{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "b87765e8-3137-4c80-bb38-9daada6c54bc", "metadata": {}, "source": [ "# 2025-11-21 PDE 2D Exercise\n", "\n", "We will implement a PDE simulation of the [heat equation](https://en.wikipedia.org/wiki/Heat_equation).\n", "At various points in this exercise, you will have the ability to modify the code to explore different variations on the project.\n", "\n", "## The math\n", "\n", "We will consider a perfectly insulated plate of metal with various conditions along each edge.\n", "We will consider the temperature change in 2D for this exercise.\n", "\n", "The partial differential equation which governs the movement of the heat through this plate is given by\n", "\n", "$$ \\frac{\\partial u}{\\partial t} = \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} $$\n", "\n", "where $u \\left( \\mathbf{x}, t \\right)$ is the function giving the temperature of the plate at location $\\mathbf{x}$ and time $t$.\n", "\n", "Note that $\\Delta u$ or $\\nabla^2 u$ is sometimes used in place of $\\partial^2 u / \\partial x^2 + \\partial^2 u / \\partial y^2$.\n", "\n", "For this to work, we also need an initial condition $u_0 \\left( \\mathbf{x} \\right) = u \\left( \\mathbf{x}, 0 \\right)$ and boundary conditions.\n", "For simplicity (and [without loss of generality](https://en.wikipedia.org/wiki/Without_loss_of_generality)), we assume $x \\in \\left[ 0, 1 \\right]$ and $y \\in \\left[ 0, 1 \\right]$ ($\\mathbf{x} \\in \\left[ 0, 1 \\right]^2$).\n", "We will also need boundary conditions for the top, bottom, left, and right edges of the plate.\n", "\n", "### Extension\n", "\n", "For simplicity, we consider boundary conditions that do not vary with time, but this is an area for exploration.\n", "\n", "### Note\n", "\n", "This sounds just like yesterday!\n", "What is different?\n", "We will use the Finite Element Method instead of the Finite Difference Method." ] }, { "cell_type": "code", "execution_count": 1, "id": "8f83a408-a789-4f2d-87b9-4aa59bf84ff0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u_0) = 1.0\n" ] }, { "data": { "image/png": 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pairs\n", " x = zeros(n * n, 2)\n", " for i in 1:n\n", " x[(i-1)*n+1 : i*n, 1] = x_1d\n", " x[(i-1)*n+1 : i*n, 2] .= y_1d[i]\n", " end\n", " x_1d, y_1d, x\n", "end\n", "x_1d, y_1d, x = make_grid(0, 1, 0, 1, n_1d)\n", "\n", "# An initial condition\n", "u_0 = sin.(x[:, 1] * π) .* sin.(x[:, 2] * π)\n", "@show maximum(u_0)\n", "\n", "# And plot it\n", "contourf(x_1d, y_1d, u_0, aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar_ticks=(0:11, LinRange(0, 1, 11)))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "290a1e11-9a89-4a6e-b66a-8ad2eb18d5eb", "metadata": {}, "source": [ "## New(ish) wrinkle\n", "\n", "We now need to handle 2D spatial derivatives.\n", "Fortunately, this is a natural extension of our 1D spatial derivatives.\n", "\n", "We will use the [finite difference method](https://en.wikipedia.org/wiki/Finite_difference_method) here.\n", "\n", "We have seen the finite difference approximations of derivatives before.\n", "For this exercise, we will need a forward and backward difference for the first derivative and a centered difference for the second derivative.\n", "\n", "$$ \\begin{split}\n", " f' \\left( x \\right) &\\approx \\frac{f \\left( x + h \\right) - f \\left( x \\right)}{h} \\\\\n", " f' \\left( x \\right) &\\approx \\frac{f \\left( x \\right) - f \\left( x + h \\right)}{h} \\\\\n", " f'' \\left( x \\right) &\\approx \\frac{f \\left( x - h \\right) - 2 f \\left( x \\right) + f \\left( x + h \\right)}{h^2}\n", "\\end{split} $$\n", "Instead of making the matrix itself, we will make a function that applies the action of this matrix.\n", "\n", "$$ u'' \\left( x_n \\right) \\approx \\frac{u \\left( x_{n - 1} \\right) - 2 u \\left( x_n \\right) + u \\left( x_{n + 1} \\right)}{h^2} $$\n", "\n", "We will make a separate function for handling boundary conditions." ] }, { "cell_type": "code", "execution_count": 2, "id": "6ffb42b1-72e3-40a4-b0b1-146eba40a810", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "961-element Vector{Float64}:\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " ⋮\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's make a function that applies the matrix A on the interior of the plate\n", "function diffusion_interior(u_0)\n", " u_next = zeros(size(u_0))\n", " h = 1 / n_1d # Note that I'm getting this from global space\n", " # Compute derivatives\n", " for j in 2:n_1d-1 # y\n", " for i in 2:n_1d-1 # x\n", " u_next[i + n_1d*(j - 1)] = (\n", " u_0[(i - 1) + n_1d*(j - 1)] +\n", " u_0[(i + 1) + n_1d*(j - 1)] +\n", " u_0[i + n_1d*(j - 2)] +\n", " u_0[i + n_1d*(j + 0)] -\n", " 4 * u_0[i + n_1d*(j - 1)]\n", " ) / h^2\n", " end\n", " end\n", " u_next\n", "end\n", "\n", "display(diffusion_interior(u_0))" ] }, { "cell_type": "markdown", "id": "802549a1-7ace-40ca-9ecb-87154e1fd715", "metadata": {}, "source": [ "## Boundary conditions\n", "\n", "We will start with simple boundary conditions, $u_L = u_R = 0$.\n", "\n", "This means that $u \\left( x_0 \\right)$ and $u \\left( x_n \\right)$ never change, so we will encode this by zeroing those entries in our result vector." ] }, { "cell_type": "code", "execution_count": 3, "id": "2db917ea-63ee-4a69-9265-14ec314ba14d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "961-element Vector{Float64}:\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " ⋮\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0\n", " 0.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Boundary conditions\n", "function zero_boundaries(u_0, u_next)\n", " # Zero edges of plate\n", " for j in [1, n_1d] # y\n", " for i in 1:n_1d # x\n", " u_next[i + n_1d*(j - 1)] = 0\n", " end\n", " end\n", " for j in 1:n_1d # y\n", " for i in [1, n_1d] # x\n", " u_next[i + n_1d*(j - 1)] = 0\n", " end\n", " end\n", " u_next\n", "end\n", "\n", "# And join them together\n", "function dF(u_0)\n", " u_next = diffusion_interior(u_0)\n", " zero_boundaries(u_0, u_next)\n", "end\n", "\n", "display(dF(u_0))" ] }, { "cell_type": "markdown", "id": "46fa6c9c-937f-4476-a50d-a18fabca2e6b", "metadata": {}, "source": [ "## Time Stepper\n", "\n", "Now we need to pick one of our for advancing our solution forward in time.\n", "This is the area where we can experiment the most.\n", "For now, let's use a simple [forward Euler](https://en.wikipedia.org/wiki/Euler_method).\n", "\n", "$$ x_{n + 1} = x_n + h \\, dF \\left( t_n, x_n \\right) $$\n", "\n", "where $t_n$ is the current time, $x_n$ is the current solution, $h$ is our step size in time, $dF$ is our differential equation, and $x_{n + 1}$ is our new solution.\n", "\n", "Let's code up forward Euler and take a single step." ] }, { "cell_type": "code", "execution_count": 4, "id": "8f13f041-eb52-4db7-b2d2-541c48c2525f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u_1) = 0.9999789421657956\n" ] }, { "data": { "image/png": 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1EE0Q0asIz4K64ReHcAxRN0xtJTwmmobXSJKR8897V4qCnQ0BSRQFOwTwSNgtIIeAnLXIXYGdErILqEpg3CJySlDnxDVOVGcnWi2YTMhgBlMw0gZjvQVMIUhvRkHhEBLZtm6vIoRjUyA2BY+5iVSXiX/84Pl9GUYqbdwVqqheqIUHw1l9RNDQp+wHPvYWbadZeNGldesYGW7yq0hxXuHnmzahf35uPPTQQwsXLgQAk8nkcDjq37Tb7QBgsVj+fmTPnj0XL148adIkt9s9fvz4tLS08HD/hqBoEF5uEMMxxkhz/0dbfO9monjLD7ryvpdFBx40jhv45F+bcF50jjpSXUqqSqGqVKkpUqqLoKoMrDUk2CRHWZRwgxyskmO1SoieWELlUL0SrFUsWmCZQJ2fAEDQX1/KTaoE17pwtQtbXbjKjq1OXF3FlO1jTrlxcQ0qsSKNmoRFoOBIxhILwVEoNBIHR4E55KJvj4CCI9BVN+OrblZyD7q+X+X8+Ut1bF9N/BVYbWm8cJNhztD1ZkYb6jr+LZHpyoqLKar6qDlvv19FMu1k3LChazb8fM6/TUxMzMnJqX+dk5NjsVjOCkIAmDlz5syZMwGgqqoqJiYmMzPTrwbQILy8IIQ1IS2dgkR0uYt+d5/6CYLD8Pgbua4DL/KHr8epFJ0kJadIyXGl+AQpLUEYlMggKdYixRmlLJMS01mOHShHmgIYda1AMWsVsxaSzv23uMrBFNUwhbVsUSFz+jBzyMYUW1GtHULDIDoRR6bi6GQcnQRBrTEqcO4WJneGOS+QymLvxi/dW57hQjtqE0ZyloSWO6M2dQwoXufJDUBXGV5Gpk+fPnHixMceeywqKuq1116bNm1a/ftvvPFGt27dBgwYAAC5ubnJyckOh+Puu+8eM2ZMQoJ/P2Y0CC8riOFNfea0XAoqXpvzxFpv8U7UdSDzrxdRtB+3owOIVJWR4pOk+IRSepwUnYS6OikxUuoYKg4OkVL7S4mhxHhJ3ZtsEiVEr4Toxa7/nAwsyGyBlT1eweYc4/duYz4tQ6ICsfE4KgVHpaLoJBQZ38q3HlFoNDP5HjzuZnnbt7ZN7zLaMF3yOC44pYVOp0mbIFTmSLX5dPeZy0a/fv3mzJmTmZnJMEx2dva7775b//7atWt5nq8PwlGjRlmtVo/HM3HixOXLl/t7ChqElxFGpc+a1kI7YxGiePJ/ceauwf3GcLNXgMHcEmc5L1kmBTnyif3KqV0k9xjoVHJauDc9VBoaJaV1k2MtgNvkXcnWxzNScqiUHApjMurfwFYnm1POHivnj/7AbqtARVUQHcMkZePkbJzcudVGs5HOyIyaAsMnKbs32b56lwvqqE+7BqsMgT8Rwsbed1k3PAE0CC8j8+bNe+yxxwRB+PscmR9//PHM65MnT9rtdo7j1OqmXATTILxcYE4d2U0d27cl6pZqC2xHPga9mn3gNRTVgkNb//CP8DtKooK9vWKEWUli16GKpS3NE2nblCCd0DdR6Jvoqv9akLnDpfyu06o/PmA+KkLhETi5O05qrVBkGNxrOO46QPrhv9bNT+uSR2sSrgj4dkKYNxp7zLbteItOnLmc8DxfvzTifAyGpl9X0SC8LCCE1QZ915sCXjERXY7ja70l25mJt+H+V7X4dFBCyOlj8vF9f4Vf71hhVpKQPZSYaPgFAs+I3WLEbjHO2wAkmTtUwu8sUG1fznxU+FcoprfwuhdezYybgbMHuVa97Nn2h6Hzjaw5wFdXfFimOn6wJ38LzULKFzQILweI4Uy97gn4rUFv2X7H4Y8hvRs3+yPQ+zcf2j+EKKePKXt/lvduJnrW2z+ehl9rYBmxa6zYNfbvocj/8QG74jncKZvpOhxn9G65RETRiezDS5TtP9V+8aYqvIu+43WIDeR/t77T9WLlUdleSkjTJu1S7QgNwkseYnh9x+sDu4Oa7KywH/5YBhdz57MooVMAaz4LKc2X925Sdv1IkOgZkux+a6LUMaLlTked199CEdk8qi0nNN/9l131Ik7tzHQZhrsNapFERAj3GYmy+oprlls3P6VPv1oVE7ixfYxNfe61bpwHMg1CqhE0CC9xmGWDU9WJQwNWoSI4c39w529mrprODrm6hdZFNOTf7p8ICJ4hyZ4XR4nZrb0VagtBMiHMpT1zhxjVnnGdPeM6/5mIX7GrX2u5RERaAzP5HtJvlGPFy+7CXw2ZUxlDVEBqxpogQ/YM+54P6MpC6sJoEF7aMKcx9bg9ULXJ9tK63W9BUjr31DIw+vccE5/YqqWt38i7fyKM7Bmd7nljrJTW5vYgxQ4vqnHhOjeudSObB9ncyObh6pyMzYVtLmzzILcAigJOCQEBUSEuCQBAkIlbBgCEEVEIAACHkZYBQMBhpGUJAHAsaBhgsGxUKyatYtCKRr1iUhOTRjFqiElDTGrFpCZmXRuJ0jOJiK0ufsMx7Xer2S8Wo8592P5Xo8SMwJ4LdUhlH3tL3vxlzfpFurRrNB0GBKRaVVQPoWy/t2Q3vVlIXQANwksYYlXGHnciLjB3VqS6wtodr7PX3YH6jApIhX9HrOXyhlXK7p89YzJdi8e2hfFPXOtiSuqY4lpUWseX1PAlVbjYBkV2hAAHs6yZ44IYzoz4IKQyIzYZcWbMWRjOhLFOixhg9BgAEIcYHQYAzCNG+4/0UgQiuwgAEIHILgUAFC9RPISIRKyRpNpaqbZarFW8NeDNJ2INEWsUqUZWakXFIaFwrRJplKKChKhgKdosR5mUKJMSZrxYAakEaT2Tsj2TsnG1Q73+qHbl09gQwY2cgdK7B/I0DMMMu57J7O18Yy4RXdqkkQGpVd9lulBxiAYhdQE0CC9hrD6SC0kNSFVSXWHd9tfZyfegnlcEpMIzSFWptOUzZdcGz5hM55rblJCLsQ2bQpjiGvZYOZ9TpjpRyhTVQLEdsYiPValjWW0HrMvA6tGcJtagijWzxsDsPoN5hPkzueVHnYpAvMWSp0DyFFa4C0oce8D9teQtEJQaAYVrlSiTkBjuTY2U0iOklFDCt+qvsBKsd03r6ZraQ7XhmP6NhcwaLTv8ZtxtUCCnE4d3YB96zbXoPiCSNnlM8+tDDK9NHec8+gV9qD11PjQIL1WIVWs7Xh2QqupTkAl0CpKSPGnjKuXoTtfkbNezd7Tmbi/ILTK5ldyxcv54iSqnFB2vYoI4bSeNuTMyTue0iYEMvIDDPNIkcJoEDuAfff0zAek4UlB3KM++WvCe9KAYvZgW7k6JldLD5LQIOUTXKk1E3pEdvSPS+S25hreWMT9+wA6dinsOD9QdZWQObchCgIBkoTpukPPY182vh7pc0SC8VGGVkQ8LwHzOlkhBUpgrbfhQOXHANaWb65XZRN8aEciU1HE78jQ7T/IHi6HUqUrRGDM5Uxajn6LWZ3ZgTRd5K+rmOxOQlsGa+plFRCTOHMFxuM52qKp2peQ+7CEMVjqFObOTxd7xUsfIlh1KRUgYklI9JIXbU2hYvJr9fhkzbDrT98qAPHg5sFmIGFabfKXrxDoi0QFS6hxoEF6SEKvWdboGoLkfcwFPQVJ0UlzzllKZ77q1t/udu1p64I6pcnI78tU7T6p25GGXYByoDRvCmh4xa5PDUDv40UYc0meq9JmqiBsa3vGWSPb93uqt+6zPbvcWC3KPaFfPVG/veDk5tOU2QxCzY63LJ3M78/Vvf81t+Ii58ham95XNP11gs1CTONR54ttmVkJdrtrBp8XlCLEqVWR2MysJcAqKovzDh9Kvax3/Gui+elTLPecBOQXuYLH6j1z1HyfR6VpdN23YED7oTrMhS9XsC4NLniqKVUWxIaN1ACBWyTW/uq1/7LY+9btQIihZEc4uSWLfBLFjREuEotgzvqZnPHeg2PjcJ8zuH7kbHkUhzZ0SFcAsRKxGEz/EnfczyGLjR1PtDA3CSw9i1br0Cc3coTGwKUjyjogfLxATdXVf3qKEBX4nZQBAdW71T8f06/fiIxX6XrqwQZxlqkbf2YTodtvnwYUwYRP0YRMAADzFUu02d9Uve2vu/1XmeNeVWe4rM6Xk0ICfVMyKrv7vTZov9ulfns0OncwMn9zMG4cBzEJtyihP3s+kOVVQlykahJcehBhVbL/m1BDIFBS98voPpB3f2x8a4hnXubm1/Q/klbjf84zf7ma2nTb100TerAkb3wFrLvkbfq1MHc1G3GCIuAEAgp3HhPJvckru2yNxKufIzu6xneXYoEZr8ANG7uu7CX0STPPWs69t5aY+hiLimlNfoLIQ80ZVdB9P4W9AN12j/okG4aWG5TWpYxBu+n9cAFNQyT0gffKCkBFk+3pWYJ8IgWTC7czXrd3Db8rVpqtjJmvC3oll9TT/AkCXziem8wkPm+p2eMu+OVJx03Y53OAY2917ZUYAJ53KsWbr+5M1n+/TvzaH7XcVM+bW5jwHMVBZqE27ylO8nW66Rp2FBuElBhGiiRvU5OKSvaR2x+vMtPtRt6ZXAgDgdojfLVP2b7bNG+Edmtasqv6OEG53ge7b/aqNOdo0Vcy16rBFMWxQG13ncElDGJn7qM191GnPmq2bXSVf7rBO+FnJirBd2c07shPRBOLhvQi5r+/mHZpifPoHbtFt/NS5qEPTf1T+ykJGpU0Y1rRKGG0IZ0kSq442uRnUZYkG4SWGC+3U5K1kiCzYdr3NTrqrmSlIju0WVy3wDE+0r5tNdIF55AWSieq7g6blW1WMED1ZGz4vUhXVtn44FbfiLZOFClm2K5JTAZlIdkIISHUKAEh2mVEUyU6QrBBAjAETFmEtg1jEagHxGKsRViPMI8aA+RBGFca0kYBHHAoeoQseoVM8wVU/OIs/21r3yg/ua7Id0/spQdrm16+E6GuXXKtZe0j/0iNM/wns6BlNvmuIzKHsg6+5FtzBGWKbvJWEJvEKqTaPSJ6mFacuS23rs4a6MMRq1M3Yg9F5Yi1JyUC9RjSnDfKPH0tbP6tdOE7sGd+ces5AMlGtP2x8d5MuSkl5wWAZ1AJ7nPqIgLtAcucJQrkslEtSuShVSkKp7K2UPGWKIoE+HAyhoDEQlRYYBgx6wgDRGAkGojUAIFCHEMwgAHDbgSjgtSFJBq8LiRJ43UgUQPQihxPZq8BRBaKLqIOxOpLhQhgukmPDWC6MU0Uw6