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November 4, 2013 10:35
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Machine learning assignment 2
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{ | |
"metadata": { | |
"name": "" | |
}, | |
"nbformat": 3, | |
"nbformat_minor": 0, | |
"worksheets": [ | |
{ | |
"cells": [ | |
{ | |
"cell_type": "heading", | |
"level": 1, | |
"metadata": {}, | |
"source": [ | |
"Gatsby Machine Learning 2013, assignment 2, Heiko Strathmann" | |
] | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"metadata": {}, | |
"source": [ | |
"EM for Binary Data" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# load data\n", | |
"X=loadtxt(\"binarydigits.txt\")\n", | |
"\n", | |
"N=shape(X)[0]\n", | |
"D=shape(X)[1]\n", | |
"W=sqrt(D)\n", | |
"\n", | |
"# fix a bug that the lower right pixel is always zero, which breaks EM\n", | |
"X[0,D-1]=1\n", | |
"\n", | |
"def plot_image(im,imtitle=\"\"):\n", | |
" imshow(im, interpolation=\"nearest\")\n", | |
" axis(\"off\")\n", | |
" set_cmap(\"gray\")\n", | |
" if imtitle != \"\":\n", | |
" title(imtitle)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 1 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def log_sum_exp(X):\n", | |
" \"\"\"\n", | |
" Computes log sum_i exp(X_i).\n", | |
" Useful if you want to solve log \\int f(x)p(x) dx\n", | |
" where you have samples from p(x) and can compute log f(x)\n", | |
" \"\"\"\n", | |
" # extract minimum\n", | |
" X0=X.min()\n", | |
" X_without_X0=delete(X,X.argmin())\n", | |
" \n", | |
" return X0+log(1+sum(exp(X_without_X0-X0)))\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 2 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def log_likelihood_image_component(x,mu):\n", | |
" # log likelihood for a single point of a single component, no mixture\n", | |
" return sum([x[d]*log(mu[d])+(1-x[d])*log(1-mu[d]) for d in range(len(x))])" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 3 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def log_likelihood_image_mixture(x,mus, pis):\n", | |
" # log likelihood for a single point in all mixture components\n", | |
" log_liks=asarray([log_likelihood_image_component(x,mu) for mu in mus])+log(pis)\n", | |
" return log_sum_exp(log_liks)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 4 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def log_likelihood(X,mus,pis):\n", | |
" # log likelihood of full dataset in mixture\n", | |
" return sum([log_likelihood_image_mixture(x,mus,pis) for x in X])" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 5 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def update_log_responsibilities(X,mus,pis):\n", | |
" N=len(X)\n", | |
" K=len(pis)\n", | |
" log_rs=zeros((N,K))\n", | |
" \n", | |
" # update image wise, since rs are normalised over the components\n", | |
" for n in range(N):\n", | |
" # log numerator for all k\n", | |
" numerators=asarray([log_likelihood_image_component(X[n], mus[k])+log(pis[k]) for k in range(K)])\n", | |
" \n", | |
" # log denominator\n", | |
" normaliser=log_sum_exp(numerators)\n", | |
" \n", | |
" # normaliser in log-domain\n", | |
" log_rs[n]=numerators-normaliser\n", | |
" \n", | |
" return log_rs" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 6 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def update_mus(X,log_rs):\n", | |
" N=len(X)\n", | |
" K=shape(log_rs)[1]\n", | |
" D=shape(X)[1]\n", | |
" \n", | |
" # precompute weighted average of all images\n", | |
" mus=zeros((K,D))\n", | |
" rs=exp(log_rs)\n", | |
" \n", | |
" for k in range(K):\n", | |
" # numerator: weighted data sum\n", | |
" mus[k]=sum(asarray(([rs[n,k]*X[n] for n in range(N)])),0)\n", | |
" \n", | |
" # normalise\n", | |
" mus[k]/=sum(rs[:,k])\n", | |
" \n", | |
" # I have to cheat here, mus get too small otherwise, which breaks the logarithm\n", | |
" thresh=1e-15\n", | |
" ridge=1e-5\n", | |
" while mus.min()<thresh or mus.max()>1-thresh:\n", | |
" #print \"mus degenerate, regularising\"\n", | |
" mus[unravel_index(mus.argmin(), shape(mus))]+=ridge\n", | |
" mus[unravel_index(mus.argmax(), shape(mus))]-=ridge\n", | |
" \n", | |
" return mus" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 7 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def update_pis(log_rs):\n", | |
" rs=exp(log_rs)\n", | |
" return mean(rs,0)" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 8 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"def em(X, K, max_iterations=50, thresh=0.001, verbose=True):\n", | |
" if verbose:\n", | |
" print \"Running EM for K=%d\"%K\n", | |
" \n", | |
" # initial parameters\n", | |
" mus=rand(K,D)\n", | |
" pis=zeros(K)+1./K\n", | |
" rs=zeros((N,K))\n", | |
" \n", | |
" # stopping criterion: likelihood doesn't increase anymore\n", | |
" old_log_lik=-1e16\n", | |
" \n", | |
" # em loop\n", | |
" for iteration in range(max_iterations):\n", | |
" # e-step, compute unnormalised responsibilities for all components and images\n", | |
" log_rs=update_log_responsibilities(X,mus,pis)\n", | |
" \n", | |
" \n", | |
" # m-step update parameters with ML\n", | |
" sum_rs_over_n_for_all_k=sum(rs,0)\n", | |
" pis=update_pis(log_rs)\n", | |
" mus=update_mus(X, log_rs)\n", | |
" \n", | |
" # compute log-likelihood\n", | |
" log_lik=log_likelihood(X,mus,pis)\n", | |
" if verbose:\n", | |
" print \"Iteration %d, log-likelihood: %.8f\" % (iteration, log_lik)\n", | |
" \n", | |
" # check for numerical problems\n", | |
" if isnan(log_lik) or isinf(log_lik):\n", | |
" print \"pis\", pis\n", | |
" print \"mus\", mus\n", | |
" print \"log_rs\", log_rs\n", | |
" \n", | |
" if abs(old_log_lik-log_lik)<thresh:\n", | |
" if verbose:\n", | |
" print \"converged!\"\n", | |
" break\n", | |
" \n", | |
" # make sure likelihood increases, with some tolerance to get around numerical problems\n", | |
" assert(log_lik>old_log_lik-1)\n", | |
" old_log_lik=log_lik\n", | |
" \n", | |
" return mus, pis, rs, log_lik" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 9 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"Ks=[2,3,4]\n", | |
"\n", | |
"\n", | |
"for K in Ks:\n", | |
" \n", | |
" figure(figsize=(12,5))\n", | |
" \n", | |
" # run em\n", | |
" mus, pis, rs, log_lik=em(X,K,verbose=False)\n", | |
" print \"K=%d\"% K\n", | |
" print \"log_likelihood in bits is %.3f\" % (log_lik/log(2))\n", | |
" print \"weights:\", pis\n", | |
" print \"\"\n", | |
" \n", | |
" for j in range(K):\n", | |
" subplot(1,K,j+1)\n", | |
" plot_image(mus[j].reshape(W,W))\n", | |
" title(\"Component %d\"%(j+1))\n" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"K=2\n", | |
"log_likelihood in bits is -4772.896\n", | |
"weights: [ 0.41962472 0.58037528]\n", | |
"\n", | |
"K=3" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"\n", | |
"log_likelihood in bits is -4483.635\n", | |
"weights: [ 0.47013607 0.24985938 0.28000455]\n", | |
"\n", | |
"K=4" | |
] | |
}, | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"\n", | |
"log_likelihood in bits is -4337.600\n", | |
"weights: [ 0.09998609 0.32969332 0.23001859 0.340302 ]\n", | |
"\n" | |
] | |
}, | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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"text": [ | |
"<matplotlib.figure.Figure at 0x2d5f090>" | |
] | |
}, | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
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| |
"text": [ | |
"<matplotlib.figure.Figure at 0x2d46050>" | |
] | |
}, | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
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| |
"text": [ | |
"<matplotlib.figure.Figure at 0x2d79b10>" | |
] | |
} | |
], | |
"prompt_number": 10 | |
}, | |
{ | |
"cell_type": "heading", | |
"level": 2, | |
"metadata": {}, | |
"source": [ | |
"Modelling Data - Geyser" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"X=loadtxt(\"geyser.txt\")\n", | |
"n=len(X)\n", | |
"var_names=[\"Duration\", \"Waiting Time\"]" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 11 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"plot(X[:,0], X[:,1], 'o')\n", | |
"xlabel(var_names[0])\n", | |
"ylabel(var_names[1])\n", | |
"_=title(\"All\")" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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whV69TIwaFadrCnB1TT2zAljcFLXGBXqkr7cxcv9Nzz0i4iw9emTSp08fTp82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\nh5ycHH+IJwjCNSwul45YJk/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FixYppZT661//qqZMmaKUUiomJsauX2xsrMNYQH7kR37k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\nEARBQJSBIAiCAPx/UjQnZ5hfbPEAAAAASUVORK5CYII=\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x32232d0>" | |
] | |
} | |
], | |
"prompt_number": 12 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Seems clustered. Now the question is: Does this change through time. Plot all four combinations of the relation between the variables, one even apart (Markov property)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"interval=1\n", | |
"\n", | |
"figure(figsize=(12,10))\n", | |
"\n", | |
"plot_idx=0\n", | |
"for var1 in range(2):\n", | |
" for var2 in range(2):\n", | |
" subplot(2,2,plot_idx)\n", | |
" plot_idx+=1\n", | |
" plot(X[:n-interval,var1], X[interval:,var2], 'o')\n", | |
" title(\"Interval: %d, \"%interval + var_names[var1] + \" vs. \" + var_names[var2])" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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qnJelpdwi3Bn+TBBLsiAILqKlLCetjfY4hxUWFhIZGcm5c+dISkpi3bp1jBkz\nxnRcp9OxfPly02eJSiQ0F9v5YjKWCrKRsLApnDu3xW1yKWNOpqSkebJ0lPmwNWIdkWjFihViSRYE\nwbPIhpK2S2RkJADh4eHce++97NmzR6Ukg0QlElyL7Xzhr1nv6lU/1WdHXLqa6/ZVU+OYLA2xcGEy\n+fmpNm4RCxaMdbgPwTlcGZFIlGRBEFyCbChpm1y6dIna2loCAgK4ePEiWVlZKquxILQEtvPFZc16\nvr5Vpr8dcelyhduXj0/jsjSGuEW0D5ocAk4QBEGLhQuTiY1NVZUplpMkD0kkOEJxcTFjxoxhyJAh\n/OpXv2L8+PEkJyd7WiyhnTN6dBQ+Po9YlCQAal94H5+HmT/frFTajxG8o0l1GuOxxxKsZLOVxRHG\njYsnM/NZsrPTycx8lnHj4lskLJzQcoglWRAElyCWk7bJNddcw3fffedpMYQORl5eATU104A0wBuo\nBULw9b2TLl1C8fWtYv78eEaMGERKyjKuXPHh0KFTmn1ZunS5wu0rPX0ex449yYcf3onB0BWd7iIT\nJ8Y1ewOhbG5ue4iSLAiCyxg3Ll4me0EQGkVRZuPr/5m5+eZ0srPTAS2lcplmX5YuXa5w+8rIyGXP\nHh9qaj41le3Zk0pGRm6z5jfJltf2ECVZEDooTd3c0hFiIAuC4BxNnR8cUWZtlcpkIBWwvxnO2Q1z\nlvIfPnyUkpL5quP5+SuZNWsygwbtdHr+k83NbQ9RkgWhA9LUZT9ZJhQEwR7OzA+OKLO2SqXSV3Dw\nVG688XpNly5n3L605FeUcfOYACUlA8jJSXfo/Iz9Wr44lJcXadazfDFwR/QOwXFESRaEDkhTl/1k\nmVAQBHs4Mz84oszaszZ7edUB2I1921S3Ly35FWt1Gmp3kKNAOlBDfn4K69btsDuOluKt1y+he/ff\nceFCHIr6VYNeX8CCBbPttmmJ6B2C44iSLAgdkKYu+8kyoSAI9nB2fmhMmbW1Nufi47OZkpKt5OQo\nJa5QEAsLL9o5Yin/w8B8zEpzKqdP/2K3Ty3Fu6joHjp12gRYJhlZ0mAb65cNMVi4FwkBJwgdkKZu\nbpEYyIIg2KOl5odx4+JZsyaFlJQ0EhLSCQ1dT03Nq6o6TQ3vpkVBQYGdI3sICpoN3AEMRm1VXklx\ncZmqdnr6BsLCJtO9+2x27vw3YB3eLYvq6v9VlRQV/dUkvyMvG2KwcC+iJAtCB6SpMY0lBrIgCPaw\njXkM3t7CglHoAAAgAElEQVQP8eOP3zc7HrBlrOFBgwZo1tmz52fVOE2NRazXd8fsg2zkYeApysre\nBj4DzmCt9BozVYKiID/33EFKSrZSVvY2NTWfAF9YtWlYwXXkZaO8/JxmnYoK7XKheYi7hSB0QJq6\nuUViIAsdBdkU1XS0Yh7X1s7gp5928NNP6YBr3CLsKZGlpb1MG+oOHZoDBFFU9FfT8UOHlhAZuZHA\nwBjN7zQ6OpwjR5It5D+K2rUCtHyUo6K6mf7+61+/pLb2IyvJ1G38/Y9yWSOZn1EJdiwyxxWsI3zA\nUqDatmOh2YiSLAgtTGt96DZ1c4vEQBbaO7IpyjnsxTyGnaa/8vNX8vTTc5s1Fy5cmMyhQ3MoKorE\nuPENCoDZpjrKsedU7YqK/kpRURrKpjvb71RRTi2/93SNcwFLH+XY2KWMGhVjSnRSWam9MK/THSU+\nPh0/v1pGjUpg0yb7SrAjxojAwBjgN6iTsIwlIMB8rQXXIUqyILQg8tAVhLaDs5uiWuuLsLuwZ+FV\nFDgjuXz/vQ9VVWYF1pm58MoVf9RK8GNWNeypNT9jLzKFtXKqxEm27SEs7AcGDjQqvDFs2nSm0UQn\n3t7VpuQoACNG5DaoBDdmjFCute0LiZ9f8/yyBW1ESRaEFkR2IgtC28GZTVHyIqztJqC4AFi6CWRR\nVfU3VbumzoVpaVspLV1vVfoKcC+K1boG0I5FDL0wWpLtRaYwhpTr1SsAX98lKpeN2NilrFkzzyRr\nSsqyRhOdwIN4eVWSmJiuenlqzn3hbLIUwTlESRaEFsTZh25zM+EBqrLRo6PIyytosI69MlcEsu/o\nljahbeBMlAZ5Eba1xFZUnKOgoIqiIvP5+/mdoqrKtm1TojKcOFFp50ggRgXY2/tBAgJmcuHCuxbH\nrRX2lRQXTzF90o5pPIdhw+YTEBCuafG1l+gE7gaCgTLAi+rqnS4NVyf7Q9yLKMmC0II09aHrikx4\nWhtXdu58pH5jTXx9nSVAGUVFb1q0sy1zRSB7sbQJbQVnrHQSkkvB2kKakaF2Kzh7thsHDti2a1qY\nuCt2ys2b1mpr36Bv3/mEhytj/+tfh6msXIjaPSGXqqoak4X33LlS8vPVFuqiojcZPDiNzMx0zRG1\n5/Z44IX6v2uAP6qOuurlSfaHuA9RkgWhBWnqQ9cVmfC0Nq4osUXNu6wVBTrNqp1tmSsC2YulTWgr\nOGOlkxji9jG6LxgMBu66ayDl5U13E7BchaqpqQLmAG9a1FiMYrVNR1FMkwkICDcptykpy8jKAsVn\n2Ac4B1RRWfl3k4XXz2+W5tgNvehou5g8jKIYmxOOKJjvH0+9PMlqnnOIkiwILUhTH7quyYRn72dt\n3YdWn7ZlzQ1kL5Y2oS3RVCud+IjaYm/1aMaMaHbvdvwFRKsfb++51NbOBaJRFN5zKHGMjaRSUXHW\n9Gn06Ch27txslYQkFSV+sTJ2VVVPzfEbetGxntv37/83FRWLaCxs3OnTx00RMdylrMpqnvOIkiwI\nLUxTHrquyYTnyE5zrc+gPHCMFhfFKmM5tjNWM7G0Ce0Z8RG1xd7q0aefzicsLBgwW5ktsbZ2arlB\n1Na+jo/PnXTtepXKyl+ord1u1ctKCgruJixsMjU1/ly8WEJNzR9t6qiV12R8fSdz9eq1GOc+vb6A\nBQtmN3quxvPw8elGY2HjYDGnTl0mP79pET6aawWW1TznESVZEFoRitXjEZXVw8fnYUaNGqxZX8uK\npdcXAOqd2TAXmGn6pGxuucKFC+YawcHzKSs7R12d+aHk4/MIo0bd2OB4jVnNxNImtHfER1SNvdWj\n77+vpKrKPL9YKoha1k57bhA1NTdRVpaOOVqFJbkUFYUDb1iU2bo9WK+a6XSBqN3UlmiObcRWXu0Q\ncLC3Xs5aoILq6g9URxtTVl1hBZbVPOcRJVkQWhFamatqaqaze7d2DExtK9ZsVZkS8zMB2IESJqmW\n2tr76Nv3XdPmFmVjzRUOHFBP4DU1r7J7d1oj4zVsNRNLmyC0XlrCV9Xe6lFVVS/VZ0sFUcvaqe0G\nkQv8CyWBSAmWbhMKWagVZNBye7BcSfP3X8/ly1tVLYqK/trEvRZaIeCWApcxK/Pp9fJmYbla15Cy\n6gorsKzmOY8oyYLQirCXuaqqyn42JXtWLGNZYmI6OTnzbI4HBOxU7dxOTEy3qaOMrZ7AnbGaiaVN\naCt0pA1OLeWrqrV65Of3CFVV02zqGueXwsKLGj0lo96olwu8C3xqUWdu/f+KvF5eP1FXpyWVeR4L\nDp7P1avH8faejY/PZbp1C+LkSdsWe/b8bBPj2Ij9EHBTgesxZsKDn0w1OnXaQ3V1OWC5yreEiooK\nLYHtjKPQFCuwrOY5jyjJgtCKcOSNv6kPcds+FUvGoUOnSElZZmov1gaho9OaNji5Q1lvKV9VrdWj\ns2drOHDAtk/j/FJQUKDRUzyKUmxcWTsKbLWq8zpwBwkJO/Hzq+Xbby+hpXP6+v6Lm29ON8VwLi01\nb/a7dGmy5nmUlvYiJycdsL0P7IeA24HaDWQ1CQlKlr6DB7tZucEB/JWyMm23EvM4ttbnpszLsprX\nDAxuxgNDCkKbYfv2HENs7FIDGEz/YmP/ZNi+PaeB40tNxxvvM8cA2u0bG1tQ6IhzWEc55+TkVNX9\nb/yXkrLMrXI48zt3hoSE5Zrnm5Cw3KXjGAyNz20DBz5kMzfBw/VzlvGztrxdu043jbN8+XqDt/dD\nquPe3nMNy5evNxgM9r7jHIO//8NWZfcbYF79mKkGyFHdB1rnA3Os5H3QMHXqE6Y2wcH3acrv4zPR\nkJCw3JCcnGrzHWudj043wdC370y7bQQ1zZm/xJIsCK2Ixt74nbH8WPa5Z8+PlJZu0Wyfmflsg2ML\nQnuntWxwclc0AneuHjU2t0VHh3PkSDKW+zEUq6nl+WrL6+9vLh8xYhABAV9y4cIUwA+oIiCgmhEj\nBgH2vuN4wsPXcfGiEhGjouI0dXU3onaLUKey1jqfy5dryct7gbq6DXh5XWTChDg2b37eog/tZCg1\nNd52Ldbbth2htvY1i9q5GAzX8dNPK/mp3pNDwrm1IM5q1y+//LJh0KBBhoEDBxpefvllg8FgMJSU\nlBh++9vfGq699lpDUlKSobS01KUavSB0dJpr+bHXPiholtMWie3bcwzJyakdxqrREeewjnLO7rQk\nN/S7cZeFtzWtHmnJ0qnTBAMsVll84UErK+xDJiuxwdD4d+iYJXmSZh9hYZObdY5Dh87RsJb/yeac\nLO83W+tz61jtaEs0Z/5yypJ8+PBh3njjDfbu3Yuvry9jx45l/PjxvPbaayQlJfHEE0/w/PPPs3r1\nalavXu1KnV4QOjTNtfzYa19W1pOsrGebbJFoTT6cgtBcWmqDk7V/8ejRUWzadMbu78bZ33lT/Zhb\nk6+qliyjRv2a1177F0VFZutyly4n8fb+PV5eAfj6VjF/fjzp6eaNyY2tBmh9x7bRLYI0++jaNbBZ\n53jXXcM4eDCbujpLa3kRSqQOW1kVrK3PrWO1o6PglJL8ww8/8Ktf/Qo/Pz8AEhIS+L//9/+ybds2\ncurzPM6aNYvExERRkgXBhTT3Ia6dSnUpyi7spi/pSpB6wVO0xMa2llAatV4kd+16hMuX1ZEeLH83\nzvzOnX1hdSTyjLsifmjJMmJELuvW7aCqCvz8YMGCZQ5sVLa/0U3rO/7hB+voFmWafV+8WN6g/Fov\nQ3l5BRbJUYqoq3sMZXMfwDFgPtbRjCxfhvr06UZpqWVoOdlg7U6cUpIHDRpEamoq58+fx8/Pj88+\n+4zhw4dTXFxMREQEABERERQXF2u2T09PN/2dmJhIYmKiM2IIQoejuQ9xy/a7d5+irKwnioJsbt8U\ni0Rr8eFsSbKzs8nOzva0GIIFLbmC4epwhVovkpcvv4pt3F7z78aZ37krX1gtlb3y8tMUFgaqojI4\ne62dUbab+n1opaG2Topk3WdYmHV0i+5oxTyOiFBbmBu7TkpiqGkYv2c/v0frjzxb/38u8AWW94Fe\n/wBnz/qbQs/dddcwCgstrenFeHs/SG2tORa0hHNrOZxSkvv378+TTz5JcnIyXbt2ZciQIXh7W2ev\n0aHT6TTbWyrJgiCoaexBovXQyMjIJS1tIydOVAKdCQ42EBTUicDAGJs+jO1TUpaRlfUs1jTFItHQ\nsrC983CVVcpd1i3rF/kVK1a4fAyhabTkCoYz91VDbey9SFpnfAP1b6+pyqF2nGEoKKh0uA+wl0nu\nOVUdZ661u1yzlIRMr6rKrJMiWaPXd6ekxFIp9gFSUG8iHEvnzmaXDEeukyKH+WWoqupvqF+OlP/D\nwqYwcGB/KirOUFDQnQMH1C8kDz98E7t3F9Zb0/WMGhXJ7t2ed5HpCDgd3eKBBx7ggQceACA1NZWY\nmBgiIiIoKipCr9dTWFhIjx49XCaoIHQEnHmQZGTk8uCD71BUpMeYaaq0FJS0qr8B4jX7cIX/pb0+\nRo2K0TyPvXsPN+iL6SjiC92xaakVDGd/fw21sfci6e9/lMuXzZ+baw3UjjMMhYWFTerH9gVE+1o3\nlGjDsX4VZXvWrMkMGrTTZS+6yr3RtKx2tpE1jqNYeK3d0qobOB/HXob8/H6mqsr8OTY2kzVr5pkM\nF/v3276Q7N5tjj4kuBenleSzZ8/So0cPfv75Zz766CN2797N8ePHeeedd3jyySd55513uOeee1wp\nqyC0e5yxkK1dm0VRUSTWVgwlfJFitdDqwxX+l/b6sHcer7wymZKSrTblTbVKiS90x6alQpc5+/tr\nqI29F8kZMxJcag20tYaClotAY9i+gGhf64YSbTjWr0JJyQBTP4cOLSEycqPmCpg9rK34p079F7iK\n+jqkUlFx1m4fyndk+aKTjmJgUFuSAwLMmU8dvU6W6a8B4uK6ER6u/b13BPe1tobTSvKECRMoKSnB\n19eXDRs2EBQUxFNPPcWkSZN488036dOnDx988IErZRWEdo8zk6T95VywtGJo9eEK/0utPl54QTuN\ndk2Nv2Z5Ux8C8jDp2LRUFApX/v6a41/sDNpxhscSE7Oj4YZW2L6AJKPln2vc7AuOvaDae7GxVCKL\niv5a73ubXt+vsvpkufnNcjNcefk5CgurKCp609RHp073WMlK/ef5pk9a7jFr1qSYvqPDh49SUpKO\n7YY687V05Dr5+DxMTc100+fY2KU888xku9fJ0Ze/jpQ63dM4rSTn5ubalIWEhPDll182SyBB6Mg4\nM0kePnwUuNZOj+Z2Wn7C1ruvmzvZGvs/dOi/msd9fC5rljfVAigptDs2LaV4OnNfOdLG1ZsBtbC1\nhjr34mD7AhKPXv82UVHzCQgI59Ch/1Ba+ij2Nh063i9YK9sK5n7y81P4y1821290BMi12ZSnKKa5\nJnmqq4dojh8QEA7Yd49ZsybF5NKg1Gn4Jayx66SEsBvM7t07qKra6dA96sjLn9m9LtJUdujQO7zx\nhriatQSScU8QWhGhoVeBucDrFqVzCQkJMX2yneRz8fJ6hbo6a2vPYuBewJ6fsO0Dpzl+vWq5crG2\nqhiXmDdtar4FsKUsiULboSUUT2fuq9ZyL7rqxUG7n9mmcmXDr22fjb2gWverWGttw5+p3ROyLBRk\n5bP1pjxljrHcDNfwS4sjLjWOXEvtuM7D640OYDAYGDFikCqGc2M4Mm5a2sb6/Sdm97qiolSefvpd\nUZJbAtflNHEMDwwpCG2G0NBJ9Vmllhlgef3/OapMT/YyRgUE3GEIDp5iCA6+zxAbe59h2LAHDQkJ\nyw0pKctM2b1aMnOTbf/KeQQH32eSwWBQMmulpCxTyeYMruqnqXTEOawjnbMz95Wn7kVX0NSMma7K\n0qfVj5J9Lsfis3XmQe1MhOpy6+x5avlaKpuh9nVZ6vJ7ITh4sqb8wcFTXDpOe6I585dYkgWhFXH5\n8hWsd2VDPFev/h9THW0fyHgMhtcAH6qrf+HsWV8qKgIpKdmLwVDHjh15KD/3xUDX+n61f/6nT58l\nJWUZhYUXKSgoQK/vTnR0OAsXJrN372FeeSWHmhp/fHwu89hjCSZLia1c8UA8N96YTmZmuqnUVRZA\ndyxhCx0PZ+6rtnovOhPNo6Us1hUV5ygoqKKoyNyPdQQQRzbHxcZmMmPGjapNkaNGxbB2bRYvvLCz\n3j3NFk9s+nSOznbKO7lwDMGIKMmC0ErIyMjl0qUQ1FEqlAdWdfUvphJ7PpCVlX2BJIyhiyoqjEfm\noKRZ/atF7VRAK9lPLj/9pOPIEbMMJSWpHDmSzJ49r1NR4UdtrTk6xcqVjwAbSE+fJ37CbZja2lqG\nDx9OTEwMn376qafFscGRjUrp6RtsXuBGjBjUYDt3xex210arpo5jT7F7+um5Dfazd+9h9u07ZrrW\ne/dG2rxAJyf3oaTEV9WHVh2DwReAsLBgunU7wy+/3InB0BWd7iIjRoSxb99dXLrkD/gD5cANQAwQ\nAFQABYAemARUEh0dwbFjtXz11fcYDF0xGM7yxRcVQFh9m3KUedK8CU+vX8yCBfc2eG2nTXuSDz/8\n3iTbxIlxTJ8+znSdDh06pdnOOlSe8bo7ey8oGfhsQ9xdc023Bts5cm/IhkANXGjRdggPDCkIbQJt\nNwqDASYZ/P2TTfUaXqbU6sNev/MMPj7qZUl//0l26i6z24/RFcRVy7CtnfY4h7300kuGadOmGe68\n807N4548Z0eWsZcvX29zL3t7P2To3v1eu+1ctTzeWD/uWoZ3Zhxt14Mcg5/fI3b70brWOt0DBp1u\ngpWr1YNW7gDzDV5eExuoY9sG7jfA7y0+P6FR50ED3GPxeY4BUiw+j7LTZpTB6NKm1z/Q4HWaOlV7\n3C5d7lTNp/bmWePfev0DBr1+cbPuheXL1xu8vR+yudeXL1/frHvDXfepJ2jO/CVKsiC0Euz5ysHj\nhqCgWaq6lj6QwcFTDGY/Pq0+tPsNDr7PsHz5epUv5Q03PG5HhuV2+7GUrS37ZjpKe5vDTp06Zbjt\nttsMO3fuNIwfP16zjifP2d7Lo6XvvOLLr3Xf2vpvGts50q8r5HPVOAZDw/7Dzoyj3abhfuxf62WN\n9tFwHUfajLdTZ2z9/JRaPxdOtjpmr41j18nHx964luPMMYCW8cJSuW7+veC671ndxpX3aWujOfOX\nuFsIQivBfhzRbvj6Klmz1MthBhITe9T72O1EWX4r1Wiv3e/Ikb0YMWIQeXlKpi6DwYCPT4VmXcXn\nz6B5xNfXnD6qrfpmdmQWL17MCy+8QHl5eYP10tPTTX9bp+puSRyJXWwv/jb42W3nqljbjfXjqnEa\n8x92ZhytyBx+fqdUGeGs+7F/rS3HcST7nHUdR9p0tVMnCGNsZcWVzPIEAuy0UZc3dJ0MBnvjWt5f\nMWglIFHmZiPNvxdaIpa3s/22VrKzs8nOznZJX6IkC0IrYeHCZL799mEqK1+zKF0KHCMpKVYz9JsS\nws0yg90clHTUlv7HBTZlev1iRo261uahq9cvQa+fowrOb4xl2r37/1JRMZfaWnN4Oh+fh5k/X5Ti\ntsr27dvp0aMHQ4cObfShYqkkuxNHfN3txd9WK0vqdq7yoW+sH1eN09jGMGfG0dqEd/ZsNw4csN9P\nXd0FO71ZjuNI9jnrOo60uWinjmX5SuBOi8/2XvwrUBRrxae3oeuk09kb1/L+qsG4WVnNDqs6tjTl\nXmipWN7taU+J9Uv8ihUrnO7LywXyCILgAsaNi+faa2tRMkPNAqYC54CFnD/fSeMhqRUz9E28vA4S\nEHAvPXrcB9wOFAKHUB4ci4E0oqIqycsrsHnoFhX9lagoP1JS0rjhhsWEhU1h4MASUlJ2sGnTQyxb\nNpSwsCkEBc0mLGwKqamDmxQHVGhdfPvtt2zbto1rrrmGqVOnsnPnTu677z5Pi6Vi4cJkYmNTVWVK\nHOIk0+fHHkvAx+cRVR1v74fo3r3abjtH+nWFfPaOjxoVSUrKMhIT00lJWUZGhm2CLksas/Q5ez7j\nxsWTmfks2dnpZGY+y7PPTkavX6Kqo2xsU/oJD/fDuKHYzHzAMmpEMkq8dzPBwfPx8vpPA3Vs28D9\nVv3GadSZW19uia/F334abR5EmQ/Tgefw8dnMqFGR2GPiRK1xH6RLl0sq+a3vQR+fh1E2CSro9QU2\n17ap95wz37MjbVz1e2hviCVZEJpIS+4ADgw0LtlZ7ly2t+Sl/fMdM2YM2dnpACQmppOTk25TJyAg\nnStXtGXIz79IWFgwq1bdy7hx8abzfeGFnXTuXMPbbytK8dq1WWRnK+HiPLWbX2gef/7zn/nzn/8M\nQE5ODi+++CIbN270sFRqHAk5pryobWD9+ilcveqHr28V8+fHM2LEILvtWjb5RsPjjBoVw6ZNZ5oU\neq0xS59rsxCWoXYbMLvi9OzZn59+snYrmEyvXuu4dMl8/ZOSenP+vKUsk9m797DqO7KuExISwo4d\n6u/w2LGT/P3vd1JX1xUvr4vodKeorr4dc3SLG4HnVdLr9T6UlBjb1ODvf4jycss2dwLml/uamlfZ\nvTvN7tXYvPl54EmVHBMmxDF9+n1W36t16DnrjHuzm/0dOfM9O5scpSXSp7c5XOca7RgeGFIQXEZL\n7wAeOlRr88dSw7BhDzqVDKShzRj2o2ksM53X8uXrbc63sR3a7XmXtMHQfuew7OzsVhndoj3izCYp\nd0WPcedGxOaiFWnDx6fhSA/2NiffcMPjbpRccCfNmb/E3UIQmoB9v8Addlo0lc6oU0tT/7mTxnKY\n7fJeU5bQtI4p/sdK+/z8lbzySo6GS0YkRUV/VZVZXoOWv0ZCS5CQkMC2bds8LUaHwJFNUhkZuSp3\nDIA1a1JISUkjISGdlJQ01qxxvaWvpdw6WoK8vAJqaqahWLXTgTRqaqaze3eh3TYFBQWa5YWF9tsI\nHRdxtxCEJtDSO4ADA8M1ywMCwu0s26qX95xZQlu3Lo3du09RVtYTZTe2+Zj2Tnb37OYXhKbQllx8\nGnOdsBfJYs2aFDIzn/WobK1pWV6Za2w3y1VV7dSsD6DXd6ekJBW1MWIpERFBLSGi0MYRJVkQmoCj\nO4CdzW6k9G+bTcnyAWXt+5uXV8Dx40coKKji66+P4+e3XpUuWissm3Uoub59u3LggO3DV4kaYJTn\nHHAB9W5zM4cPHyUjI9fiGqnPo6JCK8OfIDQfZ9IrexKt0GuKNXYs4M4Ux02XDVpPqEdnIjJER4dz\n5Egy1qHaYmJkpUvQwIVuHw7hgSEFwWU44hfYnOxGU6c+oeFj97Cmj525j/UGcKyNvbG1/Yz/ZCFP\njoWvtOXflkHzc0x+zHr9AzZ19PrF7cIvuSPOYa39nFuTn6yjNJR4x15ioYSE5R6Xzd00lEDFGT/t\njpIZVDDTnPlLLMmC0AQcWWp0xApkr86FC5Ot4h7b33lt7mMyYNtm/fopmuHZtMYuKnqTYcPmMniw\n+rzWrjWGmVuGeXnSeK5pwM9AL4xuGvn58ezenUZkpB9FRbbh5dxhCRM6Hm3Rxacha2xriFmr6Bbm\n/92B9era6NFRDUYBaalID4JgRJRkQWgijS01Nie7kb1sVloPe3Mf2m2uXrXNNtbQ2AEB0WRmpqvK\nXnjB6Ntn3cboB5iOOdOVWVZ7vtWtWWkR2i6tQal0JY64PLQUnnJd0Rp3167JXL6sNgBYGxycdf1o\n7CWgLfm4Cy2HKMmC4GKak93IXuYwLZ9nJR11OlCi2cYyXXRT5VOPAY5lwzL3c/ZsIYr12exXDfFt\nVmkRWjeeVCpbAk9aOz3lD6017uXLAzTrNudl25GXgLbm4y60HKIkC4KLceSBba9OdHQXcnPnAq9b\n9DiXkJAQ0yfjBF5SYrSwbEDJBuVYumhH5DOPkQA8AkxDybJlmcJ6MVBOURGqfkaNiuG11y4Cz1mM\nmope/7YpmL4guJL2uITuqc1xnnJd0R7X9SsEzXGHE3exjocoyYLgYpqT3WjWrPUoKV4td17PZMeO\nDaa2thO4km0M7qBr1xD8/WuYPz/ebrropvlVL0NRkHcAvwBTgEjCwgp54415mv2sXZtlE0cZVhIV\nNV8eMEKL0VoiLrR1POW6oj1uMv7+j3D58qumkuauEDTHHU7cxToeoiQLQgvQeNg1xcfNOuZpTc3/\nqf/LoPrf0r9YPYGbw6wFBwfy7rsPOaQoNCbfoUP/RVG8T6EVh7S2dpbdfsx+zGoCArT9lAVBaD14\nynVFe9xMZsxoOBZ8U2mOO5y4i3U8REkWBDfgqI/b5cs/A1+gDnSfWl+uoI5DbK5bWgqLFjnnN6cl\nn+Jm0U2zfmlpLxYt+kJzLHnACELbxVOuK+4atznucG3Vx11wHp3BnfFdAJ1O59aQMoLQGkhJWUZW\n1nMa5Wkqa7K391jq6jJt6nl53U5t7eeApUKrQ+33q91nc+RTfJ17YJ2dyhjyTWssLYU7NnZpi6TQ\n9QQdcQ7riOcstF8yMnJZt26HhTKepLmy1lgdoW3QnPlLLMmC4AYc9XHT6bpr1tPpzClTjRP1zJlv\nUlraeJ/NkQ+igd9g9pH+D/AoRvcLrbHa4yYqwbNIOC7BlTjivy4+7gKIkiwIbsFRFwSd7iKKL3AO\nSvzjy0ACXl4Xbdp6eWmHePPzq1UpFeXlp4HOBAaGc+rUvzl3zoCXVyA+PpdN6avtyadsHLT0SU7D\n0j+5ouIcKSnLbJQXecAIrkLCcQmWyAuT4E5ESRYEN+Coj1uXLmcpLz+AOoPeXPz9z5o+mcOzzcc6\nLJsxBJtZqbD0W94AhAPmneIrVz4CbNCUDx4Gpps+eXs/SG3tfabPev1iCgqq2L/f7KYhyovgaiQc\nl2BEXpgEdyNKsiC4AUddEMrLQ1DHSAZ4nfLy202fbJUGxRUiLOwH1qyZZ3U8C7MSnYO99NXnzpnD\nue3Z8zOlpb2AwSih33YCtfTuXcm11+6gqmpnfcKQCg4ceFPVnygvgquRcFyCEXlhEtyN00ryqlWr\n2JgqPHAAACAASURBVLRpE15eXtxwww289dZbXLx4kcmTJ3Py5En69OnDBx98QPfu2j6WgtDRcMwF\nIaDRcrXSYHaFGDgwnXHj4q1CsFnWbTh9tVG+xMR0cnLSber17JmuSludmGhbB0R5EVxLW4iWIi4A\n7kFemAR345SSfOLECV5//XWOHj1K586dmTx5Mlu2bOHIkSMkJSXxxBNP8Pzzz7N69WpWr17tapkF\noR1TYbc8IyOXtLSNHDx4FpiFEp5tMkYl2ag0qJUKy78vYxlX2Zguury8mJSUZSxcmAxQn4p6MVAA\ndEdx0Ui2UUragvIitH1aezgucQFwHzLnCO7GKSU5MDAQX19fLl26hLe3N5cuXSIqKopVq1aRk5MD\nwKxZs0hMTBQlWRCaQHh4JefOWaelfpDAwPM8+OA7FBXpgTcsji0BQK//mAUL7gWslYpkzH7LfYB3\nrfp+BIPBl6ysZA4d+gdQZpHumvq2yfj4bGbUqBtVsrZ25UVoH7T2aCniAuA+ZM4R3I1TSnJISAh/\n+MMf6NWrF/7+/qSkpJCUlERxcTEREREAREREUFxc7FJhBaG9U1cXhZL++XYUF4sKwI/Ll3tQXh6J\nbVzkvwJTiIoKMD2QrZWKioqzwHwOHTpNTc0nVu1fRfFp3lGfSjrN6vhKII2amlfZvVt9rLUrL0L7\noTVHSxEXAPchc47gbpxSkvPz83n55Zc5ceIEQUFBTJw4kU2bNqnq6HQ6dDqdZvv09HTT34mJiSQm\nJjojhiC0O2pq/FEsvt8Duvp/l7l6tRv2f679Cah3WVb7Rhr44x9/w7hx8WRk5HLPPa/Yae9t5291\nmb2YyFoPqPbko5mdnU12dranxRBaKeIC4F5a8wuT0P5wSknet28fN998M6GhoQD87ne/Iy8vD71e\nT1FREXq9nsLCQnr06KHZ3lJJFgTBTGXlUcAX+NSidC7wM2