475 lines
176 KiB
Plaintext
Vendored
475 lines
176 KiB
Plaintext
Vendored
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Tutorial: Multiscale PDE learning with Fourier Feature Network\n",
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"\n",
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"[](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial13/tutorial.ipynb)\n",
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"\n",
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"This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs)\n",
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"a PDE characterized by multiscale behaviour, as\n",
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"presented in [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
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"multi-scale PDEs with physics-informed neural networks*](\n",
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"https://doi.org/10.1016/j.cma.2021.113938). \n",
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"\n",
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"First of all, some useful imports."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"## routine needed to run the notebook on Google Colab\n",
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"try:\n",
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" import google.colab\n",
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" IN_COLAB = True\n",
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"except:\n",
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" IN_COLAB = False\n",
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"if IN_COLAB:\n",
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" !pip install \"pina-mathlab\"\n",
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"\n",
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"import torch\n",
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"import matplotlib.pyplot as plt\n",
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"plt.style.use('tableau-colorblind10')\n",
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"\n",
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"from pina import Condition, Trainer\n",
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"from pina.problem import SpatialProblem\n",
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"from pina.operator import laplacian\n",
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"from pina.solver import PINN, SelfAdaptivePINN as SAPINN\n",
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"from pina.model.block import FourierFeatureEmbedding\n",
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"from pina.loss import LpLoss\n",
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"from pina.domain import CartesianDomain\n",
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"from pina.equation import Equation, FixedValue\n",
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"from pina.model import FeedForward\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Multiscale Problem\n",
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"\n",
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"We begin by presenting the problem which also can be found in Section 2 of [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
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"multi-scale PDEs with physics-informed neural networks*](\n",
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"https://doi.org/10.1016/j.cma.2021.113938). The one-dimensional Poisson problem we aim to solve is mathematically written as:\n",
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"\n",
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"\\begin{equation}\n",
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"\\begin{cases}\n",
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"\\Delta u (x) + f(x) = 0 \\quad x \\in [0,1], \\\\\n",
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"u(x) = 0 \\quad x \\in \\partial[0,1], \\\\\n",
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"\\end{cases}\n",
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"\\end{equation}\n",
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"\n",
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"We impose the solution as $u(x) = \\sin(2\\pi x) + 0.1 \\sin(50\\pi x)$ and obtain the force term $f(x) = (2\\pi)^2 \\sin(2\\pi x) + 0.1 (50 \\pi)^2 \\sin(50\\pi x)$.\n",
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"Though this example is simple and pedagogical, it is worth noting that\n",
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"the solution exhibits low frequency in the macro-scale and high frequency in the micro-scale, which resembles many\n",
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"practical scenarios.\n",
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"\n",
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"\n",
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"In **PINA** this problem is written, as always, as a class [see here for a tutorial on the Problem class](https://mathlab.github.io/PINA/_rst/tutorials/tutorial1/tutorial.html). Below you can find the `Poisson` problem which is mathmatically described above."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"class Poisson(SpatialProblem):\n",
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" output_variables = ['u']\n",
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" spatial_domain = CartesianDomain({'x': [0, 1]})\n",
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"\n",
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" def poisson_equation(input_, output_):\n",
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" x = input_.extract('x')\n",
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" u_xx = laplacian(output_, input_, components=['u'], d=['x'])\n",
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" f = ((2*torch.pi)**2)*torch.sin(2*torch.pi*x) + 0.1*((50*torch.pi)**2)*torch.sin(50*torch.pi*x)\n",
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" return u_xx + f\n",
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"\n",
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" # here we write the problem conditions\n",
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" conditions = {\n",
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" 'bound_cond0' : Condition(domain=CartesianDomain({'x': 0.}),\n",
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" equation=FixedValue(0.)),\n",
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" 'bound_cond1' : Condition(domain=CartesianDomain({'x': 1.}),\n",
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" equation=FixedValue(0.)),\n",
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" 'phys_cond': Condition(domain=spatial_domain,\n",
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" equation=Equation(poisson_equation)),\n",
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" }\n",
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"\n",
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" def truth_solution(self, x):\n",
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" return torch.sin(2*torch.pi*x) + 0.1*torch.sin(50*torch.pi*x)\n",
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"\n",
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"problem = Poisson()\n",
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"\n",
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"# let's discretise the domain\n",
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"problem.discretise_domain(128, 'grid', domains=['phys_cond'])\n",
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"problem.discretise_domain(1, 'grid', domains=['bound_cond0','bound_cond1'])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"A standard PINN approach would be to fit this model using a Feed Forward (fully connected) Neural Network. For a conventional fully-connected neural network is easy to\n",
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"approximate a function $u$, given sufficient data inside the computational domain. However solving high-frequency or multi-scale problems presents great challenges to PINNs especially when the number of data cannot capture the different scales.\n",
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"\n",
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"Below we run a simulation using the `PINN` solver and the self adaptive `SAPINN` solver, using a [`FeedForward`](https://mathlab.github.io/PINA/_modules/pina/model/feed_forward.html#FeedForward) model. We used a `MultiStepLR` scheduler to decrease the learning rate slowly during training (it takes around 2 minutes to run on CPU)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"GPU available: False, used: False\n",
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"TPU available: False, using: 0 TPU cores\n",
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"HPU available: False, using: 0 HPUs\n",
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"/var/data/python/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py: PossibleUserWarning: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
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]
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "203fd6f299be4233afca490cf8648ee8",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Training: | | 0/? [00:00<?, ?it/s]"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"`Trainer.fit` stopped: `max_epochs=5000` reached.\n",
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"GPU available: False, used: False\n",
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"TPU available: False, using: 0 TPU cores\n",
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"HPU available: False, using: 0 HPUs\n",
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"/var/data/python/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py: PossibleUserWarning: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
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]
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},
