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williamgilpin/cellular_automata_complexity (1).ipynb

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cellular_automata_complexity (1).ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "2a9d54a3",
"metadata": {},
"source": [
"# Graph traversal, cellular automata, and percolation \n",
"\n",
"Imports: Make sure these are installed in your conda env, and that the conda env is active in your notebook\n",
"+ numpy\n",
"+ matplotlib\n",
"+ scipy\n",
"+ jupyter\n",
"\n",
"For interactive plots:\n",
"\n",
"+ ipykernel"
]
},
{
"cell_type": "markdown",
"id": "a84a2e46",
"metadata": {},
"source": [
"**A note on cloud-hosted notebooks.** If you are running a notebook on a cloud provider, such as Google Colab or CodeOcean, remember to save your work frequently. Cloud notebooks will occasionally restart after a fixed duration, crash, or prolonged inactivity, requiring you to re-run code.\n",
"\n",
"[Click here to open this notebook in Colab](https://colab.research.google.com/github/williamgilpin/cphy/blob/main/hw/cellular_automata_complexity.ipynb)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9ee03d2d-906b-4dee-aee1-b48f2a17a887",
"metadata": {},
"outputs": [],
"source": [
" dimport numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"%load_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "markdown",
"id": "05a02d70",
"metadata": {},
"source": [
"# The Abelian sandpile\n",
"\n",
"### Background\n",
"\n",
"We are going to implement the celebrated [Bak-Tang-Wiesenfeld model](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.59.381), also known as the \"Abelian sandpile.\" This cellular automaton describes a lattice in which sand grains are continuously dropped onto random locations at a fixed rate, resulting in the formation of random sandpiles. When the sandpiles grow too high, they topple, resulting in avalanches that distribute grains to all of their neighbors.\n",
"\n",
"If we denote the number of grains at a site $(x, y)$ as $z(x, y)$, a single \"topple\" event of the BTW model has the following update rule, which triggers only when $z \\geq 4$.\n",
"\n",
"$$\n",
"z(x, y) \\rightarrow z(x, y) - 4\n",
"$$\n",
"\n",
"$$\n",
"\\begin{array}{lr}\n",
" z(x + 1, y) \\leftarrow z(x + 1, y) + 1 \\\\\n",
" z(x - 1, y) \\leftarrow z(x - 1, y) + 1 \\\\\n",
" z(x, y + 1) \\leftarrow z(x, y + 1) + 1 \\\\\n",
" z(x, y - 1) \\leftarrow z(x, y - 1) + 1 \\\\\n",
"\\end{array}\n",
"$$\n",
"\n",
"A topple event thus consists of a single site decreasing in height by four grains, and then distributing these grains to each of its north, south, east, and west neighbors---but not its diagonal neighbors.\n",
"\n",
"After a single topple event, the entire lattice is checked again to see if any other sites now have $z \\geq 4$, in which case those sites are toppled, too. If a site located at the boundary of the domain topples, then any grains that would go out of bounds are assumed to be permanently lost from the system. After all sites reach a state where $z \\leq 4$, the avalanche has concluded. We then add a sand grain to a random new site, and calculate any new resulting avalanches.\n",
"\n",
"This idealized system has several interesting properties: the continuous addition of grains represents a slow-timescale driving process, which effectively injects energy into the system. The avalances represent fast-timescale response dynamics, and the grains that fall off the edges represent dissipation---they prevent avalanches from continuing forever undriven. Despite its seeming simplicity, the BTK model represents perhaps the earliest widely-studied toy model of \"self-organized criticality,\" a well-known hypothesis in nonequilibrium statistical physics that driven, dissipative systems tend to tune themselves into maximally-critical states (there are always sandpiles on the verge of toppling). The sandpile has been used as a thought experiment describing an incredible array of diverse systems, including: starts and stops in dragging friction, [earthquakes](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JB094iB11p15635), timings between geyser eruptions, [timings of pulsar glitches](https://arxiv.org/abs/1403.6528), [fluctuations in an ultracold atomic gas](https://www.nature.com/articles/s41586-019-1908-6), [neuronal activity patterns in the brain](https://www.frontiersin.org/articles/10.3389/fnsys.2014.00166/full), [flux pinning](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.67.919), and many other areas.\n",
"\n",
"A simple signature of self-organized-criticality observed in the sandpile model, which also represents an easy readout for experimental data, is the appearance of $1/f$ noise in the system's power spectrum, where $f$ denotes frequency. This distribution implies that avalanche durations have a skewed distribution, where larger events happen less frequently. For an experimental system, this results in \"crackling\" or brown noise in the detector. In the BTW model, the authors note that a $1/f$ distribution of rare events in the frequency corresponds to a $1/T$ distribution of waiting times between rare events. \n",
"\n",
"Here we will implement the BTW model, and then test for the appearance of $1/f$ noise."
]
},
{
"cell_type": "markdown",
"id": "0f497640",
"metadata": {},
"source": [
"## To Do:\n",
"\n",
"*Please complete the following tasks and answer the included questions. You can edit a Markdown cell in Jupyter by double-clicking on it. To return the cell to its formatted form, press `[Shift]+[Enter]`.*"
]
},
{
"cell_type": "markdown",
"id": "8e9cb0e8",
"metadata": {},
"source": [
"1. Implement the Abelian Sandpile model and simulate its dynamics. I've included a template of the iterative solution below, although feel free to re-factor if you would prefer to implement the problem a different way. There are at least three different ways to implement the Abelian sandpile:\n",
" + The iterative solution involves adding a grain and then repeatedly checking the lattice for piles to topple\n",
" + The recursive depth-first-search solution adds a grain and then traces the avalanche that results from each grain toppled by the initial addition.\n",
" + The breadth-first-search solution adds a grain and then simultaneously tracks the four potential avalanches that result from a single grain falling.\n"
]
},
{
"cell_type": "markdown",
"id": "3465df70",
"metadata": {},
"source": [
"```\n",
" Your Answer: Fill in the code below.\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "6bc995c1",
"metadata": {},
"source": [
"\n",
"2. Using the code included below, show that avalanche durations exhibit a $1/T^\\alpha$ distribution, where $\\alpha$ is some constant."
]
},
{
"cell_type": "markdown",
"id": "b131008f",
"metadata": {},
"source": [
"```\n",
" Your Answer: Fill in the code below.\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "0a9efd17",
"metadata": {},
"source": [
"3. If a single image of the sandpile has size $N$ (the total number of lattice sites), what do you expect to be the worst-case scaling of the runtime of your algorithm? What about the expected scaling of memory usage?"
]
},
{
"cell_type": "markdown",
"id": "d43059d1",
"metadata": {},
"source": [
"```\n",
" Your Answer:\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "48891642",
"metadata": {},
"source": [
"4. You may have noticed that the waiting time and avalanche size distribution exhibit anomalous scaling in their tails, as visible as a small second peak near the extreme end of the distribution. What causes this effect?"
]
},
{
"cell_type": "markdown",
"id": "b6753469",
"metadata": {},
"source": [
"```\n",
" Your Answer:\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "f523c0b6",
"metadata": {},
"source": [
"5. (Optional, Hard Problem). Try [vectorizing](https://realpython.com/numpy-array-programming/) your sandpile implementation, in order to reduce the number of \"for\" loops used in your implementation. How does vectorization affect the runtime?"
]
},
{
"cell_type": "markdown",
"id": "847cc5ce",
"metadata": {},
"source": [
"```\n",
" Your Answer: Fill in the code below.\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "4ba7c649-b71a-4741-b339-406690db8c41",
"metadata": {},
"outputs": [],
"source": [
"class AbelianSandpile:\n",
" \"\"\"\n",
" An Abelian sandpile model simulation. The sandpile is initialized with a random\n",
" number of grains at each lattice site. Then, a single grain is dropped at a random\n",
" location. The sandpile is then allowed to evolve until it is stable. This process\n",
" is repeated n_step times.\n",
"\n",
" A single step of the simulation consists of two stages: a random sand grain is \n",
" dropped onto the lattice at a random location. Then, a set of avalanches occurs\n",
" causing sandgrains to get redistributed to their neighboring locations.\n",
" \n",
" Parameters:\n",
" n (int): The size of the grid\n",
" grid (np.ndarray): The grid of the sandpile\n",
" history (list): A list of the sandpile grids at each timestep\n",
" \"\"\"\n",
"\n",
" def __init__(self, n=100, random_state=None):\n",
" self.n = n\n",
" np.random.seed(random_state) # Set the random seed\n",
" self.grid = np.random.choice([0, 1, 2, 3], size=(n, n))\n",
" self.history =[self.grid.copy()] # Why did we need to copy the grid?\n",
"\n",
"\n",
" def step(self):\n",
" \"\"\"\n",
" Perform a single step of the sandpile model. Step corresponds a single sandgrain \n",
" addition and the consequent toppling it causes. \n",
"\n",
" Returns: None\n",
" \"\"\"\n",
" ########## YOUR CODE HERE ##########\n",
" raise NotImplementedError\n",
" #\n",
" #\n",
" # My solution starts by dropping a grain, and then solving for all topple events \n",
" # until the sandpile is stable. Watch your boundary conditions carefully.\n",
" # We will use absorbing boundary conditions: excess sand grains fall off the edges\n",
" # of the grid.\n",
" #\n",
" #\n",
" ########## YOUR CODE HERE ##########\n",
"\n",
"\n",
" # we use this decorator for class methods that don't require any of the attributes \n",
" # stored in self. Notice how we don't pass self to the method\n",
" @staticmethod\n",
" def check_difference(grid1, grid2):\n",
" \"\"\"Check the total number of different sites between two grids\"\"\"\n",
" return np.sum(grid1 != grid2)\n",
"\n",
" \n",
" def simulate(self, n_step):\n",
" \"\"\"\n",
" Simulate the sandpile model for n_step steps.\n",
" \"\"\"\n",
" ########## YOUR CODE HERE ##########\n",
" raise NotImplementedError\n",
" #\n",
" #\n",
" # YOUR CODE HERE. You should use the step method you wrote above.\n",
" #\n",
" #\n",
" ########## YOUR CODE HERE ##########\n"
]
},
{
"cell_type": "markdown",
"id": "ac8071e4",
"metadata": {},
"source": [
"### Test and use your code\n",
"\n",
"+ You don't need to write any code below, these cells are just to confirm that everything is working and to play with your sandpile implementation\n",
"+ If you are working from a local fork of the entire course, then you already have access to the solutions. In this case, make sure to `git pull` to make sure that you are up-to-date (save your work first).\n",
"+ If you are working from a single downloaded notebook, or are working in Google Colab, then you will need to manually download the solutions file from the course repository. The lines below will do this for you."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8fc85fa8",
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"import requests\n",
"# Check if the \"solutions\" directory exists. If not, create it and download the solution file\n",
"if not os.path.exists('solutions'):\n",
" os.makedirs('solutions')\n",
"else:\n",
" print('Directory \"solutions\" already exists. Skipping creation.')\n",
"\n",
"# Now download the solution file into the directory we just created\n",
"url = 'https://raw.githubusercontent.com/williamgilpin/cphy/main/hw/solutions/sandpile.py'\n",
"response = requests.get(url)\n",
"file_path = os.path.join('solutions', 'sandpile.py')\n",
"if not os.path.exists(file_path):\n",
" with open(file_path, 'wb') as file:\n",
" file.write(response.content)\n",
" print(f'File saved to {file_path}')\n",
"else:\n",
" print(f'File already exists at {file_path}, not overwritten.')\n",
"\n",
"## Import Instructor's solution from answer key\n",
"# from solutions.sandpile import AbelianSandpileIterative as AbelianSandpile\n",
"# from solutions.sandpile import AbelianSandpileBFS as AbelianSandpile\n",
"# from solutions.sandpile import AbelianSandpileDFS as AbelianSandpile\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c25237ee",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Running with Instructor Solutions. If you meant to run your own code, do not import from solutions\n"
]
},
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Avalanche activity in most recent timesteps')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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AANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANgWQQcAANiWTwadlJQUxcbGKj4+3tulAAAAD7KMMcbbRXhLTk6OwsLClJ2drdDQULf3Hz16udv79LS9U3t6uwQAAErlyve3T47oAAAA30DQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtkXQAQAAtlXlg05ubq7i4+PVunVrtWjRQq+//rq3SwIAAJVEdW8XUFHBwcFKT09XcHCwTp48qbi4OPXp00d16tTxdmkAAMDLqvyIjp+fn4KDgyVJp06dUn5+vowxXq4KAABUBl4POmvWrFGvXr0UFRUly7K0dOnSIsvMnDlTMTExCgoKUtu2bbV27Vqn+cePH1erVq3UsGFDPfnkk6pbt+5Fqh4AAFRmXg86eXl5atWqlWbMmFHs/EWLFmnEiBEaO3asMjMz1blzZyUnJysrK8uxTO3atfX1119rz549euedd/Tzzz9frPIBAEAl5vWgk5ycrGeeeUZ9+vQpdv706dM1aNAgDR48WFdeeaVefvllNWrUSLNmzSqybEREhFq2bKk1a9YU29fp06eVk5Pj9AMAAOzL60GnNGfOnNGXX36ppKQkp/akpCRt2LBBkvTzzz87AktOTo7WrFmj5s2bF9vflClTFBYW5vhp1KiRZ3cAAAB4VaUOOocPH1Z+fr4iIiKc2iMiInTw4EFJ0o8//qguXbqoVatWuu666/Twww+rZcuWxfY3ZswYZWdnO3727dvn8X0AAADeUyVuL7csy2naGONoa9u2rTZt2lSmfgIDAxUYGOju8gAAQCVVqUd06tatKz8/P8foTaFDhw4VGeUBAAA4X6UOOgEBAWrbtq1Wrlzp1L5y5Up17NjRS1UBAICqwuunrk6cOKGdO3c6pvfs2aNNmzYpPDxcjRs31siRI9W/f3+1a9dOHTp00OzZs5WVlaWhQ4eWe5spKSlKSUlRfn6+O3YBAABUUpbx8mOE09LSlJiYWKR9wIABmj9/vqTfHhg4bdo0HThwQHFxcXrppZfUpUuXCm87JydHYWFhys7OVmhoaIX7O1/06OVu79PT9k7t6e0SAAAolSvf314POt5E0CmKoAMAqOxc+f6u1NfoAAAAVARBBwAA2BZBBwAA2JZPBp2UlBTFxsYqPj7e26UAAAAP8smgM2zYMG3btk0ZGRneLgUAAHiQ15+jg8qFO8UAAHbikyM6AADANxB0AACAbRF0AACAbRF0AACAbflk0OH2cgAAfINPBh1uLwcAwDf4ZNABAAC+gaADAABsi6ADAABsi6ADAABsi6ADAABsyyeDDreXAwDgG3wy6HB7OQAAvsEngw4AAPANBB0AAGBbBB0AAGBbBB0AAGBbBB0AAGBbBB0AAGBbBB0AAGBbPhl0eGAgAAC+wSeDDg8MBADAN/hk0AEAAL6BoAMAAGyLoAMAAGyLoAMAAGyLoAMAAGyLoAMAAGyLoAMAAGyLoAMAAGyLoAMAAGzLJ4MOr4AAAMA3+GTQ4RUQAAD4Bp8MOgAAwDcQdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG1V93YBQEVFj17u7RJctndqT2+XAAA+gREdAABgWwQdAABgWwQdAABgWwQdAABgWz4ZdHh7OQAAvsEngw5vLwcAwDf4ZNABAAC+gaADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsi6ADAABsy+Wgs2DBAi1fvtwx/eSTT6p27drq2LGjfvjhB7cWBwAAUBEuB51nn31WNWrUkCRt3LhRM2bM0LRp01S3bl09+uijbi8QAACgvKq7usK+fft06aWXSpKWLl2q22+/XQ8++KA6deqkrl27urs+AACAcnN5RKdWrVo6cuSIJOk///mPrr/+eklSUFCQfv31V/dWBwAAUAEuj+jccMMNGjx4sK6++mp999136tmzpyRp69atio6Odnd9AAAA5ebyiE5KSoo6dOigX375RR9++KHq1KkjSfryyy915513ur1AT0hJSVFsbKzi4+O9XQoAAPAgyxhjXFkhKytLDRs2VLVqzhnJGKN9+/apcePGbi3Qk3JychQWFqbs7GyFhoa6vf/o0csvvBB80t6pPb1dAgBUWa58f7s8ohMTE6PDhw8XaT969KhiYmJc7Q4AAMBjXA46JQ0AnThxQkFBQRUuCAAAwF3KfDHyyJEjJUmWZWncuHEKDg52zMvPz9dnn32m1q1bu71AAACA8ipz0MnMzJT024jOli1bFBAQ4JgXEBCgVq1a6fHHH3d/hQAAAOVU5qCTmpoqSbrvvvv0t7/9zSMX7wIAALiTy8/RmTdvnifqAAAAcDuXg05eXp6mTp2qVatW6dChQyooKHCav3v3brcVBwAAUBEuB53BgwcrPT1d/fv3V4MGDWRZlifqAgAAqDCXg87HH3+s5cuXq1OnTp6oBwAAwG1cfo7OJZdcovDwcE/UAgAA4FYuB53Jkydr3LhxOnnypCfqAQAAcBuXT129+OKL2rVrlyIiIhQdHS1/f3+n+V999ZXbigMAAKgIl4POrbfe6oEyAAAA3M/loDN+/HhP1AEAAOB2Ll+jI0nHjx/XG2+8oTFjxujo0aOSfjtl9dNPP7m1OAAAgIpweURn8+bNuv766xUWFqa9e/fqgQceUHh4uJYsWaIffvhBb775pifqBAAAcJnLIzojR47UwIED9f333ysoKMjRnpycrDVr1ri1OAAAgIpwOehkZGRoyJAhRdr/8Ic/6ODBg24pCgAAwB1cDjpBQUHKyckp0r5jxw7Vq1fPLUUBAAC4g8tBp3fv3po0aZLOnj0rSbIsS1lZWRo9erRuu+02txcIAABQXi4HnRdeeEG//PKL6tevr19//VUJCQm69NJLFRISor/+9a+eqBEAAKBcXL7rKjQ0VOvWrdPq1av11VdfqaCgQG3atNH111/vifoAW4oevdzbJbhs79Se3i4BAFzmctDZu3evoqOj1a1bN3Xr1s0TNQEAALiFy6eumjZtquuuu05///vfHQ8LBAAAqIxcDjpffPGFOnTooGeeeUZRUVHq3bu33n//fZ0+fdoT9QEAAJSby0GnTZs2ev7555WVlaWPP/5Y9evX15AhQ1S/fn3df//9nqixVPv27VPXrl0VGxurli1b6v3337/oNQAAgMrJMsaYinby1VdfadCgQdq8ebPy8/PdUVeZHThwQD///LNat26tQ4cOqU2bNtqxY4dq1qx5wXVzcnIUFham7OxshYaGur22qnjBKVASLkYGUFm48v1drpd6Sr+NpEybNk2tW7dWfHy8atasqRkzZpS3u3Jr0KCBWrduLUmqX7++wsPDuXYIAABIKkfQmT17thISEhQTE6MFCxaob9++2rVrl9atW6eHHnrI5QLWrFmjXr16KSoqSpZlaenSpUWWmTlzpmJiYhQUFKS2bdtq7dq1xfb1xRdfqKCgQI0aNXK5DgAAYD8uB53Jkyerffv2+uKLL7R161b93//9n6Kjo8tdQF5enlq1alXiaNCiRYs0YsQIjR07VpmZmercubOSk5OVlZXltNyRI0d07733avbs2eWuBQAA2IvL1+gYY2RZlmeKsSwtWbJEt956q6PtmmuuUZs2bTRr1ixH25VXXqlbb71VU6ZMkSSdPn1aN9xwgx544AH179+/xP5Pnz7tdHdYTk6OGjVqxDU6QBlwjQ6AysKj1+hYlqW1a9fqnnvuUYcOHfTTTz9Jkv7xj39o3bp15au4BGfOnNGXX36ppKQkp/akpCRt2LBB0m/Ba+DAgerWrVupIUeSpkyZorCwMMcPp7gAALA3l4POhx9+qB49eqhGjRrKzMx0jJDk5ubq2WefdWtxhw8fVn5+viIiIpzaIyIidPDgQUnS+vXrtWjRIi1dulStW7dW69attWXLlmL7GzNmjLKzsx0/+/btc2u9AACgcnH5FRDPPPOMXnvtNd1777169913He0dO3bUpEmT3FpcofNPlf3+9Nl1112ngoKCMvUTGBiowMBAt9cHAAAqJ5dHdHbs2KEuXboUaQ8NDdXx48fdUZND3bp15efn5xi9KXTo0KEiozwAAADncznoNGjQQDt37izSvm7dOjVt2tQtRRUKCAhQ27ZttXLlSqf2lStXqmPHjm7dFgAAsB+XT10NGTJEw4cP19y5c2VZlvbv36+NGzfq8ccf17hx41wu4MSJE07Bac+ePdq0aZPCw8PVuHFjjRw5Uv3791e7du3UoUMHzZ49W1lZWRo6dKjL2yqUkpKilJSUi/4UZwAAcHGV6xUQY8eO1UsvvaRTp05J+u3al8cff1yTJ092uYC0tDQlJiYWaR8wYIDmz58v6bcHBk6bNk0HDhxQXFycXnrppWJPn7mKV0AAZcft5QAqC1e+v8v9rquTJ09q27ZtKigoUGxsrGrVqlWuYr2JoAOUHUEHQGXhyve3y6euCgUHB6tdu3blXR0AAMDjyv1STwAAgMqOoAMAAGzLJ4NOSkqKYmNjFR8f7+1SAACAB5Up6LRp00bHjh2TJE2aNEknT570aFGeNmzYMG3btk0ZGRneLgUAAHhQmYLO9u3blZeXJ0maOHGiTpw44dGiAAAA3KFMd121bt1a9913n6677joZY/TCCy+UeDt5eR4aCAAA4AllCjrz58/X+PHj9dFHH8myLH388ceqXr3oqpZlEXQAAEClUaag07x5c8ebyqtVq6ZVq1apfv36Hi0MAACgolx+YGBBQYEn6gAAAHC7cj0ZedeuXXr55Ze1fft2WZalK6+8UsOHD1ezZs3cXZ9H8FJPAAB8g8vP0VmxYoViY2P1+eefq2XLloqLi9Nnn32mq666SitXrvREjW7H7eUAAPgGl0d0Ro8erUcffVRTp04t0j5q1CjdcMMNbisOAACgIlwe0dm+fbsGDRpUpP3+++/Xtm3b3FIUAACAO7gcdOrVq6dNmzYVad+0aRN3YgEAgErF5VNXDzzwgB588EHt3r1bHTt2lGVZWrdunZ577jk99thjnqgRAACgXFwOOk8//bRCQkL04osvasyYMZKkqKgoTZgwQY888ojbCwQAACgvl4OOZVl69NFH9eijjyo3N1eSFBIS4vbCPInbywEA8A0uX6PzeyEhIVUu5EjcXg4AgK+oUNABAACozAg6AADAtgg6AADAtlwKOmfPnlViYqK+++47T9UDAADgNi4FHX9/f33zzTeyLMtT9QAAALiNy6eu7r33Xs2ZM8cTtQAAALiVy8/ROXPmjN544w2tXLlS7dq1U82aNZ3mT58+3W3FAQAAVITLQeebb75RmzZtJKnItTpV5ZQWDwwEAMA3WMYY4+0ivCUnJ0dhYWHKzs5WaGio2/uPHr3c7X0C3rJ3ak9vlwAAklz7/i737eU7d+7UihUr9Ouvv0qSfDgvAQCASsrlU1dHjhxR3759lZqaKsuy9P3336tp06YaPHiwateurRdffNETdQLwsqo4QskoFACXR3QeffRR+fv7KysrS8HBwY72fv366ZNPPnFrcQAAABXh8ojOf/7zH61YsUINGzZ0ar/sssv0ww8/uK0wAACAinJ5RCcvL89pJKfQ4cOHFRgY6JaiAAAA3MHloNOlSxe9+eabjmnLslRQUKDnn39eiYmJbi0OAACgIlw+dfX888+ra9eu+uKLL3TmzBk9+eST2rp1q44ePar169d7okYAAIBycXlEJzY2Vps3b1b79u11ww03KC8vT3369FFmZqaaNWvmiRoBAADKxeURHUmKjIzUxIkT3V0LAACAW5Ur6Bw7dkxz5szR9u3bZVmWrrzySt13330KDw93d30ewSsgAADwDS6fukpPT1dMTIxeeeUVHTt2TEePHtUrr7yimJgYpaene6JGtxs2bJi2bdumjIwMb5cCAAA8yOURnWHDhqlv376aNWuW/Pz8JEn5+fn685//rGHDhumbb75xe5EAAADl4fKIzq5du/TYY485Qo4k+fn5aeTIkdq1a5dbiwMAAKgIl4NOmzZttH379iLt27dvV+vWrd1REwAAgFuU6dTV5s2bHX9+5JFHNHz4cO3cuVPXXnutJOnTTz9VSkqKpk6d6pkqAQAAysEyxpgLLVStWjVZlqULLWpZVpW6kyknJ0dhYWHKzs5WaGio2/uvim97BuyEt5cD9uTK93eZRnT27NnjlsIAAAAupjIFnSZNmni6DgAAALcr1wMDf/rpJ61fv16HDh1SQUGB07xHHnnELYUBAABUlMtBZ968eRo6dKgCAgJUp04dWZblmGdZFkEHAABUGi4HnXHjxmncuHEaM2aMqlVz+e50AACAi8blpHLy5EndcccdhBwAAFDpuZxWBg0apPfff98TtQAAALiVy6eupkyZoptvvlmffPKJWrRoIX9/f6f506dPd1txnsLbywEA8A0uB51nn31WK1asUPPmzSWpyMXIVcGwYcM0bNgwxwOHAACAPbkcdKZPn665c+dq4MCBHigHAADAfVy+RicwMFCdOnXyRC0AAABu5XLQGT58uF599VVP1AIAAOBWLp+6+vzzz7V69Wp99NFHuuqqq4pcjLx48WK3FQcAAFARLged2rVrq0+fPp6oBQAAwK3K9QoIAACAqoDHGwMAANtyeUQnJiam1Ofl7N69u0IFAQAAuIvLQWfEiBFO02fPnlVmZqY++eQTPfHEE+6qCwAAoMJcDjrDhw8vtj0lJUVffPFFhQsCAHeJHr3c2yWUy96pPb1dAmAbbrtGJzk5WR9++KG7ugMAAKgwtwWdDz74QOHh4e7qDgAAoMJcPnV19dVXO12MbIzRwYMH9csvv2jmzJluLQ4AAKAiXA46t956q9N0tWrVVK9ePXXt2lVXXHGFu+oCAACoMJeDzvjx4z1RBwAAgNvxwEAAAGBbZR7RqVatWqkPCpQky7J07ty5ChcFAADgDmUOOkuWLClx3oYNG/Tqq6/KGOOWogAAANyhzEGnd+/eRdq+/fZbjRkzRv/617909913a/LkyW4tzlNSUlKUkpKi/Px8b5cCAAA8qFzX6Ozfv18PPPCAWrZsqXPnzmnTpk1asGCBGjdu7O76PGLYsGHatm2bMjIyvF0KAADwIJeCTnZ2tkaNGqVLL71UW7du1apVq/Svf/1LcXFxnqoPAACg3Mp86mratGl67rnnFBkZqYULFxZ7KgsAAKAysUwZryCuVq2aatSooeuvv15+fn4lLrd48WK3FedpOTk5CgsLU3Z2tkJDQ93ef1V9oSAA7+KlnkDpXPn+LvOIzr333nvB28sBAAAqkzIHnfnz53uwDAAAAPfjycgAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2CDoAAMC2bBF0/vjHP+qSSy7R7bff7u1SAABAJVLd2wW4wyOPPKL7779fCxYs8HYpAFBh0aOXe7sEl+2d2tPbJQDFssWITmJiokJCQrxdBgAAqGS8HnTWrFmjXr16KSoqSpZlaenSpUWWmTlzpmJiYhQUFKS2bdtq7dq1F79QAABQ5Xg96OTl5alVq1aaMWNGsfMXLVqkESNGaOzYscrMzFTnzp2VnJysrKysi1wpAACoarx+jU5ycrKSk5NLnD99+nQNGjRIgwcPliS9/PLLWrFihWbNmqUpU6a4tK3Tp0/r9OnTjumcnJzyFQ0AAKoEr4/olObMmTP68ssvlZSU5NSelJSkDRs2uNzflClTFBYW5vhp1KiRu0oFAACVUKUOOocPH1Z+fr4iIiKc2iMiInTw4EHHdI8ePfSnP/1J//73v9WwYUNlZGQU29+YMWOUnZ3t+Nm3b59H6wcAAN7l9VNXZWFZltO0McapbcWKFWXqJzAwUIGBgW6tDQAAVF6VekSnbt268vPzcxq9kaRDhw4VGeUBAAA4X6UOOgEBAWrbtq1Wrlzp1L5y5Up17NjRS1UBAICqwuunrk6cOKGdO3c6pvfs2aNNmzYpPDxcjRs31siRI9W/f3+1a9dOHTp00OzZs5WVlaWhQ4eWe5spKSlKSUlRfn6+O3YBAABUUpYxxnizgLS0NCUmJhZpHzBggObPny/ptwcGTps2TQcOHFBcXJxeeukldenSpcLbzsnJUVhYmLKzsxUaGlrh/s5XFR/jDgDlwSsgcDG58v3t9aDjTQQdAHAPgg4uJle+vyv1NToAAAAVQdABAAC25ZNBJyUlRbGxsYqPj/d2KQAAwIN8MugMGzZM27ZtK/EJygAAwB58MugAAADfQNABAAC2RdABAAC2RdABAAC2RdABAAC25ZNBh9vLAQDwDT4ZdLi9HAAA3+CTQQcAAPgGgg4AALAtgg4AALAtgg4AALAtgg4AALAtnww63F4OAIBv8Mmgw+3lAAD4Bp8MOgAAwDcQdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG1V93YB3pCSkqKUlBTl5+d7uxQAsIXo0cu9XYLL9k7t6e0ScBH45IgODwwEAMA3+GTQAQAAvoGgAwAAbIugAwAAbIugAwAAbIugAwAAbIugAwAAbIugAwAAbIugAwAAbIugAwAAbMsng05KSopiY2MVHx/v7VIAAIAH+WTQ4RUQAAD4Bp8MOgAAwDcQdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG0RdAAAgG1V93YB3pCSkqKUlBTl5+d7uxQAAMosevRyb5fgsr1Te3p1+z45osPbywEA8A0+GXQAAIBvIOgAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbIugAAADbqu7tArwhJSVFKSkpys/P93YpAAAviR693Nsl4CLwyRGdYcOGadu2bcrIyPB2KQAAwIN8MugAAADfQNABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2RdABAAC2Vd3bBXiTMUaSlJOT45H+C06f9Ei/AABUFZ74ji3ss/B7vDQ+HXSOHDkiSWrUqJGXKwEAwJ7CXvZc37m5uQoLCyt1GZ8OOuHh4ZKkrKysC/5FVVU5OTlq1KiR9u3bp9DQUG+X43Z23z/J/vvI/lV9dt9H9q/yMcYoNzdXUVFRF1zWp4NOtWq/XaIUFhZWZQ5ueYWGhtp6H+2+f5L995H9q/rsvo/sX+VS1gEKLkYGAAC2RdABAAC25dNBJzAwUOPHj1dgYKC3S/EYu++j3fdPsv8+sn9Vn933kf2r2ixTlnuzAAAAqiCfHtEBAAD2RtABAAC2RdABAAC2RdABAAC2ZfugM3PmTMXExCgoKEht27bV2rVrS10+PT1dbdu2VVBQkJo2barXXnvtIlXquilTpig+Pl4hISGqX7++br31Vu3YsaPUddLS0mRZVpGfb7/99iJVXXYTJkwoUmdkZGSp61Sl4ydJ0dHRxR6PYcOGFbt8ZT9+a9asUa9evRQVFSXLsrR06VKn+cYYTZgwQVFRUapRo4a6du2qrVu3XrDfDz/8ULGxsQoMDFRsbKyWLFnioT0oXWn7d/bsWY0aNUotWrRQzZo1FRUVpXvvvVf79+8vtc/58+cXe0xPnTrl4b0p3oWO4cCBA4vUeu21116w36pwDCUVeywsy9Lzzz9fYp+V6RiW5Xuhqn8OXWXroLNo0SKNGDFCY8eOVWZmpjp37qzk5GRlZWUVu/yePXt00003qXPnzsrMzNT//d//6ZFHHtGHH354kSsvm/T0dA0bNkyffvqpVq5cqXPnzikpKUl5eXkXXHfHjh06cOCA4+eyyy67CBW77qqrrnKqc8uWLSUuW9WOnyRlZGQ47d/KlSslSX/6059KXa+yHr+8vDy1atVKM2bMKHb+tGnTNH36dM2YMUMZGRmKjIzUDTfcoNzc3BL73Lhxo/r166f+/fvr66+/Vv/+/dW3b1999tlnntqNEpW2fydPntRXX32lp59+Wl999ZUWL16s7777TrfccssF+w0NDXU6ngcOHFBQUJAnduGCLnQMJenGG290qvXf//53qX1WlWMoqchxmDt3rizL0m233VZqv5XlGJble6Gqfw5dZmysffv2ZujQoU5tV1xxhRk9enSxyz/55JPmiiuucGobMmSIufbaaz1WozsdOnTISDLp6eklLpOammokmWPHjl28wspp/PjxplWrVmVevqofP2OMGT58uGnWrJkpKCgodn5VOn6SzJIlSxzTBQUFJjIy0kydOtXRdurUKRMWFmZee+21Evvp27evufHGG53aevToYe644w631+yK8/evOJ9//rmRZH744YcSl5k3b54JCwtzb3FuUtw+DhgwwPTu3dulfqryMezdu7fp1q1bqctU5mN4/veC3T6HZWHbEZ0zZ87oyy+/VFJSklN7UlKSNmzYUOw6GzduLLJ8jx499MUXX+js2bMeq9VdsrOzJf3vZaWlufrqq9WgQQN1795dqampni6t3L7//ntFRUUpJiZGd9xxh3bv3l3islX9+J05c0ZvvfWW7r//flmWVeqyVeX4/d6ePXt08OBBp2MUGBiohISEEj+TUsnHtbR1Kovs7GxZlqXatWuXutyJEyfUpEkTNWzYUDfffLMyMzMvToHllJaWpvr16+vyyy/XAw88oEOHDpW6fFU9hj///LOWL1+uQYMGXXDZynoMz/9e8MXPoW2DzuHDh5Wfn6+IiAin9oiICB08eLDYdQ4ePFjs8ufOndPhw4c9Vqs7GGM0cuRIXXfddYqLiytxuQYNGmj27Nn68MMPtXjxYjVv3lzdu3fXmjVrLmK1ZXPNNdfozTff1IoVK/T666/r4MGD6tixo44cOVLs8lX5+EnS0qVLdfz4cQ0cOLDEZarS8Ttf4efOlc9k4XqurlMZnDp1SqNHj9Zdd91V6osSr7jiCs2fP1/Lli3TwoULFRQUpE6dOun777+/iNWWXXJyst5++22tXr1aL774ojIyMtStWzedPn26xHWq6jFcsGCBQkJC1KdPn1KXq6zHsLjvBV/7HEo+8Pby8/9nbIwp9X/LxS1fXHtl8/DDD2vz5s1at25dqcs1b95czZs3d0x36NBB+/bt0wsvvKAuXbp4ukyXJCcnO/7cokULdejQQc2aNdOCBQs0cuTIYtepqsdPkubMmaPk5GRFRUWVuExVOn4lcfUzWd51vOns2bO64447VFBQoJkzZ5a67LXXXut0MW+nTp3Upk0bvfrqq3rllVc8XarL+vXr5/hzXFyc2rVrpyZNmmj58uWlBoKqdgwlae7cubr77rsveK1NZT2GpX0v+MLnsJBtR3Tq1q0rPz+/Imnz0KFDRVJpocjIyGKXr169uurUqeOxWivqL3/5i5YtW6bU1FQ1bNjQ5fWvvfZar//Poyxq1qypFi1alFhrVT1+kvTDDz/ov//9rwYPHuzyulXl+BXeMefKZ7JwPVfX8aazZ8+qb9++2rNnj1auXFnqaE5xqlWrpvj4+CpxTKXfRhmbNGlSar1V7RhK0tq1a7Vjx45yfSYrwzEs6XvBVz6Hv2fboBMQEKC2bds67mIptHLlSnXs2LHYdTp06FBk+f/85z9q166d/P39PVZreRlj9PDDD2vx4sVavXq1YmJiytVPZmamGjRo4Obq3O/06dPavn17ibVWteP3e/PmzVP9+vXVs2dPl9etKscvJiZGkZGRTsfozJkzSk9PL/EzKZV8XEtbx1sKQ87333+v//73v+UK2MYYbdq0qUocU0k6cuSI9u3bV2q9VekYFpozZ47atm2rVq1aubyuN4/hhb4XfOFzWIQ3roC+WN59913j7+9v5syZY7Zt22ZGjBhhatasafbu3WuMMWb06NGmf//+juV3795tgoODzaOPPmq2bdtm5syZY/z9/c0HH3zgrV0o1UMPPWTCwsJMWlqaOXDggOPn5MmTjmXO38eXXnrJLFmyxHz33Xfmm2++MaNHjzaSzIcffuiNXSjVY489ZtLS0szu3bvNp59+am6++WYTEhJim+NXKD8/3zRu3NiMGjWqyLyqdvxyc3NNZmamyczMNJLM9OnTTWZmpuOuo6lTp5qwsDCzePFis2XLFnPnnXeaBg0amJycHEcf/fv3d7ozcv369cbPz89MnTrVbN++3UydOtVUr17dfPrpp5Vq/86ePWtuueUW07BhQ7Np0yanz+Tp06dL3L8JEyaYTz75xOzatctkZmaa++67z1SvXt189tlnF33/jCl9H3Nzc81jjz1mNmzYYPbs2WNSU1NNhw4dzB/+8AdbHMNC2dnZJjg42MyaNavYPirzMSzL90JV/xy6ytZBxxhjUlJSTJMmTUxAQIBp06aN063XAwYMMAkJCU7Lp6WlmauvvtoEBASY6OjoEn/RKwNJxf7MmzfPscz5+/jcc8+ZZs2amaCgIHPJJZeY6667zixfvvziF18G/fr1Mw0aNDD+/v4mKirK9OnTx2zdutUxv6ofv0IrVqwwksyOHTuKzKtqx6/w9vfzfwYMGGCM+e3W1vHjx5vIyEgTGBhounTpYrZs2eLUR0JCgmP5Qu+//75p3ry58ff3N1dccYXXgl1p+7dnz54SP5OpqamOPs7fvxEjRpjGjRubgIAAU69ePZOUlGQ2bNhw8Xfu/yttH0+ePGmSkpJMvXr1jL+/v2ncuLEZMGCAycrKcuqjqh7DQn//+99NjRo1zPHjx4vtozIfw7J8L1T1z6GrLGP+/9WaAAAANmPba3QAAAAIOgAAwLYIOgAAwLYIOgAAwLYIOgAAwLYIOgAAwLYIOgAAwLYIOgC8Li0tTZZl6fjx46UuFx0drZdffvmi1HS+CRMmqHXr1l7ZNoDyI+gAKLPXXntNISEhOnfunKPtxIkT8vf3V+fOnZ2WXbt2rSzL0nfffXfBfjt27KgDBw4oLCxMkjR//nzVrl27yHIZGRl68MEHK7YTZWBZlpYuXerU9vjjj2vVqlUe3zYA9yLoACizxMREnThxQl988YWjbe3atYqMjFRGRoZOnjzpaE9LS1NUVJQuv/zyC/YbEBCgyMhIWZZV6nL16tVTcHBw+XegAmrVqlWul3QC8C6CDoAya968uaKiopSWluZoS0tLU+/evdWsWTNt2LDBqT0xMVGS9NZbb6ldu3YKCQlRZGSk7rrrLh06dMhp2cJTV2lpabrvvvuUnZ0ty7JkWZYmTJggqeipK8uy9MYbb+iPf/yjgoODddlll2nZsmVONS9btkyXXXaZatSoocTERC1YsKDU02TR0dGSpD/+8Y+yLMsxff6pq4EDB+rWW2/Vs88+q4iICNWuXVsTJ07UuXPn9MQTTyg8PFwNGzbU3Llznfr/6aef1K9fP11yySWqU6eOevfurb179174Lx9AuRB0ALika9euSk1NdUynpqaqa9euSkhIcLSfOXNGGzdudASdM2fOaPLkyfr666+1dOlS7dmzRwMHDiy2/44dO+rll19WaGioDhw4oAMHDujxxx8vsZ6JEyeqb9++2rx5s2666SbdfffdOnr0qCRp7969uv3223Xrrbdq06ZNGjJkiMaOHVvq/mVkZEiS5s2bpwMHDjimi7N69Wrt379fa9as0fTp0zVhwgTdfPPNuuSSS/TZZ59p6NChGjp0qPbt2ydJOnnypBITE1WrVi2tWbNG69atU61atXTjjTfqzJkzpdYFoJy8/VZRAFXL7NmzTc2aNc3Zs2dNTk6OqV69uvn555/Nu+++azp27GiMMSY9Pd1IMrt27Sq2j88//9xIMrm5ucaY/71R+tixY8YYY+bNm2fCwsKKrNekSRPz0ksvOaYlmaeeesoxfeLECWNZlvn444+NMcaMGjXKxMXFOfUxduxYp20VR5JZsmSJU9v48eNNq1atHNMDBgwwTZo0Mfn5+Y625s2bm86dOzumz507Z2rWrGkWLlxojDFmzpw5pnnz5qagoMCxzOnTp02NGjXMihUrSqwHQPkxogPAJYmJicrLy1NGRobWrl2ryy+/XPXr11dCQoIyMjKUl5entLQ0NW7cWE2bNpUkZWZmqnfv3mrSpIlCQkLUtWtXSVJWVlaF62nZsqXjzzVr1lRISIjjtNiOHTsUHx/vtHz79u0rvM1CV111lapV+98/oxEREWrRooVj2s/PT3Xq1HHU8+WXX2rnzp0KCQlRrVq1VKtWLYWHh+vUqVPatWuX2+oC8D/VvV0AgKrl0ksvVcOGDZWamqpjx44pISFBkhQZGamYmBitX79eqamp6tatmyQpLy9PSUlJSkpK0ltvvaV69eopKytLPXr0cMvpGn9/f6dpy7JUUFAgSTLGFLnA2RhT4W2Wtu3S6ikoKFDbtm319ttvF+mrXr16bqsLwP8QdAC4LDExUWlpaTp27JieeOIJR3tCQoJWrFihTz/9VPfdd58k6dtvv9Xhw4c1depUNWrUSJKc7toqTkBAgPLz8ytc5xVXXKF///vfTm0X2rb0W4Bxx/bP16ZNGy1atEj169dXaGio2/sHUBSnrgC4LDExUevWrdOmTZscIzrSb0Hn9ddf16lTpxwXIjdu3FgBAQF69dVXtXv3bi1btkyTJ08utf/o6GidOHFCq1at0uHDh51uW3fFkCFD9O2332rUqFH67rvv9N5772n+/PmSVOqt7NHR0Vq1apUOHjyoY8eOlWvbxbn77rtVt25d9e7dW2vXrtWePXuUnp6u4cOH68cff3TbdgD8D0EHgMsSExP166+/6tJLL1VERISjPSEhQbm5uWrWrJlj9KZevXqaP3++3n//fcXGxmrq1Kl64YUXSu2/Y8eOGjp0qPr166d69epp2rRp5aozJiZGH3zwgRYvXqyWLVtq1qxZjruuAgMDS1zvxRdf1MqVK9WoUSNdffXV5dp2cYKDg7VmzRo1btxYffr00ZVXXqn7779fv/76KyM8gIdYxp0nrAGgkvvrX/+q1157zXHLNwB74xodALY2c+ZMxcfHq06dOlq/fr2ef/55Pfzww94uC8BFQtABYGvff/+9nnnmGR09elSNGzfWY489pjFjxni7LAAXCaeuAACAbXExMgAAsC2CDgAAsC2CDgAAsC2CDgAAsC2CDgAAsC2CDgAAsC2CDgAAsC2CDgAAsC2CDgAAsK3/By2fBC5ASVO5AAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ijEmOudWrV0tWVpa330PHb8eOHSU3N9f5LZFIqM9xumnt3mn3dNv1XnnllZHrHTdunIhI8ppTuaerVq0SY4yUlZVFzvPyyy9H+rWsrCxSx7b7tm2MnXHGGfLAAw/IypUr5Sc/+YmUlpbKkCFDZN68eWp7QslOe407kQceeECMMfK3v/1N/va3v0X2T58+XX7zm99IVlaWjB07Vq644gp58MEH5ZZbbpG//OUvctxxx0lJSUmy/EMPPSSVlZUya9Ysx6ejvr5ebUsqx7ZE586dJSsrSz799NPtOh7p2rWriIj87W9/k169egUf/9BDD8nIkSPl7rvvdn7fuHGjs92tWzd56aWXpKmpKW2T2LYviTvuuEPWr18vM2bMkPr6ejnnnHNSqvfUU0+Vq6++Wv70pz/J0KFDpbq62vsV0F4pKSmRzMxM+eKLLyL7Pv/8cxFpvv/5+fly0003yU033SSrVq1K/s/9hz/8YfI/d9tDSz5QXbt2lby8POc/krhfZOuY2bJli1RXV7c4Edplt3f8xo1t13vttdfKCSec0GKZfffdV0RSu6ddu3aVjIwMefHFF5P/2bLB37ZNrDbV1dUi4v7n7ZxzzpFzzjlHvv76a3nhhRfkxhtvlDFjxsgHH3yQ1vsX2wlsy5YtMn36dNlrr73kvvvui+x/4okn5Pe//73MnTtXxowZIyUlJXLcccfJn//8Zxk2bJhUV1dHzFwZGRmSk5PjPIzV1dXy2GOPqe1J5diWyMvLkxEjRsjs2bPllltuSQ7o7eUHP/iBZGdny0cffSQ/+clPgo/PyMiIDOa33npLFi1aJD179kz+Nnr0aJk5c6Y8+OCDXjOi/bXZFs455xyZPHlysu5hw4ZJv3791ON858nNzZXzzjtP7rzzTlm4cKEMGDBAhg8f3uY2tRfy8/NlyJAh8sgjj8jvfvc7ycvLExGRpqYmeeihh6RHjx6yzz77RI4rKyuTs88+W9588025/fbbZdOmTdKxY0fnq3FbXdvDmDFjZOLEidKlSxeprKxstdzo0aNl0qRJcvfdd8vNN9/cYplUx29LhHwdb0/5VNh3332lb9++8uabb8rEiRPbfFzoPR0zZozceuut8tlnn8nJJ5+s1r9x40aZM2eOY0acMWOGZGZmyhFHHBEpn5+fL6NHj5aGhgY57rjj5N133+UEJrLVbv7555/LbbfdJiNHjozs79+/v9x5551y//33y5gxY0Rkqxlx1qxZcvHFF0uPHj3k+9//vnPMmDFj5JFHHpFx48bJiSeeKFVVVfJf//Vf0r17d/VzPJVjW2PKlCly2GGHyZAhQ+Saa66RvffeW1atWiVz5syR//mf/3E0NI3evXvLzTffLNddd50sX75c/uM//kNKSkpk1apV8sorryT/F+e7vv/6r/+SG2+8UUaMGCFLly6Vm2++WSorK6WxsTFZbuzYsTJt2jS54IILZOnSpXLkkUdKU1OT/Otf/5L99tsvqVXuv//+Mn/+fHn88cele/fuUlBQkPwfZUv069dPhg0bJpMmTZKqqiqZOnVqm65bO8+4ceNk8uTJ8tprr7X4H6G4MGnSJDn66KPlyCOPlCuvvFJycnLkrrvuknfeeUdmzpyZ/I/VkCFDZMyYMXLAAQdISUmJvP/++/KXv/xFhg0bltRk9t9/fxERue2222T06NGSlZUlBxxwQNLM1VbGjx8vf//73+WII46Qyy+/XA444ABpamqSTz75RJ5++mn55S9/KUOGDJHDDz9czjjjDPnNb34jq1atkjFjxkgikZA33nhDOnbsKJdccknK47clCgoKpFevXvLYY4/J9773PencubN07do1Es1lG3vttZfk5eXJX//6V9lvv/2kU6dOUlFR4eiT6eR//ud/ZPTo0fKDH/xAzj77bNljjz3kyy+/lPfff19ef/11mT17toikdk+HDx8u5513npxzzjny6quvyhFHHCH5+fnyxRdfyEsvvST777+/XHjhhck2denSRS688EL55JNPZJ999pEnn3xS7r33Xrnwwgtlzz33FBGRX/ziF5KXlyfDhw+X7t27S3V1tUyaNEmKiopk8ODB6e2knbJUZAdw3HHHmZycHO8KvVNOOcVkZ2cnl4Ju2bLF9OzZ07vi6dZbb036U+y3337m3nvvbXWFEa5ua+uxAstOfXW+99575qSTTjJdunQxOTk5Zs899zRnn312xA8MV3q1tJrPmK2rnY488khTWFhoEomE6dWrlznxxBPNM88802J/bKO+vt5ceeWVZo899jC5ubnmoIMOMo8++miLK/+++eYbc8MNN5i+ffuanJwc06VLF3PUUUeZhQsXJsssWbLEDB8+3HTs2NHrB2YzdepUIyItukQY0/IqxNbOYzNy5EjTuXNnZwmzD98qxG0+advYdn98flTGNPvYINt8iZCWxtA2P7D8/HyTl5dnhg4dGvEtvOaaa8zBBx+c9Cvq06ePufzyy82aNWuSZerr683Pf/5z061bN5ORkdFmP7CW+Oqrr8z1119v9t13X5OTk2OKiorM/vvvby6//HJnifaWLVvMf//3f5v+/fsnyw0bNizS/raM321+YEhLz+IzzzxjBg4caBKJhNcPbBszZ840/fr1Mx06dGizHxjS0r3bNqZ++9vfOr+/+eab5uSTTzalpaWmQ4cOpry83Bx11FHJVdfGpOeePvDAA2bIkCHJsbPXXnuZM88801kVu+0+z58/3xx88MEmkUiY7t27m1//+tfOSsnp06ebI4880pSVlZmcnBxTUVFhTj755KS7UjrJMMaY9E6JhMSHmpoa6dWrl1xyySUyefLkXd0cQtotI0eOlDVr1sg777yzq5uSJLYmREJS4dNPP5Xly5fLb3/7W8nMzJTLLrtsVzeJEBJIrJfRE7K93HfffTJy5Eh599135a9//avjq0MIiQc0IRJCCIkl/AIjhBASSziBEUIIiSU7bAK76667pLKyUnJzc2XQoEHy4osv7qhTEUII2Q3ZIasQZ82aJePHj5e77rpLhg8fnnTIe++995LObq3R1NQkn3/+uRQUFLTrFN2EEELSjzFGNm7c2LaYqmn3LDNb05RccMEFzm/9+vUz11xzjXpsVVVVi8nX+I//+I//+G/3+bct15qPtH+BNTQ0yGuvvSbXXHON8/uoUaNk4cKFkfL19fVOwFvzf4siD5NjJFs6pLt5KZFdVrrLzt3UrdjZzly9Pqh8KqRyLu3YVAm5TmxLOvuooUtHZztn7aZd1pamdz5wtn3jNvS8eJ0h1HV2Xze5XzY621qf7UxSGbdan+L9aRwxoNWyoX2SSrsbV+kpf3YGjbJZXpIn2xQqL+0T2Jo1a2TLli2RsPtlZWXJqMU2kyZNajGGWbZ0kOyMdjaBZYbFgksnTVluIN1MpS1YPhVSOZd2bKqEXCe2JZ191JTtpu7Iztqy69oCz41v3IaeF68zhOwO7usmO9udwLQ+25mkMm61PsX7I54+De2TlJ639vK+3foN0yYJaYct4sCTG2NabNC1114rtbW1yX9VVVU7qkmEEEK+RaT9C6xr166SlZUV+dqqqalpMRlaIpFoMQ/NriK73G1jU2lzvrAmKJtZs85bV2N1NHeOc/wBracDaeia7z0W/5+F5XPWfO2eC9pqX5d2HXbZlsrjubOfe635WKjL179twdfWVK8jpC1af2vUfcdNVGof3/SWP4cTjptIW3BcBVynNu6Qui5tf4UULq11tjfsWwR1udvFL37src93HaFjIdKH3qP959LO3XDUIGfb34duu3LfSy0/YMhzHwfS/gWWk5MjgwYNimTfnDdvnhx66KHpPh0hhJDdlB2yjP6KK66QM844Qw4++GAZNmyYTJ06VT755BO54IILdsTpCCGE7IbskAnspz/9qaxdu1Zuvvlm+eKLL6R///7y5JNP7hapwAkhhOwc2l0w3w0bNkhRUZGMlB/vlFWIqMn40DSSUJsy1oeagA3qB+kE243anaq5gP7j01E0rShUl7L1olB9LVUdy4d2HTvy3IjvXNqYRa0OwXbjGM5d27zSELWe2j5ZznbPuV96z+Vra+iz6dMgQ9E0SxyXIX2KdWvvK+3ZdfYFvq80TT9dNJrNMl8ek9raWiksLPSWZSxEQgghsYQTGCGEkFjCCYwQQkgs2SGLOOIE2nV9Nma0RzeCP4d09ftsaDqIrReE+nto1+GzjUf0A8XWnYpeEKr9aFqSfR2NeH9Aa0ANxu7v7Wmbr52paCyoI4XqnyHXEaLDiuh9hm21n5m684Y5+xLrXPndp5+JSOT58l2Xpu/g87X+8N7+8tgWux0enUkk6guJ7cb3Sqb17OKxmtYXeaF7nh/NLzJSt/JO2RXwC4wQQkgs4QRGCCEkluz2JsRUQDMEmo20