hhWm8JjVWtPAsJqFDZBHzZB7ykU89/IKZu4x31dtuOmfoo5AHHoHpfp7Rdvenit8s5hbsbTSNvEGVXIEspMf8j+8RuWgU+hJi1Y5MM60wczUWehQXhJUUQ+pImDS5K9xFO4jZv3QXPOL615Rzy5teazGYGZGqoQ1YZjpjc36oLlxOf0IVe2yq4ofyIK8RRIzhzRleP15nhcxwT7CVFjQaEJxBxGosMUcxgxdiTmCGIIJqZwog703nCSF9msUFeK7FaoLUO2alSzG9dW4tOFyHoatJFY35Hj09TaNJU2ldeltV40qmO59JeCE+4z5b1xomzCHvfoLMfsgUpQc/93lGB97dLJ+hc3whv3cXNeRTpj0+rBnftKsetcp37QpVzVhOKIYTlLklh1rGlnpy5LNAgvJYwxBnFNuzwnjsOfMONmNueZEvLa/4gnt9W8PzkAXQRC+C255rc2aLXepGcNrROBRCT2fd7aP9zuIx53jmDPFXXBODRJiUuVo7KVqMlKRFLg0+4CWBUJioSgyHPM55dFqDyNynJRyQlH0bdM4euoOg+0EYw+jVOlq/U9NaY+Gs7cslOHVFFs+gJL/BxD/pK8sqsPuK/uZp85sJn75BEG2f89nLy2RbvkPv7uV5v8tGdmyn3u52epo3oxuqasAFFF9xRrTgHdhpv6Ew3CSwfDqaN7Nq2op/B3mZXYgeObfHJ57X+E3M0179/Q3BSsj8C3N2rU3uTH9SFXWppVW2MUL7Ht8dT95nH85qjZIwTHofReUmwvOepGJSIZVNo2uqiM4SAimUQkk65XKgASACgSVBagkhO49Ljj+HvsjjuRrgNj6Kcz9teY+2q54KtxfwgAACAASURBVJYKRXU0m77AknC3Ie/N3LJxe91XZ9tnDmhmHDruGwywBd68v8lZiCyhzIjJ9h0fm3v9qwnF+fDO6NB/2+j/PXUx0CC8ZCDE8OFNWainiC7HsS/ZOfObPEkhUCnInqqyzPtSh10p84xBw83NqeoCiEgcR4SazW77FnvNbiEkEVK6y6nXy2mvyrqWOmeLwyyEJ5LwRLnbKBgDEpGh8CjO3eXJWc3uvg+xJmwerNX31poHaNTRgf+lVsWw6QsscbfrTy06XjVhX+0Do5q5ZrT5WYiHTxK3/+gt3dOELZYYTRBWGWVXdRPOS12WaBBeOjDbtCd3O3O+xN2HoPiOTTttYFJQIbpPdhiWbkn+tyX6poiW2AtNrJGr1jmtX9XV7PZGpKO0XlL6LUrim7K6Ve88thLEQIdMpUOmcsWMhlA8scNz5Cv73seROpyxjDeETjTo0gIzofcMTTyXsSTIcUR36O4Njh/218yb0Jxbxc3NQoZhpj7geO9ZPjQDsSp/S/OR3d2nNtKV9ZeKTZs2vfjii3V1dRMnTnz44Yfx/1zTb9++feHChYWFhfHx8Y8++mh2tn+XR752EWRZnjt3blJSUpcuXVatWvW/BxBCFixYkJWVlZycPHny5MLCQr/aQTUGqSK7NKGYVJvvLT/ATLi1aWcNSAoyhdawW9+P/P2PPhujom82BDYFZbtS/pn9yJTiHdn5/MbyCVMcL+3wzl3tvuZhsdPgyzMFz1IfisNmyve851m0y337i8742qqc6wv2DcwveMXqzgvw1pr6TqreP0UmD3KGTXpHs3pvc6py3DfYNTxGePN+cNQ1oThO7gwds52565pQVhXZBTEBvlCgWkh+fv6ECROmTZu2ePHiFStWLF68+KwDKisrR44cOXTo0FWrVvXq1Wv48OF1df79RPkahEuWLFm/fv2GDRuWLFkyZ86cvXvP/gVYuXLlO++888knn+zcuVOr1c6cOdOvdlAXhlk1H+H/08CJYj+4krnuLtA2ZRJIAFJQIZrP94TevCx1itL983BVTMBGIBQPqfreefzO0h3d8sgXZVdeaXvhN/cdi73dRskqTfu9+4MxxGWR6+eKC7Z5bn/RFV1SdfCqgj398vJfDGQiIhbi/2Xq/lVY2Febg+esxBX2JlfVzCxkr7/LU/S7VOf3ZTdnSaHdwUvFsmXLxowZM23atJ49ez7//PNvvvnmWQfk5OSwLHv33XcnJyc/+OCDXq83NzfXr1P4GoTvvvvuv//974SEhIEDB954441Lly4964AjR44MGTIkIyPDYrFMmzbtyJEjfrWDujBFkfjQdH9LufM3KWYDbtJWas1PQabQGnrrB1GbtvX5KTJQHUFFIFXfOY/dVvp7p1OeZaXDetc+v8V9z1Jv76vbRefPLx0ylcnzhJd+dc94yh1ZVHXgyoJDo08Xv1crVEoBqT9QXcNmZaHexIy7xXHkEwA/r34w5oKbuCSfamX79+/v1atX/etevXrl5uY6nc6/H9C1a1eTybRy5cqKioqlS5fGxMRkZGT4dQqfrtBlWT5+/Hj37g09kuzs7I8++uisY66//vprr712/fr1UVFRr7766i233OJXO6gLY80d/B3JIV6b88R37MOvN+GZO81NQYVovtxrfGND0oPm2NlhAYlAySqXfFRX+p/a8Hhl6Dip2xOSrmUnnF4mEANpfZW0vsKUpyHnN+aPdcLul6pDrtRF3mHRZ/p9a+3sylmI/5cpZIT60N2bHVsON/muYXPuF+KBY6XfvncX/Kbp0N+vgnx0D9GaS7eYafsqKirM5oZ5bkFBQQBQXl6emJh45gC9Xr9o0aIZM2bodDqXy/Xxxx+r1f5NbPYpCK1WqyzLBkPDj7jJZKqoqDjrmMzMzFGjRs2cObO+oQsXLjxfbcePH//888+/++67+i/79OmzevVqvxp9SZMkv6/HUZMWTtTuWII6dW/Cxv/yj6uE3E1NXi/IVDmDHvqvUefI3Bipjg3AlpVilVz0hrVsla3LSHny+1J0utL8OtshhoNOg+VOg2VnLWz7r/TzFKemoyr2sRBjdrPWQgCAvpOq1w8Rp16uY294t+b5a4R+iY2X+R+O+wYj8Wd49xH+3iXA+fNjgzBz4/3O1x/RxPQE7MfFoiqss1NZ6W87CSEOh8PfUm2HIAgAwPNNvD+q1Wr/d6LKWYK6ZRli/Fvfad97+vtfttZnxxmzZs166aWXAMBoNLpcrvo367/5Z3Kx3u7du2fNmrVjx4709PQDBw4MGjRo27ZtmZmZvjfApyA0m80YY4fDERYWBgA2my04+Ox12fPmzSssLCwoKOA4buXKlSNHjjx16hTLnqP+1NTU8ePHv/fee/VfqtVqjSaQDy5o4875PWkEZlmLfx8uimCTXRXcDS/7eyrl6E5p6+qaz2Y0LQXZY+XB93wcN0OT8GB48zuCYo1c8l5tybLabqPk2etFc3jbuvkneEDyIpcNZAG8buR1giSC24ZUGsLwoDUBwxGVBlQ6YDnQGNtK43VmGHWHOPxWcec6ce1tXjaOj5sXZujarN4h5lHyXHPIENWBWV/YbhnkvLF3EyqxPzSUKf4Gf/EaO/lhvwqi2BSU0Mld8Icm3o9NdLHahFg1EfxLNYSQXt+K2y4EWjOD0BfBfJFCDvtVJNPoGTGo38rVX//9TZ2u4W5HfHz8mXt+ubm5RqPRYvnHcNDWrVuzs7PT09MBICsrKzMz89dffw18EHIcFxsbe/To0fre6LFjx/7eLa23a9eusWPHchwHAGPHjp0+fXp5eXl0dPQ5K+R5/qx/CXUBRBI4U4xfRdx5W3CPK0Dv37o54rJLq16oW9TEAS72aFnwXSszXjKHjm/uJ4XkUEqX1RW9Zc0YJM/4UgzpcHFSxFaJqotRdRGyFkNtIbYWoOoSVFeNZBHcLlCpgONBryccA2o1qDXAM2DQE48HCRLYHSDJyOMhbjcSRHA5geOJSoU0BgiKJEExiqUDCY4lQdEkOJpYIgkTiOc9+I7hoM/VUo+rpN+/ENdNK1KnquKeDjVkNSsOzX01vX6M3H31NiRIjlv8G6gEAECobv4Y9tr38cHfcGf/nriJR1znXv6yJn4g+HP9xZjilEr/PrKpFsKx3PlCYerUqVOnTp07d254ePiSJUumTp2KEAKAZcuWZWZm9u7dOy0t7bnnnisuLo6Ojj59+vShQ4fqQ9F3vvZObrrppldffXX48OGVlZUrVqxYuXIlADgcjkcfffSZZ54JCQnp2rXrV199NWvWLL1e/+GHH0ZERERGRvrVFOp8GG2QX2M+RJbcBVvYSa/5eyLpqzfco1KFnh38LQj1fcG7Vma8HBR6VbMW3ctOUvyf2qIlNel9pbmfi6FxrRSBigQlx1HePlxyGFsLUHUxqixBOi2Eh5GoUBIVBCmhENEPosNIsElhOdBdaEDx3G0WRPAIYHegsmoorUQlpbj4EDlQhcoqkdVKTBYIjiJBsSQslcR3VeKylFbY743lYeAUqe+10u9fiOumerVZ6g5zQ/Sd/xGHnmpv8dZyc4oxOKPx6yp1NNvz2/BdE7aDrDhmDfS3PUTL170w1nLvy1xSZ7825sap3SSNSqg4wof5MUuCD0mVqo8RhU4fbdOGDBly4403pqenG43GyMjINWvW1L+/fPnyG264oXfv3qNHj54xY0ZmZmZsbGxhYeGcOXMGDx7s1yl8DcLHHnvs5ptvDgsLQwg98MADV1xxBQAIgrBmzZpHHnkkJCRk3rx5t99+e1xcHMdxERERq1evbnQomfKRv+Oi3uLtKDbF37uDyvE9ysk9jpcbX3Ho/W0/Ex7MJv3VSWVPVATfuSJjkaWZKVj5tePk3PKMgcrNXwohLR+BNSUofz/K24ML9+GCozgsjGQkQq94EjUAokJJZJiiDugAEs8Bz4FRR6LD698gZ/6UZai0QmkVlFaiE8fRpu+Z3FMoKJwkdFViuisJXZWoVNKMhzE3oj4Oe18tbf5I/Ol6T/A1hoSnQuv3+N7/ds6vj+8JyTTbCpwZM5L7Pt218X9mKNv9i7BdE3YAyzhm+NexAwCxS4xnRBL65i1uyqN+FUTDr3P9/INfQcia4wHzoLj9bCPV2hYuXDhv3jyHw/H3/tXWrVvPvF60aNGCBQsqKirCwsI4v+4xA4DvQajValevXi2KIsuy6M9ZiEFBQWcWzhuNxk8++QQARFFsQjuo82I4PijZrxKugp/x1Lv9O4vgkT55se6ZkY0+X5BIUs3s+SDJ5iUPq4c33AqKZQqS3woKuqLpKShWyScfKZePue5d6o3LaqkIVCQ4uRvn7cGnd+O8AwgUyEiFrARy9RjoNEfWXbxb1QwDEaEQEQrdOjakoyzDyUI4lIsO/syuWgoVlSguncR2leO7K2n9iNYU+G8Rr4aRs6UBN8irX5BVOxlxQPDulw9vf+7AuC+GxF4RKdjFDzt+nTopPrhT4/1CVSTb45vwXRN+B4AmZKH9wStUE/+jHN2JO/oxR4zpMVz8aqlsL/F9AybOHEeUAG84QLUQg8FwZsLmOXEcd76bcY3y7yLTl4SjKRhYCLOM2Y++nVidQ5DMpPfw6yzSN+94+8QI/ZMabw/LsimxqoHdambP1997g+FfU5K0p3r0Owmo6SlY9YPr1MNl/caL416UWFXgP+IlLxzZhg98xx7chKLCIDuNTMqCzGuU8JCAnypgGAZS4yE1nlwDBACcbjhyCh3Kxfs/ZFY+ghI7K53HyF1GKqawAH+7tCZy8wIBoPTHH0t+fWL/tT+OiB4YDgC8gdOEqu0FTl+CEABUkWzPb8N3jv8DJNnfMVKi4eqevdL870Xc3OVI5fPlCcfhQeNdxzcbMqb6WALxesyqFT/ny1CXH7rXaFvn70wZV/5GPPIGv9YOklOH5YNbbN/M8vF49eh+iGGCV79QM+s5/ugBMRu2c7j341m+n/EMsVY5/WyF4xfn7a96k3sGeF2E4IFjvzL71uKDm3BCLAzuCg89o8SEB/YkrUSngZ4ZpGcGABCvADsOol+2MS++wumCSNexco9xcnhSIBOREHh/zpGZ/45K7aMtAQCAqgM11mN1Uf3CfK+ED2V7fhO+c8JOAPA3C4XeCd5e0XjdUvbae30vhYdM8P58kz5lPOJ9vb9K58tQQIOw7fNrpozsrhGqc/lez/txAlEU//uC7YkRvj9bRzO6f829C3W3Tuix5aGTNyz8Y13NpF9G+3HGP1X/6Mx9sKLrEHHSdwLf3MVsf3HWwKHNzP61OGcn0zGFDOkCTy0kwea2snqh+VQ8DOxOBnaHuTPkA8fRTzuYJZNZtYlkjpAzhilJ3RX/d1A4W84+l61WmnZHKOc+XSSZdjIRP876NeuOVN7o33gPH8Y0OQttjw/jxy/DXYbiZF+fdIH0FpTRx130uzZxhK8tpPNlKBqEbZ9fM2W8Rb8z3YeAP6kirV8mdLJ4h/nx4HsmNpwIYkztnk78nkOVnpTr4r4Zv3HCmmHRA3ztLkh1Sv4zFY5fnHe86k3uFZiOoKLAoU3Mtg+YvAOoT1eY1J30nSFfcG7nJQ9j6JpOuqaTB6fDwePo5134k38xhIX+06V+k5TmrFysLBU6JKs5FQKAKG/dntv3E7vQ/zm/H3gEzchColfXzRtpnv8CP/cDYH29FsQDx3hWvO57ENL5MhTQIGzr/Jwp4y75A499wvfjSWGutH297Su/d0iPHp/Ofv75mtV5A+Z373Rz0uEPcs3Jvk52r1rvzH2ovM94ceJ6kWvuJl8AAB4H/Pops/UjNkiDpoxQht2p8O3sPjVG0CWNdEmD+28kh06gT35in16CssfKQ26RmjZk2m2A4eWHCr9ZXtUhRbV8YVl5kfCfdakeXLqLRImIOXPY0ZWnTq0tHPl+f053oU8SPozp8WXYrvHb/Z1HKgxJEb4+jNd/yI67zcciOKWrpHikukLWFOvL8XS+DAW+b7pNXRSYN3Ahvq4MleoKCQLsz3MHxa9ed9w/WAn2b8FanOb00BvZHQsOdLgistPNSQCQcUuyLsKnSQ2n51cVPVF29xL39XMDkIJuO3y/mH16sKruF+aF28lHz8qjB5L2loJnyUwhz9+lfPaSkiLixZNUy+fwpSf8HirVG5k31qb+/lPdS/cXdMzW/ufn9JAILkasG+k8aZEbOk9lO6o23bNdkcmnA9fbTjcy30QVyfZYE2Fa/Zvqe/9uyNmeHC4d3+ZHAYRQj2Gekl2+Hs7rsf+PM6QuM7RH2KbxEd0Yg6/7EnjLD+Cuflxuk1OHia3UO268X02ycDU9TTsYs2Hyb2N8WWH9d/nPVro31s39wqsPau4dO48TfvmI3biU6dmJLJunxNHNG/4p2ExmX0umj0XfbEJvTVXFdJZHPyh3yPBjFDo2SfXCqrNnEWsVYbAr7xdtfGEFWnvtpkGLemTemrL/rZxP+6+/6rPBF55Ko4pku34Uuvva76qSw6RkX/eiVIL11i9uidgpIA+y5/wm2apYQ5Cx02BA572Ix136CbtfArjax1MwmhBFcDZ+HHX5okHYpnGGhk8WRRExbqSn4606iEfe4Xvl4g/vO2b3JeyFRgWE7YeEfTl8t3S+e0dgMEZKb/PvDJIBILRr0AUK/q/856vdG+oe+Ki5KehxwtaPuJ/eY3plKB88RTpEXj6zYAJOoyKTryQThqJvNuGltzAxmfLoB+QOmX7flCUEFv+7cPzNoQnpao4og1z5HxzQqMx80S/lHacldrkrLTjDrDI3fhtPn6lKmWeSn/iiauXsC//g/Z1Uaz312d11675BDKeJTheqi7RxnVMeWH2+qdEooaPitSmuaqw9e0vkc2KMkWLdaR8bQ12W6NBo26IQRSF/fU4xuobJ/vkHlp7a9/aFCnrtir0UJfm6hoEU5pLyPPf4C83Hc7z9ee39r4j7jltve67yynvEg7lZ+gMm1gYA1qN1+9/O8fFcUJ+CP9Q0MwUVBTYvZ+YNUIu78YpnlRfupSnoE42KTL5S+eoVeUgsem8G9+F9nMPq32Bpdbm4Z5uD5RpKcUS5pZ/7np3DJLe08e7tABAzONzH9YVRNxrNEYLuA19HO4VdRyoG3OosPpj0wIpu7xR0fGpj1mtHxJoy25Et5y2DMErvIVQc9PEUrDEWNXaVSV3eaI+wbbGJ1nxHDod5Dqt4rDKd/EprPajWR9urj4TGDb9AQaHiIErJBtbX32fpxw+cM3sBx5zvAGJ3Od74NOzXZdhiJIJoX7SiasIDeOUAuLYDANTm2vYuPpo+NUFlarwfEJAUrMjHnzzMqjxo+dPKxco/SYKicqiwIpcHXG5weZDTDQ4XcTrB7SIuD3K4iNOFNGqi1YBGDTotGPVIrUVaFdFpQKcBnRYMOhIXCfpmbUXXFGoebryKXDuCvPM5mj+Kv+4ZKXuMr2sGQiK45b90RAgcdXLRKW96Ny1HlKFigW1Bxmudvh/yak/e4EeQZLwe5Biy3T0kXU5pZJqxYrVZp88zPjVbO3kkk5eMihgAQJhRhSd4K/IgY8j5CuKu/bzfr1HHn/eAv2P0YYhh6ZSZ9owGYduiEEXPmSLUsYLiFYggiA5b3ndue7HXVdEh4+YLFPRWHkRDhvp4FlJ2Wj51yH3tnRdqic1BBBHpNACAeM78+IxeAx0/zPhJEzwsZkhE4rjY+NExmG28Y9H8FFQU+O2/7LqXmemjYfo4BQfiMb++cHrgdDGcLsF5hSS/kOQVobIaFG6Qw/WSllU0jKJlFR0j6zklmFW0LNFqFb1Z0XGKS8JuCblF7HRgRw12ibhWwS4ZOyXsEBm7gAtqWI2axEeS+FiU2AHFRSkJ0RDSKo9jUfNw31QyvBc88xK783M8+QXJx71p6ochd22xLZ1f8s736QYzwxElrSgfCMGcfwNLqgg2+UmT/MSXFatuA/a8l2IAIOzLYTMStZNHAoAjukBfEoMUxvr757V71sfc8H8XKIg79RRWLCKy4MvjrBldBBA6tNCu0SBsW1jMASF6zgQAjC48aFDD0vhtn4/Q6M+/jZ6iiJVHuYzHfDyL9ONHrpt7EfWFruKZ6DAuK8W+YLnxqdsAIEt/IG1SmFKWveXBnTfuHgcArZOClafRxw/zvAs+eIrERrTsp5XNCbsOoT2HIb+AnC5DNieKs0gdjN4EnWeUUYzrJcbohfN3of1T7mJP27jTtdyJQtVGB59XywkyigsnCTGQngp9sqBFe72ZyeST+WTld/iF0aqrHpQGTPX1YdFDxlsO7XTeNSZn9pNRLIte/3fRhFtCwzivFfzr4UbdaCxbU+H64FfHbRd6giCbFCMXVRC7Cxm0MuOpKPqs9sOPHcd/S37gU1VY/IVOoNHj6CSxKocPb3wxPtaGKrLgV/upywwNwrZFz5p4XcNkbkbfMHBEiKLIokp73s3BBOtxFBwFRp9mr5CqUuXIDverjU+rMc+/u+raR4BjEuaNT9XnAEDn2albHtgpuWVW03ggNDMFFQk2LmU3vMveNJa0XEdQluHwSfhjH/pjL+SVoG6RnuwgV99IIT5NDNdJLdf5DNdK4VqpV8Rf67jtAj5t4/Lq+EO/alZ8rsEs7ttF6Z2NemQQgy7wDWBZmDFeGdAFPf0ec/BHPPkFwRLhU8E5/xeT0aPmg5dKreXSsGssdz4VLdbmv/6EqcP8CM7ix2WCLwOkbFykZtyg8j4z2IQo6VQxAArtOz3xrv9wpsY3ykNd+nkPHvQlCBHDIk7r7xN6qcsJDcK2BSOsZhours/MlEEID7ph8wVKCRUHcZe+Pp5C+mmFa2oPom98zxU2PT549QvW6fMqD/xa9Xr30K5B+d8VhXS2tEIKlp5Aqx7gg3n4eL7cEltjV9WiHQdg6w6y8zAO1soDIh2zE1xdenl45qINkRl4JTPEmxniHQd2ACh2cDvLND98rX3+LU1UKOndDXp2huyOhA3or2xyHPnwWbLiW/zSVeqrHpT6T5F82Z5t6ATL0Al/jeSyoCRbHHuvKcr4Msb3LFRFsMnzTPLjX1R8PPsCA6TGx2dqrhmqVNUinYbPSrHkZXJlPm0Xizv3FTZ8Dpk+bcDNaEMkGoTtGA3CtovR+7o/tLfyIHPtNb4cSWoqlf1bXQtu97FmrlPisF1zyp//76eD1mMWq0z8hG+uaLRUc1KwviP481L2zuvJ1VcEYNvMvzueD2s3od92g9NNeke6B4W5Hhzjtqja4j6T0XoxOlmcmGwTZHSgSrX9pG7xH9pyB9u9Ixk1GAZmBywRGQZmjFcGdoOn32UOrMdTXhQtUX7/r133mMgsgp1XF3X+MoYN8jULo6Yay75pfICU65hw5rU9Jl9bHolI4z8WKDKO8LxkK2aNjT+ahzVGS7X5PjSZujzRIGy7GF3DouOS3K8NQemGoHNvMSM7K4noQrEpvtQpbf3SOyGLmHx7tI1CQj75udNDVRlv9hn8Ss+6Uw5zirHRW4P5z1d7fqx5cIVH5//sj5oyWHorH6lDH8+XQ/1bpnghkgQ//oZWfwvVtWRcfN38Xs4ks9Bac26ai2dIj3BPj3DP3VBt9TC/l2j/+6nxpaXc+Ctg0mgI1GbiSbGw/Bll+Vr04jh+6oti1nC/1xpe/ZAoS7D32qLOa2IZg6/TZzJeDbIP3e4Z2vHCS+yJKJE6Bw4xSxq3J7hSU+XTrrY4s49QftCXIGSMMYBZUHy9V0pdZug6wrbrTBAWHfvEWvLb+Q4TrSdwajefnrtECNn1k+taX9caqn84Yth4EAEBAEbFBHU0NZqClesctV/WPvBRE1Nw8Q2qMd3Q6w8pgUpBpwdWfYuuvgd9t1a8NaHiizGnZ2bUJF86KXiWILV8VaL9rcHFbw4uduQ4J9+P5r+NCkoD869hGLh1IlnyCPn0UW7v902ZFHTdY2LHzt4T95X5XkQVxSY+YDQt+enCh1WN+ZftuWX1r53hpWfed+T85io473pB1LG7YMv1pRmMNoQuJWzPaBC2XVjVsEK519hP4zLPuy+2UJeHUjJ8qZCcOqwYVVKST/fckEyM725Keczky8H1xGrl1KMVs171NjkFrxlIZowPzMMoamyw9DN09d1o9xbv/F6lrw8s7hvlarWlFy0tzig+kF356ZiCKFvdHU/Cgwvg4PHA1JyeQJY8Rj5/nNu1pilZOPlJUT7mrvzaj/tt0TOMqiMl3KGSCxxjfvk+04I59a89lmqFbVjzJ9oqc1+bSuRzLwHECelS1UmAxjvNWG3y6xGe1GWGBmHb4padZe7CQufJIvfpwuOf2qoONVpEqs1D8Z18qVze+7N7dKqPLVGtP6wLkiyDfX4+OMDJh8v6XSMmdPU7yepTcNJguGV8AAb6SirQomXountx4X7Xu1cULxxQ2inY2/xq2yCTSp7eseaLq04P1VqfeZXc9jhs3Y2avyIuJY688aj81TPskS0Nnw8Om/ztquqFDxR8s7xKkS90AlZFbl3kOTm3XKj0dZgRq1DCvQbje5svcAyXlYI0KpAVAABEPMFVRBIAwNJzgjoiufrXT89dzBgMKrXsrGy0DYwmiI6Ltmc0CNuQGqEy13ZQUDwMYhGrqizcvPv7Gbu/n+F2FJ+vCJEFxVaKon14VBNRlH1bvCN9epYFkolx6eaUx/3oDlZ85RCPuMff6/f2HGdScPrY5vYFa23omTfQjLmgL7d9Nqbgqd4VHQyX/3YhPENGJ9g/HlV4TXj1u8vlmx5Bh/x/3MRZUuPhvSeVDAUDgW3f103pdfiLpRWhkdzPX9csfLDgwmVjM8jA66Xc+yt8P13UTUZVTvGFO4Xub7bYFnxQ/7rOsePIkw2PNrT0nFC3/8fzlcLxnUTryUYbgFVGQoOwHaNB2IaUu4sSDRkddClR2riE6GHdR70/6IZf9Ja0Q788er4iUk0+ikgArvHbG8rJQ3KQWkr0aVxU9d0hXYhkGeBrd1CsVvKeMyhqYgAAIABJREFUqLh1kcffB9qcGRFtfgqu/wVNfhBMtY4vriq4LdNqVrfFuaAth8FkZLzjwxGF0zpUPvIiLFyGnJ5mVRgXBd11aPNL1U/OOHXLw5HLNnWc8XDkok+TN6+prS5v5PJi7L0i5Lsrv7T7eC6sQgn/Mpne/fkCxyCek041XBHK3QySu65y84dAFMfx39AFHtub1Emy5TfeAoQRe1k/xJm6IDprtA2RicTjhl9prLYAAMNpU3s98vOKHucrItaeQkk+jYsqezd5xvj0GHokE9PSzamv+dEdPPlQ2YBrxbgs/0blzqRgM0dESyvhhXdRZZm8sF/F5ToK6rvhcc7eke63DgZP+pf+oVvJ0F5N/95++0fNC68XrnojNeo6HSAAAEFQPC5Fkhqpk+Vh5kLPazMrTAO0fJhP9xqjphvylpSwB0ukzlHnPIDv36X2kdeVyhocagFEsNlQ/et/Ty+7hzUEpc399nzV4oRO4i/n7S/+40iVURZdvhxJtb7ff//95Zdfrqurmzhx4l133YX+eUN33759b7/9j2cSPPzww8nJfjzSnPYI2xAzH5znOOYQ6wgQRt0wU6aqcIvGcN7535ItHyX6MFOGKMr+XzyjfHpmr2rdfn0UMff3tTtY8YVDPOoee49/g5ABSUGFwFc/oZsfQ52w7f1hhTQF6xl45dHulc/2LH1rufLgC1BpbWI9T7xfuOjOuPFx5vh8BggQAi8/XNhziCE8uvENPGMzyKAbpNz7fZ1BinmUeK/e/M7G8x5g1OluGmu9fb536177qx8L5afTHluT9erhLouPa2LP+yuA4lLluiJQGt9B7cxvHNXWFBUVXXnllcOHD3/88cdff/31d95556wDzGZz9z/xPP/xxx+Hh/u6CLse7RG2IVHahAp3UZ7jKAGiOVSgOv21113ldVV0uWLx+YqI1lOMDzNlyImDSohW7tD4ogQkE9N/fklZbPCxzWKVnPdk+T3v+TcoGpAUzC2A+W8j1iO+M7Qiznj53wv0V9cwz0cjCz86Ypn2sOmOKWTiMOLXvEiFwNHTrmsGBgNASCX2eJW7Xs3b/7v9re98GlcAgKvmiPuudld8bg+7zqcfp6hpxrw3irk9hWJ27DkPMDxwI1kg1N7/ChMdFrTsSUIIH3LuI//C8ii0g1hbwAU10j9gdKFQdcyXdlKtbNmyZSNGjLjjjjsAYMGCBU888cSdd/7jgQHx8fGzZ8+ufz179uxJkyYZDL5+gtWjQdiGIEDhmtgwTYxbcuKEgUgXqtKGBUX0Yrhz72gsu62EyCik8T0i5X0b3aN9+vxSrdmvjwVTP1+7g7kPlQ+cJPk1KNr8FBRE+PAr9PkPMDujZkJy3UWf9m4XsE1gHAK2CdguMGpWMfKygVcMvGLg5EDt090EPCazMq1DYhwvrAn//hfm33eSuEhfy2IEI3qY3/qm7PZx4b8etD/+fgFSoTfXpYXHNN4drMfycOtC7ys3V5j6a1SRjX/UIA4l3mfwvrep6p2bzn0Eg41P3Gp84tb6r9x/5OjAh61EEzuJtXmNB6E2DBAGEpjVO1QA7dmzZ9Cghr2H+vbte+zYMZfLpdWe41PR7XavXr163bp1/p6CBmGbgwBpWb05aRxn6nDhI6WaUyjOhxuERJH3b/U84sOmi4SYPtia8rqvF1Plq+1yjuuqhX70xpqfgnuPoflvQ+z/s3eegXFU595/zrTtq92VdtWbZVuSezcGF7ANIWA6gYADhJbc3ITwJpAEuGAgDqEkEBKS0HHoIYSaEEPAVBtcMC7YuEmyeltppe27U855P8gYW7LOmVlT1tb8PsnymdmxZ/b85+mW9OMndfttX19GTFtM3Bmy7OiV2sL8gODFFC6q8DGVd/CaQ1CdSLNxqoPT0oSLYyGBhbjGxzReRMQpYpekOUXslnCeXa3OVWpz01U56a9HI0d75IcWtbzakPODG73nfgu+fzYR9X3vH7qm6uLb9yxb0TK62HrJt/w/P7corJFGooHuV4+SceT4perma7tqn2a3dwGAwgvc9Xe3CTs61Vr26x3353vxCT/hxk6lL0Ojx6vvDOtx/eJsdi/iJaIeXoqRyVdAV1eX17uvNtnn8w38prKycujKf/zjH4FA4NhjjzX6EaYQZinptg1sIYw0obHssB+u30b8Tq2U7ReVPmywODWd5qAaxntvCl69QtbvFFVlePBSy7nzySWnZaiCf3sJvbCSXDu1Z25xPLMz6EfW0I6QZUu3dVOnZXvIakFahRgv46Jj+ZSTU+2S6rBodk61c4whFSnCJ7AQx3yCCPG0EEmIa7udz2m+zrR1lCs1pUCeUpCclJv+StNcOQRnVoVn58fvWh/4yafSPf9HHDpyJAt94pu/G6dqROD3/RPzgkjlobXMwKWe8r/KprOTwVdj/tOdzMVIRGWXO5PPreu75Qzm4tQJleLmd9lCWFGr9D3MPBtnzUGIM8cSHj5ozDjO4HTNpuDut/71YVVV1YG/vPDCC5cvXw4ALpcrmdw3pyWRSACA2+0+5Hkee+yxyy+/HBnvjWAKYZaCEDuPSY13oJK5zGVk1yepeRV6PtT5n82l39PrFG39a9/kxVrZeAOupNf/LJS4M1fBJ19B/34DP7KoLe8rMwQVDTZ22zd3WTd1WXb3WYosqSohMlXoOc8XdXMZhiGtSLPy2sGdqLsAQCHcXsWxp939dIv71nQg16pOCaSmFaZnFSR8X40oFjrVe+a337Mx7+rlzj/eSBz6bvV+FSQEEIKCTi6SgyM5JBxSX38u1N6YLqm0LLkoz+Y49BMrSHDer+THbw36T3WCDgu48LuuvXN2oetVYmHsTuljK+3Pv87cwpC/iCQjzCG9nOgiOnrQmDBBRX3gajF0SEVN8rie6fc/9PiBvyws3OfHLy8vb2hoGPi5oaHB6XQO2IWD2LNnz0cfffT3v/89g2s2s0azEk7kLGz/pBppRwXlzGVaw8fyTFZOAQCSVen9+sDpumbfqSGt/bHwKT8yMM60bQe35in+/y7NXAVfWYn/csJXpYKdceH+Td4zXip7YJ2ztyW+iDT+PrDxBs/W852N062hjFWQgojwWCl6qrPtpzk7/ujfcKltp7M3tHIr/91XS25437+xy/ZV7MoI4OfTe8YKsat/g+JJ9voBMIHLf1e//MnWgT9WNPJvPhe6YOb29//d7/byH78fveyEHeHQsAXptfOwz4+79JUVSgHeOcEqfcDuEapW50O0HyKspFjEodwiNcbIX0UWp1lT/02BENht1lEHY7Pte1M7//zz//GPf4RCIQB48MEHzz///AGb79lnn920adP+kzz22GOnnHLKfvk0hGkRZiOI45HI8iNhBSf6BR8rlKLKsLdOmXIq80Old3Y7p9gkv65HouUvfTNO1fJK9e7VWIWnfyH+bCnJrJv2V6eCmMDGLtuLu5wbu+zTrb0/y9leJOjWhy8PhEiZmCgTE4ugM+Xk10Xzfr+mQOVyTxsTO3N0xG35MjM4BrTwno1w9W/02oUcgupS2ymz9xUYPPBs5y0PNpVWWU+/OO+k83wIwX03tv715rbr7xv2tezsn6cf/lVv4CwX0vF8FZ9r7X99S3oxqwsSh9QpZeKeLdz0E+gLUWGFFmmnxxqQ5AQ8spowHCksXrx4yZIltbW1eXl5HMe9/vrrA7+/9957L7jggqlTpwKAqqpPPPHEoGpC/ZhCmJUgjrMwhFCNdnK5RcAznE24Ybs6upA42Jl+rpWbi8/V1VxD6cWdT4av+JcBc/C/fxUL7HDKvEyMnK9IBUMp/t/1rpd2O21EnWvpOi8vKKGsyBi0Im2BvWuBvatJcXzQkP/k9tKZ+YmzqmMzC740hc5AC3/53X117qu3RW94pHn5ZWVlp9of+1tX/Y7k/95SfPl1hfde10o5fPRMHChUu56PFFxw6OjOgfhPdwrLGlEsxRwfnTqmWNrwCVsIiyu0PSyLkBMQJxDNwFNt8vWAELr//vtvueWW/v7+sWPH7g8BrlmzhuP2OTUFQWhrG7YVJRPTNZqlIAtjv9BiHXr8omTPFnl2CXMZF0vzG1ryTjl0ncYgWv7YM+t0zVeoV9U669B7f8vQKfpVqOCukOX2tbnnv1qyuQ7/wLHz/7xbF9i7skQFD6RcjH/P2fDb3E2lsZ671ngu/lfRy3XuhPrlfGcz85ECwO/+3nbHD8p/eX7RWXmem/9a8fwD3XIK2538DX9mPI1n/kxuuasXy+zHQMjhco51WN7Zw1ypzCjHuzezL7qwXE3oKO03u6xlMfn5+dXV1QcmwgiCsF8IDxNTCLMSrPES2yKE4grmmbSGjXoChNKbOz3zHIKbncwgd2tdz0RP/qHemBnR4MmfST85H+fnGhbCL10FN3TaLvxX8bJ3c929oTvyPrncXVcmZntXLTunzrd3LfNtWSLuXbWdP/Ol0ie2eZQv4/8jMy3s6lNm1TgBwJICbrOGMVEUXXe2agYurNC6novoWVx0rtW5chNz2UCYkEQZYUJUUK5GO+hrAGC4gl2Tox5TCLMRglXEFMJkJypkWYSKAo11yhS2ELpWbtLpF235Q2jOuZonX6+qvfWQ6OXg9OO/YRXsSgjXvx+4bY3vVKFxmXfz8fYuKzqSAkIcwHhL+H/cu27wfLq2nlv675J1HQYmZA1HBlp44aK8Xz/R2tYjf7g9+oMf7Tnt7FyHS2855DnXyi2/78Vp9sPgP9kubOngellzDTmkTikju7fSVyF/MY4FmbkwSEeGmslRiSmEWQo91RsAtCg7ZRQ3blerCpgBQi4U5z/ryj2RnS8q92jdz0f0m4NdDWjVw9xNVxhr7gVfqgqqGD23M+f7rxXlRMK3+rZMsfYd5gm/WfxC6sfunedZ6+/60HvNO/kdscMN8xvVwqvOKpxd65z6g61Lbtj57Vmeh34witPtVC6biEvG4K5/sNNHORvnO8lhfXMXc2XqmGLcsJGxSBC5HD+OMyZDcRYDjeZNjiZMIcxGkMgyzjDWokGUzwj+kd2b9QQIrSu3+77l5KxssWp/tH/qqZpLn5MTY3j2l+KPziXFus3HAb5EFdzYZfvev4ve28X/yrPtNEeLAFkXCMyMWim8zLulPNFz6cqih7d6Ze2w2swZ0kKE4KaLSjr+OT30ysy7fljuVrnnfix11eu9gJOvlDseCOkp2Cs62+Z8ne0dVWaUa3vYYUJUUM6soOBsZt/tEYophNkIJzBiFVoyiFy5QBnDNrBMX4DQ+frm4nPYfjacJp2Ph0+8RK85+M5jvF1GZy8ypoIrXkSvvo7/ekL7YapgV0K47r3A8tW5Z4h7f+ze6ReOttZZAiKL7B3Xe7ZtakBL/1V8mJ7SAS2sEuL/7zcooeO/iue+UL4ZJfDUNSLRd7uq52CboIXeZYdmfSfYucYQ39ZPX6ZW50OEHSaE4gotRhv8CwC8lAPom+sMa/LNYQphNoIkhpdSjXZxLHMQNA0adjMDhHxPnGvs8y5gpwn0rIwXV+OC0bqELRZC//2LePMV2JBTdN2n6KXXyV+Ob8+1HVZp83utjktfK/JG+2/1bZ5kZeykRzR5QurHOTvPsTb8do3vDxt8h5NEgwB+MT1YCIl7/2bMvjx3MbGraN0reiVk8UVy8G/sm4JElPdth+VdlneUQ+qkEtLwGeNsBWVKguEaRRYn4s2KspGIKYTZCFMIcbIHWEMnSHcL9nuYAUJx3V73HIeeMufQC+HjztRrDq56hF88hxSzOyd/QUqGOx6En08JHo4Kahj9ZZP392u9/+PeucTRetT4QulMtPQv821tbMeXv17UFhUzPg8CuHZaz0cbyYbtBrQQIfjRueSNPwo6G7NMO0Xr/SCpRtii7Z8v2TewW8wo4/yklbUsNx+nWMmlghX0NxQ3OYowhTAb4Vhp3DgVglyWELbWqzXs6ZTWjxsC89lbpxbFoTWpSYt1WRzxPvjwGeH7pxoToYeeQxNykvNKMq9nSKrcT94s2NEEy7xbqyRWwuHRhRVpV7p3z0SdV75RuKvPyHDIg3GI+BfTgnc+ALKRpnIzxpH8HPj4X7qMQqsTqmaT3tfZN9oz385/3IY0hhNCqQlo7QzDEXnzcZwlhKINdPT4NTn6MO96NsJJjDRuLd2HfAyRI+17lHF5zM+yrm/wzGOHl4L/iY8+htj0pZe//YiwcDYu9OtaPMCeJvSfd+HqKT0GjjmYlIaufTvgSsd/mLPLzo3EppEIYKGt82Jn3c/eyt8RylwLjytOVDnTK/5p7Kgfnolfv1evUXjMqUroJXZBoZTHi/misJOR5KJW55O2evoa5MkjyRB93CAn2sHsuz0iMYUwC0GcheEa1ZIhlBugr8Hte5Rqxhq+I4zisqOa3YAt9FL4mFN1dZ9KRtCav/OXnqZn7T40DZb/BX4yqddryTDGldLQNavyHanERa66Ef5MT7T0X+yqu2bVYWnhtVODL76FdjcaOGTmBAi4YeNruozCiSfivnUpNcS+3bnzLdK6vfQ1WokXRaOQoPoABBGsbi1Fi00iwWrq4MhkhG8aWQnHI4ElhPEeYFqEzfVqNWONuLYxZ76dGRZR+nH/+vQEffmfqx7mF0yHooCBHeWZ15BDVU6u1DWdYCimCg7i8LXQZ1V/OL739gcQNuLevvJMsvIeQU/6qMVGaubj4GvsoZK58yy2j1nxPw6pVQW4vYG+CnnzcZLmHUWinehMfjU5ujD3jawDIZ5eR0iwCukocufS1sT6CNFwPqNhqf3jOv88doAw+Gq0ZgG22NnalozC6mf4y4xMHOwIwlOvwPXTuzPLUjBV8JAcvhaePjpqU+Tn3zBwyOyJxO+CT/6j6z7MOlUNvRRmLvPOtfGftAMrHVap8bO9o7n5OMEQQnMAxcjE3DqyDoQ4RE2Wwck+5MwFardZ0lKnjWHP5RLXN3nnsQsnQi9FZp+qK/jzwVPCcZONVdDf/gD6Xk1/sSuTgX/ZoIIK4Xo1S53s+jiV+1a88IVI6X/ixR8l/Ttkd7tqT5FvrC7tMLUQAfxyWvDh57l2I68ol59OVt2vK2114vFaZKssBxnPlZDDWUZZxW2MTqFqbR5u3834yLwCjW4R8pIZIxyZmEUzWQdBwIm07BUt2QteRvCPtNQptYxMGb6xl+exrZKxbck9WnSrPP4h9psy0WDN08LdVxnwpr32Purt0s5bzLYMhvL1q6BMuO2yp0W292pSnyb1aVJEE1NIsBPZBrIVK5KWFrCiIj7NuRVOSnFSAiQC4Eayh1O8fDpXVAJCepKlz8t/HeN+Jlr6L4G6a1aNvntRV60vbfTwUpdywdi+ux723Pt/eg+ZM5nc/TRX9zE3egbjMRAsMP4EHHw1Xnw5o7FZ3gIptL5BmUornFWr8/HTHzAuLjegNW6jL0G8QFRzEtOIwxTCbAQJNCHEyRAzQIg7dyunMbI2pXWNPh3mYPDl2PhFWNRhVGz+L1foJTWVet+p+yPoz0/C3cd1C5zh1/CvUwXjWNia9m5IeHfKOT4ccylRK47aieLDsgVkC2bYsiriU0hKc2KaszSCtENwPi+W5HHyLHtomjVU8BXPAZ5weFp4UU348lWuN9fwJx6n6x4hBOcvxu+t4JlCCACzTlH/+WiYKYS5c632P9THfjifskYdm4/aWkDTKBM6kbcAp96nfxbiJVMIRyCmEGYfhNDnouFEiCtnFRG2NahjTqKvsX9cl3sa24vV93J48RW6/JYfrBAuXmxA0v7wNzi5PFptfHeWNfSzVfmur1gFU4TfkMz9KJHbqDgDWjhXCc1X6iViuDBDIJqTJJ34c8GTgQDqFVybU7lviLU2pM20h+bbg19dE7gJlv6lUH/Nqqo/ndg52mNsl+c58stp3b/8W+HsKeBmd2UHADh1AXnwp3x/l8ocUVI7T4v+Ukl3qJZC2kaUM8eGLm9CaZVYhl1GbCLOyyHBVkonepSbr1FjhDCQOJoeWRWoJmDGCLMQQjSOahFqShg8VLcnwaSzQxvFcI0Kn7bnzGJ099aiOLxNqdFhDfR1Qtse7viZeoWwqR3WbSFXjGe1iDwU9230Ccn0V6eCbartyf6KX3RNfSvkcUY6T4h+PCm+q1gOZqCChwQByVMjNcm9CyIbq2N1u/u5X/eM/31P7aa0j5CvpLPJFEvfeY69v3onP64Y/j8bl5s+tiDx/Eq9F+awwoKZZJOOOgpBgpp5OPQOo7KedyDLKKuwq4u+TK30k64WygKUk4sTjNkjiDdn845ETCHMPghB1G7aRI6Cm9Ymn/T3Qo6D8voMACiahnDaVsGwCMPrUiWTQLCw5W3LG/y8aUTQ7WJ44iX0nTFhK2/YKfpOs+ODFuslzq9EBRsVx23BcXcFazv61TnRLZPjuwqUEE+twj5McrRYdbJxQeQTS6T7H71F13RNfTte8FUkbMy09dYIods+pCUbD8fS6r5/vI6Sab1auGgG2bpS1/2pnaXGPmS3mHFNFPmdDCHUyt2kh9pW2+EiSpKeF8ocf2ZyVGIKYfZBNMTRInKaHEVO6ryYYDsu9tE/RNjZYRvHriCMfBivnaXLL7rtP/yiGXo38GAI3vsYnV2la1j5gXTEhLvW5f7AtdvGfclp7pigV6Ml9/TU5ES75kc+GZ1useKvL1bEEVys9MyMfjo5uvON/rzf99T248E7crcC70ZJdybZtfs4z9m0t1d4eQ+jqGYo5W5lUl7y3+/qXT9zAmndhSJBtnCOnY3DOoTQO5G37mHMjtBK3SREXYM4ZHVimeb5RELmXQhMjlxMIcw6EEKM0ohUBLm9lAW4t10tZmx24s5u9wS2+RZZkxg7m20Pxftg72fczIl6hfDZ19AplVG3xbCldff63IW2jnKRXYhtiG7N+puecRsirjmxrUVKD/rmcuhdOD4rtg3ikZu7Jm5M7XubSWK4pQ2fVac92UOWNmhvRzK8PAHw5a7dD2zxhFKGizouru57+lXQ9L1+SCIcMxU+XcXeXgKjCE6QdCvD5+wcb5F2sSooSry4r5W+Bjk9OE19/eJNIRyJmEKYfbAmQeBUmFAtQtLboZYzMvGsu9tyJjB2Q5zE0V1qxRS2XG1dxc+eTKz6vErxJPzrXfjuGMPTkdZ22OpDwol2xoZolPfjgd8Ex7viPVNjn1m+RitwOBCQqlTrlPjO90POpAIhFS7di5tleH40/2gl90gFf3sHljNV6kIheaw1+OeNtBepQzIuNx2wqG+v0+0dnUY+XcmWW4Sgajbu+5CROusYb0G7egHT/tm4xEuCjK6k4PRgmdbAiF65ZHK0Ygph1oE4atwOa0SVkZ3W/Zr0tWqljFnb4p5O10TGy2//ulTheNBTOLFtJb9omt69+Z+vo2MLE/kOY4knsobuXpf7XedeEX1pEbuoJv6xt/pf4cLp0R3ladYe+vWSo8XKo02vN5GfNuICER6o4IpEAIBiCWIa6BhhNCyn2lvXt9s2dxvOCvnemNDfXgSi7z4fO5Xs+YRLRtjCWTtLi37IMPGFHI7PFflWWqqLVuqB7m56W23k9uIUzSKk97Iw+abYsmXLZZdddtZZZz3xxBPDrXn11VeXLl165pln3nbbbUbPr1cIMcZ33nnnsccee+qpp37wwaELV4PB4P/7f/9vzpw5J5100osvvmj0Ukz2wdOEEMsRZHMBddwt7mnXimlCiFQM9f2OGoYFF/4wqSdAmE6gneu5Y6fq2iBlBZ5bCUvHGjYHn/ospxDiEyxf2pTdbemcZcGJsXh6dnSLC3/JvtYvi/UK6ZXJOTzaP1fxhT5SZUF5h1H3ZEXauY7G363L07CxDNVjixMora3fpusouxWmjSfb3mHvMKNnaZE17GJK53gLPXGUSAK47STcSzuL20u3CBG1csnkG6Gjo+P444+vra297LLLli1btmLFiqFr7rnnnquuumrhwoVXXHGFptODfwB6v0/33nvvU0899eijj3722WdLlizZvn17SclBjR4SicSCBQvmzZt31113pdNpWf7mXUxHKIguhClWpgwA6u6kW4R8Q49YYuVsjE0qviY+9ids82v7u9ykGuLSV2S28n1U7ZWrDFazdcWF53a6b/B+auio4VAI91y4bGPSOz6+x6cZTtj5OvmUkLkcCsbg7SYyowCaCdzXhX9feriOnJm23tX9BS/Wub4z1sA/HwF8d3T/Ey/6Zk/UtX7hNLJyJT/zDMauVDSWKGEt3alaCqjVhBN5aVdn+sRayhpc7INgO3iGbyWR48EdNNOf463AcWCo17jJV8xjjz02f/78X/ziFwCQSCRuu+22Sy+99MAFPT09N95449q1aydNmgQAS5YsMfoRer9R9913329/+9tZs2Z9//vfP+mkkx599NFBCx588EGv1/vggw/Omzdv8eLFp5xyitFLMRmAnsCN5QhDCOUUSSZxnpOyRNzV5ZzIMAdxmoS3K5U6HJ5bV3L6/aL/+A98d7Th2sHfr89dbOvI4w2X3g+lQXHe2D2pMcrNiW7JchUEAOHzd9WEAg81k6ua8P8GuGOcX0Kt4fnOvQ9v8fYmjZmWJ5bHGppREyN/cx/zp5PtaziZ1ScAIRg1g4RZYULXBMm6m5ELo5bkkF5aCBk5vVihZo2KEsA31h7W5JB8/PHH8+bNG/h57ty5n376aTJ50NOybt26srKynp6en/70p7fccktXF6PSZii6hDAcDjc2Ns6ePXvgj7Nnz96yZcugNR999NHChQtvuummc84554477kilvqo2GUc9iJq3htNRoKaMkp4OUuij+07F3R0eVqZM5ONUoBosNobCqWm0/X1u3nT6qn1sq0OJOJmeb+zZWNdhq+sVTnJ8CTkyW1Oee3uqK+JN4xL1usYFfdPM49AbGnkHk+c08m+NnMKhwhiSv4wLLxISx1m7//IJw7swCIEjp1ZGXn5L1+IcF9SMIjvXsDeZmtla5CNGEYVzgoVcqY3gAAAgAElEQVTfGaSvUcsZQghuhhACZ+Go3x2Tr5/Ozk6fb18GdW5u7sBvDlzQ1NTU3d195513zp07NxgMTp8+PRw21r5Y1/tgd3c3AHg8+74zXq93qOS2tLS8+eabv/71rxcuXLh8+fItW7Y8++yzhzxbfX39q6++WllZOfDHWbNmPfLII4Yu+ohGURhRN7pFSOQ45NJTRju1EkZOoKWuw3UywyKMfJSsncnOZ9mzHo0qg1yPLovw32/DGZU60icOABO4e33ud50NAhyut6pedj7SVzUlvtOjHTE9tCoROpdHnxEyCsFpPGcH6EuRD1rQ/FIQeQAAmcDaGFEIHONEDoMe0yWO1pvbp+zqs1R7DZjap4+KXrkq56rvYWqNzz4WTSdr3+AnLWLcu7GztFX/YFiEtjKBxBQUSRH3sGE8rdSDN7fSXvHcPqLS4sFIkAiinYAQEo1mODgzGxgIWklShn0D7HY7P3w3130f4S1FOjPIP6chtv3Ndz6sqqo68JeXXHLJsmXLAMDhcOy3rAZsQafzII+XzWbr7+9/5plncnNzzzvvvNWrV7/44ouD3Kd0dAmh2+0GgEQiMfDfF4vF9ovifpxO58KFC6+66ioAKC4urqmpeeSRRxyOQwSOKioqFi5c+Ic//GHgjy6Xy+Wi5UAeZYgiq70nta2MpsTASeudRsK9Wj4jXse19NtGMSruk9tTpSeytaf+Y25mtV6/6JpP4E/zjInQ+k4bj7XDz5FJE/6hUFVtov4IUsEBChAUHGyjhNNkczfMLEQhFX7ShGOYjLKgP3fhP5TxFUaq4KxIW2jreH5Hzo3HGhDCYqeSZ1c/q+cnjGHf92njyDN/ZQtm0VgSbdJwmnCW4V+TEFjKLUJrnzJu2PliOODEEdp4Xq68xrr4KqAIGauzDELoiN6vDlMI9dBQ1JjQWCOxDoZM7j9mztSHHjwoI3TA+AOA0tLSxsbGgZ8bGxvtdnte3kF7YFlZmc1mO3B9T0+PoQvQ9Q7p9/vtdntd3b450fX19eXlgzvbVlZW7r+OvLw8ynsTz/NOp3PU5/j9jCEJIw16+QTR0mCnxf9QNKT5qbVQmJDOuKWY8Q4U35UuHMMWwpaN3PjRzFUAAI1twBEoMzh38IWd7uOlL8Ep+lR/hVuJ5KuMVpPZDAZ4D5OBF+OWCLRG4PYO7Bfgn6P5e8u4HwW4OzsMG81zbd3vtTqjsjFbclYgsXZwbOTQjCqF/iBKhBleAF4ETwlKNDCeDWupwLfRXomwz4EiVJ8YQthmw9qwznmEeGa7JZMvHYTA7rCNOpicnH3F0N/5zneef/75SCQCAI899ti5556LEAKAl19+edu2bQAwf/58j8fz7rvvAkBPT8/atWtnzpxp6AJ0fQE4jrvgggv+8pe/AEB3d/fzzz9/4YUXAkAoFFq+fPmArXrxxRe//vrroVAIAJ5++umxY8cWFDAmJJgcEoZrVE0iG83gw7EenEdbwHVHea9Ee/UGIAqJN+P8CuqFAhACe7dz46p0WYQfbUHHFBirUuhJ8lt6LDNt1IR4HWxOe7elXGOSTYd5nm+WHgI7CEl+/p+9qZusj5GfFiAJAQBMtKO6tOEyewenTrL2