From 4cfd90b9044f1163ba100d8b3c3308a631c7ff34 Mon Sep 17 00:00:00 2001 From: Dario Coscia <93731561+dario-coscia@users.noreply.github.com> Date: Fri, 1 Mar 2024 18:15:45 +0100 Subject: [PATCH] PBC Layer (#252) * update docs/tests * tutorial and device fix --------- Co-authored-by: Dario Coscia Co-authored-by: Dario Coscia Co-authored-by: Dario Coscia Co-authored-by: Dario Coscia --- docs/source/_rst/_code.rst | 1 + docs/source/_rst/_tutorial.rst | 2 +- docs/source/_rst/layers/embedding.rst | 8 + docs/source/_rst/layers/pod.rst | 15 + .../_rst/tutorials/tutorial9/tutorial.rst | 226 +++++++++++++ .../tutorial_files/tutorial_11_0.png | Bin 0 -> 60120 bytes .../tutorial_files/tutorial_13_0.png | Bin 0 -> 91832 bytes pina/model/layers/__init__.py | 2 + pina/model/layers/embedding.py | 142 +++++++++ tests/test_layers/test_embedding.py | 99 ++++++ tutorials/README.md | 1 + tutorials/tutorial9/tutorial.ipynb | 298 ++++++++++++++++++ tutorials/tutorial9/tutorial.py | 191 +++++++++++ 13 files changed, 984 insertions(+), 1 deletion(-) create mode 100644 docs/source/_rst/layers/embedding.rst create mode 100644 docs/source/_rst/layers/pod.rst create mode 100644 docs/source/_rst/tutorials/tutorial9/tutorial.rst create mode 100644 docs/source/_rst/tutorials/tutorial9/tutorial_files/tutorial_11_0.png create mode 100644 docs/source/_rst/tutorials/tutorial9/tutorial_files/tutorial_13_0.png create mode 100644 pina/model/layers/embedding.py create mode 100644 tests/test_layers/test_embedding.py create mode 100644 tutorials/tutorial9/tutorial.ipynb create mode 100644 tutorials/tutorial9/tutorial.py diff --git a/docs/source/_rst/_code.rst b/docs/source/_rst/_code.rst index 4156279..a5d955f 100644 --- a/docs/source/_rst/_code.rst +++ b/docs/source/_rst/_code.rst @@ -68,6 +68,7 @@ Layers Spectral convolution Fourier layers Continuous convolution + Coordinates embeddings Equations and Operators diff --git a/docs/source/_rst/_tutorial.rst b/docs/source/_rst/_tutorial.rst index 0612e9b..5bed177 100644 --- a/docs/source/_rst/_tutorial.rst +++ b/docs/source/_rst/_tutorial.rst @@ -21,7 +21,7 @@ Physics Informed Neural Networks Two dimensional Poisson problem using Extra Features Learning Two dimensional Wave problem with hard constraint Resolution of a 2D Poisson inverse problem - + Periodic Boundary Conditions for Helmotz Equation Neural Operator Learning ------------------------ diff --git a/docs/source/_rst/layers/embedding.rst b/docs/source/_rst/layers/embedding.rst new file mode 100644 index 0000000..7ca2845 --- /dev/null +++ b/docs/source/_rst/layers/embedding.rst @@ -0,0 +1,8 @@ +Coordinates embeddings +====================== +.. currentmodule:: pina.model.layers.embedding + +.. autoclass:: PBCEmbedding + :members: + :show-inheritance: + diff --git a/docs/source/_rst/layers/pod.rst b/docs/source/_rst/layers/pod.rst new file mode 100644 index 0000000..5635ba2 --- /dev/null +++ b/docs/source/_rst/layers/pod.rst @@ -0,0 +1,15 @@ +Spectral Convolution +====================== +.. currentmodule:: pina.model.layers.spectral + +.. autoclass:: SpectralConvBlock1D + :members: + :show-inheritance: + +.. autoclass:: SpectralConvBlock2D + :members: + :show-inheritance: + +.. autoclass:: SpectralConvBlock3D + :members: + :show-inheritance: \ No newline at end of file diff --git a/docs/source/_rst/tutorials/tutorial9/tutorial.rst b/docs/source/_rst/tutorials/tutorial9/tutorial.rst new file mode 100644 index 0000000..c9bb588 --- /dev/null +++ b/docs/source/_rst/tutorials/tutorial9/tutorial.rst @@ -0,0 +1,226 @@ +Tutorial: One dimensional Helmotz equation using Periodic Boundary Conditions +============================================================================= + +This tutorial presents how to solve with Physics-Informed Neural +Networks (PINNs) a one dimensional Helmotz equation with periodic +boundary conditions (PBC). We will train with standard PINN’s training +by augmenting the input with periodic expasion as presented in `An +expert’s guide to training physics-informed neural +networks `__. + +First of all, some useful imports. + +.. code:: ipython3 + + import torch + import matplotlib.pyplot as plt + + from pina import Condition, Plotter + from pina.problem import SpatialProblem + from pina.operators import laplacian + from pina.model import FeedForward + from pina.model.layers import PeriodicBoundaryEmbedding # The PBC module + from pina.solvers import PINN + from pina.trainer import Trainer + from pina.geometry import CartesianDomain + from pina.equation import Equation + +The problem definition +---------------------- + +The one-dimensional Helmotz problem is mathematically written as: + +.. math:: + + + \begin{cases} + \frac{d^2}{dx^2}u(x) - \lambda u(x) -f(x) &= 0 \quad x\in(0,2)\\ + u^{(m)}(x=0) - u^{(m)}(x=2) &= 0 \quad m\in[0, 1, \cdots]\\ + \end{cases} + +In this case we are asking the solution to be :math:`C^{\infty}` +periodic with period :math:`2`, on the inifite domain +:math:`x\in(-\infty, \infty)`. Notice that the classical PINN would need +inifinite conditions to evaluate the PBC loss function, one for each +derivative, which is of course infeasable… A possible solution, +diverging from the original PINN formulation, is to use *coordinates +augmentation*. In coordinates augmentation you seek for a coordinates +transformation :math:`v` such that :math:`x\rightarrow v(x)` such that +the periodicity condition $ u^{(m)}(x=0) - u^{(m)}(x=2) = 0 +:raw-latex:`\quad `m:raw-latex:`\in[0, 1, \cdots] `$ is satisfied. + +For demonstration porpuses the problem specifics are +:math:`\lambda=-10\pi^2`, and +:math:`f(x)=-6\pi^2\sin(3\pi x)\cos(\pi x)` which gives a solution that +can be computed analytically :math:`u(x) = \sin(\pi x)\cos(3\pi x)`. + +.. code:: ipython3 + + class Helmotz(SpatialProblem): + output_variables = ['u'] + spatial_domain = CartesianDomain({'x': [0, 2]}) + + def helmotz_equation(input_, output_): + x = input_.extract('x') + u_xx = laplacian(output_, input_, components=['u'], d=['x']) + f = - 6.*torch.pi**2 * torch.sin(3*torch.pi*x)*torch.cos(torch.pi*x) + lambda_ = - 10. * torch.pi ** 2 + return u_xx - lambda_ * output_ - f + + # here we write the problem conditions + conditions = { + 'D': Condition(location=spatial_domain, + equation=Equation(helmotz_equation)), + } + + def helmotz_sol(self, pts): + return torch.sin(torch.pi * pts) * torch.cos(3. * torch.pi * pts) + + truth_solution = helmotz_sol + + problem = Helmotz() + + # let's discretise the domain + problem.discretise_domain(200, 'grid', locations=['D']) + +As usual the Helmotz problem is written in **PINA** code as a class. The +equations are written as ``conditions`` that should be satisfied in the +corresponding domains. The ``truth_solution`` is the exact solution +which will be compared with the predicted one. We used latin hypercube +sampling for choosing the collocation points. + +Solving the problem with a Periodic Network +------------------------------------------- + +Any :math:`\mathcal{C}^{\infty}` periodic function +:math:`u : \mathbb{R} \rightarrow \mathbb{R}` with period +:math:`L\in\mathbb{N}` can be constructed by composition of an arbitrary +smooth function :math:`f : \mathbb{R}^n \rightarrow \mathbb{R}` and a +given smooth periodic function +:math:`v : \mathbb{R} \rightarrow \mathbb{R}^n` with period :math:`L`, +that is :math:`u(x) = f(v(x))`. The formulation is generalizable for +arbitrary dimension, see `A method for representing periodic functions +and enforcing exactly periodic boundary conditions with deep neural +networks `__. + +In our case, we rewrite +:math:`v(x) = \left[1, \cos\left(\frac{2\pi}{L} x\right), \sin\left(\frac{2\pi}{L} x\right)\right]`, +i.e the coordinates augmentation, and +:math:`f(\cdot) = NN_{\theta}(\cdot)` i.e. a neural network. The +resulting neural network obtained by composing :math:`f` with :math:`v` +gives the PINN approximate solution, that is +:math:`u(x) \approx u_{\theta}(x)=NN_{\theta}(v(x))`. + +In **PINA** this translates in using the ``PeriodicBoundaryEmbedding`` layer for +:math:`v`, and any ``pina.model`` for :math:`NN_{\theta}`. Let’s see it +in action! + +.. code:: ipython3 + + # we encapsulate all modules in a torch.nn.Sequential container + model = torch.nn.Sequential(PeriodicBoundaryEmbedding(input_dimension=1, + periods=2), + FeedForward(input_dimensions=3, # output of PeriodicBoundaryEmbedding = 3 * input_dimension + output_dimensions=1, + layers=[10, 10])) + +As simple as that! Notice in higher dimension you can specify different +periods for all dimensions using a dictionary, +e.g. ``periods={'x':2, 'y':3, ...}`` would indicate a periodicity of +:math:`2` in :math:`x`, :math:`3` in :math:`y`, and so on… + +We will now sole the problem as usually with the ``PINN`` and +``Trainer`` class. + +.. code:: ipython3 + + pinn = PINN(problem=problem, model=model) + trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional) + trainer.train() + + +.. parsed-literal:: + + GPU available: True (mps), used: False + TPU available: False, using: 0 TPU cores + IPU available: False, using: 0 IPUs + HPU available: False, using: 0 HPUs + +.. parsed-literal:: + + `Trainer.fit` stopped: `max_epochs=5000` reached. + + +.. parsed-literal:: + + Epoch 4999: 100%|██████████| 1/1 [00:00<00:00, 155.47it/s, v_num=20, D_loss=0.0123, mean_loss=0.0123] + + +We are going to plot the solution now! + +.. code:: ipython3 + + pl = Plotter() + pl.plot(pinn) + + + +.. image:: tutorial_files/tutorial_11_0.png + + +Great, they overlap perfectly! This seeams a good result, considering +the simple neural network used to some this (complex) problem. We will +now test the neural network on the domain :math:`[-4, 4]` without +retraining. In principle the periodicity should be present since the +:math:`v` function ensures the periodicity in :math:`(-\infty, \infty)`. + +.. code:: ipython3 + + # plotting solution + with torch.no_grad(): + # Notice here we put [-4, 4]!!! + new_domain = CartesianDomain({'x' : [0, 4]}) + x = new_domain.sample(1000, mode='grid') + fig, axes = plt.subplots(1, 3, figsize=(15, 5)) + # Plot 1 + axes[0].plot(x, problem.truth_solution(x), label=r'$u(x)$', color='blue') + axes[0].set_title(r'True solution $u(x)$') + axes[0].legend(loc="upper right") + # Plot 2 + axes[1].plot(x, pinn(x), label=r'$u_{\theta}(x)$', color='green') + axes[1].set_title(r'PINN solution $u_{\theta}(x)$') + axes[1].legend(loc="upper right") + # Plot 3 + diff = torch.abs(problem.truth_solution(x) - pinn(x)) + axes[2].plot(x, diff, label=r'$|u(x) - u_{\theta}(x)|$', color='red') + axes[2].set_title(r'Absolute difference $|u(x) - u_{\theta}(x)|$') + axes[2].legend(loc="upper right") + # Adjust layout + plt.tight_layout() + # Show the plots + plt.show() + + + +.. image:: tutorial_files/tutorial_13_0.png + + +It is pretty clear that the network is periodic, with also the error +following a periodic pattern. Obviusly a longer training, and a more +expressive neural network could improve the results! + +What’s next? +------------ + +Nice you have completed the one dimensional Helmotz tutorial of +**PINA**! There are multiple directions you can go now: + +1. Train the network for longer or with different layer sizes and assert + the finaly accuracy + +2. Apply the ``PeriodicBoundaryEmbedding`` layer for a time-dependent problem (see + reference in the documentation) + +3. Exploit extrafeature training ? + +4. 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b/pina/model/layers/__init__.py @@ -9,6 +9,7 @@ __all__ = [ "FourierBlock2D", "FourierBlock3D", "PODBlock", + "PeriodicBoundaryEmbedding" ] from .convolution_2d import ContinuousConvBlock @@ -20,3 +21,4 @@ from .spectral import ( ) from .fourier import FourierBlock1D, FourierBlock2D, FourierBlock3D from .pod import PODBlock +from .embedding import PeriodicBoundaryEmbedding diff --git a/pina/model/layers/embedding.py b/pina/model/layers/embedding.py new file mode 100644 index 0000000..fd90a27 --- /dev/null +++ b/pina/model/layers/embedding.py @@ -0,0 +1,142 @@ +""" Periodic Boundary Embedding modulus. """ + +import torch +from pina.utils import check_consistency + + +class PeriodicBoundaryEmbedding(torch.nn.Module): + r""" + Imposing hard constraint periodic boundary conditions by embedding the + input. + + A periodic function :math:`u:\mathbb{R}^{\rm{in}} + \rightarrow\mathbb{R}^{\rm{out}}` periodic in the spatial + coordinates :math:`\mathbf{x}` with periods :math:`\mathbf{L}` is such that: + + .. math:: + u(\mathbf{x}) = u(\mathbf{x} + n \mathbf{L})\;\; + \forall n\in\mathbb{N}. + + The :meth:`PeriodicBoundaryEmbedding` augments the input such that the periodic conditons + is guarantee. The input is augmented by the following formula: + + .. math:: + \mathbf{x} \rightarrow \tilde{\mathbf{x}} = \left[1, + \cos\left(\frac{2\pi}{L_1} x_1 \right), + \sin\left(\frac{2\pi}{L_1}x_1\right), \cdots, + \cos\left(\frac{2\pi}{L_{\rm{in}}}x_{\rm{in}}\right), + \sin\left(\frac{2\pi}{L_{\rm{in}}}x_{\rm{in}}\right)\right], + + where :math:`\text{dim}(\tilde{\mathbf{x}}) = 3\text{dim}(\mathbf{x})`. + + .. seealso:: + **Original reference**: + 1. Dong, Suchuan, and Naxian Ni (2021). *A method for representing + periodic functions and enforcing exactly periodic boundary + conditions with deep neural networks*. Journal of Computational + Physics 435, 110242. + DOI: `10.1016/j.jcp.2021.110242. + `_ + 2. Wang, S., Sankaran, S., Wang, H., & Perdikaris, P. (2023). *An + expert's guide to training physics-informed neural networks*. + DOI: `arXiv preprint arXiv:2308.0846. + `_ + .. warning:: + The embedding is a truncated fourier expansion, and only ensures + function PBC and not for its derivatives. Ensuring approximate + periodicity in + the derivatives of :math:`u` can be done, and extensive + tests have shown (also in the reference papers) that this implementation + can correctly compute the PBC on the derivatives up to the order + :math:`\sim 2,3`, while it is not guarantee the periodicity for + :math:`>3`. The PINA code is tested only for function PBC and not for + its derivatives. + """ + def __init__(self, input_dimension, periods, output_dimension=None): + """ + :param int input_dimension: The dimension of the input tensor, it can + be checked with `tensor.ndim` method. + :param float | int | dict periods: The periodicity in each dimension for + the input data. If ``float`` or ``int`` is passed, + the period is assumed constant for all the dimensions of the data. + If a ``dict`` is passed the `dict.values` represent periods, + while the ``dict.keys`` represent the dimension where the + periodicity is applied. The `dict.keys` can either be `int` + if working with ``torch.Tensor`` or ``str`` if + working with ``LabelTensor``. + :param int output_dimension: The dimension of the output after the + fourier embedding. If not ``None`` a ``torch.nn.Linear`` layer + is applied to the fourier embedding output to match the desired + dimensionality, default ``None``. + """ + super().__init__() + + # check input consistency + check_consistency(periods, (float, int, dict)) + check_consistency(input_dimension, int) + if output_dimension is not None: + check_consistency(output_dimension, int) + self._layer = torch.nn.Linear(input_dimension * 3, output_dimension) + else: + self._layer = torch.nn.Identity() + + # checks on the periods + if isinstance(periods, dict): + if not all(isinstance(dim, (str, int)) and + isinstance(period, (float, int)) + for dim, period in periods.items()): + raise TypeError('In dictionary periods, keys must be integers' + ' or strings, and values must be float or int.') + self._period = periods + else: + self._period = {k: periods for k in range(input_dimension)} + + + def forward(self, x): + """ + Forward pass to compute the periodic boundary conditions embedding. + + :param torch.Tensor x: Input tensor. + :return: Fourier embeddings of the input. + :rtype: torch.Tensor + """ + omega = torch.stack([torch.pi * 2. / torch.tensor([val], + device=x.device) + for val in self._period.values()], + dim=-1) + x = self._get_vars(x, list(self._period.keys())) + return self._layer(torch.cat([torch.ones_like(x), + torch.cos(omega * x), + torch.sin(omega * x)], dim=-1)) + + def _get_vars(self, x, indeces): + """ + Get variables from input tensor ordered by specific indeces. + + :param torch.Tensor x: The input tensor to extract. + :param list[int] | list[str] indeces: List of indeces to extract. + :return: The extracted tensor given the indeces. + :rtype: torch.Tensor + """ + if isinstance(indeces[0], str): + try: + return x.extract(indeces) + except AttributeError: + raise RuntimeError( + 'Not possible to extract input variables from tensor.' + ' Ensure that the passed tensor is a LabelTensor or' + ' pass list of integers to extract variables. For' + ' more information refer to warning in the documentation.') + elif isinstance(indeces[0], int): + return x[..., indeces] + else: + raise RuntimeError( + 'Not able to extract right indeces for tensor.' + ' For more information refer to warning in the documentation.') + + @property + def period(self): + """ + The period of the periodic function to approximate. + """ + return self._period diff --git a/tests/test_layers/test_embedding.py b/tests/test_layers/test_embedding.py new file mode 100644 index 0000000..d239261 --- /dev/null +++ b/tests/test_layers/test_embedding.py @@ -0,0 +1,99 @@ +import torch +import pytest + +from pina.model.layers import PeriodicBoundaryEmbedding +from pina import LabelTensor + +def check_same_columns(tensor): + # Get the first column + first_column = tensor[0] + # Compare each column with the first column + all_same = torch.allclose(tensor, first_column) + return all_same + +def grad(u, x): + """ + Compute the first derivative of u with respect to x. + """ + return torch.autograd.grad(u, x, grad_outputs=torch.ones_like(u), + create_graph=True, allow_unused=True, + retain_graph=True)[0] + +def test_constructor(): + PeriodicBoundaryEmbedding(input_dimension=1, periods=2) + PeriodicBoundaryEmbedding(input_dimension=1, periods={'x': 3, 'y' : 4}) + PeriodicBoundaryEmbedding(input_dimension=1, periods={0: 3, 1 : 4}) + PeriodicBoundaryEmbedding(input_dimension=1, periods=2, output_dimension=10) + with pytest.raises(TypeError): + PeriodicBoundaryEmbedding() + with pytest.raises(ValueError): + PeriodicBoundaryEmbedding(input_dimension=1., periods=1) + PeriodicBoundaryEmbedding(input_dimension=1, periods=1, output_dimension=1.) + PeriodicBoundaryEmbedding(input_dimension=1, periods={'x':'x'}) + PeriodicBoundaryEmbedding(input_dimension=1, periods={0:'x'}) + + +@pytest.mark.parametrize("period", [1, 4, 10]) +@pytest.mark.parametrize("input_dimension", [1, 2, 3]) +def test_forward_same_period(input_dimension, period): + func = torch.nn.Sequential( + PeriodicBoundaryEmbedding(input_dimension=input_dimension, + output_dimension=60, periods=period), + torch.nn.Tanh(), + torch.nn.Linear(60, 60), + torch.nn.Tanh(), + torch.nn.Linear(60, 1) + ) + # coordinates + x = period * torch.tensor([[0.],[1.]]) + if input_dimension == 2: + x = torch.cartesian_prod(x.flatten(),x.flatten()) + elif input_dimension == 3: + x = torch.cartesian_prod(x.flatten(),x.flatten(),x.flatten()) + x.requires_grad = True + # output + f = func(x) + assert check_same_columns(f) + + + +def test_forward_same_period_labels(): + func = torch.nn.Sequential( + PeriodicBoundaryEmbedding(input_dimension=2, + output_dimension=60, periods={'x':1, 'y':2}), + torch.nn.Tanh(), + torch.nn.Linear(60, 60), + torch.nn.Tanh(), + torch.nn.Linear(60, 1) + ) + # coordinates + tensor = torch.tensor([[0., 0.], [0., 2.], [1., 0.], [1., 2.]]) + with pytest.raises(RuntimeError): + func(tensor) + tensor = tensor.as_subclass(LabelTensor) + tensor.labels = ['x', 'y'] + tensor.requires_grad = True + # output + f = func(tensor) + assert check_same_columns(f) + +def test_forward_same_period_index(): + func = torch.nn.Sequential( + PeriodicBoundaryEmbedding(input_dimension=2, + output_dimension=60, periods={0:1, 1:2}), + torch.nn.Tanh(), + torch.nn.Linear(60, 60), + torch.nn.Tanh(), + torch.nn.Linear(60, 1) + ) + # coordinates + tensor = torch.tensor([[0., 0.], [0., 2.], [1., 0.], [1., 2.]]) + tensor.requires_grad = True + # output + f = func(tensor) + assert check_same_columns(f) + tensor = tensor.as_subclass(LabelTensor) + tensor.labels = ['x', 'y'] + # output + f = func(tensor) + assert check_same_columns(f) \ No newline at end of file diff --git a/tutorials/README.md b/tutorials/README.md index 8403c95..f4d7db4 100644 --- a/tutorials/README.md +++ b/tutorials/README.md @@ -16,6 +16,7 @@ Building custom geometries with PINA `Location` class|[[.ipynb](tutorial6/tutori Two dimensional Poisson problem using Extra Features Learning     |[[.ipynb](tutorial2/tutorial.ipynb), [.py](tutorial2/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial2/tutorial.html)]| Two dimensional Wave problem with hard constraint |[[.ipynb](tutorial3/tutorial.ipynb), [.py](tutorial3/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial3/tutorial.html)]| Resolution of a 2D Poisson inverse problem |[[.ipynb](tutorial7/tutorial.ipynb), [.py](tutorial7/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial7/tutorial.html)]| +Periodic Boundary Conditions for Helmotz Equation |[[.ipynb](tutorial9/tutorial.ipynb), [.py](tutorial9/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial9/tutorial.html)]| ## Neural Operator Learning | Description | Tutorial | diff --git a/tutorials/tutorial9/tutorial.ipynb b/tutorials/tutorial9/tutorial.ipynb new file mode 100644 index 0000000..6299e84 --- /dev/null +++ b/tutorials/tutorial9/tutorial.ipynb @@ -0,0 +1,298 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tutorial: One dimensional Helmotz equation using Periodic Boundary Conditions\n", + "This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs)\n", + "a one dimensional Helmotz equation with periodic boundary conditions (PBC).\n", + "We will train with standard PINN's training by augmenting the input with\n", + "periodic expasion as presented in [*An expert’s guide to training\n", + "physics-informed neural networks*](\n", + "https://arxiv.org/abs/2308.08468).\n", + "\n", + "First of all, some useful imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from pina import Condition, Plotter\n", + "from pina.problem import SpatialProblem\n", + "from pina.operators import laplacian\n", + "from pina.model import FeedForward\n", + "from pina.model.layers import PeriodicBoundaryEmbedding # The PBC module\n", + "from pina.solvers import PINN\n", + "from pina.trainer import Trainer\n", + "from pina.geometry import CartesianDomain\n", + "from pina.equation import Equation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The problem definition\n", + "\n", + "The one-dimensional Helmotz problem is mathematically written as:\n", + "$$\n", + "\\begin{cases}\n", + "\\frac{d^2}{dx^2}u(x) - \\lambda u(x) -f(x) &= 0 \\quad x\\in(0,2)\\\\\n", + "u^{(m)}(x=0) - u^{(m)}(x=2) &= 0 \\quad m\\in[0, 1, \\cdots]\\\\\n", + "\\end{cases}\n", + "$$\n", + "In this case we are asking the solution to be $C^{\\infty}$ periodic with\n", + "period $2$, on the inifite domain $x\\in(-\\infty, \\infty)$. Notice that the\n", + "classical PINN would need inifinite conditions to evaluate the PBC loss function,\n", + "one for each derivative, which is of course infeasable... \n", + "A possible solution, diverging from the original PINN formulation,\n", + "is to use *coordinates augmentation*. In coordinates augmentation you seek for\n", + "a coordinates transformation $v$ such that $x\\rightarrow v(x)$ such that\n", + "the periodicity condition $ u^{(m)}(x=0) - u^{(m)}(x=2) = 0 \\quad m\\in[0, 1, \\cdots] $ is\n", + "satisfied.\n", + "\n", + "For demonstration porpuses the problem specifics are $\\lambda=-10\\pi^2$,\n", + "and $f(x)=-6\\pi^2\\sin(3\\pi x)\\cos(\\pi x)$ which gives a solution that can be\n", + "computed analytically $u(x) = \\sin(\\pi x)\\cos(3\\pi x)$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class Helmotz(SpatialProblem):\n", + " output_variables = ['u']\n", + " spatial_domain = CartesianDomain({'x': [0, 2]})\n", + "\n", + " def helmotz_equation(input_, output_):\n", + " x = input_.extract('x')\n", + " u_xx = laplacian(output_, input_, components=['u'], d=['x'])\n", + " f = - 6.*torch.pi**2 * torch.sin(3*torch.pi*x)*torch.cos(torch.pi*x)\n", + " lambda_ = - 10. * torch.pi ** 2\n", + " return u_xx - lambda_ * output_ - f\n", + "\n", + " # here we write the problem conditions\n", + " conditions = {\n", + " 'D': Condition(location=spatial_domain,\n", + " equation=Equation(helmotz_equation)),\n", + " }\n", + "\n", + " def helmotz_sol(self, pts):\n", + " return torch.sin(torch.pi * pts) * torch.cos(3. * torch.pi * pts)\n", + " \n", + " truth_solution = helmotz_sol\n", + "\n", + "problem = Helmotz()\n", + "\n", + "# let's discretise the domain\n", + "problem.discretise_domain(200, 'grid', locations=['D'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As usual the Helmotz problem is written in **PINA** code as a class. \n", + "The equations are written as `conditions` that should be satisfied in the\n", + "corresponding domains. The `truth_solution`\n", + "is the exact solution which will be compared with the predicted one. We used\n", + "latin hypercube sampling for choosing the collocation points." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solving the problem with a Periodic Network" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Any $\\mathcal{C}^{\\infty}$ periodic function\n", + "$u : \\mathbb{R} \\rightarrow \\mathbb{R}$ with period\n", + "$L\\in\\mathbb{N}$ can be constructed by composition of an\n", + "arbitrary smooth function $f : \\mathbb{R}^n \\rightarrow \\mathbb{R}$ and a\n", + "given smooth periodic function $v : \\mathbb{R} \\rightarrow \\mathbb{R}^n$ with\n", + "period $L$, that is $u(x) = f(v(x))$. The formulation is generalizable for\n", + "arbitrary dimension, see [*A method for representing periodic functions and\n", + "enforcing exactly periodic boundary conditions with\n", + "deep neural networks*](https://arxiv.org/pdf/2007.07442).\n", + "\n", + "In our case, we rewrite\n", + "$v(x) = \\left[1, \\cos\\left(\\frac{2\\pi}{L} x\\right),\n", + "\\sin\\left(\\frac{2\\pi}{L} x\\right)\\right]$, i.e\n", + "the coordinates augmentation, and $f(\\cdot) = NN_{\\theta}(\\cdot)$ i.e. a neural\n", + "network. The resulting neural network obtained by composing $f$ with $v$ gives\n", + "the PINN approximate solution, that is\n", + "$u(x) \\approx u_{\\theta}(x)=NN_{\\theta}(v(x))$.\n", + "\n", + "In **PINA** this translates in using the `PeriodicBoundaryEmbedding` layer for $v$, and any\n", + "`pina.model` for $NN_{\\theta}$. Let's see it in action! \n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# we encapsulate all modules in a torch.nn.Sequential container\n", + "model = torch.nn.Sequential(PeriodicBoundaryEmbedding(input_dimension=1,\n", + " periods=2),\n", + " FeedForward(input_dimensions=3, # output of PeriodicBoundaryEmbedding = 3 * input_dimension\n", + " output_dimensions=1,\n", + " layers=[10, 10]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As simple as that! Notice in higher dimension you can specify different periods\n", + "for all dimensions using a dictionary, e.g. `periods={'x':2, 'y':3, ...}`\n", + "would indicate a periodicity of $2$ in $x$, $3$ in $y$, and so on...\n", + "\n", + "We will now sole the problem as usually with the `PINN` and `Trainer` class." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pinn = PINN(problem=problem, model=model)\n", + "trainer = Trainer(pinn, max_epochs=5000, 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", + "metadata": {}, + "source": [ + "We are going to plot the solution now!" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pl = Plotter()\n", + "pl.plot(pinn)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great, they overlap perfectly! This seeams a good result, considering the simple neural network used to some this (complex) problem. We will now test the neural network on the domain $[-4, 4]$ without retraining. In principle the periodicity should be present since the $v$ function ensures the periodicity in $(-\\infty, \\infty)$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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O4aOPPsI111zjf0+OIu/bty/sg8MDDzyAZ555Bo8//jhuv/123HvvvXjmmWfCHnffvn0YMWJEwuUnhBCSXBYtWoQXX3yxx+SXiW4DsN0ORzzt9oIFC/DTn/4UF1xwAQBg+vTp+PTTT/0ierR2nW06IcTsvPTSS+jbty+eeOKJbp+9/vrreOONN7B8+fIQIW337t0h0c579uyBz+fDoEGD/O9Fansuu+yyhO/1sbY/kdqeRPrFJSUlyM7Oxu7du7t9FinKWC1a9N+10gC67jM/Px/bt29P6nHjabuB5LXPpaWluPHGG1V8I0G83yvacwm1BmtDOxdCksDQoUPR0NCAzz77zP/e0aNH8cYbb4Ss53A48F//9V/485//HLbBq6mpiXocr9eLhoaGkPf69u2L8vJyuN1uOBwOXHrppfjLX/7in8oHiIziL7/8Ms4//3zk5+cn/D0A+D27wj08BZNomWLF6/Wio6MjxC+ss7MT//M//4POzs4QD7PJkycDAD799NNu+1m1ahV+9rOf4e6778Ytt9yCuXPn4oUXXsC+ffvCHnfz5s0477zzEi4/IYSQ5DJ06FBcf/31ePLJJ1FVVaXLNmy3IxNru11XV4f33nsP119/vX89n88Hl8vl/z9Su842nRBidtra2vD666/jiiuuwNVXX93tb/78+WhqasJf//rXkO26Cu6PPfYYAOCyyy7rse0BEr/Xx9r+RGp7EukXOxwOVFRUYNWqVTh48KD//Z07d+Ltt9+OuJ0aEu2/a7WPrtjtdkyfPh1/+9vfwvZpFUXR5bjx9LkB67TP8Xyvnp5LqDVYG0aiE5IErrvuOvz0pz/Ft7/9bfzoRz9Ca2srfv/73+P000/vlqzj17/+Nd5//31MmjQJc+bMwciRI1FXV4fNmzfjvffeQ11dXcTjNDU14ZRTTsHVV1+NsWPHolevXnjvvfewceNGPPjggwCAe+65B++++y7OP/98/PCHP0RGRgaefPJJuN1uLFu2TLPvMXHiRADAL37xC1x33XVwOp248sorw+43kTLFitPpxJgxY/D73//e73e2cuVKf8RGcMM3ZMgQjBo1Cu+99x5uuukm//ubNm3C9773PXzve9/DL37xCwDAHXfcgeXLl4cdId60aRPq6uowbdo0Tb4DIYSQ5PKLX/wCf/zjH/Hll1/izDPP1HwbttuRibXdrqysREdHR0jEZVtbm38qNBC+XWebTgixAn/961/R1NSEq666Kuzn5557LkpKSvDSSy/h2muv9b+/b98+XHXVVZg6dSrWrVuHF198Ed/97ncxduxY1NfX99j2AMlpfyK1Pbm5uQn1i++66y6sXr0aF1xwAX74wx+is7MTjz32GM4888wQYV8LEimnlvvoyq9+9Su88847uPDCCzF37lyMGDECR48excqVK/HRRx+hsLBQ8+PG0+cGrNM+x/O9enouodZgcRRCSFzccsstSqRLZ8mSJQoApaampttn77zzjjJq1CglMzNTOeOMM5QXX3zRv35XqqurlVtuuUUZMGCA4nQ6ldLSUuWSSy5Rnnrqqahlc7vdyu23366MHTtWycvLU3Jzc5WxY8cqv/vd70LW27x5s1JRUaH06tVLycnJUS6++GJl7dq1Ies899xzCgBl3759qr/H3XffrfTv31+x2+3+fUXabyxlilS/kfbZlc2bNysTJ05UXC6XcuaZZypPPfWU8oc//EEBoBw4cCBk3Yceekjp1auX0traqiiKohw6dEgpKytTvvGNbyjt7e0h686bN09xOp3KV199FfL+T3/6U+XUU09VfD5f1HIRQgjRBtkebNy4Ma71om13ww03KACUM888M+ZjRdqmK2y3Q/fZlVja7QceeEC5/vrrQ7YbOHCg8tlnn4W8F9yus00nhFiFK6+8UnG5XEpLS0vEdW688UbF6XQqtbW1/vvuF198oVx99dVKXl6eUlRUpMyfP19pa2tTFCX2tkdRktP+hGt7JGr7xYqiKB988IEyceJEJTMzUxkyZIiyfPnysMcPV/73339fAaCsXLky6nvxljOaXpDoPsJ9jwMHDiizZs1SSkpKlKysLGXIkCHKLbfcorjd7riPG4mBAwcqS5Ys8f8fT59bUazTPsf6vWJ5LtFTa+h6Poi22BQlxqwDhBCSRjQ0NGDIkCFYtmwZbr755ri3d7vdGDRoEH72s5/h1ltv1aGEhBBCCLnnnntw6NAhPPnkkwBEBNj/+3//D1u3bg1ZL5F2nW06IYQQEp5BgwbhxhtvxJ133qlq+1Rrn2N5LtFTa0j0fJDo0BOdEELCUFBQgDvuuAMPPPCAP3N5PDz33HNwOp34wQ9+oEPpCCGEEAIIK4DKykocP34cO3fuxC233BI2+V4i7TrbdEIIIUQfUq19juW5hFqDdWEkOiGEEEIIIcSS+Hw+3HTTTVi5ciX69++PZcuWYfr06UYXixBCCEkLGPkcitHPJTwf+sLEooQQQgghhBBLYrfbsWLFCqxYscLoohBCCCEkzeFzSWrDSHRCCCGEEEIIIYQQQgghJAL0RCeEEEIIIYQQQgghhBBCIkARnRBCCCGEEEIIIYQQQgiJQFp6ovt8Phw5cgR5eXmw2WxGF4cQQggBACiKgqamJpSXl8Nu5zh3ONiGE0IIMSNsw3uGbTghhBAzEmsbnpYi+pEjRzBgwACji0EIIYSE5dChQzjllFOMLoYpYRtOCCHEzLANjwzbcEIIIWampzY8LUX0vLw8AKJy8vPzDS4NIYQQImhsbMSAAQP87RTpDttwQgghZoRteM+wDSeEEGJGYm3D01JEl1PH8vPz2XgTQggxHZziHBm24YQQQswM2/DIsA0nhBBiZnpqw2nWRgghhBBCCCGEEEIIIYREgCI6IYQQQgghhBBCCCGEEBIBiuiEEEIIIYQQQgghhBBCSATS0hOdEEKIdni9XnR0dBhdDEvgdDrhcDiMLgYhhJA0g2114rANJ4QQc8O2jkRCqzacIjohhBBVKIqCqqoq1NfXG10US1FYWIjS0lImHiOEEKI7bKu1hW04IYSYD7Z1JBa0aMMpohNCCFGFfFDp27cvcnJy2KHsAUVR0NraimPHjgEAysrKDC4RIYSQVIdttTawDSeEEPPCto5EQ8s2nCI6IYSQuPF6vf4HlT59+hhdHMuQnZ0NADh27Bj69u3LaeGEEEJ0g221trANJ4QQ88G2jsSCVm04E4sSQgiJG+k1l5OTY3BJrIesM/r1EUII0RO21drDNpwQQswF2zoSK1q04RTRCSGEqIZT5eKHdUYIISSZsN3RDtYlIYSYE96fSU9o8RuhiE4IIYQQQgghhBBCCCGERIAiOiGEEEIIIYQQQgghhBASAYrohBBCCCGEEEJSiuPHj6Nv377Yv39/TOtfd911ePDBB/UtFCGEEEIsC0V0QgghJAzxdr4BdsAJIYQQs3Dvvfdi2rRpGDRoUEzrL1q0CPfeey8aGhr0LRghhBBykjVr1sTcTgWTSn1Vrb6L2rqMB4rohBBCSBji7XwD7IATQgghZqC1tRV/+MMfcPPNN8e8zahRozB06FC8+OKLOpaMEEIISZxU6qta6btQRCeEEEK6oKbzDbADTgghhGjF6tWrkZubC5/P539v+/btsNlsqK2tjbrtW2+9haysLJx77rn+91555RVkZ2fj6NGj/vdmz56NMWPG+DvhV155JV599VWNvwkhhBCiHanUV7Xad6GITlTR0AA8/jjwj38YXZL0RFGAVauA3/8eaGkxujTpyZ49wAMPAF98YXRJzIOiiN9jMv6amoD9+4FDh4DmZnHseOipYx6u8w2wA05SA6/Piw/2f4C9dXuNLkpaoigKVu1ahd9t/B2aPc1GFyctaXI34R+7/4H69nqji5KW+BQfalpqUNdWByVKA75lyxaMGjUKdnugy7p161aUl5ejuLg46jH+9a9/YeLEiSHvXXfddTj99NPxq1/9CgCwZMkSvPfee/jHP/6BgoICAMA555yDDRs2wO12q/16hBDSnc5O0Xlfs8bokqQHyeyYdv2Lt2PahVgGkNUOFAP69FVjGvRubweOHhXLIKzW785I6tFISuDzAZdfDnz8sfj/5ZeBmTONLVO68fTTwP/8j3j9l7+IwQybzdgypRNHjgDnnAOcOAHcdRewbRswdKjRpTKe1lagVy9jjt3cDOTmxr5+Tx3zcJ1vQHTAf/3rX+NXv/oVHnvsMX8H/JNPPgnpgN97771wu93IyspK+LsRojX//cZ/45XtryDTkYnKWZU4/9TzjS5SWvHM5mcw9825AIA3dr2Bd65/BzY24kmj0d2IiU9NxJ66PRhYMBCb/2czemf3NrpYSUNRFLR2tCb9uDnOHP/vfH/9ftS11QEA+uf1R1leWdhttm7dirFjx4a8t23bNv97Ho8Ht9xyCz7++GMUFBTg73//O3r3FufywIEDKC8vD9nWZrPh3nvvxdVXX43S0lI89thj+Ne//oX+/fv71ykvL4fH40FVVRUGDhyozZcnhJDf/Q649VbA4QA++wwYOdLoEqU2VuqYdiGWAeRIA8U99VMBffqqMQ16798v6ub4ceDMM/0CltX63RTRSdy89VZAQAeAX/wCuO46irjJorMTWLw48P/bbwMffghceKFxZUo3fvMbIaADYrD5nnuA554ztkzpTtCgd0z01DEP1/kG2AEn1ufjgx/jle2vAAA8Xg8WvL0AG+ZsMLhU6UOnrxOL1wQa8fe+eg/v738f3xz8TQNLlV488skj2FO3BwBwoOEA7v/oftz/rfsNLlXyaO1oRa/7ki8sNC9sRm5mLlo7Wv0COgAcbT6Kvrl94bA7um2zZcsW/OhHPwp5b+vWrTjrrLMAAHfddRfOP/98PP3001i0aBFeffVV/PCHPwQAtLW1weVyddvnFVdcgZEjR2Lp0qV45513cOaZZ4Z8np2dDUBMLyeEEM146SWx9HpFFOI99xhbHmJaeuqnAuoHigF9+qo9ltnrhefECdxy//34+LPPUFBcjL+vXo3evXtbrt9NOxcSN3/6k1jOnSsG9/btAz791NgypRMffQRUVwN9+gA33CDee+01Y8uUTvh84rkHAH7+c7H8058Aj8e4MpmFnBwxuKz335dfioGjzz4D1q0Trzs64ivrli1bMGbMmJD3ghv/SJ1vILQD/sYbb7ADTizFy5+LG9gVp1+BDHsGNh7ZiH8f/7fBpUof1h5ai6rmKhS5inDjuBsBAK9tZyOeLBRFwXNbxaj3jJEzAAArtq2AT4lzJJao5kSbiEIodBUi05EJn+JDg7t7UrCWlhbs3bs3pFPu8/mwZcsWjB07Fg0NDfjwww9xw8mH4cGDB+Orr77yr1tcXIwTMuIhiNWrV2PXrl3wer3o169ft8/r6oTAX1JSktgXJYQQSWsrsHlz4H9auuhPsjqm4f5ychIqek/9VCC2geJw/VQgel/1Zz/7GWw2W9S/Xbt2xV/mlhbc9fTTOH/cOHzxf/+HSyZP9tuwWK3fzUh0Ehc+X8AH/brrRDTuypXA668DZ59tbNnShb/8RSyvuAKYMQN4/nngzTeBJ57gbIBksGOHGMTIyREzAp55Bjh2DFi7FrjoIqNLZyw2W0Iz12KmsxPIzgbKy8UzaXU1UF8P9I5xNn60jrlMaBKp8w2wA06si6Io+PvuvwMA/mfi/8Dd6ca7X72LVbtW4Y5v3GFw6dKDv+wSjfgVp1+Ba0ZegxVbV+DN3W9CURRauiSBvSf2Yl/9PjjtTjx5xZN4a/dbONZyDFurtmJC2QSji5cUcpw5aF6YfC/+HKcQFaRgXuQqgivDharmKpxoO9HNUmffvn3w+XwYPny4/723334bx48fx9ixY/Hee+9hz549GDduHACguroa//u//+tfd/z48d2SjW3evBnXXHMN/vCHP2DFihX45S9/iZUrV4ass337dpxyyik9eq4TQkjM7NolOjCSLVuEbzbbff1IVsdUY2LppwLqB4qB6H3V//f//h9uvPHGqGUcMmRI3GVuOHIEH27ZgntPzhYbXFaGnScHvq3W72YkOomLrVuFYJiXB5x/PnDVVeL9994ztFhpRWWlWF5xBfDNbwox8dAhJrhMFrL+L7gAyMoCKirE/0yymxw6OoRwDgD5+UBhoXjd1BT7PnrqmAOi8/1FmIsquAN+ySWX4Je//GW3ddgBJ2ZlV+0uHGg4AFeGC98c/E1MHz4dAPCPPbyBJYvKfaIRueL0K3Dx4IuR68zFkaYj+Kz6M4NLlh5UfiXqf/KAySjKLsIlQy4BAKzes9rIYiUVm82G3MzcpP/ZbDZ0eDv8fux5WXkoyBKeps2e5m4JRvv06QObzYaNGzcCAD755BPMnz8fLpcLp59+OrZt24Zly5Zh69at2Lp1K8aNGxfSga+oqMCOHTv8HfP9+/fj8ssvx89//nPMnDkTS5cuxZ///GdsDo4OhfBmvfTSS3Wrf0JIGrJzp1hOmiSWra2ATLZISBCx9FOB8H3VWPqpQPS+aklJCYYPHx71LzMzM+4yv/fPf2LPoUMYd/31GPfd72LRgw/6c5hYrd9NEZ3EhbRtmTwZcDqBb3xD/L9tW7cku0QHWltFJDQgzkF2dqAtXr/euHKlEx9+KJbfPGlfe4nof2PtWmPKk260tIhldra4B8nZch0dsVvq9NQxB7p3vgF2wIn1WX9YNBTn9D8HOc4c/MfA/wAAfHrkU3h9XiOLlha0dbRh+7HtAIDJp0yGK8OFSaeIRnzjkY1GFi1tWHNgDQDgksGi8b50iLhXf3jgQ6OKlFa0dIhG3JXhQqYjE7nOXNhgQ4evAx5vaCNeVlaGu+++G9dffz0GDhyI5cuXY8aMGRg1ahQcDgfq6+v9ScQaGxuxZcsWXHzxxf7tR48ejQkTJuD//u//UFdXh6lTp2LatGn42c9+BgCYNGkSLrvsMvxcevMBaG9vx6pVqzBnzhy9q4IQkk7sEXk4MHo0UHYykfKBA8aVh5iWWPqpgPqBYkD7vmosZd62YweW/ehH2Pruu9j68ssYd/rpfoHdav1uiugkLjZtEssJJ2e8DhoElJQIAWvrVqNKlT5s3SosdcrKAJlP4WRuJfrSJ4lt28RS2hfJ+t+yJf7kliR+ZBS6FM8djsDr5hhnp/fUMQdCO98A2AEnKcHmo+LBc2LZRADAiOIR6JXZC82eZuys3Wlk0dKCbdXb4FW86JfbD6fknwIAOLtcNCYbD1NETwZbq7YCACb1F4MX5/Q/BwCw6eimbpHQRHvaOtoABKxd7Ha7/3Wzp3sj/otf/AJ1dXU4cOAAVqxYgV//+tf+TvqwYcOwYYNIirx06VL86Ec/Qk4XH9rFixfjkUceQWFhIXbt2oXly5eHfP73v/8dq1cHZiE899xzOOecc3Duuedq9I0JIQTAwYNiOXCgEFAAiugkLLH0UwF1A8WAPn3VWMpcX1+PLKcTyMtDY3MztuzahYsvuKDbdwHM3++miE7iQg78SBHdZgtEQp98jiU6IoVyKdwCATF3I/vfutPUBMicVaNHi+UZZ4io6JYW4N/Mzac7UkQ/mUMEQMDuTkapx0K0jrlEdr59Ph969+7NDjixPJuOipFwKaI77A6cVS4alPVfczqT3nx6RDTiZ5Wf5fc/l/XPSHT9aeto8yfRHdNPJL8a3W80HDYHaltr8XXj10YWLy2QVi5SOAeA3MzckM9i5bvf/S7WrFmD0047DW63Gz/96U+7rXP55Zdj7ty5OHz4cEz7dDqdeOyxx+Iqh1488cQTGDRoEFwuFyZNmuQfMIjEypUrMXz4cLhcLowePRpvvfVWyOeKomDx4sUoKytDdnY2pkyZgt27d4esc++99+K8885DTk4OCqVfXgSOHz+OU045BTabDfX19Wq+IiHpw6FDYjlggBDSAWD/fsOKQ8xNLP1UIP6BYkC/vmrUMisKhpWXY8OOHUB2NpY+9xx+dN11yAkaFLBSv5siOokZrxf4/HPxevz4wPtSUJefEf2QdXwyhxIAYKLQQvDZZ6H5Soj2bBez8FFeDkjbrYyMwPmQMzWIfrSJILaQpOfytdaWUvF2vgFzdcAJCcan+PxRuOPLAo34WWVCxN1Wvc2IYqUVn1eLRnxc6Tj/e1JE//zY5+jwdhhRrLRhR80O+BQfinOKUdqrFICwFTmz75kAAoNMRD/CiejZGWJUvK2zLa59FRcX49NPP8Xu3bvx2GOPhUToBXPbbbdhwIABMe3z+9//Ps4444y4yqEHr732GhYsWIAlS5Zg8+bNGDt2LCoqKnDs2LGw669duxYzZ87EzTffjC1btmD69OmYPn06tssHVwDLli3Do48+iuXLl2P9+vXIzc1FRUUF2oMenjweD2bMmIF58+b1WMabb74ZY8aMSfzLEpIOyEj0YBGdkegkQSzTV+3sxHcrKrBm82acNmoU3J2d+OmsWcLO4iSW+S6giE7i4MABwO0WyRSDE/KOGCGWTGypP19+KZZBORsweLCIyvV4gH37jClXuvDZybxvMgpdInN8SL96og9er7gHAaGR6C6XWLbF1/+OiXg634B5OuCEdOXrxq/R2tGKDHsGTu8T8FQcWTISAPBFDRtxvfnyuGjEhxcHGvFTC05FrjMXnb5OfHXiK6OKlhbI5K1j+431zwQAgPGlYlBJDnIQffD5fHB7RSMuhXMAyHaK1+2dTK4keeihhzBnzhzMnj0bI0eOxPLly5GTk4Nnn3027PqPPPIIpk6dittvvx0jRozA3XffjQkTJuDxxx8HIKLQH374YSxatAjTpk3DmDFj8MILL+DIkSNYtWqVfz933XUXfvzjH2N01wfdLvz+979HfX09fvKTn2j2nQlJWRQlfCQ6RXSiAZboq3o8KC4sxKevvCIGvu+8Uwx8d4QGj1jiu4AiOokDaVUxbBhgD/rljBT9b+zcKdoIoh9SRA++V9jtgf937Up+mdIJeQ3I37xE1r88P0QfpIDucIgZABIpqHs8QmgnhHRH2lgMLRqKDHvgApIiOj3R9UeK6Gf0CTTidpsdZxSL/3kO9OXLWlH/I4pHhLwvBzXk+SH6IAV0h80Rcg9yZYiRcI/Xg04fp1R6PB5s2rQJU6ZM8b9nt9sxZcoUrFu3Luw269atC1kfEIna5Pr79u1DVVVVyDoFBQWYNGlSxH1G4osvvsDSpUvxwgsvwG6nlEBIj5w4EfCjPOUUoFTMhEKEmSUk/Rg0aBBuu+02o4uhH56TicMzM8XS6RTLDu1nYCajLtnykZiRAmJQUmD//3a7aB+qq5NfrnShvj7Q1nY9BzIynSK6vuzdK5ZDh4a+TxE9OUgR3eUS+RgkGRmBtliPaHRCUoHdx4X3bXAUOhAQEI80HUF9e32yi5U2NLobUdVcBQB+0VwiRd1dtWzE9WTvCdGIn9bntJD35aAG619fZKR5VkZWyEyADHsGnHZnyDrpTG1tLbxeL/r16xfyfr9+/VBVVRV2m6qqqqjry2U8+wyH2+3GzJkz8cADD+DUU0+NeZvGxsaQP0LSChmFXlIiIn/69hX/U0QnJ0l5EV16DssoOIroJF2QuWe6CrguV8DeZSeDqHRDCrTl5UBeXuhn0lKH9a8ve/aI5bBhoe/LQYzduxkJrSdSRM/K6v6ZtHSR6xBCQpGR6F1F9AJXAfrn9QcA7KxhI6IXsv5Le5UiPys/5DM5kMFIdH3ZUyca8WG9QxtxOajx5fEvoXBKpW7ISPQsR/dGXEajU0Q3NwsXLsSIESNw/fXXx7zNfffdh4KCAv9fPFP1CUkJjh4Vy/JysSwpEcuaGmPKQ0iykWK5FM91FNGTAUV0EjMyEv2007p/JkXFr2jnqRvS77yrgAsEIqHlOSLa4/MFItG7noNTTxXCrseTfonWfT5f0o4lc1+FE9Hle1YQ0ZNZZ4RI/l0XXkQHApG5MlKXaM/eOlG3XQVcIBAJLYV2oj2KovhF9KFFodPJhhYNhd1mR7OnGUebjxpRvLTA3SkaaCmYB5OVIRpxj9eT1DKZkeLiYjgcDlR3md5bXV2NUmkD0YXS0tKo68tlPPsMxz//+U+sXLkSGRkZyMjIwCWXXOIv85IlS8Jus3DhQjQ0NPj/DsmoXELSBRlxLsVzGYne1BTo3BCSynSNRJfLTmtauGX0vAohApn7YvDg7p8NGiSW6SYgJhOZ1Dvc7El5TpifRD+OHhXPORkZgXwwEodDWLx88YUYSOpq95KKZGZmwm6348iRIygpKUFmZmbI9Gw9kFYtdnv3Z05py9nWZt7nUUVR4PF4UFNTA7vdjkzpC0dIEthfvx8AMLiweyM+uHAw1mCNfx2iPYcahXA0sGBgt88GF4lzcqCejbheVLdUo6WjBXabHYMKB4V8lpWRhUGFg/DVia+w+/hulOeVG1NIHTFDhH2wnUtXZHS6FNrNjN51mZmZiYkTJ6KyshLTp08HIAbfKysrMX/+/LDbTJ48GZWVlSFT2N99911MnjwZADB48GCUlpaisrIS48aNAwA0NjZi/fr1mDdvXsxl+/Of/4y2IN+8jRs34qabbsK//vUvDI3w8JuVlYWscNEPhKQLMuJciugFBSISt6NDfMbZGSTVkWJ5ikSiU0QnMdE1qXRXpIgro6WJ9kQT0eUgxuHDIhqa2pz2yN/2qaeGJrWUDBwoRPR0GUiy2+0YPHgwjh49iiNHjiTlmIcPizbY4RA5AoJpaQFqa4Hm5kDuErOSk5ODU089lQm5SNJQFAUHG0QjcmpB90ZEior7TrAR1wtZ/wPyuz9Eyfo/2nwU7Z3tYSN1SWJ8dUJMlRyQPyCsiCtF9AMNqTWQ4TzZUW1tbUW2zMJtEDLKPJydS6ZDPLhKyxcz03oyQaCsWz1YsGABbrjhBpx11lk455xz8PDDD6OlpQWzZ88GAMyaNQv9+/fHfffdBwC49dZbceGFF+LBBx/E5ZdfjldffRWffvopnnrqKQCAzWbDbbfdhnvuuQennXYaBg8ejF/+8pcoLy/3C/UAcPDgQdTV1eHgwYPwer3YunUrAGDYsGHo1atXN6G8trYWADBixAgUFhbqVh+EWBopossIdJtNCOpHjogodYromsHZviZFiuVJ8ETvCS1+IxTRSUx0TSrdFSniUkTXj2giusxT0tYmBjvSIRI62Xz9tVhGes6R10A6zQbIzMzEqaeeis7OTnh1NoNXFGDaNCGQv/tu9/OwZQvwgx8A/fsDlZW6FiUhHA4HMjIydI/aJySYBncDmj3NAIABBd1vYjI6fX/D/mQWK62INojRJ7sPcp25aOlowcGGg2Etd0hifN0oGvFwv38AGFQwCEDqzQZwOBwoLCzEsZN2Ajk5OYa0P4qiwOMWIrqvw4d2pcuUsU7x5/a50W7S6WSKoqC1tRXHjh1DYWEhHA6Hbse69tprUVNTg8WLF6Oqqgrjxo3D6tWr/YlBDx48GDIQf9555+Hll1/GokWL8POf/xynnXYaVq1ahVGjRvnXueOOO9DS0oK5c+eivr4e559/PlavXg2XKzBot3jxYjz//PP+/8ePHw8AeP/993HRRRfp9n0JSWm6RqLL10eO0BddI4yYIU3iQEa4+XxiyrjUDXw+EQmnY3sq0XJGOEV0EhMyCr24WIi1XZGR6OkShWsE0WYC2GxCxN25U5wDiujaI0X0cINIQMDiJZ1EdEBENzmdTl0jsgARZS6TG0sP+mAGDRJ1f+iQaId1Lg4hluJQg2hAemf3Ro4zp9vn0k6Ekej64Y9EDyPi2mw2DCochB01O7C/fj9FdB2QIvop+eEb8YGFohFPtUh0IOCHLYV0I/ApPtQ0CLEop7m7kO/1eVHbKKKanY1OU4sfhYWFcfmIq2X+/PkR7VvWrFnT7b0ZM2ZgxowZEfdns9mwdOlSLF26NOI6K1aswIoVK2Iu40UXXWQKqyBCTE04EV1GpRt4X04ljJghTeKgqkoI505nwDLh5EwmfPVV+Gn+OqHFjHCK6CQmogm4QEBEP3JEDC65OBNZc6JFogOhIjrRHimi9+8f/nMporP+9UHeg/r2DZ9YtLRU3Hfa28W1woEkQgJIP+5wViJAwE7kYMNBdPo6kWHn46HWyHMQLhIdQIiITrTncONhAMApeRFE9JNe9alY/zabDWVlZejbty86DPIf3VWzCz946wcoyi7CupvXdftcURRc89Q1aO1oxT++9w//wJ7ZcDqdukagE0JSkEiR6ABFdA1J5gxpEgc+H3DllcKTdc0a0WkHgFmzxLXx+uvAaaclpShazQhnL4nERE8iep8+QG6umI1x8CBwOoOoNKW5GairE6+jiegARVy96CkSPR3tXJJJT/Vvs4nBvJ07ha0URXRCAshI9EhWFuV55XDanejwdeBw42F/VC7RhtaOVtS2ioibaCI6kJoirhn4uil6JLqs/1SMRJc4HA7DBODDbYdxoOUAeuf1DrEPCcaR6cCB+gM42HIQI8pGJLmEhBCiE+FE9OJisZQdfKIJyZohTeKgrg7Yu1e8LisLRMO1twvh5Phxy0XgMqsZiYmeRHQpYAH0RdcDWf/5+eIvHBTR9eWwCGLr0c7l8GHLJpo2NT150gPAkCFiyXsQIaH0FIlut9n9wvm+el5AWiMHMXpl9kJBVkHYdSii60usdi4HGw7CpzAxmdb0VP8AMKRINOK8BxFCUopwInrv3mJJEZ2kOvL3n58fOp28Tx+xPH48+WVKEIroJCZ6EtEBJhfVk56sXACK6HrTk51Lv36iXfD5AusS7ZD3oEiDGEDg+pDrEkIEPYnoQCC5KH3RtSc4qWikKaQU0fVFirj988M34v3z+sNus8Pj9aC6uTqZRUsL5D0omogu709y0IkQQiyP2w00NorXFNFJOiJFdJkHQEIRnaQ6sYjo8jMZsUu0Q9Z/NBGdntz60dkJHD0qXkcSce32wPmhpYv2xBKJLgc4eA8iJJSe7FyAgM2IFBuJdvTkhw6kh52IUXh9XhxpEonGIom4TofT/xkHMrRH3leiDeT1zxON+JFmJoUjhKQIMnmiwwEUFgbep4hO0gXp+x88iARQRCepTywienm5WDIhsvZIUTBSFDQQEHePHhXR0EQ7qqtFQmmHQ0ScR0IOZMiZA0Q7evJEBwL3IIrohIQSSyR6eZ64gKTYSLRDJrWUImE45GdVzVXw+pgQS0uOtRxDp68Tdpsdpb1KI64nk4tyIEN7YrFzkbME5PVCCCGWR0bhFheLiCsJRXSSLkSKRJd5AeRAk4XQXUR/4oknMGjQILhcLkyaNAkbNmyIuO5FF10Em83W7e/yyy/3r3PjjTd2+3zq1Kl6f420RlECwng0EZdRoPpRfXJmcWnkvh/69RPe9F5v4F5FtEH+psvLhZAeCXkNcCBJe2IZyOM9iJDwSGE8kpUFEBBxDzfxAtKaquYqAIgq4PbN7Qu7zQ6f4kN1C+1EtET+pst6lSHDnhFxPSnwciBJe/wDeVFmw/AeRAhJOcL5oQMU0Un6wEj0+HjttdewYMECLFmyBJs3b8bYsWNRUVGBY7Iiu/D666/j6NGj/r/t27fD4XBgxowZIetNnTo1ZL1XXnlFz6+R9jQ1ieS5QPQoXEai64cU0aPVf0ZG4HOeA23pyQ9dUlYmlqx/7ZF2OrKOw0ERXR84GG5tmj3NaO1oBQD0y43ciDASXT+kKB6t/h12h19k5znQlp780CVlvUQDw/rXnqNNohGX95lwyM8YiU4ISRkoopN0J9I1QBE9PA899BDmzJmD2bNnY+TIkVi+fDlycnLw7LPPhl2/d+/eKC0t9f+9++67yMnJ6SaiZ2VlhaxXVFSk59dIe6SAm5sr/iJBAUs/qkQQW1QRHeBAhl7EIuACgfqX6xNtaGkRf0D0a0Deg06cANra9C9XOsDBcOsjkyRmZ2SjV2aviOv5rRQYBao5UkSPFokOBHlCU8TVlFgE3ODPjzazEdeSto42NHmaAEQfSJL3oAZ3A1o8LUkpGyGE6EokKwspojc1AR0dyS0TIclE9hmZWLRnPB4PNm3ahClTpgQOZrdjypQpWLduXUz7+MMf/oDrrrsOuV2U2zVr1qBv374444wzMG/ePBy3YMVbiViioIGAgFhXF4hcJ9oQi50LQBFdL+S9n4MYxiDr3+UC8vIir1dQAGRni9c8B9rAwXDr44+C7tUPNpst4npSQKxurkanrzMpZUsX5EBGv17RGxHOBtCHYy2iEYkm4AKsf72Q9Z/pyER+Vn7E9fKz8v0DfRzMI4SkBJGsLIKTjJ44kbTiEJJ0IkWi0xO9O7W1tfB6vejXRXXq168fqmRYbRQ2bNiA7du34/vf/37I+1OnTsULL7yAyspK3H///fjggw9w2WWXweuNnITJ7XajsbEx5I/ETqwCYlGRELkAClhaE+9AButfWyINoHaF9a8PwfUfRQOEzcYZMVpilsFwtuGJ4RdwexAQ++b2hcPmgALFvw3RhljsXACKuHoh679vbvRGnPWvD8G//2gDeUCQLzotXQghqUAkAdHhCAjptHQhqQwj0ZPHH/7wB4wePRrnnHNOyPvXXXcdrrrqKowePRrTp0/Hm2++iY0bN2LNmjUR93XfffehoKDA/zcgWmY60o1YBVybjSKiHrS0AM3N4jVFdGOIVUQP9kRXFH3LlE7Eeg8CKKJriVkGw9mGJ0ZwJHo07DY7yvLETYxRoNrR1tGGRrcY+GEkujHISOieRHT5+2f9a0us9Q/QVooQkmJEEtEB+qKT9KAnT/SmJsDjSW6ZEkQ3Eb24uBgOhwPV1aHRTNXV1SjtwZOipaUFr776Km6++eYejzNkyBAUFxdjz549EddZuHAhGhoa/H+HDh2K7UsQAOoELIq42iHrvycrCyAgolNA1JZYZ2NIEd3j4cw8LYl1EAOgiG4mtBoMZxueGLFGogP05NYDOYiR5chCQVZB1HUpoutDzCL6ycSizZ5mNLmbdC9XuuC30+lhEAlgclFCSIpBEZ2kMz5fwK6la0e+sBCwn5SjLXYN6CaiZ2ZmYuLEiaisrPS/5/P5UFlZicmTJ0fdduXKlXC73bj++ut7PM7XX3+N48ePoyxKxr+srCzk5+eH/JHYkSJuLAIWRVztCfZD72EWLCPRdSJWETcrKzCoynOgHfEM5PEepB1mGQxnG54YsVqJABSw9CDYD70nKwuK6PoQq4iel5WHvEwRrcDkotohr4GYItHzGIlOCEkhKKKTdObECUDONJYe6BKHQ/hBA5bzRdfVzmXBggV4+umn8fzzz2Pnzp2YN28eWlpaMHv2bADArFmzsHDhwm7b/eEPf8D06dPRR6pRJ2lubsbtt9+OTz75BPv370dlZSWmTZuGYcOGoaKiQs+vktbQSsFYOBPAeOIZSAq2dCHaEE8kuqz/GNxGSA+YaTCcqCdWOxeAIq4eqBnEYP1rS6yJRQFauuhBXPV/cjaAvG4IIcTSUEQn6Yz8/RcWApmZ3T+3qC96hp47v/baa1FTU4PFixejqqoK48aNw+rVq/3+qgcPHoTdHqrjf/nll/joo4/wzjvvdNufw+HAZ599hueffx719fUoLy/HpZdeirvvvhtZWVl6fpW0Jh4RVwYnVvPZVzPUROEeOwZ0dABOp37lShfcbqChQbyOdTbG9u3AUQaxaUasdjrB68htSGIsWLAAN9xwA8466yycc845ePjhh7sNhvfv3x/33XdfyHbRBsPvuusu/Nd//RdKS0uxd+9e3HHHHRwM15F47FykiMsoXO2oahYjeqW9os/eAAL1X9NaA4/Xg0xHmA4HiQuP14MT7cJfLZZI6PK8cvz7+L9xtInXgFbEmtg1eB0mNyaEWJ6OjoC/J0V0ko7IDnm43z9AET0S8+fPx/z588N+Fs7/9IwzzoASISNfdnY23n77bS2LR2IgHhGXApb2yIjaHtwTAIhZMnZ7wH6KgZ2JIwdQMzICSdSjQTsR7YlnJoBchwN52sDBcOsTTyS6FLBk5ChJnHgGMXpn90aGPQOdvk4cazmGU/JP0bt4KU9Ni2jEHTYHirKLelyfswG0J55IdHmf4j2IEGJ5pDBoswUE82AoopNURwopkTrx0uLFYnYuuovoxPrEI6JTwNKeeOrfbhcDfdXVYiCDInriBA+g2mMwwJKDHRxI0g5GohsLB8OtTTwirlyHApZ2xDOIYbfZUZJTgqPNRymia4T8LZfklsBu67kRl3YinI2hHaoi0WnnQgixOlJA7NNH+D93hSI6SXVSNBJdV090Yn1aW4HmZvE6HhGdApZ2yIG5SPeernAgQ1vi8eMOXo/XgHbEE4ku71O1tUBnp35lIsQKtHW0ocnTBICR6EZR2yoa8ZKc2BpxngNtiTWpqESuV9Nao1uZ0g1/JHoM9yA5kFfXVocOb4eu5SKEEF3pKRKOIjpJdaLlBAAoopPURAq4TieQn9/z+rKNqKkRliIkceQ9pYu1cEQo4mpLPFHQAOtfazo7A9dALOegTx8xa1JRLNceE6I5UgjMsGegIKugx/WDo0AjzSYg8SFF9OKc4pjWp52FtsST2BUIDHaw/rXB6/P6r4FYBjL65PTxzxjgQAYhxNJQRCfpTqx2LhbrtFNEJ1GRIroUpnpCDjJ1dgL19boVK62Q56A4tv43RVyNiScKGghcA6x/bTh+XAjiNltsA0kZGYFrhbMxSLpzvFU8lBbnFMMWQyMuRa72znY0e5p1LVu6cLxNnIM+ObGNhDMSXVvURqKz/rWhrq0OPkVE1cQykCQtjQCeA0KIxZGJzSiik3QlVjsXi3miU0QnUZGDQrEKuJmZgeSLFLC0gZHoxtLTLKSusP61RT5XFhaGtxMMB88BIQK/gJsdWwOSm5mLXGcuAApYWhFvJHrfHIq4WuL3RKedjiHIe1ChqxAZ9thSccnZGDKfAyGEWBIphsiEWV2hiE5SnZ4i0WnnQlKReAVcgAKWligKI9GNRu0gRm0tLY20QM09SAZ8cCCPpDsyEj3WKGiAIqLW+M9BjAMZrH9tqWsT4kTMgxjSE72lhpZGGhDv7x9gclFCSIoQq51LfT3g9SalSIQkFSYWJelIIgIWRdzEaW0F3G7xmpHoxhDvNSAHO7xe4MQJfcqUTnAgjxD1xBuJDlDA0pLWjla0dbYBiN/OhfWvDfIa6J3dO6b1S3JFR8/tdfuT8hL1xGtnBAT86zmQRAixND2J6EVFYqkoQENDcspESDKhJzpJRyhgGYus/8xMIDc3tm04iKEtcoZdrNdAZmbgmYjnIHEYiU6IetREgTKxpXbI+nfancjLzItpG0aia0u8szFynDm0NNKQhCLRaedCCLEyPYnomZlAr17iNS1dSKrh8wUsFXqKRK+rs9RsDIroJCqJiOgUsBIn2MollsSuAAcxtEZeA71jC2IDwOSiWsJ7ECHqURMFSk9u7Qiu/1gSuwIU0bVG2rmoEXF5DhIn3pkAQFAkeivrnxBiYXoS0QH6opPURXrb2myRfYnl719RhK2RRaCITqJCOxdjSXQmAO08EyfeSHSAAxlawnsQIeqJN6klQAFRS2T9qxVw6cmdOGpEXF4D2sFIdEJIWuLzBToiFNFJOiIHkYqLAacz/DqZmUB+vnhtIUsXiugkKrRzMRYZia6m/tvagJYW7cuUTiiKukh0XgPawUh0QtRDT3RjkQKimkEMj9eDRnejLuVKFxRFSSi5bk1LjS7lSif8MwHi8USnpRQhxOocPx6wp4jkBw0EOphMpEVSjaoqsYw2iARYMrkoRXQSFYroxiLrP9IMmHDk5gI5OeI1RcTEaG4GOjrEa14DxsBIdELUo0ZApIClHWrsdLKd2X7/dJ6DxGjpaEGHTzTitHMxBjUDedLOhQN5hBDLIjvhvXtHjsKVnwOByDlCUgUpopeWRl9PdvItdA1QRCdRUSPiMgpUO9QIiABFXK2QM+uysgIDE7Eg67+GQWwJk8hMgOpqWhqR9CaRSHQKiInjt9PJjuMhCjwHWiEHkTIdmchxxt6Il+SIxCas/8RRlZeBlkaEEKsjhZCeBEQpslgoCpeQmIglJwDASHSSejAK1FiCE4vGA0V0bQgWcGNN7Aqw/rUkkdkwHg/QSDcEksYkYmVBATFx1NQ/wHOgFcFJRWNN7AoE1T8TWyZMIp7onb5OnGinxQEhxILEKyBaKAqXkJiINRLdggNJFNFJRDo6gIYG8VqNgNXYCLS3a1+udIKR6MaiJqkoAJSIIDbWvwaouQZycoBevcRrzogh6UqnrxMNbtGIq7FSON56HJ2+Tl3Kli7UtsWfWBSgL71WqImCBjiIoSVqzkFWRhYKsgoA8BwQQixKrCK6BQVEQmKCdi4kHZECos0GFBXFvl1BgUi0C1BETBQ1iUUBiuhawUEMYwlO7BrvOeAzKUl3ZBSuDTYUZcfeiPfO7g27zQ4FChMrJoiaxKIARVytkPXfOzsOPzAwsahWBCd2jfccyGtGbk8IIZYiXhHdQgIiITFBOxeSjsjfcWEh4HDEvp3NZslrwZTIgYx4/KAB+tJrhRo/boAiula0tKhL7ApQRCdEik+FrkJk2DNi3s5hd/gjp2UUKVGHHMhQK+JSRE+MYDuXeGD9a0NrRyvcXjeA+M+BjFyXeQUIIcRS0M6FpDu0cyHpiForC4CDqlpRXy+W8cwEACx5LzIlaq8BKaKfOBEQgUn8yN9vvIldAT6TEiIF8HgFXIACllZIP+d4ZgIAgShc1n9iqEmsCwAlucKTraa1Bj7Fp3m50gVZ/067E70ye8W1rT8SnQN5hBArIgVERqKTdCXW5LoWjL6liE4icuJkLp94BVzAkteCKVF7Dtgea4NaK5HgRKS8BtSjNrErwIEkQurb6wGoFNFlJDqtFBJCnoNCV2Fc23EmgDaotRIpyREiuk/x+aPZSfwEJ9aNJ7ErELgGOJBECLEk9EQn6UxHR0CISsHZGBTRSURkFHRhYfzbUkRPHEVRfw5Y/9qg1k7Hbg8MfPAcqEcOIsVb/4Al22NCNOVEm7iA4hVwgUAkOkVc9SiK4j8HRa74RsL99c9BjISoaz9p5xJnYlGnw4n8rHwAPAeJIAeR4v39A/REJ4RYnHjtXNragNZWfctESLKoqRFilsPRczSiBYUriugkImqtRABGQmtBUxPgOzmLON5zYMF7kSlRK6IDvAa0QIt7EK8Bkq6ojYIGgOJs2okkSktHC7yKF0D854B2Ltqg1pMe4GwALVBrZwQwEp0QYmF8vkBirJ6sLPLyAKdTvGankaQKchCppKTn5IrBnXZF0bdcGkERnURERoEyEt0YpICYmQm4XPFty/rXhkREXJ6DxNFiNgyfR0m64hewVESBMhI6cWQUutPuRI4zvqQOFHC1IZFIaF4DiZPQQB490QkhVuXECaCzU7yWibIiYbMx8oqkHrEmFQUCnfaODqC5Wb8yaQhFdBIR2rkYS7CAq9YPuqkJ8Hg0LVZawWvAWFj/hKgnEQGLIm7iBNd/3H7QJwXc1o5WtHe2a120tIHXgLFoMYjBSHRCiOWQUbhFRSIaric4fZakGvGI6Dk5gYhRiwwkUUQnEUlEwOKAauIkMhOgsFD4cgNsjxOBIq6x8B5EiHq0iAKlgKWeRKwsCrIK4LCJ6a+MhFZPQiI6I9EThpHohJC0JFY/dAmnz5JUQ+01YBHhhCI6iYgUcWllYQyJWIkwsaU2UEQ3FlpKEaKehPyImVg0YRIREG02GyNxNYCR6MaiRf3z908IsRzxCoiM/CGpRjyR6IDlZmNQRCcRoYBoLIkIiADPQaJ0dgZsuXgNGIMWkegWylFCiKZoIiAyClc1iVhZABRxE6XT14lmj2jEeQ0YgxaR6HVtdfApPg1LZR2eeOIJDBo0CC6XC5MmTcKGDRuirr9y5UoMHz4cLpcLo0ePxltvvRXyuaIoWLx4McrKypCdnY0pU6Zg9+7dIevce++9OO+885CTk4PCMA9f27Ztw8yZMzFgwABkZ2djxIgReOSRRxL+roSkFFJAjFdEZ6eRpAqMRCfpCpP6GUsikegA2+NEaWgIvC4oiH97i7UFpkSLxK6dnUBjo2ZFIsQy0M7FWGRiUTX1D9BOJFEa2gONeIEr/kbcfw208RpQixZ2Oj7F599POvHaa69hwYIFWLJkCTZv3oyxY8eioqICx44dC7v+2rVrMXPmTNx8883YsmULpk+fjunTp2P79u3+dZYtW4ZHH30Uy5cvx/r165Gbm4uKigq0twfyLng8HsyYMQPz5s0Le5xNmzahb9++ePHFF7Fjxw784he/wMKFC/H4449rWwGEWJl4BcSSErGMcH0TYjnijUS3mHhIEZ1EJBE7FyngNjczsaVatIpEt8i9yHRIAbdXLyAjI/7tOYiROIkM5GVnizwlAK8Bkp5IETeRpH717fXw+ryalitdSDQSnZ7QiSHrv1dmL2TY42/EOYiRONJSSo2InunIRF5mHoD0PAcPPfQQ5syZg9mzZ2PkyJFYvnw5cnJy8Oyzz4Zd/5FHHsHUqVNx++23Y8SIEbj77rsxYcIEv7itKAoefvhhLFq0CNOmTcOYMWPwwgsv4MiRI1i1apV/P3fddRd+/OMfY/To0WGPc9NNN+GRRx7BhRdeiCFDhuD666/H7Nmz8frrr2teB4RYlnhFdCk0Hj2qT3kISTa0cyHpSiICVkEBE1smSqKR6IyEToxEfv8ABzG0QKtzwGuApCOJRIH2zu4NAFCg+IUwEh+JCIgAPaETJZHfP0A7HS1I+BykaV4Aj8eDTZs2YcqUKf737HY7pkyZgnXr1oXdZt26dSHrA0BFRYV//X379qGqqipknYKCAkyaNCniPmOloaEBvXv3TmgfhKQUFNFJukM7F5KO+HwBCwQ1ApbdDsjnKYqI6qAnurFQwDWeRM+BxQa1CdEMn+JDo1s04moErAx7hn+7dBOwtMIfia4isStAT+5E0UrAZf2rh7Mx1FFbWwuv14t+XcSHfv36oUpG93Whqqoq6vpyGc8+Y2Ht2rV47bXXMHfu3IjruN1uNDY2hvwRktJIATHWKNyyMrFM4FokxDS43QEhK147F4t02imik7A0NASS8VHAMgZ6ohuLViJ6XZ0YlCLxw9kAhKijob0BCkQjnnAkLkVEVSQciZ7DSOhE0DISXWF2alVodQ44kGdOtm/fjmnTpmHJkiW49NJLI6533333oaCgwP83YMCAJJaSEAOINwpXiuhHjwYEGEKsivz9O52xC1kW67RTRCdhkeJVdjaQlaVuHxYbUDId9EQ3Fq0EXJ8vNEkpiY2ODqClRbzmQB4h8SHFq+yMbGRlqGvE09VKQSsYhWssWg1ieLwetHS0aFWstKHT14lmTzMA9efAfw2k2UBecXExHA4HqqUQcZLq6mqURojqKy0tjbq+XMazz2h88cUXuOSSSzB37lwsWrQo6roLFy5EQ0OD/+/QoUNxH48Qy6Ao6u1cPJ6AAECIVQn+/dtssW1jsU47RXQSlkQFRIAibqLQE91YEr0GsrKA3FzxmucgfmT9AyLHghp4DyLpSqICIkARN1FkYldG4RpDolHQuc5cZDoyAaSfiKsFDe2B6IECl7pGPF2vgczMTEycOBGVlZX+93w+HyorKzF58uSw20yePDlkfQB49913/esPHjwYpaWlIes0NjZi/fr1EfcZiR07duDiiy/GDTfcgHvvvbfH9bOyspCfnx/yR0jKcuKEiAQCgL59Y9vG5Qp0+OmLTqxOvElFgYCIXlOjfXl0gCI6CYscBFUr4AKWG1AyHfRENxYtB5J4DuJH1n9+PuBwqNsH70EkXUnUjxugnUuiJOyJTk/uhPCL6FmFqra32WxMLpoAsv57ZfZChj1D1T7SeSBvwYIFePrpp/H8889j586dmDdvHlpaWjB79mwAwKxZs7Bw4UL/+rfeeitWr16NBx98ELt27cKdd96JTz/9FPPnzwcgfs+33XYb7rnnHvz1r3/F559/jlmzZqG8vBzTp0/37+fgwYPYunUrDh48CK/Xi61bt2Lr1q1obhazCrZv346LL74Yl156KRYsWICqqipUVVWhxiLCByG6I6NwCwqEOB4rTC5KUgUposc6EwMIzQtgAR9cdU81JOWhgGg8TKpoLIkOYgDiHBw8yHOgBs6GIUQ9iUbhAukbBaoVCduJUMBNCC2ugeKcYhxtPsprQAVazIZJZ0upa6+9FjU1NVi8eDGqqqowbtw4rF692p8Y9ODBg7DbA7Fw5513Hl5++WUsWrQIP//5z3Haaadh1apVGDVqlH+dO+64Ay0tLZg7dy7q6+tx/vnnY/Xq1XAFCX2LFy/G888/7/9//PjxAID3338fF110Ef70pz+hpqYGL774Il588UX/egMHDsT+/fv1qg5CrEO8Vi6SsjJg504mFyXWJ97EunJdmw3o7BTR6PFeP0mGIjoJCwUsYwn2g07UzqWuDvB61Ufzpiu8BoxFi/rnQBJJVxK1EgGY2DIRtPSDrm+vR6evU3U0b7qiyUASZwOoJtGcAEB6R6IDwPz58/2R5F1Zs2ZNt/dmzJiBGTNmRNyfzWbD0qVLsXTp0ojrrFixAitWrIj4+Z133ok777wz4ueEpD2JiOgAI9GJ9VFj55KRIa6Zqirg8GHTi+i0cyFhoZ2LsWjhB927t1gqSuj+SGxwNoaxcBCDEPVQwDIWWf+AehE32Aamrq0uwRKlH1rOxuA1ED+cDUMISUsoopN0R+010L+/WB45om15dIAiOgkLBURj0cIPOjMTyMsTr3kO4ofXgLFoZacDsP5J+kEBy1i08IPOsGf4zx8joeNHUxGd9R83WtnpAKx/QoiFUGNlAVBEJ6mDmkh0ACgvF8vDh7Utjw5QRCdh0ULAYhSoerSof4AiYiJQRDcWrSPRFSXREhFiHbT0I6aAFT9azAQAOBsgETS1c2H9x43W9a+wESeEWIFEI9EtEIVLSFTUJBYFGIlOrI8UsGjnYgxa1D9AETcRKKIbi5b3II8nkGOAkHSAdi7GooUnPcBI6ESgnYuxaFn/nb5ONLobNSgVIYTojFoBccAAsfz6a23LQ0iyUTsbg5HoxOpoKSCeOCES7ZLYkfWv1g9dwtkA6qGIbixa1H9OjrA1AkSCXULSBU0i0YMEXEaBxkeDuwGABiJ6Di111MLEosaiRf1nO7ORnZENgHkBCCEWQW0k+imniOXXX3P6LLEuLS1AU5N4Ha+ILiPRKaITq6KFgCUTWwIBexISG40nA260EtEp4sZHR0cgcpkiujFocQ+y2QL3IYroJJ3QUkD0Kl6/KExiQ0bNFrgSa8QZCa2ODm8HWjpEI66JJzfrP260GMgDgN7ZohGniE5SgpUrxYPtd78L+HxGl4bogVoRXUbhejypHf329NPA2WcDf/ub0SUheiB//y5XIDlfrMiBJIroxKo0nOwvJyLiZmSIxJgARfR4kSK6rD+1UMRVR0OQXpTINUBLI/VoIaIDFNFJeqKFiOvKcPmjQKU9CYmNhnbRiORnJdaI085FHcGDPolcA6x/9WiVF6AoW2wvRXlCLEtHBzB/vuhkvPIK8Je/GF0iojWKol5Ez8wMbHPokLblMgtffgnMnQt8+ilw/fVAa6vRJSJaE2zlYrPFt62MRLeApRFFdBIWrURcKWBRRI8PrUV0CojxIQXcXr3EYJBaaKejHq0sjaSnOu9BJJ2QInqiIi6jQNXhr/9MbeqfAmJ8SAG3V2YvZNjVN+K001GPHEhKdDYG70EkZVi9Gjh2LPA/I3FTj4YGEUkOxC+iA6nvi/7yy4HXjY3A3/9uXFmIPqjNCQAERPQTJ4C2Nu3KpAO6i+hPPPEEBg0aBJfLhUmTJmHDhg0R112xYgVsNlvIn8vlCllHURQsXrwYZWVlyM7OxpQpU7B79269v0baoZWIKwUsirjxoXX9U0CMD62ioKWI3t5u+rbAdGhlacRI9MRhO249/JHoWRSwjICDGMaihZ0REIhEb/I0ocPbkWCp0gvegwjpwhtviOXw4WL54YfGlYXog4zCzcsDsrPj3z7YFz0VWblSLGUH++OPDSsK0Qkposfrhw6ITn9OjnhtcksXXUX01157DQsWLMCSJUuwefNmjB07FhUVFTgWPArbhfz8fBw9etT/d+DAgZDPly1bhkcffRTLly/H+vXrkZubi4qKCrS3t+v5VdIKRdE+Ep0CVnxoYacDsP7VIus/0d9/Xh7gcIjXPAfxwXuQOWA7bj0URdFMxKWVgjooohuLVnY6ha5C2CCmI/MaiA/NrgEXrwGSIqxbJ5Z33CGWe/cGEvCR1CDYykINUkRPRTuXQ4eAnTtFx/jee8V7GzcaWyaiPYlcAzabZQaSdBXRH3roIcyZMwezZ8/GyJEjsXz5cuTk5ODZZ5+NuI3NZkNpaan/r1/QVABFUfDwww9j0aJFmDZtGsaMGYMXXngBR44cwapVq/T8KmlFa2sg1wkFLGOggGgsWkVBM7GlemgpZQ7YjluPlo4W+BTRiFPENYZGjzaJRWnnog6toqAddoc/mp2+6PGh+UAe8zIQK1NXB+zaJV5feSVQViZef/GFcWUi2pOIlQWQ2nYuchBpzBjgG98Qr3fuFNGbJHVI9BqQli7pGonu8XiwadMmTJkyJXAwux1TpkzBOnkRhaG5uRkDBw7EgAEDMG3aNOzYscP/2b59+1BVVRWyz4KCAkyaNCnqPt1uNxobG0P+SGRk9djtQG5uYvuinYg6aOdiLFrVPxAQcZlcNHa0nA1DSyn1mKUdZxseH1K8stvsyHHmJLQvRoGqQ6tIaCkgsv7jQysBF+BAkhq0nA3D+icpgbTBGzYMKC4Ghg4V/3/1lXFlItojZ2n27atue4tE4arik0/EcvJk4LTTRKTZiRNMHJZqJDobI91F9NraWni93pAINADo168fquQIRRfOOOMMPPvss/jLX/6CF198ET6fD+eddx6+PnkjkdvFs08AuO+++1BQUOD/GyBH+UhYgsWreJPqdoVRuOpgJLqxyNmVWojoTO4aPy0tgcAEXgPGYZZ2nG14fASLV7YEG3FGgaqDAqKxUEQ3ltaOVngVLwANr4F21j+xMDJIYPJksRw8WCz37TOmPEQfamrEMlERPRXtXIKvgZwcYOBA8b+coUFSg0Q80QHLDCTpnlg0HiZPnoxZs2Zh3LhxuPDCC/H666+jpKQETz75ZEL7XbhwIRoaGvx/h1LxxqQhWvlBAxSw1KJ1UsWGBsDrTWxf6YQekei8BmJH1r/DoS4vTzCs/+SiRzvONjw+KCAaj9YierOnmYkt44DXgLFoOhuG9U9SARmFe+65YilF9P37DSkO0QkZVV1crG77YDuXVLI5cbuBzZvFazmQJBPsfvmlMWUi+iAj0Wnnoo7i4mI4HA5Uy4o8SXV1NUpjHJlwOp0YP3489uzZAwD+7eLdZ1ZWFvLz80P+SGS0FBBpJ6IOrQYyZPJrAKivT2xf6QRFdGPRcjYM70HqMUs7zjY8PnQREBkFGhdanYNgT2/6oseOltdAnxwxnex4Gz3ZYkXT2TAuzoYhFsfnA9avF68ZiZ7aSBG9pETd9uXlYul2p5YP6ObNgMcj6mXIEPHe6aeL5e7dxpWLaE+iA0npLqJnZmZi4sSJqKys9L/n8/lQWVmJybIB6QGv14vPP/8cZSeTbwwePBilpaUh+2xsbMT69etj3ifpGQqIxqPVOXA6gbw88ZrnIHa0vAaknUsqPQvpDe9B5oDtuDXRUkCkgKUOPRJbMhI3djQdSGJegLjhTABCgti1S0RH5eQAo0eL9yiipybSzkWtgJiVFbCCSaVZl9LK5dxzA9FRUiw9etSYMhHt8XgCnriJiugmt3PJ0HPnCxYswA033ICzzjoL55xzDh5++GG0tLRg9uzZAIBZs2ahf//+uO+++wAAS5cuxbnnnothw4ahvr4eDzzwAA4cOIDvf//7AACbzYbbbrsN99xzD0477TQMHjwYv/zlL1FeXo7p06fr+VXSCgpYxuLzaevJ3bu32B/PQezIa0AOQCQCr4H44T3IPLAdtx5aCbgABSw1+BSf5iJifXs9z0EcNHoo4hoJRXRCgpAC4tlnAxknpZdBg8Ty4EFh25HotEtiDhKNwgWEpcuxY0JEHD9em3IZTdecAEDAMztKXkNiMWTEoN0eaocQD9ITvapKeBE7HJoUTWt0FdGvvfZa1NTUYPHixaiqqsK4ceOwevVqf0KxgwcPwm4PBMOfOHECc+bMQVVVFYqKijBx4kSsXbsWI0eO9K9zxx13oKWlBXPnzkV9fT3OP/98rF69Gi6XS8+vklbQzsVYmpsDr7USEQ8c4DmIB4q4xqJH/Tc3Ax0dYnYGiR2249aDApaxtHhaoEB4mXI2gDHwGjAWPeq/rbMN7Z3tcGWwnSAWQ/qhhxMQOzpEB00+rBJrk6idCyBExE2bTB+JGzOKQhE9XZAielGRENLV0K+fEM69XuGvLi2OTIauIjoAzJ8/H/Pnzw/72Zo1a0L+/+1vf4vf/va3Ufdns9mwdOlSLF26VKsiki7oJSByoD02ZP1nZgJaaEpyIIMibuxQRDcWLes/ODnviROBWZIkdtiOW4uGdpFUQ0sBi37csSMFxAx7hiaCH0Xc+Glyi+l89EQ3Bi1F9LysPNhtdvgUH060nUBZXlnC+yQkqQRbWUiyssQDakODiDqmiG59FEWbSHQZiZsqIvqXXwp/68xM4JxzAu+ftHmknUsKocXv3+EQAyyHD4trwKQium6e6MS66CEgdnQALS2J7y8d0CqpqIQibvzQE91YtKx/hyMwo4zXAEkHNPVEzxajsK0drWjvbE94f+mAlkkVAYroamAkurFoWf92m90/G4PngFiO2lpgxw7x+rzzQj+TUR1dEq0Ti9LYKAQPIHE7FyB1PNHfeUcsL7hA5AWQyEj02tpAvRFrI8UOKX6oxQLJRSmik25IAasgcTtV5OQE7BNoJxIbWgqIAEV0NTAS3Vh4DRCiHi0FrPysfNht4lGRdiKxoaUnPRBk58LZADFDEd1Y/PWfqU0jznNALMuHH4rlqFHdLT5O2uLh2LHklonog4zCzc0FsrPV7yfVItHfflssKypC3+/TJ+B3zYGk1EArEV1eAxTRiZXQUsCy2ShgxYvWAiJ96eOHIrqx8BogRD1aJlVkFGj8NLi1s9MBKCCqQQ8R/Xgrp5PFipb1D9BWiliY998Xy4su6v6ZjESniJ4a1NSIZSJR6EBqiehuNyBtHy+9NPQzuz0wkERf9NRACzsXIBCJbuJrgCI66QajQI2F9W88eojobW3ij/QMrwFC1KO1gCUtXShgxYZeAiJF9NjR8hz0yRYRVU2eJnR4OeU8FvS6B/EaIJZDRuFefHH3z6SAyCjc1ECLpKJAqJ2LoiS2L6P5+GOgtVVYt4wZ0/1zJhdNLWjnQtIZrT25GQUaH1ra6QAUEOPF7RZ/gDbXQH5+YLYaz0FsUEQnRD0UcY2F9W8s7k433F7RiGtxDgpdhf7XHEiKDS1nwwC8BohF2bsX2L0byMgApkzp/jkj0VMLrSLRZSLF9vaAKGNV5CDSpZcKe4KuyLpi4rDUQJ5HrWZjUEQnVoIClrFwEMNYmpoCr/PyEt8fLY3ih/cgQtSjtSc3Baz44EwAY2nyBBrxXpm9Et6fw+7wC+m8BmJD84EkF+9BxIK89ZZYnn9++AdaRqKnFlpZWbhcQK9eofu0KsEiejhkXVn9exKBPI9aRaLTzoVYCQpYxsL6NxYpoufkiOARLeA5iA96ohOiHs1FXJnYkolFY4KDGMYi6z/HmYMMuzaNuLR0oS96bOjmic57ELESb74plpdfHv5zafshI5iJtdHKzgVIDXG5qgrYtk28/ta3wq8jxVZGoqcGWtu5HDmS2H50hCI66YZeIi4FrNigiG4sWtc/wHMQL7wGCFFPQzsTWxoJ7VyMRev6B3gO4kU3T/R21j+xCE1NgYSKV1wRfh12kFML2cmQ5zURpIhu5QGWd98VywkTAtZFXaGInlpoZeciB6JaWoStkQmhiE5CUBT9okApYMWGnlG4Vs9Pkgz0ENH5jBAfFNEJUYeiKBRxDUbrQYzgmQAKG/EeoYhuPLwHkbTnnXcAjwcYNgw444zw6/DhNLWorxfLwsLE9yVFRCtHoksRPZKVC0BP9FRDKzuXgoJAQjmT/jYoopMQ2tuBzk7xmgKWMeiVWNTjEQmySXQYiW48nA1DiDraOtvgVbwAdBBx6ckdE3olVfQq3hC/bxIeiujGQxGdpD3SC/qKK8InVARCOwccILU+WoroqRCJ/sEHYvnNb0ZeR4qtVh4sIAKvN3ANJCqiByeUM+lvgyI6CUGKVzZbIKdFolBAjA+tE4vm5gJOp3jNc9AzFNGNhbNhCFGPFK9ssCE3M1eTfVLAig+tBcRsZzZcGS4APAexoIeI7vdEbzNnRJTZoCc6SXvWrhXLiy6KvI58OGWUU2ogO/CMRAcOHhR/DgcweXLk9ThVO3VobAwMBsp7WyKY/LdBEZ2EIMWrvDzArtGvg0n94kNrAdFm4zmIh+BrQCsooseO2w10dIjXWs/GYP2TVEeKV3lZebDbtGnEKaLHhx4iLpO7xg4j0Y3F3emGx+sBoP1sGNY/sQQNDcAXX4jX554beb1evYCMk8mP2UGzPoxED/DRR2I5YUL0qEyTC6UkDuTvPzsbyMxMfH8m/21QRCchMArXeHgOjIWe6MYSPBsmV5tA2hA7F86YJamMLgJuNu1c4kGegwKXRqOAoIgbDxTRjUXWPwD0ytRmSqus//r2enh9Xk32SYhubNggHjYHDwb69Yu8XrBlATto1keKiFpEAFk9En3bNrE855zo6wV7orODZm3kTAytIuBMLp5QRCchaG0lAvD5IF4oohsL699Y9JwN4/UCTbQUJimMX8DNooBrFFonFgV4DuLBL6Jnal//tHPpGVn/vTJ7wWF3aLJPOZCnQEGDu0GTfRKiG59/LpYTJ/a8LjsIqYGiMBI9GDkT48wzo68nhVKPB2hu1rdMRF8oopN0Rg8BUQpYTU0BmwYSGa0TiwK0c4kHiujGokf9Z2cDLmEpzHNAUho9o3BPtJ2AT/Fptt9URddzwNkAPaKLJ3qO6MxxEKNn9Kj/TEcmcp1iahotjYjp2b1bLE8/ved1mbQnNWhrC4gcWojo8nchhXmrIUX0ESOir5eTE0jcZtXvSgQU0Uk6o4eAFdyW8P4YHZ8vEClLEdcY9BTRTdoOmAo96h/gNUDSAz2ioKUfsQIlxKqBdEdRFF0tdSji9gztXIxFj/oHeA6IhYhHRA/2GyTWRQqIdnt0D/BYkeKJFYWTtjZg3z7xeuTI6OvabNb+riQARXSSzughYGVkBK4nCljRaW4OWIJRRDcGPT3RWf89o7eIzn4KSWX0ELCyMrKQ48wBQAGrJ1o6WqBANOKairguCoix0uQRkQgU0Y2BIjpJe6SIftppPa/LDlpqEOyHbrMlvj8pnDRY0L7q3/8WYkbv3gFv92hIEd2K35UEoIhO0hm9BCzaicSGrH+nE8jK0m6/rP/Y0TMSva1N/JHI6H0PYj+FpDIUsIxF1n+GPQPZGdma7Zf1Hzt6RqI3uhvR4aUvYTR4DyJpTVsbcPCgeB2LiM6H09RASz90ICBEtrcDbrc2+0wWhw6J5eDBsQ0oMBI9NdBaRJfiiUl/FxTRSQi0UjCW4PrXYiBbwvqPHT2ugfx8wHEyvxYHMqLDexAh6qGAZSzBdjo2DRtxaedCT/Se0cVO56SlEcBz0BN63YN4DRBLcOCAWObnB5JDRoMPp6mB1iJ6cCfIahHaX38tlqecEtv6FNFTg+DZGFogrwEpDJgMiugkBD2SWgJ8RogVCojGo4cnvc0WCDYx6awk08BrgBD16CZgnRQRmdQvOhzEMB49zoHD7kChqxAAz0FP6HYN0NKIWIEjR8Syf//YoqHoNZgaSKFbKxHd4QDy8kL3bRUooqcnWkeim9zSiCI6CYF2Lsaih4AL8BktHvS6BuiLHhv0RCdEPY0eirhGIv248zLzNN0v6z92OJBhLP76z2T9kzREiujl5bGtzwiP1EDrKNzgfZlURIwIRfT0ROuBJEaiEyshf6d52vb/+IwQI1JE1yKxdzC03IsdRkIbCz3RCVEPBURjafY0AwDysrR9iOJMgNjR6xroky1Gwo+3cjpZNHgPImnN0aNiWVYW2/p8OE0NtLZzCd6X1cRlKaL37x/b+lb9niQUrSPRg0V0RdFmnxpCEZ2EIEVciujG0Cz635qL6Kz/2PD59J8NwHMQHQ5iEKKeJrc+kdB+EZd+xFGR9d8rU9tGnAJibHh9Xv9ABkVcY9BrNgw90YklYCR6eqKHiJ4ukejye1JEtzZ62bn4fEBLizb71BCK6CQEvUV0WilER4roetV/YyPQ2antvlMJWf+AfiIuPdGjw9kwhKjHbyeicSQ0BcTYkAKuXiJ6S0cLPF6PpvtOJWT9AxTRjUJGovMeRNKSeCPRGYWbGugpolvtt3H4sFgyEj290FpEz8kRuQEAU1q6UEQnIeglonO2WmzoZecS3KazjYqMvEc7nUBWlrb7pid6bOh9D+JAHkll9BZxKWBFx2/novFMgAJXAWwQSepo6RIZKeA67U5kZWjbiPMaiA05G4ODGInzxBNPYNCgQXC5XJg0aRI2bNgQdf2VK1di+PDhcLlcGD16NN56662QzxVFweLFi1FWVobs7GxMmTIFu3fvDlnn3nvvxXnnnYecnBwURhAEDx48iMsvvxw5OTno27cvbr/9dnQyQkcQbyS6FJxMallAYkRrAREIdN6tFIne2hqISCstjW0bK35P0h2trwGbzdS+6BTRSQi0EzEWveo/IyNwH+I5iExwFLTNpu2+eQ3Eht6zMVj/JJXRzc6FVgoxIWcCaD2IYbfZUegqBJBeImK86BUFDQR5ordxOlk09B7IS5dBpNdeew0LFizAkiVLsHnzZowdOxYVFRU4duxY2PXXrl2LmTNn4uabb8aWLVswffp0TJ8+Hdu3b/evs2zZMjz66KNYvnw51q9fj9zcXFRUVKC9vd2/jsfjwYwZMzBv3rywx/F6vbj88svh8Xiwdu1aPP/881ixYgUWL16sbQVYlXgj0aXgpCih02GJtWBiUYGcbu10xt6RYyR6aqDHNSDFKxNeAxTRSQi0czEWvQREgCJiLLD+jUev2Risf5IO0M7FWPQSEAGeg1jQyw8dYP3Hiv8epFNehrq2OihpELH70EMPYc6cOZg9ezZGjhyJ5cuXIycnB88++2zY9R955BFMnToVt99+O0aMGIG7774bEyZMwOOPPw5ARKE//PDDWLRoEaZNm4YxY8bghRdewJEjR7Bq1Sr/fu666y78+Mc/xujRo8Me55133sEXX3yBF198EePGjcNll12Gu+++G0888QQ8HlpNQQ5y9OsX2/rZ2QHLAhMKRSRGZBSWHiK6lcRlKaL36RN7NBpFdOvT0SFmIQD6XAOMRCdmJngQXGsBi3YusaGXgAjQziIW9Kx/aedCT/To6B2J3toKuN3a7psQM+BTfGjxiOQ7tHMxBr3sXICgSFzOBoiIXjMBAF4DsaJ3JLrb60ZbZ5um+zYbHo8HmzZtwpQpU/zv2e12TJkyBevWrQu7zbp160LWB4CKigr/+vv27UNVVVXIOgUFBZg0aVLEfUY6zujRo9EvSCSuqKhAY2MjduzYEXYbt9uNxsbGkL+UpKMjIPbIh/6esNlMLRSRGNFDQJEdISvNUKitFcvi4ti3oYhufYLvXXpEopvw3kgRnfhpbQ3YselppZAGASSq0WsQA2AkbiwwEt149BrIyM8PBEVwIImkIq0drVAgGli9okDTxUpBLXqKuNJShyJuZJIxE4B2LtHxW0ppPBumV2YvZNgzAKT+NVBbWwuv1xsiVANAv379UFVVFXabqqqqqOvLZTz7jOc4wcfoyn333YeCggL/34ABA2I+nqWQD5c2W3wJJk1sWUBiRI8OpOwIpZOITpHImsh7V3a2sPLRChNbGlFEJ37kPdpmEwlxtUQKiJ2d1moLkg1FXGPRMxKd9d8zwbNhtL4G7PbAbAzOBiCpiBQQbbAhx6ltIy4FxLbONrR1pHYUaCLQzsVY9MoJAAB9ckRkKes/OnpdAzabjdeARVm4cCEaGhr8f4cOHTK6SPogH/ALCwMWLbFgYqGIxIgeHch0E9E7OwOWIMRa6GFnBDASnVgDef/PzRWCk5ZkZwOZmeI1o0AjQzsXY+FMAGNxu8UzFKDvOeA1QFIRKSD2yuwFm8aZkfOz8uGwCVGAdiKR8du56JDYsreLAmJPcBDDWNydbnT4OgDoa2mU6ueguLgYDocD1dXVIe9XV1ejtLQ07DalpaVR15fLePYZz3GCj9GVrKws5Ofnh/ylJPIBXz5sxgrtXKyPHh1IK4rowZ7osZKTExh0oqWLNdErAs7Es3QoohM/eiUVBUR0O0XEnqGIayx6XgPyeaK1FWhv137/qUDwc2Jurvb75zVAUhk9BVybzea3E6GlS2SCBzK0hvXfM3ol1gUCAm6juxEd3g7N958KyHsQAORmat+Ip4uInpmZiYkTJ6KystL/ns/nQ2VlJSZPnhx2m8mTJ4esDwDvvvuuf/3BgwejtLQ0ZJ3GxkasX78+4j4jHefzzz/HMZlA8+Rx8vPzMXLkyJj3k5JIATFeEd3EQhGJAa8XaDs5Q08PO5eWFu32qTdqItGD7Y94DVgTvQQsE18DFNGJHz0FXIACVizQzsVY9LwG8vMDA+08B+GRgxjBQQlawmuApDJ6+nEDAV/0VBewEiEpkdDtrP9I+OvfqX39F7oK/a85GyM88h6UnZHt9y/XknQR0QFgwYIFePrpp/H8889j586dmDdvHlpaWjB79mwAwKxZs7Bw4UL/+rfeeitWr16NBx98ELt27cKdd96JTz/9FPPnzwcgBkJvu+023HPPPfjrX/+Kzz//HLNmzUJ5eTmmT5/u38/BgwexdetWHDx4EF6vF1u3bsXWrVvRfPIB+dJLL8XIkSPx3//939i2bRvefvttLFq0CLfccguysrKSV0FmJNFIdAqI1iQ4AijdI9HViOhAQETnVGFroreIbsJrQPsnHGJZ9IzCBWgnEgu0czEWvWdjFBWJ54u6OqC8XPtjWB0O5BGiHj39oIH0ErDU4p8NQCsLQ9BzNkaGPQOFrkLUt9ejrq0OfXP7an4Mq6PnIBIA9MlOH1/6a6+9FjU1NVi8eDGqqqowbtw4rF692p/E8+DBg7AHeW+ed955ePnll7Fo0SL8/Oc/x2mnnYZVq1Zh1KhR/nXuuOMOtLS0YO7cuaivr8f555+P1atXw+Vy+ddZvHgxnn/+ef//48ePBwC8//77uOiii+BwOPDmm29i3rx5mDx5MnJzc3HDDTdg6dKleleJ+ZEPl/FYWQC0c7E6svOSkQFoOZBkYgExImrsXIDAbAzZESfWQq8OvJyWbsJIdIroxI+eUdAABaxYoJ2LsSRDxJUiOumO3gN58pmO9U9SET0FRIAibizoORtAzgSgnUtk9LTTAcQ1IEV00h29RXR5Dzremh7ZwefPn++PJO/KmjVrur03Y8YMzJgxI+L+bDYbli5dGlXwXrFiBVasWBG1XAMHDsRbb70VdZ20RG0kOu1crE1w51HLfDRWFNGlp7mM3IsVEyeQJDGQhiI67VyIHz2joAGKuD2hKLRzMRq9B5KkiHs8Pfp/ccNIdELUo7udi/TkppVFWBRFYWJLg2nu0G8mAMBz0BP+2TAcyCPpiFpPdEaiWxu9BJRgEV1RtN23XsjfcLzJgymiW5s0tHOhiE78MBLdWFpbA20k7VyMgQNJxqJ3JDrrn6QyelqJAEBvV3pFgcZLe2c7fIoPgL6JLSkgRkbvSHRpJ8JrIDzJikRnXgBiSuiJnp7oJaDIzqjXC7jd2u5bLyiipyeMRCfpDAVEY5H3H5tNJFbUmuD6t8qAdrLhQJKxMBKdEPUkw8oCYCR6JORMAADIcWrfiAfPBJBiPQmFlkbGIq8BzgQgaYkUwdVaWVBEtyZ6CShSQARMGYkbForo6YneIroJf/8U0YkfCojGopelmkTWf0eHKQf0TAEHkoyFkeiEqEdvAatPzsko3DZG4YZDCri5zlzYbdo/XktPdJ/i8w+YkFD0tjSiiBudZCUW5UwAYkrUCoi0c7E2egkoDgeQnR16DDPj9QYEBoro6YXedi4mFK4oohM/eguI9IOOjt71n5MDZGaK17R0CY/ekdC8BqLDSHRC1MMoXGPRu/6zndnIzhAdap6D8CQtsSUHksJCT3SS1shIcrUiOiPRrYmenRcTe0J3oylocD/eAQWK6NaGdi4knWEUqLHoLSDabIEZhjwH4eE1YCzJqn8OYpBUhFG4xqK3nQ7Ac9ATfhFXr9kYJyOhWf/h8Q9iOHkPImlIolYWFNGtiZ6dFyuJ6PL3n5Ul/uKBIrq1oZ0LSWdo52Isetc/wHPQE4yENpZk1X9jo7A1IiSV0DuxKK0UoqN3FDQQ6otOupO0xJYUccPit5TSORK9rbMNbR1tuhyDENXQziU9YSS6QO3vP3gbXgPWJBl2LiZL6EcRnfihnYux6F3/AEXcaChK8gaSeA2ER+9I9MLCwOv6en2OQYhRJCuxKAXE8Og9iAHwHERDURRaGhmM3oMY+Vn5cNgcADiQREyGoiQuore3Ax6PtuUi+kMRXUARPX3ROxLd6wXcbm33nSC6i+hPPPEEBg0aBJfLhUmTJmHDhg0R13366adxwQUXoKioCEVFRZgyZUq39W+88UbYbLaQv6lTp+r9NdKCZAmI7e1AGwNIuqF3FC4QsHOhJ3p32toAn0+81nsgiYMY4dH7GsjICPRVeA5ih+24NdBbQJSJRZs8TfB42dHvit52OkCQJzdnA3SjtaMVCkSkEj3RjUHv5MY2m43XADEnwZGS8YqIwR1vWrpYDz0jgEzsCd0Niujpi94iOmC6a0BXEf21117DggULsGTJEmzevBljx45FRUUFjh07Fnb9NWvWYObMmXj//fexbt06DBgwAJdeeikOHz4cst7UqVNx9OhR/98rr7yi59dIG/SOhM7LEyIWwEjccNDOxViCB/mD79lawvqPjt6R6ADPQbywHbcOegtYBVkFsMEGADjRxpHYriTDzqW3i5HQkZD1b4MNOc4cXY4hB5JY/+FJyjXA2QDEjEjxz+EAsrPj2zYjI9DxoIhoPfSMAJK/JStEHyYiojO5rrXR6xrIyAj466eTiP7QQw9hzpw5mD17NkaOHInly5cjJycHzz77bNj1X3rpJfzwhz/EuHHjMHz4cDzzzDPw+XyorKwMWS8rKwulpaX+vyIZXksSQm8R12ajgBUN2rkYi6z/3FzArtOdUdZ/a6uYkUFCScZsDM4GiA+249ZBbzsXh92BQlchAEbihiMZdi4UcSMjB5FyM3Nht+nTiEsBt9HdiA4vE2t0xZ/YVafZMABFdGJSpICYlyc6vPHC5KLWRU8BRYrora3a71trGImevujZgTdpclHdRHSPx4NNmzZhypQpgYPZ7ZgyZQrWrVsX0z5aW1vR0dGB3lJ5OsmaNWvQt29fnHHGGZg3bx6OM6xZExgFaiy0czGWZMwEyM8PCPS8BrrDe5C5YDtuLfS2cwEo4kZD70EMgHYi0UjGIIYcRAKA+vZ63Y5jVRiJTtKWRAREgJG4VkbPKLick7OqUj0SXW7T1BTwViXWIDipnJ55AdIlEr22thZerxf9+vULeb9fv36oqqqKaR8//elPUV5eHtKBnzp1Kl544QVUVlbi/vvvxwcffIDLLrsMXq834n7cbjcaGxtD/kh3khEJzeSikaGdi7Ek4/dvt/McRCMZA0ms/9gxSzvONrxnFEVJqic3BazuJENA7JPNQYxIJGMQI8OegYIsIXZxIKM7eltKAYGBPNY/MRVaieh8vrEeybBzSZdIdEUxnVhKesDtFok/AX0j0U32u8gwugCR+PWvf41XX30Va9asgcvl8r9/3XXX+V+PHj0aY8aMwdChQ7FmzRpccsklYfd133334a677tK9zFbG4wE6Ts5MpYhrDLRzMZZkCLiAOAe1tTwH4WAkemqhVTvONrxnPF4POn2dAHQWsE6KuEzq151kzgSggNidZNQ/IM5Bg7uBAxlhYF4AkrYkKqLTzsW66Nl5SZdIdJdL+F93dor96NkRJNqid1I5k4roukWiFxcXw+FwoLq6OuT96upqlJaWRt32N7/5DX7961/jnXfewZgxY6KuO2TIEBQXF2PPnj0R11m4cCEaGhr8f4cOHYr9i6QJ8v4PMBLdKBiFayzJEHABnoNo8BowF2Zpx9mG94yMAAUYiW4UnAlgLMmof4DnIBr0RCdpC+1c0hcmFhUkcg3YbPRFtyry95+dLRIra41JrwHdRPTMzExMnDgxJJmYTC42efLkiNstW7YMd999N1avXo2zzjqrx+N8/fXXOH78OMrKyiKuk5WVhfz8/JA/Eor8/cuBQL2ggBWZZNi5cBAjMsmMRAd4Drri9QZmKzIS3RyYpR1nG94zUrzKzsiGw67DQ+xJ6MkdmWTauXAmQHeSUf9A0DXAcxCCT/GhpUNEinEgiaQdWonowVFtxBrIzoseUbjpYucSvB1FdGuht4Bl0mtANxEdABYsWICnn34azz//PHbu3Il58+ahpaUFs2fPBgDMmjULCxcu9K9///3345e//CWeffZZDBo0CFVVVaiqqkLzyZPT3NyM22+/HZ988gn279+PyspKTJs2DcOGDUNFRYWeXyXlYRSu8STTzoUCbneSMYgBBAYyeA2EEjxLi5Ho5oHtuDVImpUFPbkjkozElsECoqIouh3HivijoHWsf4DXQCRaPIFGXNeBJCY3JmYk0Ugc2fmggGg9ZAdGWq9oSbrYuQRvx2vAWugdhWjSa0BXT/Rrr70WNTU1WLx4MaqqqjBu3DisXr3an6Ts4MGDsNsDOv7vf/97eDweXH311SH7WbJkCe688044HA589tlneP7551FfX4/y8nJceumluPvuu5GVlaXnV0l5khWFy0joyCTjHMj6b20F2tvFzAMiSMYgBkARNxKy/h0OQM/bOes/PtiOW4NkW1kwEr07ybRz8SpeNLobUeAq0O1YViPZkegUcUOR9W+32ZGdka3bcXgPIqYk0WhkCojWxOcLiHt6RqKbTEAMC0X09ERvAcukkei6JxadP38+5s+fH/azNWvWhPy/f//+qPvKzs7G22+/rVHJSDCMRDeeZERCFxQIkdLrFQMZ/fvrdyyrkaxIdF4D4Qmuf5tNv+Ow/uOH7bj5SUYUNMAo0GgkQ8TNdmYjOyMbbZ1tON52nCJ6EHIQQ+9rgCJ6eIIHkWw6NuKsf2JKEo1GpoBoTdrbA6/1iEQ3qYAYFunnTxE9vUjTSHRd7VyIdUh2FC4j0buTjHNgs/EcRILXgLGw/glRTzIS+gEUsKKRNEsdDmSEJeme6IyEDiFZA3m8BxFTwkj09CRY3M7WYQaOSQXEsDASPT3R084IMO1sDIroBAD9oM0ALXWMJdn1z2sglGTPBKivFzMyCEkFmFTReORABs+BMTAvgLEk+/ff2tGK9s72HtYmJElIMTXRSHQmFrUW8ry7XIBdB1nNSpHoUkzlQFJ6oWdiXcC01wBFdALAGD9o5sQK4PUG7g3JGsigiB4KLY2MJdn3IEUJzDwkxOoky8qCAmJ4fIoPLR2iA6m3iMhzEJ5k5wVg/YeSrEGMgqwCOGwOADwHxERoJaJTQLQWekfhWikSnSJ6epLova8nTHoNUEQnAJIfie52m25AyVBkuwMwEt0okhWJThE9PMm6BzmdgWPwHJBUIdlRoC0dLXB3unU9lpVo7Qg80CTLl552IqHQTsRYkjWIYbPZUJRdBIDngJiIRMVU+WBKAdFa6C0gmtTKohudnYDHI15TRE8vknUNmEw4pIhOACQvCjc3V4hYAAWsYKSA6HAAWVn6HosieniSdQ2w/sOTrEh0gAMZJPVIloBY4CqA3SYeHSlgBZCDGHabHa4Ml67H6u2inUs4km6nw0GMEJJ1DwI4kEFMCD3R05M0tbLoRrDIz9kY6QUj0Uk6k6woXCa2DE9wFK7Npu+xKOKGJ9mR6K2toUnd051kRaIDFNFJ6uG3c9HZSsFus6PIxSjQrgR70tt0bsSZWDQ8yU7s2uhuRIe3Q9djWYlkDWIAFNGJCaGdS3qSpgJiN4JFfpfKQAJeA9YkTWdjUEQnAJIXhQswsWI4khmFSxE9PMkScfPzA7lnTpzQ91hWgpHohKgnWYlFAdqJhMOIKFzWfyjJshMpdBX6X9e31+t6LCvBSHSS1mglore3Ax0cnLMMaWpl0Y3gelAbSEAR3ZokayDJZNcARXSdefddYMQIYPx4YONGo0sTmVQVsI4fB666ChgwALj/fv2Pp5ZkRUEDyRfRf/Mb4NRTgSuuAGprk3NMNSTrGrDbgSIRyJmUa2DTJmDCBHEfevtt/Y+nFkaiEzOyt24vblx1I37w5g9Q3VxtdHEikqzEokByBawjTUdw/rPnI/dXufjpuz+FYtKM5MkScIHkJxZ976v3cPX/XY17PrzH1JHXyRpIyrBnoCCrAEByzsEH+z/AoIcHod9v+uFPX/xJ9+OpxYhrgJZGxDRo5YkOBDokxPwkK7FoZ6f4MytaCKkU0a1JmkaiZxhdgFTm8GHg298O3F+vvBL48kugoMDYcoUjmQJWMkXcOXOAv/1NvP7Zz4DTTxfnxGykav3/7W/A7beL14cOATfdBPz1r/ofVw3JPgfHj+t/Dhobge98Bzh4UPz/ne8AO3eKQQ2zkaoDecS6NHuacfHzF+NQ4yEAwIbDG7D+++vhdDgNLll3khmJ7o+EToKAddNfbsLHhz4GACxbuwxj+o3B98Z8T/fjxosh9Z+ESPRPvv4EU1+cCq/ixZ93/hnHW4/jt1N/q/tx1SDtRJI1kNTgbtD9HNS11eHbr30bJ9rFtLXrX78e40rHYVjvYboeVw3JstMBGIlOTEii3thOp7DBaG8XD+/yQZWYm2QJiIAQEZPRSVUDRfT0JU1nYzASXUfuvlsI6GPHAkOGANXVwB/+YHSpwpNMO5dkCVgffwy88YZI1jl1qnhv6VLAjIFsRti56F3/Ph+wYIF4fdllIgL7b38DPvtM3+OqobMzMMCZSiLuI48IAX3AAGDMGNH+PPqovsdUCyPRidl4aN1DONR4CP1y+yE/Kx9bqrbgtR2vGV2ssPgFxCQIWMmKhK78qhJv730bTrsT1555LQDgnn/dA5/i0/W4akimgJhMT/SfvfczeBUvRpaMBAA8vvFxHG48rPtx46XD2wG31w0guZZGep+Dhz95GCfaT2BE8Qh8Y8A34Pa68fAnD+t6TLUkMxKdIjoxHRQR0xO9E4sG+4ubTEQMQYuIfP7+rUma5gWgiK4Tzc3ACy+I1488Atxxh3j99NPmFHGTaSeSrMSiTz0lljfcALz4omjftm4FPvlE3+OqIRXtXNasAfbsEW3i//0fcPXV4v0nntD3uGqQbT+QOiK61yvuNwDwq18B994rXj/7rDkTmjISnZiJDm8HHtvwGADgkamP4CeTfwIAeHrz00YWKyJG2LnoHYX7zJZnAABzJszBU1c+hfysfOyq3YV/HfiXrsdVgxFJFfWeCbDx8EZ8cOADOO1OvH3927jg1AvQ6evE7z/9va7HVYMcxABSJxK609eJJzc9CQBYevFS3HnRnQCAF7a9gBZPS5QtjcEQT/R2NuLEBPh8FNHTFb0FRJvNtHYWIWgxmBD8+zejWEbCo7elESPR04u//EXc64YNA/7jP4CZM8VvYNcuYMcOo0vXnVRLLNrSAvz5z+L1978vjnnlleJ/M9qJGBWF69MxoO/558Vy5kwhjN58s/j/b38zX9sof/8ZGUBWlv7HS8ZA0ocfCgud3r3FAMZllwHl5SKZ6Ycf6ndctTASnZiJd/a+g9rWWvTL7Yf/GvlfuGn8TbDb7PjwwIc42HDQ6OJ1I6mJRZMQid7kbsKqXasAALPHz0Z+Vj6mnTENAPC3f/9Nt+OqxYj6r2+vh9fn1e04r25/FQBw9circUr+KZh31jwAwOs7X9ftmGqR9e+0O5HpyNT9eMkYyPjwwIc41nIMfbL7YNoZ03DJ4EswsGAgmjxNWLN/jW7HVUsyB5LoiU5MRXBkilYiIrEGeovogLVEdC0GkTo7zRntRcLDSHSiJa+f7GPMnCkGEfPzhZgOiGSjZsOISHQ9Baz33xdC+qBBwLnniveuukoszSiiG2Hn4vMBDQ36HMPnA956S7y+7jqxvPBC8Wx59KiYEWAmgn//apOKx0MyBpLefFMsr7pKzAZ0OISQDgCrV+t3XLUwEp2YiZVfrAQAXHvmtciwZ6B/fn+c0/8cAMC7e83XiCfTziUZUbiV+yrR3tmOYb2HYWLZRADAVWeIRvyvX5qvETciCleBgvr2el2OoSgK/rRTJLG85sxrAACXnXYZHDYHdtbuxL4T+3Q5rlqSaacDJGcg6c9fiEiQ74z4DpwOJ2w2Gy4bJhrxt/eaL0s4PdFJ2hIcIRnsYR0vFNGtRzJEdLlvk0XihqBFPeTmBjrhvAasQ5omFqWIrgNeL/DPf4rXl18eeP9b3xJLM4roRkSi6xmF+/bJ/sVllwXuxxUVYvnFF0BNjX7HVkMyBzGysgKBEnqdg02bgNpa8Tz4jW8EjnvJJeL1e+/pc1y1JDMKGkiOiPv3v4tl8D1I5gZ45x39jquWVE2uS6yHoih4Z6+4SKYNn+Z//9IhlwIA3v3KfI14qiW2fHuPaMSnDp0K28lG/FtDvgUbbNhdtxtVzVW6HVsNyfSDdjqcfrFer3Owo2YHDjYcRHZGNiqGioenQlchzj/1fADA6j3mGolNZv0DyRFx39//PgDgP0/7T/97FcPEuZD3JzNBT3SStkgRKStLRKyoRYroslNOzI/eVhaAaUXEELQQUu32QCdQryg/oj3JikRvbTWVlQFFdB3YvBmorwcKCoCJEwPvSwHx44/1tdGIF6838PtPFSsFKRJeemnocUeMEK/N5ouebBFXbxFRDhRdcolIOC+RgrrZ6j+ZUdCA/tfA0aPAl1+K5xE5eAeI2QCAGEgy2/OJEbMxamv1PxaxHl/UfIGjzUfhynDhvAHn+d+fMmQKAOCDAx9AMdGDXKevE22donOVjEjoZCRVlAMVlw4NNOIFrgKM6jsKALDu0Drdjq2GZA5iAPqfg/f3CQH3G6d+A9nOQGTlhQNFI/LJYXM14smcCQDo78l9rOUYdtbuBABccOoF/vf/Y6CY0vrl8S9NJyAb4olusjogaYpWQqrsBDIK1zok084l1SPRAc7GsCJ6J9eVv39FATwefY6hAoroOvDBB2J50UXCY1kyapSwVWhsFAkXzYJRSRX1EnBraoB//1u8lqKh5LyTesjatfocWy3JFnH1FtHXndQ3uta/tNZZv16f46rFqEh0vet/9GgxmCcpKREWR4oiZguYiWSeg+JisTxxQljvERKM9Bu+4NQL4Mpw+d+fWD4RDpsDVc1VONx02KDSdceopIp6+RFXN1dj74m9sMHmFw0lk0+ZDABYe8hcjbhRIq5e50BGQV886OKQ9yedMgkA8MnX5hLRk+nHDehf/x8eEIlLRvcd7R8wkccdWjQUAPDpkU91ObZajJgN09LRAnenW/fjERIVrUQkCojWQ28BETCtJ3QIFNHTl2TZuQQfywRQRNeBDRvE8rzzQt/PyADGjxevPzXRs2+ykyoG+0HrEcwn63/4cKCoKPSzyZND1zELybRzAfQV0RUlEGkuRXPJxIlipuPhw8DXX2t/bLUYNYihVyS6HCSSv/dgzhG2zqYayFCU5Hui22ziuCdO6H88Yi3WHxYXxzcGfCPk/Rxnjj8S2kwCVrKTKurtBy3rf3jxcBS4CkI+mzxA3NQ2HDFXI55sOxE9z4GiKPj40McAgIsGXRTy2aT+QkT/9/F/myqpY6p5on+wX0TjyMj/YGRuhg2HTXYNJHEgo8BVALtNdGEZjU4MhwJi+sLEogIZkcmBpPRCUfS/BpzOgDez2zyD5hTRdUAKtFKsCubss8Vy48bklacnkp1UUUbhdnSERsFrhRQHJ03q/tm4cWK5bZupbJVSys7lq6+ETUZmZqC+Jbm5AUudbdu0P7ZaUs0TXYroXQfygMA9yEwDeW63sJUCkiOiZ2QEBtho6UK6IkVcKVYFc1b5WQCAjYfN04gnM6koEIgCbetsQ1uH9p269V+L+j/3lHO7fTaudBwA4PPqz01lqZNsOxc9fekPNR7CsZZjyLBnYHzp+JDP+uT0wZCiIQCAbdXmacRTzRNdDmJ0nYkBAGeXi0Z801HzTCfzeD3o8HUASM59yG6zo8glGnGK6MRwKKKnL0wsKuA1kJ50dAQ68HpdAzabsPIAgPZ2fY6hAoroGlNdDRw4IM53sB+6RIqKn3+e1GJFJZlJRQFxjcmIdz1EXBkFHU5EHzlS+EQfPw5UmSgvWSrZuUgrkYkTw89sGCUCObF9u/bHVksqeaK73QGrlnCR6KNHi+WOHdofWy3NATeKpJ0DaelitiTDxFhOtJ3Av48LP7BwIvqEsgkAgM+OfZbUckUj2QJuflY+HDaRPE0PAUsOYsio52BGFI+Aw+bAifYTONJ0RPNjqyWVIqHlLItRfUeF+KFLxvQbA0AMZJgFowYx9Kh/j9eD7cfEA9LZ/c/u9vnofqIR33HMPI24HMgDUmMgiZC40MoTnYlFrQcTiwoooqcnwQM7el4DFNFTHxmFPnJkeFH6zDPF8osvklemnki2lYjNpp+I6PMFzkE4ET07GzjtNPHaTAMZqWTnImcCdLVykUgRN53rX/7+W1q0n5n02Wci70ZxMTB0aPfP5T1ozx7zzIqS/YXsbGH3kwykiM5IdBLMxiMiwnxo0dAQL2LJmSXiAjKVgHUyCjdZftw2m003EdGn+PznQPpvB5OVkYUzis8AAHxWbZ6BjGR7csvfph6WKnKWhYx47sqoEjESLoVeM+CfjZFkT/oGdwM6fdom1thxbAc6fB0ochVhYMHAbp/Le9DeE3t1mQmiBjmI4cpwIcOe0cPa2lCcIxrx2lY24sRg6ImevjCxqIAienoiz3tGhrBd0QuK6KmPtGk5O3zfw29lcfSoebx4kx2JDgREXK0FrH37gIYGEQEtxdquyPc/M0//O6XsXKRNy4QJ4T83cyR6suq/oEDMiAC0H0iS9T9uXHh7pv79xfG9XuDLL7U9tlqS/fsHRJJVgCI6CUX6DIeLQgeAM/sKAWt//X60eHTwI1NBsqOggYCIq7WAtbduLxrdjXBluPz+810Z3Vc04p8fM89IbCrZuXx6VESiS+uirsjzsr3GPI14suu/KDuQcOdEm7YP85uPbgYAjC8bD1uYRry0VymKXEXwKT7sqt2l6bHVkmw7HQAoyRWNeE0Lp5MRg9FKQJQPwRQQrUMy7VwYiU7MRjJ+/wBF9HRACrORBMS8PGDAAPF6587klKknjBSwtLZSkNHNI0dGHhCTAxm7d2t77ERIFTsXRQmcg0iDGFJE37UrYKNlNMmORLfbA57cWovo8h40Zkz4z222QDS6WSxdkv37B2jnQsIjo5ulbUtXinOKUZJTAgUKvjxujlGoZEdBA4Eo0JpWbS8gGd08smRkxIjW4cXDAQC7j5unEfcPZCQpElrauWg9iKEoit/OJZKIHmwnYhZf+mTPxsiwZ6AgSyS91Xo2xpaqLQDQzY9eYrPZ/AMZO2rM0Ygn+/cPACU5J0V0je9BhMSN1nYuFBCtg1azEKJhQgGxGxTR0xOK6EQrZHStFKnCMXKkWJrF0sUIAUsvEV3W/6jwAWwAgGHDxHLPHm2PnQipYudy+DBQXy8sOYYPD7/OqaeKAQ63W6xvBowYSNLL0khGoo8dG3kdeW7+/W9tj60WI+qfdi4kHFLEldHO4RhZIhpxs1i6JDsKFwgSsDSOAo2l/k/rLTzZdteZR0RPdiSujMLVWkQ/1HgI9e31yLBnRJwJMLRoKGywocnThGMtxzQ9vlqMuAb0mg0gI9EjDeQB5htIMmIgT697ECFxQzuX9CUZIqIJBcRucCApPUm2iG4WH1pQRNeUlhbgq6/E62girvTk3rtX/zLFQipFoksRPVIUNGA+Eb2jI3BPsLqdi4xCP+OM8ElFAWGbNWiQeG2Wa8CIgSQpomt5DhQlNhFdeqWnc/3TzoV0xd3p9icVjSQgAsAZfYQn994T5riAkh2FC+gXBSotQqLV/7DeohHfU2eORrzT14n2TtG5TZqIrlP9y4Gh03qfhkxHZth1sjKyMKBATKk0yzVghKWRHnkBFEXx2xSNKx0Xcb0hRUMApHf9++1cUjgS/YknnsCgQYPgcrkwadIkbJBJnyKwcuVKDB8+HC6XC6NHj8Zbb70V8rmiKFi8eDHKysqQnZ2NKVOmYHeXabl1dXX43ve+h/z8fBQWFuLmm29Gc3D2dwBvv/02zj33XOTl5aGkpAT/9V//hf3792vynS0Jo3DTE0VJjogoO9QmEhC7wYGk9ISR6EQLdu4U99OSEqBv38jrDRHPvn7B3WiSHQUN6G/nEssgxqFD5rgWg59N9ZwNFozeInq0QQwgIOKaZSDDiIEkeQ60jEQ/eFDkBMjIiDwTADCfiM5IdGIGvjz+JbyKF4WuQpTnlUdcz6wCVjKjQPvmioccraNAP68WjUgsIvrhpsNo7TA+0VawN36yRMRgP2gtLVWkPYj0/o+E2QYyjPDklnkBtBTRjzYfRbOnGXab3V/H4RhaJBpxs9yDDPFET3E7l9deew0LFizAkiVLsHnzZowdOxYVFRU4diz87I+1a9di5syZuPnmm7FlyxZMnz4d06dPx/agBETLli3Do48+iuXLl2P9+vXIzc1FRUUF2oM6Q9/73vewY8cOvPvuu3jzzTfx4YcfYu7cuf7P9+3bh2nTpuGb3/wmtm7dirfffhu1tbX4zne+o19lmB2tRfSmJiEoEHPT3h44T+keic6BpPSEIjrRglisRACK6IA+IrrbHbCniCbiFheLe7SimOMcyPrPzBR/yUBGQbe2ans/ilVEl7MBzCLiGhmJrqWILut/+PDIMwGAgIhuht8/QE90Yg6CBdxwCf0kUkT/6oQ5LiBD/Ih1iAKNdSZA7+zeKHQVAjDHOZD177Q7I0Zva40UEDt8HWh0a9fZ9IvoJdFFdCnimkVEN+Ia0CMSXf7+BxcOjvpbGtr7pIheZ46HKEPvQSlq5/LQQw9hzpw5mD17NkaOHInly5cjJycHzz77bNj1H3nkEUydOhW33347RowYgbvvvhsTJkzA448/DkBEoT/88MNYtGgRpk2bhjFjxuCFF17AkSNHsGrVKgDAzp07sXr1ajzzzDOYNGkSzj//fDz22GN49dVXceTIEQDApk2b4PV6cc8992Do0KGYMGECfvKTn2Dr1q3o6OhISt2YDq2tLHy+gDhFzEvwOcrO1u84JhQQu0ERPT2hiE60QCbpi1VET2cBUQ8R/d//Bjo7gYICoH//yOvZbOaydDEiCregQPiWA9pG4lo9Et3qIvqXJ/McyrwLkZD1X1UVePY3EkaiEzMg/bhHlURvxM0qols9CjR4JkD/vMiNuM1mM1UktBFRuNnObOQ6xdQ1Lc+BtHOJNogBBCLRTRMJbYAnd2/XSU/0Vu2m9EkR/fQ+p0ddTw5i1LTW+L+7kRiZ3FjrvABmwOPxYNOmTZgyZYr/PbvdjilTpmDdunVht1m3bl3I+gBQUVHhX3/fvn2oqqoKWaegoACTJk3yr7Nu3ToUFhbirLMCSYWnTJkCu92O9evXAwAmTpwIu92O5557Dl6vFw0NDfjjH/+IKVOmwOl0hi2b2+1GY2NjyF9KoZWVRU4OYD8pzaRaHaUi8rxnZoopwHphJTsXiujpBUV0ogXxRqKfOCH+jCZVItGDBdwoQYQAzCWiGzGIYbdrfw46OoSlERB7JLoZ6h8InAMjEotqaakjrS2lZVEkiorEH2COaHR6ohMzEIsfNxAQ0auaq0KsPIzCEBFdhyhQ/yBGDzMBgKDkoiZIrGiEHzSgvYjoU3z4okZkvLdsJHoSz4Eedi6xiugFrgL0yRbHN8NgniGR6EEDeVpaGpmB2tpaeL1e9OvXL+T9fv36oaqqKuw2VVVVUdeXy57W6dvFjzQjIwO9e/f2rzN48GC88847+PnPf46srCwUFhbi66+/xv/93/9F/D733XcfCgoK/H8DBgzoqQqshVZCks0W6IhQRDQ/Wg2e9IQJBcRuaC2iNzQkth+SHCiiEy2IVUTPzQXkM8y+ffqWKRZSRUSPtf6BgIi72/j+tyH1D2h/DvbsATwe8fseODD6usGe3Gbo+xhxDvTwRJd2RqdH738DMJcvupGR6C0tQFtb8o5LzEuwiBuNouwiFLnEKNS+euMb8VSJRI91JgBgLk9uI+of0H4g42DDQbR0tMBpd0b14wbMVf+AMbMB/HYu7do14rvrxENpTyI6EGTpYoLZAIZ4op/8/Xu8Hv/xif5UVVVhzpw5uOGGG7Bx40Z88MEHyMzMxNVXXx1xMGPhwoVoaGjw/x06dCjJpdYZLYUkRuJah2QLiGaNRPf5Ah0pLfMCEPNDEZ0kSn098PXX4vWZ0QN4AJjL0sUIAUsKuHV1woJFC2QUdE9WFkCg/g8c0ObYiWBE/QOB5LcRchTFjRRwzzgjMBsxEoMHi4CL5mbtjq8WRTE2El1LET3WSHTAXCK6EZHoeXmAnHnMaHTS7GnG/vr9AHoW0QFzWboYKWAdbz0On+LTZJ87a0Uj3lNSS0B4RgPAgQbjG3EjrCwA7QcypJXLGcVnwOkIb8sgkQJuXVsdTrQZO6VSURRDBjL09ESPSUSXyUVN4ItuxEyAHGcOcpyi455qvujFxcVwOByorq4Oeb+6uhqlpaVhtyktLY26vlz2tE7XxKWdnZ2oq6vzr/PEE0+goKAAy5Ytw/jx4/Ef//EfePHFF1FZWem3fOlKVlYW8vPzQ/5SCq080QGK6FZCy/MeDWnnYiIBMYTgSCStRHS327yDBiRAsq4BiuipixQQy8qE33RPmCm5qFFRuHK2tlZ2FlJAjCUKV84kPHhQm2MnghECIqB9JHo8Aq7LBch+gNHnwO0GvF7x2sqe6C0tgYG8eCLRzXQPSuYghs1GX3QSQIpXJTklfpuGaEgR3UwClhF+xF7Fq5mIKs+BtGqJxoAC0YgfbDC+ETfCygLQPhI91qSigPityd+A0eegrbPNP5BjRGJRrTzRO32d/vtJPCJ6ug7kAfrMiDEDmZmZmDhxIiorK/3v+Xw+VFZWYvLkyWG3mTx5csj6APDuu+/61x88eDBKS0tD1mlsbMT69ev960yePBn19fXYtGmTf51//vOf8Pl8mDRpEgCgtbUV9i6RMo6TSZZ8Pm0GVC2HlrYejMS1DmkchRtCcILVROsiuCPIa8D8pPE1QBFdI+IREAERiQukr52LwxEQEbUQcX2+gL92LALiqaeKpRlmFBpl56J1JHo8gxhAYCDD6HMg6x8wRkTXahBJ/v579w5YxURD1r8U3o3E6IEkiugknghQICCip6udS6YjEwVZImJACwHLp/jiEhBPLRCN+KHGQ4b7IRtm56KxgLirdhcAYETxiJjWH5AvGpFDjcY24rL+ASA3U2dv2iCkJ7lWkegH6g+gw9cBV4YLp+Sf0uP6ciDp6ybjG/FUGUgyEwsWLMDTTz+N559/Hjt37sS8efPQ0tKC2bNnAwBmzZqFhQsX+te/9dZbsXr1ajz44IPYtWsX7rzzTnz66aeYP38+AJGQ+bbbbsM999yDv/71r/j8888xa9YslJeXY/r06QCAESNGYOrUqZgzZw42bNiAjz/+GPPnz8d1112H8vJyAMDll1+OjRs3YunSpdi9ezc2b96M2bNnY+DAgRg/fnxyK8ksaCkk0RPdOtDORSDrweXqeSp6T2RkBOqT14D5oYhOEkWtgHj4sD7liYdU8OQ+dEi0LZmZAYE8GrL+GxuNz11hlJ2L1pHocjZGrANJZhHRpYCbnS0Gd5KF1lHQ8Q7kmaX+AePuQfIcaJmbgVgTmaDytD6xXUBSQPy60UQCVpITW2opYB1qOAS3141MR6ZfII+GFBmbPc1ocBvbiKdKFG48ftxAQMQ91GBsIyLtdHKdubDbktetkZHoWiV2DZ6JEcv38A9iGFz/QOpYGpmJa6+9Fr/5zW+wePFijBs3Dlu3bsXq1av9iUEPHjyIo0eP+tc/77zz8PLLL+Opp57C2LFj8ac//QmrVq3CqKBEUXfccQf+93//F3PnzsXZZ5+N5uZmrF69Gi4pUAB46aWXMHz4cFxyySX4z//8T5x//vl46qmn/J9/85vfxMsvv4xVq1Zh/PjxmDp1KrKysrB69WpkZ2cnoWZMCO1c0pNkCYhmt3PRuh44G8M6pLGInmF0AVKFeAXEU04GmaR7FOiuXdoIWFJAHDIkNiE0NxcoKgJOnBAiYiwWPHphVP3rFYker4hr9DVgtCd9W5soQ6LnP56kooC57kFGnQPauRCJX0DsHdsFJEVcM4noRghYe+r2aCJgyfofUjQEDnvPjXiOMwfFOcWoba3FwYaDKHQVJlwGtaRKFK7agSSzRKIn+/ffN1c04k2eJrR3tsOV4ephi+jEOxuG96DUjkQHgPnz5/sjybuyZs2abu/NmDEDM2bMiLg/m82GpUuXYunSpRHX6d27N15++eWo5bruuutw3XXXRV0nrdDDzoUiuvnR8rxHw4QCYgh6iOhVVbwGrEAai+iMRNeIeCPRzShgWTkSPV4BFzCPpYvRdi5a1H9LS2BWhdXsXIwaxMjNFdHvgDYDGWpnw9TUGN8m0c6FGI0/CjRGAVEKWEYLiEBqCFh+ATcGP3SJWSJxjbZz0SISutHdiOoWkXAw1nOQ7iJ6oasQTrtIwHqsJfFGPF4RXc4EON52HK0drT2srS+GzYbR8BogRDVaCkkU0a1DshOLmt3ORat6oKWRdUjj2RgU0TVAUdRHotfWhiY1TjYdHYF7crqJ6GYRcY22c9FCwA3245Ze3z1htvpP9u/fZgNOzspFdXXi+4v3HlRUFBDxjbaVop0LMRq1VhbVzdXweD26lasnPF6P//hWtlKQ9R+XiG6S5KKGWVnkalf/e+pEI16SU4ICV2xT80xj53LSTifZAq7NZvNHo2siotfFJ6IXZBUg1ykiIA83GtuIGz2QlIp2LsQi+HyBjryWIjqtLMxPGkfhhqCXnQtFdPOTxtcARXQNqKkR17nNBgwdGts2RUWB35uRApYcRAXST0SXkegHje1/G27nwkEMsUz2IAYQOAdaiuixRqLbbDwHtHMhAHC89bg/OeCw3sNi2qY4pxiZjkwoUHC06WjPG+hESFJFZ/KSKgJBApYWkeh18VmJAMCp+YHkokbS3GFMFG5xjriBaToTII76T/dIdADo10uMhFc3J96IxxuJbrPZAgMZaXoO/NcARXRiFMGRcIxEV89nnwFPPhnoEFiBNBYQQ5Bikla2Nul6Dfztb8Dzz4voXKuQxtcARXQNkALiqacGznFP2GzmsHSRbVVmpvhLJlqK6PFG4QLmExCNGsRoakp8NkS8Ai4QqP8jRwCvN7HjJ4JR9Q8EItETnQ1w4kRACB4WmwYIwBz3IJ8v8PzFSHRiBFLAPSX/FOQ4Y3sQtNvs6J/XH4CxnsRSvMpyZMHpcCb12FpGQquyc0lzAVEOYrR0tKCtI7FGPJGZAF83fg2f4kvo+IlglCc9AM0i0ds62vwzKmIV0QFz+KIripISllKEqKI1yEpJCyEpHa0sWlqACy8EfvADYPZso0sTO8m2svB4zCmwMhI9cTZuBK66CrjxRuCxx4wuTexQRCeJoEbABcwhYBkpIGoVCd3ZCXz1lXitRkQ3OhLdqCjcggLAeVJzSfQcqIlELy0FMjKEgH7UuEBOU1wDiUaiy/ovK4vvd2SGgaTg/oeVZ2MQ6+L3Q49DQATMIWAZGYWrlZVCp68TX50QjXhckegFIhI9Xe1c8rPy/Z7ciZ4DNSJ6/7z+sMEGj9djqIhpaCR67slI9JbEGnFpp1PkKkKf7D4xb2eGvACtHa1QIIQd2rmQtEM+xLpcgF0DWSUdBcS//AWorxev33jDOt892QIiYE5fdL1E9HSyNFq+PPD6mWeMK0e8UEQniRBvQj9JuovoWkWiHzgghHSXK1CnsSDXNdoP2ig7F5tNu3OgRkR3OIDycvHaSBHXqPoHtItET4V7kM0W8GhPFrL+q6qSe1xiLmQUdDwRoIC5RPRkW4kA2kWBHqg/gA5fB1wZLn+dxoKcCWAWP+hkR0LbbDbNzoEaOxenw4nSXqUAjJ0NYKSILiPRE7VzCbZysdlsMW9nhgTHsv5tsMU8k0crGIlODIdRuD3jdkfv6KxeHXjt9QIff6x/mbRAnnutbEwika4ieipdA83N0c9dZWXg9fbt1hlAoIhOEkGNgAiYQ8AyUkDUWsAdNiy+IICyMrE0MgoaMEckdKIirho7FwDoLzQQHDmS2PETwQx2LolGoic6G8YsgxhxaAeaUCr0H9TViVmSJD1RE4ULmEtEt3Ikuqz/oUVDYbfF3oiX5YlG/GjzUSgGTnE2g4ibqJ1IoteAkQMZRs0EAAKR6MdaE6v/eP3QJWbwpZe//9zM3LiuXy3Q0tKIEFVIP0IKiOGprwdGjhQdvjffDL/Ohg1iWVQklp99lpSiJYzW5z4Scto4YCoR0Y/WQmqqWRpt3ixEr4EDw0dtnTghIkIB0RlWFOtcAxTRSSJYWcAyQyT68ePCF1ktagcxpIje3GxsHhMzJLZMZCCjoSGwfbznQIqYRkYCm6H+jR7ESFc7naKiwLNpoueAWBe1ApYZokCNFBCDo0ATEbHVREEDQFkv0Yi3drSiyWNc1I48thHnQNZBVbP6RrS+vR61rSKpRqyJdSUyEj2R4yeKGQYxEo5Er1N3DyrPE9P50rX+tbQ0IkQVWkcjp5qVxcqVwnO1sxO4667un7e2Bjrys2aJ5eefJ698iZAsAdFmM6WI6IeR6NF54AFx3qqrgd/9rvvnUjAfNAg491zxWnbszQ5FdKIWRQH2CCvDuAUsaWVhBgHRCAFLJvXzesUgnFrUiuh5eYFnHiNFRDPMBkhEQJT1369f/EK0HMhI12tAq0h0tXYu6T6IYbcHBjJo6ZKeKIoSiMKNU8SVdiJHm41rQMwQid7h60CjW31nR20UdG5mrt9C5WiT8efACEsdLURsOYhR2qs07u+ghYifKEYmFu3X62QkeoIzAdQO5KX7IIbNZtNsNgYhqqCAGJ1//jPw+tNPu3d4tm8XkXR9+wLnny/e27s3eeVLhGQJiEBARDSjnQtnY0RGUYAPPwz8/9573dfZulUsx40LdOStIKL7fAFRmyI6iZcjR8Q91OEQA0jxYCYBywgB0ekECgvF60REXLUzAQDjLV0UxRx2LolEoquNggZ4DWgRia4o6q8BWf/V1YnNBkkEI+sfMMdvkBhHVXMVmj3NsNvsGFI0JK5t013AynZm+4+biIClVkQHQi1djMLIcyB/g4l8/0Tq3xTXQIf1E4smKqJXN1fDpxjTiBs5EwMwx2+QpDFaC4gyoqStDejo0GafRiIFQsnataH/yyjcsWOBwYPF6337dC+WJiRTRM/KEksTiYh+9JqNkQoienV1qGftxo2Be4YkWEQfcrIfcvBgMkqXGG1BFmoU0bXniSeewKBBg+ByuTBp0iRskL5XEVi5ciWGDx8Ol8uF0aNH46233gr5XFEULF68GGVlZcjOzsaUKVOwW4ZhGoAUr4YMCbWsioXgKFSj7DyNjAIFAgJWIiK22kh0wHgR3eMRM9wAY86BjERPJBI6kfo3g4BphsSidXXqn5WPHRPfwWYDhg6Nb1sp4nd0JDYbJBHMIqInOhsglUnldlwKiIMKByHTkRnXtjIKNVErh0QwUsAFAiKiFpHQ8c4EAAKR0EZFonu8Hni8IqGCkSK6JvWfiIjekp4DSTIKura1Fl6fV9U+6trqVNvpyON7FS+Otx5XdfxEMfoe5B9IM3A2CkljtBYQgzuDVrd08XgCQsmVV4pl16Sh27aJZbCIXl0dKtCZFXnus7P1P5YJRUQ/es3GsPrvHwj8/gcPBgYMEKLPunWh60gRfexY44WpeJDnHdD/GjDh719XEf21117DggULsGTJEmzevBljx45FRUUFjkUIu1y7di1mzpyJm2++GVu2bMH06dMxffp0bN++3b/OsmXL8Oijj2L58uVYv349cnNzUVFRgXaDKjURAVEKaG638JU2AqMFrETvFR4PsH+/eG1FET24fdA7uXc4tLBTsbqIbuQ10Lu3mMUCqJ8NINvngQMDgQqxkpUlygAYdw6MvgfJ+zAj0cOT6u242ghQICAgtnS0+IWkZGOklQWQeCR4h7cD++v3A7BmJHrwebesiK7Szkir4yeKoZZGJ/MC+BQfjrepE7HlIEb/vP5xfwenw4niHOGNaNQ5MPoeVJqb+GwMQlSjtYCYmRkQjKweiXv4sJjmmpUFXH21eK9rJLoU0ceMEYmKMk8GM1ghskXrAZRoyA6eGe1caGkUmWC/1fPOE683bgx87vEAO3aI1+PGBbyeg6PXzUrwIJJd57jsYBHdqMjjLuj6jR966CHMmTMHs2fPxsiRI7F8+XLk5OTg2WefDbv+I488gqlTp+L222/HiBEjcPfdd2PChAl4/PHHAYjotYcffhiLFi3CtGnTMGbMGLzwwgs4cuQIVq1apedXiUgiAmJ2NlBQIF4bJeAYGYULJC5i79sn2ufc3MC+knn8RJECYnZ2QExNJlp8fy3sXNI1saXdnvhsgETqHzB+IMPoe5DR39/spHo7nkgUbq/MXsh1is6T0QKWYVGgCUaC76vfB6/iRY4zx58kMZnHTxRZ/64MFzLsGUk/vhYithxISiQS3cgoYCOT62bYM9Anuw8A9ZZGiQzkAcYPZBh+D2IkOjESPSw9UkVElJYUp54KnHOOeL11a2AKtqKE2rnYbNoli0oGRniimygS14/W9SBnY1j99w8EroHBg4GJE8XrTZsCn+/cKaaDFxSIaDijhal4MOL3D4iBBxOgm4ju8XiwadMmTJkyJXAwux1TpkzBuq7TGE6ybt26kPUBoKKiwr/+vn37UFVVFbJOQUEBJk2aFHGfAOB2u9HY2BjypxWJClhGtxVGR4Emeq+QgxjDhom2N9nHTxSj7XTk91c74Kko2tjpmMGT26hzkKgvutqkohKjI7GNvgclKqJv3iySqf/4x9qVySyYpR3Xsw2XUbhqBSyjLV0MF7B6JRYJHjyIYVPRiCd6/EQxUsAFEhdQgxPrqrkGpIBZ1VwFxaDoIKOvgUTvAYneg9JeRJfJbVVaCn1e/TkqXqzAL//5Sy2LRdIFrT3RgdSxs5AC4oABopPSq5ewadm1K/B5Q4Pwwx0+XLxntDASDxTRBXrauRglDmjF4cNi2b9/QETfvDnwebCdkc0WiERvbAx0kM2KUSK6Sa4B3UT02tpaeL1e9JM3w5P069cPVRHUiqqqqqjry2U8+wSA++67DwUFBf6/AQMGxP19IpGIgAgYHwVptICllYiutv6NFtGNjsKV37+2Vt3A3vHjQH29eB2vHzcQEJA7O4UvuBEYfQ0k+ryYSGJdwDz3IKMGMRKt/y++ANav7547KRUwSzuuZxueSBQuYLyAZXRSv0TtVPz1r8JKRIvjJ4rRVhZSQGzyNKHF09LD2t053nYc9e31AIChveNvxKUnvtvrRoPbGF9C/znIMuYcSF9ytclFE70HaZGXIBEMF9ETjETffmw73tn7DtYcWKNhqUjaoIelR6pEossH67IyMfV2/Hjxv4zElQLiiBEBGxeriOiKYkxi0XSyc1GU7kk4rYaMUiwvByZMEK/37QuIHsFJRQHRGZb3ErNHoyfz9y/vD0Dqi+hmYuHChWhoaPD/HTp0SLN9P/kk8NRTgXYhXswiYBkt4iYqoquNwjVaRDe6/vv0CSTEVfO8IgXcAQPU3UMzM0UZgPS9BuRAgtrnxUSvgXS/ByX6/ffsEcth8eWDI3GgZxu+7FvL8MC3HsC40nGqtjdaRDdcwErQTsXvx61SQJQWMEbbuRhV/70yeyHHKRpfNb9BORPglPxT/PuJh2xnNgqyClQfXwuMPgdSxFYbiW51OxezzMZQO5C2p0404mrvQSTN0UNIShU7C5nsSfpWShFRRuIGR+FKrCKid3QA3pPJpNM9El0K3VoNJAV73Fr9GggW0QsLAxGH8hroKqIDxotTsSLPezIS69psgWvAJANJuonoxcXFcDgcqO5yE6yurkapVC26UFpaGnV9uYxnnwCQlZWF/Pz8kD+tuOACYM4coLhY3fZGtxVGC1iJ3icSjcI1+j5ldBSu3Z6YL3miMwEAY0VcRTHPbAA19e/zBURciujqSNTOJthSKtUwSzuuZxv+n6f9J35y3k/8lgzxIpPaqY1CTRSjBUS/iK3WziVBEd1wOxeDZwLYbLaERNRE6x8wVsRVFMXwayCR768oinYiuko7k0Qxuv79di4qLYW0uAZIGkNP9Mh0FdG7ekJLAdGKIro87wBFdK2vAZst9a4BGTEXfA0oSngR3SrJRZOZWBcw3TWgm4iemZmJiRMnorKy0v+ez+dDZWUlJk+eHHabyZMnh6wPAO+++65//cGDB6O0tDRkncbGRqxfvz7iPs2OWQQsoz25jbJzkfVfVycGlZON0QIukJgvutVF9Pb2gN2aUeegf3+xVFP/X38tvoPTKfL2qMEs9yCjI9GbmkKfif9/e+8eJkV1oP+/3T33gZlhuA13EERAURSVoCSaSIToN5Fs1qhhQ2IIbFwxuuanq3lcNZrEXaPmYtwYNUbd1dWYRGOMixJvJEpAUBQRiCIIAsNtrsx9uuv3x+F0Vc/0pS6nqk5Pv5/n4ammp7qr+lSdOlXvec977CI7MbzUAV1hO54bKb4XqgvXa5RCMhPdZZyLLP+mziZ0x4OfbCjsKBHAm4jrZWJdiTUXPWjae9phQAinYXck7T3ivBHfd2Qf2nraEIvEMGnIJFfbD9uJfqQn3Egj+fu7491o7Gx0/Hkpok+pHYA94cR//MxEHygCYl8R/a23hIt77Vrx/1NPNT+TbyJ6LGYO6faTQopzAQbGvACGIXJvAXPYvXU0xs6dQGMjUFQEzJhhfk7WF/lZXQkyzgUoHBEdAK6++mrcf//9ePjhh7FlyxZcdtllaGtrw6WXXgoAWLJkCa6//vrk+ldeeSVWrlyJO++8E1u3bsXNN9+M9evXY8WKFQCE4+aqq67C97//fTzzzDPYtGkTlixZgtGjR2PRokV+/hTfKHQBSwq4LS3OBazOTkCO6ncrYNXWCjc2IHLBgybs8gfMDk83HRleRwIA5jkQRh2wztkRVEdqX7x0OMvynzxZtMFukNegsO5Xw+5Iqqoy22U3ZTDQ41zYjmcndAFLk0zuwx2HHYvYnb2d2NUsJh5zK+LWlNWgKCoufgfbDrr6Di+E3YkBeBTRG7x1Yli3H0akjix/AK7iaFQwZrDoCd/b6rwRly70SUMmoSRWkmPt9OhyDQqrDpQWlWJI2RAA7s7BZJyLhzpAChg/M9HzWUAETBFdDtc/7jghuLW3Ay+/LCZdjEbzW0SvqBDOab/RTEBMgaMx0tPWZnZ6SBFddiStXQusXm2+JztJAGCIaM9CmyzOLmGJ6B0dwWwvBy5lF3tcdNFFOHjwIG688UbU19dj1qxZWLlyZXJCsV27diEaNXX8M844A4899hhuuOEGfPe738Wxxx6Lp59+GieccEJynWuvvRZtbW1Yvnw5mpqaMG/ePKxcuRJl1llb84iw2wodBCzZnu7b52xyyu3bRSdfVZXZaeeUaFR8dv9+4MABU9ANirBHAgDeRgN4zeMGvMXJeEWWf0WFGb8WNFJElxN4O0FFJ0ahd+RFIuI6/NFHogwmOTADNjSY9zhuJtbNB9iOZ0cKWIUa51JbXouSWAm6492oP1KP8dX2h8R82PghDBgYXDI4OTmjU6KRKIZXDMe+I/twoO0AxlSNcfU9bgk7DxowI4W8iOhuo0S8bt8r1vM/GglnmifpRN/T4rwR9xrlAlBEB8RoiMbORuw7sg/Hjzje9ueaOptwqF04aCYPGaCNOPEXCoiZke40+ZAeiwkn7l//Ctx+u3hv5szUDggZe3Ew+E5xR4QlIOrmRPdrgtWBMC+AdJKXlprn+Ny5YkK4jz4SEysCwNlnp36utlYsG52PrAqUoOuAZqMxfBXRAWDFihVJB1pfXnnllX7vXXjhhbjwwgszfl8kEsEtt9yCW265RdUuhgoFLCHibt/uXES3Rol46QS2iuhBE3YnBuA+zsUw1IroYTrRdRgJsHevKFMn57LK8j90SEQaBTEq0YoOHUl1daaI7gTpQh89OryRDEHAdjwzclLB0Cb10ySTe1fzLuxr3edIRLdGuUQ8NOLDK00RPWjCHgkAuJ9Y0ZrHrSQTPYRMbh0E3GSciwcn+tRa7yJ6Q0cDunq7UFpUmuMTatGhI2nUoFF47+B7jp3o0oVeN6gu1Egmksf4EecyEAREoH+cCwB8/vNCRF+1Svz/zDNTP0MBMT1SQNTNid7VJR5eAXYk9cUa5SLvcSsrhWj+wgvAmjXivbPOSv2crAN0oqei2WiMcGwbJIkUsA4cMLOZg0QHEdGtE1pFHjcQbqd3Ppf/vn3i3jEadebe7UuYIroOnRhSRO/sBJqanH1WOtG9iOhDhwpziGEUbh2QufRORwMM5ElFiT2sLlA3k9p5RQcR0e3knqom9JMu9oPtjHNxQv2RehzpPoJoJIpjhhwT+PZVoEP5SxG9tbs1KSjbRYUTvba8NhlpFGZHUj7WAdmRxzx04ho/41xUC4gvvAD89rem6OknXV3m/ltF9C9/OXW9L30p9f8yyqKxMZj9dEuBC4hJ/Jpg1Y86sGcPsGwZ8OST6r4zG33z0CWf/7z5uqYmsxOdInoqmjnRKaKHjBRwe3uDryu9vea1OB9F3G3bxNKLgAiYxyAMJ7oOLly3mehSwJ00SYxMckuhO9HLysz20uloABUdSbGYWQcK9RiMHSuWH3/s7HMDeVJRYg85sWV3vBvNXc2Bbrs73p3MIQ87SgFwnkesQkAETBE9DAEx7JEAgFn+Tp3QshNjQvUET+7lMEV0Hcp/cOng5EgEpx1JKupANBINdUSMDiK62468ZB66x448UsDkS5zLc88BCxYAF14I/OlP6r43EzLKJRYTQqFk4kRg6VLx+qtfBT796dTPSRG9q0ub7OO0MM5FIEdilJS4n5wrHX7UgeXLgQceAC66CNiyRd33ZiKTiL50KTBvnhB/7rwTKC9P/TtF9PRo1pFEET1kiovNuhW0gCWve0B+iuhSxD3uOG/bD1NE18EJHfZIAGlQKNSJXQF3ueg9PcCHH4rXXjuS5NwMFNGdfW6gTypKclNWVIbq0moAwQtYbd1mI15ZEl6ekBSwnIq42w6LnvDjhnprxEdUhCei6xDnMrZKXMA+bnF2AVPViTG8UjTihTqxK+AuF7030YvtjdsBeD8GsjMvjLkZknUgxDiUZEeey9EwdKIT1+SLiP5f/2W+fuQRdd+bCSkg1taKIctW7r9f3HA//HD/DMvBg81JqnSOdGGci8CvclA9uW5TE/D88+K1YQD/+79qvjcbUtjoK6KXl4tJRRsbgW98o//nGGmUHjrRSV+kEzfoyUWleFVcnDopcNCE7USXIm6hRlnI8t+/X4xOsIuKKBHALP/Dh4OPNNJhJABgxok4caLv2AHE46LtkiK8W8KqA4mEHnXArYjOOBcChOfEleJVSawEJTEPw4E84tYFShFXDeOqxgEQcTadvfYfsGWUhefyrxDlf6j9UOCRRjp0YgBITmjrpCNpZ9NO9CZ6UV5U7nlCXHkMgq4DhmFoUQfkNcjp5K6qIqVIAeNHJrpqAREA1q83X7/4ov9RKc1HR+ZZXeiSSEQ8+KSbCyUSMT+js4hY4C7cJH6L6Ko6ktatEw/Nkr/8Rc33ZkN2JA0b1v9vkYjZWdQXORqDTvRUNKsDFNE1ICwBSwfxCnDnwm1qMp3jjHPxxvDhZia2kzJQ5USXHbTxePD3S7rVASciulXA9TKxLhDeaABrlF6+ieiGYXYkMc6lsElmcgcsYOkiILqZWLGlqyXZ6aAszqW9MONcastrUV4khgM7caP/vcH7pKKA2YnRk+gJPNJIBwEXcFcHZCfSlNopiEa8PY7JY3CoPdhGvKO3AwaEGBfmMZATGu9u2e3oc8mJdYeyEScuyYdM9H37Up16DQ3mUEq/kCJ6dbXzz1pz0XWlwF24SfwqB9WT627cKJbTponl22/735GUKc4lF9Y4F84LYKJZHaCIrgGygypoAUuHKBEAGC/ufbFrl/3PSPFq1CjzXsMthR7nEouZoyGciIiqnOglJeY9FjuS7H9m61axlPcDXgi7Iy8SCa4NTodVRLd7v3LokLi/j0Qoohc6wypEIx60gKWDgAsA46qFE9qJgCXFq5GVI1Fd5uIh20KYmeg6RFlEIhHzGDQ7PwZeOzHKisqS52BYHUlh14HRg47GubTab8S3HRLDKacN896IJ53oAU+ua51ItaI4vEZciugft3yMeCKeY23BofZDaOgQTj860YkrEgnTFanyJla1gPjWW2I5fTpw+ump7/mFFxE9H+IsCtyFmyRfnOgyvuCLXxQPbo2N/j/0NjWJZbrRGNmQ5393d6rbTDcKvA5QRNeAsAWssAVEq4huV8BSJeACZvmH6UTX6RjYIR4HtosoTyUCYlh1QIdODMAUcXc7MFHJ+wGvcwIAZkdemNcgr256L8hOjK4u+52ZshNj/PhwOwBI+IQlYOkiIEoBa1ez/Z5wKSAeN8z7BUyWf5gietjHQEa62O3IiCfi2N4gGnEVLtywRdywy1/GsTgZCbD1kGhEvM4JAJgdeWFdgyqLKz276b0wavAoxCIx9CZ6befCy2vQ+Orxoc4pQfIY68SXfmWiq3CivvOOWM6aZT405IMTXec4iwIXEJPki4i+Y4dYzpghJrcFzAc5v5D77rQOVFaKrGWAdcCKZpPrUkTXAB0ErDCRsWidnfYFLJUConSih5mJHnYm94QJYvnRR/bW37VLdJCWlJgCvBcKvSPJafkD/jjRgx4No0v5l5aak6vaHY2h8hpE8puwnOi6CLhSRG/pakFTZ5Otz0gXtAoBMaw4HUAfEdepE313y250xbtQHC3GhOoJnrcfVpyILnVAluFHzfYbcTmxrkoneqGWf1G0KBmpY7czT2UnBilQZB46ICYLVIUUEBMJNU7UnTvF8thjTedTPojodKKbaBZlkcSPOQEA9SK6rAMTJ5oPbvJBzi/kvjuNTLDOC9AcbESeIwp8cl2K6BpAAcuME7ErIqp0oksRvbU11VQQBLo4oZ2KuDKPe/LkzPNiOCHsOpBvnRiAWhG30EcCAM5z0SmiE0lyYssCdaJXFFckOxLsClhSQPQaJQKYInpbTxvauttyrK0WXY7B2MHiAmbXiS4nFZ1SOwWxqPdGPKyJLXWZF2BCzVERvcl+I54UcVWMxghpcl0d4owkTkfEyGsQRXTiGikilZcDUYWSSmWlOTxThYgohxmPHy8mUgIoonuFTnSBH3MCAGon1+3tNevApEmm+2zLFu/fnQ0vdUB1J4IfFHgdoIiuAYXuwgVMEdFunIhKAauqSjiqgWCPgWHocwycirgqOzEA1gFZ/s3NZoRaNhobzfihfBbRdSl/wL2IrmIkAMlvklEKBZoHDZgCll0RUaUTfVDJIJQViZvrIDsyDMPQRsR1mkuvekLF0DqSevSoAxNrJgIQv99OR05TZ1MydkRFHSj0SCnAuYguOzFUjAQgBYpfIlIkolZEtIro0oku3VB+QRFdLZpFWSTJhziXjz8WObQlJWIyPdmRJN3pfuHWiQ6Y9YZOdBPNRmNQRNeAsCYW1UnAcpLJnUiYbb8KATESCUdE7Ogwo+7CdkLL8ncqoquaULHQRdzKSvM6YOcYSAF37Fg1+17okVIAME5oULbrgIzToROdFHqUAmDGWdgRsAzDUDapJSAm1gzDCd3Z24m4ISYxDPsYJDPRbca5JEV0RRMqhu1ED7v8a8pqUFUqHpTt1AGZxz168GglLm525Jkiut06kHSiKxgJQAoUv6IsAHUiomGYN7YTJpgCYn29eRPuB15EdEZZ9EezKIsk+SCiS7F8wgQxYsTNRGRu8CKi04neHzrRSV/CjlIIW8AFnIm4e/aIeltUZM4N4RUZ6RLk5KKy/CMRtVF6bnA6EmDzZrGcMUPN9sOuAzqIuE5GA6gWcGX5NzcDPT1qvtMOusTpAMAxx4ilnHsmG93dwIcfitcU0UlYLlyZxx22Cxpw5gLd27oXbT1tiEViOGbIMUq2LyNdgpxcVAqIAEKfmFA60e26cDcfFI34jOFqGvGwJrbUJZMecJaLrtoFLa9Brd2t6OoNzqXV2q1P+SevQS2560B3vDs5sS6d6MQ1fkVZAOaNsVcRranJvNkeN04I1FKktvvQ5wZGWahFMwExiV/lIM//ri7vzmM5xFiKTdI1ZXfosVtUiOjsSDKhE530xepEVzEJt110coE6EXGlC3ryZHPyYq+EIaLL8q+sVBul5wZZ/o2N9kYOShH9+OPVbJ9OaHciuqookSFDzHMwyBExOpW/FNGlOJ6NDz8UIwMrK8XEyKSwsU4sagTYiOvoArUjIEoH6DFDjkFxTE0jHqaIXllciWgk3EZ8Us0kAEBzVzMaOhpyri9F9BNGnKBk+4wTMSNd7EQaqc7jrimrQSwisu2DHBGjU/nL0Rh2OpI+bPwQcSOOyuJKjBnMRpy4xE8RSZWQLB+shw83HVtOhx+7gSK6WgotzsXqrvIaaVRfL5ajRomldKLv3y9cUX7Q3W12eHiJc9G1DhhGwXckUUTXACkgxuP28pBVoZOA5aQ9lwKiqjxuwBTRgxRxdXLhDh5sRtDlOgaHD4t2B8h/J7pOx0COqnAS56LKBR2LAbW14nUYdUCHa5AU0bdvz72udSSAnPuJFC5SRO+OdyedmUGgk4DlxIkuoyxUxiiEIaLr5MKtLKnEqEHiAVE6bDPR0NGA+iPioVKVE50TW5pO9J1NO3Ouq9qJHo1EMbRiKIBgOzJ0ugbJTowdjbmHk8lr0NShUxFhI07ckg8i+t69YimFQ8BZhqpbVIjoKvLg/YJxLgK/yqGoyPxOr3VAiuh1dWI5fLjIRzcMs36oxnruuhEZdO9I6ukRwiVAJzoJj9JSs34VqgtUCoh2XKCqXdBAOE5onaJEANMJnWuejffeM9dXte9SRC/keQHslj/gTx53GMdApzowSRg50diYey4jWQc4qSgBgIriClQUi5vIQF2gmkyqCFgErKbcAta7B94FABw/XF0jbh0NEBQ6CYgAMLl2MgDgg4YPsq63+YC4iZpQPUHZvnNeAGBCjfM4F1VOdCCcY6DLxLqAef43djbicPvhrOvKkRiMciGeCCIT3auQLIdYS7cY4DzD0w10oqtFMxduElkH/Ig0UnUe9BXRIxH/c9HlPldUiA4Bp+ge5yLPf6Bg6wBFdE0Iw4mrk4Ao5zlpbBRO52xs2iSWJ6gZhQwAGCoMPDm3rRKdyh8wnbgfZH/+9qUTw3r+F2qkkexIypXJ3dlpTqzr1zEICp3Kf9AgYORI8TrXMXhXaIBKr0EkvwljYkWdBMQptaIRrz9Sn8ypzsS7B0UFUhUlAgBDy0UjfrgjuEZcJxc0YB6D7Y3ZnejJTowR6hqQsOYF0KkOyI6kXE70rt6u5MSuvhyDAr0GVRRXJKNZ3m94P+u6mw6IB4kTR57o+36RAYyfmeiqBMR0InoQTnROqqgWzVy4SYIYjeG1I2nfPrGUIjpg5qL7LaK7Of8B/eNc5HGPxdRlK+dCs0gjiuiaYM1FDwqdBKyKCvN6JjPP02EYpoA1c6a67UsRPYzy1yFKBDBdzdnKH/BXRO/q8neyeCuGoVcdOPZYsfz737N3JGzZIkZQ1dYCo0er234YozF0Kn/Afi667MhTeQ0i+U2hO6FrymqSkSrZBCzDMJIirlIRvSJ4EV2nSS0BYPIQm070oy5clSMBZCdSe0872nvac6ytBsMwtKoDshNDCuSZ2HJoC+JGHDVlNUrzuMPIpdep/AHg2KHiRur9wzlE9P2iEZ85go048YCfAqKqiUWzieh+ZaJ7fcCiiN4fKSDG40BvbzDbtEM+RBr1daIDphPdr8lFvYroutcB63EPKhJNs0gjiuiaUOguUCBVRMzE3r0iNz4WUxtlIQXEIJ3oOkVZAGZ5yrztTPgholdUmO1vUHWgs9OM89LhGEyeLM7rI0fMTvN0WAVcle1WGHEuunUk2RHRu7vNOB2K6EQShhNXNyf01KFiopJsIuK+I/vQ0NGAaCSqNEqh0DsxAPtOdD9E9EElg1AaEw84QTmh23vaYcBIbj9sjq0VN7GHOw5nPQ+tAq7KPO4w6oBO8wIA5jHI1pHXHe9OTuw6cyQbceKBfBAQw4hz6e42H7DcuPTlb29v10swthKWiA5oIyICyI+OpHQier440XWPcwnq/AcY50LSE2YesS4Clpwo9P0sBhIpIE6danZIqYBxLmb5h+FEB4LvSLI63v0YiemUkhJTxJUibTreeUcsVQu47MizN7notm3inr6qyjTzEBJGnItuTmgpYGUT0aUL/djaY1FWVJZxPack41xyZCGrRKc8aMCBE/1oJrrKKJFIJBJ4R5Is/wgiyTkJwqSypDI5wa6cuDIdfkWJFHqkFGBPRN96aCt6E72oLq3GuKpxQe0aGYjkQx50Nif6xx+bYrdKZLkA7srGKkzoOrloWHEugDZxFgD070jq6gIaGsTrfBLR88WJHqSAolmkEUV0TWCUgj0R168s4jBFdF06MaQT/eOPU+9/rBw8aN6PTZ+udvtB1wFZ/hUVwgGuA3ZGA8iOpBMVR3lSRDfLf8uWzOtY52QIagQb0R86oe050aWIrtoBGkqci2YuXGsuvTw3+nKg7QAOth9EBBFMH6a2EQ9axJW/sbKkEtGIHo8zcqJQ6XROxzv7RU+46iiRUEfDaNKRZCfORY4EOGHECUpHApACRHcBEUgvotfVickO43ExxFs18iGypMRdXnJJiek61VFETCSAjg7xOigRPRYzJ6jUxIkLQP86IB9qYzFgyBDzfb9FdK9xA/kysSid6CRswoxS0EXAsiOib9wolqpduFYRPaiJLXWLc6mtNcsh02iAN98Uy6lT1Xc+Bl0HdDv/AWDa0XSDbCK6X070MOZl0K0OyM65d9/NfB1gHjpJB/OITRE9mwt0Y/1GAMAJw9X2hEsnekNHAxJGQul3Z0K38h9SPiR5Hm45mL4ncMPeDQDEsaosUduIB92RpFv5A0hGFNlxoqvuSGJHnulE/6DhAxgZGnG/OjFIAZIPkyqmE9FjMTMT2o9IF/mA5eVBUWcnrlXEC1JE1MyJC0B/EV26I4cOBaIW2VOK6H5losuOJLcPuPkysWgBn/8U0TWBTnQzE/3990UnbzreeEMsTztN7baleByPB9fpp1v5A7md0OvXi+Wpp6rftjwGctSV3+hc/pniXOrrxb9IRP1oDDrRRfnHYkBjY+ZcenkNOvnk4PaL6A8FLFNE33ZoW0YB6429ogKdOlptIyKd6AkjgebOYBpx3Vy4gBkRIoXCvqzfKxpx1eUPBD8aQLeRAIDpRN96OH0jfqDtAPa27kUEEaUT6wLsyAOAybWTEY1E0dzVjH1H0jfi6/eJOnDKqFOC3DVX3HPPPZg4cSLKysowZ84crFu3Luv6Tz75JKZNm4aysjLMnDkTzz33XMrfDcPAjTfeiFGjRqG8vBzz58/H+31cMw0NDVi8eDGqqqpQU1ODpUuX4siRI/2+54477sDUqVNRWlqKMWPG4Ac/+IGaH51PSKFMVwHRMNKL6IC/uegqYm50FtGlgAgA5eXBbVczJy6AYCKNvHQkSVFBigwSKaIfOOCPKOu1I0nn8x/w99qXCc3Of4romhC0gBWPmyORdBGwjjlGdDK1twM7d/b/e1OT6VJXLeKWlZnXgaAiXXSLcwFyx1n4KaLX1oplUOWvmwsayC2i/+1vYnn88er3O+hODEA/Eb2szOzMk45zK4mEKaLPmRPcfhH9CTpKoSfeg664uPHXRcCaUjslq4DV0tWSdOieNkZtT3hJrCRZDkF1ZOiWSQ8AJ408CQDw9v630/5ddmKcNlqxEwGpowGCQDcBF8jtRF/78drkelWlLrNSMyA7MYIqf0C/Y1BWVJbsyHi7vn8diCfieGOPqANzxurdiD/xxBO4+uqrcdNNN+HNN9/ESSedhAULFuCAFEX78Prrr+OSSy7B0qVL8dZbb2HRokVYtGgR3pU5mABuv/12/OxnP8O9996LtWvXorKyEgsWLECnRZRYvHgxNm/ejFWrVuHZZ5/F6tWrsXz58pRtXXnllXjggQdwxx13YOvWrXjmmWdw+umn+1MQOuNnLrCKSRVbW8Ukn4ApNEhkLrqfIrqXm3udRUR53EtLg80D1cyJCyB/nOhSZJDU1podIH640b12Lkgnens70NOjZp9UQic6RXRdCFrAsmZe6yJgFRWZ7loZ22JlgxiFjEmTTOe+SuR3FrKIK3O205U/YAqIdKL7w4wZYvnRR+lHRKwVz9++CLjWToygIo107EiSMS2W584kf/+7uJcrL1c/EoDkN0FPbNnWYzbiOglYUkSUsS1WNuzdAAMGJlRPwIjKEf3+7hU5GiAoJ/SRHr0ERAA4qU6I6GE40WvLRSMSVB3QTcAFgOnDRc78Bw0foKOno9/f1+4RjbgfAq61/DONBFGNjh1J2UZjbDu8Da3dragorsCM4TOC3jVH3HXXXVi2bBkuvfRSzJgxA/feey8qKirw4IMPpl3/pz/9KRYuXIhrrrkG06dPx6233opTTjkFP//5zwEI9/hPfvIT3HDDDbjgggtw4okn4pFHHsHevXvx9NNPAwC2bNmClStX4oEHHsCcOXMwb9483H333Xj88cex92h29pYtW/CLX/wCf/jDH/CFL3wBkyZNwuzZs/HZz342kHLRCt0FRNnhMnhwf8e0FNE/+sj992dioMe5hCEgAto5cWEYZln44chX0ZFkjXOxEon4m4vuVUTXfXJdZqJTRNeFoF24sn2LxVInfA6bk8TzX1oRV45iVB3lIgl6clEdBcRTjo5uldnnVvbtA/bsEe2OH1EWYdUBncp/6FBzhOVbb/X/u58iujz/u7rMUSp+kkioMauoxpqL3hd5DZo925zfhxAgeBeoFK9KYiUoiZUEsk07zKqbBSC9iJ50QSt2oUuC7siQx2BwqT6NiNWJ3ldI3du6F/uO7EM0EsXJo9Q34snyD6oTQ8M4nVGDRmFE5QjEjXja0QB/+1gMJ5szRn0jLsu/J9GT0snmF4ZhaNmRkW00xro9ohE/dfSpKIrq24h3d3djw4YNmD9/fvK9aDSK+fPnY82aNWk/s2bNmpT1AWDBggXJ9Xfs2IH6+vqUdaqrqzFnzpzkOmvWrEFNTQ1OtThl5s+fj2g0irVHb0D/+Mc/4phjjsGzzz6LSZMmYeLEifjmN7+JhiCHMepCvojofaNcAMa5eCFsEV0TJy66u0W0AeBvnIsfIjqgt4heXGx2TLAOCOT539trnnchQhFdE2TdbmoK5ryQnVqDBwtRVBdmzRLLdAKiFLD8GjEYtIiuoxNdlv/u3f3LQQq406f7s89hdWLoVP6AEGgBc+SFJB73N0pk0CBTGA7iGHR0mI53nY5BttEwfl+DSP4iXaCNnY2BTGypo3gFALNGzgKQQ0T3IUoECD6TW0cRd9qwaSiKFqGpswkft6QOUV6zWwhlxw8/HhXF6h98ZB0o5DiXSCSC2aNEI/7mvlQ3QsJIJOuAHyJ6RXFFskMtiI6kjt4OGBCNuFYdSUdHY2zYt6Hf32Scjh/lr5JDhw4hHo9j5MiRKe+PHDkS9fX1aT9TX1+fdX25zLXOiD6Ca1FREWpra5PrfPjhh/joo4/w5JNP4pFHHsFDDz2EDRs24B//8R8z/p6uri60tLSk/BsQBJGJ3tEhRCM3ZBPRg4hzoYiuFul61MSJmxJroKuInikTHdBbRAfMSJegJutzQphxLoAWHUkU0TVhyBDzdWOj/9vTXUBcuzY1UiKRAFavFq/POMOfbYclouvkhK6qAqZMEa+lYCt55RWx/NSn/Nm2dKIXcpwLYI4GkPnzknffFftcWSky0VUTiQQbqSPP/0gk2Hl5ciEF8nfe6T+C7i9/EUvmoZO+SAExqIktdRQQASQdzjK2QmIYBl7d+SoAYO7Yub5sO3AnuoYTW5YWleL44aKBkK5byUs7XgIAnDXhLF+2HVYnhk7lDyApom/Ymyribjm4BS1dLSgvKsfMkTOVbzcSiQSaSy/LH4AvnTJukQL53w//HQfbUueoWL1LPEh8YuwnAt+vgUIikUBXVxceeeQRfPKTn8TZZ5+NX/3qV3j55ZexbVv6uQBuu+02VFdXJ/+Nk+JVvhNEJjrgPs5Biuh989ABf0V0FQ9YFNH7o1mcRVIoLi4W/1TjZyY6AIwdK5Z+iuisA+qQ5z+gRR2giK4JRUVmh1MQApauAuLs2aKOHDwIWO/F3n5blMvgwf7HuRwKZk4ybY/BmWeKpey0kLz8slh++tP+bJcjAQSfOPps95e/pHYkrVollp/6lH/z2AQZqWONTIxq1BKNHStGuSYS5ugLANi/XwjrgH91gOQv1oktgxARdRUQPzH2E4hFYtjVvAu7ms2H83cPvIuD7QdRUVzh24R+UkAMemJRnVy4ADBv/DwAwKsfvZry/ss7RSP+6Un+XMCCnlhUxzxuADh9jOiJ/evuv6a8/+cP/wxAHB+/okSSuegBXoMqiysRjejTiA+tGIrpw0Q2/eu7X0++v6dlD947+B4iiODsiWeHtHf2GDZsGGKxGPbv35/y/v79+1FXV5f2M3V1dVnXl8tc6/SduLS3txcNDQ3JdUaNGoWioiJMnTo1uc706aK8d2UQZK+//no0Nzcn/+32Q7QKAz+FpJISUzRyK6LJm/l0E4lJEb25Wb3TlU50f9BsYkUlxzkb8hzwkgluJ87Fj4lFVc4LQCe6oKjIFAw0qAP63PWQUAQs3QTE0lLT5WkVca0Col9ZxHSiC84+Wyyl8xwQeehSQJR/Vw0nFhWccYa4d96zB3j/ffP9F14Qy3PP9W/bQR4DXcsfMDuS/mrRQF58USxnzUpv6iEkDBeobgLioJJBmD1aOHH/8tFfku9LAfGT4z/pW4Y7ndACKRC+svOV5HsfNX2ELYe2IIKIb050Tiwq+OSETyIaieLvh/+eEqnzwoeiET93sn+NeJBzM+ha/kD6jiR5DTp19KnJc1VXSkpKMHv2bLwobzwgHOAvvvgi5s5NP5Jn7ty5KesDwKpVq5LrT5o0CXV1dSnrtLS0YO3atcl15s6di6amJmyw5Am+9NJLSCQSmHP04ezMM89Eb28vtm/fnlzn73//OwBggszZ7kNpaSmqqqpS/g0I/IxzAbxPrChv5tO5cCsrzZt+1W50iuj+oKsT3W8RvRAz0QE1nQh+wTpAEV0ngoyz0FnAkiLt//2f+d7vfieWn/ucf9uVHfWFnskty/+NN8xz8amnxPITn0gfracCef63tQXTwahr+ZeXm5FFsvOosRF49eiz4IIF/m07yI4kHSd2lXzmM2L5xz+a7/3+92LpZ/mT/CZIEVFnAetT40Xm1/Pbn0++9/utogItnLLQt+0OqxCNeFAiuoxz0SkTHQA+NUGU/6YDm7C7WTwc/n7L75N/k0KrauT3tna3ojve7cs2rOiYSQ8ANWU1yUiXFz8UgmVrVyte3iFGAvgpogd5DdJ1JABglvEz255JTrD75HtPAgA+N8XHBwmFXH311bj//vvx8MMPY8uWLbjsssvQ1taGSy+9FACwZMkSXH/99cn1r7zySqxcuRJ33nkntm7diptvvhnr16/HihUrAIi4n6uuugrf//738cwzz2DTpk1YsmQJRo8ejUWLFgEQjvKFCxdi2bJlWLduHV577TWsWLECF198MUaPHg1ATDR6yimn4Bvf+AbeeustbNiwAf/8z/+Mz372synu9IJAdxExW5QF4F+ky0CPc+noEEs60cUyCCd6wuVcQ/mciS4fkCmim2hUByiiawRdoIJ/+Aex/L//E9eNDz8UE/pFo8CXvuTfdoMUEHt7zTZYNxFx4kTgxBPFPsrOi8cfF0s/y7+62owpKXQR97zzxFKW+5NPiknQZ84Epk3zb7vsyBN84QvievPmm8DOneIe/tlnxd8uvjjUXSMaE6QLVMc8bskF0y4AAPxh2x/Q2duJPS178Nqu1wAA/zgj8+RzXgkyEz2eiKO9RzxE6HYMRlSOSArpT2x+AoZh4NFNjwLwt/yrS6sRgZipvrHD/8l9jvTo25EkO4t+895vAIhOjI7eDkwdOhUzR6jPQ5dwNIxg4ZSFKI2VYnvjdryz/x0cbDuY7NS7ZOYlIe+dPS666CLccccduPHGGzFr1ixs3LgRK1euTE4MumvXLuzbty+5/hlnnIHHHnsM9913H0466ST89re/xdNPP40T5GzpAK699lpcccUVWL58OU477TQcOXIEK1euRJkla/bRRx/FtGnTcM455+C8887DvHnzcN999yX/Ho1G8cc//hHDhg3Dpz71KZx//vmYPn06Hpc3rDrS2wt89avCIdEnzsbTd3Yf7SzUVUTPJiACpoj+0Ufuvj8TKl24jLIw8eLCra8XmbnLlqVmhXrBbxFdPqAbRuokpk7I1pEkRfSGBvOYqoIiuj9o5ET3KRiDuCHIOBdd86ABIRQed5zIRP/1r81s9HPOATJEASohSBHd2hboeAy+8hUR33LffUJQ/8tfRIzORRf5t81IREywe+iQaM+Oml58Q2cRd/Fi4LrrRJzIO+8Ad98t3v/qV0U5+UUYTnQdy3/4cOCss8Q8APfcI8qlqwuYMQM46aSw947oShh5xLq5cAHgjHFnYMzgMdjTuge/e+93eHv/2zBg4JPjP4mxVWN9226QcS5tPWYjrlsmOgB85YSvYPVHq3Hv+nsxY/gMbNi3AWVFZfjy8V/2bZuxaAxDyoegoaMBhzsOY+Sgkb5tC9BbxP2nE/8Jt66+FSs/WIldzbvwX+v/CwDw1RO/ioiPjXgo1yANz/9BJYNw/tTz8fstv8eda+7EqEGj0JvoxamjT8W0YT46ERSzYsWKpJO8L69YMxePcuGFF+LCCy/M+H2RSAS33HILbrnllozr1NbW4rHHHsu6X6NHj8bvpMsmH1i1Cvif/xGv/+u/gO99z/t3BvEg5zXOIVucCyAmAAL0jnOhgGjixYX7ox8JZ9Cbb4qHfBWTO/k5sS4ghmbHYkA8LjqSnLreDCN7R1J1tfjO1lbhRj/uOO/7LFEpous4GiMf64Bi6ETXiDCc6Dq6cCMR4F//Vbz+//4/4N57xevvftff7QY5sai8JyguNq8HOrFkibgnXL9eiImAaHNlp61fUMQVjB4NXCDMnDjlFODdd0UHw9Kl/m43SCe6zh15gLj2AMCPfwzcdJN4ff31/nZikPymtkxUoEJ3gUYjUVx26mUAgBX/twI/W/szAMC1Z17r63aDnFhUln8sEkNpTL9G/Cszv4K6QXXY3rgd5z92PgDgmyd/EyMqfcpjO0qQTmid40SmDp2KT034FBJGAif/8mSs27MOlcWV+OYp3/R1u3Sim1x35nUAgP9+579x++u3AwBuOuumMHeJhIWcVAgAnn8+83pOkA8RsZiYyMgP8jXORQqIXm7w6cLtjxcXrnWiuT//Wc3++O1Ej0S81YHmZiHAA5lHY/gV6cI64A8aOdEpomsEJxY1WbpUiIc9PSIG68IL/ZvQUhKkgKu7gDhqFPD974vXXV0iL/7WW/3fLkVck5/8RHSSy/b/9tsz3wergp0YJp/7HLBwoSj/7m5g3jzgkvwYBU5CgpP6mfzr3H/FhOoJaOpsQle8C+dMOgfnH3u+r9tMOtHbDydzkP1CCriDSwf76ix2y+DSwbjnvHsQjYjb/Cm1U3Dz2Tf7vl3OC2Dy88/9HMXR4uT14MazbkTdIB+HUyIcJ7qu5X/amNOSnXkAcOGMC32/BhFN2brVfP3OOyKKxStWAdGvNiCoOBe/MtEZZaEWKSA6deHG48Dbb5v/37hRzf74LaID3kYkyPO/osIsu75MnCiWlomSPROPmyIvR2OoxW0d8AHGuWgEM9FNioqAF18E7r9ftKPf+Ib/25Tl39Eh/pWX+7ctnUcCSL79bWDsWGDzZhEjIu+1/IQirsn48cDatcD//i9w2mnA+QE8+zET3SQSEZOJPvCAuB/65jfNzH5C0kEBy6SiuAKvfP0V/Oi1H6GmrAbXzbvOd7FZunC74l1o72lHZYl/D3a6Tipq5R+m/wPeXP4m3jv4Hs6fej6qSqt832aQkTo6x4kAwMyRM/HCV1/Aw28/jE+M+QSWz17u+zY5L0Mq95x3DxZNW4SeeA8WTlmoZYcXCQCriN7RITLAJ0/29p1BCIhe4hysURa5nOg6ZqIzyqI/cui6UxfugQPClSj54AM1+xOkiO7mPMg1EgMQES7PPWdmB6vAGvXEjiS1uK0DPkARXSPoRE+lpga45prgtldVJcT73l5xDMb6F92avB7qLKJHImIiUT8nE+0LI41SOe444Oabg9teGJ0YOpd/eTlwxRVh7wXJFxilkMrEmom45/x7AtveoJJBKImVoDvejcMdh30V0fOh/AHgpLqTcFJdcBM5yI4k1gHB2RPPxtkTzw5se6GMBCjWt/wjkQjOnXxu2LtBwiSRMKMaKiuFwKVSRPfzQdqLgNjWZk58misTfe9eIbIWFzvfTqZtA97KxurCNQy9shTDduE6FRD37En9/4cfCrGjyKMMmC8ieqaRGICZg+6HiB6JZHbA24EdSf1hnAtJB12g4RKJBCcisvzTw46kcGH5E+KeIAWsfHCBBk0kEkl2ZPh9DKxxLsQkqPIH8kNEDxp25BHSh4MHxXDCSASYM0e8t3On9+9VEVmSCy8CohQTSkszC10jRog890QC+Phjd/uYDpVxLtZoDF2QAqKfQ9bT4XZSxb17xXL2bCFC9vaqGX2g+2iMXHFGADB1qlj6IaJ7jXqiE70/nFiUpINxLuET1OSi+eBED4OgOjEMg3UgHdZrkM+Rwix/MuBgJnr4yGPg9+SiLP/0JEV0n+NcDMPgMUiDdSSA3/MC6B6nQwgA04U7ciQwZYp4rUJEz5c86NrazEJeNGo6cd95x/k2MqGibKyf1c2Jm28uXFkHxo4164CKSJeB5ETfsUOdMKuqXCii94dOdJKOIF2guk+qGBZ0oodLUKMxOjvNCTt5DExk+ff2+t9m8xpEBhphZKLrnMkdBkGJuPmQiR4GQcW5tPe0w4AQiSmim8hOpLgRR0uXv8ITOzFIXrBvn1iOHm1OIpgvLly/86ABMekSAKxf73wbmVBRNtGoviKi/H354sKVIvqYMWaMkYqJNAdCHRg1ChgyRIzG2LTJ+TbSoSrqSdeJRRMJU8TOlzrgAxTRNUIKuC0tqfM/+AFF3PQEJaLTiZ6eoDsxAH/b/nzDOoG53x0ZvAaRgYYUEJs6mxBPxH3dFgWs9CQntgwozoXln0pQE4vK8z+CCCqKA36I05iyorJkeQR1DFgHiNbIocXDh5siuso4Fz9vYv2OsgCAU08VyzfecL6NdCQS6kRE3UX0oB8gvTrRx4wR/wCzc8kL+SKiZ6sD1pinv/3N+TbSoSrqSdfzv6PDfE0nOtGBmhrzdWOjv9vKh0n9wiCoSB26cNMTlBNdnv/l5UAs5u+28o2gRsRQRCcDDSmiA0Bjp7+NOAWs9ASVCc2RAOkJyokuy7+ypBLRCB9lrAR1DDgvA8kLrLEmciLNQnCiW393NqSIvm6dGIbqFavApkpE1C3OJYhJZdOhwok+apR4rVJE91NIVRFplKsjae5csVyzxvk20qE6zkW3819GuQD5My+AD/DOUyNiMVNIpws0HOS9BjsxwiFoJzrLvz9BdSTxGJCBRlG0CFWl4oY/KBGRAlYqQ8qGAPC/E4MCYnqCmliU539meAwIsWAVk6WAuH+/94l/dBfR7ca5nHyyiLNobFQjIspyAbyLq7rGWYQlorh14VpHY/ghouteB+yK6H/5i5oJwVSL6F1d/kdUOEGK6GVlInYpSOhEJ5lgJne4DBHP33Sih4T1/PdzTiye/5mhE50Q9wQlYDFOJD1BO6E5qWIqQc0LwE6MzARdB3gMiNZYRfSRI8Xrzk7v7k7dBUS7TvSiIuD888XrP/zB+Xb6Im/uKyq8C2y6xlmoiutwilsXblOTWA4ZAtTVidf19d73J4g64MWNbbcj6cwzhaN6924xIsMrqkV0QK86ENakokBhONEbGhqwePFiVFVVoaamBkuXLsURaxBxmvWvuOIKHHfccSgvL8f48ePx7W9/G83NzSnrRSKRfv8ef/xxv35G4AQRZxGPm+c/BaxUgo4ToQs3FVn+3d2po4VUQwE3M0E70XkM9IRtuDuCELB64j3oiosbSApYqQQdZcE4l1RkJnpnbyc6ejpyrO0eCriZCTqXnnWAaI1VTK6oMIVpryJiEDexVie2U2eR3SgLAPjSl8Ty4YdT41jcoFJY1TXOIqw4F7cuXCmi19TQiZ6OigrgH/9RvL7pJufb6YuqcikuNo+5TiJ6WBPrAoXhRF+8eDE2b96MVatW4dlnn8Xq1auxfPnyjOvv3bsXe/fuxR133IF3330XDz30EFauXImlS5f2W/fXv/419u3bl/y3aNEiv35G4AThRLeKkxSwUglKRKcTPT2VlUBJiXjtZx1g+WcmKCc6j4HesA13RxACVluPOVyaTuhUhpQHE+dCETc9g0sGoyhaBMDfOkABNzO1ZXSiE5KkryNbutG9iuhBCojxuHNx264LFwD+3/8TefGHDgH//d/OttMXP0R0nQTEeNwU8PJhYtFEIr2Ivn+/+C1ekIKSrk50Jx1JN90kRmU8/zzw8svOt2VloHckhdWJBAx8EX3Lli1YuXIlHnjgAcyZMwfz5s3D3Xffjccffxx79+5N+5kTTjgBv/vd7/D5z38ekydPxmc+8xn84Ac/wB//+Ef09pnooqamBnV1dcl/ZbJABwBBiLiyLYpGzXORCGScCzPRwyESCaYO0AWdmSCc6IlEuG0wyQ7bcPcE4YSW4lVxtBglsRLftpOPBOZEPxqnw06MVCKRSKB1gAJuf5IdeT5GShmGwWNA8oO+IrqqOIsgRPTKSvFgBDgX0ezGuQBCPLzqKvH6zjvFTbpbVN7c65iJbs18z4eJRa2jGIYMEbnokYg4xgcPetufIOqALGNruduhtxeQI2Ht1IHJk4F//mfx+vvfd7atvqgUGXTsSApTRBnocS5r1qxBTU0NTpUzPgOYP38+otEo1q5da/t7mpubUVVVhaKiopT3L7/8cgwbNgynn346HnzwQRh+hicHTBAClvXcl20zEQTtRKeI3p8gRmOwEyMzQTjROzrMezqK6PrBNtw9QWSiU7zKTNBxLjwG/WEdCJdkHej0rw509HYgYQihjceAaE0mEX3/fm/fG4QTJBJx70R14sIFgKVLgepq4O9/B/70J2fbsqIyL1xHF678fdGoKegFhRsXrnShl5aKzxcVASNGiPfyoSPJrYhudUNKh2QurrlGLF9+2VvczUAfjRGmiD7Qnej19fUYISvoUYqKilBbW4t6mxX20KFDuPXWW/sNH7/lllvwm9/8BqtWrcKXvvQl/Mu//AvuvvvurN/V1dWFlpaWlH+6EoSARQExM4xzCZ8g6wDLvz9BduRFIuFEqpHssA13D1244TKk7GicS0ejr50zjBPJTBCTi3Ji3cwE2YkBABXFbMSJxvjlRA9qckm3mdBO4lwAIQrI+7X/+R9n27Iy0AVEa+dJ0E5ENy5cKSbX1JjvqchFDyrWRn53ljmZ0iLP/5oa0XFghwkTgE98Qri8fvc7Z9uzorIO6Dgag050AA5F9Ouuuy7tpGDWf1u3bvW8Uy0tLTj//PMxY8YM3HzzzSl/+/d//3eceeaZOPnkk/Fv//ZvuPbaa/GjH/0o6/fddtttqK6uTv4bN26c5330C0ZZhIvsrOzs9D63SjbYkZGZoEdjkFSC7MSorBRmDhIMbMP9JwgXqBQQK0sCzuPMA2T5d8W70NHrXyNOETczMk6EHUnhEGRHXkVxBWLRmG/bIcQT8bjpxM3HOBfAnZBsGM7iXCQLF4rlG2/Y/0xfBnqcS765cOX5b3VjyzrgRUS3TrAXhBP9yBFnk+u6Of8B4POfF8vXXnP2OSsDvSMp3+qAT9jsmhF85zvfwde//vWs6xxzzDGoq6vDgQMHUt7v7e1FQ0MD6mTFzUBraysWLlyIwYMH46mnnkJxcXHW9efMmYNbb70VXV1dKM0wrOb666/H1Vdfnfx/S0uLtg/hQURZ0AWdmaoqIBYT912NjUB5uT/b4THITBAiLss/M+zEGLiwDfefIFygMkqkqrTKt23kK4NKBqEoWoTeRC8aOhp8c8kmnejMRO9HkE5ojgToTxCTG7P8SV4gBUTAFBHzTUR3E2fR1gb09IjXduNcAOCUU8Ryxw4xyeiwYfY/KymUOJegJxUFUl24hmHPCW+dVFQinehe6oA8HyMRfyfYk+d/IiF+t91tuRXRZ80Sy02bnH3OykCfWJROdAAORfThw4dj+PDhOdebO3cumpqasGHDBsyePRsA8NJLLyGRSGDOnDkZP9fS0oIFCxagtLQUzzzzjK3JxjZu3IghQ4ZkfPgGgNLS0qx/14kgJxalC7o/kYi4zzp0SByD0aPVb8Mw6ETPBkXccGEnxsCFbbj/BOECTU5qSQGrH5FIBEPKhuBg+0E0djRibNVY5dswDIOZ6FlgpFG4sPwJOYoUnsrLAdmhr1pE9/tG1k2chbyBLy115garqQGmThW56OvXm850Jwx0F25Qxz0d8p46kRATZ+YwqQDwL87Fepz9jLWxnkdHjvgvos+cKZbbtgHd3UBJibPPAwO/DtCJDsCnTPTp06dj4cKFWLZsGdatW4fXXnsNK1aswMUXX4zRR1XJPXv2YNq0aVi3bh0A8fB97rnnoq2tDb/61a/Q0tKC+vp61NfXIx6PAwD++Mc/4oEHHsC7776LDz74AL/4xS/wwx/+EFdccYUfPyMUgnSiU8BNjzQrWOekUEl7OydVzAYnFg0XWf6NjeI+zQ8oousN23D3BOEClQIuXdDp8VtE7OztTE6qyI6M/iSd6H46oXso4mZCln9jRyPiibgv22CcEckL0j3w5lsmuhsnulVAdCpwSifu5s3OPidRKTLrLCCG6UQH7Dtxs8W5eKkDQQmpsZgpnLrpSHIyEgMAxo4VE+z29gJu4y1Vlo3OdYBOdH949NFHsWLFCpxzzjmIRqP40pe+hJ/97GfJv/f09GDbtm1oP5qp9Oabb2Lt2rUAgClTpqR8144dOzBx4kQUFxfjnnvuwb/+67/CMAxMmTIFd911F5YtW+bXzwgcOtHDx+9jwEkVsxN0JjdJRZZ/IgE0N9uf1NwJ8hpUxTQKbWEb7g460cPH72MgOzEA5tKnI8iJRVn+/RlSLhptAwaau5qTx0Ml7MgjeUG6B96RI8XywAFxo+tmYh7DCC7OxY0TXT7AOhUQAWDSJLHctcv5ZwG1D1g6ZqKH6US3iuidnfb2IV2ciwoRXY7yCOJBbtAg8XvddiQ5IRIBTjhBZKJv2QKceKKzzwOcWNRPNHKi+yai19bW4rHHHsv494kTJ8KwTBBw9tlnp/w/HQsXLsRCN0OL8ghZ148ccT+KJBfyukcRPT1+i+jyOshJFdMjy9+vkQAAO5KyUVoqzs22NtGR4aeIzvLXF7bh7pAu0JauFvTEe1AcszHc1iFJAYsielqkiNjY6U8jkhRwiysRjbAR74scjdHY4V8jznkBMlMSK8HgksFo7W7F4fbDvojoLV3iQYLXIKI16W42R4wQy3hc3OTaiLjrR3e3+DygpxNdupCcCogAMH68WH70kfPPAoWTBx2GCysWExEuPT32RcR0YrcKET3IB7nKSpGz66YjyW0deO014OOPnX8WKJw6UOAiOu/+NaOmxhx55ZcTlwJWdvyOc2H5ZyeI0RjsSMqO3x0ZrANkoFJTVpN87ZsTuosu0Gz47UTnpKLZ4WiM8PF9NEYXOzFIHpDuZrO42Jww062IaBW0dXaiuxEQJ0wQS51EdLpwTZzGWWSLNNq/3/1+BO1EB4KJcwGAMWPEcs8e558FWAf8RKM4F4romhGNBifiMkohPUHFuVBATE+QkUasA+kJajQG6wAZaMSisaSQ7psTmk70rNSWBRPnwjzo9AQiojNOJCtBRRrxGkS0JtPNplcnrvzesjJ7kzt6wUsmuhsBUYroXuNcVAhs8iGtu1sL0QxAuHEugHMnbrrjIc//1lZn55WVIB/kvM4L4BQpou/d6/yzAEV0P6ETnWSDAla4BFX+nFQxPdbyz5EO4RrWgezwGkSIe2Ski18CVjJKgQJiWpJxLj7FiSSd6BQQ02LNRM8V8eQWWQfohE5PUE50XoOI1uQS0fftc/e9Qbpw3TjRvcS5SBG9ocHZNiUqBUTrg7IuImLYk2o5deKmEzwHDTInZXPrRte9DqgQ0d040Xt7zWNDEV09dKKTbFDAChe/RwLQiZ4def739LjvIM8F60B2/L4GBXnvRUjQ0AUaLsny7/RXQKQTPT2y/Lvj3WjvafdlG4xzyY48BhwNQwoav5zoYURZBOXCHTzYfBB240ZXKaIXFQHl5eK1LiJivjrRrXUgElE3GiNIJ3pQcS6jR4ulGxHdWk9VjsZgJrqATnSSDYro4UInerhUVJgT6vpxDOJxoP3ocz3rQHp4DSLEPcwjDpfAOjHowk1LZXEliqMi4sCPY9AT70FXXLiQeAzSwzpACDLfbEqRbKA60b3EuQDm5KsHDzr/rGqRWZaxLiL6QHCiA+o6kgZ6nIvT0XRyH6NR81h5gU70VGSZxuPC9R8iFNE1hAJWuDATPVwiEfO+z49jYG2H6IROD69BhLiHAla4DCkLJs6FTvT0RCIRX+uAPP8BOqEzEVicC8uf6EwuEd1t5rHuTnQvcS6AOfHqoUPOP6taZJbHThcnbr450TM591Q50XXsSOrpMc8XN3VAXh+6usy6ZBfrSIxIxPm2+0IRPRV5/gOhR7pQRNcQCljhEtTErnSiZ8bPOiDLv7hYTSfxQITXIELcQwErXFj+4ePnMZB56GVFZSiO+TypX57idx1gJj3JCzLdbI4aJZb5IKIHnQcNeBPRVca5APqJiGEKiEBhO9Ht1oGmJvN1TY3z7ZWUmJ9zWgf8Ov+PHAESCTXf6YVEItyOJKtwQxGd9IUCVriw/MMnCBGd5Z8Z1gFC3EMnerj4Xf6cWDQ3vjrR2YmREzkag9cgUtAMhDgXL1EWbuNcpIju1IULqBfYdBXRw4pzUZGJDuSXE91pHZDnbU2NyNV3g6w7XpzoKrAeN78minNCR4cZcRNGHSgqAmIx8TrkXHSK6BoS1KR+FLDSI8u/qcmfTr+wO7HzAYro4SLL3+/RGDwGZCBCJ3S4DCkXAmJzVzPiibjy75cCIuNcMhNEnAsF3MzwGkQIMguIVie608xjQG8numF4j3ORAqJTF25vr+kOVSWw6Taxoi5xLnZcuIaR24nutSMpiAc5p3XA60gM62edChGqRfTyclM01qEOWI9BRUU4+6DJ5KIU0TXETwGxt1d0IgEUsDIh41wMA2huVv/9FBBz42cdCPLeN18JyonOY0AGIn4KWN3xbk6qmAPpwgWAps4m5d+fdKKz/DNCJ3q4cDQMIcgd59LR4U6Y0tmJfuSIOeFe0HEu1n0c6HEuYU8sakdA7Ow03YB9RXQ5eeaePe72Iwwnej6I6KqdkpGIXnXAev5HQ5KRnUYa+QRFdA3xU8CyXn8oYKWnpMRsG/08BnSiZ4ZO9HDhaBhC3BOEgAhQRMxEcaw4WTZ+OqHpRM9MEJnoFHAzQyc6Ich8w19RYWYeuxERdXaiyxv3sjL3TlGvInospm7SKZ0ERCD8h3gnLlxrmfU9F8aPF8tdu9ztRxiZ6E7jXNzGGVk/G3acC6BXHQj7/AfoRCeZ4aSK4UMRN1xY/uFiLX83I12zYZ2ThMeADESCiLIojZVyUsUsyEiXxk71mVQUEHMTRB3gpJaZsZa/obgRTxiJ5GgMHgOiNdmiN7yIiGE40bu7gZ6e3Ot7jXIB3Me5WF2qkYj77VvRLc4l7OHMTly48nhUVJiRIJJx48Ty8GF3WdtBPkznkxOdIrr/0IlOMkEBMXz8zITOFNFHTGT5u5nTJhesA7mR5d/To34eE+s9EI8BGYgEEmVBF25W/DwGUkCkEz0zyfLvZJxLGMjyjxvxZKeDKtq622BACPO8DhGtaW8Xy3SO7IkTxXLHDuffG4YTHbB3Q65CQPTqRB+oAmJXl+jMAMIT0Z24cLMJDtXV5m/Yvdv5fuTDaAwVIrpOTnQdOpJ0ENHpRCeZkPW2udmMNVMFBUR7yFx0PzsyGOeSmSAy0VkHMlNebnb0qj4G8vyPxcx2kJCBhBSwmjqblE9sSReuPTixZbgEUv4U0TNSXlyOsiLRwKo+BrL8o5EoyovKlX43IUqxI6Lv3On8e4MUEEtKTBexExFdRZQFRfRUrCJmWA+RbpzomQQHt6MxurrMUREDPc5FBye6vM7oUAd0ENHpRCeZGGLOiYWmJrXfTRHdHhwNEC5BlD/nBMhMJOLfMbCe/6pGexKiE3JiSwMGmrvUzk5NF6495DFo7FA/nIxO9NwMLRcPoMxEDw+/OjKs16AIG3GiK4nEwBDRIxFncRYq4lxkXnxrKxB3YATwQ2DTKc5F7kNlZf94lKBw40RXLaIH3ZkQZpyLTk50iugCOtFJJoqKzDbDTwGLZCaIOBc60TPDTozw8Ws0BjsxyEDHz4kt6YK2RyCROuzIyEgQ5c/RGNnxTUTnNYjkA1aBJZ9FdMAU5IKKc6muNl/bFS6B7Bn0btFJQAw7Dx1w50TPJOhOmCCWTiON5LFIl7XuB2HEubh1ovsh8rAOpEInOsmGXyIioyzs4ZeAaBgUce1AET18gnCiEzJQCcIFSjITRJwIneiZYZxL+PAaRAoa6UIH8jsTHXDmxFUR51JWJmJkAJEtaxcKiP7jxIUr60AmEX3qVLHcutXZPoR1/re1CSElF3Si+4c89taOtqChE51kgwJWuPhV/tYYMTpxMyPLv7MT6OhQ+93sSLIHO/IIcQ9doOGSjHPpVDucrKu3C91xMbFYdVmIDxGaI8//9p52dPaqfdBhHbCH39cgjgQgWiMFxLIyIJpG7pgyRSwPHnQmlCUSwQ+pdOJEVxHnAriLUcnlfHaDTpMq6iCiO3HhZoszAoDp08VyyxZn+xC0mCRF9ETCnnCqIhNdisROz7uBPrGoDnVAiuh0opN0UEQPF78FRIBxLtkYPNgcIcY4kXDgNYgQ99AFGi5+C4gAj0E2qkqrEIuIRlz1MUhmorP8s1Jb5k8dYCY9yQtyCYiDB5tu9M2b7X+v1Q2rsxPdq4guRUQnTnQ/4lx0mlRRJwHRiRM9Ux2YMUMs33/fdPjZIWg3lHX/g6oDVve3Hfe7ZKBPLKpDHZAdSXSik3T4LWBRQMyOjHNRnYkurz2DBoU3J0k+ENTEliQzLH9C3CNF3MPtDoeC5oACoj38EtFl+VcWVyIWZSOeiUgkgiHl4kbKr44kOqGzI+uA6sl12ZFH8oJcAiIAHH+8WL77rv3vlQ9yRUWmoOk3QWeiA96c6Ixz8Q+VIvrYseJY9fYCH3xgfx9kx0pQkR6xGFBeLl7nqgM9PeZx8lIH5DGOx50NiZd1QOVDLutAKoxzIdmggBUufjvR2YmRG9aBcGH5E+IexrmEixRwVce5SBGdAm5uWAfCheWf/9xzzz2YOHEiysrKMGfOHKxbty7r+k8++SSmTZuGsrIyzJw5E88991zK3w3DwI033ohRo0ahvLwc8+fPx/vvv5+yTkNDAxYvXoyqqirU1NRg6dKlOJLB/fnBBx9g8ODBqKmp8fQ7fUGKbdlE9BNOEEsnTnTrg1wk4m7fnOLEia4iygJw50T3M86lo0OIvWGiw0O8kziXXK7oSMR0o2/caH8fVHXUOMFuHbC6H6Uj0g2VlWb9ZkeSSb7VAR+hiK4pFLDChSJ6+DCTO1w4GoYQ9zCPOFz8dqKz/HPDSKNwSZZ/J8s/H3niiSdw9dVX46abbsKbb76Jk046CQsWLMCBAwfSrv/666/jkksuwdKlS/HWW29h0aJFWLRoEd61uKxvv/12/OxnP8O9996LtWvXorKyEgsWLECnxdG3ePFibN68GatWrcKzzz6L1atXY/ny5f2219PTg0suuQSf/OQn1f94Fdhxos+cKZYbNtj/3jAe5MJworvJhPYjzsX6sBa2iKjDQ7xKJzoAzJkjlmvW2N8HKVR7EamdIutALhFdnv81Nd6G/Eej7sRrP0V0ZqIL6EQn2aCIHi5+x7lQQMwNRdxw4TWIEPdQwAoXq4BrOMmzzAFFdPv43ZFBJ3R22JGX39x1111YtmwZLr30UsyYMQP33nsvKioq8OCDD6Zd/6c//SkWLlyIa665BtOnT8ett96KU045BT//+c8BCBf6T37yE9xwww244IILcOKJJ+KRRx7B3r178fTTTwMAtmzZgpUrV+KBBx7AnDlzMG/ePNx99914/PHHsXfv3pTt3XDDDZg2bRq+/OUv+1oOrpECYjZX9Lx5Yrl+vT2XNwA0NYllUFEWgCnI5RLRDUN9nIsbJ7pKAbG0FCgpEa8poqudWBQA5s4VS91FdLt1QKVL3o14PdCd6PJ6kC91wEcoomsKBaxwkeXf2eksCisXFHDt40cdMAx/4soGIhwJQIh7GKUQLkPKxMNdd7wbHb3qGnGK6Pbxow4kjATaesRDNI9BdvzOpGdHnn90d3djw4YNmD9/fvK9aDSK+fPnY00GsWvNmjUp6wPAggULkuvv2LED9fX1KetUV1djzpw5yXXWrFmDmpoanHrqqcl15s+fj2g0irVr1ybfe+mll/Dkk0/innvu8f5j/cKOgDhhgvgXjwOvv27ve6WAGGSUhV0XbmurGXkyUOJcAH1ERB1EdNVOdCmib9xorp+LMOqAFKVznQOq4owAfeYF4MSiqdCJTrIhr0uqndAU0e0xeLA5CkiliKjDtSdf8EPEbW8HEgnxmnUgO+zII8Q9jLIIl0Elg1AULQKg9hjQBW2f2jL1deBItykisQ5khx15+cuhQ4cQj8cxcuTIlPdHjhyJ+vr6tJ+pr6/Pur5c5lpnxIgRKX8vKipCbW1tcp3Dhw/j61//Oh566CFU2XyY6erqQktLS8o/37EjIALA2WeL5Suv2PteeVOsswu3rMyciNEtusS5APrEWejwEK/aiT5hgphgtLfXfkdSGHVAdszkEvpVOtGditdWp95AdaLLOhDkSJy+0IlOskEXaLhEIv5EuujQ/uYLftQBWf6RiHqjxECDIjoh7qGAFS6RSMSXY0Anun38KH/ZiRSLxFBWVKbsewcivsfpsBOjIFm2bBm+8pWv4FOf+pTtz9x2222orq5O/hs3bpyPe3gUOxOLAsBZZ4mlXRE9H/KgVQqIYce5WPclbBFRh4d41U70SAT49KfF65dftrcPYdQB+RvCENHtdt50dAghHfAvE11hPKFjDCP/6oCPUETXFApY4eOniEsRPTd+lL/1/JeTbpP0yPLv6PAn0ojXIDKQoRM9fGSkS2OHup7wpIhewkY8F352YgwuHYwIG/GsyPLv7O1ER4+6Rpwdef4zbNgwxGIx7N+/P+X9/fv3o66uLu1n6urqsq4vl7nW6TtxaW9vLxoaGpLrvPTSS7jjjjtQVFSEoqIiLF26FM3NzSgqKsqY13799dejubk5+W/37t12isEbdp3oUkRfv97eza5Kkc4uTp3oKqIs3DjRGefiP26c6LmOB0X09DgdAWHt5Mp13XFCTY1YxuP2I3f8oKsL6OkRr3UQ0elEJ+mwCogyfkIFFLDsQxE9XPwW0Ul2qqrMSCOVozE4LwApBKwCYsJQ14gzTsQ+dKKHiy9OdE5qaZvBJYMRi4hG3I/RAOzI84+SkhLMnj0bL774YvK9RCKBF198EXNlhnEf5s6dm7I+AKxatSq5/qRJk1BXV5eyTktLC9auXZtcZ+7cuWhqasKGDRuS67z00ktIJBKYM2cOAJGbvnHjxuS/W265BYMHD8bGjRvxxS9+Me2+lZaWoqqqKuWf79gV0SdNAurqhDi0fn3u79XZiS7zoMOaVJFxLv7jxIVrdzSGFNHfeMPeBLthZKLL35CrI8mPTHS7nTfWTqSoQom1stKfB3KnWOuf6jruBNmRRCc6SYdsmxMJdR2vhkEBywl+xrlQxM0NRfRwsUYakdVIGwAAZhlJREFU8RgQ4gzpgk4YiaTo5BXDMJKZ0BSwckMRPVz8jHPh+Z8bvyKN2JERDFdffTXuv/9+PPzww9iyZQsuu+wytLW14dJLLwUALFmyBNdff31y/SuvvBIrV67EnXfeia1bt+Lmm2/G+vXrsWLFCgDifLjqqqvw/e9/H8888ww2bdqEJUuWYPTo0Vi0aBEAYPr06Vi4cCGWLVuGdevW4bXXXsOKFStw8cUXY/To0cl1TjjhhOS/MWPGIBqN4oQTTsCQIIXlXNh14UYiwJlnitevvZb7e8OcVDHIOBe77ncrfjnRGediojrOBQAmTgTGjRO56JYOtIwUWia6Uye6aoHZ+kDe1KT2u50go50GD1bbSeAUxrmQbJSVmdc8VQJWZ6cYCQJQwLIDnejh4mf58/y3hx8THFNEJ4VAeXE5yovExF6qBKy2njYYEHmIdKLnZkj50TiXTh/iXCgg5mRohXCC+SHg8vy3h68dGTwGvnLRRRfhjjvuwI033ohZs2Zh48aNWLlyZXJi0F27dmHfvn3J9c844ww89thjuO+++3DSSSfht7/9LZ5++mmccMIJyXWuvfZaXHHFFVi+fDlOO+00HDlyBCtXrkRZmTm/wKOPPopp06bhnHPOwXnnnYd58+bhvvvuC+6Hq8KugAgA0t3/xhu51w1DQJS/IVfcjMo4FylauhHRVYuIMlomTAER0OMh3iog5srHdlIHTjxRLDdvzr5eV5d5Hg70OBddRHTAjHQJ04keRpRVOjSZWLQo1K2TrNTWimtFQ4MYbeYVawdumKMw8gWK6OFCJ3r4qD4G1jlJeAzIQKe2vBZ7WvegoaMBk4Z4b8SleBVBBJXFnBk5F7VldKKHia+Z6HSi28JPJzqPgf+sWLEi6STvyytpJsK88MILceGFF2b8vkgkgltuuQW33HJLxnVqa2vx2GOP2d7Hr3/96/j6179ue/3AcCIgHn+8WG7blnvdfIiyULFvTkX0eNx0hqoWGfxw9Dilt9c8p8J8iC8vN193dZmiejqc1IETTgD+9KfcIro8BpGI2bkRBHbrgMqOJLeZ6H6IbH7EIzhFFxGdTnSSC9UClhQQVUc1DVT8jHOhiJ4bef4fOQJ0d6v5TsYZOUP1NairS9yHAhTRycBHtYBldeFyUsXcMM4lXGT5t3a3ojuuphGXHUksf3uorgNdvV3JY0knOtEau3nQADBtmli+/745ZDsThRJl4VREt66nOs7Fj2xJp1iF1DAfYKwieq6RCXYjjQCzI8muiF5TE6yYZLcO+DEvgJ2ceOt6foroYY7G0EVE18SJTilVY/wS0Sle2YNO9HCprhYd3YC6jgzWAWf4dQ0COBqGDHyUi+jMg3YE41zCpbq0GhGIRryxQ80xYJyLM/zqyAOAQSVsxInGOHHhjh8v3I3d3cDOndnXDWNiUadRFipcuHZz2CVyvWg0uzvaDTq4cOW2KypMES8MiovNSSaznQ+G4W40Ri4RPYxOJCCcOBe725QUSpyLiuuLF+hEJ7lQLWDJ+QAo4NqDInq4xGJmm8GOpHDwczSMvAckZKCiWsBq7hKNeHVZgENo8xhOqhgusWgMNWU1ANiRFBZ+deRVFFegKMpEUKIxTly40Sgwdap4vXVr5vW6uszvDSPOJUgXrtX5m0jkXl860QcNMh1QqvDjgdwpugiIgOlGz+ZE7+oyM9PtiOhTpojloUPZRx+E0YkE2KsDPT2m0BLGaAzGuQQDnegkF6rbDHldCTLCKp/xI4KNIroz5L2K6jpAEd0eqkdQshODFBKqBSy6oJ3BOJfw8asOUES3h2+RUix/ojtOXLiAKaJ/8EHmdax50EE+yMnf0NMj/mXCjzgXIHdsCGAKiKqjXAAKiH2xI6JbhV9rBEwmqqrMh7M9ezKvF8acAIA9QdsadSJdeH5v0wrjXIJBOtHtXJd8hCK6xvjlRKeIbg/VAqIuc5LkE345oVn+9uA1iBD3KHeidx51opeyAtlhSNnROBdFUSLxRBxHusVDEkV0e/gl4rL87SHLX1WkkbwGsfyJ9jgV0ceMEct9+zKvY42yCDIP2vobsglHKt3SVuHVjojop4Cow8SiKl3+XrEjosvzv6QEKLI5amjsWLH8+OPM6+jsRJfnf3W1/d+cDZ1EdJ3iXMKuA/L8Z5wLyYRfTnQKiPbwMw+aTlx7+FUHWP72YKQUIe5JCoidauNcKGDZQ7WAKwV0gMfALr450ZmJbgu/yp+RUkR7nEwsCgCjRollNhE9LAGxtNSMSMkkIhqGWpErGjXLzk4uujXORTU6TCyqi4AImMfFjohu9/wHzI6kbCK6zpnoqiN3dBLR6UQ3sdOJFAAU0TWGLtBwkeXf3Jx7snY7SBG9tDTcOUnyCdaBcGH5E+Ie3wQsOtFtIcu/uasZ8YT3RlyWf0msBKVFbMTt4Nu8AKwDtmD5k4LFqYjoREQPWkSKRMzfkUnQa20VQ54BdfsnxUAnTnQ/4lzk7+nqCk84y7dMdCdzAkjywYme7VxULfLqKKLTiW6eC11dagQ6l1BE1xjVHa8UsJwhy98wzLLzAkcCOIfzAoQLy58Q9/gW50IXqC3kpJYA0NTZ5Pn7mMftHNaBcPGr/DkSg2iPWxF9797M64TlwgVSJ/pMh9y38nJ7GdhOthl2nMvgwUAsJl6H5UbXRUAEnInoTpzoUkTXORM9mxNddeSO3Ql9JQM9zkWXSCPr9S3ESBeK6BrDOJdwKS42r4MqjgHL3zmyDsjrtlfYkeQMxrkQ4h5OLBouxbHipOCt4hiw/J3D0RjhIucFUO5EZycG0RnDcO7E1TnOBcgt6PkhcOkiokci4YuIugiIgH8iuoxz2b078zphO9HtxLmodqLbdTwzziUYrCK63Q4OH6CIrjGMUggflXOZUER3DutAuMjyb2kBenq8fx/LnxQSjFIIH5XHgCK6c/yaF4Airj1k+bd2t6In7r0RZycGyQu6uoSQDjh3ojc0iM+nI0wRKZeI6Me+SRHRTia630NNw55cVBcBETBFxGwCotM5AQCgrk4sDxzIvI4OmeiybvfFLxEdCL8jKew4l0QivFEIfYlGzVzkEHPRKaJrjFVAzHS9cAJFXOfIa5YKJzQntXQOndDhIo0fgJrOb4ropJCwCriGgkacAqJzKKKHi29xLhRxbWGNNGrs9P7wzfIneYFVXLQbbVJbC5SUiNf19enX0dmJ7kdmt5NMdL8fsMKeXDRfM9GdiOjyt2UTPcKOczGMzBEeqkX00lIh2ALhi+jygbytTY2rzSktLUJIB8K5/vXFadSOD1BE1xh5DejuVnOOUMByjkoRl50YzlFZ/j09Zj1iHbBHUZFZVirrAMufFAJSQOyOd6O9x3sjThHXORTRw0Vl+Xf1dqErLhyi7EiyRywaSwrpKo6B7MhjHSBaIwWvkhJxI2uHSMR04u7fn34dnZ3oYce5+P2QSye6id8ierYHvrA6kuxEeKg+RpGIu0gjPybXVe1qc4os24oKoKws+O33xU4d8BmK6BpTWSlyuQE1AhZFdOfYaU/sQhHdOSpF9NZW8zXrgH1UHgOOBCCFRGVxJYqjohFXImDRBeoYKeIe7vA+nIwiunNUiuhSwAU4uasT/DgG7MQgWuNGQARyRybkgxN9oIroYTvR8zUT3YmgK0WPxsb0GeCGEV4dKCoyR4oEORpD1ruwR2PEYub3hlEHdOpEAga2E72hoQGLFy9GVVUVampqsHTpUhzJkal19tlnIxKJpPz71re+lbLOrl27cP7556OiogIjRozANddcg97eXr9+RqhEInRCh42dkU12Yfk7xw8Bt7zc7JwiufHjGLATQ3/YhnsnEonQCR0yQ8tFI87yDweV5S87kQaVDEIsGvP8fYWCH9cgduQRrXEroudyO4eZCRxGnAsz0QU65UED5rmg2okuf5thpHc7d3SY8wWE2ZGUSdD2czSGHbHW74fc4cPF8tAhf74/G7qJ6Bo40W2OcXLO4sWLsW/fPqxatQo9PT249NJLsXz5cjz22GNZP7ds2TLccsstyf9XWCp/PB7H+eefj7q6Orz++uvYt28flixZguLiYvzwhz/066eESm2tGFVGASsc5LWCIno4yPJvbgZ6e+2PykwHz393+NGRx2OgP2zD1VBbXov9bfvpAg2JpBO9nU70MJDl39TZhN5EL4qi7htxCrjuUOpE72ScC8kD3Lhwgdxu57AmVQRyu8IHepxLmE50ax60DiKiX3EuxcVi4rbWVnE+9e2QkR0JsVg4E7xVVgpxX8fRGL295jp+iujbt2ef+NUvdBPRB6oTfcuWLVi5ciUeeOABzJkzB/PmzcPdd9+Nxx9/HHv37s362YqKCtTV1SX/VVkuxi+88ALee+89/M///A9mzZqFz33uc7j11ltxzz33oLu724+fEjqqBCzDoIDlBsa5hIv1PtVrBBhFdHcwzqXwYBuuDlUCVsJIoLVLZFJRRLTP0IqjTuhOOtHDYEi52Yg3dTZ5+i52IrmDcS6k4GCcixp0mlh02DCxDNOFm0950G7rQLYh+NbzPxJx9r0q0DnSSIo8gH9Cw4gRYkkRXQsnui8i+po1a1BTU4NTTz01+d78+fMRjUaxdu3arJ999NFHMWzYMJxwwgm4/vrr0W6pKGvWrMHMmTMxcuTI5HsLFixAS0sLNm/enPE7u7q60NLSkvIvX1AlYLW3m/FWFLDsQyd6uBQVqYsAo4juDsa5FB5sw9WhSsA60n0EBgwAFHGdIONElDjRuymiO6UoWpQsL691gHMCuKO2TL0TnceAaI0UvFTGuRiG3hOL+hnnooMTXd43Zpr01U90FRCzuXDd1oFs7sEwO5GA7HEu8bjptgtDRJcPuGVlZna7aiiim2jgRPclzqW+vh4j5IGWGyoqQm1tLerr6zN+7itf+QomTJiA0aNH45133sG//du/Ydu2bfj973+f/F7rwzeA5P+zfe9tt92G733ve25/TqioErBk3Y5G/Zk0eKBCJ3r41NaKslNVB1j+zuBomMKDbbg6VInoUrwqjhajrEgDJ1SeoHJiUTkSgCK6M2rLa9HS1eK9DtAF7QpV1yDDMDgag+QHXp3o6W5429pEZIN1vSCxK6Kr3DedMtHDFNF1mlQU8G9iUSC7Ez3MOCMgez65dbi6yv2zO7FoEA+4FNFN8s2Jft111/WbNKzvv61bt7remeXLl2PBggWYOXMmFi9ejEceeQRPPfUUtm/f7vo7AeD6669Hc3Nz8t/u3bs9fV+QqBKwrAJuGCNw8hVOLBo+qusABVxnqJrLp63NjBRkHQgHtuHBo0rASuZBl1UjwkbcNsk4F04sGhqqO5JY/s5QVf7tPe2IG2JIKzsyiNb4EeciH0JKSpx/rwpyieh+uITtunCtLhm/bvClgBimE12ly98LYce5hCWkZqsD8hhVVYlsd1U4daIHIaIfPOjfNjKhWx3INyf6d77zHXz961/Pus4xxxyDuro6HOjTS9Lb24uGhgbU1dXZ3t6cOXMAAB988AEmT56Muro6rFu3LmWd/Ucvptm+t7S0FKWlpba3qxOqnegUEJ3BOJfwYR0IF9XlH4uF8/xB2IaHgTIBsYsCohs4sWj4KO9IYpSII1Rfg2KRGCqLOaSVaIwfIrp0utbU6JkHbd0/VdgVELu6gJ4e8drvOJfGRqC727/IjHTkowvXbR3I9tCnS5xLNhFd9THK5n63EqSITie6Fk50RyL68OHDMXz48JzrzZ07F01NTdiwYQNmz54NAHjppZeQSCSSD9V22LhxIwBg1KhRye/9wQ9+gAMHDiSHmq9atQpVVVWYMWOGk5+SN9CFGy6yw62pScRtxWLuv0segzAmtM5nKKKHix/lTyNtOLAND56kgOVxYktmEbtDZqI3dzWjN9GLoqj7FEMpIg4uYSPuBNUiLuuAM/wYCcDRMERr3EZZZLvhlSK1jgJiR4cQsgG1+2d3YlHrPDXyM6qprRUP4fG4cOKOGePPdtKRjwKiWxFdPiSnm3sobBE9W6eOX5E7OjrRKaJr4UT3ZWLR6dOnY+HChVi2bBnWrVuH1157DStWrMDFF1+M0aNHAwD27NmDadOmJV1p27dvx6233ooNGzZg586deOaZZ7BkyRJ86lOfwoknnggAOPfcczFjxgx89atfxdtvv43nn38eN9xwAy6//PK8danlQrWARRe0M6zthNc4C3kMVJoECgGK6OHCa1DhwTZcHapduHRBO2NIudmIN3Z4a8SliFhTVuPpewoNVRNbJjuSGCXiCHkNauz0dv7zGkTyBr+d6GGQTcyT+xaNqhWx7Waiyxv8wYPFPvhBNBpepItumejyvPZDRJcPaTqK6GE60XUQ0aUJKgwRXbc6oIET3acrHfDoo49i2rRpOOecc3Deeedh3rx5uO+++5J/7+npwbZt29B+tCKUlJTgz3/+M84991xMmzYN3/nOd/ClL30Jf/zjH5OficViePbZZxGLxTB37lz80z/9E5YsWYJbbrnFr58ROhQQw6W42GxPvByDeNxsjyiiO4N1IFyyzbPkBI6GyS/YhqtBuQuXAqIjiqJFSeeyl8lFE0YiKSJSRHcGnejhwmsQKTik4DWQRPRsAqLc35oatSK2XQFRlo3fN/hhTS6qWx60n050iujpt6mDiC47kQ4dEsJSkNCJ3g/341pzUFtbi8ceeyzj3ydOnAjDMJL/HzduHF599dWc3zthwgQ899xzSvYxH/BjYlHijKFDRfl5yUW3tkUUEZ1BJ3S4WCcWTSTc35+zEyO/YBuuBuZBh8/QiqFo7mr2dAxaulpgQJzvFBGdQRE3XORojMaORiSMBKIRd404I6VI3uBVQGxr65/hqbOI7te+2XE8A8GJzGGL6LoIiHZEdLcdSdlE9LAf5LIJ2oXgRB82TCwNQ4hSUlT3G8PIzzrgM7450Yka6MINHxWTi8r7m/JyYICmFvgG5wUIF2k4SCTS31PZhdcgUoj4kUdMnKFictGmziYAQFlRGcqKylTsVsGgug5QxHXGkDLRiBswkmXoBk5uTPIGtyK6ddKqvhEmQbmtM2HHia7aIWzX7RmUiO40E7qnB/jnfwYWLgR27HC/XV0FxGzHxe28ALIOZBPRw440yuZEV30O6iSiFxWZv89uHejuBp591puIdeQI0NsrXutSBzRwolNE1xx5rra3A52d7r+HAqJ75PXKi4gbtoEhn2FHUriUlZltlZdjwJEApBCRAmJ7Tzs6e9034oyycI+cXNSLiCtFdEa5OIfzAoRLaVEpKouFEOB1NAbAkQAkD3AropeWCqEKAFpbU/8W9oNcmE709nbhRs1EUCKzUyf6r34F3Hcf8PzzwNKl7rerq4juZ5xL3/Mf0LsjSR4j1R1J2YR7K0FF3ciOpIMH7a1/+eXA5z8PjB0LrFnjbpuybEtLzXMvbOhEJ7moqjLjE7xMbEkByz0qnehhxYjlMxTRw0fFMWBHHilEqkqrkvEJXia2pIDlnqQT3UMmOkV09zDOJXxUHAOOBCB5g1sXbiRiOnHzSUT3S8CTQpVhCEdrJoKadNCpiG6NJHz5ZeDtt91tV/4+HTPR03VuGEbhxbn4JbTYdaIfOiSWMnLFL2Qd2Ls397rxOPDEE+J1ZyfwX//lbpvWTqRIxN13qIZOdJKLaFTNxH5hX/fyGTrRw4UievioOAYsf1KIRCPRZJyCJwGLUQqukU50FXEuFNGdwziX8FEiovMaRPIFtwIikFlEDzvKIkwneqbtSnR0ovf2Ahs2iNfTp4vlb3/rfJuJhL5OdADo6ur/9+5usd+A844knUX0bK5wv1zydicWDaqjZfx4sdy9O/e6772Xeh178kmgvj51HTsitG7nP2Av0shnKKLnASpdoHSiO0deD1U40SmiO6fvxJZuSCTMdoQirnNUiui8BpFCgy7QcBlawTiXMJHl39gpJrZ0Q2+iF2094iGWTnTnqBTReQ0i2uM2ygLQ14kuBcTOTuEwteKXE7242Iy30UFEHz1aLPfsyb3u9u1inysqgH/7N/He00+bf29qAr77XeDBB7O77FtbzYdPXYaTW0X0dHEW1mPlNH7DGudifei2TowVthM93bnoVyeX3cl1pRPdbxF93Dix3LUr97qvvSaW55wDnHGG6HD58Y/Nvz/2mLiunHKKWX7p0FFEt3tcfIQieh6gQsAKKqppIKIyzoUiunNUTGx55Ig54o0iunPoRCfEPSoELIq47mGcS7jIkRgJI+F6YksZZwRQxHWDimsQI6VI3uCniB62gAj0F478fMi0E5sQlMgmXbi7dmXPaAeADz4Qy2OPBb7wBSAWA95913x/xQrgtttEVvqyZZm/R/628nJ98qCLi8XvAdKLiNI1XVws/jnB6nSyTq6rw4O0ndEYfjnRczmepUjkd5yLEyf6m2+K5Sc+AVx/vXh9771ilMaOHcDixeK9t94C7r8/8/foKKLTiU7soELAoojrHsa5hIuKiS2lgFtcLObFIM6giE6Ie1QIWI2doid8SDl7wp2idGLR0hoFe1RYqJjYUorv5UXlKI45FAWI0o48xrkQ7RmITvSyMvN1X+HIT6ecnQn8ghLZxo4Vy7a23BPFbd8ulpMni3I5+2zx///9XyEaPvqoue4TT2T+fbrloQMilzqbiOh2TgBAPCRL4d3qXLM+SFvPxSDJlk/u10OmHRG9vV2MEAGCc6LbEdE//FAsjz0WOO88ce1qaQHWrgV+8YvUdVetyvw9OorodKITO9CJHi50ooeP1zpgbVt1mRMjn+A1iBD3KBHRj05KKl29xD50ooeP1zogXdAUcN2h8hokv4sQbRmIIno0mlk4lTfYYTnRg5pYtLwcGDFCvM4lIlpFdAC49FKx/MUvgG9/W7y+5BIREdPVBaxfn/57dBQQAWDQILFMJyh7Of+tk+umE9HDfJDOdC7G42Z99SvOJdv5L6NcSkrM4+IX1tEYudi5UywnTRLXj/nzxf/nzQN+9CPx+pprxHL1arMjoC861gE60YkdvApYhuHfpMWFAJ3o4eO1DrD8vUERnRD3eBWw4ol4Mo+YTnTnyExuTiwaHl7rAEdieCNZ/p0KRsOwI4/ojhQW3Thx04no1gfpMB8kMgl6fj7kO4lzCcKtbVdElLEtU6aI5YUXAnV1wL59wF//KtzUP/iByIMGgHfeSf89OgqIgCnWWiNXJF4m1gXSTy4adpwRkPlctO6n6v2TYm1XV+aJ2ayjFfzuYJBO9MbG9MdekkiYdWTCBLG85ZbUdWbOBP7jP8R+d3aKiUjToWMdoBOd2MGrgNXaas5BQgHLOZxYNHy8dmToeP3PJyiiE+IerwKiFNABirhuUBrnwvJ3hWcRnSMxPKF0NAw7MojOGIZ6J/qRI6aApqOIHqYTvbc3uDxowL6I3teJXlIC3HOPmCg1EgFuv104dGfOFH/ftCn99+j6AJlNRPcS5wKkF9H9mrjTCfJc7Ou+l/tWXi6Osx/bBDILtkFNKgqIYyM7CrKNxjh8GOjpEa/lhLzTpwNf+Yq5zt13C4f6sceK/+/Ykf67dKwDsnOju7v/RMsBQRE9D/AqYMm2tbRUnzkx8glZ/keOZJ/AOxsU0b2hqg5QwHWH1/KPx817MR4DUmh4dYFK8aqiuAIlMcUPCAWALP+2njZ09Xa5+g4polNAdIdXEVd+jlEi7vBa/gkjkYzUYUcG0ZrublPwViWiW/Ogw3yQDsOJnisT/cAB0XERjQLDh6vffl+kEzeXiP7xx2IpRXcA+Id/APbsEZ+94grx3tSpYilF977omIkO2BPR3TrR02WP6zCxldyvjo5UV7ifLnlrfc/UkRRkJxJgLxd9716xHDEidXLZRx8F1q0TUS9nnSXeO+YYsZQZ6n0JKq7JCdZzO6RIF4roeQAFxHCpqTFH5zBOJBy85tKzDnhDVZwOwGNACg+vAlZSwKV45YrqsmpEI+J21+sxoBPdHYxzCRfPo2E6m2HAAMBjQDTHKqioEtGtIl2YEyulEzfjcX9dwrmc6PX1YjlyJBCLqd9+X+w40dvazDKqq0v924gR5gSlgOlUzySi6+jCBfyNc9FVRLf+Hmt+t5/nfzRqTqSaqQ4cOCCWQYnoduqAFNGlC93KaaeZES9AbhFdxzpQVmZeiymik0wwDzpcolFT+HMr4vIYeIMdSeGiqvwrK1M7xAkpBCgghks0Ek12QLidXJQiujcY5xIuqq5BHA1DtEcKKkVF7m44s4noYT/EpRO0rZEbYYrofcVqv7AjIO7fL5bl5bknepQC4q5d6WMhdBQQgcJ0omdyhfud155rEss9e8RyzBh/tt8XO3Vg3z6xHDUq9/fZFdF1Go0RjZrnad9JoIPahVC2ShxBATF8vGZy63L/la+wDoSLtfwNw/nnWf6kkKGAGD5yclE60cPBc6QRJ7X0hCz/xo5GGC4acV6DSN7gVUDMNxFd3mCXl4vcVtXkinNxItapQAqIH32UeR2rOz7XyAG5Tjye3imnq4guz1M/MtHl56znmQ4ieixmusKDFPhzTWIZtIguXeTZ6kA2J3pfsonohqF/HaCITjJBATF8vMSJWPOgw77/yle81gH5OdYBd8jy7+lxN2qK1yBSyNCJHj7yGBxud96IW/OgKaK7g3UgXGT59yR60NbTlmPt/rD8Sd7gNcpCOnytIp18iJMTLoZFOhHdzzz0TNu0ErQTXQqI+/ZlnqhMOtFHjsz9fUVFZgyH/C1WdHThAv7GuaSbwNNvt7dd0p2Pfk96mqsOhCWi79yZeR0nIrrMWN+zp79TrqMD6Do6l5CuInq6OhAAFNHzAHnOtrSYE+06gQKWd2Tb6UZEt460C7vtyVdUdSTpdv3PFyoqzAnP3RwDXoNIITO0XDQgLV0t6Ik7b8TpAvWOPAZu4lxaulqSedDVpWzE3aBqYlHWAXeUF5UnY1jcdCTxGkTyBin8uXXhphPMpNNRijZhkc2JHpaAGLQTfcQI4UZOJMzJQ/viREQHzA6AdCK6jpMqAoUZ5wJk70jy24mui4g+caJYqnKiy3rS0ZF6zAHzob+oKHc0UtDI/aETnWTC2i5aJ+izCwUs73iJc5HHzCpEEmdwNEa4RCLmMTh0yPnnWf6kkLG6l2UsiBMYJeIdL3EusvzLi8pRWuTDcPkCQFWkkfwe4oxIJOKpI4lOdJI3eI2ySOfClUJl2CISnejigSSXE1eliK5rlIUdEX2gxbkA6etnmE50wzBFdDuCtQrk+f/xx0Bvb/p15GSndupAZaX5Gw8eTP2b9fwPc1LldDDOheSiqMi8ZrlxQvvdSV0IeIlz0SVKL5+hiB4+w4eLZd/21Q4sf1LIxKKxpAB+qN15LxTzoL1TW+Y+zoWdGN5hnEv4DK8UjfjBNueNOJ3oJG/w6kRPJyDq7ET3W9zMlYkuc5RlVnkQ5HLiqhLRdc6DDjrORRcRPV39DGpi0XR1oKXF3JegnOh1dcKVGY+bAn5fnMYQyYd8Kb73/R7dzn+AcS7EHl4ELL87qQsBL3EuFNG9w4ktw4ciOiHuGVYhMjcPtrsQsCggekY60d24cCmie8cqonNiy3AYXnFURPdyDWL5B8o999yDiRMnoqysDHPmzMG6deuyrv/kk09i2rRpKCsrw8yZM/Hcc8+l/N0wDNx4440YNWoUysvLMX/+fLz//vsp6zQ0NGDx4sWoqqpCTU0Nli5diiMWkeKVV17BBRdcgFGjRqGyshKzZs3Co48+qu5He0WVgGgV6XRxoqcTEP3Oa8/mwk0kgG3bxOtp0/zZfjqkiJ7Jie7EhWtdr6+I3toqhEpAPxEx6DgX2ZGk47wAYTrRd+82t+22vJ0SjZqdVpnqgNMYohEjxDKfRHTGuRA7yDkvKGCFg5fyp4juHXnt7u11fq00DNYBFcg64CbOhR15pNCRApYrJzoFRM946cSgiO4dGSXSm+hFa7ezRjxhJNiRpABZBzxdg1j+gfHEE0/g6quvxk033YQ333wTJ510EhYsWIADfUWOo7z++uu45JJLsHTpUrz11ltYtGgRFi1ahHfffTe5zu23346f/exnuPfee7F27VpUVlZiwYIF6OzsTK6zePFibN68GatWrcKzzz6L1atXY/ny5SnbOfHEE/G73/0O77zzDi699FIsWbIEzz77rH+F4QRVmejpBERdnOhBTnqaTUDcs0e8X1wMTJrkz/bTkUtEd+rClU506WCXSCGyrMx0I+tCECK6jh1JumWib90qllOn+rPtTMhIl3SjMRIJ5+J3PorodKITO0gXKPOIw0HFSACK6O4pLxf3MIDzOtDebk7gzjrgHjrRCXGPpygFCoieSbpwXZQ/RXTvlBeXo7xIiBBORdzWrlYkjAQAdiR5wUsdoBM9eO666y4sW7YMl156KWbMmIF7770XFRUVePDBB9Ou/9Of/hQLFy7ENddcg+nTp+PWW2/FKaecgp///OcAhAv9Jz/5CW644QZccMEFOPHEE/HII49g7969ePrppwEAW7ZswcqVK/HAAw9gzpw5mDdvHu6++248/vjj2Ht0orrvfve7uPXWW3HGGWdg8uTJuPLKK7Fw4UL8/ve/D6RccqIqD7qzU4hRgN4CYlAierooCykgTp4shPSgyJWJLoU/uw8dUkSXk6RK5AO8jgKin5no+TYvQJhO9C1bxHL6dH+2nYlsHUktLea1qxBEdDrRSTYoYIWLivKniO6eSMS8vjs9BrL8dZxYOp/gNYgQ93iKUjjqAqWI655kJwbLPzRGVIpG/EBbeidtJqSAWxorRXmxZm7APMJTHWBHXqB0d3djw4YNmD9/fvK9aDSK+fPnY82aNWk/s2bNmpT1AWDBggXJ9Xfs2IH6+vqUdaqrqzFnzpzkOmvWrEFNTQ1OPfXU5Drz589HNBrF2rVrM+5vc3MzanURWVQ50QFTOJYCoi5O9CBFdOnAzubCDTLKBcjtRJcPHXbPSelY7zvxls4uOD8z0dPFueSDiB5GJnpYIno2J7o8jysqTAdiLvJRRGecC7EDRdxw8VL+cjSY3VFlJD1uj4FVwNVtYul8wkucC0V0UuiocELTBeoeKeC6KX+Zoy5zvYk73I7GkJ0YLH9vKIlz4TUoEA4dOoR4PI6RfTKdR44cifq+uc1Hqa+vz7q+XOZaZ4QUU45SVFSE2trajNv9zW9+gzfeeAOXXnppxt/T1dWFlpaWlH++4VVAtMZ2yO+SIo2OAmKYcS5h5KEDpoi+Z4/I+eyLUye6FAjlw4okX0V01XEu8bj5Wsc6EGacS9gierqOJKdxRkB+iuiMcyF2cCsgGgbziFUgry1NTUBPj7PPOp3bgaRHhYhO3EMnOiHucesCNQzDFNHpAnWN7MRo7mpGd7zb0WcbOsRDhMz1Ju5wOxqDLmg1KJlYlMeAWHj55Zdx6aWX4v7778fxxx+fcb3bbrsN1dXVyX/jxo3zb6e8RllEo/3d1zq7cMMU0cNyoo8cCZSWCnH3449T/9bTYx4vuw/e8uFkoDjRVce5WI+9jnUgrDgX68S6YcW5pHOiuxGepOAuPyvJBxGdTnSSDbcCVkcH86BVUFsr7qsA505cNx2CpD+ZOklzQQFXDRTRCXGPWwGrtbsVcSMOgC5QLwwpH4JYJAbAuRNXOtGHVrAR94LrOBe6oJXgaV4GHoNAGTZsGGKxGPb3mehw//79qJP5zX2oq6vLur5c5lqn78Slvb29aGho6LfdV199FZ///Ofx4x//GEuWLMn6e66//no0Nzcn/+3evTvr+p7wGucC9BfNdJtYNIw4l2yZ6Mcd58+2MxGNAuPHi9d9nbhWN7ldUVU+nBw5kuqU89vh7AWriG4YqX9THecihXprB1NY9K0DnZ1AV5d4HbQT/aOPRL0oKQl2Yl3AdKLv2mXmn0vcCN+yrsgOCYnOTlDGuRA7eHXhxmLhdx7mM9GoKYI7PQaMc1GD2zrgdFQfSY+Mc3Fa/omE2SbzGJBCxWuUBfOgvRGNRJMiuNNjcLidcS4qcBtpRBe0GmSci9OOvISR4GiYgCkpKcHs2bPx4osvJt9LJBJ48cUXMXfu3LSfmTt3bsr6ALBq1ark+pMmTUJdXV3KOi0tLVi7dm1ynblz56KpqQkbNmxIrvPSSy8hkUhgzpw5yfdeeeUVnH/++fjP//xPLF++POfvKS0tRVVVVco/3/AqIFo/21dEDPtBWicnemuriFMBghfRgcy56FL4qK4W4ocdrGK7FM6tr3V2ovf2mm5Jieo4F+v5H3Yuat/zUT5gRiL+dXJlmhdARrlMnSomXguSMWPE+d3T039CXDfCk+yA6Cui54MTnXEuJBvMgw4ft8dA5068fIJxLuEiy7+hQYygtEtzs2mS4DEghYrXKAtOaukdt8eAcS5qcBtpJMufLmhvyPO/saMRvYk0OcIZaOlqgQHRiPMYBMfVV1+N+++/Hw8//DC2bNmCyy67DG1tbcns8SVLluD6669Prn/llVdi5cqVuPPOO7F161bcfPPNWL9+PVasWAEAiEQiuOqqq/D9738fzzzzDDZt2oQlS5Zg9OjRWLRoEQBg+vTpWLhwIZYtW4Z169bhtddew4oVK3DxxRdj9OjRAESEy/nnn49vf/vb+NKXvoT6+nrU19ejoW8URlh4jbKwfraviBi2Ez3dhI9hieh//7tYjhwZzs291YlrxY3oV1Rklp/Vya6ziG49v/uKiF5FdGsnkmHo04kE9D8f5TGqqjIjA/zaZt/RGGHloQPinB07Vrzu25Hkpg7ks4hOJzrJhlVA7DtqJxucVFQdXp3QdKJ7w6uIruP1P5+Q569h9I8NzIYs/4oKMeKNkELE6kQ3HDTiyRgFOkA943Y0ACcWVUNyclenHUmMElGCHIlhwEh2TNhBln95UTlKi0p92TfSn4suugh33HEHbrzxRsyaNQsbN27EypUrkxOD7tq1C/ssDsQzzjgDjz32GO677z6cdNJJ+O1vf4unn34aJ5xwQnKda6+9FldccQWWL1+O0047DUeOHMHKlStRVlaWXOfRRx/FtGnTcM455+C8887DvHnzcN999yX//vDDD6O9vR233XYbRo0alfz3D//wDwGUig1Ux7kYBicW7btNILwoF8mYMWK5d2/q+26dU+ly0f3O2vZCLGY6pK0iumF470iSn4vHhctdJxG9bweXPP/9jNzJVAfCFNEBsyOpby66m/M2H0X0kONcAh57QNwiBcTubnGu2G0rKSCqg070cGEmergUF4sybGwUdUDWh1yw/AkxXaA9iR60dLWguszeDb8UuyjgesetE13GuTAT3Ruy/B1noh8djcE64I2iaBFqy2vR0NGAg20Hk50auWCcTnisWLEi6STvyyuvvNLvvQsvvBAXXnhhxu+LRCK45ZZbcMstt2Rcp7a2Fo899ljGvz/00EN46KGHMv49dFSK6G1tIm9ZDr8M24neV8yzCvx+Z6L39oroiOJi8f+wJhWVHB0Z0U9Edyv61dYKMTJfnOiAEBE7OlJF9M5O023pNc4FEOeaTiJ63zoQxCiRTCL6e++JZVgiupygue/kum461uQ53tZm1vPubvM361gHGOdC7FBRYdZhJyKunART5hkT97gR0Ts7zesPnejeYJxL+LjJRWf5EwKUF5ejslg8mDgRceUkmFKAJO5xk8nd1duFth4hyjDOxRuu5wWgiKsMN7noHAlA8gqvURZAqtvV6nL0IsyroK9DvrNTiNuA/050IDXOQhcRXeayS7w60fNNRAdSRUSr0Ou2DhQXmxnfbW16iuhBzleQTkQ3jPCd6KNGiWXfTHQ3Irp1Xfl567XPz3ks3GKNc3ES06EIiuh5hBsRkSK6OmT5O3FCyw7xWEzPyb3zCU4sGj7yGMjrih3kunad64QMVNyIiFJEl+IXcY8sfydOaDkSIBqJ2h49QNJjjXNxFWlEEdczsiNJXlfsIOOMeA0ieYHqOBcp0pWX25+o0i+somhnpyl2RSL+CfylpeakalYRcds2sQxLRM8U5+I2gmWgiOjy/C8t9Xa+WvP3dRTR5bkYRNSSHI1h7UQ6cECcH5GImFg0DDKJ6LIOOBGeiorMYy4/L68v5eXmCBSdsE6u29UV+OYpoucRXgQsiujecSPiyigXTuzqHRnn0tGROqdOLtxMUk3Sw448QtzjJk6EIro63JS/dVLLaIS3zF6Q5d/Z24kj3faH37IOqMNNR55cl+VP8gLVcS66TCoKmGIeIEREKXINHuzfpIqRSP+JFeNxc2LRsDLRpRN9/37TjQ+4z4iX8S/WTHTdRXR5TlpzrFWMxABSR2PoLKKH5UTfvl0sx41LrZdBotKJDvTPRfd7vgWvWI95CJEufCLIIyhghYub8uekouqorATk3EdORgPQCa0ON3EuvAYRInAjYNEFqo5k+TsQ0WX5Mw/dO5UllSgvEg+bTo6BXJd1wDvDyp3HuTBSiuQVfsW56CAgFhUBJSXidVtbcCKXFAll2e7dK5yfRUXm5IZBM3y4cFobBlBfb77vtkykUC6Fc+trXUV06Z637rMqET1dR5IOdUA3EX3yZP+2mwu/RHR5Pukuosdi5rEJYXJRiuh5BAWscPHiROekot6JRNwdA7ku64B3WP6EuIdO9HBxk4kuJxXlpJZqcNqRZBhGcl35WeIeRkqRAY9fcS46ONGBVIE/KJGrr4i4c6dYjh8fXsRNNGqKiNZIF7dlIteXYlwiYX6XriJ6OuFfnv+qnOj5IqIHPbHoQBTR5fmUL050IH2kUUBQRM8j6EQPFy8iOp3oanB6DDo7zesqnejeYaQUIe5xI+JKAYuTWnrHjRNdxrmw/NUgc9Ht5tK39bShKy6yLinieieZid5hvxGX67L8ifZ0d5vRHqpEdJ2c6EDqvlnjXILaJgDs2CGWkyb5u91c1NWJ5f795nteRXT5+ZYWc7JCXSc1k6KnNcddHiOvGfn5EucSdCa6PCekiH7MMf5tNxdSRD9yJFVELpQ4F6B/vQ0Qiuh5BEX0cJHl39Ag4uDswDgXtchcdLtxLvL8LyrS9x4on5Dlb71fzQWvQYQIpIjrSMCiC1QZUkBs6GhAb6I3x9oCGedCJ7oanI7GkB1OZUVlqCz2aeK8AkJ2Yuw/Yr8R5zWI5A3WCZO8iIjpXLi6ONHTiehBOdFlJrp0ok+c6O92c5HuoVCViC6FxLIyMUmnjhR6nIthBBvnAgh3HqCHE33wYHPfpBvdMApLRE/XkRQQFNHzCApY4SKFcMMwHea5YJyLWpx2JFnPf07s6h1p+rDGD+aCmfSECChghYs111zGtORCrkcnuhqcxolY87gjbMQ9UzdINOL1R+w34pxYlOQNUkAsKgKKi91/T7450YPORC8EEV33PHQgvYBYKHEuiYQYeRLEvvWd0BcAPvpILMMcjRGJACNHitdSGGlrM93yAz0THTA7kiiik2zIURt2BazeXvOcoojuneJiUwx36oSmE10NTkV05nGrxYuIzmNACh0pYO07si/HmoKu3i60dosHeApY3imKFiXFcLtxIpxYVC0jKoToYduJzklFlTJqsHiQcCKisyOP5A0q8tCB9JnoOgiIQLhO9L5xLhTRw8VPJ7ruIjoQ3JwF1gl929tFHIF8EB4zxr/t2qGvMCLP31gsVfy3Qz5molNEJ3aQAlbf+QMyIc+nSMQ8x4g3nIqIsl2XHYXEG27jXOiCVoPsyGtoALq6cq9vGOzIIEQyapAzAUsKuLFIDNVlzKNSgVMnrhTb5SgC4o3kaIw2e6Mxkk50TiqqBHn+N3Y2orO3M+f6hmHwGJD8QZWIbhUQ5XfqICAC6V3yQWWiyziXPXvEctw4f7ebC5UiuizDfBLR0znRVZ0T1hxwnUT04mIhagPBdnJZy+PgQeGEj0TMczAs+oroUgCvqnI+BD8f41yku1XmJwcIRfQ8QgpYBw/ay+SWAuKQIeb1hnjD6WgA2a6HfY0dKDjtSKKAq5baWnOErJ1YqdZWoKdHvOZoDFLoSBfowbaDtjK5k5OKVgxFNMLbNRU4deJKEX1kJXvCVeC0E4NRImoZUjYEJTHhqLMTK8WJXUleoToPur1d3XeqIp1L3m8RvW+ci3wACNsh1ldE95IHLdeXInQ+iOjpnOiqRHRrx4lOIjoQTtySdZtShBgxInyBLZMT3c1EcPkootOJTuwwfDgQjYrOLztOXMYoqMepiEsRXS1OOzHoRFdLJOJsNIYs/4oKfZ4/CAmLYRXDEIvEYMCwJWAxRkE9TiN1pGOaTnQ1yE6Mfa32yt+aiU68E4lEHHVkyE6M8qJyVBSzESea40ecSz6I6F5/r5Ntdnaa4lrYIrrcvnzY7uoynTte4lwMIz9E9HROdFWCt65OdMA834N0oqcT0aUoESZS5OsrorsRvpmJ7giK6HlELGa2F3ZEXIro6nEiIBoG41xUQyd6+LgR0Vn+hADRSBQjB4nGwI6ISxFdPXWVjHMJE6edGMxEV4+TY8BrEMkr/Ihz0VlEDypqxrpN+WBbXBy+wNzXiS5FP8B5mUihsLdXdBTkk4juhxPdOvpANxE9jNEYuoromZzoXkT0fHSiM86F5MKJiEgBSz1OnNBtbWZ8HJ3oapDlf+iQmJQ7F3Siq0ceAyfXIJY/IQInuejJOJdyZiGpIumEtiEgtnW3ob1HCCgU0dUgz/+GjgZ09eaeWINOdPW4uQZRRCd5gSqxTwpmOoroYUz4aI32kFEuI0Y4z1xWjVVATCRM0W/wYDF03wmVlebvaWnJDxFdCogdHeZEVX5movs94sEuYUz8Wwgiej5OLCoz0QeSE72hoQGLFy9GVVUVampqsHTpUhyRJ3oadu7ciUgkkvbfk08+mVwv3d8ff/xxv36GdjgRcWXHLEV0dTjpxJD3GRUV+rQ7+c7QoWb8mJ1II9mmUMRVhxMnOkcC5C9sw/3BSZyFjHxhHrc6nERZSBd6WVEZBpVo4sDKc2rLa1EcFRNr2JlclE509TipAxTRSV6hSvSxCohSRNflQS4MAdHqStYlDx0wJ1uKx8Wx93L8o9HUyUWlkOgmWzoorJNHStFfdUeSznWgrS24THTrNWGgiujy/Jdlmg8i+kCMc1m8eDE2b96MVatW4dlnn8Xq1auxfPnyjOuPGzcO+/btS/n3ve99D4MGDcLnPve5lHV//etfp6y3aNEiv36GdjhxgUqRS4c6PlBwIiAyD1090SgjjcLGSUcSO/LyF7bh/iBdoHac0FLkkqIX8Y4TF651UtFI2I67AYI1k9tOR1LSiV7JnnBVOCl/WQdY/iQv8MOFKyNTdHGih52JrlNOaVmZeawaG72LflYRXYrSOovo0Wj/HGvVdaClRUTcAPrVgaYmc1h6GJFGOtQBKaJLwcNLHZBlSBHdFr5MKbtlyxasXLkSb7zxBk499VQAwN13343zzjsPd9xxB0aPHt3vM7FYDHV1qQ+KTz31FL785S9jUJ+KUVNT02/dQsGJgCXXKdCi8gUnnRgU0f1h1Chgzx5nx4BOdHU4GQ3Djrz8hG24fzgRsOrbKKKrxo2AyCgXtYwaPAq7W3bb6kiSozEY56KOZEdSW+5GXB4j+RlCtEaVgCgFs85OvUX0MDLRdXKiA0JE6+gQmcheRb+qKvGAaXW16yyiAyKCo6nJFBFVi+hSnAX0qwPSfQ0EWwdkWQ/VIGpRpYguz5m2ttR4pHwQ0RsaxGSEARpefHGir1mzBjU1NcmHbwCYP38+otEo1q5da+s7NmzYgI0bN2Lp0qX9/nb55Zdj2LBhOP300/Hggw/CMAxl+647bgSsAtUqfEGWZVOTuLfKBkV0f7BbB3p6zPaVIq46nIzG0GnEG7EP23D/cONElxEwxDtSRG/uakZHT0fWdWXcCEV0tdiNE+no6UBzlxhSzzqgDidxLhwNQ/IK1QIiYE5Yp5uAGEYedEeHfg+31kxkFSI6kCqi+z1hpVekiOhXnMvhw2IZjQIlJd6+UxVy3+S5WFoqJroNYpvt7eY1QZZ9mMh9aG8XrnwZQ+RFRDcMcR7Jc0lnEV3W/+5ucyLCgPDFiV5fX48RfS6uRUVFqK2tRb0d5QXAr371K0yfPh1nnHFGyvu33HILPvOZz6CiogIvvPAC/uVf/gVHjhzBt7/97Yzf1dXVhS454QKAFuvszXmGmzgXiujqGDJEtCHd3aIzfsKEzOvqNNpnIGF3NIY0SxQV6dFZPFDgNWjgwzbcP6QYSAErHGrKalAaK0VXvAv72/ZjYs3EjOvSie4PyY6kHKMBZEdTWVEZqks1dwPmEU7mZaATneQVqoRPq4guHZ6FLKJbM9GlgKjLg5XViapKRG9tVdch4zdyMki/nOhSRK+oCH8iWYmsA/JB3+/zH0iNeJJlLQXcMLGe6147ksrLRWdJIgHs3Zt+G7oxaBAQi4l5ERobA71OO3KiX3fddRknDpP/tm7d6nmnOjo68Nhjj6V1sP37v/87zjzzTJx88sn4t3/7N1x77bX40Y9+lPX7brvtNlRXVyf/jRs3zvM+hgUFrHCJROyLuLp11g8U7NYBef2vq3M+STvJjNWJnstATCe6XrANDx+7TnTDMCii+4CTTG6K6P5gtw7I4zNq0Chm0ivE6kTPNQqI1yCSV0gB0avoU1Qk/gGmKKWbiN7WZsa5BJmJLgVEHVy4gH9O9HwT0f3MRAf0Of+B/k70IET0dE50HUT0WCw1F99LHYhEzLLcs0csi4uF019XIpHQctEdSUvf+c53sGXLlqz/jjnmGNTV1eGAPLGP0tvbi4aGBls5qL/97W/R3t6OJUuW5Fx3zpw5+Pjjj1Ncan25/vrr0dzcnPy3e/fu3D9WU6wCbrZ73yNHzLaVIrpapCBo7aRLh+wgpYiuFrtxIhRw/UGOrOjuNu/ZMsFjoBdsw8PHroDV2NmI7riYMGlkJYczqUQ6cfe2Zm/EKaL7Q7ITI5eILl3QjHJRirye9CR60NiZ/aEz2ZHBY0DyAZXCZ1/R0G+h2i7WSRXlhI9BxrnIG38p3oaNH070fBLRpZB7+LAZwwGoi3PJ9P8wCVNEt0b96NKRZBWRvWb5y/NdilxVVfqMQMiE9RoQII7iXIYPH47hNmbomzt3LpqamrBhwwbMnj0bAPDSSy8hkUhgzpw5OT//q1/9Cl/4whdsbWvjxo0YMmQISrP0kpSWlmb9ez4hxaiuLhF7lKkNkwJjZWUw15ZCYuxYYO1a4OOPs69HEd0f5JyGuToxKOD6Q1mZaK8aG0UZZ7qH6Ogwo9nYkacHbMPDRwqI3fFuNHQ0YGhF+iHR0gE6pGwISosGxm/XhbFVYwEAH7dkb8SZie4PoweLRjxXJ4bViU7UUVpUitryWjR0NGBf6z7Ulqd303X2diZFdh4DkheozLEuLze/D9BHROwrIAL+C/zWOJd4XLzWRUC0OtHb28VrryJ6c3N+5EEDwLBhYnnokPj90pyhMtII0Of8B/rXgSA6OuQ2reKDTh1JO3eqGY0hy1I60XU//4HUa0CA+BJyMH36dCxcuBDLli3DunXr8Nprr2HFihW4+OKLMfqoArZnzx5MmzYN69atS/nsBx98gNWrV+Ob3/xmv+/94x//iAceeADvvvsuPvjgA/ziF7/AD3/4Q1xxxRV+/AwtKSsz62y2OAtGufiHTBLIZYaU158xY/zdn0LDbvlTRPcPO6Mx5DWorEz/ye1JKmzD/UMKWED2XHTGKPjHuCrRiOxuyd6I7GkRjfiYwWzEVTKu+mj5N2cvfymyU8BVjyzTPa17Mq6z/4joRCqNlaKmrCaI3SLEGyrdw7qKiFIwlwJiWZkZPeMX6eJcdBIQAbUCYn29yIW2vqcr0qxy6JB5/kci3s/Xvud/3/+HSZiZ6FZx2e96Zxc/6oD8nfnwAB+SE923pOBHH30U06ZNwznnnIPzzjsP8+bNw3333Zf8e09PD7Zt24Z22Wt4lAcffBBjx47Fueee2+87i4uLcc8992Du3LmYNWsWfvnLX+Kuu+7CTTfd5NfP0BLpxN2T+d43KSBSRFePHRHXMCii+4Us//p6MSIjExTR/WP8eLHctSvzOtZrkO4jwUh/2Ib7hxRlszmhKaL7hx0R3TCM5PGRznWihvHVogE52H4QHT0dGddjnIt/yGOQrSNDln/doDpm0pP8wM84F11EdLkf0hEeRMyMVUSXcS66OdFVxrnIoebRqD7HPRNWJ7p0z1dWep8MTNfzHzD3pVtEHgYa5yLPDR3y0CXWyWW91gFZltY4F92RdUBOghsQvnWh1NbW4rHHHsv494kTJ6bNA/3hD3+IH/7wh2k/s3DhQixcuFDZPuYr48cD770HfPRR5nWkC5QConrsiOhNTeaoMoroahk2TBgvOjtFWzZ5cvr1KKL7hx0Rndeg/IZtuH+Mrx6PTQc24aPmzI04RXT/sOOEbulqQVuPmFhmTBUbcZUMKRuCyuJKtPW04eOWj3Hs0GPTrpcU0elEV44U0Xc1Z27EmYdO8g5VE4sCqc7boiIxwZ4O9BUzg86DluK9jk50iVcRXbrgBg3S3wVkFdELYSQG0L/jKMg6IB9udRLR/XSi55OIfuhQoJv1zYlO/GPCBLG0I2DRia4eOyK67KgcOlSvEVADgUjEFHGzHQOK6P7hxInO8icklQnVohG3I2BRRFePHSe6dKEPKRuCimKNHh4HAJFIhCJuyCTLvyVz+bMjj+QVhqE+E12ik4AYhoguy0IK6IA+IrofTnTpwtU9ygUoTBE9zI4kiS4jMQBzX/buNesoRXTfoYieh0gRPZsTXV7/KaKrR4ro1mtVX+S1ZyxHgfsCRdxwceJE5zWIkFSkgJXNib73CPOg/UI60fe27kVvojftOoxy8Rd5DLKK6HSi+0byGtSU+RrE8id5wcMPAzfdBGzZojbH2ioiBhGZYhcdBMSqKiAW83+7dlDpwrVOLArkn4gu41xUnBMlJamRMDqL6EEcp76dCjqK6Dt3imUk4v6aRRHdNpok4hMnSAErm4guHbpyXaKOujoxsq+3Vwi16YRy6URnlIs/5BoNEI+b841QRFePnWuQbH/lHA6EEMGEGtETnk3AkuKiFLuIOuoG1aE4WoyeRA/2te5LCrpW5ISLFNH9YXzV0UzuDKMBuuPdONQuHojoRFePndEwnNiV5AU/+QmwcSMwaZL5ngrR2yrU6SwgBiHw9xUQdXGhA6lOdFkWXkV0ST6J6G1twMGD4rWK/Y5ExHFvE7F2WteBsDqSdEHWR/lQXlXlPoZIlqWM69Tpd2aCTnRiFztxLvJv4/o/GxKPxGKmMJhJxJUiOp3o/pDLCb1/vxDSo1FgxIjg9qtQsMbpSONPX+SxYUceIalIASubE50iun9EI9FkznkmEZdOdH/JFeeyp0V0YpTESjCsYlhg+1UoJCcWbdmNhJG+EZfXJ16DiNYMHy6WO3aI5aBB3idVBPSNcykuTnWBByEgRqNiMiqJji7cI0fMiQULSUSvqjLz+mUdULXfutYBiuipyDogH7y97Fvfc0en35mJ444DvvEN4ItfDHSzFNHzECmiZxKwDINOdL/JlcnNOBd/yVX+sjN2zBh95gIaSIwdKzq5u7pM40Nf5DHgNYiQVKQTfU/LnrRxIvFEPCkiUsDyh2QueobJRaWIPmYwh5P5QS4RXQq4E6onIBrho4pqRg8ejWgkiu54Nw60HUi7jjw28npFiJZIF+KHH4qlKtFHVwExEkndnyAERCC1PHRyolv3pffo/VQhieiRiFkHrB1JKsiX0RgU0cVSxvlUV7v/rnwU0U84AfjVr4DvfCfQzfLONA8ZNUp0Qvf0mLnPVg4dAjo7xXWVcSL+IB3+mZzQdKL7S67ylwLuxImB7E7BUVxsjsZIdwwSCbODYwKfvwlJQcaJxI14MjLByr4j+xA34iiKFnFSP5+QES6ZRgPQie4vVid0OmTUEQVcfyiOFWP0YNGIp4uVMgyDo2FIftBXQBzoLlwgHBHduk2dhLVYrL9o6PYcyEcRHSi8OhBGJnoY27RL35EhXupn3+uJTnVdMyii5yFFRaY4m07Aku/V1QGlpcHtVyExebJYfvBB+r8zE91fpDC7c6cZ22VFiugUcP0jWy76gQPCpc6OPEL6E41ETRE3jYAlxauxVWMRi2oyedcAY/IQ0Yh/0JC+EWcmur9IcXxn0860cSJWJzrxh2wTHB9sP4jO3k5EEGEdIHrT14muStzS1YULpOagBzXpqbUMdBIQgVQ3enm5+yHI+ejCBfxzoltF9L65+GEShhO97+/X6dxQKaLnax0IAYroeYpVROwL89D959hjxfLvf+//N8MwhUUeA3+YOFGYD9ra0o/GoIjuP9Llv317/7/Ja9Do0YzTISQd2XLRpYguI0eIeo6tFY34+w3v9/ubYRjJzg0KiP4wvno8iqPF6OztTLr+rSSd6BTRfWNizUQAwIeNH/b7m7wGjRo8CiWxkiB3ixBnyEx0+TAw0F24QPhOdN1EdKvQ50X0KylJdR/q9jszIUV06eBTFbejax1gnEsqfY83RfRAoIiepxxzjFimE7BkZzyjLPxDiujv93/+xqFDQGurcOFaJ4sn6igpMcs2XUcGRXT/Oe44sdy2rf/fmIdOSHam1E4BALx/uH8jsr1BNOzHDDkm0H0qJKYOnQogffk3dDSguasZAI+BXxRFi5J1YNuh/o2I7FySQi9Rz3FDRSO+7XCa8m/ipKIkTxjWZ+JhP0T0oNzedgk7E103cdka5+JV9LN+XrffmYm+dcBLJrYVXUdj6CCi63Ru0IkeChTR85RsApaMGJFCL1HPVPH8jY8/BtrbU/8my3/s2NTJzIlastUBOaKNHUn+YecaNGVKcPtDSD4hRdy/N/TvBZTuaCkyEvUcO1TcIO1p3YO27raUv8mIlzGDx6C8WKMhzAOMZB043L8OSHc0RXT/mDZsGoD0nRiyDsjYI0K0pa+AONAnFgXCd6IHtU27UERP/f9Ad6L3FVeCOE7FxSJPWaKTuFxcrG7OAmai24Yiep4iRdx0LlzpjqaI7h9Dh5odf31z0SkgBkOmOtDba47QYB3wj2ni+TutiC6PCcufkPQkXaBpBCwposvIEaKe2vJaDC0fCqB/Lrr8Pzsx/CWTE7qztxM7m3YCMIV2oh5Z/lsPbYXRZ3IZ2bHB8ifa45eIrqsLF0jdH2aiU0QvNBE9Egl/NIZu4rL1mNOJHggU0fMUq4DYd2JFKaJTxPUXeQz6RrpIAZfl7y+y/PuKuDt3At3doqOacSL+IQXyw4dFhJEVKaJP5fM3IWmxunD7ClhSxJVuaeIPsnz7OqEpogeDrAN9RfQPGj6AAQPVpdUYUTkijF0rCOT539jZiEPtqY24HCHDjjyiPX0FxL7RBm7RVUAEwhcQdROXVWWi9/28br8zE36J6PnSkcR5AdR1JFFEtw1F9DxlyhTREdfUBBw8aL7f2Qns3i1e0wXqL5kmF5Wi+mSOgvUVGSfSt/ylqH7ssUCUVzjfqKw0Oyn6dmTIOkARnZD0HDPkGMQiMbT1tGFP657k+y1dLTjQdgAARVy/yTS56AeNFNGD4LhhohHv24khR2ccN+w4RCKRwPerUKgorkhO3Nq3I4NOdJI3FJoLF6CA2JdCd6LLyXUlhVAHrCMwghqNUWKZZFs3cdkvEV23464RlJjylLIyc3LRTZvM999/XzjTq6v7X1OJWqRAuHVr6vvvviuW06cHuz+Fhiz/Dz8UznOJFHSlyE78I10uemOj2bHHjjxC0lMcK04KVO/sfyf5/nsH3wMA1A2qQ1WpZjfpAwxZ/lsObUl5/90DohGXmdHEH2T5f9T0ETp6OpLvS0FXxo0Q/5AdGVsPmTeyzZ3NyY48joYh2lNcnCogqXKihxGZYheK6KkUuoheyB1JpaXiGhAE8bj5Wrdzw3rMvUws2/c408iQEYroeczJJ4vlW2+Z723cKJYnnsjz3m9OPFEsreXf3Q1sOfo8ftJJwe9TITF6tLjXicdTOzJk+VNE9x9Zxu+9Z74nO/XGjdNv7iFCdOLkUaIRf2uf2YhsrN8IAJhVNyuEPSosThopGmlZ5gDQE+9JdmTIvxN/GF4xHMMqhsGAgU0HTDeI7MSYPoxOBL+ZNlR0FG05aHYkyU69MYPHsCOP5AdWEdEPAVE3wYyZ6KlQRE/9vxcR1Uo+xLkEeYx6e83XpaXBbdcOquoAxUPbUETPY2bNEst0Irr8G/GP2bPF8r33gI6jJqpt24CeHnH9Yh63v0Qi5jF44w3z/Q0bxPKUU4Lfp0JDduStX2++9+abYimPDSEkPSfXHRXR69OI6CNnhbBHhcXs0eIi9d7B99De0w5AxFh0x7sxuGQwJtRMCHP3BjyRSASnjj4VAPDGHrMRX79XNCjy+BD/kB15b+w1y//NfaIRZ/mTvMEqIvqRia6bmGoVzulE9y8TXbfIjkwMHZr6f1X7bT3OuoroQbq1rCK6bqjsSCK2oIiex2RzolNE958xY4ARI4QT+p2jo/HfflssORIgGE4Vz99JEbez03RCy78R/5gzRyzXrzdHubETgxB7SBFdilYAnehBMmrQKIysHImEkUi6b9/eLxrxmSNnIhrhLbLfnDb6NADA+n2iEW/qbEpm1M8eRRHXb04fczoAYMO+DehNCIHgzXpxPTqljo04yROs+aV+ONF1E6Ws+xaUiGgVanUT0VUKiNbfptvvzERfgVvVhGAjR5qvreecDoQhore1Bbctp1ive7pdrwYofELIY6RIuGWLyCDu7TUFLIro/mN1Qv/tb2L52mtiSRduMJwmnr+xdq1Yvv22qAfDh4s4EeIv06aJe8y2NjPShSI6IfY4dfSpiEai2NG0A7uad6G9pz0pop8yihXIb6xO6DW71wAAXtslGnEKuMEgy/9vH4ubqA17RQMyqWYShlYMzfg5ooZpw6ZhcMlgtPe0J2OM5DHgNYjkDX440XV2XtfVma+DEhFHjDBf61YehR7n4hfWzik60YGuruC25RQ/nOiqOiQHKBTR85gRI8xc7pdeEpEWzc3i/oF53MHwmc+I5fPPi+WLL6a+T/zlzDPFcuNGYP9+4JVXxP9PP50jAYIgFjPd6C++CHz8sejUi0TM9wkh6akuq046Qf/84Z+x+qPV6Ip3YXz1eEypnRLy3hUGn5kkGuvnt4tG/MUdL6a8T/xl3vh5iEVi2HpoK3Y07sAL218AAMwdNzfkPSsMopEoPjH2EwDENWhPyx5sPrgZEUSS75PwuOeeezBx4kSUlZVhzpw5WLduXdb1n3zySUybNg1lZWWYOXMmnnvuuZS/G4aBG2+8EaNGjUJ5eTnmz5+P999/P2WdhoYGLF68GFVVVaipqcHSpUtx5MiRlHXeeecdfPKTn0RZWRnGjRuH22+/Xc0PdotV7CyEOJdLLhFOlbPPDi4T3SpW6lYe1v055hhv3yUFyCAnrNSVGTPM17qVRRiZ6DpjzWhXJaLX1qr5ngEKRfQ8Z/58sXz+eeCFF8z3YrHw9qmQWLhQLF9+WeShv/++GEV11lnh7lehMHq0uI80DOD//g94+mnx/v/7f6HuVkEhy/qpp4A//Um8/sQn+s9zQwjpz2eP+SwA4Ln3n8PzHwgh99xjzkWEvYCBsGDyAgDAqx+9ivcPv49th7chGoni7Ilnh7tjBUJteS3OHC96w5/9+7P4w7Y/AAC+MPULYe5WQfH5qZ8HADy19Sk8974QXU8fczqGVw7P9jHiM0888QSuvvpq3HTTTXjzzTdx0kknYcGCBThw4EDa9V9//XVccsklWLp0Kd566y0sWrQIixYtwrvvvptc5/bbb8fPfvYz3HvvvVi7di0qKyuxYMECdHZ2JtdZvHgxNm/ejFWrVuHZZ5/F6tWrsXz58uTfW1pacO6552LChAnYsGEDfvSjH+Hmm2/Gfffd519h5KKoyHytSkCyiui6RVmUlYkcxZdfDs4xZC1X3cpj6lSRsfrJTwJzPXbAyt+Zb+KsFCSku1IFkyYBv/898Oc/6+dMC8OJrjPW4+O1TOTnKaZkhSJ6niPP79/8BvjFL8RreR0l/nP88WIC0c5O4PzzxXtnnqluYmySm8+L5z/ccosZ6/IFPn8HxqJFYvmXvwC33SZen3deaLtDSF7xxWlfBAD8bsvv8JO1PwEA/L+pvHENihnDZ2BC9QR09nbic49+DgAwd+xc1JTVhLtjBcQFx10AAPj2ym9j2+FtKI4W43PHfi7kvSocFk1bBEBEGf3wrz8EAJx/7Pkh7hEBgLvuugvLli3DpZdeihkzZuDee+9FRUUFHnzwwbTr//SnP8XChQtxzTXXYPr06bj11ltxyimn4Oc//zkA4UL/yU9+ghtuuAEXXHABTjzxRDzyyCPYu3cvnj7qQNmyZQtWrlyJBx54AHPmzMG8efNw99134/HHH8fevXsBAI8++ii6u7vx4IMP4vjjj8fFF1+Mb3/727jrrrsCKZe0WEV0VXnQOjvRgeBFzTPPBD71KeDrX9dPUK2sBHbtEkNive5bvorot94KXH21cJSp5ItfBM45R+13qiAMEf3mm8XyRz8Kbpt2sZ73Xq+B69aJ8+mHP/T2PQMciuh5zllnAdOni0zi/ftFfNGFF4a9V4VDJAJcdpl4vX27WH7rW+HtTyFy6aXi/nnHDuFIP/dc4VAnwTBhghj9YhjARx+JY7FkSdh7RUh+cPKok3HWBHPo0uQhk3H+VApYQRGJRHDZqaIR394oGvFvncpGPEi+PuvrqCo1XY7/dOI/pfyf+Mu46nE4d/K5MGBgZ9NOFEWLsOQkNuJh0t3djQ0bNmC+HG4MIBqNYv78+VizZk3az6xZsyZlfQBYsGBBcv0dO3agvr4+ZZ3q6mrMmTMnuc6aNWtQU1ODU+WkWwDmz5+PaDSKtUddKmvWrMGnPvUplJSUpGxn27ZtaGxsTLtvXV1daGlpSfmnFKuIroqKCuDuu4Ef/5hDKwFRxq++Cvz612HvSXqiUTWRI6efLoY4f+1r3r8rSE49FbjzzsJ5AJbieZCdHTfeKMSe73wnuG3aRWX0yvTpwA03BBcVladQRM9zolHgV78Sdae0FLjvvvzrPM13rrrKjG/58peBiy8OdXcKjgkTgLvuEnVh7Fhxz0uC5ec/FyMpYzFxLMaPD3uPCMkfHlr0EM4cdyZOGXUKnvjHJ1AU9UEQIBm58hNX4tMTPw0AuHDGhfjKzK+EvEeFRW15LZ74xydw/PDj8bkpn8Od594Z9i4VHHd/7m6MGTwG0UgUd557JybUTAh7lwqaQ4cOIR6PY+TIkSnvjxw5EvX19Wk/U19fn3V9ucy1zgjrBJIAioqKUFtbm7JOuu+wbqMvt912G6qrq5P/xo0bl/6Hu+Vb3xI3oF/+strvXbFCPOSRwmHwYGDDBuCmm8LeE5KNiy4SrrkgOzsiEZG5r9tIDEDMk3DBBcBPfhL2nhQMfFIbAMydC+zZI5ygusWUFQJlZSKWrqlJ3Xw2xBlXXAF84xvChGAxx5CAOO444MMPgZ4edlwT4pSJNRPx12/8NezdKFjKisrw0tdeQkNHA2rLOZFSGCycshALpzCLMCymDp2KHVfuQE+iBxXFFWHvDhlgXH/99bj66quT/29paVErpI8fLx7CKnjuElIQzJwpJgQkgpISc2I4EggU0QcIZWVh70FhE4lQQA8birfhUlLCDgxCSP5CAZ0UMsWxYhTHFMQhEM8MGzYMsVgM+/fvT3l///79qKurS/uZurq6rOvL5f79+zFq1KiUdWbNmpVcp+/Epb29vWhoaEj5nnTbsW6jL6WlpSgtLc34e5XACQYJIYQEBONcCCGEEEIIIYSQkCkpKcHs2bPx4osvJt9LJBJ48cUXMXfu3LSfmTt3bsr6ALBq1ark+pMmTUJdXV3KOi0tLVi7dm1ynblz56KpqQkbNmxIrvPSSy8hkUhgzpw5yXVWr16Nnp6elO0cd9xxGEI3ESGEkAKAIjohhBBCCCGEEKIBV199Ne6//348/PDD2LJlCy677DK0tbXh0ksvBQAsWbIE119/fXL9K6+8EitXrsSdd96JrVu34uabb8b69euxYsUKAGIS5auuugrf//738cwzz2DTpk1YsmQJRo8ejUWLFgEApk+fjoULF2LZsmVYt24dXnvtNaxYsQIXX3wxRh+dsPArX/kKSkpKsHTpUmzevBlPPPEEfvrTn6bEtRBCCCEDGca5EEIIIYQQQgghGnDRRRfh4MGDuPHGG1FfX49Zs2Zh5cqVyUk8d+3ahWjU9MKdccYZeOyxx3DDDTfgu9/9Lo499lg8/fTTOOGEE5LrXHvttWhra8Py5cvR1NSEefPmYeXKlSizZII++uijWLFiBc455xxEo1F86Utfws9+9rPk36urq/HCCy/g8ssvx+zZszFs2DDceOONWL58eQClQgghhIRPxDAMI+ydCJqWlhZUV1ejubkZVVVVYe8OIYQQAoDtkx1YRoQQQnSE7VNuWEaEEEJ0xG77xDgXQgghhBBCCCGEEEIIISQDFNEJIYQQQgghhBBCCCGEkAxQRCeEEEIIIYQQQgghhBBCMkARnRBCCCGEEEIIIYQQQgjJAEV0QgghhBBCCCGEEEIIISQDFNEJIYQQQgghhBBCCCGEkAxQRCeEEEIIIYQQQgghhBBCMkARnRBCCCGEEEIIIYQQQgjJAEV0QgghhBBCCCGEEEIIISQDFNEJIYQQQgghhBBCCCGEkAxQRCeEEEIIIYQQQgghhBBCMlAU9g6EgWEYAICWlpaQ94QQQggxke2SbKdIf9iGE0II0RG24blhG04IIURH7LbhBSmit7a2AgDGjRsX8p4QQggh/WltbUV1dXXYu6ElbMMJIYToDNvwzLANJ4QQojO52vCIUYBd5YlEAnv37sXgwYMRiUQ8fVdLSwvGjRuH3bt3o6qqStEeBke+7z+Q/7+B+x8u3P/wyfffoHL/DcNAa2srRo8ejWiUiWvpYBtuku/7D+T/b+D+hwv3P3zy/TewDQ8WtuEm+b7/QP7/Bu5/uHD/wyfff0MYbXhBOtGj0SjGjh2r9Durqqry8qST5Pv+A/n/G7j/4cL9D598/w2q9p/uteywDe9Pvu8/kP+/gfsfLtz/8Mn338A2PBjYhvcn3/cfyP/fwP0PF+5/+OT7bwiyDWcXOSGEEEIIIYQQQgghhBCSAYrohBBCCCGEEEIIIYQQQkgGKKJ7pLS0FDfddBNKS0vD3hVX5Pv+A/n/G7j/4cL9D598/w35vv+FTL4fu3zffyD/fwP3P1y4/+GT778h3/e/kMn3Y5fv+w/k/2/g/ocL9z988v03hLH/BTmxKCGEEEIIIYQQQgghhBBiBzrRCSGEEEIIIYQQQgghhJAMUEQnhBBCCCGEEEIIIYQQQjJAEZ0QQgghhBBCCCGEEEIIyQBFdEIIIYQQQgghhBBCCCEkAxTRbXDPPfdg4sSJKCsrw5w5c7Bu3bqs6z/55JOYNm0aysrKMHPmTDz33HMB7Wl6nOz/Qw89hEgkkvKvrKwswL1NZfXq1fj85z+P0aNHIxKJ4Omnn875mVdeeQWnnHIKSktLMWXKFDz00EO+72cmnO7/K6+80q/8I5EI6uvrg9nhPtx222047bTTMHjwYIwYMQKLFi3Ctm3bcn5OlzrgZv91qgO/+MUvcOKJJ6KqqgpVVVWYO3cu/u///i/rZ3Qpe4nT36BT+fflP/7jPxCJRHDVVVdlXU+3Y1DosA1nG+4WtuFsw73ANjz8a5AVtuH5CdtwtuFuYRvONtwLbMPDvwZZ0akNp4iegyeeeAJXX301brrpJrz55ps46aSTsGDBAhw4cCDt+q+//jouueQSLF26FG+99RYWLVqERYsW4d133w14zwVO9x8AqqqqsG/fvuS/jz76KMA9TqWtrQ0nnXQS7rnnHlvr79ixA+effz4+/elPY+PGjbjqqqvwzW9+E88//7zPe5oep/sv2bZtW8oxGDFihE97mJ1XX30Vl19+Of72t79h1apV6Onpwbnnnou2traMn9GpDrjZf0CfOjB27Fj8x3/8BzZs2ID169fjM5/5DC644AJs3rw57fo6lb3E6W8A9Cl/K2+88QZ++ctf4sQTT8y6no7HoJBhG8423Atsw9mGe4FtePjXIAnb8PyEbTjbcC+wDWcb7gW24eFfgyTateEGycrpp59uXH755cn/x+NxY/To0cZtt92Wdv0vf/nLxvnnn5/y3pw5c4x//ud/9nU/M+F0/3/9618b1dXVAe2dMwAYTz31VNZ1rr32WuP4449Pee+iiy4yFixY4OOe2cPO/r/88ssGAKOxsTGQfXLKgQMHDADGq6++mnEd3eqAFTv7r3MdMAzDGDJkiPHAAw+k/ZvOZW8l22/QsfxbW1uNY4891li1apVx1llnGVdeeWXGdfPlGBQKbMP1gW14+LANDx+24cHDNjx/YRuuD2zDw4dtePiwDQ8eHdtwOtGz0N3djQ0bNmD+/PnJ96LRKObPn481a9ak/cyaNWtS1geABQs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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plotting solution\n", + "with torch.no_grad():\n", + " # Notice here we put [-4, 4]!!!\n", + " new_domain = CartesianDomain({'x' : [0, 4]})\n", + " x = new_domain.sample(1000, mode='grid')\n", + " fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n", + " # Plot 1\n", + " axes[0].plot(x, problem.truth_solution(x), label=r'$u(x)$', color='blue')\n", + " axes[0].set_title(r'True solution $u(x)$')\n", + " axes[0].legend(loc=\"upper right\")\n", + " # Plot 2\n", + " axes[1].plot(x, pinn(x), label=r'$u_{\\theta}(x)$', color='green')\n", + " axes[1].set_title(r'PINN solution $u_{\\theta}(x)$')\n", + " axes[1].legend(loc=\"upper right\")\n", + " # Plot 3\n", + " diff = torch.abs(problem.truth_solution(x) - pinn(x))\n", + " axes[2].plot(x, diff, label=r'$|u(x) - u_{\\theta}(x)|$', color='red')\n", + " axes[2].set_title(r'Absolute difference $|u(x) - u_{\\theta}(x)|$')\n", + " axes[2].legend(loc=\"upper right\")\n", + " # Adjust layout\n", + " plt.tight_layout()\n", + " # Show the plots\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is pretty clear that the network is periodic, with also the error following a periodic pattern. Obviusly a longer training, and a more expressive neural network could improve the results!\n", + "\n", + "## What's next?\n", + "\n", + "Nice you have completed the one dimensional Helmotz 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. Apply the `PeriodicBoundaryEmbedding` layer for a time-dependent problem (see reference in the documentation)\n", + "\n", + "3. Exploit extrafeature training ?\n", + "\n", + "4. Many more..." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pina", + "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": 2 +} diff --git a/tutorials/tutorial9/tutorial.py b/tutorials/tutorial9/tutorial.py new file mode 100644 index 0000000..fd8ff11 --- /dev/null +++ b/tutorials/tutorial9/tutorial.py @@ -0,0 +1,191 @@ +#!/usr/bin/env python +# coding: utf-8 + +# # Tutorial: One dimensional Helmotz equation using Periodic Boundary Conditions +# This tutorial presents how to solve with Physics-Informed Neural Networks (PINNs) +# a one dimensional Helmotz equation with periodic boundary conditions (PBC). +# We will train with standard PINN's training by augmenting the input with +# periodic expasion as presented in [*An expert’s guide to training +# physics-informed neural networks*]( +# https://arxiv.org/abs/2308.08468). +# +# First of all, some useful imports. + +# In[1]: + + +import torch +import matplotlib.pyplot as plt + +from pina import Condition, Plotter +from pina.problem import SpatialProblem +from pina.operators import laplacian +from pina.model import FeedForward +from pina.model.layers import PeriodicBoundaryEmbedding # The PBC module +from pina.solvers import PINN +from pina.trainer import Trainer +from pina.geometry import CartesianDomain +from pina.equation import Equation + + +# ## The problem definition +# +# The one-dimensional Helmotz problem is mathematically written as: +# $$ +# \begin{cases} +# \frac{d^2}{dx^2}u(x) - \lambda u(x) -f(x) &= 0 \quad x\in(0,2)\\ +# u^{(m)}(x=0) - u^{(m)}(x=2) &= 0 \quad m\in[0, 1, \cdots]\\ +# \end{cases} +# $$ +# In this case we are asking the solution to be $C^{\infty}$ periodic with +# period $2$, on the inifite domain $x\in(-\infty, \infty)$. Notice that the +# classical PINN would need inifinite conditions to evaluate the PBC loss function, +# one for each derivative, which is of course infeasable... +# A possible solution, diverging from the original PINN formulation, +# is to use *coordinates augmentation*. In coordinates augmentation you seek for +# a coordinates transformation $v$ such that $x\rightarrow v(x)$ such that +# the periodicity condition $ u^{(m)}(x=0) - u^{(m)}(x=2) = 0 \quad m\in[0, 1, \cdots] $ is +# satisfied. +# +# For demonstration porpuses the problem specifics are $\lambda=-10\pi^2$, +# and $f(x)=-6\pi^2\sin(3\pi x)\cos(\pi x)$ which gives a solution that can be +# computed analytically $u(x) = \sin(\pi x)\cos(3\pi x)$. + +# In[2]: + + +class Helmotz(SpatialProblem): + output_variables = ['u'] + spatial_domain = CartesianDomain({'x': [0, 2]}) + + def helmotz_equation(input_, output_): + x = input_.extract('x') + u_xx = laplacian(output_, input_, components=['u'], d=['x']) + f = - 6.*torch.pi**2 * torch.sin(3*torch.pi*x)*torch.cos(torch.pi*x) + lambda_ = - 10. * torch.pi ** 2 + return u_xx - lambda_ * output_ - f + + # here we write the problem conditions + conditions = { + 'D': Condition(location=spatial_domain, + equation=Equation(helmotz_equation)), + } + + def helmotz_sol(self, pts): + return torch.sin(torch.pi * pts) * torch.cos(3. * torch.pi * pts) + + truth_solution = helmotz_sol + +problem = Helmotz() + +# let's discretise the domain +problem.discretise_domain(200, 'grid', locations=['D']) + + +# As usual the Helmotz problem is written in **PINA** code as a class. +# The equations are written as `conditions` that should be satisfied in the +# corresponding domains. The `truth_solution` +# is the exact solution which will be compared with the predicted one. We used +# latin hypercube sampling for choosing the collocation points. + +# ## Solving the problem with a Periodic Network + +# Any $\mathcal{C}^{\infty}$ periodic function +# $u : \mathbb{R} \rightarrow \mathbb{R}$ with period +# $L\in\mathbb{N}$ can be constructed by composition of an +# arbitrary smooth function $f : \mathbb{R}^n \rightarrow \mathbb{R}$ and a +# given smooth periodic function $v : \mathbb{R} \rightarrow \mathbb{R}^n$ with +# period $L$, that is $u(x) = f(v(x))$. The formulation is generalizable for +# arbitrary dimension, see [*A method for representing periodic functions and +# enforcing exactly periodic boundary conditions with +# deep neural networks*](https://arxiv.org/pdf/2007.07442). +# +# In our case, we rewrite +# $v(x) = \left[1, \cos\left(\frac{2\pi}{L} x\right), +# \sin\left(\frac{2\pi}{L} x\right)\right]$, i.e +# the coordinates augmentation, and $f(\cdot) = NN_{\theta}(\cdot)$ i.e. a neural +# network. The resulting neural network obtained by composing $f$ with $v$ gives +# the PINN approximate solution, that is +# $u(x) \approx u_{\theta}(x)=NN_{\theta}(v(x))$. +# +# In **PINA** this translates in using the `PeriodicBoundaryEmbedding` layer for $v$, and any +# `pina.model` for $NN_{\theta}$. Let's see it in action! +# + +# In[3]: + + +# we encapsulate all modules in a torch.nn.Sequential container +model = torch.nn.Sequential(PeriodicBoundaryEmbedding(input_dimension=1, + periods=2), + FeedForward(input_dimensions=3, # output of PeriodicBoundaryEmbedding = 3 * input_dimension + output_dimensions=1, + layers=[10, 10])) + + +# As simple as that! Notice in higher dimension you can specify different periods +# for all dimensions using a dictionary, e.g. `periods={'x':2, 'y':3, ...}` +# would indicate a periodicity of $2$ in $x$, $3$ in $y$, and so on... +# +# We will now sole the problem as usually with the `PINN` and `Trainer` class. + +# In[5]: + + +pinn = PINN(problem=problem, model=model) +trainer = Trainer(pinn, max_epochs=5000, accelerator='cpu', enable_model_summary=False) # we train on CPU and avoid model summary at beginning of training (optional) +trainer.train() + + +# We are going to plot the solution now! + +# In[6]: + + +pl = Plotter() +pl.plot(pinn) + + +# Great, they overlap perfectly! This seeams a good result, considering the simple neural network used to some this (complex) problem. We will now test the neural network on the domain $[-4, 4]$ without retraining. In principle the periodicity should be present since the $v$ function ensures the periodicity in $(-\infty, \infty)$. + +# In[7]: + + +# plotting solution +with torch.no_grad(): + # Notice here we put [-4, 4]!!! + new_domain = CartesianDomain({'x' : [0, 4]}) + x = new_domain.sample(1000, mode='grid') + fig, axes = plt.subplots(1, 3, figsize=(15, 5)) + # Plot 1 + axes[0].plot(x, problem.truth_solution(x), label=r'$u(x)$', color='blue') + axes[0].set_title(r'True solution $u(x)$') + axes[0].legend(loc="upper right") + # Plot 2 + axes[1].plot(x, pinn(x), label=r'$u_{\theta}(x)$', color='green') + axes[1].set_title(r'PINN solution $u_{\theta}(x)$') + axes[1].legend(loc="upper right") + # Plot 3 + diff = torch.abs(problem.truth_solution(x) - pinn(x)) + axes[2].plot(x, diff, label=r'$|u(x) - u_{\theta}(x)|$', color='red') + axes[2].set_title(r'Absolute difference $|u(x) - u_{\theta}(x)|$') + axes[2].legend(loc="upper right") + # Adjust layout + plt.tight_layout() + # Show the plots + plt.show() + + +# It is pretty clear that the network is periodic, with also the error following a periodic pattern. Obviusly a longer training, and a more expressive neural network could improve the results! +# +# ## What's next? +# +# Nice you have completed the one dimensional Helmotz tutorial of **PINA**! There are multiple directions you can go now: +# +# 1. Train the network for longer or with different layer sizes and assert the finaly accuracy +# +# 2. Apply the `PeriodicBoundaryEmbedding` layer for a time-dependent problem (see reference in the documentation) +# +# 3. Exploit extrafeature training ? +# +# 4. Many more...