T3QtHJSN9rke4g6AbcF2RpajK3WhCcRnUsFrDF3K610SDucNCXMkoptt7XugLY2Ontsfosm+Lp+5Csu2hGa6tqkZ6jdJFS9r8O7X6svdd0jz3+u0keQHr8t3P5CQ5eUi0Xuwfu/mp7X0ZSVUVOD9yfS0XWtn6PPzbQgfZcMvMEIIIbGEExghhJBYwgmMEEJILKEGFkBoSJiILVxLkeJZFhyqcWmamaMfwL7QsDxow6+zrhOvCbdDtT1Nd7TBJd2hqUJC3Aui1+nu15aIrxrcekqhssXuNupreJ26Hme1A3QpbBceW1fi/p+3vsTN8Ve0vPUEjKH3I7LcHLVa79EukSXgoNsWij9cmq17aW4O2hjFJfuYNsb3bCKh7hr2s5tuXX1XwC8wQgghsYQTGCGEkFjCCYwQQkgs+dZrYKlqR/bxmjaE9ufQlBq+shp4rnSGfUnFd0T1iQm8P9gvdp+n6h+l6QmOT05gn6C2FNUqmjWwhmI3xJLtgyQS1a208E9aW3ztquvirxs1L6zb7vPQ1Cza82PXFxqSDP2rQnw0UbPSyH7uNWc7F0LQRTWx5r9D/dc0fO+BUF+69gC/wAghhMQSTmCEEEJiCScwQgghseRbp4GFal4p+ZaAbVvAPq3pWL54eaEpS7S4iyGaWKjm5dOONF0K7f+hqUPsOIwYgzESNxGOxevM1VK3eOJHhqZTwbb1nPtlq/vQR6y+JMvZLltcLyHY407zzYr4OMF+1OcKl7buuxWqU6WCdj8QvPe+mJshKZha3B+giRUuDYunikRSNlltwetQdffA695umhpE2ii38QuMEEJILOEERgghJJZwAiOEEBJLvnUaWKr47MARvxQ8FlODKz4b6E9i274xll6oPqDGM7RTi+M+OJfmi+KN4Qj2/kaw96PfEPo0YR9FtCerLT7doi1ofWb3Q2agD1lI21BXSqxz/cIwH1XoddtjSzsW92PbMF9YRHOx/MC0/tX2h8SyDPXZxPI+n8FUtR88/ivQwn1+etjO0HeOfTyOYY32GBuRX2CEEEJiCScwQgghsYQTGCGEkFjyrdDAQuIVIlq8NdvGjFqRahNWfFHqPDmiNB1KIzTHl69spC7leLvtmCsM7f0aIfHzQv2MNF+uSD9Y11Kn6DGatuTXNEGPWaf1uEuIjhjJ99Wl9TEpoutviO/+afcL9R0cOV+dNKT5PNBu9F9LVQ/1vQc08D0R0ds8Odhy31O0b0Xz8ml5qfrdpRIbMV16Gr/ACCGExBJOYIQQQmJJLEyI2ie4/UmvpZbQUiFETD+eT3RMS659FkdSjUMYJcecA6aX7MDP9cjnfUAYmEj/akvyPaY3vB+Ykh4pn7Pc2cZQUwi6G/jalc79Wtr4MJOhe79y1/UOaheaokPQQklp5xbNhOgxGfvuXVuw2661O2QJvkj0/mZ6QjBpREJPYYHAtqWCbQpF874G06kQQgghaYITGCGEkFjCCYwQQkgsabcaWHZZqWRnbg1bE7o03kdoim7bdo528Uj6FDhWWwrfaba77S4LhvAyEIIpksolBTT9BnUsXPaLKR1qhjbfL1wCjsuwQ/sI75d9fyJ6i6K/aW3RltnbaJqXph9giC2b0BT2kbo9eihqoXgvUTvS3Boi49YaK7gvNARWRAsPOFYLkYXPti9liqZ1h6ZbQXw6sZZ+SNV17ecnQJdNlch7Nk2pc/gFRgghJJZwAiOEEBJLOIERQgiJJe1WA7PRtAnN98tmzXnDnG3UQXyhV1LxhxKRiC8W2oVD/Fo00O4ekj5cDQ8U8e1xy9t9ivcG684O9KWL2M5tDUzxMUM9ztbqRERKX3bL++4n7gsNy+PTvDrN/pf7g3IvRXoHndsmVX0Zn5dc2O/TzLRxlBugHYWmhYmcG3Vgj68pEgl5Fah5YVtzrbah5oVjvG4ohh1ru98llo2kcUFfVEV319YT2PhCdTWazW2uh19ghBBCYgknMEIIIbGEExghhJBY0m41sMZVNSIZHUREtynb2pEaCxFSoKMOgqks7PJa/DuMaYblG0D38Nnp0UaP/h7ogxbRljCWm8c+rfrIeFKci7RgGw85F/RJJqZ6B30BcTSXvft4y0aOVdKU+PzAUJtAXy3Nhwb7zNbEIvoYlLX9BVsi4jemxBK1CY11iHg1L0WjxNcR6mk+fzaMWar7mKUv/iA+W6ExUhGf75wWK7S2T5a37rLF9a3WrYHjMiR9keYb58RlbGoQaaMLGr/ACCGExBJOYIQQQmIJJzBCCCGxpN1qYD58PjedFM0kwt7DvLttOzHm74roUmkE60atDvWbSFpyJb6hDfanFg8vEhMS/ZSse1Aorj6AGqWWjwq1DU0T84EaDPahdp2+3GTVP3L1t+Jl/piBqeBLQd8W7Put+YFpum9k2xMLEfUb7DMNn46LYzhX8ctD/0PNh8n3zolopUrcPyzvG3eoAyKodxYuTV/dWtxLLUaqdg9sHH/bLfXUwAghhHy74QRGCCEklnACI4QQEktioYFpeZlSyVuDdnnNPm2j6TlYl5Zny9Fo9kYlyo/mN+az4Wu27ojmBYT0v9ouxe/IF+OxfI5bVtNYon5Jbh+uj+hazT6B6+H+aD5lyKrBiVb32b46Iv64iSLR2InotRfJo2XrDaAFaVeBMQKRui7umPZpr6F95iP0HRHxzVLK2y2N+DApGpeaV84z5lPNLYb44nki6KuI/ofa82NrbL4xmAr8AiOEEBJLOIERQgiJJZzACCGExJJ2q4Fl9t9HMrNa1wl22HnBLmz7i6AWgX4Pml8E6gFoQ64vyUj+nVhnvO3U/MQE2+Kxs2uxEFPRGJGInxfs1/Q2xPa50RQVTXPR4sjZupfmh6f1KepcIWh5mTSdxB7jmWqusR2H5pen6SR2n2px+bQ+CbluNa4fvEPQf7AQ6vO1Xcvrp527LhIb1hqHit8j1h2JsQmglm5ft3bs9sIvMEIIIbGEExghhJBY0m5NiCHYn7qhJhDtk9zZVkw3ucpy54iJEc1Q1tc/mldwuT/Sdaq7HFpLueEjEpoI6oqkvAd8YXnQTIFmIjRD+NKOILi0HdGW8NeVuMvmbZNuqoRch2Yi1AhZer1TTYZwbzG1EaKF9vLdbc38qC0hD0F1Q1GkBp/7TUTSCDSF+kJLRSQNuI5g9xk83rpuNKNqJve2wi8wQgghsYQTGCGEkFjCCYwQQkgsabcaWObq9ZKZudXKrdmzbVtsKmkRtLoj+0DHCA0vhHZgl/TeGmybralhyCWt3aiv+VKiaHZ2LQRWA/SxLwQTuh7gdWghf7B88bLW05bgknv/vWy/aMu0Q8H7h3qPr6x2fxA7DFaqIZa0frDfK77wcm0Bl5SHhFUK0uwl6lri05o0HUobGz6dd0c9H/wCI4QQEks4gRFCCIklnMAIIYTEknargfnw2ac1QtMuaKksfGihcrRwQ+kkJHVFNE2CgieEFl5T1dGuFlewAs6NIbEUvu7dfK6i5a7fFtrdNf0NWX4ShpZq1tj6zHZDQWFdOWvcI7VxlKrvl1NXCnpQutNeoM6VCuhL1Gl287Maqt1p15kZkFYpNPxZOgkNLWVfZySsG7yPUtVDt9e3KwR+gRFCCIklQRPYpEmTZPDgwVJQUCClpaVy3HHHydKlS50yxhiZMGGCVFRUSF5enowcOVLefffdtDaaEEIICZrAFixYIBdddJG8/PLLMm/ePGlsbJRRo0bJ1183fypOnjxZpkyZInfeeacsXrxYysvL5eijj5aNGzemvfGEEEJ2XzKMMf68HR5Wr14tpaWlsmDBAjniiCPEGCMVFRUyfvx4ufrqq0VEpL6+XsrKyuS2226T888/X61zw4YNUlRUJN8v+4VkZ/pj220jJE02kk7NC3WMz64+1NkuWr7F2fb5T6GmoqUj0GzhqB/40OIwot+YD4wn2FDsH26bi90+yv/Y7QfsQ1vnwj4L9T1BfQ7bUvFc87VosdxsHyURfVylU0fRNGL7GdHGDeqG2nXiuXy+Wqg7oSYTcj9D+y9U2/P1GaJpkNp122B/p/p+8/mzafdWI2Qtgo/GLfXy3Du/ldraWiksxOQzcM5UTlRbu/UF3LlzZxERWbFihVRXV8uoUaOSZRKJhIwYMUIWLlzYYh319fWyYcMG5x8hhBCisd0TmDFGrrjiCjnssMOkf//+IiJSXV0tIiJlZe7/QMrKypL7kEmTJklRUVHyX8+ePbe3SYQQQnYjtnsCu/jii+Wtt96SmTNnRvZlZLhmI2NM5LdtXHvttVJbW5v8V1VVtb1NIoQQshuxXX5gl1xyicyZM0deeOEF6dGj2UZeXl4uIlu/xLp37578vaamJvJVto1EIiGJRDS+XVO3YmnKajnuHdqBfXZhze8rhNBU7pg2XvM7SoWI/TmS68rvk2bTdeoi9we4LjzWV/eXA13NCzUt1MQ6v9G675WIyOqD3HP1nGedV9Gl0OaP97PyOffMqGHWlTS3JXetWzai30C8SGybT7NJRZ8R0ePh2fWnOiIjeg8+m9b+EO1HRNcw7eepDjTedPqfibhaYE6K75Qa8HVEnRjfGzaoZaM2jvsxH5gdmzLV+ITavQ9he/0Ng77AjDFy8cUXyyOPPCLPPfecVFZWOvsrKyulvLxc5s1rfqs0NDTIggUL5NBDD8XqCCGEkO0m6D9gF110kcyYMUMee+wxKSgoSOpaRUVFkpeXJxkZGTJ+/HiZOHGi9O3bV/r27SsTJ06Ujh07yqmnnrpDLoAQQsjuSdAEdvfdd4uIyMiRI53fp02bJmeffbaIiFx11VXyzTffyLhx42TdunUyZMgQefrpp6WgoCAtDSaEEEJEUvQD2xFs8wM7qv+vJPv/NDAtT1CIr4kW+xCxc1+F6BgtgfbpSKw+y6bfafa/vHWFXidi+3Kh5qX5AiGYo8vWtbq93na9rCWwfPGyBmfbznOGdYX6amn+O/l/a67vkw1uf2dN6+I9FvHlhEpFp8W6NPBcmt9XKmiaV+i5bD0HNS/NhyndMR99aJqXlsfO2ed5Z6SKlp8N0fosxN/Qrmun+YERQgghuwpOYIQQQmIJJzBCCCGxJJb5wCJ+YB7tQrPjhsQMjPiBBeZd0n1TmjUCjJ0X0W+UmjRNzIlvGHgdaHfH+IS2bqVpXrgf9QGsG+MV2hqbL7akiMhHY8FmP3ZYq3W11LYv325uy4ofT3X2nXzZ95zt9x7f19nG6wjRLFONvReC5juXiiamxTYM1v4sDQzbmRvYJ5pmFhLnDzUvpP7ATe4Pb3Z0NnM93YD9X9fFzcWXTv83TeNSNU3r7x010fALjBBCSCzhBEYIISSWtFsTYkOXjtKUnbt1A80DAcvXtTQiuJx5Ry5TDUFLUa+BJhE0OfrMTprpAE1rpS+7Ng/fwldt2TZe9+dHuUuMs4u+cbZr19vmF9ecUtvHDUtVsMLvMYLnEnHNfh3WN9d3fc3+zj5cVo8mQ3SL8Jm9U8VeXi6i3y8bvD+5KS7pd+pSTE7RMEhtN4dFTOyBbiWqGdY6HuvG/kYzOYY/K/2H63ZihygTcd9Bmsk21GRovxd8aXbagpbsKtPTZ76ymU0NnpJwXJtLEkIIIe0ITmCEEEJiCScwQgghsaTdamC5//5csjO3WlkjOomim4SgaWS+kE6hdnYtJJaNtsRYW1qt4Ts+E9qF/YvhnELahtoP6pmYFkOj04ia5mPXdQs6dvS4l5zt/nluW377+1Oc7Y2VrZedtd51e9gT7l/IUnct7A6Ofy0pBmoy9jLv8jnpHVc+sqHuryDlDILaEhKi/2h9GnLdjdD/qLUiOevdbdQkI+Ut3atqdGdnH4adwmdRexfmdm0ep6EuEaHvO7tPuYyeEEIIseAERgghJJZwAiOEEBJL2q0G5sNOoYFoKTUwHBTa4dEvzD46JJyMiG53j/iPpJjiOwSvHxhsa1pDxDbu0fawbk3n6DPb9adaNdgNu7P2QGtjpOsj1qX4K7fs+k7ONupYj6w+yNnucNxqZ/vmvZ5N/n37R27oqL1vrZN0ERLeTCR83NjPCOppqFMhGOIsFTSfy5DrUsMawbNbh+WxH+A94bvunnO/dLa19Cm4bacfEhEpfbn5b1+YNpFon2nh1Hz7Qn3+fGmtEO1duL3wC4wQQkgs4QRGCCEklnACI4QQEksyjDH+AHE7mQ0bNkhRUZF8v+wXST8wtJ/6/EfQbo5+RqGpKXy+WiF+ECJRDQ1t0LY9OzRFukYqsQ81/7WQGGqanqPpbb4+qzm+3tnXWOtqpYP3/8jZXvz2Xs62HetQRGTA4R8422980jP5t6Z54f1Kxeav9RmCOi6Culc68fkh4bOJfkioHaGe7dN3tPio1T/q492P/lSIrbtrKYGwLmwbtgU1MdvXC+NWhsYS9b0PtXGA7Q59T2wvjU0N8syqe6W2tlYKC32RVfkFRgghJKZwAiOEEBJLOIERQgiJJbH0A0Mbv22bTXfMwFSI6B7QNvRmy33Pk6cphdhtLZVPJTafz8+rpfI2nWb79UxNB0FsXST3Plcfqzra1bSWvLiPs90B6ur2unuujTPd2Ip7S7PuFapJphaLr7ezhZpL+ZzlAXX5fb00Py/0j0Jd15fiXstRV9zVPTf6e6IaYmtoeM3p9FcLJZLLD54XLX6hHVsR/SSLUQMLjANrvyvVY0EjQ80y5F2rjfft1Yj5BUYIISSWcAIjhBASSziBEUIIiSWx1MBCCM37E6L3pOIP1VJ5uz7Njyj0unz+bWhnD8mzlCqReHglOd79PtBGv7nY1cCyi1ztIWNlnvdcO7Jfon5Jfj+lnQVqXEhoPNAdifP8QLtwLBTDsbgf/QtXDU4422WLXR9Dm9y17jZqS9o4Qt3Q9gMLjnOp+NrZ14ntwHZqmhe+/0ImE8ZCJIQQslvDCYwQQkgsiYUJUQvvZH/aamY97dM1YkIMqFtDWzpq19cAy4DRkKCZerQ+s00JkRQNsJRdhg5zNjG8DWKbmbTl5pG05rB0Gk05mFLdLv/lQDf1ROc3MNU7mAxhiT62Bd0a7NA7mJ4Dwetec96wVkqGE7psPhVCTYY+k1dImDYR3YXCRjPTRcaZAo4z+3g0N2LdPleCloiEe1rbSkHRwz9pplEfWiqWbJQ14Ph0ueo0ms1tPo5fYIQQQmIJJzBCCCGxhBMYIYSQWBILDUyzlfuWn2tW9IgOhTZ/WwODujG8k0a6lo6KRNsZuW6lz2xbeTHs03SnqtGd4Qh320kHIX4NBe3sGGYHwwkhtu6F6VA2Vrpl95rpalqom+B2J+jTXOtv1CIiS47h/qBuiCGzfHSdusjZDltYnRqRMQ/XhX2Geo6T8kTRjLXQRhE9x6PvaO0K1cRCQE1ZFH3OlwpGS5ei6Va+ujFNj9pHnndjS9i6lvbuc/Y3NYi0UdblFxghhJBYwgmMEEJILOEERgghJJa0Ww2scVWNSMbWhBfYSK8fGJQN9vvyaEc+fawtdYf4wYSm88b0EVoYGAewmxctd/2p0KbfUOxqYpuL3fL2HdPSo2h29+IWG2zX13yu2j5uanZsp0bEXwdThXhS2EfGkeI/hZrYR2Ob+6lghdrUXQZqYoWgceL91nwGbew0IiLRcYh6qK2XhmpB+Dxp+pt9XajTot6WKnbb8HnIWZPWU3nR/Fy1UFI+/0SmUyGEELJbwwmMEEJILOEERgghJJa0Ww1sewm1pUbKY8puO/4dxjwDHw2fz0VLoI3ZqS/Qhq/VjTg2aPQ1Ac0Lbf4i6JvlahfFy5pTT6BPWS40K6o9+GO3YXlbQ0MNpdvrrt6WTq0C73022PS1GJBfnTTE2bZ1xC8HumW7bkf7dhZ4nej3Z/sMJtb5x2zPuV969xfCtq1z4XjXfM40fH57OAbxeQmJ4Siixzf0ge8FfDI1f8W27ks3TKdCCCFkt4YTGCGEkFjCCYwQQkgsiYUGFvEZgP22HhSaoyskZmBIbp3tObdtz474qSi2bM1+7fPJwNxixeL6lKHNX80HZt+DwXs5+z4/yvXNqnjO9d3Cc2H5/I9dncvWH9BvKJRILMTZ/3ILgK9dCOgXhn5LhUub/7Z9wkREVkxyc4lVXuvGRmxPhMR4xHGk6YaIM1ICNZXIewLuve86NM1Ly/+F7xGfrotoOnw0p52rkdnl8TyR+JFK3rMQ0uX3hfALjBBCSCzhBEYIISSWcAIjhBASS2KhgWk4sRBT9I8K0bk0m3A683/FCdvOHtWl3CFX28dfV/7H7naqOpePiOYVgJafTcMpP9bVvEyvb5ztNee5+xHMH7YrsXPDYbvCvKX87CiNZRu2zhXJ9xWIFt/Q1qJ8elhLdeH7y5dNL6KndSmCbfdZ1eIwRmLUetYm+N7TTVvqmQ+MEELItxtOYIQQQmIJJzBCCCGxJJYamC/3kmZrTSXuWFCOLQm3y/vswpqtG+3VxSnGgnPqBps/xqTzxRhcfRD+H8n160J9p3B+nrOdqq9QOrF9anAcRbRTxWfMG5NuvesbV9+rjQ38P1Aj25GamKbH7SxQg6xTYokiOE4j96Ck2f/Q1vXa1LbA90Ru1+axE/ERe89fF8aAxLpzPHnqNL0NCbmuTMyFCM+xlj+v1TZs11GEEELILoYTGCGEkFgSSxOilgLFJvKZG2ha8IWp8oVn0urSwHOtP7y3t3zxix8721rbfObMNXv7Ft9GQfPLgMM/SP69ZYN7zV8tKHW2Ox34lbO9WVwTYiRFvbRuatjR5kW7T3Nhn2aaxnH23o2uXTD/40NbPTbxZkdnu+vUhc62ZsbbmSbFndmOELMT3p/1MMbRZIjYZkMMHYXPHj7nkeXl8GxHzJ+W2VAz64XKFPa5I+8IMHujmTti9tPOZV0XukxkBrwLvedISy2EEELIToYTGCGEkFjCCYwQQkgsiaUGhnhThSh2WrSNo1bhtRkHnitiB/Zod5FUK4FLXHdkGKuCu1Y72wNkdSslRb58s5uzffO5M53td75x+//RElcjw9BRuGTfTl0RuhQ3Fc0sMhYUDeyDKd2d7WxpcLYbipuXaaMes8dtruaFoJYUoomF6lCpLJvfkZoXaqXFy9z+jbiZwP5VgxPOdq/pH7nHW/dXCyEXmtIJy2MaE5tQ3d17XuhPNSwV9r9ynSEh/rYXfoERQgiJJZzACCGExBJOYIQQQmJJu9XAsstKJTszzB9pZ/PVSUO8+zG1uGYb9/mc1XnCNYlE/ZI0fOcqn7Pc2UYftE82+O3ZWdO6JP8ugKL/+dqPne2ffuc1Z/s7P1zqbH/2h72dbV+6dk3TQpt/KilQUGPM9qRuFxFprHXHcnaRq8F0ez19yUVCNLFQTStUb/Oh+YVpmqate2maF6Ltj4Rgsp4X1IYwfJNWFxKiV6s6L7TFV3dIipPtKe+DoaQIIYTs1qQ0gU2aNEkyMjJk/Pjxyd+MMTJhwgSpqKiQvLw8GTlypLz77ruptpMQQghx2O4JbPHixTJ16lQ54IADnN8nT54sU6ZMkTvvvFMWL14s5eXlcvTRR8vGjRtTbiwhhBCyje3SwL766is57bTT5N5775Xf/OY3yd+NMXL77bfLddddJyeccIKIiEyfPl3KyspkxowZcv7556el0SHxv9BOm/2cq7k0QvwvX8zB3LXbn4ol3WCKE7zOSHoPwPb5QL0G/UEw1pu86G6uPGsvZ7vTOTXJv79c2dnZhwOuf56rHY0tfsXZPk/GO9vp9ANDUtHEEPQn7LC+j1tgPcR8PL45rUzpP1yfJNRaO83+V1BbUtGt6ktcnzStjzeMdNPj9Dl1SfLvz6524z1iWpIVk9x2abqgnWoHxwWOWS2WqJYixau3Kc+PBMYrtMeOFkcxEoMz4LmPaHkwZnEFQiqaF94fO2UMtiuE7foCu+iii+TYY4+V73//+87vK1askOrqahk1alTyt0QiISNGjJCFC1t2xqyvr5cNGzY4/wghhBCN4C+whx9+WF5//XVZvHhxZF91dbWIiJSVuf/DKCsrk5UrV7ZY36RJk+Smm24KbQYhhJDdnKAvsKqqKrnsssvkoYcektzc1hduZ2S4ZgdjTOS3bVx77bVSW1ub/FdVVRXSJEIIIbspQV9gr732mtTU1MigQc32yy1btsgLL7wgd955pyxdutWHp7q6Wrp3b479VlNTE/kq20YikZBEItHivm2konlFcu9o/jtgK/fFIAy1syOR67L+xuuI+D+BTVnTvKJ+L/mt7stZ460q0rZOI2paKSmS/zGe193e/9DPne236yuc7do+Wc42xkZ02hXoB6aB+qitEWhjEvdXXutuox4k65tzfu1xmd8XLlV8MQk1faxqtKtpft3bfT46z3e1vch1WmBerY2V7v+nMc8cUlfSuibz4WV9Wt0nouf/wn5ALXBH4vPRjMRIVfwPfdoS5kQrXRPmB4Zg22zdKzSWa1sJ+gL73ve+J2+//bYsWbIk+e/ggw+W0047TZYsWSJ9+vSR8vJymTdvXvKYhoYGWbBggRx6aOsDmRBCCAkl6AusoKBA+vfv7/yWn58vXbp0Sf4+fvx4mThxovTt21f69u0rEydOlI4dO8qpp56avlYTQgjZ7Ul7KKmrrrpKvvnmGxk3bpysW7dOhgwZIk8//bQUFBSk+1SEEEJ2Y1KewObPn+9sZ2RkyIQJE2TChAmpVp1E0xdsbQPttCH6mUjUxyaVvFqoS2E8w8KlYHMOyCOENmW0hUfKw7ZtK8e6InmA4FjUQb5T6Go2S17cJ/l3z8X1zj7Mu4RgfjAENTGR5j79/MJDvMcifWa3rqe1hG3jxwcn4o+jaBENxa7f0ebi5ra89/i+zr5EiVu2U1sa20Y0zUvzj/q69/afGzUuuw9ERPrdvf0uNcXL3DG8/CQcN+52wQp/fbb2quXNQiL+hf5TuWUV3yvcr7XN1rtRg0RfLaRYebdmenIYbq+flwZjIRJCCIklnMAIIYTEEk5ghBBCYkm7zQcWgq17RWIfKsdquXp8ZVEfQ7+w6h+5viiazbnQc26fLVskqnFpbXVs4aCBob0adcWGYr9dfsDhHyT/Xjuvt7cs+n0he9zmhiBDv6It56xN/o1q5SqMwwg5uD75uVt+z/tcXQTjZoqlZWjaA/qkVUG7Nxe7fV7W68vmfW90Ex9aHq0QQuMk2vEHRUQ6HOdeR/5sd0zbvkZ4LozxWHO8e3/s+IOp0vkNdxv9unLXufobxhq1t1ELQo04JA5putF0rBB/LHzHRN9nvZ1tX64+Le6iTWZTQ6v7ImXbXJIQQghpR3ACI4QQEktiYUIMWQqvhV7B/doSfXtbW1IfCfOyzr9gFpeE26Fx8Fj89I+k1MAQWbAdaZtVnxZKCsPydD5wtbN9Y48nnO0zJ16R/Lt+sGuqqT9wk7N9SoF7Px52Ty2vHfADZ7sMluUv791sJrTNcC1tr13vX4AeMQPCfnvsvHdjL2dfh/XuvcwZ7ZoMMdzWdwrd67bDRX3Vx+2zSLimN9xz7UyTYsFd7r1ft8EdV5/83DXFFc5v/htNhmimQxNuXRf/82Mfrz0vCIZR0rBNpyHhmkTCQ7XZ5rZoCDg/mhxggyZa7EO8Pwjuz0X3G0/qFu293Fb4BUYIISSWcAIjhBASSziBEUIIiSXtVgNrXFUjktFBRHSdyt7vS1HSFnxp5UPTpaA9WrNnb6xs/ru+xNUDcIkqqgOhIbNs+zTa5DFUVOcDXf1m86PuMu/zpo13tjceZJWF5eJS62oPgyZc6Gz/6peuCva7OdOc7Zs+HeNsf/JJz+TfqHHtfWuds732GgkC06l8YIUjQn1tlbh9NuDwj5ztj/68j7P92bouzrbtgrH6INAcQfMqn7Pc2cblzenUxJDFb+/lbKNrAvZ5zdDm9CqomdjjXUSkvsQNM4Z6J+o5qLn4iLhE7O32EYa16jnPvS5fahDNxcW3vBzrRkLTkITqbT6Kl7l9ELr833ElgWfJF66uaUu9SBu9m/gFRgghJJZwAiOEEBJLOIERQgiJJe1WA9tZoD9CJAwM2G5DiNjdwQ8GU1UkLFeI4mWu/R/t5J3e8p87EiIrQCNLrHP7BEMy5UfSq7v/D+r2uq3QuWXRfw11Jo0Tur3e6r6vT3SHcyTFibg+Sl2Kv3K2a4a62h6GTer8htUvrhuY5H/snvuTXn4fGww7ZrPXTPe8qEmi5qX5bvnCQ6WqjzWCptnQ1dXr7OtGPQc1Lw30FcL0RM554VyobeP9QM0Z0/7Yz2ruWvHiu7ci0XGJbXV91LK9ZTEkU472PrOPhT5ArS6qzfnDQUV8u6w+D01B01b4BUYIISSWcAIjhBASSziBEUIIiSXtVgPLLiuV7MyW45V5YyGmkL5bJGrXte3VqN9o8Qa1c/v8LNJlI24Lmn8b6jsNxa5212u665dk14d9hvcHbeO/eWCssz3rwt9727ZPp2YftUXfOcRbd+JNV0uSEa4G1uE4N87fR5WetCZvuvtwpH61oNTZ7nSO60u3Xnq7+61+WgMaF6LpViEpUtLtMxaNhdjcM3UloJfBOCpY4daFPk3rPf2ixR3FuH/47Glx/5x2QBxFrCvVOH92qpfiZX4/ME3Dx/eZ71nX0teg9hcSExLTC+XAe2B74RcYIYSQWMIJjBBCSCzhBEYIISSWtFsNzIfPxhyaDwz3o13X9uXS8hlF7PD7uuUx/xdS16XZ7wJ9Mux96SDqI9UM+j+hXb3qaFcDwHxhdhw51LwQrLtouauh2LnFRET+/OspzvYfrz85+Xeu+PWCnnPd+IVVUtpKya0YyF2WsbI5rl/ltX6t6LOr3XxgGKdxz4AYd+gvGIpP1wrxGRPRc6yhX9iXA5vvZ5/Z7r3NXee+fvD52Fjp8y900Z6tevBd1HQsX74wTW+L+KspWhH6W9nPAOqA+M6pB3+1PW5b6DbGs15A6zOMRYlosRGd+JFdXX/P0LiKrcEvMEIIIbGEExghhJBYwgmMEEJILImFBhbiV4H25kgOLrA3a/l2QmP1OedWfEvQBm3bviP+HEpsN/SzQHzXgbHb1D4ETK9v4Jfm69L82VBr0PSFS8+92C2v6F42Pq1BJHo/Sv+Bsfqa24Z6qKYn7Hmff38Imq6o4RsrtmYlEs331YhxMcFHUEA3tDUxLU9W7lp3rGA8QsTuc7yX+OxpOqI2Du36sO7Cpa6eg+8rTe/BsWO3FbU59MXCPsLn/DOlD22wDxEt9iFi3198D0TygW2nJsYvMEIIIbGEExghhJBY0m5NiI2rakQyOmz9G9MPeJapastOEQxvE7KcViMSrgbahqY73yd5aGipVEyfiGbqqTo6z9leflKzKaLzG655BJczo2kH75e2pN82a2D/oclQS+3eabZrWkMzoY+ve7umzIhpLQBc9o5L8jG9imb6weu2TZB4rno419e93bq068Jl9B3WN9//4hfdkGNoqsZnTVvGbV/XR2Pde49L7jWXl9UH4bgDNxYrzBKOYS18kxbuyWfK1pb7Yx/50sCIuCZivJc4TrCdoS5J9vOnPXu2WbvJbPaWddrQ5pKEEEJIO4ITGCGEkFjCCYwQQkgsyTDGpBanJs1s2LBBioqK5Kj+v5LsrJaXgPqWYGJKAC1ttoZ9LrQva0t3ES2tfGP1qlaPDQ3JhCw/ydWibG0iZ71r08eQS8i/LyxstS4RN5QU6n7+9OlRyucs9+4P6TNNE9NcEWww5JK2/NwOQyXi12hwnKQa8gcJWbKspdhAUB9CbdCm4jm3bCRMEtSluT3Y4BhGjQzHPGpFvnNr7ew1/SNnW9PA8H6kM5USvrPsFDZ7zfSneQkNy+dL1YLPmu9ZbNxSL8+981upra2VwkL3XRNpo3cvIYQQ0k7hBEYIISSWcAIjhBASS9qtH5iNZhO294emOtCwfc56rvHbstGnTGsL2owLl7Zdb0Absp2SXkTkg7sP8R5vawCY2h39jJDOb7jlN1a6+227u+ajhH4tiE/j2tnYvnXavUXNC0G/IxtMIyLi9jfqNxp2SiAREfHoqTiu8P6gXoO6IWqDiXWWH1iKPpY1x7taX+LNjq2WxTFcsALHrLvdUOwej+Vt3Qs1L0QLsYRgn9vn0p4PDdT2EtbrD/VN9LlE8F43gK+pLyxfyDu8sbHtYdf4BUYIISSWcAIjhBASSziBEUIIiSXtVgNr6NJRmrJzW9yHscYwpppNxNcnMF6eo6/heeFYtI2jllGwotVmbq3PsklrGguCcfvKerl5FzD1e9Hy5rZ+fpRrJ+/2ut/Gj34wqMnYvj+2BrIVv19YRK/ZgaBO0lP8KWp8aWUw5uOGkW6KGdRrfNpgqN8X9hnGwfTFxURNS/PXEQEfJtDTMLaij67Pudvot7fuVnds1MMYrrdStxTOdzXH6LPob4vmE2WjaUeanxdqf774oFoqo1Bsv8rqH/Vx9uHzkFiHPrW9ne1IjE3P+oKoLpgeXzd+gRFCCIklnMAIIYTEEk5ghBBCYkksYiGiFhGS60qLM5aKjVmLfRjJG1Tcdn8eLIux89D+jLHeUG9DDcD0cjUam4F7Vjnb7z2+r7OtxaTrNKKm1bpRi+tz6pJWy6aKFgsR0bQnW5vA/sT7o8V89OkeWvzOkJiNItHnJWTMh8YODW2bD7x/OMZt8FlCnVCLyZlO7RXbjX2CejWOO3ssoL6mPecYOxTXB/juPfomYt2hurw9dkLiOzY21slLC25iLERCCCHfXjiBEUIIiSWcwAghhMSSdusH5gN1LZ+2Udel9ThjInqsN9u3Ae3JtX1azle2DV8csq3ndu30mLvHBmMdYjw7zV5dvMy1+Vcd3Xqsvk+KXTs7alqFc91hs/ogt/yXb3ZL/o1aG/pDYey8VPJ/aWh+K3Ulrl+MD+zvqH6gxcVs/f+OUS0O4l6+1ZYWNoP6jq1ChujJbUHTf0KIxuR0nyc775zmG6ppksXi9kMqmph2zdgWvN+2D+HGSn8esy8HNsJ2L2cb89KJNOvX6DunvUN8sQ5Fovqa/V7Wjt1e+AVGCCEklnACI4QQEks4gRFCCIklsdDA0K6O2PoQ+lggofl1fLl90NcE9TMN1O5s3y8t51PEzj50WMsFW8H2W0L9Bn21ULcqkS9brUtEZMs5bhxGp+4D3e0E2OFR48ouL/Nup6KJ4bHlc9peHrU7Lc5liI+ZRjp1Jk07Qv8d1Ia0Z9PeH9rOPW5b6Gx/dvWhzrajY+3t6pcYkxHvVyi2VqjpY6grauUj99563uy4oiLROKUYaxT9C+sPdN93jbXNffblQNefs8N6HKPueyEXHmscOzkBedBC/MJ88AuMEEJILOEERgghJJbEwoSIoCnCNlNooW9w6TSaCEM+bX1L7ltCSzVum+LQ5ITmEww1hdSXuMej+4C9RBbNlQ3imvUwdBSaPjEdS7Zlgvzpd1zzyaz1rnkFl803oXlMXPDe2ybFVMyJLZHO+rAP8X740tRjWX9wHd2sZ4/xbDADoVkonX2gtUuj1/SPnG07HQgu+cbnBdFMtj73As31IBK2SgnlhffeHit22iMRfdxEXHfARG/3Ez63aAYPlVvwvWC3NXRJflvhFxghhJBYwgmMEEJILOEERgghJJbEUgPzoWlcWvkc2O/TxDTNSwP1OjtVuZayBHWrqE2/7cuyfentRaLL7DE8VFnxV862HUrq+X+4WkQp1L3+8N7ONtrGUZPBEFpi3QPNhQLJ7epqExGrPCwpt0F9AEMTaaknQtKpaGl7UtGWcNl8aAglLdWRz7UEny3NDQWfZV/Ysdo+e3nr8mmOLWH3i5aeBp9r1IZwjPvK43Mf1b7d7aLl/rFjn7vzG/i2c8HQdug2hM+uT2ffUfALjBBCSCzhBEYIISSWcAIjhBASSzKMMW0XS3YCGzZskKKiIjlsxI2SnZ0rIm2wjVt2eNQDQnUqtLPbdWMYIyTUZ8bXVtvHRUTXRXA/2s4xJE3Fc80aAKZqQS0Jz2WnexARyVjp+prY/myaX56mg2j7bd1Qs7ljn4SmnQ9B00UwVUj9gZuSf/v6syWw7pCQTZpPE2pi6U6/EkKI3yVqe75URSJRDVlLs+TD56caiuZzieGf+v4B/Co9fq44RvH50LTxEM1Lew/YNG6pl+fe+a3U1tZKYaHf65FfYIQQQmJJ8AT22Wefyemnny5dunSRjh07yoABA+S115r/l2aMkQkTJkhFRYXk5eXJyJEj5d13301rowkhhJCgCWzdunUyfPhw6dChg8ydO1fee+89+f3vfy/FxcXJMpMnT5YpU6bInXfeKYsXL5by8nI5+uijZePGjeluOyGEkN2YID+w2267TXr27CnTpk1L/ta7d+/k38YYuf322+W6666TE044QUREpk+fLmVlZTJjxgw5//zz23yunLWbJDvLb4PdRoiNOdQvLNOje6UaJw5t5TWelA/FL37sHgvXgbZytOl/3dutz7Z3F0L/RezVUPeXta7/SAdoa4i9G0HNC+306/d2r9u2u2saF4J1pwJqJDlr/OVRX6g5sJWComtxkZQn/lMHEap5hWhmofqaT/PCZxFTexQt92uStpYqEvXrE2u79GXwNVU0R00TC9HMbO1aRCR3ravV4XsBtdaec+1USPCsKf6GoX5eTnnFFy40FdU2gr7A5syZIwcffLCcdNJJUlpaKgMHDpR77703uX/FihVSXV0to0aNSv6WSCRkxIgRsnDhwpaqlPr6etmwYYPzjxBCCNEImsCWL18ud999t/Tt21eeeuopueCCC+TSSy+VP//5zyIiUl1dLSIiZWXuV0tZWVlyHzJp0iQpKipK/uvZs+f2XAchhJDdjKAJrKmpSQ466CCZOHGiDBw4UM4//3z5xS9+IXfffbdTLiPD/cw1xkR+28a1114rtbW1yX9VVVWBl0AIIWR3JMhc3r17d/nOd77j/LbffvvJ3//+dxERKS8vF5GtX2Ldu3dPlqmpqYl8lW0jkUhIIuH30dDw+YEhqBeE5D/S0tsjmkbmS3OOsdpWnuXGdkONS7NHo7+I7Rfmt5NH9YLVB7l2dvRTsvtY8+vSdKio/uOWt+3sqHmF6lII6oo+bU/TQXBcRur6R/O5ao53/eyWn+TqMX1mu/pZaPxC37GhfmGh9adSNpUMUpqvXNe33PL4bNp+YSF+di2BepsMdc+FGpsN6rwR3Qq0O4ydaD/rqMNq8T2xXVruxNy1re/bXs0LCfoCGz58uCxdutT57YMPPpBevXqJiEhlZaWUl5fLvHnzkvsbGhpkwYIFcuih/gRzhBBCSAhBX2CXX365HHrooTJx4kQ5+eST5ZVXXpGpU6fK1KlTRWSr6XD8+PEyceJE6du3r/Tt21cmTpwoHTt2lFNPPXWHXAAhhJDdk6AJbPDgwfKPf/xDrr32Wrn55pulsrJSbr/9djnttNOSZa666ir55ptvZNy4cbJu3ToZMmSIPP3001JQUJD2xhNCCNl9abexEI/q/yvJzmpZGwvJI6T5WKBvSYgGFgr6aKAt3JejSNO8UCv65OeufbsRfLfyP279/y5aLjKtvK03aLmQNA0sxKdM0zcxPp6mzyF2eU0H0cYKtsXuh5rjXS0P7106NbBvK5oWHqpjhfizIT6tW0OLgfrlQHcsoNZdsMKtz37H4DvFp721BL47cUzbz5/27NkwFiIhhJBvPZzACCGExBJOYIQQQmJJOsOm7TBS0bxC8WkXqI9hWS3OImpeaN8un/Nxq3Vp+gxqSY21EBewl+vbtUqa/UFQD9PyAuF+1KlQ97LBe5f7nt+OrmloIaAmhtR52i3i9yML1Ufxftl5nvChzC5y/XNy3/vC2U7FP6o9k0oerdC6I/EkQdeyt1EPw208tuvURc52iCamxSXtd7cbek97x+QGyFyqz6byvNQd3rv5vCk8tz74BUYIISSWcAIjhBASS2JhQsRPcgyaFGJqwKWfmtnPORbKrk/RvOUrr5oC4NjVB+H/RVyz36qVbriozm80mwFLX3bNixqFS/Uy28B2am4L2bCdC+YZLbyNjXZvIyYSWKKMoXWc8mhGgrrR3KLdrw7rm//eLP5l899W0mky1GQHzSSPZkH7fu4oc9g2fGM69Ny+FEPYJz7Tf0vn1lxg7HPThEgIIYRYcAIjhBASSziBEUIIiSWx0MBSQVve7EtTLuLqKGg315aPh9p919vLThXNC+3Pm4v9OomWijydeENJpflcvtQtGpEl/dCnkbTyAeD9qzrarQtD/NghgSL3Sln+n2qIMx+YxgfZ47aWM63vbLRnT9O8tLQydn3auCgWf0oaLW2JfS3aOwSv2xeOTsQdS6g/F4rftUBzgUHNOXdt8/FRvaz1+9HY6A9dZ8MvMEIIIbGEExghhJBYwgmMEEJILGm3GlhDl47SlL1VMclJo3+IFg4KcTQyNYW2a69eNdhNB4PpC3C/Tc+5rm8W2qPRj6jPbNeunq6U3SK6T1pIKCkN9AXSfE1sQn1/sG4tVYXPHwt1jGgKGvfeY92oe4XgSwEkEqaRVf+oT9C5P7vazbSeiiYWks4mVbQUKL79msaFY0HTpXzPOuqfUd9Gf58hvrGC6wFQ6dPWC/jun6bl2fc2c0u9pyS0qc0lCSGEkHYEJzBCCCGxhBMYIYSQWNJuNTCbkHQqkXhqYLcN9Zmxbc6aDT7Ubwg1MZuq0W7sQrSTd3s9fbcOz4XpUzRC/N/Qht8I6VOQaF3bf92oJ6wHvUdLz5793CvJv786aYhbN+iCGyvd/xui31fxstb7OKLNeVK1i4SPaVsHQQ0L6TX9I2db8wsLasdRfi0Jr9On33R6y193pK42tK81NP1M9nbTpfiec5Goxox+YjaYLioX7j36WeLYsftFvQ4FrNuHpkfb2/QDI4QQ8q2HExghhJBYwgmMEEJILGm3GljO2k2SnbVVJ9D8Q2y7MGpgqLlo+agiWPtRa9DyTaGW1Gn2v7zl7fpRa0A7OZK71t3W+szng4Y+TJpvj0/L0OL4ab51kfoCchLlrHG3o/c6zOdpxaRmbQNjT+5z4SvOdu7a1vNJiUT7xdYT8Bojcfra2N7k8TBud2TsRB9avq9U/Lw0zSvyHoBt1JZSwZfPSySqGePz5otXqGHHUxXRx1II2vvOlwMv4kMW+Ny3Br/ACCGExBJOYIQQQmIJJzBCCCGxpN1qYDZaLpmQi0A7Lh4bYnNGu27uuu2PAYho/jeor6EPGvolIfbxGAMQ/VA0zSTbo3NpsSe1PEwhoL0/YndXNJj8j93R0FDcuv8Oll1znuv703XqIrdtcF2oVRS/+HHy71DdQ8NfX5hfF+qh6EeG274+RN84zMeWizoJ+B3Z7wWMx6npNUhEO0+jJqb5WeKz7rtf+Hxoemg6/d+QqGbZur8u+ozhO92+f4yFSAgh5FsPJzBCCCGxpN2aEO10KmgeiJT1mJ18SztFRHKVUFP257xmDgtZ4t0SjZ4l+2hmQBNJHSyz//wo13SDJi8tvE0IqZi88Dq/CuyzkLBVmsm3vsRdzrzXzNaXQ6NZSANNpT6TYvGL7rHpNina4DjQUn8gmknRB54rF7pbe37s9wIuTY+YFMEkqC3pDzEpanVpodlCTIYatilaxC+Z4D4UHfB5CTXL+sDnlqGkCCGE7FZwAiOEEBJLOIERQgiJJe1WA/OFkkI9IceyQWupPSKhVFIIq6OFbUF7dMgSVk1vQ3Dpe32JGyoKlzMnLPN2+Zzlzr5IypMUNBht2W9EG1rrT9EQSTXi1UnccbMedEJ0NUA9x6etplND3JXgvUd3jWpIOdN1qjsWUP/BtD/2s6uGd1JS1iOpaDKpamI+Phrrtqvb6+4400LK2efSNHx8fpqgnZGQciEhnJT3LvaJLxSYdu+dermMnhBCyLcdTmCEEEJiCScwQgghsaTdamC2H1jEtuqxR6P/R8SurqRE8dnhMY18KD4fMw0si+kgsI+Klvtt5yGEhtnx+a6E3EsRXQOw968+yP3/WM761lPGiIiUvgz+hYpN39YTMFQUhpLSQkuFkGr6k3T6kWl+XmWLXf3Cl04nOLURYI+MSNipQHBM4xi20w/5wmOJRENkoRaO7yAMs+TsK8FvDPd5KMb3mbdlYWial4ajv8H9CdHEfPALjBBCSCzhBEYIISSWcAIjhBASS9qtBmb7gWnY9mtNLwi1tYboXj57v0h6tQi02Ueue9+2p3ZBG7yW2j2V1BMRvxQA08Kgf5sPjF2o+QTifsQXgzNUD9Cw24b+hUhEU1EI0V61ND6a/xtqljnW85aq5rUjwftpa14i7nUnFHe1iN6paF4+X0b0VURNLOIvCsfnSNsJ9Y1D8Nn2vUd8aw8ym9r+zPMLjBBCSCzhBEYIISSWcAIjhBASS9qtBuYDba25lo05VOPCujBeng3GjdPYkTb+UN8gn7YUiacGx4bGibNt35rmhURs/kpOKFs7wnNhzLlInynaXw2MhdKXw2L1+c7t88rTfPZ8fkMiuhZrt0XT21Dz0jQZLR+Vj2BdMTB2og8cOz6tT30PKM9mVBtq/RnB5xZBf0NNM/bVV14DWl3gs4vX5fOpTVduMX6BEUIIiSWcwAghhMQSTmCEEEJiSbvVwJre+UCaMjqISNQ2HhJHK1SDqS/JcLZD8j5F4hWm0VcI7cmadoGgbTySF81DKv4hmk8Z1t0J9qMfHmoudSXNNn3UqDIV/6dcONeHl/URH8XLmscS+gkVLXd9FjVfLRzDtq6F9wb1M81vD3N4oW7l09iisfdc8NhOs/35qOxxm+7nI106ikgLuuHerfch9i+i5ddDNO3VRns/4bjEuI0Yp9EGrwuvQ8t/uCvgFxghhJBYwgmMEEJILOEERgghJJa0Ww3MRouhZl8E2pvRj0iz8aNN2dZVsG5NG9L0N1++KaROidsX8cdJQfPSCIl9mG5Qz7GJ3A/UwCDH04qj/T42ptc3znbV0Xn2Xu+xkTGq+AaF3B/UazBeIVJfktXqPoz3qOXVivj64HUFxDtMNfZeOonoo+t6b3ddO1IrwliVmh6Hmpf9PsNYoLV93HGC77tQHz/ffp+PWAj8AiOEEBJLOIERQgiJJbEwIWrYn/94QYVYWDHFBaWqUEweISZCRAshg6a0jZXu/vI5rplp1y94bRsh6WtEouGi0knizY7Oti+VPJri0NAZYlIMDRNWtrje2cal1Lg/BHUMK6ni0wmanWwTleauEQq+B2yzoLZMXkvTo7W1NCANiRbWCsvb908zbUZDqbn78TrxGbDPhdfsMy82bakXaWMUPn6BEUIIiSWcwAghhMQSTmCEEEJiSbvVwLLLSiU7s2UdKCRFOtrsQ9Oxp7IUVA/31Lp+kNvFfywum8flshhuCMMmtad07iGkonmhS4VviXFL/PvCZkW14jk3pI8vxU8ooUvw8bowrBVi6xGRMQzXERqKbUeOK6y70ZNWJp1uIyJRfceH9o7R+ijbkx5KdSmCsYLl7TdqZMyCJpa71m0XamKow2uamA+7nZlN/pQwznFtLkkIIYS0IziBEUIIiSWcwAghhMSSdquB2Wh2XntbS5mh2ZSRkLTYoXqBD9R6MAySnUZERKTr1EXONobl0TSx9gJeN/qF4bZdHscFapCoG2qaV9Xozs52/sd2Xa5PWPGLO87/Cce05ivn82HaSvM4xRBlGE4IQxdpqVyqrj7U2d7jtoXJv1MNFeU7PuJ/FqCTp5vQd8yOJJWUM6itoubl8/sS8YecC/V1bA1+gRFCCIklQRNYY2OjXH/99VJZWSl5eXnSp08fufnmm6WpqXlmNsbIhAkTpKKiQvLy8mTkyJHy7rvvpr3hhBBCdm+CJrDbbrtN7rnnHrnzzjvl/fffl8mTJ8tvf/tb+eMf/5gsM3nyZJkyZYrceeedsnjxYikvL5ejjz5aNm7cmPbGE0II2X0J0sAWLVokP/7xj+XYY48VEZHevXvLzJkz5dVXXxWRrV9ft99+u1x33XVywgkniIjI9OnTpaysTGbMmCHnn3/+9jVSsZfadt5MTHkCZTU/Ch9og/f5WIiI1HVx9YWInwXY7X3XgaB+o6W1QP8eWxcJ8dcQidq6Q+LQoa8I6jVrzhvmbKPd3ecHhvoMgilmorHe3D7D1Dp2OncsG+q7hfh0XAS1POwj7AfsYzsFBx6L14zpOjClvYgbdxF90D6zNLGec7909n001u3/nvPc+xPR10CTtGM8RjTewJiM2v3y6ViaxhWqv9nvgYivVop6mtNW5Tlev7ff7wvBPrffdunSvJCgL7DDDjtMnn32Wfnggw9EROTNN9+Ul156SY455hgREVmxYoVUV1fLqFGjksckEgkZMWKELFy4sMU66+vrZcOGDc4/QgghRCPoC+zqq6+W2tpa6devn2RlZcmWLVvklltukbFjx4qISHV1tYiIlJW5s21ZWZmsXLmyxTonTZokN9100/a0nRBCyG5M0BfYrFmz5KGHHpIZM2bI66+/LtOnT5ff/e53Mn36dKdcRoZrZjDGRH7bxrXXXiu1tbXJf1VVVYGXQAghZHck6AvsV7/6lVxzzTVyyimniIjI/vvvLytXrpRJkybJWWedJeXl5SKy9Uuse/fuyeNqamoiX2XbSCQSkkgkIr83rqoRyeiwtZFgP03FtwEJ0de0fWivRm0pxOcM68bYbg3gF+bPHuZH07RQtwpJka4dq+lWqPcUe+4Xtipyri7+4Y6aGOo9tr4T6TP0uwvUCe17Hzre0XdL62Of/1sxjFHUwFAjixwPeltdSfPxqGEVrHDrwjxmqK8hVUc3j/q9ZvqfrVANJlVNM4QQ/7bIe0Gr2/PO0erGcYLPckTPhnP5dN1d4ge2adMmycx0D8nKykouo6+srJTy8nKZN29ecn9DQ4MsWLBADj3UdXAkhBBCUiHoC+yHP/yh3HLLLbLnnnvKd7/7XXnjjTdkypQpcu6554rIVtPh+PHjZeLEidK3b1/p27evTJw4UTp27CinnnrqDrkAQgghuydBE9gf//hH+c///E8ZN26c1NTUSEVFhZx//vlyww03JMtcddVV8s0338i4ceNk3bp1MmTIEHn66aeloKAg7Y0nhBCy+5JhjPEbtXcyGzZskKKiIhkpP5bs/9PAEJ/9VNNUUIvQdCmfT0aIroF1aeXTqfOJRNtu60FaTLNITDTQWHz9EBofEs8V4qOmtVsDr2v93q6yuLGy+W/0WUK0c/uuS9MNo1qRi+0f1RK++4Xx69KpP6PGWD5nubONMRtR2/OBPmah8Qe1+IX2fq2PQvWekJyDqb4X7PpC8pKJRO9PiMas+cDabWk0m2W+PCa1tbVSWFgoPhgLkRBCSCzhBEYIISSWcAIjhBASS9ptPrDsslLJztyqQaDd1x+Ry09Ek1F0rRANB+3VqMehpoJ+Fj79LhUdquX9zdcVqh2FaH8Yu03TKDHWIcZ4DNEA1JiBJfj/N/91by5u9gNDHaqh2JWSc9a7PmSaLmXrQ+h/hloQxhvUNDIsn7Om+W/Nnw1jaqaS26p8Tpieg+3G+2VrklF9re3adlv229cdiTuqEKpb7UgtPCQuI5YtftHdH80zt/PhFxghhJBYwgmMEEJILGm3JkQbzTRngyGXcCkoHhs1l4Ut+/bVjaa2XDgXmj3sdB+hJkNf+u6WsE1FkZQNgeZJJN1mDx9229FEq6V/wPQqmum0z+xmk9b6vXGJt2v2Q5MimvUS61oP/oXmRrwuRDMZIvYy/UioLiiLJuDQ1CA2GDJJG3dIbR/3OjcX2+Xd+4HmLQxxpS1Pj6baab1dWFfE9aD1Q0VElzVsNIlDey+kMyQWmvt3ZMi/1uAXGCGEkFjCCYwQQkgs4QRGCCEklsRCA0O8oXBgO2KzV5Zxb+95WwJDAiGo0dj120ud24IvJYMGhnXRlrpHzu3RKLHPNG1Ps6PjuWyNpljCwohpGkxdSevak5ZqIrqE378k3NdO1E4RTfNC/cfWh3AMRlw91vjTd4SEI8Jn0xdOqCUSew9zthuKm3UvTe/EMY3njoTvgvrs/RgGTBujGr70RTgmI2NWSYkSeS+k4AaBYN14B3z94E0L09Qg0kaplV9ghBBCYgknMEIIIbGEExghhJBY0m41sMZVNSL/l04FdRGfbRXDvGh6TiQFeho1srou/rQYSIjNWPNjCfEPiWgTsK3pB3hu+1zYTkyOEAljpfjS+a4zVKNMRfvTrktAU4mkT1E0Mxtt3CDoCynwTNj+O1+dNCSo7tCU9jaRMQn7G5V7b4eOEomG67LB/kaNq+qyPs52t9e1MGPN5MJ1oG5YvMwfmg3bhmOp2NoOfR40fGlhEM1vDwlpWyohyZx60lILIYQQspPhBEYIISSWcAIjhBASS9qtBmanUwlNfe3sAz2g8ahBzraW8sT1BwmLk6il0fYRqnkhaI+OHG/9rflehbRbxLWV1ym+cKgHaHZ23G/fL81fCvVO7Tpzu/R2tm0tI0fRHPHeowaDKVLs+IcRnyQldbumkeHzs2JSsz8Vaj9dpy5yDwYdBNuG2l9I3FIN7NOe89zYlfa9X32Q+3/xwqUC2+44W31QCWy7xxesaL1dWsxMjchY8ehBPh8xkfDnxx7jWqqiUM0rFV3LHqONZnObj+MXGCGEkFjCCYwQQkgs4QRGCCEklrRbDcwGNRq06dvbEZ8xsOFrvj8YA83WF9RYekpsN82bx257qOYVGiMtnTce22qriOgLF/GHAjS7Ompq9SXNvkC5YIJHXx41F5yiPdlt0+JcRmMhuuMqLOdX2N1Cnbfq6NbrxmvEY7XyiM9nEMegpvVF/NmwLV1sHza3vzXNsdvr2x8/UtNSI2MWcpMhvmcbn+tQzStVvzEfeJ2p5Irb7jbs9DMSQgghaYATGCGEkFjCCYwQQkgsiYUGloofmOabgDZizMNlH++L+deWdmnX4dXyFE1Ma0uIpqb1GV4HttW2y2tx31RdRLHxo5ZkU7jU7ZOaoX77P+pUqME0WPoQXpdat6IdFS9raHWfFksPdZDlJ7l6T4f1bn2V1zb7emmal9aW3PdgrEBb7PuL91bTktAHDbH7oVjxP/PFNmyJ9aBbYVttQvXqqB9Z63FLNd1dQ9PGffhU2fYCv8AIIYTEEk5ghBBCYkm7NSHa6VQQn8kwUo9i7krFtKaZCtK5rDR0+atqdk1jXbjfDrOkpdDQQjBp2MvP0QwXSVOxzJ9iBsFQO9mW+QVNVD4ToIge/smXggaXYVeN7uxsoxm1w3rXhOhDDbWmhE1CUxtel31/cR8ea6d5aQv2s4xjEFMClb/nbmsuFb62ojkx8o6Bc2sphBDffs2crOGTKZBQKWFXwC8wQgghsYQTGCGEkFjCCYwQQkgsabcamI1mq/XZYrVjU0lbkq602OlASw+OhNjCNXeAyPFWv2hLcbXQXiGpK7AspjzRNC/ENzZQO9L6EDUZvE57GT5qdahz1JWkFg5ozXnDWt23sdLdxnQrvuXkIi2ET/Ms04/oN7BsPuT5Cn1H4P0QuB84VuyQaFpYNk2v1paye59NaGfoOwh13ba2o73CLzBCCCGxhBMYIYSQWMIJjBBCSCyJhQamaS4+fxAknekEdibpTl0Q4kuXyrGozWnHapoXhgTy+V9FfNCUsDwhGlkq/dfSuYqtvyOpVbypVqL0/cNyZ/vDy/o423YKmsQ64+xDzWv1QdDfL7rnUv0NLa0Q+0zTnzV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"text/plain": [
"<Figure size 500x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Run sandpile simulation\n",
"model = AbelianSandpile(n=100, random_state=0)\n",
"\n",
"plt.figure()\n",
"plt.imshow(model.grid, cmap='gray')\n",
"plt.title(\"Initial State\")\n",
"\n",
"model.simulate(10000)\n",
"plt.figure()\n",
"plt.imshow(model.grid, cmap='gray')\n",
"plt.title(\"Final state\")\n",
"\n",
"\n",
"\n",
"\n",
"# Compute the pairwise difference between all observed snapshots. This command uses list\n",
"# comprehension, a zip generator, and argument unpacking in order to perform this task\n",
"# concisely.\n",
"all_events = [model.check_difference(*states) for states in zip(model.history[:-1], model.history[1:])]\n",
"# remove transients before the self-organized critical state is reached\n",
"all_events = all_events[1000:]\n",
"# index each timestep by timepoint\n",
"all_events = list(enumerate(all_events))\n",
"# remove cases where an avalanche did not occur\n",
"all_avalanches = [x for x in all_events if x[1] > 1]\n",
"all_avalanche_times = [item[0] for item in all_avalanches]\n",
"all_avalanche_sizes = [item[1] for item in all_avalanches]\n",
"all_avalanche_durations = [event1 - event0 for event0, event1 in zip(all_avalanche_times[:-1], all_avalanche_times[1:])]\n",
"\n",
"\n",
"## Waiting time distribution\n",
"waiting_times = np.diff(np.array(all_avalanche_times))\n",
"plt.figure()\n",
"plt.semilogy()\n",
"plt.hist(waiting_times)\n",
"plt.title('Waiting Time distribution')\n",
"plt.xlabel('Waiting time')\n",
"plt.ylabel('Number of events')\n",
"\n",
"## Duration distribution\n",
"log_bins = np.logspace(np.log10(2), np.log10(np.max(all_avalanche_durations)), 50) # logarithmic bins for histogram\n",
"vals, bins = np.histogram(all_avalanche_durations, bins=log_bins)\n",
"plt.figure()\n",
"plt.loglog(bins[:-1], vals, '.', markersize=10)\n",
"plt.title('Avalanche duration distribution')\n",
"plt.xlabel('Avalanche duration')\n",
"plt.ylabel('Count')\n",
"\n",
"## Visualize activity of the avalanches\n",
"# Make an array storing all pairwise differences between the lattice at successive\n",
"# timepoints\n",
"all_diffs = np.abs(np.diff(np.array(model.history), axis=0))\n",
"all_diffs[all_diffs > 0] = 1\n",
"all_diffs = all_diffs[np.sum(all_diffs, axis=(1, 2)) > 1] # Filter to only keep big events\n",
"most_recent_events = np.sum(all_diffs[-100:], axis=0)\n",
"plt.figure(figsize=(5, 5))\n",
"plt.imshow(most_recent_events)\n",
"plt.title(\"Avalanche activity in most recent timesteps\")"
]
},
{
"cell_type": "markdown",
"id": "c2556633",
"metadata": {},
"source": [
"\n",
"### Additional information and follow-up\n",
"\n",
"+ Another member of our department, Michael Marder, has a [paper from 1992 in which he and his student Steve Kramer propose a cellular automaton model of river formation.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.68.205) (Figure 2 is gorgeous!). The update rules and structure of implementing this simulation have many simularities to the BTK model, but, unlike the BTK model, there are not any open-source implementations of which I am aware.\n",
"+ Among cellular automata, the BTW model is not only unique for its asynchronous nature, but also because it has a \"derivative\" ruleset in contrast to the \"integral\"/totalistic ruleset we see in better-known systems like the Game of Life: instead of updating a cell based on the sum of all its neighbors, we update all neighbors based on the state of a cell.\n",
"+ The BTK model is called the \"Abelian\" sandpile because the final stable configuration is invariant to the order of toppling events. For example, instead of toppling the pile to completion after each addition, we could add $M$ several grains at once, and then perform a series of topples selecting unstable sites in any order until a stable configuration is achieved. The final sandpile would be identical to the one we would get if we simulated the pile through $M$ full additions sequentially.\n"
]
},
{
"cell_type": "markdown",
"id": "aa2b3764",
"metadata": {
"tags": [
"no-pdf"
]
},
"source": [
"### Extra code for animations\n",
"+ No need to run this, but this code allows you to visualize the sandpile as it evolves over time."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c9c9af2b",
"metadata": {
"tags": [
"no-pdf"
]
},
"outputs": [
{
"data": {
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" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_imgf8f9a70eec1d4d5e817d77b2618d979a\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_sliderf8f9a70eec1d4d5e817d77b2618d979a\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"animf8f9a70eec1d4d5e817d77b2618d979a.set_frame(parseInt(this.value));\">\n",
" <div class=\"anim-buttons\">\n",
" <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.slower()\">\n",
" <i class=\"fa fa-minus\"></i></button>\n",
" <button title=\"First frame\" aria-label=\"First frame\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.first_frame()\">\n",
" <i class=\"fa fa-fast-backward\"></i></button>\n",
" <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button title=\"Pause\" aria-label=\"Pause\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.pause_animation()\">\n",
" <i class=\"fa fa-pause\"></i></button>\n",
" <button title=\"Play\" aria-label=\"Play\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.play_animation()\">\n",
" <i class=\"fa fa-play\"></i></button>\n",
" <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.next_frame()\">\n",
" <i class=\"fa fa-step-forward\"></i></button>\n",
" <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.last_frame()\">\n",
" <i class=\"fa fa-fast-forward\"></i></button>\n",
" <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animf8f9a70eec1d4d5e817d77b2618d979a.faster()\">\n",
" <i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectf8f9a70eec1d4d5e817d77b2618d979a\"\n",
" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_f8f9a70eec1d4d5e817d77b2618d979a\"\n",
" >\n",
" <label for=\"_anim_radio1_f8f9a70eec1d4d5e817d77b2618d979a\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_f8f9a70eec1d4d5e817d77b2618d979a\"\n",
" checked>\n",
" <label for=\"_anim_radio2_f8f9a70eec1d4d5e817d77b2618d979a\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_f8f9a70eec1d4d5e817d77b2618d979a\"\n",
" >\n",
" <label for=\"_anim_radio3_f8f9a70eec1d4d5e817d77b2618d979a\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgf8f9a70eec1d4d5e817d77b2618d979a\";\n",
" var slider_id = \"_anim_sliderf8f9a70eec1d4d5e817d77b2618d979a\";\n",
" var loop_select_id = \"_anim_loop_selectf8f9a70eec1d4d5e817d77b2618d979a\";\n",
" var frames = new Array(500);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAJYCAYAAAC+ZpjcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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"FgBAmIAFABAmYAEAhAlYAABhAhYAQJiABQAQJmABAIQJWAAAYQIWAECYgAUAECZgAQCECVgAAGEC\\\n",
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