{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial: Learning Bifurcating PDE Solutions with Physics-Informed Deep Ensembles\n", "\n", "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial14/tutorial.ipynb)\n", "\n", "This tutorial demonstrates how to use the Deep Ensemble Physics Informed Network (DeepEnsemblePINN) to learn PDEs exhibiting bifurcating behavior, as discussed in [*Learning and Discovering Multiple Solutions Using Physics-Informed Neural Networks with Random Initialization and Deep Ensemble*](https://arxiv.org/abs/2503.06320).\n", "\n", "Let’s begin by importing the necessary libraries." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "## routine needed to run the notebook on Google Colab\n", "try:\n", " import google.colab\n", "\n", " IN_COLAB = True\n", "except:\n", " IN_COLAB = False\n", "if IN_COLAB:\n", " !pip install \"pina-mathlab[tutorial]\"\n", "\n", "import torch\n", "import matplotlib.pyplot as plt\n", "import warnings\n", "\n", "from lightning.pytorch.callbacks import Callback\n", "\n", "from pina import Trainer, Condition, LabelTensor\n", "from pina.solver import DeepEnsemblePINN\n", "from pina.model import FeedForward\n", "from pina.operator import laplacian\n", "from pina.problem import TimeDependentProblem\n", "from pina.domain import CartesianDomain\n", "from pina.equation import Equation\n", "from pina.optim import TorchOptimizer\n", "\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deep Ensemble\n", "\n", "Deep Ensemble methods improve model performance by leveraging the diversity of predictions generated by multiple neural networks trained on the same problem. Each network in the ensemble is trained independently—typically with different weight initializations or even slight variations in the architecture or data sampling. By combining their outputs (e.g., via averaging or majority voting), ensembles reduce overfitting, increase robustness, and improve generalization.\n", "\n", "This approach allows the ensemble to capture different perspectives of the problem, leading to more accurate and reliable predictions.\n", "\n", "

\n", " \"Deep\n", "

\n", "\n", "The image above illustrates a Deep Ensemble setup, where multiple models attempt to predict the text from an image. While individual models may make errors (e.g., predicting \"PONY\" instead of \"PINA\"), combining their outputs—such as taking the majority vote—often leads to the correct result. This ensemble effect improves reliability by mitigating the impact of individual model biases.\n", "\n", "\n", "## Deep Ensemble Physics-Informed Networks\n", "\n", "In the context of Physics-Informed Neural Networks (PINNs), Deep Ensembles help the network discover different branches or multiple solutions of a PDE that exhibits bifurcating behavior.\n", "\n", "By training a diverse set of models with different initializations, Deep Ensemble methods overcome the limitations of single-initialization models, which may converge to only one of the possible solutions. This approach is particularly useful when the solution space of the problem contains multiple valid physical states or behaviors.\n", "\n", "\n", "## The Bratu Problem\n", "\n", "In this tutorial, we'll train a `DeepEnsemblePINN` solver to solve a bifurcating ODE known as the **Bratu problem**. The ODE is given by:\n", "\n", "$$\n", "\\frac{d^2u}{dt^2} + \\lambda e^u = 0, \\quad t \\in (0, 1)\n", "$$\n", "\n", "with boundary conditions:\n", "\n", "$$\n", "u(0) = u(1) = 0,\n", "$$\n", "\n", "where $\\lambda > 0$ is a scalar parameter. The analytical solutions to the 1D Bratu problem can be expressed as:\n", "\n", "$$\n", "u(t, \\alpha) = 2 \\log\\left(\\frac{\\cosh(\\alpha)}{\\cosh(\\alpha(1 - 2t))}\\right),\n", "$$\n", "\n", "where $\\alpha$ satisfies:\n", "\n", "$$\n", "\\cosh(\\alpha) - 2\\sqrt{2}\\alpha = 0.\n", "$$\n", "\n", "When $\\lambda < 3.513830719$, the equation admits two solutions $\\alpha_1$ and $\\alpha_2$, which correspond to two distinct solutions of the original ODE: $u_1$ and $u_2$.\n", "\n", "In this tutorial, we set $\\lambda = 1$, which leads to:\n", "\n", "- $\\alpha_1 \\approx 0.37929$\n", "- $\\alpha_2 \\approx 2.73468$\n", "\n", "We first write the problem class, we do not write the boundary conditions as we will hard impose them.\n", "\n", "> **👉 We have a dedicated [tutorial](https://mathlab.github.io/PINA/tutorial16/tutorial.html) to teach how to build a Problem — have a look if you're interested!**\n", "\n", "> **👉 We have a dedicated [tutorial](https://mathlab.github.io/PINA/tutorial3/tutorial.html) to teach how to impose hard constraints — have a look if you're interested!**" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# define bratu equation\n", "def bratu_eq(input_, output_):\n", " u_tt = laplacian(output_=output_, input_=input_, components=[\"u\"], d=[\"t\"])\n", " return u_tt + torch.exp(output_)\n", "\n", "\n", "# define true solution\n", "def true_solution(x):\n", " alpha1 = torch.tensor([0.37929])\n", " alpha2 = torch.tensor([2.73468])\n", " u1 = 2 * torch.log(torch.cosh(alpha1) / torch.cosh(alpha1 * (1 - 2 * x)))\n", " u2 = 2 * torch.log(torch.cosh(alpha2) / torch.cosh(alpha2 * (1 - 2 * x)))\n", " return u1, u2\n", "\n", "\n", "# build problem class\n", "class BratuProblem(TimeDependentProblem):\n", " output_variables = [\"u\"]\n", " temporal_domain = CartesianDomain({\"t\": [0, 1]})\n", " domains = {\"interior\": temporal_domain}\n", " conditions = {\n", " \"interior\": Condition(domain=\"interior\", equation=Equation(bratu_eq))\n", " }\n", "\n", "\n", "# define problem and discretise domain\n", "problem = BratuProblem()\n", "problem.discretise_domain(n=101, mode=\"grid\", domains=\"interior\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Deep Ensemble Models\n", "\n", "Now that the problem setup is complete, we move on to creating an **ensemble of models**. Each ensemble member will be a standard `FeedForward` neural network, wrapped inside a custom `Model` class.\n", "\n", "Each model's weights are initialized using a **normal distribution** with mean 0 and standard deviation 2. This random initialization is crucial to promote diversity across the ensemble members, allowing the models to converge to potentially different solutions of the PDE.\n", "\n", "The final ensemble is simply a **list of PyTorch models**, which we will later pass to the `DeepEnsemblePINN`" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# define a single model (ensemble member)\n", "class Model(torch.nn.Module):\n", " def __init__(self, *args, **kwargs):\n", " super().__init__()\n", " self.model = FeedForward(*args, **kwargs)\n", " self.init_weights_gaussian()\n", "\n", " def forward(self, x):\n", " return x * (1 - x) * self.model(x)\n", "\n", " def init_weights_gaussian(self):\n", " for param in self.model.parameters():\n", " if param.requires_grad:\n", " torch.nn.init.normal_(param, mean=0.0, std=2.0)\n", "\n", "\n", "# define a list of models with different initializations\n", "models = [Model(1, 1, inner_size=50, n_layers=2) for _ in range(10)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the networks output before strated training" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjMsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvZiW1igAAAAlwSFlzAAAPYQAAD2EBqD+naQAA5v9JREFUeJzsnXV4FOfah+/13bi7QxLcrbi3FNpCKVBvqVPqdk7l9NS+up26QF2AQinSFi/uToBAiLvLus18fwzdkOIQA+a+rr2SmXln5t1kd+Y3jypEURSRkZGRkZGRkWkBlC09ARkZGRkZGZlLF1mIyMjIyMjIyLQYshCRkZGRkZGRaTFkISIjIyMjIyPTYshCREZGRkZGRqbFkIWIjIyMjIyMTIshCxEZGRkZGRmZFkMWIjIyMjIyMjIthrqlJ3AqBEGgqKgIX19fFApFS09HRkZGRkZG5gwQRRGj0UhUVBRK5altHq1aiBQVFREbG9vS05CRkZGRkZE5B/Lz84mJiTnlmFYtRHx9fQHpjfj5+bXwbGRkZGRkZGTOhLq6OmJjYz338VPRqoXI3+4YPz8/WYjIyMjIyMhcYJxJWIUcrCojIyMjIyPTYshCREZGRkZGRqbFkIWIjIyMjIyMTIshCxEZGRkZGRmZFkMWIjIyMjIyMjIthixEZGRkZGRkZFoMWYjIyMjIyMjItBiyEJGRkZGRkZFpMWQhIiMjIyMjI9NiyEJERkZGRkZGpsWQhYiMjIyMjIxMi9FsQuT1119HoVDwyCOPNNcpZWRkZGRkZFo5zdL0btu2bXz++ed06dKlOU4nIyPTAoiiCNQ3uSovL6e0tBSHw4HdbsfhcOB2uxEEAUEQ6Nu3L/7+/gAUFhaSm5uLRqPB29vb0+jSx8cHpVI23MrIXMw0uRAxmUzcdNNNfPnll7zyyitNfToZGZkmpLCwkPz8fIxGIyaTqcHLYrEwffp0QkJCAEhLS2PNmjUnPVb79u09QiQnJ4fly5cfN0ahUBAQEMBVV11FUlJS07wpGRmZFqXJhcj06dMZO3YsI0eOPK0Qsdvt2O12z3JdXV1TT09G5pLHbrdTVVVFbW0tNTU11NbWUltbS11dHbW1tUydOpWgoCAADh06xNq1a096LIvF4vk9KCiIuLg4dDodOp0OrVaLWq1GqVSiVCrx8fHxjA0NDaVLly44HA5MJhN1dXUYjUZEUaS6uhpvb2/P2B07dnDgwAG6du1Ku3bt0Gq1TfBXkZGRaS6aVIjMmjWLnTt3sm3btjMa/9prr/Hiiy825ZRkZC45HA4HNTU1VFdXU11dTU1NDQMGDMDX1xeA9evXs27dupPuX1tb6xEiUVFRdOjQAV9fX3x9ffHx8cHHxwdvb2/P62+6du1K165dz2iOKSkppKSkNFgnCAImk4mKigpCQ0M963Nzc8nMzCQzMxOtVkv79u3p1q0bCQkJHreQjIzMhUOTCZH8/Hwefvhhli9fjl6vP6N9nn76aR577DHPcl1dHbGxsU01RRmZiwJRFDGbzeh0OjQaDSC5RbZs2UJ1dTUmk+m4fVJTUz1CJCAgAC8vL/z9/QkICMDf37/B61gR0K5dO9q1a9cs70upVHpiRY5lyJAhBAYGsnfvXqqrq9mzZw979uwhISGB0aNHExUV1Szzk5GRaRwU4t8RZo3Mb7/9xoQJE1CpVJ51brcbhUKBUqnEbrc32HYi6urq8Pf3p7a29riLkYzMpYbNZqOsrIzKykoqKyupqqryvBwOB7fffjsJCQmA5L5YtGiRZ1+dTkdQUBABAQEEBgbSvXt3j8AQRfGCtCSIokh+fj579uxh9+7duN1uwsLCmDZt2gX5fmRkLibO5v7dZBaRESNGsG/fvgbrpk6dSrt27fjXv/51WhEiI3MpIggC1dXVlJeXU1FRQfv27QkODgZg3759/P777yfd12g0en5PSkriuuuuIygoiMDAQAwGw0n3u1Bv2gqFgri4OOLi4hg0aBArV66kS5cunvcjiiKiKMpZNzIyrZwmEyK+vr506tSpwTpvb2+Cg4OPWy8jc6lSXV3NwYMHKSsro7S0lPLyclwul2f7398ZgJCQEPz9/QkODiYoKMjz82+xoVbXf50DAwMJDAxs9vfTUgQEBDBx4sQG67Zt20ZGRgbXXnvtKYWYjIxMy9IsdURkZC513G43xcXF5OXlERcXR0xMDAAVFRUsW7aswVi1Wk1ISAghISENTJqJiYk8+uijzTrvCxWr1crKlSux2+188cUXTJ48mcjIyJaeloyMzAloshiRxkCOEZG5UBEEgaKiIrKyssjNzSUvLw+n0wnAoEGDGDFiBABms5nFixcTHh5OWFgY4eHhBAYGyu6ERqCoqIg5c+ZQU1ODWq1m7NixdO/evaWnJSNzSXA2929ZiMjINDLV1dXMnDnzuGwVvV5PXFwcnTt3pnPnzi00u0sLi8XC/PnzycjIAGD48OEMHjy4hWclI3Px0yqCVWVkLgX+ztwwGo107NgRAH9/f0RRRKfTkZSUREJCAvHx8YSFhcmWjmbGy8uLG264gdWrV7N27VpWrVoFIIsRGZlWhCxEZGTOAYvFwu7du9m5cycVFRV4e3uTmprqqRx6++23HxdAKtMyKJVKhg8fjkajYeXKlQiC0NJTkpGROQb5KikjcxZYLBY2btzIli1bPDEfGo2G5ORkHA6HR3gcWwRMpnUwaNAg4uLiiI+Pb+mpyMjIHIMsRGRkzpD9+/ezYMECHA4HABEREfTq1YtOnTqdcfVgmZblWBFit9tJT08/4zL0MjIyTYMsRGRkzpDQ0FAcDgfh4eEMGzaM1NTUC7YY2KWO2+3mp59+Ijc3F1EU6datW0tPSUbmkkUWIjIyJ6G6uprc3FzPTSosLIy77rqLqKgoOej0AkelUhEbG0tubi4LFy5E1BgoFf3JrjDjcgu4RRG3ICKIIhF+eoa3Dyc6QC6KJiPTFMhCREbmHwiCwI4dO1i2bBkul4vQ0FCio6MBPIXIZC5sai1Ohg0bTk1NDWlpaSz4dS6/WVKoEb1OOD4qwOARIvlVFtIKaxnePgydWm5VISNzvshCREbmGCwWC3PnziUrKwuAuLg4uTz4RcS+glq+35zDwj1FfHlrL8aPH4/RaCQ3N5cx+iPY2wxF5+WNUqFApVSgAPKqLHSM8vccY/a2fD766wh+ejVju0QyoXsMveIDUSplN52MzLkgCxEZmaNUVlby008/UVlZiUajYeTIkfTu3Vt2w1zgiKLIkrQSPlubxZ78Gs/6VellDEoOZcqUKcycOZPKykriTXuYOmkqOp3upMcL8NIQ6a+nuNbGz1vz+XlrPinhPjw6MoXLO0bIgkRG5iyRK6vKyAA5OTnMnj0bq9WKv78/N954I+Hh4S09LZnzZFdeNf/3+0G251YDoFEpuLJzJLf0i6dnfKAn2Li6upoZM2YgiiK33norERERpzyuWxDZkl3J/J2F/JlWgskuNSrsERfA3Pv6y2JE5pJHrqwqI3OWFBcXY7VaiY6O5vrrr8fX17elpyRznrgFkUdm7ya30oJeo+TuQUnc1j+BEJ/jrR2BgYHcdNNN6PV6goKCTntslVJB/zYh9G8TwnPjOjBzXRYz12fTLVZ20cjInC2yRURGBsl8v2vXLjp37oxGo2np6cgACG5QHhMMWnGk/netF+j9QeMFx6RQO1wCaqXCIwb+3FfMyvQynhidSoT/2dV6sVqtZxUfVGV2oFRAgJcWgMOlRubuKOCRkcl4aeVnPplLC7npnYzMGXDo0CESExPRarUtPZVLE5cd8rdCVVb9qzobzJVgrYbUMTDp6/rxL4WA4Gx4DKVGEiTxl7Gj34c8/etebu+fyI1Bh8A3EkJSQH32/9/Dhw8zb948Jk6cSEpKylnvL4oi1366kV15NcQGGXhtQhcGJoec9XFkZC5UZNeMjMxp2Lt3L7/++iuxsbHccsstshhpagQBindL4iP+Mmmdyw7fXgWc5FnIWt1wWe8vCRERcJhAdEvLlgoOFNVy3WcbEUX4cm0mNzhuReG0SEIlNBXCO0JEF4jtA5FdQX3yYFSQRKrdbmfu3Lnccccdp40Z+ScKhYIHh7fluflp5FdZuXnmFq7vHct/r+qIQSun/MrIHItsEZG55Dh06BCzZs1CFEV69+7NlVdeKVdIbQqs1ZC5Cg4vgyMrwFIBcZfBHUvqx/