{ "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 squared 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": [ "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", "Missing logger folder: /Users/dariocoscia/Desktop/PINA/tutorials/tutorial3/lightning_logs\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 84.47it/s, v_num=0, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000, t0_loss=0.0419, D_loss=0.0307, mean_loss=0.0121]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "`Trainer.fit` stopped: `max_epochs=1000` reached.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 68.69it/s, v_num=0, gamma1_loss=0.000, gamma2_loss=0.000, gamma3_loss=0.000, gamma4_loss=0.000, t0_loss=0.0419, D_loss=0.0307, mean_loss=0.0121]\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" ] }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "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": [ "
" ] }, "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": [ "
" ] }, "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(pinn, fixed_variables={'t': 0.0})\n", "\n", "# plotting at fixed time t = 0.5\n", "print('Plotting at t=0.5')\n", "plotter.plot(pinn, fixed_variables={'t': 0.5})\n", "\n", "# plotting at fixed time t = 1.\n", "print('Plotting at t=1')\n", "plotter.plot(pinn, 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 gets 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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 0: : 0it [00:00, ?it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 52.10it/s, v_num=1, gamma1_loss=1.97e-15, gamma2_loss=0.000, gamma3_loss=2.14e-15, gamma4_loss=0.000, t0_loss=0.000, D_loss=1.25e-7, mean_loss=2.09e-8]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "`Trainer.fit` stopped: `max_epochs=1000` reached.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 999: : 1it [00:00, 45.78it/s, v_num=1, gamma1_loss=1.97e-15, gamma2_loss=0.000, gamma3_loss=2.14e-15, gamma4_loss=0.000, t0_loss=0.000, D_loss=1.25e-7, mean_loss=2.09e-8]\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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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plotting at t=0.5\n" ] }, { "data": { "image/png": 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wnwP3lVgCABDJ/tesoGjhHooVAGwXnJ6URUgsJE/Hb1LD/oIsKO+Dacezad93AP5g2m+Lab+9iRaUc2hrgvI+mHY8m/Z9B4CWbO+dwsW2XeSHC2zX9S/wugkAPMKMimZ4NQLSpI6GaZ2wRPF75zkR9n+P/Dg6ktGQAJA8fowniCVa5/fZFsQSAIIqUUUGLrbtnsZihc2zK5hZ0ToKOvAjelmIyG9JhaCM8HODX987k45xkwqUABKHQQ9m/da2lV/Ph8nix/fPpOPbq++9l8vbAfAHZli4x/bZFSTigeCJq6cwY8YMFRYWqn379iouLtaSJUta3H769Ok64ogj1KFDBxUUFOimm27S7t2742qwn5mSWDCp09UWfuwQe81v76lfjvV4kVyAl4gl/M8vv7F+Ou+Zwk/vqUnHuSl9CSBZiCX8hYKFOyhWALBJzD2E2bNna8KECSovL9eyZct07LHHqrS0VBs2bIi4/QsvvKCJEyeqvLxcFRUVevrppzV79mzdfvvtbW48Es+kzla8/NT5NZlfihamHPMkFxAkxBLuMeW3xJTf1nj55RxnOr+8z7Yf74CNiCX8i4JF4lGsAGCLmHsF06ZN07hx4zRmzBgdeeSRmjlzpjp27KhZs2ZF3P7999/XSSedpMsuu0yFhYU666yzdOmll7Y62sFLXowyNiGxYHsnyw8dXVvZ/t7bfuwDtglCLBFkNv+m2n4+s5nt770px70JfQogGYgl/I+CRWJRrABgg5h6A3V1dVq6dKlKSkq+fYLUVJWUlGjx4sURH3PiiSdq6dKloQDgq6++0ty5c3XOOec0+zq1tbXatm1b2B8QiV9G4vmFzZ+FCQkGkgsIAmIJ95jwG2LCb2k8bD5/+Y3NsZ2tx39bsZQkko1YIlgoWCQOxQr/4L2AX8XUA9i0aZPq6+uVmxveEc7NzVVVVVXEx1x22WW65557NHToULVr105FRUU69dRTW5xiOXXqVHXt2jX0V1Dg7y8giYXY2dqBDQpbPx/bvgeJQHIByRaUWCKI3y0bf0NtPV8FhY2fjwnfAxP6FoCbghJLmMjLggEFi8TYWpRpdcGCBD3gb65H/osWLdIDDzygxx9/XMuWLdMf/vAHvfHGG7r33nubfcykSZO0devW0F9lZaXbzQw0EzpU0bKxwxpkNn5eXn8fSC4ATRFLtM7r3w6vfztjZeP5Kchs+7xs+z4AQUAs4R8ULBLD9mIFBQvAn9Jj2Tg7O1tpaWmqrq4Ou726ulp5eXkRH3PXXXfpiiuu0DXXXCNJOvroo7Vz505de+21uuOOO5Sa2rTTkZmZqcxMe380Y0FiIXo2dVARrvGzqzm4weOWRGfv+o5Kz6/xuhmALxFL+A+xBJKl4zepxBJRqqjKVf+86tY3BCxELAEpfHZHl68dD1tir61Fmeq6qtbrZsStrn+BMiqCV0CkSAM/i6m3lpGRoUGDBmnBggWh2xoaGrRgwQINGTIk4mNqamqanPTT0tIkSY5j3skkSEs12JJYsG0UHZpn02fp5ffD6wIm4KYgxBLJ5uVvBrEEks2mz9KW70ciBKkPBe8RS+BAbZll0fjYRP/ZwuaZFVLwkvZB218ET0wzKiRpwoQJGj16tAYPHqwTTjhB06dP186dOzVmzBhJ0pVXXqlevXpp6tSpkqQRI0Zo2rRpOu6441RcXKwvv/xSd911l0aMGBEKDIKKxELLbOmEIna2zbAAkFh+jyVI2JmDWMK/bIklvJ5ZAfiV32MJE9mQfDepjY1tsWG2BzMrAJgi5kLFxRdfrI0bN2ry5MmqqqrSwIEDNW/evNCFrNauXRs2UuHOO+9USkqK7rzzTq1bt045OTkaMWKE7r///sTtBWJiepGCpEJwmL6Eg5fJhWQu2bBwUz+dnr0iKa8FSMQSicSgh+YRTwSD6bGEl1j+CX5GLAFb2FKwaJxZYWvBgmIF4A8xFyokqaysTGVlZRHvW7RoUfgLpKervLxc5eXl8bwUAoakQvCYPiKSkZCAO4gl7GZykYJYIniIJYBgIpaATbb3TjG+WCHZPbuicVkkvxYsWPYJQUBPziNejYA0NbFg03rDcIfJn7+p3xv4y+bNmzVq1ChlZWWpW7duGjt2rHbs2NHiY3bv3q3x48frO9/5jjp37qzzzz+/yYUlP/roI51xxhnq1q2bDjroIJWWluqzzz5zc1eQJMQSTZl8LoH7TP78vfrecN2r4CGegBtMWlLJZrZcv4LrVpjHj/sERGJuNO8Bv68pbWpiweROJZKLglU4kgvBMmrUKC1fvlzz58/X66+/rnfeeUfXXntti4+56aab9Kc//UkvvfSS/vrXv2r9+vX64Q9/GLp/x44dGj58uA455BB9+OGH+tvf/qYuXbqotLRUe/bscXuXgKTh/IFGJh8LpsbiieL3vpQtiCcA89lSrLC5YOGnxL6f9gVojZlRvM+RfPyWqR1JeMvE48LvyQV4q6KiQvPmzdNvfvMbFRcXa+jQoXr00Uf14osvav369REfs3XrVj399NOaNm2aTj/9dA0aNEjPPPOM3n//fX3wwQeSpBUrVmjz5s265557dMQRR+ioo45SeXm5qqur9fXXXydzFwPD74k6E38LTTxnwHscF9+i7xEcxBOAPZhd4T4/JPj9sA9ALIjgA8K0xILJo91gBhOPDy++R8lKLvg9uWq6xYsXq1u3bho8eHDotpKSEqWmpurDDz+M+JilS5dqz549KikpCd3Wr18/HXLIIVq8eLEk6YgjjtB3vvMdPf3006qrq9OuXbv09NNPq3///iosLHR1n+AuLxKPpsUSkpnnCpjDxHjTxO8R/IN4ArAPxQp31fUvsDbZb2u7Y2HzsQV3mBW5BwCJBZIKiJ6JCQZAkrZt2xb2V1vbtgvOVVVVqUePHmG3paenq3v37qqqqmr2MRkZGerWrVvY7bm5uaHHdOnSRYsWLdJzzz2nDh06qHPnzpo3b57+/Oc/Kz09vU1tRrCYGEtwfkC0TDtWTPs+wTvEE7CBDYl029kwu8L2hHIQkv6AHxBV+JxpHSHTOoqwQ8dvUlVzcIPXzZC07zuVnl/jdTPQjL/++3C1