{ "cells": [ { "cell_type": "markdown", "id": "eff6b6a5-4360-4d83-9c6f-241cdeca014b", "metadata": {}, "source": [ "# 2025-10-10 Polynomial Interpolation\n", "\n", "* Interpolation using polynomials\n", "\n", "* Structure of generalized Vandermonde matrices\n", "\n", "* Conditioning of interpolation and Vandermonde matrices\n", "\n", "* Choice of points and choice of basis\n", "\n", "See the [FNC](https://fncbook.com/polynomial)" ] }, { "cell_type": "code", "execution_count": 1, "id": "c4278884-f9ee-45e9-8713-a32db4ea4c33", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Aplot (generic function with 1 method)" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using LinearAlgebra\n", "using Plots\n", "using Polynomials\n", "default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n", "\n", "# Here's our Vandermonde matrix again\n", "function vander(x, k=nothing)\n", " if isnothing(k)\n", " k = length(x)\n", " end\n", " m = length(x)\n", " V = ones(m, k)\n", " for j in 2:k\n", " V[:, j] = V[:, j-1] .* x\n", " end\n", " V\n", "end\n", "\n", "# Our visualization aids\n", "# Let's use the peanut blob again\n", "function peanut()\n", " theta = LinRange(0, 2*pi, 50)\n", " r = 1 .+ .4*sin.(3*theta) + .6*sin.(2*theta)\n", " r' .* [cos.(theta) sin.(theta)]'\n", "end\n", "\n", "# and a perfect circle\n", "function circle()\n", " theta = LinRange(0, 2*pi, 50)\n", " [cos.(theta) sin.(theta)]'\n", "end\n", "\n", "function Aplot(A)\n", " \"Plot a transformation from X to Y\"\n", " X = peanut()\n", " Y = A * X\n", " p = scatter(X[1,:], X[2,:], label=\"in\")\n", " scatter!(p, Y[1,:], Y[2,:], label=\"out\")\n", " X = circle()\n", " Y = A * X\n", " q = scatter(X[1,:], X[2,:], label=\"in\")\n", " scatter!(q, Y[1,:], Y[2,:], label=\"out\")\n", " plot(p, q, layout=2)\n", "end" ] }, { "cell_type": "markdown", "id": "4377599e-a1b0-4b6b-a6a1-f70b25f418e7", "metadata": {}, "source": [ "## What is interpolation?\n", "\n", "Given data $\\left( x_i, y_i \\right)$, find a (smooth?) function $f \\left( x \\right)$ such that $f \\left( x_i \\right) = y_i$.\n", "\n", "### Data in\n", "\n", "* Direct field observations/measurements of physical or social system\n", "\n", "* Numerically processed observations, perhaps by applying physical principles\n", "\n", "* Output from an expensive \"exact\" numerical computation\n", "\n", "* Output from an approximate numerical computation\n", "\n", "### Function out\n", "\n", "* Polynomials\n", "\n", "* Piecewise polynomials (includes nearest-neighbor)\n", "\n", "* Powers and exponentials\n", "\n", "* Trigonometric functions (sine and cosine)\n", "\n", "* Neural networks\n", "\n", "Interpolation fits the data **exactly**!" ] }, { "cell_type": "markdown", "id": "1f8b649a-5268-46be-ac89-a99fe19e1340", "metadata": {}, "source": [ "## Polynomial interpolation\n", "\n", "We've seen how we can fit a polynomial using Vandermonde matrices, with one column per basis function and one row per observation.\n", "\n", "$$ \\underbrace{\\Bigg[ 1 \\Bigg| x \\Bigg| x^2 \\Bigg| x^3 \\Bigg]}_{A \\in \\mathbb R^{m\\times n}} \\Bigg[ \\mathbf p \\Bigg] = \\Bigg[ \\mathbf y \\Bigg] $$\n", "\n", "It's possible to find a unique polynomial **$p$** when which of the following are true?\n", "\n", "1) $m \\leq n$\n", "\n", "2) $m = n$\n", "\n", "3) $m \\geq n$" ] }, { "cell_type": "markdown", "id": "6af682ce-2f4c-4b4a-b54c-3274a9091def", "metadata": {}, "source": [ "### Polynomial interpolation with Vandermonde" ] }, { "cell_type": "code", "execution_count": 2, "id": "91815d57-95bb-45c2-9f47-fc09638cb9eb", "metadata": {}, "outputs": [ { "data": { "image/png": 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"cell_type": "code", "execution_count": 3, "id": "35646eb8-766a-4985-a244-80f39e956867", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k = 1, cond(A) = 4626.449923375609\n", "k = 2, cond(A) = 2.7224082423906505e8\n", "k = 3, cond(A) = 1.8388423738279527e13\n", "k = 4, cond(A) = 9.028174036334257e17\n", "k = 5, cond(A) = 5.645434903563094e18\n" ] } ], "source": [ "for i in 1:5\n", " A = vander(LinRange(-1, 1, 10 * i))\n", " println(\"k = $i, cond(A) = $(cond(A))\")\n", "end" ] }, { "cell_type": "markdown", "id": "50e38d64-80a3-4afd-b8e2-5cd6b622329e", "metadata": {}, "source": [ "Is this due to the points $x$?\n", "\n", "Or is this because of the basis functions $\\lbrace 1, x, x^2, x^3, \\dots \\rbrace$?\n", "\n", "Or something else?" ] }, { "cell_type": "markdown", "id": "f615fd71-bcb8-4100-b49f-90e3973df1eb", "metadata": {}, "source": [ "## Lagrange interpolating polynomials\n", "\n", "Suppose we are given function values $y_0, y_1, \\dots, y_m$ at the distinct points $x_0, x_1, \\dots, x_m$ and we would like to build a polynomial of degree $m$ that goes through all these points.\n", "This explicit construction is attributed to Lagrange (though he was not first):\n", "\n", "$$ p \\left( t \\right) = \\sum_{i=0}^m y_i \\prod_{j \\ne i} \\frac{t - x_j}{x_i - x_j} $$\n", "\n", "* What is the degree of this polynomial?\n", "\n", "* Why is $p \\left( x_i \\right) = y_i$?\n", "\n", "* How expensive (in terms of $m$) is it to evaluate $p \\left( x \\right)$?\n", "\n", "* How expensive (in terms of $m$) is it to convert to standard form $p \\left( x \\right) = \\sum_{i = 0}^m a_i x^i$?\n", "\n", "* Can we easily evaluate the derivative $p' \\left( x \\right)$?\n", "\n", "* What can go wrong? Is this formulation numerically stable?" ] }, { "cell_type": "markdown", "id": "93b67014-25de-4cd4-a929-dbb197631d9d", "metadata": {}, "source": [ "### Lagrange interpolation in code" ] }, { "cell_type": "code", "execution_count": 4, "id": "ee284b4b-7162-410c-ab1b-32ad0d33b5b2", "metadata": {}, "outputs": [ { "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" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function lagrange(x, y)\n", " function p(t)\n", " m = length(x)\n", " w = 0\n", " for (i, yi) in enumerate(y)\n", " w += yi * (prod(t .- x[1:i-1]) * prod(t .- x[i+1:end])\n", " / (prod(x[i] .- x[1:i-1]) * prod(x[i] .- x[i+1:end])))\n", " end\n", " w\n", " end\n", " return p\n", "end\n", "\n", "# Let's visualize the polynomials\n", "k = 5;\n", "x = LinRange(-1, 1, k)\n", "s = LinRange(-1, 1, 50)\n", "B = vander(s, k) / vander(x)\n", "\n", "default(aspect_ratio=:auto)\n", "plot(s, B, label=[\"\\$l_{-1} (x)\\$\" \"\\$l_{-0.5} (x)\\$\" \"\\$l_0 (x)\\$\" \"\\$l_{0.5} (x)\\$\" \"\\$l_1 (x)\\$\"])\n", "scatter!(x, zero.(x), color=:black, ylims=(-1, 3.5), xlims=(-1, 1), label=\"roots\")\n", "scatter!(x, one.