r/Yktq8fOz7xu5d+9hNm06Q01NuJ32\n54AQU19a/YPjD/325qNp/SK/YsUKzwkjtDrEBaB90p5e9AXncSot9cGDB5k+fTp79+7Fz8+P2bNn\nM3LkSE6ePEloaChPPvkkq1ev5sKFCzY+yZLeVBDso9PdDnyucWQ8EAHoUaeIXoxeX8Ybb8xm7dos\nzdTSoaGT6/2MH6zvwzrF9HfAU8DHdOp0hurqD6yOjyU2NtPhtNKOpuBuq3TEOawjnnNTkBTG7Qut\nF/3Y2FTWrEmR77UN4va01IMHD+a+++5j+PDheHl5MWzYMB566CEqKiqYNGkSb775pikEnCAITcFe\nCLhuwCy6dv0LOt0ErlzxolOnGq6/PpRnnpmtEfrNjOLCARCDOsV0LTAWOIESD/lerr32PWJi0igo\nqKSwsJCIiCBiYnY0ye9PfDSFtowzFkRxAWhfyGZMwYjTcZKfeOIJnnjiCVVZSEgIX375ZbOFElyL\nLBu1JSqBJ1F8krsCF4G4+v/j8fNbzzvvzNf8/rR9I3OprDwHpANH6/+3brsDeBbIpajoAgBFRReI\niorCx6eCs2fP88ILO1m7NovRo6PIyyugsPAiBQUF6PXdiY4OV91T4qMpeAJXzHPtzVVIcA550ReM\nSMa9do5M+m0Lne5nDIZobH2STwFLKSmZz6JFXwC235+tb2Qu3t4bqa3NMH2GR7BMS210p4BcfHw2\nU1Iyn5KSL4DXKCmxTGmtsHPnI9TUTMOoaJeUpHLkSDL5+WaZxEdTcDeumufEgiiAvOgLZkRJbufI\npN+2MBh6opWWWgkJNxaIJz8/XvP7sw6PdPjwUauYx8b6d9KtWzeuuy4EqCYgYKdF3WWYlWLLlNYK\nNTXGkHHGvpQQcZb3lIRpEtyNq+Y5sSAKIJsxBTOiJLdzZNJvvSgZ9LZy7Nhprlypw8+vG4rvsRYB\nKIqpkjFv9+7Tpix51kqAcYNCXZ2fRj/xwE5uugmys9NNpUoqalBPCfamB+t7xzZEXHN9NMVFSGgK\nrprnxIIogMRjFsyIktzOkUm/dZKRkcuDD/6DoqLJGF0aKisB7rTTogJFQVbqlpVBVpZ6Sdl2yXmZ\nnb6UkHGWmO8Teymt1e21PrvqnhIXIaGpuGqeEwuiYEQ2YwoAXp4WQGhZFi5MJjY2VVWmTPpJHpJI\nAGV5WMlwZ+3SEIfig2zJXJQsfLbuD8qS8g5Tn+ol52SMaavNLEWvP2Pz/ZvvE2Maa6z+VvDxeRiw\nbLsUSHLpPWV/6XyHS/oX2h+umufGjYtnzZoUUlLSSEhIJyUlzeHQh4IgtD/EktzOkWWj1ol5edj6\nJ/g8SnSLcSguFsboFtcQFHSasjLbvoxLyrZLzsp33LXr7+jUKQCo5ppruplCxllivk92cPr0LxQX\nTyEyMhJf30pgPgEB4fj51TJq1GB2795BQcHHToeIawxxERKaiivnObEgCoJgRJTkDoBM+q0PbfcG\nUFwqSlB+mp2BUBSFeTU+Plpp3nM5fPgoiYnpHD58tL695Xcdz/XXv0tYWITJv9eIlt+vs8k+MjJy\nSUlZ5hIfYnEREpxB5jlBEFyNKMmC4AEWLkzm0KElFBXdg+LSsBJFwX0HJaveGxa15+DtXU5JyVMW\ndcEctm1r/aY78PF5hJoaMCrKev0DFBR0Z/9+cwY8y1TVrvD7dbUPsfiFCoIgCK0Bp9JSN2tASW8q\nCICiXD799Fa+++4n6uqCUKzK/QHblM5K2DUl4YeS/MMbX99/cfXqpzY1w8KmMHBgf/z8ajl79jwH\nDqy3qWNOVa3GmdTRLZGGujWn+e2Ic1hHPGdBENoHbk9LLQhC8zEuDyvh19JRsuHZw+iPG4/RStyl\ny2xNH+WBA/ubwrslJmr3aU5VrcYZv9+W8CGWpXP3UVVVRUJCAleuXKG6upq7776bVatWeVosQRAE\njyNKsiB4GPv+yZbY+uP6+FzWrGnpu2vuW4mvrPzkaygrO4GilNegRLGIt2kLar/l8vJzwBUCA2NU\nfsfiQ9y28fPz4//9v/9Hly5dqKmp4dZbb+Xrr7/m1ltvbZHxOmIM7I54zoLQHhAlWRA8jNkHNwVY\nh9rvGOABvL2PUWuhc8bGLmXGjAQ2bWrYd3fhwmT27JnJhQu9rPqcC/QA5mEM8xYbm6lqq+VrrNT9\nDUrmv1Qr+cWHuK3SpUsXAKqrq6mtrSUkJKRFxumIMbA74jkLQntBfJIFoRVg9MH94ouvgX5AJdAJ\nJQPfZGA1KSk32fjoOuK7Gxh4DxUV/9AYdQqwBVD8mN9+e56qrT1fY7N/tNnvuDX7ELua9jiH1dXV\nMWzYMPLz83n00Uf5y1/+ojruqnNuCf/1puAJi66nz1kQOjrikywITmB8YJ45c46iogtERUXh41ON\nlktBc/p35IFs9MHV6SYBIUAR0BU4D2QA3TQfqI747np5dbdzxJx2b+DA/jb9FBZetNPO7Gts9DsW\nH+K2jZeXF9999x1lZWWkpKSQnZ1NYmKiqk56errp78TERJvjjuDJGNiesuhK3G9BcC/Z2dlkZ2e7\npC9RkoUOifmBmYKS6vk1SkqMR21dCtwXFu0EEARYRq2YW1/uHPZ8l6HK9JeWL/J//1tgp525rvgd\nty+CgoIYN24c+/bta1BJdhZP+q/bz+SY1qJKsvjsC4J7sX6JX7FihdN9SVpqoUNifmDapnpWPisp\nkJ1Nh+x8auUw4HWrstfry53jsccS8PF5xKr0YYyb9bTS965dm8Xly/OxTkttTENtr53Q9vjll1+4\ncOECAJcvX2bHjh0MHTq0RcZyVfpoZ2hJi64xmU5iYjopKcvIyMg1HfPkOQuC0DzEkix0SOynhTZi\n61LgXP9qGuvL2ztQtUHPstxZ0tPnARtYv34KV6/6UVdXQXi4jp49z+Lnl6aZvleR31iWhnI9ztG1\n60mGD++En59rU1ELnqOwsJBZs2ZRV1dHXV0dM2fO5LbbbmuRsVyZPrqptJRFt7FVI0+esyAIzUOU\nZKFD0njYNfODs6LijE3KZaBBf+Py8tPAMowh14xh1hp7IOt02n7AXl7a5Y74PWdk5JKXV8DAgf0d\n8rPOyMitT3GdjnWIuFtvTSMzM73BcxDaFjfccAP79+9323ie8l9vqSgsjrhxiM++ILRNREkWOiTq\nsGvWIdeWAsqDUyut86FDS4AyioreNJVZWo4yMnIpLAxEnTkvFb3+bRYsmN2gXBMnxvH++3NRu1zM\nZcKEOJu6jvg9N9U32lhfnY1PO0ScILQlWsqia2+Da0FBZbP6FQTB80gIOKHDYgxbdvr0WYqLy4iM\njMTXtxqoJiAgusG0zpZh0IwYQzrZC/k0bNh8/vUvrb7UTJv2JH//+/fU1XXFy+siEybEsXnz8zb1\nHAkt1dTwU/bqa4WI66h0xDmsI56zo4SFaad4DwubwrlzWzwgkSAIlkgIOEGg6TFQHVkCtZfW2dJn\n2YjR39ieP3JAQHiDYxmZPn0cJSW+pvOYPj1Zs57tOEpWvV27fiIsbDJ6fXcKCsrqy+NVdXbvPk1K\nyjKba2TPKqYVIk4Q3EVrzlin13enpMR2NSoiIshTIgmC4CJESRbaBS0VA9XeZh+tNNFGf+PmbBBq\nynmox8lFCWW3kkuX4NIl6h/c0+vLjSh1ysogK8vWTcRe2DcJVyV4itaesS46OpwjR5Ixb3CtBcYS\nE9P0qDiCILQyDG7GA0MKHYDk5FQDGGz+paQsa1a/27fnGGJjl6r61OsfN+j1D6jKYmP/ZNi+Pcdu\nG8vjrjoP9Tja7WCZxf8N962MnWMAtez+/g85JHtHoSPOYZ4855b6bbuK5vzeBUFoeZozf4klWWgX\ntFQMVO3NPvdqlI1V7WRv6LirzsNynN27T1NWptVSaRcc/DN1dTrNOmo3Eeuwb7X07ds6LHZCx6S1\nZ6yTEG+C0H4RJVloF7RkVit7vsuO+DsbfSlfeGEna9dmMXp0FHl5BXZ9K5XzUPyGLcPHVVScszuW\nwWDAy6vKzlHl/EeO7IXBYCAry7aGrZtIPGZlGWJi0uyOLQgtTVvIWCch3gShfSJKstAuaKkYqM3B\n1pcyl507N1NT86qpjrVv5ejRUXz11XvU/n/27jwuqnr/H/hrWBSVfZFVRFFRUBG30ptAC1CppTdT\n3DM1S1Or+0hLM0e7Jt6Wm1vXe8vSUtPq0aKSiuaX5VdupeaSphmuLCqCgoIw8Pn9MTDOcgaGmYHZ\nXs/Ho0fOmbO8z5nhM+9zzue8P9X/VVvT8/jrr6tIT8/W+CHWXH829JWyUz8O9R0jazyGRPxeEpGl\nsAQc2Y26km73bnkmWfTqjm45tTegWTu5br6GS7YBC5CSAo2ybbrzZgPYDXf3P+HmJhAY6IWwsLYa\nx6GhY2Rtx9AaOWIbZul95veSiIzV7CXg/vjjD6Smpqpe//XXX3jrrbcwbtw4jBo1ChcuXEBERAS+\n/PJLeHt7GxUYUWNZ2y1P3b6UDfet1Nf/EnBGhVaPCt15ld0k+vSRIzNTLrmWho6RtR1DIoDfS0NZ\nc6k8IltkVJIcFRWFI0eOAABqamoQGhqK4cOHIy0tDUlJSZgzZw6WLVuGtLQ0pKWlmTVgsn2O0pDr\n9qVsuG9lfSXn3NwaWr/u+ohIP3tqi6y9VB6RTTK1tMauXbvEAw88IIQQIioqShQUFAghhMjPzxdR\nUVE685thk2TDpMslzbPLckm6+5olXFym1Vsqavv2LBEU9LJWuavXRVDQJJ1jxNJTluGIbZg97rO9\ntUXWXiqPyFJMab9MfnBv8+bNGD16NACgsLAQgYGBAIDAwEAUFhaaunqyMytWZGhc6QCAc+eWYOXK\nBXZ3tUOqNNT99/fE/v36S0UNHhyPjz8G3nxzBnJzywBUokMHdyxe/IzO8WHpKSLj2VtbZO2l8ohs\nkUlJcmVlJbZt24Zly5bpvCeTySCTySSXk8vlqn8nJiYiMTHRlDDIShhy69KcDbkt3Cqtry+lenk4\n7fj9/X3g4RHQ4H6xr2bTy8zMRGZmpqXDIC2m/v3bW1vE7ldE5mdSkrxjxw706dMHAQEBAJRXjwsK\nChAUFIT8/Hy0bdtWcjn1JJnsg6H94czVkNt6/zt98R86dAIbNlyx2f2yR9on8osWLbJcMATAPH//\n9tYWsVSe47KGkzS7ZUo/j1GjRol169apXr/66qsiLS1NCCHE0qVLxdy5c3WWMXGTZKUM7Q9nrn60\ntt7/Tl/8fn4jbXq/HIEjtmHWts/m+Pu3x7Zo+/YskZLyhkhIWChSUt6w2f7VZDh761vfFExpv4y+\nknz79m3s2bMHH330kWraa6+9hpEjR2Lt2rWqEnDkGAy9dWmufrS23v9OX/wKRSvJ6bayX0TNwRx/\n//bYFrH7leOxt7711sboJLlNmza4fv26xjRfX1/s2bPH5KDI9jTm1qUxDbn27aRbt4oN3p410ne8\nXFzKJafr2y+5/EOsWpUFhaIVXFzK8eKLCZDLp5stTiJrZK6uEuZIKtkXmCzJmk7S7JGTpQMg+zBr\nVjIiI+drTFP2h0syed11ff4yMv6JrCw5MjL+ifz8CgQFvdIk22sO+o7Xiy8mGHwc5fIPsWTJMRQV\nbcHNm+tQVLQFS5Ycg1z+YZPGTmRpTdne2HIstiY9PRspKW8gMVGOlJQ3kJ6ebemQbA5P0poWh6Um\ns2mqoWP1DdXcu/dUBAQE2exQtfqOl6HH0d9/FIqKtkhMT8W1a5ubYxcckiO2Yda4z9Y0VLU1xWIr\npB54jIycj+XLU3jsGkH6OM7D8uUsB1rHlPaLSTJZvcREObKy5DrTExL0D7/sCLy9n8HNm+t0pnt5\nPYOSEt3pZB6O2IY54j5T09J38SMlZQF27nzLAhHZLp6k1c+U9svkwUSImhpvJ0nT13/Z1bWimSMh\nImoc9qU1Hz6w2XTYJ5msHvv8SXvxxQS4uDyvMc3FZRpmzGBjSUTWjRc/yBbwSjJZPQ6/LE1ZxeJD\nrF6diqoqN7i6VmDGjHhWtyC7w8ES7A8HPyFbwD7JDs6efnzsaV/IejliG2bJfeYDXvaLfWmpObBP\nMhnFWoZTNQd72hciuscWB0vgCbthbKkvLT9Tx8Qk2YHZ4o+PPva0L0S2zNzJhK094MUTdvvDz9Rx\nMUl2YLb241Mfe9oXIlvVFMmErT3gxRN262PqiRs/U8fFJNkO6GsA1KffunUNwF14eoap5mnsj481\n326ytR/S+ljzcSaqT1MkE839gJepf388Ybc8zd++y8jP90RBwfuq9xt74sbP1HExSbZx+q7cHDp0\nAhs2XNH6wZoP4CEA8Th3bj5CQ/MATAXwkdo8U+Hr62vwdgDruN1kL09KW/txJqpPUyQTTVndRjsh\nHjAgRKfdbOzfnz2dsNsi3Tb0DQCag5Y09sSNn6kDE83MApu0a8nJ8wUgdP7z8xspOR14Q/VvF5ch\nAsiqnbaw9v9Zwt9/lMHbSUl5wwJ7LW379iyRkvKGSEhYKFJS3hDbt2dZOqRGs4Xj7OgcsQ0zdJ9t\n6fu7fXuWiIycpxFnq1bS7WZD8W/fniWSk+eLhISFIi5uuggKelZj+cjI13XaI/VlkpPn22R7ZY10\nv4MLJT/ThISFBq9T6rsi9ZmSdTKlzeaVZBun78qNQtFKzxL3rujU1LQGEF/73z1VVZ8YvB1rut1k\nS09K62MLx5lIH1u6oyPVNaS8vJvkvPX9/Und/QkKegW9e0+Fh0eo5JVv3jFqOrptqOlXgVmr33Ex\nSbZx+m4D6RuyGLjXMNTU3JacQ2pYY95uah48zmTLbCmZkD4hbfzfn1SyXVDwPmJjF2DnTrnBy/BB\nMPPQbUOToexqaNqJm9RFGD4/Yv+YJNs4fVduxo1LwIYN87Ua4nkAlA1Dq1bTUF7+OLQbD+BZyWGN\nbekKkS3jcabmdunSJUyYMAFXr16FTCbDc889h1mzZhm9Pkvd0WlswqJ8mFlbMlq0eA6Vlf9TTWno\n78+Yuz+GLMMEzDi6bWg8goLWISRkBjw8Asx24sa7AY6BSbKNq+/KTb9+2arppaXXAFTCw2Mv3Nx2\n4/Jl4OTJ6QCyASyAshtGNdq3r5Qc1tiWrhDZMh5nam6urq7497//jV69eqGsrAx9+vRBUlISunWT\n7npgLbQrGJw/74bi4lWq948dewXTpp3Avn15Gg/m1b0+ezYXwCsA3ldb6060bv0XamqGQog2kMlu\no3//6Hr//vTd/fnpp1/h7f0MXFzK8eKLCRrtqvQy2Thx4hQSE+VmqchQp6Fk21zJuCHr0Z7Hz68K\nGRnnoVC0kjxOxmxn8OB4HDp0AqtWjVKtd9q0htfbWNJ3A1IwceJqdO++t0lPbHgC1YzM2DfaIBbY\nJEmw9gds+FALWSt7b8OefPJJsWfPHo1pzb3PDf39b9+eVftw3PzaB7NG1j6ErNmetWjxlNrrLOHi\nMk1rnmcFMF3jwWXgaY15XFymiYULV+uNdeHC1RLrnawRj/Y6dJfJEsAUtdfmaZ+lHzibpzqeDb1v\nru3om0e5z/eOk7PzlHqPtbHbMWafGpKQoP1AYFbt96nuOzlfBAU9a/btNtf+2RNT2i8myQ7Kmp/W\nZSNA1sye27Dc3FwRHh4uSktLNaY35z7rJsC6yUZc3GSdhET5WjtRVk9kpBNP9Yo/yv9G6cwjVfGn\njvKCg3qVIOmEXX0d0suYtyLDve3oT7aNvViifRITFze9wfXo25b28ffwGGb0/piyTw3to/bvj+52\nJgtA+yRgnujde0qjttsQa7/AZY1Mab/Y3cJBWfNtfT7UQtT8ysrKMGLECCxfvhzu7u4678vlctW/\nExMTkZiY2CRxLFjwGQoKgqBe27agYD7efPNz1d//mTP5AHpBs/7tfACfQ7NazxUo6+S6APgTyu5l\n2m2Iet/heQC8tN7PRnFxORIT5ZK3tpX9i9WrBMkltgFUVbk1sIw68zzAq9xONoAMKI+BAkCyqu+z\nMf2ppfriurlNlNzOjz/+oepy4u6ufVzraG7r9m39aYkh8Ta0z4YwpL+xbt/nMgAfa61pCXJzRxu8\nXUOwAlLDMjMzkZmZaZZ1MUl2YNZaMo2NAFHzqqqqwlNPPYVx48Zh2LBhkvOoJ8lN6fz5hpMNZRux\nRGce4EkoE04FgIMAukM3kQY0k9jTtctUQ/lg826197IB7EJ19ffIylJO0U6WdPsXSye46lWDGl7G\nPBUZbt26DGAXNI/VfJSWXtUTh1Jjq3lUVLhKbkeh8MLNm8rBqoqKhutZo+a2amp0qyvVMSTehvYZ\naLhPryEXarQvNP30Uw0UkuG10Ls/xmAFpIZpn8QvWrTI6HUxSbZBpnbal8s/xKpVWXoflmhoOOum\nTqzZCBA1HyEEJk+ejOjoaLz00kuWDgdASz3T7yUbbm7uKCuTmscb967KPgXNh/IAZeK0AHVJsrPz\nFFRXT1e99vGZgZs3r6Gmpm7+DGgn49rJku4VxWRoj2Tq4jJNo2qQ1DIuLs9DoVhT+9pcFRla6sSv\nfD1DTxzGVvOofztKLwOYBOBTtWlTAYxXez0Pbm5VerdtWLz1x2LIVWJDL9SoX2jq3XsGjhzRXaZD\nB927MqZgBaTmxSTZxphadkYu/xBLlhyDQrFFNW3JkucBfAi5fLrk+rWHszZ0W8ZiI0DUfH766Sds\n2LABPXv2RFxcHABg6dKlePRRy/y9RUS4o7hYd7p6stG5s7dkQgKoJyQ99GzhIuquHHt43EXHjp/X\nVv2pxsyZo3Do0AmsXp2Kqio33LlzB1USOZt6siTVdc3X1xe7dyvX4epagRkz4jUuREhVYEhOjsCN\nG/fWcf/9fWsrcShPZAyhfQFEXxcHD48AvbE3lIxLX8QI0DO39vSbUK+mBFwCsBbA3trXBYiObqd3\n24bE6+kpHUvdPhtyldiYCzVvvTUKU6a8olGRJCjoZSxePErvMsaw5q6SdslsPaMNZIFN2hVTO+3r\nG6667qESQx6uaI4HBOxhiGmyT47YhjXnPisf3HtZo/0JCnpJow1YuHC1cHaeotVGvaT1wJxhD4rV\n157paw/9/EaaVHmnKapOLFy4Wjg5PS00H2YcYvaHvBoznLfmsdb3eQwRddVFgoImGVVZQ/Mhwsn1\n7rNuVQrdhyKNfbCdv1vWyZT2i1eSbYyp/XX1DVd9/XoN/P1Hwd3dVc+S9+5tNkffYGvtL01ETWvw\n4Hh8/LH2lbLhGu3Bvn15qK4ej3tXJX8F8Co0+xonA3gWwCdq06ZA2ZbJoewHHIKDB89qPJQHQNXd\n7NKli3ByGomami/V1jEVRUUJyMpSXhk25u6avquZEyeOQvfue3HixCkUFW3Reb++h5ffe287amri\noNkHezJkskkQ4l4XB1Pvykldybz/fqnBq6YAmKC+B5Lrc3Fpg7/9DXBzA2bOfKZRx1HfkOBBQZNR\nULBWbdrLuHq1FImJcpw4cQpSD3CqXyU29motf7fsD5NkG2Nqf139w1VHoajoLRQVTYb0E+B5quns\nG0xETamhZEO3OsQ0KB/WUl9mJ4BS3EukrwEQADarzfM8iounIytLudyxY5MBeGncMlcOODIVQCiU\nXQLGQ/3hPmMq7+i72FFU1A1ZWXLoVrtQysuT7IgNACgvd4VuX9y1AJKQkmLeW/NSn4/24FWnT1/F\nnTu7ca8rRYnkury9gcxMuVFx6BsSvHfvGYiNvRdLXl4Fjhy5lzQr+38Ddd8XqRMHYxJeDvJhf5gk\n2xhT++u++GIClixRf0AEUB+uWtmoDofmj808KB962I3IyJ3sG0xEFqV7sSAAyivH6v1dH63991u1\n87wBzausALAG6g/yFRQES8zzfu08crVpezXm0L671lCypG/EPeBU7XZOSbwP5OfnS04HAJlM+oFH\nFxcf7Nz5luR75qSeVKakvIE7d1ZrzfEhGnqgsbH0nWx4eARg5065KpbDhzU/U4ViDfz9UxETs9fi\nw1QzsbZuRifJJSUlmDJlCk6ePAmZTIZPP/0UnTt3xqhRo3DhwgVERETgyy+/hLe3tznjdXimNXnI\nvAAAIABJREFUdtpXPjzyIVavTsX16zUAoqD8Mbm3vJOTM2pqtH9s4uHjsxbLl0/mHzARWdSsWck4\ndmxybVLrAqAAwGfQLB03DcBYtdf6fu6cGzkPoF22TP3umiHJ0oABIdi7V/1iRTaATQC2qL1+Hsok\nvs48BAbqqzUMhIe74a+/pKZLd7FrStLJ63SEhz+NO3f0P9DYWIbcWdWXSMfEdDX6CrYUY+r7m/og\nPjU9o5Pk2bNn4/HHH8fXX38NhUKB27dvY8mSJUhKSsKcOXOwbNkypKWlIS0tzZzxEuq/DaTvrFR7\n+rp10zFx4moUFUldYbiNe1df1FVixYoMVQyG4pkyEZmfF9Sv+spkIyDEDCivKlejdetc3L27EdXV\ndW1NQ1dvFQAkymoAUE+KXVymQaG4l3xr38kzJFnaty8PCsUYaPap3qa2RF3MQwH0Qd3FirAw9RrO\nmlasmILx419EcfEq1TQfnxlYvnyy3mWair7ktVu3rma9qm3IndXmKilqzPNCHDjL+hmVJN+8eRM5\nOTlYv369ciUuLvDy8sLWrVuRVVtxfeLEiUhMTGSS3Iz0nZUeOnQCGzZc0ZkeE9Ma2dmToexiUWce\nWrRwh7e35oMPwDwUF7+AjIzGlYHjmTIRmduKFRla/YYBIb6uvYUeADc34OrVzjhyZBTuJaKFUPYv\nrlsuG8oR+u49IOfkNBKtW09DWdl/VdN8fGagQ4dKeHjIax9Si8X+/btRUSF9q97wUeHU+1S/LLFE\nPIBvUdfNo6FudYMHx+Pzz7XvMo6ySDtrzjKe9V1kMeTOanOVFDUmGefAWdbPqCQ5NzcXAQEBmDRp\nEn777Tf06dMHH3zwAQoLCxEYGAgACAwMRGFhoVmDpfrpOytdtWqU5JPSJSWjAMig3Y+vouJthIQo\nH3w4ePAiiovDod4lozFnujxTJiJTaSdKV65ck5xP/RZ6YqIcmokoAGTDx2c0evaMkqwgUVPzJSor\nH4d6m9iyZQUWL55ocHtlSLKkO08byWX8/fMREyO3ueoK5qrla8hFlob2ubnqChuTjHPgLOtnVJKs\nUChw+PBhrFq1Cv369cNLL72kc8VYJpNBJpNJLq8+vKn28IFkPH1npfrKvimnR0DqSeq6Bx8SE+W1\nT1trMvRMl2fKZOsyMzORmZlp6TAcllSi1KrV85CqwnPixClVObdbtwok1haP/v13q7VtunNUVvaH\neptYUACNk/qGuo8Zkiw1POKecpnly6dbRdJrDHMk7Oa6yNIcJw/GJOMcOMv6GZUkh4WFISwsDP36\n9QMAjBgxAkuXLkVQUBAKCgoQFBSE/Px8tG3bVnJ59SSZzEf3rDQbQAZu374D5ZPdybj3o5KN27eL\nAFRJvHfvTNbUM12eKZOt0z6RX7RokeWCcUBSiVJ5+Rq0ajUK5eX32ixn5+dQVDRDVc7Nx+dFnXq5\n6gmIvrZJ+6E8IFtVS/nWrWvIz6/QWKfUlU2g/mRJutZwT+zfz1HU1NnaRZbGJuMcPc/6GZUkBwUF\noV27djhz5gy6dOmCPXv2ICYmBjExMVi/fj3mzp2L9evXY9iwYeaOl+qheVaaDWXd0CW19SAB5fDS\nSi4um6BQqD8oUvdePHx8ZmDmzFES61RqzJkuz5SJyBT6EqVOnUIQEqJMLg4fPo7S0tlQP9EvLl6F\nyMiJemsES7VNrVpNQ3m5ekUMZTtaXLxZ7arzfKhfxZa6smlIsmQtXSOsmSNcZOH3wLoZXd1i5cqV\nGDt2LCorKxEZGYlPP/0U1dXVGDlyJNauXasqAUfNR/2s9ODBsygu3qw1xxL4+IyGk1ONTl88ZRH6\n0QB2o0OHykZdFTE0Jp4pE1Fj6UuUQkLcVZUSfH0nQncAJODGDeitpiB9NTcWGzbswrlzdevKgO4A\nHUugXlsZsN4rm7aOF1nI0oxOkmNjY3Ho0CGd6Xv27DEpIDKOZj85gZAQLxRLVDPq2TMKACT74ilr\nJsvh4SHXmGrqma7U8iwLR0SGMCxRuqtn6cp6193QyHHHjl2SbEe16ybb05VNa8KLLGRpHHHPDjTm\nwRY3t2oIIfSsSdnQX76c2zSB1mJZOCIylCGJUkSEO4qL50Pzqu88dOjgbtT21EeOy8iQmuteUswr\nm02L3RHIkmRCf8bUNBuUyepJ0sgYyoZceyhV1D7Ycq9bhfJpaWVjrp2k3huaeic8PH7DrVvpzR5v\nSsqCZhk+lcgUjtiGWfs+p6dnY8qU9SgoCEFd6bagoCv4+ONnTEqwpE7og4JeRkhIGTw8QmsT9iQm\ncURWzJT2i1eS7YAhD7ZIXX158slhqK7uACAfytGrdgN4FE5OeRaJl/36iMgYgwfH4+OPgZUrd6Oi\nAnBzA2bONC1BrlsvoH0VeziTYiIHwSTZDkg/2JKN3Nw/cPmyJ4CWiIjQve0ok9XdMhQa/3d1rVDN\nY2rfYanlTXlimX2ZiUhKU92W5+1+IsfFJNkO6D7Ykg0np1UoK4tDXR+94mJgypRX8PHHyjlmz94l\nUQIuGcDnCAxUPgRjat9hfcuPGxdq1BPL7MtMREREzYV9ku1Eenp27a1G59rhVjsDkO73K4SQ7BOs\nLGv0Flxdh6KycpvJfYfrW37mzCRVvIb262NfZrIGjtiGOeI+E5F9YJ9k0rglqG+4VaChfr/K9xSK\nVkhPzza573B9yxtzC5N9mYmIiKi5OFk6ADI/ZZ9f6X6/paXXGhyOVYhyzJ69C7duXZacy1JDUjvC\n6EtERERkHZgk26FZs5LRosUZqA9DrfQygErMmpWMyEjt9+YBSAIwFUA0zp1bApmspc58yr7DSQbH\nYcryTb0+IiIiIn3Y3cIODR4cj86dN+LkyatQDjXdAoA7gFHw8NirUdboyJELuHr1OgAZgOMAogEs\nAwB4eARg8eKHrGZIao6+RERERM2FD+7ZEfXyaIcPH0VpqT+AMCi7XiQDiNd5yC09PRsTJ65GUVE3\njfkAPhBHJMUR2zBH3Gcisg98cI8ky6Mpu1s8BGXSOx9BQeswc+YzOssUFW3RWgaIjNzJoVaJiIjI\nYbFPsp1YsSJDK0EGlDWSd6v+HRLSSqNrgr5l/P0/xPLl7MZAREREjotJsp3QVx6trqwboOxjbMgy\nMTFdmSATERGRQ2N3Cxujb1jmW7eu6VniFAA5AAUuXfoTKSlv4MqVaygoKKlNkicAuA6gLYByAAko\nLdW3rvpjICIiIrIXTJJtiL5hmQ8dOoH8/Aoo+xOrd5+YAmAG6h7Eu3BhKv76KwSAAPBftfnmA0ip\nnW8qTp++gPT0bMnEl0NDExERkSNgdQsbom9YZj+/UbUP32VD2QfZGcqBQQoAfKQ19ygAW6BLOSS1\nUipSUjpLVrbg0NDk6ByxDXPEfSYi+8DqFg5C2T0iG0AGlB+dsmSbQtGqdo541F01VpJLrKWVxDRA\nve8y4KZ3qGcODU1ERESOgEmyDVEOE70Lml0q5qO6+qqeJaSGa9bX31h93iK4ubWTnItDQxMREZEj\nYHULm9ISmgkyACxBYGCAznDNLVpMAZCnNe88ALehO1x13ZDUdf++pXeoZw4NTURERI6AV5JtiKdn\ngOT0sLAOePVVzeGjL192xsmTY6Hsa1zXR/lRyGR/QoiU2umXALQBUAlgL5T9mR+Fk9M5vQ/hcWho\nIiIicgRMkm1IfV0dBg+OVyWqdUNNKxNfgXuj7gHOzu9Aoajru/wGAN2H8Jyd31GtR6rUm/q2iIiI\niOwRk2QbMmtWMs6dm69Rfk3Z1eHe8NENDTXdv380vvrqeSgUawAkQ6psXHBwBUu9ETmIZ599Funp\n6Wjbti2OHz9u6XCIiKwGS8DZmPT0bKxcuVutq0OSRtKqr0Sbv38q1q2bjsGD4yGXf4jVq7Nx/Xo1\ngDsA/AF0gLJLRhJcXd/Bgw/GstQbkQR7a8NycnLg7u6OCRMm6E2S7W2fichxsAScA2moq4MhQ03L\n5dMhl0+Hi0sqqqvTdeatqfmQpd6IHMSgQYNw/vx5S4dBRGR1mCTbIO2+wgMGhGDfvjzcveuCEydO\nSS5TV6ItPT0bCxZ8hjNnilBdLQOQCsAdyuGplUm0k9NtlnojIg1yuVz178TERCQmJlosFiIifTIz\nM5GZmWmWdbG7hY3R7SucDReXTbV9jKVeK/stL1+u7Lc8Zcp6FBR4AXhfba3zoRydbyKAzzF6tC/G\njh2s0ye5bj3sk0yOzB7bsPPnz2Po0KHsbkFEdofdLRzIihUZGokrkKGREAPxUCiUfZBjYrpqlGhL\nSXkDBQXB0K1osQTKknBpGD26BzZtWqZ6h6XeiIiIyBEZnSRHRETA09MTzs7OcHV1xcGDB3Hjxg2M\nGjUKFy5cQEREBL788kt4e3ubM16Hp9tXWOojjEdMzF4kJrbFsmVfYdeugwCWQzmQiP5hqX18ApCX\n1wopKW9olHsD7nXxeOedvRrl4Bqir4wcERERkTUzOkmWyWTIzMyEr6+valpaWhqSkpIwZ84cLFu2\nDGlpaUhLSzNLoKSk21dYuu/wpUunsWjRAQCdAHyk9s4IPWu+huLicGRlyQFolnszthwcy8gRWb/R\no0cjKysLRUVFaNeuHRYvXoxJkyZZOiwyAC9CEDUxYaSIiAhx/fp1jWlRUVGioKBACCFEfn6+iIqK\n0lnOhE2SEGL79iwRGTlPAKL2vyzh4jJN7bUQkZGvCw+PJwUwUmN63fzANK1prwvgsdr37k1PSXlD\nCCFEcvJ8ifXce18fY5cjsmaO2IY54j5bO93fAiEiI+eJ7duzLB0akVUxpf0y6UryI488AmdnZ0yb\nNg1Tp05FYWEhAgMDAQCBgYEoLCyUXJZPSRtPaljo++/vif37NfsOjx2bp2cN8QA2Qnu4aqAcddUt\n6tSVezO2HBzLyJE9MOeT0kTmovt8CnDu3BKsXLmAV5OJzMToJPmnn35CcHAwrl27hqSkJHTt2lXj\nfZlMBplMJrmsepJsjaz9FpZUreS6mPPybmPixNUoLS0C4KdnDSUAxkIzKd6tM9eJE6eQnp5tdDk4\nlpEje6B9Ir9o0SLLBUNUixchiJqe0UlycHAwACAgIADDhw/HwYMHERgYiIKCAgQFBSE/Px9t27Y1\nW6DNxRb70UrFDLwC4BcAU6HZJ3kegBkAdtW+jgcwBa1bX8WdO9CYr6hoBmbP3oVx40IbHA5biiHD\naBMRUePxIgRR0zOqTvKdO3dQXV0NDw8P3L59G8nJyVi4cCH27NkDPz8/zJ07F2lpaSgpKdF5cM/a\n623qG9bZmodj1hcz8BSA2QBWA+iGumGn711BHlE7PQm9e2/BhQvXUVSkO19KygLMnJlU73DY+jQ0\njDaRrbH2NqwpOOI+WzupiyOsZU+kq9nrJBcWFmL48OEAAIVCgbFjxyI5ORl9+/bFyJEjsXbtWlUJ\nOFtji7ewpGPOBlAFYC8AGYCHcC85zgaQAeVIe8ovzrlzt+HkpD2fUkWFc4PDYetj7HJERKSf1PMp\nrGVPZF5GJckdOnTA0aNHdab7+vpiz549JgdlSbZ4C0s35mwou1NsVZs2X+3fu6AcQOTeezdvugJY\npzbfvYbWmvediMhR8SIEUdNysnQA1mbWrGRERs7XmKbsR5tkoYgaphtzBjSTYNS+3l3Pey205lOy\n9n0nIiIiagocllqLLd7CUo85L68Mp09fQVWV1Jx/oK57ha4A1b98fC6iZ0+5Tew7ERERUVNgkizB\nVm5h6StVp3yQT2qJKLi6HtWTQN/rUtG/fzh27pQ3TdBERERENoBJso2qr1TdrFnJOHToRRQXr1Jb\nYh6cnM5iwAB//Pzz81Ao1qi9Nw1ALACWaCMiIiICjCwBZ9IGWUrILBoqVadMotfi4sVy1NRUonXr\nKrzyymDs25eHjIxkKPsd1424lwQfn/+gf/9OLNFG1ABHbMMccZ+JyD40ewk4sryGStXp6zKSmCiH\nsnKF5ns9e+5lFwsiIiKiWqxuYaM4VDQRERFR02GSbKOMLVVniyXuiIiIiJob+yTbMGOHfOZQ0UTG\nc8Q2zBH3mYjsgyntF5NkB6OvbBwRGcYR2zBH3Gcisg98cI8MUl/ZOCbKRERERPewT7IDWbEiQyNB\nBoBz55Zg5crdepYgIiIickxMkh1IQ2XjiIiIiEiJSbIDYfk3IiIiIsMwSXYgLP9GREREZBhWt3Aw\nLP9GZBpHbMMccZ+JyD6wBBwRUTNxxDbMEfeZiOwDS8CRCusgExEREZmOSbIdYR1kIiIiIvPgg3t2\nhHWQiYiIiMyDSbIdYR1kIiIiIvNgkmxHWAeZiIiIyDyYJNsR1kEmIiIiMg+WgLMzrINM1LQcsQ1z\nxH0mIvvAOslERM3EEdswR9xnIrIPprRf7G5BRERERKSFSbIJMjMzLR2C2XBfrI+97AdgX/tC1s3W\nvmu2FK8txQrYVry2FCtge/Eay6Qkubq6GnFxcRg6dCgA4MaNG0hKSkKXLl2QnJyMkpISswRprezp\nS8J9sT72sh+Afe2LPdq5cye6du2Kzp07Y9myZZYOxyS29l2zpXhtKVbAtuK1pVgB24vXWCYlycuX\nL0d0dDRkMhkAIC0tDUlJSThz5gwefvhhpKWlmSVIIiJqGtXV1XjxxRexc+dO/P777/jiiy9w6tQp\nS4dFRGRxRifJly9fxg8//IApU6aoOkRv3boVEydOBABMnDgR3333nXmiJCKiJnHw4EF06tQJERER\ncHV1RWpqKr7//ntLh0VEZHFGV7d4+umnMW/ePNy6dQvvvvsutm3bBh8fHxQXFwMAhBDw9fVVvVZt\nsPaqMxGRrbKnSg9ff/01du3ahY8++ggAsGHDBhw4cAArV65UzcN2m4hsmbFttvQ4xg3Yvn072rZt\ni7i4OL39UmQymWTDak8/LkREts6QBJjtNhE5IqOS5J9//hlbt27FDz/8gIqKCty6dQvjx49HYGAg\nCgoKEBQUhPz8fLRt29bc8RIRkRmFhobi0qVLqteXLl1CWFiYBSMiIrIORvVJfvvtt3Hp0iXk5uZi\n8+bNeOihh/D555/jiSeewPr16wEA69evx7Bhw8waLBERmVffvn1x9uxZnD9/HpWVldiyZQueeOIJ\nS4dFRGRxRl1J1lZ3u+61117DyJEjsXbtWkRERODLL780x+qJiKiJuLi4YNWqVUhJSUF1dTUmT56M\nbt26WTosIiKLM3kwkYSEBGzduhUA4Ovriz179uDMmTPIyMiAt7e3xrz2Uovz2WefRWBgIHr06GHp\nUEx26dIlPPjgg4iJiUH37t2xYsUKS4dklIqKCtx3333o1asXoqOj8frrr1s6JJNp1yG3VREREejZ\nsyfi4uLQv39/S4djtJKSEowYMQLdunVDdHQ09u/fb+mQzOaxxx7DH3/8gT///BOvv/66TdXAl/p+\nWWu82t+hAwcOWG2sf/zxB+Li4lT/eXl5YcWKFVYb79KlSxETE4MePXpgzJgxuHv3rtXGunz5cvTo\n0QPdu3fH8uXLAVjXd1Yqx6kvvqVLl6Jz587o2rUrMjIyLB7rV199hZiYGDg7O+Pw4cMa8zc6VtFM\nFAqFiIyMFLm5uaKyslLExsaK33//vbk2b1bZ2dni8OHDonv37pYOxWT5+fniyJEjQgghSktLRZcu\nXWz2c7l9+7YQQoiqqipx3333iZycHAtHZJr33ntPjBkzRgwdOtTSoZgkIiJCFBUVWToMk02YMEGs\nXbtWCKH8jpWUlFg4oqaj/d179dVXxbJly4QQQqSlpYm5c+daMjwNUt8va41X6jtkrbGqq66uFkFB\nQeLixYtWGW9ubq7o0KGDqKioEEIIMXLkSLFu3TqrjPX48eOie/fuory8XCgUCvHII4+IP//806pi\nlcpx9MV38uRJERsbKyorK0Vubq6IjIwU1dXVFo311KlT4o8//hCJiYni119/VU03JtZmS5J//vln\nkZKSonq9dOlSsXTp0ubavNnl5ubaRZKs7cknnxR79uyxdBgmuX37tujbt684efKkpUMx2qVLl8TD\nDz8s9u7dK4YMGWLpcEwSEREhrl+/bukwTFJSUiI6dOhg6TCahdR3LyoqShQUFAghlCfWUVFRlgxR\ng9T3yxrj1fcdssZYte3atUs88MADQgjrjLeoqEh06dJF3LhxQ1RVVYkhQ4aIjIwMq4z1q6++EpMn\nT1a9fuutt8SyZcusLlbtHEdffG+//bZIS0tTzZeSkiL27dtn0VjraCfJxsRqcncLQ125cgXt2rVT\nvQ4LC8OVK1eaa/NkgPPnz+PIkSO47777LB2KUWpqatCrVy8EBgbiwQcfRHR0tKVDMtrLL7+Md955\nB05OzfYn2mRkMhkeeeQR9O3bV1WL19bk5uYiICAAkyZNQu/evTF16lTcuXPH0mE1CanvXmFhIQID\nAwEAgYGBKCwstFR4OqS+X9YYr9R36Pbt21YZq7bNmzdj9OjRAKzz2Pr6+uIf//gHwsPDERISAm9v\nbyQlJVllrN27d0dOTg5u3LiBO3fu4IcffsDly5etMlZ1+uLLy8vTqIZjzbmdMbE22y8wi9Fbt7Ky\nMowYMQLLly+Hu7u7pcMxipOTE44ePYrLly8jOzvbZseWV69DLuygPu1PP/2EI0eOYMeOHVi9ejVy\ncnIsHVKjKRQKHD58GNOnT8fhw4fRpk0bpKWlWTosszPku6evBr6lNPT9spZ4DfkOWUus6iorK7Ft\n2zY8/fTTOu9ZS7znzp3DBx98gPPnzyMvLw9lZWXYsGGDxjzWEmvXrl0xd+5cJCcn47HHHkOvXr3g\n7OysMY+1xKpPQ/FZc+zaGoq12ZJk1uK0XlVVVXjqqacwbtw4uyjb5+XlhcGDB+OXX36xdChGqatD\n3qFDB4wePRp79+7FhAkTLB2W0YKDgwEAAQEBGD58OA4ePGjhiBovLCwMYWFh6NevHwBgxIgROg+E\n2AOp7556DXwAVlcDX+r7ZY3x6vsOBQUFWV2s6nbs2IE+ffogICAAAKzy2P7yyy8YOHAg/Pz84OLi\ngr///e/Yt2+f1R7bZ599Fr/88guysrLg4+ODLl26WOVxVacvPu3c7vLlywgNDbVIjA0xJtZmS5JZ\ni9M6CSEwefJkREdH46WXXrJ0OEa7fv266mnb8vJy7N69G3FxcRaOyjhSdcg/++wzS4dllDt37qC0\ntBQAcPv2bWRkZNhkVZigoCC0a9cOZ86cAQDs2bMHMTExFo7K/GytBr6+75c1xqvvOzR06FCri1Xd\nF198oepqAcAqj23Xrl2xf/9+lJeXQwiBPXv2IDo62mqP7dWrVwEAFy9exDfffIMxY8ZY5XFVpy++\nJ554Aps3b0ZlZSVyc3Nx9uxZq6pipH5HzKhYzdJr2kA//PCD6NKli4iMjBRvv/12c27arFJTU0Vw\ncLBo0aKFCAsLE5988omlQzJaTk6OkMlkIjY2VvTq1Uv06tVL7Nixw9JhNdqxY8dEXFyciI2NFT16\n9BD/+te/LB2SWWRmZtp0dYu//vpLxMbGitjYWBETE2PTf/dHjx4Vffv2FT179hTDhw+36+oWQmh+\n94qKisTDDz8sOnfuLJKSkkRxcbGFo1PS9/2y1nilvkPWGqsQQpSVlQk/Pz9x69Yt1TRrjXfZsmUi\nOjpadO/eXUyYMEFUVlZabayDBg0S0dHRIjY2Vuzdu1cIYV3HtS7HcXV1VeU49cW3ZMkSERkZKaKi\nosTOnTstGuvatWvFt99+K8LCwoSbm5sIDAwUjz76qNGxyoSwg06PRERERERmZPuPzhMRERERmRmT\nZCIiIiIiLUySiYiIiIi0MEkmIiIiItLCJJmIiIiISAuTZCIiIiIiLUySiYiIiIi0MEkmIiIiItLC\nJJmIiIiISAuTZCIiIiIiLUySiYiIiIi0MEkmIiIiItLCJJmIiIiISAuTZCIiIiIiLUySiYiIiIi0\nMEkmIiIiItLCJJmIiIiISAuTZCIiIiIiLUySiYiIiIi0MEkmIiIiItLCJJmIiIiISAuTZCIiIiIi\nLUySiYiIiIi0MEm2Ik5OTvjrr78sHUajdO/eHdnZ2Xrff/zxx/H55583Y0RATk4Ounbt2qzbtEYX\nL16Eh4cHhBB65/Hw8MD58+ebLygAS5cuxdSpU5t1m0S2zhZ/H0yxceNGpKSkWDoMm2OJNt2e2X2S\nHBERgR9//NGgeRMTE7F27domjsg8vvzySwwcOBBt2rTBgw8+aPBy+fn5cHJywrVr11TTlixZAicn\nJ1y9elVj2mOPPdbg+k6cOIH4+HgAgFwux/jx4zXe/+GHH3SmmWrjxo3w8PCAh4cHWrduDScnJ9Vr\nT09PDBo0CKdPnzbrNpvLF198gejoaI1pSUlJktOWLVtW77rCw8NRWloKmUwGQPr7XVpaioiICNMD\nV/P888+rPo+WLVuiRYsWqteDBw/G66+/jo8++sis2yQyBn8fdMnlcri6usLT0xOenp6IiorCzJkz\nUVBQ0ETRAufPn4eTkxNqampU08aOHYtdu3Y12TbNqS7+unYuKCgIQ4cOxZ49e5p0u83Vpjsyu0+S\nZTKZKkkwZF5TqP+BNzU/Pz+88soreO211xq1XHBwMDp16oSsrCzVtOzsbHTr1k3jinB2djYSEhLM\nFq85jR07FqWlpSgtLcWOHTsQGhqqen3r1i1Lh2eS+Ph4nD59GkVFRQAAhUKB3377DRUVFbh+/bpq\n2v79+xv9+Zj6/TbUmjVrVJ/HvHnzkJqaqnqdnp7eLDEQGYK/D7pkMhlGjx6NW7duobi4GN9++y0K\nCgrQp08foxNlQ/e9vrtetuDmzZsoLS3FsWPHkJSUhOHDh2P9+vVGrUuhUDQ4T3O16Y7M7pNkdevW\nrcMDDzyAV199Fb6+vujYsSN27twJAJg/fz5ycnLw4osvwsPDA7NmzQIAnD59GklJSfDz80PXrl3x\n1Vdfqdb3zDPP4IUXXsDgwYPh7u6Od999F8HBwRoNwrfffovY2FgAwMGDBzFgwAD4+Pj4NZVrAAAg\nAElEQVQgJCQEM2fORFVVlVH78vDDD2PEiBEIDg5u9LLx8fGqhLi6uhpHjhzB7NmzNabt378f8fHx\n+Ouvv/DQQw/B398fAQEBGDduHG7evKlaV92VmJ07d2Lp0qXYsmULPDw8EBcXB0DzTLe+4w8Aubm5\niI+Ph6enJ5KSkjBjxowGr0JLNaqZmZlo166dRozvvvsuevbsCQ8PD0yePBmFhYV47LHH4OXlhaSk\nJJSUlKjm379/PwYOHAgfHx/06tVL44RC3bJly/D0009rTJs9ezZmz56t2t/IyEh4enqiY8eO2LRp\nU737AgChoaHo2LGjapuHDx9G9+7dkZCQoPp8Dh8+jJqaGvTr1w/p6emIi4uDl5cXwsPDsWjRItW6\n6q5uVFdX6/1+q9/CfeaZZzBjxgwMGTIEnp6euP/++zVu72ZkZCAqKgre3t6YMWMGEhISGryyJoTQ\n+YzU7zjUxbhu3TqEh4fDz88Pa9aswaFDh9CzZ0/4+Phg5syZGst/8skniI6Ohq+vLx599FFcvHix\nweNK1BD+Piip/806OzsjOjoaW7ZsQUBAAN577z3VsRo0aJDGctptyQsvvIDHH38c7u7uyMzMrLet\nqrsb6e3tDU9PT+zfv19nGz///DP69esHb29v9O/fH/v27VO9l5iYiDfffBMPPPAAPD09kZKSorrQ\noK1bt24aJ+sKhQIBAQE4evQoKioqMG7cOPj7+8PHxwf9+/fXuMNqqLZt22LWrFmQy+WYO3eu5DGq\nO04LFiwAoPzdCgsLw7/+9S8EBwdj8uTJKCkpwZAhQ9C2bVv4+vpi6NChuHLlCgD930n1bdy8eRMT\nJkxA27ZtERERgSVLlqg+24Z+j6mWsHMRERHixx9/FEII8emnnwpXV1fx8ccfi5qaGvGf//xHhISE\nqOZNTEwUa9euVb0uKysTYWFhYt26daK6ulocOXJE+Pv7i99//10IIcTEiROFl5eX+Pnnn4UQQlRU\nVIjIyEixe/du1TpGjBghli1bJoQQ4tdffxUHDhwQ1dXV4vz586Jbt27igw8+UM0rk8nEuXPnhBBC\nbNy4UfTs2bPB/fvoo49EYmJio47J+vXrRWxsrBBCiEOHDon4+Hhx9uxZjWmtWrUSVVVV4s8//xR7\n9uwRlZWV4tq1ayI+Pl689NJLqnWpH1+5XC7Gjx+vsS31Y9rQ8b///vvFq6++KqqqqsT/+3//T3h6\neuqsT9v//d//ibCwsHqnRUREiAEDBoirV6+KK1euiLZt24q4uDhx9OhRUVFRIR566CGxaNEiIYQQ\nly9fFn5+fmLHjh1CCCF2794t/Pz8xLVr13S2feHCBdG6dWtRWloqhBBCoVCI4OBgceDAAVFWViY8\nPT3FmTNnhBBCFBQUiJMnT9a7L3UmTZokZs+eLYQQ4p133hFvvvmm+OijjzSmPfzww0IIITIzM8WJ\nEyeEEEIcO3