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "6827edaabfe847b68eddfd4d280a5af9",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"Training: | | 0/? [00:00<?, ?it/s]"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
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]
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}
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],
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"source": [
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"from pina.optim import TorchScheduler\n",
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"\n",
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"# training with PINN and visualize results\n",
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"model=FeedForward(input_dimensions=1, output_dimensions=1, layers=[100, 100, 100])\n",
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"pinn = PINN(problem=problem,\n",
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" model=model,\n",
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" scheduler=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, # Pass the class directly, not an instance\n",
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" milestones=[1000,2000,3000,4000],\n",
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" gamma=0.9))\n",
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"\n",
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"trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
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"trainer.train()\n",
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"\n",
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"# training with PINN and visualize results\n",
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"sapinn = SAPINN(problem=problem,\n",
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" model=model,\n",
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" scheduler_model=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, \n",
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" milestones=[1000,2000,3000,4000],\n",
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" gamma=0.9))\n",
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"trainer_sapinn = Trainer(sapinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.)\n",
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"trainer_sapinn.train()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
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"text/plain": [
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"<Figure size 800x800 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
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"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 800x800 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"#define the function to plot the solution obtained using matplotlib\n",
|
|
"def plot_solution(pinn_to_use, title):\n",
|
|
" pts = pinn_to_use.problem.spatial_domain.sample(256, 'grid', variables='x')\n",
|
|
" predicted_output = pinn_to_use.forward(pts).extract('u').as_subclass(torch.Tensor).cpu().detach()\n",
|
|
" true_output = pinn_to_use.problem.truth_solution(pts).cpu().detach()\n",
|
|
" pts = pts.cpu()\n",
|
|
" fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 8))\n",
|
|
" ax.plot(pts.extract(['x']), predicted_output, label='Neural Network solution')\n",
|
|
" ax.plot(pts.extract(['x']), true_output, label='True solution')\n",
|
|
" plt.title(title)\n",
|
|
" plt.legend()\n",
|
|
"\n",
|
|
"#plot the solution of the two PINNs\n",
|
|
"plot_solution(pinn, 'PINN solution')\n",
|
|
"plot_solution(sapinn, 'Self Adaptive PINN solution')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We can clearly see that the solution has not been learned by the two different solvers. Indeed the big problem is not in the optimization strategy (i.e. the solver), but in the model used to solve the problem. A simple `FeedForward` network can hardly handle multiscales if not enough collocation points are used!\n",
|
|
"\n",
|
|
"We can also compute the $l_2$ relative error for the `PINN` and `SAPINN` solutions:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Relative l2 error PINN 95.80%\n",
|
|
"Relative l2 error SAPINN 95.80%\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# l2 loss from PINA losses\n",
|
|
"l2_loss = LpLoss(p=2, relative=True)\n",
|
|
"\n",
|
|
"# sample new test points\n",
|
|
"pts = pts = problem.spatial_domain.sample(100, 'grid')\n",
|
|
"print(f'Relative l2 error PINN {l2_loss(pinn(pts), problem.truth_solution(pts)).item():.2%}')\n",
|
|
"print(f'Relative l2 error SAPINN {l2_loss(sapinn(pts), problem.truth_solution(pts)).item():.2%}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Which is indeed very high!"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Fourier Feature Embedding in PINA"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Fourier Feature Embedding is a way to transform the input features, to help the network in learning multiscale variations in the output. It was\n",
|
|
"first introduced in [*On the eigenvector bias of Fourier feature networks: From regression to solving\n",
|
|
"multi-scale PDEs with physics-informed neural networks*](\n",
|
|
"https://doi.org/10.1016/j.cma.2021.113938) showing great results for multiscale problems. The basic idea is to map the input $\\mathbf{x}$ into an embedding $\\tilde{\\mathbf{x}}$ where:\n",
|
|
"\n",
|
|
"$$ \\tilde{\\mathbf{x}} =\\left[\\cos\\left( \\mathbf{B} \\mathbf{x} \\right), \\sin\\left( \\mathbf{B} \\mathbf{x} \\right)\\right] $$\n",
|
|
"\n",
|
|
"and $\\mathbf{B}_{ij} \\sim \\mathcal{N}(0, \\sigma^2)$. This simple operation allow the network to learn on multiple scales! \n",
|
|
"\n",
|
|
"In PINA we already have implemented the feature as a `layer` called [`FourierFeatureEmbedding`](https://mathlab.github.io/PINA/_rst/layers/fourier_embedding.html). Below we will build the *Multi-scale Fourier Feature Architecture*. In this architecture multiple Fourier feature embeddings (initialized with different $\\sigma$)\n",
|
|
"are applied to input coordinates and then passed through the same fully-connected neural network, before the outputs are finally concatenated with a linear layer."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"class MultiscaleFourierNet(torch.nn.Module):\n",
|
|
" def __init__(self):\n",
|
|
" super().__init__()\n",
|
|
" self.embedding1 = FourierFeatureEmbedding(input_dimension=1, \n",
|
|
" output_dimension=100,\n",
|
|
" sigma=1)\n",
|
|
" self.embedding2 = FourierFeatureEmbedding(input_dimension=1, \n",
|
|
" output_dimension=100,\n",
|
|
" sigma=10)\n",
|
|
" self.layers = FeedForward(input_dimensions=100, output_dimensions=100, layers=[100])\n",
|
|
" self.final_layer = torch.nn.Linear(2*100, 1)\n",
|
|
"\n",
|
|
" def forward(self, x):\n",
|
|
" e1 = self.layers(self.embedding1(x))\n",
|
|
" e2 = self.layers(self.embedding2(x))\n",
|
|
" return self.final_layer(torch.cat([e1, e2], dim=-1))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We will train the `MultiscaleFourierNet` with the `PINN` solver (and feel free to try also with our PINN variants (`SAPINN`, `GPINN`, `CompetitivePINN`, ...)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"GPU available: False, used: False\n",
|
|
"TPU available: False, using: 0 TPU cores\n",
|
|
"HPU available: False, using: 0 HPUs\n",
|
|
"/var/data/python/lib/python3.12/site-packages/lightning/pytorch/trainer/configuration_validator.py: PossibleUserWarning: You defined a `validation_step` but have no `val_dataloader`. Skipping val loop.\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"application/vnd.jupyter.widget-view+json": {
|
|
"model_id": "2de22bd0d1374bfa810f88a4fefde20d",
|
|
"version_major": 2,
|
|
"version_minor": 0
|
|
},
|
|
"text/plain": [
|
|
"Training: | | 0/? [00:00<?, ?it/s]"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"name": "stderr",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"`Trainer.fit` stopped: `max_epochs=5000` reached.\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"multiscale_pinn = PINN(problem=problem,\n",
|
|
" model=MultiscaleFourierNet(),\n",
|
|
" scheduler=TorchScheduler(torch.optim.lr_scheduler.MultiStepLR, \n",
|
|
" milestones=[1000,2000,3000,4000],\n",
|
|
" gamma=0.9))\n",
|
|
"trainer = Trainer(multiscale_pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False, val_size=0., train_size=1., test_size=0.) # we train on CPU and avoid model summary at beginning of training (optional)\n",
|
|
"trainer.train()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Let us now plot the solution and compute the relative $l_2$ again!"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Relative l2 error PINN with MultiscaleFourierNet: 2.73%\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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aSmxs7LBbNoqIiIhI8JmmSVNTE1lZWUM25TjiktXS0lJycnJCHYaIiIiIDKGoqIhx48YNOuaIS1ZjY2MB64uPi4sLcTQiIiIi8lmNjY3k5OT05G2DOeKS1e63/uPi4pSsioiIiIxigWzZ1AErERERERm1lKyKiIiIyKilZFVERERERq0jbs+qiIjIcPl8Prxeb6jDEDmiREREDFmWKhBKVkVEZMwyTZPy8nLq6+tDHYrIEcdms5GXl0dERMQhraNkVURExqzuRDUtLY2oqCg1kxEZId1NmsrKyhg/fvwh/d1SsioiImOSz+frSVSTk5NDHY7IESc1NZXS0lI6OztxOp0HvY4OWImIyJjUvUc1KioqxJGIHJm63/73+XyHtI6SVRERGdP01r9IcIzU3y0lqyIiIiIyailZFRERkRG3bNkyrrnmmlCHEXS33HIL8+fPP2yv98gjj5CQkHDI66xevRrDMMKiEoaSVRERkTBy6aWXYhgGt99+e6/rzz77bFhtaXjkkUcwDIPTTjut1/X6+noMw2D16tUBr3XppZdy7rnnjmyAR5D+fnA49thjKSsrIz4+PjRBDYOSVRERkTDjdrv57W9/S11d3WF/7ZFsnuBwOHjttdd48803R2zNw8U0TTo7O0MdxkGLiIggIyMjLH7AUbIqIiISZpYvX05GRga33XbboOPWrFnDCSecQGRkJDk5OVx99dW0tLT03DcMg2effbbXnISEBB555BEACgoKMAyDxx9/nKVLl+J2u3nssceoqanha1/7GtnZ2URFRTFnzhz++c9/DvvriI6O5pvf/CY/+9nPBh1XVFTEBRdcQEJCAklJSZxzzjkUFBQA1tvwK1eu5LnnnsMwjJ6nsl/+8pe56qqreta45pprMAyDHTt2ANDR0UF0dDSvvfYaAB6Ph6uvvpq0tDTcbjfHH388H374Yc/87rfNX3rpJRYtWoTL5WLNmjV9Yt27dy8TJ07kqquuwjTNPvdN0+SWW25h/PjxuFwusrKyuPrqq3vu19XVcckll5CYmEhUVBSnn346u3fvHvB7099T5WuuuYZly5b13H/rrbe45557er4/BQUF/W4DeOqpp5g1axYul4vc3FzuvPPOXuvm5ubym9/8hm9+85vExsYyfvx4/vznPw8Y20hRsioiIoKVRLR4OkPy0V9SMxi73c5vfvMb/vCHP1BcXNzvmL1793LaaafxpS99iU8++YTHH3+cNWvW9ErgAvWzn/2MH/7wh2zfvp0VK1bQ3t7OokWLeOGFF9iyZQvf+c53uPjii/nggw+GvfYtt9zC5s2befLJJ/u97/V6WbFiBbGxsbzzzjusXbuWmJgYTjvtNDo6Orjuuuu44IILOO200ygrK6OsrIxjjz2WpUuX9tpK8NZbb5GSktJz7cMPP8Tr9XLssccCcP311/PUU0+xcuVKNmzYwOTJk1mxYgW1tbV9vhe3334727dvZ+7cub3uffLJJxx//PF8/etf57777uv3qeVTTz3F3XffzZ/+9Cd2797Ns88+y5w5c3ruX3rppaxfv57//Oc/vPvuu5imyRlnnHHQT7TvuecelixZwuWXX97z/cnJyekz7qOPPuKCCy7gq1/9Kps3b+aWW27hF7/4Rc8PLt3uvPNOFi9ezMaNG7nyyiu54oor2Llz50HFFig1BRAREQFaO3zE/PjxkLx2851fIdo1vH+SzzvvPObPn8/NN9/MX/7ylz73b7vtNi688MKevYpTpkzh3nvvZenSpTzwwAO43e6AX+uaa67hi1/8Yq9r1113Xc+vf/CDH/DKK6/wxBNPcPTRRw/r68jKyuKHP/whP//5z/vdd/r444/j9/v5v//7v57k7+GHHyYhIYHVq1fz+c9/nsjISDweDxkZGT3zli1bxg9/+EOqqqpwOBxs27aNX/ziF6xevZrvfe97rF69mqOOOoqoqChaWlp44IEHeOSRRzj99NMBeOihh1i1ahV/+ctf+MlPftKz7i9/+UtOPfXUPnGuW7eOs846i5///Of8+Mc/HvDr3b9/PxkZGSxfvhyn08n48eN7vme7d+/mP//5D2vXru1Joh977DFycnJ49tlnOf/884f1vQWIj48nIiKCqKioXt+fz7rrrrs45ZRT+MUvfgHA1KlT2bZtG3fccQeXXnppz7gzzjiDK6+8EoCf/vSn3H333bz55ptMmzZt2LEFSk9WRUREwtRvf/tbVq5cyfbt2/vc+/jjj3nkkUeIiYnp+VixYgV+v5/8/Pxhvc7ixYt7fe7z+fjVr37FnDlzSEpKIiYmhldeeYX9+/cf1Nfx05/+lKqqKv7617/2+3Xs2bOH2NjYnq8jKSmJ9vZ29u7dO+Cas2fPJikpibfeeot33nmHBQsWcNZZZ/HWW28B1pPW7rfK9+7di9fr5bjjjuuZ73Q6Ofroo/t8bz/7vQArAT311FO56aabBk1UAc4//3za2tqYOHEil19+Oc8880zP3tft27fjcDg45phjesYnJyczbdq0fn+PR9L27dt7ff0Axx13HLt37+5V1P/Ap8mGYZCRkUFlZWVQY9OTVRERESAqwk7znV8J2WsfjBNPPJEVK1Zwww039Hr6BdDc3Mx3v/vdXvshu40fPx6wko3PbkHo7+3m6OjoXp/fcccd3HPPPfz+979nzpw5REdHc80119DR0XFQX0dCQgI33HADt956K2eddVafr2PRokU89thjfealpqYOuKZhGJx44omsXr0al8vFsmXLmDt3Lh6Phy1btrBu3bpeT4cD9dnvRXccWVlZ/POf/+Sb3/wmcXFxA87Pyclh586dvPbaa6xatYorr7ySO+64oyeJHi6bzRbQ7+FI+WzbVMMw8Pv9QXs9ULIqIiICWP/oDvet+NHg9ttvZ/78+X3ehl24cCHbtm1j8uTJA85NTU2lrKys5/Pdu3fT2to65GuuXbuWc845h4suuggAv9/Prl27mDlz5kF+FdZWgnvvvZd77rmn1/WFCxfy+OOPk5aWNmASGBER0W9Lz6VLl/LQQw/hcrn49a9/jc1m48QTT+SOO+7A4/H0PEmcNGkSERERrF27lgkTJgBWwvfhhx8GVCs2MjKS559/njPOOIMVK1bw6quvEhsbO+j4s88+m7PPPpvvf//7TJ8+nc2bNzNjxgw6Ozt5//33e7YB1NTUsHPnzgG/t6mpqWzZsqXXtU2bNvVKKgf6/hxoxowZrF27tte1tWvXMnXqVOz2g/thaqRoG4CIiEgYmzNnDhdeeCH33ntvr+s//elPWbduHVdddRWbNm1i9+7dPPfcc70OWJ188sncd999bNy4kfXr1/O9732vz5Oz/kyZMoVVq1axbt06tm/fzne/+10qKioO6etwu93ceuutfb6OCy+8kJSUFM455xzeeecd8vPzWb16NVdffXXP4bLc3Fw++eQTdu7cSXV1dc+TxWXLlrFt2za2bt3K8ccf33PtscceY/HixT1PSaOjo7niiiv4yU9+wssvv8y2bdu4/PLLaW1t5Vvf+lZA8UdHR/PCCy/gcDg4/fTTaW5u7nfcI488wl/+8he2bNnCvn37+Pvf/05kZCQTJkxgypQpnHPOOVx++eWsWbOGjz/+mIsuuojs7GzOOeecftc7+eSTWb9+PY8++ii7d+/m5ptv7pO85ubm8v7771NQUEB1dXW/T0J//OMf8/rrr/OrX/2KXbt2sXLlSu67776Devo80pSsioiIhLlf/vKXfRKQuXPn8tZbb7Fr1y5OOOEEFixYwE033URWVlbPmDvvvJOcnBxOOOEEvv71r3PdddcRFRU15OvdeOONLFy4kBUrVrBs2TIyMjJGpCj/N77xDSZOnNjrWlRUFG+//Tbjx4/ni1/8IjNmzOBb3/oW7e3tPU9aL7/8cqZNm8bixYtJTU3teUI4Z84cEhISmD9/PjExMYCVrPp8vp79qt1uv/12vvSlL3HxxRezcOFC9uzZwyuvvEJiYmLA8cfExPDSSy9hmiZnnnlmrzJh3RISEnjooYc47rjjmDt3Lq+99hr//e9/SU5OBqzDY4sWLeKss85iyZIlmKbJiy++OOAPEStWrOAXv/gF119/PUcddRRNTU1ccsklvcZcd9112O12Zs6cSWpqar97ixcuXMgTTzzBv/71L2bPns1NN93EL3/5yz7bS0LBMIdbL2OUa2xsJD4+noaGhkH3jIiIyNjW3t5Ofn4+eXl5wzoZLyKBGezv2HDyNT1ZFREREZFRS8mqiIiIiIxaSlZFDjOvz891T33ATf/dFOpQRERERr3wq9EhEsb8fpPrV/6HK/J/QisR7Fz8DtMyk0IdloiIyKilJ6sih4lpmvziiTf4bv71THVUMt9RzEdrXgh1WCIiIqOaklWRw+SDvaWcs+VHTHd8WovQvkvJqoiIyGCUrIocJqUf/ZejnYU0GTE0HX8jAEs871FS17cOn4iIiFiUrIocJmbpBgD2pSwj9sSraMXFeHsd69auCnFkIiIio5eSVZHDJKVhGwAROYvAGUlRstX32bv1P6EMS0REZFRTsipyGNS1tDPDzAcga4aVpMbPPw+A+c1rqWv1hCw2EZHDbfXq1RiGQX19/SGtU1BQgGEYbNq0aUTiktFJyarIAPZVN3HiHf/hin+8e8hrbdu5lVRbMx2mnfjcBQBkLD4HL3ZmOsrZ9PH6Q34Nv9/kpn++wo/+/Dhen3/oCSISdgzDGPTjlltuCXWIQXPppZdy7rnn9rqWk5NDWVkZs2fPDk1QcliozqpIPzaX1HHz/Q/wjOM+tmzNpLjuHcYlRh30epW7rIS3OCKXiQ6XddGdwL6IKUzr2EFL4Uew5LhDivkPz77C1Tu+SbTRwTsbJnHyUYsPaT0RGX3Kysp6fv34449z0003sXPnzp5rMTExPb82TROfz4fDceT+U2+328nIyAh1GBJkerIq8hkFNc3cft8d/MN5J8m2FpZG7OHt99Yc2qKlGwFoSprV63Jz3CQA/JU7Dmn559bv4OSNPyLF1kKk4aXi/ScOaT0RGZ0yMjJ6PuLj4zEMo+fzHTt2EBsby0svvcSiRYtwuVysWbOm3yeS11xzDcuWLev53O/3c9ttt5GXl0dkZCTz5s3jySefHDSW+++/nylTpuB2u0lPT+fLX/5yzz2Px8PVV19NWloabreb448/ng8//HDAtW655Rbmz5/f69rvf/97cnNze+6vXLmS5557rucp8urVq/vdBvDWW29x9NFH43K5yMzM5Gc/+xmdnZ0995ctW8bVV1/N9ddfT1JSEhkZGUf0E+kjwZH745bIQXrrnVWsdD2Aw/DTaThwmJ20bnkOTv/8Qa+Z0rgDDHDl9H7aaUuZBtUvEN2096DXrm1ux3z2CuY4S/FjYMMkr/J1vD4/Trt+HhUJmGmCtzU0r+2MAsMYkaV+9rOf8b//+79MnDiRxMTEgObcdttt/P3vf+fBBx9kypQpvP3221x00UWkpqaydOnSPuPXr1/P1Vdfzd/+9jeOPfZYamtreeedd3ruX3/99Tz11FOsXLmSCRMm8Lvf/Y4VK1awZ88ekpKG37XvuuuuY/v27TQ2NvLwww8DkJSURGlpaa9xJSUlnHHGGVx66aU8+uij7Nixg8svvxy3290rIV25ciXXXnst77//Pu+++y6XXnopxx13HKeeeuqwY5PgU7Iq8hlR+a/iMPwUxC8mas45pK35BbMb1lLf2kFCVMSw16tpameWuQ8MyJ55bK978TmzYQdkdhRhmibGQfxj9cnGNZzr3EAHdozz/g/bM5fxOfse3v74E05cOH/Y64mMWd5WuC0rNK99QylERI/IUr/85S+HlXR5PB5+85vf8Nprr7FkyRIAJk6cyJo1a/jTn/7Ub7K6f/9+oqOjOeuss4iNjWXChAksWGDtx29paeGBBx7gkUce4fTTTwfgoYceYtWqVfzlL3/hJz/5ybC/ppiYGCIjI/F4PIO+7X///feTk5PDfffdh2EYTJ8+ndLSUn76059y0003YbNZP8DPnTuXm2++GYApU6Zw33338frrrytZHaX02EXkM5IatgPgmfh50o4+H4DPOfN546NNB7Xeth2fkGRrpQMHsePn9bqXNcn6fJJRQVXjwT3Radhj7YfdHTkX59wvstc9E4CS9/99UOuJSHhbvHh4+9X37NlDa2srp556KjExMT0fjz76KHv39v+uz6mnnsqECROYOHEiF198MY899hitrdb/w/bu3YvX6+W44z7dh+90Ojn66KPZvn37wX9hAdi+fTtLlizp9YP/cccdR3NzM8XFxT3X5s6d22teZmYmlZWVQY1NDp6erIocoK7Vwwz/PrBD5vQlEJtJUdRMclq3Ub3hWTjh6GGvWbvnPQCKnHlMsvd+MutOzaPddOI2vOTv3UrawuGvH1GxCQBPmpX4dk47Gz7eRk7ZKnz+X2G36WdSkYA4o6wnnKF67RESHd37Ca3NZsM0zV7XvF5vz6+bm5sBeOGFF8jOzu41zuVy9fsasbGxbNiwgdWrV/Pqq69y0003ccsttwy6L3UwQ8U40pxOZ6/PDcPA71cVldFK/4qJHGDzzu1k2RvwmQZxuYsAMKafAcCEqrdo9/qGvaa9ymoGUJ8wve9Nm51Sp/WPQ23hJ8Ne2zRNxrVaJ4HjJh4DwMQTvg7AEtsu3t96aAe3RMYUw7Deig/FxwjtV+1PampqryoCQK8DSTNnzsTlcrF//34mT57c6yMnJ2fAdR0OB8uXL+d3v/sdn3zyCQUFBbzxxhtMmjSJiIgI1q5d2zPW6/Xy4YcfMnPmzAFjLC8v75WwfrZ2akREBD7f4P8PnjFjBu+++26vddauXUtsbCzjxo0bdK6MXkpWRQ5Quet9AEqdOT37x7KPsbYCLHPsYEtB0bDXjGwqBMBIntLv/YboiQB0VAw/scwvq2KGrQSA8bOPB8CZnMte52TshknD1leGvaaIHFlOPvlk1q9fz6OPPsru3bu5+eab2bJlS8/92NhYrrvuOn70ox+xcuVK9u7dy4YNG/jDH/7AypUr+13z+eef595772XTpk0UFhby6KOP4vf7mTZtGtHR0VxxxRX85Cc/4eWXX2bbtm1cfvnltLa28q1vfavf9ZYtW0ZVVRW/+93v2Lt3L3/84x956aWXeo3Jzc3lk08+YefOnVRXV/f75PXKK6+kqKiIH/zgB+zYsYPnnnuOm2++mWuvvbZnv6qEH/3OiRzAX2KVmGpI/LTElJE6jUojGZfRScXu4RfvT+2wksnYrH6erAL+riTWXb9n2Gvv3bIOh+GnmgQiEj99AlIbP8Nau2rXsNcUkSPLihUr+MUvfsH111/PUUcdRVNTE5dcckmvMb/61a/4xS9+wW233caMGTM47bTTeOGFF8jLy+t3zYSEBJ5++mlOPvlkZsyYwYMPPsg///lPZs2y/t95++2386UvfYmLL76YhQsXsmfPHl555ZUBqxPMmDGD+++/nz/+8Y/MmzePDz74gOuuu67XmMsvv5xp06axePFiUlNTez257Zadnc2LL77IBx98wLx58/je977Ht771LW688caD+dbJKGGYn90kEuYaGxuJj4+noaGBuLi4UIcjYeb1W07kFONjdi38OVPPvr7n+rb/Xc7Mlg95MutHfPnyWwJer7m9A/9tOcTZ2mm47B3ix8/tM2bnmyuZ9vbVbDAnsvCWjcOK99k//w/nlv2RT2I+x9wff/oUdf3jv2TxjjtZ7fgcy36up6si/Wlvbyc/P5+8vDzcbneowxE54gz2d2w4+ZqerIp0qWn2MNOfD0Dm9N4lprzJ0wBw1g3vSWVhUSFxtnb8pkF81tR+x2TkdVUEMEtpbu8Y1vpR1dY+186MBb2ux42z9oWldRT3mSMiIhJOlKyKdNmyazuZ9kZ8GMTmLux1LzLb6jud0rJvWGtWFlqHqypsyeDo/8lN/LgZ+EyDeFs7e/MDbw7g8/vJbbeS5+QpS3rdy8yznuBONMppaGkbVswiIiKjiZJVkS6VO616pSXO8X3KyGRMsp5cTqKExrbAy6m0lFsn9Wtcg5xCdbgotVtFrisLPg547Z2FRUy1VwAw7jPNBmIzJuExHbiNTvL3qSKAiIiELyWrIl3sFdZb6g0Js/rci8uxnqxm2BrZVZAf+KK11pPY9tgJgw+LzLXGlQVeMLt4m3W4oNRIwx6T2vumzU6pPROAmv1bPjtVREQkbAQ1WX377bc5++yzycrKwjAMnn322SHnrF69moULF+JyuZg8eTKPPPJIMEMU6RHXUgCAP3VG35sRMZTb0gCo2Bv4IajuslW25EmDjuuIt07c2usDT4Q7Sq0ktCJmWr/366KsBLm9TE9WRQZzhJ0zFhk1RurvVlCT1ZaWFubNm8cf//jHgMbn5+dz5plnctJJJ7Fp0yauueYavv3tb/PKKzrNLMGX0mF1ronO6L8eak1XPdS20q0Br/lp2ar+E8puztTJ1riWwOu4OrtKXXkT+4+3M9Fa01Ef+D5YkbGku4tRd5tQERlZHR3WoWG73X5I6wS13erpp5/O6aefHvD4Bx98kLy8PO68807Aqru2Zs0a7r77blasWBGsMEVo8XSSQxUAaTn9J5adydOg6T0iancGtGZzewcTsPaUpk3ov2tLt/jsafAxpHcG3uoxqdV6ahuZ2c+TYMCVMQ2KIKFrnIj0ZrfbSUhI6OkJHxUV1aunvIgcPL/fT1VVFVFRUTgch5ZuBjVZHa53332X5cuX97q2YsUKrrnmmgHneDwePB5Pz+eNjY3BCk+OYIWlJcy0tQAQl9n/k8qo7NlQAKltgb1VX1hUyKwhylZ1y8i19slOMKqpbWolKXbwPuFen58cfynYIDVvTr9jUibMhg8hx1eCz+/Hru4tIn1kZHQdbuxKWEVk5NhsNsaPH3/IPwSOqmS1vLyc9PT0XtfS09NpbGykra2NyMjIPnNuu+02br311sMVohyhKot2MROoJY4kV2y/YzImLYC1MIVi6ls8JES7Bl9z/3ZmYZWtyhygbFW3yOTxeEwHLqOT7YW7SZo9b9DxBSXFTLFZP5ilTZjdf7xdSWyWrYH88nLysrIGXVNkLDIMg8zMTNLS0vpt3ykiBy8iImJE2tyOqmT1YNxwww1ce+21PZ83NjaSk5MzyAyRvprLdwNQHZFJ0gBjYsfNwm8apNha+LBgH0fN6v/t924tZdZ2gVpXNplDBWCzU25PZ4K/hJqi7TBEslq27xOmAOUkkeHuP7m2RyVSTTwpNFC29xMlqyKDsNvth7yvTkSCY1S9L5iRkUFFRUWvaxUVFcTFxfX7VBXA5XIRFxfX60NkuDprrLf2W6MGqYfqjKKsux7qvgAqAtRaB5vaYnMDiqHebb12W+XuIcc2lVjNBqrd4wcdVxFh/eDW0DVeREQk3IyqZHXJkiW8/vrrva6tWrWKJUuWDDBDZGQ4m/YD4E8Yoh5qtFViylM2dPL3admqiQHF0BGfa42vC2BPbJWV0LbFDb52S6wVr1m9J6AYRERERpugJqvNzc1s2rSJTZs2AVZpqk2bNrF/v5UY3HDDDVxyySU947/3ve+xb98+rr/+enbs2MH999/PE088wY9+9KNghilhbnNJHWfc/yYPvLProNeIb7NKTLlTB6+H2plkHb6KqBs6+UvrsMpQxY8bfLtAN0eK9drRzfuHHBvTbDUbsKcNXhLLTLKS2cjmwEti9eeZ9zfz2388g9fnP6R1REREhiuoyer69etZsGABCxZYrSqvvfZaFixYwE033QRAWVlZT+IKkJeXxwsvvMCqVauYN28ed955J//3f/+nslXSL9M0+eNbO7nirgf4acl1FL/4Ozo6fcNex+83yfCVA5CQ3X8lgG5RWVbimdRWMOi42uY2JhrWlpaMAU7rf1ZcV8WAVO/g5atM0yTTWwxAQk7fblsHikqzktUET1lAMfTng10FzHzhi/x41zdZtVo1j0VE5PAK6gGrZcuWDdq9oL/uVMuWLWPjxsA7BMnY9fj6fEpf+BWrY1/AYfhZ6C/i7R2/YPnswd/K/6yy+mYm2GoASM2ZPujYtNx58C7kmSW0dXQSGdH/X6H8/F0sMjrwmnai0wdPgLulT7ASz1yjkobWduKj+q8gUNXQTJ5hldnJmjT4QazETKsxQIa/AtM0h10+pLHNy/5/XMWX7dbrdXz0GJwSeO1kERGRQzWq9qyKDEfjB3/j19H/xWH48WEj1uZh5/v/HfY6Jfv34DT8dJh2nAmDHLACEsZbCWWmrZE9RcUDjqveb3W5Kreng90ZUBwx6RPxmnaiDC/79+8bcFzhvi04DT8tpgt30uCVL7obHGTaGqmoqwsojgM99sj/8mXjnZ7Pj255m5pGdfsREZHDR8mqhK2smvcAyJ98MSUTvwxAXOGqYfciriux9rpW2tPANnjpGsMdT6VhFbcq3/fJgOPay3ZYa0cNflq/F5uDclsqANX7tw84rLZwCwClznEwxJPSiNgUmkzrCW1Z4fD29JbX1vGV8nsBKJ71HRqJJsvWwLrVzw1rHRERkUOhZFXCUlO7lyle65BT4twzyTjqSwCczEY+Kqwe1lrtVVaJqXp3dkDjq93WNoPm0q0DjnHUW2t6EwY/sPVZdV3lq1orBk4sOyqs+q2NXZUJBmUYVhIONJQNryLArk3vkGRrpYY4xn3xNgrSTrZubHlyWOuIiIgcCiWrEpY27SlkmsPaR5kw6WgiJp9EmxFJtr2B9e+/PsTsz6gvAKAjLrCnoJ6uBNReM3BCmdBila1ypQ9+Wr/P2nFd+21rB94G4KqzXtdIHbyFa7cGt9UMoL0qsDax3Rr3Wk+ui6Jmgs1B+rEXAXCcZx3F1fXDWktERORgKVmVsFS6410AKuxpEJUMDheV6ccBYNv54rDWimqxyjrZkwJ4Ugk4M6yKAPHN/Sd/nT4/2T6rFFbyAK1QB1w71ToQFdXY/9qmaZLVbj21jc+dH9CaHTHW01qjoXBYsURVbQLAm7kQgPQ5p1JjJJBka2XT208Nay0REZGDpWRVwlJn8XoAahM+TQZTFp4HwBLvh1Q2tQe8VnKHVdYpJmNyQOOTxluvOa6zGJ+/b93Rwspqxtusw0zpuYGVreqWkmeVeZvgzaezn5qmpbUNTDWseLOnHRPQmrZE62ltZPPAB8I+y+f3k+exthskTz22ayE7exOtHwgcpR8GvJaIiMihULIqYSmh3uog5Ri3sOda9Owz8GMwx1HKtj17A1qnxdNJDlUApOYE9pZ9+kSrXFSurZrCipo+90v2bcFmmDQShS0mNaA1u2VNPRqAifZq9pb0rbe6b8cGIgwfDUThTg6sRFdUurVtIaGjPOA4duXnk2ez9v5OmH38pzdSre/RQE9+RURERpqSVQk7Nc0eZvitZDRz2rGf3ohMosKeAUDVvvUBrVVYVkaqrRmAuMzA6qHaYzNoJBq7YVK0t29FgIZiK5Euj8gZ8rT+Z9likqkwkgEo2tH36WV9/gYASl0TA147Ocv6urLMyn6fBPenaMtbABTasrFHJfZcj82eCUBaR+BPaUVERA6FklUJOx/v3sNEu/VEMyZvUa979XHWk7/O0o8DWquyyHqru45YcMUFFoBhWIko0FDUtyKAv8o6ANUSkxvYep+NKcrajtBctKnvS1daZataEgdvXnCgtBwrWU2xtVBWVRXQnI79VqJcHd97z23mRGtbQy7ltLR3BByDiIjIwVKyKmGnYqd1Sr3UkQ3uhF73jAwruYqt3xnQWk3luwGodmYOK4bWeCuh7Cjf1udeZPdb5CmBPan9LG+q9fTSVd03EU5qsuJ1jRu8c9WB7FGJ1JvRAFTsD6zWalLdZmvu+KN6XU/InEKHacdtdFKwb0fAMYiIiBwsJasSdswy663whsRZfe4lTbSetE7oyKej0zfkWr5qK7FsiR68c9VnRY+fD0By/eZeTQj8fpOU9v0AxGbNGNaa3WLGd52+b+2977bN42WyvwCAzMmLh7VmpSMdgIau5Hwwze0eZvqsmqzZM0/ofdNmp6R7q0Xh5mHFICIicjCUrErYSWu2ng6aGfP73EvtSuKm28vYUTL0W97OJquck5kQ2GGlbuPnfx6AxexmT8WnbUw/KSxnus0qWzVh+vASym7jpluHrKYbRVQ2tPRc37lvD2m2ZnymQXLe/GGt2eS2nhx3VBcMOXb71o9IsLXRbjpJnbSoz/26SOt71V4e2NNrERGRQ6FkVcJOmrer1FR23yeXRnwOTUTjNPwU7to45FpxbVZi6UodXqcpV/Ycmogm1uZh68Z3eq7v+Og1ogwvtbZEnGnDawjQLSp9Cq1EEGV42b1jU8/18t3WPtISexZGRNSw1uyItfbYGvX7hxxbu9c6nFYQMRHszr5rJUwEwF47vI5YIiIiB0PJqoSVulYPOYZVUil1XD8dnAyD8u4DSvsHT1b9fpMMXwUACVnD3F9q2CiJt/aNtu1569M1960GoCLlmGFXAuhhs1McYTUoqN33Uc9lT7F1aKwmNrDOVQdyJOUCENU69Cl+X4W1D7cxrv/X6U7C41qH12RARETkYChZlbCyv7SMRFsbAJGp/Xec6ki2nrg6q/oefjpQeX0zE2xWVYHUnMBP13ez5Vr1R1OqrYSy3etjcpP167gZy4e93oGaE6x4zIpP94W6aru+nvS+e3WHEttVliulo2/t1j5jG619rbb0mf3eT8qxXj+rs6TXfl0REZFgULIqYaWq2NonWUs8RET3Oyaq6/BTWuvuQZOp4qK9RBg+vKYdZ2LOsGMZN99KSBezk8LqBj7cuZdF9gIAsuafNuz1DuTMmgtYVQ18fj8b8ktZ4LUS1/Ezjxv2epl5VpWEPKOCpjbPgONM0ySnowCA5K5uWp+VNdGKLcdWR0VN36YIIiIiI0nJqoSVlgrrhHxNRMaAYzKnWOWWZhlFlNW3DjiutsQ6qFVhTwObfdixRI1fRAtuEm1tfLJxHYUbXsVumJQ6xmEkDD/5PVDuLCshXWzu4Ml3NvDhi/9Huq2JWnsyybNPHfZ68ZmTAyo5VVxRRW5X56rsqX0PVwG44lOp6yqFVbxXFQFERCS4lKxKWPHVWKWm2qKyBxzjzp5NJzaSbS3s3DNwYtZeZSW+9e6B1xqUzUFxrFUkf+eHL2PmrwagMfPYQSYFJnbSMZRFTyfW5qHt9V9zVPm/AWiZd1m/h54CibW0q+RU9f6+9Vu77d9lHa6qIoGIuLQBx5U5rVJf9cWDb7UQERE5VEpWJaw4m60DQv6E8QMPcrgpc1pPNqsPOKD0WUadlfh2n5Q/GI6ufasXtj/N6f51AKTMXXHQ630anI3kc38HwCW2N1no2I8HJzmnXHnQS9Z2lZxqKxs4gW/cb7WPLXP3vx+4W1NXd67OysCaDIiIiBwsJasSVmLbrANCrpTBk6nuk+z+soHfpo5ssRJfe/Lgaw1m4vFfodMRRaa9kRRbC35spMw65aDXO1DE5KUUp56IzbD23RbnnAVRyQe9njfe+joddXsHHlS1HYC2hMErDphJVsUFd3e3LhERkSBRsiphwzRN0rpKTcVnDl5qyt51QCmuceDC9ckdXfVa0ycfdExG2gwcP94BF/wNjroc2zn3QWTiQa/3WVlf+h3+rr+m40/70SGtFZE+dMmpxCardqora86ga7lSrVqrcZ7yQ4pJRERkKI5QByASqIrGtp5SUynjBk9WUyYtgs2Q11lAu9eH29n7AFV9awc5VAKQdhBlq3pxx8OML1gfI8yWPgO+/gR4W3FmzTuktRLHz4KNn5acMj5TB9br85Pr2w82SJ3YfyWAbnHpVrKa5hu6S5iIiMih0JNVCRvFxYVEGx34TYOIpMHboyZPtE6yT7FVsq2orM/9LXut1qUAsVnDL7J/WE05FWaec8jLZOVZT0vH22opq6ntcz9/fwEZtkb8pkHmpPmDrpWWbT2NzjTqaGptO+TYREREBqJkVcJGTVepqWpbEjhcg441YjOoM+KxGybFu/oesirf+QEApfZMcMWOfLCjUERcGvUMXHKqZLf1fSq1pWFzxwy6VmzqODpMO3bDpKxE+1ZFRCR4lKxK2GitspKiOldmQOMroq2tAq37N/W55y21rtXHH+IWgHBiGJQ5uktObe9zu3m/1c61KmpSAGvZqDCsw151pXtGLkYREZHPULIqYcNfWwBAe3RgdVE7U6y2oK6avnVF4+utZM2WNX9EYgsXzTHW9on+Sk5FVmwAwMwIbG9sndOqw9pcVTAywYmIiPRDyaqEDVdzkfWLhMH3q3aLnTAfgMy2vb3arrZ2dDLJuw+A1MlHjWiMo52Z3F1yal+v6x6vj2kdVoH/tFnLAlqrNdJ6wu2rHbi6gIiIyKFSsiphI8FjHZRyd5VNGkp329WZRjFFtc0917cUFDPNYVUCSJo0tpLVqExr20NSe1Gv65t3bCHHVofXtJM98/iA1vLFWVsK7E0lIxukiIjIAZSsSljw+f2k+60EMyEzsLqoERnT6cBBnK2d3bu39Fwv6TpcVW1LxogZuKXokSijqyJArr+UmqZPT/GXbX4DgIKIiRiuwQ9XdXMmWl3EottVa1VERIJHyaqEhfKGVsbb6gBIzh68xmoPu5PSCGvLQNH2D3outxdtBKAqZtrIBhkGUibMoYlIEmxtfPDuqp7r9hLr+9OYuijgtaLTrI5YSd6KkQ1SRETkAEpWJSyUlRTiMjrxmQaOhMAOWAGQOR8AM381Pr8fgOha68CVmTF3pMMc/exOChKOAaBt6/MA+P0m45s/ASB26gkBL5WcZVUNyKQGn883woGKiIhYlKxKWKgrs/rZV9uSwO4MeF72kq8CcLbxPm9sK8Lr8zPBY6011vardoucdRYAU+rW0tHpY3dRMTMNa99p7ryTA14nNdvaOxxreCiv1NNVEREJDiWrEhZaqwsAqI9IH9Y855STqXckkWJrYfM7T/Lchr3MtJcCkD716JEOMyxM/NwX8ZkGc+zFfPjJJvI/fhObYVJiyyAiISvgdeyuGKpNq6FCVcnuYIUrIiJjnJJVCQv++v0AtEcF1hCgh81B69TzAMgreZ63nroHp+GnxR6HEZ8z0mGGBVtMMnsjZwKwd92TVG1+FYCKhPnDXqvakQpAY4W6WImISHAoWZXDosXTyUNr9/CFB1fz/ObiYc93NFlPQ/1xw08wM4+/FIAzHJ/wv+5/AuA+8RowjGGvdaTomLQCgFMqH+NCr7V3NX3eimGv0+TKAMBTU3BQcbz98VYe+Mu9NLV1HNR8ERE58ilZlaBbtb2McTc+ydNP/ZUzC+7gsWceH/Yase1WjdWIpPHDnmtkzqUichIuoxOX0Yln0unYT/jRsNc5kuQt+TIA2fYGbIZJzfSvkX38JcNep6Orm5jRMPwfQMpqG0h+6nyuKP4Fbzx937Dni4jI2KBkVYLutdUv8777F7wU/0e+G7mGn3n/wq6KxmGtkdxp1ViNTQ+sIcBnJR57GQAdCZNxnf9nMMb2H/3orJlUxUzDj42mZf+P5AseAJtj2OvYEqzGAK6W0mHPXf3ojcyyWwe7Mvf8q1eXMRERkW7D/9dJZJiOKX+cqY5KOp2xGN4W5jlKeGj9h0w985SA5je0dTDOqAE+LZc0XBFLvgcxyURMXg6uuINa44hiGKR+fxW01xMbYPva/rhTcmE3xHcMrxrAm++u5bz6f0DXToyj2ckHGz/g6IXHHHQsIiJyZBrbj5ck6Moa2pjj3wOA97y/UB4/D4DWLc8HvEZxeTmJNqvbUnRa7sEFYnfC/K/DGOtYNSh3PBxCogqQkGk96U7zVQb8ZNQ0Teyv/hS30cmumMVsjrJKiFW8/ZdDikVERI5MSlYlqDbu3ssURxUAkblHEznbqvE5q3EdNc2egNaoLt0HQCPReio6ymTkTLf+a2uktr4+oDlFpSWcyGYAsr72RyIWfwOAxXUv09jSNthUEREZg5SsSlBV7FgLQLlzHEQmkrTAKiO11LmL1z7eGdAazZVWWaRqh56KjjaR8ak0mW4ASvcH9vu57+O3ANhvZBCTNZ2pJ1xALbFk2hp4d9U/gxariIiEJyWrElS20o8AaEqeY11InkSlazxOw0/Zxv8GtEZHbSEALe6MoMQoh8AwKLdbjRrqSwNrDNCW/y4A5XHWnwnD4WJ32ucBcOS/HoQgRUQknClZlaDx+00ymrYBEJn3uZ7rnVNOAyCrfDV+/9D7HG2NVlkkb2x2EKKUQ9XgtrpetVftC2h8Yu0mAGw5n3YQM7LmAxDfXDCSoYmIyBFAyaoEzY7yBhbZrAQmY/pxPdfTFllbAU6xb2VfddOQ60S2WmWR7Aljs+PUaOeJ6fp9qS8ccmybp4MZndYT2KzZJ/ZcTxo/y7rWWaISViIi0ouSVQma7Ts2kWJroQMHjqy5PdcdOYvxYifZ1sLOXZuHXCehw6qxGpWWF7RY5eDZknIBiGwZujHAts0fEG9rp8V0kTl5Uc/17IlWlYgsWx3VtbVBiVNERMKTklUJmvo97wFQHjkZHK5Pb9gjKHVZiWfd3g8HXcPr85NpVgOQmHFwNVYluKLTrN+X5I6yIcdW7XgbgH2uaRh2Z8/1yPgUqk2r0kPx3k+CEKWIiIQrJasSNNFVmwDwZCzsc68teTYAtvLBE5P9VfVk2eoBSMpUsjoapeRMBSDLX4nP5xt0rLN0PQDNaQv63CtzWt2w6ou2jHCEIiISzpSsStDkeay9iRE5i/rci5xgXUtv3jHoHsX9hbuwGyYdOLDFpQcnUDkk6V3JarytnfLKgZ+umqZJTot14C5u8rF97jfF5ALQWblr5IMUEZGwpWRVgqLZ4yUHqxlA0oS5fe5nTrOqA8yxFbK/tnnAder3bwWg3JENhv64jkZ2VwxVZjwAFYPUWi0qLWaqzUpmJ847qe+A5MkAuBoCqyogIiJjg/71l6DYX1lDlr0BgNh+9ppGZM2hExtptma27d4x4DreKiv5aYzR4arRrNJp1cBtLNsz4JjCLVaDiCIjnciEvk/Jo7NmAJDiKQpChCIiEq6UrEpQVBZbSUsrLohM6jvAGUl5hNWXvmb3BwOu4+56ymYmTxn5IGXENEdatVY7qgd+KtpSaDWIKI+e3u/99FyrSUCuWYq3s3OEIxQRkXClZFWCorHcSlarHBlgGP2OaU6aCYBR/vGA66S0W7U7u5+6yejUGTceAHvj/gHHRNVYB6d86X23hQCkj5+G17QRZXjZXxBYNywRETnyKVmVoPDWFADQHJk54Bh3jlUlIKVpZ7+HrOpaPUykHID0vDkjH6SMGGdyLgAxrSX93jdNk5x2KwFNmHR0v2MMRwTFNms7QUWByleJiIhFyaoEhdFg7Tv0xg7cdSpj+hIAZpNPSX1bn/t79heTYWsE9GR1tIvNsLZppHRW9Hu/uKyUPJt14C53Vt9KAN2q3dYT2pbSgfcxi4jI2KJkVYIiuqtFqiNpwoBj3OPm4ccg297Axh19k5PKAqu7VZWRBK7Y4AQqIyItZxoA46imvcPb537htncBKCYNd1zKgOt44icCYKsd+KCWiIiMLUpWJSiSvdbb9zHpgxTyj4jpOWRVueOdPrdbS62anLWR40c+QBlRSZl5eEwHLqOT3Tv7ttBtLrCaAZRHTx10HWeadT+uOX/kgxQRkbCkZFVGXFO7l3GG1SI1OXvwU/wt6VZzgIjSvm1Xu5+ueRImj3CEMtIMu5N8p1VerHT72j73I6utw1XetP4PV3WLSbd+r5M7K0c4QhERCVdKVmXE7a+s6dlr2l+N1QMlTD0egEltW2nt6F2uKL6lAABn+rSRD1JGXEOSdQjOLPmo13XTNMlus7pSJUw8atA1ulvqZlI7ZOtWEREZG5SsyoirLLYSk2YiwZ046NiUGUsBWOTYz/p9n7bq9Pr8jPNZJ8uTx88KUqQyklwTrFP+qY1be10vq6xkss06eJU7e+DDVQBp2dbT2UjDS2VlaRCiFBGRcKNkVUZcY7lVGL7akT5gjdVuRtJEGmzxuIxOCras6bmeX1HHxK7T4ykTVLYqHIyfdQIAM8186ptaeq7v27oOgDKSiUzIGHQNe0QklWYcAFXFOmQlIiJKViUIvDXW4ZiWQWqs9jAMqhLnW/MK3+u5vHvXZiIMH224sCWMC0aYMsKSxs+kwYwi0vCyc8unv5f1W18DoCxmZkDr1NhTAWisKhz5IEVEJOwoWZURZ2/sqrEaF9gpfleeVW81vf5j/H6rOcC2jW8DXZUADP0xDQuGjcJIa39xzS6rVJXP72dS9ZsARMw8K6BlmlzpAHiqlayKiIiSVQmC6K4uRs5BaqweKHPWMgCOsu1hZ0UDFY1tzKh+FQD39M8HJUYJjrbUeQA4KzYC8NHGD5hhK8Fr2pl2wgUBrdER3fVEvrE4KDGKiEh4UbIqIy7Zax2miUmfGNB4x7gFdOAg3dbEypdf55l1GzjNaR3SST720mCFKUEQN+lzAIxr2Y5pmpR/8G8AdkbNwxmTFNgi8da2D1dL2RADRURkLFCyKiOq2XNgjdXBC8D3cLh7nsil7/g7hW8/isPwUxE7C1ICXENGhdw51iGraUYpu4tKySl/AwD/tLMDXsOVbD2Rj/X037pVRETGFiWrMqJKqmpJtzUBEJOeF/C8+OU/BeBHUW9wteNFa/7RF418gBJUkUnjKDeSsRkme/78FRbY9uE3Daad+NWA14hLywUg2V8dpChFRCScKFmVEVVdZlUCaMU1ZI3VXqauwLfo2wBk2hvx4iB64VeCEaIEmXn8j/FhcIbTaru6yz0TV2JWwPNTs60uVpnU0e7xBCVGEREJH0pWZUQ1VhYAUGNLHrLG6mfZV/w/OpKs0+QdE5dDVPJIhyeHQebJ34dvv0l5rNXMIebY7wxrfmJqNl7Tht0wKS8pCEKEIiISThyhDkCOLJ5aq2xVkytt+JOdkURc+E9Yey/Rx/5ghCOTw8mevYCMH62B1lrGRacMa65hd1BhJDOOKmpK95A7Ue12RUTGMiWrMqL8DVbZqo6owTsVDShpEpx9zwhGJCFj2GCYiWq3Wkcq4zqraFZjABGRMU/bAGRERXSXG4rLDm0gEtZa3FZjgM66/SGOREREQk3JqoyoGE8lAM7EnBBHIuGsM8Y6kGU0loY4EhERCTUlqzKikjqrAIhJC6zVqkh/bAnWDzuRbUpWRUTGOiWrMmKaPV4yjToAkjMmhTgaCWdRKVZjgPiOqhBHIiIioaZkVUZMSVUtqbZmQE9W5dAkZFgNJdLUGEBEZMxTsiojprshQBsRw2sIIPIZaeOmAJBia6ahsT60wYiISEgpWZUR09RVZqjaljLshgAiB4qOS6bZdAFQXrw3xNGIiEgoKVmVEdNeYzUEaD6YhgAiBzIMKgyrRmt9+b4QByMiIqGkZFVGjNlYDIDnYBsCiBygISIVgFY1BhARGdOUrMqIcTaXA2CqIYCMgLbITAD89cUhjkREREJJyaqMmOiuhgARieNCHIkcCfyx1g899uaSEEciIiKhpGRVRkxPQ4DUCSGORI4EjiSrMUBUe0WIIxERkVBSsip9mKZJp88/rDktnk4yjVoAkjLzghGWjDExqbkAJHkrQxuIiIiElJJV6fHo+/tI+emTOH/4T9w/+hcPrd0T8NyS6lrSuhoCxHYlGSKHovuHngxq8Q/zh6eXn36I9Tcv4KP1a4MRmoiIHEZKVqXHa2+8yP22P/Jy7O95LfYu3nvruYDnlpdY5YXacUKkGgLIoUvLngxAjOGhqqY84HlVNdUs+vhWFtv20f7KL4IVnoiIHCZKVgWAZo+XbzQ/ygXuDSyP2MmyiN18reVxiutaA5pfX2YVbq+2p6ohgIwIpzuaGjMGgMphNAb48F+3kGprAuC4zo/YtEFPV0VEwpmSVQHgg30VHOMssD5ZeoP1H+duVn28M6D5nirryWpTpMpWycipslu1Vpsq8gMan1+4lxOrngCgFKupQO1rdwYnOBEROSyUrAoAe7e+S4zhocWIhqXXU+Mej9PwU7HpxYDm2xqswu3euPHBDFPGmKaIdADaa/cHNH73UzcRY3jY4ZiC59z/A+D41tXs3RvYD10iIjL6KFkVALz57wJQnTgPDBv+KSsAGFf1Nq0dnUPOj261Crc7kicGL0gZc9qjrcYAZn3RkGM7OztZ3PCGNf6kG8mbdxJbnLOIMHzsfenuoMYpIiLBo2RV8Pn9ZDRsAiAi7zgAUhacA8AKxxbe3Fk66HzTNEnxWgdgYjOmBC9QGXu6uqFFtJQNOXTXto9IsrXSYkYw7agzAGiZ+VUAUus2BS1EEREJLiWrwuaSOo6xWWWq0mYtBcAY/zlabTGk2prZ+uFrg86va+1ggmE1BEjJmRbcYGVMcSVb20piPEM3BijfuhqAPRFTsTkjAEjKmw/AuM5iTNMMSowiIhJcSlaFj7d+Qra9gU7s2Mctsi7andRnnwhAzP43Bp1fUFpGaleN1cg0bQOQkRObZtVaTfFVDTnWVvwBAE2pC3uu5UyeB0CqrYmqysHfIRARkdFJyarQvOcdACqip4Izqud6/NwvALCkcyNVTe0Dzq8q3gVAnRELrrggRipjTUqW9cNPBnV0dHQMOnZ8y2YAYqcc33PNHR1PqZkEQPGej4MUpYiIBJOSVSGheiMAneM+1+t69FRrS8BcRwkb9g18wKWl3NpCUBuRFaQIZaxKTp9Ap2nDafgpKy0YcFxJSSETDWurwOQFy3vdK3dZWwkai7cELU4REQkeJatjnNfnZ7bPKusTd8ATKetCFrX2ZOyGScn2dwdcw1dr1cBsjR4XtDhlbLI5nJQbyQBU7t8x4Lh9G18HYK8xjuj45F73WuImAWBWqXyViEg4UrI6xhXVNjPVXglAQt6iPvfrkuYC4C/6cMA1IpqsGphmQu7IByhjXmX3k9GizQOO8eSvA6A8YV6fe0aqdegvunFfEKITEZFgU7I6xpWWFBBpePFhYMT3fTLqGn80AKmNWwc8TR3fbh1ciUybFLxAZcxqTegqh1Y18JPV7tJUjglL+txLyJkFQHrH0LVaRURk9FGyOsbVlVr7TattKWB39rmfPsOqu7rA2MeeqqY+970+Pxl+a69gYtbUIEYqY5UzfQYA8U17+73f1NzEdL+1FWXCvFP63M+eNB+AHKppamoMTpAiIhI0SlbHuPZq663RBldmv/edOYvwYTDeXscnO/s+2SqqbSLPVgNAUraSVRl5ybnWW/s5nUX9Pt3fsfFtXEYnVWY8GRNm9LmfmJpNrRmNzTDZv1sVAUREwo2S1THOrLP2m3piBjgcFRFDhSsXgNpd6/rcLinah8voxIsdW4IOWMnIy5lq1U1NtzVSVlbS5379rrcBKIiaBYbRdwHDoMSRA0Dt/k+CF6iIiASFktUxzt1i7eOzJU4YcExr2gIAnOUb+9yrKbZOWFfZ08BmD0KEMta5ouMpIQWA4t0f9bkfXWFd68g6asA1GmNyAfBWDLzvVURERiclq2NcgqccGPxwVPykYwCY0Ladto7OXvcq928HVLZKgqvCZf0w9dmKAD6fj6ke689g6sylA873JVtbVFz1/e97FRGR0UvJ6hjW7vWRZVptLJOyJw84LmWadchqkb2Qt3aX9Vw3TZPoKutpqzNrThAjlbGuuyKAUd27Vuqu7RtIsTXTZjqZNOe4AefHZFsVAVLbC4MXpIiIBIWS1TFsf3Uj4221AMRnDJysGmkzabHFEGdrZ+uHb/Rc31fdzGK/9VQrffbygaaLHDJnxkygb0WAsi2rAdjjnILd6R5wflK2VWs1w6wesASbiIiMTkpWx7Cykn1EGD682DHiBmmVarNTn3kCAO6C13r+sf9g61amOSrxY+CeNPBTLZFDlZI3H4Dxnft7JZtG8fsANKQsGHR+WnYeAHFGOw31tcEJUkREgkLJ6hhWX7obgCp76pCHo5LnnwXAks6N7Kq06q3WbnsTgPLISeBOCF6gMuaNmzwfgDRbE2VlxT3Xc5qtPawxkwf/YSkqJoF6MwqAqlLtWxURCSdKVscwT00BAE3uQZ6qdnHPWIEfg4XOIt7asAmAuIoPAPCOOzZYIYoAn60IsAGA0tIiJhvWAcFJC4fehlJlSwagvkL7VkVEwomS1THMqLf+0e4YqMbqgaJTqYy19g02bn2JgppmFnbtV02b3bdrkMhIq4icCEDlxucB2LRqJQD7jGxiE9OHnN/gTAWgrWZ/kCIUEZFgULI6hkW2WAXWbUkD11g9kGPaCgAm163jN8+8xSyHVRkgcvIJwQlQ5AAxn/smAMvqn2PTtq3M3fcXAGpnXBjQ/Da3ldD66ouHGCkiIqOJktUxLLHDegs1On3gGqsHSp5/NgCnOLYzbtffAChz50FUcnACFDnA1BO+yh7HJGIMD9GPn8c4Wy0VJLLgnB8FNN8fa7UUtjWXDTFSRERGEyWrY1SLp5NsrBqryVlTAppjZM3HG5lKrM3DTdEvARA7dVmwQhTpzTBg2c8AmGKrAKBkzpXYI6ICmu7oagcc2VYRnPhERCQolKyOUUXV9eTY6gCIHaTGai+GDee5f4Spp0PGXEidQcySbwUxSpHeJh97Pruc1g9XZSQz/6yrA54bmZwDQIK3KiixiYhIcDhCHYCERk15AdMNkw4cRMSkBT5x6grrQyQUDIO48+6h8Nkf4Fv6P9giBm4E8FkJGVat1TSzJljRiYhIEChZHaMaq6wT0TW2ZDINPWCX8JEx4ziYsWHY81KzrL3ZCUYrTY11xMYljnRoIiISBMpSxqj22iIAGiNSQhyJyOERG59Eo2k9ia0qzQ9xNCIiEiglq2OUr6EUAI976PqUIkeKKiMJgLqKgtAGIiIiATssyeof//hHcnNzcbvdHHPMMXzwwQcDjn3kkUcwDKPXh9sd+L40CYyzxSrf44/NCHEkIodPfVdjgNZqNQYQEQkXQU9WH3/8ca699lpuvvlmNmzYwLx581ixYgWVlZUDzomLi6OsrKzno7BQ7RFHWmS79f13xGeHOBKRw6e7MUCnGgOIiISNoCerd911F5dffjmXXXYZM2fO5MEHHyQqKoq//vWvA84xDIOMjIyej/R0vVU90uK91QBEpYwPcSQih48vpqsxQJMaA4iIhIugJqsdHR189NFHLF++/NMXtNlYvnw577777oDzmpubmTBhAjk5OZxzzjls3bp1wLEej4fGxsZeHzK4Tp+fVLMWgPi0wFqtihwJbF2NAdxt5SGOREREAhXUZLW6uhqfz9fnyWh6ejrl5f3/YzFt2jT++te/8txzz/H3v/8dv9/PscceS3Fx/2/b3XbbbcTHx/d85OTkjPjXcaQpb2gjy9YAQGK6klUZO7obA8SrMYCISNgYddUAlixZwiWXXML8+fNZunQpTz/9NKmpqfzpT3/qd/wNN9xAQ0NDz0dRUdFhjjj8VFSW4DY6AbDFZ4U4GpHDJz4tF4BUvxoDiIiEi6A2BUhJScFut1NR0bsXd0VFBRkZgZ1CdzqdLFiwgD179vR73+Vy4XK5DjnWsaSu3DqwVkscSfaIEEcjcvikZU0EINloprWliajo2BBHJCIiQwnqk9WIiAgWLVrE66+/3nPN7/fz+uuvs2TJkoDW8Pl8bN68mczMzGCFOea01ljJaoNTDQFkbIlLTKXFtH5AqyzdF+JoREQkEEHfBnDttdfy0EMPsXLlSrZv384VV1xBS0sLl112GQCXXHIJN9xwQ8/4X/7yl7z66qvs27ePDRs2cNFFF1FYWMi3v/3tYIc6ZnjrrYYAra7UEEcicngZNhuV3Y0BygtCG4yIiAQkqNsAAL7yla9QVVXFTTfdRHl5OfPnz+fll1/uOXS1f/9+bLZPc+a6ujouv/xyysvLSUxMZNGiRaxbt46ZM2cGO9Qxw+gq2+ON1tNqGXvqHKnkdZbTosYAIiJhIejJKsBVV13FVVdd1e+91atX9/r87rvv5u677z4MUY1drjZrD7EtToerZOxpdadD82a8dWoMICISDkZdNQAJvtgOq2yPK2lciCMROfw6o63Dnbam0hBHIiIigVCyOsaYpkmSzyrbE5uq7lUy9ti6Wgx3v8MgIiKjm5LVMaa+rYNMox6ApIzckMYiEgrursYAcR1qDCAiEg6UrI4xpdV1JNtaAHBrG4CMQd2NAVL81aENREREAqJkdYypLc8HoI0IcCeENhiREEjJygMgzWjE09Ya4mhERGQoSlbHmIZKq1xPrT0FDCPE0YgcfkkpWXhMqxBKZVlBaIMREZEhKVkdY9prrGS1OUINAWRsMmw2KroaA3S/0yAiIqOXktUxxmywakt6olVjVcauWrv1w1pLlRoDiIiMdkpWxxhXi1Vb0kjICXEkIqHT4k4DoKOuKMSRiIjIUJSsjjFxnnIA3Cm5oQ1EJIS8XY0BDDUGEBEZ9ZSsjiF+v0mqzyrXE5+eF+JoRELHFtfVGKC1PMSRiIjIUJSsjiHlDa2Mt1ndq5KyJoU4GpHQcXU1BohRYwARkVFPyWoYqm5u563dFXh9/mHNK6koJ9bmAcCRqFarMnbFpU0AINmnxgAiIqOdktUwdPGj61h2z2vk3vQsv355C50BJq21ZXsAqDPiwBkZzBBFRrWUzIkApNOAt8MT8LyKsiJW/flHlBYXBCkyERH5LCWrYaaxzcv8gpXsTrqZH3T+kz+9+Ca/XbUtoLktVQUA1DnTghihyOiXnDYOr2nDZphUlRcEPG/P367g1LK/Uv7I1/EP850NERE5OEpWw8zbu8v4ceQqJtur+FnUq+xNuoniDS8GNNdXa9WUbI1UjVUZ22x2OxVYjQFqSgNrDFCwdyufa10DwELfVtY++4egxSciIp9Sshpmtn+8lhRbC+1GJN6MBTgNP6c3/4fyxrYh59qbSgDwd52EFhnLqh3WOwyN5XsDGp//wu+wGyaNphuAGZt/R121qgmIiASbktUwYyt4C4DatGNwnnMvACdH7OLVLQVDzo1qt/5hdepwlQhNUVZFAG/10MlqdWUpR9da72DsPfEedjOOFKOZzf/8aVBjFBERJathpbyxjdntmwCIn3kqpM+h0ZlMjOFh/6bXhpyf7K0AIFo1VkXwJVp/Dxz1Q28D+OQ/dxFtdLDTyGX+sguo/ZyVpObUvhfUGEVERMlqWHlzWyEnOK0T/dEzloNh0D7+JAASS94atCpAU7uXLKwaq8mZqrEq4kqbDEB829AtV7NLXgagZs43MWw28uYuA2CCWUFbS1PQYhQRESWrYWX/J6uJMrw0OpIhZRoAyfPPAuBk2ye8VzBwzcii6joybY0ARKfpyapIcvZ0ADJ9ZYOOq62uYIpZDMDUJecBkJo+jmozBpthUrhrY3ADFREZ45SshpGo4ncAaM4+DgwDAPvkk/BhY4ajgvc2fDTg3MqSfdgMk3acEJVyWOIVGc2yJs4CIMVopr62csBxuzeswmaY5JNBSoa139uw2ShyWI0FagqUrIqIBJOS1TBR1+rhaP8WAJJmf/7TG+4EqhPnAeDf/eqA8xsrrX15Nfa0nkRXZCyLiUui0owDoCR/4FrFrXusHxKL4+b3ut4YZ20j8JYFVudYREQOjpLVMFFQWcdiRyEA7inLet2LmH4aANNb1tPa0dnv/NauhgBN7vSgxSgSbsodmQDUl2wfcExKzQYAjAlLet9ImwlAdMOu4AQnIiKAktWwUVG0G7th0oYL4sb1upcwczkAxzn28kF+Vb/zPdVWovvZuSJjWWOU9bZ+R+Wefu+3tTQxzWeVtho/75Re9xImWO9oZHkKghegiIgoWQ0XjWXW05tqZ0aft/GNzHl4DBfJthZ2bl3fZ65pmiQ07QYgOntm8IMVCRO+hK7yVQ0F/d7fuXE1EYaPcjOBnLxZve5NmLYIgGyjlsb6mqDGKSIylilZDROdNdae05aofrpP2Z1Uxs8GoD1/bZ/bpQ1tzMR6spo2+ajgBSkSZlxpUwCIa+2/fFX9ztUA7Iuag2Hr/b/LhKQ0Ss1EAAp39P0hUURERoaS1TDhbNwPgC9+Qv/3u/bTpdVtwufvXW91S34RUxzW9gBXzoIgRikSXhLHWSXgBipfFVthJaHe7GP6vV8SkQtAfeHHIx+ciIgASlbDRmx7KQCu1P4L+qfOXAbA0bbdbC1r6HWvfM+HANTYUyAqOXhBioSZ7DzrHYk0o5H6ut5v5Xs7PEztsA5epc8+qd/5LfFTAfBXqiKAiEiwKFkNAz6/n/TOcgDiMqf0O8Y+4Rh82Jhkr2bj9t4nm73F1lOf+vjpwQ1UJMzExCdTbcYCUJK/tde97R+9TqzhodqMYersJf1Nx55h7QGPa9wd3EBFRMYwJathoLiuhYk262385Oz+k1VccVRFTgSgfuc7vW7FN1jJqy1zbvCCFAlT3eWr6kp29Lpeu/kVAHZFLcBmt/c7Nzl3PgA53sLgBSgiMsYpWQ0D+0tLiLe1A2BPHrhVqnecta8uuuJD/H4TgPrWDiZ1FgCQosNVIn00RuUA4Cnt/VZ+csU6ADpzlw44N3vSHABSjCZamxsGHCciIgdPyWoYqC2x3mKsNRLBGTXguPSufasL/DtYvbsCgE/2VzDbYe13jZ2wMLiBioQhY3zX4cSKt3uuNdRXM8Nn1V7NO+rsAefGJyTTYLoBqCjeG8QoRUTGLiWrYaC1q2B5nTtz0HERk07Aj8EiZxHPvW1tBSjavZEIw0ezEQ0J/VcSEBnLpp3wFfymwRxzL4UFVj3jHe89j8Pwk08GOXmD7/WuMqxDi3Xl+4Ieq4jIWKRkNRzUFQDQHjN+8HGxmTRnHw9Axt6nqGn2ULfPKr1TFTO1TzMBEYGk9PFsc1in+veseQIAz67XAdifMPTWmXpnGgCt1dq3KiISDEpWw4C72SpYbksc+slo3LHfBuCSiHWc96fX8ZValQAisucFL0CRMFc//lQAYgtXAZBT9wEArqnLh5zbGpkOQGd9cZCiExEZ25SshoEkj1WwPCp98tCDp51BqzORbHsDJ1f8jW+63wUge+bxwQxRJKzlHnsBAPO9m3n9sd+QRzmdpo3pnztryLm+mCwAbE2lQY1RRGSsUrI6yjV7vGTTVbZq3NShJ9gjsM3/OgC3RL9IrM2DmXsCzPhCMMMUCWvjJs9jn5FNhOHjlD2/BWBdwmkkJKYMOdeRaFUTiGqrCGqMIiJjlZLVUS6/sp4JNquzTkzGADVWP8N99KU9vzYz52N89R/gcAUjPJEjRkn6p12q1qV+keN/8PeA5kWlWNtzEryVQYlLRGSsc4Q6ABlcTVk+TsNPBw4iYgevBtAjZSoccyVU78A47yFwxQU3SJEjwPQzr2Hb3zbQOvEMjr3gxoAPJCam5wKQZtYMPlBERA6KktVRrrkyH4AqeyrZxjAehJ92W5AiEjkypY6bQuoN7w57Xtq4SQDEGe001tcQl5A80qGJiIxp2gYwynnqSgBojkgNcSQi0p+Y2ATqTKtZR2XJnhBHIyJy5FGyOsqZjdYJY09XeRwRGX0qDesgVn15fogjERE58ihZHeUcLeUAmIHuVxWRw64hwmoM0Fa9P8SRiIgceZSsjnKRHqtslTMhK8SRiMhA2rve+fA1qDGAiMhIU7I6yiV0VgMQmTwuxJGIyED8sdkA2NUYQERkxClZHcU6On2kmXUAJKTlhjYYERmQPcH6YTK6XY0BRERGmpLVUaysoZUsWwMACWk5IY5GRAYSnWo1BkjsVGMAEZGRpmR1FKuoKMVldAJgxGnPqsholZSZB0C6WYPp94c4GhGRI4uS1VGsodI6WVxnxIE9IsTRiMhA0rOtxgBRhpf6Wm0FEBEZSUpWR7HWGitZrXekhDgSERlMZFQM1WYMAJUle0McjYjIkUXJ6ijmrbdOFre51L1KZLSrsVltVpuqVGtVRGQkKVkdxYymMgC80RkhjkREhtLgtN4BaastCXEkIiJHFiWro5irzdr7ZsSpe5XIaNfutt4B8TWq1qqIyEhSsjqKRXdYDQFcidkhjkREhuKLtn6otDWXhzgSEZEji5LVUco0TZJ8NQDEpo4PcTQiMhR7vJWsutuqQhyJiMiRRcnqKNXQ5iXTsLpXJaXnhjYYERmSO9HqYhXnVbIqIjKSlKyOUqW1DaTZmgFwJ6t7lchoF5dmvQOS5K8NcSQiIkcWJaujVE15IQAdOCAyKcTRiMhQkjKslqspNOHt8IQ4GhGRI4eS1VGqsatWY60tCQwjxNGIyFBSUrPpMO3YDJOqrh82RUTk0ClZHaXau2o1NkWoe5VIOLDZ7VSSAEBdhZJVEZGRomR1lPI1WMmqJzI9xJGISKDq7NaWnaaqohBHIiJy5FCyOkrZW6zuVf7YrBBHIiKBao6wGgN01BWHOBIRkSOHktVRKrrd6l7l7CqHIyKjX0eU9U6Iv7EsxJGIiBw5lKyOUgldtRqjUyaEOBIRCZQ/JgMAZ2tFiCMRETlyKFkdhdo6OsnAqtWYqIYAImHDmWBt24lsV2MAEZGRomR1FCquaybbVg9ATJqerIqEi6iuBh7xndUhjkRE5MihZHUUqiwvwmn48WFgxGaEOhwRCVBCqtXFKsWsC3EkIiJHDiWro1B9ZQEAtUYi2ByhDUZEApaSmQdAvNFGS1N9aIMRETlCKFkdhdqrre5VjRFpIY5ERIYjLiGJJtMFQFVZQWiDERE5QihZHYV89VZDgHY1BBAJO1WG1RigvmJ/iCMRETkyKFkdhezNVo1GnxoCiISdekcyAC01SlZFREaCktVRKFINAUTCVovbOhTprS0McSQiIkcGJaujUHdDgKjk8SGORESGqzPWKl9lbywKcSQiIkcGJatBtG5fFX9esxuf3x/wnHavj/TuhgAZuUGKTESCxZls1UaOai0NcSQiIkcG1UUKEq/Pz7l/fovq5jY+KKzhz187BpvNGHJeSV0z47oaAsSmqiGASLiJTp8MWyDZWx7qUEREjgh6shokq3dVcI/xAMVJP2fjh2/y/Sc+xDTNIedVVJTgMjrxY2DE6YCVSLhJyZ4CQJZZjd/nC2hOwbb32fer2Xzwr1shgP9PiIiMJUpWg+T1D9fzNfd6suwNvBr/B9a9+yaPfzT0gYv6igIAao0EsDuDG6SIjLjMcRPpNG1EGD4qAqy1Wvbib5joL+LonXfxwUPfAzPwrUMiIkc6JatB0OnzY9/5fM/nybYWXku4l3UbPxpybltXuZtGZ2rQ4hOR4HE4IyjFKl9VVbRzyPGNdVUsaF7T8/nRZf/i/YeuDFp8IiLhRslqELy9p5LTjA8B8J14A82J00m1NTOh8Gn8/sHf4uusKwagTQ0BRMJWtdP6+9tUsW/IsZtffQi30ckOxvNi3k8BmFH6LKY/sC0EIiJHOiWrQfDqhxs4zmH9I2VfdDHu438AwPFs4eOSukHnmo1dJ4i1X1UkbLVEWn9/vTX5Q45N2vVvAEpyz+OUC66l3XQQZ7RRWrAtqDGKiIQLJasjzOf3w47nsRkmdcnzIS4bx+STAVjsKOTtzYO/LRjZYrVajU5RJQCRcNUZZ9VItjcMXmt139Z3meHfR4dpZ/Zp38HldrPHZv3dL9nxXtDjFBEJB0pWR9jeqmZOMz8AIG7Bl62LcVnUROVhN0zqt7824Nxmj5fxPmsbQPKE2UGPVUSCo7vWanTb4LVWS976KwDr3ceQnm51rKuOnQaAZ/+GIEYoIhI+lKyOsILSEk507gHAPuucnuvGJOvpanbN+7R2dPY7d2d5PdMcVqvV2HFKVkXCVWz6ZABShqi1ml5tPT31zzy355qZMQ+A6DptAxARASWrI652/1ZshkmNLRkSPm2Xmjh7BQCnOLbx9u6Kfufuz99JlOGlAwckahuASLhKHWfVWs2kBl9nR79jGmsrmOy3tglMXnRaz/XkSUcBMMGzRzVXRURQsjriPJW7AWiIHNfrupF7PJ04yLPXsOGT/ktYNRZtAaAqYhzY1FxMJFylZ+fRYdpxGn4qSvs/ZLX7o1XYDJN9ZgYZ2Z/+cDpp1jF0mjaSjWYqS/cerpBFREYtJasjzF5n/cPUkZDX+0ZENDVJ8wEw9r3R71x/9S4AWuImBS0+EQk+u91BKSkAVBXt6ndM8553ACiKm9/renR0DHsM64fdom3rghekiEiYULI6wmJbraL+EamT+9yLnH4qANNaNlDb4ulzP6bReopiT5sWxAhF5HCo6am12v/T0ZRq6x0WY8Kxfe5VRk8FoLVQh6xERJSsjiCvz09mZxkA8dnT+9yPm24dslrq3MM7e8r7zM3yWvvXEnJmBTlSEQm2lqhsADpr+7ZZbmtuYKrPSmInLPh8n/ud6XMAcFdvDWKEIiLhQcnqCCqoaWaSvQqApHF9k1WyFtBuuEm2tbBzc+8ainsrG5lutxLYpAlzgh6riASXLyEXAFft7j73dm18A6fhp8RMYnxe3/9XxOctBmBce9+5IiJjjZLVEVRQUkSyrQUAI2li3wF2J3Upi6z7Be/0urW3qIBkWwt+DIyUqUGPVUSCK2GK9fZ+XuvmPqf6G3a8BcC+6LkYhtFn7sTZSwDINOporB28/JWIyJFOyeoIqi3aAUCNLQkiovsdEzPtJACmtn5MTfOn+1brCjcDUO1IB2dkkCMVkWCbOn8ZXtNGhlFPSWHvznVxlR8C4MtZ0u/cxIRkKsw4AMqL9HRVRMY2JasjqL3SagbQEJkz4JjYrn2rJzp38/aesp7r3vLtADTG5PU7T0TCS3RMHDvs1jsshZs+7VzXVF/FLK9V8H/c/NP6nQtQZUsFoKG8/9JXIiJjhZLVEWSr2weANz534EGZ82izRZFoa2PPZqssjWmaOOqsRNfUFgCRI0Z14gIAfIWflqDa+ta/cBp+djKOSdPmDTi30WVVE2iv6XtAS0RkLFGyOoJiW63T/M5+ylb1sDmoT7UOT3h2r8bj9fHGrgrSPdY/SJl5A//jJSLhxT3pOAAy6z/uuWbb+TwAxemn9LtftZsnKhMAf31RECMUERn9lKyOEK/PT6a3BOi/bNWBkmYuB2Bh5xbuWb2DP72ylhOd1pPVmNyFwQ1URA6bSQusv+uTKaa+ppz2lkbmtFr1VdOPuWDQuWa81RggoqU0uEGKiIxySlZHSGFtS0/ZqsQhklXXdKuu4hmurfznlf8yr/hx3EYnnvQFkDk/2KGKyGGSlpHDXqwnpHs2vM6Wd54k0vBSaKYya17fZgAHcidbLVhj21UNQETGNiWrI6SgpJiUrrJVtpQh2qWmzcCcYz1VudP9T74f+TYArmXXwSBvC4pI+CmJnQuAZ/uLmJv/DcCelJMwbIP/7zcu3TpsmeKrCm6AIiKjnJLVEdJUavX/rrElDli26kDG8lvx2SM5xllAgq2N9vhJMO2MYIcpIodbzucAOK7ueY5qtQ5aJS384pDTUrOtve9pNNDZ0R68+ERERjklqyOks8YqL1MXkRXYhLgs7Cdc2/Ope+m1YOi3Q+RIM/uki/jImEGFP5ZO08Z6Yzpzjj51yHmpaeNoNx3YDJOKkn2HIVIRkdHJEeoAjhT+RusQRHtURuCTjv0B7HrRSlLnDn7YQkTCU1JKGkk3vYdpmrR4vCyMcGKzDb3dx2a3UUYyeVRQW7qX7LyZhyFaEZHRR8nqCHG0WIcgzJhhJKvOSLh8dXACEpFRxTAMYtwRw5pT60wjr7OC5ko1BhCRsUvvO4+QKE8lAM7EcSGORESOFC1u64dfb93+EEciIhI6SlZHSLy3GoCo5IFbrYqIDEdnrPXDr62xJMSRiIiEjpLVEdDW0Uk6dQAkpI8PcTQicqSwJ1r/P4lsKwtxJCIioaNkdQSU1reSbasHIDZFyaqIjIyoFKsxQEJHZYgjEREJHSWrI6CiqhS30QmAERdg6SoRkSEkZlkNRtLNajDNEEcjIhIaSlZHQEOFdfih3ogDhyvE0YjIkSIz20pWYwwPjXV6uioiY5OS1RHQWlMEQIMjJcSRiMiRJDomlkozDoDKkj0hjkZEJDSUrI4Ab30xAK3u1BBHIiJHmmpbMgD15epiJSJjk5LVEWA0Ww0BOqOH0RBARCQAjU7rh+D2utIQRyIiEhpKVkdAZKuVrNris0MciYgcadoj0wDwNah8lYiMTUpWR0Bsh9UQwJ2k7lUiMrL80ekA2LvewRERGWuUrB4iv98k2V8DQFyqaqyKyMiyx2cC4GpXNQARGZuUrB6iquZ2sroaAiSkTwhtMCJyxInsescm1lsT4khEREJDyeohKqmuI8XWAoAzQdsARGRkxXa9Y5PiV7IqImPTYUlW//jHP5Kbm4vb7eaYY47hgw8+GHT8v//9b6ZPn47b7WbOnDm8+OKLhyPMg1JbUQiABydEJoY4GhE50iRnWO/YpBhNdHa0hzgaEZHDL+jJ6uOPP861117LzTffzIYNG5g3bx4rVqygsrL//Vfr1q3ja1/7Gt/61rfYuHEj5557Lueeey5btmwJdqgHpbna6l5Va08GwwhxNCJypElJyaLDtANQXb4/xNGIiBx+QU9W77rrLi6//HIuu+wyZs6cyYMPPkhUVBR//etf+x1/zz33cNppp/GTn/yEGTNm8Ktf/YqFCxdy3333BTvUg+KptRoCNEeoIYCIjDyb3UYFCQDUVihZFZGxJ6jJakdHBx999BHLly//9AVtNpYvX867777b75x3332313iAFStWDDje4/HQ2NjY6+NwmhXdCkBEomqsikhw1NmtLlbd7+SIiIy4R8+GB4+H0g2hjqSPoCar1dXV+Hw+0tPTe11PT0+nvLz/moHl5eXDGn/bbbcRHx/f85GTkzMywQdodmwbABMmTD6srysiY0dzRAoAnnp1sRKR4PCWboGKzXj89