From 212c79f113d0b4eb8a9753254e67a87b6cc975b4 Mon Sep 17 00:00:00 2001 From: Mauro Donega <mauro.donega@cern.ch> Date: Tue, 30 Mar 2021 19:09:21 +0200 Subject: [PATCH] cleaned --- notebooks/binnedLikelihood.ipynb | 297 +++---------------------------- 1 file changed, 24 insertions(+), 273 deletions(-) diff --git a/notebooks/binnedLikelihood.ipynb b/notebooks/binnedLikelihood.ipynb index 83c2523..0394524 100644 --- a/notebooks/binnedLikelihood.ipynb +++ b/notebooks/binnedLikelihood.ipynb @@ -9,7 +9,7 @@ }, { "cell_type": "code", - "execution_count": 205, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -23,7 +23,7 @@ }, { "cell_type": "code", - "execution_count": 151, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -44,243 +44,34 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1-D Maximum likelihood fit" + "## Binned ML fit" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n", - "\n", - "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n", - "\n", - "where for one of the two peaks the parameters are known already\n", - "\n", - "$p_b = 91.0$ \n", - "$\\sigma_b = 5.0$ \n", - " " + "With the data above, we perform a binned ML fit and compare with the unbinned fit.\n", + "First, create a histogram of the data using np.histogram." ] }, { "cell_type": "code", - "execution_count": 228, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ + "# this is my model for the data\n", "def likelihood_point(x, position, width):\n", - " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n", - "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n", - "\n", - "Complete the functions below which return the likelihood and negative log likelihood (NLL)." - ] - }, - { - "cell_type": "code", - "execution_count": 347, - "metadata": {}, - "outputs": [], - "source": [ - "def likelihood_1d(params):\n", - " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n", - "\n", - "def nll_1d(params):\n", - " return -np.log(likelihood_1d(params))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL." + " gauss1 = 1./np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0)\n", + " gauss2 = 1./np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)\n", + " f = 1./3.\n", + " return f * gauss1 + (1-f)* gauss2 " ] }, { "cell_type": "code", - "execution_count": 355, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "position: 117.72333147980623\n", - "negative error: [3.31211666]\n", - "positive error: [3.39091994]\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "solution = minimize(nll_1d, [100.0], method='CG')\n", - "min_pos = solution.x[0]\n", - "min0 = solution.fun\n", - "scan_points = np.linspace(110.0,126.0,50)\n", - "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n", - "\n", - "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n", - "print(\"position:\", min_pos)\n", - "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n", - "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2-D Likelihood fit" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time." - ] - }, - { - "cell_type": "code", - "execution_count": 350, - "metadata": {}, - "outputs": [], - "source": [ - "def likelihood(params):\n", - " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n", - "\n", - "def nll(params):\n", - " return -np.log(likelihood(params))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Minimize the NLL and find the best-fit result." - ] - }, - { - "cell_type": "code", - "execution_count": 353, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "position: 118.31548192622421 width: 13.629783202046086\n" - ] - } - ], - "source": [ - "solution = minimize(nll, [120.0, 10], method='CG')\n", - "print(\"position:\", solution.x[0], \"width:\", solution.x[1])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution." - ] - }, - { - "cell_type": "code", - "execution_count": 354, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "scanA = np.linspace(110.0,130.0,50)\n", - "scanB = np.linspace(5,20,50)\n", - "minValue = nll(solution.x)\n", - "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n", - "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Compute numerically the error matrix of the NLL for the 2-D fit." - ] - }, - { - "cell_type": "code", - "execution_count": 301, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[11.95694692 -3.06065748]\n", - " [-3.06065748 5.72672173]] \n", - "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n" - ] - } - ], - "source": [ - "from scipy.misc import derivative\n", - "\n", - "# compute the error matrix\n", - "A = np.linalg.inv([\n", - " [\n", - " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n", - " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n", - " ],\n", - " [\n", - " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n", - " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n", - " ]\n", - "])\n", - "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Binned ML fit" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n", - "First, create a histogram of the data using np.histogram." - ] - }, - { - "cell_type": "code", - "execution_count": 374, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -311,7 +102,7 @@ }, { "cell_type": "code", - "execution_count": 375, + "execution_count": 8, "metadata": {}, "outputs": [], "source": [ @@ -330,22 +121,22 @@ }, { "cell_type": "code", - "execution_count": 376, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " fun: -138.93433719876123\n", - " jac: array([-1.90734863e-06, 1.90734863e-06])\n", + " fun: -138.93433719857785\n", + " jac: array([-5.72204590e-06, 1.90734863e-06])\n", " message: 'Optimization terminated successfully.'\n", - " nfev: 60\n", + " nfev: 45\n", " nit: 6\n", " njev: 15\n", " status: 0\n", " success: True\n", - " x: array([116.43876363, 15.33581135])\n" + " x: array([116.43867707, 15.33584649])\n" ] } ], @@ -363,52 +154,19 @@ }, { "cell_type": "code", - "execution_count": 377, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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YcTMmTNkRnKk2VNV/IdL8FyH6RKTGM4grzulYxpgqYgXOVAuqHnTvfVD4McSe55+VxC5rY0xYs79wE/ZUi9Gcm6B4GsRfhyTcZJ1JjKkGrMCZsKa+fDTnWiiZgyTdj8Rd5HQkY8xRYgXOhC315aLZV0HpIqTGY0jsEKcjGWOOIitwJiypLx/NvhxKlyPJzyIxpzkdyRhzlFmBM2FHtcQ/DKB0KZL8PBJzitORwpaqsreomF15+WTmF7ArL59d+QXsKSwiv6SE/OJS/31JCfnFJRSU+J+Xen34VPGpD69PA48Vr09RVSLcLqLcbqIi3P57t5vIwOPoiAgSo6NJjIkmKeaP+6ToaJJio0mKiSE1IZ7UhHjioiKd/icyDrICZ8KKqs8/9VbJj0jSo1bcjpCqklVQyIbd2WzMymbT7hw2ZeeQvieXXfn5ZOYVUOr1/uV9AsRFRREfHUl8VBRxUf77ekmJxEdFEhXhxiUuXAIulwu3CC4RXC7/vcfro8TrpcTj/fO910NRqYes/AL2Fhezt6iYgpLS/eaPi4qkTqDYpQTu6yUl0Ci5Bk1q1qBxzRokREdX4b+gcZIVOBNWNO8pKPoCSfgXEneO03FCSl5xMcvSM1iavpMVOzLZmJXNxt055BYX/75OhMtFo+QaNEpOomVKLVIS4kiJj/ffJ8STGu+/T4yJxnWUeqqWer3kFZeQW1TM3uJisgsK/UeUeQVk5uX/fluxI4Mf8vL/UhBrxsUGil0yjZNr0Lx2TVqn1qZFSi1iIu0jMpTZ/54JG1rwKeSPhtgLIP5Kp+MEtYKSUpbv8Bezpdt3sjR9Jxt2Z//+ev2kRFqk1OTsTu1oVrsmzWrVpFmtZBokJxHhCq4JkCLdbmrGxVIzLvaQ1s8tKmZrzh42Z+9hc3YOWwL3i7ZuZ8qyVfhUAXCJ0LhmDVql1KZ1am1apfrvW6TWIsrtrspdMpXECpwJC1ryC7r3XojqiyTda+Pc9lHs8bBgy3Zmb9jCzxs3s3T7TryBD/J6SQl0rF+XIZ3a07FBXY6pX5dah1gsQlFiTDTt69Whfb06f3mtxOtlS1YOazJ3/35bm7mbH9ZuwOPzARDpctGmbgod69flmPp1OKZ+XdrUSbGiF4REA7/koSAtLU3nzZvndAwTZNSzCd09HFw1kdofIq4aTkdynNfnY1l6Bj9v2MzPGzezYMt2ij1e3CJ0bliP3s0a07VhfY6pX4c6iQlOxw16JV4vG3dnsyZjN8t3ZLBsx06WpWewt8jffBvpctGmTgodG9SlS8P6dG/cgGa1ku2LViUSkfmqmnZY7zlYgRORN4GzgAxV7RhY9jgwGCgB1gGXqWqOiJwKPApEBV77l6pOK2ebDwBXAZmBRf9W1SkHC2sFzuxLfXvQ3SPAl43U/giJaOp0JMeUeDzMWr+Zr1esYdrqdewJfPi2rZNC3+ZN6Nu8MWlNGpEQHeVw0vCgqmzN2cPS9AyWpfsL3rL0nb//u9eKi6VbowZ0b+y/daxfh6gIazSrqKoqcP2BPOCdMgVuIDBNVT0i8j8AVb1DRLoBO1V1u4h0BL5W1YblbPMBIE9VnzicsFbgTFmqPv9A7pLZSK23kKheTkc66rw+H3M3bWXy0lV8vWINucXFJMVEc1KbFpzQqjm9mzWmdrxNKH20+FTZsCuL+Vu2s2DLdhZs3c6mrBwAoiPcdG3UgOOaN6Ffy6a0r1fnqHXECQcVKXAH/TqhqjNEpNk+y74p83Q2cF5g+cIyy5cBMSISrarFGFPZ8kdDyUwk6YFqV9yWp2cw8dcVfLFsFZl5+cRFRTKwXSvOOKYtfZs3sfNBDnGJ0DK1Ni1TazOieycAduXls3BrOvM2b2POxi089f0snvp+FrXiYjm2RVOOb9GU41o2JTUh3uH04acyjpcvBz4oZ/m5wMIDFLcbRORSYB5wq6pm72c9Y/5CS1ehec9DzOkQe6HTcY6KUq+XqSvX8s7chSzcmk6k280JrZpxVsd2DGjdwrq0B6mUhHhObdeKU9u1AvwF78f1m5i1fhOz1m9m8tKVgL8p+fiWzTipbQu6NqyPO8h6q4aiQ+pkEjiCm/xbE2WZ5XcDacA5WmZDInIMMAkYqKrrytleXWAXoMB/gfqqevl+fvYoYBRAkyZNemzatOnQ9syELdXSwHm3dCRlCuKq5XSkKpWVX8AHC37lvfmLycjNp0nNGlzcsytDO3egRmyM0/HMEfCpsnJHJj+u38jMdZtYsGU7Hp+PWnGxDGjTgpPbtOS4Fk3tywtVdA4usOFm7FPgRGQkcA1wsqoWlFneCJiGv+PJrIpse3/sHJwB0LyX0bynkeTnkJhBTsepMsvTMxj7y0ImL11FiddLvxZNuaRXV/q3am7nbsJUblExM9Zu5LvV6/hh7QbyikuIiYjguBZNObltSwa0aRHWQzgOpErOwe3nBw0C7gBO2Ke4JQNfAHcdqLiJSH1VTQ88HQYsrUgOU/2oZy2a9wLEnB62xW1Z+k4e+3YmszduIS4ykvO6deTitC60TK3tdDRTxRJjojmzY1vO7NiWEq+XXzZt5btV6/hutf/mFqFv8yYM7tiOU9u3Ij7KesQeyKH0ohwPnAikADuB+4G7gGhgd2C12ap6jYjcE3htTZlNDFTVDBF5HXhFVeeJyFigK/4myo3A1WUK3n7ZEVz1pqpo9t+hdBmS8jXiDq8P/IzcPJ7+/icmLF5GclwsVx2bxvBuHUmKsWbI6k5VWb4jg29WrGXyspVszdlLbGQEp7RtxZDO7enbvEnQzTBT2aqsiTJYWIGr3rToazTnH0jivUj8JU7HqTRFpR7emj2f0bN+odTr5ZLe3bi2Xy8rbKZcqsqCrduZuGQFXy1fzZ6iYlIT4jjzmHYM69yBdvVSnY5YJazAmbClWohmng6uRKT2BERC/6S7qjJl2WqemDaT7XtyObVtK/51yvE0rZXsdDQTIko8Hn5Yu5GJS1Ywfc16Sn0+OjWoy4hunTjjmLZhNajfCpwJW5r3PJr3PFLr3bAY87Y8PYP/fDWNhVvTaV83lbsGnkDvZo2djmVCWE5hEZN+XcFHC35ldeZu4qIiOeuYtgzv3olO9euG/LRhVuBMWFLvNjRzEMScjCv5GafjHBGPz8crM+fw8o9zSY6N4eYBx3FOlw425slUGlVl8bYdfLDgV75cvorCUg/t6qYyonsnhnRqH7JHdVbgTFjy5dwORV8hqV8j7vpOx6mwjNw8bp3wJXM3bWVwx3bcO2iAjWMzVSq3qJjJy1by4YKlLN+RQVJMNBf26MzFPbuG3CTbVuBM2FHPenTXGRB3Ga6kO5yOU2E/b9jMrRO+pKCkhAdOP5mhXTo4HclUM4u2pvPm7PlMXbkWt8vFkE7tubxP95AZfmIFzoQdX86tUPwtkjItJIcFeH0+Xv5xLi/88DMtUmrx7Lln0rpOitOxTDW2OSuHt+Ys4JNFSyn2eBnQugVXHtuDHo0bBvV5OitwJqyoZy2660yIvxJX4r+cjnPYducX8K/PvmTW+s2c3akdD5xxsg3MNUEjK7+AcfMW8+4vi8gpLKJLw3qMOq4XJ7dpEZSFzgqcCSu+nDug+Csk9fuQm29y8bZ0bvjoc3IKirh30ACGd+sYlB8axhSWlvLp4uW8NXs+W7L30K5uKtcd35tT27UKqinhrMCZsKG+bDSjH8QNx5X0gNNxDsu8zdu48r1PqR0fxwvDB9O+Xh2nIxlzUB6fj8m/ruTlH+eyMSubdnVT+eeA4+jfqllQfDmrSIGzvskmOBVNAUqR2BFOJzksS7btYNT4z6iXlMj7l11gxc2EjAiXi6FdOjDl2kt5fOgg8ktKGPX+Z1z8zkfM37LN6XgVYkdwJij5do8ALUBqfx4U3x4PxfL0DEa++zE1YmMYd+kI6iaFVjdsY8oq8Xr5eOFSXpo5m8y8Aga0bs5tJx9PK4d6XdoRnAkL6tkIpYuQmCEhU9zWZOzisnGfkBAdxZiLz7PiZkJelNvN39K68M31l3PrSccxb/N2zn51LA9+OY2sgkKn4x0SK3Am6GjhREAgdrDTUQ7Jht3Z/P3dT4h0u3n74vNomJzkdCRjKk1cVCSjjuvFNzdcxoVpXfhg/hIGvvAWb/w8jxKPx+l4B2QFzgQVVYWizyGqD+Ku53Scg9qxN5e/v/sxPlXGXHyuTZRswlatuFjuHTSAz6++hO6NG/DYtzM545V3+H71eqej7ZcVOBNcPGvBuxmJOd3pJAdVVOrhug8nkVtUwlsXnRsyM0IYcyRaptZm9IVDeeNv5xDldnPNBxO5/sNJbN+z1+lof2EFzgSXkhn+++gTnM1xEKrKPZOnsjw9gyeGDQrba3AZsz/9Wjbls1EXc+tJ/fhx3SbOfPkdxs5diNfnczra76zAmaCixTMgonXQT6r8/oIlfL50JTedeCwntWnpdBxjHBHldjPquJ5MuXYkPZo05KGvp3PRmA9Zl7nb6WiAFTgTRNSXDyXzIKq/01EOaHNWDo9NnclxLZpwTb/QvzadMUeqYXISr104lMeGDGLD7myGvDaOl2bOodTrdTSXFTgTPErmAKVI9PFOJ9kvr8/HnZO+xu1y8cjggSEzjMGYqiYiDOncninXjuSUti15dvpPnPv6eyxL3+lYJitwJmhoyRwgGqIOayznUTXx1xXM37Kdu087gXpJiU7HMSbo1I6P45lzz+TFEWeTVVDIiDff59Uf5zpybs4KnAkepUshsgMiwTnjflGph2e+/4lODeoytLNdz82YAzmlbUsmX3Mpp7RtyVPfz2Lk2I/ZsTf3qGawAmeCgqoXPMshsqPTUfbrnbkL2Jmbx+2n9LemSWMOQXJsDM+ceyaPnj2QZekZDBn9Lj+s2XDUfr4VOBMcvBtA85HIY5xOUq6sgkJenfULA1q3oFfTRk7HMSZkiAjDuhzDx1f+jbqJCYx6/zMe+3bGUemAYgXOBIfSpf77iE7O5tiPl2fOoaCklNtO7ud0FGNCUsuUWnx4+YWc370Tb/w8n0ve+ajKB4cftMCJyJsikiEiS8sse1xEVorIEhGZICLJZV67S0TWisgqETltP9usJSJTRWRN4L5mpeyNCVlauhwkFiJaOB3lL3bm5jF+3mLO7XqMYzOpGxMOYiIj+M+Zp/D0OWewOmM3w14bx88bNlfZzzuUI7i3gUH7LJsKdFTVzsBq4C4AEekAXAAcE3jPSyLiLmebdwLfqWpr4LvAc1OdebeAuzHl/7o46+OFSyn1+Rh1bE+noxgTFs44pi0TrrqI1IR4rhj3KWPnLqQqLt120AKnqjOArH2WfaOqv00jPRv47aTEEOB9VS1W1Q3AWqC8kbBDgDGBx2OAoYcf3YQV7zZwN3A6xV94fD4+XPgrx7VoQhObSNmYStO0VjLvX3YBJ7ZuwUNfT+feL76lpJLPy1XGObjLgS8DjxsCW8q8tjWwbF91VTUdIHC/38sei8goEZknIvMyMzMrIa4JSt7tQVngZqzdwI69eVzQvbPTUYwJOwnRUbwwYjDX9uvNRwuXctV7E9hTWFRp2484kjeLyN2ABxj326JyVjui405VHQ2MBv8VvY9kWyY4qS8PdC/iKu+7kLPen/8rqQnxDGgTfOcGg1XungIy03PI2Z1Pzu489mTl/f44JyuPPVn5eEr//E297LALAeKTYklKjiOpZhxJNeMDj+NJqhlHjVrx1G9cm/jEmKO8Z6YquES4ecCxNKudzD2fT+X8t95n9AVDK6XFpMIFTkRGAmcBJ+sfjadbgcZlVmsEbC/n7TtFpL6qpotIfSCjojlMGPAGfkWC7Ahu+569zFi7gWuP702kO/jODQaDooIS1izbyoqFm1m5eDNrl20jM33PX9ZzR7hIrpVAjdrx1KiVQFTUHx89us93YJ9XKcgtYt2K7eTmFJC7p7Dc8zM1asXTsFkKTVrWoXHLOjRuUYcmreqQWr8GLpd1EA81Qzt3oGGNJG746HNGBIpc54ZHdk3IChU4ERkE3AGcoKoFZV6aBLwnIk8BDYDWwNxyNjEJGAk8GrifWJEcJkxojv/eVcvRGPuavmYDCpzdqb3TUYKGp9TLvJmrmD9zNSsXb2H9ynR8Xv8UTA2a1uaYHs1o3rY+DZrWJrl2Ism140munUB8YkyFB8d7vT7y9hSSm1PAnux8snflkr45i+2bd7N1QyY/f7ecrz765ff1Y+OjadelMR26N6VD92a069KEuIToStl/U7V6Nm3EB5ddwJXjJzDy3Y95+fwh9GnW+OBv3I+DFjgRGQ+cCKSIyFbgfvy9JqOBqYFf2tmqeo2qLhORD4Hl+Jsur1dVb2A7rwOvqOo8/IXtQxG5AtgMDK/wHpjQp4X+e4lzNsc+ft6wmQY1EmlWzTuXqCprlm7ju4kL+OGLxezJyic2Loq2XZow4qoTaN+tKW07N6ZGrfgq+flut4sateKpUSueRpR/3b09WflsWZ/B5nUZrF+RzoqFm3jvxWmoKi6X0KxNvd8LXseezUmtV6NKspoj16x2TcaNHMEV4z7lqvcm8Ox5Z1b4klRSFV0zq0paWprOmzfP6RimkmnR12jOP5DanyORbZ2OA/ivGtD3yVc4pV0rHhk80Ok4jshMz+H7zxfx7WcL2LIug8ioCPqc1J6Th3anR782REQGd7Ntfl4RKxdtZvmCTaxYuImVizZTWFACQLM29eh1Yjt6ntCW9l2b4I4I7n2pjrILCrnyvQms2JHB/4YM4uzO7eer6mHNxH5EnUyMqRS/H8HFOpujjNUZu9hTVHxEzSOhSFX5ZcYqPn1zJkvmrEdVOaZHM2787zkcP6gTCUnB8390MPEJMfTo14Ye/doA4PV42bB6B4t+Xscv01fyyZsz+HD0dBKSYujerw29TmhHj/5tSK6V4HByA1AzLpYxl5zLtR9M4q5JX1doG1bgjPN+L3DB0ytu4dZ0ALo1Cq6OL1Vp7fJtvPrIZJb+soE6DZO56IaTOWlIN+o3Do/ZW9wRblp1aEirDg0574r+5OcWsWDWGn75YSXzZqxixpQliAjtuzVhwOBunHhWl5Aq6OEoITqa1y4cxsKt2zn2npsP+/1W4IzztNR/L8Hz67gqYxfJsTE0Sk5yOkqV83p9fPz6D4x9biqJNeK4/r4hnDa8J5FRwfP/URXiE2M4flAnjh/UCZ/Px9pl2/nlh5XM/OpXXnzwM17/3xf0G9SJQcN7cUyPpnYFCYfEREbQt3mTCr03vH+DTWj4rWlSi53NUcbOvbnUT0oM+w+1nVuzePz2D1k2fyP9T+/MDQ8MJTE5uDr7HA0ul4s2nRrRplMj/nb9yaxdto2vPvyF7ycv4rvPFtCoeSqnDe/JKcO6WxNmCLECZ5z3e4ErdDZHGTv25lE3KXw/yFSV7yYu4KX/TEIE/vXY+Qw4u2vYF/RDISK07tiI1h0bcdWdZzLjyyV8/dEvvPHYFMY8/TX9TuvEuVccT6sOwTcxgfkzK3DGeb+de9PKm6LnSO3MzTviQabBKj+viGfv/oSZX/1Kx7Rm3Pa/EdRtFFxjEINFTFwUA89NY+C5aWxau5MvP5jLNx//wvTJi+jSpyXnXt6ftP5t7ItBkLICZ5wXZEdwJR4PWQWF1E0MvyO4vL2F3HPlm6xZuo3Lbh3EuVf0x+22WT8ORdNWdbnm7sFc/I9T+OrDuXz2zizuG/UWTVvX5ZzLjufEwV3/NEOLcZ79Zhvn/V7gCg683lGyK9+fo05i1QxcdorP5+OhG8aybvl27n7uIkaMOtGKWwUkJMVy3pUn8Na3t3Pb/0bgcglP//tjrhz4OFPen/OXeTaNc+y32zjPleK/9wbHlKRen3/qqYgwm8/w07d+ZPGc9dxw/1COPeUYp+OEvMioCE4e2p0XJ97EQ29cTu26NXj+/glcd/YzzJuxyul4BitwJhi46wECvvLm5XaC/3xK6Mzxc3DrV25nzNNfc+ypxzDwvMOaDMIchIjQo18bnnr/Wu5/6VK8Xh/3XvUW9416i63r7RJfTrICZxwnEgWuFNSb7nQUAH7rLxBCs9gdUHFRKY/d9gGJyXHc+J9zrENEFRER+pzcgZcn38IVt5/B0nkbuWbw07z26GTy9gbH+eXqxgqcCQ7u+hAsBe73I7jwqHBvPfkVm9bs5J+PnFdlEyKbP0RFRXDeFf1545vbOHVYDya8PYsrT3uCKR/MwRu48oI5OqzAmeDgqv/HdeEc5goc4YTSROT7s3TeBia+M4vBF/clrX9wTGRdXdRMSeSmh87luU9voHGLVJ6/bwI3nvs8G1btcDpatWEFzgSHiGbg3YpqidNJSIyJAmBvUfDMrFJRk8b+RFLNeC6/7XSno1RbrTo05LF3r+aup/9GdmYuNw9/gS/Gzw6LL1DBzgqcCQoS0Q4oBc9ap6OQEB1NXFQkO/bmOR3liOTmFPDzd8sZcFYXYmKjnI5TrYkI/c/ozIsTb6JTzxa88MBnPHzTOHL3BMfQmHBlBc4Eh8jAVbNLVzqbI6BeYiI79+Y6HeOI/DBlCZ5SL6ec08PpKCagZkoi/3nt71xx+xnM/m45Nwx9jmXzNzodK2xZgTPBwd0UiEE9QVLgkhLYkRvaR3DfTphPszb1aNm++lzyJxS4XC7Ou6I/T46/Fpfbxe2XjGb8y9OsA0oVsAJngoKIGyLbgmeF01EAf4HbGcIFbvO6DFYt2cKp5/SwYQFBqm3nxrzw2Y30P70T7zzzDXdf9jpZmaHdahBsrMCZ4BFxDJQuRdXjdBIa1khi59488kuc7/RSEUtmrwPguIEdHU5iDiQ+IYbbn7iAWx45j5WLt3DLiBfZsi44ZvQJB1bgTNCQqJ6g+eBZ7nQUOjaoiwLL00PzwyZrVy4ul5BSr4bTUcxBiAgDz03j8XFXU1xUym0XvcraZducjhUWrMCZ4BHVy39fMtfZHECnBv5L5SzeFppjlnJ255FUM94mUw4hrTs24on3riEmNpI7Lh3Nr7+sdzpSyLPffhM0xJ0K7hZoyRyno1A7Po5mtZJZsCU4Bp8fruzMXGqmhN/lfsJdo+apPPHeNdSuk8Q9V7zJ3OnB0ekqVFmBM8ElqjeUzAuK83DdGzdgwdbtITkgN3t3HskpiU7HMBWQWj+Zx8ZdTdNWdfnP9e8wffIipyOFrIMWOBF5U0QyRGRpmWXDRWSZiPhEJK3M8otEZFGZm09EupazzQdEZFuZ9c6otD0yIU2ievnPw5X+6nQUujduSHZBIWsydzsd5bDl7SkksUas0zFMBSXXSuD/3rmKDt2b8thtH/DDlMVORwpJh3IE9zYwaJ9lS4FzgBllF6rqOFXtqqpdgUuAjaq6aD/bffq3dVV1ymGlNuEruh/gRounOZ2EE1s3R4BvVqxxOsphq5mSQFbGXqdjmCMQnxDDf1+