Bayesian+linear+regression+approximate+inference+GAN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using gpu device 0: Tesla K80 (CNMeM is disabled, CuDNN 4007)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pylab as plt\n",
    "import theano\n",
    "from theano import tensor as T\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create a regular grid in weight space for visualisation\n",
    "wmin = -5\n",
    "wmax = 5\n",
    "wrange = np.linspace(wmin,wmax,300)\n",
    "w = np.repeat(wrange[:,None],300,axis=1)\n",
    "w = np.concatenate([[w.flatten()],[w.T.flatten()]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fba0e46db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior_variance = 2\n",
    "logprior = -(w**2).sum(axis=0)/2/prior_variance\n",
    "plt.contourf(wrange, wrange, logprior.reshape(300,300), cmap='gray');\n",
    "plt.axis('square');\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#generating a toy dataset with three manually selected observations\n",
    "from scipy.stats import logistic\n",
    "sigmoid = logistic.cdf\n",
    "logsigmoid = logistic.logcdf\n",
    "\n",
    "def likelihood(w,x,b=0,y=1):\n",
    "    return logsigmoid(y*(np.dot(w.T,x) + b)).flatten()\n",
    "\n",
    "\n",
    "x1 = np.array([[1.5],[1]])\n",
    "x2 = np.array([[-1.5],[1]])\n",
    "x3 = np.array([[0.5],[-1]])\n",
    "\n",
    "y1=1\n",
    "y2=1\n",
    "y3=-1\n",
    "\n",
    "llh1 = likelihood(w, x1, y=y1) \n",
    "llh2 = likelihood(w, x2, y=y2) \n",
    "llh3 = likelihood(w, x3, y=y3) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#calculating unnormalised log posterior\n",
    "#this is only for illustration\n",
    "logpost = llh1 + llh2 + llh3 + logprior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fba0df9d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting the real log posterior\n",
    "#the red dots show the three datapoints, the small line segments shows the direction\n",
    "#in which the corresponding label shifts the posterior. Positive datapoints shift the \n",
    "# posterior away from zero in the direction of the datapoint, negative datapoints shift\n",
    "# away from zero, in the opposite direction.\n",
    "\n",
    "plt.contourf(wrange,\n",
    "             wrange,\n",
    "             np.exp(logpost.reshape(300,300).T),cmap='gray');\n",
    "plt.axis('square');\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax])\n",
    "\n",
    "plt.plot(x1[0],x1[1],'.r')\n",
    "plt.plot([x1[0],x1[0]*(1+0.2*y1)],[x1[1],x1[1]*(1+0.2*y1)],'r-')\n",
    "\n",
    "plt.plot(x2[0],x2[1],'.r')\n",
    "plt.plot([x2[0],x2[0]*(1+0.2*y2)],[x2[1],x2[1]*(1+0.2*y2)],'r-')\n",
    "\n",
    "plt.plot(x3[0],x3[1],'.r')\n",
    "plt.plot([x3[0],x3[0]*(1+0.2*y3)],[x3[1],x3[1]*(1+0.2*y3)],'r-');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Fitting an approximate posterior\n",
    "\n",
    "This part is for the actual GAN stuff. Here we define the generator and the discriminator networks in Lasagne, and code up the two loss functions in theano."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from lasagne.utils import floatX\n",
    "\n",
    "from lasagne.layers import (\n",
    "    InputLayer,\n",
    "    DenseLayer,\n",
    "    NonlinearityLayer)\n",
    "from lasagne.nonlinearities import sigmoid\n",
    "\n",
    "#defines a 'generator' network\n",
    "def build_G(input_var=None, num_z = 3):\n",
    "    \n",
    "    network = InputLayer(input_var=input_var, shape=(None, num_z))\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=10)\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=20)\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=2, nonlinearity=None)\n",
    "    \n",
    "    return network\n",
    "\n",
    "#defines the 'discriminator network'\n",
    "def build_D(input_var=None):\n",
    "\n",
    "    network = InputLayer(input_var=input_var, shape = (None, 2))\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=10)\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=20)\n",
    "    \n",
    "    network = DenseLayer(incoming = network, num_units=1, nonlinearity=None)\n",
    "    \n",
    "    normalised = NonlinearityLayer(incoming = network, nonlinearity = sigmoid)\n",
    "    \n",
    "    return { 'unnorm':network, 'norm':normalised }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from lasagne.layers import get_output, get_all_params\n",
    "from theano.printing import debugprint\n",
    "from lasagne.updates import adam\n",
    "from theano.tensor.shared_randomstreams import RandomStreams\n",
    "\n",
    "#variables for input (design matrix), output labels, GAN noise variable, weights\n",
    "x_var = T.matrix('design matrix')\n",
    "y_var = T.vector('labels')\n",
    "z_var = T.matrix('GAN noise')\n",
    "w_var = T.matrix('weights')\n",
    "\n",
    "#theano variables for things like batchsize, learning rate, etc.\n",
    "batchsize_var = T.scalar('batchsize', dtype='int32')\n",
    "prior_variance_var = T.scalar('prior variance')\n",
    "learningrate_var = T.scalar('learning rate')\n",
    "\n",
    "#random numbers for sampling from the prior or from the GAN\n",
    "srng = RandomStreams(seed=1337)\n",
    "z_rnd = srng.normal((batchsize_var,3))\n",
    "prior_rnd = srng.normal((batchsize_var,2))\n",
    "\n",
    "#instantiating the G and D networks\n",
    "generator = build_G(z_var)\n",
    "discriminator = build_D()\n",
    "\n",
    "#these expressions are random samples from the generator and the prior, respectively\n",
    "samples_from_grenerator = get_output(generator, z_rnd)\n",
    "samples_from_prior = prior_rnd*T.sqrt(prior_variance_var)\n",
    "\n",
    "#discriminator output for synthetic samples, both normalised and unnormalised (after/before sigmoid)\n",
    "D_of_G = get_output(discriminator['norm'], inputs=samples_from_grenerator)\n",
    "s_of_G = get_output(discriminator['unnorm'], inputs=samples_from_grenerator)\n",
    "\n",
    "#discriminator output for real samples from the prior\n",
    "D_of_prior = get_output(discriminator['norm'], inputs=samples_from_prior)\n",
    "\n",
    "#loss of discriminator - simple binary cross-entropy loss\n",
    "loss_D = -T.log(D_of_G).mean() - T.log(1-D_of_prior).mean()\n",
    "\n",
    "#log likelihood for each synthetic w sampled from the generator\n",
    "log_likelihood = T.log(\n",
    "    T.nnet.sigmoid(\n",
    "        (y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * samples_from_grenerator.dimshuffle('x', 1, 0))).sum(1)\n",
    "    )\n",
    ").sum(0).mean()\n",
    "\n",
    "#loss for G is the sum of unnormalised discriminator output and the negative log likelihood\n",
    "loss_G = s_of_G.mean() - log_likelihood\n",
    "\n",
    "#compiling theano functions:\n",
    "evaluate_generator = theano.function(\n",
    "    [z_var],\n",
    "    get_output(generator),\n",
    "    allow_input_downcast=True\n",
    ")\n",
    "\n",
    "sample_generator = theano.function(\n",
    "    [batchsize_var],\n",
    "    samples_from_grenerator,\n",
    "    allow_input_downcast=True,\n",
    ")\n",
    "\n",
    "sample_prior = theano.function(\n",
    "    [prior_variance_var, batchsize_var],\n",
    "    samples_from_prior,\n",
    "    allow_input_downcast=True\n",
    ")\n",
    "\n",
    "params_D = get_all_params(discriminator['norm'], trainable=True)\n",
    "\n",
    "updates_D = adam(\n",
    "    loss_D,\n",
    "    params_D,\n",
    "    learning_rate = learningrate_var\n",
    ")\n",
    "\n",
    "train_D = theano.function(\n",
    "    [learningrate_var, batchsize_var, prior_variance_var],\n",
    "    loss_D,\n",
    "    updates = updates_D,\n",
    "    allow_input_downcast = True\n",
    ")\n",
    "\n",
    "params_G = get_all_params(generator, trainable=True)\n",
    "\n",
    "updates_G = adam(\n",
    "    loss_G,\n",
    "    params_G,\n",
    "    learning_rate = learningrate_var\n",
    ")\n",
    "\n",
    "train_G = theano.function(\n",
    "    [x_var, y_var, learningrate_var, batchsize_var],\n",
    "    loss_G,\n",
    "    updates = updates_G,\n",
    "    allow_input_downcast = True\n",
    ")\n",
    "\n",
    "evaluate_discriminator = theano.function(\n",
    "    [w_var],\n",
    "    get_output([discriminator['unnorm'],discriminator['norm']],w_var),\n",
    "    allow_input_downcast = True\n",
    ")\n",
    "\n",
    "#this is to evaluate the log-likelihood of an arbitrary set of w\n",
    "llh_for_w = T.nnet.sigmoid((y_var.dimshuffle(0,'x','x')*(x_var.dimshuffle(0,1,'x') * w_var.dimshuffle('x', 1, 0))).sum(1))\n",
    "\n",
    "evaluate_loglikelihood = theano.function(\n",
    "        [x_var, y_var, w_var],\n",
    "        llh_for_w,\n",
    "        allow_input_downcast = True\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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roR9aCUcAQAKZYAauAwAgwYtMCP3QKhGOAACyAAAA03iVzZEYWgEAdmNgNQ/X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fba018b2a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#checking that theano and numpy give the same likelihoods\n",
    "import seaborn as sns\n",
    "sns.set_context('poster')\n",
    "\n",
    "X_train = np.concatenate([x1,x2,x3],axis=1).T\n",
    "y_train = np.array([y1,y2,y3])\n",
    "llh_theano = evaluate_loglikelihood(X_train, y_train, w.T)\n",
    "\n",
    "plt.figure(figsize=(16,8))\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(wrange, wrange ,np.log(llh_theano).sum(0).reshape(300,300).T,cmap='gray');\n",
    "plt.axis('square');\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax])\n",
    "plt.title('theano loglikelihood')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.contourf(wrange, wrange, (llh1+llh2+llh3).reshape(300,300).T,cmap='gray');\n",
    "plt.axis('square');\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax])\n",
    "plt.title('numpy loglikelihood')\n",
    "\n",
    "assert np.allclose(llh1+llh2+llh3,np.log(llh_theano).sum(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "300 loops, best of 3: 1.52 ms per loop\n",
      "0.8448745012283325\n",
      "1.9514195919036865\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9600536823272705\n",
      "2.1756317615509033\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.1132714748382568\n",
      "2.1207809448242188\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9374406337738037\n",
      "2.033437490463257\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9812651872634888\n",
      "2.122642993927002\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9524849653244019\n",
      "2.1304209232330322\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9748408198356628\n",
      "1.9830398559570312\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9469156265258789\n",
      "2.034944772720337\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0123794078826904\n",
      "2.0215725898742676\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9374747276306152\n",
      "1.8552474975585938\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.990984320640564\n",
      "1.9634348154067993\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.8005599975585938\n",
      "2.0340428352355957\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0441194772720337\n",
      "2.078402042388916\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9515339732170105\n",
      "2.0935752391815186\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.014158010482788\n",
      "1.9193150997161865\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9064014554023743\n",
      "1.9159090518951416\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8740888833999634\n",
      "1.8587417602539062\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.045501947402954\n",
      "2.0620100498199463\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "1.102818489074707\n",
      "1.9564135074615479\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9090922474861145\n",
      "2.018059015274048\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9764355421066284\n",
      "1.9801956415176392\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9260282516479492\n",
      "1.9836033582687378\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0356860160827637\n",
      "2.0456244945526123\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.941687822341919\n",
      "1.9629082679748535\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9731559753417969\n",
      "1.988584041595459\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0802245140075684\n",
      "2.0056726932525635\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0316039323806763\n",
      "1.9496046304702759\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9684480428695679\n",
      "1.869762897491455\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0378801822662354\n",
      "1.902108073234558\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "1.0136998891830444\n",
      "1.9007588624954224\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0407465696334839\n",
      "1.9785401821136475\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.032365083694458\n",
      "1.8645954132080078\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9352719187736511\n",
      "1.9393141269683838\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0411553382873535\n",
      "1.9759348630905151\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8414285778999329\n",
      "2.059307098388672\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.980594277381897\n",
      "1.9248079061508179\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9445054531097412\n",
      "1.9292949438095093\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.045969843864441\n",
      "1.9180612564086914\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0355181694030762\n",
      "1.9287148714065552\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0907528400421143\n",
      "2.0063419342041016\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.030317783355713\n",
      "2.0014772415161133\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.962618887424469\n",
      "1.8605748414993286\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9774050116539001\n",
      "1.910995602607727\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9333393573760986\n",
      "1.9094206094741821\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9691608548164368\n",
      "1.8858442306518555\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.8662000894546509\n",
      "1.9423495531082153\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.8949613571166992\n",
      "1.9160100221633911\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9095511436462402\n",
      "1.924254298210144\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "1.0445687770843506\n",
      "1.9673411846160889\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.978882908821106\n",
      "1.8847665786743164\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9121913909912109\n",
      "1.89730966091156\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9401355385780334\n",
      "1.8624334335327148\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9630769491195679\n",
      "1.992774248123169\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9487576484680176\n",
      "1.9473307132720947\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0263659954071045\n",
      "1.89525306224823\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9195380806922913\n",
      "1.9877896308898926\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9764193296432495\n",
      "1.9331001043319702\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9087851047515869\n",
      "1.8820929527282715\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9978067278862\n",
      "1.9613386392593384\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.985075056552887\n",
      "1.9285860061645508\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.8952118158340454\n",
      "1.9643129110336304\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9691531658172607\n",
      "1.9074223041534424\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.018507480621338\n",
      "1.9238728284835815\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0125757455825806\n",
      "1.9139434099197388\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9592885971069336\n",
      "1.9897146224975586\n",
      "50 loops, best of 3: 1.54 ms per loop\n",
      "1.001117467880249\n",
      "1.9631487131118774\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0618159770965576\n",
      "1.865829586982727\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0544630289077759\n",
      "1.8829889297485352\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9327152967453003\n",
      "2.012500047683716\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9645974636077881\n",
      "1.8529531955718994\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0016453266143799\n",
      "1.9349000453948975\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.875522255897522\n",
      "1.8374173641204834\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9100744724273682\n",
      "1.9483352899551392\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.8262972235679626\n",
      "1.9207834005355835\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0230774879455566\n",
      "1.8619059324264526\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8782156705856323\n",
      "1.8719462156295776\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0510547161102295\n",
      "1.9405272006988525\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0219957828521729\n",
      "1.952405571937561\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.1573123931884766\n",
      "1.8239548206329346\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.064415454864502\n",
      "1.9159923791885376\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0200016498565674\n",
      "1.8292263746261597\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9069321155548096\n",
      "1.9733787775039673\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9966238141059875\n",
      "1.9710220098495483\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9025123119354248\n",
      "1.8472779989242554\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0376310348510742\n",
      "1.8177932500839233\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.011881947517395\n",
      "1.9010998010635376\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9227458238601685\n",
      "1.9468706846237183\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.862939715385437\n",
      "1.9307807683944702\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9486161470413208\n",
      "1.8571929931640625\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8988595008850098\n",
      "1.8314225673675537\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9509600400924683\n",
      "1.8611066341400146\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9949578046798706\n",
      "1.878565788269043\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8730878829956055\n",
      "1.9759849309921265\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9754554629325867\n",
      "1.9739391803741455\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.863519549369812\n",
      "1.8903473615646362\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0119316577911377\n",
      "1.8875197172164917\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0236506462097168\n",
      "1.9025930166244507\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9017845392227173\n",
      "1.8345367908477783\n",
      "50 loops, best of 3: 1.54 ms per loop\n",
      "1.0171787738800049\n",
      "1.871687889099121\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.932150661945343\n",
      "1.8545056581497192\n",
      "50 loops, best of 3: 1.54 ms per loop\n",
      "0.8963805437088013\n",
      "1.8622294664382935\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9883332848548889\n",
      "1.9165235757827759\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0065093040466309\n",
      "1.9213820695877075\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9831069707870483\n",
      "1.8940064907073975\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "1.0976672172546387\n",
      "1.859683632850647\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0611366033554077\n",
      "1.838294506072998\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0289955139160156\n",
      "1.8952610492706299\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.8878443837165833\n",
      "1.9366623163223267\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9999676942825317\n",
      "1.9656920433044434\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0331406593322754\n",
      "1.8805748224258423\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8540570735931396\n",
      "1.9150948524475098\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.053358793258667\n",
      "1.962748646736145\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0905137062072754\n",
      "1.9155274629592896\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9880650043487549\n",
      "1.9293056726455688\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.026888370513916\n",
      "1.8844863176345825\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9923015832901001\n",
      "1.9336037635803223\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8971617221832275\n",
      "1.8725190162658691\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.920857310295105\n",
      "1.8894339799880981\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0053694248199463\n",
      "1.9092943668365479\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9656652212142944\n",
      "1.9232662916183472\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9977065324783325\n",
      "1.8844738006591797\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.2036333084106445\n",
      "1.898746132850647\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0021357536315918\n",
      "1.940970778465271\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9431014060974121\n",
      "1.9282381534576416\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9904188513755798\n",
      "1.904990553855896\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9765397310256958\n",
      "1.8933037519454956\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9893286228179932\n",
      "1.951127052307129\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8894766569137573\n",
      "1.9410812854766846\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8829526305198669\n",
      "1.8478164672851562\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9760034084320068\n",
      "1.8913582563400269\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8971577882766724\n",
      "1.9102680683135986\n",
      "50 loops, best of 3: 1.54 ms per loop\n",
      "0.9775246381759644\n",
      "1.977861762046814\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.91898113489151\n",
      "1.900395154953003\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0857927799224854\n",
      "1.9142166376113892\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "0.893352746963501\n",
      "1.937159538269043\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9891102313995361\n",
      "1.8830279111862183\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9243213534355164\n",
      "1.9274885654449463\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0036383867263794\n",
      "1.9389046430587769\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.7969959378242493\n",
      "1.9497418403625488\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0847009420394897\n",
      "1.9572519063949585\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.864370584487915\n",
      "1.9119330644607544\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9453173875808716\n",
      "1.96038019657135\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8675397634506226\n",
      "1.8303234577178955\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9847473502159119\n",
      "1.8589293956756592\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9194648265838623\n",
      "1.915841817855835\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9463154077529907\n",
      "1.844448447227478\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0360722541809082\n",
      "1.858137845993042\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.04253351688385\n",
      "1.968713641166687\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "1.0069658756256104\n",
      "1.8724918365478516\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.0952907800674438\n",
      "1.9573665857315063\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.802614688873291\n",
      "1.8787537813186646\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8913273811340332\n",
      "1.8159719705581665\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9341927766799927\n",
      "1.867208480834961\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0589802265167236\n",
      "1.9539941549301147\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9097493886947632\n",
      "1.906331181526184\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9541696906089783\n",
      "1.909193992614746\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9327772855758667\n",
      "1.9232544898986816\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "1.146897792816162\n",
      "1.8370968103408813\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0738775730133057\n",
      "1.8403311967849731\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "0.9754031300544739\n",
      "1.9976423978805542\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8779315948486328\n",
      "1.9406893253326416\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0117578506469727\n",
      "1.8763118982315063\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9227365255355835\n",
      "1.8432515859603882\n",
      "50 loops, best of 3: 1.54 ms per loop\n",
      "0.9738056659698486\n",
      "1.8978081941604614\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9701780080795288\n",
      "1.9601927995681763\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "1.0007644891738892\n",
      "1.883573055267334\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9890692234039307\n",
      "1.9037498235702515\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.9662845134735107\n",
      "1.9076638221740723\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9601151943206787\n",
      "1.8417010307312012\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9368103742599487\n",
      "1.8808245658874512\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9241345524787903\n",
      "1.9551916122436523\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9748488664627075\n",
      "1.962646722793579\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8990902900695801\n",
      "1.9472965002059937\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9632441997528076\n",
      "1.8204729557037354\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "0.9495596885681152\n",
      "1.950182318687439\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9088999032974243\n",
      "1.8404701948165894\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8672885298728943\n",
      "1.9343440532684326\n",
      "50 loops, best of 3: 1.53 ms per loop\n",
      "1.020755648612976\n",
      "1.8917264938354492\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8814740180969238\n",
      "1.8805466890335083\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9514379501342773\n",
      "1.8690009117126465\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.017188549041748\n",
      "1.8670145273208618\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9998301267623901\n",
      "1.9476951360702515\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8669408559799194\n",
      "1.9175958633422852\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8989511132240295\n",
      "1.9025661945343018\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9505672454833984\n",
      "1.8321565389633179\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0252314805984497\n",
      "1.8379268646240234\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8472341299057007\n",
      "1.875765085220337\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.9293055534362793\n",
      "1.8557850122451782\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9614561796188354\n",
      "1.8672025203704834\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9699405431747437\n",
      "1.9759284257888794\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.933645486831665\n",
      "1.8617061376571655\n",
      "50 loops, best of 3: 1.52 ms per loop\n",
      "0.886096715927124\n",
      "1.9568455219268799\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "0.9915707111358643\n",
      "1.9972354173660278\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9266557097434998\n",
      "1.928452491760254\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "0.8907764554023743\n",
      "1.8821607828140259\n",
      "50 loops, best of 3: 1.51 ms per loop\n",
      "1.0371427536010742\n",
      "1.883976697921753\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.9632725715637207\n",
      "1.9309386014938354\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "1.053124189376831\n",
      "1.883291244506836\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "0.9354572296142578\n",
      "1.922497034072876\n",
      "50 loops, best of 3: 1.5 ms per loop\n",
      "0.8532063961029053\n",
      "1.9385792016983032\n",
      "50 loops, best of 3: 1.49 ms per loop\n",
      "0.9147511720657349\n",
      "1.8892595767974854\n"
     ]
    }
   ],
   "source": [
    "batchsize = 200\n",
    "KARPATHY_CONSTANT = 3e-4\n",
    "learning_rate = KARPATHY_CONSTANT*10\n",
    "\n",
    "prior_variance = 2\n",
    "# train discriminator for some time before starting iterative process\n",
    "%timeit -n 300 train_D(learning_rate, batchsize, prior_variance)\n",
    "# print initial values of training errors\n",
    "print (train_D(0, 100, prior_variance))\n",
    "print (train_G(X_train, y_train, 0, batchsize))\n",
    "for i in range(200):\n",
    "    %timeit -n 50 train_D(learning_rate, batchsize, prior_variance)\n",
    "    print (train_D(0, 100, prior_variance))\n",
    "    print (train_G(X_train, y_train, 0, 100))\n",
    "    train_G(X_train, y_train, learning_rate, batchsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ru3dvjB07Fh06dEj34RGRxBi0EhERERERkWJlzJzWSIsdExERJap79+7pPoSM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\nOCA7OLkA5DYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9fabefef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,8))\n",
    "\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(wrange, wrange, evaluate_discriminator(w.T)[0].reshape(300,300).T)\n",
    "\n",
    "W = sample_generator(100)\n",
    "plt.plot(W[:,0],W[:,1],'g.')\n",
    "\n",
    "W = sample_prior(prior_variance, 100)\n",
    "plt.plot(W[:,0],W[:,1],'r.')\n",
    "plt.axis('square')\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax])\n",
    "plt.title('estimated log density ratio $\\Phi^{-1}(D)$')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.contourf(wrange, wrange, (llh1+llh2+llh3).reshape(300,300).T)\n",
    "plt.axis('square')\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax]);\n",
    "\n",
    "plt.title('log likelihood');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FyHgKgOkPKXIVwZFuLq0BAFneLOb5srxZEY81EhVmoyZmRE8s4kMrJrSRI9cJ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\nSDMj+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9fabdf9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.contourf(wrange, wrange, np.exp(logpost.reshape(300,300).T),cmap='gray');\n",
    "plt.axis('square');\n",
    "W = sample_generator(1000)\n",
    "plt.plot(W[:,0],W[:,1],'.g')\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax]);\n",
    "plt.title('true log posterior');\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MphETQogX0eMvpnsRFeaXncxsM0X5rZkFTc6BnAOQcwBF4xw8qQNExuwLIYQQ\nQghRTEmwL4QQQgghRDElwb4QQgghhBDFlAT7QgghhBBCFFMS7AshhBBCCFFMSbAvhBBCCCFEMSXB\nvhBCCCGEEMWUBPtCCCGEEEIUUxLsCyGEEEIIUUxJsC+EEEIIIUQxJcG+EEIIIYQQxZQE+0IIIYQQ\nQhRTEuwLIYQQQghRTEmwL4QQQgghRDElwb4QQgghhBDFlAT7QgghhBBCFFMS7AshhBBCCFFMSbAv\nhBBCCCFEMSXBvhBCCCGEEMWUBPtCCCGEEEIUUxLsCyGEEEIIUUxJsF+IdLY6UiunorPVFXZThBBC\nCCFEMWRe2A14UWm9tCQ1TwIzIB1sDttgFWhV2M0SQgghhBDFyDPr2ffz80Oj0TB79uxntcsiS2er\n+y/QBzCDpOZJ0sMvhHihyH1BCCEK3jMJ9v/44w+uXr2KSqV6Frsr8tJd0v8L9DOZ/W+5EEK8AOS+\nIIQQz0aBB/sxMTF8++23TJgwAUVRCnp3zwWzSDN4PK5P/99yIYQo5uS+IIQQz06BB/vTp0/H3d2d\nTp06FfSunhvqRDU2h23+C/jTweaQDepEmS8thCj+5L4ghBDPToFO0A0ICGDbtm1s27atIHfzXLIK\ntMLimgXpLumYRZpJoC+EeCHIfUEIIZ6tAgv2U1NTmTx5Mn5+flSuXLmgdvNcUyeqUd+RIF8I8WKQ\n+4IQQjx7BRbsL1y4EK1Wy3vvvVdQuyi2dLY66fEXQhQ7+X1fuHz5cr7UkxdJSUmF3obCJudAzgHI\nOYCifw4KJNgPCwvjl19+4euvv0ar1aLVavWTsFJSUoiLi8POzg61WgLZxxXn/PvyJUaIF5fcF4QQ\nonColAJIhXDy5EneeustAINMCyqVCkVRUKlUbN68GY1Gk+M6T58+Tbt27fK7qUWKzlZHrF+sYVrO\ndHBY5PDcB8fF+UuMEIXhzz//xNvbu7CbkWP5fV84ffp0oR5/Zg9erVq1Cq0NhU3OgZwDkHMAReMc\nPOmaWCA9+x4eHvz2229GywcOHEi3bt3o1auXjNc04Un595/nsf1ZvUTM4prFc/8lRgiRM3JfEEKI\nwlEgwb69vT0NGzY0ua58+fI0aNCgIHb73NPn33+sZ/95z79fXL/ECCFyTu4LorApikJwcDB3794l\nPDycuLg4nJyccHV1pVq1ajg5ORV2E4UoEAWaevNxKpVK3pb4BJn59w2GuxSD/PvF9UuMEOLpyX1B\nFLQbN25xdGAeAAAgAElEQVSwc+dODhw4wN27d02WUalUNGjQAF9fX9q3b4+dnd0zbqUQBeeZBvtF\ndZZyUVIc8+8/yy8xMglYiOeL3BdEQVAUhdOnT7Nq1SoOHTqUo/KnTp3i1KlTzJs3Dz8/P7p37461\ntfUzaK0QBeuZBvsiZ4pj/v1n8SVGJgELIcSLTafTcejQIRYtWmTyi2TdunXx8vLC1dUVBwcH7t+/\nT0hICEeOHCEsLAyA6Ohopk+fzpIlS/D396dLly6SJUo81yTYF89MQX6JkUnAQgjx4lIUhaNHjzJv\n3jyuX79usM7JyYl+/frRqVMnXFxcTG4/duxYzp07x/Llyzl48CAAUVFRTJkyhQ0bNjBmzBi8vLwK\n/DiEKAgS7ItiQSYBCyHEiykwMJCffvqJM2fOGCyvVq0agwYNon379lhZPfkpr1qtxsvLCy8vLy5c\nuMCCBQs4duwYkDHUbMiQIXTq1IkRI0bg7OxcYMciREGQYF8UCzIJWAghXhyKohAQEMCiRYsICAgw\nWFezZk2GDh1Ky5Yt8zT8xtPTkx9//JFjx44xY8YMbt++DcCOHTvYt28f3bp1o1+/flSoUCE/DuWJ\nFEUhISGBhw8fEh8fj6IoKIqCra0tLi4uMpFY5IgE+6JYKK6ZjIQQQhg6e/Ys8+fPN+rJL1++PP7+\n/nTo0CFfxtg3adIEHx8f1q5dy4IFC0hISECr1bJu3To2bNhAs2bN9HMA8iotLY2IiAhCQkIICQkh\nLCyM0NBQwsPDCQ8PJyIigtTU1Cy3t7Ozo0aNGnh6euLl5UXjxo1lUrEwIsG+KDaKYiYjyQ4khBD5\n4+rVq8ydO5e///7bYHn58uUZNGgQXbt2xdLSMl/3aW5uTv/+/fH19WXRokVs3bqVlJQU/UTgQ4cO\nYWVlRf369albty4ajQYXFxecnZ0xNzdHp9Oh1WqJiori/v37hIaGcu/ePf1/oaGhpKWl5bl9CQkJ\nBAYGEhgYyIoVK7CysqJJkya8+uqrtGjRAnNzCfOEBPuimClKmYwkO5AQQjy9+Ph4fvzxRzZt2mSw\n3M3NDT8/Pzp16lTgQa2zszOffPIJQ4cOZf369WzYsIHo6GgAtFotf//9t9GXkKdlbW1NmTJlcHZ2\nxtHREXt7e8zMzFCpVMTFxekzCUVGRuq30Wq1HDhwgAMHDuDm5sbQoUPp1KmTZBN6wUmwL0QBkOxA\nQgjx9E6ePMkXX3xBeHi4flmZMmUYMmQIXbt2feY916VLl+bdd9/Fz8+PkydPsm7dOgIDA4mPj891\nXRYWFri5uVGhQgUqVKhA+fLl9f+5urpSokSJHL1wLjw8nPPnz3P06FEOHjxIbGwsACEhIUyePJmt\nW7cyceJEKlasmOs2iuJBgn0hCoBkBxJCiLzTarX8+OOPrF27Vr/MysqKIUOG0Ldv30Ifl25ubk6T\nJk0oVaqUfsLsuXPnCA4OJiIiggcPHqAoCmq1GnNzc5ycnHBycsLV1VUf4JcpUwYzs6dPIlG2bFnK\nli1Lu3btSEtL49ixY6xYsUI/p+Hs2bP06dOHESNG0Lt3b3lj9QtIgn3xwqtSpUq+1xkUESTZgYQQ\nIg8ePHjAyJEjDV6K5eXlxeTJk59JBpzcUqlUVKlSpUDuJbllbm5OixYtaN68OceOHWPq1KmEh4ej\n1WqZNm0aly5d4vPPP5ex/C8Y+bRFsWNqUuyzvghXK1ONyIuRhHqGoqgVVDoV5S+Wx6WMiz6NmxBC\nCEMPHz7k/fff5+bNm0DGUBd/f3/69ev3VL3gKakpXLx6mXNXLhIXH49Ol465uTkvVamOp3stypVx\nLVY93iqViqZNm7J27Vpmz57N5s2bAdi+fTuxsbF8++232b57QBQfEuyLYuXRSbEqnYryF8rjEmT6\njYkFzSXIhZIhJUlyTMImxgYLrQVg/MVDgn8hhMjILDN8+HB9oO/k5MTMmTPx8PDIc53nr1zktw2r\n+PvMSbQpKVmWc3Upy2ttfenc7lUquJbP8/6KGnt7ez799FO8vb2ZPHkyaWlpHD58mLFjxzJjxgzp\n4X9ByOBhUWy4ubuR3CJZP3RGUSuEeoaSapV1juKCZqG1wCHCQR/om5L5+LcoPAIWQojCkJaWxrhx\n47hy5QqQEej/8ssveQ70rwZd5/0JH/J/H/nz1/EjTwz0Af6NDGfRmt/oMaQvIyd9zKl/zqAoSp72\nXRR17NiRmTNn6nvzjx07xpQpU9DpdIXcMvEsyFc68Vx7NECOdYxFURtenBW1QpJjEhYRWQfbRcmj\nxyM9/kKIF8WCBQv0qSvt7OyYM2dOnjtAduzfzdS50w0C/JIOjjSq15D6dV6mfJlyqNQqEhITuXTt\nCucunyfw0nl9cH/s9AmOnT5B9cpV6d25Jx1btcPWxvapj7GwvfLKK8yYMYORI0eSlpbG9u3bKVGi\nBGPGjClWQ5iEMQn2xXMnqxuATYwNKp3KIOBX6VTYxNg8o5blr8zjTLVK5XbybXkxlxCiWLpw4QJL\nly4FwMzMjGnTplGzZs1c15Oens6sRT+xZtsG/bLyZV0Z9Ho/OrfriJWl8Rj1Nk1aABAW8S9/7NvF\n5p2/E/ngPgA379zim3k/8OOSn+nYqh2dWnegjqb2cx0YN2rUiC+++ILPPvsMRVFYs2YNzs7ODB48\nuLCbJgqQBPviuZFdL4+F1oLyF8obToq9UP6JQ2iKushqhpN8rQ9Zy4u5hBDFhlarZfLkyfrhJG+/\n/TY+Pj65rken0/HNvB/Yume7ftlrbXwZN2wM1jmYiFqujCtD+w5m8Bv92XvkAGu2buDyjasAJCQm\nsHHHVjbu2Iqba3laNmpKk4aNeblWnVy3syjw9fUlPj6eb775BoC5c+fi5uZG+/btC7lloqBIsC+K\nvNw8ys1qUuzzKNUqVR/oQ8aQpOQWyVRLqkbI1ZBCbp0QQjy9BQsW6Ics1qxZkyFDhuSpniXrVugD\nfbVazZihH9Crc49c98JbWFjQqXUHXm3VnovXLrP+j83sPXyA1LSMuV8h/4ayaut6Vm1dj5mZGW5l\ny1OtYmW8POtSoZwbrmXK4ljCkZIlHLCysiqyTwFef/117t+/z8KFCwGYNGkSpUqVokGDBoXcMlEQ\nJNgXRVZex2taaC2emzH6T5LkmJTlHITMcyPj+oUQz6tLly6xYsUKIGP4zqRJk/KUHSbw4jkWrFqi\n/3nSh+Po1Mb3qdqmUqnwdPfA092DMe+OYN+Rv9j5114CL57Tj+1PT0/nbmgwd0OD+evEEZP1mJub\nY2Zmhor/gn61WoVabYaVpSU21jbY29pRumQpnEqVpkI5Nyq7VaRa5SpUdquEWl1wQzffeecdgoOD\n2bVrFykpKYwZM4ZFixbx0ksvFdg+ReGQYF8UOZKVJkNO5iBUqVJFAn4hxHMnLS2NKVOmkJ6eDmQM\n33F3d891PUnJSUya8bV+GNDgXv2fOtB/nIN9CXp07EKPjl2IjnnI36dPcPzsKS5evczd0HtP3DYt\nLY20tDST6+ITst9v3Vqe+Hg1oHWTFri6lMnrIZikUqmYOHEiDx8+5Pjx4yQkJPDhhx+ydOlSnJ2d\n83VfonBJsC+KFAn0/5PTOQjSyy+EeN4sXbqU69evA1CtWjX+7//+L0/1/Lp6GaHh/wLg6e7Bu/3z\nVk9OlXIsSac2vvovFAFnThMcFoKZhRnBYSHcj44iJjaWmLhYUlJSSE1LJe1/X2iAjKcCikJaejra\nFC3JyckkJCWa3FdsfBxHTv3NkVN/M2PhHGpWe4mOLdvxausOOJd2ypfjsbS05LvvvmPIkCFcv36d\nf//9l9GjR7NgwQKsra3zZR+i8EmwL4oECfJNy80cBOnlF0I8D44cOcIvv/wCZPQuf/bZZ1haWua6\nnvD7EazZthHIGC7z+chPnvlLouxsbNFUq0GtWrXyXEdaWhrRMQ+JiIrkbsg9bt+7y5UbVzl35SLx\nCfH6cteCbnAt6AZzly2gWcNXeLv3ADzd8/7CMf0x2Nkxa9YsBg8eTGRkJJcuXWL69Ol89tlnT123\nKBok2BeFTgL9J8vNHITi2suvs9WR7pIu6UeFeM7duXNHn/YRYPDgwdStWzdPdS1Zu5yU1Ixc+q+/\n2o1qlarkVzOfKXNzc1ycnHFxcqZ2zf++NOh0Oq4F3eDA34c4dOIoN24H6ZcfOnGUQyeO0qheA94f\nMITa7nn/sgFQtmxZZs6ciZ+fH1qtli1btuDj40OHDh2eql5RNMhdUxQqCfQLRnE6r1ovLbF+sST0\nSCDWLxatl7awmySEyIOEhATGjRtHfHxGb3XTpk1577338lRXyL9hbPlf9h1rK2ve7j0g39pZVKjV\najQv1eT9gUNYPXcJa39axqDX+1K6ZGl9mRNnAxg85j2+nPUt96Ojnmp/Go2G0aNH63/++uuvCQmR\nzG/FgfTsi0JR1IPRnLavKPegF4dhPTpbHUnNk8DsfwvMIKl5EhbXLKSHX4jnSFxcHCNGjNCP069Y\nsSJfffUVZmZm2Wxp2q9rluon977Z5XWcSpXOZgtI16Xz94XT/HPjIpduX+deRCgqlRoztZoStva4\nubji5uxK1fKVqFGhKpVdK2BhXnQyu1WrVIUP3n6Pd/q/zba9O1i2YRXhkREA/P7nTvYd/YsP/YbR\n3bdznlN+9uzZkxMnTrB//34SEhKYNWsW06ZNy8/DEIVAgn3xzBWVQD8/2pFdHc8q2E61SjU5rv95\nD/jTXdL/C/QzmWUsV9+RYF+I50F8fDz+/v5cvnwZAHt7e7777jtKlCiRp/ruhASzY/8eAOxs7RjQ\n881stzl+8Qw/rv+VGyG3syxz6fY1g5/NzcypVr4SNStWo1r5ylQpV5HKrhVwKemEtYm38QLEJyUS\n/iCSiOhIwqIi+DcqgoiHUUTHPSQ6LgZtSgpp6RnZeext7HCws8elpBNVylWkarlKeFbTUKqE4xOP\nxcrSil6v9aB7h86s2baBX9csIzEpicSkJKbOnc5ffx/msxEf4+KU+4w6mXMozp49S3R0NAcOHODC\nhQt4enrmui5RdEiwL56pwgr0Te032TyZGJsYHJMcsU4rmKwDj++3IALvx9+yW/5CeVyCXAza8LwG\n/GaRZpCOYcCf/r/lQogiLzExkZEjR+oDfUdHR+bOnUvNmjXzXOfCVUv0qTb7detFSYesg+PE5CQm\nLZrOwcC/jdbZWdtgpjYjLT2dRG2S0fq09DSuBQdxLTjIaF0JW3vsbWzRpWe0I01JJz4xAe3/5hA8\njWrlK9Ow1su0rt8Ur5dqZ5lr38LCgoGv9+XVNh2YvWg+u/7aC8Cx0yfoP8KPbz6ZjHfdernev4OD\nA35+fkyfPh2AX3/9lVmzZuX9gEShk2BfPDPPOtB/0v5uOt/kQvkL+gDZM9ST6verP9M25UcAbuot\nu6GeoZQMKVksevjViWpsDtv8N5QnHWwO2cgQHiGeA+Hh4YwePZqrV68CGUHk/PnznyrQv37rJnsO\n7c+oz74E/br3yrJsdFwMo36cZNBjX6NCNQZ2fJ061WpR3rmsfrhLkjaZ0Pvh3A0P4WbIba7fC+LG\nvdsER4SarDsuMZ64xHiT657E0txCP3QpSZtsskxQ6B2CQu+wdt82XEo60bFRa3q36ULZ0i4myzuX\ncmLKR5/RpkkLvpn3A9ExD4mOecjwiR8xceQ4Xm3dPtft7NGjB0uXLuX+/fscOXKEoKAgqlWrlut6\nRNEgwb54Jp5VoJ+T/SSbJ+sDfcgIkC+Uv4DbQ7cC6+E3JT8C/ye9ZffxDD7Pa8BvFWiFxTULycYj\nxHMkKCiIDz74gPDwcABsbW358ccfnyrQB5i3bIE+k8+Anm9ib2dvslxYVDgfzPyMu+EZE0ztrG0Y\n3eddOr3SFjO18ZNBGytrqrtVprpbZVrXb6JfnpCcyM2QO9wKvcvtf4O5FxFGVMwDImMekKRNJiU1\nBZ1Owd7WjhK2djjalaBsaRfKlnLB1akM5ZzKULaUM6UdSlHS3sEgNWhaWhqxifGE3v+XW2F3uR58\ni9NXz3P93n9PEiIfRrF89wZW7d1EG+9m+HXuR7XylUwec+smLXjZow6ffv8lAefOkJaWxsQfviIu\nPo7eXXrm6jxbWVnRp08f5s6dC8Cff/7JO++8k6s6RNEhwb4ocM8i0M/NPmJsYkwGyDE2MVjHFc5L\nRPKaMjMnb9l9fD/PY8CvTlTLGH0hnhOBgYGMHj2a2NhYICOt46xZs6hRo8ZT1Xvs9AmOBhwHwLm0\nE326vmGyXGJyEh/OnqgP9Es7lGL2yC9xr5T7p7d21rbUrV6LutVNp7bMHJ6Ulzz75ubmlHYoSWmH\nknhW0+iXP4yP5cg/J9hz6hCnLp8lXacjXadj76lD7As4QrfmvrzTbQBODqWM6ixdshRzvpzG1LnT\n+f3PnQBM+2U21tbWdG3fKVfta9++vT7Y379/vwT7zzG5e4rnWpUqVXL9ZcIxyRGVzjBTgUqnwjHp\nyZOinoXcHk/mW3Yzjyert+w+vg8hhCgIv//+O/7+/vpAv0aNGixduvSpA/1krZbpP8/W//z+AD9s\nrI07NRRF4evfZnMrLBiA8s6u/PrJ9DwF+oWlpL0DnZu258cPp7Dlm6UMfrU3DnYZk5l1io7Nh3by\n5ufvcvT8KZPbZ75grH+P/yYufz1nGsdOn8hVO9zc3PRfYm7cuMGdO3fyeESisEnPvihQBRVYPk29\n1mnWeIZ6Go3Zf5ZDeLKTm57+3LxlVwghCkJqaio//PADGzZs0C/z9vbmhx9+wN7e9FCb3Fi0ZhnB\nYRk99Z7uHnRu96rJcqv2bmbvqUNAxtCcGR9MpkKZck+9/6cRFf+Q62G3uR5+l9jEOBJTkknTpeNS\nohSuJV2oXqYi7uWqmpyIW7a0M/49BzO405us3LOJ5bs3kJyiJTYxnlE/TuLtTm/yTrcBRkOTVCoV\nI//vfZK1yWzcsRWdTsfE6V+xeu6SXGXpadmypf7pxalTp6hcufJTnQtROCTYFwWmIAL9/Kqz+v3q\nuD10K/BsPE8rp0F/bt6ym1nv8zicRwhR9ISFhTF+/HguXLigX9alSxfGjRuHlZXpFJW5cf3WTZZv\nWgOAmdqM8cPGmAyMz928zJwNi/U/f/bWh1mOby9I2tQUzty+xLFrZzh2/Sz3HoRnu00pOwcavfQy\nvnWa0fill42Oz9bahqFd+9O9RUe+XjabYxcCAFiyYy3XgoOY+u54bKwM72MqlYqP3/uQkH/DOH7m\nJDFxsXz14/fMmvxdjvPwN2jQQP/vs2fP8sYbpodOiaJNgn1RIIpyoJ/JOs260MboZyWrdKAFEZxL\nwC+EeFpnzpxh0aJF+mE75ubmjB07lp49e+b5xU6Pik+I59Pvv9C/QGtAzz7UrPaSUbnUtFS+XjYb\nnZKRCnOA7+u0b9gi2/pT09K4GXGXiNgHxCcnkpyajKW5JbaW1jjY2OPiUBqXEqWxtcr6XqEoCnfv\nh/LP3ascvXaG4zcCSUrJ3Zu+oxNi2fXPYXb9c5iqLhXwb9+P5u7eRufQpaQTMz6YzJIda1mwbQWK\nonD0/Ck+mPkpc0d9jfVj7VSr1XwxegJ9hg0mOuYhx06f4Pe9O+ja4bUctcvDwwNLS0tSUlI4e/Ys\niqLky+cqni0J9kWRVxhjzAvjDbrZpQPN6yReIYTIb2lpaaxevZodO3bol7m6uvLNN99Qp06d/NlH\nehoTvv+CW8EZY8UrV6jEkL5vmSy7au9mboXdBaBmxWr4dzddDiAuKYGtp/fx1+WTXA27RUpaarZt\nsbOywcWhNKXtSmJtYYmVhSXJKVpCo8K5n/CQhBTjPP0AapWKWm4v4eFWnZquVSjj6IStpTUqVETE\nRhEaHcGZ25c4ffuiPkf/rch7jF31PW1qN2Zcl6E42hq+fEytVuPXuS8eVWoy/uepJGqTOHfzMp8t\n/J5v3/8U88feSly6ZCnGDRvDJ1M/B+Cn5b/SoUVbrK2z7+yytLTE09OTM2fOEBERwb1796hYsWK2\n24miRYJ9ke/yMzgviED/0d5zTQVN9hs8QVbty21Anpt0oPnZIy+9+0KI3AoLC2PChAmcP39ev6x5\n8+ZMnjwZR8f8SXSgKAqzfv2Jv0+fBMDezp7pn36FtYlhQf9GRbDoj9VAxtCV8QM/MEhxmSkmMZ7F\nBzew7fR+ElNM57jPSoI2iYTIEG5HhmRbtoS1HU1r1qNJzfo0fskLR9snz1kY2LwbyakpHL4SwPIj\nW7kadguA/RePc+7uVT7v/j6Na3gZbfeKpzfzxkzF/4fxJGmTOfTPcX7avJQRb/gZlW3TpAXNGr7C\nkVN/ExX9gDW/b2Rwr/45OnZvb2/OnDkDQEBAgAT7zyEJ9kWRVRCBfnTNaA7bHEan0qFW1CQlJVEv\nJfdvGMxObt+cm9t0oBLwCyEKQ0BAAJ988gkxMTFARi+zv78/gwYNyvJNr7mVmprK9F9+ZNOubUDG\nOP1vx02mSkXTk0NnrVtI8v+GzXRv3pHaVd2Nypy9fZnPN8wmMvaBwXJXR2dqV3iJys5ulLC2w9rS\nipS0VJJSknmYGEtk7AMiY6OJjHtAZNwD0v43nCiTChX2VrbUrvgSdSrWxKtyLbwqazA3y114ZW1h\nSfs6TWhbuzE7/znEjJ1LiU9O5H5cNB+u+IYRHQbSr2lno+1qV3Xnm3fHM3rOF+gUHSt2b6R2VXfa\nejczKus/aChHA46jKArLN67mjde6Y29rl23bGjZsyMKFC4GMz79Hjx65OjZR+CTYF/kqvwL0gng6\nkKBKYJvNNnSqjDGdOpWOwzaHqZlaEzsl+wtefrQBTAf+melAH8+X/6R0oIUVpOtsdfKCKyFeQCdP\nnmTUqFFotRmBtZOTE/7+/nTr1i3f9nE/OooJ307m7MVz+mUfvTeCRvUamiwfeP0i+88cBcDR3oH3\nexgP31l97A/m7FlBui7j2m9hZk7Hl5vT55XXeKlszifw6nQ64rWJaFNT0KalYG1hxb93QzBTm+Up\nz74parWa1+q1okE1T77c9BMBty6gKAqzd/+GlYUlr/t0MNqmSZ2GDH/9bX7csAiAb1fMxbtmHUqW\nMLx/1KhanfbNW7Pn0H5i4+PYvOt3Bvbsk22bPD09sbKyQqvVcuLECdLS0kw+ORFFl9ypRb4paoH+\n4znrI80i9YF+Jp1KR7B5MLfNb5OgSsiX/ea2XfBfOtBH8+XnJB3os57PoPXSEusXS0KPBGL9YtF6\n5W4SmhDi+RQQEGAQ6Pv4+DBlypSnfiNupvT0dNb9sZne7w3SB/rm5uZ8NuJj3ujU3eQ2iqLoA1yA\nd7r2p6S9g0GZtcd3MGvXb/pAv24ld9aNmMVn3d/PVaAPGYF45qTdCqVdcS5RyuTbePNDWUdn5rz1\nGYOa/fdFatr2Rfx54ZjJ8v079KTFy40BiImPNTgvj3q79wD9v9f9vom09LRs22JpaYmPjw8ADx8+\nJDAwMMfHIYoG+WomipT8CF6zqsMl3QW1ojYI+FWKij22e/TDeponNS+QYT1Pamdm73xe04HmRw9/\nTurQ2epIap4Emfc2M0hqnoTFNQvp4ReiGLt16xYfffSRPtBv0qQJ06ZNIygoKF/qPxEYwI+L53Mt\n6IZ+WemSpflu/Bd41a6b5XYHzhzlQtAVACqWKU+P5oa59w9cOsHMncv0P/dr0plh7fvleohNXsUk\nx3My+CIXwm9y80EIt6NDSVd02FlY42Btj08FD7rWakl5B9N579VqNf7t+5Gansbqv7ejKApfbpqH\nW6my1HIzfEmYSqVibD9/Aq78Q6I2iT+O/UnPlp0M3swL8FKV6vh4eXMy8DT/Robz19+HadesdbbH\n0rZtWw4fPgxkvE330ZScouiTYF/ki4IM0vNrezvFjuZJzfVj9lVKRi96bob1JKgSiDSLxCXdJVdD\nf5603aNBf1bpQLNKyfloHQU9pCfdJf2/QD+TWcZy9R0J9oUojhRFYdKkScTHxwPQqFEjpk2blm/5\n82cv/okTZwMMlvu2bMuHfsNwLu2U5bYpqanM3bhE//Pw1982GFpyLew2kzbOQVEyhkb2b9qFEb4D\njeqJSoxh7/UTXLl/mzvRYYTERpKu6FABVuaWONk64mJXCld7J9wcy+Dm4EJZ+9KUsSuNg5Wtvv5Y\nbQJRCQ+58eAeF8OD+CfsGlci76CgGO0zOikWYiO4FBHEsjPbaV3NmzHNB+BkazxsU6VSMcJ3IA8S\nYth97gjatFTGr53BqmE/GKUDLVvamaFd+zN7/a8AzNu0lPkffWtUZ99uvTgZeBqA1Vs35CjYb968\nOWZmZqSnp7Nv3z5Gjx4tQ3meI/JJiSLhaQL93GxbL6UeNVNrEmkWSbIqmV12uwzW61Q6Is0isUsz\nDuTPWp41mNyb06cAOd0uq9Sa2aXkzC/ZfWEwizSDdAwD/vT/LRdCFEunTp3i0qVLAFSqVInvvvvu\nqQP91NRUFq39jaXrV+rz5wNUq1SVj98biXfd7K+rK/ds4l5kGAB1qteiVb0m+nXa1BQ+3zBbn8qy\nnecrDG9vmHnmYngQy8/u4PCdQNJ1hpNuM8WnJBGVGMO1+3ezbIcKUKvUpB/UZVkmk72lDdbmViSm\nJpOYmpENSEFhf1AA58Nv8FV7f14uV8NoO7Vazafd3uPu/TAuh94k7GEkc/es4OMuQ4zK9m7ThfUH\n/iD0/r+cvnqOC0FXjHr3m3g3opJbRe6GBHPu8gWu3ryGe/UnD8dydHTklVde4ciRI0RFRfHXX3/R\nrl27bI9ZFA3SHSeea3n5kmCn2FElrQoV0yqiVgz/BNSKGpd0F6NtElQJ+oAd/nsKkN04/7xs9+gx\nZZWSM9ncOG1cQY/fVyeqsTlskxHwA6SDzSEbGcIjRDG2bNl/w2D8/Pywt39yGsns3Aq+zaBR77Bo\nzW/6QL+Mswufj/yEVXMW5SjQv/PvPRb9sQrI6Pke8+a7Bi96Wnxwoz5F5ktlK/F5d399pqDU9DTm\nH63ZBhQAACAASURBVN/A0M1f8det00aBvotdSdwcXHBzcKGUtWF+e1MUIF0xHehXLulK7zrtmPbq\nSLYN/IG9/zePP96ayf4h89k6cDp+3l1xtM44n5EJD/Hf9h0bL+w3WZeVhSVfvPEBVuYZb0rfeGoP\nZ25dMipnYW7BAN/X9T//tmuDURm1Wk2v1/6bB7Fqy/psjxMweHvuunXrcrSNKBqkZ188tYIeflMQ\n+wTjYT1mmNHNthu1S9U2Kns59TK6BOPJveryaqpY/NeWx3vGs5oUnNXTg0yZveyFmZLTFKtAKyyu\nWUg2HiFeADdu3ODEiRMAlC1bFl9f36eq7+adW7w7bgQxcRlv21Wr1Qzs2Zchfd8ymT/flJTUVL5Y\nMkP/IqxerbvgUfW/XunLoUEsP7IVADO1mok9h2FtmVF3ZEI0n+yay6WI/+YaOFrb08m9KW2rN6Ra\naTdsLQyvq2npadxPjCE0LpKQmAhC4+4TER9NePwDElOTiUuIR6foKFPSCWfbkpQr4YRn2erULlvd\n5LCcTGXtnRjq04PutVvx6Z75nPv3Oum6dKYdXo6Z2ozuHi2NtqnsXJ532rzJnD0rAPj+j19Z4T/N\n6CVanZu049dtK3kQ95CDgX9z5997VHatYFim3av8vGIxCYkJ7D60D/+3hlLWucwTz32TJk1wc3Mj\nJCSEM2fOcP36dWrUMH4SIYoeCfZFoXo8aM9ubLqpbZ5mv1WoQltdW0LSQ3Azc8NB7WCyvJuZG2aY\nkc5/vUBmmOFm5vbEtiXcSTCaFJzV0wNTbUy+l5zrlJxPIydfFtSJahmjL8QL4OrVq/p/d+3a9anG\naIeGh/HB5x/pA/0qFSoxefQEatfMecpKRVH4ftU8/aTcsqVdeL/HIP36lLRUpmyap8+8M6BpV9zL\nVQUyJsuO+H06t6JDATBTqRns3YW36r+GpZlFlvs0NzPHtYQTriWcqF/e+CWMly9fBshz6k0Xu1L8\n1PVjZh1bw4YL+wD4/tAyStmUoGXV+kbl+7zyGrvPHeHav7e5FXmPP84eoHsDw+E01pZW9G7blZ+3\n/IaiKGz46w/G9HnPoIy9rR09O3Zh+aY1pKens2rzOkYNHf7EtqrVanr16sWsWbMAWLVqFZMmTcrT\ncYtnS+7Y4qnk51j7m8432e2xm7+r/81uj93cdL6Z7/szlfbSQe1ALYtaWQb6mWW62nTF7H8D1s0w\no5tNtyduA1C7cm262XbTDxdSK2paJLXI8eReTQVNrlNyPs05SrVKJbVyKjrb7MefCiGKt4cPH+r/\n7ebm9oSSTxafmMAHn39E5IP7ANSo+hKLp/+U60B/zsbFbDuyBwALc3O+fmccdta2+jKL/9rIzYhg\nAKqVqciQ1r0ASExNZvT2mfpA38WuFL90n8DQht31gb6iKNyNDWfHzeOsvLSX+We3MufMJpZe2MWm\na4c4FnKBkLj7+i8S+cnczJwxzfrzhmcbAHSKwsS9P3P+3xsmypoxsuN/X3AWHlhPkom3Afdo8SoW\n//tytv3YPpK1xmX6duuFxf+GBW3a9TsPYx4alXlc9+7dsbPLuH/t3LmT+/fv5+AIRWGTnn1RJGQ1\nNt3toZs+sM1rEJtfY9lbWrWknkW9bJ8CxOpiDco8up0uVJfrF3i1tW+L26XcpeTMy3CeyGqRhHqG\nZnwG6WBz2AarwKfPuCGEeD49GuyXLFkyz/XMWfwzd0PvAVChnBs/fvk9JeyzHw+fKV2XztyNS1j5\n/+y9eXxTdb7//zone9MmTdt0SfcFSksLlLVQNllVFEVxQx1Rx1FnnJk76nyd64wo6nhnu86dRQd/\nguLGqKggi7ILFEpZC7SlpXRf0iVt2qTNnpzz++Mk55w0SRcEQec85zGPx2nO55yc5GDO+/P+vN6v\n954v2Nf++8FfYEImN1kob6nB+0e2AvDKd1b8FFKxBG7Kg+d3v4lKr3QnUh6ON5b/P6RExgMALE4b\nNl88iG9azkI/MHzgKiHFSFPHI12dgAx1Ash+JxLkGtA07Vc3MFoIgsCviu5Hr60f++tOwuFx4fk9\nb+K9lS8hKsz/WTM1Iw+zxhSg5FIZuvt78e+SnXhk/p1+YzQRaiyYPBu7TxzEgM2CPScPY/ls/4Zc\n2ugY3LroJnyxaxvsDjs+3v45nnjg0SGvMzw8HLfddhs2bdoEt9uNTz75BAsWLLjszy3w3SAE+wLX\nhMEB+HDa9Gul6x+MilQNmc0/5DiEbbZt8MADEUSYIZ2BG+U3svuTk5OhIlWjDsTHJY27qlp8l8zF\nBfqA4KEvICAAp9PJbvNdc0ZDZ3cXvtyzEwAgk8nwfy/9ETGa0Jaag+nq7caLG/6C0xe5jrrP3PsE\nbpnFSVc6TT147t9/YbPuP5p9O+tD/6/Sz1DaUg4ACJPI8X+3PIOUyHjQNI1vmsuw7tw29Nr7R3w9\nLsqNS72tuNTb6ve6vPZzJCijEa+MQoxCjdiwSMSGaRCn1EAXHjOiYl8RSeLFhY+ha8CI8s46GCy9\n+N3ef+Hvtz4L8aDmXT9bcj+O1Z4FTdP48Og2rJyxFCqFf/H0nfOXYfeJgwCAzd9sx61FiwMmJA+u\nvA9b9+wARVH4+MvPcO+tdyJSPfTE7r777sMnn3wCj8eDL774AkVFRVfEilXg6iEE+wLXBWqbOqQ2\n/XID/cEZ9quNiTKxgT4AeOBBibMEJc4SECBAg4YIIixXLMe8NKb4ajQB/Giz9aMZb1PbAiZbgoe+\ngMB/NtnZ2ex2eXk55s0LLBodji++3sY63ty9bAVSE5NHfGzxueNY++7rMFuYYJwkSPzqnsdwz8Ll\n7Jh+mwXPfPQH9AwwqxB5SWPYLPe+2hP46BxjrywiSPzhxqcwTpsGm9uB/yn9CMf0lex5CBDIiU7B\njIRcJEVooZYpISJImJ1W9DkG0NbfjWZzJxrNHeiwGAOu1e52osHUjgZTe9DPEq+MQm50KqbGj8O8\n5Ikh6wSkIgl+v+RneOizl9BrM+OMvhpvlm7GL2bd6zcuKy4FN02cg6/OHobFYcPHx77CTxbc7Tdm\nYlYuspLSUdvagIvNdThfdwETs/wNKJLidbjphiXYuX8XLDYr3v30w2G1+wkJCViwYAH27t0Lk8mE\no0ePCtn96xwh2Be4bK6krEbuliNPnxfgJz/SLrKDzz04w75csRzzZKN/UI0GvUfvV8DLx9dYxQMP\nttm2oUBSABWpuqoB/GhQmBQBky3BQ19A4D+byZO5AtGysrJRH+9wOvDF19sAeIs7b1kxouOsdhv+\ntnk9thz+mn0tWq3B2kd/jek5k9jXBuxWPPPRH3GpowkAEKeOxp9W/RpSsQS1PS34/TfvsGN/NvNu\nTE8aj36nFb8rXo8LPU3svmnx4/CzghVIjAjeyXYwFpcdjaZ2NJo6cKbxAjrsfTDDji5rLyg6sIkW\nAHRYjOiwGHGguQxvnduGG9On486x84Jm/GPDNXh18ZP4xfY/w0NT2HRuN6Ym5mJWqn834UfmrcTu\n80fgoSh8fGwn7p15s192nyAI3LNgOX7//t8AAJ8e2B4Q7APA4/c/jD2H9sPldmHzzq24Z/md0MUl\nDPkdrFq1Cnv37gUA7N69GzfcMHxjLoFrhxDsC1w3ZHZnIrHPX5s+mgmFb2ywDDs/wB7peUYCP/AO\n5tgTDA88aPO0sdfyXXS/HQ6JQwJdhc5fsy946AsI/EcTHx8PnU4HvV6PiooK6PV66HS6ER9feuYk\n+swmAMC8wtlIiI0f9phztZVYs/4vaO/pZF8ryp+GNQ8/DU0E50LWYGjFb/79v2jsZvz0VQol/vrA\nfyM6PBJt5i78aufrsLkdAIDFWTNw34QlMDkG8Nyht1DXxxTqysVSPDvtXsxNmsDKW9yUB83mLtSZ\n2mG094OiadA0jQipAtEKFbQKNZIjtBgfk47xMenIcDKSl5ycHLg8bnTbTOi2mWCw9aHL0osOixEN\npnZc6m2Fy7vCYXJY8En1N9hRdwyP5i/DzRmFEJH+v7VTEsfhyRkr8c9Sxs/+1W824MO7X/HT7ydH\nx+PGCXOw8+whWBw2bDq6A08s8l8BWDpjPv7x+TswW/px4PQRtBk6kKj1vw8JsfG4+9Y78NGWT+By\nu7D+3+9hzX/9Zsj7lJ+fj/Hjx6OyshJ6vR7V1dXIzc0d8hiBa4cQ7At8p1xO8D7ascEy7IMD7NG8\nT6+rFw22BqQr0qGRaIY8dvnF5X4TjWCEsuxsbGyEhbDAIDJA69GGLOQdzeRgNGO19VpEtkXCprah\nu6JbCPQFBASwZMkSbNy4ER6PBxs3bsTzzz8/4mPPV3MymUWzh8/87ji6F6998A+4PW4ATCOpp+58\nGHcvWO6nNd9ZdhB/2rEBdhcTzIfLw/DXB55HZlwKugaMeGrbn2GwMLKeMdHJeH7+w7C7nfht8Xo2\n0FdJw/Da3MeQHZUCAOi09GJ7/XEc01fBRbmHvE4CgC48GhnqBKgcIqTKmRoEiUiMhPBoJIQH1iQ4\nPS5UdDdgR90xHG2rAEVTsLjs+PuZz7G36RR+N/NBxIb5P19WTVqK0pYKnGq7AKPNjN8ffAd/uemX\nft/Fw/PuxK7zxfBQFD4p/Qr3zrwZkUruOSeXynDHvJux8atP4KEovL9rM/77wZ8HXN/qu+7H1l3b\nYbFZ8dWBPVh91wNISUwKGMdn5cqVqKxk7vHRo0dxxx13DDle4NohPM0FLourUfzKt97cM34PyqQj\nWzYefC2+DDufwQF2KBvOweww7MBjFx7Dy/Uv47ELj2GHYceQ4x/Kfgjrx6/H0uilIL3/eRHe//mu\nI5RlZ1NCEzaoNmBr+FZsUG0Y8vNfrW65EocEqi4VMmIzrsr5BQQEvl/cf//9kMsZOeW2bdvQ0dEx\n4mMrL3IdXieMC5SP+KAoCm988S5e3vhXNtDPyxiHD9f8E/csvI0NbgfsVrz8xRt4ecubbKCfGqPD\nOz95DXnJY2Cw9OLn2/+C9n7GVSdFHY//u+UZSERivHLsfVw0MrackbJw/OWGnyI7KgUDThvePv81\nnivegMOt5cMG+gDTNbdtoAfFbRXY2X0Ob7YewK8PvY33K/fhbFcdnB5XwDFSkQST48ZizayH8MGy\n53FDCtcpuKqnCT/f9/eAol+SILFmwY+hkjGJn6NN5/B55Td+Y5Kj47Fs0nwAgNVpx0dHtwe8932L\nbmcbi20/uhedRkPAmEiVGvcsZzrkeigP1n+8cdjvYcGCBWxh7okTJ2C3B9p7ClwfXLVgf+fOnXj8\n8cdRVFSEvLw8zJ8/H6+++ioGBgau1lsKfI8ZbL1JERSKFcWwEJYhjwsW9A7liT+SAN+H0WXERv1G\nuGnmx99Nu7FRvxG9rt4hj9NINHgy+UlsGL8BazLWYK1qLdaq1uJx5eN4UfUi5srmBhzjkx75mm+N\n9PMLCHxfEJ4J3080Gg3uuovxq3e73XjrrbdGfGxto9fuUqVGnDZ0d9aNX3+K977ezP69fPYSvPXr\nP/p1fS2pKcOqN57BzrOH2NdunDgHGx//A1JjdDijr8bqz9aiqY8pkI0Pj8Y/lj+LSHk4/nD8I5zs\nYBpxhYll+J+5jyFdnYC2/m68dOxDFLdVsFp7uUiC6fHZuG/cfDwz9U48N+1uPDftbjwxcRnuGjsH\nRYnjkRgewyZwfHRa+7CvuQyvn/4CP933T/z19Bc40lYBm9uJwcSGafB84QP4w9yfQBvGyICMdjOe\nPvAGStoq/MeGa/DbGx5h/37j2KfQm/0tQh+ZfydEXreezSd2wThg8tuviVDjzvnLADAdgTd+/WnQ\n+3D/irsRrmQ0/7sO7kNrhz7oOB9KpRLz588HANhsNhw9enTI8QLXjqsm43n//fcRFxeH3/zmN9Dp\ndLh06RL++te/oqKiAh9//PHVeluB65ihguxg1psUQcEgMkDpDi1nCcVgT/wJGUxh01CSnME02hrZ\nQN+Hm3ajwdYw7LEAE/RrJBrAm8RXNYauFwgmPRrJ5x+JROd6qAkQEBCeCd9fHnjgAXz++eewWq3Y\nvn07fvSjHyE9PX3IY+wOB9stNykhMaQH/anqc/j/vvyQ/fsXKx/F/UvuYMc73S7839fv4fOTe9gx\ncokMzyx7GLcW3AAPTeHd09ux/uRWeGgmWRKr1OAfy3+N6LBIvFb6EQ63ngMAiEkRXip6GFmaJJzr\nqscbZ7fD7mGCcblIiqVpU7A0bQrCpYphvxO724naPj2O1JSh0daNdqeJNWJwUm6UddWhrKsOUnIv\nJseNwdK0KciM9C96nRKfjX8u/CXWHH0HF40tsHuceLnkPayZ9RBmJeax4+alT8ay7NnYefEI4yR0\n6F38/ZZn2e8oIVKLWwrm48vT+2FzOrDx8BY8ffNqv/e6f8kd+OzgTjicDmwt3oUHltwZoN1XhUfg\n3uV3Yv2/3wNN09jy9Tb8/GH/zruDWbp0KXbv3g0AKC4uxsKFC4f97gS+e65asL9u3TpoNFxANGXK\nFKjVajz99NM4fvw4ZsyYcbXeWuB7SDDrTZImofVog44fibWmzxPfNynYYdjBZurFhBirdatxi/aW\nkNeUrkiHmBD7BfxiQox0xdAPuVAMFXQHK+4d6vMLCHzfEJ4J31+io6OxevVqvPnmmwCADz74AGvW\nrBnyGFM/l12OVKmDjunuM+J3b/8JlDdIX33zPXhgKdccSt/bhf/+5HVU6+vZ1wpSc/D87U8gJToB\njb3tePnAelzo4u1PyMYri5+AWh6OV499gKNtjMe+iCDx28IHURA3Bic7avDm2e3s5CApPAb/NWUF\nYsM4f3mD1YSm/m5028zo8frwS0RiKERSxIWpkaDUIDsqGSKNDfM0QHJmGip7mnC2qw7nDA0YcNkA\nMIF/aXsVSturkBOVgtuyCpEbncq+T5RChb/M/yn+dOLfKG49Dw9N4dVj72Pt7EcwLX4cO+6XRfei\ntKUcPVYTTrZewPbqYizP4VaJH52/El+fOwyn24UvTu7BvTNvhk7DrabEqKNw9w234oPdn8Hj8WD9\n9k148ZGnA+7JHTcux7uffAgP5cG2vV/h8QcegVQiDXr/AGD69OmQSCRwuVw4cuQIPB4PRCLBxe16\n46rJePg/6j7GjRsHmqbR2dkZ5AiB/2R81pskzfyTJGkSc21zgxappqWl4ZDjENaa1+Ity1tYa16L\nQ45DQcf5An2jy4h39e+OSpKjkWiwWrcaYoKZE/smCCPJ6oci1GpEMOlRqM8/kvMJCFxvCM+E7zd3\n3XUXwsLCAABfffUVDIZA3TcfnwsPAESqgwf7r773fzCamd/gKdkT8JPlD7D7ajub8dC637CBvkQk\nxrPLHsGbD78IXaQWG0/vwI82r2EDfQIEHph0E/6x/NcQiUR4vvhtNtAXkyKsmfUQZifl43TnJb9A\nvyA2Ey/MvB+xYZGgaBrVxlZsqNyP/y3bjs9qj+FgWyXKe5pR3tOMM131ONpejS/qjuON87vw8vFP\ncaC/Dpcc3RCRIsxIGIfHJy7DPxf+FL+Zfg/mJeVDIeYC5SpjM/5w4lO8eXY7TA5OoikXS/Hbwgcw\nJ4lZgXZRHrx09F1UGLhJjEqmxHNzf8T+/beSj2GwcM+vOHU0Vk5fyhzvcePtbwKlOg/euBJKBXMP\nvy49gKaO1oAx2ugYzC0sYu/hwZLioPeOvXa5HOPHM/UYfX19KC8vH3K8wLXhOy3QLS0tBUEQyMzM\n/C7fVuA6YCRBaWZ3Jh41P4rbB27Ho+ZHMck5Kei4UNaaZsoc8v0+6fgEHtpfJuOT5AzFLdpb8Hbu\n21iTsQZv57495ErASAlVNzBPNg8vql5ktf23627/1u8lIHA9IzwTvj9ERERgxQrGJ9/tduPLL78c\ncjy/WFMhC5TF1OubUVJxCgAQpdLglR//P4i9GeE2Yyd+8d6rMNuYeo6ESC3efuxV3DXjRtT0NOPh\nz1/GuhOfw+kt5tVFaPHmbc/hqZl3o6a3FT/d+1ec7aoFAEhIEV6ctRqzEvNQ1lWHf5ZtYwP9woRx\n+EXB7VCIpTA7rFhfuQ8bqw7iUl/wxliDcVEetLj6UGJpwu9Pfo6Pa46g3tQJAgRyo1PwaP6N+PuC\nn+JHuYsQo+AmPKXt1Xju8AaUtlezr4lIEZ4vfACFOsa+0ulx46WSjX4NvOamT8biLGYFzOK04W8l\n/vK31XNXQOn9rr8+V4yajka//ZHhKqxaxNxDiqbwwe7Pgn6u25YsY7dLTh8f9nuYOHEiuy0E+9cn\n35n1ZmdnJ/7xj39g1qxZ7CxQ4PvJ1cwmK2llSI26772rXFVDWmsOvj6jy4h9PfsCziUiRH6SnPD4\ncFw0XUS2Ohsxcq65ShrSUICCgON9XEk9vE96xL73FdLbC7p9gesN4Znw/eOuu+7CRx99BADYsmUL\nCgsLQ0o2SJ5vvE/Lzmfbkd3s9qrFtyMmMgoAYDAb8dR7r7AdcbMT0vGPh16ASqHEp+X78PeSj+H2\n+tUTILAyfyGenHEnxKQY71Xswr+r9rPBfKQsHL+b+SAmxmahrLMWfy/7kt03PT4bj09YBhFJotrY\nhs2XSmDx+vIDgFoahmlxWUhQahCjiICIEMFJuTHgtKHd0os2ixGX+trZAlw35cFZQyPOGhqRqIzC\nvKTxyItOhkwkwaLUAtyQPBGHWs/j04uHYXU7YHU78ObZ7Wg0deDu7LkgCRJiUoQXZj6E3xx+C+WG\nepgcFrxwZAP+tuDnCJMwjki/KlqF0uZy9Dut2Fd7AreOm4sZycx/P+qwCPxo9m341/6PQdM0/rn7\nI/z9od/6fe/3LFyOj/Z8AavDhq+OHcBPlj+AWI1/M7EpeZMgFovhdrtxpuJc6H8QXjIyOPe2mpqa\nYccLfPd8J8G+1WrFk08+CYlEgtdee+27eEuB7yEjnUQE07f7rDWDnaPR1hjU935x1GJoJBqkpaVh\nU90mvL77dVbP/3Te01iVuWrU130tuuEKgbzA940r9Uyoqqq6glc1Omw22zW/hmtBfn4+ysvL0dnZ\niRMnTmDSpElBv4PmlmZ2u6enx2+M2+PG9iNMwa2IJDE2JhVVVVWgKAqv7F0PfW8XACA+Iho/K1yJ\n5oZGbKj+GqVdnJWnLiwaD2ffiCx1IorPn8BHrYfR7uBkLakKLR5JXQRpjwvbWg7ii65ToLyTjuyw\neMyXZaLm4kVU27tw3NrCHqcgxJgWloxUqQakhQAsAzDC3zEqFiRiEYOJEdFosfSgxWNGM2WCyzuR\naLMYseliMdQiOWaGpSJOwjjcJECGR+PnYI+xAhetjIXpVw0nUd3RiBXaKZCSTEh2X8ws6PsM6HH1\no9HUgd/uews/Tl0M0luQuyK1CO9fYrrXvrZ/A16Z9jAk3mMnRWVCo1Ch12bG8bpz2HxgO/ISsvyu\nf27edOw6fQhujxtvfPIO7p13a8D9S09KxaXGOrR3daC45AhiNIG9A3xER0eDIAjQNI3z58//x/03\nAVz/vwdXXcbjcDjw+OOPo62tDRs2bEBcXNzVfkuBHyi+oDqUtabPcWcwvkJbPiKI8Oy0Z5GWlgaD\n3YDXK1730/O/XvE6uu3dwU437DVe6cZhgi5f4IeE8Ez4frNgwQJ2++TJkyHH+awgAUb2w6ehswX9\nNkazPjE9F2plBADgREslGoxMR1yNQoVnb/gRImRKrK/e6RfoL0ycjJemPoTUiDhs7ziJ1+u2sYE+\nAQILY/Lxi4xboJEocX6gxS/QHxeWgNu0kyEiSFxydPsF+jqJCreqc5Eui2IDaw9No4eyo52yopWy\noJWyoI9ywkPTIAkCsSIlpkgTcHfkRBQpUxEpkrPnM3ns2NV/EccsTXB6ZaThYjlWaKdggSaHNe+s\ntxmwuesk22E3XCzHT9KWQEZKAAAV/c043MM1KJunm4iMCMbZp9PWiz2tp9l9MrEUd0zg7tHn5w+A\npv1XVpZOnsfenyMXTsLtCUyGjU3nJghNbS0B+/lIpVLExjLFwKPpwyDw3XFVM/tutxtPPfUUKisr\nsXHjRmRlZQ1/kMAPjqsR0A621gzmxuPDV2jLd+J5Ju8ZVqpTY6oJarF50XTRT84zGq5Wl1sBge8z\nV/qZkJOTc4WubPT4MnjX8hquBZmZmVi3bh0cDgdqa2shl8uDfgea6Ch2mxCRfmMudHKFp3OnzERO\nTg4oisKrBzawr79w509RNHYyNpz6Ese7GG27hBRjzYIfY/GYGajv0+O10g/RZOaKu9PU8Xh22r3I\njkoGTdPYWluCnd2cDGVa/Fg8OfEWiEkRzhkacaymid03WzcON6dNYYP8toFeVPbqUWfqYoNwPgQI\nxIepEEWRiCMUyMvNRT6AW2gaF3vbsLv5HNq9BbQ1jm50E3bcO3Y2UiKYZ0oucjG1Ow9/P7MVdo8L\nzfYe7ByoxNNT74BMJEEOAHmsCi8efRcAsL3zJJbkFyEzUsd8PzGP4ZHPXwENGl+1HMcjc+5AVBjz\nHBybnY399SfRaGhDg7ENPaQVc8ZN9bv+2Sen49DZY+i3WdBP2zArZ5rf/ryGi9j5DSO1CgtXDvnv\nvKqqii3e9ng8GDNmDMTi70wlfl1wPfwenD59OuS+q5bZpygKTz/9NE6cOIF//etfmDAheNZVQGAk\nhGqelSPJCarTH4yv0PaNmW9g19JduC/zPnZftjo7IPMvJsTIVmd/62u+Ull5C2FBo7gxZJMtu9iO\nzohO2MVCB0OB6xPhmfDDQCqVIi+P8YDv7e1FV1dX0HF8u02+Mw8A1LU1sttZiWkAgCM1Z1DbyUh/\nshPSMWtMAQ7UncLbJ7eyY9cu+gkWj5mBA01n8PP9f2MDfZIgcX/OIryx6FfIjkqG3e3EG2e3Y0tt\nCXvsvKR8NtCv6dXjk0tH2UqCwvixWOYN9J0eN/a0VOLz+tOo7m0PGugDTB1Cu9WESk8vDrvbcaqr\nERRNgyAIjItKwlMTb8LNaZMh8WbQjfYBrCvfjcNtF9hMe15MGp6dthJyEZPBrzI242+nt7A1JABV\nMAAAIABJREFUCbMS83Br5iwATDHwa6Ufwu6tEciJTcfN2YxrjtVl9/ueRCSJx264i/17/cHPArL7\nS6Zztp0Hy44FfL7oSG6y1tNrDNg/GKmUcx1yuQI7CAtcW65asL927Vrs2bMHDz/8MORyOc6dO8f+\nX7BZE7iSjDSgLhhTgKK4ooBsfYw8Bk/nPe1nscnP/H8X1zfUmEOOQ3hH/Q62hm/FBtUGlEnL/PaX\nScuwO3c3jmUew+7c3aiLqfuWVywgcOURngk/HCZPnsxuX7p0KegYuVwOmUwGAOjt87c4buRZPmYk\nMp7z207vZ19bPXcF7G4n/nz4ffa1x6bdjgWZ07C/6TT+cHwT68STporHPxf9Eqvzb4JUJEa3zYRX\nSjfhRMdF9tiVY2bjkbylEJMidNvM2HSxmO2YO1mbgeUZ00AQBIx2Cz6pPYHqXs6NR0KKMDYyDrMT\nxuCGxHGYkzAG2ZHxUPEab7lBo6SjFlvrz2DAxRT5iggScxNz8ctJy5CoZAJniqbxVeMZfNV4hg2+\nx2qS8MzUlZB5A/6KniZ8VHWAPffjE5cjVcVI3ZrNnfigkmsu9vj0OyD3WntuqzoEvZmzQ12QW4iM\n2GQAQLW+HmcaORkUAMzKnwaJN/vuc0Xio1FzPQd6TX0B+wfDL8h2OgO7BgtcW65asF9cXAyCIPDW\nW2/h3nvv9fv/5s2bhz+BgICXK5EdH+4cqzJXYdfSXUEz/1eCy/0Mg21GKYJCsaKYzfBbCAuKFcVs\nMzKapFGhqxAy/ALXHcIz4YcDX6rQ0hJazx0bxSRMunoMfpnlARu3QqmJUIOmaZS3MC4uSpkC83Km\nY1dNCXq9zaxmpuTjkSnLcdHYjD+f+Jh191mYOgX/WPRLjNEkAQAu9DThpZIP0dLPBL1ykQQ/nXQr\nlmfNBEEQcHhceL/qEOweJvOcrdHhzjGFIAkCfQ4rvqg/jV6HFQAT5M/TZePHuXNxY0o+JmtTkR+d\nhAJtKpam5OGh7Fm4I2My4ggu6G+19GJTTSlaB7jJTYxChScnLMVcHfedFeursLX+BDvhyI5Kwq+m\n3AERwYRk+5vP4psWRn4kE0vwfOEDEHtXCL64dBgtZmY1JTZcg3vyFwMAPDSFD8q+Yt+DJEk8OHs5\n+zd/MgUASnkYslMYGV1XbzfMln6//R6ejl8yAkmOb8KuUCgQEREx7HiB75arJqo6cODA8IMEBPDt\ngvkrWQ8QI4+5Ytn8UNcxlDY/2H69Rx/gJEQRFAwiA5RuJQwiAyiC8ttPkzRMChPk/XIICFwvCM+E\nHw58q8W2traQ4+K0cWhpb4PD6YSp38xKexxOJvstk0ghIkVoM3aiz8oEm7mJWSAJAlsuHGTP8+iU\n22BzO/Ba6YesdeaStGl4ZtrdIAkSFE3jy9oSbK0tYaU5WoUav5pyB5K8GnmKpvDxxSPosjGSohh5\nBO4bOxsigsSAy44t9Wdg9UpkNDIllqVOQJQ8tA00QRBICo/CBHEUeig7qol+WN1O2D0ubG04g4WJ\nOciJYvT1YlKEm9OnQC1TYnsDk0U/3nEJbsqDO7NmgiQYX/4HcxdiYyXjsvN+5T4khcdgjCYRGZE6\n3DFmLj69+A3clAdvlG3B/8z9CQiCwL0Tl+CT8r2wu53YUX0ED09ZjthwpoHdgtxC/O9X72LAbsWB\nC8fxjG0AKkU4+xkyE1NRUc/UQ9S1NaFgbB67z2Kzsts+PX4orFYrjEZG6pORkeGX5Re4PhDuiMAP\nmsudSPj09gqtArWohUKrYF8brMXvtnfjaOfRy3LvGQ6fzSgfkiah9WgBAFqPlu067IOgCKhtwTtW\nCggICHxbdDod5HImmdDaGtiF1UdMFGfXaOjhfh/tvGAfAC60cdLD8UlZqO1pQU03o98fE52M8XEZ\n+HfVfugHegAAWZGJ+OWUlSC9mfDNNYexhRfo50Sl4MWZD7CBPgB801qBql5mYiIlxXgwZx7kYinc\nlAfbG8+h38WshmpkYViZOWXIQH8w0aQcq8bMQKKSCbIpmsbe1gu41OcvTyvSjcOdWYUgvD48p7vq\nsbvpLLt/Qcok3JDMNKjy0BTeOrcTTu8qxP25ixAlZwpwT3fW4FQnI1PSKFS4PXc+AMBFubG5gusp\nI5fKsDR/NgDA6XZhX4W/Nj9Tl8pu1+mb/PZZ+cG+PLApGp+mJu5YoUHe9YkQ7AtcNwQrQh0qWB8u\nkB9toD84kF9Xtg55G/KwcutK5G3Iw7qydezYTksnalGLzZ2bcePuG/GzYz/DjbtvxKa6Td/qmgbv\nH2wzStIk5trmQkkzDyIlrcQc2xw24CcoAnn6PMjdQlZfQEDg6kCSJHQ6Jmvd19cXUPzpgx/sdxt7\nAgd4nW+6+7kC0JToBFQbGtm/F2fNAEXT2NPIZMRJgsTzhQ9AKmKECWVdddhZf4I5HYDbs2biuel3\nQSXjstF6Sy/2t5SzY+4fNwdxYYwm/XhnPQw2ZlUhQiLH7emToRBzxaYOjxuXzD0o7+1EWU87zhs7\n0Oe0BXyUMIkMt6cXIFejY1/b21KJDqt/cfK0uCzcM3YWa7t5qK0Spzq5yc6DuQuRoWZsNbtsJuyo\nP+49vxw/nsB1tv20+ht2e9XEG1kXoV01JfBQ3Grv0gmz2e0zjZx9JwDERcWy26YB/+vsMHCF11GR\nmoDPy+fo0aPstlB4f33yn+WNJHDdUiYtQ7GiGBRBgaRJzLHNQYEzdNfab0O3vduvU26wALzD0oEX\nil+Ai2KyKi7KhReKX8CKsSuwpWaL3z4fPn/+JYlLrqgciG8zSukpNtD3UeAswFjXWFR0V0BtUwuB\nvoCAwFXHp8v2eDyw2+1QKAKzvzEanqNLHxfQS70ZfaeLkc0M2LkscrhcibO9XPCbFZ2Es12XYLSb\nAQBT4sYiWcUEqUZbP94+/zU79u7suViWMcPvGtyUB5svlbD6+Dm6HGRrEgEAHVYTzhiYrDQJAjen\nTkCEVO49jkKNuRsXTd1w0/5SyYvmbsQrwpGrjvV7XUSSWJiUAzftQU1fJ9w0he0NZ3F31jSoeZOP\nSdp09Dtt2Nl4BgCwpe44tAoVUlVaiEkRHslbgjUl74OiaeyoO4GZulwkKKOwIKUA71fuRofFiLNd\ntagxtmBsVDJiwzWYnpSH0pZyGCx9OK2vwvQkpqtuTmImpGIJnG4XzjVd9LteuVTGbvtWW3w087z1\nU5NSEAqLxYLS0lIAjF5/8eLFIccKXDuEzL7AVWUk2XVfkalPe+4rQjWQBlS5qmCmzFfsfTfVbfLL\nxO/q3RV0XIWhIiCYd1EuHG45HDTQ9+Hz57+caxsKn83o4EDfh5JWIq4/Tgj0BQQEvhNUKq63iclk\nCjomVGZf6s2cO1xO0DSNAQc/2A9Dg1HP/p2mScQ3zZwD2aLUKez2u5V7MOBisuwTtOm4KX16wDXs\naz7P+t1rFSosTmFkMhRNY3/rBVb6MzU2DXFen3qb24W9+lpU9nUFBPo+OmwDONBRDzPpv6pBEAQW\nJeUiIYyRUto8LmxvPBdg4Tlbl4PpcUyBrIemsOliMWurmaKKxeJUxvHITXuwqYrJ4otIEe4cO489\nx5ZLxez2TWNnstu7LnKWo1KxBLmJ3kJccw/a+zjHnqGCfX0n50iUFK9DKPbv3w+Hgzl20aJFUCpH\nLn8S+O4Qgn2Ba06wIlOKoLApYhPesryFtea1OOQ45Lf/cgLmYJ1yXyh+AZ2WQNu/fG0+JN7uhT58\nf4cK9H1j+P78V1PPLyAgIHCt4DdN8gTpwAoAGjUn/+DbN8q8nuw0TcPhcsLl4ZoaSkRiGG3c5CE+\nIsqvcdZMHZOxtrmdOG9oAABESMPwk/ybWSmLD6vbgZJ2JvkiIkjcPWYWJF75z6W+TvTYGclotDwc\n02LTmc9CUzhmaMaAm7OPTAuPxOzYVMyPT8cETTzkIu6zt0opOAn/gF9MinBL2kSovfacRocFxfoa\nvzEEQWB5xjSkRjD1VyanFQe8UiMAuGPMbETKmMD5nKEend4Jy9K0aVCImSD9ePsFVrIzL30ya995\nWl/t917jdOnsdktPO4JBUf6fobmNqcUIUyigVgWvAaNpGh9//DH796233hp0nMC1Rwj2Ba45wYpM\nQQO09wfUAw+22baNOMMfaiIQrFOui3Kh3FAeMDZOGYdX5rzCBvgSUoJX576KRlNjyPf1jZnq7VQ4\neBWBr+f/NrUIAgICAtcas5n7PeZn+fmE87K8/ILPiDDu9QGbBTKeRt7pdrGSG5IgQBIkLN7iWalI\nDIWECXTr+vSsBefk2Ew/jb6PEx21cFLMb36BNh3J3oJdmqZxsquBHVeUkAURSYKmaZT1tKPHwawW\nyEViLNZlYlpMEhLCIqCVK5GtjsHNSWORoGBkTBQBtEgpUINWABRiKZalTmQnIBXGNtT0dfiNEZMi\nrBwzk7XcPNJejS6vxl8hlmJhCidlPapnfPIVEhkmxTKZ+n6nDZd6maBcLpFhTAwjt+kcMKLXxt0f\njZIL1k3WAb/v3odKybn0mPrNMBiZBFVmSjqIQZMoH6dOnUJNDTOJSU5ORkHB1ZHeCnx7hGBf4JoT\nUGRKE8Cg3xYPPGjzhLZ4GwnBOuVKSAnytflBxz9R8AQqHq3AZ7d/hopHK3DbmNvwp+N/Chj3X1P+\nix3z+KTHAQRfRXi94vVRZ/jNlPmypUwCAgICVwtfsE8QREjphpIf1Fu5wDJc4f+6z5UHAOxeaQ8A\n1rXGF+wrJVxdQG0fJ/UZ49Xg83FTHpS0cxnuOYmcz32d2QCjg7meOIUKqeGM3KhhoBcNXo98EgRm\naVMQKQ2sRRARJKbHJCLMm0m3kUB5b+AKcYwiHHMTxrJ/72+tQh9PsgQw0qLZXg9+iqaxs/E0u68o\nMZfdPtpWyU6CpsRx5zzdyclGx2k5d51qA+eQow7jfO9NNs5Pv58X+PPvSX0TNxHKSOVWBQbz4Ycf\nsts333xzyEmBwLVHCPYFrgoumQvmWPOwzZ18WewCZwEeNT+K2wdux6r+VQGZfhFESBQF/qCPBl+n\n3MHZ+jhlXMhj4pRxWJS2CHHKOPyx9I9BJTyzk2ezY3yY5KaAVYSR6Pn5HHIcwlrz2pBSpquB7765\nZEK7cwEBgeDQNI2uLsatJTw8PKSvulLBZdttNs7Bhh9Y9lstUEi4WiOr0waR93wUTcNDUezvrpjg\n3qeHl7lOUHKFwD7aBowwe11zsjU61n0HAC7wagKmxTKZa4qmUNHLOdAURCcgWh7aX14qEqMwNhk+\nBc8lsxE2d+DvZn50ErK8hbwuyoND+osB7kULkvPYjrwXe/UweycEMQo1sr0Nwww2EwxWRgo1KW4M\ne+xFI1dImxXNFdI293FyHaWMm7BYHdx96O3n5FL8zP6lxnp2O1SwX1dXx7rwaDQaFBYWBh0ncH0g\nBPsCVxxDhgEXll5A/ax67M7djbqYuuEPApPhT3OnQUtpMcc2h7WbFEGE2xS3QUUGXyrmM5wE5vmF\nz/tl632Z+OHosHTgg4oPAl4PtTKQr80PWEUQE2I/Pf9QDO6c65My8W1JrzT8+3Zh6QU4JjmGP0hA\nQOA/jvb2drYoNyUltFNLKPiB5YBtABolr9jX2o8oBfM3DRp99n7WX95o72c16pEy7hy9di5D7cPA\nmwxkquPZbafHjZYBxhlIIZYiTcVIe1otZji8kp8ERQQyIgInEIOJloUhyk2w11rbH2gvShAEFibl\nIswrVWrq70HjoHEykQSTYtLYv+t5NQppai6J1O39TFoFJ8vpd3IrBUopN2ly8uogbE4u6RbGC/zb\nDNyEIDEmgd2uqb/EbmenZwV8JsA/q79kyRK/Gg6B6w8h2Be4orhkLujz9KC9DgU0SaNCVzFshn8w\nBc4CvKh6EY8rH8eLqhcxVzY36LheVy/OmM+g19UbdH8w+Nl6gPHM39e4L2ihro8KQ0VAph4AHhz/\nYNCVgThlHF6d+yob8IsJMZ7Je8bPknOoiUmwzrkeeGAQGUIc8e0Idt9sc2ygwoI7UQgICPznUlVV\nxW4P9TvGz2DzJR4RYVygbrb4B/s9A32IUXJZeIOlF7FhTKGvh6bQY2cmGfFKrvi3w8LZerLH8Yp8\nYxTc+Zv6e9guvBmqGFZTX8vz+h+j4lyEhiPaQ8Bn6VPXbwxw3QEAmUiMogQuG3+0/RIryfGRGclN\nSGp52v5oOXft3Tafnl/GNhTzuREBgITkAm4XxT2v+nna/HBebUOrgXufRC0/2K9lt8dmBAb7FosF\ne/bsAcB0173hhhsCxghcXwhTMYErik1tYwNGHzRJw6QwQd4/OltIFalis/lmyow2TxsSRYmYkME0\n7dhh2IGN+o1w026ICTFW61bjqbSnQp4v2EPpz8f/jD+W/hFu2g0JKcErc17BEwVPBIzzufPwZTxi\nQoznCp8L+X5PFDyBqYqpfp7+I8XXOZcf8IsgYjvnXmmC3TeIAI/WA7JJyAkICAhwVFZyzZnS00Nr\nuvlFq6GC/X7rABJ1nETTOGBCTDz3W9k5YEQ8T6bTbO5CbJjGT7rT1M/Jb3z08LL9WnkEbyyXVc/w\n+vUPuJzo8UpnIsRSxI6ie66UJqD2EDCJabgoCi0WU9BVgXGR8ThraIbB3g+jw4KWASNSI7hJRZoq\nFiQIUKDRMsDVdkXxrt1oZ/T2BEEgTCzDgMvG1jMA8HMj4jskmWw8bT7vszV3MnVwMokU2kjmml0u\nF+q8mn1dXAIiwrn393H06FHWbnPJkiWC3eb3AOEpLnBZhNJ2K0wKEJR/kQ5BEVDbglt3AcE75/IZ\nrF3fYdgBo8vIBvoAo4ffqN84qgLYP5X+Cb8/9nv2HL7GWcEy/MHceX4/7/dD6v0Bpk6gKK5o1E22\nBnfO9UmZlLRy2O9rMHaxHZ0RnUPq8IPdN3gAkUE0qusWEBD44XPy5El2e8yYMSHH2excIKqQc8ke\nv8y+dQCxai7o7TR1I5knXWkw6jGOp0U/28VITJIjtGyn23JDg59sBYBf5lzCs8r0FeYCgM7rUmPk\nFc0mKdWjLjSN8nDjWy3BzRQIgkCBlvscrQP+qxEykYStfeAn/fnBvK9A2eZysBl9/mSgnTeR4a+O\nNHRxuv6kKOa7NVn6oe9mMvuZiWnse9c3N7DNznKyuEJgPvyOuUJW//uBkNkXGDWGDAMr+SAoAroK\nHbT1TMZZ4pBAV6Hz25+nzwvZ7Gm4zrnBtOsb9RuhEqlCFsD6AuvBnXL5dFg68Mfjfwy4Hp8VZ7Ag\n/omCJ7Bi7AqUG8qRr80PGeh3WjrZMWlpaWhsbAzxTQ4Nv3NuoigRKlKFLdIto+o0XBdThwpdBXMv\n0v3vFZ/B9w0eQHFYAdIq5AMEBAQ4+vr6UF3NuNwkJCQgKiq0tt1i4clHeAG+SskFqP3WAcSER0Is\nEsHt8aCjrxtZ0cns/jpjK27JmcP+faaTCfYlIjEKYjNRoq+C3eNCRXcjJsdxkhMRP8tNcSsMPjcc\nhVjK+tIbnZwUJkoW6L4zHGEUoBCJYfO40WUfgMPjhkwUGF4lhXPSozZLn98+iqbh9kqAJCSXZOmy\nceNivY26Wgc4OWdSOPd73mLiZDkpfFlQZzMAQCaWIDmaketUNXK6/Jw0bsJ24RJnIpEzZlzAZ6Ao\nCiUlTNMumUyGKVOmoKGhIWCcwPWF8CQXGBVUGBWg7dbn6f2yxtp6LXJ35yKjJAO5u3OR2Z0Z9Fx2\nsT1o51x+xjqYdt1Nu2HxWEAO+ufLL4AdyuMeYDT4HjpQWykmxCGtOEfCurJ1yNuQh5VbVyJvQx7W\nla277HMBXOdcFamCiTIN+33xsYvtbKAPBL9XfPj3TbVBBdk5WdBxAgIC/7kcOXKE1eLn5w/9W8n3\ncVeGcVpx1SDNPkmSiPMWyrabDEiNTGC952t7WhATpkaaigleL/W2otcrZ5nKs6A82eHvdOYnafHK\niexuF+we5vdPw9Ou9/IcajRBrDaHgwCBRG8gTgNo59lb8gmXyNlGW51WMxvcA4DTw/0u81ci+PUI\nWq+jUCMvqE+KiGW3+Z2Hk71FyWbbANs1NyM2hXU6utDINfnKSeWC/apaXrCfFWgoUVNTg95epkZu\nypQpkMuFru3fB4RgX2BUeLSeoJp8m9rm95rEIYGqSwWJw78LLR+TwhS0cy6/CNWnXedDgsT6tvWg\nwB0rIkRsAWwoj3u+PCdYh1wA+E3hb0Jm7IcL5DssHXih+AVW1++TBV2p7rl6j37Y74uPSWEa0b3i\nI3FIYDxhFDL6AgICQfFldQFg8uTJQ44dGOBpxZXBM/smr+xFp2GCVofLiX7bANI0TAa6sbcdFqcN\nU+O5wPNYG1MzkK9NZ7PzZ7pq/Trx+l4HmG67ANgGWwCg4O1382oL5EEy8iMhXsFrSuUMbUih9DYF\no0HDw9PrNPVzv+NRXqchm8uBckMjc71iKWsfWtx6nh2bHcWsglicNpzvYAproxQqaL0yntMNXH1F\nTmIGu33mIneO8encd1tRfYHdHhdExnP27Fl2e/r06SE/p8D1hfBEFxgVIoMoqCZfYRp9NkRtUwec\ni6RJvyLUYNp1AAHZfpqm2W6KwTrlumm3X6fcwRp8ESHC72b+Ds/OeDbotYYK5PkTiApDRYAPv4ty\njcpbfygSRYkB/Qd831cwqVCw7/dy75WAgICAx+PB8ePHAQByuRxjxwbXdPvot3DBfkQ4FwxHhvOs\nNgeYLHhKNOcG09zTjvFxzIowDRqVXfWYncStIhxuPQeACegnapkA1uZ2oqKHayQVwcvQ93v17X6p\nD17mX8Tz7/cMcskZKRG8xmD9Xs17MHwTDxFBQsqT61QbuaaR2RodAOBERw07QZkePw5iUoQ++wBO\ntDNuSJGycEz2eu6XtlSwDjyz0yaxdQfHLnHBeWHWJACA0+XCuVomqI9Wa5ChY2oJLFYr6poZSU56\ncipUQYpzy8u55+iECRNCfk6B6wsh2BcYFaSVhK5CxwaRPs3+UBn8UMjdcmR3ZDMdc8EErnNtc6Gk\n/Sv758nmsTacqxSr/DL6PihQbIfakXbK5XfIvfDjCyEDfSB0IM+fQARbLZCQkhF76w+HilT5dRoO\n9X35kLvlyNPnXZF7JSAgIFBdXc3660+dOhUSydC/Jf0DnJwlgpfZV8jkkIqZY00DTGY/eVCwnx/H\nyT/LO2qRE52KaK+F5tmuWtZffkYC9/t6giflUfGDfWfo1UzAv1kXP8s/GsLEUrbx+4ArdI8SqzfY\nV4glbEBO0TSqeplgnwSBMd5VjSNtFexxsxPHAwD2N51mZUkLUydD5J0wHKrnOu/OS2dWXGiaRmkt\nE+yLSBGmZuQBAMrrq+DwTkimZk9kr6OqthqUt74hL5vr3sunooK5JolEgnHjAjX9AtcnQoGuwKix\nHLAgty0XNrUNCpPisoPHupg6XIy/CJqgQdAEZthnYJJzUtCxPhtOM2WG2C4O6nnvK9AtiivC03lP\ns1IeMSEO2Sk3Thk3rKMOENx6c/AEwrda4FsB8HXoHa0Tz1AUOAsw1jUWBpEBWo82ZKDvI7M7E4l9\niagx13yreyUgICBw4QIn8Zg2bdqw4y02zuUmjNdNlyAIREao0dXbjR4zo/9O4TV1au7W47bMxezf\n59ovgSRIFCXmY1vtUXhoCic7qrEgZTImaDMgJcVwUm6cNzSAommQBAG1lK/JZ2oHJLyg3sHrdsuX\n7nTbLUhShnaPCwUBgCRIeGgK7hCrA712CxxeqVEEr2twlbEVfd5rTFVpESaWoaK7ERd7WwEAsQo1\nxmoSYXHZ8XH1Afa4RalTAQBGqxkHG5hgP0wix9REJlCvaLmEThPj0DMpdRzbSffoec5NaXou98w9\nX8VJfvLGBQb7fX19aGtjJiVjx46FVCoNGCNwfSJk9gUui5Fo8ocioHiUoHFcfnxYO0kVqcJq3WqI\niEBLSH6B7qrMVdi1dBfemPkGdi3dNeJOuaEIZr0ZbALBXy0YrkNvKJee4V73dRoeLtD30VHbMeJ7\ndbnOQQICAj98+L8PWVnBO6vycbs5uaVE7P/74/N177cOwO50IF2bxO5rMLQhNTIeGq+tZHlHLdyU\nB4U6LgD16fZlIgmyo5hj+51WtHq17zG8LrO+brqMAw8T2PfwLDiTecF9w8DIGzTysbidbMZdLQ1u\nblBr5voB+Dr30jSNb1q5FeIi3ThQNI2Pqw+xr92WNQsEQeDT6m/Q52CkUbN045GlYfoTbK7Yx1qP\nLhs3GzLvd/31+cPsOZbkF7Hvd7CMqbsgCAJF+Zzu/uwFTsc/KTdQonPxIrdyImT1v18Iwb7ANSFY\n8ejgYtNQgWeeJQ/rc9djafRSVsPva6rFz6LzPe6vRBA70kCe36FXCJ4FBAR+KPAtFofqnOvDw3Ob\nEYv9hQTaSO63urvPiHh1DGRe3XujoRUEQWBiAlMTYHM7UNPdhInaLISJmUD6RHsV62CTG53KnqvS\nq9vXyJWsFt9gZaRHBEEgSqb0ntPJ6ufjFOFsdr/DNgDLEJr7UPTwHH0ipcEdaupMXLCfpWYKki/1\ntbOe+3FhauRGJaNEX4lmb6Ow5IgYFCXmosvai89rmAkASZD48YRbADCFuZ+V7/e+TuDeCcyKiMvt\nxr6KYwAYd58F4wsBAPX6ZrQa2gEAEzJzEKViCnk9Hg/KvcW56ggV0pK4ngA+amo4B5/s7CsjTxX4\nbhCCfYERQ4VRcKW6QIVdnqaRz0iKc4dCI9HgyeQnsX78eqzJWIO3c9/GLdpbvvV1DQc/kP+29Lp6\nccZ8Br2uy8sk+RAmFAICAt8Fej1j7SiTyRAbGzvMaLD672BoI3mNtHoNIEkSaTFMprq9zwCb045J\nCVwBcHlHLaQiMWZ4s/tWtwMV3czkYzwv2K82MtIXEUEi2rsyYLQPwOGdGMTIudqB5n4myCYJAmnh\nXBOqEkMzq60fCW7QqOjlzBqieBIiH3pLH7q8lpxRMiU0MiU8FIWdjZzWfn5iHsxOCz4iQ8zYAAAg\nAElEQVSq+oZ97e7seaBp4M8nPmY/w7KMQiR7u/++c2obW7+wKGsGEr2vf1N1HCYr835FYydD5XUL\nOnD6CHvuuZMK2e1LDXUY8BZU548bzzbZ4lNfX89uZ2YGt9QWuD4Rgn2BEeGY5ID5UTMsKywwP2qG\nISO43eNgXDIXzlvPwy72tyIbXDw6XLEpHzNlZoNkjUSDyarJ0Eg0wx53PbGpbhMeu/AYXq5/GY9d\neAw7DDuu9SUJCAgIDInLxQSbcrl8RF1m+UW5fGceANDFcAkTXyfXNG0i+xrjyMNZRVYbmIz9FJ63\n/nkDE3ymqLSQe600a/v0bB+AlAhm9YACjeZ+xgI5U81NUiq8EwMAGKOKYbP7fU479unrYLAP36Wc\nAo1mKQWrNxCPlMqRwOsjADDSmWNeW0wAmBDD2GWWtFej07vqEB8WifyYFLxXuY/tmlsQm4UJMen4\nrOYgznZ5bTXlEXgobykAoMHYho/L9wIAxKQIP556G/senxz7it1eMXURex17TnLyoIVTuGZlx86c\nYLenT5oa9LPyM/sjkXEJXD8IBboCw0KFUbDNsYG1uxcB+jw9Itsih9SB8zvtNlANyNPn+TXY8hWP\nmhQm5MXkjSjQP+Q4xHTUNXtY6c53kdG/XIJ18Q3WB2CjfiOKIotgajMFPc/g7L2FsLBFunzsYjtM\nChPUNjXkbvmosv7CCoGAgMBQuN3Mb9ZgSU4o1CrOYtPcb/bbl6jlOrzqu5mseGqMjn2t0dCGeTnT\nQBIE41bj9ZufoOW59HiDfZIgkRGZgAs9zeh3WtFl7UOcUoN0dRxOddUBAOpNnRgTmYDk8CiopQqY\nnDa0WfpgtFsQJVdCLhJjTmwqjnQ1w+ZxwUF5cLCjAUlhKiQp1dB6x/igaBpd9gE0SSlYvc9GGSlG\nUWwKSMI/j9oyYGQ75qokcozX6NDvtGFfC6fVX5E5A6c7L+G0t0OwUiLHI3lLUNvXho0Vu9hxv55+\nH9SycFA0hT8Xf8hKpe6feCPbNbeytRYVrcx50mISMSNrIgCgpqUeTR3MBCcvY5zfhOt4GVe0Wzg5\nMNh3u91sZj8xMRFK5chqxgSuD4RgX2BYPFoPBvW1YpszSbqCB/sumSug026FrgKJfYmQuzk9o9wt\nh7xfDmX08D8cJsrEBPpej31+kHw9ZvZf2/+anyPQ03lPY1XmqpB9ABpsDYhC6NbzPsqkZWwnXYIi\nkBfDTKLqYurYomeCIpCnz4OoMbCQWUBAQOBy8Mlygkk8gqGO4Apfe03+csVELee+09rFaMh9Mh6A\nCfaXTpiNdE0i6oytaOpth9VlR7wyCjEKNbptJlT1NMHlcUMiEiMrUocLPc0AmOx+nFKDdBWXxa/p\n1WNpKuM/nxeViKPeTPsh/UUsT5sEEUkiUqbAIl0mjnU1o9vBSGNarWa0WpmJioQkIRdJ4KY8cFIe\nxpPf+xNLgkBRbArCxP4ONW7Kg8N6LiM+Iz4DJEFga/0JVpYzWZuBMLEUGyv3suMeyFkAiqaw9uhG\nttPunWPnss3F3j/zFc7oqwEAceFRWD3lVvbYj45uY7fvLryJXYXZdZyTBy2dPp/dHrAM4FwVY6kZ\np41FWhIni/JRX1/PruwM119B4PpDkPEIDIvIIMKgHlaAB0M2Z7KpbUG7t5oUwTPXoeBnm/UefUAz\nLV+QHGz8UOe62nRYOoJ28Q3VB0BMiJGuSA96LjNlRqO4ERbCAgthYQN9gJtEmeQmf3cj7+sumSvo\nOQUEBARGS2Qko2s3Go3weAY/FAJJjOcC+oaWJr99Sbxgv6WLqQVI4WX2W4zMBGCMV/JCg0Zjrx4E\nQSA3Og0A4KLcaDQzEqCxGs7Np8rYAgDQyJSIC2MmHG0WI/QWZsKRG6VjZT8tA0bsb73ASn/kIjHm\nxacjV61lm175fPhdFIV+lwM2j9uv+ZaIBgq1yYiWB2r1T3Q2wOh1/omRhyM7MgFnDQ2o7Gnxvp8U\ni1Mm4I2z2/3kO9PixuLlkvfQaWWuOTNSh0fybwYAHG+pwFsnvmDf47m5D0Hh7cxb39WKAxeYxmfq\nsAjcPGkuAMDt8eDrUibYF5EkFk3jJDxHT5WyqzazpxYGlWidOMHJfPLz8wP2C1zfCMG+wLCQVhKK\nYgUX8HsAxeGhPdsVJkXQ7q1qm79/sV1sR2dE57CWmwDTQVY0aIlhqCB5pHRaOrGvcZ9fN9xvy/6K\n/UGz9ycMJzDQMYDVutVswO+TIwWT8BxyHMJLppewNXwrNqg2oFReygb6PmiSRruqPejkyqYeupmM\nD0HCIyAgMBwJCUyA7vF40N3dPez4jJQ0NnCsbWzw26eQyREVwUwefJr9pChOVtLSw7yWEcVl++u9\nXWbHRnGBfY03sB+rSWTdd6q9GX6CIDAtjtOWH29nMuwKsRQ3peaD9F5bdV8HSjpq2YCfJAiM18Th\nlqRsFMWmYJw6BjGyMMhFYhAgICVFUIql0CkikOQkkG0nkajkJEs+2i19OO2tNSBAYFFSLvqdVnxZ\nz0lmbs+chr1NZ1BvYiY3MQoVHsu/EevObWMLkCNl4Xi56BFIRRLozd14Ye86tmP8w1NuxaxUziZz\nw8HP2M+xauYyKLzOQMcvnIHR29NgZt5URKu41fCDx4rZ7fkz5wZ8DsA/2J8xY0bQMQLXL4KMR2BE\nyM7KIKmRwKP1QGQQgbSSQFro8RKHBLoKHSvl8clK+BIevuyklCrFXPtcFDgLQp5TRaqwXLGclfL4\ngmSNRINeVy8abA1IV6QjbYgLa2xs9LOMW1e2zq8J1itzXsETBU+M4psJji97PzjgX3NmDVtnUBRZ\nxF6zRqJBo6XRb6xPtuQL7imCQqW0EgRNgCa4wJ6gCCSYE5gGZaT/60OtvggICAiMhvh4ns5er4dc\nHtxi0odCrkBivA6t7W1obGmCy+Xy67qri4mDsb8PfQNmWOxWKOVh0EZoYOjvRUtPO2iaRoaGC/br\nvMF+dhRnC1ltbMayzJmQi6VIV8ejtk+PLpsJBmsftGGRKNBmYHfTWbgoD0531WGWLhtxYZFIDo/C\nkuTx2NXMyFdOG5pgsPVjfuI4RMqYDL2IJKELU0EXpkJOZHD3oSpjVdDXLS4Hvm4uZ4PyqbGpiFGE\n453KA7B75Tv50SkATWFnPZOJJwkCT068BXsbT2F7HeOFLyZFeLFoNWKVGvRYTfjVzv+F2btSUJic\nhx9PvZ19z7NN1dhXwRynUiixcsaN7L7tRzmJ0LJZi9hth9OBktPM+4crwzElP7Cxpd1ux5kzZwAA\nGo0GY8aMCfqZBa5fhMy+wIghrSQkTRIm0B8B2notcnfnIqMkA7m7c/2KcwOaapE0ihXFw2b458nm\n4UXVi3hc+Thrt7nDsMPP2eafJ/85ouvrsHSwgT4AuCgXXih+IWSGf6QrAI2NjYiRx+DpvKcDViJ8\ndQYjcRIKJluiCAp5jjyQNHMPfJMotV3t525EUAR0FTqhY66AgMAVIyODc8c5f/78ECM5xmUygaHL\n7UJV7UW/fXzdfpuByeQnRzNSHovDhj5rPzKjuSx+XQ9TXDpGk8Rm5Su7uRWDvJg0drtEzwThSokM\nM+KZa3DTFDZdLIbL24BqbGQ8ZidwgWvzgBEf1ZSipL12VNabg3FRHuxoPIcBlwMAEKdQYXpcBr5p\nrUStifmc4RI5ZiWMxbpzO+FL0azIKkKX1Yh/nf2SPdfPClYgLyYdJvsAfrH9L2jqY47XRWixdtHj\nEHnrJxwuJ/7ny7fY4x6ZdyfCvbKibpMRh84ynvsqZQTmTOAy86VnTsJqY1aAi6YW+k3GfBw8eBB2\nOyMxKiwsHHHNhsD1g3DHBC6bkUg/QnXaHUlTrVDvoyJVyJHkwNRmgtFlxEb9xgBnm2576CVm3/kq\nDBVsoO/DRblQbigPOGZd2TrkbcjDyq0rkbchD+vK1g15boDp4vvKlFcCxgyuMwj2GQFGtuQL6n2Q\nNIlCRyEeNT+KmXUzsfTCUnYSldmdiaUXlmJm3Uzk7s6Ftn5kPQsECY+AgMBImDqVc2k5derUiI4p\nyOMyxWcqzvntS47lNPqtrG6fmwA0d+sRHx6NcCmzQlnr1bkrJXJkRjIZ/5Z+A4zeDrlFvA67B1vO\ng/J2tF2SMglaBSOz6bSasL2Bu/bJ2lTclJIPpbew1kNTOGVoxLtVR/BNWzV67P6WocPhojz4quk8\nOr3XpBTLsCxtAprMBuxrZiZIBIA7MgvxTsVuWN3MhGCiNgM5UUn4Q+kmdjXgruz5uCVzJgYcVvzX\njv9FndcqNCYsEn+/9VmoeT0DNh7egsZu78pHQjrumnETu2/bkT1sjcWtRYsh5QX0+44cZLcXz7kh\n6Gfavn07u71s2bJRfR8C1wdCsC9wTfi2TbV8NNoag2rjD9ccDnGE97jGRuRr8yEh/SchElKCfC1X\nfNRp6cTm6s343eHfDbsCECxonq6dHmDDRoIcUZ2BilRhjm0OG/DzexEYGgyI64/zk0UBjLtRXH+c\nkNEXEBC44mRkZECjYVYiy8rKWHeWoeDLQk6Xn/XblxTLL9JlNOvJUZxUqKmHKcjNimaKdI02M3q8\nvvQTeRacPg/6OKWGbbDVYzejzGu7KRWJcV/2HLbQ9kRnLb6sO8G63IyJjMMD2bMwIToJBJjnkoem\nUN7Tio9qSvFZ7SlUGfXs+FBY3U5sqT+Dpv4eAExh761pE0HRFP5/9u47PIpye+D4d3eTbHoIaSRA\naCEEElqA0HtVaRZAQUEERFFUvKA/xYJdwV5QVPBeEBVFaaL0FnoLJRBKAqEkARJI79nd3x+TzKYn\nlECynM/z3Ofuzr5TdjA7Z94573l/PRmqBvG96gWxO+4Y51KUWXI97Fx4sGlX3tixgCyD8kShe71W\nTGx1HynZ6Tz/9ydq6VFXWye+GjqDeoXnC7hwmv+FLgeU1KNXh03GSqc8Vc7Ny+XPLavVtvf3MN8E\nZGVnE7pnBwAOdvZ0Cu5Q4jvFx8er+fpeXl506FCyjaj+JNgXt03hYLj4pFoao4bAmMBK1dovzCrB\n6roq2xSWGZ/JO93fUQN+a6017/Z4V50dt6A3f9KaSSVuKIo/ASird9yECUylflTmuinGFCJyIzh2\n7hhtc9oyIWUCw9OGMyFlAm1ySuZTVrQ9IYS4FbRarRrsZWVlcejQoQrWUAbpurooA3HDjh0mOydb\n/czXy5yPf+6S0mtfuNb+2StKT3aAR0N1WUG5yeA65vKP68+Ze+r7+LZWX/8asZmc/Px4HwdXhjQ2\nB6q7Lp1i3tH1JOTPaqvXWdGrbgDjApSgX1eokyY2I4n1F4/z4/FQNl2M4FzqVfIKzQ5sMBk5nHCB\n307v4VL+zYi1Vsfghq2pbevA4hOhpOZX2mnk7ImNRsOWC0fUdk+2vIcPdv/M1fynAU1d6/FSyCMk\nZ6Xx7MrZHLui1Ld31jvw5ZDpNHI1n6PYxCtM/2W2Wm//kc6DCfAxp1ut3rmR+CTl5qNryw5FzvnW\n3aGkZyolRrt37IreRk9xq1atUgf8Dho0CJ1OyjnXRBLsizumcNpJ4XSU0pQVwDprnUutbONq7Vqp\noHeQ6yDCJ4SzdPhSwieEM7nNZKBkPn9xhZ8AlLefU8mnMFK0eo4RY4k0ngJbs7fyVspbzEufx3zn\n+YTZhOFgcqBhXkP1RuhWBvNyYyCEuB733GPuGd62rfwnqKBUxOnYVgmys7OzCQs35/o39DYPtD0T\nq1TQ8fc2d9SciFV+JzvUM6fn7L1wDIBgz6Z42CnV3fZfOklcmhLQtvPyp0kt5YnBlcxkVkTtVtft\nWKcpwxuHqIH8hbQEPgtbxcoz+0jLD8adbezoVTeAJ5p3o5t3U1xs7Ch4Bp1jzCP8Wgwrzobxw/Gt\n/HJqN7tyr7At7xJbY0+qOfr2Vjbc3zgYXyc3/ok+yLlUJT3VydqWbt4B/ByxUT2mR5v34ZeI9Wo1\nHk97V97pNoHM3CyeXTmHUwnKeXGxdeTLIdNp6m4+Z6mZ6Uz7+QMS05UbjFb1m/Fkn5Hq53l5efz3\n39/V92MHjSjyb7Nqw7/q68F9B1KcwWBg2bJl6vthw4aVaCNqBgn2xU252WCxIO2keDrK9QhKD+KH\nFj/wRuM31EG71yMzPpN+DfupPfpQej5/gcJPACr6/hXV1C+8fvFJw4waY6UGLQshxO3SuXNn3Nzc\nAGWQblJSUoXrdGlnHhC666C5hKOjnT2ersrM4mfjzmMymfB0rk0teycATl06i8lkItgnAGut8ju6\n+0I4JpMJnVbHPY07qdv6O796jVajYXzgAHUA7+ozezgSb+5c6eTtz+SW/XGxUQavGkxGdsadZPb+\n5SyP2svlDOX72FnZEOzRgLHNujC8cTDNatUp0tufazSQkJVGGrnkFXp8W8/BlZF+Hahj78LuuFPs\njDupHteDfp1YEL6G3Pxe+J71WhGdHMfO2GP5+9TzbvcJWGm0TF31sZqj72bvwrfD/q/IE460rAym\n/zKb6HglT79ebS/mjJ6B3to8qdeavVvUsqbB/i1p6x+kfhZ35RJ7Dx0AlIm02rcKLvHvtnv3buLi\nlJuQkJAQfH19S7QRNYME++K2qig4vtFJscqqbFPZm5Ho6OgibUvL5y9gNBq5evVqpbbtbute6ScP\nZVXfKTxo+WbO3820FUIIACsrK+69V5ncyWg0sn79+grWgA5tzIFk2LGig3Qb+yg59pnZWcTEX0Kj\n0dDMW0lDScvK4Gx8DHbWelrnV82JT0/kcNxpAO5p3FEdE7UycidX8ieg8nX25L7Gyg2G0WTii4PL\nOBx/Rt2nr5MHL7QdTM+6gWoef44xj92XTvFZ2N/8GL6B41cvYDQZ0Wg01HeszUDfICY0786A+oH4\n1/JSJ+UCZfbcpi5ejPLrwANN2uFsY8epxFhWFqqnf1/DdqyL3k98ptIL39DZC79aXvwSsQFQ6vC/\n0mkMHrYuTF01Rx2MXNvOmW+GvlxkvoGk9BSe/e87HDqnVBxytnPgs0dfoVahWv85ubnM//sX9f0T\ngx8pct5XrFutpufc16f09JxffjGv/8ADD5T4XNQcEuwLi3CrZs4tCPoz4zOZFjitRK88gAGDOhtu\nZbY32GNwpZ48lDZp2I0MWhZCiKr04IMPqsHhunXrSElJKbe9u6sbvj5KCc1TUZGkZ2SonzVvYJ70\nKvysko/frlGgumxPpDIuYJB/Z3XZ0mNKGoy7nQv3NAoBIMuQw9ywFWoA+4BfV1p7KDcNuUYDnx9Y\nxuYLh9XP7axsuKdhW6a3G0aIlx9WWvNvb2TyJRae2MrHB1ey99JpdWCurZU1Aa7eDPJtyZOBPXmu\nVT/6W9elr7UP9zRoqc7Weyk9icUnQzHm9/h39m5GRk46+y+fVvc90r87n+3/Q93nEy3vob1XM/5v\n7Tdq6o6rrRPfDH2Jhq7mgcyXkxN4asEsImKVwceOtvZ8+ugrRWYfBli87i+1nGmbpoF0CDCPZcjL\ny2PFOmXQrkajYdiAeynuxIkT7Nmj1N/38vKiV69eJdqImkOCfXHTbnUP8a0K3G92vdFNRrNm4Bqm\nBEwp8VmeKY+TySdLWavkPgtP+FXw5KG04ymYNKy06juV+Q7Sqy+EuB3q1aun5u5nZWXx22+/VbhO\n2yAl2DQYDRyOMBc3CGocoL4OP6P8pnZuai5EsOu08iSgn19HnPXKb+HmMweIT1d68ce3vAen/NKc\nO2KOsvG8MvmTTqvlubbDCPZUbiYMJiM/ha/j84PLSMg035zU0jvwgF8nXmn/APc0aEstvblIxLWs\nNP6K2sPHB1ey73IkBlPR8VelOZcSz/fh68jOHxjczNWHwNp1+fXEVrXNuBb9mXtoOen54wS6+AQy\nsllv3t/yE/tjjgPgaGPHV0Nn0KhQj/6J2DOMn/cqZ+OV9B5XBxe+fWIWLeubBysDxCZcZsE/yr+J\nRqPhhRGT1JmMAbbt2UHCtfxBu+074ePlTXGLFy9WXz/66KNYWckcrDWZBPsWyGhvJLdBLkb7in+Y\n7oSqCjRvZTBcwN3WnQcaPlBq3n0zl2YV7qv4hF9/x/9d7nE0iGtw3dV3hBDidhs/frwaQC5evLjC\n3P3gwiU4j4SprwsH+0cilUC3aZ0GuDkqFXwORh8jJTMNWysbhjTvASg3DAvD/gHARe/IlLb3q9v4\nfP8fRFw9B4C1zopn2w6lRz1zOeWwK1HM2PoDcw+t4nRijNrT72Ctp2e9QF5qN4zHAnrSyNlc2jIp\nO50/I3fz2cFVHEk4p9bvL+741Qv8cGyDOiGXt4MrDzbpyLzDq8kzKU8H+vi24fjVM5xOVAL2Og61\nmR7yML8eWcu/p5RxB9ZaKz4a9JxachRg/5lwnl4wi6tpynmu4+LO9xPewr9OwxLH8emSeWrVo/t7\n3EOLRkVvBv5YbR50++C9JQfdXrt2jQ0blPQiR0dHGZhrASTYtzDZbbJJmZBC+v3ppExIIbtNdsUr\nVdLtvIm40d79qgr4Xwx6sUje/X+C/oO7rXup2y/YR1kTfqUYS3/kXbBe8eo7lTlu6dUXQtxODRo0\noEuXLgCkp6fz888/l9u+Q6EBoAUDQwFcnVxo5K0EtSfOR3I1JRGNRkPP5koFn1xDHmuPbAdgRFBf\ndaDu0qMbCb+kpLL09Q2mt29bALINuby+fT7R+TPVWml1TGw5iKlth+JgrRSCMJiM7I47wTu7f+Gl\nbfP541Qo51OuYDKZ0Gq0BLrVZ3LLAUwOGoCfi7nuf0JWKr+cDGX2gRVsOH+EcynxXMvL4EJOEj+E\nb2Dhia1qyk8jZ08mBfXjz9M71EG/DZw9aefZhD9ObgFAp9HyWuexXEy6zNw9f6r7eb3PBNrVNd8E\nbT95kGk/f0BGjvIkILCuHwuefL9E6g5A6OE9bDu0Wz23T98/rsjnJ8+cZn/+zZaPlzedg0NKbOOv\nv/5S51AYMmQI9vb2JdqImkWCfQtitDeS2T0TNe1bB5ndM29JcF7RTcT1BpB3MuAsbd8JWQnsuLyj\nzDz8gpSebzp/w5qBa3ikySMl2hTfblkTfsUYYm742IUQorp44IEH1Nz93377jWvXrpXZ1sPNnUa+\nDQEl4ExMNj8J6Bxknpl3V7hyIzA0uI+6bOmetZhMJuo4ufFE+6GAMofJe1sWkGPIRaPR8J/2o2jh\npmw/OTudFzd/o/bwA3So04zZPSZwX6MQNegHuJyRyKqo3by243/8X+gClp3eQUL+INpGLp5MDOrH\nk0H98XUyd+4kZaez4cIRvj26llUpEWxKiyIq/+YCIMjNlycC+3LoShSbLyhpSNZaKyYEDeLzA0sx\n5j9NGN28H75OnryxYZ65Tn7rgQxoaq4ytPn4Hl7+bQ45eUrw3cmvNd+MfwM3p1olzvG1lCTeX/Sl\n+n7qQxNwcXAq0ua3lUvV16OGPlhiYG5eXh5//qnceGg0GkaOHImo+STYtyAGDwMUH1Cvy19+E6ry\nJqI8VdW7X9CmoN0vUb8waO0gntn1DIPWDuKXqF9KXcfd1p2uXl1L9OgXr+RToJFdoxLpPzp01NXV\nLdG2+PrpmnSiraKV/5defSFENeTp6UmPHkpqTVZWFv/73//Kbd8pv96+yWRi7yHzRFhdWponu9px\nRCnN2bxuE4LqKRV4ohNi2HFKycV/rM09anrL2cRYvs3vEddbWfNOtydoXEvp7U7NyWD6lrmsjtql\npt042dgzKqAnn/d+ivFBA2jqWvS3OC79GssidzJ96w98c2gVZ/ID+MYuXjzdciBjm/cq0tNfXC29\nA0MatWd0s25cSr/GgqNr1c8eDujJlgthnE9RZl5vXMuHR5r3Ze6epVxIVpb5u/vydMcH1XX2RR1l\n5u+fk2dQruG9mofw8eiXsbMpWaraZDLxzn8/42qyMpahfUBr7uvct0ibhMSrrN2iDG52sLNnaP+S\nA3M3b95MfLxSAa5Lly7Ur1+/RBtR80iwb0F08TooHtcb8pffhMreRNzu3v1bMZD34OmDfBr+aZFU\nm+uptFNROdDCZTd16BhmNwxnrXORdsW3EWYTxnzn+Sx3XM6PTj8S5R5Vqe8ihBC327Bhw7C2VspQ\nLl26lISEsn87OwWbg/rQvbvU1238AnG0U9IWtx/ZS1qGMrfIw53vU9t8vW4xeQYDVjorXuv9hFrz\n/tfDa/nr2GZAmWH2k15TCHRvCECOIY/PDyzl+Y1fceraBXVbep01veu35vVOo/m811OMDuitTsQF\nSrnOPXEnmLVzEV+HrSQhMxmNRkOL2vWYGNSPGe2GMcC3NZ3q+NPExo0mNm6MbtadGe2G0dUngOy8\nXL4KW0GOUbmudPFpTmBtX34/oRynVqNlRodRnE2M5c9wJfi20VnxVr/J2OSX9IxPucbrS79Qe/z7\nt+zCeyNfwLqMgbKrdqxnx1Gl1KeLozOznvhPkUG5AEtXLyc3/wnB0AH34Whfcsb63383T8IlvfqW\nQ4J9C6LN0GIXamcO+A1gt80ObcbN/TNX1U1EZdzMDUGlevjLSLUpq9JOQYBf2eMa7DGYN5zeYLLD\nZN50fpMe+h7lHmO6Jp1Qu1CMGqUnyqQ1Ee4TTpZVVpnHU1nSqy+EuNXc3NwYPnw4oMyQW17vfvtW\nbbG3Uyrn7Ny/m7w85bfXxtqa/h2U38bs3Bw2HAgFoG9gJ5rlz6h7Nv4if4cpwXKAR0Omdh6lbnfO\ntkWsj1TKRDra2PFRj6cY0NB8Y3Hi2nme2fA5r277gV2xxzAYzU+la9s5MahRe97s/Cif9JzEkCad\niqT57L10kpe3LeCv09vVCjtutk70qd+S4U1C6ObYkG6ODWnl3gCdRktWXg5fhq3gUn61oHqO7jwe\nOIBvDi0nNz/4H+bXlSa16vLFjl/VlJ5xwYNp5Ko8lTAYjbyx9CsS05XxXR0at2TWA1Ox0pUe6MfE\nx/HZknnq+/979Fl1srICWdnZ/PnPCgC0Wi0PD32Q4iIjIwkLU/L569evT+fOnVB/VPUAACAASURB\nVEu0ETWTBPsWRn9Ij/N8ZxyWOeA83xn9Yf1Nb7MyNxEFg3dz9aXPOluWquzdr8znpaXaWGmssE+x\nLxLYX0+AX3z/zlpnmls3L9GjX5p4Xbwa6BcwaU0k2yWXum0hhLjTxo8fj42NMnPrsmXLSE1NLbWd\njbUNndoqA0JT09M4fNxcgvPezuYc/dU7lUowWq2W5wY+pi6ft2kJSfkB8KhW/RnVsj+g5O/P2viD\nGvDrrayZEfIw73efhI+jOejdd+kEb2xfwIiVb/LerkWsPbtXzc8H8LCvxQj/7nzeazKjA3qrQX+u\nMY/lkbt4JfQnwq6U/aQ1JTuDD/cu4Vj+WAG9zppn2w5lb1wEe+OUCbBq6R0ZGziQ7ecOcyBWmVeg\njqMbY9rco25nYehyDkYrs+rWdnThrYemYlXKpFegTEY2/Zu3Sc/KBGBASE/6tutWot2aLetJSlG+\na69O3Ustt7lixQr19YMPPohWKyGipZB/SQukzdBifc76pnv0CyvvJqLw4N1jA44R3zi+nC1dv5sN\n6MsL1Iun2hSe4fZmVObmoLTPPQweap39AhqjBpdMlxs+llx9LqdNp6ttKVYhRM3m6empzqqblZXF\n2rVry2zbtYN58GnoPnMqT6smLajvqfRsH448zsnzSlDdvnEQ3fyVSj7X0pJ5d/m3mEwmNBoNz3d9\nmHv8lYpABqOB19d/x1c7l6gVcTp4B/DDwBlMbHUf7nbm39DUnAy2XDjEx/uW8Miqt5m4ZjbfH15F\nZH4pTr2VDYMatWd2j4n0a9AWDUo6TEJmMp8d+Iu3dv7Mztjj5OT39GcZcll/7iCzdv2s5vnb6mx4\nsd0D1NI78O0hcxD9dJth2Fvr+X7vX+ZlHR/E1kq5WYpLimfBVvMA2bcffE4tQ1qcyWTio8XfEBWj\n3FzU8/DmpdEl54UxmUz8usI8MHf08BEl2uTl5bFmzRoAdDod9913X4k2ouaSYF9UWmk3EaUN3o0N\nir2uHv6KguIsqyz2XN1Duia9yPLrGcRa3n4qO8NteRJzEzmYcpDE3MSbOhYHkwOBMYFojMrFRWPU\nEBQbhG1e0QFZle3Vj28cz/GBx6ukFKsQQhQoSOUBWLlyZZntunXorOaSb929Xa1zr9FoGNHb/Nv7\ny3pzMDxj8ESc83P6Q08e4I89SlCq1WiZ2Wt8keo1iw+vYerKOeqgVxudFaMC+vDzfTN5s8vjdPJp\noQbWBc6lXOaPk1t4ev2nPLn2Y1ZF7iTXkIeTjR1jW/Tjna5jaepaF51Gi06jJSo5ju8Or2bius+Z\nc+4fvrywnkXHN6pPCVxs7Hm148M0d/Nl0bF16vJgr6b09m3L1rMHOX1VGUPg51af/k07qscyf8tS\ntfLOQyED6dCkJWVZsX0t/+xScv71NnpmT3kN52LVdwD2Hj7AmfNnAWjRNIBWzYNKtNmzZw+JiUrq\nUdeuXXF1vbkOL1G9yJRo4qaUNnjXpDWR6ZKJ9RXrm95+lHsU4T7hmLQm9pj20D2zO21z2hJmE6bm\ntmtNWrpndodoaNiwYbnbKwiSi7dztXa94d78v+P/Vuvp69Ax1G4oPfU9KzyGsjRJaELdpLok2yXj\nkulyw4F+rj6X2KBYTFrlYlpQRcn61K196iOEEIGBgTRu3JgzZ85w/PhxIiMj8fPzK9Gudi1XWjcP\n4tDxo1yMi+HM+WiaNFDy8od0G8C8lT+TnpnBun3beHLoY9T1qEOdWu7MHPY0L//2MQBfrl1ES99m\nNPdpjJXOirf6Pkkz9wbM3f0HBpORsLiTjP7tNUa27MeYNvdQ294ZnVZHt3ot6VavJTmGPI4lnOXA\n5ZMcvHxaneAKIDrlEl8e/JMlJzYxLmgQfRsE4+vsycyOjxCeEM3iiE3EpZtLjOYVm2CraS0fnmx1\nL14OroQnnOWv08r4A2utjqnBD2LCxPz95puhie2Hoc0fbHwuIZbVYVsAsNfbMbHXQ2We7yORx5nz\ny1z1/cujp+BXr1GpbX/+0zzD8SPDHioxcBdQe/UBdXZkYTnkii9uSlmDd+2S7a5rO6UFsFlWWWqg\nD2DUGAm1CyVeG19kEGvB8sr28Bfs71bkvF/LvcZPMT+pg3wNGFiZubLCibPKOy4A2zxbvFK9SgT6\n1yPTJdMc6Be4BaVYhRCiOI1Gw9ChQ9X3q1evLrNtj07mnPJNO7aqrx1s7RnRS+ndNxgM/LjKXAa5\nV4sQHgoZCCgTbb2w8D2iLp9X9z2mzSC+GjoDN3slXSfXmMfiw2sYuuhFZq6by67zR8k15A8I1lnR\n1qspE1sNZm7/aSwZ8iZT2gzH39VcZvJyRiKz9/7Ky1vnEZd2Fa1GQyuPRnzY/Qle6jCCTt4BNHHx\npraVA7Ws7OldvxVvdxnL653H4OXgypWMRN7a8V+17OfIZr2p5+TB5jMHiMzv1fd396VnI/NkY//d\n9pe5Bn/n+6jlUPo4r7irl3lp7rvk5g9wHtptAIO79i+17ZGIcHaHKVV6vDw86du1V4k2WVlZbNmy\nRfk3cHCge/fupW5L1FwS7IubUtbg3ZiTNz9xVLJdcolg1agxcsb6TIlBrEaNkXidMlbgeivU3Ejg\nX7DOnug9GIrd7RgwlJg460Zz+G+kTQG7ZLs7VkVJCHH3GTRokNprvHHjRjVFp7i+Xc1PPtdtK9pu\n9IAHcLBTZmz9Z/dGIi+eVT97buBjtKjbBICkjFSe+e87nI0398oH+wSw5OH3ebjVAKy0yu9cntHA\nxqh9TFv9KQN/msrLa75i2bHNXEi+rO63tp0z9/t355v+L/BZ72do7dFE3eahK5E8ufZj/jq1DYPR\niEajIci9IVPaDOHNLo8yuV5vnq7Xh/FBA2no4gVAVl4Os3b8l6TsNAAC3RvyaOAADEYjP+xbrm57\nUof71fMVm3hFnSnY0daeR7qUnk6akZXJ9K/f4VqqMilZa79AXhr9TKltAb77eYH6euyDo9UyqYVt\n376dzExlgG+vXr2wtb3xTiZRPUmwL27araoAVDyQdcl0UXPXC2iMGmzP2ZYYxKo1afEweJS5rcru\nv7L/K1BXVxddsTym4hNn3aog/nq/U8zJmCopxSqEEKVxd3cnOFjpqY6NjeXYsWOltvPx8qZlsxYA\nRF88z6mzkepntRydeWygkr5iMpmYu8xcylNvbcPnj83Ev05DABLTk5ny01uERR9X2zjq7Xmh6yP8\n/siHjGrZH2e9uZZ8Rm4WW88e5KNtCxnxy/9x/+IZfBy6iAMxJ9RynEEejZnT62ne7vaEOqg3y5DD\nt4dW8PymL4lMLL8jKyEzmddCf1RTgzzsa/Fml8ex0upYF7mb6MRYAFp4NqZbg9bqej9vX6kew4iQ\nQTja2pfYtslk4v1FX3L64hkAvN08mT3lNWxKCeAB9h85yL7DyozEdTy8GD6w9EG369evV1/371/6\nEwJRs8lVX9wSpQ3evdGAu4Btni1BsUElBqu6ZLkQGBOoBvwak4aOmR1xMDmUua2q4qx1ZqjdUDXg\nLz5x1p0K9AtURSlWIYQoS+Fgcdu2bWW362Ge3XXd1o1FPnuk33DcXJQxVNuP7GVvxCH1Mxd7R74a\n9xp+Xr6AUqHn6Z/e4pv1v6hpLQA+zu5M6zaaVWM/453+T9HPLwQnm6IB9KXUqywN38QzKz9i+M/T\nWXzoX9JzMtFoNHT2C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viE+5TI2bfOtq5wXSGqo6q4JjRvXn66QlUq6MG7k8dwp1V0DsaO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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9faa80160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('whitegrid')\n",
    "plt.subplot(1,2,2)\n",
    "\n",
    "W = sample_generator(5000)\n",
    "plot = sns.kdeplot(W[:,0],W[:,1])\n",
    "plt.axis('square')\n",
    "plot.set(xlim=(wmin,wmax))\n",
    "plot.set(ylim=(wmin,wmax))\n",
    "plt.title('kde of approximate posterior')\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "plt.contourf(wrange, wrange, np.exp(logpost.reshape(300,300).T),cmap='gray');\n",
    "plt.axis('square');\n",
    "W = sample_generator(100)\n",
    "plt.plot(W[:,0],W[:,1],'.g')\n",
    "plt.xlim([wmin,wmax])\n",
    "plt.ylim([wmin,wmax]);\n",
    "plt.title('true posterior');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}