lCH0kfYVwO44YYbaGho6PkoKio6vAEc+wP4xguw8BuH93VFZMzo6Opi5W9UFysRCYJOD05PLQDr6yJCHExfjmAunpKSgt1up6Kiotf1iooKMjIy+p2TkZExrPEulwuXyzUyAR+M2EzrQ0QkSPwxGVAHjpaKoQeLiAyT2ViKAbSbDtLSskIdTh9BfbIaERHBokWLeP3113uu+f1+Xn/9dZYsWdLvnCVLlvQaD7Bq1aoBx4uIHOkcCdY/HpHqYiUiQdBcbb0rXeqPJzsxOsTR9BXUJ6sA1157Ld/4xjdYvHgxRx99NL///e9paWnhsssuA+CSSy4hOzub2267DYAf/vCHLF26lDvvvJMzzzyTf/3rX6xfv54///nPwQ5VRGRUikqy9uLHeatDHImIHInqKwuJBSpIYmJE0FPDYQt6RF/5yleoqqripptuory8nPnz5/Pyyy/3HKLav38/NtunD3iPPfZY/vGPf3DjjTfyP//zP0yZMoVnn32W2bNnBztUEZFRKT7VSlZTzLoQRyIiR6LWrier9Y7kEEfSv8OSPl911VVcddVV/d5bvXp1n2vnn38+559/fpCjEhEJDymZuQAkGK14WptwRcWGNiAROaJ460sAaHWlhTiS/oV9NQARkSNdQkIyLaZ1QreqvDDE0YjIkcZosiqNdEb3f5g91JSsioiMcobNRhWJANSpi5WIjLCINqvSiBE3OqsbKVkVEQkDdY4kAFpqikMciYgcaWI7qgBwJR3exkqBUrIqIhIGWiNSAfDWKVkVkRFkmiT6rIYAMSnjQxxM/5SsioiEAU/XXjKzsSTEkYjIEaWtFhdeAFIyJ4Q4mP4pWRURCQNG3DgAXC1quSoiI6f73ZpKfwxZSQmhDWYASlZFRMKAK9l64hHrKQ9xJCJyJKmtKACg1J9ISkwI29cPQsmqiEgYiM+YCECKryrEkYjIkaSpyqowUmNPwjCMEEfTPyWrIiJhIDV7EgBpRiNeT2uIoxGRI4Wn1toG0Nx1iHM0UrIqIhIGUlIyexoDVBTvDXE0InKk8DeWAuCJTA9xJANTsioiEgZsdhvlRgoAtWVKVkVkZDiarYYAZuzobAgASlZFRMJGrcN6m665siC0gYjIESPKUwmAMyE7xJEMTMmqiEiYaI20nnx01qnlqoh8hrcV3vgVlHw0rGnxndUARCWPzu5VAI5QByAiIoHxxWZDE9gCbAxgetvZ9dRNmJ4W7DHJpM0/k/hJxwQ5ShEJibX3wjv/i7nx7xg/+AgiYoae09lOgtkEQEL66GwIAHqyKiISNuyJ1pOPqLbAGgNsevF+pu38E9ML/s6ULffA387F7OwIZogiEgodLXjffQAAo7kc1twd0DSzvgiAZtNFeqr2rIqIyCGKTs0FIMFbGdB4247/AvCOOZtG00280Urh9veDFZ6IhMqGR3F21NPodwPgX3sv1BcOOa2xdAcAe3ypZCVEBTXEQ6FkVUQkTCRlWrVWM8xqTL9/0LHtjTXMbNsEQPx5v2eLcxYA5VveDGqMInKY+bx41twDwE9azuP1jmnY/B2Yq24ecmpdsZWsltgycDntQQ3zUChZFREJExnjrGQ1yvDSWFsx6Njt7zyO0/CzwxzH7DmLaUpbDIC9RE9WRY4oW5/G1VJGuT+OyonncZP3KwCY254DT+OgUz2VewCojxy9h6tAyaqISNiIioqmwowHoLJkz6Bj/dusLQD5qSdhsxnETzsRgNyWzWCawQ1URA6bxq2vAPB/bcfyq3OP4bzPn84eXyo2/JgF6wada6/bB0BnfG6wwzwkSlZFRMJIlc1qDFBfvm/AMd62Jma2fAhAyuIvAzBjwVLaTQepNFBVtD34gYrIYdFQtAUAW9Z8ZmclcNXSaazpnApAzbY3Bp0b22odsHKmTg5ukIdIyaqISBhpdFktEdtrBj48sX3t00QaXgr8qSxcfAIA8bGxbLNZ2wgKN74W/EBFJPhMk+R26/8Fk2csAsDttFOaZG378ee/PfBcn5fkTms7UUL29ODGeYiUrIqIhBFPdBbwacmZ/rRsfQmAXUknYLd/emiiOmkBAJ2F7wYxQhE5bBpLiDLb8Zo2svJm9VyOmnoSAClNO6G9vv+59ftx4KfVdDIuZ+JhCPbgKVkVEQkjZpx1EMLVPHBjgKyGjQC4p5zU67or7zgAMuo3BSc4ETms2susLT17falMy0zuuX7UrFns7EzDhh9//tp+5zYdULZqUmpc8IM9BEpWRUTCiDvTersurS2/3/uNVUVMMMvxmwZTFp3a697khcsByDVLaa4LrLGAiIxeVQWfALCXLFJj3T3Xj5qQzBrfNABqt73e79zaYivRLbJlEu0a3Q1NlayKiISRCTOXWP81y2hvaehzf8+GVwHYaeSQmd67I012Zhb5ZhoAhTs3BjlSEQm29tJtANRG5fa6HuGwU5F8FABmwTv9z62wKoo0uMcFL8ARomRVRCSMZGWNp9RMxGaYFGx9r8/99j3WP0wl8Qv6nV/tsA5oNVfsDV6QInJYOOp2A+BNnNLnXszUZQAkN++G1to+9231VkURb3xe8AIcIUpWRUTCiGEYFEZYp/pr9n7Q535q7QYAHLnH9Tu/JTIbgI7q/rcRiEj4SGy1KgG4M2f0uXf07Fls7czEhol/X9+qALEt4VG2CpSsioiEnZYk69SvUf5Jr+utDdVM8u0HIG/h5/ud2xlnveVnbxy4moCIhIG2WhL89QCk5s3pc3vR+CRW+2YCULvl5d43fV5SOssBiM+eFtQwR4KSVRGRMOMevxCA1KYdva7v2bAKm2Gy18xgfE5uv3OdydZbftFtpUGNUUSCq7PC+vu/35fI1HGZfe477Taq0qw97o6C1b071zUcWLZq0uEI95AoWRURCTPZ0z8HQJ6/GK+nted60663ACiMmYdhGP3OjUm36ikme8uDHKWIBFNVvvXOyi5/JjkJ0f2OSZuznA7TToKnDOo+7XrXXNRVRcCXyqS00V22CpSsioiEnQkTplLtj8Fh+CncbrVVxTTJqFxj/XL8sQPOTR1ntWHMMGvxd3qDHquIBEdLiVUJoNI9AZut/x9OT5o1kbVe6wfUjp2fdq5r2/JfAD40phPjcgY50kOnZFVEJMzY7Db2dR2yqtpjHbIq3LKGSf4i2kwnM5Z+ZcC5Wdm5tJsOHIaf6tJ9A44TkdHNqNkJQHvCwG/jT0+P4z37XADqt1pl7fB1EFtg/XpLwkkDTR1VlKyKiIShxgTr9K+/dBMAZW8/BMB77mPJSu+7f62bw+GghBQAKot3BjdIEQkad4vVxc41yGl+wzDwjl8KQGzZu+DvhPy3cXc2Ue6PY1JXo5DRTsmqiEgYcmZbdVTTGz6hs62RGVXWkxL7wouHnFvj7Kq1Wq5aqyLhKsFbDUBK1sRBx02ddzzV/mgi/S2wbzUtm54C4GnPPM6bnxvsMEeEklURkTCUM+ckvKaNyf79lN65hHijjUJ/Cp876dwh53bXWvXWFgY5ShEJCk8j0bQBkJo5eLJ6yvRsnvHMB8D/5Dex77T2q+5IOomshKighjlSlKyKiIShiZOm8d+pt9Jh2hnvKwZge8ZZRDiHPizhi88BwKFaqyJhyVtn/d2t9UeRlZYy6NjUWDePxH+bNd5J2DwNuDubqPLHMGnxisMR6ohQsioiEqa++PWreWXBPTSbLtpNB3mnfCegec6kXEC1VkXCVX15AQAl/kTSYtxDjv/JGUdxZuOVvO/NBeBJzwLOmz/626x2c4Q6ABEROXhnn3Mx7+fOpa25nmVTZwU0JzZjEnwCKZ0VQY5ORIKhsaKAVKDanjxg2aoDnTsvh3u+fhLLHzM4L2ITpRnLuCKp/9qso5GSVRGRMHfMvHnDGp+WY7VXzDBr8Xs92JyuYIQlIkHSXmttA2iKSA14zqWfm0Sn3+SG/8Rz38mLghVaUChZFREZYzIycmgznUQaXsqK95KZNzPUIYnIMPgbrLJVnqiMYc379rGT+faxA5e6Gq20Z1VEZIxxOOw9tVarS3aFOBoRGS5Hi9Uu2R+bHeJIDg8lqyIiY1CN03oi01yhWqsi4Sa63dpvHpE4LsSRHB5KVkVExqA2t9UYoLNeFQFEwk1Cp9UQIDplQogjOTyUrIqIjEG+aCtZNbreThSRMNHRTBwtACRm5oY2lsNEyaqIyBhki88CwN2q8lUi4cRXbzUBafC7yU5NC3E0h4eSVRGRMciVaB3MiOnqLy4i4aGuqyFAsT+R9LihGwIcCZSsioiMQbGp4wFI8tWEOBIRGY6GygIAqmzJ2G1jI40bG1+liIj0kpRhHcxIoQm/tyPE0YhIoNprrIYAjRFjYwsAKFkVERmT0tLH4TVt2AyT2qqiUIcjIgHqaQgQmR7iSA4fJasiImOQ0+GgggQAasoKQhqLiATO3lwGgBmXFeJIDh8lqyIiY1StLRmA5mo9WRUJF90NARwJY6MhAChZFREZs5ojrJar7bXFIY5ERAKV0FkFQHTK+BBHcvgoWRURGaPaI60DGv5GdbESCQveNuLNZgAS03NDG8thpGRVRGSMMmMyALC3qDGASDjwN1j7VVtNJxlpGSGO5vBRsioiMkY54q3GAFHtlSGOREQCUd9VY7XEn0BmQlRogzmMlKyKiIxRkUlWshrrVWMAkXDQWLkfgCojCad97KRwY+crFRGRXuLTuxoDmLUhjkREAtHadRiywZES4kgOLyWrIiJjVEpGLgDxRhuelsbQBiMiQ+qstxoCtLlTQxzJ4aVkVURkjEpKSqHJdAFQXVEQ2mBEZEhGV0MAX3RmiCM5vJSsioiMUYZhUEUiAHXlhSGORkSG4mqzDkPa4pWsiojIGFHnsLpYtdSoMYDIaBfbUQ2AK3HsdK8CJasiImNaq8va+9ZRp2RVZFQzTZL81mHI2NSx070KlKyKiIxpHVFWYXGjqSzEkYjIoNpqceEFICVDyaqIiIwVsdbet4jW8hAHIiKD8dRZlQCq/DFkJiWENpjDTMmqiMgYFpGUA0BMu1quioxmteX5AJSaCSRGRYQ4msNLyaqIyBgWl5YLQLKvOrSBiMigmqqKAKi1JWMYRoijObyUrIqIjGHJWZMASKUBv7cjxNGIyEA8XYcgWyLGVvcqULIqIjKmZWSMw2M6sBmmGgOIjGJmo3UIsj0yPcSRHH5KVkVExjCHw0FZV2OAmtJ9IY5GRAbiaLEOQZqxY6shAChZFREZ82rtVq3VpsqC0AYiIgOKbK8CwJmQFeJIDj8lqyIiY1yzOw2AjtqiEEciIgOJ77QOQUYmja3uVaBkVURkzPNGdb2t2FgS2kBEpH++DpLMBgDi0yeEOJjDT8mqiMhYF58NgKtVXaxERqPuw1Udpp30tOwQR3P4KVkVERnj3MnWk5pYT+Ww53rz19Kx952RDknkyNXRDB89As2B/31r7KrUUeJPIDMhOjhxjWJKVkVExri49Fxg+I0BSl7+X5yPngF/O4e22uIgRCZyhOlsh398BZ7/Ibzwo4CnNZTvAaCIVNxOe7CiG7WUrIqIjHEpmRMBSDUa8XW0BTSn4PEfk/3+rwCIMHzsfueJoMUnckTwd8KT34TCNdanO16C5sDaHLdW7AWgJmLsVQIAJasiImNeWlomraYTgMqS/CHHl25+k9wd/wfAR53WFgJj1wvBC1DkSPD2/8LOF2g3Hez1pWDDh2/D3wOa6q+1/l62RY+9SgCgZFVEZMyz2+2UkQxAbdneIccXrX8OgFX2JTSfcR8A01o24murD1qMIuGuYfPzAFzT/GV+3Xo6AG0fPAymOeRcV9N+6xcJY68SAChZFRERoM5h9Rtvrioccmx86VoAOvNO5tijjmO3P93aCrDumaDGKBK2/J24a3cCEDX1ZDKWfI1Gv5uYliIoGPqAYoKnFAB32qSghjlaKVkVERFa3Fa/cW/d4I0BOppqmOLdDcD4xWfidNjZmXACAG2b/xPcIEXClFm1CxcdNPldfOXUk7j0+Dn8w7MYgNb3/zr45M52kv21ACRlTwt2qKOSklUREcEb3XVwo6l00HG7P3wBu2Gyy5/JjCkzAYieew4Ak+vfxez0BDVOkXDUkP8RAB/7xjEnO4mp6XF8kmJtBTD2rALTP+Bcs856t6PR7yYnS3tWRURkjLLFW/8IuodoDNCy/TUA9sUtxmYzADjquBWU+eOINdoo+PiN4AYqEoZq960HoDBiIlERDgCOO34FzaaLSF8zVO0YcG5dyS4A8v3JjE+OCX6wo5CSVRERwZ1iHdxI9AyerGbWvA+AY/LJPddi3C7yI6YAUJm/OUgRioQvo8L6e9GSNKvn2ulzxvO+NxeApl0D71utK7WS1XJ7Ok772EzbxuZXLSIivaTmzgUgx1+G2dnR75iGst3kmOV0mjZmHHNmr3stMeMB8FUPXU1AZEwxTVKarMNV7nHzey4nRbvY5bK20tTvfHvA6Z4q6+9Ug3vstVntpmRVRETInTidJtNFhOGjrGBLv2P2fmCV3vnYmEx2Rnrvm4lWY4GIxoJghikSfhqLiTWb8Zo2xk1d1OtWR9bRAERXrB9wuq3BKlvljR0fvBhHOSWrIiKC02Fnny0HgPI9G/od05lvlayqTD6qz73IjKkAJLWr7arIgVoKrb9PW31ZzBvf+4e8tJkn4DMNkrzl0FjS7/yoFuvvlD05L7iBjmJKVkVEBICaKKuGY1tJ/09Wsxs2ARA5+fg+91JyZgCQ5S8f9GSzyFhTtedDAHbbJpAc4+p173NT8/i40zrc6Nm3ru9k0ySlw9pHHpMxObiBjmJKVkVEBABfynQAIrqKlx+oqbKQbKrwmQbTFi7vcz8ndxpe04bb6KS+vCDYoYqEDV/pxwDUx8/ocy83OZqNNqt2atX2t/pObq0hinYA0nKmBi/IUU7JqoiIABA9zjpklda2r8+9fRteBWAbE8hMS+s7N9JNEakAA+55FRmLYhusJhqOrLl97hmGQWOqtY/VUfx+n/vdh6uKfQnkpSUHMcrRTcmqiIgAkD11IQA5/go621t63Wvfa5XWKY1fMOD8Cqd1WrmxtO+TWZExye8jsbMSgKy8mf0OiZtqbatJbd0D7fW97tUUW3+XCs1UUj6zhWAsUbIqIiIA5GTnUuWPwWaYFO/Z1Oteaq11SMSRu2TA+S3R3eWr+j6ZFRmLzKYynPjwmjZyx/e/53TBzNls70zHjh/fnt5NNToK3wOgOGIChmEEPd7RSsmqiIgAYLPbKHRYCWfVvo091z2NNUz0FwGQO7/vftVu/sRcAJwqXyUCQFNFPgDF/kTGJ8f2O2ZuVgJv+OcAULPphV73YkqsChwF8X0rcIwlSlZFRKRHfYz19Kej7NN9p3s2rrL+609nYu7EAedGpXeVr2orCmKEIuGjtszac1pqpBDZ1Wb1sxx2G7VZSwGI3P8GmKZ1o7GUlLYC/KZB7LSTDku8o5WSVZH/396dx8d11ff/f90ZaUb7vo0Wa/O+xUkcO85CAqQJpEDShaXkGwKlpJTQR1laCF8ooQnbjx9taSktD9KWQH+hoUsSUgghkIU0e3DsxEm8W7Jk7fu+zMw9vz+OJFvWSJqRNZLGej8fDz/A9557/IGLyUfnnvP5iMgUU2hPLKf2Hpm6NnDYnlKuz9g+56fIvDX22YDbpvJVIsBwRz0AvckzDyWeqWLHbzFkfGQGu6H1VQCCx54A4DehNVy5dfVWAgAlqyIicoasNfbEcmDUfr40wRHWtthPk6HKq+d8tqJyIyHjIc0Zp69dq6sioR7792AkLTDnuGu3VPLYuC1hNfT6zwHoOvALAJ5ztrK1NCd+QSYAJasiIjJlzYadBI2HAN00vnA/Bx+9mwL6aHRz2fW2D875bGZ6Go2mAIDWOpWvEkkasN2n3MzyOceV5qTxaprdlzr0xs/BGNKangZgsPTyVX24CpSsiojIGQLFJTyU/i4Akh79LBkvfxeA3wTeS15WxrzPtyfbFaQ+la8SIX20FYDkvMp5xyZvuBaAgp5X4dUfkxXsYsQkU7Ftde9XBSWrIiJylotv+gaNbi4Bt501bhO9bioX3fDJqJ4dTK8AINil8lUi+cE2ADKLq+Yde9mFF7M3WIEHFx78YwD+N1jL1ZvnT3TPd0pWRURkmqrSYl7Y+Nmp3z+V89tUBkqietbNtI0BPIMtcYlNJGGM9pHBCAD5gdp5h++pLuBD4x/j30Z3MY4XgOd9u1iTlx7XMBOBklUREZnhXe++lf/0vJXXwqXUvuOz8z8wISnH7s1LG2mLV2giCWG8qwGATjed8qLCeccneT189B3X8OHhP2RN55e5tvfjtG+4Kd5hJoTIRb9ERGRV8yV5eftnfkzP8DgVudGv7KTl220A2cHOeIUmkhC6mo8RAE65eVwQZavUj71pPTduL+cf//cIL57s4hNv3RLfIBOEklUREYkow59Mhj85pmdyJvbmFZkuW9x8lZ9iltWrv/0EAaAjqSim0/ylOWl8+Z074hZXItI2ABERWTRFZdUApDnjDPdrdVVWr8ltAIMp0e33ltkpWRURkUWTk5VNp2u3DXQ0qyKArF5On20IEMwoW+ZIEp+SVRERWTSO49DusY0BetvqlzcYkWWUMmwrYnhyKpY5ksSnZFVERBZVX7I9+TzS2bDMkYgsn+wx2xAgNb9qeQM5DyhZFRGRRTWSUgxAqPfUMkciskzCQfJNDwA5UdRYlbkpWRURkUUVzrAtV71qDCCrlOlvxoNhzCQRKC1f7nASnpJVERFZVN4ce6AkRY0BZJXqabdbYJrdbMpzM5Y5msSnZFVERBZVav4aALKDHcscicjy6GutA6DdycWX5F3maBKfklUREVlUOcWVABS6XcscicjyGO6yZat6k+ZvsyrzU7IqIiKLqrC0BoBMZ5SxgZ5ljkZk6YX6mgEYSSla5kjOD0pWRURkUeXn5tHjpgFqDCCrkzNgDxeG0tW9ajEoWRURkUXlOA5tTj4APWoMIKvQ5OFCT3bpMkdyflCyKiIii6432XaxGu48ucyRiCy9jHF7uNCfq7JVi0HJqoiILLrhqcYATcscicgSM4Z8txuArMLKZQ7m/BDXZLW7u5ubbrqJrKwscnJy+PCHP8zg4OCcz1x99dU4jjPt10c/+tF4hikiIotssjGAM9C8zJGILLGRHvwEASgIKFldDEnxnPymm26ipaWFX/7ylwSDQT70oQ9x66238qMf/WjO5z7ykY9w5513Tv0+LS0tnmGKiMgi82aXQSukjLQudygiS2qku5FUoMPNoDQ/Z7nDOS/ELVk9ePAgjzzyCC+99BI7d+4E4Nvf/jbXX3893/zmNyktnX3TcVpaGiUlOkEnIpKoUvIrAMgaV2MAWV26W+opA5pNLttTkpc7nPNC3LYBPPfcc+Tk5EwlqgDXXHMNHo+HF154Yc5n7733XgoKCti6dSuf+9znGB4ennXs2NgY/f39036JiMjyyi6uAqBAjQFklRnstK1Wu735OI6zzNGcH+K2stra2kpR0fRiuElJSeTl5dHaOvtnofe///1UVlZSWlrKq6++ymc/+1kOHz7M/fffH3H81772Nf7qr/5qUWMXEZFzUxiwjQFynGGCI/0kp2Ytc0QiS2Os23avGvSpe9ViiXll9fbbb59xAOrsX4cOHVpwQLfeeivXXXcd27Zt46abbuKHP/whDzzwAMePH484/nOf+xx9fX1TvxobGxf8Z4uIyOIoyC+k36QA0NFct8zRiCwd028PFY6nFS9zJOePmFdWP/3pT/PBD35wzjE1NTWUlJTQ3t4+7XooFKK7uzum/ai7d+8G4NixY9TW1s647/f78fv9Uc8nIiLx5/E4tJFHFs30tNZRWnvBcocksiSSh21DAJMZWOZIzh8xJ6uFhYUUFs6/tL1nzx56e3vZu3cvF198MQCPP/44rutOJaDR2L9/PwCBgF66iEgi6UkqhHAzQxN7+ERWg7RRu1CXnKOGAIslbgesNm3axNve9jY+8pGP8OKLL/LMM8/w8Y9/nPe9731TlQCamprYuHEjL774IgDHjx/nrrvuYu/evdTX1/PQQw/xgQ98gDe96U1s3749XqGKiEgcDKXYcwvBbm3PktUjJ2QPFWYUVCxzJOePuDYFuPfee9m4cSNvfetbuf7667niiiv43ve+N3U/GAxy+PDhqdP+Pp+PX/3qV1x77bVs3LiRT3/60/ze7/0e//M//xPPMEVEJA5C6ZONAVqWORKRJRIaJYcBAHImKmLIuYtrU4C8vLw5GwBUVVVhjJn6fUVFBb/+9a/jGZKIiCwRJ7sM2sGvxgCySrh9LXiAYZNMSZHqxS+WuK6siojI6pWSZz+DZo63zzNyJtO0D3Pop4sdkkhc9bTVA9Dk5lCclbq8wZxH4rqyKiIiq1fWZGOAcGyNAcxwN8P/cj3pZpiu3/kx+