7nGN6NOWJ2z9k4U+h93votIMWOFWdAWTts2yFqh7sin4XAuOPIJuphsRVA6J6QtG3TkchNSGetCYN+SoEC1yDpils3xR6R57mz6JjIrn/5ZE0ap7Kf68fy5qlW52OFFKq8hzc+Ry4wN0gIksCTaA1qzCHCTESfQp416GejU5H4bT2rVmTuZt1IdZM2aBpbbIycynMD/0Jo6u7hKRYHnr9chJrxnHfqLfZuS3b6Ugho0oKnIj0BgpUdel+VnkZaAl0BdKBJw+wrVEiMk9E5mVm2tVxq4WYk/33xd85mwMY2L41AiF3FNegSW0A0reEVmE25atdN4n/vnY5JcWlPHjtGPvicoiq6gjuAg5w9KaqO1XVq6o+4DWg1wHWHa2qaaqalpqaWgVRTbARd0OIaI8WTXU6CnUTE+jeuAFfLl8dUr0p6zf1F7htG3Y5nMRUliYt63DX039j05qdPHnXRyH1++iUSi9wIuIChgPvH2Cd+mWeDsPfacWY30nMIChdgHqcP+dwdqf2rMncHVKDvpu0qktsfDQLZoXWkac5sLT+bfn7Pwcx6+ulTJu40Ok4Qe9QhgmMB34G2orIVhG5QkSGichWoC/whYh8XeYt/YGtqrp+n+28XmZIwWMi8quILAEGALdUyt6Y8BEz2H9f9LmzOYCzOrYjPiqK8fNDp6t2VFQEvQe056epy/B6vE7HMZXonMuPp0P3prz80CR27dzjdJygdii9KC9U1fqqGqmqjVT1DVWdEHgcrap1VfW0MutPV9U+5WznSlWdF3h8iap2UtXOqnq2qqZX7m6ZUCcRjSCyJ1r4meNNMQnRUQzp3J4py1aTXVDoaJbD0W9QR/bmFLDklw1ORzGVyO12ceujw/F4vDx79yeO/30EM5vJxAQtiR0G3g1QOt/pKFzYozMlXi+fLl7mdJRD1qNfG6JjI5n1tZ0BCDcNmqZwxb/OYN7M1Xz10S9OxwlaVuBM8Io5AyQRLXB+OGWbOin0aNyA9+cvwRci35hjYqPodUI7fpq61C6mGYbOvLA3Xfq05LX/m8zOrVkHf0M1ZAXOBC1xxUHsMCj6CvU638HjorSubM7ew7TVoTPL+wlndiF7Vx6zpzl/CaLKkJudx4s3vclrd7zLR09M4psx05kzZQEr564hfcNOCvMKq02Tncvl4pZHzsOnyltPfX3wN1RDEU4HMOZAJG4kWjAOzR+DJN3haJbTOrSm8fQavPrjXE5u0yIkrpTd5+QO1G9Sm49G/8CxpxwTEpkP5MPHJ/HZ818SEenGU1p+55naDWpyy6tX0/vMHkc53dFXt2FNhl56HB+8Op0Ro06gRbsGTkcKKnYEZ4KaRDSGmNOh8H3U5+zcihEuF1cdm8aS7Tv4ecNmR7McKrfbxXlX9mfVki0sDlzlO1Tl78ln0ktf0X94X6YUjeeznDGMWfM8z/70MP+ddCe3vnEdVz56MTVSkrhn8KO8cusYSktKnY5d5c69oj/xiTG884zz40aDjRU4E/Qk/kr/FQaC4FzcsM4dSE2I55VZoXNi/5Sh3amZmsiHr/3gdJQjMumlbyjYW8iFdw5DRIhPiqNBy3p06NOGPmf1YNBlAzj/9iE8P/sRzr7uND55ejI397uXbWvDu5N2Yo04zrvyBOZ8v4IVi0Lji9fRYgXOBD2J7ABRx6MFY1B1doqiqIgIrujbgzkbt7Bwa2hcDDUqOpJz/t6PhbPWhOxkvcWFxXz67BekndaFVt2aH3DdqJgo/vHCldz/yW2kr9vBdT3uYNp7M49SUmcMueRYkmsnMPbZb5yOElSswJmQIPFXgm8XFH7idBRGdO9EcmwML8yY7XSUQ3b6Bb2JT4zh3eedv0pDRSybtYqcjD0MuKDfIb+n37DevLLwcZp3bsL/XfwcaxaETuegwxUbH825V/Rn4U9r2bAyvI9YD4cVOBMaovpAZHc07xVUSxyNEh8VxdXH9eLHdZv4YW1oDKKOT4jhgmsGMHf6SubNONiVroJP+z6tqdMkhY+emHRY59XqNEnlX29dD8C6xZuqKl5QOGVod1wuYcaXS5yOEjSswJmQICJIwj/AtwMKP3I6Dhf37EKzWjV56KvvKfZ4nI5zSIZcehwNm6Xw6iOTKS0Jjcy/iU2I5cYXr2Tjsi18+Pikw3pv3aapuNwu0tc5P9SkKiXXTqBTrxbM/OrXajNU4mCswJnQEXUsRPYIHMU5fy7uvtMHsDl7D6//NM/RLIcqMiqCUf8+i60bMpn07k9Oxzlsvc/sQf/hfRn30Cf8/Pmh/5tHREZQp0kK29fvrMJ0weH4QZ3YtnEXG1eFdzE/VFbgTMjwH8XdCL6dUPCh03E4rkVTBrVvzauz5rIlOzQmve11Qjt6ndiOcS98R1aGs8MuKuKG5y6nSfuG3Dfkfzx77WiKCg7ti06DVvXC/ggO4LiBHXG5hJlf/ep0lKBgBc6Elqg+EJmG5r+KapHTabhr4Am4xcVDX38fMs1Co+46C0+pl+fumxAymX9Ts24yz/38CMNvHczkV6cyqvOtvPfIp6RvKP/oLDtjD9+MmU7m5l2kr884ymmPvuTaCXTq2Zwfv7YCB1bgTIgRESTxFvBlQP47TsehXlIiN514LNPXbOCLZaHReaNhsxQuu3UQc75fwcevz3A6zmGLio5k1OOX8ti391GrfjJv3TOeS1vewI3H/psJz01h/tTFjHvoE/7R99+cX/8qHr/sRQpyCxl87UCnox8V3Y5rzZb1meTnOv8F0Gk2VZcJORLVE40+Ec1/FeJGIK5kR/Nc0qsrU5av4qGvp3Ns8ybUio9zNM+hGDryOFYs3MTbT31F644N6dq3ldORDlu3kzrR7aRO7NyUyffvz+L78T/y0s1v/f56u16tuPSBEfQ5qwctuzYL+WnKDlXztv7rSW9YtYOOac2cDeMwCaUmirS0NJ03LzRO6JuqpaWr0d1nQ9zfcSXd6XQc1mTsYthr4xjYvjVPnXOG03EOSUFeMTePeJG92fk8/+k/SK2f7HSkI7Zx2RaK8ouo2zSVmnWTnY7jiIztOYwc8CjX3z+Us/72l0tzhiwRma+qaQdf8w/WRGlCkkS2gdhzoGAs6nF+LFrrOilce3xvvli2iu9Whcacj3EJ0dz7/MWUFJXy8E3jKAmxoQPlaXZMY9r1al1tixtAav0axCfGsGGVDfi2AmdCliT8EyQa3ftQUHSWuOq4nrStk8L9U75jb1FonP9o3LIO/3x0OKsWb+HVhz93Oo6pBCJC87b12Lg6/HuNHowVOBOyxJ2CJNwMJTOhaIrTcYhyu3nk7IFk5Rfw36++dzrOIet3WifOu6I/U96fE5Lj48xf1W9Sm53bsp2O4TgrcCa0xV0EER3R3IdQX47TaehYvy7XHd+bSb+uZEqI9KoE+Putg+hzUnteffhz5v6w0uk45ghFRLrx2VXcrcCZ0CbiRmo8DL4cNPcxp+MAcM3xvenSsB4PTPmObTmhMZja7XZx+xMX0LxdfR69+T2bsDfERUS48XiswFmBMyFPIttD/OVQ+DFa7PwM/xEuF08MPR2vKjd/8gUl3vKvPB1sYuOjeeCVkcQlxnDf1W+TsT3H6UimglxuF15PaPzeVSUrcCYsSMI/wN0E3XtvUMxw0qRWMv83eCBLtu/gsamhM5g6pW4N/jP67xTmF/Pvy14nKzPX6UimAtwRLrzWRGkFzoQHkRgk6T/g3YTmPe90HAAGtm/N33t3Z+wvi5i8NHTOa7Vo14D/jL6M3Rl7uXPkayE5Z2W1pwrOdyx23EELnIi8KSIZIrK0zLLhIrJMRHwiklZmeTMRKRSRRYHbK/vZZi0RmSoiawL3NStnd0x1JtHHQux5kP8mWrr04G84Cm47uR9pTRpy9+dTWbkj0+k4h6xD96b8Z/Tf2ZWew78ufpXM9BynI5nDkL4li7qN7GP1UI7g3gYG7bNsKXAOUF7byzpV7Rq4XbOfbd4JfKeqrYHvAs+NOWKSeCe4aqN77nL8wqgAkW43z5x7Jkmx0Vz/0SRyCp1vPj1UnXq24OE3ryBndx7/uuhVdmzJcjqSOURb12fSuEWq0zEcd9ACp6ozgKx9lq1Q1SPpAz0EGBN4PAYYegTbMuZ34kpCkh4AzyrIf83pOACkJsTz/HmD2bk3j1snTMHrC51zI+27NeX/3r6K/Lwibr/kVbZt3OV0JHMQnlIv2zfvplGLOk5HcVxVnINrLiILReQHETl+P+vUVdV0gMC9/U+YSiMxp0DMGWjeS2jpGqfjANC1UX3uO/0kfly3iWenh9Zg6jadGvHomKsoLvJw+8Wvsnld+F92JpSlb96N1+OjcXM7gqvsApcONFHVbsA/gfdEJOlINigio0RknojMy8wMnXMYxlmSdB9IPLrnjqBoqgQY0b0TI7p15NVZv/DV8tVOxzksLds34LGxo1BVbr/4VdYu2+Z0JLMfv30BaWRNlJVb4FS1WFV3Bx7PB9YBbcpZdaeI1AcI3O/3K6GqjlbVNFVNS021/zBzaMRVC6nxEHiWorlPOB3nd/cOGkC3RvW5Y+LXLE8PrSOhpq3r8ti7VxMdE8m/Ln7VrhodpOZ8v4K4hGiat63ndBTHVWqBE5FUEXEHHrcAWgPry1l1EjAy8HgkMLEycxgDIDEDIe5SKHgbLZrqdBwAoiIieGH4YGrGxXLNBxNJ3xNa48waNU/l6Q+uo3nbejxy0zjefvprfCF0TjHclZR4mPXNUo4b2JGo6Ein4zjuUIYJjAd+BtqKyFYRuUJEhonIVqAv8IWIfB1YvT+wREQWAx8D16hqVmA7r5cZUvAocKqIrAFODTw3ptJJ4u3+uSr33IV6tjgdB4CUhHheuWAI+SUlXPnep+wJoZ6VALXqJPHoO6MYNLwnH7zyPQ9e+45dPTpIzJuxioK8Yk44o4vTUYKCXfDUhD31bEZ3D4OIZkit8YhEOR0JgNkbt3DlexPo3KAub150LjGREU5HOiyqyhfj5/DKw5Oo16gW9790KY1bWn8xJ/3fLe+x6Od1jJv5byIi3U7HqVR2wVNjyiERTZAaj0Dpr2ju407H+V2fZo15bMhpLNiyndsmfBlSwwfAf92xs/7Wh/97+0ry9hZy0/AXmf3dcqdjVVuF+cXMmbaC4wd1CrviVlFW4Ey1IDGnBc7HjQma83EAZxzTlrsGnsDUVWt58MtpQXHh1sPVqWcLnv/0HzRqlsKD173DW09+ZRP9OuDzcT9TXFTKyUO7Ox0laFiBM9VGMJ6PAxjZuztXHZvGBwt+5cUZzl8NoSJS6yfzxPhrOP38Xnw4ejp3XPoa2zfvdjpWtbFzWzbjX55G7wHtad+1idNxgoYVOFNtiEQhyc8Aiu65OWjGxwHcelI/hnXuwPMzZvP+/CVOx6mQqOhIbvzPOfzr8fPZuHoH1w95li/Gzw7Jo9JQoqq8+OBnAFx779nOhgkyVuBMteI/H/d/QXc+TkT471mncEKr5jz45TS+XbnW6UgVdtLZ3Xj585tp360pLzzwGfdc+SaZO/Y4HSts/TBlCb/8sIpLbxpI3YY2wXJZVuBMteMfHzcycD7u64O/4Sj5bWLmTg3qcsunU/hl01anI1VYav1kHn7jcq6/fyjL5m/k2rOe5tvP5tvRXCXLzSng1Yc/p02nRpx9ybFOxwk6VuBMtSSJ/4LILv6pvEpXOB3nd3FRkbx6wVAaJddg1PufMX9L6E6J9Vsvy5cm3kTT1nV58o6PeOCaMXbpnUpSWuLhsdveZ29OATc9dA5ut32c78v+RUy15D8f9yJIIpp9DeoNnnlOa8bF8vYl51InIYEr35vAvM2hW+QAGjRN4bF3r2bUXWeyeM46rj7zaSa+MwtPqfW0rCifz8dTd33EvJmrufHBYbRo18DpSEHJCpyptsRdB6n5KmgOmnM9qsVOR/pd3cQExl56HnUTE7jqvQkh3VwJ4Ha7GPb343n585tp17UJrzz8OdcOfoa501das+VhUlVeefhzpk9ezGW3DuK04T2djhS0rMCZak0iOyA1HoPSRYGLpAbPh22dxATGXjqcekmJXDV+AnNDvMgB1G9cm4ffuJwHXhmJqnL/1W9z9xVvsnH1DqejhYz3XvyOz9/9mXMuP57hV53gdJygZgXOVHsScxqS8E8omgz5Lzsd509SE+IZe+l5NKyRxKjxE5i9MXjG71WUiNB7QHtemXwL19w9mDVLt3L9kGd5/r4J5OzOczpeUJv83mzeff5bThnWnStvPwMRcTpSULO5KI3B3+yje26HoolI8nNIzCCnI/3J7vwCRo79mC3Ze3jlgiH0bR4+g3lzcwoY9+J3TH7vZ6JjIhl+1YkMueRYYuOjnY4WNLxeH5+N+ZE3HvuSXie2494XLsYdUb2m46rIXJRW4IwJUC1Bsy6F0uVI7feQyI5OR/qTrPwCRr77CZuysnlpxBD6tWzqdKRKtXV9Jm88PoXZ01aQkBTD6ef35uxLjiWlbg2nozlq87oMnrn7Y1Ys3Ezfkztwx1MXEh1T/S6FYwXOmCOk3t3o7nMBL1L7Y8Rd1+lIf5JVUMjfx37Mht3ZvDB8MCe0bu50pEq3cvFmPn1zJrO+WYrL7eKEM7tw7mXH07xdfaejHVWeUi+fvDmDd5//ltj4aK65ezADBnetts2SVuCMqQRauhLNugDcLZDa4xCJdTrSn2QXFHLFuE9ZlbGLR88+jcGd2jkdqUqkb9nNZ2Nm8c0n8ygqKKHbca059/Lj6X5c67D/kF+3YjtP//tj1i3fTr/TOnHdfWdTMyXR6ViOsgJnTCXRou/QnOsg+mQk+XkCF6oPGrlFxVz34STmbtrKPaedyCW9ujkdqcrk5hQw5YM5TBr7E1mZuTRrU5eB5/bkxLO6hN2HfkmJh/dfnsaHo6eTWCOO6+8fQr/TOjkdKyhYgTOmEmn+O2juQxB7IZL0QNAdNRR7PPzz0yl8u2od1x3fmxtP6Bt0GStTSYmHHyYv4vN3f2bNsm243C569GvNgMHd6HNS+5DulFJS4mHOtBWMe+FbNq3ZyclDujHqrrNIqhnvdLSgYQXOmErmy30c8l9DEm5CEq53Os5feHw+7vviWz5ZtIwLenTmvkEDcLvCf/TPprU7mTZxId9/vpDM9D1Ex0TSe0B7+p/ZmZ792xIVHfydMFSVNUu38e2E+Xw/eRF5ewqp0zCZ6+8bSq8Tw7PZ+UhYgTOmkvmHD9wBRZ8hSf9F4s53OtJfqCpPTvuR136ax6D2rXl86CCiIiKcjnVU+Hw+li/YxA9fLGbmV7+yJyufiEg3Xfu2okvvFnTu3ZKWHRoE1TyNWRl7mTZpId9+toBNa3YSFR1B31OO4dRhPeh6bKugyhpMrMAZUwVUS9Hsa6HkRyT5BSTmFKcjlevNn+fzv29n0Ld5Y14YfjYJ0VFORzqqvB4vi2av45fpK1kwaw1b1vvnF41PjKFTz+Z07t2SLn1a0KxNPVxH8Si3qLCEtcu2s3LxZhbPXseCH1fj8yntuzXhlGE96H96ZxKSgqsjUzCyAmdMFVFfAZp9KZSuQmq9jUT1cDpSuSYsXsbdn0+lfb06jL5wKLXj45yO5JisjL0smbuexXPWs2TOOrZv8l9hPDY+miYt69C4ZSqNW9QJPK5DvUY1j3jwtKqyfdNuVi7azMrFm1m5eAsbVqXj9fgAqN+kNv1P78QpQ3vQqEXqEe9jdWIFzpgqpL4sdPeF4MtCar2HRLZ2OlK5pq1ex82ffEFqQjyjLxhKy9TaTkcKCpnpOSyes47Vv25ly7pMNq/dSVZm7u+vR0S6adQ8hZR6ycTFRxMTF0VsfDRx8dHExkcTG3heXFzK3uwCcnPy2ZNdQG5OAXuy88nNKSB7Vx6F+f5Ju2Pjo2nTqRHtujahXZfGtOvShOTaCU7tfsizAmdMFVPPFv8YOdxI7Q8Qd3AOPl68LZ3rPphEscfLc+edybEtwmvWk8qSt7eQLesz2bIugy3rMti8PoPsTH+RKswvprCgmML8knIn4Y6JiyIpOY6kmvEkJsdRo6b/cfO29WjXpQmNW9ax82mVyAqcMUeBlq5Asy4Cdz2k1jjEVdPpSOXalrOXaz6YyLrM3dx3+klc0KOz05FCkqpSXFhKQX4xRQXFRMVEkpQcFxI9NcNJRQrcQb9eiMibIpIhIkvLLBsuIstExCciaWWWnyoi80Xk18D9SfvZ5gMisk1EFgVuZxxOaGOcJJHtkeSXwLMZzboC9eUe/E0OaJicxPi/j+C4lk25f8p3/N83P+D1+ZyOFXJEhJi4KGqlJtKgaQopdWtYcQsRh3L8/Daw79TqS4FzgBn7LN8FDFbVTsBIYOwBtvu0qnYN3KYcYl5jgoJE90GSnwfPKjT7KtSX73SkciVER/Py+UO4pGdX3p6zgOs//Jz8khKnYxlzVBy0wKnqDCBrn2UrVHVVOesuVNXtgafLgBgRCd3pBYw5AIkZgCQ/BaWL0ZxrUC10OlK5Ilwu7hk0gPsGDeCHtRv429sfkr4nOI86jalMVXkG9FxgoaoW7+f1G0RkSaAJdL8nMURklIjME5F5mZmZVZPUmAqSmNP8VwQvmYtmX49q8B4dXdSzK69eMJQt2XsY/uZ4FmzZfvA3GRPCqqTAicgxwP+Aq/ezystAS6ArkA48ub9tqepoVU1T1bTUVBs3YoKPxA5Gkh6Gkh/RnFtQ9Tgdab/6t2rG+5edT2xkBJe88xFj5y4st4egMeGg0guciDQCJgCXquq68tZR1Z2q6lVVH/Aa0KuycxhzNEnceUjiPVA8Fd1zF/5f7eDUpk4Kn1z5N45v2YyHvp7ObRO+tPNyJixVaoETkWTgC+AuVZ11gPXKDh4ahr/TijEhTeIvRRJugaKJ6N4Hg/rIKCkmhpfOP5t/DjiOKctXM+KN8azblXXwNxoTQg5lmMB44GegrYhsFZErRGSYiGwF+gJfiMjXgdVvAFoB95YZAlAnsJ3XywwpeCwwlGAJMAC4pbJ3zBhHxF8D8VdB4Xg07/GgLnIuEa7u14s3LzqHrIJCznvjPb5avtrpWMZUGhvobUwlU1U09z9QMA7ir0ISbgv667Tt2JvLTR9/waJt6VzWpzu3ntSPSHdwXeTVVG9VMtDbGHN4RARJvBdi/wb5r6G5jwb1kRxAvaRExo4czsU9u/LW7AWMHPuxDSUwIc8KnDFVQMSFJN0PcRdDwVto7iNBX+Si3G7uHTSAJ4aezoqdmZw9eixTlv1luKsxIcMKnDFV5PcjubiRUDAGzf1v0Bc5gMGd2jHxqotpXrsmt3w6hbsmfU1esfWyNKHHCpwxVchf5P4NcZdDwbuB3pXBO4TgN01qJTNu5Aiu7debz5asYNhr77Jk2w6nYxlzWKzAGVPF/EXujkDvyvfQvfeHRJGLdLu5ecCxjL30PDw+Hxe89T4vz5xjEzabkGEFzpijQESQhNv8wwgKP0D33hsSRQ4grUkjJo66mEEd2vDM9J+4dOzHbMvZ63QsYw7KCpwxR4m/yN0C8ddB4Ufo3ntQ9Tod65AkxcTw5LDT+d/Zp7FiRyaDXx3L+/OX4AuBc4qm+rICZ8xR5C9yN0H89VD4Mbrnn0E9QXNZIsLQLh2YOOpiOjWoy/1TvmPk2I/ZnJXjdDRjymUFzpijTERwJd7kPy9X9CWafW3QXmqnPI1r1uDti8/lobNOYfmODAa/Opa3Zs+3c3Mm6FiBM8YhEn8FkvSQ/yoEWZehvtA5ryUiDO/WiS+uuZS+zRvz6NQZXPj2B6zJ2OV0NGN+ZwXOGAdJ3Agk+Rko/RXNugT17nY60mGpl5TIy+cP4clhp7MpK4dhr7/HizNmU+INjXOLJrxZgTPGYRJzOlLzZfCsR7MuQr2hNd5MRDirYzu+vHYkA9u14rkffmbY6Hf5ecNmp6OZas4KnDFBQKL7I7XeAN9ONOtvqGeL05EOW634OJ465wxeOX8IRR4Pf3/3E278eDLb94RO06sJL1bgjAkSEtULqfk2+HIDRa7c6wUHvQFtWjDl2pHceEJfflizgdNfGsNLM+dQ7AneK52b8GQFzpggIlFdkFpjAQ+6+0K0ZJHTkSokOiKC6/v3Ycq1IzmhdXOenf4TZ77yDtNWrwuJ+ThNeLACZ0yQkch2SK33wZWEZl2KFk1zOlKFNUxO4rnzzuLti88lyu3m2g8mMer9z+zq4eaQzdm4hQe/rNjfgBU4Y4KQRDRFan0AEa3QnOvRgo+djnRE+jZvwsRRF3Pnqf2Zv3k7Z73yDndN+sam/DL7VeLx8Pi3Mxk59mN+Wr+pQtuwK3obE8TUl4/m3AglMwPTfF0T9FcHP5is/AJG//QL435ZjKpyQY/OXNOvFykJ8U5HM0FiTcYu/vXZV6zYmcn53Ttxx6n9SYiOPuwreluBMybIqZage/4NRZMg7mIk8W5E3E7HOmLpe3J5aeZsPlm0jKgINyN7defyvj2oERvjdDTjEJ8q7/6yiMe/nUlCdBQPDz6Vk9q0BEBErMAZE45UfWjuY1DwJsScjtR4HJEop2NVio27s3n+h5+ZvGwVSTHRXNk3jYt6diUhOjz2zxyanbl5/HvSN/y4fhMntm7Ow2ed+qejeitwxoQ5zX8Dzf0fRPVBkl9EXIlOR6o0K3dk8sz0WXy/ZgM1YqK5qGdXLunZlVrxcU5HM1VIVfly+Woe/HIaRaUe7hzYnwu6d/5LU7wVOGOqAS2ciO65CyKaI8mvIhGNnI5UqZZs28HoWb8wddVaoiPcnNu1I5f36U7jmslORzOVbMn2HTw2dQa/bN5Gx/p1eXzoIFqk1Cp3XStwxlQTWvyTv/OJRCDJLyNR3ZyOVOnWZe7mjdnzmbRkBV5VBrVvzZXHpnFM/bpORzNHaFvOXp76fhaTl66kVlwsN57Yl+HdOhHh2n/H/iopcCLyJnAWkKGqHQPLhgMPAO2BXqo6r8z6dwFXAF7gRlX9upxt1gI+AJoBG4ERqpp9sLBW4Iz5g3rWodlXg3cHUuP/kNjBTkeqEjtz83hnzkLeX7CEvOIS+jZvzMU9u3Fi6+YH/EA0wSe3qJhXfpzLO3MXIgKX9enBVcemkRAdfdD3VlWB6w/kAe+UKXDtAR/wKnDbbwVORDoA44FeQAPgW6CN7nPZYhF5DMhS1UdF5E6gpqrecbCwVuCM+TP1ZaPZN0DpLxB/PZJwY8gPI9if3KJi3l+whHfmLiQjN5/6SYmM6N6J4d06kmpDDIJaqdfLBwt+5fkffmZPYRFDO3fgphOPpX6NQz+HXGVNlCLSDJj8W4Ers3w6fy5wdwGo6v8Fnn8NPKCqP+/zvlXAiaqaLiL1gemq2vZgOazAGfNXqiXo3vuh8BOIOQOp8Sgi4dvVvtTr5fvV6xk/fwk/bdhMhMvFqe1acWGPzvRq2ihsC3woKvZ4+GTRMl7/aR7b9uylT7PG3HFKfzrUr3PY26pIgYs47J9yYA2B2WWebw0s21ddVU0HCBS5w99bYwyAf7hA0iPgboHmPQmx50F0P6djVZlIt5uB7VszsH1rNuzO5v35S5iweBlfLl/NxFEX065uqtMRTcCExct58MtpdG1Yn/vPOIn+LZsd1S8glV3gykt+RL1YRGQUMCrwNC9w9FfVUoBwuTSx7UtwqsJ9Ob5qNrt/QfP/0v6+fx7pJoJmXypJUOzPauDDI9/MQVv59lXZBW4r0LjM80bA9nLW2yki9cs0UWbsb4OqOhoYXbkxD0xE5h3uoXCwsn0JTrYvwSmc9gXCa39E5LDPT1V2F6RJwAUiEi0izYHWwNz9rDcy8HgkMLGScxhjjKnmDlrgRGQ88DPQVkS2isgVIjJMRLYCfYEvAp1JUNVl+I9ElwNfAdf/1oNSRF4Xkd++STwKnCoia4BTA8+NMcaYSnPQJkpVvXA/L03Yz/oPAw+Xs/zKMo93AycfYkYnHNUm0Spm+xKcbF+CUzjtC4TX/hz2voTUTCbGGGPMobJpAIwxxoQlK3BliEiyiHwsIitFZIWI9HU6U0WJyC0iskxElorIeAmxkb8i8qaIZIjI0jLLaonIVBFZE7iv6WTGQ7WffXk88Hu2REQmiEiygxEPWXn7Uua120RERSTFiWyHa3/7IiL/EJFVgb+fx5zKdzj28zvWVURmi8giEZknIr2czHioRKSxiHwf+AxeJiI3BZYf9t+/Fbg/exb4SlXbAV2AFQ7nqRARaQjcCKQFZp9xAxc4m+qwvQ0M2mfZncB3qtoa+C7wPBS8zV/3ZSrQUVU74x8mdNfRDlVBb/PXfUFEGuPvMLb5aAc6Am+zz76IyABgCNBZVY8BnnAgV0W8zV//Xx4DHlTVrsB9geehwAPcqqrtgT7A9YFpIA/7798KXICIJAH9gTcAVLVEVXMcDXVkIoBYEYkA4ih/PGLQUtUZQNY+i4cAYwKPxwBDj2amiipvX1T1G1X1BJ7Oxj9mNOjt5/8F4Gngdo5wYoejaT/7ci3wqKoWB9bZ7xjdYLKffVEgKfC4BiHyGaCq6aq6IPA4F/+BRkMq8PdvBe4PLYBM4C0RWRgY1hCSM7iq6jb83zw3A+nAHlX9xtlUleJPU7wB4TLF2+XAl06HqCgRORvYpqqLnc5SCdoAx4vIHBH5QUR6Oh3oCNwMPC4iW/B/HoRKK8HvAvMgdwPmUIG/fytwf4gAugMvq2o3IJ/QaQL7k0Db9BCgOf6rOsSLyMXOpjLlEZG78TfJjHM6S0WISBxwN/4msHAQAdTE3zT2L+BDCd3Zm68FblHVxsAtBFqnQoWIJACfADer6t6KbMMK3B+2AltVdU7g+cf4C14oOgXYoKqZqloKfAoc63CmyrAzMLUbB5viLRSIyEj811q8SEN3vE5L/F+kFovIRvxNrQtEpJ6jqSpuK/Cp+s3Ff1mwkOg0U46R+P/2AT7CfxmzkCAikfiL2zhV/W0fDvvv3wpcgKruALaIyG8Tep6Mf0aWULQZ6CMicYFvnycToh1m9hE2U7yJyCDgDuBsVS1wOk9FqeqvqlpHVZupajP8BaJ74O8pFH0GnAQgIm2AKIJgsuIK2g6cEHh8ErDGwSyHLPCZ9QawQlWfKvPS4f/9q6rdAjegKzAPWIL/F72m05mOYF8eBFYCS4GxQLTTmQ4z/3j85w9L8X9oXgHUxt97ak3gvpbTOY9gX9YCW4BFgdsrTues6L7s8/pGIMXpnEfw/xIFvBv4u1kAnOR0ziPYl37AfGAx/nNYPZzOeYj70g9/B5klZf4+zqjI37/NZGKMMSYsWROlMcaYsGQFzhhjTFiyAmeMMSYsWYEzxhgTlqzAGWOMCUtW4IwxxoQlK3DGGGPCkhU4Y4wxYen/AUxO4kokNQAVAAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "scanA = np.linspace(110.0,130.0,50)\n", - "scanB = np.linspace(5,20,50)\n", - "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n", - "\n", - "fig1, ax2 = plt.subplots(constrained_layout=True)\n", - "\n", - "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n", - "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Repeat the same for 50 bins:" - ] - }, - { - "cell_type": "code", - "execution_count": 373, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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fmmjU2QURQSIvQcRpdUTDMA5DJBKJvgNJ+QaJfQx866BiGqgPfBsAQt0PNFhnmcwZnBEWVAOhe20lo0DikcQ3wN4cvItB4q2OZxhGDYktCqLvhMgbQmd0paPR/GtQZ1/wLUNifhM646sDpsAZllP/LrTwsdDI/vYW4DoDiRgYetHRytJshmHUjtiiIeYuiLoRyt5DS94EgqhvFfh3AoHQ9FSuvictgylwhqW0fBpa9AcAJP4fqG8toKjqKTsLsWE0JKFCdw9E3YCWvgVl76C5w0JfZoNZkDInNIrKSWDuwRmWUA0SLP4HWvibUOfRhP8ikcOR2KdCLbNMcTOMBkVscdhiH0aSv4bIKyCwFRQon4CqDy37EA0WndBjmgJn1DkNlqEFD0DpaHBfA8ECKP8IwBQ2w2jgxJ6CLf5ZpNFkcHVDi59Fc4agRX9Gyz49oceqtsCJyBgROSAia6sse0FENorIahGZKCIJlctbiki5iKysfLx2hH0michMEdlS+bPhzLBnHJUGstD8G6FiFhL7ByT+WSRpDBL3N6ujGYZRh8TZAUl8O9SgTNyAQsVc1L8tNFqKd9lxH6MmZ3DvAEMPWTYT6KKq3YDNwBNVXtuqqj0qH0dqKvN7YJaqtgVmVT43Gjj1rUPzrgb/DnC0qZx4VBBnp1DLK8MwTikigkQMRJKnILFPgn9VaHCHgkfQgt8ddyfxagucqs4B8g9ZNkN/OvJCIOMYj3s5MLby97HA8GPc3qhntGJO6MwNByS9H+oCIKaoGYYBIk4k+lYkeQZEDofgHtAyqPiaYNAfmn28Fk5EK8rbgY+qPD9NRFYARcAfVHXuYbZJU9X9AKq6X0RST0AOI0xp+dRQNwB7S0h8DZujOer8r7nfZhjGz4g9GYl/Do28LnRPruBBcHRBA7tqtb/jamQiIk8BfuD9ykX7geaq2hN4BPhARI5rVjwRuVtElorI0pycnOPZlWEBLX0PLXwUHD1Co5IUvwCYxiSGYRyZuLojjT5FYn8P/szQaCi1UOsCJyIjgUuAEaqqAKpaoap5lb8vA7YC7Q6zebaINK7cT2PgwJGOo6pvqGofVe2TkpJS27iGBbT0XbT4LxAxCGn0NhL7CFJHIxgYhlG/iTiQ6NuRlOlI3GO12ketCpyIDAUeBy5T1bIqy1NExF75eyugLbDtMLv4HBhZ+ftIYHJtchjhS8snoMV/BWc/iLodkQgk8lLE2dnqaIZh1CNib4pEjajVttXegxOR8cBAIFlE9gB/JtRqMgKYWXmpaWFli8lzgb+IiB8IAL9S1fzK/YwGXlPVpcD/AR+LyB3ALuCaWqU3wpJ6ZqKFT4KzP2gRFP8FdU1GxHS7PBnySssorfDSPCkBVeWTFWvJKy3jgg5t8AYCjFu8gkBQuaxrR7wBP2/OX4rDbuOG3t1w2Gy8vXAZcZFuRvbricNu55XvFpAWG8MD5/Ynzh3BmwuW0jIpget6dQNg0qr1pMfH0r9lMwCKPB5iIiKwmcvORpiRyquL9UKfPn106dKlVscwjkJ9a9C8EeBshySOBS0B9SGOY21oa/wgp6SUPQWFJEdHs7ewiHcXr2Bbbj59W2RQUFbOop17KPf6iIt0U1BWji944kdrt4uQFB1FbEQEuw4WkBITzTmtW5AaG8PbC5fRu3lTHh54FmlxMTz75TcMaHsaw7t1AiAzJ48m8XFEucxMEEbticgyVe1zTNuYAmecKBrICvVzUwfE3IVE3WgakxwDVSW7uISPlq9hTuYO2qU2Yk9BEev2Z1Pq/eVN9uToKBIi3dhsNqKdTtqkNiIh0k2sO4KkqEiiXS5cdjtOhx2X3Y7rh592Bw67DVXFHwji12DoZzD0CASDVPj9lFR4KfZUUOSpoKiigpLK3/PLyigo85BfVk5eaRmH+wRJiHTTpXEaTRPi+Gj5Gi7r0oH7z+1PSkwUf/nyG67o3pn+LZvxw+eP+XdiVKc2Bc4MtmycEBosRQ/eA1oK0fdA8TOhmQAizrA6Wlg6UFTMvqJituTk8+WGzSzesYdIp4NCT8WP62QVFdMsMZ4+zZsS53bTr0UGzRLjyUiIIz0uFqfdbuE7CPEFAuSWlJFdXEJ2cQkHKn/uLShiZ34By3fvA+DztRv5fO1GbIDYhM0H8hjY9jQaRUfx0uz5/GP4hZzfvg0lFRVszM6lc+NUIp3mjM84PuYMzjhuqgG04H6o+DY07I7rHPAuQCLOtDpa2MgqKmH9/gOs3pfFzI1byMz9aeyECLudKJeTc9q0pEfTxrRLTaZDWgqx7ggLE58YqkpeaRk7DxawM7+AnXkF7Mg/yOYDuezILyBY+fnjdjjomJ5CXKSb77Zs5+lhg7i6Rxf2FxazaOceLuzYhji32+J3Y1jJXKI0LBEseg7K3oGou5Do2xB7stWRLFdQXs68rbtYuz+LuZk7fixodhHapDQiyuXkim6d6H9ac5olxp+SDTQ8Pj9bcnLZmJ3LpuwcNlY+iiu8QKjopcZGs+tgIc9ecj6D2rVmU3YOC3fs5u6z+hET4bL4HRh1yRQ4o85p+Rdo4cMQOQK888Ceji3pXatjWaKkwsu3W7bxxdpNzN4S6h3jstvp2iQNEIZ368iwzu3NB/NRqCp7C4tYvTeLVXuzWLF7H+uyDuCvbDiTGBVJaYWX5y4dwtmtWzJv606yi0u444ze5j5eA2cKnFGnNJAVmrjQ0RZJeg/8W4Eg4uxkdbQ6U+ypYPbmbbw2bzE78g8SVCUlJpr0uBgu7dKBG3p3w+Uwt7qPh9fvZ+3+AyzdtZflu/eyZOdeSrxehFBjFofdzstXDaN708Z8vHwNiVGRDOvc3urYxglmGpkYdUZV0aJnQkPoxD6JiBOcHayOVSf8wSCTV61n3JIVbM09iC8QINLpoHliAs9dNoSeGU1OyUuOJ4vL4aBXsyb0atYE6Is/GGTtvmzmbdvJ/G07Wbl7HyPGfkK0y4UInJaUSK9mTUiPi2XSqvX0ataE5kkJVr8NwwLmDM6oFfV8GRoINfpOKBsfmtst6iqrY51U2UUlfLJiDR+vWEt2cQkA1/XqyhXdO9GtSTp2m+nIboUij4dFO/Ywb9tO5mZuZ29hMQAd01PYmJXDjX2688eh5xFUZdXeLLo3NX9X9ZG5RGnUCQ0WhC5N2tIgaSyUvIpE34HY06yOdsIFVfl+2y7GLFjG/O07ATi7dQsu7dKBrk3SaZ2cZHFCoypVZVveQWZtyuTrTVtZtTcLgJZJCXRpksbUtZt4cfhQLu3aEX8wiE3EnG3XE6bAGXUiWPhnKP8YafRZg73f5gsE+HDZat5ZtJw9BUUkRLpx2e08NPBMru7Zxep4Rg1lF5cwe/NWvt60lYXbduFXJTU2miu6dSLa5eKjFWv4YOS1pMfFWh3VqIYpcMZJp/5taO7FEHk1aBESfT/iPNyEEfWTqjJjYyb/nDWXnQcLiXQ6eGbYYC7q1M40Fqnnijwevtuyg6nrNjIncwdBVRIjI3lwYH8u7tyB2Zu3ElDl6h7mC0w4MgXOOOmCB+8H7/cQ/28o/B2S+Abi6m51rBNi2e69PP3FLDbn5NE2pREXd25PvxYZ9G7e1Opoxgl2oLiEKWs3MnHVerbk5OGy24mPjCA5OppP77wRh81GdlEJaXExVkc1KpkCZ5xU6l2B5l+HxDyExNyPagUi9X+0jW25+bw0ez4zN2UCcE3PLjw9bDAO0xChwVNV1mUdYNKq9Xy+ZgOFngrSYmO4vFtH3l28gjvP7MsD5/a3OqaB6SZgnESqihb/A2zJqOs8UK33xS23pJR/fTOfCSvX4XY5eXDAGcRHurmmZxdT3E4RIkKXxml0aZzGY0PO5dvN2/hoxRremL8EmwhLd+1l4Y7dNI2L5b2lq7jjjN6kxpqzuvrCFDijZiq+Bd8yiHkU8q+FmPsh5l6rU9Xa52s28Jfp31BSUUGk08n0e0eahganOJfdzgUd23JBx7bszC/gw+WrmbByHSPf/ZTUmGjyy8q5vlc3iIVynw+3w2FGTwlz5hKlUSPBvBsgmA2NJiGe6eA6q17O8Vbu8/GXabOZsDrUAfi203uRHhdLt6bpVkczwpDH5+fL9Zt5b+lK1uzLJiHSzQ29u5OZm0e518foG68wRa6OmEuUxkmhvjXgW4bEPonY4iDqOqsj1crWnDwe/HQqmbn5dG+Szru3XGMuRRpH5XY6GN69E5d368jyPft4e8Fy/jdvES67ne5NG5NTUkpqbAwLtu+iX4sM04E8zJgCZ1RLS8eCRKO2VCj/AtwXIVK//iNPWrWep6fPwu10cmHHtgzr1M4UN6PGRITezZrSu1lTMnPyeH3+Yqau3cTgV8YwuH1rpq/fzJ+GnseIvj2sjmpUYQqccVQayAbPdIi6ETxT0MBexD3M6lg1Vu7z8cy02UxcvZ6uTdL4zzWXmabfxnFpk9KIF4ZfxK/PPYM3v1/ChJXrsImwYs9+zmzVgoNl5ezMP8ilXTuaL1EWMwXOOCotGw/4kaibwZ4BwQP15p7D1tx8Hvp06o/9nM44rbkpbsYJ0zwpgb9eMoT7zunPWwuX8vHyNXyxbhMZCfGUeb0M69zeFDiLmUYmxhGpKpozEJztsSW+YXWcY5KZk8eIsR9jE+HFKy6ieWI8GQnx9aY4G/VPbkkpYxYu473FKwmocku/ntxzdl9enDWPa3p2oXvTxlZHrNdMIxPjxPJvgeB+cN1NMPdKJOY+xH2+1amqtTO/gFve/ZRiTwUPDTyTs1q1sDqScQpIjonmsfPPZeTpvXj5m+95e+EyPlmxBgV6ZjQ2Bc4C5vzZOLKK70I/nZ3BFgMSaW2eGthXWMSt732KPxDgzNOa07NZE6sjGaeYtNgY/n7ZBUy8awSdG6dRUuHl9XlLmLVpK1PWbODFWXPx+v1WxzwlmEuUxhEF82+GYAG25ClWR6mRnJJSRrzzEXml5Yy75Wo6N2540/cY9Yuq8u2W7fzj67lsy8uncXwsMS4Xk+++yXQpOEa1uURZ7Z+wiIwRkQMisrbKshdEZKOIrBaRiSKSULl8iIgsE5E1lT8HHWGfT4vIXhFZWfmoP83yThEaLAHvMnCdjarH6jjVOlhWzm3vfsqegiJaNEqgfVqK1ZEMAxHhvHat+Pyem/jT0PMo9/rYmpPH32d+x4HiYh6dOJ2tOXlWx2ywavIV4h1g6CHLZgJdVLUbsBl4onJ5LnCpqnYFRgLvHmW//1LVHpWPaccW2zjpvAsBP9gS0AP9Ud9GqxMdkTcQ4N6PJrPzYCF3nNGHSzp3MK3XjLDitNsZ0bcHX91/G9f17sZ7i1dyyWvvMnvzVg6Wl1sdr8GqtpGJqs4RkZaHLJtR5elC4OrK5SuqLF8HuEUkQlUrjj+qUZfUtwawg+sMCOaCo5XVkY7o7zO+Y8We/bx81cVc1KnhzE1nNDwJkW6eHjaYq3t24Q9TZrIhO4dxi1bQIimRuVt30DwxgT5meqYT5kS0orwd+Ogwy68CVhyluD0gIrcAS4FHVfXgCchinCi+deBog83VDVzdrE5zRBNXreODpauIjYggIdJtdRzDqJEujdP45I4beHvhMl75biHfb38Ht9NJj4zGpsCdQMd1HUdEngL8wPuHLO8MPA/cc4RN/we0BnoA+4F/HuUYd4vIUhFZmpOTczxxjRpSVfCvA0dHNLCXcG2ItH7/Af48bRY9mjamU+MUmsTHWR3JMGrMabdz91n9mHz3TbRLTSanpJSicg/7C4vJKy1jzb4sqyPWezVqRVl5iXKqqnapsmwk8CtgsKqWVVmeAcwGblPV+bXZ95GYVpR1QwNZaM65EHUnlI1G4l9GIsOrHZDX72f4m+9TUuFl4l0jaBQdZXUkw6i1oCrjl63mxa/nYrfZ6JCezLr9B/j2wTuJN1cmgJPUivIIBxoKPA5cdkhxSwC+AJ44WnETkao9Hq8A1h5pXcMCvvWhn67eSNzT4OptaZzDeX3+Erbm5tMhLYXYCJfVcQzjuNhEGNGnO5/fcxPtUhuxZOde2qcm//h6scc0Y6iNmnQTGA8sANqLyB4RuQN4FYgFZlY283+tcvUHgDbAH6t0AUit3M9oEfmh+v6jsivBauA84OET/L6M4xHYAYC4eiNRNyIjhMU9AAAgAElEQVT28OpPll9axpgFy2iTnERuSSmY4beMBqJZYgLv3nINvxt8Dmv3ZXPFm+/z/pKVDHrlLVbs2Wd1vHqnJq0obzjM4reOsO6zwLNHeO3OKr/fXNOARt3TQBZIJBrIB/Ui9lSrI/3MmwuW4vH7GXXNpTRPjMdpt1sdyTBOGLvNxp1n9qFfiwx+89kX/O2rb+mYnkq7lOTqNzZ+xnQWMn4pmA22dCh6DC18zOo0P5NTUsr7i1cyqG0rWicnmeJmNFjdmqYz8a4RDGzbirX7s/ntpOnklpTy7JffsL+w2Op49YIpcMYvBbLAno7E/A6Juc/qND/zxvwleAMBZm/ZZlqZGQ1efKSb/1x7KU9eMIC5mTsY/ub7fLpyLct3m8uVNWFmEzB+KZAFrv5IxOlWJ/mZ7KISPly2mmGd29EhLdWMNWmcEkSEkaf3omdGEx78dCr+QBBP5WDNu/ILaJZopoE6ElPgjF8K5oaG6PKuBEdLxJZgdSIAxi9bjT8Y5OHzzqZZYrzVcQyjTnVrms6EO2/kkYnTeHLKDNbuz2Lq2k2M7NeTBwacYXW8sGQuURo/oxoEfKAeNP9a8C6wOhIQ6if0+doNtGqUSE5JqdVxDMMSSdFRjL7xSq7r1ZUPlq4mPTaGYZ3bWx0rbJkCZxzCF/phS0IS3wRnePSBW757L3sLisgqLmHK2vAd+DnclJVUUHTwpy8E2XsPsmf7TyMCecq8BAJBK6IZteSw2Xhm2GAeO/8cNufk8eSUGeSXlvHm90vYU1BodbywYi5RGj+nXgDEFotEDLA4zE8mr95AlNPJjPtuM93eqti7I5esPfn0Pjs0yPQ7L33J5jV7uPPxYXgr/Ix5cTo5+wp5+LmrCASVsS99RVFBGff+4TJi4iMZ88I0POU+Rn32ACLCa89+jt1p567HLwZg0+rdxCVG0bhZIyvfpnEIEeGOM/qQkRDP7yZN58q3PqC4vIIyr4+HBp5pdbywYQqc8XOVBU6DPvAuAWcXxOKZvCv8fqav38KQDm1oFHNqD8m1YkEm389Yy+Dhvdi7PZcpHyxg6/p9dOvXipysQvbvysPvC3D/5aN+tt3jt7z5s+d/uvvtnz2/rOsfiE+Kxuf1E+F2UZhfSvPWqUx5fwHNWqXw7Fu3Y7PZeOPvU2ndsQmDh/c66e/VqN6FHduSFhvDvR9NRgROb9kMAH8waKaMwszobRzix3EoI6+F8o+R5GmIo42lmb7etJX7P/6cDmkp/O3SIXQ5hVpPZu/JZ+bEZQy8tCdrl2zj8/e+Z/umLKjy3zY2PpK0jCTSmiaQ0jiB1CaJJKfHExHpxG6zYbMLtp/9DH3wFReWUZhfWuVRQuHB0O+5WYXkZRf9eAx3lIvT2qWzd2cubTtncOujF9KyXRqP3/Qmw64/3RQ8i+0+WMjd4yexu6CQ5y+7kNfnL+ahgWcyuH1rq6OdMLUZi9KcwRk/JxGhn7YmSOJYsDWxNg+wbNdeHDYb/kAArz9gdZyTruhgaPixHZv2M3X8IuZOX837r84CIDk9jqHX9KXXWe04rX06KY0TiHA7T0qO0hIPuzIPsGtLNts37Wfrxv34fQGWzdvMsnmbiY2Pwumys37FTrr1b43L5eCZ+8Zy6yND6dYvfOcPbIiaJcYz/rbruP39z3hs8pe0Sk4ixozRagqccQiJDv0QGxIRHk2PV+zZR9cmaXx42/VWRznp9u/O555hL+Fw2ikvrcBmFzr3akH/wZ3oO6ADzduk1lmfp+gYNx17NKdjj+Y/LlNVsvccZP3ynSz/fgvL529h2oeLmPbhItIyEvF6fGxZu4d2XTLI2pPPN1NWcsVtZ5OQFFMnmU9lCZFu3rnpKm5/fwIb9h+guCJ0uyGvtOyUnW3DXKI0fkZV0ezOEHVTqJGJsxNiS7QsjzcQoPfz/+Gmvj14fMi5luU4mYoLy1g+bws7Nmcx9YMFlBR5aN+tGVffeS49z2pLdEz4Tpeiquzcks3y+VtYMX8La5Zsp8LjIyLSSfM2qWzfmMXbsx8nOTWOnVuycbrsNGlhxlQ8mYo8Hu78YCLr9h/g3rP78eb3S/nfdZdxZqsWVkc7LrW5RGkKnPELwew+4OoPFTOQxLeRiLMsy7Jq736uHfMhjeNieWTQWVzWtaNlWU6G/bvz+PM9Y9m99QAAZ13QmWvuGkj7bs0sTlY73gof65bvZP5Xa5n75RqKDpYSE+fmrAu6sGd7Lvt25vHe3Cew2WyoqhmB4yQp9lRw5wcTWbMvizNbNeflqy4mJiLC6ljHxdyDM04MiQaJQJI+AEc7S6Os2LMfgLapjYh3h++ZzLGaPG4+a5ZsY8HX6xGbcOb5nbjt0YvIaJVidbTj4opw0vOMNvQ8ow2/eupSVnyfyXdfrGTOtNWUl3kruyZ8ybAb+vGvJz7l9PM6cvWd4dMdpaGIdUfw1ogruPODiXy/bRcLtu/mvHat2JB1gK5N0q2OV2dMgTN+yZYIWoS4junL0kmxM7+AeHcEb95whdVRTphVi7by2nNTsIkwfORZXHHbOSSnNbyhxxxOO30HtKfvgPZUeHws/nYj30xZwaRx85jw9hxSmyTi84bGVAz4A+zfnU/GafW7wIeTmIgIRt94JXd+MIGHJ0zjok5t+WrDFqbfeytNE+KsjlcnTIEzfsneGPy70Io5YEtHnNadxeWVlJIcE23Z8U+01Yu28tf73yU2Poq/vH4rHao04GjIItxOzhnalXOGdiUvu4hJY+fxxfiFjPv3TDau3k3bzhl88J9ZvPTRvXTofmr8mdSFmAgXr10/nBHvfMSsTVu556x+p0xxAzNUl3E49iYQ2IcW/Bot/9TSKDmlZXh8fq58831LcxyvYDDIn+5+mydue4uk1Dhe+eyBU6a4HapRWhx3PDaMsd/+npsfHMLGFbt4/9WvSWuaSHFBOarKigWZ7NmWU/3OjGolRLp5a8SVxLndjF+2mn2FRezKLyCvtMzqaCedaWRi/IKWvoUWPw+J7yKOVojdustGQ14dQ2JUJJ3SU3l62GDLchwPVWX8f2fz7qiZJKfH89/PHyI2/tRstn04njIvX36ymM/GzCU3