253h2vPv2Vkn6a8qKAgPdMvLyzVlypQm20+cOFEPPvhgi89ZUVGRwBaG27Vrl8aOHauTTjpJ//M//6P6+no99NBDOvfcc/XRRx+pQ4cOrr023BP0ZVyIJRAPk2IJL1RU5ap/XnXrG8L1WEIingAQ2fbeKeryteN1M5rVWKzouqptRVWvNBYrMioqPW5JyyiqIMgoVPx/LHviPhILaAuTEgzJLlaQXDBPZWWlsrKyQv/OzIw8wujmm2/WVVdd1eJz9e3bV3l5edqwYUPY7Xv37tXmzZuVl5cX8XF5eXmqq6vTli1bwkZBVldXhx7zwgsvaM2aNVq8eLFSU1NDtx100EH64x//qEsuuaS1XQWMGvRALIG2CHIsATMRTwA4UOPMCtMLFrYWK6R9hQBTixUUKRB0FCqSKNkjIE1JLJBUQKKYlGBAsGVlZYUlFpqTk5OjnJycVrcbMmSItmzZoqVLl2rQoEGSpIULF6qhoUHFxcURHzNo0CC1a9dOCxYs0Pnnny9JWrlypdauXashQ4ZIkmpqapSamqqUlG+nkjf+u6GB7xJaZ0osIRFPIDFMiiX8OPBh4aZ+Oj17hauv4SfEEzCd6csR+ZnpBQs/FCskM2ZXUJwAvkWPD64iqYBEM+WYSnbyLhmFTmaWead///4aPny4xo0bpyVLlui9995TWVmZLrnkEuXn50uS1q1bp379+mnJkiWSpK5du2rs2LGaMGGC3n77bS1dulRjxozRkCFD9L3vfU+SdOaZZ+o///mPxo8fr4qKCi1fvlxjxoxRenq6TjvtNM/216+S8R0K6rJPpvz2wx+4xgn8ingC8B+Ti0VbizK5doXlrw+YhhkVPmXCCEg6gOE6r2vbaKMdvXg/G5kyGpJlG5BIzz//vMrKynTGGWcoNTVV559/vn71q1+F7t+zZ49Wrlypmppvj7lHHnkktG1tba1KS0v1+OOPh+7v16+f/vSnP+nuu+/WkCFDlJqaquOOO07z5s1Tz549k7p/sI8JsYREPHEg4onEMSGeIJZAohFPAP5jw7UrmF0R/+sC+BaFiiRJ5ghIExILQU0qtDV50JbnDlriwYTkApBI3bt31wsvvNDs/YWFhXKc8A5K+/btNWPGDM2YMaPZx5155pk688wzE9ZOIJmCGE+4GUu09vxBiyUkM+KJZBYruO6V/xFPAP7EUlDuc/vaFRQmgNZRqEDCBSWp4HYiIVaR2uP3hAPJBQBBwqAH/yGWMIMJ8QQAmMbkJYeCzOTZFY3LQNlcsEjk7AoKE0DsKFTIX+uye51Y8HNSwbRkQjQObLMfkw0kFwDAf/waTxBLmMvreIIloAAA0WJ2hfv2LzK0VLSgGBE/269vAndQqEiCoFz40m9JBRuTCa3Zf5/8lGgguQAAicOgh8TyWzzh58KF1/FEsrg9Q3Phpn46PXuFa88PANjH5IKFH4oVjShGAMnjn54FPE0s+CWp0HldQ+jP7/y2r345BlsTlMInYBu3Z2cm67tPkSIx/HaObYnf9tPLY9Dr7x8ANErksk+1BXWhP7jD1GW6thZlMmoeQEz80RuEp/yQVPBbJztWfkmokFxoOz8thQfALrbHE345l8Yr6PsPAGjqwOLE/kULChiJtb13itEFCwDemzFjhgoLC9W+fXsVFxdryZIlLW6/ZcsWjR8/Xj179lRmZqYOP/xwzZ0719U2svSTy4IyAtJGdKQja3xfbF3KwctlG1gCCoDNmJkZH+KJpmxfajIIsYTbyz8BQCwOLFZkVmZ4+vrNSXa74mHqxbb9tBQUYKPZs2drwoQJmjlzpoqLizV9+nSVlpZq5cqV6tGjR5Pt6+rqdOaZZ6pHjx56+eWX1atXL3399dfq1q2bq+2kUIE2sTGxQEIhOjYXLPy+xjTJBSBY/L7kG7GEv9kaT/g9lgAAt7VlpkSiCxeJmrXR+DymFyxMLlZIomABeGDatGkaN26cxowZI0maOXOm3njjDc2aNUsTJ05ssv2sWbO0efNmvf/++2rXrp0kqbCw0PV22tVjQERejYC0LbHAcgTxsXUpB6+OT2Y3AbARsUR0bDwfmsLG945YAkAQmbh8UDTLRDW3rJQbS0vZsGQVS0HBZBwDibNt27awv9rapoXAuro6LV26VCUlJaHbUlNTVVJSosWLF0d83jlz5mjIkCEaP368cnNzNWDAAD3wwAOqr693bV8kZlS4uh67n0dA2pRYsK1TbLLO6xqsGhHJaEgAMBexRDDZNsOCWAIAzGJSgcCGGRaNxQrTZlgwuwJ+93b14Urf4V5BZu/OWkl/UUFBQdjt5eXlmjJlSthtmzZtUn19vXJzw/PUubm5WrFiRcTn/+qrr7Rw4UKNGjVKc+fO1Zdffqnrr79ee/bsUXl5eSJ3JUzgCxW282LElS2JBZIK7rAtwQAAaBmjt1tGPOEOm+IJL4oVybhWhZtLSS7c1E+nZ0fu+ALwP5OKCclgS8HCtGKFxLUrgLaqrKxUVlZW6N+ZmYkpjjQ0NKhHjx568sknlZaWpkGDBmndunX6xS9+QaECiBVJBffZkmAguQDAbczOjJ0Ngx6IJZLDttmaAOBnpi4VZAvTCxbMrgD8JysrK6xQEUl2drbS0tJUXR2eQ6qurlZeXl7Ex/Ts2VPt2rVTWlpa6Lb+/furqqpKdXV1yshw53eOXoHFmE3RlI3rH9vOhvfc9OPWNG4mXQGYhViiKRvOa35jw3vuxXHLbCcAsJPp17AwtSDFdQsAd2RkZGjQoEFasGBB6LaGhgYtWLBAQ4YMifiYk046SV9++aUaGr6N0f/xj3+oZ8+erhUpJAoVrvHjCEiTEws2dHD9zvT3P9nHL8kFAGjK5FhCMv9c5nemx3OmH78AYAKTE/TJZnLBwtSLbVOs8D8+Y29MmDBBTz31lH7729+qoqJC1113nXbu3KkxY8ZIkq688kpNmjQptP11112nzZs364YbbtA//vEPvfHGG3rggQc0fvx4V9vJ0k+WSnYS1OSOmckd2qCxZTkoALCBHwc9mIpYwiwmLweV7CUl3V5OkqUkATQyMWntFyYvCWXitStYCgpIvIsvvlgbN27U5MmTVVVVpYEDB2revHmhC2yvXbtWqanfxt8FBQV68803ddNNN+mYY45Rr169dMMNN+i2225ztZ0UKmAtkgrmMjXBQHIBAL7FoId9iCfMZGosAQBAvEwtWJh87QqKFUDilJWVqaysLOJ9ixYtanLbkCFD9MEHH7jcqnBE/xYisUBSwQamLt9g4vEMAH5n4m+vqecpfMvUz8jE4xkATGDqMkemMXVJKBNn1WwtymSpICBAAh1lu3XBWD8t1WBiR8zEDiuaF/TPi2tVADBR0H+bgn5uso2Jn1cyY2S3v69+6rsAgE1MLFhw7Qq4ic8RrTEvCw00w9RRdWidaZ+biQU4ANifnxKHpv3mmnZOQnT43Ozj1qAwAIlnYmI6SEwrVkhmHhPMrgD8z6yeI1qVzBGQJiUW6Jzaz7TP0KTjuy38lMwEbEQirmWm/daadi5CbEwbtOKnWRUA0FYmJtttwuyK6FGsAPzLrN4jjGFSYsGkDinaxrQEQ7LYmFwg+Qr4l42/SW0V1POPX5n0WZoUMwMA7GdqwcI0zK6wD58XokFknWBujm4OamIB/mPK50pyAQDcY8pvrCnnHCQWnysAJIaJSWiYV7BgdgWAZDCjBwmjkFhAMgTt8w1ioRFAfPww6IFYAslgyuebrOPdze8vS0kCgJkoWLSO2RWAf5jRiwQOYErHE+4y4XM2JZnWFiQXAKApE84xcB+fMwB4z6REul+Z9h6bVqyQmF1hMj4bRMv+DF1ABGkEJB3OYDHh8zbhuAcAvzDhN9WEcwuSx4TP2w+zKgDA7woLNob92cbE2RWmYXYFYLd0rxsAc5BYgFc6r2vQjl7eH39u27u+o9Lza7xuBoCACkqCk1gimIISSwBAIpmYaE6UaAoR+2+zpjLHzeYkVGOxIrMyw+OWfHsMdfna8bgl4bYWZarrqlqvmwEgRoEtVCzc1C/hz8nyK21DYiHYvE4wdPwmVTUHcwwCQFt4PeiBWCLYiCXapqIqV/3zqr1uBgDLmDLCv60zJGwsWlCwaFnjzAoKFt5ihgtiwbAjCyRjBCSJBZiA4wBA0DHoIX6cQyB5fxwkI6a2aXaUG4PDAEBydxkn25aHMqVYJJk5S4floAB7BHZGBczhdYcSZvFyNGQyRkK6tfwToyABtMTvgx6IJbA/r2dWAIANvEwox1oAWFOZ41nRoPF1TZ9lYdrsCpNmVjRiOajko0CEWBHBg8QCAABxYKSwGYglEImXx4XXM5UBIFniGckfT8HBhJkNtsyyMOWC29t7pxg7uwKAuYiiDWfT1O5YkVhAc0gumIEkLIBo8dsJE/k51vRzHwEATGdLwcIEJhYsWAoqOXiPEQ+WfkoQW9eU9iqx4OeOYyy6rN7V7H3b+3RIYkvM4+dlG9xa/gkAIvFzQpN4gljCVLZeWJulJAEgeqZfgJvloFrGxbYB81CoAFzUUvKgrY8NQvLBq2KFrckFAHZj0ENsglKkIJZoGz8PfACAeCVihHuyln2yhcnXsjClYNF43JlYsKBYkVjMpkC8KFQYzO0RkCQWEqstiYREvJ5fkw0kGKLHKEgAQeHXWEJKbjwR6bX8GE/4deADMzQBwDwmz7KoLajzvFghMbsCQPMoVCCp/JZYSHZxoiV+Llx4kWAguQDAD/w46IFYwl37t4dYAgCA+Jk4y4LZFS2jYNF2zKZAW1CoCCgSC/EzLaHQHL8mGgAAsB2xhDcoVgBAYpZ9ioefl31qDQWL5pk4u0JiOah4UaRAWxGpJ4Cta0ojNl1W77ImsXAgm9veyItCl1fLowGADRj0EDubz8c2t91LxBIA/Cie61NgX8HCtIKNCZ/l9t4pnhXQWrK1KJPEO5BkgYycF27q53UTWuX2Ug3JZmtiobFT7peOue37YutxBABoO5vPAbaff/dne2xk83EUiRt9BgZhAYC7TCtY1BbUGVOwMBEFi+jwHiERAlmoCLpkj+yysUNocwc8Gn7fP1uQXADQyI3vrpuDHhglHh2/n29t3b9kx6ZB/77YMEgMALxAwaIpU2dXSBQsWsL7gkQJdtQMHMDWDne8bNxfkgsAEDy2DXqw8fzaFkHbXwCwVSISwPEksk1KxpvIxIKF10wtVkgk5Q/E+4FEIgNnID+NgLQpsRDkDrZtCQabjisA/sQI4eSx6TfftvNpotm07wx8AACYxqSCBbMrWsbsin14D5BoRMxwjS2JhaAnFfbHexEZyQUAtvHToAcbcP78lk3vhS2xamv8dm07AAg6ChbhTC1WSMEuWAR1v+EuepptxHrw9rKpI51sNrwvJBeSg1HjALxkw2+9DedML/C+2I0+DuA/XiV7TUm424iCxbdMnl0hBa9gEaR9RXKle90AJE8yR0Canlig89y6xvdoe58OHrekeZ3XNWhHL+qtAJAsxBLfIpZoHbFEuI7fpKrmYLOPawBoidcj6yM5M29Fs/fNr/LHoKvGYsWayhyPW7LvGMiszPDs9bf3TlGXrx3PXr81W4sy1XVVrdfNcBVFCriJQoVhTB9dHQ0SC/7SZfUuoxMMyWJTcqGiKlf986q9bgaAKDFy2T7EErEhlnDf3vUdlZ5f43UzACApWipOtLadzcULUwoWJhQrJBlbsGhM5PuxYEGRAm6jUBEQrCdNUqEtTE4wMKsCAMIx6MFdxBPxMXl2BbEEALgjkcsWRVuciPV5bCxcmFCwaJxdQ8GieX4rWFCkQDJQqEBCmZpYIKnQdiYnGJLFrVkVjIIEYIOgD3oglkgMUwc/JKtYYdMMTQD+kYi1/b1Y9ilRxYlYXsOmwgUFi31sWA5KsrdgQYECyUShAr5HYiGxTEwwMBISAPzDxEEPxBKJZWIsAQDwVjKKEtHYvx22FC1MKVhQrGiZbQULChTwApm9Nkj0mtJuLdWQrBGQJBaCg/cVSLzNmzdr1KhRysrKUrdu3TR27Fjt2LGjxcc8+eSTOvXUU5WVlaWUlBRt2bIl4nZvvPGGiouL1aFDBx100EEaOXJk4ncASABiieAw8X1N1vEX9NlJcBfxBGxkSpHiQGfmrQj92aCwYGNCl9uKVW1BnacXXN/eOyUhs4fcZnoBYGtRpvFthH8RJcO3TOwA+4lp7y/JBdhu1KhRWr58uebPn6/XX39d77zzjq699toWH1NTU6Phw4fr9ttvb3abV155RVdccYXGjBmjzz77TO+9954uu+yyRDcfhrB90INpTDvX+Q3vb2Il+vuf6EFZSA7iCRzIq8StlwlzN+xftDC9cEHBwvyCRWMxwJSCgGntQXAFbumnhZvsmLpnG9NGQNLxTQ6WbkgcrlMRbBUVFZo3b54++ugjDR48WJL06KOP6pxzztFDDz2k/Pz8iI+78cYbJUmLFi2KeP/evXt1ww036Be/+IXGjh0buv3II49MaPuBRCCWCCbTYgmWk4TNiCfgFi+TzqZqLFaYvDxUYcFGloMyfDkoyZsloShIwFRE4T4XxBGQJBaSy6T327Qkl5cYBWmXxYsXq1u3bqGkgiSVlJQoNTVVH374YdzPu2zZMq1bt06pqak67rjj1LNnT5199tn6/PPPE9FsJADfVTOZdG4LgiC+30GM0eE+4gnYyPTZCa0xfZaFCbMrvGTD7IpGbs9oYNYEbBC4GRVIPJOSw0Hs6JrAtNGQbuv4TapqDjbnuEfybdu2LezfmZmZysyMP+CrqqpSjx49wm5LT09X9+7dVVVVFffzfvXVV5KkKVOmaNq0aSosLNTDDz+sU089Vf/4xz/UvXv3uJ8bwZGMhCqxBEyKJZhVkXgLN/XT6dlmJvG8RDwBv/Lbsk/RMvlC3F5ecLuxWMHsiuhQSECQUagwhFtrSgcJiQVvmZJgILkQbCurc5TWsb1rz19fs1uSVFBQEHZ7eXm5pkyZ0mT7iRMn6sEHH2zxOSsqKhLWvgM1NOxL/t5xxx06//zzJUnPPPOMDj74YL300kv60Y9+5NprAzYilvCWKbGEzVhKsu3cjiUk4gkkjy0jyf3I1KWhglywaPw+2FKwAIKIQoWPBWkEJIkFM5BgQFBUVlYqKysr9O/mRj/efPPNuuqqq1p8rr59+yovL08bNmwIu33v3r3avHmz8vLy4m5nz549JYWvIZ2Zmam+fftq7dq1cT8vzGTroAdiCezPlFgiGQMfmKEJ4gnYwM2le0xdLimRTJ1l4eX1K7h2BYDmUKiA9UgsmMWEBIOtyQVGQdojKysrLLHQnJycHOXktN4BGDJkiLZs2aKlS5dq0KBBkqSFCxeqoaFBxcXFcbdz0KBByszM1MqVKzV06FBJ0p49e7RmzRr17t077ucNuoWbzOlkui0o6+gTS5jFhFgCSAbiCSBYTCtaMLuC2RWAaYLR+3QBF780YwQkiQUz8bn4S5CSsl7p37+/hg8frnHjxmnJkiV67733VFZWpksuuUT5+fmSpHXr1qlfv35asmRJ6HFVVVX69NNP9eWXX0qS/v73v+vTTz/V5s2bJe1LgPz4xz9WeXm5/vKXv2jlypW67rrrJEkXXnhhkvcSMBPnLDOZ8LmYEOsCsSCewP68WvYpqNeniJVJF+D28oLbJlxsG4A5KFT4VBBGQJrQgYW5SC7ANs8//7z69eunM844Q+ecc46GDh2qJ598MnT/nj17tHLlStXUfDvrZubMmTruuOM0btw4SdIpp5yi4447TnPmzAlt84tf/EKXXHKJrrjiCh1//PH6+uuvtXDhQh100EHJ2zmgGV7/VhNLmI3Px3sMzrIP8QQSyeskchCYVrDwQm1BnafHGsUKwBws/WQAG9eUJrGA1rBsAxCb7t2764UXXmj2/sLCQjlO+NTkKVOmRLzo5v7atWunhx56SA899FAimokEMj0BGIRBD0Br3F5OkqUkkWjEE7CFKcl5U5iyLJTXy0GxFBQQbPRAAbjG64KS2wU105N4pidBASQOgx5i5/U5CtHhcwIAe7DsU2KYUMTxajkoE2ZXMMMC8I7ZWTYYicQCYsHnFRsbk40AYBvOTXbh8wIABE3jklBeFy1YDgpAMlGo8CHTR3m3BR1VxMrrwhoAoCkvf5uJJezk5ecW9BmaAOzEEjb+YUKxIogX22Z2BZB8RMWwBokFe/n5syO5AMCP+G0DAABu8TrxbiNTZld4tRyUlyhYAMlDL9Rjti3zwuh0xMvPxQoAgB04F9nNz7MqAADxuSBrmddNSCpTChbJ5vVSUBLLQQHJkO51A4BokFjwhy6rd2l7nw5Jf93O6xq0oxd1WQAwgVcJX2IJf/AqlrDN3vUdlZ5f43UzAHisy9dOm5KrmZUZnieH99dcUSKeYsXL277b1uZ4av9ixfyqfkl//cZixZrKnKS+bm1BnTIrM5L6mvvb3juFZdUAF5G5i0NFVa7XTWiWH5dqILGAoLFtphUAb/GbAdjPjzE8gOCJNmkdT2I90TMnLshaFvqznZezLLxYDsrr2RUsBQW4h4gYUWPKOxLBj4UnkgsA/MTN3zRmUyARvPo8gxoLmzxIC0BwuDkDwk8FC68E9doVABKL7BqMRmIBiRLU5AIAM5H4Sx5iCX/icwWA6LBMTfT8ULBgdkVyMbsCSKxAFSoWbkr+un1+QZIXiURyIXlIhgIAAACIl5fXAziQ7deVSCavCxbJZsLsCgoWQNsFqlBhmkSvKe235WdIZvsbny8ABIsXgx441/ibF5+vm8ex32J5AHCDm8WKl7d913fFEK8KFkGcXSGxHBTQVkTDMBKJBbiBmUEA0DISpYB/JHpQVFsxux0IBjcvqO0mvxUoDhS0goWXKFbAVDNmzFBhYaHat2+v4uJiLVmyJKrHvfjii0pJSdHIkSPdbaAoVCAKJHfhFj8VpEjuAfCCaYlIk/jpHIPm8TkDQOv8dp2KxpkPiSgu+HEWRUuCshyU17MrWAoKppk9e7YmTJig8vJyLVu2TMcee6xKS0u1YcOGFh+3Zs0a3XLLLTr55JOT0k4yazAOHU6A5CMAf2HQA9yU7NiR4xlA0Jh0nYpEClKBwgRBvXYFYIJp06Zp3LhxGjNmjI488kjNnDlTHTt21KxZs5p9TH19vUaNGqW7775bffv2TUo705PyKnAdo7lhqy6rd2l7nw5Je73O6xq0oxffFwDwMwY9AAAQrsvXji+TpgcWGy7IWhbVdvBGY7Ei2iXCEqGxWOFVwa3xe+e3mU2wR11dnZYuXapJkyaFbktNTVVJSYkWL17c7OPuuece9ejRQ2PHjtW7776bjKYyowJmIbEAADAZa6wDZvJLDMngIwBom0gFCYoU5gnq7Ao/FgvhrW3btoX91dbWNtlm06ZNqq+vV25ubtjtubm5qqqqivi8f/vb3/T000/rqaeecqXdzWFGRYwqqnJb38hHmNqOZEj2rAq3dPwmVTUH850BYCe3EqTJjiX8krCG2ZihCQDNW1OZ40kiuhGFCTsUFmxM6swKaV+xwuulzLb3TmF2RQCsXZet1A7tXXv+hl27JUkFBQVht5eXl2vKlClteu7t27friiuu0FNPPaXs7Ow2PVesKFR4hPXnmwpCYiF91bq4H7u3qFcCWxJsJBdit3BTP52e7c2F1wAA3yKWaJ5fBj4k0t71HZWeX9Pm56moylX/vOoEtAiAl0xb/ml+VT/PLu4cVPOrmB3s9VJQEstBIXEqKyuVlZUV+ndmZmaTbbKzs5WWlqbq6vBYrrq6Wnl5eU22X7VqldasWaMRI0aEbmto2Df4LD09XStXrlRRUVGidiEMhQrARW1JJrT0XH5MNJBcAAC0lV8HPSQqnjjwefwYTwAA3JFZmeH50jloG4oU4ZhdAT/IysoKK1REkpGRoUGDBmnBggUaOXKkpH2FhwULFqisrKzJ9v369dPf//73sNvuvPNObd++Xb/85S+bzOJIJAoVPuCHpRr8llhIZIGitecnyQAAdknUMpLMzvQ3t2OJ/V+DWCI+zNAEACB+yV72yVTMrkAyTJgwQaNHj9bgwYN1wgknaPr06dq5c6fGjBkjSbryyivVq1cvTZ06Ve3bt9eAAQPCHt+tWzdJanJ7ohFZAwmUvmpdUhILXr+mW5JZsLLh+iskIQHYjkEPsSOWaBs/HAdcUBuAm5KVDI02Cc0o/+TgfY7MpFlCJi3LBv+5+OKL9dBDD2ny5MkaOHCgPv30U82bNy90ge21a9fqX//6l8etZEYFkBAmdO4ZFWkGEy+ozbrSAFpDYtR7xBIAANOx/BMShdkUkTG7Am4qKyuLuNSTJC1atKjFxz777LOJb1AEFCrgOZtHvpmQVDgQSQYAQNAQSySW7bEE170CAOBbzKZontfXqGgO165AUDF8DhHZsCyO10xMLOzP9PY1x+ZkEwAAsTD9XG16+0xAzAwAQGxMmU1hapECCLK4ChUzZsxQYWGh2rdvr+LiYi1ZsqTF7bds2aLx48erZ8+eyszM1OGHH665c+fG1WD4i41JaZvWcbalnV4huQB4h1jC//iNbZkt52ib4p792RhjAogNsUT8uE4FvGJKkQKAmWJe+mn27NmaMGGCZs6cqeLiYk2fPl2lpaVauXKlevTo0WT7uro6nXnmmerRo4defvll9erVS19//XXoauFBlMgL5LKmdHLZ2FG3cfkGlmwA/I1YAolkW0LaxlhC2tdum2IJAP5GLOEdrlNhF4pAkTGbAjBTzIWKadOmady4cRozZowkaebMmXrjjTc0a9YsTZw4scn2