xwnfQzKOnoKxF8wsEQAIYg0J/key+K4DCxZu8Rvli6gyIzZIuRTOoZwzMjYwmcNwXK08Fed/y+bUfCzfPql5020DR027hcLn788Ueys7Px8fHhjjvuOKPYkX9isrt4a0k6323ORRQhOcyHT27qQXK4HIMkc3Eju2ZkZE5CVlYWP/74I263my5dujB+/Hg5Pbex2TcXdv0A2Wslq8Xf6PygzTCY/N15n6KszsYLi/bzx74SABKCvXh1Qmf6tz3G/SGKUJsPpfuhNA0Kd0H+Fuh9Fwx7WhpjroR320NML0gaBklDIboHKFVYrVa+/vprysrKCAgI4I477jjn69DGzAoenrWbcqMdvUbJ7Hsuo2tswPn9EWRkWjGyEJGROQEVFRV88cUXOBwOUlNTmTx5MiqVbCZvdH6cBBnLpN9D20HyaOkV1w9UjRMIvDu/hms/2YBCoeDewUk8NCIZveYM/peiCG5HvWvm4GKYfVPDMV7BnjkbI/ry9U/zqKqqIiQkhKlTp+Lt7X1Ocy432nl09m6sTjez7umHRiULYJmLF1mIyMj8A4fDwYwZMygrKyMuLo5bbrlFzo45X5w22PcLbPsSbpgNfpHS+owVULgDukyS3C2NRJXZQZB3fSzPtxtz6J0QRIeo87g2iKIUIJv5F2T9BVlrGrpzrvqAmjbX8NVXX1FXV8fAgQMZOXLkOZ/OLYgYbU5PZo1bEKkyOwj1PXXMiozMhYYsRGRk/kFxcTHfffcdKpWKe++9V64Tcj6YK2DbDOllLpfWDX4Shj/XJKcz2V28t/wwP27JZfGDg2gb5tMk5wHA7YS8zZCxVIptuXUB+EVSUVHBtkVfM9q6EFX7MdBurBT8ep6xRa8sPsDCPUV8cWsvusmuGpmLCFmIyMicgJqaGsxms6eBncxZYqmCjR/Ali/AaZbW+cVA33uhx61SgGkjIooiC/cU8eofBymtswPw5OWpTB/WtlHPc8Z8N16ymgAulJh92+LfYbgkSuL6g+rskhAtDhcTPt7IoVIjOrWStyZ15equUU0wcRmZ5kcWIjIyRxEEQQ5GbQycNni/U70FJLIbDHgI2l9z1jfgM2FnXjUvLz7ArrwaQApGffGaTgxJCW30c50xlio4vBTx4GIWHBbIEGO4gYXEUCJl+jySdtY1S4w2J4/M2s3K9DIAHhqRzKMjk+UsLpkLHlmIyMgAZrOZb7/9luHDh9OuXbuWns6FhyDAsSLuz39DznoY9oxUbKyJbpbPzt/Hj1vyAPDSqpg2pA13D046s2DUZsBms/H1VzMpLStHrRCZoFlDx9gguOXX+kF//htCkqW/k9+prRxuQeTNJel8vlbq+DypZwyvXttZDmaVuaCRC5rJXPKIosiiRYsoKytjxYoVJCcnyxkyZ0PGClj2HEz4FKK6S+tGPA9qfUNx0gTEBXmhUEg35CdGpxLmd3al2ZsavV7PHXfexdy5c8nIyOAXx1BKQnsyxOVCrVZDbSFs+VQa/PtjkvUo9UpIveKEcSUqpYKnr2xPYog3z/6Wxi87Cqi1Ovn8lp6yZUTmkkC2iMhclOzbt4958+ahVCq55557zroy5iVLxRFY+owUrAnSDfSGn5vsdDanm2835pAa4cvQ1DAA7C43R8pMdIzyb7LzNgaCILBs2TI2b94MQHBwMGPHjiUp3A92fguHlkDBNhpUjvWLlixK3W8+4TFXpZfy4E+7eHtSV8Z0jmyGdyEj0zTIrhmZSxqj0cgnn3yC1Wpl2LBhDBkypKWn1Ppx2WH9e7DuHanOhlINfe6FIU81ehAqgMst8OuuQt5bfpjiWhvJYT4seWQwqguwc21aWhpLlizBZDLh5+fHQw89JFlGAExlcHgpHPpTCnR1WmDiTOh8tKJsdQ7kboTky8E7GDg+TVkURdkyInPBIbtmZC5ZRFHk999/x2q1EhERwcCBA1t6Sq2f3I2w6GGoOCwttxkBY96QYhwaGVEUWXaglLeWHuJImQmAKH899w5p0+jnai46depE27ZtWbVqFUlJSR4RYrPZMNmUhPS4BXrcAk4rZK+DuL71O++bC6teBoUSYvtBu7EEtb8KvOMBKKqxMu2HHbx2bZfzq5ciI9OKkYWIzEVFWloa6enpKJVKxo8fL8eFnAml+yUR4h0KV7wOnSY2SSDq7vwaXlq0n51HM2ECvDRMH9qWWy6LbzWBqOeKXq/nyiuvbLBu9+7dLFmyhKSkJHr16kVqaiqqlNENd/QJh/DOULoP8jZKr2XPSo352l/Nu7l92VNQx5QvNjHztt70STz7fjcyMq0dWYjIXFQUFxcDMHjwYDku5FTY6uobyvW6A2y10PtOMAQ22SnLjXZ25tWg1yi5c2Ai9wxug7/h4q1uW1VVBUj9jbKystBqtcTHx5OYmEhCQgIREREo/7aWVOdK7puDiyQxUrwHKjP5z4Pp5JnT2JpTxT0z1/Duzf0Z3i68hd+ZjEzjIseIyFx0ZGdnExcXJ1tDToStFpY8I93s7lsP2nPrm3Im1FgcHCox0jdJin0QRZHP12ZxbffoVpcJ01RUV1ezY8cOdu3ahdls9qzXarX861//8nxG9+zZg0KhwNfXFwM2DIUbMLjr0Ax+FLtLYPoPO/hX9u2Y8ELZZRLdxtzliSkRBAGn04nT6UQQhAbXykOHDmEymbDb7TgcDs9Ph8OBXq9n7NixnrELFiygpqYGlUqFWq1GpVKh1+vx9fXF19eXHj16yLEqMmeMHCMic0mTmJjY0lNonRxZCQsfhLpCQAGZq6D9VY1+GkEQ+XFLLm8vk2JO1jw5lAAvLQqFgvsu4FiQcyEwMJCRI0cyfPhwSktLyc7OJjs7G61W20Ao//XXX9TU1By3v3LNy0RERPDZhBGoPi5CicjnaTn8mfY2gkKDW6FCEOqfJUNDQ5k+fbpnefny5VRUVJxwbv7+/g2ESFlZGYWFhSccazAY6Nmzp2d56dKlmM1mIiIiiImJISYmRi4cKHPOyEJEptUhOp3YMzJwFBTgLCzCWVSELrktgZMne8bk3XMPCoUSdVgohIezSRDp17EDIampaKKiUMgXxXqcVlj+PGz9QloOSoJrPoH4yxr9VEfKjPxr3j525FYDkBLuQ5nR7mnydqmiVCqJjIwkMjKS/v37N9gmiiJt2rShoqICs9mM1WrFarUiCILnpQltg/DoQZb88inGfDN2hU7KCv6HQfufBu6EhASCg4PRarXodDq0Wq3n5eXl1WDsyJEjMRqNuN1u3G43LpcLq9WK0Wg8zrp48OBBampq2Lt3LyAJlTZt2pCSkkKbNm3OuUOxzKWJ7JqRaRUIVivVP/2MectmLNt3IFosDbb7DBtG7KefeJYPtmvv+T2tY0f2d+6Eb10dY/74E+9+/Yj/5mvPduvevWgTElBdip+hot3w6z1QcUha7nMPjHyh0V0yDpfAZ2sy+WjVERxuAW+tiicvT+XmfvGo5QqhZ40oih5Xyt8um7/Xz1ixl2EhNQTnLUOZvgiVtQztlG9Rp46SrBJ2o1R4TtV08TeHDx+muLiY4uJicnJysNlsnm2BgYE89NBDshvnEkd2zchcELiNRlRHL7AKjYaKzz5DMBoBUPr7o0tIQBMdhSY6Gn3Hjg32jXz9NUSHg8riEtKrKgHoXlqGQqNBGxfnGSfYbORcfwMIApqoKHTt2qFLSUaXlIQ2MRFtYiIqnybs5trSrHlDEiE+ETD+Y2h77i3sT0at1cmUzzeRXiL974alhvLKhM5EBxga/VyXCgqFAp1Oh06nO2793aO6Sgvdh8C4F9i3Zh7tkkfUu0bWvQN7ZkOfu6DnVPBq/EyblJQUUlJSAHC73RQUFJCRkUFGRgbt27f3iBCXy8W6devo2rUrQUFyxo/MiZEtIjLNimA2U7toETW/zkcwGkn643fPRavi009RGAx49+uHLiXljNwrP/30E4cPHyYpKYlbbrkFXC4Eq9Vj/XDk5pI39Q6cRUUn3N//2muJevX/AHCbzJS/+w7qsDBUQUGofHxQenuj9PFB6eWFOiQEdajUdE10u3FVVIKC+ic/hQJUKhRKJQqdDqW+FQRkGktg5csw+uUmuSH9zXO/7eOPfSX896oOXN01Sn4abiZ+3VnAY3P2MDQ1lE9u6oGXRgWfDoCy/dIAtR66TIF+0yCs/akP1kgc22jywIEDzJkzB4VCQadOnRg8eDChoS3YuFCm2ZArq8q0Otw1NVT98CNV33+PUFsrrVSrSVq4AF1S0jkd89ChQ/z8888olUqmTZt2ygucu7YW26FD2NPTsWdm4cjKwp6TTdCttxJy990A2DMzyRo77qTHCJo6lfB/PQWAs7CQIyNObl0IuOF6Iv/7X+ncdXUcGT4ChUGP0uCFKjAAdVAwquAg1MEh6Dt1xG/UqHP5ExzPwUWQtxku/7/GOd5JEAQRq9ONt04yqjpcAkabk2Af3Wn2lGlM/kovY9qPO7A5BbrFBvD17b0J1Imwfz5s+hhK9tYPbjsKBj4KCQOabX55eXmsWbOGzMxMz7oOHTrI6fWXALJrRqbV4Covp/Lrb6iZNQvhaNyHNj6egOuvx//qq1AHB5/TcZ1OJ3/++ScAl1122WmfslT+/nj36YN3nz4N1ouC4Pld6eND8LT7cJWW4a6pQTCZEMxmBJMJt8WM0rfehSO63aBSScGCf7+OQaGsD+4TrDYEkwlMJtyAMy+vwVj/CRM8QkRwOMi5bhL69u3Qd+2KoUtX9KkpKDSn8fc7LFKPmB1HY2OShkJyI4mbf2Cyu3h8zm5MdhffTu2DWqVEq1bKIqQFGNYujB/v6scd32xjd34N1322ke/u7Et01+slS0jeJtj8CaT/DkeWg39MswqRuLg4brnlFoqKili7di3p6ekcOHCAAwcO0LlzZ8aNG3ec+0nm0kO2iMg0KcYVKyh44EEAdO3aEXLvPfiOHo3iPGt8rF+/nhUrVuDn58f06dNbxcVM/FuQuN2gUKA4WupbdLlwFhQgWK0IFgvu6mpclVW4qypxVVTi1bs3fldcDpzYKqPQ6TB06YLP0CH4jhyJNj6+4YlLD8DcqVCeLi0PeBiGPQfqxs9UMdqc3PjlFvYV1qJVKZl1bz96xDVdETSZMyOj1MitX22luNZGhJ+e7+7sQ0q4b/2AykzY9BFc9gAEH02hLj0AJfukSrqq5nkmLSkpYd26dezfv5+YmBjuvPNO2Y13kSK7ZmRaDNHlwpGdjS5Z6lMiiiKlr/wfPoMH4T14cKNddBwOBxs2bCA8PJwOHTo0yjFbA4LZjGX7dqx792Hdswfr3r0IdXWe7cHT7iPs4YeBo9acnd+iWPJvcNmkcuETPoc2w5pkbjanm9u+2sqW7CqCvbV8eVsvWYS0IopqrNz61VaOlJnw06tZ8fgQwnxPEac051Y4sAACE2HQ49D1+ibNtGkw16IilEqlxz1jt9vJyMigY8eOsjC5SJCFiEyLYN64kZJXX8VdXkGb5csuzXTZRkYUBBw5OZg3bcK0eg2hDz2IoXNnAEzv3ErprI34J1rxH9oDza1fgU/TBAK63AL3/bCTFQdL8dWp+fmefnSK9m+Sc8mcOzUWB3d+u50+iUH864p2Jx8oirDhf7DxA7BIWWf4x8Hgx6HbTc0mSP5mxYoVrF+/nrZt2zJu3DgCAgKa9fwyjY8sRGSaFVd5OaVvvEnd4sWAFI8R88nHeB1TibGxMBqNeHt7y1UcgcJ7b6ZuzQ5pQanEZ9Aggu64A68+vRv1qVIQRJ6cu5d5OwvQqpV8d0cf+iWdW2yPTNNjc7rRqpQoldJnwOpwo9coT/yZcJhh+1ew4QMwl0nrAuJh1IvQcUKzzXn9+vX89ddfuN1uNBoNI0aMoE+fPvL3/AJGFiIyzYLodlMzZw5l774n1f9QKAi88UZCH3oQlX/jPy0LgsAXX3yBUqlkwoQJl14aoChCdQ4ESSXs3SYzxvk/U7NkNdYdOzzD9J07E3zXXfiOGtkoFWazK8xc9eF6rE43n93ck1Ed5KZrFwo2p5ubZmwhJdyXl6/pePLick4rbP8a1r8L5nIY9TIMeKhZ51peXs6iRYvIOxrMHR0dzTXXXENYWFizzkOmcZCFiEyTI9jt5N16G9Y9ewDQd+hAxIsvYujcqcnOuXPnThYuXIhOp+Ohhx666MtIC4ILiyULm62QEO/usGA65Kyn/PrXsCiMaLUh6PXR6PVRUGyj5vufqf11PqLdjjYxkaTfFzdaqfu0wloyy01c0y26UY4n0zz8daiMO77ZhijCoOQQPrqxx6k7HjvMsONb6Hk7aI+WgM9eBw4TpFwh1cppQgRBYOfOnSxfvhy73Y5KpWLixIkXVRzYpYKcvivT5Ch1OnQpydiPHCH0kUcIvPGG886EORU2m42VK1cCMGTIkItWhJhMhygs+pm6un2YTAcRBDtKhYYhe9Qoa/JBpaWkcC5l9j3/2FOBflQ0PuN6EropGe+Ezh4RIjqdWHbsxLtf33OeV6dofzkm5AJkWGoYn9/ck4dn7WZdRgUTPtnAV7f1JiHkJN8frTdcdn/9suCGP5+CsgMQ2xdGPA8JA5tsvkqlkl69epGSksLChQvJz88nKiqqyc4n0zqQLSIyZ4w9MxOllxeayEgA3CYTgsmEphkKEy1fvpwNGzYQHBzMtGnTUKsvLg1tNB4kO+cjysuXNFivQoNPrZXOB2vRecfDpG8oEA5QW7cLh70Mm70Im60IQbADoFTqGTJ4D0ql9PfJzHqP2oPrEH5NI8C3B9H3PI/hDJ4uBUHkibl7mNIrlr5yPMgFT1phLXd/t53iWhv+Bg2f3tyD/m1CTr+j0wqrX4ctn4PLKq1rO1LqVxTRuUnnLIoiVVVVBB9Ta6igoICYmJgmPa9M4yC7ZmQaFVEQqPr2O8rfew+vXr2InTmjWVPsKisr+fjjjxEEgRtvvNHT4+JiIifnEzKz3gEUhIVeQWjgYPw2z8GQthwFQPur4ZqPQH+8VUIURRzOSizmTOz2EiIirvFs27R5FBZLlmdZWQc+jkQiet1McMQQvLwSTzifGeuyeOX3g/jq1Kz/9/BTm/NlLgjKjDbu+W4Hu/NrUCsVvH99N8Z1OUNrQ10xrH0Ldn4LggtQQJfJMOxZCIw/7e6NQUZGBj/++COdO3dm7Nix6FtDCwWZk3I29285JFnmlDhLS8m/6y7K3ngD0eEAtQrBbDn9jo3I0qVLEQSBtm3bkny0PsnFgCjWV3WNibmFyMhJ9O3zB507f0TEoUN4pS1HodTAmDdh8ncnFCFwtEGaNoTAwL4NRAhASsp/SUiYjr+hGwq3EsEP6kKyOZzzMjs33digbbzDUYEoihwuNfLmUqlb7zNj28si5CIhzFfPrHv6cU23KLy0KjqfjavNLxLGvQvTt0LHawER9s6G0v1NNt9/UlVVhUKhYN++fXz++ecUFBQ027llmhbZIiJzUuqWL6fkuf/grq1FodcT/u9/EzBlcrNaQ2w2G99//z3FxcXcf//9hIScgTn5AqCw8GdKy36na5eZqFQnqArrtMG8O2HgYxDTOGnQgmCndONPFK76BGtYNZpCBUkB0wh7/DEEwcnadT1Rq/3ZWZLI9qIYggJ78u6N41Eqmy72R6b5EUWRvCoL8cH1cSJWhxuD9iz+z4U7IW0ejH6lPoC1cCeEdQBN01kq8vLymDdvHrW1tSiVSoYPH07//v3lNN9WiOyakTkvBGMNpa+8TM2CPwApIybq7bfOuTndec9HECguLiY6+sLP2BBFkeycD8nO/h8AqakvExN9I9iNsG0G9H8ImvjGL9jtVH7+OZVff0PCTz+ib98ek+kwW7ddhSi6GoxVq/3x9+9BZOS1hIdd2aTzkmkZVh8q46m5e/noxh70STzHDs3WavhfN9D5wvDnoPNkaCJxYLVaWbx4Mfv3S9aYNm3aMGHCBHx8fE6zp0xzIrtmZM4MwQ0VGQ3X/XAd4usJWFYtBESC+/iScE8HdO4s6WbZAiiVyotEhLg5dOg/HhGSkDCd6KgbpJ4fXwyDFS9IfvgmRqnTEfrQQ7RdtRJ9e6k1vI9PCvHVr/Ll1jtYlHk5bk0PlEo9LlctlZV/YbXkePa32YrYs/deMrPepaR0ESbTIQTB0eTzlml8RFHkszWZlBnt3PjlZmauz+acnk2rsqWMm9p8mH8vfDlUSvttAgwGA9dddx1XX301arWazMxMcnJymuRcMs2DbBG51BBFyFwltQk/vETq2vpUFmj0iKKI4pfb4MACbDVa3HbwDj/mBqPSwr3rIOwUpaMbCaPRyLZt2xgwYECraGjXGGRkvEpe/kxAQWrKC8TE3Ay7f4LFj0kZCb5RMOlriOvX7HOzpu0na/IUajReLBt7Ny++ejeC4MRkOkhN7Q4CAy/D10f6v5eVLWFf2vQG+ysUagyGWLwMicTG3k5QkNThVRCcgMKTxSPT+rA4XPxr3j4W7SkC4IqOEbw5qQt++rOMDXJapU6/698H+9H+SCljYNRLENo0AeZlZWUcPHiQIUOGNMnxZc4d2TUjczyiKLUCX/MGlOytX6/zR5gyl5Ivf0OXmkLwpHGSa0DnLz3d5KyH3A3S003CAJjwWbNMd/78+ezZs4d27dpx/fXXN8s5m5Jjb94dO7xHRNBI+PNJ2PWDNKDNcLj2S/BumRgYW3o6hY8/gSMzE4CgqVMJe+xRFJrjb0YWSy6VlX9hMh/GbM7AZDqM223ybO/U8QPCw8cCUF6+gn1p09HrozDo4zB4xWHQx2IwxEnCxSsRlcqred6kzEkRRZHvNuXyyu8HcLpF4oO9+OSmHnSMOofaMeYKWP2aVKlVdEsPMI+kgW/TV+Q1mUwsXbqUyy+/XHbVtDCtRoi89tpr/Prrr6Snp2MwGOjfvz9vvPEGqampZ7S/LEQaicIdsPBhKN0nLWu8pU6bHa7GQSwFjzyG/fBhFDodbVeuQH2igFBRlNL2/m6GZa6A/K3QrvHjBvLz85k5cyYAd9999wXvlnG77WzcNASHo5y4uLtIDpgkdT4t2w8KJQx9GgY90WQ+9TNFsNkoe+ddqr//HgBD165Ev/cumtMUlBJFEbu9GIslG4slh5CQYVK1VyAv/2syMl456b4dO7xHRMTVgFTMrbJqHT7eyfj4tEerDZU7sTYzu/NrmP7jTgprrGjVSpY9Mvjkxc9OR/lhWP68JK6v+ah+vSg2WYXWWbNmkZ6ejo+PD9dddx0JCQlNch6Z09NqhMgVV1zB9ddfT+/evXG5XDzzzDOkpaVx4MCBM6qMKQuRRqIyEz7qJQmQvvdAv+ngHYxx1V8U/etfCEYjqpAQot95B+++fU5/PFGEn6ZAxlLpWJf/X6NdWNxuN19++SUlJSV069aN8ePHN8pxWxqT6RB5+V/RLvUVlGXpMGMk6Pxg4gxIalmz8pEyI2F+eo8p3rhiBUVPP4NgNKL09yfq9dfwHTbsnI4tigJ2eylWaz5Wax5WW97R3/OxWnPp1u1r/HyltgD/FC0aTRA+Pu3w9WmPv38PAgP7o9HI14Gmpsbi4LE5ewj10fHGdV3O/4BuZ/0DTEUGzLoJRvwH2o1rdEFSVlbGL7/8Qnl5OQqFguHDhzNgwAA5q6YFaDVC5J+Ul5cTFhbGmjVrGDx48GnHy0LkHHE5JHdKm2NuHgcWQMIg8ApCdLsp/+gjKj+V3CyG7t2Jfv99NOFn2FzK7YKVL0otxAHGvgu972yUqW/cuJFly5ZhMBh44IEHLp5S7v98Cjy8FCK7NYu5+lS4BZGxH6yjtM7G57f08mRNOAoKKHzkUWxpaYQ99RTBd0xt8rlUVKyiuGQ+JtMhLJZsQGiwvWeP2QQE9AKkgFkUSvS6pq/qeykiCCIuQUSrlm7gFSY7BdVWusUGnN+B598He36Wfk8YBFe81ugVWh0OB4sXL2bvXskFnZyczIQJE/Dykl2AzUmrFSJHjhwhOTmZffv20anT8c3R7HY7drvds1xXV0dsbKwsRM6Ggh2w8AEoT4e7VkJ0jwabRUGg4P7pmFavBiDwppsI/9dTKLTasz/Xhv9JpleVFu5Yety5zpaamho+/vhjnE4nV199NT16nN/xWpqSkoXoDdEEOP3h17vhyrcgpldLT6sBv2zP58m5e/HTq1n71DACvOo/B4LDQe1vvxEwaVKzu0jcbuvR+JN06ur2UmfcS88ec1CppBoVhw6/REHBt/j4tCM4aAjBwUMJCOiJQiHXPGlsBEFk6jfb2HCkgqeuSOWugUkolef4ebAbpWDWTR+BywYooMetMPw/4NN43bRFUWTXrl388ccfuFwu/P39uemmm+ROvs1Iq0zfFQSBRx55hAEDBpxQhIAUU+Lv7+95xcbGNtf0LnxEUfqCzxwlNagyBIKl8rhhCqUSrz59UOj1RL35BhH/ee7cRAhINS9Sx4LbAXNuA0vVeb2F5cuX43Q6iYuLo1u3bud1rJbGbD7CwfR/s3PH9dT9OBSKdkrNw1pRbLjN6ebd5YcBmD6sbQMRAqDUagmcXF/Azm0ykz/9AWyHDzf53FQqA35+XYiKmky7dq/Qp/dCjwgBcDoqAQUmUzq5eZ+zc9cNrN8wkMOHX6a2dve5paDKnBCHW8BHp8YliLz6Rzq3fb2VsjrbuR1M5yu5ZR7YBh0nAKJUNv7DHrD1y0abs0KhoEePHtx1110EBQWhUqnkh9lWTLNZRKZNm8aff/7J+vXrT9q0SLaInCPWGvjtfjj0u7TcaSKMeQu865tFiQ6HR3CIooizsBBtYzSPstbAF0OgOkdqE379z+ccdFlbW8uyZcsYMmTIBf3kIghOtm+/FqPpAEFVDrql1aFIGCRlxfhFtvT0PPzdTyY6wMDKx4eg15zamlDy8itU//gjCi8vol57Db/LRzfTTE+Mw1FFVdV6KivXUFH5Fy5XLQA6bTgDBqyTrSONiCiK/LQ1j5cXH8DmFAjy1vLWdV0Y0f48XYu5G2HJv6F4D4z4Lwx6rHEmfAw2mw2z2expnieKIk6nE+25PoDJnBGtzjXzwAMPsGDBAtauXUti4ombbJ0IOUbkDCjZB7NvgepsyUUy5g3oOdUTjyCKIlXffEvt/PnE//QjqqZIaSveAzNGgd4P7loBgQmNf44LiMy9T5NTMQe1U6Dfjhp0lz0JQ/7V5BVTzwa7y83gN/+itM7Oa9d25oY+cafdx1VdTeFjj2HZtBmAkAceIGT6/a0is0UQHFRWraO0dDEGfQxt2jwO/F1E7r+EhY0hMLB/q5jrhcyRMiMP/rybg8VSnZBb+sXz7Nj2pxWxp0QQpHLxHa4G9dGaQUW7QOsLIW0bYdYN2bx5M1u3bmXy5MlENEPn8EuVVuOaEUWRBx54gPnz57Nq1aqzEiEyZ0jOekmE+MfCHUug1x31IsThoPi55yh74w3shw9Tu3Bh08whsitM/lYqdnYOIqSy8ngX0oVKbfav5JbPBqBdgRrd9fNh2DOtSoQAzNtRSGmdnQg/Pdf2OLP0aHVgIHFffknQ7bcDUPHRRxQ9/jiC7RzN9I2IUqklNGQEnTq+5xEhAJWVayks+pldu29l85bRFBb+jNttP8WRZE5F2zBffpven7sGStfydRnluIXzfJZVKqHLpHoR4nbB/GnwST8pBq0RKzq7XC62bt1KVVUVM2bMYOfOnbIbrxXQpBaR+++/n59++okFCxY0qB3i7++PwWA47f6yReQMEEUpaLTHreBV3yfCXVtLwUMPY9myBZRKwv/9bwJvubnVPRHm5eXx9ddf06lTJ8aPH49K1bpu2GeD221hy9arsFpzCLcG0mnokhYrUHY6XvvjIF+uy+K5sR24Y+DZPyDUzJtH8QsvgtOJvlMnYj7++MyzrpoRiyWH/PxvKC6Z7ym6ptWGEhs7lZjoG1GrfVt4hhcu6zLK8Tdo6BITAEhBrSKgOtdA1r8xV8Jv90HGMmnZNxJGvQydr2uUdF+LxcL8+fPJyJDaW3Tt2pWxY8fKrppGptW4Zk520/v666+5/ehT1amQhcgJcLtg04fQ+27QndjN4sjPJ//e+3BkZaH08iL6/ffwOYN06UZBFOHgIrDVQo9bTjnUbrfz2WefUV1dTdeuXZkwYULzzLGxObICYnqTX7GAw4dfRKcNo2+fP9FoA1p6Zqcku8JMuJ8OL+25lV83b91K4UMPg0ZN4i+/oGnFZm6Xy0xR8Rzy8mZgt5cAoFL50Kf3b3h5yZbaxmDm+myWppXwzuSuxAY1QqrsoSVS/Eh1trQcPwDGvAkRJ052OBsEQWDDhg2sWrUKURQJDQ1l8uTJhIY2XubOpU6rESLniyxE/oHDDHPvkHrEpFwBN8w67gnBmraf/HvuwV1VhToigtjPPkXfrul7w3g4vAx+mgRaHyky3u/kVTkXLVrEjh078Pf3Z9q0aej1Tdc+vElwmGHZc7D9K+h6A+L4Tyks/AkvrwRPr5WLHUd+Pu7aOgydOrb0VM4IQXBQWrqInNwvUKkM9O413/PAJIpuOcD1HLE4XAx64y8qzQ58dGpeuLojE3tEn78F1mmTHrzWviP1Y1Ko4O5VENWtUeadnZ3N3LlzMZvN6PV6Hn744TOy1sucnlYTIyLTiFiq4JtxkghR66H7zSc0U6pDQ1BoNOg7dCBh9uzmFSEAbUdCTG9wmKSb9Ek4fPgwO3bsAGD8+PFnJUIEUcDitFBrr8XitOASXKffqbHJ3wafDZRECIAhEIUoEhNzU6sWIfsKasmpMDfa8bSxsQ1ESN2yZVR+9XWr9bsrlVoiIyfSr++fdO06w3OjdLmMbNw0gqys93G5WqbL9IWMl1bN/PsH0Cs+EJPdxRO/7OHe73dQYTrPeByNHgY/KT3UdLgG4vtLMWmNRGJiIvfddx8JCQkMGjRIFiEthGwRuRAwlcP346E0DQxBkiUkru9Jh9uzs9GEh6NsqUqCRbvhi6GACLctgsSGbiGLxcInn3yCyWSiX79+XHHFFYAU3FxuLSejOoPs2mwGRA8g0V8ymy/NWcrLm1/G5rJhP0Gw4bN9n+X6dlJzvKzaLD7c+SFhXmFEeEfQJqANqYGphHmFnf8TmsMCf/2f1GVUFHD7R5E9eCQJXV9t9fEGoihyzccbSCus5X/Xd+eqrqfuIXO2OAoKyRo3DtFmI2DKFCKee/aETfNaI/kF33P48AsAqNX+xMfdQ2zsrXJDvrPELYh8vjaT95YfxukWCfbW8uq1nbm8YyO57ZxW0BwVC9YaWPSw1KvpPDuCC4KAQqHwXB/Ky8tRq9UEBgae54QvXc7m/i335m7tGEvgu2ukSqk+4XDrwgZfOlEUKX/vffQd2uN39Iaua+nspKhuUsn3bTPg9ydg2ob6XhPA77//jslkIig4CJLhja1vcKDyAEdqjlDnqPOMe0nzkkeI+Gp9qbXXnvSUOpXO83tubS4r8lYcNyZQF0hKUAo3tLuBEXEjzv59le6HWTdKNVMAsctkDiX7UFy+kJo9ZfTsMavVBQMfy/ojFewtqEWvUdK/TfDpdzhLNNFRhD7yMGVvvEnN7Nk4CwqIfv89VL6tW6ABxETfhFYbTFbW/7BYjpCZ9RZ5+V+RkDCN6KgbUR3z+ZI5OSqlgvuHtmVoShiPzdlNeomRB37ayV9PDCUmsBFEneYYi8WaN+DAb1JX8QEPSZYTzblZNI7tRWO325k9ezYmk4nx48fTrrmtypcgskWkNSOK8NXlkL8FfKMk68IxefWi00nxc/+hdsECFFotbZb8edpOqc2GtRo+7ClVdx31Mgx4CIvTglNwUppbyuLFi0kZnsLTe55usJtSoSTeL542/m2YlDqJ/lH9pcO5rBSbitGr9dJLpUer0uIUnDjcDnQqHXq15N7JN+azrmAdZZYyikxFHK4+TE5dDm7RDcA7Q95hdIJUjOtI9RE2FG1gVPwoonxO87ezVMHHfSVRNe59Cr2rSD/0LKCke7dvWrVLBmDK55vYkl3F1AEJ/PeqpovpMK5cSeETTyJareiSk4n9/LPW87k8DaLopqRkIdnZH2C15QGg10XRr99S2Tpylthdbt5fkYGvXs39Qxu/HgjVufDnv+Dwn9JyYAKMfUdyD58HRqOR2bNnU1BQAMCAAQMYPnz4BZ3R1xLIwaoXE8V7YMEDMPk7CKq3dAgWCwUPP4J53TpQqYh86UUCJk5swYmegF0/ULXoQVb7BfBXh9FsKtvB1E5Tmd5tOi6XC4tgYeqSqXQP607X0K4kByaT6J/YwLrRWNhcNjJrMkmvSmdk/Ej8df4AfLrnUz7Z/QkAPcN7Mi5pHKMTRuOn9ZMKLR1eAqlj6uNxCndCcFvqHDls3zEFUXTQJulJEhLua/Q5NyY786q59pONaFQK1j41jEj/pvWFW/fvp+C+abjKy1GFhhD76WcXTEArSNVxi4vnkp3zEYEB/ejY8R3PNjmo9dxJK6zlp615PHNle3x0jWCQF0VIXwx/PAXGImldx2vhitfPq6Gky+Vi+fLlbNmyBYC4uDiuu+66S/c+dA7IQuRC55+dWv+x7K6tJf++aVh37UJhMBDz/nv4DGnZVvLH4hScrCtYx/yM+awvWIMLEbWgRufW0TOxJx+P+Lilp+hhac5SZh+azfaS7UhVEECr1DI8tDu3FWbQKX83TJwp1TA4itWaz46d12O3lxAaMorOnT9t1S4ZgHu+286yA6VM6hnDW5MaL9jvVDiLi8m/9z7shw8TdOcdhD/5ZLOctzERBDsulxmtVqrRYzZnsXv3bcTG3k5U1BTU6iaoVHyRIggiV36wjvQSI9EBBt68rgsD2jZSnR27Ef56DbZ8CqIg1VW6+sPzPuz+/ftZsGABDocDb29vJk6cSFJSUiNM+OJHFiIXMuYK+PkGGP3KCQNSnWVl5N95F/aMDJR+fsR+/hle3bu3wERPjCAKjJs/jnxjvmdd+8D2dC/ujlApMHnSZJKTk1twhiemxFzC71m/szhjPkeMuQAYBIG/SmrwHv0q9LwNAKu1kJ27bsBmK8TLqy29e81t9UGqR8qMjHx3LQoFLH90MG3Dmm++bpOJ6h9+IPjuu1FcBKbtQ4dfoKDgewDUal+io28mNuY2dDq5/sSZsDmrkifn7iG/ygrADX3ieObKdvjqTxzULAhOzJZMDPpoz/esunoLubmf4RbsiKILrTYEnS4CvS4CndWO344/8Lrmu/puvv98sDtLKioq+OWXXygtLSUhIYHbbrut1T94tAbkYNULFWsNfD8BSvbCgulw/2ZQNfwX1c6bhz0jA3VoKLEzZqBPTWmZuR5FFEUOVx8mNUiqnKtUKOkZ3hOL08JVba5ifNvxFKcVs2LnClQqJV6OSqD1CZEIpY47S/K448B20pUufvDzJTgoGe/pKzyN6naU7qCdTxCiKGAwJNCj+/etXoQAZJab8dOr6ZcU3KwiBEDl40PIffVuK9HhoPrnnwm88cYLJqPmWJLbPo2PT3vy8mZgsWSRm/speXkziQgfR3T0Dfj5dZdvUqegX1IwSx4ezBtL0vluUy4/b81j9aEyXru2M0NTwxBFN7W1u6ioWElV1QZM5sOIopPOnT4mLEwKxnc4q6isWnvSc6QMeQGvoyLEZi+hbsk9BAb2QzPgqeOup2dCSEgId911FytXrmTAgAHy/7cJkC0irQWHWRIh+VvAOxSm/gkhx9+wRUGg/L33CJg8GW1sbAtMVEIQBVblreLrtK/ZW7GXWWNn0TFEigGotdfipfFCo9SQlZXF999/jyiKjFOto1eYS2qMp2plN6HvxkPWX9Lvsf1g5AuIcf08F50dpTu4fcntdAntwmNdbqVjSBf0+tbTSfd0mOwujDZnk8eGnI6iZ5+ldt6veA8YcMFk1JwIURSoqFhJbt4X1NbuBECrDWFA//Uola3ss91K2ZxVyb/m7SW30kKEVymvjd6FyrkJp7O6wTiVyofk5GeIjpoCSFbJ6ppNqJR6UKhwOCqw20uw20qw2YtJSXkeXx8p06Vw7yukV3yNQhAJsOkJTbyFkKSbMRjO/9q5bt062rRpQ9QFEojd3MiumQsNlx1+mgxZq0HvD7f/DhGdPZvtWVloY2JQtIJeCKIosq5wHR/u+pD0qnRAiql4pu8zTExpGCz7d2Mpi8VCt44pXHPkaRT2Ginvf+i/W2D2x2Aqk8SQ4WidgKw1sORpGPE8pFzewJRrt5exLOMbXt4zF6tLMimPih/FIz0eIc6vYdda0S3gqrLhqrDiqrDirrHjNjvxH52AOkjK6rHsLce4tgClToVCr0YdoEPfPghdoj8K1cVdY9C4ahWFjz+BaLWibduG2M8+QxsT09LTOi9qa3dRWPgTBkMciYkPAiAILg6m/5uQ4GGEhAyTM27+gSA4cbpqcRPA20sPU1BxiCnxTwBSHZfg4CGEBA/D378Hev25V2gtLv6VnMNvYnGXN1jv492OiMjxREVOQaM5+3vLwYMHmT17NiqVirFjx9KjR49zmt/FjCxELiQEAebdAfvnS2XRb10AMb08my07d5F/zz14DxxI9NtvoVC3nDdtW8k2Ptj5AbvLdwPgrfHmxnY3cmP7GwkxNAw6M5lMzJw5k+rqaiIjI7njjjvQpC+AeXeCUg23LYb4y5r/TVQcgU0fwe6fYMDDMPzZ+m2CIHUCPYa6un3s3XcfDkcl8Slv8H3uLuYfmQ+CiEap4d5u93F7p9tx7KzCuDofV5UNTtCNNOSuzujbBgBgXFtA7R/Zx41R6FXoU4PwGxmHJvT8b1w1Fgd7CmoZnBzSqszJ1v37KZh2P66yMlRBQcR89CFeF9mFvLJqPbt3S3FFSqVeEiShIwkK7I9O1/qaAzYHbreVqqp1lJevoLxiJYEBvenS5TMAnG6BosKZ+Pl2QWPoyv/9kcHDI5KJ8G+ctg+W8u1UbHyKcncGtf4aRIUCBUoGDNyETnv2AbNWq5X58+dz+PBhAHr27MmYMWNQt+D1ubUhC5ELiS1fwJ9PglIDN8+FpKGeTebNm8m/fzqixYKhV0/iPv8cpbd3i0zT6rIyZt4YKm2V6FQ6bmx3I1M7TSVQf+LKg0uXLmXTpk0EBARw55134vu3Cf6X2yXRpTbApK+l1NimxmmTGvHt/BZy1tWvTx4NN/1y0t1KSxdz4OC/EAQbBk0iKcrXUZX6Y8yvxF1q5dmYD9nnnUH/qP68G/gS1XOli5JCo0QdYkAdakAVqEflrcHQKcRjEXFV2XCWWRBtLgSbG0eBEVt6FYLJCUDEU709Y8+HD1Zm8O7yw4zvFsX717eegGYAZ2kp+dOmYT9wEDQaIl98kYBrL9CmhyfAas2jsGgOZWW/Y7XmNdjm7Z1CSsrzBAW2gBBvZszmLGpqtlBRuZqqqvUIgs2zTa+P5rJ+K49zZb28+AAz12fjq1Pz1Jh23NQnDuX5dvQFKWj1wG84lzxBqY8JW0AQba/b54kb2Zf2EDptKNHRN+Lt3ea0hxMEgfXr17Nq1SoAoqKimDx5MgEBAec/14sAWYhcSDhtMP9eaDcOukzyrDatXUvBgw8h2u14DxhAzEcfomzmPggWpwWD2uB5ml6UuYg95Xu4p8s9hHmd+qnO7XazdOlS+vTpQ0jIMU8cDrMkRjKWgUIJY9+FXlOb7k2seQs2fywVWANAIQmQAQ9LfSv+YSkQBREUIlnZ/yMn5yMAvMu7ELnvPlSuhlaKggFWnjS/zLP9nmVU8HCcJWY0YV4o/bRnbYEQBRFHgRFHbh2+g+pdFeadpejbBqLyOzu3nNXhZsAbq6gyO/jf9d24plv0We3fHAgWC0X/fhrjsmUofX1ps2wp6ouspLYoihhN+ykrW0JV1TqMxv2ASJ/ei/D17QBASclCysqX4OfbGR+fVLy8EtHrYy6oWBNBcGGzFWCxZBMcPNTz+d+1+3aqqurFv14fQ2jISEJCRxLg3xul8ngLQnpJHf+at489+TUAdI8L4NUJnWkf2Uj3AHMF/P4Y9LrD8+BnseSyafNwz5DAgH5Ex9xMaMioE87xWI4cOcK8efOwWq14eXlx3XXXySm+yELkwuMf6WXGVX9R+PDDiE4nPsOHE/3+eyibMT5EFEX+yP6Dd7e/yxO9n2BM4plZLf7+KJ32Jux2wuJHYNcP0O1muOaj80qvO2YCUsGxqG6gPJoq+vsTsO1L8IuRGgV2vxkCYhFFEXeVDUeRCWehWfpZZMJrdCC5+nepqJBKxAfmXEHo4cmo/fRoonzQRHp7XupgA0aXEV+Nr+c9byvZRrA+mKSA878QOQpNlH20C4VWhf+YBLz7Rp6xwPlqfTYvLT5AbJCBvx4firqVxp6IgkDFRx9j6NEDn4GtuzJtY+BwVFFTs5XQ0NEoFNL/5MDBf1Nc3NAyp1Co0OujMRji6djhbbRH3Qcm02EcjgrUah/Ual9UKh/Uam8UCu1pb5inQxRFRNGJIDgQBAei6MTttuB2W/D2botSKRUarKxaT3X1ZhyOChyOiqMCJBdRdAAwcMBGdDqpmFhu7hdUVK4mMPAyQkNG4uPT7ow+w25B5IfNuby19BAmuwuVUsFdgxJ5eEQyXtrGd3+IO7+j0rSbQn8jFZWrAQGQhFNs7O1ERU46Zc2Y6upqZs+eTUlJCZMmTaJjxwuneF9TIQuR1k72Wikwddhzx8UkGFeupOCRR8HpxPfyy6W4kGZMcywyFfHSppfYULQBgF7hvfj6iq9Pu58oiixduhS3282YMWMa9G44yQ6wdzZ0mlifQVOVDQFx9SLiTKgtkAJNs1ZD9howlUrBvgkDpe2l+6G2ENqOAKUKZ7mFmt+O4Cg0I9qO79prHbyLPP3/UCi0pLZ9iWDbSDSR3qh8Ti8EyyxlXLfwOmxuG0/3eZrxbcefV2yGs8RM1dzDOAtMABi6hhI4MRml9tR/H6vDzaA3/6LCZOfVCZ25sW/cKce3NsxbtqIODUF3iTxV1tXtpbpmC8a6NMyWLCyWbATB6tk+ZPAez03wYPozFBXNPsmRlAw8JuYh48jrFBfPOyp4FICIKApHf4r07fs7ep3UjC4j41Xy8meedI6X9VuJl1cCAEeOvElu3ufHn12pw8srkY4d3sPHp3HKCpTU2nhx0X7+TCsB4LbL4nnxmk6NcmwPxhKpHYXDBAmDsF35AoXGNRQW/ezJ4GmX+n9ER19/ysM4nU4yMjLo0KFD487vAkWuI9KaKT8Ms24Gey34RkKfuxtsVnp7o1Aq8b3ySqLefKPZglPdgpuf03/mg10fYHVZ0Sq13Nv1Xm7reNtp9xUEgT/++IPt27cDkJqaStu2p+ktoVBA12O+2IIbvrpCctd0ulYq0+wTKgW2KtWg9ZZeAKUHpIZXJXuhKqvhcbU+CCX5OOxV2POMOPJF9G064Jsi3byVejX2zKPN81QKNBHeaKN80ER7o4nyQR1+GUJOFZGRE/Hz68zZoFQoSQ1KZXPxZp7f+DybijfxfL/n8dGeW/VNTYQ3Yfd3w7ShiNo/s7HuKcdVZiH4lg6njCH5cUsuFSY70QEGrut5YWWkOPLyKHjwQXC7iXrjdXxHnl/fkAsBP78u+Pl18SyLoojDUYbFkoPVlo9KVR8XplH74+2djMtlxOUy4Xabgb+fJQWUivqHFrfLhNNZddLzisIxQvwEglmhUKFUGlCpvBBEp2d9QEBv3IIVrTYErTYEvS4KL68k9PpIj5WnsYjw1/PpzT1ZebCUN5cc4v5hx/TaEsXGCcL2CYfLX5Wy5nLWoZ95LW3Gvk3CZWspLv2NkpLfiIgY7xleW7sbnS4Mvb5h2q5Go2kgQurq6li0aBFjx46V40ZOg2wRaU7MlTBjBFRnQ2xfqZOu5vgbii09HV3bts0mQrJqsvjPhv+wt2IvIPVceeGyF0jwTzjtvm63m4ULF7Jnzx4Arr766nNLZSs/DDNHgu0kHXYHPAKjXpR+L9kHnx21eCiUiJG9segmYXen4qgy4KqwNdhVlxJI6B31T1HmXWVowrzQhHthtOwnO+cjOnZ4p1HKdQuiwFdpX/HRro9wi25ifWN5f9j7pASe3xOiPbuWyh8PIpicKL3UBN3QDn3y8fEUFoeLQW/8RaXZwRsTOzOl94VlDXFVVFD4yKNYjora4Gn3EfrAAxdFVdamQBQF3G6rx6Wi1YZ4xIDdXorTWSO1LhDFesuIQoECBQZDHEqlZOlzuYy4BTtKhRalUotSqWl1/XT+KTwembWLuCAvpg1ti+E0VsIzojITfr0HCqXPHp0mSjFshoBj5uBm85bLsVoLiIycSEL8fSetSfLjjz+SkZGBl5cXU6ZMIT4+/vzneAEhu2ZaIy67VDQrb6PkfrhrlacEcd3SZejaJKE7nRWhidhQuIH7VtyHj8aHR3s+ynUp16E8gycbt9vNr7/+yv79+1EoFFx77bV07nx2VoQGuOyQsRz2zZFcLS47CC7pNehxGPE8oiDizK9C2LUIfccYiO2NqPWj6MVNiHa351DqEAPaWF+0cb5o4/3QRjUUGS6Xkcys946W6xaIibmN1JTnz33u/2B32W6eWvsUxeZiDGoDrwx4xdPx91xx1dqp/P4AzgITAVe3waf/8YWUMstNTP9xJxaHm5WPD0HTSmNDToXodFL61ltUfyeVUvcePIjoN99EJT9VyhxlT34N13wsuY+j/PU8fWV7xnU58xiqk+J2wbq3Yc2bILohIB7u3+SxxtodFaSlPURNjdQMT6FQExV1PYkJ049Ly66pqWHWrFmUlJSgVCoZN27cJVVvRBYirQ1RhN/uhz0/gc4P7lwGYe0BqPvzTwqfeBJVQACJv8xptnbpTrcTzTHVTeccmsOQmCGEe59Zx0q73c68efM4fPgwSqWSSZMm0b59+0afpyiIOEvM2I9UY8+qw55Ti2hzow7WE/Fkb8+4mj+yUagUkuiI9UXlfeK4GlEUKSv/k8OHX8bhKAMgPPxqUpKf9QQENhY1thqeWPsEW4q3cFXSVbw66NXzPqboFLDsKcerZ5jnoivYXSiP6WQqCCLFdTaiA1q2iur5UrtwIcX/eR7RbkcdFUnMu+9i6Natpacl0woQRZElaSW88vtBCmukeJreCYE8P64jnWP8z/8EBdulmkcdr4WR/z1uc03NdrKzP6Sqej0ASqWB2NjbiY+7p0GBNIfDwW+//caBAwcA6NevH6NGjUJ1CVj4ZCHS2lj3Lqx8ERQquGkOtJX83nVLllL4+OPgduM/YQKR//cKitMFeZ4noijy25Hf+Hj3x3w35juifM5N+BQWFjJz5kyUSiVTpkxpkkZ2NYuzsOwqRTA3DCpV6FToEv0Jvqk9Cs2Z/72MpnSOHHndk05oMCTQLvUlgoKaLlvDJbj46eBPTE6djF7dOMWZjkWwuih9fweGjiH4XR7fQJCcCaJbxF1rx210oIuv/45Z06tw19lR+WpR+WrRRHq3SNVX28GDFDzyCM7cPAJvvJGI5//T7HOQab3YnG6+WJvFp6szsTrdKBRwXY8YnhvbAX+v8wzyt9WBxlAfTF+dI8Wr+dfHXVVXb+ZI5tvU1e0CoFvXrwgObtgJXRRF1qxZw+rVqwFo06YN1113HYZmLsfQ3MjBqq0Nv2hQaaWAqL9FyNJl9SLkmmuIfOXlJhchNbYaXtz0IivypNTUHw/+yJO9z601e3R0NOPHjycgIIC4uPOLQxDsLuyZtdgza/C/MtFzwxOdbgSzC4VWiS7RH12bAHRJ/miifFCcQ4GjgoLvqKpah0KhJSH+PuLj70Ol0p3X3E+HWqnm1o63epYFUeDd7e8yJXUKsX7n3+/CeqASd60D08YiqraX4JMahHdKILo2AccFtAoON64KK84CE45CI44CE84SM7hFUCuIfmmA5+9q3lqC7UClZ1+lnxafy6Lw7hNxUmtTU6Bv357EefOo/OJLQqbf32znlbkw0GtUPDQimUm9Ynjjz3R+213ExsxKdGfxgHLygx9z83Q5pPpH1Tkw/jNIlRrwBQb2o1fPX6ioWEFF5V8EBQ327GKzFaHTSe6ioUOHEhoayvz58zEaja2q0nFrQLaINBdV2RCUCIBxxQopRdflwu/qq4h67bUmD8bbXLyZZ9c9S5m1DLVSzfRu05nacSqqM0yVFUWRbdu2ERcXR0RExHnNRRRFXKUWbIeqsB2qxp5T5ymLHnpfF3QJkmnVWWpGsLrQxvqe09O43V6OKDo90e12eylHjrxJYuKDnlTE5mbGvhn8b+f/CNAF8P6w9+kZ3vO8j2nLqCb3p4N4W90N1qsCdEQ83hOFRvofV805hGVn2fEHUCtQB+oJm9YV5dGnyLq/8nHk1uE2OnBV2jypzgqNEq+e4QRc3eacxGBjILrdFD35FAGTJ+Pdr2+LzEGmdbIjtxqz3cXgFCn+zi2ILN5bxNjOkedXS8dUJvUDK5IsH1z2AIz4L6hPnNbvcFSxafMI/Hy7kJz8rCeduaioCC8vr0sii0Z2zbQGrNVS4NPRgNS/MW/ZSt5dd4HTid+4cUS98XqTihCH28FHuz7im/3fICKS4JfA64Nfp2PwmRfcsVgs/PHHH6SlpREQEMB9992HXn9ubgbr/kpqFhzBXedosF4VrEefHIjPZZFows+vjL3ZnEVe/gyKi+cTHDyYrl2Or3nQUpRbynlw1YPsr9yPRqnhxf4vclWbq87rmBUmO6PeWk28XeSZjtEkGKWy8QgQ+UwfVH6S1admUSbmHWVoo73RxPiijfZBG+2DKlB/SlEhuqS4FNP6QpzFZvQdggm5teVqJVT98COlr7wCCgVBU6cS+sjDzVrwT+bCYfa2PP41bx9JId48NjqFKztFnnu5eJcdVrwAmz+RlqN6SG0qAhOOG1pevoJ9aQ8iig4UChWxsXeQlPjQcc0PN2/ejK+v70VZAE0WIi2N2wU/XgcVGXDDzxBZXyPAbTSSf/c9qCMjiH6r6ZvYfZX2Fe/teA+ASSmTeKLXE3hpzryh2pEjR1iwYIHHnDhy5Ej69+9/RqZFV4UVa3oV2hgfj5XDnldH+Sd7UGiU6NoEoE8JRJ8aiDr4/PyloihSU7ud/LyZlFes4O/aCn5+3ene7ZtGSc1tLKwuK8+se8bjIrunyz080O2BczbXPvHLHubuKKBTtB8Lpg9EpVQg2F048k1o43w9BdBEQTwvK4Yoijiya1Ho1Z4sJNElSOmgquazjghmM6Wvv0HNL1I1Ul1qKlFvvYk+pXGKaMlcPMzdUcD//X6AaotUB6VjlB9PXp7KkJTQc3ePpP8Bv00DWw3o/GH8x9D++IcJqzWPjCOvUV6+DJB666SmvEBIiFRKPjc3l6+/lopFjhgxgoEDB15ULhtZiLQ0S5+VOrxqvKQMmYiGKa2C2YxCq22Wiql2t537V9zPje1vZETciDPfz25n+fLlniJlwcHBTJgwgZhTtGwX3SKO3Fqs6VXYDlbhKpei2b17RxA4UQpmFQUR+5EaqeV9Y/hxgZKSBWRlf4DVmuNZFxIykvi4u/H379kqv9yCKPDBzg+YmSZVsxyTOIaXB7yM7ixjVnbkVjHx000AzL+/P93jmq9XiyiKVM85jNvsJPjGdij1zRtyZly1iuJnn8NdXY1CqyXk/vsJvvOOZq1ELNP6MdqczFiXzYx1WZgdkvuyT2IQj41KoV9S8LkdtCYf5t4BBVshshvcveqkFaErKv7i0OH/YrMVAhAWOoZOnf6HKCpYunQpW7ZIqcC9evVizJgxF01GjSxEWpK9c+DXo9VSJ30DHSdg2bkTW9p+gm69pclPX22r5oeDPzCt6zTUR3tPnG0FQrPZzJdffklNTQ0Affv2ZcSIEWhPYv4WnQLV8w5jPVSNaD0mw0WpQJfkj1e3ULx7nV9cybE4HBUoFFpPmlxh4c+kH3oOlcqL8LBxxMXdibd3y9RkOVvmZ8znpU0voVAo+P7K78/KZeYWRK76cD0HiuuY0iuWN67rcvqdGhFnuYWyD3YhOgXUYQZCbut43pats8VVUUHxs89hWrMGAP9rryXq1f9r1jnIXBhUmux8sjqT7zfn4nAJXJYUzM/39Dv3A7qdsPo16H6LJ/7vpEPdFrKzPyQvfyZRUdfTLvUlz7YtW7bw559/AlJV6okTJ570WnshIQuRlqJ4L8wcBS6bpwCXdV8aeVOnIphMRL39Nv7jxjbZ6TcUbuA/G/5DubWcB7o9wL1d7z3nY/3www+UlZUxfvz44zpJuqptOEstGNoFedaVvLMdV7kVpZcafWoQ+vZB6FMCG+UpWRQFzOYMKipXU1GxgtraXSQnP0tcrNS11+UyUla2lLCwMajV5xdf0hJsLt5Mrb2WyxMuP6v9vtuUw/ML9uNv0LDq8SEE+zRtBtCJcBSaqPx2P+46B6pgPeHTu3kCXpsLURSpW7iQ0rffJm7mTNlFc4Eh2O04CwtxVVQgGI24jUaEOiOCxYw2KQm/0fWFAKt//hmVvz+qgADpFRiIOjT0rFzcRTVWPl2dydXdouidIF3DKk12jpSZ6HuuFpK/2fA/CG0HKSf+LhtN6eh1UZ6HKJutGIVCRWZmBfPmzcPtdhMTE8MNN9yAt/eFdy07FlmItASWKvhiKNTkQttRcONsbBmZ5N16K+7aWrx69SL2yy9QNkHuuNVl5d3t7zLr0CwAEv0TeWPQG7QPPrMCY2azmXXr1jFo0CDPh7+urg6dTodOp0MURZxFZqwHKrEdqMRZbEahVRL1n8s87hVrehVKvQptnF+jZFO4XGaKimZTU7OVmtrtnuZTfxMddQPt2r1y3udpjRyqOoTFZaF7WPdTjiuotvDy4gMMTA7lln4tVz7aXWen7NM9uKvt6JIDCLm9U7PGjPyN4HA0CFqtnDEDbVISPsOGtUr33KWGYDZjS09HodVh6Cy1XHBVVJAxcNBJ9/G94gpi3pdi3ERRJL39CYKk1Wo0ERH4DB1KxHPPelY7y8okkXIG//vX/jjI52uz6J0QyAPDkxmcHHL2n5ncjfD1lYAIAx+DYc+C6uQCSRQFdu2+FaPxIKkp/8Vu78rPP/+MzWY791YZrQi5jkhLsPIlSYQExMO1X2DPySPvjjtw19ai79qFmM8+axIRklaRxtPrnianLgeAG9vdyCM9H8GgPv25jEYjGzduZPv27TidTpxOJ1ddJQVd+fn54cg3UrOrAOv+Sty19vodFaCJ9sFtdHhqVRxrHTlT6pt7ZWMyHUKlMhAVNRkApVJNZtZbCILj6LKegIDehIaMJCRkBHp95Fmf70Kg3FLO9JXTqbJV8dKAlxiXNO6kY2MCvfj8ll609LOEyk9H8K0dKf9kN/aMGmr/zCZgXPN3zj1WhNgzMih7731wu/EeNIjwZ55Gl3hq87lM4+IsLcWyZQvmzVuw7t2DIzMLRBHfyy8n5n/vA6AKDkah06FQq1GHhaH080Xl64fS1weltzeGTsfE14kivqNG4q6uwV1bg6umBnd1DbhcOAsKcB91JQOILheZI0ehUKvRJSej79gBfecuGDp3QpuYeFymolsQ0aqUbMup5ravttI52p/pw9oyukP4mWfZRPeUmphu/QLWvwv5W+G6meB7Yre001mDy1WHy1XD/gOPEhE+nttvf5CMjPwLXoScLbJFpLGw1sCih2HQ4zjcQeTedDOu0lJ07dsT/+03qJpg/vMz5vPiphdxi27CDGG8POBl+kf3P+1+dXV1bNiwgR07duBySTEdUVFRjBg6gqTERI+Vo+6vfOqW5gBS/QhdciCGjsHo2wWdUVErt9uO221Cq603d2ZlvY/Zkil1FrXm4HZbPNt8fNrRt8/vnuUjmW+hUfsRENAHX9+OngZdFzMWp4Wn1z3NqvxVAEzrOo1pXac1eDorN9oJ8dG2uqd8y75yqn5MB6WC8Md6oglpucqRgtlMxWefU/nNN+B0gkZD8G23Enzvvah8fVtsXpcCostF9oQJ2DOOHLdNHR6Oz7ChRL7wgmedu64Opa/vOX2eRUHAVV6Os6AApZcX+qNtJhwFBWSOuVL63/8DpZcXgTfdSNjjjzdYX1Jr44u1Wfy0NRebUwCgTag3Dw5PZnz36DOfVNo8WPgQOEzgHQbXfQWJJ7b6CIKTnNxPyc7+EBAw6OPo2Ol9/P26AmCz2aisrCQ6+izO30qQXTMtiGA2kzV+As78fLRt2xD/3Xeog87eWnAmZNZkMmnRJIbHDec//f6Dv+70PRb++OMPtm/fhii6USjcREeG0TOmHWEV3oiHFQROTMarWxhG40HslZWYdxeiiTegjtAgKF0IbhsqlYHw8Pon9SNH3sRqyz/amrwOh6MKp7MKt9uMt3cy/fou8YzdvOUKzOYMz7JCoUKvj8bbqy1+fl1ITHywcf9IFyCCKPD+zvf5Ok1K7Ts2o6bCZGfsB+sY0DaE/xvfuXG6jjYixjUFaGN90CUFtPRUAHDk5FDy2muY16wFQOXvT/A9dxN4000oz7EWjkw9ztIyTH/9hbOwkLDHH/Osz5lyPdZ9+9B36IB3v74YevbE0KkT6tDQUxytcRGdThy5udjSD2FLS8Oatg/b/gOIViuhDz9EyLRpALjKy8m/fzreffvgddllWFM78fX2Yr7fnIvR5uK2y+J58ZpOpznbP6jIgDm3QtkBUChh5Asw4OGTDq+p2c7+/Y9isxehUKhJSnyUqKip/PjjTxQWFjJ58mRSLrDYJ1mINBdVWVKX2J5T4Rg1X/nV11TPnkX899+jCQs7+f5nid1tZ1vJNgZGDwQk10Zm1R7CtTocjjLs9rKjrb+rcbpqMehjiYubjkqlQqFQsGnz5ZjN+YADhaLhv11XF0/C5hfx7htB4IRkNmwcis2Wf8J5eHklcVm/5Z7lzVvGYDYfPuFYnTacgQM3epYLCn9CcNvw8krAYEjAYIi5JCwd58KvGb/y8qaXcYkuuoZ25e3B7/LErGzWH6mgbZgPC6YPwPsse8tcqhj/+ouyd97BcSQTpZ8fbZctlbv5niOO/HyMy5ZjXLYM65490kqVipQN6z1/U3tWFuqQkCaxBJ8PosuFPTMTVUAAmnCpwWfdkiUUPvKoZ4xCo8HQowfqPn1Z49+WgWP6Excsxc7tzKvm973FTB2QQEzgaeoxOSzwxxOw+0e45mPofvMphzuddaQfepaysj/w8mpDt66/8Ouvi8nIyECpVDJ+/Hi6dGnezLjzQRYizYHTKmXIlOyTSv0OeqzBZsFiQel15oXDToUgONmat5Bf9/+PUksFTwydTefQzoiiwOo1HT1xFMfvF8+unVcwadIkEhMTWb9hIHZ78fEDRQVepNCz/RypuZlCwc6dN2Gzl6BUaj0vhUKDSuWFXh/VIP2suHgeLrcZtcoHtdoXjTYIrSYIjSYYtfrcTK4yEluKt/Do6kcxOowkew1n547RGDQqFj4wgOTw1u1icJZZsO6vxG/Y+ffUaQxEt5vaBQsRXU4CJ0uxSKIoUvf7H/iOGolS1/xZRxcSdX/8QcWXM7AfPNhgvaFrV3yGDSPw+ikXpLhzVVZiXr8e86bNmDdvxlVS0mB75OuvETB+PAD3fb+DJftLUCkVjOkUwd2DkugaG3DqE+RuhPhjXOZOq9RM7wSIokhx8Vx8fTvh69set9vNb7/9xr59+wAYO3YsvXv3PuG+rQ1ZiDQHCx6AXd+DVwjCrcsomzGL0IcfahT/s8WSTU3NNmprd1FdtxeT+TAqJJ9lsVNDUuev6B8lfbA3b7kCh6MSnS4ctSoIs0VDeZmN6moHNps3FRUJdAhpw+QHbsFszkShUFH9fRYKtwZD+wi8O4ajDWtlf1uZBuTW5fLs6tfYsGUUolvPe1O6MqH7yQvLtQbcJgclb2xDdAoET+2IIbVp3JPni2ndOvLvvgdVaAjBt91GwPXXo/JpPVV4WxJ7Zibq4GCPuKiePYeS//4XlEq8+vTBd/QofEeMRBPeeFbflkaqHpyDedNGzOs3YN6yhTZ//ul5j1ve/5KKP5eyxD+ZzREdKfcKpGd8IFMHJHBFx4jT97MxV8KXQ6HHbTDw0ZMWQTuWvLxvOXDwEJs3aQAFo0ePpn//08cCtjSyEGlqdv0AC6YDCoQpc8h/82csmzbj3f8y4r766qwP53BUodXWX6g3bBiEzV7UYIxVAIc6nJSI0XRq94JnvSi6cThczJ8/n4yMDNxuqXKgEgVx7hBS3FHEKIKJea4/SsPRAmdOt6cRmkzrp7jWytgP1lNldnBDnzhendCJxVmLuSLxCjTK1ltFtGZxFqb1haj8dYQ/1gNlK3Qj1S1bRumrr3megpW+vviPH0/gDdejS2r+zJ+WRBRFbAcOYFy+HOOy5Tiysgh/9lmCbpFcCq7qaowrVuA7ciTqwOar4NuSiE5ng0q9uVOnYtm02bOcGRDN+sjOrI/qQkzXdsy657JTH3DTJ7D0aen3xMFw7ZcnzaoBMJkOsXXb1YiiC1G8jA3rExFF1QUhRmQh0pSU7IMZI8FlQxz8DAXz8jGtXInCy4v4r7/C0LXraQ8hCA6qa7ZSWbmaioq/cLnqGDRwCwqFpKYPHnyaPUXL2WU0UuBQovNK5uE+L9E1rBsAbrebiooKwo/6OEVR5MN3P6DKWE2Q4ENbdwTJ7kgMCi3aBH+8uoTg1SOsVd4IZE7PTTM2s+FIJR2j/Jg3rT/zjszi9a2v0zW0K28OfpMon6iWnuIJERxuSt/fibvKhk//KAKubtPSUzohosNB7eLfqZwxA0dWlme9V58+xHz0YauLc2hMRJcLy9atGP9ajWnVKpyFhfUbNRqCb7+9QRDqpY49OxvTqr8wrlqFddcuEATPNnNsEj3/XIBCrcbmdJNdYaZ95D8+O6IIu3+SYkecFvAKgQmfQfKoE55PFEXy8r7gSObbgICCJHbv7s9NN93vuf63VmQh0lTYaqWiZVVZiG1HUbQ7kbrFi1FotcR+8cUpW5KLopvqmq2Uli6irGwpLleNZ5tCoaZvn98blCWfc2gO7+54l+ndpnNDuxtQoiQ/P5+0tDT279+Py+ni8YcfRecj+RoPLNqGa2MFQfigS/TH0DkEQ6cQVL5yIOiFzpasSh6ZvZtZ9/QjPtib1fmreWbdMxidRny1vrzU/yVGxo9s6WmeEFtGNRUz00ABofd1RRffCr7HJ0EUBMwbNlD98yxMq1eja9uWxAW/eWKc7FlZaBMSUCgbp0dSSyHYbJ6MIbfJTMZllyEeTXNVGAz4DBqE76hR+AwdIqc6nwJXVRWmVauoW7oM86ZNGPr2I2Hml4DUbG/J2zNQdevONVf2YVSHcDTHum3KD8PcqVCaJi1f9gCMeB7UJ45TqqrawL60B3G5atFqwuja9XP8/Fp34KosRJqKAwvhl9sQfaMpqbqKmrm/gVpNzIcf4Dts2Cl3zcx8h5zcTzzLGk0wISHDCQkehtanK9+lz6FjcEdGxEuN6VyCi2pbNfYqu0d8GI1Gz/46UcPkAVfRZrT0YXQbHVj3VWDoLIuPixGb043+GHdaoamQp9Y+xd7yvQBMSZ3Ck72fPOumec1B1ZxDWHaWoQ7zIvyh7ijUrf9G7iwqwlVe7rFwCmYzhwcMRBUQgN+YMfgMHYpXj+4XRIM9wWzGsnMX5g0bMG/cCCoVSfN/9WwvfOopFBoNvsOG4T1gQJMUXrzYcdfW4q6pQRsvVTj+ZNZ6hr0g9RxLD4xle9u+xE68hokjOhPqe/Q76rTB8v9IBdDA0xbkZFgsOezZey8WyxGUSh3t27+BzdqZ9PR0Ro8ejbKVCWRZiDQlWWson7OCim/mgkJB9Dtv43fllQ2GCIKT8ooVeHsl4eOTCkBt3R52776dsNArCA8fR2BgPxyCi1nps5ixbwY19hqifaJZOH4hWpUkJDZt2sTSpUs9x9WIKhKEMJLc4UQLgfj2iyZw/IXR3E3mzKk2O3ho1i6eHduedhEn/9w7BScf7fqIr9KkuKTkwGReG/gaqUGpzTXVM8JtdlL67g4EsxP/cUn4DrzwijNZd+8m7+57EI55GFB6e+Pd/zK8Bw3CZ8jQVhW0aVq/AdPaNVh37MSWng5HY8cAUCpJ2bjhgsxwuVCwHTpE/v+9hnPbNhSi5L5xKZTsDG9H3aCR3Pv07Wi9jgq+9D9gzRtw6wIwBJzyuC6XkbT9j1BZuZr4uMf55Zda7HY7PXr0YNy4ca1KjMhCpImxHzlC3p13EfLAdAInTfKsd7mMFBR8T37B9zgcZURGXEuHDm8Bkq9PFB0olTpcgouFmQv5ZPcnlFpKAWiva88V+isY1HEQycnJAFSUlPPZZ58R7w45Kj6C0If74tUtFK8uoc3e6VSm6Smrs3Hb19s4WFxHSrgPSx4efNoS0xsLN/L0+qepsdfw45U/0inkLIsvNQPWtApc1XZ8Lou8ICwiJ0Kw2zGtXYtpxQpM69bjrqrybIt44QUCr58CSD1OHJmZaNu0OeNeJ+c0H6sVR14+jqxMbAfTCX1gOoqjZe6Lnn6G2vnzPWM1UVF49b8Mn/798brssksm2LSlcVVUULVoMYVz5qPPrq+1FPnaawRMGC+NcQuolYr6WlSiKAmTbjdBwPGp76LopqzsT8LCxrJ3715+++03RFGkW7duXH311a1GjMhCpDExV8Jv98Hlr0FIvfXBbTKj8pGK3DgcVeQXfENBwXe4XNITk0YTTGzMLcdVCt1YuJFXt75Kbl0uBpeB9o72tHe0x1ZtA6BteAI3T7vdM7545h4ot0vio1sYmogLuyOjzMlZebCUJ+fupcrsIMRHx8939z3jWiGV1ko2F29mbFJ9d+cySxlhXq3nKf1iQhQEbPsPYFq3FvO69US88AL6VKnyZfWsWZS88CIgWU20SUloExPQREahDg7G9/LRnmJa7ro6BKMRhVaLQqNBdLsRbTYEux3BakWXmOipR2Rau5a6Zctw5hfgyM09rt5F4vxfPSXOjStXYt6wEUPPHnj16IEm8uLszXQhYc/MJOOHOSg3rqPdr7+g9PamrM7GS4/9j0EhSvrdezPxiZGw8ztY+CBofWDUi9DzDjiFuNizZyv79v2XnJxudOjQm/Hjx7cKMSILkcZCEODH6yBzJbW17VFPehfvf6RMZWV/QF7el56eKV5ebUlImEZ42JUnrBi6tXgrr8x9hURLIoHW+qcSJQqi3UEkC5H0f+oq1P6SH9FtdqI0qBulo61M68TmdPPaHwf5dlMuAO0j/fjkph4khpy76MysyWTK4imMSRzDg90fbFWCRHQLCGYnKr/WF8/SGFT99BNV33yLs6CgQVbF3yTMnuWJPan44kvK3333pMc6dmzlzJmUvfV2g+1KPz+0CQnoU1MJmnr7JZdyfCEiiqLHSvbFmiPEPHkPiXXFOJRqjrTvQ9yEIfS0fo+ycKu0Q/xAuPoDCD5x1tm+tAcpK/sDi8WftLRhtEsdyDXXXNPiYkTuvttYrHsbMldSV+RH0XojipXTSPhlDvrUeh+8AiVutwVfn44kJEwnNHSUJw3XKTj5M/tPjHYjN3W4CYA+kX0YKA7EYpWES6QQQBt3BAnuMPQqLfp2QYiOen/umTSXk7lwqTI7uOGLzRwqlSxpdw5M5KkrUtGpz6/Oy/rC9djddn478htLc5Zye8fbub3j7XhpGqfa77niKDRRNSsdpUFN6LSuF2XV3aAbbyToxhsRHA6ceXnYs7JwZOfgKivDVVmJOuIY64QCFDodosMhmeRBso4YDFKl12OeE7169yb04YdQR0aijY9Hm5CAKiDgovwbXswc+/+6o38C26ZMpmTBfCLK8uiwfyPs38ga/zD8+15Fl4BVqHPXw6cDYNgz0O9+UDW8bSckTKe2didQQrduS0hLc7BtWxR9+548i7O1IVtETkbWavhuPKYSLQXrwxBdbvwmjEf72Cg0Wn8C/HsC4HbbqK7ZTHDQEM8HzOF28NuR35i9bTaGMgMx5hgefvBhIgOkC9COhesp3ZJDG3c43ujRxvri1TMMry6hKL1aXnjYBYEKhwuHIJLoVf/U+mleGaUOJ0aXmzqXgMntxuoWsAki0XoNMzvVt1m/My2bHKsdtUJBgFpNpE5DpE5DlF5DtE7LoEBfNLKVB1EUuevb7ewpqOHtSV0Zmtp4lovdZbt5e/vb7CmX+oGEGEK4v9v9jG8zHo2qZT5n7jo7JW9vR3QIBN2QilfX1mOpaUlEUQSXC1SqCz49WObsEUWRrA3bSf/yO6J2rEXvktp26Af3J3FAGWRLTRvpNFHq5vsPbPYS9uy5C5PpIIKgpVvXzwkNHdycb+E4ZNfMeZ+4CD4fjCWnlry1YYhOAcM1Q6i90U1F5Sp8fNrTp/cCFIqGT61Wl5U5++awcvNKgquC8XfWd8Md2W0wA8cPB0Cwuyj7aDeGjlKhMU1Y8zylCqKI0eXGX1OvqF/PKibHaqfE7qTC6aLc4aLWJVlkOvsYWN673vpz2eYDZFtP3Ncm0aBlU78OnuUhW9M5ZLadcKy/WsWBgZ1QHRVuWRY7MXoN2kvgAlxutPPp6kzuHpxIpL8UbFxlduAWxPq0vkZEFEWW5y7nvR3vUWAqAKBDcAdmjZ3VYk/SdSvzqFueiypAR8TjPeUqvzIyx2CqrmXDZz8StGIR7V96Dp/+/WHnd9T98jwZwXfR9cGnUOuPv1a4XEb27ptGdfUmFAoNHTq8RXiY1CW9Jb7rsmvmfHA7Ye4d2AqqyV8XjuB0I9ySTO7ALbgq61AoNAQFDUQQnKhU9RfQFQdXMO+PeYQaQ0lC8tMqUZAghJHiiiQ+p16UKHVqwh/r2WQfjiKbgwyLnQyLjQyzjSyrnXybgyKbkw4+Bpb0qm8nvaCs+oTiQq3AIxT+5obIYGqcbvzUSnzUKvzUKryUSrRKBX7/cCW8lxpLnduNUxCpdrkptjkpsjsotjuJN2g9xxZFkcl7juAQRB5NiOCmyKCLTpCIosieglpmb8vjt11FWJ1urE43r13bGYAg76ar+6JQKBidMJqhsUOZfWg236R9w6j4UZ7PnltwU24tJ8L75GWmGxufQdGYtxbjrrFjXF+I37C4Zju3jExrxyfQn8ufvh/x39OkFQoFe8OvYXHaeiYc+YltP/1O7airGDhEi09ogNT9XaVGrfalW9eZ7D/wBGVlf5CR8Ro7d7gQRS1XXnllq3bhyULkn9jqcFTbyVsditMgYHzMG0vcAXCDr29nOrR/w1MbRBAET0BQQmACYcYwFCgIxpdUZxRt3OHo0KCJ9sG7VziiIHqCThvrQ1HhcJFvc9Ddr96qcs2uI+TbTmy5KLY3XH9PbBh2t0CETkOoVk2oVvoZoFYdN8eH4s+8pHAP/zMLtKx0urG5RSqcLp4+XMBneWU8lRjBhPBAlK34i3MmVJsdLNhdyKxt+aSX1Nef6BobwLguzZvFoFVpuaXDLUxJnYJbrI9B+iv/Lx5b/Rh9IvpwTdtrGBE3osnjSJRaFf5jEqmadQjjXwV494qQi/BdothcNvRqvWf5u/3fkWfMw+gwYnaa0Sg16NV6dCod/jp/Hu35qGesS3ChVl68t7Bjr78RfnqSO6VQXbCXQGstAQt/IH+xiH+8Fd/en+J78+uQPAqlUkenjv8jUx+LSC9WrpBcOhqNhlGjRrVaMSK7Zk6AaLOQ/cKd5A7egaB3o1BoSUp8mLi4u1AoVOw8tJPf1/yOw+HglQdf8ez35/tziCr1IVj0RWFQ49UtFO/eEWijGq+bp8UtsLnGxJoqI6urjRwy2wjVqtnbv6PnQ3br3iyyrHaSvfS09dLRxktHvEFHrF5LhFYj5ay3IhyCwI/FVbybU0K5wwVAe289H7aPo5NvywZXng+D3/yLvCopKFmnVjK2cySTe8fSNzGo1VwQ3tj6Bj8c/MGzbFAbGBk3kiGxQ+gf1R9fbdOU+BZFkfJP9uDIN+LdN4LACclNch6Z1oFbcJNdm01aZRr7K/aTXpVObl0uAfoAFo5f6Bl3/eLr2V+5/4THCNIHsWbKGs/yvcvv5UjNEbqFdqN3RG96R/QmyT+p1Xy3mgKrxcaaL2bBr7OJL8vxrPeNsRJ9S1cUV7wK4R0967dv387ixYvx9q6iZ89rGD58RLPNVY4RORecVtDUFwgTXA52774dt2ilfYc30WriWbl5JZu3bEZhrv+gT7xuPJ07dQPAeqgK09oCvHtHYOgYgkLTeC6GX0qqmFNSxZYaM45//MuSvXQs7JFM4NHYj2PTwy4kzG43M/Ir+CivFKNbwFelZHHPFFK99affuYWwOtxsy6liw5EKduXX8NNdfT2twP+7II3tudVM6R3LNV2j8W8FgcgnoshUxKLMRSzMXEieMc+zXq1Us2bKGvy00nevsT9X9uxayj/fiy45gJCpneQU9YuUp9c9zcq8lVhd1uO2aZQatt20DZVScu3+nP4zldZK/LR+eGm8cAkubC4bNrcNrUrLHZ3u8Ox7xbwrKDQVNjhekD6IfpH9uDzhcobFDrsgr4NngiiKbP19LWVffkGbwzsJSrUS0a0aUFCXci36Uc+jDU0AYMOGbzFb/o+qyhiio59n0KChzTJHWYicLQ4Lro9HUl4aTOgLP6DWS/EcTmcdJpOdP9Yu49C+Qyhd0g1GiYJkVyTt3TEkDGlPwBWJpzr6WVHrdJFmsrLPaGVKZJBHXLx4pJBP88sBiNZpGBrky5AgPwYG+hCkubjMk1VOF3emZROoVvNFx4RWZcFxugX2FtSyOauS9RkV7MitxuGurxXx8939uKxNMHC0YqLqwol3EUWR3eW7WZm7knWF6zCoDcwaN8uz/a6ld+EQHHQJ6UKnkE60CWhDvF+8pyXBueAoMKKJ9rlobxiXCiaHiZ1lO9lavJUDVQeYMXoGyqNlDJ5Z9wyLshZhUBvoENyBjsEd6RjckaSAJOJ8487ZFVhrr+VIzRF2lO5ga8lW9pTtweaWAuQ7Bnds8Nm9UB/OzoTarFy8XBVodn8AB36jttzAwY1xVI2ZyIBH78YubmVf2kOAm6qqKGJjXqFfvyFNPi9ZiJwNooj757s5/NtflFwP/ta29Lipvr/L98u+J3NjJgA+op5OrliS3ZHolBr07YLx6R+Jvu25lUvOtNhYU2Uk1+Ygz+rggMlK7jGxHbO6JjE0SHrfe4wWttWaGRLoS1sv3UX7pfob29Gbu/7ojbylLiSiKOIWRI+g+GT1Ed5ccqjBmEh/PQPbhjAwOYShqWH4G1qn5eNsMTvNeGuOVg92O+j3Uz+cgrPBGJVCRaxvLINjBvNk7yc96w9VHSJQH0igLrDFUoVlmg6z08yusl1sK9nGtpJtHKg80CD2aO5Vcz09j7JqsxAEgUT/RI/loylwuB3sLd/LqvxVtA1oy7XJ1wKSSLr+9+sZHT+aiSkTifa58HodnSm5aRs48NSLJGTlA2BR63D0akvYQ+PIqXkDcFBXG0r/AbMID0to0rm0OiHy8ccf89Zbb1FSUkLXrl358MMP6dOnz2n3aw4hIqz7lAPfvk3pdYAWlESi9P8PQ3pefnQOtcx5+1vau2KIFULQhnjh1Ssc757hJwywq3K6OGiyUu5wUepwUmp3UeZwUupwUmJ38kpyDEOCJL/7nJIqHjqYd9wxYvQauvh4MS0ujN5nGPR5MSOKIo8dyqetl57pcU1fd6LCZGddRjnrDlewNqOCF67uwLguUQDszKvmjm+20S8xmP5tgxnYNoTEEO+LXhiKokieMY+95XvZU76Hg1UHya7JxuiUgnCHxw7nf8P/5xnb+8fe2N12AHw1vgToAwjUB+Kn9aNbaDfu7Xqv59iz02ejd2iIzPbD2l2DQWPAoJZe/jp/Qr1Cm/8NyzSgzlGHTqXzdHf+YOcHfLnvywZjYn1j6RPRh14RvRgcM9jj0mtp5h2exwubXgBAgYL+0f2ZnDKZITFDmlQYtRRWi411n/2I+pcfiawuBkChFKkbFkjdhDoUShs+Pu3p1u0bdNqQJptHqxIis2fP5tZbb+Wzzz6jb9++vP/++/zyyy8cOnSIsLBT31SaWogImRtJ++QWyscASqiqiuHggYFoRANPPvdv1Ecr2JX+fpgyu0BNh0DKAzSUOFyU2p0UO5yU2p08mRjBwEBJXMwrqWL6CcTF37ydGsvNUZLpfp/Rwrs5pcQZtMTptaR46enka/C4Y2QkVlbWcdPeLAB+6JLEyODG/yzkVppZtr+UpftL2JFXfWxBS27oE8tr13YBQBCkDadrRHcpIIoi5dZysmqz0Cg19AyXivwZHUbGLxhPhbUCQTy+xPk/RUufb/sw48jzBLsCeCnmczb57vGM7RvZlxmjZ3iWr/z1SlyCCx+tD74aX/y0fvhqffHT+dEmoA2TUuqbUBaaCvHX+uOtufiFYmMiiiJF5iL2lu9lZ+lOdpXt4nD1Yf437H8MixsGwKaiTby46UVPkGifiD7NmgJ+NjjdTv7K/4u5h+eyqXiTZ320TzQ3tLuBickT8dE2XkJBa8HtcrP78w/wmjUTyiVrldjWReUjGhxKOwZDAj26/4xe3zQPd61KiPTt25fevXvz0UcfAVLKa2xsLA8++CD//ve/T7lvUwoRobqInR8Po7a/CxHIKO3G7uLBWPR+aHQR3NgzgZHdpAZSc0uqeOAMxcXmGhOPp+cTplMTrtUQdjQdNuJoZdFUbz2hWtlUfbY8e7iAmYUVBGvUrOqdSriu8f6GhTVWBry+qsG6jlF+DE4JZVByCD3jA8+75PqliCAK1NnrqLJXUWOrodpWTZ2jjnCvcPpHSz2b3IKbp9c9Ta/0NvTP7kCZoZqXu3yF2W3B6rLSJ6IP7wx9x3PM7t93xyW4Tni+3hG9+ery+qqTQ2cPpdJWiUFtINQQSqhXKBHeEUR6R5ISmMKYxDFN+we4wMiozuCDXR+wt3wvVbaq47Y/2P1B7ulyD3Dhxlzk1+UzN2Mu8zLmUWuvRalQ8se1f1zU7hpREDj07Qcof/yK0IhydJ1s7Orij+gIY3vGRCZMvp74+PhGP2+rESIOhwMvLy/mzp3L+PHjPetvu+02ampqWLBgwSn3bzIhIop8/u0tLI/rRTFRFApx2FQNMzOeUvvy2CCpydCKnApuzywg0AVBTgh0K6TfBQWBgoKhScEM7C2Z7m1mJ3v/KkCjVaHWKtHoVKi1KrR6FVqDGp9APT6BF2ezr6bE5hYYu/Mw+002hgb68lPXpHOqM2JxuFi6v4TiWhv3D63vpjz2g3X4GzRc3jGCUR3CiQownOIoMo2NYHNR8tY2BLOLgAlt8el7fJ0VURTJrs3G7DRjcpqoc9RhdBgxOozU2muJ8olicupkQBI4g2cPps5Rd8Lz/VO0TF40Ga1KS4xvDDE+McT6xnpeIYaQC/Km+08cbgc5dTlk1WRxpOYIh6oOMTh2sMeKlFuXy7j5UiVOtUJNalAqXUO70iO8Bz3CelxULjKby8bvWb+TW5fLY70e86z/fM/ndAjuwIDoAZ5g24sGUUTMXoti/XvYC1Yzt2oMGT6pKN0Cd95zD9GxMY16ulZTWbWiogK32014eMNCWOHh4aSnpx833m63Y7fbPct1dSe+iJwvgihQbU1ivWKotEIFClEk0CzgbxIINLsJiK2Pzeik0PLvX6o42aVIY6gfazU62LY4+6Tn7jIshkFTUjxjf355K3pvDXpvNQYfLV5+Wgx+0s+QWB8iEv1PeqxLCb1KyScdErhi+yFWVxv5PL+caWcRL5JfZeHbjTnM3paP0e5Cp1Zyc794/PSSZWXB9AEXVIbLxYZSr8Z3eBy1i7KoW56LV7dQlLqGlyeFQkFSwJl1l1UpVWy4YQNWl5UKSwVl1jJKzaWUWEooMZcQ6xvrGWt32zlYdRDA05fnWPpF9uPL0fXxEL8c/oUgXRARPhFEeUcRoGs9jedsLht2tx1/nXTdqLHV8J8N/yGnLod8Y36DgFIAvVrvESJxvnH8u8+/6RjckXZB7RoUGrvY0Kv1TEyZ2GBdfl0+H+/+GBGRBL8Erm93PVe1uarVxLqcNwoFQsJAdnl588e2VHwXavDX+aEVRQL9W/Y+06qCEV577TVefPHFJj+P4HIj7i7kCnbhqNBisoejs7hRiBAf6k3n2AAGJwV7xvsH6xl+SztpQZTiBERBRHBLr4ik+g+qVq+m46AoXA4Bp8ONy+7G6XDjsLlx2lx4+dcHuFpNTqx1Dqx1J66C2mlItEeI2MxOfnltG77BBvxDj77CDPiHehEY7oWqEWuWtFZSvfW82Daapw4X8GpWMQMCfehyioJnoiiyJbuKr9Zns+JgKUfDO4gL8mJijxiODV+QRUjL49M3EvPGIlyVNoyrC/C/POG8j2lQG4j1iyXWL/akY1QKFbPGzaLAWCC9TAXkG/MpMBZQbC5uEPtgd9t5edPLiNQbkg1qA2FeYYQYQhgYPZC7Ot/l2bYybyV+Wj/8df74aHzQq/XoVXr0av0pn7hFUcQlunC4HZidZhQoPBYJp9vJnMNzqLRWUmWrotJWKYkscwnV9mquTLySNwa/AYC3xpt1hes8AsRH40ObgDa0DWhLcmAy3cK6ec6pUCi4qf1NZ/cHvojQq/Xc0uEW5mfMJ6cuh9e3vs77O97n8oTLuS7lOrqGXpjdos1OMxsKN7CmYA3rCtZRY6vlxp3P4zIE4VPlpLe/Bke+Ea+OTVO88ExoVa6ZE1lEYmNjmyRGZOuCuaz76Rt8wqOxXvUYyw6UcaC43gIz655+9DtGjDQFLqebmlILNpMTm9mF1ejAYpSEiaXOQZvuoaT2k0zUFQUmZr+y9YTHUSgVdB8dx2XjJVeSIIhYah0XpQtIFEXu2p/D6iojH7eP54rQkyv5r9Zn89LiA57lQckh3DEgkSEpoXKwaSvFmlZB5Q8HQa0k4oleqANa9jPsFJxYXVbPU3GNrYaXN79MibmEInMRFdaKBuOvbnM1/zfw/wBJtPT6oddJjz02aSyvD3odkKy0A2cNRBAFnG4nTsHZQOyMih/Fu0PfBSS3U/fvuzfYfiz/tOAszFxIiCGENv5tCPMKuyBvps2JxWlhQeYC5hyaw5GaI571bw1+6//bu+/wqMrsgePf6ZPeeyUFQg81VAFFRQRBUexl17rqz7rr2tbedV131bW7urpW7IIiokjvnZCQSnpvk5nJ1Pv7IxiI0gJJJuV8nicPzJ07M2duJnPPfct5mTVglgcjOz6KoqCgtCW6j69/nE/3LsKlbh1b5af3I8b1F7aGJfD34GDmjU3oks9Ej+ma0ev1jBkzhuXLl7clIm63m+XLl3PzzTf/bn+DwYDB0D1fPCNPn83GLz+lubKUcwJque3WqRTUmPlmRxkbCmoZnxjctu8z32dR0dTCOSOjmZIS2mlXz1qdhtDY48tCA8K8OPfO0TTVWmmsstJYfeCnyoLN4sTL9+DgzfoKMx89shHvAD3hCf5EJPoTnRpIRKJ/r285UalUPDcojkani0Sv339W7E43em3re5yXHs1LP+cya1gkf5iUSGqE5zJ+cXyMQ0MwJAWgDfPq1MrEJ0qn1qE7ZHB5oDGw3eBZm8tGhbmCKksVNdYaIrwPdkO3OFsYGTaSRlsjjbZGLE5L25RmaP0ubPu/4sZkP7ge0aE0Kk272UcatYZzU89Fr9YT7BVMiDGECO8IIn0iifSJ/F1XwjnJ55z4AeiHvHXeXJx2MRcNuogd1Tv4dN+nrCldwymxp7TtsyR/CU32JmYmzCTUq+umwB6vKksVWyq3sL58PWtK1/DElCcYHzUet8vNsJopGLcPgxnlnDJhDLlVYdxe2wBASZC2RySm3TJ998orr+S1115j/PjxvPDCC3zyySdkZWX9buzIb3X19N3VH/2XDV98QmTKQC557O+H/YU4XW4ynlhOrbm1+yTYR8+sYZHMGRFFxoAQNB6+slaU1tYPjVaN8UAykr+9mu9f343ibv+r1ejURCb5M+bMROKGBB/u6XqtKlMLj367lwaLnfeuzmjb3uJwYZRl5nsVxaWg0nj+y7EruNwubC4bVqcVtUpNkLG1GKKiKBQ0FaBVaVuTH40OnVqHXqPHqDH2iJNFf+ZwOdoV5jv/6/PJrm8tbDg4eDAToycyMXoio8JHtdVa6UqNtkZ+Lv6ZrZVb2VK5pd3SDABXD7uaBd5XsOqTHOrLzQAkjgjF/5xYLsnej0OtYmZuIa+efwq+QV1zLugxs2Z+9dJLL7UVNEtPT+df//oXGRkZx3xcVycilsYG3rjpjzgddi742+PEDxv5u30URWHL/nq+3lHG4p3lbQkJQKivgSsnJvB/p/W8Bbscdhc1RSaq9psoz2ukLKceq6m1KubZN40gcXhrFl9Xbqa2pJm4IcEYfXrXtGJFUVhe28Q72RXs+nE/jVYHKhUsu/0UUsKl9aOv6K1TRUXf5HK7eH/v+3xX8N3vFugzaozMiJ/BM6c807bN5rKdUHLicDsoby6n2FRMsamYAQEDyIhqPW/mNeQx/6v5bfuqVWoGBQ1ibORYxvlMwrLKj8JttQAYfLSMPSsR1YhAFuzIo1mrYkq5mWcH+TBgTHrHD8Bx6nGJyInqjsqqy99+he1LF5MwYhTn3/foUfd1uNysy6tl8c5yvt9TQaPVwXWnJHHv7MFt92/ZX8+4xGCPt5T8lqIo1FdYKMtpIHVcBAav1l65dV/ksXXpflRqFXGDg0gdG8GA9LC2+3uyDZWNzNuTDyoV+g3VDPc28vSCEQyLkZlGfYGj0kzD4gJ8M6LwGtq147WEOBE11hrWl69nXdk61patpcZaw6zEWTw77Vmgtctt0oetNXN+rWUTagxFr9GjVWsZFjqM8weeD7QOKr3151tpsjXRaGuk0lLZbpbTnKQ5PDn1SaA1Gbr+x+sZGjKUMRFjGBU+Cj+9H3tWlbL60xycdjcqFQyfHsv4uQMoc7uYs24vtVoVI+rs/K1lP1MvvYCu1GPGiPQGY+ecR/X+QkbNmnPMfXUaNacMDOOUgWE8On8Ya/JqSAw5OHV3TW4NV/1nE2F+Bs4aFsnZw6MY20OSEpVKRXCUD8FR7UvGewfoCYryob7cTNGeOor21KH+XxYJQ0MYOD6SAemhaHrgjJKvtpdy7+e70KT44YrzITQjgi+mDkUvhcf6DMv2amz76nHVtWAcFIRK2/M+h6J/C/UKZU7SHOYkzWnrXjt0DHGpqRSzo7VrxOwwU9hU2O7xFqelLRHRa/RsKN/Q7n6jxtha28YvlsHBg9u2a9SadhWHf2Xw1uG0u4lKCeCUiwYSGuuHoig89v1eao0qUpqcXLd3NZPvvbWTjkDn6PctIp3pk83FPPZtJk0tBys/hvsZmD08ijkjohgdH9RjZ2vUV5jJ3VJFzqZK6issQGuT3h+emtLjBrha7E5m/v0XyhpbGJEUxK5BPljdCq8OSWB+xIktQCh6HrfNScWzm3E3OwiYPQC/Uzq34JIQ3cHsMFNtqabaWk21pZoaaw0OtwOX4iI5IJnTEk5r23dJ/hJ89b746/2J8okizDvsqNO8f515+eukB0VRKMqsI35IcFt3ZtPPRVQt28/zg/SM3/kDCx/4P7wDArv0PYN0zXiU3elmTV4Ni3eWs3RPBaZDkpIlt0xlSHTPfh+KolBXZmbfxkp0Bg1jZye2bncrLPtPJgNGhpI8Kgy1h1tJdpU0siyzgltnDuSfRZU8U1BBrFHH6vGD21bsFb2feXMF9YtyUOnVRNw5Fm1A35uSLsSJqCho5Kd399JidnDxAxl4/WYRVqdbQatW0by+jIav8si0rWfIdbOJTRvaLfFJInICrKYmtv+wGKfNxtRLruqU57Q73azOrebbHeXk1Zj58sZJbVnqs0uz0KjVzE+PJims5y+4VJJdz1f/2AaAb7CBETPiGDIlutvGkuwtb6KwxsxZw39f+tvicjNp/V4q7A7+lhzdLSv0iu6huBWqX9uJfX8TXsNDCbl08LEfJEQf5nYrbF5SyObFBSgKePvrOetPw9tV4ba53Vy5s4BR/t7cNSASZ5UFdYgBjbb7RmNIInICSrL28PGDf0Wj1XLty//BJ7Bzm/gPHfnf4nAx9rEfaba1tpYMjwlgXno054yMJty/Z5ZVtjTZ2fVLCXtWlrbNvtEZNAyZEs2oM+Lx6cIr1dU5NVz/3mYcboXP/zTpsINRPyqv5basYvy1ajZOGEKgrGDcZ9jLzVS9uBXcEPrHYRgHSveb6J/MDTaW/WcPpdkNAAwcH8HUCwe2m/HocCv8cUsuy5rNeKlgRcZgEg5Tc6mrdeT8LW3YB8QMGkLUwDRcTifbvv+m05//0OmHKhU8Nn8Y0weFoVGr2FXayGOL9zLhyeVc/tYGlmVWdvrrnyxvfz0Zc5O44olJzLg8jaAoHxw2FzuWF/Pe/euoLW3uktf9dmcZf3hnI2a7i7EJQcQGHX4xuoWRwcwLD+QfafH4y4DVPkUf5YPvxNZFJZvXlnk4GiE8o2hPLR8/vpHS7Aa0Bg0z/zCE0/84tF0S4lIU/rQtj2XNZvQuhYXfL8K2Y5MHoz4+ctl4gEqlYtzc8/j670+w/YfFjJ9/AXpj16zAatBqmD8qhvmjYqhttrFkVzlfbi9jy/56VuXUMDYhmNOHtBZ7c7haKyrqesi4B61Ow5DJ0QyeFEVRZh2bvi3A6XATHH1wNo7brXTKoNz31hXywNd7UBQ4e0QUzy8cieEISYZapeK1oYkn/ZqiZ/I/PQFNoBHfib/vmhOiP8jZVInV5CAk1pdZ1w4jMKL9OltuReG2XYV829SM1q3wwKYyWkr24R92pYciPn7SNXMIt9vFO3f8ifryMqZfcS1jzp7X5a95qKJaC19tL2VeegzxIa0fsiW7yrn/y93MHRHF/FExpMf1nJU+obXLqcXswMu3daCUvcXJoqc2kzYxipGnxp3QjBtFUXjhxxz+uTwHgMsnJPDQOUM7NA3apShoetBxEkKIk2FvcbL9x2JGnxmP9jfVot2Kwl8zi3ivqh6NW+GBrTU4tr7B1D9excjTZ3skXumaOUFqtYaxc84DYMuSL3E5ncd4ROeKD/Hm/05LbUtCAH7MrKTObOfddfs5999rmfHcCp5fto/86q7pCukolUrVloQAZK2roL7Cwrov8vjg4fXkbqmio7nud7sr2pKQ22am8si8409CnG6FV4qqyFifSZXN0aHXFb2D4nRj3lzR4c+VEL1JfYWZNYty2j7neqOW8XMG/C4JAdhQY+K9qnpUisJ9OxtRtr9D0qTxjJh5VneHfUKkReQ3nHY7b9z8RyyNDcz+vz8zeMr0bnndI8bjcrM6t4Yvt5WydE8lVsfBSnsjYwP48LoJeOt7Tg+b4lbI3lDB+i/zMDe2lsOPGRjI9EvTfteUeCRut8KtH29nfGIQl09M7NjrKwpnb81ha5OFa2NDeTRVak/0JYpbofrVHdiLTASem4JvhnTViL6ncGcNy97eg73FxeTzU0ifGX/EfRWHm5p39/BRixmN24l+45toI7y55PG/d9nwguMhs2ZO0qavP6O2tJjx884nOLrnnMjMNifLMiv5cnspq3JqGBYTwFc3TW67f+W+akbGBhLg7fk1Yxw2F1t/2M/2H4pwOtxodGrGzx3AqNPjD9u11Ghx4KXXtK2cezLri/xSZ+LCHXkY1CrWZQwm2qg/9oP6OHOjjZriZky1VlLGRrQNcNu3qYLS7Aa8/fV4+enw8tPjH+JFWLyvx2vFHIlpdSmN3+aj0qmJuHU02lDPfdkK0ZkURWH7smLWfpELCkSlBDDruuF4+//+O8ytKJicLnwtLqpe34mzwcry4vdpoo5Ln/gHIbFxHngHB0mJ95M07pwFng7hsHwM2rZBrjXNNqqaDi4p3mh1cM27m1FQOCU1jLNHRDFzSAT+Rs8kJTqDhoy5SQyeGMXP72dRklVPZUHTYZOLknoLV769kaHRAbxwYTpqteqkxsGcEuTLhAAf1jea+ef+Sp4e5Nk/yO7mdrmpKGiiaE8t1UUmqoubsTYdXKwxIimgLREx1baQufr3M1H0Rg3RA4OYOD+53UDknsB3UjQtmbXY8hup+ySbsBtGouqhFYuFOF4ul5uVH+0jc1Xr3+PQqdFMvXAgmsMsbeBSFO7IKmanycKn6SmEXz8Ce62F1E2nEBwd6/EkpKMkEemlQn0NhPoenBte3mglKcyHrAoTy7OqWJ5Vhf7A2jhzRkRx6uBwjyQl/qFenHNrOlnrKogfenC5aafDhUajZlVuDXd8soOaZhsWu4sqk43IgJOrpaJSqbhrQBTnbc/lg/I6bk6IIK4ftYpsWlzI5iWF7TeqICjCm8AIb7SHDCCOHxqC26VgabJjNdmxNNmpKzNjszgp3FnD1AsPrizdYnZg8NJ6/KSvUqsIWjiQyn9sxV5kwvRLCf4zetcXrxCHsludfP/Gbooz60AFU85PZcSpsYe9IHO4FW7Zu58vqhrQqGBbk5nTQwPw8jcwecBlHoj+5EnXzFFUFeazZfGXjJ17HmHxid3++icip9LEtzvL+XZnGXnV5rbtD58zlCsnJXousEMoisLSt/ewt7CB122NWNWQFunH21eNIzqw85rZz9+Wy+qGZs6PCOKlIQmd9rw9haIoVOQ1krm6jCFTY4hKbi30Vp7bwOJXdhI/JITolABC4/wIifFFZzi++iput0JNsYmK/CZGzDjYNbnklZ00VFoYdUYCAzMiPL4YonlLJfWf7gONivCb0tFH9/wKxUIcTkV+I1/8fStqjYrT/ziUpPSww+5ndbm5dncBP9aZ0LoVnvcOJKFiE2POno9W37MutmSMSCf55h9PsW/9aoZOn8msP93W7a9/MhRFYV9lM4t3lrFkdwXvX53R1tLw0cYivthWymmDwzltcARJoT7dOiV4e2Y1K1/chUYBk0rBPi6Iv1w2Ei995xYi29Zk4awt+9CqYP2EIcT2kVYRu9VJ5poyMleXtS1QOCgjkpl/GAK0DuhUFKVTx3i0mB28/7d12CytM8n8QoycenkasWnBx3hk11EUhdr399KypxZ9vB9hfxrZo6a2C9EROZsrCQjzIjzh8Oc6k9PFFTvzWddoxuBSeGaHlQHqAlat/5DEkaNZcO8j3Rzx0Uki0knKc7L54P47u6zsu6dc/tYGVuXUtN1ODPHm1LQIpg4MZXxiMD6Gruuxc7kVZj7/C6ZKC/OtBoKcKlQqGDdnAGPPSuz0Zv9Xi6qYFuzHYN/eP6DRarKz46didq0oxW5tTQi0ejUpYyMYOjW63VoTXcFudbJ7ZSnblxe3jTkZeVocE+YnHXZKYXdwNdup/zyXwNkDZNCq6FX2767FN9hAyHG05NU5nFyyI4/tJis+ToV/bLOSFm/nmy+eA5WK8+5+iAHpY7oh6uMniUgn+vBvf6Fs314mnHchky+83CMxdLbiOgvL91ayPKuK9fm1OFwHPwLeeg3bHji9rYKpw+U+6aqu2RUmIgOMBHi1jlFZl1fLayvzeOKcoexdXETW2nIAktLDOO2qweiNMnTptxRF4YOHNtBQ2doCEhTpzYhT40gdF9FtCw/+ymFzsWZRDnsODKoLjvZh9p+GExB2