1qlbghfCeljaK7b760+c5s0x\nKfrE9ZutNkefieL0KVxfGk9cx86IvjVMx2U3b6Lt+li+eS01I/brbPkza42IbFUdVVbb5GPunYTs\n96u2UkCSJOtZphkMKHftwP6XVaj+2AQaDdreEVDMOnKOVvJKkxM/H0/TPdx0KIpDblX4vnoA2iwd\nUXvRgEaQF/p+W5MKp/Dh4cUtjullWWAICkLQaHDvE07Sz+swNAnG4OWVO139AFIWfk3atDew2/E3\n6hGjjVNDkgTp6cgSjB8I0dvHbD1CUhLy6IsoHnxIZImJAKTO+x8ZY1/Ild7h6y+w274N0cPjwSjC\n+K+2czcMgUHWvQgWUJheseJ0lMnqxtqKPhPRpwoAsrt3Hip8rRbZvbvZPgDmsLYZsTWDZfcOrGG1\nhdyC3km3Hp3RNwsl9YNPil+ZTodn2xbIr8Wg969P+iuvoR48FLFGTdyK+UHpUMuHF6+f4auaQXl+\nOPIbrWS93yMbZ1+c/bZGIw66VcGrmGbjxaFCKvyKisE/gITN23F7aiDukY+T/P0qdB065Zle9KuN\nesTohwcEAZycEJ2cEGvUzPOBVI8ZhzqrrbPBgJCYCCrz5maihweSmxuyuPvI/rtoXLdIiEdydjGr\n8OVvvI5s0ybc3dyzrUNoBgzKNsedtX7kls9cFqZXnD7pFXj5VYvLLgpilaoAyO7dNR0T1BmonxqG\nPjikQDnz4om7MfSOu0bcvYvY1XDAUKcuYt26SM4ueeaxdrDsgU3rFLusghAS4lGcPIF6hJUWzZVK\n0l+agj6oMfqwVtYbNaSl0WTSOD6LPUPY5AlsvZ9a6DWX/O73zAd+mWqVYVhMm8IvZaSqVUna8Aeu\nI5/BbegAkr9ZirbvE4Uux/nVl0GSSH9pSsHTNHI5kpmRRCaaoc+gGfpMDkEl458ZxNatQa/HcPsu\nQkK8aTSha9UGzCh8l5fGo/pjo3FqycMTycMD0cOTjOdfRN+yda70p46cwEOnJlGhQhIEBEmiR9wN\ntnnVNFlimXrFhfiQFJXMkZTs3j3TMcnVjdRPvyxWud46NW2T7lL/9iUcx+w0HU+d9Q4Zk17OnUGt\nZkNUIUMJ5sOGElb48svROHz9JbqWrRAkCW3HzpZn1uux2/k3oreP2U5Eto6QNVCrcRvxNIrTUST+\n8ht9W7Umt3lGxcem8MsAycWVpFVrcH5jKmLNojlaMtSpi+OXn2K/6gc0/QeRPnkqhoaNrCekIOTZ\nc5L6D8DQfwApSZYFeFEPeRp9k5Bs6xWyuPsIWq3Z9ANWLuLbGxcxIJCgtEMnyKiuzaBLaF92efoC\npRw8XKVCdHdHfiYKxbEj6EPDLM6a1yIgwNIajVhaoxFDOrbgiwHdkMdcQR5zGX1j81Y0zm9OZ93K\nFVxy8eaSq4/p789ajbnian56Lz9KPCKb3oDD90uw2/qHcfRigZWM/NxZoy+bNauR371D+tjx5keN\n1kSnw3XcSJQH95G08lf0rXJ3QixlYBVnOLqLT2vnPfIrSxPVSqHw7VcsB50O9eixZS2K5ahUpH7y\nRZGzZ0ycTMao53D4cTkOXy7EY+0vaPoPJOXrJeXOZYOuc9dCbTb5Iqgtyzxq4aXT4KVV42bQstnL\nz6TsywL1kKdRnDmNQ98e3I/N7U8lL8wuAkoSDqKBjAfRj9oH1UeqWhV91aroW7fJW4aBTzL/QiJ1\nk+7hn3yP/jEn8EuN56nuz5lV+J1iLyIgcc69OncdXHI9FyUdkc0Q0AB9PX8Uly+RMTz/Hrk8+j9c\nXngO5cnjiO7uaAYMNnYUSlrZA07z3sFu+zaSl60suqtrScL+x+/5YNE8YmR2fFejEal57NgtSxPV\nSqHwlf/uRHb3bsVS+NbAyYmM5yeQMfI57FevQnb3TrlT9kXBpUP7Ai0lSruXlDZ3PvZLFqM8sK9Q\n+czJueHkVjLkCoYGP5ZnGnPo27RlQbOrGMSHU20K0WCKzJWTd45upMutiwDEqxw5516dc+7V+F+z\nnkS7VS1UO4qEIKDr2AXF5UtoO+U/nWOo7otYy4+kSa+g7dHLuAGxlMgYPwFdu/Zoe+Ttqz4/hLg4\nXF6eiOrPzdwfOITmcY6mDWfmsPXwi4no7YPi7JmyFsN66PWgKMStUanMOgGrqBTVNK48Ys5kMda7\nGk/evMDCcU/SrnH9QpkR54zIppflvYbRs/ckApLuEph4m8CEWwQm3ibs/lXkDz4QOSOyqVavMi7U\nN2iIoU7dIu34zmlO2/KemrXAX7EJ1L0XT907NzHU8wfHHNHDnJxIXrqi0PVZA7FadbTVqhcpr+LU\nCVyfHoyg1ZC0ZAVSRCS7zJgUP1a3OqNiL+A2bBjVy9DbaqVQ+JK3D7L79wpOWAFQ/fQjDt8vIenH\nX622qcrpnTfRtW6LtufjFWIEUNYbeSxB9fNK45SFBT6Rcpos2v3ZHLfhQ3m6tjdiIV/+YF+PAkNw\nZqKVKznjWYMznuZNR3NGZHP6cD7yazEASEolhnr+GAIakrLgMySPguU0Z057E+NHJXL2y5z5YC6e\nqXEkf7MEzYDBFrWhvGOoXQdd566kzXrbGNsY8yaq8uj/8Gw3hcR+fcntsq30qBQKX/T2QUhIKHzP\nuBxiaBSI/NpV3PuGk7R6PWLtOsUrMCMD5aEDOH75GfrAxqS/PA1NRL9SsW4pKpZs5Clrn/TO78wi\nY/S4IjnB0z1YFFQe3I+mbr1C5S1sRLZ8y8oRkS3+sNEZnPziBeT/XUBx4QLyy9HmzUQlCcf5czHU\nqYchoAGGBg1zLaS3SbzDGzHGDWJKSeKKgws3X5hEq76RVpG/PCC5uZPypQVusx9smCzXvnR0Oh2j\nR4/m6tWraDQaZs2aRc2aNenbty8NGhjdBrz44osMHjyYb7/9lsWLF6NQKJg1axZ9+vQplQYAiF7e\nCJKEEB+PVKVKqdVbEuibtyBx0zbcnhyAe59wkn9agz648AFZTDg4kLhpG8p9e3D8+ENcx41C7z+P\n9Ndnouk30HqCW5nyuLnO5EtHrUYWF2fcC1EEJE8v9I0CUR7Yl9sctgCKGpEtJ2aDZQsCYnVfxOq+\nBS6yCynJ2P+6GvmN66Zjz7i4U8/Ohb7NeoEg4KPLoJYmlUkN2vFTNX/u2zkwxKU6rezydz9cktgv\n+w559EXS5s6HUnRNLGgeBEMpY4Wfb4tXrlyJj48Pu3fv5s8//2TChAkcO3aMqVOnsmPHDnbs2MHg\nwYO5ffs2n3/+Ofv27WPr1q1Mnz4dbR4mdyWBvmkzUj78FBwqh7MxQ736JGz+C7FqNdwie6Pc+2/x\nChQEdO07krT2dxL+2I7Bvz7yC+cLzmfDhHD3LrK4OJJW/oIs1tjDNhSwyzY/dO06IEtKKnS+okZk\ny4o1gmVLrm7EHzvDvcuxJK7bRPIXi1hVsxGXHF1N04YbvWvTovVAPvdrwn0749ROqZrT5kD1y0+4\nvP4KgsFQ6KlN2Z3bOM141dRTLyyZJsiSqmx1VL49/MGDBzNo0CAARFFEqVRy9OhRLly4wIYNGwgI\nCODTTz/l0KFDtG/fHqVSiVKppH79+pw6dYqwMMvtlYuDWLOW9TdilDGZG7Scp0zM04VCUdCHtSL5\nx1/y3FRlwzzy27G4vP4K+qbNENKNc+hF7eEDpL7/UZHXU4oSkS0r855oWXw/Omo1qq1/oPp5JXb7\n9xJ3/Cwf7LnM9fsPbftH3LpIlLMnx1x9cNVrCwwsUpLYbfodl0kvoB76DKnvfVioa2+3ZTMuL08A\nmRz18NEYGhUhHKHa2MOXynB0AwUofKcH3gZTUlIYPHgw8+bNQ61WM3bsWJo3b857773HO++8Q7Nm\nzXBzczPlc3FxIamA3otCIcfNzSHfNBUVhcI4P17s9rk5wK+/YN5zdwkgScgWL0J8cgh4eOSZzGrt\nK6eYbZ+/cdOQc2oiQpLRN5FzI39wLptrMLNvKPb2SpP3S0sQBJjfrxXTejRFrzcUqV7hyGFky5cj\n+/UXhMRExJYtMbw/H1dvN7o0bcCKvw8CoBBFvriwl/fqNOc/RzeOH1zL2ip1Od31pRJ9bszdO2Hr\nVhTPj0Lq1x/Zku9ws3SdLy0N+bSpyJcuQXy8N/rF3+Jc1CnjBvUwTHwJF7/qxve6iGS2r6gUOKa7\nfv063bp1Y/jw4QwdOpT+/fvTvHlzAPr378/x48dxdXUlJeXhnGJKSgoe+SgMG+WU8+eRvzoNZYA/\n8lkz4e7dgvM8KvgYR1nCndtI9etjmDwlzyAapcXUx4L5eUw36vsUHBA8oIorP43uxrRiTgfJFn2D\nbPMmxOfGoj1xCv2efYjjXwBnZzoFB5jStU6+i7NBz3bPGqTIlXxRszGvXj3FR8sXGAP9lBaiiPyd\n2UjdH0P//Q+WG3Xcu4eydStkq1aiX/g5+vW/QXHWBwMDMSz4ON+OVGkgSFLeY/s7d+7QpUsXvvrq\nK7p2NS7itG3bloULF9KyZUs+//xzbt68ycsvv0x4eDiHDx9GrVbTpk0bTp48iV0+wxetVk+ShVvz\nKxqZvYsSbV8hHZJZiuzObRy++hyH75eAJJExbAQZEyZn8wpZKu0rQ/Jqn1dgXTKeG0/61NfLQqw8\nMYgiv0VdY0PUNU7lCHGYM1h2ce+dkJiA5OJq9tnLapY5+9IRplw/jVfn4YiCsV8pbTdas+gbB5P0\n4+piTYllrTOrNZdMJtApOICW9euYrLmEuDgkR0dwKETPWpJwevdt1EOextCgYbHltBZubg7Y2RXd\nEjFfhT958mR+/fVXGjZ82OD58+czdepUlEol1atXZ/HixTg7O/Pdd9+xePFiRFFk5syZ9O/fP69i\nAZvCLw4Oi7/C7u+/SFqyosR6mUJcHA7ffoXDd4tJm/5mNu+bj7LCN9TyI3HbrrIQyyrke+8kCcXB\nA9ivXoksOZnkJT8UuvxMBRw+dRwxBhnjOg4wmdP2P7CdmgveN3pnVdqRsPtArpiyha3LnBvtrBQl\nuEx5pkQVfklibYVvv/RbhPR0MiZOtlqZRaWkFaJyx9+4jRqGvkEDklauQfKx3qJuToTkJCQ7VbZw\ni4+qwvds0QT59Wvcu5tsnYpEEeWuHYh+fhj8AwpObwXMtU12/Rr2v/yE/epVyGOuYKhRE/WQp0l/\nfWaRFpaF1BS8GtQmde78bB0F+aX/8GzbgpT/fQyAetRzxWrLz7sOM2nR6nzTLHx+SLky7S0uxVX4\npWeIWsIojxxCtWVTWYtRKui6difxt83Ib1zHvW84spgrJVaX5OpmPrauToc86lSJ1VseMIgia07E\n8OyPu2n2wQam1G6PTiaj2QcbePbH3aw5EYNBFItegSDgOmEsqtU/WU/owmIw4NGzK44LP0YX1orE\nNb8Tf/Q06W/MKtau7NR3/2f0iZO1Kv8A9AENUB47UmxlD+aDy3hp1dl8CxUUgEZITsL5lZeQXblc\nbHkqApVG4YvePgiVxL2CJeibhZKw6S8EUcSjT3ipK1/Z+nV4du+A61MDURw8UKp1lwbrT8TQ/rM/\neHHNfraev0lscjqiJIEEscnpbD1/kxfX7Kf9Z3+w8cz1ggs0hyCga9W20A7ZrIpcTtKKn4k7/R8p\nX31r9BZZzA1JkrML6tFjEWv55Tqn7dUHu7/+NO6KLyY5bfqradI5cPg35l46nGearCgO7Meja3tU\n69eiiL5YbHnyQ3H4IPbfLy3ROiyhEil8b2RxcWUtRqki1vMnYfN2dE2bIbnkHSWpROoeMJDkLxYh\nv3YVj4geuPXvg3LXjkph379gexRDl/xjdjerUhKZfWQj1dKNZseX41IY89Mevvj3XJHq0rVpi/L4\n0SJv6LEE2ZXLOP5vHqrf1po9r2/R0rgQWwpo+kSga9na6AolB/JzZxGKaBn2xN0Yjh1ci4OoZ4lv\nAXEhdDoc58/Fvd/jiFWqkvDPHrThvfLPU0zs/tmO40fzS7QOS6g0Cl/y9kGWnFSiL055RKpSheRV\na0o/OLlCgebJp0j49xBJS35ASErCfXAkyh1/l64cVuaLf88VaNv+9rFNOOvU2Y7N2XqiSEpf16Yd\ngkaD4vixQufNDyE1BftVK3B7ohderZvh+PUXyK5ZL1pWUdGHhpG8YnXudSdJwuWl8Xj06orcQs+3\n7YL88dKqWRX1NxtObeOYizetW/bjiqNrtjTZEEXcBj2B46cLSJ/6OokbtyIW0p9RURC0WijjXbZQ\niRS+6GX0LCmLf7R6+WWOTIY2oh+Jf/9L4q8b0HXpVtYSFZmNZ67nu3v1rsNDRXLDKbc99ZytJwo9\nvaNvEoLo5IzyoPWmdeQXL+DVuD4uUyaAUkny599w//R/ZEx6xWp1WB1BIHnZj0gurrj3CTdO+xRA\n+0B/3r10mF5x1xke1IW+zXpx0945V5psyGSonxpG4u9bSX91euk5W9SokfKIKV2aVGzXklnQN21G\n8peLS31qo9ySGZO2tBxECULeDrfUaqPddhH8q5cWBlFk3raT+ab5q0YgSUp73HRq1Hm4CXjvr5P0\nDqxhuZ8ahYKMSS+bDRZfVAz1A0h7fRaaiEiz8+jlFbGWH4mbt+Hy/Ghcnx1K2jvzyBj3Yp6Lx+2C\n/Onh35I59UK5pXLKM01OCuuwzhoIGm2Z+9GBytTDr1YdzeCh5l25PoI4LvgfLhPGQSk6scsLh2+/\nwbN1M+yXfmvyKVLeWH/qWoEeKFUGPW66/OW/dD+F36KuFaru9JdfLXS0JSEpEfsfliG7fSv3SZmM\njBdfKn1lL0m49+yCavWqohfh7ELyDz+TMe5FnN+cjuLk8TzT+vl4su3rOUyfNJohncKo5e1B7Sqe\nPNu9NQufH1KubPAFjRpsPXwbJYWhTl0cP/kQWdx9kpeuKNMPobbbYyhOncB5+jQcP/6AjBdeImPE\n6DJ3TZCVDacLVtL37S2Td0PUNQY2rVNMicxgMKDctQP71StRbdkMGg0pzt+Vm2Ai8svRKI8fI929\nmO4D5HLS5ryHevBQDMHGYODCnTsIaamI9bL32HO60TbtM7ibiNO8d9C3CEMTOaB48lgBbeeuyILz\nDmxeWlSaHr6N7GgGDSFp5a8oDh/CrX/fIls/WAND4yakfLuchD2H0XXtjtO7s/Fq0RjZrdgykykn\nUbG5rUZyIj6Ypjnpmb9LgFMWlFVY7LZuwbN5EO5DB6CIOkXa1NeJP3623Ch7AOXuXUhyObp27QtM\nK7t2FZfxY8yPUB5gCA4BSUL1y094dmyJ8yzLXFoIZ8/g0bMrDksWIdy/b7H8JYlm4JNkjH2hrMWw\nKfzKjK5LN5J+24z85g08SniDliUYAhqQ8vk3xB88QfqkqaaQcOWBTP8z+SFIIie8arK/av5WHZaU\nVVgMvjXQ9uxNwh/bSdh7hIzJU7P5NyoP2O3eiT40zCITT8nJGdVva7HbuiXPNLJbsbgOexLXic+j\n7dKNlIXfFFCohOyrL1G0bQNaDYlb/s6209eGTeFXevRNm5Ow+S8MtfzKPNpOJqJfbTImTCprMSzG\nWatmzuENHPjtf9y3dzbZ4FsdvT7PTViG4BBSP/wEfVir8hmX2GBAuWc32o6dLUoueXmha90Wuz83\nmz2vWrMaj46tUR4/RtLSH0lZvBzJ29vo62eV+WDnztOnoXh5CuLwESRs/xd9SLMiN6eyUqnm8B0W\nf4WQlGQ0t7JhQqxbj6S1G8taDItwfG8Osrj7pE+cUqL20Tm9LOLsB7Lsr4NcNDD6wl7mHNmIhyad\nz5p0I9rNB50sfy+lVQvpI19+9gxOC/6HauNvAMQdOJ5rrrq8I4/+DyE1pcDQiFnR9uyN03vvIKSm\n5FpjElJS0Ib3JHXe/7I5WFP9uRnHLz9DfvECaW++k81rp3roMyj69Ebq2xcqqZ+n4lKpFL7idBTy\ni+dtCr8CI3l5oVqxDPuVP6DpP4j0KdMwNCxg52QhMetlUe4JTu6mn11vnmfhvtU0SYjlJ/+WzGjZ\njxhXb4vKD/G1bNFS9evPOHzzJcqok0gP1gcyRj1XKhuBrI2hYSPiLl5FcnC0OI+mV2+c356Jcsff\naCP6ZTunHjnGrL+dtLfmIPpUwemdWcgvR5P81XemxX99s1CkShqUx1pUqikd0dsHWTlZpKkQlEM3\nCBnPTyDuyGnS3pmHcu+/eHZsheuY4VbxvZKJWf8qadkXWn3TE0m0c6B1vzd4uvtzFit7gMicwcHz\nQH41BrFGDZKW/sj9q3fQBzZGyMgon1M2FiC5uBZqI5NYzx99w0ao/vwj98m8roEgkPHiSyR//xN2\nu3fhEdET2c0bRZS49LBftaL4samtQKXq4RsV/qPjQK24OL09C4C02XNLb4OWJTg5kfH8BDJGPmd0\n2fvfRavuiDTrQTE1Htyrg51xc8zK+q1ZWb91NsUz8PJRApLuMr953jbz/t4u9Muq8CUJISHerN/3\n9GlvZPuta9MWuwrumqJQiCK6dh3QNyrEpjNRxOHLhchux5KwaRtuI59Gcf4sWisEUylJHD5bgLZX\nH3TtO5apHOXoLS8+ore3McB0WlpZi1IhEKtXx/Hrz8vNBq1cqFSoh48ibe77Vi32aNQFmqbc55lb\n//Fe9CHqZDzwb59w82EiQcjVy+xzLYr+MXm7XhAEmBHeFLlMhnDnDg5ffY5Hl3a4Rz5u0WhK16Yd\n8pgryO7cLlK7KhKyK5dxGxiBw7LvkF/O34WxKc/NG7gNegLnuW+BQomhcRPi9x5B271HCUtbfASN\nBsm+7I0mKlkP/4E/nbj7iE7mt1rbeEjG+ImIVari8tJ4ZPfvGX2ZVKCdyo6ffoS+URDano9bNA3i\n+MF7qH5by/lL0cgfKOCbKke2etYkxsEV0hIh7gZ4me8t1kpL4EaWef6cvPVYCAMvH8X+/anY/f2X\n0c9Qj8dRD3naqPALkFHXph0AygP7ysVmoRJBFHFYsginee8genqRuHo9uq7dC8ym2rAO52lTkBwc\njD6bMheHy4nlWUEIWg3Ylb2slUrh60Oak7T0RyTP8rGduiKgGTAY0csb15HP4NavD0mr1iAVJ1hz\naaHXo/xnO07vzUEfGISm/yD0AQ1R/HcBbYdORvPFHEgeHug6dWFVo5Ysv5XCGWcPEpQ5/Jsk3TH+\na0bp10pN4O8ajXjz6CY21Q7huLdx6kYQ4M0ezZjQoRFOXcYg2alIfXc+mn6DkLwsD+EnVvclce1G\n9M1DLb8O5QDlgX3omoRYtHPa+bVXcPhhKRkjxpA2e45FHQz7FctxmToJTZ8nSFnwmWVhES34wGZi\nEEXWn7rGhtPXiMoREzjY14PIJn70D/Gz3D+SOdSacuFLp1IpfMnbG23fJ8pajAqHrnNXkn7fgtOs\nN0okMHqJoFCgHjYCuwP7UJw7i+LcHNMp8cNPzSr8zJ2O6bsOsye/0HhJdxjfszXbriQ/9K8jSdRK\njeeKixfvHfqNeJUTx7398Pd2YUZ4UyIa1wIgceNWY5SwIqKz0I69vCAkxOMW+TipCxaiHjaiwPQZ\no55DE9m/UO3URPZHsrdHM2iIRUpc2L4d9zlzSFqyosDOy8Yz15m37aRZP0qxyemmYDcf7TjNzB4P\n73NhEbQamy8dG+UHfXBTkn77o9xYiAj376M4fxb5hXOINf2M0zY5kBwcUT/5FPpGQQhpqaj+/ANd\nq9aoR4zOt2xzHhRz8nKvMGbb2fNb1DU2RF3j2qXrOBp0tLt7BaUk8sW+n2nyzgz6BWfv+RVH2VdE\nlHv+RZAktJ26WJTe0LgJBnMnUlOR34rFENAg1ynJ1Q3N4KGWC+XqgvxSNB69upL04y8YghqbTfbF\nv+fydYedlcxAN2/1bMbEjoGWy/KAjLEvoAtpXuh81qbSBDEvTzyqQb6Li+LAfpw+fA/FubMmaytJ\noSBj1HOkzfvAskIMBotGKbk2XmH8ELQP9Kdn68bUqeplbJ8koThyCIcli7Ff96spv+ToxP2YvP3A\nlFesfe+cX3sZu53/EH8oh2tpvd4YjMjCtTSXsSORx1whcdvOYnU6MtuXcvoCbsOGILt2lZTFS3NF\ntCqMss9JUZW+NShuEHNbD99G/hRiLjRf0tNR/HcB+bmzIAhohjydO43KDsnFlYzhIzE0CkLfKAhD\nPX+wK8RQOA9lr1q9Cm3Px5EeeHLM6WUxK25ZNu/IYq7g0SccQ7XqpE96BfWQp3F6a3rFmfoqYZS7\nd6LtlH13rfzcWVymvIihQSNSPi/A/80DtOE9cZ34PJ4tQ4jfe6TYi7E5feunzl+AeuQYoOBANwUx\nZ+sJans6F3l6pyyxKXwbeSNJOE+bgsG/PhkvvlTo7LLr13Ce+TryC+eQx1xBeDCY1HboZFbh65u3\nIHn5ymKLnUuOmzdwmTYZafqrqEePJf35CblD7OWBWLceCZv/Qh8aZlLyYpWqKM6ftbqc2VCrwb7s\nF/nyQ3b9GorLl0ib8ZbxgE6H4+ef4Ljgfxj8apPx7CiLyhESE7D/5WcA5NeuIui0SFawvsn0re80\nd16tTpYAACAASURBVDaG+gGAZYFuLKHQgW7KCRVLWgtw+OIznN55s6zFqDRIHh44vz0Tp7dmgCg+\nPGEwIL/0H3abN2K/ZJH5vE5OCGlpRp8oCxaSsPkv7kdfJ2ndplKS3ohYoybxR6JQPzsSh+++wSus\nCU6zXkcWexMkCeWBfTi/PBHFKfO9Pn3L1tl69JrI/qiH579OUBxUa3/Bu1EdyCjfU4KCVoO63wB0\n7TshPx2Fe69uOH7wHhnjXiThn73oW7UusAzlnt14dGmH4oQxpq+2SzfrmgbL5aS9/S66Dp0AywLd\nWEJRAt2UBypdD19+ORrFyaIP12xkQRBIm/U2YtWqOM16A/nNG0hyGYqYywjnz+P5IHqV6OWFesSY\nXLthJU8vktb+XhaS50KsWo20d+aRPukVHL79CqePP8Rh6beINWshj7mCoUZNtI/3AQs8LOq6haMr\nQVkNAQ0Q0tNRHj+Krl2HEqypeBj8A0hZvBwAhw/fQ9BqSNz8F/oWuafJzKE4cQy3gRHo2rQj5YtF\nqP7YiNOctxCSk0ps8duSQDcWl1VSgW5KkEqn8Cuje4X8FhjbBflbJ4ybJCHcvYvi/FkU58+SMfI5\n0zxqxtgXEH2q4DLxeQStFrH/AAxPPU1qnQAMgUGIVauVG+uegpC8vDAENARA0OvRtWxNyoKFxi3v\n5WR4rm8cjOjsYrRvL8cKPyupb84xjoIKMQ2lb9qc5O++R9s7AuRyNL36oDh2BCE5ucQUftZAN75p\nCcSaCUZvKZYGuhHu3sX+l5/QDB5ifFfKkEqn8CVvb2Rx96232FjGmPXsCKzefYTVu48AFCt2p+P8\nuSgP7Edx/iyy+HgAJDs7tI/1wOAfYEqn6TcQ0csbxw/fh0WLwc0NXQW1QtJ26EzyZ1+hjYjMPX0g\nSQino5CaBGc77DxtCtqu3dH2iSh5AeVy9C1b5ekbv1xSlJ3tgpDNS6ZYuw4pi5ZZUajcZG6q6hR7\nka1bPmNC+6dY2qhoH1VLA93Ib17Hec6b6Dp1LnOFXz66NFZE9PJG0GoRUpLLWhSrYNazo6VpUlNR\nHDuC/aoVeYYTlN2+jeTlTcaY50la8gPxe49wP+Z2NmWfia5jZ5I2bAG38m9rLrtyGYeFH2dfd3iA\nVLUqmqeGmZ0rVu7YjrJFKIonIlAcPPAgg4T96pXIb5TenK2udVsUhw9Z1UuoNVAcP5pvYPE8KWft\n2F+1HisC2rBk9wo+OLAGmZnnJBNByvucJQgaDUC52Glb+RS+t9H6orzEsiwuZj075pPGfuUPuA57\nEs+wYHzq+eLRqxsuUyagOH7MbN7UT78keckPpL86HW1EP+PGl/w8U5bjUZOQkoz9j9/jHtETr9bN\ncPzkI+TR/xWqDF2nruiXLkO4ehWPiB649euNat2vCBoNhlIMKahr0w7Jyan8uP5Vq3GaOxv3x7vj\n8OVnhcpq9/c2PNuGIr8cXULCWU5mcBqdXMG4jsN4pc0gpp7azsHf3ueDA2typW9xL4Zzv7zNkOjD\nuRS/xYFuMhV+YcyLS4hKp/D1IU1J/HkdYpWqZS2KVcjZe/fRZjDgzmWapMabTSOLvYmg1aLpHUHy\nZ1+RsHUH9y7Hou3dt9RkLgscP/kQryYBOE+dhGSnIvnLxcSd/g9Dg4aFK0ihQHxmGLrjJ0hasgIh\nJQXXF4yBOLLGkHWc/y7KEnRlrGvTjvioi4i165RYHZaiOHwQj+4dcPjmC9JfnU7Kp1/hMn50nlZN\nJjIycJ4+DbenBmGoWw/JqWBfOyVNcNbgNILAJyHhRPZ8gWoZyaQqVbm8mqYpVFxy9eHnf77j+Np5\n9L160pTG0kA3gsZo3FAezGwr3xy+hye6bo+VtRhWQ2kw0Ckhlp5xN+gZd4MWKcaRy5v1wjjtnHve\nvtSjfYkiLi+NR9u5K5onnyrdurOgrx9A+pRpqAcPRaxphQ0xMhnaiEi0fZ/A+dWXcfhhKWIWn+v2\nv/xkXPS1wNNjUesvDzgu+B+OH7yHPqQZCX/txhDUGMWB/divW/N/9s47vqmyi+Pfm9mZDlrKLKuM\nsvcqFJANAgIioCiIKCLIEHAA8ioCKrgYDlBxIYIiCsiUvffee8/ulX3v+0do6UjSJE3aUvl+Pn7e\nl9znPnluk5x77nnO+Z0MbSJryE8cRzPsJeSXL5Ey9SO0Q14tFNfUo2Y4687czPLaP+Xq8E+5OlbH\nnwkqSdfOr9Pi9nmm7/+bleu+YnfxCgxs/SI9ajVz7E31FulxqRCoZRb8J/AYu7ytv8PWg//wys3T\nnPMJYFD1VpRp8SxTKzzU5XBEG8ZjiCLIZGhGDMV77iyPdtESEuJR7Nlt9Zih21OkjRnvHmOf5U0F\nTNWqISkUiKEPhbjE0FBLHr/RkwmaBY85ojKpE/9HwpqNGZo0qm2bETUBmOpY14YRkhIJfKoLyGTE\nr9uC9pXXnDL2srt30LzQH/mJ4265hsz0rB1OxWLO5/nvKFmZ6G7j6NT5dbQKFf6lS2RtdGMHc4WK\npA17HakQSLYXOQ//kSQlBcWlC5is5YD36EXj2ykc1IQgCtZ/NFGRBWjwFQqSZ3+NGFYCvynvIrt7\nm9T3p7vPmzOZUG3dhHrxItRrVyH5+xN7/Hy+ShsY2nYgqUSpLO8pFg/Da+kSlHt3kzZ8FLpnny8U\nj+zuxpouv2r7Vksaq429HkkTQNIvizHWa+DS30QMDEK5YxvqmrVIy5YtlVfkMhkTO9Thpd92OH+y\nILCubE3Wh9fku+5RDlfZmmvWItXN1+Eqjw1+QSCKKE4eR7l5I6rNG1Hu22MxZCcv5jBk9ZvWZ/9v\na+1OV6AePuQo0JLdu0vy7G9y6KE4VU8gSfhOex/14l+R37uLqXIVUsdPQN+nb77r2IgVKmLI1lhc\nDC2OpFRirN8Qv3fG4fPZDLTDXkc7cLBDuvCPKkJKMoqD+0n54CO744zNolx/E7UaQ9v2qNauJu3N\nCa7PY4NuNcoyuWNdl/V03u1Q16qOjvz4MSR/f8TyFfK6RI/xWC3TA9hVJDSZCG5U21K16u2NsVmU\nJb/7ifYWvQ8rWTD5UnjlBPauT718GV4/fEfioqXg45Pxuq16gsxkryfwf3UwkiYAXb/nMNVrkG8Z\nQo4oSvp89AFeixYSd+ws8gvn8Zn9GeqlS5D8/UlYvcFqWqsryC9dQHbjBkYH5Ydzw9q1CSnJFr2Z\n8hXRDhth93zVv2sJeO4Z4nYesGR0eUjzR/3n72iGDSH24AnEso6FTsA5NVBnFTPTG93YUsrUPPs0\nqi2b0A0YSNrYtzJy7t35+82rWmaRNPjesz5FfvsWKR996pH5cyMgwBsMBhKTdKBU5jjuteBbzBUr\nWVraPYJhgFx/VFaK3hZv3c9IK01HFKKIxmQgTuXF7KF9rapX5jeOGA3FoQMoTp3M0vRDdu0qXksW\nkTb2LbeFtPzeGYfq3/XEHTjmlvmyX5ty62b833gdWcx9Uv43Fd3gl+1PkJaG8sA+jC1boTh0AM2w\nIaS+NRF972fcsr50hMQEikVWJGXKdHRDXnX4PGfln+01QMlM9kY3VklJwfv7efjMnYVg0KN9aSjn\n+g+k3v++tju3M4WTeTX4RXLTVn7zBsrd+V+lKLt8Ca8F36Lo3QtlyTBUG9ZbHacb/DLG1k88ksbe\nIax44tnrCWonx/Lpud3c2PErn53fbXVMYcZUv2GODk9ieDlLlpQbs1GMTZsjv3bFZuGcqwjJSfiN\nHUlgnx6Yy5QlbvOu3I09gI8PxuYt8PlsBoFPdkAMCLS5eZsXpIBAjM1aoPJg6itYwjs7R3Xh6z7N\n6FStNKU0PshlAnKZQCmND52qlebrPs3YMbJL7nLIfn5oR40lbv9R0oYOx3vBfMKf6ZFrIoMjxZXu\nokjG8J3V08nrI5d6ySJ8P/0Y+ZXLSHI5UuPGmN8Yi6ma400SCips47F+ngYDQlISQlIisuQk2LyJ\nDgmJVEtNYNCtc9RLiSVGqWZRiQh+KGnJlc/PL35+4/3VHOQXz5M2YjRitv0Ae2RpbN7zabetx2/c\nKNTr1pL84Ux0L77s8E1KdvUKmuGvoNi/F+3IN0gd/45z/QqcIHn2V4jFQjwyd2bkMhm965R3mxCa\nFBhE2oTJaIe8ytzP5tH6yGkqaZP4vnQ1q+N3nr6Yb0+2RTKk47XgW/wmvknMzdhcv8iuxJazo1qz\nCtWGdRhat8UY3QpNeEnA8cdKd6zBFRx9nK3rI/BJUBqNAlXIkhLxMmgREhPRaoLQjnwjx3jF3j0E\ndetgda5kuZKNwaX4qWQVVoWEY5Q93IAtGxLEwdkT83ZRbiBzWEB+6iR+700k+dPZTsWSs+O14Ft8\nZ05HiI9H36sPaaPGYq5q3QBkJ7hxHQxt2pLy8Wcuv386GR2hjp0GcK6wS5II7PwEsrt3Sf5yfqEU\ndits3eYajJzGmJ2r6Bx7ncjmfa2OceZ7/7jjVSbSvWTTobOMMZtpO2wy1evVtOsl5+ZVhhq0xMyb\nR43bl5G8vEj5dHaOMYbOXS3Sui7iqF5OeCsHDL5ej5CUhCw5Ecyi1R6hshvXuTrubTSXb/KNQUvA\ng/8u+xejc5dROee8dpW2X0wDsDSmCAgATQCK2taLVcyVIkj+fC6iJgBJowGVCu3ggZSMvceblZvw\nTZnqVs8r8GwjK8gvXkC1ZVOedVB0g19G1/dZvBf+iPeXswn683cMXbqR9PV3uYb2jE2bo7RRf+Aq\nLlXwCgLJX85HDAlFCgh063qKMl6iGZ0sk6mVJARAKgCZkiJj8DN7ydHxtxgDGO/cZsk2nV1VSWtx\n4wCjnjevHn1Y2boNTJHV0Xft7pG1Z1+D2myiRmo8ASYDgSYDASYDmu/n4XX5WEabtszIL5wnsEdn\nhOQkhAca9QCmKlWJ37E/x/hfdp8l6vgxAlXeJCq9ue4bRKLKm0sa64/PJ4JLU/z5mSSqvHm7SyMm\nPlkfgORsXpRw9y5ef/6O15JfSX1rUhY5h2Vzf8Hnjdf5+swONCYDM8rVAUHA32QgWWEJCVy+E8Pi\nrfsLJPPIFvJbN5BUKqQQN4QWfH3RDh2OdtAQvJYsQrl/r0P7OPoePTGXKOmSAqwQHwcms8Mdvmwi\nSQhJiW7LPvqv0Lx6JdRbzegfRBqK69M4uecPBlVvzarQchlj8osiY/Aze8mH/UNo0bA7V738c4wJ\nbxUMoojs1k3kFy+w62ROQSedTM6A2+fZFRjG3LI1OBFRg9Xf2c87dtfaAcroUzm476+sazojR377\nvFWDLxYrhnbgYCSNBkkTgOivQdJorMY/V568zpij96Gn4/nNJpmc+94awNLPs3qZYHrWLf9gYTpU\n69fgtWQRqk0bLJIEHbsglsgqA9u0dlUaVm/FLbUPH1/YRyl9Gmd8A5l86SARUf1IkyvZd+4K+85d\nATwTwnIF2c2biCVLWQ0Nprfy0/fp59ykajW6F15E94JjLQANbTtgaJs1RObIno9q9T/4jx+NoWU0\nyd8scG6NBoOlIby3JUQiv3SBoKhGJC77p1CGcgorUZGVsnj491TeKCSJesmxGQY/Pwsni4zBz+wl\nJytU7AzManDeuXyYBu8fIhADiovnER60jyv21AiuZ5tLL1dQrsWzGd5UWR83tlxzgOtefjRs3JNE\nhSrjv7DiITbjfFJQsEMFKu7q5/nuygN0r22JZ6vX/INm6GCM9eqTMvVj9D17IwUXy3FOeGgwB2ZP\nZNepi8yc/QV1Th7i6zLVmWPcyas3TvNZudpZxjscwvIwsls3bapkqjasx1yxkvMGPxe8vp+HWLos\nho6dbdZl2OuRUMyg45xvPAFrVqJv14HUyR9kGXflbizr9p60ebOokBiL/7AhmOrUI+WTLwBQbt1i\nkZmoVTv723ocIS4W+eVLDnfSKkw0r16JK+JDDx9B4IhfMeolx2QZk18UGYOfWxy8Y+wNFAo5po5P\noO/9DOaIypgrV6ba2n0c2WFFOjjTD83TH0jz6pUywk4ABpmcg5rQHGPyirv6eZ6/l8Qfhy7TuXIp\n9J26Erd9n0MbkOGhwYS3Cub10914S1UCSRD4qWQV3rx6lG/KRJImf1izkJ+ZC/aQ37yB2UblpFg8\nDNm9u+59Q0lCvWY1qm2bMUXWIG3MOPTdnspSXWzvu97r7iW+PrMDH5WCpDnfWATtMn2Xr9yNperg\nyTnOW7LtAEu27uflm2f4+uoBCCuB7tkBGcdV27ZgqtcAyV/jpgt1HN8Z01GtWUXckdOFWp7bGuGh\nwQSPHsGl67fpW6oqu05d5GLxUjx5/yqzh/bN9/BlkczDt0brht14ut1zpHw+F+3wkRg6dsZcMYLm\nNXKPSXr6kcuR+d2xBlf6eXqZDPS7sI+/132Fr/Hh/sAfhy5b/o+3t8PZJunsOnUxY8NqWvl6FDPq\n+PzcbrzMpixjCgPJM78gbdRYq8fE0OLI7ru5naYgkPjH3yT8tQoxJBTNKy8S1KIR6iWLMobYq1eo\nnxzD7oAwRr82GX3fZ3MYyG3Hzlk9L8Sg5a9j65l/ZjtnmrUmbtNOTPUbWg6azSh3bsfgpmpfZ9F3\n6or89i3XGq8UAvxefoXaU/7HnFf7cXD2RPqMGEJYfAz961bO97BlkTH4jnjA1sa4ep47yW3+5gl3\naFk675uGxx3swYkk0fzOBeZt+4U7v4znt03fE6pLplRqYsaQI9dj87wegMs+GsZWbsqgW+d4+0rh\naz5vrlkLs416CrF4cWT377n/TQUBY1RLEv9cQfyajZgjKqPa9G/GYXs3w8mVGvJUnQ6stvH5bDtu\nvSHMpMuHiY6/Q+9a7figdc8sekCKY0eQJSZgbNXGxQvKG8bmLRD9NajWriqQ93c3plp1kJRK5Jfy\n36kpMiGdqMisYRFbY7ITHhrMgVkTClSrxt4aWlUszZBRA5HGjyBxyV95KnJxtAfnrF1LGHlyM9d9\ng5hbow0/V2nKuWx7IreT0lxeR/YQ1uzwWmwNKslHF/bROPEe+wKKF8oUzeyIocURYmMsm5seEnQz\nNWhE0i9LwGTCZ+aHmHOpBbClqJqOLYP/bqWGzChXh1tevpTNdkOR3buHqVIExoKKoatUGNq1R71m\nNWlvv1swa3Aj5sjqxFy+7bGCNXvYNfhGo5HBgwdz9epV9Ho9kyZNIjIykkGDBiGTyahZsyZffvkl\ngiDw7bffMn/+fBQKBZMmTaJrV9fz0l0hL556emy5IGPG9taQ+v3PBPTpgf+4USTP+srjccwfqjZn\nRbk6bC5VFdEDTSus3ZyvevkTYDKw6eA/9KndjqhI60UqhQljq9Ykz/nG0hPA0wqeCgXKg/tR7ttD\n87b9M/5+ve5eYmNwaRKVWZVJnb1hJitUGemx2TF07GzZQC5ADJ264vXXn8iuXikUXcDyhExWIMYe\ncjH4v/76K6Ghofzyyy/Ex8dTp04d6tWrx/Tp04mOjmbYsGEsX76cpk2bMmfOHA4ePIhWq6VFixa0\nb98eVT5eVGHw1D2FsXkLkj+bg+b1Vy3NFMaMd2meMD9vbjngmR8Jyb2itKTGJ9cxtrBmjBKUatrV\n78qS4xtZcXQdN862hVaNkJ84jhQQkKcqV09hrhiBuWJEvr2fsWlzfL74lBbD3mHJtgMEG3T8eXwD\nSXIlX5atwefhtbivsqRR2trzia5VmV827rX7PoXx6crQtj3aAQOtNqV/jOPYNfh9+vTh6act+h2i\nKKJUKjl06BDR0dEAdO7cmfXr1yOXy4mKikKpVKJUKomIiODYsWM0bNjQ81eQicLgqXsKfd9nSb18\nCd8PP8Bcrjz6Xn2cnqNWqaAMg18uOYYP9q9gQuOnuGGlVWJu1C2bM/XSUezdnK8M7U/C799RftJ4\nUrQpqLZvQ3lgH6nvTLK0yctnLfzChLFpc4S0KbTFEppLUKrQCzI0ZiMjr51g1LXjzC8dySflats0\n2o4Y/AJtqGMDSRNAymdzCnoZLuH1/TxMNWpjaupgS0QPYtfg+z5oyZWcnEyfPn2YOnUq48aNyzju\n7+9PYmIiSUlJBAQE5Hj9Me4l7a2JyGJiEINce1LpUTOc3ccu8M7hNYw+sZF4lQ/fJ0W5ZPD71M9b\nkwd7N2epTRNSy5dDeXA/Sd/+gO/0D/B79x3Uy/4g+dM5mPOpe5DPZzOQnz9H8tff5cv75Yaxbn0k\nlYqyZ09yYNYErv+2BPVGkV5tn+OiJpj/xV1i2P4t9G/VCJmNp9no2hapjXpJMdRIjeO3sAjM2cJ2\nhdHDf5Tx/XQG2sEvF36DD3D9+nV69erF8OHD6d+/P2+++WbGsaSkJAIDA9FoNCQnP8zvTk5OJijI\nfkd3hUKeIXRU1FAoLF6oR67v23m4FEwxmXjpzFae+X0yPnotM2t3YEadjqSonNeIqVI8gP6NI5BE\nD+rufTgdzGY0cjnM/wbjwAEohg0jqH005ikfII6zHdYyiyK/H7zMH4cucfRGXMYGc0mND3XKBNOn\nfkWeaVDBpgJo+uenOHMSEhIKz/c0wBupUSN8Du6l1tvjqXt6P1KVqixe9cPDfZ3ERIJMJrCx5mLF\n/Lj401RMAwcSeP4EO2o3QRIEomtVtvxXuwrlw1x/eitoPPrbcxHBoEcd4I8y+5ru3gWTCUpbL+yz\nRvr1uYpdg3/37l06dOjAV199RZs2lpSsevXqsXXrVlq1asWaNWto27YtjRs3ZuLEiej1enQ6HadP\nn6ZmzZp5WthjcufK3Vi2HTvHtuPnM7IvbP5wr15FOW4syU90pm5wU5e8erDYlak9GiGXyTCJZndc\nhm0yhW+kqBYY9x9ANnMGlCtn85S/jlxh0ooDXLiflOPYjYRUbiSksurEdaauOczU7g0fSkRY48Z1\npEjHJa7zA/Mnn1qEy2JikK1Yjvn9D7Ju4md60s7BuXNQPZLy/t4Ie7Yjjh7D2XdzFmFlEB+PbOEv\niP2fBXdoCf1X0etBnXM/U9muLWKbNphn51+oyq7Bnz59OomJiUyZMoUpU6YAMGvWLEaOHInBYKB6\n9eo8/fTTCILAyJEjadmyJaIoMn369Fw3bE0mc6GRMHU3+SHRaqu8/peNezNitFn0aEJKIdt/DN+S\npRjsZGu3zLzboS49aoejNxj5cftZ9+vo58