{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "***\n", "# Lecture 5 - Newton's Method\n", "***\n", "$\\newcommand{\\vct}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\mtx}[1]{\\mathbf{#1}}$\n", "$\\newcommand{\\e}{\\varepsilon}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\minimize}{\\text{minimize}\\quad}$\n", "$\\newcommand{\\maximize}{\\text{maximize}\\quad}$\n", "$\\newcommand{\\subjto}{\\quad\\text{subject to}\\quad}$\n", "$\\newcommand{\\R}{\\mathbb{R}}$\n", "$\\newcommand{\\trans}{T}$\n", "$\\newcommand{\\ip}[2]{\\langle {#1}, {#2} \\rangle}$\n", "$\\newcommand{\\zerovct}{\\vct{0}}$\n", "$\\newcommand{\\diff}[1]{\\mathrm{d}{#1}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Lecture 4 we found out that gradient descent works, and has linear convergence. In this lecture we introduce Newton's method, an algorithm that takes advantage of the second derivative and has quadratic convergence under certain circumstances. Throughout this lecture, $\\norm{\\cdot}$ will refer to the $2$-norm $\\norm{\\cdot}_2$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Newton's method\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $f\\in C^2(\\R^n)$ and let's look again at the unconstrained problem\n", "\n", "\\begin{equation*}\n", " \\minimize f(\\vct{x}).\n", "\\end{equation*}\n", "\n", "Newton's method starts with a guess $\\vct{x}_0$ and then proceeds to compute a sequence of points $\\{\\vct{x}_k\\}_{k\\geq 0}$ in $\\R^n$ by the rule\n", "\n", "\\begin{equation*}\n", " \\vct{x}_{k+1} = \\vct{x}_k - \\nabla^2 f(\\vct{x}_k)^{-1}\\nabla f(\\vct{x}_k), \\quad k\\geq 0.\n", "\\end{equation*}\n", "\n", "The algorithm stops when $\\norm{\\vct{x}_{k+1}-\\vct{x}_k}<\\e$ for some predefined tolerance $\\e>0$.\n", "In the context of the general scheme $\\vct{x}_{k+1}=\\vct{x}_k+\\alpha_k\\vct{p}_k$, the step length is $\\alpha_k=1$, and the search direction is the inverse of the Hessian multiplied with the negative gradient. \n", "\n", "Recall that the inner product $\\ip{\\vct{p}}{\\nabla f(\\vct{x})}$ is the directional\n", "derivative of $f$,\n", "and that a *descent direction* is a direction in which the rate of change (slope) is negative. The following gives a criterion for the search direction in Newton's method to be a descent direction.\n", "\n", "**Lemma. **\n", "Let $\\mtx{B}\\in \\R^{n\\times n}$ be a positive definite symmetric matrix and $f\\in C^1(\\mtx{R}^n)$.\n", "Then $\\vct{p}=-\\mtx{B}^{-1}\\nabla f(\\vct{x})$ is a descent direction of $f$ at $\\vct{x}$.\n", "\n", "**Proof. **\n", " If $\\mtx{B}\\in \\R^{n\\times n}$ is symmetric and positive definite, then $\\mtx{B}^{-1}$ is also positive definite, since for all $\\vct{v}\\in \\R^n$,\n", " \n", " \\begin{equation*}\n", " \\vct{v}^{\\trans}\\vct{B}^{-1}\\vct{v}= (\\mtx{B}\\vct{B}^{-1}\\vct{v})^{\\trans}\\vct{B}^{-1}\\vct{v}\n", " = \n", " (\\mtx{B}^{-1}\\vct{v})^{\\trans}\\mtx{B}^{\\trans} (\\mtx{B}^{-1}\\vct{v}) = (\\mtx{B}^{-1}\\vct{v})^{\\trans}\\mtx{B} (\\mtx{B}^{-1}\\vct{v})>0.\n", " \\end{equation*}\n", "\n", "(This can also be seen by noting that the eigenvalues of $\\mtx{B}^{-1}$ are the inverses of the eigenvalues of $\\mtx{B}$.)\n", "\n", "For $\\vct{p}=-\\mtx{B}^{-1}\\nabla f(\\vct{x})$ we then get\n", "\n", "\\begin{equation*}\n", " \\ip{\\vct{p}}{\\nabla f(\\vct{x})} = -\\ip{\\vct{B}^{-1}\\nabla f(\\vct{x})}{\\nabla f(\\vct{x})} =-\\nabla f(\\vct{x})^{\\trans}\\mtx{B}^{-1}\\nabla f(\\vct{x})<0,\n", "\\end{equation*}\n", "which shows that $\\vct{p}$ is a descent direction. \n", "\n", "To better understand Newton's method, we first look at the one dimensional case. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Example.** Let $f\\in C^2(\\R)$. In this case Newton's method is described as\n", " \n", " \\begin{equation*}\n", " x_{k+1} = x_k-\\frac{f'(x_k)}{f''(x_k)}, \\quad k\\geq 0.\n", " \\end{equation*}\n", "\n", "Newton's method looks for a local minimizer in the form of a point $x^*$ such that $f'(x^*)=0$ and $f''(x^*)>0$. Setting $g(x):=f'(x)$, we are looking for a {\\em root} $x^*$,\n", "\n", "\\begin{equation*}\n", " g(x^*)=0.\n", "\\end{equation*}\n", "\n", "One approach to find such a root is to approximate the function $g(x)$ at a point $x_k$ by its tangent line,\n", "\n", "\\begin{equation*}\n", " g(x) \\approx g(x_k)+g'(x_k)(x-x_k),\n", "\\end{equation*}\n", "\n", "and then identify the next iterate $x_{k+1}$ as the root of this linear approximation:\n", "\n", "\\begin{equation*}\n", " g(x_k)+g'(x_k)(x_{k+1}-x_k)=0 \\Longleftrightarrow x_{k+1} = x_k-\\frac{g(x_k)}{g'(x_k)} \n", "\\end{equation*}\n", "\n", "![Newton](images/newton-crop.png)\n", "\n", "Geometrically this corresponds to taking the tangent to $g$ at $x_k$ and setting $x_{k+1}$ to be the intersection of this tangent line with the $x$-axis, as shown in the figure.\n", "Replacing $g(x)=f'(x)$ gives precisely Newton's method." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another way to understand Newton's method is to view it in contrast with gradient descent. While gradient descent corresponds to working with a {\\em linear approximation}\n", "\n", "\\begin{equation*}\n", " f(\\vct{x}_{k+1}) \\approx f(\\vct{x}_k)+\\ip{\\nabla f(\\vct{x}_k)}{\\vct{x}_{k+1}-\\vct{x}_k},\n", "\\end{equation*}\n", "\n", "Newton's method is based on the *quadratic approximation*,\n", "\n", "\\begin{equation*}\n", " f(\\vct{x}_{k+1}) \\approx f(\\vct{x}_k)+\\ip{\\nabla f(\\vct{x}_k)}{\\vct{x}_{k+1}-\\vct{x}_k}+\\frac{1}{2}\\ip{\\nabla^2 f(\\vct{x}_k)(\\vct{x}_{k+1}-\\vct{x}_k)}{\\vct{x}_{k+1}-\\vct{x}_k}.\n", "\\end{equation*}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the function $f$ on $\\R^2$,\n", "\n", " \\begin{equation*}\n", " f(\\vct{x}) = \\frac{1}{2}(x_1^2+10x_2^2).\n", " \\end{equation*}\n", "\n", "Starting with $\\vct{x}_0=(10,1)^{\\trans}$, gradient descent takes $84$ iterations to reach accuracy $10^{-6}$, while Newton's method, unsurpringly, takes only one. " ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RmrNg2ufgDndjb3gMta4FY+mJNSt53ZFerPt/j7bwMC804/M+rM4tZG/6LvEL\n3kboqOoKU3tkmB2f/w8aXvdmGi580+T/H/DELhyH7q+PJ8I+eU21ysGxyf7fD8CxSF72Ed+EgzvS\ni3Xf/6EtXo5xzBm+hCOFwNm+Frd7I/qS47yihCnKg53sMJW+bSiqRrB1IXqiccaAsS2LcjFPpVjE\nrJQwgiFC4QiBUJhgKIxWo1HQy2Wu62BVKpOD0DIrBEJhwpEo4Vh8xh69lBI3n6YysANpVwjOOWic\n4Gsf6w7uxN74GNqcg9APXu4fd5TSk6I++xDBFRf7SsekY5P7w08QhRzJKz5W1b1QCkHf97+JPdjH\nvGuuRw0E9juxV7o72fmFq5lz5Yd9wy92fxfZX36T6KvfSPj4M6q2Sylx1v4DZ+OTBM56a80VqCjl\nsdc/CFJ6k2iNEBh4z9Ec6sQa7sWoaybYMn/GyXIpJWa5RLlYoFwqIBx3klCDoQiBYPCfml/yCN/y\nHKZyGbNcRAhBKBIlHIkRjsZmPKG8sHLpRIskCbUtQpsini4dG2frGtzBnRiHnorWVCM6UClirvoj\nIAme+VbfHIcz2EPml98k8qrziZx0dtV2a2iAnZ+/iqa3XE7dORcArwBi7/n2f2GPjjDvC/+vSi4l\nLZPsTd9FCYVIvOUDvr0znO3rsB77G4FTLkJfUN0bGUAUs9jP/QPFCGIcdhpKqDaQnUKGSu8WpHAJ\ntR2MnmiYEenZlkWpkKOUz+G6DuFonHA0SigcfUneysthQgjMcpFysUi5mEdRVCLxOJFYkkCNDpm7\nm5Mfo9K3zXtO7YsxptBBS6uCveFRZCGDceQZNYtA3L7tmKv+QGD5WehLq1vySiG8kvrBHlLvvBp1\ntyZW0nXp+cZ1SMf21DK6vl+JfdN7LqH57e/2TZTa3dvJ/PoG4hdeXiM5bHuql9wYgbMv9V1ZSikR\nfVuxNz+BvvBItPm1m1VJIbCGuzEHd6InmwjNWThta9+Ja1RKRUqFHOVCAd0wCEdjhKIxAsHpO5L+\ns82xbSqlAqViAbNcIhgKE4kliMTiMxqHUrhYwz2Yg53oyQZCrYumDLmKsQHsdQ+iNrajLzneN5wo\nhcB+4m7c7s0EX/N237i7OzZM+uf/TfiEM4meXl33YPb1sPPzVzHnfR8ieeqKA5/Yt33yQyz4yter\nkkXSMsn8+gbUeIrEm9/nG3N3nn0QZ+OTBM9+G2qDv97U7duKvWm1p0mdW7vKVFgVyj2bcUs5Qq2L\npvVEAYR+W2uTAAAgAElEQVRwKeVzFHJZHNvyABRPEAyFDzjA1zIpJZZZoZTPUSrkUDWNWCJFNJ6c\ndiBMrmx6t6IGw4Q6ltSMU0opEf3bvHdx0NFo85b5t4XIjmLecxPavEMwjn9NFVFJKb0WzJ1bSb3n\nk1XkLmyb7uu+gF7fQMfHPr1fiX3k1ltouOjiqm1211Yyv/k2iTe+h+CyY6q2y0oR896bUaIJAqe/\n0Z8sHAv7+UeQ+fSUk6X3jkao9G5GDUYJtR88pSc6eY+WSSGboZjPousGkXiCSCyB7iNoOFBNCEG5\nWKCUz1EpFwlHokQTKUKR6dU90nUwB3ZijfQSaJ5LsGV+bfWRY2FveAyZG8E4ckXNd+FsehJrzf0E\nz7rEt9+Mmx0j87P/JnT0KUTPrG5HXdmxjZ3XfpKOqz9P/JjjDmxit7OZqt7E0rbI/OpbaMl64m96\nb3WFoRDYj92BO9hF8LWX+3szroOz8TFEZgjjyDNryh2lEJhDXViDndO+wAmzLZN8Jk0pnyUYjhBL\npAhF9416QAiJ4wocV+IKgRDS6yIwoRzAW4apqoKmKmiaiq6paKqyT65vlksUshnKpQKRWJx4qp5A\ncJo+GhPe4MBOAo3tBFsX1nyGopTDXrsKJRzzVk8+RS3SLGHeczNKLEng9Or2EFJKCnfcjN25hdS7\nP1FN7pUyO7/wcRZ94wf7Pca+u3me+rdIvPlKgoccWbVd5NOYf/812oJlXlzWxwMX+THstStR6+eg\nH3Ji7eS0WabcvQlhlgjNPWTKVRWMa+iLefKZNLZlEk2kiCWSGDW6FO6JSfkiXLsersVEsnR8HwUP\n1xPY1sexrar7QBHjuhTzOQq5NFIIYsk6YonUtM6LMMuUe7cgSnnvGdaQ5wK4fduwNz2Ovvg49I4l\n/vv0bsN84I8ETnkd+oLq9hBuLkPmp9d7rVHOeF3V9uL6tfT/6Dss/u7PDmxi3/1a0rHJ/ubbKJEY\niYv/zads3MF64I9Is0zw1Zf6qgNEKY+99n6UaArj0FNqVuM5xSzlzudRAyHCcw+ZMtY4QXq59BiW\nWfaAkUyh70UDMCEkFcuhbDqYloNpuViOi2W7KCjouoquKajqBGF7oAeP4KX0zuEKb6A4ricdM3SN\noKERMDRCAZ1QUCcc1PdqYLiOQyGXoZBNoxsBEnUN03o6wjKp9G7GLeYIz1uGnqjhRQoXZ+NqxFgf\nxlFn+U660rGxVv0B6Vjee94tQTXpuffuJPWuj1eFFYRtoQWCBxSx232dZH7xDRJveg/BpdUSTzE2\niHn3b9CPPA3j0BN9zztBHsbSE9Fa/VsHSCmwhsYn2pZ5BJvnTxn7FkJQzGXIpcfQdJ14qo5ILLFX\njoLtCCqmTXkC1+PYdhyBpnlkrY2Ttarsiu0JovewPTERCFRFITCO62DgBWwHjT2XQU6sUPOZMSrF\nApF4kkRdw7QrETs3SqV7I1okQajjkJpVtqKQwV57P2qqGX3pSb6Trhjtx7znJvSjz8BYenzVdjeX\nJnPj9V7V8anVYby9xfb+68fuuuR+9wNAkrjkg9XhF8fCvO93KLpBYMXFvg/NHevHfvYBL+ZYY7kv\nhUulbzv2WD+hjiUY07QMqJSKZEeHcV2HRF0D0Xhyj5JEjisolCyKZZtSxaZiOQQNj3SDAY1gQPeA\nq3ug3xtzhcC2BZbtYtouFcuhYjqT14qEDaJhg1jYwND3rN9NKZ8jlx5FURSS9Y3Trk7s7Ajlrg0Y\nyUZC7YtrepQTYTLjsNPQmqubH0nhYj1yOzI9RPCcy6sST1JK8n/5Oe7YMKl3XFXl/e/v5OmLse0M\n95O58XpiF11B6LDq/IE73IN5780ETjwX/aBq6ZuUAmfzk4ihLoyjz6qdp6gUKe9cD6pGeP4ytCmc\nFSEEhWyaXHqUYChMoq6RoE+hVy2TUmJaLoXyC9gWQhIOjhNvQJ90NAxd3auJwvP0JbbjYloupu1Q\nMV0qpo0jJJGgh+1YOEAkZOyRE+M4NvlMmmI2QzgWJ1nfgD7Vh3iES6V/O/ZoP+G5h2DUUno5Nvb6\nh5CVIoGjz/JV6IncGOZdv0JfdhzGET4S2Mwo6Z98jeiZFxE+rjqxvl9i7IqiBIF/AAG8b6j+QUr5\nZZ/9JsEvpST/55/jZkdJXfEfVV62tE3Me37rdQs8/fW+S32nZxPO1qcwjjijpn7XLeUp7VyHGooQ\nnrtsyv4WZqVMZmQI17FJ1jcRic/Mi5FSUjYdckWTfNHCtF2iIY9Yo2GDcHDPAPhSbGJ1UCzbFMcH\noKFrxKMBEtEgkdDMJJZSSsqFPNmxERRVIdXQTCgy9ReTyt2bcAsZwgsOQ4/V6OOTGcZae/8L9QS7\nFyFJ6RXlDHYSeu0VVV9pkkJ4zoAQJC7d1Rl4OYh9b7A9OUhf/QbCy0+vOqc70Il5/+8InvZ6tHmH\nVG2XjoX97AMgXIwjV/iuUqWUXjisfwfBtoMITFX9K6VH6GOjBEJhkg2N04bbJu9VeE5KrmiRL1oo\nCsQiAQ/bIYPAXnjRe2uOKyiVbYoVm0LphXE2ge2AMTMHxnVd8plRCpkMkXiCZH3jlMo1p5ilvHM9\nWiROeO5S/xyIlLjb1+L0biZw9Kt9m6yJYg7zrl96H4o/ekXVc3NGBjxn4MLLq5yB/ZY8VRQlIqUs\nKYqiAQ8DH5VSrt5tn0nwF+79E9bm50i999Oou4FM2ibm3b9BmSjO8EmoOVvWIIY6MY4521fuNQn8\ngR2eiqO+tSYAHdsmMzKEWS6RbGgkmkjNCKxl0yGTr5DJV1AUhUQ0SCIaIBI2UA+QZKqUklLFIV80\nyRVNHFeSjAepi4cIB6cn+QkPPjM6TCAYJNXYguHTmXDC7MwQ5a6NBJo6CM5Z6L+CqhSxnr4XNdGI\nvuzk6vCblNhP3ovbs4XQee+qUjVJxybzqxvQG5qJXfSOyWu8XB77nmBblIukf3wd4eWnEzn9vKpz\nTZL6GW/27cooKyWsp++p+WzA06SXdz6PdCzCCw5Hq6H68hQuBdLDQ+i6QaqxiUCND2Tvcn4pyRct\nMvkK+ZJFJKiTiAWJRwIEA/9c6e5UNrEyzhctckWTYEAjFQ+RioXQ9elXwq7jkEuPUsxlidfVk0jV\nbg8ihUulZwt2boTIgsNrOi7uwA7sDY9iHPEqtMaO6vOUC1Tu/CXagmUElp9Vtd0L3/0Pycs+TGDB\nC5P+flfFKIoSwfNw/l1K+cRu26SUkvITD1D6x9+oe/8XUGO7JkKlY2HefRNKot6f1IWLvf5hZClH\n4Jiz/b0Z16HUuR5hVogcdETN5akUglxmjHx6jFiqjkRdw7SFPK4ryOQrjOUqOK7wgBQPEQr88zyX\nl2IVa2IyMlEUqE+EqUuE0KcJCUkhyI97fbFkikR9Y81nJawKpZ3rUBSV8ILDfVdJ0rGx164ERcU4\naoVvwtR+8h7cvu2Ezn1nVVhGVMpkfvI1gkeeOJl0erlDMdNhW9gWmV/8D3rrPGLnX1aFB3eoG/Pe\nm2uSuihksJ66B73jELSFR/jiySlkKO14DqNuDqH2RTXljrZlkR4ewLFt6ppaCEenV8ZUTIexXJl0\nvkIooJOKh0jGgtNi40AwKSX5kjcZ5YoWsbBBfTJMPDJ9zYZjW6SHh7CtCnWNLYRjtT/67jkuGwi2\nLCDQPM9f6ZUZxHpmJfriY9Hbq9ugeOT+C/SDjsA4ujrsYm1dR/b3P6buys9Mfjxof3rsKrAGWAR8\nX0r5WZ995ERDr9SVn0Nv3LX5lnQdzHt/ixKKEXjVG6pJ3XWw197vkcGR1WQAXm+X0vZn0eP1hDpq\ndx+slEuMDfZjBALUNbVMGWsDMC2HkUyZTL5CLBKgPhEiNgPQTGdCSmwHbFeOJ0ZBSJh4J4qioCqg\nqWBoCoauYOi85BWBlJJixWYsWyZXtEjGgjSlIoSCU3tkrmOTHhnCLJepb55TkzCkFJh927HG+okc\ndCS636pKCC82Wc57k7RPwtRefRdiqIfgue+o2u5m06R/9FVi511K6IgTXk6PfUbYzt7yY6RZIfG2\nD1XhToz2U/n7rwme/ka0udWDXWSHsZ6+D2PxsWh+ZCClp7ce2EF4/jKMGt0HpZTk0qPk02Mk6hqI\n1039HV457p0PZ0qYlkt9IkRdMkxwhmGNqcwVEsvx8O0IiRC7YltVFFQVdBV0TSGgK+gaL3lMuUKQ\nyZuMZcs4rqAxFaE+EZo2n1UuFkgPD2IEgtQ1t9QUSgizTGnHcyiBEJH5h/onTIsZrDX3oM9bir7A\nJ4dSylO54+de++XDT6m+l6cepLjyr9R/4Iuo0cQB4bEngL8AH5ZSPr/bNjl03YdJvu3DBBbuGluU\nQmCtugWkJHDmW6pi6tKxsZ6+ByU0LpvzIWw7M0y563lC7YsJ1Ii5CyHIjAxRLuSpa24hEpu6nLhs\n2gyNlSiULRoSYRpS4T1KRk6Y5UjyZUGxIiiZkpIpqdge8HUNApqCriloKqjqi8AtJa4AV3iDw3Yk\ntguGBqGASiSgEAkpRIMq8bBK0NjzQeE4gtFcmdFMmXBQp7k+SjQ8tWqgUioyOthPKByhrqmlpozs\nhXeyhIBP7YGUEmfTakR6gMCxr61agUkpsR7+K7KQIfiat1cNIruvk8zP/4fUO68iMHfRy+2xT4nt\n0e9dS92Vn62qlhbZEcw7foFx8vm+kjcxNoC1diXGYafWSCoLyt0bcYs5oouOrKnmsswKo4N9aJpO\nfXPrlMoPKSWZfIWhdAlVUWhMRUjGg3vsMEjpYblQERQrkpIpKFuSiiURkkmynsS2Mu59jh/rCnBd\nD9O24x0TNBTCAYVIUCESVImFVWIhTxK5p1aq2AynSxRKFg3JMI2pyJRhGikE2fQIhWyGVGOzJ5zw\nFWS8+J0c5Vv8JStFrDV/R21ZiL7o6KrziEIW846fYRy9An1JdX1D4e4/YO/cROo9n0I1AvtfFaMo\nyheBopTym7v9v/zcle/EaFsAwIoVK1ixYoXnmT16OyI76qkhdl+W2xbWU3d7XztZdrJvws0a7MQc\n7q7pHQKY5RKjg30EQhHqpyAj8JalA6MFShWHproI9ckQ2gyVMVJKypYkXRBkioJsSeC6chKgkaBK\nJOiBN2AoezyYhJRYtjcxTEwShYqgUBYoCiQjKqmoRl3Mu85MPSAhJOlcmaF0iWBAY05DjEioNjlM\nTpLFPPXNrTW9d7dcoLRtLUZdC8G2Rb7vz9n6FGKoi8Bx51arYYTAWvl7UFQCZ148uZJbtWoVq1at\nwhnuw9r8HF+/97GXXRUzFba/+OlPTRbeTWBblHKYt/8U4+hXoS85tup87mgf9rOrMI5c4SsAEI5F\nafuzKJpBZMFhNVs05NKj5DNjU5LRxL6ZfIXBsRKGrtJcHyUWNvYII9mSh+tMUZAvCwxdIR5SiIYm\ncK0SCigYe+F9u8KbFMqWN0mUTM8hKpmSSFDxsB3TqIuqGPrMz23aLsPpEtl8hfpkmKa6yJQhJsus\nMDrQh24Y1De3+iZXX8jj7fR4xyfuLs2yR+6N7eiLq78PIbIjVO74OYFTL0Sft3Ty/1etWsXKlSsx\nn1uNYgS4/vd/3S+qmEbAllJmFUUJA38HrpdS3rHbfv5FHGv/gbNjPaHz313tsTkW1pq7URMNnk7U\nhxQq3Rtxilmii472LQd+MfDrm+dM6aXbjsvASJF8yaSpLkpDMjwjRYuQkmxRMJJzGcl7BRl14wBM\nRlXCgZdeUDSdSemRfXZ80I0VvA8HN8RVGhMe0c9kEhFSks5VGBorEgkZzGmMTbk097z3PiLxBKkG\n/w8iC8eitG2tV0Mw/zDfhKmz7RnE0E4Cx53ngwMb8+5foza0ETjR54MEj95D9JRzXg5VzF5jW9qm\nt9yev8w3luqO9WOvXUXgqDNR66u/CSDMEsWtz6CnmgjV6HXkODajA30ANLS0Teml54sm/SMFVFVl\nTkOUWGRmX0CyHclI3mUk55IuCCJBhbqYRjKikozsGcHurQkhyVck2aJLuijIFgXRoEJjQqMpqREJ\nzszpsmyXobEi2aJJ8zTjW0pJdnSYYi5Lw5y2mqowOztCuXM94blLfSWR0qqMk3uH1z9p99zLcC/m\nPTcRfM1laE27JlyFWaF0/1+In/+2/ULsRwC/BNTxv99JKa/z2a8K/M6257CfvIfghe+rqiiVjo31\n1D2osZS/py5cSjvWgXCJHOTfLtZ1HEYH+pBIGua01Y6bCclwpsRIukR9MkxzXWTamJyUknxZMpBx\nGMq6BHWFpqRGY1wjGnr5iXw6m1gmj+ZdhrMuJUvSlNCYU+cNyulbKOz2TOojNVctruswOtCPEA6N\nczp8CUYKl9LO9UjHJrroKN+EqbP1KcRwN4Hjz6uOuZtlKrff6H3D1qeg52WSO+4VtqVwvTYBkcS4\nCGA3Ty09iPXM/RhHrfD9HJtbylHc9gzBOQsJ1mg4VS4WGB3sI56qJ1FXu8eRaTn0DRcwbZfWxhiJ\n6PS5IVdIhrMugxmXbElQF1NpSmjUxzUC/wQin86EkGTGHanhnIuhK7QkNVrqdEIzCEdWLIf+kQKm\n5dDaGJ/ymVRKRUYH+ogmkyTr/dtYu6W8975a5hP0C6dZFawn70RtXoBxcHXYxenahP3wbQRf917f\nAr79HmOf8kK7gd8d6sG897eEzn1n1ae+pHCxn74PgmEvpl710QWH4rZnUI2grwcIni59pL+HaDxJ\nsqF2X/FCyaJnKE8ooNHWFJ9WD+u4koGMS9+og5AwJ6XRktIIz9Br2F9WsQRDWZeBtIuQ0Fav0Vqn\nT+tx2Y5L/0iBYtmmrSlOMuZfci6lJJ8ZI5cepXFOu6+H462wNnkrrMXHVH30QEqJs/kJRGbIi7nv\nNhGLfJrK7TcSfNUb0doP3mXbgVSgZD12JyIzTPCct1fli0RuFGvN3eOSuOoe304hTWn7s4TnLsOo\n8/kOgZTkxrw4cENrO6FwjZbVQjKcLjGSKdFUH6ExFZl2xVasCHpHHQazLomwypw6jYa4hq7tfzKv\nZVJ64aHBjMtQ1iURUemo16mPT++85IsWfcN5AgGN9inGvus4jAz0oigKDXPafPvCC7NMcevTGPVz\nfKW+0ixjPXGH992C+dU92+3nH8PZuIbQ695btWJ9xRC7KOYwb/sJximvQ9+tSENKif3cA+C6GEed\nWb1sd2yKW59Gi8QJ1Wj0VchlyIwMUd/cSqSGfMl1BX0jBQoli/amOIkahDVhFUvQM+rSn3aoi6q0\nN+ikontXYfdic1xJxQbLAcf1EqUTr0QZV8ToGgR0COq8ZOWAlJJcSdA75jKac2lOacxt1Kddzk5M\ngOGgTltTHKNGEqpSKjIy0EuirpF4qvqTZFJKzL5t2NlhoouXo/qoYZz1DyPNEsYx1X2tJ7TgoQve\ns8un9g4UYnc2r8F+9mFCF15ZLdMs5bCeuAPjkJPQ5iyoOo+dG6W8c52nlfYrchGC0YE+XNehqbUd\nrcYKtFi26RnKETSmd1ak9PJBXSMOxYqgtU6nrV4jFHhpjoqUEssB0wbbHcf2xAeUFF6k9vKwHTJ4\nyYV8rpAMZVx6Rh1cAR2NOq112pSJ1xdPgC0NXnjGN2Eq5WROqbG1w7fIS9gmxa1Po8cbCLVXh89k\nuYD5xB0YBy9Ha9vVMZFSYj9yO7KUJ3D2pbuoAl8RxC5dB/NvP0ObvxTjqFdV7WdvfByRHyWw/Jzq\n5bpjU9z6FFosRah9iS9pZEeHKRVyNLbOrdmWtlCy6B7MEY8GaW2IThl2KVuCziGH4ZxLa51OR8Oe\ng15KSb4CmSJkS5J8GQomFE2PxIMGBDQP5Jr3ESXvODyi91QDULG9xmCRIERDkAhBMqKQikIivOeE\nb9qS3lGHvjGHupjGgmadaGiqPiOSwbEi6VyF9uba3rtjWwz39RAMh6lr8u+cWenfgT3WT3TJsdXk\nLoQnbdUDGIefXl2lt+lJ7HWPeuQ57t0cCMQ+oVXffdKB8eX46tvR5h+OPndp1TkmSf2go3wTcY5j\nM9zXTSAQor7Z/wMwQkqGRouM5Sq0NcVIxmp/iEJKyWhesHPIxhUwr0mnJantMbk6riRT8rCdK3vY\nLppQtjwnJKiDoXuyRnUC29KTPrrCc2gsB0zHI/hoEGIhSIQVUhGoi0IosOdqnWxJ0D3ikCsJOhp1\nOhr0KQm+Yjn0DOZQFYWOlkTNybCYy5IeGaShpc1XMCAcm9LWp9GiSU9yXaWGyWA9eRfG4adXrdik\n62De9SvU1gW7FDC9IojdevivyEqJwFmXVA/YrudxuzcSOOGC6hir61Dc8hRaLOlP6kIwOtiP49g0\ntXb4ZrKFlAyOesQ0tyVOPFrbSzdtSeeQzWDWpb1eZ27j9GGLyXuRkrECDOVgOOf9O6BDKgqpiEI8\n7IE3GmSP1ANSelr3oulNDPmyN1Gki1CxoD4GjQmFloT375kOUsf1CL57xKEhrrGwRZ9y8iqWbboH\nssQiAdqa4r7XEa7LyEAvAI2tHb4FTVOSu+tgPXkXakO7b1xydxztb2IXpTyVv/4I42SfVejEb6lv\nxVhcrY5xcmOUdj5Xk9Qt02S4r4tYsq5mPN20HLoGcuiaSkdLouaKCiBdcNk+YONKWNhs0JiY+crT\nciTDORjKSUZykK94TkUqCsmwh+1o0HM+9kSi6CX/PWzny94kkS1BuuhNCo1xaEooNCchFpr5eQsV\nwc4hh2zRZX6zQVtd7clLSslQusRopjTuuPi3XjDLJYb7e0g1NBFL+je18xzQel/PfSLHEjjutVV9\ngGS5UIWjA57Y7S3PYD/zAKGL/q0qjuQOd2M//zCB4y9AjewaPpHC9Ug9EifUcUj1gxIuw309qKpG\nw5w2XxKxbJfO/iy6rjK3JVFT7uQKSfeIR3JzUhrzm40ZJYxcIRnIQO+YpD/jLS1bkh4YG+PslcZ8\nT8xyJKN5byIZzEGxAnNS0F6v0JpiRnFSx5V0jTj0jjq01evMb9JrHue6gt6hPGXLYX5rkpBPubmU\nkrGhfmzTpKl9rm9sstK3DTszTGzJsdU9g8wy1urbvf76uy9dHRvzjp95X4k//JT9TuzlO36B2tRO\n4Lhdv4ozGVoEjCPOqHZmChlK29cSWXgkuk/ibIJE6hpbiCb8pbyZfIXe4Twt9bVDCQAlU7C136ZY\nkRw0R6c5ObOK6ZIp6RmDvjFJugQNMWhOKjTFPULfG435TE1KSaECI3lvMhnKeiuB9jroaFCoi87M\nMcqXBdsHbMqW5OBWg4YpYvATjks8GqS1Keabm7Atk6Hebq8S22eyFY5NccsajGQTobbqSmO3fzv2\nlicJnvi6qsZh7mAX5n3/R+jCK1HjdQc+sRdvup7Que+qSpaKQgbriTsJHPNq1NSuCSMpBaVta1H0\nAOH5h1bLhVyX4b4ujIklqs9LyJcsugdyNNaFaUpFar7Q0bzLlj6baEjh4FaD8DQhF285CzuGJb1j\nHsg76hXa6iAS3L8Jp4ol6UtDz5i3YmitgwVNCs2J6QeCaUu2DdhkioKDWw2aanh0UkrGchUGRgt0\nNCd8QzMT4bFysUBT+9wqZZKUkkrvFtxilujBy6u6fIpCGuuJuwgsPxt1t4pLkU9Tue0nBF9zGXrz\n3P1L7H/7GcFz31kVInG2r8Ud6vKUPrtNbG4pT3Hr04QXHObbP31C+VJr2S+lpH+kQK5gMq81WbPu\nwBWSziEv5Da3SWduw/TtnR1X0j0KncOSbBna6jwnoSX58hL5dCalt0LtS3v3JyXMb/SwHZ2BJz+a\nd9nabxMOKCxuqz3GXVfQPZjDcQXzW5O+hYmu4zDU20UoEiXVWC31FbZFcfOTXu8kH7WMs+1p3JFe\nDxu75ZLsdY/gbl9H8IL3oOrGgU3s9oYnqj6DJm0L6/Hb0BYeWdVbQUpJuXM90nU8SeNubQZc12Go\np/aDlVIymvGKbubNSdTU7lqOZGufTbYkWNJm0JCYXhmzcxi2DkqQsKBZYX4jhPcwFvjPsoot6R7x\nJiDHhUUtCgubmXYlkim6bOr1BsEh7YGaq45SxaazP0tdIkRLvX8f9+zYCMVchub2+VVySO89P490\nbCKLfN7zUBf2hkcJnnRhlXfj7Hwee/XdRC65ar8Su1vMVkl2J+/7xAurmpkJs0xh85NepbSPjr1U\nyDM21E9ja4ev8sVxBV39WVAU5s2pvQJNF7x3GAspHNwWmFYOmCtLtg5IukagMeERZmtq/5J5LZsg\n+c5hSdeoF49fPEdhTmpq50W8aFU+r8kLs9ZyXLzQTJn5rUnfimzXdRnu7SIQClPXVN0SfKr3LKXE\nXrsSxQhgHHZa1Tbz3t+iJhsJnnjugU3sQohdfriUEvuZ+1FCEYxl1V/trvRtw8mNEl1ybLU6YpzU\nw9GYr5xRSknfcIFi2WJBW6pmMmQk57Kp16I5qXHQHGNKAJu2ZMuAZNsgNCU8EDXGX6pKxVMOVGzG\n+8Z4iSXwlAO65iWfQoaXZH0p42tiIGwZkPSnYUETHNKmTDkhCSHpHPbCMwe3GrSk/JfvtiPo7M8Q\nMDQ6mhO+HmEuPUohm65B7mKyiMlP7WRvfRqR7idw7LlVXrG1+u97Bf59ZX41GqKUw3r8b/6rUMem\nsPlJ7wtUPp5cuZhndLCfpra5BH06Mpr/n7r3jpLjus7Ev+o4OeecMYMMIjMCDJJIiqQkW9FJlmWt\ns+y112vL692fbXl/kmXLsizbsiXTEkWJFClKzCAIEgSJnMMMJoee0N3TOYdK7+4fb4aY6lc9ACiR\ngO45c3BQ1d1V9eq9++797nfvVTS4PDGUFjvQWGNeL19nhOlFFf6YjjXNDtRcxVgJJQgjHu7dddXx\nzf+nNVR0xmM/sgooKxhfEoxsr0LHMtvrp7kWt+AnvASdgP5GCW01q8eZ0jLDmFsFI2CgxZ6XGRZP\nypj3x9FcW4qKUhM2jK7D75mHw1lgqty5Z3ZuKUPVCLeRpnLDtn290ImJsikoh59Dwft+6eZW7EKC\n0vbj6GoAACAASURBVMylK25qjuJWQh7I3hkUr9kuVAhkug6few4FRUWm2Y6MEWYXY9xNaygzZb3o\njDDpVRFOMAy02lFRnH/iyyphzEOY9gOt1VwZXk8AB+BKO5gAQgkgnARiaSCR5sEimxUocPBJbrNc\nUd4rmQPLir/ICZQWAuVFQGUJUF3KN5nrraialgnjXu55tNcA/c2rL+REhmF4XkFJgQVrmu2m2Dtj\nZHBfzaxIrtyjqG9pFwLcpGtc4VU1wllv7BNJRFDPHYBUUgn7GrETzY3G2A0JSroG5dRLsDb3wtZm\nrA9DxJCavABrQTEKW8V67MvwSz6lns6qcHliqFvipptJMsNweeld9TXZVw36hxKEywuczbKmSUJH\n7bXFY648D5/DgTgQTvBgZzzNA6CKdsUgsdtWML6IUx81fcmoUQBInFBQXsT/OBGAz/HrMWaICP44\nMOImpGVgoFlCe23+wnlEhIWQjlm/iu4GOxoqzQ2XjMzHvaaiCLWVJs00dB1+9xychUWm6AFnPV1G\ncd82odQyS0WhnHoZjq3vg6VMbMd302PsK6/Fy1se5G5qTsPd5YBSce82WHN7XDKGgHsO9jy7o6Yz\nuDxROO02tNSXmr6ktMwwNLs08fMoKWBJ+S8Cox5CSxWfJNeKnWs64IkA7hD/N5rkk7V6ibFSXgSU\nFXEGwbXWFdMZD4rGM3xjCCf5RhFKcGZCUxXQvPRnv0ZFn1UJo27CbBDoqeeLe9Xx8KoIJxnWtzlQ\nWigq7mXcN5lW0NlcYYpNckpqAvUt7ULNHqZkkRw7jcK2AaHnJClZyCeeh31gN6w5GZk3k2JXh4+B\nNMU0WJqZGwVTMigyKQy1HCjNB78k0grmFmNorSszzbsgIngjnPGymncFAMksYXCOEEoCa5u5Qr9W\nFlUyCyyE+Nz2Rvi8rC3nRkZlMZ/XZYXcEr9WK1xW+e/Gl5gw4SQQjANpGaiv4HO7pRpLHvK1/WYw\nThic53z6Te0SGiryfzGZZRieU1BSyA0XM89dUXXMeKIoK3aioVqEHLnBOYui4lKUV4sVOOXAAhT/\nHEr6d4jxlsVpaJPn4Nj1iEAi+LlR7KTKkI8/z3s55riiqy5sIgS8C7BYLKiubxKVusYw7Y6ipMie\n10UNxDj00tVgR2Oe3RkAvBHChVlCaQGwsV1CWeHVx1XRAJcfmPEB7jCf6K01PHBZW3btCvx6RWd8\nEXgjwHwICMQ4I6azHuis497A1SSV5YsgmAA2tUloqc4PMfmiGiY83MJprDJnw/gjaUTiWXQ1izAY\nESES9EHNZlHb3CawmN7e2Pu2wZrTRYlFfFAuvgHnrocNuPXNoth1nwva+Bk4dj0stO9Tgm7IvlnT\nha3IMvzu2byB0lhSxoI/jo7GchQXii9UZ4Rxj4p4mm+6+fIRNJ0w4ubeZ1+jhN6Ga7PQIylgehGY\n8XMF3FINtFQBjVXLORRX/Yl3JFkFS2wzYD7Iocr2WqCrniv7q+1FfLMDLs7xtby5I7+3rTPCmFtF\nMsOwvt1hCs1oOsOMO4qiAjuaakUdo2safAsulFZUobRCbGmYmRsFU7Mo6tokWvWXj4KYDscGY37P\nz41iVy4dgmQvgH1gl+EzxBhSE2dhK69BQUOn8RwRwv5F6JqK2qZWU6U+5Y6gvMRpGsAjIrj8GrwR\nHevbHCgrypM5qRDOu3jSxeZ2CY2Vq48nEVeoIwvAXJAr8a56oK2Wu6E3QhSN38uMj1tWzVVAfwuH\nka62AANx/vwFdmBrl4TiPB5KKsswOKugutSC7kbzrlHBSBqBaBrdLZWmyj206AERoaaxWXhfStAN\n2T+HkjXbBSWoTZ0Hi/hh3/q+t793Myh2yqYgn3geji0ig0dLxZCeumC6WWmaCt+8CxXVdaaUxlgy\nC7c/gY6mClPmi6wShmZlOB0W9K/igfqihDMzhOoSbsFeDUNXNGDSC4y6OdzStWQoNFTwZKMbIbEU\n31ymFoG0AvQ1Af3N3ANeTRgjjC8CYx5CX6OENY3mHgoRwRPWMeNXsbbVgaoSEzaMzuDyxOBwWNFS\nJ6ICmqrANz+LyroGIfOdGENq8hzvGdHYZTyna1BOPA9b1yZD8/KfC8Wue6ehTV/gFk3Ogs3Mj3E3\n1WQ3i4dDSCViqG9thyUHj9d0humFCMpKnGioNskGY4TRBRUZhWF9u9OU3UHEgy8XZgmdtcDaltVr\nQGs6MO4Bhub4/wdagN7Ga7OO30uRVWDKB4zM84W6ro0vhNUwecYIY15g3EvY0MoZNKYBU51weU6B\nRQLWtjpMFUpwqZBYl5lyZwx+9xwchYWorBEr46VdlwEiFHasMwbdGeN1Nxq73sawb7RiZ4xBPfcq\nLBX1sHVvNpxnmork6EkUNvcJ9V8YY/AtzKKopBTlVSK+GkvKcPsT6GwqR6GJUk9mGQZdChoqeeaw\neWCbcHGO4IvyzXo1SALgMN/QHDDh4VZxfwu30G82YkwkyTedcQ9QVw5saOdGzGrGSypLODvD4Znt\n3RLKi8w/HEnquDyvoKvejiYTr1RnDDPuGAocVjSbKHc5m0HAM4+6plahJSFTZT4f2kWaK4sHoZw9\nAOfuhyAVcF120yt2lk1BPv4cHFvuE1Ku1agfmYVxlPbvFDCmdDKBSGAR9S0dAptC1xmm3FGUFjlM\ncS9NJwzOKrBbgYFWh6myVjX+sqNpYEe3hKqS/GOoasDleeDSLIdXNnZwju9PG9FPy0t1NTQOrQBX\nmAMFjmXmwE/HvvHH+H17wsDaVmBjOw9s5ZNYmnB6ilvv27olU6ocI8K4W0Uiw7Cp02lKoQxE0gjF\nMuhuqRQyInVdg2/ehbLKGpSUG7MuielIjp6Cs64Njpz0a5aKQTn1Ehw7HoSluPyGK3Z1bgS6e4Jn\nTa8wZ4kI6emLsDgLUdgi1kUKLrphkSyoqhf78iZSMuZ8cXTmsdQjSR2X5xT0NtlRX2G+U4cShJOT\nhLoybqWvFkiNJIGz0xw7728B1rXygOY7leV6McvMmOUOYcs1kBy2K3P7p2GWaTr3LC7N8t/d2s3h\nmnw/SUSY8QOD84S1zRJ6Gsyvn5YZLrkU1FeYb5pcuXNYxgz6TSfjiAR8qG/tEPI3tEQY6ZkhlAzs\nFLKutemLYJFF2G953zvOqn5PFbt87jVIpZWw99xiOMeULJKjp1DUvUlolKEqMnwLs6YsAcYIM54o\nChw2U7xL0QgXZ2SUF1nQ22TeUCCSIhwfJ9SXc/wtn5WuMw63nJ8GGir55Km6eitJgyQzhMUI4Ivy\nBRdJctdSVoFC51LNGJuRFaMuFVLKKDwgWl4EVJTwIFJdhYSGSs6SuZ6FEUvz55gNAJs6gPVt+fF/\nxghDC5zXvLNHQm2Zubfj8mvwRXVs7nSYliPwhXgd7O7mCoGltNo71jNJpMbPoniNCYQxOwzd54Jj\n+/2wWCw3NkHp4Pfh2P4ALDklAeTAPNSQB8V92wWaZiwUQCadQn1zm3AunVUx44nmxdSDcR2jCwrW\ntTlQaQIXEBHGvcCYl7C1U0Jz1WqMJ+DMFDC3NB/Wtl4fy4oRIRjj8zoQ40l70RRnfQF8bjtsy+Uz\nVtRA0vi8VlSgZInpVVXKy2LUVfB1dj1lgon4nD4zxdfQzl6gWcz7eluSWcKJCUKhg1vvZte6mg7R\ndYaphSjKSzkEnCv8HSdR39wuvOOsZwp6Koaini2iR3rqRVhb+mFbqjdzUyv27JEfw7H7YQO1kYiQ\nmljGnIy4OtN1LM67UFZZLVpzRJj1xiFJQFtDmegKqYQLMzJqy3jtEzPFN+MnXJoj3NIhobUm/7jN\nBoDjY1yB7uzlNKxrkYxMmPYBLh9hLsChkMZKoK6CT97KEqC8mDNjrqaYiQgZhW8EkSSP+PujHN+3\nSEBrLdBRL6G7AdeUgQfwgNipCR543dkLdDfkt3K8EcLpaUJ/Ew+4md3vfFDDQlDDpk4x8LScVyAr\nGjqaKwRMftkra2jtFGiQcmABSnABJWt2CNawcvplWBs6YW9fd2Mt9qmLsHVtNBzXM0mkJs6a4uqZ\nVBJhnxf1baI1JysaphaiaKkzrzrqi2qY9KrY0O40jRWpOuH0JJ8vu/ryx0lUDTg/AwwvcOv8ah7c\nshDxOjFTXp4c5Alxy76hEqgtl1BdxrOwy4qurZSGzjjdMprkczsQ4+U5gjGu6Ntqga4GCa2115Yo\nRcThx9MT/D5uXcPXmZkwxmEqbwS4tU9CRbH4+5pOuORSUOiQ0N8iKndV0zE1H0FdVTGqynM6gBEh\n6HXDarWiqr4x5xxDavws7BV1Ar2XJcJQzrwC5+4PwVJYfHMrdj3iE5I1ZP8c1IgPxX3G1lE8uOaG\nxSIOCAB4AglkZA2dTRVCEGRZqS/XeskVIsLFWV7T5bY1+RkvqSxwZJRTr25bwyfY1SQjE0YXgLEF\nPlna64DOeglttXyS/jQup5kQEaIpbm3N+AguH994+lskDLRem5L3hIGjo5wjf/tA/kBUSiYcGyOU\nF3Gs1myRecIaXH4NWzodQo16vhnHYLVYTKmo0aAfcjaDuuY2YS6kpy/CWliCgpyaMbwcxcsovPv6\nkzh+ViJJEjFdz9l0GJKjp+GsbRFgJE1VsTg/Y0pr1HSGyfkIaiuLUF0u8tiXlfqmTidKTJgvqSzh\nyBihuhTYsooHOhsAjozwQOjOvqtDLkSEQAy4PEcYcwMgoLuRGxMt71LWtaZzD3fWD0wvck+guxEY\naJHQ2XB1Ja8zYHAWuOjiXunmTg7VmMlckJMGtnWZezc6Iwy6FDjsEgZMlDvfjCNobShHaZGYd7M4\n70J5VY0QHGdyBsmxUyju3QprDu1bnTgLSsfh3Hz3za3Yc6+lZ1NIjZ9Bcd92gbSfiEaQjEfQ0NIh\nuDChWAaBSBo9rZVCEoyiEc5Py0u4mKjUNZ27XzoDdveZu19EPChzaoK7pVs6V6cqEhFm/cCFGa5Y\nO+uBgVY++ezvcZMCnfF7GJknTHo53XJzl4SuPFb2le/xgNmFGf6869vNg2WaTjg1RZBVbuGYWWTu\nkIa5gIYtXSIswxhhaoGzl+pyXFci4rU3CosEHjBTZSRHTprCdZprCPbODTecFbNSst5p7mbn8NWJ\niAdLi0tRVpUTOCMyYLa5EojpGPco2NThRIlJDkEoQTg2TuhvltBTb/6+swrfxP0x4I61PCi6msgq\n4fIscHGGV19c2wr0t/Iqiz9rI+VqkswSxt3A8ByHMde387lduUpMDOBQ09FRzpHfs54HWs0knOTj\n19sgoa9RfD6dXbHc1zSLyj25lGfQ1VIpFMVT5Cz87jnUt7TDntPwXAkuQAm6Ubxmu6GcBukatJHj\ncGy48+dHsRMRUuNneJPjHC77aoOQyqhweaPoaamEM2fwNJ0r9epSXh4gV2SVcHh0yeLslEzpThkF\nePMyt9b3rOdc9HyiM8LIPHBqnEAEbOmWsLb1+utHv1uiaNx7OL+kiHf0SVjfvnoQNpYGDg1xpb53\ng7klR8QhLG8UuLPfPGlrfqlK5C3dYkBV1XRMzEXQUl+KspzSyZqmYnFuBrWNLXDmWLNKeBHy4gxK\n+ncKm/2NDp6unNvLEExJ/06hD2806IciZ00pu25/Aoqmo6NRbEgdTuoYnlOwqdNpmhjmjfANd0d3\nfoquOwS8McQNjx09qyexJTKEMxOESy7udW7ulNCehx11IyScIFyaIQzOcubOrn4JzdX5742IUySP\njV2x3s0Ml7TMdUR9OQ82m5ExLroUlBdZ0N0gQrzhFUZnbiwpEYsgGRONVSLiNdxLq1Bg0oDlpsfY\nV15LDiws1eLOgWAYw+I8J/jn4uqqpmNyPoLmOlEhMMYHvMgpoc8kyJFRCG8OE5qrgPWt5j1JPWHg\n4CDQ0whs78nvtjFGGJoDjo3wTWLXGgkdeSykaxEirnjTWYKqAdoKVozdBhQ6JRQ48qdFX8vvLwSB\nk2Oc8rarX8KmzvwKnhG33IfmgLvWcYaBmYx5eMGoOwcklJrAWdOLKsJJHZs7ncK1UhkFLm/MdIPm\neLsPjW2dhsxUIkJ66iKsxWUCB/hmUexEhNTYaThqmgUIJptJI+hdQGNblxBHCMczCITzKIQMw8UZ\nGevbHaalL+aCPJnutj4J1aUmzCXGA4pjHmDv+tWt9ESGcGKUMDwHrGsHtvdKKDfBna9VdEbIyByi\nXMmKsVk4/l5UgJ+qIbaqceV+aoxQUQLcvlZCyyrxsmQWeGMQgATcs4HDj7miaIQjo4SSAs4Gy113\n6hIq0FBpRVutaEC6/Qmomo72nA2a4+0LsDmcqKzJob3KGSRHT6F4jYhe3BDFLklSC4DHANQDYAC+\nRURfN/nc25Ofu9UnTHGlaNAPVZFR09giDMq0O4riQrvAVScijCyo0BlhfZvYmDYtEw4NE7rqJPQ3\nm0Mvg0swxJ71QJtIJ35bphcJBy8SipzAHesktNZe+3jzBtGE+SDDYojgjxJCcUIsRbBaltkD0tsb\nCq8TwxeGpgPlxRKqyyTUVkhoqJLQUmtBfeXqfPtcWYwQDl/meOWeDRLWNOffkLwR4PVLwJpmYFu3\neWB12sdrjdy1VoxVEPFMPlkjbGwX30swmkY4lkVPa6XgPYV8XgCE6vom4xgqWSRHTgosmXdDsb+T\nuS3756FGfSju3Wp4XsYYvLPTqKytF5JWMrKGaXcE3c2VKHAaFX5WYTg7JaO3yYG6clGpuwK8NMCd\nA+ac7KwCHLjEC2/dnUeRAVxZnRwjnJ3iEMeuNddWBndZZIWwEGTwBAmLEUIwxhCOE1JZPq8LHBJs\nVp7YRAToOi9nkVmqlVRRIqGmXEJ9pYTGKgta6yzXtaHojDA0y42thgpgz8b8EA0j4OwUh1vv28Tj\nDLmi6RyWsVuBnb2ics+qhHNTMrobbALVlBG9nVdTV2mEG3VNw+LcjGm/Wtk3CzUe5OWrV1zvRin2\nBgANRHRBkqQSAGcBPEJEozmfe3vyp2eGeBW/nIbEy6R+M4tmMZREOqOis7lCUBAuv4pgXMeWLqeg\n5DIK4Y3LhO56CWuazIIiwFvDvN7K+zdz5ouZxFKE1y9yNsDdGyV0m2BwZhJOMIzNMYy7GVyLDEVO\nvhk0VltQVyGhupxH4h1XYQ+oGiGaJIQTBH+E4A0zzAcI8RShvd6C3hYL+lstqK24tpTAWT9/niIn\ncN9mvmGYSVoGDlzkfOO715u77y4/p0TeZWK5M+K4ZLFTQm+T2Lx6uetPc51R2TGmwzs7g6q6BiHF\nXvbNQouHDDSxd0mxX9fcXs1gCfsXQYyhusG4UemMYXKOMyoqy4ywjaYTzk1zEoCZZTgX5CQAs00V\n4AyTV84vQS+9+ROMxt18LjRV8c3+WhQqY4RZH2FsQcekm8EfITRUSWiusaCxWkJNuQXVpRJKilYP\nchLxHI5okhCMEXwRBneQsBBgcNoldDVa0NdqQV+L5ZogTlUnnJkATo8TtnRz7zRfnGs2wGHHXX3c\neMkVnRGOjhGcNmBHj+jlJzMMF2ZkbOwQ2UmKqmNyPoz2xgqh3G86mUA06ENDW5ehnAYPuJ+Cs77D\nUOL3poBiJEl6FsA/E9HrOceJiKAlIki7hlC69lZDUwUiwuLcDMqqqlFcaoxu8KBEHL1tlUJRqUBM\nx4RXxdZuMaNUVrlS76g1t9RlFdh/gaf+782jtIgIZye5JbCtV8KOvqsnCiXShPOTOi5M6oilCGta\nLVjTakVXowWleTLd3qmksoQZL8P4AsPonI5Cp4TN3VZs6bWi4ipBJcYI56auPNuuNeZp1joDDi9t\nfvffYm71TfsJwwuEu9eJmLuqE85OymirtQlZfLrOMDEfRmON2EM1m04h5POgsb3LkG1MxJAcOYmC\nxi7YK3nG6nsBxVxtbqddl3lDmBZjX4FsJo3QohuNbV1C0bN5XxwgoLXByKElIgzNKbBbzQN17jDh\n3Ex+S90dAl67BOxew9PuzSSVJbx6jtcHet8WCe11qw8fEWHOTzg3oWNoRkdZsYT+Vgt6W6xorV09\n+el6hYh7tJNuPrddiwydDRZs6bVibbvlqteKp/lmFYgBD2zLD88sb37dDRx+zbXVdMZhmSInsK1L\nVO7LZb+39RQI+ieWlOEJJNDXViXAa0GvG1abDZW1xoxrLRlFemYQpWt3v52Zf8MVuyRJHQAOAVhP\nRMmcc8QYQ3L0JJwNnXBUGh8oFg5CzmZQmwPB6DrD+FzYFFdPywznpsx3TE3nmHpdObChzYwWBrx8\njgdebl1jDjPE04SXz3Dc+8HtEqpM8MtlISLMLBKOXdYw6WZY12HFlh4LuhotP3X39WsVRoT5pYU3\nOK2jrc6C3eus6GtZvadlPE3Yd4Yga8BDO8xdWCLg3DRP335gqzklctxLmPYR9q4T2TKpLMP5afN3\nlcrwRh1mG3do0QOL1YLKWmOTAi0RRnp2mC8Ai/VdV+xXm9vqUuEybrBc2byIMXjnZlBRU4uiEqPy\njiWz8AZT6G2rhDUnGDy7wgvNnT+BOE+qu2NAQqWJdT29CBwe4TBDk1iHCgAw4SHsP0fY0A7ctjZ/\nRU8AUFQ+p44P69B1YGufFZu6Lagqe+8KxmQVwvAsw7lxHd4wwy29VuxeZ0VV6er3MO4mvHqeP+ft\n68xhy4wC7DvHiRJ3DIh1cDSd8OYI8UxzE13i8qsIJRi2dDqEd7XgT4AxQlvOxq1rGrxz06YlB9Ku\nJURjidp7QxX7kqt6CMDfENFzJufpf/2PP4KeTsJe3Yi9e/diz549AABVUeCbd6GhrVMoGTC/yJOQ\nWupzBoZxK7ClRrQCGXEXqsBuvssmMsCLZ7j7taXTXKlPegj7zhK29uS3ZAGu0IdnGQ6e16CowK3r\nuLV8o5kxika4OKXj6JAOImDPZhs2deXfZFZ6JvdslrCuzfxzw/M87fzBreaZt5dmGYIJ4K614iLy\nx3RMeVVs63EKFtdiMImMogmMEF3X4J0VF8ChQ4fw6o+fhMVRAFtJBf7qr/7qXVPs1zK3//x3Pwtr\nUSmsRWXYs2fP23M7Fg5CyWaEmJGmcYPFrDNPOKljZF7B1p4CoYxDLM2VzK4eCXXl4uOOuoHTk8D9\nW8wT6TSd8MYlwpQX+OCO1QONaZlwdEjDiWEdHQ0W7F5rRXfTtTe+frckFGc4Mazj7LiO3hYL9m62\noaFqlebrWb6W01ng4Z2SqSeraMCrF3iC1t0bROLEsvff0yChp0GMJQ3OKkvt9nI47IwwPhdGY02J\n4JEmY1EkYxHUt3YYxvTggVdx4JkfwFHTDMlmf0dz+2ei2CVJsgF4EcA+IvqnPJ+h2KW3eBeRHB6y\n3z2PgsJClOUUQYqneAGkvvYqwaIZXVDe7nySO9HOzzAkssDta0RKYyIDvHCa13hZLzavARHhyDBh\n0MUnwWoTf9KtY98pDUTAPbfYMNBuecfMFUaETJaQVfjiA3hQyeng0MY7tfqJCBNuhtfPacjIwAd2\n2DDQln9x+qKE504QuhqAvRvNLZwJL3Bi3Fy5E/HaJAAvQZB7nQmPgqwqBrkZESbneGJOLtacjEWR\njPPmHAaln00hNXYGJet2w2p3viuK/Vrndnz4OKdhrlTeKqdumhkss94YHHarwFdXNMLpiSwGTCoL\nZlXCwSHCuhYJ7SZB+5EFHhT84DaecZkriQzhJ8cJpYXA/VulvMaHqhGODuk4PKihv82KvZutqCl/\n59a5qhHSMkFRCYxxQ8puk1DolOC0v3M2mawQTozw++xttuC+bba8FjwR4cwkcGKU8MHtEjobxGvq\njMeTJAm4d6Oo3FNZwsHLPIkpl1LKsX0ZvU12oVtVKqNg1htHX3uVIe+GiOBfmEVRWTlKy42dlbKe\nKV4QsWP9jbPYJUl6DECQiP77Kp+h1NRFFOWkXWdSSU5ta+8yLlrGMD4bRkt9mZDJ5Y/xZgLbekQa\n3bSPdwa6Z72I+SWzXKlvaDdX6opGePEUj9R/aHd+VkAozvDiCQ2+MOED221Y33XtCl1WCLOLGuZ8\nOjxBHf4IQzjOkEgRnA5Oa1x+Jp0RZIVTxYoLJVSVWVBXZUFTtRWt9VZ0NNpQeI2NP4gIY/MML5/U\nUFYk4aHdNtTnsXKyCuGFU5ye9qHd5uVdl5X7QyZKRGeEQ5cJTVUSBnJiG4wRzk7JaKqyobk6h+aY\nVeHyRNHXVg2bzbgAfPMulFRUoqTMSGHIzI0CFguKWte8W4r9mua2Eg0I/QMC3gU4HE4h2SqWlOEN\nJtHXVmXYsIkIl5YawHTn5GEwdgUOWN8qvrdxD0+oe2ibefq8J8yV+i3d3AM1U6ZEhKEZhpdOqmiu\nseAD223XHIwHgHCcYcajYSGgwxdiCER1hOOMd/4q4AQBq2W5BhIhI3NFX1FiQU2FBfVVFjTXWtHW\nYEVzjfWajRlZIbw1qOH4ZR07B6zYu8WWt8bMfIDw3EnCzjUStvWYJSFxy91mBe7ZKAacgwmefb1n\nnRiwjqV0DM4p2G6Ct7sDCTCdhFjKcs5OU3u3kdqra0hcPobini2wFZfdEFbMbQDeAjAIXt+HAHyB\niF7J+RxpmaSBokZEnAJWU4fCHAqYJ5CAbjIQsko4PZnFRpM6GaEEh2D2rhPZGVkVeO4UsKaJJyfk\nSipL+NFRQk0Z8IGt5pYqY4QjQzoOXdBw50Ybbt9gvWoglYjgCTJcmlQxPKNiwa+juc6K9gYrmmqs\nqK+yorrMgrKS/LRFxgjxNCEUY/CHdXiCDHM+vjk0VluxtsOGjT12tNbnbxyyLDojnBzR8fo5DbvW\nWrF3s828zR1xl316EfjY7eZMiVE3txA/tAMozklkyiiE1wbNrZvl2Mgt3U6hpkze957JILi4gMb2\nbgOTgKkyksMnUL55z7vBirnmuZ3bz/dK4Nd4v8sGS2u92FzdHdLgjfCkrlxD4dwMQ1oBbusTvSCX\nnwe3P7iNt5LLlQkPj6Hcv01CrwkzDABiScJPjqqIJAgP32pDd9PVu8KoGmF0VsPQtIqRGQ2ypPqI\npgAAIABJREFUSuhssqK13obGagtqKy2oKrWgqMA8bwTg+H0kwRCMMfhCOhYCOlxeHfEUQ1+rHeu6\nbNjQbUdZ8dU3mFiS8PIpFfN+wkfusKGn2fwZYim+1tvrgHs2mSUh8YBqaSFw51oRqp3x81aZ92wQ\nGTczPhWxNMOmDoepoWr23sM+LySLRQikyv45aIkwSnq23HhWTN4LmaRdJ6JhpJMJoTbIMq93jYnl\nNjiroLTQgs76nMJJKlckWzokNFWJL+rFs0B9OWcJ5EosRfjhYcJAK09wMJuEwRjDU4dU2KwSfuFO\nG6qvEjiKJBhODCk4PaJAUQmbeu1Y32VHd7PtqtTGaxVVI8x4NFye0XBxgjfl3T5gx+71DtRUrL4w\nYynCT46oiCYJH99jR2O1+fOcniCcHid89HYJtSaY7oUZbr0/vF0sIBWIE45PEO5dLzJlFoIafDEd\nt3Rd+wIIet2wOxyCBZz1TqOwqfumSFACrngYpRVVQm0QTyAJXWfCxpWROV99S5dT6H40FyQMzRPu\n3SCWwFiMAvvPc7aSWar8oIvw5hDhF26V0GhSA4WIcGGS4cUTKnavtWHP5tWNFSLC5IKOE0MKLk6q\naKq1YGO3HWs7+Rz6WeHv8RTjm8aUimGXirZ6G3auc2BLn/2q62d0TsdPjqgYaLfigZ3m1ntWIfz4\nGKGkkBMjco0qRQNeOMP7AW/rEb6OM9MMmi7CjYw4v72xUvRIY0kZi8EketurDBu3rvE4UkNbB2wr\num4R05GeuoiSvq0/P4qdMQaPaxJ1TW1wFFwx95YTkSpKnKjOada7GNEwH9SwtdspuLBHxwhlhcDG\n9tzCU5z2ZZF4UCR33kWShCffIuzok7C1x3zsLkzqeOG4iru32LB7nXVV2GXGq+G1UzLG5zXcssaO\nnesc6Gy8uiX90woRYd6v49SwitPDCtobrLh3uxO9reaVLZe/c3ZCx76TGu7basPOAfP7vDzLrfeP\n3SGhLqdJAxFP044kuXLJxSXHPAR3mLuuK8eNiHBhRkFNmRWtNcYFEE1k4Q+n0NtWlYNZK1icc6Gx\nXcxzuFkyTwEgnYgjHgkJQbHsUqGovrZqQ1365bGoLrUIfPVklvD6EM8RyK08GE9zL/SudeYF6s5P\nEU6MET52u3megqwSnj2iwh0kfHyvHc01+Y0VVSOcGlZw8IwMALh1owPb+h0oL3n3mTGKShiaVnFi\nSIFrUcet6x3Ys9WJilWunZYJzx9V4QkRfuleO+orzatgPn+Cv7dHdonMoLQMPHuKJ+flUkZ1xuMd\nXXUSunPw+mUG2LYep6FWEhHB5YmhpMghNMSOhQJQFQU1jSKh/obTHVe9UM7kj4WDUGVZeBC+qNPo\nbas0LIrloJJZqdLJRYIrwDnUubjcmSneK/GhbWIhr2iS8IM3CbcOSNjcZRZMIbx0QsPYPMMv3WtH\nUx6rFgCm3RpeOpaFP6Ljnm0F2LXeccOYMYpKOD2i4LXTMooLJTx4awEGOvLXYw1EGb7/uoqmagkf\nvt28q/3oAuG184SP3yla7oxx17WsiFeHXClEvPZGdamEdS3mkMzWHicKcxYA39wLUF1hpIKF/YuQ\nJElwW28Wxf42vFhbLyRWzbijpovaG+F1dbZ2O3OyVTkTo61WQm+DaFE+d4p37jKLF12YJhwfJXzy\nTnMWSDDG8L0DKpprJHzodnteTFrVCEcvKThwKoumGivu27G6sfBuSzCq441zMk4Nq9jWb8f7dxag\nYrWA6biOV05p+NBtdmzoMmlzx7hyZ8TjSbmWezjJ43Lv3yJmqCYyPJi61wRvn/Hx5jMbcjKus4qG\nqfkI1rQb0Yi3Dd3mNjicRlzz50axM12HZ3ZKKPLFiDDuCqHZJGA6sqDAZoFAJ4pn+OS/2wRXd/l5\nadKP7BKTahIZwvcPcUv9lm5xzNIy4fEDKuw24ON77aaFrgA+0X58KIs5n4b7dxdg5zrzFnHXIssB\nJU27woopcFreMXTDGOHsmIqXjmZRXW7BL+4tRGONOUSjqIRnDqsIxQi/9n6HaSLVyDwvp/DJu0RO\nv6wCPznJ4xf9OUZHRiEcGDSvZeLy8wbMGzuMLygjq5hxx7Cm3ZjcoWsqd1vbuwx1zG8WxZ6MR5GK\nxwR4MZFS4A5whpclx2A5NZHFpg6xuNfleYZwEri93+juE3H2htNujgEPzRLeGuLvySwnYcqj44mD\nKu69Jb+XRkS4MKHiJ29mUV9lwQdvK0B7w3V038j5raxCkBUeLIXE68QU/hRsr0SK4cBpGSeGFNyx\n2YH37yzIu07cQYbvHVCwtc+Ke28x64REePY4wWrlTLhcj3w2wLPTf8FEj0z5CNN+wj05RiVjhNOT\nMrrq7ajNKQXhCSRABCHbOh4JQ86kUNvUajj+c6PYY+Egdzty0quD0TQSKQWdzcatMZZmGJqVsbOv\nwKA0ifiO2V4jckvjaa5ozHZaWSU8/gZhXZuEXf3ieEWThEf3KehtseDBnTbzbEydcOC0jINnZdy9\n1Yl7tonc7HwSTeiYnFfh8qhwBzT4QzpCMR2KRihwXGHzaDpX9HarhKpyK+qqrGius6G90YaeVgeq\nTWqHmImuE966qOCV41ncusGB+3ebLwIiwuvndZwd0/GZ++2mjIiLM9wS/JW9ImsokgSeP82DeLlV\nMedDhMvzhPtyKJSMEU5NyOhpFGlic4txOOwWoTZQJOADAIPVfjMo9mVrvaquAQVFRpLAxHwEdZVF\nqCg1WmNjbt4zNtdgiaQIh0f4eOWyki7N8lZwj+wQoa/pRcLLpwmfuEtCjQn8cmFSx4snVHzybnve\nAGkwquOHr2UQSTB87J5C9LVdW1d2xggLfg1TCyrmFzV4AhoCEQ3RBIPFwumVVivfmBSVK/uSQgtq\nK62or7aipc6GrhY7uprtcJp04TKTSJzhJ29m4PLq+Pi9hVjXZX6viTThsVcV1FVa8JE7bIJlrumE\np49w8sS9m8U42+lJYDHCKb4rmddEPDO1ulTC2pbc9aBjdEHFjj5jqRNNZxibDQkF8PJZ7T8Xin35\n5nOtdZ0xjLnC6GwuR+GKKBwRp8e1VNvQUGm0GMa9BE+Y18owBuC4m9rTyLvCrBSdEZ4+TKjO8wID\nUYb/3Kfg1nU23LnR3EJxB3Q8ti+NsiIJn7iv8KoKljHCxJyKsyNZDE7KiCUZeloc6Gi2oaXOjvpq\nK6rLrSguFO+HiJDOEsJxHb6QDrdfg8ujYmJeRaFTwoYeJ7YOODFgkvWWK7EUw9OvZ+AO6PjV+4vQ\n2WT+fGfGNOw/reHTH3CY4q5HhglTXm4R5rrw4x7edu8ju4wlGoh4ILW0QMwEDiV0THhU7Og1xk4U\nVcfEXBh97UZMWtNULM5Oo7G9+22s/WZQ7KlEDMloBHU5fPtoIvt2KVeDFZ9huOSSsaOvwMCuYIzj\n6r2NEjpy+Or+GM+S/PBODn2tFF+E8NQRwod3m+dfHLus4c2LGn79Aw7ThB4iwuELCl48lsW927ix\nYr2K95nJMpwblXF+LIvhaQWlRRb0tNrR3mhHY60NdZVWVJZZTQ0JXSfEUwyBiI7FkIb5Rb4pLPg1\ntDfasLnPiW3rClBv0kw6V0ZcKp44kEFPsxUfvafIlAasaITvv6ZCkoBfukeEHGWVe/Hr2iTsXJMD\nNxLw8lmgvoKXHlgpaZl7pHvWiuUdhmZlFBeIZA9/OIWMrKG90RjxjkdCbye0LcvPhWKPR8KQs2nU\nrrhxIP+DLkau1PVeuSiWB9MMgjk1weuafGCL6KbuP8eQyAAfuVV0uQJRhm+9rOC+rTZsXyNOJiLC\nkUsKXjySxYfu5Dj6alhjOK7jzTNpHLmQQYHDgu3rCrBpjRPtDeZewPUIEWHep+HSuIzTw1lEEwy3\nbSrE3u2FqK1cfSGcH1fww9cyuHurE/fuEKl1ADA0o+PZoyp+3US5Ey2VWtCBR3aKm9Ebg4DVymGC\nlZJVCPsvmS+Aiy4ZVSViINXtT0CSgKZaowsQ9nthsVhRsVT+9EYrdsYYFudmUFFTZ8DWiQjjs2E0\n1ZagdEVJjOWAaV25VWBPjHkIvhjhjhwIRtWAH50AdvYAXcYKC0hlCY8dJOzdKKG/RRyGI0Majg3p\n+OyDdtMknnSW4XuvpBFJED79QBEaqvMbK0SEMZeKN86kcWlCRl+7A9vWOrG+24