s2bN0ubNm/X++++rXbt2kqTCwsK2tRrwgK2JhUYkGACYglgCQUUsgWh1/CZVNQcnZlbS3vUdlZ5fk5DnAkxBLAG0zrQiBbMposf1KRBUMQ3Hr6ur09KlS1VSUvLtE6SmqqSkRIsXL474mDlz5mjIkCEaP368cnNzNWDAAD3wwAOqr69vW8vhmmQt1WDTCEjbEwuN/LIfpmOmE9A8YonEYHamffxyDrZpP5IVa7LMGZBcxBKJYVoi1LSkuu14P5tn+mwK076bQDLFNKNi06ZNqq+vV25ubtjtubm5WrFiRcTHfPXVV1q4cKFGjRqluXPn6ssvv9T111+vPXv2qLy8POJjamtrVVtbG/r3tm3bYmkmkFA2dcijYctoyGQt/9R5XYN29DI3SccoSPgNsUQwMOghHLEEACQOsYRd1lTmqLBgo9fNAABYwPXsXENDg3r06KEnn3xSgwYN0sUXX6w77rhDM2fObPYxU6dOVdeuXUN/BQUFbjczKhVVua1vBF/xW2KhkV/3C4A/+SmWQPD49Zzr1/0C4E/EEoll+oj0oDNxNoUpyz6ZfuwymwJBF1OhIjs7W2lpaaqurg67vbq6Wnl5eREf07NnTx1++OFKS0sL3da/f39VVVWpri7yBZgmTZqkrVu3hv4qKytjaSYsYMMISL93wP2+fwDMRCyBRCGW8J4N+2fDcWILBm3BFMQSiZOspGi0SWoTE+y2MfE9NKVIAcB8MRUqMjIyNGjQIC1YsCB0W0NDgxYsWKAhQ4ZEfMxJJ52kL7/8Ug0N3y4B8I9//EM9e/ZURkbkSmZmZqaysrLC/tCUG2tKs8buPjZ0vBPB9P0kuQD4D7EEgsL0c2yiBGU/AZiDWAJAPJhNAZgv5kz3hAkT9NRTT+m3v/2tKioqdN1112nnzp0aM2aMJOnKK6/UpEmTQttfd9112rx5s2644Qb94x//0BtvvKEHHnhA48ePT9xeAAkUtA530PYXgPeIJfyNQQ/BO7cGbX8jceO450L3QPOIJQA7mDKbgiIFYIeYLqYtSRdffLE2btyoyZMnq6qqSgMHDtS8efNCF7Jau3atUlO/DaoLCgr05ptv6qabbtIxxxyjXr166YYbbtBtt92WuL2AVUweJU9HO5hMv6A24DdBjiVMWzrF1kSoybFEUJl8ge0uq3dpe58OXjcDQAIFOZZItC5fO9reOyXmx2VWZqi2IPKyWZFEe1Ht+VX9dGZe5Iuiwy6mFClgv66raiVJW4syPW4J3BZzoUKSysrKVFZWFvG+RYsWNbltyJAh+uCDD+J5Kd/Zu76j100AmiC5kHgdv0lVzcGMKgaaQywBv2LQAwAkB7EEEM7E61OYgNkU9mosUOz/b4oV/mbnMLo4LNzEDzZaFvTEQtD33+9MG8UNAH4U9HNp0PffZAyWAgB/o0hhJ4oUzTuwSNHa7fCHwBQq0LpkrClt6lINdKwBAEBbEEvsY+r7YGoMCgAmSFayNNqlgEi6x8bE98uUZZ9Mn02ByForRlCs8C8KFQg8UzvUXjD1vSC5AADfCvrIaM4JMBUXkgcQNCSBgfgxmwJoikIFgDCmFivcRnIBANouqL+lQT13Nof3AwCA5GA2RfNMLqRRpGhetLMlmFXhTxQqLNXxG/s+OhNHQNKRhg2CPnoaAExGLBEZ70ti2Bjzt4TrBgLmYvkn+/AewW8oPsBfkS+AhCC5AAAA/MbEQTMAYDuTR60j+ZhN0TpmUwDNo1CBwCIZ3zLT3h+SCwCQWDaO1DbtXGDaudI0vD8AALjDxNkUFClaR5GiecymgEShAv9fUNeUBtxkYxIQAAAAQDDFm0SNNTHM8k9tw/tiJ4oUQOvIoiGQGOEXHd4nAAAi4xwZnaC9Twz+ARBUJo9ih/uYTYG2YDYFGlGoQFKYtlQDEAnJBQCIH7+hsAExKQAbdF1VG/bnR6Yktm3DbIrmmVykYDYFEB0KFQicoI3sayuT3i+SCwAQXCadA0w6N9qA9wsAotNcYSKZBYu2JFTdSBSTmP+Wqe8FRaeWUaRomV+LsYgPhYok2ru+o9dNAAAAAAAAhokmWUdCL7hMLVKYwuTZFACiR6EiShVVuV43AQnAiD4AQLwWbqKDCGKJePG+AUBimF6siCVhzEh8+/EZtozZFC1r6++Z6b+HiB2FCgt1/Mauj82kpRoQH5ILgPs2b96sUaNGKSsrS926ddPYsWO1Y8eOFrf/yU9+oiOOOEIdOnTQIYccop/+9KfaunVrxO3//e9/6+CDD1ZKSoq2bNni0l4AAEzF7O5gIJ6wU6zJNreTc6YlV4M+myDo+98aU2dTmPY9AmxgV8YbrgjKxS9JtgMw2ahRo7R8+XLNnz9fr7/+ut555x1de+21zW6/fv16rV+/Xg899JA+//xzPfvss5o3b57Gjh0bcfuxY8fqmGOOcav5ANAqU2Ix2wbR2DZICd4inggOk0cSm5o4tpHJRQpmUzSPIkXrTP4Ng3eIegFEheQC4J6KigrNmzdPv/nNb1RcXKyhQ4fq0Ucf1Ysvvqj169dHfMyAAQP0yiuvaMSIESoqKtLpp5+u+++/X3/605+0d+/esG2feOIJbdmyRbfccksydgdIOFN++005F8Jsfh4ExHK4ZiOeCB4/JPpIdtvJlM+NohjgLxQqAACI0bZt28L+amvb1klcvHixunXrpsGDB4duKykpUWpqqj788MOon2fr1q3KyspSenp66LYvvvhC99xzj373u98pNZXTvu0StXRLokdo+zkxCwBuIZ6AyUwbEW7yzAK3BHGfY2FqkcK07w5gk/TWNwHsxwhIRKvzugbt6EXny1b1VR3ltG/v2vM37N53bBQUFITdXl5erilTpsT9vFVVVerRo0fYbenp6erevbuqqqqieo5Nmzbp3nvvDVveoba2Vpdeeql+8Ytf6JBDDtFXX30VdxsBIBHSV63T3qJeXjcDaJbbsYREPIHE6rqqVluLMr1uRhOZlRmqLajzuhnWMrlIYcpsChNRpIiOH2aDwR1k4wBEjYJP7BI1atmEC2Au3GRusJxslZWV2rp1a+hv0qRJEbebOHGiUlJSWvxbsWJFm9uzbds2nXvuuTryyCPDEhyTJk1S//79dfnll7f5NYCg4xwIINGIJyAlJmFne9KPxHc4ihStM3U2BYC2YUYFXGXKmtIAkEhZWVnKyspqdbubb75ZV111VYvb9O3bV3l5edqwYUPY7Xv37tXmzZuVl5fX4uO3b9+u4cOHq0uXLnr11VfVrl270H0LFy7U3//+d7388suSJMfZN8InOztbd9xxh+6+++5W9wEA/KjL6l3a3qeD181AwBFPwHRdvna0vXdK3I9P9KyK+VX9dGZe24tyiI8pRQpTMZsiOoksrJo4mwxtQ6ECvscISABeycnJUU5O6wH9kCFDtGXLFi1dulSDBg2StC8p0NDQoOLi4mYft23bNpWWliozM1Nz5sxR+wOWqnjllVe0a9e3BeOPPvpIV199td59910VFRXFuVeIFxehBfZh+ScgNsQTiIZbS0C1tVgRrTWVOSos2Oj665jO5NkUpjBxNgVFCiAxKFQAiIkJyQVGQcJv+vfvr+HDh2vcuHGaOXOm9uzZo7KyMl1yySXKz8+XJK1bt05nnHGGfve73+mEE07Qtm3bdNZZZ6mmpkbPPfdc6EKc0r6ERlpaWpPkwaZNm0Kv161bt6TuIxAvE2ZnMugBgA2IJ2Dq9SoQHZOLFKbMpqBIAfgbhQoAAAzw/PPPq6ysTGeccYZSU1N1/vnn61e/+lXo/j179mjlypWqqamRJC1btkwffvihJOnQQw8Ne67Vq1ersLAwaW0HAABmIJ6AG9oyq4LlnwA0sv16OnAfhYqA67yuwesmuIoRkABs0b17d73wwgvN3l9YWBhaE1qSTj311LB/RyOexwAAAHsQT8DmJaCCvPwTsylax2wKwP9SvW4AACA5WB8fAGAKvw8m8ftgIABmc2vUcrxJWRMTzCYxuUiB5lGkABKPQgWAmPk9uQAAQCPOeQAAt9i4DIoJyVk/JfZN3xdmUyBRbPy9Q/JRqIBrTLj4JQAAcBcjxwEAMI+tSUFTEuNAS0wo2AF+RKHCMh2/4SMDAAAA2opBNQAQn3iStIyIb4rZFNEx7dihSBE7WwunSD6y3vAtlmpAvBgdDACA+4jVAMBdbiYH3UzWRpMgNz3J3xrT20+RAoAX0r1uAAAAABCJ1yPeSaTDFB2/SVXNwQykAGC3zMoM1RbUed0MT5leoEDLmE0BuIsZFQDi4nXyxuvkFQAAAACYztZZFdGwLelvS3uZTRGZ18e7rVj2CbGgUAEAAAAAAABjmJIsDxpT3neKFEAwUagAAAAAAABIomSOMjZpVoVpCehksWU2BQB4iUIFAABAgHT8hvAPAAD4gw0FABvaKDGbojnMpogfyz4hVvRUk2Tv+o5eNyFQvL5+AgAAAFpHzAYAyWFSwjDaRLQpifMg4L2OjCIFkFwUKgAAAAAAABAXkrnNs2U2hSlMm00BILkoVAAAAAAHYKQ/AMBvTJpVEa1oRvqbWAyYX9XPyHZFYspsCtOKFBTg2sbG3xt4j0IFgLiRxIkO68EDAAAA8DMuqv0tWwoUEkWK5lCkALxB9gyu6LJ6l9dNAAAAAAAA+/HrKGdTigOmtCMaphQpTEORAvAOhQoAAAAACIC96zt63QQABui6qtaVgoVbsypIqPubabMp0HZ+LYjCfRQqAAAAAAAAAoZkYmIxmyJ2phUpmE0BeItCRYB1XtfgdRMAAAAAz7BcKQAvmFQgSHRbvJxV4VWhwKYLZ0vmFCkA4EAUKgAAAAAAAALKraWggsCmAoVpmE3hT/yWmGvGjBkqLCxU+/btVVxcrCVLljS77VNPPaWTTz5ZBx10kA466CCVlJS0uH2iUKgAAAAAAAAIuEQlGL1M+CazcGBjkYLZFEAwzZ49WxMmTFB5ebmWLVumY489VqWlpdqwYUPE7RctWqRLL71Ub7/9thYvXqyCggKdddZZWrdunavtTHf12QEAAAAAAGCFrqtqtbUoM6mvmVmZodqCula3W1OZo8KCjUloUctsLFBIZhUpmE1hjlgKlK39NjCbwlzTpk3TuHHjNGbMGEnSzJkz9cYbb2jWrFmaOHFik+2ff/75sH//5je/0SuvvKIFCxboyiuvdK2dzKgAAAAAAACAJJKNfkSRonlBLVLEs+Qbvw3m2bZtW9hfbW3Tz6iurk5Lly5VSUlJ6LbU1FSVlJRo8eLFUb1OTU2N9uzZo+7duyes7ZEwowIAAAAAAAAhbZ1Z0eVrR9t7p0S9fSJnVcyv6qcz81ZE/dqxsHU2BSILUpEiUUWGxudJ9swr22R8k6G09u4V5ep3N0iSCgoKwm4vLy/XlClTwm7btGmT6uvrlZubG3Z7bm6uVqyI7rfytttuU35+flixww0UKgAAAAAAABDGi2WgTGVzgYLZFHBjJsSBvw/MtvBGZWWlsrKyQv/OzEz8b/bPf/5zvfjii1q0aJHat2+f8OffH4UKAAAAAAAANNGWYkWssypMRZHCn4Iwm8Lt4gHFCe9lZWWFFSoiyc7OVlpamqqrq8Nur66uVl5eXouPfeihh/Tzn/9cb731lo455pg2t7c1XKMCAAAAAAAAnop2tH00yfdEFRdsLlKYxqTZFBQpECQZGRkaNGiQFixYELqtoaFBCxYs0JAhQ5p93H//93/r3nvv1bx58zR48OBkNJUZFQAAAAAAAIgsiLMq/FCgMGk2hUlFCj+jOIHmTJgwQaNHj9bgwYN1wgknaPr06dq5c6fGjBkjSbryyivVq1cvTZ06VZL04IMPavLkyXrhhRdUWFioqqoqSVLnzp3VuXNn19rJjAoAAAAAAAB4zoRZFRQp/M2vsykoUqAlF198sR566CFNnjxZAwcO1Keffqp58+aFLrC9du1a/etf/wpt/8QTT6iurk4XXHCBevbsGfp76KGHXG0nMyoCbEevVHVe1+B1MwAAAABPbO/TwesmAIAVgjKrgiJF4pk0m8KPRQoKFIhWWVmZysrKIt63aNGisH+vWbPG/QZFQKECAAAAAAIgPb/G6yYAQKsyKzNUW1CX1Nf0Q4HCRCYVKfyIIgX8hqWfAAAAAAAAksDmxGJb2u7GSPZELf/kpyKFSbMpTCtS+G02hc2/JUBzmFEBV2zv00FdVu/yuhkAAAAAACBB2rIElGn8VKCQzCpSwF0UKeBXzKgAELe9Rb28boIVag7mWjAAAAAAEC03L6o9v6qf74oUpmE2hXsoUsDPmFEBAAAAHGBvUS+lr1rndTMAADBOvLMqvLyott8LEybNpqBI4Q4KFAgCZlQAAAAA8ASzMwEAzTEt4W0qk4oUcAdFCgQFhYokSc+v8boJgUKnFwCAyFiODgAAtFW8iVOvLqqN5DCtuOSH2RRBKFJkVFSG/hBsFCoAAAAAAAAAy1CkaR5FCjscWJygWBFsFCoAAAAAAAAQk2TMqkjkRbX9ZE1ljnH7bNpsCtv5vUjR0gwKihXBRaECAAAAAAAAQFxMK1LYPpsiCEUKIBIKFQDi4vV1QLb36eDp6wMA/M/rcx0AAKZjVkXymbafFCkSiyIFgoxCBQAAAIxEUdrfKARFr+bgBq+bAADN8nti1SSmFSlMQ5ECsBuFCvgWnV/Ea0cvfhoBAAAAwE1uzKrwMxOLFHwuiROEIgWzKdAasnGWYTQVAAAwCcVd2IoZOwDgPyYm8xPBxP0yrUhh82wKihTAPvQs4Ro6fwAAAAAA+J9J16rwGxOLFKaxtUjRdVVtIIoUQLQoVACIGctqAQCCgnMe4sFMIwDwDol99wW1aIT4MJsC0SKChq+RXAC+1T+v2usmAAAgiRgNAPyIkeGJZ2LRxbQihc2zKYKAIgViQaEi4BjtBQAAAAAAEiGe5CvLP0VGkaJ1NhYpWO4JaB5ZagAxMWEEJNc/gR9t3rxZo0aNUlZWlrp166axY8dqx44dLT7mRz/6kYqKitShQwfl5OToBz/4gVasWBG6/7PPPtOll16qgoICdejQQf3799cvf/lLt3cFAAB4hHjCbCYkJzMqKkN/fmZikh+JZWORImj8/juDxKNQAQCAAUaNGqXly5dr/vz5ev311/XOO+/o2muvbfExgwYN0jPPPKOKigq9+eabchxHZ511lurr6yVJS5cuVY8ePfTcc89p+fLluuOOOzRp0iQ99thjydglHIDl1+JjQnHahCK9n/B+Au4hnkBLDkwaulWwYFZF25lYaAnC++42E4qVgMnSvW4A4La9Rb2Uvmqd180AgGZVVFRo3rx5+uijjzR48GBJ0qOPPqpzzjlHDz30kPLz8yM+bv/EQ2Fhoe677z4de+yxWrNmjYqKinT11VeHbd+3b18tXrxYf/jDH1RWVubeDgGA4UwogAGJRjyBlgRxZPOayhwVFmz0uhkxMbFAIZlXpLBxNkXQihRB/M1B2zGjAq6iEwjAj7Zt2xb2V1vbtqBz8eLF6tatWyipIEklJSVKTU3Vhx9+GNVz7Ny5U88884z69OmjgoKCZrfbunWrunfv3qb2AgCAtiOeQLK0ljBkVoUZTC1SmMbGIgWA6DCjAkDUWKohdjUHNyTkedLzaxLyPG1xevaK1jfyWId1qUrLdK8GX1+777kP7LiXl5drypQpcT9vVVWVevToEXZbenq6unfvrqqqqhYf+/jjj+tnP/uZdu7cqSOOOELz589XRkbkjtv777+v2bNn64033oi7rUBQMUMzMYglYDq3YwmJeALJFW0RIqOiUnX9my9O2cqWWRUmFyn8WBRKpqDNpJCYTYH4MaMCgUCnGNHa0YufRbSusrJSW7duDf1NmjQp4nYTJ05USkpKi3/7X6wyHqNGjdInn3yiv/71rzr88MN10UUXaffu3U22+/zzz/WDH/xA5eXlOuuss9r0mvBOooqWiSqiNuK3EwBiRzwB0yQ6uej2rAq4z7QihW3HRxCLFEBbMKMCQFRMKfawnBhMkJWVpaysrFa3u/nmm3XVVVe1uE3fvn2Vl5enDRs2hN2+d+9ebd68WXl5eS0+vmvXruratasOO+wwfe9739NBBx2kV199VZdeemlomy+++EJnnHGGrr32Wt15552tthsAALiPeAJui6fwYNPMiszKDNUW1HndjDYzeTaFSWwrUgRVIgqetvwGIfEoVCAwWLIBQLLl5OQoJ6f1jseQIUO0ZcsWLV26VIMGDZIkLVy4UA0NDSouLo769RzHkeM4YWtcL1++XKeffrpGjx6t+++/P/adAAywvU8HdVm9y+tmEEu0kSmDHtyW6BlGiZ4B1Rb986q9bkIgEU8gHqYsvdJ1Va22FmXG9JguXzva3jslYW0wefknk4sUps2msAkzKdwX6+8K7MA8fbi+XAMj4AGgZf3799fw4cM1btw4LVmyRO+9957Kysp0ySWXKD8/X5K0bt069evXT0uWLJEkffXVV5o6daqWLl2qtWvX6v3339eFF16oDh066JxzzpG0b3mG0047TWeddZYmTJigqqoqVVVVaeNGMztqAJAMxKbwK+IJJIopRY5o2JxMp0gRPWZT2MGm3w6YiUJFlEwaPWTSqCoEQ1BGQAJeev7559WvXz+dccYZOuecczR06FA9+eSTofv37NmjlStXqqZm3zUK2rdvr3fffVfnnHOODj30UF188cXq0qWL3n///dCFNF9++WVt3LhRzz33nHr27Bn6O/744z3ZR8APOCfCVom6xg3MRjwBKTHJwkQmHE0YXW5yUcA0FCnaxoTjHbAVSz8lUXp+jfau7+h1MwKNJRsAmKp79+564YUXmr2/sLBQjvNtkJ6fn6+5c+e2+JxTpkzRlClTEtXEwDs9e4UWburndTMAK1HgAZKDeAKJ5OX1KmJZ/sm2a1VQNIkeRQp7MJsCicCMCgAtMimxwFINAAATmHRuBABgf6YmC01I4JpQIDChDS0xbTaFTUw4xv2AC2kHG4UKBA7JBTTH7eu1AADiR7HaXsReAGAvLwsfsYymtyHBTpEiNjbNpgh6kcLUAinsQ1YOSUFywU4kFgAA0QpasZdzpJ2ISQH4mVvJwkQ9rwnJXK+KBaYXKUxDkQIIpmD1KIH/j+QCAACA+4IWcwWtYAcgOLwaMW1Twtpmps2mABBMRNKQRKcKTQUtseCGmoMbvG4CADSL36i241wJADCFLUuvuDn63NRku+mzKUx732wqTjGbwp7fHtiB7DQCi+SCXViqAQDAucAuxFoA4C9+mVWRzMIBRYrYUKQAgo1CBZKG5II9SCwAABAdzpmRmfi+2BiLMvMJQDSSWUBIxGsFYVbFmsoc44sUpqFIYZ9E//bU9S9I6PPBPhQqLEWnJTFM7ETDGyYvf5aeX+N1EwAAANrs9OwVXjcBgKVsmlVhS4HClKIOADQyNzMHJAnFinAmvh82joAEALeYXLw0uejrJhPPnV7i/QAAf2NWhf1Me49smU3RdVUtsykAFwWzNwkgIhILAADTmVq85hxqtmQcN0Et1AHwFheyjZ8bMx9smE1BkQKJ4OVvz9aiTM9eG+4imkZIMjpXJBcAAAD8i5jKTCbPxAJgJy9mVcSS0E52Mp5rUvgfMyncxfUpIAWoUMF6qGhN0DvWQd9/v+ufV+11EwDA94J+Lg36/gNA0DCbYx+bChTMpogPRYpwfPfhlrgKFTNmzFBhYaHat2+v4uJiLVmyJKrHvfjii0pJSdHIkSPjeVlfYDST2YLawTZ5v02dhdMaLngPtCyosYRpRUNbf6tMPjeYfE51U1D3G4C3ghpPNPJDstDNWRXRaGuRgSJF/ChSADhQzIWK2bNna8KECSovL9eyZct07LHHqrS0VBs2bGjxcWvWrNEtt9yik08+Oe7Gwh9MTi4EEYkF1pQGko1Ywt/4TeXcahpiT8CfiCfMYHKxxO3EPEWK+NlSpACQXDH3JKdNm6Zx48ZpzJgxOvLIIzVz5kx17NhRs2bNavYx9fX1GjVqlO6++2717du3TQ3Gt2wdBWm6ICUXgrSvAMxBLIEgCNI5Nkj72hw3CnTE+kDLbIsnGJXdPBtnVdhUpED8+N42ZXJxEvaLKaKuq6vT0qVLVVJS8u0TpKaqpKREixcvbvZx99xzj3r06KGxY8fG31IkBaMg9wlCh9uGfWQEJOA/xBJIFM4RZrAhnkBimLZ0HYKNeMKsZKFJbTmQGzMJbCtSMJsiPhQpkieWC2lvLcp0sSXwWnosG2/atEn19fXKzc0Nuz03N1crVkS+WPXf/vY3Pf300/r000+jfp3a2lrV1n77g7Bt27ZYmgkLbO/TQV1W7/K6GS3aW9RL6avWed0MAPAVYgkEid9jCRuKFBS0AH9KRjxBLBGbjIrKmJKNB+q6qjamBGSXrx1t750S9+sdaE1ljgoLNka1nU0oUiCRTC5Kwh9cHT6/fft2XXHFFXrqqaeUnZ0d9eOmTp2qrl27hv4KCuI/2SUSo4iCx4YOeDz8ul/xYBYRYDa/xRIIHr+ec/26XwD8KZ54gljCPxKRrF9TmUORIkCYTQF4I6YZFdnZ2UpLS1N1dXjCvrq6Wnl5eU22X7VqldasWaMRI0aEbmto2LfWanp6ulauXKmioqImj5s0aZImTJgQ+ve2bdsICuAZP42GtCmpYPMIyESuKZ2eX5Ow5wJMQCyRGOn5Ndq7vqPXzWjWjl6p6rzO/fX1bZihKfkrlpDsiicA+FMy4gm/xxJu8OusCtsKFJKZRQpbZlNQpAC8E9NQ4oyMDA0aNEgLFiwI3dbQ0KAFCxZoyJAhTbbv16+f/v73v+vTTz8N/Z133nk67bTT9OmnnzZ7ks/MzFRWVlbYH5InWSPMbUpE+6FD7od9AGA/YgnzcMHe5Nhb1MsX52Kb9iFZsSazM4HkS0Y8YXIswfIrsYs3cU+RIjEoUtjPrd+dthQ34T8xzaiQpAkTJmj06NEaPHiwTjjhBE2fPl07d+7UmDFjJElXXnmlevXqpalTp6p9+/YaMGBA2OO7desmSU1uB0xn82hIm5IKkl1FLACxI5ZAkNkaT9gWS9iO2ZlA64gnzOSnWRU2FikQP4oU5uNC2v4Xc6Hi4osv1saNGzV58mRVVVVp4MCBmjdvXugiVmvXrlVqKqOKWpLI5RpqDm5Qx2/sfb9tWbKhUWMn3aYEA4mF5jECEvAGsQQSybZYQrKvWGFjLMGgB8D/iCfM1dZihddsLlAwmyI+FCkAM8RcqJCksrIylZWVRbxv0aJFLT722WefjeclAaPYkGCwMakAIDiIJfwvWdepsJUNsYREPAHAbMQTiEVmZYZqC+q8boZrKFLALSw3h2RheAEiYqR560xea9rUdkWDEZAAgFjZeu4wPZYwtW0mIWYGkGy2JAzb0s5YR7eTDKdI0RbMpvCOzTOv4A4ia3jO1uRCI5M68SQVvMdFaQEAsTLp/G1SW+Jle2wJAHCPiQl9eIciRetsKY7CHyhUAAngdafe69dPlGQmFoI0ArJ/XrXXTQBgOIqsZvD6fO6HWAIAYA5mVSSHicWXIH8ecAcX0m67GTNmqLCwUO3bt1dxcbGWLFnS4vYvvfSS+vXrp/bt2+voo4/W3LlzXW9jcDJ1PuaH5IJfRr41JhiS1dH3OqEBd6Xn13jdBAAuCFLxMJlFYb/EElJyz+/Jjl3c5odBD36I7QHAZCYm9uNl4r7YUqRgNgWCZPbs2ZowYYLKy8u1bNkyHXvssSotLdWGDRsibv/+++/r0ksv1dixY/XJJ59o5MiRGjlypD7//HNX20mhAs0K0ohzN7jV8fdbQgEAEB+Kmf5HLAEAsB2zKtxjYpHCFhQpouPmsk9cnyK5pk2bpnHjxmnMmDE68sgjNXPmTHXs2FGzZs2KuP0vf/lLDR8+XLfeeqv69++ve++9V9/97nf12GOPudrOdFefHYjB9j4d1GX1Lq+b4YoDEwHpq9bF/Vi/8tNIWD86PXuF100AgFYRS0T3WL8ilmiKgiZgBpKi5smszFBtQZ3XzfAdG4pFfB8RNHV1dVq6dKkmTZoUui01NVUlJSVavHhxxMcsXrxYEyZMCLuttLRUr732mptNpVDhlfT8Gu1d39HrZsAjQUkYmIqlGgAgeXb0SlXndfw+JhqxBJIpSEvWAUi8jIrKuEdPd11VG9Pa9F2+drS9d0pcr2UTZlMAkKRt27aF/TszM1OZmeG/mZs2bVJ9fb1yc3PDbs/NzdWKFZEHpVZVVUXcvqqqKgGtbh6Fihj1z6tWRVVu6xv6RLKTC34eCYnmMQISALxXc3CDOn5j/7KPxBLBlOxYgiVSAXjBzWVY3NaWYoVbbJ1VYWqRgtkU/sKyT23TpdJRWoZ734n6un3PXVAQ/l6Wl5drypQprr2u2yhU+IRfkgsAAJjs9OwVWripn9fNAOBTzM4EgKaYVfEtihTxo0gBP6qsrFRWVlbo3wfOppCk7OxspaWlqbo6fIZsdXW18vLyIj5vXl5eTNsnCpltGIfR9cHCCEgA8L9k//YSSwQLnzcA2MHmGSEmMLVIAcA7WVlZYX+RChUZGRkaNGiQFixYELqtoaFBCxYs0JAhQyI+75AhQ8K2l6T58+c3u32ikLFDq0jswi0kFprHxS8BADATsTEAJF+so+GjHeFvS/Lf5HYym8J/KCr6z4QJE/TUU0/pt7/9rSoqKnTddddp586dGjNmjCTpyiuvDLvY9g033KB58+bp4Ycf1ooVKzRlyhR9/PHHKisrc7WdLP0EI7G+NGzDUg0AvJCeX6O96zsm7Pn8tJQksUQwMOgBAOxi4rUqTEeRom0oUpiF7783Lr74Ym3cuFGTJ09WVVWVBg4cqHnz5oUumL127Vqlpn7bDzzxxBP1wgsv6M4779Ttt9+uww47TK+99poGDBjgajspVADwhBeJBUZAAoB3dvRKVed1yS3qUqyATRI96MG02ZmnZ6/wugkALBfrtSqiZfJFtU0uUtiAIgXwrbKysmZnRCxatKjJbRdeeKEuvPBCl1sVjqydhxLdeXBzRLcXCV5GyAFt1z+vuvWNAACwEIMeAMBOyVpWxobR/jbj/fUnln2ClwIVaTOKBzADRSgAQUcRMXk45/gTnysABJNbI+RNnLlgYpsa2VCkYDaFeeJd9smNmVQwU6AKFbAPnVAkipsjILk+BQBEh9HoAABAYlZFa0wuUtiAIgVgJ3qLiJpXyQWKFf7C59k609aUBhAsfiy+cu7xF68+z6AOemAGGADT+H1WhSntaI6txR+0jmWf4DUKFXEwOVg3uZMDkCgCgMSjuBkdzkEAAJiFWRX2seG9ZDaFmeJd9gnBQqECViC5gLZgqREAMAe/yWgLP86mcAMFTMB/GOmcHF7PZvD69VtiQ5ECgN3sirh9yLZOhJedNIoVdvPr58csJgCwh1/PRUHB5wcA/hNvASbWUfM2JNlNLlLYgtkU8aMYChNQqADgOi8TC7aNgAQAE7hdhGXgA2Ll58+NQQ8AYBYvCgamFylsKPQAsB8ZPB8iuQCT8JkBAACbMegBANwV9FkVFCkSg9kU5uL6FIgWUTesQ+IbfpbI5eD651Un7LkAwE+IJezC5wUASLZkFQ9ML1LYgiJF27DsE0xBoQJx8XpkGR1WO3j9Obl9nLJUA4C2SGQx0Y1rXvl5hqbk/TkK0fH6c/L6OAWAoEjWrAqTUKRIDJuPAQDhiLwNYGNywQRed1zRMj4fIDabN2/WqFGjlJWVpW7dumns2LHasWNHVI91HEdnn322UlJS9Nprr4Xdt3btWp177rnq2LGjevTooVtvvVV79+51YQ8A+3CuMlsQPh83YnY3+hawB/GEeUiimsWUZYxsKVKY8n4huLYWZXrdBCQRhQoACWdCYoERkIlzevYKr5sQCKNGjdLy5cs1f/58vf7663rnnXd07bXXRvXY6dOnKyUlpcnt9fX1Ovfcc1VXV6f3339fv/3tb/Xss89q8uTJiW4+EBcTfqtNOGfBTCYcn15jGUn7EE/AZqbNqrClmOAWG4oUFALNx/UpEAui7zgRtJvReSO5YJ6gfCZBmLWE5KmoqNC8efP0m9/8RsXFxRo6dKgeffRRvfjii1q/fn2Lj/3000/18MMPa9asWU3u+8tf/qIvvvhCzz33nAYOHKizzz5b9957r2bMmKG6ujq3dgewTlDOXTbhMwFiRzwBRMfrBLwNBRCv36NoUKRIDK5PAZN4n2kG2oiOrDlM+SxMKKLFg6Uagmvx4sXq1q2bBg8eHLqtpKREqamp+vDDD5t9XE1NjS677DLNmDFDeXl5EZ/36KOPVm5ubui20tJSbdu2TcuXL0/sTgRIkGYZJaMoa+tvNtxjSjzhNgY9INGIJ+AHfp9VYUORAgC8Qs/Qx4KUXAhKhxaAGbZt2xb2V1vbto5RVVWVevToEXZbenq6unfvrqqqqmYfd9NNN+nEE0/UD37wg2afd/+kgqTQv1t6XtiJYmfbEEuYwZTPwZQYN1b8DtiFeALwjhczBmwpUjCbAoBX0r1uAPZJz6/R3vUdvW6G1bb36aAuq3d53YzAClJigRGQ5ur0rwalt3Pv89m7Z99zFxSEr7NZXl6uKVOmNNl+4sSJevDBB1t8zoqKirjaMmfOHC1cuFCffPJJXI8HTLKjV6o6r/P+t5VYwlumxBIINrdjCYl4ArBNZmWGagvatswZRYrEoUiROCz7BNNQqECbmZJckEgweIXEgnm4jo67KisrlZWVFfp3ZmZmxO1uvvlmXXXVVS0+V9++fZWXl6cNGzaE3b53715t3rw54hIMkrRw4UKtWrVK3bp1C7v9/PPP18knn6xFixYpLy9PS5YsCbu/unrfsdHc8wIHqjm4QR2/sXN0eTyIJbxhUizBoIfEC9KSebEgngAiy6iojOsCvF1X1WprUeTvUSRdvna0vXfTC8gnmi1FCgDwWuAKFadnr9DCTf28bkbSBC25IJFgSLagJRYAScrKygpLLDQnJydHOTk5rW43ZMgQbdmyRUuXLtWgQYMk7UscNDQ0qLi4OOJjJk6cqGuuuSbstqOPPlqPPPKIRowYEXre+++/Xxs2bAgtBTF//nxlZWXpyCOPbLVdcF//vGpVVOW2vmEAMPAhuEyKJYBkIp4A7BHvrAqbihTMpkCixVNwRLCR1UNCmJYgpsObHEF8n90aAcma0sHWv39/DR8+XOPGjdOSJUv03nvvqaysTJdccony8/MlSevWrVO/fv1CIxrz8vI0YMCAsD9JOuSQQ9SnTx9J0llnnaUjjzxSV1xxhT777DO9+eabuvPOOzV+/PhmR23CbvyWJE4Qz3FeMO19Ni2m9RKzM+1DPAE/SdZFtd1MzlOkgMlY9gkmIhJvg0QH7yQXEsu0jq+fbO/Twbj3l8QCbPf888+rX79+OuOMM3TOOedo6NChevLJJ0P379mzRytXrlRNTfTnirS0NL3++utKS0vTkCFDdPnll+vKK6/UPffc48YuwMeStUyNab/lpp3r/Cao7y+DHuAm4gnAPbEUHihSJB6zKQD/C9zST0GUrOWfTFqyoRFLNyReUJMKgNu6d++uF154odn7CwsL5TgtdyIi3d+7d2/NnTu3ze0DgqrxvEc8kVgmxhOmFcqAeBBPwE9svVaFTUUKW1CkCKZYvsfwB6Jx+J6Jo/9tZer7mKzEQtAufAkAXjA1WWzqOdA2psZlph53AACztFaEsK1IYctsCiQWyz7BVETkARHUJRv2Z2Kn2Ca8f+5hqQYAieTWbwrFWs6FbcX7x/cIAGKVrGtVBJEtRQo+SyA4zM0qw1oUK/zF1JGPjUw+3rzCxS8B2M7k33aTz4kmM/l9M/l4ixaDHgCgbWJJ2jc3a8K22RQ2oEhhr3iWbQPsj8p9hk6G+0xPvJvE9PcpmYkFRkACcItNxcVk/haanDwmloge7xUAoK1Mn1WRWZlhXZHCltkUSDyWfYLJzO0BIuFILoSj09wy3h8AAFrGubJlNrw/DHqIzKYCKgAkSiJmVdiAIgUAU5mfTTYcQXzzbClW2NCJTiZb3hMbjq9omD6L6vTsFV43AUAcTP9tiZYNv/W2nDeTyZb3xIbjCwCwj4mjwG2cSWETln0Cgofo3EB+SS7YxIbOtNtsSSpIyU8s2DQCEkByBLmIx29iZDadR93EexCZm98b+g6A/5mYpLdFrMluv882