{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "\n", "# *Numerical Methods for Economists: The Solow (1956) Model*\n", "\n", "Welcome to the first official *Numerical Methods for Economists* lab session! This focus of this lab session will be solving and simulating the Solow model of economic growth from Chapter 1 of Romer's *Advanced Macroeconomics*. Although Romer's treatment is excellent, I highly recommend reading [Solow's original journal article](http://www.csus.edu/indiv/o/onure/econ200A/Readings/Solow.pdf).\n", "\n", "Here is a quick summary of what we will cover today:\n", "\n", "* **Task 1:** Coding the Solow model in Python.\n", "* **Task 2:** Calibrating the model using data from the Penn World Tables.\n", "* **Task 3:** Graphical analysis of the Solow model using Matplotlib.\n", "* **Task 4:** Assessing the stability of the Solow model.\n", "* **Task 5:** Simulating the Solow model.\n", "* **Task 6:** Finite-difference methods for solving initial value problems.\n", "* **Task 7:** Piece-wise linear interpolation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 1: Coding the Solow model in Python \n", "\n", "In this task you will learn how to program a continuous time version of the Solow model in Python. Before we starting writing code, we should stop and think about the \"primitives\" (i.e., basic bulding blocks) of a Solow model. Writing code that uses the only the most basic bulding blocks will allows us to use the same code to solve and simulate as a general a model as possible.\n", "\n", "The classic Solow growth model is completely described by the equation of motion for capital (per person/effective person)\n", "\n", "\\begin{equation} \n", " \\dot{k} = sf(k(t)) - (n + g + \\delta)k(t). \\tag{1.1}\n", "\\end{equation}\n", "\n", "Thus in order to construct the equation of motion for capital, we need only specify a functional form for $f$ and provide some values for the parameters $s,\\ n,\\ g,\\ \\delta,\\ \\alpha$. A common functional form for technology is the [constant elasticity of substitution (CES)](http://en.wikipedia.org/wiki/Constant_elasticity_of_substitution) production function\n", "\n", "\\begin{equation}\n", " Y(t) = \\bigg[\\alpha K(t)^{\\rho} + (1-\\alpha) (A(t)L(t))^{\\rho}\\bigg]^{\\frac{1}{\\rho}} \\tag{1.2}\n", "\\end{equation}\n", "\n", "where $0 < \\alpha < 1$ and $-\\infty < \\rho < 1$. The parameter $\\rho = \\frac{\\sigma - 1}{\\sigma}$ where $\\sigma$ is the elasticity of substitution between factors of production. The CES production technology is popular because it nests several interesing special cases. In particular, if factors of production are perfect substitutes (i.e., $\\sigma = +\\infty \\implies \\rho = 1$), then output is just a linear combination of the inputs.\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 1} Y(t) = \\alpha K(t) + (1-\\alpha)A(t)L(t) \\tag{1.3}\n", "\\end{equation}\n", " \n", "On the other hand, if factors of production are perfect complements (i.e., $\\sigma = 0 \\implies \\rho = -\\infty$), then we recover the [Leontief production function](http://en.wikipedia.org/wiki/Leontief_production_function).\n", " \n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow -\\infty} Y(t) = \\min\\left\\{\\alpha K(t), (1-\\alpha) A(t)L(t)\\right\\} \\tag{1.4}\n", "\\end{equation}\n", "\n", "Finally, if the elasticity of substitution is unitary (i.e., $\\sigma=1 \\implies \\rho=0$), then output is [Cobb-Douglas](http://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas_production_function).\n", "\n", "\\begin{equation}\n", " \\lim_{\\rho \\rightarrow 0} Y(t) = K(t)^{\\alpha}(A(t)L(t))^{1-\\alpha} \\tag{1.5}\n", "\\end{equation}\n", "\n", "For the remainder of the lab we will work with the intensive form of the Cobb-Douglas prodution technology.\n", "\n", "\\begin{equation}\n", " y(t) = \\frac{Y(t)}{A(t)L(t)} = f(k) = k(t)^{\\alpha} \\tag{1.6}\n", "\\end{equation}\n", "\n", "Now that we have chosen our functional form for production, we are ready to code the Solow model. We being with some standard import statements: \n", "\n", "* **[numpy](http://www.numpy.org/)**: The foundation upon which all scientific computing is Python is built.\n", "* **[pandas](http://pandas.pydata.org/)**: Kick-ass tool for data analysis in Python. Pandas combined with statsmodels can do most all of your econometrics. Pandas is quickly becoming a standard tool for analysis of financial data.\n", "* **[scipy](http://www.scipy.org/)**: SciPy is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. SciPy is built on top of NumPy.\n", "* **[matplotlib](http://matplotlib.org/)**: Primary graphics engine for Python.\n", "* **growth**: A Python module for solving and simulating continuous-time growth models." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy import integrate, interpolate, linalg, optimize\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "\n", "# for the first few labs we will be working with models of growth\n", "import growth\n", "import pwt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $f(k)$ and $f'(k)$ in Python:\n", "\n", "Once we have settled on the Cobb-Douglas functional form for production, we need to write [Python functions](http://www.greenteapress.com/thinkpython/html/thinkpython007.html) which encode the intensive form of the Cobb-Douglas production technology and the marginal product of capital. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def cobb_douglas_output(t, k, params):\n", " \"\"\"\n", " Cobb-Douglas production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y: (array-like) Output (per person/ effective person)\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", " \n", " # Cobb-Douglas production function\n", " y = k**alpha\n", " \n", " return y\n", "\n", "def marginal_product_capital(t, k, params):\n", " \"\"\"\n", " Marginal product of capital with Cobb-Douglas production function.\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " y_k: (array-like) Derivative of output with respect to capital, k.\n", "\n", " \"\"\"\n", " # extract params\n", " alpha = params['alpha']\n", "\n", " # marginal product of capital\n", " mpk = alpha * k**(alpha - 1)\n", "\n", " return mpk" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Quick note about docstrings and their importance:** Python documentation strings (or docstrings) provide a convenient way of associating documentation with Python modules, functions, classes, and methods. An object's docsting is defined by including a string constant as the first statement in the object's definition. Writing good docstrings for functions is an important part of of doing reproducible research. Never write a function without a docstring! " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# we can inspect a functions docstring using a question mark...