(x), color=:grey, ylims=(-1, 3.5), xlims=(-1, 1), label=\"values\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "0ab4755a-4a51-4bd2-b3db-72ad354abbb9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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\\left\\lvert f' \\right\\rvert \\frac{\\left\\lvert x \\right\\rvert}{\\left\\lvert f \\right\\rvert} $$\n", "\n", "but this definition depends on the input $x$ and its difficult to explore the space.\n", "\n", "We also don't have an easy way to evaluate derivatives." ] }, { "cell_type": "markdown", "id": "583a82b5-40b4-4a70-af51-020a36f1099c", "metadata": {}, "source": [ "## Newton polynomials\n", "\n", "Newton polynomials are polynomials\n", "\n", "$$ n_k \\left( x \\right) = \\prod_{i=0}^{k-1} (x - x_i) $$\n", "\n", "This gives the Vandermonde interpolation problem\n", "\n", "$$ \\Big[ 1 \\Big| (x - x_0) \\Big| (x - x_0)(x - x_1) \\Big| \\dotsb \\Big] \\Big[ p \\Big] = \\Big[ y \\Big] $$\n", "\n", "* How does the Vandermonde procedure change if we replace $x^k$ with $n_k \\left( x \\right)$?\n", "\n", "* Does the matrix have recognizable structure?" ] }, { "cell_type": "code", "execution_count": 6, "id": "689a2481-5f68-4284-95e1-a82e40d25a7c", "metadata": {}, "outputs": [ { "data": 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lclxtrs1CNg14cV7ZZ8jJyUki0fu21tXVOTo6Gl8zswANYWugIbRxofE/P/pdJx7P+m9CW5LoQyC2y8ksw95Bd+8YfwffBgdgCpnoyFbZ/SvkTpqLh+vsNcygKFOoVFdkWBe172Chazl0FPhzLf2REhERQcwC6+rqIiMjqdWn1cA9wlYyLnQEA9W/RhTWFqfxH1OrDwRigcg1iqSCq4T4Yg1eVdGzyk2LG1hBTsxAz1U7TWQFQX1DyOtgWeui1sXs2bPv3bsHAFCr1SKRqF+/Jnd/LRw4I2wlLhzngf59LxXqvaSOZ/3bzbNz86dAIO2NC/mXdUG3AABXjnM/316GvzUaJsjiOI1fwO33atnXXpW6QhnRttgZoVXQs2fPysrKs2fPlpaW7t69m9gvtDqgIWw9E8NHE4bwWvHtKlm1u50btSpBIBbF6WxDwbJxoSOJNExaUbXg0AZlTjr5YKZ/mMucNXT3hmunxkUt0SiFal0boSFcX8tyGbU6xoyxBfcIuDTaerp4RIc4BeraWlx7GhYphEBIPK7KzBbm6doogo4OGaZry9Nv8jctqmcFEYQ3aLz78s2mtoIAgLpC0rqoLxulW/o+HMQMQEPYJsgZ9E/nXFBjlIbCQiCWBDnEtr9fL0+uO65WiY7tqvn5C0xq8LNHeY5uC75wmpSA0MyxQFVXZFgX5cF1UQgAABrCNhIf9BoRQSiQC5OLb1KrDwRiIQgVtVeKrhPi62Ej1fyiyh+XS5JP1qsmGN7Nc/UudlRPsylGnhHaQ08ZCAAAGsI2wqazRwbHEeLxZ/9SqAwEYjmczP5PpdUH//nwvKKKBZXfL1OX5hmOQGkOI2e5J/yP5uBiPrVwICHllLEPgIYQAgA0hG1nUkdD6tH0qidZgtzmj4dAbB61Vl0vm4yYI/r9O3KwPN3F02PZdw4jZwHErFt08iqlRq7V68ChcdwsK922BaIipTJQq9VarZZCZUwH9BptK372PrFeXVIrHurEU9nnVvZeTK1KEAi1JBZcFcj1yULtMKRP2jPyX+16xjlPXoKwKJiNNYwghI4yzbJnzx6hUHj//v0dO3YcPHiQx+OlpaWFh4cvX76catWMDDSERmBi+BjCECYWXFnYba49s/UlQyEQa+efZ6eJ9tBKLef5LAJhcZynLLXrMZQatep7ytgHQE+Z5qipqZFKpcuWLeNyuaGhoV9++SWNRnv27FlsbOyyZctQ1KZWE23qw1BFf79eXlx9pRKFRnmeVHEGAmlv3CtPyxHm69o0HAzn680g0z/cc9UOCq0gaJhcDW4QNkdaWtqkSZPu3bvH5XJXr15No9EAAHl5eTQaDTHvgrYZgDNCI4Ai6LjQET89PKgTj2WdmdRxLGpz9woE0hL+uPsr0e4pxNxUOEAQ3sDXHccvME+ARFNgGlxGqsdr72/BhhDTyjPuaCqLzTgkwvANZneMJXZt4+LiAAAHDx7s37+/k5OTrjMlJaV///7QEEIaZ0xo/K/pf6oxNQCgtK78XsWDXt6xVCsFgZgVXK16cmpLqjyP2HsbxdeiPCeXmSvYkeYLkGgKaakce151lu3CZNhb6NMPV6uqdq5R5T8x/9Ds6N5u89cB0rLnlStXhg8fTohHjx5duXJlg7OePn1qvem2dcClUePgzHZ8rUN/QvzzyXEKlYFAzI+6oqhy8/vHiq7iz61gmATv5NvNc/UuS7CCwHpybUuun6HECgIAFBm3ZQ8MSdKVSuXNmzcHDx6sE9PS0goLCydPnpyTk3Pz5k0AwJEjR9auXbtgwQJKtDUi0BAajSmRrxPt1IqHRHIpCMTmkd1NqvxhqbAyP8XN8Eh5w7u/23tf0xycKVSMjLVsEDYoTUzh6Ldu3UJRtHv37jrxxo0bvXv3dnFxOXHiRGxsLABg6tSpM2bMoEZRowINodHo6BLalVSA4sjTkxQqA4GYB0wqrtm3XnD4O1ylvOhOUz5/oniwXeLHrTJzmGDzSKzEZZTh2YHC0eme/kQ7IyNj5MiRTCZTJw4ePJjD4ezevbt3794slk2FYJpklbywsPDMmTNZWVlSqTQ0NHTUqFExMTGmGMjSmBY5IY2vTyV8qTD5nZhZnlx3alWCQEyHMueR4OAGbW0NAECLIEkehlLvU6Im0BALqvyukWnl1frYcAS16KIT3AHjZKmX1eUF5h+aFdzJrochVdZ77723cOFCQoyOjj5z5gyKojoPUlvC+IZwy5YtunBLZ2dnR0fHX3/99ZNPPlm/fv3atWuNPpal0de3R6Cjf0FtMQBAg2mPZ/37Xre3qFYKAjEBmFZ84Q/xhd8Bhuk6broiAv3MAdgxOGNC4ynTrTHqiuTgeYpTO28WjWm5i2Eo287jgy2y+1c0VaXmHJfhE8jpOojs2ftisKD1VhxsHuMbQhRF16xZs3DhwsDAQABAVlbWuHHj1q1bFxcX179//5edbd0gAJkSMX7T7e068VT2udmdphJZuSEQ20Aj4AsOfKsqeEruvODPBUCpa48OGWZpt329UHqLLzqBMFncPiOo1qIdYfzXoqVLl37zzTc6KwgACA8P/9///gcAOHv2bHOn2Qojgoa4cvTeAVK17EzOBWr1gUCMi/zhtcrvFtezgghSMGBALl1vBVEEfaPjOGqUaxqJlXjKQCjBHOsD7u7uAABbzdbaAAaNQS5S+HfmKQ3WLj44xObBVQrhH5trfvkKk0mITpqjq/uib/8jbYUP8Ovtw/OiQL9msRaXUesiOTn5559/zsrKOnDgQHGxOcP/jYw5DOHvv/8OACBHZdo2E8JHc+j6rfgqWfXlohRq9YFA2o66orBy83Lp7fPkTnZEd4+V2wXeXjdL7xGdUyPHm127l6CoUakl+qLZNBbK8bQpj0cKiY2N/eSTT3Jzc8eNG+fp6Um1Oq3H5LkVzp49u3fv3ilTpgwd2mSOQYlEsmfPHldXV50YFhY2YcKEtgyqVqvVanVbrtAWOAh7RNCQE8/Lc//++J/Bvv0QEye6x3Gc2k9NCbqPbHsJn5rH3F80jsuunZb89yuuMQyKMJi8UXPtBozDEOTPB/swXO8yE+4cEuEUZnT11Go1juOtTvQsyjdMYbl+bI1WAyxsmUaj0VCtQmvg8cxaXQDDsFbcWjQa7aV3jmkN4f379998883Q0NAdO3Y0c5hGoxGJRMTjrLy8vI3rqFqtltqV2IkhY07lnNc9HfJqC1PLH3bz6PzSs9oCjuOUf2rzo/vI7c0QmvOLxqXiuqPbVE/vkjtpHn4OM1bQvIO0GCZRSc/nG7LMTwobYwrdtFqt7g5v3el1hVKibefLssCfCfbc+RbSDK27B1ry/mRCQ5ienh4fH+/g4JCUlKTbJmwKJyenjz76KDw83FhDq9VqNpvKOKFAdodB/n2vFF3Xicdy/+3bwbRZpnAcxzCM2k9tfrRaLZvNbm+G0Gy3tzLrgfDQJq1YQO7k9hvtNGEhwtSvLh7P+0+u0WeyduO4DAt5jYGaxBcdx/FWB3HLSw3TCOdgewv8mRBB65BmoNFoJvruTLVHmJmZOXz4cDabfenSpQ4dqEyUQBUzoiYR7Ttl94nCNBCIFYBpxecOVe36hGwFUTbXZc4a56nLCCuoxbXHs/4lDpjUcawprGAbwbW4pJRUdCIAespAGmISQ5idnR0XF4fjeGJiYkhIiCmGsHwiXMM6u0cR4tHMUxQqA4G0HE11eeWPH4rPHQI4TnSygqM9P9plF/sa+cgrRTf40ipdm01njQu1xNA3abkCU+sXHpkOdKajbYaEQ9qC8V/fCgsLhw8frlarL1++bO21OdrItMgJ6VX6LPKJBVfmx8x0t3OjViUIpHlkqZdEf2/HFIbwc4CiDvFvOsS/CV7YazmaaUioOzI4zoFlbx4lX4l6gRMWnGLUAnn06FFiYmK3bt2GDh167dq1R48eSSSSKVOmBAUFUa2akTH+jHDTpk2FhYV1dXUDBw50IfHuu+8afSwLp79fb38HX11bg2mPZ/1HrT4QSDPgSrnwyFbBwY1kK0hzcndfvMFh5KwXreDjqswn1Vm6NoogFhhEr0NSCCMIWwOGYUePHk1ISBgzZszOnTtpNNqiRYsGDRo0duxYqlUzPsafEQ4fPrxRn9quXbsafSwLB0WQqRHjv7+zUyfqMq4RIYYQiOWgKs4WHPi2QXJLTud+zjM+QO0an+cdzjhKtPv49Ojw/J3P0iAnV+NZfHI1y+HWrVv9+vUrLy9XKBSRkZF9+/YFANDp9MzMTK1Wa2N5t41vCMePHz9+vMVF1FLFiOCh+x8eFilrAQB1Ksm/OYmTIyz0xRnSTsFxSfLJ2lP7cK0hlA1hMB3Hvs0b3GQ4b44w/2apIaZiamSbAn9Nh1aJySr1ud8AAuz94YywpQQGBnp4eBw8eDAyMnLIkCG6ztTU1MjISBuzgsAMAfXtHBaNObHj6F8e/aETj2SenNhxtEWVp4G0ZzBJreD37xRP6oUJ0j07uM79mOHT3D7QwcdH8OfVHKLcOnbzNG2YbKupV3TCk0VjW27RCTIXC5J/eniwXMI356ABjv6LY9/u7aMvw+vj4wMAuHLlCmEFAQCnTp0aOXKkObUyD9ZxW1g1kzqOZT9fDuVLK68U3aBWHwhEhyIzlb/hvQZWkNd/rOfK7c1bwSJxaXKx4Tae23maqVRsMxKrKjqh41FlxpfXvzezFQQAFNYWf3r1a10VOYLLly+/9tprurZQKExKSpo+fbpcLi8sLAQASKXS/fv37927NyEh4enTpy9e01qAhtDkODDtRwQZXqn+enKcQmUgEAAArtXUntpXveczbZ2Q6ETt7F3nr3WasgRhvCS4+3DG39jzyIpQ52BiDmGBWGOu7cSCq8Rs28yoMc3lwmuEmJubW1JSMmjQIJ14/vx5Hx+fHj16nDhxQpcKZ9euXVOnTn333XcXLFgwYsQIlUpFidptBxpCczA1cjz6PPvJM0EOUcUeAjE/GgG/atuquktHyWGCzMAIjxXbOJ37vfR0vrQqqeAqIc7pNNXUeXTbQl0hyVPGSmInqP1/oqQ8TSkpKVFRUUQ2bQzDevToUV1dzefzdREUiYmJf/zxBwAgNja2qqoqOzubEp3bDtwjNAd+9j79/XqnFN/Sib8/OdbVUvdUILaN7G6S8OgOXGmYJwGU5jDiTYfhM14MkGiUwxlHicpiAY7+A/37mkJPo6AUqVVivQcQSke4XtZRdGJk8NDTOecwnIJJIZPGHBowkBC7deu2fft2Qpw+fbpSqbx06dLSpUt1PSdPntTlvcvPz2cymUQZWqsDGkIzMS1yImEIb5elZtZkR7iGUasSpF2BK+XCv7fJ7l0id9KcPVxmr2YFd2rhRarlgrN5FwlxVvRk1IITvZLXRXn+HIRmuaqSiXLr+MXAj/c/PFQoLjabOWTT2QEOfgmx8/xJYTAxMTHkY1AUnTdvXr2znmf+/Oijj/bt28flcs2gqimAhtBMdHaP7OIR/agyQyf+lv7nN6/9H7UqQdoPquIswW/faqrLyJ2cLv2cpzcZJtgofz09odLq94F8eF5xgYOMqaWxsUZPGR0D/fsM9O9DtRYt5ZdffnnjjTemTJlCtSKtB+4Rmo+5nQzOdTdK72bWWOt6OsSawHHJ1RNVP35ItoIIg+k08T3Xt9e+khUUK+tOZ58jxDej37DwQKD6ydWsw1PG6rh48WJgYOC0adMKCgpKS0tffoJFAg2h+ejh3ZWchvvg4yMUKgNpD2ASUfXetaLju8nB8gyvAI8PtzYTLN8URzJPEhWXXDnOZF9oSwQHkhLS0qiVuIxaFzdu3Pjpp5/u3LnzzTffrFixwsXFhWqNWgk0hGZlTuepRPt6yZ1nNTkUKgOxbRTP7vM3LlLUr6lr1zPO48OtDO/AV72aVC0jV1x6M2oyk2bRJfSkFQqtQl90gsGjs10sWlsr5eHDh4GBgUKhsLa2tnv37hyOtb5twD1Cs9LLO7aze2R61VMAAA7wQxl/fznoY6qVgtgauFZTlxjXoc4AACAASURBVPin+PxhcoAEynVwefNDdnQrd56OPTsjUenrvDuw7MeEDjeCoqZEYoURhFZHQkIC1SoYBzgjNDezOhm2lFOKb8GCvRDjoqksqdz8fsNqgmExnqt3tdoKKjTKo5mnCXFa5ETLzx1vjaH0EKqAhtDc9PHpEekarmvjAIc7hRAjIrubxP9+qbok19CF0hxGznJP+Ibm6Nrqy57KPqtLHA8A4DLsJoSNaqOeZqBeKL1VuYxCzA80hBQwh5Sb8WrRjTxRIYXKQGwDTCETHNwoOPwdOVie5uLhsXRjo9UEW45aq/6LVIB3csQ4HtPSw8UwFSarIBWdgDNCSLNAQ0gB/Xx7EtH0cFIIaTuqoqzK7xbLUusFy3NiBniu3MkMim7jxf/LS6qW1ejabDp7UkcrqMsqLpTjmH5lmOPGpNtZdJgHhHKgIaSG2Z0M7qNXiq7lw0khpHXowgS3fKipLif69GGC8z5D7Ropkf1KaDDtH0+OEeKEsFFOLMc2XtMM1GZLiLZjiKXPXy0WuVx+/vz52tpaAIBCobh48eK1a9d06bZtDGgIqaG/X6+OrqG6Nobjh0jFviGQFqKtE1bv+cxYYYKNklRwlagHxEAZUyKto+a2iGwIw9r6NtBu2bBhg5OTU48ePW7evLlv3z4/P7/Hjx9Pnz6dar2MDzSE1IAAZFa0wX30UmFKkbiEQn0gVociM7Vy0yJFZqqhC0F4g8Z7rNzeijDBRsFw/E/SdHBsaLwbxwoiprVKTFKsD/wHCHAMhTPC1pCbm9uhQ4fQ0NCcnJw7d+4sWbKkY8eOgwYNOnbsmFarpVo7IwMNIWUM9O8T6qwvf4rhGNwphLQQXKMWHdtVveczrZhUTZDn6PbOeqdJCQidYayBrhZdz68t0rXpKG161ERjXdmk1OZIiQ1CO0820x5GS7cGkUg0adKk69eve3p6LlmyRNeZkZHh4eFBo9naniu8RSgDAcjsTlPXpWzQiUkFyXM6TSOnfodAXkTDL5b++j9teb3wU1ZYV5dZq9oSIPEiGF7PjWt40BAvrocRr286yOuiTuFWOR3UKjD+XaGcrzRbLSaUgdh5sT26O6IM/eyoe/fuAIArV6689tprhOW7cOHC0KFDzaSTGYGGkEoG+fcLcgrQecpgOHYw4+9P+i6nWimI5SK7myT8ezuuUhi6UJpD/AyHETOBscshXSy8misq0A+CoDOj3jDu9U2HKEtKtJ2scINQI9c+/DFPXqV8+aHGpuKWoMuSYJRuuJeuXLny7rvv6tpqtfr48eP79+/HcVytVjOZTADArVu3ysrKhELhxIkTYa5RSGtAEYRckiIp/2ppXXkzx0PaLZhCJjjwreDwd2QrSHfx9Fi6yWHkLKNbQQ2m/fnh74QYFzDIWtYq1BKNjK//FyEo4hBsfaH05Sk1lFhBAICkSF55T0SIQqHw4cOHgwcP1olXr17VaDSjRo26fv16amoqAODSpUsPHjyYNGlSWFjY4MGDcSqKCRsFaAgpZnCH/kFOAbq2FtcezPibWn0gFoiqMLNy02LZ/SvkTk7XgR6rdjCDopo4qU2cyTlfJqnQteko7e2YN00xiikQZUnB86cxz59D51jfbpa8WkXh6AqSDU5OTnZ3d4+IiNCJWVlZAwcOZDAYV65c6dOnDwAAwzBd6SU/P79nz56p1WpKdG470BBSDIogs0nuo4n5l4kHEASiDxPculJTQ1oqYLKdpy5zfetTlGOSdT+lVkV+IRsXOtKH52WKgUxBbQ5pgzDMKjcIef5U5sEhj67VapctW4Y8X2+YNm1aQEDArl275s2bp+scNmzYV199BQA4duzYihUrdIul1gjcI6SeIQEDfk3/Uxc+ocG0hzOOruq9hGqlINSjFVULDm1Q5qSTO5n+Yaw3lnIDw0037t+Zp4hUMiwac1b0ZNONZXTIG4RWGkHo1ddF8Fgsypa+/FBj4xbj6BZjSJgwadIk8l9dXV23b9/e4BSpVPr777/fu3dvw4YN5lDRNEBDSD0ogs7pPPWr6z/oxHN5F2dGT7aid3CIKZCn3xT+uRmTig1dCMIb+Lrj+AUSmbzp89pKnUpCjh2cEvG6m50xnVFNilKoVgj064ooHXEItMoUoygd6fRekChLQnwW88DxYLUiCw+Xy12wYMHw4cN79+796NEjDw/rcC1uADSEFkFcwKDf0v8qFpcCADSYdl/awbUDVlGtFIQacLWq9vR+ScqpetUEeU4ub65gR/U09eh/PDlWp9KvLtozedOjJjV/vEUhfGZYF3UI4hKRANYHApw6WsF09tChQ0FBQf379w8MDMQw7MKFC7NmzaJaqdZgtTeKbYEi6FxSSYpLhdcya7Ip1AdCFWp+UeWPyyXJJ+tVEwzv5rl6pxmsYI1c+M8zQ93BGVGT7JlW8DgmqJdi1Do3CK2LkydP8vl8AIBcLq+rq4uObmuGd6qAhtBSGBY4uKOLPvsoDvBd93+hVh+I+ZHdTar8fqm6NM/Qpa8m+D+agzkitH5L/1Oh0TsNunKc3+g4zgyDGg0c1OZYdwSh1fHVV1/V1NT8888/q1ev3rx5c7du3ajWqJXApVFLAQHIoth57yd9qhPTKh/fLL3X17cHtVpBzAOmkIr+2ip7cJXcSXfxdJnzMTMwwjw6lEv4/+UmEuLcztPZdJZ5hjYKsgqFqk6ffJzGQnn+bGr1aQ907NixY8eOUqn0jTesJt9Co8AZoQXR1bNzL+9YQtz14BctbmvJbSEvoirIrNy0uIEVtOsZ5/nRbrNZQQDAvoeH1JjekHjzPEeHDDfb0EaB7GbpGMpFUCMnGYA0BZdr9avQ0BBaFu/FvoU+j9oprC0+n3eZWn0gpgXDxOcOVW79UFNjCB5FWByXWatdZq5CWOZzeswTFV4qTCbEBTGzGaiVLRfVSzEK10UhrwI0hJZFiFPg8KAhhLj/4SFizwZiY2hFVVXbV4vPHQKkSqdM/3DPVTvsepg7r/HetN+w5+45wU4BQwIGmlmBNoJjuDhPRohWGkoPoQpoCC2Od2NmE3sz1XLBUZIXH8RmkD+6wd+4SJn32NCFILxB492X/0B38zGzMulVT26W3iPEhd3mosZOXmpqJMVyjVy/j8Dg0e284AYh5BWAhtDicLNznRg+hhAPZ/wtVNRSqA/EuOBqlejYrpqfv8BkdUQnynNye/dLp0kJCI2CBcl9Dw8T7c7uUX18rM9Fi7xB6BTOBVZmx9uKUqncu3dvfHy8j48Pm8328/MbP3784cOHba+CromAhtASmRU9xYFlr2vL1PJDGbBmr42griiq/GGZJPkkuZPdMdZz9S52JDXm52bpvTS+IYvbO12tMiC6th1vEN64cSMiImLhwoWJiYnl5eVKpbK0tPTUqVOzZs3q2rVrRkYG1QrWg8/nFxYWUq1FQ6AhtER4TO4sUibuk1lnYXkmG0B2N6nyh6Xq8gKiB6EzHMe97fbe1zQHZ0pUwgG+/+EhQuzn27OrRydKNGkLmAYXFxjSzrWrUPrz588PHTq0oKCg0b8+fvy4X79+upJJFkJCQkKPHha35AANoYUyqeNYIt2oGtOQn1YQqwOTimv2rRcc/g5XGVyf6B5+Hst/tI+bavRqgi3nYkFytlAfv48iyPyYmVRp0hbE+VJMrXc4Yjkz2C7WWgPhVSkuLp4+fbpS2Zw/nVgsnjBhQm0t3F5pDivzkG4/MFD6vC5vfn1Dn4n7UuG1yRGvR7l1pFYrSCtQ5jwSHNygra0hd9r1jHOevMScARIvosG0Pz8yVN8dGjAo1DmYQn1aTS1pg9DZGlJ0Gou1a9eKRKKXHlZSUrJx48avv/76lS6emZmZnJw8YcIEkUj0559/lpaWLl++PDIyEgBw+fLl8+fPi0SiwMDAKVOmhISEkE/EcfzMmTNXr16VyWShoaFvvvmml5f+nf6vv/7Kz89XKBR79+7V9UyYMEGXp/v8+fPXr1/n8/murq4RERGjRo1yd3d/JYXbApwRWi7DAgeHPX8w4QDfm3aAWn0grwymFf/7W9WOj8hWEGVzXeZ+bOYwwUY5kfUfseROR2lvd7Ga6rsNENVLMdpeDKFMJjtypKXeA/v378dIUTot4dq1awsXLty6dWuXLl12796dmJiYk5ODYdjs2bOHDh26f//+1NTUzz//PCoq6sABw6NJLpfHx8e//vrrf/zxx61bt9asWRMeHp6YqM9YtHfv3uzsbLlcvuE55eXlOI7PmjVr5MiRv//+e25u7unTp999991t27a9krZtBBpCywVFkPe6vUWID/jpt8ruNX04xLLQCPiVW1eKE/8gp89mBkZ6rN5p120whYrpEClrf0k3TAfHhMT72ntTqE+r0SoxSbFCLyDAMbS9bBDevHlTJpO9/DgAAAB8Pv/Zs2etGGXr1q2nTp0qKyvLy8sbNWrUzp07Dx069Pbbb5eXl9+9ezc3NzcsLGzBggVZWVm649euXZuUlLR27drS0tL79++npaU5ODhMnz5dIBAAAC5evBgfH+/s7Jz7nJiYmPT09MOHD3/11Vc5OTlJSUnp6enl5eXTp09vhbatBhpCi6aHd1dy0rWd92HSNetA/vBa5XeLVQVPDV26MMGlm+guntTpZeCntIMSlX5F0Y7BmdvZrM8dI1KbI8Ux/asG14vNtG8v2z1lZWWvdHxJSUkrRklISIiPj9e16XT67t273dzctm7dSqfTAQA+Pj6bN29WqVT79+8HAGg0mp9++ikyMnLdunW6U6KiotavXy8QCP7888+mhqioqAAAREQYsgk6OztHRUW1QttWAw2hpdMg6doFmHTNssFVCuEfm2t++QqTGdbraI6u7ou+pSpM8EWyBLnk/NrzOs9w5VDjttp2RFnttPQSi/VqKdHZ7NYkGRgwYADRlslkT5486devHzm56NChQxkMhs4xNTs7u7a2dtiwYShqsCwjRowAANy71+RqVs+ePd3c3ObNm7do0aITJ060ZNfT6EBDaOk0SLq279FhmHTNYlFXFFZuXi69fZ7cyenUx3P1LlZYDFVaNQAH+NZ7PxEJ1QIc/SdZV7ml+tQLpW83G4QAgKCgoFc6Pji4NZ5QZI+Vuro6HMcb1KCn0Wiurq466yUWiwEADQ7Qic24rTo7O1+9ejU+Pv63336bOHGih4fH5MmTX3W+20ZMaAgFAkFqampmZqbphmgnzO8yk0nTe4RXy2qOZp6iVh9II+C45OqJyu+W1AsTZDCdJr7nOn8dynWgTLEXuJB3Ob3qCSEu7f4OHaVRqE9bUEs0Mr5+gxBBEYcQO2r1MSfdu3f39GzpMntMTIyvr28rRkFIsT0ODg4IglRWVpIP0Gg01dXVzs7OAABHR0cAQIMDdJV7nZycmhklKirq6NGjQqEwOTk5ISHh+PHjc+bMaYW2rcb4hlAmk02dOjUkJMTV1bVHjx7z5s0z+hDtDU+u+xsdxxLiwYy/+dIqCvWBNACT1FbvWy86vhvXqIlOuqe/x/LNvMETKAwTfBGpWrYn7TdCHOjft6e3tRZTBQCIsqTguSsSz59DZ1urRW8FKIouX768hQevWLGi7SNyOJxOnTpdv35dKjXMwi9evKjRaHr27AkACAsLc3JySkpKInuonjt3DgDQq1cvncjlchUKBWgMJpM5cODALVu2vP766ykpKTjJy8zUGN8QKhSKpKSk4ODgNWvWvOoqNqQpZkZPJpKuKTSKban7qNUHQqB4dp+/MUGRcZvcye032nPFdoZvSFNnUcXBx0dq5EJdm0ljLo59m1p92kj90kvtaINQx/vvv9+1a9eXHhYXFzdzpnFSJSxevLimpmbJkiVqtRoAUFRU9MEHH7DZ7Pnz5wMAaDRaQkLC06dP165dqzNjjx49Wr9+vZub27Rp03RXCA4OlkgkiYmJGo2++OW1a9dOnTpFpEUVCAQZGRkhISGIGd8gjW8InZ2dBQJBYmLiN998w2AwjH799ok9k7ewq2GtIKX45o3SuxTqAwEAAEwrPneoevenWrGA6EPZXJc5a5ynLkOYFvcWWFpXfjTTUMxkRtQkb55FuLC2GnIoffuJICTgcDgnT54MDw9v5piePXseOXKE7L3SFhYsWDB//vxff/3V3d29S5cuoaGh+fn5v/zyCxFTv3bt2jFjxnz99dceHh7R0dGxsbFyufzvv/8mlkYXLlwYEBAQHx/PYDAQBLlz586TJ0/Gjx/v7OwcExPTu3dvPz+/ioqK3bt3G0XhFmJ8HzZzmvF2xeiQ+P9yL2ZU6/dct937qYdXDLF3CDEzmupywYFvVUX1YrNYwdEusz+iOXs0dRa1bLm3V43pF2/d7dzejJpErT5tRClUKwQqXRulIw6BFCcooIQOHTrcvn175cqVv/76a4NaEywWa8mSJV9++SWH05r/TFxc3JEjR8LCwsidKIru27dv/vz558+fFwgEc+fOnTJlSocOHYgD2Gz2mTNnEhMTr1y5IpFIFi1aNG3aNDc3N+IAHx+frKyse/fu8fl8jUYTGhoaGxsbExNz69at4uJiGo02f/78qVOnNr+naHQQk67D2tvbd+rU6ebNm80f1rFjx9OnTzf/XqOjXAa+TtNWyl9ymEaj0YW52BgaTVFN9YcA6G93Lm86jzeN9Ffb/NTNQNVH7l5yeXL6TpbGEM6MIWhi+IzEsOkYYnJP7NZ9aqXirkj0P0J0clrFYvczql4mRLfn1GBaE10kikvXZ8YpduUe79OhkTOtBGFWatnexRkPWr/MU1hYePLkybS0NKFQ6Obm1qNHj/HjxxO5zWyArVu37knOiU7YDAAIdQCfdqNxjffTt4jnplqtzsjIqKvTl2dzdXUNDAxs9MgZlzVXy1tiuVEAXi2fkJXgF8IY4Uv/TyfU1f1zpbq/HCfquNrqp24Gc39kHib/rOLnmYJz5M4yhtsyvxW3GZ1AATCLPq/8qRGg6cH6hfPcjtRqI5PLe1vh3VJP4egSwwbhWRrn73yr+zgkSrGwtqkfEBCwbNkyI2ljoeTV4U+ef8tCFdjV32i+URZhCAUCwaeffkrEe0ZFRTW1QPxYwATtreZmfQrUM9xpN5mIEACAIupQ5v505f9RrVR7obM8Z0fxpiBVvQin8w59VvouE9HsqdKqJfjTT3BQ/eQJB2iOZoG1/44QHHSTGZaGUrntzlOmnZNerZFIXrY2CAAAgM1mv3QFxSIMoaen54kTJ1qyNLo4SvvFA2t+72szWmCXp54TwdyiE53RNDfa7Wptb2q1snkQHH9bcPrTil8YuIboVKLMbzzn7nd9nULFWgILqfGnHyfEMs1IKRZAoT5GIUildHnudihFac84FueaBDEdKAIWd2LweEb70i3CELacz7vTJgai2eKXrI7K5fLW7Q9bCUNOZFwqqdVXFe/F+3lmbCwdYalUqvYWr6JUKplMpqn9sxhyUciFH5zL6+WIkrt2yBr50Qi3oBEmHbsxXvX2vpB1IKtaH7nFptuv6zmDzbCyeDuNRoPjONkLnZumALn6Ni2A80eclT3KGpCbjv55lmolLJ5hvsicOBoNAZ2dkTBHY/7qre/u6eqKdHV9yb+grg6zt7fl7HE9Xd6b/98yDaYFAEhU1WLxkYVd58pkGJdry5/6RaRSzM4ONakhVGY9EPy5iRwgAQCw6xnnO2VZGEUBEq90e6dXPd1RfZ0Ql3SfMy7U0TR6mRCVCuA4YLEMn/rxeQmRkjIqxt4nyLrv/Hs16D/W/QnMQbA9MsU0XzT831slgY7+UyLGE+KRpyfzRIUU6mObYFrxuUNVuz6pFybI4bnO/cRl5ioLDBN8EQzHfry7G3+efCXMOXhMyHBqVTIKaqm2NodUjDfSojdoIZaPSWaEq1atKiwsBAAoFIrs7OypU6cCAAYMGGDzTk3m5K3O0y8WJFfKqgEAWly7NfWnr/t+TLVStoOmpkJw8FtVQb1MuazQLi6zVtOc3Jo6y9I4lX0uR5ivayMAeb/nQtT00R1moCZdbCi95MvmuMNoWkibMMmvoqSkJC8vLy8vLyYmJjAwUNdukIkV0kbYdPaS7u8QYho//UrJ9WaOh7Qc2d0k/saEelYQpTmMnOW+6FsrsoJVsuq9aYbS4cODBnd2j6RQHyNS/dBQysAtxvpWeiGWhklmhH/88YcpLgtpwOAO/Xr5xN4pu68T9z0+PCR4IJfRjhLwGx1cKRf+vU127xK5k+bs4TL7I1ZwNFVatY7vbu+UqvUh/3YMzsJub1GqjtHQyOuti7p1saDKHhArxRbWSdozH/R8j8iyJlSI9j88TK0+Vo2qKIu/aXEDK8jp0t9z1Q6rs4Ln8i7dKjO4uS7sOteN40KhPkak5pEY1z5fF/VmczysYLMWYuFYn9cohIwPz2tG1KTf0v/Uicez/h0VEhfm3JoKnO0aHJckn6w9tQ/XGsIEEQbTcezbvMETKNSrddTIhTtS9xNiZ/fI18NGUaiPcal+JCbarjY0HZRKpbo675BGKS4uNt3FoSG0emZFT07Mv1ImqQAAYDj2w51dO+I3ojD1eYvBJCLB4e8UT+uFCTK8AlzmfszwDqRIqTax+e4usUqfsJBNZ33cd7nN3A8auVaUZcis5tbVRjYIvby87O3tFy5cSO7EMMxYVSOsiGY+dYP/jxGBhtDqYdKY7/d896PLX+jEJ9XPjmSemB45kVqtrAXFs/vCw5u0YqGhC0G4fUc5TVhoFQESL3KxMCWl+BYhzo+Z5WvvTaE+xkXwuI5YF+V4sOw8rfI7ehE/P7/bt2836Kyrq7O3b3eRIZR86nb3umGT9PHpMdC/LyHuf3g4v7aIQn2sAlyjrj39c/XuT8lWEOU6uL2zzjKrCbYEoaJ2y909hNjJPWJyR0vPAPdKVD8y+Iu628p0EEI50BDaCMt7LLRn6guTqrSqr6//oMY0zZ/SntFUllT+uLzu4hFAKkPGCovxXL2LHd2HQsXayI93d9cq9VtoDJSxqvdSm1kUBQBolZjomWFd1JY2CCHUAg2hjeDKcX6/6wJCzBbmHXx8hEJ9LBnZ3ST+90vVJbmGLl2YYMI3NEdX6vRqK9dL7lwpMsSSzo+ZGejoT6E+RqfmsRjTPF8XdWdxfdjU6gOxGaAhtB36+fQaGjCQEA89/vtJdRaF+lggmEImOLhBcPg7XGko4EJz8fBYutFh5CxgzY4JYmXdptvbCTHMOXhq5PhmjrdGakj+om4xcDoIMRpW/MuHvMiKXovc7fSpT7S49pubPyq1KmpVshxURc8qv1ssS71M7uTEDPRcuZMZZGVhgi+y5d5eoUKfhpqB0j/t9wENsbISE82jVWLCTNK6KEwoAzEe0BDaFDwm96M+S5HnNVeLxCU/kZJstV9wXHL1RNWWFZrqcqIPYTCdJr7nOu9T1I5HoWpG4Ubp3aSCq4Q4t/P0ICerrzjYAFGmFFPra5GyXZg8X7guCjEa0BDaGj29u40JNVQY+OfZ6Qf8dAr1oRxtnbB6z2ei47vJwfIMv1DP1busMVj+RaRq2Q93dhFiqHPQjKg3KNTHRIge22D4IMRCgIbQBlna/R0idAzD8W9vbiFyTrY35I9v8b9dqMgkJexAEN6g8R7LN9PdfanTy5hsu/dTlaxa16YhtI/6LKOjNrUoCgDAVFhtluEehhuEEOMCDaENwqazP+67nCi4UyGtJCfcaifgapXo2K6a/Z9jUoOHBcpzdFvwudOkBITOaOZcKyK14uG5PENy1FmdpoS7hFCoj4kQPZNqVaR1UT8OtfpAbAyYWcY26eweOTni9SNPT+jEf3MTB/j36efbk1qtjIVWhWkVmEaulQoVShzDlJhGrmXw6I6hXDqHBgDQ8ItrDnyrLs0ln8UK7+oyc5VVB0g0QKKSbri1lai7G+QUMLvTVGpVMhGC9Prhg7YTGwmxCKAhtFkWxMy6U5ZaUKvPVLvp9vbfxmx3YFlfxiaVWFOWXFObI1FLtRqFVivHiKKsDUBQxCHIjmdfgaT/SlcXGv6A0hziZziMmAlsKLocB/i3t7bypVU6kYbQPu7zPgO1wV80psZqn5HqLsF1UYixscGfDUQHk8b8pO8Hiy6s0mBaAIBALvzh7q71A1ZTrdcroBCoSi9V8+8IiTDq5sExvDZXWgvsAVhKR4Qc8JSDP7V3FrvOXckMtJGatAT/ZJ5JKb5JiNOjJnZ0DaVQH9MhzJRolfp1UZYTw74DrLgJMTLQENoyHV1DZ0VP/TVdXyf5cuG1gX594gIHUatVS5BXKksuVlfeFxEZll8VDeJcB/rVIf2qZagg0c4lSuAW48Dg2cgNn1mTvfvBL4QY4Ro2r8ubFOpjUqof1q+7ZDuzeoilYCPPBUhTzO409Wbp3WeCHJ344909MZ6dLLlGq7RMUZxUVf2wFjRtAVEmSmehNA4NZQKGHYPORjFhkaRYoQJeLx6MqTHh0zrh07qCMxX+w9x9BruhdOt+lErU0nUpG4hcsjwmd/2A1Ta5KAoAwDS44Ak5oQwMnIAYH9v88UAI6Cjts/4fvvPfcl2KGbGqbm3yt1uG/88Cn5t1hfLipErBk7oXTSDbhekX5+YUzqOxaXQ2itD0lkwqlbJUUuGhTcrCdAcANMBZjkTIQaQcDcfxhh9Qq8QK/uVX3BQGjvOy3n0mHOBb0n6qkFbqRAQgH/VZ5s3zpFYr0yF6JtEq9OuiTAe6QyBcF4UYH4t7GkKMTgcHv3diZu24/7NOzKjO3PPg1yXd36FWKzLyKlXuP2XkgqsEdp4svzh391hHBG1kGqd6crv2xG4iQIIOhPbglvdAD/sx0eJ8peBJnfBpnaKmXpI5hUCV+VuRYwg3aLyXNXrhH808fbP8LiFOjhg3iFSBy/aofmiou+TaxRGui0JMATSE7YLJEePvlD+4W/5AJ/6deSrSrWMcKUM3hUjLFI93F6glDYtGcX3Z/sM83JrYE8LVqtrT+6XJJ8mdKM/Js/D4PwAAIABJREFUZeYKdmRPAIBzBMM5ggeAt7xSWZMuLrlSrZFqiSNrc6Vpm3M9ezoHjPZkOljNr+BJddaeB78SYqRr+MJub1GmjenBtbggo44QrXceD7FwrOYRAGkLKIKsHbDy3bMflkv4up4NN7d0cPANcw6mVjFJifzxngKyiQIA2Afa+Q9zd4m0b+r1X80vEvz2jbosn9zJCu/mMmsVzaHh9ifHg+UX5+7V16XoQmX5dYHB+wYH/DvC6oe1fnHuvq9ZwcahRCX94vom8tbgugGrLHCJ24iIsiQauf7eYPBoDkFwXRRiEmBmmfaCA9P+q0Efs2hMnajUqtalbJCopM2fZVLqiuSPd9Wzgo6h3E4JQTHLgl2imrSCsrtJld8vJVtBhEZ3GDnLPeF/L1pBArodLXiCd+yqUJeoepGUWiVW+B///rfZ5CU4C0QXNUi8xyAAWWPTW4M6yP6iztG8RpfHIZC2Aw1hOyLUOXhl78WEWFpX/vWNzRjeyviENiIukD3enU+87wMAfAe7dU4IcgrjNnUKppAKfvtGcPg7XKUkOumuXu5Lv3MYOaslwfIcD1bUOwHR7wbaebLI/QqBKvO34mcHi4l4NUvjyNOT5KjBKZHjB9r01iAAANfiNY9JhrCz9eWCgFgL0BC2L+KDhowNjSfEG6V3Dmf8bX41anOlGXsKCG9AAIBfnHvQeK9mXCGUOen8bxfKHlwldzK7DfZYtZMZGPFKoztH8LqtCg2Z5EPn1ktOXfWg9uGWXHmlsqkTqeJpTRa5nFaYU/C7XedQqI95EGVLNTJiXZRuHwTrLkFMBTSE7Y4PeiZ0djekWfn50eHbZanNHG90anOlT/YVkudefkPdA8c0vcqHacXnDlXt/Egrqib6ULady+zV3MnLEFZrPD8RFPEe4NLjk3C/oe7k3UFZhTJtc65FLZPWqSSfXzNsDdozeWt6LLPtrUEd5G8BrotCTAo0hO0OOkpbO2CVE0sfmIzh+FfXfyiTVJhndGGmJGNvPSsYMNozcGyTVlArrKza/pH43CGAGU5hdgj3WLndrvvQNipD59ACx3p2XRHK9THMNrRKLPNAccHpiqYympoTHOAb6m8NftRnmaedO7VamQFciwtI66Iuna2+eDLEkoGGsD3iYee2dsBKok6TWFW3PmWjSqtq/qy2I3hS9/TnQqLOOAAgcJyX/7AmH+vyR9f5mxYr8x4buhCEN2i8+/s/0N18jKWVnScrZlmwR3cnQxcOSi5XNxrUYWYOZ/yTUnyLEKdEjh/o34dCfcxGVVqt+rkXFZ1Lsw+2vohPiBUBDWE7pbtXzIKuswnxmSDnh7u7TTpiTbr46S9FhvTZCAie4O03xK3Rg/XVBH/+EpMZwsho9s5u737pNCkBoRl5YRBlouEz/UIm+RA5awAAtTnSB9/n1hVQVtP4YmHKvrSDhBjl1nFh17lUKWNmylJqiLZHdye4LgoxKdAQtl9mRE0iJyU5m5t0Oue8icaqflibeaDYEMOHgOAJ3j6DGi8NqK4orPxhmaR+sDw7orvHqp3syB4m0hAA4D3AJeb9YLYLk+hR1aofbc8vuVRlukGb4mFlxjc3fiRqDTow7dcPWGV7pecbRVwgkxTJ9QICvPtbbmpciG0ADWH7BQHIJ/0+CHT0J3p+vLs7veqp0QcS58ueHSwhW8HQKb4+Axu3grK7SZU/LFOXFxj0pDMcx73ttvArmoOz0XVrAM+PE7M8mBzCgWN4wRn+s8MlRIV0M1AkLvns6v/UmFon0lHa+oGrPbkeZlOAWspJ00GXSHuOO6uZgyGQtgMNYbuGQ2d/PnANh653FdFg2vXXNhIJnY0CpsGz/yolHE8QFAmf4efVpxGThknF1T+tbxgm6OnvsfxH+7ipZqupy+DRoxcG+g11J8dyVKWKHm3NU4nNsWUoVIhWX/5crNKvCSMAWdP3/e5eMWYY2hJQ1aqrHxncZJpaNoBAjAg0hO2dQEf/NX3fR54/9atlNSsvrRMqjBY/UHS+0hCZh4DwN309eji9eJgy+yF/Y4Ii4xa5065nnOeKbQy/EGMp00IQFAkc6xn5Vgca2/ADkZYpHm3NU1Sb1qVIoVGsufIl4SYKAJgfM3N44GsmHdSiIKfBs/NiOYVBf1GIyYGGEAJe69B/etREQiwWl350+XOp2ghOItIyRekVQ/CfVx8X99gXrCCmrT3zS9XONdpaw4IYyuG5zv3EZeYqhElZGLVrZ4euH4RyvQ0KKASqh9vyJCXyZs5qCxiOfX7tu8yabKJnbGj87E5TTTScBYJp8IpbQkL0GegKy01AzAA0hBAAAFjYbe6o4DhCfCbI+eTq120MqMAxPPvPUuLtnunICBzXMF5QU1NRuXVFXdJfgJTpjRkU5bFqB6fboLaMbhQ47swu7we7RBuSe6nrNOk782tzTJKjdVvqvhuldwixl0/sh70STDGQxVKVKiJCVugcWr2YFgjEZEBDCAEAAAQgK3sv6eNj8MlM46evv7ZRi2ubOat5Si9XkydPIZO86ex6To/yh9cqv1+iKsgk6YHwBo13X7KR7mIp6aRpTDRyXgfypqZWgWXsLTB69pk/nhw79uwMIQY5BawfsJqGtAs3UQJy1IRXX2eUCR9QEHMA7zOIHjpK+2LQms7uUUTP9ZI7G25tw18sGN8C5FXKoguGqAP3WEfXzoZicrhSLvzjh5pfvsJkhmK8NCc398UbTBEm2EYQFAmd4us31BD4j2nwZwdLKm4KjDXElaLre9N+I0Q3O9eNQ9ZxGe2r6lBtjlRaptC1ERTx6gejJiBmAhpCiAEWjblhyNpQ5yCi53zeJXJMd0vBQfZfZUQGGTqXFjzBm/ijuiSH/90S6e0L5DM4nft6rtrJCu3SStVNDQICx3oGT/AmtqxwDM/5u6zgDL/Z01rE05qsb27+SJQB4TLsNg5Z52HXeKoBG4Y8HXTtbE8O6IRATAo0hJB6cBl2G4as8yKFrB3KOPrX0xOvdJHy6wJxnmEXLWSiN4NHBwAAHJdcPVH54weaqlLirwiD6TTxPde316JcS68/7jPINXyGHzn7TMmlqtxj5a2aM+spk1SsufylQqN3rKWjtC8GrglxCmybptaHUqgmF6NvKswUAjEF0BBCGuLGcflu6OdEVm4AwK77v1zIv9zC05VCdcG/hhTezpH2Ok9RTFJb/dM60fHduEZN/JXu2cFj+Y+8wRPMFibYRjx6OEXO64AyDD+c8ms1zw6T0gW8ChXSyg8v/p9Iqd9uRACyuvfSHt5djaOrVVGWUkMEm3J92Q7BTZalhECMDjSEkEbwd/DdOHSdHUOf6VhXA+FG6d2WnJtztIwoLkFjo6FTfAAAimf3+RvfUzy5Qz6S22+058rtDN9go+puclyi7DstDKBzDG4sVfdFT34uwl4x9UyxuHTphTXkkMF5XWaMCG5rSQ1rRKvC+LfrR01AIGYEGkJI43R0Cf160KcMlKETNZh2fcqG9KonzZ9VeU8kfGpY4Aoa68VyQMXnDlXv/lQrNjzpUDbXZc4a56nLEIZV7gM5BHO7LA1mOjKIHuHTusd7Clpe4D5fVLgs6ZNKmSHIcnTIsLmdpxtZUSuh8p5IIzfU4G0k2BQCMSXQEEKaJNarC7lak1KrWnPlyyfVWU0dr5Zo8k6WE6JjCNctTFH54wfic4fIYYKs4E6ea3bbxb5mMsXNgZ0Xq8vSILabwZCL82UZewu0ipfbwixB7vtJnwrkhjeDYYGDV/ZebBJFLR+8XnJRrz7O5FLJEIgZgIYQ0hyD/Puu6JVAJGCTqKQfXPysqYr2ucfKNc9ryKEM1K9zWeUPy1RFJMOJog4jZ7kv2UhzsoXSsmwXZszSYJ6vIfWMOF/2eE8BMblplIzqzA8uflarNKTTHBsa/2m/D9tbyCCBKEsi4+t9hRAaAmtNQMyPCQ1hRUVFUVGRRkNxaVNIGxkbOuIdUuVChUbx8ZWvzuRcaHCY4ElddZohxtzN46n02JeYnBQm6OzhvmSTw8hZALWd1y+GPb3T4iD7AEPAX12h7PHOfOKFoAEPKzNWXlonURlcaseHjVrRazFqJb5CpqA02TAddItxJC84QyDmwSSPpNu3b8fExHh7ewcEBHh5eW3ZssUUo0DMxqzoyeTtKy2u/e72jj+eHCN6NApt7tEyQmTSK+2KfyZfgdOln+eqHazgaDNoa2bobFqn9wIdQw1ejpJSRfrufPULtvB2WeqqS+tkakO2nZnRkz/sldCeraCiWiXMhFETEIoxviHMzc0dMWKESCQ6dOjQ2bNn+/btu3z58t27TVv9HGJq3u7y5kd9lhHLdzjAdz/4deu9n3Rh4IVn+EoRERShdVMfAkBvBgxhgnb2jVzXJqCx0Kj5AWSPf2mp4vGufCJtJgDgRundz5K/UZLSt74Z9ca7XeeYVVHLoyylhojCtO/AsQ/gUKoOpJ2C4HgbgoEbY+7cuQcOHLh371737t0BAGq1unPnztXV1SUlJWx245UEOnbsePr06fDwcGPpUFdXZ29vs4/dRsFxXCaTcbmmjb5KKb715fXviKd57TOBKrlWUSRTClRh7hFTYmfH+MY64knO+DndAQyvDi5zPmb4BDV9yTYhlUrt7OwQy5hRaVXYk32FRD7uElHRX49/zZY+EdWKvIN9ZF0wt74+uj8hAFkUO29q5ITWDWQDt7dQKNywYcPFpEv5mfm+Th36BQ2eGjur05xg9yaybKtUKhzHWax2UaFXo9Hs2LHj+PHjmZmZvr6+gwcPXrNmjYdHeynLTMntbWRDqFar3dzcfH19nzwx+NmvW7fuiy++OHPmzJgxYxo9CxrCtmMeQwgASKt8/MmVr6RqWUVycdZPD8nuoCiCfjx85cLIDARoAAB2PeOcpyxDmCZ8eFmUIQQAYCrsyc9FoizJ04r05f8skKnqFanwGRYY+lZnBCBLeyx4o+PYVo9i7bc3n88fMGBATk4OuTPGP/bm02scbuMzwvZjCDUazbhx486dO0fu9PX1vX79ekBAAFVamRNKbm8jL43m5OSIxeIBAwaQOwcOHAgAePDggXHHglBCV49O2+K/tVfb5f6WDuq/RWE49v2lzTUyGcp1cH1nvcvMVSa1ghYIykSj3glwibb/9sLaBlYQAFCWVFD7RLCm7/ttsYI2wMcff9zACgIAHhbf37INOhOA/fv3N7CCAIDS0tIPPviAEn3aCUY2hKWlpQAAd/d6zvE6UfcniA0Q4hQYr+qvVTbiGKnQqFPkbM/Vuzid+phfMUsApSN4b2leTcMHvY6AIveR7TJ3DAGO4//880+jfzp69KiZlbFAmvonnDlzRi43VUVoiJHr3ei+KgeHetmTHR0dAQBSaZO1TEtLS3v27Ik+96rv3bt3G38SUqnUcpbLzAOO43K53Og7vk0hLG+yAlFNcE85jQUkkqYOMCIymQzDMEv7rvML8v6/vTsPbKLM+wD+TO6kbdqk95W20ItiufFADgEBQVhcFZVDWE9cREXUBd3Vd9ddX0URVNR3VXZXAbGiq4AKgqCIKB4td4Fe9C5t0yZpmubOzPtHSjotbemRZHJ8P38lT5OZ35Ahv8wzz+95evqTQ2szDPpfxq9Pb4PBoNfru/1TbW1tT/84zq5Rm83W7V8DSU1NTbftNputoqIiOTnZy/F4n9tPb4lEIhBcIdO5ORE6h8N0OZud571U2uN4sISEhO3btw8dOtT5NCws7Ipx945hmNDQ0MFswe8wDMPj8bxwj5AQQpuNEVWne/prHV8dEhriqsH3KIqifOoeoVMpU9nTn6IjYgZ/Zvr16R0SEiKVSru9uImNje3puILnHmFsbOz58+cvb+fz+SqVyjv/wbnFyent5q7RuLg4QkhzczO7UaPRuP7ULYqi5HK54pJBZkHwKGtVceP6lROoJiG/m5OHEvBORZQ8cfC5Ztb8YcHDbDf//cdXP2/5WhLd/Zq6w+3j2i6avRyVT6Eo6uZZ3Q+amzdvnpeD8UE9/SNMmzYtGLIgV9ycCDMyMiQSyS+//MJudD4dOXKke/cF3sYwhu93ql9fbW+qiw+VrLru+stfknpbljhSWlB/8p6vHvmx5tfLXxDAqvS1D3395IGK7wlFZdw7grrsh8KU9BuvSZh05v8qXOuwB6cHJ6xSyroWzg8fPvzJJ5/kJB6fsmLFivHjx3dpjIiI2LhxIyfxBAn+X//6VzduTiAQHDt27NChQ4sWLYqMjCSEMAyzatUqvV7/9ttv99Sz8eabb7pe7xZWqzUYelG6sNlsIpGnFnNwtGo1779g+GE3YdonlVYlrVJFjVO3NugteqFAmDUyW7UwM+qGROdfLQ7LwcrDdYb6q+NHC3ieusS32WxCodAXukaP1Pyy9tDzrtUkpLEhCWOSE+kYk95ot9uHJmbcNXLZyilP8SgebaWbjreEp4eKIwY4l5hfn966IoP2kHl61k06k1Zv1plsxiFDhixZsmTr1q0RET0uOuFwOAghwdBXJBQKFy1aZLfbGxoadDpdbGzsnDlz8vLysrOzuQ7NSzg5vd1fUH/8+PFrr702Ozv7zTffVCqVb7zxxrvvvvu3v/3tueee6+ktqCMcPI/WEZrPF2i3r2evo2SlVHXUo87HNEOPWp0uT5Zpzbr/Pfrar3XH2O9NCU9+7von0hUeWXTQF+oIHYxj84ltH539jGEtVJ8Snvz8pLWp4cmEEIfDwefxL+y6WMeaVFMg4Q9/MCUstfse1N757+lN25njr5Sa1O1TbIeqpLkrU/mCK882Hjz3CNl0Ol0vPw4CVSDUERJCRo8e/emnn9bX10+ePPmqq676z3/+s3r16r/85S9u3xF4AWO3tXzx76Z3/tJpNcEQuSlthetp5DC5PFlGCFFIItbd8D/LRy8T8Dq+2ipbqv+470+fnv+CnScCxmn12eV7n9h+9r/so5s1ZNq7N21wZkFCCJ/PJxQZckt88o0dZUV2s+PMPyt0JT0OpQ5INd+qXVmQUCT91oS+ZMGgxefjH8dLPNLVMG/evJqamuPHj5vN5pycnKioKE/sBTzN3lDdvOUlW20Zu1GcMUp28+ryN9Xk0ld/4tSOz5dHUYtybhsbO/LvP71arW+vHLU6rJsK3vv14rGnr3tMIQmQX7hNxub/O/7+wYrD7BQo5AkfHffA7zJu6vYtKXNiKT5Vta/R+dRhpc/+qzLnXlVEpr8OAe0Xi9ZW+23HQsTx10eGqjCzKPgETy2IIxQKr7766smTJyML+injbwcaXn2kUxbk8eU3LYle8eLFfDtDt3/7hyRIItK7fo9nRaa/N3vjnKE3sht/qStY+uXDH5/baWVNPO2PbA7btsJPl3zxxwMV37OzYGxIzFsz1/WUBZ1Us2JS58a6ntJW+uzmSk1hay9vCRhln9U5rO03mIWhgpTZwTJ5Jvi+wL/5DP1Fm426HW8Yjx1iN/KVMZF3rxGlDbcZ7I2/6VztSdOiu60YlAoka6599JqEset/eavV2l5Xqre0vn3s35+c3/2H3LtmD53uj0vR/lT765sF/6ptvchupAg1PXXyY+MelIuvfG8jaVo0oaiKL+qdT2k7c+79quylyZG58t7f6Ne05w3sfJ86L1Yg9b9PHwIVEiF0Yq0q0mx5yd7U6YteOnKS4q7HeNJQQkjdEQ1ta/9dL1GKokb19vV9g+r6nKisF37ccKLxjKtRbWx65Zc3Pz73+X0jl0xRTfBO6f3g1bTWvVmw+Whtfpf2dMWQx8Y9MCKmH0stJk2N4vGpC7suOq8nGQdzfkt15qKk6NHhbgzYd9B2puy/HctVylNlseMUHMYD0AUSIVzCMIbDu1p2b2YcHavoUUJR+Nx7Q6e0LxjksNIXf+wY+pgwOZLiXSGNxciiNt74j4/P7dx6Zkebzehqr9LX/s8P67Ii05ePWjY2zqdrTI0205YzH396freNtrPb5eKw+0cumZc+i0f1+xZDwuRISkCV/bfOlQuLtlVb9bbEKQF4K6HmW7W5ub0/nOJRQ29L8JMfPxAskAiBEEIcrVrth+vN5wvYjaLkDOXStYLoRFdLwy9a+6WF1wUyfuw1ffpdz6N4C3NuvTl9xvbC/35W9CV7cdqi5tLVB58dGzfygVF3D4t0W/2Mu9S01n1Zun9P2YEWS6fpMfkU/3cZN907cpFcNPBx3vETlAIxr/ij2vYbrgwp31Vv0diG3BIfSHnCorXVdBojowxJ7H5dUgCuIBECMZ0+qs3bSLexvuspKnTS78LnP0DxO84Qhmbqvu+4HIy/XskX9+NKSC4Ke2j0H27Lmvv+6by9ZQcdTMfiFQX1J499fWpS8rW/y7hpTNwIzu8d2hy2wzU/f1m673j96curPkbF5j467oGhEamD31H02AhCUcUf1TCO9r3U/dBsM9gzFyVR/ABJhmWf1dGuMTJhAtVNGCMDPgeJMKgxNmvLF/8y/LC70/q6oeHKRU9Icq7u8uKmE3qzpv1ijieg4icOZCagaFnUU9esvHPY77ee2XGg4hB9ab8MYQ5XHz1cfVQuCrs2cdzUlOuvTRg3gC7HQapprfuq9Ju9Fw5ozS2X/zVKFvngyLtnDpnqxvua0WPCRXLBuX9X2c3tvwzUx1usrfZh96oEEr8fTtJljEzavDiMkQEfhEQYvGwNVZotL9lqO60ZJM4cpVz8FD+8myRXe6ijgyvmaoUobOAnj0qe+OcJj9+ePe/dE1vyL55g/0lvbd1f/t3+8u+iZVFTUyZOT5mUHZkx4B31kfMS8IuSr080nOm28F8uCrs1a+7CnFslAvdPbhKeHjLikbTC9yotuvZlhlpK2069UT78wZQBT8PmC2gb3WmMTJosZmyAVJFCgEEiDFLG3w5oP3mTsbJmf+bx5TMXymctJt3NWKYrMRhqLi2dQ5HEKW6YGDZLmf7qtOeP1Z9698SWc83FXf6qNjbtOLdzx7mdiWHx01MmT0uZmBaRMvidurTZjOebS841FZ9tLjqtPqe3dF/MNyJm+Lz0WTeoJoj4nprHlRAii5fkrkwrfLfS1Ng+8Yqx3nxq04WrlqdKY/x1XrHqAxgjA/7B/XONDgDmGh28vs81SpvbdDveMB77nt0oUMYql64VpQ7r6V2F71Zoz7eXA0aOkA/7g2qQAbMxhDlef/pAxfeHq4+6ig4vJxeFqcITU+TJqvCkFHlySnhSGAkJDQnt41yjDsZxQVd5tqnoXFPxuebiKn0N3fPJLxeFzRoydV76rJRw7y2Fam9zFP6rsrWiY2ytIISfc1+KvPOUpH5xeqsLdEXba1xX1wmTI4fcEj/grQXnXKN+8UG7HSdHjSvC4GKtOK/Z+pK9uZ7dKB01SXFne5lgt4wXzdqijvyUdIObh/hThBoTN2JM3IjHr/7jbxePHaz44ceaX0z2rmsV6a2tZ9Tnz6g7li0V8oQqeaIqPEklT1JIwp1vabO20Qxjpa0Wu5UhjMHaRghpNmmKNWWWPkxq451LwG4JQvi5f0w9v6XadV/N3uY4838VWXcnRV7lT+X2mrOtxXm1riwowhgZ8G1IhEGDplu/+1S/Z0unMkGxVHH7Stn46b2/tSFf5/pSkw8JGdiaCX0h5AkmJF49IfFqi8P6U82vByt/+KWuoJcp2Wy0rUxXUaarGPyu5eKwWWnevgS8HE/IG3aPquy/F+uPapwttI0+/3512vy4hEluW6fMo/TlxvNbql3jYHkCKnNJUgAM/IEAhkQYFBw6tWbry5ay0+xGUXKmctlaQVTCFd7MkKYTHUMo469XeiLCLsR80dSUiVNTJrbZjEeqfz5Y+cPJxkLzZdeIg8GjeCnhycMiM3KisoZFZqZFqDgv23CieFT6ggRRuKBqX2N7uT3NXPj8ov6CMf3OBB/PKG115rObK131EhSPylycHJERFLOKg/9CIgx8plM/afM20kbWYJDuygR7oq8wWrTtoxn5Ip5yuFe770OEsllDps0aMo0Q0mTSVLZU1xnqy3VVFS1VFw0NdYb6K26BLVKqyFKmZyrTsyKHXhU9bDDl8J6mmhkjDheWflLnmt+86WSLocaUvTSZ+OrQS3OztfCdCrvpUoUoRYbeFh810p86dSE4IREGsvYywcO72I280Ajl4ickw8b3cSPqYx1TbCuHh/FF3q7tc4mSKqOkyrGkYz62el1Do7W5Sl9Tra812c0hQhkhRCaU8nl8AU8gFUgIIaHCEIqixHxxuiI1WuZPE5jFXqMQhgmKtlU7zO0XWOZm68k3LiTMVITdGOZrIzCtevuZf1ZYWzs63lPnxMZd543+A4BBQiIMWLb6Ks2WF2115exGceZo5ZKn+PK+fj0xNNN0qmPGmegxvnUxEiYMjQ2PGRGTw3UgnqLMCRvzVMb5LdWtle1DSRkHU7tXY6qyZS5MEsh8pZvUbnYUvlfhKpYghCRMikyaHt3LWwB8B2e/7sGjjL8daNzwCDsLUnyB/KYl0X/8375nQUKIrrjNduk3vkDKj8jCzR5vEyuEuQ+nJUyKZF8Cagpbj68v1Zcbe36f99A2+ux7lW21HXdwY8ZFDKZYAsDLcEUYaGiTQbvjDdPxw+xGQUxS5NKnhUlD+7u1puMdw2QiR8h5Ah/rjwsOPAE15Pfx4RkhJXm1dmP7HTiLznb6rfLkGdGqmTEcdpMyDubc+9XslKwcHpZxV6Kv9dwC9AKJMKBYSk9ptr3s0DWxG2XjpytuX0mJpf3dGm1nms+w+0UDc7U8fxF5lTz0CWnRto6sw9BM1b5G/QVj5pKkwcx4N3AMKdlRqz3XMQ4rPD0ke5nqiotzAfgUJMJAQTvM3+4wffcJoWlXG08ii1iwUjZ22sA2qT3X6hoBKAwThA+98rQ14FFihTB3RVrxzmr1T3pXZaeuxHBifWnyrJi4axTeXLOCtjMXPr/Y+FvHWKrQJGnOvSnoNgC/g0QYCBzaRs3WdZYLhexGkSpTufRF24KsAAAfmElEQVRpQdTAb9WoWf2iUSPD8TPfF1B8KmGmInqYouSjGtultSGtrfayT+tqv2tSzYqJHuONT6r5tL58dz17dIw0Wjz8wRS+BMMOwP8gEfo906kftXkbaSNris7+lAn2xGGhNWc7uryiR6Nf1Icoc8JGPZFetK1Gf6HN1WhuthZvr6k5qFbNjo3KlXvoLl3bRXP5znpdSacpYcURwqseShWG4vsE/BJOXD/WbZkgP0yhWPykJHvsIDeuKdS75gcRK4Ryj02rBgMjjhDmrkit/kZd812T65MihBgbLOffrwpNkqbMiVVku3OUr63NUbm3oeFnravG30kkFwxfnipW+PGKURDkkAj9la2+UvPBi7aLFexGSfZYxaIn+XLF4LevPtbRLxo9OgKDAH0QxaNUs2Lir1fWHmquO9xE2zvyk6HGVPhuRViqLHVObHj6YG/uMg6m4Vdt5Z4GV2esK4DYaxQps2NwLQh+DaevH2KYtqN7dZ//k7F13KGhBELprLuVNy7odjXB/rKbHOzlJqLQL+rDhKGC1LmxcRMU1fvUjQU69uVaa4Xx9NvlEVmhUSPk8lSZLE4ygB802nOtF3bVuxZKdInICh0yP14WF1xLI0FAQiL0M3SbXrN9g7nwZ3ajIDZZefcamyLeLVmQENJ0Uu9aPUAaIw5NlLhls+A5EqUoY2Fi0vSoyq8bm062EFbnpa7IoCsyEEIEUn5YqkyeIg1LCwlTSfni7ga2MMTSYjM3WU1NVnOztbXS2FLa1uUl0mhx2u/ivDzrLIDnIBH6E0vJSc22lx0tzexG2fjpigWPEKHYZnTbPCPsOnoMk/Ej0hhx9tJkQ2101d4G9lgnJ7vJoT3X6iz7o3hUSLw4LC0kLFnqsDhMTVZzk9XcbDU3W9ldrF0IJPzkmdEJkyK9WacB4GlIhP6Bcdj1e7e2HtxBWIuq86Shijsfk46aRAhhel5svb+srfaWso6LACRCvxOaKMm5P0VfYazc03D59ZwTQzOGWrOh1nyxb9vE7UAIYDin/YBD09i8dZ21vEuZYJZy2VpBpPtndGw60eK6zxSaKJHG4CaQX5KnynJXpLVWmVpKDPpyo77SaO881KXvwtNDhtwSH5KAHnIITEiEvs5Y8J3uk020mdXtyePJZ9wln7WY8Dyy+ECnOnofW24C+itMJQ1TSQkhhCEmtUVfYdSXG1srjMZGC+mhE0EYwpdEiSSRYkmUSBopCkmUIAVCYEMi9F2MxaT979vGX79hN/IjopRL1ojTcz20U7PG6lrxh1AkehT6RQMFRaQxYmmMOPZqBSHEbnToK4ytFUaT2sqX8KRRIkmUSBIpkkSJBBJfWd0JwDuQCH2Uraa0+YMX7epadqM09zrFXY/zQjy45HfT8Y4Bh/JUGaqkA5VAxlfmhClzMPITAInQBzGM4fCuli/+xdhtrjZKKAqfe2/o5PnuKpDoifp45zp6AIBAh0ToW2hDi2b7q+azv7IbBbGqyKVrhYlDPL13U6Olra59eVWKR0WN9OClJwCAj0Ai9CGW4hOabS879Bp2o2z8dMWCRymRN4ZuNrKmVQvPCBFyssQdAIB34ZvON9AO/f6P9Ps+7FQmKAmJuPNR2egpXosCdfQAEISQCLlnV9dqtqyzVhezG8Xpucolf+JHRHstDEO1yaRun0+S4lORV6FfFACCAhIhx0wnftB+/DptYq3uxuPJZy6Sz1xEeF5d45Q9TEaZEyaQYQw9AAQFJELO0Gaj7pM3jQXfshv5ypjIu9eI0oZ7OxqGNJ1EvygABCMkQm5Yq4s1H7xkb6pjN0pHTFDc9ThPxkFpV8uFNou2vVqDL+IpUF4GAEEDidDrnGWCuzczDrurrb1McMotXAXFHiajvErOF3m1VxYAgENIhF5FG3SaD181n/uN3SiMS1Eue1oYn8pRUIQQ0lzYsWQP+kUBIKggEXqPueiY9sP1HJYJ9sRYb7G2XOoXFfMiskI5DAYAwMuQCL2Bcdhbv8nrWiYYIlcuWi0Zfi2HgTlpizouB8OHhvAEWHMVAIIIEqHH2Rtrmre8aKspYzeKM0Yql/yJHx7JVVRsuuKOtVsjMnE5CADBxf2JkGGYwsLC/Pz8goKChoaGjIyMF154we178RfG3w5oP32LsZg6mnh8+cyF3i8T7AnjYPSs9ejRLwoAwcb9iVCr1ebm5hJCBAKBw+G45ppr3L4Lv+BbZYI9a7lgdFhp52NxhFAWi/XoASC4uD8RSiSSTZs2jR07duTIkbGxsW7fvl+wVhVrtrxob7rIbpSOnKi4cxVP5luXXLrijkltcDkIAEHI/YlQJpOtXLnS7Zv1Gz5ZJtgLXRErEeIGIQAEHwyWcSdHq1b74Xrz+QJ2ozA+Vbl0Lbdlgj2xtTkMtZfuX1IkIiOE03AAADiAROg25vMF2u3rHXptRxNFhU76Xfjv7qcEQu7i6o2uyEAuFXSEJkmFoTgfACDo9PWLz2w29/4CiUQy4CDUavXSpUtlMpnzaW5u7iAHmra1tVGU94rhGLvNvG+r5ee97DJBKkQecuvDgqyxbWYLIRaPx8AwJpOJYQXQF+rCjrQdkiYyGAy9vNgHGY1Gmqa9+Vn7Ai+f3r7AarUyDGOz2bgOxKuC8IMmHjhqiUQiEFwh0/UpEZpMJleW6snFixfj4uL6Glpncrl8+fLlSUlJzqeRkZFX3F3vHA7HILfQd/aGau22l221ncoERekjFYuf9GaZoDMF9veo28o7MnRUToTX/tHchWEYmUwWbF8W3jy9fYRAIGAYRiwOriHNQfhBEw8cNa8PhWp9SoQikWjDhg29v0YuH/g6rmKx+Prrr8/MzBzwFrrg8Xh9OfjBM/52QPvJm4yVdbnsLBOctZh499uZYZj+HrWx3mLRdaw4ET4klMfzs4ziPORgS4ReO719B4/Hc57hXAfiVUH4QROOjrpPiZDP5z/++OOeDsW/0GajbscbxmOH2I0CZazy7jWitByOguofduFEeDpmVgOAIIXBEQNhrTyv2bLO3ty5THDUJMWdj/GkflOBoEXhBACAhxLh2bNnTSYTIYSm6ba2toKCAkKIUqlMS0vzxO68qtsyQbE0Yv4DIRPmcBhXfzEORn8BM6sBAHgmES5atOjkyZPOx6dPnx43bpyz8cMPP/TE7rzGoWvSbFtnKT3NbhQlZyiXrhVEJ3IV1cC0XDA6LO0zq4nCMbMaAAQvjyTCf/7zn5cPxB/wmFIfYTp9VJu3kW7TdzQ5ywTnP0Dx/a+HmX2DUJGNy0EACF4e+Qa/9lru19hzI8ZmbfniX4YfdndaTTA0QrnoCUnOeA4DGwzMrAYA4OR/lzJeZmuo0mx5yVZ7gd0ozhytXPIUX67kKqpBwsxqAAAuSIS9Mf52QPvJJsbKmheGozJB9+o0s1oiZlYDgKCGb8Du0eY23cdvGI9/z24UKGOVS58WpWZzFZW7YOklAAAXJMJuWCvOa7a+ZG+uZzfKxk9X3L6SEku5isqNOo2UQSIEgOCGRNgZTev3b9fv305o2tVGiaWKBY/Ixk3jMC43MjZ0mlktLDXoJjMEAGBDIuzg0Kk1W9ZZLpxhN4qSM5XL1gqiEriKyu3Y40XlQzGzGgAEOyTCdqZTP2nzNtLG1o4mfy4T7AV7ZjX0iwIABNRX/MC0lwke3sVu5IVGKBc/KRk2jquoPAQzqwEAdBHsidBWX6X54H9tFyvYjZKsMYrFT/HlCm5i8iR9OWZWAwDoJKgT4eVlgpRAKJ99d9i0BX5dJtgL9IsCAHQRpImQbtNrP9pgOvMzu1EQkxS59Glh0lCuovICzKwGANBFMCZCS+kpzdZ1jpZmdmMglQn2pOvMapmYWQ0AINgSIe3Q7/+oS5kgTyKLWPCIbOxUDuPyDl0xZlYDAOgqiL4KHdpGzdZ1lguF7EaRKku5dK0gKp6rqLwJM6sBAFwuWBKh6eQR7cev0UbWKokBWibYC9wgBAC4XODngG7LBPlhCsXiJyXZY7mKyvvYM6vxRDx5GmZWAwAgJOAToa2+UvPBi13KBKVXXatYuJoXIucmJo6wLwfDMbMaAMAlgZsIGcZweFfLF/9i7DZXGyUUhc+9N3Ty/EAtE+wFVpwAAOhWYCZCpk3flLfeXPgLu1EQmxy5dK0wMZDLBHvCOJiWMsysBgDQjQBMhJaSE4atL9N6DbtRNn66YsEjlEjCVVTc0ldgZjUAgO4FViJ0lgnu+5AwjKuNJwmJuOMR2ZgbuAuLe60VRtfjiAzU0QMAdAicROjQNDZvfclafpbdKErJVi5dI4gMijLBXuhZiRDjRQEA2AIkEZpO/qDNe502scoEebywqbfL5ywNnjLBHjGktdLkeoYl6QEA2Pw+STAWk27Xe20/7WE38sKjIpeuEQ/N5Soqn2JuttoMdudjvpiHG4QAAGz+nQit1SWaLS/Z1bXsRmnuBOHc+8WxCVxF5WvY/aJhKTKKF3SlIwAAvfDbROgsE9y9mXHYXW3tZYJTbmltbeUwNF/TWslOhIG8vAYAwAD4ZSKkDS2a7evNZ39jNwpiVZHLnhYmpHEVlc9q7XxFyGEkAAA+yP8SoaX4hGbby45uygQfpUS4+9UVbaXbLlran1BIhAAAXflZIjQc+VL337c6lQnKwhQLH5fmTuAwKl/WWm1i6PZ/LmmUWBjC5zYeAABf42eJsHV/p2J5cXqucskafkQUhyH5uE79oqm4QQgA0JWfJUKePNKh1xJCCI8vn7VYPuMuwuNxHZRPY1cQytEvCgBwGT9LhMq7/9Sy+9+EtstnLhKl5XAdjh/oNGQUpfQAAJfxs0QojFVFPfBXrqPwG+Zmq7X1Uim9iCeLw2AiAICu0K8YyNiXg6EqKUrpAQAuh0QYyPQVrBuE6BcFAOgOEmEg6zynDBIhAEA3kAgDFm2j2+rMrqdhKtROAAB0A4kwYBmqTYyjveZSEiUShvnZwCgAAO9AIgxYelQQAgD0ARJhwOo8pwwSIQBA95AIAxZWXwIA6AskwsBk0dqs+vZSep6IF5Ig4TYeAACfhUQYmDqtSp+MUnoAgB4hEQYmVBACAPSRR4bUX7hw4csvvywuLjYajUOHDp09e/aYMWM8sSPoCVZfAgDoI/dfEb722mtDhw597LHH8vLyjhw58te//nXcuHHPPfec23cEPaHtTKdSelwRAgD0zP2JUCgU/vnPf66qqmpqaiouLj537lxWVtbf//73I0eOuH1f0C1DjYm2XyqlV4pEKKUHAOiZ+78iH374YfbT9PT0F1544bbbbtu7d+/EiRPdvju4HCoIAQD6zhuDZaKiogghDMN4YV9AUEEIANAf3kiE27ZtI4TMmDHDC/sCQkhrJVZfAgDoK4/fPfrqq682b9581113TZ06tafXtLa2vvPOO5GRkc6nGRkZt9xyy2B2arPZbDbbYLbgdxiGcR61tcVu0bUfO09AiaL5AfxP4TxkigquKskgPL1tNhvDMDxecJV7BeEHTTxw1Hw+/4pnTl8T4bx58xobG3t5wXvvvTdixIgujfn5+YsXL87MzNy0aVMv73U4HDqdzhVrQ0MDTdN9DKxbNE0Pcgt+h2EY51HrK9pcjbJEMUMxDB2wndLOQw62RBiEpzdN084znOtAvCoIP2jigaPuy++nvibC6Ojo3jcnEom6tJw6dWrWrFkKheKbb75x3ibsSURExJo1azIzM/sYzBVZrVaxWOyurfkFhmEcDodYLDbXalyNEUNCA/vfwW63i8XiYEuEQXh6UxTFMEywHXUQftCEo6PuayL897//3a/tnj17dsaMGSEhIQcPHkxOTu5/YDBA7NWXUEEIAHBFHulzLykpmTFjBkVR+/fvHzJkiCd2Ad2i7UxbDTsRYsgoAMAVuH+wTGlp6dSpU+12+3fffZedne327UMv2mo7SunFCqEoXMhtPAAAvs8jU6zV1tbq9fqJEycqWR588EG37wu66LToBPpFAQD6wP1XhDNmzAgNDb28fdSoUW7fF3SBCkIAgP5yfyKcP3/+/Pnz3b5Z6AusvgQA0F/BVaAa2GytDou2o5Q+JBGr0gMAXBkSYeBoq7a4HocmSXmC4KquAwAYGCTCwNFWjTUIAQD6DYkwcLRVsRIhRsoAAPQNEmGAYByM6WLHTLUopQcA6CMkwgDRVmumbe0z1YrkAnEESukBAPoEiTBA6FmFE/K0EA4jAQDwL0iEAcLAvkGIflEAgD5DIgwQhmosOgEAMBBIhIHAYaVNTZeKCCkSkoBSegCAvkIiDATGi2ZyaRV6aZSYL8bHCgDQV/jGDARtdR03CHE5CADQL0iEgaCtlpUIMcUoAEB/IBEGAlwRAgAMGBKh/2NIWz0SIQDAACER+j2zxuowt88pI5DyxeGYUwYAoB+QCP1e1xuEWHwJAKA/kAj9Hm4QAgAMBhKh30MiBAAYDCRCv4dECAAwGEiE/s1udpi1VudjikfJ4pAIAQD6B4nQvxnrOiZXE0cJeAIMlQEA6B8kQv9mYA0ZlcaJOYwEAMBPIRH6N/YNQmmciMNIAAD8FBKhf0MiBAAYJCRCP8bQjLHB4noqjUciBADoNyRCP2ZSW2lr++RqwlCBMJTPbTwAAP4IidCPoYIQAGDwkAj9GDsRhmIZQgCAAUEi9GPsRCiLR+0EAMBAIBH6sbZak+sxukYBAAYGidBf2dscVr3d+ZgnoKQxuCIEABgIJEJ/ZajruByUxYopPiZXAwAYCCRCf9V5yKiUw0gAAPwaEqG/6rowPQAADAgSob9CESEAgFsgEfolxtFpcjVZPBIhAMAAIRH6JWODhXG0r0MojhAKQzC5GgDAACER+iX0iwIAuAsSoV9CIgQAcBckQr+ERAgA4C5IhH4JiRAAwF2QCP2PVW+3GS5NribkSaKwHi8AwMAhEfqfTpeD8WKKh8nVAAAGTuCJjTY0NBw7dqyhoUEgEAwZMmT8+PFCodATOwpObXVYdAIAwG3cnwjXr1//1FNPsVuSk5O3b98+ceJEt+8rOGGWUQAAN3J/12h6evrrr7+en59/8eLF8vLyt956S61Wz58/v6Wlxe376slNN91kMBi8tjsv63aW0aNHjz7++OMcRcSZ1atX//TTT1xH4VUGg2HWrFlcR+FtH3zwwVtvvcV1FN72+9//vqGhgesovOr06dPLly/3/n7df0V4yy23sJ+uWLGivLx8/fr1R44cufnmm92+u26VlJQYjcbQ0FDv7M6baDtjUlvbn1AdC9Or1eq6ujrOwuJIXV2dWq3mOgqvMplMJSUlXEfhbQ0NDa2trVxH4W3l5eWtra2xsbFcB+I9zc3NNTU13t+vNwbLREREEEJCQkK8sK+AZ6w3M3T75GoShUggweRqAACD4vFEmJ+f//bbbw8fPvz666/39L6CAVZfAgBwL4+MGiWErF69eteuXc3NzS0tLUuXLn311Vd7GThqMpl2794dFxfnfBoeHp6QkDCYvdvt9pMnTyqVysFsxDfZTgoIab8K1BNtQUF7x2BZWVlLS0tBQQF3oXFAp9OVlZUF1VFrtVq73R5Uh0wIqaura2trC7ajtlgsZ86c8eboCs4VFxcbDAb3ftBJSUlX7F6mGIa54obKysreeeedXl6gVCrXrl3LbsnLyzt27FhdXd3333/f3Nz8/PPPP/nkkz29XaFQWCwWimqvh5NKpSqV6opR9aKiokKlUvF4AVglmRCSFCYKdz6uN9a1WLTOxyaTSafTxcfHcxcaB+rr68PDw6XSIBo6S9N0VVVVamoq14F4lU6no2k6IH/a9qKqqioxMZHPD6LbHxaLpampKTEx0Y3bvP3225955pneX9OnRHjkyJG5c+f28gKVSnXq1Klu/2SxWBYuXPj5558fOHBg+vTpV9wXAACAN/UpEQ5SQUHBuHHjHnvssddee83T+wIAAOgXb3QeOvs8TSbTFV8JAADgZe5PhJWVleynNE1v2LCBEIKZZQAAwAe5v2tUpVKpVKoxY8bExcU1Njbu3bu3uLj4hhtu+OabbwQCTw1SBQAAGBj3J8KNGzfu2rXr3LlzjY2NcXFxaWlpCxYsePjhh0UirBYEAAA+xxuDZQAAAHxWgPdVmkymDRs2/PzzzxUVFUajMSEh4YYbbli1alVkZCTXoXlQXV3dZ599tn///tLSUh6Pl5GRsWjRogULFnAdl2c55xMoKCg4deqUxWJ55plnRo0axXVQ7uRwODZt2vTRRx+p1eqUlJSHHnrozjvv5Dooz6qtrc3Pz8/Pzy8pKaFpevv27QF/e8VoNO7Zs8fZqabX61NSUqZNm7Zq1arALpb99ttvd+zYcfLkSbVaLZVKs7KyHnrooRtvvNF7ETABraamhs/njxs3bvHixffee+91111HCImLi6uoqOA6NA+67bbbCCE5OTl33HHHokWLoqOjCSGrV6/mOi7PevTRR52ntLMAec+ePVxH5GZ33303IWT27NnPPPPM1VdfTQhZt24d10F51lVXXcX+TC0WC9cRedzmzZsJIfHx8XPmzLnnnnuGDx9OCBk7dmxbWxvXoXnQH/7wh9jY2Llz595333133HGHc3rqZ5991msBBHgitFqtGo2G3eKsZXzkkUe4CskL3nvvvd9++831VKPRZGdnUxR19uxZDqPytD179uTl5ZWUlLzyyiuBlwgPHDhACLn//vudT2022+TJk8VicWVlJbeBedTmzZu/+uqrhoaG2bNnB0kiPHTo0I4dO+x2u/Opw+G45557CCEbN27kNjCPamxspGna9VStVqempgoEgubmZu8EEICTkLEJhUKFQsFuWbp0KSGkoqKCm4C84v777x83bpzrqUKhePDBBxmGyc/P5zAqT5s9e/add96Znp7OdSAe8Z///IcQsmrVKudTgUCwcuVKi8Xy0UcfcRqXZ913331z5syJiYnhOhDvmTJlyoIFC1zTqvF4POc657/++iuncXlWdHS0a4pNQkhUVNTs2bPtdrvXlmQK8ER4uWPHjhFCRo8ezXUgXmWxWAghcrmc60BggI4ePZqYmOjsKHOaOXMmIeTHH3/kLijwBqvVSoLsPy9N0ydOnJDL5UOHDvXOHgP8zrNTY2Pj999/bzQaCwsLN2/ePGnSpNWrV3MdlPfo9fp33303Li5u2rRpXMcCA0HTdEVFxZgxY9iN4eHhoaGh5eXlXEUF3vHKK69QFLVw4UKuA/G4b7/9Vq1W19fX79y588SJE++//77XVrH1y0To7EDv5QUCgYB9oX3mzJk77rjD+Tg7O/vFF18MDw/3bIgeYLPZen9BtwtdMQyzfPny8vLyHTt2hIWFeSY0T6Fp2uFw9PICPp8fkGuMdGE0Grtde0GpVOr1ek5CAu/44IMPPvzww3vvvXfKlClcx+Jxf/nLX44ePUoI4fF4a9as6X2lB/fyyy+RrKwsUa8OHjzIfv3kyZM1Gk1lZeWePXvkcvmUKVM+++wzroIfmObm5t4PWSQSdfud+PTTT+fl5a1atcofyyeefvrp3g95xYoVXMfoDc6aAWcXGZvFYullmU/wd/v371++fPk111wTJMsV7Nu3T61Wnzx58tlnn12/fv2NN95ot9u9s2u/vCJcu3atTqfr5QUZGRnspwKBQKFQKBQKlUo1YcKEoUOH/vnPf7711ls9HKY7hYSEvPzyy72/RiLpumD9s88+u27duocfftg53avfufnmm6Oionp5QYBVCvZEIpHIZDKNRsNuZBhGo9EMcuVO8FkHDx6cP39+Tk7O119/7Xd9OQMTFhYWFhYWFRU1YsQIhmGef/75nTt33n777V7YtV8mwgceeGDA7w0PD8/Jyfnxxx8dDocfrXgpkUicg8f67h//+Mc//vGP+++/f9OmTeyOYj8yefLkyZMncx2FT8jOzi4pKbFYLGKx2NlSVlZms9mGDRvGbWDgCYcPH54/f35mZuY333zjLKoLNhMmTCCEFBUVeWd3ftk1Ohgmk6moqCgmJsaPsuAAbNiw4dlnn122bNk777zjp1kQ2GbOnNna2vrdd9+5Wnbv3k0ImTVrFndBgUccPXp07ty5SUlJ+/btC+w5sHpx4sQJQkhcXJx3dueXV4R9l5eXZzAYZs+enZCQQNN0YWHh2rVrGxsb165dy3VoHvT6668/8cQT48ePX7FixfHjx13tiYmJXjuxvE+n05WVlRFCamtrCSGlpaUFBQWEkOHDh1/eaex3VqxY8frrr//pT38aMWJEQkLC6dOn161bl5KS4pxFKFBVV1c3NjYSQlpaWgghx44dEwqFIpEoNzeX69A8JT8//6abbuLz+a+++mptba3zZCaEhIWFZWZmchubhzgcjkcffXTZsmW5ublSqbSlpeXjjz/+29/+plAo5s+f76UgvFO3z5UXXnjBeZgikcg54oCiqPvuu89qtXIdmgdNmjSp28/6xRdf5Do0D+ppAFRRURHXobnHp59+KpPJhEJhSkoKj8eLjY1lzx8UkFauXHn5B5qcnMx1XB7k+srqYsqUKVyH5ik2m801haxMJnM+UKlUR44c8VoMgb/6RGFh4U8//VRXV+f8BrnuuuuGDBnCdVCelZ+f3+1govT09NTUVK+H4yWNjY2nTp26vH3ChAmu/13+rqamZufOnfX19WlpabfeemuXWZMCT1FRUXV1dZdGiUQSwKt8V1RUlJaWXt6uUCjGjh3r/Xi8Q6/XHzp0qLS0VKPRJCQkZGZmTpkyxZsjogM/EQIAAPQi6AbLAAAAsCERAgBAUEMiBACAoIZECAAAQQ2JEAAAghoSIQAABDUkQgAACGpIhAAAENSQCAEAIKghEQIAQFD7f1OtnUoOBCMTAAAAAElFTkSuQmCC", "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" ], "text/html": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function vander_newton(x, abscissa=nothing)\n", " if isnothing(abscissa)\n", " abscissa = x\n", " end\n", " n = length(abscissa)\n", " A = ones(length(x), n)\n", " for i in 2:n\n", " A[:, i] = A[:, i-1] .