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@karlnapf
Created January 31, 2017 05:48
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{
"cells": [
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib.pyplot as plt\n",
"from scipy.spatial.distance import squareform, pdist, cdist\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solve standard ridge regression problem, i.e. GP regression predictive mean. $\\lambda$ here is the regularisation parameter, which corresponds to the observation noise in GP land."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f55f0fd7c10>"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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KigIApKWlYcCAAWjXrh1eeOEF+Pn54dtvv8Xo0aOxYcMGjLIQ+lWxatUqXLt2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\niogLQRAEQRC0IuJCEARBEASt/H8WqfRRNZmhtAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f55f1483c90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 20\n",
"D = 1\n",
"freq = 10\n",
"sigma_noise = 0.4\n",
"sigma_kernel = 0.1\n",
"lmbda = 0.1\n",
"\n",
"X = np.random.rand(N,D)\n",
"X[:,0] = np.sort(X[:,0])\n",
"y_true = np.sin(X*freq)\n",
"y = y_true + np.random.randn(N,D)*sigma_noise\n",
"\n",
"\n",
"K = np.exp(-squareform(pdist(X, 'sqeuclidean')) / sigma_kernel)\n",
"K_reg = K+np.eye(N)*lmbda\n",
"L_lower = sp.linalg.cho_factor(K_reg)\n",
"alpha = sp.linalg.cho_solve(L_lower, y)\n",
"alpha = np.squeeze(alpha)\n",
"\n",
"res = 100\n",
"X_test = np.linspace(-1,2,res).reshape(-1,1)\n",
"y_test = np.sin(X_test*freq)\n",
"K_train_test = np.exp(-cdist(X, X_test, 'sqeuclidean') / sigma_kernel)\n",
"y_test_pred = np.dot(K_train_test.T, alpha)\n",
"\n",
"\n",
"plt.plot(X,y, 'b.')\n",
"plt.plot(X_test,y_test, 'r-')\n",
"plt.plot(X_test,y_test_pred, 'b-')\n",
"\n",
"plt.legend([\"train data\", \"ground truth\", \"predictive mean\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\"Update\" the solution, which essentially is \"recursive\" kernel least squares (IEEE paper). That is, given the $\\alpha_{n-1}=(K_{n-1,n-1}+\\lambda I_{n-1})^{-1}$ construct $\\alpha_{n}=(K_{nn}+\\lambda I_{n})^{-1}$ in $\\mathcal{O}((n-1)^2)$ computation. Note I here also construct $K_{nn}^-1$ from $K_{n-1,n-1}$. Also note that storing these matrix inverses is unstable and needs to be replaced with Cholesky factor updates. But this gets the idea down."
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# new observation\n",
"x_new = np.random.rand(1,D)\n",
"y_new = np.sin(x_new*freq)[0]\n",
"\n",
"# for readsability\n",
"alpha_old=alpha.copy()\n",
"K_old = K_reg.copy()\n",
"K_old_inv = np.linalg.inv(K_old)\n",
"\n",
"# kernel of new observations\n",
"# costs O(1)\n",
"k_new_new = 1plt.legend([\"train data\", \"ground truth\", \"predictive mean\"]) # gaussian kernel\n",
"k_new = np.exp(-cdist(X, x_new, 'sqeuclidean') / sigma_kernel)[:,0]\n",
"\n",
"# new kernel matrix\n",
"# costs O(n-1) where n-1 is the number of previous observations\n",
"K_new = np.zeros((N+1, N+1))\n",
"K_new[:N,:N] = K_old\n",
"K_new[N,:N] = k_new\n",
"K_new[:N,N] = k_new\n",
"K_new[N,N] = k_new_new + lmbda\n",
"\n",
"# low rank update to kernel matrix, note this requires a system solve using the \"old\" kernel matrix\n",
"# costs O((n-1)^2) for the matrix multiplication/triangular solve\n",
"a_new = np.dot(K_old_inv, k_new)\n",
"gamma_new = k_new_new + lmbda-np.dot(k_new, a_new)\n",
"\n",
"# construct new inverted kernel matrix, wqould be required for the next update (see above)\n",
"# costs O((n-1)^2)\n",
"K_inv_new = np.zeros((N+1, N+1))\n",
"K_inv_new[:N,:N] = gamma_new*K_old_inv+np.outer(a_new, a_new)\n",
"K_inv_new[N,:N] = -a_new\n",
"K_inv_new[:N,N] = -a_new\n",
"K_inv_new[N,N] = 1\n",
"K_inv_new /= gamma_new\n",
"\n",
"# construct the alpha using the residual of the prediction using the \"old\" alpha\n",
"# costs O(n-1)\n",
"alpha_new = np.zeros(N+1)\n",
"y_pred_old = np.dot(k_new, alpha_old)\n",
"error = np.squeeze(y_new-y_pred_old)\n",
"alpha_new[:N] = alpha_old-a_new*(error/gamma_new)\n",
"alpha_new[N] = error/gamma_new\n"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.6076029396572267e-13"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# constructed new inverted kernel matrix is the same as naively inverted new kernel matrix?\n",
"np.max(np.abs(K_inv_new - np.linalg.inv(K_new)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compare predictions oif the \"updated\" solution to a naively (recomputed from scratch) one. As handling this with matrix inverse in unstable, this might differ depending on the seed. But works most of the time for smallish $n$."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f55f0bd1450>"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Tc3Lx73/btOlbjodHyXsUSovOZ4ZDYffNbU2LkrSb3/7u7u5W97MGY44ZM4bu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\nJcmFEEIIIZxKkgshhBBCONX/AwpXFJUN5p3KAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f55f0c9d350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# kernel between training and test data\n",
"K_train_test_new = np.zeros((N+1, K_train_test.shape[1]))\n",
"K_train_test_new[:N,:] = K_train_test\n",
"K_train_test_new[N,:] = np.exp(-cdist(x_new, X_test, 'sqeuclidean') / sigma_kernel)\n",
"\n",
"# naive prediction (and computation of alpha)\n",
"# costs O(n^3)\n",
"y_new_naive = np.zeros(N+1)\n",
"y_new_naive[:N] = y[:,0]\n",
"y_new_naive[N] = y_new\n",
"y_new_naive = np.atleast_2d(y_new_naive).T\n",
"L_new_naive = sp.linalg.cho_factor(K_new)\n",
"alpha_new_naive = np.squeeze(sp.linalg.cho_solve(L_new_naive, y_new_naive))\n",
"\n",
"plt.plot(X,y, 'b.')\n",
"plt.plot(x_new, y_new, 'ro')\n",
"plt.plot(X_test,y_test_pred, 'b-')\n",
"plt.plot(X_test,np.dot(K_train_test_new.T, alpha_new), 'm--')\n",
"plt.plot(X_test,np.dot(K_train_test_new.T, alpha_new_naive), 'y--')\n",
"\n",
"plt.legend([\"train data\", \"new data\", \"old prediction\", \"efficient update\", \"naive update\"])"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.04121180964e-14\n"
]
},
{
"data": {
"image/png": 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MUPz6U9JtYHbjONSk+LWHIxEOQqzZVMSEWOWHFIImJebRaSnG75dVa0NJbV1O\nfHH15KSp23OQnWLDZz0idlALQ40+BxlmdVYqnOjHN10DnhjuX/9v1dsKR99e8whSfxKP3f4FVa4/\nKysLgN2V4iFACSIchFBVQxve+BrmjVMvHMzOzEOOOcb+wy2qtaGk4DJGpU9jPFWO2EEtLPW5PDjj\n9pOXpt58g6D0lDjG9V3Lh8fE0ML5OtzcwV7TkyyIupPURKsqbcydEliyXFxbo8r1hxsRDkLov9v2\nAHBVgXrh4NL8wIqF4CQtvQsuY1T6NMZTzcwO3DjEDmrh5R37QTC7WTRZ/XAAcMuMlbiSHKzfvj8k\n7YWLO//+NzC5efwL31Ctjcy0RCRXEhVHxWdcCSIchNAH5XZwx3FF4WTV2rh4xgTwWNhWZYxJicUN\nleCOU20ZY5DYQS08bSwJhOCr56g/rABwz43LwJXIH98Uex4MVI/TzYaOR5nkuoXp49NVbSvaZaNO\n7HWgCBEOQqi4tYiE3pmqTpyKiowgpjeX/a3GCAdV7RXE9KlzGuOJgjuoVbaKG0c42V3nIKIngwlj\nUkLSXkJsNBM9K9je84Jh5vVo7XtP/wd/3BF+d/1dqreVRBYt7hrV2xkOVA0HkiTdI0nSTkmSuiRJ\napYkaa0kSeo9Nutck2QnO0a9IYWg0RF5HPEaIxw0uysZodJpjKeK6beJHdTCTFWPgxRvaIYUgr4w\nZyWehAr+9b49pO0akd8v88+DDzCiYykrLsxTvb1RFhtdkviMK0HtnoNFwJ+AecBlQCTwtiRJMSq3\nqzv1R7vwJFQwN0P5nRFPNTUlj15riSHW+3ZFVjAuNjThIEmy0eoRex2Ek2NmB+NjQzOkEHT3ikuR\nnKk88p4YWjiXh9a9jzNpL99doPymR6djS7ThttaIXh0FqBoOZFleLsvys7Isl8myXAx8AcgE1P8X\nUmde3hqYjLhspvo9B/PH50NUL1tL9Z2gA8sY65iq8jLGoFHRmXSLHdTCRnVjO764OgozQttzYIky\nkyvfxB73C4YI4Fr63eYHsHRM5/ufuiwk7U0ZlQWRTsrrW0PSXjgL9ZyDJEAGht3Zp++X2cFjYdmc\nqaq3tXRWoPvunX36HloI1TLGIFuSDXdMrXiqCBOv7w78fl+WH9pwAHDHwlX44ur525tbQ962Uby2\no4yjSW9w68S7VJ9TFDQ9M3g8e01I2gtnIQsHkiRJwMPAR7IsD7t1QI6jdmJ7Z2CJMqveVuGkseBK\nZOdhfYcF93mkAAAgAElEQVSDHZWVgPrLGIMmj7JBpJOy2qMhaU9Q16ZyB/giWVo4JeRt37H8QiJ6\nMvjLZrHnwZnc/dIDmHrTeeALK0PW5rwpWQA4akUP4VCFsufgcSAXCN1vio4ckYvIjgrNaIrJJBHv\nzKO8Xd97HTiOVIA7jrysUSFpL/hUsbtC3DjCQXGLA0t3LlZLZMjbNkeYmBl1M6W8KHbdPI0tpYc5\nGPNPrky6i4TY6JC1O2FMCrhjOdgiPuNDpf5jLCBJ0mPAcmCRLMvnPPN09erVJCYmnvTaqlWrWLVq\nlUoVqqulvRd3wgEKU0IzKQdgXHQ+hzxbQtbeYBxqryTGo+5pjCeaO9kGm4NPFXNC0qagnnqPgzER\noR9SCPrWxSv5/JYHeGjde9zz6Ss0q0OPvvrM75CkJJ78zp0hbddkkoh22jjsqwlpu1pYs2YNa9ac\n3HPV2dmp2PVVDwfHg8F1wEWyLA9oqvhDDz1EgYq7CIba2m37QJJZOj10/03TRuaxv+tJ+lweTZ6s\nBqLJXUGKKTTzDUA8VYQTr89Pj7WYxbE3aFbDrZcUcvubE3lq1wsiHJxgV3k9pVFPckX0L0hPiQt5\n+wlyFi394f8ZP90Ds91up7BQmR5qtfc5eBy4BfgM0CtJ0qjjfyxqtqs375bawRvFNfOmhazNCyfl\nQYSHd/dWhKzN89UVWUlmbGjmG8D/nipqO8P/xhHuNhVXQ1QvCyZo13NgMknMi1tJhfm/dPX2a1aH\n3tz+1O+RvLE8+dWva9J+WpSNTqlGk7a1tnarckPJas85uANIAD4AGk7482mV29WVvc1FWHvyiYuJ\nClmbywsDKxY2Futz3kFHjwtfbB1TRoau5wAgQbbR0i/2OjC6d/YFfq+vmq1dOAD43rJVYOnkty+/\npWkderG3qhFH5N+4OGY1GSMTNKkhMyELl2X4PQDsKq/n17uU24VS7X0OTLIsR5zmzzNqtqs39T47\nmZGhHSaZlDECU+9o7PX6XLGwqeQQSDKF2aHrOQBIjcykk+F34wg3O2ocSM5Upmeru1f/uVx7QS6W\nznye2ytWLQDc/uQfwWvhH1/9pmY1TEqzQXQXh5s7NKsh1Nq6nCz56/VIsnJDyOJsBZV19LhwJZQy\nKz30cyiS3HlUdekzHGw/GBjuWJgb2p6DcQm2YflUEW4OdjpIck0P2WTWs1mcsoo663paO/u0LkVT\npTUtFJn+wqKob2EblaRZHfnjAquSth+o0ayGUPL7ZQruvY2+2P3ct/BBxa4rwoHK1m51gMnH0vzQ\nbwqZZc2j1aTPcFB8pBLcsSF/8puYakO2tNNwrDuk7QrKapEcZMVoO6QQdNeVn4JIJ39Yu0HrUjT1\npb8/AHIET331O5rWMXdyFgD7Dg+Ph4Dl9/+OwwlrWJ39T66crdwmeyIcqOydEjv4I7hufmj3fweY\nnp6HJ76KlvbekLd9LlXtFVj6QreMMSjv+FPFjgPD48YRjlrae/HEVzJjdOg/U6ezdPZkojun8VLJ\nWq1L0Ux5XSs75T8z3/TNkJ2QeSa5tjTwRnOgqUbTOkLhZ8+9xgbvj1jo/wkP3naTotcW4UBle5rs\nWLqmkRQX+gUaS3LyQZJ5q6gs5G2fS5O7khFSaOcbAMyeGAgH+2pEODCq13eVgiRzca4+eg4A5sSv\noDryVfpcHq1L0cRt//cwAE99Rf1jmc/FHGEiss/G4Y7w/oyv376f+/Z/hvTOa3n/Z/cqfn0RDlRW\n67EzzqzNOVPLZucCsOmA/oYWQnka44lmjB8NPjMHmsL7xhHOPjxQDH4Ty+fkal3Kx+64aAWypYPH\nXvtQ61JCrrqxnS3eR5nNnUwZl6p1OQDE+2w0ucL3M17V0MaNL15HtCuTop88izlC+X/KRThQUY/T\nTV9cMTPStNnQKS05FnP3ePY26iscBJcxTh0Z+p6DqMgIzH3jqG4P3xtHuNvb6CCqZxKpiVatS/nY\nqiWziOi28cyu/2pdSsh98YlHwOThqdu/q3UpH0uLyqJdrtG6DFW43F7m/v5mvJFtvPX59YwZEa9K\nOyIcqOjVHaVgdnPZNO12e0z15VHTq6+9DoLLGEN1GuOp4rw2mpxirwOjOux0kCbrZ0gBAhsiTY9c\nQZm8blgd41zb0smH/Q8zy3cHedmhOSNlIDLibbiiw/MBYMHPv0db4vv8Ye6LLJkxXrV2RDhQ0QaH\nHfwmVsyfoVkNE+LzaY/SV8/BjorAaYyLQnQa46lSzJm0+cLzxhHu/H6ZTouDyUn6mIx4oi/OX4E/\ntpGn39mpdSkhc9sTj4HZxd+/9D2tSznJxFQbcswxmtp6tC5FUV/601PssTzMTfGPcPcNl6jalggH\nKtp9pIjo7qmkJcdqVkNBRh7+2AaqGto0q+FUJRotYwwaG2ujL0qEAyOyVzYgx7QxL0tfPQcAX112\nIVLfSP62eXgMLTQc62Zj74Pke26nYNIYrcs5Sf64LCC8ViU98cZWnmq5g6m9X+GFu76mensiHKio\nxm1njKTtAVIXTwtso/xmUammdZyoUqNljEHjR9jwWxvpcbo1aV8YvDeKHABcOVN/4SAqMoLJ/uvY\n61qL3y9rXY7qbvvr48hR3fzf53+gdSmfUDghsCppb5isStpRVsfXPryBhO557Lr3TyG5d4pwoBKX\n20tv7D6mj9Q2HFxeMBl8Zj46qJ95B039lYyQtJlvAJA7xgaSzM7yOs1qEAZn+6Fi6I9nwTSb1qWc\n1qpZK/AkVPLKNv2EcTW0tPeyofuP5Li+xLyccVqX8wmzJo4Bn5myxhqtSxmy1s4+Lv7b9Uj+aLZ+\n56WQndEjwoFK3tx1ACJdXJqrzTLGoLiYKKJ7plLSop95B53mCsaF8DTGU83KDvzDsudQeDxVDCdl\nbQ7i+/JVWbqlhNXXXQr98Ty2Mbw3RPryE08gR3Xwt8/9UOtSTitcViX5/TKFv7wNp/UAz1/9CtOy\n0kLWtj4/YWHgjb1FAKyYP1PjSmCUlEddvz7CQVdvP7642pCfxniiOVMCTzqlR4x94xiOmmQH46L1\nN6QQlBAbzTjXcra1h++8g7YuJ6+1/55Jzs+xMC9L63LOKM5ro7GvRusyhmTZ/b+lNuEFVo9/mpsv\nCu2/JSIcqGRXvZ3IrkmaHVt6oslJeXTHlOhiHPTj0xiztOs5SIqzYOpNp7pNLGc0kh6nG1dcGflp\n+lupcKJP5d6AM2kvmxzVWpeiii//9f/wW1r56y0/0rqUs0o1Z9EmG/cB4KfPvsrb3h+zyP9TxbdG\nHggRDlRS7bSTLms73yBoji0P2dKOvbJB61LYcTCwjPHCHO16DgBiPJkc6THujWM4emv3AYjwsniK\nfnsOAL63Yhl4o3nwjXVal6K4jh4X61p/x/jeW7hk5gStyzmrsXE2nJHG/Iyv376fX5XdwujO63jv\nZ7/QpAYRDlTg9vjoit1Dfqq28w2CrpgReNLasEf7oQXHkQpwW5k5YbSmdSRLNlo9xrxxDFfvlQYm\n1V49V989B2NGxJPWcxnvN4XfvIM7n3gKf0wTj92s714DgImpWfhjm+jocWldynmpamjjUy9ei8WV\nhf2n6myNPBAiHKjg3T0VENXLkin66DlYmJcFbivbD2kfDqraKzVdxhiUHmOjO0KEAyMpqncQ0W0j\nMy1R61LOaVn2CrqSPqKkulnrUhTT43TzYtNvsPXczLI5U7Qu55xyxwZPYDXO8GFwa2RfZAcbvvAK\n6SlxmtUiwoEKXrfbAbhh/iyNKwkwR5iI7ZtG2THtlzM29ldochrjqbKSbHitdcNqq1ujO9TrINWn\n7yGFoB9cfy3IEr9/Zb3WpSjma0/8E19sPY986sdalzIgBeMD4cB+qEbbQs7D/J9/l7aED3jwgpdY\nPD1b01pEOFDBjjo75u4szc81P9EYcx6NPu17DrrMlWRYtZ1vADA13QZmN45DTVqXIgxQW6SDifHG\nCAc5mSNJ7FzEW4fDY2ihz+VhTf39ZHTdyHULpmldzoDMnpwBfhNlDcboIfzCo0+y1/IINyc+wneu\nX6J1OSIcqKGqt4hRfn3MNwjKHZFPX+x+3B6fZjV09fbjja1lapr2PQczsgJPFbsrjXHjGO7K61rx\nxzZQOE7f8w1OdMmYFRyN20htS6fWpQzZt/7+PN74Gh5a8ROtSxmwuJgoIvrGUNVWo3Up5/SX17fw\nz9Y7yen9Kv9afafW5QAiHCjO6/PTYbWTm6yP+QZBF0zIg0gnm0u0W171UWk1mPzMsmnfczB3SiAc\nlNSJcGAEr+8ODIldPt0YPQcAd191PZjd/GHtG1qXMiQut5dnqn/N6I7ruXGRcf7/A8R6smjo1fdn\nfNv+Wr6+6QYSui5g572Paj4fK0iEA4VtKq6G6C4WT9JXOLiyIHDGwtv7tJt3sK28AoBFudr3HGSm\nJYIrkcqjxpmsNJxtqSgGbzSXzdL+d2egLpxmw9pRyLpyYw8trH7yBTwJlfzhmp9qXcp5S4mw6foE\n1tbOPi79v+sx+WLYftfLIdsaeSBEOFDYq7uP74x4gb7CwfTsdCRnCrtrtZt3UHykUhfLGIMs/ZnU\nden3xiH8T8lRBzE907BEmbUu5bwsSFlBfcybhltOF+T2+PhH5a9I67iaWy7R1z1tIMbE2uiNrNG6\njNPy+2UK7v0STms5/7r2FXIyR2pd0klEOFDYtho7ET0ZId0DeyBMJokEVz4VHdqFA61PYzxVgmyj\nxS3CgREc8ToYG2GsLm2Ab16+AqJ6eHDdu1qXMijfe/ol3Anl/HaZ8XoNACakZOGzNujyBNYrf/0b\n6hL/zXcnPMOnF8/QupxPEOFAYRU9dkZ69ZmwMy15tKBdOGjsryRFw9MYTzUq2kanJMKB3rk9Pnpj\nS5iWarxwcPXcHKK6pvDCPuOdteD1+Xmi7D5GdCzli1fM1bqcQckZYwOTn90H67Uu5SQ/fnY97/h+\nwkXyz/nDlz6ldTmnJcKBgvx+mXaLnalJ+gwHeWl59MeX09Xbr0n7XeYKxln1M2Y8LsFGv+WwLs6c\nUIrb48Neof022Up6f18VRDpZMNE4KxWCTCaJAusKKiPW43J7tS7nvNzzz7X0J5by68t/pnUpg1Yw\nPgsAu45OYH1layn3H7iF0Z3X8+5P9fv/VoQDBW0rq0WOOcaiCfpaxhi0cHIemHy8bS8PedvBZYxa\nnsZ4qslpNoju5nBzh9alKObLjz9F4dOTaetyal2KYt7e5wDgqtnG6zkA+MqiFcgxx/jrGx9pXcqA\n+f0yjxXfR3L7pXx1+QKtyxm0eVMzAdivoxNYV754CxZnNvafPqPbo8dBhANFrd8V2Bnx+nn67Dm4\nak5gxcL7paEfWtDTMsagvHGB5Yw7D+rnxjFU7x9+B6J6eWnLXq1LUczuumJMfaN0N49noD576WxM\nPWN5eodxVi389PlXcSXt495L9PtkOxDBE1grW2u0LgWA0poWXEn7+ErOjzXdGnkgQhIOJEn6uiRJ\n1ZIkOSVJ2i5J0pxQtBtqW6vtmPpG6WY2/qlso5KI6Mlgz5HQh4Ptx09jXKiDZYxBcyYFwsG+w+ER\nDvx+mSPmzQC8XbJb42qUU9HpIKnfmL0GENi+fFrECkq8aw0xhOX3yzxs/yWJ7Yv55rWLtS5nyGI8\nNt2cwPr8pm0ArLxwvsaVnJvq4UCSpJuBB4CfA7OAfcAGSZJS1W471Mq7ihjhLtTNbPzTSfbmUdUT\n+r0Oio9UgidGV8Ep15YG3mgONofHXgcfOA7hj20En5k9zeETDo5GOMiONW44APj83BX44up47r0i\nrUs5p/teeJO+pCJ+vMjYvQZBKZKNVm+N1mUA8N7BbZh6xzBv6jitSzmnUPQcrAaekGX5GVmWDwB3\nAH3Al870hn6PsSbuQCBtt0YVMSVBn0MKQVnWPNoiQt9zUNkWWMaopzE2c4SJyL5x1HTo46liqJ7b\nvAlkCVvvTdT7d2ldjiIajnXjjT9EwRhjh4OvX70YyZnCE5v0PbTg98v8YdcviW9fwN0rLtG6HEWM\ntmbRY9bHZ/xAz3bSvRfo+gEySNU7tSRJkUAhsDH4mizLMvAucMZ+laKKI2qWpYq9VY3I1hYWZOs7\nHMwak483voaGY90hbbexv5JkWT/zDYLifDaanPq4cQzVR7WbsXTmc1n2FbgTDoT8Z6yG13YGguzF\n04y3UuFEligz473XsLtH3+Hg9y+/S2/SDn4w/2eG+AdsILKTAyewanmuDAS2oe6M3cWskfofUgD1\new5SgQjg1EPNm4H0M73Jfki7/f8Ha+32QHfhtXP0HQ4uyglMSnxz9/6QtttprmBcrH7mGwSlRtro\nkMMjHNT4NzMpehFXzZoNkszLW/ZoXdKQfXjAAf4Ils3O0bqUIbt5xg24E8t4Y+cBrUs5Lb9f5v4t\n9xLbMYd7brpC63IUkzM6CyK87KnUdonvyx85IKqPq6YbIxxotRepBJxxZs66f/yJ1t0fnPTaqlWr\nWLVqlcplDd5Hh+xIzhHMz8nUupSzWjY7Bz40selAMbctnReSNnucbryxh5mSrL+eg4w4G5V9r2ld\nxpDtrWrEk1DJxWN+xbI5U+ENK2+X7jL8hLLi5mKi3VNIirNoXcqQ3X3d5dz/u1geeXsty+feo3U5\nn/DwKx/QnbyFn054NWx6DQBmZtmgAoqqDjMvR7ux/lfs28AXyaqLlFnqvmbNGtasWXPSa52dyp0A\nqnY4aAV8wKhTXk/jk70JH7MuymX9s+vVrEtxBzrsJMsFuv9QpSTEENkzEYc7dPMONpcEljEWZOmv\n52BCqo33W1to63KSkhCjdTmD9s/3A6sUPr9kEZYoMwm9BThcxp+UeNjlYJQBt00+nZSEGMY6r2RL\n31pAf+Hgvg9/SYw0i1985iqtS1HUvKk2eAeK62qAhZrVsatxG7H+WYoF3dM9MNvtdgoLlQkfqg4r\nyLLsAYqAS4OvSZIkHf/71jO975jfeMMKR812JsXpe0ghaKScx2Fn6MLBjuPLGC/M0V/PwbSxgeWM\nO8qNvWJhY+VmzF0TKJg0BoAJMbNpwNiTEv1+ma4YB1OTwyMcAFw7eQW9SbvYUVandSkneezVzXQk\nf8C3Z4bPXIOg9JQ4JOcIKlu1HT6sZzsTLRdoWsP5CMXU8QeBr0iS9DlJkqYCfwWswNNneoPLUo3X\n5w9BacoorWnBF1fP/CxjhIOJCXl0RocuHOyrrwBPDLMmjglZmwNVMD4QDvZWG3veQUX/ZrKkRR//\n/QLbbLwJVVQ3tmtY1dDsOFAHlk7mZRl7MuKJfrDiKvBF8ofX1mldykl+vvE+LJ353HfrtVqXogpL\nv436bu0+46U1LXgTqlicbYz5BhCCcCDL8n+Au4FfAnuA6cBSWZaPnvFNZhe7yvV1UMbZvFEU2Dfg\nypkzNa5kYArH5eG3NlNWe+YfgZKq2iuJ7pugq2WMQbMnZ4AscaDRuD0Hh5s7cCU6WGT73/yC62YH\n9hl7cYv+19WfyZv2wLbJywrCp+fANiqJEd2XsPGIflYt/O3NbbQlv8Od036qy8+oEpKlLFrcNZq1\n/6/N2wG42QCbHwWF5DdBluXHZVnOkmU5Rpbl+bIsn3Mw9L3islCUpohtVSXgjebiGRO0LmVALssP\nPIm9WRSa3oMGVwUpsv7mGwBYLZGYesdwqM24PQdPvbsFJJlbFv6v5+DSWROhP4GNB4w7tLCjphhc\niYbYMOZ8LM1cQUfiJsrrWrUuBYCfvH0f0Z25/P4L+jwdUAnpFhvdEdp9xgObH43W/YT1E+kzJnqj\n2VUd2qV2Q1HWWkpMTw5RkRFalzIgl8ycCN4otlaGJhx0mivJsOpvvkFQrMdGQ69xw8FbZZsx9aaf\nFE7NESaS+gopaTPupMQD7Q4SnNPDbgz8B9ddB5Kf3617VetSeObd3RxNepMvT/lJ2PYaANiSbHis\nhzUbri7r3ka6d76hfpd1+dsQ7cqivM04PQf17hLSTXlalzFgligzlp4cSo+qHw4CyxhrmDpSnz0H\nACkRNo55jRsOSns2Mda7+BM3nslxc2iOMG44aJYd2CzhM6QQNH18OvEdC3jjkPZDC997/RdEdk3m\ngS99WutSVDU1PQvM/ew/3BLyto22+VGQLsNBspRNg9sY4cDvl+mxljAlxTjhACDdlEe9W/0zFraU\n1oDJz0wdncZ4qtFWm262Vz1fbV1OehJ2M2/0ok987cLs2fjiaimtCf0Ncag6elz0x5czPT38wgHA\nRaNW0Bz3Nk1tPZrV8LW/Pk9L0ut8I/dXhun1HKwZtsDE410Vof+cr91aDFF9LM83zkoF0Gk4GBeX\nTbdlvyFOMNtxoA6iu5ljm6Z1Kedlako+PdYS1f8fbyuvAGCRjk5jPFV2sg1fbD0ut/HO9HjmvR0Q\n4eGmeZ8MBzfMC0xKfGmr8XoP3txdBiYfi6eEz0qFE929fAWY+/nD2rc0af+jkhr+Uvs1srpu4cHb\nbtKkhlC6YGoWAI7ampC3/UrRNvCZWblYmf0HQkWX4SAnfTxyTFvIZtMPxTv7SgG4Yqaxeg7mZeVB\ndHcg3KjIcaQSPBZdLmMMmjraBiaf5turDsb6fZuQXElcP/+Tv38Lcm1IzhF8UGG8SYnvlQZWKlw9\n11ifq4FaMmM8lo4ZvLz/vyFv2+3xcdXfP0uEO5kPf/DnkLevBduoJOhPoKIl9D0HOxu2Eds9y3Cb\nrOkyHMzKzgbgnb36n5S4o7oE3HFcYKBZqACXHw8zb+9Vd95BZVsF0To7jfFUM7MDXY5FVcYbWtjX\nvpmRrgtP2y1sMkmk9M9mf4fxeg72NBRj7h7PmBHxWpeimguSVnA4+nV6nO6QtnvVb39LV+JWHl3y\nHJlpiSFtW0sWZxa1XTUhb7eObUy0GGu+Aeg0HMyZPA58ZnZU6X/ewYG2EmL7cnX9j9/pzM/JhP54\ntlerO++gob+SFB2exniiuZMDwW7/EWPtddDn8tAWu42C1E8OKQTlJMyhNXK3IYboTlTd62CkLzzn\nGwR9/ZIVEN3Fw6+8F7I2n3p7J+96f85CfsTXrtZuK2EtJGKjxR3aBwAjbn4UpMt/0WKizUT1TGL/\nUf2Hg0ZfCWPMxuv6NJkk4vryKG9Tt+egM6KCDKt+5xtAcHvVFCqPGqvn4N+b9kBULysKzny40qIJ\ns/HHNhnuGPSOaAeTEsM7HNxwYT7m7vE8bw/NqoWmth6+uuEWYrsK2XDPz0LSpp6kRdvokmpC2uYL\nm3cA8OkFxpqMCDoNBwCp5FDn0vewgtvjwxlbRu4I44UDgIyoPJr86oWD4DLGySP13XMAge1V6zTc\nXnUw/lu0GTwxfGbJmSc63XDB7MD3bjfO0EJJdTN+azNzM8M7HJhMEjOjb6BcWofb41O9vYt+8x08\nlkbW3vocVkuk6u3pjS0xi/6YwyHtRdt4cBum3nQW5NpC1qZSdBsOxsfn0hml756DzSXVEOnkggnG\nDAe5qXk448pUm6UfXMZYYNN3zwFAEjaOeowVDna3bCapZx5xMVFn/J7Zk8di6h3N5irjhIPgduSX\nTQ/PlQonuv3CFcjWFv6+YZuq7Xz/qf9yMO5JPj/qES4v1P/nUQ2T02wQ1UtVQ1vI2izr3sYoj7E2\nPwrSbTiYPjoHf2wDtS3KnU+ttHcdgafuK2Yaaxlj0IKJeWDu5729lYpd0+X2sqOsjsdf+4hfvfos\nABdO1X/PwSiLjW7JOOHA6/PTHL2Z6UlnHlIIGumZzYEu46xY2FLpAE+MYbYjH4rbll6AqTedf2xV\nb2hh98Ej/LH8y4zpvIF/fONLqrWjdzNsWQDsKK8JSXsut5eO2J2G2/woyKx1AWeycGoOjzfD2/Yy\nbr9Sn+M1u2tLkVzJzJwwWutSBmX57Hy+Wwwbi0tYPnfqgN5Tf7SLXQdrcRyupbyplpr2Whr6DtPu\nq6U3shaf9QiYjneRmiC6M5fCyWNV/K9Qhi3Rxt6eQJejEVL+6zvKkGPauGramScjBuUmzeYD5yOG\n+W/b31pMrC8v7DfmgcA211O4jn3utfj9f1T85+P1+Vn6+BeQoix8cNffDPHzV8ucyTbYAo7aw4D6\new4ENz+6aroIB4q6fNYU+EBia4V+w8HBjhLifXmG/cDlZI5E6kujqK4EuBG3x8e+Q43Yq2opqTtM\nZWst9V21tLhr6aIWl+UwWE7oyfFHEOHMIM5nY0REFnkxi8lKymRKeiYzbJnMmZJpmKVok0fZoN9J\neX0rOZkjtS7nnP69fTP4I/jcJef+bCyZPIf3D7axqbiaJTPGh6C6oTniczDOPEvrMkLms7Nv4Edl\nT/Di5n3cfJGyJ7t+6g8P05b8Lr+b9g6TMkYoem2jmZKRCp4YyptrQtLe+qLthtz8KEi34SA10Yq5\nJ4tij34nJTbLJUyMPveTm54l9eexSXoM83efxhdb/7+nfkByJRHtziSBTCZGLSQj7jNMGmljWkYm\nBRMymTF+dNg83U3PtEEtFFXUGiIcbD2ymVh/Iekpcef83k/NL+TnB+GVXbt1Hw5cbi/OuFLy4j+v\ndSkh881rlvCjPYk8/v5aRcPBfzbtY33vPRT67uL7N16m2HWNymSSiOrL4rAvNMOHOxu3YfXNNNzm\nR0G6DQcAyb4cavv0OSmxz+WhP66c3IQ7tC5lSO4o+BZr9r3IaGsmWYmBp/7ptkzmTM4kY2SC1uWF\nTOGkTPgodF2OQ+H3y9SbNjHTcvOAvn9aVhoRPZlsqd4N6PuAnXf3VIC5n0WTw3ulwoniYqLIcl/N\nzv61wL2KXLOty8nn1n0GizyV9351vyLXDAcJso1mV2jCQZ28jZzoZSFpSw26Dgc2ay57+0O/vehA\nvLu3AiI8XDjJmCsVgu7/3HXcz3Val6G5YJfjwWb9T0rcuv8wvrh6rsgeeK9Vum8OFb36n5T4jiOw\nbfJVs8N/pcKJbpy2gj/WPc/GPZVcOmvoE3gvvv8H9FsPsW75bhJioxWoMDykRWVxyK3uyhCAstqj\neGUIF9UAACAASURBVBIqWZxuzPkGoOPVCgB5o3LwxlXT1uXUupRPeL8ksFLhygJjrlQQThbocrRx\nuFP/4eC5TZsB+OIlA9/hLi9lNh3WIs3Osx+oorpiTL1jht34+PdWXAkeCw++OfRVC79c8yaOmD9x\nY+IfuG6BuD+daFy8jX6L+p/xf324HYCbLxThQBUXTs4FSeadPeVal/IJRXUlmHrTmTIuVetSBIXE\nh7DLcSg+qN5EdOe08/oH9NKcORDdzTv2ChUrG7rKbgcpnuEzpBCUlhxLeu9SNrUMLRyU1rRw794v\nMrJjGf++++sKVRc+Jo20IVs6VF8i/17Fdkx9owy5+VGQrsPBFQU5AHx0QH/zDiq7Skh0i1QeTkZG\n2uhA/+Gg2r+ZCZHnNxH2xgUFAKzfre+hhdYIB+Njh184ALh64gp6krext6pxUO/3+2UueeQ2ZPy8\n+81/GHYVlZryM7MA2Fmu7ud8f9c2RrmNuflRkK7DQWZaIqbe0ext0N+KhVZTKbYYY883EE42Lt6G\nK1rf4aC0pgV3QjmXjD/35kcnyh6dTGTXRLbX6nenxNqWTnzxhynMGJ7h4IcrrgF/BL9bt25Q77/1\n4SdoSXqNn+T/g+nj0xWuLjzMnhh4kt9Xo97nPLj50cxU4w4pgM7DAUCiO5fqbn31HLR1OfHEVTI9\nXYSDcDJxpA05po2mth6tSzmjp98LzDf43JLzX0I7hjlUOfUbDl7bGdg2+dK84RkOJoxJIblzCW/X\nnf/Qwhs7D7Cm7S6m9d3JL2+9WoXqwsP08engjaKsqUa1Nl7ZVgJRvSw36OZHQboPBxmWHFrRVzjY\nYD8AJj8XThbDCuEkLyPwVLHzoH6Pbn63YjPm7izmTMk47/fOGDmb7ji7amdpDNWmcgf4zCwtnKJ1\nKZq5LGMFbQnvU93YPuD39Djd3LjmFqL6bHzwoz+qWJ3xmSNMRPZlUtOhXs/But3bDL35UZDuw0Hu\nyBz64w7S5/JoXcrHNpWVArB8tggH4WTW+EwA9lbrd2ih3LWZTM5vSCHostzZEOnk9Z36CttBxS3F\nWHpyznqQVLj7/rXXQ4SX3697fcDvuezXP8MZX8w/rn6e1ESritWFh3hfFk3OGtWuv7NxO9buGYb/\nWeg+HFwwIRcivHzgqNK6lI/tOVJCRM/w2iRoOJg1cQz4IzjQqM9wUH+0C2fCXhaOG9yunDctLABZ\n4jW7Picl1vU7SJeG55BC0OzJY4ntmMcrBwe2v8vD6z5gh/n3LIv+FbdcUqBydeEhNdJGu6zeZ7xO\n3saEaGMPKYABwsFlMwIrFj4o1c+kxOreElK8Yr5BuLFEmYnozaC6XZ/h4OmNW8HkZ+WCwYWD9JQ4\norty2HVEf/MOWjv76I6zM2OksbtilbAodQWNsW/R2tl31u+rbmznu1s+S1LHRaz7/t0hqs74MuJt\nOKPU+YyX17XiSahgUZYIB6rLtaUhOVPYU6+frtBjESVkWcWQQjiK89po7NNnOHhz/2akvjSWFk4e\n9DXGmmZT49ZfOHho/bsQ6eLOy67SuhTNfWfpCoh08sC6t8/4PX6/zEV/uAO/uYe3vvpM2JxxEgqT\nUrOQrUdpae9V/NrPBzc/WiDCgepMJok4Vw6VHfoIBw3HuvHFH2bmGNFzEI5GmG20hehglvNV0rWJ\nMZ5FQ1o7XTBqDr1x++hxuhWsbOhecqwnqmsKS2cPPviEi6WzJxPdmct/is+8auGOvzxLXeJ/+PaE\nJ5iXMy6E1RnfNBUnHm88uA1T3ygW5mUpfu1Q0304ABgTmUOzXx/DCm/uDtRxUY4IB+FoTKyN3kj9\nhYOOHhdd8TuZmz60U0CX5s8Gs5t1W4sVqmzovD4/labXmG65RutSdGNO/A1UR64/7UTsD/Yd4v8a\nvs6E7s/z0O36PkhLj2ZPzALAfqhG8WuXdW0nzX2BoTc/ClItHEiSZJMk6e+SJB2SJKlPkqQKSZJ+\nIUlS5Plea+qIXJyxB3SxL/zm8hKQJZbNztG6FEEF41Ns+GMbdPdk/dz7u8Ds5qa5g1upEHTDghng\nM/OmQz9DC89u3I3f2sznL7hW61J0446LViBbOnjstQ9Pet3l9nLNU7di7h/JBz94VKPqjE2ticdu\nj4/2MNj8KEjNnoOpgAR8GcgFVgN3AL8+3wvNzsqBSCfby7Rff+5oLCGye4Jhz+gWzi5njA0kGXvF\nEa1LOcn6vZuhP4FPXTi02fwpCTHEdOexu0E/Kxae/Gg9kjOF25eGx01VCauWzCKi28azu04eWlj2\nm1/Tk7iTP1/6vFgtNUhqTTxet60EonpYnh8ev8eqhQNZljfIsnybLMsbZVmukWX5NeCPwA3ne62L\n8wNP6Rsd2g8tHHaWkuoXQwrhakZWYK8D+yF9DS3Y2zaR+v/t3Xl8VOd97/HPM5JG+4IQu0ASIJCE\n2LSweQEbMBBvaRzbUeKbhNRpUjsbN72x6zZ22yTXbZqEtE2cxE3qpba5aeIN2cYYY2MEFqvYRhKb\nkBBCrALt+8xz/xiNjUDLjDRnzszo93699Io1Ouc5jzM+o6+e5Xfalnhl4dmU0Dyqu/1n5GB/UyGp\nXZ8hwurXT5D3KYtFMTvss5TpNz4ZMX12UzHbHD9iqfp7/mpNcPwCMktMdyq1rVVebdNV/KhgaZ5X\n2zWLr9ccJABXPD1pYcZk6Ixm32nzFyXWW21Mi5NwEKwWznSGg9Kz/hMOOrvs1EV+TM7o4U0puORN\nyqc9zjboVjlf2Fl6mvaEw3w2S6YUrve1xZ/DEV3L81v2UFvXxKNbHyKmMZ93n/h7s7sW8IxYeLy7\ntjgoih+5+CwcKKWmA98CfuvpuaEhFqJaMzh+xdxwUFF7BUf0OXKSJRwEq8S4SFTrWCou+084+FPR\nIQhv4t55w1uM6LJmTh5Y7Lz28SGvtDccv3ynEOxh/O97VpndFb/zjTU3oVrH8J87Xmfp09+hO/wi\nhV99WUZYvCA5JpVWa5VX2zyjdzEtfJFX2zSTx/+VKaWeBh4b4BANZGqtj19zziRgE/BHrfV/DXaN\ndevWER8f3+u1aHsEtenmTits2u8sm7wsS2ocBLOozhRqHP4TDv68dzt0h/PQbfleae/exdnwoZX3\nbPtMH57+8GwhiSyT+fM+WMNCSHfcwx79DMQ283DS8yybO9XsbgWFqYkpbFfnaGzpIC46fNjtnaip\noyvuODePe9ILvXPPhg0b2LBhQ6/XGhoavNb+UCLoz4DnBjnmlOsflFITgQ+AHVrrb7hzgfXr15OT\n07sU6KofP82Wlp/icGjTtonsPG4Deygrc2QvdjBLUClc7vKfcLDnQhHxjoVe+RADiIm0Et08jwNt\n5i5KrLnUSF3ch9wX+3NT++HPCub9Bf948g8kN9zP7374ZbO7EzSyJqXAVdh7/AzL508fdnuu4kcP\nLPZd2C4oKKCgoKDXayUlJeTmeqfKqMfTClrrOq318UG+uuGTEYMPgb3A14bT0ZzJmeiIeg5Xnh9O\nM8Niu2gjvHnmiH4wzEgwPjKF5hD/CAcOh+ZcWBHZcd6ZUnBJs+ZR4zB3UeL6je9BSBffWyP1Dfrz\n+P2r+GLcb9nx2LNBsXfeX+ROSwVgf0WVV9p7/1gxqnUst85O80p7/sDIOgcTgG1ANfADYKxSapxS\natxQ2ls2KwuArYfMW3dwpsPGWGRKIdilJqTQFVXtF3U13t13DB11iTWzvBsO8pPz6Iw7Sm1dk1fb\n9cQb5YVENMwOimpyRomwhvLyum+QMi7B7K4ElQUzJ4NWlNV654+AssZixnUuDqoAZ+SCxDuAqcDt\nwBmgFjjX878eWzpnKnRb2X3KnHDgcGgaI0pJT5DFiMFuxrgpENpJ2emLZneF//dxETgsrF2xxKvt\n3p2TD0rzpx0lXm3XXZ1ddipD3yYnRkYNhO/FRFqxtEykoq5q2G0FW/EjFyPrHLygtQ657suitR7S\nRu0IayjhLemUXzJnUaKt6gI6so68KRIOgt3cFGft9b0nzJ9a2FlTRFTjfCaOjvVqu2vyM6AzivfL\nzJla+P3mYnRkHWuXSDgQ5ojuSqG2Zfj3+MZdpWBtZnV28OxUgAB5toLLGLKo6TBn5ODdEhsAK2ZL\nOAh2C2Y4w4HtjPnh4DTbmRnh3SkFcIbt2Jb5HL5sTjh4YVchqnUsX125wJTrC5EYksLl7qpht/P6\nvmJwhFBwa3AUP3IJqHAwNS6TRqs54aC4wgZdEc7pDRHUUsYlQEcspedOmtqP3eVnsMeeZuVM7xQ/\nut70yHxqMWfHwsHWjUx33EVoSEB9BIkgMjEq1SsPWdt9tpjIxrmMHRXthV75j4C6M+dOzMQRfZ7K\nc1d9fu3yy6VEtmTKc9NHAItFkdy+mg8af0t9c7tp/XjxoyIAvnr7zYa0vyglj+64Cp/fT1v2n6Az\n/iifny1VEYV50hJTsEedpb2ze1jtVOtipocH13oDCLBwcGumc8fCewd8P3pwttvGhBCZUhgpni34\nEfaoWr76q9+Y1ocPT23H2pBB5pQxhrR/d65zGPSPO3w7tfCrLYXQHc737l7h0+sKca2sialgsbPv\neM2Q2/ik+FGqhANTrZg/AxwWPj7h20WJDoemObKUmaMkHIwUa/JnktH2NTbW/4Tqi96rOuaJU91F\nTA01ZkoBYGVOOnTE8eEx34aD7ecLGdO8POiGYUVgmZ/mXFu0v2LoUwuvbN8NwOcXBddiRAiwcJAQ\nE0FocxqlF3w7crD76BkIb2JBqtQ4GEn+++Gn0KEtPPRr31fwO3bmMh3xZSxL8/5iRJfQEAsJrbnY\nrvguHFSeu0p9fBErp8iUgjDXooyehcc1VUNuw1n8aAzLgnAtWkCFA4DRjiyq23wbDt476NypsHKe\njByMJHkzJrGA71DU/QtslRd8eu3nP9gBwEO3GhcOAGbE5HMhxHeLEn/25iaw2Fl3510+u6YQffHG\nQ9ZKG4Kv+JFLwIWDlOhMroT4dlphd6UNOmNYnDnFp9cV5nvlkcdQjjC++Lsf+/S6W44VEdI8mZtm\npRh6nZvS8rDHnPFZ+HnrRCFR9bnkzZjkk+sJMZCozhRqmocWDpzFj3Yzd3TwrTeAAAwHcyZkYY89\nzcWrLT675rGrNmJas4MyHYqBTZuYyB3Rj3HE+ju2HTo1+AlecrStiMkO49YbuHw237ko8dXi/YZf\nq7W9i2rrJhYkSOEj4R9GqVQud1UN6VxX8aM1syUc+IUl6ZkAbDlwzGfXPGcvZWKorDcYqV769new\ntCex9kXfPI71/JVmWuJKWJJs7JQCwM3Zqai20Ww7YfzUwm/eKYKIBh6+RcKB8A/jI1NoGuJD1t7Y\nvysoix+5BFw4WDk/A4Adx3wztdDZZactuoysJFlvMFIlxUfx4PgnqYp9hf/Zfsjw6z2/tRgsdh5c\nbHw4sFgUiR15lNUbvyjx5b2FWJonUbBsvuHXEsIdaaNS6Y4e2kPWdtcUE9k4J2h33QRcOEgeE0dI\nczKHz/lmUeJHh09BWDuLp0k4GMl+/8hfEtY0jW+9/oTh13rHVoRqS+KuBZmGXwsgIzaPy9a9OBza\nsGs4HJojXRvJsNwt03PCb2SMT4GQLg5WnPP43GpdzDRrcE4pQACGA4D4rkwqm3wTDt4/4typsDpH\nwsFIFhURxl9n/JhLCe/wHxu3G3qtIw1FjO+42We/RG+dno8j6gL7T5w17Bpv7SmnO/YUD86TLYzC\nf8xN7al1cNKzqYWK2it0xh0LyuJHLgEZDiZHZlJn8c20wv7qUlRbItmp43xyPeG/fv61+4msz+GJ\nDx437K/sxpYO6mN2kT/O+CkFl88tcs6ZvrbLuKmF32wthM5ovnP3bYZdQwhPLZzpDAeHq6s8Ou+l\nbbsAuH+xhAO/MmtsFp0xJ2lu6zT8WsfrbcS1y04F4Swa9MPFT9M8qpgfvlxoyDU2fLQfwtq5L8/4\nnQouOdMnYmkZz/YK4xYl7ry0kQmtK0mIiTDsGkJ4KnlMHKp9FCc9rHWw9dguVFtSUBY/cgnIcLBo\nWiZY7Gw9cMLwa13ExuRwmVIQTo99fiUJV2/j5weeoLPL7vX23zhQBJ0xPHDrPK+33R+LRTGmK59j\njcaMHJRXX6IpoZjVU2VKQfifiPZUqhurPDqntKGYsR3BWfzIJSDDwR3znQ9g2l5u7LqD5rZOOmKO\nMWusbGMUThaL4hef+Wc64kt59NmXvN7+/svbSWxZTIQ11OttDyQrIY8rEfsMmS75+ca3Afj+3Xd6\nvW0hhiuBFC51uT9y0Nll50pU8BY/cgnIcDBzchKqLYmDZ40NB1sPnICQbm5Kl5ED8am1dyxgYsPn\neK7qSRpbOrzWbmeXnUsRO5mf6LspBZel6XnoyCtsP1Lp9bY3nSokpmEhs1LHer1tIYZrXEQKTcr9\ncFC4uwzCm1iTLeHAL8W2Z3KywdhFiR+UunYqyMiB6O0/v/AT7FE1fMWLj3R+o9gGEQ3cPdd3ixFd\nPr/EuSjxzb3enVqob26nNnIzS0bLlILwT6kJqXRGnXZ71Oz1fcXgsPDFpfkG98xcARsOJlmzuOgw\nduSgpMaGpWUC6cmjDb2OCDyfWZDBjNa1vHn1J9RcavRKm/+zezvYw/hfty3wSnuemJU6lpDmKeyo\n9O6ixF+9tQ2sLXzzNqmKKPzTjHEpENZGefUlt47fc3ZXUBc/cgnYcJCRlEl79DFDFoW5VDSWktAp\nowaiby9+7Sl0WBMP/foXXmlv97kiYhsXkBgX6ZX2PDXens/JFu+OHPzxQCGhTWncu1juI+Gf5qWm\nArDneJVbx5+2FzM1iIsfuQRsOMhPzYSwdnaUVhl2jcsWGymRst5A9G1h5mTyHN/mo66fU1p1cVht\nORya2tAiZsX6fkrBJTsxj/qo/UMqJdsXh0NT7ihkVphURRT+a8EMZ62DI2cGX3dQUXuFzvij3Jwi\n4cBvrZjr3LGwzWbM1MKVxja6Yk8yZ4KEA9G/V/76cdAWvvS7nwyrna0HTuKIPs/qTPPCwe0ZeRDe\nxHv7j3ulvT8VHcIec4Yv5sqUgvBfaeNHQUcsxy8OHg5e/mg3ENzFj1wCNhzkpk+Cjlj2nTZmUeKm\nfeWgNLfMlHAg+peePJqVkY9xKOw3bD889JX+r+wsAq1Yu+ImL/bOM/fflAtA4X7vTC08+1EhdMTx\nyJ2+330hhLssFkV4ewrVDVWDHvv+0WJUWxK3zZ1mfMdMFrDhwGJRRLdlcOKqMSMHRUdLAViTl2VI\n+yJ4vPSt72JpH83aF58achs7qouIbJjLlLHxXuyZZ9ImjCKscTq7qr0TDnZd3cjk9tXERFq90p4Q\nRonXKVzoGHzkoLRhF2M6Fo2IabKADQcA40OyOGc3JhwcqLUR0