nKsmvzIlcTWWEY\nm1VxfjSLM8My6qqs2LOtEDvXF64KS2YVwk/ezGDUpeEzDxWZQkc6I/zwDRVZBfiV+0TlHk8TvneQ\n8IGtErobxWDqj44D79vE2wCulMlFwnyIz20jps5welLGjl4jt50xwqgrhK7mCkNFzyuGbwfsDu7F\n3fSKffmmaxpbDE2LubUeQldO2VKdEU6NyxhotQt1qI+NM5QXAutykjUWozzB4Bd3i3jYhWnC6QnC\nr94t1jIJxRn+40UF922zYVufOCEUlfDEgTQW/Do++3Ax6qvyT+B5n4qXDqdwaULGrg2FuGtrIdpM\nivL/LMUT0PDmWb6JrGl34ME7itHdIjZBXpZwnOHRF1IoKZLwq/cXocikzdplF6eNfeZ+hxA41nTC\nDw4Repsk7B4QA3tPH+OB1Nxa7vkWQDLLcGFaxs41Rut12WrPDTapigLfggtNHT2wWCw3XLHzin1+\nNLR1CtZ6MJpGd4vRWg8ldEx6VWzvNW6sGYXw6iVzg+XwMKfu7t1gvL7OOLOrrRa4Y534Ho8Pazh8\nScfnPugwDaTO+zV8+7k0NnTb8MidhXkhRcYIJwaz2Hc0BU0n3L29CLs3FqLEpO/qz0o0nXBpQsah\n0xlMe1Tcvb0Q79tVvOo1z41xw+Wh2wtw+yaxYt2ycpdVrtxzY2LuEKdCfuoukU004wdOjHH9kuuR\nvj5E6KmX0JFTTG3Sq0LTCf056zGfMRsN+cF0HVV1vCXoO5rby9jgu/0HgJLxGC3OzVCu+MMpcnmi\nwvG5gEoXZ7LC8cUoo5fO6aTpzHBc1YiePEw05RW+QothRv/0nE7BOBPOxVOMvvxElk4Mq+IXiSiW\n1OnL34vToy8mSVbE7y9LIKLRvz0dod//so9efCtBqYye97PvlmRlnV49nqQ//IqPvvaDMHkC5s9E\nRKRqjJ48kKK/fjRGwahm+pmLUxr97eMZCsXEZ4mnGf3zCzrN+sQxWQgRfe8QUVYxHmeM0asXdZoN\niN8ZnpdpyqsIxxd8cfIEEsJxv3ue4pEQERHxqfzezOXcPwDkW5ilRCwiPOuYK0jxZFY4fmo8Q36T\nMT8xrtPgnDjWC0Gix98Ux5OI6OBFnZ46rBNj4phemNTo/37f/P0REV2aVOhPvxGl0yOy6fnl+z03\nkqE/+3qAvvitIF0Yy5pe690WT0Cl/3w2Sr/z/y/S84cSq67FxZBGf/2fMXr69RTpuvg5TWf03f0y\nPfG6TLrJs5yfYvTt/Topmnju4CWiIyPiNUMJRs+f0UlRjd9RNEaHL6cplTW+A03XaWjKTxnZuEY1\nVaW5yVHSNH78nczt9648G3hCUmmlsdwcY4RgNC1QwHRGmAuo6MrBpogIF1yEje0iNencNFBRIrqp\nssrTiO/dLLIyFJXwnf0Kbum1YueAaKn7Izr+/gdJrO204dMPFJm6gopK+MkbSfzvfwuirsqKL3++\nBg/eUWJqBa8mRISMzBBL6ogldWSyDIxdn0fldFhw365ifPnztehtdeCL3w7hyf1xZGUmfNZmlfDx\ne4tw+0Yn/uGJJOb9mvCZjV08RfvRV1SkssZ7KS2U8MA2CS+cJuFccxXnVp+cMP6eJEnY3CFhcI6g\n5zxbZ50N7rAGRTMer60sQjiWga4bn6G0sgqJaGRZud5QUeQsinOqNyZSCiBJQqJVIM4gSUBNWW6s\ngeCPA/052aGqzlkZtw+ISWBTXt6e8cHtIiQ27WV4/hiH08wqMR6+KOOJV9P47Y8UY1u/uXe3GNLw\n949F8NSBBD7x/lJ84TeqsKnPed3ep64Tkmk+r+NJHYrKrvu9NdbY8JlHyvGXv1kNl1fFn/9zEOdG\nsqafra+y4o8/VQJ3gOHbL6Sh5swpq0XCJ++2I5Ik7D8lzvtNnUBtOfD6BfEed/fzCpq+qPF4VYmE\nhgpgxGP8jt0qoaXGBpfPeB2rxYKa8iIEImnjcZsNRcWlSMVyLnAd8p5CMQvT42jq6DFMinA8g2g8\ni64WI2g1F+A0uPXtRldqxs8567mufCQFPH+Ku0i56e37zjAQgAe25TRWJk5pLHRK+MU7RajEE9Tx\njR8l8eCtBbhto3nrmWm3iv94JorGWht++f4yVF8l4xPgCtztVzE2I2NqXobbp8IXUhFN6LBZrzTd\nUFROfSwrtaKuyoaWeju6Wpzo63CirfHqwVIAiCV1PLk/gfFZFZ/9cBkGOs2fY9l9/a0PF5sGVV8+\nqWI+wPDZBxzChnpokCEU53GLlWMoq8BTxzgmWZ/DTDo2xlBVItbJH3MrsFkloVbKnDeGwgK7wQAg\nordx7aKS0hsKxUSCPlRUG9udTS1EUFVeiMpSYwLe6QkZ3Q12VJdZDcffGCZ01krozHHlT03wXrT3\nbTJeNy0THj1AeGSn2MkrGGP45gsKPrHXbppaf+BUFkcuKvi9jxaj1mTOMkbYfzyNFw8n8dAdJbh3\nV9E10XhlhWFiVsbErAyXR4HHryIY0ZDOMhQ4LLBaeSBSlhmsS2yvhho72hod6G51YqC7ABWl14bT\nj0zL+O6LcbTU2/Dph8pN4RlVIzy2L41khvBbHyqGM4dhlMoS/u05BXdtsmJ7v3HeyyrhO6/xuEVf\ncy68Apyf4RTIlSyZZSjtvg3GbGtNJ5wYywqZxZrOYei+9ipDyWolm0HAu/A21Hi9c/s9VezRoN+Q\nDk5LNLCG6mJDrXWd8UHYmMPt1Rlh3wXC7l6j5U3Ea6u31ogsmCkv4cAFwq/fK+Lqr5/TML6g4zcf\nFLnniyEdX38qiQ/vKcT2AdGaYYyw72gK+46l8SsPlGLnhjytl5bvXScMTmRw4mIa54bTsFkl9Hc5\n0d3KlXRDjQ0VZTYB39R0QjSuwxdSMb+oYnpexuhMFsk0wy0DRdi5qQib+4uuSrW8OC7j0ediuH1z\nIT5yd4kp22FoWsX39nELrqMxpxQyIzz2qoqqMgkP32pUuprOA3e8WbbIkhmc4yyOlfvBcv7B/ZuN\nzJqMwnBmUsauHKw9neU12/s7qo3MkmgE2UwKdU2tN1Sxq4piqOCYyapwmdxvIK7D5eMF7FYe90R4\ni7v3bTRujrE08OxJ0WAhIjx7glBZDOzZaFRoskr41+cU7F5rxa614ib92uksjl5S8PmPlZgm90QT\nOv79mRhUjfDffqH8qsH4eFLHiYspnBpKY3Q6i7ZGB/o6nOhsdqCl3oGaKhtKi8SS0ZksQyimwetX\nMetVMDErY2xGRk2lDdvWFeHWLcVoa8wfJwKW8i9eT+DUUBaf+0g5BrpEw4UxwvdeSSOWJPzWh4sF\nr9sfZfj3FxT82vsdaKszjsdCkFc7/fX7jIqaiJf+7qwXE8QG5xiyKrC92/hbLp+KjEIYaDU+04I/\nAZtVEmi9i3MzKK+ufUdGy3uq2FVVMSSVJDMK3D6etGGY5GENgZiOTTnW5YSX4IsTbl+TM2B+7vL/\n4m4jr1dWCd9+lfDQdgltOVbQ+IKOH72p4vc+5ERZTqp2MKrjH59M4uE7CrFznTixMlmGb/4ohmSG\n4Xc+WrGqlR6Jadh/NIHXTyRQU2nDrVuKsW1dERpNWp1djwTCKs5czuD4hSQWfCr2bC/B/XeUobYq\n/+/Gk1cW7O99otK0sNLglIrv70/j9z9aguZa43OlZcK/PMtZQ5t7jOd8UcIP3yJ85j4JJYXGBfD8\naV58rd9IhMLpKYZCh1itcGReQaFTQked8Vkm5yOorSxEeckVDcd0HW7XJNp6+m843XGlzC/G4XRY\nUVdl5LOfm5LRWms39C8l4gyvdS0SmnPquew/D9RV8L4BK2VknnB0hPDpeyQht+PJN3hNIzMv9K3z\nMl4/I+MPP1GCShOlPj6r4F+eimLP1kI8fJe5AbB8nZHpLF5+K47B8Sy2DBRi58ZibOovvG4IcqXo\njDDhknFqMIVjF1IoK7Hi/tvLcPvWklWNl8FJGd/6cQzv312EB24vFp6bMcJ396WRznLLPfe5Lrt0\nPH9MxR98xCnkZxy8yJDMAg/vND7Xclbqx2/jrSOXRdG4AZobAFeXrPbtOaUGsoqG6YUI+jtqDJtf\nMhZBJpVEXXPbzR08zRWXJ0qBSMpwjDFGJ8YyFE4YA0uazgMT4aQxMKHrPGA66xd+nl49p9O+MyZB\nvxSjLz6eoUm3GLxKpHX6/74do0PnxKAtEVEwotEX/jlA33k+SqpJYGVZwlGVvvWjAP3aF1z0racD\nNL+YPzj108piQKHvPhukT3/BRd/4gZ8WgyYRtiXRdUZPH4jTH3/VT26/eWD19IhMf/HNKIXj4ti5\ngzr99WMZCpoE4w5d0unZ4+JxX5QHUpWcyyUyjJ49rZOcE2xKZHQ6MpwWgl7hWIam5sPC7we97hse\nPF0pqqbT4KSfVM04FtGkRsdGM0Lg0R3iAeXc454wD5iqOdM0IzP6xgs6zZsEoE+PqvTVp7NCAI+I\n6Py4TH/+r1EKRMwD5ccupul3v+SjC2Pmc39ZLo2l6S/+yU2/98U52nc4Rul3iSSg64zODafob77p\npc/9n1l66c2o6XMtSyiq0V/+a4C+9eMoqSaf03RG//pMgr63L2Ua/H3phELf2S8L5xSV0b+9rNO0\nV/zOW5eJjo2K9zI0z+jUpDgu426ZJjzi+pyaD1M4njEc03Wd5iZH39HcvnGTX9VpyGTyB+ManRoX\nJ/+kl9HhEXGgLs8TPX+aKPc9eUKcsZGWjScYY/ToPpn2nRIHV9UY/cMTcfrxobRwjohoflGhz3/F\nR/uOJvOyAmRFpydfDtOnv+Ci7z4bpEjcfBG9G5JIaW9f+zvPBlddcG+eTdHvfclHE3PmG86rJzP0\nt9+JUUY2mcwXVfqXZ7MCK2m1BfDqBaKzU+J1Tk7odHnejJWQJW/YuBPoOqOhKT9lc1kEmnpTKXZ/\nOEWzXpHlNTgr03wOS4kxRgcu6TQfyp2nRD8+QTTuEX4mr8ESiPJN1xsSz7m8Kv3pN6Lk8ppv5i8d\nTtIf/b2P5hfzGwULPpn+5t+89LtfnKO3ziSE9/9uyuRclv7237302389R8cv5F9/WVmnrz4epi9/\nJ0RZWRyHjMzoS4/Fad/xjHBO1Rh9/cdZOn5ZHKNJD6NvvqwLxlwqS/RfB4niOSpDVrnRkswYP5+W\ndXrrclr4nUg8Q5MmRoumvrO5/Z6yYlZKJJFFabHT0FEEABZCGlqqjS4kEWHMS0KgTWc8y3FHThNa\nIt7I9s71Yjr22XEdiTThvq0ibvj0wQyKnBIeubNAODe3qOLvvhvBx99Xig/cKrp6ADA6ncWffMWN\n+UUFf/cnzfjVR6qvORC08t5VlUF9B6yBkiIrPn5/Jf7xz1qQTDP80ZcXcGE0bfrZO28pwmc/XI6v\n/SCKMZcinL93uxOt9TY8/kpauI/bNlhht0k4MqgbjtttEu7dJOH1iySwebb3AIOzPKC6UvqbJUwu\nigyZlhobFkJGFoHFIqGytACRuJEJYbW+sxom74YQESLxDKrKjDEXWSVEkjoaKnOascc5N705J+Fl\nLsiP9+QwvAIxwugCcNf63MxIwjNvqdhj0iYukWL41nMpfPK+QtOknecOJfHWuTT+12er0VIvQnm6\nTnjmQBR/+XUvtgwU4mt/1oI7tpbk7R+QT3TG57amXT/8293qxBc+14Df+UQNntwXwd896kckLrJZ\nnA4L/uATFagsteDvvxcR2GAFDgm/9eFiHL4gY2jKOBltVgkf32vHq2c0hBPG73U3SqgtB87ksLyK\nnMDaFs7IWykOm4TOOmB80fishQ4LKoot8EWNa6e8xAlZ0SArOcwZ2zub2zekVgwRYWIujKbaUgMV\nLKMwnJ2Usbu/wDBpFsJLhe3XGyfs8DzgCgAP3GK81ugC4cQo4dfuMQai4mnCPz0j4zceEBNuTl5W\n8MqJLP70l0uFdOQFv4q/+04Ev/JgGbavE5W+rhN++EoEb5xM4jc/Wo0dG0xa2OSIqjKMTmcwMpWB\nayELt09BMKIikdLfDjIy4sq6usKG5non2lucGOgqRH93EQqcV9+TB8cz+NcnA9i6tgi/+kgVHHbx\nO0OTMr75TAx/+KkK9OQEdVSN8NUnktg+YMfd24zPHYoz/MuzCn7nEYehbRoRr22/plnClpziagcH\nebelW7qM93BklKGpUkJXvXEzPz4mY0O7wxBAz8gaXJ6oEJS80QlKy3M7nVUx541hTc79zfhUKBph\nTbNxjM2fndc52tQBdOco9qcOM3Q1SNjWa3zUE8Mazk3o+K2HHEIxqm/8KIX2RiseuUMM8L90OInD\n5zP4s1+vMjVCfEEV//R4AAVOCb/9idqrBlIBHlcaGk9h3JXBrFuGL6giHNUgKwwWqwTGCFaLhIoy\nK2qr7GhtdKK7rQBre4vQ3nR1KqWqEZ7eH8HBk0n8t49WY7vJemOM8F/Px+EP6/jvv1wpsGGm3Rr+\n47kU/uRTJULvgjcuaJj2MHzmfmPbzXCC15j6jfcZ6yRlFeDJo5whU7piiDMKYf9FwgNbjASBcELH\n1KJJAD2QgEWS0JDTLvGmzzxdvlZGVuHyiIyB6UUVOiOhINIblxl6GiS0Vl/5rM6AJ4/w3oQrqXQ6\nI3x7P08Jbs8JmD5xUEFliYQP7Mip27DEVf/8x8SAYSim44vfCuGj95Xi1k3iwogndXz1u37YbBJ+\n/1O1KF/FQlc1wtmhJA6diOHccBItDQ4MdBehu60ALQ1O1FbZUVpshW1pEug6IZHSEYyocC8qmJ7P\nYmQqjZkFGRvXFOGuneXYual01YJJqQzDv/8wCF9IxZ/+Rj2qK8SFeWEsi/98No4//0x+A4LHAAAg\nAElEQVQVmmqN54NRHV/5fhK/+4vFaKs3nnvrkoaJBXEB+KK8Hs/n7jdO6GiK1/D51B3GrD1/jHDO\nRXh/DiPE5Vchq6IynJgLo6GmxFAB9GZR7O5AAlaLkeGwvEltbHegZMUmlVhiBj14izEnYyEEHBsF\nPnqr0ROd9RP2n+OKZeXnE2nC156R8bkHHUK7w1dOZDHqUvH7HxMt7DfPpvHCWyl84TeqUGVSCuDC\naBrf+H4AH763AvffUbYqvTYcVXHoVByHT8fg8StY11uE/s5CtLcUoKnOgapyGwoLODOGiPc/jcY1\n+EIq5jwyJmezGBxLgTHC7i1luHt3ObrbClZV8mOuLL72mB93bC3BJ+6vFO6PMcJ//DiGjEz4/Ccr\nhPOvn8ni/JiKP/qkcWx0RvjGTxTctUkkCbx2gYEIuG9LjmE4ASgqcEdOGY2TkwwVRRLWNBmNlhPj\nMta1OgwlyH+mRsv1Yjfv9A8rcEhPICFkEjLG6OhIhhLpnIBTigdNcwNp4x6i504JkBRdmGb0xCER\nW5v26PR/v58RstU0ndFXHo/TwbNiwCid1ekvvhGglw4nxQsRxxx/94tz9PgLoVXxxnhSox+84Kdf\n+eMx+h9fmqZ9b4YpGs+fEXo1SSQ1eu1ohP7iH1z0qT8apf96ZpHC0fy/xxijZ1+L0Of+zyxNzZkH\nxt48m6I//qqfYklx7E4Py/RX/xkzHbt/eCpLQzNiHOHZ4zodHxHHZP95oksu8f5euaCTL2r8fGYJ\nj8wdW384RXOLMcMx3AQYO2OMLk8FhBhAaClulCvnZ3S6OCuO9wuniUYXxDF67HWdhmbFMX3qkEIv\nHhex8dlFjquHTQLdgxNZ+v0v+8gbNJ83rxyJ0Wf/cpaGJ8X7XinjM2n60r/P08f+YIT+8b/cdP5y\nwjRweS3CGCPXQoYef9ZHn/mf4/SHfzNFb5yIkrYKSSGa0Ogvv+6mrzy6aIqpqyqjLz0aosdfignn\ndMbo608l6KWj4jPOeM31RTLD6GvP6RRLiVj7o68TpXOWVzDOs+RzYwIzPoVGF4zxLcYYjbqClEwb\nj7+TuX1DJv/wdIDSObnRoYT55D87rdNQToo1Y0Q/+n/UXXeYFFX2PdU5Tc45E4ecQXJQ0XXFjAHD\nGgEVXVyzoouuilmRNWJYs4JhFck5wzDDwCQm59DTPZ1j1fv9UcxMv3o1Coiyv/t9fDrV1an6vFv3\n3XvuuXsJqWmjzw3yAnnrJ5YtwAsCee1bLymsZB3Qhv0e8tqXDqatWBAE8uqnFvLB912yhZqqei/5\n2+N1ZPM+O/NYt/n8PPniv+3kmnvLyKurm0hN468vkjOxxlYveevTZnL1PaXkw29bf7Vguq/ISW5+\ntJYcOyFfHP56o508855ZdiG9+71Ttqh8ojFInv/cyxSDOmwCef0HlvHSYiXk0x2ESO+DJ1oEsreC\n/exHqr2k1Uo7H58/SI5VtlO/2f+CY3e4fKS8rpP5DsdkiqZBXr64ZrYT8vE2QiScAlLdIpB3f+EZ\nnDZ28GT5fzxMkTsQFMjy1Tay/zhbHG/tDJBFz7WR0hr2MUEQyFfrLOTuZxpIS8evFFJbveTpN+rI\ngqXlZO0GM3G6zi5JIMgLZF+hnTzwXDW5/dETZN8Re58FU39AIK990kYefa1JFv9ON08efK2dbD3k\nYh6z2Hnyjze7SGM7+/k/3+wj6w+y12DbUZ78cliGFXaMkIOV9LFuCY0W66kFLa2dTtLYRvuUM8H2\nWSmechz3PsdxbRzHHf2tcz2+IDiOg05Db+vbu3gkSHJdvEDQ0AlGVKfNJm57pAJTpQ1iDlcqWXq0\nSoBSAQzNpr+uuYvHxoM+XDtHzygcrtvths0p4Ia54WyrdoMPz77TituuiMGMcRLh8ZNWWOrEoier\ncKLWi5cfycK9NyUjM4XNz/9eS0nQ4q5rk/DmshyYrUHc+Xgl9hU6ZM8dN9SI+xbE46UP23G80sM8\nftkMEzRqDt9udjKPXT1Tj/3H/YzsQG6KEnGRHPaX0sWg2HAO6XFAoaSolBgJ6NRAfQd9PD0WaOkC\nIyeQGKlEu6TQpFErodUo4XKzRd+zaaeDa0CcaRlponsveIHA4uARL8F2s0XEqpQzfaweGJzG6qzv\nLSOYMIBVJF13IIiZI1TMtK5NB32IClNgzEA67egPELz5RRf+Os2IAZlsj8aXv3Rh71EXnr47CYmx\nbCE1EBDw6ffteOC5WgzKM+DdZ3Nx6ewYGA2/X9Ux1JQKDuOGheH5f2Ti9msSsfrbNjz1RgPaOwPM\nuWoVh8XXxiE9SYPlb7fC46ULn0a9AvfMj8I3Gx2oa6GfHxWmwCWTdfh0vZsp+J8/Ro19JSLZItRG\n53EoawCcHvp4fjpQ2iimibuN48RO4toO+lydRgGTTsEUaSNMWticvu6A4YztbLFiVgM4/1ROtDl9\niDCxI8A67DziJfnfZgsQaQCMkmLm8QYR/FImzP5ygvESHWVeINh4OIgLxrLNGl9v8WDWaC1TPKlq\n8GPdbhcWXRXZk+/utqY2P559tw23XxWLcUPZok0gIGDVpy147cNm3D4/EY8tSkNS/K93z50Ni41S\n4+9/S8EDt6Xgg6/b8OJ7TQzAAWBIPz3uvzEeL3/Ujsp6H/WYQsHhjssjsbfYg6Mn6MfCjAr85Twd\nvtzogUCkC0CFbYVB+AP08fH9ORw8wTJe8tPF3zDUNCoOSZEiG4T6XuFKWF0CAjz9GhEmHWxO+jP+\nAXbKuCaE9GA71Mx2HuEGBaNbX9MhygeEmi8AVLexE6iaLQQ2NzCQHqyDyiYeVgfBmAHSupCALYd9\nuHqWnsH8lxscSIxVYdZYiZg7gO83d2F/kQtPLkySLaTWN/uw5Jka1DT68PoT2bj8/FjZgvzZNI7j\nMCrfhDeezMHAHD2WLK/G1n2shopCweG2K2KQkaTB8++3wR+gsZ8cp8J1c8Ox8qsu+Pz0YxOGaKBU\nAnuK6UAhKozDiDwlthbSwYxRx2FQOnC4ksZkTJjor2rb6c+WHiuqzkqDlvgIJdptdNCi06igVHJw\ne1nGz+nYWeGJEUJ2cRyX8dtnAg6XDynxtFiS1SnAqFVAJ2n1rTMTZMiAv74DmNSfft26kxczkx6F\nicJKARFGjpkWU1ITQJtFwG1/pReiP0Dw7lobrr8ojOkotTl4PPNOG667OEqW+WK2BPDMqgbERavx\n5pM5vxnFuNw8ikodKD3hQlW9Gy3tPlhtQXg84o+t0ykQGa5GUrwW2el6DMw1YvjgMIQZ+/7Z8vsZ\n8foT2Xj781bc/2w1HluUhpQE+jvm5+lx19VxeOH9Niy/NwnxId2qYUYFbpsXgXfX2LB8USyMIcW+\nCUM02FXkx+GyACWzkByjQGaiAvtLeUwOGU6SEMUh2kRQ3gQMCnFK2QniAGyHh2YRZMRyKGki1DQs\nlZJDlEmBTjtPDVoJN2pQZXUjGAzi7bff/tXrfKZ2Orj2+IJQKjhqIg4AdNh4qssUEHXDLU5gYj/6\nNSpbgdQYVm768AmC0bnsGLnNR4KYMYKdBvT9Dg+mjtAyA2COV/lQUOrF8kWxjMPffcSJX3bbsfye\nZESYWNzuOmzHW/9pwU2Xx2P2pMjfZK40t/lQeNyOsio36ps9aOvww+4MIhgk4BRAmFGFmCg1UhN1\nyMsyIL+/CQNy2I7QblOrOFx9URzGDgvDv1Y1oqzKg9uuTqQCL47jcOsVMXj1kw689YUZ914fR33O\nCUP1OHrCh683OnH9Rb0+SMFxuGqmHiu/cWHUAA3Fips2TIWXv/Fh2nAVwkNmCIzO4/DJFoKJAwnV\nETswFShrotlMGhWHhAiCxk4R+90WF6FE1UnCSOhvGG7UwuHywaBT4eDBg796nfuyP5UA7A/wCPAC\nDDoJ+O08o3TnDxJ0OIBxefRrVLaI4NdJguDDlQSjcmlWhUAIthUG8ddJrO7J2u0eXDpVx2jErNni\nQFqiGuPyaQZMIEjw4uo2TB5lxPSxbPqlqt6Dp99owMUzonHFBTF9Aj8YJNhxwIpNOztxrMKJgblG\n5Pcz4eKZcUhJ0CIqUg2jXlxYHi8Pqy2I5jYfqurd+GW7GS++XYu8LANmnReD6ROjZRkxOq0C996U\njHXbrXjwhVo8dEcq8vvRN6LR+Qa0dUbg+ffasPzeZOhD6JODsrUYMUCHz35x4LZ5vVrRCo7D5dP1\n+PAnF4bn0UMKpo9QYfUvfowfpKSOj8zlcKCcYFBaqLMWgV/RDIzK6f1MCRHAgSpRmCk0RREXrkSH\njXbsWo04rGTvvoNYvHix7LX+M83u8lGDNICTaRingH4SVk+DBUiOAoO98iZ2Oo/TQ1DVCsweQR+v\nbRVgcwLDc+nfv6YliKqmIK47n47IvT4BH3xvw81/jaBu1gBQVe/D+9924om7EhnWFCEEX6/rxLrt\nFjy9JB25GX1rIpktfqzbasbWvRa4PAJG5odhQI4RM8+LRmKsBuFhKmg0CggCgdPFo73Tj8YWL8qr\n3Xh9dT06LH5MGh2JC6fFYlCeSfY9slJ1eOXRLKx4rwnLXq/Hw3emUgGUQsFh0fxYLFvZijUbu3D5\nHLpB4Pq54Xh0pRmjB+kwIKv3d0mLVyE/W431+724dErvdwwzcBiZp8SOo0FcPL43AIoycUiOIShp\nEJUguy0zHthdxgYt6bEcTrQSitaqUXEI0ytgcQqIC2El2SxteOe91fj5h29QXl7e5/X+VTvdpHxf\n/wBkADj6K4+TBx58hCz5+4PkySefJFu3bu0pLuwqcRO3pKJd0yaQ3WVsgWLNPlY+wOYSyKvfsYW6\n47VB8voaVjv6QImPrPiULcY0tPrJoufaiM3BFlJWrzWTf73bKqvtXFbtJtfeV0Z2HmIr793mD/Bk\n7fo2Mn9xEVm6vJxs3t1J3J7TLzj5fDzZccBCHnmhglx5VyH54ocW4vH2XTAtOO4g85eUkSPHWT1z\nQRDIys/ayWuftDGPebw8WbKijZTJFNhWrXGQrTIsovd/9pGDZWy36Jv/5UmbpHjU1kXIZzvZjuFD\nVTwpa2I7WrcfowtNW7duJfcvfYhMOm8KAfCHFU9/C9cnzyF3L/kHefiRxyhsd9iCpKCKvU5bjvGk\nySKRS3CIRVMpvPaUCLJdph+t95E9Mh2Sr3/lILuK2Pf8Yr2d/PsbK3Pc6Q6Su56uJ/uKWOaXIAhk\n9betZNGTlcRs7buQ2truJS++XUPm3XaEvL66jpSc6Lsz9NeszewjX/7YQm5YcpTcu6yUHC7uez0F\ngwJ585Nmct8zVcQhU7i1dAXIbU/WkaPlbMH/4HFRW15a8LfYebL0jS6GGWZ1COSpj9gCdWWzQD7c\nxP42O44TUiDpsg7yAll7gCceCcumviNASht8xG63k9WrV5Pp06f34Dn0Hzld3J7uE/p8oVNw7DVN\nXcRioy+0zcWTfeUsW2RnGU9q2wXJuYR8uIVlDOwuEWSr1O/810cKTtA/Os8L5Kn3baSkhgaqIAjk\n2fc7ycZ9LMALSlzkjmV1xO5kAVRRIzr1/YV9s2P2FXSRG5YcJQ8/X0HKq+Wpk2diNQ1u8tQrleSa\nRUVky57OPhdTcbmTzF9SRgpL2Pf2eHly77MNZNsB9vPvO+omj77ZwbBk6loD5OFVXQwVrLw+SF75\nhr2Rbi/myaYjLLPp852igw+1FqtANhezv+XhSi8xS+QZbE4vGTNu4v+EYy+ubGdu+mWNPlLXTuPM\n4xMXuJQNceAEIbslmiOCILaxN0nkBsw2njz1EUvFO9EQII+/Y2N+r+aOAFn4r1ZG3kIQBPLS6jby\n3jdmImcffttKFi+r7JOa6/Hy5L3PG8m824+Q1V81EpvjzCm8oRbkBbJ5dydZcF8xefi5CtLYIs8m\nEwSB/PuzFnLfM1XE5WbXZmGZm9z+ZB3pcrDfe8VHneTnXex6+HKTi3y7lb0ZfLrJR3YWS4IWQSAr\nZYKWZgshX+5iP++ecp5UhQylCQaD5LsffyazL7qa6PV6WYduMpnOuaQAd/Jfn+by+JmhAxYHjxhJ\noSbIE3TYgSRJm3V1myiTGcoYIITgWB3BkEyJFKdVQLtVwJAs+isWngjAoOMwIIPech4p98HpFjB9\nNL2Fdbp5rPrCjLuvi0OYZDxfa4cfT7/ZgMU3JGHsMDY94/HyWPF2Ld76pAH33JyBZ/+Rh35Zv92V\neqqWmarHE0ty8Ng92fjsuxY8/Vo1HC626JLfz4iH70zFC+82oraRbsfXaRVYsiAOH31vQWcX/dyx\n+ToYdBx2F9EMmvQEFdITlNh3nC425aUqwAtAraSNekgmh5IGUEVUjhPzjdVt9GeNDwfsHjEPHWox\nYQpYHHShiQR9OHL4gMyVOav2m7gGAKNOTeXACSGwOAQG2y1dYspJmhevbmXlA5o6xdmx0nWwv5TH\n6P7sgOj1+704fxw7gPqrDQ5cdJ6JKYjuKnChsd2PGy6RvAGAH7dYsPeIA8vvz0BEGJuxrax1485H\nStBq9uHd5wbjpitTEG46O5ldpYLDjInReP+FwRiRH4Z7nizDT1s6um+iPcZxHG6/JgHZaTo893Yj\neEmBfVh/Pc4bacJ735iZ5103Nxw/7XTC5aELqXPG6bCn2M8cn5Svwt7jPPUZFByH/AzgWJ2UySWO\nh7RKyGUp0RyaLQTFxcV44IEHkJaWhkv/Mhcbf/oSHk/vGlMoFJgxcxZeW/ku2tokC+QU7WzRHT8D\nsAdAP47j6jmOu1nuPKVSQYnJA4DFJSDKRH+MdjsQZQDLJGgHsuhZBmi1iv+Vgv9AOY9R/ZVMHnPL\nYR9mjWZZOd9ucuLyWaxM6X9+tGLsEAMG59K5RbeXx9NvNuCqC2MxYQRdDAaAxlYv7n6iDIQA/352\nIEYPZc85Wza4nwkrlw9EbLQGCx8tRWUtqw8zpL8Rt12diKffbIDNQTvwzBQtzp8Ujg/WdFLHOY7D\nlbPD8N1WJzOBZuZoHbYe9lEMGY7jMLa/EgfL6dePMnGINAK1EoxmJYi/aeh6VSg4xEeILAL6NZSw\nOOnFtmPHdgSDv4898Gt2qrgGAKOepgZ6/QQCIZSGNwC0dBEkRdHHrE5xSlKcBCLH6wkGp9N1oyBP\nUHCCx1gJE6bFzKOhjcfYQXTgVNXoR21zALPG0QGLw8Xj4+8tuOvqOIbZUnDcia9+NmPZPemyTv3n\nrWY89NwJ3HhFMh5dnI2YqN8nQd2XqVQcrrwoEa8+OQDfb+jAc2/VMowWjuNw17VJ4Djg3S9bmde4\n6oJI1Db5cegYvSaSYlUYOVCHn3e5qOORJgWG5qqw+ygdtKTHc1ApgRpJ0DIonUNpAyTrQMy114Sw\nY1pbW/HF6pex4K+jMHToULz44otoaWmhXis/Px8rVqxAQ0MDfvp5HWZfeCn0+l+f89CXnS1WzLWn\ncp4U/LxA4PQIiJTogrd1ESRG0uB3+cSW9GR6sh5KGwgGpoECPy8QFFaKuhmhVtcShN1FMDSX/hwH\nS7zQqDmM6E8Xv8prvSgodeOVB2khcUII3vi4BQNy9Lh4BhvtlJxwYtkrVVhweTIunhnHPB5qnRY/\nDhZ14WiJHdX1brSbfXC4xMjUZFAiNlqD7AwD8geEY+zwSCTEyU9A0qgVWLQgDYPzjHjouRN4aGEW\nczOZNi4CtU1erHi3CU8vSacizHmzIrB0RTMOHXNjdH6vE8hL1yA1Xo3th92YNa53t5GbqoROw6Gk\nJoj87N7rOSJPic1fBeHzE0qfY2Aah9IGQk1+jw0DBEGcfhUdUitLiuTQaiNU/0KYnoM/SOALkJ6B\nKRs3bvzVa/t77VRxDQBGPY01q0tAlEnJFPPbbcDITPq5te1ARjxN3xUEgvJGYMFM+tzyBgGxERyl\nzwMA2474MHmYhtEsX7vFiUummpjo/rOfrBg/zIg8yYSyDksAL7/fhAfvSEViHP2dCCH44Mtm7Dpk\nxStP9Edact99GYJAUFHtwqGiLpRVOlHX6IGlyw9/gECpACLC1UhO0CEvy4iRQyIwPD8cOq08iywt\nWYc3nh6Al96pxQPPVGD5A7nU7kCp5PDAbam4/5kabN1nw/TxvQV/rUaB26+KxVufd2BIv1SKbPDX\naSY8/pYZ5080UrMJZozSYdUaJ2aO0fbsrDiOw+j+ShwqDyI7ZPhHbDgHg46gsQNIDwk6M+OBXcUe\nVBz4Hh9//DE2bNgAnqd3nACQkJCAeVfMx7QL5+OquWN68CKmVIBAkKUsn4r9qawYo452qHa3AKNO\nwWxL22zAOAk7oMEssmGkaZiKZuCyCfTzK5sERIex4N9Z5Md5QzXMlvmnnS7Mm25iFCU//t6Ca+dG\nMSyCLXttqG/24eVHshj2y/EK0akvvSMT44bT08e7jecJdh2w4Pv1raiodmHU0AgMHxyOC2fEIzFe\ni7CToHW6eLSbfaisdaHwmA3v/qcOGWkG/GV2AmZMioFKxW64pk2IRmy0Bk+9WoV/3JmJMcPoz3DD\nX+Px8Iu1+G5jJy47P7bnuEatwI1/jcYnP1gwYqCe2rlcMtWIf39rw/TRhp7jHMdh8nANdhX5KMdu\n0nPISlSgpE7AiLzehdovBdhdCoraxXEix7e+g3bs8RHi1CVCSM/15TgOkQYFbK7efocNGzbIXt9z\nYXotvZS6XGzAYnWKVEZpM1G9GRghEUZr7ATCDUCkZAhMYSWPkXksfbKgPIBHb6LTgXUtATS0BXHv\ntXTUV9/ix4FiF15/hA5YBIHgpfebcMnMaAzpT6cMCSF4+9NGHC1z4rUnByBcJpIHgC5bAN+tb8Uv\nW9uhVikwdngkZkyKRWaaHjHRGug0YrrOagugsdmD8ionPv+uCf98tQKTx8Xg8ouSkCeTrtRqFHh4\nURbe/rQRD/3rBJ5/JI+i/ZoMSjx0Ryoee6UOg3L1SIjtdb5D8vTISdPi5x12zJvVKywVE6HE6EE6\nbN7vwrwZvdcuNV6J6AgFiqsCGJ7X+zrDc5TYXBBEIEhTHPslc6hoJkiP5yAIAnbt2oWPPvoYn3/5\nNTwuO/tdtDrMm3cpFixYgNmzZ0OAEvvL6RQpx3Ew6NRwedmGrFOy003Kn+k/AMw07upWP6mUTKV3\nnywuSQtwGwoJKZXoZ7R3iRIC0nO/2OIjuySFDo9PIH9/3cpUvEuqvOTB19jC1/6jTvL3FxqZIleH\nxU+uva+MVNWzBZ3KWhe54s5CcqCQ1eLutj0HO8l1iw6TOx8sIpt2dhCv99SZMX4/T3bsM5N7Hy8m\nV952kGze2dFnwfRYuYNccWchKSphi6It7T4yf0kZqW+m2ROCIJAn32wmG/ewbIR/vmsm+4vp7+z1\nCWTpG13E6qCvaWFlkHywjmXTfLiJJ7Vt9OetaSPkBxnNn58KeNIl0eOoa/eT8pP6GrW1tT0FJq1W\n9z8hKRBqu0s9zFT6kkaBHKmhj3n9hLy/iR2msamQJ7uO09/f6xPIE6s9xCWRIdh91Ev+vZZlPf37\nGyv57w72+L/ebSU/bmUx+v0mM3nguWpZ3aPVXzeRux4pIXZnX4XUIHn7k1py0Q37yfMrT5DySsdp\nMWPMnT7y6bcN5PK/HSQPLi8hDc3ysheCIJBVn9STRY+VyLLBvl7XQR5eUcMOM2nzk5sfrWUIEE3t\noryCtBC9t9hHVn7DXrv3fvKRoir6Ndq7BPLUO2XkscceI5mZmbJFUABkypQp5JU33iXf7WZ11/eV\ne4hdopPVZhHlBc4E23+qHrtWTUcadrdAqZsBgNkBxIZDEj2LXagpkjRMdSuQm8SmYcoaBAzJot+r\n6EQAOSkqZhzcpgNuzB5vZKL4r9d34eoLI5ndxLtftuLCqVHITqO3oVZbAE++XIVFC9KYKBkAHK4g\nnn6lAm+srsXdt2ThrX8NwczzYqHtY/spZ2q1ApPHxeDVp/Px2H398Mm3jXj42TJYutjW+sH9THjw\nriw882Y12jroDs3EOA2uuTgWb33aQhWDOI7D/LlRWLPRhqCkEDVnvBGbD9D5SK2Gw9AcNQrK6Pcf\nkK5AbavAFEBzEoFqSY4yOVqsqQQlu9S4cFGrPNTCDQrYTxa1QtMwo8eOZ77/uTRfQNSjl84CMNsJ\n4sIlOXeruEORlJ5Q3QrkJNHHyhsEZCQoYJDIEBwoCTAjHO0uAYXlPkyTkAGqG3yobvRhziQ6uu/s\nCuCL/5pxz43JDOa37LFg865OPPtgrmxz3LEyO25aUojWDh9WvzIM/1iYi345pj57OeQsJlqDay9L\nxeerRmLY4HAsfKgYX//YzLT5cxyHO65LRWqSDi+9W8sUVOfNiYHLI2DrPht1PDlejTH5Bvy0gwZV\ncpwKmUkqHDhOR8zD+6lR1RSEw02nQvKzFDheK4LVYrFg1apVuOSCiXjy9gFYvnw5amtrqfNTM/Lw\nz3/+EzU1Ndi+fTvuXvg38KoIZn1FGBSwS97LoFXDIx1gcIr2pzp2aarD7hEQrpc6doLYMBoQVheg\nUdGEf0B0ElkJ9Lk1LQJiwzlmjumhMj8zlLrLwaOk2o+JQ2knXVjmgSAQjB5ML4qjZS5U1npx5YWx\n1HFeIHjmjWrMmBSNaRMkdx8AJ2pcuPX+IoSbVFj98jCMGxl1WqCXs6EDw/HuiqHIyTTg1r8X4Wgp\nu+UbPTQcV1+ciCdfqYJfUnS6aHo0nC4euw/TujL9s3SIj1FhdwFd0h85QIsWM4/mDrpYOXqgGgdL\nafBp1RwyExXYcaAew4cPx5gxY9De3o6sRA7VkvqWRgVEG4F2eh0iNoyD2UGDP0yvgMsrShSEpmGm\nTZckos+x2d0CwvQKBu+dTrGuEGotVrZuZHMReP20HDUAlNTzGJRBr5cuh4CmDh6Ds+g0564jHowc\nqGPSiGs3d+GSaRFMwfTDb9sxZ3IkUhPpnHt1vRtvfdyAp+7PQWQ4/R6EEHz+XRMef6Eci2/OwhP3\n9UNcjHwN6FRNrVZg/qUpWPX8UGzZZcbDz5bC5aYxx3Ec7r81Ay1tPnzzM12RV2180sIAACAASURB\nVCo4LLwuER+uaYfbS0cL82ZFYsNuOyO1MWOMAVsO0MVVnYbD4Gw1jlTQ2M5J4vH999/jsssuR1JS\nEhYuXIh9+/ZR50RFReGuu+7CL5v34rmPy/HYY48hMzOz5/NFGoFOCWMmXMax67UqeH1sXv5U7JxN\nUPIGCJQcegph3WZxAJJh3Wi1AomSGmWAJ2ixAGmS2mR5g4D+6ZIhzF4B1U1B5OfQwNx31IuRA3XQ\nS4bv/rzDjr9Mi2AW5odr2rDgsnim23PNujYQADdekcx8z6LjNix96jjuWJCBJbdln1aE/lumUilw\n23UZeGhxLh57vgy7D1qYc+ZdEI/EOC0+XtNMHVcqOPztygR8vLadoYldMj0C63bSNwqVisOkYXrs\nLqSpj/3SVbDYBXTaaFAOSFfglZdfQFFREQ4dOoRXX30VSdFiR57LK6GHRbEsmJgwcViw9DMbtBzs\nriA2b97cc3zW7NnsxTmH5vAICJPsRO0eQKtm8d5iZRldvcVUmrlV0SBggATbhScCGJKtYoqmuwo9\nmDKCjoTM1iCOnfBi5gT67lLb6MWREieumksHLIGggOdX1eLW+SnITqeDHEIIVq6uxcbtHXj7haE4\nbywb0PweS0nU4Y1n8hEfq8W9jx9Hl412sBqNAk/cm4Mvf2xDTT2Nyf7ZBgzpZ8CPm+n1kBirxqAc\nHXYcooE1rJ8W5i4erZKJXSP7q1FYEQAhBAcOHMDixYsxIDcFX75+FdauXQO/v3enqlKpMOa8S/Dt\nt9+ipaUFb731FuZMH48gz8FFbwYQYwI6JTp9YXoFHBKKpVKpkK2jnYqdM8fu8BBq6AAggtfmAaIk\ntZO2LpEbGmotFjFlI10oJ5oE9EuVTFqqCSI3lVXA21fsYaL1lo4Aqht9mDiC/hAHjzrh9xNMHk0z\nTeqbvfjyxzYsvT2T2cIWl9rx+IpyPH5fP8yYRC8a6jWa3Ph8bQMe+9dx3HTPIcy7aS/m3bQXN959\nCA8vP4ZPvq5HVS2ruNhtY0dE4flHB+KFlZXYd9hKPcZxHO69JR0bdnSirIpOpQwbaERMlIrZtg4f\noIfDJeBEHZ3CGT9Uh/3HvNT2V6ngkJ+tRrFkzFheigKH9m3q+XvDhg1QcBxSYoBGidBXQqT4G4da\nmA7wBVnhJJNegT37DsFiERdtYmIiJk8Y08eVOTfm8AoIkwQLVheL6yAvFlSlNMdGM0G6RCOpuZPA\npOcQaZJgrCrAsLwa2gLw+gTkpdPHN+61Y/IoEyUfAQCf/diBy86PhUFH3zQ+/74V8TEanD8lhjre\n7dSPlTvw2nLR+cpZkCfYd9iCtz6sxr2PFeGa2w9g3k17cfkt+3DH0gI893o51m1uhd0pn25QqRS4\n/45sjB0Rib8/dRx2B31efKwGt16TghfermGCk2svicP3myxwuemI94LzwvHLLjuNYSWHsYN12F9M\ne2CTogVfffw8BgwYiHHjxmHlypXo7KQpwWPHjsWbb76JEzXNuHbpWlw6bx60WvF6cJyYZmuT7Eaj\nTRysLvrzGrUcPH5WMC8vnWXdnYqdM8fu8gow6dioxqBlNTTabeIFCrVGM5Aq8ZVOD0GXkzCyvcdq\nAky03mENotMmMNKlW/Y7MHVMGLNV/XZ9J666KJYRYvr3Jw2Y/9dEJMXT4G5u9eLxF8rx6D15GD1M\nclc6aYXHunD3I4VY/FAhmlq8mDIhFg/d0x+rXhiBf68YgUeX9MesqfHotPrxwFPHcPvSAuw91Mnk\nFQFgYF4Ynnl4IJ594wQqa2gHHhWhxu3XpuKND+upnCXHcbjmojh8u95MN14oOMyeGIbN++ioPT1R\nJXJ5m+nIJj9HhePV9KJzWuthbqno+bugoAAdHR1Ii+XQaKY/f0KE+BuHfi2RBSM6xFAz6RTYtKk3\nvz5nzhwopRq359hcXgKTTppOJIiSpAfNDiDSxObXG81ACu1LUdkkIDeF/p4+P0F1cxADMiX03WNe\njM3XUVjlBYKt+52YPZGO1ptafTh+wo25U2kH0trhw3cb2nHvLemsKup/W3DkmA0rnhgkm3P3+QV8\n+V0jrrhlHz74vBZ6rQLz56Xh+cfz8faLI/H6s8Ow8OYc5OWYsGt/J666dT+ef6Mcre1e5rU4jsNt\n16VjRH4EHn+hnMlNnz81BiajCj9toXWgUxK0GDnYhPU76UBncK4OAgEqaumgZdwQHQ4c88LhcODD\nDz/EjBkzkJebid0/LUdFBa3XkpSchjlX/AOlpaXYv38/Fi1ahMzUOBi0QKckIyoXtEQZWVwrFBz0\nWo7ZzSoV/88idpdXYLSobW5R9jLU/EHA6WWjnRYLQXKMJL/eKhaXpIXQirogBsp0mg7vT3fpEUKw\n+4gLU0bRb1bd4EVrhx8TJY1IBcfsaGz14pLZdD7I5xfwxIpyXH9FKsaNZO+4nVY/HnvuOJ55tRxz\nZyVizerxWLowD3OmJWBAbhgS43VIiNOhX04YZk6Ox5Lbc/H1e+Nw7bw0rPygGn9fViy7CPL7h+Hu\nW7LwxIvlcEo6UGdMjAYRgB37aaAPHWAAx3EoKqORdt5IE/YfdVONSRzHYcQAHQrL6Pful6ZCdXOQ\nWnSbNm2iziGEYPPmzUiKFtMPoWbUAQpO/J1DLcIgYoI+l8OObb2Offb/WBomyBMEgoTZHdrc4vcJ\nNbOdjdbdPgK3T9yNhlptq4CsRHq5VjYFkZ6gZN7rSLkPIwfQO9GSKi8iw5RIS6QDmZ+2WTHnvEhm\nhu6HXzfj0jnxiI2mzz9aasdna5rwzEMDZJ36wSMWXH/XQRQe68KKZUPwzosjcfP8TIwfFY2MNAPi\nY7VISdRj2OAIXH5RCp55ZDC+fGccIiM0uGXJYXzydT2CQZkmpBszoVJx+ODzeuaxO65NxafftcDt\noaPzv8yMxk9brZKOZw6TRxmxq6AX7zzPo/L4Fnzz/p1ISEjAzTffjK1bt1KvZTKZcNNNN2HLli2o\nrqnB2LlPITuHlphNjhZJHqEWG86mXYxa0a9Jd6NGrQJu35nx1qV27hy7j8AoAZPNTRBhYHPuUSZA\neuNqlclN1rWJjj3U2iwClEowmuuF5T4M60dH2ZX1fqhVHDIkM1d/3mbFBVOjGG32D79uxi1XpUAt\nyYO9+2kdkhN1uHyupEccQEmFHbfcexipSXr8560xuHBG4inl0ZRKDtMmxeHD10dh+OAI3HpfAQ4V\nWZnzZk+Jw6ihEXj1vRrquELB4db5Kfjwm2Ymar94ehR+3ka/VmyUCqkJahwtp/OXI/prcaScjnaM\negXio5SobeldWHIc8w0bNiAxCmjvAsN2kFsAEQYONsmQA8HvQlFBb7Fq1qxZzPucS3P5xG5TaZQr\n69gdbDG1u54kre/UtwvIkDj2ivog+knSLRYbD4udR24afXzvEReTXvT5RfbIhVPp/HhtowcFx+y4\nYi6tge328PjnKxV4cFEOEuPpGwchBO/9pwb/er0Cf1+Yh389lo+8LHmFRqlFhKtxx4IsfPDqKBQc\n7cK9jx2Fw0kHJkolh8eX9MOG7R0oKKZzG7mZBowYHI7vNtBC6P2z9IgIV6LgGJ3GnDTChL1FLhQV\nHe1p7Z8790JUFH7LtPZPnT4Hl936Htra2rB69WpMnz4dOo0SSdEcGjpoJ5wUzaHFIsF1mHgDl+5G\nI/SAXSZocfnOzgzqc+LYCSHw+gmlewwADq+YWw01i6QrERC3ugFebOAItSazgFRJbrK6OYicFDqy\nCAYJqhoCGJhFO/DDx90Yk2+gFlUgIGD3YTtmTaTTKSUnnOiyBzB5HH13qap1YeP2Dtx/RzazuAuO\nWvGPp4/hgcV5uPPG7F8dQt2XqVQKLLgqA/98aBCWrSjFjr1m5pyFN2ai6LgNRcfpBTBicBiMBiUO\nFNLHp46NQGGpC05Xr2PmeR5FO5bjtluuQmNjY8/x7FQ12q08nJIKfk6KEtVNwZ7nSiN2QHTsGhVg\n0rOF0SgTq60RrheLraG2Z9c28CdlBIYNG4bERPbmeS7N4xNgkAQsvgCBQMTJUaFmdYrfO9Tau4B4\nSebO4iBQqUDpgQNAdVMQual0wFJa48eATLYJ71CJG2OG0AvmQJEDuRk6xMfQH2ztL+24ZHY8DHr6\ntT/6qgEjh0Rgwmj6RkAIwcv/rsSeQxa8/8pIjB91ZoXUxHgdXnpqCPrlmLD44UJYJTTeyAg1ltyW\njVfeqUZAMkjj6osT8cPGDqZTc9bESGwJqSG1trbii/+8iR/em4vhw4f9Zmv/ls2/IGvo5eAJ7ZhS\nYhVolqQU4yNYdpdBK+baPRJGcphe9HfUuRoOnv/PEbsvQKBSskJIUg1jQAR/pCQN03Ey5y5t1242\nE6TE0l+puolHVrJKciyAhBglQwU7XOLGKAnFsaDEhbQkDeKiJeBf345L58RT34EQgtc/qMHN16Qz\n1LDySgeeeL4UTz84COeN7buQeqo2YkgkXlo2BC+srEBBMZ3E0+uUWHhTJl57jy4qcRyHyy6Ix9r1\ndGRjNCgxbIARe0NG6n311Vf48dtVOHLgJzz++OM9x1VKDnlpapTX0UjNSlahpkV0uIcPH4bVKu4A\nTBGJiIgQCyRNTU0oKytDnMwCkMs7hulY8IfeMObMmdPX5Tln5vGz/HXnyYBF2pvRJVNQ7bARxEfQ\nz2+SwXWQJ2js4JGRSGO7rNZP6YwDQG2zH1o1hxTJJK8dB+2YMpYuXtmdQezYb8VFM2iMNjR7sG5r\nO+64gZ078vbHNSivcuCNZ4chKvL3TQtTKDjcc2sOJo6Jwd+fLIZHQlmcNCYKifFarFlH82az0vVI\nS9Zh5356LUwaFY4DhWZ8/MlnmDt3LlJTU3H//fejo+U4dV5CQgIWLl6Cq+7ehKKiIixduhTJyclQ\ncBwyk1SobqE/R0ochyYz7YTjIwGzDUwNTC5oCdNzcEhG6+m1Cnj8/48jdm+AQCeJVgkhcPkAkyRi\nt7tZx97pAGIkOUibU6STSfP2De08MhIlo+8aA+iXTgPQ4eLRZg6gn0Q74+BRByPy5XQFcaDQhtkS\ntkBRiR0dnX5cPDuBOf+x50pw3525GDlEvpB6JtY/NwxPLh2Ip1aUotNKO9ppE2Kg0Siw6wCd9Js8\nNgonat1oN9Pnjx8ehoNHex37zz//3PP/P/20DoLQC+LcNA2qGuliaXqiEvVtIvhDm4cGjpiFiefN\n6Pl7w4YNiAkDOu3SBg02n65Vi/MjQ/P8oSme/0XHLmKbdexSXHv9YiQnHRjT6WDz621WAUnREppk\nJ4/ocAXzXpUNLLaPVXgxtL9kcExAQFGZC+OG0VuGbXstGD00HFERdGDyn28bccVFSYiWOO6d+8zY\ntKMdK54YAqPh7CiUcByH22/IRFaGES+vOsE8dteCDHzxXRMjCHbR9Fis3yHuYAVBwI4dO/D3++7E\nT6un4MYF12HdunWUXotKrcM111yDn3/+GY2NjVj5xitIzRyCdgv9uhmJSjS00amhxCgFWq00hrVq\nDlo1m2KRw7ZJB0gnO+rUHNPUd6Z2bhy7nzBj8LwBQK1io3i7W9ySh5rFQRAtoX21dwlIiKK/Ds8T\ntFl4JMfSjr26KYCsVBq4ZTVe5GWwxdTDx5wYPYQG/66DXRgxOJwpHn3xfTOuuSSZYfW88X4VxgyP\nwszJEmnKs2Bjhkdh7qxErFhZwXaRXpqCL75ros7XqBWYMjYKW/bSDn9kvglFpS4EgwSCIFDOuaOj\nDcXFxT1/Z6eqUS1x7DERCnh9oqhbqPMdM2EWho3pzYOLjp2DRZJPDzewC4LjOBi1ogAcANTV1fVM\nlNHqdDjvvPN+4+r8+eaTwbbLJxbMQs3mYXFNCIHFAURL8u7tVsJgu6ldQGocjWuPT4C5i0dKPI3L\n0movBmbTd5bjJ9xIS9IyUrtb9lgwcxKdSjFb/Nh90IpLL6DTXlabHy++dQJPLh2IiPCzq/DIcRyW\nLszD0VIbk27MzjCif44J67fRO88JoyJRcKQUSx94FDk5OZg6dSref/99+Lw02KZMmYK3Vr2DeQv3\n46OPP8WFF14IlUq8DlkpbNCSEqdEUwcdscdHcTDbWHpidBhYbOtFxl+oheK621RKQCBgmD9nYufE\nsfuDhOGfu32ARKodhJzMu0sWQJdLpImFWoeNIFayhTXbBEQYFYyyXX1LABlJNKAr633Iy2Q57YIA\npEqYBPuO2DB5LB15t5t9OFbmwJxpNEOmtMKO/YctWHyLROXpLNot8zNQ3+jG/gK6AHre2Gh0WPyo\nqhNzHF1dXXjggQfQWPEl9hXQW9aocBXiY9SorPOguLiY0YEOddYZSSrUtwYYberEGCWq6m3Ys2dP\nz/Fp02ZhwLDeztBt27ZBr/bBJkm76DWidG1AosJr0ALuk5uL0JvNmHGTodP1rS54rswnh20/gUEa\nxcukHd0+cXFLny+H7dZOHkmSgKWhNYiUeBUTWFTW+xgVx6IyF4YPpLfCNkcQNQ0ejJKogq7b0o7p\nE2MQHkY77w8+q8OMyXEYMlBe7O73ml6nxIN398cb71Uxw6kvvygJ/90oYrS7tX/a1EnY9PWleOnF\nZ5nW/ojoTDz99NOorq7G9u3bcdedtyE9JQZ1zbQT78Z2qCXFKNHaSb+/RsXBpAdsTtoJR5rY6DxM\nplZk0AAeiWPnOA5aNQdf4P+tYxdbyUPNGxAXd6j5gqKao1pyrl2GYWCxE0RLdDjarQLiJZGOP0DQ\naeORGE2/aG2TH1mS2ZSllW4MyqWLqcEgQWGJAyPzafBv3mXGlPHRjPToe5/W4qZrMmA4S9tUOVOr\nFbj9hiy8959apvFiztQ4bNwucnyXLVuGF198ES+98CD27t7ANG8MyjWgpMrTJ6Ol28KNCnAcYJPo\no8dFKbBh49YejfThw4cjJysR2vAs5OSIw03dbjdKj+5hIhiOE2mP0ihGrxbTFtLPMGHy/5aMQLf5\nA4SZI+D1sykXl0/8vqFmd7OEADGKJ4gOY3eoUmw3dQSZaL3LwcMfIIiX4L20yoNBufSbHTlmx9CB\nYRTLixCCDds7cL4kYGlt92LzznbcdPUpzfo+Yxs5JBKZ6Qb8d4OkwNlfj6NHNuLCuZf+Zmv/rl17\nMGv+z1hy/yPIysrqeTwrVYPaJhpwKfEqRjYjNlIBi12Qic4VsEhkL8L1HGzS5iOdeNMONa0a8PMs\nO0yj4hga5JnYOYvYZcEv2c25vezEduBkkVWyAKxOgihJesbcJSA2UjLEwxJEbKSSoS7Wt/gZmuOJ\nWg/6ZdFhVWWdG/ExGiYHuWNvJ2aeRxec6hrcqKxxYe6sP565MWVCLDxeHkdL6A6JGZNisWOfBYQQ\nfPfddz3HvdbdOFZBV3T6ZelRWeuR1TnfuXNnDxWM4zgkx6rQIlkAcREKbN9KNw9FmThYnYTKh+/a\nvhEeH5iFIrc91WnEmz7P85SMwNiJ/1s0R0BcpLzANhx5Ayy25dIzDg/r2N0+keMvZZCZu3gG2y0d\nQSbt2NDiR3qyhpEnqKrzMtguLHFgxCCJ9G+jBz4fj8H96eNrfm7GRbMSz3oKRs5uuDIdX/3QBEEQ\ncPDgQdx9991IS0vB/s0P4Jd13zOt/cmZ0/DNN9/0tPZPmjQBuRl6VNbR0URGkgZ1LXStKTlOhWZJ\n2kWt4hBm4GC104FMVBgHq9SxG2Sicy0YWQGO46BVidgINY0KzFCbM7Fz4tgDPGG2iz6ZKN7jZ6N4\nsQGEXSgOF2HoYFaHgKgwichYF89w2n1+ATaHgLgo+gPUt/iQnkyvvopqF/rn0KvP7eFR0+BG/gA6\niv9laxtmT41nulj/CFMoOFwwIwFLljyAESNG9LBHsjMMcLqD2H+gBHV1dT3nN9XuQXkV7dgzUrSo\nrrdhx44dPccSEsRCsM/nw86dO3uOx0YpYbbRCyAqXIHD+3ud75w5cxBmAOwuutC5ceNG6LVsFKML\nic67rTuCKSgo6JERSEhIREbuoFO9NH+aBXnRqUtprv6gGKGFmlcG2y6ZQMbhZnENAF1OIottKYZb\nzQEkx9HHzNYA9HoFM+qxosaN/jl0eubIMRtGDo2kFVR5gg1b2/6UgAUAIoxdKDnyIXLzBva08PfV\n2t/c3IyJF7yKKdP+0tPaDwAZyVrUN9OAS4pTo9VMBycxEUp0OXgmko4KU6DLyTpxaV3IIBOc6DWA\nR0Y1QaMSsRFqahWHwJnpflF2Thx79wIINdkoXibScfu6uaFSqiSBSRLt2JwCIiXg77QJiJE49g5r\nELFRSmYsXmOrH2lJ0ijezcwtPV7uQL9sE8NL37KrHXOmnf2CaaiFslUSohqxbdO7KCwsxOLFiwGI\nDn/YoHB8+vmP1PM6zY3Yf7CEOpaaqEVx0V74fCIyBwwYgGuuuabn8dBUSEyEEp1ddATjsjWgtUlk\nMeh0OkyaNAnhBpHWNX36dCiV4nUvKCgA7+mAWxLF6DVyjl286Ye+94yZs8ALv08d848wuYAF6CP1\nKLdD9ck4do+oEUO9T5DA52ePW2w8YiTDZVrNQSRIeOoNLX6mbsTzBHWNHuRkSBRNSx0YPpgOWIpL\nbYiK1CAr/ezN75VaaGt/VlYWig+uQk11BXVOamoasgfdiGPHSnpa++Pi4pCXZcCJGtrjpiZp0SCJ\nzhPjVGgz0x5XreJgMijQ5aCxHWFij4UZODjcv512USvFSWFSaWqtjGNXKbn/v8VTnidQSdgvQZ7N\npctFOr4AoJWhyrp9opBOqDllFoXdJRZUQ81q4xEdQb95IEhgdwSZeY5NLT6kJkmkTetcyJU4+3az\nDy4Xj7zsU+u+O10LBoO44IILEBUVhW+++QYAcHB/bxt0eXl5TwEpN9OInTs3M69x5NB26m+dVgFL\nc2/hc86cOVSkTeXZTQpGq7ogJFqfOnUqdDpdz29qMIZj3LhxAMS8bWXxZtltqF8CfrVSxEboe8+e\nPYdJ4/wvmFwahhCxmU7NBDKAhoniWaqk28vm4p0eAqOO7W61uwSES+YHW+1BREfQb262BpAQQy+i\nNrMfURFqRlqgus6F3Ewa24XHbBgz/OzRdruN53msX78e119/PdXaH1o3Cm3tr6urxejJdyMiKpN6\nndQkHZra6KghPkYNs5UGXHSEClY7z/DOw40stsMMHJwS3rnhpHBXqOnUgE8SnHCcfHSuUoGJzpUK\nEUe/187WMOsLOI4r4ziuguO4B3/rfF6gR9wB4heUdtb7g+yC8AXEOx39egQ8zy4Ut5cwQwkcLgEm\niWPvcvDMBHerLYCIMBVDv2zt8DGCX7WNHmSm0vnKknI7BvUL+92666HW0tKCyy67DAsXLsSPP/6I\n9evXw2639zQQSYue3bnytGQ1So/vZV6vumIXA+qOpt7z5syZg6lTp0KpEi9scXFxT5demEEBh4tG\n4J5dbPMQx3HiVtRPp2OOH94I6QwBtWwEA9jtDoppM3v2rLMC/lOx08E2LxBGJI4XxBy5XHqGwbZs\nykbO2bO4BgCHW4BJIhfcZWexbbYGECNN2XT4mBmnwaCA5jYf0lJobB8vt2Nw/7M3nL24uLintf+C\nCy7Ap59+yrT2z54zB4PHPIba2qae1n6FQoGsNANqGiSDquO0aGmnvWtMpIpx7N0ql15JG3+YQQG7\nBNtGHSvQpdeyzBatGgyuAdE3SRlfagUbxSsVHIJnIWj53Y6d4zgFgDcBnA9gMID5HMcN+LXnCIRd\nAAJhnb1cBBSQi+wD4oWTLh6fTLOI18+2fLs9AoySBeFw8QgzsdrpXY4gUzjt6PQzQ6abWj1IT5Xk\nhk7TCCHYt28f5s+fj+TkZCQnJ2Pt2rVYtWoVFi1a1HNeWVkZSkpKKOcH9Dr6lsaj8PtEfmF4eO+C\nNLcchCOkS6KlpQWdbWUAALVajalTp8JoNKL/oN4JRd25e72WoxYEz/PYsZ3Or3ebRs3BH6ALqEcP\nbWKKRCqlHNCBggPbe5g2w4YNQ3JSIoQ/wbGfLrYFAkgzMXIYBoCgzPGgXGQfYAMWn4yz57trT5Lj\nLo8Ao4F+UadLYPLrXfYgoiLpN7LaAjAZlEyKsanl92O7tbUVr7zyCkaMGIGhQ4f+Zmv/hvXrMWTk\nX+B004s/PlYDs4V24lERKtgctBcNN6koyYxuM+oVcEsGb+h1HOPstRoRw6GmlmGwqFQshgExaJXO\npVYqRMyEmoKjdWXO1M4GB28sgBOEkDoA4DjuCwB/BVDW1xMIoSeyA72RjfQY4+xlInu5nD0gUs+k\nAwh8fsLw2j0+gemE9XgFGCSywj6/ABAwz7faAoiUOnuzH8mJp8+z5nm+p1ni10y6CB599NEe59dt\nmzZtAs/zOHxwW8+xq666Cps2bUJtbS34oBvbtu/BJRfP6Dm/2yZNmgSTSUwjjRozHSVHxcLphg0b\ncMMNN5zk2/Yi9fDhw+g6KSOQlJSEwYMH9zzW7bDHjBmDiIgI2Gw2dLY34sSJMgzO6C2CKjkwDlvB\nAYf20Ewbjjs5RDJk2PUfZKeFbTlcC4TFNSCP7SAPKE/F2QcJ1BIM+gMif156Pbx+Ap0kRen28DDo\naWw6XUGYDDLOXoJrQgg6On19arD/mnk8Hvzwww/4+OOPsX79eqoLtNsSEhJw3XXX4YYbbsCwYcOo\n7xMfo0V7pw8Zab03lcgINaySIRxGo5JRNzXIOHBATD9K9Vk0MlxytYpjuPRqmUCk24FLsamQSbHI\nHuNYZ38mdjZSMSkAGkL+bjx5rE+TWwAE7AIQ+lookk8tCOyx7uPShSIXQQV5UWQp1AJBArWEzeIP\nCNBoFOzi8fLQS4YUON1BmGRkTX/LTsWpy1kolbHburq6cOjQIezc0RtJn3/++VTkvHlzr9Psq11/\n1NheSYCNGzdCEAQolRwFajoHPpsGNXfyuqtUmDmzl3++ZzudOuJkIhhO4thDX/tPyLKfFrZlcS1z\nrPu4FO9yx3gZvMsGPDJYB8S+C2lBNxBkAx5/gDDsLa+Xh06Ca0EAvD7hlFxC9gAAIABJREFUtOUD\nGhoakJiY2NPCH+rUdTq6tf+ll17C8OHDmXVmMqpYh61TwiOR69VpFIzcQPeuUWpqFSezc2QLmHK5\nbznH3Bc25Rw2BzY65/6HIvZTtmXLlgEA6toD8F0+C7NmTv8z3/5XjQO7+uRiwb7iQ7nF+8cGk31b\nRGQKbF2ilMBXX32FgoJDAMRc5YwZM8BxHN555x0AwI7tmwD8C4QQir8eqnOe028oTGHRcDosaGsT\n5QUMUQOp9wx9LqPhEnId5syZgzVr1gAA9u7aCGCJ3Gk91lBfh8ZaUUZAFyIjUHRwB7Z9s+ePjthP\n2ZYtWwaXV4DTK+DqS2dh2rRp5/oj9dip4lgWw6d43m9ZamoqUlNTUVLSy8SaMmUKFixYgCuuuKJH\nKO7X7FTXmBwmfjdKTuMFTvnUPk48sHc7vnp/96m/oYydDcfeBCA95O/Uk8cY63bsO0s8GN+P3gpy\nYO9yfYGKuaP1dZfjACK9o0IuKuQgSE7kOLaBRsFxsmwMpZJjZERVSnbrdir21ltvYeHChaf9vG7T\naHSYOO0OrPvuCQDAypUreyiRY8aMQXR0NGbMmAGFQgFBEFBUeBgWiwWNjY09MgIREdEYMWJEz2sS\nKDBo2FQc2LUWgBidX3LlwJ5F5XDQxU2pRnpo1Bp6wzi0fxt8Pl8P31juN9y6pfeGMWXKFOj1YiFv\n2JgpmHbznJ5F/NRTT53ehTo1Oy1sd9h4tFqDGJLZm6boKwKTi9Ygc0w2qjvF5wJ974IYbCvAjJdT\nykSu3MlCcDAonNY8To7jsGDBArz33ntYsGABrr/+eqoL9FTMHxCYnUYgSBiacjAoX8SWG7QlCAQK\nyY1ALn1GhD52Y5AeIyCQ8V2y57InEgBjJ0zFTVf1rpMzwfbZSMUcBJDLcVwGx3EaANcA+OHXniAH\ndrmtitxWRylThFApxdy71ESyv6RlV2ZLptOwxRK9TgkvU1QRt3jSBRARrmaKNXExWqaocyp21113\niRS5QAArV678Tb3xUAcMAIPyx2Hs+F7H2s1JB3qdalRUFMaMEeeEdk82Ck2ljJ0wrYdzDoi1hRGj\n6XSMuHUXUblt27ae/H5cypCepqZuC80TZ2dn98gLeD1u7N3by8KRW3xbt7BMm24mz58QrZ8WtjkO\nkN7K+8qZKmQcrlLJ4l2uoCyXPpDLCwNiWsIrSUsY9Ep4JXllo14JlySlIeKazl8rFBxiotiC5anY\nfffdh4qKCjz++OOn7dQBwNzpR2wMndvvsgcYiWynm60XuD08M7QekK9BhGK755hMn40cRbv7piDF\nJi9DDpErtsul487EfrdjJ4TwABYD2ADgOIAvCCGlv/qmHAeBsBGDtHCmknHsKgXrxOVocsDJ5hYJ\n2LUaDj6/1ImzBRSjXgGnZGq4QsHBaFDCLpnuEhWhhqVLOmhXi9Y2dnzdqZpKpcLChQvR0tICv9+P\nQ4cO4corr8SKFSugVotAzsjIwJIlS6jnZeVORE52CoYPH868ZmiKZNas3ohgw4YNlGOfMoWOuN1e\ngtHjetNmO3bsgM3hhvYkAyP0uTmDZkBqAUmety9uvNSx8zyPHVtZx95XQfJs2+liWyGzQ+zLscsG\nKDL0N7WKpclp1CJbRnoeIWK0Gmo6LQePVwbbUp62UQW7Q9JJHKGGtYsWewNOYltmNONvmUajOeOb\nMSEErR1eJEiKtpauAMPmERlttMd1eQRmWDcg1guk3H2fnxVyC8j0Hcg1pPVF5JALWuRqg4IMieRM\n7Kzw2AkhvxBC+hNC8gghz/3W+XKFCDk6kFopD2qflA/a09klaSDQcfBIuKcmGVBHmJSwSUAdHaGC\n1SYD6hgN2jvpaCU9RY/6RppL2y/HhNITEv3OMzS1Wo1Ro0bhq6++wtKlS/HRRx/h0ksvxSeffMLM\n/NSGjUT/HBOT59ZqjRg/vpe2OCbEUa9bt46SEbjwQvq5dgePnOx0DBwo5tV9Ph/27NkJ08lBJaHO\nuf9Qtm4iFcHqy7EHeLpDs6CgAFarKCOQmJiI/Px8AH1vq/8IOx1si7iWpjPExS7FUZ8OW3JMp2E1\nug06Dm4JrjmOkw1GRGxLNE4iVLDa6DeKj9WgzUyTsg16JYwGJaPdfzaxfarW3OaFVqNgBnnUN3qQ\nLuHZt5n9iJM0YFm6goiOlExS4wncXpb775TpB3B72YlvcuJuvgDbZQyIv7U0ug8KLMOPl6GCn4md\nk85TWccuu+VkgS7XAMBxnGyzgFGnYJoKwowK2CWOPTJMCaudfnODXgmO4+CSnJsUr0VzG/1GGal6\n1NTTjj0n04h2sw9dNpluhd9p8+fPx9q1azF58mQkJSXh0ksvBQBMmDgJHV3xGNgvnHHsQ4ZP6on0\nASAxdRg0WrGjsKmpqSdlY4rKxtDB9DbZag8iMkxJvebenZsQZlSgrq4OFRViq7dWq8PAIROp5/KC\nyK8O7RYWm0t65QU6OkT1Sb8E/H0xbeQagf4XTKngZOhrXA8rKNQ0ShknLqOV093cFWpiswxbvwkz\nsB2TUeFKdNkleihRanRYJNK08Vq0dvgZjZTMNAOD7fwB4TgqGbv4R9vR4zYMlmgx8TxBQ7MHGRJO\nfUubD8mSJkKzNYAYiWO3OXiEGZTsJDe3gDBJE6PLIzBDfDw+dlqWL8A2mQHyDWly0f3ZClrOiWNX\nKdiijFzLrVbNqp/pZXSMARHs0pbfcCPH6CVHhSsYJx4brUJ7Z5CJqpLjNWiSdLBlp+lRLVGJG9wv\nDMfKHdTzVSoFxo2MxrY9HeyHPcv29ddf4+DBg1i2/AsM6h+BMJMKkyZN6ik0AsAF59OOvr45iP6D\nJjGvlZZ9HkPzbLcEERetohz7of2bERWuoNgwI8ZMRkwUvchcHsCgA1WgioiIQNYAcffQneMHWG2g\nvuiXfW13z7WplOyuEzip2CfVCZEJUHQatkXdpGdxrdeKNxBpSjEqXAGLTSqlrEK7lV5YyfEaNEtw\nbTQoERGmQnM7vbi6sR1q40dF48ixLoZ6+Efall0dmDyOVk89UeNCUryWmc1aVedGdjodxTe3+ZGS\nQDv7blyHGiEEVjvPCKzZXISRa3B6xPm9oebxiR2pocYL4j9pJC/v7OX1hk7Xzo1jV7JpEzkdYjlR\nqJ5xaTzrxKWCPJFhCnRJNMNjI5QwS8Srwk/enaUpmnQZRbh+2UaUV9NTIpISxMlLDc103vH8GfFY\nv5UeWPFHmEqlwujRo7F1dxfOny4WLnU6HS655BIAgEKhwU03Xk49p6LGhSlTWU3zYSOnUX8HeQKz\nVRSSmjp1ak/U31hXAuJrp5zvsFEzmQVhdxOEyagT5g6lc/wALYz1a0ybAE+gPgvgP9umUrJFTaC7\n1kMfk4/EWQEpOaEpjuNEUSoptiOV6JQobibKKBimJGjQ2uFn8vH9sgyoqKKj8+H54ThSTEfn4WFq\njBgSiW27//igBQAsVj+KS22YMoF27EeO2TA8n6ZJerw82sx+RuJDTqm1tSOApDg6vLa7BOg0HNNt\n2+UQECVx7A4ZbMvJMXfjWlpekNPCkmtIOxM7J45dreIYsae+onO3BPwcx4nzAiWaxxFGDl0Sgfvo\ncAU6JRFMfIwKbZLonOM4pCSo0dBKv1lmqhbV9bSzHpgrOvbQaegcx2HciCjs2k9LiY4fGY22Dh9K\nK2iN9D/CGps9OFpiw/SJveBfuXIl/nbnMlx32/vIyc7sOU4IwbEyJ66+ci71GkqVGlMmT6WOtZpF\nXRG1ioPRaKTG0R0v2kJ1q+YOnoHocDbSiTBKt6sE/Yb1OuqNGzeCECLKNJ9cFNu398oIDBg0jGIH\nBYLkrID/bFv3FlqaZ9fJROd6LevY5XAdZhDlfKWBkBy2E6KVjBNPjmdxrdUoEB+jRp0kEBmYZ2I0\n+vP7h6G20Y1OCQvmkvOT8PWPTUzq5o+wNT81YfqkOKYJcPcBCyNGdrzChdxMAzNvoarei8xU2uM2\ntAWQEk971lYzzwwlEQiBxf5/1H13mBRV9vZbnXtyzsNEYMg5o4JKMmdR0VXXsKZ1XXPOeXVFVH7q\nqhgQ00pQBAkCkgYGmBlgcmZiz/R0zt1V5/ujRPrWbVARF7/zPPPH3K6qrr517qlzz3nPeyQkKnTb\nFkG3I3nxngDvxQOyvVPyXsm6/f+pxx7RO48QX4zSy2NKtEwkHuSkCKT3aYkq9Fl571ytFjgKzvxs\nHVo72RsYUhSF6kb2i+JiNcjJNKCmgfXaZ52agnVb+rhwzFWX5OLdpa34o+X9Za24+NxsplNTcnIy\nolMuxg3XzmOOPdTpg0YjYNrkocjPz/95PCdvHMaMYDvltHSwnaXCk7XvLn4F1jAaAV18CVIVXX0i\ndf9xeIBhoyb8XJTS0dGB2tpauH1AzE8LIHwncNrpbIJYZkb883nsgiBE5A8xRODjjonQfCGSXqtV\nAuKiBI4LPC1RhV6FbmenadDZyxt2m0OEW5FUHVIUhZom9i0yfkQc9uxnvXO9Xo3pE5OwYRvbd3Ty\nuCRoNAI2/cFeu9UewPLvurDgkgHMeFePD+1dXkxUGPa9BxwYO5xtCtJvC8Lnl5CdzmY6Wzv8KMhh\nxyJ1obK7CHqdwCVPI3Vtc0Tgz3f7eC/+cMQhIn35CdDtk2LY9RGw5JG8c7VKXhRK4vq4KHA9M5Pj\n5Oay4SIrv8hBK3PTNFzX8aJcPZra2RsozjOgyxSAS9FCbsLIOOwqZxfAiCFx8AckVCnikefNzkS3\nyfeHblv37bei/IAN8y/IZcYPdXrR2u7B5HGJzHhpuR3jRsRBpVJhzpw5P4/HpU3FkCLW3Whq96Mw\nzNMJj3XX1BxB/s2aNStiK8J+OyFZofx2N5AYw9ILrFmzDkHxCMog3LCfeYbSsPOY4j+L6CNAbI3a\nyGEXp8KwxxoBl4/3+JPjBPQ72LH0JBVMFlYvc9K1aDexu1G1SkBelg4tHYrY+cAoHKxj3yL5uQYE\ng4S2Ttbgzzs9Dd+uNzHeuSAIuO36Irz5fvMfGmt/6/1mzJ6ZjuxMVi+/3WDCGaekMvkgIsKuCjsm\njGLDMwfr+BaXkkRo7gygQOnF9wQ5w26yiEhLYvVa+qllYbLCabFHaG/o8sm7sXA53EQoEnHhidDt\nk2bYfQrlj/ppa8pxI0fo8J0YI8DCeTACem1KWJgKUQaB27LmZ2vR0sm6UIML9KhpZleaTqvC0IFR\nqKhm3yKnTUrCpp0WRtFVKgGXnJOFz1Z2McdqtSo8/I/BePX/GtBrjpD1/Z3icAbx3MI63Hf7IC6J\n9PmqLpw/N4PjAPlhhwUzJsud6B9++GFMmjQJk6eejulnXIP4WFapa5t9KCk4opVjxoxBXHwydx+n\nzTgTHh9x7dpMNglpiayi9jvlbu7hL4k1369DrFGOQ7a1taGuTqYR0OkNOH3mdOZ8X4Bg+BN67IAc\n5lAa9mi9ALeiAC4uCnAqvHON+qcGyQqnJS1RQK9VkdhPUaPTzBr25HgVJIm4Fm6DCwyobWF1e+yw\naFTUuJhiO0EQcOqkRGzaYWGOHTU0DnqdCqWKZuljRyRgyvgkvLK4gVu3J0I2be9DZbUdNy5gUVoe\nr4hv15tw8dmZzHhjqxfBoITBhaxl3XPQhbHDWE75DlMQsVEqjtK4pTOIwmw2PNPVJyJb0XLQ6iRE\n6fFzLcdhsbiAJEULBkeExuWRvHhRIoQiJFmPR06KYTdEqJJTqwToNLxnEznsAlgUMNrUeNmrUcYi\nc9LUaDexC6AwW4umDtawZ6dp4Q9IHAxs/IgY7N7PflnBACPiYjWoqGbHzzojDVV1TjS0sCtzeEk8\nLj0vBw89WwWP58R5N4GghEdfrMZpU1IwZTxrbLtNPmzZ2Y8L57KVq42tHjjdIYwcImtfbm4uSktL\n8dc7l2LaeHahuL0SOkxBFA04sl1VqVQYPJyNwwNAyciZyE5VM+gXIkKvlZCuMPYWl+zphBv27Vs3\nw6iWX3zhSJsho09BYhy7KvxBvoDkzyKGCE5LtIEPu8QY5B2qEgaZFCO/+MIlPVFAj5XX685edjcq\nCAIKs3Wcbg8rMuBgA3sDSQlapKfouFDjrFOSsX6rhdk1CIKAKy/MxpLP27mY+h1/LUJzmxvLlnfg\nREpdoxOvvNWAp+4byjksX33bhXEj45GtYE9d96MZZ0xP5tr47atyYfwI1tpWNfowpIg9PxAkdPaJ\nyMtUdJzqFZGTxt6DyUpIV+xOJYlgdwGJSsMewYuPlGT1Bwl6Dc/QeTxycgz7T0UXyrd8TITtaWI0\nYFN4MKnxQJ8CRqvVCEiKFWBSLID8TA1au1nDPjhPi4ZDAW5rObokCvtq2O3BlDGx2F3p5Hhfzjsz\nFcu/72XGjAY1rpufi4XvNnO/bcEluRhYFIO7nzgAh+v3Y9u9PhEPPVuF2BgNbr2uiPv8jQ9acfl5\nWVxBx4p1vTj3jFQGBy5JhO17HZg2nsUJ76/zYmiRgfP4E3NYwz569Gg4QynIz1TEJt2yB65sPN5n\nl59hQUEBiouL5d/j9aCjQaYXCDfsE6fN5hTdG5B+bpLwZxNjhIKiGIO8HQ8XtQqINchb93CJpNuZ\nySp09bP6F2NUISZKhR7F+OB8LepaWe9oaLEBTe1+jrZ22thYbN3DJvaL86OQnKjFzr02ZnzG1GSo\n1QLWbGJ13mBQ4+XHR2D56i4sW96OEyHV9Q7c++QB3HvbQJQMZOPlpj4/vvymGzctyGPG3R4RG7db\ncNZMFjmzv86NtCQt0hQFS/uqPRhTwipmU3sAuekazgtv7RZRoNDtLjMhK5n31mOjwPHZ2NyyHQsX\np48Qo8TFB/giqOOVk1SgJECrBufZxBr5Dt8J0fKEhUtSjOwBKb3+7BQBnWZWeQuz1GjuVJLuq5EQ\nq0ZbNzs+bqgRe6vYlZaSqEVhrgG797M3ccb0ZNQ2ujmI49lnpCMQlPDdD+wCEAQB9946EEMGxuL2\nByrR2q54W/0G6erx4h+PVCIxXosn7h3KkSBt321BS7sHl5+fxYxbbEFsL7Ph7NPZBOnBBg+ijGrk\nZ7MezJ4qD8YNZZW/zxpCVuGpzNisWbPQ3BlCQRbr1XSaJWQlszTHEhHMPxn2w+celsrd6yCKIoO0\nOeU0Nr4eEgkhkUcT/FnEqBPg8StDMTICQrmbTIgBrArdTksQ0KvIFWUmCTDbiINSRtLtkgIdalpY\nw27Uq1BSYEBlLbu4Tp0Yj217HByB3UVz0/DfNb2Mc6JSCbjrxkL8Z+khWG3s9dNS9HjzxdFYvb4H\nr73dCL//+Lsx/7CtD/c9dRD33zEYp01l9ZSI8Pp7LbjorAxkprO6umazGeNGxHEGfFOpHadNUkAi\n/RLqWnwYVcLuBGtaAigpYM93eiQ4PRIyUhTNRvolZCnGem1H9PqwhET5pa702J0RwjORCp6OV06a\n22PUq7gFEG8U4FAUYyRHCLuoVAJS4wET61RgQJoKbSbeY+8yi5wXNaJYh8p6NuY9ZkgUalt8cCo6\nrcyanojvNrNxR71OhQvnpmHJV2xMXa0WcP/txXj74zauYk+lEnDHDUW46Ows3HZ/Bd5b2vqbQjN+\nv4hPv27Hjf/ch1OnpODBOwdzxQw9vT68vLgJD9xezHnanyzvxuxTkxGniKOv2WzF7OksuiAQlLC3\n2oMJIxTNjRsCmDwuH0OHHmmQccaZs9DUGUJxDnvdNpOEAWmKZKpDhoMdDqWEh2N2bVuHffv2wWKR\n5zolNQOjRw9nzj/s1fxZ6HqVEqUX4FHwDgmCgNgIuaLkSGGXBKCHDWVDqxGQliig08zq8MBcDRra\nWf3Jz9TC5hLRb2N1eNLIKOyoYN8iGak6FOQasG0vexOnTEyE3RHEnv2sNz+oKAZnnZGGp19r4Ijw\n0lL0ePOF0bDYArj2zr3YUdb/m+Lu7V0ePPRcFd5b2oqXHhuOaRP5PM7X3/XA1OfHlRflMONuj4gv\nvu3B/PPYsKPDFcKuSidmTmat7Z6DHpQUGrhGOpUNfowoUjSvbw+hKFvDhRgPRdDtHishQ5FPsrqA\n+Ci+mtThBeKVsEg/393teOWkGfZIZdHxUfzWNMYgkygpkTGZSUA3a2uRn6FCaw9PsJ+XoUGjYgGM\nKdFjXy3rbRsNKowabERpJetNTx8fh/buANo62eMvmpuO6noXqhvYBVOUF41brsnHYy/XwalADAiC\ngAvmZeG918ahq8eLy2/ejf/7sBl1jU5usQA/Ze/b3Hh/WSsuv2k3DtY6sPilMbjq4gFcWb3PL+Lx\nf9Vj/vlZGDmEDau0d/mwpdSCqy5g4+hmaxD7ql04cypr2MtrvMjP0nFNvstrfRhbYsBLL72EAQMG\nYMGCBSgedhoSY1U/F3odltYeCfkZ7D12W4HMMJDOzJkzf2aS3F+5D0uXLv35s3FTz0SCsrTbJyH6\nTxqGAeQXVqQCuki6nRIHmBUlDsmxMsRX6fTkZ6jQotDtwQM0qDsUYuLsarWAkQP1KK9jdXXSyGhU\n1nm5cMy5pyfh2x/YhaRWC/jr/By8u6yTQ+hcN38AJInw3rJD3G+Pj9PiqfuH4rbrC/HWB8246Z5y\nfPN9N8yWyKABr0/Ern0WPPFyDf52TzkGF8Xg/YXjMHQQ30/1QI0DH33ZjifvHcwVD325ugfjR8ah\nKI91QtZttWHyqFgOELB9nwvTxrCxEYtdRJ9VxKA81rDXtoUwOI89v89O0GqAhBiFbltY3QaAPieQ\nqvg5gZDc4DxKEWN3+4mjLTheOWkb2hiDCnYlGVcUYPOwbaUEQV4AfXYgOu3IsVnJAmrbWULj9CQB\nXj/B7iLEh036kHwNqlqCGF50JCkyaIAOFoeEXkuIKUiYMSEWX62zYdbUI09DqxFw1oxEfP19P+66\n/kgDHYNehesuy8YbS9rx+pMlTFHEvNPT0NTmxn1PVeNfjw/lOs5kpBnw6N1D0NbuwTfruvHUK7Uw\nW/zIzjQiMV4LQRBgswfR0e1FXKwGk8cl4eUnRmBggSIz85P4AxIefqEWA7KNXAiGiLBoySHMPy+T\n89ZXbujH6ZMTuL6YG0udOG0C+10uj4TG9iBuu1wH47Cz0dbWBgBYvd2LIflswskXIPRYCAPSFVtY\nRWwyPj4eY8dPRtmu7SAiLF68+OfPho+fhQQOOnbilP+PEEEQZBSMT0JCWF/RhCgBNg+rr6lxQJ+D\n5asXBAGZSYTOfmBg2GMszFShtFrEzDDSzuR4NYx6AR0mEQMyjjzX8UMNWLfTgzMnHTFesdFqjBho\nxPZ9Lka3J4yMwXtf9OBAnRsjBh85fuq4eHy91oSV3/fionlHaJg1agGP/3MQbn/4IOJjNbj8fL6h\n1PSJKZgyLhk7yvrx/SYT3lrSDKNBjcx0A6KMagRDEvrMAZj6fBhYGIOZ01Pxz1uKERcTgWQFQF2T\nC4+8WIuH7xzIJUzbu3z4ZkMfFj83lBn3BySs+sGCx+9gIcD9thBqW/248+o0ZnxPtQ+jB+uZsCYR\noboliJlj2XXQ1CWhMJPV65BIMNlkhzNc+uy8Ybe5ZW9dUOwCXCfQaTlprk+MgWei02sF6DV8AjU9\ngQ+75KYA7WYWHqkSBBRnq9DQyW5DRxRpcaCJZWpUqwVMGKrHrgPsl40eYoTdKaLpEOtlnHt6EsoO\nuNDRw47POiUJcbEafP5tD/cbb7s2H8WF0bj7yWrYHJETpnm5Ubj9r0VYungCvnh3Eu69dSAuPicb\nF52dhbv+Voxl/yeP//NvA49q1D1eEQ8+V4PYaA3uv72YC1N8u9EMr0/ERXNZZbbYgli/zYaL57Lb\nXpM5iMZDfkwdzXo1ZdU+DC/Wc4nLA00hjChiF2Vzt7xVVWJy283yswuX8VOPhGMCgSPx26HjzuTw\nvy6vhFijgrbAdeJhpL9HYowqjt8lMZqPp0cb5AIVpSefmyKgvY89vyhLhbZeiYuzH9ZtZqxYj3ZT\nEBYFJ9KcaXH4fruTw7nPPycVS1f1cdXYd92Qh6UrutHRw66RxAQd/v3kMKz83oSPvmyPGHJRqwWc\nMjkFzzw4DKuXTsWi50fhr1fl48KzsnDFhbl4+oGhWL10Kha/NAaXnZdzVKN+oMaB+5+pwT23FGHi\nGNYdFiXCy2+34pqLs7jY+potVgzKN6JIwRmzYacT08dEc9zspQd8mDyCPbajT4RaJSAjmT22oUPC\nwBzWEeqxymg9JVqrxybbr3CxunnkjD9IUAn8+d1mhdL8SjmpoRiPn7itXlIMnyzNSJAnKFxijQKM\nOqBXgSAYlKNCXTv7wshIVkGrEdDWwyr6lJFGbK/0coo+e1osVv/IXjgmSo0LZiXjo+V8UvSfN+Zh\nxfe9XEhGEAT886ZCjB0Rj1sfOIDaxmM/pPg4LYYMisPUCcmYOiEZwwbHcagWpbS2e3DbQweQlW7A\no3cN4mLurR1efPhVF+65OZ9Lsn76jRlnTE1ASiK7qNZsdWDGxFhuy7ujwospI1lLa7aJsDolFGaz\nil7XLmFgDs8b4w3wCaZBoxWt9AAMHT4KRXkZnFfj9EmIMSiv+9ubPvyREmtUwalwWhJj5N2oEi6Y\nHkG3B6QChxT1bAadgKwkAc3d7HVHDdSivJ417DqtgHFDDNhZyQb1hw80IBgiVDWyhnrGpHjYHCHs\nOcDqZ06GAQsuzMILb7YgoGjWkZaix6JnhmPLzn4893ojPN6jJ0xVKgHZGUaMHZGAqROSMWlsEgrz\noqHXH50Xgoiwal0PHv7JUz9lEh9zX7q8G3q9CueeySZZXR4RX60146rz2XF/QMKGnU7Mmca60D3m\nEPqsIoYWsmutoj6IUQO1jA6GREJzt4TiLFYH23rl5xYuvoAM8lDi2vtdhCRFGMfpJU6viQj9NkVi\n5lfKSTPsapWAKL3Aee3JsQLMCmqA9HjA7OQZ8grSgRaFozw4V42GTolBIAiCgHElWuypZRfAwAHy\nQ6trZcdnTY1FeY0Xpn52/Pwzk9DU5kNFDbsA0pJ1uPvGPDy1sJm7Ouq1AAAgAElEQVTrLCMIAm5a\nkIcbrhyA+5+pxodftB9XyzylhETCl9904e+PHMRFZ2Xi7r8Vcobb4Qrh8VebcPNVOchTcFY3tnlR\nWu7AFeekKs4RsXmPC2efyip/hymIXquIUYPYwOCe2iDGDtYy1KdEhJpDIobkserVYpKfGWusgdis\n8VzPywlTz0QKi3SDN0BQqwTOq/EqSYZOssQaVXAo9FqrFhBrkL21cMlKBLoUuaKsJHm7rqScHpKn\nRnUbe92CLDV8ARl/HS4zxhmxea+XK6I7b2Y8vt7AvknUagE3XJaOdz43cbp5wZxUpKXo8Nr7hzjP\nPDlJhzeeGwGtRsANd1di34ETQ+Xba/bjkRfrsHJtD15/ZjjHBwMA28qsWLvZjAdvLeByTUtX9WHi\nqFgU5LBOyObdLhTl6pCbqUDO7PHglDFGxikiIuypCWJ8iWIn2iUhLUHgyL9aTISCCPmkjAS2mQYR\nwewEp9sOr4Q4BQe8PyD+pvaD4fI/NewhRTVGXJSKQ8GkxPIJJa1GHleGYwozBDT3KCCTUQLSEwU0\ndrLfNWGIDntrA1zhxekTjNiwm90LRxvVmD0tFl+vZ79Qr1Phpisy8NYnPVxrscljE3DB7DQ8+kpj\nxBLr06en4J2XR6G+2Y1r76zA6o38Ivo1EhIJG7b24cZ7KrFjjxVvPj8C585K58IvPr+EJ19rwpSx\n8Zh1CuvthEKENz7uxjUXpSEmmvWaVm2yY8qoaI67euNuD04bxyt/WXUA44ewC6XDLJdFp8az99Tc\nQyhI56tQow0svQAADBs/iyvXdngkxBnZMYkIvkjts06iRBvkAjxlAjUlVnZQwiUrSTbs4TZTpRKQ\nlwY0K5yWoXkqVLeJrLEWBIwv0aGsWkEvnaOFQSfgYBM7fur4GHT3BVGrqLIePyIWeVl6fPEdywkj\nCALuvTkfzYc8+HQlH240GtS477Zi3HptPl5Y1IBHXqw97iYc/dYA3l3ahhvurkRhXhQWvzgS+Qqu\ndQCoaXRj4fuH8PhdRUhSdE+qb/Fi6247/nIhG3YMBCUs32jDxbPZl4Q/IGF7hRczxrOOT2u3CJUK\nyE1n10dVm4SheeyYN0Dos/Mhxk6L/HzDxeWTOyRFKTbiDg9v2D3+IIzHiev9nxp2j8Kzio9Swa6A\nFiZEyZhfJS91TrIcnw2XAWmysfcqEAQjC9WobGKvm56kRnK8ClXNrBGYPsaImhY/ei3s+Lkz4rGn\nysMx400aFYuB+QYs+S9Px3v5uekYURKLB15oiGjc01P1ePaBEtx7axE2b+/HJTfuwWvvNqOswnZM\n7G8gKKH8oB1vLWnFZTftwcrvTbjxqgF49YmhyM0ycsf7AxIee6URack63HhlDvf5l2vMiI1WY9Y0\nVsn7bSFsLHXiEoXyO90SSg/4cPoEdpG1dImQSMZTh0tlo4hRRSpuC9tqAopYUM7PMfdw2KPBYEDO\n4OmcV2P3SIhXvIh8/hD0fwKqR2WuJ9aogt2t4EaPF9Cr4HyJj5ITp0pPvjhTQGM3e2xqggoxRoFD\nx0wersOu6gBHDzBnajTWbGcvrNUIuGxuIj75xsJ54LdclYE1W6yoa2G3/0aDGs/eOxAbtvXjs294\n4w4A0ycm4aNFYzB6WBwef7kON95Tic9XdqK13XNM2KPVFsD6LX14+IVaXHNHOVxuEW+/NBJ/vWIA\nB9cFgNomNx57pRH33JyPwYVsDsjnl/DvDzpx0xUZHBJm7TYnCnP0GJjHevE/lnsxKE/HMTruOBDA\npGFsKz9RIhxsETGykL2vpm4gLw1cGLS9X7Zb4dLnkJOpSt4aZwSP3eMLIcoQOffwS/I/RcV4vEHE\nhdXRJkSr0NgdVKBgBKTFEXodQF7YGzA3Bdh0EJgy+MiYVi0gP43Q2A2MyD8yPrJQjfV7Q1xT2ukj\n9dha6cfI4iOTZdSrcNq4KKzZ7sZfzj0SDoiJUuOCMxLw0UoLHrqJ9YhvuTITdzzVjDHDnJg06oj1\nEQQBtyzIweJPOnDPs/V45p5ipCTxMfIxw+MxZng8unp82LC1Dx9+0Y66Zjey0vVIT9UjNloDQQCc\nrhB6+wPo6PahcEAUJo5JwL+fHMZ1jAkXhzOEx//dhIxUnRxXV2xTqxo8WL3ZgtceKeS8/E9XWzFr\naiznra/f5caEYQaOV2NbpR/TRuo4Ja1sFnHj2ezvbusF0hJknHe4HDIDYwqA/HPOgdFohNfrxZx5\n5yMj2cgtFJtbQpZiAXq8weNW/hMpgZDEvGASomXDnhJ3ZCw1FihrkufocPhAEIABKXJMPTwWW5wJ\nbKjguedHF6lR3iihKOxlmpGsRlqiCpWNQYwdfGTeJw834L8bnGjpDKIgjP/k1PExWL3FgdJKD6aE\nJciTE7S45cpM/OvdDrz2SCGDlEpO1OLlhwfh3mfr4XaLuO6yLC4EYtCrcck5WbhwXibKD9qxeUc/\nvl5TA6crhLwcI5ITdTAY1BBDEmyOENq7vPB6RYweHo+pExLx0N+LOfRYuOw94MALb7XgnpvyMWl0\nPPf5f77oQWGuAadOYD+zu0Ss/MGGJ29nvYqQSFi73YO/XaIsYCKU1wfx6PWsZ9HQISElXuCoqRu6\nCAOzeDKwkCjDV8PFZCdkJiji6z65MElJ1+vxBpEUp0AP/FohouP+A3AJgIMARABjf+FYamy3kFJ2\n1nrJ6RWZscZuiUob2DFJIvpoM5HVxZ5f1SbR5z+yxxIRvb/GT3vqQsyYPyDR/W/aqKefHbc7Q3TL\ncz3UZ2XHA0GJ/vF8O+0oV3wpEVU3uunKu2rpUJeP+0ySJFq2spvm31ZJFdUO7vNI4g+I1NDsou1l\n/bR2k4nWbjLRtl39VNfoJJ8v9MsXIKK6ZhctuHM/vbO0nURR4j7v6w/Q1ffUUdl+/p7213vo5ifa\nyKN4Fk63SLc+30M9/UFm3OYS6Z5FNnJ62ONr2kL0xnJ+Tr7ZJVJZPXtPHj/R+xuJgj/9vNLSUlq4\ncCFtLu+jqnb2WF9Aoh+rPCRJ7Hhrl40sdg/Jqnz8uqz8+626bbF7mPuyukJU1uDl5mH9fpFMNvY3\ntPUSrdjFHUrLtohUo5gHu0uiJz70kj/Aju+t9dMrn/LPdX2pi/71UT83Xt3opZsebyOXh187by3t\noideb6NQBB2y2gN05xM19Mi/GsjuDHKfRxKrPUAVVXb6YXsfrd1konVbeml3uZU6u70R9VQpoijR\n599006W3VFDlUdbTmi0WuvmRBnJ7+LXy+ie9tGSFmRv/ocxNL3zAz82GMi+9/w2/5j9e76fSavY3\n+wISvbpcJI+f/R0VLUSbD7LnS5JEK8pEcvvYY1tMAarv9DNjwZBIBxp6SZTjbkS/UX9/byjmAIAL\nAWz5NQd7fSEOFZAYo4JF0Ug6I1FGChADvwLyU4FWFpSC4iw5RqlMNE0YrEZZLRsO0WkFTB+pww97\nWXhcXIwap0+IwvJNbFJUqxFw82Up+GB5P0fdO6QoCtdenI4nFx2C3ckXIc0/LwP/vDEPz73RjA+/\n6vrFeLpOq0JxQTSmjk/CnBlpmDMjDdMmJmFQUcwx0QOATHT05WoTHn6pETdckYMbr8zhvCmPT8ST\niw7hvDOSMH4E60b4AxLe+cKMGy5O4WBgq7fK3nq6wlP+sdyPcYO1Pze0PixldSLGD2bvNxiSd1VD\nWEgx2nrlrephTupJkybh73//OzxIQqYSIuYSkRit4rG/3gCijcdGDh2n/CbddikI1+OMcmW1Ep6Y\nmQB0K1hIs5NlJJiye9LQAQKqD/GdwvLSVahsZvVx1EAtrE4JrQqajBnjotDVJ3L8MUOKDBgzxIhP\nVysytwBuuCwDfr+E977gw40JcbLnnpWmx60P16C86pebyCTEaTFqaBxmTk3BnBlpmHVqKiaMTkBW\nhuEXe9eaLQE88q9GbCuzYdGTJRg5JJY7pqLahU9W9OLR23I5wrDKWg9qmny4bC4LlQwECas2u3DJ\nmSxkRZQIm/b6cfo4FiTg8hIaOyWMKmKvX98po2GUVACtvUABG+ZHv0um6lXuWq0uCUkx7HXlnShb\n8fpb5HcZdiKqI6IGhFddHEMMejUXZ0+KUcOiaPEVrZehjP0KdGBBOtCk0DWdRkBxJlCt4B8akqeC\nxUUcedKpY/TYVxfkGm3MmxaNAw1+tHax91dSaMDkUdF45wu+RHrWtAScNjEej712iKMhAIAJo+Lx\n5jND0NTmwc0PVmNbmfWE0psSEcr223HrIzXYXWnH60+W4LRJidxxPr+Epxa1Y3BhFC6ew8PGPlpl\nQdEAPcYPZ0M8JksIP5Z7cN5prPJ7fBK2VQZw+nhW+a1OQku3hNEK5a/rlJNIysKiZhOv/A6vzAWT\noCBNsjglJClCQb6AjDPW/QEx9t+q2y5PgONWSYhWweJi9SIzUUCXlXVa1Co5HNOi0O3B2XKIRlmF\nOnmIGqXVIgfTPX2cAd/vYpOiGo2Ai86IwbK1Ds6pWnBuEvZWebCvmgUPaDUCHrolFxXVbiz7lu8j\noNWocMvVubjj2gH419ttePaNZq7B++8Vr0/E0hXduPnBapQURePVRwcjPZVvQ1TT6MFL73bigb/l\nIDuD/dzhErH4czNuvjyFq71Yu8ONgmwtihSNNsqqg0iJVyFPQfq1q0bE8AI1DAoDfrCNMCyPb6xh\ndckv7HDpshCyFMszJMrx9XhFhbXLG0C0MsP6G+R/mjyNidLBqcAcJ8ao4PBIHEFSdiLQaVFwUCcB\nHh/P9jgiX8D+FuIUfcoQDbYfZBdWXLQKk4fpsG43uwCijSpcdEYMPl4daQEkoqsviI2lfLZ/wfmp\nGFkShUdebYPDxSdMUxJ1eOruYtx6dS4+/robtz1Si007LUxrvd8qokjYsceGu56qw1sftWPBhZl4\n6cGByEzjFd/rk/DE64eQkarDLVdlcHH1XfvdqKjx4sZLUrhzP/3OiXlTo5EUxxrOzfsCGFagQVoi\nO76zOoSxA9UcO96BVsLIAgVE0Q+Y7ECeAvvbaQGyk/iqPItLRJKymbAngBhlXfZJlIACj5scq0a/\nwoFIjJapepW8McWZQKMiL6nXyk7LwTZ2fFCuCv4AOF6kaSN1aOsRuSYyU0YYoFYL+HEf+6UxUWr8\nfUEq3vrMDIudPScmWo1n787Dll12fKooXjosk8bE4z8vDUVethF3PFaDl/6vFc0KfqTfKnZnCEtX\ndOPauw+itd2L158swTUXZ3Gt7gCgutGDZ95qx91/zcbwQawnQER46zMzpo2JwajBLMDAbBPx/U43\nrpjLev+iRFhT6sPZ09jjQyJhV00I04ez+m5zyWiYYgUgoLEHyE9j+WGICJ1WIJvjkpGTpsp8ktMT\nQOzvMOy/mDwVBGE9gPTwIQAE4GEi+ua3fNnrr74IpyeA5HgjZsyYgRkzZkCjFhBnVMHqkpAaf2Ti\nspMEbK8jjBxwJLGqEoDCDKChG5hQfOS6A1LlxdLZD+SE2aeJQ9R4+XM/5ozXIC6sN+GsiXo884ET\nZ4wXkRz2naeOMWLLHi9+3OfFjPFHvFedVoW7rknFo4u6kZelYzLrgiDg+kvS8eHyXtz7Qise//sA\nZKXxD2TCqHiMGxGHXRV2/Pc7E95YcgiTxyZg4qg4DBscg5TEYz9EmyOIqno3yirt2LHXhvQUPS45\nKw3TJyRy+PXDYrYG8fQb7SjOM+C2BZnctre9J4B3vjTjgRvSEa0Iqeyp9qGnP4Tb57MxEZdXwpZy\nP+6+kvXifQHCnjoRt1/A/o5+J8HsiKz8A1JlKGu4dFgIIwcoE1ESdFoBhrCCqc2bN2P5qjUwGrQw\nHGdnghOp2++8+Qq0GhWiDNqfdTs5VoUWUxAS0c9bakEQkJNE6OgnxIdhoXOSgc0Hee7uUQUC1u4j\nTBiIsHUgYNpwNX7cH0J+xpH51mkFzJ5owKptPtx28ZHno1IJuOacOPzrIyvGlOgRH7btH1pkxNzp\nsXhlSS8ev5VtypIYr8Hz9+Tj0X+3weoI4eb5GZyBNRrUWHBhJs6fnYpvNvThkZcbEROtwdTxCRg3\nPBYDC6JhOEaZvCQR2rt8qKh2YleFHVX1LkyfkIgXHxzENaQOl217HXjrk27cc0M2xg7jK7K/Xm+D\nwyXi7mvZLSER4ePVDsyaFI3URFZvSg8GkBSrwsBcdryySUJaggoZii5KlS2EYQN4NExDNzB5EHs/\ndo/c4lO5EzU7RSQrdqLrN2zE8lVrkZoYxTliv1aEExEaEARhE4C7iWjfMY4hSZJQ3WzGoLwkaMOa\n/XX0h+DwSBiae0RJiQjfVxLGFwlICcMz9zuBteXAFafIhv6wlDUQui2E8yaxk79qRxAqFXDOZBY5\nsXq7FyarhOvPYWe63RTEix9Y8MTfUpCSwE743ioP3v7SjGf/nonUJB6JsWaLFUtX9uLO67IwYQQf\nCwyXXnMAO/baULbfjppGNzRqAVnpeiTFaxH1ExrB65NgtQfRZfLD55dQUhSNcSPiMGVcPHIyjp0t\nP1jvxkvvduLc05NwydxkTkHsLhEPL+zCpbMTcNoE9l6dbgkPv2nG7ZcncKRIX2z0gAi4/Ew2bLOp\nIgSTRcL809nj15dL0GuBU4eHtzADvtopI5zC4WBOL2FTNeHcsSx7Y0NXABq1gIL0I3MuShJqmvsx\npDAZapUceyeiE04i82t12+bwot/hQ2E2+yIsa/ChOFOLxDBj2u8klDUR5oxif+f2Wrl7TrjTQkT4\nYANh5kiBqQEIhggvfebH9fN0yAwreQ+JhKc/cGL+mUaOv+eL9U70mEO4Y34Ch2R67aM+aDTAHVel\ncrri8Yp48Z1OBIIS7rspB4lxR3+RShKhqt6F0nI7KqqdaOvwIjVZh/QUPeJjNdBpBYgSweUW0WcJ\noLPHj8R4LYYNisaEUfGYNDqei5OHiygRPl3Vhx922vDIbbkcZQAA7Kxw48OV/Xj+H1lIVJDYbavw\nYs12N564OZnhTfcFCE+958DNF0YjL4x3R5IIr34VwAXTNCgOq64OioTFqwlXny4gMayK1OwA1lXI\n9il8Gg8ckkAEjAwr2pOIsKPGh/HFesZp6bd54fYFMCBDRuscl27/1mxrpD8AmwCM+4VjiIiordtG\nZhuLIDiMeFBmyKvaJdrbzGftv9pJ1NbHjvkCEr22QiS7m72G7ScUgUMx7vNL9NBiGzV28Jn9VVuc\n9Pz7/REz9t9uttGdz7WTzRkZqXKw3k3X3FNH733RQz4/f++RRJIk6jX7qaLKQZtLLfTdpj76blMf\nbdrRT/sO2qmn1/er0ANEMpLn01W9dNVdtRHRL0REbq9I97/aQUu/5REBkiTR68ss9OkaO/dZZ1+I\n7nvDRk43+7t8fome/thLPRZ23OuXn4nDw957r51o6RYZ6RQuBw+JtK9FiYaSaHsNj5yyObzU1HEE\nZYUTjIqh36jboZ9QDCGRvc8WU4DqOljEgyRJtHqfSBYnOwFmB9HHm4kUl6CKZom+2Mrr0uaKIH2y\n3s+Nl9f76en37RQKsdcPBCV6aFEfbd3n4c7x+UV68N+d9NHKfg55REQUEiX6eIWJrrmnjnZX/jqk\nF5GM9mpt91BpuY3W/Wim7zb10ZrNfbStzEo1jS5yuH4dsoaIqLvXTw++3EIPvtxCVnvk8w7Ue+j6\nR1qpuZ1HZvVZQ3TbCyZq7Qpwn63Y4qElq3kkTHlDiN5c4ePmpLwp8jP5sZqorJEdkySJvt0rktXF\nXqPfERk51dxhJYvjyPjx6PbvVfoLALQD8ALoBrDmGMcSEZHV4aWmDiv3Y/Y2+ajXzhpLl0+GBylh\nV9XtRGv2cZegDeUibajgJ3vVjgCt2MY/zD01fnrmA34BiKJEz73XT19vjKzAn67up7tf6iD7UYy7\nzRGkF95upxseaqDdRzGuf4QcqHPRbY830mOvtVFvP/97iYg8XpEeWdhJb3/eF3EBryt10SNv9nFw\nOlGS6NVlDtq8j18w6/cGadkPvIHZUSPRN7v457HpANG+JnbssPJbFMpvdYWotM7L3Wtbt436rO6f\n/z/Rhv14dLu5w0pWB7tQ3T6RtlZ7SJR+ndOyvJSo2cSOBUMSLfpGpF4FTNIfkOiZT7zU0ce/DBd9\n6aR1u3ijcagnQLc930MdJt4wOlwhuuvFdlr2nSWibhARVVS76PoH6unFt9up7yg6dqIlEBDpyzV9\ndMU/aumrtX3cej0sVY0euu7hVjrYwL+4gkGJnnzbTKu38sa76yeHxeZk5zEkSvTSZz5q6GDXuShJ\n9M4akVpNiucRJPpgI5FLMe09NonWVfLPuqbdT2297ByGQiIdaOylUOjI8cej278XFbOCiHKJyEhE\nmUQ075fOiY3WweMLcvQC6fFq9CqaA0TrBSREywm1cCnOlCtOlb1QJwwScLCVRxHMHK1BZZMIs6Kp\n9djBWiTEqLBhD5vRV6kE3HJpPDbv9WJ/A5/tnz8vEWOHGvHEW92w2vmEaXysBvfflIOb5qfjnc9M\neHxhG2qbfl9S6VjS3O7Dc4vb8cp7nbjs7BQ88ffciKEil0fEM2/3ICdDhxsu4cMzje0BrNzsxu3z\nE5jCLgDYeSCAYAg4ZZSywwxhx8EQZo1jt7zBEGFvA2HSYGX7L6ClFyhRFMT2OuQwRGI0e3yvTUR6\ngpqv1HMHEB/zxyVOj0e342L0sCuYJqP0Khi0AqwK5FdeqlyZqCTBGz6AT5Zq1ALGFwvYWcseq9MK\nOGOMBmt2hQ6/YADIW/fLzzRifZkffYo1lZuuxeVzYrHoMyu8Cm722Gg1Hr8lE2UH3Fj6bWQE16gh\n0XjziSJkpupwx1PN+Gh5Lwf3PVEiioQfdtpw6+NNqGrw4F8PFuDiOSkRc0r767z41we9uOuaNAwr\n5sMzy753Ij5GhXnT2BCiJBE+Xe/B2VMNiFck53fXiEiKFZgQDCBDHPU6nvSrvktGwkQroqQtvYT8\nNAUVhkToc4hIi2ev7XAHEG3QQq3szPEb5X9OAqZWqRAbpeMWQFq8GhanyPFrFKYJaFZk/7VqoCQb\nOKDg+o+LElCSC+yuV/ScNAo4daQGq3dFwJvPisIPe/wciVJCrBq3XZaAd762o8MU5M674qxETB8T\ng4cWdqGtKzK74IQRsXjrySJMGhWLl97txD0vtOCHnTaOZ+Z4JBCUsG2PAw+90oonFh5CSVEUFj9V\njFMnxEdMuPSYg3h4YTcG5+tx4yXJXCK1zxrCos9suOGCOA6z3m8XsWqrDwvmRHHnfV8WwthBaiQr\nqvH2NQHZKeD4YqrbZdiqEnrebCIURFD+Xrts2MPF6QnAoNcweZo/g8TH6OH0BCBKCnbRBA16rLzT\nkhgtG/dwKUiXE21KvqQxRTLu36ygJJhQoobDQxw5WGqCGrMn6vHxWg+H8jplTBRKCnR48wsb19wl\nPlaNx2/NRHWTDws/7otYf2HQq3D1hWlY+GgBHK4QbnqkEQuXdKGm6dj0Ab9W+ixBfL66D399sAHr\nttlw+9VZePyOyKAEQO4d8PonvbjnujSMGMQb9Q273Khq8uOGC/m18cNePwQBmD6avbbHR9iwL4R5\nk9i1IBFhezVh2hA2PyIRcKANGDGA/W5/kNBjY6voAcDslFlKDQoGVbvLh/jY3++wnBR2x4QYPewK\n0nWtRkBiLO+1ZyfK/OxyceERGT4AaOiSqTHDZUqJgMoWvmBp+gg1eq2EunYFJC1ehQtONWDJajcC\nih6qg/J0uHJuLP691MpxWwuCgItmJWDBOUl4anE3dlZE7mEqN+lIwrvPFuOi2cn4scyBv9xbj+cW\nt2PdVivau/3cwoskRITu3gA27rDh5Xc7cM099VjzoxWzpyfivRcG4qLZyUdFH1TWevDI6904+9Q4\nXHM+b9RdHgmvfmLDOadEY/Rg1t0QJcKS7zw4c4IeWamsIW3vlVDXLuLMsazy+4OE3fWE6UPZ7wmJ\nQFU7MIrtQwxvgGToYwTljzaoYFQov83pQ0LscZZa/4GiUasQbdDC4WKVMj0hstNSnC6gSeG0qFWy\nble2stfWawVMGChgW7XyeAHnTtFgdWmIK4Y6fZweKgDry/hd59VnyeydH612cMY4LkaNx2/NAAF4\n7I1umK2RPfK0ZB1uvzoLbz9djMw0HV77oAs3PNSIdz/vQdl+56/25ANBCbVNHny1xoz7XmzB359q\nRp8liMduH4AX7s3HqCHREc8LhggfLO/Hio02PHlHJoYW8Ua9