{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a1cc726f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Physics Informed Neural Networks\n",
    "\n",
    "**Presenter:** Filippo Maria Bianchi\n",
    "\n",
    "**Repository:** [github.com/FilippoMB/Physics-Informed-Neural-Networks-tutorial](https://github.com/FilippoMB/Physics-Informed-Neural-Networks-tutorial)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e363db51",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduction\n",
    "\n",
    "What are PINNs?\n",
    "\n",
    "- PINNs are Neural Networks used to learn a generic function $f$.\n",
    "- Like standard NNs, PINNs account for observation data $\\{ x_i \\}_{i=1}^N$ in learning $f$.\n",
    "- In addition, the optimization of $f$ is guided by a regularization term, which encourages $f$ to be the solution of a Partial Differential Equation (PDE)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cffd09a7",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Traditional PDE solvers\n",
    "\n",
    "- Simple problems can be solved analytically.\n",
    "- E.g., consider the velocity:\n",
    "\n",
    "$$v(t) = \\frac{d x}{d t} = \\lim_{h \\rightarrow 0} \\frac{x(t+h) - x(t)}{h}$$\n",
    "\n",
    "<img src=\"figs/simple_pde.png\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "- Solution: \n",
    "\n",
    "$$\n",
    "v(t) = \n",
    "\\begin{cases}\n",
    "3/2 & \\text{if}\\; t \\in \\{ 0, 2 \\} \\\\\n",
    "0 & \\text{if}\\; t \\in \\{ 2, 4 \\} \\\\\n",
    "-1/3 & \\text{if}\\; t \\in \\{ 4, 7 \\}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "08b1c65b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"figs/numerical_pde.png\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "- In most real-world problems solutions cannot be found analytically.\n",
    "- Differential equations are solved numerically.\n",
    "- E.g., they apply the definition of derivative for *all* the point of the time domain."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45aec619",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Limitations of PDE solvers**\n",
    "\n",
    "- Computationally expensive and scale bad to big data.\n",
    "- Integrating external data sources (e.g., from sensors) is problematic."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6ee24fff",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Neural Networks\n",
    "\n",
    "<img src=\"figs/neural_net.png\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "- Universal function approximators.\n",
    "- Can consume any kind of data $\\boldsymbol{X}$.\n",
    "- Are trained to minimize a loss, e.g., the error between the predictions $\\boldsymbol{\\hat{y}}$ and the desired outputs $\\boldsymbol{y}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bf86ecd0",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Imports\n",
    "import torch\n",
    "from torch import nn\n",
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "82760add",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's start by creating a simple neural network in <a href=\"https://pytorch.org\"><b>PyTorch</b></a>."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "980ee1b5",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Define a simple neural network for regression\n",
    "class simple_NN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(simple_NN, self).__init__()\n",
    "        self.linear_tanh_stack = nn.Sequential(\n",
    "            nn.Linear(1, 16),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(16, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 16),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(16, 1),\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        out = self.linear_tanh_stack(x)\n",
    "        return out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a908a777",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Then,\n",
    "- Create a small dataset $\\{x_i, y_i\\}_{i=1, \\dots 5}$.\n",
    "- Use the NN to make predictions: $\\hat{y}_i = \\rm{NN}(x_i)$.\n",
    "- Train the NN by minimizing $\\rm{MSE}(\\boldsymbol{y}, \\boldsymbol{\\hat{y}})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3a554192",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# Define dataset\n",
    "x_train = torch.tensor([[1.1437e-04],\n",
    "        [1.4676e-01],\n",
    "        [3.0233e-01],\n",
    "        [4.1702e-01],\n",
    "        [7.2032e-01]], dtype=torch.float32)\n",
    "y_train = torch.tensor([[1.0000],\n",
    "        [1.0141],\n",
    "        [1.0456],\n",
    "        [1.0753],\n",
    "        [1.1565]], dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6d76616a",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0, loss: 0.865811\n",
      "epoch: 200, loss: 0.000253\n",
      "epoch: 400, loss: 0.000151\n",
      "epoch: 600, loss: 0.000068\n",
      "epoch: 800, loss: 0.000017\n"
     ]
    }
   ],
   "source": [
    "# Initialize the model\n",
    "model = simple_NN()\n",
    "\n",
    "# define loss and optimizer\n",
    "loss_fn = nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)\n",
    "\n",
    "# Train\n",
    "for ep in range(1000):\n",
    "\n",
    "    # Compute prediction error\n",
    "    pred = model(x_train)\n",
    "    loss = loss_fn(pred, y_train)\n",
    "\n",
    "    # Backpropagation\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    if ep % 200 == 0:\n",
    "        print(f\"epoch: {ep}, loss: {loss.item():>7f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aa4644a4",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# evaluate the model on all data points in the domain\n",
    "domain = [0.0, 1.5]\n",
    "x_eval = torch.linspace(domain[0], domain[1], steps=100).reshape(-1, 1)\n",
    "f_eval = model(x_eval)\n",
    "\n",
    "# plotting\n",
    "fig, ax = plt.subplots(figsize=(12, 5))\n",
    "ax.scatter(x_train.detach().numpy(), y_train.detach().numpy(), label=\"Training data\", color=\"blue\")\n",
    "ax.plot(x_eval.detach().numpy(), f_eval.detach().numpy(), label=\"NN approximation\", color=\"black\")\n",
    "ax.set(title=\"Neural Network Regression\", xlabel=\"$x$\", ylabel=\"$y$\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce277406",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The NN does a good job in fitting the data samples.\n",
    "- However, it has no information on what function should learn when $x>0.8$. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "cd3a8bf4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Physics Informed NNs\n",
    "\n",
    "- Use PDEs to adjust the NN output.\n",
    "- Train the model with an additional loss that penalizes the violation of the PDE.\n",
    "\n",
    "$$ \\mathcal{L}_{\\text{tot}} =  \\mathcal{L}_{\\text{data}} + \\mathcal{L}_{\\text{PDE}}$$\n",
    "\n",
    "\n",
    "<img src=\"figs/neural_net_pde.png\" style=\"width: 50%; display: block; margin: auto;\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ad6a57a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Advantages**\n",
    "\n",
    "Combine information from both data and from physical models.\n",
    "- Compared to traditional NNs, $\\mathcal{L}_{\\text{PDE}}$ regularizes the model limiting overfitting and improving generalization.\n",
    "- Compared to traiditional PDE solvers, PINNs are more scalable and can consume any kind of data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7379c57",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example I: population growth\n",
    "\n",
    "Logistic equation for modeling the population growth: \n",
    "\n",
    "$$ \\frac{d f(t)}{d t} = Rt(1-t)$$\n",
    "\n",
    "- $f(t)$ is the population growth over time $t$\n",
    "- $R$ is the max growth rate\n",
    "- To identify a solution, a boundary condition must be imposed, e.g., at $t=0$:\n",
    "\n",
    "$$f(t=0)=1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b8b0ee7a",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "R = 1.0\n",
    "ft0 = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c6782f4",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Use the NN to model $f(t)$, i.e., $f(t) = \\rm{NN}(t)$\n",
    "- We can easily compute the derivative $\\frac{d\\rm{NN}(t)}{dt}$ thanks to automatic differentiation provided by deep learning libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "308d79c8",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def df(f: simple_NN, x: torch.Tensor = None, order: int = 1) -> torch.Tensor:\n",
    "    \"\"\"Compute neural network derivative with respect to input features using PyTorch autograd engine\"\"\"\n",
    "    df_value = f(x)\n",
    "    for _ in range(order):\n",
    "        df_value = torch.autograd.grad(\n",
    "            df_value,\n",
    "            x,\n",
    "            grad_outputs=torch.ones_like(x),\n",
    "            create_graph=True,\n",
    "            retain_graph=True,\n",
    "        )[0]\n",
    "\n",
    "    return df_value "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46db65df",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We want our NN to satisfy the following equation:\n",
    "\n",
    "$$ \\frac{d\\rm{NN}(t)}{dt} - Rt(1-t) = 0 $$\n",
    "\n",
    "- To do that, we add the following physics-informed regularization term to the loss:\n",
    "\n",
    "$$ \\mathcal{L}_\\rm{PDE} = \\frac{1}{N} \\sum_{i=1}^N \\left( \\frac{d\\rm{NN}}{dt} \\bigg\\rvert_{t_i} - R t_i (1-t_i) \\right)^2 $$\n",
    "\n",
    "- where $t_i$ are **collocation points**, i.e., a set of points from the domain where we evaluate the differential equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f7b2db5f",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Generate 10 evenly distributed collocation points\n",
    "t = torch.linspace(domain[0], domain[1], steps=10, requires_grad=True).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0babb74f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Only minimizing $\\mathcal{L}_\\rm{PDE}$ does not ensure a unique solution.\n",
    "- We must include the boundary condition by adding the following loss:\n",
    "\n",
    "$$ \\mathcal{L}_\\rm{BC} = \\left( \\rm{NN}(t_0) - 1 \\right)^2 $$\n",
    "\n",
    "- This lets the NN converge to the desired solution among the infinite possible ones."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3de1ccf0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The final loss is given by:\n",
    "\n",
    "$$ \\mathcal{L}_\\rm{PDE} + \\mathcal{L}_\\rm{BC} + \\mathcal{L}_\\rm{data} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "66cb667d",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Wrap everything into a function\n",
    "def compute_loss(nn: simple_NN, \n",
    "                 t: torch.Tensor = None, \n",
    "                 x: torch.Tensor = None,\n",
    "                 y: torch.Tensor = None,\n",
    "                 ) -> torch.float:\n",
    "    \"\"\"Compute the full loss function as pde loss + boundary loss\n",
    "    This custom loss function is fully defined with differentiable tensors therefore\n",
    "    the .backward() method can be applied to it\n",
    "    \"\"\"\n",
    "\n",
    "    pde_loss = df(nn, t) - R * t * (1 - t)\n",
    "    pde_loss = pde_loss.pow(2).mean()\n",
    "\n",
    "    boundary = torch.Tensor([0.0])\n",
    "    boundary.requires_grad = True\n",
    "    bc_loss = nn(boundary) - ft0\n",
    "    bc_loss = bc_loss.pow(2)\n",
    "    \n",
    "    mse_loss = torch.nn.MSELoss()(nn(x), y)\n",
    "    \n",
    "    tot_loss = pde_loss + bc_loss + mse_loss\n",
    "    \n",
    "    return tot_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e4655d8b",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0, loss: 3.063274\n",
      "epoch: 200, loss: 0.000948\n",
      "epoch: 400, loss: 0.000451\n",
      "epoch: 600, loss: 0.000110\n",
      "epoch: 800, loss: 0.000090\n",
      "epoch: 1000, loss: 0.000087\n",
      "epoch: 1200, loss: 0.000085\n",
      "epoch: 1400, loss: 0.000084\n",
      "epoch: 1600, loss: 0.000083\n",
      "epoch: 1800, loss: 0.000082\n"
     ]
    }
   ],
   "source": [
    "model = simple_NN()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)\n",
    "\n",
    "# Train\n",
    "for ep in range(2000):\n",
    "\n",
    "    loss = compute_loss(model, t, x_train, y_train)\n",
    "\n",
    "    # Backpropagation\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    if ep % 200 == 0:\n",
    "        print(f\"epoch: {ep}, loss: {loss.item():>7f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c4ed19a2",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# numeric solution\n",
    "def logistic_eq_fn(x, y):\n",
    "    return R * x * (1 - x)\n",
    "\n",
    "numeric_solution = solve_ivp(\n",
    "    logistic_eq_fn, domain, [ft0], t_eval=x_eval.squeeze().detach().numpy()\n",
    ")\n",
    "\n",
    "f_colloc = solve_ivp(\n",
    "    logistic_eq_fn, domain, [ft0], t_eval=t.squeeze().detach().numpy()\n",
    ").y.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "705c3b81",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# evaluation on the domain [0, 1.5]\n",
    "f_eval = model(x_eval)\n",
    "\n",
    "# plotting\n",
    "fig, ax = plt.subplots(figsize=(12, 5))\n",
    "ax.scatter(t.detach().numpy(), f_colloc, label=\"Collocation points\", color=\"magenta\", alpha=0.75)\n",
    "ax.scatter(x_train.detach().numpy(), y_train.detach().numpy(), label=\"Observation data\", color=\"blue\")\n",
    "ax.plot(x_eval.detach().numpy(), f_eval.detach().numpy(), label=\"NN solution\", color=\"black\")\n",
    "ax.plot(x_eval.detach().numpy(), numeric_solution.y.T,\n",
    "        label=\"Analytic solution\", color=\"magenta\", alpha=0.75)\n",
    "ax.set(title=\"Logistic equation solved with NNs\", xlabel=\"t\", ylabel=\"f(t)\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7ce2baa",
   "metadata": {
    "run_control": {
     "marked": false
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example II: 1d wave\n",
    "\n",
    "- Now, we want our NN to learn a function $f(x,t)$ that satisfies the following $2^\\rm{nd}$ order PDE:\n",
    "\n",
    "$$\\frac{\\partial^2 f}{\\partial x^2} = \\frac{1}{C} \\frac{\\partial^2 f}{\\partial t^2}$$\n",
    "\n",
    "- where $C$ is a positive constant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "980f2ca0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Differently from before, $f$ depends on two variables: space ($x$) and time ($t$). \n",
    "- We modify our neural network to accept to input variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2ba361a9",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "class simple_NN2(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(simple_NN2, self).__init__()\n",
    "        self.linear_tanh_stack = nn.Sequential(\n",
    "            nn.Linear(2, 16),    # <--- 2 input variables\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(16, 32),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(32, 16),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(16, 1),\n",
    "        )\n",
    "\n",
    "    def forward(self, x, t):\n",
    "        x_stack = torch.cat([x, t], dim=1) # <--- concatenate x and t\n",
    "        out = self.linear_tanh_stack(x_stack)\n",
    "        return out"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "473d690a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- The function we defined before, `df()`, computes a derivatives of any order w.r.t. only one input variable.\n",
    "- We need to modify it slightly to differentiate w.r.t. both $x$ and $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ba9d5e25",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def df(output: torch.Tensor, input_var: torch.Tensor, order: int = 1) -> torch.Tensor:\n",
    "    \"\"\"Compute neural network derivative with respect to input features using PyTorch autograd engine\"\"\"\n",
    "    df_value = output      # <-- we directly take the output of the NN\n",
    "    for _ in range(order):\n",
    "        df_value = torch.autograd.grad(\n",
    "            df_value,\n",
    "            input_var,\n",
    "            grad_outputs=torch.ones_like(input_var),\n",
    "            create_graph=True,\n",
    "            retain_graph=True,\n",
    "        )[0]\n",
    "    return df_value\n",
    "\n",
    "def dfdt(model: simple_NN2, x: torch.Tensor, t: torch.Tensor, order: int = 1):\n",
    "    \"\"\"Derivative with respect to the time variable of arbitrary order\"\"\"\n",
    "    f_value = model(x, t)\n",
    "    return df(f_value, t, order=order)\n",
    "\n",
    "def dfdx(model: simple_NN2, x: torch.Tensor, t: torch.Tensor, order: int = 1):\n",
    "    \"\"\"Derivative with respect to the spatial variable of arbitrary order\"\"\"\n",
    "    f_value = model(x, t)\n",
    "    return df(f_value, x, order=order)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6013750a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Loss definition\n",
    "\n",
    "- For this example, we do not consider measurement data.\n",
    "- We train the NN with a loss that only accounts for physical equations.\n",
    "- The first term of the loss encourages respecting the 1-dimensional wave equation:\n",
    "\n",
    "$$\\mathcal{L}_\\rm{PDE} = \\left( \\frac{\\partial^2 f}{\\partial x^2} - \\frac{1}{C} \\frac{\\partial^2 f}{\\partial t^2} \\right)^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80aa22c1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- As before, there are infinite solutions satisfying this equation.\n",
    "- We need to restrict the possible solutions by:\n",
    "    1. imposing periodic boundary conditions at the domain extrema.\n",
    "    2. imposing an initial condition on $f(x, t_0)$.\n",
    "    3. imposing an initial condition on $\\frac{\\partial f(x, t)}{\\partial t} \\bigg\\rvert_{t=0}$."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a3d7795d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We define the domain of $x$ as $[x_0, x_1]$.\n",
    "- In this example, $x_0 = 0$ and $x_1 = 1$, but they could be different values.\n",
    "\n",
    "<img src=\"figs/boundaries.png\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "- The following loss penalizes the violation of the boundary conditions:\n",
    "\n",
    "$$\\mathcal{L}_\\rm{BC} = f(x_0, t)^2 + f(x_1, t)^2$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "fde287b2",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Next, we must define the initial condition on $f(x, t_0)$.\n",
    "\n",
    "<img src=\"figs/initial_cond.png\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "- The following loss penalizes departure from the desired initial condition:\n",
    "\n",
    "$$\\mathcal{L}_\\rm{initF} = \\left( f(x, t_0) - \\frac{1}{2} \\rm{sin}(2\\pi x) \\right)^2 $$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3b477992",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Finally, we must specify the initial condition on $\\frac{\\partial f(x, t)}{\\partial t} \\bigg\\rvert_{t=0}$.\n",
    "\n",
    "<img src=\"figs/initial_cond2.jpeg\" style=\"width: 40%; display: block; margin: auto;\">\n",
    "\n",
    "The following loss penalizes departure from the desired initial condition of the 1st order derivative:\n",
    "\n",
    "$$\\mathcal{L}_\\rm{initDF} = \\left( \\frac{\\partial f}{\\partial t} \\bigg\\rvert_{t=0} \\right)^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a631559d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The total loss is given by:\n",
    "\n",
    "$$\\mathcal{L}_\\rm{PDE} + \\mathcal{L}_\\rm{BC} + \\mathcal{L}_\\rm{initF} + \\mathcal{L}_\\rm{initDF}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f2934df9",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def initial_condition(x) -> torch.Tensor:\n",
    "    res = torch.sin( 2*np.pi * x).reshape(-1, 1) * 0.5\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b1e50e13",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def compute_loss(\n",
    "    model: simple_NN2,\n",
    "    x: torch.Tensor = None, \n",
    "    t: torch.Tensor = None,\n",
    "    x_idx: torch.Tensor = None, \n",
    "    t_idx: torch.Tensor = None,  \n",
    "    C: float = 1.0,\n",
    "    device: str = None,\n",
    "    ) -> torch.float:\n",
    "\n",
    "    # PDE\n",
    "    pde_loss = dfdx(model, x, t, order=2) - (1/C**2) * dfdt(model, x, t, order=2)\n",
    "\n",
    "    # boundary conditions\n",
    "    boundary_x0 = torch.ones_like(t_idx, requires_grad=True).to(device) * x[0]      \n",
    "    boundary_loss_x0 = model(boundary_x0, t_idx)                                    # f(x0, t)\n",
    "    boundary_x1 = torch.ones_like(t_idx, requires_grad=True).to(device) * x[-1]    \n",
    "    boundary_loss_x1 = model(boundary_x1, t_idx)                                    # f(x1, t)\n",
    "    \n",
    "    # initial conditions\n",
    "    f_initial = initial_condition(x_idx)                         # 0.5*sin(2*pi*x)\n",
    "    t_initial = torch.zeros_like(x_idx)                          # t0\n",
    "    t_initial.requires_grad = True\n",
    "    initial_loss_f = model(x_idx, t_initial) - f_initial         # L_initF\n",
    "    initial_loss_df = dfdt(model, x_idx, t_initial, order=1)     # L_initDF\n",
    "    \n",
    "    # obtain the final  loss by averaging each term and summing them up\n",
    "    final_loss = \\\n",
    "        pde_loss.pow(2).mean() + \\\n",
    "        boundary_loss_x0.pow(2).mean() + \\\n",
    "        boundary_loss_x1.pow(2).mean() + \\\n",
    "        initial_loss_f.pow(2).mean() + \\\n",
    "        initial_loss_df.pow(2).mean()\n",
    "\n",
    "    return final_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5a39ad2a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
    "\n",
    "# generate the time-space meshgrid\n",
    "x_domain = [0.0, 1.0]; n_points_x = 100\n",
    "t_domain = [0.0, 1.0]; n_points_t = 150\n",
    "x_idx = torch.linspace(x_domain[0], x_domain[1], steps=n_points_x, requires_grad=True)\n",
    "t_idx = torch.linspace(t_domain[0], t_domain[1], steps=n_points_t, requires_grad=True)\n",
    "grids = torch.meshgrid(x_idx, t_idx, indexing=\"ij\")\n",
    "x_idx, t_idx = x_idx.reshape(-1, 1).to(device), t_idx.reshape(-1, 1).to(device)\n",
    "x, t = grids[0].flatten().reshape(-1, 1).to(device), grids[1].flatten().reshape(-1, 1).to(device)\n",
    "\n",
    "# initialize the neural network model\n",
    "model = simple_NN2().to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "36cc375c",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0, loss: 0.133278\n",
      "epoch: 300, loss: 0.058259\n",
      "epoch: 600, loss: 0.033736\n",
      "epoch: 900, loss: 0.026548\n",
      "epoch: 1200, loss: 0.023956\n",
      "epoch: 1500, loss: 0.076558\n",
      "epoch: 1800, loss: 0.014723\n",
      "epoch: 2100, loss: 0.012283\n",
      "epoch: 2400, loss: 0.003159\n",
      "epoch: 2700, loss: 0.001655\n"
     ]
    }
   ],
   "source": [
    "# Train\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=1e-2)\n",
    "for ep in range(3000):\n",
    "\n",
    "    loss = compute_loss(model, x=x, t=t, x_idx=x_idx, t_idx=t_idx, device=device)\n",
    "\n",
    "    # Backpropagation\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    if ep % 300 == 0:\n",
    "        print(f\"epoch: {ep}, loss: {loss.item():>7f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "65b3ec36",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. 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We ignore the initial 0/0 size\n            // that occurs as the element is placed into the DOM, which should\n            // otherwise not happen due to the minimum size styling.\n            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n                fig.request_resize(width, height);\n            }\n        }\n    });\n    this.resizeObserverInstance.observe(canvas_div);\n\n    function on_mouse_event_closure(name) {\n        /* User Agent sniffing is bad, but WebKit is busted:\n         * https://bugs.webkit.org/show_bug.cgi?id=144526\n         * https://bugs.webkit.org/show_bug.cgi?id=181818\n         * The worst that happens here is that they get an extra browser\n         * selection when dragging, if this check fails to catch them.\n         */\n        var UA = navigator.userAgent;\n        var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n        if(isWebKit) {\n            return function (event) {\n                /* This prevents the web browser from automatically changing to\n                 * the text insertion cursor when the button is pressed. We\n                 * want to control all of the cursor setting manually through\n                 * the 'cursor' event from matplotlib */\n                event.preventDefault()\n                return fig.mouse_event(event, name);\n            };\n        } else {\n            return function (event) {\n                return fig.mouse_event(event, name);\n            };\n        }\n    }\n\n    canvas_div.addEventListener(\n        'mousedown',\n        on_mouse_event_closure('button_press')\n    );\n    canvas_div.addEventListener(\n        'mouseup',\n        on_mouse_event_closure('button_release')\n    );\n    canvas_div.addEventListener(\n        'dblclick',\n        on_mouse_event_closure('dblclick')\n    );\n    // Throttle sequential mouse events to 1 every 20ms.\n    canvas_div.addEventListener(\n        'mousemove',\n        on_mouse_event_closure('motion_notify')\n    );\n\n    canvas_div.addEventListener(\n        'mouseenter',\n        on_mouse_event_closure('figure_enter')\n    );\n    canvas_div.addEventListener(\n        'mouseleave',\n        on_mouse_event_closure('figure_leave')\n    );\n\n    canvas_div.addEventListener('wheel', function (event) {\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        on_mouse_event_closure('scroll')(event);\n    });\n\n    canvas_div.appendChild(canvas);\n    canvas_div.appendChild(rubberband_canvas);\n\n    this.rubberband_context = rubberband_canvas.getContext('2d');\n    this.rubberband_context.strokeStyle = '#000000';\n\n    this._resize_canvas = function (width, height, forward) {\n        if (forward) {\n            canvas_div.style.width = width + 'px';\n            canvas_div.style.height = height + 'px';\n        }\n    };\n\n    // Disable right mouse context menu.\n    canvas_div.addEventListener('contextmenu', function (_e) {\n        event.preventDefault();\n        return false;\n    });\n\n    function set_focus() {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'mpl-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'mpl-button-group';\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'mpl-button-group';\n            continue;\n        }\n\n        var button = (fig.buttons[name] = document.createElement('button'));\n        button.classList = 'mpl-widget';\n        button.setAttribute('role', 'button');\n        button.setAttribute('aria-disabled', 'false');\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n\n        var icon_img = document.createElement('img');\n        icon_img.src = '_images/' + image + '.png';\n        icon_img.srcset = '_images/' + image + '_large.png 2x';\n        icon_img.alt = tooltip;\n        button.appendChild(icon_img);\n\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    var fmt_picker = document.createElement('select');\n    fmt_picker.classList = 'mpl-widget';\n    toolbar.appendChild(fmt_picker);\n    this.format_dropdown = fmt_picker;\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = document.createElement('option');\n        option.selected = fmt === mpl.default_extension;\n        option.innerHTML = fmt;\n        fmt_picker.appendChild(option);\n    }\n\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n};\n\nmpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', { width: x_pixels, height: y_pixels });\n};\n\nmpl.figure.prototype.send_message = function (type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n};\n\nmpl.figure.prototype.send_draw_message = function () {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n};\n\nmpl.figure.prototype.handle_resize = function (fig, msg) {\n    var size = msg['size'];\n    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1], msg['forward']);\n        fig.send_message('refresh', {});\n    }\n};\n\nmpl.figure.prototype.handle_rubberband = function (fig, msg) {\n    var x0 = msg['x0'] / fig.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n    var x1 = msg['x1'] / fig.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0,\n        0,\n        fig.canvas.width / fig.ratio,\n        fig.canvas.height / fig.ratio\n    );\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n};\n\nmpl.figure.prototype.handle_figure_label = function (fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n};\n\nmpl.figure.prototype.handle_cursor = function (fig, msg) {\n    fig.canvas_div.style.cursor = msg['cursor'];\n};\n\nmpl.figure.prototype.handle_message = function (fig, msg) {\n    fig.message.textContent = msg['message'];\n};\n\nmpl.figure.prototype.handle_draw = function (fig, _msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n};\n\nmpl.figure.prototype.handle_image_mode = function (fig, msg) {\n    fig.image_mode = msg['mode'];\n};\n\nmpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n    for (var key in msg) {\n        if (!(key in fig.buttons)) {\n            continue;\n        }\n        fig.buttons[key].disabled = !msg[key];\n        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n    }\n};\n\nmpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n    if (msg['mode'] === 'PAN') {\n        fig.buttons['Pan'].classList.add('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    } else if (msg['mode'] === 'ZOOM') {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.add('active');\n    } else {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    }\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Called whenever the canvas gets updated.\n    this.send_message('ack', {});\n};\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function (fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            var img = evt.data;\n            if (img.type !== 'image/png') {\n                /* FIXME: We get \"Resource interpreted as Image but\n                 * transferred with MIME type text/plain:\" errors on\n                 * Chrome.  But how to set the MIME type?  It doesn't seem\n                 * to be part of the websocket stream */\n                img.type = 'image/png';\n            }\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src\n                );\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                img\n            );\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        } else if (\n            typeof evt.data === 'string' &&\n            evt.data.slice(0, 21) === 'data:image/png;base64'\n        ) {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig['handle_' + msg_type];\n        } catch (e) {\n            console.log(\n                \"No handler for the '\" + msg_type + \"' message type: \",\n                msg\n            );\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\n                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n                    e,\n                    e.stack,\n                    msg\n                );\n            }\n        }\n    };\n};\n\nfunction getModifiers(event) {\n    var mods = [];\n    if (event.ctrlKey) {\n        mods.push('ctrl');\n    }\n    if (event.altKey) {\n        mods.push('alt');\n    }\n    if (event.shiftKey) {\n        mods.push('shift');\n    }\n    if (event.metaKey) {\n        mods.push('meta');\n    }\n    return mods;\n}\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * https://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys(original) {\n    return Object.keys(original).reduce(function (obj, key) {\n        if (typeof original[key] !== 'object') {\n            obj[key] = original[key];\n        }\n        return obj;\n    }, {});\n}\n\nmpl.figure.prototype.mouse_event = function (event, name) {\n    if (name === 'button_press') {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    // from https://stackoverflow.com/q/1114465\n    var boundingRect = this.canvas.getBoundingClientRect();\n    var x = (event.clientX - boundingRect.left) * this.ratio;\n    var y = (event.clientY - boundingRect.top) * this.ratio;\n\n    this.send_message(name, {\n        x: x,\n        y: y,\n        button: event.button,\n        step: event.step,\n        modifiers: getModifiers(event),\n        guiEvent: simpleKeys(event),\n    });\n\n    return false;\n};\n\nmpl.figure.prototype._key_event_extra = function (_event, _name) {\n    // Handle any extra behaviour associated with a key event\n};\n\nmpl.figure.prototype.key_event = function (event, name) {\n    // Prevent repeat events\n    if (name === 'key_press') {\n        if (event.key === this._key) {\n            return;\n        } else {\n            this._key = event.key;\n        }\n    }\n    if (name === 'key_release') {\n        this._key = null;\n    }\n\n    var value = '';\n    if (event.ctrlKey && event.key !== 'Control') {\n        value += 'ctrl+';\n    }\n    else if (event.altKey && event.key !== 'Alt') {\n        value += 'alt+';\n    }\n    else if (event.shiftKey && event.key !== 'Shift') {\n        value += 'shift+';\n    }\n\n    value += 'k' + event.key;\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n    return false;\n};\n\nmpl.figure.prototype.toolbar_button_onclick = function (name) {\n    if (name === 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message('toolbar_button', { name: name });\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n    this.message.textContent = tooltip;\n};\n\n///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n// prettier-ignore\nvar _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n\nmpl.default_extension = \"png\";/* global mpl */\n\nvar comm_websocket_adapter = function (comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.binaryType = comm.kernel.ws.binaryType;\n    ws.readyState = comm.kernel.ws.readyState;\n    function updateReadyState(_event) {\n        if (comm.kernel.ws) {\n            ws.readyState = comm.kernel.ws.readyState;\n        } else {\n            ws.readyState = 3; // Closed state.\n        }\n    }\n    comm.kernel.ws.addEventListener('open', updateReadyState);\n    comm.kernel.ws.addEventListener('close', updateReadyState);\n    comm.kernel.ws.addEventListener('error', updateReadyState);\n\n    ws.close = function () {\n        comm.close();\n    };\n    ws.send = function (m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function (msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        var data = msg['content']['data'];\n        if (data['blob'] !== undefined) {\n            data = {\n                data: new Blob(msg['buffers'], { type: data['blob'] }),\n            };\n        }\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(data);\n    });\n    return ws;\n};\n\nmpl.mpl_figure_comm = function (comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = document.getElementById(id);\n    var ws_proxy = comm_websocket_adapter(comm);\n\n    function ondownload(figure, _format) {\n        window.open(figure.canvas.toDataURL());\n    }\n\n    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element;\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error('Failed to find cell for figure', id, fig);\n        return;\n    }\n    fig.cell_info[0].output_area.element.on(\n        'cleared',\n        { fig: fig },\n        fig._remove_fig_handler\n    );\n};\n\nmpl.figure.prototype.handle_close = function (fig, msg) {\n    var width = fig.canvas.width / fig.ratio;\n    fig.cell_info[0].output_area.element.off(\n        'cleared',\n        fig._remove_fig_handler\n    );\n    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable();\n    fig.parent_element.innerHTML =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n    fig.close_ws(fig, msg);\n};\n\nmpl.figure.prototype.close_ws = function (fig, msg) {\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n};\n\nmpl.figure.prototype.push_to_output = function (_remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width / this.ratio;\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message('ack', {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () {\n        fig.push_to_output();\n    }, 1000);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'btn-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'btn-group';\n    var button;\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'btn-group';\n            continue;\n        }\n\n        button = fig.buttons[name] = document.createElement('button');\n        button.classList = 'btn btn-default';\n        button.href = '#';\n        button.title = name;\n        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    // Add the status bar.\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message pull-right';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n\n    // Add the close button to the window.\n    var buttongrp = document.createElement('div');\n    buttongrp.classList = 'btn-group inline pull-right';\n    button = document.createElement('button');\n    button.classList = 'btn btn-mini btn-primary';\n    button.href = '#';\n    button.title = 'Stop Interaction';\n    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n    button.addEventListener('click', function (_evt) {\n        fig.handle_close(fig, {});\n    });\n    button.addEventListener(\n        'mouseover',\n        on_mouseover_closure('Stop Interaction')\n    );\n    buttongrp.appendChild(button);\n    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n};\n\nmpl.figure.prototype._remove_fig_handler = function (event) {\n    var fig = event.data.fig;\n    if (event.target !== this) {\n        // Ignore bubbled events from children.\n        return;\n    }\n    fig.close_ws(fig, {});\n};\n\nmpl.figure.prototype._root_extra_style = function (el) {\n    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n};\n\nmpl.figure.prototype._canvas_extra_style = function (el) {\n    // this is important to make the div 'focusable\n    el.setAttribute('tabindex', 0);\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    } else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n};\n\nmpl.figure.prototype._key_event_extra = function (event, _name) {\n    // Check for shift+enter\n    if (event.shiftKey && event.which === 13) {\n        this.canvas_div.blur();\n        // select the cell after this one\n        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n        IPython.notebook.select(index + 1);\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    fig.ondownload(fig, null);\n};\n\nmpl.find_output_cell = function (html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i = 0; i < ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code') {\n            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] === html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n};\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel !== null) {\n    IPython.notebook.kernel.comm_manager.register_target(\n        'matplotlib',\n        mpl.mpl_figure_comm\n    );\n}\n",
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+uvd/Pnz3dFHH+3PEYfPjXOZtijTBbumy0VABERABERABBomIAHcMHA9TgREQAREIB8BC2Blga6iLs/RWqoSwNR73XXXeQF8/PHH+8dEXaYR5WFALUu9FE27lK+nukoEREAEREAERKApAhLATZHWc0RABERABHITMJfnxx57zN9zwAEHjDrvG1dRnQI4+rwsQWxpl7AMmyjOOpecG44uFAEREAEREAERKE1AArg0Ot0oAiIgAiJQB4HQ5fmmm25yiMiFCxeOpDdKeqYFyDJLcSdtwwV67ty57oQTTshVTZhuifZbG0IrcfQMsQRxLrS6SAREQAREQAQqJSABXClOVSYCIiACIlCWgOX2RcjyQyEYFUJx0aJFmdVWaQEuKoCjjYsKYl6nHxLEmcOoC0RABERABESgVgISwLXiVeUiIAIiIAJ5CCTl9l25cqW3pi5evDizmioF8IoVK9zs2bPdm9/85szn5rlAgjgPJV0jAiIgAiIgAvUTkACun7GeIAIiIAIikEIgmtvXLKXcggDm9bPPPjuTYS8L4GjjJYgzh1MXiIAIiIAIiEAtBCSAa8GqSkVABERABLIImMuzRXnm+mhuX1ygh4aG3JIlS7Kq80KZa62ezBtSLrjhhhvcnnvu6U488cROqsl1LxwodnbY8hwnuUxzJjrKKdeDdJEIiIAIiIAIiICTANYkEAEREAERaJxA3ty+q1evdlu2bHFLly7NbGPVAniPPfZwJ510UuZzq74gSxCHeYgtyrQEcdWjoPpEQAREQAQGlYAE8KCOrPolAiIgAj1IoGhu31tuucVt2rTJnXPOOZm9qVIA33jjjW7WrFldEcDRjoaC2KzEXGMWYku5FEaZliDOnC66QAREQAREoKUEJIBbOvDqtgiIgAg0TcBy+yJUzc03S6jdeuutbsOGDe7cc8/NbC514gJdRRokBPDMmTPdySefnPncpi+wHMThOWLaEEaY5t8SxE2PjJ4nAiIgAiLQDwQkgPthlNRGERABEehzAnldnqPdRAC//vrrbtmyZZkEqhTA5B+eMWNGTwrgKAgJ4sypoQtEQAREQAREYISABLAmgwiIgAiIQG0E4nL7Zll9w8bcfvvt7pVXXnHnnXdeZhurFsDTp093p5xySuZze+2CqCB+4YUX3KOPPuoOP/xwN3fuXG8ploW410ZN7REBERABEWiKgARwU6T1HBEQARFoGYGoyzNnVu0nLwoE8Msvv+zOP//8zFuqFMA333yzmzZtWl8K4CioZ5991t13333umGOO8QLYzhQnuUwTWKvoOGUOji4QAREQAREQgR4hIAHcIwOhZoiACIjAIBEwMWpBm8LcvkX6uWbNGocF84ILLsi8rWoBPHXqVHfqqadmPrfXLzABfNxxx7m9997bC2D7CYNqxQliizItQdzro6z2iYAIiIAI5CUgAZyXlK4TAREQARHIJJAnt29mJcEFCODnn3/eXXjhhZm3VSmAV65c6aZMmTKQAjgKMiqGQwtxKIpNDBNci7+riIAIiIAIiEA/EpAA7sdRU5tFQAREoAcJWKArfvNTxuU52q277rrLYcG86KKLMntcpQBetWqVmzRpkjvttNMyn9vrF0QtwFntzSOIwwjTEsRZRPW6CIiACIhALxGQAO6l0VBbREAERKAPCRTN7VukiyaAsQAjqNOKBHA8naICOFpLnCC2zQ2zEEsQF5nVulYEREAERKCbBCSAu0lfzxYBERCBPidQJrdvkS7ffffd7uc//7k/A5zldrt161ZvLebs7h577JEpmNPasXr1ap9Hd8GCBUWa25PXdiqAJYh7cljVKBEQAREQgZIEJIBLgtNtIiACItB2AmVz+xbh9pOf/MQ988wzPgo0gjSpvPrqqw6xvHHjRn8J51Vnz5498kNKoywLcli3BHD+USpqIbYo0/mfoCtFQAREQAREoDoCEsDVsVRNIiACItAKAp3m9i0C6b/+67/cunXrfB5ghFO00Jaf/exn7oEHHvCRjQ8++GC3fft2nzrptddeG7l88uTJowQxKY7Syi233OIF8+mnn16kuT15LRb0n/70p86iQNfdyKggZqMkGmHa8hCHUabrbpfqFwEREAEREAEISABrHoiACIiACOQmUEVu39wPc87dc8897umnn3bLli3zQanCMjQ05O69917v9oygPeGEE9yMGTN8AC4EFq8jhF966SX/s2HDhpHbcZMOLcREfA6LBHCRUUq/NhTElnYpKQexnSUuYq2vrqWqSQREQAREoA0EJIDbMMrqowiIgAhUQCAut2/d+WERuE899ZQ799xzHVZcK6+88op3ed60aZPbZ599vHUT8bRt27YRARztMmeETQzzm3ut4CIdCuI777zTW5TPOOOMCsh1t4qmLcBZvbWgafab6y1PtP2OBtWSIM6iqtdFQAREQATyEpAAzktK14mACIhASwlUndu3CMb77rvPuzifc845Pi8vbXniiSfc2rVrvWg66qij3IEHHuj/HaZhygqYRRs2b948ShBv2bJlpGncz88xxxzj9tprr1j36yL96Oa1JoCPP/54N3/+/G42JfbZEsQ9NyRqkAiIgAgMNAEJ4IEeXnVOBERABDojgDjBlbjK3L5FWsTZ1SeffNItXbrUC1JcotevX++w2J544ok+2rOVogI4bAf9xCJsFmKewd8oiOtZs2aNWIj33HPP1IBcRfrXxLW9LoCjDCSIm5gVeoYIiIAItJeABHB7x149FwEREIFUAhZMCgssbsa4CDftinr//fd7iy9il0BXWG33339/b5mNBsXqRABHQdx6661e+BNUC1HMWWLcq00QI4LNZRoRnsfi3K3p1m8COLoxwf/t7DC/KfSJ8TjkkEM8e7lMd2t26bkiIAIi0H8EJID7b8zUYhEQARGolUAY6Oq5555zd911lzv22GO9q3HTxQQwz0XkHH300e4Nb3hDrBCvUgDffvvtXgAvXLjQdxkmRJU2CzGC2MQY7QoFMdbipjcK0salnwVwtF9mleeMNimvLEp33BliizBtAbeanrt6ngiIgAiIQG8SkADuzXFRq0RABESgKwSiuX1ffPFFt2bNGm9xPeiggxptE2dyyceL1ReX55NPPtnNnDkzsQ1h29NyBufpBAKYoFlnnXVW7OU8i9zDJogJymXiDOHFuWGzEBOZupuCeJAEsA0GcxKXdRufqIXYBLGd5ea3BHGema9rREAERGDwCUgAD/4Yq4ciIAIikEnAzl1aFGX+j2hA4N12223e8oo7cFPlhRdecOQAtsBUZ555preyppUqBfAdd9zhn50kgKPtwF0cEWyCGHFshfRNYYRpUjY1KYgHUQAnjY+lXArPETMOUUEcukzLQtzUu1rPEQEREIHeICAB3BvjoFaIgAiIQNcIRHP70hATBQg6zsMSbZnzlnUXROwjjzzifxApc+fOdbhhI0RxLW5SAGN5XrRoUakus5EQ5iB+/fXXR+ohmnUoiMlJXGcZRAGcZaE3nkmCOC0PsQRxnbNRdYuACIhA9wlIAHd/DNQCERABEegagajLs+X1NQslVk3ckI844gh32GGH1dpOBOdPfvITb0UlsNSb3/xm98wzz7iHH364cQFsLrZlBXAUFO7UoSDm/KoVLMKhIA7zHVcBHIacpe7VNEhl+hg9o523DgnivKR0nQiIgAgMLgEJ4MEdW/VMBERABBIJWG5fXHf5ocRZvnDlXbVqlXvTm97k3vjGN9ZGlLRDuDwTeIqzxlicaQ+W4Iceesg17QJNkKUNGza4xYsX19Jn3KvNXZpz1mEOYs4MmyDmLDEu1J2UQRTAuOUzb5kXnZSigphzxLZJ1Mlzda8IiIAIiED3CEgAd4+9niwCIiACXSFQJLcvkY9XrlzpxS8iuOqCBRqB+9hjj/kgRVgpSblk5dFHH3UPPvjgwAngkCPjgfXbBDG/sRhbCXMQI4iLBvgaRAGMWz7czjjjjEqnZBFBbEG1JIgrHQJVJgIiIAK1E5AArh2xHiACIiACvUMAq1kY6MqCAyW1ECvoTTfd5N2fcYOusuAGjMszbtYEuMLlmWjPYUEYr1271qe7wSqaVqoMgkXqJ8T/2WefXWWXc9WFCINNKIjDHMS4h5uFGG5ZOYgHUQDfcsstnmXVAjg6QCaILcq0RfqOniE2MczmRNZ45JoEukgEREAERKA2AhLAtaFVxSIgAiLQOwTM5dnELy3LE+wHIXbjjTe6Qw891B155JGVdejZZ59199xzjxfj1I11OU44PP744+6BBx5olQCOE2EE0QpzEIdu65aDeM6cOT5NVJSjCeATTjjBzZs3r7Ix7GZFCGA2bywPcFNtSRPE9n4KI0xLEDc1MnqOCIiACOQnIAGcn5WuFAEREIG+JGCWUX7zEw10ldYpXHNXrFjhUyCRCqnTwvMRtE8++aQ/24oomz9/fmK1TzzxhA/gdNppp/mI0GmlSgvw3Xff7S3TS5Ys6bTLld9PP7FOhzmI+RsFwRUG1OI8MVGgYThIApjAbPR1wYIFlfMtUmGcILb3lwRxEZK6VgREQASaIyAB3BxrPUkEREAEGiWQlNu3SA5agjNdf/31PjDVMccc01H7cafG5ZnAWog0XJ6zUgAhlH/6059KAKeQxxoM0zAHsbnqsskAYwQzFvz999+/0RzEHU2YlJsJzEbf2BjppSJB3EujobaIgAiIQDwBCWDNDBEQAREYQAJpuX2LdJdgTNddd5074IAD3HHHHVfk1lHX4oZ77733+si9BNTiJ89ZyZ/97Gfuvvvuc6ecckqqpZiHVWkBtnRMS5cuLd3nbt2IWznWaxPEiF8rYQ5iAmqRgqkfC4HZSBfVawI4yrKoILYo0/04JmqzCIiACPQLAQngfhkptVMEREAEchLIyu2bsxp/GWLqmmuucW94wxt8hOaiBcGL++1TTz3lEF+44Wa5MofP4D6EswRwUfK7r4chkbThjks7lngrdecgLt/q9DsRwMynU089ta5H1FJvVBDzXg0DauGdYWeIwyjTtTRGlYqACIhASwlIALd04NVtERCBwSOQN7dvkZ4jYK+++mrvOot4LVII3MRZWn4jvrgf0VKkPP300z5Y1sknn+z23nvv1FstvRNtLpoqKFoxOYlfeOEFd8455xRpbk9eGw2CFeYgxkqMKLZSdQ7iuoDcfPPN3nrNxkg/l1AQv/zyy36uE3GdDSeEsf2EUaaLHGHoZzZquwiIgAjURUACuC6yqlcEREAEGiQQdXkuEugqrZnUu3z5crfvvvu6E088MVePuAfhiuUXC9fhhx/uF/VlFu7r1q1ziNGTTjppVH7guIZIAMcPT1YU6E2bNjnEF2L4xRdfTMxBTLRphFgvFFJzkTKr3wVwyBL2bBjxfmHDyQKbWaoy+x2NMl3mfdULY6g2iIAIiEC3CEgAd4u8nisCIiACFRFgoTw0NOQXzIjArNy+RR975ZVXevGJCM0quEwTtArhSvAlAl1l5e9NqxPxxnlcxDciPEus83x+OrUAY4lbv369O/fcc7O63POvMxZE3s4TBZr5gyAOcxAztyjMqzAHMf/ulHNZeKTmIuUTngGDUvA4YK4fddRRXgBTLJCd/bZxCN2mJYgHZQaoHyIgAk0RkABuirSeIwIiIAIVEyib27doM7AAkz82y9pGJGIsWOQOJrURZ4YJVNRJIYUPdSKk99tvv8YFMC7Q/W5hKyKAo4CZY5wZDgVxXA5iNjlmzZqVK7BZJ/PB7kUA87w8mzJVPK+JOp5//nnv7UC6saS5LkHcxEjoGSIgAoNOQAJ40EdY/RMBERhIAp3k9i0KhDPACJykgEMsyonWjJWRf5Nuh7zBVQjHZ5991t11113eemlWsaT2mxt4FRZgAm8999xz/gxwFf0oyrzK6zsRwNF2MO840427LqKYaNNhDmIiS1seYiy0dbG74YYbHC7Zed3yq+RZV13MN+Yd6cayvB2sDRLEdY2G6hUBERhkAhLAgzy66psIiMDAEagit29RKESBRmzEpZzBPZY0RVhqCUqEpRYbbRTUAAAgAElEQVQRVFVBFNx5553emkxgoLRShwAmDVKedE1V9beOekwAMzZFInDnaQviN0y5hBeA5SDmvLCJYX5zZrcqQbxixYqRXNJ52tkP17DZw3uJdGNZAd/i+mPc7ShE1hlixsdcqfuBj9ooAiIgAlURkACuiqTqEQEREIGaCVSV27doM8kDTHTg008/fdStCB/ckzkzyhlhFu6TJk0qWn3q9ZzDXbNmja+bXMRNCWCECIJEArjYcOIebQG1sBCHOYhxhw8FcSc5iK+//no3Z84cv+EyKMWClbHZwxGCTkuWII6LMi1B3Cl13S8CItAPBCSA+2GU1EYREIHWE6gyt29RmIgNxMoZZ5zhb2Vh/cQTT7i1a9d6ix5Bew488MDKrHth+zgXeccdd7hjjz3WP6MpAUwgL6zaS5Ys6Vqgp6LjlHR9nRbgrDbiIRAK4jAHMUHSQkFcJEUWc9JSa2W1oV9er3ucLOVS6DYNGwuaZ4I4DKolQdwvs0ftFAERKEJAArgILV0rAiIgAg0TqCO3b9Eu4G6K9W7hwoU+RY5FSMallTOYRAOuqxAZ9/bbb/fnIg866CAJ4BKg6xZWRZrE/AkDauE9YIX5ZIIYN/q0AGp4JVigtSLP7+VrSR3GphLvKazbdZckQRxGmObfEsR1j4TqFwERaJqABHDTxPU8ERABEchJoK7cvjkfP3IZEXdZBCNCSdOyefNmH6UWq2zdeWEJtnTbbbf5yLgE1korVZ4BJocxLqlnn3127X0sOh5Fr+8lARxtO3MpFMRbtmwZuYQgWqEgtrnGOGMBHjQBTCC5hx56yEe27iR1WNH5YddLEJclp/tEQAT6jYAEcL+NmNorAiLQCgKW25e0KIhAhBiuilUFESoCEQFMZGXcWXk+QpiAVE20BXF06623ejfrQw45RAK4yMDturaXBXDYnawcxKQ9QhgSkI33BYGiOBs+KOXJJ590Dz/8sE83Rh+7XYoKYjYouvUZ1W1Wer4IiEB/EZAA7q/xUmtFQAQGnEA0ty8WVyIhX3jhhY0IziheLHIIYIIbYZHDPZPfTRXOj95yyy0+tdKhhx7amAAmpRPCcfHixZUH9mqKnT2nXwRwlEs0BzFzgY0YKwRcIzAaohg3/H6P1v3444+7Rx991Kcbq/NYQdn5V0QQI4bxGpEgLktb94mACNRJQAK4TrqqWwREQAQKEGCBiZUV6y8/LB6xdBGM6YILLmh8gc/5W56PCGYxe+655zYeEIpI06tXr3ZHHHGEO+ywwySAC8wnu9TOltaRBqlEc0rfwvuDqNJ4RCAUeX9YpGPEb5iDGGtxEx4KpTsTc+Njjz3m+FmwYEGjm0xl+1BGEPf7JkVZVrpPBESgtwhIAPfWeKg1IiACLSWAhRXrluXwtEA0CFAseOedd15jZ1FZ2OKK+cgjj3jBSzAi2nXOOec0PjrklV21apV705ve5N74xjc2JoAJRoRwXLRoUWowpsaBlHjgoAhg6zrvE7wSSL2FK76dIWazJMxBHApi0nj1uiBG1GMFJt0Y7e23YoLYPsPCzQk20eCP90g0qFa/9VPtFQER6H8CEsD9P4bqgQiIQB8TyMrte++997qnnnrKW1/TouJWhYCgRLhdIypww8RqSBtIX0Mbmi5Y/FauXOkOP/xw/5NWzH2cSMOdBueSAG56pPM/Dy+Jm266yQdiIziaFTaREMEmiJk7JsJwl47mIO41QcymE+eASTdGROx+L6Egvuuuu7wnCeLe0i7xOxTD/FsW4n4fdbVfBPqDgARwf4yTWikCIjCABPLk9iUfLYtirK9F8qSWwbV+/Xrv8ozAIOUQgadYkBKFGTGxbNmyMtV2dM/rr7/ubr75Zm/9xQrclAB+8MEH/cbDWWedVTv3jgDluHnQLMAmgPfff38/R5MKluIwBzFzyQrvpVAQk5O424UI0ESCJt1YL7SnSh58hjAeiPvQQmxnhM3jRYK4SuqqSwREIImABLDmhgiIgAg0TADLiInfqMtztCkEY8ItcsmSJW7atGm1tJQ2sPjm/CGWUyLr7rvvviPPuuOOO7xV7fzzz6/l+WmVYnnG2sf5X84BSwAXH4Km88sWb2GxO7DwsymC+zPB0fIW7gsF8caNG0du5b0VCuImvC2i7R6kTZdo3whkh9jFAmwlzmU6TRBblOm8463rREAEREACWHNABERABHqAQJbLc9yimLOBRCOu41zgpk2b3N133+1dR0m9gstz1P1yzZo1joBYBOJquiBSOO9JBOgssVOlC/QgWeMGTQDjSotbfFEBHJ271BPmIMb93wrvtTAHMS7UdZdBijweZcU5fhiedtppiRijgpiNObMMRy3EYZTpusdF9YuACAweAVmAB29M1SMREIEeJZDH5TnadIQYwahwxSWybZXl2Wefdffcc493TURg4mIcdwaP83tce9FFF1X5+Fx1IdBvuOEGnwM4zd2VymxzARfZTs8AmwA+88wza7O85wJQwUWDKoBJgZTlFVAEH3MtFMRYjK1YDmJEMcG1cNWtutx///3umWee8Tm/O52/Vbet0/qw2GNlJ8dx3pIliPms4sfEsKVdylu/rhMBEWgvAQng9o69ei4CItAQAbNMEqSHH4pZNLKagPhFjCHEsNBWURDiBHl64oknvFXmhBNOcPPnz0+sGgsxqZi6kYsYq9yKFSvcwQcfPCrgUVxjqxTAFpBIAriKGVdtHcwJLIoHHnhg5rnwsk9mLuF9EApiy0GMmy4B4sxCzPuyiuBN9913n99o4rhDHQK7LIsq7sOLg02Ek046qXR1dnQk/G0i2AJrRc8Q91qgs9Kd140iIAKVEpAArhSnKhMBERCB0QTicvvaObc8rDiXi1jl7BwL7k4LZ2qJ8kx6IerD5Tkr4A7XY5nqRi5iE8AE5TrmmGNSu1+lAGbjgQ2CQYjIO2gWYCy15IZmTmRFBu/0/WL3M7cIomWCmLPE4WYWItgEMUKvjCAm2vpzzz3nA94NmnBjE8s+b6ocE4uhwG9KGGGaMZAgroq26hGBwSIgATxY46neiIAI9BCBaG5fW5wVaSIiDNdIzs7NnTu3yK1jrkXEssimXURV5ifPQh03aURUk7mIrfG4oV533XXe2nfsscfmFsCdukNKAHc01Wq9GcssQZWaFMDRDiG4iIwe5iA2EcbcC3MQk/s2j6AlAvvzzz/flXRjdQ4YmwfXX3+99zI5/vjja3tU1EIsQVwbalUsAn1PQAK474dQHRABEeg1AubyjMukLYrzujxH+0JaFFwjTz31VDdv3rxSXUXwIqJJ60N0W6y+RcS05SImDVITwYDCTpoA5rwn0anTSmgB7lQAE3iM6NtY3usIPlZqIEveNGgWYLwYbr31Vu8WzyZOLxTeY3hVmCDm32EO4lAQE2QuThBb/u2lS5f2QpcqawOfgViA99lnn8xNrMoeuismgCzEVRJVXSIwOAQkgAdnLNUTERCBHiAQpjfi3+bunMcCFNd8xAsW2JNPPtntvffehXuI2yZnePmN6OW8b9F8wk3mIo52kE2Ea665xkf8zbIeSQDHTw82Pkixc+KJJ7o5c+YUnkO9doMJYAKjkR6rFwvzlsjqJoixFlthEypMuWTpzSwaO2eAB6nAgjPA++23X+Y5/rr6bZsReQUxgbXKblrW1QfVKwIiUB0BCeDqWKomERCBFhMoktu3CKZ169Y5XCMRL2Fu3jx1IJ4Rr1iniPCMWCgjxLEe44qNZSrrvHCedhW5xgTw/vvv78V7WkEYwYozogg9RAa/iwp+nsHZa34WLFjgcGHt5zJoApjNnNtuu81HLuenHwqRycMcxMxVK7ynmKsIZlIzDZoALpu3uc5xzRLEYdolizItQVzniKhuEWiWgARws7z1NBEQgQEkUDS3bxEERF/GMoT4QwTmKYhGhC/iGfGHy3Mnlj/yk+IOTHqWaI7gPO3p5BosNldddZW3HtGPpBKmdMKihgi2YjldYYArap4UMxLAnYxavfdiTb399tv7SgBHiSAKwwjTcfPVUi41feyg6tGzoGV1Ru3utM2hIDYrMXVa3AaLNh0G1ZIg7pS67heB7hGQAO4eez1ZBERgAAiUye1bpNtEhb3zzjv9+VfOwWYVzh5ylhALkwWdweWyk4L7LGdiFy9e3Ph5WBPAWL+xgkcLr9M+BDpCAU5E4WUTAIvbiy++6H8spysLWl43C3FSChvqo88EH6s6/3InY1HmXrMAk4KmikjiZdpQ5T0mgPFowA16EAoikXzbzFPmMZZgK2EOYuZrng2cXmLSi2e2s/hYDuIwsBb3mOiVIM4iqNdFoLcJSAD39viodSIgAj1KoJPcvkW6RFTYO+64w6