sGX/KFIAwUShImCSnVywaaRaUBMMQd1vAIAdbIolpOAm6m2LJ2w7rgAAFGzaiiIFkvUd4kLaiBcROnAA2zrabWHjfjKbomUsRwcgGRj40LKgxRK27attx5PtgjwDDYAZmFXhz32Cv20tyvS6CfAAUXoAkVyIjo0d72g07peN+2brsdQclmoA0MiNIiO/Md6z9XwbDT/vW6LZNugBAEzGrAp/YzYFEGz+yvpFyYZRPX5LLticYLY5sb8/P+xDspFYAABzEEt4zw/7YfNxFIkbfQZmZwLwoyDPqvDTviB+FPlgA39F6h6xMZj3IgHrh46hbZ1zPyQUGvnh+AEAPyGWiI+N52Ub2xyJF8cPgx4AAF6yqUjBbAp/4PoUaIt0rxsA2Gj/znqX1bs8bElTfkgkHMgPiakD+W3WFAAky45eqeq8zv7k74Hna+IJd/kxlgAQHHX9CxgNvZ+Misq4kqFdV9Wy7j0AGIxChcHS82u0d31H156/5uAGdfwmuZ02vyQX9mdCosFvyYT9eZVYYAQkAD/wYyzhV14PgvBzLOEVt2MJBj0AgLu6fO1oe+8Ur5sRN2ZTALANhQoknR+LFfuL1NFPVMKBJAJaYuMydAAQD2KJxD+/nzGbAgD8J95ZFUFBkQL7S9aMLL6TaCsKFQHn1UhIvycYDhS0hECi+HU2BSMgAUTSP69aFVW5XjcjZsQSyUEsER+/xhIAgPjEuvyTjbMqbCpSAMD+GF6UIIxkjh2j29ASjg8ASAw/F0c5V6Alfj4+3Ppe06cBACQTsykQCdeSCS7/Ru8+kYzkAiO+YBovEwt8H751evYKr5sAwBJe/nb6ORmN+BFLAID/xbucTazJcZtmKNjUViQHyz7BJvTs4CmSCziQ348JP49sBoKGYp45/H7uAAAAaI1tRQpmUwA4EL06SGIkJMzg9bFg8whIlmoA0JIgzND0+hwCc/h9NgWDHgDgW8yqAAD/oEdngSB0RkguwOtjwOsEGwBIFB3byutzCbzHMRA/N35/mHkGAMlhWyGF2RT+wrJPSJTARvJuBM22Jxe8TtTSsQyuoHz2QSg6Agg2r2MJBJvX8QTHPwB4I+izKkxtF7yXrOtTAIkSjOwgrOF1BxPJZ8JnTmIBQBAkq1jq9W+qCecVJF9QPncGPQAA9mdjkYLZFP7CbAokUjAieh8ISnJBCk5HE3zWAAB37OiVyjkmQEz4rE2IoQEAMB1FCrRma1Gm102Ah7yP6oEITOhwwl2mfMbJSiy4WWy0fdk5AOHc/E4HaeCDZM65Bu7hMwYASMFc/smktgBAIhDZJxjJhcSh4+lffLYAgGThnONPJs2aYdADACDZKFKgNcm4PgXLPiHRzIjuYRyTihWmdEKRGCZ9nqYc5yY6PXuF100AYDmTfmNNOveg7Uz6PE06zgEg6II4q8ImLPsEoDXmRPlAC0zqkCJ+Jn2OyUwscOFLwL9sLOol8zfJpCSuSecgxI/PEQAQdDYWSihS+A+zKeAGIn3LBDW5INExtR2fnztYqgHwJ77b7uBcZDfTPj8GPQCIBheG9SevigU2FimQfMlY9glwg1nRPoxDsQJtZeLyXSQWACB5TIwlTDsvoXWmfWamHddt4VZh1MYZZwDsl6zlnxA93ltEi8IuzIr4k8yt4NntUZBBT3ySYLCHiZ+TnxILABCvoMcSkpnnKDRF3Mf3FQBMlezZDcymgClY9gluCXbUj6iYmtgNeqfVdHw+AIBGxBKIh6mfj6nHMwBgH2ZVmIP3FEAszIz+YRxTO2SmdmCDzOSRj8k+jt0eAcka9oC/+W2GpsmxhKnnraAy+TPxWywBAGibZM1yYDYFouX29SmYTQE3mdkD8AG/JRdMZnJnNmhM/hxMTZABQJCY/Fts8jksSPgckotBDwAQzsQZALYWKUx8LwG0bvPmzRo1apSysrLUrVs3jR07Vjt27Ghx+5/85Cc64ogj1KFDBx1yyCH66U9/qq1bt8b82vQEEDWTkwsSBQsv8d43RTERgA34rQrH+cw7Nrz3psfCAIBvuT2qfH+2FhKAWDGbIhhGjRql5cuXa/78+Xr99df1zjvv6Nprr212+/Xr12v9+vV66KGH9Pnnn+vZZ5/VvHnzNHbs2JhfO70tDYe30vNrtHd9x6S+Zs3BDer4jdmdyB29UtV5HR3JZDA9odCIxEJsTs9e4XUTAKucnr1CCzf187oZ1rAllpBEPJEkNsQTXsQSFBIBABRBACRTRUWF5s2bp48++kiDBw+WJD366KM655xz9NBDDyk/P7/JYwYMGKBXXnkl9O+ioiLdf//9uvzyy7V3716lp0dffjC/VwDj2JD0tWFUnu1seX/9mlhgqQYgGJLxXfciGWpDLCHZc66zlS3xmi3HKwB/YyRz8piyZJHNRQpT3sOgcXMmkdu/QVuLMl19fr/atm1b2F9tbdu+e4sXL1a3bt1CRQpJKikpUWpqqj788MOon2fr1q3KysqKqUghMaPCVf3zqlVRlevqa3gxq8ImjIhMPBsSCo1ILACAuWyYWSERS7iBWKJ1tg96YHYmABNkVFQmrcDT5WtH23unJOW1TEeRApCyVtcqPd2934S9e/d9zwoKwn/jysvLNWXKlLift6qqSj169Ai7LT09Xd27d1dVVVVUz7Fp0ybde++9LS4X1Rx7egkuIYiOj20JYFtG7JnMtvfQz4kFAEg0r367bIonbDsPmoj3EABgC6+T7TbPpoD/MKPLXJWVldq6dWvob9KkSRG3mzhxolJSUlr8W7Gi7Tnybdu26dxzz9WRRx4ZV8GEGRU+4NWsCltGQu6PUZGxI6FgHpZ9AgDvEEvEztZYgkEPAGA/G2dVUKSASShSmC0rK0tZWVmtbnfzzTfrqquuanGbvn37Ki8vTxs2bAi7fe/evdq8ebPy8vJafPz27ds1fPhwdenSRa+++qratWvXarsORKHCZclY/slLNhYrJJIMrbE1odCIxAIAP0lWLMHAh9jsf64knojM5njCptk+8WDQAwCYyfYihdczUYLMzetTwH45OTnKyclpdbshQ4Zoy5YtWrp0qQYNGiRJWrhwoRoaGlRcXNzs47Zt26bS0lJlZmZqzpw5at++fVzttLf3gDBeJkht7sg1LkFgc0c6kfzwXth8PAJAUNn+2+2H82ei+CG28vJ4ZNADAJgjnqS77YUGYH/Jmk3BhbTN0b9/fw0fPlzjxo3TkiVL9N5776msrEyXXHKJ8vPzJUnr1q1Tv379tGTJEkn7ihRnnXWWdu7cqaefflrbtm1TVVWVqqqqVF9fH9PrM6MCCWHraMj9BXVkpM2JhAMFIbHg9ghIrtsDBJtXsyokYgmbEUsAAEyWzOWf2sL2IgezKQB/eP7551VWVqYzzjhDqampOv/88/WrX/0qdP+ePXu0cuVK1dTsy4MtW7ZMH374oSTp0EMPDXuu1atXq7CwMOrXplDhI14mFyR/JBga+T3R4KeEQiMSCwC8dHr2Ci3c1M+15/f7UpKNiCXsQSyReH4Z9AAAftJ1VW3Mo73juVYFRQpEo3F5pwMLb24s+2RDcQ/u6N69u1544YVm7y8sLJTjfPubdeqpp4b9uy3818OIg9sjiIPUGfC6g+cGPyxhsP8+2LwfzfH6uGOZBgB+4vVvmte/6W7wyznYL/sRidfHndffu0RidiYAE7F+P2yXzGOYIgW8wowKn/F6VoXkr9GQBzqwY27qCEk/JhCa43ViIZmCVPQEEGxBiiUkM+MJYgkAAOIXy6wK22dTwF2RChS2LGcGxIpChQ9RrEie5jrxyUw4BCmRcCATEgt+GgEJwGzJXP6JWCK5vC5eEEt4K5mxBIMeALvV9S9gZoAH4ln+KVp+KFKw7JM33CpWJLsAwoW0sb/g9kqSLIidAhM6fl45cKklN/+CyoTjiyIFEmnz5s0aNWqUsrKy1K1bN40dO1Y7duyI6rGO4+jss89WSkqKXnvttbD7PvroI51xxhnq1q2bDjroIJWWluqzzz5zYQ+AxDPht94rxBLuC/LxBf8ingCaR5EHtmntmM2oqEzocc0sDXgtuD0TnzMlgUoHEG4I4nGVjGIna0p7a9SoUVq+fLnmz5+v119/Xe+8846uvfbaqB47ffp0paQ0nVq+Y8cODR8+XIcccog+/PBD/e1vf1OXLl1UWlqqPXv2JHoX4DPEEvAzU44rU75n8A/iCcAd8cwaaG22hB9mU8A9yS6sUaSACShUJFEQZ1VI5nQE4Q+mHE8kFpBIFRUVmjdvnn7zm9+ouLhYQ4cO1aOPPqoXX3xR69evb/Gxn376qR5++GHNmjWryX0rVqzQ5s2bdc899+iII47QUUcdpfLyclVXV+vrr792a3cCKxnFvmTHEqb81pny2w9/MOV4Svb3K6h9kSAhngDs4ZciBcs+uYPZPwgqChU+ZkpyQTKnQwi7cRzBrxYvXqxu3bpp8ODBodtKSkqUmpqqDz/8sNnH1dTU6LLLLtOMGTOUl5fX5P4jjjhC3/nOd/T000+rrq5Ou3bt0tNPP63+/fursLDQjV0BXMM5AInAceQuZmd6i3gCaF2yE8CRChJ+KVLAP5hNAVNQqPj//BpUU6yAH9Qc3GDU8cMISGzbti3sr7a2bSOJqqqq1KNHj7Db0tPT1b17d1VVVTX7uJtuukknnniifvCDH0S8v0uXLlq0aJGee+45dejQQZ07d9a8efP05z//Wenp6W1qM7wT1FkVknnnA9jFpGPHpO8VvEM8AdiF2QNIhiAt+cSFtHEgoook659XrYqqXK+b4ZnGDmLHb6iRITomJRUkEgum67Jml9LT3RuhtHfvbklSQUF4MFdeXq4pU6Y02X7ixIl68MEHW3zOioqKuNoy5/+1d//BVdX5/cdfCSGJVENgCCRZIyxUNyggW7Jmg7JWCcLiWO3QETXDAl+EdSSdLjhdo1JDl11By6qF0nXW1br7/YJYW6WuS9MiyO6IKdAI46+YXflREA1IIz8kShJyvn8wibnkJjn35p5zPp9zno+ZzMDNvTfnfu7nnPs67/c5577yirZt26Y9e/b0eJ8vvvhCCxYs0LXXXqvnn39e586d0+rVq3XzzTdr9+7duuiii5L624iejMJmtX08KOjF6NR8aTtZAq6RJTjoIRFeZwmJPAFETccZFKdHpoXqbAoaN6kXpSYFEA+NiggwrbggUWCAO6YVFoAOhw8fVk5OTuf/s7LiHwly3333ad68eb0+1+jRo5Wfn69jx47F3N7W1qampqa4l2CQpG3btmnfvn3Kzc2NuX3WrFmaMmWKtm/frg0bNujgwYOqra1Vevr5be6GDRs0ZMgQ/du//ZvuuOOOPl4pYC6yBNwgS8Bk5Akko2VsEdevD9DgfWeTPgo8TE0K2I8