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Last active March 26, 2024 22:54
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Estimation exponential mixture models
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exponential Mixture Models and the EM Algorithm\n",
"\n",
"This notebook explores Exponential mixture models, their esitmation, resulting classification, and the EM algorithm when labels are not provided."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np # for numerical python libraries\n",
"\n",
"import scipy.stats as st # for statistical libraries\n",
"\n",
"import matplotlib.pyplot as plt # for plotting\n",
"\n",
"import matplotlib.pylab as pylab\n",
"params = {'legend.fontsize': 'x-large',\n",
" 'figure.figsize': (15, 5),\n",
" 'axes.labelsize': 'x-large',\n",
" 'axes.titlesize':'x-large',\n",
" 'xtick.labelsize':'x-large',\n",
" 'ytick.labelsize':'x-large'}\n",
"pylab.rcParams.update(params)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generate some random Exponential mixture model data\n",
"In the mixture model, a generative model, the probability that a point in feature space is generated is Gaussian with a class specific mean and covariance matrix"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# prior distribution over hidden states\n",
"pi=np.array([0.5,0.25,0.25])\n",
"\n",
"# intensity conditional on hidden state \n",
"# (here we have two visible exponential variables)\n",
"lmbda=np.array([[1,10],[2,1],[4,0.6]])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def GenerateData(pi,lmbda,N):\n",
" # this function simply generates exponential mixture model data \n",
" # pi represents the probability of each class (in this case, we have 3)\n",
" # lmbda are the vector of intensities for each state\n",
" \n",
" d = lmbda.shape[1] # data dimension\n",
" K = pi.size # number of classes\n",
" \n",
" X = np.zeros((N,d)) # store features (i.e., the visible inter-arrival times)\n",
" Y = np.zeros(N) # store labels (these are not visibile to us when we have real data, but we store them for experimentation)\n",
" Y = Y.astype(int)\n",
" \n",
" # used generate random labels\n",
" cpi = np.cumsum(pi)\n",
" U = np.random.uniform(0,1,N)\n",
" \n",
" for i in range(0,N):\n",
" \n",
" # generate a label for point i\n",
" Y[i] = int(sum(U[i] > cpi))\n",
" \n",
" # generate random point in feature space conditional on being in class Y[i]\n",
" for j in range(0,d):\n",
" X[i,j] = np.random.exponential(1/lmbda[Y[i],j])\n",
" \n",
" return X,Y\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot a random sample"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t,y = GenerateData(pi,lmbda,500) #generate the mvn data\n",
"\n",
"ax = plt.subplot(1,1,1)\n",
"ax.set_xscale(\"log\", nonposx='clip')\n",
"ax.set_yscale(\"log\", nonposy='clip')\n",
"\n",
"for i in range(0,lmbda.shape[0]):\n",
" plt.scatter(t[y==i,0],t[y==i,1]) # plotting the points\n",
" \n",
"plt.xlabel(r'$t_1$') \n",
"plt.ylabel(r'$t_2$')\n",
"plt.title('Random sample of labeled mixutre data')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimate the model from the data using labels"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def EstimateMixtureModel(t,y): #No EM here - this is straight up classification with known labels\n",
" \n",
" Y = np.unique(y) # get the unique list of labels\n",
" K = Y.size # number of unique labels\n",
" d = t.shape[1]\n",
" \n",
" pi = np.zeros(K) \n",
" lmbda = np.zeros((K,d)) \n",
" \n",
" # estimate the parameters for every unique point with the MLE estimates \n",
" for k in range(K):\n",
" idx = (y==Y[k])\n",
" pi[k] = np.sum(idx)/y.size\n",
" for j in range(d):\n",
" lmbda[k,j] = 1/np.mean(t[idx,j])\n",
" \n",
" return pi, lmbda"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.506 0.254 0.24 ]\n",
"[[0.98027245 9.02516435]\n",
" [2.15256329 0.83039297]\n",
" [3.76774373 0.56241834]]\n"
]
}
],
"source": [
"pih,lmbdah = EstimateMixtureModel(t,y)\n",
"\n",
"print(pih)\n",
"print(lmbdah)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayes classifier\n",
"This provides the (posterior) probability that a point in feature space comes from a given class $\\gamma_{k}(x)=\\mathbb P(T=t|Y=k)$ and equals using Bayes rule\n",
"\n",
"$$\n",
"\\gamma_{k}(t) = \\frac{\\pi_k \\; f_{T|Y=k}(t; \\lambda_k)}{\\sum_{k\\in{\\mathcal K}} \\pi_k \\;f_{T|Y=k}(t; \\lambda_k)}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# compute the posterior probability of a point in feature space being from a given class\n",
"def Posterior(pi,lmbda,bins):\n",
" K = pi.size\n",
" \n",
" nbins = bins.shape[1]\n",
" p = np.zeros((K,nbins,nbins))\n",
" \n",
" for i in range(0,nbins):\n",
" for j in range(0,nbins):\n",
" \n",
" denom = 0\n",
" # for every quantile, calculate the probability of it being in a certain class\n",
" # divide by the sum of probabilities for that point, across that class\n",
" # what results is the probability of the point (i,j) being in class k\n",
" for k in range(0,K):\n",
" p[k,i,j] = pi[k]*(lmbda[k,0]*np.exp(-bins[0,i]*lmbda[k,0]))*(lmbda[k,1]*np.exp(-bins[1,j]*lmbda[k,1]))\n",
" denom += p[k,i,j]\n",
"\n",
" for k in range(0,K):\n",
" p[k,i,j] /= denom\n",
" \n",
" return p"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# use the true and estimated model parameters to compute the posterior\n",
"bins=np.zeros((2,100))\n",
"bins[0,:] = np.exp(np.linspace(np.log(1e-4),np.log(100),100))\n",
"bins[1,:] = np.exp(np.linspace(np.log(1e-4),np.log(100),100))\n",
"\n",
"p = Posterior(pi,lmbda,bins)\n",
"ph = Posterior(pih,lmbdah,bins)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# plot the results\n",
"ax=plt.subplot(1,2,1)\n",
"ax.set_xscale(\"log\", nonposx='clip')\n",
"ax.set_yscale(\"log\", nonposy='clip')\n",
"plt.contourf(bins[0,:],bins[1,:],np.argmax(p,axis=0).T,2,alpha=0.25)\n",
"\n",
"for i in range(0,lmbda.shape[0]):\n",
" plt.scatter(t[y==i,0],t[y==i,1],s=4)\n",
" \n",
"plt.xlabel(r'$t_1$') \n",
"plt.ylabel(r'$t_2$')\n",
"plt.title('True')\n",
"\n",
"ax2=plt.subplot(1,2,2)\n",
"ax2.set_xscale(\"log\", nonposx='clip')\n",
"ax2.set_yscale(\"log\", nonposy='clip')\n",
"plt.contourf(bins[0,:],bins[1,:],np.argmax(ph,axis=0).T, 2, alpha=0.25)\n",
"\n",
"for i in range(0,lmbda.shape[0]):\n",
" plt.scatter(t[y==i,0],t[y==i,1],s=4)\n",
" \n",
"plt.xlabel(r'$t_1$') \n",
"plt.ylabel(r'$t_2$')\n",
"plt.title('Estimated')\n",
"plt.show()\n",
"\n",
"# the estimated comes very close to the true. We are able to identify the regions quite well"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Estimating without the labels... EM Algorithm\n",
"Responsibilities at iteration m for data point n in class k is\n",
"$$\n",
"\\gamma_{n,k}^m = \\frac{\\pi_k^m \\; f_{T_n|Y_n=k}(t_n; \\lambda_k^m)}{\\sum_{k\\in{\\mathcal K}} \\pi_k^m \\;f_{T_n|Y_n=k}(t_n; \\lambda_k^m)}\n",
"$$\n",
"where the probability that data point n occurs given that it is in class k is \n",
"$$\n",
"f_{T_n|Y_n=k}(t_n; \\lambda_k^m) = \\lambda_{k,1}^m e^{-t_{n,1} \\lambda_{k,1}^m}\\lambda_{k,2}^m e^{-t_{n,2} \\lambda_{k,2}^m}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# now we actually use EM - we no longer have the labels\n",
"# this function represents the e-step\n",
"def Reponsibilities(t,pi,lmbda):\n",
" \n",
" K = pi.size\n",
" \n",
" g = np.zeros((K, t.shape[0]))\n",
" \n",
" for n in range(0,t.shape[0]):\n",
" \n",
" denom = 0\n",
" \n",
" for k in range(0,K):\n",
" g[k,n] = pi[k]*(lmbda[k,0]*np.exp(-t[n,0]*lmbda[k,0]))*(lmbda[k,1]*np.exp(-t[n,1]*lmbda[k,1]))\n",
" #posterior probability that point n is in state k\n",
" # similar to what was in the \"Bayes\" function, except here we are given \n",