r9xLe7UayjEF8XWf6PosDsHYUaTpU7a2FI7BiV2MXGJHOce103QO5zohcuh3nf5NK3f+5uSNlwdW31mz6omp7zw967M1y+TkkEeLF5CphFnGySeffNxxx02YMGH27NkrV6689dZbB35/++23v/XWWwAgiuL9999//vnnL1q0aOLEiZdeeunxxx9v6CP05owtX778tNNOq6ysDIfDV1555dy5cwEgFArdeuut//u//2uz2ebOnXvRRRfV1NT4/X5Zlp955hlD12HyBXTnjJYCK10I+3AubVoh39ZvKWU4RhL1Sk4xu9d2dyNy2kkuo4nNPtZtgtMC7K6SB/Libvdsa68FHVZySASLf+urnBTffURkx1AIIPgB/0VgTtHAj1CbDFUWAIAne/B0eyY7+DxL5zM7x3yn2kDsdnJeqn4NF4ljPYOZJo0ijZu52rkMa7V0jLaTJYT2Ul78jGbTY48NEsmhUwmD76xo/fuywtOvKf3uclfUKdR3pZM9rbue27zqx7OW/P3AlYgTzRH12QbHcU899VRDQ0M4HJ44caLweWv/N99802LZFww4/fTTFy5cuHPnzrKyskCAMbd8KHqFsLCw8OOPP25tbXW5XPst1tGjR6vqF/kUt91223XXXReNRouKioxeh8l+GOUTahLZqM0vor3YN4ry90J72FbG9IvKhToiQE2b9fpFFRW27kG3LDEwhFbD6NU619Xu7foPGQoBeLSvqjjd7dGO4ASH/Qyo4C5CrADlCC0G9Pt2vNaN6tKwLUFWjMqkvnCMFEVxvKnbNi2g9+6IPEwMpDdul06YxX5IJoyGZzbqsAhH4y1vMtKJrWWCtIrqHuAQdtohHgb3QSHw4Dsrqq5+yj1uAQCIzWFrt2RzlXoCU95/7gQ52SvZvpjIgThBb+8ck6+XUaMGb2sDySv7cTqdM2bMyOzkxr45JSUl+1XwkLhcLlMFDxOGECpJukUI4X56ESHf3u8sY2xMiZ1yyRi2/dT0CZqkbx795p1Q6VVdkoEg1gdt9gCfLDq8Ae7vxvM7UuKoFKP+7MgCAbyBSQIggOB7iAursDlOlhVz1dYMfXrzLJ0v7DSWADLbH1+3SdetnzAGGraw95nCMTi+i5GzYy0V+DZGWjzJdZEh3lHE8fvljfD7Liad6NbUBD9o9icnmJ7REYg5oT7LQIjeWQZYQkjCYZxLMxnFjl7rcYyNKb0rWbyILYSNn3Dfu0DXbrhuC5rtN5au+cJO13ypzdAhgwiq1pciJTMS27/BaRJfBWMR6kTwsIorEeoGkojCH8u5OYdRZT/HFry+s7Q/xXuser3HswsTz33oAx01LXkeIglcTzPKK6PdhfxKEm/GWCacNOw/xFYuklaGZU98DhINITgoET+w+Ad1914YOPGH9tLxUopHe+qjoZ2dDa+V1i7lD24uinjJtAhHIKYQZhmIo2eNYiXJU5JlVBkpMnHS+iUK7X3WMkYJR2KXUvA/9CWgpqFjLxpboWvXWLsJfjnOgG3XEhXr+sQr8jKZXz8AJuj+vqqqVIsTH5ZNmZ3M51ANQu2EjEWoCiFXEsBYvstBWJF2mbdeQKzCngOocCtYxc0dqKyQ/QCMH00aN3N5ZTSVFSTIKYZkg0Jpgcu7OCQgrj+BPcO+6mm59qH5MrlzLxC9hcF3VoQ3r9QiIQvncXpGT170J09g2qCViBPg6HptMtGDKYTZBod42k0hcgKswxt8kX7iYfi4uPaIrYxWREgUEm3S8lk+z+ZtqKwULDrqkXrD0NWLanMNFKu9uNt1nC0ooMy3pJejxbKMS2XDzZaOFAIIAp/XF27utz1Pxtzo357xaI6JQijd726VhM44dklofK5g5Rkm5qyC5Nqt9rJhi/q+YNIo8tkmbsbpDHOzcAyJ75LpveDFEgvXEaEIIcmzkeghEmrc4493jz8eAPhw2rl2eFe5GSMckZhjmLILhBChvJhjDbAG0rAGH4n2EffhFhEmGhRPETtldO8WbqK+won1W7lpBSlOt6rJGnqjwTnP2q1z/VAaFce78cCERF3GZziysOMkklMvRErYSw9Fuww3t+HxL/XPeCZ4xVv95/w7VPlY95vNjBeXYwIJnUUUE0aTpk1sz23JGDWxk5E4yiwl1Hw2iNMyS4lA2/QQJ9IHOZkclZhCmGUghLhhOxhhLY0kms7hjr1A7fLKheK8S6QXESYblMAo9gbXsY2rrWCuAgDYtI1MzzVQOLG2w14sJvKEzNvVPt5XWZ1slLJgyu7XRm2iYU3SH1QNTxHalCBLGzQBwZ0lqOP7/rrvBxovy3/8W54fvxOmPwQz8hObdvF6zKfqSmjZxTFXFlQSuZ5x0+2lPN9Ja5WOvTacGKyUvauf/eTKQi0ZBQAQaQ8/4nliWoQjD1MIsw0EaPibosn0BmzIYlfH0rJ2UV+Cz2X4w9Mdqq+AvReEWrhifeU6e1tIlceAX3RTl7VaMNYz90BaFHufJhYqmccXj0REohbJwXcThvs0PRYkV+VzNxVxMxxIi+6rhjqpzCJrpD9Fs43cFizxWq+O5nd2K9hsEO1hGIWeAqJ0MtrbWn3A99HaMmCHBdKD37qcY+dU/vAhTrQAAKH21CbAmTHCEYgphNkGAm5YoSKagkRqUC6dIHZaygMXTgpeVs/coObNY2cP9rRBkV/XltHYyVW4DXRW+6TDMlrMfEDSm7GCUrlrBG5npamu1fGAavBLncIw+vMOpYl+BQAwgT9tjtsE5LEyTlXpUffqS+wtyIdQK0MIc/wk1c1wS4o+jo/ShJA4JDJECC2BCu+M05AgwQHlE4fkwEILk5GDKYRZBze8RUiwAgI1tS+VIE6aUnLhlOhh3HStU3Gz7AqsQjgEAUbjbgCAUAQIgP68/KTKNcekSinDkfFJzH+S9hXJmccXj1zsJOXCiY1JHXflAE5wo7s6yNsRsilBXtybvuHDyNRngg9vSzz7bS8zrFfuUva26SrbKMzDPayVbj+kuhnPiejlhH6am53YJUgNXpDqrGv753ItFQMAQPt6qClyZP1rFyipQQFFs4pwJGIKYfZBGW+DFRBo8wVIOqE5qRZhX0LyMW662q24A4yX4lAH8noRax4LAEBTG1R6DJiD23osFdZExkOXPkr5/WrYgo219j5qKEp3vhU31l/qglx0Ug56sodc34IfalNbw9r/zXSu+27eFD+7mqLCmWps1vUpxbmIaRHa3AQrgJO0Wy94eRShCqHDQtKDC2aU/s72F3+7c/lJaiQICAamdYqS2+Ys6Wp6c9BixJlaOOIwyyeyDIQoA7KJpgDdNZpKAlUIUSRpYRkM6U7NwxTCNlTIWjPA3jZU4TKQtLK5y1rFZe4X/TDuK0gfVhn+EU2+0veZUtWnSV5e7/85Arg4D12ct2/3L51gd/v1DnOqcCvvt+haWZhHNrCEEACcfkh3Y1v5sO9qoodDYVpCDXFIkBoshJzFYa+cmjP5W58tWzD2un+5eR5hDQA8gamxvqEDg0whHHGYFmH2QbEIWUJI5Dh2UF2j0aTkYXzP093Y5WcYZL2tqChPX4CwBcodBjJlPum0jJYyFMIIFjtVe66aeaLNkQ4CElD7NqeMeUcPZCBMqJNyt7xX34yswjwINbMFxuUHuYt2AYKH5yIMIUTJwULIW504HS857+aCJT/bccvCUMf6gd8nY22CNLjulj6Y1+SoxLQIswsEALTyCQVRJ2oSOU7stPoKMRIXq6lvPwRSIc3F2khDrajIh/QkpDS2wKyA3r0VE7S733pZXoazczelfH6tnxt5aTIH4ldC6xMFJzg69R/ySZy8GyU/L+AAIB42YL777VpKRtE4cbHGUBQFoLeN/dqd4ycyNUwoeDhCvUJil0hysFJyFsdAgDCw+ErJV7T1j5f48mfykrNr7xuzT39+0GKEDqOPg8mRiWkRZhcEAA3vGgUs02OEkEqAnaaUfCRBzxpVejXJiag1GgAA/S1cob6U0b3tUOHWu7fuDYseQbFzjBz64Vif8ObJI6tqYih+tb9JdcawgX5pIQ36NVAIAEA6rhGsVwgQQLlHberQMVzCDz3t7HxMjx/LXVQhzOFIXEHasCciVhFpKmgHnYS3OvaX53qmnTpn6RtOX7UouWd8+3GnZ+j8FHNXHHGYtzz7oCXLqCAxkmWwg7YAhZMiVQjT3arLz97XQi1QqKNiLZlGkTjKd+gVtp0hS6WYoTmYxPxexeVXddS1HdVwBAe08Kdpj/5DFrvRr4u5gUJzgkk6rhGAjd3KliDblC93yY06YrI2C7FYSSzEKiX0Y6Wb9rQgDnF2HmJU76jVCgfny/D2nMl/+iIWKLryq6ZeVT37hhz/pEN9hhkjHHGYQph9UMonNBlEuhAmCT1GGEkJ1PIJuUtjpowCQG87KsrVMbCwHUq8qv4svB09UgmXoRBuS3v8OHKkT9/9UshTQusTXqNHbU6Q5e349524qUf+n1XhxS/0Ln6x97o1jHhtpSPdqG/IVUEAelkrc/xE7WK8NvFekR4mBPshEke/IBZOt22mHU7paGFylGLe8iyDEEqLNYIxCDR7DqkykWhxX5RQeAdNl9QwtrnYChfpA68OkyMYggK7AT9nW1QI8Bl2VmtUHE75aJi+e/h4lUizqmN4/AFsSZCfNGEAwAQuWR3b3a+2X5m/65LAi3Wp9jjt3cJvV7uDulyp3hyI9TLeiRw5RO1nvMogO4cS1DChRQRl2Pws3LFX/uw/tPObFuHIw0yWyTIQAjLs9xCBRkmlAQBQVaD2FAZVQyJtAU4TK6vdNiEgy8iqY+5EPAl2wUBFYCTNOfkMSwB7VMlKMizDP8qwEDlORGzkPXdVhFySx13pRwDwRJLXXKJNQDYBLSiWPulWiiqHfersEqb2uP4CqwRyiqExvIhImvHAcCKHVOoanhsUIzwIxGiiRszyiZGHaRFmG4QSoiCY0CKI+0xG6gKZcFQB05JEsjKEUJVB4OkXso94wpgQRmXezmXo2wxpopWMoC7bFDggImiG8mUkBPtjx2Ns6LW9qVAK96bw+i7FLdHutF0gCX02vN0CMmulaCWY2uAUAJCEQKG5GYjAAR72KUIcRzDtI0wZHIGYQnhEQTBDfzSNPmUGVA1Ru++TNKGX7ANAOo4s1FlP+4mnwM4bEUKFc2QqhGFNso7UhjJDsRO5XzMghDMd6OU+EtEgjuGFDuW0UdZxTwZHrege4xGOLaQ9EE4RJ5K6tMNqATnOWClYAKcZ72GcCEC1CBHHkeGFkHA8a9CSKYUjDtM1ml0goCWtEYLprlGENYZSKpijCqGWYluESgqY7tMBkklwGBHCuMZlXDsRJZJpEe7HSpR+TSoT9U6/muVElf3kW7s0AjDDxf32WPf1M5zBJB7rZWwRNgHH9VmENolQR4QBAEgWwCnGo4VEhBTa2xIReKQN+xQhhBiDlswY4cjDFMLsggBQXkgRYbhGQdWISA0islyjJI3ZFmECrPqacMUSUCjqFcKkynGAMusymsACAuDNlNHPkTS5D+vtlAYACGB5CXelDCqB6hxe4MBr5bys6RMA4BD1CqFdRJHhczkHECyEbRFKCKhCCDzNNUo4HhjPiSmEWceuXbv+/Oc/h8PhM8888+yzzx70t4SQ66+/fv8f58yZc8YZZxg6v+kazTII1SJkJstoGvBUzycrWYbIWGJZe3IKWfXNf03EDcQIozJy8Bmag/1YdICBRm5HPSJOG3KNDlAmwSgLtKek1pjeV2S7SJJpXcphkUDRYRFqrNvIiYAU2kNFBFqyDEIcofceMnUwywgGg8cdd5zP5/v2t7991VVXPfvss0PX3HnnnVar1ev1er1eu91u9CNMizDroI8NpRc5EYyBMm6NEIQBUe85SRHByRJC3RZhPAkOm942JRGZd/IZmnT9mmQlZoDwCyya3KMO7qKpk3Wx3N31jh9M1pUMahNwSgXMCl4DgM1ClBgrRmgFjeUaZVqEiOMI0Yb9JI6jxwiRqYRZxooVK2bPnn3rrbcCgKZpv/vd7y644IKhy66++mqv13D57ACmRZh9MGKE1G8pPVlGwUANEII+16icRHqFMEHsol5ti8mZBwj7sGTRzADhF1iJ3KfpKHA5FHZODaf07gwIwCZAUoc1brWCzHKNihJhWoRIBI4RI0S08glW1qgZI8w21q5du2DBgoGfFyxYsHnz5tShos233Xbb9ddf/5//0IpEh8MUwmyDUMqYELCSZTQNhh8SiBSG4xQASIqILLennCQ2fXtsIoUcul2jEYWzo0yFUJNEUwgPwIqVfpypECI1IhsQA7uFJFgKBwA2CWRWfqlgRZhVR8iLQKhZo3TXKCAOUS1Cs+N2ttHZ2Zmbmzvwc15eHiGks3NwT/kLL7ywtLTUZrNdeeWVP//5z41+hOkazToojS0IIQyLEGuE4hrVMD1ACABYxgIrtCQndVXTA0AyBTZR78YSl3lbpkLYr4oi0bEZjxgkkKPGY4QD2JEalQ2MIrKLOMGqlAcAqwUUVhKrKBKVaVxaEKLXEXK0ZBngOHrWqNlZ5jAhfJmAjD17wfYd77+3fsaMGQf+8txzz73uuusAwGq1yvK+19x0Og0Ag6KACKGnn3564OczzzxzypQpN954o89nYBiZKYRHFojewJ8gjpYbzgiOAAAgHtH9RgDAiaDpM/MEgahY77Yi8UTJ9IG0c5pmjpE7ABUEC8ow4CoDb+EN2EWyxokCME0pRQWOtT1iDTjmI6BSG9MDcIQw+oVSH0nmiAwTOv+1iUZHY+8Z5Rg3Zdx9v//zgb8sKSkZ+KG0tLS5uXng5+bmZqvVmpeXN9ypxo8fz/N8R0eHKYRHOBSxQgjoTTF4DlQMwwXwRAGo6XYAgKxIYb3dSzZIsnLcB3DYIKbodb+7JC2O9WWjDsHLKwqf4bFHJSlOzOEzTKONYyHHYqT6U0F2Vu0pAKTSYLGzxDKNeAvj8cMKEIn20kM0jCgBAqwB453JVMKvG46DHE/O9OnTD/m3Z5999rXXXnvTTTfZ7fYnn3zyrLPO4jgOAN58883y8vKxY8eGQiG32y0IAgA89dRTDoejqqrK0AWYQpht0Gw+hBCjyo7nacaawBOmEFp4lSVyFvtAxjx7v7BbIaHqtQhzJJzEGT6QHkFOo5zMjj0qSSPJl2nX1gQW3FYDQphMI4edvT6VBpGV1q6kgWflYWGZsFrP00LpBGO68xOZJmGWsWTJkhUrVkydOrW0tHTXrl2rVq0a+P2NN954wQUXjB07duXKlddee21tbW0kEmlsbHz88cetOgu8PscUwmyDUBw3BFGDHwDAc0gddqwq4REiQDBBwwcaOSuSWYaExQrMFiEDOB2QkPVahE4Jx0iG7k0vl04z/W4jiRSSSoUMs4eSwOdLeoVQ1hAgEHVsJMk0kli1NEoaeFYVP5YB6KFuDRN++KwwjBk1SKZFmGXwPP/yyy9v2bIlHA7PnDnTZtvX4PGVV15xOBwAsHTp0rlz5+7du9fpdNbW1g780hCmEGYbiPI9RCwhJLxAy5cDICIiCiDKS7cVqaz6aNFOUvqyCu12FA/r1Ta3pMXVTC1CXkmiDJMkj0oUXvLxGQphAgSnbiFMqpxd0qUcKRlED6ufexo4tmuU0NsnIQ3TnJ/MNoSmDmYlkydPHvSbgoKC/T+Xl5eXl5dnfHKzfCK7QIgaIwSOHiMEjjGhBgkcVmhfdE7iFJbIWayQYlU9D+CwG3CNOkScwhwZfgoVhRykpJBoDtDZj8xJHi5TISSCW3eMMK5wDh0BQgBIykRi9WpX0sAM9RKF4RolKi1GCITmdBlYwbgCk6MOUwizCwIEDf81RAgxmmLwPKjUr7HEg0zNHbcgmSWEkh1S+vIwbHaUUPVahBwCK48TGXlHESI2UEzv6H7SnOTN2CLEgkvSm3GqM1MGAJIy2zWqphHTIiQyYGqyDFIxpZoWsIbMBGOTgzGFMNuguUYJYlqEPGOBgOijingLx4wRSjaS1lE3BgBOG0loBp4xl6glMs2XyeGUlOkd/ZwkkjyZCmEcC27drtGEyjn05SUkZRBZFqEsg46sUYZFCBjTijAwZvSOYdYYmRx1mEKYbbCyRqkVfITnGcO7RR7LtAWcFRRWjNBi02sR2q0QVw0JIY4fVr6MKYT7SIDoyTRrNE54l+6ZIQmF09niOCkT5hhLNYWQlWkREkKdFUy3CAkrWcZkBGI+ENkFItQYGWKVxAs8qFSnlsgRavMWzsLOGkU88DyRdWyzDptBIZQytwh9gmxahAPISJSQltlAKwCIq4LbYsA1qtciTCGJWUcos5NliAo0z+dAsszw5ROIaRGaMcKRhymE2QVBCA0/LI2zepDDTTkc8SJ9ZilYBC1J2x95J5dijREHAJsDojpmvrpdENFdPgEAPpsWybRDZr4oJ3mWxTEyiHG23EwzZRTCKQQ5dDfGi8i8W9+Ui3gSrE7GmnQcODurfCKFQaK+LWka8MMuIMCMEZpCOOIwhTD7GN41aimcJpx4Ee1YyQJJ2g5I3FatnyaEkl+I9rCFMDefdPeyl5UXkKawgQSWmly1WTNcAzTAJEtft2igqdJRTFDyTbXpGqI0lGbFXumUOUrK1qD1MamsVFfAuKsHfIWM00Z7kJDPeGC0fpXkUN94EilEccLKaUYbN7OgfuRhCmHWQYapFExGW3vb1oTWvxD+9C01Ejz0wVYHitNclthtVcI0IbTk89Fhzn0guSXQoWOZ3wcpBUV1G4U1uelmjWU1DEOhkLRyWoTP8PCjiaDonW4NZXZsk+qs9RvozdYYs1QUsZdhDL294ClgLOvrQWKAIYQ4omhuqjc2ngbb8HFLRUE8zevAGNJkcjRiFtRnG4QMcY32d2/avf6OSM92yZbHb8/T0lG5r8N37HdG/eBBJB5UG48sdi5O28Ww2670xSkLxAAf7yGEMMIo3jLS3s3pcSKV55PmiDQ+T1crmmpfuimdTwhCui2SA5lhC9WnfG4tlsGxRw1RzsFxqETU4bk+FM2ac16eAbdqY1ioLGbfrGAI3B4kWBgr+7o5cQrNb6nFCXAcDF8+gVSMsAbC8FKnyIhRZmMK4YjDtAizjcGVgooc2bzqxwWjTj1+6dr55787+aaPJv+5bspf6pVQe9cbfx18tMUGcdouprntah81a1RCoh0l+hlX6S3B7b2MNQNUlJDGiF7vqFPEeVa1Rc0w1DfdFgpKGY6oPmroEn0zrPruzaGoV5zjcvVahEmViyS5/GEnAXxBexDyitkCEw4iSwFNCJV+DXmoUeSEDPQ+k0oakOkaNTkIUwizDTKoiVq0Z3tO3sSycRcLohMAECYAIHoKAgBGyEAAACAASURBVCf9T7xx8+CjJQeXoAmh6rYr/YzvuTXARVhhQl8paQ/p2i8qy7jGqIH8l8mBVJ1CSwiiUCHGCeJj3IhOmQlavDMyDRBGsBjVxFE5ei3C5ohYlk/oIzIH6OzhvCU6LqAbSQGaSmn9GHJobbm5eBpsNCEkqszRLUKzjnDkYQphdoEAyMHfQ4s9EOvbo6T2bW0DQojTiZ73nrQVVQ86nJMciGoR4hxbmhojBAApwIe7GXtbbhF0BHU9PBUlpCluQAinFaTrtQyFEAFMtfZ1S7mZHX4UEOdsChJHSdHMDt8juybkpvQI2wB7w2JFia73ofYgeEvZK2NBkPIZFiHOoekcisvESi1sVGT6XERiCuHIw4wRZheEDH4hdXiq8kqPX/PiKb7CY0SrR6tzJmNt0Z2rndXH5Z/y08HHW+18nDq8222TtzOuQSoQI0whLMVdXYzzDFBRTBqNJI5O8qf+lCoAfRn5Q1ng6L47WT0q1TYyk+BbLfnz7PreUA5FneKeWm4gU6YpKlXU6hrI1RYC3xSGwKhppCSJ6KEJoRrG2Emz+FFCRlbqAiXNMYb/jsQnZ4RjWoTZBgE8WMlq5yybfvIKp3cMx0kAyD1xYc2yt6qve5UfUpaFLHaI0S1Cqxxi7Ed8QAgHGUJodQLHQ1iH4VESgO4oL+ueU1/sVAQeBdUMp+yWigkvL3cJnswOP6LBiGuT8hbYdaTzDkO96p7qT+pf3xi3VOpweAJAe5D4WLZjpAeseRy9IbbSq2lemsGHEjJQhZAoCqt8gvaXJkclpkWYfRzKM+Py1bh8NQCQHB+QS4Y3lyx21EMrnyAeu9LHaBoiBsRwC/sNKbeIdPSiHBdj2+B5KMojLRGxyqM38jTJn9wTc/kFfTMPh7DY1f26UpAfyzBOduTSLuRWivG8TP/fUoTvUKzVPiMpoxGpvEiXbnQEUS5LMsNBZKP6RQFADmE1h1Yhg+IystBKUVE6jSit+DAGXSauyVGFaRFmG2SoECYiTal4x+d/T7XnrDaOFSPU+hlCKOXzIZZFCAC5xbijm7kKAKCiiDRFDIQJpxbKdWqGYUIAmGXt7ecdCZShTXnk0m4tWOTQ57A+FHWyc4wnLfF6RUDDqCPMlbJKAwEAE+jpQb5ChisiEkQiNVMGAJR+rLmpOpdgtDQlShpodYQaa0iTyVGIKYRZBgEyxDX6yX+vbNh8/8DPjJ7aNicXphkEOM+hBWX6C6+1VAzqsAj9Y0l9K3MVAEDNGPRpyIAszSlMbE15FZLhwykifKKja6ejMrPDj1DaRL8ooMkWVuHL8GyS8+aWGKg+3NlnKcsnko74b0sn+PxEoCV7AgD0tiKhhHG6ZBfBeTTXKBdOIiv1LSqVQvywn4KxhsyW3CMP85ZnG3hoZ5ljznix9tib9/1Bo04TdHtRiFZOTqwiOEQ5SDMK7dVSsI5dTFUxlWxt0PXufMxk2NCtb0IBAAAUO5UxPvmTVOb90pY42ySJb5Z0WCtHBQlk3W0v/6G3PrNGBACQxPzGlG/JaAO9CNZ12I6Zqmvltj2ogpUpAwCte3hbDeOFKdGMtWJaABj1JjgH9clJxpE47NOINJUwWnKbHIWYQphlEEKGDAwUROf+NsFI2behaKkYVoYYf84cFKY1jgEAKHalmmlxRNHD8VbUz/KxVU7G23cjPcXH1ZUklOK7EgYC0ufWRD+QM5cxDpEfeevrbSVRzoAAH6EQgM+cVae52jPuJgMAH6X8xxQmvLqHTgDAuh7H7Mm6Vm6tR2XTdWSW7uEc1QyLMN2SxoU5lAV8KAVOaqpUMsaJw8otIQoyd8WRh3nLswsCGGmDXaM7P/r17vV3DLRe2+8aDb79WP29Fw5aiewukBUk0yoo1GIPXQgBwFUtdO5hPBvuALHYSLuOmBSHYMZ4sqHTgHd0bnEihC2tSual8X4hdY6r9TPHaHy0h3z2WotzRLLY0cFeOjwfpAvOqTZQfRhXuPpecXK1LgN0Wz1UTmZbhME6cIyl+U+JQnCPjPNpnk++J4lyaBYhSSWQMLwQaurR/ryYHAJTCLMMTPAQizCV6O5oeG3rOz/DWnq/EAYWXR7e9jZRBld9oRwXCtEsA7kwN9XMePG31tja97D3g4rJZFudPu/oVFgXNNAOm0PktNHR1anD8m0e7+gqtMgNVn0J/kcmEc7RIhVe6Ws4nG/ybtmFeG5ywEC66YZO26Qx2KIjBSotQ0srFI9jCGF/F0ISiLm0f0eqTQW/nQjUqby9MeSittlLxUEY/gULq+auOAIxb3m2QYg2WNsE0T525i843rLxjcvV+L6qAM7iED0FcniwRUbcXr6X5h1VC72xVsauZK22tNWxPZll07HeMOEksqHDio0EsM4aE1uXyktlOrB+gMs9De2WQIjPPAc1m8GI2+4YvdTT6OMNVMEP5f10wbm1EUOG0Ppu+zHTdB2xcy8qqgKRlSnTsQe5qhm6mmpRSBGj1QIfioGLahGmE/zwMUKiKaZFmIU0NTXdcMMNP/7xj998803KssbGxjvvvHP7dlbTkCHoFUKM8f3333/WWWf96Ec/amhooKx8+OGHly9fbvQ6TL5AG1z/wAs2rCkTF9yV45/8yVNnxOrWA0CieZsa6RHd/kGLkduLemkpD1pxTqKJYRE6qsU2lmsUACqm4G31zFUAAH4f5OXA7j7WdngAuTZ1aiC5PnVY/dJcvHKpd+9njiqVMYv1iGS3tXy0LTHLlnmLbQCIYXFbynNyhbGRHeu77HMm6/OL1kHFVLZftGMPZ61hPB6pZlUtYqRQob4octNihCSdhOFdo0BUUwezjVAoNHv27FQqNWnSpKVLl7744