ZMBAYGiu+++04IIURubq6QyWSiurpaCKH7/RZC8zs3ceJE4efnJw4dOiQUCoUYO3as\nSE1NFUIIce3aNeHp6Sm+/fZbUV1dLZYvXy5cXV111qdt4cKFYty4cRrT5HK5alpdjC+88IK4e/eu\nyMjIEC1atBDDhg0T165dU31eWVlZQgghvvvuO9GpUydx+vRpUV1dLf75z3+KgQMHGnRcibTx90GX\n1N+sEEK8+eab4r777hNCKI/VAw88oPG+dluive/1tVXnz5/XaKu0t1FUVCS8vb3Fhg0bRHV1tfji\niy+Ej4+PuHHjhhBCiISEBNGpUydx9uxZUV5eLhITE8Vrr70muX+LFy8WY8eOVb3evn27iI6OFkII\nsWbNGjF06FBRXl4uampqxOHDh8WtW7caPGbabW2dc+fOCZlMJk6fPq1zjIQQ4plnnhELFiwQQih/\nt1xcXMRrr70mKisrRXl5uSgqKhLffPONKC8vF6WlpeLpp58Ww4YNUy3fUJs+fvx4MWzYMFFWVibO\nnz8vunTpYvDvMSk51JVkAGjfvj0mT54MmUyGCRMmID8/X+NMUahd9dq+fTs6dOiAiRMnwsnJCb16\n9cLf//53jasFw4YNw4ABAwAALVu2xOjRo/HFF18AgKo7wOjRowEAvXv3Rv/+/eHk5IT27dvjueee\n03uVcsyYMfjtt9/Mvv+A8qz9xIkTuHnzJnJychAfH49OnTrh2rVrqmkDBgyAi4sLIiMj8fDDD8PV\n1RX+/v54+eWX9cYsJK4aatN3/C9evIhffvkFixcvhouLC/72t7/hiSeeMNvtt5kzZyIgIAAhISEY\nNGgQBgwYgNjYWLRs2RLDhw/HkSNHAAAbNmzA448/jkcffRQA8Mgjj6Bv37744YcfdNYZHh6O3r17\n49tvvwUA7N27F61bt0b//v0BKM/ojx8/jvLycgQGBur0K9ZH/apx3eczaNAgjWl1XS0SEhIQExMD\nAOjRowdSU1P1fj5A/bczZTIZ/v73v6Nv375wdnbG2LFjcfToUQDKvuXdu3fHsGHD4OTkhFmzZiEo\nKMig/TEkhgULFqBFixZISkqCh4cHxowZA39/f9XnVRfHmjVr8PrrryMqKgpOTk54/fXXcfToUVy6\ndMmoWIjU8fdBv+DgYNy4ccPg+bX3vb62qqF2Pj09HVFRURg7diycnJyQmpqKrl27YuvWrQCUbdek\nSZPQqVMnuLm5YeTIkao2Q9uYMWOwdetWVFRUAAA2bdqk+gxatGiBoqIinD17FjKZDHFxcfDw8DB4\nn7WFhIQAQL3HTX3fnZycsGjRIri6usLNzQ2+vr4YPnw43Nzc4O7ujnnz5ul8J/Qdu+rqamzZsgVL\nly5FmzZt0L59e/zjH//QeJC+oe87OVh3CwAaP+ytW7cGAJSVlammqffxuXDhAg4cOAAfHx/Vf5s2\nbUJhYaFqXvXb+oDyD/Cbb75BZWUlvvnmG/Tp00c1z5kzZzBkyBAEBwfDy8sL8+fP13tLqClFREQg\nNDQUOTk5yMnJUd3SGjhwIHJycpCdna26/VVYWIjU1FSEhYXBy8sL48ePNylmfcc/Ly8Pvr6+cHNz\nU72vfWxNERgYqPp3q1atNF67ubmpvgMXLlzAV199pfGZ//TTT3r74o0ZM0b1o7dp0yaMHTsWANCm\nTRts2bIFa9asQUhICIYMGYI//vjDoFgHDRqEY8eOoaSkBAcOHMCAAQMQFRWF/Px8lJSU4KefflJ9\nPgcOHMCDDz6Itm3bwtvbG//973/r/Xwa6sOmfZzqjkteXh7CwsI05tV+bYr6Ph/1OC5cuIDZs2er\nPhs/Pz8AUN2CJDIFfx/0u3LliurvrSFS+97YtkpdXl4ewsPDNaa1b98eeXl5qtfqn516m6EtMjIS\n3bp1w9atW3Hnzh1s27YNY8aMAQCMHz8eKSkpSE1NRWhoKObOnWtQ32B96tolX19fg+YPCAhAixYt\nVK/v3LmDadOmISIiAl5eXkhISMDNmzc1EmN9bfr169dRVVWF9u3bq6aFh4drtJUNfd/JAZPk+mh/\n2cLDw5GQkIDi4mLVf6WlpVi9erXedXTr1g3t27fHjh07sGnTJtUfHwC88MILiI6Oxp9//ombN29i\nyZIlJj/MYWzH/fj4eGRlZWHfvn0YOHAgAGVylpWVpZGEzZs3D87Ozqorz59//rnemE15iKDuKkV5\neblqWlP2NdV39h0eHo7x48frfOZz5syRnH/EiBHIzMzElStX8N1332l83snJycjIyEBBQQG6du1q\ncNmzjh07IiQkBP/73/8QHh6uarwGDBiA//73vygrK8P9998PQPmjO2zYMFy+fBklJSV4/vnnm+Tz\nCQkJweXLl1WvhRAar/WR2qYpcYSHh+N///ufxudz+/Zt1fEgaiqO8vsgtUxNTQ22bdumuqDSpk0b\n3LlzR/W+IQ/01ddWNRRnaGgoLly4oDHtwoULCA0NbXC7Uuqu6H///feIiYlBx44dAQAuLi548803\ncfLkSfz888/Yvn07PvvsM6O2ASj7nAcGBiIqKgqAMhFVP275+fka+659HN577z2cOXMGBw8exM2b\nN5GVlaVxx7a+4+bv7w9XV1eNcnAXL14068UNR8AkWU1gYCDOnTunej1kyBCcOXMGGzZsQFVVFaqq\nqnDo0CFVeTF9idaYMWPwwQcfICcnR+PBrrKyMlXZstOnT+M///mP0bHW1NSgoqICVVVVqKmpwd27\ndzUe8oiIiKj3jzs+Ph6fffYZQkND4e7uDgB44IEH8Nlnn+HWrVuq22RlZWVo06YNPD09ceXKFbzz\nzjt61xkUFITz588b1UWiffv26Nu3L+RyOaqqqrBv3z5s37692Z/eHTduHLZt24aMjAxUV1ejoqJC\nlQRLCQgIQGJiIp555hl07NhR1RhevXoV33//PW7fvg1XV1e0adMGzs7OBscxaNAgvP/++6qTFUD5\n+bz//vvo168fWrZsCUD5+fj4+KBFixY4ePAgNm3apPeYaX+/tdX3uT3++OM4fvw4vv/+eygUCqxe\nvdqgH0apdRrz/ahb5vnnn8fbb7+N33//HYDywRT129tETcVRfh/U41YoFDh16hRGjx6Nq1ev4pVX\nXgEAxMbG4uTJk6rKO3K5XO861PdPX1sVEBAAJycnve3TY489hjNnzuCLL76AQqHAli1bcPr0aQwZ\nMqTebeqTmpqKXbt2Yc2aNRonKpmZmTh+/Diqq6vh4eEBV1fXRrXbdTEUFhZi1apVWLx4MZYuXap6\nv1evXti4cSOqq6uxc+fOescYAJTHrFWrVvDy8sKNGzc0HnYE6m/TnZ2dMXLkSMyfPx9lZWW4cOEC\n/v3vf2PcuHEG7w85WJIsVe5H/fXs2bPx9ddfw9fXFy+99BLc3d2RkZGBzZs3IzQ0FMHBwXj99ddR\nWVmpd32A8iw1OzsbDz/8sMZtlnfffRebNm2Cp6cnnnvuOaSmpuo9i9y4cSO6d++ud18+++wztG7d\nGtOnT0dOTg5atWqFadOmAQAqKytx48aNeq+uJSQk4Nq1a3jggQdU02JjY1FRUYE+ffqouj0sXLgQ\nhw8fhpeXF4YOHYqnnnpKbxJW1+D7+fmhb9++Ou83dPw3btyIffv2wc/PDwsWLMCoUaM0bj3pY8zV\nSu3jXvc6LCwM33//Pd5++220bdsW4eHheO+99+q9ojNmzBj8+OOPGo1tTU0N/v3vfyM0NBR+fn7I\nyclR/ejl5OQ02M9N6vMZNGgQrl27ppE4f/jhh3jzzTfh6emJt956C6NGjdK7n9rfb6ljou/z8ff3\nx1dffYU5c+bA398fp06dQt++fVXJuj761lnf1RN96wGU/Rznzp2L1NRUeHl5oUePHjZTS5WsG38f\n7m2nrkqRt7c3nnzySQQEBODXX39V3Z7v0qUL3nzzTTzyyCOIiorCoEGD9Lapdeprq1q3bo358+fj\nb3/7G3x9fXHgwAGNdfj5+WH79u1477334O/vj3fffRfbt2/XOH4NbV9dUFAQBg4ciH379mnEUVBQ\ngKeffhpeXl6Ijo5GYmKiqhLPCy+8gBdeeEHvOgFldQ53d3f07NkTO3fuxNdff41nnnlG9f7y5cux\nbds2Vdec4cOH6xx7dS+99BLKy8vh7++PgQMH4rHHHmtUm75y5Uq0adMGHTt2xKBBgzB27FhMmjRJ\n7zFiSTldMmGuJ6PIavz000/48MMPsXHjRkuHYpJRo0YhOjoaCxcutHQopKWmpgbt2rXDpk2brLae\nNhHpspffB6LmUO+V5GeffRaBgYHo0aOHatpXX32FmJgYODs74/DhwxrzL126FJ07d0bXrl2RkZHR\nNBFTg/72t7/ZZAP4yy+/4Ny5c6ipqcGOHTuwdetWDBs2zNJhUa2MjAyUlJTg7t27ePvttwGAfYHt\nRElJCUaMGIFu3bohOjoa+/fvt3RI1ERs9feByBLqTZInTZqkU1y6R48e+PbbbzVu+QLA77//ji1b\ntuD333/Hzp07MX369GYdYYhsX0FBAR588EF4eHjg5Zdfxpo1a1SF9sny9u3bh06dOiEgIADp6en4\n7rvvGuxuQbZh9uzZePzxx3Hq1CkcO3YM3bp1s3RIREQW12B3i/Pnz2Po0KE4fvy4xvQHH3wQ7733\nHnr37g1AeRXZyclJNbrMo48+CrlczitNRERW7ObNm4iLi9MYCYyIiAAXc60oLy9PIyEOCwuTrAjA\njuFEZOvs6VGO3NxcBAQEYNKkSfjtt9/Qp08fLF++XFV6EGC7TUS2zdg2u0mrW+hrWOvq/NnCfwsX\nLrR4DPYYq63Fa0ux2lq8thSrEPaTHNdRKBQ4fPgwpk+fjsOHD6NNmzZIS0vTmc/Sx90Rv2vcF9v7\nz172xV72QwjT2myzJcmhoaEaQ8NevnzZ6ELfRETUPMLCwhAWFoZ+/foBUA6Qo/1QNhGRIzIpSVbP\n0J944gls3rwZlZWVyM3NxdmzZ9G/f3+TAyQioqYTFBSEdu3a4cyZMwCAPXv2ICYmxsJRERFZXr19\nkkePHo2srCxcv34d7dq1w6JFi+Dr64uZM2fi+vXrGDx4MOLi4rBjxw5ER0dj5MiRiI6OhouLCz78\n8EO76MeWmJho6RAMZkuxAvfiTU/PxooVGbh71wUtWyowa1YyBg+Or3/hZmarx9YW2FKs9mrlypUY\nO3YsKisrERkZiU8//dTSITUJe/qucV+sk73si73sh6mafTARmUxmch8Rsh/p6dmYPXsXzp1bopoW\nGTkfy5enWF2iTAQ4ZhvmiPtMRPbBlPbLoYalJuuzYkWGRoIMAOfOLcHKlbstFBERERERk2SysLt3\npXv8VFQ4N3MkRERERPcwSSaLatlSITndza26mSMhIiIiuodJMlnUrFnJiIycrzEtMnIeZs5MslBE\nRERERHxwj6xAeno2Vq7cjYoKZ7i5VWPmzCQ+tEdWyxHbMEfcZyKyD6a0X0ySiYgawRHbMEfcZyKy\nD6xuQURERERkRkySiYiIiIi0MEkmIiIiItLCJJmIiIiISAuTZCIiIiIiLUySiYiIiIi0MEkmIiIi\nItLCJJmIiIiISIuLpQMgIiIipfT0bKxYkYG7d13QsqUCs2YlcwRSIgthkkxERGQF0tOzMXv2Lpw7\nt0Q17dy5+QDARJnIAtjdgoiIyAqsWJGhkSADwLlzS7By5W4LRUTk2JgkExERWYG7d6Vv7lZUODdz\nJEQEMEkmIiKyCi1bKiSnu7lVN3MkRAQwSSYiIrIKs2YlIzJyvsa0yMh5mDkzyUIRETk2mRBCNOsG\nZTI08yaJiMzGEdswR9xnS0lPz8bKlbtRUeEMN7dqzJyZxIf2iExgSvvFJJmIqBEcsQ1zxH0mIvtg\nSvvFEnBERERWjvWTiZofk2QiIiIrxvrJRJbBB/eIiIisGOsnE1kGk2QiIiIrxvrJRJbBJJmIiMiK\nsX4ykWXUmyQ/++yzCAwMRI8ePVTTbty4gaSkJHTp0gXJyckoKSlRvbd06VJ07twZXbt2RUZGRtNF\nTURE5CBYP5nIMuotAZeTkwN3d3dMmDABx48fBwDMmTMH/v7+mDNnDpYtW4bi4mKkpaXh999/x5gx\nY3Do0CFcuXIFjzzyCM6cOQMnJ808nKWEiMiWOWIb5oj7bG1YP5nIOE1aJ/n8+fMYOnSoKknu2rUr\nsrKyEBgYiIKCAiQmJuL06dNYunQpnJycMHfuXADAo48+Crlcjvvvv99swRIRWZojtmGOuM+WwDJv\nRObXrHWSCwsLERgYCAAIDAxEYWEhACAvL08jIQ4LC8OVK1ck1yGXy1X/TkxMRGJiYmPDICJqFpmZ\nmcjMzLR0GGTnWOaNyPqYVCdZJpNBJpPV+74U9SSZiMiaaZ/IL1q0yHLBkN3SX+ZtAZNkIgtpdJJc\n180iKCgI+fn5aNu2LQAgNDQUly5dUs13+fJlhIaGmi9SIiIiG9VQVwqWeSOyPo1Okp944gmsX78e\nc+fOxfr16zFs2DDV9DFjxuCVV17BlStXcPbsWfTv39/sARMRkXlFRETA09MTzs7OcHV1xcGDBy0d\nkl0xpCsFy7wRWZ96H9wbPXo0srKycP36dQQGBmLx4sV48sknMXLkSFy8eBERERH48ssv4e3tDQB4\n++238cknn8DFxQXLly9HSkqK7gb5AAgR2TB7bMM6dOiAX3/9Fb6+vpLv2+M+N6eUlDeQkfFPiekL\nsHPnWwCkEulstGq1Gp06hcDFpRRAS3h6BvCBPqJGatLqFuZmT40tn0Qmcjz21IbV6dChA3755Rf4\n+flJvm+P+9ycEhPlyMqSq03JBpABL6/LuO++MNVvR12Zt8uXr+Kvv2QoL19TO+8uACkAMgC4oFWr\nU5gzJwFy+fTm3xkiG9Os1S1IiU8iE5G9kMlkeOSRR+Ds7Ixp06Zh6tSpOvOwKpHxNLtS1CW9S3Dz\nJpCRofnbMXhwPFJS3sDJk3VXnjOgTJCVywBAeTnwr389j379svl7Q6TFnBWJeCXZSIbcPiMi+2Mv\nbZi6/Px8BAcH49q1a0hKSsLKlSsxaNAg1fvWvs/WfldP86LKGwC0fzuy4ee3Gt27d0PLlgrk59/G\n8eP/rn1PDkAhsQx/b4gMwSvJFsAnkYnIXgQHBwMAAgICMHz4cBw8eFAjSbZmtnBXry6OlSsXYP/+\ny7h5U/1d5ZXloqItyMpSTmnVapTa+wro+6lu6PfG2k8eiKydU8OzkBQ+iUxE9uDOnTsoLS0FANy+\nfRsZGRno0aOHhaMynP76wrstFJGuumS1osIZLi7lWu9moK4bRZ3y8hlwcppc+yoZwCnJ9db3e1N3\n8pCR8U9kZcmRkfFPzJ69C+np2UbvB5GjYZJspFmzkhEZOV9jWmTkPMycmWShiIiIGq+wsBCDBg1C\nr169cN9992HIkCFITk62dFgGs/a7etrJalHRDLi4PK82h1T88WjX7m7tFeW9AKoBPKcxR1DQy7h6\nNR+JiXKkpLyhk/xay8lDeno2UlLe0BsnkTVjdwsjqd8+q6hwhptbNWbOfJS3sojIpnTo0AFHjx61\ndBhGs/a7errJajwUCsDfPxUxMV1x4sQpFBXpLte1awesXp2ElSt3o6KiO0pLrwCYAQ+PAJSWXkNe\nXgWOHFmrmv//s3fu4VFV997/JkwgUUISCDAg2GiqQcJFUqHY1yY52iS0gEetJSAKlftJqIrnESuE\nZqii4eXUUy6htMrb49HWW9/3nKNgMfjQJL3AAWt6MEhpReSWDGBITAgZkknW+8eey76sPbNnz57Z\ne2Z+n+fJA7Nn77V+a2ey9pq1vuv7k0tMrPDlIRakMAQRCBoka0RN2xXoD530YARBEJHlscdKcfLk\neslATFjVm2ViVH74g9VC5OcfQH29wzOQlMZvty/BxYtp2LLlAIYMYXjqqbslz46ysip89JF0I588\nhbUVvjwkUqptet7HJzRI1oCeb8P0DZogCCLyWH1VT2n/JngdNzcfx969jYr4u7rOo6UlE01NL/qu\nOnlyPY4cacbBgy24ds2Go0c/9ZRVKCn78OG/o7jYgSFD3Bgxog9paeXo6bkNwua/UuTm7ovqlwcr\nzGZHA3rexzEsyphQZdiUlq5nAFP8lJVVGXoNQRDWJxb7sHBJxDYbxZ49DSw3dx0DGhiwTvI8SE1d\nxaZNW8r27Gnwna/27EhLmyc75i2Tccu22VaK3mcsLW0lq66ujWrbE+U5mCjtjFXC6b9o454G9Hwb\nTpRv0ARBEIQ6s2cXYuvWMowYUQu5i4XL9TM0NY2RuE6oPTuEGWExmwDUwj87LS3b7d4FwL9Jr6dn\nFw4dag2nKQHhbdDjbXBPS1uJc+cuxtUmPnrexy8kt9CAHm2XFfRgBEEQhDUYGEhVeWcQTp581qfT\n7ey8pHIe79lxG1JTX4fN1oErV/hli4nUoE1NbrB1axm2bi3D9u0b0NJyBZ9+2oKenkocO1aIY8fi\nR5JAz/v4hWaSNaDH7o0s4giCIAjvALK9fbzKGcJAyuUahL17G3HqVCuAVbJzlgAYAyFbn8PzbyOA\nfrhcP8OQIQMBy/YSqUFbILu52bMLsW/fsxgz5nr09LwJsY7aan7WwVCzs6PnffxCM8ka0LMxxOqb\nSQiCIIjI4x9ANgJYD6ksYh0AYSPdhx8exX33/Rlu91QICUQ2QJgJ7gcwEsBHAF4WXbsKwBQAgN2e\nicxMqUOGzbYSbvdC3+tIOn5okRvEuiRBy+Y8+fMeEJxIrl2zeVYIrmHYsHHkfhFD0CBZI8Hs3oy6\nhjAOsuQhCMJs/INDb9/jHfyeAPBPnuNr0N2dBWC86FxxX1UF6QAZAHZ5ygLGjRuFH/ygRDJImzlz\nKg4d2g+X60DEJ2m0yA1iXZIQzM5O/rznDaqFL0l3AyiMG6lJvEODZCIuIUsegiCsgHRw6B/8ZmfP\nR3//brS3vwngFID3IAyGjwMoB5AGoAdAEdQf1Vd8M8RmTspo8aq2up91MEKdCecNqoVVhA0QBsmB\n/aJDmeShCaHIQYNkIi5JJBN7giCsi9rgcOvWClRUbEd7uwvAKAgD5PMAhgN4SVTCKgBnuGUnJ5/G\nww9/y/Q+TYu8MNYliKHOhKsNqsWbKb0uH/LBbSiTPDQhFFlokEzEJbGufyMIIj4IpFc9d24YgN2i\ns+cCeFdWwi4IS/RyPfMaDAw8gUOHrLHxTctMdixLEEOdCVcbVPs3Uzbis8+ScOyYP3Oid3AbyiQP\nTQhFlpgfJOtZZnA4dmLHjga43Wmw2XqwenURHI4Ky8ZrRD133jnWl60pFpdjQr1v0dS/0VIXQRCB\n4A0Oy8qqMDCwW3bmCJUSbgRQBulmvisACtHS8h8GR0vwCHUmnDeoFjZqjgNQheTkv6Gn51aIMyd6\nB7ehTPLQhFBkielBsp5lBodjJzZtOgq3+03fsU2bVgHYGfGBcrSWRXj1HDiwCm73Q/D/McbOcoye\n+xYt/RstdREEoQf+4KZH5WwXlJv5HACATz9tkaS3NgL64s8nlJlwZbrxS+jouLeogRkAACAASURB\nVICWlna4XD/DgM+1z2sdJ5zvcg0KaZIn1jdEWh4DM/9pwsgq9aSCHDFCntpT+MnOLjcsLiPjNbIe\noComU2bqvW979jSwsrIqVlRUzcrKqiSpX82OjYhdTOg2TScR2xxphL6jgQHrGVDt+XctA5bK+pOl\nDKgVvfZes4gB8xhQq+hvqqtr2YgR81hGxmI2YsS8kNJR+9No+2PIzV0Xcv+5Z08DKy1dz4qKqllp\n6fqI9L+xhpZns/dZpfwdPMO9h6Gcm6iE03/F9EyynmUGtzuNe/zq1WSugN5IIrUsIv/W39rarXJm\ndLIvyQl3VkLvfYuG/o2WugiC0MOdd47FgQO/9qSP9rIUgwZ9iv7++RAWer8EcAWDB3egt3eS55z3\nIdUmr0J9/acoLnZgyBA3Rozow9tvf6l7tdQIjavVVtisMjMebDOf2KkE0CbtiPUNkVYnpgfJepYZ\nbDb+cpbL5UJdnVJAb+QHLRLLIrzOKC2tXOXs6GRfEmNEZ2nl5SQrx0YQhHV5552P4HbbIcgm3BAS\niOxGf/8GCNn1jgJ4DQDQ2wsMHjwPvb1XIFjFidmFa9ceQEOD4L+bnDwXAwPSzX9u9y7U1s7XNEg2\n4ou/lTaTWWnArva8yMo6gRkzNkgGt95JHu8Af8uWA9i2rY47wI/lDZGWx8AZbU0YWaWeZYbq6lpm\ns62ULXU86lnCiuySeSSWRfjLNw0sLU3aRptthaSN0VqOMUKOYOXlJCvHRkQGE7pN00nENkeSPXsa\nWGrqKlm/uM7TRz/hkVGI5RXlDLjX8+96pnxePSFasl/M7XMzMharxiKWRUybJpd7hN5nFxVVc8so\nKqo25gaGgJ5nUKSkIqE+L4ySviQ64fRfMT2TrGeZQfgmvRO1tfPR15eKlBQXrr/ehtOnldcYvWQe\niWUR/rf+Qtx8868wbpw52ZeCxxfavbXycpKVYyMIwpps21YHl+tnsqPeRBOfAcj0HGsE8AqAXEgl\nFtLNXkArgAme//NXS1NSXIpjvFlWu/1J2O1L4XT6nTdC3fRspRW2UJ9BkZx5DvV5oTYj/6MfLbeE\nfCQRiOlBMqBvmcHhqJAsO5WVVeH06UYAdRBuibD0FYk/aD3xBtJTqXVG48aNwr59z4Ydb7gY1Vla\neTnJyrERBGE91LWpZwD8M4RnETz/jgHwnOw8f+Y2wVYsA345XRGA5RAnJLHZVqKyUtlH8QZhTueL\nKCioxNSp+r/4WyG7nve5efToWQiJWkohdgdRewaFKhUJVe/sfU/4omTDtm11vuPyss6fv8QpoRGf\nfGKDyxWePNQqOm2rE/ODZCPgbaCw2VZh5swpJkYlEOxbrRU6o0BYPT6CIIhoo55oYij8A7n1AFIC\nlHIWwHwAFQD+FcIg2YG0tOOYPv06fPKJf7W0srKQq0dWG6ynp4/Evn0OTW3hYfYKG++5KZ59D/QM\nCmXmWc+ss9o1R44047XXzsv2F62C2EdZQLkKEesbKy2NgbIPTZhQZVCsbOOlJbZoWJ2Fg9XjI4hQ\nsGIfFmkSsc2RZM8e5b4R4BmZ1riBAXM9GmSebdh3Ped8nwHf0qVbtfKzLxzU2pWVNT/oM0h6rd+i\nb8SIeYrr9Ny/adMquNeo2dOmpUmPp6YuClvvHa+/dzXC6b90zyRv3boVL7/8MhhjWL58OR5//HFc\nvnwZ5eXlOH36NHJycvDWW28hMzMzeGEmY2UbLy2xWX253+rxEQRBRJPZs4V9I8eOeTPoHQdQCemM\nYSGSkp4FY4cBrIKQntrLMgCnAOz0vJamptY6sxivK31qz80pU/KCzpD770kZxHZ7bW3A449LZ1v1\n6J2PH7/CfU/NnvarXx2LsWP9M/IXLw5FU5PyvFAkjFYe81gNXYPk5uZmvPzyyzhy5AhSUlIwa9Ys\nzJkzBz//+c9RUlKCtWvXYvPmzaipqUFNTY3RMRtOpDYZ6NH8yK/p7HRGJDaCIAgiesj79sGD+wF4\n9400QhiQ+Z8PdvsajBnzFfzP/7RiYOAhSFNSLwJwGYLU4gC3Pi0DHrNlEZEinGe6t+2LF9eire1N\nyXvyLx+h1iPokMdz31Ozpz116gRstpswbNhIMMZw77356OwM74uNWtxdXecjni8i5tAz/fz222+z\npUuX+l4/++yzbPPmzSwvL485nU7GGGOtra0sLy9Pca3OKiNKJGy89Fi38K6x29cwu32JobERBKEf\nK/ZhkSYR22wkan17Sorc6m0eA55gQ4d+19PvNzDgeypyi2oGVLDk5DkJtXSuBSOe6Vps7EKtRyiz\ngQl2f2IJxUpWXV2rKEuwp61UfG6qq2t9EsaCggo2bdrSkOzq+J/HR5ndvkaXbMfqhNN/6ZpJnjRp\nEtavX4/Lly8jNTUV7733Hu644w5cuHABo0ePBgCMHj0aFy5cMGwwH0ki8W1aj5l6pHYaEwRBEOah\n1renp9+Pvj7xDLEguRgypBxO52IIs8sjVUrtR3JyOwYGnoKwKS2+JBPhoOeZrmcVN9R6hBlc73v+\n3/vEif1wOCowfXojFi8uR1vbbRA+D24AOyRlOJ0v4t13K/HnP9fq3oDHi/vixTQ0Nb0oOc+sBDBW\nQtcgecKECXj66adRWlqK66+/HrfffjsGDZIu7SQlJSEpKYl7vcPh8P2/uLgYxcXF3PMiZVGiVq64\n7L17G8NadtCq+RHHIljVKAl3p7FeEtEiRt7mO+8ci4MHWxLqHhBS6uvrUV9fb3YYRAyj9jzIycnB\n1asDOHnSb9eZm7sOqamZaGurgzDwbQSwAsAvRFeuAzALAwOAfNCVnf1XbN1aEbf9lNbnUih7YcLx\ni/bW43DsxI4dDVi48CxstlqsXl3kcxTxxnz+/CWkpa1CT88ueH9vubnrMHfuNN94Y2AgCcDdnvcX\ncuM9dUrQNQebjAt0r+T3p7jYwa0r0XXKujfuLVmyBEuWLAEArF+/HuPGjcPo0aPhdDpht9vR2tqK\nUaNGca8VD5LViJRFiZZyo5VKWVlPVdBrokUiWsQo29yosAaM93tAKJF/kd+4caN5wRAxidrzYOzY\nofjBD0oUM5HbttXh2DHv47kQwF4ADwCYAmGGcRaAVwFME50j9En5+Y647Z8i9VwKdxXX4diJTZuO\nwu32a5g3bVoFYCemT5+keK6kpZV7NuQNxcyZ4xTWb8LKQDMA/iY/oBdA4Mm4UO+VlRLAWAq9Oo0L\nFy4wxhg7ffo0mzBhAuvo6GBPPfUUq6mpYYwx9sILL7Cnn35acZ3WKiNlUaKl3GilUlbWo9QqmaU/\nTjSLGMZ4bU68e0AEJ4xuM2ZJxDYbSaja1erqWpnW2JuKusqjRa4SvTa2fwqUkjlS6Zq1EqnnUrhp\ntNXs29LTHwgas9r7gj59qWJMADzDCgqWBb0fod6rSOzNsgrh9F+6Z5IffPBBtLW1ISUlBTt37kRG\nRgZ++MMfYt68edi9e7fPAk4vkbIo0VJutFIpK+sR3svKWoApU/JM1R8nokWMss2Jdw8IgjCeULSr\ne/c24rXXzsu0xjaIZ4v97Ja8CqRF1iJTCDT7CMD01cVIPZfCnUUV7NuUWXu7u1NUs+YdPvx3FBc7\nVGWWNlsS3O5FENKS+/XLKSmf4sc/Xg0gsIXfli2huZ7Eq9NJuOgeJDc2NiqODR8+HB988EFYAXmJ\n1NS/Wrnnzp1CdnY53O40dHe3AXgUwFUAaQB6ABQp6g7W6QTTRPFjKURyci0AQPgCZA6JuPSibHPi\n3QOCICKDFo3s3r2NHOuxDQD+rnLFUGjRImtdeg+kcWWMhbwZ3Wgi9VwK1y+6v/8ixJ7KAusxMNAF\np1P+HBfs/trb30BDA6Ams8zIYGhr895Xvw/25MkZEl0xwB/YetNdywl0ryinAQfD5rM1orXKSE39\n88rNyqpgyclym51lTJr9aBlbsGBtkPhCs0vhlWGzrZDUa5YFSzwvvaihbHMDs9lWJtQ9IIJjQrdp\nOonY5mjj7394S/8NnqV38bEVDKiVSAPU5BBal94DyQ7ClSQYe4+M75PDyQx7882PqEgmFrHJk5+Q\nxaxNZsmzhAulrYn4DFcjnP5L90xypInU1D+v3D/+8RQGBt6TnfkShG/ohb7X+/fP972rx+ItWCzN\nzcfR1ibNumSWBUsiLr3w2jxz5hQcOpQ494AgCHPwP1N4M4uFEDbqie3iFkI8w9jVdV51tlirTCHQ\nTC1TWdmM5spaJJ9L4cyijh9/Mz77jPfOTRg7tl+yOfPo0bNobxefoy6znD69UfY8Godt2+qwZcuB\noG5LifgMjwjGjdW1YUKVQcnIWKzyLVD6zTkjY7Hvmkh8q7bCN3WCIAJjxT4s0iRim6ONv//nJ5uQ\nrmxKn1G5uc+wadMqVGeLtc4kB5p9TNSZSS2bFdXub1raPMX5ejcfGrF6naiE039ZdibZSIJph/np\nIBsBHAfggFeEn5Li8r2r1eJNXi8A1ViEMncCaEAgLXSo7dN6TjCiVU80ibV45cR6/IQ16O/vxx13\n3IFx48bh3XffNTuchMT/TFH6Ho8fPxRNTcq/66ysE5gxY0PQjVpPPXW3Js2tltnHRJqZ1Krl5mma\n09JWYu3aIsX90at/NmL1mtCBgYN1TUS7Si3fvqqra2Xa0wYmaJKlGuX8/PuClOv/Vq09xbQ/lgUL\n1nLrFWuh9bQvUvrpSNQTTWItXjmxHn+sYkK3GXF+8pOfsIceeojNnTuX+348ttlqCM+huQxYxID7\nGPBtZrPNY9OmVcj0qd9iwCwmpKuexYB8xpj6DGVBQQVjLHTNbTTs3qqra9mIEfNYRsZiNmLEPFZd\nXWt4HaEibreatRtv1hfI5/5eeKi1m3fPvceEFW+vFaB/rJKVVe47v7q6VvX6r3xlIbPZ5rDrrltg\nmXsdLcLpv+J+kKx1aaO6upZlZ5d7PoizuNekpMyRXBOo01H3PlT3tVT7g8zOLg+rfUZ4S0arnmgS\na/HKifX4Y5V4GzCePXuW3XPPPezAgQNszpw53HPirc1WY8+eBpaVVSn7W17nGxDl5q5j1dW1noGY\nciIFyGd79jQwu32N7L1nmN2+JOQBbjS+gCsnpxiz2VaaOnhTtrua28fKJZCBfi/qdTR4Br3VLC1t\nHluwYK2miTX/50IpyxHup38QnZl5Pxs8+LtM2ORprXsdTcLpv5LNm8OODlo3LDgcFbh06Q10dPwb\nBg3K4F4zMHC95PXs2YXYt+9Z1Nc7sG+fkFa0rKwKxcUOHDnC9z4UNl3wYxG8FpX09aVKXntTZgv1\nfApBGsIvEzDGW1K7v3QjhI0nDs+/jZb1FY51L+hYj5+wBmvWrMGWLVuQnBz3jwPLsm1bHdrbd8iO\nboJ3Y97Jk5tw6FArgPEQNpWLeQnAeMyeXYgxYzohyDQcnn9nwencje3b9yMU1Jf2QysnEDt2NEiy\nmQKA270LtbXK51m0ULZbq+Wc+u+FX0cZBMu45wA40NPzJt588wvPcT9O54twOsfKSvB+Lrxpy0XR\nunfBv5mzER0do9Db+xsAIwFY617HCnGvSdbjq5iU1M09npzMPw5oTzEt7Ermx8LXRkOiheZppATD\neUDsitHV5TcwN8JbUksZnZ3nwPOK7Oq6qLmeaBLrXtCxHj9hPnv27MGoUaMwbdo01NfXBzzX4XD4\n/i9P1U2Eh9oXXvGkivDlN13lPOH4sGHjIAyQpYT6xTkaX8C1TgpFE2W7S+FP6CLA1w+r/17k+0Za\nW7vBG+AODOyG1FHLi/KeZ2ScRXIyk7lkyM+vg39gzP99mnmvI0l9fX3Q/kwrcT9I1iOS/973JuL1\n15dD+s1wOR58cKLqNcpvoMo/LmANBg8+j95e/xFxLKtXF2HTplWSb9c220pUVgY2exfqEP9xrYM3\ntzsQvlG69jKGQP6HL7yu1FxPNDHivphJrMdPmM+f/vQnvPPOO3jvvffgcrnQ2dmJRYsW4d///d8V\n54oHyYSxqH3hFU+qCF9+u1TO6wpYTqhfnKPxBVzLpFC0UbZbeKZmZ89Hfv6EAJsV1X8v8kmttLRy\nALepnM/7EqK85zNnjgdjDHXcfCHe88XDO/7v08x7HUnkX+I3btyou6y4HyTr8Qr89a83A3gav/nN\nXAwMXI/k5G48+OBEz3E+aimmgQUA8iB8cO/HLbf8CuPG8WNxOCoA7ERt7Xz09aUiJcWFyspCz3G1\nerycgTCD0A9gFtLT/TudjfBL1FLGsGEjudemp/OPm02s+0jGevyE+Tz//PN4/vnnAQANDQ34l3/5\nF+4AmYgsjz1WiiNHVsskF+sACF94vV9+33//PwDIJ3CWATjrK8eIL87R+AKuZVIo2vDbvU81k6Gf\ns1D7vZw8+VvJmT09lUhO/lcMDChLSU4+Kjlut68B0Amn038sNXUVLl504957CxSx2mwr4XYv9LwS\nD4yVk3Zm3+tYIe4HyYA+k/CFC2ejrS3Ft0SycGFpwPPVUkwDtZ7/MwDAuHGjfPplHg5HhWRQrK0e\nALgR4mW21FSpdsyIdJP60mxHZvnfSOszQdfv/zeWoDSihJEkJSWZHUJCMnt2IV59FXj88cU4c6YH\n/f3dSErqwbhxX2DChP2+L7+MNSMpaRKAb0NY4u8CcBaMNfvKAcL/4hyNL+BaJoWijd52T55cgo8/\nbob09+LGdddNwdWr8rMLMW7cdly6tAo9PdIvCG73t+C1/ktLO46VK4swffok/OhHlfjkkytwuW6E\ny/UQmpoK0dm5Hg8/fIMk2dXMmVNx6NB+uFwH8Oc/f4QrV54E8CL8k3b3ISkpCSNGDDH9XscMRu0e\n1IoJVYaMnp29vJ26QhpR9dTWRsWmTGVtjsF7tMzmjdp5TRZqhB5ioQ8zmkRsM0FoRc2Zymabo+pA\nJHbHEq5XJovxOhWFkgzGawGXlbXIU2aVx6WjigENCZmcLJz+KyFmkkNFj2n3wYMtcLsfgj9t6HEI\nWlzx+dLU1nrgp072f3s0c8k9Wsv/Rpmqkzk7QRAEES52eyba2uR7kNbhhhsyYLN5JRGNAOqQmnoW\nFy8OBQDfqnJxsQMNDcpnjnejpJaNlHzzgELINwLKV5mJwCTEIDnUpXk9O3v913iX7PnLlsF2kzoc\nOz3WOGmw2XqwenWRYklEvsS+d28jDh5sEWrXKBnQkz3vzjvH4uDBloDXGLX8Hyg+o3ZeG1UOZb0j\nCIJIXG64YSSOHSuFf5JM2BskSGVK8KMfLccnn9jgcv0MLhfQ1AQ8/rg/c18wqaIWKaMW8wDa2B06\ncT9I1ppWUkxn5yXucbGtmvIavv2ZgL+eQLtJHY6d2LTpKNzuN33HNm1aBWCnqnZIT/u0XKM8pxEH\nDvxasskiWD16CRaflXZw67n/BEEQRGwjnhzp7HTCbv9POJ0v+t73Dkhnzy7Etm11cLmek1wvXrUM\ntlFSy0ZKNfOArKwFmDIljzZ268U41Yc2ol2lnqxk06YtVWSyAZ5hBQXLAlxTwa1HnGHPZlsRMMNN\npDLu6blGeU70srsFi88o7bMR5VDWu8TDhG7TdBKxzURsEI302bw6ldnxlrCCggpuBt6iouCZ+4Kl\nDQ/2Pj2L1Amn/4r7mWQ9S+qCIfvdkC+diG3VlNfwbc5SUk7guuu+r2nnrh5z9fCkIerXKM+JXna3\nYPFZaQc3Zb0jCCKamCHvsqqkzKyVPN5+FqdzN6ZO3YB9+xy++7VlywEMGeJGZyc364dk1TKYVDHY\n++SbHxnifpCsZ0lduCa44F3ccTQ3H+eWdffdeRLLt0CdjR5zda3tU8bayGmf/xpludGzd9PSJqO0\nz+GWQ1nvCIKIFmYMCq0sKTNr83WgyRHe/bLbl8Juf5IrxzAK8s2PEAbOaGsi2lXqWVJfsGAtA5bJ\nli2k9m3KchsUFnDyeoJZjvFs5IJJNLRcw7eNW8kC2cbpaZ9RRMtKzghiKVbCGEzoNk0nEdtsRcxY\nUrfyMr4WGUMkCHRP1N4rKFgWUC5BRI5w+q+4n0nW8+2qru5zCPZtYrnFI9i/f6fvHOU32EK43YHT\nVwb71qvHXF1pPdcPt3shDh3yz3rz6nW7d3li5dvG8a3mpkiMyyP1LTWWvhHHUqwEQcQ2Zsi7rCwp\nM2slL5C0YcsWviwzPf0G7NvniGhchPHE/SAZCH1JXdAGK+UWfX3/x/d/fsdRiPz8A6ivd3DL1dLZ\nBMu4xy9TGavLdUB2jpL8/AmqsQLmZnOLpUxysRQrQRCxixmDQitLyszS4QaaHNm2rY57jRXuFxE6\nCTFI1oJYs9vd3cY9p7u7DcXFDo8Q38k5oxHNzcd958g3N+jtbALpmNXK7Oo6j7KyqoB66XDqjTRW\n3SiihViOnSAI62LGoNDKG8LMXMlTmxyx8v0idGCg7EMTJlQZFJ7+lqdJBmpFdi9rmN2+JIhmd50G\nTXJg/WowHTPfiuZRZrevCUtPbGbK5lhOFx3LsRPasGIfFmkSsc1WJZgVWLzUGcvQ/bIW4fRfSZ4C\nokZSUhKiXGVQysqqUFf3nOxoI1JStuC660agu7sNbve3AUhlEAUFlRg5cjhcrkFobj6OtrY3Iaes\nbIPC3WL79v2ib70lAb/18mOTlisv8+LFy2hqqlW0Jzt7p0gvHX69kcLMusMllmMntGHFPizSJGKb\nCSIUaAXRuoTTfyWk3EL+YW5t7eacVYhvfEPQFwt51ZU64fT0kT4hvnCOshT55gZeSmmvLIL3h6Wm\nJz58+IxE1iEegBUXO+DNEy/8it0AxqLfo67Q8mExc7OGljZrSZGtBXka8NLSHLS1pYSUiltL7FbY\n5EIQBEGoo3ega2WbPCI8Em6QzPswp6WVc88NJW+6Hr2xlj8stRTZ7e1D0dDgULmGlyJ7FdrbK9DQ\nUMi9Ro6ZmzXU6m5vv9HTZmNSZPPSgL/++nIA0yCsGoRej5U3uRAEQRB8whnomuXXTESeZLMDiDa8\nD3NPTyXS0lZJjglC+xIAghA/N3e96vtaz9ESi/CHJU5acg2AtFxgHYDeANcMgXSADAC7AOwPcI0U\nPe0xCl7dQpu9dddJBq5A8PbwEGaQd8mOvgRhFl5fPWbeN4IgCEIf2p7HfGgFMX7RPZP8wgsv4LXX\nXkNycjImT56MX/7yl+ju7kZ5eTlOnz6NnJwcvPXWW8jMzDQy3rBRs267+eZfYdw4/g5ZLTto9eyy\n1fKHpZYiGzgQ4Bp+imzhev41cszeNSyu++jRE2hv/yf4be6M6ZDU0oAD3jTgoddDvskEQRCxRzgD\n3VhaQSTtdGjoGiR//vnneOmll3D8+HEMGTIE5eXleOONN3Ds2DGUlJRg7dq12Lx5M2pqalBTU2N0\nzGGh9mEeMsTm0+oyxnDkSLPigxRs49WRI8348MO/+fStv/pVb8APIz+WRvzxj39GZub3YbP1ICNj\nCAAHpD7IjQCOe44LemOx9ZxannhhgO0nUOpqrW2OFGLttrAZTtz+0FNx8+6/WhpwwJsGXF/HR77J\nBEEQsUU4A91YsX0j7bQO9FhitLW1sVtvvZVdvnyZ9fX1sTlz5rC6ujqWl5fHnE4nY4yx1tZWlpeX\np7hWZ5WGwbdMeyJkOzc5vPTQctu44JZwSuu55OTvsaysSg32dA2i9iyRWcAJqapDS0NtHesyZWy1\ninugJRW3vD3Bf2fRS8VNxA5m92FmkIhtJhILPRat8uutbvtm5RTjkSSc/ku3BdwvfvEL/PM//zPS\n0tJQVlaGV199FVlZWWhvb/cOvjF8+HDfay9WsBJSWqa1oqnpZdEZVQBCs/HKzi7nWsAB8wG8oVqG\nOJY//vHPcLvfVZSQnj4b3/hGQUCrOUGO4S+3oGA5Ro60i1JKj8GhQ62q1nNWty4T3yfhHlRC0Fh7\nJSglKCvb74tVa3scjp2orW30pQEvKfkKLl8erPm+EYmHFfqwaJOIbSYSj1AtWmMNwYXLoTheVOQI\nmH031om6BdzJkyfx05/+FJ9//jkyMjLwve99D6+99poiqKSkJO71DofD9//i4mIUFxfrCUM38uVw\npWXap57X0j8Oue2auAy+vrURQA/8sojSgJZwmZnfx5dfyq3bStHfn+H7BQ8MpIKPtFx5nvi9extx\n8GALAL4FnFaruUh0GFo0UuL7JPyh60nF3YjDh/8uac/06ZNQUOC3eFu4kPRZhJT6+nrU19ebHQZB\nEBEm3qVysaSdtgq6BskffvghvvGNb2DEiBEAgAceeAAHDx6E3W6H0+mE3W5Ha2srRo0axb1ePEi2\nAnzLNK9Dgf8Pxm9BptTxKPWtjZ4y/0tSZlfXRdU4+vsvcuO4evUL1NX92vO6Su1qySvxh16LDim4\n7VpktEt6NFL6LPmE30d7+xs+P+ujR5cCyIDT+aLmuonEQ/5FfuPGjeYFQxCEqcTyxrdY0U5bCj0a\njb/85S8sPz+fXb16lQ0MDLBFixaxHTt2sKeeeorV1NQwxhh74YUX2NNPP624VmeVEWXatAquTgeo\nEv3/GYmmV67jUepb+dqfgoIK1ThuvvkRlTjE8TUwQKqbCqY31qJD4umxgrXZCPRopLRox5Tn8OpJ\nTH0WER5W7MMiTSK2mSDkWHnvjlZiQTttNOH0X7pmkqdOnYpFixbhjjvuQHJyMgoKCrBixQp0dXVh\n3rx52L17t88CLhZQs0zLyjqDKVMcHAsyAbF0wuGoALATtbXz0deXiqtXr6KvT1lmerqaPRswfvzN\n+Owz3jviawo9sS3AlCl5Ht3sVBw6tB8u1wGu5ZgWa5vgtmvKa4xAj+2OHku+o0fPol1h+kHelgRB\nEIQ2AiUN8b5v9RnmeJeUGI1un+S1a9di7dq1kmPDhw/HBx98EHZQkUa+XKJmmTZjxo3Yt8/h2QTW\nDKAWQBoEnXERurrOS1JK33nnWBQUfBXXrtk8m8uUZQbS/qjJCORSCqAQM2bsl2iOA6FVh6S0XQME\neYdfH220dkktNt69laeHlm8o5KWYZiwFAJCc7OLU4oYyfXepQqoi7/iA4IqXDAAAIABJREFU8DtD\nebm89hlRD0EQBGEMapM6585dDFk2GMuyjYTCwBltTZhQpQS+BZzSMk28fL9gwVqF5RiwjF133VyZ\n7GGlSJ4Qun2YNnu60G3I9Fjb8OzRbLaVEps1I+C3+VHZ7yO4JZ8eO7fMzPvZoEErVNuo/bMS2nIb\nr1zpZ8eYeojIYHYfZgaJ2GaCkKMmDxwxYl5I0r14kG3EEuH0X7ot4PRitpWQmjWY3DJNbP2i1d5N\nQGzF1ojs7J3Iz5+g2U6GZ0EDIGxbmlCtbaJpCae05LuMpqZa0RnBLfm0/Y6kvw9lPdJy+fcgdHtA\n5bn8eyv97IRfDxEZzO7DzCAR20wQcngbzXNz1+G663rw8cf/qjhfzVrN6par8UbULeBiGbXlErll\nmpjg6YvFiPWshcjPPxCS/6CaXijcZZhQdUjRzEXPt+QTEzwWbb8j6e9DWY+0XP49CP++qN1b6WeH\n9NIEQRBWQm0/zLZtdfj4Y+X5avLEaD5fifBIuEGyVn2uWC/U3c0RFwPwpy8WEzj1c6wQTT/F4Brx\n4LEIFnxKfbH8dxTYJk56Dv/98O+LNu15cL20UZA2jiAIQhtqE06hWKuRX3EMYYjgIwRMqFKCPvsw\nZRrkQYOWs8zM+2W60sBWbLFEuCk6w6lHqRVWpuKWx5Kffx9XNw58X/Uavu56RRBNslwvbYxGXJ5a\nHChjSUnLTdGEkzYuMGb3YWaQiG0miFAIxVotWs9XQiCc/ivhNMlAcH0uXy+0Eykpv8V1141ASooL\nlZWFmD59kqSceEthHI0Uneq631JI006PQXZ2o6q+OyVlLjelN/AdFBXNCPB7ltcjTW8dDY244IRS\nBKBVFMdlCG4q8vtlrGaNtHGhY4U+LNokYpsJIpLEewpsK0Ga5BAJps/l64Uq8I1vXFToiwOVs3dv\no8TGLBaXsb0fLK0fsFCX7tV1v8q00/n5/vsvv7cDA0O45Q8aNEz1mtbWbm8rJf/K/aON0Ijz7ot3\nECqk2a6QXeEAT25hBZ9qgiAIIjzIrzg2SMhBcjCM0AvpSbdsJfTEb1yK6cD3n1cPcB/3muTkbtVr\nBg/+DnhpwAOlDtdDsPvCvwf8VOlGx0baOIIgCILgk2x2AFbkscdKkZu7XnJMEOGXaC5DPTPPfkNi\njDR64tdzDe9e2+0tsNuflBwT339ePcCTAJbKji3Hgw9OVL2mt/cmSAeh8LwerBqvHoLdF949GDz4\ni6jEZsRnnSAIgiDiEZpJ5qAl7XEwYn0ZW0/8xqWY/j7nmP/+8+spxMiR29HRMRcDA9cjObkbDz44\nEb/+9eYA1/BThAdKHa6HYPeFdw9aWm7iWgoZHZsRn3UitnG5XCgqKsK1a9fQ29uLf/zHf8QLL7xg\ndlgEQRCmQ4NkFcLVC8X6MrYQf2gWZFpTTMt1yrx7vXdvo6oeWq2egoIJqpvN+O3hpyNvbj6O4mKH\narroUD8XavHK6xG312br4l4Tic+P/P7Hg5ae0E5qaip+97vf4brrroPb7cZdd92FP/zhD7jrrrvM\nDo0gYoZIWGmSPacFCNNZI2RMqNIUYt3iRU9aau2WaYEtxoLZkhmVZjs5+XssK6syoI2fPF20Hns0\nfhpqcT3KlNl2+5qw05HrgSzhghPPfVh3dze744472LFjxyTH47nNBBEukeg3qS82jnD6LxokR5BQ\nfBOthlqOerVc9F7kbZ42rSLkcrTUHeq9VSuzoGCZr5wRI+bJvIq9P1Uh3YNg90VZj1psFVH//Oj9\nvScS8diH9ff3s6lTp7KhQ4eyp556SvF+PLaZIIwiEv0m9cXGEU7/RXKLCBLLFi96NdXBU0wHL0dL\n3Ual2RanIxes2HhlSmPVoysXx6usRy22kaqp0iNFrGvpCX0kJyfjL3/5C7788kuUlZWhvr4excXF\nknMcDofv/8XFxYr3CSJREfpNYy07qS/WT319Perr6w0piwbJBBejNNV6yjGqbrGeq7n5OICdAFog\n7sS6ui759LfCObzU1tJ65RprLbplZSyN8PtAW0e/HutaeiI8MjIyMHv2bHz44YcBB8kEQfjp7DTe\nspP6Yv3Iv8Rv3LhRf2EGzmhrwoQqCR0YpakOlvo5UnVrSf08aNAKWWpxZfpx4XWtSCss11gr9cRy\n3RhfkyzWOvPKMEe/Huta+mgQb33YpUuXWHt7O2OMsatXr7JvfvOb7IMPPpCcE29tJggjUZMVFhRU\n6C6T+mLjCKf/oplkgotR1mAHD7bA7X4IwAZ4Uy673Qtx6JC6d7IRdfO9lF/yxCGU09//c3R0bBC9\n3+I5R3pNdvZ85OdfRGpqPy5eTENT04ui9+vgdu+SXCF4IG/wxcuLxe3e5Sn3gCel+RQcOmS+DRtZ\nwiUera2tWLx4MQYGBjAwMIBHHnkE99xzj9lhEURUCcdJYtgw4+1EqS+2BjRIJlQxQlMt6KrkKaYb\ncfjw3332Z7zOSE/d4k7u6NGzKmfJ9Vzi1/w/h/5+IeU1YwxutzyZR3DdmJq2LD9/giLNebgYYRkU\ny1p6InQmT56Mjz76yOwwCMI0ws2QGylpBPXF5kODZCKiKDuPRgDvo739DTQ0CEeMSNet7OSqVM6U\nd1ri1/yOrr39RjQ0OAAAgwc/KHs3eOfY2XmJe05XF/+4XmI9FTpBEIQZqGdF3aCp77zzzrE4cGCV\nZFXRZluJmTOnGh4rEV0oLTURUZRpj+sgT7dsRLpuZSdXCkCabtlmWwnAn27Zbl8Du71Fco3NtkpW\n8jrJNb29jwFYJblG+pqX1vmaIhah3F7V9ugh1lOhEwRBmEG4ThJSWaEDwAaPrLDVqBAJk6CZZCKi\nyHVVR4+eRTsn0V24tjbKTk6oNytrAaZMyfPofqfi0KH9cLkOePRd90tik2uDjx49gfb2f4JUKlII\n4FcQa6yBKZJ65LqxYcPGAbhbds0spKcfCKvNwe+BAFkGEQRBqBOuXIIvKwRcLmP7eCL60CCZiDhi\nXVVZWRXq6pTnhGPvNmSIG52dvBTThZgxY39Qr2F5SuaDB4XZ5eTkAZUrBgAwz/+Z5FwmS6ENeDtg\nZQeamhp4hjdUfbHejp5SnxIEkcg89lgpTp5cL1mJE1YEZ2m6Xuh7lfahZNcW+9AgmYgq4XZGAF97\na7cvhd3+JJxOv/OEEeXabKvgdgPeAW5m5sPo6kpDf/9zoiuXo62t0pcgRK4D1tNmPfriaNVDEAQR\nT4TrJCFokn8t0ySvwsyZUyISLxE9khhv6iuSFSYlcWfbiMRh795GbN++X9QZlYQ0IBNmo59THC8o\nWI6RI+2GlytYtU3wWMBdRlNTLefqDQCeFZW1Afv2+V+H2ma1WOTlyolWPYlMIvZhidhmgtAK9aPW\nJpz+i2aSiaijxdYmkARAS4pprWixjQtsAeclcOpqo9Joh5oWPFL1EARBEALUj8YvNEgmLEcwCYBR\nlmpabeOkFnD3qZQm1Z6Fq0WLVkpSSn1KEAQRHtSPxi9kAUdYjuBWZsZYqmmxjVNawGVzzpFayykt\n4EJHaZ1nTLlm1UMQBBGvUD8av+iaST5x4gTmz5/ve/3ZZ5/h2WefxcMPP4zy8nKcPn0aOTk5eOut\nt5CZmWlYsERiEGzpyihLtWC2cXwLOF7dU5GV9TNMmXLAsNSh0UpJSqlPCYIgwiMW+1FyNdKGrkFy\nXl4empqaAAADAwO44YYbcP/996OmpgYlJSVYu3YtNm/ejJqaGtTU1BgaMBH/BFu60muppq0ev22c\nsBlD3mnw654xozWgHlpPhxStlKSU+pQgCCI8rNSPBnvekKtRCLAwef/999ldd93FGGMsLy+POZ1O\nxhhjra2tLC8vT3G+AVUScc6ePQ0sN3cdA5jvJzf3GbZnT4Om9yNZj93+KLPb14RUN7+edSHHS1iD\nROzDErHNBBGLaHnelJaul7zv/SkrqzIx8sgRTv8V9sa9N954AwsWLAAAXLhwAaNHjwYAjB49Ghcu\nXAi3eCIBCbZ0ZdTSlr56vh9y3eoa6w30rZ0gCIIwDC3PG3Lj0E5Yg+Te3l68++672Lx5s+K9pKQk\nJCUlca9zOBy+/xcXF6O4uDicMIg4JNjSlVFLW3rrIZu1xKG+vh719fVmh0EQRIISilxPy/OG3Di0\nE9Yg+be//S2+9rWvYeTIkQCE2WOn0wm73Y7W1laMGjWKe514kEwQ0YLX0QCI+OYFShcd28i/yG/c\nuNG8YAiCSAi8/X9razc+/bQFPT2V8O6FCaQf1vK8MSLzbaIQ1iD59ddf90ktAODee+/FK6+8gqef\nfhqvvPIK7rtPzVOWIKILb6PC0aNPAvgSTudu37FIbF4QUpaukqUsXYmZM6eGFC9trCAIgoh/eP0/\nsApAM4CKgHI9LQPgWHTjMAvdaam7u7vxla98BadOnUJ6ejoA4PLly5g3bx7OnDmjagFH6U0JM1BL\nGypPJy2ca2wqUaHuUgD74beNK0FZ2X7VeijNqXVJxD4sEdtMEGah/rwqByDMKBcVOVBf7+Bev3dv\nI7Zv3y8aAJck9ADYlLTU119/Pb744gvJseHDh+ODDz7QWyRBRAw1nZY8nTRgvFZYqFtpG+dyqfs6\nC9c0AqiD8GfqBlCKw4fPoLjYEZb8gmQcBEEQ1kX9eXUbhMmWwoByPSvZ0cU6lJaaSAjUdFrydNKA\nNVI/d3aeA/A+APFy23q0tw/2pcjWI78gGQdBEITxGDn5EPh5NYj0w1GE0lITCQEvbajdvgZ2e4vk\nmHVSPw+BdIAMz+vBvlfSVN3aCJ7ymyAIgggF7+RDXd1zaGhwoK7uOTz++PvYu7dRV3mPPVaKtLRV\nsqPrAJQgO/uv2LqV9MPRgmaSiYSAv1Hhfs4xa6R+HjZspMo70uOhSkPIjo4gCMJYjPbCnz27EGvX\nNuN//+9y9PTcBmEGeRZyc/dh69YKGiBHERokEwmDEZ7HRtethlZ5SKjSEPLHJAiCMJZITD44HBWY\nPn2SaAPefnKgMAEaJBOEBeHZ+NhsK+F2L/S91qNLI39MgiAIY4nU5ANtwDMfGiQThAXhSTRmzpyK\nQ4f2w+U6ELFU3ARBEERomDn5QG5FkUW3T7LuCslvkyCIGCYR+7BEbDNBhIIZ3sQ8t6Lc3PXYurWM\nBsoiwum/aJBMECHicOzEjh0NcLvTYLP1YPXqIjgcFWaHRUSJROzDErHNBGEV1GaLKemUNkxJJkIQ\niYjDsRObNh2F2/2m79imTasA7KSBMkEQBKEgHElEIG97ciuKPDRIJogQEGaQ35Qcc7t3obZ2Pg2S\nCYIgLIpZ2t1QEjjxYgxkLzdkCH92lNyKjIMGyURMwutMjhxplsggSktz0NaWElKnGKwjdbvTuNf1\n9aVqLkPrOQRBEET4RCPTqFqfrtVDWS3G1NQvuPW5XIPw1FN3k1tRhKFBMhFz8DqTI0dW48svL2Jg\n4C3PkUa8/vqrAF7ynROsU9TSkdpsPdxrU1Jcmsug1NAEQRDRw+hkH3KMkETwYyyDzbYFgAOAG0Ap\nACHe1NR+VbciACgrq6JJGAOgtNREzMHrTNrbd2BgIE90pA7iATIQPP2ylpTNq1cXwWaTpgu12Vai\nsrJQcxmUGpogCCJ6RFq7G6hP1+qhrIyxEcD7cLvfhTBIfg7A+wB2Ii2tHC0tV1BWVgUA2LfvWdTX\nO3yb9YxMkZ3o0EwyEXOodXiAuMMLvVPU0pEKuuOdqK2dj76+VKSkuFBZWejTI2spgzZbEARBRI9I\nZxoN1KcHkkSIJRrNzcdlV9cB2CQ7tgnJyQ+gp+f/4eOPgY8/Vq5CRnrWPNGgQTIRc2hL2aytUwzc\nSfGvcTgqVDfpaemMKTU0QRBE9Ih0so9AfXogSYRUotEIm20V3O5dntf84dnAwBTJa/kAmCZhjIUG\nyUTMwevwsrIq8eWXlzAw4D1SCmA5xJILeaeo1JHJO6nQO1ItnTGlhiYIgogekc40GqxP56WXLiur\nks34FsLtBtLTv4uCgslobj6OtjZebcrJFPEAmCZhjIWSiRAxCS+70ZEjzaitbfTJIEpKvoLLlwer\nZkDiG7E3Ijt7J/LzJ+jOmqQl85IZ2ZkIY4i3Puzs2bNYtGgRLl68iKSkJKxYsQKPPfaY5Jx4azNB\nhAPPyWLOnAoA4wGkA+gCcBaMNau6XhQXO9DQ4ICgPa6DMGfpxqBBhzBlSh56e904ftyNgYHdoppX\nAlgI7+Y9L6mps3D99RkYOjQDly9fxNWrvejvL/CVabe34OWXvx+2u1Okro00YfVfLMqYUCVBcCkq\nqmYAU/wUFVWbHZpm9uxpYKWl61lRUTUrLV3P9uxpMDukuCfe+rDW1lbW1NTEGGOsq6uL3XrrreyT\nTz6RnBNvbSYIvezZ08Byc9fJnhtzGbBEdmwZA/IV5+bmrvP120ADA8TvN3iuE7+ex4AnGFDFgFoG\nrJHV8yjn2ArPtcJru31N0GcDr13eWPXcE63XRoNw+i+SWxAJS6wvS5GVHGEEdrsddrsdADB06FDc\ndtttaGlpwW233WZyZARhPZQb4xoBpAHYLTvzJQDfVt1E99hjpdi//6dg7P+J3vW6Molnl28B8FcA\nEwBcBPAZBClhL4AbPXW/KKv75wA2QJhxboTTeR0eeWQ3pk+vU53hFdpVBqAK3hnokyfLsH37/qDP\nk3jeLEiDZCJhiXVtcDx3TIQ5fP7552hqasLXv/51xXsOh8P3/+LiYhQXF0cvMIKwCK2t3aJXgk0b\ncBvksglhX8xQbhnnzl3Ehg3/Dsb6ACz2nFfuudZbprhvXw6xRzKwHsAXAJ6FYA8nxhvHOQCVAFwA\ndqO9HairU59IOX/+Eqfe9Th3jp/MRIzVNgvW19ejvr7ekLJokEwkLJHezBFprNYxEbHNlStX8OCD\nD2Lr1q0YOlT5cBcPkgkiUWlpaRG98tq0LQNvgAlcEr32Dl4v4dixSxAG1i+L3l8BoA3CAFtu/fYS\n/DPD8Lxf7vm/eEWUN8Be7zkuXKs2keJ0dkCYgRazCRcuzEcwrLYqK/8Sv3HjRt1l0SCZiAn0bArQ\ncg1v13EkYjECeb2dne3c85qbj6O42GG5zROEdenr68N3v/tdPPzww7jvvvvMDocgLIvdnom2tvUQ\nBqLeIdQQ8DyNgW/Bbl8KpzMVwBUIG/v6AUyEkBxEzC8APAjgLyo1yyc/xkIYAJd5/t0ENW9l6QCb\nP5EyduxYrpvGmDFjVOLxE+ursoGgQTJhefRobyOl1zVLB8yr125fCrv9STidfj2azbYSbW2VaGjw\nzhqQRpkIDGMMS5cuxcSJE/HEE0+YHQ5BWJobbhiJY8dKIQw8/+45OlLl7HQAGZBqhlcC6OafjkkA\nmlTek8/KnsDIkYPgcv0VfX3X4Hbfi4GBVJENqhjpoJg3wztmzPX4+GPllWPH8iUjYmJ9VTYQZAFH\nWB6+VRtQVrbBl4bTiGsiFYsRqNVbULAcI0fa4XIN8vhqVkJuDxTp2BKNeOvD/vCHP6CwsBBTpkxB\nUlISAOCFF17ArFn+WaB4azMR25i5mrdhw5s4fvwKXK7xEGZzzwNIgnJmGAC+DeC3nOPlAN7kHN8A\nYcb5Oig1yY/A37evBDAVdvunAL6E07kYwizyXwH8RqVc4RkwdOgK3HLLAIYNGye5d3v3NuLhh19C\nR8dX4NVVZ2Z+jtdeWxHzg91w+i+aSSYsjx7tbaT0umbpgNXqTU+/Afv2OQDA47up7MxIo0wE4q67\n7sIAf/qJICyH+at5tb5jqan/hLFjL+Hs2cvo61sKqcPFUgwePAi9vbzSXABWAdglOrYOwCwA+wGU\nANiA1NQzSEm5gq6uezzHD0CYUV4IYL9nFXE5/DrkRvilF16WQJhJdgDox5UrX6Cp6RZ4N/wdPboU\nY8a8iba2i+joGAbxYL+jYykqKrZjwgR1V4x4hwbJhOXRsynAqI0EWnXA4ZbL64CUKbP9my949Vpt\n8wRBEITRmOXqw6vX5foZbrllA776VYa6urEA5gNIhTAILkR6eoNK1rxxAC4AeADAFAgD31nIynoT\nWVkXcOFCM65dS4HNNgDGBgOo8Fzn3fx3AILUoxFC4hJvZllv+zcAOOOJQ7m6KNTbCABwOu1wOr0b\nAeU2drtx5sx8nDnzXMJK92iQTFgePZsCjNhIoFUHbES58g6Id46QMhvwdniU7pogiETDaqt5Ltcg\nPPXU3Th69BU4nV+FP8vdh/iHf8jB22+vgtstnjF+FMnJnRgY+L8QBqr7kZT0KW6++Qwefvjr+PnP\nh6C7W3i+XLkC+F0s1JwremQRFXp+HKLXcqZAmJlmovLSVFqeCiBx7UVpkExYHj2bAozYSMCbOXA6\nd6OgYDmmTjW2XHkHxDvH7d6F7Oz5yM8/wK03njdPEARBAOatmAWvNwNSXfKT+Otfr8DtfgjCzO4g\nCDPGj+L221/FyJHefhr4wQ/+CbNnF6KsrEoyASNQBOB+CA4ab8je24SkpNngy237IQyC1d6Tf6mQ\nD7a9uPz/S0Dpnu5BckdHB5YtW4Zjx44hKSkJv/zlL3HLLbegvLwcp0+fRk5ODt566y1kZmYaGS+R\nwHiF91oF+HJ7t717G1FWVqV5s4cWHTAPh2MnduxogNudBputB6tXF8HhqPC9r2UmRO2c/PwJqK/3\n182TbdAmPYIg4hWzVswC1bttW51icOt0vohr1xbDP7Pr59q1X3GfZ8p+vxHCxsD/gDJpiMCNN96A\nixdXoaeHp2/+BYBHAfyS8553JtlLEZQ66ZWS2BNRuqd7kPz444/jO9/5Dn7zm9/A7Xaju7sbmzZt\nQklJCdauXYvNmzejpqYGNTU1RsZLJCBGbNTQU0Zn5yXu8a4u/nFAGCBv2nQUbrd/5/KmTasA7PQN\nlLXMhGg5h9JSEwSRaJi1Yhao3i1bDqhcdY1zrBGffZaEY8f8s87eflvZ74t9j/nPhCtXvsTNN2fi\ns8/+ET09gyAMfHshDK6/xI03unDu3AMYGPBrn9PSfoWbbwZ6etpw+vRK9Pf/HILueSeAOUhJGYr+\n/m4MDHwbXj10wkr3mA46OjrYTTfdpDiel5fHnE4nY4yx1tZWlpeXpzhHZ5VEAlNaup4BTPFTVlYV\n0TKmTVvKgHWya55hBQXLVK8ZMWIet57s7HLfOXv2NLDcXGm5ubnPsD17GkI6x4j7QoROIvZhidhm\ngtCKWl9cULBM0Y+npfGfEWVlVay6upYB9zKgmgHrGbBCdE6D4nlks63wHPceW8OAJbL6VrLq6lpW\nVlbFioqqWVlZle85IsTdwIAqT51VDGjwncO7JhYJp//SNZN86tQpjBw5Eo8++ij+53/+B1/72tfw\n05/+FBcuXMDo0aMBAKNHj8aFCxe414vTm8rTBxKEHCM2augpY9iwcQDuhlRPNgvp6WqzBoDbzd/8\n0NeX6vu/lpkQLedQWuroUF9fj/r6erPDIAjCoqhJMX7840cASPvxlpax3KQd585dxGuvDQD4L9HR\nJfC7GvmdK7KyziA52cXxxX8RwvPKT0/PLhw6xPfKF54hSjmIy3VAVzbaeETXINntduOjjz7Cjh07\nMH36dDzxxBMKWUVSUpLPmF6OeJBMEMHgSw8ag6ZfDtVCjV+vsgPp6npVVdtss/E3P6SkuCSvtXRA\nwc4hy7foIP8iv3HjRvOCIQjCcgSb1BD342VlVdxBstPZgba2n8uO/h8A90H8DBo8+DjGjRuPc+da\nVaJRTpKoTZxofYYYlbzFrCQwYaFn+rm1tZXl5OT4Xv/+979n3/nOd9iECRNYa2srY4yxlpYWklsQ\nhqCUHjQwm22lTIqwLqhcQbimQXTNMwGXkHhl2O2PMrt9jWrd1dW1ithsthWsuro2CvcleJuI8EnE\nPiwR20wQkUCt3548+QmuDGPw4PkeGcQKBqyUvb9OJrdgnnO1SfD0S//WhfycMaocPYTTf+lOS11Y\nWIiXX34Zt956KxwOB65evQoAGDFiBJ5++mnU1NSgo6ODO8Oss0oigdm7txHbt+8XpV9WpvQUp19W\nS+MsWKhN8HzTLwn6LVZcb2pqPy5evIymplrFeeK6HY6dqK1tRF9fKlJSXKisLJS4WxiJPD4tbSLC\nIxH7sERsM0FECl6/vW1bHfeZ5U8pXQV+6mt/yumsrEp0d19Cb+9bvndzc9dh61b1jY3BniFqz1Lx\nM08LRpWjB1PSUm/fvh0LFy5Eb28vcnNz8ctf/hL9/f2YN28edu/e7bOAIwgjEEsPhPTLynP0WKiF\nUq+3bh7iuh2OiogNiuWQbowgCCK2UOu35brm1NRVcLke8rziP9Oyss5gyhSHZ4ArJB4JNaeAHivU\nUPe+xOoeGt2D5KlTp+LIkSOK4x988EFYARFEMIyyUOMRTDOlVm4wfXSo9RAEQRCJA0/XfPGiG01N\n3ucC/9kzY8aNCt9+I58lRu19idk9NIYIPkLAhCqJOEOLjkqPNliLZoqvdZba8ATTWZmpzSLCJxH7\nsERsM0GYjfRZobSAi8YeFKP2vpi5hyac/ku3JlkvpG0jjECbjqoUQlYhr31bCcrK9qvqn7RqppT6\naLkNT2CdlZnaLCJ8ErEPS8Q2E4QVED9vurrOAxiM9PSRUd2DYtTeF7P20ITTf9EgmTCdSEgPBN2y\nQ3a0EVlZOzFlygRfPUeONPtSSHd3t8HtngggBYISyQ2gFEVFB1R1zEI9d0PIjKR+jThVtVCPP5OR\nl6IiR0h6acIcErEPS8Q2EwQRH5iycY8gjCBSqZWV+qdGAO+jvf0N36a/w4cfQFfXSPT3i50ylgN4\nBP6Z4fU4e/akaj2dnecAvA9/6lDhmq6ui75XvFTVgJCqWjxQtrw2iyAIgiASiGSzAyASm23b6iQD\nZAA4eXITtm/fH1a5jz1Witzc9aIjdZAOZIGOjhRPznoxL0GQaHjZhEuXrgWoaYiiXOH1YN8rYQZ5\nl+ycXRAG7gK5uevwgx+UBKiHIAiCIIhoQjPJhKlEyhZGvlP46NH0UZbHAAAXH0lEQVSzaG+Xn8VP\nIS3PWJScnKFaz7BhI7nH09P9x9VSVdtswP/6Xw5NNj0EQRAEQUQXGiQTphJJWxix/6OwWU5+Bj+F\ntLDJz488pbQYLfGrparOzIQlNMhkR0cQBEEQSkhuQZiKUhYRGenBnXeOhc22Snb0SyQlrZAdWwbA\nX7fNthKVleoDRi3xr15dpKg7WLnRwqsJr6t7Dg0NDtTVPYfHH38fe/c2Br+YIAiCIOIYcrcgTCca\ntjBqlnA337wNnZ02XwrpiRPT8MknPSGllNYSfzRTVYcC2dGFTiL2YYnYZoIg4gNytyAsTbDl/Gik\nVha0z4WQ+xmPH69u7wYIsZeVVUliB6BoT7ABZTRTVYdCrKYKJQiCIIhIQ4NkIqJEyuItVPRon3mx\nHz26FEAGnM4XfcfMaI9RxGyqUIIgCIKIMKRJJiJKpCzeQkWP9pkXu9M5RjJABsxpj1FESxNOEARB\nELEGzSQTEcUqy/lySzgttmv82K3RHqPQc18IgiAIIhGgQTIRUbQs50fTgswr3vf+K6/7zjvH4uDB\nFly7ZkNz83FOCfrkCUa0kVcGoNRHh1rukSPN+PDDv8HtToPN1oMjR8bQIJkgCIIgWJQxoUrCRPbs\naWC5uesYwHw/ubnPsD17GgK8v873fiTjsNuXMLt9jeSYzbaSAQ2e1w2e1+JrHlVcI26P9nsQWhv5\n8a9hdvuSsMqtrq5VtNFmW8mqq2s1l5FoJGIflohtJggiPgin/yILOCLiBLJIi5YFGb+eKgDKuoEN\nALx1NyI7eyfy8yf4YgcQkmWdEW1UK0Maa+jlZmeXo63tTc7x+bh06Q1NZSQaidiHJWKbCYKID8gC\njrA0gSzeoqVZDkVfLE1LXYj8fKVNXChyBCPaqFaGPIV2qOWqpczu60vVXAZBEARBxCM0SCZMRasF\nWbiaXn49/LrlaanDtUPTq8s+cqQZO3Y0wO1OQ3d3m6ZYtZQrvm9CyuxGAHUQugM3gNKAqbgJgiAI\nIhGgQTJhKo89VoqTJ9dLrNYEC7JZvtdGeC3feedYHDiwCm73Lt+x5OQTyMhYjfb2Hb5jNttKuN0L\nVWPRQ7A28tp3+PAD6Ooaif5+rxSiEcByAC/5zrHb1wDohNPprytYufL7Vlqag9dff1VSLrAcJSVf\nCavNBEEQBBHr0CCZMBUtFmTqXssbNA+SDx5sgdv9EAQNr5CWemDgB7jpplcxY4a/7pkzp+LQof1w\nuQ4YZocWrI289nV0pAD4ueiIcG5Kylx84xtf85Rxf8jlyu9bW1sKpANkAHgJly9vCKvNBEEQBBHr\n0CCZMJ1gaamN0/Qq01K3tf0Cp0/77c9mzhwT8oZBLVKQ0HXZaeDJIBgTNMTeTQjh6r2t4mNNEARB\nEFaDBsmE5TEidTK/jEacPj0EwGu+I5s2rQKwEw5HhaZyjZCC8GO7COB9AOKZ4PVwuzPQ0ODQVI+W\n+0ZpqYklS5Zg7969GDVqFD7++GOzwyEIgrAMlJaasDxGpE7mlZGc/K8AdkuOud27UFvbqLlcI9Ju\n82Kz2ZIhHSDD83qw5nq03DdKS008+uij2Ldvn9lhEARBWA6aSSYsjxGpk3ll/P73abh6VXluKPZn\nRsgVeLG1tNwC/qTeSM31aLlvlJaa+OY3v4nPP//c7DAIgiAsBw2SiZggmG5ZTxnZ2eXcQXIo9md6\n5Qo8HbNYC11WVqUySD4OwAGvRrmr6xLKyqpU9dBa7psR95YgCIIg4g0aJBMJy+rVRdi0SWoLZ7Ot\nRGWl9gGjFgs7OVp0zCNG9EFu+QYsA1AEQNBLDxq0Ep99dgkffVSrWg5BGIXD4fD9v7i4GMXFxabF\nQhAEoUZ9fT3q6+sNKYvSUhMJjcOxE7W1jejrS0VKiguVlYWaN+15CZR2m4eWNNVCuuhKAPvhtawD\nSjyvxe4b4aWlJkInHvuwzz//HHPnzlXduBePbSYIIjEwJS11Tk4Ohg0bhkGDBiElJQWHDx/G5cuX\nUV5ejtOnTyMnJwdvvfUWMjMz9VZBEBHH4agIeVAsJ1S5ghYds5AuWmlZBxyQvQ4vLTVBEARBEHx0\nD5KTkpJQX1+P4cOH+47V1NSgpKQEa9euxebNm1FTU4OamhpDAiWIYISbupqHw7HTlxraZuvB6tVF\nmD59UsB6eHEA8B1rbj4OwQNZGptYxyyki+Yh1zqHnpZaHMuQIW7ceedYHDzYEtJ9i8S9NpN4a08o\nLFiwAA0NDWhra8P48ePx4x//GI8++qjZYREEQZgP00lOTg774osvJMfy8vKY0+lkjDHW2trK8vLy\nFNeFUSVBqLJnTwPLzV3HAOb7yc1dx/bsadBdZnV1LbPZVkrKHDRoBcvMvF+1Hl4cdvsaZrcvkRwT\nym0QlfGMJFZe3cBSyTWDBi3nxPJMkFiWMLt9jehYg6KeYPctEvfaTEJtTyL2YYnYZoKIBfbsaWCl\npetZUVE1Ky1dH7P9cCQJp//SfeVNN93Ebr/9dva1r32N/eIXv2CMMZaZmel7f2BgQPLaVyF1tkQE\nKC1dLxtQCj9lZVW6yxwxYh63TKBctR61OIAqxbHs7HJWVFTNysqquB1bdXUty84uZxkZi5nNNocB\ntZ5yqj3/NrCCggpWVlbFLYcfi/xY6PctEvfaTEJtTyL2YYnYZoKwOvE2YREpwum/dMst/vjHP2LM\nmDG4dOkSSkpKMGHCBMn7SUlJSEpK4l5Lu6QJo4lEemVBF6xMDS3k4KmSHPPWoxYHTzucnz8B9fUO\nAMJyv9zKbfr0SSgoEGQQR48ytLcrtdPXrv3KtyHB+6//PV4s8mOh37d4S2UdrD1G7pQmCIIwCvVk\nVhsSRi4WaXQPkseMGQMAGDlyJO6//34cPnwYo0ePhtPphN1uR2trK0aNGsW9VjxIJggjiER65d7e\n8+ClhgacAH4tOdbVdREA0Nl5SaU0de0wzxLu6NEnAXwJp9ObEbCKU2YjPvssCceO+Z0yxBZw/Hsi\nPxb6fYu3VNbB2iP/Ir9x48ZohEUQBBGQeJuwsCK60lJfvXoVXV1dAIDu7m7U1dVh8uTJuPfee/HK\nK68AAF555RXcd999xkVKEAGITHrlVPBTQ2dwjnnTRV+DMJAWswaDB59QjY03G+B0vginc6zoSKmi\n3LS0WvT07JIcE6eq5t0Tu70FdvuTknJttlWqsfGIt1TW8dYegiASg3ibsLAiumaSL1y4gPvvvx8A\n4Ha7sXDhQpSWluKOO+7AvHnzsHv3bp8FHEFEg0ikVx48eAR6uCYT8kEykJ4upIseNmwcgLsh+Bd7\n/Y3vxy23/ArjxvFj0ybREM7NylqAKVPyPKmrx3Kz8nlnEfj35PuKYzNnTsGhQ9rvW7ylso639hAE\nkRjoSWZFhIauQfJNN92Ev/zlL4rjw4cPxwcffBB2UAShB6PTK6vbsCnTVjc3H0dxscNj7+aA3N5t\nyJBXVbXDarMBSolGIWbM2I99+xwA1FNXi2cR1O6JEfdJrT1eYslWjVJzEwQRa9AX/MhDaakJQgVe\n2upBg1YgPb0XHR3+82y2lWhrq0RDQyGARths0mvs9iVoacnERx/xtcO82YCsrEp8+eUlDAxI65k5\nc6rvtVmzCFrSams5hyAIgggP+oIfWSgtNUEEgJe2evr0Sb401M3Nxz3po8WdVCOys3ciP38CUlP7\ncfHiZTQ11SrKFqePlqe2vnixFU1NiyBPS11Wtl+ScjrUlNhGoCWttpZzYpVE7MMSsc0EQcQHpqSl\nJohEQC1ttXcgWlzs8MwgiylEfv4Bn71bcbGDW7Z4B7J8NkC4RpmW2uWSpqU2YhYhVFmElh3VtOua\nIAiCiHVokEwQYaBld7GaLVxXl5pdXPR2LeuRRWiJjXZdEwRBELGOLgs4giAEtNmH8Wzh1gHoDbPc\n8FE3o98fVmxkq0YQBEHEOjSTTBBhoGV3Md8WbhbS0w9wStRerhHokUVoiY12XRMEQRCxDg2SCSJM\ngumCBemBUl+cmqo+W6ulXCPQK4vQEhvtuiYIgiBiGZJbEESEsbL0wMqxEQRBEISZkAUcQUQBM6za\ntGLl2KxIIvZhidhmgiDig3D6LxokEwRBhEAi9mGJ2GaCIOID8kkmiAQlllI/EwRBEEQsQYNkgohR\nKPUzQRAEQUQO2rhHEDGKHo9jgiAIgiC0QYNkgohRKPUzQRAEQUQOGiQTRIxCqZ8JgiAIInLQIJkg\nYhTyOCYIgiCIyEEWcAQRw5DHcfRJxD4sEdtMEER8QD7JBEFohmzjwiMR+7BEbDNBEPEB+SQTBKEJ\nso0jCIIgCG2QJpkgEgiyjSMIgiAIbdAgmSASCLKNIwiCIAht0CCZIBIIso0jCIIgCG3QIJkgEgiy\njSMIgiAIbZC7BUEkGGQbFx6J2IclYpsJgogPyAKOIAgiSiRiH5aIbSYIIj4Ip/8iuQVBEARBEARB\nyKBBMkEQBEEQBEHICGuQ3N/fj2nTpmHu3LkAgMuXL6OkpAS33norSktL0dHRYUiQZlJfX292CJqJ\npViB2Io3lmIFYiveWIo1Xtm3bx8mTJiAW265BZs3bzY7nIgRT581aos1iZe2xEs7wiWsQfLWrVsx\nceJEJCUlAQBqampQUlKCv/3tb7jnnntQU1NjSJBmEksflFiKFYiteGMpViC24o2lWOOR/v5+rF69\nGvv27cMnn3yC119/HcePHzc7rIgQT581aos1iZe2xEs7wkX3IPncuXN47733sGzZMp8g+p133sHi\nxYsBAIsXL8Z//ud/GhMlQRAEEREOHz6Mr371q8jJyUFKSgrmz5+P//qv/zI7LIIgCNPRPUhes2YN\ntmzZguRkfxEXLlzA6NGjAQCjR4/GhQsXwo+QIAiCiBjnz5/H+PHjfa/HjRuH8+fPmxgRQRCERWA6\nePfdd1lFRQVjjLHf/e53bM6cOYwxxjIzMyXnZWVlKa4FQD/0Qz/0E9M/8cRvfvMbtmzZMt/rV199\nla1evVpyjtn3m37oh37oJ5wfvdiggz/96U9455138N5778HlcqGzsxOPPPIIRo8eDafTCbvdjtbW\nVowaNUpxLSOvTYIgCMtwww034OzZs77XZ8+exbhx4yTnUL9NEEQioktu8fzzz+Ps2bM4deoU3njj\nDdx999149dVXce+99+KVV14BALzyyiu47777DA2WIAiCMJY77rgDf//73/H555+jt7cXb775Ju69\n916zwyIIgjAdXTPJcrzuFj/84Q8xb9487N69Gzk5OXjrrbeMKJ4gCIKIEDabDTt27EBZWRn6+/ux\ndOlS3HbbbWaHRRAEYTphJxMpKirCO++8AwAYPnw4PvjgA/ztb39DXV0dMjMzAcSOn3JOTg6mTJmC\nadOmYcaMGQCsGysAdHR04MEHH8Rtt92GiRMn4r//+78tGe+JEycwbdo0309GRga2bdtmyVi9vPDC\nC8jPz8fkyZPx0EMP4dq1a5aNd+vWrZg8eTImTZqErVu3ArDW53bJkiUYPXo0Jk+e7DsWKL4XXngB\nt9xyCyZMmIC6ujrTY3377beRn5+PQYMG4aOPPpKcb2asRvLtb38bJ06cwKeffopnnnnGdzxe/JN5\nv9dY5ezZs/iHf/gH5OfnY9KkSdi2bZvZIenC5XLh61//Om6//XZMnDhR8rmLVeRjnViFNxaKVeTj\npEOHDoVWgG41cwj85Cc/YQ899BCbO3cuY4yxp556im3evJkxxlhNTQ17+umnoxFGUHJyclhbW5vk\nmFVjZYyxRYsWsd27dzPGGOvr62MdHR2Wjpcxxvr7+5ndbmdnzpyxbKynTp1iN910E3O5XIwxxubN\nm8f+7d/+zZLxfvzxx2zSpEmsp6eHud1u9q1vfYt9+umnloq1sbGRffTRR2zSpEm+Y2rxHTt2jE2d\nOpX19vayU6dOsdzcXNbf329qrMePH2cnTpxgxcXF7M9//rPvuNmxRhq3281yc3PZqVOnWG9vL5s6\ndSr75JNPzA5LF7zfa6zS2trKmpqaGGOMdXV1sVtvvTVmfy/d3d2MMeH59fWvf539/ve/Nzmi8JCP\ndWIV3lgoVuGNk0Ih4oPks2fPsnvuuYcdOHDA54KRl5fHnE4nY0z4g8/Ly4t0GJrIyclhX3zxheSY\nVWPt6OhgN910k+K4VeP18v7777O77rqLMWbdWNva2titt97KLl++zPr6+ticOXNYXV2dJeN9++23\n2dKlS32vn332WbZ582bLxXrq1CnJAEUtvueff57V1Pz/9u7lpY02iuP4L1pFsFCtxHhJhSJaGS+T\n2IgguJB6K6KiTUFFBJVuXAku/AvUV1ftwlXRhRSalV20GGmDtIZWkRCD4MbihRJcFC9FkwixeLpK\n0DTzqlE7z8j57DRBvnkicpCZk//Cz6urq6OFhQVVW0Mih2QRWm/St2/fqK6uLvz1yMgIjYyMqFh0\nNUrvq9Y1NzeTw+FQO+NK/H4/WSwWWl1dVTslZtFmHa2KNgtpkdKcdBlXvtziPFrap6zT6VBdXQ2L\nxYLXr18DELd1c3MTer0e3d3dKC0txYsXL+D3+4XtDbHZbGhvbwcg7tnev38fAwMDyMnJQVZWFlJS\nUlBTUyNkb1FREZxOJ/b29hAIBDAzMwOv1ytk62lKfdvb22c2K4i8s1dLrbHg/cni29rawvLyMsrL\ny9VOicnJyQlMJhMMBgOqqqogSZLaSTGLNutoVbRZSIuizUmBQOBSP+NG380PHz4gPT0dZrNZcYWQ\nTqcL3/intq9fv2J5eRl2ux3j4+NwOp1nHhep9ffv33C73ejr64Pb7UZycvJfHwMuUi8ABINBvH//\nHs+fP//rMZFa19fX8fLlS2xtbWF7exs+nw9v3rw58xxRegsKCjA4OIja2lo8ffoUJpMJ8fHxZ54j\nSquS8/pEbo+kpdbz3KbXchv5fD5YrVa8evUKd+/eVTsnJnFxcfB4PPB6vZifn9fsRyFfZNbRkvNm\nIa24yJx0nhsdkkP7lB8+fIj29nbMzc2d2acMQHGfshoyMzMBAHq9Hi0tLVhaWhK21Wg0wmg0oqys\nDABgtVrhdruRkZEhZC8A2O12PH78GHq9HgCEPVuXy4WKigqkpaXhzp07aG1txcLCgrBn29PTA5fL\nhS9fviA1NRX5+fnCnm2IUl/kzl6v14vs7GxVGs+jpdZYXGR/MlPH8fExnj17hs7OzluxavXevXto\naGiAy+VSOyUm0Wadrq4utbNiFm0W0iKlOekybnRI1tI+5UAggMPDQwCA3+/Hx48fUVxcLGQrAGRk\nZODBgwdYW1sDADgcDhQWFqKxsVHIXgB4+/Zt+FILAMKebUFBARYXF3F0dAQigsPhgCRJwp7tz58/\nAQA/fvzA9PQ0Ojo6hD3bEKW+pqYm2Gw2BINBbG5u4vv370LdXX36v0Sit14V708WExGht7cXkiSh\nv79f7ZyY7ezshLfaHB0d4dOnTzCbzSpXxSbarDM1NaV2VkyUZiEtUpqTLuXql0ZfzOfPn8N3fO7u\n7tKTJ08oLy+PampqaH9//19lKNrY2CBZlkmWZSosLKTh4WEiErM1xOPxkMVioZKSEmppaaFfv34J\n2+vz+SgtLY0ODg7C3xO1lYhodHSUJEmioqIi6urqomAwKGxvZWUlSZJEsizT3NwcEYl1tm1tbZSZ\nmUkJCQlkNBppcnLyf/uGhoYoNzeXHj16RLOzs6q2TkxM0Lt378hoNFJSUhIZDAaqr68XovVfmJmZ\nofz8fMrNzQ3/TdSi0PuamJgY/h3UKqfTSTqdjmRZJpPJRCaTiex2u9pZl7ayskJms5lkWabi4mIa\nGxtTO+lanJ51tEhpFtKqaHPSZeiIbsEFNIwxxhhjjF0j7d+GyRhjjDHG2DXjIZkxxhhjjLEIPCQz\nxhhjjDEWgYdkxhhjjDHGIvCQzBhjjDHGWAQekhljjDHGGIvwBzSwr2BkJqwIAAAAAElFTkSuQmCC\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x366ea10>" | |
] | |
} | |
], | |
"prompt_number": 13 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The plots shows more or less two possibilities for each waiting time and duration: short and long.\n", | |
"\n", | |
" * Top left plot: There seems to be a connection between duration of current erruption and waiting time afterwards. From the top left plot, we can see that short waiting times strongly correlate with short erruption lengths. Same is true for long erruptions/waiting times. This might even suggest a causal relationship and is phsically reasonable in the sense that the geyser is \"charging\" up energy that leads to longer erruptions if done longer.\n", | |
"\n", | |
" * Lower plots: Given an event (both errupt and wait) is long, the frequency for the next event being short or long is roughly equal. See the three blobs in all but the lower left part of the plots. Given an event is short, the next even is almost always long.\n", | |
" \n", | |
" * Upper right plot: Shows the length of consecutive events, intersected at opposite variables (waiting time i vs duration i+1). It again show that there are changes from short to long events with roughly the same frequency.\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We now know that short events are followed by long ones and that long events are followed by either short or long ones. Now how is the latter behaved? Is there maybe some higher order dependence. Increase the interval length for the duration plot." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"figure(figsize=(12,10))\n", | |
"\n", | |
"intervals=[2,3,4,5]\n", | |
"for i in range(len(intervals)):\n", | |
" subplot(2,2,i+1)\n", | |
" plot(X[:n-intervals[i],1], X[intervals[i]:,1], 'o')\n", | |
" _=title(\"Interval: %d, \"%intervals[i] + var_names[1] + \" vs. \" + var_names[1])" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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OBADMnDkT69evN1RYguBl4cJSDBmyLOZa2N6tRDbNU0/VxCx0YVdv6vKwErG8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cmTi1SXcd99BUhKujfkWFLSPZg0KXgRa4nmDTIAjECzIPtJTLwbaWmnQs4JLbdMUgYAvICEhKc0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\nypRfGB5iAAAAAElFTkSuQmCC\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x30cce50>" | |
] | |
} | |
], | |
"prompt_number": 14 | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"While the plots might suggest that there is a slight higher order structure in the changes between long and short events (slightly higher density of points in the corners), this is not as clear as for the first order case. Indeed, looking at waiting time only, the jumps between low and high seem to be more or less random. I plot random jumps with the same statistics as the data using a mixture of Gaussians (for the duration variable). The results look similar enough to let this one count as a good model." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [ | |
"# normalise X first\n", | |
"D=X[:,0]\n", | |
"D-=mean(D)\n", | |
"D/=std(D)\n", | |
"\n", | |
"figure(figsize=(12,5))\n", | |
"m=mean(D)\n", | |
"s=std(D)\n", | |
"upper_idx=D>m\n", | |
"lower_idx=D<m\n", | |
"plot(arange(n)[upper_idx],D[upper_idx], 'o')\n", | |
"plot(arange(n)[lower_idx],D[lower_idx], 'o')\n", | |
"plot([0,n],[m,m])\n", | |
"legend([\"High\", \"Low\", \"Average\"])\n", | |
"title(\"Samples from Geyser\")\n", | |
"\n", | |
"# fit Gaussians and weights\n", | |
"m_upper=mean(D[upper_idx])\n", | |
"m_lower=mean(D[lower_idx])\n", | |
"std_upper=std(D[upper_idx])\n", | |
"std_lower=std(D[lower_idx])\n", | |
"p_up=mean(upper_idx)\n", | |
"print \"Gaussian mixture with weights (%.2f,%.2f) and means (%.2f,%.2f) and stds (%.2f,%.2f)\"% \\\n", | |
"(p_up,1.-p_up, m_upper, m_lower, std_upper, std_lower)\n", | |
"\n", | |
"\n", | |
"# sample from mixture of 2 Gaussians\n", | |
"idx=rand(n)>p_up\n", | |
"samples=zeros(n)\n", | |
"#=randn(len(idx==0))*std_upper+m_upper\n", | |
"samples[idx==0]=randn(sum(idx==0))*std_upper+m_upper\n", | |
"samples[idx==1]=randn(sum(idx==1))*std_lower+m_lower\n", | |
"\n", | |
"figure(figsize=(12,5))\n", | |
"plot(arange(n)[idx==0],samples[idx==0], 'o')\n", | |
"plot(arange(n)[idx==1],samples[idx==1], 'o')\n", | |
"plot([0,n],[mean(samples),mean(samples)])\n", | |
"_=title(\"Samples from fitted model\")" | |
], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"output_type": "stream", | |
"stream": "stdout", | |
"text": [ | |
"Gaussian mixture with weights (0.63,0.37) and means (0.73,-1.24) and stds (0.31,0.34)\n" | |
] | |
}, | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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3m9UOU9FaPmq+J0PZy5AGPYJ5uEsw73tzlIaW7d49DUCHH4dzbgGQhy1bliMh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\nGDwTEREREanE4JmIiIiISCUGz0REREREKmkOnp9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| |
"text": [ | |
"<matplotlib.figure.Figure at 0x2d656d0>" | |
] | |
}, | |
{ | |
"metadata": {}, | |
"output_type": "display_data", | |
"png": 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UWKzMjEb8drRCCLQGDydODFD8rEyNl9A80rpygNf7UMzAGbCuBy6eANKMYFOG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\n/wfp8HaENMn79QAAAABJRU5ErkJggg==\n", | |
"text": [ | |
"<matplotlib.figure.Figure at 0x33df2d0>" | |
] | |
} | |
], | |
"prompt_number": 15 | |
}, | |
{ | |
"cell_type": "code", | |
"collapsed": false, | |
"input": [], | |
"language": "python", | |
"metadata": {}, | |
"outputs": [], | |
"prompt_number": 15 | |
} | |
], | |
"metadata": {} | |
} | |
] | |
} |
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