\n", "cobb_douglas_output?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $\\dot{k}$ in Python:\n", "Next we need to write another Python function encoding the equation of motion for capital per effective person." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def equation_of_motion_capital(t, k, params):\n", " \"\"\"\n", " Equation of motion for capital (per person/effective person).\n", "\n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " k_dot: (array-like) Time-derivative of capital (per person/effective \n", " person).\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " # equation of motion for capital\n", " k_dot = s * cobb_douglas_output(t, k, params) - (n + g + delta) * k\n", " \n", " return k_dot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding $\\frac{\\partial\\dot{k}}{\\partial k}$ in Python:\n", "The final piece of the Solow model is a Python function returning the value of the derivative of the equation of motion for capital (per worker/effective worker) with respect to $k$ (i.e., the [Jacobian](http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant) of the Solow model). " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def solow_jacobian(t, k, params):\n", " \"\"\"\n", " The Jacobian of the Solow model.\n", " \n", " Arguments:\n", "\n", " t: (array-like) Time.\n", " k: (array-like) Capital (per person/effective person).\n", " params: (dict) Dictionary of parameter values.\n", " \n", " Returns:\n", "\n", " jac: (array-like) Value of the derivative of the equation of \n", " motion for capital (per person/effective person) with \n", " respect to k.\n", "\n", " \"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " delta = params['delta']\n", "\n", " k_dot = s * marginal_product_capital(t, k, params) - (n + g + delta)\n", " \n", " return k_dot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our model coded, we need to define some parameter values. Recall that the of exogenous parameters of the Solow Model with Cobb-Douglas production are...\n", "\n", "* $s$: savings rate \n", "* $n$: labor force growth rate\n", "* $g$: growth rate of technology \n", "* $\\alpha$: capital share of output \n", "* $\\delta$: rate of capital depreciation\n", "* $L(0)$: Initial value for labor supply.\n", "* $A(0)$: Initial level of technology.\n", " \n", "To store the values of the exogenous parameters of the Solow model we will create a [Python dictionary](http://www.greenteapress.com/thinkpython/html/thinkpython012.html). Where do we get these parameter values? Common method is to pull \"sensible\" values out of ones arse. A better method, which we will cover in the nest task, would be to calibrate the values of the parameters based on real world data. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# sensible parameter values for the Solow model\n", "solow_params = {'alpha':0.33, 'delta':0.04, 'n':0.01, 'g':0.02, 's':0.15, 'A0':1.0, 'L0':1.0}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are ready to create an instance of the `SolowModel` Python class which will represent our Solow model!" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# inspect the SolowModel object...\n", "growth.SolowModel?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create an instance of the SolowModel class representing our model!\n", "solow = growth.SolowModel(output=cobb_douglas_output, \n", " mpk=marginal_product_capital,\n", " k_dot=equation_of_motion_capital, \n", " jacobian=solow_jacobian, \n", " params=solow_params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coding the steady state value of $k$ in Python \n", "When analyzing growth models we are often care about the long-run steady state of the model. Because the Solow Model is so simple, we can write down an analytic expression for the steady state value of capital (per worker/effective worker) in terms of the structural parameters of the model. \n", "\n", "\\begin{equation}\n", " k^* = \\left(\\frac{s}{n+g+\\delta}\\right)^{\\frac{1}{1-\\alpha}} \\tag{1.7}\n", "\\end{equation}\n", "\n", "We code this expression as a Python function as follows..." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytic_k_star(params): \n", " \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " return (s / (n + g + delta))**(1 / (1 - alpha))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "..and then we add this expression to our `SolowModel` instance by first creating a Python dictionary containing the steady state expression and adding it to the model. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# create a dictionary of steady state expressions...\n", "solow_steady_state_funcs = {'k_star':analytic_k_star}" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# add the dictionary of functions to the model\n", "solow.steady_state.set_functions(func_dict=solow_steady_state_funcs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 2: Calibration:\n", "\n", "In this task we a simple strategy for calibrating a Solow model with Cobb-Douglas production using data from the [Penn World Tables (PWT)](http://www.rug.nl/research/ggdc/data/penn-world-table).\n", "\n", "### Capital depreciation rate, $\\delta$: \n", "The PWT provides estimated depreciation rates that vary across both time and countries. As an estimate for the rate of capital depreciation for country $i$ I use the time-average of $\\verb|delta_k|_{it}$ as provided by the PWT. \n", "\n", "### Capital's share of output/income, $\\alpha$: \n", "Capital's share for country $i$ in year $t$, $\\alpha_{it}$ is computed as $\\alpha_{it} = 1 - \\verb|labsh|_{it}$, where $\\verb|labsh|_{it}$ is the labor share of output/income for country $i$ in year $t$ provided by the PWT. I then use the time-average of $\\alpha_{it}$ as the estimate of capital's share for country $i$.\n", "\n", "### Savings rate, $s$: \n", "As a measure of the savings rate for country $i$, I take the simple time-average of the annual investment share of real GDP, $\\verb|i_sh|$, for country $i$ from the PWT.\n", "\n", "### Labor force growth rate, $n$:\n", "To obtain a measure of the labor force growth rate for country $i$, I regress the logarithm of total employed persons, $\\verb|emp|$, in country $i$ from the PWT on a constant and a linear time trend.