Lectures/Lecture25/3dasm_Lecture25.ipynb

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    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "# Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 25\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor\n",
    "\n",
    "### Suryanarayanan M. S. | <a href = \"mailto: s.manojsanu@tudelft.nl\">s.manojsanu@tudelft.nl</a>  | PhD Candidate"
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    "# Outline for today's lecture\n",
    "* Recap of previous lecture\n",
    "* Zeroth-order optimizers\n",
    "* Optimality criteria\n",
    "* Gradient-based optimizers\n",
    "    \n",
    "**References:**\n",
    "* J. R. R. Martins & Andrew Ning, Engineering Design Optimization, 2021 - Chapters 1 & 4\n",
    "* For practical details of algorithms (Extra):\n",
    "    * Nocedal, Jorge, and Stephen J. Wright. Numerical optimization. Springer Science & Business Media, 2006.\n",
    "* For Adam, momemtum & Adagrad\n",
    "    * Ian Goodfellow and Yoshua Bengio and Aaron Courville. Deep Learning. MIT Press, 2016 - Chapter 8"
   ]
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    "## Recap & contextualization\n",
    "<img align=right src=\"./figures/recap.png\" width=40%>\n",
    "\n",
    "**1. Unconstrained minimization**\n",
    "\n",
    "**2. Convex functions look like bowls**\n",
    "* Well behaved     \n",
    "* Every function has convex local approximations!  \n",
    "\n",
    "**3. Optimizer tradeoff**\n",
    "* Exploration vs exploitation  \n",
    "* Order of information (Taylor series expansion)"
   ]
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    "# Basic plotting tools needed in Python.\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
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    "class FunctionPlot():\n",
    "    \"\"\"Simple class to manage plotting of a function.\n",
    "\n",
    "    Plot the function, its first order model and its second order model.\n",
    "    All of these can be plotted one by one interactively.\n",
    "    \"\"\"\n",
    "    def __init__(self, bounds=50, convex=True):\n",
    "        self.count = 0\n",
    "        self.saved_x = []  # Saved every input received\n",
    "        self.line = None\n",
    "        self.bounds = bounds  # Bounds on the decision variable\n",
    "        self.convex = convex\n",
    "\n",
    "        self.random_coeff = np.random.choice([-25, -15, 10, 20])  # For the underlying function\n",
    "        self.sine_coeff = 100\n",
    "        self.sine_freq = 0.2\n",
    "        self.show_canvas()\n",
    "\n",
    "    def underlying_func(self, x):\n",
    "        \"\"\"True function.\n",
    "        Sum of two functions:\n",
    "        1. A quadratic function with a random coefficient\n",
    "        The form is ax**2 - bx + c, where a is 1, b is random_coeff and c is 1.\n",
    "        2. a*sine(b*x) \n",
    "        \"\"\"\n",
    "        if self.convex:\n",
    "            return x**2 - self.random_coeff*x + 1\n",
    "        else:\n",
    "            return x**2 - self.random_coeff*x + 1 + self.sine_coeff*np.sin(self.sine_freq*x)\n",
    "\n",
    "    def gradient(self, x):\n",
    "        \"\"\"The gradient of the underlying function.\"\"\"\n",
    "        if self.convex:\n",
    "            return 2*x - self.random_coeff\n",
    "        else:\n",
    "            return 2*x - self.random_coeff + self.sine_coeff*self.sine_freq*np.cos(self.sine_freq*x)\n",
    "\n",
    "    def hessian(self, x):\n",
    "        if self.convex:\n",
    "            return 2\n",
    "        else:\n",
    "            return 2 - self.sine_coeff*self.sine_freq**2*np.sin(self.sine_freq*x)\n",
    "\n",
    "    def first_order_model(self, x, x0):\n",
    "        \"\"\"The first order model of the underlying function.\"\"\"\n",
    "        return self.underlying_func(x0) + self.gradient(x0)*(x - x0)\n",
    "\n",
    "    def second_order_model(self, x, x0):\n",
    "        \"\"\"The second order model of the underlying function.\"\"\"\n",
    "        return self.underlying_func(x0) + self.gradient(x0)*(x - x0) + 0.5*self.hessian(x0)*(x - x0)**2\n",
    "\n",
    "    def show_canvas(self):\n",
    "        \"\"\"Shows the figure on which to plot along with the bounds.\"\"\"\n",
    "        fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "        ax.set_xlabel('x')\n",
    "        ax.set_ylabel('y = f(x)')\n",
    "        ax.set_xlim(-self.bounds, self.bounds)\n",
    "        ax.axvline(x=-self.bounds+3, color='r')  # To show the limit\n",
    "        ax.axvline(x=self.bounds-3, color='r')\n",
    "        self.fig = fig\n",
    "        self.ax = ax\n",
    "\n",
    "    def plot(self, x_value, with_first_order=False, with_second_order=False):\n",
    "        \"\"\"Plots the function, its first order model or its second order model.\"\"\"\n",
    "        self.count += 1\n",
    "        self.saved_x.append(x_value)\n",
    "\n",
    "        self.ax.plot(self.saved_x,\n",
    "                         [self.underlying_func(x) for x in self.saved_x], 'bo')\n",
    "\n",
    "        if with_first_order:\n",
    "            self._plot_first_order_model()\n",
    "        elif with_second_order:\n",
    "            self._plot_second_order_model()\n",
    "        else:\n",
    "            pass\n",
    "\n",
    "#         self.ax.legend()\n",
    "        plt.show()\n",
    "\n",
    "    def _plot_first_order_model(self):\n",
    "        if self.line is not None:\n",
    "            self.line.pop(0).remove()\n",
    "        x = np.linspace(-self.bounds, self.bounds, 100)\n",
    "        y = self.first_order_model(x, self.saved_x[-1])\n",
    "        self.line = self.ax.plot(x, y, 'r--', label='First-order model')\n",
    "\n",
    "    def _plot_second_order_model(self):\n",
    "        if self.line is not None:\n",
    "            self.line.pop(0).remove()\n",
    "        x = np.linspace(-self.bounds, self.bounds, 100)\n",
    "        y = self.second_order_model(x, self.saved_x[-1])\n",
    "        self.line = self.ax.plot(x, y, 'r--', label='Second-order model')\n",
    "\n",
    "    def plot_minimum(self):\n",
    "        \"\"\"Shows the minimum of the function.\"\"\"\n",
    "        if self.convex:\n",
    "            min_x = self.random_coeff / 2\n",
    "            min_y = self.underlying_func(min_x)\n",
    "        else:\n",
    "            x = np.linspace(-self.bounds, self.bounds, 200)\n",
    "            yvals = self.underlying_func(x)\n",
    "            min_x = x[np.argmin(yvals)]\n",
    "            min_y = np.min(yvals)            \n",
    "        \n",
    "        self.ax.plot(min_x, min_y, 'x', markersize=20, color='b', label='Minimum')\n",
    "\n",
    "    def plot_func(self):\n",
    "        x = np.linspace(-self.bounds, self.bounds, 100)\n",
    "        y = self.underlying_func(x)\n",
    "        self.ax.plot(x, y, \"b:\",label='True function')\n"
   ]
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    "# Exercise: walking as an optimizer\n",
    "\n",
    "* Understand different optimizers\n",
    "    * How they perceive the objective function landscape\n",
    "* Blue dots - Underlying function\n",
    "* Red lines - bounds\n",
    "* Red cross - Minima\n",
    "\n",
    "#### We will see how important information is!\n"
   ]
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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 453,
       "width": 846
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the object separately in a cell\n",
    "plotter = FunctionPlot(convex=False, bounds=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Zeroth-order optimizers\n",
    "* Black-box / derivative-free optimizers\n",
    "    * Only access function's outputs\n",
    "* Used extensively for hyperparameter optimization\n",
    "    * Decision variables are discrete (or mixed)\n",
    "    * Discontinuous functions\n",
    "        * Gradient and Hessian are not defined (or not used or not accessible)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "image/png": {
       "height": 448,
       "width": 859
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 13  # Make guesses!\n",
    "plotter.plot(x)\n",
    "plotter.plot_minimum()\n",
    "plotter.plot_func()\n",
    "plotter.fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Issues with Zeroth-order methods\n",
    "* Not very efficient.\n",
    "    * The number of function evaluations increases exponentially with dimensionality.\n",
    "        * `Curse of dimensionality`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Usually do not know when to stop!\n",
    "    * **Cannot identify minima**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# How to know a minima if we see one\n",
    "\n",
    "* Minima are defined as points better than their neighbourhood\n",
    "* To identify minima\n",
    "    * \"Look\" around a point\n",
    "* We need a local model of the objective function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Local model using Taylor series**\n",
    "\n",
    "\n",
    "$$ f(\\mathbf{x} + \\alpha \\mathbf{p})|_{\\mathbf{x}=\\mathbf{x}_0} \\approx f(\\mathbf{x}_0) + \\alpha \\nabla f(\\mathbf{x}_0)^T \\mathbf{p} + \\frac{1} {2}\\alpha^2 \\mathbf{p}^T   \\mathbf{H}(\\mathbf{x}_0)   \\mathbf{p}$$\n",
    "\n",
    "$$ \\text{Gradient: } \\nabla f(\\mathbf{x}) = \\Big[\\frac{\\partial f}{ \\partial x_1}, \\frac{\\partial f}{ \\partial x_2} ..., \\frac{\\partial f}{ \\partial x_{D_x}} \\Big]^T$$\n",
    "\n",
    "\n",
    "$$ \\text{Hessian: } H(\\mathbf{x}) = \\begin{bmatrix} \\frac{\\partial^2 f}{\\partial x_1^2} & \\cdots & \\frac{\\partial^2 f}{\\partial x_1 \\partial x_{D_x}} \\\\ \\vdots &  \\ddots & \\vdots \\\\ \\frac{\\partial^2 f}{\\partial x_{D_x} \\partial x_1} & \\cdots & \\frac{\\partial^2 f}{\\partial x_{D_x}^2} \\end{bmatrix} $$\n",
    "\n",
    "**Need gradients and/or Hessian information**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Optimality criteria\n",
    "\n",
    "* Mathematical conditions to identify minima from other points!\n",
    "* In practice,\n",
    "    * Used internally by gradient-based optimizers\n",
    "        * to find minima and to stop.\n",
    "    * In constrained optimization\n",
    "        * Optimality is checked with KKT (Karush-Kuhn-Tucker) conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### First-order condition\n",
    "* **At a local minimum, gradient vanishes.**\n",
    "    * $\\nabla f(\\mathbf{x}^*) = \\mathbf{0}$\n",
    "<img align=right src=\"./figures/1d_optimality.png\" width=50%>\n",
    "* In one-dimension:\n",
    "    * Slope = 0 at every minimum (High school calculus!)\n",
    "* In multi-dimensions:\n",
    "    * Gradient = collection of slopes\n",
    "    * **Gradient** = **0**: Slope in every direction is zero\n",
    "* If the gradient is non-zero\n",
    "    * We can travel **opposite** to the gradient to reduce the function further.\n",
    "    * (Remember that the gradient points in the ascent direction!)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "🚨 **Gradient can be zero at other places too** 🚨\n",
    "* Stationary points\n",
    "    * Local maxima\n",
    "    * Saddle points!\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* So how do we check ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can look at the Hessian..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Second-order condition\n",
    "\n",
    "* Hessian is the **curvature matrix**\n",
    "    * Eigenvalues are curvatures along different directions\n",
    "* Local minima\n",
    "    * If Hessian = positive definite (all eigenvalues are > 0)\n",
    "    * In one-dimension: $H(x^*) > 0$\n",
    "* Local maxima\n",
    "    * If Hessian = negative definite (all eigenvalues < 0)\n",
    "* Saddle point\n",
    "    * If Hessian has positive and negative eigenvalues\n",
    "* If semi-definite (some/all eigenvalues are zero), then we are not sure!\n",
    "\n",
    "<img src=\"./figures/hessian_stationary_points.png\" width=60%>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gradient-based optimizers\n",
    "\n",
    "<img align=centre src=\"./figures/opt_spectrum.png\" width=50%>\n",
    "\n",
    "* Spectrum: from first order to second order\n",
    "    * Based on Taylor series local model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Common steps:**\n",
    "\n",
    "**1. They need a guess to start - Initialization**\n",
    "\n",
    "**2. Update rule to make better guesses**\n",
    "\n",
    "$\\mathbf{x}_{k+1} = \\mathbf{x}_k + \\alpha \\mathbf{p}$\n",
    "\n",
    "* $\\mathbf{p}$ is a **search direction**\n",
    "    * Which direction to move ?\n",
    "    * $\\mathbf{p}$ depends on $\\nabla f$\n",
    "* $\\alpha$ is a **step size** (in ML, sometimes called learning rate)\n",
    "    * How much to move along $\\mathbf{p}$ \n",
    "    * Usually it is a scalar\n",
    "    \n",
    "**3. Stopping criteria**\n",
    "* E.g. $||\\nabla f(\\mathbf{x})|| \\leq \\epsilon $, where $\\epsilon$ is some tolerance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gradient descent (GD)\n",
    "\n",
    "* Simplest gradient-based optimizer\n",
    "    * Utilize only gradients\n",
    "    * Pure first-order"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Search direction , $\\mathbf{p} = - \\nabla f$\n",
    "    * Steepest descent!\n",
    "    * We are decreasing the function's value most rapidly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Step size, $\\alpha$ = scalar\n",
    "    * Same for all directions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* **Stochastic gradient descent (SGD)**\n",
    "    * Common ML optimizer for large datasets\n",
    "    * Gradient is estimated using **minibatches** (subsets of the training data; more on this later)\n",
    "    * Full batch, i.e. when using full training data, SGD = GD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Choosing step size (a.k.a. learning rate) matters\n",
    "\n",
    "<img align=right src=\"./figures/lr.png\" width=40%>\n",
    "\n",
    "* Most important hyper-parameter\n",
    "    * For most gradient-based optimizers\n",
    "    * step size = learning rate\n",
    "* Too small, slow convergence\n",
    "    * Less exploration\n",
    "    * \"Bad\" local minimum\n",
    "* Too large, can diverge\n",
    "    * Oscillations\n",
    "    \n",
    "Common strategy in ML:\n",
    "* Use **learning rate schedule**, instead of a constant learning rate\n",
    "    * E.g. decrease learning rate slowly at each increment $t$:\n",
    "    \n",
    "$$\\mathbf{x}_{t+1} = \\mathbf{x}_t + \\alpha_t \\mathbf{p}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Question**: Can you try to anticipate when **Stochastic Gradient Descent** (SGD) is used instead of **Gradient Descent** (GD)?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "1. For very large datasets and for models with many variables because GD would need a lot of memory to save all the gradients at each point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. Also, because SGD does not use the complete gradient for the entire training dataset to update the model parameters, this causes \"noise\" and that can act as regularization!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We will discuss this in more detail when learning about artificial neural networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 453,
       "width": 846
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotter = FunctionPlot(convex=True, bounds=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SJEmSJEmSVLIYnKlMWLSo4PHvv8OkSdHUIkmSJEmSJEmSSiaDM5V65cvDCy/A0UeH43LlYMAAOPPMSMuSJEmSJEmSJEkljMGZyoSsLHjtNTjySHjpJejRI+qKJEmSJEmSJElSSZMZdQFSqlSqBEOGQEZG1JVIkiRJkiRJkqSSyBVnKlMMzSRJkiRJkiRJUiIGZ9KfFiwI+5798UfUlUiSJEmSJEmSpCjYqlEC5s2Dww+Hr7+GGTNCS8fKlaOuSpIkSZIkSZIkpZIrzlTm/fADHHhgCM0ARo+G7t1h1apo65IkSZIkSZIkSallcKYyb9UqWLKk4Llp0+CXX6KpR5IkSZIkSZIkRcPgTGXezjvDBx9ArVrheKed4KOPYNtto61LkiRJkiRJkiSllsGZBOyxBwwdCvvvH1o1GppJkiRJkiRJklT2ZEZdgFRStG0LH38MGRlRVyJJkiRJkiRJkqLgijNpA4ZmkiRJkiRJkiSVXQZn0iYaNAjuvz/qKiRJkiRJkiRJUrLYqlHaBC+/DCefDLm5kJUF550XdUWSJEmSJEmSJKm4ueJMKsIzz8C//x1CM4Dzz4d+/aKtSZIkSZIkSZIkFT+DM6kIixdDXl7Bc5MmRVKKJEmSJEmSJElKIoMzqQgXXwy33rr++Pzz4dFHo6tHkiRJkiRJkiQlh3ucSZvgmmtg5crwcffdkJERdUWSJEmSJEmSJKm4GZxJm+jmm8N/Dc0kSZIkSZIkSSqdDM6kTWRgJkmSJEmSJElS6eYeZ1IxWLMGTjsNRo6MuhJJkiRJkiRJkrS5DM6kLbRqFZxwAjz7LHTuDJ98EnVFkiRJkiRJkiRpcxicSVtg5Uro3h3eeiscL1sGnTrB+PGRliVJkiRJkiRJkjaDwZm0BTIzoVKlgudyc2HJkmjqkSRJkiRJkiRJm8/gTNoCmZnw4otwzDHhuGpVGDoUDjss2rokSZIkSZIkSdLfZ3AmbaGsLHj1VfjnP+H99+Ggg6KuSJIkSZIkSZIkbY7MqAuQSoMKFeCll6KuQpIkSZIkSZIkbQlXnEkpEou6AEmSJEmSJEmSVCiDMykFvqYFB/IROWwTdSmSJEmSJEmSJCkBgzMpyT5nDzowik84gEMZztyf/bKTJEmSJEmSJKkk8g6+lESffVGeQxjBAuoBMIOdObR7DX7+OeLCJEmSJEmSJEnSRgzOpCRq1DCPBvxS4Fy9OjGqVImoIEmSJEmSJEmSlJDBmZRE9evFGM6h7Mw3ABzIaIYMXEy1ahEXJkmSJEmSJEmSNmJwJiXZ1vzMcA7lNJ7hXY6matWoK5IkSZIkSZIkSfFkRl2AVBZsw1ye4T9RlyFJkiRJkiRJkgrhijOphFi5MuoKJEmSJEmSJEkq2wzOpBLgjjtgv/3gt9+irkSSJEmSJEmSpLLL4EyK2K23wtVXw2efwRFHwKJFUVckSZIkSZIkSVLZZHAmReihh+C669YfT54MHTvC6tXR1SRJkiRJkiRJUlllcCZFqHNnaNy44LlTT4WsrGjqkSRJkiRJkiSpLDM4kyLUtCmMGAGNGoXjhx+G88+PtiZJkiRJkiRJksqqzKgLkMq6Zs1CePbJJ3D66VFXI0mSJEmSJElS2WVwJpUAO+8cPiRJkiRJkiRJUnRs1SilgcWLYenSqKuQJEmSJEmSJKl0MziTSrhFi+CIIyA7G5Yti7oaSZIkSZIkSZJKL4MzqQT77Tc4/HCYOBFGjzY8kyRJkiRJkiQpmQzOpBLsxBNh8uT1x6NGQc+e0dUjSZIkSZIkSVJpZnAmlWD33AO1a68/3mYbuOWW6OqRJEmSJEmSJKk0MziTSrA994Thw6FOHWjUCEaMgKZNo65KkiRJkiRJkqTSKTPqAiQVbl14VrEi7LRT1NVIkiRJkiRJklR6GZxJaWCPPaKuQJIkSZIkSZKk0s9WjVIpMGoULF4cdRWSJEmSJEmSJKU3gzMpzQ0dCh07whFHwKJFUVcjSZIkSZIkSVL6MjiT0th770HXrrB6NUycGMKz336LuipJkiRJkiRJktKTwZmUplavhv/7P1i1av25SZPg4Yejq0mSJEmSJEmSpHRmcCalqawsGDIEGjVaf+7kk+Gaa6KrSZIkSZIkSZKkdGZwJqWxnXeGkSNhm23g3/+GAQOgfPmoq5IkSZIkSZIkKT1lRl2ApC2z007w6afQoIGhmSRJkiRJkiRJW8LgTCoFttkm6gokSZIkSZIkSUp/tmqUSrm1a+Haa+GXX6KuRJIkSZIkSZKkks3gTCrF1q6F//wHbrsNDjkE5s2LuiJJkiRJkiRJkkougzOplMrLgzPPhOeeC8fTpkGHDpCTE21dkiRJkiRJkiSVVAZnUim1cCGMHl3w3I8/wsyZ0dQjSZIkSZIkSVJJZ3AmlVL16sGoUdCsWTjOyoI334SDD460LEmSJEmSJEmSSiyDM6kUa9w4rDrbYw945RXo1CnqiiRJkiRJkiRJKrkyoy5AUnJtvTVMmgSZfrVLkiRJkiRJklQoV5xJZUBRodnatampQ5IkSZIkSZKkkszgTCrjZswIrRwnTIi6EkmSJEmSJEmSomVwJpVhs2fDoYfC11/DYYfBmDFRVyRJkiRJkiRJUnQMzqQy6qefQmiWkxOOlyyBjh3h00+jrUuSJEmSJEmSpKgYnEllVO3asMsuBc+1aAHNm0dTjyRJkiRJkiRJUTM4k8qoSpXgrbegc+dwvOee8N57UKNGpGVJkiRJkiRJkhQZgzOpDKtYEV5/HS67DD74IKxCkyRJkiRJkiSprMqMugBJ0crKgnvuiboKSZIkSZIkSZKi54ozSUWaNi3qCiRJkiRJkiRJSj6DM0mF6tsXdtsN+vWLuhJJkiRJkiRJkpLL4ExSQk8+CRdcALEY9OwJffpEXZEkSZIkSZIkScljcCYprokT4ayzCp678EKYNCmaeiRJkiRJkiRJSjaDM0lx7bMPXHttwXN33BHOS5IkSZIkSZJUGhmcSYorIwNuuQVuvz0cX3MNXHlltDVJkiRJkiRJkpRMmVEXIKlku+oqaN8eDjww6kokSZIkSZIkSUougzNJRTrooKgrkCRJkiRJkiQp+WzVKGmL/P47XH45rFwZdSWSJEmSJEmSJG0ZV5xJ2mzLlkF2NnzyCUyaBG+/DVWrRl2VJEmSJEmSJEmbxxVnkjbLypXQtWsIzQCGD4eOHWHx4iirkiRJkiRJkiRp8xmcSdosM2fChAkFz333HSxcGE09kiRJkiRJkiRtKYMzSZtl993DKrM6dcJx7drw4YfQtGm0dUmSJEmSJEmStLkMziRttr33htGjoXlzeO+9EKZJkiRJkiRJkpSuMqMuQFJ623VX+PJLKF8+6kokSZIkSZIkSdoyrjiTtMWKCs1WrEhNHZIkSZIkSZIkbQmDM0lJNXx42Pfs00+jrkSSJEmSJEmSpMIZnElKmjFj4B//gHnz4LDDYNiwqCuSJEmSJEmSJCkxgzNJSfHVV3D00bBsWThetiwcT54cbV2SJEmSJEmSJCVicCYpKXbYAfbbr+C57t1hzz2jqUeSJEmSJEmSpKIYnElKisqV4e234YQTwnGnTvDss1C+fLR1SZIkSZIkSZKUSGbUBUgqvbKy4MUXoW1bOOeccCxJkiRJkiRJUkllcCYpqcqXh0svjboKSZIkSZIkSZKKZqtGSZFauxYeeQTWrIm6EkmSJEmSJElSWWdwJikysRicfTacdx507w4rVkRdkSRJkiRJkiSpLDM4kxSZq66Cfv3C60GDoFMn+OOPaGuSJEmSJEmSJJVdBmeSIjF7NvTpU/Dc2LHwxRfR1CNJkiRJkiRJksGZpEjssAN88AHUqBGOy5WDl1+G9u2jrUuSJEmSJEmSVHYZnEmKTPv2MGoUNGwITz8NXbtGXZEkSZIkSZIkqSzLjLoASWXbnnvCN99A9epRVyJJkiRJkiRJKutccSYpckWFZmvWpKYOSZIkSZIkSVLZZnAmqUSbNQuaN4fBg6OuRJIkSZIkSZJU2hmcSSqx5s6FI46A776DLl3gueeirkiSJEmSJEmSVJoZnEkqkRYvho4dYfbscLx2LfToAa+8EmlZkiRJkiRJkqRSzOBMUolUtSq0bl3w3N57w1FHRVOPJEmSJEmSJKn0MziTVCJlZsIzz0Dv3uG4aVN4912oXj3auiRJkiRJkiRJpVdm1AVIUiIZGXD33bDddtCpEzRoEHVFkiRJkiRJkqTSzOBMUol37rlRVyBJkiRJkiRJKgts1Sgp7T3xBOTkRF2FJEmSJEmSJCndGZxJSmuPPw5nnw3t28P06VFXI0mSJEmSJElKZwZnktLWa6/B//1feP3jj3DAATB+fLQ1SZIkSZIkSZLSl8GZpLS0di3ceivEYuvPLVwIkydHV5MkSZIkSZIkKb0ZnElKS+XLw4cfQtu2689df31o2yhJkiRJkiRJ0ubIjLoASdpcdevCsGFw7LGwww5w441RVyRJkiRJkiRJSmcGZ5LSWtWq8M47YQVaRkbU1UiSJEmSJEmS0pmtGiWlvaysEJwlsnAh5Oamrh5JkiRJkiRJUnoyOJNUqv3xBxx+OHTtCsuWRV2NJEmSJEmSJKkkMziTVGqtXh32P/vsMxg8GA49FObPj7oqSZIkSZIkSVJJZXAmqdQ691z48MP1x+PHQ48e0dUjSZIkSZIkSSrZDM4klVo9ekCtWuuP69WDPn2iq0eSJEmSJEmSVLIZnCXB5MmTuf322+nUqRNNmjShQoUKVK1alZ133pnTTjuNjz766G/NN3ToULp3707jxo2pUKECjRs3pnv37gwdOnST51i+fDn33HMPbdu2pXbt2lStWpUWLVpw2WWX8eOPP27yPF999RVnn302zZo1o1KlStSrV4+DDjqIJ554gtzc3L/165KS7YAD4JNPYNttoXLl0K6xWbOoq5IkSZIkSZIklVQZsVgsFnURpUmHDh0YPXp0keNOOeUU+vXrR1ZWVsIxsViMs88+myeffDLhmF69evH444+TkZGRcMysWbPIzs7mm2++iXu9Ro0avPjiixx99NGF1ty/f3/OPfdcVq1aFfd6u3btGDRoEHXq1Cl0ns2Rk5NDkyZNAJgzZw6NGzcu9s+RFPPnQ/36Bc/9+mtY+qSUmTsXvv0WDj446kokSZIkSZIkqQRJ43vYycoNXHFWzH766ScAGjVqxIUXXshrr73G+PHjGTt2LPfffz/bbLMNAM8//zynnXZaoXNde+21+aFZq1atGDhwIOPHj2fgwIG0atUKgCeffJLrrrsu4RxLly6lc+fO+aFZz549GTZsGGPGjOG2226jatWq/P777xx//PFMnTo14TzvvfcevXr1YtWqVTRo0IA+ffrw6aefMmTIELp37w7AuHHj6N69O3l5eZv2myWlSKNGhmaSJEmSJEmSpKK54qyYde7cmVNPPZVjjz2W8uXLb3R9wYIFtG/fnm+//RaA0aNHc+CBB240bubMmbRo0YLc3Fxat27N6NGjqVSpUv715cuX06FDByZOnEhmZibTp0+nadOmG81z4403ctNNNwFw991307t37wLXx44dy0EHHURubi6HHHIIw4cP32iO3NxcWrRowcyZM6levTqTJ0/e6HOde+65PProowA8++yznHrqqUX9Vv0trjhTMr3xBowYAQ8+CHG+bCVJkiRJkiSpdErje9iuOEsTgwYN4oQTTogbmgHUrVuX++67L//4tddeizvugQceyN8zrG/fvgVCM4DKlSvTt29fIARbDz744EZzrFmzhoceegiAFi1acOmll240Zr/99uOMM84AYMSIEUyaNGmjMW+++SYzZ84E4Kqrroob0N1zzz3UqlUr/7WULj7+GP79b3j4YTj+eFixIuqKJEmSJEmSJElRMTiLwMEb9IybNWvWRtdjsRhvv/02AM2bN6ddu3Zx52nXrh277LILAG+99RZ/XTw4cuRIFi9eDECPHj0oVy7+H/eGLSPfeOONja6/9dZbccduqHLlypxwwgkAfPnll8yYMSPuOKkkmTYN/vEPWLdt35tvwuGHw7Jl0dYlSZIkSZIkSYqGwVkEVq9enf86Xpg1e/bs/L3SOnToUOhc667n5OTw/fffF7j20UcfbTQuntatW1OlShUAPv74442ur5tnl112oWHDhkXWkmgeqaT59tuNQ7LddoPKlaOpR5IkSZIkSZIULYOzCIwaNSr/dfPmzTe6Pm3atEKvb2jD6xu+7+/Mk5mZmd9+8a9zLF26lJycnC2uRSqJunSBoUOhevVw3LkzPPooZGREW5ckSZIkSZIkKRqZURdQ1uTl5XHnnXfmH69rb7ihOXPm5L8uajO7dRvf/fV9Gx5XqVKFmjVrFjnP1KlTmT9/PqtWraJChQpAWMm2rgXkltRSlHXhXCLz5s37W/NJm+qQQ8I+ZzfeCM89B5n+qyhJkiRJkiRJZZa3iFPsgQceYPz48QB069aN1q1bbzRmyZIl+a+rVq1a6HzrWixCWB0Wb56i5og3z7rgrLhqKcqGoZuUai1bwuuvR12FJEmSJEmSJClqtmpMoVGjRnHllVcCUL9+fR577LG441auXJn/Oisrq9A51wVcACtWrIg7T1FzFDZPcdUipbNVq+D55+HPxZeSJEmSJEmSpFLKFWcp8tVXX9GtWzdyc3OpUKECr7zyCg0aNIg7tmLFivmvV69eXei8q1atyn9dqVKluPMUNUdh8xRXLUUpqrXjvHnzaNu27d+aUyoOeXlw+ukwcCB89FHYA812jpIkSZIkSZJUOnn7NwVmz55Nx44dWbRoEeXLl2fgwIF06NAh4fhq1arlvy6q5eGyZcvyX/+1leK6eTalbWKieYqrlqIUtX+aFJVrrw2hGcBTT8GcOfDKK7DBl4YkSZIkSZIkKYk++gj69IH//hc2ocneFrFVY5LNnTuXww8/nLlz55KRkcHTTz9Nt27dCn3PhiFSTk5OoWM3XKn1133C1s2zbNkyFi9evEnz1KtXr0DLxeKqRUpHX34Jd95Z8NzHH8MPP0RTjyRJkiRJkiSVNS+/DIcfDq+9BmeemfwtdQzOkmjBggUcccQRfPfddwD07duXU089tcj37brrrvmvp0+fXujYDa+3aNFis+bJzc1l1qxZceeoWrVqfgi2JbVI6Wj33eHVV2Fdx9Ly5cM/zrvvHm1dkiRJkiRJklQWPPYYnHgirNtJ6vnn4YYbkvs5Dc6S5Pfff+fII4/k66+/BuDOO+/k3HPP3aT37rDDDjRq1AiAUaNGFTp29OjRAGyzzTZsv/32Ba4dcMAB+a8Lm2fixIn5bRbbt2+/0fV183zzzTf8/PPPCefZ8HPEm0dKR8ceC8OHQ9268MQTcOSRUVckSZIkSZIkSWVD27ZQuXLBc1OmwNq1yfucBmdJsHz5crKzs5k8eTIA11xzDVdcccUmvz8jI4MuXboAYRXXuHHj4o4bN25c/iqvLl26kJGRUeD6wQcfTI0aNQB49tlniSVYvzhgwID81/HaSHbt2jXu2A0tX76cV155BQgr3Xbeeee446R0tN9+8O23cMYZUVciSZIkSZIkSWXHPvuEVo3l/kyz/u//4M03Q3ewZDE4K2arV6+mW7dufPLJJwBceOGF3HrrrX97nosuuojMzEwAzj//fFasWFHg+ooVKzj//PMByMzM5KKLLtpojqysLC644AIApk2bxr333rvRmLFjx9K/f38AOnToQJs2bTYa061bN5o2bQrAHXfckd/WcUO9e/dm0aJF+a+l0qZWrcKvz5qV/N66kiRJkiRJklTWdO4MjzwC99wDDz8Mf0YnSZMRS7QMSZvl2GOP5Y033gDg0EMP5cEHH9xoJdiGsrKyEq7Ouuqqq7jzzjsBaNWqFVdccQVNmzZl1qxZ3HXXXUyZMiV/3O233x53jiVLltC6dWu+/fZbAHr16sWJJ55IpUqVGDFiBLfffjtLly6lUqVKjBkzhr322ivuPO+++y7HHHMMeXl5NGjQgGuvvZa2bduyaNEinnrqKV5//XUgtHUcOXIk5Ys57s3Jycnfa23OnDk0bty4WOdPmvnzoX79gud+/RXq1YumHiXFl19C+/bQvXto55iVFXVFkiRJkiRJkrQJ0vgedrJyA4OzYlZYSBbPdtttx/fffx/3Wl5eHj179uTpp59O+P4zzjiDJ598knLlEi8enDlzJkcffTQzZsyIe7169er897//pXPnzoXW+tRTT3Heeeexet0ufH/Rtm1bBg8eTN26dQudZ3MYnKmkmjsX2rWDOXPC8WGHweuvw59dUiVJkiRJkiSp5Coh97BHjYKMDDjooE1/T7JyA1s1lmDlypWjf//+DB48mC5dutCoUSOysrJo1KgRXbp04d1336Vfv36FhmYAzZo1Y8qUKdx11120bt2amjVrUrlyZXbZZRcuvvhipk6dWmRoBtCzZ08mTZpEz5492XHHHalYsSJ16tThgAMO4LHHHuOTTz5JSmgmlVR5edCly/rQDGDYMLjttuhqkiRJkiRJkqR08uKL0LFjuNc6bVrU1bjiTGnCFWcqqd55B048EZYvD8f77RfCs0qVoq1LkiRJkiRJkooU4T3sWAzuuguuumr9ue23h7FjoWHDot/vijNJKoGOOSYsI27QAJo1g//9z9BMkiRJkiRJkooSi8GECQXPff89PPRQJOXky4z200tS+mvdGsaNg9xcsFupJEmSJEmSJBWtXDl4/vmwFc66AO288+DWW6Oty+BMkorB9tsXfj03N2xuWb58SsqRJEmSJEmSpBKvcuXQxWu//UJodskl4T5qlAzOJCnJYjG44ILw5MTAgVC1atQVSZIkSZIkSVLJ0LAhfPklVKkSdSWBe5xJUpL16QOPPQaDBsGBB0JOTtQVSZIkSZIkSVLqjBwJa9cmvl5SQjMwOJOkpHrnHbj44vXHn30GHTrA6tWRlSRJkiRJkiRJKRGLwS23wCGHwOWXR13NpjE4k6QkqlkTatUqeO722yErK5JyJEmSJEmSJCklVq2CHj3g+uvD8f33w+OPR1vTpjA4k6QkOvBAGDcOdtopHN9yC/zzn9HWJEmSJEmSJEnJ9sUX8NJLBc+ddx58/XU09WwqgzNJSrKddgrh2d13wzXXRF2NJEmSJEmSJCVf69bw1FPrjzMy4L77oEWL6GraFJlRFyBJZUHt2tC7d9RVSJIkSZIkSVLq9OgBM2bAgw/CwIFwzDFRV1Q0V5xJUgkwe3bYIHP27KgrkSRJkiRJkqTic/PN8Pnn6RGagcGZJEVu8WLIzoaRI2HffWHs2KgrkiRJkiRJkqRNk5cHc+Ykvl6uHDRtmrp6tpTBmSRFaM0aOOEEmDYtHM+fH1aeDR8ebV2SJEmSJEmSVJSVK+Hf/w4LAgoLz9KJwZkkRei332Du3ILndtopbJwpSZIkSZIkSSXVzz+HRQAvvwzz5kHnzrBkSdRVbTmDM0mKUIMG8MkncOSR4bh+fRg0CKpXj7YuSZIkSZIkSSrM1VfDuHHrj6dOhZNPhlgsupqKg8GZJEWsRo0Qll14Ifzvf7DddlFXJEmSJEmSJEmFu/9+aN58/XG1avB//wcZGdHVVBwyoy5AkgSZmfDgg1FXIUmSJEmSJEmbpmZNeOedsL9Z9ephUUDLllFXteVccSZJaeKWW+Ctt6KuQpIkSZIkSZKCZs1gyBAYP750hGZgcCZJaeGFF+D666F7d7jjjvTvEyxJkiRJkiQpPSxaVPj9yLZtoV691NWTbAZnklTCjRsHZ54ZXsdiYdPNM84wPJMkSZIkSZKUXJ9/DnvuCbfdFnUlqWNwJkkl3Ouvw6pVBc+1bZv+m2xKkiRJkiRJKrneegvat4c5c+C668J9yrLA4EySSri774Z77lkflJ13Hpx9drQ1SZIkSZIkSSq9vv8ejj8eli1bf+6UU2Dy5MhKShmDM0kq4TIy4LLL4H//C3ucPfBA1BVJkiRJkiRJKs223z480L+hvfeGxo0jKSelDM4kKU107hyWQ2dmRl2JJEmSJEmSpNLuoovgjDPC6x49YNgwqF8/0pJSwuBMkkqJefPgwgthxYqoK5EkSZIkSZKU7jIy4NFH4YUX4JlnoEKFqCtKDYMzSSoFVqyArl2hTx84+OAQokmSJEmSJElSUZZTKeG1rCw46aQQopUVBmeSlOZisbBkevz4cDx+PLRtC199FW1dkiRJkiRJkkquWAzueKgSezCV+dSNupwSw+BMktLczJkwaFDBc1ttBQ0aRFOPJEmSJEmSpJJt+XL417/g6tuqMotmdOcNVpEVdVklgsGZJKW5nXaCsWNhhx3CcbVq8M47UNeHRCRJkiRJkiTFcckl8PLL648/5kDO4TFi0ZVUYhicSVIpsNtuoUXjwQfDSy+FY0mSJEmSJEmK56aboEmT9ccZ5NGc6dEVVIJkRl2AJKl41K0Lw4eXrY06JUmSJEmSJP19DRrAW2/BAQfEyFrxOy/yb45mSNRllQiuOJOkUqSo0Oyhh+C991JTiyRJkiRJkqSSa++94eUn/+BT9jU024DBmSSVEYMHw8UXw9FHw733QsyGxZIkSZIkSVKp9scfhd8HPObI1ezCt6krKA0YnElSGTB9Ovz73+F/knl50Ls3nHaa4ZkkSZIkSZJUWn32GbRsCY88EnUl6cXgTJLKgP79w9MlG9p1V/dDkyRJkiRJkkqjV16B/feHH3+Eiy6C4cOjrih9GJxJUhlw991w223rg7ITT4TLL4+2JkmSJEmSJEnF7+uvw/2/FSvC8dq1cPzx8N130daVLgzOJKkMyMiAq6+Gt9+Ggw8OK9BcbSZJkiRJkiSVPrvuCtdeW/BcixZQpUo09aQbgzNJKkOOOSYsy65cOepKJEmSJEmSJCXLjTdCly7hdc+e4Z5ggwaRlpQ2DM4kqYwpbKXZb79Bjx4wf37q6pEkSZIkSZJUvMqVg+efh+eegyeegKysqCtKHwZnkiQAcnPhn/8M/zNt0wY++yzqiiRJkiRJkiQlEosV/gB8tWpwyilu2fJ3GZxJkgC4/HL48MPw+ocfYP/94f33o61JkiRJkiRJ0saWLg0PwR9wAPz+e9TVlC4GZ5IkFi2CV18teK5WLdhjj2jqkSRJkiRJkhTfjBnQrl24n/ftt2FVWV5e1FWVHgZnkiRq1YIJE6B9+3C81Vbw+uvQsGG0dUmSJEmSJEkq6Oyz4auv1h+/8w7cemt09ZQ2mVEXIEkqGRo2hOHD4YILoFWr8NSKJEmSJEmSpJLl6adhn31g4cJwXLMmtG0baUmlisGZJClfVhY8/njUVUiSJEmSJElKZLvt4JVX4IgjYLfd4M03oWnTqKsqPWzVKEn6Wx59NCwHX7Uq6kokSZIkSZKksunQQ+F//4OxYw3NipvBmSRpk338MVx4ITzxBBx8MMydG3VFkiRJkiRJUuk0dWrh17OzoUqV1NRSlhicSZI2ydy5cPzxkJsbjseNC72UFy2Kti5JkiRJkiSpNFm7Fq6+GvbcE55/Pupqyh6DM0nSJpk6FX7/veC5006DWrUiKUeSJEmSJEkqdX77Lawku+OOcNyrF0yeHG1NZY3BmSRpkxx1VOiZvMMO4bhjR7j11mhrkiRJkiRJkkqT99+H995bf7xyJXTrBn/8EV1NZY3BmSRpk+25J0ycCGecAS++COXLR12RJEmSJEmSVHqceCKce+7648xMuPxyqFYtuprKmsyoC5AkpZfataFfv8LHrF4NWVmpqUeSJEmSJEkqTe6/Hz77DGbOhFdfhQMPjLqissUVZ5KkYrV0KbRpA3fdBbFY1NVIkiRJkiRJ6SUrC157DSZNMjSLgivOJEnFJhaD//wHpk4NH+PGwYABUKNG1JVJkiRJkiRJJceoUbDttrDDDvGvN2yY2nq0nivOJEnF5t57w/Lxdd56C3r2jKwcSZIkSZIkqUSJxeCee+Cww+C442Dlyqgr0l8ZnEmSis3atZCRsf64Vq3QslGSJEmSJEkq6/74A449Fi6/PNxHmzwZzj8/6qr0VwZnkqRic+WVMHQo1KkTjp9/PvFyc0mSJEmSJKksyciAr78ueK5fP3j33WjqUXwGZ5KkYtWxY3ha5qmnIDs76mokSZIkSZKkkqFaNXjjDahSJRxnZMBNN8FRR0VblwoyOJMkFbttt4Uzzyx8zF+frpEkSZIkSZJKu113DavM6tSBIUPg+uuhnElNieIfhyQp5V58EXbfPXxjsHZt1NVIkiRJkiRJqXPiiTBzJhx5ZNSVKB6DM0lSSn31FfTsCbEY3HILdOoECxZEXZUkSZIkSZJUPD78EO65p/AxNWumpBRtBoMzSVLKLFsGxx4Ly5evP/fBB/D++9HVJEmSJEmSJBWHvDy47Tbo2BEuvxwGDYq6Im0OgzNJUspUrgxnnQXly68/17Mn/Pvf0dUkSZIkSZIkbalYLDwwfu214TXAKafAd99FW5f+PoMzSVLKZGTAxRfDiBGw9daw997Qp0/UVUmSJEmSJElbJiMDOnQoeG7xYnjiiUjK0RbIjLoASVLZc+CBMHkyrFoFFStGXY0kSZIkSZK05S68EMaOhVdegXLl4PbboXfvqKvS32VwJkmKRMOGhV+fPTt8o2EbR0mSJEmSJKWDjAzo1w9++QVuuAEOOSTqirQ5DM4kSSXO6tXwz3/ChAkwciQ89BBUqhR1VZIkSZIkSVK4d5WVFf9atWphm5KMjNTWpOLjHmeSpBKnd+8QmgE89RS0awc//BBtTZIkSZIkSSrbYrGwZ1nz5mFVWSKGZunN4EySVKJMngx9+hQ8t2IF1K4dTT2SJEmSJEnS0qVw8slw9tlhi5GTToK1a6OuSslgcCZJKlH23hteeAGqVAnHFSvCq6+GZe6SJEmSJElSFHr3hhdfXH88bBjcemt09Sh5DM4kSSXOSSfBxImw++5h9dmee0ZdkSRJkiRJksqym2+GbbYpeG7JktC+UaVLZtQFSJIUT/PmITxLtNEqhG9M7BktSZIkSZKkZKtXD156CQ4+GKpWhWeegW7doq5KyWBwJkkqsSpUKPz6DTfAwoVw332hpaMkSZIkSZKULAccAAMGwP77w447Rl2NksVWjZKktPT++6GP9KOPQvv2MGtW1BVJkiRJkiQp3Q0fXnj7xZNPNjQr7QzOJElpZ+7c8E3Kum9iJk+GffeFP/6Iti5JkiRJkiSlpxUr4Mwz4bDD4MEHo65GUTI4kySlnc8+g6VLC5678kqoXj2SciRJkiRJkpTGpk0LD2X37x+OL78cxo2LtiZFx+BM6aewdbKSyoSjj4bx46F583B8zDFw6aXR1iRJkiRJkqT0NHcufPnl+uPcXPjnP2HZsuhqUnQMzpR+2rSBnj3h7bc3XnIiqczYfXeYMAEuvjhsypqREXVFkiRJkiRJSkeHHQZXX73+uEoVuOOO8F+VPQZnSj+//AL9+kHXrlCnDhx1FPTtC999F3VlklKsalW4/36oXTvxmC+/9OkgSZIkSZIkFe7GG6F9e2jZEiZOhH//O+qKFBWDM6W31avhvffgggugaVPYdVfo3RtGjoQ1a6KuTlLE5s+HI4+E1q3h88+jrkaSJEmSJEklVWYmvP46fPrp+u1BVDYZnKl0mTYN7r0XDjkE6tULjWiffx4WLIi6MkkpFovBaaeFHtXTp4cNXh991G0SJUmSJEmSyqL586F7d5gyJfGYBg2gUqXU1aSSyeBM6ee66+DQQ8MjAIX5/Xd45RU49VSoXx9uvTU19UkqEfr0gXffXX+8ahW89ZbBmSRJkiRJUlkzciTstRe8+WZYa7FkSdQVqSQzOFP66dULhg0Lq8hefRV69AirywoTi0GLFqmpT1KJkJ0N++yz/rhBg7AAtZz/55MkSZIkSSoz3n8/rMOYOzccz5gB550XbU0q2bx9qPRVowYcdxwMGAA//wzjxoXVaHvvvfHYrbaCI46IP8+SJdC5MzzyCHz/fTIrlpRCzZrBmDFwySUhLHvuuRCeSZIkSZIkqew4+GBo3brguffeC7eUpXgMzlQ6lCsXNjC6+WaYNAl++gmeegq6dIEqVaBDB6hePf57P/wQBg8OjxnssAPsthtccQWMHg25uan9dUgqVllZcN99YfvDjh2jrkaSJEmSJEmplpUFL720/vZwx47w+efQsGG0dankKmKTKClNNWoEZ54ZPlatgl9/TTx20KCCx19/HT7uvhtq1oSjjgo93zp1gjp1klq2pOTYeefE12Kx0AG2a9fwpS5JkiRJkqTSZccdwzqL2bOhd2+38lDh/Ouh0q9CBWjSJP61vDx4993E7128ODyOcMopUL8+tG8Pd9wBU6eGu+2S0t5jj0G/fqFj6yWXhKxdkiRJkiRJ6WXmTFi+PPH1E04IjcYMzVQU/4qobMvLg4ceglNPhbp1ix47ZgxcfTXsuSdstx3cdFNq6pSUFFOnhrBsnQceCB1eJUmSJEmSlB5iMejfP9yyveiiqKtRaWBwprItMzM8avDss2E3yLFj4ZprYK+9in7vnDkwf37SS5SUPM89t/EKs/PPj6YWSZIkSZIk/T2//QbHHx927Fm+PLRjfPnlqKtSujM4k9YpXx7atYNbb4UpU0Iw9sQTcMwxUKlS/Pd07px4vkcegXHjklOrpGJxzz3hS7VChXB80UXucyZJkiRJkpQuFi+G998veK5Xr7CXmbS5DM6kRBo3Dv/K/u9/sHBh2Avt3HNh++3D9cqV4eCD4793wYKwbOUf/0hVtZI2Q0YG/N//waefwr/+BXfeGXVFkiRJkiRJ2lQ77hgeit7Qv/4FDRpEU49KB4MzaVNUqgSdOsHDD8N338FXX4UebxUrxh8/dGhorhvPMceEu/Nffpl4jKSU2nNPePHF9SvP4hkzBlavTl1NkiRJkiRJKtrJJ4ewrHZtePNNePzxsOZB2lyZURcgpZ2MDNh11/CRyODBia99+mn4uOoq2Hbb0Beuc2c45JDELSElRerLL+HQQ2H33UPAtvPOUVckSZIkSZIkCLdrH3sMli6FbbaJuhqVBq44k5Jhr71gjz2KHvfjj+Ff9exsqFMnBGiPPw55eUkvUdKmWbkyPLW0ahVMmgStWsHTT0ddlSRJkiRJUtmwaBGccAK8+mriMTVqGJqp+BicSclwxRXw+ecwZcqmv2fFirBSrW9fKOeXplRSXH11WHG2zvLl8MUX0dUjSZIkSZJUVowaFbbYePVV6NUrrEOQks2781IyxXvM4fTTQ4vGRDp3Tnztiy/CIxaSUubkk2GXXdYf77EH3HFHdPVIkiRJkiSVBZ9/Hna3mTMnHC9eDKecAmvXRlqWygCDMynV7roLvv8+hGB33gkHHFBwhVlhwdkpp0C9enDQQXD33fDVVxCLJb1kqSzbe2+YPBnOOgsqVgx7nFWsGHVVkiRJkiRJpdsee8CJJxY89+WX8O230dSjsiMjFvOuu0q+nJwcmjRpAsCcOXNo3LhxxBVtovnzoX79gud+/TWEXxv67TcYOhSGDYMnnoDMzI3nysmBP38PCth++7BHWufOcPDB3tGXkujHHwtfMJqXZ6dVSZIkSZKk4vL776FV4w8/wKGHwnPPuZdZsdvUe9glULJyA2/vSSVB7drw739D//7xQzOAd9+Nf/777+GRR6BTJ6hTB/7xD3jySfjpp6SVK5VVhYVmK1bA/vuHLz8fSZEkSZIkSdpyNWrAf/8bmnh98IGhmVLD4ExKF7/8UvRqsuXL4Z13Qk+5xo2hVSu49loYN87mv1KSXXklfPpp+PLr0iV8yUqSJEmSJKlwQ4bArFmJr7dvD5dfbpcfpY5/1aR0cd11sHBhCMbOPjsEY0X57DO47TbYbz9YsCDpJUpl1ZAh0KfP+uN33oHTT4+uHkmSJEmSpJJu2TI45xw4+mjo0cPn/lVyGJxJ6aRy5bCX2WOPhc2WPv8cbr899Icr7JGLNm2gQYP411atsq+ctIXGji14XLEi3H9/NLVIkiRJkiSVdN9+G5plPf54OP7kE7jnnmhrktYxOJPSVUYG7LEHXHVV+D/LL7/A88/DiSdCzZoFx2ZnJ57nqqugWTO48EJ4//0QpEn6W26+Gf73v/X7qN59NzRvHm1NkiRJkiRJJdXWW2+8wuz660OgJkXN4EwqLerWhZNPhoEDYf58GDUqNP/dbbfCg7NBg+C770KfuSOPhDp1oFs36NcP5s5NXf1SmjvmGPjiixCinXtu1NVIkiRJkiSVXNWqwXPPrW+iVbky9O0LO+0UbV0SQEYsZo82lXw5OTk0adIEgDlz5tB4U/b3Kgnmz1+/BGWdX3+FevWiqeevZsyAnXcufMzee4fgrXNnaN3aXTilLXTnneFLqmXLqCuRJEmSJEmK1jXXwLBhoZGWoVlESvo97EIkKzfwDrhUln34YdFjJk+GW26BffcNa6hPOw1eew3++CPp5UmlzaBBoTtq69ahb7eb3kqSJEmSpNLs559hzZrE12+8ET7+2NBMJYvBmVSWnX02TJkCt94K7dqFfdMK8+uv8OyzcPzxoaXjsGGpqVMqBebPhzPOCK9Xrw6dVP/xD3DdtyRJkiRJKo1efTXsInP77YnHbLUVZGamriZpUxicSWVZRgbstVdYEz12LPzyS2gufMIJUKNG4e+NxWCffVJSplQa3HlnyJ431LVr0Xm1JEmSJElSOlm8GE45Jdxi/O230Mxq/Pioq5I2ncGZpPXq1Qv/V3v55bA8ZsQIuOwyaNFi47EHHAA1a8af5733oHt36N8f5s1LaslSurj9dujde31Q1rkznHlmtDVJkiRJkiQVt1mz4KWX1h+vXQsnnwzLlkVXk/R3GJxJim+rreDgg8NGTF9/Hf6P16cPdOwIWVnhrn8ib7wBb74ZUoFGjcKGTjfeCBMmQF5eqn4FUolSoQLcfTeMHAlt2kC/fq42kyRJkiRJpc8++8D11xc816oV5OZGU4/0d2XEYu6uopIvJyeHJk2aADBnzhwaN24ccUWbaP58qF+/4Llffw0ru9LZ0qXhUZF47RxjMdh2W8jJif/eBg3g6KMhOxuOOAKqV09urVIJFIsVHpp98knoAZ5oUackSZIkSVJJlpsbGlZNnw6PPgr/+pcPEJdYaXwPO1m5gdvuSfr7qlZNfG3q1MShGYR91J55JnxstRUcdFBYvZadDTvtVPy1SiVQYd8ozp0bviSqVg2r0o48MnV1SZIkSZIkbaq1a6F8+fjXMjNh4MDw3z9zDSlt2KpRUvHabjsYMACOP77o1WRr1sCwYXDxxbDzzuHjtddSUqZUEsVi0KtX2EQ3JweOOioc28pAkiRJkiSVJJ9+Ci1bhi0pEtlhB0MzpSeDM0nFq2ZN6NEDXnkFFiyA4cPh0kthl12Kfu+MGVCxYtJLlEqqZ5+FwYMLnlu2LDydJUmSJEmSFLVVq+Dqq2H//WHaNDj9dFiyJOqqpOJlcCYpebbaCg45BO69NzQ0njEDHnww7G221VYbj69YEQ49NP5cixbBTTfBpEmQl5fUsqWoHHooHH74+uOGDaFPn+jqkSRJkiRJ2tCLL8Idd6y/Pff999C7d6QlScXO4ExS6jRrBhdeCO+/DwsXwhtvwH/+E9IBCKlB5crx3/vee3DjjdC6NWyzDZx5Jrz5po+0qFTZdtvw5fH442GPsyeegDp1oq5KkiRJkiQp6NEDDjqo4LnJk2HFimjqkZLB5k+SolGtGnTrFj7y8mDKlMJXkm3Yv+7nn6F///Cx1VZw8MGQnR0+mjVLeulSMmVkwFlnQffuUK9e4nHz5kGNGomzZkmSJEmSpOJWrhw88wzssQesXg3XXw9XXuk2Eypd/OssKXrlysE++yS+vnYtDBkS/9qaNfDBB+HjoovCXmrZ2dC5MxxwQPyWkFIaKCw0y8uDE08M4dmAAaGvuCRJkiRJUirsuGO4H7HTTrDnnlFXIxU/WzVKKvmWL4dTT4Wddy567DffwP33h7aPdevC8cfD//6X/BqlFOrbF0aPDtsGHnggXH45rFwZdVWSJEmSJKk0+OYb6No17LSSyHHHGZqp9DI4k1TyVasWwrBvvoFvv4UHHoDDDit6Ndkff8Brr8GoUampU0qBb7+Fq65af5yXB6++GhZfSpIkSZIkba61a+G++2CvveDtt+H886OuSIqGwZmk9LLTTqEl44cfwoIFIRg7/XRo0CDxe7KzE18bPhyWLi32MqVkKVcu9BHf0NNPh3xZkiRJkiRpc113HVx22fquNgMHwuuvR1uTFAWDM0npq3p1OPbYkBrMnQvjx8MNNxTcL6169bDXWTzz5oWVa3XqwFFHhf53332XmtqlzdSsGXz8MdxxB2Rlhae/Djkk6qokSZIkSVK6u+ACqFWr4LkHHoBYLJp6pKgYnEkqHcqVgzZt4MYbYeLEEKT17w/XXx/ShXiGDAn/Xb0a3nsvfHfQtCnsuiv07h1aPNr/TiVQZiZceSVMnhwCtERWrYJly1JXlyRJkiRJSl8NG8JDD4XXGRlw4YXw/vvhtVSWZEZdgCQlxdZbw3/+U/iYwYPjn582LXzcey/UqAFHHgmdO0OnTlC3bvHXKm2m3XYr/Pptt8ELL8BTT4XFlZIkSZIkSYU5+eTQ1OnEE6F9+6irkaLhijNJZdfatWHpTmF+/x1eeQVOPRXq14f99gtpxOefp6ZGaTN9/nlYjTZ7Nhx+OPTsGf46S5IkSZKksmvcODj33MTtFzMywm4mhmYqywzOJJVdb70FCxbAq69Cjx5Qr17h42Ox8N3FtdfC6aenpERpc6xZE/6K5uauPzdgQAjRJEmSJElS2bN8OVx6Key/Pzz6KDzzTNQVSSWXwZmksq1GDTjuuJAq/PxzCMauuw5atSr8fdnZia8tWVKsJUp/1+LFUK1awXNXXgl77RVFNZIkSZIkKWrZ2XD//etXml1yCfz0U7Q1SSWVwZkkrVOuHOy7L9x8M0yeDDk58OST0KULVK5ccGznzonn2Xdf2H13uOIKGD264LIfKQXq1YMRI+CRR6BqVdh117BQUpIkSZIklU29exc8/v13eOCBaGqRSrqMWCxRN1Op5MjJyaFJkyYAzJkzh8aNG0dc0SaaPz/si7WhX38tuiWgSp6VK2HUKBg0KOyQOnZsCNr+avZs2HHHgudq1oSjjgqP9nTqBHXqpKRkCeCHH+CPP6Bly8RjlizZeIWaJEmSJEkqXXr0gOeegwoV4KabQuvGzMyoq1Lk0vgedrJyA78sJGlTVKwIRx4ZPgozePDG5xYvhpdeCh/lykG7dmHFWnZ2SDMyMpJSsgSw3XaFXx81Crp1C+0aevTwr6MkSZIkSaXVAw+Eh2fvuAN22SXqaqSSy1aNSfDrr78yaNAgrr/+ejp16kTdunXJyMggIyOD00477W/PN3ToULp3707jxo2pUKECjRs3pnv37gwdOnST51i+fDn33HMPbdu2pXbt2lStWpUWLVpw2WWX8eOPP27yPF999RVnn302zZo1o1KlStSrV4+DDjqIJ554glzb0UkhhShMXh6MGQNXXw177hlSjXPOCYHb8uWpqVH60/LlcMYZsGgRnH56WBD5/fdRVyVJkiRJkv6uWCw8s92nT+IxtWvDG28YmklFsVVjEmQU8rh+jx49GDBgwCbNE4vFOPvss3nyyScTjunVqxePP/54oZ9z1qxZZGdn880338S9XqNGDV588UWOPvroQuvp378/5557LqtWrYp7vV27dgwaNIg6SWhDZ6tGpY21a0Mrx8GDw8dnn236e6tUgV9+Cf+VUuCyy+C++wqee/xxOOusaOqRJEmSJEl/3w8/hOeyhwyBrCz4/HNo3jzqqpQ20vgedrJyA1ecJVmTJk3o2LHjZr332muvzQ/NWrVqxcCBAxk/fjwDBw6kVatWADz55JNcd911CedYunQpnTt3zg/NevbsybBhwxgzZgy33XYbVatW5ffff+f4449n6tSpCed577336NWrF6tWraJBgwb06dOHTz/9lCFDhtC9e3cAxo0bR/fu3cnLy9usX69UKpQvD/vtB7feClOmwJw58MQTcMwxUKlS4e/day9DM6VMLBa+B9pQ+/bQs2c09UiSJEmSpL9v0aLQ1GjIkHC8ejX06hWaHknaPK44S4IbbriBNm3a0KZNGxo0aMD333/PDjvsAGz6irOZM2fSokULcnNzad26NaNHj6bSBjfdly9fTocOHZg4cSKZmZlMnz6dpk2bbjTPjTfeyE033QTA3XffTe/evQtcHzt2LAcddBC5ubkccsghDB8+fKM5cnNzadGiBTNnzqR69epMnjx5o8917rnn8uijjwLw7LPPcuqppxb5a/w7XHGmUmHFChg5cv1qtL/2xLv9drjqqvjvvfZamD077I125JFhbb1UDN55B84+O/xz9dlnsOuuUVckSZIkSZL+jt694d57C557992wJYNUpDS+h+2KszRy00030blzZxo0aLDZczzwwAP5e4b17du3QGgGULlyZfr27QuEYOvBBx/caI41a9bw0EMPAdCiRQsuvfTSjcbst99+nHHGGQCMGDGCSZMmbTTmzTffZObMmQBcddVVcQO6e+65h1q1auW/lhRHpUrhO5aHH4bvvoMvv4S77oIDDwwr1Tp3jv++WAxeeAFefBH+/e/wP60DDwzv/fLLcF3aTMccA19/HXqcFxaa/XV1miRJkiRJKhluvBG23z68btgQXnsNjjoqyoqk9GZwVgLFYjHefvttAJo3b067du3ijmvXrh27/LmT41tvvcVfFw+OHDmSxYsXA2GlW7ly8f+4TzvttPzXb7zxxkbX33rrrbhjN1S5cmVOOOEEAL788ktmzJgRd5ykP2VkwG67weWXw+jR4cmO3XePP/brr0Oz6nXy8uDjj+HKK6Fly/Cd0bnnhkeJVqxISfkqXWrUSJzbAixcGP66nnSSAZokSZIkSSVNlSphp5BevWDaNDj22HDrSdLmiSw4y83N5ZdffuGPP/6IqoQSa/bs2fz0008AdOjQodCx667n5OTw/V/avn300UcbjYundevWVPlzX6WPP/54o+vr5tlll11o2LBhkbUkmkdSIWrVSvwdzaBBhb/3xx/h0UchOxvq1AlLiB5/POyvJhWDyy6DBQvCosfmzeGZZ1zoKEmSJElSqixcCKefDp98knhMx44hPKtZM2VlSaVWSoKzOXPm8MILL3DWWWfRsmVLatWqRYUKFWjUqBG1atWiYsWKNG7cmE6dOnH77bfz0Ucf5bcpLIumTZuW/7p58+aFjt3w+obv+zvzZGZm5rdf/OscS5cuJScnZ4trkbQFTj4ZHnssLAmqWLHwsStWhKDtnHNg223D7rB+PWoLDBsGG27NuWhR+Cvmk2uSJEmSJCVXLBYeYm3RIvxs3rMnrFoVdVVS6ZeZrIlXrVrFf//7X/r378+4cePyz/+1nSDA6tWrmTt3LvPmzeP9998HoFatWvzzn//knHPOYfdE7ctKqTkbrBIpajO7dRvf/fV9Gx5XqVKFmkU8atCkSROmTp3K/PnzWbVqFRUqVADCSrZ1f2ZbUktR1oVzicybN+9vzSeVKttsA2efHT5WrIARI0JyMXhwWG1WmOnToZg2xVTZtGhReFrtz86/VK8Of26xKUmSJEmSkui118K2CetMmxa2vL/++uhqksqCYg/Oli9fTt++fbnvvvtYuHBhgaCsZs2atGrVivr161O7dm1q1arFihUr+O2331i0aBHffvst33zzDbFYjN9++43HH3+cxx9/nI4dO3LTTTfRtm3b4i63RFqyZEn+66pVqxY6dl2LRQirw+LNU9Qc8eZZF5wVVy1F2TB0k1SISpXg6KPDRywGX34ZArRBg2Ds2LD/2YY6dIBq1eLPNWoUfPppWMnWooVLiBTXccfBAQfARRfByy+Hb9AbNYq6KkmSJEmSSr9u3WCffWDSpPXnHn4YLr007GsmKTmKNTh79tlnufrqq/n555+JxWJstdVWHHXUURx77LG0a9eOnXfeucg5lixZwsSJExk2bBgDBw5k9uzZvPfee7z//vscd9xx3HfffUWufEp3K1euzH+dlZVV6Nh1ARfAihUr4s5T1ByFzVNctUhKgowMaNkyfFx5ZWh4PXRoCNKGDg1LhTp3Tvz+AQPCxxVXwPbbh7HZ2XDwwUW3hFSZ0rAhvPQS/N//hRAtkZwcqFrVfuqSJEmSJBWHzEx46ilo0wbWroWuXUNwZmgmJVexBmenn346EPa6uuiiizj++OOpVavW35qjWrVqHHLIIRxyyCHceuutjBs3jn79+vH888/z2muvsdtuu3F9KV+LWnGDG9arV68udOyqDZraVqpUKe48Rc1R2DzFVUtRimrtOG/evDKz4lDabHXqhPX7J50Eubkwbhw0axZ/bF4evPvu+uPvvw/feT38MFSuDIcfHkK07OzQKlICDjoo8bVYDHr0gK++gvvvh3/9y0WMkiRJkiRtilgs8c/QrVrB7bfDTjuFFWiSkq9Yg7Pdd9+da665hhNOOIGMYrpb1q5dO9q1a8cNN9zAHXfcUSDIKa2qbdBWraiWh8uWLct//ddWiuvm2ZS2iYnmKa5ailLaVxFKKZeZWfjSoIkT4ddf419bvhz+97/wAbDXXutXo7VpA+XLF3u5Sn8DB8Lw4eH1SSfB00/Dc8/Z1lGSJEmSpERiMXj+ebjnHhg9GhKtQbn88tTWJZV15YpzsqlTp/LPf/6z2EKzDTVp0oRHH32Uy8vAvxIbhkg5OTmFjt1wpdZf9wlbN8+yZctYvHjxJs1Tr169Ai0Xi6sWSSVM9epw9tmwKaH1Z5/BrbfCfvuFnn2nngqTJye9RKWPxYvh4osLnvv22/DXTJIkSZIkbWzaNDjkkNC95csv4eqro65I0jrFGpypeOy66675r6dPn17o2A2vt2jRYrPmyc3NZdasWXHnqFq1an4ItiW1SCphmjeHxx6DH3+Ezz+H226D/fcvurfeggXhUagFC1JTp9LCihXw1266ffqE/c4kSZIkSdLGrrsORo1af/zEE/Dpp9HVI2k9g7MSaIcddqDRn72tRm34r2cco0ePBmCbbbZh++23L3DtgA3atBU2z8SJE/PbLLZv336j6+vm+eabb/j5558TzrPh54g3j6QSKCMD9tgjPNb0ySehfePzz8OJJ0LNmvHfU6UKdOgQ/9pvv8H778MGex6q9Nt669DZ8803wyLGzp2hS5eoq5IkSZIkqeS6776wzfw6sRi89VZk5UjaQEqCs6+++mqz3/vII48UYyXpISMjgy5/3nGcPn0648aNiztu3Lhx+au8unTpslGLzIMPPpgaNWoA8OyzzxKLxeLOM2DAgPzX3eLsMNm1a9e4Yze0fPlyXnnlFSCsdNt5553jjpNUwtWtCyefHDasmj8/PPrUuzdssIKVI46ADVq6FjBoEBx5JNSpA127Qr9+MHduSkpXtDIywh/5tGnhjz3R4sXVq6F/f8jNTWl5kiRJkiSVKNttBzfeuP71O+/AHXdEWpKkP6UkOGvTpg19+/b9W+/55Zdf6NSpExdccEGSqirZLrroIjIzMwE4//zzWbFiRYHrK1as4PzzzwcgMzOTiy66aKM5srKy8n//pk2bxr333rvRmLFjx9K/f38AOnToQJs2bTYa061bN5o2bQrAHXfckd/WcUO9e/dm0aJF+a8llQKZmXDQQXD33fDVV/Ddd9C3b9gbLZHBg8N/ly2Dt9+Gnj1hm21gn33g+utDz4G8vNTUr0hUrQoNGiS+/sADcOaZ0Lo1JHguRJIkSZKkUiE3NzTnSeSii+Dee+Hrr0P3FkklQ0Ys0TKkYlSuXDkyMjLo2LEjzzzzDA0bNix0/Ntvv03Pnj1ZuHAhAGvXrk12icXq448/ZubMmfnHCxYsyA+T2rdvz5lnnllg/GmnnRZ3nquuuoo777wTgFatWnHFFVfQtGlTZs2axV133cWUKVPyx91+++1x51iyZAmtW7fm22+/BaBXr16ceOKJVKpUiREjRnD77bezdOlSKlWqxJgxY9hrr73izvPuu+9yzDHHkJeXR4MGDbj22mtp27YtixYt4qmnnuL1118HQlvHkSNHUr58+U37zdpEOTk5+XutzZkzh8aNGxfr/Ekzfz7Ur1/w3K+/Qr160dQjJdOaNWHF2h9/FD6ufn3o1Cl8R3jEEfDnyliVft9/HxYvrnsWJCMD7rorLGqUJEmSJKk0+fRTOOussKXBO+8Uva28FJk0voedrNwgJcHZvvvuy4QJE8jIyKBOnTr069ePf/zjHxuNW758ORdeeCFPP/00sViM8uXLc80113DjujWraeK0007j2Wef3eTxif4I8vLy6NmzJ08//XTC955xxhk8+eSTlCuXePHgzJkzOfroo5kxY0bc69WrV+e///0vnYt4rOGpp57ivPPOY/Xq1XGvt23blsGDB1O3bt1C59kcBmdSGpgzB/75z7CMaFP/15KZCQceuH5TrD9Xt6p06tIl7IW2TkZG+EEizmJnSZIkSZLS0uLFcPnlYRuDdbdH3ngD4uyQI5UMaXwPO1m5QUpaNY4ZM4ZrrrmGcuXKsWDBArp168ZZZ53F8uXL88eMHz+evfbaKz8023HHHRk9enTahWbFqVy5cvTv35/BgwfTpUsXGjVqRFZWFo0aNaJLly68++679OvXr9DQDKBZs2ZMmTKFu+66i9atW1OzZk0qV67MLrvswsUXX8zUqVOLDM0AevbsyaRJk+jZsyc77rgjFStWpE6dOhxwwAE89thjfPLJJ0kJzSSliSZNYMwY+OUXeO45OOGEoleT5ebCiBFw6aXhO0qVapdfDrvvvv747LMNzSRJkiRJpUtmJrz7bsFnii+4AJYsia4mSX9PSlacrTNmzBhOOeUUZs+eTUZGBjvttBPPPPMM77//Prfddhtr164lFotx2mmn0adPH6pWrZqq0lTCueJMSlNr1sAnn4S9zwYNgunTE4/96CM44ID41+bP9+umlFizBh56CB57DCZNgpo1o65IkiRJkqTi9fLLcOKJ64933z2sOttpp+hqkhJK43vYad2qcUNLly7lvPPO47nnngsF/NncNRaLUbt2bZ588km6d++eypKUBgzOpFJi1qwQog0eDCNHwrrWr7Vrh5VqmZkbv+fHH2H77WHvvUNLx+xs2GcfKGK1rUq2NWtgq60SX7/ySth5ZzjtNP+oJUmSJEnpJRaDww6D8ePhhhvgoosK/xlYilQa38NOVm4Q5w5lclWtWpUBAwawZs0aBg4cCITQrEaNGkyYMIEddtgh1SVJklKladPQn+CCC2DpUvjww7ASrVq1+KEZrO9vMGlS+LjpJmjQAI4+OoRoRxwB1aun9tehLVbYDwzjx8Pdd4c/9ieegEcegdatU1ebJEmSJEmFyc0Nu1Scckr8n28zMsKOFBUqwDbbpL4+SVsm5c9wL1q0iOOPP56XXnqJjIwM1i14++OPP/jHP/7B1KlTU12SJCkKVatC167hO8kHHkg8btCgjc/98gs88wwcdxzUrQuHHw4PPggzZiSrWqVIXh6cd976XvDjx4en9P74I9q6JEmSJEkCGD0aWrWCM86Avn0Tj9txR0MzKV2lNDgbNmwYe+yxB2+88QaxWIyWLVvy0UcfcdxxxxGLxfj666/Zd999ue+++1JZliSppFq7NqwyK8yaNTBsGFx8cejtt/POcMklMHz4+laQShsffggTJhQ8d+21LiqUJEmSJEXv5puhQwf48stwfOONMG9epCVJSoKUBGdr1qzhsssu48gjj+Snn34C4OKLL2b8+PG0b9+eV155hWeeeYZq1aqxatUqLr/8cg477DBycnJSUZ4kqaQqXx5++CEEY5dcEkKxosyYEVawHXYYHHVU8mtUserYEYYOXf9HvcsucOGF0dYkSZIkSRKE3SI2tGQJXH55NLVISp6UBGdt2rThgQceIC8vj0aNGvH+++9z3333kZWVlT+mR48eTJkyhf33359YLMbIkSPZY489ePnll1NRoiSppMrKgkMPhfvug2++CcHYgw+G9oxF7ax7yCEpKVHF68gj4Ysv4K674OGHw1+BeGIxWLAgtbVJkiRJksqu/faD005bf7znnnD22ZGVIylJUhKcTZ06lVgsRrdu3Zg6dSqHHXZY3HE77LADo0eP5uabb6Z8+fIsXryYk046KRUlSpLSRbNmYQnSBx/AwoXwxhvwn/9Aw4Ybj+3cOf4csRgcdBCceSa89RYsXZrUkvX3ZWWFp/YOPzzxmNdfDz3jH3ggdOyUJEmSJCnZ7rwTtt8+7G82cSK0bx91RZKKW0YsFosl+5NUq1aNhx56iP/85z+b/J4JEyZw8sknM3PmTNauXZvE6pQOcnJyaNKkCQBz5syhcePGEVe0iebPh/r1C5779VeoVy+aeqTSLC8PJk+GwYPDx7x58OOPkJGx8dhvvoHmzdcfZ2WFJuWdO0N2NjRtmrq6tVmWLYMWLWDOnHC8667w2GMhD5UkSZIkaXMsWxaCsSVLQrObRHJzITMzZWVJyZXG97CTlRuk5Mt7ypQpNGvW7G+9p02bNkyePJlLLrkkSVVJkkqVcuWgdevwccMN4bvdeKEZhGBtQ6tXhxVsH3wQVrM1bx4CtM6dw6NjRbWEVMrdeef60Azg66/ht9+iq0eSJEmSlL5iMXjxRbjiCvjpp3A74bTTYK+94o83NJNKt5S0avy7odk6VapU4YknnijmaiRJZUKVKomvDRpU+HunTw97qh1ySHi65oQT4LnnwhM4KhH++kdx6KHQpUs0tUiSJEmS0tsvv0CvXiE0gxCkXXRR+K+ksiclwZkkSSXK44/D/feHtKWox8R+/x1efRV69IAGDeDAA8EWwpF7/HEYMwb23jssNnzwwcQLDCVJkiRJKkzDhnDllQXPffwxfP55NPVIipbBmSSp7Nl5Z7j4Yhg2DBYuhNdeCz0Y/trP+a9isdC2sXz5lJSpwu23H4wfD6NHQ8uWicc9/TSMGJG6uiRJkiRJ6eeyy2DbbcPrjh1DaJaoVaOk0q1Yg7Ps7GwmTJhQnFPmW758OXfffTePPvpoUuaXJJVR1avDscfCM8/AvHnw6adw/fWwzz7xx2dnJ56rb9/w8d13yalVGylfPmxDl8hPP8H554fFhd27+0cjSZIkSWVVLAbDhyduv1ipUuhu8s47MHQo7LZbauuTVHIUa3A2ZMgQ2rVrR3Z2NsOHDy+WOefNm8ftt9/O9ttvz1VXXcWCBQuKZV5JkjZSrhy0bQs33QQTJ8LcudCvH3Trtn7PtETBWSwGd9wBF1wATZvCrrvC5ZfDqFGwZk3qfg0q4MorYfny8PrNN2H33d2qTpIkSZLKms8/D9uYH3YYvP124nGdOkHnzm4FIJV1xRqc3XDDDVSsWJEhQ4ZwxBFH0LhxYy6//HLGjRvH6tWrN3meH374gaeffprDDz+cbbfdluuuu44FCxaw7777ctxxxxVnyZIkJbb11nDGGfDGG6Gl44gRsMsu8cdOmRJWrK0zbRrccw8cfDDUqwcnngjPPw8+AJIykyfDCy8UPHfKKeGPQ5IkSZJUNtx4Y9gfe9SocHzZZbBqVaQlSSrhMmKxRItTN89PP/3EzTffzIABA1izZg0Zf8bzW221FS1btqRVq1bUr1+fWrVqUatWLVasWMFvv/3GokWL+Pbbb5kwYUL+qrJ1pbVo0YIbb7yR448/vjhLVRrJycmhSZMmAMyZM4fGjRtHXNEmmj9/4z2Tfv3Vu7ZSaXTLLaHFY1EyMqBdu7ByrXNn2GMPH2VLktzcsGDwuutCXlm9OsyYUfRWdpIkSZKk0mPgQPj3vwueu+uu0CRGEml9DztZuUGxB2frzJ07l0ceeYRnn32WuXPnrv+ERdwcXFdO+fLlOfzwwzn33HPJzs4u8n0q3QzOJJV4w4fDc8/Bu+/+vV6AjRvD0UeH4M1EJykWLw6/vdttFzppJvLrr/4RSJIkSVJpE4vBAQfAmDHheNtt4aGHoGvXSMuSSo40voeddsHZOrFYjI8//pgRI0bw0UcfMW7cOJYtWxZ37E477cSBBx7IgQceyFFHHUWDBg2SWZrSiMGZpLSRlwcTJsDgwTBoUGjhWJRKlUIryEqVkl+f4ho7NnTVPO88uOYaqF076ookSZIkSX9HLJa4ocvEiWGPsyuugEsv9cdvqYA0voedtsFZPIsWLWL+/Pn89ttvVKxYkXr16lGvXj2ysrJSXYrShMGZpLT1009hFdrgwfDhhxDv4ZHs7BCyxTNlCixdCvvtB5mZya21jIrFoH37EJ4B1KoV2nb07BltXZIkSZKkos2aBVdeGfYxu+qqxON+/x1q1EhdXVLaSON72MnKDSK5A7dufzNJkkq9bbYJCUzPnrByZdiNeN1qtNmzw5js7MTvv/deePHFkOYceWTYF+2oo6BOndTUXwa8/vr60Axg0aL4+aYkSZIkqeT47Te49VZ4+GFYswbeew/OOCNxC35DM0mbqlxxTlarVi3q1KnDN998U+D86NGjGT16NCtWrCjOTydJUnqpWDGEX336hEfivv4a7rkH/vGP+ONzc2HIkPB60SJ46SU4+eTwU8ABB8Add8DUqWHJlDbbDz/AhovemzaF//u/6OqRJEmSJBXtxx/hwQdDaAawZAnceGOUFUkqLYo1OPv9999ZvHgxa9euLXD+4IMP5tBDD2X2uifrJUkq6zIyoEULuOyysCotnnHjQmD2V3l58MkncPXVsOeesN12cM45YRXb8uXJrbsUuvRSmDYN/vnPcHznnQWDNEmSJElSybPXXnDqqQXPvf562O1AkrZEsQZn5cqF6XJzcze6FsFWapIkpbfly8NPAkWZMwcefxyOOSa0cMzOhsceC/2otUl23DEs6JsyBY49NvG4//4XLroIFi5MWWmSJEmSpARuvTU0d8nKCg9FTp8OVatGXZWkdFfsrRoBvvvuu+KcVpKksqljx5DkzJkDTzwRgrFKlQp/z8qV8O67odfg11+nps5SZK+9wmLAeJYvDxtOP/RQaOd4773ht1uSJEmSlBzffReeE02kcWN49tnQReTee8P24JK0pTKLc7J99tmHDz74gGuuuYYKFSqw8847s9VWW+VfnzdvHlU3I/Lfdttti7NMSZLSS+PG0KtX+FixAkaOhMGDw8f338d/T40a0L59/GtLloQm8LVrJ6viUunBByEnJ7z+/Xfo3Rtatgzb1kmSJEmSis+CBXDbbfDoo+HH13btEjdkOeGElJYmqQzIiBVjD8XBgwdzzDHHkPGXR7XXfYq/nt8UGRkZcVs/qmzJycmhSZMmAMyZM4fGjRtHXNEmmj8f6tcveO7XX6FevWjqkVS6xGJhVdngwWF/szFjYN0+o8cfD6+8Ev99/frBWWfB/vtD586hteNuuyVeaiVWroQmTcIPb+scdhh88IG/bZIkSZJUnHJzQ5ePH39cf86fv6QkSuN72MnKDYq1VWN2djYPP/ww1atXJxaL5X+ss+G5v/MhSZLiyMgIgdfll8Po0eEbnYED4aSTCn/kbtAgyMuDjz8OvQdbtoQddoBzz4UhQ8KqNhVQsSJMmAD/+lc4zsgIbUD8oU2SJEmSildmJpxzTsFzw4aFH1clKRWKdcXZOitXrmTChAn89NNPrFq1itNPP52MjAxuueUWttlmm789X48ePYq7RKUZV5xJUjFZtQrq1IFlyxKPqVQpPM7XuTMcfXRYaqV8EyaEbpm9eyce88IL0LYt7LxzysqSJEmSpFJj+XLYaSeYOxe22grOOw+uvdYdB6SkSON72MnKDZISnP1VuXLlyMjI4IsvvmDXXXdN9qdTKWRwJknFZPLksPfZypWb/p499gjtHDt3hn33hfLlk1dfKfDjj+EHvLVr4cwz4frroVGjqKuSJEmSpJLl44/DDgLlEvRE698fRo2Cm2+G7bdPaWlS2ZLG97DTolVjIgcddBAHHXQQVapUScWnkyRJiey9NyxcGNo1nnPOpq0mmzoV7rgjBG533JH8GtPcjTfC6tUhOHviCdh1V/jjj6irkiRJkqSSYeJEOPxwOPDAxFtzA5xxBjz3nKGZpNRLSXA2cuRIRowYwXbbbZeKTydJkgpTuXJYQfboo/DDDyEYu/32EIwletRvnY4dE19zX1K+/hqefbbguVNOgerVo6lHkiRJkkqSq66CNm3CnmUQ2i+uXh1tTZL0VykJziRJUgmVkQEtW4afXj7+OCzFf+EF+Ne/oFatgmPr14fWrePPM2sWNG0K558P773391pBliJbbx32PqtYMRxXqRJ+EJQkSZIkhb2gNzRrFvTrF00tkpSIwZkkSVqvTh046SR48cUQoo0eDVdcAbvtBkcfnXhF2uDBMHs2PPwwHHVUmKdLF3jqKfjpp9T+GiJUqxbceSfMnAm9esHll0ODBonHf/KJC/UkSZIklR1du0K7duuPt9kGateOrBxJiisjFvN2jUq+ZG3yl3RpvLGiJG1k9WrIyop/rWNH+OCDxO9t1Sq0h8zODn05ypdPTo1p5OOPQ0//ffeFW2+Fww4LCwAlSZIkKZ0tWRL+W61a/OujRoUA7aqrQtOSSpVSVpqkeNL4HnaycgNXnEmSpE2TKDRbujT85FOYKVNCOrTffqGfYY8e8Oqr8PvvxV9nGojFwkI+gE8/hSOOgJNPjrYmSZIkSdoSK1bA/ffDjjvCXXclHtehA8yZEzp0GJpJKokMziRJ0papUgXGj4fbboP99y962dT8+fDcc3DCCVC3Llx8cWrqLEHeeQfGjCl47qCDoqlFkiRJkrbUBx9As2Zw6aWwYAE8+GD40S+RqlVTVpok/W0GZ5IkactkZMCee8LVV4dNu379FZ5/Hv75T6hZs/D35uZCw4YpKbMkqVAh/FC5zvbbw+mnR1aOJEmSJG2RJk3g55/XHy9bVviqM0kqyQzOJElS8apbN/QdfOmlEKKNHAm9e8Ouu8Yfn50d/3wsBmeeCf36wdy5SSs3CkceCV9/DU8+GX7AvOGGxJ0wV6+G6dNTW58kSZIk/R3Nm8MppxQ8N2dO+LFOktKNwZkkSUqerbYKDezvvhu++gq++w769oWjjgrLrrbbDnbbLf57v/wS+veHnj1hm21gn33g+utDW8i8vNT+OpJgq63CL23GjML3N3v66fBbdOqpMGtW6uqTJEmSpA3FYvDHH4mvX389ZGaGPZzHjYOXXy66k78klUQGZ5IkKXV22AHOOw+GDIGFC8NmX4l+kho0qODx5Mlwyy2w776w9daht+FrrxX+k1saqFAh/HAZz4oV4Zeclxe6X+6yCzzwQGrrkyRJklS2xWIwdCi0aQP/+U/icTvuCNOmwfvvhx/bJCldGZxJkqRoVKkCLVsmvj54cOJrv/4KAwbA8cdDnTpw2GFw//3w7bfFXmaUnniiYJfKtWth772jq0eSJElS2TJ7Nhx0EHTqBJMmweuvh2caE9lwL2dJSlcGZ5IkqWQ65xw44QSoXr3wcbm5MHw4XHppWJK1005w5ZWpqTHJ8vKgatX1x4cdFjpfSpIkSVIq1KsXVpFt6Prro6lFklIl5cHZoYceymGHHcYPP/yQf+7777/PPy9JkgTASSeFpvgLFsCIEXDZZWHH6aLMnAmffZb08lLhkkvCE569e0OlSqFtYyK//FJwdZokSZIkbamqVcMzihuaMQN+/z2aeiQpFVIenI0cOZKRI0eybNmy/HPLli3LPy9JklTAVlvBwQfDPfeERx1nzoSHHoKOHSErK/57srMTz/fmmzBxYljOlQbq1oW774affoL99ks87qabwp4CF1wQxkqSJEnSpojFQjf8RM47D2rXhu22g6efhq++gho1UlefJKWarRolSVJ6ado0pEPvvQcLF4Yg7MwzYeut149JFJytXQu9eoVdrRs1gjPOgDfegCVLUlP7FqhVK/G1nBzo3x9WrYK+fUOA9uqrqatNkiRJUvqJxWDoUNh//9ASfu3a+OOqVYMPPwxbSp9+OmRmprZOSUo1/5mTJEnpq2pV6No1fMRiMGUKfPJJSI7imTAhtH6E0Nvw6afDx1ZbhZ8Us7Ohc+e029H6rrtg9eqC5wpbnSZJkiSpbJs/H445Bj79dP25V1+FE0+MP75Vq9TUJUklgSvOJElS6ZCRAXvvDeefn3jM4MHxz69ZEx6hvPhi2Gkn2GWXsMHY8OEbJ1IlUPnyIftb58wzoXHj6OqRJEmSVLLVrRs6Vmzo5psTrzqTpLLE4EySJJUd9eqFUKwo334LDzwAhx0WfqI87jgYMABWrkx6iZvjwQfD1m/nnBMW4V15ZeKxX30F332XstIkSZIklUAZGXD99QXPrVgBP/4YTT2SVJIYnEmSpLLjggtg+nSYMSOkTYcfXnCpVjxLlsDrr4eVbOVK7rdO224Ljz4Kc+dCkyaJx51/Puy8c9ibYObM1NUnSZIkKbXy8sKDc4l06QJ77BE63ffvH54f3GGH1NUnSSVVyb37I0mSlCzNmsGFF8IHH8DChSEY+89/oEGDxO854gjIyop/bc6cELCVANWqJb720UcwYkRovzJgQFh8N2JEykqTJEmSlAJr1sDzz8Puu8O++8Jvv8UfV64c/O9/4dnC//yn6GcKJamsMDiTJEllW7Vq0L17eMRy7lyYMAFuvBFaty44rnPnxHNcfHFo6dixI/TpA7NmJbXkzXXzzQWPGzWC9u2jqUWSJElS8Vu5EnbdFU49FaZNg2XLwo8oiWy3nYGZJP2VwZkkSdI65cqFwOyGG0KANm8ePP10CNY6dYr/ntWr4f33w38/+CCsZGvWDJo3h8suC0u61qxJ7a8jjtxc2HNPqFx5/bnLLku8iE6SJElS+qlYMawy21CfPiWmQYYkpQWDM0mSpEQaNgybgb3+Omy9dfwxH38c/6fQb76B++6DQw8Nq9FOOAGeew7mz09uzQlkZsK998Ls2XD55WHvgjPPTDz+1VfhzTfDvgiSJEmS0seVVxY8btwYcnKiqUWS0pHBmSRJ0paYPj2kUoX544+QRPXoEfZRa9cObr0VpkyBWCw1df6pfn24666w8XeVKvHHrF4Nl1wSFtrtvnvI+0rAojlJkiRJhA7z/folvr777tC1a/ix45134PPPoUWLlJUnSWnP4EySJGlL/N//wYIFIRg77bSQTBUmFoNPP4XrroO99w6vI1BY1vfCC+ufSJ02LeR9Eyakpi5JkiRJ8X33HZx1Vuge0bNnCMQSeeEFGDMmbNWckZG6GiWpNCji8WhJkiQVqUYNOO648JGXBxMnwuDBMGgQTJ6c+H116kCbNvGv5eWFPddSbO1auPPOgucOPBD23z/lpUiSJEn605o14XvyX35Zf+7OO2HgwPjjE3WXkCQVzRVnkiRJxalcOWjbFm66CSZNgp9+gqeeCr1S/vrTa6dOUL58/Hkefxx22y1sSDZ6NOTmJr30dW66CVq2XH989dWJx6a406QkSZJUJm21FZx7bsFzr7wCM2ZEU48klWYGZ5IkScnUqBGceSa8+SYsXAjvvQcXXAA77gjZ2YnfN2gQfP013HMPdOgA9erBiSeGnisLFiSt3PLl4V//Cm1f3nkHzjgDjjwy8fjzzgttYqZPT1pJkiRJkgjfe1etGl5nZUGvXlC5crQ1SVJplBGLpfY54XLlypGRkcEXX3zBrrvuCsBXX31Fy5YtycjIYO3ataksR2kiJyeHJk2aADBnzhwaN24ccUWbaP78jfe6+fXXcPNTklS2xWLhI147xuXLQxvHlSvjvzcjI+z03blzCN/22COSjQvmzYPtt4fVq8PxMcfAAw9A06YpL0WSJElKa8uWwdNPw1tvhWftEu1JfPPNsGQJXHIJbL11SkuUVFql8T3sZOUGKd/j7NRTTyUjI4NatWrln6tVq1b+eUmSpDIhIyNx2DViROLQDELgNnZs+LjmGmjcOARo2dlw2GEpe+y0b9/1oRnA+++vfwJWkiRJUtHWrIFbboFHHoHffgvn3ngDTjgh/vjrr09dbZJUVqV8xZm0OVxxJkkqU9auhQkTYPDg8DFlyqa/t2LF8Kjqv/6VvPoIW641aQI//7z+XM+e8OSTSf20kiRJUqkSi8G++4Zv/9dp3RrGj4+kqYSksiiN72EnKzdwjzNJkqSSpnz50Irxlltg8mTIyQmJVJcuRa8mW7kSWrRIeomZmSHPu+YaWNdI4JJLEo+fNg1++SXpZUmSJElpJSMDLrus4LmJE0NwJkmKhsGZJElSSbfNNmE511tvwcKFMHRo2Bl8hx3ij91zz/jzfPMN/Pvf8OKL6/vAbIGGDeHWW2HOHHj7bWjePPHYs8+G7baDs84KZUiSJEllRV4efPll4uvdu6//1j47G0aOhLZtU1KaJCkOgzNJkqR0UrEiHHlk2GBs1iz4+mu4+27o0CGsVMvOTtzT5X//g4ED4aSTQsuFAw6AO++EL74IPWI2U5Uq8I9/JL4+fjyMHg2rVoWFcy1awLBhm/3pJEmSpLSwZEn4tn2XXUI7xkTPrmVmwlNPwVdfwaBB4Vt72zRKUnQyoy5AkiRJmykjI6RQLVpA796waBEsX554/ODB61/n5cEnn4SPq66CbbcNoVt2Nhx6KFSqVGxl3ntvweNGjeDAA4ttekmSJKnEWbECmjYNWwet89hjodV5PIcdlpq6JElFc8WZJElSaVGrVmjVGM/ixfDxx4nf++OP4Sf5zp2hTp3w38cfD30Yt0BeHtSsCVlZ689deGHBY0mSJKm0qVQJOnUqeK5v37AlsSSpZDM4kyRJKgvKl4dHHoFjjil6NdmKFWF12jnnhJVoe+zx/+zdd3iUVd6H8XtC6EV6bwoioCJIERUpNpAEFVRcxd7X3lFXRd+1YS9rL1hWRcWeUNSVuoqg2EAsCCi9ifQWmPePs2kwkwRMJffnus6VmXnOeeY3rPsQnu+cc2DYsF1624SEsDzj3LmZE9suuCB+/wcegDPPhGnTduntJEmSpGLjiiuyP69fH+bPL5paJEl5Z3AmSZJUGlStChdeGPY5W7EiBGMXXwzNmuU+9vvvw4y1v6BBA7jrLpg9G/bYI3afLVvgoYfg5ZehY8ewnOMXX/ylt5UkSZIKxNKl8H//B6eeGr/PgQdCz55w/PEwbhx8/TW0bFlIBUqSdpl7nEmSJJU2FStC376h/etf8MMPYRfy1NSw59m2bTuOSU6Ofa5t2+CRR+Doo6Ft21x3MS9TJv6xt9+GBQsyn0+aFDZKlyRJkoqL5cvh+uvhtddg06bw2uDBcMABsft/9BGULVt49UmS/jpnnEmSJJVmkQjsu2/41/6ECWH38tdeg0GDoGbN0GfvvUOLZdo0uPpq2G8/2HNPuPRSGDVqlzZvePLJ7M8PPTTMPJMkSZKKi6pVw/fN0kMzCN8ji8fQTJJKHoMzSZIkZapZE045Bf7977D+zKRJYf3EeFJTMx//9lvYR61v33CeY4+Fp5/O80YOI0bAP/8ZlnUEuPLK+H1/+AFGjoStW/N0akmSJClflC8fVjzP6rXXYOXKoqlHkpT/DM4kSZIUW5kyYdpXUlL8PlmDs6w2bIAPP4SLLoImTaB9e7j5Zvj887hpV506ocvcufDGG2EviHjuvTeUtffe4fHy5Xn9UJIkSVJ80WjYZ/fDD+P3uegiKFcutLPOgsmToUaNQitRklTACiU4u+eee1i0aFFhvJUkSZIKy7Zt0KULNG2ae99vv4U774RDDoH69eGMM+C992J2LVcOBg6Mv7/Z8uUwfHh4PGdOWGXy2Wd37SNIkiRJEL73NWwYdO4MXbvCJZdAWlrsvvXqhS96/f57GNO+faGWKkkqYIUSnN100000a9aMfv368d5775EW728dSZIklRwJCfCvf4UpYt99B3ffHWaoJeTyK+by5fDKK/DCC7v0tsOGZd9Tolw5OPfcXTqVJEmSBMD06XDOOfDVV+H5vHnxF1eAsDpCvXqFUpokqZAV2lKNaWlpjBw5khNOOIFGjRpx7bXXMmPGjMJ6e0mSJBWUSAT23x9uuCHsibZ0adgj7ZRToHr1+OOSk+Mf+/Zb2Lgx5qE998z+rd6TToK6dWOfZssWmDUr108gSZKkUq5z59CyevzxoqlFklS0CiU4+/7777nyyiupXbs20WiUZcuW8dBDD9GuXTu6du3Ks88+y5o1awqjFEmSJBW0WrVg0KCwS/qyZTBhQlhPcd99s/fr2zf2+LQ06NkznOe448I6jAsWZBw+8USYNg0++wxOOy0soxPP+++HfdD69IEPPoi7vZokSZJKgRUrYOHC+Mez/l7ZrBkccUTY80ySVLpEotHCu/ynpaWRkpLCsGHDGDVqFGlpaUQiEQAqVqzICSecwDnnnEOPHj0KqySVEPPnz6dJkyYAzJs3j8aNGxdxRXm0bNmOX4FfuhTq1CmaeiRJKmpz54Y1b2bODMs8xjJhAsT6fbB9+zBLLSkpfB24TJlc365XLxg3LvP5CSfAiBG7UrgkSZJKomg0fOHq2WfDvmRnnAFPPx2778aNcPrpoSUl5enXTUkq+UrwPeyCyg0KNTjLaunSpbz88su8+OKL/PDDD6GY/4Voe+65J+eccw5nnnkmjRo1KoryVMwYnEmSVIoMHgz33ptznzp14Jhjwh2N3r1hjz126DJjBuy3X/bXXn0VTj01H2uVJElSsfbUU/D3v2c+r1QpLGaQ04riklSqlOB72AWVGxTaHmfbq1u3Ltdeey3Tp09n8uTJXHDBBVSrVo1oNMrs2bO55ZZbaN68OX379uXtt99my5YtRVWqJEmSCtPixWHftJwsWwYvvwwnnwy1a4epZfffDz/+mLGezs8/Q40amUPq1AkzzuJZvTofapckSVKx0r8/JCZmPl+/Hl56qejqkSQVf0UWnGXVpUsXnnrqKRYtWsTLL79M/fr1iUajbN26lTFjxjBw4EAaNWrEDTfcwKJFi4q6XEmSJBWkl16CJUsyg7EYs8mySUsL6zFedx0cfHDGRmb9+8P8+fDCC9CxI5x/PpQvH/sUS5dC/fpw/PEwcqR7oUmSJJUkK1bA5s2xj9WrF7bNTVe2bPhVU5KkeIpFcAYwd+5chg4dyq233sqSJUsylm2MRqNEo1GWL1/OfffdR8uWLXnwwQeLuFpJkiQVqDp1wuYSw4eH2WXpwVjbtjmP69Mn21eKK1WCs8+GL7+E2/4RfwWDl16CDRvg/ffD6o9t24Y8TpIkScVTNApjx4ZluBs2hA8+iN/3ggugRQu45x6YNw/uuqvw6pQklTyJuXcpOBs2bODtt99m2LBhjB8/PiMkA2jTpg3nnnsup59+Ot9//z3PP/88I0aMYMOGDVx33XXUrVuX0047rSjLlyRJUmEoWxZ69Ajt3nthzhxITYWUlHC3JOvXi5OS4p/mlBPDhhZJSaF16gQJCUSj8Nxz2ft27Zp9SR9JkiQVL6edBq+9lvn8mWfgxBNj9z3yyLCMd0KxmUIgSSrOItH0pKoQff755wwbNow333yTNWvWAGFmWaVKlRg4cCDnnXcehxxyyA7j5s6dywknnMDXX39Nhw4d+Oqrrwq7dBWRgtrkr8CV4I0VJUkqEdauhf/8JwRpo0fDtGlhz7PtbdwItWqFTS3S1asHxxzDLx3/RvvBR7N+fea+ahMnQrdusd9y06b4Sz5KkiSpcLzyCpxxRvbXfv0V9tqraOqRpBKrBN/DLqjcoNCCs/T9y4YNG8Yvv/wCkDG7rGPHjpx33nmceuqpVK1aNcfzfPzxx/Tu3ZvKlStnhG7a/RmcSZKkXEWjEInEPjZ6NBxzTNyhqxNr8nqLm3l23amsL1+dGb+Uj3uqbt1CcHb22TBgQFgOUpIkSflv8eKwD20sGzaEJRr//DM8L18+LL998smFVp4k7R5K8D3sgsoNCmUBmqSkJD766CO2bduWEZZVr16dU089lfPPP58DDjggz+fac889AVif9dvCkiRJUrykC2DMmByHVkv7gwt/upoLuZo/qEFkn9phOcfkZDjsMChXDoAZM+C//w1jPv0ULr4YPvsM9tsvvz6EJElS6bZ6Nbz1FgwbBlOmwPz5O97PBahYMcw4+/jjsIfZ6aeHBQYkSfqrCiU4GzVqVMbj7t27c95553HiiSdSoUKFnT5XpUqV6N69O5GcboxIkiRJWd17Lxx7bObeaD/9FLdrTVbCLyvh4YdDq1oVvvkG9tqLZ5/N3rdqVWjTpiALlyRJKj02b4YWLWD58szXXn0Vrroqdv977gm/rnmbUJKUnwplS8y6dety3XXX8dNPPzFu3DhOO+20XQrNABo2bMi4ceMYO3ZsPlcpSZKk3VbZstCrF9x/P/z4I8yaBY88AkcdlTGbLK5KlaB5c6LRkLlldcYZUKZM7GGrVmXfUk2SJEk5K1cOevfO/tqwYWFF7lgqVjQ0kyTlv0IJzubPn8/QoUPZe++9C+PtJEmSpJy1aAGXXw4ffRS+0vzOO3DuubE30UhKgoQEIhGYPh2GD4c+fSAhAc6s+r9x77wD2+2/+9BD0KBBWDros8/i3/CRJEkqTdatC99hiufss7M/X7Qo7HUmSVJhKZTgLDGxUFaElCRJknZe1arQvz889xwsWABffgm33w6dO4fjSUkZXStUCBvOjxoVbuK0/vQJeOEFOOGEsKnGUUfBI4+w7edZvPhi2KPj2Wfh0EPDKSVJkkqjbdtg7NjwfaMGDeDMM+P37dUrfMfp2GPh3XfDr2cNGhRerZIkRaJRv/uq4m/+/Pk0adIEgHnz5tG4ceMiriiPli3bcQfbpUuhTp2iqUeSJO2cJUugWrWwDtD2Vq+G2rVhy5YdDo2lJ4eTfWnxr76CAw8sqEIlSZKKr48/hqOPzv7ajz/CPvvE7r9pE5QvX/B1SZIo0fewCyo3KJQZZ5IkSVKJVK9e7NAMwh2gGKEZwJd0IsK2jOf7J0ynw10nwYsvhn+AZLFtW9g7bdOm/CpakiSpeOnVa8d7si++GL+/oZkkqSgZnEmSJEm74qCDwkZmRx4JZctmO3Qd9/M7TbmLG2nFT5y17QUib48Im3bUrx/Gfv45EPY/69cvvHz++TBunPuhSZKkkuXPP+H552Hu3NjHExPhlFMynyckhIn9kiQVRwZnkiRJ0q5o3BiuvDLMPFu+HN5+OwRj9eqFwyzgRu7hR1pzGY9ljotGYcoU2GMPAF59Nbz8559hm7WLLy7cjyFJkrSrxoyBE08MXwA67zx4+eX4fU87DfbfH+65B37/PWwTK0lScWRwJkmSJP1V1arBgAHhDtDChSEYGzIEOnUiApQlLXv/PfeENm3YvBnefDP7oUG9lxN57FH49ddCK1+SJGlXpKSE7w6lLzn973/HnznfsSN89x0MHgyNGhVejZIk7SyDM0mSJCk/JSRA585w220wdWoI0p5/Hvr3hypVQp+kJIhEWLIE9tsv+/BTE4bDFVdAy5bQpg1ce21Yv3HLFh57DJ56aodt0iRJkorEoEHZn//yS/j1J5ZIpODrkSQpPyQWdQGSJEnSbq1BAzjnnNA2bYKJE6FhQwCaNIHx48NyRa+/Dj/9BHt+/lrm2B9/DO2BB9hSrRb/t3E2yzdX45JLovTqFeHBB6FduyL6XJIkabcVjcK0aWFm/JQp8OmnsYOvgw6CFi3CRPmyZcN3g7bb+lWSpBLH4EySJEkqLOXLw5FH7vBy06Zh2SKWLYN6k2MO/Wj1QSynGgDbtkX4z3+g+suPwqDDoH17v8YtSZLyxdKlcMgh2VeNnjoVunTZsW8kArfeChs3hr3OatYsvDolSSooLtUoSZIkFRfr18OZZ0LdujscepXsayEdzGc0feAKOPDAMHXtggtgcgjdNm+GlSsLpWJJkrSbqVMnrDyd1RtvxO9/xhnh1xBDM0nS7sLgTJIkSSoumjWDYcNg0SL44ovwFe4DDwRgEK9yMsOpxDoABvJm5rgFC+DZZ8OaSsCoUVCvXlgu6aWX4M8/C/uDSJKk4uzHH2Hu3NjHIhEYODD7a2++Cdu2FXhZkiQVCwZnkiRJUnGTkBDWQ7r9dvjqK1iwgKTnBjD8+DdYVqk5b3EiJxPjq99JSUD4VviWLTByJJx1FpwwIAoTJkBaWuF+DkmSVGz8/DP83//BAQdAmzbw4IPx+558cvi5115www3w4YeuCi1JKj3c40ySJEkq7ho2hHPPhXPPpdKmTZw4fjykNoKUFJg9O/TZd19o1owNG+CDD7IPP+HAOdCjB1SvDn36hICtTx+oXTvfSly9GubPh7VroUoVaNwYqlXLt9NLkqS/6N13YciQzOcjRsBDD0GZMjv23W8/+OYbaNfOwEySVPo440ySJEkqScqXh6OPhkcegVmzYOZMuP9+uPJKINzkyjqxLCEBBmz53+y0P/+E4cPh9NPDWo6HHsrg7p9z39WLmPVLdKdLiUZh7Fg48cSwr8m++8JBB4WfNWvCSSeF49GdP7UkSdoFOf2d279/9ueLFsGkSbH7RiJhZpqhmSSpNHLGmSRJklRSRSLQunVo/3PwwbB0aZiM9uabsGkT1B83fMex27ax5rPveJgD2TyxPNc/BPvVXMBrt89i/3M6Q6VKOb71tGlwxhkwY0bs41u3hm+yjxgRgrSXX87Yrk2SJOWj9evho4/CjLKJE8P+ZeXK7divVavwd3L6393168OSJYVbqyRJJYHBmSRJkrSbqVYNTj01tOi69XBYjDWYgFEcw2bKZzz/6Y86NL2sLVy3GXr1Cks6JidDs2bZxn38cfjW+rp1eatnxgzo3j3c0DvqqF3+WJIkaTurVkGjRtn/Th47Fnr3jt3/ggvCKs8DBsChh8ZeplGSpNLO4EySJEnajUUqVwrTw+bPh5EjITUVPvkE1q/nXbKv2dSLsezBatgIjBoV2rhx8NZbrFgBn38elmDcmdAs3bp1YdyECc48kyQpv+yxR9iP7IsvMl979934wdnllxdOXZIklWTucSZJkiSVBo0bh6+Zv/8+rFgBo0Zx/vHLuaDKa9RjMQD9eXfHcUlJALz3HvTrB926ZYZmFdiwUyWsWwdnnumeZ5Ik5cXWrfDZZ3DjjeG7L/EMGJD9+fvvw7ZtBVubJEm7M4MzSZIkqbSpUAH69OHwdy/j6dWnsOC7P5j091c58eCFO67ZdMwxQPj2OmSGXglsZSENmcBhDOYe9mU6kHsiNn06jB+fj59FkqTd0KOPQr16YTnFe+6Bl16K37d/f0hIgJ49w7gpU8JzSZK0a1yqUZIkSSrNIhHK7N+WQ59oCwyClSthzJiwpOOKFVCvHmvWhH3NsmrDD9TgTw5jEocxiXu4kd9oSipJDOdkptCFTVSM+ZZPPBFu7kmSpNgqVQp/DacbPRq2bIGyZXfsu/fesGxZWE5ZkiT9dX7/RJIkSVKmGjXgb3+DV17JWBdq8WLo1Cl7t78xfIehzfidi3mSzZRnG2U4gK85mP/SgAXZ+r3zDqxeXWCfQJKkYm3LljD7+qmn4vf530rJGVavhokT4/c3NJMkKf8440ySJElSjvbeG559FvbdN/O1fqTE7LuUOkyhC1ES+JYOAHzEUdRlKakkkUIyX2w9iAULylCtWmFUL0lS8bBgAVx+OXzySQjCypaFU08l5t+HDRqEL618+SXst1/YZ7Rp08KvWZKk0sjgTJIkSVKu1q7N/rwrk+nFWJJIJZkUmvE7AKM4hmiWhS2qsIbuTKA8mzmA77iJu5lJa9as/oFoNMKMGSGQi0QK89NIklT4atYMk7k3bgzPt2yBjz6CE0+M3f+JJ6BOHWjevNBKlCRJuFSjJEmSpDyoUiX7841UZBR9uZTHac5c9uN7BnMPE+lGOTZl9DuKjynP5mxjp9CFqtUifP897L8/NG4MZ58Nw4fDtm2F8WkkScpf0SjMmAEPPAC//Ra7T8WK0KNH9tc+/DD+OTt3NjSTJKkoOONMkiRJUq4aN4YyZWDr1lhHI8xgP2awHwDV+YMufEEZtpLMjncERyck0b8RPP10eL5wIbz4IowbByd/cj5UKB82d+nVCypUKKiPJElSvrjhBvj3v8NSjADly8Oll8bu27s3jBkTHrdvD+3aFUqJkiRpJxicSZIkScpVtWrQvz+MGJF73z+pySS6AzCJw3iBc0kilSRSacNMyvc7mmrVwvJUWfU+fAuRf78CmzbB449DpUpwxBGQlMTv7Y9lU80GtGzpso6SpOJl8eLM0Axg9Oj4wdmAAWHJxqOPDvuYSZKk4selGiVJkiTlycUX7/yYrSTyX7pxE3dzAN/RiAWcdWV1tm6FefOy9z267jchNEu3fn1Yw+qii3ik62u0agVN91jFmX2X8vHomFPfJEnKN1u2wOefw513Zs6SjqV37+zPx47N/tdZVs2awZlnGppJklScGZxJkiRJypOePWHfff/aOertV5cePcKyjzNnwo8/wiOPhJUZj1j077jjxhDuSs5fswcvj6rLlyfcDWecAW+8AX/++deKkorYpElFXUHB2F0/l0qH116DWrXgkEPg5pvhySfj9z3qqMzZ0E2bwqBBsGZN4dQpSZLyn8GZJEmSpDyJRODll6Fy5V0bX7kyvPRS5s3FSAT22QcuvxxSUmCP6y+Eu+6CQw+FhMx/qsynUcb+aekOX/8hvPIK/O1vULt2SPVWrgTgmWfg3Xfhjz92rU6pMN12Gxx2GAwdWtSV5K+hQ8Pnuu22oq5E2jVNm2YPv779FpYvj923du3wV9IPP8DcueHvodq1C6VMSZJUAAzOJEmSJOXZgQeGUGpnw7PKlcO4Aw/MoVPbtnDjjWGaytKl8O9/wymn8GuVA6jPooxuVVlNR77KHLd1K8yeDdXDEpDXXx/2kKldGzp2hGnTdq5WqbBMmgS33x4e33DD7hOeDR0aPg+Ez+fMMxUX0WiY7fz003DaadC+PWzbFrtvly5hq82sxo6Nf+5Bg6BNG/fhlCRpd5BY1AVIkiRJKlmOOgomTAgrJc6YkXv//fYLM81yDM22V6tWuAs5aBA90tJY+Nnn/Pjya3yauoFVi9eTyHZ7nCUlQSTCN9/AqlXhpWg0hGb1vh4N0+ZD377QsOFOFCEVrG7d4J57MkOm9J+DBxddTX9V1tAMwufr1q3o6pGyWrIkfEcjq++/hwMO2LFvuXLQvTuMHh3+Hjv8cNh778KpU5IkFS2DM0mSJEk77cADw83G8ePh8cfDbLKtWbKsxETo3x8uvhh69PiL38BPTCTS/TDadD+MNhDWwUptBKmp8OmnsGlTCM4IT7PaZx9o9NJdMHFieKFDB0hOhqQkljTtzMGHJtCtW7ixf9hh0Lq1swVUuNJDst0hPIsVmpXEz6GSa8MG+OKLMJOsevUdj9evDy1bwqxZma99+mns4AzgoYfgxRehXr0CKFaSJBVbBmeSJEmSdkkkErYW69kTVq+GBQvCfjBVq0KjRlCtWgG9cfPmcMkloa1bF+56Hn54xqGjjgpLw23YAL0O3ggv/zdz7Ndfh/bPfzKx2tnMWf0Cc+aEvWmqVg37oiX6ryQVst0hPDM0U1H65z/DzLCpU2HLFnj77bBkbyyHHbZjcHbVVbH7tm6d/7VKkqTiz38SSpIkSfrLqlUrwKAsJ5UrQ79+GU9POim0TZvCrIOakz+Nu4HNpNXtsj0/OHEqiY9MCDPSWrXKNvVs1iz46Sc46KCwd5qU30pyeGZopqI2cSJ89lnm8wkT4gdn3bvDxx+Hn4cdlvG9C0mSpAwJRV2AJEmSJOW38uXDTdH9DqkGAwfCHnvs0Gcih2V7ftjK9+Haa8MUg733hiuuCMtCAm++GfK0OnXCMl+33VYIH0KlzuDBIXRKd8MNIZQqzgzNVFBWrAgr8t5yS5hJ/Mgj8fselv1ynrE6byynnw6//w6vvgoXXRS+JyFJkpSVM84kSZIk7b7SNzDbsiVMR0hJCXdiZ87kJc5kAt2ZRDcmchiHkeVO66+/wqOPwuWXA2H2WtZDK1bEf8uNG0Nw515p2hUlaeaZoZkK0u23w2OPZT6vWDF8nyGWrMFZQgKULQtpabGX3i1TJn/rlCRJux9nnEmSJEna/ZUtCz16wH33wQ8/wK+/st+jF3Jx79m8Vu5sfqcp3ZmQfcw++0CLFkSjMHly9kNdWy6HKVNiLgN56aXQoAEcfzzcfTdMn15wH0u7p5Iw88zQTLtq2zb45RcYPjzM5o2na9fszydPhmg0dt+DDoJ//APGjIE//wx93a9SkiTtKoMzSZIkSaXPXnvBZZfB6NGwYgWR994jcv750LBhZp+kJADWrAmrN1asmHmo66x/hzu1DRvC2WfD22/D6tVAuGG7ZAm8/z7cdBN88klhfjDtLopzeGZopl314YdQo0ZYHvGUU8Kssni2D86WLYM5c2L3rVgR7rgDjj4aqlbNv3olSVLp5PdvJEmSJJVuVarAcceFFo3CN9+E5Rz79AGgWjUYPz4s+zV9OkydCns9+UoYu2QJvPhiaGXLsvqQPvzww/tA5jqNBx0U/60HDgyzLw48EDp2hIMPDu8nQfFcttHQTPGkzySbPRuOOSZ2n4YNM75jAIQJwH/+CdWr79h3zz2heXNo2jSEaAcfDHXrFkDhkiRJ2zE4kyRJkqR0kQh06BDadhIToX17aF9vEVwwbcexW7bw5fi1RLOEZmUT0ujw50TYfCiUK5ete1pa2HJtw4YwYQ3CMmNHH52fH0glXXEKzwzNFMusWXDuufD112GGbrlymT+3t99+YeXcLVsyX5s6FY46ase+kUgI4dwvUpIkFTaDM0mSJEnaGfPmhbUbf/xxh0O9GMvP7M0XHMRkurJ2WxUq9D07rB121FGQnByWgKxbl5kzQ2iW1YEHxn7LbdvCsFatYP/9oV27EOLFujGt3U9xCM8MzUqnaBQWLoTvvguXsFj7htWqBROybBG5eTPMmBHz+weULx+uYdOmhdljHTuGIC0eQzNJklQUDM4kSZIkaWd06QIzZ8Kvv4YlHVNSwlqOmzcTAfZmFnszi9N4NXPMmjXwzjuhPfssnHce07abtNa0KdSuHfst584N27GNHp352oIF2bdk0+6tKMMzQ7PSZ+PGsNzid9/BH3+E12bODN8Z2F6NGmHbyNmzM1/76qvYwRnA88+Ha12jRgZjkiSpeDI4kyRJkqRd0aIFXH55aGvWwCefhCAtNRUWL44/rm9fAHr1ghdeCDeYp02DvZpvgzXrwuy07Xz/ffbnNWtCgwaxT794MfTrF2al7b8/tG0LRx4JCQm7+kFVXBRFeGZotvvZsAF++ikEYYcfDvXq7dinQoXQJz00g3AdihWcQZg5lh6c1a8PmzbFf//27Xe5dEmSpEJhcKad9vvvv/Poo4+SmprK77//Tvny5WnZsiUDBw7k4osvplKlSkVdoiRJklS4qlaF/v1D27YtbPaTPhtt6tTMfh06ZEwTa9oUzj47NADGTYBaR0OPHmFdxuRkaNkSCLM+smrXLv5Mje++gy+/DA2gevXsN7+z2rIllFu+/K59bBW+wgzPDM12P4ccApMnhyUYIeyvOGBA7L7t2sGiRZnPv/sOTjopdt8rroDTTw8BmjNhJUlSSWdwpp2SmprKoEGDWLVqVcZr69evZ+rUqUydOpXnnnuOkSNHstdeexVhlZIkSVIRSkgId487doRbbw1TwEaNCkFa587xx6WkhCTrk09Cu+qqsKlZcjK9W/yN6K0d+P6HRL77Lv4SaLDj7LTWreOHbOPHQ58+YZm11q3DHmu33bbTn1iFrDDCM0OzkmPBAvjhhzCDbOZMOOMMOPjg2H0rVMgMzSD0j6ddOxgzJjyuUiXnWWSHHrrzdUuSJBVXBmfKs2+//ZaBAweyfv16qlSpwo033kivXr3YsGEDw4cP59lnn+Wnn34iKSmJqVOnUqVKlaIuWZIkSSp69etvN7UsjtTUHV/7+Wd48EG68CBdqlWDo4+Gm5KJ9jkGqBvzNNvPTmvTJv5bzpwJW7fCL7+EtnBh/ODsl19gypQwCa5FC6hVy/2JilJBhmeGZsVLWhps3gzxFnc580z4z38yn++1V/zgrE0bGDs28/mPP8Z/39NOC4FYu3bQrJnLvUqSpNLD4Ex5duWVV7J+/XoSExP56KOPODjLb+KHH344e++9N9dffz0//vgjDz74ILfeemsRVitJkiSVIIsXw6+/5txn9WoYMQJGjCASiUCXLplLOrZvn5FiXXwxHHBAmHk2fXrOs9O2v2meU8g2enTYzi3d4Ydnv1mvwlcQ4ZmhWfHwr3+FLH3WLJg7F+64I/7/Di1bZv//Yk6zyLL+f7xZs7BfYjzt2oUmSZJU2hicKU+mTp3KuHHjADj33HOzhWbprrnmGoYNG8bMmTN5+OGHufHGGylbtmwhVypJkiSVQPXrw/Ll8PHH4W75yJGwZEn8/tEofPFFaLfeChddBE8+CcBBB4WWF9sHZ61bx++7fa5Xv378vs89Bw88EGa+NG0Khx0Gp56at5q0c/IzPDM0K1hz54YlFX/7LbQuXeLvL/bttyGsTjdrVvzz/m8rxAw5BWcnnBD2OdtnH6hcOc+lS5IklSoGZ8qT9957L+Px2XGWmElISOCMM87gxhtvZOXKlYwbN46jjjqqkCqUJEmSSrhq1cJd7RNOgG3b4KuvQoiWmgpffpnz2MMO26W3fPfdEJ6lt8MPj993+xv3LVrE7/vDD5nnBFi/Pn5wNnIkTJgQZr80bRrCu5zOrR3lR3hmaLbrtm2DZctCGFalCrRtG7vfvfdm5NsAnHNO/OBs+zAspwmpLVqE923dOswo69Qpft8GDUKTJElSfAZnypOJEycCULlyZTp27Bi3X48ePTIeT5o0yeBMkiRJ2hUJCdC5c2i33QaLFsGoUZCSEmalrV2bvW+fPrHPs2EDdOsWErGkpLBhUZZVIapVC7NeunTJvaRGjcLN/Llzw55LOYVb24dsTZvG7ztmDDz6aObzM86Al16K3XfyZJgzJ/Pmf6NGITDQXwvPDM1i27YtTATdujV+2HT77WEZxbS08Pycc+D552P3bdYs+/Pffov/3tsHZznNODv22LCSq3sOSpIk5Q+DM+XJzP+t9dCyZUsSE+P/Z9M6y9ouM3NaH2I78+fPz/H4okWL8nwuSZIkabfToEG4I3/OObBpE0ycGEK0lJRwLN5GRWPHwrRpod1/P+yxB/TuHfZFO+YYqF07zyU8/XT4mZYG8+ZBjRrx+24/Oyan4Oz33/Pe98UXM+sAuOCC7M+z+uqrsNpl7dqh1au3+y9NtyvhWWkLzdLSQhi2bRs0bBi7zyOPhP+7LF4c+g8aBP/+d+y+lStnhmaQcxi2/X/b2/+3n1XHjiGUa9kyhNQ5BdVlysQ/JkmSpJ1ncKZcbdy4keXLlwPQuHHjHPvWqFGDypUrs27dOubNm5fn92jSpMlfqlGSJEkqNcqXhyOPDO2hh2DNmvh9U1KyP1+1Ct58M7RIBLp2DTPRkpLggAPyNGUlMRH23DPnPs8/Dz/9FIKB33+HDh3i992Z4Gz779PltOTc44/DsGGZz6+4Ah5+OHbfMWNCvXXqhJBt772hefP45y7OdiY8K+mh2caN8Mcf8Oef4T/tqlVhv/1i9334Yfi//4OVK8PzAQPg7bdj901Lg6zf7Vy4MH4N24dvOQVnzZuHALdp0zD7rFWrnPveemv845IkSSo4BmfK1Zos/xCvkod1UNKDs7VZl4+RJEmSlP8ikbDeYizRaNgfLZ5oFD7/PLSbb4bGjaFv3xCiHXHEX5qe1bVraHlx7LFhNs1vv4UQLafAameCs/999y9DTpPrhg8Ps9nSXXllyCRjeeCBsFrmHnuE1qdP/H2qFi0Kq2VWqhT+OCtVKpzZQXkJz4oiNItGQ9i1dWv8JTa//BImTQpB2KpVYc+u88+P3ffBB+Ef/8h8nlMYlpCQGZrBjv99ZLV9GJbX4CwxMbRoNHYGffDBYRabJEmSijeDM+Vq48aNGY/LlSuXa//y5csDsGHDhjy/R26z0xYtWkSXvGy8IEmSJCnTW2+FWWepqWG5xpzMnw/PPBNa+fJwyinZp2wVkCFD8t53r73CXk6LFoWf8Zbag50Lznam79dfhxlq6WrUiB+c3XJL9v2ucpr19sQTMHJkCNcqVAgrag4aFLvvJ5+EpSjLlg1tv/2gV6/sfWKFZ998E2oYPz52aPbtt6Ft2RLa3nuHDDWW1FT48MPQb/Nm6NQpnDuWe+8Ns73Wrw+h0gknwIgRsft+9FH2MCw5OX5wVr169uc5hWF16mR/vmxZ/L7b/3e1ZEn8vh07hrCvQYMwm8xlEyVJkko+gzPlqkKFChmPN2/enGv/TZs2AVCxYsU8v0duS0BKkiRJ2kmRCHTpEtr//V+YNjNyZAjSPvkE1q2LP3bTpjB1ppgZPjzz8bp1OZdYpw40ahQCks2b8y84W7Uq+/M99ojfd/367M8rVYrf99tvs08QrF07fnD2/vvwr39lPj///B2DMwhhWEpKmMEF4c/vnXfCn0e6rDPN3n4b/vnPzGOnnRY/OPvqq+z7y61bFz84Sz+ebvs/l6y2D8P+/DN+3+3/7HMKw7b/3zSnkK1du/Bn3LBhaHXrxu9btWoIzyRJkrT7KH7/ElKxU7Vq1YzHeVl+cd3//kWUl2UdJUmSJBWShg3hvPNC27QpTDtKn402e/aO/ZOS4p/rjjvCmorHHAO1ahVYyTnJbSXJ998PP6PR3EO2Tp2gXLkQpixfnnNQsn2Qk1/B2fZ9y5aN3zctLe99u3TJDM4gfmgWy5Yt8Y9t/5459d3+c+cUnG3/57l9UJlV1pCtcuWc/xw6dYKxY0OAVqcO1KwZv2+NGmEJUUmSJJVOBmfKVYUKFahduzbLly9nftYdkmNYuXJlRnDWpEmTwihPkiRJ0s4qXx6OPjq0Rx6Bn37KDNEmTgzrzR15ZOyxq1bB7beH9CYhIWxmlpwcgrb994+9uVMRikTi76eV7rHH8n6+K66Afv0y9+Bq3z5+350JzrZf6T6nEGj7kCqnvvHUrJn7nmY7E5zltDjJ9iFnTpMdmzULs+eqVw9tzz3j9z3iiBB0VquW+59BjRrQs2fOfSRJkiQwOFMetWnThokTJzJr1izS0tJIjPN1zR9//DHbGEmSJEnFXCQCrVuHdu21YUrVN9/ET5s++ihzytO2bfDZZ6HddBM0aRICtKQkOPzwnJOiEurEE/Ped/Ro2LgxBGjr14eAJ54zzoDOnUO/jRvhsMPi923XLvwRp+9F1qpV/L4NG0L9+rB4cfbX//gDhg7NHp41aAAdOoQQqly58J9EPAceCJdcEvqVLQv77BO/b9++8Pnn4T+HypXD8obxdOsGn34a/3hWFSqEJkmSJOUngzPlSbdu3Zg4cSLr1q3jq6++4qCDDorZb/z48RmPDz300MIqT5IkSVJ+qV4956k5WTfi2t68efDUU6FVqBDCs/QgrVmz/K602EtICGFRXvLDY4/N+/KAl18eWl6kpWUPzWrWDKEZwA03hJ/p4dnf/x5aXhx+eGh5Ua9eaJIkSVJJkFDUBahkOP744zMeDxs2LGafbdu28fLLLwNQvXp1esXanVqSJElSyda7d0h4ckuDNm6EkSPDtKTmzcMyjjfckPOafspXQ4dmhmMQ9jRbsSL8THfDDaGfJEmSpMDgTHnSpUsXDvvfWiHPP/88n3/++Q59HnjgAWbOnAnAFVdcQdldWWhfkiRJUvF2yinw/vshgRk1KjMYy8306TBixK5tyKWdFis0S59ZNniw4ZkkSZIUj8GZ8uyRRx6hYsWKpKWlcfTRR3P33XczefJkxo4dy4UXXsj1118PQKtWrbjmmmuKuFpJkiRJBapCBejTB/71L5g9OwRjQ4dC9+5QpkzsMUlJYU+1WP77X/j+e4hGC67mUiKn0Cyd4ZkkSZIUm3ucKc86dOjAG2+8wWmnncbq1au56aabdujTqlUrUlNTqZrTbs+SJEmSdi+RCOy7b2jXXw8rV8KYMWE/tJEjMzfVSk6Of46rr4YpU6Bp08x90Q4/HCpWLJzPsJvIS2iWLv319P7b73kmSZIklUbOONNO6devH9999x1XXXUVrVq1olKlSlSvXp1OnToxdOhQvv76a1q2bFnUZUqSJEkqSjVqwN/+Bq+8AkuXhtlkN98cZqPFsnQpTJ0aHv/+Ozz5ZAjZatUKP596CubNK7z6S6idCc3SOfNMkiRJyi4SjboOhoq/+fPn06RJEwDmzZtH48aNi7iiPFq2DOrWzf7a0qVQp07R1CNJkiQVRy+9BGedlXu/du0yZ6N17Rp/SchSaFdCs/wcL0mSpBKqBN/DLqjcwBlnkiRJkqSitXUrNGuWe7/vvoO774Zu3aBePTjtNHj9dVi7tuBrLMbyI/Ry5pkkSZIUGJxJkiRJkorWOefAnDnw/fchvenWDRJy+efqihXw6qtw6qmZe6iVQvk5U8zwTJIkSTI4kyRJkiQVB5EI7LdfSG8mTgxLxqQHYzVrxh+3//7QtGnsYytXwsaNBVNvMVAQyysankmSJKm0MziTJEmSJBU/NWuG0OzVV2HJkhCm3XBDCMqySk6Of46hQ6FWLTj2WHjmGZg/v2BrLkQFuSeZ4ZkkSZJKs8SiLkCSJEmSpBwlJoblG7t1C3uc/fYbjBwJqakhFIsnNRXWr4cPPwwN4IADQtiWlARdukCZMoXzGfJRQYZm6dLPl/4+6T/z+30kSZKk4sbgTJIkSZJUsjRrBn//e2jx/P47TJ++4+vffhvanXdC7dpwzDEhROvdG6pXL7CS80thhGbpDM8kSZJUGrlUoyRJkiRp9zNlCiTk8k/e5cvhlVfgb38LIVrPnnD//TBzJkSjhVLmzijM0CydyzZKkiSptDE4kyRJkiTtfk48MeyNlh6M5TabbOtWGD8errsO2raFt94qlDLzqihCs3SGZ5IkSSpNDM4kSZIkSbun2rXhtNPg9ddh2bIQjF1/fQjGchKJQK9ehVNjHhRlaJbO8EySJEmlhcGZJEmSJGn3l5gI3buHtGfGDJgzB/71L+jTB8qXz963SxeoUyf2eT7+GDp2hFtvDctBbttWoGUXh9AsneGZJEmSSgODM0mSJElS6dO8OVxyCYwaBStWwAcfwAUXQKNGkJwcf9yHH8K0afDPf8JBB0GDBnDWWTBiBKxena8lFqfQLJ3hmSRJknZ3iUVdgCRJkiRJRapyZejXL7RoFDZvjt0vGoXU1OyvLV0KL70UWvqstqSkEL61arXLJRXH0Cxdeh3p9aX/LC71SZIkSX+FM84kSZIkSUoXiey4dGO6n36C2bPjj01Lg08/hWuugX32gb33hiuvDMs7btqU5xKKc2iWzplnkiRJ2l0ZnEmSJEmSlBctWsDYsXDttdCmTe79Z82CRx6Bo4+G2rXDnmq5KAmhWTrDM0mSJO2ODM4kSZIkScqLsmWhZ0+47z744Qf49Vd49NEQjJUrl/PYtWuhfv0cu5Sk0Cyd4ZkkSZJ2NwZnkiRJkiTtir32gssugzFjYMUKeO89OO88aNBgx76JiSFgi2XNGoZ2HlHiQrN0hmeSJEnanSQWdQGSJEmSJJV4VarAcceFFo3C119DampoU6ZA9+5QrVrMoUMv/o0bvjwx4/k9LZ5lcLm18Ety2CetBEgP+dLDv/SfJSX8kyRJktIZnEmSJEmSlJ8iETjwwNBuuQWWLoXly2N2HToUbvj3fhnP72Ewg3+9F64Grr46BGfJyZCUBIcdlvuSkEXI8EySJEm7A5dqlCRJkiSpINWtC23b7vDypEnb7WnGYAZzb/ZOv/wCDz0ERx4JtWvDiSfCsGGwZEkBF71rYi3bOGlS0dUjSZIk7SyDM0mSJEmSikC3bjDkH2kA3NPyOQaXezjnAWvWwNtvwznnQP360KULPPFEwRe6k7KGZ0OGhM8pSZIklRQu1ShJkiRJUhG57Y5EjuwD3bqdB2tOhk8+ydwbbfHinAdPnQqdOxdOoTtp8GA49FBDM0mSJJU8zjiTJEmSJKkIZYRLVatC//7w3HOwYAF8+SXcfnvO4Vhycvxjw4fDrFn5WuvOMDSTJElSSWRwJkmSJElScZOQAB07wq23wpQpsGgRvPACnHBCCNgAKlaEnj1jj1+xAgYNgr33htat4ZprYOxY2LKl0D6CJEmSVBK5VKMkSZIkScVd/fpw9tmhbd4MEyfC7NkhPItl9GjYti08/umn0B58EKpVg969ISkJjjkG6tYtvM8gSZIklQAGZ5IkSZIklSTlysERR4QWT2pq7NdXr4a33gotEoEuXUKIlpwM7duH1yRJkqRSzKUaJUmSJEna3dSvD/Xq5dwnGoUvvgjLQR54IDRuDOefD++9F45JkiRJpZDBmSRJkiRJu5sHH4SFC8P+aEOGhP3ScrNwITz3HNx0kzPPJEmSVGoZnEmSJEmStDtKSIDOneG22+DLL0Mw9vzz0L8/VKkSf1xycvxjv/0GW7bke6mSJElScWFwJkmSJElSadCgAZxzDrzzDixfDh99BFdcAS1aZO+XlBT/HMcfD3XqwMknwyuvhPNIkiRJu5HEoi5AkiRJkiQVsvLl4aijQnvoIfj5Z0hNhbFj4ZBDYo9ZsAC++SY8fvPN0CIR6No1hG3JydCuncs8SpIkqURzxpkkSZIkSaVZJAL77ANXXw0ffghly8buN3Lkjq9Fo/D553DzzdC+PTRtChdeGM6zbl2Bli1JkiQVBIMzSZIkSZKUux9+yL3P/PnwzDNw7LFQqxYccwz8618wZ07B1ydJkiTlA4MzSZIkSZKUu4ceygzGjjsOKlXKuf+mTTB6NFx2Gey1FyxbVjh1SpIkSX+BwZkkSZIkScqbRo3g/PPhvfdgxYrMYGzPPXMe16kT1KkT+1g0mu9lSpIkSbvK4EySJEmSJO28ChWgd2949FH49dewlON990GPHlCmTPa+SUnxz3P99XDooXDXXfDddwZpkiRJKlIGZ5IkSZIk6a+JRKBNG7j2Whg3DpYvh+HD4fTTw15nOQVnH3wAn30G//gHHHAANGsGf/87pKTA+vWF9hEkSZIkgMSiLkCSJEmSJO1mqleHk08ObetWSIjzvd1ffoGff87+2rx58NRToVWoAIcfDsnJIXxr2rTAS5ckSVLpZnAmSZIkSZIKzvbLNmY1cmTOYzduDH3S++2/fwjQkpOha9eczy1JkiTtApdqlCRJkiRJRePCC2HUKLjkEmjePPf+338P99wD3bpB3brw+ecFXqIkSZJKF4MzSZIkSZJUNCpUgD594F//gtmzYfp0GDoUunfPfTbZqlXQunXh1ClJkqRSw+BMkiRJkiQVvUgE9t0Xrr8exo+HZcvg9ddh0CCoWXPH/oceCjVqxD7X2LFhFtvIkbBhQ8HWLUmSpN2KwZkkSZIkSSp+atSAv/0N/v1vWLoU/vtfuPFGaNcuHE9Kij/2jTfgiSdCn1q1oF8/eOopmDevcGqXJElSiZVY1AVIkiRJkiTlqEwZOOSQ0O66C37/HSpWjN03GoXU1MznGzZASkpoEIK3pCRIToaDDsp9SUhJkiSVKs44kyRJkiRJJUvTplCnTuxj330H8+fHH/vdd3D33WGpx3r14LTTYPhwWLmyYGqVJElSiWJwJkmSJEmSdh9164ZgrFs3SMjltseKFfDqq3DKKSGI69EDPvqocOqUJElSsWRwJkmSJEmSdh8NGsANN8DEiWFvtFdfhVNPDXum5WTrVpgwATZuLJw6JUmSVCwZnEmSJEmSpN1TrVohNHv11RCiTZwIgwfDfvvF7l++PBxxROxjf/4JzzwDCxYUWLmSJEkqegZnkiRJkiRp95eYGJZvvOce+P57mDsXHn8c+vaFChVCn169oHLl2OPHjIELL4TGjaFDB7j5Zpg8OcxUkyRJ0m4jsagLkCRJkiRJKnTNmsHFF4e2fj18+ilUqRK/f2pq5uNvvgntzjuhdu0QviUlwdFHQ/XqBVy4JEmSCpLBmSRJkiRJKt0qVYLk5PjHt26FkSNjH1u+HF5+ObT0WW1JSaG1bg2RSMHULEmSpALhUo2SJEmSJEk5WbUKjjoq99lkaWkwbhxcdx20bQstW8Lll8N//1sYVUqSJCkfOONMkiRJkiQpJzVrwuuvh2Dss8/Cso0pKfDDDzmPmz0bHnsszEQ79NDCqVWSJEl/iTPOJEmSJEmS8iIxEbp3h6FDYcaMzGCsd28oXz7+uKSk+Me+/x62bcv/WiVJkrRLDM4kSZIkSZJ2xZ57wqWXwujRsGIFvP8+XHABNGqU2adqVTjssNjjFy+Gdu2gQQM46ywYMSIsCylJkqQi41KNkiRJkiRJf1XlynDssaFFo/Dtt2FJx40boVy52GNGjQo/ly6Fl14KLTExBG3JyWGmWqtWEIkU3ueQJEkq5QzOJEmSJEmS8lMkAu3bh5aTlJQdX0tLg7FjQ7vmGmjZMgRoSUlhmcicloSUJEnSX+ZSjZIkSZIkSYUtGoX583PvN2sWPPIIHH001K4NAwbA88/DokUFX6MkSVIpZHAmSZIkSZJU2CIR+OKLEIw9+mgIxuIt6Zhu7Vp491047zzo27dw6pQkSSplDM4kSZIkSZKKSosWcNllMGYMrFiRGYw1aJDzuKSk+Me2bs3fGiVJkkoR9ziTJEmSJEkqDqpUgeOPDy0aha+/htTUsBfa1KnhtXQ5BWedO0OtWqFPcnLYJ02SJEl5YnAmSZIkSZJU3EQicOCBod1yCyxZAqNGhSBt2jTo0iX2uLlzQ+AG8MkncNVV0KpVZojWrVvuS0JKkiSVYgZnkiRJkiRJxV29enDWWaFFoyFYiyU1dcfXfv45tIcegqpVw35qyclwzDHhvJIkScpgcCZJkiRJklSSxAvNIMxKy8maNfD226FBWNYxOTnMSOvQARIS8q9OSZKkEsjfhiRJkiRJknYXr78eQrFzzoH69XPvP3UqDBkCnTpBs2awcWPB1yhJklSMOeNMkiRJkiRpd1G1KgwYENq2bWE/tNTU0KZOzXls06ZQoULh1ClJklRMOeNMkiRJkiRpd5SQEGaSDRkCU6bAokXwwgtwwglQpcqO/ZOS4p/rnnvg2mth3DjYsqXASpYkSSpqBmeSJEmSJEmlQf36cPbZMGIErFgBn3wCV14Je+8djscLzqJRePppeOAB6NUL6tSBgQPh5Zdh2bJCK1+SJKkwGJxJkiRJkiSVNuXKwRFHwEMPwc8/h9auXey+M2fC3LmZz1etgrfegjPPhHr1oGtXuOMO+PrrELJJkiSVYAZnkiRJkiRJpd3ee0MkEvtYSkr8cdEofPEF3HILHHggNGkCF1wA778P69YVTK2SJEkFyOBMkiRJkiRJ8SUlwa23QseOufddsACefRaOPx5q1YI+fWD27AIvUZIkKb8YnEmSJEmSJCm+ffeF22+HL7+EhQvhueegf3+oXDnncZs2waefhj3RJEmSSgiDM0mSJEmSJOVNgwZw7rnwzjuwYgV89BFcfjnstVfs/j16QNWqsY998QW88gosX15w9UqSJO0kgzNJkiRJkiTtvPLl4aij4JFHYNYsmDkT7r8fevWCxMTQJykp/vinn4YzzoC6deGQQ+DOO+Hbb8O+aZIkSUUksagLkCRJkiRJUgkXiUDr1qFdcw2sWhVmox18cOz+27ZBamp4HI3C55+HdvPN0Lgx9O0LyclwxBFQqVLhfQ5JklTqOeNMkiRJkiRJ+WuPPeCkk0IIFstXX8HSpbGPzZ8PzzwDxx4LNWuGEO3xx2Hu3AIrV5IkKZ3BmSRJkiRJkgpXQgIcdxxUrpxzv02bYNQouPRS2HNP2G8/GDwYfv65cOqUJEmljsGZJEmSJEmSClfHjvDee7B8OYweDZddFoKx3MyYAffeC3PmFHiJkiSpdDI4kyRJkiRJUtGoUAF694ZHH4Vff4UffoD77oMePaBMmdhjKlUKx2NZtQq++y7smyZJkrQLDM4kSZIkSZJU9CIRaNMGrr0Wxo0Ls9HeeANOPx1q187sd+SRIXCL5YMP4IADoFkz+PvfITUV1q8vlPIlSdLuIbGoC5AkSZIkSZJ2UL06DBwY2tatMGVKCMI6dYo/JjU1/Jw3D556KrQKFeCIIyApKbSmTQulfEmSVDIZnEmSJEmSJKl4K1MGDj44tHi2bAn7pW1v48YQqKWHavvvnxmide0Kid4ekyRJmVyqUZIkSZIkSSXf77+HWWq5+f57uOceOOwwqFcPBg2C116DP/4o8BIlSVLxZ3AmSZIkSZKkkq9FC5gzB6ZPzwzGypTJecwff4TQbNAguPfewqlTkiQVawZnkiRJkiRJ2j1EIrDvvjB4MEyYAEuXZgZjNWvmPDYpKf6xTZvyt05JklRsGZxJkiRJkiRp91SzJpxyCvz73yFEmzQJbrwx7HOWVY0a8fdPmzcvnOfYY+Hpp2H+/IKvW5IkFRl3P5UkSZIkSdLur0wZOPTQ0O66K+yJNnIkpKSEvc4S49wmGzkS1q+HDz8MDeCAA8IMteRk6NIl9yUhJUlSiWFwJkmSJEmSpNKnaVO46KLQcpKSsuNr334b2l13Qe3a0KdPCNF694bq1QukXEmSVDhcqlGSJEmSJEmKZcsWGDcu5z7Ll4elIP/2txCi9ewJ990HM2dCNFoYVUqSpHxkcCZJkiRJkiTFUrYszJ0bgrFTTgl7oeVk61YYPx6uvx7atoUTTiiUMiVJUv4xOJMkSZIkSZLiqVULBg2C116DpUthwoQQjO27b+5j27cv8PIkSVL+MjiTJEmSJEmS8iIxEQ47DIYOhenTYc4cePxxOOYYKF9+x/5JSfHP1b8/3HILTJ4cZqpJkqRiweBMkiRJkiRJ2hXNm8PFF8PIkbBiBXzwAVx4ITRqBA0aQIcOscf9/DO89x7ccQccfHDoe+aZ8NZbsGpVYX4CSZK0ncSiLkCSJEmSJEkq8SpXhn79QotGYeFCSIjznfWUlOzPly2Dl18OLTERunWD5OQwY22ffSASKfj6JUkS4IwzSZIkSZIkKX9FImHWWTypqfGPpaXBuHFw7bXQpg20bAlXXAEffQSbNuV7qZIkKTuDM0mSJEmSJKkw3X47XHcdtG2be9/Zs+HRR6F3b6hVCwYOhG3bCr5GSZJKKYMzSZIkSZIkqTB16wb33gszZoRg7LHHoE8fKF8+53Hr1oVlHeMtASlJkv4y/5aVJEmSJEmSisqee8Kll8KoUbBiBbz/Ppx/PjRsGLt/UlL8c730EowYAatXF0ytkiSVAolFXYAkSZIkSZIkoHJlOPbY0KJR+PZbSEkJe6J98UV4LTk59thoFG66CRYuhMRE6N49hGzJydCqVeF+DkmSSjBnnEmSJEmSJEnFTSQC7dvDzTfD55/DkiXwxhuwzz6x+3/zTQjNANLS4NNP4ZprQv+994Yrr4RPPoHNmwvpA0iSVDIZnEmSJEmSJEnFXZ06MHBgCNRiSU2NP3bWLHjkETjqKKhVCwYMgBdegMWLC6ZWSZJKMIMzSZIkSZIkqaRr0waOPhrKlcu539q18O67cO650KABdO4Mt90Gf/5ZGFVKklTsGZxJkiRJkiRJJd0JJ8CYMbBiRQjGzjsvBGO5+fJLGDo098BNkqRSIrGoC5AkSZIkSZKUT6pUgeOPDy0aha+/Dss4pqTA1Knhte0dfjhUqhT7fD/+CImJ0LJlQVYtSVKx4YwzSZIkSZIkaXcUicCBB8Itt8AXX4Q9zYYNgxNPhGrVMvslJ8c/xz//CXvvDfvsA1dfDZ9+Cps3F3ztkiQVEWecSZIkSZIkSaVB3bpw1lmhbd4MkyaF2WjxgrOtW2H06PD4559De+ghqFoVeveGpCQ45hioV6+wPoEkSQXO4EySJEmSJEkqbcqVC0s0Hn54/D6TJ8Mff+z4+po1MGJEaJEIdO4cQrSkJOjQARJc5EqSVHL5t5gkSZIkSZKkHS1eDPXr59wnGoUpU2DIEOjUCRo3hvPOg3ffhbVrC6dOSZLykcGZJEmSJEmSpB2dcAIsWABTp8Jtt4VgLDeLFsHzz8OAAWGcJEkljMGZJEmSJEmSpNgSEkJgNmRICMIWLswMxqpUiT+uWjXo1i32sY0bYcuWgqlXkqS/yOBMkiRJkiRJUt40aADnnANvvw3Ll8PHH8MVV0DLltn7HX00lC0b+xyvvgp16sDJJ8PLL8OyZQVftyRJeZRY1AVIkiRJkiRJKoHKl4cjjwzt4Yfh558hJQVSU+H44+OPS0mBVavgzTdDi0TgoIMgKQmSk+GAA8JrkiQVgUg0Go0WdRFSbubPn0+TJk0AmDdvHo0bNy7iivJo2TKoWzf7a0uXhm9VSZIkSZIklTabNkGtWrBuXfw+jRpB374hRDviCKhcufDqk6TSpgTfwy6o3MClGiVJkiRJkiQVjq++yjk0A1iwAJ59Fo47LoRsxxwD//oXzJlTODVKkko1gzNJkiRJkiRJheOQQzKDseOPz3022aZNMHo0XHYZ7LVXWBJSkqQCZHAmSZIkSZIkqfA0bAjnnQfvvgsrVsCYMXD55SEYy83BBxd8fZKkUs3gTJIkSZIkSVLRKF8ejj4aHnkEZs2CmTPhvvugZ09ITMzet04d6Nw59nlmzw6z2e66C779FqLRAi9dkrR7MjiTJEmSJEmSVPQiEWjdGq69FsaOhWXL4I034IwzoHZt6NsXEuLczkxJgc8/h3/8A9q3h6ZN4aKL4MMPYf36Qv0YkqSSLTH3LpIkSZIkSZJUyKpXh4EDQ9u6Fdasid83NTX78/nz4emnQ6tQAXr1gqQkSE6GZs0KtGxJUsnmjDNJkiRJkiRJxVuZMiFIi2XtWhg3Lv7YjRth1Ci49FJo3hz22w9uuAEmToS0tAIoVpJUkhmcSZIkSZIkSSq5ypeHDz4Iwdiee+bef8YMGDoUuneHunXhjjsKvkZJUolhcCZJkiRJkiSp5CpbFnr3hsceg19/DcHYvfdCjx5hplpOVq6ERHezkSRlMjiTJEmSJEmStHuIRKBtW7juurB847JlMHw4nH461K4de0xycuzXo9GwpGNqKmzYUGAlS5KKF4MzSZIkSZIkSbunGjXg5JPh5Zdh8WL47DP4xz/ggAPC8aZNYd99Y4+dPj0s6ZicDLVqhZ9PPQXz5hVe/ZKkQuc8ZEmSJEmSJEm7vzJl4OCDQ7vjjhCAzZ0bZqnFkpqa+XjDhvA8/bX99w9BWlISdO2a+5KQkqQSw+BMkiRJkiRJUunTpElo8WQNzrb3/feh3X13mI3Wp08I0Xr3hpo1879WSVKhcalGSZIkSZIkSdre8cfDYYdBQi63UFesgFdfhVNPhbp1oXt3ePjhwqhQklQADM4kSZIkSZIkaXvXXAMTJsCyZfDaazBoUO6zybZuhYkTYdSowqlRkpTvDM4kSZIkSZIkKZ6aNeGUU+Df/4YlS2DSJLjhhrDPWTzJyfGPjR0L8+fnf52SpHxhcCZJkiRJkiRJeZGYCIceGvY2++47+O03eOKJsL9ZhQqZ/ZKSYo/ftg1OPjnsrda+PfzjH/D552GmmiSpWEgs6gIkSZIkSZIkqURq2hT+/vfQ1q8Ps8mmTIG99ordf+rUsPQjwLffhnbXXVC7NhxzTAjceveG6tUL7SNIkrJzxlkBWLt2LRMmTOD+++9n4MCB7LnnnkQiESKRCM2bN9/p882YMYOLLrqIli1bUrFiRerUqUP37t15+umnSUtLy/N5hg8fTu/evWnQoAEVKlSgefPmnH766UyePDnP51ixYgVDhgzhgAMOYI899qBatWoccMABDBkyhBUrVuz0Z5MkSZIkSZJ2C5UqheDr9tvj90lNjf368uXwyivwt7+FEK1nT7jvPpg5E6LRAilXkhRbJBr1ypvfevXqxbhx42Iea9asGXPnzs3zuZ5//nkuueQSNm3aFPN4165dSUlJoVatWnHPsXHjRk466SRSUlJiHk9ISOC2227jlltuybGWqVOnctxxx7Fo0aKYxxs2bMj7779Pp06dcjzPrpg/fz5NmjQBYN68eTRu3Djf36NALFsGdetmf23pUqhTp2jqkSRJkiRJUtG59Vb4179g5cq8j9lzz7BnWlISHHFEWC5SkvJLCb6HXVC5gTPOCkDWLLJGjRocddRRVKlSZafPM2bMGC644AI2bdpEvXr1ePTRR/niiy8YNWoUAwYMAGDy5MkMGDCAbdu2xT3PueeemxGa9erVi/fee48pU6bw/PPP06JFC7Zt28att97Kc889F/ccCxYsoF+/fixatIjExESuv/56JkyYwIQJE7j++utJTExk4cKFJCcns2DBgp3+rJIkSZIkSdJu7//+L9yQnjABBg+GfffNfcycOfDYY3DCCe6FJkmFwBlnBeCZZ56hSpUqdOnShZYtWwLQvHlzfvvttzzPOEtLS6NNmzbMmjWLatWqMW3aNFq0aJGtzyWXXMITTzwBwEsvvcQZZ5yxw3nGjx9Pz549AejXrx/vvvsuZcqUyTi+fPlyOnbsyO+//06NGjWYPXs21WOsoXzWWWfx0ksvAfDmm29y0kknZTv+1ltvMXDgQADOPvtsXnjhhVw/485wxpkkSZIkSZJ2S3PnwsiRkJICn34KcVaeon9/eOed2Mf++AP22AOy3PeTpDwpwfewnXFWglxwwQWceuqpGaHZrnj33XeZNWsWADfeeOMOoRnAfffdR40aNTIex3LvvfcCUKZMGZ544olsoRlA7dq1GTp0KAArV67k+eef3+EcS5Ys4d///jcAvXv33iE0AzjppJPo3bs3AC+//DJLlizJ0+eUJEmSJEmSSrXmzeHii0N4tmIFfPABXHghNGqUvV9SUvxzXHghNGgAZ54Jb74Jq1YVaMmStDszOCum3nvvvYzHZ511Vsw+lSpVypjlNX36dH755Zdsx9euXct//vMfAI466qi4aeuAAQOoVq0aAO/E+NbKBx98wNb/TQM/++yz49acXufWrVv54IMP4vaTJEmSJEmSFEPlytCvHzz1FMybB998A3fcAQcfDH37xh6zZQt89FGYNfLyy3DyyVC7NvTqBQ88AD/+CC46Jkl5ZnBWTE2cOBGAffbZh/r168ft16NHj4zHkyZNynZsypQpbPrf1O6s/bZXrlw5unbtmjFmy5YtMWvJ7Tw51SJJkiRJkiRpJ0QicMAB8I9/wGefhRllsUyaBKtXZ38tLQ3GjYNrr4U2bWDvveGKK+Djj+MvBSlJAiCxqAvQjtauXcv8+fMBaN26dY59sx6fOXNmtmNZn+flPB999BFpaWn88ssvtG3bdofz7LHHHjmGeA0aNKBatWqsXr16h1pyk/5541m0aNFOnU+SJEmSJEkqFSZPzr3Pr7/Co4+GVrkyHH10WPqxb9/4gZwklVIGZ8XQ/Pnzif5v+nRum9mlb3wHYfO7rLI+39nzZA3O0s+Tl431mjRpwowZM3aoJS/jJEmSJEmSJO2kG28MyzOmpoY2dixs3hy//7p18O67oQFMmwYdOhROrZJUArhUYzG0Zs2ajMdVqlTJsW/lypUzHq9du7ZAz5PbObKeZ/tzSJIkSZIkSSoge+0Fl10Go0fDihXw3ntw/vnQsGHO42rWhHbtCqVESSopnHFWDG3cuDHjcbly5XLsW758+YzHGzZsKNDz5HaOrOfZ/hy5yW2G2qJFi+jSpctOnVOSJEmSJEkqdapUgeOOCy0ahW++yZyN9sUX4bV0xxwDZcrEPs9zz8Hw4WFJx+TksE+aJJUCpTY4S0tLo2zZsn/5PMOGDeOss8766wVlUaFChYzHm3OaVg1syrKZZ8WKFQvsPOvXr8/1HFnPs/05cpOXZSAlSZIkSZIk7YRIJCzD2KED3HwzLF0aZqWlpMCYMSEUi+fdd+E//wnt6qtDcJYeoh12GOThS/aSVBK5VGMxVLVq1YzHuS15uG7duozH2y+lmN/nycvyi+nnycuyjpIkSZIkSZIKUd26cMYZ8OabsHw5nHBC7H7r18Onn2Z/7Zdf4OGH4cgjoXbtMHbYMFiypMDLlqTCVGpnnCUmJjJz5sy/fJ4GDRrkQzXZZZ19NX/+/Bz7Zl3isEmTJjmep1OnTrt8niVLluRaS9bzbH8OSZIkSZIkScVITqtxffopZNkGZgdr1sA774QG0LlzmI2WlAQHHggJzteQVHKV2uAMoHXr1kVdQkxVqlShSZMmzJs3jx9//DHHvlmPt2nTJtuxtm3bxuyX03kSExNp2bLlDuf56quvWLVqFYsXL6Z+/foxz7Fo0SJWr14dsxZJkiRJkiRJJUTPnmGpxpSUsDfa4sU59586NbTbboP69eGZZ6Bfv8KoVJLyndF/MdWtWzcAfvrpJxbn8BfT+PHjMx4feuih2Y517tyZcv9bazhrv+1t3ryZyZMn7zBm+1pyO09OtUiSJEmSJEkqIapUgeOPh+eegwUL4Msv4fbbw8yy3CxeDFlWwpKkksbgrJg6/vjjMx6/+OKLMfusX7+eN998Ewizwlq1apXteNWqVTniiCMA+OSTT+IutfjOO+9kzBTr37//DsePPfZYEv43vXrYsGFxa06vMyEhgWOPPTZuP0mSJEmSJEklREICdOwIt94KU6aEYGzYsLDHWdWqO/Zv2BDat499rl9+gWuuCUtBbt5coGVL0q4yOCum+vfvT4sWLQC4++67+fXXX3foc91117Fy5cqMx7Fce+21AKSlpXHJJZewdevWbMeXL1/O4MGDAahevTrnnXfeDueoX78+gwYNAmDMmDGMGDFihz5vvfUWY8aMAeD000+Pu5yjJEmSJEmSpBKsXj046ywYMQKWL4f//AeuugrSv9SflASRSOyx778PDz4IRxwBderASSfBiy/C0qWFVb0k5SoSjUajRV3E7mbWrFlMmjQp22vXXnstK1asoFatWtx///3ZjvXp0ydm0DRy5Ej69evHtm3bqFevHjfffDNdunRh5cqVPPvss7z99ttAWEpx3LhxlClTJmY9p5xyCsOHDwegV69eXHnllTRs2JDvv/+eO++8MyOUe+qpp7jwwgtjnmPevHl07NiRZcuWkZiYyDXXXENycjIAKSkpPPDAA6SlpVGnTh2mTZtG43yejj1//nyaNGmSUUt+n7/ALFsGdetmf23p0vCLgSRJkiRJkrQ7+eWXEJq1bBn7eK9eMG7cjq9HImEZyOTkELx16BA/fJOUv0rwPeyCyg0MzgrAiy++yNlnn53n/mPHjqVnz54xjz377LNceumlbI4zdblLly6kpqZSu3btuOffsGEDJ554IiNHjox5PCEhgVtuuYXbbrstxzq/+OILjj/++Lh7rtWvX5/33nuPgw46KMfz7AqDM0mSJEmSJKkE+/NPqF0btlsRK6YGDUKAlpQERx4Z9lyTVDBK8D3sgsoNXKqxmDv//PP56quvOP/889lrr72oUKECtWrVolu3bjz55JP897//zTE0A6hYsSKpqam8+uqrHHXUUdStW5dy5crRpEkTTj31VCZNmpRraAZw0EEH8f3333PzzTez3377UaVKFapUqcL+++/PzTffzPTp0wskNJMkSZIkSZJUwm3dCjffDJ065d530SJ47jno3x9q1YLeveG99wq8REkCZ5yphHDGmSRJkiRJkrSbWLQIRo2C1FT46CNYuzb3MQ88AFdfXfC1SaVNCb6H7YwzSZIkSZIkSVLJ16ABnHMOvP02LF8OH38MV1wRf280CPufxbJtG7z2Wrj5L0n5wOBMkiRJkiRJklQ0ypcP+5g9/DD88gv89FOYXXb44ZCYGPq0bAmtWsUe//XXMGgQ1KsHBx8Md9wRXnOhNUm7KLGoC5AkSZIkSZIkCQgB2dVXh7ZqVZiNtmVL/P6pqeFnNAqTJ4d2yy3QqBH07Rtmqh1xBFSuXDj1SyrxDM4kSZIkSZIkScXPHnvAiSfm3CclJfbrCxbAs8+GVr489OoFSUmh7bln/tcqabfhUo2SJEmSJEmSpJInLQ2aNMl9NtmmTTB6NFx2Gey1F+y7L1x/Pfz3v4VTp6QSxRlnkiRJkiRJkqSSJzER3n47BGPjx4dlG1NSYPbsnMf98ENoP/4IH3xQOLVKKjGccSZJkiRJkiRJKrnKl4ejj4ZHHoFZs2DmTLj/fujZM4Rr8SQlxT82b17YN01SqWNwJkmSJEmSJEnaPUQi0Lo1XHMNjB0Ly5bBG2/AGWdA7drZ+/btG/scaWnQrh00bQoXXRRmsa1fX/C1SyoWXKpRkiRJkiRJkrR7ql4dBg4MbetWmDo1LOk4a1bYHy2Wzz+HP/8M7emnQ6tQAXr1guTkMFOtWbNC/BCSCpPBmSRJkiRJkiRp91emDHTtGlpOUlJ2fG3jRhg1KrRLLoF9980M0Q4+OOclISWVKC7VKEmSJEmSJElSuu++y73PjBkwdCh07w5168Kpp8Krr8KKFQVfn6QCZXAmSZIkSZIkSVK6kSNh+vTMYKxMmZz7r1wJr78Op50G++wTloSUVGIZnEmSJEmSJEmSlC4SCUsxXn89jB8Py5ZlBmM1a+Y89sgj4wdt0Wj+1yop37nwqiRJkiRJkiRJ8dSoAX/7W2hbt8IXX4R90FJTd1zWMSkp/nlOPRXWrg19kpKgSZOCrVvSLjE4kyRJkiRJkiQpL8qUgUMOCe2uu+D338PSjqmpMHYs9OkTe9zGjfDBB7B+fQjdANq1ywzRunbNfUlISYXCpRolSZIkSZIkSdoVTZvCRRfBhx/CH39AnTqx+40fH0KzrL77Du6+G7p1g3r1wlKQw4eHPdMkFRmDM0mSJEmSJEmS/qpy5eIfS59lFs+KFfDqq3DKKSF8694d7r0XZsxwbzSpkBmcSZIkSZIkSZJUkG6/PQRjp54a9kzLydatMHEiDB4M++0He+0F8+cXTp2SDM4kSZIkSZIkSSpQNWuG0OzVV2Hp0hCM3XBDCMZys2EDNGxY8DVKAgzOJEmSJEmSJEkqPImJYV+zu++G77+HuXPh8cehb1+oUGHH/n37QkKcW/nDh8PNN8Pnn4eZapL+MoMzSZIkSZIkSZKKSrNmcPHFkJoa9jr78EO46CJo0iQcT0qKP/b55+HOO+GQQ6B+fTjjDHjjDfjzz0IpXdodJRZ1AZIkSZIkSZIkCahUCZKTQ4tGw4y0Fi1i912zBsaPz3y+fDm88kpoZcqEWW1JSeFcrVtDJFI4n0Eq4ZxxJkmSJEmSJElScROJQLt2ULly7OMffwxbtsQ+tnVrCNWuvx7atg3h2+WXw5gxsHFjwdUs7QYMziRJkiRJkiRJKmnatAnB2L775t53zhx47DHo0wdq1YLjj4dvvy3wEqWSyOBMkiRJkiRJkqSSpk0bGDoUpk8Pwdi//gXHHAPly+c8bv16eP99KFu2cOqUShiDM0mSJEmSJEmSSrLmzeGSS2DkSFixAj74AC68EBo3jt+/TZvYx+bMgbfeglWrCqpaqVgzOJMkSZIkSZIkaXdRuTL06wdPPQW//w7ffAN33gkHHxz2TQNISsp8vL3XX4eBA6F2bTj8cHjgAfjpJ4hGC+0jSEUpsagLkCRJkiRJkiRJBSASgQMOCO2mm2DZMhg9GvbbL/6YlJTwMy0Nxo4N7dproUULSE4OoVv37rkvCSmVUM44kyRJkiRJkiSpNKhTB04/HTp0iH18+XKYPDn2sV9/hUcegaOPDrPRBgyA55+HRYsKrl6pCBicSZIkSZIkSZKksD/aUUdBuXI591u7Ft59F847Dxo2hE6dYMgQmDmzcOqUCpBLNUqSJEmSJEmSJNhnHxgzJgRj//kPpKaGtnBhzuO++iq0unWhTZvCqVUqIM44kyRJkiRJkiRJmapUgeOOg2eegfnzYdo0+Oc/4aCDwr5p8SQlxX5961b4+eeCqVXKZwZnkiRJkiRJkiQptkgk7Il2881h/7PFi+HFF+Gkk6Batcx+bdtC8+axzzFlSpjN1qoVXHVVmM22eXNhVC/tNJdqlCRJkiRJkiRJeVO3Lpx5ZmhbtsCkSWE5x8aN449JSQk/f/kFHn44tKpVw35qycnQty/Uq1cY1Uu5MjiTJEmSJEmSJEk7r2xZ6NUrtJykpu742po18M47oQF07hyWekxODjPcElwwT0XD//IkSZIkSZIkSVLBWLMGli7Nvd/UqXDbbdCpEzRqBOeeG0K1NWsKvEQpK4MzSZIkSZIkSZJUMKpWhfnz4csvQzDWuXPuYxYvhhdegBNOCAGaVIgMziRJkiRJkiRJUsFJSICOHWHIEJgyBRYtygzGqlbNeewxx8Q/tm1b/tYpYXAmSZIkSZIkSZIKU/36cPbZMGIELF8On3wCV10Fe++9Y994wdnmzdCsGQwcCC+9lLflIKU8SCzqAiRJkiRJkiRJUilVrhwccURoDz4IP/8MqamhbdwYQrZYJk4MS0C+9VZokUhYBjI5GZKSoEOH8Jq0kwzOJEmSJEmSJElS8dCqVWhXXQVbt8bvl5KS/Xk0GpaBnDIFbr0VGjaEvn1DkHbEEVClSsHWrd2GSzVKkiRJkiRJkqTip0yZ+MdGjsx57MKF8NxzcPzxUKsW9OkDjz0Gs2fna4na/RicSZIkSZIkSZKkkmXcOHj+eejfP/fZZJs3w5gxcPnl0KIF9OhRKCWqZDI4kyRJkiRJkiRJJUuDBnDOOfDOO7B8OXz8MVxxBbRsmfvYZs0Kvj6VWAZnkiRJkiRJkiSp5CpfHo48Eh5+GH75BX76CR54AA4/HBITd+yflBT/XNddB3feCd98E/ZNU6ljcCZJkiRJkiRJknYfrVrB1VfDf/4TZqO99RaceSbUqRP2TevdO/a4devCPmg33wwdOkDTpnDhhfDBB+GYSgWDM0mSJEmSJEmStHvaYw848UR48UVYvBi++w6qV4/d9z//gU2bMp/Pnw/PPAPHHQe1asExx8Djj8PcuYVQuIqKwZkkSZIkSZIkSdr9JSRA27bxj6emxj+2aROMHg2XXgp77gn77guDB8OECZCWlv+1qsgYnEmSJEmSJEmSJJ12Glx2Gey1V+59f/gB7r0XevQIS0CecgqsWVPwNarAGZxJkiRJkiRJkiQddhg8+ijMmgUzZ8J990HPnmFftJz8+SdMmgRVqhRGlSpgBmeSJEmSJEmSJEnpIhFo3RquvRbGjoXly+GNN+D006F27dhjkpLCuFg+/hhSUmD9+oKrWfnG4EySJEmSJEmSJCme6tVh4EB4+WVYvBg+/xz+8Q9o3z6zT3Jy/PF33AH9+kGtWiFge+IJ+O23gq5au8jgTJIkSZIkSZIkKS/KlIGuXUMY9vXXMG8ePP00HH547P4rV8J//xseb9wII0fCJZdA8+aw//5w441hmce0tEL7CMqZwZkkSZIkSZIkSdKuaNwYLrgAKlWKfXzMGNi6Nfax6dPhnnvC3mp168KgQfDaa/DHHwVXr3JlcCZJkiRJkiRJklQQqlaF7t3DTLWcrFwZQrNBg6BOnRCm3XMPLFlSOHUqg8GZJEmSJEmSJElSQUhKgvHjYdkyeP11OO00qFkz5zHbtoXlG2+8EdasKZw6lcHgTJIkSZIkSZIkqSDVqAF/+xu88gosXRr2PbvxRmjXLv6YVq2gZcvYxxYvDvurKd8ZnEmSJEmSJEmSJBWWMmXgkEPgrrvg22/ht9/gySchORkqVszsl5wc/xxPPQVNm8IBB8BNN4UgLt5eatopiUVdgCRJkiRJkiRJUqnVtClcdFFoGzbA2LGQmgonnhh/TEpK+Pndd6HdfTfUqgV9+oTlIfv0CbPctNMMziRJkiRJkiRJkoqDihWhb9/Q4lm0CL76asfXV6yAV18NLX1WW3JyCNLatoVIpODq3o24VKMkSZIkSZIkSVJJ8dNPuc8m27oVJk6EwYNhv/1gzz3h0kth1CjYuLFw6iyhDM4kSZIkSZIkSZJKip49YenSEIzdcEMIxnLz22/w+ONhJtsrrxR4iSWZwZkkSZIkSZIkSVJJkpgI3bqFvc2+/x7mzoUnngjBWIUKOY/NaRlIGZxJkiRJkiRJkiSVaM2awd//DqmpYa+zDz+Eiy6Cxo2z92vfHho1yvlcl14Kb74Jf/5ZUNUWawZnkiRJkiRJkiRJu4tKlSA5GZ58En7/Hb79Fu68Ew45BI49Nvfxb74JJ58MdepAr15w//0wcyZEowVfezGQWNQFSJIkSZIkSZIkqQBEItCuXWg33bRz4VdaGowbF9p118Fee0FSUmg9euS+JGQJ5YwzSZIkSZIkSZKk0iAS2fWxs2fDY49Bnz5QuzYcfzw8+ywsXJhv5RUHBmeSJEmSJEmSJEkKDj8cypfPuc+6dfD++3DBBWHPtBtvLJzaCoHBmSRJkiRJkiRJkoLhw2HFiuzBWG7226/g6yokBmeSJEmSJEmSJEnKVLkyHHssPP00zJsHX38Nd9wBXbvuuNxjQkJYvjGWDRvCsQcfhJ9+2rk91oqIwZkkSZIkSZIkSZJii0SgfXv4xz/g889hyRJ4+WUYOBD22AMOPhhq1Yo9duxYGDMGrrkGWreGVq3gyivh449h06bC/BR5lljUBUiSJEmSJEmSJKmEqFMHTj89tC1bQpAWT2pq9uezZsEjj4RWpQocdRQkJ0PfvlC/fsHWnUcGZ5IkSZIkSZIkSdp5ZctC48axj0WjOwZnWa1dC+++GxpAp06QlBRax45hCcgi4FKNkiRJkiRJkiRJyl/RaJhZdt550KBB7v2//BJuvx26dIGGDeGGGwq+xhiccSZJkiRJkiRJkqT8lZAAxx0XWjQKX38dZqClpsKUKeG1eJYsgeXLC6/WLAzOJEmSJEmSJEmSVHAiETjwwNBuuQWWLoVRoyAlBcaMgTVrdhyTnBz/fI8/DrVqFUipBmeSJEmSJEmSJEkqPHXrwplnhrZ5M/z3vyFES02Fn36CcuXgyCNjj121Cq68EtLSCqQ0gzNJkiRJkiRJkiQVjXLloFev0B54AGbNgm+/hSpVYvf/+OMCC83A4EySJEmSJEmSJEnFRcuWocWTmlqgb59QoGeXJEmSJEmSJEmS8kuHDtC5c4Gd3uBMkiRJkiRJkiRJJcPll8OUKTBtWoGc3uBMkiRJkiRJkiRJJUudOgVyWoMzSZIkSZIkSZIkCYMzSZIkSZIkSZIkCTA4kyRJkiRJkiRJkgCDM0mSJEmSJEmSJAkwOJMkSZIkSZIkSZIAgzNJkiRJkiRJkiQJMDiTJEmSJEmSJEmSAIMzSZIkSZIkSZIkCTA4kyRJkiRJkiRJkgCDM0mSJEmSJEmSJAkwOJMkSZIkSZIkSZIAgzNJkiRJkiRJkiQJMDiTJEmSJEmSJEmSAIMzSZIkSZIkSZIkCTA4kyRJkiRJkiRJkgCDM0mSJEmSJEmSJAkwOJMkSZIkSZIkSZIAgzNJkiRJkiRJkiQJMDiTJEmSJEmSJEmSAIMzSZIkSZIkSZIkCTA4kyRJkiRJkiRJkgCDM0mSJEmSJEmSJAkwOJMkSZIkSZIkSZIAgzNJkiRJkiRJkiQJMDiTJEmSJEmSJEmSAIMzSZIkSZIkSZIkCTA4kyRJkiRJkiRJkgCDM0mSJEmSJEmSJAkwOJMkSZIkSZIkSZIASCzqAqS8SEtLy3i8aNGiIqxkJ61YseNrCxfCpk2FX4skSZIkSZIkSVmV4HvYWbOCrBnCX2VwphJh2bJlGY+7dOlShJXkg/bti7oCSZIkSZIkSZJiK4H3sJctW0bz5s3z5Vwu1ShJkiRJkiRJkiQBkWg0Gi3qIqTcbNy4ke+//x6AOnXqkJjoZEkVjEWLFmXMapwyZQoNGjQo4ook6a/xuiZpd+N1TdLuxuuapN2N1zUVlrS0tIzV6vbff38qVKiQL+c1fVCJUKFCBTp37lzUZaiUadCgAY0bNy7qMiQp33hdk7S78bomaXfjdU3S7sbrmgpafi3PmJVLNUqSJEmSJEmSJEkYnEmSJEmSJEmSJEmAwZkkSZIkSZIkSZIEGJxJkiRJkiRJkiRJgMGZJEmSJEmSJEmSBBicSZIkSZIkSZIkSYDBmSRJkiRJkiRJkgRAJBqNRou6CEmSJEmSJEmSJKmoOeNMkiRJkiRJkiRJwuBMkiRJkiRJkiRJAgzOJEmSJEmSJEmSJMDgTJIkSZIkSZIkSQIMziRJkiRJkiRJkiTA4EySJEmSJEmSJEkCDM4kSZIkSZIkSZIkwOBMkiRJkiRJkiRJAgzOJEmSJEmSJEmSJMDgTJIkSZIkSZIkSQIMziQpV6NGjSISiWS02267LU/jZsyYwUUXXUTLli2pWLEiderUoXv37jz99NOkpaUVbNGSBPz+++88+eSTnHzyyeyzzz5UrlyZChUq0LhxY4477jhef/31nboeeV2TVNR+//13rr32Wtq0aUPlypWpWbMmXbp04f7772f9+vVFXZ4kATBt2jTuuusujjnmGJo0aUL58uWpUqUKrVq14qyzzmLixIk7db7Ro0czYMAAGjduTPny5WncuDEDBgxg9OjRBfQJJClvrr/++mz3zMaNG5frGK9pKgki0Wg0WtRFSFJxtW7dOvbdd19+++23jNeGDBmSa3j2/PPPc8kll7Bp06aYx7t27UpKSgq1atXKz3IlKcOtt97KHXfcQW6/6nXq1Im3336bpk2b5tjP65qkopaamsqgQYNYtWpVzOP77LMPI0eOZK+99irkyiQpU48ePZgwYUKu/U4//XSee+45ypUrF7dPNBrloosu4plnnonb54ILLuCpp54iEonsUr2StKu+/fZbOnXqlO1LlGPHjqVnz54x+3tNU0nijDNJysEtt9zCb7/9Rt26dfM8ZsyYMVxwwQVs2rSJevXq8eijj/LFF18watQoBgwYAMDkyZMZMGAA27ZtK6jSJZVyCxcuJBqNUrlyZU477TSGDRvGpEmT+PLLL3nllVfo3LkzAF9++SVHHnkka9eujXsur2uSitq3337LwIEDWbVqFVWqVOHOO+/ks88+4z//+Q/nn38+AD/99BNJSUk5Xs8kqaAtWLAAgIYNG3LFFVcwYsQIpkyZwueff86DDz5Io0aNAHjllVc466yzcjzXzTffnHGDuUOHDrz++utMmTKF119/nQ4dOgDwzDPPcMsttxTcB5KkGLZt28b5559PWlpanu+ZeU1TiRKVJMX01VdfRcuUKRMtX7589JlnnokCUSA6ZMiQuGO2bNkSbdmyZRSIVqtWLTpr1qwd+lx88cUZ53rppZcK8BNIKs2uv/766NChQ6OrV6+OeTwtLS06cODAjOvR//3f/8Xs53VNUnHQs2fPKBBNTEyMfvbZZzscv/feezOuQ7fffnsRVChJQVJSUvSNN96IpqWlxTy+bNmyaKtWrTKuWRMmTIjZ75dffokmJiZGgWinTp2i69evz3Z83bp10U6dOmVcG2P9jiZJBeWhhx6KAtHWrVtHb7zxxoxr2tixY2P295qmksYZZ5IUw9atWzn//PPZunUrN910E3vvvXeexr377rvMmjULgBtvvJEWLVrs0Oe+++6jRo0aGY8lqSAMHTqU66+/nqpVq8Y8XqZMGZ544omM5YFGjBgRs5/XNUlFberUqRn7ZZx77rkcfPDBO/S55ppraNOmDQAPP/wwW7ZsKcwSJSlDSkoKAwcOpEyZMjGP165dmwceeCDjebzfwR566KGM5c8ee+wxKlasmO14pUqVeOyxxwBIS0vj4YcfzofqJSl38+bNy5gV9uSTT+a45Gw6r2kqaQzOJCmGhx56iGnTptGqVSsGDx6c53HvvfdexuN4y25UqlSJgQMHAjB9+nR++eWXv1KqJO2yWrVq0a5dOwB+/fXXmH28rkkqalmvQ2effXbMPgkJCZxxxhkArFy5Mk8b00tSUcm6/0+s38Gi0Sjvv/8+AK1bt6Zr164xz9O1a1f22WcfIFwro7nsbStJ+eHiiy9m7dq1nHnmmXH3M8vKa5pKIoMzSdrO3LlzGTJkCABPPPEE5cuXz/PYiRMnAmFz+vr168ft16NHj4zHkyZN2sVKJemv27RpExBuOsfidU1SUUu/DlWuXJmOHTvG7ed1SFJJsXnz5ozHsX4HmzNnTsZeaVmvbbGkH58/fz5z587NvyIlKYY333yTlJQUatasmefVRrymqSQyOJOk7fz9739n/fr1DBo0iCOOOCLP49auXcv8+fOB8A2anGQ9PnPmzF0rVJL+oqVLl2Zcg2Jdt7yuSSoO0q8pLVu2JDExMW4/r0OSSorx48dnPI71O1bWa5i/g0kqLv7880+uuOIKIGwNUKdOnTyN85qmksjgTJKyeO211xg9ejTVq1fPtu58XsyfPz9jGnnjxo1z7NukSZOMx/Pmzdv5QiUpH9x3330Z68ynL7WYldc1SUVt48aNLF++HMj9OlSjRg0qV64MeB2SVHxt27aNe+65J+N5rN/Bsl7D/B1MUnFx/fXXs3jxYg455BDOPffcPI/zmqaSyOBMkv7njz/+4KqrrgLg7rvvpl69ejs1fs2aNRmPq1SpkmPf9Js6EGZ0SFJh++KLLzI2XG7cuDEXX3zxDn28rkkqajtzHYLMa5HXIUnF1UMPPcSUKVMA6N+/P506ddqhj7+DSSpuJk2axHPPPUdiYiJPPfUUkUgkz2O9pqkkMjiTpP+59tprWbp0KQcddBAXXHDBTo/fuHFjxuNy5crl2DfrvmkbNmzY6feSpL9iyZIlnHjiiaSlpRGJRHjppZeoVKnSDv28rkkqajtzHYLMa5HXIUnF0fjx47nhhhsAqFu3Lk8++WTMfv4OJqk42bx5MxdccAHRaJSrrrqK/ffff6fGe01TSWRwJqlESb/J+1fbiy++mO2848aNY9iwYZQpU4annnoq5gbNualQoULG46ybPceyadOmjMcVK1bc6feStPsoqOtaPGvWrCEpKSlj77K77rqLww8/PGZfr2uSitrOXIcg81rkdUhScTNjxgz69+9PWloa5cuX580334y7yom/g0kqTu666y5mzpxJ06ZNGTJkyE6P95qmksjgTFKpt2nTJi688EIALr/8ctq3b79L56latWrG49ymk69bty7jcV6WHZKk/LBx40aOO+44vvrqKwCuvvrqjG89x+J1TVJR25nrEGRei7wOSSpO5syZw9FHH83KlSspU6YMr7/+Oj169Ijb39/BJBUXP/74I3fffTcAjz32WLalFPPKa5pKosSiLkCSdkZiYiIzZ878y+dp0KBBxuN33nmHn3/+mcTERNq2bcvw4cN36P/DDz9kPJ4+fXpGn4MOOog999wTyL7BafpMjniybnCadeNTSaVPQVzXYklLS2PgwIGMHTsWgPPOO48HHnggxzFe1yQVtQoVKlC7dm2WL1+e63Vo5cqVGTdbvA5JKi4WLlzIkUceycKFC4lEIrzwwgv0798/xzH+DiapuHjooYfYvHkze+21F+vXr495z2z69OkZjz/99FMWL14MQL9+/ahcubLXNJVIBmeSSpzWrVvn6/nSp4GnpaVx/vnn59r/7bff5u233wZg2LBhGcFZlSpVaNKkCfPmzePHH3/M8RxZj7dp02ZXS5e0m8jv69r2tm3bxumnn86HH34IwMknn8zTTz+d6ziva5KKgzZt2jBx4kRmzZpFWloaiYmx/xnrdUhScbN8+XKOOuooZs+eDYTZGmeccUau49q2bZvx2N/BJBWl9Htms2fP5pRTTsm1/z//+c+Mx3PmzKFy5cpe01QiuVSjJOWjbt26AfDTTz9lfMMmlvHjx2c8PvTQQwu8Lkml24UXXpjxzcDk5GReeeWVPO/l6HVNUlFLvw6tW7cuY6nZWLwOSSpOVq1aRe/evTNWL7nnnnu45JJL8jR2zz33pGHDhkD2a1ssEyZMAKBRo0Y0b9581wuWpALiNU0lkcGZpFLvrLPOIhqN5tjSlzYDGDJkSMbrZ511VrZzHX/88RmPX3zxxZjvt379et58800gfJOwVatW+f2RJCnD1VdfzXPPPQfAEUccwYgRIyhbtmyex3tdk1TUsl6Hhg0bFrPPtm3bePnllwGoXr06vXr1KozSJCmm9evXk5SUxLRp0wD4xz/+weDBg/M8PhKJcNxxxwFh9sXkyZNj9ps8eXLG7IzjjjuOSCTyFyuXpOxefPHFXO+ZDRkyJKP/2LFjM15PD768pqkkMjiTpHzUv39/WrRoAcDdd9/Nr7/+ukOf6667jpUrV2Y8lqSCctttt/HQQw8BcMghh/D+++9Tvnz5nTqH1zVJRa1Lly4cdthhADz//PN8/vnnO/R54IEHMvaLvOKKK3bqCwKSlJ82b95M//79+e9//wuEa9Idd9yx0+e58sorM5amveyyy9iwYUO24xs2bOCyyy4Dwp65V1555V8rXJIKkNc0lTTucSZJ+ahs2bI8+uij9OvXj9WrV3PooYdy880306VLF1auXMmzzz6bsT9at27dOP3004u4Ykm7q8cee4zbb78dCMtc3HvvvcyZMyfHMfvss88ON5u9rkkqDh555BEOPfRQNmzYwNFHH81NN91Er1692LBhA8OHD+eZZ54BoFWrVlxzzTVFXK2k0uyUU07ho48+AuDwww/n3HPPZfr06XH7lytXLuZs/VatWnHttddyzz338OWXX3LooYcyePBgWrRowa+//srQoUP5+uuvgfDFpb333rtgPpAk5QOvaSppItFoNFrURUhScTdu3LiMJX+GDBnCbbfdlmP/Z599lksvvZTNmzfHPN6lSxdSU1OpXbt2fpcqSQD07Nkz1/Xjtzdnzpy468h7XZNU1D788ENOO+3/27t/kKr/PY7jr5MllihCTS6GmFtQpFHkIC25hGthVlBSi0NbNoS0RUuDJEj/yEIIghqUwKHEIgjKUGiKiIhoqUgSSeqc3+bl8uv3417u/Xk88nhs3/P9HHgPh+/wfX6/n3Mk8/Pzvz3f2tqa8fHxtLS0rPBkAP/y324t1tTUlHfv3v32XLFYTF9fX65fv/6X3z9x4kRGRkb+4/+vBfh/GxwcXH5o89GjR+ns7PztOtc0KolfIMA/oK+vLy9evEhfX1+am5tTU1OTzZs3p6OjI8PDw3n69Kmby0BFcV0Dyu3gwYOZnZ3NmTNn0tramk2bNqWhoSFtbW3LTymLZsBasm7duly7di3j4+Pp7u5OY2Njqqur09jYmO7u7kxMTOTq1atuMAMVwTWNSuKNMwAAAAAAAIg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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "image/png": {
       "height": 448,
       "width": 871
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = -10\n",
    "plotter.plot(x, with_first_order=True)\n",
    "plotter.plot_minimum()\n",
    "plotter.plot_func()\n",
    "plotter.fig"
   ]
  },
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   "source": [
    "# Summary\n",
    "\n",
    "* Zeroth-order optimizers\n",
    "    * Common choice for black-box functions\n",
    "    * Curse of dimensionality\n",
    "* Optimality criteria\n",
    "    * Gradient and Hessian to identify minima\n",
    "* Gradient-based optimizers\n",
    "    * General format is to have a search direction and step size (a.k.a. learning rate)\n",
    "* GD and SGD\n",
    "    * Simple but can oscillate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
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   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
 ],
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