fNOzhejvdq8sZeWH2fgEGbjg7nGHnRVzqFKrjblrsjC7XLy0xcqI8YF89O4DOO02Jiy4mMkLL+2myI+fzJrpRGPmzKfs+b1sX/Yd4+dfgM7QMxel64i4YG+umjyAqyYPoNnmZHVONT9nVbMmr4aYQK92ZdTnvrgal1thRGwgw2P8SQj1ITbQi5ggr8PWL1EUhaI6CztLGtlV2sjW/fVs3l/PX2el8afpyQBMTA5hYnIIANFXDCY6JYAVH2STv70a278dzLt9VJc0sWeZrcQZ9Pj0krVobFYneoMG1YFZRMNOiSF7QwVjzkogaWSYxwaN6gwapl+aRuKIUH56Lwun3fW7Jcg9xZpVh0qnxpgc6OlQhPgdxa2w/qs8ti4tAiB2UBAGn6OfhhW3gte3+3l5rwmHWsXIMxL47INHcNptJIwYxcTzL+qO0LuUJCLHkDJuAgHhETRWVZK58mdGnt47KtUdL1+DllnDopg1rLUw1K8rAkNr3ZLsShOKAjlVzXy2tf1jpw8K450/jG+7PfHJ5TS3ODHZ2lekVataZ/UcyeBJ0QRF+rD0jd2MnZ3YJUnIv/ZX8nRBObfER/DXpJ5dBMvlcLN7ZSmblhQw7eJBpI5tXXdo+PSYI46k94TE4aFc/LfxmBvtPaIVy5pZS+17mai9tITfPAptcO+/aBB9h8PuYvk7meRtrQZg/NwBR/2+W1lnotbhZH54IGqDhjirQtCFA1m+/E3qy8vwCwlj9v/9GbW6d1xYHY3nvz16OLVaw+izzuHnd99gy+IvGXHamajUPbPQU2fwPWR8iI9By8Z7Z7KzpIEdxQ1klpsoqbdQWm/FZHO2dbX8qspkw+VW0GvUDI72Z3iMPyNiApmYHEJc8NGb7SOTArj0kQntxhqY6lrw66STSYq3AZcC/y6u4uKoYOI9sCz2sSiKQsGOGtYsyqGppgWA7A0VbYlITyww5uWnb9cakrmmjMrCJqZdPKhTFj7sCGNqILoYXxwlzdT+N5OwG0ei7uQB0EKcCHOjjSX/3knVfhNqjYpTL09j0IQjXxAtqqjjtqzWVpN4o57Rc5LwHhWORddM8Z6dqDVa5t5xN97+XTsurLvIGJHjYLda+N+9dzDklFMZM+dctDrPVy71tEarA7vTTZjfwRP67tJGDFo1CSE+bRVST1RduZnPnt7MwIxIpixMPempooqicMH2PFY3NHN2WABvDRtwUs/X2Rqrraz6ZB/7d9UC4O2vZ/zcAQyeFNUjE5DDMdW18P7f1uF2KSSNCuP0Pw7p9kGszgYbVS9tw93swDgkhJBL01D1kuMn+q4f38kke30FRh8dZ90wnOjUwMPupygKzxdW8mxhBQDzwwL455AEDIdc/DZWVVCZn8vACVO6I/QTJoNVu8DJlBwXHbdnVSkrPsgGBWLTgjjz2mFt1UBP1N5mK6dtysYNPDMwlitiQjsn2JO0Z1Upqz7JweVwo9aoSJ8Zz5izEnpEd0dH5W2r4oe39uB2KsQMCuTsG0ced/2SzmIrbKT6jV3gUvAaGUbwhYM8XoRN9G8tZgc//XcvkxakEBh++NZhq8vNbVlFfFXVAMDlBXb+6hdA6AWDujHSziOr73YBSUK619CpMZx1/XC0Bg0lWfUsenoz9RXmYz/wKAb7evHXAa3NoffmlLCuoWesYOwf5oXL4SZmUBAX/W08E89N7pVJCEDyqHDm/l86OqOG0uwGlr6xG5fL3a0xGBIDCLlsMGhUWHdUU//pPhR3j73eEn2Q4lbI317dtnKu0UfH7D+NOGISUmFzMH9bDl9VNaB1K9y/u4XbS134T4rB5XTy5bOPUbBtc3e+hW4liUgHuN0u9m1Yw8avFnk6lH4hKT2MBX8ZjW+wgcYqK4ue3kL+9uqTes5bEsKZFx6IU4FrdhfS4HAe+0GdzG51Urqvvu12XFow5/15NPNuSycosmet63IiYgcFcc4t6Wh1avbvrmXF/7Lp7oZXr8EhhFycBmpQ++lAriNEN7FZnSx5dRffvbqL3b+UHtdjvqysZ4fJSqBD4eXNVhaY1YRdPxJ9jC+rPvgPeZvXs/jFZ2kx94yLp84miUgHVBXk883zT7Lm4/cxN9Qf+wHipIXG+nHB3eOISg7AbnXy3au7KNxVc+wHHoFKpeIfafGM8ffmb8lRBOq6t+WhcFcNHz6ygcUv78RU19K2PSolsE+1ukUmBXDmtcNQqVVkrS2nYPuJ/85OlNewUML/bzQBZw3oU8dW9Fx1ZWYWPbWZwp01aLRqtMc5WPoKk5o/FNp5Z52ZCd5ehN+Uji7cm+x1q9iy+CsAzvzTbRh9+uYyBr2z/ddDIpNTiR44mLJ9e9n+w2ImL+ydCwz1Nt7+eubdMYp1n+VRVdRE3JCTKyvurVHzzehU1N14cmppdrD60xyyN7QOQvMPNWI12TttVlBPlDgilOmXDsJU28KAdM+Mx9FHHWxhcttdmH4qxu/UOJlNIzrdvk0VrHg/G4fNhW+QgbNuGH7Ecu0tLjcvFlVyY1w4Xi6Fhs9yuMnixDAwiJBL01AbtNSWFLH0lX8CMG7e+aSOm9idb6dbSSLSQaNnz6Ns3152/LCEjPkLe9xCQ32VRqNmysJUXA532wwap91FZUETMYM6Xnr/0CSk3GZnUUU9N8eHd8mVc+6WKlZ+lI3V5EClghGnxZFxThK6fnAyHDI52tMhtKn/PAfr9mpacuoJuWII2oCeN4Vb9D72FierPtpH1vrWi4yYQYGcec2wIxb5K26xc/XuAnaarORbbLwyNJGQywZj2VFN4DnJqDRqbBYLX/39CRy2FuKHjWBKH6nqfSSSiHRQ6viJ+IWGYaqpZu/qFQw/9QxPh9SvaA5Zwn7jNwVsW1bE4ElRTFqQckKzamxuNwu355FjsVHSYufJgbGd1lKiKAo/vLWH3M1VAARF+XDqFWldviZMT2VvcbLqkxzST4sjJKb7m5h9M6Kw5dTjKG2m6qXthF4xBH2cX7fHIfqWujIz2RsqUKlg7OxExs5OPOKU+2U1jdyyt4h6p4sgtZoLo1pbdw1JgRiSAoEDq5O/+gL1ZSX4Bodw9i13odb07YsWGSPSQWqNhlGz5gKwdclX3T4IT7RSFAW3SwEV7F1bzocPbyB/W8cHshrUam6IC0cFvFtWy61ZRTg7aYaFSqXCP8SIWq1i7OxELrx3XL9NQgDWfp5H1tpyvn99NzZr9w8SNgwIIPymUWgjvHGb7FS9thPz5kr5GxYdduhnJjIpgCkLU5l/x2jGz006bBLS4nJz374SLt9VQL3TxZBmN++tMTPZ+fu2ALfLhZevf2vRstvvwTsgsCvfSo8gdUROQEtzM6/feBUOWwvn3/cYCSPSPR1Sv1WW28DP72W1LQY3YGQoGeckdfiK+4vKem7eux+XAmeHBfDKkAT0J1BBt3RfPQZvLaGxrVfaToeLhkorobF9c5BZR1hNdj55YhPN9TYGjAzlrBuGe2QQqdvmpO6jbFr21gFgHBxM0IJUNL7SzSqOrabExC8f7GP6ZYOOa+XcQquNP+4qINPcOjj9kmIHN+9twSvYSOgVQ9BFHH6mXF1ZCcHRsZ0ae3eSOiJdzOjry9DppxGVMgh1L1lAra+KTgnkwvvHMXpWAiq1ioIdNXz02Eb2HljR93idGxHEW0MHoFepWFzdyB93F2J3H3/9i4ZKCz+8uZsvn9/WOl31QKuKVqeRJOQALz89s64bjlrb+nva9kORR+JQG7SEXD4E/zMSQKPCXmKSgmfimJwOF+u/yuPTJzZTkd/I2kW5x/U4H42aGruTYDe8sMXCHZkt+CUHEnFTerskxNpswu12td3uzUlIR0mLyAlyOhxS6r2HqS1tZtO3BezfXctlj03E58BgREuTHaOv7rjWPvmlzsRVu/KxuhWuiw3jkdSYI+6rKArleY1sX1ZEwc4aUEClai3GNvn8lOOeutff7F5Zyi8fZKNSwTm3phObdnKzoE6Go8KMy+xoW61XcSu46lvQhnh5LCbR8xRn1bHqo33UV7S2vCaNCuOUiwa2fcf8Vo3dSYhOg0qlwlFj5ZfP9xJaYiHUoeA3PQ7/mQmoNAe/j1xOBx8/dDd6L29m/9+f+8QaMh05f8tg1RMkSUjPExLjy6zrh2NpsuPtf7CZfekbu2msspAyNoLUcRGEJ/gdsUtgWrAfbw0bwBP55VwfF3bE16rIb2T1pzlUFjS1bUscHsL4uUmExcsAyKMZOjWayoJGstZVsPTNPVx433h8gzwzg0UX6cOhf8mWrVXUf56Dz7gI/E+LR+MvM2v6s4ZKC2s+y6VwZ2sdHC9/PdMuGkjy6PDD7q8oCh9W1PFgTilPD4rjvIggzJsqSMs3o/bREnxZGsaBv5/lt+K/b1Kek43Bxwe7xdInEpGOkETkJLU0N7Pr5x8YfuoZfbbYTG9zaBJib3FSW9aMzexkx/JidiwvxifQQHiCH+EJ/sQMCiIquf0f/akh/kwL9kOjUuG0uzA32mmqtuIXamwr0WxtdlBZ0IRaqyItI5KRM+MJjur9VVG7g0qlYtrFg6gpacbcaMdU1+KxROS37EVN4FYwb6jAsrUK38nR+J0Si9pbLjz6o+K9dRTurEGlVjF8Wgzj5gw44uy8khY7d2UX81OdCYDPKuo5LyKIgNMTUOwu/KfHoTlMC0rmyp/YvnQxALNv/jOBkUdelbevkq6Zk/TBfXdSnpvNtMv+yNi553k6HHEYLoeb/XtqydlcSeGOGpyOg2M/BmVEMvMPQ4DWomOfPLEJvZcWt1vB0mjDZnGyJ641sbliaBQT5icDrQnO9mVFDD0l5ojNs+LoGqut6I2aI9Zb8BRbfiONSwux729t7VLp1Hinh+MzMQr9cQxOFL2X3eqksdra1qrpdrlZ9XEOw2fEHvFCw+FWeLOkmmcLK7C43OiBm+vV3HHOULTHGENYVZjPh/f/GafDzoQFFzN54aWd/ZY8RrpmutGwU8+gPDebbUsXM/rseajVMi6gp9Ho1CSlh5GUHobD5qK6yETV/iaq9pvaVWltsTjalV0H2B+m5YuJPqgVGGt3M+HAdr1Ry/i5Sd34LvqegLD24zB6ygrXhqQAwm4YQcveOpqW7cdRbsa8qQKXyU7oVUM9HZ7oAnark50/l7D9xyL0XloufXgCGq0atUbNtEuOvPrtDpOF2/cWtc2IGe1Qc/cGE0lmNy0RFfhOPvIYM2uzia///jhOh53E9DFMPP+iTn9fvYUkIidp8NTprPrwXZqqK8nbvIHU8ZM8HZI4Cp1BQ3RqINGpgb+7zzfIwIK/jsFudaJSq/AJMGD011FfUMo31Y0872djts1BpEGa6Tvbvk0V7F1Tzpz/G9lWOdeTVCoVXkNCMA4Oxr6/iea1ZfiMi2y731Fppml5EV7DwzAOCpKS8b1Uc30Lu34pZc/KUmyW1to2Xn56THUtR1wp91BWl5tMcwuBqLhln405BTbUKvCdFovP+KN3sSx77UUaqyoJCI9g9v/9uV9fxEoicpJ0egMjZ85iwxefsHXJ15KI9GJaneawBcf+NTiBPMs+Ms0t3LCnkEXpKWhlumenaTE7WPnhPmwWJ5sXF5JxTs9paVKpVBgSAzAktv9cWHbWYD3wo9KrMaQEYUwNxJASiDbUq0e07Igjqys3s2lxAXlbq9um2gdFejP27ERSxkQccYadze1ma5OFiYGtXXSjzfBIKUzMNhHkUNBGeBN0XiqGI6wxc6gJCy6ivryUs26+Ey/f/j3AXcaIdAJTXQ1v3nw1bpeLy5/+F+GJPeeLVHSOPEsLZ27eR7PLzS3x4dyb3HPWUOkLcjZX8sObe1Cp4Ly/jCEyqWfPGnBUmDFvq8K6sxpXva3dfZpAA2HXDpcpwD3MoV1/lYVNLHpqMwDRqYGMPDWOxJGhR0xAFEVhcXUjj+SVUWl3sGp8GvFeBqrf3IUttwGVXoP/6Qn4TopC1YEWPcXtRnUChRN7g46cvyUR6STf/vMZsteuZOi0mcy68TZPhyO6wFdV9Vy/Zz8A7w0fwOmhPftk2dsse3sP+zZWEhjhzUX3j2+3rlBPpSgKjtJmWnLqseU0YNvfhEqrJvqBCW0npPqvcnFWWtDF+LZOF470QRfujaoXvL/e7teB6tnrKzD6aJlx+eC2+zYvKSRheAhhR1lvSFEUVtY381R+OdtMrTVEInVa/j00kUlBvjgqzZh+LiZg9oDjmupdX1GGtamJ6IFpJ//mejgZrOoBY2bPI2fDGlD1nEF3onPNCw9iQ4OZt0tr2NRolkSkk51y0UBKsuppqLSw5fvCXjEYWKVSoY/1Qx/rBzPicdtdOKss7a6KbbkNOKut2PIbDz5QDdpQL3SRPoRccvDk6LY6URk0Uun1JNhbnBTtqSN/ezWFu2pwtLRWK9Xq1UxZOBCdoXUsxtjZiUd9no0NzTxZUM66BjMAXgpcut/Bn4J9iAlq7ZrRRfgQfNHxJRWOlha+fu5x6spKmXPbXdKNfwhJRDpJVOogrn/l3X6xQFF/9mBKNDOC/SQJ6QIGbx1TFqbyw5t72LJ0P6njIgiK7F21WdR6TWtScoiQSwdjLzJhL2/GUWHBUWFGsTpxVlmB9glH9es7cVRb0AYZ0QQZ0QYZ0AQa0AQY0AYbfzdWRbS37ss8diwvxnXIFH2fAD2p4yNJmxDZloQcS6PDyYU78rG63egUOL/EwZW5NkLtCto4M4pLaVcZ9VgURWHpa/+ipng/PoFBRKUceSZOfySJSCeSJKTvM6jVkoR0oZQx4WStq6BoTy1Fe+p6XSJyOL92x/z6ThRFwd1kx1FpaRso+StXow2cCs5qa2sryiH3acO9iLxjbNvtmvcyUewuNP4GNH561H46NH56NL56NAH6Pj1Gpbm+hbLcBsr2NTBhfnJbkTGdXo3L4cY/zIvk9DCSRoURkeh/zBYmt6KwrqGZSYG+qFQqjGUWrqyHyiY7V+fbiWxR0EV64zcjHq/hoR1usdq65Cuy165ErdEw5/a78Q0OOeH33hdJItIFakuKsVnM/aIfsD+rsDm4I6uI2xMjGRfQ+0+YPUFr1dWBNNfbDjvFui9QqVRoAgyHrbIZdV8GrkY7zroWXPUtOOtbcDXYcDXa0AQZ2+1rL2jEfWDK6W/pIr2JuG1M2+3a9zJx212ovXVofHSofXSofbSttwMMxzXLw1PcLje1ZWaqCpsoz2ukPLeBppqD9X5iBgWROjYCgLSJUSSOCCMkxue4usctLjdfVNbzekk12eYWvhiVwsRAX2y5DVyzvrUrzZgWjO+UaAzJgSfU5V68Zye/vP82ANOvuIbYNKlF81uSiHSyzFU/891LfyciKZVLn3hexor0Yc8XVvBTnYk8i43l4wbhKysxdwr/UC/8Q/vu1fzRqDRqtMFGtMHGY+4bfFEariY7LpMNt8mBy2TH1WzHbXKgCW5//GxHS1qifIi4dXTb7cp/bcVtdqL21h5IWA4kL95aNEFGfMZEtO3rtrtQ6dSd9j3ndrmpr7Bg9NHhE9iaqOVtreaHt/a020+lgtA4P6JTAgmMOFjvwzfIiO/vl3L5nf1WG++U1PBBWS2NB1bZ9lWpKG6xMxHwHhWOy2THd1I0uuOoJ3IkTTXVfPPC0yhuN0OmziD9zDkn/Fx9mSQinSxx5Gg0Oh2V+TmU52RLq0gfdn9yNMtrm9jfYudvuaX8Iy3e0yH1OU01VvK3V5M+U47tbx1u8bQjCb5wEC6zA7fZgdvsxG12tN62OND+JulzNdhwW5yt3US/oYvyaZeIVL24DWd9S2uXkL8BjZ+u9d8DXUNew0KPGJPVZKe2tJnaUjN1Zc3UlLT+3+V0M/HcZEafmQBAeKI/eqOG8ER/Igb4E50aSGRSAHpjx05filuhurSJW/NLWeGyoxzInWIsbi4osnOhrx8DprdWWtYGGwman9Kh5z+cXcu/x9rUSFhiEjOvvUkuTI9AEpFO5u0fQNqkaez55Ue2ff+NJCJ9mL9Ww4uDE1iwPZcPy+s4PcSf2WGBng6rz7A22/no0Y04bC5C4/yIHXT8J17RnnFQ8LF3OiD8pvTWRMTiwG1xHkheWpMWzW/WBXI1O8Cp4Kq3/a6eii7KB69hobSYHdSVm2FxPhoVaAIMOLRqdm+spEVRaHGD1a1gOjC+VGfU4LS72p7HP9TINc+fctzjMhSHG2d9C866FlRqFaZEX8L0OhSHC9u/d5I72QfFR82EGicXlrs4LdQPn3HRGAd3/riNSQsvQ+/tw8CMSegMx27l6q+kjkgXqMzP5f17bkOt0XDtS2/LwKQ+7rG8Ml4qqiJYp+HncWlESAn4TvPLh9ns/qWUkFhfFt477ogFp4RnKA4XrgPdQo6GFpr2m7BUmnHW2zDZXOxudmJptAMwJ1iPxn34043dR4d7dhJh8b74h3hR8+au1jEtek1r18+Bf1Gr0AYZ8T/tYAtZ7f/24mywoViduK2tyVOxl4ofInX8GGegylfDjklDMWrUVL2yg01+KqLDfRgyKAx9rF+HZr+I4yd1RDwsIimFmLQhlGZlsuPH75i88DJPhyS60F0DIllRZ2J3s5U7s4t5b/gAaYLtJBlzk8jZVEltSTN715QxdOqRFxET3UNRFJrrbVQXmdDo1CQMDUEbbEQV4c0Xr+w+7GN8A/VUpAUzYnwkrkYbrgYbzkYbitmBq8mOd4Q3wWPC2/a3lzWjtLgO+1y6WN92iYi9xISz3kaBj5qV4VqWR3izN+DgeC2ty8V2k4UJgb6E/2kkZ3fScTiSsn172fHDEmZecxM6o7SCHA9JRLrIqFnnUJqVyc4fvyfj3AvR6uQqua/Sq9W8PCSB0zdlk2+xUeNwEqaX33dnMPrqGHf2AFZ/msOGr/NJGRuBwUu+trqTvcVJZWET5bmNVOY3Ul1swmpyAK3l0ROGtrb46o1aIpP80Rm1BEf7EBzl0/pvpA/6Dv7OQv8wDLfZgeJwozhcKHY3brsLFH7XPRQ4N5l3zSYeam5o26YBpgT5MS88kLPCAgjSdc9nxtxQzzfPP0lzfR3egUFMu+yP3fK6vZ38RXeRlHET8A0JxWm3U1daLOvP9HGDfIx8MDKJ0f4+ePeA1WP7kmHTY9i9srS14uqSQiYtOPlBhOLIFLfSNh5DURTe/9u6tsTjV2q1iqBoH0JjfdttX3DXWDrD4aYTuxWFPc1WVtY3s2p7HgujgjkvIgivISHMMPvw5OZGJgf6cmZoAGeHBRKq797Tm8vp4Jt/tCYhIbHxTFxwUbe+fm8miUgX0Wi1nHf3QwRGRqHTH3sNAtH7TQnq3ytodhWNRs3k81NY/PJOdvxUzJCp0ce1RLs4fqa6FvK3VVOUWUtzvY2LH8gAWmuehCf6U1dqJjI5gKjkAMIT/QmJ8UGr69rp6g63wuYmMxsbzGxsNLOlyUyD82B3TYhey3kRrQOYB3obyJwyDB+N56bQr/jvm5RmZaL38uacO+9D7yWf0ePVZYlIYWEhjz76KD/99BMVFRVER0dz2WWXcd9996HX64/9BH1AWHyip0MQHuBSFN4orsZfp+GSKBmo3BkShoWQlB5GSKxvW30JcXIsTXbytlaRs6mS8rzGdvc1VFnakr1Z1w5Dq+/aE7zN7SbL3ILdrbQVB7S4XJy3LZdDh7f6aNRMCvTllCA/pgcfTPxVKpVHk5DdPy9j+9LFAJx1850ER8tYpo7oskQkKysLt9vNa6+9RkpKCrt37+baa6/FbDbz3HPPddXL9kiK2011UaF0z/QTX1c18FBeGd4aNZMDfUnwkhPnyVKpVMy6fpgMAu4kmxYXsGlx4cES8yqITgkkcUQo8UODCQg7WFuks5OQfIuNHEsLe5ut7DW3sLe5hXxrC04Fxgf48PXoVAACdFqmBfnhp9UwPsCHcQE+DPX1QtfDZk5V5O7jx7f+DcDE8y8hZWyGhyPqfbosEZk1axazZs1qu52UlER2djavvPJKv0pEbBYz/7v3DhqrKmQqbz8xLzyQd0trWN9o5rasIj5LT0EtJ9CTdmgSoigKKMgqtcfJZnGguFsH/wJEDPBHcSuEJ/iROi6ClDER+AZ1TsLsUhRKW+zst9opbLFhdytcHRvWdv/CHbmUtDh+97ggrYaQ3wwq/Sg9uVNi6koupxODtw9RqYNkXMgJ6tYxIo2NjQQHH7mwjs1mw2Y7WBSnqampO8LqUgZvH7wDAqgvL2Xn8u+ZdMGlng5JdDG1SsU/B8czY1M26xrMvFNawx8P+SIWJ6d0Xz1rP8tlxKlxDMqI9HQ4PZrVZGfr0v3sXlXG8GkxTDqvdaBv3OBgLnt0AgFhHR/H4FIU6h2udoNBn84vZ0uTmeIWOyUtDhyHlKcK1WnbJSIjfL0J1NpJ8zGS5mNksK8Xg32MRBl0vbLFKyZtCJc9+QJ6Ly9UahmofiK6LRHJzc3lxRdfPGpryJNPPsnDDz/cXSF1m/Qz5xwylXchGq1M7ezrErwM3J8Uxb05pTyWX85pIf7SRdNJKvIbqdpvap3OOzocjU6+/H+rxexg27Iidv5cgtPWOsCzsqAJRVFQqVSoVKpjJiFbG83ss7RQ0uKgpMVOSYud4hY7ZTYHgToNuyYPa9t3U6OZ1Q3Nbbf1KhXxXnoSvQwkeulxK0pbq+Dbwwd0wTvufuaGenwCWwfL+oUcuZS9OLYOV1a9++67efrpp4+6z969e0lLO1javLS0lGnTpjF9+nTefPPNIz7ucC0icXFxva6y6m+5nA7euPlqzPV1nH3LX0ibPM3TIYlu4FYUFmzPZV2DmUmBvixKT5Yumk7gsLt4/2/rsDTambIwlZGnxnk6pB7DaXexbVkR25cVYT9QECw8wY/xc5OIHxrc1uLQ5HRRYLVRaLW1dqFYbTQ6Xbw17GCSsGBbLmsOSS4OpVOpyJk6HOOBqepLaxppcLiI99ITZ9QTZdCh6cOf9d0rfuSn/7zGrBtvY2DGZE+H0yN1aWXVO++8k6uuuuqo+yQlHRyUWVZWxowZM5g0aRKvv/76UR9nMBgwGPreVaNGq2PEabNYt+gDti1dLIlIP6FWqXghLZ7pG7PZ2NjMTpOVdH+Z0neydHoN4+cMYMX/stm8pJDBE6M6XDCrr1r7eR67VpQAEBTjS8LsOCaNjmxLQO7dV8I31Q1U2w+/Eq/V5cbrQHIxPsAHrUpFrFFHnFFP7IGfOKOeyN8kGmeGBnTxO+s5ynOz+fHNl3E5HNQUFUoi0gk6/NcbFhZGWNjx9XeXlpYyY8YMxowZw3/+8x/U/bj/bMTMWWz44mPKsjOpLMgjYkDPH4QlTl6Cl4F/Do4nxdvAEN/+ubR9Vxg8KYrtPxbTUGlh27IiMs7pvzPSFEWh0u4ks9nK9nQffiQAU5SBYlzYmyrJd0dgPLCeitXtbktCQnVaBngZSDjQhZLg1b6swl+Torr9vfR05oZ6vn7ucVwOB8ljJzBxwcWeDqlP6LLLiNLSUqZPn05CQgLPPfcc1dXVbfdFRva/AWa+QcGkjp9E9rpV5GxYK4lIP3JOeKCnQ+hz1Bo1E+Yn8f1ru9n+YxHDpsXgE9D3WlN/S1EUilrsxBn1oMD2H4t4xtbICl/3wZ0iNOBuTTaMahWlNjvJ3q1rnvwpLpyrYkJJ8jLgp/Vc3Y3eyOV08PXfn6C5vo7gmDjOuukOGZzaSbosEVm2bBm5ubnk5uYSGxvb7r4evOBvl5pw3oWMPGM2sYOHHXtn0SftMlkotNqZK8nJSUtKDyNigD+VBU3sXVPO2NmJng6p0zU4nGxrsrClycLWJjPbmizUO10sHTiAvA9zKc9tRJ1mRD3Sm+QDrW5DfLxI8zUyyMdInFHfrgtloI8swnaifnr7Ncr27cXg7cO8P9+PwVu6WTtLhwerdqeODHYRoqfb0mhm3rYc9Go1P48bJLNoOkFFfiOm2hZSxoT3qZoi31Q18GxBBfssLb+7TwdcuM7MgCIbOoOG0RckM2RCFN7SwtFlcjet56vnHgOVinP/+gBJo8Z5OqQer0sHq4rOYW+xotXrUavly6O/GOXvzVh/H9Y3mrk9q1hm0XSCyKQAIpN670DJcpud1fXNrK5v5sroEEYfKG+uVdGWhAzw0jPG34fhRgOuX6pwbqpB44aolABOu3JIuyqoomskjR7H6Nnz8PYPkCSkC0iLiAes/fQDti75irNuvpPkMeM9HY7oRoVWGzM2ZmN1u3k8NaZdoSdxcuwtTmwWJ37BPbf7wepys7ahmZ9qm/il3kSu5WC5gtsTItoGiDY6nKxrMDM2wIdQvRZFUVj01Gaq9ptQa1RknJNE+unxqPtQK1Bv8GsdFnFsHTl/y0gbD7C3WLFZzOz4YbGnQxHdLNHLwN+SW082j+WVU3DIiUicuJKsOt5/YD3L383ssWPQcswtDF69i0t35vNWaQ25FhtqIN3Pm5vjwzk99OCXdYBOy6ywgLbqpSqVivFzk/AP8+L8v45l9JkJkoR0MYethQ1ffILLebAcvSQhXUO6Zjxg5OlnseXbLyjYsZWGygoCI/rfLKL+7KqYUBZXN7KmoZnbsor4YpSsRXOy/MO8sFkclGY3UJxZR/xQz67plG+xsbi6Ab1axfVx4QAkeRvw1qgJ0ak5NcSfGcF+TA70JUB3+K9hp8NFfbmFsPjWVWYThoVwSVoGGq1cP3Y1RVFY+so/yV63iqqCPObecY+nQ+rT5BPtAUGR0SSOHA2Kws4fv/N0OKKbqVUq/pEWh49GzYZGM19VNXg6pF7PP8SL4dNbZ+et/SLv4Kqy3ajK5uC14ipO35TNpA17eTy/nFeKqnEfaKHRqFQsHzeIzROH8OygOGaHBR4xCTE32vji79v46oVtNNVY27ZLEtI9Nn61iOx1q1BrNIw6a66nw+nz5FPtISPPOBuAXT8vw2m3ezga0d3ivQw8lhrDY6kxzJOpvJ1i7KxE9F5aakua2bepstte97vqBi7ekUf62j08mFvGrmYrWhVMD/LjjsQInId0FUUZ9Mds3q8paW4dD1LYuuhnc4N033WnvC0bWP3RfwE49Q83SLmFbiBdMx6SNHosfiFhmGqr2bd+NUNOOdXTIYludnGUZ7sP+hqjr47RZ8az/st8NnzVfQvirapv5uc6EwBj/L05PzKYc8ICCdF3/Ou1cFcNP7y5B4fNRWCEN2ffOILACKlX0V1qivez+F/PgaIw8vTZjDz9LE+H1C9Ii4iHqNUaRsycBcCOZdI909+ZnS6+lS6akzbi1Dh8Ag2Y6lrY9UtJpz//+oZm/rCrgE2N5rZtf4gJ5faECNZmDGbxmIH8ISa0w0mIoijsWF7Mkn/vxGFzETMoiAV3jZEkpBtZTU18+eyjOFqsxA0dwYyrrvN0SP2GtIh40PBTz8ButTBipmTd/ZnJ6eLMzfsosNr4VJfMlCA/T4fUa+n0GsbPHcDP72Vhqvt9MbAToSgKK+ub+UdhBesPJCBGtYpxB2p+pPoYT3pdluz1Faz+NAeAIVOiOeXigWg0cp3YnepKS7A2NREQEcnc2+9Go5XTY3eROiJC9AB3ZhXxv/I6og06fho3iMAjDGIUx+Z2K1QXmYhIPLnvDEVR+LG2iX/sr2RrkwUAvUrFhVHBXBMbxqBOLJfudLj45l87SBweSvrpcTJN1ENqS4oBhZDYeE+H0ut15PwtiYgQPYDZ6WLm5mwKrHbOCQ/ktSEJcjLysKt3F7C4uhFobQG5PDqEP8WFE23UH+ORx8fe4kRn0LT9nt0uN2ppBel2DlsLOkPPLYLXW0lBs16mNHsvXz33GNuXSoGz/spHq+HfQxLRquDrqgY+rqjzdEh9QlONlTWLcnCfwHTeiYG+GNUqbowLZ9PEITyaGttpSYi5wcbnz25l/Zf5bdskCel+hTu38eb/XUNx5i5Ph9KvySe/B6gqzCN303q2Lf22x1aFFF1vlL83f05sLW53z74SMputx3iEOBqX081nz25h+4/FZK4qPeq+drebFwor+KGmsW3bldGhrM4YzAMp0YTpdZ0WV0Olhc+e2UJtaTNZ68qxNsv0fU+oLS3m2388haWxgcyVP3k6nH5NEpEeYMjUU9EZjNSVFlO6d4+nwxEe9H8JEcwI9sPqVrh3X+fP+uhPNFo1Y2YlArD+q3yspsOf8Lc2mjlj8z6eKqjgwdxS7G43ADq1ithOagH5VdX+Jj57dgumuhYCwr1YcNcYvHw79zXEsVmbTXz5zCPYLGaiBw3htKtv9HRI/ZokIj2AwdubtCnTANghlVb7NY1KxctDEjg/Iog3hiV6Opxeb9gp0YTE+mKzOFn3ZV67+8xOF3/LKeHsrTlkmVsI1mn4c2Ikui4am1O8t44vn99GS7ODsHg/zvvzGPxDZeXc7uZyOvnm+SdpqCjHPyyceXfei1bXeS1eouMkEekhRh6Ywrtv/RosjQ2eDUZ4VLBOy0tDEjq1O6C/UmvUTLtoIAB715RTml0PwLqGZqZtyuKNkhoU4PyIIFaNH8yCyOAuGSScs7mSb1/agcPmIjYtiPl3jMLbX1pCupuiKPz09qsU79mJzujF/LsewDsg0NNh9XuSiPQQEUkpRCan4nY52b3iR0+HI3qQzyvrWXWgcqfouKiUQAZPbq3z8cNbe9hY3sh523IpaXEQa9Tx4YgkXhqScEKVUI+X26XgdimkjAlnzk0j0RtlerYnZK1ewc7l34NKxdm3/IWw+ERPhySQgmY9yojTz6IiL4edy79n3NzzUKklT+zvvqys58bM/QTrNCwZM5BEL4OnQ+qVpi4cSGVBE3VlZmyrKpk7NBAfjZpHU2Lw1Wq6/PUHZUTiE6AnemAQarVMy/aU1IzJpG3bTERSCsljxns6HHGA1BHpQRwtLSx64gHSJk1lxMxZaLTSNN/fWV1u5m3LYafJSpKXga9HpxLahVfufdVnFXWMcmqp2FBFxrwk3GoVui5MCBw2F2sW5TB29gB8gyR57El+PeVJnZ6uJQXNhOhDKm0Ozt66j5IWB6P9vVmUnoK31Jw4LhaXm3v3lfBRRR1nhwXw5tDELj8BWZrsLH55B1X7TUQM8GfBXWPkpOdBptoa9vyynIz5F0grczeSgmZC9CERBh0fjkgmSKtha5OFG/YU4jyBAl39TZ6lhbO37OOjijrUwDBfL349ai6Xmw1f59NU07m1Wkr31fPx4xup2m/C6KNj8oIUSUI8yN5i5YunH2bNx++x6sN3PR2OOAJJRHogR0sLO5cvZc8vyz0diughUn2M/HdEEka1ih9qm7gnp0SK3x3F11UNnLl5H3vNLYTptXySnsztiZGoDyQFaz7NZfOSQr55cQcNlZaTfj23W2HT4gK++sc2LI12giK9WXDXGKJSAk/6ucWJcbtcfPvC01TvL8A7IJD0M872dEjiCCQR6YFyN61j2esvsubj93G7XZ4OR/QQ4wJ8eGVIAmog2iDjhw7H4VZ4MKeU6/YU0uxyMyHAhx/HDvrdisbpp8fhG2SgodLCoqc3U5x14iX1W5odfPOv7Wz8pgBFgbSJkVxwzzgCI7xP9u2IE6QoCsvffoWCbZvR6g3M/8vf8A8L93RY4ggkEemBUjMmY/Tzx1RbTcG2zZ4OR/QgZ4UFsjIjjdsTI6XJ/zBMLhffVjcAcHN8OIvSU4g4TNLmH+LF+XePJWKAPzaLk2/+tYNdK06slUlrUNNidqDVqzntqsGcduUQdIaun4kjjmzT15+x88fWabqzb/kzUamDPB2SOApJRHogrV7P0GmnAbT+MQlxiBTvgyuFNjldvLi/Erd00wCtxeDeGJbIf4Ylcn9yNNqjzIzxCTAw/45RDMqIRHErrPxoHz+/n4XTfvRWSKfDxa4VJdgsDgC0Og1nXjuMC+4ZR9qEqE59P6Ljstb8wqoP3gFgxhXXkDpuomcDEsck8wB7qBGnzWLLt19QsG0LTTVV+IdKs6Joz60oXLEzn/WNZrLNLbyQFn/UE29fpCgKb5bUEKDTsDAyGIDR/j7H/XitTsNpVw0mOMaHdV/kUbizhumXprXd31zfgsPmorHKSkOVhYYqK4U7azA32LA2Oxg/ZwAAgeHSDdNTqNQaNDodI2eexejZ8zwdjjgOkoj0UMHRMcQNGU5x5i52/bSMyQsv9XRIoodRq1RcFRPK5iYziyrrMbvcvDwkod9M7TU5XdyeVcS31Y0Y1SoyAnxIOIGCbyqVitFnJBAa40tdubmt4JjiVlj01GbMjb9fLM83yIB/qPF324XnDZo4hZCYWIJj4zwdijhOkoj0YCNmzqI4cxe7f1rKxAUXodZIv7Nob35EEN4aNdfuKeS7mkbmbNnH28MH9PkKrJnNVq7ZXUi+1YZOpeL+5GjiT3Kl3PihIcQPDWm73VhtpcXiRKtXExDuTWC4N4HhXgTH+JCcHo5G1z8Svt6gua4Wt9uNf2gYAKFSur1XkUSkB0sZPwnvgEBCEwZgNTXhExjk6ZBED3RGaAAfj0zmmt2FZJpbOHPzPl4eksDMkL5ZBPCj8lru3ldCi1shxqDj9aGJjAk4/u6Y4xUY4c11/5yGSiVVOHsym8XM508+iLXZxIJ7HyE0LsHTIYkOkkSkB9PqdFz9z9fRe0n/szi6CYG+LBs3kGt2F7KlycKDOaVMC/Lr0jLm3U1RFP5vbxGLKltX0J0R7MfLQxII1nXd15isC9OzOR0OvnrucaqLCvEJDEJnkO6y3kgSkR5OkhBxvKIMer4YlcJjeeVcHBXcp5IQaG2VSPDSo1HBnxMjuTUhoq1Ameh/FLeb719+nuI9O9F7eXHu3Q8REB7h6bDECZBEpJdoqqmmoaKc+GEjPB2K6MH0ajWPpMa02/avA9N7b4wPR9/L1tqwud3U2p1EHxj/cXtCJGeFBjDMTxL0/kxRFFb8902y161CrdFyzh33ETEg2dNhiRPUu76V+qmSzN28efPVfPfSc7hdUmlVHL8iq41nCyp4qqCCMzbvY3Oj2dMhHbdVdSZmbsrmil0F2NxuALRqlSQhgg2ff8zW774GYNaNt5EwIt2zAYmTIolILxA1cBBGPz+a6+vI37rJ0+GIXiTOqOeFtDiCdRqyzC3M2ZrDVbvy2WU6+fVVukppi51rdxdywY48ciw2KmwO8i02T4clegin3c6+jWsBmHHVdQyeMt2zAYmTJolIL6DR6g6ptPqdh6MRvYlKpWJBZDCrMwZzUWQwKuD7miZO37yPP+wqoMjac07wZqeLf+2vZMqGLL6pbkANXB0TypqMNAb7enk6PNFDaPV6LnzwSc684VZGn3WOp8MRnUASkV5ixMxZABTs2EpjVaWHoxG9TbBOywuD41k5Po3zIoJQASvqTHgdUvzMk6v5VtgcjFmXyRP55VjdbjICfFg2bhCPD4wloAtnxYjew9xQ3/Z/g7cPw2ac7sFoRGeSRKSXCIqMJn7YSFAUdv/8g6fDEb1Uqo+Rfw9JYOX4NP6RFkeY/uCCcOdvz+Ou7GI2NZpxdXFSoigK+w9pjYk06BjoY2SAl56XBsfz5agUhkoriDigNHsvb916HZu//cLToYguIJcavciImWdRtHsHu35exoQFF6PRyq9PnJhUHyOpPgdrLmQ2W1nT0Myahmb+W1ZLkFbD1GA/pgf5MT3Yr23WyslwKwpbmiwsqW7g+5pG9lvt7Jo8jBB96+f4jaGJhOq1aGRKrjhEZX4uXzz1EI4WK4U7tjJ69jmo1VJlui+RM1kvkjIuA++AQOwWCzXF+2W6mug0aT5GFqUn82F5HctqG6l3uvi6qoGvqxoAuDcpilsSWms0NDtdZDZbCdJpCdRpCNBq2qYFO9ytLSm/1jDZYbLwWUU9WWYru5ut1DkOzvoyqFXsbrYyLdgPgAjDwdYZIQBqS4r47IkHsFnMxKQNZd6f75MkpA+SRKQX0Wh1zP/L3wiOicPgLVMYRedRq1RMCfJjSpAfTrfCNpOFn+ua+KXOxLYmS7t1XDY2mrlkZ367x3upVTgVcCgK/x6SwHkRrcsRFFhsvF5S3bafn0bNzBB/zgoL5NRgP3y1clIRh9dQUc6nj92P1dRERFIq5/71Qamc2kdJItLLRKUO8nQIoo/TqlWMC/BhXIAPdw2IotnpalfBtMnpIt6op9HpotHZ2sJhdR8cU2I+pNbNKH9vrosNI83HSJqvkWG+Xr2uqJrofqbaGj597H7M9XWExiWw4N6H5eKrD5NEpJdSFAVzQz2+QcGeDkX0cb9ttZgfEcT8Ay0eLkWh6UBColep8Nao8T1klegEL8PvKr0KcSz5WzfSVF1JYGQU59//GF5+fXMBR9FKEpFeqLGqkq/+/jjm+jqu+/c7MmhVeIxGpSJIpyVIptiKTjTy9NkADBg1VlYd7wekjbQX8g0OwVxfh6WxgbwtGzwdjhBCnDRLYwN268GKvyNPn41/aLgHIxLdRRKRXkij1bYV89n54/cejkYIIU6OpamRTx+9j8+efAibpecuPyC6hiQivdSI084ElYr9O7fRUFnh6XCEEOKEWJoaWfTofdQU76exqgKrqcnTIYluJolILxUQHkniiFEA7FwurSJCiN7H3FDPJw/fQ3VRId4BgSx84AkCIyI9HZboZpKI9GIjTj8LgN0/L8PpcHg4GiGEOH7N9XV88vA91JYU4RsUzIUPPUVwdKynwxIeIIlIL5Y8ejy+wSFYmxrJ2yyDVoUQvYOptoZPHr6burIS/ELCWChJSL8mc+56MbVGw7TL/ojOaGTAqLGeDkcIIY6L3WqhxWzGPyychQ88QUC4dMf0ZyrFk2t/H0NTUxMBAQE0Njbi7y8FbYQQoq+oLirE4OWNf5hM0e2LOnL+lhaRPkRRFFSycqkQogeqKszH2tREwoh0AMLiEz0aj+g5umWMiM1mIz09HZVKxfbt27vjJfsVh93Gmo/f4507/oSjpcXT4QghRDul2Xv55OF7+PK5R6nI3efpcEQP0y2JyF133UV0dHR3vFS/pNXqyFqzkrqyErLWrvR0OEII0aZw5zYWPX4/NouZiAHJBEXL2kOivS5PRL777jt++OEHnnvuua5+qX5LpVYzYuYsAHYs+87D0QghRKusNb/wxVMP47TZSEwfw4J7H8Hg7ePpsEQP06WJSGVlJddeey3vvfce3sexhLPNZqOpqandjzg+Q6fPRKPVUpmfQ0VejqfDEUL0c1sWf8Xifz2L2+Vk4MSpzP/L/egMRk+HJXqgLktEFEXhqquu4oYbbmDs2OObWvrkk08SEBDQ9hMXF9dV4fU53v4BpGZMBqRVRAjhWTkb1rLiv28AMGrWXObc8hc0Wp2HoxI9VYcTkbvvvhuVSnXUn6ysLF588UVMJhP33HPPcT/3PffcQ2NjY9tPcXFxR8Pr10YeqLSateYXWpqbPRyNEKK/Sh6bQfLYCUy5+EpmXHUdKrXUzhRH1uE6ItXV1dTW1h51n6SkJBYuXMg333zTbjqpy+VCo9Fw6aWX8u677x7ztaSOSMcoisJ/7/o/aooKmXb51Yydc66nQxJC9BM2ixmt3oBG21oVQnG7JQHpxzpy/u6ygmZFRUXtxniUlZVx5plnsmjRIjIyMoiNPXY5X0lEOi5z5U+UZmcy+qxzCImN93Q4Qoh+oLGqki+efpio1DTOuP7/pJ6R6BkFzeLj258EfX19AUhOTj6uJEScmCGnnMqQU071dBhCiH6iPCebL599FEtjAzZzM5bGBnwCgzwdluhFpLKqEEKIE7Jvwxq+e/HvOB12whKTOPeuByQJER3WbYlIYmIiPXhZmz6nPDeb7d9/y4QFFxEUJQWEhBCdR3G7Wf/5x6z99H8AJI0ex9m3/AW917HLNAjxW9Ii0ketW/QhBds2Y/TzZ8aV13o6HCFEH7LsjZfY9dMPAIw6ay7TL78GtUbj4ahEbyVDmvuoUbPmArBnxY/YW6wejkYI0ZcMnDAFrd7AGdffwqlXXS9JiDgpkoj0UYkjRhEYGYXNYmbvqhWeDkcI0cu1mA/WJkocOZprXnyT4aee4cGIRF8hiUgfpVKrST9jDgDbl34r43OEECdEURQ2frWIt265lvqKsrbtMihVdBZJRPqwodNPQ2swUFO8n5LMXZ4ORwjRy9gsZr7+++Os+uAdWppN0roquoQkIn2Y0ceXoQdqimxe/KVngxFC9CrV+wt4/57byN20Ho1Wy8xrbmLi+Rd7OizRB8msmT5u9Ox55G/dTNzgYSiKIhUPhRBHpSgKu5Yv5ed338Bpt+EXGsY5t99DZMpAT4cm+qguK/HeGaTEe+dwu12o1TKqXQhxbJkrf+K7l58HWgelnnXznXj7B3g4KtHb9IgS76LnkCRECHG8Bk2ayo4fvydlbAZj55wrC9eJLieJSD/hdrnYt2ENdquVEaed6elwhBA9hNvlYtdPPzBsxkw0Wh0arY4LH3pSLmBEt5FEpJ/I37qJxf98BqOvH4OnTENnMHo6JCGEh9WVlfL9y89TnptNc10Nky+8HJBWVNG9pM2tn0gaM46AiEhamk3sWbHc0+EIITxIcbvZtvRb3vvrLZTnZmPw9iE4WlZFF54hiUg/oVZrGHP2fAC2LP4St9vl2YCEEB7RWFXJZ08+yE9vv4rTbiN+2EiuePYlBk+d4enQRD8liUg/MmzaTIy+fjRUlpO7ab2nwxFCdLPcTet59883sX/nNrQ6PTOuup7z73sU/9AwT4cm+jFJRPoRndFI+hmzAdj09WdS9l2IfiY0PhFFUYhJG8rlz7zI6LPmyqwY4XHyCexn0s+cg1anpyJ3H4Xbt3g6HCFEF3LYWsjZsLbtdmBEJJc89hwXPvgkwdExHoxMiIMkEelnfAKDGHnm2USlDsLg4+vpcIQQXSR38wbeufMmvn7+CUqy9rRtD0sYIK0gokeR6bv90JSLrkCj1Uq5dyH6oIbKCn5+5zXyt24CwDckFKfd7uGohDgySUT6Ia1O5+kQhBCdzGYxs+HLT9m65CtcDgdqjZaxc+Yz4byL0BmlbpDouSQR6cdazM1sWfwVYQmJDMyY7OlwhBAnSFEUPnn4XqoK8wCIHzaSU/94AyExcR6OTIhjk0SkH9v54/es/+xDgqKiSRk7AbVGqikK0VsoigKKgkqtRqVSMXr2OWz48lOmXfZHkkaPk65X0WvIiKV+LP2M2Xj5+VNfXkbmyp88HY4Q4jgoikLhzm18cP+d7P7lx7btQ6bO4MpnXyJ5zHhJQkSvIi0i/Zjey5vx887nl/ffZt1nHzJ46nQ0Whk/IkRPVZqVyZqP36M4cxcAjpYWhk0/HZVKhUqtRiOzYUQvJIlIPzfyjNlsXvwlTdVVbPv+W8bOOdfTIQkhDqEoCsV7drL+848p3rMTAI1Wy4jTzyJj/kJp/RC9niQi/ZzOYGTSBZey7PUXWfPJ+6SOn0RAeISnwxJCHPDLe2+xZfGXAKg1GoZOO40JCy7CPzTcs4EJ0UmkHU8wfMbpxA4ehtNmY+X7b3s6HCH6NafDgc1ibrudMn4iWp2e9DPncPW/3uCM62+RJET0KSqlBy840tTUREBAAI2Njfj7+3s6nD6trqyUtZ/+j+lXXINvULCnwxGi37GamtjxwxK2Lf2WtMnTmHHlte3u8/KT70DRe3Tk/C1dMwKA4OgY5tx6l6fDEKLfqczPZdvSb8lesxKno7UCauGOrShud1spdklCRF8miYg4rMr8XCKSUjwdhhB9Vs6GtWz6+jPKc7PbtoUPSGbsnHMZOGGKrAcj+g1JREQ7iqLw3cvPs3fVz5x794MkjRrn6ZCE6DMURWmb5VKWk0V5bjZqjZZBE6cw8oyziR6YJrNgRL8jiYhoR6VS4R0QCMAPr73IJY8+h3+YDIwT4kTZLGay161i108/MOmCSxmQPgZoLSho8PZh+Kln4BMY5OEohfAcGawqfsfR0sL/7ruD2pIigqJiuOiRZ/D2D/B0WEL0Gm63i6JdO9jzy3JyN65rG/sxMGMyc++4x8PRCdH1OnL+lkREHJaptoYPH/gLpppqIpJSWfjA4+i9vD0dlhA9msvpZPVH/yVrzS8019W2bQ+OjmXo9JkMnXaatH6IfkESEdEp6spK+OiBu7CamogfNpJz734IrU5KwAtxqJbmZoy+vm23//uXm6kuKsTo48ugydMYNu00IpJTZeyH6Fdk+q7oFMHRsZx3z8N88si9FGfuonzfXuKGjvB0WEJ4XHN9HfvWryZr7Upq9hdyw+vvoTd6ATBp4WUobjcDRo+TxF2I4yCJiDiqyORU5t15Hy6nQ5IQ0a9ZmhrJ2bCW7HWrWhed+7UxWaWiLCuTxAODUFPGTfBglEL0PpKIiGNKGJHe7nbh9i3kbd3IlIuuwODt45mghOhGWWtXsuRfz6Eo7rZtUamDSJt0CgMnTME3OMSD0QnRu0kiIjrE7XKx/D+v0lBRzr71axg/73xiBw8jND4RjVY+TqL3MzfUk7NxHYERkSSOHA1AdGoaiuImIimFgROmMGjiVFkcUohOIoNVRYft37Wd5W+/Sn1ZSds2rU5PRHIKI2eexeCpM4DWxbt2/LAEvbcX3v4BePkF4B0QiE9AIDqj0VPhC/E7ptoacjauJWfDWkqy9oCikDR6HOf+9cGD+9TV4Bcc6sEoheg9ZLCq6FIJw9O54pkX2blsCYU7tlKek02LuZnSrExCYuPbEhFHi5UV/33j90+gUhE/bCTpZ8wmdfykbo5eiFaKorDl2y/IXr+aitx97e6LTBlIwvD0dtskCRGia0giIk6IVqdj9Ox5jJ49D8Xtpr6ijPKc7HZjRtQaDYMmnYLdYsbS1ITV1IilsRGn3UbRru0ER8dKIiK6jaIoNFVXEhAeCbRWEc7bsrE1CVGpiBk0mNTxk0jNmIR/qFQTFqK7SNeM6HaNVRVkrvyZ5LEZhCcmAdBUU0XuxnWMOuscqbcgOo3idlORl0POpnXkblxLQ0UFN7z+Xlul4JxN6zDX15MybgK+QcEejlaIvkO6ZkSPFhAeycTzL2677XI6+eYfT1GRu4/izN3MuvE2mY0jTpjb5aJk7x5yNq4ld9O6dhVONTodVfm5bVNtU8dN9FSYQogDJBERHqfWaBg2fSbVhfnkblrH+/cUcs4d9xKWMMDToYleKHPlTyx99Z9tt3VGL5JGjSVl/ESSRo2VpQqE6GEkEREep1KpGHn6bCIGpPD1P56koaKcD+67kzm3/5XkMRmeDk/0UHarhYLtW8jZsJb44SMZcdosAJLGjMfLP4CkUeNIzZhEwvB0tHq9h6MVQhyJjBERPYrV1MSSl/5O4fYtaHV6Ftz7CLFDhnk6LNFDWJoayd+ykZyNa9m/azsuhwOA2MHDuPChp9r2U9xuVGq1p8IUot+TRe9Er+Z2ufj6+SfI27yB8MRkLnvyH3JS6ecUReHzpx5i/45t7aqbBkVFkzJ+EqnjJxKVMsiDEQohDiWDVUWvptZoOPvWu1jx7htMPP8SSUL6odrSYkqz9rR1t6hUKtRqNYriJiwxidRxE0nNmERIbLzMshKil5MWEdFruN0u1GqNp8MQXUBxu6nIzyF303pyN66j7kDV3mtefKutlHpNUSE6o7GtDogQoueSFhHR5+z5ZTnbl37LBQ880bbcuuj9qgrz2fnj9+RtXk9zfV3bdrVGS/zwkdhbrG3bQuMTPRChEKKrSSIiejy71cLK//0HS2MD37/8D+befrd01/RSLeZmFLcbL7/WK6T68jJ2LFsCtE6zHTBqLCnjJpA0aqzUkhGin+jSrpnFixfzyCOPsHPnToxGI9OmTePLL7887sdL14z4VWn2Xj595B5cTicTFlzM5IWXejokcZwaqyrJ27KRvC0bKMncRca5FzLpgkuA1iTzl/ffJmXsBOKGjUSr03k4WiFEZ+gRXTOfffYZ1157LU888QSnnnoqTqeT3bt3d9XLiT4uZtBgZl57M0tfeYH1n31IaFwCgyZO8XRY4jB+Lav+a/JRU1TY7v7a4v1t/9d7eXP6tTd3c4RCiJ6kS1pEnE4niYmJPPzww1x99dUn/DzSIiJ+a8V/32TL4i/R6g1c9PDTRCSleDokQfu6HS6nk1euvRSbxQyASqUmZvAQkkePJ2lMBsHRMZ4MVQjRDTzeIrJ161ZKS0tRq9WMGjWKiooK0tPTefbZZxk27MjFqWw2Gzabre12U1NTV4QnerFTLvsDtaXFFG7fwpfPPcYVT/+rbbyB6F7NdbXkb91E3pYNNFZVcuVzL6NSqdBotQyaOJUWczPJYzMYkD5GfkdCiCPqkkQkPz8fgIceeojnn3+exMRE/v73vzN9+nT27dtHcPDhV7l88sknefjhh7siJNFHqNUazr7lL3x4/58ZOHEqRh9fT4fUbyiKQm1JEbmb1pO3eT0VeTnt7q8rLSEkNg6A06+T7hYhxPHpUNfM3XffzdNPP33Uffbu3cvWrVu59NJLee2117juuuuA1taO2NhYHnvsMa6//vrDPvZwLSJxcXHSNSN+x2FrQWcwejqMfmX1R++x4YuPD25QqYhKGUjymAySx4wnJC5BiosJIYAu7Jq58847ueqqq466T1JSEuXl5QAMGTKkbbvBYCApKYmioqIjPtZgMGAwGDoSkuinDk1CHLYWMlf+zIiZs+RE2AkURaEibx/Za1cxeOoMIgYkAxCbNoTNWi0JI0aRPHYCyWPG4xMY5OFohRC9XYcSkbCwMMLCwo6535gxYzAYDGRnZzNlSuvMBofDQWFhIQkJCScWqRCH4Xa7WPTY3yjbtxerqYkJ513o6ZB6rdqSIvas/InstStpqq5q2/5rIhI3bCQ3vvkBei9vT4UohOiDumSMiL+/PzfccAMPPvggcXFxJCQk8OyzzwJwwQUXdMVLin5KrdaQNvkUyvbtZc3H7+EXEsrQaad5Oqxew2m3s3P592Su/InK/Ny27TqDkeSxGSSmj2nbptFq0WilBqIQonN12bfKs88+i1ar5fLLL8dqtZKRkcFPP/1EUJA05YrONWrWXJpqqtn8zecsffWfqDUaBk+Z7umwegW1RsOGLz7B0tiAWqNhwKhxDJk6nQGjx6HTSzepEKLryaJ3ok9Q3G6WvvpP9vyyHFQqTr/2Zkacdqanw+pRLI0N7F7xI/t3bmXBfY+2LSC47ftvABg06RS8/QM8GaIQoo/weB0RIbqbSq3mzBtuRavXs2PZdyx7/UVQFEbMnOXp0DyuqjCfrd99TdbqFbicTgD279jGgFFjgdYWJSGE8BRJRESfoVKrOe3qG9EajOxZ8SPRA9M8HZLHKG43eVs3sXXJVxTv2dm2PTI5lZGnzyZ28JELCwohRHeSrhnR5yiKQnN9LX7BoQe3HVKCvD8o2bubjx+6G2hN0AZmTGb07Hn9OjkTQnQf6ZoR/ZpKpWqXhBRu38KaT//HnFv/SkB4hAcj6zp2q4Wqgnxih7S2dMSkDSVhxCjCE5NIP3MO/qHHnnYvhBCeIC0iok9zu128c8eN1JeXYvDx4ayb7iB5TIanw+o0VlMTW7/7hm3ff43idnPty/9pK3uvKIoUeBNCeERHzt/9p61a9EtqtYbz73uUyJSB2MxmvnzmUVa89xYOW4unQzspzXW1rHjvLd646Y+s/+xDbGYzPkEh7QqRSRIihOgNpEVE9Asup4Nf3nu7baqqX2gYM664lpTxE3vVCdtUV8P6zz5izy/LcTkcAIQnJpNx7gWkjp/Ur8bBCCF6ro6cvyUREf1K7uYN/PSfVzHVVANw2VP/bCth3hs0VlXy1q3XorjdRA8awoRzF5KYPqZXJVNCiL5PBqsKcQQpYzNIGD6SjV8twlRb0y4JsTQ24B0Q6LngfkNxuyncsZXy3GwmXXApAAHhEUy77I9EJKUQkzZUEhAhRK8niYjod3QGI5MXXsahjYFN1VW8fdt1JI0ez7hzFhCVOshj8dlbrOz5ZTnbvvuG+vJSANImTyc4OgaAMWfP91hsQgjR2SQREf3Woa0JhTu24nI6ydm4lpyNa4keOJghp8wgNWNyt5Q9V9xuSrMyyVz9M9lrV2G3WgDQe3kz/NTT0RuNXR6DEEJ4gowREeKAmuL9bP7mc/auXoHb5QJaF4VLGDGKmdfc1KW1OPZtWMM3zz/ZdjsoKppRs+YydNpp6L28u+x1hRCiK8gYESFOQGhcArNuvJ0pF11B1ppf2LvmF6oK8ijN2oPXIX9Ie1evQKVWE5UyCL/Q0LbF447FabfTUFFG8d7dFO/eSXhiEhMWXATAgPQx+IaEkjhiFIOnzCBuyDCZASOE6BekRUSIo6gtLaaupJjUjElt296+7fq2sRtqjQa/0DACwiLwDwsnKCqG8fPOB1oLii199Z80VJTRWFVJc30dHPLnFpGUwmVPvtB22+12HXdSI4QQPZm0iAjRSUJi4giJiWu77Xa7GDBqLFqDgbqSIlxOJ42VFTRWVgAQkZTaloioVCqK9+xsV2RMZzASlTqI+GEjiR82st1rSRIihOiPJBERogPUag0zrrwWaB1g2lxf15qIVFdiqqn+3fTfKRdejkqtJiAikoDwSLz8/GXKrRBCHEISESFOkEqtxi8kFL+QUGIZdth9Bk+d0c1RCSFE7yKj4YQQQgjhMZKICCGEEMJjJBERQgghhMdIIiKEEEIIj5FERAghhBAeI4mIEEIIITxGEhEhhBBCeIwkIkIIIYTwGElEhBBCCOExkogIIYQQwmMkERFCCCGEx0giIoQQQgiPkURECCGEEB7To1ffVRQFgKamJg9HIoQQQojj9et5+9fz+NH06ETEZDIBEBcX5+FIhBBCCNFRJpOJgICAo+6jUo4nXfEQt9tNWVkZfn5+qFSqTn3upqYm4uLiKC4uxt/fv1OfWxwkx7l7yHHuHnKcu4cc5+7TVcdaURRMJhPR0dGo1UcfBdKjW0TUajWxsbFd+hr+/v7yQe8Gcpy7hxzn7iHHuXvIce4+XXGsj9US8isZrCqEEEIIj5FERAghhBAe028TEYPBwIMPPojBYPB0KH2aHOfuIce5e8hx7h5ynLtPTzjWPXqwqhBCCCH6tn7bIiKEEEIIz5NERAghhBAeI4mIEEIIITxGEhEhhBBCeEyfTkRefvllEhMTMRqNZGRksHHjxqPu/+mnn5KWlobRaGT48OEsWbKkmyLt3TpynN944w2mTp1KUFAQQUFBzJw585i/F9Gqo5/nX3300UeoVCrmz5/ftQH2ER09zg0NDdx0001ERUVhMBgYOHCgfHcch44e5xdeeIFBgwbh5eVFXFwct99+Oy0tLd0Ube+0cuVK5s6dS3R0NCqVii+//PKYj1mxYgWjR4/GYDCQkpLCO++80+VxovRRH330kaLX65W3335b2bNnj3LttdcqgYGBSmVl5WH3X7NmjaLRaJRnnnlGyczMVO6//35Fp9Mpu3bt6ubIe5eOHudLLrlEefnll5Vt27Ype/fuVa666iolICBAKSkp6ebIe5eOHudfFRQUKDExMcrUqVOVefPmdU+wvVhHj7PNZlPGjh2rzJ49W1m9erVSUFCgrFixQtm+fXs3R967dPQ4/+9//1MMBoPyv//9TykoKFCWLl2qREVFKbfffns3R967LFmyRLnvvvuUzz//XAGUL7744qj75+fnK97e3sodd9yhZGZmKi+++KKi0WiU77//vkvj7LOJyPjx45Wbbrqp7bbL5VKio6OVJ5988rD7L1y4UDn77LPbbcvIyFCuv/76Lo2zt+vocf4tp9Op+Pn5Ke+++25XhdgnnMhxdjqdyqRJk5Q333xTufLKKyUROQ4dPc6vvPKKkpSUpNjt9u4KsU/o6HG+6aablFNPPbXdtjvuuEOZPHlyl8bZlxxPInLXXXcpQ4cObbftwgsvVM4888wujExR+mTXjN1uZ8uWLcycObNtm1qtZubMmaxbt+6wj1m3bl27/QHOPPPMI+4vTuw4/5bFYsHhcBAcHNxVYfZ6J3qcH3nkEcLDw7n66qu7I8xe70SO89dff83EiRO56aabiIiIYNiwYTzxxBO4XK7uCrvXOZHjPGnSJLZs2dLWfZOfn8+SJUuYPXt2t8TcX3jqPNijF707UTU1NbhcLiIiItptj4iIICsr67CPqaioOOz+FRUVXRZnb3cix/m3/vrXvxIdHf27D7846ESO8+rVq3nrrbfYvn17N0TYN5zIcc7Pz+enn37i0ksvZcmSJeTm5nLjjTficDh48MEHuyPsXudEjvMll1xCTU0NU6ZMQVEUnE4nN9xwA/fee293hNxvHOk82NTUhNVqxcvLq0tet0+2iIje4amnnuKjjz7iiy++wGg0ejqcPsNkMnH55ZfzxhtvEBoa6ulw+jS32014eDivv/46Y8aM4cILL+S+++7j1Vdf9XRofcqKFSt44okn+Pe//83WrVv5/PPPWbx4MY8++qinQxOdoE+2iISGhqLRaKisrGy3vbKyksjIyMM+JjIyskP7ixM7zr967rnneOqpp/jxxx8ZMWJEV4bZ63X0OOfl5VFYWMjcuXPbtrndbgC0Wi3Z2dkkJyd3bdC90Il8nqOiotDpdGg0mrZtgwcPpqKiArvdjl6v79KYe6MTOc5/+9vfuPzyy7nmmmsAGD58OGazmeuuu4777rsPtVquqTvDkc6D/v7+XdYaAn20RUSv1zNmzBiWL1/ets3tdrN8+XImTpx42MdMnDix3f4Ay5YtO+L+4sSOM8AzzzzDo48+yvfff8/YsWO7I9ReraPHOS0tjV27drF9+/a2n3POOYcZM2awfft24uLiujP8XuNEPs+TJ08mNze3LdED2LdvH1FRUZKEHMGJHGeLxfK7ZOPX5E+R5dI6jcfOg106FNaDPvroI8VgMCjvvPOOkpmZqVx33XVKYGCgUlFRoSiKolx++eXK3Xff3bb/mjVrFK1Wqzz33HPK3r17lQcffFCm7x6Hjh7np556StHr9cqiRYuU8vLyth+TyeSpt9ArdPQ4/5bMmjk+HT3ORUVFip+fn3LzzTcr2dnZyrfffquEh4crjz32mKfeQq/Q0eP84IMPKn5+fsqHH36o5OfnKz/88IOSnJysLFy40FNvoVcwmUzKtm3blG3btimA8vzzzyvbtm1T9u/fryiKotx9993K5Zdf3rb/r9N3//KXvyh79+5VXn75ZZm+e7JefPFFJT4+XtHr9cr48eOV9evXt903bdo05corr2y3/yeffKIMHDhQ0ev1ytChQ5XFixd3c8S9U0eOc0JCggL87ufBBx/s/sB7mY5+ng8licjx6+hxXrt2rZKRkaEYDAYlKSlJefzxxxWn09nNUfc+HTnODodDeeihh5Tk5GTFaDQqcXFxyo033qjU19d3f+C9yM8//3zY79tfj+2VV16pTJs27XePSU9PV/R6vZKUlKT85z//6fI4VYoi7VpCCCGE8Iw+OUZECCGEEL2DJCJCCCGE8BhJRIQQQgjhMZKICCGEEMJjJBERQgghhMdIIiKEEEIIj5FERAghhBAeI4mIEEIIITxGEhEhhBBCeIwkIkIIIYTwGElEhBBCCOExkogIIYQQwmP+HzWS/7RPwd0ZAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot solution\n", "with torch.no_grad():\n", " pts = problem.input_pts[\"interior\"]\n", " for model in models:\n", " plt.plot(pts, model(pts), \"--\")\n", " plt.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see we get different output since the neural networks are initialized differently.\n", "\n", "## Training with `DeepEnsemblePINN`\n", "\n", "Now that everything is ready, we can train the models using the `DeepEnsemblePINN` solver! 🎯\n", "\n", "This solver is constructed by combining multiple neural network models that all aim to solve the same PDE. Each model $\\mathcal{M}_{i \\in \\{1, \\dots, 10\\}}$ in the ensemble contributes a unique perspective due to different random initializations.\n", "\n", "This diversity allows the ensemble to **capture multiple branches or bifurcating solutions** of the problem, making it especially powerful for PDEs like the Bratu problem.\n", "\n", "Once the `DeepEnsemblePINN` solver is defined with all the models, we train them using the `Trainer` class, as with any other solver in **PINA**. We also build a callback to store the value of `u(0.5)` during training iterations." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# define the optimizers, one per model\n", "optimizers = [TorchOptimizer(torch.optim.Adam, lr=0.006) for _ in range(10)]\n", "\n", "# define solver\n", "solver = DeepEnsemblePINN(\n", " problem,\n", " models,\n", " optimizers=optimizers,\n", ")\n", "\n", "\n", "# callback\n", "class StoreValue(Callback):\n", " def on_train_epoch_start(self, trainer, pl_module):\n", " input = LabelTensor(torch.tensor([[0.5]]), \"t\")\n", " output = pl_module(input).tensor.flatten()\n", " if trainer.current_epoch == 0:\n", " self.store = [output]\n", " else:\n", " self.store.append(output)\n", "\n", "\n", "# define trainer\n", "trainer = Trainer(\n", " solver,\n", " max_epochs=500,\n", " accelerator=\"cpu\",\n", " enable_model_summary=False,\n", " callbacks=[StoreValue()],\n", ")\n", "\n", "# train\n", "trainer.train()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The training finished, let's first plot how the value of $u(0.5)$ changed during training" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with torch.no_grad():\n", " metrics = torch.stack(trainer.callbacks[0].store, dim=0)\n", " plt.plot(range(metrics.shape[0]), metrics)\n", " plt.title(\"Ensemble Convergence\")\n", " plt.ylabel(r\"$u(0.5)$\")\n", " plt.xlabel(\"epochs\")\n", " plt.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, different networks in the ensemble converge to different values pf $u(0.5)$ — this means we can actually **spot the bifurcation** in the solution space!\n", "\n", "This is a powerful demonstration of how **Deep Ensemble Physics-Informed Neural Networks** are capable of learning **multiple valid solutions** of a PDE that exhibits bifurcating behavior.\n", "\n", "We can also visualize the ensemble predictions to better observe the multiple branches:\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot solution\n", "with torch.no_grad():\n", " pts = problem.input_pts[\"interior\"]\n", " u_ensemble = solver(pts)\n", " u1, u2 = true_solution(pts)\n", " plt.plot(pts, u1, label=\"Reference solution u1\")\n", " plt.plot(pts, u2, label=\"Reference solution u2\")\n", " for idx, sol in enumerate(u_ensemble):\n", " if idx == 0:\n", " plt.plot(pts, sol, \"--\", label=\"PINNs\", c=\"k\")\n", " else:\n", " plt.plot(pts, sol, \"--\", c=\"k\")\n", " plt.legend()\n", " plt.plot()\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What's Next?\n", "\n", "You have completed the tutorial on deep ensemble PINNs for bifurcating PDEs, well don! There are many potential next steps you can explore:\n", "\n", "1. **Train the network longer or with different hyperparameters**: Experiment with different configurations of the single model, you can compose an ensemble by also stacking models with different layers, activation, ... to improve accuracy.\n", "\n", "2. **Solve more complex problems**: The original paper provides very complex problems that can be solved with PINA, we suggest you to try implement and solve them!\n", "\n", "3. **...and many more!**: There are countless directions to further explore, for example, what does it happen when you vary the network initialization hyperparameters?\n", "\n", "For more resources and tutorials, check out the [PINA Documentation](https://mathlab.github.io/PINA/)." ] } ], "metadata": { "kernelspec": { "display_name": "deep", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 2 }