os6HVVvc+OeCRA751dErYv1uP66Z\nG8UVAq3bG8KIAjWyFFzste3yzrKQ7cKHFpPsrGQocOotvTJ8V9mXoNsSQqYCLhwSJbi8QcRH/37D\nfkJQMb/qiwSBDn+XJBFqWswYOCCJKS7pd4po7glifLGeeRtWdRC8AcJ4BfnOliq5vVQ4igAANlZI\nCEnAnLHs8XXtIlZuD+EfF+uYUAMR4f1vPYgyCLhiFs/DsnqrC1vLvXjo+iTExfBeYlO7H68u6cXI\nwUZcc34SVwyhFLszhLL9LpRXu1Db5IXdFUJWmh4pSRrERat/NtC+wGH0QBBdpgCio1QoKYzC6KHR\nmDAyBskJx+ZICQQlfLbGhm37XLhzQWrELarHJ+GlD60oyddi/hy+Jdk327xo6RJx+6XRjPKLEmHR\n8gBOG6nBmIHsnPx4UILDA5wzUdGQow3osgJzRoMdPyQhKAJjC9jjK1r8yEhQIyMMliaKEmpa+1GS\nnwxN2Hb1j0LF/BoJ122rwwerk0fHVB0KID5KhZyUI7+FiPBdBWFyscAwWQZCwLKtwAUTgfgwmxYI\nEd5dS7hwisB0oQKATzcGkBQrYO5EVicsDgkvfeLEDedFcz1pvT4JLy6xoKRAh8tnx3LeLBFh1Q92\nfLPZjusvSsbUMZEbvYQf39Lux679Thys96Cx1QudToXMVC2SE7SIjlJBq1FBkggenwSrPYTe/iDM\n1iByMvQYWmzEhJGxGDk4CtoIBGDh0mkKYNGnfUiIUeP2q/mZXzkAACAASURBVFIRE8Wvy6omPxZ/\nZcddVyagKJf1yH0BwosfOzFvigEThyp4jUwSPlkfwF2X6BEVVlQXEgn/WUeYN05AXlq4/QD+WwqM\nL5Lx64dFkuTnO22wwIQYfQEJZY1+TC0xMFxO/XYvXJ4A8jJZ7prj0e2TYtgBoMPkgE6rRlrSEc0l\nIpTW+TFsgI5hOvMFCWsrCPNGs1zcDg/w9S5g/nQgnAfKGyD853vC/FN56tjPNgUQbRBw7hR2AXj9\nhJc+cWL2RD2mjODfmMt/cKKs2o/7r01kcMCHxeOTsGR5P6oafbjp0mSMKjk6URd3rldEpymAPksQ\nLrcI309NDfQ6FWKi1EhJ1CA7Xc9R7B5Lapt9ePsLM7LTtbjp0pSILyS3V8IrH1uRn6XF1WfzC3t/\nYxCfb/Tg/gWxXD/TTeUhtJokXDuHbUTg8MjwvOvOFBAXFb4ogGXbgHlj5FaHR8YJq8sJZwwXEBO2\niDx+Cfua/JjyByr/iZJf47RYXSLqu4KYOJB1Whq6CWYnYcogdn73Nsn6PXME+137WwmVzYQFM9lQ\ngNNDWPi1H9fN1SE7hb3WweYglq3z4L4FsVwc2eWRjfvwYj0umxUTMYzX0ObHoqV9yM/S4boLkzgI\n4dGEiNBnCcFkDsBiC8HtFRES5bqUKIMK8bFqpCXrkJmmY6CHx5KQSFi92Y6Vm+y4fF4iZk/l9RY4\nYtRvvzwBJfms4SYi/GeVB9FGAVfOZtdpSCS8/nUAZ47VYKSignpXHaHDTLh4mqLPQK8cerxoMgtx\nPGQmNPcSZgxlj2/uCSIkEQZlsffV2G5BWlI0Q5QInES446/5w0/IgcPi9gaopsXMox16A1R1iEdY\nlDWJdOBQBMjXQaLSem6YyuolWrZF5K7v8spIgsZOHtFyODveFAECSUS0YpOT7n2tl0z9R4do7at2\n0y1PHaIX3+uh9h7+d/zR0mMO0MKPTXTjY220fZ/zqOgGqyNEj7zZRx+vtkc8prNXnovmTv63dppF\neuojL1kc/Hkrdoq05QD/nCpbiNZGQDLVd0m0vZY/vr7TT40RYGn1bf1kd/HIHPxBcMdf86fU7fYe\nO/X0s+gLSZKotM5LFgWSKhCSkV9Or5L0jGjJD0QWBYhDlCT6YL1IB9v4ud9bH6JXv/RRIMh/9t0O\nL738iYNDOxHJRG+PvtVHH6yyHRVx4vOLtPTbfrru4Vb6ap2VvL5fB+U9USJJEu3e76I7n2+npxd3\nU0/f0RE5ZVVeuu0FE9W2RF5/q7d76aVPHBHnaXVpgD5a5+fWhNMj0cKVIpkdSrQY0RfbiVoUSCZJ\nkpEwnRb2+JAo0bZqD7kU8F2vL0hVTZGRasej2yetg5JRLxPcKMmTMpM06HeI8Cvi3SVZAppM4OKI\n44qAmg6ZwD5cxhbJCIwaBYdMtEHAJadq8cXmIDyKOHxmihrXzIvCOyvdMFl47pfzZ8RgzpRoPPMf\nCxoPRU6YjhkShX/fn42SAgMef6Mbr33ci9bOP74nZ2dvAG991ocHXu1CZooWCx/MwdQxkT2wdlMQ\nT73Tj/FDDbhqHu/x2JwS3vrahYtnGlGQxXpngRDhsx+COGeyFomKRhjNPYQeq5znCBd/EChvASYM\nZO9DlAh13YQh2cpYPKHHJiI7WdHQ4Cc0lbLU2mm3Hn1iToIkxRthsbMtFwVBQE6yBu1mNu6sVQso\nTgdqOlld1GuB0QXA7gb22ipBwOwxAjbvJ/gUPQvGFKuQliBgzW4+tj13sh7J8Sp8+B2fTI2JUuHB\n65LQaxGxcJkN3gjJfb1OhSvPTsKzd2ahrSuA25/twIqNNriP0RLvRIgoEXbtd+OBV7vw2Rorrj43\nCQ/fnI70FD4MSURYu92Nj1c7cPfViRiczydbSw8GUHowgJsuiOZ2CY2dIiqaRFx0ipZbExsrCaML\nwTV/aeiSq6eV1BjdNrmEWUlm12sTEWNQIVpBttdv9yIp3sBRaZh7Oo82NceU/6lhVyp6cryR6+mn\nVQtIT1Cjo1/BXWEQkJkANCj4NGIMwJAcoKyRHVepBMwZK+CH/cQ14hicq8bwAjW++lEu9w6XYYVa\nnDvdgLf+6+aIwgDgjIlRuP78OLy2zIbNeyOjAPQ6Fc6bGY83Hs5FfpYOz79rwmOLurCx1MmxRP4e\n8fok/LjHhacXd+PxRd1ISdDg9YdycOncRI6l8bDsOujFix9YcOmsWJw/gzf8bq9s1E8ZredijwCw\nakcIWckCF1cPhgjrywlnjha4BbOvWY49Kns/tvbKjSYSFf0fu60ikmLUHGKg3+5FUpyR74Nq5RkK\nT6ZEGbTQqFVwutmXf0aiGg6PBI/CcA7MlInBlAn/YbkyOoZrnZcsYGAWsPkAe7wgCLjwFC2q20RU\ntfLJ/gVzo+D2Eb7Y6OX01mhQ4Z8LEpEQq8LT71rQbY6c+MxM1eKff0nDY7dk4FB3ALc93YG3PuvD\nwQYvB938PdLdF8SXa62449kOrPzBjotmJeDle7IxbljkMnt/gPCf5XZsrfDisRuTUZDFG/6DTUGs\n+NGLWy+O5ki3nB7CF5uDuPRULUdW19RN6LYCU4aw40ER2NMk0weE3xIRobqDMDRb4HS1vT/E5FkA\nuYra5vQhKY7NgQV8XgR8Co/1V8r/NMbudtgRFXskwCpKEmpb+rl4pDcgYW+jH5MHGxgeBqeX8EMV\nYe4oNtYeCAGfbwPmjAHSFPz7GyokePzgqAZCIuGdbwMYkqfGzNF8zHD9bh92HAjgH5fHcHFJAOjq\nC+GNz23ISdfgL+fEcRl35XftrfJg614X9td5UZirx8hBRgwpMqAgW3dMLo1w8QcktHUFUNvix/56\nL+pbfCgpNOCUcTGYNDIqYseZ8HM/XetEVVMAt12eEFHxPT4Jr3/pxqBcDS48zcAtoN21IWw7IOK2\nC3Rc39ENFRK8AeBcRcLU5gZW7gYumQqEhw5DImFtJWHqIIFp7CtJhNJ6P0bk6RAbNqchUUJdaz8G\n5SVDG9YH0udxw9rXg6z84pMaY5dEEUJYc0urwwurw4fCHBYm0WIKwh8klChYBQ+2y3o6sZidv8Zu\noKJVjt+Gg5n8QcJ76wjzxgtcu8H2XglLvg/gb+fqkJrAXs/rJyz60oXCLDUunmmMmDDdsteLrzY4\ncdnsWJwyhj8mXKz2EH7c68K2fW7020IYXWLEiIFGDMrXIzNV+4u0vIfF5hTR2OZHVZMXFTVeOD0S\npo6OxmnjY1A04NgokUM9QSz+0o78LA2uPTeOa8IOANUtQXz4nQd/uygaBZlKw0p4d3UARVkqzBrH\nrgtfgPD+esJZ4wXkK+a5rFHW71mj2O/qtBCqOgizRrCG3ewQ0WLiwSFmmwcuTxD5WazxMvd0QafX\nIz4p5c+dPDW1tyEthwV6dvXJjIlZqSxfSXV7AFF6Aflp7ETvbZagUQOjFI2S6zplKN0Fk9gFEAwR\nlmwgnDJcQEmOgi/FTXhzhR8XTtdiSB6fXFxb6sPu6gDuuCQGiXG8sgSChM++d6Kizoe/nBvPNXqO\nJP6AhAP1Phxs8KK21Yf27iASYtXISNEgMV6DGKMKWq0AQZCv7/FKsDhEmMxB9NtF5KRpMahAj+HF\nRowcbETUUTzzcKltDeD9lXYU5WhxzdlxEb15p0fCm/91Y2COBhfN4I16a4+Ej9dHNhZtvYRvywh/\nnSUwtKZEwHf7ZD6YUfmKe+oiWFyEqYqkYZclhD67iFEF7Fz2WtzwB0TkZrDIHXN3J/RGI+ISk0+q\nYXc5bIiOPbIwJYlQ29qPwuwEGML6VgZDhNJ6HyYo+EGCIcKaCsJpQwWGHIwI+GYPUJguwyDDpaWH\nsGYv4XrFvAPyS3jrARG3nqeDUcH/7fFJWPSlGwVZalxyujEi53eHKYjFX9mRlqTG1WfHcQyfkaTP\nEkRFrRdVjT40tPlhd4nITNUiNVGDhFg1DHoBGo0ASZI9bKdbRL8thO6+IEISUJSjw9BiI0YOMqAo\nV/+LL4VQiPDddjfW7XTjirlxmDqK11tA9tQ/XuvBTRdEoyibNepEhBXbQ7C7CNfM0XJzsbpMglYD\nzB7D6qnDAyzfBVw8RY4aHBaJCOv3y0R2mYmst76vyY/cFA3SElhkVF2bBTnpsYgJK+4QRRFdrY3I\nyi+CRqP9cxv29qY6pOfkQas7smgDQRENhywoyU9mqq3cPgnlzbzX7g0Q1u0nnDlcYLZMRMCqMqAo\ng18AXRbCf7cTrjldQLyisvGQScKH6wK4fh6PJgCAjXt82LTXj1svjkFWSmTlrmryY8k3DuSmazB/\nTizXP/FYEhIJvf0hmPqDsDpEeLwSgiGCRHJlYZRBhYRYNdJTNEhP1v5q9AAAWB0ivljvRE1LAAvO\nisP4oZGx32abiLe+dmP0QDkMpVwcZruE//smgEtP02JwrqIhgF9+cc4dJ6BQ0aW9sQcob5a9zfBC\nOn9Q9tZnDhOY5tSSRNhV78eQXC0SwhBAh41kQXYC09xXDAXR1daM7PxiqDWak2rYuw+1ICM3nxk3\nWdwIRHgZNfUEERIJg7NZr72+m2CyEU4ZwuqhxQV8UwZcMoWvalxfLsHtA86fLHDPbdWOIExWwnVz\ntRwDoccn4f+Wu5EYp8KCOVER9SoYInyzxYWNZR6cPT0GsyZHPu5o4vZK6O4Lot8Wgs0ho71Cokyh\nqdcJiItRIylejYwULZLi1cfcGSjlQKMfn65xIDVBg2vOjeMI+w5L6cEAVvzoxc0X8p46AGzdH8Ke\nehG3nKfjXo5Vhwg7qgl/OVNgcOiHHZbsJDkPEi7NJkKbmTBjKPs8+p0iGrt5VJTd5UevxY3i3EQW\nXWbtR8DvQ0pG9p8fFWM1m6jf1M1lfdu6bWTq5zkcqtr81NLDZ7+r2iXaUcdn5S1OGUng4KkiqLRW\noo828rwzRET7m0P07CdeMtsjZ/p3VfnpvjdsVNN69Ey8PyDRys1OuuW5Hvp4tZ2sjl/Xzu6PEKdb\npC/WOeiW53ro83UO8hwDwdDSFaQH37LRpr080oSIyOGW6MVlPtpVw6NjJEkmQtoUgQfD6yf6aBNR\nN08LRHubRdoXgSelwxyk8mb+Psw2DzVH4Beymnup39RFRCcfFdPRXE8+L6t4wZBIBxt7yR9QtGgM\nyqR3HgVJnChK9F25SN1WXkd3NxCtLeeJ04Ihid5fL9K+Rv4cUZTow+/99OlGP8dVQyTr7NsrXPTq\nMgfX4jBcuvuC9OrHFrr71V7aWu45KnLmfyGN7X56cUk/3fPvXtpbw3MIHRZRkujbbR569B07dZsj\nr8WKxhA9t9RLVid/jX6HjILpifAs6jqJvtxBFFJMWSAo0ao9PLmbJElU1uClHmuQG2841M/xC0mS\nRB3NDT/r0/Ho9v80eRobnwiP0w5RZBMzaYnRMNu8XLY+P12Djv4QAgokzKBM2YvptSvb7AEj8uTC\nJeVGZOIguTJs035+hzKiQI2ZYzR477sgbC7+84lDdfjruVFYstqD9bt9EROmOq2A806LwfN3yOWT\nD71hxvsr7WjrDnLH/lHS1RfCx6sduG9hHxxuCU/fkoLLZsVGLJgiImyr9GPx127MnxWFGWP5MJLb\nR3hvTQBjB6kxsYT3dnbUyIiXU4bzzsS2Wnn3lKFscecmdFiAoYqwmCj9P+reO1ay/Lrz+9zK9XLO\nsV/onKd7EidyyCE5JIeUREmUrSx5sQ6ADa93ZWtheAUDXgtY2AsYa0BQWFlaUZRWFMOIHE7OM909\nPR2m4+uX86t6lfNNx3/8XnW/qnvrdfdwONNzgAaHr26lW7/f+Z3zPd/zPcJ8xGBXdyX0JiJEEzk6\n26o1PmyyqQSNLW0178cnaY0tbWSSlVVOn9dDW3OYaKJSJyjgUwyZuaqBGB6PxpFhjXPz4ihEHtsF\nqZxzGIfPq/Hs/aojdSVW+RyPR+PbT/pJ5YQfvG061m3Ar/F7X6tjuMfHH/9VlsUN94JpT4eP/+G/\nbOX3vtHMG2fz/Mt/v8nz7+TIFX52aYw7McsSzl4t8m//Is7/890kx/eG+D/+2w6O7XGHXvJFmz/5\nfo6r8yb/4tca6Gl3RvNXFix+9K7Bb38pQEtV8b5kCP/4rvDIfo3uqsHTuSK8ex0e21+ZhYJqpOxp\ncZIBNtNKsrdaFyZbUJlbteZRIZvB6/MRDNXWo7+dfeINSrH1VXyBAM1tlf3jC2sp6kJ+OlsrN/DU\nio6mwUQVmX8lLny4KHzhkFbRwGLbqlg30eeEZIq68P+9IjywW3NM9AGVlr131eK/eiZAc4Pz8Xja\n5k9/mKOxTuPXv1RHQ13tczGTs3nlTJ7X3s/T3Ojl4cMh7tsXovUOsMq7sXTO5oOrRd4+X2AjbvHo\nsTCfP1m34/sUSsLfvpRnJWLx+8/W093m0rxUVAWlPYMenj7hc2ygG6uKBfMbT2o0hKseW1MNG7/4\n4K15pqCc9CuXlSbMripdmPmIQa4o7B+q/J3jW0XIsaoiZCaZoJDP0tWnBql+2g1KlmmyOj9Dz9Ao\nPv+tw8kwbaYWYo4ZBKYlnJoqcmgkWFEkBnj7uk1rveY4/KJp+PFZJ64LML0q/HTr92is+j2KuvDn\nP9Hp6/Dw7EPO3xLg7DWdv3u5wJcfDPHY0cCOsMjMks6Lp/JcmCpxaCLIg4dC7B8L3hVMczsTERbX\nTU59WOSdiwXam708dX8dJ/aHHLDSdptbM/mL5/Ic2OXjFx4Pu157dcHiH940+M2nAwx2Vt57EeH7\n7wqhAHzpeDWrRUEw3S2qy3S7JXPCG1eVxv52YoEtwumpEpN9/orRjiLC7HKStuYQrdvYMCLCxtI8\nTW3t1DUoCO8z0XlqlEpsrCzQNzKOZxuLoFAymVtJsnukDe+2v+umcHqqyNFdwQrup4jw9pTQWq+x\n31EUhe+fhq/eB+1V8y4208J3XheevV9jqMt5r964aPLeFYvf+bKfjman4zYt4UdvFTlzReeXnwpz\nZGLnyUeWJVyZ1XnnYoELUyU6Wrzs2xVgYijAaL+f1kbPHWOLIkIqazO/anBj0eDqnM5q1OTAeJCH\nDoU4NBF0HSG23a7OG3znhQJ7Rnz80hNhh4ojqKLyn/9EZ++Qu1NfTwh//5bwiw85W9vLRaWvHIfO\nKoWC6XVhcVNh69tfs2QIZ24UOT4WrMgubBGmFmIMdDXRUFc5hGVtYYa27j5CYRUIfNqOXURIbG4g\nttDWVSkkshrNIAL9XZWLcSVmEklZHBmtdKS5kvDSh8KT+51O+oNZWI6ptV1dW3znqnBjVfj2Y5pD\nm6Ts3DtbPPzCI76KYKhskYTFXzynOjK//YU62l3W/3bL5GxOXSpw6sMiSxsmk8MB9o4GGBvwM9Tj\nu2O2F6h9sh6zmFnWub5gcGW2pFQt94V4+HCIge6d5TMMU3j+vSJvX9T51afCHJl035cXZyx++K7B\nb34xwGCX8/O9/qHN0ib86qOa41C4OK9mLj97Ara5KGwRXrkk7OrS2FXNUNo0iWUsjlSRATJ5nZVI\nht3DbRW/fTGfIx5Zp3d4182/fyYcO0B0dfkmk2G7La6nCPp9dLdXiv4sRg0SWZtDI5UbIF8SXvxQ\nFSq2MwlASWiem4VvPqBEe7bbQkT44Sl3yQFQjIIXz5r8xhedJ3rZppdN/tNP8/S0e/jWk3W0ubBm\nqs20hNllgyuzOjPLOvOrJpYtdLX5aG/20FTvIRxUrBhQi7VYEtI5m3jKIhI3sQWGe/2MD/rZOxpg\nfDDg6pyrLZ2z+d7rBaaXTL79xTr2j7pvlI2EzV88r/PgPh+PHXbCL6mc8NevCk8d1dhd1VhkbWVL\n471wqEroq+ysqgumoBhQQb/GWE/lZ9pM5knndIfuSi6dIptO0j1w603uBcdumSZrCzP0Do/h9d26\nd2Wq5vhgK8Fti9EW4f3pEiNdfkeafmNNWI47i3C2qKi9u8WpkSSiWDK5IvzCQ5rDeZcM4a9fNPB5\n4dtP+l3XjWUJL54p8crZEl88GeSJY8Gaoxe3WyZnc3VO59q8WturUZOmeg9drT5amjw01HkIBdRn\nskXQDSFXUIHKZtIimjBpbfSya0Ct7X27gvR23FlB9fqiwXdfKtDT5uVXngq70pMB3r5k8vpFk99+\nunLqVNnOzQhnbii5hroqJtFGEn56Hr55PzRWISTXV4W1pPBYleLjTkHp9FKCztY6h5jdxvIC9U3N\nNDTdWvOfGceuF4tEV5foHRmriNrLDJlqrrJtC2emS+zq9lfMRQWYjQgzG8Ln92sOetTrlxXH/alD\nlQ0EAFcWhdc+FH7tMc2BsQFcnrf43psG3/ycnwOj7rCGYQovnSnx6tkSjxwJ8NSJkINadjtLZy0i\nCYtYyiKdsykW5WZ3rc+nEQpqNNV7aGvy0tXmpbnhziN8ULSy186VeOX9Eg8cCPDlB0OO6n/ZbqxY\nfPdVgy+f9HN80vmdswXhb14Xjo9rHB93gbKuQF6HLx52Nmy8cVXoatYcXabJnMWVRZ2Tk5UptmXb\nXJ+PM9rXTHibEJCK1mdp6+ohVHcrALgXHDtAPLKOpmm0dnZXXLMRy1HUTYfGTTJncWVJsSW2f38R\nNSZwoE1jsreK0VKC770Hj+xzdjxatvC9d4RwAJ454WTKmJbwvTcNIgnh178YcLDEyhZJWPzdywXi\naZtnHwlxaNzZjbmTWZZsOWyLZNYmk7Mp6aLqaJpSq6wPe2hq8NDR4qW7zevKP9/J1mMWP3xLZQvf\nerKOQ+PuwYplCz8+ZTK1bPPbX/LT1uh8n6tLwisXhF97XHNg5IWS0qR6eE+lyBdAuiC8etmpdQRw\nbVnH63HCyMlMkWgi72DCFAt5Yuur9I2MVfz9M+PYAaKrSwTDdY6ofTWawbaFge7KPD6Rtbi67L4B\n3r4uNNfBwaHqJiRFgRzpUsWnajs3I5y6rlJXtwW+HLX565d0jox7+eJxX01ebTxt809vF7k0a/Do\n0SCPHQ3QsEPD0idhhZIqjr78fonxAR9ffyREV6v7ASUivHHR4q0PTX71ST9jfe6Y+3feEPYOaDy8\nz3kfrizDh/OqjyBYtb+m1tTw5sf3axU84fKBPdrtjFjXN7Pops1QFVUwm06SSyXpGhj+mRf/x2Xb\n17ZpGqwvzNIzvAuf79aNsG3h+kKMoZ5m6sOVN+jqko7P63QA2aLw8iX3jHQ9CT89B18/Ca1VqraG\nqaCy1gYnTgzq937tgsU7l02+/WSAXb3ua1VEuDxn8sM3C3g8Gl96IMihcSfX+5O21ajFC6eLXJ03\neepEkMeOBmtmrdmC8DcvqyzlV5/0OyJxgKkV4YUPhF9+RKOrqlhq2fDc+9DbCierJDFsW/0+u7o1\nxqogmFr+qrwOBrud8GJkZZH6xmYamisz1M+UY9dLRSIri/QNj+Hx3trUlmVzfaHMWa7aAFsnYLUq\nWtFQTQH3j2t0VUEruaLCfB/eo4YYVNvZaeHMlPCrj2m0uDj3bEH4zisGIvArT/hrRjigopyfnipx\ncdrg2G4/nzsUYKDr7vi5P6utxyzeuqhz+rLOnhEfT98for+zdiE1VxT+8+sG2YLwXzzlZAiUr/nb\nN4TJfvjcPqejWI3DSxfh6yecU9gTW0Wl6r4DUF2YmYLNweFKiO1W5lZZcBQRVudnaO+5ha2X7V5x\n7ACJ6AYiNm1dvRXXJdIFNpMFR6Smm8LpG0UODQcrVE1BTd+ZWhOeOuiEVq6tKA2eb56EUBWkrJvC\n378ptDXC08c1V2d8fcni7183ePiAj8cOeWsGLrYIF28YvHC6RKEkPHokyIl9/k80eLEs4dKcyZvn\n1VCcx48FefRIcMcMeWbV4ruvGRyf8PKFGoHZ9S2n/q3PafS0Vh+A8MYVNfPhi0ecWf+FBZtMER6e\nrNwTlq0gNjeEIRLPkS+aji7TQi5LIrpRga2X7TPl2AFi66t4/T5a2ivzm1iqzISonKZubG2AfYOB\niqnvAOtJNfn9CwedXXjRlKpmP33USb8D+GBGeO+a+nHdMHfbFl49b/HuFZOvPuDn8NjOcEgqa/P2\nRZ13PiwRDmoc3xPg8Lifnva7g1Hu1CIJi4vTBmevGaSyNvfvD/C5wwHam3dm4FxZsPj+WwaHx7w8\nfcLnyiBIZoXvvikcGNZ4aC+Ozx/PwHNn4cmDqsN0uxmmqoEcGNQY6qh8XrZgc36u5JjQDjC/miQc\n8tPdVnlKpBNxivksXf2VdCczl8Lf0HLPOHbLMlmbn6V7sLIZT0SYWU7Q1hSmrbkSqF1PmCxGTe4b\nr+y4FBFOTwseD5wYczrS96ZU9P7V45UMJFDO/R/eFuqCCpap+fu+piM2fOtxv2MS1nYTEWZWLN48\nX+LSrMHkkI+jkwEO7PLdUQf03ZplCdMrJuenDD64btDV6uHhQ0GO79m5Uc8whefPmFyctfjWo34m\nB933wYU54c3Lwrce1uhudb7e2RmlZ/S1E8463Wpc+GBe+ZtqeY3pNYOibnNguLJgWg5YxofaCPor\nA5b1pTmaWzsqJFcAjMQGgbaeT9axa5r2x8DXgBIwA/y2iKRrXCu2ZaJ5tlG+DIP1xTkHRaxcXGhv\ndm6AzbTFjVWDE1UpDsDlJZtoGh7d68TbF6Pw2mX42n2K715tV5aEl8/XZsuAgmb+7jWD9iaNZx/2\nu0a3280WYXbF4oPrOhenFZ99z7CfsQEvw90+uts9ruyEHV/TFiIJm8UNi5kVk+sLJiVDODTu5+ik\nn8nB2pBR2bIF4bl3DRYjwi895q+Ziq8nlGN4aK/G0THna2YKCuq6f0IVTLebiPDulKKNVQ/QsG3h\n7EyJgQ4fva2VOyadLbG6mWVyqK3ie9iWxerCDF39QwSCtwpOIkL26ns07X/oY3Xsd7u2q/dROh6j\nVMzTuUXHLFuhaDC3mmRyuHJQiIhweVEnHPQ4isimpQrPu/s0x/hAEXjlEpim0izxVP2UpiX86LRQ\n0uEbDzqDHlDr9J1LFq+cM3n8iI+HD3hvuy4LJeHCD0sZbQAAIABJREFUDYPzN3RuLJn0dniZGPQx\n1udjsNtLU70zs7udFXVhJWoxv2YyvWxyY8mks8XL4Qk/x/f46azRXbrdplcs/vEtk4FOja8/5BT0\ngq21eQ0uzin4pa3Rec3VZZUNfeOkGuaz3bJFRdt9eFJzqD0mcxaXF3VOTIQczKT51RThoJMckk0n\nyaYUGWD7PTOzSfLzl2g++Mgn7tifAl4REVvTtH+L6pD6n2tcK8X1eYLdlXSJ5GYE0zTo6Omv+Hu+\naDC/mmRyqB2fr3K1XlvWEWDvgFNA/61rQkMYjo44ndXUqpJB/doJpSpYbfMbahM8ekDjsAvPHdRG\nee2CxTuXTB464OPRg947YqWICOsxm6klk5kVk6UNi3japr3ZQ1uTh5YGDw1hjWBAuxl5WbZa7GX2\nQDxts5myaar3MNTtZVe/l8lBP/2dd5YJmJbwzmWL1y+YHJ/08tQxX83Pfn1Z+OkHSipgst95Ta4I\nP3xfKRBWM2AAriwrpsDj+5wQwvSaQb7khGAs22ZqIc5Ad5NDmjcRXVdUwu7KE0SPraJvrtK458TH\n7djvam1bpQKewLYDx7ZZXZilvbu3osgLqo5kWeKQGtBNRft0y0jLRbrP7XY6E8tWeHvQrwZzVPtk\nW1RhcH5DsWXcHBlALG3z/bdMUjnhmQd8TA7c2boyTGFmxWR6yWRuzWIpYmHb0NXqobXRQ1O9Rl1I\nI+DX8HrUYaSb6nDI5m2SGZtoyiZXEHrbvQz3eBkf8LF7yEdj/Z1lAvG0zU9OmyxFbb7+kJ99LtpP\nAIYl/PSssJmGX3rY2YMBqg/jvSkVBFZDi4alqI1j3RrjVRIapqVqRuM9TggmlS2x5haw2BZrC7N0\n9PQT3AYvigi5G2cJtPUS7Bz49KAYTdO+AfyiiPx6jccldeE1Gvc9hFZRVLJZW5hxfDGA1WgWw7Qc\nTALTUhjWaLeP7hanXvgrl4SJXmdBA9RJ/MGs4gG7OfdYWvjeu8JwJ3z+iNMplS2REX5y2mBu3ebJ\noz5O7Pbu2DjhZrohRJM2ibRNKqcWdskQjK0GQJ9XdQfWhzVaGjy0NGp0tXgJ1mC11DLLFs5P27x4\n1qCnzcNX7vfR1eK+YWwR3rwkXFmCbz7oxB0BciV47gxM9sFRl6L0ckw4v6CYAuGqzxrPWFxb1rnP\nJaJZiajCucPhlUpEVhboHdpVQSMU2yJz5V3qRg7gb2z9uUExd7K2c/OXqRveV/H3fDZNKrZJz9Co\n+wHW1Uhj1bScWMbi+orBiXFnw89qQjg7q+5rdRHQtOAn56AhCI8dcDp3UGSBt64opcKxXvdbJSJc\nXbT58SmT5nqNp0/4GHLhe+9kIkK2cGttZ/JCvqgojuWG2oAPwiGNhrBa1+1NKsC5UzXIsmXywqvn\nTc5PWzx8wMejh7w1YZp0XnWUttTDl+9zcv1Bdfa+ew2euc8pM13unQn54fioU5L3ypIq0lZrAFmW\nzdRi3FEwhdqBrZHapLhyg4a99+PxeD9Vx/5D4G9F5G9qPC65+ctoXj/hgcryci6TIh2POTaAbQtT\ni3F6O+pprmq1yxRsLsyVODYWpK6qEaKcKp0c0+hpcd6PK0sqzfrKcSejABTf95/OCJkCfP1+J/1p\nuy1HbV5432QjYfPwAeXg75by+POykiF8MGXx1iWLpjr4wn21YRdQssjPnVbr4ev3O4ud6hr4p7PK\nqbsxjWIZ4a3rwqN7K+c8lj/P+9PuEWk2r7O4nmZyuM0BUURWFqlraHTIB5TW5zFzKerHDv9ci6d3\nsrZTF16jfuI43vAtbyAiRFeXCNXVO9hfmZzOciTN5FBbhfgd1M5oQDGM5qPCE/ucuveGBc+fg7oA\nPH7A2fIOsLwp/OCUsH9QSUHUClwsW3j/usWr5006mjw8csjLxIDnU2fElC2atHnrksXFWYtjE0p6\n2y36LtuNVeH5s8LJSY2Tk85aEaiM/tSU8gvVjY0iwoUFIZmHR/c4od7VuMnypsnx8aDjni6tp/F4\nNEeDmqGX2FhaoHd4FK9vOxRtk716ilDfOP6Wzp9P8VTTtBeB7XwSDTUc5A9F5Edb1/whcExEfnGH\n15H/9V//IXp0mUBHP0889QUef/zxrS8iRFeWCNU7N0CuYLCwlmJiqLWCIQGqc28l5n4zNzOKBvnI\nnkq977JdX4FTN+BLLhru5c90dlp18z12UOPQiPtiKNty1OatSybXFm0OjHo5udvLYNfd44w/q4kI\nqzG1KS/MWIz2enjkoI+Rnp2jrmvLSiLg2JjGg3tx3cCJrCpCHxx2h1/SBeG1K8KJXZWSpaAO6XNz\nOu2NHocUczmi6e9qdMx7zKaTZJMJugdHKu7lKy+9wIv/+W/wd/Th8QX4N//m39z94v8Y1/Yf/ov/\nHruYx9/WwxNPPHFzbRu6zsbSvKOOBGrurwiODMUW4fysTpvLvRIRzs8LqTw8stfpmE0LXryg/vup\nw+B3QSTyJeHHZ4RsEb56UqOjqfZtMy3hwoxa27oBJ/d4OTbhpbHuk3fwhqmyidPXLNbjNif3eHlw\nn2/Hz6KbCoaa24CvndQY6HC/9uKCGrb+lWPuNbhrq8JCVDXYVUf66bzNxfmSoxEJyhBMhomhyo76\nnQKWF77/97z28ov423rRNO2jre2fNWLXNO23gN8HnhSRmjPgygWm4vocVi5N/VilOv2tDTCCz1+Z\nrqxvZimUFEWoOv25tmJg27Bv0NlAsRoXzs6pjrAmlx9/PqKamB7b72w8KFs0pbTG64Pw9DF3vvt2\ny+SF96cszk5ZiMCBUQ/7hr0MdNaOjn5Ws0VY3RSuLlpcmrPRDTg26eHEbt9tC7zZgvDSeSGagmdO\navS1uV9fpjQ+MKmi9WrLlYTXLgv7BzVGOl2ioRWdoiGuUejiehqPhqN3wTJN1hZn6eobJFAliJRf\nuILm9RIe2A38fOiOd7O2bdsie+U9Qv0T+Fsqu4ZSsSilYpHOvgHXjLSnvd7RgVjObvb0B2iv0v0R\nEd67oWCNByec0aNlwxuXIZmHp484i3/l1zg/C29eFk5MaJzczY7rU0RYjAinr6npTIOdHvaPeNg9\n6HWMSPw4ragL0ys2VxYsri3a9LZ7OLHby4FRz22hz9l14YVzwmAHPHXEyV4B1cl7akqRK75y3NlV\nCopyemVZeNIFWtRN4ex0ibFeZy+GYVrcWEww3OvsXcimkmRTzoDFNg2yV96lfvwo3joV4X/idEdN\n074E/DvgURGJ3eZaERHEtshefY/QwG78zZVCYOl4TAk79Q85HPjMcoLmhpBDJMyyhfOzJdoavYy6\n6EksRIWLi6qIV627AapV+IULKgI9NOzkqpbf4/QUnJlSXZf37+a2i0pEWNkULs+rBZnMCSPdHkZ6\nPAx0avS2e1ybJe7EirqwHheWojYLGzZzazb1IY3dgx72j3gZ6nbnLVd/pw9m4N2rwuFReGifhr/G\nd7q2DKen3SmNoCLA164IEz0aEy7Y7UrMZDlmcnzMyWRKpAtE4nkmqopKAJtry3j9flo7KhsQzFyK\n/OwFVa/xKsz943bsH2Vtm+kY+cVrNO57oIL9JSKsL87R1NpOfVNlepjfYslMDFZOEQNI5Sw+XNBd\nI0HLVqwjnxdOjjt/bxFF17u+qpx7R5Vuz633UM4vlVPOr3pKkJvphnB92ebKvMXUsk04qLGr18NQ\nl8ZAp4eOZndq5e1MRH2OlU2bpYjN3LrNWlwY6vKwd8jDgRGvqzhftaXzKkpfT8AXjznnBNz8Hia8\n8iEYW4yi6l4AgPmocGlJBYfV/qOchbbWe9jV48ys5laS1IX99LRXpgCmqdiA1QwvgMLiVUAjPLTn\n5t8+Dcd+AwgA5YX/noj81zWuvUkJM1KbFJev07DXuQE2luapb2qhsaVSzU83LG4sxRnta6EuVHkT\nS4aiz431OIupoE7cy8sK963WKQGFG79wHloa4NG9ajitm6VyWwsmCY8d0Ngz6A5ZuFkmL8yuKUe8\nHLVZTwhBP7Q3qcaohjoVDQT9t/jIpg2GoYaLZPJCMifE00K+BN2tahMNd3kY7fXcNjIvm4gwvabm\nZTaF1WZur5GKW7aSKF2JqR6AaoYAKKf++lUlgLS7z/k6sa1i6bFdQYd8cFE3mVlOsKu/tWKABkA+\nkyYZi9IzNFohOyEiZK+dJtg1RKD9FkPm5+DYP9Lazs9+iCdUR6ivUv5PLxaIrC4pSMZXuX6jiTzJ\nTJGxwVbHelpPmMxtqEOxmsFk2QpuDPjg5JgzcgdVDHz7qmrQq6aklk1EuLEKr1wQOpvhsYM7wzPb\nzRYVZMyuKWe8sikks0Jrg0Zbk8qUG8JKQsDvU7i/oOiZRUPIF5UjTmaFzZT6Lr3tHga7NEZ6PAx3\ne1yLnG5W1IXTU8K5WTXM/oE9tYOVZE5pv/S2qnvjVo8oB4WP7XP6DRHh6rKBbStF0uosdCOWI1tQ\nOkfVQWp0dYlgKExze2VmZ+bS5GfO07jvwQqCyWeqQSk/exFPsI5Qf6WSUbmgUN3cAQqvWo1mmBhs\nc1Ags0Wb87Ml9g85C3OgTt4PFxXm7tZhaljw1lWIpOALh6Ct0XHJTVuMCK9fEkomPLRHY88Ad13N\nt0VI5xTFLJVTjr+oCyUDrK05xF6vOmTCAY2GOmiu124eBHf7fmWH/s5Vwbbh0QMau3pq1w1SeXj5\noprY8/h+p0wAqGLrG1cVA6laz0Q9rgrcB4YDFRORQDFDppcSdLbUOXoVyhFNZ+8gwXDlY6WNBYzU\nJvUTx+5JSQFbL5K9dspRSAVIxqLoxQKdfYOOzb6wlsLv8zoKbKA6dDfTFkd3OTMeyxbemRI8Gjww\n4Q73babhxYtq4s9Du52NTGUzLVVXOj0lDHfBg3vcG/ZuZ4apApBYRkjnlChZyRB0E8QGNIX9BwMQ\nDirn39KgDpM6l4L97aygCx9Mqy7ysV54ZL879Fq2qVUVsJycgL0D7tfMrAtXV2sHgzPrBsmczZHR\ngOOeZ3IlljYyrnXBTDJBLp10QDAi9raApRLr/Ew5dtsokb36HvXjx25iSWXLJOPk0inHlweFt+eK\nhuMkBKXPcHlR5/CoU+MaFA3vgznhwUmNzhoRyfUVxWE9tkvpudcKyEWE2XV495pauMfHNQ6O4Irj\nfZqmm8KVRXh/WvB51Gad7K/t0EXUwr/dPUjkVM/A/kGntjpAvqRGG072BRycXuXI0vi8mgNXL0c0\ngVCYlqqIxi4VyF47Tf3uE3hD966kQCm6jBFfo37yPocDVxlps6NgZlk2N5YSdLU6DzoRYWrVoFAS\nDo0EHIe6bQunZ4SiDg/vdrJlQMEOb1xRncJPHqwNzYBywudm4P0bQncrnJjQGO7amTzwaVgiK5yd\nFi4vwEQ/PLC7Nkcf1FCYt67CZkYJA1YzX2ArEl9RgeCje53CXqDUZtcSFsd2OSmpJcNiZim+hatX\nYjs7Ba3F9XmsTJy68aOffUkBfXOFUnSZhj0n0LTKdDu6tow/EHDgqyLC/GqKgN9LX2eD4yZEUxZT\nq8q5N7i0OUdSqvB0eFhj2KXIB0rP/ZVLKj17bL873327rcSE92+oyvtEH+wf0hjqunOY5uM2EWEl\npmY2XluCgQ518Nxuc2aLSqExW1Sb323hg+JTn5kR7tul0e9SbC3oNudmdUa7fPS6zH9dj2XJ5nV2\n9bc6nFQ6vkk+l3V04amGjQ/wN7UT7BmpeI6dTeBtbLtnHHu5ucTf3OloyDN0nY3lebr6hgiEKvHV\nMjQ14uIUyp2pAuwfCrhg6ootE0nD5/Zo1LvUb0RU882712HfoDq43SCIm5/VUk7zgxnVW3FwRGPf\nEK4Z7ydlJUOYWoFLC6rJ6OAwHBvfOUIHWIiqtT3cCQ/sdmcL2bYiWyRz8Mge9y7d1bjJQsTk6K6A\nQwrDsmyml1XHfEeLc+LXxtI8DS2tNDZXwsxWIUfuxvs07D6JJ1h5qNvJCN7W7nvbsdt6Ec1fqZ2R\nnzmPt67JgUlalsn64hxtnT2EGxqrHtu6gU1hOlqdXncjaTK9ZnBk1Fl0AkjlFdd6uAP2D7hTEm2B\nS4tK0/3gMBwe2XkTgBLLuryoJIGzBRVFjPdqDHXysU6XcTPTEpY2YWZNLfyAH/YPauwf5raL3rbh\n8pJq3No/BEdH3b+riDC1prjUD7m0UwMUt5z6UKeP/nanU0+ki6zHsowPtlVIMwOUCnmia8v0DDqp\ngaXIEkZi3RkFWyb6u98n9Mi37hnHDmCV8uSun6F+8j68ocriRC6TIhWL0jM4WiGAB7fS+LHB1go9\nEVCO59KijkeDfTWc+/S6ouY9OKnRUSN6zRVV5JrMwyN7oe820wVFhLU4XNoKFFrqYaJfY6wHOpt/\n/pF8tqiy4+lVYSECQ52wf1hjvPf2JIZcEd65rqL0x/bV/q4lQ3j3hipGPzDuXvxdi5vMRUyOjAYc\nvTMiwtxqiqDfHU6Lb6xh2xbtW8Opbz3PJnf9ffztfQQ7K3EhK7aCcfkdwo/98r3t2PXLb+Hf93DF\n3229RPbaKerGDuOrr2QMlDd698AI/kBlBKMbFtNLCfq7Gh0zA0EVnWbWDQ6PBF1V6IqGYhX4t1gF\ntQo0mQK8fU1xuO+fhNGu2vDMdktklYOdWVPV+e4W6O+A3laN7hZorv/oG0JESOdVPWAtrqLz9YRK\nr8d6FdRyJ8UvETWN570pCPnhc/vcG7ZgC3+dU+/78G5n5yMo+OXCnM5gh4+BDqdTz+Z1FtZTjPW3\nEqoqllqmyfrSHG1dPYTrqw7yYo7c1PuuTtK4cRbJpQge/fyn6titxAaelkrObCm6jBFbVYdRlYhL\nPLKGZVp09PY71sFmMq9UIAdaHbWksnPXNNg/6IRlANa2Mqr9Axq7umuvs7kN5fS6mhXefLvMFBSm\nvxRVDT+z6wriGeiA/naNnhbobMFBCbwbMy0hllZstdW4sLypMsiRbhUkjfdSc57AdjNMxU2/tKiy\nk6OjtWsLiZzyBQNtcHDIPdBbiZksRAyO7HI2RIoIK5EMhmk7KNmgejHS8Rg9gyOOg7y4NouVTTog\nGLFM9He+j2/P/fi6hu5tx1547W/xH3wUb1tled5IbFBcnaZhz/036WtlyyTjSiBncKSCHQG3qGLD\nvc00hJ1cpcgWLHNwKEBzvfNXtW1V9V5JKD6wWyNT2ZY2lQP0edXkmv62O3PwoHDulRhbDliIJJUU\naEuD2kwNYcU1Dm0xB8pf07ZVUbekKyZMtqiKmomMisi7mqGnVW2qgY67w/fXk3BmWkU0908oHn+t\n75PKq2imvQGOjrhHM9mizcW5EiPdfvpc4JdCyWB2JclwT7OjrVpEiCwvEKyrd+DqYttkr58m2DlA\noKMyorHTMfSzLxB86Fk8ofpP1bEX3/oHAg98vWL9qoz0At5wg4MkILbNxsoi4foGx/xfgLXNLbhq\noKWisQXUur2ypGPacGAo4Pp7ZArqN2sKq/b3WhmjYanGnA8X1PDxo6OqYH6nlsop57saVwHMZlrt\nkdYGaKpTr7Wd7eXRVEBh2Vt6MbqqUWUKCgLNFNS+6G6BvjaN/nboarlzWNOyFT33gzml5Hr/hPoc\nbiYizGwoXaOjoxqD7e7vsRA1WI1ZHNkVIOwyDGQ9liWTc/+tymyorv5hAsHKANTMJsnPXqRhz/14\nqjB34/pppJQncOjxex9jNyOLmNdOEXjw2Qo6D0B+4SrYFuGR/Q5sNb6xhi02HT3O6CaT11lcT7nS\nIEHR7a4u6ewZCNBRY8Dzclz4YFaxO3b31V5EIoo+dnYGwgEFzwx33rmD324lQ0hmlaPOFiFfFIqG\n6hy0toa/ez1qMwT9UBfUaAipSL+l/s6iFrfPvxKHC/OK7nVsl2o2qgUxlRf+5WXh8JDGSA3Vy2TO\n4tKizkSv35VuWtRNZpeT9HU2OBpxRIREZB3LMunoHXD8voWl69h6kbpdhyrXhW2hn3oO79A+fP0T\nn3rxtHTuZbS6JvyT91U8Zhu6ykiH9+FrqmwCME2DjaV5Wjt7qKuCG0WE5UgGw7AY6WtxFkxFmFox\nyBZtDo0EXTNOy1a4+0YK7h93h87KVtDh/JwiD4z1wKGRO4vgq01EdbQms2r+ba7ETbaXYak1CFs6\nSD4VzNSFVGNQeW1/lEY+3VT69B8uKI2X+8adM3e3W8kQ3p9VAdMDE+49LiLCzLqaWXp4NEjIJXCK\nJvLEUu7ZVTkLbe3odsjximmQuXaK8MBuR0ObnYygn3+F4EPfQAuE7n3HLiIYl94Ej8cByYht3aL7\ndPRXPaaim1C4jpYOZ4toKltiJZJhtL/ZMZwDIJW3ubRQYrjLz4AL7guKj31mRjBtODHmTnEqm23D\n7IZykIalFA4n+hSccS+absL0msLRRdSmnejduWaQK6qFb9qKI+228EFBXtNrBvsGAxVT2MtW0k1m\nV5J0t9U72B4A6URMMaAGhh1pqpGIUFiZUhFNVSBg3DiLZBL4j34eTdM+dcduF/OU3v0BgSNP4Gmp\naqjKxMnPXaJhz8kKBUiAUrFAdHXJtZgqIiyup7FFGO5pdjh3EWFuw2QjZXFoOOBaTwIVuJyb26op\nDe7cAZ0vKfji6rKKmvcNwmD7RwtePglL5JT20401lUUfHnGXCNluyzHh3PzO98OyhatLOroJB4cD\nrhnPZjJPNJFnbKDV0Vxm2zaR5QWVkVVnoSLkZy/gCYQJD+6ufMw00N/7Ib6J43i7R4DPCCtGDJ3S\nuz/Av/cBvJ2VWtU3sdTxo3jrnO3lG8vzNLV2OEZHgZojuBrNbk1ecoECdJuL86pLbLzPfbyXiDC7\nAZeWVRfl7r7btVkrLPDyEixuwmCHcpgD7bcvtP68zbJhLaEW/HxEFY32D94eQrK3CnBXV4TdvRqT\nNTKYm04laXFwJODKQCo79a62etpdnHo+myERWad7cMRRLLWKeXJTZ6gbO+KovdjJDfTzrxJ88Oto\nQRVWftqOXUSwNhYwp864ZqTFtVnMdJz6yWMVDDBQzViJzQ26B5z3oUwNFdydO8BawmRmzWDvYIB2\nl8MVVE3p3JwSsTo+6pw0Vm2GpYKBK8sKNpzoVQ1OrfWfvpMv6DAXgRurKiuY7Id9A+5yANstX1IZ\nTLqggrdaGUzREC4tlKgLetjT73e957FkgUgix64BZ5FbRNhcW0HzaLR39zmy0NL6PEYqSv3EcUft\nxbjyDmKZBA4+evNvnwnHDmDH19EvvlaxMctmJDYorNxQ1B+/Cw90eYH2rl4HUwbKzj3DSA1YxrS2\nsElLUcZqYdL5kjrRU3k4MqzR23r7QmdRh5l1BdXEs8rJD3UoJ++m1fHzsIKuoJbFqKoJNIZhvEdt\nyDv5DJGU+t4hPxwbrR2lG6ZwdVndxwPDAVcYoFgymVut7dSLhTyba8t09g0SrNKBEcske/0Mgc5B\nB1NADB39vR/g230Sb9ctKuG94NgBjMtvIbZdsTHhFt7uCYYID+5xvEY5c+kaGMZblbnYIiytp7Fs\nYaTX3bmXBzz0t/sY7vTVXK8rceXc2hrg0LA7LbLaNtMqQJjdAJ9HsVKGOlR955MIYEQUeWEpptb2\nZkbtq4letc9u9xks+xaba7wb9vTvIMedtbiypDPQ7mOoxn2MJvJsJvPs6m8hWDVaSURIRDcw9BJd\nfYNOx52OUVi4rPxbVfZmRRYwr51WgcE23/eZcewAxvQ5JLmB//gXHRFMcWUaM5fc6i6sosRtpa4d\nvQOOuZegJvAsRdKuRTrY4sFHTFbjpqt87HZbTypd8bBfVct3Kq5ut3xJ8WYXN5V4Vl1QFXK6mhVz\npbW+doX+Ts2yFU6+mVbsmPWkwup7WtSmG+q8fQRTtlRe+HBJMV4ODWlbUb37d03nbS4v6nQ2e9nV\n43ON5tWQlBS9HQ20NjkrceV5t+3dfYTrK7szVZp6Ec3nJzy011FvMS6+huYP4d/3YMXz7hXHrlLp\nH+HbdQhvX1XB1DIV3Ng97IAbQc1KLRULdPUPOYgCIsLyRoaSYTHa1+yQ+gWFG19a1PF71RCaWgVT\n0xKurwrTG7CrC3b31WaFVX4GiKbV2l6OKWfb2aQgm84m1ffQGP7ZI/qiroKj6BY7Zj2peOf97beC\npTvZPyLCYkzRNFvr1UHm1nB089qo0jTaO+AOK4oIG/EcyUyJXf0tDvgFVHdxIZehu98JLaos9H3q\nRg/ia6zkskshS+nUjwgc+byDXfWZcuxi2+hnn8fb1odv7EjFtWUMSvMFHJsb1ODX2Maqa7QHZW3v\nFL2djbQ2upf44xmLq8s6Pa0+Rrtqj5OzRZiLqMp5WwPs699Zn935fNXtt55UDjiWUQXTcACawtAQ\ngnBQ4fMB3y3mQPm5pq2oW0VDHRhlBkGupDZRR6PiEve0qI11NxFUKi9cXVFNLbt7NcZ7akNP5YW/\ntGky2R9wKNmVLZ0rsbSRZqCryZWGauglIsuLtHR2U9/orG4VV6Yxs1uHepVzMxevYq1METj5jIM9\nda84dgA7E0d//3kCJ76Cp6ESNlRw41nqRg/ga6wkVYsI8cgapmHQ2Tfo6tzXNrNk8jqjfe6OxRZh\ndt0kkrLYM+CnbYfAJV9SqoUrCRjvhoneO3PwZSsZsJFSznczrdZ2yVAslIaQ+hcKqLVd1onRNGCL\nFWNYZWYMN1lf6bxa960N6rDobFJ6LncapJTv01JMwYl+rwrKanWag4Jeri3p2KJUYqsbj8qvuRLJ\nUCiZjPa1OAqloLKu8oi77QNhQB342etnCHQNObNQ20I/8xO8XcP4Rg86Xvcz5dgBpJSn9N6P8O//\nHN7qgqllkp16H39rD6GqTkNQ+Gw8suYq6QpQKJnMryZpaw7T1VrnGoHqpnBtWadkCHsH3XHislm2\nwt+vrykK2WSvRvdHbM6w7a1FXFD/W9BVlKKbypHbW6wYj0elvgGfYsaEA2qzNIbVv4+SBosImxmV\nlsayMNmjGk1qiSWB4qdfWzbQNNg74L7wAWJNIj1VAAAgAElEQVTJPBvxvKtMKWw59ZVFmts7aWhy\n1kn0zRVKG/PU7z6Bx1eZbdnJKPq5lwic/AqeKszd2ljE1zN8zzh2AHNlCmv+EoH7v+bA28vF1PrJ\n4w5evogQW1/Fti06ewcch5uIsJkssJlU99kNcoStSVUrBh1NaobqTrWibFEd8CtxGOlUDv5OIBo3\n003lnLPFW2tbN9U/21ZOW9PAq5UnhKl1Xbe1tpvq1P//KFG/aQkLUZhaF4I+2Dew8x4VETaSFtNr\nhoJeutwzUMuyWVhPowFDvU0OSiOoQeuZZJzugWFnncS2yU2fw1vXSHhg0vFc49p7SCGL/8jnHRmq\ntXQd//Dee9uxW8koniqp3jLeHjj5DJ4qzRhbL5Kdep9Q71iFkl/Zys69VuRumBbzqymCAS8DXU2u\nUbmIsJ6wmFk36GvzMdzl23ET2LawuKkWj23Drm6N4bvkkH8appvqc89GBMuGiR6Nkc6dO/dsEZY3\nTRaj5hajyFujS1dYiyre9Uh/i6OYBNuceluna/HbSG1SWLji7uxKBUqnfoR/z/0VuDqAnUtR/OGf\nUP9r//LTZcXYlgM2NC6/hZgG/i0u8nbTY6sU12Zp2H0Cj78ys1HOfQXbtunoHXBE7gCpbJHlSIb+\nzkYHhfTm+1vCjVWDVN5md5/fFV7YbvmScGNdmI+qTHC0SzUd3StTk2pZKi/MRYSFTfW5d/dqtDfu\nHHQVdZupVYOiroI6N20pUASA+bUUDeGAq4QJqEg9k0y4O3URCvOXENt2UHYBrLUZzOlzBB74WkVX\nPoBx7Qzm9bPUfeOf39uOPf+P/4HQV3/PGcEsXsFa3kqxqx6zCllyNz4gPLzPod8Ot5x7R0+/Y2gw\nKEe8HElT1NXsVDenAwqfvLGqky0KE71+x3CDaitHvnMRYXWr63OoXRVad4p+P0mzbGEtCUubwnoK\nepphV5dG1x1kGsmcxdSKQcCvsbvf79qYAerwXFhL4/VqDHU3uWK/5SaN1o5uhx45lBs1LrgyYMS2\n0N9/Hk9bL/7xY47HSs//Jd6+MQJHH/9UHbt+4U38hz5X+fksE/395/F2DDjgRoDi2hxGYoOGyeOO\ndS8ixDZWscqwjNe5HgslVctobgjR21Ff8zeNZdRv2VTnYazHVzPjKptpKWx6LiLkSjDUDoPtGm0N\n944QWK4kLMdgcVOprI50wmin+zjH7WbbwtKmghQHOnwMddSGYcv1up72BlcCgIiQjm+Sy6Tp6h9y\nderF5SmsfIb6iaMVEuUAdiqK/sGLBO77Ep4qWM6Or1N8/i8JPfO7eFs6723HXnz5u2ihMIGHvlbx\nmIhgXnkH0Yv4jzzhiHxubvxdh/A1VBYdAIr5HJvrK7R19ToaPcqvH0sViMRz9NfAfssWy1jcWDUI\nBzXGevw7wjNlMyyVxi7FlLPvaISeZpUGqmLSJ7MZRNRG3Eipwm8krZo1Bts0Btq5I/y0ULKZ3TBJ\n5W3Ge/10NtWeVF+eU9reHKarzR3uuvXb9FDX4MTUrXyG3PQ5wiP78Vc18IgI5uW3EbOE//CTzqj3\n7MvYkWWCT/86Hu/dD/z9uEzTNMn9p/+T4Od/FW/3UMVjN+HGPfff5CXffEyE4sqUmig2ftRRN1AM\ni3X0YpHOvkEHbgtgWjaL62lEhKGeJodMbNksW1iImKzETQbafQx2+O5oGEamICxuCktxVevpbVVr\nu6v5ztbTx2WWLcSzsJFSwUq+pKi7Q+0anU2332MiwmbaZmbdoC6oMdFXO1gREdZjOZKZIkM97rCi\niJDc3KCYz9PVP+T62xTXZjGSERomXA7uYo7SqecU7bsqCxWjRPGHf4L/8KP4xj/aPN9PVgSsVLj1\ngSeqCqa2hXH2BbSmdvy7Tzqeb6Zj5OcvuUZ1oNgym6vLNLV3ONTTypYrGCyup2iqD9Lb0VC7YGoL\nK3GLhahBe4OXkW5fzUVQbYapouONpOr4s2xV1Gxv0GipV918If/H4+xLhuIlJ3MQz6pDBaC7Gbpb\nNHqa7xwiKhnCfMQgmrIY6FAbvxYkZYuwEcuRSBcZ7G6ksd79oMxl0iSi6zWzqZvZ2OBu/K3djsfN\n2QtYG/METnzFmcktTaG//SNCz/4ztHDDp148NRevo7/zI0JfV59nu9npTfSzLxA4+gU8Lc5mlcLi\nVexSgfrxI46oTkRIxTfJZ1J09g065F7L10QSeWLJQk3tpLIVdJu5dZNEzmK4009vm/eOOz0zBeVU\nN1JqrdUF1Npuq1druyl8e1GuOzFblMxAMq80l+JZiOfU63c3Q0+LglruBCISERI5m7l1A1tgrGdn\nSKqkmyxtpPF6PAx2N7kWScW2VTZlqTqIWzZVXJ/f0gk67oTaTAP9zI/x9oziGz3k+Lz6q38PgSDB\nzz0LfEaKp3Zig+JP/iOhp38DTxVuLkYJ/fQ/4R3Yg294n+M1FA57uaZzN3Sd6OoS4foGWjq6XJ2n\nZdksRzIUSyaDPU01i09QVkxUFKiOJi/DnT6HANDtLFcSYhnleJN5xYgRUYWi+qAqFAX9GgEv+LaY\nA+V9VtbUMLfYA0VDbjEISurx5jrVht1WrxZ7ffDuDo2CbrMUVd2Lva2Ku7tTJFYsqYXv83oY6G5y\nKDSqzy1bDIEEnX2DjvFfsOXUpz8g1D9JoK3H+fjaDMaNswRPfhWtSnvdTscoPvdnFRHyp+3YRQT9\ng1ew1+cJfuk3HQ7aiixiXH1HMWXqnBr0hYUr2EaJ+rHDjueCmpGZjEVq0nxBBS5L6ynq6wL0dTS4\nwmJlyxRs5jYMsgWbwU4/fXfh4EEFP8k8xLLK+Sbziq0V8it9mLqAWtsBn1bB9iqzYsqML9NSQUXR\nUIXW7BbzKxSAljporVcQUHvD3SmkigjxrM1CxEQ3hdFuH13N7jWim9dvKY92tdbT0RJ29x+mSXRt\nGZ/PT3t3r6O4DVDamEffXKF+4j6HBozYNsb5l9CC9fj2PeR4D+PDt7DmLhP8yu/cDGY+E44dwJy7\njHHmBUJf+31ndFPIoJ/+Mf7JE3h7dzle56ZzrwHLWJapur40jY6eftfTFCCRKbIWzdDaFKa7rX7H\niUSGKSzHVBrbFPYw0O6jtaE2RHE7KxlKTyNfgoJxa7qMsaUTU/5JNO2WXkzAqw6AcEDx4huCiinz\nUT6DiJDK2yzHLBJZi75WFaFXj17bbrbIzcaMnvYG2ppC7oVU2ya+sYZp6HT0DTjGwMEt+CU0UMOp\nb65gXHqDwPEv4anm++pFis/9Kb69J/HvvZXZ3QuOXWyb0kt/g6ehhcBDX3VcZy5dU0yZk19xNObd\ndO56gfqxIw5YBm7RfJvbO2tmpZZl36RE9nc10lQjmypbOm+zGFXTgHpbffS1e+84O622MhSYK0Je\nVxTdkiEY1pYGkgBba9vjUWvbv00zpsz6qg9+9MjfshXTZWnTRNNguNNHZ7N3x+heNyyWI2ksSxjs\nbnIoj968rlgkurZMfWMTze2djvUvIpTW5zDi69RPHHM0IN2UVDFKigFTdShYy9OU3vxHQl/7/Qqa\n7Cfu2DVN+yPgWcAGNoDfEpH1GtdWUML0sy9jr80T/PJvOhaxnYmjn/0p/gOP4O1wzq4qwzLh4f2u\nBdVy91cxn6Ojd8ChqnbzdUyblWiGQsmgr/P2m6C8aFZiJpYNvW1eelp89zwjpmy6KUSSFqtxEwH6\n23z0tHpvr2ld0FmOZAhsjW5z408DmIa+NSAlSFtXryubo1wvCQ/ucYVf7GRE0RqPfB5P1eNi25Re\n/g6euib8D321YmN93I79o67tWgdP2cyZc1iRRQL3fcnBghARikvXsPIZ6saPOCifsJWVri0RDNXR\n1tntGjGCEsdbiWQIB330dTbUxN7LVtBtljeVRERTnYfeVh/tjZ67HsH4aZiIkC0Ka3GVebbUe+hv\n99Fav3PwZYuwmVB6L52tdXTWoEUD5NIpEpsbtHb2uPZfqHrJNGZajW10YzqZ109jp6Lqt6/2ecko\nxR//BcEnfwVvTyXm/mk49gYRyW79938H7BORf17j2soGJbHRX/k78PkJPPoLjhtqJzfQz72M//AT\nDplfuCV5GRqYIODyOCgd5ORmhJaOLlfedNkyuRIr0SzBgJfejgZCAfcT+9ZnF9J5m7WERTRl0Rj2\n0NnspaPJe885ecMUNjMWkZRFOmfT3uilt81Ly20WPahIpjyKsLejgeaGYM3nlNlJTa0dNLa0ul5n\npKIUFq7UPJDt9Cb6By/i3/8I3k7nga6f+gl2fIPg07/ugCt+Do79I69tOx2n+E9/RvDRb+Ktluvd\nvsGPP+3KhrnpIMaPOqI+ANu2iG2oRqaOnn7HrIJb1wmReI5YqkBnax0dLXW3ddSWLURSFmsJi3zR\npqPJS2ezl9b6e8vJiwi5ohBNq7Vt29DT6qW31Xtb1o+IkMnprG5mCfq99HU11mTL2ba9VSQtB4nO\n30PEVnWSQo668aMOwToAY/oD7MgigRNfdh7ohRzF5/5U1R4njzqe+6lCMZqm/QEwKCL/TY3HnQ1K\npk7px/8Rz8A4gWNPOp5jxVYxLr7mGr3BFk47c55AxwDB7mFXZ6KXimyurxAIhmnr6sbjgl+C2gSb\nqTzReJ6WxhBdbfWu+LHjM9hCLGMTTVnEMxbhoEZ7o5fWBg9N4U9+M9giZAtCPGsRz9hkizatDR66\nmr20N94+OgfFtIgm8sRTBdpbwnS11oaq1MKPUMhl6ejpdwyfLpu+uUxxddZ1oAqUs7QXFEugij0C\nYFx+F/P6WULP/C5a1fgwMxbB33H348Pu1D7K2rbWFyi98t2tWlIl3CQimFffwc6mCBz7gsO5gxra\nXYosUj92xDETuPwa2VSCVHyzJo305mvpJuuxHPmiQXd7Pa2N7jBatRV1m0jKIpq2yW+to7attR3y\nuw+k+HmaYQnJnE0iYxHLqC6+jia1tpvq7gwazRcN1jazmJZNb0fDjlm6XioRW1/ZykB7XGFdsUzy\ncx8CUDd6CM3lGnPmPNb6nIrUq9aumDqln/wlnr5dBI5/3vnc6Cr+rv5P3rFrmva/A78BJIEnRCRW\n4zoxYxt42yp1EKSQpfjcn+E7+BD+PSccz7NiKxgX3yBw+Ak8LnisrRfJbY3XCw/ucU1NbdtWOhyF\nHG3dfTWLT6DgmUhCMT7amsN0ttS5VsbdTBWUbOIZm0TWoqALDWHl4BvDGg0hD+Gg9rE1fNgiFHWV\nhmYKNpm8TbpgE/JrNzdhS73njotipmWzmVTsiuaGIN3t9Tum8HqxQGxjDX8goKAXt4VfjkBTEerG\njjqGUEM5Un9JUQJ7Rp2fa+4yxqmfEHzmdx2Yu5VJkvh//4jOf/V/feyO/W7Wtm1ZTgmE2UsYp39K\n8JnfcdYKRDCvvI2dSxM49hSaG+yS2KCwdI3w0D6HZnfZbgYugRCtXd14XbD5suUKOmubOSzLpqut\nnpbG2hmY432MW8FCImcB0FznobHOQ0NI/Qv4Pj5qr2kJuZKQLdhkCmpdF3Whqc5D29barg/e+eGS\nLxpE4jnyRZPu9vqaNSLYiuiTCdKJTVrau6hvck5Fgu2+p5nw0G4HTVtEsGYvYK3NEjjxJWddxbYU\nauEPuKIWhXNvk3/1h3T8j3/88Tt2TdNeBLaHy1t1bf5QRH607bp/BYRF5H+r8Tqy+X//L7T+s3+N\np6pL1E7HKf34z/Hf/2V8o/sdz1WR++v4Dz2Kt90pniSWSX7+EmKZ1I0ecqhClq0sExtubKSlvcsV\nAy6bblhEE3mSmSItjSE6WsIOJbfbmWkpyCZdsMkWbLJFoWQIQb8alBvyK20Ov0/D71U6LZ6yngaq\niGrbKiswLRWxlAzZYhEopx7wKWGjhrCHxrCH5jrPXc9X1Q2LzWSBRLpAU32Qrra6Hb+r2DapxCbZ\nVPLmEAG3hV+OZlTX3UFXzNhORtHPv4R/74Oukbq1MkPp9X9wj3wNncSf/zHB8QM0PPXNu1/8H+Pa\nzrz0PRo+/03HY8aV9zCvnCb0zO84iAIqcn8XOxNXkbvfGT2auRT52YsEOgcIdo/ULFinYlHymTSt\nXd2u/QLb3zOb19mI5zEtm87WOlobQ3eVWcpWQJHKK6ebLQq5oo0talpSKKApppdPw+/V8JXXtsbN\nO2xv/bMswbAUeUDfWtcF3ca0tobLhD00hjw01XloCGl3/TlzBYNIIk+xZNLVWkdbc3hnooReIr6x\nBkBbd19NmMvMJsnPXSTYNUyga8i1kGreOIu9uUTguEukLoL+1g+QfIbgU992YO7G4jTJv/r3tP7e\nH+DvGfhUoZhB4Mci4lSxUY/LH/zKs0gxT/DQAzzx5JM8/vjjNx+3Y2sUf/pXCpccmHA8305soJ9/\nBf8+dwcgIpTWZtHja0o9zSXdB7Asi2R0g2IhT1tnt6v873YzTOX04qkC9WE/7c1hGuoCHzkysW2h\noKsFXHbShiVbk5Pkpp4GKHqYR1ObwudVdK+AT7t5MIQDOw9N2MlEhHzRIJYskMnrtDaF6Gipq1kY\nLVsxnyMeWd+K0nvwusAIoGCy/OxFfE1thAYmHdEMbDuwD3zOoc0PYEWWKL30HdeC0quvvspP/8O/\nA9smeOAEf/RHf/TzhGJuu7b/p6ceIDC2H1/PAI8//njF2tY/eAVr8TqhL/+W6wY3p85gx1YJHP+i\nI6oDFRnmZy/iCYQID+9zZcyAkkKOb6zhDwRp7ex2dEJWv2/+/2/vvcPjqq71/88p06QZdblXcKEY\nA6Z3c+kQCCW00BII5JKQ5AZISCBfMIQaEmrCDQRuIJjmUEM33TbYGBv3Inf1rpGmzyl7//44I7nM\nGUnGNpL56X2eeSzP7HPOnjPvWXvttd+1dsoxesmUSXFBgNLCQI+/f3cwra25bVgS03JKWNhCIqTj\nrChsVnxp6mbHxudRMsov599v+ozZQtAeTdPankQiKS/Ko6iHwUsKQaS9jWi4jYKS3OtEUkqM5hrS\nDRtdk+qcNgJr1ZeISDPeKSejuKlj5r+PaKp2pLHbOKIfvfk67z98L969DkAvG8Ltt9/+rS+ejpNS\nrsv8/QvgGCnlBTnaSmGZdDz7EGpRGaHvX5FdN6HzQZ76A7Rh2VJHEWnFWPQh+h77o7vUtAYw25tI\nVq3CN2Qs3vKROcmRjMcINzfi8XopKhucc2Tu6tsWZLGFoKQgQFHIt91efF/DMG3aoynCkRQApYUB\nigv83WqeASzTpL21iXQyQXF5916h0VpHqnYt/uHj8ZYOc21j12/ArPgS72T3EJvdUkt65nM5B/rY\nB69grF9B8ZU3oXh9u2LxdLu4bdZXEf6/P1F48XV4x26zK07ng9xYhe/Uy10fdHvjUuzaNXimnJxV\n5AycaXuyusLZ+Hjsfq5xd6edoCPcSqw9TKi4hIKikpzKmU6kDIu2jiThSIqAT6e4IEBh0NevFkt7\ngrOYahKOpIjE0tvlhG1pC5wB0d0WSNsiWbUKOxUnb+xk17CitC3MZbMcSeOBJ2SF2KSUmAs/wq5Z\n6zrQi2Sc8BN3EThkKnlHngz0jSrmZWACjiSsEvhvKWV9jrZOglIqSfuT9+CbdAj5U8/Mamc3bCL9\n8Uv4jr8AbWh2vFUkophfz0QdPBp93EHuSQTpBIkNyzIezt6uIQDYepTOLyyksLgsp+696xgpSaYt\nwpEU7bEUXl2jKOSnIN/bb428YdpE4mk6omlShkVh0EdxgZ88v6dH0gshiGaKHAULiygoKcsZwpK2\n5RifeAd5e0xG2yb0ABkjtmk5VtVKvFNOyqqRASBa6kjNnI736LPQR2UP4Mn5n5KY8y7FP70FNd8Z\nYHaBYd9ubhvrVtAx43GKf3IT+qBtqpVKiTn3bURbA76TL80y7uBUhLTWfu2sJ7mIBSAzaNasxTds\nT7xl2XsAd8I0DNpbnA0fikoHEQiGevFbSyLxNOFIinjKJJTnpTDoI5Tn7XHg7wt0zjo6Ymk6YmlU\nVaE45Ke4wN+jvBOc9Yn2liYs06C4rPvZuxWPkNy0DD2UmYG6iDCkkcJY/DGKPw/PpGNcs4jNrtnb\nFSjbFrszDdqf+Qv6sDGETr+46/3dJkHJjoQJP3EX+cedSeCQ47La2vUbSX8yA99x52XJxaDzBn6E\n4svDs+/RrqoCKQSpunWY4UangJjLlKnrepZJe2sLyXiUUFEJoaKSbuPvXdeQkljCpCOWIhI3UFWF\nUJ6XYJ6X/IAHvY8eBtsWxFMmsYRBNGFg2YKCPB+FQR/BPG+vPDEpBNGOdiLhFvyBfIrKynN6MuDE\nHJObVqCFigmMmOAaLpDCxlo1DxFpwXvgCSj+bMPfOWvzHnUm+ui9sz5PrVhA7D/PUnTNzeilm41f\nf0hQAkgt/oLYzJcpvuYWtKJta98IzLnvIFrqHMmmL1tBZLfUYC6bjWfioWjD9nS9np2Kk9i4HNXj\ncxwXl9h8J1KJOOGWRhQUCkvL8eflLha2JSxL0BFPE4mliSdNAn69i9sBX+4dmnYlpJQYliCe4XUs\nYeDRNQqCXoqC/pyJRdvCMg06WltIJmIUFJcSKizOOauRUpBuqMRorsI/YqJrQh2AiLdjLvoQddBo\n9PEHu8bczQUfOJ76qVdkr7fYNpGXHgNFpeDCa7fqz25j2AGslgban7yX4PcuwT/JRQ2TkYt5jzoL\nfXS21yaFjbnic2QsjPeAE7JuVNd1om0kKlfiKSjFP3x8zvgkOAsnHa0tpJJxx8AXFvfowXf1R0pS\nacshXNIgkbLw6Cp5fg8Bn07Ap+Pz6jvd2Nu2IG3aJNMWyZRJImVhmDYBv04w4CWUv30PohCCWEc7\n0XArHr+fotJyV+1uJ6SwSdVtwGyrJzBqLzxF2ZuNg1N611jyCYrHh2e/Y10HY2dA/ze+Y85GG5ld\nt9pYv5KOl/6XoituwDN8zFaf9RfDDpD4/H2S8z+h+OqbUYPZ5QPM+e9j12/Ef8plrrwV0TDm4o9Q\nB49Bd9lFDDLJWg0bMFrq8I+YgKd4cLcqj0QsSkdrM6qmUVhS1msDD04YMp4wiSUdY2pYgoBP7+K2\n36vj9Xaf3bm9kFJiWoKUYZFKWyRSFomUCUAwz0Mw4Awy27MmYBppIm2tJOMxgkXFFBSVdPt828kY\nycqVKJpOYPQ+rjkFsHkw1iccjD48O2wopcCc9y52UzX+Uy7PKpEhpST62j+xO1opuux/sp6N3cqw\nA5h1lbQ//RcKzrsK38T9s46xW2pJf/A83oNPRB+fLdyXUmJXLsfatALPfsei5YjnStsiWbMWK9Li\nFJzKYXy6+pVO0xFuIRWPk19QSKiouFtv1fWamZBNMmU6/6Yt0oaNqoLXo+HRNTy6iq45L0cR4ywY\nbamKkVJm1AMCWzhkt2wbwxQYpo0tBD6vTsCrE/A7D5vf575hQHewLZNoR5hYRzs+fx6FJaWuG5hs\nCSvSSrJ6NVpeAf4RE3OqkUR7M8bST9CG7ok+boqrQbEqV2N8/ga+qee7rq8Ym9bQ8fyjFF78c7xj\nswf6/mTYAWIfvoqxahFFV92EmpethjEXfYK9YblTmTKUXR5AGinMJZ+AquLZ7zjX0A04qplk5cqu\nHe9Vl1nAltdNxCJE2hzVZqiohPxQQY8x+Kxr2qLLiUimLVKGhWnZeHQNr0d1uK2p6LqKpjq5HGqn\nKiYji5HSkesKIbFtiSUEliUwrc3cVlUFv1fDnxlE8vwePPr2lfKQUpJOJYmGW0mnkgQLezboUtik\nGzZhtNTgG5o75NUpZ7RqVjtrRS7hMylsjNmvI6Pt+E76oevieezt5zFrNlD049+gujhRu51hBzCr\n19P+7EMUnP9TfOMnZX0u2ptJz5yOPvFg9MlHu8fUW+swl89CH7kX2tj9c/7wVrSNZNVqVH8egRHd\nPwTgLBhG29uIRzrwBQIEC4u3y9PZFlJKLNshrWE6JLZsgW1LbCEQUnYZcwAFx8irqoKmqmiagq6p\neHQ18xBp2030bfuTTiaIdbSTTMTIDzmDmFsFwS0hjDSp2rVY8XYCIybm1FhLKbGrVmFtWIJn3yOz\nypN2wlz9Fdaiz/CedHHWTlqQkX5NfzgnR9reeYPSM87uV4ZdSkn8/RkY61dRdOVvUAPZ1S3NlfOw\nln6O76QfZhXEA8crt9YtdJJbJk/N2gtzy3bpxk0YTdXOfqqDRnVrrKWUpBJxou1tGOkU+QVFBAuK\nehQQdAchJIZlY5o2huUYaYfbAjtjwJ1bJKGT14qS4baC1sVrh9s+j7ZDcX1h28RjEWLtYaSUhIqK\nyS8o6jHEakZaSVVXoPrznYEyx4AqjRTm8tlIy8A7+fgsLxycoobpj18CVcN3/PmuC6mx917C3LDa\nlSN2Ik7razMYfOmV/duwN7/6ImXnXJj1mVG5lo7nHqHg/Gvwjc9WlIlEhPT709EGj8Rz+OnuCxep\nBMayT1EUzVm4cLnRkHkImioxGqvwlg3HN2RMt+EZcMITiWgHsY52bNsiP1RIXqgAj7f3CR79CaaR\nJh6NkIh2oCgqwcIi8kOFPS8cC5t0U9UW926sa6YdZIi/8nNkMo5n/6lZFQ0hM0Vd+LFTze6US1Fd\n1kG6jPp5P3Gd