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Created June 20, 2013 19:52
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{
"metadata": {
"name": "LinearRegression"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Stochastic gradient descent and on-line mean estimation\n",
"-------------------------------------------------------\n",
"\n",
"Readings :\n",
" \n",
" - An overview of practical aspects and algorithms based on SGD and theoretical convergence proofs for learning rates from [Bottou (2004)](http://leon.bottou.org/papers/bottou-mlss-2004). It may also be worth having a look at this more recent and [hands-on approach](http://leon.bottou.org/papers/bottou-tricks-2012) from the same author.\n",
" - The `sklearn.linear_model.SGDClassifier` and `sklearn.linear_model.SGDRegressor` [documentation](http://scikit-learn.org/dev/modules/sgd.html).\n",
" - The wikipedia page about [Tikhonov regularization](http://en.wikipedia.org/wiki/Tikhonov_regularization), the original paper which coined the term ['Ridge Regression'](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.3796) and nice [slides](http://web.as.uky.edu/statistics/users/pbreheny/764-F11/notes/9-1.pdf) about the ridge regression as a solution to ill-posed problems, the bayesian analogy and model selection. \n",
" - The analogy between SGD early-stopping and regularization is discussed in that paper by [Zhang (2004)](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.58.7377) and that one by [Friedman (2004)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.3.4934&rep=rep1&type=pdf).\n",
" - The original [lasso](http://www-stat.stanford.edu/~tibs/lasso/lasso.pdf) paper and the [LARS generalization](http://www.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf) for efficient computing of the regularization paths.\n",
" \n",
"$n$ points $(x_i)_{i=1,\\ldots,n} \\in \\mathbb{R}^2 \\hspace{.3cm} $ sampled from $X \\sim \\mathcal{N}( \\mu, \\Sigma = \\text{diag}(1,1))$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"mu = [0, 0]\n",
"cov = np.diag([1, 1])\n",
"n = 30\n",
"x_n = np.random.multivariate_normal(mu, cov, size = n)\n",
"x_lim = [-3, 3]\n",
"y_lim = [-3, 3]\n",
"\n",
"x_grid, y_grid = np.meshgrid(np.linspace(*x_lim, num=100), np.linspace(*y_lim, num=100))\n",
"least_squares_grid = np.reshape([np.linalg.norm(x_n - [x, y]) for x,y in zip(x_grid.ravel(), y_grid.ravel())], (100, 100))\n",
"\n",
"def plot_ls_contour(ax, x_lim, y_lim, ls_grid=None, x_n=None):\n",
" ax.vlines(0, y_lim[0], y_lim[1], alpha=.5)\n",
" ax.hlines(0, x_lim[0], x_lim[1], alpha=.5);\n",
" \n",
" if ls_grid is not None:\n",
" cont = ax.contourf(x_grid, y_grid, ls_grid)\n",
" #plt.colorbar(mappable=cont, ax=ax2);\n",
"\n",
" if x_n is not None:\n",
" ax.scatter(x_n[:,0], x_n[:,1], color=\"grey\", alpha=.9, s=10, label=\"$(x_i)$\")\n",
"\n",
" ax.set_xlim(x_lim)\n",
" ax.set_ylim(y_lim);\n",
"\n",
"f, (ax1, ax2) = plt.subplots(1,2)\n",
"f.set_size_inches(12, 6)\n",
"\n",
"plot_ls_contour(ax1, x_lim, y_lim, x_n=x_n)\n",
"\n",
"plot_ls_contour(ax2, x_lim, y_lim, ls_grid=least_squares_grid, x_n=x_n)\n",
"\n",
"mu_ols = np.mean(x_n, axis=0)\n",
"ax2.scatter(*mu_ols, marker=\"x\", color=\"grey\", alpha=.75, s=80, linewidth=3, label=\"$\\mu_{OLS}$\")\n",
"ax2.scatter(*mu, marker=\"x\", color=\"k\", alpha=.75, s=80, linewidth=3, label=\"$\\mu_{Oracle}$\")\n",
"plt.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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iGvCNrDfwyLDf4cb4U5otl+tM/0Q68Y3hlygITqcT77zzDurr61FVVYW//e1v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\n",
"text": [