* (x .- abscissa[i-1])\n", " end\n", " A\n", "end\n", "\n", "# Let's view these polynomials again\n", "s = LinRange(-π, π, 50)\n", "A = vander_newton(s, x)\n", "plot(s, A, ylims=(-3, 3), label=[\"\\$n_0\\$\" \"\\$n_1\\$\" \"\\$n_2\\$\" \"\\$n_3\\$\"])\n", "scatter!(x, [zero.(x)], color=:black, label=\"roots\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "88af4ff6-4718-477d-9024-8432579164bd", "metadata": {}, "outputs": [ { "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" ], "text/html": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's fit our example curve\n", "x = LinRange(-1.5, 2, 4)\n", "y = sin.(x)\n", "\n", "# Solve \n", "p = vander_newton(x, x) \\ y\n", "\n", "# Plot\n", "scatter(x, y, label=\"data\")\n", "plot!(s, [sin.(s), vander_newton(s, x) * p], label=[\"fit\" \"true\"])" ] }, { "cell_type": "markdown", "id": "2d920707-2af7-4c1a-aff7-f9298ce6632d", "metadata": {}, "source": [ "### Newton Vandermonde matrix structure\n", "\n", "How much does it cost to solve with a general $n \\times n$ dense matrix?\n", "\n", "1) $\\mathcal{O} \\left( n \\log \\left( n \\right) \\right)$\n", "\n", "2) $\\mathcal{O} \\left( n^2 \\right)$\n", "\n", "3) $\\mathcal{O} \\left( n^3 \\right)$" ] }, { "cell_type": "code", "execution_count": 8, "id": "f61a8a1d-e9b0-4ccd-9525-c8708bb35dd6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5×5 Matrix{Float64}:\n", " 1.0 0.0 -0.0 0.0 -0.0\n", " 1.0 0.5 0.0 -0.0 0.0\n", " 1.0 1.0 0.5 0.0 -0.0\n", " 1.0 1.5 1.5 0.75 0.0\n", " 1.0 2.0 3.0 3.0 1.5" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vander_newton(LinRange(-1, 1, 5))" ] }, { "cell_type": "markdown", "id": "afd6dd42-3358-4955-979f-980fb67d19ea", "metadata": {}, "source": [ "How much does it cost to solve with a Newton Vandermonde matrix?" ] }, { "cell_type": "markdown", "id": "2fbb73e4-b842-4628-a29a-939be83ea578", "metadata": {}, "source": [ "How is the conditioning of these matrices?" ] }, { "cell_type": "code", "execution_count": 9, "id": "53c9fa8f-3fe0-489d-9513-f8defdbe305c", "metadata": {}, "outputs": [ { "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": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Maybe Newton is better?\n", "plot([vcond(vander_newton, LinRange, 20)], yscale=:log10, legend=:none) " ] }, { "cell_type": "markdown", "id": "969be176-d707-4a65-bb09-b4dd649af406", "metadata": {}, "source": [ "## A well-conditioned basis\n", "\n", "Recall the Legendre basis from the assignment." ] }, { "cell_type": "code", "execution_count": 11, "id": "9826e33e-45aa-4efb-9a62-107dca1a7bb8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "vander_legendre (generic function with 2 methods)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function vander_legendre(x, k=nothing)\n", " if isnothing(k)\n", " k = length(x) # Square by default\n", " end\n", " m = length(x)\n", " Q = ones(m, k)\n", " Q[:, 2] = x\n", " for n in 1:k-2\n", " Q[:, n+2] = ((2*n + 1) * x .* Q[:, n+1] - n * Q[:, n]) / (n + 1)\n", " end\n", " Q\n", "end" ] }, { "cell_type": "code", "execution_count": 12, "id": "a7ba0538-83d1-4a9f-a8fd-ff562ec4fb29", "metadata": {}, "outputs": [ { "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" ], "text/html": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CosRange(a, b, n) = (a + b)/2 .+ (b - a)/2 * cos.(LinRange(-pi, 0, n))\n", "\n", "a = 20\n", "plot(range(2, a), [vcond(vander, LinRange, a)], yscale=:log10, legend=:topleft, xticks=range(2, a, step=2), xlabel=\"rows\", ylabel=\"cond(A)\", label=\"Vander, LinRange\")\n", "plot!(range(2, a), [vcond(vander, CosRange, a)], yscale=:log10, label=\"Vander, CosRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, LinRange, a)], yscale=:log10, label=\"Legendre, LinRange\")\n", "plot!(range(2, a), [vcond(vander_legendre, CosRange, a)], yscale=:log10, label=\"Legendre, CosRange\")" ] }, { "cell_type": "markdown", "id": "def5f384-d148-4932-aca6-96f6214ec9c0", "metadata": {}, "source": [ "## But do we care about ill-conditioning?\n", "\n", "What can wrong with poor conditioning?" ] }, { "cell_type": "code", "execution_count": 14, "id": "162fc1f7-dee4-4f21-b4f9-607561ef04fd", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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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" ], "text/html": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's solve for a fit\n", "ourvander = vander # try vander_legendre\n", "p = ourvander(x) \\ y;\n", "\n", "# And see how good it is\n", "scatter(x, y, label=\"data\")\n", "s = LinRange(-1, 1, 100)\n", "plot!(s, runge1.(s), label=\"true\")\n", "plot!(s, ourvander(s, length(x)) * p, label=\"fit\")" ] }, { "cell_type": "code", "execution_count": 16, "id": "71725d5e-2d93-4f87-b8c2-15298a834740", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LinRange:\n", " Vander:\n", " Condition number: 2.7224082423906505e8\n", " Vander Legendre:\n", " Condition number: 7274.598185486983\n", "CosRange:\n", " Vander:\n", " Condition number: 7.423193943616384e6\n", " Vander Legendre:\n", " Condition number: 8.502660254099549\n" ] } ], "source": [ "println(\"LinRange:\")\n", "x = LinRange(-1, 1, 20)\n", "println(\" Vander:\")\n", "println(\" Condition number: $(cond(vander(x)))\")\n", "println(\" Vander Legendre:\")\n", "println(\" Condition number: $(cond(vander_legendre(x)))\")\n", "println(\"CosRange:\")\n", "x = CosRange(-1, 1, 20)\n", "println(\" Vander:\")\n", "println(\" Condition number: $(cond(vander(x)))\")\n", "println(\" Vander Legendre:\")\n", "println(\" Condition number: $(cond(vander_legendre(x)))\")" ] }, { "cell_type": "markdown", "id": "9c972abe-3491-4404-a87e-0f7371aa7d32", "metadata": {}, "source": [ "What is the \"worst\" normal vector?" ] }, { "cell_type": "code", "execution_count": 17, "id": "9660b05b-2427-4467-bca7-1bc9c4e91dd5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] } ], "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 }