cAIuptUqE9BMzCWsu/jzjiCC8Oyrg8R59BHmKiIi9atKhxd2D6snz5ch9AJ5pDlBRJFjgIyy4WYsQDIiIMghXmdEUMY3kLU9jYeUxEMdZimEkAF5mlzV7LJg/vCQJgEQhrUApu3cxLUm8hiEMLMS7UlGgOYvIR93rO4EGw2KcJYjbh+GGjkR+zEstCPCjvTPVjEAlIAA/iqKpPIiACtRKIujx3GugqrbEINhbGRx11VKK1i8UxkaJxl8b9FyGIIKyqIH4RwQsXLnQsuJsuV155pQ8ARiAwKy+88IIXv4hdhD6Cn3FAQEQFcLS9YQob+HL2MozYiyDm/+vXr/fRt7vR5yoZD5oFmPFas2aNzwGctilUJcMm6iKyNfMOARwW/oYVNRTE4QYO89POu5fNQVxn/2y8BmnDIhTEeOkQJ+HII4/0G3Wh27RcpuucWapbBMoTkAAuz053ioAItJAA4gnBaefEyuT2LYINN15ynrK4igv4w+KSM8JYjFh84QJc9ZlBXIFxMz7zzDMdLphNFyzApIA65ZRTvEBAkD/88MPeFZT+hsHBcH3OEsDR9iMmLEARgpggS1Y4Q82zzUpcNdsmWA6aAGasOBYwaAJ49erV3sWW1Ftphc8e5qgJYnh0moO4znlIO3HvJhAf54AHrZBfHQHMZxGR9sMzxEku03x22cbpoPFQf0SgHwhIAPfDKKmNIiACXSdQZW7fIp3B3XPVqlV+8RjmPKU9RGZeu3atr+7oo4/2i8sqXJ6j7SMgFM9hYd6NM6QEwcI9mUBgRHnGLRxLF2eCozl6EbOcn+wkDzACGos3gbVwabTzw3Cx85i0h82AXnc/pc2DJoAHVVDxPmeDhXPnRQqCK8xBHHo0ILTClEtJOYiLPK/oteatwSYe6cwGrcTl2S5yhtiiTEsQD9rMUH96mYAEcC+PjtomAiLQEwSqzu1bpFOcn1u5cqUXv4hgCoLs3nvvdbjesaBFCNbppovQxsJBSqBOokkX6Xd47dVXX+2FLv3m3C/BwBD8ceLTXKA7PX/35JNPeiszVmdEsJ0d5jdWZgrPQASH7qd1bECU5Wb3DaoAxu09T2C4Tvk1df/NN9/s04zhdt9J4T0Q5iBGHFuJ5iDmeXXPWY4SkMuc9yzR3AethJ8VSR4yJojNOmxHLiyYlnkSmRjms43XVERABOohIAFcD1fVKgIiMAAE6srtWwQNZ/9uuukm7/6MBQXrF2dfEYIsJo899tjao8KywCOtEpYpXPyaLIwBApiFIwtC+ptmRapKABNQDCsw547D89S0B/dTiy6N0DD309DaxkYB57HrFhd5xmLQBDDscfsfNIsi73M2esKz7nnGN+sai4huLtOhi7/lIDYrcZmc2VnPx5OCGAW4CHOWf9BKmZRpWYL4Ix/5iMf07W9/uyc+QwZtzNQfEZAA1hwQAREQgRgCdeb2LQKcs7033HCDD/bDYhVRhqgiKjRCsAmBhYDC4ow1lNRKTRUW7liOWEAjfjmDnJWSqGoBnJU6iOdhYTMLcWhtQ0xYuiV+d5qOqiz3QRPAg+pSe+ONN/r5HY12Xnbck+7Dk8LOvCOKN27cOHIpHiUmhtn4qWLO2hlZjjBwnn7QCp4ibBISvKxsnvSoIGazkbo48tHEZ/ygjYn6IwJZBCSAswjpdREQgdYRwKKH8CT4Ey5tiL5unc/iPOv111/vxS9W35kzZ/ooz1lCsMpB44wbQhTLVFMWHFy/CZzD4hzxS38RwFmlKgFcVjQSIM3yD0fFBWNn7tJN5nM1a3aWmM9iW+b1m/bJd551wrQJbuHjt+R6hAlgIqPvv//+ue7ph4tWrFjh5wfv7yYLnythhOkwB7HNWdqFIC6TgzjujGyT/av7WQQI5PPirLPOclVY0BHDeDew6UkARAngukdQ9beRgARwG0ddfRYBEYglEOb2NddjFiFYW7tVsH4iBClpZ1/rbN+6deu8JYKzxmHE5bqeyWISl2vGA5FD1GfciZsUwFUt2k1cmIXYAmpZPlcsw/zUmb6maQG86pDhND7bN20fM0V2Du0c+du4SeNip1CWGCYIGvNx0M6UstHFEQMspd0qvOfSchBbEDgEcd4gcEnHCbrVx6qfS3wErNxnn312qQ2CaHsYAz7rsQJfe+21VTdX9YmACJBTfaedxBcOERABEWgxgajLM+63LEhZiHB2relCe3CtQ/xRsL5E84M21SbyC3PmEstUnUFssN4ifBGfWLwR3PQbyxiumOQhzipVWYCrEsBhe8N8rghiLMWWz5WgN+Z6iiCuMlpvEwLYRG+S8OXvofiNjiNiePzE0YJ44h4T3en3rxoz5IMYVIm5wecN3ibHH3981jRv7HWbs6HLtAWBYxPHgsAxdwnEFxe4iSB6fI4NQk7tOPAWkPCcc86pxFrLZwIbIW9961vdf/7nfzY21nqQCLSJgARwm0ZbfRUBEYglYFGeWXiw4GNhx9+uueYa72LZtEUGqyEWLkQSFhfcgbG8Igi7UcwKDYe6XE6xuCOy6SvnBHmWnT/kDDTpYZoUwFi9H3jgAS/66wr8FaavYaw5P2x70hat184QsyFQttRpgbtzwWK3+bmhUU3LsvzG9WPCtPiIt4hgSiiEiX6O6MAzowmPhLLci9zHXGCjh1zeBHrr1WJB4MIcxLaJg/hlw8o2cvjs4rO0TJCoXu1/XLsISgiPpUuXVtJsPgvZaLzkkkvcd7/73UrqVCUiIAKjCUgAa0aIgAi0lkBabl9eW758eePCE+sW4pezpLhfcxaMKMicva06OmzegUdw3Hnnnd4SXkfaGSzMnDFmIU2qp8MOO2yUJYXgQCyuFy1alNnkqizATQjgaGfCaL0IYhbCVrAImxhGYBQ5i1mXAA7FrwnYba8Op4gKy45tu92eo1bgJOEbrSO0BpsARigiGAehMG/Z6EHQd/PIRVGWCHc2rcIgcGFUdAQxfUMgkkc8mre76PN68Xo+G4msjQt0FYXvANLevf/973ff/OY3q6hSdYiACEQISABrSoiACLSSAAIXkclijR8LchUGHEEAY40k+nHdhTYQ4RlrCeIGsWnWrauuusqLn07zg5btA2cu77jjDm+ZOvDAA8tWM1YY7djh1q5d63CRxOKZZG0lPQzj0qQA7oXItQQjQjiYuAiDE+FuGgbUSssZWrUARvhShl4bfcY3S/xGJ0DU5TlrYpk1+JAVVwxcWh0+i5jnWP4429yvJZqDGHFsXg18roWbOL2SJqxT1nw28t4kCFYVhe8APgt/53d+x33jG9+ookrVIQIiIAGsOSACItB2AizSsLYhOlmcIR7iIm3iAs0ZN4KR1FkIOoMbHefseB6LnzCdRlPtSOojUXdvv/12vzA/+OCDK0ER9tki3ya5+d58881+rPJYWKqyAPeCAA5BW3AiE8MIYzuLaa6nJi6I3BvO5yoFMOJ33IRxbuvLoy29ceKX9ofW3+jEIdgVZefQjsQ5NXnOpFGvTZw5wT97w19+2Z+VbTItVyUTP6ESgqMxz0lthtfHoBTmKDmA+QzB+ht6NRAx2dyl+d2Jm383ed16663+e6SqGA14wyCmP/WpT7kvf/nL3eyani0CA0tAFuCBHVp1TAREIEqgaG7f6667zi/acN2rq3C+lvOMWIAOOeQQd8QRR4wJJNNEO9L6h9hikUdEZtrYaQndvA899FDv9pxmwVy5cqV3o8wrgGHZadoq3LIJyNWrIosNAdwuEcT8vPLKKyOWNs5LhwG1sODjXYALPS6pZctdZw67eEbFL38rav018TtK5EeEsFl8xwTHmjksnA/4z+8PjADGgsg854gBnwGDVHgf8X7i/ctncJhyKcxBjEU4FMRV5CBuguOqVat8jIKqNkr5rD3//PPdZZdd5j75yU820QU9QwRaR0ACuHVDrg6LQDsJxAW6yhJJBKXBSpEn/U5RqrTH3H9ZPCG0knLs1tmOPO3GMk0+SixTCNayJYxsjTskga7y5BVmgYmFLE+QGYRyGwRwdAzM9dQsxLieWmF+wYSxw8JYRliY+I0TwEWtv3Hi19pq1mATv/b3JBF80uoby07HnroPj4jVq1f7c/+HH354T7Wt08ZYlGTev9GNLnPzN1FMAEArbD6aIGbjhnnciwXXdTx2qjoqw4bnxRdf7P7sz/7MffSjH+3FLqtNItD3BCSA+34I1QEREIE0AoguE79ZLs/ReoqcPS0yCrgB4vJM1N8s91/qJQgUaXKqOmNWpK1ci3WRxTmWWoKzlCksdAnuhSsk51eJaB26eafVybO5v0kBjGUe103OYucR6WWY1HkPGwZsXCCIsbgjgK2EuVwRFsytpPLAW853m17eMvKyWX8nzdp9T/QscFxdW1/c/fw0Acy9SYGxBlkEYwllk4kjBmXfY3XOp07qtvc9aYKySjQHseXN5r4i8zbrOVW+TvAyjq5UFaWf1Efvfve73T/8wz+4973vfVU2VXWJgAjsIiABrKkgAiIwsASKujxHQRRxvc0LkbOlWESw2LHQ5SfN/Zd6ORtIXxYvHg4+1HTBmggLLFNlrFNYd0hxhIgliBau1GmiK9o/hAEL4zwL6KoswP0ugEOGTz75pM8pjXURCxvjYYLYcrlyfpgfS13D/VHxu3P77mjOVn8e8Rsdz+2bks/8mrBOOjs8qCIYd/bbbrvNHzEgCvogFd77bKItWbKkULf4zGNjIEy5FM5bCwTHJiICNOtztNDDc15cR/5mUh/91m/9lvuXf/kX9yu/8is5W6LLREAEihCQAC5CS9eKgAj0DYEyLs/RzhWxPGaBQZjdf//97qmnnvIuqLj/EmE6T0F8Ekym6AIyT915rmFxjghnYV7kfCKLw8cff9w9+OCDfnFKFOkyeYQ5E4fV/Nxzz81sblUCeJBS7ZgAxkUToRDmcsVCjKU4TF2DoJj0vz4+YvmdOHU4F+/QhtH5fv3fIpGg0wYoKl6j94ZWZasnTggPoghmk4lAc7zHqjhnn/lGafAC0gTx/u10Ay8rBzFzO8xB3IQgriN9FamPPv7xj7sf/OAH7q1vfWuDI6VHiUB7CEgAt2es1VMRaAUBy+3LwoQfSlKU5ywgWGRYmC5btizr0tTXEZBYQfg9d+5cL345W5y3IMSx3OWxgOats8h1WGFww+YMad4ItVhqsHRjSeUs30knneSITlymFBmHqgUwOVktHVWZtvfCPVEBHG0T4hcLnaVcmvmZ4cA7Q5t3pznqVPz69+HEcWNwmAiOE795RfDUeVPcts3DUan79Uww/NesWeM9QqqKtN4Lc482VJ0maGRe7MpBbBZiGNpGDh4muPebII5GRq+KjUXvZmMPz5Yqyp/+6Z+6z3zmMz4vdJ7Af1U8U3WIQNsISAC3bcTVXxEYYAJ5cvsW6T4LNxZXROQsW55++mkfTRhhxhlaLDxxKZfS6i9iAS3bzrT7cD9mMcbCPE+OUs4233XXXd5tmbymWH4JelW2YBljcXveeedlVlGVAObcLOlI2iCAQ6i4PUfFr/9/xdbfzIEMLoizAk+bP9mNmzB+5KpJUyd4i/WUWZPdMVddU6T6nrgWKzyWUj4jqsy13QudYwOL92UdwQTD/oUbOXxu8zlkOYgJoBUKYuIPFP0cjmNpwcsYM8auikL058svv9xviBC5XUUERKB6AhLA1TNVjSIgAl0gEM3ty+KmUxc4FqQIoQsvvLBwj3BZRviuW7fOW3vJ7csZyzKliAAsU3/WPVifiUTNGVIEYVJhsYmLN67e/BuxzMKw04VmkY0IE8C0sZPxNwFMHxDx/VyyLMDWt7rErx+LGOuvPZfcvpRtr++2OEd5mwhG+IYlKoJ5bcf2nX0nghFsbBpxxIBUSINUOMPPZ0Cd6eTiePEZbJ4N8A0jo3MMJUy5RAqmMgXXbjYoqzy7Tf7fP//zP3cPPPBAbo+bMm3XPSLQZgISwG0effVdBAaAgLk8s9gx97eyLs9RHLgtk7/yggsuKCSmWGhxL4uj+fPn+xRHZVLPWHuwBBA9mXZ0o+DmR2oOxCzW3KTFpgn+qVOnepdnzuRVUYr0vyoBTO5cote2RQCb+J0wZaLb/MruqM+MX2j9nbLHsADdvnWsWN25YzhI1uYXRp8VThO/XG8COE0E4+a8c/vY4FmhAOZ+LMH9KIJ5fxMZniMGpKoapFJ1ntyybDiWgaXdXKb5fLbCZ1YoiPMeUcHKzAZdla7rv/u7v+sjQOM9VCZmQlk+uk8E2kRAArhNo62+isCAEQjTG/Fvy+vbqcXRMOECyyIE19s8LryI8Z/97Gd+555/Y83BMtBpe7AMcZYWS3SndZWZAiwcr732Wr8wR8xHS3jGuQrBH62/iCW+KgFsgoRzff2+CM2yAD/57v/HbXl967B4jRG/JnptXOLEL6+ZAI6O39ZXhs/nxpVQ/NrrUUsw4tdKlgg2Acz1k2dOdof96w/LTPnG7xmkDZcoPALoYWGtKk9uVYPDxp6JYX7jzmwFF+lQECflIDbLfZWu6x/4wAd8BGis10S6VhEBEaiegARw9UxVowiIQM0EOsntW6Rp5IFF0BJ9OMuCi0jkeizGLPZweebMWRWlrCW6imdTB6Ly6quv9qY95S0AACAASURBVEKQAF5hCdM6IfgJlFW1SC+yAWCu8MyRTlyg2ySAH7r4LSNDagKYs7SUoY1jIz+nWX/j5ty48cPBr7a8NLauOAHMtSaCQ/FbVAT3kwC2qOODcOY8OgcIoEd6LbxCerlYijATxaRts0IQLRPEfK7bhqhtXFS5Ufaud73L/fCHP3QI9Dwbr73MVG0TgV4lIAHcqyOjdomACMQS6DS3bxGsnGV94okn3NKlSx0uckmFnXpEKhaEffbZxx133HEuyWJQ5Pl2La64nCXOa4ku84y0e7CuX3XVVT4a8oknnugv5W9YurEudnrGOau9tgGQxwJelQWY9EA8dxBcUtMswFHxa8LXxiQqgItaf038Wn2hCE4Sv3atpV+Kmx9RS3CSK3S/iOBByjsdHS/iByAe2RTsl8L3DJ/noYU4zEGMoKdPbPaR6o2jIXz2V1EuvvhinxMad+0i+dKreLbqEIG2EJAAbstIq58iMAAEqsjtWwQD+WsfffRRn7+SVD7RwiIJgbx27Vr/UlVBn6LPIZ0QwaXyWKKL9C/vtfRz+fLlfoGHFYeFIeIQ4U9gLxa2ec/M5X1meB1nI7E05zmLLQE8lnCSAH76f/w3t/HFjSM3RF2Y81p/qSDJ/TkqgEMhnCWAEePbh8ae+/XPyzgP3G+u0MxvNtw4YsAxgkEpfHZcf/31I7EQ+rVf9IMzwyaIEafEnbDC98Pee+/tPw8Rx514n5B1AFHNpmcn9fQra7VbBJogIAHcBGU9QwREoCMCVeb2LdKQhx9+2PFz1lln+UVNWHBPQ5jiush5MSyjdZ3XIrgUIoY8wHUKzTQ2CGAW5gTCwiKNNYSUTocffnjtizSzgLMwzLKIVCWABykqb5wADsXvlJmT3eZXRwe+Yi7kFcBFxS91Y93d8trwueO4Elqi84rgaXOmuQmTdqdG2rrrXDNWYEovnwdG7OBRwRGDefPmFfmY6ulreT+SQo3Ns6QAej3dgYTG8Z1EsEOEKm7QCNUwBzEBAM1lmu+OvMdCqHfhwoV+k5Hvnrz3lWWI2/dXv/pV993vftd/xyDgL7roIvfFL36xo2jkDz30kJ/L1I/nzpVXXlm2ibpPBGohIAFcC1ZVKgIiUBWBqMtz1YGu0tqJ9RcrMPkrw4jGiCOskny5V5HnNosVC2MWWkuWLPHni7tREMC4gbMww70bSxUWjyZKkWBkEsBjRwQvhUceecSdeuqpfpOGoFcTJk/01l/ELyUqgPOKX+4tK4CtpXFCOOqKnSWCEb+UUADz/4lThvNPb9uyracFMMH28CRhI61surQm3otFn8FG2U033eQ/J/PkEC9af7evt80lPGP4bjILMd4xloOYc7xhDmKsxUnClnvwqEE08x1TpwDm+2vZsmWOKN2MD55OfM/gfs1m5+rVq3106zIFbyVc3+mPBHAZgrqnbgISwHUTVv0iIAKlCbCjzgKK33yRVpHbt0hjWAwgPhcsWOAXpbThsccec+xu0xYC1hAZuc5FCu1lYcxzk1yxi/SpzLUEg7HFDBsBLNCwejdVzAWcxVrW2eqqBDAujkSfrjK6a1O8os8JBfDLH/7vY8RvJwI4SfxSZ5L7c9zZ3lAER8UvdaUJYBO/1u9QBJsA7nURTLA9PlcQUlgOB6Xw2bFy5UpvTSRI3qAVPpf54TuCQFlW+BwKcxCTLskKARVDQcympn2H8B3DZw7eNQjQOstnP/tZ96Uvfclv8BLjwdr/9a9/3V166aXu7LPP9tb7ouXv//7v3W/8xm+43/zN33R/+7d/KwFcFKCub4SABHAjmPUQERCBIgTqzO1bpB0sSonsjOWMHXkskbi7sVCwXfoi9ZW9loUxFrw4V+yydea9j2BQWCJYyOJ+jRW66XNpRaJxSwCPHdlQAL/2u+/zF2zfuvv8Ypr787TZu4O/xYlQE8CbXtydQiZN/PJaUnArE8FxAti3OeY88PQ5U92O7cP5h8MSJ4KxAk+bPd3t97f/mnf6N3ZdVqqqxhpS8YPwGEHIHXTQQf64xKAV3JQZO0RkmncO54XDHMSkjrPC5yrvUQQz1lI+56mPyPt1FTaW8eCxjb5ohG6+3zh6Qo7jIumrOBJERGzu+dSnPuWP7cgCXNcoqt5OCEgAd0JP94qACFROoO7cvkUajFsiopcdeRY5iEAsGbjyZZ1FLfKcrGsRv4jgqCt21n2dvB5auxG8WCgQ/meccUYn1Za6t8gZaPMa6DQNEovRNWvW+EU7i/d+LiaAj/zOX/puhOKX/0cF8MQpE8Z0N9ECu2Os+EQMJ1l/qTgtunMW57AdiF8rURGc5Ao9afrknhTAeJtw5MLc1LM49MvrBI669dZbfT50rJqDVvDO4Xti0aJFmanywr4TQyIUxJdddpn3srECr6997Ws+A0EdQdEITIabMi7OiPhowTKMhfhzn/uc+/znP5972C655BL3H//xH/57k8CNEsC50enChglIADcMXI8TARGIJ2C5fcm/yu44u9OcnarbvThtPIjMivWTguAliAu5cJsuuNix0Dr99NMbcY/EOsDu//r1673o5VwilgAsFYjwpkvedFS0SwJ47OgggCd+4eP+hUnTJrnNr+y21pr4nbbXbjE5tCkm92+M9TXP2d+oZThL/GL9TQuORR8QwaH49eOe0wqMAKb0mhU4yZW26fda1c8jUNTtt9/uxS+ibtAKm3PkfsdduJOcvbxHibNw3XXXuR/96EejMBFMCrFKGry3vvWtlSD8xje+4T72sY+5d77zne573/vemDrJQ/y2t73NkZLpiiuuyPVM2k37CKD1mc98xgt6CeBc6HRRFwhIAHcBuh4pAiIwmkAY6Ap3V9s57lbEY1pHgBBEH2Kc4E+nnXZabCqkJsaSxREi0M4i1/nMMKcxYp9zzizsOAvGb9zzmi5FgoBVJYA5s8f4YyE5+OCDm+5ypc976fd+3W184fUx4tfP81e3uCzxa6Iz2qg8Aph7QhGcJoBD1+c0ERwngONEcJoVmLZPvvz/82cxOxEuVQ0U1l+swGxyxaVcq+o5TdczSJ4UcewsEwBCr4rNWvJB43GEJRXBiyDmB5GNdwCbCVWUj3/84+5P/uRPvAjmzG+0sPHLxufJJ5/sPWGyCpZ+Noj5rmTzlHPOEsBZ1PR6NwlIAHeTvp4tAiLgLXacj+LsJkKYqMsIvm5EPL5m5gmJIzJxj+FoskvX3dn4qIVnketKkQJ7noPQZiGHmzfu3raoI5Ir/8bVr+liQcCwsmQF36paAA+C5YqUR1h+veANrL+TZ051QxtHpz/Ka/2lrrwC2OZLXGTpcC5Fz/4mieBps6e5Hdu2x07DNFfoMCAWluD7L/mQn9Oc7yfIHcGnCPLW9Bl3OmJnSTlikDXHm37/dfK8QUonFscBoUgfcVWuonDchfO4oTDls5lNQJ5DiqQqCgGq/u7v/s6f0/3yl788pkrmI0KcwGWW5z7tubQXqzJinc0AigRwFSOlOuoiIAFcF1nVKwIikEogKbcvX7wsAhBaYVTNunGmid/w2d0QwnYWmd34OlIPsQGB5R2XbwK5sPMfpn2i/zfffLPfrECENl3YFMFClicKdlUCeFBcN7H+msg18YvwpUTFr/9bhe7P0XmCAN300uhgWXZNXOCrOAGM+LUSJ4KLnAWmnvX/8zNeWLABR0H8Wv5WRHFaypoq3wec8WcDCoGDFW1QCkdaEIkERurG8ZG6ORIpHusnn01VFFhR16c//Wkfobmu8oEPfMB985vfTHwO8xHxm0cA4ynDxs2v/dqvuW9961sjTZYArmv0VG8VBCSAq6CoOkRABAoRSMvtm5R7t9ADCl6cJX4nTBs/pkYTwosfuaPg04pfvm7dOu9WhjDdd999i1eQcgcu3nfddZdfxCGuye8bl2qIXJGcDcYy33SxKNh5NkWqFsCHHnqo46cfSyh+aT8C2MQv/89j/eW6tOjPUS6pwa925eTlnqgQTor8HBXBWQKYupNE8PS5M93W1zePNBkr8JRZU91ef/gtx4YHEc8Rw2EOV94LCGKzENeVh5tNHo5+cMSgm0c/qp7nxBEgIBJHKar+7Kq6rWXqwyWZgFZVHQ0hYjZRky+//HL3iU98okyTct1TlQs0m6ccDyJIJFbqMGCXBHCuodBFXSIgAdwl8HqsCLSVQNTlGRdE+4FJNPdu3Zyunf1mt3NobCRbe+64SeNGmjB+4u5/80cTwfy7TiHM+a+7777bEQylSisKwhrLL2PCTj9BapLOsbEwIwp2Va5+RcYVrwB+8qSBqkoAszFw2223efHbrwL4lT94v9vyygaPOkv8ekGc0/rLtUXdn0P3Yxv7UAQnCWCuNREcil+rI8sKPHPv4dys48bv3sSytgxt2upfiwbEwhpsEXoRxWHKGgSwiWGEcVZe6rzzHPHA+xHrX1V15n12ndfx2UWgqOOOO64W75U6256nbiJcs6FbVXT8a665xr397W93f/EXf+E+8pGP5GlCqWuqCoLF9zWfj2xuHHnkkaPawnsIizbvE7678Oj6wQ9+UKq9ukkEqiYgAVw1UdUnAiIQSyBvbl8770oewTrSP4SNQ/xGi4nhUPiG10RFMK/VbQ0mtyKudiwiOZfbaWGBz4Ib1libsCyzSEkrt9xyi9u4caOPRtp0sTRQuIfuscceqY+vSgD3e/qWUPwCLGoV7Yb7c9zAIYLTxK/dgwiOE8C+bzHngafPnTHqcXECmAsQwViB5/zxtxPnFRY+LMNmISZAnhXOD5uFmGMDZdOjcfaeIwidRhNu+r2Z9TxEPZ81CKC64hdktaHO1/GMYcMCK2gV5d///d/de97zHveP//iP7r3vfW8VVcbWkTcNEqmQvvCFLyS2wwRwnoby/kAUq4hALxCQAO6FUVAbRGDACSB+cZ9FnPATtfqG3Td3XwKB7LPPPrWRiRO/eR/WtAh+/vnnfURi3Ag7zUmLiMWaTJTjuXPn+oVpHpdLrKG4iS5btiwvpsquK+IWLwHsHK7P4ydN9NbfSdOn+HHY8tpu0eaFX47gV1w3HHF5utv44saR8Sxq/eXGOAuwVZgU0CqcQOMnjs1NnHR/VPzadWlW4CwRbHXwWbZp06ZRghg3UArnh1nkmyBGHOeNDIwnBhGAOWJQVkRX9oarsCLcunHvZpMNy/mgFYIDck6c+AxVlH/+5392H/zgB92//uu/une84x1VVBlbB5s6HHnB3Z/NVb5vw/LmN7/ZH7vhc7+suJcLdG3Dp4orICABXAFEVSECIpBMAGsjC0SECYtHFolpi0IWgZxJrdrdN2xhmvidMG33Qnv7pvhIs36xO3GcmzxnOLKulYkzh+/d+vK2Sl2isTyxECEycycpebAks6hhPEjvc/jhh+deoHPWjd37888/v/HpbnmQcTMkbU1aYb7Bi0BCeYR9Ul1sFGD1hjes+qWUEb/0beLU0XOZv+3YtiOz2xueH3axpiSd/00Tv5NnDOflDaNTxz106p7T3NYNwy7LccVEdJL4HW7fWDdo/s4mwfatQ6lW4KTn8pmGizRzjh8EBZ91nunEiaMCauE+nfTZV3U6ncyBa+gCzoZyfAGBmPXebahJlT4GkceGB4KxikJk5ksvvdT9+Mc/dhdddFEVVSbWQaCtr3zlKz7w2lVXXTWSfou0SLSBmAsIfCu4ZfPzy7/8y+6rX/1qZtskgDMR6YIuEpAA7iJ8PVoEBplANNAVfc0Sv1xj1k5yCh544IGVIjLX358veldivaEAtouiQjgUvmPOBe8Swdx7+ppbKmk/whMxxhmrMudRWZATSAohibsemwtF3cvJBUlE1wsuuKCSPhWpxM6FkyM1zVUbqwbWbYQIBXfpsult+lUA4/pM2TE0bJWkJFl/p83e7SZs52HDcckjgMPrQytx+Pc8Apjrk0Qw4tdKkgjOI4CpI04Em5W8rAgO+8pnDCLYXKbxmrDChozNR36TK9UKgaIIGNWNIwZF3otFr+W9iwcHOWyzji8Urbvb1/Mdhysxn6UED6yikJv3c5/7nBeedaecw5WfmA6cY95vv/38+XNSEPJ/vIP4zmGT1MrnP/957w7967/+6+6f/umfMrsrAZyJSBd0kYAEcBfh69EiMKgEsgJdpfXbrJ2kzSAoU1UFKw3iaMe7fmekyqHXdosE/hgnfu1iE8FRqy+v1y2CcVfmrBl5GYtaI1nkWK5K3DNxRSwTyRY3ORboRChtuuQJjIbowHOA/uI6b4GMzD0Vt9Iwmi+5VtM8EXBzJfAXLufhIrDpvhd5Xpz45f6oAI4K0jjxy31FBHBo/Q2twtSTVwBzbZwIDgUw1ySJ4Kl7ZqcPSrMCU/eeX/2HIsgzr+XoBxtYdn6YjRUrBAWyOcl5fK7rRpC5zE50cAHil/cvm1e4Cg9S4TPmhhtu8AGgOJ5SRSEn79e+9rVYt+Qq6o/Wwecc1lxcr5mDzEcsz6Rgim5ASwDXMQKqs1sEJIC7RV7PFYEBJMCOuInfvC7PUQwIGYQHUYkPO+ywSiiRR5dIpFPe//ux9SGE08Sv3RSXDsleSxPBBPk5ccWNpfuCFWnlypVe/CKC8xbLwYllFFdeLMhY4csUxCXu6QjgvOcayzwn7h6sEgQJ4iwaloloYeHG+NIu3MQRwHbWnM0Dc0/l38xRilnjqC8umm+/CmCsmRb5mX6G4hchuW3z0Bh+VVh/49yfEcJFxK81LCqC8wjgGfOGxdX2oeRjC1Z/mhV40oypbvqn/6qqqTumHjZoTAzzG4EcFjw8sA5zfrjse7W2xpeoGPdn3KDPPPPMUhtvJR7Z2C18rpIf/Q1veMOYCMhlG/EHf/AH3s2Yc9NFPuvLPk/3iUBbCUgAt3Xk1W8RqJhAWZfnaDOw1LKoKCr24rqD9Q9hRGAtBM+EX/9/E3uNuB16LXnxPGnW8PneHdviUybFBsYK3KE7EcFEJMYljsVxNNVEXIcYCywvuD1j+cQ9r9McnFiRiVKLC3TTC3MW0IwjbpRhJFksMAhjAu1w5pdALggHO3MebSd/N9dUxAci1wr3ITz4wVLO4harO1aQfliIZll/TUQ2KYCHBfiWxPecnf+NXhAK4Kj4tWujVuBOBTD1miv0xGlT3IzP/nXFn5Bjq+N9ynubOcnxBPNW4ErzWDALcZbHQu2NLfmAQc1vDI46Nsl++7d/27sX81nb6Wd2ySHTbSLQCgISwK0YZnVSBOol0InLc7RlLCpwK8P9GTfosgWrKS7PLDA5o7Xhl38zVfyGL0aFsIlfu6aMCLZUL2UswcYEKy4WzrSCcCPQFWepEXW4PFfhekidbCScd955PrhPkyUuNRZMsEpbNGuC0HCmMvRAyBLq1GHWYURI6C7NeUX+xiIU5k1bvYvwNfEbZ/2NCsg6BHBS8Cv6YBbgqFs0ryUJYF4zEZxHAJv4NWa9bgWOG1vO2OMezWaVWYhDjwXmdujCz4ZPP5RBzW8Me8sVzndVVd5K73//+30EaL6/cJFXEQERqIeABHA9XFWrCLSCgOX2xRLHDyVPoKssAXfdddd5yxuBsIoW2oRFEMsg/8aVmgXKTQefGltVkluzieCo+C0qgi0yNPeVFcFbtmzxwVY4j5p21owzhIh+3Cxxy+PaqlKqEKUWrqRBIpBWk4Xn8nwiyZK6A9du+on7KAtPLLQmUIsI4LAPzJUsd2mzEDfd/zTWmy7/qNv66kZvvQxdn7knKkzrEL9xz7H2Rt2fQxGcJn7zzi2swFHxy71lBTD3mhW4blfoaB9Jc8b7/Kyzzhp5iQ0Z3tPmtcBmnhUswhZQC2Hc9KZU3jHCc+PnP//5wKV3ov98XjBueCt1Ep0/ZHnJJZe4K6+80s+FXh3TvGOv60SglwlIAPfy6KhtItDDBIrk9i3SDRZ911xzjdt///19tOIihXsRSiy4sJBg/ST1xo0HnZJYTdq5XkRwkgCmwjhL8LT5k924CaPP2U6aOsFtenmLm7bXFLdj+043bfY0d+QVy3N3DaF37bXXugMOOMAdd9xxY+5jLHATxtqCEET4cm2VhTylWGKJUhtGr63yGUl1cYabKLmMJ1Yy3CpZHGIti+aKLiuAo89GbBANFes5fMPgRVF36SxLc52MsP6O5Pp9ZbdAmjxruhvasNvFmzZ0WwDTBhPBeQQwuXmjAbyiLCdNi9+MyRLBnAOesfeeI9XZ5kG3BDBpzvj8IiVNUkEUmRjmN/+3gseCWYhx4e/mnAzbP6jpnegjY4AXCpusVX3e/tIv/ZIPgEXdvTKGdX5+qW4R6BYBCeBukddzRaCPCURz+yK6qvqyRmwsX77cu54iePIWgmdxThWhgihCKJql7tZTzvDVbFk/OuBMmvjlerPebns9+WxwKIIRv1biRLC9hggu4goN76uvvjp2UyAU/ViFYFZHuhEsOYhsotQ27X6J6zUu2CzsGWdcAznvG+faHbrjd2L9jga4MXdpEyChuzSbLGYdbvKs5tY//pjbtmm3CELEIXwpUfFblwDO4/48ZnPh+Q2p7s92PQLYv29f2xz7MTBt9vRYUc/FaQLYhO+oYFhBHuStrw1vHDRpBWazhc8+cl3nKbYpw3y0H5uTfBbbnEQU837plgs/71s8Ns4555w83eqrazhmQv84qsOGbaeFMeWICR4v/FT1ndppu3S/CAwiAQngQRxV9UkEaiJgLs8WZIjHdOryHNfUq666ykf7PeWUZMut3UebiBK8du1a/ycWI7gK24LPxG/4HBPCaQI4dF324iFDBIfi155VlQhO2hTgnBgWiDjRX/UUwLpMOpMlS5Y0Hs2VAEE2vmyMsLmR5B5YlwAOeTIesGdhj/hAlEejS5t7al3Wclyfd27bvTETil/aWtb6y71l0x9F51xSBOiJu8Tmppd2pwSK3mvil7+nCWD/3oyJbM3foyI4tPjyeiiA+b+1qxsCmMj3fJaSLqhMYd5zJtXOtIdzko1AhLBZiMukQSvTJu7hqAJt4XNj0ApR8fGM4ahO1BOlTF/5DCFaNptveLl0a9OiTNt1jwj0GwEJ4H4bMbVXBLpEIHQttRQzfEHX8SWNuy9upgsWLEjtLQsFc7FLsn7GCWAqHT9hnNv6yug8wOHDogI4TQRPnTfF7dy+Y0xb0wTw5JnD1uKj/uPqXCPKuTDOv3IOloJbMIsvFk1EhuYMWh1jYY1DgCJEzz77bAfrpgru7FhZmHP77befd4tP62dVAhi3cyJvY9nJCsZmZzVNfDThLh21/u7cMTo6eVkBXET8DovIcbFTIS39kQlNbkwSwaEA5rqoCMb6ayWPAI6KX7s3yQo8Ycrw+xMLe51pkawdRBxHqJLqq4piebDNOsyGjRU8OMxjAUtxXZs0PA93Xo4TLF68uIpu9VQdeKawMchnUhidvmwj+SwnmB+eLmxs1vl5XraNuk8EBoWABPCgjKT6IQI1Eagit2/RphHwiUUau+FJhYUdLs8EfEqyCiaJX+pEAFuJCuE48Tuy2I5YghG/VuoUwWYVx8U5TP3DggnLTt2FlEqPPPKIW7RoUSPRSRGyPBPRjbUXkcmZX4J7pZWqBDDPu/HGG73ozoq8HW0P7tJhuqWq3aURv+OnTHZbXx4WNVnil2tCkTh19nB02dfWvTjS9Onz9hiua1cwO3thw/rdwimOex0COCp+7bmhCA4FcLR/YTuxAieJX67LI4An7zHTTfztr9X6FiP1G595pPqqo7BZSEAt26Thc9MKm41mIUYQd3J0INr2uOBedfSvG3XipoylluMYVXwG8117+OGH+6B+5H1XEQERqI+ABHB9bFWzCPQ9gapy+xYFgfBgERZGRLU6aBOiCHHEDjnihAAkcbvladbfaJtCEZwmgP1ie5cIDsXvsHgYawX2i+yYoFj2/LyWYAKDcZYPyw7WHFzELfVPUb5lrn/44YcdP4wJC+Y6C4t1XCdZrGMNISI4ln5cn7OCzfSCAA7ZmLt0nGsquanNEscCOq8lbttffGJE/E6cMc0NvTbalTju/C+5bUcJw63x3g9RARwd51AQlzn/G1p/re6oFbiMAPbvyxhX6CwB7N+f43cHrQvb16QVGG8DPCvyHPuo4r0XnmlnswaPB89i3Dj/nrN5yXu9E0skwb34zErbzKyiP92og6M3bAqyaVFF3AU+K9hwY5OROBgqIiAC9RGQAK6PrWoWgb4mUGVu36Ig2P1m0YS7bViIeko0YIKPEAAJa2iaGCsigO05BKjKKgjgqPi1e8pagVmEp0WGRgCbJRErAak3OlmYZvUx+joLPTYdWMiyQK6rhKmcEL5scHDWljypnLXjb2mlKgHM/CMfNd4FaamninLo1F0a8UvB+ov4paQJ4CmzZ7ntm7eOaeb2kgI4rGjjC6/Hdj+v+3N4cyiCkwQw12MFjlp/rZ44ATx9/p5uR3BWOq7BWQIYzju2bqvVCsymH59lWBObLggvzg+b1wLvQd5HFLwvoueHi3zudHq2uWkWRZ736KOP+rgIHNWpImcvnw1sPFx88cXuiiuuKNIUXSsCIlCQgARwQWC6XAQGnUAduX2LMrvlllscFoowcigiiLOgiGDcYBFGaXkS87o/R9s2afokt+W1sYLBriOVkRcdm5MjQ5cVwbMPmef2+dPvjmoSC1Hc7FhosfDEQlTFebOiY2KBqIhSi5tkHYU0S0Sbpp+IXXN3ZsMDV0qEKAHO0kqvC+Bo23FFNeswv8NIvha0iEUx1sGhr398xPU5S/wifK3kFcBZ1t9o2004blj/6qiXyghgKkAEp4lfrpk8a9qoyNfRNoUiGPFLyRLAXBMngs0CbKzHf/CyOqa9r3PFihX+fVUk8n1djeE9ROAq5iOimHy3VvBasHnJb/6fVtjMxLOhqrPNdfW5TL14xBAZn03BKgKLwRkPl3e/+93u29/+dpkm6R4REIGcBCSAc4LSZSLQBgJRl2cLclVkx78KTrfffrtfgJESgjZhMNYgowAAIABJREFUfWSxgVs0wihPyoky1l/Er5UkEWwCmOuKiOAZ86ePCRgUCoVtW4ZdUsOgWIgjXIGxyBAhlkVWt4LJIMAJ+EKU2irOu4XzBGurnWumj1jBQpdCNj+YE2x6EOwrrVQlgKkHUUJ0V+ZcEyXLXfr0u/7TN2PH0G735aj1d/zkiWOaWrcAtgeaEC4rgH3ftsUfI7Bn5BXAJn7tviwR3G0rMHEPONZQNPd5E/MS92g+g8xCHAZ5wxPHIp4j4KObkk27djfBw55BYECCEeKynPf4Qlr7nnnmGR/Q8IMf/KD767/+6ya7omeJQOsISAC3bsjVYRGIJ8CCn4UOv1mIV5nbtyhz3F2x+pE6A6svlgjcAznzmsfV7J4LlvpHbnxhbP7QMPhVtF2hAOa1qAgOxa/dmySCzQqM8LUSPTMZJ4CxgB36nf/r+0+QL8bkkEMOcc8995wfk24JYCwdWGex5LBQr6pg6SfiKdYPLNsIgOhikvHnLCHRmGGRVvpZAEf7FbpLH3bV348Rv/whFMCT95wxxjqaV/xSVxELcDSFUNj2La/GpzeKO/8b7TNnlS0NUdw4I4ApYf7jMdw2D7lOBDD1WVujVuAJ06e5ne/5TFXT39fD5y0CeP78+T7QW68XNuZMDPObM/sUPp/YuDILMf9GAPO7G67ddXPk85Ao9XxPVRE4jCMmePhceuml7o/+6I/qbr7qF4FWE5AAbvXwq/MiMLz4wgJXd27fIqyxerKwQAixuMLtlZ3xvIsME8DhMxHDRcSv3WsiOE782jVJInj6nKljup1XBK9990e8NYUFMVZIXAkZo27l08Q9mbRLBHypygU7FPmcaeZsc5y3AYvsW2+91c+BQw89NHUqVSWATZSQeorgW90unP2dMG2qG3p197lbE78I3yRRmFcAFxG/XuwEgaNCNuMnDVugN70w2i06FJVJLMNAXUkiOI8AnjwrPk1Xr1qBu+FtUNV85n1CmiNLt8Rvvk8ofF7zb6zEeFHwu2lvoqr6GVcP8SjWr1/vj+pU0S++94h78dnPftZ94QtfqLPpqlsEWk9AArj1U0AA2kyAhRfubFgXWZywU19Xbt+8nGkTOTEJysICCgFIIKIiJU4A26J904ubYquKWn/DixDBRQVwnPi1OtNEsFmeSG2zz9/+y0jOXYLJcP556dJh63bThZQfRGImDzGisJNikbw524zIx+qbViful5wLb6sAtsBXcQLYxC/jEWcV7ZYAjhPBWRbgLAFs4tfmXpIVeNrcPVxckK8iAnj6vnPd1peHRfwYK/CMGW7nf/9UJ2+BUffWFXCtsgYWqIjPb6LUh1HP7XY2NMOAWqR96ueChw6Cv6rPZDY53/KWt7ivfe1r7vd+7/f6GY3aLgI9T0ACuOeHSA0UgeoJhLl9OWuLuMICR/7BbhbcYVlUIHgoZQIuJYlf6gutVlEhnCaAuTfNeszroRU4TfwOt2N3DmL+H7pChwIYV2grWECxtJx77rldGaJ169Z5d3RcGbFIly1YsamHTRfc2amPzZe0YnOU+ck8TStVWYB5xnXXXdd1t9Rx/+cyN/TSK2Osv3HzqNcEsI0T1uAs8evfB5FUTVErcFQAc0+0z4hfShkBjOjd9NxLjt8UE8BT588ZsbwTEGtCxQKYYw64CpfJOV32fdjEfSbsEb281xGLbGxaIbCbuUtzfnjSpN0xGJpoX6fPuPPOO/1nclXHUsj1/o53vMP91V/9lfvQhz7UafN0vwiIQAoBCWBNDxFoGYFooCtE58033+xdS7GwdasgiHApYzGIJZozobiDsUgqUtKsv9F6TARnid8psyb7W4c2DufKTCqI4Czxa/cWFcFhYLAiPKq6lgAtbE4QpbaoRd7awOKXRSNeByz2cYtMi+Rt9zEX8ArII4CZ38whFt9xLvNPPLthDJKD94kX4L0ggM312c+/wP05LgdvVAzmtf5SdxEX6LTzv+YCHYUcl5s4ek1UAPO6ieA48cvrSQKY14qIYBO9Yd/Cvhh7iwhdpQjmmAefwUQ97+ZncFWfFVaPCXuCFnJ+34/n1q0j0aWxEuPVYsXODyOKSbWW98hL1e3OWx+fyfRx4cKFeW9Jve7f/u3f3Hvf+173rW99y73nPe+ppE5VIgIiEE9AAlgzQwRaRCAuty8LEqLdkl+1qWi3IXLaRDTNJ554wlsAcHnG4kfkZ6Jr5gl6FdZXRADbfds2746qGzcdTAB7EZIigqsWwDxv6p7T3L5//i8+Dy7RkC+44IKuzNhnn33WB6vCXTlPFO5oIznTzQYH480in2jOec/N4VKJe2AeL4UyAjhsayiGux2ZF+vvjs3DAsEE2KSZwxtC2zaOduXvVeuvsZ0weaLb/NJriXM3Tvx6wfTacD+TBLBnsWmYkVl/7SF5BPD0vec4F/HIiBPB46dMdlvWv+imzJ/jtm/cVKkVGBHI/CYFzhFHHNGV93cdD83qF+9VNmAt3RIW4jANGCKYCNP88D2Q9/Oijr7E1cmxDNpEZPwqyne+8x334Q9/2H3/+993b3/726uoUnWIgAgkEJAA1tQQgRYQSMvti6Xs6quv9qKm6RQcWAIJ/IGFDxc4ojyTBufRRx/1uW/Jr8giKG/J6/4c1jdxygT/382v7LZEhK+H4tf+niSCp+41LdbqlNT+PFZgBDAL8nXv/V8OEXrhhRd2ZSGIhR7rLRsUlp83z7iEeYw5A4gFmQVtkYLlGAtZXgHMIpqfvBbgrLYkWYiz7uvk9VD8Ug8C2MQv/+9HAezfZwkiOEkAcw8iuIwA5t4sEZxXAFMXItjXuWvzoSorMCKQYygE+yMQ3KCUov0K04AhhtkI5fODwuZoeH64iry7nXKuOsfx3/zN3/izv8uXL+/aRmenTHS/CPQLAQngfhkptVMEShLIyu3L63zhcq6zyVQVuNQSVRihcthhh/mFH7luKViDyQu7YMGCQmKpjPXXBLBfnMeI4LwCGPFrJW7RnTR8oQiO5k+1c5OI4J+//5M+MjYWYONUckqUuo1op1ih8RLAWyBPwQKE2zQWHjY4EL9lAt9wzo4zknnc9G2+VymAw76OczvdQfvMzNP9jq6JCmC3SwhQaVT8+r/tsoKOzMHNw6lpooW5OW3+XqP/HNS98bmXMtudFQE6WgHW37DEieA0AUxU562vxadWsnonTZ+S2N/oCxYMy4tfK4EVONo/c4U2AcwtVVqB2QjEmohXRNYZ98zB6aELeN8Su4DUZXzGFy1sziKCzUKMJ4gVPkfs/DC/q8jDW7R9fCYRv4DAgFWUP/7jP/bRnxHWVblVV9Eu1SECg0hAAngQR1V9EoFdBOJcnuOiPGMBRqCQ47XuwqLmgQcecKTVYdGC1TmaVsciDpMTkdyYeUunApjnhCI4TvxaW6JW4LICeMb8WaO6ZyJ44wuvjwQOQgBT7n7r+9x5552X69xsXmZ5r8P9mjNvxxxzjLdUZRUCmeEyjQjmes4AlhXuCIQbb7yxYwEcd/43qx/h64jfpFKlKE4Tvzy/iPV36pzdHhQ7dqWnGdOHQABHX4sK4jLnf6MC2L/PAktwmvjl2k4EMPdHN6Sm7T3H7dw2nKpnpORwg+ZaE8Hjd0Uw3rFla8cRofFwIM91WaFYZA43eS2Clc8MxG9W/u487eK8raVbQhRjYbaCizSeJYhhvsuaOD/M0SGeh+dSFeVLX/qS+8M//EPvFVVVnVW0S3WIwCASkAAexFFVn1pPoGhuX8464lJG1OU6Cws9LIIsjFisIH7jLIIWcbhIwKVO3J+jfTYRnCaAucdEcCh+ra4sK/D0ubsDL0VFRWgJ3rph2DXbXKHn/NH/7kq0VBacLNIRsmmLWeYemxtY8NlswWJcxGU6bv6x0L3hhhu8hezoo49OnaJpFuA6BXC0USaWD9xn9AZH1vtr4v/9C7dz61a37eVX/KUTZkx321/bHTmXv2UJ4Cmz93QIs2iJFcAp4jd6P2K4qPXX9yFiAbZ6TQTnEcDck2QFnjp3WORv37Q5Fm/dAnjCrJlu28W/kzW0ia9XLRRLN6TiG7He4jWCd0+eTbOij+dzAUFsFmIEMoXPHY7OmIV41qxZpTffktpUR57w3//93/cRoB9++OGB8gQoOq66XgSaICAB3ARlPUMEGiRgQYCw/vJjFt+0ACJY19gxP+uss2pr6dNPP+1++tOf+ui8LIhw9UtqU5mAS49c8guj2r7xxWGXyTSLVej+HO04eXjzlKTFvV+Qb40PrhWK37g2hgIY184N6191M+aT23TIzf6j/+2mTIl398zT3rLX5MnFy9gyxow1Gyq41BPZtdOyefNmH6itHwVw2Pdx43bPqQP2jucy4ftfLyR+J+25h9v08/X+MQhfK3UIYF/3+PE+VVC0JEV/5rq09wjiNy04FtbfsMSJ4CICGOuvlV6xAhMD4Y477vCficzxQSkIU6yZBPYiwFedhe89NljNQsxvOz/Md1voLk1mgU4DanHEgu9NIuLjFVNF+ehHP+ojQPP912mu9SraozpEYJAJSAAP8uiqb60jwCKAqM588fNvXE7zfNFz5gjxQtqhqgsLBayBiCKEG65dWUGQnn/+eb8gLHLeNCqArR+bXo63CvF6mgCePGOK2/Ja8r1Wf1EBjMvzzhirW5oV2M43IoApRIVuulguXhazcef5woBmuLRj3a/qXB5u1HgpYEXKWmz2ggU4yVU6FMA2fuG1B1z9lw7XWqy/WH4padZfxC8lKnbjxK+/Ls4FuoAF2D9s1zl9/hkK4SQBnCV+jUOSCC4igD2vDCtwXQK4Eyswm0sEmCPNV97z9U2//8s8j89xcn7jNVImcnyZZ9o9fAfymWUWYqzsfDZQ+B4KA2qV2VCsI3XV+973Ph8BmrPTRdP/dcJK94pAGwlIALdx1NXngSaAWEDM5hW/wCAAC+5k55xzTqVsWHRgAeALvYgoYtFC8JQsd1trbJL49ev1icNRnjc8Pzr/a5r45XoEMCVNBNvZ3KFNyfmBQytweN43KoLzCGC/wN865M9EzrnsHysdq6zKLBUR1vtopFoWuri244KIFYvX82y8ZD3TXmexSU7ePKm60gTwvU8NL4BnTUoPqJTUrrQzwOE9cdfFiV/uCa896Ka/99Xs3OXK6cc7xv3ZhC+vx1p687o/+wqGo+zmKoH4Da8fP2GC2/T8y7FV5BXA3BwngqMCmOtCK7BZf+3haQI4FL+ec/QcMH8sGAzLzgKPmzbNbfvF/5kLY/QiPu84L9+EpbRUA0veROT4e++9129alc0dXvLRY25jIza0DvOdZIVAVmYh5vxwntzkRSNc5+nHr/7qr/qMDNSdpw156tQ1IiAC8QQkgDUzRGDACCBCEMBFBAjWVhYH559/fiU0ECEEssLyy79Z2HFuNG+bzNqIRSRPVNQkAWzi1zoViuAs628IIkkEmwDm2iwRHA121W9W4LhURIwtKaseeughv2DD6luH6x5z+tprr/VulMcdd1zqHE0SwCZ+427OI4jzil/qzyuA48RvmvV33KRJY5rfkQAuIn69OByO0h4tCGBKnAguIoCpIxTBceLXnm0iOCqAeT1OBE+ZO9vtjLGAV+UGjQB227eXOgtMgDk2kMiP3el5+Uo+wCuqhKj1HIkgdVqRYIYVPT61GjaK7ewwv9lk8+/dceP8sQ2zEHOWOC54nwUuIzI9P1WUt73tbSNR88sGDKyiHapDBNpAQAK4DaOsPraKADvdCOAiBetDVTlmeT67/ix+CHCFyzOLiSKlSN5X6s0rgK0NCOEiApj7oiI4FL+8niaAo9daO8pagTk3yb1NWoGjqYgQpffcc4/DykMEVs77YkmpozCnrrnmGi8OWEynlTICOFof1tqZE3dHmPUL45QI0GPuj7k2y/05y/o7cc89RvLPhs/rJQFMu6IiOEkApwW+MhGcJYDjxC9taFIA8zyswF4A+4cXF8HmKkyAt/3226+Ot1BX6iSYIRH/+Q6YO3duV9qQ56F8ZnCEwwQxm8H2HYoQDd2l+YxDJFcd4Is2nHvuuf5788knn6w8aFceDrpGBNpEQAK4TaOtvraCQBkBzDktFitYgDtJH8GiAEsGiwksgYiVSTFWq6yBsKi/WI1xg84qRQVwmluzuT5Hn5klgJNE8Ix5w6Jw+9BYV9OyVmATD02K4HBMEKJsmjDOLNg5q12nyx6LUVwDOUeIlbkJARx9htk+Z0xMd58uc/43Tvz6ObPL/Rnx6/+/cbQozyt+ubfq878hH7MA299MBBe1/tr9eQSwF56Tx1rErY5QBGP9tVLUCpyUE9g/f8pkX23oBl1GAJNjm82kXnAVzvqsLfI6XkAPPvig3xwrugla5DlVX8v5YY58mCDme83OD/N9RgwL4hsQ7b4qt3XqP/30073wXrt2bW5vqar7rvpEoC0EJIDbMtLqZ2sI8AWKCC5ScFNj15kzwGUCgvDl/cQTT/gvbgqilYBFeV2eo20tcuazqPjlWbYwJ9dutCQJYK4LRXCSVTdqCU4TwNTZiRWY+2d/efjcaN3FIjFzltsirOKySdTasuOct80sSK+66iovtrPyY3ZqAU46qxvn/Bu9dvqETbndn+k7YvmQn3zf7Xj1ZTd+ylS3/fXXRpAgfk342h/LCuAy+X/HjE2C+zPXRQWw3bv11bHvL3stK/XRjrjzuZFGNSGA/TgFfQ+DfcUKYK6fPsMNLXtf3untvW/uu+8+795fxxGC3A2p+EK+U0jpQz53XIn7tfCdSqAyE8R4KFlBEDNmZiUus+Hrvwd27vQbxljKSR1V92dqv46F2i0CVRGQAK6KpOoRgR4hUEYAI1wfe+wxHwW6aPRJxCouz7jCci8CpdPFThGLXycCmCGLiuA0Acz1iOAk8cvroQA28TsiYPrYCmwCmL6wSUKO5qasOiwOly9f7gPp8Ny0YjmwcdEOvRnSzgCH9cUJ4PiTr5wXHJsqK84CPH7cWOs/f5s6fovD+ov4pYQCOGp5jIpfrs9rAW7S+huyHD95otucEBwrSwBPnDnDbX351cShnrzXsFU8mhM5vAErcGj9tdeiVuC0YFhT9pk/6uzzuIm7rc7jJk10255/3lcbWoGLCuBePivbydfa448/7mMEnHbaaY5cvINS+M6jb1i4EbyWf5j+0U8sxHw28j2Y16OKzy2i6+MGf9NNN9WOis/zr371q+673/2u3/ymzRdddJH74he/mDtlFZsCP/rRj9wPfvADH+ySTXBcxvFkeNe73uU+/OEPl/IAq73zeoAIsFG50/w6hEMERGAgCJQRwOzS80Me4CILFSyBuDzzZYo4wYJRhSusCZ599tnHu8+llaICOMktEyGcJX5pB+I3Kz0SIjgqfr3AiRHA/L1TK/DkPWe4Gb/3Z7XNXwLG4PLMggfXv4ULF/rz3U2WK6+80uWZDyaAWaTaXMwrfulPXgGcJ6qz8UkSwEfd88/ObRlOtRWK3/EzZridm0a7O/erAKZvURGcJX65BwFMSRLBVQpg/x6MWJyn7Lf36OkdWIGjIpgLd+yyCtpZ4CIi2M7K4t6Ph8WgFMQvQhHX3rriA3SLlY0ZVlv6ZumW+G0eWIhBRLBFmOa7Ncmyi5cL36FLlixxfNbVWfi+XrZsmVu1apX3qlm8eLEfp9tuu80HK1u9enWu4JOf/vSn3Ve+8hUvevmeJvo/7vykVeQ7Y9GiRX7jsuimep19V90iYAQkgDUXRGDACPBFGu5I5+ke1l+swCxU8lj1EBncQ/RfvtDZtSZCb5VuW7i84g6G+1xSKSp+qSftXOK2zcnpjKwNnQhgL3RyWIFn7L3nKLfLaLuHNuzOT4yYqFMAI3oRvyxoKHnckPPMuaLXsJBicXbyySen3tpNAZx0/jdOAB9z73dGXJ9DARwnfv3rfXL+1wYH629YQhFcpQDmGUlW4Mmz94y1kmedA56y73x2QgoJYBPB4+fOczs3bvBu0G7HTjd0/v/InOrkSOfzF++GrBzpmZX10AVsqmJdPPPMM900CxLWQ+3rpCmc/+X7L3q+mc8fzg+bIOb8MN/JFDbkTAzzGyb2ncl3Nt93b3/7230u4DrLZz/7WfelL33JjwvfswQxpHz96193l156qfcEu+GGGzKbcPnll/u+YukNo5fD5bzzzvNj/8lPftJddtllmXXpAhFomoAEcNPE9TwRqJlAGQHMFxXngE899dRMCwSWNYJmEbmUnW8WbUWsxnm7T9ob6l2wYEHiLVULYL+YzhDB5v6cZgWeNnu6C/P/hh1IswIjfK1EXWBD4T5hymS3+cVh91ATE1WLYBZyLPJIZcUiDbc2XN27JYDzbIjAo9cEcJz4pZ0I4Kj1F/Hr+1CR9XfyvDmxqX+GHzK8KN+y/sWROTdl/pxR/x95ocT536gApi4TwVkC2Ky/9vyoFdisv+H7Kk4EJwlg3/2ElEhe/I68CQMRHGFgVmDcoHcDHPaKQABT8lqBk8RU3s/KXr2OAFi4CeNZVCa2RK/2i3aZezffmaRNSip4ZCGCTRAjGK3ABEZcAyM2oN/znve4b33rW7V1HaHNmWU2Nu+8884xHlYcYeL7ndSIaZvPWQ3EtRo3aAJZslmuIgK9RkACuNdGRO0RgQ4JlBHAuHPxpcduNm6mSYUgILg8Yw1kxxfLbxUuz3HPW7FihV80sUudVIoK4DTr76Rpu8/2bXopOdJveP43SQQjgClFRPD0eWPPyGWJYOOybdMWbwWmVOEKzYKMoDzMC6wUzAs2I/Kew+1wCsfeThRorCYsONNKJwK4kwBYtCnv+d9Q/Pp58vprzsQv/y8jgCfN2cvtHBob/C5O6Hl+uwRwlGUoiEdey8j/GzcecQKY6xDBRQUw94UiOI8ARvxaiTsrHceFDYNRpagVeNdZbo/XrMDTZrihhb+SOmcHJVhUtJNsnj3zzDPexbZscKg6PkuqqLOsezcCFDFsP5/4xCe8h40VBChnc7HC1uE2fv311/t0S2984xv9sadowTKMhfhzn/uc+/znP18aFRvqZAfgyIx5D5WuTDeKQA0EJIBrgKoqRaCbBMoIYKKQ8iXMGTRSzUQLouKRRx7xX5gE9cAaGLo81dHfG2+80Z8t4hxRUvn5R3915KUN63fvrI+fOCH2lk4FcFzwq6gINvFLA/IK4Djxy/1FBDDXV2EFJrURAU1effVV73LMnLDFa1435DrmA3mAOU9HQJ20YlGgWWgWPQOc9/yvH5sOAmAd8+D3nHttd4CnnYEYjYpfP48i7s/8DVGH6A1LbgGcIH6jXEfEcIUCmGBRW194KXUMoxZgLs4SwFwTWoGzBDDXhyJ48vy5uA+MbldRAczdJoIn7zojv3Wz2zFnX7f9pLck9jmvNbGO91WddbKJxncL51rzBoOqsz1V1o2bL5b7Tt27+U798Y9/7INJcXbWCp+51I0r8S/8wi90ZI0N+/2Nb3zDfexjH3PvfOc73fe+970xSH74wx+6t73tbe7iiy92V1xxRWlkBMb6xV/8RZ8NguBYKiLQawQkgHttRNQeEeiQAAIAN+UiBXdmXJ4QtnxhhYWAGViHsf5iBWSH2s4MFXlG0WtZDGCJZCc8roTiN3wd0RiX3ohr8gpgro2zAhcVwNSTJYKTxK/1qYgInjpvL7djaKi0FZgAJow14pGAJlgJwnPded2Qi451nuvzuMRTT1QA91oArKj1NxS/vv0R92c/hwIBPHGvPd3OobFn1ePEr68vxtU3yfqbNA5bXng59qWk9EdJ1l8qsWjJSSI4TvzawxHBcdZfe90EcCh+7bU0K7AXv1bSRHCCGzS3jrhCxwhgXk9Li4SLKD+DFi2Z3MZ8ppBer8r4EHk+L+q+5oEHHvAeMmzQYuXstLABzUbBhz70IZ9bmA0/vKA2bNjgLrnkEh+tuYry/7N3HuCWFGXer5NuvjN3MjkjCIgIEkWiBJVdERVzQBR3V8X06a4BERUxY8AVRRTlMa8rLKsrSJYoiGIiKKAEgWHy3HzS9/zfc95zqquruqs6nHtnpup55pmZc6qqq9/uPt2//r/h3e9+tzj//PMJghHzqzZ4eCGsCbkWUI4paTvuuONoH97+9reLL30pvwSNSdfnx3kLeAD254C3wGZmgSQAjHig2267TaCu684779yxCMAYQASg3n777am+b6/e5GM9U1NT9PCka1EAjP4qBLvAL29PhuCo0kesAsvqL89hAuDBJQuETa1TWwAuDw/SJpMAMM4ZuPRB1YBqipccUH/VBjfksbGxWBU2j0vq2muvJZdAxMlFtbkCYBv3Z4JfPCyz+js42IkX7fCXIf4X4NvpYwnAru7PWruWgt4UMytXd7qlAWBMooPgKAC2Oa8AwbYAjPlgI2sAxoCYbNC0Rh0ER7hCJ3WntbHHXPYBTMHV96ijjprLZeSybbj4onxVVuo2Sh+98IUvFJ/97GcpERVdH7OzlJkZWZTjkv/Z7uQZZ5whLrroIvHBD35QfPzjHw8NgyK9++67E4QjMVuSduGFFxLI414BLwCdV1mSef0Yb4EsLeABOEtr+rm8BeaBBZIAMBJzQHGF6oc/cKPGjRAPZgAilDdCiYZetjvuuIOSh8AFTNfiABhjZAhOAsCYgyE4CoDRDxCsA2B8p4NgWwDG+DwhGGovXnJAqYHCj3hfU9kKWxU2j/MEsWuIRz7kkEMip5cBGC9r/vSY/WpsXaCTuj8HXJ/bWXE5YRKvkhXg4mgrsU6zXSZJ3gtbBTgPAKZzfeVqYYJffG+jAPP+qBCcFwBjezoVWHUjbxk9whU6CQC3gbh60Iu1JyNnS8a5vTmVjIGqiXuLyYvH/sqcfz2zVrdR+ujUU08VgMe3vOUtue3wm9/8ZvGNb3xDoIQR4n3VhpeggN+kAIzs0ccffzx5ESGb9YtfrD/nc9tBP7G3gKUFPABbGsp38xbYlCzgmnQCcZ+IuYX6CxdovLnnLrj3AAAgAElEQVSHKozslnCHmouHMmSoBJSdcMIJWtPbADAPBAgnBWDMAQiOA+BiuWg8RUwATA/lSv1R3SRJALgyOiL6/iW6/AQeTvGQiuOPt/RIWhKl8NuqsHlcKzZJ0Vrs0qQ6nHgAw77c9NdBsWgwWFNXa2NNTC/BnKZzEgAm+EWD+hsBvwy+vFkVgHXwS/ttmwDLMv63s9uKAsyfF0olMSupwbKZTADM7s9yXxcALo+2yrXUNo4bT7HKooXamGm61maCoSEVuD5rXcRTxgJLybAExwLjs1pVmxCL40nnor52HtcqzwkXWnjxROVxyHP7ec6NPAl4QQsFOIsGWDzttNPEpZdeKl7zmtdkMaV2jjxdoPEiFfbAswPcnuH+7Ju3wHy1gAfg+Xpk/Lq8BVJYAK5TAAHbhv6Am6VLl9JNHfCw4447kks0ElHNRcMDBlzM8DZZXYML/PLao8oWyRmgdftaGR4QsxujIap/4bCoTpj7yBAM9ZebDQCjrwzBKsyjLBI3W1doZGdFWSOo/XBtx4uPuDg9qLADAwORmbnzOlegLCAxDCAhquG8Hx8fpwdvvMC5+YFWRm656YA4jfpLx0eErze5BFIHgGvd+F1V/eXSOrzWNOov5sgi/ldEADC2oUKwi/rL+8kQHKf+5gLAWIQKwXkkw2Io1kDw5louCF48uJfEXbN5/WbkOS/gHi8OkeE6i/ad73xHvO1tb6PEU0hAlVfLKwkWkmTiRQfu2cgejSzSvnkLzGcLeACez0fHr81bIKEFXAEYDylwb0UDZDzjGc+gWoFz2eBi9thjj5ELtFpqyRWAi1Ktzqk1QfUoDn7JJhkAMD1nz9aEDL9sXxsIdlWBS0OtmOC+M4JxXgBexHYhMyfKTEHhR3khm2YLoTZzufaBhwIUXdTLjGo4ZxB3hv2sbP8C680g4e+iwWD5q8zVXwl+sbBOvdjhdgksxd05DQBn4v6MRcYAMBuYQTgJAGMOnXuyevAYgPG5TgWG+stNlzlb3g6pv53O9fB5YukGjYHyi4tQMiy6CNsZoQ0qcNYJlaxP+pw73n777fQiNi5sIedl5DJ91nD/1a9+VaAkEvIsmMJ+stgR2zJIKIV0zjnnWG2Sk4Ehkds73vEOAcj2zVtgvlvAA/B8P0J+fd4CCSzgAsBy2RtW2BBrOdcNSUZQHxNJsABqcksDwJhHhmBbAMY4kwoM9ZdbnAqcBwBj26wCswJMnwGCG42OKzRc46GsIzENoBfJrqDo2jab0lS2c7n2Q5IYKNQmd0o8aAPsUVIG5wu8GVYWn2m9GbXiDYGNxi26pPmsXGyEtlMsthThg566XBTG17UgaLJbqisOfjF2zgHYEn555wHBSQEYc0RBsAy/vD0VghMDMCbsoQrc6BsU9f1O7JwzXC8XsbJ51VW3vhAy7HjrrbfSS6uDDjoow1nnx1RI0ojfo7ikfLar/cxnPkMxubfcckuuHjZ4NsDLbXh6IcwIOR/khnsCXJmRfCuu5BzG4V6C8xbeRHDhvvjii2M9iWxt4vt5C+RpAQ/AeVrXz+0tMEcWsAVguCvhxoWYSdzMAUXz5WEFMIM3yri5qjHIOgBWFVLZ9LICzJ8zBMcBMNRfuekgWAZg9DVBMOBXFw9sowATkEnu6ENbLREza9Z3lqZzg5ZVYDyoAH4BwUnd22+66SZSdLJy+3O5PKK2jfMdceurV6+mzKPwYMD5fOtDrZhRm5YXAB/80LdD8Iv1AIALrPziA12yK1UR1mR/prls43+pcxjWjfZxBGDMU1vXPScD12DMixY+V6tr9eNdARjbNqnApQVtxV1eYC8AGNvrHxAAYLTZZxxHgLi51stFYkW8jHr2s59tcwluUn2y3jeorZ/73OcIPvH7lWdDAqxzzz2XXNNR2g7Z9dFQFgkZqPGSES8cuV1wwQUCf5DQ6rzzzut8jpfnxx57LFWQQAKv733vez2rEpGnffzcW4YFPABvGcfZ7+UWZgG4NMMF1NRQXxdud4888gjVMMQNFyBsk2W3V6ZEYhjEFcHlFdmJubmqvxinA2B8Xh5oxc5Or+0qc+r+qQBMD65SPLAKv/jeFYAxxgaCh7cJliZS92t2XWs/dCrwdTsfSbHUSHSVtCxFXG3mPM8N07aRyAtKBmJ+t9tuO/H0pz+dIB1QbAvAtvCL/XNRgDvwi4GS+isKGufqDN2fsblexP+qx7tQqXQ+qj61KvC1LgGW3CEJAGM8q8Cy+svz6gC4vGSxto6yazKs4oqtg7tf7u67KLZLR01s6PaR3aBxvQOCm01xp9iKzlXUe0W5oLnKuZDHtQuIAlxlVcInjzUmnRPeMCMjI5nt2/ve9z7KAI3KC3IpwqTrixo3PT1N5xpc1Lfeemt6oYmQGPx/yZIlBLSoBsENMb0A9Ne//vXikksu6XyOWsJwd8ZLnJe//OUUPqVr8pg89sfP6S2QxAIegJNYzY/xFpjnFogCYCQIgloGcFi8eLHYd999yQ3WNsayV7uOBwEkhzn00EPFwoXd2D5XADbBL4FiG4DxbxMEJwFgzKdCsOz67KoCQ+3lpird8v7JAMIP/wwWpdERMXnSWwMvE1yPJdzz8LA+F3U9sW2c13LWVXgwIFYcL3sAvqhVjYYXPHkAsAv8BlyfsSgG4MFhIaaVZGkW6i+msC1/RH212Y0d1F9M4qgAy+cfXQMSBNsCMI1TVGCd+svnbhQA07kwGbQ1ANhkSxs36OJyqRyc/OZEB8A4DpVW+EZBfgEiq8Cjy8QNf2+p3gAI/CbzHzX0w/V6nev+yBmA327kGdjcGrLScxhJFvv21re+lTJAo/IBwjfybnhhCDUXqi1ehGNfTjzxRHLD5t9RXoMJgN/whjeIb3/727FLdUnIGTuZ7+AtkJEFPABnZEg/jbfAfLKACYCRIAixtQAEvOHdddddO/E6c6nu6WyHN9KIjYNLNh4IueUFwJhfhWAd/PI6WAXWKcD0EC9lhFbjfnUAjDE6FViGX3qQVrJyxwEwxgCCAcClV/5HqtMUygAenBCX3euGeEK4bwO+8UCF2qnwEIAHAx6w5XMELv033NfNjB23VlsF2AWAteov4JdOtHwBuNcJsNi+KgDTddCGYBcApnESBEcBMF0T5bbiqjnQMgAz/KKbtpxUjBt0SPV1AGDaZqVPFNevJjdout4RC9w/JO4YH6QXklAU8YKSG9RThmG49keVKIs7x+fieyRcgqKIl6ybU8PvD/YNsbT77LNPJrsGdRUZoPH76pKXIZON+0m8BbZAC3gA3gIPut/lzd8CAABALjf8HzAJAIaqgAcSPJjIDe5PcMM75phj5oWBHn30UXLLPuCAA8SyZV3X3/UffQutb+qpdZ11usb/8kBZAebPZAiOAmB68I4pEcUQrEt8ZaMCq/DLa7SF4OJAv6iuWddKhgUQTgnBOEfwgI64r143ADBc9xCfhjg5KCUoc4QkLmrSNpz719+rd8fTrTtrAD5k9WWiMDvd3RTUPxP8opeF+3NhdIForFlNcxYXx2Qw1qm/7dXUnlppd+gc1V+6HgwukPWIur10XrbPT3VhDMFpABhzMgQ7AzAGt7NBh+CXdrgQXHKMCgwApuM3PUF/10YWieLsNEHwDSub5N0Az4U1a9Z0/uD/rU0VKL6dgRiwHFe2zO5A59MLXhlQSbOExHxW6j4r7qfwmIL7MDxPsmgve9nLCKoRV7upvejIYv/9HN4CvbaAB+BeW9xvz1ugBxaQARjKApIfAW7hWgX4hWqmtjvvvJMyOh533HE9WGH8JlCnFq7aUPe22qrldsjwK48GCCcBYB388rwMwVkAsA5+6aF8tqY1AqvAJvilh2FLFRgAzK0xPUP/TAPBKP2B7KF5lukwnRkM3zh3cS4jjhnxzLqHRRcA1sFvCzjCdX1tFOBI+MXEqvqLz2IAuLBwkRANTakeE+hGALBqXyMQOwKwCX7Jln19orZ6jfGiTwvAxdER0ZyKqMHddoOWARiLsVWBtfDLe5NABcbQRrkNw+0XJYBg8fQjAjaC0ohznYF43bp1ndwO891dmiERv9177bVX/A/+JtQDnijwmELOgac97WmZrPwFL3gBJUNbtWrVZhUHnolx/CTeAjlYwANwDkb1U3oLzLUF8PCBP1BRofziQWr33Xen5Bom1eC3v/2tePLJJ8UJJ5wwL5SFlStXUnIjJOjadtttyaQ6AMbnxVJJTK5cGzK7bfyvOhAAHAe/GNM3OiSqE5LSpznw5QGzEmlSgaPgt/PcLUGwup8yjDAEZwHAc/mSBFmg2T10zz33pEzWpnM5LQAnhV8cm4M3/FwU5eRHatZlS/dngl655QTA8iYCMJwxAGM7Jgg2ATDB8+CgaEQoyIBfgtkYAFbh1xaAAzG/uh/2lABMv19tFZimVyBY3iTOa7yAYiCez+7SUK5xzeJFFa7XzalBpUU4yA477BBIFpV0H3F/RmgH4Bdl3DanRGhJbeLHeQvkbQEPwHlb2M/vLTAHFoCrKNRTJAlCPBFq+yHJRVSDWykK2kPdmw+1KPEwAOCCeoAHDbQoAOZ9k0E4KQBjrvpsNdJegF9uJgjuX9TKXl2f0kOyDoAHly8WzYgM3rzNpCpwedEi0axVE8UD/+Y3v6GHNLwk6VXDwyESoiErOBpKqsQlibnmT5osy4YFZ+n+DPWX4jwnNohGf8vtnN1d6T8W6q9YMCbEbEutDzRbAHZQf6OOYa3tbq32KZjA2OD+jPFQgLnpIDgOgDHWBMEMwOgTBcEAaV2LUoFj4Zd2LpkbNO1TWwXmvwv1mqj3DYvSrgdYXV5x7tL4zUeoy1y4S+MehMR1WaqkVkbpQSe8eECdXLxQziJjM37juPwgXljPZ9f2HpjXb8JboCcW8ADcEzP7jXgL9NYCABWovxx/pXN5VleE5FgPP/wwJTiaD9lH4Y4Nt1eoBzvttBMt1waAeb8AwnHlj6KOChTgqPJIWQAwti9DMOCXHuRTAjA9l0tAwipwcbAF7QDg4tbbicJRr3E6MXvtJQAvBmR5hmcCXJ3xoHj88cfHrnkuADgWfrFqFYBHFgixeqUg6OVmC7908ji4RcdaTeogQV1tdbCckSsAy/DLW5AhOAp+6TyWwFUHwTIA07mtUYKLY4tEU5Npm/rraivX68IKfnmHMlCBk0IwL8HGXRpAjBjiXiRZyloldTl98+4LFR73WCSS5JezabaJY4dwDtyv8dLXA3Aaa/qx3gJ2FvAAbGcn38tbYJOyAOLGoOainIHtzfS+++4TDz30kDjiiCPE0FBX3ZyrHd+wYQMpCHDdRrZqF/jlNZsANir+l8eyC7RuDhl+ub9OBWYFmFglRgVm+O080KaEYB0AY24Zgl2zQiOWHF4FgNC83fTwAA0XeKgtiCNEZnO8FJmvAAzXZ2q1rudAQP3FdwzAAF+0aivBUaDZAnAG8b/Ga1sjiwOETfCLeUwxwDoAJjO1Y4Jt1F9epwrAKvyinwmA6TtduSkNABeXBOttx/4GmgCYLrhWhmouh9T6d1cRV1XgermVIbrQbForwbr12bhLA4jxJ4+kS6yS4uXlLrvsEmvCTakDXNDxW7jHHnt0wnPSrB8ADDsh3Aelo3zzFvAWyN8CHoDzt7HfgrdAzy2ADJwABpeGsjL485znPCdVrViXbUb1xQMUYsjw8IREI64AzKVR5GzRvL04AFbjf1UItgFgGX6xXRMA03ezNZE1AKtQolOB0ccFgtlNHonS8nho5uMDN2u48OMcxrGHmyFg2Nb9+ke394slI/Hnv637M9lJSYpVLnZr6lrBLyaRswTj/5sQANN5ui4cZ6+eZ+o1bQJg9AMEuwAwxsgQrANg9JEhGOovNxsVuLh0eat7O/uz1e+Zoxs0Td+GYAZg2re2S3RWECyvPcpdGrV6oQxn6S6NF5hQM/H7zR48VrbcBDohAz08U5ABGpmg0zbcr6H+ogLD//3f/6Wdzo/3FvAWsLCAB2ALI/ku3gKbmgWSADDUX6jABx98cGy8cC/sgXqIeBuOZEd40EgKwLxWGYTzAGDiGSkhlgrABBAGFbhvrK0IKoZN6wptowIXh0dE4Z/fZnVI8dCHUlp5xYlDCUESGJyHiENH7DqXwAIAIzHaiSeeGLtWALDakNhq8XAw87YtAEdlf372zA2iNDNB8CIrvvK/G4OjoljVxIFvYgAsSmUya331UwHzxmWA1h2wAgPghvXG42mK22UIdgVgAs8YFTgRAGPihG7QMviqAFwvtZTi/h2zqTXLho5zl2ZX6TTu0shYjWsWHjzwRNqcGrxgEDKEGsAA17QNWaXxO/fSl75U/PjHP047nR/vLeAtYGEBD8AWRvJdvAU2NQskAeBHHnmEyjDYJBnqhT2gWFx77bX08IT4qLQAjDUDguPgF/10GaBZBdapv7I9AME6+CVw0ADwwLLFolHVl0TKG4AZMAon/ZvVIUVdZsSWQ6mwiSu3mrTdCS6bmB/lr4aHh8X+++9Pf3OzjT/WwW+LT8JljYpK/iL005V2LhXDY8vtz06oXhaCX5qnXesV8Ev/VwHYFn6JkCxjfTNKgBVK7MQHoQ3A/F8GYVf3ZzoeshuwAYKjANgEv7w2qMCy+tv5PCIWuAO/6OyiALdOsO7prir9bTdomrbSejmjc4OmQ62owHlBsHxtRrlLIxyGaw+7uEtn7Sbs8luSd1+EF9177730gg6qedoGW0Elf8Mb3iC+9a1vpZ3Oj/cW8BawsIAHYAsj+S7eApuaBfCGHwDp0nBTh4vrs571LLFixQqXobn0xUPZL3/5SyqjseNlX9FuA+WPTI1doNXvqxsnI9cbVf4IEJwGgLFhFYIBwPTgq4HgtABMz+WaZFj4nGOBCTIaDSsVOK9EaVD7Abhwm4SiglrVaiZy2/jjXgIw4JehRVV/GXz5ZEsMwDr4pRPJEopdr05TYWQFfnlaQHAeAGyCX9vdMQEwxutU4FDZKeoYfvFh/sFxywZN00fEAtMhbscD9wKC5f2ycZcGFI+OjhpzTCBcAfeTrNyEbY97L/rhZTGy0uMl3diYlMAu4cYxH17yvvWtbxUXXHBBwln8MG8BbwEXC3gAdrGW7+stsIlYIAkAI9MuIATwAeic64Z9uPLKKwnGd7niQu1yTABsgl9MUurvE9Or1hl3L67+b6OmAQ9ptigFmB5qJRWY4ZcgKqUK3Leim7hHTlZUKFdEdVUrky/HAdO/2xmhO6BhAcEo0fH3v/9dHHnkkWLQUFbG9bxhpQgP3Uh2hsyqusRtiAmGOhwXf2xyf1bXpVN/yS6aCko6BfiEvmtEeWqDVv0VheAkm5P7c+j4lsuisSaYKZr7RMX/ygownf+KChwHwIXhUdGc2Gg83XoOwFhJBm7QZAtFBabfjbY7dK08IIa33c31Mkvcn92lkYAO1yr+hocRWqVSoXAZVojl7NIIV4BHB8BuPrxQTWwAzUCEaaA0G7ylFizQh6+4bA9qMsogve997xOf+tSnXIb6vt4C3gIJLeABOKHh/DBvgflsgSQAvHr1anHHHXcE6u7O9T5CAcYD1u4/v0i7lKQAjMlMEBwFwOWRYTG7bkOkWRDPW5uciuzDECwDMD34JlCB+wG+CrWp2XoBwdzq4y1oYACm53ZLFTjLTOE4R1F2Cw9/yCiNFy9RD8q2darTALAt/ML9mV2fyZbs7tzfyp5enA3G+27uAMznlgrCJgBW4bczXoLgKAAG/KJFAXABpaVM7s7K54Ul7ThOKYN354JJqALXlmwjmpLrM2eDpnVLnzeK3Wuz0VbZy7MT3etVUYHxRa8hWP4xA/wivpdheOPG7ksI2V0aL7RwbSOzMcfxz/X9JKvtP/DAA/QiEPky5DCNpPOjpBLKD370ox8VZ511VtJp/DhvAW8BBwt4AHYwlu/qLbCpWCAJAOOh5rbbbqPSDsi6Ox/aNddcI0ZGRsSeV35TuxxXAIb6KzcdBMcBMMZHQTAntIqCYACwCr+Y10UFJvCVWwQEywAs+ro24Gy5HdgYHhWFo19rPPT3338/KR+HH344HZekDQ/RcKdGPDEemuF2D3fKqGabgKsXAAz1V4ZaAHDDAL/Yp8Tuz3RSWLo69zj+t3Osyq3EWNwYgl3U38D4DesDtX915wQDML4zQTABMJoFBGcFwPUlW4umpP4nBWA67IVueAdDcrHRymxeLQ+KerEsyo2qqJb6xdhWc5dkSnaXhjqMhE5yQwmz7bbbLtJdOunvyFyNg/sz3JYPO+ywTGoq33jjjeKkk04Sn//858W73vWuudqtzWq7X/rSl8TXvvY1qmyBcxReS9dff/1mtY9+Z9JZwANwOvv50d4C89YC6oNI3ELxJv/mm28mF1T8mQ8NNywkW9r76m+HlpMk/lcFYEwqQ3Cc+zMUYG46CJazOScBYHrwtVCB+5cvDbpbYqAtAKNvG4LlcjE2EIwHP6gfaUplTU9Pk6v9+vXrxdKlSymRDFwp45pNAq5exP9GwS8dhrzVX2wkr/hfzO0YAywUAKZzeM0qkRSAMb6pSxAmnSBZAnAHfnl+VQW2VIABv7R2CwCmfhoVmBVgsqEGgOnQF7svHPjf3Bd/L1mRvixP3LVo+h4vXlG/G+owssXj39yi3KWTbm+uxkHZRs6M5z73uVa/XXHr/PnPfy5e8YpXELCdccYZcd399zEW+O///m/xkpe8hLzHjj32WFLp99xzT/Ef//Ef3nbeAh0LeAD2J4O3wGZqAbz1xAOJbcPDCt5EIxslbhbzoaEM0qH3XBlYytTK1fR/V/UXY3QAjM8ZgrMEYMxrguD+JWOiMaNPUhanAhP8oulARYLgKDdoWQUW/QOiuW5tV3WLUIEBv4BgKB9JYt/gZQD4xcsZeBmgxq8u3ld37iFDOVSXqAzUtuovnT8JMkCfWL6KEhOVZ1pun43KgCjOBt3d0wJwY2E3q2xBp/42u/WHZTsV1Gt99Ur3S9gVfrEFDQDj4+a4OVTA5ALNC3YBYNqWEgvcUX95wggVOBaAaQPRv6MMv9RVif/OWgXGNnQQTOejDM3tf88VECO8AeobrnFc74Bik7s0EkmpSe/cT97ejcBvEXJmQFXMoh46Sh+dfvrp4rvf/a541ate1bsd2Uy39LrXvU5ceumlAh5kuF/45i2gs4AHYH9eeAtsphZwBWC17NBcmwXusVD9jvnbjdqlzKzWJ7KKS4Bl2i9AsI37szxeVYF19Xx1EAwApgdWBwhGRugO/PIiVGCxVYElN2gAcKcxKBggGO7PcIM+5JBDnLOf4njiwRHAi7jArbd2U6o4A/VRRx1ldDu0BeAk8AsbHTdwoxP8YkxU/G9jdFHX9pr401QArJ7oNkDsCsAG+KVNlyuiua71skpucfBLfQeHRHOD4fpux/+q88oQbAvAYkSTwMghDlgGX3k9NipwXBww/T5YqMDoJwOxDoJVKF+6PP8s/6grjz8HHnhgJ7wB9xhOpgUgZi8l/CYsXLiwk0wrKrv0XN+XsH3kI0CWa8Tt2r7Ai1r3JZdcIs4880xx+eWXi3/+53+eD7u4Sa8B0HvdddfR+YcX+r55C+gs4AHYnxfeApupBVwBWC47hIREc9WwDsAOXOjwcHH0Qzfol9KGvZmn1gQfsMv60kgm9ReDSwOt2pyza9cbd1t2f5Y7MQTr4Bf9VABm+KUHXAcA7lvaKpcU3FlFxnRIhqWqwDSvBMD4rxoPjOyncP9D8he4l9k0xPtiDBQhZIlF6ZAk6jFnoJ4rAAb8okH9hfKLlkT9bQx03eg79tNBF+yfRgGOOjgmGM4YgLEEFYJjAbidnZzGaiBYdn+Wd5EBOAS/3EmnAo8tEUJnews3aBP80rpTuEHT74JUcsoVguvtpFpNEXZxUEGYTZMHEMclipLdpdXs0lCDObM0/pazS9v85uTdByXZEMIBBTiL9pWvfEW8//3v94plSmN+5CMfEeecc452FgAx7h2+eQuwBTwA+3PBW2AztUC1Wu2Uq7DZRbnsEJISzUWbmJgQeLiAqxziQwHDz/rt5fqlKLDHIGxSgG0AGBsyQXBSAMacMgTLAEwPuxYQ3ClxpMZ+xrhBY361JFLHmFEq8IJFQtRrorp4a9H3zOd1hiDzKUAUqs6SJV1XXdO5AoUHxxOqDx5k99tvP4rpTtIA0QDwI444ghJnqS3P+F8b+MV6ZPfn+uCIqGxolQeqDXdrhRbrrURGgWar/mKQxgU65P4cY+CmdN4UVj3Z7Z0VAEtZx3lyBmEXAKbdVSDYBMDUd2KjsAZgwC8dHLvjIbtBR8EvrSMnN2j6vZCyRsvKL5JhhbargWAG6oIwu3VnAcScKOrQQw+1KpmGF2WASsDwfHeXRtZm1C5HMsAsGkofnXvuuZSEEi8XfUtmgcsuu0zgzy9+8QtyUUccMCdrRPzvfAntSrZ3flTWFvAAnLVF/XzeAvPEAq4AjGWj7BDisQA4vW5PPPGEQKZfQO/uu+8udtllF1H92gf1y9DVqwHsVcpiph0jrA5MA8Am+OVtQAU2KcD0jN0ui6TCLz3QxgCwXN9Xm/zIwQ0a2zNlhO64QvcPtnarXqO/ZBUYKi7UedS/xAuKqIaHWcT7IunVjjvuSNnFUe4oaYsrwdQLAOYsvNgHk/oL8OVWaNtQ3uf5BsCdtQKEcwRgbAcQnAaAo+CX5s8KgOmiVcC4HQccB79sTxsVOBAfrMCtjQpMl2k7KRYAmGygwrcEwbKaLJ+TUTCMfkmAGNcrvHgAiUlees1nd+lf//rXolarUS6ELNrZZ58tzj///E7d5Czm3JLngNKL/CHeBXpLPgvi990DcLyNfA9vgU3SAkkAGG5Cg4ODFOPZq4Y3/3hYgrqIByVkBWZ1cfbCD+iXEQHAGKCDYFsAxnhVBY4DYBtbAYJ1AIyxOghGMqwA/PJG4lTgtG7Q2I4Ewc2BYVE89BTaOsdlH3DAAZG1PZEhFUfoYzYAACAASURBVPHbaHvttReVQUnb4kow2cb/Yh02McClYkshY/VXhl+aQ0p+Ve8bEsV6OKmZCsBa+MVktgqwbQKsCGPL6m+gWxucCqueCI6W3HFD05pigDUKMI2t9AmhiQsOzCu5QPPnrALHATDF9E51a+iG1stu0Kz+cgcbFbjZFLbwi2mNAEwnTzdMwzUWmH4v2irwTGVI2Lo61wvBclWqbXBeFA3nl9rXBojhKfL444+Tx0baBFfzzV361ltvpZd5Wam1/+///T/x9a9/ne6BO+ywQ9qfyi1+vAfgLf4UsDKAB2ArM/lO3gKbngWSADCyQCOrJcrc9KLBjezuu+8WyA6MmFLArxzvlRSAsXYZgl3gl/dbhuA4AC6PjojaxvFIk5UGWwqNrqUCYEzooAIHFGCM1blCKyowQzAUHaj0cJFfsSKcSAcvMwCqcFXu7++nfvAoyKJxCSZTDeILr+q6Vi9e2Ip/LBTCbp428IuxAGDALytx5Wo32zPDL8CXmwrAadRfWntO8b9xAMz70wFhEwDHJMDSHnMAMJoJgjXwy/MAgucSgOuLt3I6jdO6QWNjJhV4qn9hYC1xEFxrA7PJVV53TsTBMG9z2fLlWrtwpmTASBrPD+3v5Ry7S6NcIH7f4AmTRfvXf/1XygC9evVqChXxLZ0FPACns9+WMtoD8JZypP1+bnEWgIsW3IldGm7sGJdVco+obT/11FOUTROgjpI4cHtWH5TSADC2zRCcBIAxniHYBoDRPwqCK4sWisb0tNYkOgCuLFsqmrb1Xh0AmOBKVuhMscBtCG70tRI+4eH5yZ0OpRcWiOXdaqsgEMBlEd/hIQ7QC/jFQ2JWDSVV8MdUg1gGYN6mzlGATbW4nQB4zQYhyqVwwqBTtr9TlOut4yXDL/6vAoeN+otx89X9uXWA9e7phbWtOOZQc1V/MQEDMP6tg+AIABaD7eRhEeWVOlmdo1RgnkfdoQgV2BV+eWobN2g6nzQ1gfG5DMCT/cEXSTbxvujD8CvvrgrCppciURCsg25sg4EYL8rwG59VpuSo35E4d2m8XIVXUVbZpfGiGHNllSsDZXsQu4qcCUncxbP6jd1c5vEAvLkcyXz3wwNwvvb1s3sLzJkFkgDw7bffLpCIKs/aeXBnA8ggSyhc41ASR6cmwnBaAI6II0UMsK7V1rfqtuoaZ4A2fV8cGhRR46H+cksKwPSwK8UCA347D9E2EJxHMixWgbG2vgEC4JU7H0ZJrZAlfJtttumsEUnL7rrrLkoMA3dnuD1nrfpE1SDWwS8WFwXA8vFWAViGX/STAVj34L85AzCDcWGNUlc4LQDDsCoE2wAwxukgWC5pNN8BmE7OeDfoycHFQoZT9dyzgWCODVZ/3xiCjR4BuO6bwYz6ZdGKizbBL30n/Rb9+U9/6nnmXdVdGt5F/CKYs0sDiKG0ItwnSUOoEIA6q2oJSNb0q1/9SoyPj2dSVzjJPm1OYzwAb05HM7998QCcn239zN4Cc2qBJAB85513Usbe4447Lpe14w03VF+ohCiFAyVRl9EXG0+r/so7UKxUxOyqYLkk/t4GgNHXBMEyAFM/jSs01F9uNiqwMwBjcgcVuLBsKyHWSjVaHVTgq9YP0UuLbbfdlnaJk5fB/fnpT396bjFsXIMYWWVRM1RutuqvzkwEuJIC/JLtfy1KUjwvw2+t3FLCS7WZ0LWR2P2ZTphwFuK83J9VQOnsiEH9VVXhAATPZwDGjmkgmOsuF2vheG1TNuik6m/L1kFVPZD0ygDAE0PLgvHD0nWdBIBniwPaUIC4H3gVfuX+JdFKkKe2KJhevmxZ3CZz+T7r7NKY7/rrrxfLly8X++yzTyZrPvHEEykPxsqVKzN/cZjJAjexSTwAb2IHbI6W6wF4jgzvN+stkLcF8NYbEOzSkLUX5QNOOOEEqsGbZQNYQz0EBEMlBCwh3tjUsgZgbEeF4Dj4xRgowNx0EJwVAGMbUIFl+OXtWrlCGwC4uKwdq6vGcsoP4OWy6Li69rdAj5qiAtMaB4bFk0v3IgBGXC7AFG57cAe0rQ2c5LxCRk88JCJBmxpXbAvAulNaVX9P3vG3oq8qJVJqZ//lNasAnLX6i+3kBcC28b+d42Nyi4Ya7ArAsvuzfAKwChyl/qK/6rqsqsCyAoz+rgCMMcrLiNrYcv2xsDyBbQF4YmRFQFUNuE4rJ60LBAN+ueni4evNlsdMqRC+T0QBcEO0wL4igi8SogBYNtlcwTDWgJAbLrWEv3E/omuuUKCXslx/GP/W3QNxT4UL9NZbb033sLQNijUSheH+iN+4rD1n0q5vUxzvAXhTPGq9X7MH4N7b3G/RW6AnFkgCwFBnkcH3ec97XurMnbyTuMEjKRKSI+HmvvfeewfcZ03GyAqAof7KTYbgOACW4ZeejxVXahV+eTuyCiyrv/y9SQUuLWgHpipGsQLg1lNcZ2Rx+VZhVViGYAmAMagpAU1hspXQq7FgiSjOTLb+3Y4FBgCj/b6+hGL88KC4//77B5KX5XGC4xxCLWBkXlVBOysAdoVf7OeWCMDN9nlUXKu4RcMgURmgTSfGTDfBmLaLKW6XIViFX55EgmBWf/mrOBUY8EuXlC4ZmcMJbooDnhzdKqj0SuWKQuAcAcFqX7qWRUHI8MvLlSGY4VfeFQZhG/hVTVAuaOopx9hpLkGY7NRsisnJyQ4Qq+7S7Cotu0sDmJErAy9xn/a0pzmcCfquWAOSacE9G4nDsn7xnHqBm+AEHoA3wYM2B0v2ADwHRveb9BbohQWSADBqvKLWKxKXZJHACG/bUQ4HqvLw8DC5PCN5iE3LC4CxbYZgVwDGWBmCTQBM/dqu0C4AXF68RDQ1LrEuAEzg233iDZo6RgXmzs1yN3kVAzC+kyEYD973FpbTC40oJd/mWNv0QYkQlFY56KCDAplSs4r/leG3XmplK1bV3qTuz5hrU0yAZUqMxQBM+yVDsAl+0dGkALfPq+LGtebTICkAY8Y2BFsBMF24LZDLA4AnF2wTjOmVFPYoZVdVVuNU4OnisCiIhtaegGAd/HJnQHASAOY1VQoa93LNSprNoIfRiuXRdcVtfiPS9olyl0a8MEAY9zG8zEVt81133TXtJgnCoSQjpwLqC3sATm1Sijv3dYDT23Fzn8ED8OZ+hP3+bbEWwM0cAOrS4GIKNyy4ZJlic23n27Bhg4BLNRIjIWMw4qVc6kFmlQBLVYB5/YDgJABMD8dtJTgpABNMKhmhAb9oOgCmzy2SYRVXbB0+PLJ6FAHAtA1JBZYhuFnpE6XxdSEVGBDc98zn2Z4SqfrhxQxe0Bx44IGdOtGYMAsABvyiwfU5DfxiDl35o1r/iOib7ALe7NAi2l6xqcnS3q7FWtmgZF/W1Gg1lbUxGTorF2gZgGk/GIITADC/VKF5TBBsAmAMggpsUoDxvQGAaXuGWGCGX7ZjGhWYFVrAL11jckyvGiOcUAVuzdtySwb80nloAGD67RHm0JPW2HD5sNY4faZw2r60dvw/DoRVAJbP2fkAw1gP7p9wTUbOCtldGt/hBTGgFVBscpe2+cEDAKP2L0JIkFzLt/QW8ACc3oZbwgwegLeEo+z3cYu0QBIAjis1Y2NI3NAfffRRUuv47fb222/v9Ga7+d9foE1VVyouloYM0Kbsz/SQq7hAdx5q+/pEbU2E6qTE/8r7DgCOgt/ONsrmB00TANPDZAIVuBPrq9pIDXxNoAIDgDv7NNsqDcSu0JX9jrc5LVL3eeSRR8hFEO6CS5d21aK07s8Mv6VG8GWRjfpbr0jx0u091MGS7jMt/NLB1yt3sgEr61vXRSYAbJkAS96+CsD8nRFgY9Rfee7QHFHw2z4Pi9NSzLbmTGuUu+dvYFs9AOA/vPMTreulHobKXS+90OgGTaeCrBBbxAIz/HauVQ0EV0Xbu0HoS+TV2nHBmKOiuDWbADgqK7QJhE0A3JQge6vl86cmLrtLI0QIv0VQavEZGl7s6tylbX70cJ9etmwZJZ782c9+ZjMkcZ/p6Wlx3nnnie9///vk6QV4RwKuj370o+TS7dLgLv6Rj3xE/PSnP6VEiHjJffLJJ4tzzjkns9rvLuvxfb0FXC3gAdjVYr6/t8AmYoEkABwVZ2mz20gQApUODwkDAwP0VlvN2GszDwOw3Jdg2BGATfBL8NDOfGyCYDX+N7Tuhl4lkfsVIgCYHorbKjCrvzzWVQXuwC8myAiA6QFccoVmCG5UBkRpYp2oD4+JQr0Fjb2AYLxUgTv9AQccQA+M3NIA8Et3+R1NEwe/1Kc2I6p97Vq07Y3rILYXAKy7hvrWPRl5aeWl/sobbZZKorROUzfYAYDpFJaV4B4DcHXBUm3cr40KfPfbzw3/TFT1oFmsdF+OVQZa/97+G181JsOi69EAwVMlc1iJrAQz/PIiSwoEy/DLfWQIdgXgRjOoGPcXu3XQbQBYNuZ8gWEowUjmiPhfuEPj/1CJ4fHEjd2lAZgA4yjPJ0ApMkqfeuqp4oc//KHN7TFRH2zn2GOPFbfccgsl8Hruc59LuTngdo3f01tvvdXapRuKOLLxIwniLrvsQi8l8XISf3bbbTdx2223Bbx0Ei3YD/IWyNkCHoBzNrCf3ltgriyAt9Ozs3bxWLxGk8pmsw+oYYgHA/yNGypK5SA7cJKmA2Cap1gQ1ZVPhaY0KcA2AIzJdBAcB8DF4WHR0JQ86jxcthNaNSbN6pQJgOlh11IFLi7WxM65QHBEMiwdAGNtgGA0BuB6ZVAM7P3cJIfaesxjjz0m/vCHP1DCLTwwcksKwIDfRqEFHpV698Ec/5fV31p5UBQVdZhORY37sgmSrBVgC/XXxmA6GM4bgAG/nXNfhWBHACb7MgRbADD1N6jA9aFWYrlC23NBtZ/sBg34pb6axFemY/vn936SxlSnw6DbMMDvwu1bZbym14WTf233jQs7S7RJhhUFvzwRQ7AKwHSuSxCsA+DOMS3oQZ5+qxT3Zx6jAjB/3lcIlxJrzaN3sZbn33p5K3xgrhoS/+F3CLXOoXpyM7lLq9mlkQNDzvQMmNx5553FaaedJr75zW/mtlsf/vCHxcc+9jEC16uuukqMjLTq13/+858X73nPeyjsCXGzNu11r3uduPTSS8Upp5xC0M6Af+aZZ4ovf/nLAt9/+9vftpnK9/EWmDMLeACeM9P7DXsL5GuBJAAM5RaZoKHcrljRLp9jsczHH3+c1Dkk3sKbcdzQ0yTziALgzgOHBMJpARhzqhAcBcCAX7S0AIw5ikNBVZH3zwaAi0uXC9HQuMy6ADAtogsvpjhgekBtgwwDMD7rFQTrzs2k8b9x8AvolVsaADaBU1T8r8UlZ92FYbiXAIzFBZRgAwDL8b/qDtkAMLvh0ymcIQDTea1AsPp/Bl/0TQK/8v42Nd4kyz7fCgOJguCJ0kJjvK5qz5polTzSNUBwFPxiTF2URJ8mwVWU+3MeAMzrnysQhrsvvJzwglf2RAkcz2aTcl9wuSUoxLg3orG79KpVqyiGGJ5SmOttb3sbwWMeDXCOl4ZwW77rrrvo/i63Zz7zmXTfv/POO8nDJqph/1ECD4kP8cJcfk5AhmyEO2G/8cLS5Rkij/32c3oLRFnAA7A/P7wFNlMLJAHglStX0g0SN2Tc5OIa3KxRmgbxRFB7cSNdsqSVzClN0wJwUV+XGIqwKwCz+7O6RhmCbQAY400QLJc0ilKBXQAY2+NkWAS/3FQITgHAtI2IZFidTUrxr5w4qtBs5KYE4yXL3XffTZnEWXmxVX+xZvYe/aen3S8q9a4CxepvrdiOjWyEa6JmDcBp4n8TX1eFoqiseyI83DEG2BT/KyvA8kYIhBMAcLNddgtzlSa77qXy3DIA43MdBLMCTOdAhArM6i/Pb1KB/3rO58Xs+KwolFq/R7MTmhq6GuV38S4t5bJe1cd4qxAcB8CAX9onQ8Kq0G9bBADTNa9kZZbHA37lJoOwq/pLv5miKAYKYfXbRgEOHP+2Yrzt8pYtetEAdkgW6XKvw30SLtIMxPg34m5xrwWY4r4LNfVb3/oWJdTKuiG51jHHHEMuzsjzoTYow1CIzz77bIrrjWpY4xvf+EZyp7766qtDXU8//XRSstHvDW94Q9a74ufzFsjMAh6AMzOln8hbYP5ZAG9kXRrcse644w5y70JmyqiGN9xweV6/fj3FOeGBAG+z0zYb9TewjWJJ1FZr4g5jEmCZ1gkItnF/DjyIKa7Qaj1fEwAXx9rufAZXdZMKHIBfeqJMqQKncIPG5mUAxv/zcIeG8oDzDecZYtjQPvnjoMvk2MKyNkw8Cn4ZfDFfKWP4xZzW7s/onJELtPbcVkCXYNgRfmmJahK19sZMANwsVUR5w2rtkqIUYBmA6dhoIFgFYPSTIViGXzoWKQH4nvec2wFfzOcKv3RtLBzUQvD0+ilhA8Eby4tC0GsDwTPNflEyuDFXG61a6eVCGObp+tZkjWYIdgVgNY5YBuGkAMwnVy9AGKonYl8RijE2NpbodgdF9sc//rH4xS9+QW7HUIjpHC+VyEUZCbGOP/74Tn3gRBuRBn3hC18Q73rXu8TLXvYy8aMf/Sg0HZJvnXTSSZTECkmtoto73/lO8cUvflG8973vFZ/+9KdDXb/yla+Qmo1+559/ftql+/HeArlZwANwbqb1E3sLzL0FXAEYLlJIYLHHHnuQG7OpIQ4KLlO4kSMJBhJfyHFNafY8CQDz9mQQto3/VdeqZmfW7Qu7QPN3qgqsAjD66SA4CQAXlsDtWROPl6EKLCvAWHtcLDA9JLdr53JmZDwYj+6+f5pTITAWtaRRVmvfffcl10E0FYDxmc71Hpz3ugMf6Ci/9WLLHbRcD8bIb7YAbABdHKO+9ZrkWab+Bvilc0SKAZYPHACYbK2B4DQArINfbCcKgOn80EBwbXRJx5VfXju/vHjg7M+I6lQwS7gKv6VKUdSmwwAJqN3mWa3zVW46JbgpXcPT66fFwMIBMXr2JwNu0EkAGPDLTQfBDMB0nDQQrANg9FWzRMv7Z3J/NiXSQv/Bok4V1nv+RJVkyhOEkTjqwQcfpHJstjXto34Er732WgLPl7zkJXQ/xf+RRwPt3/7t3wSAMm1797vfTTAKCEbMr9rYswZQ/5vf/CZyc1CqAcmAYMT8qu3yyy+n/UG/n/zkJ2mX7sd7C+RmAQ/AuZnWT+wtMPcWQBIsLtVgs5qNGzeKm2++mVyldt9999AQuHLBhQoPAJVKhVyl5YRENtuI65MGgDE3Q3BSAC70D4j6+nXGZarwyx1lCNYBMPrJENyBX57AQgUm+KWJEgAwxkWVRMpIBcZmGIJrpX4xtss+cYfc6nvVPV8Hv61dDD4wv/7gB2h+uD0z+OL/KvziMxWAda7P6GebAGuu4387ho0AYO4TAGFHADbBL+ZmACabSxDsAr+8RlkFNgEwHZ/pCaGqvzyHKwCb4BfAKzcd/OL7rZ+pqc0d6Qod9uYY+cinBcC3sw8at+coFVgGYDrPJSVYhl+eX4ZgE/zSb22z5Ro9KGV35jmSAHBrriAEGxVmi4RZmG+75dm6FD/wwAPi73//uzjkkEPE0NCQ1W9XVCeor6985SvFRRddJN70pjcRBN9+++2UqAr1bOG6nLadccYZNP8HP/hB8fGPfzw0He7puN8jfwfcu6MalOlf/vKXnfWqfeEWzQr2lVdemXbpfry3QG4W8ACcm2n9xN4Cc28BVwCenJwUN954o9hpp53EnnvuGdgBqMl4U4w4JsQpIRYziwcA1UppAZgezFaviqz/azoygF9uJgg2ATDGAYJN8EvfSxmhcwdgbDBFLHAaFRibzhqC4XUAdWKfffahmpU26i/DrwqsNvBL5rPM/oy+LpmDe5UAq3MyWwAw9yUQzgmAsQ2G4CQAjPEMwUkBmI6VpAJD/aXP2iW95N+Gh85uuXjOTrRCSYrtsmbVyaAaTL85GvV3+4N3pHG1aX02fnM8cBCCmx+/KPSTpQKvCYBV+CUbxgAwHae2EmwDwLw4BmET/NJvoAFc1TEMwmkBmNeWFQjff//9VOf+sMMOyyTkB1mU3/zmN1Nt3le84hWmW1OqzzH/N77xDfGhD32IMkGrDS7dgF8bAAbcAnIxH+J91QY4BiTjjwfgVIfND87ZAh6Aczawn95bYC4t4ArA6A8XLGRy3HvvvTtLB/QCfgHBiA0GHGfl8qzaxyUBlpy9OGTnSkU0NLHBpgRY9BAsATD+r4PgNABMD4BtCA4BMD1p6x+UEQvcUX95R5OowFEKMD3hd5PdVBetEE3p/+WJ9R0TczZoWvLQIlGudlUb1RWaAKDUL+rFiliy0x6JLwdkTUWWUpyXOD/jAPh1Bz9I2yo1w26pWQNw6vJHWGgP43/5IJjgApmH+zWu0Unif3UHHBCcFIDpOtWd+8qG5HNXXYMOgGneNgQ/eNYnRaH98gjwy+CLPq7wS+e/AYDxXd/okJha03J57RwXTUy/CsE64FU/m2oMimJBn3QLEKxTf+V1FArmWues/qq2BQS7qr/0u6jUDOZ5BzTqMvW3VIA7Nm0n+dp+hblmss2P0z333COQkA91dOEFlbYhYRTiZa+44gqKw82jeRfoPKzq59zULeABeFM/gn793gIRFoA7FdyWbRtKNeANLmIsEWsJ9+mHHnqIkn4AeKG+cQIi2zld+mWh/tL2pAcTFYJdABhTyRAcBb+8nwVTYqF2BwCwFn7xvalu80JN7UsbAMacESpwffFWorR+lagtapW8UqEh9P923Vx6AG3HdvK/+6ZbmXoZgOnfUqZoQDBaUpdoNUGbCYAZfPl4qABsC7/VcjduUj6HC80wFAxOt5LYqG2+JsCiY22o3aqW3ZFBOCsAptPSULaI1iZlgLa1q9yvNtCqcVqaDceUdq7T2WnB6m/ns3pVsOqLz2ozwZcnOvilfhHqb+c87NfDkq4EUutibIrJ1Rs7u5VEBQYAk60NEByl1HZsYoBgEwBjXL+mXBI+t1V/edt1CXKHi5OBUyEpAPMkSUH4T3/6k0A+ArgnZ/ESGKWP4JqMF89HH3209nck7Yc+CVZaC/rxm6MFPABvjkfV75O3QNsCrgAM4IXbEuJ6Ed+LRFdwPR0ZGSGXZ/ydZ8sDgOnBS1KC8wTgwvCoEJKbs85WmQEw7ZgSC+yQDRrwS8/ZauyvXBNY/c4AwLQUGYjbSabo4budWblaHhQok4RWLfWLZTuGY8yjzi14Ifz6178WT3/608X3fx1O0PbqQx8V5WbQNVWF30ah1FmDvC1tTK8uzlIDv5iHyj/NdBVy+sygUs5n92c6HzQvcADBJvilMTEJsNTj2ii3Sk6Vx8MvDuLgF+PqfYOiPB1UTeVtJAXgJz7zOYHkU2iI8Z0ZD3pkmNTfvuEg3K7Yp5v0Cgovt/ps2HWa7KepAwwA5gYQHloyKibeFUxgFKUCM/zSNWgAYLpuDcrrbDszNPr0l8KeKSYArjW69YaHS3bQalqDDMBsC4BwWvjlufASaIcVbvc03BPxMi4rWP3kJz8pPvGJT9BvGxJr5dFsyyChFNI555wTuQTbMkhQtk877bQ8dsfP6S2QiQU8AGdiRj+Jt8D8tIArAGMvEN8zPDws4A6NUkdQg1EWqSzVhs1rb/MCYHrQa0OwCYBV92d5H1kFjlOACYDRoiB4wUIhps3KVEgFXry0NWddl/jKPRlWfUkwKU+s6isDsQTAZFNFBWabNSQApqUXu4DAiajqhTIlk7IFYZQKQXIYuN//4I5dOocH4IsG+JXhTQu1GjdjU01eLVxoAJihXr0mTDGZQ5Oakl3zzP1Zd33jPOnfsDL0lW0CLHkgAzAdNwWC4wAY8MvNBMEMwOhnUoGrg2OBGG+GX05uZYLf8kAX8Bqaer/Y5vaH7qb9iXQCYMygnG8qAKOLLhZYhl9eiA6Cp+stL4e+YhjMZQBGHxmCo9RfGYAxjiE4KmuzCwDT706z2JlXNrTRq8FQ41jtbwPDyESPOr5HHnmk9hi7fnjWWWdRRuU///nP9HIvj4Z7OV5qo2Qhag8/61nPCmwGpeUA9jYQDvdv5GDA8wBKQslJMBEihfAUvCBAvWSu157HPvk5vQXSWsADcFoL+vHeAvPYArVaTcCt2bZBAb7mmmsExiGbLsAXNztdaRnbOV365QnA9Dy5seWmq2tRANzpPzAomuMRczAAY4AJggHAaCYIlt2gGX7RPykAY2yxKOqLW27O1BSVL28VWAfAtEuFLkygzzbbbW88PnKJrkpfS0GkXXOBWsu+JnjVuT+7ArBpB4cmwnDpcu2YT+xgtmLuZ+sC3ekvvQiRQdhV/cV8MgDj/zIEuwAwjVWUYBl+8b0NAMfBb7m/HCqDRPuhAeCdj9lb1KbM9dedIFjzwiVOBR6vD4uypt5vWgDG/jIEuwAwnz+DpZayrmtJAJjnkVXmtACMOeMgGHkIpqenxeGHH57J5Yn4XCSUAkziXptXQwKsc889l5J3IcM0XnKjoSzSe97zHtqfX/3qV53NX3DBBQJ/XvziF4vzzjsvsKzXvOY14rvf/S6VbvrBD37QeTn+jne8Q3zpS18S+P7SSy/Na1f8vN4CmVjAA3AmZvSTeAvMTwu4ADD6Ir4Jb3gBvCjzsHBhG9Z6tHtZJsDSLrlcEc21q7VfxQLwQEt5MgFwR/3l2XUAzPCLPjYqsAzAGJMQgutLlVIsDgBM+5xABcY4WQk2QTDtlgLC6gFqGOKqdfCLsb1Sf7EtHQBHlaRxuZQygWKHDNB0rE39FXd4huAsABjbBQTHwS+dK5ICTONiABh9VAiG+stt5ac+KaqTQRdfVn8BvmhqDWA6tw3qb6YATAckGHMepwKbAJiuC8kVmtVftoOsAqvqr3zOAoJt3J/V89wEwK7wS7bXuG0DhHsBwFBJ8VL50EMPdbmUjX3f8pa3UAZohHgsWqTJ9ZDJVgRBO+KW4UWDPB5IHRJjXQAAIABJREFU4oVyTvj/kiVLxG233SZ2263rufCRj3yE3KFf//rXi0suuSSwCiQkxPMBSkKhZOKzn/1senb44x//SP/HXEuXtj2XMlq/n8ZbIGsLeADO2qJ+Pm+BeWQBWwAeHx8XcO2amJigt7n4g5tlL1vzxu8LserJ8CaLwbqunQ7KA3nn86jMnOWWK64Ogm0BmMZrVOAQAKOjCsEyAOP7KBVYhV/0TwDAIfhlQ0VAcKxbdIJYYFq+xhWalyNDMGJ1TSDG/flhV4VNW/glIGjqvSNs3Z8xR54ALF8MiWFYA7Su6i+d84brrW9C/0JJrv8r74eq/srfRSWt6pwnCgDjc4ZgVf3lMSYABvyWKiUxvb4bkgD4ZfDl8bYADPjlZqMCDyxRXjC2Y/inVkteJg4qMOCXm04FpnO+DcEqAOM7huAoAEa/UlF/3ajuz/KxrTWKYrQSjAnG964AbMww3YbikfJE6B7StHSBxsA4BfjWW28VpVJJHHTQQaHtJPngta99rbj88supwkKf5NmSZK64MQhpgpr7ve99jxRnAPeJJ55IpZHguiy3KABGP4SknH322eKyyy6jpGArVqwQL3rRiwiaFy9eHLcU/723wJxbwAPwnB8CvwBvgfwsYAPA//jHP+jtLbJFow4gbmaoB3zMMcfktzDNzATAcmMYzgGAsRkZgmPhFwPaCjAvUYXgOQNgeooMJ8Mygi/vgIMKHJUNmjZviAWm76R4YBmA8R3HA9eKLZdmWzAz9ZNPHzkBlslN2Tb5FebN0/3Z5ULDvg9PaF4U6SbJSf3tXANtKO7fqIsN1mc9jgLgRqlfVKbWGc2hqr9yR0CwCYDRjyGY1V8d/JYHKmJmY9B92RZ+sY04AO5fvICW3KiGS3O1vtBn7J9aFUywpqrAG2sj2kRXJldoHfzanoOz7SRXg+Wwm7cJgAG/3FQIzhqAeTsMwlnCL+a+6aabqP4vVM8s2imnnCJuueUWiisGWPvmLeAt0BsLeADujZ39VrwF5sQCcNUCBOsavrv33nvpTXB/f79AIgy8uUWME97uouB9L1sIgHnjawyxka4KcFv9lfeJITgtAGvhlzfEKrCq/vL3OhV4bIkQNX3GWBsVOBDvazqIDgCMKWxLItFzvCEjNL5TIXim3M2Sy0s1AS6U4bSt3Gi5u+al/mLurFygdfuq2iYShnsEwLxOGYSTKMAAYDQTBEcBcK0yJMrVsMIo2xAQDABm+MV3rP7q4Bff2wKwDL+BbQ7qy2m5QjDmZBAeXLpQrHrt2Z3NuAAwBsUpvFHXGAMw+sgQHKf+ynMyBEeVYdJlgKbfFkPWatPnaibqqN+YOPUXY2+44QaxYMGCUCKppL9Lxx9/PLkSP/HEE5mUVUq6Dj/OW2BLs4AH4C3tiPv93aIsYAJgKLy/+93v6K0zoBfwCwhGgys0VOATTjihZ8mvsF0jAPMRU0E4AwCm7a5dLWIBWFF/Ow9RbVfoSABGZ0CwKwBjnA6CY9ygreCXdyAjN2h6MLVUgacrI6JSnxGzpYHOtahzd1ZBLwv4NV38ffWWC6xL8ivqr0mq1Uv4VfcnBMM9BmCsBxBsgl86T9olkNS1M/zy5zoITgvA2IYKvwBfbjbqb99wn6jPhusDqwDcN9bKCF+fCZcQIjs4qsCqvRiAAb/cdImuVBV4ota67ioGN+aoG6QMv9yPIdgFgHnscNmcGCsrAGYFWHWN1r1kswFglBRCzOy+++4bZSqr75B0ErG4yM780EMP9fR+a7VA38lbYDO2gAfgzfjg+l3zFtAB8MqVK6nkAZRhJKxA4gs5y/Mf/vAHKmHwvOc9ryelj/goxQIwdwQIm+CXnuz0rpdCowB3zpCY2r2q+7N8ZsEVOhUAYzJZBYb6y81RBXaCX2wjhQrcjCiJRA/4EhBP9S0IxfSqD6BREJwn/AaOZaEbbz5Q68YS6tyfyXzzDIA7YMEu0nMAwHTsCyUxMKEp9+QAwHQpS+7QUfCLvlCA0aJU4PUXf13MjregC8pvFPyiD9RfAK/cVPjFd9sd8rROFwZf/sAEwGQnHQQb3KDVu1leADxTb/1+9pd0pZG6Wdvl9QCCkwBwvVkSCyrhmF1X+CVbGpRh1QW64xotwrkl4gAYYULXX389xbvuvXc33ls9Nrb/BwDvv//+5FKN+26vqi3Yrs/38xbYnC3gAXhzPrp+37Z4C+CGjVrA9IDQaIi//OUv9Ka5UqnQG+xly5aFbIR6hA8//LA4+uijO6pwLwxpDcBQbUslUVitcY22SIAV2pe+thK5Tp/Mh/obFGD6TpOkJrSNkQVCTEe4Z2YAwPWxBFk3UwAw7XoEBE8MSiCvyS6sU2B0ECwnx9Kdh3VRFiVhiKl0PHGbEgCrQwer44GPsip/5LJEm9hneT7Yc0QTL2xre57LlADL9Dm/sFAhOC7+V2cLQPD06HJRmdkYaSoGYHTSQbAMv+hTmwmeM7L6C+jVuT5jnAmAVfCVF5uXCvzQKz8TsIlOASZ7tMsisfrLg3QqMAMw+sgQrFN/5Y2bFGU5/lc9gABgbjIIuwKwLfzK2x8uh3+P4wAY91KUCkIW5Sxq9gKA99hjD7HDDjtQ5mQPwC6/hr6vt0A6C3gATmc/P9pbYF5bgAEYJRDuvvtuiu1FaaP99ttPDA62yvqo7b777iNIPuKII8TQUDg+M48ddoFfbF8uvRIA4TQAjIl1EBwFvxgzOCzEZBCOQjaKA2AMAATL6i9PYukGnQiAsQ0HCI5LhjUxvDyw62r5IhVwo0CsJmWMpmVqXjQAfuWWBoSj4Fd3zg/N6utBz6ULtLxO1dYMwraJxnguV/jFOFmxlyE4CQBjvnrbbdoEwTL8or8OgJ/64pdol6D6ylmf8RnDr6z26gBYB787H7efKI2OiMZkN5O0er70CoCx3Sg3aBWA0V8FVxmA8T1DcBQAz9a71+FwJZgcywTAMvyyvRiC8wbgupQVmrcZB7/0Ez09TQmrUK8XCSPTNgAw5kJCrWuvvTbtdH68t4C3gIMFPAA7GMt39RbY1CwAAEZyDcDv7Oys2HHHHemNc7HYzcqp7hMSckApPuywwyjZRy9aGgAmOGI1OIn7MyvAvKMqBNsAMMaaIBjwyy1OBbYFYKKCbubn+qI2eGpccmOPnwMAYy4ZiCaHlwcyN6vQFQfANJ/GFbHaToakrl2FYBWAuX8SEM4CgPOEX5OtTMfXVEZqeEKfVM62/i9vL079VdcFELaN/5XHMvzyZzoIVgEYfWUI3nDJxWJm/UTH5VkF4GYjWGsX420BeLdTDqelJQFgjKssDP/GzqxaY8wILdvmwVd+NhS3blKBVbDt2FOKBTb1AQTbAjDmlSHYBYB5TcMV/csE1wRYpgzQMgDzNvfZzlBuTzI4cmdAqcV9FOFDaRtClFAv9/nPf7644oor0k7nx3sLeAs4WMADsIOxfFdvgU3NAihxdMcdd1B5hWc84xliq622it2Fv/3tb5Qd+uCDD6Y6gb1oaQGY11jYsFa/3Kj4XxWAMYMMwbYAjHE6CLYE4MboYlGsGpLCRKjAHfjF9nsAwBOjWwdsHBfLGwfBOgCeLQ6IQiEMJdgwQ7AJfglGRPcFT0XokxCpJ4oLAKsP1sPVVpmaPAE4ifuz7mKQ93NkvFtOKW8Axlr6ZvSquZoAS163CsD4ToVgHQCjHyC4F/DL642D4L7F4d/Tpi6pneZannlqjfa3TXWDRicVgserA5FJr1gFNgEwnduG6xHfyQowLxIQbOv+LO8Yj1nYH44NnmsA3rhxI91Pd9llF7HTTjulvjUCqHFPfsUrXiG+/32lDGDq2f0E3gLeAlEW8ADszw9vgc3YAlB977rrLnLXGh4ettpTlEVCXWC4ZeHtdC+aCwDL7s+htRXLorDuqfCSXQEYMzAERwEw3J/lFgfA6GtQgZ0BGCLwgmCcLS0lBwieWLBNYDdlWHIFYFqiqjpLKjDgl1vUQ3dDih9UD7gMwPxdFAi7wC+tX3Kh1F0fI1VzLduk11MeAMxrAQjnDcCsGPdPhV9SuQIw1s0QbIJf9Jm86Mu0i7ILMqu/fcOtrPczG8MvnVzVX7ajCYDLYwtF05T1GeeTDoJ113GhKGZWBpOL2ajAAGCyWUTm56iSRBhruhZ18Mv20CXS4u90LtD4ToVmBuGo9bnGACdVgNetW0f30913311sv/32SS/lzrinnnqKlOTTTz9dfOMb30g9n5/AW8BbwN4CHoDtbeV7egtschZAjBEg2KVBNUaWaMQJ2yjGLnOb+mYCwMVuHFoIgk0ArFN/24tsVvpEYWMMyKgATE/dUjywrP7yzmsAGPDLzVYFro0tF4VG1w26M0GGADw1uoKmVbMwx8XyJnWFluHX9NBda3azfBdFI3RK6eC3AyiiKPpFGHiyBmB5UVnBcJ4AzHOPKO7RJjdn7J+rC7TaXwZhEwDr1F/ZtoBgEwDbwC/mUgHYJfkVuz/La2IIBvSqzQTBtiowzSe9PAIM6wAY3VgFZvjFZ2kAeKpWEUOV8L0kCQCb4Bdr1KnGgOA81V9s18YFevXq1RROhDCibbfdNvWtD7k2UILwzDPPFF/84hdTz+cn8BbwFrC3gAdge1v5nt4Cm6QFZmaCSUnidgJlkvCWGy7TWdzk47bnAr/04F3qZg4NzC0BMH9OIJxE/cV2Kq3yJ5EQnASAMakCwfMNgCcXBhXfrAGYjqOiAk8Xh0VBA7Sy8iTDLx9jGYLj4Fc+X2QQzhOAm5I79mhV78Yad42QvTSx0qZxRjXXkOVanZtBOG0CLHl9urkAwUnUX8xbL/aJganVkQBcHugTM+u7L6QateALExv1t3+0X9Rnwy+atj/u2VrzF/uCZZMCNjCowEkBmOe+99h/D61FB8DoZILgyVqfGCiZs6kDgNFUCO4FAGO7AONFA/Zu0VnH/2INUGxRrmivvfbK5OXwH//4R8q18YEPfECce+65Nj8Dvo+3gLdARhbwAJyRIf003gLz1QKuAIy33Ihzwk0e5RnybnkCMAHseISKG6MARwKwDn7ZWKwC6xRg7tOGYBl+8ZWNAgz1l1uWKrAKvvKxzxqCZUgD/JKtNQBMn7fjD3UATDZrj3MBYN63voLbC6I492f1epEBWP7OFYZ7CcC8zuEpfWkwV/UX85nGVGbN5cGiFGAAMFq5Fk6YBPVXhd9Sf5+oTgTVfxMAA3rlZgvApXbSwOa0IZYfdnCBYIMbtHqO3XPsf2jjzwG1uqZCsNxPB8EMvzwXQ3AU/FbrrTj8kb7w9WXr/iyvXVaGZRDulfsz1oKEkigTiJfDuhKCrvfK22+/XRx33HHiE5/4hHj/+9/vOtz39xbwFkhhAQ/AKYznh3oLbAoWgAs0XKFtG+KckOkSbl4777yz7bDE/fIG4GapLIrrg3FzncUaAJjVX+6nVYGjABgDIzJt07wGAKahEcmwZPhF3ywAeHLhtqDMyGOYNQBjY1Ol0dA2TRAclfQq7uSLBONm60F9oGguYyPPnxUAy0C7oBpRg9pR/cVa0yrAvL88z8hkMK7eFYCjXKnrxYoYmG4lEVObDQBjjAzBDL/4nNVfG/jtHx0Q1amwi68OfjG3rAAz+HbslhUA08EMu/mrpct6DcBYFiDYBoDRV4VgVwDWuUUzBPcSgB977DGBMoEID1q8uBu2Evf7Y/oepY9OPvlkcn+GG7Rv3gLeAr2zgAfg3tnab8lbYE4s4ArAyHR58803U3IOJPvIu7kAcFwCLN1aAcBoIQi2UH/l+UIQnBaAEVtb6SZ8krflAsAYlwaCCX659RCCdfDbWYZBCY6C4FqzdZzLhbAbpw0A87bjQDgLADapuSYQdlF/iZkU9/IOmFm6QHf7d7NpyxCcNQB3bC+BsC388lhAcPO/v91ReWX4RR+T+gvw5WYLwDudfKSoT7TccVX47djOAMFOCjAdzHgARjcVgjfOtvarVNSMl1yhdSqxqgKrCnDH5oa5yd5tBVj+XQMIu8b/Yrwpm3SjWRCLBvQeBHm4QD/88MPir3/9qzjggAPEwoXhGG/d/SfqM5Q+evWrXy0uvvhi8cY3vtF1uO/vLeAtkMICHoBTGM8P9RbYFCzgCsBTU1PihhtuoDIPe+65Z+67mAkAa+J/Ow+ibQDm/3dA2BGAMT4AwTEA3BgaFcXpcMyabFATAKOPDoKrC5ZqYTcJAAfAlxeVMwCPl8esSwWpSvBss+WWWiqE4zEZfjsP5goEmwDYpB5FQbALAJvcn01AK3++sNr1WsgTgI1rMUA0QDgrAIb6qzZWg10BuPSjCwOQCwCG8kswprg+637UdPCLfjoFGABcGB4VzYi63q5u0CUois2mqK1SvFUSADDDb1IAxjiGYBP8os90rSRG+qohc+rglzsNVsxxxibQjQJgzKtCsAv8YrxNAiz0Q9Iq/DnwwAPF6GjYe8X1ZvmDH/xAnHHGGeKHP/yhOPXUU12H+/7eAt4CKSzgATiF8fxQb4FNwQLValU0GnoVQLd+ADNcs1DmYe+99859F/MEYFZ/1Z0gCE4AwJiHINgCfnmbURBcH1ogClV9lm4VgAG/tH1N5mdXANbCL02erRs0ppTVyKQAzPDLNlUhWAVg7gc12EX95XEyFA4WuwqTC/zSvksJsORz0AaAuT9A2AWA81B/5bWzK/zoVNAtWnWRD+xvUZ+4TgfAGAcInhxcLPqrUkZ1aUKO/5W3MfvVT1PcL1ptOnhNyQBcGR7QArGL+gv4peMbAcCt78OxwMXFS4SohqGxNaE5VKX21Mrgz5jygkJWgGUAxiCTClxtGBIK5gjAM/WSGBsIxwVH1QyOA2A2DIOwCwDbwi+28cADD4i///3v4pBDDhFDQ0Op740offTud79b/O///q944QtfmHo+P4G3gLeAvQU8ANvbyvf0FtgkLeAKwPV6Xfzyl78U22yzjdh3331z3efZP1zXmb+y9onYbblkgKbnSUX9lTdQnNI/XKvxv7pFNfoHRWlig3G9UH+5mQAY8ItmAmB8J0MwAzCNSQHBRvjlBWcMwQAygK/cCsIuJh0qsAq/PA9DsAl+O/Yv6F/+RNUV1QEnQHguAJjO43YGaFkVNp18vQJg3j6DsAmA4+J/tddXoQtmKgTr4FdWf0v9FTGzvut5ocIvtqdThG0BeOdXnxRYso0KTNArtwQALA8nGNYo9IDg8dlgAi+MSwLAdN7F1LuGAoymqsBRCjAAGE2FYFf1F3PABVrXxvr18fxJ6//yNu6//37x6KOPiuc85zmivz9sZ+MNwfAFYn/POusscf3114sjjzzSdbjv7y3gLZDCAh6AUxjPD/UW2BQs4ArASJh11VVXUZbL/fffP9ddlAFY3pAJhrMC4Ga7NFJp49rQ/tkCMD1YGiBYBmD000EwAzC+j1OBZfil/gkBOBZ+afJsVeCNlXCyGFsAnmn2dzI8605EQHAUAFfbccH9xbDK7grA2P5AwS5RFq/VRQF2VYVNF2avAZjXMTytL/FkAmCT+ktgIwEwz88grAJwFPxiLGAXqi83W/hFf537sy0AFxYuEsLg3UFrSQnBmEJ1lzYBMP1WKfG64zMttby/oqkl3jbW5GxZDEZ8zwCM7jIEmwCY4ZePhQzBWQJwvVEQSwbDscFpAfiee+4Rjz/+uDjiiCNEudytO5/0JnneeecJ/Lnzzjsprtg3bwFvgd5ZwANw72ztt+QtMCcWqNVqAqquS7v66qspyQdinfJsJgDmuqx9ax4PbD5rAKYHQwWC4wAY6q/cVAhW4Zf7yhAswy++j1OBbQCY5lHBWIoftIJfmsQNgDFEhS7AnA58ZbvZQHAcANO2I+rjMgDzdmUQNmaPNczH/YeK0XHdvC0X+I3ajzgwHqsqGZpzSIAlHzej0tu228h0MKN1VgCMNQCCZQAeuOp7oj4xJWbWbRRQftFk9Vf322ULwDbw2znWkis0ga/cTBCcAQDzZhiEb33OOfRRWZOcygTAZFcD5EYBsAy/vA5AsI36K5uHIdgVgE3qL+BXbjIIpwVg1O1duXKlOOqoo0QxLsu/xY3zgx/8oPjyl78s7r33Xqq64Ju3gLdA7yzgAbh3tvZb8haYEwskAeDrrrtODA4OUqxTni0OgHnbAGFX+CWoMLhAswLM88sQPBcAjHWYILg+OKI9BLYq8OSCrd0PoSMEqwC8oaK4fGpWEAfAgF9uXOdXtyOzzYqoaDI/q/DLYwHBSdRfdUwcCPcKgHm/GISzUIBNc0TG+UovDmQIdgXgqG2U60Elv/LTi53gF7ayBeC+4bCL61YvOMZ8LZlcYnsAwLyoX+3xdvqnDoDxuQzBrADjcx0AA3656VRgHQDTXCXzy1ZVAeb5a/WCGBvU50Kwjf/luVQA7lwfA3rvDZcY4N///vdi9erV4uijj3b/TdWMeOc73ym++c1vCpRXQsiRb94C3gK9s4AH4N7Z2m/JW2BOLJAEgG+88UZ6w3344YfnumYdALP6G9pwoSgq6zRxwoYM0FHxvyoA08PhxrUiDn7RT1WAaazkCm1SgNEPKrCq/vJ+6gC4NtJSkwr1cNIcGwBOBL+0QTcVmIHJBnzl42qCYBl+ub8OggG/3FQINgEw+uuAmecxKa4maDaBcK8BGOtHzOZYPVzz2nRNuWaAjlN/1WsW58XIjN412uQCHQXA9fa13l+dFHB9LlYqWgDuG2m5PM+OB5NQRcHv4KLhwPLrs+FsxVoAHmnF8otqOLFTZ0IXCHao2a77cY6CYAZgGX55DhWCZQBGHxWCswZgbEMHwVkBMKu/siLsAr9Y329/+1uBMoFwgc6iIQM0MkGvW7cuk7JKWazJz+EtsKVYwAPwlnKk/X5usRaA+zMg2KXdcsstArHDeSbmsFV/O+uWXDsDIJwRAGM7cWWL0EcHwPgcEBwFvzy/CYDxvQrBUQBM/SNigRPDL00cDcBkBylOc33fMpfTq3tINcmwdPDLA1QIlgEYfWSwjQJgrkU6UAxCS5Q7tQmA6+1Mz6PFjQEb5AnARnBVkgIxDM8lAMMoKgS7xv+yYRmAx37xLVHbMB6AX/SB+7MJfvG9CsD9C4dFfSasPDrDL02eEQBjrhQQbKMCJwFgLIsh2AS/6GNSgE3qL8ZAAeYmQ3BUZmhbF+jOuaNcGwBhVwBGrO709HRmL4ZRAxgZoGdmZkSlEi4JluhH1Q/yFvAWsLKAB2ArM/lO3gKbrgWSAPDtt98uJiYmxDHHRLj8pTRJGgDmTRMIOwKwTv3l+RrlPlEeDyfG6nyvxP+qJihYPLhGZcWVAZjhl7fhqgKnAmBs1FIFTgq/nf1SIHiiMSTKmlq/6C8DsAq/nXOiUBM28Mv9ZQh2VX8ZfuXzgEFYB8Bx8bzq+eTc35AVd2EjGJfL2+mFAizvE4NwEgBm+MV8Iz/6Mk1bm+oqvDL84jtV/cVnDMAA3w4Y2QLwS/9JiMl2/DervuoBM0GwiwKMOS1+R0w/v3EAPFU1J29iFVhVf3lbNgA8XS2KhQNhjxVbAMa2GIJd1V+MNblA6+J/j9zdLakd7osoKXjooYemvPu1hp988sni17/+NSnApZK5JFUmG/OTeAt4CwQs4AHYnxDeApu5BZIAMN50r127Vhx33HG5WScLAMbiKhvCLp/0DGkZ/yvvIAAYzQTBJvWX54gD4NpAK563NGt+8GIItgFgzKWqwPh/aviliePdoNPCL21GAmDAL7c4CDYBcNwJy+qv2g8gnAUAY16oxQtKQUWYzklDgq3MPjcAMM8/1gheK70GYLb5YDVsG7KbJvszj2EA1sEv2VZJ9Kdzf5bBF2N06i99rnN/BgCjGWoa03cJVODmgmDSrMLqlakAGMuIguB1U32iv6wvDRYHwJgbEBylAAOA0VQIjor/NV2zI/16zyVX9ZeOqebaOHTH9aKvr/Wbb9PgGYXszwcddJBN99g+uL8+9NBDlFk6i6RasRv0HbwFvAU6FvAA7E8Gb4HN3AJ4Yw13Zpf2u9/9TjzxxBPihBNOEAULd1iXubmvEwCbMttKQNG3QcmGmwKAsUYdBEcBcKOvBW+lGXOWYFsAVuEX8+oUYPpccYOeGl2R+gGadiTiuK/rX0FdolyGXc4JQLAMv2R/gwqM72pNs1oyW2890PaV9El1TACsK5XE+xDn/qzuq9xfBuHMQNcE0jEAzOtkENatxzUBVtQ5YEzIJQpiqBquox0HwOz6XOzvE7PruuPj4LdvwZCoTYZdlK3dn9vw2xgcEcWZGNXQAMFNqTZ44HyRMrXLn4depgGMLZsJgAG/aCYApu8qdWFSgPH9xExJjAyYE10xAKOvDMFJALhaL4hFQ+F7lysA6+C3/sjPyBajo6Ni8eLFYsmSJWLBggWRIHrTTTdRcsgsShah3CDqCcPT6oEHHsjtPmt5yvhu3gJbnAU8AG9xh9zv8JZmgSQA/Ic//IEyUz7vec/LpN6havP169eLwYfvCh2KqARYuuOme/gGCLsmwMLcrP7K25EhOE79ZQDGeB0EM/zy/FEqcL0/mJCHx8S5QRP8oqVwoQzYWQPBDL+0mYgSRC7X2WQjWFqKx5ogeKo+ICpF/UsdBmDMoUKwCX7Rt9poQfVIOQw4aQCY9wUgPBcAHHeMVPforAA4Cn7lc0MGYRMAy+qvCr/l4UFR3TAeON1k9Rfwi5YGgJe/9pWB+SMhWALgxmi3BrbpBZawBWB5BTEwzACMIXJGaAZgfG6C4PGZkhjs0yvEGOcCwOgPCHZxf+bdBPxyUyE4CwB+2siDlNF5zZo1nRwZcEMGDPMfwK7cbrjhBoLkZz3rWS4/b9q+AOD99ttPjIyMiLvvvtsDcGqL+gm8Bdws4AHYzV6+t7fAJmeBJAD85z//WTz88MNU7qHfVN4joSUeeeQRgfmP3ibsepYFAGNZlQl9HG9c/K9ulxiCXQAY86gQbAvA1cExUWzo4S5KBe7AL+9EFhAsAbDKpgOxAAAgAElEQVQMvp1NZADArPyaMkKrEAz4pWOsAWAZfnmNMgTbADCPYxB2hV+MN43B5wvLYeXTBYxtE2C5HiMG4V4DcGed0rk2WA0CLQB40S+/I+qTrZcTrP7q4Je+H58WDL74vy38oq/O/dkFgBsD+pdXmNsFguPCKTq/VRoY1gGwDL8YmwaAMV6nAsvqr/xbOlAxA7WcAEseIwMwPpchOAsA5vhfgOiGDRsIhAHE+De3oaEhUoYBxAsXLhSojrB06VKx7777Jrz7dYdhu7vvvrvYZZddxK233pp6Pj+Bt4C3gJsFPAC72cv39hbY5CyQBIDvu+8+ik167nOfK4aHzQ90LsZALPI999wjHn30UXHMtuEam5grKwBuFsuib2PQJZrmL5szbeoUYN6/RqkdGzwdhhcCnrb7s2yPOABGX50KDABGc4Hg6eGl4UORIQDr4Jc3GKcwRp0jstuzDQAz/PKcKgTrABh9GYJNAMzqr7pWQLArAEfBrzw/g7AL/NI5nNL9Oe6aXdDUvzxKUgJJty1z3HEw5lyG4AXXfE9U164XUH/RAMCAXzSd+ivDL/rYArAN/PI+qSpwfbQby2uq6Z0LALd/NwurngyYW4VgFYDRWYVgqL/cTCowFGBuKgSbAHi2WhALhsJu0yb4peMqKcCB62bQXNEgiwRYCBcCDDMQz862QikQo4t7KRTbvffeWwCO04QHAYC33XZbcfDBB4urr7467rL033sLeAtkbAEPwBkb1E/nLTDfLIAbLd/EbdeGmKS//OUv4rDDDiOXr7RtamqKaiji7Tq9Qe/XJ8HJEoB5zTIIJwFghl+er6yBYB0Aoz9DsKr+8lwqADP80gOXpQo8NbycpisIRWXJAIDXDWwVe+iTArAa89vah6Z2e6wCqwCMzgzBJvjt2Lpojls0ATDGDpX05W10GaDR3xaAeV0LyoZrwTVhlmX8b9wB5eO5sBms39trAO5cv/XpkPrL8Is+MgBXRoZFta0Sy/uZJwDL4MvbzAKA6XqwvIbl300GYRmAx2f0mZ9dAViGX95XGYKjABj9VQhOAsAYs2Qk7CHjAr9Yi00GaNw7EaMLGF61ahVla+YGzyhWh6EQIzmWS8MLYYz7p3/6J3H55Ze7DM28L5J7ffzjHxe33XYbPSvstdde4q1vfat4/etf77St3/zmN+KKK64Q11xzDcU1Q1Ffvnw5lVN83/vel4ly7rQg39lbIMICHoD96eEtsJlbIAkA/+1vfxP33nsvvZ1etCiYpdTVXHhwQIwT3qzvuuuuYrfddhPVP16vncYFgCOT7yilkRiCTQBso/7KC1Yh2ATAGAMINgEwfS9lhJYBGN/ZQLARgDGB5QO07mDYwC+Pc4XgjfURUSyE3SKjAFgHv7x9QHAcAJOtDRBsAuB6oyRGK5PaczUrAG62wXVhJehd4KwMZwDApm0ChnUA7JpFOjphlj7r+IpffL3j+owD0ZAS+qnwi+9VALaFX4xlBZizRaO0kur+zCcD6nkXa/pEa+jjBMFJ4oCVs1L97bxpyamdHmsnK6JS0r9ckiFYVoAxWFWBowA4Dn55MTIE27o/y7sqj5FB2AWAbeBXvehR/xegiBe4AwMDBHd4sUvHulCgF8UMxEisFacOj4+Pi2222Ua86lWvEt/97nddb6uZ9f/pT38qXvayl5G6fcQRR9D+AWAB++9617vE5z//eatt1Wq1Ti1jzIFM2VDJ8eIbMIw6x9/73vfES1/6Uqv5fCdvgbwt4AE4bwv7+b0F5tgCSQAYcbp/+tOfKNvlsmXLEu0Btgs36vvvv5/ejiNuCm+D0bLOAC0vEO7PplaZ6r7Bl/ukAeAo+MU2jFAvLQAQrMIvvo4DYIZfeghTFWDauP6hN+qAuoAvz+MCwIBfbi4QXG2Y3ddbu2ou2zTb6J4Tg+WwohsFwJhbhWAT/KKvqwKsrptBOAsAdjkuZMOYmO5RsT5w6mQFwKZrBPALt2e4P5NtlWz2AGCovtySqL8Muzr359FTXymK08Gs7gDfzvmbFQCT8TUvhByuXxMAA37R4gBYhV/eRxmCdQCMflCBbQEY/RmC0wIw5mIIzhuAoQSjDvCOO+5IL3LRAMCcSAtlA6Hqkq0rlU4iLUCxrtTSk08+STHAb37zm8XXv/71qJ/k3L7DmnfeeWeBpJQ/+clPxCmnnELbwtoOP/xw8de//lVce+21lAskrgGAMeass84Sz3/+8zvZtAHWH/7wh8W5555LGbcffPBBgmzfvAXm2gIegOf6CPjtewv0wAIzM3o3TtOm//GPf4jf//73lKVyq63i3WDVeXAzRCZp3EgRM4WsmXIssQ6AXdRfel40uYgaALjRLovUPx6uG+wKwNg+q8BxAFyrDIpSbTryKJsAGINMEDw9EFbm00Lw+oHWC4qmaNXytG1x4MTzyPBL+2apAk/WOPGV2Y3ZFoCxXRmCo9yfoQDLjUHYVf3FHCYwNq17QcWhjnAG6m/UNaU7DwDDeQPw1tdd0oHf0mB/KN5XNIIveGwBuDwQfpkSB8Ay+Mr2MKnATgowGV+fKCqJGzSvDypwHACjL1TgOAA2wS9vq2xQmBH/q2tD/ebEWKb43yiX6bEhfWywrgRSEgUY4Tt33nknJa3aaaedQrsE0ANIMhBD4eWGe6CcTAvxxABB3F/f+c53ivPPP9/2pzbTfp/5zGfINflFL3qRuOyyywJzQxkGEJ900knk1pym4WU43KrhVXbJJZc4u1an2bYf6y1gsoAHYH9ueAtsARZwBeCVK1eKu+66SzzjGc+gRB0uDTd+uD3hjTngeZ999gnFR80lANMDnwLBJgBW439VOwCCbQAY46IguNo/KkoGNUkHwFODi7XxgWkAmOG3BUJuAGwDTxtqcAsMK9JxEMzwi21UIuJ4p2oVMVDSPwTLCjAfQ4ZgFwDGWECwKwC7wq/80L6oT6p3m3MCLNsXGWxD9FdVYToXLOp2y9eS7uWXrP7awC/mi3J/7ii9M4b60LPhcwcKMO1P0Vx3er64QetseMXgqwM/WSYV2AScnWulr0Hlj6KaDoBN8It5ZqoFsWhE/0LLFYAZjJeOamKDNS+HkgAwXIJxT4Rqu/3228feEnHP5WRa+BshQGjf+ta36HMA4de+9jXxoQ99SHzsYx+LnS+PDojNRWbrSy+9VLzmNa8JbAKxwMh8jQalGG7fadqpp54qfvzjH4tPfOIT4v3vf3+aqfxYb4FMLOABOBMz+km8Bea3BXAzw1tY24a32HfccQfdpHfYYQfbYeKJJ54g5Rdvw/fYYw9yF1NjodY8dE9gvpHxJ1oPmZqas/SF68N0jAIsbxwgnET9xRz1SluVnAmWbJHnh/orNxMERwEwxqsQbAJgMpdjMiwZfHmtWQMw4JfWZgnArf1ona8yAOP/JggGAKOpEKyDX95PQHCc+7Pu5K81i2JBXzg2OK37M29Lp1oBhPPOAO0CwLq+pAq7Xq+a616FX9hFjvctDw2K2njQ/ib1l8G3Y1sHAB58zZs6hz/qBZYJgqsD+gSCxabBk0FRgSvrV1onwtL9htoC8MapkhiIqP0LN+goAJ6eLYiRwbCiGwfAWLMOgpMCMB8sBmHddYQ+SQAY90Tksthzzz0pdtel4d67ceNGUofPPPNM8atf/YrukWgIMXrlK18pTjzxREoWhbjZXjXk9wDYI9wJ93q1HXjggaR6/+53vxPPfOYzUy3r2c9+tkCSrG9+85vitNNOSzWXH+wtkIUFPABnYUU/h7fAPLeAKwDjpoiMkIBYxAjFNdzMEeuL5FmId4JrFzJc6poKwNwHD84j44+Hh2geqF0SYPGE7AKtbqBiKG2EflEKMAMw+lUMEGwDwIBfbjYqMOCXm8490kUF1sFv53g4qsCmY8Lw21mzJQQDgFX45TlUCGb45e9lCI4C4HIxqqSKXvEC/HJTIThPAMY2YWNZEe4cqwxcoF3gl9eiu775xcVwIfhiyLb8EeaE6zNdf9Pd0AEGYMAvWhwA9y0YEfWpcOhBXQPAOvdnGX6xPRsAnh0KhiUUGnrQtQVg1b5964KljtTv1ZeIKgDTb5XGVTkOgMenimJowPwCFQCMpkKwDQBjnAzBUWq0yQVa9zkgOCv3Z6wRXlF//OMfCRSThAXJx+qpp54Sn/vc58R//ud/irGxsU52aWSWRiKqd7zjHeKFL3yh7vLK7DO4dLPCC9dtXbWHF7/4xeQa/T//8z+UrTppu+mmm6ikIp4N8Iyw9dZbJ53Kj/MWyMwCHoAzM6WfyFtg/lrAFYDhxoybFpJ9wOUrqsHVC2/G4daFmzngN8pdKgqAeTsdEHZVkxzUX94Wstv2Txlqn7br/+r2XwZgerDUQLAKwLoHaRmAW9/rXTShAsvwi75pADgKfjF3FiqwCr+0ZksA3jg7KMpFfZxgVgA8U29B7nAlHCOvxv/yOSADMH/GINwLAOZtBlyjNQCcFdCarn3T/LpM3oBhWwBOAr9YIyvAAF80HfzS5wkBWHftzrZrduO7Yj3sfkvnuwsEG+KAdcdAB8NJ3KABv9xMKjAAGM0EwQzA6CNDsAmA4f6sNoZgV/UX85jAGE5Pi0eDL7mSqL/YxuOPP0517BEWlDQxpLzPKH302te+Vlx88cVUbeHKK68Uv/jFL8QNN9wgLrzwwtxVUuT54PAmuGfryjjBLRoZqpG9GSp1kgbQhvqLsor//u//Lj75yU8mmcaP8RbI3AIegDM3qZ/QW2D+WQA3OHa5slkdslviRoxkH3D5MjUoxXCPQokIuEqjLxJ8RDUbAJbHj0yEVY+kCbB06+LyLioE26q/8pwyBOvgl/uymqTCL753AWB6wNa4tse5QcfBL+ZNC8Dray33TxWIsgBgzMsQrKq/bGOowFHqL/oxAOPfMgSb4JcetiUFOHCeVvSJzkxQTDY2KLc65SrK/VmrCsdkdFavhayA2VTKirc3VOhmVVaBbds7/ks02smDVPWXlV86Bgb3Z4Zf9LFVf6mvJv5XVYB5/eqLL/681wAsh4b0rW15ztgAMF07kgqcFoBl+MXcDMC26q98HgKCswZgnp9BOCkAP/bYY+K+++6L9G6KvPEpXwIq/+Vf/oXiYuXSQJOTLdd+G1dojIMq7dK+853vUIki7M92221HQ00A/OpXv5rgNykAIys2Emz97Gc/o23C9VuXEdtl/b6vt0BWFvAAnJUl/TzeAvPYAq4ADMUY5Q+Q7GPvvfcO7RlimlAqCW/EEeOLPrbJsnQAbIobDACGBMJZAbCutimDcBIApofLthKcFIAxhw6CpwbGhM510gqA6em45cJoA79s96QQzPCLeXRAFAfBUH+5mVRgsnWxLkwAjO+L5spIAfjlbTEEJwHgWqP14mesPxibmiYBlnz+28T/2iTMMv1MZQHAcfCrblvtv/MNX6UuLvBL51g57K5uC8C28FvtbynLxYbZbd4FgpO6QXdsqPGOAQi7uEHL8Mvzqiowq7/8vaoCqwCMfoDgJADMY3XnqIv7s/RzF5rqxfuHs6ubrgn584cffpjKAqE0ILsO24wz9bnooovEe97zHvHzn/+cygYlaRxX6zL2uuuuE0cddZTohQv06aefTjG/CKWCR5kvf+RypHzfvC3gAThvC/v5vQXmgQVcARhq8VVXXUWxOmryC7zV/fOf/0xvkAcHB6nEkS5+yLTbSQGY54MinCcAYzuA4KQATA/kBrdH2SaNkrmurQrAgF96+DYkz7GB4PX97vWckwDwulorcyi3PAGYoTPqEjNBsKz+yuMBwS7uzzxWXosMwb0EYF5LVMIsk61cANjF/Tnq2Mjnxq53/0A01q0Vhb4+Ud8gZb6uBeNoZfW3zO7Ok1OBzaR1f66c9nZRrk4Jhl51H0wQ7ALAxuvZwQ1alyAQx6ZvXTeXgi4OGNuGCpwEgDFWhmAdAKNPX9kcM6xzgcaY2bYX+eIF4dCHLAA4Kfxibahpjz9QMlHWKG37whe+QPVxkYUZ8bFz0RCyhPjfPJJgvfe97xWf/exn6SX6zTffbJU5ey5s4Le55VrAA/CWe+z9nm9BFkBdXoCrbYPCCwBGrNP+++/fGQb3LLg84+0x3ubuu+++Ti5Nru7Pxof1QkGMjGtcox1jgHUKMLbZKFZE//Q67eZNLpDcuV7qo4fnuFatDItSQx/vi7EyBDMAmx6a4wA4Cfzy+l0geG11TBvj6wLBsvrLazCpwJPVPtFnKH2EsdPtzNBDlXB8pgmAMc5UTsnk/owxOhgHCM8FAGM9poRZuvPSBX55bt08SRXgXX9zKbk+q/BbHBwU9Y3BZFoMwCb4xbps1V/qq3F/Fm9+H+1e2XB9zncA5mMDEJ4d21pcOXNM6HCZAJjOfykjtKoA43sGYBP8dravgWAT/GIMAzD+rULwXAMw1F+owIcccoiVe3Lc7/+5554rPvWpT1FpJbxEnosWVQYJL83xYhvPAgh1cimDdN5554kPfOADYvny5QT4UIB98xaYbxbwADzfjohfj7dADhZwBWAs4eqrryZXL5RCQFu1ahUlu8KNEcmxdtttt1CJo7ilZwHAqosfg3DTEX6x1igAxvc6CI4CYMAvtygIBvyi2QCwDL8YY6sCcxxwGvjF9mwBGPDLTXVxtgXgiWq/9hTSATDgFy0JAEfB72ytJBb0h5NiYVsmAI5Sohf06WODXeJ/W8dB78+tm0fXVxcnzMaeCwBW1d/mZCs2mNVfG/il/or6S5+lyP7M8It5TABM16HBFdpFBc7DDVp3LHUAvHZjUQzqL7cOAOvgl88ZQHAUAPMhWDgSVIJtARjbYQg2wS9dk3XTdRH+KUmjAKPKwaOPPiqe85znCGRrTtsAiBdccAFVT4hLNJl2W6bxn/70pykxFeJ0ke1Zbj/96U/FKaecIl7wghdQDK9t+/rXvy7e8pa3UEJMuFsjKaZv3gLz0QIegOfjUfFr8hbI2AJJABg3L7z1xRvvBx98kLI4IlMkVF+82U3S8gBgXsfw5Grtkkzlj0zwi0mgAHNTIdgWgOkB2qAEMwCjTxQEz5b1NSFtY4E39C9JcpgCY2wAWIZfDNbF+NpA8IaZQVEyZH5WIZgBGNszQTArwOgjq8C9AuB6Oy4Y21800I0NNsEv+rkmwNId4CigzSthVmL1V3J9pv3fsEEAfunfivorNAn28gRguoYjvDQAwVN9wVq/xRgX5qHJVZ1DNl8BGAuEChwFwOgTle8wCwBmQy0Y1rtTR4Gxrux9GgBGvgtkgkaZIl3GZNcfWtQDvuSSSwSyMc9VWSBUbkCZQ3h0/eQnPyHgRUPJJ4A+VG+8CD/22GMDu8eJMa+55ppA7o//+q//Ei9/+ctJIYcH2aGHHupqFt/fW6BnFvAA3DNT+w15C8ydBeD+DAh2acjYiDY8PEw3RMQ9wVUL/0/a0sb/Yru6TKf0uSiIEenhkteYFoAxD0OwjfuzahsVgmX45b4mCE4DwBsHFhuzDLsevygIVuEXcycBYMAvmg0Ay/DL+6JCsAy/3IchOA6A0V9VgV3dnzGHDMD4P0NwnuovXws2x5hh2EUBzjL+d9cHfi7E+AYhq78Mv2Q/CYBLI8MhtTcN/GL+ykj4t2z6JW8JmG62PBjhdaEv0xUHwfIGChIwD08+1foqgzhgeRtXTBwbiMmF+svNpAJvmGiKoYGILHKWAIztyCpwXPyv7ryt1ppiSTC1AHVzUX/RPw0AI9sy7oNHH320s+eTbp/e9KY3iR/96EcEn6Oj3VrwNtdtln0Avqeeeiq5OsMlGqFNgF64PQPSv/jFL4Y2h8SXaIiJRqUINNgG8b5IoIlSUXLolDzBySefLPDHN2+BubaAB+C5PgJ++94CPbBAUgBGzC9ujHhDjUzPad985w3AbEoZhF0BWFZ/1UPTKLayzfZVu6VcuI/s/qyOkyHYFoBnKq1EK/IDsjxvlAoM+OUWpTbanno6ANaBrzyfixs0wy+Pj4PgpACM+U1z87bhAi03BuEsAJjnHevXx4jr1F+McXF/juofdbzH+uyy42YBwKwWI/EVwy+tu9qN1Y6DX/SPA+DKWEudnX6ypbr2Lw5SVEMT/7vh5e/UmskcehCG4KQA3LlmpQzPnZro/5+99wCzrCjz/6tzmk4zIBkkKsiiqyQluiDIgglEHxUDrrv+F1wMa9ZV2NV1AdFVV2VXfypi4lHMgSEoOS+sBMlxUDIzw8z0dO7/86nbb9+6deucUyfde3u66nn6gbm3Tp067wn3fOr7hqiT58gGbZ+jMgB4w8aKKjs44IZk2wsdCE7j/mweLgBMsyE4DQDngV/2TfjP6tWrdQblIhp1dX/3u9+piYmJ3L+reedDkqrPfOYz6tprr9UAu/vuu6uTTz45shaxC4AffPBBrSYntU9/+tPq1FNPTeoWvg8WKN0CAYBLN3HYQbBA8y2QFoBx9eIHn4a70w477JB71bsI92f9kjy/+mxb1fViDgiXAcDs24bgOACmv84qOx/767oiTBVY4Ff6uSA4CoBN+NX2iqg1m+aqtAE4CX4ZO40K7AvAjDs50xk5dVMFdinAsmEUBNvwK/2B4Czxv7YCLOPNzFagYUVfbcmkZgKwadQ4GC4KgIFf1dml5p6tJJsz4Zd/CwCj/Op/u2J9I+J/BXzlmOyx+dwFv52nnKGeeqKSXM91f7nvuXwqcNQCl6s0nBOGPQCY45E4YFP9Ffu4VGAUYFqUCiwATB8bgh0h2Hqs3pjQWTMBlnktCvzKZyYENxKASVa1fv167QJdRHv1q1+tE2AB1e1xvuRF7CyMESwQLFBngQDA4aIIFlgCFqCsEcmrkhr9SMrBaq6s8h555JFJm3l9XwQAp4Ff/VI9/3I4MP5MzRx943/NjUT9NT8zITgvADOuQLAPALte0tf3jNadiyIAWNtSVdwmfeBXJuGjAq+b7HVeP5GQGgPADAQEx8EvfcanOtRAT/39EAXAbNPf7b5/ohJgRcEvYwkA8/8mBLcKANsnxARiFwBnif811d+23j41u65a+kjv3writAHYBcTtPdUkdOYxpAFgc7vHnqg+N7rnKsnMfCG4SBXYdYMswLAnAIsK7APAAr/6uo9wg84CwIwXBcG+ACy2AIQbCcA33nijVmuJjc3b8Kp6xSteobNKU04wAHBei4btgwXSWyAAcHqbhS2CBRadBXwAmB93ShyxIk0Gx66uLvXkk08qAFhgOM+BNxOAmbcJwUUBsAauqQ0qCX6nOiqQ1zkTXfaI7wFgG37F5kkqsAt+ZdsiIPiZqapbte91kKQCrx6vJPlyZXl2AfD6ifnMz51u1U2fD08A1teEBcFRADw1U4H/4b767NBpAdiEX9OOgHAaAI46p2nieX3Po9kP2B3qrg0BSAvAu/zxhwvqbxb4ZT4mAHcOV2IoZ8frz48LfnVfh/szCrCrmSBs2rdvtlKiyX1vRl+j9j5c27sUYNfcNAh7QDAAvGGj213ZVoBNAGafNgSb8CtzMlXgKAWYvhOTc2p4sHYeUfBLf1sBlv2R0mLFSGMyQLPP6667TocDkRQyb2Ocl73sZWp8fFwnlyzi9zXvnML2wQJLzQIBgJfaGQ/HuyQtkATAJLy4+eab9Qr39ttvr92eb7/9dr06ffjhhxcSo9RsAJYTDwgnlT9yXSQuBVj6dczGq+sCwPSPg+DJzl4VpRzFxQLHwS/7zAvAWeBXg0FbffZWgSWBX22TiMzPNgT7APD6iU7V3x1d8xr1d+FaMAA4Tv0VAGY7G4KLAmCBX9stuhHxv74PxSjQbW+rwN5gV61Lt2tcG37pY6q/7QMDuiaw2aLcnwV8pW8eAI6CXxn7occ3qJ62CmDHLTL0z1SVbF8VOA8A6/nMh4UMrn9swWyuOOA165Tq6kyG4CwArM//fDxwEgDr+8iA4KwAzDg2BLuyP9Mvbwzw1VdfrX8H9913X9/bJbIfAPzCF75QlxnkdzcAcG6ThgGCBVJbIABwapOFDYIFFp8F+MEluYXd+HzVqlWKEg/8CO+5555q66231t3+9Kc/aRctkn5QDilva1QCLHOeUSoKL4f9E5XYQ7P5JMBy2WGmvVN1T7sTG5nwK9tGQTAATEsDwWNWGZao85QVgrPCr8wjyg3aBGD6JqnAAr8ybneECgwA06Ig2ARg+okK7AvAbGNCcNEALMcnILyYANi89jocix98v9dd51a6TVbVWgFgF/zS1Qbgtq76OHAX/LJtVvfnqPtIQNhHaafP4PTqxEdnmjhg12B2aAgg7JrfuY8dlgjANvzK/kwV2KUALzzbOqIzR6P+mk0gOK37M2PYRQ0EhIsufyTzpSoC5X1e8pKXJJ7PpA787u6yyy76D7AOLVggWKDxFggA3Hibhz0GCzTcAi4AJjEWKi91CPv6+nSJo6Ghak3Lu+66S5c5OOigg3KVPpKDbTQAx7kQysuhDcFRAByn/gK/0lwQ7AJg+tsQLPDLd74A7Au/GgRSJsNaPT2aehvXhe1SgdeMV0oemS1JBU4LwIztgmAbgOkHBKcBYJm3K45YvktKgGUfv8v9GQhudQAW9dc+HhcA73X7t2pcn9nGhF/97xj1t2Owkhl9drwSj2u2POqvvh8j3J9d1zQQTOtuiw9p0PedqgXCKCDOowK7ciNo+DYUYeYCANPiVOAoANb3U2+bioNfbccUAEx/ILgIAGYsILgsAL7sssu0YvuiF73IdUmk+ozfYxaacYOmXm5owQLBAo23QADgxts87DFYoOEWsAGY8kbE+1KDcPPNN1d77bWXjvk123333afjk/iRNsE47+RNEPaNc9MvkimyP1f6V2tdmnN2AYWAcF4Alv0ICEfBr/QzIdgEYL5PguA08KvtkQKAgd+028RdFyYEP72xX0Wpg1EqsA2/C3a2VGBRf+V7G4Bd8Ct9uzrcMZum+7N9jJMzbWq0vx6CfBNgmeNFxv/OKbWiv967oBkxwE8eDpcAACAASURBVC4XaF8A3mvVz5Qam3dtttRflF9pUQAs8Eu/ZgMwcwCCZ+cqz5je9nogl+NJUooFiIsGYH3/zsO3gHArAjCq8MiQ+1kdF/8b9byZnVNqMys2OK/7M7+ff/jDH/RvJTVu87bp6Wm1fPlyXQ/3Zz/7Wd7hwvbBAsECGSwQADiD0cImwQKLzQImAJPY6pZbbtFZoXHB2nnnnZ0xSGSCvvPOO9V+++2nRkfrswsXZYOnH7zLa6gyAVi/LLa1q75Jdy3UKAXYVH/tgwCCkwCYbYBgG35lLBcE86KcFn4XXsYTIFjA1zyWNOAcdSIFgIFfaS4IjlKBN07FlD4yINgGYPZlQnAUAEfBL9snATB9bAguQv2tnrOqVQWEWwV+mZk3ADtcn/WRzVbjtW341d931NZl1pvkUIDTJL9KejCZEExfFwgnAfDCeVZtaniqUq944bOIRTzXvKJUYLPvz+99wcI/XSrw2nWzqr8v2oVZPyfrw/oXxhzbOKeGlrlhlk62C7T5mQuC0wIw8Gs2AeG8AIy3FArwFltsoV7wgqoNk66PqO9ZeN52223VCSecoM49dz4kIOtgYbtggWCBTBYIAJzJbGGjYIHFZwEyTt5///1a1SWZB0k4WNGOasQG4yJNzFNcvyItEQfDjQBgjsWGYF/3Z5cd2uLeFolja+9yllWRsVwAvLGr4gaapcXBrAt+Ky+88S/EPvMAgE34ZRtfAF6zsVv1xGV9nv/OBb8yN4HgMhRg2YcJwUUBcNTls7zPrTj6wpbPObP7JCXAMvvb53ZB/e3pVWrd2mpXA375sA6Ac8CvvnYdpd+KBGA5kAceqyr0eSGYMU0Q9vWS8QFgxhYIzgLA69bPqmUD0YALANNcEOyCX/qan9sQnBeAGf/v/6Y2oVqWa5/8GVdeeaV2WyZBZN722GOPqd122029+93vVmeffXbe4cL2wQLBAhksEAA4g9HCJsECi80CqL3UMXziiSfU4OCgjvcloUdce/TRR9Uf//hHHfO05ZZbNvSQXSDcKACWAxUQzgrAM20V1bIzIkM08CvNVVu0+l3VNTcP/Mp4NtBGgW9U/ywXwlNj/aq9vV468oFgAJiWBMFJABwHv4w/PtWmBnvrs0dHKcC4P9tNILhsADbPoeke3bIAjPprw29fv1Ibaj0uBIDbl83H+m6sd/3Oo/5yvsoAYMY1IXhGtauB9mpGbN/z4uo3NF1bwzzq/ssLwKi/0qJUYACYFgXBAsD0sSHYB4DZTiA4Cn7pYyfAknnbCjCfFwHAGzduVNdcc43abrvt1K677prlEVizzb333qte/OIXqw984APqrLPOyj1eGCBYIFggvQUCAKe3WdgiWGDRWYDyRpdeeqmOO8KFq8OhrNgHBSzfdNNNOuZpm222adoxCwynAeA08b8cmE/CrN7p2tqnce7PAr9iNBcEmwBMvyQILgJ+9bEaiu7ameGFOMa4E5xXBc4KwAK/zC0PAGv7JgjZADDNhGAf92eX3YZ6p53mjKoBHBf/6xrIdT4AYV/QynIzZ43//atHf63anl1dC8Ae8MscZ0sA4A4j3ljsMPOWj6n29mhl08dedz86pbraKucdAJYmIOxzblx9zM+Gp5+OnEpaAGYgUwVOA8Bs64LgtAAcBcVAcFr1V18vDvfsIgB4w4YNug7wc5/7XLXTTjv5XA6xfci/cfDBB6tPfepT6rTTTss9XhggWCBYIL0FAgCnt1nYIlhgUVpg3bp1OtGVb83Bp59+Wt1www1qjz320LWBm90o1bR5f208YGSG3BQJsDiuNMAsIJwGgNmHCcE2/IptoyAYV+giARjwNZsk84k6x3kAGPil+SrA2lbzdYFNAObzKAh+drxT9Xa5k1jJMW2cbFcDPe4+Ar/SVyA4CwBPzyvDywfqa0OXCcACAJsNRCdkynoPZ3V/roFfdo77M/BLc6i/ovzKPG0A9lV/9T097/7cOVK91uem6hcmJt74oQWz8GwEhOW/ae112yNzaqCzYn8Tgvl3f7u7TJq5jyQAlr5RIOwDwVFxwCYA6/lascCi/socbAA24Vf6mCpwXPyvy84D/e4Vqyj1V65/e6wiAJiYXTyogF8gOG+76qqr1FFHHaVOP/109eEPfzjvcGH7YIFggQwWCACcwWhhk2CBxWgB3KBnZ+MhwTyutWvXarcvYpWKWPXOa7O7775bxzBTlmnjU3/WwzUDgOU4umardUztY7MVYPkeCI6CX+njguCJznh39TS2XTs9XGe3sgBY4Hfh2FK4QdvwyxhZARj4pfkCMH2B4DwAzBgmBKeFX319OxStqMUIl/pVFAznAuCJefAz4ZeDswDYvobzqL+doyNqzlX33AHAU2/6iCJJIH9mA4IFhNOowwLBNgDPzFYW7wY742NSfSFYroORmWrirLQAzHxQgW34FTuYEGwDMH1MCHYBMH2AYF/3Z9P+k1OzanS4PgFaGvdnxisCgFevXq1uvvlm7f6MG3TedtFFF6njjjtOffWrX1UnnXRS3uHC9sECwQIZLBAAOIPRwibBAovRAmkBeP369TrxB1mii4h7ymszV1kmVO3xZx6rGzqNoqtBI6Ni3D1Tr+pEwW+a4zchuCj4BXyl2S/ZSQBcgbF0ybBs+GUMXxUYBdgFwIxhQzDqr7QoFVgAmH4uCLYV4Op47pS3rvhf2UYUYPN8A8JpATgqAVYaADbnkAeGswCwVn8FfpnItKGIm/DbN6DUxtrwArqnBWCgd+H6dsCvvoYdANz+jk/phUEy/fJfG4b5twnDPuowEEzr7awtkSUQzHdRIJwWgOWYAWEfAKa/rQKXCcD6nu12PzuiwBj4lWZDcBoALgJ+mcdTTz2lKyeQAItEWHkbpY/e/va3q3POOUe97W1vyztc2D5YIFgggwUCAGcwWtgkWGAxWiAtAJP4g9IPuHwVkfkyr83sskyPP/64finhpZX59avqy6YLaNOqxfqFeb6Opj13e3wThOMAeLatqmjEx/xWkjGVAb8LkGAdWxIEpwFgF/zKfn0gePVYl+rqcMNnHABr6HC4QpsATB8TgqPgd2KqohoP99cnxkoLwHqcvoi44IiFhaIB2LyGiYde3u/vKp0m/nd8ukvt/9RP1Vxnt2rfMJ/x2YRfJiIADPzSMgJw5/CImjVqCi9c2ykB2LSNQLAJxPb976MOA8FTsx1qsLu6SGYCsIxpg3BWAJbn1cisVUrJ8QwzAXj12hnV0x0d/4wK7FJ/Zf6owFHqr/QZH59Rw0O1pcyi4JdtTADm3yYENwOAyYdx22236fwZlELK2773ve9p5ff8889Xxx57bN7hwvbBAsECGSwQADiD0cImwQKL0QJpAZjSD7///e91vcI999yz6Yf88MMPqz/96U+6LNOaNWsUinB3d7fOUk1yL7M98fB9dfP1hdmFl2hP+DV31BGR8Vn6mADMZy4InuroKczWz84MLYxlA2xaFdgXgOPgVx9zghs08CstCYJN9Ve2sQHYhl/pJxCcBMD0tyE4CoBd6q/sb3qeo1csqwXhIhJgsQ+XC3TUhRSVECwKin0BGPilAcCi/s5196i2McvtFwAW+GUDC4CT1F/AVx+zA3753Nf9GfU3qcWpw7KtxA3b6rAPBMvC03DXs9V71Xr2OKE4auFkflsThO3tiwTgyj0d7R0C/Op7KAcAsz0Q3Iz4X/ZNRQRyUOy1115qs802S7pkEr//7//+b/WhD31IXXDBBerII49M7B86BAsECxRvgQDAxds0jBgs0JIWmJ6e1m5+vo0XvwsvvFBttdVWumZws9uf//xndeutt6rh4WFFfPLQ0JAu59TX1xc7NYHhRgCw7KNzttb1Ub+sG+qvOWETgouC3w0zy+qS8CQBsJ7jXHwm3CQIToLfystyfDmkvADMPkwIbgUAFviV825CcCsBMPWa7eYqVUWfTodC39U+U6P+Ar+0GgBOgF99HRrZn9uH5l2bJ+oV66LV36RnnK86LEB848M9qr9zskYJtlVg+54DhPOqwOZxAMJJAEz/OBV4ZsbtjSH78QFg+poQnEYBlv1MTc6q5aPVBTL5PGrxpygX6EceeUSRg8K12Jp0zbi+/8IXvqBOPfVUHWJ0wAEHZBkibBMsECyQ0wIBgHMaMGweLLBYLJAWgDmulStXqs0331zXLGx2Exdo5gGUo0r7lHOSeT/+8P3OQ8ga/2sPZr9kmhAcBb8LL5BzM6pI+GVcOwkPnyVBcFYAfmJs3pUVwFXxL8vMIwqCTfilX5QCrF/YO2eVSwHmOx8Aph8qsI8CrF/e512hs7g/2wDMeALBaQA4a/yvfa1GCXa+AOyCX/bxsvGVqn1yfMH12an+2on4YtyfF+CXwVsAgG07+qjDdz/RpQFYGkBcN4618MQ1MdpdVYT1vevwSHFdD1HwbLtGowLj/iwtCoCfXTetBqzs++b8N4xVxhhcVuviLH1EAZZ/CwT7xP/adgKAaTYEl1X+SPb/0EMPaY8jvI9YgM3b/u3f/k2deeaZinJIrbC4nPd4wvbBAovRAgGAF+NZC3MOFshggSwAfPHFF+sf/H322SfDHovb5Mknn9QvCyjYW265pX5p8C3n5JqFwHBR8Bv1gsrngHASANMvrqySjyU3zvbXKbg2BJcBwCb8Ms8iAZjxoiB4YjperQaCo9RfsWeHQ43mO4n/te0OBBcFwIw9O9umlg/WxwaXGf+rz5HDY9UFv/R1KcBR6u9+a36tTUbsb53629PnjPV1uT/XgK8+Ie545TwKsI/7s899J32AYfPPzCqdBMH2wpO5KCIgnBeAzWMBhm0A5nsXBAPAtCgIFgCmjwuCbQCmHxCcB4DlWASEywbgBx54QPG37777qmXLlqW5LJx9P/rRj6qvfe1r6t5779VJJkMLFggWaLwFAgA33uZhj8ECTbEA8AgEp2mXXnqp6unpUS996UvTbFZYX14iefHA/Qy1l2PYfffd1Q477FDYPh5b9WDdWEW5S5sDRyW9KgJ8F17CbSVJ1UNikRBsw6+GHw8FWPez4POZ9V1ut9qIZFhrxzpUb3e82hwFkmKvtADMdn0RtYT5LioG2KUA0x8AXniZN0C4TABOo/4yN18APuiZHy8kvnLCL4PZaq/972VDSk04yot5qr/sosj436wPGXGVFiDmOXbbo9XYfhThYSM5lsvzwvYMAITt51IaBdg+lp/dUB/LWjQAu+BX5tHbW1/iiO/sBFjSX9Rf+ziA4LIBGFAlBwW/g0khNz7XzCmnnKK+853vqMcee6yQpFo++wx9ggWCBWotEAA4XBHBAkvEAlkA+IorrtBK64EHHthwKwHrZN7kJYFV91122UWrwM973vPUjjvuWMp8BIbLAGCZsAnCRcKvLwQXBcAu+F04Rg8INgEY+KVFudbaKjDwS8sLwBsn2tSyvvra2FEKMPucmFJqZFn9Nj4JsOyL1gRgvhM1uFUAOE3874HP/kIfXttUVa3Vsb8ov9LiABj41QbODsAu+GXIqPJHpTxEHIMCwtc90KmIkZaWBMEu13hAeXnPfGbt+YGyQrALgBnShGBRf2XOLhXYVIDpZ6rAcQC8ceOMGh3trrNWWgAW+LXdoouK/2WCd911lyIHBb+DJF7M2975zneqn/zkJ2rDhg2qv7+4Gu955xW2DxZYShYIALyUznY41iVtgSwAfPXVVyuyRx9yyCENtd3Y2Ji6+eabFXV+KTvxV3/1V4qyTFdddZUGYf7Kbo+ueqhmF2ndpZPm56rZGbfN1Fy36mqrxA9OzPYudJ21VN46d0rr+7wA/PiGZBdAHxXYBcAclNO91lKBBYDpHwXB6zdW1NWBXrdKDPxKsyE4CoCBX7OZIJxW/WUcG4Bl7FErU7R8XkQMcBoF2Ff9dcEvc24zk+45Yn21IizgKwe5CQKwHNo197UvQLAZF4waHOcGLdtLHxOCmwnANvzKPAWCkwCY/iYER8Ev/aIUYFP9FQjevfsCtWLFCv1HhYDOTnd8ctIzWr6n+gALsQcffHDusRjzjW98o7rooov0b1reufkeQ+gXLBAsUGuBAMDhiggWWCIWQIUAZtO06667Tq1fv14ddthhaTbL1ffpp5/WSi9z3XXXXdVOO+2kVWig+PLLL9fqLypwIxswXCQAp4FfwNdsLnfJRkDwkxuqia5mI0pEyTx9AJi+QLCov7Jtkgpswq9s44JgAWD6uCA4CoCT1F/7uhMITgvAUfA7Y4jLmw1VQxaKgF9t84Ljf186ebHqGN+gZrt6VMdYVZ2sgV92bANwh8MFNgf8sguXAtwxNKSmn36m5rT9ae9jdXI/4Kirqz6rcJnPFoFgE4DZ32BXvfJtq8D2vQ8IZwVg9pmkAtsKsL6XjIRYUQCsj2dZp/IBYPoKBOcFYDlvh257uVZXafx2kMeCcw0Q402UNn8EnkjUAn75y1+eelvXtXTMMceoP/7xj+qZZ55RZAwPLVggWKDxFggA3Hibhz0GCzTFAlkA+H//938VQHrEEUeUPmfi5Mi2ibsZ8b7UXHzOc56zsN+JiQn1hz/8QW2//fZqjz32KH0+cTv4yyOrFr6OcpeO294HgGfnKoAwo+pBwX4RLhuATfhlTkkArEHLww16zVi9MtMMAGa+ogKnBWC2BYLLAGC5hgDhVgVg1F8bfud6+lX72LraW8AE4IFBpcbH6m+RkgDY3tHK3soCGiA0MjKia7vyNzAwUAjgRN37jz/+uLp//Vb6a9yhkyA4yg3aHJ8+m9lu0a6M0Y7P4gDYBb+yX4HgOADu6oyuDYz7s92A4LTuz/pZ5HDw+MhxE1pdBTD5/eK//P7RyGkhMOyrDgOrq1evVoceemju3x1+51hQ/stf/qJWrVoVADi3RcMAwQLZLBAAOJvdwlbBAovOAlkAGCUW168jjzyy1BdD3LNvv/12/VLASyj1fe1sm8QEk5V6m2220S7RzWyAeG9v70JysD8/8oj3dJLgV8C35iW3wRD8zMYBNdK7UT29sRqfZiuWSRCcFYA57igIHpuIVktMFdhUfxde2g1XaFP9Ne0MBGcBYBwrRofcrtY+CbBqznV9eLH+mrjgzYbqwSGqBqrrgszr/myfm/1nLlOdG9bUALAX/DJQwQDc3l/1UKg59tl6m204/O/UU089pf9MOCLBkcDw6OhoqjJrSQ8AYkhxpSWGdG6Lwysw1lU7t5nZyvU90rNR/9cHgM1+Jgj71BKOAmDGnJiIuBDnVeA4+GX7tADMNgMRpZR83J9N+wPAZuO3b82aNRqG+cObiCbqsLhLRy2A3HTTTVpRPuigg5JOc+L3APD++++vE1Ky2JtWjU7cQegQLBAs4GWBAMBeZgqdggUWvwX44Z2crK9BGXdkt956q07+cfjhh5cWq8RKPfG+zz77rHZLRPl1uSXyEnPhhRfqMkgvetGLmnpCLrvsMm2PAw44wDmPKCBOgl8ZrAgIzhoLDPy6Xr6LBuCn5xNfuTIxlwHA+gV7HoKjALjy4u6+tOz4X7OXRBa4ILhIAJZ9miDcSAA2z4sJv8wL92fgl+ZUf1F9zWYDsKf6yxBm+aP24ZHKqFHhHQ4Ann3VexZmwuIbECxAPD5eSeKFayoKIc8koJgFr6yNDMLADmNQS5bER5feWXG9NiFYAJjPgeC0ALxwfeAa7aEC/+jK5aqnp35Rae2aSdXbly9uNi0AT01VFgNGRqvZsuV48gKwfd74zREYRtk11WGBYRZAJD73hhtu0L+dUc/7NNcFv8Ms4LIfPKwCAKexXugbLFCcBQIAF2fLMFKwQEtbIAsAo1jw8obrV54XwCjD8PIB/PJyQT1EklvFvRCsXLlSv5C++MUvbqqtr7zySoU94xQBVvhxnaOGMW6W2263Xeo52yBsu0MX6Qr99Mba5FZ18YdGyR4NIQlxwBoiItygBX7pE1WKyAXBq9e1q56YJKyowC71VwzvA8Bj43NqeFm9+6YPALMfE4Kj4Ffbz7KnzNGMATYvmKjM0MsH6xXOqAutyPhfALh9sqJUmvCrz7vt/mzHOeZQf1WfkVXaPFAXACfAr20n7mmUPoFhVEOp54tHCiDM82doaMjLdZVt77//fv2HushzS56jAsDMIQ0E+5RMYkwA2Mc12qUCA8C0rBC8caySa2JoyH2zulygBYDZzobgNABsq79JD10WQEQdZiHEVId5bgOqLALTiigHyDXBbx15LPgdCS1YIFigORYIANwcu4e9Bgs03AJZAJj6u7y8AXq8wBXZAOs77rhDv0iyIo6ym9RwgSahyT777JPUtdTvk7Jj8xKF2xwJxHDZfsELXuB8YX5k/sUqabJxIJwGgmeMjNDPTvar6XmXS9m/DWV5IdgFwCb8yn59VGDgV8NCDgBmeyA4TgHOC8DsQyC4DPU37lpJguGiANiEX+bTPlNNrmfC72zvwAIk18w7CwAPDVeGmIrwYikAgG3bkogPpVCAWJII4qECGAHE/NdVGofnLc9PnnODg4Mafu1+Lgg2VWDmMznTrlb01cZL+2SMthVgYNilCrtU4CQAXr+ucg6WDUYA7jwA08eGYBf86tM6rwDLORAIjoJf+kXF/yY9T+O+59ktscOmOszC7FZbbaXPt6kOp90XajPj8JvKgm5owQLBAs2xQADg5tg97DVYoCkWIJFUmnbfffepe+65R73sZS/TqkcRjRcAlOVHHnlEEXPHiyEviD6N2Fu2IYaqme3aa6/VSVbICmo3M4s1q/zPfe5zU7u5xYGxZIWenqu6KLararze+GyP6m6vAgkvy+unq6qZmXinbADGNiYEP/Fsl+pwhPH6qMACwIwZB8FxqqueT3RuHn0qAWCarQJHKcBRnrdAcKMB2L4WbSD2BeCo+r9jUx3qiK5L1Gx7l+ocf1bvzoRf/e959Rf41f+eV4lr5ubj/qxPdL07rBOAM7o/p3mGALSEaeDRARBTok0ai3LiKi25C3jGkdMAFZGQDVdYxy//r08N9VYyfY9Pd6jhvknlAmC+NyHYRwV2ukCTMKu3to6wDcACv3JsLhVYAJg+LggWBZjvswIw2wLBjQZg85oQdZhQIJq4SkvyNHGXxqXd15WZRRS2O/bYY9X555+f5hIsvC8LuZ/5zGcUv2d4YZFc8uSTT1Zvf/vbc++LWsff/va39TjXXHNN03+zcx9QGGCTs0AA4E3ulIYDChaItkBaAH7wwQfVnXfeqfbbbz+96p23EV9HYi1czngJeOELX+hUT6L2Q+wtL5IAeTMbMWFr167VsdFmE1WbLNYcGy/FRbUktXjt9LxCppSanq2N35ueq1KnnXk2DoLzKsAcuw3AfGZDcBIAm/DL9lEAvG7DnOrrjSfcDWNzanAguo8AMPsRCPZ1f7bP9eTUnFoxH6JqfleU+3Oaa8v2Ql6+rOI63dZWTd61ZkPlunHWYu6s9AOABWrJ/tw5vn5hGjb86vNvA7CP+ktt4KmIxTqXAtwAALZtzbNM1GH+Cyzpa7OnR8MQ3xNDDPzyPIhqaSCYMQBhHwCmbxQE852AcNkAzL5MCE5yf7btNDDgLlMVFfue1gXa5x669NJL9ULGbrvtthA7zG+YADFu7WbscNz5ZjsqGbz1rW9V3/3ud312X0qfn/3sZ+r444/Xx0B9Y7wZLrnkEv3b/P73v1994QtfyLxfFqr/5m/+Rt8HLBwFAM5syrBhiRYIAFyiccPQwQKtZgFWeSWmzWduqLTUQCRxS16Y44eVeF8gHFWUl4m0NRB9Ym99jitvH7s8FC8RLBQAwKgBqNp2Fuu8+5Ttk0BY+knZnGemlisTgPm+kSqwADDqrzRfFVhAzAZgDRoO70sAmBYHwQAwzQXBJvzKXIHgLAAM/EqzIbgVADjuXEQBcBz8Mh4ALMqv/reH+js3MKzannmiMh3AV5oLgBvo/pzmfuX+x10WdZh4UQEjnm8sHEpmaZ4Nriau0KjA2gw91frP/Bs3aLON9lYSdZnNlTArDoDNbS++sUMnw7LVX+ljqsCm+ivfmyqwqf6a+wCCfd2fze0mJysLC6OjtUnIynB/dp0bfi8BOn7/zOoDLHhwziWZlpk8TWKHWQCx1WG8Ap7//Oerf/zHf1Rf+9rX0lxmhfVl3jvuuKNexEWFRo2mUabrwAMPVPfee6/6/e9/7/RwSpoEdiCRJe7+eEagMgcATrJa+L4ZFggA3Ayrh30GCzTJAmkB+NFHH9WJnFAxfGJ0ow4LkKbMESvCe+65p9p6660zWYAfUgC6iHqMmSYwvxEgz8sC5aFwacNGvAiJ4uOKCcyzP3tbXrD/8uijsUNG1Y19YnKzuvqjpgpcRhywCb9M2heA6btuzK3WZgFggV/G9QVg+vb2RCvGUeKjCcCMYUJwqwCw6zwwVxcAH9138YLrM8qv7meovzPdfapjfEPNNRkHwICvtLbJeqBzKsAtCsAcB88B8W6hfjkQhKs0sCGLjuRRQCkEpvheFgBFBRYAnphqUyuWVcMYbABmf1xDK/orSchozQRg9i8QHAXA9OnqcivhdvyvHJPAr/zbhOBGATCgi+cRv39R9ec5vxI7zDk3k6eJOsz1scMOOyh+U/fee2/1wQ9+UJ155plF/ix4j8V+P/zhD6vXvOY16uc//3nNdijDAPExxxyjfvWrX3mPKR0/8YlPqM997nPq8ssvV5/85Ce17QIApzZj2KABFggA3AAjh10EC7SKBdIC8BNPPKGTObHyTTKntA1Qo/zHQw89pLOfUt+XVeGs7frrr9exd4cddljWIQrZ7pZbbtHxfWQFBX55+dluu+3U7rvvnlrVTjMhXrT4w67YdNWqVWqXXXd1DhEFwK7OD41tVfNxHASnLYf05NpO1ebgRx8IfubZ+HqiJgSL+isH4lKBTQCmnw3BLgVYxouCYF8AXniJH3LDdNrsz2muG/raLtB85joHUSWojhq4TMf9+sKv3qfD/dkEX/p4wy+dYdrTpAAAIABJREFUW8T92bY9z1WekzybcG/Fu0ViQskGb5ZZkjAU3GQlkRYK8co7RlT3vJs545sQHAXA9IuD4DQKMGONb6xVns3jFBXYpQDTzweAx8em1OBwfTkpXwBmPwLBjQJgzi2eR/z+kdPBp7nU4dNPP13deOON+tpgMfif/umf1Je//GWf4Qrvc8ghh2hAPffcc9UJJ5xQMz7HK7/RLN6kqf6AtxjeT29729vUN7/5Tb1QHQC48NMXBizIAgGACzJkGCZYYDFYgFVocc/zmS+qJvGugB2r12kaP6QoIrz84QaIikx8XJ5mux7nGSvPtvzQo2rzEos9sQ8vvmU2E37Zp7xgU7YF18s+h3tlGgg25/7A+lqFPmssMPCrIScHALN9VE3ROABmOxuCbQCmj0BwHPxqOBifUyPDta6oUfBLf1sBFvsCupuN1BukTAB2wS/z8QVg4JfWPlONyxX1F+VXj+Wh/s511MdzLnYAxuUT+OU+3GmnnfRfVEIk7mEgWbJK44IqjSSDj/ccugDBADBNlGAbgu2FKEA4qwqMC/TaNeOqpye69i8AHAW/cgwdHfHx9wCwvucMCI6CX30Pzbs/28/Vudk5NbK8vhxWGfG/JDtEwWSBc9eIxca4576ow1//+tfVb37zG/2bKPHilP076qij1N/+7d8qoJQEj41o/B6jUgPiLlWbKgvAOnMll4VP4zeJOsm4T7PojTdUAGAfy4U+zbJAAOBmWT7sN1igCRZIC8C8oPHjz6o1L3a+jWypvBTycggYEvOUNt7XtS/T9dg366bvnH378UJz3XXX6ReIzs5OrWqj5JTZRPXlJYP/59hd9nzwL2tUT3utO2lWCJ6bL5n04Pot616sk1RgAV/TJjYER7nfSkIs1F9pUQDM90Cwrf7KdiYAu+BX+gHBcQAM/NKKAmDZrwnCrQrAh43+r+qeXF8Dv8wfABb45d9xADzTV6kx3T5Zn9jKG4Bb0P0Zzw8W5XjOoQ6mXQRjkVBgmMXGdaN/WwfA2A0ITgJg+k3PtqnNBqpu0XzmowILAOv7KQaCp6er2eZdz7uNGybVsiH3IqfA78I9Nw/BWQFYxhEQLgN+2Qel7PA8Im9Fmt/AqN8DXIzJskwZJLx4yBtBQ2n9yle+ot71rneV+VOiM5mLwsvvu6u6w+te9zrtGv3LX/5SvepVr/KaD3M/5ZRT1DnnnKMVYFoAYC/ThU5NskAA4CYZPuw2WKAZFkgLwPz44/618847e69+4xqMQgqoUf922223LexQxfX4Fa94RWxm1cJ2aA0EgLJqTqIbGivljYZfwDcO/oHgWdWu+tortUPzArBpgvvWVV2loyD4qWcrKtJcNQeU/ndaFdgEYLaPU4GjAJjtBIKLAGDGMyE4rfsz29ugKxDcaAD2jf9F/Z3p7FZdE9WyP0nwy3Hi/izgW/m3J/zSeREkwELJZZFPysdkCREx7y2eLQDJFQ9t7YTgwb5KMqjabWoVVwBYmoCwDwCzzfkXV9TZVgHgKPVXP1sc/s+f+3tHfbUCfggARtRQfgPTekG5dk/SqRNPPFG7H7/lLW/RJQF/97vf6b9Pf/rTOiNzmY3fZ7lWeR9gEdduuEV///vfVz/4wQ/Um970psTp4A2FkkyyTBKGSQsAnGi60KGJFggA3ETjh10HCzTaAsSjifuVz75x/yKGhx9+3HzjGsB79913qwceeEC7OqOMkuilyAZ8EvdKiYWyE03Z8yZ2DwUa5ZfMnqg/ZMwsK9uzftGbm9Pny8wq66N8CwQzBiBcJATLC/W9a624YdWmBH4rc6+1YBoAtuGXkcoEYMaPqVSj3Z/NJhCcFoCjIJexRyNig207Zrmfssb/ulyfZzt6VMdUZXFFmq3+zjmM6Q3ALV7+iGMGVIFf7k3yI2yxxRZZTotzGxJi0YgHFjdo6WhDsL0IZQIw2wDBaQGY7VwQvG5txbOkb8CRfl0phforzaUC2wowfXGFThP/K+M3EoCJg+W5jxdUEYu5lD56z3veo1CCX/va12a6bl7/+tfrReY0jf3uu+++evFWjiMKgAFz4NcXgEmmdcEFF+h8GHh7SQsAnOYMhb6NtkAA4EZbPOwvWKCJFkgLwKgblEPgB5PszVFNMqDixgf0Eu+bJnmGr0nuuOMO7TbWyHgp5ma6dOMKx6o5sU7UI3a5kPkeT1Q/O96XfknKr2us+/9S9SOmdmh/e22W3qR5ihu02c/1Qn3tI9srW5RxgZsPBOMC7QJg5uCC4LXrZhNr/87Ge27Gwi/7tQGYz4DgogB4dsYomTRaVbKKgN/KtVN/ppPif1++4v9U7/jaGvXXB35negdU+1R9VudSAXjECkGYdailByUrWUn3A9+T04DYSO5R4iNJYFV0O++6Srmk3u7ahZep6Ta1fLCaqMqVTdyGYMZZMVB/PuxFMVGA6R8HwHzvgmATgOljQ7ALgCcmptXwqDvuNS7+12XvshRgXNTxPALsslYvMOd79tln6wzMF154ocKTKUsjizSu92kayixAWrQLNIo2QP4v//Iv6l//9V9rphQAOM0ZCn0bbYEAwI22eNhfsEATLZAWgFEe+aHeaqutIpNh4ArICjmKKKCMK1QR8b4uM6Ew33///aUrr+a+KXfECxC2EJduVG4Sfey33346wVeRzZXsCtXXR/l1zUMgGACW5gvCvgBs7vfqVdVkYFlU4KfXzCmHV57eRRQA65fy3ugEPEkAvGFsVg0Nul0oXfDL/khyNTrsLusSlwDLdY5MANbAMg/BRQBw1gRY4vqs7T6xTgG/tCj1F/CVVjgAG/G/c8NV2G2brpYKWti5A375brYAACYr/q233qqfbyzyFX3vm9eGC4IBYJpAsC8Ay+LU5suqIBwHwOzDhmBRgPW95lCB4wDYBb+MAwDTXBCcBoDLgl/mxvMfzyOe/UUo/Z///Oc1KFIflyoCzWgsUuPFUEQSrHe84x067nf//fevS3LJQhH7wRuMhWKUb2A5tGCBVrBAAOBWOAthDsECDbJAWgBmWitXrtR1KylvYDcTDnGRJlNmVlDzMcF9992n7rnnntKUV3MOgCiwzf5wt+ZHXF54SVxC7FbRMcC+ya58bGX2cUEw3/uAcBYIZmxA2EcFNpVI4FeaC4JtAEb9lRYHwM+um1XLBqJjBAFgmguC4wCYbWwIjoJf+ka5QNsALMcEuGxmKMJpzzv9fdVf+koJJNTfrulKMiUTfvm3C4ALg1924HCBnusfdB66LwAXAb/UbwUY8P7gWViG54d5kALAfGYqwQLBfA4IJ7lB08/2zgCEXWERUSqwCb8L95sBwTb8Sh9RgZMAWPoLCLdK/C/zImb2zjvvVHvttVchav9pp52mzjrrLL2oivt8M1pcGSS8ubi2+S0i3CfJk0sA2Oc4vvjFL6r3ve99Pl1Dn2CB0i0QALh0E4cdBAu0jgWIWQOC07SLL75YZ40E9qTx44gLMEAKHKKGUPag7Pbggw/ql5EylFdz7tgJpeexxx5Tg4OD+oXXLFFB0g9isEj6weJAEc2G3ywuz3HzcEHwzHym58H2aoIje4ysAMw4uEtf/fB2NUPGuUEnATADmRBsAjDfuSAY+F14IXdAsMAvfbIAMNuZEFw0AMvcs4KwLwC74Jd9d0xXYztt+HVdb3nU31ncp9c9o2YHa58lbTP1Sq8TfplQCe7P5B3guUNuA+75gYGq2l3EvR81RpwKLNuMDNS6e7tcoF01c2VxavNl1eRkJgAzvqjAWQGYMYDgKPdn13EDwa0EwDzr8TwyF0DznHPcn3GD5reziKzSWeZyxhlnqI985COK2F2yPZuN2ORjjz1Wl2aibFOeFlyg81gvbFu2BQIAl23hMH6wQAtZIAsAX3rppfrFT9y1AGiSXVB7lpViXgwaVb+QF1FUGGKgyoi941RJXU9ipXB5Y5XezpSJKsAKPuC/5ZZb5j7DkuxK3J+Lhl8mSEKz+57sVL0dtdl4BYLpEwXCNgS74oBdRrD7AcNRAGzCL2MluUHb8Ms2eQHYBcEuBdgFuQLBad2fK8xmZQybN6YLXPgqDQynAWBT+WU/JvzqfxvJr2a6+uvUYPpkBeCZwVHV5ih15IJf9tMoACbcgcU+nnHAb6OedRzjj67tX7hfRAU2FWD6TM8otdlQPATHAbB5315+7fqa2xgAdsGvdBJX6CgFWD9PxyiN1Fv3eBD3Z9dzIyrRliv5FduX6QJNzglgld+cIlR/3IBJSIU7fVGLp2l/gIhj33HHHXU8MDG8AC+NOUktXxa+DzvssJqhJcHVJZdcspBJOm7fAYDTnpnQv5EWCADcSGuHfQULNNkCWQD4iiuu0G7NZDymLBLxvhs2bNAJQYiL6ohLn1vw8Qp4At1FxGPZ08Pli+Mj4zNlL3bZZRenSzeu3/TDLS5PYpSikl0lmZk4LOKxSGq21fMOrYFgE4A1jM21q+GOtTVDZlWBo0D5mlW1qvBTz8yqzs76GN44CHYBMJO2IdhUgPnedoU2FWA5aFGCk9yfXXYf6He7Wmdxf046r/J9FBD7xP+uXV+Bb5T1V+1wi+qZqkDQTHu3rv8rTeAX8LU/k3/7wO90/5Bqn5lSHetWK6DXbK0EwOLlgtcJmd7xAmEhsNHNdoW2AZj5AME0AeG0KrAckw3AfD45ns5jyLYPAKzvOwuC4wB4empGDY7UJ8dqZPZnOQ7CYLgGyKBcRMZ/XIZ/+tOf6pwZjVxMsc8L4PuGN7xBuzrjEs2CMtDLbyD1fL/0pS/VXeoS3sSiEMkgk1oA4CQLhe+baYEAwM20fth3sECDLUAiJ2J80jSSdbANMb6onijArARTGqnMeF/XHHFJBuTygqdrbKlfzHeoviT+imqo32ThJDN21tIYjYJfYF1KZjBfFg5ue3gqEYI5dgHhIgHYhOJrV22rgF9aGQBsw6+cTxOCXQBMPyA4CwBPTc2qkeH62pplAjDzbXfkAGvvqP+wu8t9VR+7862R8MsWAHAc/Oo5RGR/BnrNBgC7Wm4ALsj9mXsTl2fcXwn/YMGtqyvCcGkephn6fuOSPjW0rHIexyeUGhmcUy4VWIYGgrMCMGPYENxoAAZ+pdkQ7ALg094+rX+HxGum6ASM5IDA8wgPqCKA9fjjj9e1cgHgRi4euy69q666Sn3mM59R1157rV4c5Tf+5JNP1nWKnffnvPtOAOAMN3LYpOUsEAC45U5JmFCwQHkWyALA/DjiKsW2vASWVfrD56iLAE97P7zs8pLDSj8KD0oPL71xjXJPN9xwg854vf321azHPsdAH1eyqzyZnl37ZR8oF7hvSpy2HBcAPDVbyWA82DWmXCqwOSYgXJQbtD5+VQtmv/7j1k4Apq9LBV69dkb1dEcntRIVOAmAo+CX/XZ3RWeVjnJzBn6l2RBcJgC74Jd5+AIw8EtD/UX51cdvqL9TXX2qa6qSFEuaKx7YBuDp3iHVPl3rcq/n5Yrpdbg/07fR8b885wizYLGNvAY87+wQCN/7vKh+AsEAMG3AEkdFAV649pbV1/3K4ga9bk3lnPf0RsP/hnXjamCw3sWZ7UT9lXmJCpyk/tp2ExCOAmC7PxAsf3nPAdn+qZ2LB1QRteePPvponV+C35CiYT3vsYbtgwWWkgUCAC+lsx2OdclbIC0Ao/ZefvnlenVY3AD7+6sukI02KLFL119/vV6pRoHO2zg+VG1in0TpScp6yT5Xr16trrvuOvW85z1Px1KlaQK/8t8y4n05z2SpJnMt541YZVu9SAvBuEaPdNqu0dGQKDZxuUFHfbby9q3rTFkGALMTVOA4AKaPC4LjklyZAMz2AsFR8EuftPG/rmstDwC/fqf/U7NtHanglznYAGzCL+BLc8Gv/twTgBsd/yvJ71hoIz4TT5Bmq3RyvoFguR4nJufU8uHqvWcDMNtMTSu1+UgVhPMAcBQEA7/SXBBsA7C+74Z6F8ofua5lUwE2v3fFEfP9v7+rTS/O8scz1W551WGeoyyG4Cac91pgfi9/+cv17w2xxQGA0/xyhr7BAsVaIABwsfYMowULtLQF+AEGZn0aLlo33XSTjvulkRCjWW6AMl9iWa+55hq122675c6gyfERx0sdY9ydcQ/2fcFBEcc1fNddd9Wxwr6tEcmuOL8kKSOWi7guVxIvma8Jwf1d1ZdZvjfrBtv/FhD2SYaVBoBlXjYImxCM+istTgWemnInlpJtkwB4fLyyn6HBWnfmNADM9kBwmeov+/B1f6av7QKN+ts5U/tMQP1F9ZXmq/4K+Mp2vuov/XO7P+uLtDYZlP7Is/4vi2GEV7C4xfOgzHrmvs8Ls58JwHyeBMEAsDQBYR8IFhdoUX8X7jWHCpwFgBmvq6c+RED2EwXAs/M30dBodQH2jP+vqkwLALOIIeElNhCLl00adRi1lgURwDVvyA/zIZaYdscdd+QeL8t1FLYJFggWqFggAHC4EoIFlpAFfAH4qaee0hAlNQEBvsMPP7zproDAKnFLQCfwmbXxkgvcc3zANCpumpcbFgWuvPLKVPMwVQrOQxnKL8nJgHoyPuOazbElHdfND1ZVoum5djXUPbZg1jgIptNw57Nep8AHgl19BITLAOANG6bVsmXRL+ICwBygCcFpAZjtp6bn1PLRejfSItRfxvcFYBf8zrR3qh4ju3MS/LI/U/2d6qnU6O1wuTqX4P6sX1ymHTHEOeCX5wD3DQtsxPST4yDpvvG68AvuZKvADC9KsK0CmwBMPyA4DwAzhu0KbQIw39sqsEsBpt/k+KQaGK73JIqCX7YRADZNevbHokNVeN4CwwLGLnVYnsGiErtOF7+D/F6Q0ClvYw4kjsS7gBwSrXiN5T3GsH2wwGKxQADgxXKmwjyDBQqwQBIAS9wocU/EvZFsilgl3LV4AfBxDy5gmpFDoNrikg2w4n6cpZHYhhg/Xn44vizZpGUeZMKU0hBRc2lUsivcw3lZ46UP22y3XW2m5ThbCQQDwDSB4CQApu/cXJsa6ap1jbb35QPAeiwrNpixab+/u5KQzFR/ZR8uFXjt2gog9fdHAy4ATIuCYBOAtU3mlWCf+F/7+AFgmg3BRQBwVvdnlF8bfqc7ulXXdG2sr63+chwAsICv/rcDdPncVwF2qb9s34j4XzK+i6cL93NU5vcsz5qitwGAabhCowBLA4Kj3KDNOczOKrX5aG18sMNrWP3mgiedUzcB2IZf2UAgOA5+F/paEJyk/tqTigPg2uOuuEebQGyPFaUOc22wsHjQQQflPp3Mgd8uIJjfsdCCBYIFmmeBAMDNs33Yc7BAUyzAC5+r8XIAGJINeWBgQGc+JX707rvv1gmieAHg82Y25k4GTdRNXBTTNJQAwB6YJx6WZFeDgxX1Km3znYeZ7Ir9m4pD2n3G9SdJCy51uHDj8pylRrILgm0AZg72ZwKpMj8XDGcFYMY0xz//hufUmaEMALbhV3ba21tJHOZqdvyv2UcAmM9MCG4WAB/1/AdU90zF5V3UXxf88r0NwLPt9TbwVX8Zr5Xif/GUQInjv4Bv2nj+Iu9h37GiIFgyRdded7WjAsDSBITTALC+XuZdoYsAYMYzleA0AOwLvy67plGHuT5wj3/Zy17me4oi+7FfFlxxp/7d736Xe7wwQLBAsEB2CwQAzm67sGWwwKK0gAuAeQHEBRBXZ9yzzMyn9913n86SzAvA0FBtOZNGG4AXEWoVbrPNNhr0fBsujqijuHaPjo5quM+T0ZPxLrnkEu0uSeywq7kyPRed9MSsVYo6L4sWvnYx+11/f5vqap9RogLLd8sSYoNtAGY73rOXW6pwnbprqb1s5wTleRXYnKsNwjYEiwLMNi4VWNTfhWO0XKGjAJj+URAcBcAm/JrHAAiXBcCu7M/sGxfoKPjl+zj1V2KCO6x4YbbzBeDSyh/piy5d/C+qHnDD8xAvjjQeE1nuryK3EVdoUwVmfBuCbTdobSYrQTQgbEPwz3/xaGScbhIAsw9UYB8FWGwCBBfp/pzG1mbssCuRlrgq77PPPgvlltKMb/blWuP39fWvf7368Y9/nHWYsF2wQLBAARYIAFyAEcMQwQKLyQIkSTLjoXCdJfkLnxNba7sAUkqHmpgk76AsSDMbLygXXnih2nLLLXVmY5/Gi664sQGsRSS3QS2/6KKLdLIcFgvs1ohkV8yB+r6SwRp75IF6jsEFwdOz7WqkJzoumO1sCDbfsQWEs6rALsCWsX56w+ba9CYAm/Ar58WGYBuA6We6QjcCgAV+69yi43N31V1raeJ/TfhloI7ZaqYkG375HvXXTIalt7EAuJHuz+x/xqopzGdtDvhte+ERkY8HFvp4JrCghjtqXM1vn2dMo/t86dc9epcjQx01rtC45282Wi0P5gPA5tw3m88aHQfA9I+DVb6fGJtQ/YNWrab52N8oW/X0V47J1dLG/+Y5H6Y6TPZnPKBYNOU6kZa1zBK/tbjZv/3tb1ff+c538kwzbBssECyQ0wIBgHMaMGweLLDYLCAADKStWrVKu87yg46iCljajZhZQOslL3mJXr1udlu5cqV28WU+Sc1M5oXKQ+mkIhKPYDvmgTsbqqvZJNkV/6WVkexqfHxcL1qQFIxzBtT7ZrBOstnld3eqwe7JGiUYCKYJCCe5QdPXrkQ62lWfMMsbii0V2N4OEBYIzgrAzFkgOA6AxzfOqJHRSq1cab7uzzXXyUwt6QoIuxIVxZ2zNAD8ml3vWBjKhF8+dAGwvd886q++FzzLH9F3pm9Z3WG7QJdOaQCYhEbcO9yf5ABohWda0j3p+l4guK+3CrxmfLqAsA3BtgIcte8rL/tzpAq8Ye2YigNWAJhmQzDJr6La1MR8TP5obZiNC34ZI48LtI+9CQUiJAjPGhY5WVzMW2aJ31Ke1SeddJL66le/6jON0CdYIFigJAsEAC7JsGHYYIFWtQAAjHpIfUN+kKnrC8RFxcNSSxb3YRRGFyA3+jhxgaZmLy5pUY0XlYcfflgr14AhLzBFv+iiRK9YsWIBxBuV7Ar1ihd43Ol22mkn/VcE1Ju2BIL7uqrqoAAwfYDgLADMtmy3onvNwq6yAjADuLb9weXRHgqiArvUX5kQABwHv/QDgLUdDAguAoBlDiMj9dmio67zNAmwXr3ng6pntpLgaqatcyEGWMYWAJ7uqChxnTP1uQLyAHCU+/NMT31egcj6vw6ll7n6ArAsiHG/8DxrtkdLnmfnF3/Zo9rn2TcOgosGYOCXVhYAM/YyA4Ibqf7K+eA3j0Vf4HfvvffWOSPEPdrO5m+fwzh1WDypPvzhD6vTTz89z+kP2wYLBAvktEAA4JwGDJsHCyw2C6Aa4v5HnVgAjhfBuPq+uNjSn1hXXIib3UiCxQvJ/vvv75wKLyio2qjbwD3JrkjmVXQzQVzifeW/klG0aDDlXFCXUspplOW6CQDToiCY74a6a+sGx7lBi+1NcBYQ9ooNdsQBx8HzDy8frTvdPgCswa+zknna1QR+5TuB4LTxv2wfGf87LwEvX16rMrvm4wvAAr+AL00SYMmYwK+Ar3xmA7ALfumbJf53qm9k4XDaZ+tLGpUBwI8//ri+d8huz4Ifi2iLvYkKrO/VeSXYzlI+PFhViBfuQ9s9w2EIFGCaXbNXAJjvXBAs6q8MKSqwj/prTkMguNEAbMIvXkb8hria6eljxw7zfDazSkuZJeKJSYB12mmnqU996lOL/fIL8w8WWNQWCAC8qE9fmHywQDoLoPwCbrjQkvHUp04sZZBuuOEGtfvuu2sX4mY3ykeg6h5wwAF1U0HdJpkXbo4+cJ/nWATE99tvP60OyEtQXE3JrPvjhYrs1SQjY7GCRYuRkSpEZB03bjsgeHK6Qw33VZRAUwXm3zOz7Wq0txobHJUMy9yHK6s03y/vri2j5JMMy0c9tkEYCI5TgJlLGgCmPxCcFoCT4Nc+L1Ew7OP+bMMvY5sAPN3epbostbdo9Xeqb1i1z1Q9CuT4XPDLd2kA2KX+/uHpTn3/EyrBH8ovHi+4sQI1ZSyIlXEP+owpEDw+PqtGRzqVDcDT8yW4VoxWs3f7uEH7ADDzsyHYBmD6AMFpAVhvN1QfR8znbzvk9oVzy3OwqOSCxPyySNLT06OV3yj4tc+LmUhLPIFsd2l+F6hh/+pXv1qdddZZ6gMf+IDP6Q19ggWCBUqyQADgkgwbhg0WaFULkNWZF4att97aa4pr165V11xzjYZl3G2b3a688koNmwcffHDNVETZJqM1oE4t3KJejFzHfNlll2kYFQDmhaeMeF+OFdc5Sh1JeSoU8Ea0OAgGgKUBwj4ATP8oCOY7AWEfAKa/j3pMPwHh9esm1cCyaGV1bGxKDQ1Ff28rwIw9OTWjRkfdCXyiMkCnBeCoc73Zivq5rltfzYb81gMe0Zt2zlVVVoFfwJdmw6/un9L9ebKnWk6sw6HoMmZeAE4T/3vj5Kj2cDEbyi+JjAiFKNozoxH3YtQ+PvPDDjU4X6M6SgW2IdgHgNmfDcGm+ivz8QFgfU11xZQQm4//tY9xdq4qVS8brrrKv+lllaSNetzOTu3Kznll0QN4zdLEQ0AWSfKU/Isqs/Q///M/6uMf/7j653/+Z3XGGWeU+vuUxQZhm2CBpWSBAMBL6WyHYw0WQMmbntYxwL5t/fr1CugkQ/Suu+7qu1lp/YBx4l8PPfTQhX3gGkycMi8eJBlpREmTK664Qrsiiyt2GfBLuaVbbrlFkT2UlzsSlcW5q5dh9Iv/VHmhRAl2qcCyTxcEuzwt4wB4YaxuR8KslG7QLlt84zcDiQDMdi4IdsEvfQFgmguCywTgjg63q3ZnZ2VhAvidVR2qe67qqm7DL/2yqr+T3cvqMkIznguAXfBL3zLdn3lGEArx5JNP1lwKABKwhDIMOBWVPK6Me893TF8VeOH+Go6GUXOfAsD6OunpVC4A5juBYJf6q++R+eRXrszQkvzKdawmAMv33/siYWeUAAAgAElEQVSPrfVzlwVPlH3+WKSVRqk+Uf75f5/FDn4/eM7ybEX5zQO/9nGIOszv01FHHaWoSvDJT35Su0H7zM33Ggj9ggWCBdJZIABwOnuF3sECi94CaQEYRRW1E1UVN+hmt+uvv16//Bx22GH6RYgyTXfddZd+eSG2r+zENuLidu211+q6ybjJ8UL9nOc8R8cVFvVSMzY2ppNd8cJE7HXZinbUef3trb2qu6OSsXigpzZe01SB+X5mtk2t6Ku6RfOZDcE+AMx2KMrLeyzX6IRs0Ho7R31h+9h+cFl9jDB9UIBpWQB4AS7m1eAo+NU2sTJAy7azKVJAxwGwC37ZR/tc7cJXGvUX4DVbZEywQwFuNACrvV6hy9eQCI/kfoQMcD8Bw/zxTNP2aG9fUA+BJpIeLcZmqsC4Qg8M1AKuKMDmsc3MUjKpEhMe1UwAjnNhZnsgOAmA6WdDcBYAtueLGiwwTMgOv3E01FyBYRYQUYvtVib8yr5wvwd++b34yU9+ov/fNZfFeO2FOQcLLFYLBABerGcuzDtYIKMF0gIwKuQll1yiIYxEWM1uJBLhJQcApkwF5SqI6SPZlW/MVtZjMDM9ozqwb168UJvkhQsY5i+PukQMM4oBtsf1fPvtty8MrLMcu6jAbGtCsA3AfA8E0wSEs6rAtks1MBxXE1iOyweApa8NwgLAfG9DcJICbNoVNTit+sv2eQEY9VfgV1+P8+rvbFuH6pytL0GTBMCTXZUEQHbJJP2ZVQ+40q8+oRWf53V/ZgxnpueIrNB/6txG35vEh9pJ/riHBYa5d3GVlnhNYFnUYV/1MMv9VMY2QHBXVzUsIQmCAWBpcSAsELxh7QbV1eOfodw8RhueTQiOAmCX+suYKMBxDcWVZzPnlsUOFhD19dPWpq8HgJhzzG+FZAVn8bSs2HAWZwFefrPOO+889brXva6pz/Iyrr0wZrDAYrRAAODFeNbCnIMFclgA92dZIfcZhhcKSv6QcZhyQs1uqKIkK0Ft5UWHlxnmVfaKumR4tpNd8Tkr+7xsoSbICxeulagOKMO8dPm6LvPijmIgtZmLLt+U9fwJBE/OVAB3tL8CVC4VWPYBBBcFwDLmqOUe7ZMMy3XM5nY/vGxkQf01+5oQHBX/G2XPZYPuWOIi1F/26VKA337I4wvTAX4BX2k2AEfBr0CvbOeCX71/TwBOo/5qUHHVCk5R/ugWtYW+D7n3eC4kuTizyCTqIf811UOBYcZKGifrfVXkdiYET0zMKDN5mq0CmwAsc3CBMAAM/NLiAHh8bFz19tcr6FHKMRBchPqbZD/Ufjm/hJJIfXbUYZRjzituzyx4FN3uvfdeDb/EF//gBz9Qxx9/fIDfoo0cxgsWyGiBAMAZDRc2CxZYrBZIC8Ac58qVKzVoorI2u6EAS1yfbybrvHO24Tcu3hcAFldLScSD+jA6OqptyJ8riRX7IEHZAw88oBO5xNVmzns8WbY3XaFNCI4DYNnPqO0WPVdfmsU1J5fia/YDhosAYBnz//2uviYtEJxG/ZWxpqdm1Mjy+mRlRQBwEvx2qlolNkn9nZqv/dsxV5+p2Vf91VDcAu7PFz/RprbYYgvtrZI2CZ6oh9y/QJMsZjGO3L8sZjUqCV3a+9QGYNkeEI5ygzb3YeScUpuvqLgLmwAcB8EAMM2G4DjX6a7uaEU5Kv43rU3M/vz2AcGPPPKIPr/SOL9m1vAiXOEJzXnlK1+pkxeec8456i1veUuA3zwnL2wbLFCwBQIAF2zQMFywQKtbIAsA4wKNe+C+++7b1MND+cU1GFgk2RWuwWU39oXNRDlIk+wK12hetFCkTPVBXC1Rh3HfZmzcuVEKUCJw28yazbRMewgECwCzL5TgJAiemY/d3ay/oiTRfGKBkwBYxhrpXld32D6u0FF9bBDujshgKwmw7J0Dv2YzQbgMABblV46nS9W6O7vUX4FemacLfvnOF4DTuD8zblkJsHB/5tlQRCy+6SpNWIK4SnPPymJWq7lKR0Hw0FA9bLpUYBOCOU83XXV/3b1lK8ECv9LRhOA4AJ6emlJ9A/V1drO6P/s8+3BFxouI5zjXCQoxCx54E9nnl8WOLHkdqEF/5JFH6hj0b37zm+rEE08s5Hr0Ob7QJ1ggWMDPAgGA/ewUegULbDIWyALAl156qQayl770pU2xg6ijuJTx4gIwHnLIIaUqMWa8bxb4tQ2F3Xn5AoaBYlwvadiVfeGOx0s1mZ5b2d3SBcFDvbXKocQBiw0EgOXfgHCRAFwDm/MwnAeAZTwB4bwAzHgCwUUC8JsOXq262yZrVPA4+J1ur7hluxRhX/VXQ7Gn+7MG3ZLq/zK2szTSXq8oBTa4X1nEEnVY7l+fREuNfmgKBOMGbTYbgn0A2AXBSQDMNkBwEvyaczNBuAz1l32Z8EvMr+n2zPnke3GXlvNL6IqpDieFshDCgvKLN8/Xv/519e53v7uU67HR11TYX7DApmaBAMCb2hkNxxMskGABYE5+3H2NRckfFJUDDzzQd5PC+gGOt956q4775YUFV8SHHnpIzwUlpoxmwy/HLn9F7I9zgHs07nGovqI88HIlSVr4byuCMABst6npNrViWdXt1gZg+tsQPDvbpjYbqM0Y7bKtrwrs2na4e33i6fIBZQY59+LaGMEo9Ze+tgIsk5iZmVOjLrfoFNmfGQsXaOC3q63W1dmG3xnVqTpUvVtzHgAuK/uzBtqc8b9kfy5C+U26aLhfUQwFhikVp+ff1qaT38k93AxXaeb22R916pj23t7arMdTUzNqxYrq/ZsVgDlWgWBb/RXbpQVgthMILgOAWby4+eab9QKqDb/2+ZbzKzBM1QFpkkiLc8zvj3m98RtFzC8ZyL/85S+r97znPQ25HpOu1/B9sECwQL0FAgCHqyJYYIlZIAsAX3311VqhNGvvNsJsuKfx0kKSqS233FKro8RW3XPPPVqNxj2t6BaV7Kro/fByRe1JAH+nnXbSw/NCLS9bZokWlOFWcok+/8Z+Ndw/o0xXaCCYJiCcpALTFwimxYFwHgA2z1kUDPsCsIwlIJwVgBnHhuC02Z/ffPAzejqdbVW4FfgFeqXlgV/G8HV/rvStzwCdJgHWRM+Q6h17uu42m+wbcd56bbavLqrjzs3JUSButNzTgJYsaFFPVlyls7jSpn3msF9qH7Ow9oeHD9ObmxAMAEsTEPaBYJcbNOMAwVEAzPdxMdi4P7tajyORFv2Ssj/H2cqEX/JYpP3dGB8fX1CHUYl5ZtPI8Ew5vKOPPlrtt99+6o1vfKNOYPj5z39efeADHwjwm/YCDv2DBRpogQDADTR22FWwQCtYIAsAm7V3G3UMKKQ33XSTBu9ddtlF7bzzzvqFAgC+8847dTxy0TV/0yS7ymMHYsOkdvFee+1VcxzyMg0Mm3GHKA/yMs2LdbMbENzXU83xLADMvIDgNAAsx+IC4aIAWPbR1janhrqqsch8nhaC2caVMEv2EacA2+cNGPYF4Le+fPXC5ib8Mv8OVevuSsc8AJw3+7MGIIf7M5/bNYX5rM2qUSwHatcuXjiPLQTA5jkli7TpKs3ziybeHSiHuNQmudKmvb95dpFH4NFHH9XPk+9c+nw1ONKnxsemapKx2RBcFgBPjldKw/X21yeCi4Jf+s9OV58pfUOV+OA88MszlN8RYDwL/Nrngd9PxmSx46yzzlLf//73dRd+mzgHxxxzjPrP//xP/XsVWrBAsEDrWiAAcOuemzCzYIFSLCDxpmkGl9q7RxxxRJrNMvdFwbjtttsWSgGh/kojwQgvepSu4GWyqJYn2ZXvHHh5wj2OY6AOJcmu4mBWSrQQN2wqD6IskUSrWUl4vn1ZvxoaUJEQPNJf73rrcoOOsp0Jw0VCMABst8GuZFfsuHNswnAU/LI9LtCuNjc758wYLX2PP2RM9bZXgILW0VYLu3ngV4+XMvvzePdgzWEMjFcUaWkbeyqeGe2O8kVRYL2pALBpB7NEGsAk3h2SFd6sSev7DHH1kyR6uOAyJotqhE98/P9VYNKEYBOA+Y7Fl+WGWzSfOdYWnMmwNm4YU929Pc6pCwDzpQ3BvgAsA5//tV0ymUcWUdkY+GURseh2zTXXqBNOOEGH6Eh+Cvbx/Oc/XyvD1P094IADit5tGC9YIFggpwUCAOc0YNg8WGCxWSALAEvtXQA4bWmRNPZhbgAipYAoRcFLi12fkSQjuA5TJohyJ3lb0cmuouaDMsS8AVnimKlRmkYFkhIeUmJJlCWS8ADCqMMoP2WeH/vYUIFpogSbKjCf2xCcBoBlX4BwkQDMuC4IblNVOF3WtTHTZQUIp1F/K7BRD8WSMMsGX/pnhV+29Y39nejoVy7lNSpTtKuvC371/GfrF0b0OUmhALeS+3OaCwVXWokbNrPCsxgmNYeBtDT3MPBLjgQWyRgD+DW3B4IBYH0/Lu9TNgDzuXggCAinAWC2tyHYhF+xjwnBUQBsqr+mXbMAcCPgl9Cc17zmNQoPqY997GPqox/9qKJiwm9+8xv129/+Vqvxb37zmxdU4jTXSugbLBAsUK4FAgCXa98werBAy1kgCwCjxlI78bDDDksFbWkOHkCkxBEviLwEAriuuFeSRhEXzIve1ltvnWYXdX3LTnYlO8StmUUEkuUw59133z3VS649cTMJDy++lGvRcNHRUZNEKw1gZzVkHARPz8zH+A5WXsBtAK68fFf6xDVhxM0HsoGpPXYSAEt/6TfQWalx6tuA6bN/Wev6Gaf+2uO++9gZ1W0luNLn11J+9WcZXJ8n26uJkNpV1eVU5hHlduwC4Ki+aQA4Dfwyx8UKwOZ5jlrQ6uzs1Pew/MXdw8Avi2o8M+NqHydBsO2CDwjbEHzD5ffUJOVD/TWbCcEuAKYvENwI9ZcEZXgt0fgdYcGx6MazHHWX/BjE+5555pk1z3TODc98zh+5K0ILFggWaC0LBABurfMRZhMs0BALUJ82TSOxCpmXSYKFMlt0A+CI0xJA3HPPPSMBkZc9Xm5e8IIXqO222y7zVFzJrorM9CwTQ4kA7FFsd911V7XDDjsUnhxlw4YNWgGSepYaEtra9IufqMNlnDc5RhOCbRU4CYJ9AJj92EJpXhhOC8HmhdYx70bd2+G+j0w1me2A4TgABng7DBB1gq4n/EbFM7c7QNkFv8w3r/qrx1ji7s9pHkw8i3CPFnUYZVHuYRI2Sew/SrFkHQagea7gUUKICM/DKOX4n87aoLq6q8nRBgYr5bCkuWLQ5+YdE5Yvrzzvn3lmXD14x18WtskCwLJxZ1dtduqFeRjxvwvPlpTuz8AvvyUAKB5EZcAvv1fHHXecuvzyy3Wm5y996Uu5FjTTXCuhb7BAsEAxFggAXIwdwyjBAovKAmkBGLfk+++/Xx100EGxMatZjCC1GYl3fd7znqee+9znxgIiroO4nBFjRd8srVHJrogLI16ZhgoAjJbdOLfiJo1tJSPt4ODgAgzb5TvyzkkAeHxSqWV9tS69AsCyj9FltS6wWQGY8drnxeMV/emVYV8AroBIvZuyQLBpu/a2WjW1u31KCQzbUOyyeVSfNHN1KroO+NX2c6i/+nOHO3KruD/r89GiCbDy3keyPa7SUoKHe1jqkFNWSUIdWJAkGRMeJXvssUfiolpaCBYANo/pvttWaRXYhl/pgwocpf5Kn5nJyv3fM1C7kFqE+zMLByyOYi+U36KTJDJvvHnI9oyrMzV+v/a1rwX4LerCD+MECzTQAgGAG2jssKtggVaxAGqkgJHPnO67775SSg+RDIqyESgXxMT6ACIr/CQe2W233RbKB/kcg/SRZFfi/sy+i64dytjEMWM3YnRJdpW29EaaY4rqi1s5L9Cow7xQ82+avEhjb9zNizj+KAi2AXh6RqnNh9NDsKtUrgCwefzA4vI+P5dlX7B09WOfPhAscxM4drk2x8Gx7xxjgTYFAKdxf46C5TTuzxWgrc9gHTW2C37p26wSSEXcp3FjoPQCuqIOA8fSuI933HFHDcU8Z5LaB75S9ViYnp5Rw6NVN/04FVjGBYDH14+p9s6OpF05vxf4lS9NCHYBcJrYXxN+ed6SabvoxuIiMb0XXHCBOvHEE9U3vvGNlqzVXvRxh/GCBTZFCwQA3hTPajimYIEEC6QF4KJLD7FCTykjygHxEoerGgqlT8NN+sorr9RlJnApTtPYL39lwi/jA/UkQOGYeBkr0/3Y9/ilfIeow/IiTYyauFjy0ojCk7V9/+pKUqzJKaWWD1VVUxcE009AuAgV2JyzCxpdUJwGLn1VYOZhKsETM11Oc3a1z6j+jo0LCrHdKQq66RcFzGWpv+wzxP9mvSuK2w4vGRRO3KUBXkmExx5MV2myxLsWtUwVGACWBgj7ADD9b7/2rkgAntxYAezuPndmaBuAZf+AcB4Axh7YhcWCsuAXW7/1rW9Vv/71r9Vb3vIWdc455+R6VhZ3VYSRggWCBbJYIABwFquFbYIFFrkF0gIwCbBIhPWSl7xEw1KexkscyUFQJnFR44XFR72QfRJ/RewV7s+4Qfu0RmV6xq7E5RH3SxIb3J5JatNqzYw5RB1mUUGDW3u7Vk5Qhpl/mvPC9pRG6p7nPROCowBY7LJi0K0A2nZLowLb27Y5cm25FNzh3nEnYJpAumGq+oIPyEa1zvb6BFPSd3Km/rp4Tm+1zm8UAKeBX31OG6z+6n2G+N/Cb3mem8S2onSSR4DFP543PEdZ1DLLpLHgJlml7czwaSDY5QYNAOtz7FCBBYBdEBwFv/QFXGl2uSQfBdiEX7yIiiyNJycR27/zne9UP/3pT9Ub3vAGndW5FZ/rhV90YcBggU3YAgGAN+GTGw4tWCDKAvygS1yZj5VQMwE7YNWsyeuzrdkH0OIlDoglgVWWbMi4of3hD3/Q25P4Jak1KtkViajITk2M2Pbbb69dtItwLU46viK+Z86SRAt3S2m4R0sSLRLw+DSBYACYhhKcBMD042V7s6F4EM4DwOzDF4I72t31ejsigNYXgl3Qy7wmZ2pV98mZdm27nYcfrzF5nKt0ZDxvzuRXTCDE//pc+eX1AXR5bgJ7uDzj/WI/W6I8PPDoYFFLskqTWV8g2FSBmT0q7PCK2vvchmABYPqbEGzCr1jCVIJ9AFi2A4R94JffkxtvvFGHdvDbVAb8Mjaxvj/60Y/Ua1/7WnXeeeelXhgs78oIIwcLBAtktUAA4KyWC9sFCyxiC6QFYOCIFzCyM2+77baZjhyVAohmtR/wBRKzNF5ILr74YrXNNtsklpdwwW+aGpu+80N9oRwJx4YqndVGvvsrsx8v28QLS8yhLJSQOEtcpanNHAX3tgrsC8Hmi3YcCOeBYF8A1tBXIASPT3ep7g433EfBr5xjM6v21Eyb2us51Uy80icN/GpwSZH8KgqAiyh/xNhp4n8r/etV9U01/pfj5X7EvRfY22mnnfRf0sIazz0W5OQexiNFGvcu9/F//HC5WjbUp0wINt2QBYTjVGATgl0AzPcCwVEALOqv/Uz7zXfiSweZ8Ivym9czyfVMZW4nnXSS+t73vqeOPvpo9ZOf/KQlwlnKfP6HsYMFlooFAgAvlTMdjjNYwLBAWgCWzMuAK+53aRovY2QsJeaXeNO8MVqMt3LlSq1EM1ZUa0SyK/aNezjHhtJCbeIykq+ksXeRfaVWqajDXDc0VCReOFGHKTNiLyrYKjDbDA3UzswIQdRfuF60XSBcNABrwHNleU4JwIxjKsFAr91MCLbBV8POvPIr29klpQBgaaaqzv/vv+3DdftrFfdnbePZ2sRnMlkXAEfB9VKDX7xdgF9gdpdddtHqb5Zmu0pLMrwfX7+P6u23SiJZpYhm5+bUyIram9dUgZnP9JT73JpzjcotkAWAsQfKL88jnrk+yRPT2o2Fv/e+973qW9/6ljriiCPUz3/+c52vIrRggWCBTcMCAYA3jfMYjiJYIJUFeAGKevFwDZQ187IkhAISScxCsiv+m7ddeOGFGjSJSXa1RiS7ArApDyWJvIBxVNJNtXG8KEmoSgAxbtM0YuFwPZSYQ2CYJGA3PL2vjgcWV2j6Tk3NqRUjJsTVWsuGYIHd5wxX1dM8AMzeylSBxyY7VU9ndNxv3LWRB36rUFzdg9hpPrxSPb26YsM37P2wUwEuIvsz44f432KeACSpA34JFyGcIu3CY9QseDbKfXzWT7bQ3aYmptTgaOW57EpGBQSb7c/3PFLzb9TfuMzQM/MLZ92OGvKu36E49bdR8PuhD31InX322erlL3+5+tWvflXI71YxV0YYJVggWKAICwQALsKKYYxggUVmgbQAnCXzMuoFya6IKQWQcFNDAS6iUYORDMv77rtvzXCNSnaF/UgKBgwSJ8uxpU0YVYQdmjWG6WIJDJOYpwKXbRqIUWbumXmV/qyvrxLPql+0pyov0gLBPiqwDbzAcB4IdgEwc0qjAuv+8/HAQK/doiB4fKo21re3qwKlaeCX/rb6K/sXe5r2efLpyj5gGI79vcdUS+HEXT+cY+BLsoabbrRc8+IOn2dBa8MDtzqnsNQVYBaXgF/+S230rOEiPs+Hf/jsGg3AtCgItgGYvgLBpuuzC4IFfmUuJgSnVX9N+CXB4BZbVAC+yMYCwSc+8Qn15S9/Wde9/+1vf7tJL2wWabswVrDAYrJAAODFdLbCXIMFCrJAWgBGjbj00ku1CoEbdFKTzJxsR7ZmXuKS4taSxjS/JwkWmU5f+tKXLnzcqGRXHBNgzzFutdVWao899qhzAU5zLJtCX2zyl7/8RVEuy3yptSFYAJhjBoJtABZQM23igl3ze3GTjqoJ7LJvHhV4/UQFeLs64pVeE4Jt8DXnND7Vpvp7qmPFuT2zXRL80kdsZsIvn7/vVX7w67JZVGw4ydEEhtPUlDYhj4zGPCdCU3rRAfjlnuJZ24h8AjYE+6rArrhfG4JtAJZzDAinUX+xC27PXIdlwS+/Iaeddpo688wz1f77769DbYiZDi1YIFhg07NAAOBN75yGIwoWSLQALx4SB5bYWSt3UwrVlZcxEmHFtccff1wnhGIlnSzNZbzAUQaJmLIDDjhAT6VRya5QOoFf1G0ysRKTVyTY+5yLVuzDYgAZsLELSXqAIinNcsfEUXrKogSbEMznw4O19Ymi3KCTjtsEYDN22Fnr11ESifFNFXjtxqqy293pzgqdBMGVazNiZ0op4NduXR21+4qK+62H4cpIwO/TqytALbVd06q/SbaW2HBRh6UeLR4e4g5PiEJUqRjJBs/10ijISzqmVvgehRP4xS48O7feeuuGTevETz1Zs6+Bwdp4V5cK/MAt9znnJxAcBb/6vphfpensqY1Bdrk/C/xiF+A3TyWCKIPyG/K5z31Offazn1V77723IsyG/AahBQsEC2yaFggAvGme13BUwQKxFkgLwMAsLwQonrj7uhovEPfff7+65557tDvwX//1X5f2AnHVVVdp9eDggw/W8Mv/i/szMahlQCmuvrfeWnHZ5OW0jJewxXjZkgGb7N5cIyyOmHaR0izn3bCNPjQg2Abg6ek5tWK06ibtSoaVpAKL3VwqcHt16AXzdlqQKV84Spvqr6IAmO+iIHjDRMXdub+7Xil2gS99xydrJ4tn6vBAdfso9feJp6t9Zub/tyz4ta9R7jsWhgSGpaY09yA1aEUdxmODRl8yyrMAx33EMyU0pbM8A78sJnAfNcMuJgTPzl9IgyPzscGOGzMKgDmfQLAPAJvnfuUP63M64CmA8osiXpZduIY///nPq1NPPVX/vlFloIySSuE6DxYIFmgdCwQAbp1zEWYSLNAwC6QFYCaGOxgvBa7EU4xHTCz1gonNJdlVmRkzr7nmGv1CdMghh2jwklI9ZcCvZLEWsOcFCVfP0JT685//rO644w6txpMELEox+doFFfhxqcAAMC0OgosGYPZXFATbACzga14fJgSngV9zDDuZmHwn9uPfLvjl8zyuz2mvc4BFYJj4f+4fGs8F/vAQ4X4tq3RN2vm2Qn8JGWFRoCz3Xt/jfOP7H1L9g5VawALB+vyNDKg0KjDwG5UYS9Rfe042ADcKfon3/fjHP64XZH7/+9+XklXa1/6hX7BAsEBjLBAAuDF2DnsJFmgpC/ACKiVtfCcWlXgKEMX9lUzRlKOgLEWU66PvvpL6XX/99VpJOvTQQ0uFX+wE4BHfSrIfVO0ywT7puFvle1H7UfxR9rBLUgZsE4JdKrAcGyBchBu0aauyVWD2NTkd7eosc2l3lFviO5fya87fhF8+N+0nACzwq8FlfsUAO65dO6k+fYLbhbvs6wmgw0NAModLzCeu0iQwQh1GJS6jNnfZx1bU+KYiXlZJn7RzFQg2AZgxTHBdNp812qUC28qvDcIuAHbBryQCK8sdnOcYmZ4/+MEPald8fuOaobynPT+hf7BAsEB+CwQAzm/DMEKwwKKzQBYAJgkW9V/NxFNAL+6MEhNLrcoy3I9NA/PSwosRL9a8GBFryAt10ftlgQDXXlQs9tEIsF8MF5K5KICiB/xyXfi0KAg2VUzGAeY2X17rDtwoFTjKDZp5uVyhnx2rzLO3Ox4yN060qYFehzu05fbMWPNJeRdMmlX9XbN6Up36tubAr3k9SF4APAWAXp4bUkaLz7i/pIzWUsqmLs9P7imeL9igVZoPBMtcn1z1WM20Xa7PAsE+6i+Lqrg9c42QZHCbbSohFEU2fkeo8XvKKacokrCh/JaRr6LIOYexggWCBYqzQADg4mwZRgoWWDQWyALAV1xxhYbMAw88UB8n7s4SE0tsViMStkiyK5TH++6rJGBBPUJFQlHCRbuIF2iS0ZDsiuQr2223na7DuZRVKrmwUfRYFHjmmWe0rXHXTKP2/8ePO9XQYKfaODGrBgdqSwK5IJj9Cgg3CoDZp08ssICvedO7IBjwtZuAsK38poFf+sapv6ufaQ34xU2eutDcl4RP4Clglhy3dhkAACAASURBVNFCHQYEpRVVYqnVH8aUlcJzhmcx4QMsArRaA4JnZ2ZU/2C1drsLYE0Ajov75fjaHO4Ypvprwm9ZCdK4/s4991x10kkn6ezjLO6WWWqq1c5rmE+wQLCAUgGAw1UQLLAELZAFgIm7Rekl7vbee+/VAIryR7zv8PBw6Va0Mz2TLMaONQTQeYHGFZs/SbyTZnIovkAeCnDZNTjTzKvZfcXVnWQ9KDLPf/7zMy0KnPWLStbXqcmKGrp8tFIbOgqA5bgBYR8IdiXCYowi3KDXrm9TVtLautNiQrALfmWDDkdyrjjlV9tsvo6ybS879hf4bWtXTXN9lmN86KGH1N13363DBnhOkB3c1cx7Gc8Oiekn7ECSaPGMKdrLo1n3FM8Y4JcG/LKA16pNIJj5CQhHQXAS/NrHKDD82X+e0+eZc3z77bfrhccy4fe8885Tf//3f68VX0rqkbk+tGCBYIGlZYEAwEvrfIejDRbQFgAmpXSJr0kk7halApdGXlZwf80Cmb77lH6S6Coq2ZXUKCVTs/kCTQ1HgWFeppMasb6oVai9qJut5JKYNPcyvzfLHOHmjmqSB0ZcEJwEwHJ8ZrKsqGP2zQbN9j7JsABfs8VBsABwHPyOjVdHm883FOv2TO8k+KUPsb/AL62Zrs9mjDj3HfDr+5yIK7EkbtJxJZbKvA+KGJvnE94l3D9lZsovYq7mGMefcv/CPwFhG4Ifu39Vpl2e/tFO7VEiz3YGYUGAEnMsZhbpecN1+dOf/lSdeOKJOls9bs9494QWLBAssPQsEAB46Z3zcMTBApkBmBcVGolCcHsmfq/MJqWN0mR6lsQ7wPBTTz21UO+YF3FgmJdowNgEOPaDqv3ggw/qF3VUGeJbQ1N6QYG6zoBJUWVrcIXu6m5fUIH1S+9oV6IK7DofLiDOqwKvWadUV2d0Uqs4AN6wUan+StJrZzPhVzqMT8ypoWW1+4uK+2UbV+bnp5+aWNhfs+EX1ffhhx9eyAifNSwhqsQSUETGcbvEUqvfrzyP8C5h/o3ynCnSJiYEu1TgZ5+s/D74tgvP20d3Nev8ElIhNer5fzM+nFwPWRvX0q9+9Sv11re+VY+J8ovKHFqwQLDA0rRAAOCled7DUS9xC6RVgHHZu+GGG/QqPQrgzjvvnEsB9DG/Db8Aq/z5bE8f5gu0A8O4S4vqDeTy8gwQA7qovvQBjIFf36ROvvNYrP1EEWehg7I1RbpquiCY+GCzmZmNfW0oQOyrAj+zdk51R7xXp4Vg4FeaC4Kj4Nc8NkDYJ+sz22Cf1asn1exMNdFVM12fzQRpqHconGlixJPOcVyJJbmfiTHO452QNIes3/P8AX6xB/DLs2axNgHhvBAMAPNMJuEVeRcIOSHnAh4n2IsFA7Jk0zineB2JFwALmr7nmd+SCy64QL3pTW/SY6D84uETWrBAsMDStUAA4KV77sORL3ELEM/r0x555BEdl0XjReKwww7TWZfLbHa8Ly86eV3hGJNkO4Auf5KFlrH5jhd2IC+rWlWmPRo9NvZ44IEHdJy3b5mjLHMEgu1WBAQzpivGtr3DrermBWATfM3jMSHYBb/0Rf0128REbabo/r5qsDDK7+o1U7r7jAG9JgA3S/0FfkmKx72Fwsa9VKaHCDH6UmLJ9PSQxS1ACZU473Mjy3Vtb0PICLYBfkkEtql4lwDCWSFY4JeM/uQVwBV5hx12qDM3v1MCw2Z4C3HlAsNx55lnGeWN3vCGN+hSdhdffLFemAktWCBYYGlbIADw0j7/4eiXsAVYeeflIKrx3V133bXgFsxLBpmfqb3rG8+Xxbw2/PIC67vS77s/9sFLKcqv1CbV0NTRobMby4tV2aDvO99G9rPLHKGIl3W+P3VO5cj6+6sgPDmfHGuzFZVkWVlU4CgA5vMiIZjxpmeyn50k+J2aqoVhsY0JwK0Av9xDqJsACtnYCY9oJHhyzZJVWZLimSWWmn0/P/bYY+q2227Ti4aSBTv7FdOaW77qnbfpifX09+n/ToxtVFMTlVj0WccNYsMvZYjIK5DUuM7wRhIgJjGfPLfFVZr/mh48l112mTruuOP0ZytXrlT77rtv0m7C98ECwQJLwAIBgJfASQ6HGCzgskAcAEsNXJQVwBcIIqMr5Ycog4SbYRkNMOUlJyrZVVH75AUKRYb9UGcS9VeUYSnJAnTj8itxw0vBLZrYO+J9AZlG1T4Ggl0AzLkGgrMCcBQEpwVgxnG5Qq9bX4HTPkOhdV2fG8Zm1UB/fcpnG341OFjqrwnArQq/PCtI6gSAkh2cuMqiF6zS3PdRJZYkQ7zEDUdlpE6zr6S+hBDgPcOzA/j1ScSXNGarfy8wLPM0QVhifrlmUH5xdSakhoRXaRvnGeWY3yizlBZJrhj78MMP19mdP/axj2nlHRdos4Z92v0V2Z/5XXTRRYrEktddd53iOuEaEaBPuy/uvVNPPVX97Gc/Uyy4kODrta99rTrttNP0b1towQLBAvUWCAAcropggSVqgSgAJhbrpptu0jFZvNCS+Ag1B3fYe+65R79EFF32KEuyqyynjf2sWrVKK9soMrhpAvhmE5c7gJj4YVHJzfJKuN9tao2XL0CGl9I8ZY6y2CUOghlvdLSiBqdtLjdoxkgLwSYAC/jKXKIAGPA1mwnBRcAvY4v6u3bNRvXFU2Iyb6U1nGd/niE8K7hmcF9FyWsm/Lqmzf0skNTIEktS/xjvCeC3EcDtedqa2s2EX3JJFFWCSCoB/Pu//7v60Y9+VBPiAgy++93v1t5LrbCQyXx+8Ytf1JyHrADMNc1vMr/N2HLvvffWiy78sbhw7bXXtmSN6aZehGHnwQLkFZiL84EMJgoWCBbYZC3Ai4hZeoIDlRIdfEedV15q5YUWBfiOO+7QLmRFJkMqItmVz0niWAFfYppRYlC1k15KsQMvz5JRWuxFDF+rJ93xsYn0QUmhLikQzEspikyjQeYj/zOtRkcrEGeqnfxbfqaWL+9Jc1i6bxGxwIwzPh4dLmBDsA2/5qQ7HHHIccqvbQ+J/W02/HKtoGSRwbdZ10zaiyGpxBL3NM+2vIm7WGS78847df1j4HdTXDBLa3v68zxlwYTEVsAa100Z7eqrr1avfvWrdYItzimqKI3n/hFHHKEzQb/uda8rY9deY55++un6vtlnn330H4ptVgB+29veps4991x17LHHKuoby7V7yimnqK985SuK7885Zz7WxGt2oVOwwNKwQADgpXGew1EGC9RZwAZgypYAuJLx166BCzgSy8YLXVH1cctIduU61RwrLs8APi+4e+21V+pEXrw8S9IdXO4Yk8bLrdQaRhlvNDjmvbRRuYnf5PhwB996663zDplpe1TgiYlkCGbwNCCcBoAZ206ItfbZipLb0x1dFqlyHVTcnOPgd+PGSsDwsmXVmGcbfiugUFWPXa7P9AGAm6X8ipcIEEzm3u233z7TOW/mRnEllnhGSB6AtPHvPEdZaOO5gBqXdvtm2qTMfTcKfnmWHX300VoB/vnPf65e8YpX6MUISiD9+te/VsDxe9/7XvWFL3yhzMNNNTa/GVkAGLDHW4ffbBZdiL+XhucDGbV5vuONYH6XanKhc7DAJmqBAMCb6IkNhxUskGQBAWBJesQPKIooJTpcMb4kwOLlAuWUFeu8rRHJrpgjL0Kom+LSjbKdN0GPJN2RuGHJqE0GaYHhVslAG3eeOKe4yvECxaIAcb/NbALBzGFgoNbt2XZWmptVasVmyYpwFjdogV7bFkkQPBstEiuBXxkTCF6M8Iu7Myoe6hrhEc1aMCn6Oo0qsUS5IokbTiqxRB1xXFFRGnmOBvitnCVyC3DNkF8B75KyyujxLDvqqKO0S/7555+vQdhekGQRk2uXWvat0rIC8Le//W31zne+U1dmILu13f7u7/5Ofetb31L0e8c73tEqhxvmESzQEhYIANwSpyFMIlig8RYAgCXuk1ViKV0SVQYI1ROXRzK8brvttrkmLMmuxP25jEzPTJDkIMS1cqzEJ5ou3bkOwNhYlCSBYVzbaLiiyYszmWjLLAmT9ljMMkcoD5QFaZXSLLhCSzMh2BWtAwSbLQqIfVTgNfPlhXp6OiLNGQXAG8aqqaD7+uq3t+FXdsDnQ0PVkmI+WZ9XP125vmiNjvvlfmIxCW8B6qhuqqpSlhJLJAgkTwKQDPy2Qqxp2udCGf1N+CXTM3GpZXjJoPICv/yW4QqMi3MZ+ynDRlkB+H3ve5/60pe+pD70oQ+pM844o25qX/3qV9V73vMeRb8vfvGLZUw9jBkssGgtEAB40Z66MPFggXwWoJzEDTfcoBVSXBiTlFFeLMhaSZZXV71Gn9k0KtkVc0HdpMwRjZd1lNlGNOJpWSygzBJKBA3AZ4FBMko3s7wS6jUvi7jF8bIO/LaaUiUQPDUxo0aWVxOOuVRg+5y21SdcVh0RMnBnp9utOQ0Em/DLXGwAjoNfc+64f4+MVBVt0/X56Ser0Cs2aDT8opzhAcL+8QJptrdAI+5l9pFUYonFLe5zXJ9ZRAJ+Qy3xytkBflkwYeGkzCRpqO7AL4uQP/jBD9Txxx+/aOAXO2UFYOJ+yfwMBBPzazcSbZFwi34o4qEFCwQLVC0QADhcDcECS9ACvMRefvnl2iUNoPWJ4aPvNddco3bbbbdMmTsbBb/sBzWGP1QYXtZxY2xGE7dKXsxYcJCXHdyjBYYbCZ/NKHOUxe4f+MqE6ppXYk0I9lGBXQDMHFwQHAXA9PeBYBt+5VgFgn3hl+0AYGlTk1VFedqIB24W/HL9Uh4LLwYWTJZqaZWoEkuV66tD17IlPCQpuV6We2KxbYOXAG7PwC+/L/xulKHIPvDAA+qVr3ylLiX03e9+V735zW8uZT9l2j8rAJPQi3JK3/jGN9S73vWuuiniFk0MNP2ogRxasECwQADgcA0ECyx5CwC0xMX6Kjkom1deeaWGX15m0jRXsit+9It+IeKlC9WX5CCoMcBvIwEzzibEnaEMS3klyShN4izJKF1mnVDilFFjUKuI22ThI28sdJprIG1fgWAAWBpqcCuowNPTlu91ioNzQbEJvwzlAuBmwa/EiePSTwK8VnGVT2HyUrpyPkgaiCcFtuF+lnua+1jCHxZjYry8BuM5zLOGRb8y4RfVHfjlv9/85jfViSeeWPhvSl5b+GyfFYCBWyCXYyfe127AMfAbANjnLIQ+S80CQQFeamc8HG+wwLwFeElBEfRtxAtfeuml2pUNePJtAr/y37LifQFM4n0Be14+cXtupbhb017YHZdS3KQps8S5oPHiLEm0AI2iFgjMMkcsYPBX1Ni+10GWfi4IHp4vlSTj2XHAfF6EGzTj2Crws89OLhxGf381k7N9bBvWV+6rASPbM/9ebPAr5XxYRMK1t8wFmizXR7O24VlGGAGZ8VHDUcW5nwgTYZGLP55HNMIdBIZZbGzVZ1JRtuRZxnMYW5CFmCzhZTxrWHjA7Zm467PPPlv9wz/8Qyn7KcouceNkBeDgAt2IsxP2salaIADwpnpmw3EFCyRYIC0Akxjmkksu0QmwSITl0xqV7MoEvDITrfgcc9o+qEa8LEoSLSmvBHQIDPOSnfUlslXKHKW1i/QnHthUgfl8ZmZWLd+sf2HIsiBYANgEX/M4XBAs8Cv9BIKzwi/jcB81OuYX19J77713ITN8qGVbOaOm8ku5JLxMbKgtq8RS1nuoUduZ8MvvBHklsj634uaMhw/we/fdd+tatyeffHIp+2mU3bICcEiC1agzFPazKVogAPCmeFbDMQULeFggLQADahdeeKGOceOlL6mJS2DZmZ5RUolP5Hh44cqboTrpuMr8HlsRMycwjOpOExUJIEZF8nVdFvdV+r/whS/0dncv8xjTjn3SGZVEYr191bJIALA0QLgsAAZ842KBbQC24VfmODY2qZYN1pZsinN7ZjuJ/W00/LI/wJeSPiGjce3Vim0otcN9JVnzfRTdIkospb1vGt2f5y9J0ngeU5sWL6Ey4JdnI+WNCHU566yz1Pvf//5S9tNI+2UFYN8ySJRCwj08tGCBYIGqBQIAh6shWGCJWgBAFbXR1wQAMC9+xAJGtUYlu2L/uGjeddddWoEB8FBkNpWGHVG2cZPGpZL/p3GsZJ4Fhvkv8Yd2Y1sABpBptTJHWc4PEDw1Ma0GR6qqrwnBjDm6vPod/06TDIv+ZkIsU/GNA2C2A4KjwJfvgV9pJgT7xv2uWzOmPvePM/ra9oGtLPaVbUx1k9hVXHubmbE8z7EUvS3Py9tuu03fj9x31M3Ocj6ylFgq+liKHg/bAL+Ec5QJv8A18Hvrrbeqz33uc+ojH/nIoodf/axqa9PPaVnw9D0/LMSw4MtvAL+FZqUDcj7ggo7NcBdn4Tq0YIFggaoFAgCHqyFYYIlaIAsA4wJNbOq+++7rtJqZ7IrxJd63aCWA/eD+RvITXDN5Ud/U4xOpLyzKMHHO8uLEgoQk0aL8CnZnUYD4xFYtc5TllrMh2AZge0yA2DcWeO3qjaqrJzqmNw6C1z87oQaW1aq7MhcTfs35dXXX1gp2Jb16dvUGvckbX/q/+r/cS4AX55r/Fl1qh+sGdRP3UmCbBSXX4kqWc7fYt8E2QBf3H5BBfgFfL4y4Y48qsYTd5b7mXLfyIoQJvyTX22OPPUqBUjxjjjnmGJ1c69RTT1Wf+tSnStlPM67VJAD+r//6L8UftY0Bf7OdcMIJ6vvf/7467rj/v70zAbeqqvv/KrWcslfzzQlBRg0sMhlEBRFkUEFTxBFkULScEFELEBFFUNOQQaVARVEBJcMBAUHUEAUcygFFFEQcoNTKnLL+ve//+Szf33VzuPeefc7Z0zn3u57nPih3n73X+qy1D+u7flMvN2vWrKp3dvDgwW7ixImO38+YMSONYemZIpBpAhLAmZ4edU4E4iNQjAAmCRYn1e3atduiY9Vleo5ik5j7IBJIsRnF2kBsLBv1qMVAfNSjuTOWAssoTaZVyxAMDyxMZPdGxGClyvLmuVAahYrgb36z+jq/W29dTbFgXM0LFMGIX2u5Irgm8fvPL/692bCxbFv7f//+OuM1czrt8l0cBx8214gAa5TSsoOPUuNzcV8ljIB3KusJ5ApdM6VeHxR4u+22m89/EMf3Wk0llhBHvNeWSCtLJZZgw7phfe6xxx6uRYsWsYjSf/zjH+6YY47xdeuHDx/uxowZE8tzSl0rYT8/b948d9VVV1VdvmLFCj+e4MHyyJEjvbWbhuAfPXq069evn5s+ffpmj+GdPeigg3wysMaNG7tWrVr5gyy8Ffj/5cuX+wMzNREQgc0JSABrRYhAHSXAhssylYZFQBkkPte+ffvNPpJUsiuEHxYA3IHZcGFtiGMzGpZHFq5D8LIBxXKHu5s1LPWWRAvreNRW+LTGPuiqr+op4w6dzwrMddWJ4FIFcFD4BjmYCC5G/HIfE8AmfnMZ876y4cUSyVxb2R0s/SaGC80ezoESWXs5SNE7tTnxYFxr0mxwYWWuebeDc52VEktBq3ic4pfv+p/+9Ke+Bv3QoUPdddddV/bf+YjYfDG5xPf2798/rwDmAt7dUaNGublz53oXfQ5qjj32WC+aKyksKK1/c/TcyiQgAVyZ86pRiUBeAsUIYDYhbMw6duxYdX9LdmWb8bjKHOH2y0YdEdCkSRNHtudKEXV5JyvPBVh8X3jhBR9DxuaHOWDjbGWusBqZGN5pp53KnpuJYLBs/51ta6UTpRU4aK2t6aHfqMHqXJvlN4z4zX0e4gxhZGV3gtnDzVqIlbi2AyLeJQ6UsLDFWbKm1PWdxueDGY3jdO0NMzb6Ul2JJTxfzC0+yRJLQfFLbClW8Ti+i/F+wLX3D3/4gzvvvPPchAkTyl78hplvXSMCIhA/AQng+BnrCSKQSQLFCOCVK1e6Tz75xHXu3NlbgoNuzwwyLvHLqTYuXTQ2W4g8ta8IcPrPwQCbZDKvkoSGxiaV32EtRCRxcEHDhd2shfkEUpYZmwj+n/+robzjf+1QY3ejsAJ/8vcv/P233W6bGp/zxWdfJbzaPifjc6745ZrqXJ9rsvzmmwfmmgMim2uyDtOIJbWEaQikYEwv64FDEyxsDRs29O6ScYiYfH3P4u85OOJgAJfzOMv5FDP2MCWWeL95z+NowWRgcbqEs4ZPPPFEt2TJEnf22We7m2++WeI3jgnVPUWgjhKQAK6jE69hi0AxAvj555/3bnldu3b1AssEMBtn+4mSbDCbMdYOyi+RnVbtKwK4PXMwwMED8b41xXrZptmSaGFZMYFkYjhJC1JU85crgrlvdUK4WCuwid5gf2sSwCZ+7VoTwXGL31yWFktqc82BFY33E3dIPAFwkyaOHpHRtGlT702h9hUBLOmIXw4UysEqzrtsrtLBfAB4epgnAC7yURxuJCV+OZw55ZRT3MKFC72r8NSpU4vKuK01LQIiIAI1EZAA1toQgTpMwKyCYRFgaUR0YQGmsdlmYxVHHC6bLWo9UuqBDRzit9RkP2HHmfXr4P7222+7N954wycA+8lPfuJFTZhWk0CyLMNWXqlckmdVJ4L/53/+1+20y46b4SjECvzJx1+4bb5Vc1boXBGcK37twf/84l9buGhXZ/n99O+fupk37B1m+gq+pqaEadwIgYQArvQM6mGhIX6xiuMS3qBBA88mCuEY9vmlXkf/g3HDFgKx7bbbVonhYr0++N7gsI3v/ygzYeeOGbf8vn37uocffthnMCZetphyU6Wy1OdFQAQqm4AEcGXPr0YnArUSYLNhGYTDoMJqRE3BDh06eHfKuFye6Rd1JXFBxKpJ2RGVZPlqhpgvyhxR9xHhQgmoUg4GsAKatdCyDLPpZ6NsccNxuVOGWXNhrjn14nfddjtuHguMCA62rbb+qvRQsJYwNXa33mbzkkT2mdoEMNcggmsSvvwe8Zvb7J6fffy5+3///ir7M/MZl/jNfT5xpOYuz7trcfsWI44gxsOinERfmPUR5hq+cxC/WMwrwSXcQiAsRtxqzBZTYok1SmZhDiNZI3ibxHHoiYAfOHCgu//++737M+V99L0fZvXqGhEQgUIJSAAXSkzXi0AFEShEAFt9WSyPbEricp0loRMuiAiz+vXru2bNmtXJDXl1y4w4Xw4h2NQiUCkBFaWllvVgcaQkWLLDEUSRieEslWEJMsoVwbkCmGtNBOeyLUYEf/7JF267HapPwFWd+P1XQBCb+L3n+nqJfZtYrDjvMQIGl3dLrMScW0Z4PArMdRaX6bpgfWPshHcQD00sdKNGjRKblyQexHvM2PjewEIcrCOer8QSn8UT5/33349V/GKtPuuss9zs2bN91mf+rGvl7ZJYC3qGCIjAVwQkgLUSRKAOEwgjgIPJrnCZxgLMRspiC9kgY6UlIUpuop1C0bIhx/KL0Nt33319DJ7aVwSCGXuTKMnChtRK7vAnc0LDHd3EcFSxhaXOMWt0zZo1bvTUHXw/d/zuVwmxworgmgQw98i1BCN8gy1XBGdR/DJ/vFdYdgklyC2NEowR593mEMofGGy1lX+ny80tvpD1xHca4pcxk10e62+lN8ZslmG+c80TILfEEhxM/PIdz4FbHJZf3tlzzjnH3XXXXb727e9+97vYknhV+txqfCIgAuEISACH46SrRKAiCeByZpuf6gaYm+k5mOwKCy3ZmbEemUWBzREbZsQwG6ZCrJMI69dee81vunF5rimhU0VORJ5BBa3iabhnWhkWsw4HS+6YGMaSlIbrLOsX90xiE+nD+Nl71CqCi7UC5wrfXBFcnfD1BxcpW34tURpeG7jLh0kix3ozgZTrFm/W4VLc7rPyDuMWjPglkRSeJsT91rUWLKfFQUnQE4A1AxsOTFg7cYhf3t/Bgwe72267zSdXpJZtJayturaONF4RKDcCEsDlNmPqrwhESKA2ARwscZQv2RUbSYsjxdWSZllnEcNsmmtyZ+Peb775plu/fr0jWQsbLSyLal8RQIAQt4lFdr/99vNlWdJsbFjpEwKJObfYQnOdRRCzYY5js5w7bpi89NJLvh4ua4yDEw5QcIc2izWf2f4722/20bAi+NOPv7KEfnvbb9WK/J+ff1Viarsdt6u6Lih8+cs03J45VMKCx9wceOCBRb1XWAvNEyBoLSTpmoVBZMUToJD3ggM8xC9/8l7J2+SreHQOM3m333333ao64rzLvNN2+BFVTgC+Sy655BI3ZcoU16lTJ/fQQw+5rIZYFLK2dK0IiED2CUgAZ3+O1EMRiI1ATQI4V/wWkuzK4kgRR2yYLY6UmFUTwwhdGiKFzKJci2UK90zFfX093Vb/mMMExB0b0Cw15hZXeDv8MNfZ2urPRtX/oEs4tY8RMbmi+6Qhb1f7OARxdSL4n5//s8buVSeCTfjmfuhf//zSbbfD16L7k7//w/3+lmZRDT3UfYjVxy0caxpZwqMQFhw4cNhg1uFglmEOPlifWOGTOPwIBaGGi7BqIn45vKF2dtqHSqWMJerP8k6vXr3aC2CL/ecAhEOvYE4AE8O4TRfj+YH4HT58uJs0aZJr3769e+SRR4o6oIl6/LqfCIhA3SAgAVw35lmjFIFqCbCBDVrKuIhNDn9nrtGFiN/chyCwzVLIxtnuycYKiwLCCdG0++67u+bNm9eJhDthl6IJGA4EsIpT1zPrjbk0N+mgW7zVn63NE6CQsWG1I2MvQiafS/ixg15z2+64uQXYnlWdUNuqhqzQfCYogmsTv3Z/s/omKX55f9etW+d/ECeIXztwKoRxvmtr8gQg7IHwBeaaP7OWRIs1ivjFst2iRQu355575htqnfl9MMM87ywHkjZ/NZVY4oDF5jtsiSXWzhVXXOFuuOEG165dO7dgwYKy+H6rMwtBAxWBOkBAArgOTLKGKAI1EQgK4Nx4Xz5TivjNfWYwqRKi2MQwAg/3Q6zDqkcafZmjtFZ/TfVnrbwSAqmYFZuxoAAAIABJREFUWD8szmQJR8CQKI1M4WFadUK4JktlbSL4y8//6b617be3eCRW32BD/CYpfO3wykpkcWDCwUkSHhWWZdgOPyxBnrnOmnU4ib7UthbIhIz4Rcwhfkkmp/YVAUskt2HDBp9hnrVT0+FFKSWWeM7YsWP9T6tWrdyiRYu814CaCIiACCRJQAI4Sdp6lghkjIAJ4NqSXUXdZTbJlPJhE8XGh02puVJmMcNw1OOv7X5Bl/A4yhwlOZbgs2ryBECkmTgKE/dtpXzgtP/++3vPgUJbrhAOI4IRvdU1E8JB8ZuG8KVvvE8kkaNcDe8VAiatGqpY6M1Nmjkz19lgyZ2kD7sQ5YhfvmsIJ+DATe1r8fvGG284vE6YI7wGwlrugyWWmPN//OMf/qZWSxzeePwQosC1v/rVr9zo0aO9dRnxm7VkhxzcjRs3zs2cOdNxGIAlvHv37u7KK68s2FUey/aECRPcs88+62Or+U5v06aNGzJkiOvcubOWnwiIQIoEJIBThK9Hi0DaBNic8MPmmZ98ya5K6S/3ZoPFRgs3STZAbLZ4LrHCFkdqGYaJWbQMwwilYuLMSulv0p8lppVkV2yU2Jwj8LIeS1kMI8QrMYW5caT55tsOTlgHlGMh23gpDSFs7Rvf/Ga1t9rm29vU+oh/fbG51feBqT8opUtFf5Z3iEMlGCEoqPMbVsAU/dCQHzTXWfpGGISFXFjJHd7xuN9vRBku83zXwYZnqn0tfi0JYRQHJ7kllsjuTGbnffbZx3+vrVixwlvflyxZkrl5QPwiTJ9++mnvHUBsMskZV65c6V36n3nmGV8nOkz79a9/7YYOHer/3TrkkEMceQoIS0AM02655Rb3s5/9LMytdI0IiEAMBCSAY4CqW4pAuRBgQ4jwMvEbpctzkAH3J7EKWWnZ+GKdqs791eIK2SyTAMpKchDDyKaVDRTWhEoTw8EyR2wUqUdaaWOs7p0wV0o7/LD5JstssLwSVk2sm3HEQxcqhLMieo0ngpIav4jLrB+cWDktO/wIltwxT4CoM4hzoIT4Za1xcJI1i2Oa/1YEM/DzvYrlN0qvAeabzM6zZs3y1l7LGI+YPPbYY90xxxzjBWcUCdqi4Hj55Ze7q666ysclP/roo1VJuUzMdujQwT355JN5H8X6tsRqjz32mDv00EOrPkON4969e/t///g3LoznS94H6gIREIGCCUgAF4xMHxCByiDAxvCwww5z3bp185sRKyET9eiwAFGqBisvm1ssMGHqA1tJDqs1HCy3Y2K4HDLO5uNpZY7gVJfLsdh8mxjGjZbGoQziBfHLBp3yO0m0o/u/XO1j5k3/YRKPD/UM1gxeA6whLExkNC6Xg5NgyR3mnIRmNCzXwSRaYb4raoIFF8Qvz8LjpFSvgVCTUiYXwWTt2rXurbfe8oeKUYtfw8Bzbr31Vl/rlzX605/+1D3++OO+PBcNIXj66af7UkhpNt4l/l2xNcMhbbBxeMK/Y88995wvKVZbe/jhh13Pnj296/T8+fO3uJS1yKEV1nBcotVEQASSJyABnDxzPVEEMkEAt66jjz7au6PScO1CCB933HF+sxiF+y2bWjboWDg5ESdpUTH3tXI7JoZts8zm2GqRsrkt5t5pToa59dIHDgayVuYoLTYWV8gm2WIKTRwxz2xUEUmliKO0xhbVc7GeIu6IbW3QoIFr2rRp2Yjf6hhUl0Hc4kjNOlxINmsO3PjuofF9xuGb2tcEEL+45OJ+jviN413iPZ4xY4Y755xzfLZ2hK8lrcPtGuvwgw8+6A9fJ06cmOr00DdqEfPvIH3LbViGsRCPGjXKZ7CurWHt7tq1a14BTDgQ3j5qIiACyROQAE6euZ4oApkhwCYaly7csojTQmDS2KQghjmtb926dVHxhCS/4ZSbk/VmzZr5e0ZhnWJTxWbZxDBJtGhWexY3UERSVmIga5psEqyQsRfLJht0rDBqXxHA4kt9aOaYxDEcnFicOBYaGmspWF4Jt+m60vCGIKETB0Fs2BEXUbxbWeFncaS5tcQRa3bgVVv9WdzBEb8wQdwpy/DmM5uU+MX1edCgQT7L/xNPPOHXaXXNck+kuf5uvPFGn5wK9+R77713i67MmzfP9ejRw/+b+Pvf/77WrvIdRSgLXiy5LtD333+/O+GEE7yb9bJly9Icsp4tAnWagARwnZ5+DV4EviZAPPBTTz3lxTD/wBOvS8NtjVgtBDH/aIeJEdu4caNbtWqVt8hyuh+nZdMsR2yWzVrIc7EQIob5M0yfk1oLwXIjxL6xQS+mHFBS/U36OaxDDk4QvFj+WD9By35N4sgyDPOZrMQUxsGO9Y7lFxFcSBmoOPqSxD1ZDwha3m+8VSxjPO+MiWHm3g4AuIb1w5rh3dLB0uazhNUXAUwoAa68cVl+EXoDBgzwmdpJeMUhaJbbRRdd5MaPH+9FMDG/uY01xUEla4rDp3xtzpw57rTTTvMHwJYEC3dzkmDhGj19+vTMJQHLNyb9XgQqiYAEcCXNpsYiAhERYJNJfJKJYTJh0hCUdgpOhszczVMwIQ8WOeKokorZpH+cuFsMqVkKrRYpfWfDHMeGLyz2YJkjNu1sqNLsT9h+J3Ud4pYav7j14jJPTHRtlk3LMEzSGYSPZRiu1HJacEH84rlBJt0999wzqanJxHOC9Wd5z1kvNAuFwJuC7yr+H6GCxVjtawIIMNx74xa/uDb37dvXHz4ifolNz3o766yz3NSpU92IESPcmDFjtugu3AgzQMjjuROmMfaTTjqpKszI/g29+OKLvdDOupdSmDHqGhEoVwISwOU6c+q3CCREgE0nJ96caGMZJm6JhpsxMcS4hB1++OF+M8qJN5usSZMmeWtxmm6p9MfEsNUiDbrNYilkw5xUyy1zhIDRBuhr+rjzIu44xCjGrdcyDDPnCGIrp4Wl0DJKl3MGcQ50OBxgnCrl43xiKw4EbL4tFIIVhds8hwMIsCTf8aS+S4p5DgcDfHdzOITlNw4uzAlJn0499VTvdo77Lx4c5dBw1Z42bZq77LLLfCbo3AY7xG9YAXzDDTe4Sy+91P/7SMxwo0aNfMw1ccSEG/Xq1cv/m6omAiKQDgEJ4HS466kiUJYEEMNkwuQfblzcKE1Dw6KApZXM0pSKmD17dqasL4hPRJHVImWjZhtlE0eFJNgpdPIQd4gX/qyEhEWFjj/f9biuw4d5wlpkJUTyfa6m3wfLaQUthWz6zW026nI7xfY1zOdwAcYFU9mMq6dFyAUx4xwoERscTJyGELMkWpXsGl/bOqL++po1a2IXv4sXL/YWT+aA/87NpBxmrad1TZQu0OTV6Nixo/dCwOU5GMLBARZ5Nfi+W7hwoU+WpSYCIpA8AQng5JnriSJQEQTYjBPne/PNN/uTc7O4YWE48sgj/cl3ly5dfDxmlhL0mNusxRQilmhYB628UpQxuRwKsNmp62WOalr0lq2X9YS1iDmIsnFfBJEdgBBDS7OkaZZROqvWeNYph070D0GhhE6brw5qRPM9hLcJlk3EFwcpuMTbgZe943w32QEIh3ZZ+l6Kcs0H72XiFy6tWrWKxfLL80hyhVWTg0Rq6CLyyqlFmQTrjDPOcLfddpt3pcalOrfx9yNHjnTDhg1zY8eOLSdM6qsIVAwBCeCKmUoNRASSJ4C7Gyf+JOQZPXq0t1DhJk2tRBrilxNuEmiR+CNrm05O49kok204GENKP80yzKa52BYscxSHuCu2X1n5HNxffvllL+6Ih8Z1Ne5WU9I0K6+Udpx4cPyIO0pBWUxrkvH0cc9DFPd/9913vRcKogvxW52Fl3ccCzoHIEHXeASzWYZZd+VWQi0MP8s0j/iFT1whKSRPPP744/17vGDBAh/+Um4tbBkkXJj5t6621q1bN38IQGmn888/f4tL+XvqIp999tmp1z8ut3lSf0UgKgISwFGR1H1EoI4R+M1vfuPrO2KRwh36sMMO8wQQwcQB83f8PPPMM/7v2aR27tzZi+GjjjrKfy5LFhiLIUWUsVG2bLNsHs0yjBgO22fbfCJesNwpG+3mL8g777zjVq9e7S1SuAqmIe44uAkmTbNyLAgisxTG6Rpf21eG8eH58GEdqn1NwPjgrYG4C+O1wfwSS23eAMSb08wbgDnPWtb4Yufc+HAogOU3LvG7fPly7+0D20ceecSRHLEcG14DfM/jsUMuglz37ZYtW3pPjJUrV+a1bvfr18/deeed7vTTT3d33HHHFjhIEHbXXXe5cePGuV/+8pfliEt9FoGyJyABXPZTqAGIQDoEHnzwQfeLX/zC8SfZMatrbIqw0pgYxlKAOyKikMRZbJxIpIX1LaywTGK0lm3WxDCbI5olVCKjNBlmq+szYyZhCq6HbD7ZSNXV2MOa1gRlWDgkyVIZKHObZc5xyza3WebZvAGSEKGsHxIWkXU2S3ySeO/CPsPceuGD+C3mkMLqiVsSLYsbtkR5iGF+irl32HHEdZ1ZxkvhE6ZvJEekKgCHhWR+7tSpU5iPZfYaEmBdffXV7uCDD/YWXHvfKYs0dOhQd+ihh7qlS5dW9X/y5MmOn+OOO86LWWt4QZlFnP/u2bNn1e8eeOAB/zsa3h2UMlMTARFInoAEcPLM9UQRqBgCxLWGLePDhnPTpk3eRRpBTMwYVlesL1gNEMNsFBAbWRLD9Jss0mYptNIr5kKJGDZrNuMhHhERhcUXt944sq2W6wJCVGL1pcY0wpLDgSzyqan2rHkDsEbjcOdnrSF8EcB4G2D5jctyV65ryEr5RO3WizeAuUlzAGKJ8niPTQzzzCx9N1U3hyZ+OazD8huXgCcpG4eXWNERdZWQzIk1QPIqSgDuscce/t8lDlv4fw5psXY3adKkCjvZnXGHxuJLXV9rrB1Cg+677z7/V8xDw4YN/aGfhQchtIcPH16ur6H6LQJlT0ACuOynUAMQgfIjwAaBzSYbJ8Qw5TIQ08ThcfqOGD7mmGN8KZMsbTgtoRICF0FsLpSIODZIWJGIMUUg7b///ipzFFiaHA4Q78u8w4pSPhx+ZL0h2hFEZik0bwCEhblJcwBSagwpa4t4Vg4HEF0cDoQ9XMo6w6j6RxkZvAfiLOVDX/kuIm7YEuVZfWksqjbnWSypxdrBqhi3+OWQj0SHlKGiVjxCOEvf06WsN77Tsebec889DjdywiHIX0FppL333nuzW9ckgLmI9/n222/3LtC4TlOmi++JNm3a+Lhg7qkmAiKQHgEJ4PTY68kiIAL/t1HAwoorNWIY1zOsrGyo2rZt62OG+alfv36mNllscNjUIIaxbJsYRghhFeYHoVeqMKqERYKg+NOf/uTjL3fffXdHDeRy5MKcEyNo3gA25wjVYHmlQjNKI7IRFawjyjPhOVDoPSphndQ0Brib2zyWdyzjSXkO2AGIWYfNA8RKajHvzFna82XZsAuJiS5mzeDBgfjlO5tydxxWVor4LYaHPiMCIlCeBCSAy3Pe1GsRqEgCJjDmzZvnxTAZRamdSyPWD6swG67GjRtnZtOFIELcYRkkgQ4bZCwjNDbFJoz4Xdqb5DQWDW6FlIHisIBDjGbNmmVm7krhYQcgJoYZn805c23llfJZubEuYiEiCzmfIVt4OR4OlMKyts8GY+pxm0f8pmUZr6mkFu81h13mKp10/0z84pWAu22YhGDFzBe5DRC/rPmZM2e6E044oSLe5WJY6DMiIALlTUACuLznT70XgYolYAIDEYybHRlGTVjiPosYJvkISUTSskBgFUK80IJljhDtJowQyDREjQkjNsr5hFElTCzu4GRURQSTKK1BgwapzVXcPKubc0uoZEm0cq2WxBpzeII1jZjD5s2bS/wGJorvgDVr1jgyqmfRLZz1bZZhvBtozDmurlZiKS4xapg2btzoXnnlFR/rG6f4JX4Vt13ENhmOTz311Ip9l+P+rtD9RUAE0icgAZz+HKgHIiACeQiwEcbdFPdoxPDDDz/s3WlpP/jBD7yLNGI4SQFhZUaw9uCyyqa3umaldnCVDm6Sg3Vnk3LnTHKhIfyx/CLymBfiuetKwwvASu0EEyqZMEIcYTWED3HjxBameZCTxXnhncfdlqROcCMmOsuHRniABOfcsogTr2xiOOrEabjME1dPojTEb1zZ5jmAoLYt33m33nqr69+/v8RvFl8a9UkERCA0AQng0Kh0oQiIQBYIsDFGYJA4CzdpEmmRsIZGhk4Tw9RtjMOVNJipF+sOLplhN54mjBDDWP2CdWfNSlgJWX9x58Uyzviw1mPxrquN+Gd4WEIlE0asTf57r732cvvtt18sa7VcmbNuSOaEtbEcY6Jxaw8m0WIN0KJMnMZ3COKXw7M4xS+JtbD8koBsypQp7qyzzpL4LdcXS/0WARGoIiABrMUgAiJQ1gSwvFBSCTE8d+5cn5SKhrstYpiY4datW0ciMILJikotc8SmGIsR/WWzbGVXglbCuN0n45h4XDJJ6ISFE6tdTZbxOJ6d9XsijOCDW69lFqbPVl+aQ5AsZhdOkivvGOIXTnhJcJBVzrHzjAfPD7MO4xFCw5ptMcOMsxDrtolfvE8Qv3HVp8bCTMwv63XSpEnu3HPPlfhN8mXQs0RABGIjIAEcG1rdWAREIGkCiMply5a5OXPmeDGM9YJWr149HzOMIG7Xrl1RG2ruTe1LLLdRlznCTRgrIRtb/jQrIUl/eBYZpcNamZNmHnweNTPZLGPFxjKO+6fa1wRIlEVMNJ4AWH2ZUxNGwezC5g1ACZY4vBiyOiese+JZeQ+Il4/LiyOt8QcTpzHvltOAOcbSbYK4Ni8QPAnwrohb/DIHlDeiNNcNN9zghgwZIvGb1sLRc0VABCInIAEcOVLdUAREIAsEEJUrVqzwYvj3v/+9Q5zRKMPTo0cPbxk+9NBDQ2WUJf6YeE2S3sQdr2nukyaGGQfNYgkRw1h80kr8Vd3cBt3C6RviF3dPta8JEOuL+GU+qRHNOrRm2YUtcZplPjcrIYIYK2E5W0LzrQXELy69MKgr2bD5XrEkWhYSASe8ACxuOGjdDYpfsuLHdcDEIRzil8MIauL+4he/yNT3Tb61pN+LgAiIQD4CEsD5COn3IiACZU+AzfVzzz1XJYbffPNNPyasTGz0EMMdO3astrYom06sILhaU8IH1+qkGv22WEI2yhZLiOUQIcwmOerEOoWOLeiymsVMvYWOJ47rETccoISJieYaDlpMDAethMHEaUmX2omDi90zWAqKdc0BQV2yfMMhGCvOO28u8ghgLMPMN2WIzPIbl/hlrXJASHby0aNHu5EjR0r8xrn4dW8REIFUCEgAp4JdDxUBEUiLAIINV2azDCNuacSqIoZxk+7cubN3473vvvvc0KFD3ahRo1zPnj296Eyr0W82pyaMEOQ0LK0mhpOOHw0KFw4TSHhVyVbKYubeSmVhsSdbOK6uhTSzEjLvzD+Ne+EebVbCcra2s4Z4HxF9lIJq0aJFnRdcMCF7uFmH7V1n7plzEqexjqI+JMBLgVCRZ5991g0fPtyNGTOmzs9FIe+qrhUBESgfAhLA5TNX6qkIiEDEBLC2kbCJ0kok0bKavsTe7rPPPt4lEwvMXXfd5bp06RLx04u/Hf0msY6JYUusg2i3+FEEfdQb5GCP2ZRjJaLcESWOKEcV5/OKp5XeJ0kihBsprswkBOOAopQWLLUTTJxWk8tsKc9K4rMIPdYQYo81RLmsLLn2J8Eg3zMQwRwQwIWMz/auc9DEoRPWYf4s1SOA+HQ8YZ555hl/6Hfdddfpfc43Ofq9CIhA2RKQAC7bqVPHRUAEoiSAqCSBE5bhyZMnO8QLDesamVCxDFMLM22X49wxB+NHiRvGYkhjQ2xiOGprEZtw4llx1eWggPJTEi6bzwz1a/EuQLTEEa9pidOsvFLQZdbmPWtrNUiI/uMWzkEOSepICqY1tPka4pCDAwLELmuI+TT3eIQxh0808whADDP3hXoEcM9evXq5pUuXuvPPP9/deOONEr9R/uOie4mACGSOgARw5qZEHRIBEUiLABa2gQMHurvvvtu782IRefTRR93y5curxPARRxzhxTCiGCtrljbtwSyziGE2trQokykFMxknHROd1roo9LmWDbvQOtGFPseuxz0eK6p5BATrzgY9ArKyVukf4hcBV79+fR9bn5W+FTsHUX/OxC9eFYhfvFJym9UVRwwHPQIQyuYeT6xwbWw5MDvxxBPdkiVL3Nlnn+1uvvlmid+oJ1P3EwERyBwBCeDMTYk6JAIikAYBLFHHH3+8e/zxx30c3D333OPdnxGVGzZs8JmkcZOmzBKCA8ve4Ycf7kXyUUcd5bP0Zm0Tb9YixLAlUzLXSTbIuE4WUn8URggXrI3EahKzqfY1AdbK2rVr3VtvveXXThrZsGtyjzePAKyErNW03NURv3gPEG8q74Hq3x4OM3jPahO/uZ/Eoo4Itrhhyx7PIYyVV8oNi0BAn3LKKW7hwoX+4O+3v/1t5mL48TYhE/XMmTP99zDeLN27d3dXXnml9xwotJEA8dprr3WLFi3yXj4cFjRt2tQdd9xx7pJLLin0drpeBESgTAlIAJfpxKnbIiAC0RJ455133EEHHeQ3QhMmTKh2I4i42LhxoxfD/DzxxBNeDCIiO3To4MUwGVQRl1kTw1h6sBAihs11kg122MzCwWRO1Gflc2qbi9/XX3/dsY6w1hHzyyFJmo31ysEH8878Yb2nlXIIUsp48LBA/NKnhg0busaNG2fuPSllfFF8Nih+OUApJm7cEuaZGLa44fXr13vhR0I/PFjOPfdc9/DDD7s+ffq46dOnZ1L8kpDw6aef9odt7du3d4xh5cqVXtQTr8waCtv4zj711FN9HW7eTzwPODSwXA9WHSDs/XSdCIhA+RKQAC7fuVPPRUAEIiaAUGBjFUa8Ii7YYM6dO9dbhnEhxLqFqDzkkEO8GMaSzMYtzP0iHkqtt2NDTN8Rw8HMwlhXzGU2KN7ef/999+qrr0aWzCnJsSbxrGApKLIzk+25EMt6En3kGXgEMO+s8+AhiM07az8u0Y7oQPwiwhEtjRo1SmrYZfMcK5dFh3F7Lkb85g7WDkGY95tuusn95je/8ZfwPcW6bd26tXvggQcy6c1x+eWXu6uuusq1a9fOh6JY6adf//rXPlEXh45PPvlkqPklkVibNm28xZfvbGrAW4MDa7NVq1ah7qWLREAEyp+ABHD5z6FGIAIikDIBNplYbh566CGfURorCxt+hC9WZWKG+dl7770zJ4axylnsKGNgLDQrs8M4sLqQWAeLFK69al8TYPOMBQmG5VQKyg5BrLxS7rwjhnGfjaIFk6bhborrs9rmBAgvQITReM9wV46jkZV8wIAB/kCL7yfm3Q7t7HuKpHZpNw4TOYwzLlhsgw0vFLL2U9+dw4J8DbFMki++o/HSURMBEajbBCSA6/b8a/QiIAIRE2BDiXVt3rx5XgwTX/f555/7p2BhwCqMdRgLWNYsw2w6zUKIayDijsYGuUGDBr7+aFSiKGLsqdwuWMaHWsz7779/arG1pQCweWfuP/zww6p5t2RKCBEOPopZr4hfRAou+Pvuu69PeqWWjvhlvZ5zzjm+rBsiEGvw4sWLvQV4wYIF/nuKUmochG2//fapThO5GDp16uS9BapzTcYyjIWYGu1XXHFFrX0lGzsltnB5JkxBTQREQAQkgLUGREAERCAmApaVef78+V4M86clo8KCgRgm5jhrWXCDVk2SJ7FxNjGMKELsmSiKCV3mbxvMZMzBAHWQixGIWRsoc83hh8UNWzIlBJG5xxPjHGasiN7nn3/ei1/KHOEBobY5AQ7LsPzyXYGVE8+LOBrv7wUXXOBuv/12X86NeNjgYRZz9Nhjj7l169b569JulGIaMmSI6927t7v33nu36A4HjIh4DhMZS22NsnaUdyLm+frrr3ezZ8/2hzKsYbL9kwW7uizbaTPQ80VABOIjIAEcH1vdWQREQASqCLDBZZOJRZiYYZLP4N5HwzqB+yFiGCGVVoZe+oLgwbUQEYTgwapJq04UYRU0MZyv3EolLYVgMics47j1hhGE5cbAkimZizzjpmEltDI7CLbq1ivWRMQvFmDWN4cEatWLXzgjfonFjqNx/4svvthbfEkq9eCDD6Zu4c03zosuusiNHz/ei2BifnMbMb3E2uMuzjqrrf385z93U6ZM8Qxwgc61AhO6wAElbtJqIiACdYOABHDdmGeNUgREIEMEEMPE1uJ+iBjGBRG3QxpiysQw1okkxTACh/IrlKipyapZU81ZrEkmhsNaCDM0JaG7gqBjw43AI1aSeNZKFL+5QMy135KncZhDq67GNMm2YMQap1zWnnvuGZpvXbmQdwxGSYjfYcOGOaygCDwsp5ZMKsuszzrrLDd16lQ3YsQIN2bMmC26ils035Vh3JpPPvlkb/VlrXJgw0EA7tUkARw9erQvecffr1q1KpPJwLI8T+qbCJQrAQngcp059VsERKBiCCA8iXlDDJOhFIsbDXGFGMbNj/jhOMUwggZXTIQd8clhYpTZvGPFNgshgodGwixzlyWZT6UIRIQdjBDBddmlFzFsNaaZe3PrZ30y37j14kr9wx/+0O2+++4V855GNZCg+MWKGVdJMd5P4mNvuOEGn0mZON9ycfUdNGiQmzZtmrvssst8Jujc9sYbb3jxG0YA40Y9Z84cfws8cLp27brZ7cgO/eyzz9YotqOad91HBEQgOwQkgLMzF+qJCIiACPhSSk899ZTfsCGGKUFEq1evXlU2aTJLU8s1qoaAQdghxIsVdmYhtFrDVnuUsjomhmtyl41qHHHexxgxP7j0yqr5NW2rMU2NbBPD/BZhRzZp5h+3aTXn+WD55YAgTvHL+zh27Fj/Q6kjygjFlVk6jnmN0gV64MCBPvYZr5Z33313i+7ecsstPjkY5ev47lUTARGofAISwJU/xxqhCIhAmRIMDCVpAAAgAElEQVQgHnf58uVVYvjtt9/2I8Gq1rNnT28Zpp5lKTVncb0mns4sdrgxl9qs9qiJYcuCTUItE0SIozgt2qWOIfh5rNy4hsMIt3QEndrmBMyqyZol2RWimLhxK69ETVs7CEk7w3Bac2fiF0aIX2JP42gw/9WvfuXde3kOoRZxWZnj6D/3jDIJ1pVXXumzRR988MFu2bJlW3SZ5IRHHXWUd6les2ZNXEPSfUVABDJEQAI4Q5OhroiACIhATQRwZ8RND8swWU/Xrl3rL0VQHn300V4MH3bYYQ6La9iGQKWGLS7KbJTjSMJj7rLE2/G8Tz/91HcP0Y4AQHCzOY/Soh12/GGuQ8RxQMA44rTYhelLVq+xTMasUbKbm7BD6FFWiXnnTw4QaMSgmhiuK8nTWPdkHoYJjHhv42is0wkTJnh3XhLYkdm5HA9swpZBohQSQr+2RuIrMu7j3UJJpNxGWai+ffv6RGRWizmOudE9RUAEskNAAjg7c6GeiIAIiEAoAgiNP/3pTz5zKWLYNnW4GCOGiRsmyQtupzXF3+IKyOcQzGz8kooNxBpsYhirIQ1LsIlh/izFoh0KYMiLEG5kxEacw6icXEhDDrHky/72t79563i+AwLEL94GVl4JV3IaydPMK6CS4sWDYBG/uD0z5rjFL+68l1xyic8mv2TJkrKNwSYcA+Fuhyu8f8EGR97NlStXehfv2hrfOdyLe3JwmFuO68wzz3S33nqrO+OMM3zcsZoIiEDlE5AArvw51ghFQAQqmADC45VXXvFimCRaWHRpCNojjzzSW4aPOOIILzQQw4jnkSNHusaNG/sEMpQRScsl1WJHEUVWEgoxjCUayzDCCLfpNBqx16+++qp/Poyof6y2OQEELQcxtEJq2FryNDJKM/fBeHETw6yBcnGRr21dkCwMyy/iN073eb4HEG8XXnihd+XFglrupadIgHX11Vd712VimCm7RqMs0tChQ334x9KlS6vwk+maH8rJjRs3brNpIRP2Nddc4w8IyQht9yIxGOEkHNAQbkJCLDUREIHKJyABXPlzrBHWUQJsKtkEzJw5023YsMGLiu7duzvioUioVEhDnJBNFGvjpk2bvFUBYYXrmaxihZCM91o2wdS4NDFs7nxs9rp16+Z69Ojha4CSXItNJbWIs5KciAzSlk0aqyJjQbBj1TYxnFRf33nnHbd69WqfzRrxa5vleGevvO6OazjiF5FainU8GC/O/CMYaeYij+UOF/mseAUUMktJit8ZM2Y46t2SvR3xW79+/UK6mslr+TesY8eObsWKFb48Ufv27R15EPh/1gSClVJk1vg3in+T+vXr56ZPn77ZmLgXB4HEAHOvtm3b+u8b7sGBDEJ7+PDhmeSgTomACERPQAI4eqa6owikToB/7Dt37uyefvrpqo3D+vXrvbsYFpZnnnnGWwDDNDa6lNCg7ASbK8rxUC+RHzYfbCDKLcFKmHGX+zUIC9z9sArzw6bRGocWbBRPOOEER3KirJUpwlXRrIPBREr022oNI06jbjDjPaHGKFZxxC+Wc7XNCTA3uJ8ifmHEGoqqBcsrBV3kOcBDDPP9VUice1T9KvQ+VguZtUw5qCiSy1XXB9Ysh5zUzUX0In4bNmxYaHczez1eIhzkUquXgykOxDjIpTRSritzbQKYATIX119/vSPmd926df6Ai3/PhgwZ4i3DaiIgAnWHgARw3ZlrjbQOESAxCBsEhCuuYySaoZnrWIcOHdyTTz4Zisjpp5/usC4cf/zx3nXMLDEXXHCBmzRpkuP3d9xxR6h76aJ0CGDBxx3aDisQlTSExOGHH+6t+WwAERlZE8O4jgYTKWGtoUWdVRghwSEPFibeF4RdUhbndFZFcU+1uGi+B2AUZ+w4B3l2EGJeAfQaEWRJtOI4CCmOzNefIuYUt2cEF4mo4qqFzJrF22PAgAH+oBPxi/uzmgiIgAiIQO0EJIC1QkSgwgggGNgcInpwga0peQgbtAMPPLDW0ePuTBwZSYA4fQ9aMXBZ5QSeOMD33nsvNgtHhU1P4sNhDhG/uKuef/75bvz48d6NHXd2fjgIIf4NQUMWacQwrtJY2rImhumniWGEkWUVJj43mFW4UMgICRKCsY4R1rwzacUeF9r3JK8neRkx5mnERSMmbe45wLGDEAS4zX0WXNURvyS8Qrxj+Y1T/BLOwAEkieNIeEXiKzUREAEREIH8BCSA8zPSFSJQVgTClo+gLiIuY7W122+/3Q0cONC7U1NLMreRNfO2225zXNe/f/+y4lQXOouwI9YXyy8xbiSCCYpafo9F74EHHvCWJNYOBygceBxyyCFeDFM+hE18FsWwZRVmDJSXoSGCEEQc1oQpsYOQIokY4g4LOKWOslqSKc01u3HjRs8JrwEOzsyrJI0+BQ9CEMXBubckWgjjpNcs7rocLCJ+sfxilY2j8d4+8sgj7rTTTvM5GCh1hNhWEwEREAERCEdAAjgcJ10lAmVD4MYbb/QxTb1793b33nvvFv2eN2+et/AhbrAA1tbIKEpNScpqXHfddVtcetNNN7nzzjvPZx7FsqiWPQJYo4jXxE2ytsamGkGJVQkxzIEHVn5ExEEHHeTXC+WVSKCWtLDIRxURi4ssIhbLMNZCGvG7JoarE0QIKdggorgOEVEJmYfz8Sr092TEJuYfl3DEbxYsrTaGmuYe1+hgeaW45zUoflu0aOH23HPPQjGHup73dNGiRe7kk0/284D45dBGTQREQAREIDwBCeDwrHSlCJQFgYsuusiLUUQwMb+57cUXX/QbJuL3EEe1NeJ+EcmIYGJ+cxuWQ4QR1yGa1CqDAJts6m+SJZp5XbhwoWODT6PmJlZh5p1kO1kTw/Qd93+rNYyIpyHezFWWGFLEL27hCGcsdc2bN5f4rWb5Wr1oBCXiN62SWWHeLFu3lk3c1iwu28HySlFb+LH4YvnleXGKXxjgpUHyOg53yO9AEic1ERABERCBwghIABfGS1eLQOYJkA106tSpbsSIEW7MmDFb9JcMtyRKoQYsJXNqa127dvXWBu535plnbnEpVsIuXbo4rkMkqVUeAStTM3/+fC+G+fPTTz/1A+UgBTFM3U3WVBbFMJmETQwHBRH9x90bi/Z+++2Xub5nYSVZOSjEFuK3nDJis25ZpyaGbc0ifslaz2EIsbOlxnoHxS+HKHHW3n3qqaf8u0a8Pt+3eGaoiYAIiIAIFE5AArhwZvqECGSawKBBg9y0adPcZZdd5jNB5zYy3SJ+wwhgxC0il/sR75vbEMeIXwngTC+JyDqHqEBELliwwJdWwkKMpZiG5QsXaTboJOPJohhGBJHoCqsmY6EhJrAOEjNMDHDU1sHI4Cd8I7Jhr1mzxlt8Eb9ZzLZcCBKSU1lGaTwEaKzRYHmlQrN+I37xouHerPlC66sX0n9K1/FuWfwvNXHVREAEREAEiiMgAVwcN31KBDJLQC7QmZ2aiuoYG3HcizkEQQwTO0wMMY3DFRPDWYqrRbwjWPizQYMGXvxiIfzkk098vxG/WAURw/xZV8XwW2+95WshE2OK+C1UGGZ9obNuTQyzZu0whIRS5iafz9rNPXB7RvziQZBbkzZKBqxZ8jaQ7ItDJ0qXqYmACIiACBRPQAK4eHb6pAhkkoCSYGVyWiq+UySeIj4RN2liwxGWNOKEEcPEDCOm4k5GVBNorL+UBUO45FrrEDHmKmsWbfqJCI7KVbYcFgBCcN26df6HLM/MF1mfK7kF60xTXslKazH+YGmtoEcDawhR+tlnn8UufsnZcNRRR/nM0rxXeNuoiYAIiIAIlEZAArg0fvq0CGSOQNgySJdffrkbPXp0rf0PWwaJUkj5sgxnDpQ6FBsBRMXSpUvdnDlz/KadLMI0rGSIYX7atm2bmIUVUfvHP/7RW9AoT1NbbVaEholhEmTRED8WN4q7dCWKQsTv2rVrHdZf6iqTJK8Sx1nbokf8WmktLMSsY5plE0cQ898mfvfdd19Xv3792N4jyk4hfvFQ4GDp6KOPzlxoQWyD141FQAREIEYCEsAxwtWtRSANAlji2Kix6cfidcABB2zWjZYtW/rSLytXrvQZfWtr1P4krg1XURLicF9rWEEQNFhNiKusTVSkwUHPzAYBRCfxi4jhuXPnug0bNviOkXmZBFqIYWoOs8biaAgasj0j8H70ox/5eN+wjXfJxLC5yiKGySJt1sFKcA+GDbkBiPulXBTit9TkUGEZZ/U6yisRK2zzb9nEmX94kewK1+e4PBpee+01L345hJk9e7b3oMhaXH1W5079EgEREIF8BCSA8xHS70WgDAmQAOvqq692Bx98sC+VYXU7KYs0dOhQd+ihh3oLnbXJkyc7fkiyMm7cuM1G3KdPH3f33Xe7Xr16uVmzZlUJlcGDB7uJEyc6fj9jxowypKQuJ00AC9uzzz5bJYaxONIQpVab+rDDDotMfGHF47AH4cBBEMK12IY1kPuRURoxjECiFRI3Wuyz4/wcYo5s8Bxwffe73/XiN67DiDjHEee9YcRBHxZZswrzPDgF3eSjihnnMKJ79+5+vc2cOdOXPZL4jXOGdW8REIG6RkACuK7NuMZbJwjgxtmxY0e3YsUKb2kjYyjWHf4fV87ly5e7Jk2aVLG44oorvDt0v3793PTp0zdj9OGHH/pyG4iVxo0b+7qTq1at8ptB/p97sQlUE4FCCCAgcUvGtZNa06tXr/YfJysvli8sXp06dfJuuMVs/jdt2uTXKCIFUYdlM6qGVZv3AjHMnyaGeYZZhu3QKapnxnEfhB2WRjw4OBygrJXE75ak8QTA7Zk4csp9cWBjlmHKbNGwBAfd5Iu1oBN/feSRR/qwAQ4WTznllKLWfxzrRfcUAREQgUohIAFcKTOpcYhADgEy3WLNveeee7x1hw0uVgVKI+VmLK1NAHNb3PBGjRrlXVjZ9JMlF9dVRDOCRU0ESiGAEHv55Ze9GCajNMKVhqA0MXzEEUf4UjxhxDBljhB2uCcjfkloFFfDqo110MQw4phmSZR4VxDDYfodVx+ruy/MX331VS+0eIcRv1FZMJMcR9zPwuKL+CUOl0NDkroFWzBmHJdpuAbd5BHLYUtIcUjJdzTf17feeqvr379/5tZN3Lx1fxEQARFIgoAEcBKU9QwREAEREIFQBBAQWIPNMkwcuwnKbt26+YMX/qxJVGJBw1uBZEVkMc5XziZUp0JehCUYMYx1MJhEiVq6WIYRwySYSlsM00+8OLCSY7UkL4DE75aTHBS/eLs0atSo1pWApThYXqkQzwCs8KxrkpBNmTLFnXXWWamvk+oGi+DnYBXXbOL5OTxBtF955ZUl1UHG7ZsYfe4PB2qNq4mACIhAXAQkgOMiq/uKgAhESiCKjRcWmkceecTX0iQxEhYXXBebN2/uTj31VHfOOedEFn8a6eDr6M0sM7GJYVz4aYjaLl26eDHM5pvYVa6lBjYb6WHDhnlX/bCWtzjwWhIlLMMIYsQRjT6ZGKbfSYth+oWFnX5hnUR0xJXIKQ6uSd0T8cvhCy7OCF8EcCENTwA7DMFN3jwDOLhh/vkdSQhhz0EE65i1O2nSJHfuuecmvi7CjI3v4M6dO7unn366KrRm/fr1PqEia4lkd4VysucS7vDEE0/491gCOMxs6BoREIFSCEgAl0JPnxUBEUiEQFQbL0sOxqaTpEi4NGKxWbZsma8PS3KwhQsXOix2atkiwMaYAwvihXGTZs74O9yciXfHTZ+NOKVpSPyWpbh0+klWdhPDrGcafbeYYZJpxS1EEb8kBWPN89wf/vCHsT8zW6soXG8Qq4hf5gyX52C+hHB32PwquAfLK2HlReQyB2RAf+6557zbM0kKL7zwwkyKX0ZE6TxCaNq1a+ffMQstsOSKHTp0cE8++WTBiHD3PvPMM73V+7e//a0EcMEE9QEREIFCCUgAF0pM14uACCROIKqN1zXXXONj+bD0UsbEGpYXYkxx6cN6OHbs2MTHqAeGJ4CgJHYVMUx5pT/84Q9eDNPIIt27d29fMxWrVNIW1nyjoJ9YFS2J0ueff+4/QtIkE8O4lUYtholVRvxijaRkWYsWLSJ/Rr6xl8Pvc8UvFs0o1xDzjwWerPsctnEYQcMyfOKJJ7rjjz/efxel6b1Q3TxhEWd94kVTW3k9xDyhB2Eb7wHlpPjMiBEj3OGHHy4BHBaerhMBESiagARw0ej0QREQgSQIxLXxyu07MW24Qe+zzz4+Dk8t+wSw2jNnWIT3339/v0FHDCNiiGnFok82aeoNE38bpZCJgg5iiMzCJob5bxqZmBHvjIcY3VLjcxG/L774one7JSs84jdrLKLgWeo9WDdkJkfk8T2A5TcuTngscEjDvHBog4WYRHA0LKskf0MQ4qKehfb444/7rOwcCLz55ptbdAnLMAeVJEskqWLYdvLJJ7sHHnjAj53kdRLAYcnpOhEQgVIISACXQk+fFQERiJ1AXBuv3I6TERdhQNkdhJVatgl89tlnvm71okWLHJvoO++80wtHRN6DDz7ok2g99thjfi4RMbhtIoaJG8b6H5ewKYUaY0IM4yqNpwIN8RusNVtomSLEL6IOwcW4f/CDH2Ry7KVwi+KzQfHboEEDX+4orjWCazXrkJrYiFzEI89CWOLVwA/xtGSfJot5FtqNN97ohgwZ4r0r7r333i26NG/evKpa3vQ/TCMfA4cAJNAaOXKkjwGWAA5DTteIgAiUSkACuFSC+rwIiECsBOLYeFXXYRJj9ezZ09WvX9/Hmqplm8DUqVN9zCA/N9988xZWUqyrWPKYVyzEuJtSGozWpk0bbxVGEGPpi0volEKQvpoYRjDRCq01GxR1lD4jPjqLYy2FUxSfDR4S8P43a9YsNk4cbHBwg8C9+OKL3bXXXlutK/rGjRu9q3pW5osEc+PHj/cimJjf3IYlm1JaCHaEe77GYQ8Hjrh645rPwaMEcD5q+r0IiEBUBCSAoyKp+4iACMRCIOqNV02dJKvw4sWL3fnnn+8mTpwYy1h00+gIIHAfeughf2iRTyRwLcIDixNieP78+d71mEYyNMQwoiROl9dSRk7SLGJFsQxjyaUxZmKFLW4YARFshA5g+UU8xy3qShlb2p9NUvwi+nr16uWWLl3qv2c43Is61jsunhw0ceiExXrMmDFbPAbrNVZzDg9ef/31vN1ASDP+JUuWeKsvTQI4LzZdIAIiEBEBCeCIQOo2IiAC8RCIeuNVXS+pu/nzn//ckYmX+qh77rlnPIPRXVMngBjGuooIRgzjumkWVuKIcU3FMpxVV2GrNYsYJm7Ukn/tvPPOVWIYt2mscIj+uGNZU5/QEjqA+KUcGhzjtpCz5nAfJqTj7LPP9l4L5SJ+QTxo0CA3bdo0RyZ9XLZzG4kEEb9hBDCJsg466CB32mmnuTvuuKPqVhLAJSxmfVQERKAgAhLABeHSxSIgAkkTiHLjVV3fKdvRtWtXh8WMuFEsgWp1gwDikRhh4oiZeyzKiCEa7sKIYdYDwjiLYoU1S1ZnxDCxz5TbodFX/jtuUVfOqySYGKxevXo+E3E+T4Jix4sF/5RTTvGlgwYOHOhL/ZSa2KzYvhT7uag8cXDLp/4xGfdXr17tk71ZkwAudnb0OREQgUIJSAAXSkzXi4AIJEogqo1XdZ0m9owMrMSK4vaMW6Ja3SWAGMZChxgmM62VqGnUqFGVZZgYxyyKYYTFpk2b3Jo1axziztp3vvMdnwEbV2lK7ag5z8eyYsedGAyLfZ8+fbynQd++fd3tt99eduKXNRNVLob169f72srEN3PIFGx8DzMveDOQ/Zps2MTwx91OOukkn9jr0ksv9THZwYZI550n+RzeAnwXqImACJQ/AQng8p9DjUAEKppAVBuvXEhr1671ZXIQDZTtoHyHmggYAayrlFSizjBimKRENKyqWIb5adu2bWbEDFZG3J6pK0ypGsQDSbQQ8YhjGgLYxDC/j8vimeVVhGUckYXlPG7xyxrq37+/mzt3rkNk3XXXXV5IlWMLm42fUkijR4+ucYgmgMMw+O53v+sPJ+NuxNUjuKktTub4jh07+kcyf7zjxNJzcMFcqomACFQGAQngyphHjUIEKpZAVBuvICA2Oohf6v0OHjzYWzfURKAmAgjIp59+2luGKfHyzjvv+EuJFSeBFmL44IMPTk3cIH6JqyTOFKsaSa+sIfhw67Zaw2zqadttt12VGN5pp53qhBgOil/mrnnz5rGNmzVD+AaWRdzoZ82a5TMdl2vDko0XAfHyL7zwgk8eF2wtW7b02ZxXrlzpXZyLaWm6QPPvzBFHHOEPRRgH+SB+8YtfuOuuu86dcMIJ7r777itmSPqMCIhARglIAGd0YtQtERCBrwhEvfHitL9Dhw7ulVdecQMGDHC33nprbJtgzWHlEcB9lk2+ieF169b5QSIOevTo4RNosb622WabRAaP6EX8IoJJ3EU8a02NmGfWv4lhq3dNKRrLJs3GvxItw4hfhA0W8T322MOX4IlrnKwRkurdfffdfk3gRfDtb387kfUQ50NIgHX11Vf7wx7imc2lnrJIQ4cO9YeKZLi2NnnyZMcPBwDjxo3L27U0BTCdwwX6V7/6lY/XJvli586dvav2yy+/7DOuq4mACFQOAQngyplLjUQEKpZAVBsv3EPZ1CxfvtydeOKJ7p577smMC2vFTl4FDwxRhXskAgfLsJV/YbN89NFHezFMiRcsf3GILdYzbs+IX6yZWK/CNsQw1jyrNcw9aPTVxDCxmFmMdw47RruOeULEMNa4xS/PIpfA9OnTXbdu3fy6wNpeCY01gnvwihUrPMf27dv7mun8//e+9z3/vUopMWuEluAO3a9fP88jX0tbAHPYSnZq3mm8IsiijtDHMqwmAiJQWQQkgCtrPjUaEahIAlFtvKz2JBlYicmryUoXZrNWkaA1qKIJICgRWSaG8TCgEcd41FFHeTHM4QvW1ijEMDVlsfyyaSdLNYKk2GZ1kk0MI6xpvB9k6UUQI3DKUQwHxS/WPFhFwb861jwLSyhZnpnrBx980G2//fbFTksmP4fHAdZcDg8JBeCQpHv37r40EvHxwVZuApi+4yWAOzdNNeEzuQTVKRGIhIAEcCQYdRMREIG4CUSx8SKJSbDuZE19ttqqcY9J969MAqyf1157rcpNGosSjcRTiAVihrEOIo6KEWOffvqpt/wSz4ugQ9hF2bi/iWH+m0bypl133dWLYf4shzI+CFIOIigTRfKvOMtZ8axhw4Z5l19c4Mn6zHyrlReBESNGuLFjx/pO49JNmbxyPPgpL+rqrQgkT0ACOHnmeqIIiIAIiEAdIYAYfvPNN6vEMPHDNMRvly5dvBhGFIdNRIVbJuKXJEtkrkWQxtmwBpsY/sc//uEfhSAwMYyFOIuZjRGkq1at8lneYfTDH/4wNiHDs8giTyxsu3bt3IIFC/x8qpUXAeKXcfHmQIm60EuWLPExz8OHDy+vgai3IiACeQlIAOdFpAtEQAREQAREoHQCiGHKwBAXev/99/vM0vwdCZJwmUUM4y6NW2l1lmFKwmBNJskSbpqIzyQboQgmhq08Df3EPRoLK/1JKvlXbeOGKZbfJMQvz0Ik4RZM9mNiRkkkplZeBDjc4UBpw4YN/gCDAxN++Hve01atWpXXgNRbERCBWglIAGuBiIAIiEBKBBAUbJxnzpzpN14kT8IaeOWVV9aazTdfd9944w2/meP+uNqyoVPLFgGEE+W4EML8UHMYSyICEisUMcMk0sLSisikPikutvzgYovoTLORQdqySZNZmvHQT8S7ieE0Mh/TDyy/1G1GkPMexOXCyrMok8P7+uMf/9gtXrw49XlJc02U87P79Onjs3ZfcMEFbsKECX4oHFQdf/zxrlmzZv7gqdLiuct5vtR3ESiVgARwqQT1eREQAREoggDiFKsf1gXLqIp1EBdZNu7PPPOMa9y4cRF3dq5Tp06OjKps0CWAi0KY6IeYJ+JU586d612lmTtcnImzJdMuG/A777zTzyf1ZLt27Zpo//I9jERclBdCEH/00Ue+nzQsoYhhXJBJ/hV347mvvvqqP1jg4AAreZzil/rhZKgnthh32aQt8nHzrCv3552i9BGlsUgsF1yrAwcOdLfffrs7++yz3ZQpU+oKEo1TBCqegARwxU+xBigCIpBFApdffrnPnErMIG6TljDHampi5SMBS6GNusZnnnmmr2NJNloJ4EIJpns9Ig4R+cADD3jLMGsDMUyjzi8b8mOOOcaXPComgVbco6OvJoY//PBDb9WmERNrYjgOS1rS4vfmm2/2dWOZE8Rv1InI4p4n3f8rAmSyxkuAWHfKOWHJDzaSwHGQQr1v3knePTUREIHyJyABXP5zqBGIgAiUGQGy92IVI47yhRdecAcccMBmI2DDRTkOrBEHHnhg6NFhgSN5C58hmyk1aCWAQ+PL3IULFy70rtBYMX/yk5/49WD1etu2betjhvlp0KBBJsUwscqIYNYlopj/p3HYY2I4ikzJlnX7vffe8y7IvD9xZanmWdOmTXMXXniha9q0qXv88ccLqr+cuUWmDomACIhAHSQgAVwHJ11DFgERSJcAm2bclHFxJkNwbsMyjIWYzLLU0gzbTj75ZG+loB7tu+++KwEcFlwGr6OMDvGHO+ywg7cCc6hBQp5HHnnEW4bnz5/vqAVMQxxjmUIsN2nSJJNiGEswlm0TwxwC0Rgfh0H8fOc73ym47wjS1atX+/WehPjFFf2cc85xjRo18uK3fv36GVw96pIIiIAIiEBtBCSAtT5EQAREIGECxA4OGTLE9e7d2917771bPB3x06NHDy9oSMQSpiGMSJpEQp6RI0f6OFJZgMOQy941CMV99tnHxyIuWrRoC7dMRB8um4hgxDDrxUoUkbkWqzBrB2+ALLpJI4ZJnGVJtIghpm233XZVYvi73/1u3r4HxS8J5HBfjdPyS7I6QiTi9LsAACAASURBVAsQvYjfhg0bZm/xqEciIAIiIAJ5CUgA50WkC0RABEQgWgIXXXSRGz9+vBfBxPzmthdffNFv5rHsUfM1X8MSSAIXBBOu09/61rckgPNBy/jvEbW4NpNgqbaGCMQtGqFMAq2HH37Y/fWvf/UfQQAjho877ji/PuJKCFUKSvpPKICJYXPxJoO0WYarKwvF515//XUfw5mE+IXtgAEDfMI6xC/uz2oiIAIiIALlSUACuDznTb0WAREoYwJYkaZOnerjdMeMGbPFSHCLZoNN9l82+fkaQhqrMsl4sPrSZAHOR60yf095ItYBgg13eGJwabjbm2WYmPOsimEs2VZr+IsvvvB950CHDMvEDZsYXrNmjS8dxv8znjgtvw8++KDr27ev7wPil4MFNREQAREQgfIlIAFcvnOnnouACJQpgUGDBvlEOpRQId43t1HHF/EbRgCTGOmggw5yp512mrvjjjuqbiUBXKaLI8JuE2dLJnHEMCWWNm3a5O+OC6+J4datW8cmHksZChZeMvBSHgpBbPHOW2+9tcM6zP/jJk1sdJzil9AC3i1KOnGwkM8iX8qY9VkREAEREIFkCEgAJ8NZTxEBERCBKgJRuUBTcgYBgyWMREDBOqQSwFpwQQKsFWpOz5kzx8eVkzSKRjmlnj17+phhSnIhMLPYELyIYVyeLWYY4Uu9XyzD/BmlEEaA41Z+0kkn+azVjz322Bax2FnkpD6JgAiIgAjkJyABnJ+RrhABERCBSAlElQRr/fr1PhEPNUj33XffzfpIXCWxxLiIUueSTTzxoWoiQDmilStXVonht956y0NBSFrytfbt27ttttkmM7AQpIQGsObJFk18MO7dH3/8se8jLt1kgTYxXGrfsfaSpI7EXGThbtWqVWZYqCMiIAIiIAKlEZAALo2fPi0CIiACBRMIWwaJUkijR4+u8f4mgMN0AHdRRLGaCAQJkJGZWtRmGSa2loaYJKs4lmHiyhGUaWWURvyuXbvWIdRZxySHM0s1SbMsgRaZpWn0k8RYiGG8IoghLqQtXbrUl6DiGdRiJsRATQREQAREoHIISABXzlxqJCIgAmVCABdOLFhYrxAfJPEJtpYtW/pszljpcHEupskFuhhqdfsziGFqSJsYXrVqlQeC6EQMEzd8xBFH+BjcJMUw4nfdunVup5128uK3Jusu75WJYTJhI5zpJ14QllGavtfWcBMnazaNMlOHHnpoJhcFwn/cuHGO0kyEQCD4u3fv7sug1atXL1SfORAjxhnPkD/96U/u7bff9pb05s2bu1NPPdXXOy7Vkh6qI7pIBERABBImIAGcMHA9TgREQAQgQAKsq6++2h188MHexXKHHXbwYCiLNHToUL/xxhJlbfLkyY4fNudsfPM1CeB8hPT72gggHl999VWfQIuYYQQSDfdjhBZiuGvXrm777bePVQwjfBHAPJeEV2EFGQnAPvjgAy+IqauMuKeRzMrEMO7NwUZCOeKhiZdGFFpG9aytFMRv586dfUw3ZZlwV8cbhAMzLN7PPPOMz/qdr9l3EKKXQ7gmTZp4ZsuWLXNkE+c7CAs4c6wmAiIgApVEQAK4kmZTYxEBESgbAmxiO3bs6FasWFG1icUCw//jfrp8+XK/IbV2xRVXeHfofv36uenTp+cdpwRwXkS6ICQBxDCZye+//37/8+yzz/pPIowQwYhhRDEiNUrLMC7PxP0WKn5zh4WgJV4YMcyfxEDTyJpORuyTTz7ZC2Ss3LyXlI9iXFlthEaQPZ6kZRyeEd9Ps8OzDh06+Ozf+do111zjPvnkE2/pJRmaNeYaSz+W5WHDhrmxY8fmu5V+LwIiIAJlRUACuKymS50VARGoJALUOcWae8899/jstrhqIiTY3O69996bDVUCuJJmvnzHghjG2mhiGGsjf7ftttt6qyRi+KijjvKW1lLEsIlfxB2W30LjeGsijPjFIoy4w9pL3WGa1UWeOHGi+/nPf57JOsn0E8s2Fmzcl2sLn8CaDbdiG67VuEHvs88+PvZaTQREQAQqiYAEcCXNpsYiAiIgAiIgAgkRQPi+9957XgzjJv2HP/zBW1JxU8Z9mARaWFXxaChEDCOwsUJGLX5zsWDt/c1vfuM4XLLSSlzTtGlT16tXL/+DiCyk73GjD5tAb9SoUX5cxTbc31u0aOEPHnCHVhMBERCBSiIgAVxJs6mxiIAIiIAIiEAKBBDD1OlFCCOIccHH9ZhMysSoIoaxuGK9rE1QEgZAJuq4xS+IeM6RRx7p3aJnzJjh42dNzG/cuNFT7NOnj/9dVlpUJdTyjYcYaOYLF3HmRE0EREAEKomABHAlzabGIgIiIAIZIRBFltrgUIgFvfbaa92iRYvcpk2bfFwoljqSgl1yySUZGbW6AQHEMKKSWFoE5WOPPeYtrLgZk/QNMXzMMce4PffcczMxfMstt/ia1pQvou5uVG7P1c0KybUIN0Do3nXXXT4O2IQ5Vmxcu0kA1rZtW3fSSSdlZmIvuugiN378eDdkyBAf85vbqP394x//2GfLfv7554vud5cuXdzixYvd+eef73ALVxMBERCBSiIgAVxJs6mxiIAIiEAGCESVpdaGglWReERcMclW26xZMx/HSckesmcjjtWySQAxTH1eLIoISpI2sT4Qm4hLYob5IQ5+zJgx3nWa6/KVKypltFg0Eb/E3d92220+sVyW3JxrG9tZZ53lpk6d6kaMGOF55TbeBQ6GeEdef/31ojBNmTLFx0ETx00pLA4q1ERABESgkghIAFfSbGosIiACIpABAlFlqWUoWLTatGnjLb5z587drC4rljoSAWEtVMs+AcQwSaeoPYvIXbBggfvss8+qOk694VmzZnmX6bgE6bvvvuvFL4mdiP8dNGhQbM+KY0bo77Rp03wZNZLl5TZipxG/xQpgskeTAZtkW8yR1USOYyy6pwiIgAikRUACOC3yeq4IiIAIVCCBqLPUUtKFesgPPfSQ69GjRwUSq5tDQgwjfql5/dvf/taLUP6O9qMf/ci7SCO+9t1338gEKu7OxPwiEidNmuTOPffcyO6d1CzG6QL90ksvucMOO8xnmMbtGfdnNREQARGoRAISwJU4qxqTCIiACKREIMosta+99ppr3rx50daslBDosSEJ3Hrrre7MM890jRs39tZg3G2xOuIujds07Qc/+IF3kUYMsxasXFHIR1RdRoIuyjOtXr3ax85eeOGFZSd+GUxcSbDWrl3rvSuIryd7NFmk1URABESgUglIAFfqzGpcIiACIpACgSg36JMnT/ZWKCx1119/vZs9e7ajvinWQqyEJ554ottpp51SGKUeWSqB6dOnu4EDB7qGDRv6jNHButfEepM4iwRaJNIioRatSZMmXgyTRItET2HF8AcffODLMSGwr7nmGnfppZeWpfiFQdgDJsIQRo8eHWqa3n//fS9+cQsfPHiwF9lqIiACIlDJBCSAK3l2NTYREAERSJhAlC6aJOIhIc/FF1/sXaBzk/rsuuuu3mKIm7RaeRGYM2eOGz58uM80TKmdmhrZo4lLZZ6JAceSS2vQoEGVGG7dunWNYhhLMuKXWPIrr7zSx87GFV+cxAzAg1JSH3/8sY9/JylcsLVs2dLhyrxy5UoHl3wNPrw/r7zyihswYIDDKl/OfPKNV78XAREQAQhIAGsdiIAIiIAIREYgyiy1lKbB6kst2Z133tknLerUqZMXQVi3yBzM32PZ22OPPSIbg26UDAHEXCGljqgrvGzZMod4RgyT0IpWr149HzOMdbhdu3Zuq6228n+PSOTv8RogazJJoypB3CHir776al9SiqzaZEKn4dpNTDXWXOLmreFJwQ9u5OPGjav6+88//9x17tzZLV++3HtT8D4Zu2RWgJ4iAiIgAukQkABOh7ueKgIiIAIVSSDKLLW9e/f2Yoe2cOFCn5022MgO/eyzz9ZYEqYiAWtQnsB//vMft2LFiioxjPsujTrCJEvr1q2bu+GGG7y4o040rs9hXaazjpgyUh07dvTj5+CHrNmUduL/v/e97/kx4y5ujZheDowo94TruTVqCePujOil1vE222xT7dCDn8k6G/VPBERABMIQkAAOQ0nXiIAIiIAIhCIQpQs0MaK3336722uvvaqsfcFO3HLLLe6cc85xhxxyiHvqqadC9U8XVR4BymE9//zzXgxTM5osz9aIHyejcaWIXxvXF1984a25WG2pZ4wnBOWdsHIH46m5viYB3L9/f3fHHXfkXRCWnTvvhbpABERABMqEgARwmUyUuikCIiAC5UAgyiRYxGySjRZXT1xfc9v8+fN9Zt+mTZu6NWvWlAMe9TFmAohhYmCHDRvmNmzY4F5++eWKE78xI9TtRUAERKDiCUgAV/wUa4AiIAIikByBKLPUkviKGM799tvPURIpt911112ub9++PhEQCYHURCBIAMtlJcT8alZFQAREQASiJSABHC1P3U0EREAE6jSBKLPUkqSHjLfckzqlua6d1JAla+0ZZ5zhpk2bVqe5a/AiIAIiIAIiIALhCEgAh+Okq0RABERABEISiCpLLY/DlZUERpSyISO0ZbxdsGCB69mzp0+GRNIfEmKpiYAIiIAIiIAIiEA+AhLA+Qjp9yIgAiIgAgURiCpLLQ/lXkcccYSPASbjbdu2bd1f/vIXL3qJ96QcDPVk1URABERABERABEQgDAEJ4DCUdI0IiIAIiEBBBKLIUmsPxAX6+uuvd8T8rlu3zm277bauVatWjjIuWIbVREAEREAEREAERCAsAQngsKR0nQiIgAiIgAiIgAiIgAiIgAiIQFkTkAAu6+lT50VABERABERABERABERABERABMISkAAOS0rXiYAIiIAIiIAIiIAIiIAIiIAIlDUBCeCynj51XgREQAREIGkCJOYaN26cmzlzptuwYYPbZZddXPfu3d2VV17p6tWrV1B3yGY9YcIE9+yzz7qPP/7Y7bzzzj6jNfHNnTt3LuheulgEREAEREAERCA/AQng/Ix0hQiIgAiIgAh4AohfhOnTTz/ts1K3b9/erV+/3q1cudL993//t3vmmWdc48aNQ9H69a9/7YYOHeq+8Y1vuEMOOcTttddePskXYph2yy23uJ/97Geh7qWLREAEREAEREAEwhGQAA7HSVeJgAiIgAiIgLv88svdVVdd5dq1a+ceffRRt+OOO3oqJmY7dOjgnnzyybykPvjggypr8WOPPeYOPfTQqs/87ne/c71793bbbbed+/Of/1z1jLw31QUiIAIiIAIiIAJ5CUgA50WkC0RABESgPAhgiWzYsKE77LDD3BNPPFEenS6jXv773/923//+993f//5398ILL7gDDjhgs963bNnSvfTSS+65555zBx54YK0je/jhh13Pnj296/T8+fO3uPbHP/6xe/HFF92KFSu8S7SaCIiACIiACIhANAQkgKPhqLuIgAiIQOoEJIDjnYLHH3/cderUybs4v/nmm1s8DMswFuJRo0a5K664otbOLFq0yHXt2jWvAH7jjTdckyZN4h2Y7i4CIiACIiACdYiABHAdmmwNVQREoLIJSADHO7833nijT06Fe/K99967xcPmzZvnevTo4X7605+63//+97V2BivyPvvs47744guX6wJ9//33uxNOOMG7WS9btizeQenuIiACIiACIlDHCEgA17EJ13BFQAQqkwAWx9GjR1c7uH79+rnp06dX5sATHNVFF13kxo8f70UwMb+5DZdlXJd/8pOfuOeffz5vz+bMmeNOO+00h2u1JcF66623fBIsXKOZM1yu1URABERABERABKIjIAEcHUvdSQREQARSIzB37lx31113ORIo7bbbbl5AWSPB0plnnpla3yrlwWeddZabOnWqGzFihBszZswWw8ItumnTpq5Zs2bu9ddfDzXsJUuWuJNOOsl9+OGHVdczfxdffLEX2ltttVWo++iidAhEWRILrwAOsvAe2LRpk9t99929NwEHW//1X/+VzgD1VBEQARGoQAISwBU4qRqSCIhA3SQgF+h4533QoEFu2rRp7rLLLvOZoHMb8bqI37AC+IYbbnCXXnqpFzkIn0aNGvkySMQRc6DRq1cvh5VYLZsEoiyJ9dFHH3mXd9YQ66BVq1Zu1apV/ocY8OXLl7vvfe972QShXomACIhAmRGQAC6zCVN3RUAERKAmAhLA8a6NKF2gKZXUsWNH7y6Ny/M3v/nNqs7/5z//ca1bt3Z//OMf3cKFC32yLLXsEYiqJBYjO/30092MGTPc8ccf72bPnu223nprP+ALLrjATZo0yf/+jjvuyB4E9UgEREAEypCABHAZTpq6LAIiIALVEZAAjnddRJkE64wzznC33Xabd6XGpTq38fcjR450w4YNc2PHjo13YLp7wQSiLImFu/Nee+3l3d3feecdH8Jg7csvv3R77723++tf/+ree++9zX5XcKf1AREQAREQAU9AAlgLQQREQAQqhIAEcLwTGbYMEpbBmhKSWQ+7devmHn30UTdx4kR3/vnnb9Fx/n7w4MHu7LPPdlOmTIl3YLp7wQTCroUwJbFuv/12N3DgQNe5c2e3ePHiLfpihyVc179//4L7qg+IgAiIgAhsTkACWCtCBERABCqEgARwvBP5r3/9y2dl/vjjj90LL7zgDjjggM0e2LJlS/fSSy+5lStXehfm2hqZue+8884aXVv79u3rk5qNGzfO/fKXv4x3YLp7wQSi9Aa48MIL3YQJE9wll1zirrvuui36ctNNN7nzzjvPcR1ZyNVEQAREQARKIyABXBo/fVoEREAEMkNAAjj+qSAB1tVXX+0OPvhgb8HdYYcd/EMpizR06FBHxu2lS5dWdWTy5MmOn+OOO86LWWtk+iXeE7dX/rtnz55Vv3vggQf872ivvvqq23fffeMfmJ5QEIEo48GZa9YAIpiY39zGeiBRGteR5V1NBERABESgNAISwKXx06dFQAREIDME3n//fR9LSE3Zp556KjP9qqSOkPmX5FUrVqxwe+yxh2vfvr17++23/f+TpZdsvWTttWb1mXNrMf/v//6vL3903333+UvJ+tuwYUNHHeDnnnvO/x1Ce/jw4ZWEr2LGEmVJLJKcLVq0yJfYqq5cGW7RXbp08cnQSIqmJgIiIAIiUBoBCeDS+OnTIiACIpAZArjo7rjjjl6Ivfvuu6ohG9PMfPHFF96ae8899/ikRTvvvLOvu0xpJBIWBVtNAphrEMHEdZLdF9fpTz/91Nd7bdOmjY8LDtZyjmkoum2RBKIsiYW4ReRSYot439yGOEb8SgAXOVn6mAiIgAjkEJAA1pIQAREQgQoicMwxx7iHHnrItWjRwpfY+da3vuUtwgMGDKigUWooIpAuAblAp8tfTxcBERCBUghIAJdCT58VAREQgYwR+Mtf/uIuvvhi71L5wQcfOGrK5rrfZqzL6o4IlB0BJcEquylTh0VABESgioAEsBaDCIiACIiACIiACBRAIGwZpDAlscKWQaJutDw5CpgkXSoCIiACNRCQANbSEAEREAEREAERqCLw/PPPew8CyjmR3Ivkat/+9rcdCcCKaX//+98dsdBkOt60aZPbfffdfVZjaiUT81yOLcqSWBs3bnT16tVzW2+9tY8pp9SWtS+//NLHlX/00Ufuvffe8+zUREAEREAESiMgAVwaP31aBERABERABCqKAOKU0jvBVqwARri1a9fOvfHGG65Ro0Y+2/WqVav8D9myyZpN0rZybFGVxGLsffr0cXfffbfr1auXmzVrlhfDtMGDB7uJEyf638+YMaMcManPIiACIpA5AhLAmZsSdUgEREAEREAE0iNw7bXXus8//9y1bt3a/2B1LFYAn3766V64UcN29uzZVcKOereTJk1y/J4s2OXYoiqJxdg//PBDd9BBB7m1a9e6xo0bVx0UvPLKK/7/OSjYddddyxGT+iwCIiACmSMgAZy5KVGHREAEREAERCA7BL7xjW8UJYBxd6Yu9VZbbeVde3fbbbeqQZlr71//+lfv2hv8XXZGnr8nUZXE4kl/+9vf3KhRo9zcuXPdn//8Z8/k2GOP9a7iu+yyS/7O6AoREAEREIFQBCSAQ2HSRSIgAiIgAiJQNwkUK4DDJnfiuv79+9dNuBq1CIiACIhA4gQkgBNHrgeKgAiIgAiIQPkQKFYAX3jhhW7ChAnukksucdddd90WA77pppvceeed57hu/Pjx5QNEPRUBERABEShrAhLAZT196rwIiIAIiIAIxEugWAFM3C+ZnxHBxPzmNhJtkXCL6373u9/FOwjdXQREQAREQAT+j4AEsJaCCIiACIiACIhAjQSKFcBdu3b15ZSmTp3qzjzzzC3uv3jxYtelSxfHdQsXLtQMiIAIiIAIiEAiBCSAE8Gsh4iACIiACIhAeRIoVgAjbhG506ZNc2ecccYWg0ccI34lgMtzXajXIiACIlCuBCSAy3Xm1G8REAEREAERSIBAsQJYLtAJTI4eIQIiIAIiUDABCeCCkekDIiACIiACIlB3CBQrgJUEq+6sEY1UBERABMqJgARwOc2W+ioCIiACIiACCRMoVgCHLYN02223uQEDBiQ8Kj1OBERABESgrhKQAK6rM69xi4AIiIAIiEAIAsUK4I0bN7p69eq5rbfe2r3zzjvu+9//ftXTvvzyS7f33nu7jz76yL333ntu9913D9ETXSICIiACIiACpROQAC6doe4gAiIgAiIgAhVLIJ8Anjx5suPnuOOOc+PGjduMQ58+fdzdd9/tevXq5WbNmuXFMG3w4MFu4sSJjt/PmDGjYtlpYCIgAiIgAtkjIAGcvTlRj0RABERABEQgNQLz5s1zV111VdXzV6xY4RDBbdq0qfq7kSNHuqOPPtr//xVXXOFGjx7t+vXr56ZPn75Zvz/88EN30EEHubVr17rGjRu7Vq1auVWrVrlXXnnF///y5cvdrrvumtpY9WAREAEREIG6R0ACuO7NuUYsAiIgAiIgAjUSQMTmi8klvrd///55BTAX/O1vf3OjRo1yc+fOdX/+85/dbrvt5o499lgvmnfZZRfNhAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgwFIagAAAb9JREFUgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJEpAAjhR3HqYCIiACIiACIiACIiACIiACIhAWgQkgNMir+eKgAiIgAiIgAiIgAiIgAiIgAgkSkACOFHcepgIiIAIiIAIiIAIiIAIiIAIiEBaBCSA0yKv54qACIiACIiACIiACIiACIiACCRKQAI4Udx6mAiIgAiIgAiIgAiIgAiIgAiIQFoEJIDTIq/nioAIiIAIiIAIiIAIiIAIiIAIJErg/wOnJAOBbQkmqQAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction\n",
    "y = model(x, t)\n",
    "y_np = y.reshape([100,-1]).to(\"cpu\").detach().numpy()\n",
    "\n",
    "# Plot\n",
    "X, Y = np.meshgrid(np.linspace(0, 1, 150), np.linspace(0, 1, 100))\n",
    "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"})\n",
    "ax.plot_surface(X, Y, y_np, linewidth=0, antialiased=False, cmap=cm.coolwarm,)\n",
    "ax.set_xlabel(\"t\"), ax.set_ylabel(\"x\"), ax.set_zlabel(\"f\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd07f2dd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusions\n",
    "\n",
    "**Growth rate**\n",
    "\n",
    "- We saw the difference between:\n",
    "    - Fitting a NN only on observations.\n",
    "    - Adding a regularization term from a 1st order PDE."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "132a6a45",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**1d wave**\n",
    "\n",
    "- We saw how to include:\n",
    "    - A 2nd order PDE.\n",
    "    - Multiple constraints on the initial conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0e47416",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Next steps**\n",
    "\n",
    "- With more complex equations, convergence is not achieved so easily.\n",
    "- Also, For time-dependent problems, many useful tricks have been devised over the past years such as:\n",
    "    - Decomposing the solution domain in different parts solved using different neural networks.\n",
    "    - Smart weighting of different loss contributions to avoid converging to trivial solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49a91deb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## References\n",
    "\n",
    "[[1](https://www.sciencedirect.com/science/article/pii/S0021999118307125)] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. \"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.\" Journal of Computational physics 378 (2019): 686-707.\n",
    "\n",
    "[[2](https://maziarraissi.github.io/PINNs/)] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. \"Physics Informed Deep Learning\".\n",
    "\n",
    "[[3](https://www.sciencedirect.com/science/article/pii/S095219762030292X)] Nascimento, R. G., Fricke, K., & Viana, F. A. (2020). A tutorial on solving ordinary differential equations using Python and hybrid physics-informed neural network. Engineering Applications of Artificial Intelligence, 96, 103996.\n",
    "\n",
    "[[4](https://towardsdatascience.com/solving-differential-equations-with-neural-networks-afdcf7b8bcc4)] Dagrada, Dario. \"Introduction to Physics-informed Neural Networks\" ([code](https://github.com/madagra/basic-pinn)).\n",
    "\n",
    "[[5](https://towardsdatascience.com/physics-and-artificial-intelligence-introduction-to-physics-informed-neural-networks-24548438f2d5)] Paialunga Piero. \"Physics and Artificial Intelligence: Introduction to Physics Informed Neural Networks\".\n",
    "\n",
    "[[6](https://github.com/omniscientoctopus/Physics-Informed-Neural-Networks)] \"Physics-Informed-Neural-Networks (PINNs)\" - implementation of PINNs in TensorFlow 2 and PyTorch for the Burgers' and Helmholtz PDE."
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