{ "cells": [ { "cell_type": "markdown", "id": "06e95097", "metadata": {}, "source": [ "Title: Symmetric Linear Systems and Quadratic Forms\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "markdown", "id": "6b8b433a", "metadata": {}, "source": [ "# Symmetric Linear Systems" ] }, { "cell_type": "markdown", "id": "ca6c9296", "metadata": {}, "source": [ "(system of linear equations)\n", "\n", "\\begin{eqnarray}\n", "2 x_1 + 4 x_2 & = & 2 \\\\\\\n", "4 x_1 + 11 x_2 & = & 1 \\\\\\\n", "\\end{eqnarray}" ] }, { "cell_type": "markdown", "id": "741daa9c", "metadata": {}, "source": [ "(system of linear equations in matrix form)\n", "\n", "$$ M x = b $$\n", "\n", "$$ M = \\left(\\begin{array}{cc}2 & 4 \\\\\\ 4 & 11 \\\\\\ \\end{array}\\right) $$\n", "\n", "Note that $M$ is symmetric in this case. Symmetric linear systems are special." ] }, { "cell_type": "markdown", "id": "120efb3c", "metadata": {}, "source": [ "(factorizations)\n", "\n", "There are a number of common factorizations of the matrix $M$:\n", "\n", "- $A^TCA$ - source of problem, dynamical systems or statistics; $A$ may be a rectangular matrix\n", "- $LDL^T$ - Gaussian elimination, $L$: lower triangular, $D$: diagonal\n", "- $Q\\Lambda Q^T$ - orthogonal $Q$ (eigenvectors), diagonal $\\Lambda$ (eigenvalues)" ] }, { "cell_type": "markdown", "id": "2d05f7ee", "metadata": {}, "source": [ "(minimization vs solution)\n", "\n", "minimize $\\frac{1}{2} x^T M x - x^T b$\n", "\n", "solve $M x = b$\n", "\n", "Note that you can derive this basically by differentiation:\n", "\n", "$$\\nabla_x (\\frac{1}{2} x^T M x - x^T b) = M x - b = 0$$" ] }, { "cell_type": "markdown", "id": "d8632baf", "metadata": {}, "source": [ "# Quadratic Forms" ] }, { "cell_type": "markdown", "id": "0e684ca6", "metadata": {}, "source": [ "(quadratic forms)\n", "\n", "Quadratic forms are \"quadratic functions of vectors\", like this:\n", "\n", "$$ f(x) = u x_1^2 + v x_2 ^ 2 $$\n", "\n", "We write a quadratic as with a matrix, like this:\n", "\n", "$$ f(x) = x^T M x $$\n", "\n", "where\n", "\n", "$$ M = \\left(\\begin{array}{cc}u & 0 \\\\\\ 0 & v \\\\\\ \\end{array}\\right) $$\n", "\n", "Therefore, a matrix $M$ is sometimes used as a linear function, $f(x) = Mx$, and sometimes as a quadratic form $f(x) = x^TMx$." ] }, { "cell_type": "code", "execution_count": 3, "id": "99fd679f", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-3.0, 3.0)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VuVZzhbommKJKdj/iVAHGR5UOuq5TUlKCy+WisLBwv9yUVS3EjlA6RgQ1WZw0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\n6dpVxu/PY8sWP2PH5nPKKfV4/HGVI46I0rixycs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yLUQGbwv7jmfOSDRs6ETTYP9+Nzly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9++NXv/qVrX4LB8XBIcx2DJZlsWHDBjQ0NGDbtm0YOnQoamtrMXDgwJLJUxAExONxW7Zf6D1x\nRBRFU9p92vMBxW6pb57nMWPGDPTt2xczZ8601W/hoHg4hFkh4DgOTU1NaGhowDvvvINBgwahtrYW\nQ4YMydiQ8pnpqRyKa6fNQq/G/mygBS96ia60GuTtgEKjeat43GqRpSAIuPnmm/G9730Ps2fPttVv\n4aA0OIRZgeB5Hm+99RaWLl2KTZs2oX///pgwYQLOPvvsjIhLTS3q8XiQSqVsN1cRKI+KV61uXMhc\nRcAcL16joFfq22yP22xkOXPmTHTu3Blz58611W/hoHRUFGE2NDRgzpw52LFjB/71r3/hhz/8oerr\nevXqherqarmmsmXLFpNXah54nsfmzZvR0NCAjRs3ol+/fqitrcW5556bIYQhGwjLsgBg2XqTGqwy\ncaSYodgk9a0cF2UHELLUc36oUnFrRMtUNrKcPXs2QqEQ7rnnHlv9Fg70QUUR5o4dO+ByuTB9+nT8\n6U9/0iTM448/Hm+//XbFNfcKgoCtW7eisbERTU1N6NOnDyZMmIDhw4fLDkTPPPMMPB5PyTM9zYJV\nW17UUt/KuYp2HeUGGEOWSpDonYzI00Nxq3W4EgQBc+fOhSAIeOCBByxzHzkwF/YZG68D+vbtm/dr\nK+gcIcPlcmHQoEEYNGgQBEHABx98gIaGBsyaNQuHDh3C7NmzwXGcTI7KgcSpVCqvmZ5mQTlxxEqE\nQyzmfD5fm2tIBC8sy8Ln89muTmwGWQJHnJr8fn/GASSRSBSdAVEjS1EUcc899yCVSuHPf/6zQ5YV\nDOeXVwHDMLjwwgsxYMAA2dS40uByuXD66acjHA6D4zgsWLAAzc3NGDduHK688kosW7YMsVisjT1a\nMBhsY4/G87zpBxA7TRxRXkOfz4dUKiWTAD1ey+ogPsJGk6USenjcqlkMiqKIP/zhDzh06JBDlg7a\nX4Q5YsQI7Nu3r83f33PPPRg3blxe77Fx40Yce+yx+PrrrzFixAj07dsXw4YN03uplscTTzyBxYsX\nY+PGjejWrRvGjRuHOXPmYOfOnWhsbMQll1yCzp07mWodlwAAGWRJREFUo7a2FiNHjkR1dbWcWgwE\nAnK9iSZWM5r87SySEQQByWRSNlMo1zUsBnq36xQL+jrRilv6GioVt1pk+dBDD2Hv3r14/PHHHbJ0\nUFk1TILhw4dnrWHSmDt3LqqqqnDLLbeYsDJrIRaLIZ1Oo0OHDqr/XRRFfPbZZ1i6dClWr16Nmpoa\n1NbWYvTo0Rn/RtnkDyCjx07Pjd/OIplsZuTlUovmC6uQZTZoXUOSEqcHhYuiiEcffRQ7duzAk08+\naUh5Yd26dbIH7DXXXINZs2a1ec2MGTOwdu1ahEIhLFy4EP3799d9HQ7yR8UembTOCfF4HNFoFIBE\nGC+//DL69etn5tIsg3A4rEmWgHSSP/HEEzFr1iw0NTXhkUceweHDh3H55ZfjJz/5Cf72t7/h22+/\nBXBkIHZVVZXcdK/3WDI7i2RyTe5gGEb+Xlqj3coxnQawB1kCmdeQTPghwiFRFPHpp59i2bJliEaj\nmD9/PrZt24YnnnjCELLkeR4///nPsW7dOmzfvh2LFi3Cxx9/nPGaNWvW4NNPP8WuXbvw+OOP4/rr\nr9d9HQ4KQ0UR5vLly9GzZ09s2rQJY8aMwahRowAA//3vfzFmzBgAwL59+zBs2DCcccYZGDx4MMaO\nHYuLLrqonMu2BRiGQa9evXDLLbdgw4YNePzxx5FOp3HVVVdh4sSJeOqpp3DgwAEAxsz0JPUqn89n\nO7LkOE6e3JGPpy3DMG1Gu7lcLqRSKUSjUcTjcdPI0y5kqQaO48DzPCKRCCKRCJqbm/HEE0/gpJNO\nwkMPPYTzzz8fhw8fNuSzt2zZghNPPBG9evWC1+tFXV0dVq5cmfGaVatW4corrwQADB48GM3Nzdi/\nf78h63GQH+x1h5eIiRMnYuLEiW3+vlu3bli9ejUA4IQTTsB7771n9tLaFRiGQY8ePTBjxgzcdNNN\n2L9/P5YvX47p06eD4ziMGTMGtbW16Nq1K9xut7z5k7Qt8UoltaZcPXZ2nasIlN7YD0C+hn6/X46Y\nUqkU4vF4UR7B+YL8VnYb5wYcMbGg07ADBw5EXV0dOnfujHHjxmHVqlX41a9+hTPPPBPLly9HTU2N\nbp+/d+9e9OzZU/5zjx49sHnz5pyv2bNnD4455hjd1uGgMFQUYTowHwzDoGvXrrj++utx3XXX4Ztv\nvsGKFSswY8YMxONxjBo1CuPHj0fPnj0zyJPe+BOJhGaDuh6EUy4YEZ3RrRa0UYLyGpYqYLEzWbIs\n24YsRVHEokWL8NJLL2HJkiXw+XyYMmUK4vE4mpqaUF1dresaCnF5KubfOTAGDmE6MA0Mw+Doo4/G\ntGnTMG3aNBw8eBCrVq3CzJkz0dzcjJEjR6K2tha9evVqs/GrkScxJXDIUh0ulyuj15OIrkrpUwTM\n8eM1CvTa6e+9ZMkSrFy5Eg0NDRlZilAoJJdu9ET37t3x5Zdfyn/+8ssv0aNHj6yv2bNnD7p37677\nWhzkj4qqYVoFDQ0NOPXUU+F2u/HOO+9ovm7dunXo27cvTjrpJNx///0mrtAcdOzYEVOmTMGqVavw\nwgsv4LjjjsMdd9yBiy66CA888AA++eQTiKIok2dVVRWqqqrgdruRTCbluYqAvYwmyEzIcDhsWt2P\n9CmGQiHVPsV8ez3bC1nSa1+2bBmWLFmCJUuWIBAImLKWAQMGYNeuXdi9ezdYlsXixYsxfvz4jNeM\nHz8ezzzzDABg06ZN6NChg5OOLTMqsq2k3MjHoo/nefTp0wevvPIKunfvjoEDB2LRokU45ZRTyrBi\ncxGNRrFmzRosXboUe/bswfnnn4+JEyeib9++YBgGCxcuxBlnnIFTTz01I3Iysl6nF6xGOKSlgqRu\ns/V6Wm3thUBr7atWrcLTTz+NFStWIBQKmbqmtWvXym0lV199NW699VbMnz8fADB9+nQAkJW04XAY\nCxYsyKsVzoFxcAizjMjWD/p///d/mDt3LtatWwcAuO+++wAA//M//2PqGsuNeDyOdevWobGxEZ9/\n/jm6deuGrVu3YtWqVTj55JPl1+kxENtolGNaSiHINlaL53lLrz0btMhy7dq1mDdvHlasWIGqqqoy\nrtCBXeCkZC0KNYXc3r17y7ii8iAUCuGSSy7Bc889h2HDhuHtt9/G+eefj2uvvRa//e1v8c4770AQ\nBLleR6zRvF4v0uk0WlpaEIvFwLIsBEEo2/egVZlWJRzSpxgMBhGJROSIKx6PI5lMwuPxQBRFW6W/\n0+m0KlmuX78ef/nLX7Bs2TKHLB3kDUf0YxBKteizSlRkBQiCgBtuuAHvvPMO3nnnHXTq1Aksy2LD\nhg1YuHAh3n//fQwdOhQTJkzAwIEDDRO7FAN6+gWtyrQ6SK8nqWuGQiHwPC+3/BgxVktvaCl5X3vt\nNTz44INYuXKl7upXB+0bDmEahPXr15f07/NR0VUKXC4XBgwYgAceeACRSAQA4PP5MHLkSIwcORIc\nx6GpqQmLFy/GrFmzMGjQINTW1mLIkCFwu92qU0GSyaTh5GnV0WL5QplC9nq9BbX8lBO0Cpkmyzff\nfBP3338/VqxYkdXFyoEDNTg1zDJi+PDh+OMf/4gzzzyzzX/jOA59+vTBq6++im7dumHQoEEVI/op\nBTzPY+PGjWhsbMSmTZvQv39/TJgwAWeffXaGIpUmTyNmetJDiEOhkG3JMldUrDWTspy1Y62WnY0b\nN2Lu3LlYsWIFOnfuXJa1ObA3HMIsA5YvX44ZM2bgm2++QU1NDfr374+1a9fiv//9L6ZNmya7Dqmp\n6BzkD57nsXnzZjQ2NmLjxo34wQ9+gNraWpx77rkZvXZq5EmbwxcKeg6n1UeLqSFfslRCS3ilh1FC\nvtCaxbl582bMnj0bK1asQJcuXUxZi4P2B4cwHVQEBEHA1q1b0djYiKamJvTp0we1tbU4//zz4ff7\n5ddpKUXzJc9KJUsl6NpxOp02pXasRZZbt27FrFmzsHz5cnTt2tWQz3ZQGXAI00HFQRAEfPDBB2ho\naMCGDRvQq1cvTJgwARdeeCGCwaD8umzkqTaPkgytBiBPZLETUqkUWJbVvd6qlf4mMyn1gBZZvvfe\ne7j55puxbNkydOvWTZfPclC5cAjTQUVDFEV8+OGHaGxsxPr169G9e3fU1tbi4osvRjgcznidVo8i\n2fTtTJZqA5SNQKGHkHygRZbbtm3DjBkz0NjYmNGi5cBBsXAIs4Jx8OBBXHbZZfj3v/+NXr16YcmS\nJarKwV69eqG6ulpOq23ZsqUMqzUeoihi586daGxsxEsvvYTOnTujtrYWI0eOzGg/EEVRFrvQY7Rc\nLpctBT5mkaUSauRZ6GBxLfP97du344YbbsCSJUvQq1cvA7+Fg0qCQ5gVjJkzZ6Jz586YOXMm7r//\nfhw6dEh2FKJx/PHH4+2330bHjh3LsMryQBRFfPbZZ1i6dClWr16Nmpoa1NbWYvTo0RmHCjIvkfa0\npWueVo80y0WWSqgdQnJdRy2y3LFjB6677josWrQIvXv3NvNrOGjncAizgtG3b180NTXhmGOOwb59\n+3Deeedhx44dbV53/PHHY+vWrejUqVMZVll+iKKIf//731i6dClefPFFBAIBjB8/HkOHDsXkyZNx\n0003ob6+HgzDZERMViZP2lCh3GSpBnIdOY6DIAhtej3JDFQlWe7atQvTpk3Ds88+m2GdqDec7Exl\nwiHMCsZRRx2FQ4cOAZA20I4dO8p/pnHCCSegpqYGbrcb06dPx7Rp08xeqmUgiiL27t2LBQsW4E9/\n+hMGDx6MMWPGYPz48Tj66KMzSJHneVnsorbpl/M7WJkslaAjT57n4fF4wHEcgsFgRnvQ559/jqlT\np+Jvf/ub4f3KTnamMuE4/bRzaFn03X333Rl/ZhhGcxPfuHEjjj32WHz99dcYMWIE+vbti2HDhhmy\nXquDYRgIgoBnnnkGv/71rzFt2jQsW7YM06dPB8dxGDNmDGpra9G1a1d5IHa2mZ5mk6fdyBLIHIqd\nTqcRj8fhcrn+v717j2ny+uM4/i4tV61OlOisZLpoJDgmEBXnJsoiknJpURNAYeIFwzTe5hLJMjc1\nWzaXqZn56dwlmYsmOkMBLUthqAvEaZAlGl1mnLc4QQE3EZUiBWp/fxgaEcFujD7Ffl+JicDh6fev\n58M5z3m+hwcPHvDll18SHBxMVFQUq1at4rvvvnNLcw+z2UxFRQUA2dnZzJw586mBCf3r6DnRM5lh\nerGwsDDKy8sZMWIEtbW1xMXFPXVJ9nGbN29m4MCBvPvuu26q0vMkJycza9Ys1q5d6/yew+Hg9u3b\nHDp0iKKiIpqbm9Hr9RgMBkJDQzuF4pMzpo5l274Oz/7eqq9jGTYgIMDZ6tBkMrF//34qKiqIjo4m\nOzvb+QdLX5LVGe8kgenF1q9fz9ChQ8nLy2PLli00NjZ2+Su5ubkZu92OVqvFarUye/ZsNm7cyOzZ\nsxWqWnktLS3PPGi4oaEBs9lMYWEhjY2NJCQkYDQaGTNmTJfwdMexZM9bWHaora0lMzOTrVu3UldX\nR2FhIRaLhezsbHbs2NGrz+xpdSY7O7tTQAYHB9PQ0NBlbG1tbafVmf/9739euzrzPJDA9GINDQ2k\npaVx/fr1ThsXHm/Rd/XqVebOnQs82pWYmZkpLfr+obt37/Ljjz9SUFDArVu3iI+Px2g0Mm7cOLeE\n5+N9bftj96HuwrK+vp4FCxbwxRdfEBMT4/y+zWajrq6Ol156qc9qktUZ7ySBKYQbNTU1YbFYKCgo\noLq6mjfffJM5c+YQFhbWKcg6Wsv1ti9rfw/Lhw8f0tTU1CUs//rrLzIyMti2bRvTpk1ze12yOuOd\nJDCFUEhzczOlpaWYTCauXr1KXFwcRqORV155pVMo/tu+rM9LWHZs+Olw+/Zt0tPT2bJlC7GxsYrU\nJqsz3kkCUwgPYLPZKCsro6CggPPnzxMbG0tqaiqRkZFdwrMjOHsKz+c1LO/cuUN6ejofffQRcXFx\nClYovJEEphAeprW1lZ9//hmTycTZs2eZNm0aqampTJ48udvwfLKpuc1m67cnpjx8+BCr1Yqfn1+n\nsLx79y7p6el88MEHxMfHK1ih8FYSmEIxpaWlzvM+c3JyyMvL6zJm9erVlJSUEBQUxPfff09UVJQC\nlSqnvb2diooK8vPzOX36NFOmTMFoNDJ16tROJ308OfME8Pf3/9dneiqlu7C8d+8eGRkZ5OXlodfr\nFaxQeDMJTKEIu93O+PHjOXr0KDqdjsmTJ3PgwIFOL51bLBZ27tyJxWLh1KlTrFmzhsrKSgWrVpbd\nbufEiROYTCYqKyuJiooiNTWV119/3dn9Zt++fcybN4/AwEBngP7TMz2V0hGWvr6+nV7baWpqYv78\n+axdu5aUlBQFKxTeTjr9CEVUVVUxduxY50kSGRkZHD58uFNgms1msrOzAYiJiaGxsZH6+nqGDx+u\nRMmKU6vVxMbGEhsbi91u59SpU5hMJjZu3Eh4eDi3bt2iqamJjIwMZ0AGBAQ4+7Jardb/5DitvtBd\nWFqtVrKysli5cqWEpVBc/3p7WTw3bty40emMwlGjRnHjxo1njqmpqXFbjZ5MrVYzbdo0tm/fzi+/\n/MLNmze5fPkydrudd955h5KSEmw2m/PIrMDAQLRaLYGBgTgcDqxWK01NTc5mBkouNHUXlg8ePCAr\nK4ucnBzmzJmjWH1CdJAZplCEqzObJ2/knjIj8hRtbW1kZWWhVqs5d+4cfn5+nDt3jvz8fLZu3cro\n0aNJTU1l1qxZBAYGotFo0Gg0BAQEOFv0PXjwQLGTVR4Py8efWba0tLBw4UIWLlxIWlqaW2oR4lkk\nMIUidDod1dXVzq+rq6sZNWpUj2NqamrQ6XRuq7E/aGhoYOjQoezdu9c5O4uMjCQyMhKHw8Hvv/+O\nyWRix44d6HQ6jEYjCQkJDBgw4KnN4d0Znh0zXY1Gg7+/v/NzbDYbixYtIi0tjQULFvTJZwvxb8im\nH6GI9vZ2xo8fz7Fjxxg5ciRTpkzpcdNPZWUla9eu9epNP73hcDj4448/MJlM/PTTTwwbNgyDwYBe\nr2fQoEGdxrrjTM+OsFSr1QQEBDiv29raypIlS0hMTGTp0qWyoiA8igSmUExJSYnztZKlS5fy3nvv\n8fXXXwOQm5sLwMqVKyktLWXAgAHs2bOH6OhoJUt+LjgcDq5cuUJBQQEWi4VBgwZhNBpJTEzscghy\nX5zp2V1YtrW1sWzZMuLi4nj77bclLIXHkcAUwos5HA6uX79OQUEBxcXFBAQEYDAYSE5OJjg4uNtj\nyf5teHYXlu3t7eTm5vLaa6+xatUqCUvhkSQwhRDAozC7ceMGhYWFFBcXo1KpSElJISUlhZCQkF6f\n6dkRlj4+PgQGBjrH2e12VqxYQWRkJOvWrZOwFB5LXisRQgCPdiCPGjWK1atXU1ZWxr59+9BoNOTm\n5mIwGPjqq6+ora3F4XDg4+ODv78/AwcORKvVolaraW1t5d69e1itVlpbWzvtcO4pLNesWcOECRP6\nPCzz8/OZMGECarWa06dPdzuutLSUsLAwxo0bx2effdZn9Yj+R2aYQvDsNn3l5eUYjUZefvllAObN\nm8eGDRuUKNXtHA4Ht2/f5tChQxQVFWG1WklMTMRgMBAaGvrMMz01Gg1tbW1dwvLhw4esW7eO0NBQ\nNmzY0OczywsXLuDj40Nubi7btm176vNwVzpQCe