q5BWHRtTdLCMtKaJvPjBr6yO12BsOZDLDe98TGpMFKU+Hx3SUnj9+uFWx6qx2jQyMWdwxi/ZGgMgtgRLixtAbkkZPTOa1Nvi5vf7efXpSbw7aiZnD+3K6Bm/NcXtEO4oF8NHns2Ymb/jN3+7Ck+Zl9ysQnxeH5nr9lJeWsEnb36Ht8JnddR6rW1qMq9eeym7DhYS547g0UFnWx3ppDMFzvgle1MA1LsQLZ9kWQx/MEiZz0esu/42b37qtjFM+3ARV952Nk/86wYiIk7OqCMNgdPl4MKr+/L6F49w/58u58C+Qh66+lWee+h9xrw4ncx1Zhbr49W/ZTP+dukFbD6Qx/hlqwHYfCDX4lQnjylwxi852gACnq/Rwt+jWmFJDLsIAkxevZ5HJ063JMPxWD5/C6sXb6Nx8yTufPxibGbw2xpxOO1cMuIM3vzyUYZdfzrL5m0hITmGgvwSABZ/u5HigoZ//+hkubxbR24/ozcfLF3F01/M4rLX32XJzj1WxzopTCtK4xfEFo3am4FEISnfANaMaSciOO12UmNj6N60fvXdyckq5PlHP6RF2zT+9dF9pkNzLcTERXL/n4czeHgvRv1xAn+9/136nNuOdct2cs7Qrjz83NVWR6y3Hh10Nmv3ZfPZqrWMPL0nPTIaWx3ppDBfKY3Dc7SHwA7E3tjSD2eXw06n9FRu6dfTsgy18Zd7x1Fe6uEPo24iMrr+XmINBx26N2fUZ7/mjseGsWbJdgKBAM1apaKqlBZ78Fb2pTNqzmGz8a8rh5EYFcWszdso8/oo8/rw+BrWn6U5gzMOz9EeKmYRLPsIsWdYNlyXy27HG6hfMwisWrSVzPV7Oa19er0fmSRcOJx2rr7jXM4Z2pV//3ECb70wjTVLt6EBpaigjH9+eC92u/m+fiySY6L599UXc/PYT3h04nQOFJfQtUk6f7t0iNXRTpga/YsQkTEickBE1lZZ9oKIbBSR1SIyUUQSqrz2hIhkisgmEbnwCPs8TUQWicgWEflIRMzcDmFEnO2BIJSMQss/tyxHhMPB3MwdjHzX2v54x2L8f2aRlBrL06+NtDpKg5PWNJFnR98WGgZsfibrV+6ka9/TTHGrpZ4ZTXjiwoHM3bqDtNgYhnW2dmi+E62m/yreAYYesmwm0EVVuwGbgScARKQTcD3QuXKb/4qI/TD7fB74l6q2BQ4CdxxzeuPkcXYP/Yy8Hon/u2Ux0mJjcDnsnNO6pWUZjkVBXgmrF2/nomv7kdrEulkYGjKbzcblt5zFqM8eID4xmknj5jP948WsW7aDsf/6imAwaHXEeuXG3t24sEMbFmzfRaOohtWFpUYFTlXnAPmHLJuhqj9csF0IZFT+fjnwoapWqOp2IBPoV3VbCd3UGQT88LV8LFB/ehyeAsSeHprsNJCJiHXfjjMS4/EGAtx5pvXjYtbE15OWoaqkNkmofmXjuLRsl87Ln9xPj/6tGfXHCfz3r5OZM3015aVeq6PVKyLC0xefT3ykm99//hXvL13FY5O+pD4NAnIkJ+qT63bgh3bcTYHdVV7bU7msqkZAQZUCebh1ABCRu0VkqYgszckxQ/fUKVcvqFhKsPgltGKuJRGaJcSzv7AYj8+Hvx58M184az1Ol4M2nQ/7z9k4wWLjo3j69Vu55q4BbNuwn7iEKLwVPoLBICVF5VbHqzeSoiJ55uLz2ZCdw9cbM8krK8Pjr/8NTo67wInIU4Af+GGwwMM1uTv0q0BN1gktVH1DVfuoap+UFHPDvi6JsxdoDpR9BL41lmRolhhPUJXe//gvi3bsrn4DC5WWeNi0eg+XjuhPqw5NrI5zyrDbbdz+24t4/KUb2L4piwevepVRf5zIQ1e/SnGh6S9XU+e3b83lXTuyaMduHhl4FpHO+j8owXEVOBEZCVwCjNCfzmf3AFVna8wADh2CIBdIEBHHUdYxrObqFfoZ+xgSc58lETIqRz6/oEMb0mNjLMlQU0vnbMLvC3DmkC5WRzklDby4Oy+O/xUaVL79YiUde7YgJi7S6lj1ylMXDiQpOoonpswgp7iE95astDrScal1gRORocDjwGWqWvVr0ufA9SISISKnAW2BxVW3rSyG3wA/9NQcCUyubRbjJHG0B0kA70LLIrRNaQRAp8aptK78PVxlrtsLwO5tByxOcupq06kpL310H41S41g4az1b1+8jP6eY7D351W9sEB/p5umLBrHpQC5/njaL5776lh15B62OVWs17SYwHlgAtBeRPSJyB/AqEAvMFJGVIvIagKquAz4G1gNfAveraqByP9NE5IdrN48Dj4hIJqF7cm+dwPdlnAAidogYAJ5vCR58AC37sM4zJEVH0TIpgeW79rGvsKjOj38sCvNLcbocNG4W3oW4oUttksDf37mL6Fg3T942mqduf4u/3P+uaV1ZQ4Pbt+bsVi1YtGMP791yDS0b1d/WwDVtRXmDqjZWVaeqZqjqW6raRlWbqWqPysevqqz/N1VtrartVXV6leXDVHVf5e/bVLVf5X6uUasGPDSOStxDgEII7AX1WJKhR0ZjFuzYxZBX36bcF74jypeVeGjSohHd+7e2OsopL1Tk7sTpcpB3oIjr7z3PjAVaQyLCkxcMwOP3M3H1egBKKurnx7P5GzeOLuIcwA2uHkj0rZZE6JnRhHKfn18POINwbrlckFdKQlLDmX28vmvSIpnn3rkTEWH089M4sK+AZXM3U1ZSPz+s61LrlEbc3K8Hn6xYyz9nz+P8V98mv6z+tUo1Bc44KpHIUJHzzEQ1iGrdn0H1zAhd1W4cF0uUK3xbdmXtyWfd8p0/3oszrNeiTRp/G3M7pcUeHrvpNZ65byzj/j3D6lj1wv3n9CcpOoo5mdu5qFM7HLb6N2C4KXBGtcR9IQQPoHlXoYWP1fnx26QkEeeOYM7W7WE9rYffH6BxsySSUuOsjmJU0aZTU/46+nYK8ktp0rwRNz1QPyfPrWux7ggePu9MNmbnclarFsS53VZHOmamwBnVixgMEgU4ENfpdX54u83GuW1OY+bGTO74YELY3odLb5pESpMEklJirY5iHKJjj+Y88tw17Mw8wLhRM/F5/ezd0XAn+jxRrujemeaJ8bz63QI2ZB3go+WrrY50TEyBM6oltmiIGAKBbRBpzYhqg9u1osIf4PdDBuCyH25oU+slp8eRm1WIz0zfEpbOHdaNK287mynvLeD3I9/kiVvfpMITnl+WwoXDZuO+c05nQ3YOL82ez0uz51PmrT9/ZqbAGTUikcNBi9HyGaiv7r/FndO6JU6bjb0FRdjDtDVco7R4dm/L4ZU/T7Q6inEEtz4ylHZdM9i+KYsb7htEhDt87+mGi0u7dqR5Yjz7i4r56r5bw/o++KHC85PCCD+u/mBLg9JRaN4NaLBu+6TFuiPo1zKDrzZsYfT3S8NyINjktHg0qHTrZ7oJhCuny8HjL90AqsyevIJAIGjOuKvxw1nclpw8lu4ODTgVqCd9Ck2BM2pExA6Rl0FgD8Q9B1L3QyANatea3QWF/HP2PLaH4egKKY3jAWjVMd3iJMbRNGneiAeevoK1S3fwyp8ncueFL1KYX2p1rLB2adeONEuM5415i7nj/QmM+m6B1ZFqxBQ4o8Yk8iogiAT3I1L3lyku7NgWG6H5q1olJ9X58avTsUdzABZ9s9F8YIa5QZf3pO+A9nz3xUoaN2+Ep8z0jTsah83GzX17sGpfFrFuF2lhPi7sD0yBM2pMHK3AdTpa9iHBkrdR/846PX5KTDTntDmNmZu2huUlkrSMJBo3S2LcyzOY9qF143cejwO7c9m8bCsAgUCAGWO/pbSwYRbrux6/GJ83QNMWyaRlhN8XpnAzvFsnIhx24iMjubFPd6vj1IgpcMYxkcjrIbgPSp6Him/r/PjDu3Uku7iE2977jDmZO+r8+NXpfU47HE47/QZ2sDrKMVNVnrr4OZ4Y+jceOvspRt03mhdu+w9Lv1oFgM/rIxAIWJzyxGnWOpVLbjyDLz9ZzJrF25jx2VKrI4W1+Eg3F3duz+drNlDkqWDd/myrI1XLFDjj2LiHgC0JXGci0SPr/PCD27cmNsLFuqwDZBcX1/nxq9PzrLb4fQFK69FwULl78/hm/Dx+N/gZdqzdTWlhKZ6SCqa9+TUAU9+Yyaz35/LFG19zU8v7yNsffvc/a2vE/YOJjovkpSc+4d9/+Iz9u/OsjhTWru/djTKvjz9MncmVoz9g98ECqyMdlaP6VQzjJyIuNPIqKB2DBrIRe1qdHj/C4WBY5/ZMWrWeoR3b1emxa6L76a0RmzDjsyVERrlo2yXD6khHteTLFTx18d9RVdJbpnDHczdy4e2DSEyNZ9/WLGaO+46v3/2O/7t5FC63kzY9TyMpPcHq2CdMbEIUNz84hP/+ZTL3/uFSMxNENbo1SadjWgpbc/J4YfhQUsP8Xpw5gzOOmUReBwTRgt8RLHi4zo9/Tc8uVAQCTFi1joJya2Y4OJLoWDfd+7fmmymrGP2PaVbHqVZRXjGqyuUPXMTYzFe5/vdXkJgaag3apHU6I5+5jrGZr/LiN0/Tc3BX1i/YzHt//ZTJ//mSBVMaxiW9Ydf1I61pIvNmrLU6StgTEa7s0ZnM3Hy6NE4jwhHe50imwBnHTBzNIWIQ+FeBBlGt235EXZuk0zOjMa98t4DLX38Xb5jdF7rkhv4EA0Euuraf1VGqdfaVp+OMcOJw2I44nYzNZqP7gM48M+kxhtwygHFPf8y4pz9izqf1o6l4dewOOxff0J81i7fzf4+M56168MXEShd0aAPA1LWb+GzlurCeENUUOKNWJOpm0HLEPQCRuv8Wd0u/nhRXeDm7dYuw6/Tdf1BHGqXGMWvyClQ17PJVFREZQZezOzBnwkKevf6lo2a12+08+ta9DLrxbIrzSxj5zHV1mPTkuuCqPjhdDrZv2m8mRq1GelwsPTMaM3NjJk9NmcHMTZlWRzoiU+CM2nGdAY62aOk4gv79aLBubzYP6dCGtNgY9hUWh91lErvDztBr+7J0ziZ+c81/WDZ3s9WRjqrX+d3I2ZXHrg17Kcw9+gg1drudO/4+ArHZmPK/hjPtTHxSNAMu7saBfQXceP/5VscJexd0aMvmnFzGjLiSO8/oY3WcIzIFzqgVEQmdxfnXQ+75aOmYOj2+027npr7d+X77LsYuWs53mdvr9PjVueTGM3C67GTvPYin3Gt1nKPqPaQbAFf8ehgJKfHVrp/aLJneF3Rj4qhprFuw6WTHqzOXjjgTT5mXrycuMx31q3FBx9BlyvVZOYiE7zxxpsAZtRd5OUgC2FsgUdfX+eFv7NOduAgXo75dwNsLl9X58Y8moVEMw67vT9HBUho3D++Wea17tKRJm3Re+fVbTHplOn+87P9YNG05+VkH2bBoC77K0eNLC0vJ3plDIBAgLikWX4WPg1nh3Uz8WLTrmkHrTk2Y+M48Rp73f/h94XVvN5xkJMTTKT2Vb7Zs44Wv5/Ll+vC8SmEKnFFrIpFIzN0QyIRA3c9iHRMRwb3n9KfE6+X203vX+fGrM+KBwcQlRjPqTxP4dupKDuaGX789CDUieXnes/QY1IX/PDSGNXM3cDC7gPmTlvDgGU+yd0sW+7Zm8f7fJnDTaffxxRtf882H8xl807mcfUXdzw94MvU8ow25WYVcc9cAMwhzNU5vmcHqvVnM3JTJhqwcq+McloTzDfBD9enTR5cubRhNkxsK1XI0ZwjYUsHRFol7HLHV3bBHXr+fof8bS1xEBB/fcQPBoOJ2hs89udmTV/DCYx9hs9u49q4BjHz4QqsjHVEwGOSzf33BW0+8R8AfxBXhxFtx+Lm/ktITeGP1P4lPblizly+ctZ5n7hvHP967m659W1kdJ6zN2rSV+z7+nHE3Xc3ppzU76ccTkWWqekw3/MLnk8Col0QiIeY+tOhp8G+FyIsgYmCdHd/lcPDwwLP47aTpDHllDJd06cDvzj+nzo5fnfMu68GMz5awec0eLrmxv9Vxjspms3HNo5fS47zObFi4hazt2UTHRxMdH0VUXCTR8VE/Ppq0SSc6LsrqyCdcp14tAFi9aDupTRJJa5pocaLw1ad5UwRYsntvnRS42jBncMZxU/WiuUOBGCR5EiJ1e+U7qMrVb33AzrwCnr1kCBd1Dq8RTvZsy+Hey17m3Iu68eu/XAEK7iiX1bGMI/jVJf+iIK+ExORY/jflN1bHCWuXv/EeMREu4t1uhnVuxyVdTt4YrLU5g6v2k0hExojIARFZW2XZNSKyTkSCItKnyvIRIrKyyiMoIj0Os8+nRWRvlfWGHUtoI7yIuJCYByGwETzT0cD+Oj2+TYTHzz+XEq+XnWE4Nl5GqxSuuXMAsz9fwR1DXuDN57+wOpJxFB17tqDC4+OmX5vuAtXp26Ipa/ZmUejxUOQJv/FXa/JV+x1g6CHL1gJXAnOqLlTV91W1h6r2AG4GdqjqyiPs918/rKuqZuiA+s59KTjao0XPoDnno/7ddXr401s2Y0j7Nvxv7kJem7eI5ZUzD4eL6+89j5bt0igv89J3YHur4xhHkdokAU+Zl771cEaIutYxLZWKQIBnLxkSllPoVFvgVHUOkH/Isg2qWl0HmBuA8ceRzahHROxI7G9BC8B1ZmjGgTr2+JBzCQSV/81dzNS1G+v8+EfjinDy2AvX4/P6mfHpUlSVQMCMmBGO4pOiAdi4chde05LyqNqmhLrAZOaE5ywMJ/NmyXUcvcA9ICKrKy+Bmju5DYHr/9u77/CoyrSP49970nsPhBJC7x1WqnRQkKoIiMgqduwFX1fXrouKDd21K7ZFVBBBpIk0BaQoXXoPoaW3STIz9/vHDC4iSCjJmQnP57pykZmcmfwOycyd85zn3M+lENgOStYD5X9ut3pMFDd1bIvd4eDyRt51Hg6gZoMk/n5fH5Z/v5kXH5zCuJFvU2Q/9SxFwzpRMe4C99Cod0jdfcziNN6tdoL7D9nvt+yg75sfcTgnz+JEf1QmBU5ELgEKVPV07bnfBGoDLYA04KW/eK6bRWS1iKw+etQ7r7Uw3EQEiXgQNBPNeRJX7ml/rGXm5o5tSYqM4Nm5i8gsKCTXy84LDP57J5pfUosf524kKCQAdfnOJK+LRWSMe3bosFu7El+5Yl0GcaGFBQZSNSqSo3n5pMTGUOTwriPesjqCG85fHL2p6mFVdaqqC3gXOG3bdVV9R1XbqGqbhISEMohqXEgS0BSC+4F9FhROQ13l22k8JCCAcT0789vho/R84wNeXbSsXL//mdhsNu5//mqCgv3JyykEAUeJ06sbMl9somLda5yl1K1MRFTFuxTiQquTEMex/AL+M2wAybHetVbgBS9w4p4jPhT4/C+2STrh5mDck1aMCkLCPWvEBXZEbOU/+nx5o3q0S6lOicNJz/q1y/37n0lCUjT3/WsoOzcf5MnbPuKRMe/z+Zs/WB3L8HB6WnSlH84x7bpKoVp0JIdyvLRLz5k2EJHJwHKgvogcEJExIjJYRA4A7YFZIjL3hIdcChxQ1V0nPc97J1xS8IKIbBCR9UA3oPxXzTTKjPgnQ+hosH+Dq3gj6thTvt9fhCf79kCBz1atc0/o8LIlUNr3bMzdz1zJ2uU7OXQgg/jKZ25ybJSPzHT3eaT3XviOnKwCi9N4v9iwULLtRYyYNIXnv19y5geUozN2MlHVEaf50ten2X4R8KeWDap64wmfjyplPsNHSfhtaOFUyLoNxQHx8xBbRLl9/5S4GO7q2p4JC35k7BczcKry1rCBXtX5vPeVbSjIs/P2c9+yfuUuegxqRX6u3QyLWSzLU+BufvgKYuLDLU7j/eLD3L+vteNjqRHjXUOUplWXUSbEFgnhd6G5T0HodawKHYcAACAASURBVCDl/0ZxQ7vWLN6+myU799C7QR1KnE4CvWztuEGjO1GQV8QnE+dTXOzgl6XbuPuZK+nUp6nV0S5axwtcryGtveoPIm8V5ylwI9s0p2HlRIvT/JFZTcAoO6HDwL8e2OeDlv9Qj5/NxvMDLyPI35+0nDxsNu/8dR9xe3eG3NCZJbPWk1AlhnpNq1kd6aKWeSwPPz8budlmeLI0YsNCADiW733/X975ijcqBJEAJPIpcKWh2ffjyrgO1fJd/LNqdCSPX96dX/Yf5Pl5ixk3fQ4Fxd517ZmIcOO4vlw+7G/s3pLGnC9W4XK52Lq+fLvBGG57tqbhdLr49r8rrI7iE6KCgwH3+e6B73xqcZo/8q7xGqPCkcBWaOhIKPgM/GqBKwP8KpdrhgFNG/LTrr18smotoYEBXNu2Bc2qlm+GMxER7nhiEOpSJr/5A9s3p7J68VazbEs5c5Q42bh6Nx37NPH61R+8xfFh3MSIMOoklH8Ho79iCpxR5iT8ftT+g7u5iQUtvAAeu7w7aw+kkV9cQrUY75yxaLPZuPOpwYhNmD1lJS071Pl9+RajfGxZtw97YQndrmhBUnXvXondWxw/S9k2uRr9m3pX/04zRGmUObGFI1FPgWsXmjsRzf8Y1fK9vigsMJCXh/Qlq9DOP2bM47tNW9mX4X0rD9hsNu54YhD9r23Pr8t28K97/suh1Ayeuv1jjqZ5X96KZuVCdw/TStVM98DSOn4Epxa05zsTcwRnlAsJ6oIGD4SC91BciH9dCGpfrhkaJ1ViXM/OPDt3Ect372Ngs4Y81c/7lkSx2Wzc9ugAkqrH8u7479i7/Qi52QVkpeeRkORd07ArmuXfbwIgN7vQ4iS+w+YpcF+t3cSkn39h2o0jLU70P+YIzig3EvkPkGjwqw2BbS3JMKptC7rVrYXD6WRQ80aWZCgNEWHw3zvz2L9HcexwNn7+NlyevpU7Nqea1l5lYPfWQxzYc4xrxvagWduaVsfxGcd/F2vFxdCplncNqZsCZ5QbscUgkY+BcycUfIQ608r9jVpEGD+wD5UiI3hg2mxSs3L4fsuOcs1wNtr1aMRLk28lIMCfB0e+zaRX5nLXkDeYN9WsbH+hvfPcTMIjgxl0XUf8/P2sjuMzji902rVuTe7r3sniNH9kCpxRvoIvh6AeaO7L6NHeYD9lQ5wyFR0SzKtX9eNIbh6jPv6Su6fO4kBWdrnnKK1aDaowceodNG6dwpS3FtK4dQ069m4CgNNheiVeCMu/38TaFTup16w6EdGmk8zZyCxwD+dGhwRbnOTPTIEzypWIIJFPAEFgi0MDyvc83HHNqlTmyX49Sc3O4dI6KVSN8u5lUSJjwnjmvesZckNnNq7ew5O3f8yxQ9mMu/Ydvnx3sdXxfJrL5eKT178nNCKIa8b2sDqOzzle4MZ+MZPx873rd9EUOKPciV8lJPJhcB1EihejqrhXTipfV7ZozE0d2vDDtl18tPJX1qWmsT/Te2cq+vn7cdND/Rg3YTjbNxxg7KDXCAjyJ7GqmXhyPhbNXMfuLWnc8fhgGrdKsTqOz8ksdBe4wc0a0aZ6VYvT/JGZRWlYI+QqsH+L5owH+wIksA2E31LuMe7r3ok96Vn8a95iokOCaVEtibeHDyr3HGejW/8W1GqYxIRxX7BuxU5i4iNo3q42a5fvZM/WNEbe0ZOAQPPSLo3DBzKY+Ng0qtdKoEu/ZlbH8UkZ+YX422zc36OT1/XuNEdwhiXcQ5XPAAIl61GLfhVtIrww6DIaJyVSWFzC6L+1tCTH2apRpxKvTLmda+/syY9zN3BL31f4/us1rP95FzY/87IuDUeJk3/dO5kiewn9rmnntb1Kvd2+zCySoiIo8bIlqcAUOMNC4l8diXoWNBPUuqHB0MAA3ho2kLjwUMZ9M5fUrBy+3bgFl5dPxfcP8GPkHT15fdqdJCXHsmbpNkIjgkg/nENhfhGvPTqVtP3pVsf0Si6Xi/88/Q1b1+/n7meGMHBUR6sj+awdR9MJDQig5fg3OJybZ3WcPzAFzrCUhPSFkBGQ/y6u/A9w5TxpyTVeiRHhvD18EIUlJVz78Rfc//Vs5nvx5QMnSqlXmZcm38bND1/BxtV7uLXfy0x6ZS6Lvl1Hdka+1fG8jtPh5M7BrzN7ykqG3dKVy4b+zepIPqvY6WRPRhaNKydyU4e2JIaHWR3pD0yBMywnkQ+Df33IfQ3sP4DrmCU56iXG89qVV3AoO5fGSYl0r+c7TY79/GwM/nsn3v72Xhq2qsGMT5ZRqWo0edmFqLobOH8ycb65QBz4edEWdm1JI6V+Ja67p7fVcXza3vRMHC4X7Wslc0+3DuYcnGGcTCQYiX7VfcNWGWzW9QHsVLsGT13Rk01pR3h6zkLSsnP4Zv1vluU5W5WqxfLMezfwf6+MoKjIwT9v+pCHR7/LlrX7OLg3/fc3IJcXni8pawV5RaxesoUJ476gdqMqvPL5WHPe7TztOJYBQGhAgFcO6ZufruEVxL82EvUkOH5Fc193N2R2WTOeP7RlU27u0JYpv2zg9i9m8szchWQU+E5vQhGhS9/mvPPdfdz2zwHs2X6YlYu2kJ9byI7NqRxNy2JM7wmsW7HT6qjlprjYwZjeL/LYzZMIiwjm8TdHExwaaHUsn7fh4CH8RRj75Uy+XrfZ6jh/YuYSG15DQgahRcug4C0UQcQPQq1p3Hpv945kFhby5a8bGdG6GbGhIZbkOB8Bgf4MuLYDvQa3Zsany/jq/SXcOfh1WnaoTVRsGJWquo+UD+w6SlZGHo1bp3jdENP5yjiSg72wmJce+pKs9DyaXVKbf7x6DVGx3nWuyFet2LOfplUqc2XLxnSu7V19KMEUOMPLSOTjaMlacGWjQZdh1dutTYSn+vXE6VImr1lPQngY1aKjKHE5uapFE4tSnZuQsCCG3dKNK65pz9eTljLtwx8pzC/i309Op/+1HVjxw2YWzVzLp0sfITQ8CFWtEIVuw6pdPDz6PcRPCA4OYNyE4XS9onmF2DdvkF1oZ3PaEe64tB1DWza1Os4pmQJneBWxhUH0q2j6UMh5GFfEU4hmIQHlv5CiTYRnruiJS11MXLycmrExVImOYEjzxr8vEeJLwiKCufbOXgwc1ZEZny5j1uc/8/gtk0isGkOPwa1+72v59NhPqNu0GiNu625x4nOTn2enML+Iyf/5AafTRZNWNRk3YTgJlb1zoVtftWpfKgr42YS8oiLCg4KsjvQnpsAZXkcCGkHEQ2juM1AyHLWFQty3iJT/KWM/m43n+vfGpcqMDVvo37Q+NhGfPsqJiA5l5B09ufrmriz7fhMzP13Ot5+tYP7UNXTp1xxwz8oE92SUt56ZSfeBLWnQPNnK2KUy8bFprFq8lcJ8Ow6Hi7GPD6LfiEt89mflzVbs2UeAzcari5bToFIi3bxw1rEpcIZ3Ch0FxcuhaDGEP2dJcTvOz2Zj/IA+uBQmLl6BzWZjfeohejWow5DmjS3Ldb4CAv3p0rc5Xfo2Z9eWg8z8bAULZ/xKkb2EtP0ZOB1OajZIYuHMX2nQIpkGzZPJzSrgx3kbadWhDolVYywvHFvX7+frST96OrpsZOXCLaQfyaF+s+o8+OIwqqbEW5qvolJVlu7YS9sa1Rh76SU0qlzJ6kindMYCJyIfAFcAR1S1iee+ocATQEPgb6q62nN/CvAbsNXz8BWqeuspnjMWmAKkAHuAq1U187z2xKhQRASixqPpV0PeeDSoLTiPQUAzS95U/Ww2nh/YB1Xl1YXLSImNpsRZcZaqqdWgCnc/PYQbHriMBdN/4ce5G/n4tfkAxCZEsG7FTkJCA8nPtTPxn9MIjwzmi5WPA7B6yVZUoW2X+mWeMz/XzpLZ62nVsS5RMWH8NHcjP83byOJZ6wBo0iaF6+7pTY+BLc2abmVo86Ej7MnI5Ib2rWiTXM3qOKdVmiO4ScAbwMcn3LcRGAK8fYrtd6pqizM85/8BC1R1vIj8n+f2Q6XIYlxExBYFMW+i6UPR9OvAtR+JmgAhAyzJ42+z8cKgy1BVvtu8jYLiEgAOZGVTNSrS8qOZCyEiKpRBozsxaHQnMo7msnrJVlYu3sLSORuYN3U1fv42GrZMpnqtBDas2k3tRlWY8s4inA7n7wXusze+JzounH4j2gGwfeMBIqNDqVQttlQZCvKKcLlchEeGkJdTyIRxX9BrSGs69m5CVkYeE/85jfrNq7Nv+2EKC4qpVC2GXoNb031gS5Kqx5XZ/43xPzM3bsFPhNSsXPKLiwkL9M5LLqQ0nQ08R2bfHj+CO+H+RcADJx3B/Wm7UzzfVqCrqqaJSBKwSFXP+OdfmzZtdPVqs5LxxUaLfkQzx7i7ncR+gc1m7cKKDpeLB76ezezN27ihXWumrtvEiNbNuLdbxe1nWFLsYNOaPaxavIWVi7ZyYPfR37+WlBxHcu1EmrRJoU7jqnz2xvckJcdx37+GAnB9zxdo0DyZh14aDsCDI9+iebvaXHtnLwBGdxvPpZc3Y8y4vgAMbPYog6/vzPBburF90wFeeOBzEqvGUJBrZ++OI6hLCQ4NpEvfZvQc3LpCXt7gzZwuF10nvkdoQAC5RcUsvvtGAvzK/mhZRNaoapuzekwZFLhNwDYgB3hUVZee4vmyVDX6hNuZqnrG9hWmwF28NP8jNPdZCLsNCb8NXOmIn3VrTzlcLh6ZOY/p63+jVfUqjB/QhxqxF8+6bJnHctmx6SA7NqeyY1MqOzanciT1fw2zY+LDiYoNIyo2HIDouDCSa1ciOi6cH+duICk5jkYta1BYUMyPczcQGR1KQlIUhQXFbFt/gLycQo6mZeFy6e/PV6dxVeo0qkrdJlVp2bEuwSHeedRQ0S3fvY+/fzqVV4b05dI6KeU2e9IbClwQEK6q6SLSGpgONFbVnJMeV+oCJyI3AzcDJCcnt967d2/p986oMFQVzXkECr8C/0aghUj8TESse5NzqfLigqV8sHwNfRvV4/mBffhy7SYua1iXuLBQy3JZJScznx2bD7JjUyqHDmSQnZFPVnoe2Rn5ZGfkkZdj/8vHh4QGEhwWREhoINVqJVDXU9DqNKlKXGLFGAKuCB6eMZc5m7ez/P5bCQ4ov3mK51LgLmg6VS0CijyfrxGRnUA94OTDrsMiknTCEOWRv3jOd4B3wH0EdyHzGr5DRCDyCdSxG0o2QMT9lhY3cF8n91DPS4kLDeXFBUs5lJPHpkNHyMwv4I4u7S3NZoXImDBadaxLq451T/n1kmIH2Zn5ZGfkIwLBoe5iFhIaRGCwv+kL6QOO5eUzc8MWQgID+PLXDYzy8vUTL2iBE5EEIENVnSJSC6gL7DrFpjOA0cB4z7/fXMgcRsUkEgjRb6DpQyD/QzS4P1ACtsqW/nV/Y4c2xIeF8o+Z80iJi2FoS/dAhy9fK1cWAgL9ia8URXwlc8G1r/pk1VpKXC66pVSneoz3/xzP+CeTiEwGlgP1ReSAiIwRkcEicgBoD8wSkbmezS8F1ovIOuAr4FZVzfA8z3sicvzwcjzQS0S2A708tw3jjMQvDol5E1xZaOYN6NE+UDjZ6lgMat6IN4cN5GB2Dtd+/CWb0w4z7MPPfWZNOcM4k/ziYiavXkev+nV4fWh/utb1vgu7T3bGIzhVHXGaL319im2nAlNP8zw3nvB5OtCjlBkN4w8koBFE/QvNvhf8G6GBvSzrWXmiLnVrMunaq7jl8+mM+e/XVI6MICLY+9oXGca5mLp2E9n2Ivo1KfvrHS8UM+ht+CQJ6Qdht4FjM2L/0j0JxWH90VKLakn8d/TVBPn7syc9k0LPtXJLduwh115kcTrDODcOl4tJP/9CWGAAExct95mFc02BM3yWhN8DwQPRvFfRrLFo+pWoY5/VsaidEMeU64dTMy6G26Z8w8s//MRdX83kxQV/umLGMHzC5NXrSM3K4Z+XdeNfA3r7zLll04vS8Fnudl7Poa4MKPoBQoaCX3WrYwFQKTKcz/5+NY/OnM/bP63kkhrVuK3TJYD78gJfXI3AuDil5xfw2qJldKyVzKBmjXymuIE5gjN8nEgAEj3RfW1c4TdQsg51HkadR8/84DIWEhDAhMGXM65nZ1btS+WWz6ezNyOL26fM4J2fVlodzzBK5eUffiKvqBhBcPnI0ORxpsAZPk9sYUjMu+CXiGbchGaMRLPu8YrzBCLCmPZteGfEINJychn6/n8pcjgI88K1swzjZOsPHmLq2o20Tq5KzfgY/HzsWkXfSmsYp+G+fOADsPmDKx/CbvGqoZTOtVP4asw1JISHsWL3PhxOJ6rK6n0H+GX/QavjGcafuFR5evZC4sNDeXv4QB7t083qSGfNFDijwhD/ZPeRHHbIm4C6ctGiFag6rI4GQI3YaKbcMIJu9Wrz3LzFPPTNHCYs+JHHZ33vc0M/RsX36aq1rD94iCtbNPHK1bpLwxQ4o0KRgCZI9Ovg2IFmXI9mjoaCj6yO9bvwoEDeuLo/d17ajhkbtpCRX8i93TpiE6HE6eRwbp7VEQ2DLYeP8sL8JYQGBLA/M9vqOOesVM2WvYVZTcAoLS2cjmaPg4DmEPMhNlu41ZH+ZMWe/Tw4fTaZBXbG9exMZkEh/129jpm3jCIxwvvyGhcHe4mDK9/7jGy7ncmjhxETFuIVR3Dn0mzZHMEZFZKEDEIiHoKSdZDzJC5XAZr/Maouq6P9rl1Kdb65eRSdaiXz7NxFrNmXyvDWzUxxMyw1fv5idhzL4Lkr+lA9Ntoritu5MgXOqLAkbIz7YnD7N5B5k3s9uZI1Vsf6g9jQEN4cNpBH+3TllwNpTF27iRV79pOalcOISVPYeviY1RGNi8iCrTuZvGY9AEVO7zh3fT7Mhd5GhSbht6NaDPn/gaDLIOCsRjjKhYgw6m8taZNclXunfcffP/mKgU0bkllQSFhQgNXxjIvEgaxs/jFzHo0qJ3Jftw50qp1idaTzZo7gjApPwu+GsBuhaA6a+zyu4g24cl/1iuvkTtSwciLTbhzJkBaNmb7hN8ICAyjw9LJ8bdEyVu09YHFCo6LKsdu5/tOpOJwuXh7Sl851anrVZTbnyhzBGRWeiED4g6gWQsEH7vNyzkMQdh1IrNXx/iA0MIDn+vemc+0Unpz9A0Pe/Ywb2rdm1qatuFRpW6Oa1RGNCsZe4uDWz79hX2Y2NWNjSImNtjrSBWMKnHFREBGI+CeqdiicCmG3I7bY34/ivO2v1csb1eOSGtV4es5C3v5pFfUS4+nuWX9rc9oR0gsK6FwBhpAMazlcLu6dNotf9h9kXI/OdK6T4nWvhfNhLhMwLiqqTjT7AbDPQiIeRV2ZoDlIxCOIeOeI/fwtO3hy9gIy8gu5qUNbdqVnsDY1jfljbyA4wPyNapwbVeX+r79j1qZt/POyblzbtoXVkf6SuUzAMM5AxA+JegGCeqC5z0DJr6CF4BVLpp5arwZ1+PbW0Qxo2pC3flrJ9qPpPNijM8EB/rhUmb5uM8VOp9UxDR+iqrz0w4/M2rQNf5uNPg3rWh2pTJgCZ1x03CsQvAZBXaB4GfjVRURQVxaqJVbHO6XokGDGD+zDOyMGYS9xMG76HJ6Zs5Dvt+zgoRlz+X6L9Yu9Gr7Bpcpz8xbz7rLVDG3ZhC9vGE5CeJjVscqEGaI0LlqqxWjWfVA0D8LugqL54F8TW/SrVkf7S3lFRbz8w09MXrOeqJBghjRvxH3dO+Fvs7Fy7wEqRYRTowJNFDAuHIfLxdgvZrBo+25GtmnOo5d185m1Cc0QpWGcBZFAJPpVCB4I+RPBFgvBV1od64zCg4J47PLuTLvxGmrFxfD+8jUM++Bzft1/kCe+W8BD38yxOqLhhYodDu75ahaLtu8mOiSYMe1b+0xxO1emwBkXNRF/JOp5CBkBxT9B8QJUXWjxStTl3Y2PG1ZO5LPRVzNh0OUcyctj+KQp1EuI477unQAoKC7hs1VrKXL4fkcK4/zk2O2M/vQr5m/dwSN9urL0npuoGh1ldawyZ6ZgGRc9ERtEPoFKKBS8jzqzoHghBA9Cop60Ot5fEhH6N21A9/q1eHPpz0xa8QtLd+3ljkvbERkSzFNzFtKwciKtqlexOqphkf2Z2Qz/8HOO5RdwX7eOXPe3llZHKjemwBkGx6+TGwe2cDTvNQhoC+F3Wh2r1MICA3mgR2eubNGE5+YtYvz8JVSLjuTOLu1oVrUyAJPXrCMmJITLGtWzOK1RXuZv2cEjM+fhUmVI80aM6eB9rerKkplkYhgn0fz30dznIagHRL0Mec8jIVcjAY2sjlYqqsqSnXt4beEyNh06Qs24GO68tB0frfyVypERTLzqCqsjGmWsyOFgzGfTWLUvlcaVE3n1yn4k+/jEozKZZCIiH4jIERHZeMJ9Q0Vkk4i4RKTNCff3EpE1IrLB82/30zznEyKSKiJrPR99zya0YZQlCRuDRD4ORQsgczTYF0DxKqtjlZqI0KVOTabeeA2vX3UF/jYb9309m8LiEnrVr42qcjgnj+Effs7GtMNWxzUusF3HMrj6g89ZtS+VatGRfHTdVT5f3M5VaYYoJwFvAB+fcN9GYAjw9knbHgP6q+pBEWkCzAWqnuZ5X1HVCWcX1zDKh4SOBIlAsx8Gv2Q0qDcCqCsHsUVaHa9URITeDevSo35tvtu0jdeXLOeB6XP4eOVa+jdtQHahnajgYAD3ygWBAQT6m7MWvuyJ7xYwbe0mQoMCeXPYALrVrVWhWm+drTMewanqEiDjpPt+U9Wtp9j2V1U96Lm5CQgWEd9dLc+4qEnIACTmXXAdgoxhuOzL0GN90fyPz/xgL+Jns9G/aQNm3Xodz1zRi2P5+Tw7dxGhgQFsSjuM0+Xi+flL6P/2pzhc3rMgrFF6GQWF3PPVt0xes56woEC+uelauterfVEXNyjbSSZXAr+qatFpvn6HiFwHrAbuV9XMU20kIjcDNwMkJyeXSVDDOB0J6gCx/0Uzb4KsOyCoPQS2tzrWOQnw82NoyyYMbNqAaes288GKNdw9dRbJMVFcWqcmI9s2x9/m/pt32rpNtE9JJikqwuLUxl/JtRfx2KzvWbZ7H/lFxfz9klbc170jQeZIHCjlJBMRSQG+VdUmJ92/CHhAVVefdH9jYAbQW1V3nuL5KuEezlTgaSBJVW84Uw4zycSwijoPohljwLkfiX4JCe6D2mdD4KWIzTfbHDldLr7fupP3l69mXeohYkJDGNmmOT3q1eLK9ydzT9cO3NLpb7hUUVX8bOayWW+yfPc+/jFzHgezc6mbEMvLQ/pRLzHe6lhl5lwmmVzwMi8i1YCvgetOVdwAVPXwCdu/C3x7oXMYxoUkflUgbjKaeQuadRcaNhby30TCx0L4HVbHOyd+nia7vRvUYc3+VN5fvoY3lqzg3WWruLxRPVpVc1879/Oe/Tw8Yx7vjBhUod9AfYGq8uHPvzBzwxY2HzpClagIHuzRiTHt21z0w5GnckELnIhEA7OAh1X1p7/YLklV0zw3B+OetGIYXk1s0RA7yd2/Mv8NCB6Eht7knnyiLq9dbudMRIQ2ydVok1yNnccymLRiDdPX/8asTVtpUTWJdjWr06hywu/9LZfv3keRw0GXCrLqs6/IKrTznyUr+Gjlr/iJcH/3Toy+pKUZjvwLZxyiFJHJQFcgHjgMPI570snrQAKQBaxV1T4i8ijwMLD9hKforapHROQ94C1VXS0inwAtcA9R7gFuOaHgnZYZojS8gaoDzXkCCr+A4H4Q+Rhk3oqEDkdCBlsd74LIKrQzff1mpqzZwK70DCKDgxjYtCHDWjXlhQVLScvOZeYtoxARUrNySIqKqPB9Da0yZ/M2np6zkPziYuwlDvo3acADPTtTKSLc6mjl6lyGKM2F3oZxDlQV8t9B814GvwZgi0DCbkCCT3npp89SVVbvS+XzNeuZu2UHJU4nLasl0aNebYa1bkpYYCBdJ75H59opPNe/t9VxK4zUrBzS8/P5dtNWJq9eT7HTyaW1U3igR2fqV7o4h4lNgTOMcqb2BWj2/UAYEvsOEtAYLV4J/g0RW8WagZiRX8DX6zcz5ZcN7M3IIsBmo32tZKpERtCtXi261q1FdqGdUR9/ycO9u9C+ppn1fLZUlflbdnDXV9+igJ8IVzRpwM0d21InIc7qeJYyBc4wLKAlW9DMW8GVAZFPQu7TENwbW9R4q6OVCVVl/cFDzNm8nTm/beNgdi4BNhsda9egVbUqLN6xm//r1YVmVSuzOe0I7y1fzb3dOlI9puJ3rz9Xj8ycz7YjxygoLmbHsQzCAgMY3KwxN3dsS6XIi2so8nRMgTMMi6jzGJp1O5SshZChEH4vNr94VLVCT8Q4XbG7JKU6neuk4Gez8faPK5lxyyhiQ0NYsmMP61LTuKVj24u6a8qyXXuZt2UH9SvFM2vjVlbtSwWgWZXKjGzTnMsb1zOTR05iCpxhWEi1CM3+B9hnQvAAiHwGch5B/Gsj4bdbHa/MqSobDh5m9m/bWLRtN7vS3Q2QqkRFcGmdmnSuncKv+w/y9frN/HTvzYgIk9es42huPnd17WBx+rKVmpXDnN+2MaBpQ5bt2sdbP678/f+ndnwsVzRpQL/G9c1K7H/BFDjDsJh78slbaN4r4N8C/CojAY2Q8FutjlbuDmRls3TnHpbu2MvyPfsoKC4hwGajebUkOtRMpkW1JGZu2EJqdg6fXDcUgH/NW0xUSDC3d74EcK9C7YtHekdy85i6dhN9G9ensKSET1eu5cu1Gwnws1HidJEUGU7fRvUZ0LQh9SvFV+ij/AvFFDjD8BJqn4Nm/x8QAtGvYgu6BC3ZBDiRgGZWxyt3xU4nv+w/yNIde1i6cw/bjhzj+DtPzdgYWlRLolnVyvywbSfJMdE8drl7Nmrvf39Iu5TqPNWvJ+Be36xOQhw142Is2pP/ybHbcSlEhwSTWVDIk7N/oH+TBiSEhzFvy3beXbaakAB/CkvcP7uQpQAACsxJREFUK6rXiI2mS52a9GlYl1bVq5jLKs6SKXCG4UXUsQPNvAOce5GIB1D7D+A6hsTPQsT3jkoupFx7ERsOHmJdqvtj/cFDpOcXAOBvs1E/MZ6UuBiyCgqpXymewc0bUzUqgksmvMX17Vpzf49OjJs+h8O5eXw06ioAZmz4DYABTRsCsPNYBoF+NqrHuIf9XKp/WVScLhfq+f4Aaw+kER4U+PvsxRe/X0qzqpXp07Au9pISWox/g/5NG1A/MYGth48y57ftuNSFw+V+T60eHUW7mtVpk1yVS2pUN309z5MpcIbhZdSV5z4vVzQHArtC+Fhsgc1RdQElmMU23FSV1Owc1qceYmPaYbYdSWfXsQxSs3N+30aAypHh1IiNoUZsNIdz8vDzs3FVi8YkhIfx1OyFhAT68/Eo93DnsA8+JywogA9GXgnAkHc/Iykqgn9fPQCAwe9+Rq34WF4afDkAPd/4gJbVknhx0OUUOxx0nfgezapUZnDzxhzNy+fVhctIigwnLCiQ7UfTySsq/j1bYkQY9RLiqZsYR/OqSbRJrkpCuG/2KPVWpsAZhhdSVSj4EM19EfySkeg3oGgBap+NxH7iM+vLWaGwpIQ96ZnsPJbBrmMZ7ErPZHd6Jkdy88goKDzlY2JCQwgJ8EcVAv38iA0LITjAn/S8AoID/KkeE02xw8nOYxmIQGRwEMUOJ0fy8lFVHC4XWYX2Pz2vnwjx4WHUiI2mbkIcdRPjqJsQT92EOKJCgsv6v+KiZwqcYXgxLV6FZt0DmgchI0HzkcgnzASDc1TidJKeX8CRvHyO5uZzJC+Po7n5ZBQUYi9xYHc4PP+WYC9xUORwUlhSgkuVID8/Avz9CPL3J8jfj0A/z7/+/kQEBZIYEU5CeBiJEWEkhoeRGBFOTGiIOW9mIa9YTcAwjFOTwLYQ9zWadTcUvAehI4Fi1JmN5r2KRIxzN3Q2SiXAz4/KkRFUjjTntoxT883254bho8QvEYn9GEKvh4LP0PSrUPt3YJ8LrmNWxzOMCsUUOMMoZyIB2CIfRqLfBtdRyH0JwseCX20AtOhHVB0WpzQM32cKnGFYRIK7IXEzIbAt5I5Hs8biKvoZzbwBCj62Op5h+DxzDs4wLCR+CRDzHhRMQnNfgpINEHYnhF4DgLqyQSLNRBTDOAfmCM4wLCZic68lF/clSCjkv4Hm/RuXqxDNuB7NfsjqiIbhk8wRnGF4CQlo5J5lmfss5L8NRT9BUEckoAnguZ4OzNGcYZSSOYIzDC8itlBsUc8i0RPBeQDyPwDHXvekE/s3aNZY1JVndUzD8AmmwBmGF5Lgy5D47yCoG5o3Ac0YgTr2guaDhFgdzzB8gilwhuGlxC8eiX4diXoZHHsh/10I7AS4e1y6sv+JOg9ZnNIwvJcpcIbhxUQECbkCiZ8FQZ0h70U04xrUPhfsM8CZZnVEw/BapsAZhg8QvwQk+j9I1ARw7IKcJyDsRjg+AaVgqme9OcMwjjMFzjB8hPtoboDnaK4T5L2Opg/BVbQSzXsDzf/A6oiG4VVKVeBE5AMROSIiG0+4b6iIbBIRl4i0OWn7h0Vkh4hsFZE+p3nOmiLys4hsF5EpIhJ4frtiGBcH8UvEFvMmEv1vcGVD5igIvATC7wJAnWmofYHFKQ3DeqU9gpsEXHbSfRuBIcCSE+8UkUbAcKCx5zH/ERG/Uzzn88ArqloXyATGlD62YRgS3Ms90zJ0NNinQ8ZwtHAmmv8BmnUv6sqwOqJhWKpUBU5VlwAZJ933m6puPcXmA4HPVbVIVXcDO4C/nbiBuK9U7Q585bnrI2DQWWY3jIue2MKxRf4DiZsGflXQ7PuhZBtEPY/YYgHQwm9QV84ZnskwKp6yOAdXFdh/wu0DnvtOFAdk6f9app9qG8MwSkkCGiGxXyCRj4Njg/uIDlDHPnerr4JPLU5oGOWvLFp1naqP0MnLhpdmG/eGIjcDN3tu5onIqY4aL7R4oKIszmX2xTuV8b78Crxzwu2xno8yUZF+LlCx9qci7Uv9s31AWRS4A0D1E25XAw6etM0xIFpE/D1HcafaBgBVfYc/vlLLnIisPtul0b2V2RfvZPbFe1Wk/alo+3K2jymLIcoZwHARCRKRmkBdYOWJG6i7a+xC4CrPXaOBb8ogi2EYhnGRKu1lApOB5UB9ETkgImNEZLCIHADaA7NEZC6Aqm4CvgA2A3OAsarq9DzPdyJSxfO0DwH3icgO3Ofk3r+QO2YYhmFc3Eo1RKmqI07zpa9Ps/2zwLOnuL/vCZ/v4qTZlV6kXIdEy5jZF+9k9sV7VaT9uaj3RY6vMWUYhmEYFYlp1WUYhmFUSKbAnUBEokXkKxHZIiK/iUh7qzOdKxG519NKbaOITBaRYKsznY3TtIeLFZH5nvZu80UkxsqMpXWafXnR83u2XkS+FpFoKzOW1qn25YSvPSAiKiLxVmQ7W6fbFxG509NmcJOIvGBVvrN1mt+zFiKyQkTWishqEfHW00K/E5HqIrLQ8x68SUTu9tx/1q9/U+D+6DVgjqo2AJoDv1mc55yISFXgLqCNqjYB/HC3T/Mlk/hze7j/AxZ42rst8Nz2BZP4877MB5qoajNgG/BweYc6R5P4874gItWBXsC+8g50HiZx0r6ISDfc3ZiaqWpjYIIFuc7VJP78s3kBeFJVWwCPeW57Owdwv6o2BNoBYz0tIM/69W8KnIeIRAKX4pnNqarFqpplbarz4g+EiIg/EMpprjP0VqdqD4f7jecjz+c+097tNK3u5p3QyWcF7mtBvd5pfi4ArwDjOE3DBm90mn25DRivqkWebY6Ue7BzdJr9USDS83kUPvA+oKppqvqL5/Nc3AcaVTmH178pcP9TCzgKfCgiv4rIeyISZnWoc6Gqqbj/8twHpAHZqjrP2lQXRCVVTQP3iwBItDjPhXIDMNvqEOdKRAYAqaq6zuosF0A9oLNnpZPFItLW6kDn6R7gRRHZj/s9wVdGCgAQkRSgJfAz5/D6NwXuf/yBVsCbqtoSyMd3hsD+wDM2PRCoCVQBwkTkWmtTGaciIo/gHpL5zOos50JEQoFHcA9/VQT+QAzuobEHgS88zeF91W3AvapaHbgXH7reWETCganAPap6Tt3CTYH7nwPAAVX92XP7K9wFzxf1BHar6lFVLQGmAR0sznQhHBaRJADPvz4zfHQqIjIauAIYqb57vU5t3H9IrRORPbiHWn8RkcqWpjp3B4Bp6rYScOHu5+irRuN+/QN8ifdee/wHIhKAu7h9pqrH85/1698UOA9VPQTsF5HjDT174O7G4ov2Ae1EJNTz12cPfHTCzElm4H7Bgo+3dxORy3B38xmgqgVW5zlXqrpBVRNVNUVVU3AXiFae15Mvmo57KS9EpB4QiG83Kz4IdPF83h3YbmGWUvG8Z70P/KaqL5/wpbN//auq+fB8AC2A1cB63L/oMVZnOo99eRLYgnth2k+AIKsznWX+ybjPH5bgftMcg7ul2wLcL9IFQKzVOc9jX3bgXlZqrefjLatznuu+nPT1PUC81TnP4+cSCHzqed38AnS3Oud57k8nYA2wDvd5rNZW5yzFfnTCPTlm/Qmvj77n8vo3nUwMwzCMCskMURqGYRgVkilwhmEYRoVkCpxhGIZRIZkCZxiGYVRIpsAZhmEYFZIpcIZhGEaFZAqcYRiGUSGZAmcYhmFUSP8P64RD3VjKZGQAAAAASUVORK5CYII=\n", - "text/plain": [ - "<Figure size 432x288 with 1 Axes>" - ] + "metadata": { + "needs_background": "light" }, - "metadata": {}, "output_type": "display_data" } ], @@ -419,17 +177,10 @@ "\n", "fig1, ax2 = plt.subplots(constrained_layout=True)\n", "\n", - "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n", - "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n", + "# p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n", + "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5])# , linestyles=\"dotted\")\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { -- GitLab