\n", "\n", "$$ \\ln\\ \\verb|emp|_i = \\beta_0 + \\beta_1 \\verb|t| + \\epsilon_i \\tag{2.1}$$\n", "\n", "The estimated coefficient $\\beta_1$ is then used as my estimate for the $n$. To estimate the initial number of employed persons, $L_0$, I use $e^{\\beta_0}$ as the estimate for $L_0$.\n", "\n", "### Growth rate of technology, $g$:\n", "To obtain a measure of the growth rate of technology for country $i$, I first adjust the total factor productivity measure reported by the PWT, $\\verb|rtfpna|$ (which excludes the human capital contribution to TFP), and then regress the logarithm of this adjusted measure of TFP, $\\verb|atfpna|$, for country $i$ on a constant and a linear time trend.\n", "\n", "$$ \\ln\\ \\verb|atfpna|_i = \\beta_0 + \\beta_1 \\verb|t| + \\epsilon_i \\tag{2.2}$$\n", "\n", "The estimated coefficient $\\beta_1$ is then used as my estimate for the $g$. To estimate the initial level of technology, $A_0$, I use $e^{\\beta_0}$ as the estimate for $A_0$.\n", "\n", "All of this is being done \"behind the scenes\". All you need to in order to calibrate the model is pick an [ISO 3 country code](http://en.wikipedia.org/wiki/ISO_3166-1_alpha-3)! Now let's calibrate a Solow model for the UK." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'A0': 0.94757946906339341,\n", " 'L0': 22.66865316643656,\n", " 'alpha': 0.36286396,\n", " 'delta': 0.041320667,\n", " 'g': 0.018602292580074467,\n", " 'n': 0.0036491168322516018,\n", " 's': 0.18750289,\n", " 'sigma': 1.0}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# calibrate the Solow model for GBR\n", "growth.calibrate_cobb_douglas(model=solow, iso3_code='GBR')\n", "\n", "# display the results\n", "solow.params" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k* = 5.46097822832\n" ] } ], "source": [ "# display k_star for our chosen parameter values\n", "print 'k* =', analytic_k_star(solow.params)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "{'k_star': 5.4609782283190977}" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compare with our model's dictionary of steady state values \n", "solow.steady_state.values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Short digression about numerical precision:\n", "\n", "The equation of motion for capital (per person/effective person) should return zero when evaluated at the steady state, $k^*$. Let's check whether or not it does..." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "capital(k*) = 0.0\n" ] } ], "source": [ "# very close, but not exactly zero!\n", "print 'capital(k*) =', solow.k_dot(0, analytic_k_star(solow.params), solow.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To a human this is almost, but not \"exactly\", zero. But for most computers there is no difference between this number and *exactly* zero! Why? No computer has infinite precision. Eventually, at a small enough resolution, a computer can no longer tell the difference between two floating point numbers. My computer, which is a 32-bit machine, has the following machine-$\\epsilon$ (i.e., machine \"epsilon\")." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.2204460492503131e-16" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# this is your machine epsilon\n", "np.finfo('float').eps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " If you have a 64-bit computer, then your machine-$\\epsilon$ will be even smaller!. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1: \n", "\n", "#### Part a)\n", "Derive analytical expressions for the deterministic steady state values of output per effective worker, $y$, and consumption per effective worker, $c$, and then use your results to fill in the blanks in the code below." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytic_y_star(params): \n", " \"\"\"The steady-state level of output per effective worker.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " y_star = # insert your code here!\n", " \n", " return y_star\n", "\n", "def analytic_c_star(params): \n", " \"\"\"The steady-state level of consumption per effective worker.\"\"\"\n", " # extract params\n", " s = params['s']\n", " n = params['n']\n", " g = params['g']\n", " alpha = params['alpha']\n", " delta = params['delta']\n", " \n", " c_star = # insert your code here!\n", " \n", " return c_star" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part b)\n", "Create a new dictionary called `new_steady_state_funcs` containing the expression for $k^*, y^*,$ and $c^*$." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part c)\n", "Use the `set_functions` method of the `SolowModel` class's `steady_state` attribute to add the new dictionary of steady state functions to your model. Then use the `set_values` method of the `steady_state` attribute to re-compute the steady state values." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Part d)\n", "Examine the resulting dictionary which should now contain three values (one for $k^*, y^*$ and $c^*$)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2:\n", "\n", "Try calibrating your model and computing the steady state values for at least 5 different countries. How different are the steady state values across countries? Are there any groups of countries that you think might have systematically lower/higher steady state values?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# insert your code here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Task 3: Graphical analysis of the Solow model using Matplotlib\n", "\n", "In this task you will learn how to recreate some of the basic diagrams used to analyze the Solow model using the Python library [Matplotlib](http://matplotlib.org/). We start by changing different parameters to see how each change impacts the long-run steady state of the model. We then focus on short-run dynamics by plotting impulse response functions for various parameter changes.\n", "\n", "### Long-run comparative statics" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# set up inline plotting!