brD0KKVv62zrSsu3A/iX7fb2Jyx5wt69I/P/m16+ii\n25Bm53P0nv05yOVoh4908ALySCWL0qj3N3NRShIJ3Z9GcuB7pji4n6DObRE7dkIKD0eWkkJCt96I\nds5VrVpHwLixxLbugKj0ddsleJLCJo+MJBGq16OV5Oiyrcm/eg3kBw85tVaPyiPPmjWLWbNm5Xh9\ny5YtOV4bMmQIQ4YMcXkhj3GOzMU3dZJjOOpXLEe6ZnY9GrFkKYAMA+dqP097XvStpDRuJaWx7sxN\nPtl8gokdcmkL5wypqfiPeo20tybmkH3+cutJpqw/6nTKavrfIEefUoMB2f17iKXK2D1feeSQpTdA\nfhn8B0hKFbrnBiIVL+7QeFOdeiTNnYf/nM+RrVsLgPzaVUvDbRt/M9W2LZjLV0AMt/1Eld8IiQlo\nXhpI2muvY3yiXUEvJ3cMBuCBrHg2TDXroF6/1qN1HNkpMpW2/zXSy+srpyZwYN9fTLhyGLXZxFtX\njvDjyc1ZxlhjRMtIvu/fgorFcheGqxTiz3f9WjCiZSRzt5+m3/ebrBr77FyKTeal33Ywd/tpB6/K\nPrKkRBSnTxLYrQOKA/syXl958jopn3zCqrVzCU92vgJ4yrojrDyZTULv5k0ESULMJb5qqbZ1s56O\nA+heeoWUmZ87foJCgf6Z/hhXrc54KbBPD7x+/dnmKcptmzG0bJ2HVbofSROA/PJF1KtWFvRSHCZt\n5BuYq9fI8bqpVm2EtDTkly/l21oeG/xHlHQP/7xvINPL12PaxQNc2rmYqRf3kyRXIRfFXPVonO3n\n6UzIJDNT1h1xi9EXS5YiYeU6zBUjCOzdDdW/azMUQM8FhFE39jon/3ifUcc3IHMyX3v6v0cxZz6n\nTBnitu3F2Lip/TWFFne/gJonKVEC47K/iTl/jcRFf6Dv/pTVYbLr11BcvoShVev8XV9uCAL6Tl1Q\nrV/zaOTkq9WkTnoPU+26OQ6ZalqURxXH865g6yhFRlrhv8z/KjYgxKijhD6NCRGNOevreDciR/t5\nrjx53eW4P1iMfrlgvzyHd6TgYiQsXYFm6ItoXujPoVGTuZRSgkvl67C1VBU+2ruML3b/wXMX9jEk\n+nmOFXPs/S7GJPP38WsP/w5KpU0NncyIxcOQxcWB0QhKZa7j3YYoWkIBzr6nUonUtStSohZDu442\n51Zt2oAkCBijovO+Vjdj6NQVn2+/QXHk0EOBt0cQKTQUQ4v8/fs+9vAfUbLkSgsCw6u1oHedDlmM\nvbvyqd2lo5/Di3YVHx+SfvgVXf8BSFs2WzpBAUkqb15r+Rwtuo/Hz6jnkz1/OjXt8uPOq4mKoZYY\nuizGzaqZdhCSkyhWvSLqFX/lOGYWRZYeucLzC7dRd8ZySk5eTMnJi6k7YznPL9zGb/sv5voZqNat\nwX/8aMyVqyD5Fr7NWmPT5ogBgajWrs59cCEncdk/bm1OnxuPDf4jSn5JKoP7dPTTvWi3oFCQ8uls\nBrUelGPTcWeJCOr2nsTzbRzrKJXOMUfVRDNhrN+QxAULEfNRJ17y1yAGBuXoc7vy5HWiZq3mtaW7\nWXfmJreS0jCLEmZRythIH/TzVmpPXZZzzyIT5oqV0PXohfz8OYIb1sL7y9mQkuLpy3IcpRJD+46o\ndu8s6JU8cjw2+I8o+Snr7IqOvs253GXwAQSBW2kGq4cMciV3faznpDe9exFlJu39dBxVE82MVLw4\nhie7Z5ET9hTyc2cJahOF/NIFS2Pzvbsyjs3dfpqXftvh0I35wv0ku5vp5qrVSP72R+J3HsD4RDt8\np71HsQY18jXWnBsp0z4m4a+iIZecnzyO4T+i5KdYnMM6+g7gihftTkqmJrB7+QwSlV6sKVuTKE77\nzwAAIABJREFUFeXrsKZsDRLUhSt0Ya1n7VfXDtH26hWuqHyIaNoc70W/IMTFMufkvVz3V8onxZCk\n8iLO6+GNyWZK6gPMEZVJnv01qePexvunBZiqFp4iNMlFeZH8RnbjOuo/f0f3/CCrrT/zm8cG/xEm\nv8TicvN8S6fEM+HIGlrcuUDbrmOI8bad6umKF22P7AqgAfo0vt6xiHFNe3PLN6e8x22fAOr3mkj3\nK0fpfvUoizZ9j0mQ8WtEYyb0GJ4xTlGvLl4vvoxu4GC3rtcRrBXVKUUzTfZvZ36JCEa/+RnHxj5H\nLeDw0n+Yci13VdpP9iylXEosjXpl7YvsyGa6GF6O1Hffd+la/uvIL13Eb9r76Ls9VSgM/uOQzmPy\nzJPXjtHv4n4qJsXw7qH8fcyuVSqrUQ/TJtHyznl2LZ9BtfjbOU8QBA6HhPN+w2406D2J8Gc/ZGTz\nvuwKq0Tt9Lm0WmSnToKiYPwha+m03e9fJdSo4/tSVQHYkmzEVDacXVvtN/0BCNKl0u3aMX6LaGz1\neF4209WLf8Vv7Ehk+ZhL/igh6B+0BfWyrVmlOH403zagHxv8x+RKmJ99IaoFVaOo0H86H9btxLBT\nW4lItJ2XnttcztKjZlad/HOBJWje4y1SFWp2rJhJ07v2axGu+wXzdY3WzK8eTY9aD+a6eRMAc6nS\neP20AL8xIyw/yDTXu3w5g7WCuZdunWWfJpTj/hYvceeZS3w3fznvVWie63x9Lx1ALokssmHwM2+m\nK/buIahNFLJbNx1aq2AyoV69kuBm9fF/7WXkZ884dN5/Bv2DSltVzkrbdNS//4bfpLfzZTmPDf5j\nciXdiw7SpaKwIphmlCtIUnnzee123PXRMH3f3zbnql3Kvoqqs/SsHZ6jWvi6XzAtuo/nbGAYG//5\nnCev5r7ZWCnEn6ceGHzhxg0AxNJlQBRR7tpBwAv9CKlWHs3zffH65UfE2NiM9MfZ/V5jUdueWdIf\nlx654rLXnN3DV5tNlNMl812palnG/H3aMaM88Nxu1pWpwR0bm9jwcDNdtXUTsuvXEIuHOTS3bsBA\nYg+cIPX9aSh3bCMougmaFwcgJOWPPLrszm2Umfr9FjYeevi2Db6pZm3k164gJCZ4fD2PDf5jcqVP\nhSD+d2All3+bwMBzu22O0ypUvNriOb6u3srmmAwv2k3IZTImdqiT4/V4L1/adR3Dv2Wq0+n6Sbtz\nCAJMaF8nQ+hNuGFJWTSXKo3uxSHE7zlM3M4DpI6fgCw+Hr9xo3h5xqKM9MeQe7foeO1ElvTH15bu\nJmrWarvpj46ilyuo0bQPCx6Ec9JxZDO9SsIdmt67zM+V7VcMp2+mq7ZtwRjV0rlwlq8v2qHDidt/\njJSZX4AoIuVTmqrX4l8JGPw8aAuJWFp2DLl7+BkVtyeOe3w5jw3+Y2yTkoLPF5/w4otdeefoWn6s\n2pxV4fabj6wqV5vNpatZPZbZi3Yn3WqUZXLHnKXrWoWK3u2HMrJ5P7vnv9uhbtZNyxs3kAIDH6Za\nCgLmylXQvj6aqW/NImzADFYqHm7A3fHWEKa1pEM2v3Mh4ynIWS0hITkJ9fJlNI+saOWgkKVRSfPq\nlRzaADfJ5HwTGc3y8jlvipm5m6JFSE5CcXA/hmjbN2y7qNXoXniRpJ8Webzvcjr6Tl0R0tJQbd+S\nL+/nLOZqkaSNGG23ItpcpSqSWo3ixDGPr+dxls5jrCK7dJGgru0QkpLQPfsCy7s+y+gNF1yeL7sX\n7W5sKYCaZbZVCDMrgGZGHPMG4oDnc4zP0BLyzuq93vXWEGRIo3rcLXaumEmCypvVZWuyolwd1pat\nYT/9URRR7t6J128LUa/8G3Q6un7xA0tyud6oyEosvWV/fwLgkiaUYS2fy3UcgHL3TgSzGWN0G4fG\nO4t6ySKkwCAMHTq57YZgrloNc/kKqNauxtChYButW8NUrwGmeg3sD1IqMVWrjuL4Y4P/mAJCLF8B\n7aAh6PoPQAwvR1tgstwvTzr6bpNJtsGIlpGUC/Zj2vqjuRYgVQrxZ0J7G9LNajWUKZNFc9+eltAd\nH8sNIFWpotFT79D96lG6Xz3Gsxf3YxRkLKgaxauQI/3Ra+FP+Mz6FPnVK5jDy5M28g10fZ+lutoX\nVu6y+l7pNK9eibC9t0iOiaXNrbOsDq+Fyc7NLTfC/LxRHDmMuWQpzBGVXZ7HHup/lqNetwZT9Zqk\njR6LvttTeZcFFgT0nbri9efvpDwKYmo20A0YmC9aTIIkSR7sU2cbg8FUeJoUuJlC14TBjTirmGnL\ni/YkZlHk7+PXWH78GseyNWepXSqIvmV86bt0PqnTPrZ0j8pG9s/PLIpEzVpt8yZSL+Yah5ZNo/FT\nb7O/+MNev+WSY+h29RjJSi9+qtqcSiH+7BjZJeMpx/vbr1EcOYyu/wCMzVtApqcfa4VX2Yvqnl+4\njeQtW9m5YiZNnnqbfcVd7zPcqVppfh4QjRAX67l8cUlCuWsHPp/NRLV9C6ZKEaSNfAN9v+fy5PEr\nd+8ksEdn4lf9i2+71kDR/O2BhxugPKaIYzTi9ftvIIronh/k0CkjWkZSvUywzQYomannK/DD3f2U\nrtuV/PQqclMAVRw+iHrdGpTHj5L425+Ipexr3uemJXQuoDgdO4/kXEDWzJar/iHMrdGGUJ3l3ByK\nnKKI5OWFkJZqaYPn/TBl1ZGiuh41wxl9shw6uYKWt8/nyeCnb6Z7tDhIEDBGtSQxqiWKg/vx+eIT\nvJb9gb7/gDxNa2zUhLTho5CCH43q24Lk8abtfxGzGfWSRQRHNcR/zAgUhw86dXrPuuU5NqlXrjr6\na59rRu0/f8Z7zhceuhDXMNVrQMKKtQgJCQR2bY/83Fm743PTEkpVerG+bA0S1Q/by4dokxl9bANH\n//yAvX9/hCBZwg1ZtIQkCdXWLQQM6GtJ+XyhP16LfnE4Pa9n7XDKFA9mb/EKtLzzcH9FLpqpknDH\noTnAc5vp9jA1aETSL0tIXPh73idTKEj93weYK3kmFFWUeOzh/5eQJNR//4nPzA9RXDiPvkMnkr7/\nGVMt+xkc1nBUR1/7ymv4fDMX3aCXcvWk8xND1Wr8OvNHWo0dgqZda3p1GsHuEpUI8/WiXrkQ+tSv\nSMeIEshlMse1hCSJrteOM/jsTrpdtWzArSxXmwVVozKGZNYS0r46Au3Q4cjPnkG1bjXqtavxGzMC\nY+OmmK2EmrKTnpK6fW0Ew05tQ5BEJEFG34sH+GXzD1Tu9wGXNKF25/D0ZnquWGn9B6DauB5jw8ZW\nQ26PEqoN6xDu38/zU4y7eOzh/5cQBLwW/oRYNpz4NRtJWvi7S8beGdJGvYHk44PvR1M9+j7OkC4j\nPHDbZep1HM3JgBJ0unIMsyhR/fRBFo3txeQvl2Xk0Tus/yMITDq8msqJ93izSW9KDZhB7w7DWFWu\nNpJg+anlmEsQMFeLRDtqLAlrNhJ74oL1TVNJQrlnF5iyqnx2q1GW8K6dKKZPJTL+DoIkMvHwGtaX\niczV2EP+bKY7TVoa/q8OIbheDXynvodwP/96Dbgb1T8r8P7xu4JeRgZF1sN3ZNPrv0jiL0vAxyf3\ngW5C0gSQNvYtfCe9TdrQ4Zhr1My397ZG9k3n9AItw4NskbIp8WiMOu55+6N7kEfvzH5i586vk6Dy\ncXkTUgq1bqTlJ08Q2L0TYmAghrYdMHTqguGJdkj+GroMfprDO9YjCgI9Lx+hesJtXom271Fm3kwX\nYmKQ376JqUatLBvHBYaPD/E79uH91Ry8v/sG72+/Rvv8ILSvjSxUT4mOIOh0SGrbOjqZURw7gtfP\nP5Ly8acea2peJA2+NbVBgCXbDrBkm0Vs6sCsCUXX6EsS8ssXMVeMyHksH419OtqBL+H13TxUWzah\nLUCDbyvDSK94mA5XNjWOGLUvOsVDBcrseWxBulTqxV5jU+mcmUe5ySy7qiVkrl6D+DUbUa1bg3rd\narz+/B1JqUT74hBSp35Mmd9/Y/yJazTu/yRbSlZhZwkrn/0DKhfX8Hbb2hmevXrFX/hNfJPYs1eQ\nNLblF/ITMawEqe9PI23kG3h/+xXe381HFh9P8pfzC3ppTiEYDGCnyhYsWWB/HbvGjaWbmfbzAhrq\ny3E2qCRhft7UKhVEj5rh9Kwd7pawW5E0+Lk1704fE96q6Bl85Y5t+H40FcWxI8QeOIFUvHhBLwlU\nKuI37siXJiG2cLQnb9mUeK77Wf9eBOlSGX1iI6OOb0SrUBH+7IcY5Zaf0OAzO+hy7QRPd3jV7vwu\nawnJZJgaNMLUoBFpEyYju3IZ9fo1iCEPnwh63zlNwN0rrPx4Pp2UpaympPZvEkGf+hVISdZnnKfa\nvhVTvQaFxthnRipWjLS330X72kiE3OQTDAYUbTohvjgYejyTPwvMDb0OyY6OzsqT1zPqRkK1PkwD\nat2/zqmAEtxKSsuQ6vhk8wkmdqjDgOZV8rScImnwrakNWhvjaR35/ESxZze+M6ah2rENY83aJH37\nk83wQIFQgMbemZ68ZVLjue4blKHxP7bp03ibjBmGXiWa+bp6NDPqdMww9gAhuhTa38xdQsFdWkJi\n+QpoX3kty2umWnVIeX86TQf1pc3sz5Dfv4GhU2cMUdEZ8rzpNQYZmM0od2xD+9IrblmXp5A0ATZv\nSLKrV7jio2HXqYt0vn6Hy+99xEsbzxeKEK6gNyBprOsKZX/ivO+t4aZPIPVir7EkIqttSpfpuJum\n550u9VxeT5E0+I56+EUF71mf4jftfUyR1UlcsBBDlycLRyy2kOBMT96SaUnsKFGJ6gm3efHsLmrG\n3USrUBF9+3yGobfWOvGOTwAaow5vkwGtwnpDEk+nP4phJdAOG2H5hyCg2vQv3j99j+Tji6FNW/Qd\nO8OzfcH/obqo4tgRZIkJGKNbe2xdnkR+4TxBUQ3ZG1yGxRXqcVMdwuRLB4m5e58lMfEFHsLV9+yN\n5J0zjGcrvHg4pCz1YmwL7k1Yvh+FXMb4jq4lWxRJg5+dqqkJnPfRIApF0wgaunYnKbwc+h69Cr2h\nL4jNdGd68tbrPREvswmtQkW7rqNZue5L1GYTLbuP42BoeZvn3XmgrxOWlsQVTUiO4/md/qgd+Qba\n18cgP30K9brVqNatxn/Uaxg7d8hi8JXbtiD5+GBs8Gg+7ZrLV+Df4W9R/odv2HlgBXdU3viIZtrH\n3mBF8fIZ4woqhKt77oUcr9kLLx4uVpahp7dbNo5sbPy/uWyvywa/cFsHF8ncvDvEoOXM7t/pdyeT\nRy9JtKn0aO3228McURl9z6cfCWPfcNR0Rs5bwtqNO7keE8/1B17YyHlLaDhqOtfux7n9fR3No1eZ\njUiCLMND31UigpbdxhOn9uWv9d8QGX/L5rl3Hxj8ElrrOvD5kf6o3LIJv7fHPnxBEDBXr0HamPEk\nrN1M7MmLEJ71CUMsUxbtiy+jPHwwR8rnI4FCwYLiFanZtA+9a7XjtsqSlLD82PoswxwJ8+YHuYUX\nf4toxCvRAxA8VJteuC2Ei0RFPjT4TRLvAbAnU9n7mGvH+WLBx8jPOCZbWxiQnz+H/9AXkV84X9BL\ncZl0j77/nQtc2rmYEEPOTThPhNocyaOvHncL/fcj2PDPZww5vZ0acTcRJJFTwaVo1uMtElXedL12\n3Ga2ZbqAWrpMcjqCAJM75o+WkOzuHbwXfIsQG2v1uBSS88lD3/sZ9J2fJLB7J4rVqIT/8FdQrfwb\nIcWxEFhhYNepi0iCwLKwitRv0osTvkGsLlY2x5jCQG7hxdNBpVhevm5G3Ya7KZIhncweftPEe9xX\nenEpU2PtVSHhTBNj8er0BEmzv8LQvWe+rs+ZsIbs0kV8P/0Y9Z+/I4aVQHbzhsfUDD1Nupe1Ibg0\nSknk3cuHGJWpCjV9TEFspt/10bChdDWqx99m3vZfkSGRqPRidPNn+LFqFE2eeps0hQq5IDC/X1QO\nRc77Xv606D6ek0ElM16zq8jpJuTnziKLi8XYtDnGppZ2h8q9uy37OA5iatCQ+FX/ol63BtW61Xj9\nsRhJpUL76ghSJ73noZV7CEHgiQZPEmAyWD+clFig2UjOhBc9QZE0+OGhwRyYNYFdpy7S5s1tHA0t\nTdnQ4CxGNdVbiWzUcAKGDCRt+CFSJ/4vX5pWO1ojUE404vvRB3gt/hUpuBipH3yI9vkX7TZDLuyk\n39zuq7z5uFwd/nf5IJ+H1+JKJn15T3hiYX7e3Eqy34821suP9l3HAOBv0NL43hWa3bvEiSBL6C9N\nqc6Yq1uNsvRIvcmGW2p+SlJy9E4id1O07ClVmTA/b5qWCqJHrXCequWe3Gl7WFJwjxK35xBieDnM\nJUuh3LPLKYOPXI6pURNMjZqQOuk9ZJcuol6/BnPpQlaBa4Pm1Stl/HbA8v26r/LOMUaxZzdB3TsC\nkDZkKIYu3TA2bgoq65vsnsBhmQ4PUSQNPjxQG2wRQLF7N6gw6g0Ojh6X5bgEJH33E95fzsZ36v/A\naCB16sceX5ejGUTlq5ZBtWUTqZPeR/vikAIpmPIkuwPDUEoSxQ26LAbfE9QqFZSrwQfwNhnQyRUk\nq7zZWCaSjWVyhmHS8+g1k9+h76GD9PHXYKrXAGPDRpgaNcbQrEW+fVbyM6dR/7Oc5E9mZTgrxqbN\nUO61r6WfG2LFSmhfHWHzuM9HU5HFx6Hv2MXSDtGGHk5+ERWZ1eDbGiMVe+jZ+3w3D5/v5iEJAoZO\nXUmat8CuM+VqsoH3nC8wNo/C9GBT3FZ4US6aCU+Jo1LSffaHls8ixOdOiqzBBxDi4jDVqYuxSTMb\nAwS0I0ZhqlMXcwUrbeUykV4Nt/zENY5nK2hxphrOmRqBuAPHPVZiXRBk9sT63r3IVS8/9mfTe8kc\njnMXPWqGs+5M7g2/5+74jciE2zR/6m3bcz1Iq0z8YznqZUvxHz8aZALeC+Yj+2wGsXuPIObyXXIX\nPrM+xVyyFLq+z2a8ZmzSHPWKvyElxXO1DzIZqvVr8f7hO0RfP4xPtEPfsTP6rt3B136lsSdw5DvT\nvHolzKHB3L+XhPz8OYs08x+LESTJ0lowF2PvauW+78zppE78X4bBz8y4o+tod/MMlZLuUy45FuUD\nRdV2XUZbdTbcQZE2+FJoKIl/r851nLGl/R6emavhsuNsNVx2D19jMhBi0HHJx0pYowgZe8jqiR3w\nD+WIXzGkbLugmTfc3UXP2uF8svlErrn4ZVPjuW0lxz6dzHn0kr8GSaNBksmQvH2IPXIG+a2biOWt\naNKLIppBz2KqXhNTo8YYGzRCCnSs4taWZ9kl0Ivn/1pK6pTpWTxsQ9duJFaLzNXrVm7djHrNP6RM\n+dDpkEbamxNIG/8O8hPHH6R8rsF/1GsYnmiPVAAGP3MId/+FK2w7fh5RlGx64ObKVUj+cj6pb03E\ne/5XpL010eq8imNH8Pl0BonhVSitS+Gml+0b6K5TFwmPDrLoEl25hPzKZeRXLiPodFlaF2YOL4bo\nUtDJlawoV5uLmtCM/67459xcdxdF2uC7A2c6PGWuhhvbzn6z73Q+Or+Xytok2tfvmpdlPhJk9sS+\nteHBeMLDT5cRfum3HXbHlU2JY13ZGlaPWcuj1/d8GsnbB80rgwh85ikSf1lsNXdaSEoEkwnvH75F\n9tkMAEyVq2BsEU3Kx5/ZXI89z7LFmR3cl6u40akHmSPtYlgJxLASdq8TQP3PClRbN8FHn+Y61iqC\ngLlWbdJq1SZt3NsIMTFWs4AwGFAcOYypQUOPOjDpDWOGdo8GHOt4JYaXsxvGFVJTkd2/R+u1q7gh\nSRz3DWJNSFkWh0VwOFutxc7TFxny9094//rzw/n9HzhxhocyFpnDi2836e3w9bmLxwbfFqLIqeFj\n+M6rKvg6p38yYfl+AIY0yilglWWDSZLoGnONFaHlcowpimT2xPJbxbRbjbJM7ljX