ouHXEYIueKKK26//fZNmzYZ/Qi9+Qt33nnn008/fccdd3z44Yfz58/fvXu33X6It6p33nnn5ptvVlX1pptuMnopJgOQQwihXVMTAGjszF/Y/FW7fnuq6M6Te9uKzr6ekwY7eTinj+uluUZxkSfVTAsiAoCj1rJ9DzCHMZVNxHubQFZATw79MVNhbbutxmfAdjmnJnrPh4XzbfrKFYdhsqVvgtW7S60Yn9An2kcIPUJOr+S9OufTwzzP6kTghNK4SzLQYLM5KiqEq9AxTQIAPm1AZWezc3Ba9/C26QwhTLZqciFNCFFCBkAgDa9zmgpEo8wjJJpqFtNnG48//vikSZPuueceAJAk6c477zz77LOHLnvggQdqamr6+jLppKHLIlRV9U9/+tN99923ZMmS3/72tyUlJc8999zQZYlE4uqrr77tttsyuA6T/RBtcIzQnTfB6tw3/LRk7Hcm3bu9dOmdtb9+r+is64cejhx5PN0iLMpR21L0UkLRw/EWYLbelqyQXw57mumr9jFrMjEUJgSAmQVJjeP3KhnOrN/PUk9TTHJ1HkXz6xUkfGavusJX7+AY7zR0CMDqdL6hNBkAWNdpO0afOQgA2+pQxVT24vY6zsFyjcabsVpESxnleuPEQ08ZjSORWm6PFbOgPttYvXr1woULB35euHDhhg0b0unB79NtbW333Xffb37zm8w+QpcQtrS0dHV1zZ07d+CPc+fO3bBhw9BlN9xww/e///1Ro0Zldikm+xiSLFMw6tRA2aJ9f1Cx6A54Z57uqBymhsvt44K0dpHEJoJDkHsYG6irWurQky8zFW/XsQwApo+DPT1iXDEQlkYAZ1XH3ksW6j/kkFiQ9iNf3U5bpUzprXVEsdM+ara9t1aKHOZ5tqc9HhuuNmKmA8CGoGPONF0rQxFIJsFfzrYdu+vAXs2yCJs1ehEh1xNHOdRMmWR8qBPlQAhWkdlgLcvo6Ojw+/fFgAKBACGks7Nz0JoBp6iH/ho0PLpco52dnS6XSxT3+b9yc3Pr6wd7mdauXbt27dq777579erV9LM1NTWtWrVqv8KPGzfujjvuMHjZRzCqylAgPMQ1eiBy+2b80S5uzreHW4BcXr6FVU9W7E41qZKfdvctNZb23bHauYwzlU3Hm18VztOxd0giTKgiH3fZFpSwKh0PYMmoyIpPSyNYdHOMkg86FWL8eEf3Rjx6amwHd4TvdM1SgSLZznV/CZ7et1OF50wypqYyRps6rMsm6PKLbtuNKiZhZoV6fxdCAqKnjAJAqlnGhVQhDMWRkyaEOBUHiVpaihV6aSwhJBYzFk/NKmRZBgBJyvCN0G63cxzjNtlxaQCMNTisbwltWPPhiSeeeOAvlyxZcvXVVwOAxWIZuGz4/PqtB89eXrFihdvtPuOMMwx96IHoEkKHw5FKfZFanUqlnM6DfFypVOrKK6986qmneJ6dklBYWDh+/Pjrr9/n1isoKBh0tqMbQWD9n1OFkKTDZE8dUITQG+DWhemfoIwKxHcE3TNoD6trum33v8RFlzGiO7Vz8cvLkaKCqONROnE+vLbSbUgI3RZ8+ujoC63ll7rq9B91SM50tbWrY7ZC9cT4bv6InTnXIuW32Iqu8+0Q0eH+E7alc3rAflJ5yNBRbzc5Jo7B1MbXX/DuJlR9PDtA2LCRy2EFCLUoxn2qRneNtvWhHGrJTbSPk6iXrikAtP9YhNARvV8dphDq4aXQ+O2KsberpDVeMSb4q1/96sBfjh49euCH4uLi1tZ97RxbWlokSdpvIA7wwgsvbNy4saqqCgDa2tquueaa3bt3//rXv9Z/AbqEsKSkRFGUjo6OwsJCAGhsbCwpOag2q7m5eceOHSeccAIAqKoai8V8Pt+GDRsGrmwQkiQVFBQsXrxY/1WOKMjQfjEHwFlcEN5FWYD8hXwbY2tLjS0Ob+ugOxw9x9k234iY+TKefJJfjjftQLMmss2sbx1L7nvSEkzyfpuBDiZXTu47v7Fkd9o91nJYnkAOkR959/wNVa5FkyYk6nK0I+y9XkHCDvsoWbT9Km+Hn89wxMQXZyPcc7HKXxzbq7/L9gCvNHkuvEDXgAaMYfVG9PNl7Hu9ax3vPI7RAyj2aZpU5wJ1arDYHEW5NdSzhDmJVktD1BS7u6DJlw0SBF9e3nCicOaZZy5btmzZsmUWi+Xvf//76aefPmCVrl69uri4uLKy8pFHHkkk9rnBTj/99Msvv/yiiy4ydAG6AjY+n2/RokWPPfYYAHR3d7/22mvf+c53Bn5+9NFHAaCqqioYDNbX19fX1z/zzDMDvtOKigpDl2IywNAWawfCSW6IUhsru3womabPqVdqAuFPGR5aS5HAO7muenb8b8LJ+O2NzFUAABYJTpwDL9XRXuqHYuXJVdNDz8YrMTncLAYekcu9DRf6WjY7a/bYysiRkxbRI7g/ck2qcKq3BLYFDlsFAeC/iaIxeeqcImNd2er6pdaYMFdH8gsAbNqJvIU4T8dg+l3reQ9TCLen5WpGtJhvCaPcItqKSB8n0uw5oskDLZxMsoczzjijpKRk9uzZZ5555iOPPHLzzfsaL19zzTWvvPIKABQUFIz6HIvF4vf78/LyDH2E3syFu+66669//eu8efOmTJly0UUXTZs2DQDq6uquuOIKAOB53vs5LpcLIeT1evW4SU2GMrSg/kA4i4vEqEKIEAQCXDttjVpTmPwswXynzznWvmcd+wmZeor2zjqks1h+6WnwUoM7oRrr5LC4PO53wbvJfENHDcf0/8/eecdHUa19/DnTtpdsNr2ThJZCD71FulQRAUWwgVgRCyJXrHAVy1VQLhfBchXUC4qgIAgKSO/SSUInpNftu9PO+0d4ERF2ZjaLJrDfj3+syZkzEzKZ3zxdXf165GGVTrvXkOUiAu/i9tcgIuKkJvG4Lv1By9n7zGeZentEAaBaUP3iiX6qvTKnKAAsLQgbcztIevfr2LgPZQ2UFhVXLdSWgCFTwjVac0TwpvsVOQDiYg2K8CeW2CEphD4QG6vb/GaFpul169bNnz9/4sSJ+fn5mZmZdV//+uuvx48ff9XiJUuWDBo0SOkp5NYRtmnT5vTp04cPH46KikpKSqr7Yk5OTmVl5VUru3btWlBQoPQ6QvzOn8Yw/QGVEbskQoBgjaUu1gjpkdf7PjaowKjynOc0yf4KAA1dtSfWO7rfI/Esi0jCOgscP4Uy06XFMC4Kt89AP5w2jm6mbGDQsx2rHv4poZ262kQomBx7PYwENyU8f4sr6hsio4m3KMlXr0adNw4HoT2qS09Se2ebD9ezUuJKvnamjG1hj9Er27DMTe0o1j7XR5ZOYAyb98HkKdK3xMk9pCVHBVKvzY4jnHC73zchjInSGhTuN0ZYW0v4nUmCeW9oLG8DhCCIrl27XvXFlJRrjFpr0aJFIPvLX6pWq3Nyci6rIABQFBUefnXjD4qiAs5hDQHXqiO8EoJSYywC6zeOGBZHXJSQGbF5hPOYhKKYu6hP7pLlPMweKGzcJ9fNeP9I+LLAzCn0P6WY2MGpju9cicoOuz4IoKeu7B/W47Va6wF9S1/Dq6y4oIrZb2g52Fz2uKUgiCp4zGcqBd3dLaVep/7EV/nmEbmiQV5VZ95ZRKogJl1aNfN3k7ouEptiHnwnPXza1X2UroQod4BO66+aHgAc1Ujlr0kb5vyVHoW4WQn1Gm14+I0RAgChMWK/YUIUHkddkMgr8abHOY5KCKE6kQYalZ+Tvkla9Rc27pUrhOlJOCkO/1Io0TTyzzyYXZvHmQtYxQf6IZryvBxxrL3BsVOfVUb7LUH7C/ESqn36DKcufKb1WE9t4EPn/wyP0dfOlGdyqhhCmd1j9xHrzhtG3y53/aY9qPXtsl528veQ5i4SDmr3KRaidVjr72WFKqxFkRJd2rGjllD5S5a5xmizELcAISFscGBR9O+cQSojOPy1EULhsVShhBCyzaJrD0s/p8xdNCd3SytcQgYWED4lr8UMANx7B/pvXphSD5SOFqe0r/rK2STg4fXXhEB4uPHiU9aCc7qkI9q0v70raSkdvkuflWO0/8N6PIIK8nP5B1dCupXvojBHBgC+OWXq1QFbZb8q/LIfWg2QvsE8Dqi6AIZWEgFC51Ef30IiQkwU1YBFIoiInbUE49ci5EMW4a1ISAgbHoiQ8I6qDBIWYUQMeVGi4R7fPMp1XLqfiKGLLm+PrEByVj9xk2zvaKdsrNahncWKp+b2SXK1jOK+dl4jNlBPmtDOVyOPxuvxDkPr0+r4v95TKgJRTFv3GTKL9fHTrCeGGy4GPG7+epxgjbvYyOc7Kc6R8Qro21Omu4fIXX+hBLm8KFFGRc3JPWRYWwbREneO4xjnTY/zv4a8aCMsCf7XYJeNUPstn/CbqhbiZiUkhA0PggDen9OSoCUSR1F4NCqpBr95nEJ8mFDDc7USIRxzV42cxFEAyB4gbNyvoBrh3hHoi4JAmn8+36n6LJh2efyFiwJDjYQHw848Y82LNDHbDa2O6JpVUX/F/CY3UheoE7cY27qMkXdaSl6NOFKfWfPXwy7Sn9rTX+lWYVErDjeuPmPMbgYp8XKF+Zc90HqgINlQBgAK9hKGrtJRx9rDAtdMwiKkLtiJcL8poz4PAPjpuA0AmA8J4a1ISAgbHAiRouDPIUYyBmTza/AxatDryDK/3lGEcPNw52EJz5umCS1gokzG0MHUtmKVDc4VSS68RG5HXMnSu0sUVy9oKHF2j/LlrqQC3w1RqQTaPcF89p2o33qE2c4bUrYY2+VpUqooY9CLDp2E5owqbo8ha48xM9mM/hF5/HnribbqajLYhiAAuETqg9rmo1o42kcpdv25OGJJvnn8Ndr9X5d1u4hWMgonAOD4dsokVUEIGFxHPXxzifgfeb4GrH5do45aQitRw/rn2S8hbgVCQtjgQAiB/+Yy6jBcI5FAQcSlkAUS04s8bVOrt0m//1qH6vetlg6bIRK6jhW+3iBXLUgSnpsozjkQqbSmEADSzOycXuULHU1PsDfKYlMjobeubFbk4ekRJ1qHccWGpE2m9se0aaVMuJdQMFXxKgRE1JKGAlXiDmOrg4aWUSZmgvXC+1EHxpguRJE3KjrlFqm5thYdk7j7MpWVrNSx8Eh4x1aQmSZXnvcfRz7AaTnS+aJlZ5C9Ehk7SAUIT/iwQSVG+k2SEjF1poyI8+czxzVlhFbCCYH5ULLMrYjcOsIQfyFI4D1+lIfQhEOlRONNIjadzi9je6b7WePLSa5cePgaTfD+iHWEYddj9tuflPandb9HmN2PevwuQS8v9te5FbTKQB8fC3uileLRsq0ivHN6lT+/uelDxoL6D2HwQzTlGWQoGmQoqhGY33yWXxzxx7CKB6TFnAb71CJHiaxKYFWYVYusGrMM5gREehDjI2gPUnGIYUmGJRkvol2gwoAspLeNuma05nQy7foLGtu4Rep9W4ucRG6K8vJ5ADhepfrlov7rp7H86rqv16Me9/Ny/KJ7f6AiRhiQ365pAFC71cvmSMy0IQtrwGgAjd8uoFVlhDokhCGuQUgIGxxYqpiJ1FjwOQlrD8U2pY8f87+Ga5PgOe7hnSKl92eTGdupfSxRlI/imkk8Co2RuGVP4fvN6O5Bch+az9yPxzxt6JfgVDoJCP5CLawjjGRztaW52lIA4DBhE5gaka4RGJvIVPFMtaArE1S1Iu0UaRUSTIgzk2wE6bPQXBhpNxFsGMmaCU4bvHJAOdRTBQURzTkQ+eyD2GyU+wstq4T9J9Dri2UV3e/5kUr6UNqmL9/CuftIvLBR+WUoPk1io5oySiUlhH7z1ELcrISEsOGBRcz5y5UgtOFirZQQxqdSGyTWYIbCmVH2XV5LH78WHALrcMO+1VxcM+nwSc8H+M8mq0b1E+QMowAAkwGeHI9m/S/y0z4XKYWVbXCFFk40FjS/8Vp4GRqJVsprhQZtPdRTBQHg8xNmazTZp7OC38uStajznbxKK31IUR7hcSNjWyk/swCO3S7uBYlGCnReORHT1P8aXFFGqP22oBSFUFuZW5NQjLDhgUX//hmC1gIG8PgbnoCiEoiKWuSWkC53h9SqbdJPc+sIw+41pJym/MmtcGSquGaLAp/fwO6iNYr8X4GyTtyXqdPCRfameTcsXtgYqb8KXnDQy06ZXpis4JCqWvTjViJ3oqw0mb2ryYg7jZIZSI7DXhylF8MlJh/RJypQnL9AAABAVSnpN0aIOQ8QoQ7JtyIhIWxwYMxjXiJ7ntSHi9V+DT6CwHEJ1KkK//v4cppU/ipt5xmyVZgmC4/KulsGPs0vWok4JS7AGZPxknzzRWeA/olWEd43e4a08Hfqr4IY4O0DkQ+NgqhwBRbSf1ejnBGCKVLWIXt/pCKGSzcJqt7i9XaQCBBCnWs0TsJ9iqvLSI1fIeTdCIUeibciod96w0MURVZidC2hsUC1ZOJoOpVX6n8NnxXrO+fjaqRf4cOGGfaskfWynNJWjEjFa7cqMAqjI2DCCPTG3qiA3VKtI0NaeIn6qyAArDxp9NL0nf0U/EKqbLBmC7ptsqw3oPOHkUAS+izp/NuKrZy3g4TCIZsHXF4ULlFoiO2VhNafa1TgvfB39xUK8bcQEsKGCGYlZsaS6nDwbxECkDHp9ImrZ4NcfSKKEFrH1O6Q9o5GjTTsW03JHFk66Gnuo5WEIqNw7CDRTdNrzwbeR7R1pHd2j4pFtqbHfAF6WW8CbCLzXm2LnCS+PipY7aUWHbO8+DgQSh4Pn69G7YcJZnkvM3vWUNY7pH9NIoud+1xse4kAIVVQhhJTJEZIO2qBYvxX0wPvCcUIb01CQtgQESWFUGXG1RLWHopLpfIkXKMA4GmfVrVVOmNTm84QRvLsAVl2XpN22JosrtuuwCgkCHjpMZh/OLzaG/grebsoz5ze5Z+70le5EnC9p/g2Ok6wplnVWX2a+qa0U1yOciVvH7CO7A9NZPeRAYBaO1q9hejziKyUS4xh/1rKOlwi7AcA9v1enGzGRr8DJS5lykgECHFNGam9elTO1Ws46SGdIW5KQkLYEPGfNQoApCYcKiVcoyg+lTpd4r/RGgCwHVMq18kq5Q6/w7h7tb/5hVcy4Gl+8SokKJm1lJaEB+fCewfr1TutVYT3i8FFJeqwf9laVguBV743LniMVjkTPnOmz+pZ+UBWIFXzl/n1ou6sR33fHcoE4b+rof1gPkyi98slzuwnCAOpaybdzbV2m9ebI1npCvSJSiJWSgirywm/AUIAwJwXIDSV91YkJIQNEckYIamLwOVS3cw0ejCFkacljEKuRTRXw3nOSr/LR4w07ltN+p2E+DtpHcSINPz5GmVm2cRR+Dyr/uhIID1ILxOmEubeVtqzKTerJmudK46/2U3D4z7Ta9WtqnWmLwYXtY2sV3uawxXqOfsjXnoMM3JfeAAAzl5EP2xFfR+X+9bz69e09S5Z7uuStT5PV6lcUAD6cDFKlKydKCY1Eu9YIufCosI5mSFuCkJC2BCRjhEaYnBFIUiF7FDTtsy+8xInI5BveKvSFRLSCwCaJMrcUb37W7m5nWPmcF+uJc5cVKBDKgYWvIp32owfHpLwYvmHQDAho/aL24vsJtMr1a2P+m7OSdG1IvOJPe0rb+rUzrZ3csvDVPV6iB+pUD2/PXrmY5AloSl/QMTw+ido8DNyo4P2Sji6kYgeJ53T5DnL+UoEvl2S/2VEtYuockimjELROUonYbGKXgeEhPCWJCSEDRHJPk+I0gCtxjaJXBiySRvVrmLJ07kHZhUtlzXuIGayZf1ntCjPe2SOwrc/zb32EZK5vg6jDj58Ge93GOqphQAQqRVe7V45o1v1t74m823NK28iT6mA0S/umNerspsnk18PLeoWJ/0e82e+zvfsLLlUPHOkQjVte8xLj0O3tsqcokvXIEGPu46Vmxm16XM68g4DHSYdCS5Z5vQOyMCkxIsUvfc8pGdJJvbgknOkwd9sCgAQvdWhZJlbk5AQNkSwyIGUepDGWFwqYe0RzdvQB85KGo5cdhzvI5xHpVNmTF002ET9tlZuPkvXuwXCipf+qOw2M+pg3ouwu9ZQTx9pHR2iPUsHX+zRo3gaSwAAIABJREFUXHijJusHZ0Jwh/r+LeSxxtdrWp3XhH88qGRiqxqls+YBgBfh+W32ib/UfnLs0gvQDxXW155SrIIXStBnq9HYOZyczqIA4LGjLV9RsY/IGu9bstLrGpQluUy1t5BMbSu5DFdcpPQSFqHgtcm5sBA3H43+oXBTgghK5CS8o7Q2GqSEEIzhoNZLltUDQu7+WaUrZBmFCdMjvp/HyDTyEILRb3L/Xa1gPFMdZiP+z2tB8JHWQZMwprntk4EllTrTc5VtN7mivLjxlYthgBOscb6t+VJP2pROtndzy+P0gTTGrPaKw3+oLqjhvxwQ9sNZHycCkWacOZ3qlK1MBUUMry1Gg6YK1iS5B274mAwfqNOkSEcgHYd9HEvwGRIT5wGA2VWI0ltLLLJXIUQhRiJPFbN/XZe+EA2KkBA2SBAlXUGhixGLpIQQgEhvQ0uGCQHcg7JKvnXJcQtZcrXYyuz7Qa6QhMfjgU/xry4iFDlIIag+0jpi9dw7ueVT2tUU6iNeqGz7lSOliFc8DfFvwSVSG1wxL1e1/o5t0jeDD9gXCgDlbrHbssqcaPrbwZZBKWqagO2YQi1lmWhXsewnwk1D93vkOkVdNbB5CR0/1W+3z/+n5FuXe0C2RGlgXYCw0k5I9pQpOUeYJPyiICNJLcTfRUlJyT//+c9p06Zt3779z99lWfarr76aOXPm888//+WXX3Kc4hfEkBA2RBBC2CeZLxMNReckt5IZJhTSIwWdxrZHVkpo/LTw7+fRoux6+e7jBN6Al8seVXiZy1o4P0haCACDUx1zepV/PbSoaSo939Fydk32r+6oBusvPc/pljib/KOqTbnBMr1bzdIhxSPS7QH4Qi8ToSX+2z/spY4GAgGJYEgrw6qLgYyiLS5HH69E4/7FyS+6/2kxHTFMr0mSkWyFoWyV2zMgU3Ihvfc8NJUOEIqlFyidtBD6n/oS4u/CZrN17Njx/Pnz0dHRQ4cOXbNmzVULqqqqVqxYodPpoqKi3nrrrTvvvFPpKULTJxoiGGPMOvyvoQ2xuFza1EPN29Kr5gHGki/XzgHZJd8eMXWUKF4GgLDu2qJY1Z7v+U53yBJDgoB73uHeHabq2lqIl2iDdTV1Wvj4q4b5h+Ax5WMLr4dFzY/PqB3XsnZ/mWZFvnVaWWJbddVtmtJYSpZ/+EbDA7HXE77RF+sDalhTx/S0i6b6ZYReBgF0iLrkmSRSjcOiTI+8f+b9x1OkZgL+AYzh9Y9Rv8f4yGS5Zr6zGm37H9Vmk6wXmtodXl6v5dOkK0pVewvJJu2ldyw6R+sk7zwcGk/fMPn8889TU1MXLlwIAHq9/o033rj99tuvXBATE7N8+fK6z0OHDm3atKndbjcaFXRbbKAvwrc6WBCkXKNIZQRRBKdEeB+Z5IUJAbwDsspXObE8Oy9hRsSquTQv+7lhTcB9HuVeW0TIbNJ2JXVauC+odmEdBIIO0Z43elZ8Oqg4Pp55r7blPFvLPZ5wu6ikjC548EAUsIYvnSnPVrQ7qY2a2rn2mxGF4zNqg6WCV0KkGlFG2G1tjS6PsDdP4ma7im82ELUY97pPQQ+9dR9RkXcY1HGy3rxLVricA6XCfgBQFyBs2kZ6XdE50iARbhTZUMftBsqvv/7ar1+/us99+/bdsWMHy1730bNz587k5GS9Xrpv0ZWELMKGCBZ5SYsQAEhjrFh6gUiTyKwj0lvT+87z6ZH+lwkJZiHeXLPVbektPWDe1FHNNFHt/o7rOlru07D3A8KRdeS3P6M7+yoWwxtkF14mTs893rZ6UquazYW6tadjl1Y1MZF8Gm1Po+zptCOCuoFzB90idYrVn+KNpwXjea822cB2T3ZPTbto1dzAgrY6FQQAFU0MyDGv2l7dsYXcB0dpBSxcAVP+x8tvT22vQDuWUW23ysoBxhwuX+3yLW0puVJmgBAAxPILZFMJ1yjmnEBQIN/jH+KvoqSkJCLiknsgKioKY1xaWpqYeHUH2m7duhUUFBAEsW7dOkJRn9yQEDZQsCh6pBtlUfporuQcSAkhmdpOtXOVZ2wHyQ2dA1oXLd8jRwgBIPEF6+qHfB2G8Yy0MxUAgCBg7Bzu/VFMTiYkxgSihXNfxJNfNp75lX6je1l94mTXgyFxv2Rnv2SniOGMjfmtXH2wJHJVRZKIcbrKkYicyYwziXJpiHpJlIBRMa85z+nPifoznKGSUzU3e9sk+QZG2TPCKzVU0Fp8CRgWHXX/csGXZaWebK0zqy49Goh0I2rxe3bM8K6Wlz4r/OdDEo2t6+B5ePUj4raJYky6gutc8yEdNcaoipH1tKne5BaTwoQ46R4I9N7zqGmmdAWh2wE8R6glNsSsC0IWYTCIxTpO4T9kUbnryL79d91115Vf7NOnz6RJkwCApmmev/SCUveBpq/hs1mzZk11dfXixYtHjhx5+PBhnU4n/wJCQthAETzSdg+lT+TO5UP3If6XES070N/8C/l4rJL4dXuGZFUP3sxW8EyE9I1hbK/WddZ+97YweqZcD2lUKh42g3/kDeqjGThOXl/KKwkzwtx/iK98oBn/U8L0duWtI2+UoUYgSDOzaWZ2VFMAgCInfbRCdaLK9FNlxOlKFUWIekLQEbyG4HWI1yBehzkNIWgJXkcIaiRwInKJlAcol0h5MOUGyo0pN6bcIuUUSJdAxWjZ5hZf20h2XHhN8zAfeQNEHQCe22ovqOHvaa755qSn1dKKtcPDW8aqiCwLivnDi07/HDNNyYoQ8jzM+JDgw8U+kxRk5Z3eR+zfINccBIBzi132kT3lrFSvP0W26Cu5DJ/Po8KkZZ40xhOMXpBq8xtCEv5wS1etwlKc8rPRMVtHjRp15Rezs7PrPsTGxhYXX8r4Kyoqomk6MvIa/i2TyWQymWbPnr148eLdu3fn5ubKv4CQEDZQRI/0GB3akuI+sU16L70JDR0LrABSQohNGk//lhcWXkx7UVZPstQ5kfu6e9r249M7yrUPOt0pYBEm/ZNa+A9RaeIMAERb4T+vilsPEK8uim5tcU9tXWlU3fAuyXF6Lk7P9U9xAoCIwcaSdh/hZEkbSzh8hJ0jnSxj8xJlPmT3kR4OKBqMKsGkwhaVaFSJBkY0qLxGWtQzopERzGrxRpizV8EKePFR15n7o6waYmwzzcu7HAN/qN7xYWZizKWKkdJqLtpCA4BBQw7rKq1SoggvLyQqaTxpASffKcp64dNpTJM5UXJayQCA84jPcZTzvi2dL4q8HLPjJDHzVelNz56gTCnSG5IM5kLlE38PiFJFRsdeJYSXGTJkyBtvvDFz5kyapr/55puBAweSJAkABw4ciIyMjI+P93g8Gs2lG/vs2bM1NTUJCQmKLiAkhA0U0Sfd5IIyxOPqUvC6QC3hBGC63UtSO3xlF8WyaiLSQkZfN+vE+WD3orsWJk020FbpJxdlJFPfjvpseulLa7wqrdyHe+e7BAB4eHaAWggA3dvitv+CBV9p7/kp8dHsqoHJ0vHUYEEgCFMJYSoBIJBi9r8MAiEthcrcolVDgIF5/bn0s/++8Mi8c2veaAEAG/bbxs0+uX9hdnyE9AgIABBFmLmAKAE86SOWUtKo7ru3GU2OPuJ2uU6qk2/anQ90A0b63mO2nEIpLcAg/caGTx2jzTnS5xbZy3WEDq6WImgNqcC3FuLGMXLkyPnz5/fq1atJkybr1q376aef6r7+yCOPjB079qmnnvr666/ffffd1q1b+3y+X3755bnnnktPl+7VfiUhIWygYM4NgAH8+qwIkrQkiRfyiab+WkxhgavY+En5ywu8p/IIiwnbXfrJIw3Txl9zsRBj8vRveW5BYfpMWUXW4f10Vat0K94Wxr6sIPW8/lqo08CzD+B+3WD2gvCNRfpn21REaUNpDr9DETAwRf3WfucXjyWiZmYg0AdPpmTcf3DLYXuPbGOftqb3HkuOtd5YFTyzH+1bR7fZIneuluOwz/Yb657dTs5izY/5VKuB0uswFi+coLvfdc1v2iuPVJfsUetjNfo4FfH7z1btKzcyYSEhbCAwDLNp06aNGzdWV1e/++67l/2in3zySXh4OABMmDChTZs2J06c0Gg0b731VkqKtAPgKkJC2EDBiMQ+F1JJ5PLRxmT27Am4vhB6S08VvDkUi0LEiMn8/xKIiDCxxl45eKp6SHe6xbVvF8fDPYvvXJD0iJGRYRQCQJM3Ig50d7cbwDeV7SCFYGghAGQ3haVv46WrVff/ED+hRe2o9FpF9XA3N7MGhrddWPJVsXB3CwQAFgM1qmf4z/ttPbKNCMHdt8nq8BKwCrJe+OQ5VZM5kTKdogBw6k2746HukpFsqPOL7jpNvNxVciWuLEaE6nqZMtUlewpPLKFovcdVLHBuAhEMoWIItUdwWdXSBfgh/jJomu7fv/9VX8zIyKj7QBBE69atW7eWVXJzTUJZUg0URFCCt0ZyGW1OwSePX++7gseR91pfS6eR2e8di+09ldHFAQARZqTbNuOOnLreUWKEwdM/4/x8uX0XKSOZNjf6s+dVXoURls53CQOe5h+eTVyUmDHs9+wUTBiO//MqbKwJe3Rz/Hn731MC2HDw8MS8Q9a1bHTioPiFzzR55P0zq3deupE8rKhVK/iTD1gFAWDFm4y2k946SK5R5Tjssx3iPHdIt88GAGbzSUhtCXrpoYb4zHHK0uR63yUptSW2c+cRP+SO29+514dphqxoTZKeNgmYZ4ibZ1ZJCElCQthgQaJHWgipsFR87tj1vuvI28pYE+LHvI5ICgA0VVEAwB7I867fxbRu5mdbx6SexUsdbIVcZ6Oll1bfVb/iLVmutisJihYCQEo8/miW2G8ANXlT3LyD1gpP4+upXX9YAX1/2nDPT4k2s777ABUAjOwRvnBqk/vmnLrzlYIJb57addw58Xa51nd9VPD0PmL/Bjp5lkTp6pWcesPumCjLHAQAzdoCstVtclbiM8dpY/L1vqszpzLqS4lCBM9pKb2ZCY9QxwIATSi+mUM0XkJC2FARBcErXUpIasIQInFV6TW/S5uiRO/vQ7ep46ztpf9UjXre9Npkqqm/hHLRqncPzDr3gYJm/Cmzrb9tpE5sVXxHBUsLCQSj+uMv38FEsv7enxJn7406a7tVnmVOjvjiRNjINUlb3OGvToVXnsCm//epj8m1Hv2kdfdsQ/ds484PM8ONspSmPiro86BPpqlS/xVJm+XeDI5DPtsx3j1CljmIPBy95wyRLe0XhTohDLuuRWiJ6ZTe/tm6z+L//7lhLMZoJKYBh7jJCMUIGyhYZOVUUAAAZUkRz51A4deoy9M1acdEJB5/sZsmvoWnON91er+mW3vrynfprDTJbZ0PdS8ZcSTpUaMqWtZNQhnJ9HkxX0wtemmNVyqJ9WqCEi+swxoGU8bjh0bhHzZpn1qlbWr23tu0JjviBraG+Xup9pIrTpuWnzS1aorfnQEtmlwjdzfaQk+5Q0HEqz4qCADfvEnpuujC+yq4CQpm2+wP9pSTLAoAqk0FRFoG0snoJMlxuPw83VZWr4DLQkggss4oDHHrEBLChgrGgkuWiUQZUnxnjkO73tf8bvrTy6t3fcNWFRpadDc9vdzbxmdPPCNnW9Gq9wzJPvfh2Waz5M7oCeupqeyuXz4b3/tP6Rm/VxFELQQAnQbGDBJH9oMNO1T//DZaI/J3pdn6JzsJdPPMHy9y0MtOm9ef1/XrCksnilGycl+kqacKnthGHNxIt90qN1MUAOz7vPY8wfNOK5nrNWvzyVbD5KzEhfmEKQ7kOTnlhORD3KyEhLDhIrplNdVkwpp4T6663ncRSYV3HfP7/1a4ZAohADgf6F4y8nDiA3pNE7kZKCmzIw/18/60UOj/sOJihs53CaIAY6fRb04RuyoclX5NaAoG9cADusGmPdTnK8I/PRE2JMVxe4rdor6BbTxvNJwA24p0q86bT9Ywowbg5U//7gWtP2VV6NVFiDOLkxbwAahg4TH0ydOqph/HUka5MVos4vxXbM6HewMt6xBk89B7zxGDu8hZLJ4+xpiSZV5JXUgeA863/RalSQhjFGh5iMZOSAgbLoJbemQEANCWVLz/InZUI4O//iBY4BBJ026dqtbiM8tyugpWnXNSz8OP7uy4JhrkPdkoPZG1MmHTsEKB9w56TLEWdh0rqE34jTfo9nvRM+NEQzDquAgCbuuEb+sER08RK9ebxvxoTg3nOkY4O0Z7moX5Gku5RZmb2l2i2V2h21eqSY8XRwxHvXJEJngZshjDqk1o/jLU6wG+72SBUP5guHgczXtA1eTdaHNXec1n645a5HD49O7hcs1B7fLfUKuuoJUn/gd3MJG95CzEAl/nGsUYR6rj1aSsdrshbhpCQthwEVkXFnkk+UwiSDqipXhsD+o04NoLMM6bPVAT3yLpvvcAwFiYVPH/QigUlQNNkZHXVVDX2BzNxmMXPrIlPiKdql4HE0lmrUrYMqwQIBAtbDdIzL7Nt/Z9atQ0avp9Yq8OQXNmZqbhzDSYNhEfzKP2Hja/ddBcWgXtYrztw92dY9xRugZXj+8T0OEK9d5yzd5yXZmbattC7Hgb8XQbMdICAMH08ZZUwGuLiQofPLaEjW8ZyM4Xj6O596uavBNjld1EBgA85/kz/7JVf/4gyHsfQV5O+9991BNz5e3uFIpO0RmT/a/CosDzLsLnAiwCAIEIi0pBsmuIm4OQEDZcEMkI7kpKL92dWmXNdB3cSVxPCBGK7PuwLvnSS7eq1sLYzayxFgA8P2z1/bI3fPmb192aQDWv3nF23CJrP602Va4BUk8tpFUw9Hk+s4/w/rPMup1o+n3YbAzac5+hIScL52TBY/dAZQ3sOqzedUD10S/hYWohJ9LdMcrdOtKjJv+2UCIGOFXD7C7V7i7XnqhQNU8SO7UjZrTGzZJEhAAgyI1VMYbvNhILlkPuRPGBSQqaiF5JYCqIRXz08SrHwz2FRLn9uDXLDhDp2SgmWc5i8fg+OqIpIq8bIGQ9lfm736gs2sqzDgBQkRodZYxSx6lIjczrCXHTEBLCBgxCgrNcjhAyUdnOzcuA54C6tlZZOo648n+NhUmVGbUAoH/4Ds+qX30b96lyrzvmW4g3Oyb2OPKYAgcp1FsLAaBJO/z8Ot/a96nR08nnJ0Bux+CLkzUMBvfEg3uCiMX8s8SuQ/ovDuimbyUi9GKKmU3SsUkGX4qJTzSwBuaGtPbmBLjoZM7b6XN2+qxLfcFOn6+hIsNwTiu4uy+0y8AaFQRd/C5TXI5eW4TsBDy1nI1KDfCfNzAVhDqnqFfvGi09HewSrKD7dC/10ByZy8VDO3TWDD8Ljm6dodZFdxi0hNFYnSd/rM5b4eBqCuyHEnTpZibII6BDNHBCQthwwQInusrlrCRUBtIQI5454qfpaO1vP3qL8qMHTwUAfKTSNu9d08JnACHtqD6en3b4EUIIyEEKwdDCOtMwu58471n6h63wjwexVW4GqzIIBC2a4BZN4P4RIAhiUTk6W6Q6d1H9WyH+7gScL0dqCqeY+SSDL1nPRmh4LSUaGFFD1f2H/cikV0AennBzhJMl3Bzh4gk7S5yz0xdczFkbU+Ygo8NwShxOTkJdE9A9cTgxVtQpCLEFyGVDsPdEoe8kBSN2ryJgFVTqFAUAzXeHiPh0lNhU1mos4hN76S7T/ayoLd/f++7ddaEHRhRNjMXEWIyMpdh9LiSEtxohIWzAiDxvL5S5VmXN9B3a5afpKO+odp8/XPdZHZPu23aQ3X2U6ZgplFZir1S/7IAcpBAMLQSA5Dbi9B996xdQY1+gHh2FR9x2Y+cukSQkxuDEGOjZ/rKRhMur4VwRda6IOluo21eF3V5wuMDjRW4f8rDg9CKdCmtorKVFLY05Ebk45PYRTh+iSaxVg1aFDRqsUSOtBox6nJyJBsVCSjyOjxKpS3+COLhhPz8UlcIriwk3jZ/6lotKCfykAatgnVPUrsQpigSs+3QvNeYluac4l0eojKTWX00JSWlryw+GRbcHAMF56Y1TQ2pFfMMHe4VoaISEsEEj2ItlrqSjsj2HPyFGPXq9BcaMXoVfzhB9bkKlRQSpjki1/+MjjAT+bFH40lnSVxKQgxSCpIWUCgY9xWfkCkueZTb/Rjw6UmymuL98vYi0QKQF52Rd9eXf1cvpBo8X3D7k8RIUiXUa0GlFveaq8en4Tx/+UmwOWPojsWIzDHpK6D6OR/XImA1YBQGg8CO7w6dzy3eKAqjWHCFMMShVek5hHeKRnUyE/8WoWccXDv482RrfIyymk1hzAvMuHrPlnqKQOXgLEhLCBo3gqZS5kjYlgNeNK4pQRNw1FzDh8aZW/c598kT86Ncdeds8RXnpy3ZU1K6gmieTMbKKsQNzkEKQtBAAkrLxc6t9274kp7xHt0jGD4/Azeth0AQXvRb0l1LuG8olXUmtHS35Eb7bRLQdwE9bLVhi6nWR9VFBz3n+7Hv26i8UOEVBxPrFe6hh0+SfBR/aoUq99pTXy0SnDDJFtCo88WXxyW+dlccBgCYYMxMepVE20zXETUBICBs0IusCkQNCjjcSMZGZ/NFdqPfI661ImvDuqXn3HnwshdJbUib+2+BKc3fqzms8cq+GQDWvDD9778eW7mp9prJy62BpIcVAr/uEbncLu76hpr5HpcTgR0fhzLSGqD0NhFo7+t8GWL4etewlPrfSZ02q779VfVRQ9OHDEyvsD/cUEuQ6RQFAteEEQRqJpm1krse2KlxTQYelSq7U6OOadniOtxfVbHpZ/vWEuPkICWGDBpGM4KogDbI6HzKR2exvO4jrCyGpNTWb/r3gsZNqAyAEGAwrq+09fEKc9JjvOoQES830QQcnrOu0IZqyKEuxYCLJzBXxvw4trDhHjH+TDThBAwAoBrrdzXcaKexYRj73AZmegB4aKmbLy6K4daisRUt+hB82E+2G8NN+rK8VWEf+DmLxU6qUd6ICUEEAyHu+2mGNdY9R4BQFjPULd1P9HpN/hHhkJxOVcZVX2g++oj0KrifEzUho+kQDB/EOuWFCxtoCF+aDQ2JmBakxwv9Hh9QnvcaZ6wAreET6BmQ4+rfZN7Kcq1HcqEwVQ7Vam3hkP/PmnerSU/Xt6UKpcI97+Zd/9aUM4//xETFuJvHjFsRy9dz1ZuBIAcyYj0ZPI0pMePo6712v8/VXQdYLX7/GLH5Ok744NmJwIF3dTr5aU3aArH59BCgJTmq+PUhiPZHRScGZ9m1WRchtVQOi4Dm1TsHmIW5GQkLYoMGCl6uR2xoUUSomupW47xf5+5O97qBrKO2Kw4quyv5EbnWnVvtGlPPVirWQtpId9yUbJkW9PVb9039oXO+unxQD3e8RZm729Xme+/YQDHmSeG8JcTAPibeeu7S4HC1dg8bNJGZ8RIT1FF/Z6h31KhcmXYYqzZn96PXb1Ser9W1/TQzrFki9+alZtYU/o8qF47FWwWwsosJhmLuVHjtdvnZiW5V4IV8VI1cIOUeRzK7cIW5iQq7Rhg3GXGWB/OWa+M727Sv9eEevBhH03dN17z3h7ZYiRsmYa/P/OJ7MBYC9dxzqsCJSqY8UAKJGG0xd1DumlB7Y4HvgLV/A1dyXIQjIzBUzc9myM2j/D+Ssr0h7BerVAXq3FdtnAH1T3+anC2HzXmLjflReDa36Cv1f5Jt1FWX7BSXgfPDDXHrHd3Tq21Hyx81fxalZNYU/QdVHE0Szsh6exlfWkz3ukNlKpg5x13pVbHv52ibUnoP6v46FaOTc1E+ImwLBUQyAAWS9EVPhzeCIE589jlJaytwfRSeR3UeYXvmpZoFElt1V1FML1Ql05rcJxZ/b3xpT0e9Bvt/EAPt7XUVUEzxoCj9oCl9dhA6tJz/aQEyfR7RpKfbrAD1z8F9Qq/6XceYi+nkXWr8HuVncopdw23Sc2TOQZtl+OHuA+HSais7UtNsaFcCvuI46FaxUroLq1Ufpc27y2bsVHCOKeMv3muwH5R/BVZ3CglQdbYibnZAQNnyQ4KoidbIqHBAitEm93T9/Q02UW3oMAFT/8eK721TrjvsGyJXPOuqphYAgdoLR0luz48myAz97H3jLF3WtubKBYYnDve/ne98P9nJ0aAOxfC05579kuyzxtrbQtgWOaZwzdpxuOHIStvyGft1HqA04e6B493whMSP4BeC8D76fS29fQae+FRlYRLCOgFWQqPEY3t7ETJpzva6B10Q8vJ2gjZRZQZEpV31a0YWFuCkJCWGDBxG87ZxMIQQAVWI318YXcE0FCpP9sCdJeux04z+frcpJEi3K3F/11UIAdSKd+V188ef2t0YH0zS8jDESd79H6H6P4LahoxuJNeuJD5aTmIcW6Ti7Cc5IhYxUrG+oU3cEAU4WomMFcOQsOnIaVVZCUkuxeW/xsWe5IL40XMW534iPp6mYDE27rdF0eOA+1tOzawNTQQAwzlpP5fRHic0UHSVuWK5PypW/Hou84JZbqhvib6S6uvrLL7+sqakZMmRI69atr/quKIo7duzYvXs3x3HdunXr1q2b0v0VCGFZWdmCBQsqKir69es3bNjVE6J9Pt/69eu3bdvm8Xg6duw4ZswYkgzq8+xWpS5fRhXrrxfolRCUWh3fmd38HTlikvyzoIR0skN/wxu/2N4eqvQK66+FdaZhWA/NtidLD2/23TXDl5Qd/Ke81oRzRgg5IwQAzlaOzh8hLh5Bu7ehk/NIgx5nNcOZSah5Cm6ZioM45y8AKmvgxBl0/Bz8dhLlFSBLFI7PEhO6i6MeEZOzRepGJnY4q9CPC+jdq6l6GoIAcHp27YV1ODAVZH49yRypJKc/oOgoXHgSKktVmdftMvhneEcxIhnMyy6lDfF34HQ6c3JycnJymjVr1rt37+XLl/fp0+fKBV999dXs2bMHDRqkUqnuuOOOJ554YubMmYpOIVcIvV5v165de/Xq1alTpyeffLKVyoB+AAAgAElEQVSsrGzSpD88Zzdv3jxr1qzhw4cnJCTMnj173bp1X3zxhaJLCXFtFObLAIAmOde7fTZ5+3hgFMTEqNsnMm89oNpY4MtVXJEXBC0E0KTQWaviS5fYP3y0KqmlOGyKLyHjRhk9pkicfZuQfRsAABa44pPEuYNozwFi+RdEaSFhDcfRVoiNgNhwHBcBMRE4xgoRFgjuq12tHZVUQmkFFFegoioorsLF5ai8HKm0OCVbTGyHe4wQx2WJ6mBMJ5bEVQvrF9Fbv6ai7jC022qtjyEI9VNB5PSaXltPjXsFaGVNG4QNy7WJveWXD0IoU6aRsGTJkqioqKVLlyKEwsPDZ8+efZUQDh069O6770YIAUCXLl3uvffeF198ESmp0pErhMuXLzcajYsWLUIIRUVFTZ06deLEiVeeKTc3t3///nWfe/bs2aZNm4ULF2q1DdXl1KhQlC8DAKTWyliaibvWox5KzDuaZkY9a5z9SmVOItYrzioJihYiAsWMN0WNMZZ+ZZ87sSo2Tbjzee5GxMD+cFIS4pqLcc2h6xgBAHgWakpQ1UVUXYSKCtHRQlS9E1UVI1sNWCwoOgJbjFirRjQJBi1WU4ihQa/BNA06DTAMqGgQMbjcwHLIy4LLDZyAXV7wsIjlsdON3CwuLkNlZUAzyBorWuIgLFG0dBCzE3DvOLDEiRrDDf1xr8brgk1L6J8XU2G52tYbrJrk+prD9VFBADDM2UhmdCPSshUdhZ01+OhOVe/Zio4KZco0CjZu3Dhw4MA6uRk4cOCUKVM4jqPp329Ug+H3vxmSJBmGUaSCIF8It2/f3rt377rdc3NzT58+XVJSEhv7e8eTKy/LZrOp1WqVStkLXYjroyBfpg5NUq59w1Kq+2BACl6QUdNWZEZP0z/W1r4/XFHVcx2OJ3ORIOwdeqT1FxGalMCfpwSDYieYoscay76yz5tYlZQhjJga4OT0AKAYiEjCEX9qRSZwUFOMqoqRqwZ5XcD7wOFE1T7gveCxI2wDrxNYD+JZQAg0RkypMK3Baj0iVFitB0aNdSoUbsCMBnLjxfB4/NeYen7wudHmz6mfFlHm7ppW6+r1K6tDZHHe9OqyfWTFovuwKZByQ9W646pdxeS01xWfetNKdXxHglH2bxrKlGkUFBcX9+3bt+5zdHS0KIqlpaUJCddoCevz+WbMmDF16lSlp5ArhCUlJZ06XWruoNPpdDpdcXHxlUJ45aU89dRT06dPv16MsKioaOvWrSNHXqp1y8zMfP7555Ved+NFEJS7YhTmywAAbW1KAC0e201kdlZ0Kmr4Y8y8x/ULdzgnd1V4lQAA9ql9+VjzntyNqS+Y4ycp6819FQSDYiaYou4yFC22vXdfTfOuQv+Hbrh16AeSBmsSrn+vzoaAswpt+ZLa+DkVdpu29Xpr/SUQADznuMOTqxzm6OpP7sC6QCKZ1IlS46wNzKP/QmqFpiTrFbd8r+70rKKDAsuUwRi73W6lRzUcWJYFAJ4PsN+vWq0mpJzPJgqiFXqUvK6yowf23nXXXVd+cfDgwePHjwcAkiRF8dIfft2Ha4oLz/NjxoxJSUl59llldwLIF0KGYa78t+M4Tq2+xs/Kcdzo0aOTk5NfeOGF621lNpsTExMv/8wxMTG3lO0oeRv9GSx42bJD8vNl6tCmDXX+799Es/ZAK3nM0TQz8Z8w9wlMk64HlfS1+n/cozuIRu2p+b9U769s+UZYwG7SOggNkfBEWOwD5uJPbfMm10QmCH3vZbNyReoWumWCyYUjxK9f0b+tJSKG6rPWhGnTgpF7g6HwE/uZt2odD/Vw3dMxAF8CAFAnSsMmLaPHPI8S0pQeK675L2NtSemVNdHhq08GkCmDEGrUz6s6rx7DBPh7l+NyFDcXeS94le17xhMZGTNq1B9KmZs3b173ITY2tqSkpO5zcXExSZKRkZFXbSAIwr333stx3IoVKwLI05QrhHFxcRcvXqz7XFZWxrLsn81BQRDGjRsnCMKyZcv8XIpOp0tKSho9erTSa705UOq8BgDAmC1V1gUNAFTR2d6L24QNX5GDxis70hhOP/Whbt4UEATXpEDsQu/ADN9tzTwLNtV2O9jiLUvE4Po6AUkdSnjcHD/ZXLHaufK/NV/MYDNyhY638y26i+TfmuHZWCjKR/tW03vWkAJBRIwxtt9tpq3ByfzxXuCOPlljd2prPn2AT1HgtLgSKq/M/PAyevRzRCvF9xsuOS9sW2Pq8YrSA30lB0H0KT0KrmOONBbqLr6h/QgEpYmMvloILzNw4MC5c+fOnDmTJMmVK1f279+foigAyMvLs1gskZGRoijef//9VVVV33//fWAaL9c6GT58+Jo1axwOBwB89dVXPXr0sFgsALBv376CggIAEAThvvvuq62tXb58ecCvGyGuBxYF3l6k9Ch9xlhx47e4skTpgchgoZ+cq1txUvfRdqXH1oEZyj6lb+V7dx99zXPogQquKgguTURB5HB95ncJHfYmu/vEfLfMOK2z+uNnmMO/kEKo1/a1qLqINn5Gvz5U8/6DmuNsWPKHce12pyQ+HR4cFcRQ9F/H7r4lpR3aV372YL1UcNL/mLueI1opLv8CjIUv39M3HUaoFfvhfSUHsBgaRt8IqHMf9u/f/5FHHpkzZ87l0ogJEyZ8+eWXAPD5559/8cUXbrd7yJAhffv27du3b51UyUeuRdizZ8/OnTt37NgxIyNj8+bNK1eurPv6K6+80rp161mzZn3//fdLlizJyMi4XMy4YsWKxMRERVcT4rqIPFt6iDJee+ju9SA1YZqUfr6l/yKnvK30hJe0cN4UAAjMLgQALjuuYvlk74JNtu7BMQ3roCxk9GhD9GiDr4Sv+N75zSL7Z9O4jF5Ch0FC0NuMNUZqitFv68k9P1JVFwnrEEP0m4bmHdWyk45l4b3AHX2y2u7U1ccQhHqqIADevR7V2tUZPZQeKHqqsc8ZwBlD/PWo1ert27evXr3abrfPmDHjcprMhx9+GB0dDQB9+vTZsGHDVYcoOoXcZwZCaNmyZbt3764rq7daL9368+fPrztlr1699u3bd+Uhf3bjhggYLPK+4n3apoOUHqhr0s+3fZZ4aFsAD5qgaGGdaejp3fLozO8sK9wt3w6vZ43alahiqPiHzfEPmz3n+crvHF+/bxNmCpm9heY5Qnon0Rx1MyS2yMTnQWf2o5N7iCPb6OpCFDFMZ33J2KSTGskfBC8TDEWfO079s8Yxvpt7QmdMBr5/fVXQ7eC//Y+p3WOKUqPr8JUeDuCoEH8XarX6zjvvvOqLHTpcGmwZHx8fHx9fn/0VvDwjhC4njl4mKSmp7kNYWFi7du3qcykh/MM7ijHnQbTCrHSCMLQca/t6HmreDqkUZ7QHRQuhzjRcNtn3wUZbz8NNZ5qj79RDUIMUmiQq4amwhKfC3KfYyo3udT+7v5rlVRugaY7QoiOfniNa4m5CUfS64PReIn8vmb+bKs3HYVmMtpsu4mVN0y7a4P7zXsZxyJf/Yq3dq6/+70NCkoIp83+mnioIAMJ3i9TR7egwBZ1FL+Mr2o2FQAKEIW5KbnkvUuMBkRRbcUxp7igA0OHpjLkpv/ozcuQjgZw3SFqIVZTt2X7ufhnc3PWn3y1KfdYYPdIQ9Oe1No3RpjEwyQwYXPls7Xbvhq3OZW96aBWk54gtO/Gp7XFkciOODLlq4fR+Mn8Pkb+HqjwNYa1oXVed9WVtk3ZqQh1s4+8KHId9p+bY7Yc4x8QerjvbQf0MzfqrIL6QDwe36Xq+FsjBIsfVnAvsvCFuSkJC2GjAnJct3h+AEAKAoeWo6l9fwR37ofjUAA4PlhYCAJcdV/nx/fSBQt+CX07NKWrypDF2XPDlEAAAga45o2vOwINGAHCfYmu3ezfudK2Y6+FsOCIN4tLFuFQhtqkYnYYtcTignP8bjtuGik+i0pNE0Sni4kmi7CTyucHSltF11UXN1qa3VRHMDb9u5wn29Nu2mh0+57gu7tk5WFXfh0b9VRCwKCx5T9d8pGIHCQAAcJX5BEmJYijDKsQlQkLYmPCVHTUo6bV2GcTodemDXV++Rz33QWBlXshgoR9/XzfvCaBI1wOB1BdeCdc2oWLRffSBQvbfv5xdUJI61RB0Z+lVXLIUJxgBgLcL7nzOnseWnmS3f+51FbCsTbSmEbHpYkIqH50mmiKwKQoMFvxX1mY4q5C9CmzlqPICKjpFFp0iSgsQ5wVjOqVprlI1U+sHMlFNGVX8X/c368pjT8+1V2/yOsd1cb8UBAmEy/WCo+uhggDirysJDqnjOwZ2uLfkNzHkFw1xBSEhbFxgzlZImwLJxVUl9XDv3CXu/onoNCCwcyNTOP3kB7oPnyIv1Npn9AWmvsLFtU2oWHwffaDQN3/D6bnFqVMM0XfeGOvwj1BG0tiBNHb4Pa9McIiuAs51wvdbgY/9xseWCZ5SwVslqo1IbwVjFJisYlikaI7AxnCsD8cAoDUBAGgMGCFQ64CggFEDpboUicQYPHYEAG47AAavE0QR+Vwg8MB6oLYU2atQTTlRW0HYKwl7GXZXAW0AdQSpiiLpBFrdTK2/ncluyqjj/p6/UFc+e+Z9R/Umj+PeLu61HbA6OG8EqvUnjK+tp8c8H0C94GWwo1pY/XlYp2cCeCOsgy05CKHCiRBXEBLCRoXIs8UHAhNChAhDxt22b+ehZu0UjCq8ahNTOP3MQlg4nRnw79oFd/HNogLb50q4tgkVHz+g2nqa/c/G03OLkyfpo+7QUca/tOCXNBDGdipju6s7hrCVAlshsCW8u0KoKRX4MlY4ynNVAgLM1mIEmLNjwJhzYswD7wGBxSSDBBYDgMqEAAFtIBABlB4hEpE6hGhEaAg6hqIiKbodrYomoyOopBiStpJ/gZNTGgGqt7rPL3bZ9vmcE7q617YPlgQSTp/+nU3qrRfoR99FCemBb4Sx8Pm7moTupOEa/R3lIDhKMK+w70mIm52QEDYmsMh7z/+qazEssHdh2pSoTenr+fAFauq7oA+wEShSa5kp88QDv4Y99J53RKbj8R71Nw0BwNc9tbx7Kr3vvOfrXSdfPWfupo29U2Ptr7uhCSCSMFaSsZLQQkGDCNGHCVUDkDSF2Pf7Sr51la10CZEGxx3dvK9nBksCAUC19bTh1Z/IlDbUc4uQzlifrYQV/yHKK7SdFDZLugLvha2AA+y0GeJmJSSEjQwscGxlHmNtEdjh2tT+mPd635tKTX0vYC0EAKJtTyY9Cy1/XzV0kf31QWyH4HRO4NonVbVPQk6vbdPJqi8OkVMuhOVq4+7Sht+mRXTjUJfGpYKufLZspbvkWxfHkp7+ma6P2wjJ4UHcHzl8xnc2qbYX0mNmoGb1La8SvlsMv+02d5yKAm2agEXec34bFkMzCEP8gZAQNjIw73WdWMV0D1AIAUDXbBjkQ/21EBkszAOviYd3mp9719sr2THtNqwNTms9rFd7h2R5h2Qhm8e+5VT1v/cRTxRa+mjjx+jM3W9Ahfith7eIr1jtKlnp9RQK7ttael7O4NpeY6hNPWE2nzS9tp5s0Zmc/loANaxXIXy3GPZvC+s4FTH6gDfxXtwFOBQdDHE1ISFsfPD2Qs52IbBIYR3B0kIAILI7M2mfoR/+rRq+2PbaQLZTINXN1wObNJ4hWZ4hWWRRrWPdscp/HKTslVFDdeE9VKYuGkof6gyiBAEch73VW72lP/o8Z1lf3xaux7K5Ngn1rAi8JmSly/D6eqbATt0/m0gO/KXtMkFRQYxFd973oQBhiD8TEsJGiMB58lbRHZ+ozx5B1ELQ6unR0/DxPaYZ77AdYu0z+gQ2lNUPQpzZ9WBX14NdqVMVtk152nmniYcuqFtoI3rQlu4qU47m7w0lNlwwOPPY2i2eiq2sfacbR+m9OU28DzZlO6Vg6ka9RqjWnzC+voHsNJB67kFlI8CuQ1BUEAC4kt8w14hHCYa4cYSEsBGCRbb8hOAqJ3X16uaqazYM8oKkhQCoZY7qhU+J7//DDF7kHt/OPbYd1iuczikDPi2CT4twTeyOeJEqKKvceVb7dgFx8JwqTRPZm7b01Jo6qRtXlO5G4DnH2XZ7K3dxNT+7RZrytU7w5jTxPZsqRtUrUUUCjFWbTuoX7CRZNf3YeyiuSVB2DZYKAoAzb1XIHAxxTUJC2CjBWHDnf29o+1A999E1r9PCp6mp/6q/FoJaR9/1DM69m/hlie6Tf3uGZLkndRGswZk4cRWYIriWMVzLGNeDXZCbZfYX1u49rZl5Gi6UabO0pizKmEnpM1W65kyDKEu4wXjOcc5jrPMoW3tEcB7yCphgOyZ7ctLY8cli9I0UvzpEzGw5ZfhgG+mjqV7jiJw+wepnHUQV5CpOCO6qoFxViJuPkBA2TrDgLT6ga1lLqM313CnIWgiArDH06Odw3/Fo09fq4Yu8gzJdD3UUIw313/l6YC3j657q655qB0B2L328pCyvTP1zMT2/FJ8vZpI1+kwmLJMwZKn0GUywBtL+jYhe7MpjnUd89qOc7ajgOe4BPSU2j/CkN2H7RvNPRgsJYX/RpfCCeu1x/YKdhMZC5T5GZHUKrG/RNQmiCgKA88QKENj67xPipiQkhI0WLLpP/qjPurv+OwVdCwEAWaLokVNwv3vJTcs0wxb7eqQ5H+8qJNRrXoEcsFHNdkphO6VcigVxAnWqgsovLS4oUf9YgvKLCBVSJas0SaQ+kdAkkupESh1Pq+OphlmewZYL3guc9wLnvcA7L2L3ecF3nmOLfaiJmU2P8jaL4ydF8c2igh6UlYYT1GuP6/+9g9BZqdufIrI7B3f74KogX3tWsBcB3IQTSEIEhZAQNlpE3nt+m7bZMIIJgu9R13wY5PHed6eQj72BrDH137AOZLBQQyfj3NHExuXMmM/Z3k2dD3UMbqWaBDTJt4jmW0R7obUdAACIUjtVWEuU2siLNfSmGrq4iiipgnI3Gc4w8Yw6kdLHIyYc0WEkFUbSZoIOIygzSZmI4IceMXC1Al8r8rUCVyPyNSJbI/A1gqcMu86L3gscd9FL6GmIMwpxJl9MOBdnEXJMYpyZTwwD6m+zawmnT/3NQd1ne1BiC3rcayipeZBPgLGwYiH6bbep49MoGPc2ALhOrMShFtshrk9ICBs12Hl4ibH9w0HZS9d8JL+3jHvncfKhV4i0rKDsWQfSh1FDJ5F9xlK/fsvc+6WYGOYZ1Mzbr7kYcQP9pddDjDayfwqbIV4kyh1kkY0otRElNrrASdpdpM2DbB5k84Ldh20sohBppgkzSaoIwkAiEBGFSD2JQCQYILQEgTBBI1KHMAeCSxAxIbIgegQRE6IPRI+AAWEfFj2iYBeEWl60ccjEIBMjGtXYpBZNesGk44w6Mc4g5JjEWLMQZwpie5d6glie2XpavTZftf0UZHSgJ/8rWOkwV4KdNeIX/4LSUlPHqUF5wwMAtvQwV3UScMgcDHFdQkLYiMECx5Ye8hXuUCV0CcqGpg6PsqW/ORa+CpkdiJGTg+UmrQNpDeTA+8j+48Uzx6i9G/ULPuOTwrwDm3n7/z2KeCWYIoRYkxDr7+dFbhbZvYTNA6xAuHwAgDgRPCwAIFZAHg4AEMeDh8d6BBEqAMAMgTUMAABD1kkaZihQU6JBJRo12KgOYkTtRsEKzI4zmrV5qi0nITaRbNWHmPkyMtwAFzcW8dbV/PefqBO66DqNC7h3zFWIPrv9wGIcig6G8EtICBs3WGAdh5eSYU0ofXRQNmSi21giMtynf/K8ch8xaBzZe0SwMgAvQRBEWhaRlgUjnqDOHKP3bdT/51M+yeId2NQ7oKVoDUJA6AaBtQzWMn9FEmYDAAmYOnRRu+qYav3xOv0jX3wJjDcqxIsLTwlL3yV92NzxacoYF7RtsWjb/WFoEn0ISUJC2OjBAmvfNdeS+xoQwXGjIZLRNR2ijmpj/3Upt2Mdde8zwY8DwRWKOPRRKm8vvWWjfv4ivlmse1A617mJkFDfbNgQAYCcXmbfBfX6U6rN+TgumWrdh3zxhRunfwAAHqew6lNx38+61EHqlFwU1LcuT/73guMihDqLhpAiJISNH4xFr8155Gt9q3uDuCtpig/rMs1buMv5wQtE+1xy+AOgviEVgUDTRFYXIqsL8Cx1bC/98yY8/0tMYbZ9kq9TAtc+8a8rBrglQQ4fvf+Cek8hvbuQuFiJmjSjMrqjGTOQ6YbnNImHdwpfvceY0w09XkOqIDsD2KqTrlPrQyUTIeQQEsKbASyw3os7mahMJrpNUDdG6oTOTHQrV8EPvpcnkCMmEZ36BXX/P0IxRKuudSNbcWUJffqI+pdD4gfLgPdx7RJ9XZK4NvF82v+1d+/RUVVnw8Cffc6ZayYzk0kmmVxIQkgJF0FQYggU0BhB4eVSV6kv0retaLFruVr7roVWrdYF/ZaLZVFf237FG/rVFm2NLLmkCpHLKxdBLkIMVwXMhZD7ZC6ZOWfOZe/vjxPSmHCLTmZC5vn9wTpzsnPOk2Fmnjln7/3sb7mSIuqNhGXDF42mT2uNhy9y51tITi6fP4m7+14yamJUiqJdE2trpO/8D7S1Oic+JLhGRf34VAkHD/0Fs+CwEQwG33//fb/ff8899xQVFfVvIMtydXV1bW3trFmz0tMHXHILE+EwwVQ5cORNV9lKzhLlG1mcwZo8/j5LdkngX+9o+z7klv438eRF9xT9kbRMkpbJlcwGANbWaPjymOnjI+zPFUxg8uQRyrg0tShDK/IMUtma4YeICn+2zXC6xXC61XisiVzoIAVj+FG3cHP+k+SNAT6GnwNKRNv6Lt21wTLq7qTvL49yD3Q3Fjz0CsVqasNFOByeOnXqqFGjioqKpk6dunnz5hkzZvRp43K5PB5PQ0PD1q1bMREmNhoJHPyzc+bTg/HhIjjzXdOeCNduD//hl+SmUr78h99pnfGBIO5s4s7mps8DPSmeP0FrvqLbTrCGSuCJ9j2PfJNbHe1Wi9K1kWmDV0v6xsK1BIQzLYYzLcKpdsOpFq4twLKzuZxRvKeELCiKdfLTdfnp3i3azg8MrtHOWSs5czTHJPcmntuueM+BhhMHh4l3333XZrNt3LiR47jMzMzf//73VVVVfdo0NjY6HI7MzG85BxoT4fDBKFWDzV2nNtrG3TsoJ+A4a8FsS+4MqX5f+E9Pgd3J3bWYm3In8LGb3N2dFKH7Di3ztbEL50wXz9EPzrALB6Gjneamq4Vp6gibOsJJs13qCCdNTx6MlYaGDuIXhQs+rtHHN/gM9X6h1s9/dZHxAskp4LNHk5zvk6mjSPqIWP439cFaL9CdH9CDVcaMicnFvxLsOYN3LtVXHzr1Ac6XGE6qqqrmzZvHcRwAzJ8//7HHHlNVVRC+kbwcju/0vQoT4bDCNFk6v523ui35fW8dRAsRLJaCcvPIMrmlRqzarG56k8xayM34D2KNw1xA4nQTpxtumtr9GS9LrKnW2NLAGhvpF43MexjamyEYYBmpanaKNsKh5idrOSk0LYmm2Whq0tCZrn5NRKXEF+a8Yb4lSJr8QqNfqPXzFzq5i15ghKRnQFoml5LDuSbC97PIfQWDMtVvoBhjZz6nH79H67605M2y3v5/oj4ipg8t1Orf/wLDa8HhpbGxsby8XN/OysqilDY3N+fkRPPrFCbC4YZpcqjmHc1fG91BpH0Qwpk8N5s8N6u+r8PHdshV73JT7iTfn8vF6n7p5RnNJG+MPtnj35c/qszamwztF6G9iR5rpDsaWMhLfJ3gDwAH1GVnLht1WbR0m5ZqZikWmmKlNhOYjSzJQJPNYDFSq4FZjYMSsKwRUeYCESLKRJSJqJCAxAUl0hHiO0TeK/GtYeINEl+IBEPMbge7nThSOaeHSxkHI7NIsYekZka37kFUsKCXHtzB/ncTAZM1r8x057JoTZC/CtXf4P90DVVErCkaXyYDS7IOrIeCUO+pE188/PA3imTdfvvtS5YsAQBCCLtUGEjfINGuRIGJcBhiVJEa9mthr33KcmIY3HLMgnOkfdJDVPKJ9bsj//dp1WwhpXO4iaUkM39QzzsAgpF48vQBPn3enSwiQsALgU7W5QdfO2voZGe8LNTOImEmiyBJJNwFUgQiEkgRZrOA2cTMRmY1ATAgwCwmEHggDIAxixEEnpHutythBABIlwSMAeMAgARFAAaMEEUlkky6RBAjQAiYTJCUBCYzM5qJyQJWG2dKIrZssDlJZgqMSSHJLkh2kCTnDVCGpstPTx5kB3fS8zVGz2TLuP8yuApjc2bx/M7QyQ2MylhKLe6aP15VW/PVgH6lU25LzrHeeuutvXcWFHTX8MvKymppaek+eHMzx3EZGRlRCbUHJsLhiWmy3H66Y8dTjtseicGHEWd2Jo1ekDR6vtL+VeT44cjOD4DnyE0l3KTpZPQkEAbncuo7IyYLuLPBnX09GYaFgyBLEJEgInbviYSJpl3alkBT+/6ONYnApWNbkvRBTIwX9IRHTJY4jFgZBKzhLD1xgB37lLXUGzLGmtNuNt75X0QwxejsSjj4+Rty2xmsIHPj4oDLzspevnz5ZX86e/bs11577emnnyaEbNmypaysTO8grK+vT05OTkmJwjzj4fA+RJdHFRZR/PtesBTOto5ZGN2aHVdADGmjDWmjbQBaqE1uqY5seFvuWMnlFpFJ07nJM0nKDTwLkFiT4Zv9oOQK29c4TrQCii8lws4dp8c+Zcd2A3DGtLHGzHLjxPEktqld6TwfOPhnJou4uMQwtmTJkhdffHHRokVFRUWvv/76pk2b9P2LFy9esmTJr3/9awB47LHH6urqfD7fypUr165d++KLLw6oExET4TDHqBI+/7HSespe8sjgDVjvj09yWwrKLQXlVAkrrccjh47I//orcbjJhFJu3GSSN2aw6tSgwaNp7OLX9HwNq95Pz58wpI40p443Fv86WnVuB4iJ5zp/PsIAABRLSURBVD4OndqIA0SHPavV+tlnn1VUVPj9/s8++2z06NH6/ueff74n282ePdvn8y1evFh/aLcPrCYwJsIEoMqKv86747f2KQ8bM6K5vtL14AxWU/ZtpuzbgFGl87xcf1ypeUPpqCUpGVAwjhs1HvLHcpn5wOH8v6GI+TtY7Sl27gQ7d4I1nuWSXIJzlCntVuNdPyFCzFcDvoTKgcDBtaqvHrNggrDZbA888ECfnbNmzerZvuuuu77L8TERJgamMVULHFprGjHNNuE/YzCE7zIIZ3AVdndYUqoGLqid5+R9+5V/vaOGfXx2IRTeREaN4/LHgD2GK/eiPmSJ1n8Ftafo2ROs9iSosiG1QEgeacycLYz9OTFY4x0fKG2nAodfoYoEDKtpo+jARJhAmCZHGvYrbceTxt5rypoyONWtrg/HCc5cwZlr1gNTRKXznHrha/lkheI9D0C4jFzIzIXskcSTSzx5xBXlQWKoW7iLNdex5jrWVAcXallrPQ16hZRcwTHS6Cgy3HY3lzTgalWDR/U3hE5vkttOYhFRFF2YCBML0yJaKBKsfrur5l3r9+ZaRs4CLv5DOonBYky/yZh+k365QeWAFmzSAk3K0TNa+BMt2MQiIZI2AjJzuZwC8IwgrnRwpRMbrkoxELLEOlqgs4W1NbGL5+FiPW2pY3JEcGbxtkzBnME7S4QRi3hrWjy/IV2B0vFV+MwmxXueURUYjXc4aLjBRJiImCIxkEKnPwid3mQpKLcWzhns6YYDwhntXKrdkFpkvrSHqaIabNKCTdrpC+rnR6jo1cIdTIkQRzrnSodUD0lLh9RMcKWTlAzicIEhRmP3hxxKoauTeVtZZyvztkBbC2tvhs4W6msDReJsbt6ayltSjUkePuNOblQGH+0S7VGntJ3qOvGeFmplGs4RRIMFE2HiYqoMAOGz28RzVabc6Umj/yOWw0oHhAgWQ0qBIaWg906myTTcoYkdVPRqX7Wrx7+kklcLeZnoBSKAzUVsDrA5iSMFnC5IdhKbk9idzJbCWWxgsYJlcMt9RZ8SATHExBAL+iAUAH8H6+oEvw+CPubvgC4fCwWYGCQWO29NJRaXweTkLamcbTKf7uLMLs4Uhxp43xpjVG6pCZ2ooBEfU3AdCTS4MBEmPKowAKl+b6R+ryF9gqXgDkNqUUwmHX5XhDfyyZl88mXqzTNVpJEAjQSp3EVFP/MFNbWZKl004meRoKqIVBZBDhNzEpiSiMkC5iQwW4nZCknJYLGCIOjz34nZyjiemKzA88RkBl6APrPgL02T/zfBAGq/OW1i6Bs39MJBAGBiFzAAsYsxBlIIKAVJJJrCxDCIIQh3gRRmUhikEJPCTA4D4TiDlRgtxJTMGW2c0c4bbMRo44yjSZadMyZzpmRitN0Q/3dXoYVapfq9Yu1uoApTcY48igVMhAgAADSFASjNR9W2kwyYMX28KXOKMX0cMd5ol00AAEAECy9Y+KRrDLGhShgUkaoiUyVQJaqINCwyfxhAYcpF4BhVJQD9X8pUiTHKFAmo1jMrniki0TMcAQYEAJgqk0uVdEjPrTyjtXsmPQMAIEYrASAGKwEggoUA6f6XNwERiGAngpuzW8Bl5gwWIlg5wQIGc3zG+sYG1WTvV3LzMfni5zTSBUAZ7VemB6FBM3zfWmjgGGNMlQAgcvFzufUEUI2zpJoybzZ6JhtSC4dNUZQenMEKhgGWB0bRQyNBpeOM1PCZ0nYCCAEqM4q9gCgOMBGiy9PvSmmhFvH8drF2DwAzpI42ZxcbPZOG1MgadGNhjGqBBrnleKTxM62rFTge73+iuMNEiK6BUQpUBAC55Qul40s49v84s1NwFhjSvmdw5PGOEYSP/wQMNGQxRmmoRemsUzvPK96vtGAT8Aamyt3T4fEWKBoCMBGiAdBvnGrhDi3cEWk+SngBVIWYkgVnntE9VnDkCc48zIuISj7FV6d6zyve06qvgQEjhGOq3N1HiskPDTGYCNG3RVV9RAOTfHKzT2k7CURgmsyZ7HxShuDM4W2ZvC1dSMrgLCnDr38R6agS1rqaaahN62pWAw1qsJmG24HjAQhTZYDusbLY9YeGMkyEKDqYpgAoAEClTip1Kh2nCScAEfQRgLzZySe5eccI3pbFW1M5Swpvdg6FwpXoOjFNpZKPSp1U9GqhNjXQoAYvaqIXqEZ4IwFC1V7FP/GaD91QMBGiwcKoCtD9gaiJXk30QvsZwpuA44FRRlVgwJlsnMnOWVx8coZgcRFLKm+yE2MyMSVzgvnqx0fRxTSVKUEa6aKST4v4abiDhtu0cAcVO6ncBVQGzgiEAAOmRXpPi2RUxQs+dEPDRIhiimkR6LVmAJV8VPKBvx6aAXgDIQIQAkwDTWXAiGAmBgtnSOLNdmJycpYU3mQjhmRisHT/SLAQgxVHsV4F02SmiEwNU0VkqsSUMJXDTA5QKaCJnUwOUrmLKSGmiIxRwgmE8IwQoBqj/UqaUazwgoYnTIRoyNAUBt+oycKUMFPCFDpUv76DEF4AwgPpmdBOGaVAFeCNhDdwvIkYzMCbOMECvIkzmIghiRMsIJiJYCKcQAwW4IwcbwCOI4IZAIhg6T4sbwJ9ZuEQwDSZURWopo9OYvqMfk0BTWGMMlUETaGawpQwUJWpYaqEmSIxVWRahCkRpkpMk5gmM00G4IDjOMIzwulddYxqcIXS1UyT8doOJSBMhOgGwnp6IvvSZKbJGoRAvNzvEY5wHBABALqTKCFAKRAOKAUCwKieGP5d0IQ3kEsDfAgnAMcBEABCOIERvteRgcA1Z+Qz1uvSihCmV3nVB5IwTem58GL00jbhCUcYAMcJjDEgHLBLkTP274AZu44KLBpoGr3sk4YQAgBMhCghMMo02tNheV00pSd3xWEZdKZ1z7LTcNQJQoMOy0shhBBKaJgIEUIIJTRMhAghhBIa9hEihBAa0iRJ2rJlSzAYLC8vz83NjfrxB5AIa2pqNm/ebLfb77///tTU1P4NvF7vO++84/P5FixYMHHixOgFOXxEIpHdu3fHOwqEUIKqrKzUNG3x4sXxDmQAJEmaPn260+ksLCxcsWLFRx99VFJSEt1TXO+t0d27d8+YMUOW5YMHDxYXFwcCgT4NgsFgcXHx/v37VVWdNWvWrl27ohvo8BAKhc6dOxfvKBBCCaq6urq6ujreUQzMe++9xxirqqp69dVXH3/88VWrVkX9FNd7Rfjcc889/fTTK1asAICysrK//vWvv/zlL3s3+Nvf/padnb1+/XoASElJee655+64446oh4sQQiihfPTRRwsWLOB5HgB+8IMfPPPMM6qqCkI0+/Wu64qQUrpz5865c+fqD+fOnbt9+/Y+bXb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"contourf(x_1d, y_1d, u_1, aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar_ticks=(0:11, LinRange(0, 1, 11)))" ] }, { "cell_type": "markdown", "id": "089a4598-cf31-4662-b74a-f029312366b4", "metadata": {}, "source": [ "### Exploration\n", "\n", "Implement backward Euler for this system instead.\n", "And maybe the $\\theta$ method." ] }, { "cell_type": "markdown", "id": "342abc5b-9bae-4215-b3df-d9cbd67f6238", "metadata": {}, "source": [ "## Building it out\n", "\n", "Ok, now it seems like we need two things right now.\n", "\n", "1) Something to take our time stepper (`euler_forward`) and our finite different matrix (`A`) and create a series of outputs.\n", "\n", "2) Something to automate and animate the plotting process.\n", "\n", "Let's start with 1).\n", "We'll make a basic function `run_simulation` to produce our values $u_n$ via our PDE and time stepper." ] }, { "cell_type": "code", "execution_count": 5, "id": "33149a77-4311-4a03-aba6-cfc85ac655de", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u[end, :]) = 0.005169326243333146\n" ] }, { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function run_simulation(u_0, h, dF, time_stepper, t_f)\n", " # Setup\n", " num_steps = Int(ceil(t_f / h))\n", " u = zeros((num_steps + 1, maximum(size(u_0))))\n", " u[1, :] = u_0\n", "\n", " # Simulate\n", " for i in 1:num_steps\n", " u[i + 1, :] = time_stepper(u[i, :], h, dF)\n", " end\n", " u\n", "end\n", "\n", "# And run it\n", "h = 1e-5\n", "t_f = 0.25 # s\n", "u = run_simulation(u_0, h, dF, euler_forward, t_f)\n", "@show maximum(u[end, :])\n", "\n", "# Plotting the final u as a sanity check\n", "contourf(x_1d, y_1d, u[end, :], aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar=:none)" ] }, { "cell_type": "markdown", "id": "c4a803db-3895-4a6a-a8c4-2fc905335ebb", "metadata": {}, "source": [ "It looks like the temperature went to $0$ on the whole plate, which I would expect given the boundary conditions.