\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RQmDkyJFwcnLCjz/+qHeeqvu/ISEhWvcNd+/erTV+TEwMunbtqvWHhJubG+zs7DTOCkeP\nHq0VtAUKFFCfeb77y16Xzz77DEIIjT8QACAlJQWDBw9GdHS03nmobN++XePSv8rr16+xYcMGSJIE\nb29v9fBPP/0UhQoV0lo2AGzbtg0AMGvWLL3LdXBwwJgxYxAfH48DBw5ofBYTEwM/Pz/UrVsXnTt3\n1pq2Z8+eUCgUmDlzpvpSOyB3CVusWDHs3bsXAQEBOqfNiitXrmDy5MmwsrLC5s2bUbBgQb3TqL5L\np06d0upARtd3qUSJEujfvz/i4uI0/jgE5Oe1X79+nen6VbUcPnxYY/jhw4eNDvLc3N0u5V4MckpX\ntWrVcPToUURGRqJZs2b4888/ERERgYiICGzcuBGdO3fGqVOnsHXrVp0NxADNy5zFixfH8OHDIYTA\nqFGjcOzYMYSHh+OLL75Q/xLUdVl0ypQp8PX1RVxcHAICAjBp0iS8efMGkydPVo8jSRJWr16Nn3/+\nGVFRUbh9+zaWLVuGgIAA9OvXT+sKgK5lTZ48GT4+Ppg9eza2b9+Op0+f4syZM+qaZ8yYYdB2kyQJ\nDx8+RKdOnfC///0Pd+/eRXh4OH7++Wf07dsXMTExGD9+PFq2bKmexs3NDStWrMC///6LYcOGISws\nDI8fP8aqVauwbt06DB48GH369NG7jQFg0aJFqFOnDj7++GMcPHgQCQkJuHLlCjp37gwHBwf1HxLv\nUp1pR0dHq8/CAcDGxgYdO3ZEbGwsmjVrBgcHB4O2g646VbVGR0fj2LFjmD17Npo1awZHR0f8888/\naN68eYbTq9SvXx9t27bFixcvMGLECFy4cAEhISGYNGkSAgMDdW6Xr7/+GqVLl8bHH38MPz8/PH/+\nHBcvXsTChQvRokWLDG/vZPTZ1KlTIUkS1q9fjw0bNuDRo0fYsWMHZs2aBUmSjJqv6t/pTcN75KRT\nDrWOJwv26tUrsXjxYtGlSxdRrlw5UbRoUVG7dm0xZswYERISojHuf//9p37USvXYVdrHet68eSP2\n7dsnBg4cKIoXLy6qVq0qRowYIXbt2qUx3f3798Xbt2/Fb7/9Jvr06SOqVKki7O3tRaNGjcScOXO0\nnp0+e/asGDt2rKhVq5YoVqyYqFKlihg3bpz4448/RHJysnq8d2t79/EtpVIpVqxYIZo3by4cHR1F\ns2bNxLJlyzJ8bOpdISEhYtWqVaJr166iRo0awtHRURQuXFhUr15ddO/ePcNOPc6fPy+6d+8uypcv\nL5ydnUWbNm00Or4RIvXxuXe3cVqvX78Wc+fOFY0bNxZFixYVNWvWFMOHDxePHj3KsPZKlSqJKlWq\naA3fuXOnsLKy0vmMfUZatWqlri/tNndychJeXl5iyJAhYuPGjTofldP3XXr58qXYuXOn6NGjhyhW\nrJioWbOmmDJlivjuu+80pkvr4cOHYuDAgaJcuXKifPnyYsCAAeL27duif//+QpIkjWfPhw4dqvVd\nSa+P/Bs3bog5c+aIqlWripIlS4rWrVuLo0ePavQnoHrcMb199+7yrKyshL+/v/oxw7R1vPvoJOVv\nkhD8E4+I8i8hBMqUKYOUlBQ+3kUWiZfWiShf+PPPP3Xenrh+/TpiYmLUfRkQWRoGORHlCwkJCfjz\nzz8xZ84cBAUF4dGjR1i9ejU++ugjlChRAsuXLzd3iUSZwkvrRJQvREVF4YcffsDhw4cRERGBFy9e\noHLlymjZsiUWLVpk8s6AiHIKg5yIiMiC8dI6ERGRBWOQExERWTAGORERkQVjkBMREVkw07/CyIQe\nPHiAGTNmoEyZMnBwcEBKSgqmTJlidOvSBw8ewMfHR+cLKQD57VJLly6FQqFAQkICFAoFFixYoH5j\nEiD3mzxq1CjUq1cPhQsXhp2dncb7nj09PTF+/HgAQJkyZdCvXz8MGjQIJUqUwC+//II9e/aoX0Zh\n7PrdunULK1asgI2NDUJDQ1GyZEnMmTMHHh4eRm0Hc8rKvjR02uzYnpGRkZg3bx6sra3h4OCAIkWK\nYObMmRovPHnX8uXL8fbtW62+0R88eIA1a9YgOTkZtra2KFq0KCZOnJjuG830fW+Dg4Mxc+ZMvHnz\nBgkJCWjWrBnmzZuXbne5uUVWj2tjpzfF8a9iyPfB0PoM3X+mOv79/f3xww8/4OzZs3BxcUHXrl21\n3iBoKjm9j1XSO/bSzjej74Kh29rQfWfIehiTLekyY69yGXr79q2oUqWK+PHHH9XD5s6dKzp06CCU\nSqVB83jx4oU4evSoqFatmlZXjSrx8fFiwIABIjo6Wj3sxo0bolatWuLBgwfqYcuXL9fqajJtl4lp\nu91UDVP9FClSRBw4cCBT63f79m3RoUMH8eLFC/WwAQMGiGLFiol///3XoO1gblnZl4ZOmx3bMyYm\nRlSqVEmcP39eCCFEXFycqF69uli1alW69YaHhwt7e3utLjRjY2NFjRo1xPbt29XDNmzYIDp37qw1\nD0O+t6GhocLb21tERkYKIeTvcZ06dUSdOnXEw4cP063P3LJ6XBszvSmPfyEM+z4YWp+h+8+Ux//I\nkSOFEEIkJiaK2bNni08//dSo6Q2Vk/s4rfSOPSEM+y4Yuq0N3XeGrocx2ZKeXBvkO3bsEHZ2diIp\nKUk97M6dO0KSJLF582a904eEhIiePXuKOXPmiObNm6e787Zv3y4WLVqkNXzmzJli5cqV6n+PHTtW\nhIeHi7dv32rshLNnz4qJEydqTFuhQgUxZswY8cEHH4jVq1eLsLCwTK/fV199JaytrTX+EFD1S/75\n55/r3Q65QVb2paHTZsf27NWrl1i9erX63zExMaJChQpi06ZN6dY7atQonX1hf/jhh8LZ2VljWExM\njJAkSezatUs9zNDvbc+ePdWBonLu3DkhSZKYNGlSuvWZW1aPa0OnN/XxL4Rh3wdD6zN0/5ny+K9Z\ns6Z4+fKlUdNkRk7t43eld+wZ+l3IaFvPmTNHPczQfWfoehiTLenJtUFet25d0bZtW63hVapUEb17\n9zZqXqqXEegyZcoUUa1aNfH69WuN4bNmzRLz589X/3vcuHFa0yYmJoqOHTuKV69eaQz38fHRW5Oh\n6/fHH3+I8uXLi3PnzqmH7d69W0iSJJYtW6Z3OblBVvalodOaenvu2bNHFChQQCQkJGS8cmns3btX\n/PLLLzp/mZQuXVp4eXlpTePi4iIGDRqkc34ZfW9LliwpatSoIRITE9XDUlJShJ2dnahdu7bBNee0\nrB7XmZneFMe/od8HQ+szdP+Z8vjv16+fGD9+vFHTZIY59nFGx15aGX0XDN3Whu47Q9fDmGxJT65s\n7Pb27VsEBQWhWrVqWp9VqVIF/v7+JltW06ZNcffuXQwZMgTPnj0DACQlJeGvv/7CBx98oB5v3bp1\nWtPOmDEDX331lUHvT07LmPXr1asXIiIi0LRpU/Ww8+fPo2DBgujatatRyzWHrOxLQ6fNju35+++/\no1q1aihWrJgBawm8ePEChw8fxoABA7Q+e/bsGaKjo2FnZ6f1WcWKFTP1fa5WrRoiIyORlJSkHmZj\nYwM7OzvExsYaPb+ckNXjOjt+Lxh6/BvyfTCmPkP3nymP/+nTp2P9+vX4+eefjZrOGObYxxkde8Yw\ndFsbsu+MWQ9TZItRjd3i4+Mxf/58ODg4wN7eHra2tpg2bZoxszBITEwMhBAoUqSI1meFCxdGfHw8\nUlJSYGtrm+Vl9ezZE+3atcOePXtw6tQpLF26FHv27MHKlSvx3nvvpTvd2bNn8fjxYzRu3Fjrs9ev\nX2P58uV49uwZXrx4AaVSialTp6JixYpZXr9///0XO3fuxObNm1GjRg2963fo0CHs2LEDCQkJ2LJl\nC54+fYpff/0VSUlJuHDhAhYtWoQWLVronU9mZWVdDZ328ePHJt+e169fR5kyZRAQEID9+/cjKioK\nCQkJWLZsGapUqaI1n2+++QZz5szRuQ0cHR1RoUIFJCYman326NEjREdHQ6lUajRw0efkyZN4+fKl\nRrBEREQgMTERPj4+Bs9HqVSq34Nub2+PevXq4dy5c2jWrBnGjBlj8HwMkdXjOjt+Lxh6/BvyfTCm\nvszuP2OP/7RiYmLg4uKCTz75BG3btoWbm5tR0xu6jJzexxkde1mR3rY2ZN9lZTtklC3pMTjIlUol\nmjVrhr1798Ld3R337t2Dl5cXvLy84O3trTHuyJEjcfXqVYOLAIDVq1ejZcuWAIDo6GgA8gq/SzXs\n2bNnKFGihFHL0MXW1hb79u1Dv379cPjwYQwdOhRdunTR2yL0008/xbx583R+9uTJEwwcOBBly5YF\nAPzwww/o1q0bLl68CHt7+0yt319//YUzZ85g69atWLVqlcbZQnrevHmDAwcOYNeuXahTpw5Gjx6N\nDh06qOteunQpxo4di5s3b6Y7D3PuS0OnNfX2fPnyJe7evQs7OztcuXIFixYtAiC/Patx48a4dOmS\nRphfv34dRYoUQaVKldLdJl27dsXOnTvx+vVr9Zl5eHg4Hj58CEmSEBcXBxcXl3Snf5e1tbXW2eG6\ndetgZWWF2bNnGzSP5ORkDB48GAUKFMDu3bsBALNmzcLu3bvRu3dvrfHNfVxnx+8FQ45/Q78PxtRn\n7P7LzPGvcu/ePQwdOhTdu3fHH3/8gZYtW+KLL77A1q1btca1tH1syLFnLH3b2pB9l5XtkFG2pMug\nC/BCiNOnT4vChQurW/Q9ffpUrFy5UiQnJxs6C4MFBQWle69jwIABQpIk8eTJE4Pnl9F9ESGE2Llz\np/jkk0/EX3/9JSpXriwkSRKVK1fWarWqcuzYMVGyZEnx9u1bg5afkpIi7O3txWeffSaEyNr6vX37\nVrRr1060adNG7/2T48ePi927dwulUimcnJxEv379ND5fvHixcHFxMWgdMisr62rotKbentHR0UKS\nJFGoUCGNxkFKpVK4urqK/v37q4cpFAoxdOhQkZKSoh6mq5bk5GTRtGlTsXDhQpGSkiKeP38u5s2b\nJ+rXry9sbGx07kt939u07ty5I4oUKaJxX1efuXPnCicnJ417fX/99ZewsrIST58+NXg+hsrqcZ3Z\n6bN6/Bv6fcjK+hm6/4w5/oUQIiEhQbi7u2s0rmrYsKGoVKmS3mkzIyf3saHHXlrGHFOGbmtd+y6z\n28HYbFEx+Fqes7MzkpKSULduXXz66acIDg7GlClTdN73y6r33nsPBQoU0PnZy5cvUaBAgXSfvTXW\nli1bsGvXLqxduxadO3dGUFAQJk+ejPDwcPTv31/nNOvWrUOnTp1gbW1t0DJsbGzg4uKivi+SlfWz\ntrbGl19+iRMnTmDcuHEZLtfd3R09e/ZEUFAQ4uPjMWnSJI3PAwMD0bBhQ4PWIbOysq6GTmvq7al6\nxrNq1aoazwdLkoTSpUvj0KFD6mEbN27E8OHDYWOT8cUtOzs7HDlyBOXKlcO0adOwZs0ajBo1Cm/e\nvEHlypWNbmeRVnJyMgYOHIgJEyYY/Jf8w4cPsXLlSvTp00fj8t+5c+fg7u6eLW8Cy+pxnR2/Fww5\n/g39PmS2PmP2nzHHPyCf3dna2mL48OHqYY0aNcLTp0/1TpsZObmPDT32MsuQbZ3evsvsdjA2W1QM\nDvKaNWti48aNSElJwffff4+WLVvihx9+MGphhrK1tUWNGjUQHx+v9dmLFy9QsmRJky1rw4YNmD9/\nvvrf9vb2WLlyJdatW4cLFy5ofeFTUlJw9OjRdH/R9ejRAz169NAa/vr1a9y5cweAcesXGRmJGzdu\naIxTt25dAPKlPYVCke66ubq6omDBgvjnn39QqFAheHl5aazHkSNH0K5du3SnN4Ws7EtDpzX19rS1\ntUXp0qVRvHhxrfkVLlwYSUlJ6kv6wcHBaNWqldZ4QsdLBYsVK4Zhw4Zh9erV+Pzzz1G2bFnExcWh\nTp066W4DfYQQGD58ODp37oxvvvnG4OmOHj2KV69eaV1CP3nypPoyqall9bjOjt8Lhhz/hn4fMlOf\nvv2XleNfCIGDBw9ixIgRGsNtbW11tvMwhZzax8Yee4YwdltntO8ysx30ZUtGjPpT5uOPP8bHH3+M\n4OBgDBo0CJs2bcLYsWO1xhs9ejSuXbtmVCErV67UaHTl4eGBiIgIjXEUCgWuXbuG5s2bGzXv9Lx8\n+RIBAQEe3P2SAAAgAElEQVQava2pjB49GjNnzsSLFy80/nIKCAhAUlJSuq1XL126pNVI7vHjx3j8\n+DE6dOigHmbI+iUnJ6N27dpISkrC7du31feBXr16BUBut6BQKPT+9XbixAk0a9ZM4y/Xw4cP48WL\nFxg8eDDevHmD2NhY9T39d7eDOfelodOaenu2bdsWly9f1qonOTkZ5cqVg6OjI3bu3InQ0FD06tVL\n/XlKSgoA4JdffsH169cxZMgQjc/TunPnDqKjo9GnT58Mt0FGvvjiC9SuXRuff/65etjWrVsxdOjQ\nDKdT/cJS/aJSrdvly5fxySef6JzG3N8FU0yfljHHvyHfh8zUl9H+y+rxf/PmTcTFxWm197l582a6\nDeosZR8fP348S8feuzKzrfUde8ZuB33ZkiFDrr+PHj1a1K9fX2PY119/LYYMGWLUdXxjLF++XDg7\nO2vcmzh//ryQJEn8888/GuNGRERkeA9j6NCh6XYC4OnpqdXrmhDyA/66nsfdsmWLkCRJrFixQuf8\nRo8eLeLi4jSGHT58WEiSpNGZhCHrp1AoRNmyZUWDBg002iL4+voKSZJEr169NJYTFRWlVY9CoRCO\njo5anV706dNHtGvXTggh9zB27do1netjClnZl4ZOa+rtuXfvXlGoUCERHx+vHqZUKoWDg4MYPnx4\nuusaHh6u897Yxo0bRcWKFTXui3311Vc6nzNVyeh7K4QQmzdvFl9++aXWcFUPXiq6vhdff/21KFSo\nkMawQ4