9s1bkiibGs8N\nX+v667by6A2dupCwdCUBA/oQUrU8YkiIJd89k+GXAoNIWrTUImp38QKKA/tQ7t9nWxtGq0XQ6+zu\n97wT0ZiFJSvz3OVb9At3vqZEuX0LhpatnT7PFlaNPaDctYPAZ55CLFYMQ/tO6Dt2wdCqTYFKbTiC\navU/qDauJ+nL+bT5aAE1zp+gc8x1Bt06R6zSK4fB33XqIrrnBmB4oh1i+QqYHzzphVQqg6HTQ2fO\n0fCip3hs8G2wact+Wqz5i0OSmT7tXmF7SedEiyYs30+YjzqHkcgc1qialki4PpV1xXKOKao40rrP\nU6Tnwlsz+kH6NHxNBq77Zr3hONKT19S4CQn//Etwi0bIYmIQUlOQ/PxzDhQEzBGVLYVy/Z6zOZ9q\n0wYCXnyOXiEl8FVq2B0Yxu6AME75BmWEwFIUKvYGhFHelTTWq1dRXLpI6oTJzp3nAsaWrYhfsS6j\n2tdr8a9IajVpo8aSNs72XklBIyQnoV69Eq9ff+a9spFMKlmdxSUiECQJlWi2eo6pSdOsc8TEACBl\nUst0NLzoKR4bfCuYRZEJR++T2msCv2+Yz8Z/Pmdssz7MqdHGKZ3z6f8epUtk6SxhgMzee8fY6xgE\nGZuDSmU5r6h6+IWBES0jKRfsl2NPJlSXTJLSi+t+D5/mnMmjN1epSuKChQQMHoDs3l3M1gy+g5ga\nNiJp1ldsnTWPhveuM+j2OWTAPyHhdKvTMct30JU0VtnmTUiCgDEq2uU1OoxcjqlpM0xNm5H6vw+Q\nXziPat0azFVcU33MLVumVoB7Kuj1fZ9F/2QPvBf+SOsZH3Pi6kn+Ci3Pq5EtiVHl1Max+ptVq0gZ\nM47Voh8/LdyWkewhZdfbdpI89HsvugZfuXkjgsmIoX0np8/NqIbzCaDtk28wc89SZu9aQpN7l3k5\n+nmb4ljZydG0mqxhjagJuzgQWobgEsV5shAo++ULdjRC8otuNcrSJbI0fx+/xvLj1zh2K56LspIE\nvzSbMF8vniwfSp/6FehQqYRTefTmSpYQnnDvPljrReAgYlgJ9P0H8Pbuq1yPicffZKBx4j0O+4c4\n97czmazWlgibNmGqVQepmAcbltvAHFEZrZ3CQd/3JiHodZaUz+YtsmwoO5Itc3bBFMqHuem6fH3R\nDh3O75XqcmzKNPrevUSCwvpmuLWn8hXXEpnmVZ9L++66Zz0P+LhnE5fPLbIG3+ebuSAILhn8zNVw\nJpmcMc37sj+0PIPO7cbkZMnz8mwGHx6GNfxrVcPUoBEHXx7m9BofRYS4WII6tiFpzjxMTW2kyuYT\n9nrypksIO7Lxlxkx1NJ7QHbfPT/w9P2eZIWKjcXK2BxjDb/Rw5HFxZL08+Icx8wffkTqxatuWaPb\nUShQ/fUP3t/PR/TXYHiiHYYHKZ+OPM1sO3aO8u3d+91qWieSEWWqM79MdZtjsn8OziR7OIogwLTu\njVwWToMiqqWDKKI4eMBlBUBr1XCLKjehQ5dRWTTQHeGYncq65G8WoP2PGHsA9crlyK5fQ6xgJXWx\nCCAFByPJ5cju3ct4TX76FD5ffJKzbZYDZPcah9w8Tbf7V+yOSUcsUdLSA1cUcx4sXRpTHdc11T1J\n6qT3iDtymvgN29AOfQ35pYv4jx6OYDY5VMOy7bj7tabSn8pnD+1L3+iGlA0JomxIEH2jGzJ7aF8u\ndKtPxME9GZ+xJ4x9pRB/vuvXwuHsP1sUSQ9ffuE8sqREjA0bu3S+TbEtF0IRDjfA/g+g/mspxqho\nh9IGH0lkMuI3bEcs89AbV+7chu/0KciuX7OkYDoh35HZa9SYDMw8v5cfS1Zh5QOZZrkoEh1qfa/A\n2LQ5vp/NQH7mNObq1lNNCy2CgKl2XUy165L25gSE2FgkP/8cHr5CFKmgTeJ8pswqTxh8sJ9s4P/K\nl3j9vQxTZA22Pz2Iqbf98qRcKxNAEISMLmXulOkokgZfcdCSFmmq38Dj71U8LYlAQxrnAouoEXMT\nsls3Ue7eScrncwt6KR4le5N23ZBXwdsHv3GjkN2/R9I3CxyWXsi83xP6zRx8RBOL6rWkb8N6REVW\n4pnlvxDywjMkrFyLWDLrxr+xYWMkuRzlnl2PnsHPhq29hp73L/P78Y2sLVaGOWVrsqZYwWj/JM/7\nAd0Lg/H+fCZtPhjP6YDifFSnEz9VaYbogpGuUMyfHSO7eESHqUiGdJQH9mGqUhUpwHpOdW4402j6\n3UOrOPLnVEYf24DMyuOzq02rixrqv5eBUom+a7eCXopVZDdvgMG6wmJe0T33Akk/LUK1dTOBfXog\nxDuu+R8eGky/htV55vA2zM8NZNV3HzPn1X70a9UIxag3wGggoE+PjBTADPz8MNWqnWddncJE9jj5\nypByDI6MJkyvZdWRtZzbtYRpiZchISF/FyYIGFtEs+DdOTTt8RZnAkrw2qktVEq6z8RDq/Az6Jya\nLj3ZwxMUSYNv6NCZtNfHuHx+LScaTb/VpBffVYvi8z1/sOWfT6mUeC/LcZebVhcx5BfPY2jX0eWb\nsEeRJIKb1cd7wXyPvYWhQ2cSlq5AfvE8yh3bnDrX+5cfEBITSXt9dJbXxXLlSVy6AllcLAF9e1oq\nejNhbNIc+c1MRT4pKY9mk5MHZN+v0MkV/FC6GvWb9CKqYXcOaELov3YpwsYNBbK+5SeusTesIj06\nDSe6+3hqxN9i6oEVeJuddySWPzb4jmPo2Bl9JkEpZ+lR0/G+o2lKNSOj+vNE1zGUTYnn6J8fMOzk\nlodzWelh6vXj96g2rHN5fY8iKZ/OJunbHwt6GVYRYmMRdDrMpa1nwrgLU6MmxO05jKHbU06dp165\nHH2vPlZ1esyVq5Cw5G/k164S8GwfSE3NOJY6eQoJ/zzs/OTz1WyUkVVd2kAuDNisTxEEdgWWoH+t\ndlzZfQCpe4/8XdgDMid7aBUqvMxGAHRyZcbr0bfOEaDPXbnVXrJHXiiSBj+v9KwdTsVizhXObC5d\njVpPT2ZhRBPCUyyP7FabVosivjOmo9xpX9elSKJU5j6mAJDfugGAWMrzbS8dFU3LTMIZz4p4AAAg\nAElEQVTfq0mZ+pHN4+ZatUn8bSliQACClCmsmO3vrdq2BaluvQKvg3CV3LJlDsyaQJk6Na1+z4Tk\nJLznzkKIs94NzB1kT9BQmy1PU/oHmX0K0czijd9yfsm7hKVZb4Vpay53USQ3bfOKo2Jb2UlRefFq\n9ACQJJtNqxUnjyOLuY+h9RPuXPJj8oDsQdhDdIOHr9yyCf9xo4jfsM0l4259UiVSkP1iPFPDxiT9\n+ofN40JKMopDBzB/4qJYWiHBVWkOxYH9+H44Bd8Z09D16oP2paGYa9X20CotpHv4BpnFzJpkcpr0\nfIfjf7zPxMOrGRnV36Pvb43HHr4N0sW2XEIQmNa9kdWSfOXmTUje3rY1+h+T78hu3UBSKDIKp/KE\nQoH82lVk9+87fsqhA3j9tCDv720H5e6dCCYT4hNtPfo+hRVjm7bEHjpF2qixqDb+S3DbFgR264hi\n7x63vUf2BA212YROrsjyRHXdL5iZdTow9PR2yifFZJ8iA0mC5xduY+mRK5it1VK4iEMGf+/evbRp\n0waAw4cPU6ZMGdq0aUObNm344w+LV/Htt9/SqFEjmjVrxqpVq9y2wIJkRMtIp42+IMD0Ho1yFEgo\nd2xD/dtCVFs2YmwW9Ui3KixqCKKIqUYtt8j3isXDAJDdv5fLyIeo1q3Gf/xofD76wGPxdeW2LZhL\nlQYXNWyKAlJYGGlj3yLu0EmS5v9geRI3u28TO3uyx4HQckyv2znHuC9qtSVe7cP7B1fanEuUJNad\nuclrS3cTNWs1K09ed8sacw3pzJgxg4ULF+L3QM704MGDvPHGG7zxxhsZY+7cucOcOXM4ePAgWq2W\nFi1a0L59e1T52CsSQHb5En6T3iJl6sdu6zpkS2zLGuliW9YaoKg2bcBn7hcApI0YneN4kcRsxnf6\nFHTPDsBcqfA2Xte+PMxtFc9iqKWDl+ye4/IKaW+/C94+lgKte/dImfG5e/or6/Wo//4Tc5WqKE6f\nxtChE/JHNH7vVpRK9E/1Rv9Ub0snuyNX8tzJDnJKH+8qEcGuEjk1lVKVXkyt14VRJzbhbTLkqs2V\n3mdjcse6THyyvpMXm5VcryIiIoJly5ZlKLwdPHiQVatW0apVK4YMGUJKSgr79u0jKioKpVKJRqMh\nIiKCY8eO5TKz+1Hu34v633VIAe7tSt+tRll2jurC132a0alaaUppfJDLBOQygVIaHzpVK83XfZqx\nY2QXm8qKqZOnWLwKwGfuF6iXLnlksyUcRblnFz5zPke4b/vRtaghBQYhKZVOefgIAmmjx5E06yu8\nfluIZtCzBPTuhmr9mjytRfXvOjSvv0pQxzaYIiMtN5LHZLDy5HWiZq3mtaW7WXfmJreS0jCLEmHJ\ncSz55T2KrVzGqCXbHfawnUn2mBcZTfU+7zksxAgWWe9PNxx3eLw1cnUjevXqxZUrVzL+3aRJE155\n5RXq1avH9OnTef/996lbty4BmYysv78/iYn2d6EVCnmGSJW7kB87hBRRGU0Fz6TXDY6OZHB07r0m\nFQpLaCDH9Q0cgKFrJ+SjRqJ57WXMh/djnvulJ5bqUWxeXzbkK5chhYfj2751nkrN8xtHr88mYWF4\nJ8ahcvb8V1/GFF4adU9LWqEweTLeefmNPNcX09ULKN5/D595X6GYPSvv11bIsXd9ZlHk94OX+ePQ\nJXZcuEOizmh1jiB9GkaZnF83L+DTPUuZF9mSSdeuc/fZ9rlq2Ux/qhH9vt+U6zqd1eRKZ8Ly/VQp\nEUDv+q5FMJz+Ffbs2ZN69epl/P/Dhw+j0WhITn4Y7khOTiYoKP8LjoR9exGbui4dmi+EhGD+dRGm\nXxchFlC+cL5gMCD7axlin2ceKWPvDowbN2N+8y2XzpU6d0YqVx4xKgqpZcs8r0V8ZwKSv8XrlH3x\n3/Xw/zpyhdpTlzHo562sOnHdprEHOBlcmie6jaXW05NZXq4O4479y9VF73D+4y9y9bB71i3P9B6e\nbe4z4e/9Lp/r9G2mU6dOzJ49m0aNGrFhwwYaNmxI48aNmThxInq9Hp1Ox+nTp6lZs6bdeUwms9Py\ns3ZJTSXk+HFS+7+Azp3zuoBD8rrtn7T8bwGv1RUcuT7VujWo4uNJ7NoT8yN2ja7KI2cQFAYiLn22\nyk0bCLx6hcSPP8OY5FxJvi3k//xLcKumKN56kxulyrI2qDQbDp3J1xaT+YW1z85V9coTwaV5NXoA\nbzfpyYtnd7GrRCV+sNHJLjNDGkWg0xndrpiZzrm79qMn9nDY4AsPNnu++eYbhg8fjlKppGTJksyf\nPx8/Pz9GjhxJy5YtEUWR6dOn5/uGrfLoYQSzGVPD/G+d51YKQYMQd6D+6w9MVavlEBMrbAiJCchu\n3cJcuYp7NkrziO/nMzHWrYexjfvSJ81VqyEGBCIZ9FRZ8C/abOGEzA1EDsya8Mgb/cy4Q6o4Qe3L\n57XbZ/w7eyc74f59pAeb9emMaBlJ9PFdrD5wjs9K5Z7ppzYZMcjlSE7223AWQcprvy0XMRhM7vXw\n9XoUR49YFDIL+Idr1UM0Gh2qNPWZMR355UukTJ+Ra7FNQeGIByzcvYv81g1M9TyvWJoXVCuXE/DS\n88ScuIBU3JKHn2cP30WExAQCencnbexbGDp3zXJMuWsHQmwshm7OhQGVO7cjxMWhOHOKnVqJjmfs\nC7fNHtq3QPoNu4vMn93Kk9edLp50lK/7NKN3nfLIT50kqG0LDJ26oh0y1NKl64HDpnnpBUhM4Id3\nZ7P8+DXWn72FaMXcFtOlcOjPqYxv2pvfKzn2t5fmveLSuotOcFWtxtS4SYEbe6uYTBSrUw2vRb/k\nOtQcXg7V+rUERTdF9e/afFicZ5DCwgq9sQeQ376JpFIhhYQU9FKQAgJJ+Hcrhk5dchxTL12CZsgL\neC341qk5vb+bh883c0kb/w4Liue+0edIk5FHAbMoMm39UY/Nny5uJoaHkzL1I+RnThHYsytBrZvj\n9fMPFk0jvQ7UanrXKc/PA6JtPrjHevlxKqgkc3cuZtbOxczZ8ZvH1l10DH4hRnHoILKY+5gcyEXX\n93uO+G17MEdWJ+C5Z/Ab9VoOFcTHuA/ZzZsWLfnCsrEsCFZDeimfzEL70iv4vz0Wnw+nOJbSazaj\n3LENQ8tWgGMNz11pil4YyehL7SHSxc0kP390Lw0lfucBEhYvw1y2LH7jR+Mz70sEvR7UjhVYzqjT\nkVBdCiNPbqZBjOfaTxaSb3nRRrVlI6ImAFODhg6NF0uXIXHJXyR/Mgv1ir/xm/S2Zxf4H0Z266bb\nVTIVRw9TrHpF5GfPuG9SmYzUaTNImfQevp9/gt+YEblKHSuOHUGWmICxVZuc00kiDRPvEWp4tDbU\nHSVzX2pHcUTFMp0c4mYyGcYn2pG08Hfi9hxGO/Al0OuRMu1l2uuNsbl0tYz/f0kTanNcXnls8PMB\n1eaNGFu2ci7cJAjoXniR+K27SZ0w2XOL+48jv3nD7SqZkp8fspgYp6ptHUIQ0I58g6TZX+P111IU\nRw/bHa7cvhXJxyejt3NmeWGFJLF//988eT+rN2lTgvgRw1pfaluEaJP5cO8ybvz6Ni1u571Folih\nIlKxYggGPVImCZVaJQN5/txumw1RIvu8B0CbW2fzvAZbFA2Dr9cX9ApsIiTEozh80GV1TDG8HGKJ\nkm5eledQHD4IZnNBL8NhxJKlLDo67pwzXU/HUYPv5PdX3+85Yvcdw9TA/gafausWDM2i4IGXmbmB\niEGQYRIEfMSsTwm2mqI/ajgiL+xv0PLh3mVc/m0iI05uYW6N1pxxsFWpI53sdP2fx9Dx4X7Mi756\nft7yI8k/juKLXUuonJD1+3HFvxh3vDXMrN3BoTW4QiHc4XSewB6dMDZqQuoHtjXDCwr5hfNIAQFu\nl0MW7t5F8vMDX1+3zpsXZDdvENjpCZJnfYW+33MFvRyHSPr+Z7fPKfn5I3l5IbuXu7yC/Pw5Art1\nIPG3P53a5JbCwnIdox30kuU78oDosAC+PLOD2WVrctY3kFSZAt9s4mFFxcPPjUqJ91i9dg6lUxOY\nU6MNn9ZuT4y34z0wHOlkpxs4+OE/TCY6xV/J+OeoE5sYdWITa8rW4MO6ndhesgo6hYqSz8/Mdd4q\nYa5Lxzz6Bl+rRXHsKLqn+xb0SqxiatiY2NOX3b4p6D9mOIoL50ma/Q2mpoVDajm9b621LJP/FIKA\nWDzMIT0dn1mfIilVmCLd32g8ewpnqbKlGXbnHHW7tmd26Rrod/xKSbWCvtENi0zhVTphft7cSrId\nk7/v7c/JoFI82XEE5wNzv3lmx1onO1sot2zCb/I7KM6c5nyH7rQObU6c2pf+F/bz+snN1Ii/zfaS\njqmYCoJFvsFVHvmQjuL4MQSTKdfH2wLFAxkgqVM+RCwWQmCPTvi++w5oC37zTf3XUgxtO7iv8ccj\njBgammtIR3blMuo/f0f72ki3yGWrNq5HuXO77QG+vkj169Mk9hZzXu1HsRLFeSW6QUZT9KJi7CH3\nvtRJKm96dRjmkrG32snOBl4/fEfgM08h+fkTv3YTgQsXMqRXG3QKFT9Ui6J+r4nMr+a4hMa07o1c\n1tGBIuDhKw/sQ/LycnsctrBjjqj8f/bOO76p8vvj73uTNE26W6DsDbLKkj1akCUo04ULB24Bx9cF\nCCoKKOpPGSoo4ESmIqJsGUUZgqyyNy0USqG7aTPv74+0pSO7SZNC3q+Xr5ckz33uc5vk3HPPc87n\nkPHHBlRfziboow8I2LSe7NlzMXTo5JX1yE6fQnHoAJnjXG8efzORuWg5UlCwzTHq2Z8jhYWRN+oJ\nt5wz8LsFBGz5i6wvv0E3ZLjFMVL3HohLFoMkoW/bDlO0YzFrXycxNY0dR8+w5/R54hNOkS0Ggdrx\nhjaCZGLDmpn8X0xf1ta1bkusdbKzhnbIcKTwcLTD7ilKtx3T0yzAOGX9AfPToCOV9ZJEmDbNrnib\nPSq9h6/4bw+G1m2LNqZuKWQy8sa+TPqm7UjBISh2eK9PrvLX5ZiCgtH1u9Nra/AlpMgoUCqtvi8m\nXyJwyU/kPTfGbfswWfN/QDvwbkKffpzA+XPLvG80mdgW3Rjh8mWGTvyG4Op3En6lKm1nrPJId6WK\nIjE1jQ4vTWPcvKX8+NduLlxNI+1KEhRkw3S9cgalwbpYWiF9Lx2npp1es5P6t7Wpo1MaKSoK7fB7\ny9RWjOnZnG6RFK2xNF1SzhBo0Jn/ocuHq2cJ1ZW/HqfSG3wh7XpR2tmtirFZczLWbDKHBryEoXlL\nNK++AarKI7srO3oE2dEjXjm3kKdBN2AQeU8+7b5JlUqy5y0k76lnCZnwBkFT3ysq0CrUfr/vqDn0\n1/RUAkaThNEkkZyl8Uh3pYrCarFY2kVeP7Ce7as/ZsyRLeU6hyDA5AFti7zz0ii2bUF+YN+NFyQJ\n9YxpyA9Z1/EZeXtjuHgEUs5CbgYYdCBJhGg1bP7jM17+70/zexePQG6GWzbUK31IJ3Pln76ZBqjV\nEvjDt2jvHmL29jyNAzo9nsRZjRdfIOjj6QhZmWT+Yr3VnKcwNmpC1kL7UhtOI4ogN38XVPO+IP/+\nB5l5xXhDQCwwmMEDXmB3tQYWDy/eXcmacfM1LMlBhBp0fLtzOSNSzzOjdX8+j3FdjK6wk50lz152\n9jRB70xEuX4teY8+QU7bgo5UBgNBn3yIsU5dcwTCAkUGPDfd/F8B9ySfQGXU83NwRInX3ZEyW+kN\nPuCWXqTuRtixg5DXXsLQth2GijD4VlBs3YwpqgrGmNZeW4OvIiZfxNi0mf2BlYyA9WvIG/Ukmldf\nZ9aZrDJqkX/Ua2N3jsJjKoPRL+3hN8tNZ9XBDVTXahjRuh8rm3QG0TkbESgT6VQvigdvb8ywmLIt\nDoXMDNSfzkC1YB6mqtXI+mo+2hH33XhfWxCqsRFqrls1kr0zJ7Dj6Bk27D/KH/+atfZHXT7Jloga\nJJZKE/V7+D6MuHEDpipVMLTyrqFVz/4Mxc5/0PzvTTTjXvX6k4AvISYno3OjDLFFKljuWkxKRH72\nDLkT32FVuqlc0sBT1h+gXmSwUzFrX+D18wcxItCx03BOBoVDZgpRKgVhdRrb1depFhzIggd72L5m\nk4nwu/sjS7yA5uXX0Lz4EqjVJcdozfF3yY6WTt2qkdSNi2RkXEcSU9NI2LaD3pu+5n+dBlKnSoTb\nexX4Db6HEDZuQBfb2+uiXJk/ryDo4+moP55OwLo1ZM/6CmPzFi7Pl5iaxv5/E4lPOMXWgyeBStpA\nQ6dDvJqCqaZn2mGKF5OI7NGJzG9/cqu2vT0Ctm9DEgTyu/Zg6o+7bI6tlZNOtfxs9lexnmJYWvvd\nF+nWolGRnj/Ai816EGgykqG4sWnet2l1Pn9mEL8lJLIqIZFDpRqWt64RzuqPvubl/j0Q7GkriSI5\n0z7G2KixVVmOIg9f6XgySd2qkTRLOoakUjF+8Te8FRLq8LGO4jf4nuDKFcRDh9A9/YK3VwJKJblv\nv4v2zkGEjHueiH6x5Hz4KfmPPOb0VIXZECWQJJbGp1e6BhrilcsIkoSplnt1dAoxRUQiaHJL5uLn\n5CBmZ5nVOT2EIn4rhpg2/Hoxx6I3O+zcfs6FVOFglTq8cHQrD5/+l/oPTbc635lr2fyWkMg9bep7\nbM3lpXvzkgY/XyYnv1STl+7NGyETRe5pU7/EtRSmc/5z7AwvHj0D+8845MDoCxRIrVIgl2HPwy8z\n7+0dyZ0wGckDxh4qscEXr1xGTEz0iYYnpRH/2gSA3s1yCuXB0KET6X/9TdD09zE0uc2lOUrHShUm\nI0d2Luetxp34Nbph0Zi6cb5v8DEY0PXug7GB60UsNgkKwhQUjJiaWvSSauE3qD/7mLRDxz33g97/\nH7q7hlhUixQkE28eXE+L9MsM6/88+TIF6sLUPxus8nGD70hs29IYiw4MNzqAhRp0HLm9Bsr/ve60\njZFCw8j935sY61veHLeGPrYX+theTh3jDL5lKZ1A+ftKgt6bxLUzl3zO4EsxMRimTvO9ohaVitwp\nZb/gjlI6G2LA9Ys0ycvitDqsxJjK0DHJ1LARmUtXevQcUvFqW40G9dw5aIeN8JixB0j/ew9Cfh4J\nX5VNQ5QEkf6DXmLlhq/Y/KfjDc0POaE8WaEYDKhnf0bdp58v2vwsLLwymSS7nrq1dE5RMjH60gk+\nOLOHiB0SOQMGYCjMvnEQKSoKzZsTXbosT+JbltIJ5P/twRDT2i0l6e5Gat0GqXWbStmg3BalfyBD\nUi9wRhXCoeBIq2NuZYrr6agWfY+Qdh3NWA9XIisUSAqFVbXI7AAVgwaOZedvH9H+ujnfXpBMNnup\nOqI8WeHk5hL6zOMEbN6Evk076t7Rl7pxkTw7JBZwrD2lpXTOuLRkPj+5k7Y511lUvTE7Hn6Kd500\n9r6M7+7E2EHx3170XpIRuBkJev8dc3WmE5WWp9Wh1NJqCDbar2K8FTFVrYZ4LRW0WlRzZqIdfi+m\nht5Xo9TJFHQYMYFlDc3qnI6EdXwJ4do1wu+5m4B/tpP101L0d/R1aZ7SzknvtEts3fcHOlGka4eh\nPNLqDlZf8tGnGxeplAZfSElBlnjBtwXTKhOShJCdRciENwi7ZzDihfMWh5WOgy6v1pBAk5G7ryVa\nHXMrk/XF12QuXUng0p+RXU5G89L/Kuzc9vTaJUHkqxZx/BPdCLmdm7wj2u8VhXjhPOF390OWeIGM\nlX+i6+M+7XhjQfrsnNot2eWCqFq5yLcsseBuKqXBV/y3B+CWl1RwG4JAzozPyFi6Etm5s+ZGzN8v\nLNM3tXSl3zl1KLtCq9GkmP7IzdJAwy2o1ebWd917kD1tBsZmFVfEZE8tEmBrzdvoMfQNMpVqm+Mc\n0X6vKFTz5yIYjaT/sdGp/gGWKO2c/B1ene9qNOW7o1t5uKDzVUU4MEJ6GlEtGxOwfq3Hz1UpY/hS\naCj599yPqY7jmtR+7KPv3Yf0+F0ETZ5AyOsvI2RmkldM/dLSl79HhyEYi+VoVxYPP+D3lRjatsdU\nt57Hz2Vs1ASjAw3sy4PsyGGkqKii7mhDW9Vl/fFLbpnbGe13T5M7+X00L72GVKWKy3Mo/tmOeDWl\nTDqnSRAZ3cK8B/BDgfbOqSv1uX3cVMC5ehPZkcMo//zd/FRnQ0QPzH0khNwc9BWwVyBIUik3roLQ\n6QwObaxUJhSbNxL08YdIf/4JERGV+voC/tqAvt3tZXSAElPT2H+ukhde5edTtW41sj+bQ/7Do8q8\nHRZmDmFUps8v/O7+mKKqkPX9z4BZGbP7zDV2K0vt0ahKCH+PG+TThVfFsfXZiefPEfzu2yjXrEbX\n6w4S5iygw8tlaxBEycSCo/GMunySh1vdwZLqjcuMsVdvolyyiNBxz5OalGrX4IcP7IMUFkbmkl/t\nXR5hYSoCAlz30yulh++rBGzagHjlMsbwcG8vpdxYi43WrRpJTONajOrXtVIZxOKIyWbP1+jm5uXe\nQsjJRr5vLznFWnzKRJGJ/dswerHrktnOar/7KkJ2FurPPkH19ZeYIiLJmj0X7X0jqSuKRemc/xw7\nU7SJWyMyjNFAllzBCbXl37K9ehOhsE+xHdl22ZlTKP7bQ9bcBS5dm7NU7k/SxwjY8pe5d20FaqdU\nNEJmRpnYfmVDVmDwTfZK6N2B0Qh6z2YxKXb+g2AwoI/rXeL1wS3rMHmAZaVGR3BW+92tmEyoZn+O\nkFH+LBnZs6MJmPclK7v2o2WPB2n1zznGfr2MJdvMe4Ej4zoy+7mR/DdrIv/NmkiD6lUwCSIv3dad\n/aGWQ0eWUjqLI+i0SEqlXVugXL4EU3AI2jvvcu3inMRv8N2EmHgB+ZnTnhfj8iZGI2H3DkV+372Q\nYrt9ny9TER6+/MA+5IcOUKV2FZS/LPPYecAsp2CsURNjo7KhhzE9m1s1+qLJRNcrZ6imySrxuj3t\nd4+j1RLy7JMEffAOiu3byjVVYmoaXXLDaNTpHu5R1OJEZi5J18xSIOPmLaXDS9NITE0rccy/h0/S\nOTOFZrnWbzZ2603ytUgBtkM5AILeQP7Ih8qKr3kIf0jHTQRs3Ywkiuh7xuE7SWxuRiZDM/ZlQt/6\nH4p2bVBO/8Tcug2Q/7sb+aH95D/1nJcXaR9Z8iVMYeEQbLsFoctIEsHjXwNRhqQOstvbtrwExG81\nl+Nb8SbH9GxOvchgpm44WCKmL5NM7Ph9Bk/EjeK727oDtrXfKwIhK5PQxx5CsWc3Wd98h27wsHLN\nt+PoGbNipg12HTpBwzAZih1/E/DPdhK2xxNk0DOrTkteKvi7OIug09qN3QPkTnrPpfldpdIZ/KCp\n76HtfyeGjp29vZQSyP/bg6Fde6SISrBpWQ50Q4ajH9AX+dgxhD7zBPl//E7Oh5+i2LWDoI+noR35\nMFJwiP2JvIixfgPy7x/psfkV8VtR/LeXzJ+XEzRpfFG1rUcwGtF362H3yXJwyzoMal6LDWeusHzf\nOfZduEZKtgaDIFJTBnc2q8XQmLoWtd8rCvFyMmEj70G8dJHMZb+h79bD4WOFnGxUsz+Dl8ZBjRpF\nr9sLvQBIK5YS8ctCJLUafacu/N7rbmZlmNgbWtXqMfay0fRduiEF+p7r5/MGv7ia3bH9CRxcOZuF\nF9ORNKJPZYXkfP4FQlqa/YE3A9WqYViylPzvfiT4rf+hXL8G7ZBhBH/wDgEb1pVoBOGLaIfdU/Rk\n4gnUn32MPqYNuj79Uc36zLMevkxGzvRPHBsqiozs0IiRHRoVbbiLP7/O+O6NyXsk1nNrdJDA7xci\nZKST8fs6jC1aOnaQ0Ujg0p8JmvoeQlYmhq6dkYbeeCpwROpjnimYh//caNbLUSi4tm0Pu+YttXmM\nvXoTffee6Lv3dOwaKhCfNvil1ezuSr0AwOeXczlT8IH4jByvICBFea+zVYUjCGhH3Icutrf5ugUB\nfeu2KH//zecNvidR7NpBwI6/yVzwIwiCWU/nqgc9/HIiqdUImlxvLwMAzevjyXviaaRox6pcFbt2\nEDTxTRQJB8kfOoLcyVMIaWVdCTZaq0EmSSQHlmwan6lUlYgYuKq+WRnwaYNf+u7cJfMqqYpAzqhC\nS4ypFHK8NynFC2C0Q4YT9Ml0yMnxXHzcx1F9MRND09vQ3TUYAFO1asiSLnh5VTZQqRA0Gm+vwoxM\n5rCxF5MvETb8LgytWpP++3oMXbpaHFe8Ocp7Z/dy97VE6nV/yGaxYPHWg8XTNStdvYkFfNrgl46/\ndcm6yq6waiU2pyqLHO+tQGFYR7lxHabo6hhatkIKq/w1Cc6Q/elsZJcvFXU6y/3gI693PbOF/vaO\nmGp6riGLpzDVrEXG6vUY2new+fctrKatm5fNk8knmNSoYwljXzimNMVbD7obISWFkFdeJPf96R6v\nwC6N734TKenhi5KJzpkFBt/KGD/exVS/AZnfLkLXPZaQ558iIq4ris2bvL2sCkWqVg1Dm3Y3XvBh\nYw+Q/dV88p59sWJPKkmo5s5BKGeoy9Chk92/b6H3PuH8fjLlAXxRu2x7z4oOzwT+upyAbVsweSHB\nw7e/jcUQJXiiRRzLq3moQ5GLyM6eRnbqpLeX4TPo7hqMVK0aGavXY2zYiPCRIwj+3ziEnPKV+LsL\n8dxZAn/6HvIqZ5VwcdQfT0e5bLG3l+EcBgPBr44lePIElJvW2x2u2LUD9UdTXT5d3aqRHHpzFE9d\nOcWGuEFEVI+mTpUIHojtwKxnH/DYHqBy2WKUvy63+F7gssXo+t1ZRrakIvBpg1/8zmsQRX6Jbsip\nUjm13t48Uc2ZSegoz6X4VVZMdeuRueJ3sqd/QuAvy4iI64r8393eXhaKXTsIeXWst5dRfoxGVF9/\nhexsJXrCzc0l9LEHCVyyiKyZX5L/0KNWh4qJFwh56jHCh9xJwMb1UI59hsY/LEAIC6P/13OKqmln\nPzeSkXEdPRaLD1yxFOXqVWVelx1OQH4kgfz7H/TIee3h0wbfEaldr8rxShIBW6fvUIMAACAASURB\nVP7yqd61PoUokj/6GdK27MBYvyFSUJD9YzyM7NJFTJGRoPK9HGlnkB86gJiZUUZOwVcp3bRE++Aj\nlgfm5KCeNoXI7h1Q7NpB1swvyVi/pVyVqHkvjCF71lcVWx+i1SIpy+roBC5fgikiAl1f9+n4O4NP\nb9r6WnpU8ZqAHUfP0CjrOlsuXWRT1brUTE2rtDv3nsbUoCGZv/zu7WUA5uwOY033auio5s5B364D\nhs5dLA/QaMydxNyYuaSI32ouFKokPSECly0ualpiS8de/cVM1F/NJu+5MWheetUtRroi5KlLI+i0\n5EgCS7btuZHpI0n8veUXMjrFos/M8Yq98Hl55NJGFryTHmWpw/24xAQ+PrWbyLjHyJUriuKBlVFe\n1xkcur78fMSM9CJ9dl8h7IHhSAEBZP1ovbDGmc9PTLxAZJd25E58l7wXx1kcE3VbPbMBe+V11xZt\naY33DAaFwiFJ3RLHlbo2MfECYupVz3ePkyTEqymYoqvbHCZkZSKkp2OqV9+l0/jKby+oZ2e+z4EX\nmpcsvlKYjAQb9aQrAl3aP7jp5ZE9mR7lDJaygQZcv8g/4dHkyhVFY/w1AWbCRo5ACo8g67tFNsep\np09B13dAhUlliJeT0Xd1TR/FEuo5nyOFhJD32JNWx5iLr9xYbZuXh+LfXeSOn1zuqVQ/fofyl2Wk\n7TvihoXZQBDsGnsAKTQMKTTMs2upAPJzcskXQ8u8rhdlpIsywDv2wqdj+L6EJU2Of8KjWVjzNptj\nblV0d/QjYPNG29k5ubkEbN1M+OABBE2ZXCF9PbVDhqPr7VrT69KIVy4T+POP5D3zgs1wjalqNfdW\n2yqVZPyxAe095a9ollSqiq+0zclB/eH75VbC9GV+a9udtVVsdwrzhr3weQ/fV7Dk4U9r0N7umFsV\nh7R1goLI+HMT6tmfof7kQwI2riN79lyzpomH0Lz2ltvmUn05G0kZSN5Tz9ocZ6pWDTE52W3nRRRL\n5vqXA0mtRnBniqokEbjwG3QDBmKqXUpx02RCuXwJQVPfQ0y7Tk7VaPQ948p9yuJh313HzwIwPvcS\nwXG9aDagj1di5e+G1CUpyraWvzfshd/D9+MRTPUboG/TDuXvv9keKJejeeV10jdsQ1IEED6wDwEb\nPN/Mudzo9Sj/WEXe6GfsVhObPXzf7B8gqYPMBt9kKv9kJhNBk94iZPxrKNesLvGWfPcuwu/sTejY\n5zB06ETa33vIH/1MuU9ZuLc2bt5Slsbv5cLVNKQLF3jy95849OU8i3r3tzJ+g+8gvpYxVBnQDh5m\nP6xTgLFlKzLWbSb37ffQdfM9lcEyKBSkxe8mb+zLdoeaqtf02S5oUmF6ann1dAqalqi+mcu2J8fy\nlCmS28dN5fZxU3l5zk8oHnsIfV4+GSv/JGvhj5jqNyj/4rHsJd+oqm1pdYynsWQLWmdfZ/WBdQQZ\n9FbHeBq/wXcQn68J8EG0Q4ah63WH47LRAQHmTJfKIrwWHIwUUnZjrjR5L44jfee+CliQ85hq1kLX\nrQeC0eDyHEJWJmEjRxCw5g/ua9WHXolalsbvJelaOknX0vl5xwHaNutDSO3unGnqoOyxgxSPgwcb\ndHTKvMqTySf4uF6bomQKb8TKLdmCfFHGHWmXmHF6t9UxnsYfw3cQv4fvPKb6Dcj6YYl7JjMYQO7/\nugpZmW7NYtF370lmOXXblb//hjzhEL9NnM4vf5+wOOaM2rxmZzJThNRUZOfOIqanIaRdR7x+HTHt\nOvpu3dH1HVA0XyFvXDjIpHP7uRKgKvLuS4+pKCzZgpNB4bzZuDOzT+5gVdV6XrEX/l+Qg5SQTD16\nmrjFC/m9XnPCuner9JKpPk9eHhF33kH+iHvJe/Ellw2/cpU5Z107dIQ7V1ehhPeLQzd4GLlvv1sh\n53OkDib/4VHo+vRj/+xv+TnhLx5r2Qt9Qephcerk55C38leUyScQ09IQ064jpF1H3yMW7T33lxkf\n+PMPBE+90QLQFBSMFBmJqVo1KDD4xfmxehO2RNQkITiyyLv3ClotzebP4fCYe9isl5f4213rMYqk\nX/JZfWkfWXKo6CIony+88kWEq1ep0qoxmQt+RDd4aJn3faX4w1NU+PXl5xP04QeovpqNoV17smfN\nxdjUeqMLa4TdOxQpONhubYCvfn5iUiJRt7cic/736IYMd2kOZ67NUrFhafbOnEB9nYag9ycT+OsK\nDgRHMbRNfxJVZStkxyYeZtbJHUCB8Y6KwhQZSf79D1rshSxeuYxw/bp5XESkxR6xY+cuKdK7t8YD\nsR2Y/VzF6V0Jadep0qyBVfsgXrpIRFxXdH37kT13oVNzl7fwyqEY/u7du+nd26zZcfr0aXr06EFs\nbCwvvPAChfeLb775ho4dO9K1a1f+/PNPlxdUGZBdTATAVNd2nq0fNxEYSO67H5Dx+3qE9HQi+vRA\n9eVsMBqdmkZMvoixVi3X15GXR9i9Q5Hv/df1OcpBwPZtSIKAvnvFtCO0FwpRG/UY35lEZLfbCYjf\nypsdB3B75+EWjT3ADzWa0HHoC6QmpXL9XDJpexPI2LDNauN7U/UaGFu2MldrW2kI7ot7a4JWa/4f\nC1o6AKZatcn5dCa6/gMrcFVm7Br8GTNm8PTTT6MtuIhXX32VadOmER8fjyRJrFq1iitXrjB79mx2\n7NjB+vXrGT9+PDqdzuOL9xayJLPBN9bxG/yKxNC5C+lbdpA36gmC352IYtsWxw+WJGTJlzCVQ0cn\n8OcfUGzfihQR4fSxQtp1hGvXXD43gCJ+C4aYNh5rpZmYmsaSbXsYO3cJt4+bylvfrSwz5olLx2mS\nmwFA/+sXabdyMXmjnyVt134uDL4HEwKfndjB3allu3xlKpQ0ur2tVePtCj65t1ZgKyVloPUhQ0d4\npRWo3WeDxo0b8+uvv/Loo2Yp03379hEba/YwBg4cyIYNG5DJZHTv3h2FQoFCoaBx48YcOnSIDh06\neHb1XkJMTDQ/knqhgUGlRKcjZOyzaAcPR3f3kPLNpVaTO3UG+Y88jrF52WYW1hAy0hE0Gte7O+l0\nqOfMRDtshEtCXOHD70bfuQs5Mz5z7fwmEwHxW8l/4GHXjreG0Yhi904uhFehwwfzrQ4TJRNTzuxl\n4vkDTG54O+83vJ3fqtan56CnWT15CgDdmzUk9uvPeeHiUY4EW74putvbLt2OsLDwqkuzhl7bW7vh\n4bvvxuYu7Br8ESNGcP78+aJ/Fw/5h4SEkJmZSVZWFmFhYWVet3liuawonljZkKVcgvr1CAu3LNkq\nl5s3rCrr9dnD+etTIb9wjoBVKzA8/IB7FtHFuuKiJYQLZu9a1bQhgXbWben6xG8Xm6WV3/7dpc9V\nrFEdZUYaMle/EykpUL06ikF3lut7VXht6fka4g+d5J/9x/h20rNMat8fIutbPCZaq2HR4c30Tk9m\nfKOOfFi/rfkNQeBKSJh5PZLEo6t/JPziUZ5p1pP5tZpbnGtA55Zu/13EhNUipnEtnh0SW3R9BoNz\n4T53IhREcoKiQpHcfK2F1+fy8c4eIBZrKZaVlUV4eDihoaFkZ98orsnOzibChcfeyoJp6DCEbt28\nvYxKhemee5FNeQ+ysyHEc7rkwqGDSK1iyrS+kyIiMb49CalJU+cnNRiQzZiBachQ89wuIFWPRjh3\nzqVjAYiOxvDfftePL8b5K9e47ckC4TVJ4htBQMrNAQuO8F2pF/jjoLkzVZ/2d7E5suQeSGxME3O4\nbNxYwn/8npTpH9MppjP5CaeITzhVNCY2pgmxrZtSP7riuzxVNFK1aAzvvItUWlrC7oGSxwv0nDb4\n7dq1Y9u2bcTFxbF27Vr69OlDp06dmDhxIlqtlvz8fI4dO0arVq1szmMwGH0uC8JhOhaoLVpZv69m\nebgLV65P7HcXURMnkL9ipcdil0JKClE9uqPv1JXsmV+U1HIJrQLjCuSJ7ay7jITwubOEG41kjXkF\ng4ufaVBYFMrLO73+nQgLU7F5//EbLwgCuaKcoNKFV5LEQ1dOs+iIeZ9kbq3mZYw9gMkocXJjPC1/\n+onsT2YijnqCocDQTm0tnt/T1+8Tv72gCHjxVfP/O7gO5ZJFBK5YRubSX0Fm3YuvMHlkoeDO8+mn\nn/L000+j0+lo0aIF9957L4IgMG7cOHr27InJZGLatGkEBFjeofZza2Kq3wB967Yof//NYwZfio4m\n67tFBL8ylojYLuS+P93cRs8JrykxNY39/yYSn3CKrQfNvYq7tWhEj4++pmut+ri6TW+WSHajYmY5\nKPS8C8mVKWidc6MaulPmVT4/uYOumVdZVaUebzTpzMkgy3pBi7b+y6Kt/3JgzRZqtmjm0XXfzJjq\n1kOxfSuqL2c7JNfhKv48fA/gE16GB3H1+lSzPkP9xedcTzgFHnQIhIx0gt9+i8Bli9H26UfOZ3Mc\nasTiaN65K5uAylW/op42hfRtuyDQevaGpwkLU9H0iUlcuHrDwB/YtYI2OWlExD1GhkLJmv1rqZ2f\nw8u3dbPo1Vti1rMPeL1nBVTu357p9Vepsuh7xj8zniVp5o3f0kVuN30DFD+VA4cqMh9/krwnn/ao\nsQeQwiPInjMP7V1DCH5ngsM6+46U4LvatEI7dITPVvgObDeQQKORDLn5c3m0ZW8y5AEYRceltv45\ndsYnDH5lJTE1je6JJv5TBvPwD3OY2Wk4OlHG0vi9RYVle2dOICasHHUk+A2+HzdgzTMu/WV1V3qc\no20vdQPvIq3/nTZjosVxRGTLG4Yt8Mfv0Hfo5FQaqi1iY5rw41+7i/59WVmyufz1APtPII8mn2R4\n6nkOBkdyKCSKS7uBZ+4vs1nuxzF2HD2DViZnVMte7NrzG5PO7mNS445lxsQ0Lp/B9386ThKwehVB\n703y9jJ8Ckc9Y3dQWv+8UJFxafxexs1bWlb/XCYDSSJo4hvI9/9X7jVWtBCXkJ1F8BuvoNjxt9vm\njI1pQsfMq2z67w/q5lmWro4MVlOnSgQPxHYgMrhs+rFeFAkz6Bh78Qi/HtrI9j+/JqpRbZSLf3Lb\nOisr8v/2oP7wfXPWjYMUOhv7QqvyZIs4vqtZNpvMHaqffoPvJAHxWwnYvNHby/ApHPWM3YErRlm4\nfh31N3MRLyaZX5AkVLM/t1v5unHfnzyebFn9saJQ7PwHwWhEH9vLPRNeusT9C2fx757fiNblEanX\nWhy2YerL/DdrIrOfG0m/9mWfLJZUb0yf2++mSuwoavV4mA8fGYvmldcwtrScnRf47XzUH00lYPUq\nxLNn3NNwxUdR7NuLes5Mp5IFin9nf6rRtEhd1NoYV/GHdJxEvJjol1QoRfEvYveMK9ydegERiVyZ\nAo0oRyOT8/d+JVBWwEpMvgQyGZJKhaRSg8K2yqErYRdZ8kXArP0OZhEy9ZzPUH81i+wZnxdV/3Zr\n0aiEEFeXzBTWRpXMpa7oMn3F9m0Ya9TE2Nj56t4SaDSov5yFYs7nKFQqLkx6n60tO3PbyfNctxEW\nA3N1rFWBMkEgOTCIoKHDyLMR6pKfOIZy5QrEdHPbP0kdhKF5C7JnfIYxpnX5rs3X0OqQAnyvyhb8\nBt9pZEmJbunDebMy49RuGmsyyZYrUBsNBBX8N6BhMXVLjQblhrXo+vYnbOQI5MePFb0lyeVIKjUZ\nazZhvK1sml+vn+fTPzMDjcx8I9GIclKUahbWvA1dgSTvxpMpPPpTPAnJ6aTk5DH43AFWAi/uukhP\nWVWGt65Levxugl97ibAnHyF/xL3kTPu4pGGTJNRGAxpZyZ9IeaQBxCuXQafDVLeew8cExG81e/fl\nLMgRr1xGPWcmpqefwThhImpByQPAA3d0sXusO/Rqcj78lJzpnyBeuYz86GFkRw4jP3rYqi5R4I/f\nYYqIxNCyFaZ69SvV3oCgzYdA5wx+aWfD2pjy4jf4ziBJyJISya/j+A/2pqWYOF7xL+uI1v24GqBC\nKm6gJIkHutzQVRKvphD6zBNkzV1A9iezzLroeRpzb1VNLoImD1PVqhZPWy0vl1q56aiNBtQm880k\nzKBjZ1g1DlZvDBG1SAsIZP3xS0XH1MpOQy+ILL2kYfGKnXyy5TAT+7dh8A9LUC79meC33yJye2fu\nmH8j/hxoMiICuWLJn0h5fnQhL72ApFQ63BRGSElBfuwomjHlz8s2NWzE9QNHCa1XoCXkRNpiab0a\nWxvlNhEETDVqoqtRE/r0tz5OklDP/BRZolmAzRQUjLF5CwwtWpH77vtIwa5Vaju62V9udFqnPfzu\nzRsRv3Eb3TNSWBHd0OqY8uI3+E4gXLuGkJeH0QkP7WZCPHeWwFW/Il/1C1JcL3h3OlDykT9FaUFf\nSBDo3qJx0T+LNzi3p01fmmWjXyrjCamNejSRtSHKshJmndw0koPCMRV4iWevZzN68d9MHtCWMSMf\nRh/bC/Xsz6h2e3v2zmzK/nOJ7Nu1D7aAKiKcB2I7uMUomKpFIzt90vEDAhTkvD8dXdwdLp+zOFK4\n63IndatGUjcusmIylASBtD2HyjwNyA/uN4f9SiNJBKz9E0PzFtC6ucWngYrMJBPytUhOCqfFVg+n\nz74/CTXoWVOlDhpZ2dCm38OvYCSViqx5CzF0uHXyjYWMdAKXLEK5cgWK/fuQVCpMd92NaeCgojGu\nPPJrBw8j6ONpCDnZTnlsluLJtow9wKp6bUmwUEA0Zf0BAMb0bE7O9E8As2GLaVyLUU1rwgcvM2PM\nI+hseaNOYKpazalsGykikrxnX3T8BHl5qL+ajezkcacba/gcjj4NYG4oEvb4QwBIwcFIrVoR3LQF\nhnbtyX94FODZGovS6O7oi9GJJu1CRjotnn8ClDKWfvB/DM42eOwJxG/wnSE4GO3we729igpF0GoJ\nmjYFXVxvsuYuQNt/IGG1CsItBWEBVx75tUOGEfzBOwRsWOeU1EKZm0tQuE1jD7CzeiN2Vrd8U5qy\n/gD1IoMZ3LKU0FX16qRv2IqxgeXHa1cwVauGeDXF/SJZkoRy1a8ETZmMeOUyeaOfMTeHcbD+oLJj\nqlWb6wePIz96mKAzJxASElDs3oH8yKEig198s19t1FNDq+GsKrRE6NFdNRb6uN7o43o7NFbIySbs\nwXuQXUwk49c/GdAqhrLNG92H3+D7AQqaYwcFlzESpujqXDt6FoKDbR7v7CN/8bCOMwa/+M1l+9HT\nrEzUYbAwTq3XolE49lg9beNBBjWvhax4KECpxNigIWEP30/uGxPckhZpqhaNoNUiZGe5rRG5/MA+\ngt9+C8W/u9D2G0Dust/Kn9FT2Sj2NKAaYW4pmJmZVyL1s7iHH5d+mTUH1rEntCqdOg23OKaiCHnx\nWWQnTpC5YhVGF5VYncFv8G8CXN6Mys1FuXEdypW/EPDXBjIX/2I5A8mOsXcVzWtvOVWcUkjhzUUe\nVpXll3aWef/es//x2c5l9BjyOhdCqtid78y1bH5LSOSeNvVLvC5oNEgyGeH3DiHv8dHkTH6/XH8L\nY606GFq0QsjJcZvBD1i3BiEzg4wlv6K/o69b5rxpsJLZszMsmoU1mnL3tcQKXlBZcl97C/H5MRja\nV0yzKL/Br+S4shkl370L1cJ5KNevRdBo0LdpR+6EdzA0rVi1Q92A8vX0XHXY8g92e/XG6EUZa9bO\nofvQ18koJR1gcS4LBt9UoyaZK/9ENX8uQVPfI2DzX2TP+hJ9tx4urdfQuQvpW3e4dKw1NC+/Zr5x\nyv0/ZVsUzyTLUCi5FBiEvtQNocJbIQLGmNZUZKuWypPc6scirlSeyo8fRX70CJpxr5K2ax8ZG7eR\n98JYpOhoTy3TIyQkp1t8PUUdxqA7x1I9L5OVG+YSYNTbneuQlbkQRfKeeYH0zX9jqlaNsOF3ITtz\nyvJYd2E0EhHXlYA/fr/xmiRZfhoKDPQbewcondKoMJnQC6LNMTcjfoPvKJJE2MgRKDZv8vZKSmCt\n8lSQJBpqsiyOyX/kMdLjd6N59Q2MDRtbOrxSkJJjPZf8eEQNhvV/nl6XT6JdMIZAg87qWHtzARgb\nNSFj9Xoyl/zqUk9bZ5AfOoD82JGiZuXyg/sJH3InARvWefS8NzOlvXeFVNbgu8vDD/x+IQG/l20A\n7wv4XQMHEVJTCdi8ibyHH/P2UkpQ2nuvk5/DuMTDPJByBpXJQI2ej5Z9CrhFsje212jKA32e4skT\nO9DKnPuqi8uXEf7pp2Ss23Ijo0YmQ9+7jwdWWhJF/FYktRpj7ToEv/QCgUsWYWzSFMlDeym3AqUz\nyRYHKfhDr+WBLu6psShO4JKfMDa5Dd2QGxvChQJ+xsZNyX/yabecxxX8Bt9BZBfN8WJTXR/V0ZEk\nnrl0jE9O7UYniiyr1pAl1Rth9HCPTLeh1YKTxSrRwSqSszQ2xyxr1JFljexnDkUHl2o2nXQR2cmT\nDqdPiilXMEVXd2isPZQb1yNoNET27IykDCBn2gzyRz1pV2fIj21KZpKV1XVyG6W1dCSJoPffQT1/\nHtkf/Z/nzusA/pCOg8iSzAbf14TTCh9DZ5zezbzjf7MsuiGNuo3kheY9iY+oiSQIXtmMcoaA1auI\natUEIceyVK81Ymq6Xjlamtal59LkgkpleXAp5AkHiby9FeppU8w3LhuIF5OQHTlsfUBeHop/d5n/\n9+FHSdu1n/zRz/qNfSVC0OYjFdPSUX/6Eeo5n5Pz3jTyn3jKiyvzG3yHERMTMQUFI0W4SW/DTRRu\nNM2v2YyBbe/kqRZxZJbKP/f1zShDTGvEzAynY9RDW7nv5js0puRcgkaDpLaf3QNgaNYCzbhXUc/5\nnIj+vZAnHLQ6Vv3pR4S8bL16Vn4kAUkQSF+3mdypM3zu++bHPoJWBwUevuqLWQTNmEbumxPJe36M\nl1fmN/gOI0u6YA7n+FiIpNB7PxkUzroqlg2gr3v4xYuwnGF467o0jHJNSKs4jaqEMKyUwSc3FynI\ngm6LJRQKNG9MIGPdZkAifEBv1B9PB33Z7CBT1WqIqcWamRtLJuUZOnTi+vFzGNq2d/Iq/PgM2nwk\npRIhPQ31F5+jGfsKmlff8PaqAH8M32E0z41BvM+DcT9HkSTQaCDI7H26TcnQy2gHDyPok+lOaevI\nRJGJ/dswerHr3aAEASb0a1OyyhZAk4vkYEinEEPrtqRv2Ib6049QffsNeaOeLJPqaqpWYPDz8lB9\n/SWBvy4nfd2WEuEjv1dfuckb9wqGmDZIEZGkb9mBqVq0zziKgiS5UOroBnQ6Q6XsLO8IYWHmH6+7\nr09MSiTklbFIoaFkLfzRrXM7gyeuTzx/jqhObcx6PU5ILQDM2X6sSAjNWSYPaMuYns1LvBYWpoKk\nJHJS0jA2KdtqzhGE7CykkNAyrytX/Uro049jCg1DyM0h74mn0IyfZHGsJ/DUd9NXcPT6gse/BpJE\nzoefVsSy3EZYmIqAANf9dL+HXxmQJAJ/+Jagd99GCg0l5/9meXtFbsdUvwG6nnGI1223HbREocF2\nxugLAkzqX9bYF1GnDsZQ+7IM1rBkwGVHDhP69OPm90NDyfhzo8UmL348j3j+3C25Ee43+D5OoVcf\nEL+FvIceJfe9qUhh4d5elkfIXPG7y4++Y3o2p15kMFM3HOTsddvZPo2qhDChX5uyCpkeRlbYUxfI\n/GmZ39h7EUFvsKytXw7Ey8mYatR065zuxm/wfRzVD98iO3WCzMUr3KbL7rOUM845uGUdBjWvxW8J\niaxKSORQQYtDMOfZt64ZwdCYugyLqVs2Zl8BSCHmvQl9h06gDCjzvmLnP+jbtnc4HdRPOTDokRTu\nM3+Knf8QNnIEWXPmoRs8zG3zuht/DN8DuDVOmpeHoNP6lFfviThwhbWfc2ANe06fJz7hFCaT5Noa\nJAkMBoshA8XOfwgZ+zxiagq5E98h76nnQBQRkxKJur0VmfO/L1mh6Wb8MXwz4Xf1w1i/AdlffF3u\nc8r/20PYvUMxtG1H5s8rPHrDLm8M32/wHSDwuwUo1/5B5lLH9DH8PyrnsKb4WRx3tZ/z9BpkCYcI\nnjwefafOaMZPtjwoJ4fg9yej+nY+uq7dyfr2J5Tr1hD8yhiuHz1bpKHjCfzfTTPhA3phaNGKnM/m\nODSvNYdkaKDEfR+8jqnJbfwwaRZrj1yg96qf+LJhJ06GVyc6WEVMzQiGtqrL8Nblf7L0b9pWAPIj\nhxGvXPboOcSkRMRrqRja3e7R8/giFdl+ztE1bN27mh9qNGFhrWYlxlhbg3D1KkEfvk/goh8wNmyE\noWNn6ycLDibno/9DO2gwgT//gBQWjiJ+C4ZWrT1q7P3cIOurBQ5LeVhzBg6t2cjs/1ZzSB3KY91H\nc3jNIRpkpfLLv3+wqkojjoVGk5ylITlLw/rjl/hky2Em9q/4vaPi+AuvHEC8mOg5SQVJIvD7hUTE\ndiF48gTPnMPHKa3mOehaIuPP7bc5xtNruD07lfBSCpsW1yBJqGZ/TmSXdihXryJ3yjTSt+1C19d+\nozp9XG+y530LokhA/Da3dNXy4ximho0w1bLdGrMQaw6JSRDYF1GT/kPf5HC+ef9JaTT3X7Mk1nf2\nejajF//NnO3HXFx1+fEbfAeQJSVi8oDBF5MSCbtvGCGvv4x26HAyf1rq9nNUBkr/oAZeS+TN8wds\njvH0GtRGA/mizOYYAAQBxYF9aO97gLRd+81NxwPKbsgWR7xwHsXOf4r+LTt2FPFaKjq/wfdJrDkb\nJ2rexp3D3uR64A0V08CC3gv5Muspn1PWH/Ca0fcbfHtIErKkRIx16rl1WuUvy4iI7VKUgZPz+Rc+\ntTHrLbpmXOGZS8f5sYZ3+7LmiXKUJsd6EWV98x05H/2fw+GYwMU/EfLMEzdeMJnQDh6GvnNXwBwe\nCnnuScTkS06v24/7sXijDwqHqLJPCLY8/OJMWX+A1UeSbI7xBH6Dbwfh2jWEvDy3h3SkkBC0Q4aR\nHr/r5k+3tEOh1k+0VsOKQ5vYG1qVV5t2tTjG02soJEuuILRUSCeuiZXYZyVC1QAAIABJREFUq5Mb\ncaaq1RCvpRY12Ta2iiFrwQ+gNueFyxLPE7A9nojYLiiX/uxS318/HiaiFgC1ckp2SnPEwy9k2saD\nGIs1Wq8I/AbfDlJEBGn/7EUf18ut8+r6DyRn5pd+rx6zmqfcZGJpwl/IkLgvpi/6UuEUTyt+lp4/\nSx5AWIHBDzAZee38Qb7+fILL7Q2NJhMrDpzn0Z/ieXVnIoLRSMybC2g7YxWP/hTPigPni378hg6d\nSNu+G13ffoSOfY7QUSMRUlLKd4F+XKaMsxEcCQGBRObnkLBiCr9s+KrI8J8PiWJ8x2FcVdnXgzpz\nLZvfEiq2kbrf4NtDLjd3GwoN8/ZKblq6tTA3atkQVYv7Y/qQHFhWlriiPfxhbfrzUf22DL16niM7\nl/Ph6X/JHjQEU7jzmUKrjyTRfeYaXlixk/XHL3EMc3ZI1dzMogyOF1bspPvMNUWP+VJkFNlzF5K5\n4EcUe/8lsndXhOys8l+oHwDCB/UlcNEPDo0t42wEmXsnpCmDeKHHg3RPOcOx5e8w9vBmkoIi+bDd\nQDKUjklrr6pgg+9Py/QkBRo4QnY2eWNe8vZqfJa6VSPZM2siO46eocaxM9TxQuFVcdXRPafPc2HH\nv8zfvY7uVy+QGNOe4+9Pp1q3rjgbXLEk7HZFZdbZidZkcTiyVtHrhVkcxQXddIOHktalGwHbt1aY\nwNqtgPzoEYSMDIfGlnE2lAWSDILAksadWFenJR/uXsmsHUt59NQunox7rMTnaotDyen2B7kRv8H3\nFBcuEDb6KQK2byVv1JPmOKyPSKR6GqPJxMpDiaw6nEhCKXkDa0UoJdvPeYfCNTw7JBbu7YU4bAeZ\nny5F1f9OVC58dtZUPK+oQ9lYqzl5cstx3sJjCo2+VLWq0wqifuxg0IOD0gqlJciXJpWMu2cog3gu\n9hF+aNqFL/9eTEDBxq0jFP42Kgp/pa2T2JUAqBJBxPKfkL31JqaQUHI+nelQTnZlwlY14+ojSQ4J\nmDWMCvF6EYo1iq4vQ+PyTXr1kSS7Ov3Bunzm/r2Iqe0GciyirOjWggd72P/75OU5Vcrvr7Q1UyU6\njJzpn7jUULzG5CUYTVbMppOOnUwUuDzF8T4b/krbCsRaxd3S+L0sjd8LQHIjJfJ5szE+9hjpb79/\nS23KOqNLf+5aJhMW/MmF4XHWJYorAklCyM2x3HTFRWNvNJmYusF6m8NCYq+c4uHT//J++7ssvj9t\n40EGNa9ltRxfsW0LIS8+Q84nM9HdOciltd6SGI0IkuSyPHJ0sIrkLI3lN538zkQHV6xQnn/T1haS\nRGS7FubUOBwr/lnXthv6337H+PV8v7G3wcT9azm04n1mr/rHa0UosqNHCLtvGKGPP+LW1MeVhxLt\nPuEA9L14jItB4ZwIi7b4vr0sDmPT2zDEtCZs1EhCxjyLkFGx8eBKS0HrSclFgx9TuuF9MXoln2Dy\nf6sdnqu1jbk8gd/g20C4dg3ZpYtFzawdKe9fn5qNNHCgp5fmU6w+kuSUsb8z8TDv7V3NvOY9SQ8M\nqvAiFOHaNYJff4WIO7ojSzxP3uhnyowRF/1EeN9Yl+ZfddixzIu+l46xqVZzm16hrSwOU42aZP28\nguzP5hCw5g8iYrsQ8NcGp9d7yxEQQNq2XegGuPY7HdrKek1O9yunGXNkq+Nzle6l7GH8Bt8GsqQL\nAObm5Vjw8C14hZ6WAPA1HA1fFNIgK5VFWxawoXZz3r19cNHrFVWEEvjdArPuza/LyZ00hbTt/6Ib\neFdZo6vRoDh0oKg4yhkSHMi8iNZkEpOezF81bTdBsZvFIQjkPzyK9PhdGJs2I/jVcea4vh/riCLG\n5i1c7h08vHVdGkZZzrNXGg1Uzc9h5Ol/URrKNrEvTqMqIQzzG3zfQZZk9q4sVdk+mnySdfvXEuBg\n+f3NiqPhCwCVQccvG+eRGaDioTuewlQsNl1RRShCTg7aocPNujcvjrOumBhqToEUcnOcPocjmReD\nEg8D8Fct2wbf0SwOU+06ZC7/jYw/NvgbqHgYmSgysX8bi+8VVtou3rwAuWTdNggCTOjXpsIb8fgN\nvg3ExERMQcFFnkBhPu5LiQn8cHQryUo1Rkp6hp4uEPI1HA1fAMQln6Rx1lVG9HuOdAvFVRVRhJI3\n5iVyPp2FVLWqzXGFhXZCtmM3M2fZGd2Q1zuP4HKQG/d5BMEjIn9+yjK4ZR0mD2hb5vVCLR2DIJIr\nty6/PKl/W69kqPkNvg1kSRfM4ZyCx/3uzRoy5cwePj+5k0/rxjC6RRzGUndoT0sA+BqOhC8KWVe3\nFQ0enMaBKpaNkjuLUIT0tPJtxIaaH9mFLOerWx3JvDgeUYNP2thP13VLFodOh3zP7vLP46cEY3o2\nL2P0Cz38dKXa4t6MIFCisK6i8Rt8G+RMnUHGioIdd6ORB375jknn9jO+UUdea9IFycIHeqt5+M4W\njhSXki3vXBbR6VB9NYfIjm1Q/u5YhzKLFIZ0XJAzsJXF4SzuyOIIXLKIiLv6ETTxDdBYSSf04xJj\nejZnwYM9imL6vzZoR2pgMBkBZRukN6oSwvyRPbyahuzPw7eFQnHj0V+SCMvK4MI706jZqjMPeLH3\nqh8LSBIBG9cR9M5EZGfPkP/I4+i69nB9uiZNSdv+L8a6zstiD21Vl/XH3SNt7I4sjvyHRyHk5BA0\nfQps3oRh/nxo2d4Nq6ucyM6eJvSxh8j6cj7GmNblnm9wyzoMal6L3xISWZVQi40XD9HkynlkokB0\nsIrWNSMYGlOXYTHlb3FYXvwG31HkcrK+W4RaEBgJXpUA8CVsFqG4MJcrCKmphL7wFAHbtqDr3pOs\nb77H2CqmfIsJDMR4m+0NVWsMb12XT7Ycdngz2xpuy+KQych7YSy6fgMIf/l55Hf0Jui5MeS+/a7L\nxUeVGSE3F/mJ4wh6nf3BDiITRe5pU5972tQn0HAK8fo1Lv/P8QraisJv8J3hFtHCcYaYmhFuM/iu\nhi+k8HAkhYLMbxehG3S31z+nwiwOe9IKtvBEFoexSVMMW+MRP/s/ZDt2gfwW/fkXFF556maX//ho\nj8zrDlz+NrVv357evXvTu3dvRo8ezenTp+nRowexsbG88MILeEmix08FY6sIpZBAg45TS97moVO2\nNw5dDl8oFGT9vALdXYO9buwLsZbF4Sgey+KQyzG9/gZZ3/7kM3+rCkdvzqSRrIjX3cy4dIvPz88H\nYMuWLUWvDRkyhGnTphEbG8vzzz/PqlWrGDZsmN257IqReSgmbuu8vYNkNPnqc7JmfQVBjula36o4\nEr7IlwcQYDTQ7noSPzfpbHGMQ+ELSUK8moIpunp5llxhFG7OOVOFLAhmY+/xjb1b1dgDgsGzHr4v\n45LBP3jwIBqNhgEDBmAwGJg6dSr79u0jNtZcij5w4EA2bNhg1+A7Ika2d+YEtxt9W+c98cc67j+w\nFqUuj6qrfyP1qr/phC0cDV8cjKpNm+sXLb7nSPhCduI4wZPHIzt6hLRd+yvNjXhMz+bUiwx2SEG0\nUZUQJvTznoKoeOE8gSuWohn7it1G7JUanTl276qWji1UX83BWK++ObTog7hk8IOCgnj99dcZPXo0\np06d4s477yzxfnBwMJmZmbZPLJex/5z9Qpv95xKJaexYMwFH2f+v5fP2TL/M6gPrOKMORdOhE/Uy\nrxXJrTqDXG5uz+fKsZWB0tf3SLempGi0TFi1x+oxB6Lq8Oyx7RblY6cO6cgj3ZpaPvD6dWTvT0H8\neh7UroNh5kzCakR51EMtvL7IMU9D7doYp39Yrvke6daUB7s0Zvm+cyzfd44DSde5XLDvUSNUTds6\nUdzXvgH3tW/g8SwOW99N8eAeZJ98iGrdHxgXLERyQwZLRePQb69vL/T/7SOkaSO339gUi3/E1KcP\nxgc907+g8PpcPt6Vg5o2bUrjxo0BaNKkCVFRUezfv7/o/ezsbMLD7VcQxifY7w8an3CKUf262h3n\nDJbOe3fqBZYlbGJ3aDWGtB3A9uT/oHF9t573ZuZ/fc1ZMdaM/sGo2lTLz6Z6XhZX1AVVrILZ2Bce\nWxpx+TJkY14EgwHje1MwjR0HgYGeuQALCKmpYHC8mYUtZKLIyA6NGNnBd+s0TI+OQmreHPno0ci7\ndsH49iRMr71+823uBgcjlTeLyxrZWYiLf8b48itQ1/eqnl36JL/99lsOHTrEF198QXJyMtnZ2fTv\n359t27YRFxfH2rVr6dOnj805DAYjWw+eLPFa7fwcumWksKz6jR/F1oMnyczMQzx/zmIhjaluPbTD\n7inzuq3xpc8LcH/KGTZE1uaBmD5oZXLUV5LR9uxKjguNIm7VJhNPdWxMtFppMXxxMKo2AM3TL3NF\nHVYifGHt76RQh6EcNBjN+EnmuL1WAq3n/6aF1yepghDS0m+qz9Hud7NJK9iwjaAZ01C99y7SmrVk\nrFoLXs4fdxRv//aqXjLXX+T9+x+6MNvyHa7glQYoo0eP5oknniiK2X/77bdERUXx9NNPo9PpaNGi\nBffee6/T89bOz+X+lDMlDH4hssQLqGd/XuZ1fY9Yiwbf1nhCym6IjW4RhwnBLJUgSdTOzcRYx/mi\nm1udkkUoiRwqaHF4PrwazcfMpX7D2nzlYBGKvkes+fPyElJICGLKZa+d32sEBpI7eQragXchO32q\n0hh7X8IU6pu9MFwy+HK5nB9//LHM61u3bnVqnm4tGhVtzgLsCo/m3vD+ZcYA6GN7cf2U4+JatsZ3\nm7ukxHkB9OKN2FikXotMAJ1fiMolihehOIKQngYyWZFgma9gCg1F7iHxtMqAoWNnDB0tZ1X5sY0U\n5lvf5UK8eut2RGjME2Jk9uZMCwhk3qK1Zp10P55Drydw/lwiO7dF/dkn3l5NGaSQEI+pZVZ6KqB3\nQWVE1zMO8Bt8izgiNOYJMTKHztuqyc23WeVDBPy1gYheXQme+CbaQYPJe+5Fby+pDHlPPW/Wl/dT\ngoDVvxE2bBDiubPeXopLKH9dTkSvbh6ZO3/kwwCYfOxptRCvWrS6VSPZO3NChRdeeeu8fgC9ntDH\nHkS5aQO6Lt3I/vIbDG3aeXtVFpGqVMFfL14WKaoKsksXiezdjZzJ75ulBCpRnF+8lorsdNnEDXdg\nqlPXbPTVZdUyfQFB8pIGgk5nuKmyH4rj7UwBT1Ou69NoCJ7wOro7+qIbPMwnKz5v5s/PXdcmZGcR\n9O4kVD9+i65nHNmff+ETzVccuT7VF7MI+ng6185Xvg358mbpVJ7bsp+bgog+PZDUanRDhvuksffj\nGFJIKDmfziRjya/ITp8i9IlHytdwpiIx6D1SZVsZ8AepLSCkpCBVqQKy8lW13erITp7A2PS2Eq8Z\nm7dEfuSwl1bkx93o7+hLevwuxCtXKs0NXNDrQXFrmj6/h18aSSKqU2tU87709koqLbLTpwh96F4i\nYjsjO1OyqtnQspXZ4FcWb9CPXaSwcJd7B1QUialpLNm2h7FzlzD/jy2k5OYzdu4SlmzbQ2JqmlvO\nIaSkEPTu24iJF9wynye4NW9zNhCuXUPIy8PoA/HIyoaQkY76049QLfgaU/UaZM9biLFh4xJjDC1j\nELMyEZMSMbnQTaoiEa9cJvzuAWR/PserBWCVltxcxJxsr6ublhZL3FylMV+F1eGEm0UaxaspqL+c\nhXbwUJ/9bvs9/FLIksx3Z5MP6mD4Moq/44ns0g7Vj9+hee0t0v7Zi3boiDKP+YYCDZPKENaRlEpk\niecRr1/z9lIqJUH/N4OInp1Q/rLMq090hVl4haQGqDgRFG5zjCsIOi0A8oRD5Z7LU/gNfilkSebq\nXL+H7xyGJrehvWsIabv2o3n1DVBZVis01aqNoXkLBE1uBa/Qcc6nXOeHjTt56ec1AHzw9RK3P/7f\nCmieH4u+Zy9Cn3+K0CceMYvReYF/jtk35o6MsYegNRv8gE3ryz2Xp/CHdEohJiZiCgpGivDn4TuD\nFB1Nzqez7A8UBNK37fL8glyk9OP/16IcQ0aGx3s03IxIVaqQteAHlL/9QvCbrxIZ24nsj/7PnKFV\ngTjivbvDw6fA4JuqViv/XB7C7+GXQjDoMbZoWWkyDioaISMdzrjhx+GjlP7hZ8kVhBp0Nsf4sY12\n2D2kxf+LvmMXlGv+8PZy3ErxzeD/zTHri61NuuazT4N+D78UmldeR/PK695ehtswmkysPJTIqsOJ\nJBQoVwJEB6uIqRnB0FZ1Gd7avnIlBgOBP3xL0Iyp0K49hjVrK2D1FU/pR/sseQChRn2ZMSPjOlbk\nsio9UnQ0Wd//XNRtqiIpLdJobYyzlH4abGt28Fmbms38eUsB33sa9Bv8m5jVR5KsttZLztKQnKVh\n/fFLfLLlMBP7W2+tp9i6meDJ45EfP0b+/Q8ifjjd00v3GqW9937t7yJLprA5xo+DCAIolRV+2u7N\nSxr82cf/RiZJvNC8Z4kxzlJ2M9jcnCdZGVRiTN04v8H34yCuNnmfs/2Yw82zz17PZvTiv5k8oGzz\n7JAxzxK4bDH6Dp1IX7cZQ/sON23rRkskBQZ7ewk3PbJjR5FdSkLXd4BH5i/tvTfKy0Zb6onWFQ+/\n9NOgXhD5snYLTqtCS4zxpadBv8H3YVxt8u6MsS9O4THFjb6uZxy6O/qiHX6vW/c1ZCeOI2RmYujk\nW3rrnnr892OdwEXfo/76K/IeepTcKdPc3hehtFhi2KF1XAtU8UBsh3KJJZb28K8q1bzYrIfNMd7G\nb/B9GEezC4o/Mq4+kuSSsS9kyvoD1IsMLgrvaB94yOW5bKH+7GNkF86RsXazR+Z3ldKP/9bG+HEf\nue9/iLHJbQS/M5GAbVvI/mwO+l53uPUcdatGUjcukpFxHQlf9Q3Gxk3o+txIt56jMuDP0imGcPUq\n4tkzPlP272z+sNFkYuqGgy6dq9uV0wiSuanFtI0HMXq4wYWhZQzyY0fBaPToeZzFWz0abmkEgfzH\nniRt206M9RsQfv8wgt5923Pn02qRlIHlnqYyflf8Br8YgUt/JqJPT/sDKwhn84dXHkq0uEFri8aZ\nKfy2/kv++f1jhlwwVwieuZbNbwmOt5N0BUPLVggaDbLzvtVEo27VSE4snMK3z93DU7ffRp0qEdSp\nEsEDsR2Y9ewDPpd1cTNhqlefzF9Wkz39YwzNyvaddheCNh8psPybx6Wf9AZeS2TCuX02x3gbf0in\nGLKkC2ZJBR/Nwa+dn8P48weY3LAD1wNKeigBa/7g6rYjtMqWcS4kilyFbQ8mVJfHpH1/Mu7wZlJU\noTx0x2hW1WtT9P6qhESHe9K6gqFlgcTC4QSMjZp47DyuUD86ioY5V3hsxmtcP3waqWpVby/p1kEU\nyR/9rEdPkfnTMrc0KCntvfdKT+aeq+eY1qC91THex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6QVY/ZAu32BQwbg9tZMnCi7rvmU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\n/wMfja/f8t3dvAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1679f990>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Bm5s7zz//98IKscTw9fXEza3w+sHVwy4iIiIi16Vy5SoMGHAXXl5e+Pr6Mm3a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"text": [
"<matplotlib.figure.Figure at 0x167ae8d0>"
]
}
],
"prompt_number": 218
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, axes = plt.subplots(1, 4, sharey=True, figsize=(16, 4))\n",
"plt.ylim(0, 4000)\n",
"#\n",
"ALLOW_FLIGHT = True\n",
"for ax, d in zip(axes, [0, 60, 150, 1000]):\n",
" #\n",
" popX = range(0, 11)\n",
" results = []\n",
" for pop in popX:\n",
" FLIGHT_DISTANCE = d\n",
" FLIGHT_POPULATION = pop\n",
" sol, _, _ = flight_sa(path, ALLOW_FLIGHT=ALLOW_FLIGHT, **ARGS)\n",
" results.append(sol)\n",
" #\n",
" ax.plot(popX, results)\n",
" ax.set_xlabel('Population (Flight Distance = {})'.format(d))\n",
" if axes[0] == ax:\n",
" ax.set_ylabel('Solution Distance')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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fobXqjBZe/DCL2vpGHr/A+oRCdCVWm53vdxczYmCoQ9qaVqvhnqkJPPvuTv71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\nu3Zt11AAAAAAALRFi9fsrlmzRunp6dYHU50/f15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"text": [
"<matplotlib.figure.Figure at 0x166f99d0>"
]
}
],
"prompt_number": 239
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Discussion:**\n",
"\n",
"In the plotted city figure, the large circles are those cities which have a population which allows them to have an airport, whilst the smaller circles are those cities that are only accessible via car.\n",
"\n",
"To assist in debugging and to gain an understanding of how the simulated annealing based approach performed, I implemented a TSP heuristic which uses a nearest neighbours based algorithm.\n",
"The algorithm simply arrives at a city, calculates the next nearest city from the list of unvisited cities, and then travels there.\n",
"Whilst there are other algorithms which guarantee better results, this was the simplest to implement.\n",
"\n",
"The minimum spanning tree based algorithm guarantees a 2-approximation (i.e. never worse than two times the optimal path) and [Christofides algorithm](http://en.wikipedia.org/wiki/Christofides_algorithm) guarantees a 3/2-approximation (never more than 1.5 times worse than the optimal path).\n",
"If the simulated annealing based approach outperformed the nearest neighbour method, these would be the algorithms I'd investigate for better baselines.\n",
"\n",
"**Results**\n",
"\n",
"For the initial task, cities were connected with a flight when they (a) both had a population of more than 7, (b) were a distance of more than 200 from each other, and (c) planes were active (see: `ALLOW_FLIGHT`).\n",
"\n",
"For the non-flight task (`ALLOW_FLIGHT = False`), the nearest neighbour method achieved a distance of 2944, whilst the simulated annealing algorithm achieved a distance of 3325.\n",
"Given the complexity of the problem (N=100) and the simple method of permutation available (swapping edge endpoints), the simulated annealing algorithm performed reasonably well.\n",
"If you observe the graph that compares the two distances, flights (where flights would have been available) and ground transport, you see that there two distances are nearly equivalent apart from a few rare cases.\n",
"This is logical as the only time flights would be available are the few times in which a large distance between two cities was selected as part of the solution.\n",
"As the simulated annealing algorithm was optimizing for ground based transport this would be rare.\n",
"This is clear when you consider the nearest neighbour heuristic, which does reasonably well by naively minimizing the distance between close cities, actively discourages large distances which might benefit from flights.\n",
"\n",
"For the flight task (`ALLOW_FLIGHT = True`), the nearest neighbour method achieved a distance of 2790, whilst the simulated annealing algorithm achieved a distance of 3340.\n",
"The clearest distance between the non-flight and flight tasks are that the flight task looks far more chaotic as it encourages jumping from one end of the map to the other as a distant city may have an airport.\n",
"Disappointingly, whilst the nearest neighbour method finds a better solution, the simulated annealing performance is worse than that of the previous solution.\n",
"This should not be the case as the previous solution was valid, though less likely to be returned due to the new lower cost flight paths available.\n",
"This could likely be fixed by performing numerous restarts and selecting the best returned solution.\n",
"This is an intensive approach, and if you did not know a better solution was possible, it may be missed.\n",
"This is a potential disadvantage to the simulated annealing approach when other methods are available.\n",
"\n",
"A potential reason that the second task was more difficult to optimize over is that it has more reasonable solutions than the first.\n",
"This is as all potentially good ground based connections from the first task are available as well as all the newly possible flight based connections.\n",
"\n",
"The second task may have been unfairly penalized as, to allow for a direct comparison, both tasks used the same temperature settings.\n",
"The second task may have benefitted from cooling down more quickly than the first, allowing it to lock in and optimize a particular solution rather than jumping between the many potentially good solution and discarding so much of the progress.\n",
"This can be seen by looking at the two trace graphs of distance.\n",
"The task that allowed flight showed far more variance, especially when the temperature was high, due to all the different possible good solutions that were allowed by the flights.\n",
"\n",
"**Results for threshold analysis (allowed flight distance, population, distance)**\n",
"\n",
"To understand how the number of potential flight routes impacts the distance travelled, I ran a number of simulations.\n",
"The parameters changed for each loop are FLIGHT_POPULATION (the minimum population for the city to have an airport) and FLIGHT_DISTANCE (the minimum distance two cities need to be away from each other before a flight between them is allowed).\n",
"\n",
"Some guidelines for considering the different possibilities:\n",
"\n",
"+ A flight population of zero means that all cities are allowed airports\n",
"+ A flight distance of 0 means that any potential flights are allowed\n",
"+ A flight distance of 1000 means that no flights are allowed (all cities are less than that distance away from each other)\n",
"\n",
"For a flight distance of 1000, only ground based connections are possible.\n",
"The variation between solutions is simply simulated annealing finding various different solutions.\n",
"\n",
"More interesting is the progression from left to right.\n",
"As we increase the minimum distance required before flights are allowed, less of the flight based connections are available to be used by the simulated annealing algorithm.\n",
"This is most evident on the graph describing solutions with a minimum flight distance of 0, where all flight paths are allowed.\n",
"As we increase the population requirement, we are again eliminating potential flight based connections."
]
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"source": [
"Question 3: Project Proposal [0 pts]"
]
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"Write a 1-2 page proposal for your final project. Discuss the problem you wish to solve and be sure to give enough background information that an educated reader who might not be an expert in your area of application (i.e. your TFs) will be able to understand. Please specifically mention the techniques from AM207 that you plan to use in your project. For those working in groups, please give a rough outline of the anticipated division of labor for the project.\n"
]
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"<style>\n",
"center img\n",
"{\n",
" margin: 1.5em;\n",
"}\n",
"</style>\n",
"\n",
"# Faster and more accurate raytracing using Monte Carlo methods\n",
"### Proposed by Taiyo Wilson, Tegan Brennan, and Stephen Merity\n",
"\n",
"Raytracing is a technique used in computer graphics to produce realistic images by calculating the paths taken by rays of light entering the observer's eye or camera at different angles.\n",
"The paths are traced backward from the viewpoint, through a pixel in the image plane, until they hit some object or go off to infinity.\n",
"When a ray hits an object, it may trigger other rays to be sent into the scene, \"looking\" for a light source, to indicate how well lit the first ray is.\n",
"\n",
"<center>\n",
"<img src=\"http://i.imgur.com/JQSlGjU.png\" width=\"450\" />\n",
"</center>\n",
"\n",
"While it may seem counterintuitive to trace the rays away from the camera as opposed to into it, this method actually makes the algorithm much more efficient as most of the rays from the orignal light source do not ever enter the viewer's eye.\n",
"An example of this can be seen above, where the ray may bounce along the wall for eternity and then dodge the camera entirely.\n",
"\n",
"\n",
"Raytracing instead works by making the presupposition that a given ray intersects the view frame (or camera) and traces the ray backwards until either a maximum number of reflections have been reached or the ray has travelled a certain distance without any intersection.\n",
"Objects are then modelled as collections of abutting surfaces, which can range from simple rectangles to more complicated shapes, with the optical properties of those surfaces, such as color, being determined by the values returned by the ray once it has ceased travelling.\n",
"\n",
"How do we end up with an accurate model of how light is transported around the scene however?\n",
"This is where Monte Carlo integration can be employed.\n",
"\n",
"## Monte Carlo and anti-aliasing\n",
"\n",
"If you take too few samples per pixel, the image looks noisy, as if taken by an old camera in poor lighting.\n",
"The reasoning is quite simple: there is too much variance for the number of samples taken.\n",
"In a real camera, the number of samples is the number of photons that reach the film or sensor.\n",
"In our digital world, the number of samples is the number of times we query that particular pixel of the image.\n",
"\n",
"Many raytracers just take a set number of random samples per pixel.\n",
"The optimal situation would be to continue taking samples until our variance falls below a user defined level.\n",
"\n",
"This means that we only use as many samples as we need to.\n",
"In areas that are almost pitch black, we will spend nearly no rays, whilst in areas that are complex, like the area below, we end up computing a smooth gradient when combined with other neighbouring pixels.\n",
"\n",
"<center>\n",
"<img style=\"border: 1px solid black\" src=\"http://i.imgur.com/iYe9B8K.png\" />\n",
"</center>\n",
"\n",
"## The light rendering equation\n",
"\n",
"The following rendering equation expresses the radiance leaving a point as an integral sum of the emitted radiance and the reflected radiance.\n",
"The radiance $L$ of a point is written as a sum of two terms.\n",
"The first is the emitted spectral radiance, or whether the object itself emits light.\n",
"The second term contains the inward radiance scaled by the its projection and the reflectivity function; these values are integrated over the hemisphere surrounding the point.\n",
"In simpler terms, the second term is how much light is contributed by other photons randomly hitting the surface and being reflected towards the viewer.\n",
"\n",
"$L_0(x, \\omega_0) = L_e(x, \\omega_0) + \\int_{\\Omega} f_r(x,\\omega_0, \\omega') + L_i(x,\\omega')(w'\\cdot n) dw'$\n",
"\n",
"where $\\omega_0$ is the direction of outgoing light from the point, $w'$ is the negative direction of the incoming light, $L_i$ is the spectral radiance of light coming inward the point, and $f_r$ is the proportion of light reflected from $\\omega'$ to $\\omega_0$ at the point.\n",
"\n",
"For additional details on this algorithm, Wikipedia provides a [good starting point](http://en.wikipedia.org/wiki/Rendering_equation) and numerous other sources such as [A Practical Guide to Global Illumination using Photon Mapping](http://www.cs.princeton.edu/courses/archive/fall02/cs526/papers/course43sig02.pdf) provide full details.\n",
"\n",
"## Monte Carlo and the light rendering equation\n",
"\n",
"The light rendering equation defines how light is reflected from one object to another.\n",
"In real life, this \"computation\" is done with billions of photons per second.\n",
"Unfortunately, simulating billions of photons is computationally intractable. Monte Carlo methods allow you to quickly approximate the colour and brightness of the given point without the need for millions or billions of photons.\n",
"\n",
"Whilst we could fire hundreds of samples in a naive Monte Carlo fashion and hope for the best, it would be better to use information about both the scene and previous experiments to direct our sampling.\n",
"\n",
"The first and most obvious improvement is to sample directly towards any potential light sources, as this is where the majority of the light in our scene will come from.\n",
"If it is not visible (i.e. we are in shadow), then the light contribution will come from other reflecting surfaces around us.\n",
"\n",
"In this second scenario, we can consult other nearby Monte Carlo sampling sessions.\n",
"These other sessions have already sampled and know, for example, that there is a large soft reflection surface near us that is in direct illumination.\n",
"\n",
"Without this knowledge, we lead a large number of samples, or else we will end up with a noisy image like below.\n",
"The noise is especially problematic in areas that are not well lit.\n",
"\n",
"<center>\n",
"<img style=\"border: 1px solid black\" src=\"http://i.imgur.com/QCw5AiQ.jpg\" width=\"600\" />\n",
"</center>\n",
"\n",
"\n",
"## Importance sampling with BRDF\n",
"\n",
"The bidirectional reflectance distribution function (BRDF) defines how light is reflected at an opaque surface.\n",
"Imagine you had a perfect reflecting surface (i.e. a mirror) and you are looking at a particular point.\n",
"That particular point is being hit by billions of photons, but the only photos being reflected into your eye are the ones that follow the angle of reflection.\n",
"\n",
"<center>\n",
"<img style=\"border: 1px solid black\" src=\"http://i.imgur.com/R1xdzhd.png\" width=\"500\" />\n",
"</center>\n",
"\n",
"If we were trying to determine what light was reflected via Monte Carlo sampling, it would be best to perform importance sampling, as we know the only real contributor is the light that is incoming from the angle of reflection to our eye.\n",
"This would be a clear improvement to efficiency rather than standard MC sampling.\n",
"\n",
"This property is also present in less perfectly reflecting surfaces, except that the importance sampling function is more \"diffuse\".\n",
"\n",
"<center>\n",
"<img style=\"border: 1px solid black\" src=\"http://i.imgur.com/puhlDuK.png\" />\n",
"</center>\n",
"\n",
"In the example above, only five rays are used in both images, but one of the images takes into account the viewer's angle of incidence ($w_0$) and hence knows the direction in which the majority of the light contributions will be coming from.\n",
"Due to this, even though both are equivalent as far as the computational load is concerned, one of the images is significantly less noisy than the other.\n",
"\n",
"## Experiments\n",
"\n",
"Our experiments will consist of implementing and showing the improvements in terms of both image quality and generation time compared to the naive Monte Carlo methods often employed in other raytracers.\n",
"Depending on time and the resulting complexity of implementation, we may achieve the full set of features listed here or might instead focus on one or two of the core ideas.\n",
"\n",
"We will initially write Python code and run it using PyPy, which runs Python code but 10 to 100 times faster.\n",
"If we find this to be a significant issue, we may fall to using C++, especially as rendering is a computationally intensive task."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"[A Practical Guide to Global Illumination using Photon Mapping: Siggraph 2002 Course 43](http://www.cs.princeton.edu/courses/archive/fall02/cs526/papers/course43sig02.pdf)\n",
"\n",
"[Introduction to Path Tracing](http://web4.cs.ucl.ac.uk/teaching/4074/archive/2010/Slides/JK2010/03_path%20tracing.pdf)"
]
}
],
"metadata": {}
}
]
}
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