dvfFofoRGbRdRyO/BzSCiC3Cip2gRPd2l5f6wnygQ4nn3VerQcuFiWrIiISF4WBagDynEHCY0N4/elRPXf0J19lvbFnGfof+RL5264DdQKSJRJ+8E/wnjqj0+a1X4U9t0X17GinrSncmawtAItJab+IiMRFUWExQ8YHQEdLfVTPuIOdlB35N/vvjUP1yEE692s7gCyRsQE49RIA+4K29FT3Sz+O+nG35yQAI+llix/bKqZkVURE4sLr9dJKHgDdrdF1sTr6k6+Qzij7wxX8KPm3ARh69E444zCuSLyETj6PF5e6cD6/N2RXU3N6XoXh6Lay+AZsmTaTXRm3GFcjJasiIhI33Um2icxg+8l5x7ojfVQcuxeA19bfRvU7v8Cg8VM5eoT2V38e1zhFANoOPAbA8+4GHvzzP2B/qBwPhvFDv4jq+cxRW6YtpbA6bjGuRkpWRUQkbob8E40BeuZvDFC37zHSGONEuIDf/p0Pcfn2Tfxv8qUT9x6Pa5wiAObk0wB0FuxkW2kOT3t22N9HsxXFDVMQ7gAgO7A2XiGuSkpWRUQkboLp9qCJM9A879juw08BcDxtG7npKQCYos0AJHUdjlOEIhOCwxQPHAQgff3VOI7DSOVbAchuegrc8JyPm/4mkgkzbryUltfEPdzVRMmqiIjEjZNlD5r4hudvDJDW9hsAxgKXTF1LLd0CQN7wiThEJ3Ja+OQLJBOiMZzDhVt3ALDxorfQ7aaR7g5gGl+c8/n+luMAnAznUZmfGe9wVxUlqyIiEjf+/InGAGPzNAYIB6kZtaunBZuumrpcWLMDgPJwCyY0FpcYRQDaXrP7VZ91N7C9PBeAN28q49GQ/YGp+5W5twJ0Nx8FoNlTREqyN46Rrj5KVkVEJG4yC+2p6MKJvXyzaTv6IqnOON1uGtu275q6XluzkQHXT7ITprPxYFxjldUtXGf3q7bn7cTrselRhj+Zk3l7ABg/Nve+6ZF2u/rf61ON1cWmZFVEROImUD3xGd8ZZLRv9oS16cCTALyetIH0FN/U9VR/Mic8ditB67F9cYtTVjk3THH/awCkrb1y2q3CTVcDkD9wBOZY3Xd7bcWL0Yzy+MS4iilZFRGRuCnKy6fRtbVWT82VbDY+D0BfwYUzbnWk2jJAw02vLX6AItjDUT6CBI2H7dsunnbvwq076HAz8BHCbTkw6xz+iRqrZK+JZ6irkpJVERGJG8dxaEq2+1Z7G2b5B70xlA/Ye+m1V8y4PZ67HlBFAImfvuZjANS7+Wwrz592b2tZLr8JVwHQcfiZWefIHrOHCFOKauMT5CqmZFVEROJqIMOujAbbDkW8P9h+giJ6CBoP63dcNeP+6YoA0XXBEolVV9MRAJqd4hmHo5K9HprSbQm1obrnI08QDpLvdgKQV6oaq4tNyaqIiMSVKbAroyl9kctP1e+zp7Bfo4qyooIZ91URQOJtpN2urPamlEa8Hw7YrQEZna9EvG/6TuHFMGKSKS1Vq9XFpmRVRETiKr3MrowWjUZuuTpywn5abcnaHvH+mRUBuhreiE+Qsrr11AMwmlER8XbRBlsRoGi8CUa6Z9zvnShbVR/OpyIvPT4xrmJKVkVEJK4CtTvsv5pOwmODM+7ndduDV56K3RGfP7MiQMtxVQSQxZc6eAoAT151xPsXrq/lSMi2Dh4/+dKM+90Te15bPEX4klRjdbEpWRURkbiqLF9Dp5uOxzG0nJh+yCo80kt1qAGA8gveMuscpysCvB6/QGXVyh237YDTiyPvN63MS+cVbAvVtkPPzrg/3mYP//WlBOIU4eqmZFVEROLK6/HQ4LUrox3105PV+ld+jccx1LkFbFq7ftY5grk2iXC61XZVFtn4IHmmD4CC8sj/G3Qch+7cbQCEIrRdzWh/GYDOrC1xCnJ1U7IqIiJx15NWBcBoy/QuVN2HnwLgeMqWqa5Bkfjy7KGVtNHW+AQoq1aw01aZ6HbTqCyNfMAKIKniEgAKeg+AGz59IzRKyaDdS+2pvDR+ga5iSlZFRCTugrnrAEjuPjrtemrrbwAYDeyc8/n0ibatucG527aKxKqj0ZZUq3cLKMpMmXXcms176HVTyXQHoPnlqeumaR/JhGh3M9i65aK4x7saKVkVEZG4Sw3YOpV5I/WnL7ohqkfsSmv+xjfN+XxewBZaLzLd01e1RM5Rf4v9Aao9OYDjOLOO21VTwi+C9n/HPft/MnW94+CvAXgutJYLK/LiGOnqpWRVRETirqjalqUqDzdjwkEA2o/9hnRnjD43ha3b5/58GiirImwckp0wg11NcY9XVo9gl90GMJhaNue47FQfx3IvByB06OdT10eO29JrTVnbVQkgTpSsiohI3FXVbKTfTcHnhGl99VcANL36OACve9eTmTb751eAzLRUWkwOAB3NOmQli8fbZ6tRhLPnL+afu+16wsahcOgY9DWCMeR17wfAs0b7VeNFyaqIiMRdqt/H46lXA9D3+F9DOEjJoR8C0FYY3T/kO7yFAPS2KlmVxZM5YlfqfYU184695sItPBey40Zffxi6jpLp9jNikqnaellc41zNlKyKiMiSyHnzJwkbh42DL9Hwo9sIhFtoczPZcP0nonq+32eLso91NcQxSllVjEthyFaYyA6sm3f4+uIsnk+2rVd7X3mI/olqFi+GKrm0du5tBLJwSlZFRGRJXLVrN496bJeqNSd+DMCjRR9gc2V0/5AfS7Nlhdy+xvgEKKuOGWglhSBh41BSMX+yChBeex0ARe3PkPHYZwE46t9MTpovbnGudkpWRURkSTiOQ/jSP536/bFwEW9+72ejnyDbJqu+wZbFDk1Wqf6W4wCccnOpKsyJ6plLLr6cfcFyPBg8JsSoSaKj4ro4RilJyx2AiIisHte+5e089sx23up5ledq/5SbC7KjftaXVwn1kDHWFr8AZVXpbKkjG2h18qn0RZcSXbmumOrxz5E70MyASaHDzeDfbpy79JqcGyWrIiKyZHxJXtLe/2/87Sv7ufWGd8T0bGZRFQD5YTUGkMUx0nkSgL7kwqifSfZ6uP9jb+OJo21k+pOpzEvn7Ztn73wl507JqoiILKk9G6rYs6Eq5ufyS+0p7EL6MMFRnOS5y12JzCfYewqA4ZSSmJ7bVVXArqqCeIQkEWjPqoiIJIRAcTkjJhmA7tb65Q1Gzgveif3P4czAMkcic1GyKiIiCcHvS6LZ2HaWnc3HlzkaOR+kjdiyVUk55cscicxFyaqIiCSMriS7t3CwvX55A5HzQlbQ7n9OzV+zzJHIXJSsiohIwhhMKQZgrFuNAeQcuSHy3R4AcoqrljcWmZOSVRERSRjBdNtAwOlvWuZIJNG5fS14HUPQeCgOVCx3ODIHJasiIpIwPDk2WU0ZVmMAOTe9bfUANLk5lOZmLm8wMiclqyIikjBS8qsAyBpXYwA5N71tdQC0O/kke5UOrWR6OyIikjCyJ/YWFoQ7lzcQSXhDnXbfc08MDQFkeShZFRGRhFFUthaAbGeE0HDv8gYjCS080RBgdOLQnqxcSlZFRCRhFOXn0+2mAdDRdGKZo5FE5hloBtQQIBEoWRURkYTh8Ti0OfkAdLeoMYAsXOqI3ffszVElgJVOyaqIiCSUnuQiAIY6Ty5zJJLIsqcaAihZXemUrIqISEIZTi0BINTTuMyRyLIa6YbuBa6uuyHy3W5ADQESgZJVERFJKKEMW2vVOxB7Y4Dx/f/B6H23QNPexQ5LlpIxmB/eiPmHnXD8sZgfd/tbz2gIoFarK52SVRERSSjJueUApI60xvZgOMjYQ58i5fCDuP/8VoYf/DMIjcUhQom75pdxWl/BMS7j//3HMBRbKbPJhgDNagiQEJSsiohIQkkrqAIgd7w9pue6Dz5Bphlg3HjxYEh75R5afvWtxQ9Q4q7r2Xum/r1vpIPQg7eBMVE/39M62RAgTw0BEoDekIiIJJTcQDUAhaYrpgSl+fkfA/AT5wr+3vNuADpff3zxA5T4Co+TcvhBAP5i8HcYM0kkHXsEDv1P1FOMdNYDagiQKJSsiohIQikpq8U1DilOiOHeKLcCGJdA88Texk3vZPOedwFQOngwpoRXll/48C9ID/fTHM5m/JI/4Z9GrgSgae9Po5+j21aSGEgti0uMsriUrIqISELJzkij1WQD0HHqWFTP9B97lnzTQ5+bwoVX3sjarZcRNB7y6WOsSyWwEknnM98H4L/Cl/L//u5OPNU2WXVOvRj1HEkDtpKEm6WyVYlAyaqIiCQUx3Ho8NjGAL1tdVE90/DsfQA87b2ItYFCKovzed3YRKXhtafiE6gsvvFB8pt/DcDAht/Hl+SlYtvVAJSM1cNob1TTZIy0AODLr1r8GGXRKVkVEZGE0+ez/dxHo2kMYAz5jb8EYKjm7YBNeJvSNwEwcPyF+AQpi260+Q2SCNHqZnHtVW8F4OJNGzkaKsSDYbQuindpDIUhu30ks2RtPMOVRaJkVUREEs5omu3nHu49Ne/Yse5GAuFWQsbDlit+d+p6qOQiANI69sclRll8rXWvAnDMBNi5Jg+Aitw09nvW2fuvPzn/JCPdpGFLlhWV1cYlTllcSlZFRCThmCx7MCZ5qHnesY1vPAvAIVPK5srTB2ry1u8BYM3YEXBDcYhSFttg8yEAOlPW4DgOYFfJe/LtDx40zr+yOthqu141h7OpLC6IT6CyqJSsiohIwknOs/tN00fnrwbQV/cbAJpT108lOACbt1xCv5tCGuP0N7wan0BlUXm6jgAwml0z7XpazWUAFA+8Pu8PHl3NRwE4RQGZKclxiFIWm5JVERFJOJmFVQDkhTrmHZvcZhPR0YKt067nZ6bymmOTnsbXn17cACUuMgfqAUgq2jDt+oatu+h1U0k1o7gtB+acY7DtBABdySVxiVEWn5JVERFJOPmldq9hkenFzNMyNTBsV+Myqy+Zca8zewsAYyejL3sky8QNUxxqAiC3Ysu0Wzsq8nkxbH/waHvj13NOE+62FSSG00rjEKTEg5JVERFJOGWllQy4fjyOoavx0KzjxnuaKKSHsHGo3rxnxv2k0gsASOk9HrdYZXG43SfxEWLEJLOmavrKarLXQ2OGXTkfOvHsnPMk9dtDeW72mvgEKotOyaqIiCQcvy+JOseujLXVz/7Zt2HicNURE6CyZOZhmtwye4o8P9gShyhlMXWetNs5joaLqC7MnnHfW34xAOldr885T8aoPZSnGquJQ8mqiIgkpM4UuzI21Hxw1jF9J14C4FTKummHqyYVltsVumJ6MMGROEQpi6W7wSahzcnlJHlnpi/F63bZfw02wdhA5EmMoTDUDkBWicpWJQolqyIikpCmToR3HZ11TFK7XY0bKdgW8X55aQUDrh+AnmZtBVjJgu2HAehPr4p4f+v69ZwK5+DBMNY0S3WH4S5SGcM1DsUVagiQKJSsiohIQkoutJ/wJ0+IR1IyZBOc9MqLI95P8SXRSCEAHacOL26AsqhS+uwpfpO/LuL98pw0XqMSgNbDz0ccM9B6DIBmN5vKwvw4RCnxoGRVREQSUvbEifCSiRPiZwv2tVJsunGNQ9XWy2adp8tnSxgNtGpldSUrGLWtddNLN0e87zgO7Rm2he5ow96IY7qabGWIJgpI9yfFIUqJByWrIiKSkCpq7OnvXAYZ72+fcX+ydupRU0xNoHjWeYbTbFercFddHKKURTHSTa7pB6C4euusw0zJdgAyuiMfshpst++426caq4lEyaqIiCSkkoJ8GlzbH775+Csz7vcetclqXcqmiIerJrnZ9tNx0kBDHKKUxTDUZMuTNYZzWFcWmHVcXq2tpVsyfhKCwzPuu1M1Vstm3JOVS8mqiIgkJMdxaEoqB06fFD9TSuvLAIyVRN6vOim5oBqAzJHmRY5QFktbg6340OCUkJPmm3Xc5nUbaXMz8WIItbw2435OzxsAjOZtjE+gEhdKVkVEJGFNngwfbz8y/YYbonLUrsblbbhizjmyA/bATlGobdHjk8Ux+fm+3z/7dg6AmsJMXnVnOWQVGiUwavcl+9bM7GYmK5eSVRERSVjhPFsr039WB6re+v2kM0a/m8KWbbvnnCOwxtZazXGGCA/3xCdQOSdur92iMTrP53vHcWjLsO9z6OTL0+6Fml4hmRBtbiZbNkYuZSYrk5JVERFJWGkBe/o7b+TktOuNB2x/+AOeteRlps05R6CwgHY3E4D2RpWvWomSB+0WDZNdPu/YUJE9ZJXeOX0fc9shu4f5ZbeajSUzO2DJyqVkVUREElZRpT0ZXuq2Qzg4dT100n4C7szZPu8cXo+HFo+ttdrddGSe0bIcMkdtO1x/fuX8Y9ddiWscysdOQP/psmYjdS8A0JKxBY9n9gN3svIoWRURkYRVVb2OIeMj2QnTc+p029XCPtvByFc59xaASd2+UgCG2k4sfpByboyhINwBQGZx9bzDL960gedDVQAMHfjp1PWs7omuVmVzH7iTlUfJqoiIJKw0v48D2LarrS/9NwCh/nbK3VYA1my/Oqp5RjPs52XTU7/oMco5GukhjTEAisrmb5FalZ/Bi377Q0rvKz+xF4e7KAra1dniDbM3iJCVScmqiIgktBPl7wIg59CPwRgaDjwBwOFwCRur1kQ1h5NrPy/7B0/FJ0hZsIF2u9rd5mZSEWWLVGfD2wEo6ngBxgcZqbdbAA6FirlofU18ApW4UbIqIiIJ7YJrbmHA9RMIt9D7xmP4nvs7AI6kXYDXE90/5lIKbVWBnDHVWl1pupqOAdBkom+Reukll3MsXEgyIYJHfkXbwWcAeN1TSyA7NW6xSnwoWRURkYS2paqcx5Ivt7958FbKh16n301h7LJPRT1HXqmttVoc7gBj4hHm6mXMOf13OtheD0B3cmHUz1xSWcCvzIUADDz1D2QdewiAntz5D9zJyqNkVUREEp674/8AkBPqAuCe9Jv4vSujO1wFUFJuV1ZTnXHG+9sXHsjRRxm9+1rcE79e+Bznk7EBzL/8FvzjLhgfWtAUoW5blmwodfY2q2fzeBwGKq8BIK/jJfJGGxg3XpyaqxYUgywvJasiIpLw3vqWd/BG2CYzL4SqefsH/hLHib48UWFOFi2urb3ZPvHZOSbGEHz673F/9B5Sml/g5EN3xT7H+cYYQg/8CU7TS9B5hNEDP1nQNJ4BW34qnDl/jdUzbbrkOl4NldLnpvC3w29hU/cX2bp914JikOWlZFVERBJedpqfX1T8KT8f38wrO7/KupLcmJ53HIc2TwEAvS2xl68afOKvSX7sL/FgP3eX970MY/0xz3M+MU//LUmH/2fq9z3P/2BB86SN2FP83tzoDstNesumct4WvpO8rm/ys/KP8/e3vpvdVQULikGWV3Q7lUVERFa4j97yxxxofi9vq4zuxPjZ+nzFMH6ckc762J997vtkAF8Zu4F3Jz3Hem87bfsepvjS9y0oloTX24B5/C4c4GvD1/K5tEcp6nwRBlogM/rP+QC5wTYA0ovmr7F6pjRfEi/f/g5GxsNUF2TE9KysLFpZFRGR80KqL4ldVQUxff4/00iabQwQ7mmM6Tkz1ElZyJa8etMffI59qXavbPf+hX32Ph90HXoKDy4vBdfQuft2ng7W4sWl/6UfxTZRaJR80wdAXqA25jhKslKVqJ4HlKyKiIgAJsvuiUyOsdZq02tPAnAwHGD3pvWw/m0ABNqfBje8qDEmivajLwFQl7KRb/7ORTyT8RYARvfGlqyOdzcAMGj8lAfKFjdISRhKVkVERADfRN/5jNG2mJ7rPmRP/h9L2YIvycuOPW+nx00lx/QzfOK5RY8zESS129am44VbcByHgl3vY8wkUTR8DNpei3qeyRqrjW4ehZkpcYlVVj4lqyIiIkDmxJ7I/HBspatSW38DwGjgEgDWB/J42rMDgMYX/nvxAkwUxlA8dASAtDUXA3Djrm08EdwAQNOrj0U9VV9rHQAd3sIFb++QxKdkVUREBCgos3siC+jHjA9H91BwhMrRw/a5TbaGp+M49Jbbz97+hqcWP9AVzvQ2kGUGCRoPVRttspqf4acneyMAvXV7o55rtKsegH5/8aLHKYlDyaqIiAhQVlzKgOsHoGdiRW8+PcdewEeYlnAWO7ZdOHW9astlABSON666jlidx+x+1dfDpWwpPyPJLN4KQFr3oajn8vTahgCjGRWLF6AkHCWrIiIigN+XRDO27FVn09Gonml+7QkADiRtIDf99J7KqrVbCBkP6YwR7G1a/GBXsO7jNlmt99XiT/ZOXc+uugiAwFhd1AfPUobsYTdPjDVW5fyiZFVERGRCV1IRcLof/XycxucB6C24eNr1srwc6l1bgL617sDiBZgIWu3hqsHcLdMu16zbzrBJJoVxwp3R/TCQM9YKQFpR7GWr5PyhZFVERGTCUGoJAMGJkklzMobSgdcByFh7xbRbHo9Dc5IttdTT+MbiBrnC5Q/YPbwpFRdOu76uJIfXwrY8WNvR38w/UWiMArcbgLzSdYsbpCQUJasiIiITghk2wXT656+1GuprJocBwsZh/dbdM+73p9tSWMH2I4sb5Eo21EGB24VrHEo3XDLtltfj4VRKDQB99S/PO1WopwGPYxgyPspLtQ1gNVOyKiIiMmGy/3zqcMu8Y5uP2oTrmFtETUnhjPvhPPvp2td3YhEjXNl6T9gV0yPhIrZVlc+4P5K7CQBP++vzztXZaJP8k24+JdlpixilJBolqyIiIhPSCqqA0/3o59Jzcj8Ap3xVeDwza4CmldhSTXkjUWwpiMZY/4qvLNB6fB8AdUmVZKYkz7jvL78AgILB+Vebe1tsQ4B2b3HE/35l9VCyKiIiMiG31H6mLnI7wbhzjnVb7ergYPb6iPcLKm2pppJwG4TGzikuc/xJzP9TxfjPPnNO80TUdQz6F6diwUj7cQBGMysj3i9dtxOAfLcbhrvmnGus065I96eULkpskriUrIqIiEwIlNUSMh58TpjRnrkTuMx+e6LdU7wp4v3qyloGXD9exzDYeuyc4mr92V04JkzS3rsxrYtYXaB5H+YfdsLfbsZ8Zze8ePc5Tefrt6vIJqcq4v0tVeUcD9sqCf3z7Ft1+uxc41mqsbraKVkVERGZkJeZRoPJA6Ctfo59lW6YsqBNpvKrL4w4JCfdz3FsdYHWulcXHJNpPUCgx+4F9WDofPD2Bc91toZnf4yD3VrgdB7C/flfwEj3gufLGrUJvr+oJuL97FQfRzxVALQfm7siQNpEjVVvbtWC45Hzg5JVERGRCY7j0JxkDwb1NM6erI62HyeVcUZMMjXrts86rsNnVwUHmg4uOKamR/8OgKeDtYwbL4VtTxM+9tiC5zuTOfEkAJ8Y/H2OhIrwYOg99OsFTuZSHLZ7fXMDkbdGAPRk2nvjTXMn8HkT+4YziiMnvrJ6KFkVERE5w+mSU7MXrm+aqBN6xJRSnJ0+67jhrGoATNcCtwEMd1FY9xMAnqj4KN8PXQ1A10+/uLD5zjTaS/mIbX165Ts+zP5ku8e27bXHFzSd29eMjxBB46F0zdrZB060Xc3onaPt6vgQeaYPgIKyDQuKR84fSlZFRETO4ObaRMvXe3zWMf0NdlWw1V+N48x+Ut1TYIvZpw3ULSiWzqf/BT/jvBys4L03vBcu+zMA8vteh+Dwguac1HfwCbwYDoWKueLCCxkpvRSA1ObnFzRfV5NtBnDSzac8L2vWcXk1E21Xx09CeDzimNEO+99Xj5vKmlIdsFrtlKyKiIicISUwUXJqdPaSU54O25VqJHfuVb+sMnv4qmhs/iYDkXS+bj/3v5h7HetLsnnvVZfS5mbixdB38pUFzTmp/dVHANjv205xVioFm98MQNnoUVsmK0bdp2w5qlZPMUne2dOLdWu30OumkkyYYFvk7REdpyYSX1NAXrov5ljk/KJkVURE5AxFVfYzdSDcPuvKX86gXXX1lW6Zc66SajtXHv2Ykd6YY8kfsAngms2X2T833c8RxzYuaD3yUszznSmj6RkARsptq9idW7dxPFyAF8PAkadjnm+ybFXvPKWmqgsyed2daLt6JPIhq/5WO1dnUsmcK9eyOihZFREROUN15VoGXD9Jjkt/c4R9q6ExykLNABTXRK4EMDVXoJgONwOAnpbZtxVEYoa6KDT2ZH7ZGa1LOzPsAaXRU/tjmm+a/mYCwUbCxqF8x7UAFGelst+7GYDW12I/wOX01gMwnjl3a1SPx6El1Xb3GmjYF3FMsMtuAxhM1RYAUbIqIiIyTWaqj7o5Sk71ndxPkuPS7aaxrnbjnHP5krw0Y1uxdp6av2vTmSZLOx0PF7CxomzqultkV3NTuxdeYaD91V8AsDdcyZ7N66auDxTvAiD51HMxz5k6UWrKk1c179jRfJsUJ3VErriQNFFjNZQ1d+Irq4OSVRERkbN0+GcvOdX8hv1E/ppTS1