8lr5UIr2e321m5cmWnm6TBYOhyk5wxYwZms1mh\nKpWjUqkYNmwYOTk55OTkcOfOHQ4fPkxeXh537twhISEBo9HImDFj8PHxwc/PDz8/PxwOB62trdhs\nNhwOByqVirNnz6LT6Rg6dCjr169nxIgRbglLeHTo87O40oFKeC9ZkhVe7/GbpK+vr/Mm+SRZjHlk\nyJAhLFq0iMOHD1NcXMzo0aP58MMPSUhI4PPPP+fixYvOsHz//fe5d+8eWq0WX19fCgsLiYiI4I03\n3uDKlSssX77co55ZutKBSngvmWEKr/e0m+SpU6c6jVGpVJw8eZKJEyei0+nYunUr4eHh7i7V4wwe\nPJjMzEwyMzNpamrCYrHw6aef8ueff6JSqdBqtYSEhDhnnps2bQIeNaHw8fEhPDycV199laysLJYt\nW9breuLj46mrq+vy/U8++cSlXrSeFN7C80hgCq/nyk0yOjqa6upqgoKCKCkpITU1lYsXL7qhuv5j\n4MCBpKWlMXfuXNLS0qipqSEkJAS9Xs/MmTNJTU3FbDZjs9nYv38/Pj4+tLS0cPToUa5du/af1HDk\nyJFe/b4rHaiE95LAFF7PlZukVqt1/l+v17NixQoaGhoIDg52W539QXt7O2+99RYtLS0cP34cf39/\nbDYbZWVlbNmyhfv373PkyBHnQdgBAQEkJye7vc7ultcnTZrEpUuXuHbtGiNHjuTgwYMcOHDAzdUJ\nTyXPMIXXe/wm2draysGDBzEYDJ3G1NfXO2+yVVVVOBwOCctuREdHU1hY6Gym7u/vT0pKCocOHeLY\nsWPOsHS3oqIiQkNDqaysJCkpyXkQ9c2bN0lKSgJAo9Gwc+dOEhISCA8PJz09XTb8CCd5rUQInt2m\nb9euXezevRuNRkNQUBDbt29n6tSpClcthHAnCUwhhBDCBbIkK4QQQrhAAlMIIYRwgQSmEEII4QIJ\nTCE8zJIlSxg+fDgRERHdjlm9ejXjxo1j4sSJnDlzxo3VCeG9JDCF8DCLFy+mtLS0259bLBYuX77M\npUuX+Oabb1i+fLkbqxPCe0lgCuFhpk+fzpAhQ7r9udlsJjs7G4CYmBgaGxupr693V3lCeC0JTCH6\nmaf1vq2pqVGwIiG8gwSmEP3Qk69PS9NwIfqeBKYQ/cyTvW9ramrQ6XQKViSEd5DAFKKfMRgM7N27\nF4DKykpeeOEFhg8frnBVQjz/5LQSITzM/Pnzqaio4O+//yY0NJTNmzfT1tYGPOprm5iYiMViYezY\nsQwYMIA9e/YoXLEQ3kF6yQohPFJ+fj6bNm3iwoUL/Prrr0RHRz913OjRoxk0aBBqtRpfX1+qqqrc\nXKnwFjLDFEJ4pIiICIqKisjNze1xnEqlory8XI5bE31OAlMI4ZHCwsJcHisLZcIdZNOPEKJfU6lU\nzJo1i0mTJvHtt98qXY54jklgCiF69KzetuXl5QwePJioqCiioqL4+OOPXb52fHw8ERERXf4VFxe7\nfI0TJ05w5swZSkpK2LVrF8ePH3f5d4X4J2RJVgjRo8WLF7Nq1SoWLlzY7ZgZM2ZgNpv/8bWPHDnS\nm9IAePHFFwEICQlhzpw5VFVVMX369F5fV4gnyQxTCNGjZ/W2hb5/htjd9Zubm7l//z4AVquVsrKy\nHk95EaI3JDCFEL2iUqk4efIkEydOJDExkfPnz/8n1y0qKiI0NJTKykqSkpLQ6/UA3Lx5k6SkJADq\n6uqYPn06kZGRxMTEkJyczOzZs/+TzxfiSfIephDima5du0ZKSgq//fZbl5/dv38ftVpNUFAQJSUl\nrFmzhosXLypQpRB9S2aYQohe0Wq1BAUFAaDX62lra6OhoUHhqoT470lgCiF6pb6+3vmMsaqqCofD\nIU0ExHNJdskKIXr0rN62JpOJ3bt3o9FoCAoK4ocfflC4YiH6hjzDFEIIIVwgS7JCCCGECyQwhRBC\nCBdIYAohhBAukMAUQgghXCCBKYQQQrhAAlMIIYRwgQSmEEII4YL/Aw+NHlArY+qIAAAAAElFTkSu\nQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# positive definite\n", "from mpl_toolkits.mplot3d import Axes3D\n", "subplots(1,1,figsize=(8,8))\n", "x,y = meshgrid(linspace(-1.2,1.2,20),linspace(-1.2,1.2,20))\n", "\n", "z = x**2+y**2\n", "\n", "ax = gcf().add_subplot(111,projection='3d')\n", "ax.plot_wireframe(x,y,z)\n", "ax.set_zlim3d(-3.0,3.0)" ] }, { "cell_type": "code", "execution_count": 4, "id": "1a6c167a", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-3.0, 3.0)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JEi6X64glcYrr+FUeUUBxxLa862yPNZay3n9xandPdGJvfvuYJUpRFMX/IBEV2b1VkZTX\nuY89H7YW+Hw+li1bxhNPPIEkSaxfv55nn32W1atXc8oppxx1e4qi8MQTT3DhhRfi9/tp2rQpHTp0\noH79+uUyfkgy0bXFw77YY0tTirNKg82xotTibMcWrUQCF+/XcLTfL+3+Y7HLq4LBIIIgFGksDhZH\nuyZK8kp8vCfuKkrcK/Jha+9LFEVq166NIAjccMMNNG7cuMjbqFGjBjVq1AAgNTWV+vXr8/vvvzui\nayMI1hLbdlRrmiZer7fYYhu/zbJIMdilSsUR21jKusHCFluwLCgVRSmXm6G8o/TC9nkiUtgrcXyu\nOHbiDgqKh1POVnTiBb60zRF79uxh27ZtNG/evCyGVyhJJbpgdSEFAoFo5GDXapaUsqizNU0zOuFS\nkmiytDdZ7HewxdZ+IBVFbI+HcJaWZBpvIlMf+7qxH4xHm7UvC8vMk7U0LZbSTKT5/X6uvvpqnnzy\nyXIv3Uw60VUUhYyMDMLhcIGVHEpKWdTZmqaJ2+1OuNpveY4hfjw5OTnFXqPNxjDANMEJsiqG2BSF\noijRZoL4FEV5rCJxshAv8H6/n7S0tGJvR1VV+vTpw6BBg+jVq1dZDjEhSSe6sa9gZRHtlEWdrV0N\nUNrOmpJgpzR0Xcfn8x1VbE0Tvv9eYNMmgfffF9m7VyA3F/bvr0JWloAgQHo6pKWBKJr8618mbdua\nXHCBQePGJonmJATB8q9QVRUgOsGRTJHoiURxa4tPtI6745HTjf17ccseTdNk2LBhnHfeedxyyy1l\nPcSEJJ3o2pR1jW1RPmN77MZPSoXD4VLtvyQXqS22mqbhdrvRdT2hw5KmwXvvibz4osimTSKZmdCq\nlUF6uiXATz+t0aRJDnl5bnr39jF0qM7AgTpvvSXywAMyVasavP++zCefCJx+usmwYQZXXaVzxhlE\nS/Y0TcPlckWL3IHo5F1RnakcCqektayxxz02h1yeHK/0Qkm1YOPGjcyfP59GjRpFJ+AeeughOnfu\nXJbDK0DSia59Qisq0o0VW6DAUj1F3UZpxxBLIk9b+zU0lu+/F5g1S2TRIok6dUwuvtjg00/huedU\nrrjC2leHDiJjx8rMni3Rpo3JunURunZV0HWYNEnnvPNUhg5VeOUVlbQ06NFDYcUKkccek0hPNxg3\nLkjfvgI+n7fAjZ2Xl4fL5UIUxUI7jU52y8aiUhqROlotq33c7ajY7j5MlCtO1mMff+xK8l1at25d\noY1JkISiC/mmJ2VxsIpSbgVHrwCoCNEtiqctwK5d8OCDMu+8I1Ktmsny5SoNG1r/1qOHwYABCjNm\naHTvbtCrl0FKisqQIenMmhWkUydYu1blyisV/H546CGdhQtVrr1W4bnnNNauDdOtm4vbbsth0yYP\nd96ZwZNPGtx+e4R+/XRiLYhjc5Dxx9UWg5L6tTocHbvKJxa/3x99EyrP1TyOV3rBTrUkA8kxygSU\nZaQbix3Z5uTkEAwG8Xq9pKenHzVXWlZjSbQNe6XfnJwcBEEgIyMj4YTd77+L3HijzKWXuqhb1+Sb\nbyI0bmwyYYJMIGB9pnVrk7feUhkzRmbxYuvUd+xoMnt2LsOGeVmxQqR6dXjvPZWNG0VuvlmmVSuT\nN98Mc+ONEp99FuKdd3KYOTONVq0k7rxTJxiEuXMV6tTxsWRJ0ZZ8t5ta7K5Bn8+Hx+NBluUCD7tA\nIEBeXh7hcDhqVuPkikuG/VCTZTk66evz+fD5fLjd7mguPhKJkJeXRyAQiJogJcOxz8nJOa6GUcXB\nEd2/t1MSsS2rsSTavt3SnJ2dHRXbRG3NhgEzZ8pcdllVPvlE4IsvItx1l06VKjB3rkbt2ibduinY\nnb7NmpmsXKkycaLMrFnWtlq10lmyJI/Ro2Vee02kcmVYuVLlu+8ErrtOoE6dw7zxRg5TpqSzebOP\ntWtVZs8WUVUYOzbEb7+JXHaZxujRXvr08fL778W7rGwhVhTlCEGwj7+u64TDYQKBQHTFD7sxxk5b\nlCUnS0fdsYg/9vZDMPbNLvbY28e/sGN/vCLdnJwc0tPTK2S/pUUwT+THVyHYT96srCwqVapUqpNs\n50ftw1CSRoJQKBStHigpWVlZUYekWE9br9db6GvT7t1www0KoRBMmXKQadMq43LBvHkadvmyYcDt\nt0ts3CiyfLlKtWrWz3/8UeDKKxVuukln2LAcJEli2zYvffootGplUL26xt69Jp9+6sIwBM4+20SW\n4auvBM4/36R7d505cyQuvzxM48bw4INuevdWmTfPhSCY9O+v8uijkTIvQbNbPyORCLIsF+hOLMuu\nL7sioyTL2hcHexHP8n419vv9xW6Pjyd+4i722MdO2ImiiNvtLnfxDQaD0XK7HTt2MH/+fJ577rly\n3WdZkNSRbmkiTDuytet9ixPZJhpLWdTZhkIhsrOzMU2T9PR0fD5fwpvRNGHGDJFWrVx07WrwwQcq\nDRtqLFmioijQu7cSTSmIIkydqtO5s0GHDgq//279vG5dk/fei/DkkyIdO6bTpo2P7t0V/vUvnY8+\nEti1C4YMgTfe0Gjb1iAvD265ReOJJzR+/RUWLpRIT4fZsz385z9uLrlE59VXFUaOjCCKJi+/7KJV\nqxSys0t1WI4gtnMrNipOSUlJGJnl5eUdEZk5lIyjvZG43e6o65eu69GouDxTFPGRbjLYOkKSim5p\nKhji0wgulyuaYzwercSxXUm2p63P5yu03jAchlGjZJ58Usblgq5dDeyPulzwyisap51m0r27EhU8\nQYDJk3UGDTJo187Fli0wdapEt24KHg/89pvAqafq7NjxF++8c4jt24MEAgorVihcfLHJa69p9O1r\ncNddCs2bm2zfrnLqqVCzpsmXX2Zx9tkGn30mYRjwxBMuLrxQIy3NZPdukUaNUtm+vfwvMztfGZ8r\njs1XqqqalPnK0lLe3y02T2//Nz5FYS8EW9iDsLRjTJb10SBJRdemOGJXWM62LGwWSyr+oVCIw4cP\no2kaoiji9XqPWtz9++/QoYNCbi58/nmE++/X6NRJYceO/KhfluGFFzQuuMCkc2eFAwfyf79/f53q\n1U0uvdTF5s0CL76osX17kI0bD/5dJF4Z00ynZk2Z1atVgkHo1k0hK8sqIfvPf6z9bdsmsHSplaoY\nODCdWbPy6NFDp0YNk9tvj7Bxo4tQSMAwTETRpFcvL2+8UfGFMoVFZvH5ykRicDIKcUXW6cZO3Nlp\nskQTd6V5EDqR7nGgKGJ3rAmyskgNFFf87TSCqqqkpaWRlpZ2zBvis88EWre20gkLFmikpsKQIQZT\np2p066bwxReu6BhEEaZN0+jY0UopfPUVTJggcdFFLtq0MXjhBY1Nm0T27QsSCPhJTxdZsCCPevUE\nrrjCxc8/Q0oKvPqqRtOmBm3bKvz0EwwaZDB/vsqQIQqLF4s8/7xG9+4RunRJZehQlaFDVebOVXj2\n2WwqVTKoUcPk0CEBTYMbb/QwZ075L7R5LOLFwC6/ixcDOwKryFfkk4FjfZ/CHoSFpYfs458oKo4X\n3WSJdKXJkydPPt6DKC52Qt9ezDFRdGg/RQOBAJqm4fV6EzY2mKa1ikJpjHOKsg1b/P1+P4ZhkJKS\nUmACxZ4YSvRd1q4VuPpqherVTWbM0IhtPDvvPJP69U2GDk2hSRODM8+0Uy/Qtq3J+++L3H67zOmn\nw+uvq1x5pcbZZwdo0iTITTdlUKWKh8aNdUQRunWTUFWBUaMU2rQxqFkT2rc3EUUYMUKhRQuDVq1M\nOnQwGDVK4bvv4KqrwlSpYjBmjJf+/SN07mxw220+7rsvxDffyJx5psHevSK6DuvWyXg8Js2bly6v\naucNy9IMPrZO2F7fy/axsM+RXVdsC4DdgBAb3RUXe92+8hRe+yHicrnKbR82qqoesT7asYiNjO3j\nrygKiqJEGzjscx57/O3j/tlnn/Htt99y7rnncvbZZ5fjtysbkrJ6wS7utt3GYsWuOE0NYJVmZWdn\nU6lSpVKNJzc3N+GTNnY8giBExxNPbm4ubrf7iBtj2TKRm26SWbhQZeFCiR07rFf7ypUL/v7KlXmM\nHJnJiy9qdOlisHcvjBpl5XW7ddN57jmZl1/OpVmzPNxuNx6Phz17RHr2VOjSReU//wmQlmZVXyxd\nau3zhResSbRPPxWYPVvi7bdFUlMhEIDMTOu/smxStapJTo7AwYMCPh+cfbbGd9/JXHmlGv353r0C\nBw6IiCLcfHOEyZNLXtlgR0IpKSkl20AROFr1Qvwsvi2+8aY0Ren4KouqgmNhr4JRmuqaolIR1Ri2\nANulg1dddRX/+9//SElJoVmzZjRq1IjJkycfM5C6/vrrWbFiBaeccgo7d+4st/HGk5TphUQTaSWt\ns42t0y3NeOJ/P9F40tLSihWdLVpkNSgsXarSurXJM89otGpl0LGjwh9/FPxsq1Yqr70WYuRImTFj\nJFq2dNG2rcEHH4QZN87P009nMXRoKqtWVY7W+551Fnz4ocqWLRLDhqXy93OKTp0MRo/WGTBA5tRT\nXTzwgEzduiZPPKGRng7XX6+za1eEffsi9OmjIoqwalWIbdv81K5t4PGYDBkSYvVqhfffl9m/X8Qw\nBM47z+pamz7dxbBhHpLvcW9RlNpW2xvjRMgVn2wpjNgKlvT0dNatW0efPn2YP38+N9xwAxkZGQl9\nSOIZOnQoq1evroARFyQpRddGEIRomqEkTQ32NspiHLHir6oqubm5JRJ/m5dfFpkwQWblSpUmTcy/\nP2O15l51lUG7dgp79xb8/fPP17noIoM5cyQGD9YYM8ZPIJCNYRh06+bh3Xc17rtP4aGHpKjgVakC\nb70VQFFMLrtMYfRoiX/9y8Wnn4o8+qhGgwYmp55qctttOiNGGGzeHOHXXwU6dVI4eBCmTQtyyy0h\nunTxsn27xIcf5lGnjs6HHyqsXh2ge3cNUTQ55RSTr7+WqFTJJCXF5PXXZdq181IG7pzlQnGFqigT\nR4ZhHJGrBAqkKZKdihL4+GOVm5vL+eefT8+ePZk4cWKRxtCmTZtSveGWlKQV3di8bknENpay6m6z\nxTYQCOB2u4st/vYY3nxT5O67ZWQZUlLMuM9ZlQQjRxp06ODixx+tbe/fL9KlixevFzZsyGXlSoE7\n7nCTkpJGamoqkiTRoIHJhx9GWL5cZORIGdsj5+BBEZfL5McfBd54Q2LGDJXly1VGjbJqgDMyoHVr\nhe++E8jMhNde0+jUyaB1axebNklce22EpUtDTJ7s4f773Tz2mJ+RI8P07JlC794aY8ao/PWXwPjx\nYbKzBSIRAVmGrVslOnb0EufVc1IRGxXHlrJ5vd6oP0J823MoFErKUraKHmvsfeWUjJUzhmGQk5MT\nnUgrqdjalFZ0Y5frtpd8L2lHzkcfCYwbJ7NqlcqECRodOrj45psjtzN2rM6ECRodOyosWiTSqVMm\nnTtHeOaZA5x1Vpj33w+za5ebAQM8+P35v3fqqbBmjcqhQ9Cli8Ktt0q0bu2jRg2D3bsjvPSSxpgx\nCi+9JGKa4PHAc89p3HKLTrt2Cm+9ZeVl77xT54UXVP79bx8zZrhp2FDngw/8fPedSM+eGdSvr/HM\nMyHuuMPN3r0Cc+cGWbDAxdChERo2NDjlFGsybetWiRYtUsjKKtmxT0Zio2IgYZNBUWfwi0JFpxcq\nsjTNprST4RVJUk6k2aU8dt60JG7xsWRnZ0f9cYtDrKet3UVW3G3Y5OXlsXOnzNVXpzJ/vspll1mn\n5dVXRe66S+att1QaNz7yVE2cKDJ9usydd+YyblywgM9vJAJjxsjs3Cnw5ptWQ4PNsmUi//63FU2/\n+mqQ5s3zosfxhx8E+vWTadrU5KmnNOy5pM8/F7j2WoU+fXTuv18nLw8WLdK4/34PhiGQkmLw558S\nkgSRCGRkWOPNzrZujnr1DA4cEMjIMKlXT2fzZpmsLIFwGNLSTDZsyOPMM499OVbERJodaZbnjWya\n1jJPRzNqsecb7BREfOttUSwyK6qluSjfp6yIPz9dunTh448/Lrbg79mzh+7duzsTacdCFMWoX2tZ\nmt4UFV3X8fv95ObmoigKmZmZpfaE3bNHol8/H089pUUFF+Daaw2efFKjRw+FTZsKbn/JEpP58yUe\nfDCXF1+UZWx3AAAgAElEQVRMZdmytAKVGi6X1SjRs6fBZZe5+OorgcOHYcQImTvvlFm2TOWJJzSu\nu87Dm2/mV02cfbbJxx+rhMNw+eUKe/ZYP2/a1GTFigjvvCNy6qku6tRxsWSJzL//HaRVKx1VFZk/\nP8Du3X/y1luHSU016do1xNdf/8Ftt/n55ReBNm1UFMXknXcUwmErXVK9ukFurkDjxj7eey8pL8kS\nUZQI1I6Ki2oGlCgqdgzMTyyS9govq8YGe1tF2Y4ttjk5lkFMZmYmHo+n1GOxyrpSqVtXp2fPI2tY\ne/Y0mD1bpW9fhXXrrJnxl1+OMH68wptvBrj1VhdvvZXDlCmeApNk1nezUgH336/Rrp3C+ee7SEmB\nzZsjtG5tMnCgwfLlIf77Xx/jx0v8veoOPp/lUjZ4sEGbNi6mTxcZNkymVSsXjRrpXHllEK/XZMgQ\nlYkTIyxapPLCC0FuvTWFe+5Jp3Fjg02b8gCFLl2q0a6dyfLlOXz9tUSdOhozZ2Yhyyann65z8KCI\nx2N5Slx9dQr33Xf8myhOdARBSNj2nMgi0xbg8m57rkjxixf4ktRJDxgwgJYtW/L9999Tu3ZtZs+e\nXdbDTEjSii7kVy+UxXaOdsHEetqKopjQ07akomsYMHSoTPv2KppmRaGaduTn2rc3WbgwzHXXydx0\nEzz4oI9339W46CIr2jnvPIM1a/wsW1ZwkswmO9vqVDMMqFHDJPbNvGFDgzVrsti1S6BzZ4V9++zv\nBC1aGNSubTJpksyePSYffXSQZ5/NYuZMneXLVR5/3MuIET6ysuDyy3U2bgzw558i7dtnsHu3yIwZ\nIaZMiTB4cCorVnhZuzbIWWeJ/Oc/mTz6aJBGjXRq19apX1+Nekg8/ribzp3dqGr52DaerBTW7aUo\nSvRNrDg2jSUdQ0UQK7qRSKREjTILFy7k999/JxwO88svvzB06NCyHmZCklp0yzu9UFRP26Nt41g8\n8IBEbq7AtGlhlizJ4c8/BQYOlIldds0W/fPPP8zw4WHmzUth+HCd+vUL7r96dYO1a61Jsh49LA9d\nVYWbb5Z5/nmJjRsjbNkS4d13Ra65Ro567AJkZpq88YZGu3YGrVq5eO01geuuk+ndW2HIEI0vvzxE\n5coaAwZUYvfuDFwuF02awEcfBahSxeCSSzx8+KFE5cowc2Yu//d/QXr18jJpkguXy2TMmAivvabQ\nsKGPXbsELrxQ5+abffz4o0ybNga7d8v06KGSnm51wG3apHDhhWn89VfwiFZcR4iLR6whTXxUHOuB\nYFdQlLTt+XilF7Kzs5PGdwGSWHTjW3lLu63YbcSKrWmaRxXbwrZRFN5+W2TePIkFC1RcLgGv1+T1\n161mgz59FAIBMzoOgE8/rcTs2R6WLrW60yZOtJy9YvH5YMkSjQYNDNq0UWjXzrJz/OgjlbPOgtNO\ns1aGOOMMk1atFL76Kj81IoowYYJOx446Q4ZYEe+mTVn063eI006TWLwYxo836NbNxdSpEroOXi88\n9FAeM2ZEGD3ay9ixbhYscPP++wqKAjNnuhg2zMunn0pce61K584669dL5OUJjBkTxjRNliyx3M7e\nflshEhGoWdPE4zH55ReJevWqs2VLaoG+fHuZmePddFBajmfTQnE9EMrDGaw0xB677OzspDEwhyQW\nXSi7vG5sV1owGCySp21p+eYbgTFjZBYtUgssbe52wyuvqFStqtG1q8jhw9Y4vv46lZEjXSxerNKh\ng8lHH6ls2SIycKBMMFhQ9CUJxo/XyckR+OorgVGjdGKvSZcLpk3TmTRJp3NnhcWLrff63buhY0eF\nH34QWbUqF0HQ6Ns3nb/+yvy7tVNg4ECDjRsjvPeeSKdOCj//LGAYVuriwgt1FixQmDQplbQ0k5Ur\n8/jjDz/TpoX4/HOJ/fsFHnooxI4dedSqZfLKKy5uu01l6dI8qlQxadNGZ8CACAcPCoC1JLyuQ8+e\nqYwZkxKN1Ow8+tGaDkorDidTF5f9Xf76S2DaNIV77nExcKCHc8/1Ubt2KvXq+WjQwEedOj569fJx\n//0pLFuWwq+/eo9qkZmXl3dEVFzR3wmSq0YXklh0S+OpmwhVVTl8+HCRPG0LG09RxxEIWK//9eub\nXHih3W0mxIhHNk8+mcMFFwj06ZPJ1q0y11yjMHOmxiWXWJ+vXBlWrFDxeKBTJ4W//soXiF9/tSwg\nR4/WeestlZEjFR555Mio+NprDVatUnngARd9+mTQurWLLl3CLF78J82aqbzzjs6AAXD55W5eflmM\nTtCdcQasWqXSubNBixY+GjSoxIQJLtq109i928/LL+ewdq2LKVPc7N8v0K+fxubNAQQBLr7Yx9q1\nEjNmhJg1K8RDD7mYOtXNnDlBOnXSWLpUYcSICL17q2RmmlSqZJfOuTjjDF+MR/DRmw7K6pU52dm8\nWeThh720apXBOef4eOIJN7t2iWzYIHHOOQYvv5xH584a2dkCV12lMXx4hLw8gTvvdHPZZT5at07h\n6add/PGHfEyLTNsEKD4qLq9Ju1jRddILFUhpRNe2WQyFQtHI1u7eKs9x3HGHzCWXGMgyDBkiEw6b\n0Qs2HA7j8/nIyEjjyScNWrY0aN9eYdw4y8gmFrcbZs3SaN/eoEOHNL77TuDnn6F9exfDhxvceafO\nZZeZfPxxhJUrRfr1k49YyaFePZNWrXS2b1fIzNRo0yZIZqbVxaYoEjfdpLN2rcqLL0pcfbXMn39a\nVQbLl4vMmSNy3nkmVaoY+HwmzZtb3gwdOmisX2+Zm7dsmcKMGQppaTBtWpiFC4M8+6yLzp29/Pyz\nwJgxEXTdpHVrH3PnKlx8sc7bbyssX65wwQXWds880zJqz8oSqF07tdAFMBOVV6WkpBzxyvxP8M/9\n8EORZs1S6NAhhVdf9XDggMANN0SoVcvgzz9FFiywHnKjRnkxDNi6NcBtt0VYtUrhrbdkxo+P8OOP\nfv773zAffijTqJGPIUM8fP+9JRmJLDLtpXPiF7os71UkksnWEZJ0CXYo/eoR4XCYUCgUdSnTNK1E\nYhs7nqKMY+lSkXXrRDZvjqAoJoMGyfTuLfDSS2G8XrGAt66mwc6dIm3amDzzjEzbtvk+DPn7hXvu\n0alVK8KVV6YjywJ33aUxalS+QNeqZXWh3XGHTKtWCosWaZx/vsnBg9C/v4TXq7N160HWrcukT59K\n3H67zs03W3aPAPXrm6xfr/LAAxKNG7uoUsXE5YInntC47LIwwWCYJUvS6dXLR//+GuPHR/D54O67\nI/Ttq/F//+dmwQKF4cMj7N8v4vGYfP65xJYtErVrG3TooHPppWHWrJHZsEGiQwedypVNli6VUVUr\nfaHrVr46EIAbbvDxyCMePvssyLF8TWJtA2OJdQqzo7RYpzAb+2flkWoojxTGCy8oPPqoi4MHBapU\nMUlLg/btI/z0k8zq1QqTJ4dRVRg92st55xmsXBmkRg2D6dNdzJ7tYtiwCF98ESIjA3bsEHniCRe7\nd4s8+6y1AGmnTl46d9aZODHM6acfeb3bbyCx95KdurOPd2zaJ35NO9uZrTjHzol0K5jiiK4tttnZ\n2UQiEVJTU0lLS4u+jpb3OH77zaokmDNHJSVFQ1Vzef75g1SuLDJkSFVycwve3BMnSni9JsuXW00M\nPXoovPNO4lPWvr2OopgEgxAKCUc4eLlcMH26xsSJVh536lRo3VqmUaMwCxeGSE83GTZM4OOPI7z9\ntkiXLgq//JL/+6JoTZrpulV+dvrpJueck2+aPmyYzief+Dl0SKBly0yWL3dhmlC1qkGHDhr79wvc\ndpuH11+XGTJEZe9eP7t2+bnqKo3XXlM4cEBk/vwQ69YFUVVYvVrm7rsjPPZYiGrVTJo316MuZQA/\n/SRRrVoqL7xQsrihKOkJ2xIxGdITn3wiUqeOj9tvd5OdbT2MIxGBQADmzfOwebPMnj0CQ4Z4GDXK\nQ7VqJueco/PkkwpNmvj46y+BTZsC3HNPhOxsgREjPPTu7aVLF40tWwL066dx660RHnkkzKpVEi1b\n+pgzRylwnRX2ECmKGdDRouJEefl4A/PjYVxTUv4Romuf0Ozs7Ojre2zLbllOxhWGYcDw4Qo33KDS\noEEOubm5uFwuqlbNYO5cg3POMbnmmkwOHrQ+v2CByMqVEnPmaEiS1SDx1lsqN98s8+yzBSPy3Fzo\n2zeF664Ls3VrhNdeExk0SCY398hxDBigMWWKn3vucVGjhsm990p4vfm+FWeeCWvXqlxxhUHLli4W\nLRL58UeBdu0U1q8X2bIlwg8/qDRvbtKypYtp01yEw9b3rlbN5PnnQzz/vJ8pU1KoV8/H+een8vXX\nEgsXBvnlFz+DBmncc4+bO+5wEwgITJ4c4bPPAoTD0LRpCkuXyrzwQohXXgnyxhsyDzzg5uqrVZo1\n0/npJ5GmTTVatVKRZWuft9/u4bTTfPz2W6lOX/Qc2ukJWZaRZfmET0/8/LPAOef46NQphUOHrHN4\nyilwxhmWxeZdd4WZMsVPzZoGLVroLF4c5P33A5x5psFLLym8+65MMCgQCAh8/LHExIlu2rTxUaeO\nwRdfBBg50lrs9LPPrCh32jQXM2eGeO+9PF56SWHAAE+B+YTiUBqLTMivWkqmpXogSb0XwHrts2dR\nBUEo1Gw61tA80coRcHQT8qJiP5UL6zt/9FGBN98UeOedg/h8+TPw+WMwuP12nY8+SuHhhzWGDlV4\n912VBg0Knp6ff4aePRXatTN49FEdXYerrlI4/XSNRx7JIT09jVAI/u//ZDZtEli8WOPcc62oLRQK\n8fHHBsOGVWL6dJU1a2Q++khk1qwI9eodonKcM/oXXwj06SNz8KDAnXfq3HlnfsoBYM8eGDdOYvdu\nePppnebNQxw+LPLoozKvvuqmWTOdbdskOnWyXkfPOMP6LllZ8NRTLmbNcjFwoMptt0WoVMnk3Xcl\nHnzQzbffini9EAxCerpJMGgt+VOtmommwZ9/WsfN7YZQiGi01by5xsqVIcpiQQm7LK0wX9b49ERs\nu228J0Jh6YnSeCIcOADt26fw00/WCZEkaN5cJyvL2s8NN0Q4cEDkxRcVLrxQ5dZbw5x5psizz7qY\nN0+hSxeNceMi1K9v8NVXAnfd5WHDBgmPB+66K8yoUSqyDN9/L3LffS62bZOYNClM//5atIklLw8G\nD/by2WcSb76ZR6NGeVERLWsSpYOCwSBXXHEF1atXp2HDhnTu3JkLLriAunXrHjNFsXr1am655RZ0\nXWf48OFMmDChzMdcGEkvusFgENM0C5ifmKY1MZWXlwdUzOoR9nLu8eY7hmGwY0eYDh3Scbth6dII\nTZseOQ7TNDl0KIunnqrG449LPPqoxo03Ju62O3wY+vdX8PmszrJQCF55JYiqBgvUK86ZI/Kf/8hM\nnZpHx465bNmSwrBhacyaZZWdgWV8c/PNMv36+XngARf2whWGAfffL/HqqxLt2+ssXSpx1106o0bp\nxKa+IxGVN97QufvuNKpXN9izR6R79wi33x7g9NNdZGfDM8+4mDnTRb9+KrffHqFaNWvf+/cLTJjg\nZuVKGVGE6tVNOnbUqFvXYNMmkQ8+UOjTR2X0aJXDh+HZZ1189JHMgAFhUlNVFi1KIRQSCIUgJyf/\nmF57bYQZMyKUptLvWKKbiKOZ08Qb04iiGJ08LY6pzsGD0LWrl2++yT8JlSqZBAICigLVqhmEwwIH\nDgjUq2cweLDKWWflsWyZj+XLXfTvrzJmTITatU2++07kySddrFghM2CAyk03RfjtN4EpU9zs3Sty\n5pkGO3aI3HJLhBtuUKPGR6YJq1ZJTJ7spkoVk27dNKZOdfHYY7n06mWU2PSpqNhpH4/Hw+7du5ky\nZQo1a9bk119/Zc+ePWzbtu2ooqvrOueeey5r167ltNNO46KLLmLhwoXUj+02KkdOiom02FZgW4jt\n9a2KYvlYHukFu+Y3GAxz661VuPdejVq1BHr1crN4sUrLlon398MPAq1aGTzyiEzjxiotWhz5ucxM\nWLZMpVUrhV27BDZujCDLRH0T7P0PGBDkzDNVRozIZOlSF+vXy8yfr9K2bf42e/QwuOiiMCNGKFx2\nmcLs2Rq1a5sMHy7zxx8CGzZEOOUUGDvWYOxYmfnzRZ5+WqNZMzufK9Cwocrpp5vs3SuiaZaLmKJY\n/56RAZMmRRgxQmXqVBfNmvm4/voItWsbzJ/vYv9+gZEjrdrcVasUcnIEWrTQGTVK5c8/I7z0kkLX\nrl6aNDEYMybCffeFeeopmXnzfDRoYHDaaTrffCOxd6+VW87JEXj1VRevvmrZSD7xRMnFtyS+zPET\ncfGTSLHNHbFtrLYoF7bPb78V6N3by6+/5m/b6zUxDEtcTz/dYPt2iYMHBdq31zj/fIONGyUefthF\nVpabqlVNrr8+wqBBKvv2WV7LmzdLjBypsm2bP7r8U06OwGmnmWzbJuD3i1x8sc6gQflOc59+KnLP\nPW5ycgSmTAnTsaOOIECrVjp9+6ayb1+Ym28u33rd/Hp0ibp16xIOh5k8eTJVq1Yt0u9v3ryZunXr\nUqdOHQD69+/P0qVLK0x0T5qcrqZp5OTklMrTtjTCG99gcfjwYQzD4PXXK2OaEqNHm/TqZTBrVr5x\nTfzvL1ni5bvvBJYu1XjxRetzr72W+BStXi2SlSVwxx06nTq5eO+9/MlAVVXJyckhFArRsqWbGTN0\nli+XqVrVpFatI7d16qkCc+dmcf31OpdfrnDBBS68XqsW127cqFfP5N13VcaM0enTR2HcOJmsLFi4\nUKJTp8p07Wqwc6efzZsDZGcLtGhRmalTXQQC1u+fcorJI4+EmTQpzPPPuxg/3kP16gYrVuTx4IMR\nnn8+zPbtfho00Onf38uVV3r5/HORCRMivP12HmlpJv37e2nSxMcrr7ipWtXg8GGBNWtk9uwRqVrV\nivpjBXb2bBeZmalcfbW7QFt1USirF8BEpVX2JJKd6iqsuUNVNebOFalZ08fFF/sKCO5ZZxkMHarS\no4fG//4nEQoJPPhgmNdfD5KWZvlXqKrAE0+E+emnP5kxI8DmzRIXXeTjyitTOP10k507A0yYEKFS\nJdi4UeLqq7306uXl3HMN/vc/P99+G6BePYMWLVJ44QUrf3v99V7+/W+VjRvz6NTJElyA884zGDQo\njxdecCf0DilrYu9rv99frJzub7/9Ru3ataN/r1WrFr+VxaRAEUnaSNfGTjNomobH4ymReXhZle3Y\naQpJkkhLS2P/fpkpUxTWrMk3c+nQwWTxYpX+/RWeeUaLuort2gVTpqSzenUEj0egY0eTFStU+vRR\n2LNHZ/z4/Av8++8FbrpJ5s03VS66yKRNG4NBg1wMHJjC+PE5gBGd/Nm1S2T4cKtMbO9eaNtW4b77\nNK6/3iD2awsCdOmi8/jjMoZh8u23Al9/LRQoURMEGDjQoEuXCHfdJXPmmS4yM00WLMjioosEIhGV\nKlUkHnvM5IYbRB57LJ3GjX2MHx+hQQOde+/1EA7D4sVB6tQxeOEFF23b+rj8co0xYyI0a2YwbpzK\njTeqzJ0rc8st1iSN1wvt21um6Ipi8t57EsuXKzRsaEW/desarFih8NprMo0aGdSrp7Ntm8h331kH\n/b33FKpVUzj1VIO5c4PRBpPjiR0VS5IUTWHYD+19+wyuv97LJ58cmdoQBKsSZc8ekeeec1GpkknD\nhjp+v5WqiUQEBg9W2bAhQK1aJp9+KnHnnWmsXu3l0ks15s0LcuiQwOOPu9m5U6RdO52VK628/dix\nEebPtxpubHr00Ni6VWLCBDetW+ts3RooYJZkGEQnPM86S2XBggCyXL6dfPFVErquFyulcbw7DZM2\np2vlQA+hqmrUjKY0BzMrK4uMjIxit/zGtkUahhFdfNI0oXdvmWbNTCZNOvJ1a9s2gauuUvjvfzWu\nucZa86xHDz+33lpwGfbffoPevRWaNLEMxUMhaNNGYdw4naFDLcHWdZ3du4MMG5ZKRobI7Nk6VaoI\n/PEHtG3r4o47tOhnv/1WYOhQmVNPNXnuOY3q1a39fPVVNv36VWXoUIPbbtOZP99aMqh3b4PJkzVi\nA4l9++CaaxQqVzbx+w3++EPgrruC9OihIghmtA4TYOtWF6NGZfLHHyK9eqk8/niIypXzz1NODsyf\nr/Dcc1Y1RefOKjt3Srz/vkyvXiqXXKLz+ecSb74pc/bZBv36afToEUYUg2zcmMGiRTIffCBzxhkG\nqakmhw4J/PqrSChkCZR1dQtAwYdHmzYaL7wQ4rTTEp/XcDiMIAjlumx5bN44KwvGj3fz9ttKgTSR\nNV4Tnw+CQYFGjTS6dAlx1lkqX33lYsUKN/v2SZxxhonfbxnXX3GFhs8H778vI4om/fsHGDQIatSw\njvuuXQLz5inMmqWQlyfQsqXOK68EseeRTRPWrJGYPt3F3r0iY8ZE6NpVY/hwD6eealWoeDywbp3E\nffe5kWW4//4wTZrklPtKwFDQwNw0Tbp27VosA/NPP/2UyZMnRxelfOihhxBFscIm05JWdMFajE4Q\nBPLy8kpdMnL48GHS0tKK1SBhiy2Ax+MhEAhEKwAWLxZ56CGJzZtVCrtvv/lGoHt3hfPOMwCBuXP/\nIj39yDHk5sLgwTKRiGWKU706zJihRSsSwuEwLpeLQCDC1KlVWbZMYtYslfHjZbp2Nbj77oKiH4nA\ngw9KzJ0r8cwzGg0bGnToIHHjjSa33JKfHz94EO6+W+bdd0Uefth6OOzYIdCnj8K//x3hppsOI4oi\nH3wg8cgjmRiGyeTJYdq0CWEYOv/7n5fhw700barRt28e8+Z5+fBDF337Bhk5MkSdOkRn+n/8UeSG\nG7zs3CkiSSbXXKMxZIhKs2bG3zWn1k2+eLHCmjUy//qXiqKI/PijRNWqBrVqmWRlwQ8/SJxxhkG7\ndho1a5r88YeVgvjuOzHha6/lGaHxyCMRLr44P/ovb9E1DFixwmDqVC9ffqkc0aJtkf+wSEmByy/X\nEAT44gurfrtrV5VOnSI0bhxm506Rd991sXy5h99+kxBFgXr1dB58MESjRrmAj+XLFV55ReG770T6\n99cYNEjltNMM7r7bzQcfyEyfHuLAAYHp011IEowbF+Gqq7RoNUgoBGPGeNi5U6RKFZP9+0XuvTdM\njx7WuCpi+XVILLobNmwo8u9rmsa5557LunXrqFmzJhdffHGFTqQltejavd2lLfeC4i3ZY1dGxE7W\ngRUtV65cmZwcqF/fqgR4//0IZ55Z+LaWLxfo319h1Cidu+8+RFpa4jFomuWnsG2b1cBQt26QUCgU\nLTa3v0OlSpVYvFhk+HCZiy4yWbtWLXQiadMmgSFDFLKyYNw4P5MmSQkfOps2CYwda1UY7N0rMHVq\nDt27h6POa7m5uaSlpfP66yZTpnioUUPnrLM0Vq50M3VqmN6989Vu716ra2r+fBdt2qgMHJjHBx8o\nLFmSwqhReYweHeavv2Ref93NkiUKhiHQr59K374q6ekwZ47CSy8peL0Gqamwe7fEmWdaInvFFTpN\nm+rs3CmxZo3E0qVWvjclxRJtO4I8Ws7R44GGDXWGDs2jSxeVKlXKRnT37YO5cxXeflvmhx9EVPVo\nK0Nb5XCKYhKJWB15kmRVd4TD1vfo2tWq8vj5Z5FVq+S/V+nQ6NJFpUmTCKpq8MorLqZN8yFJEAgI\nXHKJxqBBYTp31vF48iftdu0SmDLFxdtvK9SqZTJtWogOHfQC6SfDgPfes6Lf778XmTQpwpAhaoHy\nPL/fj8/nK/fX99g3BGul6258/PHHxdrGqlWroiVjw4YNY+LEieU02iNJatG1c7mHDx8+osa0uOTk\n5ERLywrDNvPQNA2v13tE/vjQoUNUqlSJu+6ycmRNmxo89pjM8uUq9esfeZhVFVq2VBgxQmfBAoma\nNSPMnKmRlnbkGL78UuDKKxVuvDHMs8+6mDrVT9+++amI2LK3+++XeO89EV23DMufe06jRo0jv09W\nFlx2mUKVKrBrl8mDD2oMGgSJ7pklS+DGGxVE0crz3XOPwemnC9Ea54yMjL8bUAS6dvXyww8SDRro\n3HabSteuGvFanpsL99zjZs4chbQ0kxEjwlx3XYjq1WPLrUx27nSzYIGX11/3EIlYEzbWSsM5ZGb6\nUFVrcct16yTWrpX55huRtDST7GyBWrVM2ra1It7Dh+HHH0V27pTIyhLQdZNQSMDlIs7wvWAqAuxu\nPJOqVU1OO82kZk2DOnUsc3dVtUrWNM2a+d+zR2DvXpHffxc5dAjC4SO7A+MRReuVPv5zVauaZGaa\nvPRSCJ/PZMsWic2bJTZskPj5ZxFZhsqVTf7v/8IMH25Fm3/+KfDuuxKrVsmsXy/ToIFOZqbKp5+6\nufHGEDfdFEAQdPx+WLnSy8KFXnbtkunXL0LXrjr33efh1FMNnn8+FH1YvfaazJNPWkHE2LEFo18b\n07TWR6sI0Y19C8nJyWHYsGHRVEEykPSiq+s6WVlZVKpUqVQnOzc3F7fbnfB1Utd1gsEgqqoWsBaM\nJysri/37M+nQwc3nn0eoXt3qLJs0KfHCko88IrFpk8Dbb1u52uuuM/nrL4XXXtOIrX7JyzNp0ULh\n5pv99O0b4ZtvUhk82MM11+jcd5/VGmuaJllZWWzaVJVbb5XZuDFCZib8978Ss2dLPP20Ro8e+e+w\noRB066bQuLHBY49ZK/lOnFiJ9HR46imNevWssRqGwaJFOhMmeHnjjTzOPlth+nSZF1+UGDzYElVF\nsaz1du9W6d8/hUaNNKZMyeajj9J4+mkXWVkCo0dHGDhQJTXV2vfkyW6WLpV57rkQkgSLF8t/m9zo\n9O+v0q2bitttMmuWwmOPeejSJcTll4fZtk3ho4/c7Nkj0bq1xhVXaFxyic6mTQozZ1qG6S1a6Ljd\nJj/8ILFjh0gkInDBBTrVq5v89Rd8842E3y9Qo4ZVAXHwoIAkcUQutaJwu02aNrVKvlQV2rbV2LlT\n4tze42YAACAASURBVM8/rYeCIECVKtb3uuginYsv1mnY0DIBWrJE5uGH3fj9Vr3u/v0iV1yh0bWr\nRocO2t81vAEOHUpjzBgPv/wi0qCBzvr1Mi1aaFx7bYgrrgghScbfVRQC48dn8v33Mp06RXj1VQ/n\nnmswblyEyy/XEz6QoWIXpYwV3V9++YX77ruPxYsXl/t+y4qkF13DMEo8CRaL3++PtiPa2EXYkUgE\nt9uNx+M56j6ysg4zaFBVOnUyGTs2P4+6dKkY9c5t1co63N9/L3D55QqbNkU44wzrc9nZuTz8cBrL\nlyu8/bZG3brWpNS4cSKHDgnMmaPicllNHgcOwJAhCroO8+apVKtmsnVrDr17V+ONN1Quvjj/tH7y\nicD11ytceqnB1KnWJMvgwVYKY948DVG0UhMej4+XX3bx3//KXH+9zi23BFi61GTy5HSWLYtwwQX5\nd9y+ffDwwzKvvy4ybJifjh1dDBmiMGpUhJtuCqJpVqeVaVr2gk8/7WLDBolu3TQ++USiQQOD6dND\nxL6gBIOW58KiRQrr10uIIpx2msGjj4Zp29Y6nnZ54G+/qXz0kZdZszxs324Zpp93nsall2pceKHB\nhReanHWW+ffxUZgxQ+GPP0Rq1zZwu61IeN8+61ympxtkZwvk5eV3ulmt4wKybE1k2emA/Mm5YyNJ\nlldF7N9dLsuP4vffRQzDEtxQKP+4VqtmjU2S4Pbbw6SkwPr1VoQ7YoRKhw4a334rsnmz9bOffxZp\n1EinalWrUqFdO52HH84/rocOmaxYofPBB6msXSuTnm5y4IDAtGkhrr22YJ5F100+/FBi3jyZlSsV\nOnSIMHasnwYN1ITNHbGBh32v+Hy+oh2cUmAbVSmKwtdff82sWbOYOXNmue+3rEhq0bU7ekoyCRZP\nIBCIOo7FWj7aOdOiCPqiRUEefjidLVvUI16/1q0TuO46hdmzVdq1M+nQwVrKPLbrzBb+BQu8TJ4s\n8/LL2WRnG0ycmMnmzREqVYpvX87vGps5U2XcOIGxY2H48CNnZXJzYfx4mfXrRZo2tSoOli/PLw+y\nc9qSJLF3r8Ydd8hs3OhC0wTWrlU5//zEl8mPP5qMGiWwcaOLXr00pk4NU6mSmrC9de5cmdtv9yBJ\nJo0aGQwYoNGzp0psI6Cuw+OPu3j+eYUePTQOHhRYv16mZk2Ddu102rXTaN5c5cMPde67L4NTTjF5\n8MEQmZk6X34psn27lULYsUPm4EERwxBITzdp1kyjVSuD00+30gPVqpl8/LHEiy9akXiXLhoNG+ps\n2iTx9tsKkmR931Ao36S9ShWDQ4estI293lzs3ePzmaSnm2RlCVEhrVXLJCPD5Ntvxej3y8w0CYcF\nqle3jOZlWaBSJZOffhIRBJBlmDYthN8vsGuXyE8/iXz7rcAvv1jbaNpU5+qrNZo3tyJe+1rz++He\ne928+aZM584aP/8s8uWXEi1ahOnWDTp31qhRw2TrVpFBg7zccIPKLbdE2LNH4NVXFRYsUKhSxWTg\nQCuHXrnykc0ddoNHvEOYIAiEw+EKiXSDwWDUH2PTpk2sXbuWxx57rNz3W1acFKJbnEmwwrCrEERR\njJ5Ur9dbZCEPBuGCC2SeeSZCx46JBXrTJmvSrHt3g6+/Fli3Ti2Q6/T7/dGVEN57D266KRPDEFiy\nROXSSws/TcuWiQweLNOggcr69cZR6yTHjZN46SWJQYMMHnlEi5YJ5eTk4HK5opMUW7akMWiQ5UZV\nqRI88ICWcAzr1sHgwQqPPqqxYYO15E737hFGjPBz4YX5qZqZMxUee8zF/PlBGjc2WLNGjpZ7XX65\nRv/+GvXr69x4owdZ5u9yLmt/mgZffCGybp3M6tXy3xUO1mx+r15WZHvOOUbUgezTT0XuuMODKJoM\nHBgmNVXn11+tyPb33yW+/Vbm55+tAy8IoGkCkmSiKJaY2n4O9p0hy5ZY2hNcmmb9qVLF8oUQBEtE\nVRUUhb+XMbJac23cbuvzhw8L/H2p4fNZEbSmUaB6QZKsVEG7dhqNGhmcdZbJWWdZeeRvvxW5+WYP\nVauaTJ8e+ntlZ4ktW6zo98svJapUMTh4UKRdO41nnslDlo+MQDdvFvn3v714PNZD4pprrGqGRo2K\nttBrfJedLcTF8Z4oKXl5eVF3slWrVvHDDz8wadKkMtt+eZPUHWlltXqE3S8fCoVQVZW0tLRim5k/\n/rhEzZo6/8/emcfZWL///3lvZ5nNVrKkslTahMlOdiLLx1aIiCJkKaRsMZakpBLKEmXPTjLGkq1E\nSFK0EVnDGLOd7V5+f7zdZ86ZGfvw+fD7Xo/HPDweZ8a9nft+3df7db2u11Wz5sVbICtXtpgxI8CM\nGTI1a4Z7GNjHYJvzNG3q5oknLCwLvvpKviTfmJICRYqI82/cWOPo0ez/budOiSVLFDZuFJl4mTIO\n5s2T0XUjuG+Hw8GRI7l44QUXX34Z4KefAvToYdC1q0bjxkI9YceGDRIdOjiYNu0czz1n8uGHXnbv\nTqNwYZMWLXLTooWbdeuEsH7KFI2EhHQqVDBxOODpp3VmzfLy88+p1KplMGKEgzJlIklOlnjmmXDF\nhapC+fIm1asbnDkj8fzzfqZOPUelSgK827Vzc/fdUVSrFkGZMhG0aBFB2bIGw4b5qVnTokkTif79\noUsXC49HQdMk5s9P5vjx0/zzzymOHTvB6tXnKFVKp2hRgzlz0jl48DTHjp1j2TLPBUpCAKOmWeTL\nJ+bJnTkj4fMJn18QYKnrQgFhGGLWW758FsWLm0RHW5w9K4pqAwf6mDTJg2mKQlX9+jrbt6dx770W\nU6d6OXkylZdeEoZEDgc8+aSOZQnd7datCrGxBn//LVG6dCSlSkUyY4aG2w39+vnZvz+Vn39OZ+/e\nNM6elXjxxQiSk0W2/sMPMnFxDipViuDZZ91UqmQwaJCfAwfSGDvWd8WAC1mtMe06x82e3HGrOYzB\nLZ7p2m5DlyqCXSpCGxuAYCfZ1cbp0/DYYw5kWbS6tm9/8XfZSy+pOBwWW7bINGxoMmqUTiDgw+Px\nIEkSmqYRGRnJqlUy/furrF3rp0cPldRUidmzA1lUCH//DVWrOvj66wCFCp1jypQ8TJ6sMW6czjPP\nZDxEp09DlSoO3n03owvu++8tXnlFJXdugzFjUihVysm//zqoWdPBqFHh/9/vhxkzZMaMUala1aRu\nXZOBA1Xmz/fz8MNCteH3+4P2h+fP+1i+PBeDBwuKokcPPx07BrI1vp41S2XYMCEvS02F9etFBmxT\nCjVq6GzdqjBnjsbEiV7q1Alk4Q8TEhS6dXNRsqRJqVIGp0/LHD8ucfy4zLFjUlDre+edFgUKCBN2\np9NCUeDQIZEF33WXiaZZpKRIJCcLXa9lwd13m1SoYFC4sMmxYzLx8Rq6DtHRFm63xfHj8gWTdYvH\nHxemP6dOCV7WssR+bTqiQAEB2CdOSLhcFmXK6Pz0k4bPB0WLiqw2OVkoIRITJf79VwBm0aLC/rNY\nMTP4YxjC2rJRI524OB+hCz3DgH37ZN5808FffwlPjHz5LBo00GnQQKdcOTOLouR64mKOaVdCT2TO\nii8XoXrgKVOmUKBAAZ577rmcO5kbHLd8GzBcW6YbCrYRERFBR/triTFjFNq2NWjbNpVnnonB4zHo\n0iVr1rBjh8S6dTI//ST66p99VqVVK5g0yc8dd0QTCASwLPHQ9emjMm1agMKFYckSndGjFapUcTBr\nVoZZjq5Dp04a/foZlColZFEDBujUrw8vvKDy9dcyH3ygExUlim7PPmvQtKkZNHN/8EEP69ZpfP55\nNE2a5OX55wMkJGh0726EAS6IAlDXribt2vl5/XWFrl1VnnzSvGjjh6rCxo0KFSua9OnjY+lSjSef\njOChh0xatxZcbkwMjBzpYPFijdWrPTzwgNhn+/Y6hiEoha++UunY0U1qKpQoYbJkicYff0iULKlT\nvrwwVn/nHQczZ2pMnuylXr3wlcbRoxKdO7uQZRgyxEeuXAS1rn/9JTNmjJNChUxGjfJQuLDgXwMB\niQEDVNLTZaZMSaVgQZ3jx2HKFDerVkVy3306x44pFzx9MzjfggUtJAnOn5eCdEGXLn5cLli6VCV/\nfpOdO1XcbgH83bqlsXq1kMK5XCJzfuGFAGXKiMw4JsYiMtJi0iQHX36pMWCAl9jY8O+lXLk0XnhB\neFW89JKf/fvFRI7duxXy5xdcdq1aabRoIVO06M3Pr650coddFLcz6Mx8cebp36EG5g888MBNPafr\njVs607V9F0KLYJeL7BobJEm6qDXj5eLQIZFB7tnjJyIilaNHNf7zn2g6dzbo3z8DAEwTnnxSNEE8\n+6zIbL1ei9dfz8NffyksWhQgJkbYVL75Zgw+H3zySfhLID5epksXlQEDDLp3NxgzRmHzZplVqwJB\nBYLNbaenw5tvqqxeLVOxosmZMxIrVvgxTfGykWU56C8M8OuvaTz1VG7S0yXGjdNp1y77TOiPPyTq\n1NH44IMA//wj8/HHCgUKBHjtNYt69XyoqoTPZ9CpkwuvV2XOHE+wWOf3Q0JCBpebK5eFw2Exb54n\nWx3zP/9ItGzp5sknDYYP9/HbbzJ79yrs2SPx448S+/eLduuICMF/lihhUaiQReHCJoULW+zZIzNo\nkJPu3QO8+qo/eD6WBXPmqAwZ4uSNN/w0aqSTkiKRkgJbtyq8/76T4sV18ue3OHxY4dAhOailbd7c\nH+wC+/JLJ9OnR9ClSyo//+wkIcGBzydc1u6+W1gniknN4qVVubJBkSImCxZoSBLIskWNGgF+/FHj\n22/T+e47hd69nQwdKlYFliXGE6WkSCxfrjJqlJMOHfzcc48ouh06JHPokMShQzKaZlG6tEnlykJS\n9sQTBnnzXp9n79VEaJfYtcbFrDGBMBD2+TIac4YOHUrz5s2pVq1aTp3KDY/bAnRtHvRSN9blGhvs\n7YT60V5JdOyocv/9wl/BBv+zZ108/bRGkyYmw4cLbeMXX8hMmyazcuU5LMsI6WSTGDVKYfZshfnz\nU0lMtOjcOZrdu/1kZ+976JDw0r3zTouffpLZts0fdA7LrqA4erTMqFEqrVrpDBt2njx5zGz9hYcO\nNfj2WwdvvWUyfLhKYiIMH27QuHFGa+y//wovh379hGEOiGx79ux0pk3LRWKiRdeuAbZskfF4LObN\n85PdMxgIQPv2Lg4flrnvPpOtW1Xuu8+kTh2d2rUNKlQw2LdPpk0bN716+enWLZCpO8rk11/9tG+f\njypVdBo10jl5UtAIx46Jf/fuFS5smkawUCW6vMK701wuYZQeHS0kYidOSFSvrlOxoo/ixS3uvVfm\ngw8cnDolMX++h1y54NdfZQYMcLJnj5iwXLGiTs2afpYvd/Dggzp9+yazZEkEU6ZEcPasTOvWPsqU\nMdm7V2XuXPGicDqFRMvnE9SHDcyqKgp5ERECcJ3OjOPTNHC5BLgWK2ZStGhGge1iSq1bCXSzi+ys\nMe1nuWXLluTOnZvKlSvTsGFDSpUqdVVJ08KFCxk2bBgHDhzghx9+oGzZsjl67BeLWxp07TE8Xq8X\nwzCy1QheaWODruukpaVdFSm/Z4/Ef/6jsW+fn6gowqZYnD4txqxXqGAxZIifsmWdzJyZSMWKarbH\nMHu2zBtvKLhcFmPHmjRvfvGiRlISPPigA5fLYtEinXLlMsaWhHbVnT4N5ctrjBuXyvr1CitXuhk5\n0qB9+3CHsdWrZbp3l9m0KZ177hGzzeLjZYYMUYiMhBEjhH9u/fpiYsWwYeFL+MTERHLlys2WLSYv\nveTmxAmJ//zHS4cOFtWqhU+b0HXo3NlFWprEnDlisKTdVbZuncL69cInIRCARo10WrXSefxxg8KF\nreAxf/+9RLt2bgYODNCpU3iF0e+Hnj3F1Novv/QEDdMNAxIT4YUX3CgKTJzo4a67BAhbFowZ42De\nPO1CA4iQDKamqjz3XDSmKfxif/xRYedO5YKKwSIuzkfjxjpOJzz7rBu/XwDkd9+plCuns2OHwqpV\n5ylSJMCMGS5GjIimZEmdiRNTKVnSokmTKOrV03n9dTEBxOcTxy/0wRYxMXAdgpwL1/vmgO61mL5f\nS9h6YIfDwc6dOxk/fjx58+blzz//JDExkT/++OOKt3XgwAFkWaZr166MGzfu/0D3SsIG3exG5Vxt\nY8O1jOwR2axB164CIDNPsTh3zqRZM5WzZ0X1fepU85LH8NJLEgsWaAwfbtCnz8W7f0aMUNi7V+LZ\nZ01ee02lSxcxSic9PQN0TdOiVSuZ++7zM2KEeOh27xZTIiIjRdfZQw9ZHDoE1as7mDkzhcqVrbBM\nxTCEcc+wYSpeLzz+uMny5XoWL4fExERy587NiBESa9ZoTJ2aysqVMkuWRHD2rFAjtG6tc//9Ji++\n6CIlRQqjHUJj40aFjh3ddO/ux++HPXsU9uwRRa3SpcVI9m++UenePZWWLWUKFzaxk5vz56FdOzdR\nURbTp3vDLAhPnJBo1cpNbKzBuHEZRadAAHr3drJ7t8Jrr/k4d07oYn/91WLbNvECqlhRZN/lyhkk\nJKj89JPCsmXpREUJRcDLL7s4elSmVCmT558PULasTrNmEbz/vpc//1SYNElkt1Wr6kyfnobHY9Kv\nXwQnTkjMnn0OVb22gtKVxI3KQDPHzXBlg6xNGC1atGDx4sVER0df83TlmjVr/h/oXmnYoBvKx15r\nY8PVjuzZtEni5ZdV9u7NaISwM+6IiAh8PsHb/vmnk1q1clOxosXixaJ4lF0cPQrlyjmYOfM8w4fH\nULSoxSef6GReLf36q0S9ehrbt/spXFhYP3bpopGSAhMmJFGypJDrTJsGn38eyebNAdzujPM3DJg6\nVWbkSJV27QzWrZPp1MmgQ4eUi/LiI0cqzJ0rtpE3L/TubdCsWYYuNjExkWXLcjFmjJPVq5O46y6R\n+URGRvLrrwrz52ssWKDi84n/P2mShwoVzCzgvXmzQocOLmbP9lKlSng2ffKkxKefanzyiYNq1XTS\n0kxOnlQ5dkx4EOTPb3LihMwdd5iUKSMkXk6nhdMplukrV2qUKGFwzz3CAvH8eYnkZDh8WMbvF5K7\nEiXEsr1gQZMvvlCpVk3nww8zvt+4OAfx8SqvvupjyxaV1avFOcXEwLx5Hh57zOT8eahRI5J77jHY\ns0elXj2d/PlNtm1T+frrdFasUBk0yMn58xI7d56mUKGMgZehPGbmseTXCsS3G+gahhHkdAEaNGjA\npk2brqsx6maD7i2tXsg8ssfr9QYbG2JiYq7qi7haBcRddwnx+/79EqVKZfw/XdfDjMw//tjFgAEG\n//4rUauWxtKlAUJM64MxeLDKiy8GqFQpwIYNAfr0UalWTQsOlgQBmN26qbz1lh70gS1cGFauDDB5\nskzDhrkZMCCFatUMxozJw9q14YALQkv68ssmTZv6qV1buyBdEsv+7C7XunUSn32msHWr8JJYtUrm\nww8VBg9W6dHDoH17H5s3Oxg61MmKFSncdZd4MEBIe4oVUxg8WMY0I1m3zkH16jq9ewtz8lq1DOrU\nEe5gf/wh06GDiy++yAq4ALt2KXzxhUZ8fDqPPaYHsx3LgoMHJVq0iODpp3WaNtUvLNGF2czRoxIL\nFjioW1enRg0jyI9GRVmMGeOkcGGDOXM82Iuk5GRo2jSC+vV9vP22D0URJjpxcWI+m2XBzJkOGjTQ\nKVjQz5IlGmvXppMrl2g4eP55N2fOSNSpY/HRR2n8+69E69ZuRo/2Ua9eBJIkrvO0aV7uuMMKVutD\n79XshjBerLJ/uYTiWrO/qw1bAnYz9pP5fC6137p163Ly5Mksn48ePZrGjRvn+PFdSdzSoGuH/Ta3\nGxuupzPtSm/SkiVh/HidRo00vvwyQGys4JYtyyIqKgpNE40EmzfLTJzov7CkV6hRw8HChYGwiQzf\nfSexdavMzp2iIOhyCeXCjBkytWtrTJig06yZyZQpIqvr3Dmc7zVNnfbt04mNhZ498zB6tEKvXnq2\nigA7du+WMQyJJUsCvP22yvjxuRg82Mszz2S4jB0+DJ07a8yaFaBQIfFZkyYmTZqY7Nhh8f77EiNH\nuvH73bz3npcHHhBgaXfV2S3VM2ZorFqlsXLlGfLkMRk2TObECY2NG52sWqXRt68Lj0eYb+/fL+N0\nWjz6qBmkB+LjFXr1crJokYfHHzfDurfOnYPnn3fTvHmAIUP8YZTM339LNGwYwciRPjp2zOB+DQO6\ndBGdb3PnCl4ZRBvtf/7j5o47hCF6y5ZR7N4tdNXp6RLDhnlp1Uonb17h7fvyyy4WLPAwZ47GrFka\nx49L5MoF+/alUaCARWIi1K0bQaFCFm+/7eStt3xs26aQmCjRpIke7EzLHKFAbPPzmSv79j1vy7Ey\nZ8T/7ekINypCn88rSZLWrl17ow/pquOWpxfOnDkTzAyuZ5ovXNv0iK+/tnjpJQeTJ5+ndm3xUNgK\niMycL8CyZcL85tNPdZ5+Wgjcq1TRePVVgxYt/FmKebt2SbRtq1GvnsGSJQrr1weCDmChRUK3242u\n60ycGMFnnzlJSRFj07t3N7IUY06dggoVHMyeHaBqVbvrzU9cnBuXS2bkSJ0KFSxq19Zo2dLk1Vcz\nMs9Q+sbnc1KjRi5KlPBz4IBGTIzFM8/4aNo0jQIFTDRNY906B717R7JqVQolSmStRh86BI0b56Vb\ntzSiomT27lXZu1fl998V7rvPJH9+i507FXr39lGliknhwiYFCxqYpge/P5KmTSOoXt0gLs4XBrj/\n/CMAt1cvMRTTDtOEl1928ddfMr16+Th6VEiv/vxTZts24fJVsaJBbKyPChVE9vbKKy6+/tpDyZLi\ne/zlF5n69SMoVUp49z71lCj2ffSRg82b0ylQwGL/fpnmzd0kJkrExfl44YUAO3YodO7sYtu2NPLm\nDW9nvZYIvZah9ETo9GE7Q76WMVZXE6F+CDcyMhuYP/3001ftpZs5atasyXvvvUdsbGwOHeWl45YG\nXRA8qmmaJCcnXzfoXo1xTijg7d4dRceOkUyY4KVWrVRiYmJYv14Yf+/Zk9X85ocfJJ55RqN/f1H5\nnjtXYd26AKaZfTHvzBnRsut0WqxdG+C++6xgW6XT6cTtdiNJEr/+6qFOnRi2bAlgGGL/587BhAl6\n0HXMsqBFC5VHH7WIi8sAU4/Hg2FYrFoVxbBhKn4/FCsmhlEKjWpG957gft20b+8kTx6L8ePTCQQM\ntmyBL790sXq1i9KlA1SurDNlipu5c1MpVy5r6+f58zINGkTTqZOPLl38YcDh9ZrEx7vp1y+Gp54K\nAEIOdvy4zIkTElFRJl6vTK5cFiVLhnO4hmGRkKBRrJjJXXdZpKRwQYcrcfKkGGlTtKhozxXSK5P1\n6xXS0yWWLhUFPo/Hw9GjTho0iOaTTwTlsXmzwrJlwgWtSBGL3r39tGwZwOuVqFYtgk8/9eJ2W4wf\n72TrVmGevm1bGnfcIbLoypUjefddL/XrZ9AvN2LSQig3bDfcAFky4pws2N0s0A1VSQQCAZo3b87G\njRuvaVtLly6lV69enDlzhly5clGmTBlWr16dswecTdzyoJuTnrpXYpwTOiInFPB27ZJo1kzlrbdS\neOEFF1WqaPTta9CyZfbSr8OHhZ/t0aPCxSs21rqogmLDBokePTQ6d9YZP15h8OAU2rXTiYjIMOSx\nLHj6aZmqVXUGDpSDn82fL/PmmypNmpjExeksWiQzfbrCpk3hY4RClRdLlgiVQ0yMxR13QM+efurU\nSUFRrKAJ0IcfKixapJKQ4EWWRSHTtsb0eCTmzZMYMMCNZVmULatTo4aX2rXFaCBVFZMTWrWK4pFH\nDEaNylhn20vj48cl6tePZvjwNBo39oYVmAxDon17wdn37u3H75eCHG5KCowd6+SRR4QTl+BwRcvu\nqlUqCxaorF+fHmYpOXGixuzZwhvCLlyePOnlqafy8sQTJqmpsGWLymOPGSQlSTz2mMHUqWK8sGEI\nn4w777Q4dkzi1CmZdu38TJrkYOVKD48+anLypMSLL7q45x6LSZO8wf3ejPE2doFLKFrMG1awu96s\n/UojtGB35swZevfuzYoVK27oPnM6bgvQNU0zKFu6nhv4UtMjrkQVsW+fSePGDurVs9i3T2bLlouP\nygHo319hyRKFYsUsZs0KkD9/VgVFICC0tkOG+KhVK5kDBzR69MhNiRIWEydmmJ3PmyczbpzEhg2p\nxMSEazLPnYOhQ1WWLRMdUps2BXjkkfCv3V4xpKREUL68g3nzApQrZ7B0aYCJE12cOKHyyis67dsH\n2LtXon17F+vWpZI/vwdZlnG5XMEHzjCgWTMnpUqZDBwYYOtWmYQEMc0iJUWiRg0/hw/LOBwWc+cm\n4XIpwWspSRLJyRaNG8fQrJmf3r29WTjKwYMd7N6tMH9+EppmhhSUZDp3jiYyEj79NJxuSEhQ6NHD\nRUJCelg77OrVCn36uFi7Nh3DIOhTO2+emEnXqJHwKqhbV+fLLzXmzRPgbKsiXnzRxTffqJQoYfLq\nq36aNNFp1cpNlSoGXbv6+egjB5MnOzBN+PXX1LCGl5sBuqHes5kjO08Em47InBFf7hj/G6B78OBB\nxo0bxxdffHFD95nTccsX0uyHUZbl63Yuyk7BYMvSPB4PiqJcUhXx8MOwdGkiTZrcQf36F9fZgpB6\nzZmjsGOHn5kzha/C7Nn+oFLBjsmTIX9+nZo1k4mIiKBCBY3vvgswbJhC+fIOJk8WWfIbb6jMm5d6\nwQ8gPPLkgQ8/1PnhBzEPrUMHlREjDJ56KrxJwjQtXn5ZpUMHgzJl0klN9dKokZOWLQ127DD58EOF\nt9+OwO+HYcME4LpcLlRVDQPFMWO0C38TQFWhXj2TevVExn/woMTQoRoHDihERVk8+mh+HntMv/Dj\np2RJH6NG5eLxx3V69fIGvwP7e5k500l8vIMVK84QE+MKOXaToUNdnDkDH310lvT0jEr//v0aO6MX\n0AAAIABJREFUXbu6mD/fQ9GiYs7YkSMS33yjMHSoi8cfN6hRIwJNg/LlDdLS4N57DdasSSUmRjwi\nu3bJjB3rYN26dPbskZk9W2PxYnGen37qoXlz8X1Pn65x7pxERIRF2bKR1KwpjHL69cu+w/C/GRdT\nTlxLwe6/oZJITk6+6g7S/4W45TPdnPTUDZ0eEWpNZ3eZXWp+GmRoff3+PLRsqVGihNDaZtek0727\nSt68FiNHCn5v9WqZrl1VevVK5rXXnIDFkSMeKlfOzddfp/H441qWm3rTJomXXtJwOi3q1DEZPTo1\nrDkjNGbMELTCxo0BVq+WGTpUIV8+0W1WqZLI4qdPV5g1y82KFWdwu5UgdWL3vwsKw0F6Opw4oZI/\nv0WbNgatWmWMcl+7VqZbNwfffusNfhYa27fLtG7t5JtvvNx3nxifs3evzI8/ip8NG5QLVpWiaFao\nkE7BggK4EhMVpk51M3ZsEsWLW0RGKkEud/FiB9OmuZg8OR1ZtjlcseR/990IHn1UtBIfPqzy778y\nBQqYnD4t8+STBs89J7L6woUtNm8Wxa6EhESKFFFQVZWkJMHHVqmis3u3gmVJtG4dYM4cjbfeyhi8\nefCgRNWqkeTObfHQQybDhvnYskUhPl5l+XJPlpfwzRjkeKlM90rjSgp2dsenoig3rWC3ceNGtm/f\nzsiRI2/Y/m5E3PKga+sYr2Sw5OXC9k4QhjHCFCciIiKLT8HFwp5TlidPHjweic6dVU6flliwIEC+\nfBl/99tvErVra/z8c3j2c+gQtGwp8/DDJmPGJDF8eG6ioxXGjbu4R298vFA35MkDY8emU7++j6io\n8HbokydF48WqVYGgptgwxPy2ESNUHn/cpF27dLp3j2T58nM8/rgjKPsCgoZA06fLzJ4dyYYNXjRN\nZvNmmblzVVatUqhUyaRuXZ0xYxzMmSOUBpnj9GmoWtXF+PEBGjbMek7Llyu88YbG+vVePB6hsT12\nTOKffyR++cVixQoH998vXmI+n+Bw/X5RIDt/XiJ/fos8eYTcKzoaoqIsduxQKVLEpE0bP8WKWdxz\nT4CCBXVefDGKAgUMRo1KCWZvp08r1KoVw+TJXipWTOHMGRcJCU7GjHGQlCSmErdvH6BCBZNBg5wc\nPy4xc6YXw4Bly1R69nQRE2Px6adeqlc3OH5conLlCNauFa3FmeNmgO6NLHCFZsS2ref1WDZeSYSe\nz4oVKzh+/Dj9+/fPkW3frLhtQPdaPXVDIzU1NXgTZWeKcyVhTwQWGSIMHqywcqXMsmUBihcXf/Ps\nsyrly1v07RsuxfL5fJw9m86bb+Zh1y7xoP/yi5+LdSYbhpgm3LevQYECFj16KBQvbvDhh1Zw7hpA\nu3YqRYtajBiRFejS000++shk5MiIC74AYoy5vVzUdR2v18vhwyoNG+ZhzRpfFv1vaiosXaowYIAD\njweqVTOpW9egXj2DBx4QngmGAf/5j5MyZUzi4rI6sv/1l0Tt2i4WLfLxxBMZgG2aJklJXp5+Ohdt\n2gTo2dMKPtymaXLqlEn16lGMHZtCrVqesAf+7bfd7NihsmhRSljjxyefOFm82MnXX6fickkXNN4m\nLVrEcO+9OgUKmCQkODl2TKFECYNjxxS2bk3ljjvEvfDddwodO7rYsCGd+HiVCRMcQb/cnTvTgmqV\n558X/r4DB4aNGw65brc26NoROgkYuGzBzv5+rrdgN2vWLFRVpUuXLjl9Sjc0bnlO147rmR4R6tOg\nqiq5c+e+5gfBPg7BgcHo0QbFilnUqiWKU4oi+MGZM8WDmJXGgM8+syhTRrhNLV4s06mTmWVpCjBz\npkx0NLRqJX7/7bdpfPCBSuXKbl57zaBXL4O1a2V275aZOjX8wbcLgz6fl4iIGMqWNXj6aS/t20dS\nuLBFr15+atZMBUxU1UXPnlG88Ub2DRdRUaJNt3RpkzlzfGzerLB2rcKECSqqCnXrGiQmSng8MHRo\nVsD1eOC555y8+WYgCLihvhpDh+amWDGJnj3DuxBBoWvXCNq0MWnWzIFlZVToExJkZs92sGbNmQvN\nFOJh37VL44MP3KxZk4wkiQm8O3c6mTnTye+/K5w6pdCggU5cXDL33gv16+dhzpxE3G4dj0cmPV2m\nS5c8VK2qU716BOXKGbz7rofu3d0sWOAJAu6SJQp79ypMmeLNcr72+d2MuFlcK2R8N5fqsLOz4osV\n7C7X2JHZS7e4ncncQnHLg+71jOzJrEiwBdfXc5Nmdxwvvmhyzz0BnnlGDP4bPFjH7Q739rVpjPPn\nz7N+vdj/xo0BXnxRmJFPnqyTP3/GNs+dg7g4leXLM2wPnU547TUP7dop9OqlMWuWmCL8+ecBbJOp\n0MKgqqokJ8cwdqybr79Oo2hRH507p7NypYN33olk0KA89Ojh499/hdvYyy9nb/L+008SH3+ssXWr\nlzx5oGlTg6ZNDSwL9u+XmDJF5auvFNxuKFnSRZkyZthPXJyDkiVNunQR2w8EAni9XmRZZtWqXGze\n7GDLFm+WF88776gEAhlAbheGTpwQS/0vvvBRvHjUhZeqwe7d0LZtFOXL++jePYK9ezXuvtugaFGT\nv/9WWLo0hYoV9QurDj/PP5+Pl17yUb68iiRp7Nkj0a1bBCdOyKiqj0WLzlOypEX//tE0buynTBmd\nI0dkRoxwsXixyty52Zv6ZL5fbvW43DNzowp2SUlJt9yoHrgNQNeOqwFdeymf2afB6/Ve8/SIzNvP\nHPXqWXz9dYBGjTQOHICkpFQsK5CFxrAsiSFDhNPYY49ZbNkSYMQIhQoVHEycqNOwocgER41SaNRI\njBrPfA2KFRN+DC1bqhw5IjFxosJddxncf78/OC1DLGtlXnvNwUsvBXj4YQm/X0FRdFq2NGjd2sN3\n38mMGuVi2zaVVq08bN3qITbWQlWV4EPk9Up07uxkzBh/cE5bxvGIabgJCQpz5/p46imTw4elYNFs\n0iSN7dtlvF54+GGL1q01ChYMULCgTNGi0YBCv34OZszw4b2QMLrdwo5xwwaZ6dNVVq/2cuqUMK9J\nTZU4dw7693fw+OMG8+erjBmjcfCg8MnVNDGuJzZWITZWp0wZD4qiU7t2LsaOTaJsWR+BgCgczpsX\nydmzMu3bpzN5ssbcuU5OnRJj2jdtSubhh8GyNHbskElIcLBy5TnefNPN/PluSpUKUKVKgNq1vZim\nclu35V5rZDdRInO3oi0HDeWJIaP542pdAf9X4pbndEMzt4tV7kP/1u6qyjw5AcjWIvJq41IqCsuy\nOHrUy4svujFNmVmzdAoUCNc/zpzpY9q0SLZs0cMyu61bJTp31qhTx6RzZ4MmTTR+/NHPnXdm/E2o\nEfuff0pUr67x7bd+li6VGDdOpXZtL4MH6xQvLpbhy5fLxMU52bw5BcvyBlUaoXrbmjWdNGtm4PXC\n3LkqimLxzDNemjVLp1AhnWHDYjh5UmXGjPQgGIcCzMsvOy7412blNY8elahSxcVnn3lxu/0cPmxy\n6pSDEyccHD4ssW6dQnS0daFwJuH1CirCNiCXJEFtREUJ79moKIszZwSN0aaNoHWKFhVm399/LzN+\nvMaWLd6w7HPgQI0jRyRmzEjH6xXeF0eOaNSunZsyZQLs2aNRr56fZ5/1MXx4JL16eWnRQpyLrkPN\nmjGULKmzaZODJk0CvPSSjyZNolixIpkSJTKGMGa3jE5PT7/hI8tvhhY4s/NXToedEdv+KikpKZQu\nXZrChQtTpkwZatSoQWxsLBUqVLjibfbv35+vvvoKh8NB8eLFmTFjxk3Lmm8b0L0cYNqAZFlWtpMT\ngGse2RMa2akoMmfWDoeb0aMdzJmjMHt2gAoVrAv7h8ceU5k0yU/t2lkfkvPnoW9flcWLZTp2NBg/\nPrwwFgq6LVqoVKpk0r17Kj6fD5/PxeTJkUydqvLccwG6dAlQv76bTz5Jpnx5X7Z620mTVFasUFi9\nWjQaWJZw0pozR2HpUqEK+PtvmZUrk3nooUBwqWgDzJo1LgYPjmDbNg8xMeHX2jShcWMnVav66dHj\nPKqqhnkeDx2q8dtvEvPnh5vYWBY8+6yD4sUtRo0Kbz7ZtUumRQsn27Z5KVgw47YWKgIXS5d6KVMm\n4/Nvv5Vp397Bpk1JyHKAb7+NIiHBwaJFKnfdZdG/f4DmzQNERxt8/LFKQoLG/PmJSBIEAjI9e+Yi\nPt5BnToBBg9O54EHTN54IwLThHfeSQsCrP2I2dcndBquqqo3pMpvx+0AunaEeummpKTQpUsXqlat\nyp9//klycjJffvnlFW9r7dq11K5dG1mWeeONNwAYM2bMjTr0sLhtQPdigGmP9jCMjBE5F7uxr3Vk\nT2hkVlHYmbUkSVky66++kunWTWXIEJ2XXjL55BOZlSstli3zXVSFsWGDRKdOGooCtWqZjB6tB7Nd\ne/rF9u256d1b5Ztv/iUqSgtODTBN0ZI6dqyDL75Quf9+nYUL0yhSJOsL6OhRAVTr1nl54IGst8i5\nc1C2rJsHHzT59VeZ/Pkt6tUzqFtXp3z5AOfOmVSrFsPUqUmUK+cLArH98+mnwmN3+fJEoqPdYddl\n2zaZ555z8v33njAeG0RDyUcfaWze7A3TP3s8Qo42YECAZ54JVYWI7rjy5Q0GDsygjlJSLJ54wk21\nal6OHVPZvVujUiXh1bBrl8z333uDRkH2tVi/3ku+fCbTp6tMnKiRlCTx8cfJNGkiMuSDBx00aZKb\nbdvOc8cd2dNM9pLaBiqHw5FtlT+ngPhmKCRu1nSKzAbmjRs3Zs2aNdc9rWLp0qUsXryY2bNn58Rh\nXjZueU73YoW0UEWCy+UiKirqsjfe9SggMm9D1/ULJjLGRbW+jRqZlCwZ4NlnVb77Tuabb2TmzTuP\nZWWflQgJmsq77+o89ZTJiBEKsbEO4uJ0nn9ecL1+v0XfvjLDh6eQL19U0GnKPrZ8+fy0bu1h0aK8\nlCljUalSLpo2NejZMxBUJlgWvPqqRvfugWwBF+CDDzSqVjWYNcsfnNybkKAwfLiDAwdcRERYPPig\nhSxHYBhOIiON4BJx3z6dMWMiWbkyEadTCfrvKopCWppEly4OPvjAnwVw//lHYuBABytXerM0nMTF\naTz8sEmrVuHZ/4wZCmfOwCuv6Hz/vcwPP8j88IPEmjUKug4Oh0qPHhY1angIBCA21s2CBeHjzF9/\nXaNNG53p01Vmz1Zp0MCgWjWTQoUs2rXTAEHXxMU56dPHS+7cOj6fEdY8YIOnfW+EfieZVxiZJ+Tm\nlD/CrR6ZC3a6rl+XLt+Ozz77jDZt2lz3dq40bnnQhQxS3ibiQx24rsaqMSdAFzJ8DNxu92XBvkQJ\ni82bA3TqpCJJ1iW9GpYskS+4hImpC2PHGrRta9Kzp8oXX8i88046Gza4KFIEWrRwYFkZ2ZP9EgCJ\nYcPyMnSoTpcuOiNH6kybptKwoYuyZU169w5w9qyYMDtnTvb60n37JGbOVNm+XWR4igLlypmUK2cy\naBDMmqUQF6fx2GMmY8Zo7N3r5I47LEqX1nnoIR9ffhlB164Bihd3oigCiG0Z0Rtv5KJ8eT/163vQ\n9QyOWFgyOnjllUCYaTzAli0yCxcqfP+9F78fDh+WOHxYYudOmffe07jvPpNixURWXrZsgKJFAzgc\nkezb5+HOOzO+m969NZo00SlXLkMnPGmSwvr1CqoKzz+v8/33Xs6fh0aNXOze7Qn+3YoVKn/+qTB/\nvtg2ZIBn6E/o/RX6IrZB2I6LAXF2huYXA+LbTZaWnZfupfZ7JQbmo0aNwuFw0LZt2xtwxNnHLU8v\ngOBibYIdxM0cWhC60rjakT2hYcvPbClWVFTUVfFoliU6xAYMUOjTx0ffvnIYAAcCULq0xkcf6dSu\nbYX8P4vUVA/Tp8u88040Ho9EfLyX2Fgj2MJrjxFyu9189ZXosPr2W29YNufxwPz5CuPHi8LSyy/r\n9O8f3kknrhHUru2kXTuDzp2zKj3On4cnnnDx+ed+KlcWQOLz6ezb5+fnnzVmz47kwAGF3Lktjh+X\niImBu+82KVLEwjTFyJ5XXvEQE2PicBg4nSZut8SmTU6+/dbBq6/68flk0tIkUlMlEhNFge/ee03O\nn5c4fVri7rst7r3X4vffJR591KRfvwCPPOJDkryASoMGeejRQ6dt24yseMcOmTZtHOza5UXXYcEC\nlc8/V/ntN4k2bXTGjAmQO7f4npo0cdKwoUG3bjrHjkmMGKExf77CtGl+WrbMvnvQpsG8Xi+apgVX\nIDbPa9MumeVRoZFZBZGdUU1mk5qbUay7WUMpA4FAcJq3ZVk0bNiQrVu3XvP2Zs6cydSpU1m/fv0N\nH2cUGrcF6KamppKWloZpmsTExFxz901oG++Vvrnthyk9PT2YuciyfM381oEDXl5+ORKHQ2batAD3\n3CM+nzpVZskShdWrA9nu1+1206OHxrffQmKiQs+eHl54IQ1NM4IaZK9XIjbWxaRJfmrUyN5yctAg\njb17JfLlE85cNWoYtG1rUL++gabBlCkqX36pkJDgyzYrf/VVjUBA4uOP/UHA13Udl8vFsWMOqld3\ns2mTl6JFBciePg3//CPzxx8S/fo5qFvXoGBBC48HPB6hREhMtNi6VaVixQD58xtERppERUF0NGzd\n6iAQkBg2LMB990HhwhaqCosXK7zzjsbmzWkYRsbKY8oUFytXKnz9dYYLma5DlSouatc2OHRIYtMm\nhYYNDSIiLI4dk1m82Bc8v/h4mYEDHaxe7eWjjzS++EKlcmWDo0cltm4Ndzazw15lZHZjsyO0Om//\n2EBsZ7KhfxsaoUAsSVJYsc7Onm1Av1LHsKuNmwm6toG5aZo0atTomg3M4+Pj6du3L5s2beIO26rv\nJsVtAbrnz59HlmVSU1Ov21M3tI33cpFdkexKpGuXCtEsITF5chQffaTw7rs6jRubPPqog0WLhKNY\n6H7tyvShQxZPPhnBDz+kc+pUgLg4Fz//rNG/fyotWqSjaTIffhjFvn0as2d7s23D/PNPiVq1XOzY\n4aFAAZG1Ll2qMGeOyh9/yDRsqLNsmfDQffTRrLfN9u0ybdo42bkznchIf7BQJB5GiWbNnFSrZtC3\nb9YMeeBAjX//lZg2LXPnHLRsKQphAwboFz4TILVnD7RsGcU335whb14jCFBpaSqVKsUwfXoKZcp4\ngoXNEydkKlZ0sXatlwcfFG5jW7fKjBmjsXOnTJkyJs8/r9OsmYHfD0884SYhwRt0fgsERBZfqZLB\n6tUqjRsbvP56gCZNnLz/vp9atcxMxy5WP7YZzJV6eISe48WAOJQjzvz/Qn/n9XpxOp1hWfG1dIJd\nKm7WUMpQcE9PT6ddu3bXPI7n/vvvx+/3k/eCsXKlSpWYNGlSTh7uReO2AN1QT93rBd0rGdlzqSKZ\nvZS3K6xXG6GgvWePRMeOKg4H3HOPxYIFvjAlhm1MbVkWXbu6uPtug9deSwqC8c6dGkOGaJw9K9Gj\nh4+hQ50kJCRRpEggbElr/7Rp46ZiRZPXXssKigcPSrRuLRoELAvq1DGoW9egTh2DO+8UgFSliotX\nX/XSqFFKlqxu0SKFsWM1vv3Wm2WSxt69Ek2aCLDPXDxbtkxhxAiN774LL54ZBtSq5aRTJ50OHYww\nkOrXz4nPB+++K17GtizrhRciKVQIHnnEJD5eYdMmhfvvN9m/X2buXB9162aAZp8+GpoG774buPC9\nQNeuDr76SqF+fYNhwwI8+KDF558rLFigsmpVRpZr68FtKsHlcuUI53kxIA4FUMgY1Gr/3qYzQjPi\n0N9f76y1mwW6ofs5fvw4gwcPZuHChTd0nzcibptCmv2vDSbXs62LvYdCFREXK5JdbzEu1EqxdGmL\nbdsC9O+vsHSpzLRpftq3Vy9MwbWCD8svv8isXSvz7bdnw/S2FSqYrFnjY80amc6dXTidFr/8EskD\nDxgoSsYDrOs6CQkWv/wCkycn4fEoYUtSSZL491/R7fXLLx6SkiQSEmSWL1d47TUHDzwgnL00zaBK\nldRgVmdHUhIMGKAxd64/C+AaBvTs6WD48KxqheRk6N9fY8YMfxa1wvTp4mXUvr0RvG6SJLFjB3z1\nlZMdO9KIjo7h8GGTH36QWLxYJSFBxe22qFXLoGFDD+PHm4wZ46ZCBTMMcH/5RWLZMpXduz2cPQtT\np6pMnqyRnAyTJvlp00bs0+uF0aM1vvgiQ0tsGEawkJpZIni9YSsdQrd5MSC2wwZcyFqssx317G1n\nVk2Eqi8uBcShHrc3K5KTk2/JFmC4TTLdnPTUzW4boR4NTqczTMSfOa63wSI0Uw5tqvjlFxf9+0cT\nFQXjx4slryRJeL1e2raN5MknDfr0yb6au2+fRKNGLt57z8/UqaI1uEcPnQ4ddKKjBadZsaKLt97y\n06CBP8sDLEkKDRrkpVs3H23amGFZk89nsXSpSffuUTzyiM7vvwuf3bJlha9C2bIm8+YpOBzw4YdZ\nzW4+/VRl8WKF+PisHHG/fhrp6RKTJoVTDidOSFSs6CI+3stDD9mKFR8HD+q0bp2P0qUt/H7YuVPB\nsqBsWYMfflDo3TtAr14BJMmWrkHz5jFs2nSaO+6wgUWhVasoypUzSUqSWLBA0AiRkRaJiRKffZZx\nLBMnqmzcKLNwoT/4Xfn9/iCdcbNlXfYx2LSOrQe2wTQ7pUN2j3/o7zMX6zLL4BRFwefzoapqjsi3\nLhWh3sDff/898fHxjBs37obu80bEbZfp5pTOFrIWqy41NSKnwt5/KG8bFRVFpUoy33zjYepUjfr1\nI+jY0UePHkn88ouL/fsdzJuX1RDGjuHDNfr2DdCypUHLlgY7d8p8+KHK2LFuOnbUiYqyKFjQolEj\nE0kKz6RM02T2bAVFgaZN00lLy9CfSpKwfoyPz8Mrr/iJizMwjAC//57hrzBvnsYvv8jExIhROEWK\nmNxzj0WRIhZRURbDh2tMmOBn/36JiAhwuy1cLti/X2bRIpX4eA9//SWRlia8FdLSRHb5yCMmn3yi\ncvCgGLV+7FgEDoeFLEsUKSJkX++9F6BIEYvJk1V0XeK11/QL94qKoqgMG+bkjTcM7r03+kLGb/DR\nRyrbt8vs2iXToYOHLVtSiIhQeOKJaL75JsMxLCUF3ntPY8UKb1ih7GpVKzkVoccQHR2d5RhCTcjt\n1Y0NxJmtFu2/tcNe0ttZrg3Auq4HedbsLBxz+qWT2WHs/zLd/2LkpKeuvQ27Nz67TrJLxfV2tdmy\nM5uXDeVtbb3twYM+3normp9+chARAa++GuC557KXKm3bJvPCCw727PFmcbw6dEji/fdVZsxQefJJ\ng27dhEoh9PKlpECZMi7mzfMH9as2X2lZFj/+6KBTp1xs2XKGXLnCu85Aok4dFx076jRoICr8R47I\nHDkijMmXLRMvsPz5raBSweORSE8XHr0OB+TODZGRFpGRYrikzwcHDsh07Bjgnnt83H23zv33q+TL\np1C5spsVK7w89ljGLX32rGh4+PprLw8/nPG5rULYvl0Y5sybpzBrlso//9gSMT8REQKg3nrLSVIS\nvPPOeRRFISlJZfToSHRdYvz480GOPbO29mbE9RbrstMSX8zzNjNU2MBqZ6ChFEV2fhPXC8Sh3sAL\nFy4kJSWF3r17X/P2/ltxW4Fu6Lida43k5ORgk8XVTI2ww27Fvdq3sC2vsi0NY2Jigg+Fnf3axTv7\n4RLDFh2ULGkxcqQ/zHEMROW/Xj0nHTvqFwXlt97SOH5compVgzlzVH7/XaZlS53nntMpXdrirbc0\nTpyQmDpVSMBsjwun04mqOqhd28VLL+m0aRPI8vAuWeJiypRI1q1LQdOUsGLP9u0y7do5+PFHL5ll\npLNnK0yfrrJhQ7gES5i2O+nbN52nnkoLKiMkSWLAAA2PBz76KJzC6NdPwzTh/fczPrdVCE8/bfDz\nzzJ79sg0b65z110W69YprF+fsd8TJyTKl3exfbuX6GiTCRMUJk920LSpl0GDzhMRAZkLkjerY8x+\nwWf2rbieuBgQh2qAQ3ldmwO2nxMbfDP7TeREm3Oogfn06dPJkycPHTp0uO5zvtnxf/TChbCLZHZr\n4ZW0DV/sWK7mGEJ5W4fDQUREBF6vF7/fH7wpba7Q/r19XPXrm+zf72XGDJXmzV08+aTB0KEBihUT\n+1+zRiYpSaJ16+wB9+RJ+OwzlW3bvNx9t0WHDkKnOneuSrt2TlRVmMUsWODF6/Xh9/uC10aWZebN\nUzBN4ehlH6vN66WmWrz9tpupU8XMMr/fj67rFx5YhX798jBkiJeICBPIAIuUFBg2TMtidAMwYwZE\nRRk0bOglIiJjGf/77xLz5qns3OkJ+/sDByQWLcr4/Nw5WLdOmKv//bcoQHbooLNwoYEsQ9myQsMc\nut+xY1XattVZuVLhnXdcPPmkzurV57jvPgO3OyrIm9ovfp/Pl60yJCeBOFT/fL0jqjKHDZzZmZBn\npibsUFU1TKaWuWBnA3IoEF9Lm3NmeqFo0aI5dt43M26LTNf23gzVrl5pZC6S2cuia21uuJqutuz0\ntvaDG9oyKssyDocjePNmd0OmporCzsSJGq1a6fTtG6BZMxdDhwZ4+unsQbd3b43ISBg9OmuByzRF\n51VyssWZM+D3S9Svb/DUUxY1aojJt2XLupg1y0+FClkbLUaN0vj9d4nPP88oPNkP5Ny5MlOmOFi1\n6hyWlVHgURSFUaMiOH5cNIaEXtNTp7xUqpSHhQvTKVcunFdv2dJB1aomffqES92aN3fy0EMG+fJB\nfLzC3r0yFSsabN+uMGeOL0xXO22acFRbsSKjEeKvv4TRTd68Fg88YDJoUBolS3ouWyi7lMb2eoD4\nRknRrjZs8337JZtdM0Z25uOh55HZgS3ziJ/sgNgeCSRJEsOGDaNJkyZUr179pp//9cb/t5luqA9v\n6Gh1Wyd7IyOz85l945qmGeSObc7UzmJsMIbsl7NRUTBggE6nTjrvvqsRG+smd26L2NhiTNKHAAAg\nAElEQVTsAffPPyWWLlX58UdPtr/fu1dIp7777gx58zr5+28Ha9eqTJmi8uKLDvLls8id2yIpSXSV\nhfr6Hj0q8cknKt99Fz6qRpIkPB6FuDgXs2f7iYmJCsuiDh60mDFDY+3a06SkiPO0DWI++CA3Tz1l\nZgHc9etlfvtN+ER4vfDzz6IItnKlwtatMvv3SzRoYNCvX4Bq1UwmTFDJk4cwwE1PhzFjVBYuFNfX\n54MvvxQdbfnyWXz8cTrlyomhpS7X5Qtll5N2XUtGbK/EboQU7UojVKGRHX9s03KZXzgQDsQ22IZm\ny5CRMYcCsU1p2YCenp7O1KlTOXv27H/lhZMTcVtkuqF97VfSmJA5wwxdnl1vc8OlWokzO5/ZmXUo\nbxvaNpsdn5yZb7OX7PZDazcCHDkiM368ysKFKk2bGvTqFaBkyYyvukMHB488YvL66+HZoX0tW7Vy\nU7euwSuvZJWhHTwIlSq5adNG588/hUohOtoiNlZIxNatU3j4YZO33w6QuaYZF6fx99/h0is72rcX\nxzRgQCCY0QH8/bdKw4Z52bjxLIUKCXrizBmVv/9W6dTJySOPmJw9K7F/v8z994sXzbp1Cj17Buje\n3QjSBYmJULq0mw0bvJQokXEtPvhA5YcfZCZM8PPZZyqTJ6s8+qiYE1exYhqGkfPLePtaXy4jtlc/\nNr10LcNScyJC1RFX4897JUAcuq2LtTmHPhsjRoxg06ZNHDt2jPz581O3bl0+/fTTKz6XIUOGsGLF\nCiRJIl++fMycOZMiRYpc8f+/3ritQPdyGtnQDPNiRbKcmB6RuTMuM29rm2uE2vuF8rZX82BdqgJt\nV9pnzHAxdaqTJ54w6NNHJzLSomVLJ3v3egl9t9hAt327k169Yvjxx6wWigCvvabhcMCYMYEL5yE6\n1nbvlomPV1i6VCF/fot//5W44w6Le+4RBjS5clnMnq0yaJCfQoUISsQiIsRY+rg4B5Mne/F6/SQn\nW+i6A69XYfp0jchIkVn//bfE0aMyUVEmEREW6ekSvXp5KFdODPOMipJZulTl/fdVtmwJL8QNGaKR\nlAQTJmRQF+fPw6OPuqlXT2fNGpWGDQ169vTzwAO+sDbmmwV0mTNie3xUaGfdzSzWhaojcurFc6UZ\ncejzY18P+7t45plnmD9/PmfOnOHYsWPUqlXrivefkpISxIgJEybw008/MW3atOs+ryuN/y/ohavx\n1s1Jra8kSUGdr62fDO04kyQpCHTX4kxmb+NShY88eQx69TpP584mixdH0q1bJGlpEtWrG+i6BUhh\nXVROp4vRo6MYPDiQLeAeOiSKU7t2ZdASsiwsKkuUMJg1S+W99wJ07qyj66L6f/iwxJEjEh9/rFKy\npMlvvyns2SOW9R6P0N7u3SuTP7/J2LEK0dFuoqJkIiNFYe3oUYnBg3Xuv98MArgsw+OPu5g3z0Ns\nbIZyIjHRZPjwO3n77TQCgQyvglOnbDtKkT37/YLn/fhjhfR0KFQIduzwctddIqMLBMQcuRuty84c\n9vdpF6tsKVqotePNKNZBRnarKEqO6o9tQA0tvMLFrTDt52nXrl3ceeed/Pzzz/z666+43W4efPBB\nHnzwwavaf2hSlpqaetMNb24L0IXwZYgdoUUyh8NxRd66OQW6oQUxm4MLLRLouh5cPt+IdtHMQBwV\nZdG1q0GnTsmsXq0wZ46DkiXd1K3ro1UrP9WrQ0SEm/h4B2lpEs8+mz0XPHKkRrdugTAO145vvpE5\nfFji+edFdqaqUKSIaIT49VeJEydkfvrJQ2YJ85Il8M47GmvXniMyMsOS07KgQQMn77zjp0OH8OOZ\nMEGlVCmTypUlIOPtMHOmQsGCUKuWaHawAWrkyFy0bu3ln3903nvPyeLFGiVLmrRrp7N4sZ+oKHGv\npKVdvd41J+NijRZ2pmvH9XLEl4obkd1eSWRWwNjyS/vclyxZwpo1azh9+jTlypVj0KBBDB069Jqs\nWAcNGsSsWbOIiIjg+++/z+lTuWTcFvQCZEiSUlJSyJUrV1iRLCIi4oozlmvV2dphqxeA4Higq+Vt\nb3TYVfCjR30sXx7BwoVuTp+WaN7cw6pVLuLiUmnQwAguZ+0X2s8/C2OavXs9ZGZwLAuqV3fSs6ee\nZXoDQOvWDipVMundO4NDNk2T1FQv1arlZvRoLw0bhisz1q2T6d/fwQ8/hHv/pqRAqVJuVq4Mdzvz\nekX2+8UX4YqKrVslmjVzUbCgiWFAy5YeWrRIp1gxgveF3+9HVdUbPk/sYmHrsK9HBpYTqglbmWBf\ni//Giycz6KuqyqpVq3jvvfcYOXIksbGx/Pjjj+zatYs+ffpkq8u/EgNzEHPRfvvtN2bMmHFDzyk0\nbhvQtQ2Ok5KSgg+SzdteTRiGcU2jnUN5W8hYmuYEb5uTYRhG2IBOO3vat09i9myV2bMVcuWyqFtX\njBAvX96L2y3AqV27XNSqZdCjh5EFmJYvVxgzRriIZcasHTtEI8RPP4lt2Ry8z+dj4cIoFixws2ZN\nOP9qmlCtmot+/QI0axYO4qNHq/z1l8z06eHFuI8/Vtm0SSgZtm2TWbNGISFB4fRpiXLlDF59Vady\nZRNJItjGameI9gsxlDfNbCp+I8JWZ9jdVjktA8sMxLquB9u4M5/njdL+Xk2EUhput5vk5GRef/11\nFEVh/Pjx15TVXiqOHDlCw4YN2bdvX45u91Jx24Cux+MhLS2NQCBAZGTkNRuOXO30iFCfBPtGsZdE\nmqYF+Tmbt82pzqGrjczdZBe7PpYlAHjNGoU1axR+/lmmShWD4sUNFi/W+P77MzgcGR1KqqpiWQqV\nK0fxzjv+MLcue3sNGzp59lmdjh2N4EMlwMxNbGwkM2b4qVQp/P8tXqwwfnzWYtiZM1CmjDBCt5tA\nTBN++kmiQQMXTzxhsHu3sGysX9+gfn1hvBN6yUNBP/QFmB2nCNlL9HLqO7FlYKEvwBsdNs1l88ah\n3Kl9z97MYh1kn91u3LiR4cOHM3DgQJo2bZpjx/LHH39w//33A6KQtmPHDmbNmpUj276SuG1A99y5\ncxd0oJ7r8tS1JV+2ufGlwl6K2dpJTdOCnTZ25dm+vLYL03/jZrYBxm6RvhrQSEyE9esVVqxQ2LZN\njMkpXdqkbFmd0qV1Spf2s3Gjwvz5TpYuTUJVwwFqwwaFvn0d7NiRjq6H0yoTJ2ps3CizaFF4xqrr\nok133Dg/tWuHg/Ebb2icOSPx9NMGu3fL7N4tJGsxMRYlSpi0bSs8fjPbRGZsWw/ztrgU7XS5Kvu1\nAvHFQP9mR+bONiBLEetmtDhnlqN5PB6GDBlCYmIiEydO5M7sCgjXES1btuS3335DURSKFy/O5MmT\nyX+xG+YGxG0DuvZb+0pMyC8Vl9LZ2pHZV/dSvK0NcqHV5+yWsTci+70agLnSOHMGfvxRNCCIH4WU\nFCha1OThh03uvtvg7rt1ChcOULBggB498tCzZzqNG6eHcaY2L5vZoMY0YcoUhfnzVQYNCnDkiBxU\nPxw+LLF3r1A1lC9vEBtrEhsrMtnLPZfXYwyTeTuZi1ih3gShWunstm/TO0COfSfXErZvw6UojYup\nCXIKiDM3W6iqyvbt2xk4cCC9evWibdu2t2wDxKXitgPdpKQkoqOjr+tmvhhwZ1ZDXKve9lLL2FAw\nvtYbLvNsshtZrLMsOHlS4tAhKQQchZPYwYMSx45J6HqGJtftNomMFOY1SUky+fJZF5zFpAsSMtA0\nuPNOMcJdSMTE4Mp777UoWtSiQAEriy/DxY8vgzO9UfTO5bTSoU0Ol6N3bnRkHlR6tZRGTgGxrZm3\ns1u/38+oUaP4/fff+eSTTyhcuPD1nur/bNw2oGtnHcnJydddCDh37lyYd252vO2l9LZX+2BfyUN7\nJUD8v7JszZxVKoqG1yv0uMIX1yQlxcQ0jf/X3rlHRXGeYfyZXRBYrl4xCg2oCKLInSUXNKRqQoyK\n5lRMLxo0HrUn3mLFpLVeWhWNtyRitDmm1taIVistPYIaQtC27kLEejlFMaJQFUERL1yUBfbrH/ab\nzA57353ZZZnfOTmJMtn9Ztl5553ne9/nhYdH5/8DMQM/Pzl8fORwd7fPBpajNFNA93dK5SYAFv9O\n7bkeoXwbLAnEALq0El+4cAHLli1DZmYm3n33XYfseYiJy9TpUuzZ3AB8r9tyrR5pKQ633pb+3JoL\n21SDA20DNVb+Qy8omUzmkKJ+umbuhc2tM/X2Bqf7Tfb/f559VroOVhq0tdmmm3IfW/nObGJBi/81\nGo1OVsmVJuh0W6EDsdC+Dfz6Wvqe3POk1wjw7LMpLi5GeHg48vLyUFpaii+//BJDhgyx67qcFZfJ\ndKnTmD08dR89egRPT0822DlLva2h8h+6HprdOiJT4GqVVJ+zFmO6qb6SLi7WegTYG3O9bul3iltJ\nQG/otrb9cm+Cjn7yod4oNGmZNWsWzp07h+bmZiQnJ0OpVGLDhg0WrW/27Nk4duwYBgwYgEuXLnX5\neUlJCaZMmcIG87feegsrV66023lZi5Tp8qAXPDVMphMgqO7K121pa68YcN2raDbX1tbGXpTPmg2a\nAdhPHzYFV0qwl1apr02UL8Hws0T61MHtAHS0ZmpOVmnoKcfWbjNuduuoJx+6jtbWVgBg/Ux27tyJ\nJ0+e4NSpU+jbty/Ky8tx/fp1i39fmZmZWLhwIWbOnGnwmLFjxyI/P9/6ExAAKej+H65uSwiBp6cn\nevXqpVe3lcvlTvEI7+bm1mUelqngZK9HWP46hJ4NZiw4UR2bng9dk5j1pvqkFWvfk3tz5b6+OYGY\ntqDT7NYR0gpdL/086M34xo0bWLx4MVJTU1FUVMTeUNPS0qx6j5SUFFRXV5tch7PhMkHXlOmNMfi6\nLXfKAfVM4P7cEV6mgG43maF12EMftsc6xIBmlYQQdoKzkJ4EhuB+HkLdjM0JxFzdlI5e5+qoYkGz\nbPp5MAyD3//+9zh48CBycnIQGxsryjoYhsGZM2cQHR2NwYMHY8uWLYiMjBTlvY3hMkGXwq0qMAUN\nprQLhuq2crmc1eS4zQ10rLXYmNtNZghuIKZDOw1dsMbqh4WQEqyBu1HGX4ex4ERLtgydq6UVE9xq\nEUd8HlyNmyYKvXr1gpubm84GFtB1U1KI9mZ9GnJtbS0WLVqEmJgYFBcX27TXYilxcXG4efMmFAoF\nCgsLkZ6ejqtXr4r2/oZwmY00AKzGacoPl1tv6+HhAU9PTzYbBHR1W3oBczNFczZ07IGt3WSWYqx+\nmMorjjSFAey3UWZryy+tM7Vn44k1mNNsIUZ7M79CgmEYHDx4EHv27MG2bdvwwgsvCHKNVFdXY9Kk\nSXo30viEhoaivLzcrG5TIXGpTJfevQ1lujSIUUMNugnG3STjGm7oe1Q0ppnaU0fkdpOJpR/zS39o\nYwH12qWbVS0tLaLXmtp7GKO+c+VmxNSWk3+DpYNCbe1ssxVLsmxj50o1cVsCMX0qpBryvXv38P77\n7yMoKAjFxcVQKBT2O3ELqK+vx4ABA8AwDMrKykAIcXjABVws6ALQ0bG48HVbvr8tzVxM6ZSW7jbz\nL1hTiNlNZgxDj/D21ofNWQd3g0qoahFzKibouQLQ0Y/FanCgcLNba27Ihs7V0E3HUCUMv1JDLpcj\nPz8f27dvR3Z2Nl599VVBP5e3334bp06dQkNDA4KDg7F27Vq0tz+bCjJv3jwcOXIEu3btgpubGxQK\nBQ4ePCjYWizBpeQFrqcutWbk6ra0ucGYT4K9dDlDj3SGZAln6iaztG3WUP2wrf4SzuJTwL8RyuXy\nLnW1Qm7UUcTWkI11StInxEePHsHf3x9arRbLly+Hl5cXtm3bZrUfdU/ApTJdegend22ubuvv788G\nB3osVy+1dwal75HOkCxBM22ZTObwagBrOpf0bV7xM0RL/CWMbZSJibEs2951tabg3oCELs+j6Huq\no9+Rjo4OuLm54ciRI9iwYQM8PT0RExODKVOm4O7duxYHXVONDgCwaNEiFBYWQqFQ4A9/+INoVRD2\nxqWCLoUQgkePHrF1rPp0W7FbZvV9gek6aMAlhLB6qaWyhC0IEeQsuelwAxPNKsWo/TWGJTcgcysm\nAMs1U74Tl6PkJkB3qoSfnx+am5tRU1OD9PR0zJ07F1VVVTh79iyef/551q/WXEw1OhQUFODatWv4\n7rvvUFpaigULFog+ZsdeuJS88OTJEzQ1NaGzsxM+Pj6sbksIYbNJWgZGv8COgO8NwJUShHYg48P1\nbBC7KoGvD1M9zlGTb+mahJJ5LK0ioPsMjm5p5pYKUg+JM2fOYOXKlVi6dCkyMjLs8hkZq0SYP38+\nUlNTkZGRAQCIiIjAqVOnEBgYaPP7io1LZbpUc2tpaWGzW/pleDbh1fH1paa6uCzJEG0JTNxMzlE3\nILqZQw3f6e+GG4jNqR+2F7ZuUJnCUBUB1Ye5m1e0CseRfhqA7vgcX19fPH36FKtWrUJNTQ3++te/\n4rnnnhNlHbdv30ZwcDD756CgINy6dUsKuo7Gw8OD1Zqampp0BH93d3eH9qBb28Vl72oJZ3DgohgK\ncvzJt7bow+bgKA2ZBlfasAJ8X34FgDWHod9lMcv0+Nmtu7s7ysvLkZWVhblz52L79u2i3wj4D+WO\n+t7aissEXa1Wi3nz5qGurg5xcXHw8fHBpUuXkJ2dDYVCwT6+ipEx8ddlSzeZPqzduKIXkkwmc6he\nyr2gzdEprdWHzQlMhkaei42xz4RfHSJ0mR7/M+no6MC6detQXl6O3NxchISE2PweljJ48GDcvHmT\n/fOtW7e6rdG5ywRdmUyGL774AiqVCgsXLsStW7cwZswYzJgxA2FhYUhMTERycjKGDh0KAOyjHPdC\ndXNzs2t9Kbc6QugL2lhgotkwtYGkm4li66WAruWhtZ+JPfwl9OmUjtygoo/w+j4Taw1w6DmZe176\nNu0qKipY3bawsNBhN6XJkycjJycHM2bMgFqtRkBAQLeUFgAX20gDgBMnTqCyshILFixgH88qKyuh\nUqmgVqtRUVEBT09PxMbGIjExEUqlEv7+/nprLmmGaOkXTYjZZNbA3xTi6qX88xW6WsIRUxwM1Q9T\nG0y5XO7w3w//Ed4WbGn35W/aabVa7NixA0VFRdi9ezfCw8NtWpspuI0OgYGBXRodAOC9997D8ePH\n4e3tjb179yIuLk7QNQmFywVdUxBC0NzcjLNnz0KlUqG0tBR3795FcHAwEhISoFQqMXLkSLbawRL9\n0Fm6yQDdR0Ra0K8PoaslnKXpA/i+UUar1ep0lAHi+Q9TuNmtEHPbKOYEYiq90e/stWvXsGTJErz2\n2mv4xS9+4bC6cVelxwVdfWi1WtTU1LDZ8IULF0AIwejRo5GQkIDk5GQEBgbqfIG51QN0B97UQEqx\nzoXrUWDpY7OxLiR+9m+JXmos8AuNPvcrrl5qj/l0lqzFntmtNe+vr0zvn//8Jw4dOgQvLy9cvHgR\nn3/+OZRKpVXvcfz4cSxZsgSdnZ149913sWLFCp2fO+tEB7GQgq4eqLZ1/vx5NhuuqalB3759kZSU\nhKSkJMTExKBXr16ora1Fnz59uvSoi60RCplR8h/TTckwlm6UCYk1rcT8wGSvVl+unk2HmzoCfjux\nu7s7zp8/j61bt6KhoQFPnjxBRUUFFixYgK1bt1r02p2dnQgPD0dRUREGDx6MxMRE5ObmYsSIEewx\nJSUl2LZtm9NNdBAL6blBDwzDwNPTE8nJyUhOTgbw7ItaX18PtVqNkpIS/OY3v0F1dTXc3d2xfPly\nvPTSSwgJCWEDNtXHhNik4yO0I5kl1RK0vtTRHWW2lIHZy3+YuxbaOuuI7JYLd3wONRg/cOAA9u7d\ni48//pjNbtva2vDo0SOLX7+srAzDhg1jKxxmzJiBv/3tbzpBF3DOiQ5iIQVdM2EYBgMHDkR6ejqC\ng4OxZ88eLFu2DOPGjUN5eTk+/fRTVFZWwsfHB/Hx8UhMTERCQgJ8fX31lvlYu0nHxZEaMr9agmsB\nSfVSbn2pJbKErQhRBmZtmR79HQnpkGYOXImF3oTu3r2LJUuWYMiQISguLoaXlxd7vIeHBwYMGGDx\n++hrYigtLdU5hmGcc6KDWEhB1wpiY2Nx6dIlthsnMTER8+fPZz0fysrKoFKpsGfPHjQ2NiI0NJQt\nWQsPD2fNdkw5jxmCX47m6IvZUEZpqqzJHjce/lrElDUsKdOjvzOxNuq48MfnyGQy5OXlYceOHdi0\naRPGjh1rt/WY8zrOOtFBLKSgawUymUxv+yPDMAgICMCECRMwYcIEAM++8FVVVVCpVPjyyy9x6dIl\nyGQyREdHsyVr/fr1Y0fId3Z2GtUOaUYJCNOqagmmMkpD9aVUJ7Vnd5k96n9thcoSdKQ6nfbBNb8R\nurGBi74NxAcPHmDZsmXw9/fHV199xU67thf8JoabN28iKChI5xhfX1/2v9PS0vDzn/8cjY2NTmEw\nLgbSRprIEPJsvPu5c+egUqlQVlaG27dvY+DAgUhMTERSUhJGjx7NzrmiQYlrgkInFXfXCgkufP8B\nS6sl7D1Rwha4pt7GapGF8h/mr4XrkiaTyXDixAls3LgRa9asQVpammD7C+Hh4fj6668xaNAgJCUl\nddlI4090mD59usmpvq5Etwy6hw8fxpo1a3DlyhV8++23BoukQ0JC4OfnB7lcDnd3d5SVlYm8UvMg\nhODWrVtQq9VQq9U4d+4cNBoNRo0ahfj4eDQ3N6O9vR3vvPMO6yXhCK2U7y/r6ekpyHuaUy1By/So\nxCLUWsxdr62fiz3rpbnjczw8PNDU1IQPP/wQ7e3t+PTTTwXPKAsLC9mSsTlz5uDDDz/E7373OwDP\nGh127typM9Fh27Zt7IZ1T6BbBt0rV65AJpNh3rx52Lp1q8Gg6yyD6KxBo9Hg8OHDWLlyJTo6OjBy\n5EgwDIP4+HgolUrEx8fDy8tLtM4ya0qv7Ak3G6b/Br4PSvS8xQ68QnXaWVM/zM+05XI5/vGPf2DV\nqlXIysrCW2+91W1NYlyJbqnpRkREmH1sN7ynAAB69eqFyspK/OpXv8Ls2bPBMAzu37+P0tJSqFQq\n5OTk4PHjx6yvhFKpxLBhwwDApk06Ps4yxYHqw3SuHW1rpsGIawYvxhMAXy+1t1ubpf4S1E9Do9Gg\nd+/e0Gg0WLNmDWpra/H3v//dKp8CU00OgOtMcxCTbpnpUlJTU41mukOGDIG/vz/kcjnmzZuHuXPn\nirxCYdHnK+Hh4YG4uDgdXwm6sWOpIYojDc75mJNp06BkaH4ZNxu2JUDy9VJHbmbSulu6Abt+/Xrs\n27cP3t7eiI+PR2ZmJl5++WX079/fotc1p8mhoKAAOTk5KCgoQGlpKRYvXtxtpzmIidNmuuPHj0dd\nXV2Xv9+wYQMmTZpk1mv861//wnPPPYd79+5h/PjxiIiIQEpKir2X6jDkcjkiIyMRGRmJOXPmdPGV\nOHDgAO7evYugoCB2k27UqFFgGEbvCBm+BaQzbE5ZMq7GUHZoqFqCH4jNWYuQ2a2lcMfneHt7s5/R\n2LFjMXXqVNy4cQOff/45GhsbMWfOHIte25wmh/z8fMyaNQsAoFQq8fDhQ9TX13db9y+xcNqg+9VX\nX9n8GrSsq3///pg6dSrKyspcKujyYRgGvr6+SE1NRWpqKgBdX4mjR49i9erVrK9EfHw8kpOTMXDg\nQDZ76+zsZCc60IkFtNZUbExZHpoDwzBwd3c3OK2BL0sY6h7k17o6MrvV599w8eJFvP/++/jpT3+K\n7Oxsm59KzGlycKVpDmLitEHXXAypI/SRy9fXFy0tLTh58iRWr15t9uuaWyFhju7lSGQyGUJDQxEa\nGoof//jHXXwl1q5di5qaGri7u+P+/fsYPXo0tm3bxuqlXN1QrGGZQrbN6pvWwJcl+LW0NMP18PBw\nqJkR0HV8TkdHBzZv3ozTp09j3759Fg+ENIQlHrzW/H89GceJdDaQl5eH4OBgqNVqTJw4EWlpaQCA\n2tpaTJw4EQBQV1eHlJQUxMTEQKlU4s0332QbFswhKioKeXl5GDNmjMFjOjs7WY/PiooK5Obm4vLl\ny7adnMBwfSWWLl2KgwcP4vXXX0dFRQVeffVV/OAHP8DPfvYzTJw4EVlZWTh69Cjq6urYwKfRaNDU\n1ITHjx+jtbUVbW1tbJ2prdDg1tTUxGbtYkgbVJbw8PCAQqGAr68v/Pz84O7ujvb2drS3t7NdhK2t\nraz0IuZ2CL0Rtba2wtPTEwqFAlevXsXkyZOhUChw8uRJuwVcwLwmB1ea5iAm3TLTnTp1KqZOndrl\n7wcNGoRjx44BeLaJdv78eavfw5wKCXPNPZydF198EfPnz9d5LOzo6MB//vMfqFSqLr4SCQkJSExM\nhIeHB7Rard4uK0unFlgy8lxo+C5cXNMbS2UJe8Dv/COE4LPPPkN+fj4+++wzjBo1yq7vBwAJCQn4\n7rvvUF1djUGDBuHQoUPIzc3VOcaVpjmISbcMus6CObpXd2D8+PFd/s7NzQ3R0dGIjo7W6yvxxRdf\n6PhKKJVKREREQCaTGd2k4wckviWlozenuFUSfO3WUlnCmpsPF32biDU1NVi8eDFeeuklfP3114I9\nCbi5uSEnJwevvfYa2+QwYsQInSaHN954AwUFBRg2bBg7zUHCND066NpaIdGT9CtTvhIHDhzQ6yvR\nv39/g3W0DMPg6dOngllSWoK+7NbU79dQtQTXINzcmw8f7vgcHx8fAMC+ffuwf/9+fPLJJ0hMTLTx\njE2TlpbGSncUOjqHkpOTI/g6XI0eHXRtrZAwR/cyRWNjIzIyMlBTU4