pTCxNGxhrQvgsfYUdE8MO5JTsW8\nxKs7jgypjSpdRHq4eVMKLhPIo6Jt+DsWSk7U0pqwj7tmyBZG4f/GhafSoKoGPKbb7nAWP0oM/ikF\nCPBwkD4qk5bIMkOqulW22BhtlykF4Z4/PPowoU1TeeRVzx/pXHKilu64Clakmz/8Pm9MPk0xB2jv\n7B5WO798+21whPD9e9Z4qWdCGGdyXAodEQPXOijcVQbhjawO8uJHLgEdDvKmZEF4EyUna73e9pWQ\nUtKiJRwI90RFhPHNGT/iYsJbPPPWDo/OfWFbEQBrbzd/5GBFVh6EtfH2nuGNyG0+vZH4hpuYNjHR\nSz0Twjgzx6VCeBOV56/2e8zre0dG8SMXn4QDpZRVKXVQKeVQSs3xVrvLsjMB+OCwd6cWai41Yo89\nzbyJsjdbuG/9ww8SWT+Px9/37JHOH1YUEdaYTnaa+Y8Fv++m+aAVb5UMfWrhckMrF6Pf55ZxMqUg\nAsPsyc7tjHuO97/uYNfZYiIb5zA+McZX3TKVr0YOfgrUAF4d/78lOw26w9l9yrs7Ft7d72xvaZaM\nHAj3hYZYeGLh0zSN2sk/vPK22+ed6NxOmsX8KQWAiaNjCW/MZO/ZoS9KXL/xfQhr51srZQujCAz5\n6c5wcPh0/+HgtH0XadZFvuqS6QwPB0qpNcBK4G8Ary7xtIaFENE8k6N13h05KDpmA4eFVTkZXm1X\nBL8nHlhFwtVl/LTkb92q3ll57irtcTZuTTV/SsFlkiWPys6hjxy8ergQa+NMVuXN8GKvhDBOVspY\n6Irg6PmqPn9eee4qnfHl3DRlZKw3AIPDgVJqHPAs8BDQZsQ1xqhMznZ4NxwcOV9KWPM008rYisBl\nsSj+dfXTdMTb+M5/vjLo8c9t3QlK86Wb/ScczB+XR2vsoSE9cbLb7uCEeos5ETJqIAKHxaKwtqVw\nur7vkYNPih8tknDgLc8Bz2itDxh1gWnxmTSGe3da4XSbjSSHTCmIoXl49SIm1H+WP5wa/JHO75Zv\nx9I8iVtnp/mod4NbPTsfQrrYuMvm8bn/vXUfjujzfHmhhAMRWGIdqZxvr+rzZ1t6ih8tnz/dt50y\nUainJyilngYeG+AQDWQCq4FY4F9cp7p7jXXr1hEf37sYTEFBAQUFBTccOz85i201lzh25jIzJye5\ne4kB1Vtt3BT5da+0JUam3z74E+7dNJu1v/4dr/7gO/0eV95aRLLlFr8qqvK5JXP5+sehvHNoLw8t\nz/Xo3P/aWYjqSOTrq5cY1DshjDEmLIXTXX1Pp9nqixmj/Kv40YYNG9iwYUOv1xoaGrzWvsfhAPgZ\nzhGBgVQCtwGLgA6lev0fuk8p9bLWem1/J69fv56cnBy3OnNLRibra2DLwXJmTh7+0OyJmjoc0efJ\nnSQjB2Lo7lmURfqrX+H19h9TW7e2z2JalxtaaY7dx53x/8uEHvYvMS6SyKZs9rd5vihxX2MhqZbP\nEGEdykeLEOaZHJvCsZY/3/C6q/jRisgfmNCr/vX1B3NJSQm5uZ4F+v54PK2gta7TWh8f5KsL+DYw\n95qvNThHFR4A/s4rvQeWz0sHh4VdFd5Zd/BuibNs8rIs2cYohueFtf+AtjbypV/1/UjnF7bugpBu\nHlzkHzsVrjUlNI/qbs/Cwc7S07QnHOLeTJlSEIEnfUwqOvIKtXVNvV5/e3e5s/jRrJGz3gAMXHOg\nta7RWpe5voATOKcWTmmtvVa1KC46nLDm6ZRd8E442HnCBvYwls9P90p7YuRanDWFXPujbOv8GeXV\nl274+VtHilDto7h7kf89vyN3Yh7tcTYuN7S6fc6/bXoL7GGsu2eVgT0TwhjZPbUOdh/tvSjxtZ7i\nR19atsCMbpnG1xUSvV/nGBjtyKS6zTuLEm0XbYQ3z5SHxQivePmv/9b5SOff/N8bfnboahFj228m\nNMT/CpV+Zm4+WOy89vEht8/5oGYjiY1LTX14lBBDlZ+eCsCByqperxfXFBPROHvEFD9y8dmnktb6\ntNY6RGt92Nttp8VkUR/mnZGDMx02xilZbyC8Y+bkJJZH/B8OhD7DztJP/yJpbe/ianQxeWP9b0oB\n4N7F2dBtZfMR9+od1NY1URe7jdsmSVVEEZjmTZsA9jCOnu89cnDaXsxU68iaUoAAf7aCy5wJmdhj\nztwwV+Qph0PTFFFKerysNxDe89K3voelcxRfee7TRzpv+KgErK38RY7/1De4VkyklejmuRy86N66\ng/VvvgehnXxvjaw3EIEpNMRCaOtkqq5+Gg5GYvEjl6AIB0tmOJ+xsKXk6LDaOVx5Hh15hfwUGTkQ\n3jM+MYb7xvyQipgXeX2ns3bA6yVF0BlFwVL3duWYIc2aT43DvXDwWtlGwhuyuTk71dhOCWGg2O5U\nzrVVffL9K9v3AHDfwpFTNtklKMLBHT1ljnceH97Uwrslzg/uFXMkHAjv+q9Hv05ocxqP/Nm5UWf/\nxSJGtSwmKiLM5J71Lz85j864o4OOyHV22akMfZvcGJlSEIEtKSyFq/rTkYMt5cWottGszBl5C9SD\nIhyMT4whpHkKR84PLxzsPlUKXZHOBzoJ4UUxkVb+avqPOJ+wkWfe2sGFiCLmjvLPKQWXO+fngdL8\naUfJgMf9fnMxOrKOtUtkSkEEtuSYVFqtVZ98b6svZkyHfxU/8pWgCAcACd2ZVDUPb8dC2WUbkS2Z\nWMNCvNQrIT71b1//AhH1c/juti+jI65y12w/DwcLMqEzivfLBp5aeGFXIap1LF9dObK2eongMy0p\nBR11kSuNbXTbHdRF7mZO4shbbwBBFA5SIrOoswxv5OBst40JITKlIIwRGmLh8fyn6Y6tBHsoX1nu\n3/OYEdZQYlvmc+jSwDsWDrYWMt1xl19uyRTCE9nJqQDsPlbtLH4U0TDiih+5BM3dPGtsJl0xFdQ3\ntw/pfIdD0xJVSkaihANhnB9+YQ0JV5cR37iEpPgos7szqGmReZxT/Y8cbD1wks74cu7LlikFEfhy\npzkLIZWcquL1fbvAYaFgab7JvTJH0ISDxelZYHGw9eCJIZ1fXF4N1mYWpMo2RmEci0Vx5O/eZO/f\nvGZ2V9yyOCWf7rgKKs9d7fPn/7G5ELrDWXfPSh/3TAjvy5k+CRwWys+dpvhMMRGN2X0+F2UkCJpw\ncMd853bGHUeHNrWw5aBzp8Id82TkQBgreUwc6cmjze6GW+7OzQPgjzv6Hj346HwhY5qXM3ZUtC+7\nJYQhoiLCCGlN5lRdFaftxaSFjcwpBQiicDBtYiKqdSwHaoa2KHF3lQ06YlmYMdnLPRMicK3MSYeO\nOD48dmM4qDx3lfr47aycIlsYRfCI7krhZPMhOuLLuClFwkFQiO/I4lTj0EYOjl2xEdOaPSK3rAjR\nn9AQCwmtuRypu3FR4i82vgsWO+vuvMuEnglhjKTQVC7FbgHg8wslHASFSeGZXGJo4eC8o5RJYbLe\nQIjrpUfncTH0xpGDjcc3ElmfQ96MSSb0SghjTIxOgZAuVFviiCx+5BJU4SAjKZP26GO0d3Z7dF5n\nl522mDKyxsh6AyGud/PUfOwxZ7BVXvjktdb2Lqqtm1iYIFMKIrhMTXTuWEgaocWPXIIqHCycsy2X\nuQAADS9JREFUmgWhnRQdqfTovA8PVUBoB4unSTgQ4nqfzXcuSvzzx5+OHvx20w6IaODhW2QLowgu\nsyalAjBn1MidUoAgCwfL5zh3LHxY6tmixA9spQCsyZFwIMT1bs5ORbWN5qOTn4aDl/ZsxNI8iYJl\n803smRDed9vsDLCHcn/e7WZ3xVShZnfAm+ZNmwAdcZRUlwP3un3evmobqm00WSljjeucEAHKYlEk\nduRR1uEMBw6H5khnIRmhd4/oYVcRnPJnJnPymxeYNjHR7K6YKqhGDiwWRUxbFifqPVuUeKLeRly7\n7FQQoj8ZsXlctu7F4dC8s/co3XEVPDBXphREcBrpwQCCLBwATAjN5Lzds2mFi9iYEiFTCkL055Zp\neTiiLrD/xFl+/f5G6Iziu/eM7GFXIYJZ0IWDGYlZtEYdxeHQbh3f3NZJR8xxssdKOBCiP/ctdtaX\n/3PxXnZeKmRC6x0kxESY3CshhFGCLhzkTckEazN7j9W4dfyWkuMQ0s2SdKlxIER/cqZPxNIyno1l\nm2hK+JhVaTKlIEQwC7pwsCzbuWPh/cPuTS18WOp8psKaXAkHQvTHYlEkdeVxNOJ5AL5/953mdkgI\nYaigCwdLslKgK5J9Ve4tSiypsWFpmSgLUIQYxKyEfAjpIqZhIdlp48zujhDCQEEXDqxhIUS2zORo\nnXvh4FRTKaM6Zb2BEINZmu4shrRktFRFFCLYBV04ABhryaS2071phcsWGylRMqUgxGD+cuXNjK5f\nxZN/8UWzuyKEMFhQFUFymR6fxQetm3E49IC1Cy43tNIVW8GcRBk5EGIwyWPiuLz+XbO7IYTwgaAc\nOZifnImOvEJ59aUBj9u8/ygoza0ZEg6EEEIIl6AMB7dk9exYODTwuoOPynt2KuRlGd4nIYQQIlAY\nGg6UUncqpXYppVqVUleUUq8ZeT2X2+dOB3souysGDgcHa22ENqUyPjHGF90SQgghAoJhaw6UUvcB\nzwKPAx8AYYBPxu9jIq1Ym6dTOsiixKpWG4m+6ZIQQggRMAwJB0qpEOCXwPe11s9f86OjRlyvL0lk\nUdM+8MjBldBS8iNk5bUQQghxLaOmFXKAiQBKqRKlVK1S6h2llM8m99NiMqkP6z8c1FxqxB5TzbyJ\nso1RCCGEuJZR4WAqoICngH8C7gSuAh8ppRIMumYvcyZm4og5S/XFhj5//s6+UgCWZcm0ghBCCHEt\nj8KBUupppZRjgC+7UmrGNe3+WGv9htb6ALAW0MD9Xv536NMtGc5Bii0H+p7J2HHMBg4Lq3IzfNEd\nIYQQImB4uubgZ8Bzgxxzip4pBeCTcX2tdadS6hQwZbCLrFu3jvj4+F6vFRQUUFBQ4HZHV86fCdsU\nO4+X8ZerFt7w8yMXSrF2pstjZ4UQQgScDRs2sGHDhl6vNTT0PVI+FB6FA611HVA32HFKqf1ABzAT\n+LjntTAgFTg92Pnr168nJyfHk67dICk+itDmFGxdfa87ON1mI8ki6w2EEEIEnr7+YC4pKSE3N9cr\n7Ruy5kBr3QT8FvhHpdTKnqmG3+CcVviTEdfsyyh7Fqdb+w4HDeE2psfJegMhhBDiekY+W+FvgC7g\nRSAS2A3crrX23rjHIKZEZXKo4/UbXj925jKOqAvkJks4EEIIIa5nWIVErbVda/0DrfUErXWC1nqV\n1tq95yh7yexxWXTHVHKlsa3X6++WOHcq3J4t4UAIIYS4XlA+W8FlcXomKM37B4/3en3nCRvYw5xl\nloUQQgjRS1CHg1U5zgcwFZX3LqNceslGRHMGURFhZnRLCCGE8GtBHQ5SxiVgaZnAodresxk1HaWM\nUzKlIIQQQvQlqMMBQHxnJqeaPg0HDoemKdJGeoJsYxRCCCH6EvThIDkik8t8Oq1wsOIcOuIq+Sky\nciCEEEL0JejDQdaYLDpiTtDa3gXA5gM2AFbMkXAghBBC9CXow8GCqZkQ0sW2wxUA7D5VCl2R3Do7\nzeSeCSGEEP4p6MPBirnOHQsflTnXHZTV2YhqySI0JOj/1YUQQoghCfrfkNmp41DtozhwxhkOartt\nTAiRKQUhhBCiP0EfDiwWRUxbJifqy+i2O2iJKiNjtIQDIYQQoj9BHw4AJoZlccFRzq7yarA2syhN\nwoEQQgjRnxERDmaOzqQt6iibDhwGYOVcqXEghBBC9GdEhIPclEywtvKGbRN0xJE/M9nsLgkhhBB+\na0SEg+VzsgAo5zViW7OxWJTJPRJCCCH814gIBwszJkNnFDrqIpOsst5ACCGEGMiICAehIRYiWzMA\nyEqS9QZCCCHEQEZEOAAYb3FOLSyZLiMHQgghxEBGTDiYnuCslLg6R8KBEEIIMZBQszvgK0/c8wW6\n3+hmVupYs7sihBBC+LUREw6WzZ3KsrlPmt0NIYQQwu+NmGkFIYQQQrhHwoEQQgghepFwIIQQQohe\nJBwIIYQQohcJB0IIIYToRcKBEEIIIXqRcCCEEEKIXiQcCENt2LDB7C4IL5P3NLjI+yn6Ylg4UEql\nK6XeUEpdUko1KKWKlFJLjbqe8E/ywRN85D0NLvJ+ir4YOXLwNhACLANygEPA20opqV8shBBC+DFD\nwoFSajQwHfhnrXWp1roCeByIAuTJR0IIIYQfMyQcaK3rgKPAl5VSUUqpUOCbwAVgvxHXFEIIIYR3\nGPngpZXAG0AT4MAZDFZrrRsGOCcCoLy83MBuCV9qaGigpKTE7G4IL5L3NLjI+xk8rvndGTHctpTW\n2v2DlXoaeGyAQzSQqbU+rpR6E+eagx8D7cDDwL1Antb6Qj/tfxF42e0OCSGEEOJ6X9JavzKcBjwN\nB6OB0YMcdgpYCrwLJGitW645/zjwe631TwdofxVQhTNQCCGEEMI9EUAqsLlnen/IPJpW6LnYoBdU\nSkW6TrnuRw4GWOfQ0/6w0o4QQggxgn3sjUaM2spYDFwFXlBKzempefCvOBPN2wZdUwghhBBeYORu\nhdVADLAV2AssAe7RWh8x4ppCCCGE8A6P1hwIIYQQIvjJsxWEEEII0YuEAyGEEEL04lfhQCn1qFKq\nUinVppTapZTKN7tPwnNKqaeUUo7rvsrM7pdwj1LqFqXURqXU2Z737p4+jvknpVStUqpVKbVFKTXd\njL4K9wz2niqlnuvjnn3HrP6K/iml/lYptUcp1aiUuqCUel0pNeO6Y8KVUr9WSl1WSjUppf7s6XON\n/CYcKKUeBH4OPAXMx/mgps1KqSRTOyaGygaMA8b3fN1sbneEB6KBg8Cj3LgdGaXUY8C3gG8AC4AW\nnPeq1ZedFB4Z8D3tsYne92yBb7omPHQL8B/AQmAFEAa8d00JAYBfAncC9wG3AhOBVz25iN8sSFRK\n7QJ2a62/2/O9As4A/95f0SThn5RSTwH3aq1zzO6LGB6llAP4rNZ64zWv1QL/qrVe3/N9HM7y6F/R\nWv+POT0V7urnPX0OiNdaf868nomh6PkD+iJwq9Z6R8/9eAn4gtb69Z5jZgLlwCKt9R532vWLkQOl\nVBiQi3PbIwDamVreBxab1S8xLOk9Q5gVSqmXlFKTze6QGD6lVBrOvyqvvVcbgd3IvRrolvUMUx9V\nSj2jlEo0u0PCLQk4R4Ou9Hyfi7PA4bX36DGgGg/uUb8IB0ASzucwXP/MhQs4P4hEYNkFfBVnKexv\nAmnAdqVUtJmdEl4xHucHkdyrwWUT8GXgduAHOEvgv9Mzgiv8VM/780tgh9bata5rPNDZE9qv5dE9\nauRTGb1B0f/8mPBTWuvN13xrU0rtAU4DDwDPmdMrYTC5VwPYddNBpUqpI0AFsAz40JROCXc8A2Th\n3pouj+5Rfxk5uAzYcS6GudZYbvwLRQSYnsd0HwdkRXvgO4/zQ0bu1SCmta7E+bks96yfUkr9CvgM\nsExrXXvNj84D1p61B9fy6B71i3Cgte4C9gPLXa/1DJcsx0sPkRDmUUrFANOAc2b3RQxPzy+N8/S+\nV+NwrpyWezVIKKWScT6BV+5ZP9QTDO4FbtNaV1/34/1AN73v0RnAFJzPPXKLP00r/ALng5r2A3uA\ndUAU8LyZnRKe63nIViHOqYRJwD/i/I91g5n9Eu7pWRsyHecIAcBUpdRc4IrW+gzOOc6/V0qdxPl4\n9R8BNcCbJnRXuGGg97Tn6ymcW93O9xz3LzhH+zbf2Jowk1LqGZzbTO8BWpRSrlG8Bq11u9a6USn1\nB+AXSqmrQBPw78BOd3cqgB9tZQRQSj2CczHMOJx7cr+ttd5nbq+Ep5RSG3DuxR2Nc0vNDuDvev7q\nFH5OKbUU5zzz9R8OL2itv9ZzzD8Af4VzpXQR8KjW+qQv+yncN9B7CjwCvAHMw/l+1uIMBU9qrS/5\nsp9icD1bUfv6xb1Wa/1izzHhwM9whohw4F2c9+hFt6/jT+FACCGEEObzizUHQgghhPAfEg6EEEII\n0YuEAyGEEEL0IuFACCGEEL1IOBBCCCFELxIOhBBCCNGLhAMhhBBC9CLhQAghhBC9SDgQQgghRC8S\nDoQQQgjRi4QDIYQQQvTy/wGfBWJ71MmD9gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f55f1ae06d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# constructed new alpha is the same as naively computed alpha?\n",
"plt.plot(alpha_new)\n",
"plt.plot(alpha_new_naive)\n",
"print np.max(np.abs(alpha_new-alpha_new_naive))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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