\n", "\n", "## Pretty pictures\n", "\n", "Lets make an animation now!" ] }, { "cell_type": "code", "execution_count": 6, "id": "312d2054-6871-481f-a4a7-26d7ef0920ce", "metadata": {}, "outputs": [], "source": [ "# We wrap the plotting in an annotated loop\n", "animation = @animate for i in 1:Int(ceil(t_f / h))\n", " contourf(x_1d, y_1d, u[i, :], aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar=:none)\n", "end every 250;" ] }, { "cell_type": "code", "execution_count": 7, "id": "ec0e6934-9050-42a6-9f2b-aa7058556672", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mSaved animation to /home/jeremy/Documents/csci-3656-fall-2025/source/notebooks/heat_plate_fixed.gif\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Plots.AnimatedGif(\"/home/jeremy/Documents/csci-3656-fall-2025/source/notebooks/heat_plate_fixed.gif\")" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gif(animation, \"heat_plate_fixed.gif\", fps=30)" ] }, { "cell_type": "markdown", "id": "4e69ec3b-7d94-4572-843b-b834e9aed55b", "metadata": {}, "source": [ "Note that the temperature uniformly goes to zero, which we should expect as the temperature on the edges is fixed at $0$." ] }, { "cell_type": "markdown", "id": "418c7304-b1d5-4ebe-9f4f-5eaa41bbab1d", "metadata": {}, "source": [ "## Different initial condition\n", "\n", "How about a more interesting initial condition?" ] }, { "cell_type": "code", "execution_count": 8, "id": "423e88c2-1ea2-4300-845f-9f455112ce66", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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9, "id": "46510ac7-4087-49e7-aad6-64f1749cd722", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u_1) = 0.9889907175516975\n" ] }, { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# And take a single step\n", "h = 1e-6\n", "u_1 = euler_forward(u_0, h, dF)\n", "@show maximum(u_1)\n", "\n", "# And plot\n", "contourf(x_1d, y_1d, u_1, aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(-1, 1, 11), colorbar_ticks=(0:11, LinRange(0, 1, 11)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "785bbe1f-ccbd-4c24-937e-b9c658e06c3f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u[end, :]) = 7.491934145799629e-10\n" ] }, { "data": { "image/png": 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", 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[ "# We wrap the plotting in an annotated loop\n", "animation = @animate for i in 1:Int(ceil(t_f / h))\n", " contourf(x_1d, y_1d, u[i, :], aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(-1, 1, 11), colorbar=:none)\n", "end every 250;" ] }, { "cell_type": "code", "execution_count": 12, "id": "1ec29ef7-1bec-4f90-a16e-0184f2029372", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Plots.AnimatedGif(\"/home/jeremy/Documents/csci-3656-fall-2025/source/notebooks/heat_plate_zero_2.gif\")" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gif(animation, \"heat_plate_zero_2.gif\", fps=30)" ] }, { "cell_type": "markdown", "id": "acbb0400-6f38-4f9f-8825-22a73b7d654c", "metadata": {}, "source": [ "## Periodic boundaries\n", "\n", "Ok, let's tackle the periodic boundaries.\n", "\n", "In this case, we can think of our solution as \"wrapping around\", so in our 1D finite difference equation, we will have\n", "\n", "$$\n", "f'' \\left( x_0 \\right) \\approx \\frac{f \\left( x_n \\right) - 2 f \\left( x_0 \\right) + f \\left( x_1 \\right)}{h^2}\n", "$$\n", "\n", "and\n", "\n", "$$\n", "f'' \\left( x_n \\right) \\approx \\frac{f \\left( x_0 \\right) - 2 f \\left( x_n \\right) + f \\left( x_{n - 1} \\right)}{h^2}\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "id": "df70a461-bcf3-45d0-b36e-1d8304de733a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u_1) = 0.9889907175516975\n" ] }, { "data": { "image/png": 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", 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across plate edges\n", " for i in 2:n_1d-1 # x\n", " # Compute on bottom edge\n", " j = 1\n", " u_next[i + n_1d*(j - 1)] = (\n", " u_0[(i - 1) + n_1d*(j - 1)] +\n", " u_0[(i + 1) + n_1d*(j - 1)] +\n", " u_0[i + n_1d*(n_1d - 2)] +\n", " u_0[i + n_1d*(j + 0)] -\n", " 4 * u_0[i + n_1d*(j - 1)]\n", " ) / h^2\n", " # Copy to top edge\n", " u_next[i + n_1d*(n_1d - 1)] = u_next[i + n_1d*(j - 1)]\n", " end\n", " for j in 2:n_1d-1 # y\n", " # Compute on left edge\n", " i = 1\n", " u_next[i + n_1d*(j - 1)] = (\n", " u_0[(n_1d - 1) + n_1d*(j - 1)] +\n", " u_0[(i + 1) + n_1d*(j - 1)] +\n", " u_0[i + n_1d*(j - 2)] +\n", " u_0[i + n_1d*(j + 0)] -\n", " 4 * u_0[i + n_1d*(j - 1)]\n", " ) / h^2\n", " # Copy to right edge\n", " u_next[n_1d + n_1d*(j - 1)] = u_next[i + n_1d*(j - 1)]\n", " end\n", " # And the corner(s)\n", " i = 1\n", " j = 1\n", " u_next[i + n_1d*(j - 1)] = (\n", " u_0[(n_1d - 1) + n_1d*(j - 1)] +\n", " u_0[(i + 1) + n_1d*(j - 1)] +\n", " u_0[i + n_1d*(n_1d - 2)] +\n", " u_0[i + n_1d*(j + 0)] -\n", " 4 * u_0[i + n_1d*(j - 1)]\n", " ) / h^2\n", " u_next[n_1d + n_1d*(j - 1)] = u_next[i + n_1d*(j - 1)]\n", " u_next[1 + n_1d*(n_1d - 1)] = u_next[i + n_1d*(j - 1)]\n", " u_next[n_1d + n_1d*(n_1d - 1)] = u_next[i + n_1d*(j - 1)]\n", " # Return\n", " u_next\n", "end\n", "\n", "# And join them together\n", "function dF(u_0)\n", " u_next = diffusion_interior(u_0)\n", " periodic_boundaries(u_0, u_next)\n", "end\n", "\n", "\n", "# And take a single step\n", "h = 1e-6\n", "u_1 = euler_forward(u_0, h, dF)\n", "@show maximum(u_1)\n", "\n", "# And plot\n", "contourf(x_1d, y_1d, u_1, aspect_ratio=:equal, clabels=true, color=:turbo, levels=LinRange(-1, 1, 11), colorbar_ticks=(0:11, LinRange(0, 1, 11)))" ] }, { "cell_type": "markdown", "id": "2cdccbe4-b790-4de8-9d45-6de6786bb050", "metadata": {}, "source": [ "Hmm, I see a problem here.\n", "If the initial solution has an average temperature of 0, then we will do extra work to repeat the final result above.\n", "\n", "We need to swap the initial condition so we can actually see the effect of this boundary condition." ] }, { "cell_type": "code", "execution_count": 14, "id": "4981000b-2277-4740-9fe3-5d94e130b128", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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"metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "maximum(u[end, :]) = 0.40455907051979945\n" ] }, { "data": { "image/png": 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QjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0V4ghCdOnOjXr1/btm3nzp2bl5dX4k8fPny4YMGC7t27d+zYccaMGWlpaXadEwCAcmFrCB89etS7d+9+/fqtX7/+8OHDixYtKrHgypUrDx8+nD179ooVK65fv/7222/be1QAAOzPaOO6LVu2REZGTp48WSkVGxs7aNCg+fPnOzg4FC3o3Llz586dte1PPvmkYcOGZrPZxcXF7hMDAGBHtl4Rnj9/vk2bNtp2VFTUo0eP7t+//3OLz5075+vr6+zsbIcBAQAoT7ZeET58+DA0NFTbdnBwcHZ2TklJCQoKKr3SZDJNnz59xYoVOp2uzENdv379m2++CQ4O/u8ERuOaNWvat2//wrO/igoKCrh/CcCLMpvNlT2C/WVmZr78QZycnAwGw7PX2BpCFxeX7OxsbbuwsDA7O9vNza30srS0tB49ekycOPGdd975uUOFhIR069Zt5cqVRXsCAwONRlsnebUZDAZrZc8AoNp5Vd+HqpiPy9b8BAUFXbt2Tdu+deuWXq/39/cvsebJkyc9e/bs37//vHnznnEovV7v7OwcEhLyC8YFAMC+bH0dbvTo0d9+++2tW7eUUqtXrx4wYID2FuBf//rX+Ph4pdTTp0979+7dtWvXjz76qPzGBQDAvmwNYVhY2Pvvvx8REREcHBwfH798+XJt/86dO48dO6aUOnToUEJCwqpVq3T/k5iYWF5TAwBgJy/wztycOXPefffd9PT04i+K7t27V9sYPnz48OHD7TwdAADl7MVuUaldu3bt2rXLaRQAACoe9+oDAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRACAEQjhAAA0QghAEA0QggAEI0QAgBEI4QAANEIIQBANEIIABCNEAIARCOEAADRCCEAQDRCCAAQjRBWLaYHpsoeAQCqhOXLl1ut1gp4IltDWFhYuHDhwlatWnXq1Gnfvn1lrtm/f3/nzp1btWq1YMGCgoIC+w0pSEpKSmWPAABVQkxMjMViqYAnMtq4bvXq1bt27dq2bdutW7dGjx594sSJ0NDQ4guuXbs2atSoLVu2NG7cePTo0XXq1Pn9739fDgMDAGBPtl4Rrlu3bsGCBWFhYf369RsyZMjGjRtLLNi4ceOgQYMGDhzYvHnzBQsWrFu3zt6jAgBgfzaFMC8vLzExsXXr1trDNm3aXLx4scSaixcvFi1o3br19evXc3Jy7DgoAADlwaaXRtPS0qxWq6urq/bQzc0tNTW1xJrU1FQ3Nzdtu27dutqeBg0alD7a999/v23bth07dhTt8fT0rFmz5i+Y/tXj2Kmd21utKnuK6s6qlK6yZ6juOIcvr+LOYfpZa0jXkIp5roqUn5/frFkzne6lTuPo0aM//PDDZ6+xKYRa4bKysrQNs9mspa7EmszMTG3bbDar/+WwtM8++2zo0KFG43+f2mAw+Pj46PXcv6qUUhaLpUZejcqeonqzWCw1anAOXwrn8OVV6DkMUypucAU9VwWyyzn09fV97hqbQujk5OTl5ZWYmOjv76+USkxMDAoKKrEmJCQkMTFR205MTKxXr16dOnXKPJrBYOjevbstzwsAQHmz9Tps7Nixq1atKiwsNJlMW7duHTt2rFIqIyNj1qxZ6enpSqkxY8Zs27YtOTm5sLDwk08+0RYAAFDF2RrCDz74ICcnx8vLKzQ09Fe/+tWbb76plMrKytq4caP2imiXLl1++9vfNm/e3Nvb++nTp/PmzSvHqQEAsBPdC/3cvtlsdnBweMaNLRaLJS8vz8XFxR6zAQBQ7l4shAAAvGJs/c0ysLukpKTNmzdnZWUNGzasTZs2pRdYLJZNmzbduHEjMjJy1KhRL3kP8Svp7t27mzdvNpvNQ4YMadeuXYk/zcnJ2b179+XLl/Pz8yMiIoYNG1Z0rzKKXLhwYevWrXq9fuzYsU2bNi1zTVxc3KFDhxwcHHr06KG9LYLizp8/v3XrVqPROG7cuMaNG5decPPmzW3btj158mTgwIGdOnWq+AmrOLPZfObMmcTExNDQ0DLPj8lk2r9//5UrV9zd3UeOHBkSYuefFeGHFipHSkpK69at09PTvby8evTocfTo0dJrhg4dunfv3saNG8fExLz//vsVP2QV9/DhwzZt2qSlpfn6+vbp0+fw4cMlFphMpgMHDri7u/v6+n700UdjxoyplDmrsvPnz3fs2NHJyUmv17dr1+7atWul18yZM2fixImurq5ubm5xcXEVP2QVd+bMmU6dOrm4uFit1qioqJs3b5ZYcOnSpdatW+fm5gYFBY0YMWLv3r2VMmdVNnXq1GnTpi1dunTr1q1lLpg0aVJ8fLyfn19ycnLLli1/+OEHO09gRWVYtGjRoEGDtO3Y2Ng+ffqUWHD27FlnZ+fMzEyr1XrlyhUnJ6cnT55U9JRV28cff9y3b19te9WqVdHR0c9YfP78eYPBYLFYKmS0amP8+PHvvfeetj1p0qTp06eXWHD69GlnZ+fk5OQKH63aGD169OzZs7XtCRMmzJgxo8SCCRMmTJkyRdvevn17eHh4hc5XHRQUFFit1unTp//ud78rc0FOTk7R9rhx435u2S/GFWHlOHbsWI8ePbTtMq8Ijx071qFDh9q1ayulmjZt6unpeerUqYqesmo7evRoz549te0ePXocO3bM+vNveP/rX/9q2rSpo6NjRU1XPZQ4h6U/Dw8ePNi7d+/bt2+vXLly3759zzjDYh09evTZ/5aTk5ODg4O17ZCQkDNnzmg/coYiz/2FKsXv0MzNzXV2drbzAPY9HGz04MEDT09PbdvLyys7O/vp06fFF5hMpqIF2prk5OQKHbHKK3EO8/LyHj16VHpZZGRkvXr1Fi9evHPnzoodsBoo/mnm5eX14MGDEgtu3bp15syZefPm5ebmzps3b9y4cRU+Y5VWWFiYkpLy7HPYqlWr7777TvseQnsBn3/Lv9iRI0cOHTo0depU+x6Wewcqh9Fo/Omnn7RtbcPBwaHEguL/p2N+fj5XMyU4ODiUOIdlnqLDhw+np6evWbNm8ODBZ8+e5bfaFlfi87D0CdTr9bm5ud9++62jo+OECRMCAgLmzp3bpEmTCp+0itLr9c89hzNnzoyOjm7btq2Hh8dPP/2k0+mcnJwqfNJXwfnz5995550tW7YEBgba98hcEVYOf3//ou8K79+/X7du3RL/Nvz9/e/fv69tW63W5ORkPz+/ip6yaitxDp2dncv8rX5ubm5BQUExMTHJyclnz56t2BmrOj8/v6JPs/v375f+HPP392/UqJH2xd3Ly8vT0zMpKamip6zafH19n30OPTw8Tp069fnnny9btiwmJqZGjRr169ev8DGrvcuXL/fu3Xv16tX9+/e3+8EJYeXo37//7t27CwsLlVI7d+4s+qs9ceKEyWRSSvXp0+fkyZN3795VSh07dkwpVfrHA4Tr37//nj17tOvm4ucwISFBC2R2dnbR4itXrmRlZQUEBFTKqFXWgAEDil4xLn4Ojxw5or1WP2jQoMuXL2u/PermzZtpaWk/9yMWYg0YMGDXrl3a9q5du4rOYXx8fEZGhrZtNBrDw8PDwsJiY2NHjBhhMBgqZ9ZqJScnJz4+Pj8/XymVmJjYq1ev2NjYoUOHlsuT2ffeG9goMzMzIiKiS5cuw4cP9/b2vnLlira/adOmmzdv1rZnzZoVHBz861//2tvbe9OmTZU2a1WVnZ0dFRXVqVOnkSNHenl5Xbp0SdvfokWLzz//3Gq1fvbZZy1atBg1atTAgQPd3NyWLFlSqfNWRffu3QsMDBwwYEDv3r2bNGny8OFDbb/BYNBuPrJarZMmTWrevPmkSZMCAwMXLlxYecNWUUlJSfXr1x80aFDPnj1DQ0MfPXqk7VdKHT9+3Gq1njp1qk2bNqNHj27ZsmVUVJT2v9qhuC+++CIyMlJ7ySEyMnLDhg1Wq1X7Xxy0z8muXbu6uLhE/s+7775r3wH4zTKVxmKxxMfHZ2ZmRkdHF/2XVRcuXPD19fXw8NAeJiQk3LhxIzw8PDQ0tPImrbry8vK077ujo6Pd3d21nRcvXvT29vb09CwsLDx37tzVq1dr164dHh7O5WCZzGZzXFycwWCIjo4uen3+5MmTzZo1K7o37z//+U9SUlLLli2bNWtWeZNWXRkZGXFxcQ4ODtHR0bVq1dJ2JiQkhIWF1a5du6CgICEh4fbt2z4+Pl26dOFysLQHDx4Uv4HIz8/P19fXYrGcO3cuIiLCaDRqr+gULXB1dW3UqJEdByCEAADReI8QACAaIQQAiEYIAQCiEUIAgGiEEAAgGiEEAIhGCAEAohFCAIBohBAAIBohBACIRggBAKL9H9ynOSeEyPJXAAAAAElFTkSuQmCC", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Running the simulation\n", "u = run_simulation(u_0, h, dF, euler_forward, t_f)\n", "@show maximum(u[end, :])\n", "\n", "# Plotting the final u as a sanity check\n", "contourf(x_1d, y_1d, u[end, :], aspect_ratio=:true, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar=:none)" ] }, { "cell_type": "markdown", "id": "4323cb2a-2f2b-4b01-907f-e0f308080800", "metadata": {}, "source": [ "Note that the heat went to a constant temperature that matches the average of the initial distribution instead of being uniformly $0$ like we see with zero boundary conditions." ] }, { "cell_type": "code", "execution_count": 16, "id": "1064ec73-222c-4083-9838-e0acc4e91d46", "metadata": {}, "outputs": [], "source": [ "# We wrap the plotting in an annotated loop\n", "animation = @animate for i in 1:Int(ceil(t_f / h))\n", " contourf(x_1d, y_1d, u[i, :], aspect_ratio=:true, clabels=true, color=:turbo, levels=LinRange(0, 1, 11), colorbar=:none)\n", "end every 250;" ] }, { "cell_type": "code", "execution_count": 17, "id": "3a9fc71c-d99c-4f28-b4f4-66ae9b99aa9f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Plots.AnimatedGif(\"/home/jeremy/Documents/csci-3656-fall-2025/source/notebooks/heat_plate_periodic.gif\")" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gif(animation, \"heat_plate_periodic.gif\", fps=30)" ] }, { "cell_type": "markdown", "id": "5246de46-3e86-4ab7-850f-93add2fda834", "metadata": {}, "source": [ "## Extensions\n", "\n", "There are several ways we can extend this work.\n", "\n", "- Time Stepper: An implicit time stepper would allow us to take bigger timesteps.\n", "\n", "- Fixed Point Solver: Our fixed point solver this week is terrible.\n", "Can we replace it with something better?\n", "\n", "- Boundary Conditions: Time varying boundary conditions would be interesting to investigate.\n", "\n", "- Initial Condition: What happens if we change the initial conditions (such as using an initial condition with a discontinuity when using the periodic boundary conditions)?\n", "\n", "- Recreation: We can see a hoof shaped region of high initial head on the demo gif shown on [Wikipedia](https://en.wikipedia.org/wiki/Heat_equation).\n", "Can you recreate that simulation (or another one you find)?\n", "\n", "- Finite Elements: We have used FDM (Finite Difference Method).\n", "See the \"bonus content\" notebook for a brief intro to using FEM (Finite Element Method) instead." ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11.6", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }