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PINA/tutorials/tutorial3/tutorial.ipynb
Nicola Demo 0c8072274e Tutorials and Doc (#191)
* Tutorial doc update
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Co-authored-by: Dario Coscia <dcoscia@euclide.maths.sissa.it>
Co-authored-by: Dario Coscia <dariocoscia@Dario-Coscia.local>
2023-11-17 09:51:29 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "6a739a84",
"metadata": {},
"source": [
"# Tutorial: Two dimensional Wave problem with hard constraint\n",
"\n",
"In this tutorial we present how to solve the wave equation using hard constraint PINNs. For doing so we will build a costum `torch` model and pass it to the `PINN` solver.\n",
"\n",
"First of all, some useful imports."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d93daba0",
"metadata": {},
"outputs": [],
"source": [
"import torch\n",
"\n",
"from pina.problem import SpatialProblem, TimeDependentProblem\n",
"from pina.operators import laplacian, grad\n",
"from pina.geometry import CartesianDomain\n",
"from pina.solvers import PINN\n",
"from pina.trainer import Trainer\n",
"from pina.equation import Equation\n",
"from pina.equation.equation_factory import FixedValue\n",
"from pina import Condition, Plotter"
]
},
{
"cell_type": "markdown",
"id": "2316f24e",
"metadata": {},
"source": [
"## The problem definition "
]
},
{
"cell_type": "markdown",
"id": "bc2bbf62",
"metadata": {},
"source": [
"The problem is written in the following form:\n",
"\n",
"\\begin{equation}\n",
"\\begin{cases}\n",
"\\Delta u(x,y,t) = \\frac{\\partial^2}{\\partial t^2} u(x,y,t) \\quad \\text{in } D, \\\\\\\\\n",
"u(x, y, t=0) = \\sin(\\pi x)\\sin(\\pi y), \\\\\\\\\n",
"u(x, y, t) = 0 \\quad \\text{on } \\Gamma_1 \\cup \\Gamma_2 \\cup \\Gamma_3 \\cup \\Gamma_4,\n",
"\\end{cases}\n",
"\\end{equation}\n",
"\n",
"where $D$ is a square domain $[0,1]^2$, and $\\Gamma_i$, with $i=1,...,4$, are the boundaries of the square, and the velocity in the standard wave equation is fixed to one."
]
},
{
"cell_type": "markdown",
"id": "cbc50741",
"metadata": {},
"source": [
"Now, the wave problem is written in PINA code as a class, inheriting from `SpatialProblem` and `TimeDependentProblem` since we deal with spatial, and time dependent variables. The equations are written as `conditions` that should be satisfied in the corresponding domains. `truth_solution` is the exact solution which will be compared with the predicted one."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b60176c4",
"metadata": {},
"outputs": [],
"source": [
"class Wave(TimeDependentProblem, SpatialProblem):\n",
" output_variables = ['u']\n",
" spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})\n",
" temporal_domain = CartesianDomain({'t': [0, 1]})\n",
"\n",
" def wave_equation(input_, output_):\n",
" u_t = grad(output_, input_, components=['u'], d=['t'])\n",
" u_tt = grad(u_t, input_, components=['dudt'], d=['t'])\n",
" nabla_u = laplacian(output_, input_, components=['u'], d=['x', 'y'])\n",
" return nabla_u - u_tt\n",
"\n",
" def initial_condition(input_, output_):\n",
" u_expected = (torch.sin(torch.pi*input_.extract(['x'])) *\n",
" torch.sin(torch.pi*input_.extract(['y'])))\n",
" return output_.extract(['u']) - u_expected\n",
"\n",
" conditions = {\n",
" 'gamma1': Condition(location=CartesianDomain({'x': [0, 1], 'y': 1, 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma2': Condition(location=CartesianDomain({'x': [0, 1], 'y': 0, 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma3': Condition(location=CartesianDomain({'x': 1, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 'gamma4': Condition(location=CartesianDomain({'x': 0, 'y': [0, 1], 't': [0, 1]}), equation=FixedValue(0.)),\n",
" 't0': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': 0}), equation=Equation(initial_condition)),\n",
" 'D': Condition(location=CartesianDomain({'x': [0, 1], 'y': [0, 1], 't': [0, 1]}), equation=Equation(wave_equation)),\n",
" }\n",
"\n",
" def wave_sol(self, pts):\n",
" return (torch.sin(torch.pi*pts.extract(['x'])) *\n",
" torch.sin(torch.pi*pts.extract(['y'])) *\n",
" torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*pts.extract(['t'])))\n",
"\n",
" truth_solution = wave_sol\n",
"\n",
"problem = Wave()"
]
},
{
"cell_type": "markdown",
"id": "03557e0c-1f82-4dad-b611-5d33fddfd0ef",
"metadata": {},
"source": [
"## Hard Constraint Model"
]
},
{
"cell_type": "markdown",
"id": "356fe363",
"metadata": {},
"source": [
"After the problem, a **torch** model is needed to solve the PINN. Usually, many models are already implemented in **PINA**, but the user has the possibility to build his/her own model in `torch`. The hard constraint we impose is on the boundary of the spatial domain. Specifically, our solution is written as:\n",
"\n",
"$$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t), $$\n",
"\n",
"where $NN$ is the neural net output. This neural network takes as input the coordinates (in this case $x$, $y$ and $t$) and provides the unknown field $u$. By construction, it is zero on the boundaries. The residuals of the equations are evaluated at several sampling points (which the user can manipulate using the method `discretise_domain`) and the loss minimized by the neural network is the sum of the residuals."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "9fbbb74f",
"metadata": {},
"outputs": [],
"source": [
"class HardMLP(torch.nn.Module):\n",
"\n",
" def __init__(self, input_dim, output_dim):\n",
" super().__init__()\n",
"\n",
" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, output_dim))\n",
" \n",
" # here in the foward we implement the hard constraints\n",
" def forward(self, x):\n",
" hard = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
" return hard*self.layers(x)"
]
},
{
"cell_type": "markdown",
"id": "f79fc901-4720-4fac-8b72-84ac5f7d2ec3",
"metadata": {},
"source": [
"## Train and Inference"
]
},
{
"cell_type": "markdown",
"id": "b465bebd",
"metadata": {},
"source": [
"In this tutorial, the neural network is trained for 1000 epochs with a learning rate of 0.001 (default in `PINN`). Training takes approximately 3 minutes."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0be8e7f5",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/u/d/dcoscia/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:546: UserWarning: Can't initialize NVML\n",
" warnings.warn(\"Can't initialize NVML\")\n",
"/u/d/dcoscia/.local/lib/python3.9/site-packages/torch/cuda/__init__.py:651: UserWarning: CUDA initialization: CUDA unknown error - this may be due to an incorrectly set up environment, e.g. changing env variable CUDA_VISIBLE_DEVICES after program start. Setting the available devices to be zero. (Triggered internally at ../c10/cuda/CUDAFunctions.cpp:109.)\n",
" return torch._C._cuda_getDeviceCount() if nvml_count < 0 else nvml_count\n",
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "a0d1db0bc4b445e49c45e078c9c12aef",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"# generate the data\n",
"problem.discretise_domain(1000, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])\n",
"\n",
"# crete the solver\n",
"pinn = PINN(problem, HardMLP(len(problem.input_variables), len(problem.output_variables)))\n",
"\n",
"# create trainer and train\n",
"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"id": "c2a5c405",
"metadata": {},
"source": [
"Notice that the loss on the boundaries of the spatial domain is exactly zero, as expected! After the training is completed one can now plot some results using the `Plotter` class of **PINA**."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c086c05f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0\n"
]
},
{
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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0.5\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=1\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = Plotter()\n",
"\n",
"# plotting at fixed time t = 0.0\n",
"print('Plotting at t=0')\n",
"plotter.plot(trainer, fixed_variables={'t': 0.0})\n",
"\n",
"# plotting at fixed time t = 0.5\n",
"print('Plotting at t=0.5')\n",
"plotter.plot(trainer, fixed_variables={'t': 0.5})\n",
"\n",
"# plotting at fixed time t = 1.\n",
"print('Plotting at t=1')\n",
"plotter.plot(trainer, fixed_variables={'t': 1.0})"
]
},
{
"cell_type": "markdown",
"id": "35e51649",
"metadata": {},
"source": [
"The results are not so great, and we can clearly see that as time progress the solution get worse.... Can we do better?\n",
"\n",
"A valid option is to impose the initial condition as hard constraint as well. Specifically, our solution is written as:\n",
"\n",
"$$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t)\\cdot t + \\cos(\\sqrt{2}\\pi t)sin(\\pi x)\\sin(\\pi y), $$\n",
"\n",
"Let us build the network first"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "33e43412",
"metadata": {},
"outputs": [],
"source": [
"class HardMLPtime(torch.nn.Module):\n",
"\n",
" def __init__(self, input_dim, output_dim):\n",
" super().__init__()\n",
"\n",
" self.layers = torch.nn.Sequential(torch.nn.Linear(input_dim, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, 40),\n",
" torch.nn.ReLU(),\n",
" torch.nn.Linear(40, output_dim))\n",
" \n",
" # here in the foward we implement the hard constraints\n",
" def forward(self, x):\n",
" hard_space = x.extract(['x'])*(1-x.extract(['x']))*x.extract(['y'])*(1-x.extract(['y']))\n",
" hard_t = torch.sin(torch.pi*x.extract(['x'])) * torch.sin(torch.pi*x.extract(['y'])) * torch.cos(torch.sqrt(torch.tensor(2.))*torch.pi*x.extract(['t']))\n",
" return hard_space * self.layers(x) * x.extract(['t']) + hard_t"
]
},
{
"cell_type": "markdown",
"id": "5d3dc67b",
"metadata": {},
"source": [
"Now let's train with the same configuration as thre previous test"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f4bc6be2",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"GPU available: False, used: False\n",
"TPU available: False, using: 0 TPU cores\n",
"IPU available: False, using: 0 IPUs\n",
"HPU available: False, using: 0 HPUs\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "c13be1fd7a9549e8855489ce4b5ffaaf",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Training: 0it [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`Trainer.fit` stopped: `max_epochs=1000` reached.\n"
]
}
],
"source": [
"# generate the data\n",
"problem.discretise_domain(1000, 'random', locations=['D', 't0', 'gamma1', 'gamma2', 'gamma3', 'gamma4'])\n",
"\n",
"# crete the solver\n",
"pinn = PINN(problem, HardMLPtime(len(problem.input_variables), len(problem.output_variables)))\n",
"\n",
"# create trainer and train\n",
"trainer = Trainer(pinn, max_epochs=1000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional)\n",