ba/Pspu3w28R1si21ltfO4TVbrkqrwJ3unrmdXXwxA6VjdvF22ZtN+xCajdWlbyfCfbouau+lqAMqHD8V8gCt/3K42Z5Ssm2ckpFXsAKBw6FjEFrJFQ3ZF2yma+4cBWR2UrIqIiJxlsuQUXTO3AYyffBGAzpxt0c2VbldF3e76mGIItdhOVX3Z0w9x1azfwZhJIoMRgl2xzTnJ021LaSUVT08GL9p2IafCOSQRZrh+7qL904wPkT9ZamrN/Alm+fqLCRuHHNMPg63Tbw53UTRRrzWn5pIIT8tqo2RVRETkLJ4Cuy80faB+xr28XptEeit2RjdZtv2UnTQQW0WArD57It5bsnXa9arCXA66AQCaD70Q05yT8kbsZ/a0wPRWsRV5GRzz2FXlhqOR95NGMtx+AoAuN53qKEpNbako4XC4GICeE9OT4sE6e3DscKiIHbVVUccg5y8lqyIiImfJLp8oOTU+PcE0wz1UhG1L0fItV0Y1l7/ArtJmjTZHH0A4eLqda830pNjjcWjy21qwfSdfjn7OScERisKdABRWbp1xuzfNxjvWEv2e2I5GW+C/wRSSnTr/1oh0fxInkqoA6Dy+d9q9tsPPAnDIW0t+hj/qGOT8pWRVRETkLKU19hN/Hv24Qz1T11sO2nJPJ8IFbK2tjWqurIDdw1kUbou4PzOS4eaD+AjR76awfv3M8lgj+TaZ9rTP3hJ21rlbD+NxDD1uKrWVVTPuB/NsvL6e6LtuDbTY7RKdE/tzo9GXZbc3hJunH2ILn7IJeG/uzERaViclqyIiImdZU1zEKTcHgLaTp5OpzsM2WT3q2zDt0NNcStbY5C+DUdyh7qieaT5i98UepDxiO9eUsgsAKBiMrcIAQGud3cZwnAC56Skz7qeV2pP6eSPRd92aLDU1lFYe9TOm1B4UC/T8Btzw1PX8PttwwVdxcdRzyflNyaqIiMhZkrwe6ib2bvYd+vXUdW+L/WQ9VHhB1HOV5efR7GYDpzszzWeoYT8AbalrI94PrLcHj0rcDsxIT8QxsxmcqHAwWfHgbEXV2wEodjthfDCqOZP7TwLg5lRFHUfx1jfT46aS7fbhNkzsvR1oJd/tsvVfN+yOei45vylZFRERieBEwdUApB950F4whtJBu+qXXn1p1PMkeT20OLbWanekJgMRJHfZPydYuDni/U3VlTSHbQLc1RhbvVXTaWMYyayOeH9tZSXtE40MBiOU7ooke8Tu4/UXRrc1AuBN68t4NGy3W7T95n4Aeo/bpPVguIQLaiIn07L6KFkVERGJYM3l7ydoPFSMHSfYdoixjhPkMsC48bJu22UxzdXjt6f3J0/Nz6dg2H5Wz6iIvIKb5kvilMfuD+1siC1ZTR+sB8BbuD7i/dw0P8exJ/rbTrwy/4TGPV1qqnT+GquT/MlemorfDEDSsUcA6Jio/3okaS1ZqcmzPiuri5JVERGRCK7ctpEnXXvIp/7X99Dx1HcBOGDWUF1SENNco+l2L6fbUz/vWDPaT9Fkm9XaHbOO606x9VuHW6NbrbWTG4rHGwHIKo+8agvQmVIJwFDzG/NO6fa14CdIyHgorYg+WQUou+idjBsvhWON0HkEmvcDMJCnw1VympJVERGRCJK8Hporrgeg5PC9lL5+NwBPFr4Px3FimyzH1lr1DzTNO7S30SaIbW4mNRWzH1gay7QJJT3RrdYCmME2MhnBNQ5l1TOrDEwazbF7ZT0RmiKcravJ7sM96eZRkZ8VdSwA1164nieCtirAyH9/jOo+e7AspTLKGrayKihZFRERmcWGN72PEZNMptuPB8MPg1fwnpv+NOZ5UgprAMgem7/Walu9Pa1f75SS5kuadZw33+4PTR9siDqOjvrX7Nxu3pyrw76JzlbZQ/NXBOhushUJWjzFJHljSyty0/wczLkcgNTWl0gizP83egkVW94U0zxyflOyKiIiMovd66t4zOwAbEelzBv+morcmaWk5pM7sZezONw+b63V4Yli/F2plXOOyyy1K5IF49E3G+hqsMnqKW8ZyXMklnmV9uBTSagZwsE55xxpPw5Ab8r8nasiydh+I8MmmUHj50P9N/PfVV/g0urCBc0l5yclqyIiIrNwHIf6HZ/mn0cu497ar/I7l8zf9z6SQPlawsYhxQkS7G+dc6x34tP7eM7cJ+uLK+2e03z6MKN9UcUx1mo/2femzZ0I19RsZND4SSbMeMfczQGciX2445lroorhbNftupCL+r/Ipr672PGOj/PfH7kKjyfGbRZyXotbsvqVr3yFyy67jLS0NHJycqJ6xhjDF7/4RQKBAKmpqVxzzTUcPRrDxnEREZFF9tF3Xce2j/4bX/rA7y94jpLcLJrcXAA6Gg7NOTZ7qB44/Sl+NlWlAdrcTAB6m6JrDpDUa1dBQ7lzJ8KlOWkccW21gdZ5KgKkDtkDW968yKWw5lORm85/fPpmnvr8TfzZmzcqUZUZ4pasjo+P8+53v5s/+ZM/ifqZb3zjG/z93/893/3ud3nhhRdIT0/nuuuuY3R0NF5hioiIzCnJ62F3VcE5JVEej8Mpr/1M3tM4R4tUN0wgZD/r51fOfSI+JdlLo1MMQEeU5auyR04B4C/eMOc4x3Fo9dmV0v7G1+YcmzfeAkB6SeQGBtHYXpZLdUHGgp+X81vcktW/+qu/4pOf/CTbtm2Larwxhm9961t84Qtf4IYbbmD79u388Ic/pLm5mQcffDBeYYqIiCyJnjSb/I22zt7FaqyzDr8TYsQkU1U9/5aDLr+tFjDUGsXKqhuiOGS3IORXzD/3ULbdZ2va50iEg8MUmF4ACqOYU2QhVsye1bq6OlpbW7nmmmumrmVnZ7N7926ee+65WZ8bGxujv79/2i8REZGVJphrVx6Te2bfA9oy8cn9uFtMUfb8B7lGM2wCbLrnL1813t2AzwkzapJYUxm5IcCZPMWbAMgamD3e4Tb75/a4qVSWls07p8hCrJhktbXV/rRXXFw87XpxcfHUvUi+9rWvkZ2dPfWrokLt2UREZOVJLbErjznDJ2cd03fK1lht9ZVHVcvVk29LYqUOzD7npPZ6u/2gzi0kkDN/IpxfZbtnBYKnwA1FHNPRaPff1psictJ8884pshAxJau33347juPM+evQobk3ji+2z33uc/T19U39amxsXNI/X0REJBqTe1AD4dZZy0GF2+0WgaHMmqjmzAjYvaf541E0G2i2c7cmlUaVCNfUbmbI+PARIjhLRYD+FnsIujM5EFW8Igsxe7XhCD796U/zwQ9+cM4xNTXR/QU7W0mJPXXY1tZGIHD6f/RtbW3s2LFj1uf8fj9+v39Bf6aIiMhSqa5az5Dxke6MM9x+nLTAzD2eaf32s7pTMP9neoDCNbZ8VZHpgfEh8M2+Yhpst4nlQFp0XyAr8jLY5wa4yHuS1mP7qIhQnSDUZeMdSp+905bIuYopWS0sLKSwMD6FequrqykpKeGxxx6bSk77+/t54YUXYqooICIishLlZ6ZywBSzzWmk5cSr1EZIVovG7NfBzPLNUc1ZVV5Gl5tOvmeIvpYjZFdeOOvYpL56AMK50ZWYchyHZn8VF4VO0tf4KhX8wYwxyf22e5abPXfdVpFzEbc9qw0NDezfv5+GhgbC4TD79+9n//79DA4OTo3ZuHEjDzzwAGD/UnziE5/gy1/+Mg899BAHDhzgAx/4AKWlpdx4443xClNERGTJtE2UgxqY2Jt6JjPQSh79uMahtCa6SjoZ/mROUgRAR/0cJbGAnBGbCPuL1kUd7/BERQDaI2/xyx2xyaqvcO66rSLnIqaV1Vh88Ytf5Ac/+MHU7y+80P6098QTT3D11VcDcPjwYfr6Tnfd+MxnPsPQ0BC33norvb29XHHFFTzyyCOkpKTEK0wREZElM5xZDT3P4HbOLDXVcvAZSoFDbgnrSkuinrPdXwHBOoaaZybAU9ywLVvlQF7FpqjnTireDF2QPRChQc9oH2VhWxM2s+qiqOcUiVXcktV77rmHe+65Z84x5qz+yI7jcOedd3LnnXfGKywREZFl4xSugx5IG6ibca/r6POUAnX+9Wz2Rv/hczirFrqegggJ8KTx7pP4nDBjJok1a6JfWc2vvgDegJJQM4THwXv6xP9g/V4ygPpwHlsXeF5FJBorpnSViIjI+S6zbAsAxWMzK9ckte4HYCh/e0xzeovs3teMCAnwpMmyVSfcQgK50XeKWlu7iX43hWTCjLdNT4ZbDtsa6Ac9teRn6KCzxI+SVRERkSVSNrEXNZcB3MGu0zeMITBkO0WlV++Kac7cNRMlsYKNYNyIY2ItWzWpNCeNw8ZW6Gk9vm/avdCplwHozo5+W4HIQihZFRERWSJVgSIaw7kAdDQcmLoe6qonxwwwbrzUbr00pjnX1GwhaDykMUaoJ3Kt8VjLVk1yHIfWFFs9oL/xwLR7Ob12tdZbNnsFApHFoGRVRERkiSR7PTR6bVvSrrpXp643HXwagNfcctYHYisRuaYgh2Ou7f7YNtGu9Wyxlq0601CObTyQ0rr39MXRXgKhFgACG2JLrkVipWRVRERkCTVl2BqqSXWPTV3rO/4CAKdSN+DxRP+ZHsDjcWhOtiumPQ2vRRyzkLJVk0LVbwGgamAfjPYCMFD3GwDqwvlsW6uyVRJfSlZFRESWUGj9OwGo7HoGxm3t8ZR2uyI6VrRjQXP2Z9gV01CkeqjBkalV0Mn9rbHYs3MPb4RKSCLM4Gs/B6D18PMAHPTUkJeuw1USX0pWRUREltCbrngrx8MF+AnS9crPwA1TNmJP2mev3b2wSQvsp/rUvuMzbg017CfJcWl1s6itjq6N65lqCzN51mcPfXXuvR84fbiqJzu6Tlsi50LJqoiIyBIqy03nuZTLAOh+6T8Yq3uWdEYZMj42bNm5oDkzy21JrKLRkzPuNR98BoDXqaYoK3VB84fXX2/nb/tfCI2RO3G4Kqlch6sk/pSsioiILDHP5hsAKO94muB//iEAPw9fxJr87AXNV1pra7PmMoAZ6px2b6zRHozqzFr4KujOS6+hOZxNmhkh/MMbKAm3Mm68lGzYs+A5RaKlZFVERGSJXXbFdTSEc0lllIyxdt4IlXDy0jtjqoF6ptpAMSfDeQB01r867V52j10F9ZTtWHC8F60p4DFsS1Vv43O4xuETw+/jgrXqXCXxp2RVRERkiVUVZPK/Prsq2eum8k+lX+KTb4+tGcCZ/MleTk6UxOqsP6Me6vggpcEGAIrXL7zElOM49FW9zU5pvNw08Ifs+t1Pk5Pmm+dJkXOXtNwBiIiIrEYDF3+Me57q5omM6/jOH/5+zCWrztadVgPDB3CbTtdD7a/fSxaGpnA2WzecW6epLZffwB/efYCjpow/v+VmbtgeW4MBkYVSsioiIrIMPnzt5fw4/7v8zeZSMvzJ5zxfb+mVcOwnlLf9GtwweLy0HnqOLOANTw2/dY4lpq5eX0Lb+/6CPyvJ5oLy3HOOVyRa2gYgIiKyDJK9Hv7PrmryMxanTunGXdfT66aS7fYyXm/roI5PlJjqXoQSU47j8L6dVUpUZckpWRURETkP7Kot5TFzAQBNz/8YgJyJw1Xe8ouXLS6Rc6VkVURE5Dzg8Th0VVwLQEbdL6CnntJgEwAlGxZ+uEpkuSlZFREROU/UXnojIyaZwlAr43f/Fh7H8Hywim3r1i13aCILpmRVRETkPHHlpiqeCNv9qb6RdurDeXyv7A6yU1ViShKXklUREZHzhC/Jy8mS3wKg3c3gz9P/kr/70DuXOSqRc6PSVSIiIueRqqs+yIe+30ZT9g5+dNv7yUw597JYIstJyaqIiMh55O1bK8j9+JfYEshWoirnBSWrIiIi55lLqwuWOwSRRaM9qyIiIiKyYilZFREREZEVS8mqiIiIiKxYSlZFREREZMVSsioiIiIiK5aSVRERERFZsZSsioiIiMiKpWRVRERERFYsJasiIiIismIpWRURERGRFUvJqoiIiIisWEpWRURERGTFUrIqIiIiIiuWklURERERWbGUrIqIiIjIiqVkVURERERWLCWrIiIiIrJiKVkVERERkRVLyaqIiIiIrFhKVkVERERkxVKyKiIiIiIrlpJVEREREVmxlKyKiIiIyIqlZFVEREREVqyk5Q5gsRljAOjv71/mSEREREQkksk8bTJvm8t5l6wODAwAUFFRscyRiIiIiMhcBgYGyM7OnnOMY6JJaROI67o0NzeTmZmJ4zhL8mf29/dTUVFBY2MjWVlZS/JnyuLR+0t8eoeJT+8wsen9Jb6lfofGGAYGBigtLcXjmXtX6nm3surxeCgvL1+WPzsrK0t/SROY3l/i0ztMfHqHiU3vL/Et5Tucb0V1kg5YiYiIiMiKpWRVRERERFYsJauLwO/3c8cdd+D3+5c7FFkAvb/Ep3eY+PQOE5veX+Jbye/wvDtgJSIiIiLnD62sioiIiMiKpWRVRERERFYsJasiIiIismIpWRURERGRFUvJahS+853vUFVVRUpKCrt37+bFF1+cc/x//ud/snHjRlJSUti2bRsPP/zwEkUqs4nlHd59991ceeWV5ObmkpubyzXXXDPvO5f4i/Xv4aT77rsPx3G48cYb4xugzCvWd9jb28ttt91GIBDA7/ezfv16/f/pMor1/X3rW99iw4YNpKamUlFRwSc/+UlGR0eXKFo521NPPcU73/lOSktLcRyHBx98cN5nnnzySS666CL8fj9r167lnnvuiXucERmZ03333Wd8Pp/513/9V/P666+bj3zkIyYnJ8e0tbVFHP/MM88Yr9drvvGNb5g33njDfOELXzDJycnmwIEDSxy5TIr1Hb7//e833/nOd8y+ffvMwYMHzQc/+EGTnZ1tTp06tcSRy6RY3+Gkuro6U1ZWZq688kpzww03LE2wElGs73BsbMzs3LnTXH/99ebpp582dXV15sknnzT79+9f4sjFmNjf37333mv8fr+59957TV1dnfnFL35hAoGA+eQnP7nEkcukhx9+2Hz+8583999/vwHMAw88MOf4EydOmLS0NPOpT33KvPHGG+bb3/628Xq95pFHHlmagM+gZHUeu3btMrfddtvU78PhsCktLTVf+9rXIo5/z3veY377t3972rXdu3ebP/7jP45rnDK7WN/h2UKhkMnMzDQ/+MEP4hWizGMh7zAUCpnLLrvM/PM//7O55ZZblKwus1jf4T/90z+ZmpoaMz4+vlQhyhxifX+33Xabectb3jLt2qc+9Slz+eWXxzVOiU40yepnPvMZs2XLlmnX3vve95rrrrsujpFFpm0AcxgfH2fv3r1cc801U9c8Hg/XXHMNzz33XMRnnnvuuWnjAa677rpZx0t8LeQdnm14eJhgMEheXl68wpQ5LPQd3nnnnRQVFfHhD394KcKUOSzkHT700EPs2bOH2267jeLiYrZu3cpXv/pVwuHwUoUtExby/i677DL27t07tVXgxIkTPPzww1x//fVLErOcu5WUzyQt+Z+YQDo7OwmHwxQXF0+7XlxczKFDhyI+09raGnF8a2tr3OKU2S3kHZ7ts5/9LKWlpTP+0srSWMg7fPrpp/mXf/kX9u/fvwQRynwW8g5PnDjB448/zk033cTDDz/MsWPH+NjHPkYwGOSOO+5YirBlwkLe3/vf/346Ozu54oorMMYQCoX46Ec/yv/9v/93KUKWRTBbPtPf38/IyAipqalLFotWVkXm8PWvf5377ruPBx54gJSUlOUOR6IwMDDAzTffzN13301BQcFyhyML5LouRUVFfO973+Piiy/mve99L5///Of57ne/u9yhSRSefPJJvvrVr/KP//iPvPzyy9x///387Gc/46677lru0CQBaWV1DgUFBXi9Xtra2qZdb2tro6SkJOIzJSUlMY2X+FrIO5z0zW9+k69//ev86le/Yvv27fEMU+YQ6zs8fvw49fX1vPOd75y65rouAElJSRw+fJja2tr4Bi3TLOTvYSAQIDk5Ga/XO3Vt06ZNtLa2Mj4+js/ni2vMctpC3t9f/uVfcvPNN/NHf/RHAGzbto2hoSFuvfVWPv/5z+PxaK1spZstn8nKylrSVVXQyuqcfD4fF198MY899tjUNdd1eeyxx9izZ0/EZ/bs2TNtPMAvf/nLWcdLfC3kHQJ84xvf4K677uKRRx5h586dSxGqzCLWd7hx40YOHDjA/v37p369613v4s1vfjP79++noqJiKcMXFvb38PLLL+fYsWNTP2gAHDlyhEAgoER1iS3k/Q0PD89ISCd/8DDGxC9YWTQrKp9Z8iNdCea+++4zfr/f3HPPPeaNN94wt956q8nJyTGtra3GGGNuvvlmc/vtt0+Nf+aZZ0xSUpL55je/aQ4ePGjuuOMOla5aZrG+w69//evG5/OZ//qv/zItLS1TvwYGBpbrP8KqF+s7PJuqASy/WN9hQ0ODyczMNB//+MfN4cOHzU9/+lNTVFRkvvzlLy/Xf4RVLdb3d8cdd5jMzEzz7//+7+bEiRPm0UcfNbW1teY973nPcv1HWPUGBgbMvn37zL59+wxg/uZv/sbs27fPnDx50hhjzO23325uvvnmqfGTpav+4i/+whw8eNB85zvfUemqlezb3/62WbNmjfH5fGbXrl3m+eefn7p31VVXmVtuuWXa+P/4j/8w69evNz6fz2zZssX87Gc/W+KI5WyxvMPKykoDzPh1xx13LH3gMiXWv4dnUrK6MsT6Dp999lmze/du4/f7TU1NjfnKV75iQqHQEkctk2J5f8Fg0HzpS18ytbW1JiUlxVRUVJiPfexjpqenZ+kDF2OMMU888UTEf7ZNvrdbbrnFXHXVVTOe2bFjh/H5fKampsZ8//vfX/K4jTHGMUbr8SIiIiKyMmnPqoiIiIisWEpWRURERGTFUrIqIiIiIiuWklURERERWbGUrIqIiIjIiqVkVURERERWLCWrIiIiIrJiKVkVERERkRVLyaqIiIiIrFhKVkVERERkxVKyKiIiIiIrlpJVEREREVmx/n+bjel3QFVMrwAAAABJRU5ErkJggg==",
|
|
"text/plain": [
|
|
"<Figure size 800x800 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"#plot solution obtained\n",
|
|
"plot_solution(multiscale_pinn, 'Multiscale PINN solution')\n",
|
|
"\n",
|
|
"# sample new test points\n",
|
|
"pts = pts = problem.spatial_domain.sample(100, 'grid')\n",
|
|
"print(f'Relative l2 error PINN with MultiscaleFourierNet: {l2_loss(multiscale_pinn(pts), problem.truth_solution(pts)).item():.2%}')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"It is pretty clear that the network has learned the correct solution, with also a very low error. Obviously a longer training and a more expressive neural network could improve the results!\n",
|
|
"\n",
|
|
"## What's next?\n",
|
|
"\n",
|
|
"Congratulations on completing the one dimensional Poisson tutorial of **PINA** using `FourierFeatureEmbedding`! 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. Understand the role of `sigma` in `FourierFeatureEmbedding` (see original paper for a nice reference)\n",
|
|
"\n",
|
|
"3. Code the *Spatio-temporal multi-scale Fourier feature architecture* for a more complex time dependent PDE (section 3 of the original reference)\n",
|
|
"\n",
|
|
"4. Many more..."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"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": "3.12.7"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|