cOCUmSxKNHj9JdZlZl9bg2ZnoVUxz/hn4fjKlP3/7L6vF///59IUmSuHTpksYwW1tbERwc\nrHN7mII59rEQ6R97aaX3XTB2Wxty7Bm7HvqyJSMGBbm3t7dGEMTExIimTZuKoKAgoxdoqPj4eFG9\nenWxdu1a9bBRo0aJpk2baox3+fJlYWVlJTp27JjuvLp16yYkSRKPHz/W+uzAgQOiZs2aIjQ0VD0s\nMjJSdOrUSRw7dkxr/G+//VZIkiQ2btyoc1nBwcFi2LBh6t58FAqF6NWrlxg8eHCm1m/ZsmVi7ty5\n6n/HxMSIDh06iAoVKmjUfOHCBSFJkpgwYYLG9JcvXxaSJIkzZ85oDG/atKlYsmSJiIuLy/aewLKy\nLw2d1tTbUwgh+vbtq9F71qZNm4S7u7t49uxZuusaGBgoJEkSU6dO1Rj+xx9/iGrVqqmnPXPmjHBw\ncBC3b99Od14ZfW+PHz8unJ2dxYcffigGDx6s/unbt68YMGCAerz0vhdBQUHCzs5O/Pfff0IIIW7d\nuiVcXV1FtWrV0q3HFLJ6XBs6fVqmOv4N+T4YWp+h+y+rx3/nzp3FjBkzhBBy463hw4frDCBTMsc+\nFiL9Yy+tjL4Lhm5rQ/edseuhL1syIgmh/4ZCcHAwjhw5gufPn6NAgQKwsbFBp06dsnRvzxB37tzB\nwoUL1Q2BkpKSsHr1ao1L3ZGRkfDx8cGgQYM0XgAQGxuLfv364eHDh7h79y4kSYKDgwOqVauGTz/9\nFIMHD1aPGxQUhCVLlkChUKjvkc6YMQMNGjTQqsnPzw8ff/wxjhw5And3d511X758GZs2bcKrV6/U\n90qmTJmi9ZywIesHyM+C79q1CwBw9+5d1K1bF/PmzUOZMmXU44SHh6N169ZwcXHBpUuX1MP379+P\nuXPn4urVqxqX1v/66y/873//Q6NGjTBx4kSTPMqXkazsS0O3kym3JwA8f/4c3377LUJCQlC4cGGU\nKlUKkyZN0vkyjcTERPTo0QNBQUGIi4uDJEnw9PTEZ599pm4zMXfuXDx8+BCPHz+GUqnEt99+i9q1\na2vMx9DvrZOTExISEiCEgCRJAKD+/7lz52LBggUA0v9eAMCvv/6KnTt3okqVKnBxccGBAwdQu3Zt\n/PTTT7p3oolk5btg6PTZcfwb+n0wpD5D9x+QteP/+fPnmDFjBh49eoSiRYuiYcOGmDp1qt59lFU5\nsY9V9B17jx8/Rv/+/Q36LhiyrY3Zd8ashyHZkh6Dgpwsx/z58zUa7xAB+r8XSUlJKF68OH788UcM\nGTIk5wojk+Lxnz/lyi5aKfOUSqW5S6BcKO33IiEhQeMROgDYuXMnbG1t0blz55wujUyIx3/+pDfI\nk5OT4eXlhXr16qFJkyZYtWqVzvFmz56NypUro2HDhggNDTV5oaTfvn37NPoJJgK0vxfTpk1Dr169\n1C1yw8PDMWfOHCxZssSo3uUod+Hxn3/pffysYMGCOHHiBOzt7fH69Ws0bNgQ3bp1Q9WqVdXjBAQE\n4PTp07h8+TKOHj2K6dOn4+DBg9laOGlSKBS4cuWK1r0myt90fS8mTJiAJ0+eYOHChYiKikJMTAx2\n7Nih8XgkWRYe//mbUffInz59iubNm+Pvv/9G+fLl1cPXrl0LhUKByZMnA5Df7hIWFmb6aomIiEiD\nQffIlUol6tati1KlSuGTTz7RCHFAPiNP28quRIkSDHIiIqIcYFCQW1lZITAwEHfv3sW6deu0ev4R\n8vPoGsNUzfKJiIgo+xjVRWvFihXRuXNnXLx4EfXr11cP9/LyQnBwsPoeW2xsLCpXrqwx7bBhw9Tv\n4wYAHx8fo96bTERERNr03iN/8uQJbGxs4OjoiKdPn6J169Y4evQoSpcurR4nICAAU6dOha+vL44e\nPYpdu3ZpNXaTJCnTndkTERGRbnrPyB89eoShQ4dCoVDA1dUV06dPR+nSpbFhwwYAwJgxY+Dp6Qlv\nb280atQITk5O2LFjR7YXTkRERDnYsxvPyImIiEyPPbsRERFZMAY5ERGRBWOQExERWTAGORERkQVj\nkBMREVkwBjkREZEFY5ATERFZMAY5ERGRBWOQExERWTAGORERkQVjkBMREVkwBjkREZEFY5Dr8fDh\nQxw8eBAjR44EACgUCr5HnYiIcg3LCHJJyvpPJoWGhqJevXq4c+cOAODy5ctwc3Mz1ZoRERFliWUE\nuRBZ/8mkNm3aYMuWLfjwww8BAMePH0eHDh1MtWZERERZYhlBbmYXL15E8+bNAQDHjh3D+++/b+aK\niIiIZJIQWThdNWZBkoQcWpTJbd68GVFRUXj79i0OHDiAq1evmrskIiIiADwj18vf3x9hYWH44osv\nYGVlhVmzZpm7JCIiIjWekesRGBiIw4cPo3Tp0rCyssJHH31k7pKIiIjUGOREREQWjJfWiYiILBiD\nnIiIyIIxyImIiCwYg5yIiMiCMciJiIgsGIOciIjIgjHIiYiILBiDnIiIyIIxyA00a9Ys+Pn5mbsM\nIiIiDezZjYiIyILxjJyIiMiCMcj1iIuLw59//olhw4aZuxQiIiItDHI9rl69itatW+PmzZvmLoWI\niHK7iAhg+3bg44+B2rVzZJEWcY9cWiBlefliXuZX87vvvoOtrS0mTJhg0PirVq3CwIED4erqmull\nEhFRLicE8N9/wMmTqT8vXwKtWqX+1KmT7WXYZPsSTCArIWwKu3fvhp+fH44dO4Z27drpHf/27dsM\ncSKivEYI4M4dzeBWKFJD+7PPgBo1ACnrJ5/GsIggNzd3d3f4+fmpQ3zTpk0oV64c/Pz8sGLFCvz8\n889wcHDA8+fPUbVqVYSHh+PChQto0qSJmSsnIqJMEwIICdEMbltbObR9fIB584CqVXM8uN9lEZfW\nc5M///wTSqUSHTp0wJIlS9CwYUMolUr07dsXAHD//n388ssv+Oyzz8xcKRERGUWpBP79NzW0T50C\nChdODe5WrYCKFc0e3O9ikBtp2rRp+OyzzxAYGIjExET4+fnh66+/hrOzM2JiYnD8+HG4ubmpf4iI\nKJdSKoGgIODECcDfHzh9GnBy0rzHbQG/xxnkRjp+/DgUCgUiIiIQFxeHJk2aIDIyEiVLlkSNGjVw\n5coVJCcno2nTpqhQoYK5yyUiIhXVpfITJ4B//pHPup2dgdatU4O7TBlzV2k0BjkREeVNQgB376YG\nt78/YG8vB7fqp2xZc1eZZQxyIiLKO8LDU4P7xAl5WJs2qcFdsaI5q8sWDHIiIrJcUVGawZ2UpBnc\nuaBVeXZjkBMRkeWIiZEvkauCOy5OvretCu+aNfN8cL+LQU5ERLlXfLwc2Kqz7qgooGVLObTbtJF7\nTrPK372NM8iJiCj3SE4Gzp4Fjh2Tf27dApo1k0O7TRugfn3A2trcVeYqDHIiIjIfhQK4di01uC9c\nADw8gHbt5J8mTYACBcxdZa7GICciopyjeiRMFdwnTgClS6cGd6tWQLFi5q7SougN8sjISAwZMgSP\nHz9GiRIlMHr0aAwaNEhjHH9/f/To0QOVK1cGAPTp0wdz587VXBCDnIgof4qOlu9vq8JbqUwN7jZt\nLLITltxEb5BHR0cjOjoa9erVw5MnT+Dp6YnAwEAULVpUPY6/vz9WrlyJ/fv3p78gBjkRUf6QmCj3\nU64K7gcP5L7KVeFdvXq+a1menfS+/czV1VX9Sk4XFxfUqlULly9fRuvWrTXGy+shPWvWLLRp0wbt\n27c3dylERLlLSgpw8WJqcF+/Dnh6yqG9aRPQoAFgw5dtZhej7pHfvXsX7du3R1BQEAoXLqwefvLk\nSfTu3Rvly5dHmzZtMGHCBFSpUkVzQTwjJyLKO8LCAD8/4OhR+bnuypWB99+Xw7t5c7krVMoRBgd5\nYmIifHx88OWXX6JHjx5an1lbW8PW1hZbt27Fvn37cPDgQc0FMciJiCzX8+fyfW4/P/nn5UugfXug\nQwc5vEuWNHeF+ZZBQZ6SkoIuXbqgc+fOmDx5cobjCiHg6uqKiIgI2NnZpS5IkjBv3jz1v318fODj\n45P5ynNIXFwcTp48CV9fX2zZssXc5RAR5QyFArhyRT7j9vOTL5c3bZoa3rVr8z53LqE3yIUQGDp0\nKFxcXLBy5Uqd48TExKBkyZKQJAn79+/H2rVr8ffff2suyELPyI8dO4ZGjRrh/fffx6VLl8xdDhFR\n9omMTL1cfvy43Jq8fXv5p2VLoFAhc1dIOugN8jNnzqBly5bw8PCA9P9/fS1evBgREREAgDFjxuB/\n//sf1q9fDxsbG3h4eGD69Onw8PDQXFAWgtwUf/Rl5W+I7777Dra2tpgwYQKioqIwePBg+Pv7Z70o\nIiJzevlSfie36nJ5bKx8n7t9e/m/eeAVn/kBO4QxgJeXF/z8/HDp0iW0adMGkyZNwtq1a81dFhGR\ncYQAAgNTz7oDAoCGDeVL5e3by92f5vN+yy0RnwcwgLu7O/z8/NCuXTtcu3YNhQsXxpYtWxAbG4ur\nV6+iefPmEEJg4sSJ5i6ViEjTs2fA338Dhw8DR44AhQsDHTsCU6bIvail6ROELBPPyI20du1adOvW\nDTExMTh69CiioqKwYcMGc5dFRCQTQm6Ydviw/BMYCHh7A506yT9Vq5q7QjIxnpEbKTo6GhUrVsSe\nPXvQsWNH+Pr6mrskIsrvdJ11d+4MfP65fNbNRmp5Gs/IjfTPP/8gJSUF9+7dQ7Vq1QAA7dq1M3NV\nRJSv8Kyb0mCQExFZgvh4zbPuokVTg5tn3fkag5yIKDdKe9Z96JB81t2yZWp4v9MNNuVfDHIiotwi\nKUnuiOXgQeCvv4CCBYEuXXjWTRlikBMRmVNEhBzaBw/Kr/5s1Ajo2lX+4es+yQAMciKinKRQyB2x\nHDwo/0RFyWfcXbvKHbM4Opq7QrIwDHIiouyWkCD3pnbwoHy/29U19ay7SRPA2trcFZIFY5ATEWWH\nO3dSz7oDAuTHw7p2le95V6xo7uooD2GQExGZwtu3wJkzwIEDcng/f5561t22LVCkiLkrpDyKQU5E\nlFkvXsgvH/H1lS+Zu7kB3bsD3brxBSSUYxjkRETGePRIPuv29ZVbmTdpAvToIQe4m5u5q6N8iEFO\nRJQRIYCQEDm4fX2B0FD57WE9esitzdnKnMyMQU5E9C6FAjh3LjW8k5PlM+4ePQAfH6BAAXNXSKTG\nICciAuRe1fz85OA+eBAoU0YO7h49gAYN2DEL5VoMciLKv54+le93//EH4O8v96qmut9dqZK5qyMy\nCIOciPKXhw+Bffvk8A4IAN5/H+jVS35/t5OTuasjMhqDnIjyvnv3gD//BPbulRuudekC9O4td4la\nuLC5qyPKEgY5EeU9QgDBwfJZ9x9/yP2Z9+wph3ebNmysRnkKg5yI8gYhgCtXUsP75Us5uHv3lrtH\nZX/mlEcxyInIcikUwNmzqeFdsCDQp48c3o0asaU55Qs25i6AiMgoCoXco9qePXJ4ly4tB/ehQ0Ct\nWgxvyncY5ESU+6nC+7ff5AZrZcsC/fvLZ+NVq5q7OiKzYpATUe6kUACnT6eGd5kyQL9+DG+idzDI\niSj3SBvef/wBuLrKZ95nzjC8idLBICci81Io5KBWnXm7uspn3qdOAdWqmbs6olyPQU5EOU+plMN7\nzx6GN1EWMciJKGeonvPevRv49VfA2RkYMIDhTZRFDHIiyl4hIXJ4794th/nAgfJbxtzdzV0ZUZ7A\nICci07t/H/jlFzm8Y2PlM+9du9hJC1E2YM9uRGQaMTFyg7Xdu4Fbt+Qe1gYOBFq0YPeoRNmIQU5E\nmffsmfxWsd275VeCdukCDBokvxqULyYhyhEMciIyzuvXwMGDwI4dwD//AK1by2fe3boB9vbmro4o\n32GQE5F+SqXco9qOHcDvvwMeHsCHH8qXzx0dzV0dUb7Gxm5ElL7bt4Ht2+UAt7cHPvoIuHYNcHMz\nd2VE9P8Y5ESkKTZWbnG+YwcQESFfNt+7F6hfny3OiXIhXlonIuDVK+DAAfns+/RpudHaRx8B7doB\nNvx7nyg3Y5AT5VdKpdyr2vbtcsvzhg3l8O7VCyha1NzVEZGBGORE+c29e8CWLcDWrXJDtY8+ki+f\nly1r7sqIKBN4zYwoP3jxQm5tvmULEBwsP+vt6wvUq2fuyogoi3hGTpRXCSG/Yeznn+VL597ewPDh\nQNeu7KyFKA9hkBPlNZGR8mXzLVsAOzs5vD/8UH5VKBHlOby0TpQXvHoln3Vv2SK/KlT1kpLGjfnI\nGFEexyAnslRCAJcuAZs3A3v2yKE9YgSwfz9QsKC5qyOiHMIgJ7I08fHAzp3Ajz/KjdhGjAACA4Hy\n5c1dGRGZgZW+ESIjI9G6dWvUqlULPj4+2LVrl87xZs+ejcqVK6Nhw4YIDQ01eaFE+ZoQckctQ4YA\nlSrJjdhWrgTu3AE+/5whTpSP6W3sFh0djejoaNSrVw9PnjyBp6cnAgMDUTRNhxEBAQGYOnUq9u/f\nj6NHj2Lnzp04ePCg5oLY2I3IeLGxwLZtwE8/yf8eNUoOcxcX89ZFRLmG3jNyV1dX1Pv/Z01dXFxQ\nq1YtXL58WWOcixcvom/fvnBycsLAgQMREhKSPdUS5QdKJXDsmNxgrVo14MYN+TJ6cDAwdSpDnIg0\n6A3ytO7evYubN2/C09NTY3hAQADc3d3V/y5RogTCwsJMUyFRfvHwIbB4MVC1KjBjBtCqFRAeLj9K\n5u3N1udEpJPBjd0SExMxYMAArFq1CoULF9b4TAihddlc4i8dIv2USuD4cWD9esDfH+jXT26B3rAh\ng5uIDGJQkKekpKBPnz746KOP0KNHD63Pvby8EBwcjA4dOgAAYmNjUblyZa3x5s+fr/5/Hx8f+Pj4\nZK5qIksXFyc/8/3DD/J7vseNk++FFyli7sqIyMLobewmhMDQoUPh4uKClStX6hxH1djN19cXR48e\nxa5du9jYjehdque+168H9u2Tu0odPx5o0oRn30SUaXqD/MyZM2jZsiU8PDzUl8sXL16MiIgIAMCY\nMWMAALNmzcKvv/4KJycn7NixAzVr1tRcEIOc8qukJGD3bjnA4+KAsWPlblNLlDB3ZUSUB7CvdaLs\nEhoqXzrfsQNo1ky+fN6hA2BlVBtTIqIMsWc3IlN6+1Z+Pei6dcDNm8DIkXLf5xUqmLsyIsqjGORE\npvD0qdxpy//+B7i5AZ98AvTuzdeFElG2Y5ATZcWNG8DatcDvvwM9esiN2Bo0MHdVRJSPMMiJjKVQ\nyG8YW7MGuH1bvvd96xZQsqS5KyOifIhBTmSo+Hhg0ybg+++BMmWATz/l5XMiMjsGOZE+N2/Kl89/\n/VV+9vu33+R3fxMR5QIMciJdhAD+/htYsUK+Dz52LBASAri6mrsyIiINDHKitF6/ljtvWblSDvOp\nU+X74XZ25q6MiEgnBjkRIPe4tmGDfAm9dm1g2TKgfXt2nUpEuR67mKL8LSwMmDhRfnXorVvAkSOA\nn5/cAxtDnIgsAIOc8qfz54G+fQEvL6BoUeDff+W3kXl4mLsyIiKj8NI65R9KpXy/+9tvgehoYMoU\nObz56lAismAMcsr7UlKAXbuApUvld3/PmgX06gVYW5u7MiKiLGOQU96VlCT3f75iBVCtmtwTW9u2\nvPdNRHkKg5zynvh4ufe1778HvL3lDlw8Pc1dFRFRtmBjN8o7oqKA6dOBKlWA//4D/P2BvXsZ4kSU\npzHIyfLdvQuMGgXUqSO/DzwwENi8GahZ09yVERFlOwY5Wa5bt4AhQ4AmTeSXmNy+DXz3HVC+vLkr\nIyLKMQxysjzBwcCgQfL97+rV5U5dFiwAXFzMXRkRUY5jkJPlCAoC+vcHWreWO265dw+YOxdwcDB3\nZUREZsMgp9zv+nWgTx/g/fflhmthYfKz4EWLmrsyIiKzY5BT7nX5MtCjB9C5s3wZ/d49uVU6e2Ij\nIlJjkFPuExgoB3jPnkC7dvIZ+JQpcq9sRESkgUFOuUdoKDBggPzmsdat5cfKJk4EChUyd2VERLkW\ng5zM7949YNgwoEULoH59OcAnTwYKFjR3ZUREuR6DnMznwQNg3DigcWOgQgU5wGfN4j1wIiIjMMgp\n58XEyPe8PTyAYsXkjl0WLOBjZEREmcAgp5yTkCA/9+3uDigUwM2b8qtF2ZELEVGmMcgp+71+Daxe\nLffCFhUFXLsmv1K0dGlzV0ZEZPH4GlPKPkol8Msv8ll4zZrAsWPyi02IiMhkGOSUPY4dAz77DLC2\nlt9E5uNj7oqIiPIkBjmZ1rVrcsvzsDBg8WKgXz9AksxdFRFRnsV75GQakZHARx8BnToB3bvLbyjr\n358hTkSUzRjklDUvXwLz5gH16snPgt+5A0yYABQoYO7KiIjyBV5ap8xRKoGdO4HZs4GWLeVL6m5u\n5q6KiCjfYZCT8c6elbtQtbIC9uwBmjUzd0VERPkWg5wMFx4ut0Q/dw745htg4EA5zImIyGz4W5j0\ne/lSfha8YUOgVi25S9XBgxniRES5AM/IKX1CAHv3AtOmAc2by+8JL1fO3FUREVEaDHLSLTRUfhd4\ndDSwbRvQqpW5KyIiIh14bZQ0vXgh3wdv0QLo0gW4epUhTkSUizHISSYE8Ouvcp/ojx4BQUFyy3Rb\nW3NXRkREGeCldZIvo0+YADx5AuzeDXh7m7siIiIyEM/I87PkZLlXNm9voEcP4MoVhjgRkYXhGXl+\n5e8PjBkDuLsD16+zNToRkYVikOc3T58CM2YAf/8NrF0L9Oxp7oqIiCgLeGk9vxAC2LFD7tClSBHg\n5k2GOBFRHqA3yEeMGIFSpUqhTp06Oj/39/eHg4MD6tevj/r162PRokUmL5Ky6N49oH17YPlyYP9+\nYM0aoFgxc1dFREQmoDfIhw8fjiNHjmQ4TqtWrXDt2jVcu3YNc+fONVlxlEVKpXz53NMTeP994NIl\n+f+JiCjP0HuPvEWLFggPD89wHCGEqeohU7lzBxg5ElAo5LeVvfeeuSsiIqJskOV75JIk4dy5c6hX\nrx6mTp2KsLAwU9RFmaVQAKtWAU2bAr17A6dOMcSJiPKwLLdab9CgASIjI2Fra4utW7di0qRJOHjw\noM5x58+fr/5/Hx8f+Pj4ZHXxlNatW8Dw4YCNDXDhAlC1qrkrIiKibCYJA66Lh4eHo1u3bggKCspw\nPCEEXF1dERERATs7O80FSRIvwWcX1Vn4N98A8+cD48fzFaNERPlEls/IY2JiULJkSUiShAMHDsDD\nw0MrxCkbhYcDQ4fK/x8QAFSubNZyiIgoZ+kN8oEDB+LkyZN48uQJypcvjwULFiAlJQUAMGbMGPz+\n++9Yv349bGxs4OHhgRUrVmR70QT5ufDt2+V3hc+cCUydClhbm7sqIiLKYQZdWjfJgnhp3XSePgXG\njgVCQoCdO4G6dc1dERERmQlvpFqao0fl4HZzAy5fZogTEeVz7GvdUrx6JV9C9/UFtm0D2rQxd0VE\nRJQL8IzcEoSEAE2aAI8fA4GBDHEiIlJjkOdmQgA//wy0bAlMnAj88gtQvLi5qyIiolyEl9Zzq8RE\nYNw44No1+d3htWqZuyIiIsqFeEaeG129CjRoABQqJL/ohCFORETpYJDnJkLIbyvr2BFYuBD48UfA\n3t7cVRERUS7GS+u5xYsXwMcfy/2lnz8PVKli7oqIiMgC8Iw8N7h1C/Dyks++z51jiBMRkcEY5Oa2\ndy/g7Q1Mngxs2iTfFyciIjIQL62by9u3wOzZwG+/AYcPA40ambsiIiKyQAxyc4iNBfr3BwoUkLtZ\ndXExd0VERGSheGk9p924AXh6yj21HTrEECcioizhGXlO8vWVW6avXg0MGmTuaoiIKA9gkOcEIYDF\ni4H16+Wz8MaNzV0RERHlEQzy7JaUBIwcCYSFAQEBQJky5q6IiIjyEN4jz07R0UCrVoCVFXDyJEOc\niIhMjkGeXUJCgKZNgW7dgB07+Hw4ERFlC15azw4nT8qPl337LTB0qLmrISKiPIxBbmq7dsm9tO3e\nDbRta+5qiIgoj2OQm4oQwNKlcsv048eBOnXMXREREeUDDHJTUCiAiRPlF56cOweULWvuioiIKJ9g\nkGfVmzfAkCFATAxw6hRQrJi5KyIionyEQZ4VSUlA376Ara384pOCBc1dERER5TN8/Cyznj0D2reX\n+0rfu5chTkREZsEgz4yYGMDHB2jQANiyBbDhhQ0iIjIPBrmxHjwAWrQAevWSX35ixU1IRETmw1NJ\nYztzNygAACAASURBVEREAK1bA+PGAdOnm7saIiIiBrnB7t8H2rQBJkwApk41dzVEREQAeGndMOHh\n8pn4xIkMcSIiylV4Rq6PKsSnTAE+/dTc1RAREWlgkGckMlIO8WnTgE8+MXc1REREWiQhhMiRBUkS\ncmhRphETA7RsCYwdK5+NExER5UK8R65LfLzc2cugQQxxIiLK1XhG/q7EROD994HmzYHlywFJMndF\nRERE6WKQp5WcDHTuDFStCmzYwBAnIqJcj0GuolAA/foBdnbAjh2AtbW5KyIiItKLrdYBQAhg8mQg\nIUF+ixlDnIiILASDHABWrABOngROnwYKFDB3NURERAZjkP/yC7BmDXDuHODgYO5qiIiIjJK/75H7\n+wP9+wPHjwN16pi7GiIiIqPl3+fIb98GBgyQz8gZ4kREZKHyZ5A/ewZ07w4sWiS/0YyIiMhC5b9L\n6woF0LWr/Kz42rXmroaIiChL8t8Z+WefASkpwKpV5q6EiIgoy/JXq/WtW4F9+4CAAMAmf606ERHl\nTXrPyEeMGIFSpUqhTgYNwmbPno3KlSujYcOGCA0NNWmBJnP1KjB9OrB/P+DkZO5qiIiITEJvkA8f\nPhxHjhxJ9/OAgACcPn0aly9fxvTp0zF9+nSTFmgS8fFy96vffw+4u5u7GiIiIpPRG+QtWrRA8eLF\n0/384sWL6Nu3L5ycnDBw4ECEhISYtMAsEwIYPhzo0kV+3IyIiCgPyXJjt4CAALinOcstUaIEwsLC\nsjpb01mxAoiOll9JSkRElMdkucWXEELrsTIpt7z+88wZOcADAtiHOhER5UlZDnIvLy8EBwejQ4cO\nAIDY2FhUrlxZ57jz589X/7+Pjw98fHyyuvj0PXsGfPgh8NNPgJtb9i2HiIjIjEwS5FOnTsWQIUNw\n9OhR1KxZM91x0wZ5ths/Xr4v3rVrzi2TiIgoh+kN8oEDB+LkyZN48uQJypcvjwULFiAlJQUAMGbM\nGHh6esLb2xuNGjWCk5MTduzYke1F67VzJ3D9OnD5srkrISIiylZ5r4vW8HCgcWPg77+BevWyf3lE\nRERmlLe6aFUogI8+AmbOZIgTEZHZCAFERubMsvJWP6Vr1gBWVsC0aeauhIiI8hGlEvj3X+D06dQf\nAIiKyv5l551L62FhgJcXcP48UK1a9i2HiIjyvTdv5GZYqtA+dw5wdgZatEj9qVIFyImnsfNGkAsB\ntG0LdO4s96dORERkQomJ8nmiKrgvX5bPGdMGt6ureWrLG0G+cSOwaZP8J5G1dfYsg4iI8o3YWM3L\n5CEhQIMGqaHdrBng4GDuKmWWH+RRUXLDNn9/oFYt08+fiIjyNCGA+/dTQ/vUKeDRIzmsVcHduDFQ\nsKC5K9XN8oN84ED5RsSiRaafNxER5TlKJRAcrHnGnZKieZncw8NyLvBadpD/8w8wYoS8R+ztTTtv\nIiLKE968Aa5eTQ3ts2eB4sU1g7tq1ZxpmJYdLDfI37yRL6kvXgz07Gm6+RIRkUV78QK4cCE1uC9d\nki/cqkLb2xsoU8bcVZqO5Qb58uXyGflff1nun1FERJRlT57IL7tUBffNm0D9+poN0xwdzV1l9rHM\nII+KAurWlf/kqlrVNPMkIiKLkLZh2unTciQ0barZMK1QIXNXmXMsM8hHjABKlQKWLDHN/IiIKFdS\nKuVHv9IGd3Ky5v3tunUBm7zVT6lRLC/Ig4KAdu2A27dzz0N8RERkEikp2g3TihXTDO7q1XlHNS3L\nC/LOnYGOHYFPP836vIiIyKySkjQbpl28CFSqpBncZcuau8rczbKC/PhxYPRo+TpLgQKmKYyIiHJM\nXJxmw7SgIPnSuCq0mzeXHw0jw1lOkAsht2CYMQMYMMB0hRERUbaJjNS8vx0RATRpkhrcnp7sBiSr\nLKd5wP798vvG+/UzdyVERKSDEEBoqGZwv3yZGtojR8rdf+TnhmnZwTLOyIUAGjYEvvgC6NXLtIUR\nEVGmvH0LXLuWGtpnzgBFimje337vPTZMy26W8XfRwYPy2XiPHuauhIgo30pKkhujpW2YVqGCHNj9\n+wNr1wLlypm7yvwn95+Rq+6Nz54N9Olj+sKIiEin+HjNhmk3bsgvE0nbMM3JydxVUu4/Iz90CHj9\nmpfUiYiyWVSU5qs8w8MBLy85tL/+Wv7/woXNXSW9K/efkXt7AxMnsqU6EZEJCSH3q5W2Ydrz5/Kv\nXNUZd/36gK2tuSslfXJ3kF+8CHzwAXDnDps5EhFlwdu3QGCgZsO0ggU1G6bVqAFYWZm7UjJW7g7y\nAQPknvAnT86eooiI8qhXr4CAgNTgvnBBboiWNrjd3MxdJZlC7g3y8HD5kbP//pM72iUionQ9eyb3\nS64K7uvXgdq1NRumubiYu0rKDrk3yKdOBaytgWXLsq8oIiIL9fCh5v3te/fkXtJUwd2kCRum5Re5\nM8hfvgTKl5f/pOS1HyLK54SQmwqlDe5nzzQbpjVowIZp+VXubEG2Z498HYghTkT5kEKh3TCtQIHU\n0J4xA6hZkw3TSJY7z8ibNgXmzAG6dcveooiIcoHkZM2GaefPA2XKpAZ3y5ZyD2pEuuS+IL9xQ37n\neHg4HzkjojwpIQE4dy41uK9eBdzdU4Pb2xsoUcLcVZKlyH1BPnGi3OffggXZXxQRUQ6Ijta8v33n\njtzztCq4mzaVXzZC9H/t3XtUVOXeB/DvjMj9KleTi9zkLoyGIIIoealThmmmpCbVKVNT09dz1srj\nyW6vKytL65SiLc2T9ZbLUpFMwxRIUZAj3sjEGyKo3K/DwAzD8/6xDwObOzqzNzP8PmvNmpnNnv38\n9szAl733s5/9IAZWkCsU3ImOubl0fJwQopcYA27c4Ad3RQXX7ac1uMeO5Y55E6INA2vfdUoK1/WS\nQpwQoifUauDSJX5wDxnSFtqrVgFBQdQxjejOwAry774D5s8XuwpCCOlWUxNw9mxbaGdmAi4uXGg/\n9RSwcSMwciRdg5sIZ+DsWq+q4r79hYWAjY0QJRFCSK9qazt3TPP353dMc3ISu0oymA2cLfKffgKm\nTqUQJ4SIqqSEv5s8P587ph0TA/zjH1zHNBo1mgwkAyfIv/sOWLZM7CoIIYMIY9zQpu2Du6wMiIri\ngvvzz4FHHwVMTMSulJDuDYxd6+XlgLc3d46GmZkQ5RBCBqGWFuDyZX5wM8a/IlhwMNdZjRB9MTC2\nyH/+GZgyhUKcEKJVSiWQk9MW2qdOcQOtxMQAjz8O/O//Al5e1DGN6LeBEeTJycDTT4tdBSFEz9XV\nccObtgZ3Tg4wahQX3ImJwFdfcT3MCTEk4u9ab2wEnJ25ERToYrmEkH4oLeUuKNIa3H/+yQ1F0bqb\nPCqKOqYRwyf+Fvnx40BoKIU4IaRHjHGXYGh/fPv+/baOaZs3cx3TTE3FrpQQYYkf5MnJQHy82FUQ\nQgaYlhYgL48f3Gp129b2smVASAh1TCNE3F3rjAGensDhw9ylfwghg5ZSCfznP/yOacOGtV3GMyaG\nO7mFOqYRwidukN+4wf12FhfTbychg0x9PXDmTFtwZ2cDPj78U8GGDxe7SkIGPnF3rR87xp12RiFO\niMErL+d3TPvjDyAsjAvsNWu4Y922tmJXSYj+ET/IZ8wQtQRCiG7cvs0/vl1czA1vGhMDfPwxMG4c\ndUwjRBv6tGs9IyMDixcvRnNzM1asWIHly5fzfp6Wlob4+Hh4eXkBAGbPno1169bxG+q4a72lhRuZ\n4eJFYMQILawKIUQsLS3AlSv84G5q4u8mHz0aMBK/ey0hBqdPv1YrV65EUlISPDw8MH36dCQkJMCh\nw+lisbGxSE5O7nvLV64AdnYU4oToIZWKuwpYa2ifPMntFo+JAeLigPXrAV9fOmpGiBB6DfKamhoA\nwMSJEwEA06ZNQ1ZWFp588knefP3uM5eZyR0UI4QMeHJ5545pXl5ccD//PPDll/Q/OSFi6TXIz549\nC39/f83zwMBAnDlzhhfkEokEmZmZCAsLQ1xcHJYtWwZvb++eF0xBTsiAVVHB75h2+XJbx7TVq7lf\nXTs7saskhABa6uw2ZswY3LlzB0OHDsXu3buxcuVKpKSk9PyizExg1SptNE8IeUiFhfzj23futHVM\n+/BDrmMaXdOIDGaMMSiaFahX1vfrtn3Gdp3X1mtnt5qaGkyaNAm5ubkAgOXLl+Pxxx/vtGu9FWMM\nLi4uKCwshEm7i/hKJBKsX7+ee9LQgElffIFJtbU0LBMhAmOsc8c0hQKIjm4beCU0lDqmEf3Vwlog\nV8r7Hbr1qnrUNdV1+TO5Sg6TISawNLbs1+3Vsa/qfH17/VW1sbEBwPVcd3d3R2pqalsg/1dJSQmc\nnJwgkUhw6NAhjB49mhfird5++23uQUoK11OGQpwQnWtuBnJz+R3TLC25wI6NBdatA/z8qGMaEQdj\nDA2qBtQp61DXVMe770v4djWfQqWA+VBzTZhamVh1DtmhbY+dLJy6DeLW11oMtcAQ6cDMrD79z715\n82YsXrwYKpUKK1asgIODA5KSkgAAixcvxr59+7B161YYGRlh9OjR2LRpU88LzM3lrm5ACNG6hgYg\nK6stuLOyAA8PLrifew74/HPA1VXsKok+U6qVnUK31/v/Pq5tqu0U1sZDjGFlbAUrE6tO95ZD28LU\n1tQWrtauvW4Fmw81h1QiFfttEow4Q7TOmQPMmgUkJAjRNCEGrbKSG5e8NbgvXuTO2W49f3vCBG7M\ncjJ4te5q7i5MewvfjvfNLc1dhm77e2sT6x5/3v7eSErHcR6GOEE+ahSwfz8QFCRE04QYlKIi/vHt\n27eBiIi24I6IAMzNxa6SaINKrUJtUy1qm2pR01SjeayZ1thumpL/vH34NqgaYGZk1n2YdhfE3cxv\namQKCR2LGTCED3K5nBvRrbaWetMQ0gvGgKtX+cFdX891TGsN7rAwYOhQsSsl7fUUwLzw7SKA279G\npVbB2sQa1ibWsDG10Ty2NrGGtXHnaTYmNrwAbn08kI/vkocnfJJevgz4+1OIE9KF5mbg/Hl+xzRz\n87bQfvNN7teHNoZ0gzGGOmUdahprUN1YjZom7r6rAO5yC7kPAdwattYm1nC2dO40rf1rzIzMaMuX\n9Er4NL14kTu3hRAChYLfMe3MGcDdnQvtZ58FtmwB3NzErlJ/KNXKTiHc5fOmztOrG6tR11QHUyNT\n2JrawsbUhrs3sYGNqQ0FMBmwhA/yCxe4njiEDELV1W0d0zIyuF+HkBAuuF9/Hfi//wPs7cWuUhyM\nMdQr6zsFcI+h3GG6Uq3sFMKa5ybcvaedp2Z6x3mtTawxdAgdpyD6Rfgg/+MP4OmnBW+WEDHcvcs/\nvn3zJjdKWkwM8N57QGQkYGEhdpXao25Ro6apBlWKKlQ1VqFKUYXqxmrNY959h2m1TbUwMTLhBXDH\nELYzs8NI25HdhrXFUAvaEiaDjvBBfv06d1kkQgwMY8C1a/zgrq5u65i2cCEwZszA75imblF3H769\nhHGdsg6WxpawM7WDnZkd//6/jz1sPDr/zMwONiY2tDVMyAMQttd6QwN3pYX6eursRvSeWs3tGm/f\nMc3YmH8N7oAAQCrSuBRNzU2oUFSgoqEClYrKTo8rFZVdhnO9sh5WxlbdBnFP97amttQ7mhCBCZum\nt25xQ0xRiBM91NjIXb6zNbhPn+Yu3RkTA8ycCWzaxH29ta25pRnVjdWoaKjQBHC3j/8b1hWKCqjU\nKgwzGwZ7c3vu3swe9mbc42Fmw+Bt593tljGFMSH6Q9hEvX4d8PERtElCHlRNDX/EtPPngcBALrhf\new3YswdwcOjfMhUqBcoaylDeUI4yeVmPYdz6uK6pDjamNpoQtjdvC2R7M3uEOIe0BXW70LY0tqTj\nxYQMAsIHOR0fJwPUvXv849s3bgDh4Vxwv/021zHN0rJt/hbWgoqGKl4wlzeUtz3vYrq6RQ1HC0c4\nmDtobsNMuXD2tvNG+CPh/KA2t6ctZEJIj4Q9Rr50KXeZpRUrhGiSkG4xxv1f2T64KysZxkY0IujR\nCniGFsPW8yaqVaXdBnNVYxWsjK00wexo3uG+43QLR+pVTQjROmG3yIuLgcceE7RJMngxxlDbVIsS\neQnu1pQgJ7cJ2adNkJdjh4KLbmiRNMPS9xwk7ichf/IIVPYXcMXSAeUWjshTOMCxoC2IQ51DOwWz\nvbk9XeyBECI6Yf8K3bsHPPKIoE0Sw6JuUaO8oRyl8lKUyEu4+/qStsfyEu55TTVK8t0hKZwIozuT\n0FQwFmZ2NXANLoDf+Hw898Y5BPqaw8XSGU4Wz8PZchVsTGxoa5kQoneEDfK7d4HhwwVtkugHhUqB\ne/X3cK/uHv++3eP79fdRqaiEraktnCyc4GzhDGdLZziZO8FG4gabO5NQf9kb6vPOqLxsiWA/htiJ\nQxCzmDuX28nJCgBdiJsQYliEPUY+dChQVweYmAjRJBFZ667t3gL6Xt09NDY3wsXSBcOthmO45X9v\nVvx7F0sXOFo4wkhqhJIS/vHt/Hzg0Ufbzt8ePx6wshL7HSCEEN0TNsjt7YHyciGaIzrW3NKM+/X3\nUVRbpLkV1xajqI57fLfuLu7V3cMQ6RB+KHcR0MOthsPO1K7b3dqMcUObtg/usjJgwoS24B47lv4/\nJIQMTsIGeUgId/UzMqA1NjeiuLYYxXXF/KBu97xMXgZHC0eMsBoBV2tXuFq7ah6PsB6BEVYjMNxq\nOCyNLXtvsIOWFuDSJX5wSyT8EdOCg8UbMY0QQgYSYYN8+nTgyBEhmiPdYIyhRF6C29W3cbvmNgpr\nCjWP79TeQVFtEWqbavGI1SOdArr9YxdLF62Ni93UBOTktIV2Zibg5MQPbk9PugY3IYR0RdjObtTR\nTedUahWKaotwu+a2JqDbh/ad2juwMraCu407PGw94GHjAZ9hPnjM6zG4WbvBzcYNDuYOkEp0t7lb\nV8eFdWtw/+c/3PACMTHASy8BO3cCzs46a54QQgyKsEHu4iJoc4aodYv6RuUN3Ky6iRtV3P3Nqpso\nqC5AqbwUw62Gw8PGgwtrGw9EuEbguaDn4GHLTTMfai5ozaWl/N3kV69yVwGLiQHWruU6pllbC1oS\nIYQYDGGD3N5e0Ob0VVNzEwqqC3hB3T6wzYeaw9vOG152XvC288bkkZPxsuxljLQdiRHWI0QdpIQx\noKCAH9z37wNRUVxwb9nCDXtKHdMIIUQ7hP2Lb2sraHMDmbpFjds1t5FfkY+r5VdxtYK7Xau4hhJ5\nCdys3TRB7WXnhWj3aHjZecHLzgvWJgNn87WlBcjL4we3Wt12bHvZMiAkBBhCQ4UTQohOCBvkdnaC\nNjcQVDRUcGFdcRVXy68iv5IL7htVN+Bo7gg/Bz+MGjYK/g7+iPeLh6+9L9xt3Afs0J9KJXdMuzW0\nT53idrTExADTpgHvvQd4e1PHNEIIEYqwvdaPHTPYsdYrFZXIK81DXlkeLpde1twr1Ur42fvBz8EP\nfvZ+GGU/Cn72fvAZ5gMLYwuxy+5VfT133e3W4M7J4a5E27rFHR1NfRgJIURMwgZ5Tg43coceq1fW\nc0Fdyg/semU9gpyCEOwYzN07BSPIMQguli56NX53WRlw8mRbcF+5AshkbcEdFQXY2IhdJSGEkFbC\nBvmNG4CXlxDNaUVFQwVy7+fi3L1zyL2fi9x7uSisKUSAYwCCnYJ5oe1m7aZXgQ1wHdNu3+Yf3757\nt61jWkwM1zHN1FTsSgkhhHRH2CAvKwMcHIRort8qGiqQVZyFs8VnNeFd01SDMJcwyFxkkLnIMGb4\nGPg7+GttIBShtbQAf/zBD26Vij/wyujR1DGNEEL0ibBBXls7IK5koVKrcLHkIs4UncGZ4jM4U3QG\npfJShD8SjvBHwjFm+BjIhsvgZeel04FRdE2lAs6d4wI7I4PrmGZnxw9uHx/qmEYIIfpM2CBXKETZ\nTytXypF5JxPpt9ORfjsdufdy4WnnicgRkYh0jUSEawQCHAIwRKrfm6JyOXDmTNvWdnY2dySjfXDT\n5eAJIcSwCBvkKhVgpPvTquRKOU7dOYX0gnSk3U7DhfsXIBsuQ6xHLGI9YhHhGjGgzsV+UBUV/I5p\neXlAaGhbaE+YQKfuE0KIoRM2yFtadLIflzGGP8v/xOFrh/HL9V+QVZwFmYsMk0ZOQqxHLMa7jRd8\nWFJdKCzkH98uKgIiI9uCe9w4wMxM7CoJIYQISdgg12JTKrUKaQVp2P/nfhy+dhgtrAVP+DyBv/j+\nBXGecbAyEf9Y/MNgjDv1q31wKxT83eShoYLs4CCEEDKA6VWQK9VK/HbzN+z7Yx8OXj0I72HemOU/\nC0+NegqBjoF6d/pXeyoVkJvbFtonT3IXEmkf3KNGUcc0QgghfHoR5JdKLmHX+V3Yc3EPfO198WzA\ns5gVMAseth5arlI4DQ2dO6aNHMkP7hEjxK6SEELIQDdgg7yxuRF7Lu5B0n+ScL/+PhJDE5EYlgjv\nYd46rFJ3Kiv5HdMuXercMW0QDkVPCCHkIQ24IC9vKMeXZ7/El2e/xNhHxmL5uOWY6jVV704NKyri\nH9++fbtzxzRz/e9/RwghRGQDJsjrmuqw6fQmfJ79OZ7xfwarx69GoGOgEKU9NMaAq1f5wV1fz99N\nHhZGHdMIIYRon+jRwhjDrvO7sPa3tZjqPRVnXzkLL7uBPR57czNw/jy/Y5q5eVtov/km4O9PHdMI\nIYTonqhb5AXVBfhr8l9R3ViNHTN2QDZcJkQp/aZQAFlZbcF95gzg7s7f4nZzE7tKQgghg5FoQZ56\nIxUL9i/A6sjV+J+o/4GRVPSdAxpVVdy45K3BfeECEBLC75hmby92lYQQQohIQb4zdyf+cfwf+H72\n94gdGStE8z0qLuYf3751C4iIaAvuiAjAwkLsKgkhhJDOBA/y7y59h7+n/h0nFp2Ar72vEE3zMAbk\n5/ODu7YWiI5uC26ZDBiqn1cqJYQQMsgIGuTn753HlG+mIG1RGoKcgoRoFs3N3K7x9h3TTE35x7f9\n/QGp/l6tlBBCyCAmaJCP2zEOi8cuxkuyl3TWTmMjN0paRkZbxzRXV35wu7vrrHlCCCFEUIL2MFOq\nlUgMS9TqMqurgczMti3u8+eBwEBg4kRg6VLg228BBwetNkkIIYQMGIIG+ZrxayCVPNw+7Hv3+Me3\nb9wAwsO5Le233+ZGT7O01E69hBBCyEDX6671jIwMLF68GM3NzVixYgWWL1/eaZ4333wTP/zwA+zs\n7PDtt9/C39+/c0MSCaoUVbA1te1zcYwB16/zg7uqijv9q3U3+ZgxgLFxnxdJCCGEGJReN49XrlyJ\npKQkHDt2DF988QXKy8t5P8/Ozsbvv/+OnJwcrFmzBmvWrOl2Wb2FuFrNXcrzs8+AOXOARx4B4uKA\nY8e4sckPHADKyoDkZOBvf+O2vgdqiKelpYldgmAG07oCg2t9B9O6AoNrfQfTugKGvb49BnlNTQ0A\nYOLEifDw8MC0adOQlZXFmycrKwvPPvsshg0bhoSEBFy5cqXPjTc2clvZGzYATzzBDbLy/PPA5cvA\n008Dp08DhYXAd98BS5YAwcH607vckL80HQ2mdQUG1/oOpnUFBtf6DqZ1BQx7fXs8Rn727FnebvLA\nwECcOXMGTz75pGZadnY2Fi5cqHnu6OiIGzduwNu78+VGa2r4HdNyc4GAAG4X+auvAv/+N+DoqI3V\nIoQQQgaHh+7sxhjrNIa6pJurhYwY0dYx7a23uF3jVlYPWwEhhBAyiLEeVFdXs7CwMM3z119/naWk\npPDm+eyzz9gnn3yiee7l5dXlsry9vRkAutGNbnSjG90GzW39+vU9xaxW9LhFbmNjA4Drue7u7o7U\n1FSsX7+eN09ERARWr16NF154AUePHkVAQECXy7p+/XpPTRFCCCHkAfS6a33z5s1YvHgxVCoVVqxY\nAQcHByQlJQEAFi9ejHHjxiE6OhqPPvoohg0bhj179ui8aEIIIYRwBBuilRBCCCHaJ8jJXBkZGQgI\nCICvry8+//xzIZoUxZ07dzB58mQEBQVh0qRJ+O6778QuSRBqtRoymQwzZswQuxSdksvlWLRoEUaN\nGqU5g8OQ7dixA1FRURg7dizeeOMNscvRqpdeegnOzs4ICQnRTKurq0N8fDzc3d0xc+ZM1NfXi1ih\ndnW1vn/7298QEBCAMWPG4I033oBCoRCxQu3pal1bbdq0CVKpFJWVlSJUpjuCBHlvg8oYiqFDh+LT\nTz9FXl4e9u3bh3Xr1qGurk7ssnRuy5YtCAwM7PZsBUOxfv16uLu74+LFi7h48WK3/UEMQWVlJTZs\n2IDU1FScPXsW+fn5OHr0qNhlac2LL76II0eO8KZt3boV7u7uuHbtGlxdXbFt2zaRqtO+rtZ32rRp\nyMvLQ05ODuRyucFseHS1rgC3oZWamgoPDw8RqtItnQd5XwaVMRQuLi4ICwsDADg4OCAoKAg5OTki\nV6VbRUVFOHz4MP761792Og3R0Bw7dgxr166FqakpjIyMNJ1BDZGZmRkYY6ipqYFCoUBDQwPs7OzE\nLktrYmJiOq1PdnY2Xn75ZZiYmOCll14yqL9TXa3v1KlTIZVKIZVKMX36dKSnp4tUnXZ1ta4AsHr1\nanz44YciVKR7Og/y7gaVMXTXr19HXl4exo0bJ3YpOrVq1Sp89NFHkOrLkHsPqKioCI2NjViyZAki\nIiKwceNGNDY2il2WzpiZmWHr1q0YOXIkXFxcMGHCBIP/Lrf/W+Xv74/s7GyRKxLOjh07DPrQ2MGD\nB+Hq6orRo0eLXYpOGPZfX5HU1dVh7ty5+PTTT2FhYSF2OTqTkpICJycnyGQyg98ab2xsRH5+PmbP\nno20tDTk5eVh7969YpelM2VlZViyZAn++OMPFBQU4PTp0/j555/FLkunDP073J13330XVlZWmDNn\njtil6ERDQwM2bNiAd955RzPN0D5rnQd5eHg4/vzzT83zvLw8REZG6rpZ0ahUKsyePRsLFy5Ec2uf\nWgAADNVJREFUfHy82OXoVGZmJpKTk+Hp6YmEhAQcP34cL7zwgthl6YSPjw/8/PwwY8YMmJmZISEh\nAb/88ovYZelMdnY2IiMj4ePjA3t7e8yZMwcZGRlil6VT4eHhmmtFXLlyBeHh4SJXpHtff/01jh49\natCnDd+4cQMFBQUIDQ2Fp6cnioqKMHbsWJSWlopdmtboPMjbDypTUFCA1NRURERE6LpZUTDG8PLL\nLyM4ONjgevl2ZcOGDbhz5w5u3bqF77//HnFxcfj3v/8tdlk64+vri6ysLLS0tODnn3/GlClTxC5J\nZ2JiYpCTk4PKyko0NTXhl19+wbRp08QuS6ciIiKwc+dOKBQK7Ny506A3OADgyJEj+Oijj5CcnAxT\nU1Oxy9GZkJAQlJSU4NatW7h16xZcXV1x7tw5ODk5iV2a1giya711UJkpU6Zg6dKlcHBwEKJZwZ06\ndQp79uzB8ePHIZPJIJPJuuw9aagMvdf6xx9/jJUrV2LMmDEwNTXFvHnzxC5JZ6ytrbFu3To888wz\niI6ORmhoKCZPnix2WVqTkJCAqKgo5Ofnw83NDbt27cKSJUtQWFgIPz8/FBcX47XXXhO7TK1pXd+r\nV6/Czc0NO3fuxPLly1FfX48pU6ZAJpNh6dKlYpepFV19tu0Z4t8pGhCGEEII0WPU2Y0QQgjRYxTk\nhBBCiB6jICeEEEL0GAU5IYQQoscoyAkhhBA9RkFOCCGE6DEKckIIIUSPUZATQggheoyCnPRJeno6\nnnnmGUydOhWjR49GYGAg5s+fj71796KhoUHr7aWkpCAwMBAqlQoAcP78ed5FD/pq27ZtCAsLg1Qq\nRWFhobbLFNSxY8fw9NNPIzo6GkFBQfj+++97nP6wunvPO342RPsWLFgAY2Njgx7Pn2gRI6QXa9eu\nZUFBQezatWuaafn5+Wz+/PlMIpGwAwcOaL3NzMxMFh8fz1paWhhjjO3atYtJJJIHWlZaWhqTSCTs\n9u3b2ixRcP7+/mzz5s2MMcaysrLYoUOHupyenJyslfa6e887fjZE++RyOTM2NmZVVVVil0L0gJHY\n/0iQge3YsWP44IMPkJeXBx8fH810X19f/Otf/8KRI0d0Mnbx+PHjceDAAa0sixnAKMSFhYW4evUq\nQkNDAUBzbfDupuuSNj8b0rXMzEx4e3vD1tZW7FKIHqBd66RHb731FiZOnAh/f/9OP7O1tcWRI0fw\n6KOPAuB2uU6aNAljxoxBbGws1q1bh+vXr2vmb7+be//+/YiLi0NgYCBkMhl+/fVXzXyHDh1CZGQk\npFIp0tPT8cUXX2Djxo0AgMmTJ2Py5Mmaq6z11mZf9bU2ANi6dStCQ0MxYcIEvPLKK7zLe7av/aef\nfsKcOXMQHh4OqVSKixcvdtt+b8ucO3cuAGDVqlWYPHkyDh061O303pbXavv27QgNDYVMJoOPjw8S\nExNx9epVAOjyPd+9ezdv/Y4cOYKoqChIpVIEBQXhq6++AgB888038Pf3h6enJ3766ac+rePDfB4P\n85lcuHAB586dw6JFi/DYY48hJCQEs2bNQnZ2dqd6QkNDERwcjNDQUOzYsaPL5f/444+YO3cuwsLC\nsGDBAly4cKHbdezJ77//jgkTJjzQa8kgJPYuATJwtbS0MAsLC/bKK6/0af7ExET2/vvva1777rvv\nsujoaN48rbu54+LiWFFREVMqley9995jRkZG7P79+5r5CgoKmEQiYenp6Ywxxr7++usud/P2pc0T\nJ070add6T7WVlJQwxhjbsGEDc3Z2Zvn5+Ywx7hCDg4MD27t3b6faY2Nj2a1btxhjjMXHx7PLly93\n2W5/ltn6fvQ0vS/L27hxI3N0dGRpaWmMMcYqKyuZj48P27Jli2ae7t7zjm36+vqypUuX8uZJTExk\nx48f71dNHfX1u/Iwn8mlS5dYRESEZl61Ws0WLVrE3nnnHd7yHRwcNOvz22+/MQcHB/bRRx91Wv6U\nKVNYcXExU6lULCEhgf3lL3/pdv16EhcXx3bt2sUY4z6HDRs2sP379z/QsojhoyAn3SotLWUSiYSt\nXbu2T/MXFxczpVKpeV5ZWckkEgm7efOmZlprqG7fvl0zTS6XMyMjI5aUlKSZduvWLV5YdHe8tj9t\n9hbkPdW2fft21tjYyMzNzdnq1at5r5s/fz577rnnOtW+fv36HttjjPV7mR2DvOP0viyvdZ558+bx\n5klOTmapqama59295x3b3LhxI7OxsWENDQ2MMcaqq6tZSEhIv9exo758Vx72M2loaGAWFhbsgw8+\n0BzzLy0tZdevX+ctf+7cubzXzZkzh1laWjKVSsVbfus/lYwxlpSUxCwtLVlzc3O369gVpVLJLCws\n2J9//sm++eYbVlFRwaZNm9bn30My+NAxctItBwcHWFpaoqysrE/zNzc3Y/PmzUhLS0N9fT2kUu7I\nzalTp+Dp6cmbNzo6WvPY3NwcwcHBOHDgAF599dV+1difNvuqq9r279+PqKgoKBQKHD16FOfOndPM\nU1NTA5VKBbVajSFDhmimjx8/vte2rl271q9lamN5rfN0rG/GjBl9bqe9RYsW4Z///Cd++OEHJCYm\n4ttvv8X8+fO1to49fVf6u+yO62xmZoaNGzdi7dq12L59O+bMmYMlS5bA29ubV3tUVBTvdePHj8e+\nfftw7do1BAQEaKaHh4drHvv4+EAul+Pu3btwc3Pr9X1sde7cORgbG+PgwYNYuHAhhg0bhg8//BC+\nvr59XgYZXCjISbckEglCQkJw7dq1Ps3/4osvQqVSYe/evXBxcQEASKVStLS0dJqXdeiAxhh7oE5z\n/Wmzr3qrLTExEWvWrOl1OWZmZn1us6/LFGt5PXF2dsaMGTOwY8cOJCYm4uuvv0ZKSorWaurLd+Vh\nPpNly5Zh3rx5+P7777Ft2zZ8+umn2LRpE15//fV+12pqaqp53PpPZcf6e/P7778jJiYGo0aNwo8/\n/ojXX39d05mRkK5QZzfSo/fffx8nT57UdIJq79atW7Czs0N6ejpu3ryJEydOYN68eZpAramp6Xa5\nJ0+e1DyWy+XIy8vDzJkzu52/4xabQqHod5t91bG2y5cvY+bMmfD19YWFhUWnTlp5eXn4+9///kBt\naXuZfVle6zyZmZm8eVJTU5Gamqp53vE972m8gFdeeQWnT5/G7t274erqCicnp37V1JOevisPu+z6\n+nqkpKTA3t4ey5Ytw6VLl/DCCy/g448/5i3/1KlTvNdlZmbC0tJSJ1vJJ0+exOzZszFz5kykpKRg\n3759UKvVD9SJkwwOFOSkR5MnT8a6deswZ84c3h+S69evY9GiRVi2bBliY2Ph6ekJf39/pKSkQKlU\ngjGGrVu3Auh6iyQlJQXFxcVQKpX45JNPIJFIEB8f32m+1te29owvKirCiRMnMH/+fHh5efWrzb5u\nGXWsTSqVIj4+HsbGxnjrrbeQkZGh6R1eV1eH1atXIyYm5oHaMzEx0coyW6f3ZXmt8xw/fhzp6ekA\ngPLycixbtgx+fn6aZXZ8zxcsWNBtLdOmTYO7uzuWLFnS6fBIf9exo56+Kw/7/pWXl+P555/H/fv3\nNT+vr6/Hk08+2em9OnHiBADg+PHjSEtLw/r162FkZNTj8jtOu3TpUo+DEzHGcOrUKU2PdWNjYzDG\ncOLECRgbG/f6XpFBSsDj8USPpaWlsaeeeopNmjSJxcTEsIULF7Ldu3fzOvJkZmayefPmsZEjR7LY\n2Fj2/vvvM4lEwgICAthnn33GGGvrwHTs2DE2ffp0FhAQwGQyGfv11181y0lOTmaRkZFMKpWysLAw\ntmPHDsYYY0uXLmXjx49nTzzxBDt58mSvbW7ZsoVt3bqVhYWFMalUysaPH9/jYCl9qY0xxnbs2MFC\nQ0NZWFgYe+aZZ9hXX32l+dnx48d5tb/22mt9en97WmbH92P69OmMMcYOHjzY5fTeltcqKSmJhYSE\nsHHjxrFZs2ZpBphpr+N73r4WmUzG64j27rvvMnd39wdax6709fPobdk9fSZyuZytWbOGBQcHs8jI\nSBYXF8dWr16tOUuh43sVFBTEQkJCeOvdfvkymYzt37+fJScn8753GRkZjDGuB7qnp2e363z//n0W\nGhqqef7TTz+xBQsWsN27d/f4XpHBTcKYAYyWQfRGWloa4uLiUFBQAHd3d7HL4RnItQ1GhvZ5VFRU\nICoqCm+99RavMyAhD4s6uxFRDOT/HwdybYORoXwelZWV2LBhA2bPni12KcTA0DFyIpht27Zh1apV\nkEgkSEhIwOHDh8UuSWMg1zYYGeLn4evrSyFOdIJ2rRNCCCF6jLbICSGEED1GQU4IIYToMQpyQggh\nRI9RkBNCCCF6jIKcEEII0WMU5IQQQogeoyAnhBBC9BgFOSGEEKLH/h/HWSfOT7eU7wAAAABJRU5E\nrkJggg==\n", 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