"trainer.train()"
]
},
{
"cell_type": "markdown",
"id": "a0f80cb8",
"metadata": {},
"source": [
"We can clearly see that the loss is way lower now. Let's plot the results"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "019767e5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0\n"
]
},
{
"data": {
"image/png": 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5LF68OIwfP75lWu/evdPnCxcubPN9k/dJLnXe3u677x4efPDBbr8n+StyYVFbVx1F/q6L/BsrSkxLiGsAkD03dKnQAWJRD8ap7s1fqnBzl7tfHhUG1Har63u++sprTf/9SRg2bFir6cklyldffXWraevWrQtbt24NQ4YMaTU9eb506dI23z+5vDnpFfK2t70tHXdx/vz54c4770zfp7vvCd0hrlWXuBanvGNaQlwDgOwpLlagsCj5oshFxioUGBtl5cqVYeDAgS3P+/evT9v1la98Jb3keeTIkaFXr15pgTG5/Nklz8UlrlHkuFakmEZ8MS0hrgFAz7gsuuQUFrFfVFeShG3/aCsRGzx4cOjTp09YvXp1q+nJ86FDh7b5vvvuu2+4++67w8aNG8Nzzz2X9kbcc8890/EXu/ueUPZLYmmcou0XRSvmFymmJcQ1AMie4mJJDwiLdqBN9oq0jxTld1dE/fr1C2PGjEkvbW62bdu29Pm4ceM6fG0y7uKBBx4YtmzZEv7jP/4jvO997+vxe5K9ovy+itJekR9xjYS4BgDZc1l0CUnA6M7+4rKy6po6dWo4//zzwwknnBBOPPHEMHPmzLRXYnKpc2LSpElpEfH6669Pn//iF78IL7zwQhg9enT6/2TMq6R4eMkll3T6PYlDEQqLYhrd2WfEtGoT1wAgW4qLJUrCJGCUORkz9mLjTJw4MaxduzZMmzYtrFq1Ki0azps3r+WGLCtWrEjv9tzs1VdfDVdeeWV45pln0suh3/3ud4fvfOc7Ye+99+70e0JniGuU+cSZuNY44hoAZEtxsSQkYNRrP5KIVdOUKVPSR1sWLFjQ6vlpp50Wfv3rX/foPcmfE2ZUQexxjcYR1wAgO8ZcLEESprBIvfcn+xSQF20QjdinYhXz8SUAQGcpLhaYBIxG719AOcVa0NDu0Mh9y/4FANAYiosFTcIcIFPV/SzG3yNQzvaG8olxPxPXAICiM+ZiAcV4YByjTQdt3uU8/Vf0y2BJis14VVAuMRYyxLXOEdfqt78ZhxEAoH4UFwuWhFU9AetMYtXI96tqMTK2RMwdNqE8qhzX6h3TuvqeVY1pMcY1AIAiU1wskColYI1IuBq5XFVI0CRiQD2JafmrckyLLa45aQYAFJniYkGUOQmLtZDYk3Uoa2ImEYNii6U3fpljWhniWlvLL64BANAexcUOSMIao+hJV9WLjTEVGAFiIK4VWyxxTe9FAKCoFBcjV5beHVVIvDq7/mUoNMaSiAGd54RZfYlr4hoAAH+huBhxElb0wmLVE6+yFxpjKDDq5QHFIq6Vk7gGAFBtiouRKmoCpqBYrUJjDAVGoBjEtWrFtSLGtBjimpNmAEAR9c57AShHApYkEwqL1dyGee+vMfQyhtjl/TvJu52oUpsc2/Yr4jZ8uYD7KwBAnvRcjCwJK9oBbRGThtgVsddHst/qwQi01z4UhZjW2O1apLiWJ70XAYCiUVykWyRgjVe0S6YVGIG22oUiENOy3c5iGgBAubgsOiJFSMKKeolT0dnmcV/yCTHz+2ifmJaPomz3IhyXAQDEQHExkiQs9gPYoiQCZVaE7yD2/RjITuztQeztaRWIawAA5aC4GIGYE7AiHPhXTezfScz7M5CNmNuB2NvQKvKd7EyPYwCgSBQXaZfkK26SMSDGAkWshUVtZvxiPe6IdZ8GAIiF4uJ2JGF/IQErlhiTsTwSMb08gCK1kxTrGESBEQCgfYqLOYrxQDXGA3qKmYzFuH8D1frdx9g20jm+NyfNAIDiUFwkJQErB8kYkJcYC4sUW2zHJrHt4wAAsVBczElMB6gxHbhTru8z6/3cpdHg9xBbO0i5vs+Yjt8AAGKhuFjxokRMB+yUs7eHRAzKL5bfeUxtH/XlewUAiJfiYkWTMAlYNUjGgKrQ3pVfLN9xlsdxVT35DQBUoLg4a9asMHz48DBgwIAwduzYsGjRog7nnzlzZjjiiCPC7rvvHoYNGxY+/elPh1dffbVbC1x0sRQWqY4Yvu8Y9nvoiLhW7N93DO0c2XByFHZNTAMg+uLi3Llzw9SpU8P06dPDkiVLwqhRo8KECRPCmjVr2pz/e9/7XvjsZz+bzv/kk0+GW265JX2Pyy+/vMcLT9dJwKqpSt+7Xh50VRnjWpV+B1Vq34jne4+hqA5ViWkAlLC4OGPGjDB58uRwwQUXhKOOOirMnj077LHHHmHOnDltzv/QQw+Fk08+OXzoQx9Kezu+853vDOecc84uezuWMQnL+0A07wNxQqW//7z3f6hSXKvK7zrvdo18+f5hZ2IaANEXFzdv3hwWL14cxo8f/9c36N07fb5w4cI2X3PSSSelr2lOup555plw7733hne/+93tfs6mTZvChg0bWj3oGQfg2A8gn7gmpjWGuEbe+0FWxfUq9USmZ+RqAOSlb1dmXrduXdi6dWsYMmRIq+nJ86VLl7b5mqRnR/K6U045JdRqtbBly5Zw0UUXddjV/vrrrw+f+9znurJo0cuzd4cEjB33h/4r+uX2O9jruZovhGhkEdfKGNMS4hqxyDOuQUzkagCU9m7RCxYsCJ///OfD17/+9XTcjzvvvDPcc8894dprr233NZdddllYv359y2PlypWNXszSqnphcfgb17b7qLKq7xeQZVzLOqaVvZdTlduvjmKauLa5kkMDQE/J1QDIvOfi4MGDQ58+fcLq1atbTU+eDx06tM3XXHXVVeG8884LH/nIR9Lnxx57bNi4cWP46Ec/Gq644or08rMd9e/fP31kIYskLK8DzzInYPVIojr7Hsuf37fHnxWjvHp6ZNF7MfldD1q2qaGfQTlkEdeyjGlZEdfqT1zrOT0Yqboy5moAlLDnYr9+/cKYMWPC/PnzW6Zt27YtfT5u3Lg2X/OnP/1pp6CUBL1EcjkZjVGmwmLevTPy/vxGKtN+At0hrhVHmdqrvONKWWNaXvtJFsX2svdIpj7ENAAK0XMxMXXq1HD++eeHE044IZx44olh5syZ6dmt5C6biUmTJoUDDzwwHWMqcdZZZ6V3LXvzm98cxo4dG55++un0DFkyvbnIWGZ59O4oQwIWe7Kz4/IVuXdjHj09jL1ITMS1rhHXuk5My5YejFSZmAZAIYqLEydODGvXrg3Tpk0Lq1atCqNHjw7z5s1rGQx/xYoVrXoqXnnllaFXr17p/1944YWw7777poXFf/mXf6nfWlD4wmLsiVdXlr+IhUaJGFUmrsVNXMte0WNaHpw0IxZiGgB56FUrwLXJGzZsCIMGDQpvO2Va6Nt3QKEuM8m6h0fRkrCiFxU7UsSELOsejI0ee7He4y5u2fJqeODBa9KbcgwcOLAu7dqVD78zDNhztzot4V+8+spr4bq3/qQuy0n9iWmdJ6bFpWhxTUzLLq6JadXW/P2PPeva0He3+uZqAF2x5bVXwy/+71V1i2sfnP/3od+e9c2RN7+yOdz+9u+WLlfrcs/FMlFYzEeZC4rb0/MDoBqFRXEtTln3ytd7EQCoqkoXF8ukCElYVZKvjtY99l4fLo8GYrtDdMzENXEt65Pi9e6RDwBQD4qLJUjCYi8sVjn5KmKRMcsCo14eQHvtUMzEtZ23hbgGAFBdios0jOSruMmYHoxAnu1PrMS14sa1rDhpBgBU0V9v60whxZiEJQmGBMy26iyXWkL84whn9TuNMaYlxLWubasYxbpvAQCUgeJiA1Q5CYs1qYhdjNstxv0rtps2AeWmqFiu7ZZVXHPSDAComspeFl30okNshZ8Yk4iiifGSMpdHA1U9YSaulTOuAQBQf3ou1lkVz1ZLwGzPnqri7waIs7AYa6+7Iotpe8a0r1Xx5DgAUE6KiwUUy4GxBKwa2zaW/Q2g0WJpd8uoanHNSTMAoEoUF+mWWBKEsotlOyswQjVlUSCJpX2Jpb0tO9sZAKB8FBfrqCpJmMTA9m4EvTyg+1wqWY4edVURw/aO4XgKAKAsFBcLJIYD4RgSgiqKIfmNYf/rDkUXiFfe7Ure7WqVVWHbO2kGAFRFJYuLig3FLG5RjWSMfMyaNSsMHz48DBgwIIwdOzYsWrSo3XlPP/300KtXr50e73nPe1rm+fCHP7zT388888wsVoWCFEYUFsk7puW9D9JY4hoAZKeSxcVGKHMSlvfBP/F8H43eD/XyyMfcuXPD1KlTw/Tp08OSJUvCqFGjwoQJE8KaNWvanP/OO+8ML774YsvjiSeeCH369Akf+MAHWs2XFBO3n+/73/9+FqsDuySuxSPvk5cKjOUkrgFAthQX6ZAELE6+F+ppxowZYfLkyeGCCy4IRx11VJg9e3bYY489wpw5c9qcf5999glDhw5tedx///3p/DsWF/v3799qvte//vX1XGwKzAkzqhLXGnHSzBU4uyauAUC2FBcLIK8krKwH+mWR1/ejl0dxbNiwodVj06ZNO82zefPmsHjx4jB+/PiWab17906fL1y4sFOfc8stt4QPfvCD4XWve12r6QsWLAj77bdfOOKII8LHPvax8Pvf/75nKwQ9JK7FTVyjpzEtIa4BQPb6Zv+RFIEErDjf0/Ln9817Merey2Ov52p5L0Zmfrb68ND3lf51fc8tG5OE6ydh2LBhraYnlz1fffXVraatW7cubN26NQwZMqTV9OT50qVLd/lZydiMyWXRSYFxx0ui//Zv/zYccsghYdmyZeHyyy8P73rXu9KCZXIJNXFr5BAFTphRtbhWJXnHtIS4BgDZU1ysg7IlYQqLxZJHIpbsl/1X9Mv0M+m6lStXhoEDB7a6TLnekqLiscceG0488cRW05OejM2Svx933HFhxIgRaW/Gt7/97XVfjipzieSuiWvFUra4VrWTZkWOaQlxDQC6zmXRtCIBKybfW8eqWnxJkrDtH20lYoMHD057Eq5evbrV9OR5Mk5iRzZu3Bhuv/32cOGFF+5yWQ499ND0s55++umurQSl4oQZnSWu0Z2YlhDXACB7iosRyzoJcyBfbFl/f8ZeLId+/fqFMWPGhPnz57dM27ZtW/p83LhxHb72jjvuSMe8+vu///tdfs7zzz+fjrm4//7793iZaawy3bVdXKMrxLVyENcAIHuVKy7WuwdTmZIwiq8sibTfVbamTp0abr755nDbbbeFJ598Mr35StIrMbl7dGLSpEnhsssua/PSsbPPPju84Q1vaDX9lVdeCRdffHF4+OGHw/Lly9NC5fve975w2GGHhQkTJmSyTsTHCTOqGtPInrgGANky5mKkJGEUgbEXy2HixIlh7dq1Ydq0aWHVqlVh9OjRYd68eS03eVmxYkV6B+ntPfXUU+HBBx8MP/nJT3Z6v+Qy61/+8pdpsfKll14KBxxwQHjnO98Zrr322oaNkQXbU5Qqj6zHX2xUXKv3uIvJyfJBy9q+WzLiGgBkTXERSVjJuNMm3TFlypT00ZbkJiw7OuKII0Kt1naivPvuu4f77rvPFwHUhbhGd4hrAJCdyl0WXQRZ9lrUu6OcsvxejVEF5dGoIQnENXrK8QoAQLwUFys8LlzVDtTfMXRp3ouQqaJ/v0X/fQHZK3q7RxycNAMA6BqXRVOpomFn571/1cjuLk4lLyUz9iKU4yZlRS7UlKmw2IiTYWWIa0W/PLre4y4CAMRCcTEykrA4eiDu+BllSMoAiJO41nlOmgEAxEdxsYKK2Lsj70uat//8ohUai97To17cWROyH4rACbP2iWvdJ64BAMRFcTEixviJK/EqU6Exi0SsEZdGu4QMKNMJM3ENAIAyqlRxsZ5jUxX1ZhNFSMJiTb46WtaiFBkByJ64Vn9OmgEAxKNSxcWqi72wWKTkq4hFxqImYkAxZdEbX1xrHHEtfob7AABiobgYiSpfEl3komIRkzGAMoi5sCiulYeTZgAAu9Z717NQBjEmYUnyVaYErAjrFuN+UNYhCKBI/M7K3fbXQ6zrVcS4BgBQNoqL3SAJK2+SUoX1bHQiVuVeuEA27UCMBaUY2/t6K3PxFACA7lNcjECVkrAqJiZVXGeAqqhiGx/b+hbtpJmT1ABA2SgullxshcUqi2n9Y9ovgO7fzKGKYmq/YmrXs1bFoioAAG1TXCQTEpBqbQeXRkN1VeH3r7DWelvEIKaiMwBA1SguljgJi+VAO5bEIxaxJKWx7B9ZXkJW1Z5eUJZLNGNot2Jov2MTyzZp5P5RhaI5AEB3KS5S+iJarGwbgM5TWIybmAYAUF2VKS7Wq8dSUXp45J2ESTKKsZ3y3k+ActlU4t5debfXRRDDScWixLWiHE8CAHRGZYqLMSprEpZ3YlE0Zd1eZd2/geoVjMraTjeK7QUAUC2KiyWUZxImoSjedss7aQeImbhmu8V80sxYwgBADBQXqRsJmO0HFEs9L82MsfDSU+JaMbefk2YAANlSXCyZvA6oJWDF3o6N2m/qWWwwPhVUk7hWbI4PAADKT3GxC/TwaJvEob5sT4B8aYeLrwgnzQAAykJxESKUR2LrMjIgNnm0SwqLtmlW9MgHAMpCcbFEJGEA5KEsvbkUFsu1bZ00AwDIhuIi3SYJa6yybN+yFB0gJlW4Q6zCUPmUJa4BANCa4mJJii1ZJ2EShHJuZ8k8UFXiWjm3cyPimpNmAACtKS7SZRKwbNne9VWFHl/QGcZ7+yvtLAAAdJ/iIlCY3ouKIRCfovfGV1jMnm0OAFAuioslKGpIwsqv6ImYS8gAyCuuxXzSDACgDCpRXIzpMsgiF1mKXuAqOtsfqAInzCiCeh3PxXzyGgCgsypRXCwzZ+OxXwF0nRM2+fMdAACUg+IinSIBiIPvAYhJkXvjU6245mQsAEDjKC6ySwpacSnq96EIAcRSACpqOwqxD/8DAFST4mKBiyvOwtNI9i8oL+O8ERPFXgCAYlNcpEMO+ONU5e9FUQToiSq3n1X/Xup90kyPfACAv1Bc7ATFDAAofm9phUUAAKg/xcWCkoRRxF4eQHnotUW9Kf4CABST4iIUWNESMcUIIC9Fay+pzkkzV8gAAEWnuJiRohVVJGEAgOMPAAB2RXERCq7RheAYe3kA5dLodsYJMxqlaCePAQAaQXGxgCRhANW1fkT/vBcBGspJMwCAYumb9wJAFv7nwCUt//7hhuNtdKCyqja+W1l7LYprAADEQnGRUiVh2ydb3ZmnqIXH5Hu7f9XIvBej05eQ9V/Rr8fFkb2eq9VpiYA8LwU19ELPYlpH8xU1phUtrgEAVJ3iYsFIwrqffHWGniDt73fLn9+3bts5hstKBy3blPdiAA1WxBNmYhoAAEWjuJjB5WNFGey7SElYPZOvXX1GUXp+6OUBUFyNjmtOnpX7pBkAQJ7c0IVCSZKjLAqLeX8mANWQV1wrgqKc9CzKSWQAgEZRXKQw8k6GilBkLEoiBtDooT5ibw/zjil5fz7VvtESAFAupS8uJmOrlUVVk7DYEqCYliVLxvsst1mzZoXhw4eHAQMGhLFjx4ZFixZ1OP9LL70UPvGJT4T9998/9O/fPxx++OHh3nvv7dF7QlXEFEdii7FFOj4hbuIaAGSn9MVFii3WhCfW5YLumDt3bpg6dWqYPn16WLJkSRg1alSYMGFCWLNmTZvzb968ObzjHe8Iy5cvDz/84Q/DU089FW6++eZw4IEHdvs9KY4iXAIac0Eq1vgR63I1kpNm5SWuAUC2FBeJNgmLPdGJtbdHrN9n0YoTVTJjxowwefLkcMEFF4SjjjoqzJ49O+yxxx5hzpw5bc6fTP/DH/4Q7r777nDyySenvRNPO+20tIDY3feEsos1Zmwv9uWDzhLXACBbiosNpohS/gSnSMtKtWzYsKHVY9OmTW32Qly8eHEYP358y7TevXunzxcuXNjm+/7oRz8K48aNSy+LHjJkSDjmmGPC5z//+bB169ZuvyfVU6VeY0WKEzEuaxFOmhFHTEuIawCQvb7ZfyQUK6np7HL/cMPxeS9GJsWA5c/vm/dilMqK3w0OvXcfUNf33PbnV9P/Dxs2rNX05BLlq6++utW0devWpUXBpEi4veT50qVtJ/TPPPNM+OlPfxrOPffcdJzFp59+Onz84x8Pr732WvoZ3XlPslGFm0bEVogqYlyrSkyr98nk/iv65TrG+KBlbRfbqhTTEuIaAGRPcbHiPTxiSsKKmIDFmowl3+v9q0bmvRjkbOXKlWHgwIEtz5Mbr9TDtm3bwn777Rduuumm0KdPnzBmzJjwwgsvhC996UtpsgcUP67FFNOgkTEtIa4BQM+4LBrqqMiJZNFUoQdWTyVJ2PaPthKxwYMHpwXC1atXt5qePB86dGib75vcITq5O3TyumZHHnlkWLVqVXo5WnfeE8qmDPEgpnVo1MnQKl2eX4WYlhDXACB7iotEIaYEpqfKtC6UX79+/dKeh/Pnz2/VgyN5noyr2JbkJi7JpdDJfM1+85vfpEXH5P26855Qpt74ZYoDZVoXqkFcA4DsKS5WmCSs3GL5fonf1KlTw8033xxuu+228OSTT4aPfexjYePGjemdnhOTJk0Kl112Wcv8yd+Tu0V/8pOfTIuK99xzT3pDl+QGL519T6p9k7Iy9xYrYzGujOtEuYlrAJAtYy52wGWXjVfWhKXMY1XV66YueQ9+z19NnDgxrF27NkybNi29tHn06NFh3rx5LTdkWbFiRXq352bJoPr33Xdf+PSnPx2OO+64cOCBB6aFxksvvbTT7wkUSwxxzXjCdJa4BgDZUlxsID08qllYjCkRg86aMmVK+mjLggULdpqWXN788MMPd/s9oYy9tcU1enpSe6/najZinYhrABD5ZdGzZs0Kw4cPDwMGDAhjx44NixYt6nD+l156Kb1cLhmPKxl8ObkRwL333tutBaY8SVgV5J1o+p6hc8Q1it7e031lvkyfahLTAIi+uDh37tx0HJPp06eHJUuWhFGjRoUJEyaENWvWtDl/cufQd7zjHWH58uXhhz/8YXjqqafScbiSy+ioLkkYEAtxDYoTv2M+aVavK1agJ8Q0AApxWfSMGTPC5MmTWwblnz17djqY/5w5c8JnP/vZneZPpicD/z/00ENht912S6clvR6prrwTk6y5PBriJq5lq4y9xMQ1IBZiGgDR91xMeiEuXrw4jB8//q9v0Lt3+nzhwoVtvuZHP/pROjZXcll0MpD/Mccck95VdOvWre1+zqZNm8KGDRtaPaDI8kw8G9HLo4zFAaopi7gmppW7N1vVCotAvORqABSiuLhu3bo0edrxbp/J8+RuoG155pln0suhk9cl4yxeddVV4ctf/nK47rrr2v2c66+/PgwaNKjlkdyZlPqRhAFkF9fENMpIURXiI1cDoFA3dOmKbdu2hf322y/cdNNNYcyYMWHixInhiiuuSC+nbs9ll10W1q9f3/JYuXJloxczWmXqIVb1RKTq6w9l0dW4VpaYZjy5nWnX86FHPtSPXA2AzMdcHDx4cOjTp09YvXp1q+nJ86FDh7b5muQO0clYi8nrmh155JFpj5Ck636/fv12ek1yR+nkAQCNlEVcq2dMWz9CbCQexhSGuMjVAChEz8UkYUp6acyfP7/V2a7keTL+VFtOPvnk8PTTT6fzNfvNb36TJmdtFRYpJ7078t0Osd5dU08o8laluPbywb3yXoRStW/iGhCbKsU0AAp+WfTUqVPDzTffHG677bbw5JNPho997GNh48aNLXePnjRpUnoJWLPk78ndoj/5yU+mgSq5s3Qy8H0yED7Zi7XIBJAXcQ26T5EV4jJVrgZA7JdFJ5KxpdauXRumTZuWXgI2evToMG/evJbB8FesWJHeabNZcjOW++67L3z6058Oxx13XDjwwAPTQuOll15av7WIkB5ZfyXxaM1lZPXtibXXc7U6viNVJK5lpyzjCItrcZwsvX/VyLwXA6IjpgFQiOJiYsqUKemjLQsWLNhpWtIN/+GHH+7ORwERFwmWP79v3osBdSGuQfc5adb65HL/FS4lJV9iGgClu1s03VeWHh7sTK8XgGIO9aH9BgCA1hQXaShJWDyMt9mau+4C1E8Z4r2TugAA3aO4WKG7aiouAUC1C2gAAFBvios0jCTM9gGgOrKO+06aAgDEQXERAAAiUMYrZwCA8lNchBzp3QkU5Q64sY1nl3WvNe01AAC0TXGRhpCExcklZAA0kvgPAFA9iosVoahEI9SjJ1I9ekQBAAAA+VBchJzp5QEQN+10vJw8BQDIn+JipOo9NlWWJGEAUF2OAwAAqqXUxcX1I/rn8rku8wQAKJ4in9wFAMhLqYuLAAA9oRceAAB0THGRupKE2W4AjWacPWLmChYAoGoUF6FiJOUANJqTjQAA1aG4WAGKSQAAAAA0guIiAEAb9L4DAADFRSgMSSxQVu7ASyO9Y+hSGxgAIEd6LlI3imMAcXr54F55LwIV5LgAAKAaFBeBHtEjCQDyt35E/7wXAQCoKMVFAAAAAEBxEQAot6zG13NJLwAAdI6eixFymWl1SWYBAACAIlFcpC4UxYrFnTUBAACAelBcBArNXXChsTYdtNkmptucfAQAKD/FRQAA+P8ZngYAQHGR7bj8FQAAAIBG0XMRAAAAAFBcBADoKeMEFo8rNQAA8qPnIpA7N4wAAACAYlJchMjoMQMAAAAUheIiAAAAAKC4SD70tAMAAACoJj0XAQAAAADFRQAAAAAgO3ouAgDQMIZPAQAoN8VFAAAAAKBbFBcBCLNmzQrDhw8PAwYMCGPHjg2LFi3q1Fa5/fbbQ69evcLZZ5/davqHP/zhdPr2jzPPPNOWBiAT4hoAVY5rd9xxRxg5cmQ6/7HHHhvuvffehi6f4iJAxc2dOzdMnTo1TJ8+PSxZsiSMGjUqTJgwIaxZs6bD1y1fvjx85jOfCaeeemqbf0+KiS+++GLL4/vf/34jFh8AWhHXAKhyXHvooYfCOeecEy688MLw6KOPph1BkscTTzzRsGVUXAQoqQ0bNrR6bNq0qc35ZsyYESZPnhwuuOCCcNRRR4XZs2eHPfbYI8yZM6fd9966dWs499xzw+c+97lw6KGHtjlP//79w9ChQ1ser3/96+uyXgBUT2djWkJcA6DKce0rX/lK2tHj4osvDkceeWS49tprw/HHHx++9rWvNWp1Qt+GvTMAu9RvZb/QZ0C/um6pra9uS/8/bNiwVtOTM11XX311q2mbN28OixcvDpdddlnLtN69e4fx48eHhQsXtvsZ11xzTdhvv/3Ss2H//d//3eY8CxYsSOdJiop/8zd/E6677rrwhje8oburBUDk8o5pCXENgHp5duYRoe9uA+q6Qbe89mrD41oyPenpuL2kp+Pdd9/d08Vvl+IiQEmtXLkyDBw4sFVPwh2tW7cu7YU4ZMiQVtOT50uXLm3zfR988MFwyy23hMcee6zdz07OlP3t3/5tOOSQQ8KyZcvC5ZdfHt71rnelga5Pnz7dXCMAqqozMS0hrgFQ9bi2atWqNudPpjeK4iJASSXBavuAVQ8vv/xyOO+888LNN98cBg8e3O58H/zgB1v+nQwgfNxxx4URI0akvRnf/va313WZACi/RsS0hLgGQJniWl4UFwEqLCkQJj0JV69e3Wp68jwZJ3FHSS/E5EYuZ511Vsu0bdv+csla3759w1NPPZUWEXeUjMuYfNbTTz+tuAhAw4hrAFQ5riWS6V2Zvx7c0AWgwvr16xfGjBkT5s+f36pYmDwfN27cTvOPHDkyPP744+kl0c2P9773veGMM85I/73j2CHNnn/++fD73/8+7L///g1bFwAQ1wCoclxLJNO3nz9x//33tzt/Pei5CFBxyWC/559/fjjhhBPCiSeeGGbOnBk2btyY3o0sMWnSpHDggQeG66+/PgwYMCAcc8wxrV6/9957p/9vnv7KK6+kd5H+u7/7u/TsWNLb8ZJLLgmHHXZYOpAwAIhrAFD/fC3xyU9+Mpx22mnhy1/+cnjPe94Tbr/99vDII4+Em266qXMf2A2KiwAVN3HixLB27dowbdq0dJDf0aNHh3nz5rUMArxixYr0jmSdlXTb/+Uvfxluu+228NJLL4UDDjggvPOd7wzXXnttuwMVA+X1ww3H570IVIy4BkCV49pJJ50Uvve974Urr7wyvbHmm970pvRO0Tt2EqknxUUAwpQpU9JHW5KbsHTk1ltvbfV89913D/fdd5+tCkBuxDUAqhzXPvCBD6SPrBhzkR7TIwEAAACgmnrnvQAAAAAAQDEpLgIAAAAAiotQBlW8zLz/in55LwIAAADQDXouAgBU/CQPAAB0l+IiAACFdv+qkXkvAgBAZSkuAgAAAACKi+zMmXwAgM5b/vy+NhcAQBfouQgAtMsNl+gJ41cCAJSf4iJ1IXkgL3s9V7PxAQAAICeKixFyOQ6N5nJ5AAAAoB4UFyEieoACdMzJEQAAiIviIgDADpzsAQAAxUUgAy7jB4D8DVq2Ke9FAAAqSs9FACg5Nz4iD3p/AgBUg+IidSOJAAAAAKgWxUWIhOIsUFZFHT5Bu1wMbvIDAJAvxcUKcNANAAAAQCMoLgIAAAAAiovkzyVk8dOTFYBGq/LxQP8V/fJeBACATOm5CBGochIGEPNJEu0zAAB0THGxAZyxBgAonqLefAgAIE+lLi4OWrYp70UAAKgUvT0BAKql1MXFIivymXNJhe0FAFkwjjAAQP4UFyvCwTexMowAEDsnzQAAoH2Ki1Ah9S4yF7mHLQD1pxALAFA9ios0hOTCdgLKox49jOt9MkKPfAAAiIPiIgDALjhpRhb2eq5mQwMAhaO4SMNIxACgOsR9AIBqUlyEnEjCAIpFux0Xl8YDAMRBcbFCl6U4CAcAaJublAEAdI/iYsTKcJCrl0c820VxubVByzZl/h0A9aVdi4d4DwBQXYqLAACdpIhGo++sDgBQNIqLNJxErJzK0LMWgJ4T5wEAqk1xsWJnrl1Clj9JWP2UcWxUKLOynJTQjufP8QwAQMGLi7NmzQrDhw8PAwYMCGPHjg2LFi3q1Otuv/320KtXr3D22Wd352MpMIlYviRh0DFxDbpHfIf4iGkARF9cnDt3bpg6dWqYPn16WLJkSRg1alSYMGFCWLNmTYevW758efjMZz4TTj311G4vLBSdJKwYPXypliLFtZ7ciKisPX3zOnmiPQdiVKSYBkCFi4szZswIkydPDhdccEE46qijwuzZs8Mee+wR5syZ0+5rtm7dGs4999zwuc99Lhx66KG7/IxNmzaFDRs2tHpQfFVPxKq+/hCrRse1ssQ0JwMoc1wryyX7IFcDIPri4ubNm8PixYvD+PHj//oGvXunzxcuXNju66655pqw3377hQsvvLBTn3P99deHQYMGtTyGDRvWlcUslUYc7LpEFiC7uCamlVeZimtF4jgG2iZXA6AQxcV169alvTWGDBnSanryfNWqVW2+5sEHHwy33HJLuPnmmzv9OZdddllYv359y2PlypVdWUwiVtVELM/1bkQSpocHZZFFXBPTyk1cA2IhVwMgL30b+eYvv/xyOO+889IEbPDgwZ1+Xf/+/dMH5U3E/ufAJXkvBkAmcU1M2/nkxPA3rq37SZR3DF1a1/ekfVUtqELZyNUAyKW4mCRSffr0CatXr241PXk+dOjQneZftmxZOjjwWWed1TJt27Ztf/ngvn3DU089FUaMGNGd5YbCkIRBvMQ16sFJMyAGYhoAhbgsul+/fmHMmDFh/vz5rYqFyfNx48btNP/IkSPD448/Hh577LGWx3vf+95wxhlnpP+u8liKVR+vqCoFt6qsJxSVuEa9VKW9z3s98z5+6YibHpE3MQ2AwlwWPXXq1HD++eeHE044IZx44olh5syZYePGjeldNhOTJk0KBx54YDqA/YABA8IxxxzT6vV77713+v8dp5dRcpC56aDNeS9GtPT0qHYSBrEQ18rBpdHlLyw2SizjCO/1XC3vRaAExDQAClFcnDhxYli7dm2YNm1aOtj96NGjw7x581oGw1+xYkV6p03iHp+KxitrEgZlI65RL2U+aSamQTGIaQAU5oYuU6ZMSR9tWbBgQYevvfXWW7vzkbmdQX754F55L0ape3mUNRErcxJWrx4eLh8jJlWJa7Eo80mzssa1GOiND50jpgGQNV0MyV3ZCnGxrI8kjK6YNWtWGD58eDqcxdixY8OiRYvanffOO+9Mh8ZIhrl43etel/Zg/853vtNqnlqtlvZw33///cPuu+8exo8fH37729/6Ugou9pMCsbR7scSBeinb+lAN4hoAZEdxkSiUJXEpy3pQLXPnzk3HaJo+fXpYsmRJGDVqVJgwYUJYs2ZNm/Pvs88+4YorrggLFy4Mv/zlL9Mxd5PHfffd1zLPDTfcEP71X/81zJ49O/ziF79Ii5DJe7766qtZrRbkqizxoCzrQbWIawCQLcXFioull0cZEpiiL3/RGPi+fmbMmBEmT56cFgiPOuqotCC4xx57hDlz5rQ5/+mnnx7e//73hyOPPDKMGDEifPKTnwzHHXdcePDBB1t6LSY3+7ryyivD+973vvRv//Zv/xZ+97vfhbvvvruOSw5xK3pciGn5G3W8EsvNXKgvcQ0AsqW4WBBVOfiNKZHpitiWO6aiMfnZsGFDq8emTZt2mmfz5s1h8eLF6WXLzZKbciXPk56Ju5IUEufPnx+eeuqp8La3vS2d9uyzz6Y3/Nr+PQcNGpRebt2Z96RxqlCUj639iy0+dFZRlzsvsQ8ZUJWYlhDXAKAgN3SBRiraYPhVSsCqUuTO0l4ra6FPv/oWfLZu/sv7DRs2rNX05LLnq6++utW0devWha1bt4YhQ4a0mp48X7q0/Rs+rV+/Phx44IFpctenT5/w9a9/PbzjHe9I/5YUFpvfY8f3bP4blPmmLjsS12i0QcvaLrRVLaYlxDUAyJ7iYgZnsjcdtLnRH1P4u0YXNRGrUmGR4lm5cmUYOHBgy/P+/fvX7b332muv8Nhjj4VXXnkl7bmYjNl46KGHppdMAzsT18rTG5XyxbSEuAYA3ae4SLRiT8RiLSwWIQlz+Vg2kiRs+0SsLYMHD057Hq5evbrV9OT50KFD231dcun0YYcdlv47uVv0k08+Ga6//vq0uNj8uuQ9krtFb/+eybxQxZNmsce1WGNaI+mNX76YlhDXACB7pR9zMZbLROqhigfBSbITW8IT4zJBd/Xr1y+MGTMm7X3YbNu2benzcePGdfp9ktc0j391yCGHpAXG7d8zGR8ruWt0V96TODk5UL4YEtvyFO2EGXER1wAge3ouEnUvj9h6e8ScgDU6Caticbsqkkuazz///HDCCSeEE088Mb3T88aNG9O7RycmTZqUjq+Y9ExMJP9P5k3uFJ0UFO+9997wne98J3zjG99I/96rV6/wqU99Klx33XXhTW96U1psvOqqq8IBBxwQzj777NzWE2ISQ1yLPaZBd4lrAJAtxUUKozkJyiMZk4BRZhMnTgxr164N06ZNS2+4kly6PG/evJYbsqxYsSK9DLpZUnj8+Mc/Hp5//vmw++67h5EjR4bvfve76fs0u+SSS9L5PvrRj4aXXnopnHLKKel7DhgwIPP1o5o3dYn9pFlCXKNKd3LPkrgGANlSXOzEwd7LB/fK4rvIXRESsayTMUVFqmLKlCnpoy0LFixo9TzpkZg8OpL0XrzmmmvSB9Axca3Yl0QbKiBO4hoAZEdxsWB3jG5kL4+i2b7wV89CY1ELikVJwmJQprFYgeKfNGt0kbGoca2RlhvqAwCgbhQXKYUdE6euJmYSr+ySsHr08HD5GJSrfXHSrDUxzQkzAIAiUVyk0L082lO1YqFei0CWw33Us0d+o5UhrlUtpgEAUCx/HaEfAIiey/opu0afMHNJNABAfSkuFlCjD4r1gisWSRhAvu0kAABUmeJiRtxJEADapicZRS0EO74DAFBcpCQH91XlewLQXgIAQJ70XCwovTwoIj08oDz8niniCbMYj5+SmywBABSZ4mInVPWgT6+4uFU1CQPKKYv2RlwDAID6U1ykQxIxAKDRHG8AABSX4mKBLyHTq6y6qpyEVbUnMVAfVW4/q67ex02GBgAA+AvFRXZJIlbN70MSBuUVa5HeSbNqcpwBAFBsiosAQKV6bilmxcN30XODlm2qw7sAAHSf4mLBZdXL436XkUXB9wCgPaXr9IoFAGicShQXndGtD4Wt6pCEAdofGq3IxxVF7bULANAIlSguxsTBKFVMwgBipF217fMW6/inAABdobhYgoO/LHuZScTykeV2b8T+pKgO5VX037e4Vn564wMANJbiIl0mEcuW7V3fIr9hEiB+ikHlJq4BAJSL4mJJZJ2ISQwAii3mHvlZE9PKu631xgcAaDzFxRwU/RIyslOGJAyovyr0wF3upBkAABSC4iLdpqdHY5Vl+yqmQ/mV5XdelnY3VrYvAEA5KS6WSNa9PBIShfJs1zz2H4DYiGvl2a6xxzVDEwAAZaG42AUOAtsmEasv2xOgGMUhqhfXytJLFwCgnhQXS3ZwmlciVqbEIU+2Y/sU94GsaIuLvy0VpgEAsqO4SN1IxoqrUUmYHh5QnaK9k2bsyHEBAEA1KC6WUJ5n6yUSth1AWYhpxdx2ei0CAGRLcTFHZe3VJRkr1jaThAGxc9KsWMp6HBDjcdugZZvyXgQAgOoUF6t28JV3waisiUUjtlNZt1WMSRhAd5S1nS7jtsr7+KezjCMMAJRJZYqL9eJgsDgJRuxi2D5FScKAYmjkSYW826synwyqF9sHAKCaFBdLLO9ELCHRsF3qQVEfiIW4Fu92aeRxj974AADtU1zMWRUOVmNIOGISy/aoYhJWteERoGzF+xhOmsXUjsfC9gAAqDbFxZKLKRGTfEjAgPIXy2M9uVBvYlpcsT2W4x0AgCrqnfcCUC2xJCFVTsASkjCgqGJqv2Jr27NUpfWud8G8SL2FAQA6Q3ExgoPCRvfyiCkRq2IyFtu6Nnp/qEqvJYBY2/mqxfDYjnMAAKpGcZHcxJacVCEBKyI9PKB4qnbSrCptfozrF+O+AABQNX3zXgCyO/ge/sa10SYq7xi6NOclKXfy1UwSBrRXxH/54F6F2jjiWnZijmuNpjc+AMCu6blYoYPXmAtLZejxUYZ16ClJGKA9+IsyxIPY41rMxzUAAFWi5yJRKWJPxpgTr+1JwoCyibX3YlvxQVyj3kN9xHrHeACgeipVXEwOwtaP6B/tJWRJr69NB22u63sWLRErUpGxKEXFhMIiUFbiWvViWlZxTW98AIDOqVRxkWIlYjH2+iha8pWlRiRhbuYC2SnqSbOiEdd6zgkzAIC4KC5SGDsW9rIqNha9oCgJ+wuXj0F5FemkWd6FxqLHtKzotQgA0HmKi5HJqpdHUROxXSVIPUnOyphwZVVYlIRB8Yf7KLqix7V6x7T23rPonDADAIiP4mJkl5BlqeiJWFUSqe6SgAExcGl094lp5YprhvoAAMqqd94LQL69wIp+oE55ScKArhLTyivL71ZvfACArlFchBKShAExFfWdNAMAgPJSXIyURIzu0nMHqDrtYLk4YbYzNykDAGKiuNhDZbl0UyJWDll/jy4dA2JtL8S1cijL91iW40UAgLZUrrjoTG/5D+CrqkzfnyQse7NmzQrDhw8PAwYMCGPHjg2LFi1qd95f/epX4e/+7u/S+Xv16hVmzpy50zxXX311+rftHyNHuuFSEfj9EQsnzOgJcQ0AslO54mKR5NErrEwFqirJ43srUq9FJxU6Nnfu3DB16tQwffr0sGTJkjBq1KgwYcKEsGbNmjbn/9Of/hQOPfTQ8IUvfCEMHTq03fc9+uijw4svvtjyePDBB3vwLVIGei/SWY5H6AlxDQCypbjIThzQQ7XMmDEjTJ48OVxwwQXhqKOOCrNnzw577LFHmDNnTpvzv+Utbwlf+tKXwgc/+MHQv3//dt+3b9++afGx+TF48OBGrUKlKZ53TEwrnrKdMNMbOHviGgBkS3Ex8oPGvHqHScaKQxJGezZs2NDqsWnTpp3m2bx5c1i8eHEYP358y7TevXunzxcuXNijjfvb3/42HHDAAWkvx3PPPTesWLHCl4Ve+XTI8Qc9iWkJcQ0Astc3+4+kSAf4w9+4Nu/FoAOSsOIb+Oymph5+ver6nlu2/CXhGjZsWKvpyWXPyViI21u3bl3YunVrGDJkSKvpyfOlS5d2exmScRtvvfXWcMQRR6SXRH/uc58Lp556anjiiSfCXnvt1e33JbuTZi8fXN/9Mm9iWvzyimlFGuYjdnnHtIS4BgDZU1wsgOSgd9NBm3P5bMlYvCRh7MrKlSvDwIEDW553dAlzvb3rXe9q+fdxxx2XFhsPPvjg8IMf/CBceOGFmS0Hccorrolp8XKyjJhjWkJcA4D2KS4WpJeHAiPNJGB0VpKEbZ+ItSUZB7FPnz5h9erVraYnzzu6WUtX7b333uHwww8PTz/9dN3eE7pDgTE+eca1RvdabMTQOVUdZ7UzMS0hrgFA9io55mJVD8p6QkErDnl/D0VMwuhYv379wpgxY8L8+fNbpm3bti19Pm7cuLptvldeeSUsW7Ys7L///r6Sgmj07zHPS1GTtjTv9pS/8D1Qb+IaAGSvksXFosp7TCAJQL5s/+5xMmHXpk6dGm6++eZw2223hSeffDJ87GMfCxs3bkzvHp2YNGlSuOyyy1oNlv/YY4+lj+TfL7zwQvrv7XslfuYznwn/9V//FZYvXx4eeuih8P73vz/tIXnOOed085uE+tOuVnv7531cReOIawCQLZdF11EZB8DfkcvJ8tvueZOEldfEiRPD2rVrw7Rp08KqVavC6NGjw7x581pu8pLc5Tm5g3Sz3/3ud+HNb35zy/Mbb7wxfZx22mlhwYIF6bTnn38+LST+/ve/D/vuu2845ZRTwsMPP5z+m8YU0dePyHb8saIP+dFMXMtvu5ed3vj5EdcAIFuKiwUTSyKWcCfp6iRgWRQWJWH5mjJlSvpoS3PBsNnw4cNDrdbxJbO333573ZaNcp80iyWuiWnZbesYOGFWfuIaAGTHZdEUPkEoK2OCAWhzyySW4waFRQCA+lJcLGDvq5gOimNJFMompu0a0/4GlFNM7UxM7W9ZVPFkmd74AECVVLa4WPSbPMSWiFUtaajKtsxqP5OEQbyq+PuMrS0usti2Y0zHT1U8fgUAyqmyxUXKn0AUje0HVFmMRR/tcs+2XWzbzwkzAIDGUFwscC+PWBOx2JKJ2MW6zcqQhOnhAcUirpVDjDENAIDGUVwsuBgTsZgLZjGJeRvFul8B+RTT98rw0uhY25+Y2+xYxLyNYt2vAADKoG/eC1BWSSL28sG9Mjtg3nTQ5kw+q6uak4zhb1yb85LEI9bEC4BdE9fa3yaxyrKwmGUhHgAgFoqLZEIyFn/y1UwSBrTFSbPWxLVixLUy9Vg01AcAEKtKFxeTg7T1I/rnvRil771Y9WSsCMlXGZMwoNjEtTgVKaZlTa9FAKCqKl1cLFMvjyIlYjsmJ2UsNBYx+cq6sNjoJEwPDyg+cS0e4hoAAO1RXCyZIiViZSs0FjHxaqbHIpRDo3vkZ33SrKjK0ktfXAMAoDMUFxssj0SsiAXGohYai5x4ARRBWWJaQlwr7wkzl0QDAFXWuzsvmjVrVhg+fHgYMGBAGDt2bFi0aFG78958883h1FNPDa9//evTx/jx4zucn/ooQ0+0JCnb/hGDGJeppyRhIK7FXkQpQ0yLMYbsuDwxLFNPlWVf2ZGhPugKuRoA0RcX586dG6ZOnRqmT58elixZEkaNGhUmTJgQ1qxZ0+b8CxYsCOecc0742c9+FhYuXBiGDRsW3vnOd4YXXnihxwtflIM1Z7MblwQ1KhHK8rPyVNYkDKoc18qqjO1VVrFGTGssx3nEREwDoBCXRc+YMSNMnjw5XHDBBenz2bNnh3vuuSfMmTMnfPazn91p/n//939v9fxb3/pW+I//+I8wf/78MGnSpG4uNmW/lKwrylj0K3OinkUSpocHXSGuFWfsRXGNjvYNQEwDoAA9Fzdv3hwWL16cXtrc8ga9e6fPk94bnfGnP/0pvPbaa2GfffZpd55NmzaFDRs2tHoUXV5ntR1sY7+AfONa1jGt7MV1cY2Y9gm9FomJXA2AQhQX161bF7Zu3RqGDBnSanryfNWqVZ16j0svvTQccMABrRK5HV1//fVh0KBBLY/kkjO6TyJGLPuDJIzYZBHXyhrT8vw9i2vYF2BncjUACnVDl+76whe+EG6//fZw1113pTeDac9ll10W1q9f3/JYuXJlhkvZOBIx8iYhh+zjWlljWt60Z+S9D2R1XFf23sjEo+q5GgAZjbk4ePDg0KdPn7B69epW05PnQ4cO7fC1N954Yxqw/vM//zMcd9xxHc7bv3//9JGV5KBt/YjsPi/vg/AqjMPIziRhkE9cyzqmVWHsxaqNwUh8MQ1iVNZcDYCS9Vzs169fGDNmTHozlmbbtm1Ln48bN67d191www3h2muvDfPmzQsnnHBC95e2BGK4LNQBebUk33fe33kM+z1UKa5VqadT3u0b1fzOxTViVNaYBkAJ7xY9derUcP7556eB58QTTwwzZ84MGzdubLl7dHIH6AMPPDAdYyrxxS9+MUybNi1873vfC8OHD28Zw2rPPfdMH+RDb49qiCEBg9iJa8XuvZjQM786xDXomJgGQCGKixMnTgxr165NC4ZJoXD06NHpWa7mwfBXrFiR3mmz2Te+8Y30zmX/83/+z1bvM3369HD11Vf3cPGLKYZELKHAWG6xJGB6dxA7ca3nxDWyUMW4VqVeyNSHmAZAIYqLiSlTpqSPtixYsKDV8+XLl3fnIzJXlXEXd6TAWE6xJGBZk4TRXWWMa1UlrpVPTDHNCTOKQEwDoNR3iybOg9MYxuSjnN9lTPs5VE3WxfaYfu8xtYP0jO8SACB+ios5iikRSziAL7bYvr/Y9m+gWmI72ULXxfb9iWsAAG1TXNyOSyolY0UkgQZiEWPxJbYCFcWMa3ns245LAYCiUFzMWYyJWCK2g3qK9T1JwiAOeRQnYoxrMRaraJvvCQCgIjd0oZx32WzvAH/TQZtzXhKKlHzFWFgASIhr8RLXAACKS8/FSMRckNHjIx6+C6AIYo5psReyqib2uJbXvuySaACgSBQXd+BgrrgJQNkVYdtLwoC824POEtNsfwAA6kNxMSKxJ2LNJGS2d5H3X6iaPE+aFaFdENNs7yLvvwAAMTDmYmRiHX+xLcauavy2LQoJGFB0Ylo227co8oxrrqIBAIpGz8UID+qKVqjR68O2rPLvFShnTCtaMSxWRdyWRdtnAQDypudipIrUg7HZ9smDO0x3f9sVjSQMilGEXz+if26fX8SYltCbsWfbrYjENACArlNcjDQRKzoJWee3UZFJwoCyFxgTTp51fTsVUQwxTW98AKCIFBcjVuRErJmErP3tUXSSMCiWGE6aiWvlUqaYBgBA9ykuRq4MiVh7SUgVLp0ua+IVQ2ERKKayxrUqxLSEuAYAwI4UFyPv5VG2RKzsxcayJl0xFhZdOgbFVca41lb7L64Vg7gGANAziosFUcZErOiJWRUKibEmYECxT5olxLX4iGsAAHSH4uIuSMTiTXSyKDxWMdFqj8Ii0Ih2pewnznYkrsUhtpimNz4AUGSKiwU9GK5aMtYWhb/sSMKgPGI6aVbVAmN7xLVqxjQAgKLrnfcC0D0OjMmKfQ3QzlAWMcY0vRYBgKJTXCzwQV+MB8iUR7J/xbiPxfp7hCKJ8XcUa5tDedi/AAAaQ3Gx4Bwo0wj2KyAv2h+qtF/FWOgHAOgqxcUSHPzFesBMMcW8P8X8O4Siifn3FHM7RLHoEQsA0Hhu6FISbvRCvfYhgBiIa9RrH4pVzAV+AICu0HOxZAeBsR9IE6ci7DdF+P1B0RThd1WE9on42G8AALKjuFjSRMxBNfYVumLWrFlh+PDhYcCAAWHs2LFh0aJFHc5/xx13hJEjR6bzH3vsseHee+9t9fdarRamTZsW9t9//7D77ruH8ePHh9/+9re+FLpFXKNs+0oRjieLTlwDgOwoLpZYEQ6uyU+R9g9JWGPNnTs3TJ06NUyfPj0sWbIkjBo1KkyYMCGsWbOmzfkfeuihcM4554QLL7wwPProo+Hss89OH0888UTLPDfccEP413/91zB79uzwi1/8Irzuda9L3/PVV19t8NpQ5t9XkdotslWUoiLZENcAIFuKixVIxBxsU+R9oki/t6KaMWNGmDx5crjgggvCUUcdlRYE99hjjzBnzpw25//KV74SzjzzzHDxxReHI488Mlx77bXh+OOPD1/72tdaei3OnDkzXHnlleF973tfOO6448K//du/hd/97nfh7rvvznLVKKGitWE0XtH2B3Gt8cQ1AMiW4mJFSMawD1TPhg0bWj02bdq5ULt58+awePHi9LLlZr17906fL1y4sM33TaZvP38i6ZXYPP+zzz4bVq1a1WqeQYMGpZdbt/ee5KuIxQ5tGkXcB4r4WytSTEuIawCQPXeL7sHB4foR/ev5XWTC3Terp2iJV9WSsH6/+V3o27tfXd+z97bN6f+HDRvWanpy2fPVV1/datq6devC1q1bw5AhQ1pNT54vXbq0zfdPCodtzZ9Mb/5787T25iE+4hpFUeS4VnZ5x7SEuAYA2VNcrGAillBkLD/JFytXrgwDBw5s2RD9+xezvYLOENfKr+hxrQonzBpJTAOAeLksuuKKeEkR1fhOJWE9lxQWt3+0VVwcPHhw6NOnT1i9enWr6cnzoUOHtvm+yfSO5m/+f1fekziU4XdXljaQcn2nZfhtFSGmJcQ1AMie4mIPleVgsfnAvegH71VWpu+vLL+rIujXr18YM2ZMmD9/fsu0bdu2pc/HjRvX5muS6dvPn7j//vtb5j/kkEPSIuL28yTjYyV3jW7vPYlHWX5/ZWoTq8hxCd0lrgFA9lwWXfHLo9vi0rLiKGPiXJbCRpFMnTo1nH/++eGEE04IJ554Ynqn540bN6Z3j05MmjQpHHjggeH6669Pn3/yk58Mp512Wvjyl78c3vOe94Tbb789PPLII+Gmm25K/96rV6/wqU99Klx33XXhTW96U1psvOqqq8IBBxwQzj777NzWk2rGte3byZcP7pXjktAZ4hr1IK4BQLYUF+ukTIlYMwlZnMqYeJGviRMnhrVr14Zp06alN1wZPXp0mDdvXssNWVasWJHeQbrZSSedFL73ve+FK6+8Mlx++eVpAfHuu+8OxxxzTMs8l1xySVqg/OhHPxpeeumlcMopp6TvOWDAgMzXD5qJa3Eqc1xzwiwf4hoAZKtXrUm2H9l1yeV0gwYNCm87ZVro2zfuxLRsBca26PmRvTInXkVKwrZseTU88OA1Yf369a1ulNKTdm38fh+p+501t2zbHP5zzbfqspzUn5gWH3Ete1WIa7HHtHrGNTGt2pq//7FnXRv67hZ3rgaU25bXXg2/+L9X1S2uNaJd21KnZYyNnot0mZ4f2ahC4lW0JAyqpoy98tsirmW/nctOTAMAqkRxsc6qkoi1lyjo/VG/bVklkjCIl7hmnMbuqnJcAwCoEsXFBqhaIrY9xcbub6uqUliE+Ilrf+UkWtvEtNa/FwCAKlFcbJAqJ2KdSTaqlpxJutomAYPiENfab8/FNLb/nQAAVE3fvBegzCRi1So6KiB2jQQMikdc63r7L65Vh7gGAFSV4mKDScQaU6DLMllTNKw/CRgUl7jWNeJa+YlpAEDVKS5meNDpMun6UfArLkkYFJ8CY/2Ja8UkpgEAhNDbRsiOA1Cqvv/7DUB5+D1TdX4DAAB/obiYMQeiVJH9HsrJSQOqSlwDAPgrxcUcOCClSuzvUH5+51SFgjoAwM6MuZgT4zBSdooNUC3iGmUnrgEAtE3PxZw5UKWM7NdQXX7/lI3eigAAHdNzMQJ6e1AWigrA9m3B+hH9bRAKTVwDANg1xcWISMYoKskX0FHboMhI0YhrAACdp7gYIckYRSH5AjrbVigwUgTiGgBA1ykuRkyRkVhJvoDuthuKjMRIXAMA6D7FxQKQkBELyRdQz3ZEoZG8DdpufwQAoHsUFwt4ACwZI699D6ARbYu4RpbENACA+lJcLPhBsYSMLPYzgEYS18iCuAYA0BiKiwUnIaNR+xNAHvRmpBH7EwAAjaO4WCIKjfR0vwGItW3SU5/u7jsAADSW4mJJKTTS2f0DoAjENTq7fwAAkC3FxQrQ+wNJF1Am4hriGgBAPBQXK6itA3KXm5WLpAuoEsXGchPTAADiprhISsGxmCRcAJ1rG51EKwZxDQCgeBQX6fIBvgQte5ItgMa0o2JaPsQ1AIDyUFykrgmBJK37JFoA8bW94lrjti0AAOWguEguiUSVkjXJFUBxiWvd2x4AAFSH4iKFT04aUaiUPAFQlrgmpgEA0EiKixTeIL0oACgRcQ0AgCLpnfcCAAAAAADFpLgIAAAAACguAgAAAADZ0XMRAAAAAFBcBAAAAACyo+ciAAAAANAtiosAAAAAgOIiAAAAAJAdPRcBAAAAAMVFAAAAACA7ei4CAAAAAIqLAAAAAEB29FwEAAAAABQXAQAAAIDs6LkIAAAAACguAgAAAADZ0XMRAAAAAMiuuDhr1qwwfPjwMGDAgDB27NiwaNGiDue/4447wsiRI9P5jz322HDvvfd2a2EByNcf/vCHcO6554aBAweGvffeO1x44YXhlVde6fA1N910Uzj99NPT1/Tq1Su89NJLO82TxJTkb9s/vvCFLzRqNXYirgFUUxnjmpgGUD3Lly9PY9ghhxwSdt999zBixIgwffr0sHnz5g5fl8SzHePVRRdd1Pji4ty5c8PUqVPThVyyZEkYNWpUmDBhQlizZk2b8z/00EPhnHPOSVfy0UcfDWeffXb6eOKJJ7q8sADkK0nAfvWrX4X7778//PjHPw4PPPBA+OhHP9rha/70pz+FM888M1x++eUdznfNNdeEF198seXxj//4j/Vc9HaJawDVVba4JqYBVNPSpUvDtm3bwje/+c00rv3v//2/w+zZs3cZqxKTJ09uFa9uuOGGLn9+r1qTrrwg6an4lre8JXzta19LnycLP2zYsDRYfvazn91p/okTJ4aNGzemwbrZW9/61jB69Oh0RduyadOm9NFs/fr14aCDDgonvfXS0Ldv/64sLkDdbNmyKTz08BfTHgqDBg3q0Xtt2LAhfY/T950U+vbqV6cl/Isttc1hwdp/CytXrkx7VTTr379/+uiuJ598Mhx11FHh//2//xdOOOGEdNq8efPCu9/97vD888+HAw44oMPXL1iwIJxxxhnhj3/8Y9o7ZMceHp/61KfSR9YaHdfENKDsca2IMa2scS3PXG3MmVeEvrsNqPMaAXTeltdeDYvn/Uvd4toJTe1anzq3a1ublvGRpmVsRFzb0Ze+9KXwjW98IzzzzDMd9lxM2vyZM2f27MOS4mJnNQWRWp8+fWp33XVXq+mTJk2qvfe9723zNU3BrNZUMW01bdq0abXjjjuu3c9p6hWZFDw9bAP7gH0gyn1g2bJlXWk62/TnP/+5NnTo0IYt45577rnTtKRt7Ylbbrml1pQ8tZr22muvpXHhzjvv3OXrf/azn6XL0ZSE7fS3gw8+uDZkyJDaPvvsU2sKbrWms2XpezdaFnFNTMv/N+thG9gHGhvXihjTyhjX5GraOm2dfcA+UO24tqMrrriiNmbMmB0nt3LaaafVBg8eXHvDG95QO/roo2tNJ6JqTSedOnxNW/o2rUSnrVu3LmzdujU0BcpW05PnSRfMtqxatarN+ZPp7bnsssvSS6+bJVXnpgAdVqxY0ePeQjFLquPJmcUdK9hlU5X1TFRlXauyns1n5psShR6/VzIG7bPPPrvLMTC6q6l9T8fL2F5Pz4Ql7fZ+++3Xalrfvn3T7dFRm94Z//RP/xSOP/749L2S4TSSOJB0yZ8xY0aP3jeGuFbVmFaltsF6lk9VvtN6xbUixrQyxjW5WmNVpV1IVGVdrWf5VD2ube/pp58OX/3qV8ONN964/eSdfOhDH0pzk6S3/i9/+ctw6aWXhqeeeio0nWTr8HU76lJxMSvtdQdNkrAyN27NknW0nuXiOy2X3r27dS+sNoNW8shbcpnUF7/4xV1eOtZI2xffmnoAhn79+oV/+Id/CNdff33dA23Wqh7TEtrAcqnK95moyrrWI67FEtMS4lpjVT2uVaVdSFRlXa1n+ZQprn22k7lachPlZi+88EI6NvAHPvCBdDzFjmw/znByA+b9998/vP3tbw9NvT/Tm8I0pLjY1FUy9OnTJ6xevbrV9OR5U5fRNl+TTO/K/ABk65//+Z/Dhz/84Q7nOfTQQ9N2e8ebd23ZsiW902a92/RkzKjkvZO7nh1xxBF1fe/tiWsA5VPVuCamAVQ3pjX73e9+l44HfNJJJ4WbbrqpeXKX4lVzz8eGFReTniRjxowJ8+fPT+/43DxIcPJ8ypQpbb5m3Lhx6d+3H8w4uRtbMh2A/O27777pY1eSdju5pHfx4sVpLEj89Kc/TeNAcxCql8ceeyw947jj5Wr1Jq4BlE9V45qYBlDdmNbcYzEpLCYx7dvf/na3enAm8SqR9GDskq4O0nj77bfX+vfvX7v11ltrv/71r2tNXSjTgZBXrVqV/v28885LB4Bs9vOf/7zWt2/f2o033lhr6qqZDlK522671R5//PFOf+arr76avi75f5lZz/LxnZZLVb7Pjpx55pm1N7/5zbVf/OIXtQcffLD2pje9qXbOOee0/P3555+vNfXISP/e7MUXX6w9+uijtZtvvjkdrPiBBx5In//+979P//7QQw+lN0hpCmTp4Mvf/e53a00BNL2pShayjmtV2o+qsq7Ws3x8p9VRtrgmV2ucqrQLiaqsq/Usn6p8p21J4tVhhx1We/vb357+O4lVzY/2YlpT78TaNddcU3vkkUdqzz77bO3//J//U2vqBVl729ve1tZHdKjLxcXEV7/61dpBBx1Uazo7VjvxxBNrDz/8cKs7zZx//vmt5v/BD35QO/zww9P5k7vP3HPPPd35WAByliROSdKV3OFs4MCBtQsuuKD28ssvt/w9CUpJopXcQXNXd0tuOpuW/r2px0itqYdIbdCgQbUBAwbUjjzyyNrnP//5TA8KxDWAaipjXBPTAKrn200xqK3YtH2fwh1j2ooVK9JC4j777JN2tkiKkxdffHFt/fr1Xf78Xsl/utxPEgAAAACovPrc8hQAAAAAqBzFRQAAAABAcREAAAAAyI6eiwAAAABAsYuLs2bNCsOHDw8DBgwIY8eODYsWLepw/jvuuCOMHDkynf/YY48N9957b0ZLmt163nzzzeHUU08Nr3/969PH+PHjd7ldivp9Nrv99ttDr169wtlnn93gJcxvXV966aXwiU98Iuy///6hf//+4fDDDy/E/tvV9Zw5c2Y44ogjwu677x6GDRsWPv3pT4dXX301o6XtngceeCCcddZZ4YADDkj3w7vvvnuXr1mwYEE4/vjj0+/ysMMOC7feemsGS0rsqhLTEuJaueJaVWJaQlxrm7hGleNaVWJalfK1qsQ1Ma1tYlqG6nTX6x5paqBq/fr1q82ZM6f2q1/9qjZ58uTa3nvvXVu9enWb8//85z+v9enTp3bDDTfUfv3rX9euvPLK2m677VZ7/PHHM17yxq7nhz70oVpTI1F79NFHa08++WTtwx/+cG3QoEG1559/PuMlb+x6bn9b9AMPPLDWFKRr73vf+zJa2mzXddOmTbUTTjih9u53v7v24IMPpuvc1ODVHnvssYyXvLHr+e///u/preyT/yfreN9999WaAnStqcCY8ZJ3TdOBQ+2KK66o3XnnnbWkebzrrrs6nP+ZZ56p7bHHHrWpU6embdFXv/rVtG2aN29eRktMjKoS0xLiWrniWlViWkJca5u4RpXjWlViWpXytarENTGtbWJatqIoLp544om1prMDLc+3bt1aa+o5VLv++uvbnP9//a//VXvPe97TalrTWYjaP/zDPzR0ObNezx1t2bKlttdee9Vuu+22Ri1ibuuZrNtJJ51U+9a3vlU7//zzCxGsurOu3/jGN2qHHnpobfPmzVktYi7rmcz7N3/zN62mJQW4k08+uaHLWU+dKS5ecskltaOPPrrVtIkTJ9YmTJjQyEUjclWJaQlxrVxxrSoxLSGutU1co8pxrSoxrUr5WlXimpjWNjEtW7lfFt30ww2LFy9Ou5E36927d/p84cKFbb4mmb79/ImmZL7d+WPQnfXc0Z/+9Kfw2muvhX322adRi5nbel5zzTVhv/32CxdeeGEWi5nbuv7oRz8K48aNS7vaDxkyJBxzzDHh85//fGgKdFktdibr2XTgkb6m+bKDprNG6eUETWcBM1nmrBSxLaKxqhLTEuJaueJaVWJaQlxrX1HbIxqnKnGtKjGtSvlaVeKamNa+IrZFRdY37wVYt25d+mNNfrzbS54vXbq0zdesWrWqzfmT6bHqznru6NJLL03HgtvxB1L09Wzqch5uueWW0NTdPItFzHVdkyLbT3/603Duueemxbann346fPzjH08PRKZPn57FYmeynh/60IfS151yyilJ7+jQdKYzXHTRReHyyy/PYpEz015btGHDhvDnP/85HW+SaqlKTEuIa+WKa1WJaQlxrX3iGlWNa1WJaVXK19ZVJK51Zz3lanK1Rsi95yKd84UvfCEdPPeuu+5KB6Mti5dffjmcd9556YDIgwcPzntxGm7btm3pGb+bbropjBkzJkycODFcccUVYfbs2XkvWl0lA+cmZ/m+/vWvhyVLloQ777wz3HPPPeHaa6/Ne9GASIhrxVeVmJYQ14AqxrSq5WtViWtiGqXsuZg0UH369AmrV69uNT15PnTo0DZfk0zvyvwx6M56NrvxxhvTgPWf//mf4bjjjmvkYma+nsuWLQvLly9P79C7faOe6Nu3b3jqqafCiBEjGrvQGX6nyV3Hdtttt/R1zY488sj0TG7Spb1fv34NXeas1vOqq65KD0I+8pGPpM+TuwRu3LgxfPSjH00DdHJJQhm01xYNHDhQr8WKqkpMS4hr5YprVYlpCXGtfeIaVY1rVYlpVcrXqhLXxLT2iWnZyj3DT36gyVmB+fPnt2qskufJeAdtSaZvP3/i/vvvb3f+GHRnPRM33HBD2ttr3rx54YQTTshiUTNdz5EjR4bHH3887WLf/Hjve98bzjjjjPTfw4YNy3LxG/6dnnzyyWn3+uaAnPjNb36TBrIYg1V31zMZc2bHAmJzkE4uky6LIrZFNFZVYlpCXCtXXKtKTEuIa+0rantE41QlrlUlplUpX6tKXBPT2lfEtqjQsr1/TPu3Tu/fv3/t1ltvrf3617+uNfVuSm8R33SGIP17Uw+o2mc/+9mW+X/+85/Xms6S1JrOEtWefPLJ2vTp02tNZxhqTY1eXqvQkPVsOgNWa2osaj/84Q9rL774YsujqWt6XqvQkPXcUVHuPtaddV2xYkV6F7kpU6bUms7y1X784x/X9ttvv9p1112X1yo0ZD2T32Synt///vdrzzzzTO0nP/lJremMZnr3wJglv61HH300fSTN44wZM9J/P/fcc+nfk3VM1rVZsm577LFH7eKLL07bolmzZtWaiqi1pgPMvFaBCFQlpiXEtXLFtarEtIS4Jq7RuN9LUeNaVWJalfK1qsQ1MU1Mi0EUxcXEV7/61dpBBx2UNtDJrdQffvjhlr+ddtppaQO2vR/84Ae1ww8/PJ3/6KOPrt1zzz1ZL3LD1/Pggw9OCxw7PpIAHbuufp9FDFbdXdeHHnqoNnbs2DTQHXroobV/+Zd/qW3ZsiXrxW7oer722mu1q6++Oi0oDhgwoNZ0RrP28Y9/vPbHP/4xj0XvtJ/97Gdt/uaa1y35f7KuO75m9OjR6XZJvs9vf/vbeSw6kalKTEuIa+WKa1WJaQlxTVyjMb+XIse1qsS0KuVrVYlrYpqYlrdeyX+y7y8JAAAAABRd7mMuAgAAAADFpLgIAAAAACguAgAAAADZ0XMRAAAAAFBcBAAAAACyo+ciAAAAAKC4CAAAAABkR89FAAAAAEBxEQAAAADIjp6LAAAAAIDiIgAAAACQnf8P7vnx2rO2nZsAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=0.5\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plotting at t=1\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x600 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotter = Plotter()\n",
"\n",
"# plotting at fixed time t = 0.0\n",
"print('Plotting at t=0')\n",
"plotter.plot(trainer, fixed_variables={'t': 0.0})\n",
"\n",
"# plotting at fixed time t = 0.5\n",
"print('Plotting at t=0.5')\n",
"plotter.plot(trainer, fixed_variables={'t': 0.5})\n",
"\n",
"# plotting at fixed time t = 1.\n",
"print('Plotting at t=1')\n",
"plotter.plot(trainer, fixed_variables={'t': 1.0})"
]
},
{
"cell_type": "markdown",
"id": "b7338109",
"metadata": {},
"source": [
"We can see now that the results are way better! This is due to the fact that previously the network was not learning correctly the initial conditon, leading to a poor solution when the time evolved. By imposing the initial condition the network is able to correctly solve the problem."
]
},
{
"cell_type": "markdown",
"id": "61195b1f",
"metadata": {},
"source": [
"## What's next?\n",
"\n",
"Nice you have completed the two dimensional Wave tutorial of **PINA**! There are multiple directions you can go now:\n",
"\n",
"1. Train the network for longer or with different layer sizes and assert the finaly accuracy\n",
"\n",
"2. Propose new types of hard constraints in time, e.g. $$ u_{\\rm{pinn}} = xy(1-x)(1-y)\\cdot NN(x, y, t)(1-\\exp(-t)) + \\cos(\\sqrt{2}\\pi t)sin(\\pi x)\\sin(\\pi y), $$\n",
"\n",
"3. Exploit extrafeature training for model 1 and 2\n",
"\n",
"4. Many more..."
]
}
],
"metadata": {
"interpreter": {
"hash": "56be7540488f3dc66429ddf54a0fa9de50124d45fcfccfaf04c4c3886d735a3a"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}