OQkBD8+c9/RkBAQJfjnLGl\nWSaTISwsDGFhYZg5c2YXX4kPPvgAtbW1GDhwIDsKafTo0SCEoKqqCoMGDQLwLCC1t7ezWaLY9cA0\nu2UYxmazHL7JD62W4PrwGpMl9GW3dXV1WLx4MUaMGIHi4mJ4enra69QlHEC3buWvq/wAAAlOSURB\nVI4Qg9TUVGzZsgXx8fFdfmaOuYcpsrKy0K9fP2RlZWHTpk148OABNm7c2OW47trSzPeV+Oabb3Dz\n5k2EhYVh7ty5iIuLw/PPP6/zmC7UqBx9azO3Btje76uviYOW53V2dqKxsREhISE4evQodu3ahc2b\nN+Pll1+2aX3d+QbvSkhB1wB5eXlYtGgRGhoa4O/vj9jYWBQWFqK2thZz585lN+z0mXtYQkREBE6d\nOoXAwEDU1dXhlVdewZUrV7ocFxoairNnz6Jv3752OT9HcPToUbz33nv46KOPMHz4cJSVlUGtVqOq\nqgr+/v5ISEhAUlISEhIS9PpK2EMnpfCn3zqy244G/7a2Nri5ueHWrVt4/fXX0d7eDj8/P8ycORMp\nKSkYN26cTefs6jf47oIUdB1M79698eDBAwDPLr4+ffqwf+biCi3Nzc3N0Gg0XS5mQoiOr8S3337L\n+kpQWWL48OE67mOAdQ5cjspuDcEdn0ODf0FBAT766CMsXbqUzTSvX7+Ov/zlLza9V0+6wTszUtAV\nAUMbduvXr8esWbN0gmyfPn3Q2NjY5dg7d+7otDTv2LHDpbvrzPGVCAgI6OLAxW/g4AZUbumVM2S3\n/PE5jx8/xooVK8AwDD7++GP07t3bru/Zk27wzkyP3kgTC2MbdjTrGDhwIO7cuWNwLlVPa2nW5yvR\n1NSEs2fPQq1W48CBA6ivr0dwcHAXXwn+4EiZTMZqqLTDzdHZLX98TklJCdasWYNf/vKXSE9Pt3p9\nxm7wXIzJM67uWeJopEzXwWRlZaFv375YsWIFNm7ciIcPH3bR2fgtzRMmTMDq1avN6rBzZXs+rq+E\nWq3GhQsXQAhBVFQUK0s8fPgQT58+RWRkJAghok1o1oe+8Tmtra349a9/jcbGRuzcudNiNzBLiIiI\nQElJCXuDT01N1SsvcFm7di18fHywbNkywdbV4yASDuX+/fvkhz/8IQkLCyPjx48nDx48IIQQcvv2\nbfLGG28QQgipqqoi0dHRJDo6mowcOZJs2LDBrNfu6OggQ4cOJTdu3CAajYZER0eTiooKnWOOHTtG\n0tLSCCGEqNVqolQq7Xh24qLVasmTJ0+ISqUi2dnZJCwsjPj5+ZEf/ehHZM2aNeTYsWPkzp07pLGx\nkdy7d4/U1dWR2tpaUl9fTxoaGsjDhw9JU1MTaWlpsfs/TU1N5O7du6Suro48fvyYNDc3k6KiIpKU\nlET2799PtFqt4J/P8uXLycaNGwkhhGRnZ5MVK1Z0OaalpYU8fvyYEEJIc3MzefHFF8mJEycEX1tP\nQsp0XRhqaHP8+HEAYDPoDz74gD1m/vz5SE1NRUZGBgDdzZbuzDvvvAOtVovt27dDo9FArVajtLQU\nZ8+eRWtrKyIiIlhtODQ01C6bdIbgj89pa2vD+vXrcfXqVezevVs0v4LGxkZMnz4d//3vf3VKxrgV\nOdevX8e0adMAPNPAf/KTn1hckSNhHEnTdWF6sj3f7t27dZoIuH4dXF+JHTt2oLKykjX9TkxMRGJi\nIvz8/NDZ2clOaDa1SacP7vgc6idx/vx5LFu2DJmZmdi8ebOom3l9+vRBUVFRl7+3p2eJhGmkoOvC\n9GR7PmNdW5b6SiQlJWHEiBHsMEx+a68+u0ua3bq7u8PHxwcdHR3Izs6GWq3G/v37MXToUME/Awnn\nRAq6Loxkz2cehnwlrl27BpVKhdzcXFy8eBEymQwxMTE6vhJarRZtbW06nXS0oaNXr17w8vLClStX\nsHjxYkybNg3Hjx+32WPCVbyeeywOVZQlBKW9vZ0MGTKE3Lhxg7S1tZncSFOpVFZvpBUWFpLw8HAy\nbNgwdrOGyzfffEP8/PxITEwMiYmJIb/97W+teh9HodVqSXNzMzl9+jTZtGkTmTZtGklOTiZTpkwh\n69atIydPniQFBQVk79695M6dO+Ty5cvE29ubxMTEkKCgIPLJJ5+Q27dv22Utly9fJpWVleSVV14h\n5eXleo8xZxNVwjFIma4LI5Y9HzVz5w4xnDx5chcPirFjxyI/P98u5yY21AktJSWFrVkl//eVKCkp\nQVZWFqqqqjBmzBioVCqEhIRAqVQiMjIS/fr1w8mTJ5GdnY3r16/Dy8vLprX0JK9nV0QKui6OGPZ8\n5l7gxMUKZRiGQXBwMK5du4aoqCgUFxfD29sbFy5cwJ/+9CcsWbJExyKUiDhrzlW8nl0RKehK2Iw5\nFzjDMDhz5gyio6MxePBgbNmyBZGRkWIvVRBWrVqlo9PSCgg+lgRcyevZdZGCroTNmHOBx8XF4ebN\nm1AoFCgsLER6ejquXr0qwuqERwjzdWfwepYQhm45mFLCuTDnAvf19YVCoQDwTPJob2/Xa+wjYRmG\nJBvujDONRoNDhw5h8uTJIq9OQh9S0JWwGXMu8Pr6ejZAlJWVsS5XljJ79mwEBgYiKirK4DGLFi1C\nWFgYoqOj8e9//9vi93B2zJmGzd1EjYyMREZGhrSJ5iw4snRCwnUoKCggw4cPJ0OHDmW9IXbv3k12\n795NCCEkJyeHjBw5kkRHR5MXXniBqFQqq97n9OnT5Ny5c2TUqFF6f+5KXhISronkvSDR7aiursak\nSZNw6dKlLj9zVS8JCddBkhckXApDXhISEs6CFHQlXA7+w5szlk8dPnwYI0eOhFwux7lz5wweFxIS\ngtGjRyM2NhZJSUkirlBCKKSSMQmXort4SURFRSEvL69LowofhmFQUlIiDYl0IaRMV8KlmDx5Mv74\nxz8CANRqNQICAqzWc01VSpSUlLCTomNjY7Fu3TqzXzsiIgLDhw8361hp28W1kDJdiW7F22+/jVOn\nTqGhoQHBwcFYu3Yt2tvbAdjPS4KSmZmJhQsXYubMmQaPEdpPgmEYjBs3ThoS6UJIQVeiW5Gbm2vy\nGFu9JCgpKSmorq42eoyxLNTWVl5AGhLpikhBV0LCSkz5Sdjaygv0vCnQPQFJ05WQsBLqJ3HhwgUs\nXLgQ6enpVr2OoWy5tbUVTU1NAICWlhacPHnSaCeeRPdACroSElZii5+EOa28dXV1SElJQUxMDJRK\nJd588012soVE90XqSJOQMIKx7rf6+noMGDAADMOgrKwM06dPN6kBS0hImq6EhAFMVUocOXIEu3bt\ngpubGxQKBQ4ePOjgFUt0B6RMV0JCQkJEJE1XQkJCQkSkoCshISEhIv8DUxa/rTDZ+loAAAAASUVO\nRK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# indefinite\n", "z = x**2-y**2\n", "\n", "ax = gcf().add_subplot(111,projection='3d')\n", "ax.plot_wireframe(x,y,z)\n", "ax.set_zlim3d(-3.0,3.0)" ] }, { "cell_type": "code", "execution_count": 5, "id": "17619f1d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-3.0, 3.0)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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JrgtoGiiKRayGYZGy/RlBsAjVNHcQtSxbv2P/vnV8sG2bwLZtAl9+6eG225oB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\ng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UhOTsa8efOQlpbmxRMyPAUrGWPwCn/RkkhKSsLly5ctGlXM4TgOMpmMDYnkEczTZfCK\ntWvX4syZMwAAhUIBoVDodDx3uEoJmUxmmBQ9b9487Nu3z+HPjouLQ2xsrENrWdqFXzBPl+FXbNy4\nEbdu3cLr168RGRmJvXv3QqvVAnCfloSeTZs2YevWrcjNzbW5xtN6EhzHYdmyZWxIJI9gRpfhV5SV\nlQ27xlUtCT3p6elobm62u8aeF+pqKy/AhkTyEWZ0GQwnGU5PwtVWXiDwpkAHAiymy2A4iV5Por6+\nHlu3bkVWVpZTn2PLW37z5g16e3sBAH19faiqqrLbicfwD5jRZTCcxBU9CUdaeZVKJdLT0yGRSCCV\nSvHpp58aJlsw/BfWkcZg2MFe91tnZyemTp0KjuNQW1uLDRs2DBsDZjBYTJfBsMFwlRIXLlzAiRMn\nEBQUhJCQEPz6668+PjHDH2CeLoPBYHgRFtNlMBgML8KMLoPBYHiR/wEL7+qZIqeaogAAAABJRU5E\nrkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# negative definite\n", "z = -x**2-y**2\n", "\n", "ax = gcf().add_subplot(111,projection='3d')\n", "ax.plot_wireframe(x,y,z)\n", "ax.set_zlim3d(-3.0,3.0)" ] }, { "cell_type": "markdown", "id": "bcc44550", "metadata": {}, "source": [ "(definiteness of matrices)\n", "\n", "positive definite:\n", "\n", "$$ M = \\left(\\begin{array}{cc}1 & 0 \\\\\\ 0 & 1 \\\\\\ \\end{array}\\right) $$\n", "\n", "indefinite:\n", "\n", "$$ M = \\left(\\begin{array}{cc}1 & 0 \\\\\\ 0 & -1 \\\\\\ \\end{array}\\right) $$\n", "\n", "negative definite:\n", "\n", "$$ M = \\left(\\begin{array}{cc}-1 & 0 \\\\\\ 0 & -1 \\\\\\ \\end{array}\\right) $$\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "6ab4af60", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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F0h59cTWxsLDApWdP0vbvf+h1mjK/Rs7O1LW1NXic29wmhxwcaGHwWJVl586z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\nkZgl/w//ssZoWLoNJwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# level sets and contour plot\n", "figsize(5,5)\n", "x,y = meshgrid(linspace(-1.2,1.2,20),linspace(-1.2,1.2,20))\n", "z = x**2+y**2\n", "contour(x,y,z,levels=[0.5,1,1.5])" ] }, { "cell_type": "code", "execution_count": 7, "id": "06d318bc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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e93zTpk0r+tpoNGI0GitSnhDCBkVERBAREfHQ7SoUfmVdtqEod1+kuLTHFQ8/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\nQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# ellipses\n", "figsize(5,5)\n", "x,y = meshgrid(linspace(-1.2,1.2,20),linspace(-1.2,1.2,20))\n", "z = x**2+2*y**2\n", "contour(x,y,z,levels=[0.5,1,1.5])" ] }, { "cell_type": "code", "execution_count": 8, "id": "bda7595c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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yBy+783tO0EyJzt2bTxRmY4Osans9UIvCzdp2tJ05HlZ7iEWvAeT6QT9UtNyq\n82RUoHlA6aF1dudK80LegzVHbd5au/pgWqBDvMx8pwRZdHzvmGVBgXhabvQc6j0eyDkq+Si8rDGs\nsa1ciQ/onAbNdsvZc1CyIPPmU/0pkz3wmTKyDe5VwXdskEW31wu1ariN9eGizaNtW9dS5rhZ/Twv\nOv+IZr/lJOo7KKgX2Ulan8w8pU8czetR70WIzKnng0T7tEVfyNia1/P+svs1oiqYoR+yWYBVeZl5\no5odaD1vLgq5zCdSxc5HD3j2E77qQsxcPD2wiSgKTR7X2prXu08zx673eGhzsnI0SdeKdcwRLzrf\njNbHNgDIZT5lelcGGfWsJrJz98aqVjs28hjC+tiGnCNtv9X62EZA2U+TKpB5c9NgG/2UsSCneVUl\n6ll1z+OqOgaokO1l3lv0A6HymEXn3Lso6D1m0WsysziIaBG3nJk3bfXnXvbgZXd+zwmaKdG5e/PJ\nwKziouiVN4ceqEXhZm072o4eD/Q6il4DyPWD7n8tt+r8me2WU/OjnzDauN4FjV6IPZ8yWrv6YFqg\nQ7yx51t1siK3du22Mrdw3GtjiKfleu2eOQ7vOTK+JOk4Wbfi2hjobaj3PjLnzfrYRtOv+lMms4Ka\ne5UW8SyNsXKLjtm7+omuznqOXeXxiC4KMsfJ6ud50flHNPstJxH+piouXnQ+2R3dexFllb0Itdyo\n1+ZUQqx3O1XnReX5VTV2FhjeuFFVnDOZfpIWAbRVq1atqtAKtFWrVu2MVqCtWrVqZ7QCbdWqVTuj\nFWirVq3aGa1AW7Vq1c5oBdqqVat2RivQVq1atTNagbZq1aqd0Qq0VatW7YxMoD3++ON0/Phxuvvu\nu/djv/nNb+jMmTN055130gMPPEC//e1vR5/kqlWrViEygfbYY4/R+fPnb4g9//zzdObMGfrxj39M\n733ve+n5558fdYKrVq1ahcoE2v33309vfvObb4h97Wtfo0cffZSIiB599FH6yle+Mt7sVq1atSqg\n8L+HdvXqVTp+/DgRER0/fpyuXr2q5v7whz/cr99yyy107NgxMW/496MysV5PU3T7Wk71vDz1bm/M\n/pVC/9lrK6/in86uUHaOyPy1nMr3PsY+bvv98pe/pF/96ldQv65/4HGz2ZgTfsc73qH2I5L/MT4P\nBtY//tbzD8NJ/xge971YpK15vaU0P2/umXlakv7RvgpFLw6e37YjXhtDvGjZMzep7eXwXO861mT1\n07zMfI8S2419AAAgAElEQVQdO3bDYujll19W5xT+lfP48eP0i1/8goiIrly5oq662slqOw59w9bY\nUU+bm5eHxNA2+h6jilx0kTkh79+aU9ULlXd8UC+6P3tVBTUtJ3pNVF576DXD32f0PAgD7aGHHqKz\nZ88SEdHZs2fpQx/6UHSIG9R7MFAvc3FUfcJET9RsKY3rvYfsRTTEorAZS9ZcqmBm7feqY1f5IYOc\nv56qIOfFqs4hE2iPPPII/cVf/AX953/+J506dYr+6Z/+iZ5++mn693//d7rzzjvpm9/8Jj399NPh\njfYcjKodas0NuTCsOWrtCMzQbfbCLTNHbYyp4YZsswdmUi7izQU1LV+LVRyv6DU5FngHmd+hnTt3\nToz/x3/8BzS4Nqnhe52h3uZ736tZcc9D5oeOyeeqzT/zPZWXr/XhnjVuz1z5vpC2P2iMHz0yeRlQ\n93xIRNUDtV5AZACXWVxEAZzZt7P/pUDPwch+OkQPHDqu1i+6Mqj6pEe96JyHNrIPK1YBvdvLvM/s\nvuw5Zh50LGVXQtpY2nWSBVnl/CyN+t/YoZJWBET+r6ART/OtOUlzQFZSbb/ISqhC0dVZZH7amIPQ\nVVu1IiCIQDs6dlbWBxzqafOxPtQj88uADJ2TNs+MZlmh9RA7u2PROVmfMl6scmUw5eqs96JvvTHB\nFd1e9n3NvTrrOR6RlY93znvKrtay80U0KtD4DrM+cbRY9lPB2ynowczCtwoSEUXh1nMRzQm27DGT\n6paX/bDIqvJDJnrM2hzvusiCLApjjx+SFvcdmhSr2LmZT6OqT5joidrzSa+NhcwnMu8hNiXYstur\ngpm136uOXeWHDHL+eqqCnBerOk9mu+XkbfRgVO1Qa27IhWHNUWtHYIZusxdumTlK/ccEW8/4PTCT\nchFvLqhp+Vqs4gMnek2OBd5Bo/4ooE1qfWzD9rx8rQ/3rHEr59rmEen7vupTGB2vAtSa731IRNUD\ntV5AZACXWVxEAZzZt4u75YwcjOynQ/TAoeNq/aIrg6pPetTLzBm5QMZSdPuZ95ndlz3HzHtPlrIr\nIW0s7TrJgqxyfpYWectZtSNbr+pgetu1LibP6xFyoWheZr6tnzkuGWWOc/a98pyop83RKnvni56P\n1jmuzduDVS/IquC2uFvONtb2l2Jaf8nz5qT1seaAzF16r5qHzG2z0f+VDcmz+vXMV3v/iFcha0zk\ngyji9XxIREqpjnoZ2EljeMDr9awY75s5b2Z5sJZfhIMiwOBxPobkSf2tXGlOaEz6zsmDhvfPA/F5\neeCSYhpEo2CT9ln0wyWiCMC0eBRkbT0CtWw51DNgs/K1mAUgadwIwJDta/Pm+ySiQ79C08bQtqcJ\n/SsDKWbN3YKXlIeWvE87rhXT5pUBm7YPEK9HUbj1gKytjwmzCLwi0LJiXBbsEABafgbAmXPm0K/Q\n+BhSTrs9r680DnIB96zQKqAm9Udi1rw8T9p/Y99qcqFwQ0HWtqeEWgReUp4X08CBgEpSFHBIjPfN\naOdWaNZ2tblIykBMiiErochtp3Ybmr0FReased7+sfZvVijAtFgUclNALVKXto9Ag8e9/RiFnpeD\nxHjfDNQO3QqNx7mn5UhzsJSBGJ+7By8pLwq1drvRW1Brnoin7cupVmkRuEVBptWrYYZsF4FcG0Pg\nxj0EWlZf1LdivH9Gh26Fpo0bXaVFbkGzt57RW822PsUKzZob6nn7g3s9igBMimcgNwXUEGB5wIvC\nDQFXBHaob8V4/wzUdmKFxv1ontUnAjE+dw8I3qqpcoUmjcvnY82Ve9b+8LwKReCWAVlb98AyJsxQ\n4LUxNC75GXhFAGfFeP+MdnaFFsnz5irlRFdokVtNKda7QmvnEYWX9kETgVjvKi0CMC0eBVlbr4Sa\n5mXrHjisuAc7ayxrTC3HivH+Gajt9Aqtzfd2DjJm5EKO3F629SjU2u2i43l1633w9z/HKi0Ktx6Q\nafUeqGlepq5BAo1rOZEXMpY1D22+Ge3MCo3n8HlEV2bWNpGLmEMbrUeh1m5XG8/y2/cQBZv1/iVv\nDKFwQ0GmeSjgkDICM3S+WbihgNKEjmHNQ5tv5vw5lCs07mk5iFDQoatFDQBovef2c6rbzQjEem81\nuVCAabEM5CqhpnnWmFa9B2KaPOB5Y1h5VoyPkdGhXKFZY0u5kblJY2Qu4AhMqqGW2SafO+Jl9k+l\nInDrARlS74GZBy2tfzsHBGJcGVghfa18K8bHyJw7s63QiPRfzbxYq+xKLQtI9OLtWS31Qk0bM1Jv\n34/3PRrfF5aXVQReWnwOqEVB5wGM+xYUEA+BUGW+BC0tJ6NZVmhE8q2LBAsPZNk3ro2nzQWdU2Q+\nGlC437PNKMwy7ykLuYyiYBsLaijQeNkLNg0EGZDx9977yowl5UvHBtXst5xWrOICyV5Q3kWKjNf7\nPRo6dnR+FsxQr2IeWfVALQO4LNyyoKuC2djgyYwvxa3cqGZbobVCL5QISPgcIreYyDaj8cw2Ws+D\nXQRiPfNo20TTrMo0RcCWgRoKL8n3oGXlZOGGAiIKMm2fZcGG9Je2iWh2oFXCLHIhRb647oFa9DYv\nskrz5urtx8qVGuplFAGX5fVArQdkXtlbR2EWgVD7/nrhiORZ845odqBpO7FV7+rCEwK3qhVZ5nss\nbQwUfpW3imN4iCqgFoWYVkf8arAhQJNiEaAgeZX9MoD1NCvQer5La/ORbaHKfHcWWQlZXuRXTOR9\noBDLrtTaHKJpbj+jYEMhZnkWyKxYD8wioMvATNpPPS9vHGTOWk5Esz62gVxwmYuI5/DtItLGH+M7\nrKovzzO3770/LhBNAzKuCNh6oTYmyHiJAMxrI4DIwArpZ+VE+2d0KB/byF5oGcBpQEDmm/leKlsi\nc47MN/JekH02hsaG2tRwQ4Dl5Xow64WYFOuBpjXPjA7lYxtRUFq51jwzY0b6Vl74vT+uRH/hzLyn\nXftRYAygtfVMuwdmfH9EQZSdhzZWRrP/KEBU80tnzy0OsnKr+jUWWRX1fIdWcduZ+YVzitvPDNgy\nEGvbVSDzcuaEWTu/yAvpl5mPtO9QzQ60KphFIILMiQi7BY7eynntCLQy7ysDRMub43u0KNgyUMuC\nzMrXcqeGmbR/el7eGMg2tJyoZgeadwIS9d/iDBd/ZF7a2JlVmZSDtitXZZI31gfF2N+jRaCGQkzz\nqkDm5VTDC+2HwKadv5VTBcFDCbTe79KsbVTdnlatypAcBBCZFZTWL3urOceqTNLYUJsCZEN9STCT\n9iUKLs3rmXNEi3psQ4ppF7D1ZtHVwdg/CoyxuhpLU6y2DtuPAhEg9XpTwEuKZaGXeUW3n9GoQNvb\n2xPjFkisEw2JD9u9fv26O7/N5n9XLt6FNuSNIWnsMbcXmUflfHqgWAG0DNzGBBrP6YEVkhOFVSS3\n8rW3t3dgHhHNesspgacCaNrYbV8EZL3iIPDAgIAjC5dKSGbG6tl+BmjeeRQBmgUoKz+SEwGW164A\nmtaHA6cHVuj2I1rcjwIo0JBVGM+ZCmSoKiFTvf2559aqGmiod5iBVgm1oV8PzLKvqA4t0NDx9/b2\n9iE298rmKGiM/YVCy4rPCTQ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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# quadratic