1YU/eo/mF59h4pMv9qlhT1VX4huxTS12KYm98wJm5VqKfnRDlucOTvKVMfftnOof\nyFSGXPk5+uh90cbsl5NzdjpBqnoNIp3AP3w8emFZj/w0DYNYR5h4tAOP10d+qIC8YEGvQ5D9CZ0D\nVjzaQTIewx/IJ1hY1CtnzE7FSdWuQyRj+EdOwFPo7qxAZte35bPQBo9FH3+Qe1JkPOIUhCsdivfI\n77kupMbfewlj/UqKrvxtFjeEaVD1x1vwDhnK8J/f0L8Ne8VPLqL8wsspPvG0rM/NyrW0P/cIBedc\niW9vl7CLkSL9yb9BSmf0c/G2pRDYG5dgVVfkTE3vhDBSpOrWY0VaHWlk2fBeTUmNdGqzUVRV8vJD\nBIIhvL7epWn3BaSUmEaaZCxKIhZF2MqUtBIAACAASURBVDZ5oRB5ocJe9VtKidlWT6puPVp+Af5h\n412lXp2wW2sxl89x6k2PP8h9IDYNjNmvIRMxfCdchOLi0RobVtHxwmMU/OBqfBMnZ30emTeH+r8/\nxJg7H8A/sm/3PK34yUWMvfthPOXbZFZ3emXrVjheWb7LZiONVaQ/fsmpFbL3oe7T/mQMY9ksFEVx\nHJcca0rgVEBN1a5F0T2Ogc+R07HV+YUgmYgRj0ZIJeL4/AHygiEC+cGcuQr9AUIIUok4yXiUZDyG\n7vE4jlewwHXzi6zjzTTpzE5WzmxnpCtfIbP4v34Rdt26zD7N2fWMwFF1pT96AX2vQ12jDFIIYm8/\nh1m1nqIf35gdqrNtav78R6QQjPztbai63r8Ne6q6kk1/uJ4hV/+CwqOy1TBmzUY6nn2Q4Ok/xL//\n4VmfS2E7C0816/CdeHHWpgWdEO1NmMtmoRQNwrPXYa4ZfZ2wExFSdeuxU3H8Q8biKXGvsZzVFykx\n0qnNxlLY+PPy8Qfy8QXy0D09Swl3JSzTJJ1MkErGSSXiKIpCIDMI+fzutaa3hZQSM9xIun4Diu7F\nP3wcejB3MTVpmVhrF2A3VTlJRy5ZwgAi1k76oxdRiwfhPTJ7s2eAdMVSIi//g8KLrsW7Z3Zt/tji\nhdQ8cBejb72XwLgJfR5jb359BuH332Ls3Q+iF20t4ZRSEv/wVdIrFlL04xvRCl0knpE20h8+jzZ4\nlDMrdVMVSYG9cTlW5XL0CYegDRvXzYKpwGytJ1W/AS0Qwjd0D3SXQcUNQgiS8RjJWJRUIobm8Wzm\ntj/Qp95853OXTiZIJeKkU0m8Pj+B/BB5wVC3SVlbQpgG6aZKzJZaPKVD8Q0Zm1MWDU4OjbliDoo/\nH88+R7k6luCUkTDmvY33yDPRx2TzVto20defxmqpp+iK61G3XUgVgrq/PYDZ1MCo/3c3qte7e8TY\nkxvWUTntJob9/HoKDjsqq53VWEP7Mw+Qd8zp5B1xouu5rDULMRZ8lLl52ZI4yBiZdQuxGzfhmXgY\nao507K5zxsKk6zdipxP4Bo3CWzo8Z5jB9XjTIJWIk0okSCcTSCQ+fwCvz4/H58fr86HpO9/YSymx\nLQvTSGGk0xipFEY6iZQSnz8Pf14e/rx8dE/vs2WlsDHbGkg3VqLoHscohEq6Pd5ursFcNRetZAj6\nxENzDqZ23QbSn72CZ9KR6JOyNxqAjGTw3RcpvOSXeEZly13jy5dQfd80Rv5uGvn7OuGZvjbsUkqa\nXniayNzZjLnzAXSXolyJ2e+SmPchRT+6Ab08e6FfGimMWa8hkzG8/3Whq3cPTsE0c/lsFK8ffe8j\nszaB3+qcwsZoqSXdWIkWCOIbPBot6J5V6Xp8ZvExlYiTTiYwUkl0jxev39/FbY/Xh7YLjL0UAtM0\nMNNpjHQKI5XESKfQPV58gQy3A/nbNdCIdJJ0UxVmWz2e4iH4hozJGUcHR3hhbViCXbMGz4SDUXMM\nplLYmF99gF25Gt8JF7qvmZgGHS/9HUyDgh9el7VQKqWk/vGHSW1cz+hpf0LLFNTbLQw7QHJtBZV/\n/D3Df/lbQgdne+Z2uJn2p/+Cb5+DyD/pPFcP2m6uxfhkBtqYffAcfGLO6ZMIN2Ku/AIlEELf67Bu\nHwJwVAbpxk3YsXa8pcPxlo/o9od3Q6ex7SSikU5hGmmEbaN7PGi6F92jo+keNE1DVTUUVXUWdhQF\nBec3lDg52EIIpBAIYWPbNrZlYVsmlmlimQaqquHx+fB4fZkHLvCNZgzCTGO01GI016DlhXplBGQq\ngblmPrKjGX3vI10XP517IrCWzMZcNd/JLHZJPpNSkpjzLsm5H1J0xQ3og7PPFV+5jOp7b2PEjX8g\nOHnz5tb9wbBLKWma/hSxhV8y+o4/uxr35NdziL8/g8If/gLPaHdpnLV0DtbK+XiPPQdtuLuWXQqB\nXbkCa9My9DGT0Ebvm/MZ6GxvttU7g7Wm4S0fhad4ULfHuJ4n4zE7DoTDa9NIoygKuseDrnvRdB1N\n11Ez3FZVFUVRHbWXooCUyEyfpJQIYSO6eG1hZbht2xa6x4PX68s4R/5vNGOQUmLHOzCaq7EibXjK\nhuEbNKpb/T84qjxr9VyUUKkz83cp9wBOPN349N+ge/FNPc+9LEQiRsf0R1ALSyg47ycoevb+tg1P\n/o1kxQpG334/Wv7m8MxuY9gBEhWrqLrrDzk9dxGP0j79YbTOG+EipZOpBOlZr0I6ife481ALsqe4\n4Iym9qYVWJXL0UbuhT5mP9fp/5aw0wmMpmrMtga0/EK8ZcMyi1E7sFIvBJZpOKS1TIfIto0QNtIW\nCOlsn9SlilEUx9ArivOAaCqapqNqOrpHR9e96B7PDk2NpZRYkVaM1jqsaBve4sF4y0e6Zo1udZyw\nsStXYm1ahjZiIvoe++dchBaJCMZnr4Gw8U79gasnKm2L2FvPYVSupeiK613DFfFli6m+/w5GXH8z\nwQMO3uqz/mDYwbmfTf/6B9GF8xlzx/3oRdlSxs4wU+jMS/FPPsz1nHbdBoxZr6KNOwDPlONzOy6J\nKNbqechEBH3ioa41d7aE83u3YDRVYyejeEqG4i0d1uPv3dM5hW1lHI0Mt217M7czjonjqDjHKBle\nOw6NhqppaJrmODu6ju7x7nA4U1gGZlsDRksdSIG3fATe0mE9iyUSEaw1XyGjYfS9Duv2ntpVFaQ/\n/w+evQ9F3/8YV/tgtTbS8a8H8e51AMFTLshyVKUQNPzjUZJrKxxPPbj1b7FbGXZwPPeqO29myE+u\no/CY47OOkaZB5JUnsdtbKbr0l6hBlxoaUmCtmIe5dDbeQ09F23Ny7rhjKoa5ZiEi3IA+bgrasD17\nNNRS2JjhRoyWWkQ6gad4CJ6SIWh57hUNdwdIKZ0tCNsaMcMNqB4vntLheEuG9Eh6KSWicRPW2oUo\nwSL0CYe41jbphFW5GuOLN/HsdTD6/se6GiiRjBN58X9BUSi46GdZ1T8BYl9/Rc2DdzPyN7eSP3nn\nbEaws7Att6WUND3/TyJfzGLMHX/GU5q9qYhZX0XHsw85NUGmnplzwTQ9+3XHcTn2XNRC9+xpKSWi\npQarYj5KIOj8Ji6lGraFnU5gttRhtNWjenx4SobgKR7coyfbnyGFjdXRitFWjxVtw1NYjrdsWK/C\nT9JMY21Yil231lEgjd435/MgLRPzq5nYVRV4jzsvq0hdJ4yNq4m8+Bj5J5xD4FAXG2fb1D32AOma\nKkbfes9WnnondjvDDpDatJ7Kab+j/OIrKDkle59IKQTxj98gtWiOM33dJuOwE6K1nvRnr6AWljny\nom48ENHehLnmKzAN9HEHog5y36RjW9ipBGa4AbOtASlsPEXl6IXl6MGi7Z7SftuQUmDH2jE7WrA6\nmkGCp3iwM0j1wluTUiJa67DWLQQpncW7HAlhkMk0nf8eor4S73Hndm06vS2spjo6nnsE7/hJBE+7\n2HVdo+PzT6l//BFG/f4O8vbO1rGH5y6i5Mgp/cawd6L55ecJf/A2o6f9Cd/Q7LCSHQnT8dyjaMVl\nFJx7FYpL/oCUAmvlfMwln+E5YCr63ofkdEaksLFrKrA2LEEtGYa+5wHdDrqbryGxom2YbfVYHS2o\n/nw8heXohWWo/m+et/FtQZgGVqQVs6MZK9qGlhfCWzwET9GgHmfm4Bhpu2olVuUKtEGj0ccdmDPs\nAk7ZC2P2646U8Ygz3BV6UpKc/wnxj16n8IJr8I5zydExDWofvAc7GmHkzXd2xdS7ziEErZ99Sfl/\nHdm/DXvdq+8z9JyTsz5L19dSedtvKT7xNMrOv8R9QW3FAqKvP0PwtAsITDnG9RrSMjEXfYq1bjHe\nQ09B2yO35rfLy1m3CJDoe+zfawMPYCfjmB1NWB0t2MkYerAIPVSCFixCywvtUMhmZ8DxymNYsTBW\ntA0rGkbz56MXlOIpGoQaCPZaGSNaarE2LAbLQN9zCmqO3ao6YVWtxpz7NtrIiXgOca8zDpBesZDI\n608TPOV8Agcf69qm7d03aJ4xndG33ot/bHa8ueXjuSy65Nec3PBl3+rYG1vwDcr2qNvee5PmF//F\nqFvvJrCHS0zdNIi+8QxmXSWFl/xiq/o3W0J0tGDMeg00He9RZ+X03iFjqCpXYFWtRC0fiT52cq8M\nPGSSomJhrPYmzI4WAPSCUvRgMXqoGMXT97kb0rawYu3YGW7bqQR6qARPYRl6YXnODOis85gGdvVq\nrKoVqCVD0fc8sNv7JE0D8+uPsTYsw3v46a57R3S2i775LGb1Buc3LXOpXppIUH3vbah5eYy4/hbU\nbZLDpBAs//k0YhUbOPKT5/q3YZ857Agm/XWaq3E3W1uo+uPvCUzch6HX/NJ9i6mMd+cZPYHQmZe6\nxt0hs7A65w2UvBDeI87IGXuHjOFqrsbasAQsE23MvmhD9+wxJLHVOSzTMZ6xMFY0jDBSaIEQWl7m\nFQii+vK3S2WzPZDCRqQS2MkYdjKKnYhiJyKoHh96qBgtWIweKuk14bvO2bAJq3I5SIE+dn/UIWO6\nHbBEPIL55XuI1nq8R5/lukAKmXj6zJdJL/+Kwot/jmdEdgkBZyHy/4h8/imjb7sXr4vH22nUp7z0\nCGXHHdanhv3T/c/g8Pefxjc4O+wS+WIWdX9/iBG//j3BA7PrIm327l4jdNblrrWTIGN0V32JuXgW\nnn0PR9/vqG55Ks20k/lbtQq1eDD6mEk5s1ddj5cSkU5gRVqxYmHsWAcoClpewWZeB4Ko3t7JZ7cX\nUkqkZSJSMYfbGV4LI4WWF8oMNiVo+YXbVRZBpuJYVauwa9eglg53nLpuZLwAdvVajHlvo5aPwHvY\naa55F+DE0yMvPIZWNpjQOVe6lggw21odWzd+L4b+9FdZdkEKwfLrphFdvoZD334ST0Gofxv29q9X\n8NWZV7PPA7cw7ILTs9rYiTjV901D0TRG3HgrWp7L6nI6SfT1Z7Aaayi86Nqs8qidkMLGWj4Xc9nn\nzo7xk92rQHa1lxIRbsDetBzR0YI2YjzaiImoge5VNK7nsswuEtrJGHYqhkglUHQPqjeA6vWjen2O\n96N7UDQPiqY75FS22UJJZhaebMt5WQbSNBBmGmEkEekk0jJRfQE0fxA1L9j14HWny83Z91QCu7YC\nq6YCNb8IbfS+qGUjulfG2BbWyi8xl85B3/sQPJOPyXmv7bZmOmb8L2peiIIfXO2ajSkMg9pH7sNs\namTULXeiF2Y/dM0zZ7P4R79lykuPUHrMIX0eY6+441HqZrzN4e89jX94ttcdX7GU6vtuZ9ClP6bk\n5OyQI4BZvYGOlx7DN2EywdMuyum4iGgYc967iI4WvIefjjYiWxK6JaRlYtetxa5cCR4f+qi9Hfnv\ndjgvkDG0RhIrHkEkoxlux5Gm4XDa53Db4bUXVXd4jaY7DoGigtJ1MqSwQdibud3JazOFNFLY6SQK\noPrzM4NICD2/ANUf3O76NlJKZHsjVvVqREst2rA90Ubt26NKTkTDTi39tka8R5yeMzsYILVkHtG3\nniP/v75P4PAT3CMPm9ZTdectFJ/8PdfohLRtlv70D8TXVXLom0+gh4K7R4w9sqyC+WdcxcQ7fs3I\nH52X1U5aFvVPPEJi9UpG3XIn3sHZ0xgpJamFs4m9/2/yT3QWJXIZHhHrwPzqfURzLZ6DTkTbY98e\nwyQi3oFdvRq7fj1qYRnasPGo5SO3+0HYts/SSDnG2EghzDTSNBxD3UlsYWeMeZd0wFHFqJpj+DXd\nGQh0L6rH5wwSPj+K179DoR8pBKKlBrtuLaKtAW3IGLSRe/e4ACelxK6uwPzqA5RQMd7DTut2gS+9\nZC7Rd14g/7jvETjyZNffzAy3UX3PrXjKBjH8Vzeh+rLDOA2vf8Cyn93KQS//jZIjHcljXxt2KSXr\n/vQE1f/3bw5775/kjcnOSkzX1VD1x5sJHXIEg6+4xnUGJ5Jxom88g9VUR+EFP0Uf0r0iw/jyPdSi\ncjyHnJQzYa8TUgpEcw129WpEpAVt6B5ow8aj9JCj0BOksBHpZBe3pZl2PG3LQFqWY7w7ud2JjCKG\nLm538tqL4vE5g4Qv4Ly/I31LJ7Hr12PXrgUp0UZOdL5zD7NXaaYxl87BWr3AmR1NOjKnsyJSSSeT\ntHItBRf9DM8w94XU6FdzqX30fob+5DoKj/2v7POYJkt+fBPpplYOfvUx9KAzK9gtDDtArGID80+/\nijHXXcYev74yq62Ukra3XqXllRcYccMfyN/vANdzWs31RP79BGp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numpy.linalg as la\n", "import matplotlib.pyplot as plt\n", "\n", "# Define the function f and its derivative\n", "def f(x):\n", " return 0.5*(x[0]**2+10*x[1]**2)\n", "\n", "def df(x):\n", " return np.array([x[0], 10*x[1]])\n", "\n", "def ddf(x):\n", " return np.array([[1, 0], [0, 10]])\n", "\n", "# Get a list of values for specifying the level sets\n", "xvals = np.array([[np.linspace(-15,-2,20)], [np.zeros(20)]])\n", "yvals = list(reversed(f(xvals)[0]))\n", "\n", "# Create a meshgrid and a contour plot\n", "xx = np.linspace(-10,10,100)\n", "yy = np.linspace(-4,4,100)\n", "X, Y = np.meshgrid(xx, yy)\n", "# The construction inside looks odd: we want to transform the set of input pairs given\n", "# by the meshgrid into a 2 x n array of values that we can apply f to (calling f on such\n", "# an array will apply the function f to each column)\n", "Z = f(np.dstack((X,Y)).reshape((X.size, 2)).transpose())\n", "# the result of applying f is a long list, but we want a matrix\n", "Z = Z.reshape(X.shape)\n", "\n", "% matplotlib inline\n", "cmap = plt.cm.get_cmap(\"coolwarm\")\n", "\n", "# Now apply gradient descent and newton's method\n", "import numpy.linalg as la\n", "\n", "# The implementations below return a whole trajectory, instead of just the final result\n", "\n", "def graddesc(f, df, ddf, x0, tol, maxiter=100):\n", " \"\"\"\n", " Gradient descent for quadratic function\n", " \"\"\"\n", " x = np.vstack((x0+2*tol*np.ones(x0.shape),x0)).transpose()\n", " i = 1\n", " while ( la.norm(x[:,i]-x[:,i-1]) > tol ) and ( i < maxiter ):\n", " r = df(x[:,i])\n", " alpha = np.dot(np.dot(ddf(x[:,i]),x[:,i]),r)/np.dot(r,np.dot(ddf(x[:,i]),r))\n", " xnew = x[:,i] - alpha*r\n", " x = np.concatenate((x,xnew.reshape((2,1))), axis=1)\n", " i += 1\n", " return x[:,1:]\n", "\n", "def newton(f, df, ddf, x0, tol, maxiter=100):\n", " \"\"\"\n", " Newton's method\n", " \"\"\"\n", " x = np.vstack((x0+2*tol*np.ones(x0.shape),x0)).transpose()\n", " i = 1\n", " while ( la.norm(x[:,i]-x[:,i-1]) > tol ) and ( i < maxiter ):\n", " grad = df(x[:,i])\n", " hess = ddf(x[:,i])\n", " z = la.solve(hess,grad)\n", " xnew = x[:,i]-z\n", " x = np.concatenate((x,xnew.reshape((2,1))), axis=1)\n", " i += 1\n", " return x[:,1:]\n", "\n", "x0 = np.array([10.,1.])\n", "tol = 1e-8\n", "\n", "xg = graddesc(f, df, ddf, x0, tol)\n", "xn = newton(f, df, ddf, x0, tol)\n", "\n", "plt.subplot(1,2,1)\n", "plt.contour(X, Y, Z, yvals, cmap = cmap)\n", "plt.plot(xg[0,:], xg[1,:], color='black', linewidth=3)\n", "\n", "plt.subplot(1,2,2)\n", "plt.contour(X, Y, Z, yvals, cmap = cmap)\n", "plt.plot(xn[0,:], xn[1,:], color='black', linewidth=3)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "In practice, when implementing Newton's method one does not explicitly compute the inverse of the Hessian. The reason is that one does not need the inverse itself, but only the product $\\nabla^2f(\\vct{x}_k)^{-1}\\nabla f(\\vct{x}_k)$, which is the solution of a system of equations $\\nabla^2 f(\\vct{x}_k)\\vct{y} = \\nabla f(\\vct{x}_k)$ that can be solved much more efficiently. One therefore replaces the update step with the following two steps:\n", "\n", "\\begin{align*}\n", " \\text{ Find } \\vct{y} \\text{ such that }\\quad &\\nabla^2f(\\vct{x}_k)\\vct{y}=-\\nabla f(\\vct{x}_k),\\\\\n", " &\\vct{x}_{k+1} = \\vct{x}_k+\\vct{y}.\n", "\\end{align*}\n", "\n", "There is a lot that can go wrong with Newton's method. In particular, the matrix $\\nabla^2f(\\vct{x})$ has to be non-singular, or invertible, at every step. If, however, we start at a point $\\vct{x}_0$ that is not too far from a local minimizer $\\vct{x}^*$ with $\\nabla f(\\vct{x}^*)=\\zerovct$ and $\\nabla^2f(\\vct{x}^*)$ positive definite, then we are on the safe side.\n", "\n", "**Lemma.**\n", " Let $\\vct{x}^*\\in \\R^n$ be such that $\\nabla^2f(\\vct{x}^*)$ is positive definite. Then there exists an open neighbourhood $U$ of $\\vct{x}^*$ such that for all $\\vct{x}\\in U$, $\\nabla^2 f(\\vct{x})$ is positive definite.\n", "\n", "For the main result of this lecture, namely the quadratic convergence of Newton's method, we make the additional assumption that the Hessian $\\nabla^2f(\\vct{x})$ is Lipschitz continuous as a function of $\\vct{x}$.\n", "\n", "**Definition.**\n", " A function $f\\colon \\R^n\\to \\R^m$ is Lipschitz continuous on a domain $\\Omega\\subseteq \\R^n$ with respect to a pair of norms on $\\R^n$ and $\\R^m$ if there is a constant $L>0$ such that for all $\\vct{x},\\vct{y}\\in \\Omega$,\n", " \\begin{equation*}\n", " \\norm{f(\\vct{x})-f(\\vct{y})}\\leq L\\norm{\\vct{x}-\\vct{y}}.\n", " \\end{equation*}\n", " The constant $L$ is called the {\\em Lipschitz constant} of the map.\n", "\n", "In particular, the Hessian of a function $f\\in C^2(\\R^n)$, considered as a map from $\\R^n$ to $\\R^{n\\times n}$, is Lipschitz continuous with respect to a norm on $\\R^n$ and the corresponding operator norm on $\\R^{n\\times n}$, \n", "if for any $\\vct{x},\\vct{y}$ we have\n", "\n", "\\begin{equation*}\n", " \\norm{\\nabla^2f(\\vct{x})-\\nabla^2f(\\vct{y})}\\leq L \\norm{\\vct{x}-\\vct{y}}.\n", "\\end{equation*}\n", "\n", "**Theorem.** \n", " Let $f\\in C^2(\\R^n)$ and $\\vct{x}^*\\in \\R^n$ a local minimizer with $\\nabla f(\\vct{x}^*)=\\zerovct$ and $\\nabla^2f(\\vct{x}^*)>0$. Then for $\\vct{x}_0$ sufficiently close to $\\vct{x}^*$, Newton's method has quadratic convergence.\n", "\n", "**Proof.** Assume that $\\nabla^2f(\\vct{x}_k)$ is positive definite.\n", " Consider the difference\n", " \n", " \\begin{align*}\n", " \\norm{\\vct{x}_{k+1}-\\vct{x}^*} & = \\norm{\\vct{x}_{k}-\\vct{x}^*-\\nabla^2f(\\vct{x}_k)^{-1}\\nabla f(\\vct{x}_k)}\\\\\n", " &\\stackrel{(1)}{=} \\norm{\\vct{x}_{k}-\\vct{x}^*-\\nabla^2f(\\vct{x}_k)^{-1}(\\nabla f(\\vct{x}_k)-\\nabla f(\\vct{x}^*))}\\\\\n", " &= \\norm{\\nabla^2f(\\vct{x}_k)^{-1}(\\nabla^2f(\\vct{x}_k)(\\vct{x}_{k}-\\vct{x}^*)-(\\nabla f(\\vct{x}_k)-\\nabla f(\\vct{x}^*))}\n", " \\end{align*}\n", " \n", "where (1) follows from $\\nabla f(\\vct{x}^*)=\\zerovct$.\n", "\n", "The Fundamental Theorem of Calculus tells us\n", "\n", "\\begin{align*}\n", " \\nabla f(\\vct{x}^*)-\\nabla f(\\vct{x}_k) &= \\int_{0}^1 \\frac{\\diff{}}{\\diff{t}} \\nabla f(\\vct{x}_k+t(\\vct{x}^*-\\vct{x}_k)) \\ \\diff{t}\\\\\n", " &= \\int_{0}^1 \\nabla^2 f(\\vct{x}_k+t(\\vct{x}^*-\\vct{x}_k))(\\vct{x}^*-\\vct{x}_k) \\ \\diff{t}.\n", "\\end{align*}\n", "\n", "Continuing by inserting this identity,\n", "\n", "\\begin{align*}\n", " \\norm{\\vct{x}_{k+1}-\\vct{x}^*} &= \\left\\|\\nabla^2f(\\vct{x}_k)^{-1}\\int_{0}^1\\left[\\nabla^2f(\\vct{x}_k)- \\nabla^2 f(\\vct{x}_k+t(\\vct{x}^*-\\vct{x}_k))\\right](\\vct{x}_k-\\vct{x}^*) \\ \\diff{t}\\right\\|\\\\\n", " &\\leq \\norm{\\nabla^2f(\\vct{x}_k)^{-1}}\\cdot \\\\\n", " & \\quad \\int_{0}^1\\norm{\\nabla^2f(\\vct{x}_k)- \\nabla^2 f(\\vct{x}_k+t(\\vct{x}^*-\\vct{x}_k))}\\ \\diff{t} \\cdot \\norm{(\\vct{x}_k-\\vct{x}^*)}.\n", "\\end{align*}\n", "\n", "Applying the Lipschitz bound to the term inside the integral gives\n", "\n", "\\begin{equation*}\n", " \\norm{\\nabla^2f(\\vct{x}_k)- \\nabla^2 f(\\vct{x}_k+t(\\vct{x}^*-\\vct{x}_k))} \\leq L t\\norm{\\vct{x}_k-\\vct{x}^*}.\n", "\\end{equation*}\n", "\n", "Integrating this out, we end up with the bound\n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_{k+1}-\\vct{x}^*} \\leq \\frac{L}{2}\\norm{\\nabla^2f(\\vct{x}_k)^{-1}}\\cdot \\norm{\\vct{x}_k-\\vct{x}^*}^2.\n", "\\end{equation*}\n", "\n", "The only remaining issue is that the ``constant'' on the right-hand side is not a constant. However, the Lipschitz continuity implies that $\\nabla^2f(\\vct{x}_k)$ converges to $\\nabla^2f(\\vct{x}^*)$ if $\\vct{x}_k$ converges to $\\vct{x}^*$. Since the inversion of a matrix is a continuous operation, also $\\nabla^2f(\\vct{x}_k)^{-1}$ converges to $\\nabla^2 f(\\vct{x}^*)^{-1}$. In particular, if $\\vct{x}_k$ is sufficiently close to $\\vct{x}^*$, we have $\\norm{\\nabla^2f(\\vct{x}_k)^{-1}}\\leq 2\\norm{\\nabla^2f(\\vct{x}^*)}$. Setting $M:=L\\norm{\\nabla^2f(\\vct{x}^*)^{-1}}/2$, we end up with the bound\n", "\n", "\\begin{equation*}\n", " \\norm{\\vct{x}_{k+1}-\\vct{x}^*} \\leq M\\cdot \\norm{\\vct{x}_k-\\vct{x}^*}^2.\n", "\\end{equation*}\n", "\n", "There exists an open neighbourhood around $\\vct{x}^*$ in which $\\nabla^2f(\\vct{x})$ is positive definite, and within this neighbourhood there is an $\\vct{x}_0$ such that $\\norm{\\vct{x}_0-\\vct{x}^*}^2<1/M$, which ensures that all following iterates remain in $U$. This shows quadratic convergence. \n", "\\end{proof}\n", "\n", "Note that the conditions for quadratic convergence in an open neighbourhood $U$ of $\\vct{x}^*$ are precisely that $f$ is convex on $U$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Quasinewton methods\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One drawback of Newton's method is that it requires the computation of the Hessian matrix, which can be expensive.\n", "Quasinewton methods use an approximation of the Hessian, $\\mtx{B}_k\\approx \\nabla f(\\vct{x}_k)$, at each step of the algorithm. These are construction in a way that $\\mtx{B}_{k+1}$ can easily be computed from $\\mtx{B}_k$. A popular method, that is used often in practical applications because of its efficiency, is the **Broyden-Fletcher-Shanno-Goldfarb** (**BFGS**) method. The BFGS method may be described as follows.\n", "\n", "* Start with $\\vct{x}_0$, $\\mtx{B}_0$.\n", "* For $k\\geq 0$, compute\n", "\n", "\\begin{align*}\n", " \\vct{p}_k &= \\mtx{B}^{-1}_k \\nabla f(\\vct{x}_k)\\\\\n", " \\vct{x}_{k+1} &= \\vct{x}_k + \\alpha_k \\vct{p}_k \\text{ for a suitable step length } \\alpha_k\\\\\n", " \\vct{s}_k &= \\alpha_k \\vct{p}_k\\\\\n", " \\vct{y}_k &= \\nabla f(\\vct{x}_{k+1})-\\nabla f(\\vct{x}_k)\\\\\n", " \\mtx{B}_{k+1} &= \\mtx{B}_k+\\frac{\\vct{y}_k\\vct{y}_k^{\\trans}}{\\vct{y}_k^{\\trans}\\vct{s}_k}-\\frac{\\mtx{B}_k\\vct{s}_k\\vct{s}_k^{\\trans}\\mtx{B}_k}{\\vct{s}_k^{\\trans}\\mtx{B}_k\\vct{s}_k}. \n", "\\end{align*}\n", "\n", "* Stop if $\\norm{\\nabla f(\\vct{x}_k)}<\\e$ for some tolerance $\\e$, or if $\\norm{\\vct{x}_{k+1}-\\vct{x}_k}<\\e$. 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