mBUxEoyIiaFbAJqYWFcJ8BGRYL3/nlZycnJjCQk/y8vKUl5fX5/3Kysp04sQJ1dXVadKkSZLOFw7a29tVWloa9zFVVVW6++67Y24bP368nnjiCd1yyy2Szl9zOj09XWlpaZ336fh/e7uZ65ntbhz2gbYdL/b87wRxhiZZArYxMU+EOUsgceSJ6Dg5Joujzw2SWX+YIi2M42cDkvkPU7FnF4CgdhZMvGQN15rGhUydDyauPwiPsWPHasaMGVq4cKF27dqlHTt2qLKyUnfccYcKCwslSUeOHFFxcbF27dolScrPz9e4ceNifiTpsssu09e//nVJ0rRp0/TZZ59p8eLFqq+v13vvvaf58+crIyNDN9xwQzAvFlYzcVtIlsCFTJ0TJq4/qcRBD8EjTwD+oOnEGKQaTQrgPBoVXRCug2PiziT8Z+o8CKqwwBGQ0bJ+/XoVFxdr6tSpmjlzpq677jr9/Oc/7/x9a2urGhoa1Nzsfj4WFxfr17/+td5++22VlZVpypQp+vjjj1VTU6OCggIvXgZ8xIEPsUz9DIG/mAeIOvIE4A6Xz4Ipotqk4Iu0EQ+XfgpIUF+qbeJlGzrwRdvRRVEBkIYOHaoNGzb0+PtRo0bJcXq/rm2830+bNk3Tpk3r9/IBNiBLRJfpWYKDHuAX8gQAIB6TmhRAT9iLiyBTj4TsYPqOJlLL9PebwgIAdEeWgElMf79NX18AAImL8qWPovzaU82vsyloUsAWSTUq1q1bp1GjRik7O1ulpaWd17eM5+mnn9aUKVM0ZMgQDRkyROXl5b3eP0qCLESavsNk6rWFkTo2vMemryepwmXvEASyRGqQJXpmw+cM+seG9zjI9YSDHhAFUc0TFB0B+9GkALpLuFHxwgsvaOnSpaqurtZbb72lq6++WtOnT9exY8fi3n/79u2688479frrr6u2tlZFRUW66aabdOTIkX4vPMLP9J1PJM6GooJkfgEOsFnYs0SUmn82bCtt+dyBe7a8pzasH6kSpe0ezBH2PAHv9bdQHMUzC6L4mm1mapOC76dATxJuVDz++ONauHCh5s+fryuvvFJPPfWUBg0apGeffTbu/devX697771XEydOVHFxsX7xi1+ovb1dW7du7ffCe8HvkM2RkH2zZWcUvbPpfQx63eAISIRd2LOE34LeZgS9zXTLps8h9Iz30J2gtwuAH8gTAGzl9dkULWOLjG1SAL1JqFHR0tKiuro6lZeXf/UE6ekqLy9XbW2tq+dobm5Wa2urhg4d2uN9zp49q1OnTsX8wBu2FBckCgy2su19s2mdAGxElkDQbPpMwlfIEwC68iNPkCUAeMGPJgVgq4QaFcePH9e5c+c0YsSImNtHjBihxsZGV89x//33q7CwMCZQXGjlypUaPHhw509RESuZl2zbkbJtRzWqeJ+SwxGQCDuyhDeC3naQJeAVG9+roNeHoLcHgB/8yBNRyxJRxeWf3IvSa7UVTQrYLqkv007WqlWrtHHjRr388svKzs7u8X4PPPCATp482flz+LA/XzATFBN2JoLeoUqGjTuuUWDz+2LjetBfXFMatrElS0Rx3bJxG9rxmWXr51aY2fq+2LgeAFHkJk8EnSX6QkESsI9XZ1PYdKknvp8CvclI5M7Dhg3TgAEDdPRobGH96NGjys/P7/Wxq1ev1qpVq/Taa69pwoQJvd43KytLWVnBTdwbh32gbceLA/v7QckobFbbx4OCXoyEdezEDvrI174bLmBjMaErEwoLJjQtAa9FJUsEYWz+UdU3juj7jh6yNUtI5AkTkCX6L4gsEcXGLILnR56IYpYAYBdbmhOAWwntiWVmZmrSpEkxXzbV8eVTZWVlPT7uscce04oVK1RTU6OSkpLklzbETClQmrCDlSyOigxGGMbc5nkP2IYsEX62b1PD8LlmmzCMue3zHrANeQImicIlkaLwGr2W6rMpaFIgjBI6o0KSli5dqrlz56qkpETXXHONnnzySZ05c0bz58+XJH3ve9/T1772Na1cuVKS9Oijj+rhhx/Whg0bNGrUqM7rRV588cW6+OKLU/hS7GfCkZCS3UdDduCoSG/ZXkzoypTCginNSsAPZAnvkCVSp+tnHXki9cgSqUeWQNSQJ5AqmfWHKfrCKsxXhFXCjYrZs2fr008/1cMPP6zGxkZNnDhRNTU1nV9idejQIaWnf7Uz97Of/UwtLS36i7/4i5jnqa6u1vLly/u39PBMGAoMEkWGVApTQaFD1AsLXKoBQYlKlojqpSQ7hCVLSOSJVApbnjAlSwBRZFueODkmK+VHpbeMLfLsmvcAUieV66nNTQq+nwJ9SbhRIUmVlZWqrKyM+7vt27fH/P/gwYPJ/InABVVcMOVISClcBQaJIkMywlZM6IrCAhCsKGSJoJAlvEWeSFxY84RJWYKDHhBV5AmYYvC+s6EtwnLZJwB+SapRgegIY4FB6r7DTKHhK2EtJnRFYQFA2NGs8AdNi/jIEgAAAOdxNgXgHo0KA5lUXJDCXWDoEOXGRRSKCR0oKgBAMMgS4RalLCGZlyc46AGINi7/lBp8TwXgrbCecYTUolEBV6JQYOgqrMWGqBUSujKtqCAFW1jgUg2AP4L8ngoTD3yQFJk8Ee8zlzxhP9PyBE0KADBHmC//hODRSEMU0KjoBcWFWFErMHTV0w65yQWHKBcRLmRaUQEAoixqBz90ZVvzgizxFbJEdxz0AAAAgFSiUWEwE5sVUrQLDBdyswPvRQGCwoF7phYWOAISgB/IEuYjS5iPLAHAdFz+yRxhO6uCL9LuH9ZLIDE0KpAUCgzuUQgIDoWF+DgCEogWmhX2I0sEx9QsAQAAosP2yz6FqXkHb5l7rjkkBV/Q7A07bjBVRmEz8xOAMWgO9oztNUxm8twMeh+B7RqAMOLod6QS8wlIHI2KPpgQwoPeEekNBQaYxvT5aPL6DCC8TN/2mL7tRrSYnm9NX58B9MzLo4ptP+I6TLhcEgAkh0YFUsLknTlEg+lFBcmMwoIJzVcAwTBhG9QbG7bjCD/T56Dp6zEAAEgt25uQXPYJiaBRYQkbdkooMCAoNsw7G9ZhAN6hSeieDdt0hA851j22Z4C5bC9oAgCijUaFC6aEcVsKnezkwS8UFQAgMTZlCbbv8Istc82W9RcAwOWfoo7vpwCSQ6PCMrbsoFBggNdsml+mrLemNF0BBMuUbZIbNm3rYR+b8qpN6y0A2IwCM0xi+1lSXPYJiaJRYSGbdlRs2gGEHWybUzatrwC8ZVKz0KZtk23bfZjPtjll0vpq0nYMQHy2FzYBANFFo8IlQnn/2LQzCDPZVlSQzCosAMCFbNtG2fg5APMwhwAAfuHyT+gPmo6IIhoVlrKtuCBRYEBybJ03pq2jNFsBhIWtnwsIlq3zxrQ8AcAOFDgBBI3LPiEZNCoSYFqhz9YdF1t3FOEv5gmAMCJLpA6fE3DD5nli2vpp2vYLsBXFO9iCM0IA+I1GheVM24FJhM07jvBOGOaFzeslgOixfZsVhs8NpJ7t88L29RJA8DirIjmMG0xg+zykIYtk0agIAdt3ZGzfkURqhGUemLg+cgQkYBYT10kTt12JCsvnCJLXMQdsnwdhWB8BmMH2YmcYcFYCALhHoyJBJhYXpHDs0IRl5xKJCdN7Hob1EEB0hWUbFqbPFbgTpvfc1PXQ1H0gAEglGjswAfMQUUajIkRM3bFJRph2ONFdGJtSpq5/FBYAJMLUbVkywvhZg1hhe3/DtP4BMAdFTySLy/cgGcwb9AeNiiSYXPgL2w4ORYZwCet7Gbb1DoD3yBL+CuvnTxSFNRuavN6ZvL0C4A7Nir4xRkilZOcT8xBRR6MihEze0emPsO6Yhl3Y37ewrm8Aoi2s27awfyaFVdjft7CubwB6xhHHZvG6OMz3VCAq2Lahv2hUJMn0I4vCvsMT9h1W20Xl/TF9PTN9OwVEnenrqOnbuP6KymeVraLy/pi+npm+nQLgHkdqAwBMR6MixEzf8UmVqOzImi5K78PY/KORWb8ARFtUtnVR+gwzWdTeh6isXwDMQbOiO8YEXkl0btk+FzmbAqmQEfQCwFtj84+qvnFE0Ivhmwt3bNs+HhTQkoRfVIoIF7KlqMARkIAdbhz2gbYdLw56MXrVsd2LSp4gS/gnqllCsiNPkCWAcGoZW6TM+sNBL4YRbC8M++HkmCwuXeUD5iJwHo2KfrChuCBFr8DQFcWG1IlyMaGDDUUFAPBK1A5+6ECWSB2yBFkCgBloVlAYBlKJsymQKjQqIiSqBYauKDa4QyGhO5sKCxwBCdjFlgMfJLKEFP8zkjzRHVmiO7IEgK44Uj1aBu87SzE3gvpqCtIwA2LRqOgnm4oLEgWGC/W0Ex2lggOFhL7ZVFgAAK+RJbqLevOCLNE3sgQA00T5rAqKw4mhqdY/8da1MM1BGnBIJb5MOwVsO+KIHaW+df0yxwt/bBS21+MXG78027btEYDzbFt3bdw++i1sn71hez1+sXFdsW17BCB5LWOLQlUwdSNqrxdm6Jh3YVvnaFKEU1NTkyoqKpSTk6Pc3FwtWLBAn3/+uavHOo6j7373u0pLS9OmTZsS/tucURFRUf7eiv5KZIfcq6MpKQp4z7a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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Plotting at t=1\n" ] }, { "data": { "image/png": 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" ] }, "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(pinn, fixed_variables={'t': 0.0})\n", "\n", "# plotting at fixed time t = 0.5\n", "print('Plotting at t=0.5')\n", "plotter.plot(pinn, fixed_variables={'t': 0.5})\n", "\n", "# plotting at fixed time t = 1.\n", "print('Plotting at t=1')\n", "plotter.plot(pinn, 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 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", "Congratulations on completing 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": "3.9.16" } }, "nbformat": 4, "nbformat_minor": 5 }