"<matplotlib.figure.Figure at 0x3754a10>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Stochastic gradient descente, equivalent to on-line mean estimation\n",
"\n",
"At step $i$ , the error between $x_i$ and the current estimation $\\hat{\\mu_{i}}$ is\n",
"\n",
"$$||e||_2^2 = \\sum \\limits_p (\\hat{\\mu_{i,p}} - x_{i,p})^2$$\n",
"\n",
"and the stochastic gradient descent step with a learning rate $\\eta$ is : \n",
"\n",
"$$\\hat{\\mu_{i+1}} = \\hat{\\mu_{i}} + \\eta \\hspace{0.1cm} w$$\n",
"\n",
"with $w \\in \\mathbb{R}^2 \\\\ $ and \n",
"$$w_p = \\frac{\\partial ||e||_2^2}{\\partial \\mu_p} = 2 (\\hat{\\mu_{i,p}} - x_{i,p})$$\n",
"\n",
"so\n",
"\n",
"$$\\hat{\\mu_{i+1}} = \\hat{\\mu_{i}} - \\eta (\\hat{\\mu_i} - x_{i}) = (1 - \\eta) \\hat{\\mu_i} + \\eta x_{i}$$\n",
"\n",
"compared to the online mean estimation :\n",
"\n",
"$$\\hat{\\mu_{i+1}} = \\frac{i}{i+1} \\hat{\\mu_{i}} + \\frac{1}{i+1} x_{i} \\Rightarrow \\eta = \\frac{1}{i+1} $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def online_gradient_descent(x_n):\n",
" n = len(x_n)\n",
" mu_path = np.zeros((n,2))\n",
" mu_path_0 = [0, 0]\n",
" for i, x in enumerate(x_n):\n",
" mu_path[i,:] = mu_path_0 - (mu_path_0 - x) / (i + 1)\n",
" mu_path_0 = mu_path[i,:]\n",
" return mu_path\n",
"\n",
"descent_x_n = online_gradient_descent(x_n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f, ax = plt.subplots(1,1)\n",
"f.set_size_inches(8, 8)\n",
"\n",
"plot_ls_contour(ax, x_lim, y_lim, ls_grid=least_squares_grid, x_n=x_n)\n",
"\n",
"ax.scatter(*mu_ols, marker=\"x\", color=\"lightgreen\", s=80, linewidth=3, label=\"$\\mu_{OLS}$\")\n",
"ax.scatter(*mu, marker=\"x\", color=\"white\", s=80, linewidth=3, label=\"$\\mu_{Oracle}$\")\n",
"\n",
"ax.plot(descent_x_n[:,0], descent_x_n[:,1], color=\"k\", alpha=.75, label=\"$(\\hat{\\mu_i})$\");\n",
"\n",
"plt.legend()\n",
"\n",
"i = 0"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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IgjdDOVR3+/aVs2nTQLOD91iqhDNmYn80cdwMEivCVyymIMmeXjsJsaBPPSt8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\n7rzzTsaMGcOECROYNWsWdXV1fjcpkB555BFOO+0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"text": [
"<matplotlib.figure.Figure at 0x3754890>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import itertools\n",
"\n",
"f, ax = plt.subplots(1,1)\n",
"f.set_size_inches(8, 8)\n",
"\n",
"for i in range(200):\n",
" permutated_x_n = np.random.permutation(x_n)\n",
" descent_x_n = online_gradient_descent(permutated_x_n)\n",
" ax.plot(descent_x_n[:,0], descent_x_n[:,1], color=\"k\", alpha=.1)\n",
"\n",
"ax.vlines(0, y_lim[0], y_lim[1], alpha=.5, color=\"blue\")\n",
"ax.hlines(0, x_lim[0], x_lim[1], alpha=.5, color=\"blue\")\n",
"ax.set_xlim(x_lim);ax.set_ylim(y_lim)\n",
"ax.scatter(*mu_ols, marker=\"x\", color=\"lightgreen\", s=80, linewidth=3, label=\"$\\mu_{OLS}$\");"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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4iGq1+krOp2kastksDMOApmkYDAZoNBrwfR/ZbJZHlkj8KAKt1Wr4+OOPkclk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\nJOb2jQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x3d667d0>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"SGD, polynomial fitting, early stopping and analogy with regularisation \n",
"-----------------------------------------------------------------------\n",
"\n",
"$n$ values $x_i \\in \\mathbb{R} \\ $ drawn from $X \\sim \\mathcal{U}(0,1) $\n",
"\n",
"$$ y_i = f(x_i) + \\epsilon_i \\sim \\mathcal{N}(0, \\sigma)$$\n",
"\n",
"$X \\in \\mathcal{M}_{n,d+1}$ \n",
"\n",
"$W \\in \\mathcal{M}_{d+1,1}$ \n",
"\n",
"and $y \\in \\mathcal{M}_{n,1}$\n",
"\n",
"$$ X W = y \\Rightarrow W = (X^T X)^{-1} X^T y$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy.polynomial.polynomial import Polynomial\n",
"\n",
"n = 25\n",
"d = 3\n",
"x_n = np.sort(np.random.uniform(low=-1, high=1, size=n))\n",
"\n",
"w_oracle = [.1, .25, -.25, -.1]\n",
"print 'Oracle coefficients = {}'.format(w_oracle)\n",
"f_oracle = Polynomial(coef=w_oracle, domain=[-1, 1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Oracle coefficients = [0.1, 0.25, -0.25, -0.1]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"y_n = f_oracle(x_n) + np.random.normal(scale=.1, size=n)\n",
"X_n_d = np.vstack((np.repeat(1, n), x_n, np.power(x_n,2), np.power(x_n,3))).T\n",
"w_ols = np.linalg.lstsq(X_n_d, y_n)[0]\n",
"\n",
"print 'OLS coefficients = {}'.format(w_ols)\n",
"ols_fit_P = Polynomial(coef=w_ols, domain=[-1, 1])\n",
"\n",
"plt.plot(*f_oracle.linspace(), color=\"b\", ls=\"-\", lw =3, alpha=.7,label=\"$y=f(x)$\")\n",
"plt.plot(x_n, y_n, \"ko\", alpha=.7,label=\"$(y_i)_{i=1,\\ldots,n}$\")\n",
"plt.plot(*ols_fit_P.linspace(), color=\"g\", ls=\"-\", lw=2, alpha=.75, label=\"$y=\\hat{f}_{OLS}(x)$\")\n",
"\n",
"plt.legend(loc=\"lower right\", prop={'size':20})\n",
"plt.figsize(8, 6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"OLS coefficients = [ 0.07242179 0.40520583 -0.294731 -0.42844065]\n"
]
},
{
"output_type": "display_data",
"png": 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DlWebPEur6q1Iy07j0z2fmrPE++bqqnqZdy2yoNnWrfDRR2q9AFshwW2E2NhY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\nTgdHSrRZtWoV27RpE2OMMaFQyNasWaO13IABA1hVVVVHhka00OdcOn7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"text": [
"<matplotlib.figure.Figure at 0x46a6850>"
]
}
],
"prompt_number": 94
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$||e||_2^2 = (\\underbrace{\\hat{a_i}x_{i}^3 +\\ldots + \\hat{d_i}}_{\\hat{y}_i} - y_i)^2$$\n",
"\n",
"$$= \\hat{a_i}^2 x_{i}^6 + 2 \\hat{a_i} \\hat{b_i} x_{i}^5 + \\ldots = (\\hat{w}^T x - y)^2$$\n",
"\n",
"$$ \\frac{\\partial ||e||_2^2}{\\partial w} = 2 x (\\hat{w}^T x - y) = \n",
"2 \\begin{pmatrix} \n",
"1 \\times (\\hat{y}_i - y_i)\\\\\\\\\n",
"x_i \\times ( \\hat{y}_i - y_i) \\\\\\\\\n",
"x_i^2 \\times (\\hat{y}_i - y_i) \\\\\\\\\n",
"x_i^3 \\times (\\hat{y}_i - y_i)\\\\\\\\\n",
"\\end{pmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def linear_online_gradient_descent(X_n_d, y_n, learning_rate_func=None, return_path=False):\n",
" if learning_rate_func is None:\n",
" learning_rate_func = lambda i : 1 / float(i)\n",
" n, d = X_n_d.shape\n",
" if return_path:\n",
" w_path = np.zeros((n+1,d))\n",
" w_path_i = np.repeat(0, d)\n",
" for i, (x,y) in enumerate(zip(X_n_d, y_n)):\n",
" e_i = np.dot(w_path_i, x) - y\n",
" w_path_ip1 = w_path_i - x * e_i * learning_rate_func(i + 1)\n",
" if return_path:\n",
" w_path[i+1,:] = w_path_ip1\n",
" w_path_i = w_path_ip1\n",
" return w_path if return_path else w_path_ip1\n",
"\n",
"random_sampling = np.random.randint(n, size=n*3)\n",
"w_path = linear_online_gradient_descent(X_n_d[random_sampling], y_n[random_sampling],\n",
" learning_rate_func=lambda i : 1 / np.sqrt(i),\n",
" return_path=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 95
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"i = 75"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 96
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w = w_path[i]\n",
"fit_P = Polynomial(coef=w, domain=[-1, 1])\n",
"\n",
"plt.plot(*f_oracle.linspace(), color=\"b\", ls=\"-\", lw =3, alpha=.7,label=\"$y=f(x)$\")\n",
"if i > 0:\n",
" plt.plot(x_n[random_sampling][i-1], y_n[random_sampling][i-1], color=\"orange\", marker=\"o\", ms=10, alpha=.5)\n",
" plt.text(x_n[random_sampling][i-1], y_n[random_sampling][i-1], s=i, color=\"k\", size=14, horizontalalignment='right', verticalalignment='bottom')\n",
"\n",
"plt.plot(x_n, y_n, \"ko\", alpha=.7,label=\"$(y_i)_{i=1,\\ldots,n}$\")\n",
"plt.plot(*fit_P.linspace(), color=\"orange\", ls=\"-\", lw=2, alpha=.75, label=\"$y=\\hat{f}(x)$\")\n",
"plt.legend(loc=\"lower right\", prop={'size':20});\n",
"plt.figsize(8, 6)\n",
"\n",
"print \"At step {}, w = {}\".format(i, w)\n",
"i += 1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"At step 75, w = [-0.06094577 0.27709357 -0.09252499 0.03007913]\n"
]
},
{
"output_type": "display_data",
"png": 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CQ4C+/RNur7hYjbyrg7eXF6xcqVPltNTUVKKjo4mKigJg0qRJrFy50iJwf/31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\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x37bfd50>"
]
}
],
"prompt_number": 97
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n_runs = 100\n",
"w_runs = np.zeros((n_runs, d + 1))\n",
"\n",
"for i_run in range(n_runs):\n",
" samples = np.random.randint(n, size = 100)\n",
" w_runs[i_run] = linear_online_gradient_descent(X_n_d[samples], y_n[samples], learning_rate_func=lambda i : 1 / np.sqrt(i))\n",
" fit_P = Polynomial(coef=w_runs[i_run], domain=[-1, 1])\n",
" plt.plot(*fit_P.linspace(), color=\"orange\", ls=\"-\", lw=1, alpha=25.0/n_runs)\n",
"\n",
"average_w = np.average(w_runs, axis=0)\n",
"average_P = Polynomial(coef=average_w, domain=[-1, 1])\n",
"plt.plot(*average_P.linspace(), color=\"darkorange\", ls=\"-\", lw=2, alpha=1, label=\"$y=\\overline{f}_{SGD}(x)$\")\n",
"\n",
"plt.plot(*f_oracle.linspace(), color=\"b\", ls=\"-\", lw =3, alpha=.7,label=\"$y=f(x)$\")\n",
"plt.plot(x_n, y_n, \"ko\", alpha=.7,label=\"$(y_i)_{i=1,\\ldots,n}$\")\n",
"plt.legend(loc=\"lower right\", prop={'size':20});\n",
"#plt.plot(*ols_fit_P.linspace(), color=\"g\", ls=\"-\", lw=2, alpha=.75, label=\"$y=\\hat{f}_{OLS}(x)$\")\n",
"plt.figsize(8, 6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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ZHXFraGi8s2iLmS7w7xeC3bt345FHHrnyVOVhk/XK1rSkhRNGWipFfrnR7p2e\nIQE6FRJ1p+f32VA1ZXeKxJU7T91aqcIbY0DjGH+3C+wdzw+d2xq2EoIaydqdEUe3DWDtV4gvMbjA\nCRbFBe0Mf4YFIJIUeQ2AwfdXrgfKOySqDwF3HDj1Oo/llNhLbZgS+cbSdiekCInaW5NA/SQJ13BE\nlLZVXNLk2kz9gNslMUnVyvE8Zp7md57p5XWr7KJYLRHL2tYEEJ/mQskqcAGUHaALW+KLYl/2adjp\nZ/QX2YKWrE7joIlbQ0PjonC50tq7d+9ee6JWCF3aYNZeJ4G1yewdqFmfd4jHcoexc3QGn7wPu28e\nJTE5FXpqd990riAubJCsq28wSrQKHJhRGD7XTGUlJLH0bJ+hUt4WYxJvjun1RGZVe7NAY1wI1CSR\nhQ0SY1hDO0JWanynJN7eNpie72KGILGAqCZOcnNUa5s5knISslQRVPke0yKJ9t0u4zi7ec7uPFA7\nSOFZUOV1NBwgbvA6JJE4uXUsWKysbGfRcMUp8T0G0mEi7gwQHOHvhrTCRT4zAnEImAbPH6rv21vV\nPw1N3BoaGheFBx54AI899himp6dx5swZxHEM27bxyU9+cq1PbXVIYpLN0kGgeohksv5e3swvtxr8\nnCEe3dIHvbJzWru04Hskg8jDY6+/iEf+y/+F3ffce67xSxxQpFU9JL3ZWSq7C5vOFaWdD2GT9ef6\n0bTWG/okf38WaM3z3BVRmxnAyDFrEMzw/XaRBJnpYeYgP5BGvFaWPdRWljXqsCGpaolg8xuBwmax\nF10EjJjkmB0Eut/Da2YVmCJvTQCz+4HFV0jMwTyo8LbBXvOYCwk1nzzTzXMwHYmcE6biE19S3gCi\nEEhaTIcnIfeVGCCTB9yvmQFg0zLVLpP01bZwJKV/8dDEraGhcVHYvXs3Pv7xj+PP/uzPEMcxLMvC\n+vXr8e1vfxs33njjlRM1XwiSJE3jNsclHV0CNvwmVcGXE3HQ7rHmvOleRslnD/E4530R9v7tf0fQ\nnBNSyAJOCYFhY+8/PYPdH/p4+tncaZJ14wRJpHQde7OzfRc2rCOO2PK28KL4fbtpj3PUIokmMQBL\n6v95IMkx+m5MAPCFoEdFyFXigii/QSJYE23TlnAJcCWqTmIAhsy99rlgSCIwco2oPLcy6etz+0WY\nNiPzu+sAIkbITpek0i2WAjI9PA+7yGuUJDxe2OQxrawIz7rkvKSWjUCmfmX43Rm2iOvy/A4MUFOQ\nxGxNiyOQqHjKAAAgAElEQVQgbsqc9CUxazmPk94FQhO3hobGRePVV1/Fzp07l/3tiu+77kTYYI3T\nnWY0FAcktv67KF66XOnwFSdujZw7xGMl+EviAT4DtyFCL3M5Ebiuy+2qr4vaPQBKm4F1v8bMwVuR\nddhir3P1ILD4MksFoYwiNUwalygCNSxpd8oAsESANgPAZOtXz3sYdSYea9O5QVkwOCS9WExQwhqj\nW8Pia5keHjNq8RoFS7JI8GX7FlXbkRBqVCdZJgaJMTsM9IxID7gpae8ySdt0xGwlI+Qv87etLBDH\nzF5409Q01I9xYWLY/PzZbvm8Bf6OhERtGGJAkwBRnuelFP+Rx2tuGKyHn8+Y5gKhiVtDQ+OicTkE\napcdkS835UmSRn4dSbo1zlRpaevqZjyf97hnuadl34YhS+SlrVGGyZpv327kuv4RmKqn2yUxENaR\n808CJ/dy/wPvlzGTK9zuI5XirpKgqq8D9RMUlHnzspAxANh8f1gTs5V1QFZSy3HEDEXcIrl1vQ8o\nbSJZR02mxPPDbKuyRf8QyhSt1jSvu18XlfgCfc2DRUbdkZiXGKCgy5TI3HSkXm7y9UwvYG9Mo2SV\nmlb+6LkhZk7MAo1YrAK3iT1eg9hlrbpxmun+0OW5ZnqByjY+m1mJ7KU+bRjik77EmSFKPOjO8PyN\nDNvbIgOILSBoAV4TcBeA+sSq/ilp4tbQ0LhoXBV914AMsZDRkv6iKLK3MVqtHWZ0VNlBEr2UiLzU\nkEWNx7xQsla19tYkCTM7QP/zjv7pBx54AI/9+Z/TezysA5ELJ1PAAw/+Z+C6T6Qp2SQRc5hZZhfq\np4D6Eaae/RmSZByR7CKX78t0S3p7PcmrtJUEmIDuY61TrPNaGWBoD1DcSLFYMMdj5ob4sHIkrfox\nYPGXQPVl1tn9WireUqYuMFLbUUd6xk1bVOSKaCXqVtakVoHXximL6Uwfa/bFUabhkySd+BU1+OzN\ncl9xlJq/JCHPv7AZyFTELCXhgiFsAsEktw2W5HudAxrTQHMBcBeBIGCt32sAbhVozmK1U8DOB93H\nraGhcdG44vuuO0dL2kVGqtkBkkTjFKO9wgY+LlVafCWyzg1emFIbkNaqSWYF7BKJM9t/LtE3TgFL\nh3DgJz/A3u/9Em5SRK68Dg/81gPYfcswFeOtMUaRrdPsSW73FkeMCJ0ecouRMKp1KhzK0XUDr0l+\nPQlO1chbE2KYUgQqN9BJzMzwXIM6yTSO+Hv9aNob7c6kZYhMma5rqpXKyqfCsEw3I1uVsg4X0sjb\nLop1qZiuWA4J3XTSRYaj+rbrolyv8zuwcryWMcTxTGrokU9yd7qkZa0hqfiGtJRNAbUzgO8BfgNo\nzlN815wDPEnNnxcGkO8G8r1ArgfIdwHZEpDNA04Oxgf/x0XzniZuDQ2NVeGKm+YVhzLRSlLhZ5uN\nePOMsu2SRN2XIC1+Nlln+8WQ5QLJunMcZhLynPPrznU/c8VDe+k1RpK5ARJwMMd50O4UMwqGCcAm\nURoiGLNyJE3Y1IH50lqVGwK6bmLLmEqp+3M8n6VD7PEOqvxMlR0UlHnTwMLLvI7BkgziqLGOHXn8\nDpQtqhLbZSVVHbsAYka3iHk+iU8Bl1dlqhwJAFNU5338jGGN6fjEkLp6gaIzy5KUf8d+bSUUk/S+\nt8AoO6hyX4YpLVqxRMfzgFsDvBbgN0nKrQUgfLO2LQPIloFCHx/ZCpAtApksYBkiTGvIOYt63bAl\nzZ+F8eFvauLW0NB4l8NfJPF5c0IW65f3W0cuI8CwQeOSbO8F7TYMgcVFPmo1Pup1oLYUoFmtoVVt\nwG2FaIUleFEJYZJDEBgIQ7737FubYQC2DTgO4Jgt2KgjazZQqOSQL5dRqBRRKADlUoxKyUMlM4tK\n8AK6op+hZJ6GYRqp5zVikqPTJa1MZfYaK8EUEiFRUUz7SzLRqodRdc+tNCZRafTmBFPoYY32nDAY\nUUc+TVDqJ7hAMUwufJwKX09AsVgSytCOfr4OQ9LbTRGzgVG2afN3M8tzhCVRdJEe4Y6ULLwZ1t/j\nkPVtpyIEaHIfdkHEZXkxSIn5GZpjTOd702zfChpAqwEEHtCqAV6NRO1W3zxqNi0gkwMyeUbKdhZw\nLMA2SM4I+ZmTJF0gqYWDIy1m2R7W+80c0pJAAuOW/1sTt4aGxrsQkS+irQnezPPio93pJpbEMkTi\ndGpzKWnnOAbm5oDJSWBmho/paT7PzwMLC0C1iuX7ij32FyeRqJPFoAMXmGpPonbPNQwhRsOW+rKf\n1nGDOp/jQOq8WWTzGfT2GujrM9HXb2BoIMS6vhqGemsY6plFf3keluGLuhoAYlE/F5haLm5hliHT\nyzRyY4yCtIWXgNqxNEsRq3YmKyVcu5SO6zSMdk0dZobq8eIWLh6UkE4pse0SSUsZmSQBr5Vh8mcj\nS3IzRYldP8zvKvK4b6fMRVamn8Iyu8jIHREjaX8OqJ8GFl8DqmMkY78FuC2pN9fSz7ASbIerKNsC\nbBNw7JSgjRjthYUp/dlWntdUObhlSoCRJ8knQsyJ9JZD3p9IS5pdkGuRg3Hbn2ni1tDQeBfBmydZ\n+wskk/zwykMv/AWgdhgNt4ixxW0YO5PF2BgwPg5MTJCwz5oiugLilFCTkDfvt0vWKgJWfc+qXh0H\nMnAi5k2/83dFWk6nUCqWR0RiSIJlEaNjRxheF2B0g4kNIxFG1zWxebSBkfUhbCsBmsfEWOYNwJV6\ndewJeUqWItMr866FoDL90ussnt9hnWnz3CijXG+aVqnNM5LCLvL9Vk7U4IaQrZ1er2wP4PSS1P05\nptwbJ3l9CyOcY13YzOOYFo/pznKhMfMSH9VTFIC1qiToKDz/5bezjJwdi5JsEyRoyyRhK+95u4vn\napfZ9uWoR5EkbXV+5/J9RB7T/IG0pkX1tFQBg9+lAa4SoxY/i1+F8eFvaeLW0NC4xtGOrs+QNPPD\njP46epKjiKR84qiPYwdncPx4gpNT/ZhbeLsq95SsTYTo6rHQ3ZtFpSeHctlAuQyUy0ChAOTzQC6X\nPhwrhJ0swY7mYQeTMN2TQPMMksgF7AoSu8J0emTz2YvgVhfRanhoxv1oGSNoRoOoNnKoLoWo1mxU\nq8DCQoJWM5aIFRJRJ2jbiJq2EInLRxLJI4BjetjUP4YtQ6ewdf0Ert84iS2bDdg91wM9t7BVyq9K\nK1RTavMO683uFDMMKn0dNUm23jzT27kRoDgMZNaRIJNIotECAINkHAdSZ8+S3BtjQO0Q09qGQ7Iu\njHKhErtA/Qww90tg4QhQOw3Up1iH9hrn/8oshzXmbF4iaAMwI8CS3mpLsiN2F1XjThdQWEdrVOWY\nZuUkQ1EU8Vw2zYio/vWwSpKOG1JXN5gtMAxR5gdyjZbEmCbhZwobfN0wAKcbxm1/rolbQ0PjGoW/\nmLqZ5Qaldl1GHDNqfuMN4MgR4PBh4NixBF6zJS1NOTHIePOouKsLWL8eGByIMdBdw0DXAga7F9E3\nVEDPUC+6BnthWmcpupOEx1CRoD8nE7vmZLyk1HURU1yVFTW75ZAEvTkZ/lHjwiMnxGVKj3Ic8Mbv\nL7LtKuTgimYzwNxSGXPVImYXS5he7MHkXAmT0w4mpx0s1BRZykQqlZJWzyptbmbh2CG2jsxgx6ZJ\n3LBlCjdcX0d3yU0nXJm2EJIpc7HneU1LW+iAlhvk+YZ1nrNT4XHiSHrAmwBMIS6P16c1JZF5QrI0\n8kBziURdHQdq4yRpv3n+LyyTowBMpbcdqTebcRrhG3Id7RwXHNl+LkasAiNq5YVuyDVSZQWo5yTN\ngESBiOf8tHxgmKnhShKlznW26A3sAskeCd9n5sS5rdB2XDM2/0dN3BoaGtcQlo2HNID8CDxjCIeP\nWnjtNeDQIT5qtc73SBuPStcaaSTuOMDoKLBhAx8jI8DwMLBuKEbRFgW1v0AyyQ2yhcu0UgvMqMk0\ncSdJx+JLrWZJJ7H0+VZJEoURplyR0NAjXErb05KQKVg1K9qwpS/4NMVhqlc4agrBWExZZ/tFDBby\nOP40e4hNG7ByaARdGJ/uxthUL05PV3BqogvHp4Yxs9SNtqVoouq2SFP2SQwkIUYHF3HT1gncvOUE\nbtlyDN3dERccOaUKl7S1Yclns5ka9qZJypErEbb0ZkceP4u3CLgNIAgBLwBai4ygg/MY9RgGv7RM\nljXorM36s60WI1bqftYWqhUpzsvKdVUpfzMrrmW2CPdEad8pcktEaKZ6vT35HqFKEpK9aA8dUdF4\nTtTrlvR6L6TfnZGhm5wlg1CsDGvzong3dl78WE9N3BoaGlcOgjp7q90ZtOJ+HDo1glcOlfHqq4ys\no5U0RklEgotDwC6gbyCL664DtmxJH+vWsWuI2yfpHGhvTkZk9jI9qhTQQU16fRfQHh0JQwZhFHlD\nTsAUqDuTpkyz/dxX7Evfssnos3EqVVYXRgCrIt7o46wPe/M0+jBAQlSRolJtRx4QLooZS537t7Ik\nAuWIFofyWiA9631A8TogN4haq4TjYyUcPWHhyMkuvHGsiMlpOyXYRPq4DSFDm1H5dZt9vPeGBdy6\naxY37mjCscXTvXmK6e6wyvO286IxMIHaFOvPtUmakzQXqOJeCYYBZJQ4zGT0bEPaqYRgTUvIMZN6\nhBu2jNLsYQYmN0KtQ6ZXatXKkjSXDi6BZB6US1pLRp66E9JnLosI0waMHK1SbSFaK8+/mVYaYUeu\nmLeI/3g7uu8B7G4uEgyLi4Ik5sLNX2AfuV/XqXINDY2rGDIbOayN4/AREz9/YxQ/f60Hr79hrUzU\n6RtRKTRx/aY5bN+Zw/ab+rH9ehPd3SttmvAm25qgYhlGqvCNPbY/JSIQQ0RSzvRI5C1zn2Opb6po\nTbVQWfmUUJxucH70LFA9TOOT0E1nYAd1wJuixaey7HQKFIeZosBOEgAB66hJmHp6GybT0JZDEkMi\nnt0uU76FEQ4m6bmV9X8YXBjUj8qCaJrRcVgDogCLrW4cntiGQ6eG8erxTTh8ooLAj2TR4bevsRLD\n5RwPt20/ht03ncIdtzbQVTRoRFIdAxZPAovHKRZbqb3KgPS/2YBjSvRsAGbCRZDpcMGS6QPyInzL\nSt0ZFok30003tOIm2qc6ZRHpBZJtEdMVv8rI119Mo31/nguOoCYagY5BI3kpU2T6ORxFWZuqzEHs\n8zpYWabNOzsCsgPsUc8Npj33qozizXJh4M1wYWaIWj0BEHkwtjyoiVtDQ+MqQ+RjZmwSL+yv44VX\nevDyoV40vQzerCa9cSOwaxewa1sdO0ePYHjYhFHZvvLQhshjhNo4KWQdMkJVtWbVspNE6RQou4R2\n73NY5Y3eypM07BLbjxrHmS63ckBhI8nGW2Bb1dLLPGbUklRuTm7kDVGAy5AJpySGKF0Asjy3sCUC\nqlwavQY1Er2qWdslbhu0uFio7AC6bwW6bybp+DUSdf0IZ2B7M7IwkXnb2X7JGOS4/7DGlHCwAD+u\n4I3J7Xj12Ab8/GAfDh3OIwpDuU4i1ot8IGjCCJvY2f9LvH/zs3j/lmfRX5xLr7ttMYrOOEAmI03r\n7F1uT+nKDzAb0H0j28jsMuvIYU1S8YaQ+DogN5xOEFOkGTbl+5HvKBQXs9iXwSMRaAYjixC7QNe1\nTI8slCypX7vcT9ggYTtlwK7Iv4WKCB+lFz2sMwOiFPeGI+cjYkB/UfrO53iOdlHc3Lr5b8ybJ5FH\nLYrTtv2+Jm4NDY0rH1EEHHyljp/9dAk/+5mJk2fKUgNceWzC5s3AzTcDN90E3Hgj0FXyJYJcAkrb\naPSh6tBhPRWLNccYYZl5SaF2MUpNfJKyUxYRUQlALJHaIt9vF0nUjsx1difTkZh2mUQS+0xxVw/R\nlCT20J4eZRfRFoYB4vs9SLI0JbIOm5LuFvGXJSnZqCXp1KpE23mx41STuAygfD0nbpW2kli8JU7v\nUjOn4xb3nyR8rykp5gTSEy6pbVW7tkRI5Z4Blo4C84eA6hm0Fup45fV+vHR0M14Yuw0TtfXnfkGm\nAZgWdo6ewN03vIIP3PQi+rvmRZAlbVbZvpSkS9cx6gxFde3PcsFiGFxQqN5o0wYXKA35LJLS7xSN\nGbaI/RRhiwGMyqZYJRGDFVKXtE6bVUumdKk6dRKkQ0LcKXq4x3EqSLMLUOYpjModfieRxzS7aZPs\nLdVjPseoO6zLdRgQ//YB9nEPf1QTt4aGxpUJ1wVeejHG/mcbeP6Aj2rVPKvumGJgAHjve4FbbwVu\nuYWKbwC8WTdPA/Xj4mnd0+FF3QJgMcIK6iRRp4c32iQiabWjqDKJO1hMU6d2KfXJtiuioJ5lb/Hi\na9wOMgnKneJrbRvRCsVTcZymV60cU7lWlgSTxGmK3SqSz60SiS1qpUTlzXFBYlo8f0vS+Ejo9Fa+\nntGpZZNc5l8G5vczJR81peVKBFN2gZ/FKdHm1C6TOJRYLqgBi68CE88Di8ekHr0E+CuLxRLLwunm\nFhwYvxsHTt2FQ5PbEbe/O1mkmDYM08HNO+bw4Q/4uPtDJRR6+ni9vXk6r7kzsmDJSfRa4feDDNq9\n6gBT/0mS1rXVseJIovIGkLjMMCibUyuTepK3F4JJmq1IpO898lheCGQamb+UptkNM/1u7YK0r6l5\n3yEJWhnUIOaiQA03iRMq6eOQC4bMIDMG+WH5tx6hsw9fE7eGhsYVhUYDeP554Nl/i/Diz1z4LS+9\nIXbMjnYcRtS3387H8DBSa+844g21dZpTpZKAPbdZMe6wCqLSFnGRKKuRk75cp4tkHXkSxS7yJm3L\nUAtHtkkSqQWfBJZ+QQcxb0rmTxeEXCSSNoVgWuOpgtopAfmN3G8Skkwi8cR2ihIZ5gDV05yX1rAo\nlGEcx+Tvo3ThikX4VNxIwi5ex4tSOwxM/ysw/yLFbrHPqC/TTUFUdoh17oxkCuKINW13DqgeBWZ+\nzlp0cx5oNenHuhKyOSCbBfJlGYph8nwM8Q93SlgKN2H/8T34t4O34+XjWxAZoqyHjL2MWsiYDdx1\n0wl89H2HccsNdZi5PqaO7XKq2EcsGQcpdSSR1JF9SWHXWetX87qDJbQJ08qJklyMUQxHyF8WUcZZ\nBjlqhKlqd4MltqS9IiqUxZIhc7PDZlonD5bAOnch/YzBgkw5m+N5mzm07VxNW4R+8jnb5wYo+1lt\neaqhobHmaDaB554Dnn0WeOnFEIHrMjIxs8vS4b29wF13AXfeSdLO5UDyDBsdNddax7jFhL7axU28\nATZPMPJunha7zY2c/5wRFXYcUozkL/BhWCI06yHhxy4VxdVDdBFrynjKqM6bb2GYYqXsIAnEnSHB\nupO8YVt5Rr65AbRtN71pySIIudt5MKWaEdXzkNRxI6D6S6B2lJ+ruInEEXskgMIGoHI9xVn+LLDw\nIjDzEy5cgkWJ8AoyOGUdkB9iOj0OuL07y5Gdi0ep7nYbtP4MViBpwwTyMq0qmwVyRSAniw8VWVo5\nOacbga4dXEy0B3iYQNhCbW4Jz+2P8ePnuvCLN4YQJ3ZHqxbdw4b6W/i1eybxq++fRn9XTQRwLjMO\nnhCjOmbki/grlGBeImmnmGZFlBhQLYZULTsWh7tYsi/K/CX2AZjyvg6luWEAkEhfbRe5y+1o2683\nhfQ9HtcuSrmlLALGKO31VvXzRF136UowC3IODozdX9XEraGh8c7D9xlZ/+hHfA48VWuM0lYcmNi0\niWT9vvcBW7cCZuIJQVdTG00rJ61QZUZb3hzVunaFUXX9GFu4VM20vIWkB1GMe/PSX+2LgEhqt4mk\napcOUljmzfIGbJekHm3TSat8PQBDhmmoUZTyWbL9tOA080BcZRYABmBKpOkU0sg6P0zyd7q5jTdP\nlzBPXMlKW/haLKn3nETKTi+FdDPPAkuv8LNGQZrKz62nAM2ptJX4aJ5mFF2f5vAM1+WXcjYMEyh0\nk5yzDok6I1GgSiUb4DUrbAK6bmEd3SmJCn6RGQ+/xsVQWJP2KYPfl1UE7Czmq2X86wub8cMDm3B8\nvNKRGqYI0ESIO3edwH94/8/xnm0nYSQx2h7gpvRYZ7pYKsh0yzSzDICIj7AltqJuWvs2syRDw2Rr\nmjJQcbqFXItC9lm0J74kkSwUl7hIjFz5HrtI7IbF1z1p9TOMtMsg0yXRvAgKI0+yPWmPNs/HTlv0\nwrqI12bleB6Mmx/RxK2hofHOII6BV18FfvhD4Cc/AZpNMdqIpD4q0czWrQbuvht4/90JRobqQtJi\nbJFEaY3TqaQKXncWWPg592UXUiK2yxQ2la4TEZcrRD0nE6+s9OafJBIlz0ivtjJXGQCKG3h+qtbp\n9PDn1gRJPZZJT6bNm3i2F4Ap86ZrshjIMqVtFfh7fh2j0kwf2KLV4PF9WUgES2w5sgokmsZJkkO2\nh3XRpVdkdvZJRv5WQdzW+rhPp0CjksZJoHYCqJ4BmotAyyNJn3PvNIBiD5Cv0I81k2FvdCJTwmDx\nGiinr/wgFwX5IUbJYZ3XVA1SSZCKw0xHBHUZwMkxgkx8IVGlPK8DQR0nznThX372HvzwxRtQc0tS\nZnDa2evRoTp+fc8p/Lt7aihUctx3gnSxpDzZkzjN2ihdRCJTuSJRe7fPTTmUdaE91MSQgTNqeEvY\nlO++JFoCaa3zF2mAE3YQueomUG5pthK2FTpc6OTfk8oYeVKWCTpaB03pSYcpPzswBu/WxK2hoXF5\nMTYGPP008MwzwOwsQEWttMJItHndtgw+eE+E999Vw7rexZSoO2+oTiVt30pivt6aIoG1pkmEdp43\nusJm+knbZYmqxeUsWOqoIUJSozWJaqbT9qf8urTm7apWnSYQBkLo86kAyRQBkZkjKQQ1/m5JFJXp\nZWSe7WWqPL8OrHc2uZ9QUr3erOxX3Nv8eab3E0m9JpEYwMzwBq9Sv04PI8Q4oiNac0pq0guA69Fx\nbKXG9nw3kO8CchnWpx0LSFqpAUxbnNfDBUZ+HWBKXVjV5b1FEmYcSIpZ1PdthzIhQVXjN03auoYt\nwIylRFBgT3amT1zeugDDhu96eO5ABt//YQW/ONiNthOckGEhF+Cj95zB/R8Zx8CgISpv1bfu8xix\nJ0I/mSaW6ZJBJT2ieZAShZoKFzbTf3vBEhcUToVkC4P7bU2yTKKIHOD3mxuUfzM9aRRtFQBYQsgi\naFOaibCG9lhPM5NqK9Tx1FAa5bhmUuy2Gt7TxK2hoXFeNJvAj38MPPUULUYBiIBI1a8djGzI4IPv\n9/HBu+YwOjjHG6Fqt1JErdy9AElBqhq0KLvd6VQtnhNTC7ssU8DGGAkhStPRZi4VK3mLjKTsHFPZ\n+SGShwGacTTP0Do1XGJEq8go20+C8pfkc/ntUiQMB8j1UBmc6QbK14k6OI+277a/KAYuAcVqrXFG\nxknIm7src6uzg7xZB4sUiiGkqjwJRKA2JVH6PNBYAFotwAsBf4WxZU4eKA0AGZkJnbPZ6hSHbLMy\nxMgkOwQUBimaK28Ce8KbgHta+p7VEAyZaKXEXE6B55vtR3sUqKr9JgnaHt0wZDHQLT3nhoiycmin\nkFUKWrXAGSbGzzj4zr8O46l/G0KzpcRa9BW3LOCe3VV84t9PY+umGsnWypGYnS7psS5LhNyBOOro\n6ZaHYXNbw0jPxZviAjGW78guAvkNQEFpEKRXXJG+v8T9+lU+R66k3lWmqEeyMt0SheewbJzsW2BN\niXvfvn343Oc+hyiK8OlPfxpf+MIXlr1+6NAhfOpTn8JLL72EP/3TP8XnP//5c09CE7eGxhWDJAEO\nHgS+9z0KzTxPvRBKfdFHpQv40D0+Pnz3HLZtXICRUTdxuZErD2xAolBF1POpWCxyaVoSeSTG4mbe\n+FunGQm1ia+PbVeJS5IOq8zX2+pmKVGOYaA97tI9QyW1O4G2EYpSkqv0elgTErcZtTtFCsmyfazz\nFjfwPTBSi9SgJulkl2K15nGSLuw0krYLJM7YY+rfnQQghOdKNO4vycxolyTthSuovA2gvJ5p74wJ\nWCF1UkZCYnLKPJbTRbK1sukoSksEa81x9p+rcaL8Irltfj1T5NlBiQytlATDpgiugHTkZQGwJdJV\nynXDFutWEe/585LGTuT7KUo2oUsyFt2AmUGrGeOHP8rgn79bwNi4CLtgtqPxW2818MCDNm66ZQUi\nDJvn6iMMEcIlYsDiST1ZjWFVg1ZyshCzilLnrskCQ6Z4IZZr27HoVK2CTmX5v+tVYs2IO4oi7Nix\nA0899RRGRkZw55134oknnsCuXbva28zMzODkyZP41re+hZ6eHk3cGhpXKGo1psK/9z2mxduI6Whl\nw8Xu22r41Q81cNvtNuyCRMgqslFIEhmAITXesNWh6i4zRT3/ArfpulH+NkWhVdiUaFtq3v4SiRZG\nmhKFkw7fgESbscc0eu0wn02LftHZAdmPRMj+LFOthsV+6GxHr215mywSStyueZrErww44ojE0Dgt\nimGxtgzrjJ5Ni+lj1SOuotxgnspptwG4ERAkgOdz8dEJpwD0bAOKXeI0VgfiOjMAlhixZCSd7pSk\nBSkjgj5J58Y+z7txilF/ElP0lh9inT3bx32YmTSaTDrEbGrRkV/XMaijwqg5jvhdNE+KeO8Mr6uZ\n5X7zwzSnUe9TyvpOO9KwwQWFCANjo4gXXynhH79dwMuvyBCUjn9HN+4K8MBvzOHWXbMwfDE0SaKU\nQNWM88RntsM0eN2V2twUAZ5KecNM6/xtUu5Ja9nKvvYdwJoR909/+lN86Utfwr59+wAAjz32GADg\nkUceOWfbL33pSyiVSpq4NTSuICQJh3d85ztMiQcqO5uEbYOTzcML+Mi/C7HnI13oGuxZOfKIJH2s\nIms7LxFWr9SnZTTn4svcJtsDwGLE45RSG8mgRdJMYqZrc0O8mYZN1n3V2EjD4Pm1JknUkdRBc0NS\noxbTE79G4oSojZ0KW71y62gXml/H6DN0mU5vjZOcnG5uY+YpcqsdTlP7SZASkSnuWV6Noiw1r9ld\nYCktr5MAACAASURBVK+0nwB+vLKIrDgE9G4HSn2AHQHhFBAuihgrxyEh2WGWAJIkJaJcPxcXysmr\neQZoHGXUm4QkocImtsjlN5Koghq/AzVUxMrLgkXSxNk+sYLNoe3B7s7I8wSPEbskwdwAFwH5Uarn\nzRxfaxuZKBtSGQ1qZPgZjEwq1FJDWNpEbeDI8Rz+8Tt9ePZAmVaryo4WCa7fOI3f/rXncduuUzDi\nQNLdEcV9ahynWjyp6FvVla0s2vPKYaZCs7YPe+e0NCPdxjQBSK1dvV/1Zxsy+MRyuBBUs76tDN+j\nppGZdiqaVANcDGYyjMLQRfPeyj6DF4jx8XFs2LCh/fvo6Cj279+/ml1qaGi8A/A8tnD9r/8FHD0K\nUGim+lgbyGda+NA9VXz0vgq2vWcXjPZoLUFnVO3NkTQzMve4vJ03sLDFFq7aURJA8xQjn1x/2vqV\nqch+Fhi9FjbSdxuxpKLHwKhNyFodL4mlx1e8v40M3+MvUsAV1dI+2vwgRVmFjUBpM9pjGP1FRv5h\nk1Ftppc1z/x6mrBM/gvPO5b0aSjKeNPkkJCgKo5lLaa9W02pTccd9QUFA+jaBPRuA7qGACdmScCd\nAtwxuq/l1gGl21lbV4M62tGptK5FrkS6MjgkbJEUihuA7jtIwLErgqmQNW2nwmi4f7eQ9ADLAlFA\nW093BqgdAWZ+ykVKKLOwDbEJzVSArl1MkycxswD+ApX4syIaa9u9iv7AzKU6A4hNaKIGdEiNvD2B\njUM4tplL+C/3Bfjd9/XhH565C0+/sBNhxEzOG8e78ejX7sUNW6bxe7/+M9y0dSJtOcz08bvL9aM9\n81rVnCFmKrAkGpeH0fFz+9+0GMIkkWRXRLkeR6JHUP3g0msep/9f2m5qcSBK+ARAKFmVMO1PT8T7\nvTNDdRFYFXEbqzx4Jx599NH2z3v27MGePXsu2b41NDSI6WmS9fe/n6Be6zCnkJvNtk1VfOzXfHzw\n3iHku7Ysf7MyNvHmlqdIy9slCjco/qoeJFm7UyL2Eb/p4nXiZNZM1eT5dUDXTYwSIyH62Z+kN7g4\nYmo9dhnZ5Aao6G5NSJ+zqts6VFL7S7yB5tfRy7u0hTd0w+b+/DmSbihjJjPdQnYBI+7ZA2mKuZ32\nVnXQlkSKTSDwAVceXgB4Z1mFGhbQvQnov551akXUrdPA0mFGZLl1wOA9QGELr3+wJAuPlliTylSy\nYFGGU3jS0iVOY6VtJFXVKmXK/Of8Fhq7ZAf4upXldWmcApZeB7x/pUjLX2CkiA4XM1ipuYmKFONQ\n3N1EV6DcxtRQFlN5eCvCitLvLnSZRWi35XVcT8MSb/KKpNrXAzCwvhLgj3//EB78jWl84we34Ps/\n2YwgsgEkeO1MD774327Ge28N8Hu/G2P7jpXS2sbyn40VCLv9bHY8y7S2zp87p4+1/68oEg7QntUe\nNkWwqQi/k/gDIA7wzHOH8MyB15HOK794rIq4R0ZGMNZRDBsbG8Po6OhF7auTuDU0NC4dkgT45S+B\nf/52jJ/+JEAcqjQlxUCZjIEP7l7Cff8+xPZb1pGEFcIWyc6bZYSX6WKEU7oObS9uf4EOX7Uj6Xxr\nw+HNLZR2p/IOkoCdZ4o6K9GRP8809MyPeSyYjGD8RQAJo/jeWxntVQ+ltXEry9qt6Uhb1RLT76VN\nbCGzMuIhnRcBU5X7d4qsw5a38T3144yuw0UuOpTXuTIZicTdKxQBmRtIa1Zz+UU2baB7I9C7FaiM\nABkbaJ3iY+k1LhwyfUDv7tTopTkGeBOsmau6qmqTcmf4+Q0nFU0lYUePdy8/n3JQU4roxJfWuoPi\n9ib+5xAVtTK4saWHuT10pSJ/l/alTEV6oQuSqrdYbVA15bDJ6+nNyoImFPJqpa53gcypRsIIXB0/\nK6l2xKnTmBLM2V1iXmJhoOzh//jd4/it36ji7/dtx/d+vA5hRF3DS68CL30R+ODdLfzeg1WsG+po\nk1uWflY+5UlKppG0lbUJ2F8eQSvXs6gl0bGQOwxJn3cQvpmh0M0piihT9aqLt0Hic/GSxNjz0R3Y\nc1+e5Rczhy89ftNF/59eVY07DEPs2LEDP/jBDzA8PIzdu3efI05TePTRR1Eul3WNW0PjHUIYAv/2\nIx/f+qaPo0fkpmU47Uhq3UAL933oND7yEQPldRt4Y00SMZGYlTRx1GEG0sMdKytSd5q1z8gDEIKR\nmy8R+RIVvPlRzlDODaXistYU1eT1Y2LGEqdtSWaG6vKuGyiSWngZmP4X+ojbBaa7YdKMxJuUVOkA\niTgnEWamV+rcvhiaZMVIxQCaE5ykVT8Jjn1UhCNTxYJF3mgjD/Bipr1bLuDWl19cwwTKg0DXCNC9\nHsjkAe+M1NubPEenzBR9eQe3b46TqP0aYFlS+83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b3wDuv3/h/q+8EvijT9jIpevu4sQp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YC11rD4TRtVgnfXa9l+9EKs37bZFjb/GHuk/WHOwLbqtCHNv5bsU68Dk3dz3nRshfRp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\nNBVTYRWPIGNLTF9KH1OfJ0tY5kfBZtpmoCqH3OgdtUDtMcA7nILZoKdgs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Viw\nYAGKi4v7YHeMI7jVz16vCbe9HPDuEBoairKyMtPrsrIyhIWF3e62mG7COfyDh+58lm4cU15ejtDQ\n0D7bI2Ob7rx/Pj4+pv+eO3cunn/+eahUKgQEBPTZPpme0ZPPXr+7ym2dy0yePBnnz59HSUkJOjo6\nsH37dqSmpvbx7hhrcA7/wKI7n6XU1FRs3boVAPDDDz/A39/fdBzC9C/def9qampMf0vz8/NNZagZ\n56dHnz3HxM3dGjt37hRhYWHCw8NDKBQKcf/99wshhKioqBDz5s0zjduzZ4+Ijo4WkZGRIj09vT+2\nylihrq5OzJ492yIdrOv7d/HiRZGYmCgSExNFXFwcv3/9jLXP0gcffCA++OAD05jf/OY3IjIyUiQk\nJNhN02T6npu9f++9956Ii4sTiYmJ4q677hJHjx7tz+0yXVi8eLEICQkRMplMhIWFic2bN9/2Z6/H\nBVgYhmEYhul7+t1VzjAMwzBM92HhZhiGYZgBBAs3wzAMwwwgWLgZhmEYZgDBws0wDMMwAwgWboZh\nGIYZQPx/grpLef5G99MAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x52b9a50>"
]
}
],
"prompt_number": 98
}
],
"metadata": {}
}
]
}
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