" # a data point as opposed to calculating the probability for an arbitrary point\n",
" # in feature space\n",
" denom += g[k,n]\n",
" \n",
" for k in range(0,K):\n",
" g[k,n] /= denom\n",
" \n",
" return g"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The m-step update rules are for class $l$\n",
"$$\n",
"\\pi_l^{m+1} = \\frac{\\sum_{n\\in\\mathcal{N}} \\gamma_{n,l}^m}{\\sum_{n\\in\\mathcal{N},l\\in\\mathcal{K}} \\gamma_{n,l}^m}\n",
"$$\n",
"\n",
"$$\n",
"\\lambda_{l,i}^{m+1} = \\frac{\\sum_{n\\in\\mathcal{N}} \\gamma_{n,l}^m}{\\sum_{n\\in\\mathcal{N}} t_{n,i} \\,\\gamma_{n,l}^m}\n",
"$$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def EM(t, pi, lmbda, iter):\n",
" \n",
" K = pi.size\n",
" d = t.shape[1]\n",
" \n",
" for m in range(iter):\n",
" \n",
" # e-step\n",
" gamma = Reponsibilities(t,pi,lmbda)\n",
" \n",
" #m-step\n",
" #\n",
" \n",
" # compute update to pi\n",
" numer = np.sum(gamma, axis=1) # sum_n gamma_{n,k} gives array shape (1,K)\n",
" denom = np.sum(numer) # sum_{n,k} gamma_{n,k}\n",
" pi = numer / denom\n",
" \n",
" # compute update to lmbda\n",
" denom = np.matmul(gamma, t) # sum_n x_{n,l} gamma_{n,k} gives array shape (K,d) \n",
" for k in range(0,K):\n",
" lmbda[k,:] = numer[k]/denom[k,:]\n",
"\n",
"\n",
" print(' -- estimated parameters -----')\n",
" print(pi, '\\n\\n', lmbda, '\\n\\n')\n",
" \n",
" return pi, lmbda"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def InitialGuess(t,K):\n",
" # generate an initial guess depending on the number of classes that are specified\n",
"\n",
" pi_h = np.ones(K)/K\n",
" lmbda_h = 1.0/np.mean(t,axis=0)\n",
"\n",
" pi0 = pi_h * np.random.uniform(0.99,1.01,K)\n",
" pi0 = pi0 / sum(pi0)\n",
"\n",
" lmbda0 = np.tile(lmbda_h,(K,1)) * np.random.uniform(0.99,1.01,(K,2))\n",
" \n",
" return pi0, lmbda0"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def loglike(t,pi,lmbda):\n",
" K = pi.shape[0]\n",
" n = t.shape[0]\n",
" \n",
" gamma = Reponsibilities(t,pi,lmbda)\n",
" logl =0\n",
" for k in range(K):\n",
" for i in range(n):\n",
" logl += gamma[k,i] * ( np.log(pi[k]) + np.log(lmbda[k,0]) - (t[i,0]*lmbda[k,0]) +np.log(lmbda[k,1]) -(t[i,1]*lmbda[k,1]) )\n",
" \n",
" return logl"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"def BIC(t,pi,lmbda):\n",
" K = pi.shape[0]\n",
" n = t.shape[0]\n",
" \n",
" return -loglike(t,pi,lmbda) + 0.5*(2*K+(K-1))* np.log(n)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-------- Kfit = 2 -------- \n",
" -- initial guess -- \n",
"[0.49809492 0.50190508] \n",
"\n",
" [[1.44636115 1.26669531]\n",
" [1.43563871 1.27685289]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.4794008 0.5205992] \n",
"\n",
" [[2.83100659 0.65732803]\n",
" [0.98497385 8.77080699]] \n",
"\n",
"\n",
"-------- Kfit = 3 -------- \n",
" -- initial guess -- \n",
"[0.33387791 0.33173456 0.33438753] \n",
"\n",
" [[1.43015684 1.26741556]\n",
" [1.43589019 1.28016097]\n",
" [1.43098238 1.2679464 ]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.22316429 0.4919953 0.28484041] \n",
"\n",
" [[2.90940303 0.48481904]\n",
" [0.95724247 9.31730403]\n",
" [2.65698095 1.03366119]] \n",
"\n",
"\n",
"-------- Kfit = 4 -------- \n",
" -- initial guess -- \n",
"[0.2509918 0.24924743 0.25154049 0.24822028] \n",
"\n",
" [[1.42474824 1.26282952]\n",
" [1.44115241 1.27729374]\n",
" [1.44058428 1.25794529]\n",
" [1.44479932 1.26478645]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.12734148 0.3873757 0.26679835 0.21848447] \n",
"\n",
" [[ 1.39855492 5.25689672]\n",
" [ 0.89413056 10.55609854]\n",
" [ 2.88303654 0.51983303]\n",
" [ 2.69585245 1.01850799]] \n",
"\n",
"\n",
"-------- Kfit = 5 -------- \n",
" -- initial guess -- \n",
"[0.20105033 0.20151482 0.19846859 0.2008225 0.19814376] \n",
"\n",
" [[1.4246904 1.27768248]\n",
" [1.4200708 1.25978002]\n",
" [1.42343218 1.26034366]\n",
" [1.44498226 1.27002182]\n",
" [1.42050762 1.26812908]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.33533947 0.17657868 0.16260484 0.14589271 0.1795843 ] \n",
"\n",
" [[ 0.86863997 11.23592413]\n",
" [ 2.56532335 0.82504945]\n",
" [ 3.07581032 0.45008596]\n",
" [ 2.8089168 0.95569667]\n",
" [ 1.29953145 5.81646344]] \n",
"\n",
"\n",
"-------- Kfit = 6 -------- \n",
" -- initial guess -- \n",
"[0.16516135 0.16637138 0.16794155 0.16690864 0.16754179 0.16607529] \n",
"\n",
" [[1.43045738 1.26621042]\n",
" [1.4357111 1.256265 ]\n",
" [1.42787624 1.26567534]\n",
" [1.43170622 1.25656559]\n",
" [1.44085698 1.27579006]\n",
" [1.44636222 1.26707865]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.12567106 0.18147799 0.13058957 0.19093108 0.26003162 0.11129868] \n",
"\n",
" [[ 1.21222956 6.34475299]\n",
" [ 2.99346526 0.46333299]\n",
" [ 1.20780235 6.37308198]\n",
" [ 2.64174578 0.87626314]\n",
" [ 0.82960341 12.53665461]\n",
" [ 2.80001586 0.94271417]] \n",
"\n",
"\n",
"-------- Kfit = 7 -------- \n",
" -- initial guess -- \n",
"[0.14303089 0.14192704 0.14219562 0.14448482 0.14255263 0.14314788\n",
" 0.14266111] \n",
"\n",
" [[1.43816292 1.26814236]\n",
" [1.43756441 1.26748664]\n",
" [1.4415785 1.27910488]\n",
" [1.44173364 1.26070398]\n",
" [1.44359513 1.27394121]\n",
" [1.42217294 1.25907902]\n",
" [1.43334177 1.26412093]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.06706766 0.06568679 0.27305435 0.16796744 0.17636172 0.13837483\n",
" 0.11148722] \n",
"\n",
" [[ 1.3166319 5.74471329]\n",
" [ 2.80407382 0.95933571]\n",
" [ 0.83774204 12.24003541]\n",
" [ 3.05574722 0.45452708]\n",
" [ 1.18925154 6.49479255]\n",
" [ 2.51944035 0.82397222]\n",
" [ 2.83045886 0.91694609]] \n",
"\n",
"\n",
"-------- Kfit = 8 -------- \n",
" -- initial guess -- \n",
"[0.12502513 0.12367559 0.12422168 0.12571826 0.12506027 0.12450538\n",
" 0.12575082 0.12604288] \n",
"\n",
" [[1.44518127 1.27850752]\n",
" [1.44490965 1.27650709]\n",
" [1.43946413 1.25715749]\n",
" [1.42301083 1.25981103]\n",
" [1.42062855 1.26721325]\n",
" [1.42305157 1.26561651]\n",
" [1.41913297 1.26093234]\n",
" [1.44004119 1.28041919]] \n",
"\n",
"\n",
" -- estimated parameters -----\n",
"[0.14159441 0.11571945 0.16867738 0.12751488 0.0734684 0.0754711\n",
" 0.11193446 0.18561993] \n",
"\n",
" [[ 1.08637404 7.3591545 ]\n",
" [ 1.15190067 6.81214417]\n",
" [ 3.01406158 0.45378798]\n",
" [ 2.60893394 0.8535715 ]\n",
" [ 1.23299789 6.27146366]\n",
" [ 2.81298384 0.92776829]\n",
" [ 2.74785899 0.89290933]\n",
" [ 0.7895542 14.36111458]] \n",
"\n",
"\n"
]
}
],
"source": [
"# generate an initial guess using a list of classes\n",
"\n",
"Kfitmax = 8 # largest number of possible classes\n",
"pe = np.empty((Kfitmax,Kfitmax,bins.shape[1],bins.shape[1]))\n",
"pie = np.empty((Kfitmax,Kfitmax))\n",
"lmbdae = np.empty((Kfitmax,Kfitmax,2))\n",
"bic = np.empty((Kfitmax,1))\n",
"ll = np.empty((Kfitmax,1))\n",
"\n",
"# fitting the parameters using 2, 3, ... 8 classes\n",
"for Kfit in range (2,Kfitmax+1):\n",
" \n",
" print('-------- Kfit = ', Kfit, '-------- ')\n",
" \n",
" pi0,lmbda0 = InitialGuess(t,Kfit)\n",
"\n",
" print(' -- initial guess -- ')\n",
" print(pi0, '\\n\\n', lmbda0, '\\n\\n')\n",
"\n",
" # use EM to update the estimate\n",
" thispie, thislmbdae = EM(t, pi0, lmbda0, 100)\n",
"\n",
" pie[Kfit-1,0:Kfit] = thispie\n",
" lmbdae[Kfit-1,0:Kfit,:] = thislmbdae\n",
" \n",
" pe[Kfit-1,0:Kfit,:,:] = Posterior(thispie,thislmbdae,bins)\n",
" \n",
" bic[Kfit-1] = BIC(t,thispie, thislmbdae)\n",
" ll[Kfit-1] = loglike(t,thispie, thislmbdae)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def MakePlot(t,Y,bins,atitle, m,n, o):\n",
" ax1=plt.subplot(m, n, o)\n",
" ax1.set_xscale(\"log\", nonposx='clip')\n",
" ax1.set_yscale(\"log\", nonposy='clip')\n",
" plt.contourf(bins[0,:],bins[1,:],Y,np.unique(Y).size-1,alpha=0.25)\n",
"\n",
" for i in range(0,lmbda.shape[0]):\n",
" plt.scatter(t[y==i,0],t[y==i,1],s=4)\n",
"\n",
" plt.xlabel(r'$t_1$') \n",
" plt.ylabel(r'$t_2$')\n",
" plt.title(atitle)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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fnALAXjXaks6GnS1mxdQKTESD9R1WarC+0l+u+NPQAs3U2rLvIgCjx4z0maEFYmoFIqLB+o7BpMF8gTtDy7yetdLQOllWza03W6vBAnb7oTA4saL2hLnuQk/qPoAmxq579hrs76/vdh2HvthqCM6GVk+7+XTH0BIEwRmrUsv1ugsb63K6XfcBNCE2c8s1JBxa7zSeFXUcjtdW+tTQqq74AnvVaC6OCfapoSUIQkes1GB/rszpkf6C3mkwM30VA2ak2H1uaAmC4IwVGsysl3pSewucNVh/qaPlydDSuxuGVrRYamh95Cjo9TiuiKklBBTe1p7QBc+2vXd1EDtmUdZV3QezcDJjNsM8iTx35/bFVkPQgtH5Ie8ZhlZP0A2tiefTxNAShB7gbe0JXfBsPXiXW7GjC7OsiPAu6z64GljQsQiqJ6Hn7lx3uNbN8oWhpbenj7wUTcHFesB9+ru3iKElCN3HGw3WleGkayY9fnVWd8tqDWamL2JAQWMZoG3FFkNLEPyLFRrMrJe6qr3lSUOZNVhnRpu3GszXdGZo6UaW/ugtJ8uqOT08lznXXOz1WK6IqSVYhhWdaczdcTpDFzzZLeUdxI5ZlBXNW8eB7xz1mPpuFk4P7/8B38u9gYf3/8DJDPMk8lyzwPra0IqJHGGJoRVohf8EwR9YcTfN3B2nM3TBk62WuxU77cIsg8O3HO007V0fa2NdDncevIE7D2awzj7TSYh5Enre3IXUjawhMc0MiWn2qaF1fWIKcRNGS4aWIHQTK/QXeKfBujKc2jVTRqf6yzzWnytz+F7uDXwvN4PNpzb0SIOB9revP/rK0BoS3PuuhGJoCYONQNFgZr1UMmtdpxrMrKE2FW1wq8E6M9p6mglmJd4YWlahG1rJE8f6pAN1sOUjCoMWs7ixoh5WZ1RMyWTMySwygseyvbXKEDvdrQehj7MuaSZnzxcDcPZ8MUVp/2MIsVXgdqyKKZnEntzCZ3HL+rWh9fKx/XxRd14MLWFQY76b5usCnlVJmcQUZJGhjGU7VYbYMdeDeG7O9m6N9beI8LZXVLZTxYpbjhrHrLavcfuZ9HNd70LqIgfwWWaWjm5oJQ5LAHqXnQViaAmDk77QXxVTMrl+dKShucz665k07+KXPpY5fr1TupNVadu90mD6PMD5b1/Dv4aWFWYWiKElDE4CTYN5Mwd9nHX2meyu1OuoOWuw1eBxLE8azF/409DKLshHiT7kM0MLxNQSLOT6+KWGoPE1RfPWUTRvHcuB5abXOxN2D+//AWfPFzNu+AT+0hrHmJNZXBiZCMD21grjuHHDJ+ANOfH3QPw9Wt2s3n6gHmCVoVV4JobZtrliaAmDmtTYpYaY8TUls9ZRMmsdK4AVpte7EnVrj/2AsqZi4sImsOlSHDEFWTSN0GKYAuhtX7z9DPo8zJi3GAIk4D9Dq7eIoSUMVvpCf4Gz4XRv7rJOjbXONJg5fnn7Gczz6Ku/fSuzs0AMLWHwEugazJ3+qkrKpCopk+yW90FR2o5UeqXB/MX24lMkjojsYGiFVrRYXoLGH4YWiKklWMiqyWt8fofQFdfMrM6EnTkTa0zRByhqK8Pq81GAzIZGsiIiuszw6mlXQ6s7aPTW0DK3nJ5tSxJDSxj0eMpm8jXmO4NdibqypmLjOaYthoU1aDHslrYY1pOuP11lZsXteZzoY1upmbaCsgUPdP9DukEMLUGwjr7QX+Cswboy1jrTYLd4qcHc0dXffljOU4QcyaZ5egZN6fd1+zN6QgwtQbCOvtBgrplZnWkwd/pL3zaYGRlBVkQ488cs88ln8MUaUse8rg2taLF8PegvQwukppbQDXpSs8GqOg+exjJnZtnfX88f39vIm6FzWTV5TYdipjrDgsOZbo9jfXQULUMjUIEft0YZ6fLu5mt/fz1znk1hSeHGHnU1tHLftG5oXZuY0GtD646E68TQEgYFPanXYGXXGk9jme8Mrq2p40hRCWtr6tx2zxkWFG6ct84+08hsUIF7ItMNQeZ6jc6KkXpTMyv62FYUtZXoY1t7/T2AGFqC0F36Wn95Gs+swdZWt8Wv6jqgY0F5M+uStJoz3miwzgrCF14oYVJkeacdn0OOZKOoDkKOZLt9vyeIoSUI3SMQNZhZfyUcWs8fDm7kraC5rLav6aDBdIYFta8hm0Ykgurgwdo6coLnAbidb28Lwlu5htxefAqAxBGRRldD/eErQ2vRzCk+N7RATC2hG/Sk1bMV7aE7G0u/I+hA5c+VOTwaGcGSpvfZfGqDUwHSvaWamLFh42LLBRxAVkQEvx0RzAx7Av8VVNt2jey2a2TzWXGl8Yg9uQWb6uhxQOmqg0ZX5FbnGQ/d0OrJ4q2gsYy3D580DC1BGCz0pNWzFe2huxrrirAE43ljXQ4zJoxjY12Ok4jZXanFpQutjdja/tneThUoQTwaFckMewKPREeyt+24vZXOizdXQeTazXDx1ZO5KibWeLhSM20FqhJEzbQVHd7rLr4ytDpb1ApCf6ev9Zen8bqrwXS2t1Zx4DtHO9VgOu4KwkO7odXV333z9AxUxUbz9IxefX4dMbQEofsEogbTM7IcqGys0+JXesv7bCra4NSER6+XZcPGxdb2NeSTQ2qZYY/nkegoSmat81qDdZferiF1jtdWkjhCKy1RVlwNYGlnQzN/LTlgGFr+0mZiagmAd3f0vGn1bMU53oylz7cdlb9FhJMVEU6rovBO6U6je05WRLjTGOZx9OP1YzIbGglSVTIbGgGMjKzqpFt6FVC66qDRGbnVeYwIyWfhlGYWTmnutaGl1swSQ0sYUHhzN8/bVs+9PcebsczzNae0m+ORs4hxrtWgj1OVlGmcs7dyZ4f4pWMeK7c6zykzy5u282ULHiDvhwd7vfXQl4aWIPRnutJgfa2/XMfrqQYbN3yC05y60mCAMc4/k5canQ1Lm97yytACaEq/j/r7d1my9VAMLUHoSH/VYO04x6+9lTsN3WSOX3qZCH0cb+IX9N6U6s0aUse85TC0osXyQvBm/lpygMTxVX41tAAUVVW7PmqQ8aWUFPX5HdalKfcH9AKfNmxed63pDHddCO3vrzc61XTW4rm783WgopcYHTd8AuXnS5yu21lHxG177yK7pZxFjhgerKkj8nwhAKfiv8H5eY/0ao5WoBtaPTWydMyGlpUFAK+Zm3xIVdXZlg0o9Jqrrk5RX8waXPHr7oPt8cDbroGd4a4DjpU1DczzNccvvVzywtgMp7oMnXXk2XrwLrLVcr55MYiHyosAaIpI5sTSvxvH6BlZgE87GXaG1YZWadNbvd5uGDVsrsSvAEQ0mPUazEr95TpfKzTYTc1BPPx5cds4ChVfutVpnh07G+L3zExfGFqXq0J6ZWbNvmq8xLAAQzRY/9VgcWET+LypxOm6nekv7b1sMhsa+VlDC8GXGwCoSr6tzwrAd8bxWt90NtQ5WVbNR44CEsdXebVutVqDSaaWAFh/R89dmrqnFPKesCwohiBVZVlQDKnxNxivl58v4Zm07U7CadXkNR1e0/lNwSGOFJXwu5KjRJ4vNPIhAsXQmji2oteGVm7pcZ8YWoIQKFh5Nw/cp6lbWdNAmy9kNjRwI7HGlkJQsWHrIJxW29fw3JztbguQri86zJGiEh4qL0JBs8XCzmnm/PHaSnKr84yMLH2bob+x0tDSszSkfpYwkPC1BrNSf4F1Gmx9gRa/Hv68CAVV02CKzaOhlRQeZzz8iZWG1qdVlZYYWoIQKPR3DabzeVNJB63Vmf5abV/DkaIy1tXUEny5wVhDBpqhVXDiLAUnzvo0Q6u7hpYvkO6HAtD9zjmd3XkD9+2lK6ZkGncKdbpz99B87PqCwzyitqJSQsWQJCKCxvBGSzmq4mDzqQ1u5/RKzmretlWxyBFDyuTfAzAqbjmTy7azzj6TbLWclQ2N/Oxcq5Mzv7amztKuE96gG1q9Xbjllh4n/3S5GFrCgKa7XXM6u/MG7ltLVyVlGnFAp7t3DvXjE5Iy+UNRGYrailpTy9qIZFaNaCR/6FCjxpa7czfW5ZAVEU6qKZPrVNwyXrnwLlkRw8lsaGRtbR0/TpjK7oMZTIq4jscuXGDS7p2Wdi70Bt3I0rHK0JKC8MJAxNcazJ3+Aus0WBFhFKkXGK+EeDxfz8rKCB7L8tTnjXn9uTKHrBHhZDacY21tHRdGJhqfL10ZxW8L86iamsrQDP/FLzNWG1qy3VAYaPQHDWY+dvWsdfzhwNMoqKg1dZA4mzdUbQ25qWiD2zl50mBVSZlsrMvhlRHDA2YNaabgxFkAnzYFCwRDC2T7oVsGY+p7d3FNle9pavt1z16jLeyUIA5856hHobb51AbeLdlOZkMjD9Y1aALtxMvaZh0lCIAZE8bRqihu0/c3fPh7jnyRC4pCkKry7HXORQfvPngDDiBIVfm4+CzT7QnG5ztSWKwFPhQO33qsx9+ZN+jbhCaOreh1nRh/GFqy/TDwGIyp793FNVW+p2ntM7e0x6/DtxztMk19X0V7DKtKyiQmvy2GATPsCUb8ck3f189tBTAdo8eLzacfcI5fiQk4VAc2xcaR0+3xK+9HH/X2q/MKq7cagm8MLdl+GJiIBusaswZ7M3Ruj7cWWqXBdP0VpKo8vahjUefNpzawt2S7ocHMx+ifJUhVOVJUgqoEGRrMeA1onrHckrpY3SHQDS3Zfhh4iAbrmr7QYDvfvl4zns6dZ+mid5j5t6sN/YUphnVHg7V/nsBYQ7rib0Prtmlzu3WubD8UukVnrZB7yuZTG3DgABTjLqCR2n7ib15fz/7+elBbUVGMu4eeuvW8U7rTKMZXMSWTnPh7OBX/DRyKjbph40FtZWVDIzYVUiJSnToXflZcydGGvaAooKpkKGM7zEUv7reyoZF19plte6z1zhi68etbA/h4bSXnh7zXbwwtQfA1vW2D7Alzx0EwpbXn/83r6yUcao9f+p3Dzjr17K3c6VQEvmTWOqqSb9Pa2g+JaItfKskRc5y6neZW57GncgetioIC2FSMY8od5SSMiXSKXzXTVjCuzfTRnv0Tv3Q+raokcVhCwBtaguBrfKG/oKMGM28t9Paa+nEXRiaiKkHd1mBF89ZR8SUtfl0YmcjKthiUEdxRX+nnGxrM5Zjr45caxZVVYF3SzLbPBxlDRrZV2YKQj7f15OvqMYFuaAmCr/GFBttU1B6/9Ewsf2gw16Luuv5qikhuX0OC2y2Uun5TwO0xgbCGdMVfhtbp4bnMueZitw0tXyDbDwc4ZrFjRXFQwBA7NhTjTp6e2o7a6vX1xpzMarvL114/wd22Rf31vaU7aFXgP4aGsvbEfzO5bDtVSbdowRBYW9fAPVGL2Vj6Br9r2A0oLIy9gdX2NSzQU1nHLOVHNXXEbLnG6Y7APZHprG27S/D11g/aPp+WUsuBp8GQVRqudwN6W8BQN7RiIkdYZmhNPJ/GlCTfBTMhMGlqaXHqctKfmVGwBUV1MLpgC7sS77Fs3LNNJcbz8dpKhsct48qybSiqA0Vt9ep6Mwq2oAAORdGOra0kJSKVow17SYlI7fDfIHLIFdRcLmPU0HhqLzQxY0sKn8UtZ9eit7jjrUWsq3WwtraOR6LPs7lhP+NGJHC2sYyFE9JJsy9md3EOC+3prK2pIzrvVWqmqcZ2wq/HpbH22FZqpq0A4POGM6AonG0sA+NeZHv8eiHvGW28CencmXIvAHF7Hie6bYyebFP0RXYWiKEl9F98ob+gowarqK4zMrW8vaZ+3LAvCjnwnaPG695osEdGR7LWlJ0/5mQW69RW1tbWgXKWddzFG60VgEJq/A14cXDsAAAgAElEQVSsmrymfdyEpdxXXceYZ68xzLFVk9ewtrqO2OIt1I+cQHZLuZYNoSj8dMWT8NvFuMawJw9t5o3T+7hx4nx+MmsVYTlPEXIkm+bpGb3K5tKNLB0xtITBjLmOlVVb53TDyYbitIUvpqB9DenN9fS1n6rYjGPdbVvUuSJsAmVNxVwRNsFpzdZhDZn/N+6szMa8hkw1rSHX1tQRc3AjVTV1lq0hwdpC+AUnzvrUzIJ2Qyt54tiA6UAt2w/dkDjlKvVXz77Y19OwhDkn/psry7bxWdxyDn7pR5aM+VblJo427CVqyBXUXv6cayJS+Xrs6m5fr6tj9etcE5HKf+fvY2FMS5tTbuNoUQmK2sr6qEheiQhnZVstGVCYYY+nVdGChzlFVA8imQ0NrKupNdJVXTFSVBsauSdqMUCHQOOaOuuaAtsdrDS0Xj62ny/qzmuGlo8DGsj2w0Bk4tVT1Ee2PtfX07CEWR9uIDl/B/nJN3DoWu/rNXTFrtMvcbhiHwAzx8xnycTbu329ro7ddfolPq54lxljvsYfTrzDgkiHEb+OFJ3BpjpwKDZ+lpjCW44aI4bp2xB1bIqNTctfNYyozC/a41feDw92uG7KH+fwaGQEWRHhLBs6hn8LTexgVq3edrOxPXHT8leN8/QY5m7czuivhpZsPwxMBsr2Q6s7DuroWwTHDk/o0GnQ22t2dZx5G+La6jrGnPiboa1s2DjiQYMpwHRTDDOXg9DHNGsw3VDT/9ZvfunfeTRyJFkR4aw8d56fjp8H0MGwSs26x4hhezM3MuqJJSiqA1WxUX//rh59rwWNZZZ1NtTxtaEl2w8Dj4G0/dBKo0VHX4tdEZbQodNgT2tkuTvWbBw9duItvhLV3GX86qs1JHTcStkd9KwsHV+v/7IL8lGiD/Xa0LJag4mp5YaBFJCswp2rfOfBDHT3+YU5vf++XAOU+Y/+SGERj0ZFkhURzvwxy3jsxFuENeS3LwBVldsaGnmwto5HoqP4W0Q4ZpcdzEEEjhSV0TQikbBzhR0CYsKh9aZaNwootg7HWJWpZbWhVXgmhtm2JL8YWiCmViAydcY09aXdr/X1NAIO1+wk3dgBWGRfYmQs9QZztlNa44emulbt8WtB4lIePZpLaG0BF6OSmBNxydiWk1dUwiPRUWRFhDtlapnnq8cvPSvL1bCK2/M40Xn6Hcwgaqat6HCMlZlaVhtahRdKjJ99naElplZgMlBMLStxV+vqe7ntGuxPab3/vsxG1+KL+9v1V9sC8JG2GJYRPJb1+R8BqlsNti752g6ZWmCuA6bFsPqIeEY2lJCffAN5c9KwjxrF1R9sJeRINqgOkwZTOmRgWZmpZeU2QzP+yNASUyvwkDWke1zXTfqaDGChqfB6T+nPa0h38/cWf2wzNGOVoQVSU0voI9zvU/Zun7C3e7Jd27WaW8Q2RSTzYG0dH9SGsNq+hrCGAhRgZUMjqCq07ZNel3gtWRERLIzN4IU52ay2r2FT0QbuPriMK8IS2sbL4PAtRwk7V9ihPaweVJoiktsK0KtuW8i6tngtmbWOw7cc7ZGhdW1iQr80tAShP7G7OAeH6mB3cQ4ACyekO73nibg9j5PyxznE7Xm8y2tEH9uKorYSfWwrCyekY1NsLJyQzsWoJB6sreMfDUO5M+VeQmtPo4D23HZHUAEuRiVRk7ISFBtToqcaWVSrt93MuPA4bTz7EvJ+eJCyBQ84XU+fa/SxrVyMSnIytMzHANyZci+blr/qZOSVLXjAGNdbfGFoDVFOMimynEmR5bLlUBDacF/ryjsN5m2dLfPWxevjNf11ffxSKqZkoqLwYG0du8Lmsb7gMErbNW9qDnLWYMnXsr21itT4DMNouzd3GZtPbTCNmcHL39rOqIYSbKqDSfk7nAyt5ukZNM9YjqrY0DSYQzO6TPxk1ir2Zm7kJ7NWAdCUfh/19+8aVIaWIPQnXNeR5i2C7mpg6QyGNST0bB3Znw0tXyCm1gBA/4PbVLTBZ9cwBwedhbEZ2LCxMDaj03NdA40n1tlnMt2ewDr7TMD5j/7E0r9z+NZPOLH0721Ha4JqbW0dt547rxXoO3ee7VQ5Bc1NRRvYXZmNAwdlTcVOrnjTiETUtmfXuT45pFabS+K1qEqQUwtZnZ4UUDxeW8nx2kpyq/MMQ6sni7aCxjJyS4+TW3pcDC2h3/NC3jOs3nYzL+Q947NrmE0m0IydRfYlTq+5w50p5IlfTJrBdHsCv5g0w8k4+uzbW8j70SE++/aWtiPbF6Np9iUEqSq3NjQSWlfUwXzLLdqFQ3VQeq6kQ2aVXiTVnLWlqK2E1hXxk9TvkNb4Ib+YNMMwuMx0x6xzh68MLd3I0h+CEOhsPrXBMG58hdlk0kmN1zRYanznGsxsVnXGuqQ2DZY0k1WT1/BM2nZWTV5D0bx1HPjuMQ589xOtQPyUTKNCzMPlJc4arLXKyXzbW7pD02Ql23mnNJvpY77G/PFXMimynNbo8ahAa/R4ksLjCDmSbRhYj0RHMT1xPL+ePANVsdE83fkzhuU8xagnlhCW81RPvk5ADC1BAP+sIaHjOnK1fY2xjnRXA0tH1pDu8ZehlV2QbzwC2dACMbUGBJ11e+gterADOrjKrk6zp8BYlZTp8Y/azHaqaFUU3qCyywDbFJGsBZOIZO6JTOfj4rPcE5neIWga30nbNtvdldnGuGHnClHansG5k0ZWRDgOHGynyqNz7m2g1dGNrGGxR5k4tqJXhtaHhSUcPBrKPz+Moz5/CnckXCeGltBvcTVyrMJslrnLTnJ9zZ25VjNthVtTyB3bWqppVRRev1zZqUF3MSoJte35zpR7eTtiLg/WNVAzbUUH881cIuDtol3GuNHHtmplRxWbkV11MdKujRtpN77TbS3VbjOwumPWueIrQystfqoYWUK/w1PHwN5iNsvMJpOO62uezLWKKZlOHQ49sb21TYO1VnZq0hXNW8eFUZoGuzAyke/Gahrsu7Hpbsy39vjlAA5X7DOM66CaMyhAUM0ZACeT643T+3CoDrZernObgWU2wHqCGFqCoOGPNeSmog1us5PMr/X3NSS0G11ZI6xfQ5rxp6GlRB9i0rVlTLq2jEUzpwSsoQViag0I3GVRWUV3gp2nY71NqdQ/B6hdXtMcTMzjr62p40hRCWtr6kxjQvKly0ZQ2lexnYRD6zsESr0DBoqWXtrVd+rOpfdEbnUeI0Lyja2GPV28FTSW8fbhkxSeieGOhOvISEomIym52+MIQiDhauRYRXfNMnfHd2dbnrdbGkPrirTth3VFTtcAeHLvs+SGX2sYbd8YOkaLXW3xa0/hTuL2PO7WbDOP29V3ajbAuoPVhlZp01uGoSUI/RF3WVRW0F2zzNPxRfPWceA7R7ssVq9/Dl2DdXbdYV9oGmzYF4VO499XXsLHRWe4r7yEwgslzBwz32mhoagqV3+gGenN0zOcsrDMJteNE+djU2zcOHG+2+s3T8/Q6tWojm5na4mhJQjtyBrSmjWkedzMc42WriHN+MvQ+mvJAUYlnzSMrP5w01FMrQGAO/fbKroT7HobGFfb1/BW0FxubWjEBlwRluDRbXcNJrrDv7Eux8n51r6bHTwzLJVbGxoJUlUyGxqNdrF6INtUtIHp9jjWR0dRlZTp1XfqzqV3h9nQ6k1A0A0ttWYWdyRc1+NxBCHQcJdFZQXdNct6a66trakz4te48DiPWypdDSk9Q+zpstwO2VOZS59hT8Rcp/gVfWyrk9mmn2/eatjVd+pqrHmDLwwt+6hRYmgJ/Rp3WVRW0F2zrLfm2qrJa3gztF2DjR2e4DFjy5z9pWeI/c8nvyU5f4dRJ2tSZDn3zVrIszf8yohftzY0GtlV5jpYTx7azHR7POujo2ientGhZpYrTen3gaKgQLeytaw2tD6tqjQel6tCxNAS+h2yhrRmDXn3wWWss89EVYK4JzLdsjWkGX8aWonjq3q9bvU30v3QDdK5ou8wtzSdbk/o0PIU3HeIcO1K4a57xJd23kRYQz4AVcm3Ob3vrr1qV3TWqSK3Os/42QpDK7f0OPmny1FrZgVUZpZ0Pww8pPth35Hyxznt8Ssxweh+qBd8B/ddBt11NnTNDLvyxVsIrS0AoCYl0+l943yXa3VGd7sd+srQ6kvBJN0PAxPpfth3XPesew32TFq7LrK/v57Yk1s4nfxljsxZya8/+AMqKjZFIWdYErHH93boQjji2XsIqi4CoHnG8g7bCVOz7jFi2N7MjV7N1duOh7qRBdaaWQCXq0KM1/rCzJLuh4GHrCH7joGyhnSHPwytk2XVfOQo8JuhZbUGC7ZqIGHg4a7lqK9ZZ59JtlpOhjKW1NjZxvX/tL+UnM9qSb8yiv85074PWQ8EqbFLjWMPz3Geqx44jBbRShAls9Y5BRTz+a54Cjwls9a5DUS51XlMHFuBfdQofYQBaWgJQiDzQt4z7C7OcSqu7mtqpq3g6bJcsiLCGRcex9nGMhZOSOfpnArePFLP4umj+H8n22tZ6WbSwgnpxlzzbuw417g9jxNaW2DEL/083ZhaPmkG21qqPWaYuTOwyhY84HWnQysNLdeC8IIguGfzqQ28U7qT6+OXWp4F5ol1STPJbinn67ZopsdO4+OKdxmpfplvbcjjuslD+cZXhjPn5BZsqoOk/H8QveJhjial8sbpfdw4cT5DZ62iPsM5roTlPEVQdVFb/LIZBpTZlLpx4nxjDFc8mVdN6fd12e3QF1sNZZuhIHTNQFlDgrYODGvI79EaUj/fdR3paQ1pRjeydAaSoeULJFPLDeKya/TEebb6mnpQvHwxBltIJS111/FOjK1b7rbh3BuvKFQl32oU6VOVIA7fcrTr87s47nhtJeeHvEdM5AjLttMEuqElmVqBh2RqafQke8nq6+pm1eWm9vj13gS1WxlSYMoAA0ChJmUlZQsecMoM02tydXp+F8e5wwpDq/BCifFzIBlakqkVmEimlsa9ucvcZkr5kntyl6HiwKYoPLv0l7z4yXZyiz/C0RyLLaSStAmzebCmzm02lidGPbEERXVoReBH2wmqOUPz9Ayj2Luq2Ki/f1fX53dxnCuDwdCSTK3AQ9aQGgNlDQmu68jurSGdzvfiWB1/bTUEZ0PrtmlzfX49HcnUEvxGV86zP66pFw4MCqkABYZEHqRk1navAxFoe6fvbdpL/tChJF+6xGtl5cQUZNE0IpGwhvwORfpcHfV9w5fy1XM7eC98KSM8XGMwGlqCEMiYs5/66rp64fmg0AoAhkQdpGzBq16bWTq/mDSDNy5VoAK3NTTyYFuW18VIO6G1BU7F3t1lZe0buYSv1u3kvVFLiPTierqRBb3PzjJnZmkEhqElCIGE2fjVmT7ma3xc8S7Tx3zN7fu+YMH4WewtOcSNE+eTFB7H3pJDKIqKLaQCRYG9JYf4ZebGDtlYndE8PYNvVX7YpsEu8lpb18LW6PEEVRfRGj3e6XjXzKx/RKYzpyaHg1HpfKmLa5m3GsLANrQEIZAZKGtIgBvtyRSpF0i+dJnXznZvDfmn/aV85fJCVgXnUtNFB0edghNn/dbRvq8MLV8gppbgkdX2NT5PGXVNT9Ufm4o2cOfBDLR20Apxw8bzeVMJqWOcg6M5eDwSHek21bVk1jryD34AQP7QoUZxwI11ObxiT2DluVruMY2zsS6HVyaMY2VdDktZx901t/NwUDOrzu2g9lC4EQyP11ZS7igHtLpZVhhaLx/bb/z8Rd15Jp5PY0qSfwKbIAwk7ky51+fbDt1tcdSv+0LeMzhUBwDDhwynqaXJrcGmm1C/MG0hdJ33tpZqVEUBICsinHvjF/FC3jPsibhEJpE8WHualD/OMbY/vjJhHCvLclmOtvC8u2IVDwddYlXdTur3DPNoqlldN0u2GgpC13Q0fjUmzVoILGz7rdzy6774yXb2lnxEasJsvn31MgCWJNwLc+HJQ5uZv+W7bQoMEkfGUXzu8w7bA80G1CPRUcYWQnOB96b0+8jf8l1A12Bax8Pfn3lf02ANX7D2iSWGifX7M+/zyoQ4Vp55nzXcx7c/X81DQa2sqsmhJWeIx+wwX3U1BDG0BKG7DJQ1JEARTaAo5Id0fw2Z81ktXw4ymid2ij+zs0AztE4Pz2XOxLGkxfdvQwvE1BL6GN1F31exnbU1dYZhpLVi1SKADYVHpv2P03mbijawuzIbRVW5NTKCBwuy2NuaYLRxdQ1IcWETKGsqJi5sAodv2QFA1sEPcKAtEtcWtO+xzrLHGa8vBdKvjGJVUS7BisPYg61nZk2MHNEmRHu///jlY/sNIwsgGv8FNkEQuo+eibWncCdra+qczKLdxTnGz00tTR22QD6w54eUnivRskfVVrZfqsChKOwuzulgai2ckM7bRW8CKgsSl1KWci+7t92MQ1HIigjnwdo6o06XOX4tbzt/8fRRrPpUi2HmWl5mxNASAoVmxyW/ZSYFApMiy0kK938H0L0lh3CoKnvPfMgf3nnNaTvhG6f3GSUbFMXGX5b8yuncJw9t5u8Fe9o02EgePJLNG4njcagO3ji9r0PXwsSIOAobykiMiKP+/j8DkLXlKA7glYhw1tXWEXIkm6b0+8iKCDdi2Brg5lmhrDqmxa+gtmPAt1lZZsTQEoTApKdrSIC1x35AWUsRyVfEsNXPa0h3+NvQyi7IR4k+RPLEsQOmA7WYWkKfkhq7lH0V27UWqXXORft2V+4AVLepq1rAArVtUfe9qMWkmlx2Vx6Z9j+aI38ii6pL6ymZtY7U2Az2Vu5kGTGgnkEFmkYkkhr7dafigrtO1fJScBqrgnM5GreQh/fmcfyMSnqKncdvGmvJ9/Dysf0Unolhtm2uGFmC0E9YOCGdPYU7yWxoJLrY2SwyG1HuMrRKz2mLdj17dNnQMR6Lvd+Zci9ra+q0bYUj6iijfZvjsiGjgRJU4GKknYX2NCN7TC9QHx89lJdatRj27sgl3P3EKRZPH8X308cAYmgJgUVocAuTIq3PTApU+upvRC/OnvlFA0rblkDdMLpx4nxeL9iD2vazK2+c3ge0a7B/n/BVbjRlarnylyW/as/qsj1FU/p93Ji0gDcK9rCyoVFbfqoOwnKe0l5vG+ex7Ea2fHSRq9s02OXpGTyW3cgrh5r4ekoQ/7rEN4sx8xZsMbQEITDp6RoSoKypWMu+GjpEK/buhzVkTVKmU9H6hSNtTtcRQ6t3SKF4N0iRP/+y9eBdRreKFXOe9+occ6bWci/P2/n29bwyYjgrz51n6aJ3jNf1An6g+fqHb/3EeG/lpjx+GfQ8Z2IPkRURzoIJ17ItZwUOVSFIgY8e8hyAHstu5NVDF7l5Vig/zwh3es98h/HDwpI2Qyup3xlaUig+8JBC8f4la+e9bL9UwbKhY8hc+ozX5/1i2+0UOi6QaBvGb5a/1OXx2/76dSN+Lb/jLeN1vQg8aPGrJiXTMNe++cQpHjbFr0t1c7lUeRMOFWwKvHb/5E4Nref2lvL28VoWTY3i7tT4TucXqMXgO0MKxQcmM2Z+Sd39/gt9PY1Bwx///jNea67mmyGj+eFNv/XqHHOm1s1enrfhz7cZMWzNd18GnIvIK2gxrP5n7Vmus39dzUMeNJgewzxh7jqrG/jeYM7M0glUQ0sKxQcesob0Lz1ZQwL88uDNFKkXsCvD+OWcrpsJ9WQNmbkpz0mDLRiTwbZ3vqZpMODxOaM9rvuePlLOrqJ6lthH8f3p1iRQQGAZWlZrMFvXhwiDkYRD65m55RoSDq13+7srm4o2cPfBZWwq2tDta22nglZFYTsVHsd0HX+1fQ15RWXkFZWwvuiwx7HN52VFhNOqKGyJCHcaqyop06kzovHT+z8mP+QOvh30Fq9GDEdVILf4IxJHBxOkaCnxnfHqoYu0qtqzmYLGMj4sLGH3yRB2nwzpt4aWIAQqcXseJ+WPc4jb83inr+m8kPcMq7fdzAt53ptSOttaqrX4danCaWzXMV1/f70wn2NFJbxemO9xbPM55vhlHqdm2gpUFGNRGH1sq/F5/xlyB98OetuIX8GRB4iPHoqiwJzJQ7vM0Hr7eC0OVXvuDD0za1JkOZMiy/uFoSUIgUxYzlOMemIJYTlPuf3dzJOHNpOadQ9PHtrco2ttvVRDq6Kw9VKNx3Fdr/GTWavIKyolr6iEhz7z3M3LfJ45humvNU/PQFXMS5F2DRaW8xSfucSw3OKPiI8OwaZo26o7480j9ThU7dlbXLca6g9BELzHv2vIKloVhWy13Gn8ztaQAG8UaRrsjSLPGqw3a8iEQ+s7aLDcih3EhAZhA66LDe103berSItfu4q8j19dEUiGli8QU0twS4xpf7C7313R9zXr2wK7Q2ZDI0GqSmZDo8cx3Y1flZRpFOzzhPm81NgMbNhQwWmsklnrOBX/DSMoDX9/LbnVeUwve5sgHCgKrDx3vm17tkpF9H+wOuV3/Pb4SrcCU+fmWaEdzK+CxjLePnySwjMx2KtGY68azR0J14mhJQgWEn1sq1FjqrPXdPTaWOY6WN6ycEK6Eb/MY7uO6fp7zbQVqEoQNdNWeBzbfM5C+xJsSlv8Mo1TtuAB8n70ETUpmcYWHr34vBa/VFaeO4+igtoaSu3on2Cf8Uf+EPYKt/3vMhZ8/BeP1180NQqboj17Qje00uKnkhQeZzwEQeg5IUeyjS2B7n4388bpfUYtq57gSYOZx3V3Dd2Qap6e4XFs83k3Ji1wimFvnN5HU/p91N+/i+YZyw0NpuuqkCPZTjFM12C1o3/C7dOe5P+dXO72JoXO4umjvDK/dKR2liBYgz/XkKmxS434ZR7fn2vIquTbjPilG2sxBVluNdj5Cf/B1VN+xUvnMhl3/DGP115i1+LXErt38csTJ8uqOVlWbRhai2ZOGZCGFoipJXjA9Y+9qz/+1Nil2LB12rrVk1N/T2Q6Hxef5Z5I51oy5jHdjV8yax2HbznqVHTP9Rrm81bb1/DcnO0sjM0A1UZz7Rz+tL+U3Oo8PpmfiqrYUFCZXPo6K85soGrqAk2wzVjOmu++jKLYUBRQFHitudqjwNT5eUY4Hz002th6qBtaas0sw8gSM0sQrMedYdSZibRwQjo2xea2npUZd9led6bcy9sRc3mwrsFpbNcxXX8vW/AAeT882KFou/ka5nPuTLmXTctfZVGbuRVr+xrffOIUT+dUGOOhBKGgEp2XxcVIu/Z5UzJZfsdbzAt7GiWoCUWB6qazjDmpicwxJ92LTIC7U+N5aU2Kx62HpU1vGYaWIAjW4WoYdWYg3ThxPjbF5raWlRlP2V4/HT+Pj4vL+On4eR7HdXcN3ZAydyN0vYb5vJ/MWsXezI3clLQABRvNNXN4LLvRGIs2DRby8TYuZT9O5dRUpxiGSYNtv1Th8SaFzvfTx/Da/ZO92noohpYgWIc/15Cr7WvICZ7Hg3UNTuP7aw2pj6Xrr5j8l0k4tJ78yBtwYCM/ajlXxr3MV5vbNVghF7T4VdJJ/Jo+lr/fNKVXWw//WnKAophqimKqGZV8kkUzpwzom45SU8sNiVOuUn/17It9PY2Ap7v/8Ov7jlUliMO3eE5X7w0z/zYNBZX1UZFkjRxJrHo9+aeWcO2EMJZNG9l+4M7HuD0ol82tabw56VY23DJeK2L68TatroNio/7+XU5jGzUkgJuHRvPQZ0eNbkHmttZmgafXziqqryf/dDlqzSwykpJ98tn7AqmpFXhITS3fodevUpUg8n540PLx4/Y8TnReFo9GRZIVEU5McCoFx5d2qAkTt+dxRh19lc2taTzcchev/2yy0/laDHOe46dVlWw88iuqm84ybvgE/tIax5iTWVRMyaRo3jrs7693+t0d/bFuVmdITa3ARGpq+QajfpUbfWPZNX672NBgW0aO5FLtHG5MuK1DXdHtj/yOb7VpsA+mfpvvLWolYd+LxH6y29BgeT/80OmcF/Ke4e2iXYDCN4bE8Jt/fkzNtBWULXjAyE7Vf+8On1ZVcrkqBAjc2lmekJpagYfU1PINfbWGLDi1hPQro/je3Pabe8c3/9hYQ/4j6d/53tx4rZB8/ssogAMbr6Ts6pC48LPTP6T00hkS1TBeL86nJmEFZ6f+nHHHHyO6ZKvxuxX8teQAieOruDaxvbxEoOk1qzWYdD90gxLsYEhMc19PI+DJrcgjbbT3LZSrkjKJKcjqNNWzu2wq2sDeymwyGxrbMr00k/aViHAcOPicfajqEjJKN3D757vZHTGfhhtv5JvBuQThYFVQLr8+eReAYUaFfLwNVJWwnKecDKrm8m9w7sRiFOCdmCCSL7Zy8+VQfo7z1gD9nNzS4+SfLqf2nB0IJfJSu6HlqwKAgiD4jpppK4yFkxW8kPcMu4tzWB48mt/882NQHShg1G74vOUdHOpS5h77L6Z+mst7kUuJ/Jdfa1spFS1+/bLlLmM8fTEXnZeldRLb8TCHrtVaU7/+wXkKT/4QBTgfFcJX6ppZNPVO7p6nCTVz5pY7U8vc0fBPbwfxVl4sK2eF8XPPO48EQQggmqdnGDffrOLJQ5t5o2APmQ2NbZle7RpMxUFw5AFePXQTN53dyJyaHA5Gp/Ol7/2E200a7Fd5d/KvS6ZSnvY7gmyPt8Uvlbg9jxsx7emcCnZ+nIpCKgmjh/JSzSVqpo/i+ws0s9+8vbwrU+vTqkpe/+A8B05d4rrJQ7lhUlS/M7MEYbDhuzWk1sFQq8/ccQ3pUJfw5YL/5JqiXN4bcQMjMh5nlTl+nbqLhSNtFAy7mxlR50mu3YaCysL6P3E2rt2gevpIOScK/xUFqB8xlKSLl1hyeRTfB6JLthqZW96YWp2tIU+WVfORo8AwtALNyPIlYmq5IWzIEK6KkX/gvCG3Is+pQ0xnHE+8h6mzOi6W9KCip3d6PL+2ssNreyp3ogKvjBjOgwVbeCQqklciwkm8dJmCkFAiWqdzQQjUPa0AACAASURBVFFZFbSbYMXBgSFHyfqgkDcir+b5uk/439Y0p5pXTen3uTWooL3guwoUVLUar/08I9wQi5VTUylpLHPKzLrDTWaWuQCgmFqC0D8oW/BAhwWTbkzpWwS7g14za/ulCtarrajA+qhIWgFFVRkbPJ8CBVYF5RKsOHjX9g9e2XYz88ZO449n89jcmsaSGc71FsoWPGAs8JLzd1A7X9sqefBUHqDFr9Ja7abN28drja2FFVMyjUwtHU+ZWW/nVeNQ2+OfIAiBT1P6fU6aRufJQ5u1mldtWwS7wxun9+FA02Brj2Q7abD8kBBa6q5jUUoLc07mEKw4yOUg9275HtMjp/JC3XFeal3I4umRxnjm+GU2qPRi7ypwpvoSADs/rjcyWL294aBvMzxwClQVDpy6xH9cJ3pfEAKdklnrnLYK6ni7hnSHXjMrWy3nEbWV9ab4dToklFiud9ZgQz/glYPLmDcmhT+WaxrMXPC9Ke5XsGuHW4NKL/iuAmfOXTJe+/70sdQkrDAytbzBdQ15sqzaeG+wGlogNbWEXnBVTCwJYyIZEtPs8TG36EnueHsRc4uepNxR3sGY+tP+UnIrdnRZIDC3Oo/zQ95jWOxRduWf5pfbP+fZ/P+LigPQCrmfTv4yWSNH0KoonA4ZykNf+RH/feM3OPRQDAej02lRbcbdw8Mjv+ClljTuGJLLr4doLWAfy25k9q+r+UdkOqpiozV6vFNtCHfdDvXXmtLv49Xb/5PnR1zLln0XOXg0tNOthlYVABQEwXd01jERtOyBtwrf7HaR+adzKvjmE6cIUTVDe7xtmFE7JmvkCFAUFEXh9xn/xmv3T+a9yKVG/HKoDt4JqSO5+a8oYBRLfjqngpueOMVjrxfyz+SlqEoQTSMnct2z12B/f73bYu/m14rmrePAd44aWVqddTR01wRDEITAo7Ouibrmeb2ge4Xm9fPu2PoCqtquwZqnZzhpsL/euJW/3fkz/nXJVKcYBiofj2xgc0sa3x6yh9+0aTA9Lu4buQRVCeJipN2Iv3qxd8U0D/PPnmoUgmZk6Q+9btbiK7UmGIuv9NwEQxCEvqWrroneriFdz8nclMef9pdyRZi2NS9B0TRYVkR7/HpuznYev+5+slan8N6IG9o1GA7eCWvXYHrB96ePlHPT30/yTlhb/BpuZ9qua41i8O7We/prZ6f+nGNLPvR666F5DalnZtXE76cmfj+J46u4bdrcQWdogWRquUVVm7jcktfX0+gXTIrs4v38HSiqg0n5O5g4J43T5VBeXW5kd735WS1fHTuSYyPrWOSIcpuNVe4oZ0RIvuE6/+ykliVQox5CUcCm2Fjz3ZcBuNF0x9FcvHjmhCEE1cHKy/DqEJWUL0Zxe3AuiupgyMfZPHT5LrZ8pGVi5Ve2MicIbNVFKOCUsRWkgH10EIXVLcyd0sScayrILYWqunN8UXeeiefTuCGh6+Lv358+VjK0BCHA6WpLy5tH6pnXFr+WDfG+6YPeav6C+jmKAsU0G/WvFpoyv3Qi/+XX1O8ZRmZZLlkjwlnZcI4Jwc9ze5AWw6KOvcrOpm8CcEP+MyQF5/JiSxqr6nNRcGjF4JPuxKbAuMgQztY1s2hqlJGlZc7I0umsZtbPM8IlQ0sQ+gGeMs8LGst45dBQHKrCNfUjODaynozgcKMOaGfo5xVffr9Ngyksue0/+QRI/WQoe0s+YuGExU7nXD1+GEFfKKy4pPDaUAfTvhjFqjYNFpn3Kr+4fBc7P67nV8HP89W6XF5sTWNVrRa/oo9thSl3OXUyfPNIvVddDc1GFmAUgp86F6caOYIgBB7mronusrRyPqs1NFiGEuPVmDmf1eJQtecRUzTtc4ZmDt9ylFRT1peZuKEKNgVWNCm8FubgK01R7ARDg0WeeZUdFzUNVtxwidYglZDGAhRwytiyKRAfPpTSxku9Kj+jryFPllVzenguiZHDuW3a3B6NNZAQU8sNIbYhg9Lh9AXmGg5p8VOxj9K25oHWsevLU0bw/OlPCK5z4FDK2Pq1jsX/ThTs5nBhHmcvpfKTWau4eVYorx66yIQh8yht/YAbJ87nsexGXj10EfvoG2isXkzzMOcMAl3YrSs9wy8UUJUy/tqSxreCcvnf1jRjayFoQeq30SPJighnZUMjrTF2tmbdQ3PNHFrVmzhd3cLE0Zf4x4lh1FcM1+ZYO4anR2wiveX31NRbV+hPEIS+o6stLYunj+KpT7X4pSpnyfPQuMd1i+Li6aN480g9VwRfT6XjXaOTobZIu4lzJ1K5GDIKTCULI/NeZR0O1tbUogAtbUVKVwXlcnrSDXBMO+72oFwejxpJVsRJ8hriGKWcJysinOaq53CoNxmG1tvHawFYMEdl2z/K2H8yjGfHPEfqF3u0bdTzvy3/DgpCP8ddHS3duFo8PZI3j9TzQt1xgvQYdkPHOqkd41eFU/xaOCGdZ3eP4c0j9cRHf4tzNTd3iF/6DYKHyop5WAFVOcuLLWncHpTLS61pxvZCfZvPmdiPmBkRx8TLlzk9dCjNZ1/Aod7Em0fqee1+rTGGfo7+83NjNjP/i138M3mpUUtQOhoKQv+lqzpa6VdG8X+L2jXY4Tkdj3Hdnph+ZRQ5n9WSfmUUIbFL2VO5k1FNXyHzL3nEhKVyrulrVNaEUtB01hhjZW02Nhw8VN4ev5IUDA32UmuacazrGvLiiCS2nVxB84U5ONSbDENL344I2jbC5yM3c33TLq+LxeuGVvLEsdKBug3pfugG6bzjH/SOga3R4wmqOdOhcyBoae47Gn+MoqjYFBt7Mze6HWv2r6tpNf2vHKTARw+1Z06E5TxF8OFs8tVxJCtnaZmZ4ZSdBVoqe+bsUG46u5F/jThOq6IQpKo4FBsqKqBw7sSjpqM11x3AoUJ+yB0EKw5aVBs/HLd9UGRiSffDwEO6H/oHvdvWxUg7oXVFHrtuPZ1TwbtNPzBi2Kblr3Y45ptPnMKhOscTm4KxeAM4+p8PcHtQLvnqOK4MOstb4V/n3qp/QQHiokIorW1GAZ6LfYkfRx014peqBOHAAdhoPPkosSNtVNRrW4YUBX53dwX3PxeLQ1WMGNaKjYaf+aY7WiAh3Q8Dk6umJ6ub3nqir6cxoLG/u8PJsPfUOdCb+AXtMUzHNX7pHVt1DVZ/zc1GdpaOAjw/djPz67OZYU+gVTFvMLRx/uSjxEcPpbTmknEtTxrs9iteNTpeD2RDS7ofBh7S/dA/JBxaT0xBFk0jEgk7V0hVUmaHbK4/7S/lPeVeLX5h47k52433Ck5optWUuNHc9PeTHeLX32+aYvw+7vhjjCo2xa8JN/PQ5bvYUegcv5YmjuLWLzbwo9i8jhpM1TSY2XXp7hoyuyC//XrRh/q9oSXdD4UBg549FVRzxmN76VcPXSQ49jqGRB4gPvgrzP51NTfPCu2w9UXP3rKPDqKoupWbZ4Ua2Vva8ffx2OW72n9PD+fnbeO3uoijb3++msUhj/FBSD1fvRTBR61TaQw7QHjTdTSiOAUkfT/0rqJ63h++lHnnd7K5Nc0IdIPB2BKEwYieeRBaV2RsHXTHm0fqGdIWw5pr5/B0ToVR3FhHz9wyb62Jjx7KN584xZzJQ/nGV4azI/leHj51F9e1/Z44LAHbhjwcanvhdxX4TtXtLBlWygehNWQEj+VA65coV/cRxZd5uM3A0uSXSnyUin3UKFbOCuPVQxeNu46bW9M4nt34/9u79zipqjvv99/V3XSDNtrcBLVRBCIoSkA6QpIngRHDRYxgFM8zkpiQJ0QmJnMS50wSZjIanZmQzDwTcyaXISETDQ5mIl7AExCJ8OhMNEhACcYICoLSGi4ttILKrXudP6rXrr2rd127qnftrs/79eLV3VW7dq3eXf781a/W+i2WGCISxvRRr5rcd1ZG/gY8/zlvaXW6XlRSMH6dVZ2cUZouhrmi0/RxDVqybr8X1xZO+7r+7uT85M9/NlgLlVyKLSWK7L88+xa91nJC1729RQ+cWa86naN37Z90ds1H9L+/OqpT8Wz6uAYdfu9dPbPjhNaf8TFNffvXWt42VZv2vKf+dX1YYgiUEVdIKobxO++XUbt6v/2KVozteA+Zcv51Ow6p1+BE/Go4lpiNNfGs3rp2WCK3cQ3e3cwp/9LA4A6Di3TbyfnJn8cM0UIlG7ZLifglSfMPz9OMvq/r6T5v6mo7WJvaLtIb1f+lc9o+op0msUGF01hfq0sGnpbTe8jVu3Z6hayEeBe0SoGZWiGYqdU93EytsBlajr8w5QpQqbOw0nGzt9zx65tf8O576Om+2ri9jwadeUr7W2tUN3iVavttlJV08vAkndg/W3Ob3tYnh070KviuKZ8LNqmVfCmxzWqm+895YbG3w0VPWKLITK3yw0yt7uFmaqWboeW4N3b+mQX+GQzpuDdvxki/uCX4Bv9nTzTr8RcO6Zx+dXr98HE1DF2lk6dtVPvxs1RVd0AnD0/UN2fNlyT9zd2HZa1UZay23DZIi1cf9WaopsbSTPdJucXsOGGmVnkihpVevvHLFa3CZpGm45+Bmnq8O2/jgFrtr75fvfo9o+pTg9VWs18nD0/UyQNz9LCviOXOsWTdfm92lzHSt+b3C/TM+tXzb2nTnvckJR6z4qZk7HQzO8JmdMQVM7XKz4iRF9nF/3RP1MMoS66IVAy5vJ/yF6ZcASrsvVkY/3u/sPd6rgi298gJ1Q5eGXgPeXz/HD1y7ehO5/GPQ+p87nTvIV1B6/qW32jEzt+Sg6XBTC1EJmx7abe19Pl9z9arR/6ka4ZP1ubbkltMuwKXs3j1Ua3YfExW0g1NyRlci1cf1W3Vd2te9XptGjBN65una+cr+2TfnCBJmvHyUi2rXa/lR6fql/0/q+b+mzoWGCoxo2L/HB1983xpaDII+Zv6uZ9TZbt/wN6HQrd6BRAvr//Z10PfDN6z7cd6fM9jkqyuHDZDC6fdrIXTBgfeHPotXrVbG7cntneeNDoxC2vV0+/o9o749d9nXqVAcxpJ/2P7v+hHteu1/O2pemz0/6UXzEYZa1VVt1/GJGLY3949Wx8b26ZpY6Vfb6vW9RP6SJIXI1Njabb7pPRNpwHES6b4teHVdTqn/ly9cfR1XXH+ND381Zu9+1Nj2JJ1+7X2uVZZSTPHN3ix7oPP36WX69Zr+amp+u2lX+n0PB98/i59v3a97mudqn+58GW1W6u2mn1e/Dq+f46WrNvfaRbrwmmDvZlZHzi/j04erAv0zBoz+SwtrWv2eub4ZWs6DRRD7141RS3eINwbYxZ1eh91974fa0PrYzqntlFvnGjWFUOma+W4ZPxKfW+2ZOs+Pbo7Eb+uuiD5Hm/J1n1eDvbU6TMl/X3geSbtvUv/Wrtey9+bqmcu+Iqe6r1J7Qq+h1yydZ8WjhvS6T3kwnFDAsU2v7D3kK6gdeVlozXiR/9MDpYBRS14dh11Tdy7x7hND2j4zt/qlZEf1NbLr5ckrdr1hKysdr/9uvfz+weP82ZW+XcclKQHtpwl29Hf6oEt76n5nUOa8fJ/6lvVG1RV3a4qI006vE7/9Mr7Zd+coFkjRkqSxry0XtVq17zq9brj8HzNHjVdjx9+tKPKPlGStGZ3qxeA/FNA/UHH/7OklOmqnZcevjn0E94nCwDiLTHb4UGvsbokbXg1UdBy38+7+INa+ni1fr2tWh8b26b/dcV+nTy13zvHph21cj36Nm4/oat2/lj/Ub3ei1+Tj6zRL9+9JfC882p88Wv7ZzRv1hQ98sqTOs2cpSPtiZkO7dbosd/X6LnbB+rbc4Lj9hev/D8Hl2x3XnoY1nQaQDyFzdba8Oo6tdt2NR/Z6/38mbE3pywlTC49fGxrq9eSwTVun/T8XfpU9a9lJH2q1wa9f9q3Oz33jR0N4W+sXq/nzv+cNry6TnUaonftn7wc7NHnWrX4s/300fGJbbb/eDCxO/ZV7+uvBntC61461GmJ4dKNyYJW6tLDbE2nAcRH2EytDa2PqV3taj7xmvfz/CE3p31vtnZPMn6593ST9t6lf/XlYB99b62eTylqBXKwPfM1e9J0Pd66VrI263vITNw4R/czGtr3qP5j7zPqP2BPoqBVfy45WBYUtSApUdD63e692v3aIPU7MaBo5/3v5ja9eMjqov5GH2msDtz3iZd/qyq1a/jLv9UK839LkkaaD2qn3agzNEhv66BGmkl6+Xfn6rcvnpKV9NsXT9Olvc7wzjG6X5v+eMh2fF+l3754mpbVbVCNaVe7NWqT0dYzrtTwd6Zq9IjkJye/OS25drmxvlarNk7WjGGzJUlr9gcLe2HB0E0fXbuntVOA9N+e+tiwTxYAlK90b+ZOntqmAc8/KGPbddYLT6h2VuJN4TXDp2jVrv8j2/H9iPpz9fi2FrVb6fFtNfr2nGByc/2Eo1qx+T0vsXJv9tqt1KYqtYyZovf12xd4TMslUzTwD09oedsVumBgjY7vm62jL07XwIHVOtDSFtg0I12hyi3nfnDLsUCRy39b6mPDZtcCKF/p4peU7As44PmHvKLWFedP6zRTS0r2vnpsa2vgPNPHNXgztdysqu/XrpcxidJ+up1jH+n1MV1z8td6pNfHdGxfYsfXD3X0x9q4/4R33MmDdfrV82/pd6++pw+c30dXX3qmxvQ/S998KdFPcN1LhwLFq3UvHfJudz+7AtfeCd9ghhYQI5kmCoStfLmiYXpwplbDdEnp37PNGNbgzdRyM6r+tXZ94D3k4ZBJCKV+D/ni4XZ99tp9eujpvnpgy1gdOtJHi2aFr3BCEj21Qpx/0Xn26z//q6iH0e12vzZInxw6sajnzLQmOZ/+UtlmQPmPm7T3Ls2rWa/D513X6bzuPNYmEq4qo047Xrif76i522uafPup+YH10K6ZoL+poCRvLfR5fWv1gyuH65qHt3vnduurc/1d4oCeWuWHncOK64bv1qrdGlUZq/tvPRG475KnH8qpx1S2GVD+4y7d+m+6sWa9To4P3w02tcdgJv4YdmfbfG2+baB3jmEDq7XrYJu36+uiWfWa/J0WvX1MOqO39OTXBmr8HS3euZ67fWBev0sc0FOrPNFTq3gy9bXKta+WlLk4lnrcB5/vyMHGXqfX/+zr3gwrSVr19Dt6ZscJpXvrYXyNlMNysGkX9te6lw7p3DPr9Ppbx72vbqnh2h2JYtbQhsTtLp+bMSpR2Mo0kyuO6KlVfsZcdKn9xT0rox5GjxC395CJLXiSft5/uVf8uqNtfvA95JETOrNOaj0uXdQ/MVv/j4cSO1MPHWD1yBfPIgfLU48vahljfi5ppqQD1tpLcnlMpTb5K8Ua8HIr4MxZud1bJ728bar+vc/Neu1I8o3qeX1rvZ/926teeOI/QhsNpm4D66Q2lTeSVoU0DcylWWE5o6hVWoXELza6KK5ySiCa7mzxegX+qvZKffnIZ0KP61UtnWwLxrC/ufQBLZpVH9hAQ5LabOdETEokUGEJVeoGHHFGUau0ColfEkWtYsq1GFUqfzx4INDI/fZf7dM3q4PFKr+z+lbrwJE2SZ1zMFfQcvnTipvGau6ybWlzsHPPrNPe1uPez/7jU5vIxxVFrdIqJIZR1Cqecn4PeV/bVN2WEr9S+WPYX57zq+R7SEnXN72lFVvOkLX+DCyRmFUb6boJvb2Ne4ykZ8nBsqqE5Yc/k/T/SlqW6wNo8lc8+awl7urOgNmC35Kt+9RupXkdy3vmVa/X7Ufmq75XlY6ebFd9ryrt9RW43Pb297VNDRSfHt2dCEpLtu5TY31toCgmJYKPK4A5My9INgP0V+rnrNxeNsEaZSnv+IXiWjSrPqdiVjF2BsxUQFu8+qjafPHr6hOP68v6TOh5TibeEwZimDufm6E1bGBiOfiug22dClojBiXuc6mW8d3nZoldN6F3WRX8UJYKil/vnTwZmN2Dwn10vOnUkyrMhN/9UCN3rtHOkVdpywduSXtcJm4W1sRRiQ0vJHkFrTH9z9LSjc2yqTmY703h0IY6NXcUoaRg/PIXoB7bkShsfXnVjtCCllFyRpfjZnK526dd2L/HzdpCSZCDRaic30PeWL0+a1HLxbBf1U5R/YBXdcHR3tp1sFbtkl5+02r4wBrtOtgmf5ZllMyznLlNyY173H3DBlar6c4W8i+fHl/UstY+aYwZFvU4kF3Y+mj/tqlumV+6AOdfo+x+Tl3DXDd4pS7r16i5bx/VeQcmyEj6aOMZenR3q46ebA+c7/ZT8/XNU/M184IGjeu4beG4Id7UUzcLy6++V5Xuu/rCwJj8YwjbXjZ1TTXgEL/iI2xnQP9Svz0tbVmTD39PK/eze8yDW451il9SogD1SkhhqtpIy/p9Tne2zNd1E3rr4x2372lp876GLV/07yI7t6l3YCfE1CKW+8TQ35cLcAqNX/ZUlU4erCv+gJDWyJ1rVGXbNXLnGm0cdqskeb2sBtVX6+DRNq+nVTrP7Dgsa6VndpxQ+7Fqrw/W1yYndiZc99KhTjHMLRN0ywj9IcnlYNNH9deYjtsWTGrUupcOyVp5s7D83DJDx1+0Si1iuVlbqX25AIccLD6ieA8pJVb47D1yolMOJiVi2P2DP675M9p0Q0Nv3SDphu9K7dboud0NktoCx7vWD07qh4ZhLSjIv5IiK2oZYz4q6a8kjZN0nqS/s9b+Q8hxV0n6lqSLJP1J0r9aa7/bnWNF8WSqhIftDOiCjJsNlakA5N821R+c6oas0obWxzRy5Ef0RvUzskb65Rl99e6f5mto31qtf/cenT76GZ08PFHH9ye3CfNv7+ofuwuObk21lJzR8M7Jdl3z8HYZJWZnpS4vdIWwNbtbddUFyfEiXohflSnTzKSwXWlc0pH4JC578uGfBeUe+8je/9RjKzZp9CUf0qsnk/Hr6BvzdUNTb63a+5+h8SvdbC83s+G6Cb21YvOxQCJmJN2/+ZhWbD7m9dkKay7vpsT7x4v4KPf41aemRmP6n1Xqp6lI6WYntYy4QYN2rVDLiLnetf/mq/tkrbzlgJtffU9fm/y+tOeefuEJ79yu8LTtvV/os5s2acpZMzXtwtn6jUnGsP/R96/UvOOQagev1OF+z6hXXTCGpRao3NhdASx1lpZRokD1wv53vD5b/hlebumi67vln7WFeCn3GIbSKLf3kFdd0JB4D3muy8Fmy70jHDHohK7/yF4N6tdXUxvHePnjBR0fcraHvIc8ckwaf0eL1+s0dXmhy73u33xMNzSRf6WqivC56yX9UdJXJe0LO8AY0yRplaS1SgSub0r6ljFmoe+YTcaY7SH/ri35b1Ah7t73Y31q+yd0974fd/lcqZVwvzfGLNLzM34XmDY6Y1iDqkyiEi4lGogu2Rr6ctHCcUO0cs5oLRw3xHvcjGEN3hav+2v+W3XvfEjWGtW98yGtnDNarx05obp+G2WMVV2/jd7zuLGGjb356AmtnDNaMy9IPMdVFzR437sAZZXYFvbStR/QOS8s9s5hfF/940XsEL9i4rtblmvKis/ru1uWd/lcqTOp/N6b9iW1fnVtYOnhdRN6q9okl/O120RhKZ1Fs+q1+baBWjSr3ntsbf9Narftam57WteOnCLZKp08PNE7pz9+udvcWMPGb5WYxbVoVr3mNiXHV50Svx7cckx91n1fDf80Q33Wfd/7ffzn8o8XsUL8ipFle36oz266Wsv2/LDL50rdHdDZO+EbevaG3wd2B5x2YX9VmcSyQCmRfy3d2Jz23AsmNWrFTWO1YFKj99he/TapXe164sCjWjCpUXXvduRg734ocU4FY5h7LjfWsLG//tZxrbhprGaMSo7P5V/tHTO42q30oV3/osvuf7+GbvkH7/fxn8s/XsQOMSwmyu095OKn9mj76y2d/k0ZVKNvf2Cgpgyq0cRBvVUlaeKg3lrf8R5yX81/q9eRSbLWqNeRSfr2BwZqz1tvBePXACvXtGF3S60+cMFQTW1MzDN1+eOeljZtvm2gl3/d0NTb+96fg1269d8C+ZcUfA9J/tVZZEUta+0aa+0ia+0vJXWeQ5xwq6TfWWu/bq190Vp7j6TvS/qa7zyXW2tHh/zLq8uoMebzxpjNxpjNh1sPZX9ABXFFoQ2tj3X5XP5iUy5c4ecHVw73kpawYJbucQvHDdEVDdNVpSpd0TBdh5s/rqPbF+tw88e9Y+e+fVTV1uqGI0d1ycDTJCX7YmUau/85XCHN33tmXs16Gdumhlcf9Apxrvjl77GF+Cnn+NXSkv2/j0ryyCtPqt2265FXnuzyuVyhKddPxlzS8cAX+nkJS1ixKdNjZ4+YrCpTpWuGT9atE+bp3R3f0vH9c7SnpU33bz7mxa+5bx/VA1/o5xW2XM+sTOP3j++6Cb0D8WvYwGr1ei6xpLLXc6u9429oyu8aoPyUW/ySUnKwQ+Rgfk8ceNQrDHWVKzblMjvJFX2+N3uUl3+lFpqyPfaKwTNVpSpNOWumJOnw3o4cbO/HvXP5c7AxgxO9uFxfrExj949v2oX9vfh1em3irc2N1YkcbMDO+73jXSGM2VnxVm4xjPeQ6ZXbe8iNB97TnkEtGf+N/8AxLZwljf/AMb3vjMtlZPS+My5X6xuzdXT7YrW+MVt7BrXoj4faAznYBy84TZKRkXT9hD4aUX+uN5Z0+ZebEZ+ag91Ys17Gtqvm2dXeh6Gu+OXvsYWkcu+p9WFJ/55y21pJ/48xptFam/4jozxZa38i6SdSYueKYp23J7iiYbo2tD6mKxqmd/lc+TT9S+WfGppNcIrqzZo/5GZJ0vFh+wLnMJLOOzBBm99cr6dOn6lPv54oCNjQ83Qeu7v/tJqqTj25lp+aqhs7dvhxyw678vsjdiKJX+Mvu4j45XPN8Ml65JUndc3wyV0+V65N48Pks1QvuMxxnm6dMC/0PCs2H/Pi16nLZum21Ue9pY67DrZ1Wi6ZOn53/+l10tsptbY9LW26Yvr8TwAAIABJREFUr3qq/ryjUfMdvoakfDJYEbotfknBGHbxJWOJYT5TzpqpJw486hWGumLBpMaCZiblu1Qvucxxtn42Kdl4PvU8a3cc8mLYb/pepc+8nigI2E7n6R869qUbm/XYjkOBZdTvdeRi/kbz31y2Le050GNFkoONGHmR3f56S5ZHVI7xvSbr2ZNPanyvyerqdZkyqEZTBiWW5OV7romDemvjgff0wYve0xWjO3/o57f08Wr9elu1Pja2TYuunKnEBpjS0mOnvNuvGN2mf1tdG8jBRv82kUi5eBSWg/llysHuO5XIv5a3TfWWHZJ/ZVbuRa2z1Xla6T7ffVkDkjFmhaT/IWmgMaZZ0t9ba7s+B7IMdXXnh3TmD0kWheIiXRP21KLS0L61uv3IfP17n5vVfDi4i6G/Ebw7T2qRyz1PakFLkjYO/Yo26iveedKt5S63LWtRNMSvPBRj98Awt04IFoXiIFMDUH9Ss+XVk7r94Hwt6/c5PTCtnx68M5jkuUTInSc1wXLPk5pMSYni2fP6C31zy3yvoXzYeNgBsccifuVp6JZ/0KBdK3RwxNzAMr6uumnYLbppWGE7EkbFv8zRX0RKLSq9sP8d3d46Xz+tX6jX3wxOuHG9r9z53Fd/P7B1Lx3q1KDZdtzw0/qFuuOt+V7vrXQN4dkFsceKJIYdrzmlPYPiV9S6csfdGte8Xlsbp+rxUZl39cvHxZqui5WYFLFH0V2XYwdbZcyZajy9v0bUZ85VHt/WonYrPb6tRt+ek3xf9u05iX/O8EGHAzmY+W2LF49c/iUVloM9P+4v9Lz+olMel4ocLKnci1qZ5PRJnrV2bqkHUkr5FDzCdn6IUjGLNUu27staHPLLdVZX89ET3lf3mMb6Wq+poJFkfFNdXRFrze7WQNP41JlaVUbeGP/Q8q5eO3JCjfW1CvPo7lbZjq8UtSpGRcSvfP5nG7Z7YNSKlSwsXn00a2Lil+usLv9Ohu5xrvm7azzqbnfP7Rq9+3dlTP2U0PXcctw5w8aT2jy+0pOqClER8UvKr+AxaNcKGdumQbtWFLWoVahiFWuWbmz2Cky57hSY68yu19867n11jzn3zDpvZ0OXg7n7/P3A3LHNrce9mCclXpxVRvre7FGBmVzpxuLuf2wHuyBWkJLFsDN6W10xOt2KyO7ln3G04Mq2jMeO37BeRu0a//p6tc++sZtGmFk+4892nud2nynJlDQHm9sU3IDHKBGLupKDbXn1pHYdbAttKSEl87MVm9kFsdyLWn+SlPouf3DH1/Bu4T1MuhlHYcJ2fohSPmPPZsO796i+Y4evqad9JuvxqTOy0hXYXAGrsb428JgvPv6KXjtyQkP71uoHVw73zuHfbafdSnuPnNCqa0eHPo/jL5yFsSlf0WNUfPzKZ8vhsN0Do1asLZMf3HJMdYNXqle/Z3R+rw9L+kzG49MtE0wtrl03obfu33zMa0DvHueKaG4HHXdbmy/IuF0Zn7t9YOjz+Mfuby6fyo3BHVvpSVUPUvHxS0o/4yjMwRFzvZla5SCfsWc7j4tfZ2uypLFZH+OfkZWpuOYKWOeeWec9ZunGZu1tPS4jaXrHDohLNzar3SbeJPbpVeUV2Zpbj+uBTyfH438uN3ZX5Ep3DcjBeqxIYlhdVa9AL6UopZtxFMafg8Vx/NnO05052PU/OqxdB9s0fFC1HvhCP+8cheRgqYWzVMSvpCh3P8zFU5JSGznNkPRqsfs5lKt8muKF7fwQJTf2xvpazVm5Pe2uhbno1W+TjLGq7bepoAJZuh0z0hWcwm4Pa1DvDyLpCmfZ/oZX+XZRRI9S8fErn8bqYbsHRs2NO9uuhbmcp1e/Z2SMVXPb03k/Pt2ui4tm1Yc2oHffV/kKUeka1Gf7vbL9DWke32NVfPyS8musHraDYJTc2M89s05zl23LuHNhtvO4+HXA/Ffej0+346IUnKnlP15KzNDyLzN0t71zIjkr3p+DhRXPcvn7uebxM0bRPL6HqfgYRg6WPE935mBhhahcNwkKG3umv+ENvl0UK11kRS1jTL0xZpwxZpykWklDOn4e6TvsLkmXG2P+0Rgz2hhzk6QvSfp2FGOOgn+HvbhxY28+eiLtFqy5OrvtI7LW6Oy2j3S6L9t2sUu27vN6LGTb0dA7Z7/l2ln3Sd3db3mnY+t7hf9n4y+cLdm6zyvkuZ0R3e2p4vw3rlTEr9zEfcvhdAlLIU4dniijqk4N67+7ZbmmrPi8vrtleZpHJncyzGVHQ0m69+xl2ln3Sd179rJOx7ndEZ3UYphL3BavPqqmjh5dbip+uqQy7n/nSkP8yp3bYS+Oy9Lc2F9/63jaolKuTh2eKNmq0Gb1y/b8UJ/ddLWW7flh6GPPPbMu8NUvrOj0swH3aWfdJ/WzAfeFHje0ofN5pGDxbOnGZs1dts17rLstTJz/xpWKGJabuP+/uRxysMWrj3qrdMIKS13Nwfz8yxOb7mzxZn9lysHi/jcupihnajVJeq7j39mSbun4/qfuAGvt7yTNkXS1pN9L+ntJf2utXdLto0XB8t2CNczOnTP11zsv1JrXluucFxYH7su2XezaPa3e9PPUwpG/oOQKUV98/BV9+J1HVWPa9dH31nY69r6rL/RmVRnJK1S5nlmN9bWdZoaFzRTzF74QO8SvCpHPJ53pPLjlmI7tn6O/fvl9unP9veqz7vvefY+88qTabbseeeXJtI/PNP3cJTSSvCRo4qF1qjHtmnhoXafjHvhCPz13+0DvUz33CaibGm+ULGK5AlfYp5Su6NWVT08RGeJXBclntlmYdS8dSsSvne/T9zb9REO3/EPg/icOPKp2teuJA4+GPj5sNpbjCkqSvNlkHzm6RjWmXR85uqbTcQsmNep7s0d5s6qM5BWr/MUzf4ErbKaYK3oVOnsNkSOGVYhi5WCL3jysZ195TX/7ZrC4ny0Hy9aCITUHu/5Hh3X5m4kc7IOHw3Mwl38ZJWeg+XMwIwVyLnKw3ERW1LLWPmGtNSH/pqQct9pa+35rbZ219nxr7XcjGnKPl23GU6GKMRNpxrAGzaterxrTrgF7H5KULAoNPvURValKVzQkZhmn/h65FtUe3Z0oPP2v936sKrWr3Zq0/ckWjhuiqo5PD1yhKrXpvHtO14vLKDiGdEsiUf6IX+Upl1lP+SrGp2AuKbuxZr3XDN8lJI3VH1KVSX56GPY75JLUrdicSHrGbP03GZuIX/edmprx9/J/Apq6ZNH/nGEzxdJNx0f5I36Vp2wzngrV1ZlIrig2r2a91wjfXxSactZMVSk5iyv198ilqOYKTx/c9S9e/FqeIX4tmNTo5WCuWJXadN49Z9hMsUxLIlH+iGHlqZxzMPcesm7raknKOQfLtajmcrCbDv/Uew+Zrkds2Aw0fw42N6WlAzlYbsq9pxa6UbYZT1FaOG6IWs+/TtZUe4UmVxTauXOm7h39kLb84WO65uHtevxw8PfItajmejPMq16vKiO1y+i2k4ltbf2zqtz3jfW1gZ5h7mfXU8stOXS7NpqUmWLFmMEGICmXWU9RcEnZyfGzZE2Vjo+b5SUk2/9wtZ6Y+xPdOmGerv/RYT2884lOv0MuSV1Y/Lqn3+ckBT/R839/3YTe3ieCwwZWB5Io/5T3XQc7zxQrxqenAJKyzXiKiiuKvTnyBllTrYMj5gaKQjcNu0U/u/xXevb3V+q6n2/Thv3B3yOXoporePnj19L6hZI6z6pyP597Zp2MErNNl25sDhSyFkxq9JYdup0U/TPFujp7DUBn5ZyDnbosmX9J6pSDPf3MVRp/R4tW7gz+DrkW1TK9hwzLwVzONWxgdeBn14zev+QwbLY+OVhn5b77IbrRFQ3TtaH1MW/GU7lINmCfr4Uzkk3wXdHIFYVeO5KYKXXi8OXq3X9T4PdYsnWf1uxulZE0s2PpYGpT96suaNCa3a26r22qbqxer+VtU71ZVK4w5X52Ox/6n9fN0Epdcui2pHaztvzPSx8toHiuGT5Zj7zyZKeeCVFL7mgzX4u+mmjCet3Jzrvc7DrYprqqierV7xldM2Jy4PH+3QwlddqJ54amxC48/vi1p6XNe6x7jJSc1j5sYLWXiO1pafOSKCmRyLmkz78ttX93HjflHkDXTTlrpp448Gho36ooJRuwf0YLbkg0wZ92MrjLoCSveORyMPd7uMefe2adN4tKUqCpuyt4Ld81VfM64pcrQj22I7GD4WM7Ers4uoKaez53LreM0c2+cse5HGzahf0DzeTd8QCKoxxzsLD8S0q2WXA5mPvw7sThy9V7wKbA71BoDubyqbAc7JWO5/N/aOjPwfwzsdztrgDmnpc+WkHGug7a8Iy56FL7i3tWRj2MinP3vh97RbX5Q272bp+zcrvabeJN1co5o9M+/ouPv6LXjpzQeX1r9YMrhwfuc+cIc9UFDZ2KS/7i06S9d3kB6t/73KzXjpyQUeftU/23uRlYqYWzXH+XuHj/pJFbrLVNUY8DSeMvu8hueOqeqIdRcb67ZbmXzN06YV7gvqY7W9RmEz0ZMhWC3DbQI3zbQPsfHyb1WCm4LfSlW/9Nf94Rv5b1+5x2HWzzEjOXaLnzuOTKjTNsG+tcf5c46H/aJOJXGbr4krH23hWrox5GxVm254deUe2mYbd4t89dts3LWzIVgr68aof2th7X0IY6fW/2qE6PT2fGqP6BWVz+wtOdve5R/5fv1/K2qbr91HzNGNVfa3cc6pSDDW2o8xriS/JmYaXuhpjr7xIXTRefRwwrM+Rg0UiXg3U1//KfI0yhOVim95BuBlZPzr+k4udgBS0/NMaMMsZMNcb0Tbn96uIMC5Uo3fLHXJfp/eDK4Xrk2tFeQcu/ZDDTY92uhFv/v69pzKNNOueFxYHlg/NqEuuwP1mz3uubZUyiGGY6zuGCkZvR4ApZqcse/c3kw9A8vvSIXyiFTNPuc50m7pq4uwTJP009HVeIWrz6qH71j/+sM74zQ3f2uttLeP68Ohm/3NR11zfL7cIzYlB1p2ntUudp96nN5MPQvLS0iF8olXTLH3Ndqve92aP04KfHegUt/zLBKqOMuxYu3disF5Z/ReN+OVZ39rrHKzj1f/l+1Zh2zaterxmj+nuzsIzvfP6ClsvBXCErddljpp0Y/WOmgXzpEMNQCulysELzLyn3HMyff/VZ9/3A8sEba8JzsBuaeoe+h/QvQUxd9phpJ2z/eCs1/8q7qGWMuUXSKkl/KekFY8y1vrvvLNbAEG+FFGeuaJgeaPjuFNpo3t+IfeG4IXrk2tG66oIG3VFzt3bWfVJ31NztNW9fu6dVN1avV7Xa1fDqg95MrXYrLT81VdZU6/B51wUKbAvHDdGqa0frkWtHa2ZHgcsqeV/YNfA3k882ZhQf8Qu5KCQxuGb45ECzUb9CG5266ed7Wtq8HQuNFIhhrjD14JZj+vOOGFbz7Grvk8LlbVN1ylbp5PhZnZI7fxLn+mtlug6pzeQzjZnmpcVH/EKuCinOpDZ8dwptNO+W/73+1nGtuClR7BraUNcpB3MzqlwO1v/l+73ZWi5+HXrfDV6fLFe08hfRpl3Y38vBXEEr7Bpk2onRP2YayJcGMQy5KGYO1pVG82E5mD9+SYkPBdPlX21Wuu/UVFnTOQdbNKtez94+UM/dPtBrDD98ULJYFXYNMu2E7R9vpeZfhczUulnSBGvtbEmTJX3DGHNrx32pOTEqVCHFmflDbta9ox8KLD3sitQZXq5Q9Ulf1XzVtaO9WVn3dSRPrpeWe/zGoV/R8zN+pzfGLEpbYFs4boiMSf7urodXu03043KFrWyzzmgeX3LEL2RVSGJw64R5XsP3Ygn7hLHKKBDD3KeK103orV/4Ypibtn5n23z9zaUP6L1pX8qY3C2aVa+qjv8CVmw+pqY7W3R/x24+bpliLp940ry0pIhfyEkhxRnX8N2/9LArUmd4Ld3YrNffOh6MX58e6xWr/DmYWzZ4R9t8fXHYGu2dkOjlla7AtmBSo5eDuZlfa3ckrsHaHYfSjinbmFF0xDBkVY45mCtU+eOX/0PBsPyr2kjPj/sLtX51bcYczN2+p6VNbTaRg/nzL1fYypZfVXr+VUij+Bpr7TuSZK3dbYyZIukBY0yjCEjokNrEPSrWBpu8u5lXn+q1QYc7dlGUOnYlHPcd/aWvobyUX9+rxvpavXbkhBrrazsV89xssWzN4WkeX3LEL2SV2kA0KltePak2m/gqKfDJ3yd7rddJ33bRi2bVS7P+WtN/9DmvL0S+jUSHDUz01bJSoH+E+w8jl/PRvLSkiF/Iib+fVJSsr6jkCm0uB3tzxFzvuAWTGqVJd+nPfH25/A3kc3HumXXa23pc555ZFyjm+f/DyHbOfJ8TeSOGIatyzMFcwSlT/vU3q//Caygv5df3yt/eIbXf1oNbjnm5Vab8qtLzr5yLWsaYamttm6R9xphx1tqtkmStPWKMmSXpZ5IuLdE4ETP5FmfcLKrG+lpvF8GuFnfW7mmVlVQ3eKX+q+4Z9Wv8kN7c+3H9tM/NGnfld9KOO3XZYq78SwtdUc//+yA6xC/ko5DEIHV3nGIkFq5fVnPVg5p8/ybVnHW52vfPSXzyN+uvQx+TbXp6Jv7HuK2m3Y48iA7xC/nKtzgTtkNhV4s761465OVgvzHPqNdZE3Vi/xw9PeKvNGbSXaGPybY8MBP/Y6ddmGwoP30Us66iRgxDPvLNwdwsKn/OUqwcrG7wSu3v94wGnD5JB/bM1j39PqervxCef/l3jXaFqFz52zv4dzskB8tdPssP3zHGDJB0k6RAoyRr7Slr7U2SPlrMwaFyuELSa0dOFK2n1IxhiT5Xvfo9I2Osjp/+tKT0/az8jytkCWBqv62VcxJN6wvpB4aiI36hpFxCYlW8fgauX1Ztv02yalevfs9k7GcldW36uXvsDU29tfm2xLT6QntRoKiIXygpN4tqb+vxovWUcn2uXA6W+KqMxbKuLP/zP3bBpEY9+Omx3vJGRI4YhpJxhaRdB9uK2lNqxKBqL36923ujpOwfGBaag6X22yIHy18+Ra1aSdXW2mZrrReQjDH9jTGrJcla+1SxB4jK4ApC5/WtVZVJLOXr6i6ArpH7x/rNUJWqdE7bRzMWq1xjd0lpC1GZGuAX2tAe3YL4hZJyCYxRYoZTMXagcY3c54ycLKMqnTo8MWOi5N9GOiwJytZ8tSsNVVFSxC+UlCsIDW1I7FR47pl1Xd4FcMGkRj3w6bGaOvgqySbiV6ZilZstlm6WWLbm94U2tEe3IIahZFxBaMSgam+WebFysGtHTlGVqdL5vT6csVjl8itJafOoTDkY+VfXGWtTV26mHGDMs5I2SVogaZakJ6217/nuP0fSa9baQvpzlaUxF11qf3HPyqiHUdHmrNyudpuYhplPX6tSP2cU4ypn7580cou1tinqcaRTifFr/GUX2Q1P3RP1MCpa050tarOJJXz59FQo9fNGNa5y1f+0ScSvMnTxJWPtvStWRz2MijZ32TYv11lx09iyeM4oxlTumi4+jxhWZsjBohdFrpPLc5KDBRU7B8tlptYKSYOV+AB6jaS3jTF/MMYs69ix4jZJrxVrQIBUul0AM820cs+ZaZZYoePK9LwoKeIXul0pd6DJ9Emfe950n1IWOq5CttdGURC/EIlS7QKYabaVe850s8QKHVO2GV4oKWIYul0UOVi2/Ksr4yIHy03WmVregcYclTRB0rmSxkka3/G1RtLfWGsfLtUguxsztXoG13ze33TezbSSFOh/5VeK2VizH94uq8T/1Vdd23NmeJX7TC2nkuIXnxL2DOmWErpP+iQF+i/4FfvTwMvuaPHi17O395xPF8t9ppZTSfFLYqZWT5BuKaGbbSUp0P/Kr9gzsq7/+TYvfj3w6Z41w6vcZ2o5lRTDyMF6hkJzsFLMxiIHy00+0z372kQFbIekDcUaAFAqYbsYul0JrVXaHQ7dMTOGNWjJ1n1as7tVRtLMCxIFMH+xzD1P6vep57QpX9HtiF+IlXQ76Lhdcdqt0u6w498O+/ofHdaug20aMahaD3yhXyBRc8+T+n3q+YhfkSN+IVZc4/l1Lx0KFK2mXdg/sStiRw6Wer//mGkX9tfSjc2BXQwXTGpMu1NjukIa8assEMMQK4XmYP78K2xXbHKw0sm5UbzNdUoX0M3SLe0LWyromrnPvCD9MkJ3jCSt2Z3YhdEquSOjv1iW7vtUV3U831UXFHc5JXJD/EI5C5tanm6aumsmOrcp/TT2RbPqvcRq18HETj3uqz9RS/d9qhuakrsiovsRv1DOwpb3pVsq6Jq5Tx+VfimhO0aS1u5I7MJoldyRMd1Ojf5Cmt+MjueaMaq4SymRO2IYylW25YT55mDufkm6f3PnXbHJwUon5+WHlYTlh+XlnBcWa8Deh/Tm0E/ojTGLOt1fqubt/qWKbqaWlCx0nde3VpcMPC2nmVo9VVyWH1YSpr6Xlz7rvq+6rat1fNwsvTftS6HHlGK6un+KvCRvptbk77To7WPSGb2lGZf0zulTwp4qLssPKw3LD8vH0C3/oEG7VujgiLnaO+EboceUqoG7f6mim6n1wv53tLf1eGJsDbnN1OrJ4rL8sJKQg5WXbDlYqZq3+3MwN1NLSha6Rgyq1oTze5GDRbT8EIjEgL0Pydg2Ddj7UGhRy79cMJOwHluZ+M/r78nlNB89oR9cOTxwrkopZgHITd3W1TK2XXVbV6ctavmnq2eSrsdDtnP6j337WPLroln1gfsqJZECkJtBu1bI2DYN2rUibVHLv1wwk3yLTv7zuuOv+/k27/7vzR4VOH7BpMaKKWYByE22HCzX/Evqeg7WdGeLd/+eljY98IV+5GBFlPPyQ6BU7t73Y31q+yd0974fh97/5tBPyJpqvTn0E6H3u+WC2QpKmZYH5nreGcMaZHzfA6hs392yXFNWfF7f3bI89P7j42bJmiodHzcr7TncdPVsCU2m6em5nnPEoOrAVwCVa9meH+qzm67Wsj0/DL3/4Ii5sqZaB0fMTXsOt1wwW0Ep3fLAfM47tKEu8BVAZetqDpZr/iV1PQe7bkJv7z1kKXZmrHTM1ELkNrQ+pna1a0PrY5o/5OZO978xZlHoDK185TqjK5OF44YwGwuA55FXnlS7bdcjrzypWyfM63T/e9O+lHaGVr7y+UQxnQe+0K8oYwEQf08ceFTtatcTBx7VTcNu6XT/3gnfSDtDK1+5zujKJHV2FoDKFqccLHV2PIqLmVqI3BUN01WlKl3RMN27LV3z967IdUZXPkoxTgDxcc3wyaoyVbpm+OTA7emaj3ZFPp8o5qIUYwQQH1POmqkqVWnKWTMDt4c1f++qXGd05aoUYwQQL2E5WKlyG3Kw8kZRC5GbP+Rm3Tv6ocAsrXyWCkZZWMp3SSOAnuXWCfP0xNyfdPqEMNdp6lEmNflMpQfQ89w07Bb97PJfdZqlletSwSgLS/kuZwTQ84TlYPnkNuRgPQdFLZSlGcMaElsw57BUMMrCUj7jBFA50m0HnSrKpCbXMQKoLNMu7K8qo6xLBaMsLOU6RgCVJZ/chhys56CnFspSPr2rutIrK98dEVPRYwtAmFx7J3SlR0M+O/F0ZYwAKkuuOwl2tU9WvjsiFjJGAJUln9yGHKznYKYWIlOsZYO59soKe75CZnnRRwtAsaas59OjIfU5C/2EkT4OQGUr1rLBfPpkhT1nITO96KUFoLtzsLDnKyQHI/8qHYpaiEx3LxsMe76w5YPZilalHDcFMyAeopiynvqc6aauZ0uaSjl2Ejag/EWxbDDsOcOWEGYrWpVy7BTMgHjo7hws7PnCcjDyr+hQ1EJkcu1H9cXHX9E1D2/XFx9/pejPlzrLa8nWfVqzO1G0WrO7NbS4lGncS7bu0+yHt+uahwsrTNF4HoiHXHshLF59VJfd0aLxd3Q90Uh9zrBPGBevPqr7NyeSphWbw5OmTGO//keHNf6OFl3/o8MFjZHGp0D5y6cf1ZdX7dB1P9+mL6/aUfTnTJ3ptXRjs9buSBStHtsRXrTKNPaujpXm80A8dHcOFvZ8qTmYP/+6f/Ox0OfLNO6ujrXS8y9jrY16DGVnzEWX2l/cszLqYaDDNQ9v975/5NrRJX2uOSu3q933n0SVkVbOyf6crjeXtZJ7eK6PDTtPoT2+utv7J43cYq1tinocSBp/2UV2w1P3RD0MdGi6s0VtHUGh2kibbxvYbc8nSc/dntvzud4QhTw27DyF9pjoTv1Pm0T8KkMXXzLW3rtiddTDQIfrfr7N+/7BT48t6XPNXbYtkIPl+nyuN1chjw07TyE9vqLQdPF5xLAyQw5WXrozB0vNv/J5PlcQK+Sx/nPEJf+Sip+DMVMLZe+8vrWBr6XkZmGd17c24yyy1GWCboaVlWQ6jrFWec/WyrU/GIB4uG5Cby8mdMcON/7nu6Ep/Pky9YZwzuitgqax59MjDED5G9pQF/haStMu7O/Frxmj0s8iS10mmFrQOr22qqBlhPn0CANQ/rozB3OzsEYMqs44iyxdDuY3bGB13jlYpedf7H6IsveDK4eX/Dn8M6Syza5ySxSlRDFr4bghgR0YF44b4s34cvcDqEzdsbtN6qdzmZ7P/2ngg1uOecf6dwBaNKve+8TRfwyAyvO92aNK/hz+GVIPZJhh5Y5zs+LXvXRICyY1BnZhXDCp0Zvx5e4HUJm6OwfLNruKHKx0KGoBCvayCitC+YteqY3mpcQMK//j/EWuMHFbZgigfPn7KKRLfsKWF6b2hvA/NtM213Gb4g6gvPl7WYUVocKWF/r7ai2Y1Bh4nL/IFSZuywwBlC9ysPLA8kNA2ZvW+4te7tirLkhfkPLP3gpbgkhDeADFkkvDVJdMGSV6NdzQlDkZWjSr3kuqUqe/V3ozUgDFla1xvStoGSWKWTNG9c+4TNA/eytsCSIN4QEUSylysEzzP3WOAAASxklEQVTIwcJR1AIU7GWV2i9LCha9cu17lalwlevOjwCQTdgOPKm9GFzSNbepd849F9IlTrnuOgQAufD3skrtlyUli17TsxSz/DIVrvLZ/REAMvHnYGH5l5R/DpapcEUOFo6iFpAirBjlClmSOhW80slUuKIhPIBSCUuGMs28Sidd4lTpzUgBlE5YMcoVvSTl3AA+U+GKhvAASiFdMSrfHCxT4YocLBxFLSBFpmJULssG3UwvSRSuAHS7dMlQrlPW3SeNkkicAHSrTMWoXJYNuplekihcAehWmYpRueRg5F+Fo1E8YsvfbF1SaOP1QhqypzZ995/L9XTItGwwW9N5AJCCzT4ldWr8WWgz0LDdfhavPur1c8g2ZT2XpqcAKpu/2bqkTo3XC23Gntr03f98LgfLtGwwW9N5AEjNr8LyrUJysHS7Leaag5F/FY6ZWogtf/Eo3QyqfGZWZVtS6M5hjDIWq+iXBSAX/uQl7BO8fD7Vyzad3Z2jyihrokS/BgDZ+ItHYTOo8plVlctyQnceY5SxWEW/LADZpOZX5ZKDkX8VjqIWYstfPEpXSMqlwJTrToS5FqsK6ZeVa2ENQM/hT17CEpl8dtTJtqQwn0Qp334NuSZ1AHoOf/EorJCUS3Epn10Icy1W5dsvK5/CGoCeITUnKpccrJB+WeRgCcZaG/UYys6Yiy61v7hnZdTDQDcpZIlisc1ZuV3tNlHBdw3p4+D9k0ZusdY2RT0OJI2/7CK74al7oh4GukmhSxSLqenOFrXZxDbVm28bGMkYCtH/tEnErzJ08SVj7b0rVkc9DHSDQpcoFtPcZdu8/Ms1o4+LpovPI4aVGXKwykIOVrhi52D01ELFS9dDqzvNGNYQ6A8GALlI17+hO7kdfZguDyAf6fpndadpF/YP9AYDgFyRg5UPilqoSOUwO8uvHAprAOKhHD4Z9CuHpA5AfJTDDC2nHAprAOKDHKw80VMLFSnXPloAUG5y7eEAAOUon15aAFBOyMHKE0UtVCR2KAQQV+yOAyDO2KEQQFyRg5Unlh+iYqQuOWS5H4A48U95j1MzUABIXXLIkj8AcZG65JDlfuWHmVqoGCw5BBBnTHkHEFcsOQQQV+Rf5Y+iFioGSw4BxBlT3gHEFUsOAcQV+Vf5Y/khKgZLDgHEGVPeAcQVSw4BxBX5V/ljphYqxpKt+zRn5XYt2bov6qEAQF4Wrz6qpjtbtHj10aiHAgB5W7qxWXOXbdPSjc1RDwUA8kIOVv4oaqFiFNJTi0IYgHJQSD8HkjAA5aKQnloUwgCUA3Kw8kdRCxWjkJ5ahTaXpxgGoJgK6edQaGNTEjEAxVZIT61Cm8tTDANQTORg5a/HF7WMMRuMMVuNMX8wxiwxxlRHPSZEY+G4IVo5Z3RefbUKbS7PTosoBuIXnEWz6rX5toF59XQotLEpu/ygGIhf8FswqVErbhqbV1+tQpvLs9MiioEYBoccrPz1+KKWpDnW2nGSLpU0QNLciMeDGCmkECax0yKKhviFghWShEns8oOiIX6hSwophEnstIiiIYahYORg3avH735orX2749saSX0k2QiHgwrBTosoBuIXosAuPygG4heiwk6LKAZiGKJADlaYyGZqGWM+aoxZZYx51RhjjTHfSHPcVR1TP48bY/YYY24t4Lkel3RA0tuSHuji0AFUOOIXgLgifgGIM2IYgFRRLj+sl/RHSV+VFNpN2xjTJGmVpLWSxkn6pqRvGWMW+o7ZZIzZHvLvWneMtfZKSedIqpN0Ral+IQAVg/gFIK6IXwDijBgGICCy5YfW2jWS1kiSMeY7aQ67VdLvrLVf7/j5RWPMGElfk7Sk4zyX5/h87xljHpE0W9KvU+83xnxe0ucl6ewh5+TxmwCoNOUcvxqHsuwVQHrlFr86xuHFsCFnn5vjbwKgEpVbDCMHA6JX7o3iP6xEhd1vraRhxpisi+WNMWcYYwZ3fF8jaZakF8OOtdb+xFrbZK1t6tdAY0kAXRZJ/Bo4kM0JAHRZt8UvKSUH608OBqDLyMGAClLujeLPVudppft89zVnefyZkh4yxtQpUcBbL+nHRR0hAIQjfgGIK+IXgDgjhgEVpNyLWplk3YHCWrtX0ge6YSwAkA/iF4C4In4BiDNiGNDDlPvywz9JSl2cPLjja2hjQAAoE8QvAHFF/AIQZ8QwoIKUe1HrKUnTU26bIelVa222aaMAECXiF4C4In4BiDNiGFBBIlt+aIyplzSy48daSUOMMeMkHbXW7uy4/S5JTxtj/lHSvZIul/QlSV/p7vECgEP8AhBXxC8AcUYMA5AqyplaTZKe6/h3tqRbOr7/qTvAWvs7SXMkXS3p95L+XtLfWmuXdPtoASCJ+AUgrohfAOKMGAYgILKZWtbaJySZHI5bLWl1yQcEADkifgGIK+IXgDgjhgFIVe49tQAAAAAAAIBOKGoBAAAAAAAgdihqAQAAAAAAIHYoagEAAAAAACB2KGoBAAAAAAAgdihqAQAAAAAAIHYoagEAAAAAACB2KGoBAAAAAAAgdihqAQAAAAAAIHYoagEAAAAAACB2KGoBAAAAAAAgdihqAQAAAAAAIHYoagEFWLJ1n+as3K4lW/dFPRQAyNvi1UfVdGeLFq8+GvVQACAvSzc2a+6ybVq6sTnqoQBAXsi/SoOiFlCAtXta1W4TXwEgbh7cckxtNvEVAOJk3UuH1G4TXwEgTsi/SoOiFlCAGcMaVGUSXwEgbq6b0FvVJvEVAOJk2oX9VWUSXwEgTsi/SqMm6gEAcbRw3BAtHDck6mEAQEEWzarXoln1UQ8DAPK2YFKjFkxqjHoYAJA38q/SYKYWAAAAAAAAYoeiFroFjdUBxBVNPQHEGY3VAcQVORhyQVEL3YLG6gDiiqaeAOKMxuoA4oocDLmgqIVuQWN1AHFFU08AcUZjdQBxRQ6GXNAoHt2CxuoA4oqmngDijMbqAOKKHAy5YKYWAAAAAAAAYoeiFgAAAAAAAGKH5Ych+pxep7ETR0Q9DADIW3XV6erXZ2LUwwCAgpzWu1YTLhoa9TAAIG/kYEA0mKkFAAAAAACA2KGoBQAAAAAAgNihqAUAAAAAAIDYoagFAAAAAACA2KGoBQAAAAAAgNihqAUAAAAAAIDYoagFAAAAAACA2KGoBQAAAAAAgNihqAUAAAAAAIDYoagFAAAAAACA2KGoBQAAAAAAgNihqAUAAAAAAIDYoagFAAAAAACA2KGoBQAAAAAAgNihqAUAAAAAAIDYoagFAAAAAACA2KGoBXSDv1v5B41YtEZ/t/IPUQ8FAPJGDAMQV8QvAHFGDMuOohbQDe575jW1Wav7nnkt6qEAQN6IYQDiivgFIM6IYdlR1AK6wY0Tz1O1Mbpx4nlRDwUA8kYMAxBXxC8AcUYMy85Ya6MeQ9lpamqymzdvjnoYQNkzxmyx1jZFPQ4kEb+A3BC/yhMxDMgNMaz8EL+A3BQ7fjFTCwAAAAAAALFDUQsAAAAAAACxQ1ELAAAAAAAAsUNRCwAAAAAAALFDUQsAAAAAAACxQ1ELAAAAAAAAsUNRCwAAAAAAALFDUQsAAAAAAACxY6y1UY+h7BhjjkjaEfU4yshASS1RD6JMcC2CRllr+0Y9CCQRvzrhv9kgrkcS8asMEcMC+O81iOsRRAwrM8SvTvhvNolrEVTU+FVTrBP1MDustU1RD6JcGGM2cz0SuBZBxpjNUY8BnRC/fPhvNojrkUT8KlvEsA789xrE9QgihpUl4pcP/80mcS2Cih2/WH4IAAAAAACA2KGoBQAAAAAAgNihqBXuJ1EPoMxwPZK4FkFcj/LD3ySI6xHE9UjiWpQn/i5JXIsgrkcQ16P88DcJ4nokcS2Cino9aBQPAAAAAACA2GGmFgAAAAAAAGKHohYAAAAAAABih6IWAAAAAAAAYoeiVhEYY6qNMc8ZY34V9ViiZIwZaoz5P8aYF40xfzDGfDHqMXUnY8yVHb/7TmPMP0Y9nihV+mshTohfCbxmiWEOr4V4IYbxmpWIX368HuKD+JVQ6a9Z4ldSoa8FGsUXgTHmVklNks6w1l4d9XiiYow5W9LZ1tpnjTH1krZImmOtfTHioZWcMaZa0ouSZkraI+m/JP21tfbpKMcVlUp+LcQN8Suh0l+zxLCkSn8txA0xjNcs8Suo0l8PcUL8Sqjk1yzxK6jQ1wIztbrIGNMoaZakn0Y9lqhZa/9krX224/ujknZIaox2VN3mA5J2W2t3WWvbJC2T9ImIxxSZCn8txAbxK4nXLDHM4bUQH8SwBF6zxC8/Xg/xQPxKqvDXLPHLp9DXQo8tahljPmqMWWWMedUYY40x30hz3FXGmK3GmOPGmD0dFfN8fE/SVyW1d3nQJdSN18Od5wJJl0na1JVxd4ciXZtGSXt9P78m6dxSjrtUiv1aidNroVwQv4KIX5kRw5KIX+WBGJZE/MqM+BVEDIse8SuIGJYe8SsoyvjVY4takuol/VGJYLEv7ABjTJOkVZLWShon6ZuSvmWMWeg7ZpMxZnvIv2uNMVdLOmCt3VLqX6YISn49fMf0lfSgpC9ba98q2W9UPEW5NqkPKf4wu03RrkcMXwvlgvgVRPzKjBiWRPwqD8SwJOJXZsSvIGJY9IhfQcSw9IhfQdHFL2ttj/+nxPrUb4Tcfp+kp1Nu+2clpgDmct7Fkpo7zr9P0ruS/jPq3zeq69FxfC9J65RYCxz579pd10bSJEmP+e67WdL/jvr3ifK1EvfXQrn8I351z/XoOD72r1liWHFeKz3htVAu/4hhpb8WHcfH/jVL/Cre66UnvB7K4R/xq3uuR8fxsX7NEr+K91op5LXQk2dq5eLDSlQJ/dZKGmYS65wzstYustY2WmuHSfqfkjZYa/9n8YfZbbp0PYwxRtK/S/qjtfafSzC+KGW7Nr+TNNwYM9wkGv7dJGllN4+xO2W8Hj38tVAuiF9BxK/MiGFJxK/yQAxLIn5lRvwKIoZFj/gVRAxLj/gVVJL4VelFrbPVeWrcPt99laar1+PDkj4l6QqTWCe71RhzTTEHGKGM18YmGvvdImmNpJck/be19jfdOL7ulu210pNfC+WC+BVE/MqMGJZE/CoPxLAk4ldmxK8gYlj0iF9BxLD0iF9BJYlfNcUdY49i8zrY2ickPVGSkZSHrNej4z/AOK8DLpSVJGvtOkmjIx5LObAV/FooF8SvIOJXZsSwJOJXeSCGJRG/MiN+BRHDokf8CiKGpUf8Cio4flX6TK0/SRqSctvgjq+hzc16OK5HelybIK5H9PgbBHE9MuP6JHEtygN/hySuRWZcnyCuR/T4GwRxPdLj2gSV5HpUelHrKUnTU26bIelVa21zBOOJGtcjPa5NENcjevwNgrgemXF9krgW5YG/QxLXIjOuTxDXI3r8DYK4HulxbYJKcj167PJDY0y9pJEdP9ZKGmKMGSfpqLV2Z8ftd0l62hjzj5LulXS5pC9J+kp3j7fUuB7pcW2CuB7R428QxPXIjOuTxLUoD/wdkrgWmXF9grge0eNvEMT1SI9rExTp9Sj1do5R/ZM0RYl1qqn/nkg5bpak30s6LulVSbdGPXauB9eG61HZ//gbcD24PlyLOP/j78C14PpwPeL6j78B14NrE7/rYTpODAAAAAAAAMRGpffUAgAAAAAAQAxR1AIAAAAAAEDsUNQCAAAAAABA7FDUAgAAAAAAQOxQ1AIAAAAAAEDsUNQCAAAAAABA7FDUAgAAAAAAQOxQ1AIAAAAAAEDsUNQCAAAAAABA7FDUQtkyxiwyxmyNehwAkC/iF4A4I4YBiCviV+WhqIVyNlHSpqgHAQAFIH4BiDNiGIC4In5VGGOtjXoMQIAxpkrSEUmn+W4+Kel0a+3JaEYFANkRvwDEGTEMQFwRvyoXM7VQjqykCR3fXy3pbEnnEowAxADxC0CcEcMAxBXxq0JR1ELZsYnpg+dIapf0hLV2n7X2oDHm58aYA8aYP0Q8RAAIRfwCEGfEMABxRfyqXBS1UK7GS9phrX3Hd9vPJM2IaDwAkCviF4A4I4YBiCviVwWiqIVyNV7Ss/4brLVPSjoUzXAAIGfELwBxRgwDEFfErwpEUQvlapwktmIFEEfELwBxRgwDEFfErwpEUQvlqkbShcaYc40xA6IeDADkgfgFIM6IYQDiivhVgShqoVz9raRpkvZK+o+IxwIA+SB+AYgzYhiAuCJ+VSCT2CQAiAdjzDBJv7LWXhLxUAAgL8QvAHFGDAMQV8Svno2ZWogNY8wKSb+VNMoY02yMuTnqMQFALohfAOKMGAYgrohfPR8ztQAAAAAAABA7zNQCAAAAAABA7FDUAgAAAAAAQOxQ1AIAAAAAAEDsUNQCAAAAAABA7FDUAgAAAAAAQOxQ1AIAAAAAAEDsUNQCAAAAAABA7FDUAgAAAAAAQOz8/5YrSf50kXRoAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1440x720 with 8 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# plot the results\n",
"plt.figure(figsize=(20,10))\n",
"MakePlot(t,np.argmax(p,axis=0).T,bins,'True', 2, np.ceil(Kfitmax/2),1)\n",
"\n",
"\n",
"for Kfit in range(2,Kfitmax+1):\n",
" MakePlot(t,np.argmax(pe[Kfit-1,:,:,:],axis=0).T,bins,r'K=' + str(Kfit), 2, np.ceil(Kfitmax/2), Kfit)\n",
"\n",
"plt.subplots_adjust(wspace=0.5,hspace=0.5)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#plot the BIC score for model selection\n",
"plt.plot(np.linspace(2,Kfitmax,Kfitmax-1),bic[1:Kfitmax])\n",
"plt.xlabel(r'$Regimes$') \n",
"plt.ylabel(r'$BIC$')\n",
"plt.title('BIC Score')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
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}
],
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