form in intensity\n", "imshow(z,cmap=cm.gray)" ] }, { "cell_type": "code", "execution_count": 9, "id": "1fef402b", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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WREVF4e3tzciRI1m8ePFN1yxZsoRRo0YBkJCQwIULF8jP13/avCAIggoMrZ/I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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# evaluation of quadratic form in matrix form\n", "M = array([[3.0,0.0],[0.0,1.0]])\n", "z = apply_along_axis(lambda x:dot(x,dot(M,x)),0,array([x,y]))\n", "contour(x,y,z,levels=[0.5,1,1.5])" ] }, { "cell_type": "code", "execution_count": 10, "id": "893bb868", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.76484219 -0.64421769]\n", " [ 0.64421769 0.76484219]]\n", "[[ 1. 0.]\n", " [ 0. 1.]]\n", "[[ 1. 0.]\n", " [ 0. 1.]]\n" ] } ], "source": [ "# 2D rotation matrix\n", "def rotation(a):\n", " return array([[cos(a),-sin(a)],[sin(a),cos(a)]])\n", "\n", "print rotation(0.7)\n", "print dot(rotation(0.7).T,rotation(0.7))\n", "print dot(rotation(0.7),rotation(0.7).T)" ] }, { "cell_type": "code", "execution_count": 11, "id": "9e045ed6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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BH/sZyWhF67MeZdmyEHx8otm/f6wQPgOQlpZPnToWqvrIIYcSirGipmxb9+Li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\nzcfaSE5OliRJktLS0qT27dtLx48ff+x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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# \"rotated\" quadratic form\n", "M = array([[3.0,0.0],[0.0,1.0]])\n", "Mr = dot(rotation(0.7).T,dot(M,rotation(0.7)))\n", "z = apply_along_axis(lambda x:dot(x,dot(Mr,x)),0,array([x,y]))\n", "contour(x,y,z,levels=[0.5,1,1.5])" ] }, { "cell_type": "code", "execution_count": 12, "id": "865795a1", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 2.16996714, -0.98544973],\n", " [-0.98544973, 1.83003286]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Mr" ] }, { "cell_type": "markdown", "id": "350946e4", "metadata": {}, "source": [ "# Positive Definiteness" ] }, { "cell_type": "markdown", "id": "de09e8d0", "metadata": {}, "source": [ "Assume $A$ is a rectangular matrix with linearly independent columns.\n", "\n", "Claim: $A^T A$ is positive definite.\n", "\n", "I.e. $x^T A^T A x > 0$ for all $x\\neq 0$.\n", "\n", "$$x^T A^T A x = (A x)^T (A x) = ||A x||^2$$\n", "\n", "Clearly $\\geq 0$. $A x = 0$ only for a linear combination of columns that is zero, but that's only for $x=0$." ] }, { "cell_type": "markdown", "id": "72ea1953", "metadata": {}, "source": [ "# Eigenvalues and Eigenvectors" ] }, { "cell_type": "markdown", "id": "14819391", "metadata": {}, "source": [ "(definition)\n", "\n", "$$ M x = \\lambda x $$\n", "\n", "If $M$ is diagonal, this is really simple: pick an axis aligned unit vector as $x$." ] }, { "cell_type": "markdown", "id": "bc2e44ca", "metadata": {}, "source": [ "(eigenvalues)\n", "\n", "$$ M x = \\lambda x $$\n", "\n", "$$ (M - \\lambda I) x = 0 $$\n", "\n", "shifting $M$ by $\\lambda I$ makes it singular:\n", "\n", "$$ \\hbox{det}(M - \\lambda I) = 0$$" ] }, { "cell_type": "markdown", "id": "f4da0638", "metadata": {}, "source": [ "(determinant)\n", "\n", "A determinant is an alternating multilinear function of the columns:\n", "\n", "$$\\hbox{det}[a_1+v,a_2,...,a_n] = \\hbox{det}[a_1,a_2,...,a_n] + \\hbox{det}[v,a_2,...,a_n]$$\n", "\n", "$$\\hbox{det}[a_1,a_2,...,a_n] = -\\hbox{det}[a_2,a_1,...,a_n] $$\n", "\n", "$$\\hbox{det}(I) = 1$$\n", "\n", "That actually uniquely determines it." ] }, { "cell_type": "markdown", "id": "73c0dd06", "metadata": {}, "source": [ "(determinant)\n", "\n", "$\\hbox{det}(M) = 0$ is equivalent to $M$ being singular.\n", "\n", "E.g. two identical columns:\n", "\n", "$$ \\hbox{det}[a,a,a_3...,a_n] = -\\hbox{det}[a,a,a_3...,a_n] $$\n", "\n", "Note:\n", "\n", "$$ \\det(AB) = \\det(A) ~ \\det(B) $$" ] }, { "cell_type": "markdown", "id": "60458b16", "metadata": {}, "source": [ "(2 by 2 matrices)\n", "\n", "$$\\hbox{det}\\left(\\begin{array}{cc}a & b \\\\\\ c & d \\\\\\ \\end{array}\\right) = ad - bc$$\n", "\n", "Calculate eigenvectors and eigenvalues from this:\n", "\n", "$$(a-\\lambda)(d-\\lambda)-bc = 0$$\n", "\n", "Note that some of these solutions may be complex numbers.\n", "\n", "If the matrix is symmetric, then the eigenvalues are always real." ] }, { "cell_type": "markdown", "id": "4522c1b8", "metadata": {}, "source": [ "(orthogonality)\n", "\n", "Let $M$ be symmetric and $u$ and $v$ be eigenvectors corresponding to different eigenvalues $\\lambda\\neq\\mu$. \n", "Then $u$ and $v$ are orthogonal.\n", "\n", "$$ M u = \\lambda u, M v = \\mu v $$\n", "\n", "$$ v M^T = \\mu v^t$$\n", "\n", "multiply from right by u:\n", "$$ v M^T u = \\mu v^t u$$\n", "\n", "apply eigenvalue equation:\n", "$$ v \\lambda u^T = \\mu v^T u$$\n", "\n", "reorder:\n", "$$ (\\lambda - \\mu) (u \\cdot v) = 0 $$\n", "\n", "since $\\lambda\\neq\\mu$, we must have $u\\cdot v = 0$\n" ] }, { "cell_type": "markdown", "id": "cf8310d3", "metadata": {}, "source": [ "(image coordinate mapping)\n", "\n", "The horizontal vector is an eigenvector of the transformation." ] }, { "cell_type": "code", "execution_count": 13, "id": "14bb31ed", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Aig1KzknNJVH05Jkk+R4hDxGyxoucXd9z8eQdPAmfAn7wKFWQ3H1MVqDTQDnJ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\nTB+TJpIQHF4NobuHoSP0PSEuMTYhyTS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iD87WvPHyVxBCE+SE0D4hxhnBSxBb6GSXzmd0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\nyONokdEz5OnvfpF//0f/Nqp3sZ4Ff0JVPmIQHVLka9JyF1vlPDmuWK0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40YBh4nC5bnh2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bmyB6tILKAQZwAsvQBG9awrxbAEJe6p+mGmsqaTWWQuviedpP7BD/7UWbv/r2Wv6+yuvPJK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\nXcRtt93Ggw8+uC9rOXLkC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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "import urllib2\n", "imshow(imread(urllib2.urlopen(\"http://upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Mona_Lisa_eigenvector_grid.png/800px-Mona_Lisa_eigenvector_grid.png\")))" ] }, { "cell_type": "markdown", "id": "6474969d", "metadata": {}, "source": [ "(diagonalization)\n", "\n", "Let $M$ be an $n\\times n$ matrix and have $n$ linearly independent eigenvectors $u_1,...,u_n$ with eigenvalues $\\lambda_1,...,\\lambda_n$\n", "\n", "If the eigenvectors are the columns of $S$, then\n", "\n", "$$ S^{-1} M S = \\Lambda = \\hbox{diag}(\\lambda_1,...,\\lambda_n) $$\n", "\n", "Reason:\n", "\n", "$$ M S = M \\left( u_1 ... u_n \\right) = \\left( M u_1 ... M u_n \\right) = \\left( \\lambda_1 u_1 ... \\lambda_n u_n \\right ) = S \\Lambda $$\n", "\n", "If additionally $M$ is symmetric, we can choose $S$ to be an orthogonal matrix." ] }, { "cell_type": "markdown", "id": "c3667672", "metadata": {}, "source": [ "(orthogonal matrix)\n", "\n", "An *orthogonal matrix* $Q$ is a real, square matrix where the columns and rows are orthogonal unit vectors.\n", "\n", "Equivalently, $Q^T = Q^{-1}$ or $QQ^T = Q^TQ = I$.\n", "\n", "If $Q$ is orthogonal, then $\\hbox{det}(Q) = \\pm 1$.\n", "\n", "If $\\hbox{det}(Q) = 1$, then $Q$ is a *rotation matrix* (otherwise it's a rotation plus reflection)." ] }, { "cell_type": "markdown", "id": "a7fe20c5", "metadata": {}, "source": [ "(trace and determinant)\n", "\n", "The *determinant* of a matrix equals the product of the eigenvalues.\n", "\n", "The *trace* of a matrix is the sum of its diagonal elements and the sum of its eigenvalues." ] }, { "cell_type": "code", "execution_count": 17, "id": "362c07f4", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 3. 0.]\n", " [ 0. 1.]]\n", "(array([ 3., 1.]), array([[ 0.76484219, 0.64421769],\n", " [-0.64421769, 0.76484219]]))\n", "trace 4.0\n", "trace 4.0\n", "det 3.0\n", "det 3.0\n" ] } ], "source": [ "# trace and determinant\n", "print M\n", "print eig(Mr)\n", "print \"trace\",trace(M)\n", "print \"trace\",trace(Mr)\n", "print \"det\",det(M)\n", "print \"det\",det(Mr)" ] }, { "cell_type": "markdown", "id": "2a345d80", "metadata": {}, "source": [ "(proof sketches)\n", "\n", "determinant:\n", "\n", "$$ \\det(M) = \\det(S^{-1})\\det(\\Lambda)\\det(S) = 1\\cdot\\prod\\lambda_I \\cdot 1$$\n", "\n", "trace:\n", "\n", "$$ \\hbox{trace}(AB) = \\hbox{trace}(BA) $$\n", "\n", "$$ \\hbox{trace}(S^{-1} ~ \\Lambda S) = \\hbox{trace}(\\Lambda S ~ S^{-1}) = \\hbox{trace}(\\Lambda) $$" ] }, { "cell_type": "markdown", "id": "60d60450", "metadata": {}, "source": [ "# Norms and Metrics" ] }, { "cell_type": "markdown", "id": "5e2bc3ca", "metadata": {}, "source": [ "(norms)\n", "\n", "Norms assign lengths to vectors and must satisfy:\n", "\n", "$$||av|| = |a| ~||v||$$\n", "\n", "$$||a+b|| \\leq ||a||+||b||$$\n", "\n", "$$||v|| = 0 \\Leftrightarrow v=0$$\n", "\n", "Norms imply metrics by:\n", "\n", "$$ d(u,v) = || u - v || $$" ] }, { "cell_type": "markdown", "id": "f78a612a", "metadata": {}, "source": [ "(quadratic form as norm)\n", "\n", "A *quadratic form* defines a norm on a vector space.\n", "\n", "$$ ||x||_M = \\sqrt{x^T M x} $$\n", "\n", "It is equivalent to a rotation and rescaling of the vector space prior to measuring distances.\n", "\n", "If $M = S^{-1}\\Lambda S$, then $S$ is the rotation and $\\lambda_i$ the rescaling of axis $i$." ] }, { "cell_type": "markdown", "id": "9a502869", "metadata": {}, "source": [ "(importance for pattern recognition)\n", "\n", "When you take measurements in the real world:\n", "\n", "- the measurements are often linear combinations of some underlying causes you are interested in\n", "- the measurement scale of each measurement/cause is arbitrary\n", "\n", "Quadratic norms allow you to compensate for these effects." ] }, { "cell_type": "code", "execution_count": 15, "id": "8ebd8b73", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }