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      "#Regularization\n",
      "\n",
      "##Introductory Theory\n",
      "<p>Regularization is a technique for reducing the complexity of a model in supervised learning. The processing of performing regularization can be viewed with multiple interpretations:<br><br>\n",
      "\n",
      "<b><u>Complexity Penalty</u></b><br><br>\n",
      "\n",
      "In the ERM framework, regularization can be viewed as the penalty or cost for adding extra complexity to a model. Usually, the complexity is a function of the weights learned for each feature. For now, we'll consider the class of linear models: $f(X) = W\\cdot X+t$. Remember in ERM we seek a function $f^{opt}$ such that:<br><br>\n",
      "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)$</center><br>\n",
      "\n",
      "where $\\mathbb{L}(f(x),y)$ is some arbitrary loss-function. The complexity of linear functions $f$ is set by the $L^p$-norm of the vector $W$, which is defined as $\\|W\\|_p =(|W_1|^p+|W_2|^p \\dots |W_m|^p)^{\\frac{1}{p}}$. The two norms we'll deal with the most in this class are $\\|W\\|_1$ and $\\|W\\|_2$. We want to add a term to the loss function that penalizes it as the norm of $W$ increases. We do this by adding a constraint to the above function:<br><br>\n",
      "\n",
      "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)$</center>\n",
      "<center>subject to $R(W)\\leq t$</center><br><br>\n",
      "\n",
      "where $R(W)$ can be any $L^p$-norm (mostly we'll choose $\\|W\\|_1$ or $\\|W\\|_2$). Using the method of Lagrange multipliers, we can set this up as:<br><br>\n",
      "\n",
      "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda (R(W)-t)=\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda R(W)$</center><br><br>\n",
      "The parameter $\\lambda$ is the Lagrange multiplier here, and in most cases we choose it using some form of cross-validation or model selection. We can think of it as a lever that controls the amount of penalty we enforce as $R(W)$ increases. The most commonly used forms of regularization are:<br><br>\n",
      "\n",
      "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda \\sum\\limits_{j=1}^m |W_j|$</center><br><br>\n",
      "<center>$f^{opt}= \\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda \\sum\\limits_{j=1}^m W_j^2$</center><br><br>\n",
      "\n",
      "The first one above is commonly called \"$L1$\" regularization or the \"lasso.\" The second is usually called \"$L2$\" or \"ridge.\" Both can be thought of as penalties that force the optimal solution into a bounded region, where the bound is defined by some sort of $L^p$ circle with radius $t$. <br><br>\n",
      "\n",
      "<b><u>Bayesian Formulation</u></b><br><br>\n",
      "\n",
      "Regularization also has a very nice Bayesian interpretation, which we will develop here. Regularization can be thought of as a Maxium a Posteriori estimation problem, which is an extension of Maximum Likelihood estimation. If you recall, we used the MLE method to find optimal parameters for Logistic Regression. This was defined as:<br><br>\n",
      "<center>$\\hat{\\beta}_{MLE} =\\underset{\\beta} {\\mathrm{argmin}} \\:L(\\beta|X,Y)=\\underset{\\beta} {\\mathrm{argmin}} \\:\\prod\\limits_{i=1}^nP(x_i,y_i|\\beta)=\\underset{\\beta} {\\mathrm{argmin}} \\:\\prod\\limits_{i=1}^np_i^{y_i}(1-p_i)^{1-y_i}$</center><br><br>\n",
      "\n",
      "In MAP estimation, we assert a prior belief onto the value of $\\beta$, so instead of finding $\\beta$ that optimizes the likelihood, we find one that optimizes the posterior distribution, which is defined as:<br><br>\n",
      "\n",
      "<center>$P(\\beta|X,Y) = \\frac{P(X,Y|\\beta)*P(\\beta)}{P(X,Y)}$</center><br><br>\n",
      "Usually with MAP, the denominator above doesn't factor into the optimization, so we only consider:<br><br>\n",
      "<center>$P(\\beta|X,Y) \\propto P(X,Y|\\beta)*P(\\beta)=Likelihood*Prior$</center><br><br>\n",
      "For logistic regression, we have already defined the likelihood. Now we can define a prior on $\\beta$. For reasons of mostly mathematical convenience, we can assume that $\\beta$ comes from one of two priors:<br><br>\n",
      "<center>$P(\\beta_j) = N(0,\\tau_j)=\\frac{1}{\\sqrt{2\\pi \\tau_j}}exp(\\frac{-\\beta_j^2}{2\\tau_j}),\\: \\:j=1,2,\\dots d$</center><br>\n",
      "or\n",
      "<center>$P(\\beta_j) = \\frac{\\lambda_j}{2}exp(-\\lambda_j|\\beta_j|), \\: \\:j=1,2,\\dots d$</center><br><br>\n",
      "\n",
      "The first above is the normal distribution, and the second is the Laplace distribution. Again, there might be no reason to assume one prior is better (or more accuracte) than the other. We normally choose based on properties of the MAP, given a specific prior. Also, we defined the above priors as functions of individual parameters $\\beta_j$. We usually assume that the prior on each $\\beta_j$ is independent, so that $P(\\beta)=\\prod\\limits_{i=1}^d P(\\beta_j)$. We can now define a new optimization task, based on the MAP formulation:<br><br>\n",
      "\n",
      "<center>$\\hat{\\beta}_{MAP} =\\underset{\\beta} {\\mathrm{argmax}} \\:L(\\beta|X,Y)\\:P(\\beta)$</center><br><br>\n",
      "Using the above priors, we can define two different MAP estimators.<br><br>\n",
      "\n",
      "\n",
      "<center>$\\hat{\\beta}_{MAP}=\\underset{\\beta} {\\mathrm{argmax}} \\prod\\limits_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i} \\: \\prod\\limits_{j=1}^d \\frac{1}{\\sqrt{2\\pi \\tau_j}} exp(\\frac{-\\beta_j^2}{2\\tau_j})$</center><br>\n",
      "or\n",
      "<center>$\\hat{\\beta}_{MAP}=\\underset{\\beta} {\\mathrm{argmax}} \\prod\\limits_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i} \\: \\prod\\limits_{j=1}^d \\frac{\\lambda_j}{2}exp(-\\lambda_j|\\beta_j|)$</center><br><br>\n",
      "\n",
      "We don't try to optimize these functions as is. Instead we take the log, and in doing so, we end up with equivalent formulation of $L1$ and $L2$ regularization defined above.\n",
      "\n",
      "</p>"
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     "source": [
      "##Examples"
     ]
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      "<p>As a starting point, we can visualize how regularization constrains our search space for possible optimum values of $\\beta$. We'll generate a high variance data set that represents a bournoulli process where $P(Y|X)$ is governed by the inverse logit. We'll then plot the following:\n",
      "<ul>\n",
      "    <li>Contour plot of the log-likelihood loss as a function of $\\beta$</li>\n",
      "    <li>Constraint boundaries of the following constraint $|\\beta|_p<t$</li>\n",
      "    <li>The path of $\\hat{\\beta}_{MAP}$ as we vary regularization strength</li>\n",
      "</ul>\n",
      "</p>"
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     "input": [
      "import numpy as np\n",
      "import math\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "import course_utils as bd\n",
      "from sklearn import linear_model\n",
      "from matplotlib.colors import BoundaryNorm\n",
      "from matplotlib.ticker import MaxNLocator\n",
      "reload(bd)\n",
      "\n",
      "\n",
      "def RegDemo(n, alpha, beta, regtype):\n",
      "    #Generate a bivariate X and a bournoulli Y\n",
      "    data = bd.gen_logistic_dataframe(n, alpha, beta)\n",
      "\n",
      "    #Create a grid of possible combinations of beta\n",
      "    dy = 0.1; dx = 0.1 ; b_min = 0; b_max = 2\n",
      "    b1, b2 = np.mgrid[b_min:b_max:dx, b_min:b_max:dy]\n",
      "\n",
      "    #Get z\n",
      "    z = np.array([[ bd.LogLoss(data, [b1[i,j], b2[i,j]], 0) for j in range(b1.shape[0])] for i in range(b2.shape[0])]) \n",
      "    z = z[:-1, :-1]\n",
      "\n",
      "    #Some settings\n",
      "    levels = MaxNLocator(nbins=15).tick_values(z.min(), z.max())\n",
      "    cmap = plt.get_cmap('PiYG')\n",
      "    norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)\n",
      "\n",
      "    #Plot Contour\n",
      "    fig = plt.figure()\n",
      "    ax = plt.subplot(111)\n",
      "\n",
      "    plt.contourf(b1[:-1, :-1] + dx / 2., b2[:-1, :-1] + dy / 2., z, levels=levels, cmap=cmap)\n",
      "    plt.colorbar()\n",
      "\n",
      "    #Plot an Lp Constraint, i.e., the Lp norm < k\n",
      "    cs = [0.5, 1, 1.5, 2, 2.5, 3]\n",
      "    x_c = np.arange(b_min, b_max, 0.01)\n",
      "    for c in cs:\n",
      "        if (regtype==2):\n",
      "            y_c = np.sqrt(c - x_c**2)\n",
      "            plt.plot(x_c[~np.isnan(y_c)], y_c[~np.isnan(y_c)], label='L2 norm<{}'.format(c))\n",
      "        else:\n",
      "            y_c = c - x_c\n",
      "            plt.plot(x_c[(y_c>0)], y_c[(y_c>0)], label='L1 norm<{}'.format(c))\n",
      "\n",
      "\n",
      "    #Now get optimums for various regularization strengths\n",
      "    b1_opt = []\n",
      "    b2_opt = []\n",
      "    for i in range(-10, 10):\n",
      "        LR = linear_model.LogisticRegression(C=10**i)\n",
      "        LR.fit(data.drop('Y', 1), data['Y'])\n",
      "    \n",
      "    #Now fit the data for various regularization strengths\n",
      "    b1_opt = []\n",
      "    b2_opt = []\n",
      "    for i in range(-60, 60):\n",
      "        LR = linear_model.LogisticRegression(C=10**i, penalty='l{}'.format(regtype))\n",
      "        LR.fit(data.drop('Y', 1), data['Y'])\n",
      "        b1_c, b2_c = LR.coef_[0]    \n",
      "        b1_opt.append(b1_c)\n",
      "        b2_opt.append(b2_c)\n",
      "\n",
      "    plt.plot(b1_opt, b2_opt, 'k+-')\n",
      "    \n",
      "    plt.xlim([b_min+dx, b_max-2*dx])\n",
      "    plt.ylim([b_min+dy, b_max-2*dy])\n",
      "\n",
      "    box = ax.get_position()\n",
      "    ax.set_position([box.x0, box.y0 + box.height*0.0 , box.width, box.height * 1])\n",
      "\n",
      "    # Put a legend below current axis\n",
      "    ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), fancybox=True, shadow=True, ncol=3, prop={'size':10})\n",
      "\n",
      "    plt.show()\n"
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      "<p>The next two plots show all of the above with different sized datasets. The first is relatively small, with 50 examples, and the 2nd has 50k examples. We know the true value of the data generating distribution is $\\beta=[1, 1]$. The dark green elipsoid shows where the log-loss is at a minimum. Its center is the optimum point of the data. With more data, we can see that this center gets closer to $[1, 1]$.<br><br>\n",
      "The circular constraint boundaries basically say that the coordinates of $\\hat{\\beta}_{MAP}$ have to be within that boundary. The MAP estimator will found the lowest value of the log-loss (i.e., darker color) within the circle. <br><br>\n",
      "\n",
      "What we can learn here is that with a very loose regularization weight (bigger circle), we are more likely to choose $\\hat{\\beta}_{MAP}$ that fits the data well, but is far from the truth (which we know because we created the data generating distribution). With the right regulariztion strength (such as the red circle in the above plot), we can see that our MAP estimate is actually closer to the truth. The problem is less severe with more data, because the dark green elipsoid shifts closer to the true optimum point. <br><br>\n",
      "\n",
      "Note that with $L1$ regularization, we can do the same analysis, though the constraint boundaries would look different. Instead of circles they would be straight lines.\n",
      "\n",
      "</p>"
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     "input": [
      "plt.clf()\n",
      "RegDemo(50, 0, [1, 1], 2)\n",
      "RegDemo(50000, 0, [1, 1], 2)"
     ],
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b/Yi6pU+Lh2yQeWoct2ybhzqsgq+nfEytotrxg+sjXlIrtw7XkxrezocHQikZ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\npEWpJL0fTWn/3rdozcrR7YEqQI7baPJdhzE886+9jtsdCevmUuNYyeH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       "text": [
        "<matplotlib.figure.Figure at 0x1057f7210>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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95u+M+vpJgg2lVIxawonpf6Q29ftYA9W+HuLVI4LC4fn8celTNETU8Ni633HT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\nK7mYa0u0b9lfzisH2LJlC9OnTwdg+vTp/PDDD83GFBUVsW/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IJeheDo642NhyqVC8k36d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wAAAA\naUlEQVRzqEuyP3r0KH/88YdJf8WQkZGRMQQODg5MnjyZLl26GPtSmtCumEOdoBcUFDSUk5SRkZH5\nK2JlZYWrq2tDxUhTQicxl5GRkZExbeS4iYyMjIwFIIu5jIyMjAUgi7mMjIyMBfD/AVr1j/vov8lA\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108b29a10>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>The above examples were a bit theoretical, and are mainly presented for explaining the underlying optimization process (and to reinforce the idea of the bias-variance tradeoff going on).<br><br>\n",
      "Below we'll look at an actual dataset. First we'll read it in and rescale it. Rescaling is very important because the norm of $\\beta$ is going to be a function of the scale of each feature. Since we apply the same regularization factor to each feature, rescaling ensures that it has the same effect per feature. \n",
      "\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.preprocessing import scale\n",
      "from sklearn.cross_validation import train_test_split\n",
      "from sklearn import linear_model\n",
      "reload(bd)\n",
      "\n",
      "f='/Users/briand/Desktop/ds course/datasets/ads_dataset_cut.txt'\n",
      "\n",
      "#Lets prep the data\n",
      "train_split = 0.75\n",
      "tdat = pd.read_csv(f,header=0,sep='\\t')\n",
      "\n",
      "'''\n",
      "For regularization, it is advised to normalize the data first. We'll normalize and then split, and if its not obvious\n",
      "we shouldn't normalize the outcome.\n",
      "\n",
      "Note too that the sklearn scale function returns an array, which we have to throw back into a data frame.\n",
      "'''\n",
      "\n",
      "lab = 'y_buy'\n",
      "Y = tdat[lab]\n",
      "X = tdat.drop(lab, 1)\n",
      "X_scale = pd.DataFrame(scale(X, axis=0, with_mean=True, with_std=True, copy=True), columns = X.columns.values)\n",
      "\n",
      "X_train, X_test, Y_train, Y_test = train_test_split(X_scale, Y, test_size=0.3, random_state=42)\n",
      "\n",
      "#The above returns numpy arrays. I'd prefer to store them as data frames.\n",
      "X_train = pd.DataFrame(X_train, columns = X.columns.values)   \n",
      "X_test = pd.DataFrame(X_test, columns = X.columns.values)   \n",
      "Y_train = pd.Series(Y_train)    \n",
      "Y_test = pd.Series(Y_test)        \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Next, we'll look at how a feature's weight evolves as we change the regularization weight.\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L2 = {}\n",
      "L1 = {}\n",
      "\n",
      "for i in np.arange(-5, 5, 0.5):\n",
      "    LR2 = linear_model.LogisticRegression(C=10**i, penalty = 'l2')\n",
      "    LR2.fit(X_train, Y_train)\n",
      "    L2[i] = LR2.coef_[0]\n",
      "    LR1 = linear_model.LogisticRegression(C=10**i, penalty = 'l1')\n",
      "    LR1.fit(X_train, Y_train)\n",
      "    L1[i] = LR1.coef_[0]\n",
      "\n",
      "\n",
      "feats = X.columns.values\n",
      "Rpath2 = pd.DataFrame(L2, index=feats).transpose()\n",
      "Rpath1 = pd.DataFrame(L1, index=feats).transpose()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p> This plot shows how the weights progress with $L2$ regularization. We can see a generally smooth progression that converges to a point as the regularization strength decreases.\n",
      "\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.clf()\n",
      "fig = plt.figure()\n",
      "ax = plt.subplot(111)\n",
      "\n",
      "for f in feats:\n",
      "    plt.plot(Rpath2.index.values, Rpath2[[f]], label=f)\n",
      "\n",
      "plt.xlim([-3, 2])\n",
      "plt.ylim([-1, 1])\n",
      "box = ax.get_position()\n",
      "ax.set_position([box.x0, box.y0, box.width*1.5, box.height * 1.5])\n",
      "\n",
      "    # Put a legend below current axis\n",
      "ax.legend(loc='upper center', bbox_to_anchor=(1.15, 1), fancybox=True, shadow=True, ncol=1, prop={'size':10})\n",
      "\n",
      "plt.title('L2 Regularization Paths for Feature Weights.')\n",
      "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
      "plt.ylabel('Feature Weight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.text.Text at 0x1064d6290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x10915fa10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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atm2rViMrcvyTJk2iVq1amJmZMWLECIYMGaK133tjKG3/JfH09CQxMVHrPevh4UFCQoKa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xQH3/a+QschIi3Duk7qxoaXiKpl/5X9CN0Uiq99v8a/nP8ldBwi0iKs66RubHiJqNpy7uUg8OdA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\nknRHd/5KTgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10915fa50>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p> Next we'll do the same for $L1$.\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.clf()\n",
      "fig = plt.figure()\n",
      "ax = plt.subplot(111)\n",
      "\n",
      "for f in feats:\n",
      "    plt.plot(Rpath1.index.values, Rpath2[[f]], label=f)\n",
      "\n",
      "plt.xlim([-4, 2])\n",
      "plt.ylim([-0.5, 0.5])\n",
      "box = ax.get_position()\n",
      "ax.set_position([box.x0, box.y0, box.width*1.5, box.height * 1.5])\n",
      "\n",
      "    # Put a legend below current axis\n",
      "ax.legend(loc='upper center', bbox_to_anchor=(1.15, 1), fancybox=True, shadow=True, ncol=1, prop={'size':10})\n",
      "\n",
      "plt.title('L1 Regularization Paths for Feature Weights.')\n",
      "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
      "plt.ylabel('Feature Weight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "<matplotlib.text.Text at 0x109164350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x108cf5ed0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Fixdp0KABfn5+dO/enaioKK1tjYyMSEhIKPA+c/Zhbm5OXFwcR44cASA9PZ3o\n6GiqVq1K1apVNTfHrV69urCHV+LI1U+IEkxRFIafPctwExOs/7lZQgghxIuzsLAgMTGRevXqUatW\nLeDfNrrr16/H0tIStVrNyZMnGThwoNZya2tr9PX1sbGxeWaXY0+2v82ZLlu2LBs2bGD8+PHY2Nig\nVqs5fPgwAEuXLmXkyJGo1eqXe8DFnEopAfXdMqa2ELlbe+sWn1+5wt92dpST2l0hRDGR33VdrvvP\n58qVK3Tp0uWpGuaSTKVSMWfOHLy9valWrZpmvrThFaKEiktL4+Pz59ncsqUku0IIUQopiiK9NPxD\nEl4hSij/8+fpX6sWjpUr6zoUIYQQefj9998JCAjQmtewYUM2btz4wmWbmZlx/PjxFy6nJJCEV4gS\naMudO4Q8fMhxe3tdhyKEEOIZ3NzccHNz03UYJZ4kvEKUMA/S0xlx9iyrLSyoIENPCiGEENJLgxAl\nzdgLF+haowYdqlbVdShCCCFEkSA1vEKUILvv3WPX/fuckKYMQgghhIbU8ApRQiRmZDD07FkWNm1K\nZQP5LiuEEELkkIRXiBLis0uXaFelCm9Xr67rUIQQokS7fPkyLVu2fCVlL1y4kJUrVz5zncjISHbs\n2PFK9v+4V3mcr5tUAwlRAvwVH09QXBxR0pRBCCGKtWHDhuW7TkREBOHh4bz99tvPXW5GRgYGpfjX\nv9J75EKUECmZmfiePs3cxo2pXqaMrsMplRQFkpIgISH7kZ6ePe/xR1bW0/Pyml+QdQs7/1V5FX3c\nF7bM4rLd61Zc4izqMjIy8Pb25u+//6ZFixYsX74cCwsL/v77b6pVq0ZYWBjjxo1j7969mJubc+jQ\nIWrUqEFWVhbm5uYcOXKE6rn8IhcYGIiRkRFjxozBxcUFJycn9u3bx4MHD1i8eDGOjo5MmTKFlJQU\nDh48yMSJE3nnnXfw8/Pj5MmTpKenExgYSLdu3Vi2bBmbNm0iKSmJzMxM6tSpw4ABA3jnnXcAGDx4\nMF27dsXOzo4BAwaQlJQEwPz582nduvVrPZ+vmiS8QhRz065cwbJiRfq88YauQylWsrIgMTE7QX34\n8N9kNb/nuc1LTARDQzAyyn6UKZOdVOQ89PS0pwsz/2WU8eT8l+1VjPRa2DKLy3avW3GJ80WogoML\nva3i4vLc6545c4YlS5bQunVrfH19+f7773Md1UylUuHt7c3q1avx9/dn9+7d2NjY5Jrs5qyfU45K\npSIzM5NB0GfWAAAgAElEQVSjR4+yY8cOpk2bxh9//MHnn39OeHg4c+fOBWDixIm4urqyZMkSHjx4\ngKOjI2+99RaQXRscFRVF1apV+fXXX1m/fj3vvPMOaWlp7N27l4ULF5KVlcUff/xBuXLlOHfuHP36\n9SM0NLSAZ69ok4RXiGLs74QElsTGEmlnp+tQXovMzIInqHklq48eQYUKULnyv4lqXs/r1Hn2OpUq\nQSn+pVCIl+5FvpAVJGl9EaampppaUG9vb+bMmZPnuj4+PvTo0QN/f3+WLFmCj4/Pc++nV69eANja\n2nL58mUge8hg5bFvL7t27WLr1q3MmjULgNTUVGJiYlCpVHTq1Imq/3RT6e7ujr+/P2lpaezYsYMO\nHTpQrlw54uPjGTVqFJGRkejr63P27NkCnYviQD6ihSim0rOyeP/0ab5t1Ija5crpOpxX4to12LsX\n9uzJ/hsbm51c5pWY5kxXrQqmps9OZitWzK7tFEKIwni8NldRFPT09DAwMCDrnzZDKSkpmuWmpqbU\nqlWLvXv3Ehoays8///zc+yn3z+e7vr4+GRkZea63adMmmjRpojXv6NGjVKxYUTNtaGiIi4sLv//+\nO+vXr8fLywuA7777jjp16rBy5UoyMzMxNDR87viKC0l4hSimvo6JoU65cgyoVUvXobw0d+9CcHB2\ngrtnT/Z0x47g6gqTJkHjxtL+UAhRNMTExHDkyBGcnJxYs2YNbdu2JSEhgbCwMNzd3dm4caPW+kOG\nDMHb25tBgwbl2vThcUo+bU8qV65MQkKCZtrNzY25c+cyb948ILsZg1qtzrUcDw8PFi1aRHh4OMuX\nLwfg4cOH1KtXD4AVK1aQmZmZ/wkoZqR+Q4hiKDopiTnXr7OwadN8PziLssRE2LkTxo0DW1to0AAW\nL4ZGjWDdOrh9G4KC4MMPoUkTSXaFEEWDSqXC3NycBQsWYGFhQXx8PCNGjGDq1Kn4+/tjb2+PgYGB\n1udz165dSUpKeq7mDHl9rufM79ixI9HR0ajVaoKCgpg8eTLp6elYWVlhaWnJ1KlTNes/WVbnzp3Z\nv38/nTp10vTaMGLECJYvX46NjQ1nzpyhUqVK+cZS3KiU/L5GFAMqlSrfb0NClBSZioLz338zqHZt\nhtetq+twCiQtDY4e/bcGNyICWrXKrsF1dQUHh+wbvoQQpVt+1/XieN0PCwtjzJgx/Pnnn7oOpURT\nqVTMmTMHb29vqlWrppkvTRqEKGbmXrtGOT09hpmY6DqUfGVlwbFj/ya4hw5B06bZye3kydC2bfaN\nY0IIUZLNnDmTH3/8kTVr1ug6lFJLaniFKEYuJCfjGB7OEVtbGhfBTFFR4OzZfxPc4GB4441/a3Bd\nXMDYWNdRCiGKupJYw/ukL7/8kqCgIK15ffv2ZcKECTqKqGTIq4ZXEl4hioksRcE1MpIu1aszxtRU\n1+FoXLv2b4K7d292zwc5Ce5//gPFoCJaCFHElIaEV7wa0qRBiGJuUWwsjzIz+fifO2l15e5d2Lfv\n3wT33r1/e1KYMiX7hrMSco+DEEKIEkISXiGKgaspKUy6dIlgGxv0X3M2mZgIBw78m+BeuJDd9tbV\nNbv3hJYtpT9bIYQQRZskvEIUcYqi8OHZs/jVrUuLxzoQf1XS0uDIkX8T3IgIsLPLTnDnzwd7e930\npPDbb78RHh4O/NvVzuPDbz7vdGG2KUgZ+vr6dOzYkbrFrAcNIYQoySThFaKIW33rFldTU/mlfv1X\nUn5WVnZSm5PgHjoE5ub/NlFwdtZtTwp37tzBz8+PsLAwPDw8AO1hNXOeP8/069gmJSWFjz76iF69\nevHpp5/StGnT13GahBBCPIMkvEIUYbfS0hhz4QLbW7ak7CtoNxARAR98AA8fQufO2U0Ufv656PSk\nEBQUxEcffUS/fv2IjIykQhHsmSI3d+7cYf78+Tg7O+Pi4kJAQACtWrXSdVhCiCLi3Xff5eeff6Zy\n5cp5rrN8+XI6d+5MnTp1XmksgYGBGBkZMWbMmFe6H12TlndCFGF+587hU7s2ds/4UCyMxEQYMwbc\n3WHECDh9GubNgx49ikaye/v2bd577z2mTJnCpk2bmD17drFJdgFq1KhBYGAgly5dok2bNnTv3p3O\nnTuzd+9eubNcCMH27dufmewCLFu2jBs3bhSo3MIMCVxSRlLLjyS8QhRRm+LiiExMZKqZ2Ustd/t2\nsLSEuDg4cQJ8fIpOrwqKovDzzz9jZWVFo0aNiIiIoHXr1roOq9AqVarE6NGjuXjxIl5eXowYMQIn\nJyd++eUXsrKydB2eEKKQkpKSePfdd7GxsaFly5asWLGCvn37apYHBwfTtWvXPLc3MzPj3r17XL58\nmebNm/PBBx9gaWmJm5sbKSkpbNiwgbCwMPr374+trS0pKSmEh4fj4uKCnZ0d7u7u3Lx5EwAXFxdG\njx6Nvb09X3zxBWZmZpov1klJSdSvX5+MjAwWLVqEg4MDNjY29OnTh+Tk5Fd7kooYadIgRBF0Lz2d\nUefOsd7CgvL6+i+lzBs3wN8/e+Sz//0P3nrrpRT70sTGxjJ8+HDOnz/P1q1bsbe313VIL03ZsmXx\n8fFh4MCBbN68mS+//JKJEycyfvx4+vXrR9myZXUdohAlRrAquNDbuiguz7Xezp07qVu3Ltu3bwfg\n4cOHTJ48meTkZMqXL8+6devw8vLKc/vHa1XPnz/PunXr+Omnn/Dw8GDjxo3079+fBQsWMHv2bGxt\nbUlPT8fPz4+tW7dSvXp11q1bx2effcbixYtRqVSkp6cTGhoKwN9//82ff/6Ji4sL27Ztw93dHQMD\nA3r37s3QoUMBmDx5MosXL2bUqFGFPFPFjyS8QhRBn5w/T++aNWlbteoLl5WZCQsXwtSpMGwYrFgB\n5cu/hCBfEkVRWLlyJWPHjmXYsGGsW7eOcuXK6TqsV0JfX59evXrRs2dP9u7dy8yZM5kyZQpjxoxh\nyJAhVHwNvXAIUdI9b9L6IqysrBg7diwBAQF06dKFtm3b4u7uzpYtW+jduze//fYbs2bNeq6yGjRo\ngJWVFQCtWrXi8uXLmmU5NbVnzpzh5MmTvPVPTUVmZiYmj43qk3NDb87zdevW4eLiwtq1azVJbVRU\nFJMmTSI+Pp7ExETc3d1f6BwUN5LwClHE7Lx7l+AHDzjxEmo4jx/PvinNwCB7mN8WLV48vpfp+vXr\nfPDBB1y7do2dO3dia2ur65BeC5VKhaurK66uroSGhvL111/zxRdfMGrUKEaNGqU1OpAQouhp0qQJ\nERERbN++nUmTJuHq6oqnpyfz58+nWrVq2NnZPfcX2Me/4Ovr65OSkqKZzqkJVhSFFi1acOjQoVzL\neHxfXbt2ZeLEidy/f5+///6b//znPwAMHjyYLVu20LJlS5YvX05wcHBBD7tYkza8QhQhCRkZDDt7\nlp/MzalkUPjvo48ewfjx2c0WfH1h//6ilewqisLixYuxsbHBwcGB0NDQUpPsPsne3p4NGzZw4MAB\nrly5QuPGjfnkk0+4du2arkMTQuQhNjYWQ0ND+vfvz9ixY4mIiKBDhw6Eh4ezaNGiZzZnyE9Ora6R\nkREPHz4EwNzcnLi4OI4cOQJAeno60dHRuW5fqVIl7O3t+eijj+jatasmaU5MTKR27dqkp6ezatUq\nrWS6NJCEV4giJODiRVyNjen8AjV8O3dm35R29SpERcHQoUVrJLSYmBjc3d35/vvv2bNnD1OnTpU2\nrGRf0BYvXszx48dRqVRYWVnh6+vLmTNndB2aEOIJUVFRODo6olarmT59OpMmTUJPT4+uXbuyc+dO\nunTp8sztH2/D+2QvCTnTgwcP5sMPP8TW1pasrCw2bNjA+PHjsbGxQa1Wc/jw4TzL9/DwYM2aNVpN\nHT7//HMcHR1p27YtzZs319pfaeipQaWUgNRepVKVmm8oouTa/+AB/aKjibK3x7gQQ5ndvAmjR8PR\no/D999ldjhUliqLw008/MWnSJEaPHs24ceMoo4sh24qJu3fvsmDBAubPn0/79u0JCAjAzs5O12EJ\n8Vrkd12X677Ii0qlYs6cOXh7e2s1DytC9T5ClF6PMjPxPXOGBU2bFjjZzcqCn36Cli3hzTezuxor\nasnupUuXeOutt1i8eDHBwcFMnDhRkt18VK9enSlTpnDp0iXatWtHr169eOutt9izZ49c6IUQooAk\n4RWiCJh6+TKtKlWie40aBdru5Elo3x6WLs0eGnjmTN0OA/ykrKws5s+fj729PW5ubhw6dIgWRakx\ncTFQsWJF/P39OX/+PAMGDMDPzw9HR0c2bdokffkKUcQ5OTmhVqu1HidPntR1WKWSNGkQQsdCHz6k\na1QUUfb21HzOtqzJyTBjRnbN7vTp2d2NFaV2upDdt6Svry/p6eksWbKEZs2a6TqkEiErK4stW7bw\n1VdfER8fz/jx4+nfv7+0gxYlijRpEIUlTRqEKILSsrJ4/8wZ/tu48XMnu7t3ZzdfOHcOIiNh+PCi\nlexmZmby3Xff4eTkRI8ePThw4IAkuy+Rnp4ePXr04MiRI/zwww+sXbuWRo0a8d1335GYmKjr8IQQ\nokgqQpdJIUqfL69cwczQEK833sh33du3YcAAGDIE/u//YP16eKzf8SLhzJkztG/fnl9++YXDhw8z\nevRo9F/SSHFCm0qlomPHjvz+++/8+uuvHD58mIYNGxIYGMjdu3d1HZ4QQhQpkvAKoSNRiYksuHGD\nH5s2fWaXMIoCS5Zk1+rWqpXdbjefHm9eu8zMTL799lucnZ3x9PQkODiYJk2a6DqsUqNVq1asX7+e\ngwcPcv36dZo0acLo0aO5evWqrkMTQogiQRJeIXQg45+mDF81aEDdZwyje/o0uLjADz9k9687axYU\ntdFno6OjadOmDTt27CAkJAQ/Pz/0ilIbi1KkadOmLFq0iKioKPT19bGxseH999/n9OnTug5NCCF0\nSq5KQujAf69do4q+Pr516uS6PCUFpk6Ftm2hTx84cgTU6tccZD4yMjL48ssvad++PT4+PuzevZuG\nDRvqOiwB1K1bl1mzZnHu3DkaNmxIhw4d6N27N6GhoboOTQhRSJGRkezYsaPA27m4uBAeHp7n8i+/\n/FJr2tnZucD7eF6BgYHMnj37lZX/LJLwCvGanX30iG9iYlhkbp5rU4Z9+8DaOnuUtGPHwM8Piloz\n2OPHj+Po6EhwcDDh4eF8+OGHUqtbBFWrVo1JkyZx6dIlXFxc6NOnD66uruzevVvucBeimImIiOC3\n334r8Hb5jaT21VdfaU3/9ddfBd5HQWLRFblCCfEaZSkKvmfOMNnMjAbly2stu3MHBg+GQYPgm29g\n0yaoV083ceYlLS2NadOm4erqyvDhw/n999958803dR2WyEeFChXw8/Pj/PnzDBo0CH9/f+zt7Vm8\neLH07CBEIa1atUozvPCHH37I0aNHsba2JjU1laSkJCwtLYmOjiY4OJj27dvTpUsXmjVrxvDhwzVf\nOHft2kWbNm1o1aoVffv2JSkpCYDQ0FCcnZ2xsbHBycmJhw8fMmXKFNatW4darSYoKIikpCTef/99\nHB0dsbW1ZcuWLQAkJyfj6emJhYUFvXr1Ijk5Oc8vuAEBASQnJ6NWqxkwYAAAlSpVAiA4OJgOHTrQ\no0cPGjVqREBAACtXrsTBwQErKysuXrwIQFxcHH369MHBwQEHBwcOHTr0zPMWGRlJmzZtaNq0Kf/7\n3/80++ratatmnVGjRrF8+XL27dtHz549NfP/+OMPevXqVeDXCsCgUFsJIQrlhxs3yFQURtWtq5mn\nKLBiBXz6KXh5Zd+UZmSkwyDzEBERgY+PDyYmJkRERFCvqGXjIl9lypRh4MCBeHt7s2PHDhYtWsTY\nsWPp1asXvr6+tG7dWqc1MEK8DMHBhX8Pu7g83y8fp06dYv369Rw6dAh9fX1GjhzJ2bNn6datG5Mm\nTSI5OZkBAwZgYWHB7du3CQ0N5dSpU9SvXx93d3c2bdpEhw4d+OKLL9izZw/ly5fn66+/5r///S8B\nAQF4eHgQFBREq1atSExMpHz58nz++eeEh4czd+5cACZOnIirqytLlizhwYMHODo68tZbb/Hjjz9S\nqVIloqOjiYqKwtbWNs//65kzZ7JgwQIiIiI08x5f9/jx45w+fRpjY2MaNGjA0KFDCQkJYe7cucyb\nN4/vvvsOf39/Ro8ejbOzMzExMbi7uxMdHZ3r/hRF4fjx4xw9epTExETUajXvvvvuU+vl1Ep37NiR\nESNGcPfuXapXr87SpUvx9fV9rtfoSZLwCvGaXElJYeqlSxxQq9H/5wPl7Fn48EN48AC2bwc7Ox0H\nmYvU1FRmzJjBwoUL+fbbbxk4cKAkRcWcnp4e7777Lu+++y43b95kxYoV+Pj4oK+vz/vvv8/AgQN5\n4zm6yhOiKHrepPVF7Nmzh/DwcOz++dBOTk6mVq1aTJkyBTs7O8qXL8+8efM06zs4OGBmZgaAl5cX\nBw8exNDQUHPTL2T/gtamTRvOnDmDiYkJrVq1Av6tcVUURaumdteuXWzdupVZs2YB2Z/VMTExHDhw\nAH9/fwBatmyJlZVVoY/T3t6eWrVqAdC4cWPc3NwAsLS0ZN++fQDs3r2bU6dOabZJSEjg0aNHVMhl\n2E+VSkWPHj0oV64c5cqVo2PHjoSEhFC1atU8YxgwYAArV65k8ODBHDlyhFWrVhXqWCThFeI1UBSF\nD86c4RNTU5pXrEhqanazhTlz4LPPstvpGhTB/8bQ0FB8fHxo1KgRx44dw6SodfwrXljt2rX59NNP\nGTduHH/99ReLFy/G3Nycjh074uvri5ubGwZF8c0phI4NGjToqRu+YmNjSUpKIjMzk+TkZE3S93gl\ngaIompHiOnXqxJo1a7TKiIqKynV/uVU0bNq0KdcuIF9WG/1yj/UipKenp5nW09MjIyNDs6+jR48W\nerRHPT09DAwMtIZKT0lJ0RyDj48PXbt2xdDQkL59+xb6fhFpwyvEa7D85k3i0tMZZ2rKgQPZPS6E\nhEB4OIweXfSS3ZSUFAICAujSpQsTJ07k119/lWS3hFOpVLRt25alS5dy5coV3n77bT7//HPMzMz4\n7LPPuHDhgq5DFKLIcHV1ZcOGDcTFxQFw7949rly5wrBhw5gxYwb9+vVj/PjxmvVDQkK4fPkyWVlZ\nrF+/nnbt2uHk5MRff/2l+d9KSkri3LlzNGvWjNjYWMLCwoDsGtPMzEyMjIxISEjQlOnm5qZp3gBo\nmiW0b99ek0SfOHGC48ePP/NYypQpo0leC6Nz585acRw7dizPdRVFYfPmzaSmpnL37l2Cg4Oxt7en\nfv36REdHk5aWxoMHD9izZ48mwa9Tpw4mJibMmDEDHx+fQsep04R3586dNGvWjCZNmvD1118/tXz1\n6tVYW1tjZWWFs7Nzvi+aEEVRbGoqn168yHd1zBn+gR5eXvD557BlCxTF+70OHz6MWq3m3LlzHD9+\nnH79+kkThlKmcuXKDB06lCNHjvD777+TnJxM69at6dixI6tWrSI5OVnXIQqhU82bN2fGjBl07twZ\na2trOnfuzIoVKyhXrhyenp4EBAQQGhpKcHAwKpUKe3t7Ro0ahYWFBQ0bNqRnz57UqFGDZcuW4eXl\nhbW1taY5Q5kyZVi3bh1+fn7Y2Njg5uZGamoqHTt2JDo6WnPT2uTJk0lPT8fKygpLS0umTp0KwPDh\nw0lMTMTCwoKpU6dqml3k5YMPPsDKykpz09rjn/d5ffY/3vPD3LlzCQsLw9ramhYtWvDTTz/luS+V\nSoWVlRUdO3akdevWTJkyhdq1a2Nqakrfvn2xtLTEw8MDW1tbre369etH/fr1MTc3z//FyYuiIxkZ\nGUqjRo2US5cuKWlpaYq1tbUSHR2ttc6hQ4eUBw8eKIqiKDt27FAcHR1zLUuHhyHEM2VlZSk9jkcp\n3TdfUGrXVpSRIxXln7d0kfPo0SNlzJgxSq1atZR169YpWVlZug5JFCGpqalKUFCQ4u7urlSrVk0Z\nPny4EhYWJu8T8Urkd10vTtf9ffv2KV26dNF1GMXayJEjlSVLljzXuoAyZ84c5e7du1rzdVbDGxIS\nQuPGjTEzM6NMmTJ4enqyefNmrXVat25NlSpVAHB0dOTatWu6CFWIQpt3Io4/zjziQqAZv/4K8+fD\nP2/pIuXgwYNYW1tz7do1oqKi6Nu3r9TqCi1ly5alT58+7Nixg2PHjlGnTh369OmDWq1m3rx53Lt3\nT9chClEk5dcPrni2Vq1aceLECby9vV+oHJ0lvNevX8fU1FQzXa9ePa5fv57n+osXL+add955HaEJ\n8cIUBb76IY2Pz59n8G1z/j6qh6OjrqN6WkZGBgEBAfTt25evv/6atWvXUrNmTV2HJYo4U1NTJk+e\nzIULF5g9ezaHDx+mYcOGeHp68scff2jdfCJEadehQwdNH7m65OTkhFqt1nqcPHnylexr2bJlT+3L\nz8+vUGWFh4cTHBxMmTJlXigmnd0qU5BvO/v27WPJkiXPHP0jMDBQ89zFxQUXF5cXiE6IwnvwALz8\nU9j3znE+qm/C//UsglW6ZN9N7OnpiaGhIZGRkZLoigLT09PD1dUVV1dX7t+/z+rVq/n000+5f/8+\nPj4++Pj4UL9+fV2HKYqB4OBggoODdR1GiXbkyJHXtq/BgwczePDg17a/56GzhLdu3bpcvXpVM331\n6tVcO7I/fvw4Q4cOZefOnRgbG+dZ3uMJrxC6cvQo9PZ/xMPJkQRa1CWgQdG82P/555/069ePoUOH\nMnnyZPSL2tjFotgxNjZm1KhRjBo1ioiICBYvXoxarcbOzg5fX1+6d++u1cWREI97sqJq2rRpugtG\nlEg6a9JgZ2fHuXPnuHz5Mmlpaaxbt45u3bpprRMTE0OvXr1YtWoVjRs31lGkQuRPUWD2bHh7VAKP\nvjzGd7ZmRTLZVRSFr7/+Gg8PD5YsWUJgYKAku+KlU6vVzJ8/n2vXrjFo0CAWLlxIvXr1+Pjjj/Ps\nY1QIIV4lndXwGhgYMH/+fNzc3MjMzMTX15fmzZuzcOFCAIYNG8b06dO5f/8+w4cPB7L7igsJCdFV\nyELk6u5dGDwYLlR4gN7sk/zYrAl9iuAoVQ8ePGDQoEHcunWLkJAQ+alZvHLly5enX79+9OvXj4sX\nL7J06VLeeecd6tSpg6+vL56enpobk4UQ4lVS/dOFQ7GWM2KJEK/bwYPQrx/Yj7zLfufTrLZoTudq\n1XQd1lMiIiLo06cP7777LrNmzSr0iDhCvKjMzEx27drF4sWL2b17N927d8fX15d27drJnexCI7/r\nulz3RV5UKhVz5szB29ubao9dj2WkNSEKISsLvvoKevcGr59uc7Dtaba0tCxyya6iKPzvf/+jc+fO\nfPHFF8ydO1eSXaFT+vr6vP3222zYsIFz585hbW3N8OHDMTc3Z+bMmcTGxuo6RCGKpMjISHbs2FHg\n7VxcXAgPD89z+ZPDIzs7Oxd4Hy9q4cKFrFy5Ms/lW7du1QxQ9uuvv3Lq1KkC70MSXiEK6PZtePtt\n2L4dPt5zg1WVz/OHtTWti9hPs48ePeL999/nv//9L/v378fT01PXIQmhpWbNmnzyySecOHGCFStW\ncOHCBSwsLOjWrRubN28mPT1d1yEKUWRERETw22+/FXi7/PoB/uqrr7Smn9Uj1qsybNgwzUhvuena\ntatmqOZff/2V6OjoAu9DEl4hCmDfPlCroVUreGflFRYlxvCnjQ1WlSrpOjQt586do3Xr1qSlpRES\nEkLz5s11HZIQeVKpVDg5ObFo0SKuXr1Kz549+fbbbzE1NeWTTz5h/fr1nDp1ioyMDF2HKoTGqlWr\ncHR0RK1W8+GHH3L06FGsra1JTU0lKSkJS0tLoqOjCQ4Opn379nTp0oVmzZoxfPhwTXOMXbt20aZN\nG1q1akXfvn1JSkoCIDQ0FGdnZ2xsbHBycuLhw4dMmTKFdevWaYYWTkpK4v3338fR0RFbW1tNX7/J\nycl4enpiYWFBr169SE5OzrP5R0BAAMnJyajVak3CWemf61lwcDAdOnSgR48eNGrUiICAAFauXImD\ngwNWVlZcvHgRgLi4OPr06YODgwMODg4cOnQo131lZWXRoEED4uPjNfOaNm3K7du3CQwMZPbs2UD2\nUMUtWrTA2tqafv36Adn9+vr5+XH48GG2bt3KuHHjUKvVmhiey0sc+U1nSshhiCIsI0NRAgMVpXZt\nRdmxM0v59Px5xeLoUeVaSoquQ3vKxo0blRo1aijff/+9DPsqirVTp04p06ZNU3r27Kk0atRIKV++\nvKJWq5WBAwcqs2bNUn7//XclNjZW3uclUH7X9WctBwr9eF7R0dFK165dlYyMDEVRFGXEiBHKihUr\nlEmTJiljx45VRo4cqcycOVNRlOyhhQ0NDZVLly4pmZmZSqdOnZQNGzYocXFxSvv27ZVHjx4piqIo\nM2fOVKZPn66kpaUpDRo0UMLCwhRFUZSEhAQlIyNDWbZsmeLn56eJYcKECcqqVasURVGU+/fvK02b\nNlWSkpKU2bNnK76+voqiKMrx48cVAwMDJTw8PM9jqVSpUq7T+/btU6pWrarcvHlTSU1NVUxMTJSp\nU6cqiqIoc+bMUT7++GNFURTFy8tLOXjwoKIoinLlyhWlefPmee7L399fWbp0qaIoinLkyBGlU6dO\niqIoSmBgoDJ79mxFURTFxMRESUtLUxRFUeLj4xVFUZRly5Ypo0aNUhRFUQYPHqxs3Lgxz32Qx9DC\nOuulQYji4sYN6N8fVCoIDVeYlnCW4w8S2a9WU/0FR355mdLT0wkICGDjxo389ttv2Nvb6zokIV5I\ns2bNmDJlimY6MTGRkydPEhUVRVRUFNu2beP48ePo6enRsmVLrKysNH9btGhBhQoVdBi90BXlNdzM\ntmfPHsLDw7GzswOya1Vr1arFlClTsLOzo3z58sybN0+zvoODA2ZmZgB4eXlx8OBBDA0NiY6Opk2b\nNgrM85MAACAASURBVACkpaXRpk0bzpw5g4mJCa1atQL+rXFVFEXr2Hbt2sXWrVuZNWsWAKmpqcTE\nxHDgwAH8/f0BNP8PhWVvb0+tWrUAaNy4MW5ubgBYWlqyb98+AHbv3q3VpjYhIYFHjx7l+v/n4eHB\n9OnTGTx4MGvXrsXDw+OpdaysrOjXrx89evSgR48eucZVmNdYEl4hnmHXLhg0CD78EMZNzGLw2VPc\nTU9nt7U1RgZF59/n+vXreHh4ULlyZcLDw6levbquQxLipatUqRKOjo44PjZOt6IoxMbGapLgP//8\nk/nz53P69Gnq1aunlQS3bNmShg0bSt/T4qUYNGjQUzd8xcbGkpSURGZmJsnJyZqk7/E2tIqiaHqZ\n6NSpE2vWrNEqI6++qnNrh7tp0yaaNGny1PyXlfQ/PliMnp6eZlpPT0/TxEhRFI4ePfpcN0Q7OTlx\n/vx57ty5w+bNm7W+0ObEvH37dvbv38/WrVv54osviIqKeup4CtOji7ThFSIXGRkwcSL4+MCaNTB2\nUiY9o6NIVxS2t2xZpJLdvXv3Ymdnh7u7O9u2bZNkV5QqKpUKExMT3NzcGDt2LCtWrCAiIoKHDx+y\nefNm+vbtS3p6OsuWLaNTp05UrlwZBwcHfH19mTNnDnv37iUuLk7XhyGKGVdXVzZs2KB579y7d48r\nV64wbNgwZsyYQb9+/TQ3WQGEhIRw+fJlsrKyWL9+Pe3atcPJyYm//vqLCxcuAJCUlMS5c+do1qwZ\nsbGxhIWFAdk1ppmZmRgZGZGQkKAp083Njblz52qmI/6fvTOPj6q6+//73jv7koUlQCI7CGFJCJuy\nuGBdUKEu1Kp1bYva1rq0tYo+6IOtWrXSX1HcarXUtSDqA4jVbkDVsMhqQBYJhCUJZIFkMpn93vP7\n485MZrIHCAlw33md19nPPTOZmfuZM9/zPZs2AXD++efHRfTWrVv5+uuvm30sZrP5uOzjL7300qR5\nbN68ucm2kiRxzTXX8Itf/IJhw4Y1OEFXCMH+/fu58MILefrpp6mursbr9Sa1cbvdeDyeNs+z89y1\nDQw6CQcOwI03gtMJmzaBOT3MJVsKGOJw8NrZZ2OSO8f3RE3TePrpp3nhhRd46623uPjiizt6SgYG\nnQaz2cywYcMYNmxY0s+mHo8nLgIKCgpYvHgxBQUF2O32BmYR2dnZ2Gy2DnwUBp2V7OxsnnjiCS69\n9FI0TcNsNsePz77hhhvQNI2JEyeycuVKJEli3Lhx/PznP2f37t1cdNFFXHPNNYC+GevGG28kGAwC\n8OSTTzJ48GAWLlzIPffcE18l/te//sWUKVN4+umnycvL45FHHuHRRx/l/vvvJycnB03TGDBgAEuX\nLuWnP/0pP/zhDxk2bBjZ2dlxs4umuPPOO8nJyWHMmDG89dZbSaunTa2kJnp+eP7557n77rvJzc0l\nEolwwQUX8NJLLzV5veuvv55x48bx17/+tcGYqqpyyy23UF1djRCC++67j9TU1KTr3XDDDdxxxx28\n8MILvP/++wwYMKCF/1Z0fHEyjF3aGcMBtcGJ4uOP4cc/hl/8Ah58EMrCQS79+mu+k57O3IEDkTuJ\nY/wjR45w6623cvToURYuXMhZZ53V0VMyMDhlEUJw8ODBuAiOxbt376Zfv34NzCL69u2L3Em++J6u\nnE4HT6xcuZK5c+eybNmyjp7KGUFTB08YK7wGBkAoBA8/DO+/Dx98AJMnw16/n0u2bOH2nj35n759\nO80pUOvXr+e6667jmmuu4ZlnnsHciTbOGRicikiSRO/evenduzdXXnllvDwUCrFjx464CH7llVco\nKCigurqaESNGJIngoUOH0qVLF0ydyNzJoHPQkh9cg5ODscJrcMazdy/ccANkZMCCBdC1K3xTW8tl\nX3/NQ7178/NOsnoqhODVV1/l0Ucf5eWXX+Z73/teR0/JwOCM5MiRI0lmEQUFBezcuZPq6mrsdjtp\naWmkp6cnxY2V1a9zuVyGMIpyOq3wdhbOPffcuOlEjLfffpvhw4ef8GstWLCAefPmJZVNnjw5yXNF\ne9HUCq8heA3OaD78UPfAMGuWbsYgSfCVx8P0ggLmDhrETVF3LB1NbW0tP/nJT9iyZQuLFy/m7LPP\n7ugpGRgY1EPTNLxeL1VVVRw9ejQpbk1ZIBCIC+DWiubEdOKO+lMdQ/AaHCuGSYOBQQKBAPz617rN\n7scfw/jxevmKo0e5/ptveH3IEKZ369axk4yyc+dOZsyYwZgxY1izZo3hW9TAoJMiyzIpKSmkpKTQ\np0+fNvcPh8NxIdyUQN6/f3+jovno0aOYzeYWhbHb7cZsNmOxWDCbzUnp+nFLZSaTyViRNjhlMASv\nwRnH7t3w/e9D//66F4a0NL18SUUFd+zcyfvDh3NBrLCDWbRoEXfffTdPPfUUM2fONG4uBganMWaz\nme7du9O9e/c29xVC4PP5ml1BLi4upqamhnA4TDgcJhQKJcVtLVNVtVXCuK1lrfHnamDQVgzBa3BG\n8be/wT33wJw58LOf6SYMAG8eOsRDe/bw95wcxrjdHTpH0DfL/PrXv2bZsmV8+umn8RN3DAwMDBpD\nkiScTidOp5OsrKyTck1N0+IC+EQI6MTYwOBEYwhegzMCvx/uvx/+8x/99LS8vLq6eQcPMvfAAVbk\n5jLU6ey4SUY5cOAA3//+9+nWrRsbNmxo4JjbwMDAoDMQO3mrPWyHH3744RM+psGZjeFI0OC0Z/t2\n3UbX44ENG+rErhCCOXv38mJxMZ/n5XUKsfvPf/6TcePGcdVVV7FkyRJD7BoYGBh0Qlwu1zH1++Mf\n/4jf72+XsQ2axxC8Bqc1f/0rnHce3HuvfkRwSopergnBfbt3s6Syks/z8ujbwacpaZrGb37zG267\n7Tbee+89Zs2aZTi2NzAwMOikHOt+innz5uHz+dplbIPmMe6oBqcltbVw++3w9NOwYgXccUedvW5Y\n07h9xw42eb2syM2lRwdvkKioqOCKK67gX//6F+vXr2fKlCkdOh8DAwMDg9bh9Xq5+OKLGTNmDDk5\nOSxduhTQXUleeeWVjBo1ipEjR7Jo0SJeeOEFSkpKmDJlCt/5zneaHfeXv/wlI0aM4OKLL6aiogKA\nCy+8kA0bNgD6faN///4AnH/++WzZsiXed/LkyRQUFLTHwz2lMQSvwWlHQQHEjg5fvx5GjqyrC6gq\n39u2jYpwmM9yckjr4FPK1q5dG/+g/M9//kNmZmaHzsfAwMDgVEeSjj20FbvdzkcffcSGDRv4z3/+\nw69+9SsAPv30U7Kysti8eTMFBQVcfvnl3HPPPWRmZrJy5Ur+/e9/NzlmbW0t48aNY+vWrVxwwQU8\n/vjj0cfV+IltM2fOZMGCBQDs2rWLYDDIyMQbnwFgCF6D0wgh4LXX4KKL9IMkFiyARLNcTyTC5QUF\n2GWZ/xsxAoeidOBcBfPnz2f69OnMmzePZ5991jiS1MDAwOAEIMSxh7aiaRoPP/wwubm5XHLJJZSU\nlFBWVkZOTg7//Oc/mTVrFl988QXuNnj/kWWZ66+/HoCbb76ZL774otn23/ve9/j444+JRCK88cYb\n/PCHP2z7AzkDMO6wBqcFHg/cdRds2wb//S9kZyfXV4RCXF5QwFi3m/mDB6N0oI2U1+vljjvuYPv2\n7eTn5zNo0KAOm4uBgYGBwbHzzjvvUFFRwcaNG1EUhf79+xMIBBg8eDCbNm1i+fLlzJ49m+985zs8\n+uijbR5fCBFf1TWZTGiaBkAgEIi3cTgcXHLJJfzf//0f77//Phs3bjwxD+40w1jhNTjl2bQJxozR\nN6StXdtQ7B4MBDh/82YuSU/npQ4Wu9988w3jx4/H4XCwevVqQ+waGBgYnMJ4PB4yMjJQFIUVK1aw\nb98+AEpLS7HZbNx000088MADbNq0CQC3243H42l2TE3TeP/99wF49913Oe+88wDo168f69evB2Dx\n4sVJfWbOnMm9997L+PHjSU1NPaGP8XTBELwGpyxCwIsvwqWXwm9/C6++CnZ7cptvfT7O27yZH/bs\nyVMDBnTo7tf33nuPCy64gAceeIDXX38de/3JGhgYGBicEsTuJTfddBPr168nJyeHt956i+zoiktB\nQQHnnHMOeXl5/OY3v2H27NkA3HnnnUydOrXZTWtOp5N169YxcuRIVq5cyWOPPQbAAw88wMsvv8zo\n0aOprKxMup+NHj2a1NRUw5yhGSQhjsVqpXMhSRKnwcMwaANVVfDjH8PevbBwIQwe3LDNFq+XK77+\nmsf79WNmB24GCwaD/PKXv+Szzz5j8eLFjBo1qsPmYmBgYHAq0NJ93bjvJxPz/rBz586OnkqHI0kS\n8+bN4+abb6ZLly7x8hZXeOfNm9eqMgODk4Gq6scD5+VBVhasXt242P2yuppLt2xh3qBBHSp29+3b\nx/nnn09JSQnr1683xK6BgYGBwQnlzTff5Nxzz+Wpp57q6Kl0aloUvDFXF4n85S9/aY+5GBg0STis\ne13IzoYXXoA//Qmefx4aO9Hy08pKrtm6lbeys/leRsZJnyvoq7qvvPIK55xzDtdddx0ffvghaWlp\nHTIXAwMDA4POx7nnnkteXl5S2LZtW5vHufXWW9m/fz8zZsxoh1mePjTppeG9997j3XffZe/evUyf\nPj1eXlNTQ9euXU/K5AwMgkH4y1/0AyQGDtTtdC+8sGl/iQvLyrj3229ZMmIEEzrAcL+2tpbXXnuN\n5557jtzcXJYtW8a4ceNO+jwMDAwMDDo3a9as6egpnFE0KXgnTpxIr169KC8v54EHHojbyrjdbnJz\nc0/aBA3OTHw+3afu738Pubn6scATJzbf508lJTxeVMQ/c3PJOclnkXs8Hl588UXmzZvHpEmTWLp0\nKaNHjz6pczAwMDAwMDBonCYFb9++fenbt6/xDcTgpFJTAy+/DH/4gy5wlyzRXY61xDP79/NqSQmr\nRo1ikMPR/hONcuTIEebNm8eLL77I1KlT+fe//83w4cNP2vUNDAwMDAwMWqZFG94PPviAwYMHk5KS\ngtvtxu12k5KScjLmZnAGcfQo/OY3MGAAbN4M//oXfPhhy2JXCMFDhYW8eegQn+flnTSxe/jwYR56\n6CEGDx5McXExa9as4e233zbEroGBgYGBQSekRcH74IMPsnTpUjweDzU1NdTU1LToNNnAoLWUl8P/\n/A8MGqS7GPvyS918YcSIlvuqQnDXrl2sqKriv3l5ZDW2g+0Ec+DAAe69916ys7Px+Xxs2rSJP//5\nz8YBEgYGBgYGBp2YFgVvz549446UDQxOFKWl8KtfwZAhUFkJ69frm9POPrt1/UOaxg+++YZCv59/\n5+bS1Wxu1/nu2bOHO++8k9zcXKxWK9u2beOFF16gT58+7XpdAwMDA4POh+sY94n88Y9/xO/3H1Pf\nSZMmNVt/5ZVX4vF4qK6u5uWXXz6ma5zONHnwxAcffADAf//7Xw4dOsTVV1+NxWLRO0kS11577cmb\nZQsYDqhPHfbvh2ef1Vdxb70VHngAzjqrbWMU+f38ZNcu7IrCe9nZ2BSlfSYLbN++nd/97nd88skn\n/PSnP+W+++6jW7du7XY9AwMDA4POf/CE2+2mpqamzf369+/P+vXr29XbVVFREdOnT6egoKDdrtGZ\nafPBE8uWLePjjz/G4/Fgt9v5xz/+wccff8zHH3/MsmXLTsqkDU4fCgth5kwYNQqcTti+Hf74x9aL\nXU0IPq2sZHpBAWM3bGCM2837w4a1m9jdvHkz1113HRdeeCFDhw6lsLCQ3/72t4bYNTAwMDCI4/V6\nufjiixkzZgw5OTksXboU0F1UXnnllYwaNYqRI0eyaNEiXnjhhfiJaE0dLfzqq6/y4IMPxvMLFizg\nnnvuAepWlUtLSzn//PPJy8tj5MiRfPnllwD069ePyspKZs2aRWFhIXl5eTz00EPt+fBPKYyjhQ3a\nle3b4amn4O9/h7vvhnvvhbZ8sT0SDvOXQ4d4ubiYFJOJu7OyuDEjA0c7Cd01a9bw5JNPsmHDBh54\n4AHuuusunE5nu1zLwMDAwKBxjmeFV3q8CUftrUD8b+u0RGyFV1VVfD4fbrebiooKJkyYwLfffssH\nH3zAZ599xp/+9CdAP8PA7XbTv39/NmzYkLTymEjiGACXX345jz76KBMnToxfc+7cuQSDQR555BE0\nTcPn8+FyueJj19TUMG3aNGOFt94Kb5NuyWLcc889SS8sSZJITU1l7NixXHXVVe03Y4NTmi1b4Ikn\n4L//hfvug/nzoS3nQGysqeHF4mI+rKhgWteuvJ2dzTkpKUhNnThxHAghWLVqFU888QS7d+/moYce\n4v3338dms53waxkYGBgYtC+tFa0nAk3TePjhh/n888+RZZmSkhLKysrIycnhgQceYNasWUybNo3J\nkye3arxu3boxYMAA1q5dy6BBg9i5cycT6zmhHz9+PD/60Y8Ih8NcffXVDc5GMBYAG6fFTWuBQIDN\nmzdz9tlnM3jwYLZs2cKBAwd4/fXXuf/++0/GHA1OIdatg+9+Fy6/HCZMgD174JFHWid2A6rKW4cO\nMWHjRq7dupXBdjs7x4/nrexszk1NPeFiVwjBp59+ynnnnccdd9zBTTfdxLfffstPf/pTQ+waGBgY\nGLTIO++8Q0VFBRs3bmTTpk1kZGQQCAQYPHgwmzZtYuTIkcyePZvf/va3rR7zhhtuYNGiRXz44YeN\n7pc677zz+Pzzz8nKyuL222/nrbfeOpEP6bSlxRXer7/+mi+//BKTSW/6s5/9jMmTJ/PFF18wcuTI\ndp+gwanB55/rK7rbt8NDD8HChWC3t67vvkCAV0pKeKO0lFEuFw/36cOVXbuitMNqLujfyJcuXcoT\nTzxBIBDgf/7nf/j+97+P0o6b3wwMDAwMTj88Hg8ZGRkoisKKFSvYt28foNvZpqenc9NNN5Gamsob\nb7wB6KYQHo+nSZMGgGuuuYYnnniCvn378uyzzzao379/P1lZWcycOZNAIMCmTZu45ZZb4vXHuqHu\ndKdFwVtVVYXX6yUtLQ3QDbSPHDmCyWQyVsHOcITQD4h44gkoLoaHH4ZbboGoM49m0YTgn0eP8mJx\nMfnV1dzasyef5+VxdjseHKGqKosWLeLJJ5/EZrMxe/Zsvvvd7yLLLf7QYWBgYGBgECf2i+NNN93E\n9OnTycnJYezYsXE3rgUFBfz6179GlmXMZjOvvPIKAHfeeSdTp04lKyuLf//7342OnZaWxrBhw9i+\nfTtjx45tcM0VK1bw3HPPYTabcbvdvPnmm0n9u3btyqRJkxg5ciRXXHEFzzzzzAl//KciLW5ae/31\n13niiSe44IILAFi1ahWPPPIIP/jBD5gzZw6///3vT8pEm8PYtHZyEQKWL9eFbnW1fnDEDTeAqcWv\nT3A0HGbBoUO8XFKCU1G4OzOTG3v0wNmOq6vhcJi3336b3/3ud2RkZDB79mwuu+yydrEHNjAwMDA4\nfjq7WzKDzktTm9Za5aWhpKSEdevWIUkS48aNIzMzs10n21aMF/7JQdPgo490oSsEzJ4N11wDrdGq\nm6Kb0D6oqOCKLl24OyuLCe20CS1GIBDgjTfe4Nlnn2Xw4MHMnj2b888/3xC6BgYGBp0cQ/AaHCtt\n9tKwfft2srOz2bBhA5Ik0bt3bwAOHTrEoUOHGD16dPvP2qBTEInoNrlPPgkuF/zmNzBtGrSkG4Oa\nxuLycl4sLuZgMMhPMjPZOX48Ga2xeTgOamtrefXVV5k7dy6jR4/mb3/7G+eee267XtPAwMDAwKAt\nnHvuuQSDwaSyt99+m+HDh3fQjE5vmhS8f/jDH3jttdf41a9+1eiK2IoVK9p1YgYdTygEb78Nv/sd\n9OypHxRxySUtC939gQCvlpTwemkpI10uHuzdm2ldu2JqZ1vZ6upq5s+fz/PPP88FF1zA8uXLGTVq\nVLteE03Tz0Y+dEgPpaV16UOHdJsPWdbtPRRFD21NH0uftqZdLv2f3I421AYGBgYGdaxZs6ajp3BG\n0aTgfe211wBYuXLlyZqLQSchEIA33oBnnoEhQ+D11+H885vvownBv6Ob0D6vruaWHj1YlZfHkJMg\noCoqKpg3bx4vv/wyV1xxBStXroxvHDhmamuThWt9IRsrKyuDlBRdLPbqpcc9e0JmJoweDWlpuihW\nVX2pXFXbng6Hwe9vvM3xjJuYrqmBw4fBbIYePeoeR8+eDfM9e0JGRut2JxoYGBgYGHQCWtxmVFtb\nyx/+8Af279/Pa6+9xrfffsvOnTuZNm3ayZifwUkiEoFt2+Czz2DePF2rLVwILVkCVCVsQrPJMndn\nZfHOsGHtugktxqFDh5g7dy5vvPEGM2bMYO3atQwcOLDpDpEIlJe3TshGIskCNhbGj08uz8gAq7Xd\nH+tJQQjweOqeh8OH69L5+cn5RKHflDCO5bt1a52ht4GBgYGBQTvRouD94Q9/yJgxY8jPzwcgMzOT\n733ve4bgPcUpL4c1a2D1aj1evx6ysmDSJPj4Y8jLa77/Fq+XF4uLeb+8nKlduvD6kCFMaofDIepT\nVVXF2rVrWbp0Ke+99x633Hwzm//7X3qbTHDwoP5AmhKylZX6ucb1ReyAAfoDTyxLSWnZduN0Q5L0\nE0JSU/Wl/eaImXIkiuBYKChIzldV6aK3qdXixLK0tDPveTcwMDAwaHdaFLyFhYUsWrSIv/3tbwA4\nnc52n5TBiSUchq+/Tha4FRVwzjn6aWgPPqin09ObHycU3YT2UnEx+4JB7urVi+3jxtGznVY4hRDs\n2rGD/E8+YfXKleRv2kRRWRlj09O50GJhu9tNjz//GRYsaCiievXSRVtiWffurfOdZtAysqw/n927\nw4gRzbcNhxuurB8+DHv36i/IxDK/v/nV4h496q6blqbPw8DAwOAUw+Vy4fV62bdvH/n5+dx4440A\nbNiwgTfffJN58+Y12beoqIjp06dTUFDQpmuuXLmSuXPnsmzZsuOa+6lKi3d/q9WK3++P5wsLC7Ge\nLj/hnqaUluqiNiZwN26E/v1184SLLtKP+h06tPVa4UB0E9qfS0sZ7nTyy969+e6J3ITm88GePdR+\n8w3rVq1i9caN5BcWsubIEVyqygSbjYm9enFXbi45Y8ZgHjwY+vXT7WR79gTjS1hDVFU3xg4G9ZCY\nrp8PBHQTDk3TzRpioX6+tWWtbdO9u77yO3x4XVkoBF5vXdi/H775Rrep9nr114rfr+cjEf04P7td\nfw04HMkhsczl0k1PEl+zsZXkxBXlxtKtLWuqvilaanO89a1t0xpa6/6pLW6i2mPME33tjh7T4LQl\n9mvo3r17effdd+OCd8yYMYwZM6Yjp3ba0qLgnTNnDlOnTuXgwYP84Ac/4Msvv2TBggUnYWoGrSEU\ngk2bkldva2p0cXvuufDYYzBunP4rdVsQ0U1oL5WUsLKqipt79GDFqFFkH4u4FEJfwduzBwoLYc8e\nRGEhRd98w+rCQvK9XlabTOyIRMjp3p2JQ4fywx//mD9deimZ55xz6nkOEEIXZtXVuk1sYwKzOfHZ\nlnRTdZoGNpsu8qzWltMmky4GJakutJRvjzY2my5gMzIabxcTcELooj4mjGOCuLZWD5WVulhOLAuH\n64RwLCTmE9N2uz6X2LUai5tKt0b4tNTmeOtbO0ZbBHFr23b0mCf62h09pkGnpKioiKlTpzJhwgTy\n8/MZO3Yst912G3PmzKGiooJ33nmH5cuX43a7+dWvfgXAiBEj+OSTT+jTp098nFmzZrFjxw7y8vK4\n7bbbGDVqVHwVds6cORQWFlJYWEhFRQUPPvggM2fOTJqHqqrMmjWLVatWEQwGufvuu7nzzjsbnbMk\nSXg8HqZNm8bu3buZMmUKL730EpIkxVecARYvXszy5ct54YUXyMnJYdeuXZhMJjweD6NGjeLbb79F\nOQX3ZTQpeD/66CMmTZrEpZdeypgxY1i9ejUA8+bNo3v37idtggbJHDxYJ2xXr4YtW2DwYN004fLL\ndR+5gwcf++dudSTCXw8d4qXiYsyyzN2Zmbw5dCiulkwBAgEoKooL2kRxy969BBwONmZkkG+1strv\nJ7+0FBSFiRMnMvGii/jBxImMHj26cxxXLYQukKqqmg7V1c3Xm836T+4uly6cWiM+Y3m3W1/5bItg\nbUzAGjffZIJB3ZanrEw3sSgvb5jev7+uzO/X/w/du+sCPGZK0Vg6I0P/Vmk85wYGJ4Ynn+zoGbRI\nYWEhH3zwAcOGDWPcuHEsXLiQ/Px8li5dylNPPdXALWZje1yeeeYZnnvuubiZQX3PWFu3bmXNmjV4\nvV7y8vIa7J96/fXXSUtLY926dQSDQSZPnsyll15Kv379GlxLCMG6devYvn07ffr0YerUqXz44YfM\nmDEjaW6xtMvl4sILL2T58uVcddVV/O1vf2PGjBmnpNiFZgTv22+/zc9//nPsdjuTJk1i0qRJTJw4\n0RC7J5FAQDdHSBS4waAubidM0D8Pxo3TNVVb8asqO30+tvt87IjG230+9vr9TOvaldeGDGFy4iY0\nIXSxEBOx9YVteTn06QMDB8KAAZR07Ur+kCHkp6ay2uHg623bGGqzMXHiRGZMmMDciRPp27dv+2xy\n0zR9Ze9YxWp1tS4c09L0kJpal46FjAw4++zG61NTTx/PDacTVqu+MzMrq3Xtg8E6MZwojsvKdPvj\n+mWBQJ1ATk1taFqRaGJRv6y5OovFENIGBm3heN4vbTBN6d+/f/yQiOHDh3PxxRcD+kpuUVFRq/zA\nt3Sa3FVXXYXVasVqtTJlyhTWrl1Lbm5uvM0//vEPCgoKWLx4MQAej4fdu3c3KngBxo8fH6+78cYb\n+eKLL5gxY0aTc5g5cybPPvssV111FQsWLODPf/5zi4+ps9Kk4P3ggw8A3b4kPz+f1atX88orr3Dg\nwAHGjh3L3//+95M2yTMBIWDfvmTThK1bITtbN024+mp4+mndoUBb3suV4TDba2sbCNtDoRCD5J7D\nnQAAIABJREFU7HaGOhxkOxxc060bD8syQyorcezbB6tWNVypNZvjgjbu2eCWWwj36cOWykry165l\n9erV5C9fjtfrZeLEiUyYMIHf/fjHjBs3rm0bHoXQRWtlpR6OHElOHznStFj1eHSh0JxgzcyEYcOa\nFqxmc9v/iQanF1YrnHWWHlpDIFC3glxTo5u1+Hz6rwWJcU2NbuLTVH39Mk07NqHcUvuYmI4dQpJ4\nEIkhsA1OZU6SPXXifiZZlrFEfZPLskwkEsFkMqFpWrxNIBA47mvKjeydmT9/Ppdcckmr+icuMgkh\n4uMllifu25o4cSJFRUWsXLkSVVUZNmzYsU69w2nRhrd///4EAgECgQA+ny+eNjg+fD7dg1aiwAV9\n5fbcc+G552DMmNaZr2pCcCAYbFTYhjSNbIeDbCA7EODCo0cZWlpK/6IiTMXFUFwMJSV6HAjoQjAm\naAcO1N03xPJRNw7l5eWsXr1aF7dvvcWGDRvo378/EyZM4LLLLuPxxx9n8ODBdW+gQEAXqnv2NC1g\n66ePHAGLBdG1K3TtiuiSjujSBdGlC1p6KlJmT8w5OY2L2pQUwxuDwcnHZmubQG4tsYNHmhPG9UVy\nWVnrxHQkUnf4SGI68SS+mBhuKd+ebU+WDfmJ6AfHthGypfr26NMUJ2PD5Bnwpapfv358/PHHAGzc\nuJG9e/c2aON2u6mpqWm0vxCCJUuW8PDDD+P1elm5ciXPPPNMkga77LLLeOmll5gyZQomk4ldu3Zx\n1lln4WhCPKxbt46ioiL69OnDwoUL+clPfgJAjx492LFjB2effTYfffQRKSkp8T633norN910E489\n9tgxPxedgSZVwZNPPsnq1aspLy9nyJAhTJgwgXvuuYfXXnvtlLXf6AiE0BcdS0thw4Y6gbtjh+7N\n6dxz4frr4f/9P+jbt/nPgKCmsdvvTxa2Hg87AwHShWCo3092VRW5JSVcv3cv2du20XPnTqioQHTr\nRrhndwI9uuDtlsquri6O9LNSnjuA0tRBFLsEJZYA1UEPES2CJkrQxEFU/3+o/rSaqt1V1Ow6ivKt\nB7cnxFmZdnp1szIhzcxVF6eSEiwndccHpK5fyJHfRdhRq5JWq5LqU1FUQZVTocohccQhc9QhcdQh\nUWmHSofEETtUugSV3aHCrlFhF1TYNAKKH03sR+IAsiQnBTWoYjtsI9OXSS9PLzLdmfRy6XGmO5Ne\n7royp8Xw4mBwCmM26yHhBtSuxDxmxARwfUF8MvOhkB63h5eQ9vBAEnv+Ep/L+uljqW+PPk1xsjZM\nHu81OgH1TfLq28HOmDGDN998kxEjRnDOOecwJMG/eaxtbm4uiqIwatQobr/9dvLy8uJ1kiSRk5PD\nlClTqKio4LHHHqNnz54UFRXF28ycOZOioiJGjx6NEIKMjAw++uijJuc7btw4fv7zn7N7924uuugi\nrrnmGgCefvpppk2bRvfu3Rk7diy1tbXxfj/4wQ+YPXt23JPEqYokmjAgGTJkCC6Xi+nTpzNhwgTO\nOecc0tLSTvb8WoUkSc3awZxohNB/PT98uC7E3Ig2FiwW3XtWbq4ucCdM0E8ya2p/VnUkwo7KSraX\nlrK9qortfj/bERywWOldXcXZJcVk79nDiJ07GXiolEzfUcJ2KE83cyhF5qBbsN8RYY89wC5bLYUW\nL3a7m3RLKr3kFLI0Fz01Bxmqje5hC13CZtLDMqlBGWuVn+DeEsIHy5DLj2D11NJNlugqSdhVlbDL\nidY1nUiXVNS0FNT0NCLpaWjpqWhd0tHS09HS09C6pusrs+npSC4XsqwgSzKKpCQJV0VWGojZ+m0a\ns/MVQlAVqKKkpoRSb6ke1+hxibcuXeotxaJYkgSxIYwNDDonscXsWAgE6rzmJZ6m3VxoS9sTHepr\n4ZMdoPXtYm1bSre23YnsD1BS0vx9/WTf9zuCxx9/HJfLFffy0FEsXryYZcuW8de//rVD59FaJEli\n3rx53HzzzXTp0iVe3uQK786dO6msrCQ/P59Vq1bxzDPPUFNTw6hRo5gwYQI/+tGPTsrETxZCwNGj\nLYvX2KmqNluyL/xYGD++Lh07edZsDVMTqqE6UE1VTTn+A3tZ/X9FlJWVc6A2xEHNTLHFzYHUbuzt\n3otam4OzDx6gb+l+upfvZ9DRfeR5i3EHq5AcFnA5MTlcBM52c/Ds7tSGe5IahPQA9A6oXHAkgu1A\nCEttAHOtD6nag6j2IPuKiVjKCdps+EwmvLKMRwiOqCoVoRC7AgE8koSrTx96Dsuh7w9GM3DiRNIG\nDNBPKEtNRekkjv4lSSLdnk66PZ3hGcObbNeUMC6qKiL/YH6zwjhJJBvC2OAMIxJpKD4T8yeirn49\n1LlWjnmos9mSzYtbE9raPhbMZv16be3XmFe/jgrQ+naxti2lW9vuRPY/0ZZBpyrtfXppS9xzzz18\n9tlnfPLJJx06jxNBkyu8iYTDYTZu3MiqVat49dVX2bt3b5IhdkfT1Dc9TdNNQZsSron5sjLdXrZH\nT0H3Xn669KwhLcOLu1sNznQvjrQaLO4aLDYPVrUcvJWoVUcQVVUITzWSpwa5pgZTTS2SP4IaVpA0\nEwgLwuRCs6RwpGsme3v15pt+fdnVuw+WSISBh4oZXHaIQeVlDCkvI7vsMP0qq7AGQpi9fpSaGqjx\nItnt+k+aqamIlBQiDgcBq5VaRaEGqNI0KiIRyoNBDvt8FHu9HKiuZt/Ro9RIEraePXH37En3nj3p\n0aMHPXr0oGdCOhZcLleHv8E6gpgwjonixBXjpLIEYdzcqrEhjA06mtgBd0195pWX6/tCmxKfmpYs\nPBsLzdUdS72xV9QgRksruGfCCu+xUlBQwK233ppUZrPZ4u5lT3eaWuFtUvAuWbKE/Px88vPz2bp1\nK8OHD4+7JpswYQIZGRnHPalPP/2U+++/H1VVmTlzJg899FCDNvfeey9///vfcTgcLFiwgLy8vEYf\n3E8fOkBppZfDR2so93g54q2h2u/F6q4hNa2KLs6jdLNW0ENU0kU9SnrYQ0rAgzvgw+H34/AHsfrD\nyJoJyeRGWFxELC7CFid+qwOf3YHX5sTjcOBxOalyuah2uvA4nVQ7nXicel21w4GQJFJra0n1+Uj1\n+0kJBEgLBBjo8TDU6yU7EGCoqtLVaq0TsW43PpOJo6pKRTjMYb+f0tpaDtbUcODoUUrLyzl8+HA8\nmEymBmK1MQEbE7EGJ4b6wjhuRpG4ghyNLYqFLHcWfVL70De1L31S++jpND2d5c7CrBh3eIPWEwo1\n/etT/VBdrf8wk/gLVGLIyNBdPjclSs3mM2JfkUEnxRC8BsdKmwXvNddcw+TJk5kYPRDgRB8nrKoq\nQ4YM4V//+hdZWVmMGzeO9957j+zs7HibTz75hPnz5/PJJ5+wdu1a7rvvPtbE3BnUe3BF6RbCZgd+\nmy5OfTYHNQ4HNQ5dkFY7dZHqcTqpdrnqQoJYrbHZsKoq7mCQlHCYlEiEFE0jRQhcioJbUUgxm3GZ\nTLjNZlxmMy6LBZfVittux242o0gSKhDSNAJ+P36/n0AgQNDvp6qigiNlZVSWlVFZXk7F4cOUHz5M\nWVkZ5WVlWCyWVgnYHj16tM3Fl8FJJyaMi2uK2V+9Px72Ve+Lp0trSslwZsQFcJ+UOjEcC2m2zmk3\nb3DiCARaFq+x1VmvV3fzW9+UqrHQtav+c7uBwamIIXgNjpU22/A2tcvvRLFu3ToGDRpEv379ALjh\nhhtYsmRJkuBdunQpt912GwDnnHMOVVVVHD58mB49ejQYr98Hn6JoGooQSNGAEAhAaBpSJIIUDiOF\nQvoySSCAFL3TSD4fks+HrbYWgkG8wSA1wSDFwSAiFEIEg/FAI2WxPEIgWa1IFoseW63I0ViyWJBT\nU5G6dIEuXaBbN8SgQdFNXumE09II2mz4JYmDkoSpkWCWJEzl5ZgqKjABFknDKqlYpAhWVCySqudR\nsRDBLEUwR8vN6GlztNxEBBNqQhzGRAQFFbOk6W0lgVkSer2kRdtpKGiY0JBRUSQVBQ1ZqEhoCBEB\nVISIIERirB5jnR7XrwMByEiSKRqUerEJaFjWfLvG62PpY2mXLpno6rIw2u1C7pOHLJ+DJFmQZQsa\nCpV+D4drKyn1llNcU0ZhWT4rCj+kqKqYvdUH0JDJSulDn9S+DQRx39S+9HL3wiQbLtg6Gz5fy2ZU\nsRAI6Kut9QXrgAH6BtfEsi5ddFtRg2NHCIFQBaggVBEPjea1trXVbzj6NWLpJvNaG9qe6Hz8yaDl\nNG3v00CIHksfA4MTTIfdKYuLi+ndu3c8f9ZZZ7F27doW2xw8eLBRwdvrupsIhgIEQgGC4RAANqsV\nm8WCzWbFarFgt1mx2SwJwYzNbsFmj8Y2E7Y0s563ObDZUrFYFGw2E1arHI/1oETLZCwWCatVirp+\nVRMEWn1RF0aIMJpWgxBHEvKxOISWUBZLC02vEyIM0TJEGFBAMkeDCRGLMSOkWDAhMKFFyzXJrMtV\nKSpfo7GKXh5BwYdCRMiEhUQIRY+FrAcUQsJEUMgEhURQkwgKmYCQiKBEPSyYUWQFk2TCJJuisTke\nm2UTZpMZi2zCLJkwyxYsigmLbMYqm7DIFqyyCasSi83YZTNWxYxNtmBTzNhkEzZZYJVEVPhrccFd\n97wnCuSGZY21a1x4N96nfjtNCzTSJ4wQoej/LznWtCBChLBpIfqJEH0sIUSXIFpaCHFWCE0TaMIP\nYhuCnWiYUMMS4TJB+SHBATVCQNWQJBOybMOs2LGYHFhNLuzmFByWFJyWNCwmJ7JsQZatcbFdF1uj\nsQn9C4R8gmLpBI+nxzoiHtfdJBNjPZ1cl9yu5bqG4zZ2LY9H4ptvrGzbZmXbNhvbtln55hsbPp9M\nRkaE7t3DZGRE6NEjTPfuYfr1izB+fJju3UPR+hBpaZGo6UD9azS8tsfTeHlT7VtXTlI6WXg00UYT\niBCIIGgB0EIgghIiKBAhCS2AXh+SENG0Fk1rwWh5MNo/JEX7RvsEpYQ2kl4WATSJ6EcrQpVAA6HF\n8sn1SW01QI3mNUBIIAv941MBZKHHCkj1ypGjaUUgydE2Sr3yxLYSkBT056xhOdH2Qk+TXCcl9q9f\nTsPy5D51121YXq8+dt1YsjkTFqltaSnxGsfQ38DgRNNhgre1G6Pqf+trqt9k3/mxBoxwjmSEMhKB\npL+vAzL4BVTL+vtJSPp7XhIgaclpSSAh9FiOxtEgJ5TJsiAigVeS9A+V6LWJ5aMxshT9wJGQFBnJ\nLCGbFWSLhGSRka0Ksk1BtiqYzAqSLOvtTDKSoiCZZGSTSS9TFCSTgqwo8TpJkZAUKfpBLNXlZZqu\ni+Xlxutki4xkkZqPzVKD/4UqBAFNaxD8qtqwrJF2NbF0JLFdhIAWanS8YL3rmSUJmyxjlWVs0WCN\nlsXzshmbbG3Qrtl+SgttE9JKOxg9CqFGvxQlCmZdLAcjtRyuOcihmoOUeYsprS2moqaUI74yjvqL\nqApUYFcUMhxd6OZIpastlXSbmzSrk1SrA7fZht1sBhGJvtc0hNBOYHzixhRCTXjN1VcJ1KtLbidJ\nDcsS60QjdSLh7huJmNi3bwCFhUPYU3h2PK6uTqNf/0L6D9jEgIG7mHH9tzwwcDfpXY7EPxP0cUS9\nMSW8qoT3EIhDsbkJvT72OISESHg9iUbnVpcWAJoMPgvCZ0Xy2RC1ViSfFXxWqLUg1dr0tM8KPgtS\n0AQhE4T1WAopehzW43g6aIKwghQriygISwTMEYRFBUsEYY6ARdXLLSrCHC2Ppa3Rtma9TV1aBYeK\nZqlrj1lFs0brTSqYRFSkagg5IS0JUARCBhQNZKHXR9PIAhFLK+hCTxaIY3ibJr4ejqdN2zmxY4r6\ny7edhG82lLN9Q0VHT8PgNKZVgtfn83HgwIEkp8nHS1ZWFgcOHIjnDxw4wFn1/JDUb3Pw4EGysrIa\nHe+HS5bFhavEkrrbQIKAhaiglXQPE0KTEUIPiLq0Xi6haTJaNK9psViK5/VPTb0t0TH0oOcl6sol\nISEJCVlLiFWQIzKyClJEQgEUWdZFr6wgSbG0DLG8pMTridaDjCRkhCYhaXpMRIKQDKqk3wQ1CdRo\nnSbFy0VCWl8FkSAiI0IyIiwhwjKEJD0fkvVVl5AEQUWfUzyYkGWTLsQVk55X9LxsMuFQTLgUE5LJ\npAv4WGzWY9lsRjbrecVsQjJbUSymZoW34lCQHTKKXUGyS2h2mZAVgoogVE8MBxPTzdRVhsPJbeuJ\n8sS+9esCmoYiSUli2SLLyIAiSciShAzIkv6/juVbW6cktKmrsyEzCEUajOwE2SXF27kkCTcQUYMc\nCdWwP+ihNlRDTbAaj7caT6AaT+Ao/ogPp8mB2WTFolgxK1bMiqUuli2YFQsmxaKv1EdjRTZjUswo\nsglFNqMoJhTZhCyZojJXPwUwMRb18o3FTfVNjNVoWj2OMk0I1OjnR+z5lARI5TakvU5EoROx14la\n6EQ9aEPpGcQ80IdloB/rNB/WgWVkZh1EVWCP1Jt99GaVdHH8fyQlxPXTiXklLLD5wVYLVp/AWgs2\nn8Baq6et0bTFJ7B69dhSSzxv9gkstQJzrcDsF4TtEhGnRNgZjV0SYaespx0SEZdMJFVC7SWjWkG1\nSmhWGc0CmkWKBr1cWCS93iIhrFK8TDPXfcGIS+/6+fpxvfrWtKkfN0ZziyetXbBsU90xXu9YOVXG\nPF5sUyFval3+wz/377jJnARcLhder5d9+/aRn58fP9Rhw4YNvPnmm8ybN6/JvkVFRUyfPp2CgoIT\nMpeWrllSUsJ9993H+++/z5YtWygpKeHyyy8/Idc+mbQoeJcuXcqvf/1rgsEgRUVFbNq0if/93/9l\n6dKlx3XhsWPH8u2331JUVERmZiYLFy7kvffeS2rz3e9+l/nz53PDDTewZs0a0tLSGjVnANib9nt8\nYV9S8If9+CK+xsvDtfjDPgIRH4GwD4vJjNNsxWm24zDZcJgdOM02HGY7DrMdu9mKw2THbrLhMNmw\nma3YZBsmrJjRY0XoQVYtyJoVWbMgRSxIqgURNhP22amtFdTWatTUaPh8Kl6vRm2tRm2tiq9Ww+fX\nUGQNl13FaVNxWFQcpggOJYxdDmMjjE2EsaphLOEQ1kgISySMw6Fhd2rYXWBygeyQUJwSsgM92CUk\nOyh2CckGsh1kG/rKScIqnG6OEWpgjpH88300aGGEqiI0FU2LILQIQtPzQuh5TaioCXa6Im7yoSHQ\n86Ai0ECK5iUN5Ij+j9UU/UuDZkISsi7MI4ouuKuiK1MRBREyQ2xVKmICzYwkTEhY4rFdMuOQzNGf\n8M1Iiv6zvqyYkU1WZFM0NluQTVYUiwXZoseK1YZss2CKxXYbis2KrFiRomOCCU0yExIKIUyEhEIQ\ncwMBpwqRnKahEDvWOpXGhKEDTaQ1UQchNYI3XIuqhYmoIcLxECSshgipQcJqkFCkmpAaoFYNEooE\nCEYChNQAwYifYCRIIOInGPETigQwyyZsJgs2xYrNZMVusmJTrNhNNuwma/x9ZDdZcZhtOEx2HGYb\ndpNdfw+a9dhpduA0O3CZ7Vhkc6NfAI61zFMF27ZKbNsqUVAABQWwdavuoSAnB0aOhJE36XF2Ntjt\nDsChi3afRqQmglqjxkOTeU9yXcST3E4LaZhSTChuJR5MKea6tNuEkqqgnBVNpySUuxWUlIS0S9F/\nuTE4ZpvQY10BNWxQTyyPdvQE2pnYF6e9e/fy7rvvxgXvmDFjGDNmzEmdS0vXzMzM5P333wdg06ZN\nbNiw4fQUvHPmzGHt2rVMmTIFgLy8PPbs2XP8FzaZmD9/PpdddhmqqvLjH/+Y7OxsXn31VQDuuusu\nrrjiCj755BMGDRqE0+nkL3/5S5Pj/Wzcz455LkIIQmqogTD2hX34I/7Gy8N+KsM+fGEvvnAZvkhM\nSDc+hjfkJaJFyHBmkJGaQY/MHmQ4M+jh7MFgZwY9XHo+w9EDt5KBOdSdmmoTVVX6gRhVVcTTB2Nl\nvmh8VERjqKkFl12QYhek2lTcJhW3ouKWIji1CC41hCMYxhkIYveFcGph0lIF6WkS6d3A3d2Ec5gD\nV64LZ44TxxAHsrljdsnEBHjjgjuSYAMdSorVcAAtECISCKAGg2jBIGowhBoKooWCqKEgIhxGjQTR\nIiG0SBAtUosaDqEFomYDWhhNhKLXCSEII6SwHsthkCKghMEUAUsEzCqYw6DE4mi9EoGIBUmzIWk2\nZM2GJOzI2JCxIcl2TJIdWdGDYnKgmOwoZjuKxYlitaNYHZisThSTA1m2oyh2ZLku1M/LHbyJTRMa\n/rD+mm85lOGt0dOHws23lZCwKBZAv1lICSYJElLC6mByGtWKXJKNuXgE1pKhWA4PxlLeF3vIjiv1\nAG53KU5XOcPtRxk/sgaHBvZKO7bPbNQutbM5aGNHwIYtWBcipggBa4CANUDQFmwY2wL4rX4CtkC8\nnT/Vr5dZA/htetpv9RMyhxDRP9A/j0SCvW1SOiAQfoE4nNy2xX7RdP22idQXbM3VH0/f+vUt9e0I\npGNcAz0TfZifqRQVFTF16lQmTJhAfn4+Y8eO5bbbbmPOnDlUVFTwzjvvsHz5ctxud/yktBEjRvDJ\nJ5/Qp0+f+DizZs1ix44d5OXlcdtttzFq1Cjmzp3LsmXLmDNnDoWFhRQWFlJRUcGDDz7IzJkzk+ah\nqiqzZs1i1apVBINB7r77bu68885G53zjjTdyyy23cMUVVwBw++23M336dLp27Rq/5qpVq7j//vsB\n/fX8+eefU15ezvTp09m4cSOPPfYYgUCAL774gkceeYTrrruuPZ7edqHFO6PZbG5wpLB8grYJX375\n5Q2+Jdx1111J+fnz55+QazWHJElYTVasJivp9vR2u44/7KfcV85h72HKass4XKvHBz0H2XhoY1L5\nEf8RUq2pcSHcw9mDjIF6PDRBIPdw6nHskANVBY9HiopjJUkoJ8alsfwRwdFKobc7ICEE9MyP0EMJ\n0j3op1ttJX0yNfoOkRk0xsLg8610G+vCkmFpt+cphm7CIQOd01etEAItqKH5NFSfiuZPTqs+FdUX\nQQ34iAR8qEEfashHJORDDfvQIn7UiA9N86OqAUKaD0EAVfgRUiVCKkaTAgglAEoQbEGwh5DsIbCF\nkKxBhDUI5hBYgghzAEwBEAqSatVFtrAhCxsydiRsdSJZdiCbdLGsmB26mMaFIrmRJRcKTmTJjYIr\nWh6NcSFhov7O79jzkVhmEzZswkY30a3JNkIWYAUsTY8jhEBogogaIewP6yum3ghajVa3UupVUT0a\nvkqN2nKNUJWG8GrIARWrpiIBYYuCsMuYUmSsgyqxdZVQXCYkdx9kVz8kl4TskpFcUjzILhnJIYEL\nZLeM5NTTRN19NSUkWyvGGxPuHdEvRn3B1lz98fStX9/WvganP9L/dv7/eWFhIR988AHDhg1j3Lhx\nLFy4kPz8fJYuXcpTTz3FqFGjkto39jp+5plneO6551i2bBkAK1euTKrfunUra9aswev1kpeXx7Rp\n05LqX3/9ddLS0li3bh3BYJDJkydz6aWXxj1gJXL99dezaNEirrjiCkKhEP/5z3949dVXkw6kmDt3\nLi+99BITJkzA5/MluaQ1m8389re/ZcOGDTz//PNtfbo6nBYF7/Dhw3nnnXeIRCJ8++23PP/880yc\nOPFkzO20w262x11KtYSqqVT6K3UBXE8grzm4hjJfcrkiKboArieEezh7kJGRwcCE8nR7OrIU+9KS\nuJlHd6d08KCZ/fvN7Nvnomi3RmFBhH/vFhxYJ3HoWRMuIvRUasjqotKnN/QbKjNorJnBE6z0HyTT\npUsLu31PEyRJQrEpKDYFc5f2FeVxcR0T1X4Vzafn42mPRsQfQfUHdJEdFdha2EckUWCrASLCj6r5\nEcKPRgChHAFbMcLmA7tPj20+sPr1tLU2GvshYoagAyka6tJOPR1yIoXsCWmnXh92xMvkkBMp7ISw\nXTc5iW3yhPhLMl6WkJesEia3ibBZ4Yhf4VCNheIjJvYeVigsUZCcCpmDTPSdoDAwR2FonsLQ0SYc\nqYYvLwODMwWpnmhsC+LCC1vdtn///gwfrh9tP3z4cC6++GJAX8ktKipqIHgbvV4LvoavuuoqrFYr\nVquVKVOmsHbtWnJzc+Nt/vGPf1BQUMDixYsB8Hg87N69u1HBO3XqVO677z5CoRB///vfueCCCxqc\nsTBp0iR+8YtfcNNNN3Httdc22DclhGh2zp2ZFgXv/PnzeeKJJ7Bardx4441cdtllPPro6W5d0/Eo\nsi5gM5wZjMgY0WxbIQTekDcuiBOF8M7Knfx3/3+Tyr0hL90c3RoVyL1cvcjtmcuFFw2L+neV0Zff\ndDQNSkvN7P5KsGt1kL1fq2xfG+afS1RKalXKJBsRWY6KYUH/bIV+Q2T69ZPo0wf69oXMTOMI0baS\nKK5pvx8hWkQIgab5UFUvkUgNqpoYGiurJhI52KBdMFKXlmULiuKOB5PJjaK4UBQ3kuTG43FTVuam\nuNjF/v1u9uxxUVXmpkcPF71zXfTv7+K6wW6ys1107eqMul87A75xGRgYNEpbROvxkCgWZVnGYrHE\n05FIBJPJhKZp8TaBQOC4r9nYL+zz58/nkksuabGvzWbjwgsv5LPPPmPRokVxu+FEHnroIaZNm8by\n5cuZNGkSn3322Qk/eKyjaFbwRiIRrrzySlasWMFTTz11suZk0EYkScJtdeO2uhnUZVCL7UNqiPLa\n8qRV45gY3nRoE09+/iQHPQcZ1XMUYzPHMi5zHGMzxzK462BkWSYrSyIry8oFVye/CVS/Su22Wg6t\n9fHt6iB7vlYp+lBjp7DxZYqTcsVGacBCuUemZ0/o01eib1/o04e4GI7Fbnd7PVsGx4MkSSiKE0Vx\nYrE0voG0LcQEdCRSw9GjXnbsqGH37hqKimooKdHLevWqoV+/GrKyKrjooiKuvdaLzeZypxZOAAAg\nAElEQVSNC+ZY2LVLzwuhoiiuBOHsigvotuQT+0uSxRDRBgYGbaJfv358/PHHAGzcuJG9e/c2aON2\nu6mpqWm0vxCCJUuW8PDDD+P1elm5ciXPPPNMknC+7LLLeOmll5gyZQomk4ldu3Zx1lln4XA4Gh3z\n+uuv57XXXmPDhg389a9/bVBfWFjI8OHDGT58OF999RU7d+4kJycnXp+SktLkfDs7zQpek8mELMtU\nVVU1sOM1OHWxKBayUrLISmncxRtAdaCajaUb+arkK5bsXMLsFbM54j/CmF5jGJc5jnFZugjum9o3\nLgQUu0LK2BRSxqZw9t36OEIIQiUhvFu8eL8uo/brWqo213KgUKPKlMJRNYXKCierN9v4yG/hwGGJ\n/fslLJZkAVw/7tHDOHHqVEXTYM8e2LwZtmyR2LLFyZYtTo4c0b0j5ObqYfp0GDEC2nqKtqaFUNXa\nBoJYD8llodBhVLWwyfpYGYg2iWZZtiHL1oTYGj3kozVlhrg2MDgVaGB7LiXbpc+YMYM333yTESNG\ncM455yS5do21zc3NRVEURo0axe23305eXl6d3b0kkZOTw5QpU6ioqOCxxx6jZ8+eFBUVxdvMnDmT\noqIiRo8ejRCCjIyMZk/KvfTSS7nlllu4+uqrMemnZenmYtHx5s2bx4oVK5BlmREjRnD55ZdTXFwc\nr58yZQpPP/00eXl5p9ymNUm0YIzx3e9+l02bNnHJJZfgjN55JEnqVAbLxpnaJ4fy2nI2lG7gq+Kv\nWF+6nq+KvyKsheOrwLGV4F7uXi2OpQZUfNt9eLd4qf26Fu/XXmq31CKEwDnSRehsN1W9Uqh0uTiM\nlQMlMvv3w759sH8/VFdDv3768asDBybHAwZAE19uDU4ytbW6u68tW/SwebOe79JFF7WjRtUJ3AED\nOu+XGF1ENy6KdTOOZIGsaQE0LRg9fS8YTQdbVSZEGP0kvDohXCeMT2yZfgS2foSYfjS2HuryzdUp\n6KfgNV4nSZ30n2lwStDSff1MuO8//vjjuFyuuJcHg9YhSRLz5s3j5ptvpkuXLvHyFm14r732Wq69\n9toGgxmceXR3dmfqoKlMHVTnHbzYU8z6kvV8VfIVL371Il+VfIXdZK8TwVnjGNNrDF0dXZPGUmwK\n7jw37rw62wUhBKFDobgAdm/5/+3dd1hT1/8H8HfCUgTBBYpYQUVlE1BUXKAFt1Kr4qzbOqu1aq1d\nWqvVar+to1XbWlex1Trq5qe14sDJnm4QFMGByJCZ5PcHNRohMgxcEt6v5/Hx3uTccz+5XjwfTs49\n5yHqRybA8kYOOlvXQh2nOjB6xwhGzkYQ2xohOccAt28Dt24V9RiePFm0nZAAmJqWnAy3bFnUO8xb\nWL3kcuDevRdJ7fMENympaA7b50mtn19RL249AcchV0TR0sz1oadXv/TCb0gul/239HTxxLhoP7fM\nrxUUZL223Isl0F9dEv2l+bIr9N6LJT1KToZ1SnnvxUI7RdsvL9khqsC++A2OLd/+c8rtpKpt5f3K\nO6a8s1686full2EeUTa8TupTag+vJqgJv+lpCrlcjvj0+KIk+L+e4JDkEDSq00ipJ9i1iSuMDco2\nUFeWLyvqDY78rzc4IguZwZkw6WwCixkWqO9TX2myfZkMSE6GUjL88nZ2NmBtXXIybGUFaMn4/EqT\nnw/Exir32kZEALq6xXtt27ThA4o1VdHT3CUnwy8WuVGVcMuU3ns+R13R//PyCu2/WOr6zetSva/4\n9GXYfvUJ/co5pnjbWFpb+abvl2URjtLff+utj2p8D29FRUVF4b333lN6rVatWkrTj2kzVT28pSa8\n1tbFl/cTiURqWXxCXXjjV28yuQzXHl1T9AQHJwcjIjUCzU2aK/UEO5s7o7Ze7TLVKX0mxYM/HuDe\nj/dQmFGIptOaovH4xmWaHiwjA4iPf5EAv5wUJyUBZmYvhka8mhQ3aFCzeocfPSrea3v9etG1eJ7U\nPk9yGzcWOloi0hYc0kAVVeGE99GjR4rt3Nxc7NmzB48fP8bSpUsrL9py4o2veQqkBYh5GKPUExz3\nMA5tGrZBuybtFA/FOZo5Qk9HdRIrl8uRcTED9368h7QjaWg4uCGazmgKY9eKTfNQWAjcvVtyMnzr\nVlHvsapk+K23NLc3UyoFbtx4kdQ+T3Kzs188SPa859bevmj5XSKiysKElyqqwglvSVxdXREaGqrW\nAN8Eb3ztkFuYi4iUCKWe4Pj0eDiYOSg9FNe2YVvoiHWKHZ//IB/3N99H8sZkGFgYwGK6BRoNbVQ0\nd62aPHmiOhm+fx9o2lT54bnGjYuSZKn0xZ/CQuV9Va9VZdlHj4p6tl8ejuDiUjQjRk3q0Sai6oEJ\nL1VUhRPekJAQxaBpmUyG4OBgbNiwAREREZUbcTnwxtdeWflZCL0fqpQEp2SloJNlJ8xoPwMD2gx4\nadW4InKpHI8PP8a9n+4hKzwLTSY0gcVUC9RqXqtSY83PL5pF4uVkODUV0NF58UdXV3lf1WvqKFue\nOho0AOrWrdTLQ0RUZkx4qaIqnPB6enoqEl5dXV1YWVlh3rx5SvPJCY03fs3yJOcJAm4G4LsL3yEr\nPwsfdfoIY5zHoJZu8YT22fVnSN6QjJTtKTDpbIKmM5qinnc9pYfciIioemHCSxVV4YT39u3baNGi\nhdJr8fHxJT7MJhTe+DWTXC5HYEIgVp1fhbCUMMxsPxPT2k9D/drFp46SZkuRujMV9368B1m2DBbT\nLdB4XGPo1dPQQbdERFpM2xLekJAQbN++HWvWrKm0cyxevBjGxsY1ft5eVQlvqTODDxkypEyvEVU1\nkUgEL2svHB11FCfGnMCNtBtotbYVZh+bjYT0BKWyOnV0YDHZAu3C2qHttrbIDM7EpRaXcHXSVWSG\naeYyiUREpBnc3NwqNdktLCzknL2lUJnwxsXFYe/evUhPT8e+ffuwd+9e7Nu3D1u3blVax5moOnAw\nc8BW362ImhYFA10DuP3shhF7RyD0vvLDlSKRCCYeJrDzt4P7VXfUblEb0YOiEeoRilT/VMjyZAJ9\nAiIi0hQJCQlwdHRU7K9evRpLliyBl5cXFi5cqFhK+Ny5cwCAwMBADBgwAADw+PFj+Pj4wMHBAZMn\nT4aVlRXS0tLKdR6gaMjphx9+iPbt2xdb/Xbt2rWwt7eHs7MzRowYodbPrqlUJrzXr1/HoUOH8PTp\nUxw6dAiHDx/GoUOHEBoail9++aUqYyQqs6Z1m+Jb728RPzse7Zq0w6A/B6Hn9p4IuBlQ7OsvfXN9\nNF/UHB1ud0CzBc2QsjUFF966gNuLbiM3kb/UERFR2bzcuyqVSnHp0iX88MMPiuT0ZUuWLEG3bt0Q\nHR2Nd955B4mJieU6z/NziUQiFBQU4MqVK5g7d65SHCtXrkR4eDgiIiKwadOmN/loWkPl0sKDBg3C\noEGDcP78eXh4eFRlTERvrK5BXXzk8RFmdZiFXdG7sODEAiw4sQDzPOZhuMNw6OvoK8qKdcVo5NsI\njXwb4dm1Z7i34R6CJcEw6frfQ249+ZAbEZGmCBQFVvhYT7nnG59/8ODBAIqmcE1ISCj2/tmzZ7F/\n/34AQN++fVGvnGutv9x54+fnV2IZJycnjBw5Er6+vvD19S1X/dpKZcL7nEQiwfr16xEbG4ucnBzF\nbw+//fZbpQdH9Kb0dfQxxnkMRjuNxvFbx7Hq/Cp8+u+nmN1hNia7ToZJLROl8oZtDGHzgw1aLGuB\nVP9U3Jp3C7JcGSym/feQmykfciMiqs7UkbSWRldXFzLZiyFwLw/11Ncv6lDR0dFBYWFhiceX9YG7\nV8/zch4GAHXq1Cmx3iNHjuDMmTM4dOgQli1bhqioKOjoqG9Oek1U6kNrY8aMQWpqKgICAuDp6Ymk\npCQYGRlVRWxEaiMSidCrVS/8894/ODD8AELvh6LF2haYf3w+7mbcLVZep44OLKZYoF14O7T9rS0y\nL2fikvUlXJtyDZnhfMiNiKgmMzc3x4MHD5CWloa8vDwcPny4zMd269YNO3fuBAAcO3YMT548Uet5\n5HI5EhMT4enpiRUrVuDp06fIzs4uc3zaqtSE9+bNm1i6dCmMjIwwduxYHD16FJcuXaqK2IgqhWsT\nV+x8dydCpoSgQFYApw1OGPv3WESlRhUrKxKJYNLZBHY77dA+rj0M3jJA9IBohHYORepOPuRGRFQT\n6enp4YsvvoC7uzt8fHxga2sLQHmM7fP9V7e//PJLnDlzBg4ODti/fz/eeuutMp/Hzs7utXGJRCJI\npVKMGTMGTk5OcHV1xezZs1GXKwuVPg+vu7s7Ll++jK5du+Knn35C48aN0aFDB9y+fbuqYiyVps3H\nR9XLk5wn2BC8Aesur4NLYxfM95gPLysvlVO8yApleHzoMe79eA/Z0dloMvG/ldyaVe5KbkRENYW2\nzcP7OtbW1ggJCVGaM5YqrsLz8E6ePBlpaWn4+uuvMXDgQNjZ2WHBggWVGixRVapXux4WdV2E+Nnx\nGGI7BDOOzkC7X9rhz+g/USgrPv5KrCtGo3caweUfF7gEukCaJUWwSzCi34lG2j9pWvOfMBERVT7O\nn1s1Su3h1QTa9JseCU8ml+HI9SNYdX4VkjKS8GHHDzFBMgFG+qrHrhdmFeKB/4OildzyZWg6rSnM\nx5rzITciogqoST28AJCWloaePXsWe/3kyZPs+S2nCi8tnJKSgk8//RT37t1DQEAAYmNjceHCBUyc\nOLHSgy4rbbvxqfq4dPcSVp1fhdN3TuN9t/cxy30WzI3MVZaXy+V4eu4pkn9KRlpAGhpPaAzrZdbQ\nqVWzn44lIiqPmpbwkvpUeEjDuHHj4OPjg+TkZACAjY0Nvv/++8qLlKga6WDZAXuG7cGFiReQlpMG\n2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t1b+UPwN0GiMpPKpJh5dCauJF/B0VFHYVbHrFzH311/F4nLEmG/3x4mHU0qKUoiqsnY\nrpO6ceEJohpILpdjceBi/BH9B46POQ4rU6tyHf/4yGNcHXcVNj/ZwGxo+RJmIqLSsF0ndWPCS1SD\nrbu0Dt+e/xYBowLKtRQxAGSGZyJ6QDSazmyKZguacQYHIlIbtuukbkx4iWq4LWFbsDJoJcKnhqOW\nbq1yHZt7NxfRA6Jh3M4YNj/ZQKzHGRyI6M2xXSd1Y8JLRHh397uwbWiLr3t8Xe5jCzMLETsiFvI8\nOez32EPXpFJnOySiGoDtOqkbu2OICOv7rMfPIT8jMjWy3MfqGuvC4W8HGLY1RKhHKHISOIMDERFV\nL0x4iQhNjJvgm57fYOLBiSiUFZb7eLGuGDbrbGDxvgXCOoch43JGJURJRERUMUx4iQgAMEEyAXUN\n6mLNxTUVrsPyA0u03tAaUf2i8HDfQzVGR0REVHEcw0tECrfSbqHDrx1wadIltKzfssL1ZIZkImpQ\nFCznWKLZR5zBgYjKh+06qRsTXiJSsvr8ahy7eQz/jPnnjRLV3KRcRPWLQl2PurBZbwOxLr9QIqKy\nYbtO6sYWiIiUzOk4B09zn2JL+JY3qqdWs1qQnJMg704eovpHoTCj/GODiYiI1IEJLxEp0RXrYvPA\nzVj4z0Lcz7z/ZnXV1YXDIQfUtq6NsC5hyE3MVVOUREREZceEl4iKcW7sjCluUzDz2Mw3rkusK4bN\nTzZoPK4xQjuFIjMkUw0REhERlR0TXiIq0WfdPkPMgxjsi9v3xnWJRCI0m9sMNuttENk7Eo8OPFJD\nhERERGXDh9aISKVziefgt8cP0dOiUa92PbXUmXElA9G+0Wg2vxksZ1tyBgciKobtOqkbE14ieq0Z\nR2YgT5qHXwf+qrY6c+/kIrJfJEw9TdHqh1acwYGIlLBdJ3VjwktEr5WRlwGHnxyw1Xcrelj3UFu9\nhU8LETM0BiI9Eez+tIOusa7a6iYizcZ2ndSN3SpE9Fp1DepiQ78NmHJoCp4VPFNbvbomunA84ggD\nCwOEdQ1D7l3O4EBERJWDCS8Rlapf635wb+qOL099qdZ6xXpitP65NcxHmiOsUxgywziDAxERqR+H\nNBBRmTzMfgjHDY44PPIw2lm0U3v9D/Y8wI1pN9BmSxs07N9Q7fUTkeZgu07qxrgUFgQAACAASURB\nVB5eIiqTRnUaYbXPakw8OBEF0gK11282xAwOhxxwffJ13F1/V+31ExFRzcWEl4jKbJTjKDQ1bopV\n51dVSv0mHU0gOS9B8o/JuDHnBuRS9vAQEdGb45AGIiqXO+l34PazG4ImBKFNwzaVco6CJwWIGRID\nnTo6sN1pC10jzuBAVJOwXSd1Yw8vEZVLc9Pm+LL7l5h0aBJkclmlnEOvnh6cjjlBr6EewruHIy85\nr1LOQ0RENQMTXiIqt+ntp0Mqk2JT8KZKO4dYX4w2m9ug0buNENoxFFmRWZV2LiIi0m4c0kBEFRL7\nMBbdt3ZH2PthsKxrWannerDrAW7MuoEWK1vAfIw5V2Yj0nJs10ndmPASUYV9dforXEm+goPDD0Ik\nElXquTKuZODWR7eQ/yAfVoutYDbMDCJx5Z6TiITBdp3UjQkvEVVYvjQfbj+74dOun2K4w/BKP59c\nLseTE08Q/3k8ZDkyWH1lhYaDGlZ6sk1EVYvtOqkbE14ieiOX7l6C7y5fRE+LRgPDBlVyTrlcjsdH\nHiPh8wRAB7Beao36vesz8SXSEmzXSd2Y8BLRG/sw4EM8znmM7e9sr9LzymVyPNr/CPFfxEPXRBfW\nX1ujXo96VRoDEakf23VSNya8RPTGsvOz4bDBARv6bUDvVr2r/PxyqRwP/nyAhMUJMLA0gNVSK5h2\nMa3yOIhIPdiuk7ox4SUitThx6wQmH5qMqGlRMDYwFiQGWaEMqdtTkfBVAgzbGsJ6qTXqtq8rSCxE\nVHFs10ndmPASkdqMPzAexvrGWNtnraBxyPJluL/5Pu4suwNjN2NYf2UNI2cjQWMiorJju07qxoSX\niNQmLScNDj85YO+wvejUrJPQ4UCaI0XypmQkrkiEaXdTWC22Qh3bOkKHRUSlYLtO6sbZ24lIberX\nro81vddg4sGJyCsUfjlgndo6aDanGTre6ghjV2OEdw9H3HtxyLmVI3RoRERUhZjwEpFaDbEbgtYN\nWmP52eVCh6KgU0cHb338Fjrc7IDarWojpEMIrk2+htzEXKFDIyKiKsAhDUSkdvcy7sFlkwtOjT0F\nBzMHocMppiCtAEnfJSF5YzLMRpih+aLmMLAwEDosIvoP23VSN/bwEpHaNa3bFMt6LMOkg5MglUmF\nDqcYvfp6aLGsBdzj3CE2EOOKwxXc/Ogm8h/kCx0aERFVAia8RFQpJrlOQi3dWlh3eZ3Qoaikb6aP\nVt+1Qvvo9pDlyXDZ9jJuf3obBWkFQodGRERqxCENRFRpbjy+gU6bO+HK5CuwrmctdDilyr2Tiztf\n38HD/Q9h+YElLOdYQreurtBhEdU4bNdJ3ZjwElGlWnluJU7Gn8T/jf4/iEQiocMpk2c3n+HOV3eQ\nFpCGZh81Q9OZTaFTR0fosIhqDLbrpG4c0kBEleojj4/w6NkjbI/YLnQoZWbYyhC2223hctoFmaGZ\nuNTqEpJ+SII0t/qNRyYiotKxh5eIKl3Y/TD09u+NyKmRMDcyFzqccsuKyEL8l/HIDM5E80+bo8nE\nJhDrs7+AqLKwXSd1Y8JLRFVi4T8LEZ8ej11DdgkdSoVlXMlAwhcJeHb1GZp/0RzmY8wh1mXiS6Ru\nbNdJ3ZjwElGVyCnIgfNGZ6z2WY2BbQYKHc4beRr0FPGfxSPvXh6sFlvBzM8MIh3NGJ9MpAnYrpO6\nMeEloipzOuE0Ru8fjehp0TCpZSJ0OG/syb9PEP9ZPAqfFsL6K2s0fKchRGImvkRviu06qRsTXiKq\nUu8feh8ikQgb+28UOhS1kMvlSAtIQ/xn8YAMsPrKCvV96kNswKEORBXFdp3UjQkvEVWpp7lPYf+T\nPfwH+6O7VXehw1EbuVyORwce4c7SO8iOyoauiS70m+rDoKkBDJoaQN/ixfbzfb2GehozVRtRVWK7\nTurGhJeIqtyBqwcw/8R8REyNQG292kKHo3ZymRwFDwuQdy9P8Sc/Of/F9r185CXnQZothUETg6LE\n2OK/RPh5kmzxYlunNucAru7kMjnk0qI/kOHFtvTFe6/dlsohl5Vh+9X6VWyreg+yol/OIIfiz6v7\nQOllFPsoQ5ny1gug7aa2bNdJrZjwEpEghv01DC3rtcQ3b38jdCiCkeZIXyTCyf8lwq8myMl50DHU\nKbGHWLHdVB/6jfS1/sE5WaEM8nw5ZHkv/pblyyDPe2U7X6ZUpirKQgpABxDpiIr+HcQlb7/uPegA\nInEZtnVERWPFS9su6VxiESACICpqO59vF9tHGco83wdKL1POei2nWbJdJ7ViwktEgkjNSoXTRicc\nG3UMrk1chQ6n2pLL5ShMKyy1t7jwSSH0zfVL7CF+OUHWNS7fUsly6X9J3fM/uf8lf7kv9kt977+/\n3+i9fBkAQGwghkhfBLGBGGJ9MUQGIoj1xUqvK96vwrIiHRGHp6gR23VSNya8RCSYbeHbsObSGlye\nfBm64vIlYqRMli9D/v0Seotf6TkW6YiKEuDG+kXHvZKwvpq4yqXyogTPQARxraJk79W/K/295wkm\n5zyuMdiuk7ox4SUiwcjlcvT2740eVj3wcZePhQ5H68nlckgzpEU9w/fzATEUCaW4VskJqEiPPZdU\n9diuk7ox4SUiQSWkJ6Ddz+1wYeIF2DSwETocIqoG2K6TuvH7ISISlJWpFT7r9hkmH5oMmVwmdDhE\nRKSFmPASkeBmuc9CbmEufg39VehQiIhIC3FIAxFVC9EPouG1zQvh74ejad2mQodDRAJiu07qxh5e\nIqoWHMwcML3ddMw4OoMNHRERqRUTXiKqNhZ1XYTrj69jT+weoUMhIiItwoSXiKoNA10DbB64GbMD\nZiMtJ03ocIiISEsIkvCmpaXB29sbrVu3ho+PD9LT01WWlUqlkEgkGDBgQBVGSERC6dSsE4bYDcFH\nxz8SOhQiItISgiS8K1asgLe3N65fv46ePXtixYoVKsuuWbMGdnZ2nPicqAZZ3nM5TsWfwolbJ4QO\nhYiItIAgCe/BgwcxduxYAMDYsWPx999/l1ju7t27OHr0KCZNmsSHWIhqECN9I2zsvxHvH34f2fnZ\nQodDREQaTpCENzU1Febm5gAAc3NzpKamlljuww8/xKpVqyAWc6gxUU3Tu1VvdH6rMz4/9bnQoRAR\nkYbTrayKvb29kZKSUuz1ZcuWKe2LRCWv03748GGYmZlBIpEgMDCw1PMtXrxYse3p6QlPT8/yhkxE\n1cz3vb6Hw08OGO4wHO5N3YUOh4gqSWBgYJnaeqKKEmThibZt2yIwMBCNGzfG/fv34eXlhatXryqV\nWbRoEXbs2AFdXV3k5uYiIyMD7777LrZv316sPk5QTaS9/oj6A8vPLUfIlBDo6+gLHQ4RVQG266Ru\ngowVGDhwILZt2wYA2LZtG3x9fYuVWb58OZKSkhAfH48///wTPXr0KDHZJSLtNtxhOJqbNMfKcyuF\nDoWIiDSUIAnvwoULceLECbRu3Rr//vsvFi5cCABITk5Gv379SjyGszQQ1UwikQgb+m3A2strEfcw\nTuhwiIhIAwkypEHd+NUHkfb7/sL3OJN4Bvv99gsdChFVMrbrpG6c/oCINMLUdlNx6e4lhKeECx0K\nERFpGCa8RKQRauvVxnyP+fjq9FdCh0JERBqGCS8RaYz3272PC3cvICIlQuhQiIhIgzDhJSKNYahn\nWNTLe4a9vEREVHZMeIlIo0xtNxXnk84jMjVS6FCIiEhDMOElIo1iqGeIeZ3mYemZpUKHQkREGoIJ\nLxFpnKntpuLsnbOISo0SOhQiItIATHiJSOPU0a+DeR7s5SUiorJhwktEGmlau2k4c+cMoh9ECx0K\nERFVc0x4iUgj1dGvg486fcReXiIiKhUTXiLSWNPbT0dgQiBiHsQIHQoREVVjTHiJSGOxl5eIiMqC\nCS8RabTp7afjVMIpxD6MFToUIiKqppjwEpFGM9I3wocdP2QvLxERqcSEl4g03oz2M3Dy9knEPYwT\nOhQiIqqGmPASkcYzNjBmLy8REanEhJeItMJM95n45/Y/uProqtChEBFRNcOEl4i0grGBMeZ0nIOv\nz3wtdChERFTNMOElIq0x030m/u/W/+Hao2tCh0JERNUIE14i0hp1DepiToc5+Pose3mJiOgFkVwu\nlwsdxJsSiUTQgo9BRGqQkZeBlmtbImhCEFo3aC10OERUAWzXSd3Yw0tEWqWuQV3M7jCbY3mJiEiB\nPbxEpHWe5j5Fq3Wt2MtLpKHYrpO6sYeXiLSOSS0TzHKfhWVnlwkdChERVQPs4SUirZSemw6bdTa4\nMPECWtVvJXQ4RFQObNdJ3djDS8UEBgYKHYLW4LVUr/JcT9NappjZfibH8r4G70/14bUkqt6Y8FIx\n/I9bfXgt1au813N2x9k4fP0wbqbdrJyANBzvT/XhtSSq3pjwEpHWMq1lipnuMzmWl4iohmPCS0Ra\nbU7HOTh07RBupd0SOhQiIhKIVjy05uLigoiICKHDICIiIjVwdnZGeHi40GGQFtGKhJeIiIiISBUO\naSAiIiIircaEl4iIiIi0mlYlvN999x3EYjHS0tKEDkWjff7553B2doaLiwt69uyJpKQkoUPSaPPn\nz4etrS2cnZ0xePBgPH36VOiQNNpff/0Fe3t76OjoIDQ0VOhwNFJAQADatm0LGxsbrFy5UuhwNNqE\nCRNgbm4OR0dHoUPRCklJSfDy8oK9vT0cHBywdu1aoUMiLaE1CW9SUhJOnDiB5s2bCx2KxluwYAEi\nIiIQHh4OX19fLFmyROiQNJqPjw9iYmIQERGB1q1b45tvvhE6JI3m6OiI/fv3o1u3bkKHopGkUilm\nzpyJgIAAxMbG4o8//kBcXJzQYWms8ePHIyAgQOgwtIaenh6+//57xMTE4OLFi/jxxx95f5JaaE3C\nO3fuXHz77bdCh6EVjI2NFdtZWVlo2LChgNFoPm9vb4jFRT9qHTp0wN27dwWOSLO1bdsWrVu3FjoM\njXX58mW0atUKVlZW0NPTw/Dhw3HgwAGhw9JYXbt2Rb169YQOQ2s0btwYLi4uAAAjIyPY2toiOTlZ\n4KhIG+gKHYA6HDhwAJaWlnBychI6FK3x6aefYseOHTA0NMTFixeFDkdr/PbbbxgxYoTQYVANdu/e\nPTRr1kyxb2lpiUuXLgkYEVHJEhISEBYWhg4dOggdCmkBjUl4vb29kZKSUuz1ZcuW4ZtvvsHx48cV\nr3GmtdKpup7Lly/HgAEDsGzZMixbtgwrVqzAhx9+iC1btggQpeYo7XoCRfeqvr4+Ro4cWdXhaZyy\nXE+qGJFIJHQIRKXKysrCkCFDsGbNGhgZGQkdDmkBjUl4T5w4UeLr0dHRiI+Ph7OzMwDg7t27cHNz\nw+XLl2FmZlaVIWoUVdfzVSNHjkTfvn0rORrNV9r13Lp1K44ePYqTJ09WUUSaraz3J5Vf06ZNlR5E\nTUpKgqWlpYARESkrKCjAu+++i9GjR8PX11focEhLaEzCq4qDgwNSU1MV+9bW1ggJCUH9+vUFjEqz\n3bhxAzY2NgCKhotIJBKBI9JsAQEBWLVqFU6fPo1atWoJHY5W4bc55deuXTvcuHEDCQkJsLCwwK5d\nu/DHH38IHRYRgKKf6YkTJ8LOzg5z5swROhzSIlrz0Npz/LruzX3yySdwdHSEi4sLAgMD8d133wkd\nkkabNWsWsrKy4O3tDYlEgunTpwsdkkbbv38/mjVrhosXL6Jfv37o06eP0CFpFF1dXaxfvx69evWC\nnZ0d/Pz8YGtrK3RYGmvEiBHw8PDA9evX0axZMw7/ekNBQUH4/fffcerUKUgkEkgkEs6CQWrBpYWJ\niIiISKtpXQ8vEREREdHLmPASERERkVZjwktEREREWo0JLxERERFpNSa8RERERKTVmPASERERkVZj\nwkvVgo6ODiQSCZycnDB48GBkZWWp/Ryenp4ICQkp1zFffvllhVZHO3DgAOLi4t64HnXq3LlzqWWs\nrKyQlpZW7PXTp0/jwoULKo87duwY2rdvD3t7e7i6umLevHklljt8+DAWL14MABg3bhz27t1brExy\ncjKGDh1aaqzqXm70+vXr6Nu3L1q3bg03Nzf4+fnhwYMHFYrtOVXXszpbvHhxuefePnToEFauXFnu\nc0VERODYsWNvXA8ApKamclVIIlKJCS9VC4aGhggLC0NkZCTq1q2LTZs2qf0cIpGoXAuTyGQyLFmy\nBD179iz3ufbv34/Y2FjFfkXrUaegoKBSy4hEohJXLzt16hTOnz9f4jHR0dGYNWsW/P39ERMTg+Dg\nYLRq1arEst999x2mTZumOFdJLCws8Ndff5Up1ooqLCxU2s/NzUX//v0xY8YMXL9+HSEhIZg+fToe\nPnxYodjUEWNZvfpZ3lR5Y5ZKpRgwYAA+/vjjcp8rLCwMR48eVexXtB4AMDc3R7169RAaGlqh44lI\nuzHhpWqnU6dOuHXrFgDg1q1b6NOnD9q1a4du3brh2rVritc7duwIJycnfPbZZzA2NgYABAYGYsCA\nAYq6Zs6ciW3bthU7x/Tp09G+fXs4ODgoehyBoh65hQsXws3NDX/99ZeiFzIkJESx6o+joyPE4qIf\nnV9++QXu7u5wcXHBkCFDkJOTg/Pnz+PQoUOYP38+XF1dcfv2baXezJMnT8LV1RVOTk6YOHEi8vPz\nFedevHgx3Nzc4OTkpPisL+vfvz+ioqIAABKJBEuXLgUAfPHFF/j1118BAKtWrYK7uzucnZ2VPtvz\nHlGZTIbp06fD1tYWPj4+6Nevn1JP67p165RiSEhIwKZNm/D9999DIpHg3LlzSjF9++23+Oyzz9C6\ndWsAgFgsxtSpU4vFnpSUhPz8fJibmyteO3PmDDp37oyWLVsqYkhISICjoyMA4NmzZxg2bBjs7e0x\nePBgdOzYUSmh+eyzz+Di4oJOnTopemMfPnyIIUOGwN3dHe7u7opEffHixRgzZgy6dOmCsWPHKsW2\nc+dOeHh4oF+/forXunfvDnt7e6VyL8cWExODDh06QCKRwNnZGTdv3iz2mV/2+++/K8pPnToVMpkM\nUqkU48aNg6OjI5ycnLBmzRoAwNq1a2Fvbw9nZ2eMGDGiWF1bt27FwIED0bNnT3h7e+PZs2eYMGEC\nOnToAFdXVxw8eLDU6/dyD/mePXswfvz4Yucp6f4Ginrnp06dio4dO2LBggXYtm0bZs2aBQBwcXFR\n/KwYGhri7NmzuHLlCjw8PODq6orOnTvj+vXryM/PxxdffIFdu3ZBIpFg9+7d2Lp1q6KehIQE9OjR\nA87Oznj77beRlJSkOPfs2bOL3TcAMHDgQC6TTEQlYsJL1YpUKsXx48fh4OAAAJgyZQrWrVuH4OBg\nrFq1SrEs7+zZs/Hhhx8iMjISzZo1U1mfql7dZcuW4cqVK4iIiMDp06cRHR2tKN+wYUOEhITAz89P\ncbybmxvCwsIQFhaGPn36YP78+QCAd999F5cvX0Z4eDhsbW2xefNmeHh4YODAgVi9ejVCQ0PRokUL\nRT25ubkYP348du/ejcjISBQWFmLDhg2Kczdq1AghISGYNm0aVq9eXSzurl274uzZs8jIyICenp4i\nmTt37hy6d++O48eP4+bNm7h8+TLCwsIQHByMs2fPKuoHgH379uHOnTuIi4vDjh07cOHCBaVr9GoM\nVlZWmDp1KubOnYuwsDB06dJFKaaYmBi4ubmV+m8bFBQEV1dXxb5cLkdKSgqCgoJw+PBhLFy4sNgx\nP/30Exo0aICYmBgsXbpUaUhKdnY2OnXqhPDwcHTr1g2//PILgBf3xuXLl7Fnzx5MmjRJcczVq1dx\n8uRJ+Pv7V+gzvGzjxo2YPXs2wsLCEBISAktLS5Vl4+LisHv3bpw/fx5hYWHQ0dGBv78/IiIikJyc\njKioKERGRiqSzpUrVyI8PBwREREqv+0ICwvD3r17cerUKXz99dfo2bMnLl26hH///Rfz58/Hs2fP\nXnv9Xv43V9WrW9L9/VxycjIuXLhQbPhDeHg4wsLC8NVXX6F9+/bw8PBA27ZtcfbsWYSGhmLJkiVY\ntGgR9PX1sXTpUgwfPhxhYWEYNmyYUhyzZs3C+PHjERERgVGjRuGDDz5QvKfqvnF3d8eZM2dU/jsQ\nUc3FhJeqhZycHEgkEjRp0gRJSUmYOnUqsrKycOHCBQwdOlTRK5aSkgIAuHjxomIsZUk9YKXZtWsX\n3Nzc4OrqipiYGKXhB35+fkplX/6Kf9euXQgNDcWKFSsAAFFRUejatSucnJzg7++vVM+rQwPkcjmu\nXbsGa2trxVf+Y8eOVWqgBw8eDABwdXVFQkJCsbi7du2KM2fOICgoCP369UNWVhZycnIQHx8PGxsb\nHD9+HMePH4dEIoGbmxuuX79erOfx3LlzGDZsGICir4G9vLyU3lcVw5uuQp6YmIgmTZoo9kUiEXx9\nfQEAtra2SE1NLXZMUFAQhg8fDgCwt7eHk5OT4j19fX1Fj6ybm5si1n/++QczZ86ERCLBoEGDkJmZ\niezsbIhEIgwcOBAGBgYlxlfez+fh4YHly5fj22+/RUJCAmrVqqWy3pMnTyIkJATt2rWDRCLByZMn\nER8fjxYtWuD27dv44IMP8H//93+KbyqcnJwwcuRI+Pv7Q0dHp1idIpEI3t7eMDU1BQAcP34cK1as\ngEQigZeXF/Ly8pCYmPja61cWqu5vkUiEoUOHqkyUb9y4gQULFmD37t3Q0dFBeno6hgwZAkdHR8yd\nO1dRj1wuV3ndL168iJEjRwIARo8erfhm4XX3TZMmTUr8uSEi0hU6ACIAqF27NsLCwpCTk4NevXrh\nwIEDePvtt2FqaoqwsLAy16OrqwuZTKbYf/4V7Mvi4+Px3XffITg4GCYmJhg/fjxyc3MV79epU6fE\nuqOjo7FkyRKcPXtW0dCPGzcOBw8ehKOjI7Zt24bAwEBF+ZKSgVdfk8vlSq89T8Z0dHRKHJvZvn17\nBAcHo0WLFvD29sajR4/w888/o127dooyn3zyCaZMmVLiZ3gew8tJxqsJR2kxvMre3h7BwcGKr/pf\n59Vz6evrq3yvtNf19PQU22KxWBGrXC7HpUuXlOp+ztDQsMS67O3tcfr06dcH/4oRI0agY8eOOHz4\nMPr27YtNmzYV++XhZWPHjsXy5cuLvR4ZGYmAgABs3LgRu3fvxubNm3HkyBGcOXMGhw4dwrJlyxAV\nFVUs8X31Pt23bx9sbGyK1a/q+r183736c1KW+1vVtczKyoKfnx9+/fVXxfCVzz//HD179sT+/ftx\n584deHp6lnhsWWNXdd+8+vNERPQce3ipWqlduzbWrl2LTz/9FEZGRrC2tsaePXsAFDVmkZGRAICO\nHTsqXv/zzz8Vxzdv3hyxsbHIz89Heno6/v3332LnyMjIQJ06dVC3bl2kpqYqPSVeEpFIhPT0dIwY\nMQI7duxAgwYNFO9lZWWhcePGKCgowO+//65obI2NjZGRkVGsnjZt2iAhIUExRnnHjh3o3r17ma+P\nnp4eLC0t8ddff8HDwwNdu3bF6tWr0a1bNwBAr1698NtvvyE7OxsAcO/evWIPXnXu3Bl79+6FXC5H\nampqmRI9Y2NjZGZmlvje/PnzsXz5cty4cQNA0Rjhkr6Gb968uaKHvqw6d+6M3bt3AwBiY2MV45df\nx8fHB2vXrlXsR0RElHrMyJEjcf78eaUHqM6cOYOYmBiVx9y+fRvW1taYNWsWBg0apDI2kUiEnj17\nYs+ePYp/i7S0NCQmJuLx48coLCzE4MGDsXTpUoSGhkIulyMxMRGenp5YsWIFnj59qvj3fO7VRLBX\nr15Kn/n5L4mvu37m5ua4evUqZDIZ9u/fr1T38/pV3d+vejmeCRMmYPz48UqzgmRkZMDCwgIAsGXL\nFsXrdevWVbqvXq7Hw8ND8bPt7++vuMdf5/79+2jevHmp5Yio5mHCS9XCyw2pi4sLWrVqhd27d8Pf\n3x+bN2+Gi4sLHBwcFA/j/PDDD/jf//4HFxcX3Lp1CyYmJgCAZs2aYdiwYXBwcICfn5/SmNHnnJ2d\nIZFI0LZtW4waNarYmNSSHDx4EImJiZg0aRIkEomi3qVLl6JDhw7o0qULbG1tFeWHDx+OVatWwc3N\nDbdv31a8bmBggC1btmDo0KFwcnKCrq6u4gGvV8dUqkouunXrBnNzcxgYGKBLly5ITk5G165dAQDe\n3t4YOXIkOnXqBCcnJwwdOlQxxdvz+t59911YWlrCzs4OY8aMgaurq+L6vezlGAYMGID9+/dDIpEU\nm+3B0dERP/zwA0aMGAE7Ozs4OjoiPj6+WH2dO3cu9gS9qnGkz7efz5Rgb2+Pzz//HPb29opYVV2v\ntWvXIjg4GM7OzrC3t1dKvlVd01q1auHw4cNYt24dWrduDXt7e2zcuBFmZmYlXhcA2L17NxwcHCCR\nSBATE4P33ntPZVlbW1t8/fXX8PHxgbOzM3x8fJCSkoJ79+7By8sLEokEY8aMwYoVKyCVSjFmzBg4\nOTnB1dUVs2fPRt26dYvV+/Jn+fzzz1FQUAAnJyc4ODjgyy+/LPX6rVixAv3790fnzp1hYWGhqO/l\nulXd36quf2JiIvbu3YvffvtN8eBaSEgIFixYgE8++QSurq6QSqWKY728vBAbG6t4aO3lc69btw5b\ntmyBs7Mz/P39FQ/0lXTu5y5fvlymxJiIah6R/E0H5hEJICcnB7Vr1wZQ1MO7a9cupV4qer3s7GzU\nqVMHjx8/RocOHXD+/PkSkzt169GjB/z9/ZXG8r6OTCZDQUEBDAwMcOvWLXh7e+P69evQ1eVorLKo\naddv1KhRmDdvHiQSidChEFE1o53/65HWCwkJwcyZMyGXy1GvXj389ttvQoekUfr374/09HTF1FBV\nkewCwLx587Bx40YsWbKkTOWzs7PRo0cPFBQUQC6XY8OGDVqbrFWGmnT9Hjx4gPT0dCa7RFQi9vAS\nERERkVbjGF4iIiIi0mpMeImIiIhIqzHhJSIiIiKtxoSXiIiIiLQaE14iGxqQpQAAABNJREFUIiIi\n0mpMeImIiIhIq/0/Nexm+uNsHT0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108cf5990>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>It is not so obvious from the above plot that $L1$ holds the feature weight at 0 for some time, but we can see this if we directly compare the paths of individual features.\n",
      "\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "fs = ['isbuyer','expected_time_visit','visit_freq','multiple_buy']\n",
      "\n",
      "fig = plt.figure()\n",
      "\n",
      "for i,f in enumerate(fs):\n",
      "    fig.add_subplot(2, 2, i)\n",
      "    plt.title(f)\n",
      "    plt.plot(Rpath2.index.values, Rpath2[[f]], 'b', label='L2')\n",
      "    plt.plot(Rpath1.index.values, Rpath1[[f]], 'b--', label='L1')\n",
      "    \n",
      "fig.tight_layout()\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SgGc2vFGsW8fyn8l4TuZoEbVGklA26WBT9ESqC12a3quJtzcQH88MVYcObKrF\n0xNYv56lBuFw1EVsLHNsCAlRLpL5u+8y4/YsHR1Hj9BIwkJZnDp1Cg4ODk3KE6kutLX/qTE4OzNP\nqiVL2NPotm1Aly6Ajw/g5ga4uLBpQRcXdjg6AsbGWlZaDagiYSGnYZ4+BZYtY0ZKIGBeeA4OirXV\nogVzmJg/n401/vavP6g9YWFdODzrbU3FE6k+UlKAiRO1rUVtKiuBggK2RvbMgQwCAYsgHRjI0nTE\nxgL//ceeTg8cYE+6Dx+ydau2bVn2XjMztn4lFrNkjM2bM3d6gYAtXtvZMSNnbMzOGxmxa3fuPF93\nqP6l4uQEdO1a+3xuLsu6WnPWwNERCAhgT9LKooqEhQBzMJo3bx7EYjGmT5+OyMjIWmXmzJmDhIQE\nmJqaIiYmBn5+fpJrYrEY/v7+cHZ2xsGDBxXSQZfZs4cl7ezbl31++WXWTxQlIIBFQ9+/HxgxQjU6\nctSPwgaquieSo6MjfvzxR+zevVtm2ZrzjGVlZRCLxbCwsJB4Ii1btkxRVfSasjIWqLXad4/WSEkB\nvv6abRjOzgby8tgUS0SE7BT0jx8DT56w/VPW1mwx2sgI6N0bGD6cGZiysufHn38Cv//OYv5VVDBD\nUlnJpm6cnJgBqzqIWFuVlbXlikRMbk1DVFbGzldHIGDnSktV9mdSGnkcjOLj43Hr1i3cvHkTZ8+e\nxaxZs5CSkiK5/tVXX8HDw0Pi0WdoxMQA4eHPP7/+unLtde3Ktk0sWAAMG8YioXP0AGViKcXHx1Pn\nzp3Jzc2NVq5cSUREW7ZsoS1bthARUX5+Pjk7O5OlpSVZW1tTu3btqKSkhNLT08nHx4d8fHyoW7du\nkrqKxGrSd06eJOrRQ9taMK5fJ4qJITp2jOjWLRbLjFM/ivTR06dP0+DBgyWfo6KiKCoqSqpMREQE\nxcXFST536dKFCgoKiIgoJyeHXnnlFTp27Bi9+uqrKtNLV8jOJmrViqisTLXtTplC5OFBtG6datvl\nKIY8fVSpjbpDhw7F0KFDpc5FRERIfre3t5eaBqzC3NwcFy9eVEa0waBJBwki4ORJFtJozZrac/Gd\nO7ODo15kORidPXu2wTK5ubmws7PD/PnzsXbtWjx8+FBjOmuSH34Axo4FWrZUbbuvvMKmo6OiWJqZ\nqmlrju7CI0lomZQU4Nm2FrWSmMgCwZqYsKmT8nK2FsTRPIqGOiIiHDp0CG3btoWfn1+Dzhr66GBE\nxKb3GrvvpomLAAAgAElEQVQpVx5eeYXth3rzTTbVFxenehmcuuGhjvSQlBT2NqNO0tOB0FD2ZDpo\nEPdi0jbKhDras2cPDhw4gPj4eDx58gQPHz5EaGioJOpEdfTRwSglha09BgSovm1nZ/aQNmAAGw9H\njzKjxdEMCjkYqX2iUQl0XD2lyckhsrUlqqxUn4yKCqLu3Yk2blSfjKaMIn20vLycXF1dKSMjg54+\nfdpgPqgzZ85I5YOqIjk52eDWoN56i6jGchyVlhKtXataOfv2EXXtSvT0qWrb5ciPPH2UR6jSIlX7\nn9T5RmNsDGzaxIO+6hLVQx15eHhg3LhxklBHVeGOQkJC4OrqCqFQiIiICGzevFlmW8ruR9QlHj8G\nfv4ZmDJF+nxBAcvtpEqGDwdcXYEvv1RtuxzVonCoI01gCOFa6mPhQuaezfMv6S+62kd1Va/62L2b\nBSd+Fj1NQmoqe8A6d0618tLT2VRiWhoLLMvRLGoNdcRRHl0OccThaJqYGOBZEmEpiorUk8vJzY0Z\nvmohQjk6BjdQWqK8nD259eihbU04HO1z+zZ7Q5IV5UGZOHz1UV7OwnOdO8ci93N0D63lg2qorqFz\n6RIbHJaWqm87PV31bXJUizz9f86cOejUqRN8fHyQlpYGAHjy5AkCAgLg6+sLDw8PLDGQtMexsSxa\nvqy9T+oyUAALejx2LDB7Nov/x9ExFPXAqKioIDc3N8rIyCCRSCTTE+nu3bt07tw5+uCDD2hdte3b\n8tSV18tDX9m0iWj6dNW3u20bkY8PkVis+rY5tVGkj8rT/6t78aWkpEh58T169IiImDdgQEAAnTx5\nUiV6aYvKSqIuXYhOn5Z9/Y8/iH77TT2yT50icnQkGjKEqI6ANhw1IU8fVfgNKjU1FUKhEC4uLjAx\nMcH48eOxf/9+qTK2trbw9/eHSY3AV/LUNXROnAB69VJtm//8AyxaBOzaxTOI6jLy9P8DBw4g7NmC\nTEBAAIqLi3HnWX4T02eZI0UiEcRisd4n/Tx7lm3QrWs9tk8fli9NHfTuDbz2GntD+/xzYOdO9cjh\nKIZW8kEpm0tK3yktBX79lbm6qpI1a1hyQQ8P1bbLUS3y9H9ZZW7fvg2ABZv19fWFnZ0d+vfvDw89\n/4fHxABTp2pvA3lUFHDsGPDFF8BHHzHvWrFYO7pwpFHYQCmz/8KQ9m4owsGD7KnQxkZ1bZaXA4cP\nsxhjHN1G0VBHVfWMjY1x8eJF3L59G7///rte56eqa++TJmnViq1FpaayIy2NJUm8d097OnEYWskH\n1Zi6+hhPrCF27wYmTFBtm7//DgiFPACmulFFwkJlQh1Vx8rKCsOGDcP58+dljgt9GDsHDgD+/iwM\nkTYZP54dAgHbh7VoEdCzJ8sf1a2bdnUzFBQaO4oucMkTrqWKZcuWSTlJyFtXCfV0lqIiIktLogcP\nVNvuvXtEf/2l2jY5DaNIH1Um1FFhYSHdv3+fiIjKysooMDCQjhw5ohK9tMGQIUS7dmlbC9l8/z2R\njQ3R3r3a1sQwkaePaiUfVF11FbkBfePbb4neeEPbWnBUhaJ9tKGxQ0T0zjvvkJubG3l7e9Off/5J\nRESXLl0iPz8/8vHxIS8vL1qzZo1K9dIkt2/Ll/fpww+JRCLN6FST5GSidu2IPviAKD9fOzoYKvL0\nUR7qSMMEBwOzZgFvvKFtTTiqQFf7qK7qVZ3/+z+WWbm+eHgiEWBmxn5qY+k6JIStUZWXA7/9xqJP\nDBvGzvfowb1llUGePsoNlAYpKADc3VkqdVUnY+NoB13to7qqVxWFhSwN+6VL9a+b3rkDeHkBd+9q\nTrfqPHwIzJ/P1qV69ABeeAEoKQGys5lOQ4YAgwezwLMODoCdHR/b8iJPH+X5oDTITz8x13LegTlN\nnS++YBEcGnLqUWcUCXmwtASio9kew6tXgYwM9jYVHw9kZrKfv/zCQjXl5LCHUGNjwNQUsLBg9a2t\nAV9foEULZuBatGBHeTlw5Qorb2T0/KeFBeDn9/yNUSBgx6NHwN9/P/9chZkZ4OPz/HPVtdJSVr46\nAgHTzdu79r2WlrL7rImpKTBjBtChg1J/SoXgBkqDxMUBS5eqts1Hj1iWXJ4dl6Mv3L8PbN0K/Pln\nw2W1baCq8PRkR3VcXIC332YHwN62Tp8G8vOB3FxmrAoLmVHy9ASePGHhlJ48YS7sd+8yl3YioLLy\n+U8zM5aaHmDnqo7SUuDixdq6mZo+D29W/YWkpoGqumZuDty4Ubud0lL2RlsTc3P2psgNlAGTmQnc\nuqX6HfGbNwNZWSznE0d/SExMxLx58yAWizF9+nRERkbWKjNnzhwkJCTA1NQUMTEx8PPzQ05ODkJD\nQ3H37l0IBAK89dZbmDNnjhbuQHE2bABef519wTeEuiKZqwNLS/ZFzlEhanLQUAk6rl6jiIoimjlT\n9e327k2UkKD6djnyoUgfVSYWX35+PqWlpRERUUlJCXXu3Fmvtmg8eMBct2/ckK/8lStE+/erVyeO\ndpCnj3IfFA2xe7fqozwUFLA57P79VdsuR70oE4vP3t4evr6+AABzc3O4u7sjLy9P4/egKJs3A4MG\nAZ06yVfe3V31IcE4+gM3UBrgyhU2VREYqNp2Dx5kUwovvKDadjnqRdlYfFVkZmYiLS0NAQEB6lVY\nRTx6xJwjeAZpjrzwNSgNEBcHjBun+j0Te/fKzkDK0W2UjcUHAKWlpRg9ejS++uormJuby6yva6GO\nvvmGPaTpeWxbjoIoEupIKQOl6EIvALi4uMDS0hLGxsYwMTFBamqqMqroLERsem/3btW3a24ODB2q\n2nY56kfZWHzl5eV44403MHnyZIyQlYL2GdUNlLZ58gRYt44FNOY0TWo+JK1YsaLhSooucCmbdM3F\nxYWKiorqlaGEejrD+fNEbm4sKRvH8FCkjyoTi6+yspKmTJlC8+bNU7le6mTTJqJXX9W2FhxdQp4+\nqtaEhfUlXXtmHBUVrzdURS5v4hlGONVo1qwZNm3ahMGDB8PDwwPjxo2Du7s7tm7diq1btwIAQkJC\n4OrqCqFQiIiICGzevBkAcOrUKcTGxuL48ePw8/ODn58fEhMTtXk7DSISAatXAx9+2Pi6K1eyaBKc\nponCU3yyFnHPnj3bYJnc3FzY2dlBIBAgODgYxsbGiIiIwIwZMxRVRWeprAR+/JElJ+RwqjN06FAM\nrTE/GxERIfV5k4zNbX379kVlZaVadVM1O3awsEaK+HJs2gSEhqpeJ45+oLCBUnSht4o//vgDjo6O\nKCwsxMCBA9G1a1cEynBz07WF3sbwxx9skyFfFDYcVJEPqilRUcEy1sbENL4uke5EkuBoB7UmLKxv\nodfR0REAYGtri5EjRyI1NbVBA6VvREfzDLeGhkILvU2Yjz9mESMU2WLx6BGLT8djVzZdFF6D8vf3\nx82bN5GZmQmRSIQff/wRw2vsqBs+fDh27NgBAEhJSYG1tTXs7OxQVlaGkpISAMCjR4+QlJQELy8v\nJW5D99i7l2W5nTlTte1WVrJ0HU+fqrZdjmZJTExE165d0alTJ6xevVpmmTlz5qBTp07w8fFBWlqa\n5Py0adNgZ2en82MmOhrYuRPYtUux+vfu8benJo8yXhiKJl1LT08nHx8f8vHxoW7duhlcwsKMDCJb\nW6KUFNW3feYMUbduqm+XoxiK9FFlPWB///13unDhAnl6eqpUL1WSkEBkZ0d07ZribVy4QOTjozqd\nOLqFPH2U54NSMSIRm84YNw547z3Vt//uuyyB2iefqL5tTuNRpI+eOXMGK1askHjfrVq1CgCwePFi\nSZmZM2eif//+GDduHACga9euSE5Ohr29PQAWReK1117D3zXzKSihl6pIS2PhjPbtA/r0Ubyd/Hy2\njjtmjOp04+gO8vRRHupIxbz/PtC2LUtypmpu3WJRKWbPVn3bHM2haKijmmV0kaws4LXXgC1blDNO\nAEsAyI1T04aHOlIhhw4BP/8MXLignn1PkZHAggXMAHL0F1WEOpIHTXvA3r/PIpv83/8Bb7yhVlEc\nPUTjoY44z8nJAcLDWXZNdSzsFhSwJGOxsapvm6NZlPWAlRdNesA+fQqMGMHSn8+bpzGxHD1CEQ9Y\nPsWnAsrLWbSI+fOVn9aoC3t74K+/uMutIaCMB6wuUlnJghbb2gLr12tbG44hwQ2UCvjoI8DCAli0\nSL1yVB0NnaMdlAl1BAATJkxA7969cePGDbRr1w7bt2/X1q3g/HkgKIg5NPzwA++jHNXCvfiU5PBh\nICKCeS7Z2mpbG46m0dU+qm69cnKYQ9DRo2wz7ptvsk21qmTDBmDgQJa0kGN4cC8+NZKVxWKEhYez\ngLDcOHGaAiUlLOGgry+LEHH9OjB9uuqNE8DG1f37qm+Xoz9wA9VIioqYJ1337myA3rih+ky5VTx+\nzOKRcTjaprycJRzs3Bm4fZuth37yCZvaVhc8Dh9HKQOlTLgWeepqmvpcIMvKWNDLLl2Y4bh8mU1t\nWFqqRx7ADOEXXyjefmPlqRpDl6cM+jB2ioufp4uxs2OR+Q8dAr7/HqjhdKiWv/29eyzYsiy08b82\n9P6sk+NH0TAVyoRrkafus7UxRdVTiGXLlkl9LitjoYXWriVyciIaM4bo+nX1yavOlStENjZEDeR0\nVJk8dWDo8og0H+pI3WMnPZ3oiy+I+vcnsrBgSQa/+YYoN7f+eqr+24vFRMbGROXlmpEnD4benzUt\nT54+qvA+qOoJCwFIEha6V1vRlJWwsKCgABkZGQ3W1TRPnwJ5ecDWrcwz6dw5Nn3n7g74+wN79iiW\nz0ZRFi4Eliyp+wmSo7/o6tiJjWWbbF99le1lCg4GTE2VblYhiovZ9GEzvlOzSaOVhIV5eXkN1lWU\n779n8+Pl5SwXTUUFIBaz/UM2NqzjFxU9PwoKgP/+YwbK3Bz4919AKGR7msaNA1q0qHnfLFJETRwd\ngRdfrH2+vvKyyM1lm32vXmVGkWN46OrYGTOGRSmpipR/9Ojza6+8IttYHTnCpryvXwcOHpS/fE1q\nln/hBZaskNO00VrCQnlwc3NrdHgXZXj4EDh6dAWOHmVvUlOnql9mfbupaxpHdctTB4Yuz83NrdF1\nDHHsAEBcnOr/9pMn131NG7m4DL0/a1KePGNH4wkLnZ2dUV5e3mBdALh165ai6nE4OgsfOxyOfGgl\nYaE8dTkcQ4WPHQ5HPhR+g6oerkUsFiM8PFwSrgUAIiIiEBISgvj4eAiFQpiZmUlCstRVl8NpCvCx\nw+HIh06HOuJwOBxO00XnI0ls3LgR7u7u8PT0RGRkpEZkrl+/HkZGRrh3757aZS1cuBDu7u7w8fHB\nqFGj8ODBA7XI0eTG6JycHPTv3x/dunWDp6cnNmzYoFZ5VYjFYvj5+eG1115Tu6zi4mKMHj0a7u7u\n8PDwQEpKitplKoIhjx8+dlSHzo4dNe/FUopjx45RcHAwiUQiIiK6e/eu2mVmZ2fT4MGDycXFhYpU\nuUu2DpKSkkgsFhMRUWRkJEVGRqpchrybO1VFfn4+paWlERFRSUkJde7cWa3yqli/fj1NnDiRXnvt\nNbXLCg0NpejoaCIiKi8vp+LiYrXLbCyGPn742FEdujp2dPoN6n//+x+WLFkCExMTAICtBiKyvvfe\ne1izZo3a5VQxcOBAGD3LURAQEIDbt2+rXEb1jaEmJiaSzZ3qwt7eHr6+vgAAc3NzuLu7Iy8vT23y\nAOblFh8fj+nTp6s9uviDBw9w8uRJTJs2DQBbF7KyslKrTEUw9PHDx45q0OWxo9MG6ubNm/j999/x\n0ksvISgoCOfPn1ervP3798PZ2Rne3t5qlVMX27ZtQ0hIiMrbrWvTpybIzMxEWloaAtQchmP+/PlY\nu3at5AtLnWRkZMDW1hZvvvkmunfvjhkzZqCsrEztchtLUxo/fOwoji6PHa0HEhk4cCAKCgpqnf/s\ns89QUVGB+/fvIyUlBefOncPYsWPx77//qk1eVFQUkpKSJOdU9TRRl8yVK1dK5nw/++wzNG/eHBMn\nTlSJzOpoesNmFaWlpRg9ejS++uormJubq03OoUOH0LZtW/j5+Wkk4GVFRQUuXLiATZs2oUePHpg3\nbx5WrVqFjz/+WO2ya2Lo44ePnSY+dtQ+4agEQ4YMoeTkZMlnNzc3+u+//9Qi6++//6a2bduSi4sL\nubi4ULNmzahDhw50584dtcirzvbt26l37970+PFjtbR/5swZGjx4sOTzypUradWqVWqRVYVIJKJB\ngwbRF198oVY5RERLliwhZ2dncnFxIXt7ezI1NaUpU6aoTV5+fj65uLhIPp88eZKGDRumNnmK0hTG\nDx87yqHrY0enDdSWLVvoo48+IiKi69evU7t27TQmW1NOEgkJCeTh4UGFhYVqk1FeXk6urq6UkZFB\nT58+VftCb2VlJU2ZMoXmzZunNhl1kZycTK+++qra5QQGBtL1Z6Htly1bRosWLVK7zMZi6OOHjx3V\nootjR6cNlEgkosmTJ5Onpyd1796djh8/rjHZHTt21IiBEgqF1L59e/L19SVfX1+aNWuWWuTEx8dT\n586dyc3NjVauXKkWGVWcPHmSBAIB+fj4SO4rISFBrTKrSE5O1ogn0sWLF8nf35+8vb1p5MiROunF\nZ+jjh48d1aKLY4dv1OVwOByOTqLTXnwcDofDabpwA8XhcDgcnYQbKA6Hw+HoJNxAcTgcDkcn4QaK\nw+FwODoJN1AcDofD0Um4geJwOByOTsINFIfD4XB0Em6gOBwOh6OTcAPF4XA4HJ2EGygdZvny5Zgy\nZUqd13fu3InBgwfL1VZMTAwCAwOV0mfq1KlYunSpUm1wOOrG09MTv//+e53XMzMzYWRkhMrKSg1q\nxVEEreeD4tRN9Vw0mZmZcHV1RUVFhSSx2KRJkzBp0iSN6qOt/Dgcjrz8888/2laBoyL4G5QOIyuO\nr7Zj+2pbPodjKIjFYm2roPNwA6UGXFxcsG7dOnh7e8PCwgLh4eG4c+cOhg4dCisrKwwcOBDFxcVI\nTk6WSiddVffYsWOSz1VvLC+//DIAwNraGpaWlkhJSak1bWdkZISNGzfCzc0Ntra2WLRoUZ0G5dq1\naxg4cCDatGmDrl274ueff5br3v777z8MGjQIlpaWCAoKQnZ2NgDZ0yZBQUGIjo6GSCRC69atpZ5s\n7969CzMzMxQVFckll8ORFxcXFxw9ehSpqanw9/eHlZUV7O3tsWDBAqly0dHRcHJygqOjI9avXy85\nX3Mqu/o4Xbt2LUaPHi3Vzpw5czBv3jwAwIMHDxAeHg5HR0c4Oztj6dKlkjERExODPn364L333oON\njQ1WrFihlvs3JLiBUgMCgQC//PILjh49iuvXr+PQoUMYOnQoVq1ahbt376KyshIbNmyQOV1W81yV\ngTl58iQANgAePnyIl156Sabsffv24c8//8SFCxewf/9+bNu2rVaZR48eYeDAgZg8eTIKCwsRFxeH\nt99+G1evXq33vogIO3fuxEcffYT//vsPvr6+9U4xVk0JNm/eHBMmTEBsbKzk2u7duxEcHIw2bdrU\nK5PDaSxVY2ju3LmYP38+Hjx4gH///Rdjx46VKpecnIxbt24hKSkJq1evxtGjRyX165rKnjx5MhIT\nE/HgwQMALIX5jz/+iLCwMADMuDVv3hzp6elIS0tDUlISvvvuO0n91NRUuLm54e7du3j//fdVfu+G\nBjdQamL27NmwtbWFo6MjAgMD0atXL/j4+OCFF17AyJEjkZaW1qj25J1ai4yMhLW1Ndq1a4d58+Zh\n9+7dtcocOnQIHTt2RFhYGIyMjODr64tRo0bJ9Rb16quvom/fvmjevDk+++wznDlzBrm5uQ3WCw0N\nldLlhx9+qNcBhMNRlubNm+PmzZv477//YGpqioCAAKnry5YtQ8uWLeHp6Yk333xTqn/WNd4cHBwQ\nGBgoGSuJiYmwsbGBn58f7ty5g4SEBHzxxRdo2bIlbG1tMW/ePMTFxUnqOzo64p133oGRkRFatGih\nhrs2LLiBUhN2dnaS31u2bCn1uUWLFigtLVWL3OpThu3bt0deXl6tMllZWTh79ixatWolOXbt2oU7\nd+7U27ZAIICzs7Pks5mZGVq3bi1TRk0CAgLQsmVLJCcn49q1a0hPT8fw4cMbcWccjvwIBAJER0fj\nxo0bcHd3R8+ePXH48GGpMvKMFVmEhYVJZgNiY2MRGhoKgI2r8vJyODg4SMbVzJkzUVhYKFMmp2G4\nF5+GkPVEZmZmhrKyMslnsVgs1ZmrI6/3XHZ2Ntzd3SW/Ozk51SrTvn179OvXD0lJSXK1WZ2cnBzJ\n76Wlpbh37x4cHR3RvHlzAEBZWRnMzc0BAAUFBVJ1qwa2nZ0dxowZI6nD4agDoVCIXbt2AQD27NmD\n0aNH4969e5Lr2dnZ6NKli+T3qrFSc1zW7Mevv/463n77bfzzzz84fPgw1q1bB4AZnxdeeAFFRUUS\nT9uacC/YxsHfoLRI586d8eTJE8THx6O8vByffvopnj59KrOsra0tjIyMkJ6eXm+b69atQ3FxMXJy\ncrBhwwaMGzeuVplhw4bhxo0biI2NRXl5OcrLy3Hu3Dlcu3at3raJCPHx8Th16hREIhGWLl2KXr16\nwcnJCba2tnBycsIPP/wAsViMbdu21dJ18uTJ+OWXX7Bz507JUyeHow6ICLGxsZIHPisrKwgEAinD\n8emnn+Lx48e4fPkyYmJiJGPF19cX8fHxuH//PgoKCvDll19Ktd2yZUu88cYbmDhxIgICAiSzCg4O\nDhg0aBDee+89lJSUoLKyEunp6fXuyeLUDzdQGqL6k1PVIqylpSU2b96M6dOnw9nZGebm5lJTANUX\na01NTfHBBx+gT58+aN26Nc6ePStzMff111/Hiy++CD8/P7z66qsIDw+v1ZaFhQWSkpIQFxcHJycn\nODg4YMmSJRCJRA3ew6RJk7BixQq0adMGaWlpUo4P3377LdauXQsbGxtcuXIFffr0karfrl07dO/e\nHUZGRujbt68Cf0UOR35+/fVXeHp6wsLCAvPnz0dcXBxeeOEFAKwv9+vXD0KhEMHBwVi4cCGCg4MB\nAFOmTIGPjw9cXFwwZMgQjB8/vtY4CwsLwz///FNrHXXHjh0QiUTw8PBA69atMWbMGMkbGN9HqADU\nAAkJCdSlSxcSCoW0atUqmWVmz55NQqGQvL296cKFC1LXKioqyNfXl1599VXJuWXLlpGTkxP5+vqS\nr68vJSQkNKQGRw4EAgGlp6drW416mTZtGi1dulTbamidhsbVvn37yNvbm3x9fal79+509OhRybUO\nHTqQl5cX+fr6Uo8ePTSpNucZ2dnZZGpqSiUlJdpWxaCp10BVVFSQm5sbZWRkkEgkIh8fH7py5YpU\nmcOHD9PQoUOJiCglJYUCAgKkrq9fv54mTpxIr732muTc8uXLaf369aq6B84zdN1AZWRkkLW1NWVm\nZmpbFa0iz7gqLS2V/H7p0iVyc3OTfHZxcaGioiKN6cuRRiwW09y5cyk8PFzbqhg89U7xpaamQigU\nwsXFBSYmJhg/fjz2798vVebAgQOSPQABAQEoLi6WeIPdvn0b8fHxmD59ei0ngZqfOcqjiumDbt26\nwcLCotYhy129MSxduhReXl5YtGgROnTooLSe+ow848rMzEzye2lpKWxsbKSu8/GjHR49egRLS0sc\nPXqUb7TVAPV68eXm5kqtiTg7O+Ps2bMNlsnNzYWdnR3mz5+PtWvX4uHDh7Xa3rhxI3bs2AF/f3+s\nX78e1tbWyt5Lk0cVoVMuX76sAk1q88knn+CTTz5RS9v6hjzjCmCbrpcsWYL8/Hwpj0uBQIDg4GAY\nGxsjIiICM2bM0IjeHPbgoK4tIpza1PsGJe8Tuay3o0OHDqFt27bw8/OrdX3WrFnIyMjAxYsX4eDg\nUCsESRVCoVCysMgPfujiIRQK5RojioyrESNG4OrVqzh48KDUYvypU6eQlpaGhIQEfP3115IoI3zs\n8EOfDnnGTr0GysnJSWrfS05OjtRGTVllbt++DScnJ5w+fRoHDhxAx44dMWHCBBw7dkziWty2bVuJ\nktOnT0dqaqpM+enp6SC2TqaRY9myZVwel9eooyG3f0XHVXUCAwNRUVEhiVvo4OAAgG09GDlypMzx\nw8eO/ss0dHnyjJ16DZS/vz9u3ryJzMxMiEQi/Pjjj7V2/w8fPhw7duwAAKSkpMDa2hr29vZYuXIl\ncnJykJGRgbi4OAwYMEBSLj8/X1J/79698PLyalBRDsdQkGdcVRkYALhw4QIAoE2bNigrK0NJSQkA\nth6SlJTExw/HYKl3DapZs2bYtGkTBg8eDLFYjPDwcLi7u2Pr1q0AgIiICISEhCA+Ph5CoRBmZmbY\nvn27zLYEgufTGpGRkbh48SIEAgE6duwoaY/DaQrIM6727NmDHTt2wMTEBObm5pJ4bgUFBRg1ahQA\nFqh00qRJGDRokNbuhcNRK6TDaFq948ePc3lcXqPQ1SHEx47+yzR0efL0UcGzgjqJQCCADqvH4ehs\nH9VVvdRNRQUQEQFcvAhYWj4/LCyAd98FPDy0rSGnCnn6KA8Wy+FwDIZmzYCoKCAnB3j48PlRUgJU\n21omxeuvA7duAR06AH36AP37A/7+AI9lrH0afINKTEzEvHnzIBaLMX36dERGRtYqM2fOHCQkJMDU\n1BQxMTHw8/OTXBOLxfD394ezszMOHjwIALh37x7GjRuHrKwsuLi44KeffpK5D6qpPgVy9Add7aO6\nqpcucv8+M2jp6cDJk0ByMjNYly4BLi7a1s5wkaeP1mugxGIxunTpgiNHjsDJyQk9evTA7t27Jekc\nACA+Ph6bNm1CfHw8zp49i7lz5yIlJUVy/fPPP8eff/6JkpISHDhwAACwaNEi2NjYYNGiRVi9ejXu\n37+PVatWKXQDHI420dU+qqt66RqlpcCJE8CRI0BKCvDoESASAY8fs+nC8nL2uXoc5cePZbdlagpU\n+TLKSsMAACAASURBVIJV8wlDXft6zc0BWVk5SkoAWf86CwvZ7T98KLu8paV0OUXLl5YCu3cDY8bI\nvg9FUXqKr3pIFgCSkCzVDVRdoY7s7OwkoY4++OADfP7551J1Tpw4AYBFBQ4KCpJpoDgcDkeVlJcD\n584xg3TkCJCWBvToAQQHA2vWAFZWbGqv5mFi8vzLu6bBqfqOrTJQ1b9ziZhBqFkWkDY41Skulq27\nlVXt9gHgWfb5WtRlcBpqvyYPHgDPtt5pHK2EOqoyYADLPNtQJtemjlgMXL/OBtPFi+wJy9pa+rCy\nYj9NTdlgatbs+c+q3wUC9lQoFj//Wf33ysrnR83PRLUPoPZgFIuBp0+BJ0+YzGe5C6UoLGRHzfbs\n7NhRk4ICdtSUZ2cHODrKLl9tqx0AQChkaw26QkNT5/v378dHH30EIyMjGBkZYe3atRgwYIBcdTmy\nuXQJeOUVwNmZGaQPPgD69q17baouTE0bV97SsnHlrawaV76xUeLUXV6V1GugBLLMqQxqvqYRSYc6\nSk5OrldGfXKWL18u+T0oKAhBQUFy6aTP5OYC8fHMIKWlAX//zZ5g/PzY4erKnoKKi4HMzOe/378v\nPTVR/WdFBTM0VQbL2Jgd1X83NmZTDlVH1ecqwwYAL7zAPlcdVfpmZT03ZlV127dnR03y8thR/d8u\nEAD29rINTn7+cwNVHXt72U92ssp7eqrGQCUnJ9fbn+VBLBbj3XfflZo6Hz58uNTMRHBwMF5/pvDf\nf/+NkSNH4tatW3LVbYrMns2moF5+Wfb1khJg7Fjg88+BGimcODpMvQZKmVBHe/bswYEDBxAfH48n\nT57g4cOHCA0NxY4dO2BnZ4eCggLY29sjPz8fbdu2rVOH6gaqKZCbC/TuzZ7sevYExo8HfHwa/1Sl\nLOXlQEICEBMDHD/O3owiI9lTZ00ePmRz9GZmQIsWsqcJDIWaD0mKRLSWZ+q8rmjm8tRtahQUALGx\nwMcfy75OBMycycYUN076hVZCHQ0fPhzff/89AOD777/HiBEj1HFvesfDh0BICDBrFrBzJzB3Lnsi\n1LRx+usvNg2ydi0wbBibXnzwQLZxAtgUho0N0LKlYRsnVVHXtHhN9u3bB3d3dwwdOhQbNmxoVN2m\nxDffsLejVq1kX4+OZtN7z/6EHD1CK6GOFi9ejLFjxyI6OlriZt7UEYmAN95g+zC0vaTQpQvwxx9A\np07a1cNQkXfqfMSIERgxYgROnjyJKVOm4Nq1a42S0xSmx0UiYMsW4NdfZV+/dAlYsoS5jzd27Yij\nWhSZHueRJHQAImDqVLaG9MsvbF2Iox8o0kdTUlKwfPlyJCYmAgCioqJgZGRUr7ODm5sbUlNTcfPm\nTbnqNpWx8+OPwP/+x/Yu1aSkhG24/fBDPrWni8jTR+ud4uNohmXLgKtX2V4DTRqnxETgyy81J4/D\nUCaauTx1mxIXLwJz5tQ+z9edDAP+rK5lvv0W2LULOH268e6uikLEvJnWrQN+/lkzMjnPUSaaeV11\nmypRUbLPR0eztdQ6Us1x9IWGoskmJCRQly5dSCgU0qpVq2SWmT17NgmFQvL29qYLFy4QEdHjx4+p\nZ8+e5OPjQ+7u7rR48WJJ+WXLlpGTkxP5+vqSr68vJSQkyGxXDvX0msOHiezsiG7c0JzMx4+JwsKI\nfH2JsrI0J9dQ0dU+qqt6aYJLl4hsbIiuXNG2Jpz6kKeP1luioqKC3NzcKCMjg0QiEfn4+NCVGv/1\nw4cP09ChQ4mIKCUlhQICAiTXHj16RERE5eXlFBAQQH/88QcRES1fvpzWr1+vkhvQV86fZ4Po9GnN\nyczPJ3rpJaLRo4lKSzUn15DR1T6qq3qpm8ePibp0Ifr+e21rwmkIefpovWtQ1fdcmJiYSPZcVKeu\nUEcAYPrMbUYkEkEsFqNVNT9QagILuPUxZw6bYuvVS3MyxWJg1Ci2sKyp6UQOR5MkJQFt2wKhodrW\nhKMK6jVQ8uy5kFXm9u3bANiOeV9fX9jZ2aF///7wqJaMZePGjfDx8UF4eDiK6woOZaBcusQiL0ya\npFm5Tk7AwoWyA1RyOIbAvn1suwbHMFBLqKOqesbGxrh48SIePHiAwYMHIzk5GUFBQZg1axY++ugj\nAMDSpUuxYMECREdHy2zbEPdybN0KTJ/O3cn1EVWEOuIox61bwNdfA198IX2+ogI4eBB49tXCMQDU\nFuqoOlZWVhg2bBjOnz+PoKAgqdBG06dPx2uvvVanDoYW6qgqdP2lS+qV8+QJi8LM35ZUiypCHXGU\nIyND9vg5fZpFQOE5nAwHtYQ6srOzw3///SeZunv8+DF+++03SSLD/Gqhpvfu3QsvLy+V3pQuExfH\nwhfVsPMqJS+PyeABOjiGyJ07sqPe79sH8KhphoXaQh3l5+cjLCwMlZWVqKysxJQpU/DKK68AACIj\nI3Hx4kUIBAJ07NhR0l5TYMsW4NNP1df+n3+yQTpzJjBunPrkcJSjoZQZO3fuxJo1a0BEsLCwwP/+\n9z94e3sDAFxcXGBpaQljY2OYmJggtYlt9pFloIiA/ftZJBaOAaFuV0Jl0HH1Gs25c0QuLkRiserb\n/u47onffZa7r/+//qb59jmwU6aPybN84ffo0FRcXExHbi1h9+4aLiwsVFRWpXC99YeFCoqgo6XOX\nLrGxVVmpHZ04jUeePspXKDTIli3AW28pti509SqLcn7kiOzrzZsDHTuy1Bjci0m3kWf7Rq9evWD1\nLIx9QECAxDO2CmrC2zRkvUFVTe/xaPqGBfcj0xAPHgB79gCNCUhdWcni5X31FQvbEhHBEu/Jgscb\n0x/kyVRdnejoaISEhEg+CwQCBAcHw9jYGBEREZgxY4Za9dU13nsPsLWVPrdvH7B+vXb04aiPBg2U\nPOml58yZg4SEBJiamiImJgZ+fn548uQJ+vXrh6dPn0IkEuH1119H1LPAWffu3cO4ceOQlZUlSbdh\nrc28whogNhYYNEj24q4srlwBRo5kG2rnzmXz6y1aqFdHjmaQd/sGABw/fhzbtm3DqVOnJOdOnToF\nBwcHFBYWYuDAgejatSsCAwNr1TXELRoAS+BZnexstq+wb1/t6MORD4W2aNQ3/6euUEcLFy6k1atX\nExHRqlWrKDIyUuE5Sn2gspLI05Po2DH56zx6RHTiBJ9T13UU6aNnzpyhwYMHSz6vXLlSZpzLv/76\ni9zc3OjmzZt1trV8+XJat26dSvTSVzZsYPElOfqFPH1UK6GOqtcJCwvDvn37GmdV9YzTp1litcY8\nwJqaMldxPqdueMizfSM7OxujRo1CbGwshEKh5HxZWRlKSkoAAI8ePUJSUlKT2qYhi/37uXu5oVLv\nFJ88c+V1hTqys7ODWCzGiy++iPT0dMyaNUsS6ujOnTuwezbXZWdnJzFohsqWLcztmxsbDiDf9o2P\nP/4Y9+/fx6xZswBA4k5eUFCAUaNGAQAqKiowadIkDBo0SGv3om3u32cpNZrwn8Cg0Uqoo5plGzMn\nr28UFbHwK199pW1NOLrE0KFDMXToUKlzERERkt+/++47fPfdd7Xqubq64uLFi2rXT184fBgYMICn\nczdUNBrq6M8//0RQUBDs7OxQUFAAe3t75OfnS4U+qom+L/R+/z0wfDjQurW2NeGoAh6LT7ucO8ci\npKxdyz7z6BEGTn0LVOXl5eTq6koZGRn09OnTBp0kzpw5I3GSKCwspPv37xMRUVlZGQUGBtKRI0eI\niDlJVC0KR0VFGayTRGUlUadORKdOyV/nu++I9u9Xn04c1aKrfVRX9VKW3buJxoxhv5eVEVlaEhUW\nalcnjmLI00e1Eupo8eLFGDt2LKKjoyVu5obI8ePMNbwxOZ8OHgQmT1afThyOPlN9k+7Ro4CvL2Bj\no12dOOpD8MyS6SQCgUCvd8yPHw8EBgLvvCN/HVdXtjm3c2f16cVRHbraR3VVL2V5/3223vThh8CM\nGYCHBzB/vra14iiCPH2UhzpSE6WlQEJC4wK2PnzInhDd3NSnF4ejz1S9QYnFwIEDwOuva1sjjjrh\nBkpNHDwI9OnTuOmHf/4BunX7/+3de3CU1fkH8O9y8QoIImyAACGbOyHJ0sRQbH4VyeaCEAsiFIQi\nBJqmODQGcScdQWSGEKzAaDIYsIBBMaCtVMcmkQLmghBQ2DRWEIIuRWQ3QC7IreTC8/vjJWsum81e\n3nf33d3nM+MMSd7znrPyHs7uyTnfA/TuLV27mDyUlJQgJCQEgYGBWL9+fZef79q1C5GRkYiIiMBj\njz2G6nYHIPVU1pO1DVCVlYCPjzDjwDwXD1AS2b1bmOKzRXU1cPdEBebBWltb8fzzz6OkpAQnT55E\nYWEhTp061eEaf39/lJeXo7q6GitXrsTvf/97q8t6spwcIdKIV+95hx4HKGverS1btgyBgYGIjIyE\nTqcDICxJnzRpEsaOHYvw8HC8+eabputXr14NX19fqNVqqNVqlJSUiPRy5KGhASgttb0DPfUUkJUl\nSZOYjDiSZm5NWU8WHg4MGgTs3csDlDewuIqv7d3a/v37MWLECMTExCAlJQWhoaGma4qKinD27FnU\n1NTg6NGjSE9PR2VlJfr27YtNmzYhKioK169fxy9+8QskJCQgJCQECoUCmZmZyMzMlPwFusLevUB8\nPDBggG3lhg2Tpj1MXhxJM7e1rCf69lshOiwqytUtYVKzOEC1f7cGwPRurf0A1V0Wn4+PD3x8fAAA\n/fr1Q2hoKH788UeEhIQA8OzzbHbvFlYYMWaOI2nmtpR1903u3dm/X4g28uAAGo9kzyZ3SbP42pw7\ndw46nQ6xsbGm7+Xm5mLnzp2Ijo7Ghg0bPOa4jUuXhGwwD8+/ZQ6wJqEFAKqrq7FkyRKUlJSYgpat\nLQt0HKA8yYEDtq2OZfLQ+U3Sq6++2mMZSbP4AOD69euYOXMm3njjDfTr1w8AkJ6ejlWrVgEAVq5c\nieXLl2Pbtm1m7+1u7wI//BB48knOBvNUYkQdtU8zHz58OPbs2YPCwsIO13SXZm5NWU/W0iL8fvdu\nVgDzcJJm8TU3N+Ppp5/GvHnz8Jt2v9Fsn723ePFiTJs2rds2uNu7wN27ATNnOjIPYc+7wM4cSTPv\nrqw3+OwzoLAQGDXK+oM/mZuzlIPkSBbfnTt3aP78+ZSRkdHlvhcvXjT9eePGjTRnzhy7s5rk5Px5\noocfJrp92/ayqalEn30mfpuYtOT6jMq1XY7IyyN69FEiM/+kMDdkzTMqWRbfF198gffeew8RERFQ\nq9UAgHXr1iEpKQlarRZVVVVQKBQYM2aM6X7u7oMPhGPa77nH9rKHDgEZGeK3iTFPUVsr/I73bqQn\n8wKcxSei6GhhI2F8vG3lbt4EBg8Woo769pWmbUwacn1G5douR6SmArt2AZcvA/37u7o1zFGcxedE\nNTXAhQu2Heve5ptvgOBgHpwYs+TbbwE/Px6cvAkPUCLZswd45hmgj8VJU/M44oixnp07Z9vRNcz9\nuSTqqL6+HhqNBkFBQUhISEBjY6NIL8d17Mnea/Of/wCRkeK2hzFP8/DDwJw5rm4FcypLKyhaWlpI\npVKRXq+npqamHlfxVVZWmlbxGQwG0ul0RER07do1CgoKolOnThGRcKLu+vXriYgoJyfH7U/Ura4m\nGjmSqLXVvvLNzcLpoMz92PuMFhcXU3BwMAUEBJhOl27v1KlTNGHCBLr33nvp9ddf7/Cz0aNH07hx\n4ygqKopiYmJEbZdc1dcT9e9v3wpZJk/WPKMWP0FZE0xpKeoo6m5YVvuoo85lFixYgH+4eezC7t3C\nzvZedk6Y9ukD3H+/uG1i8mVNIvngwYORm5uLF198sUt5hUKB0tJS6HQ6HDt2zFnNdqnPPwcmTrRv\nhSxzXxb/STUXY9Q2yFi6pi15uU3nqKPa2lpTFJJSqURtba1jr8KFiByb3mPex5o3fkOGDEF0dDT6\ndrNyhjxshV5PDhzg5eXeyCVRR52vtVSP3KOOvvpKOGBw/HhXt4Q5gxhRR44mkisUCsTHx6N3795I\nS0vDEi9IJj5wQEiRYN7FJVFHSqUSRqMRPj4+MBgMHaKPOpN71FFhofDpiZOVvYMYUUe2JJKb88UX\nX2DYsGG4fPkyNBoNQkJCEBcX59A95ezCBeDKFV5I5I0sDlDWBFOmpKQgLy8Pv/3tb1FZWYmBAwdC\nqVSCiJCamoqwsDBkdIpISElJQUFBAbRaLQoKCjoMXu7kxg3g3XeBI0fsv0djI/DQQzzAeRNbEsnN\nGXb34LAhQ4Zg+vTpOHbsmNkBSu6zD9Y6cABQqYC1a4GVK13dGmYvu2YfelpFUVRUREFBQaRSqSg7\nO5uIiPLz8yk/P990zdKlS0mlUlFERAQdP36ciIgqKipIoVBQZGQkRUVFUVRUFBUXFxMRUV1dHU2e\nPJkCAwNJo9FQQ0OD3as8XCk3l2jGDMfuMW4c0d3/ZcwN2fOMWpNx2eaVV17psIrvxo0b9NNPPxER\n0fXr12nixIn0mZkQR7n3HVvMn080dSrRyy+7uiVMTNY8oxx1ZKfWViAoSPgENXGiffdoahI+PTU0\nAPfdJ277mHPY+4wWFxcjIyPDlHGZlZXVIePSaDQiJiYGP/30E3r16oX+/fvj5MmTuHTpEmbMmAEA\naGlpwbPPPousrCzR2iU3RMCIEcCkScIm3eefd3WLmFiseUZ5gLLT3/8OvP66Y9N71dXC769OnhSv\nXcy55PqMyrVdtjp1CkhKAmJihK0czzzj6hYxsXAWn4Q2bADMbFGxCUccMWbZgQNC+HJtLWBhLRXz\nUJJFHQHAokWLoFQqMW7cuA7Xr169Gr6+vlCr1VCr1SgpKXHwZTjX4cNCh3F0bQcPUIxZtn+/sP+p\ntpYPKfRGFgcoa3a8FxUV4ezZs6ipqcHWrVtNJ4ACwMKFC80OPgqFApmZmdDpdNDpdEhKShLp5TjH\nhg3ACy8I+58ccf06759irDstLUBZGfDEE8C//iWs5GPeRZKoI6PRCACIi4vDoEGDzN7bXefHv/sO\nKC8HFi50/F6bNwvz64yxrk6cEBZI+PgAo0fzcTTeSJKoo87XmJObm4vIyEikpqa6VZr5pk3AkiXA\ngw+6uiWMebb9+20//JN5FsmjjsxJT0/HqlWrAAArV67E8uXLsW3bNrPXymmzYX098P77wgGDzDuJ\nEXXErHPgANBpjz/zNpY2SR05coQSExNNX2dnZ3c5GiAtLY0KCwtNXwcHB5PRaDR9rdfrKTw8vNs6\nLP28h+Y53dq1RM895+pWMDmx9xl15LiNnso60i65uHmT6ME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       "text": [
        "<matplotlib.figure.Figure at 0x108d83290>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Next we want to choose our regularization strength. Remember that from a Bayesian point of view, the regularization strength respresents our prior belief on the variance of the feature weights. If we assume a lower prior variance, we are effectively not allowing the weights to deviate too far from zero. Whether we take this point of view or not, the optimal strength is largely an empirical question. It is generally better to test rather than to assume what the optimal strength should be. <br><br>\n",
      "\n",
      "The various implementations of learning algorithms differ in how they treat the regularization parameter. Many implementations formulate the loss function as such:<br><br>\n",
      "\n",
      "<center>$\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n \\mathbb{L}(f(x_i),y_i)+\\lambda R(W)$\n",
      "</center><br><br>\n",
      "In the above, the parameter $\\lambda$ controls how much of the loss function is determined by the regularization function. Other implementations view it like this:<br><br>\n",
      "<center>\n",
      "$\\underset{f \\in \\mathbb{F}} {\\mathrm{argmin}} \\frac{1}{n} \\sum\\limits_{i=1}^n C*\\mathbb{L}(f(x_i),y_i)+R(W)$\n",
      "</center><br><br>\n",
      "In the latter formulation the parameter controls how much the training error influences the total loss. It doesn't really matter which of the above is used (one is just a scalar multuple of the other), but it is helpful to know which system your implementation uses. I.e., it is useful to know if increasing the regularization parameter <i>increases</i> or <i>decreases</i> the amount of regularization being done. In SKLearn, the latter formulation is used.<br><br>\n",
      "\n",
      "Here we take the above example and use cross validation to find an optimal regularization strength.\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import KFold\n",
      "from sklearn.metrics import roc_auc_score\n",
      "\n",
      "\n",
      "def LRValAUC(X_tr, Y_tr, k, cs):\n",
      "    '''\n",
      "    Perform k-fold cross validation on logistic regression, varies C and penalty Type (L1 or L2),\n",
      "    returns a dictionary where key=c,value=[auc-c1, auc-c2, ...auc-ck].\n",
      "    '''\n",
      "    cv = KFold(n=X_tr.shape[0], n_folds = k)\n",
      "    aucs = {}\n",
      "\n",
      "    for train_index, test_index in cv:\n",
      "        X_tr_f = X_tr.iloc[train_index]\n",
      "        X_va_f = X_tr.iloc[test_index]\n",
      "        Y_tr_f = Y_tr.iloc[train_index]\n",
      "        Y_va_f = Y_tr.iloc[test_index]\n",
      "        \n",
      "        for c in cs:\n",
      "            for norm in [1,2]:\n",
      "                lr = linear_model.LogisticRegression(C=c, penalty='l{}'.format(norm))\n",
      "                lr.fit(X_tr_f,Y_tr_f)\n",
      "                met = roc_auc_score(Y_va_f, lr.predict_proba(X_va_f)[:,1])\n",
      "\n",
      "                if (aucs.has_key((c, norm))):\n",
      "                    aucs[(c, norm)].append(met)\n",
      "                else:\n",
      "                    aucs[(c, norm)] = [met]\n",
      "    \n",
      "    return aucs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xval_dict = {'e':[], 'mu':[], 'sig':[], 'norm':[]}\n",
      "k = 10\n",
      "exps = np.arange(-5,5,0.5)\n",
      "auc_cv = LRValAUC(X_train, Y_train, k, [10**i for i in exps])\n",
      "for i in exps:\n",
      "    for norm in [1, 2]:\n",
      "        xval_dict['e'].append(i)\n",
      "        xval_dict['norm'].append(norm)\n",
      "        xval_dict['mu'].append(np.array(auc_cv[(10**i, norm)]).mean())\n",
      "        xval_dict['sig'].append(np.sqrt(np.array(auc_cv[(10**i, norm)]).var()))\n",
      "\n",
      "xvals = pd.DataFrame(xval_dict)\n",
      "xvals['low'] = xvals['mu']-xvals['sig']/np.sqrt(k)\n",
      "xvals['up'] = xvals['mu']+xvals['sig']/np.sqrt(k)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Now lets plot the cross-validated error as a function of C, with a separate series for the different penalization types\n",
      "\n",
      "\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.clf()\n",
      "\n",
      "norm = 1\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'r')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'r--', label='L1')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'r+')\n",
      "\n",
      "norm = 2\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'b')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'b--', label='L2')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'b+')\n",
      "\n",
      "plt.legend(loc=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "<matplotlib.legend.Legend at 0x10df969d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vXoiiiKamJhw4cABTpkzxqS4FIbsd+I//AOLilI6EiPrJYwteo9GgqKgI2dnZ\nEEURubm5MBgMKC4uBgDk5+dDr9djwYIFmDZtGsLCwpCXl4cpU6YAQI91KchxFitRyBAkSZIUDUAQ\noHAI1NW8ecC6dUBWltKREJEHvuROzmQlV2zBE4UMJnhyxXVoiEIGEzy5qqsD6uuVjoKIAoAJnjo1\nNclj4F95RelIiPwSExMDQRBCcouJienzz8XjKBoaYmw2ICqKXTSkOg0NDSE7WMOfSaPdsQVPnex2\neaExXmQlCglM8NTJZpMXGmMLnigkMMFTJ7tdfmQLnigkMMFTp451aK68UulIiCgAmOCpk90OLF0K\ntC81QUTqxgRPnTiLlSigdDoddu/e7fJaa2srVq5cicTERISFheGDDz4YsOMzwVMnzmIlCqiOsezd\nzZkzB3/84x8xceLEfg2D9Ibj4KkTW/BEAy4iIgI//vGPAQDh4eEDeiy24KkTW/BEIYUJnjrV1gLf\nfad0FESBV1AACIL71tvd5Hoqr8I7zzHBUyebDdi6VekoiAKvoACQJPfNU4L3tWwQY4In2aVLgMMh\nj4MnopDAi6wks9vlhcbGjVM6EqKQ0tLSgkuXLjn3IyIi4HA4nIujNTc349KlS7jssssCfmyvLfjy\n8nLo9XqkpKSgsLDQ7X2z2YxRo0bBaDTCaDTiqaeecr6n0+kwbdo0GI1GzJgxI7CRU2DZbPJCY7zI\nShRQixYtQlRUlHMrKCiAXq9HVFQUvvvuO2RnZ2PEiBE4fvx4wI/tsQUviiLWrl2LiooKxMfHIzMz\nE4sXL3a7efYNN9yAv/71r271BUGA2Wzu13rGNEjsdkCjYYInCqCjR4/2+HrXhvBA8tiCr6ysRHJy\nMnQ6HSIiIpCTk4OysjK3cp7WYQ7VNZpDTscY+MmTlY6EiALEY4K3Wq1ISEhw7mu1WlitVpcygiDg\no48+Qnp6OhYtWoTDhw+7vDdv3jxkZGTg1VdfDXDoFFB2OzB7NjBzptKREFGAeOyi8WUK7TXXXAOL\nxYKoqCjs2LEDS5cuxddffw0A2LdvH2JjY1FXV4esrCzo9XrMnj07MJFTYNls7J4hCjEeE3x8fDws\nFotz32KxQKvVupSJjo52Pl+4cCHuv/9+1NfXIyYmBrGxsQCAcePGYdmyZaisrOwxwRd0GV9qMplg\nMpn6ci7UH3Y7oNMpHQUR9cJsNsNsNvtVR5A8dJI7HA6kpqZi9+7diIuLw4wZM1BSUuJykbW2thbj\nx4+HIAhNVnY9AAAJTklEQVSorKzELbfcgpqaGjQ1NUEURURHR+PChQuYP38+nnjiCcyfP981AEFg\nP30wuP12IDsbuOMOpSMh8lso55Hezs2Xc/bYgtdoNCgqKkJ2djZEUURubi4MBgOKi4sBAPn5+Xj7\n7bexZcsWaDQaREVFYfv27QCAU6dOYfny5QDkL4rVq1e7JXcKInY7FxojCjEeW/CDEkAIf/OqSnIy\n8PDDwP33Kx0Jkd9COY/0pwXPBE+ykSMBvR745BOlIyHyWyjnkf4keK5FQ7JLl4AJE5SOgogCiAl+\nKDOb5RXyfvlLQBTlpYILCuTXiajferpl3/79+5GVlYUxY8Zg/PjxuOWWW3Dq1KkBOT4T/FBmMskJ\n/f77gYgIYP58eZ/DVIkCoqdb9jU2NuJHP/oRjh07hmPHjiE6Ohr33HPPgByfq0kS16EhGkQLFixw\n2X/ggQcGbO4PW/Akz2KNiQGmT1c6EqIhZ8+ePUhLSxuQz2aCJ7kFf+21chcNUQgK1jv2ffHFF3jq\nqafw3HPPBf7DwS4aArgODYW8ggL/ErS/5fvim2++waJFi/DSSy9h1qxZA3IMtuCpc6lgIhoUx44d\nQ1ZWFh5//HGsXr16wI7DFjzJXTTx8UpHQRSSut+yr7a2Fj/4wQ+wdu1a3HfffQN6bM5kHera2oCF\nC4FVq4C77lI6GqI+CdY8kpiYiGPHjrm9LggCoqKiXPbPnj3b42cM2GJjFOIcDiA3FzhzBghjbx1R\noPV2y77Bwt/qoerSJWDlSuD0aWDLFmCQ7hFJRIOHCX4oOncOuOkmYPhwoKwMaGriKBqiEMQEP9TY\n7cCNNwJJScC2bcCwYVwLnihEMcEPJVYrMGcOMHcuUFwMhIfLr9vtbMEThSAm+KHiyBFg9mzgzjuB\nwkJ5al4HjoMnCkkcRTMUfPGFPBTy8ceB/Hz391NS5Ds6EVFI4Tj4UPfxx8DSpcBLLwG33qp0NEQD\nIiYmBg0NDUqHMSCuuOIK1NfXu70ekDs6lZeXQ6/XIyUlBYWFhW7vm81mjBo1CkajEUajEU8//bTP\ndWmA/e//AkuWAG+8weROIa2+vh6SJIXk1lNy95nkgcPhkJKSkqSjR49KLS0tUnp6unT48GGXMu+/\n/750880396lu+18PnkJQvffff1+ZA7/9tiSNGydJH34o7zc3S9Lf/iZJd94pSQUFATuMYuc3SEL5\n/EL53CQp9M/Pl9zpsQVfWVmJ5ORk6HQ6REREICcnB2VlZT19SfS57qDr6+3o+ljP/MYbg3o8mM3A\n1q3Agw8C770HnD8PrFkDxMYCGzcC3/secO+9ffvsHg/XxzhVIpTPL5TPDQj98/OFxwRvtVqRkJDg\n3NdqtbBarS5lBEHARx99hPT0dCxatAiHDx/2ua4iBjnBo6ZmcI+3aRPw5JNy/dhYYMMGYOpU4PPP\ngb17gR//mAuLEQ0RHkfRdL+XYE+uueYaWCwWREVFYceOHVi6dCm+/vrrgAUYUOXlwK9/LU/N7276\ndHnST3effw60tMgt4a71vJXvUF8PTJjge/kOI0cCBw/6Xn76dKC1VR4x89lnQMeX68cfu5cloqHB\nU//Nxx9/LGVnZzv3N27cKD3zzDMe+3x0Op1kt9t9rpuUlCQB4MaNGzdufmxJSUle++A9tuAzMjJQ\nXV2NmpoaxMXFobS0FCUlJS5lamtrMX78eAiCgMrKSkiShJiYGJ/qAvJdTYiIKPA8JniNRoOioiJk\nZ2dDFEXk5ubCYDCguLgYAJCfn4+3334bW7ZsgUajQVRUFLZv3+6xLhERDQ7FJzoREdHACJq1aF5+\n+WUYDAakpaVh3bp1SoczIF544QWEhYX1b+JCkHnkkUdgMBiQnp6O5cuX48yZM0qHFBChPEnPYrFg\n7ty5uPrqq5GWloaXXnpJ6ZAGhCiKMBqNuPnmm5UOJaAaGxuxcuVKGAwGTJkyBfv37++9sNde+kHw\nj3/8Q5o3b57U0tIiSZIknT59WuGIAu/48eNSdna28yJ0qNi1a5ckiqIkSZK0bt06ad26dQpH1H++\nTtJTq5MnT0qfffaZJEmSdO7cOWny5MkhdX4dXnjhBWnVqlU9TsRUszvvvFN67bXXJEmSpNbWVqmx\nsbHXskHRgt+yZQvWr1+PiIgIAMC4ceMUjijwHn74YTz77LNKhxFwWVlZCGu/3d+1116LEydOKBxR\n/wXtJL0AmThxIqZPnw4AGDlyJAwGA7777juFowqsEydO4O9//zvuvffekFrr6syZM/jwww+xZs0a\nAPK1zlGjRvVaPigSfHV1Nfbs2YPrrrsOJpMJn3zyidIhBVRZWRm0Wi2mTZumdCgDauvWrVi0aJHS\nYfRb0E7SGwA1NTX47LPPcO211yodSkD95Cc/wXPPPedsfISKo0ePYty4cbjnnntwzTXXIC8vD01N\nTb2WH7TlgrOysnDq1Cm313/1q1/B4XCgoaEB+/fvxz//+U/ccsst+PbbbwcrtIDwdH6bNm3Crl27\nnK+prUXR27lt3LjR2b/5q1/9CsOGDcOqVasGO7yA82WCXyg4f/48Vq5ciRdffBEjR45UOpyAee+9\n9zB+/HgYjcaQW67A4XDg008/RVFRETIzM/HQQw/hmWeewZNPPtlzhcHpNfJswYIFktlsdu4nJSVJ\nNptNwYgC51//+pc0fvx4SafTSTqdTtJoNNJVV10l1dbWKh1awLz++uvS97//fenixYtKhxIQfZng\npzYtLS3S/Pnzpd/85jdKhxJw69evl7RaraTT6aSJEydKUVFR0h133KF0WAFx8uRJSafTOfc//PBD\n6aabbuq1fFAk+N/97nfS448/LkmSJFVVVUkJCQkKRzRwQu0i644dO6QpU6ZIdXV1SocSMK2trdKk\nSZOko0ePSs3NzSF3kbWtrU264447pIceekjpUAac2WyWfvjDHyodRkDNnj1bqqqqkiRJkp544gnp\n5z//ea9lg+KOTmvWrMGaNWswdepUDBs2DH/4wx+UDmnAhNqf/w8++CBaWlqQlZUFAJg5cyZ++9vf\nKhxV/4T6JL19+/bhj3/8I6ZNmwaj0QgA2LRpExYsWKBwZAMj1H7nXn75ZaxevRotLS1ISkrC66+/\n3mtZTnQiIgpRoXWJmYiInJjgiYhCFBM8EVGIYoInIgpRTPBERCGKCZ6IKEQxwRMRhSgmeCKiEPX/\nAUVkakVvtB07AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ded3f90>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>This is interesting. We can see that the AUC for $L1$ is $0.5$ where the regularization is stronger, but for $L2$ the AUC is pretty good in the same region. This is because all of the feature weights in $L1$ are zero for that range. In $L2$ they'll likely be small, but they won't be zero. This means they'll still be able to rank the instances.\n",
      "</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "norm = 1\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'r')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'r--', label='L1')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'r+')\n",
      "\n",
      "norm = 2\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['mu'][(xvals['norm']==norm)], 'b')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['low'][(xvals['norm']==norm)], 'b--', label='L2')\n",
      "plt.plot(xvals['e'][(xvals['norm']==norm)], xvals['up'][(xvals['norm']==norm)], 'b+')\n",
      "\n",
      "plt.legend(loc=4)\n",
      "plt.ylim([0.82, 0.89])\n",
      "\n",
      "plt.title('X-Val AUC by Regularization Weight')\n",
      "plt.xlabel('Regularization weight C (higher C is less regularization)')\n",
      "plt.ylabel('X-Val AUC')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "<matplotlib.text.Text at 0x10e053910>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pknORX9zFwaFkZR0cCqw8iAqqOOfOAp/nkFbIQJ+srKxiBbB161YmT56MXq/n\nmWeeYdq0aSafJycnM3LkSC5fvkx2djZTp05lzJgxANy8eZNnnnmGEydOoNPp+Oyzz+jcuXOx9isK\ndvEibNig3Tc9c0abHWLRIujRQztZWFOlStojF+rUKaDA+k3QKwo+mVLsbeZcreckirt3//q5Rg3t\nhF+tWtnEL0SFpgrw+OOPq82bN5u9/+2336o+ffoUtJpRdna28vLyUrGxsSozM1P5+fmpkydPmpSZ\nNWuWev3115VSSl29elU5OzurrKwspZRSo0ePVp9++qlSSqmsrCx18+ZNs30UEr7IJSlJqQ8/VKp7\nd6Xq1lUqNFSpLVuUysy0dWRFGDVKqaVLbR2FEBVOcc6dBdYc3nvvPZ544gk2bNhA+/btUUpx+PBh\n9u3bx+bNm4tMOgcPHsTb2xtPT08Ahg4dysaNG/H19TWWady4MceOHQMgNTUVFxcXHB0dSUlJYffu\n3axcuRIAR0dHateufe8Z8D50/Tr8739ak9HBg9pA3ldegd69y8lTMvV6bT6lOXNsHYkQ96UCb909\n9NBDHDt2jO7duxMbG0t8fDw9evTg+PHjtGjRosgNJyYm4uHhYXzt7u5OYmKiSZkJEyZw4sQJXF1d\n8fPzY8mSJQDExsZSv359xo4dS7t27ZgwYQJ37ty512O8r+zcqY0Xa9pUO7c++6zWlPTFF9pA3nKR\nGEDLaI0awYMP2joSIe5LhT5DukqVKowbN+6eNqwrxt2suXPn4u/vT3R0NGfPniUkJISjR4+SnZ3N\nL7/8QkREBB06dGDy5MnMnz+ft956y2wb4bnmswgKCiLoPh2ldvs2TJ+ujRWbO1cbh1Wzpq2jKgV7\nGxUtRDkWHR1NdAmnlS4wOdSoUcPkBK/T6ahXrx7BwcEsWLAAl5xuHAVwc3MjISHB+DohIQF3d3eT\nMvv27eONN94AwMvLi6ZNmxITE4O7uzvu7u506NABgEGDBjF//vx89xMukx2xdy+MGQOdO8Px41C3\nrq0jKgObN0NEhK2jEKJCyHvhPHv27CLXKbBZ6datW6SlpRmX1NRUDh06RMuWLZk4cWKRGw4MDOTM\nmTPExcWRmZnJunXrGDBggEkZHx8foqKiAEhKSiImJoZmzZrRqFEjPDw8OH36NABRUVFmg/EEpKfD\n1KkweLDW4+jzzytIYsgZZSe904SwmUKblfJydnZmypQpBAQEFL1hR0ciIiLo3bs3er2e8ePH4+vr\ny7JlywCIHOsvAAAgAElEQVQICwtjxowZjB07Fj8/PwwGAwsXLsTZ2RmADz74gBEjRpCZmYmXlxfL\nly+/h8OruH76SasttG0Lx45pXTQrjG+/hT59tA7+QgibKPHcSllZWbRv397Yy8iW7sdBcBkZ2nMl\nPvsM3n9fe9RxhdO/Pwwfrk2DLYQoc6UaBPff//7XbAM3btxg3bp1DBo0qOyiFMX2yy8QGgpeXnD0\nKDRsaOuILCA9Xety9Wc3ZiGEbRSYHDZt2mR2Q9rFxYXJkyfTz1qPaxSANuL37bfhww/h3/+GESMq\n8NQGO3aAv7/2zAQhhM0UmBxWrFhR4Eo///yzsSeRsKzjx7XaQqNG8Ouv2kR3FZp0YRXCLhT7SXAn\nTpxg5syZeHt7F6u3kiid7GyYNw+Cg+Ef/9DOmRU+MSildWGVmqkQNldod5DY2FjWrl1LZGQklStX\nJi4ujkOHDhmnxBCWcekSDB2qddY5dOg+GiT822/aFKEtW9o6EiHuewXWHLp06cKgQYPQ6XR8/fXX\nHDp0iJo1a0pisLAdO7SnS/bqBdu23UeJAbTqUb9+FfiGihDlR4HJoWHDhqSkpJCUlMSVK1esGdN9\nyWDQpr0YPlzrqPPmm9afQtvmNm+W+w1C2IlCxzncvHmTr776irVr1/LHH39w/fp1vv/+ezp16mTN\nGAtUUcY5XLsGo0fDzZvaLKp5Zhm5P1y7ps0WeOWK9pQeIYTFlOpJcHklJSWxfv16IiMjSUhIMJk3\nyVYqQnI4eFAbyDZokHYD2hJPXCsX1qyB9eth40ZbRyJEhVemySG3uLg4u7j3UJ6Tg1KwdCm89RYs\nWwZ/+5utI7Kx4cOhZ0+YMKFst6vXw/792iPhHn20bLctRDllseRgL8prckhL086BMTHw5ZfaiOf7\nWnY2NGigDeooi/666ekQFQVffw2bNoGrK7zwAowfX/ptC1EBFOfcWexxDqJs/PYbdOgAtWrBvn2S\nGADti/D0LJvEEB+vjRhcvBjatNFmKDxypODEcPNm6fcpRAUk015a0apV2qM6Fy/WbkCLP+V0YS0L\nTZrAuXNQxPNGAK3GEhAA7dppv5iuXcsmBiEqgAKTwwsvvFDgSjqdjvfff98iAVVEd+/Ciy9q88n9\n+KN2QSty2bxZm2a2OC5cgOXLtSaj1ash1zPJAW2MRHESA2ijDI8fhxUrYNQorWlryhTtBpBMFy7u\ncwX+BbRv39448V7etqniPAJUaGJj4e9/h+bNtdHO5frRnZYQGwtXr2ptbcUxYYL28Ip//1v7Ukur\nRg2YNAmee07rKbV4sTYS8cMPS79tIcoxuSFtQQcOwMCB8Npr8NJLMvA3XxERWtYsZKJHo4wMLTGc\nP2/ZR96lp0PVqpbbvhA2VqrnOeS4cuUKCxcu5OTJk6Snpxs3/OOPP5ZNlBXUhg3w/PPaOU/mkSvE\nt98WvxfR/v3avEuWfhZqQYnhww+1/T/88H08IEXcL4rsrTRixAh8fHw4d+4c4eHheHp6EhgYaI3Y\nyiWlYP587f7mDz9IYijUrVuwZw+EhBSvfEqK9jALW0lNhVdf1Z6yNGKENpw9JcV28QhhQUU2K7Vr\n145ffvmFtm3bGh8NGhgYyKFDh6wSYGHsrVkpK0truj58WLvHWuGn2C6tjRu1Z51u327rSEomMVH7\nBX/zDZw6BX/8oc0mK0Q5USbNSpUrVwagUaNGbN68GVdXV27cuFE2EVYgN29qU2BUrQq7d2v3OUUR\nyrILqzW5uUFYmLZkZ+efGDIytNkU5d6FKKcKrDlkZWXh5OTE5s2beeSRR0hISOCFF14gNTWV8PBw\nBgwYYO1YzdhLzSE2VjvHhYRonWjuu9lU74VS2gyDO3bAQw/ZOpqyFxkJY8dqox09PLTxFx4e2n+S\n/v1tHZ24z5Vq+owGDRowYMAAhg0bRnBwsF12X7WH5PDTT1q3+OnTtRkaRDH9+qs24+CZM7aOxHIM\nBm2W2YQErYdVQgI0awb5XVh9/bU28aCHh3bDvXp1rfrp768N1MsrM1Pr/iY3xsU9KFVySE5O5ssv\nv2TdunWcPn2aQYMGMWzYMDp37myRYO+FrZPDl19q9xiWL5fHEJTY229r4xvee8/WkViNUlprU6VK\n+ZzTz57l18jfOR+Tjv5WOvq7mRjSMzG0bsvDrz1MkyZ5yi9ezPevbecPXXMMD1TFULkKegcn9F0e\nYcDiHrRokaf855/z+Zw4jqV7o8cRvc4Rva4SBq+HmLDYxzz/fPUVS99K5tANbxQ6DDigAOXehBff\nbUrHjnnKb9zI+2/d5ND1ZgDodNrfpc7Dg3+809R8GMs33xDxrxscvtZU+2748+LTw51J7zTFrM/L\nN9/w/pwUfv6zvJG7Oy+842keT0755HzKLy6g/Fs3+flas1KVf+2dBrT5u/3XhEt1z6FevXpMnDiR\niRMncvHiRdavX8/LL7/MlStXePrpp5k7d26RAWzdupXJkyej1+t55plnmDZtmsnnycnJjBw5ksuX\nL5Odnc3UqVMZM2YMAJ6entSqVYtKlSrh5OTEwYMHi3HI1qEULFyoddHfti3/CztRhMREaNWqeGUv\nXtRuXj/3nGVj+pNS+Y9J+eYbOHZMGwZx9672b3o6TJwI+T3i5IUX4H//+6vc3btaUoiM1Ma/mPDy\n4lu8OJiiDc52qA4ONaHSNWh2CfPk8MorxNeYwslf9ThkZ6HTZ1EJA5WqVSYjI5+D6tmTGudTqX/+\nASrpDFRCTyX0ONSvQ61a+ZRv1Qqfp65Q9UpVHHQKnQ50KHSNK9GwYT7lvb1p+/gl6lxzRBm0k45C\nB64O1K+fT/lmzWjZ6xLVk/86Bel0Clx11KuXf3m/xxKpey3P+27kH49JeV3xyve5RN1ree4fuelK\nVN6laX5fZvlU7EFwaWlpfPXVV/z73//m0qVLRT4dTq/X06JFC6KionBzc6NDhw5ERkbim2u6g/Dw\ncDIyMpg3bx7Jycm0aNGCpKQkHB0dadq0KYcPH8bZ2bng4G1Qc8jK0sYvHDqkTfh5Xz6YpyyEhWlZ\ndeLEossuXw7ffw9r15ZpCJs2aVOaXLr013Lxopb0R40yL796tdY5qWpV7XlEVatqS8+e2nOK8rp8\nWfv/klOuShW5HyXsQ6l7K6Wnp7Np0ybWrl3L3r176dOnDwsWLODRYsyLf/DgQby9vY3PfRg6dCgb\nN240SQ6NGzc2do9NTU3FxcUFx1xz2tj6fkJeN2/C4MHwwAPSI6nUsrOLP39RVBTp3XuTnADJydqk\nq40bmxf74gvYskUbjpB7+ec/85/oMCtLm07Jz0/bXs5S0Bi7kSOLf3igxSlEeVXgX+fw4cP54Ycf\n6NGjByNGjGDNmjVULUG3vMTERDw8PIyv3d3d+emnn0zKTJgwgeDgYFxdXUlLS2P9+vXGz3Q6HY8+\n+iiVKlUiLCyMCWX9EJgSio+Hvn2hVy9499374wrQYNBOrpUq5T8n1Pffw3ffac/TqVLlr6vp4GDo\n0sW8fFwcJCX9We56Pe5erEfyj1qTibe3efmFC2HpUkXy+U/I/rIq9edqc+rNmAFPP21evkkTrTNQ\nrVpQu7b2b61a+ScSyKdpRwhhVGBy6N27N8uWLaNmrrPC//3f//Hss88Wa8PF6d00d+5c/P39iY6O\n5uzZs4SEhHD06FFq1qzJ3r17ady4MVevXiUkJAQfHx+6detmto3w8HDjz0FBQQQFBRUrvpJycNBm\nVg0Ls8jm7cJnn8EHH2g1pBs3tIcS1aihXXlPnWpevmpVrTnF0fGvNvXbt+HOnfy3//332j7S0yE9\n7mWqHHqAeju0Zrr8ksOoUTCkbQz1nh9C9bPHipyb6pFHtEUIYSo6Opro6OgSrVOiifcCAgL49ddf\ni1X2wIEDhIeHs3XrVgDmzZuHg4ODyU3pvn378sYbb/Dwww8D0KtXLxYsWGA2Pcfs2bOpUaMGr7zy\nimnwdtCVtTzS6/Ov+SQkaB2I6tTRltq1LVhDGjZM6+8/fHjh5d59F06fho8+slAgQtx/bPokuMDA\nQM6cOUNcXByZmZmsW7fObOCcj48PUVFRACQlJRETE0OzZs24c+cOaWlpANy+fZtt27bRRh6CUCrn\nzmm9RoOD4bHH8i/j4aE996ZZM3B2tnDTmV5fvHsOffpoVTYhhFUV+Nd5/vx5muTpP7dp0yYAdu/e\nnW8Tj8mGHR2JiIigd+/e6PV6xo8fj6+vL8uWLQMgLCyMGTNmMHbsWPz8/DAYDCxcuBBnZ2fOnTvH\nwD8bhLOzsxkxYgSPFXRGEwW6exfmzNG6YF65ol2oT54MxehPYHnZ2cXLPnkf5iOEsIoCm5WaNWtG\nWFgYU6dOpdKff8SXL19m6tSpnDp1isOHD1s10PxIs1LhlNLGmvXqBR072tlN9Cef1KaXeOopW0ci\nxH2nVM1Khw8f5ty5c/j7+7N9+3bee+89OnXqROfOnfn555/LPFhR9nQ6mDlT6zlkV4kBStaVVQhh\ndQX+ddatW5dly5bx3nvvERISgqurK/v37zfpnirsg1Kwb5/2DJpyo6C74kIIu1BgzeHGjRuEhYWx\nfPlytmzZwqBBg3j88cfZXt7m3q/g7tyBoUO1rqZZWbaOpgSKqjlIc6EQNlVgcmjfvj3e3t4cPnyY\n3r17895777F69WpmzpzJsGHDrBmjKEBCgtav/4EHtJmvy9UEnUXVHL75RrsnIYSwiQIv3Xbu3GnW\nhOTv78++ffv45JNPLB6YKNy+fdrDhaZM0R5JaoczqheuqK6sUVHSU0kIGyrwr7Ogews6na7Yo6SF\nZWRmaqOK//MfbUqPcqmorqxRUbBmjfXiEUKYkO4i5VDlytpzqsv1/dzCmpUuXNCGavv7WzcmIYSR\nPBW9nCrXiQEKvyEdFaUNzsjv2cxCCKuQvz5hG4XVHE6csJNh3ELcv6RZyc5t2QJHj8Lrr9s6kjJW\n2A3pRYukK6sQNiY1BzulFCxeDOPHQxHTWJVPRd2QLnfdr4SoWKTmYIcMBm0i0j174MCBfJ4fXBHI\nCGkh7JokBztjMMBzz8Hx49rzjWvXtnVEFiJzKwlh1+Sv087cuKFNtf399/k/mrPCkJqDEHZN7jnY\nGRcXWLmygicGyP+GdFycdvddCGFzUnMQtpHfDenlyyEjA/z8bBOTEMJIag7CNvKrOURFyfgGIeyE\nJAcbysyEzz67T7v05605pKbCsWPl7KEUQlRckhxsJCNDm1V140btPHnfyXtDeudO6NQJqla1XUxC\nCCNJDjZw9y4MHKg9f2HDhnL2HIaykrcra1QUhITYLh4hhAm5IW1l6enw1FNQpw6sXn2fJgYwrzkE\nBkKHDraLRwhhQqdU+W3x1ul0lLfwn3tOa15fufI+HwPm6KhVoe7rL0EI2yjOuVOSg5Vdu6bVGu7r\n8V9KadNxGwwyh5IQNlCcc6dF7zls3boVHx8fmjdvzoIFC8w+T05Opk+fPvj7+9O6dWtWrFhh8rle\nrycgIID+/ftbMkyrcnG5zxMD/JUUJDEIYbcslhz0ej2TJk1i69atnDx5ksjISE6dOmVSJiIigoCA\nAI4cOUJ0dDSvvPIK2bm67ixZsoSWLVuik5NIxSLzKglh9yyWHA4ePIi3tzeenp44OTkxdOhQNm7c\naFKmcePGpKamApCamoqLiwuOf540Lly4wHfffcczzzxT7pqOcqSmahfJIg+ZV0kIu2ex5JCYmIiH\nh4fxtbu7O4mJiSZlJkyYwIkTJ3B1dcXPz48lS5YYP3v55ZdZtGgRDuX0UZFJSdp4rk2bbB2JHco9\nOvrzz2HVKtvGI4QwY7G6fXGagubOnYu/vz/R0dGcPXuWkJAQjh49ys6dO2nQoAEBAQFER0cXuo3w\n8HDjz0FBQQQFBZUu8DJw4YL2COQRI2DAAFtHY4dyj45evx5GjbJtPEJUcNHR0UWeS/OyWHJwc3Mj\nISHB+DohIQF3d3eTMvv27eONN94AwMvLi6ZNm/L777+zb98+vvnmG7777jvu3r1Lamoqo0ePZlU+\nV5i5k4M9iI3VEsPzz8PUqbaOxk7l1ByysmDXLm3CPSGExeS9cJ49e3aR61iszSYwMJAzZ84QFxdH\nZmYm69atY0Cey2gfHx+ioqIASEpKIiYmBi8vL+bOnUtCQgKxsbGsXbuW4ODgfBODvfnjD+jRQ0sK\nkhgKkVNzOHgQvLygXj1bRySEyMNiNQdHR0ciIiLo3bs3er2e8ePH4+vry7JlywAICwtjxowZjB07\nFj8/PwwGAwsXLsTZ2dlsW+Wlt1LduvDvf2tzJolC5NyQ/uEHmYVVCDslg+CE9cXHQ7du2sOx33wT\nHnvM1hEJcV8pzrlTOpsL68upOfzvf1Crlq2jEULkQ5KDsL6cG9L169s6EiFEAcrnIAI7sGULvPKK\nraMop/J7RKgQwq5IcrgH//sfhIbKjed7JiOkhbB7khxK6IsvtGm3t26FLl1sHU05JXMrCWH3JDmU\nwKefwquvag8ta9fO1tGUY1JzEMLuSXIopuxs+PZb2LEDWre2dTTlnF4P58/LnEpC2DGp2xeToyN8\n9ZWto6ggcqZlL6eTKgpxP5C/TmF9er32oB9pWhLCbklyENaXU3OQm9JC2C1JDsL69HrtX6k5CGG3\n5NJNWF92tjQrCbvh7OzMjRs3bB2GRdStW5fr16/f07qSHIT16fXQvr08CUnYhRs3blTYCTxLM6O1\nNCsJ69PrwclJqz0IIeySJAdhfTK3khB2T5KDsL6cWVmFEHZLkoOwPqk5CGH3JDkI65O5lYSwe5Ic\nhPXp9fD993DwoK0jEcJueXp6sn37dpP3srKyGDRoEE2bNsXBwYGdO3dabP+SHIT1ZWeDUlJ7EKIQ\nOp0u366o3bt3Z/Xq1TRq1KhUXVWLIncFhfXJCGkh7omTkxMvvvgiAJUs/PcjNQdhfTk1B+mxJITd\nkuQgrE+vl2YlUX6Eh2sDNvMu4eHFL19QWTtm0eSwdetWfHx8aN68OQsWLDD7PDk5mT59+uDv70/r\n1q1ZsWIFAHfv3qVTp074+/vTsmVLpk+fbskwhbXJPQdRnoSHa/9f8y6FJYfilrVjFksOer2eSZMm\nsXXrVk6ePElkZCSnTp0yKRMREUFAQABHjhwhOjqaV155hezsbKpUqcKOHTs4cuQIx44dY8eOHezZ\ns8dSoQpr0+th3Dho3tzWkQghCmCx5HDw4EG8vb3x9PTEycmJoUOHsnHjRpMyjRs3JjU1FYDU1FRc\nXFxw/LMdulq1agBkZmai1+txdna2VKjC2mRuJSGKJTMzk7t37xoXvV5PRkYGd+/eBTD5uaxZLDkk\nJibi4eFhfO3u7k5iYqJJmQkTJnDixAlcXV3x8/NjyZIlxs8MBgP+/v40bNiQnj170rJlS0uFKqxN\nRkgLUSx9+/alWrVqxiU8PBwfHx+qVavGxYsX6d27N9WrV+f8+fNlvm+LdRcpTv/buXPn4u/vT3R0\nNGfPniUkJISjR49Ss2ZNHBwcOHLkCCkpKfTu3Zvo6GiCgoLMthGeqy0vKCgo3zLCzsjcSkIUKTY2\nNt/358yZU+JtRUdHEx0dXaJ1LPYX6ubmRkJCgvF1QkIC7u7uJmX27dvHG2+8AYCXlxdNmzYlJiaG\nwMBAY5natWvTr18/Dh06VGRyEOWE1ByEsKq8F86zZ88uch2LNSsFBgZy5swZ4uLiyMzMZN26dQzI\n83AXHx8foqKiAEhKSiImJoZmzZqRnJzMzZs3AUhPT+eHH34gICDAUqEKa5O5lYSwexarOTg6OhIR\nEUHv3r3R6/WMHz8eX19fli1bBkBYWBgzZsxg7Nix+Pn5YTAYWLhwIc7Ozhw/fpzQ0FAMBgMGg4FR\no0bRq1cvS4UqrE2vh3/9C158EWrVsnU0Qoh86FQ5fj6eTqersI/3q9CmToX334cbN6B6dVtHI+5z\nFfk8UtCxFeeYZYS0sD69HgwGuSkthB2T5CCsLztbSw5y30EIuyXJQVifTJ8hhN2T5CCsLyvrrwnJ\nhBB2SZKDsD6l4OOPbR2FEKIQkhyE9en1ULmyraMQwq7l95jQAwcOEBISgouLCw0aNGDIkCFcvnzZ\nIvuX5CCsT0ZIC1Gk/B4TevPmTSZOnEh8fDzx8fHUrFmTsWPHWmT/0pdQWJ/MrSTEPenTp4/J63/8\n4x8Wm09Oag7C+qTmIESZ2LVrF61bt7bItiU5COuTuZVEOWKvTwk9duwYc+bMYdGiRWW/cWT6DGEL\njz0Gv/wCycm2jkQIuz2PNG3alE8//ZTg4GCzz/744w+CgoJYsGABI0aMKHAbMn2GKF+ys2WMgxD3\nKD4+npCQEN58881CE0NpyV1BYX3Z2XJDWohiyHlMaI6kpCSCg4OZNGkSzz77rEX3Lc1Kwvq6doX4\neMjz2FghbMFezyNNmzYlPj7e7H2dTke1atVMXqempua7jdI0K8nlm7A+qTkIUaSCHhNqLXLPQVif\ndGUVwu5JchDWV6UKrFxp6yiEEIWQ5CCsT+ZWEsLuSXIQ1ifNSkLYPUkOwvpkbiUh7J4kB2F9UnMQ\nwu7J5ZuwPkkOwo7UrVvXbGrsiqJu3br3vK7Faw5bt27Fx8eH5s2bs2DBArPPk5OT6dOnD/7+/rRu\n3ZoVK1YAkJCQQM+ePWnVqhWtW7fm/ffft3SowlrS0mDCBFtHIQQA169fRylVIZfr16/f8/di0eSg\n1+uZNGkSW7du5eTJk0RGRnLq1CmTMhEREQQEBHDkyBGio6N55ZVXyM7OxsnJiXfffZcTJ05w4MAB\nli5darZuRRcdHW3rECxDrwcHh4p7fH+S4yu/KvKxFZdFk8PBgwfx9vbG09MTJycnhg4dysaNG03K\nNG7c2Dj0OzU1FRcXFxwdHWnUqBH+/v4A1KhRA19fXy5evGjJcO1Ohf0PajCAk1PFPb4/yfGVXxX5\n2IrLovccEhMT8fDwML52d3fnp59+MikzYcIEgoODcXV1JS0tjfXr15ttJy4ujl9//ZVOnTpZMlxh\nLXLPQQi7Z9GaQ3Fu8sydOxd/f38uXrzIkSNH+Mc//kFaWprx81u3bjFo0CCWLFlCjRo1LBmusBaD\nQbqyCmHvlAXt379f9e7d2/h67ty5av78+SZlHn/8cbVnzx7j6+DgYPXzzz8rpZTKzMxUjz32mHr3\n3Xfz3b6Xl5cCZJFFFllkKcHi5eVV5PnbopdvgYGBnDlzhri4OFxdXVm3bh2RkZEmZXx8fIiKiuLh\nhx8mKSmJmJgYmjVrhlKK8ePH07JlSyZPnpzv9v/44w9Lhi+EEPctiz/PYcuWLUyePBm9Xs/48eOZ\nPn06y5YtAyAsLIzk5GTGjh3L+fPnMRgMTJ8+neHDh7Nnzx66d+9O27Ztjc1T8+bNo0+fPpYMVwgh\nBOX8YT9CCCEso0JMn/HBBx/g6+tL69atmTZtmq3DsYjFixfj4OBQqkEt9ujVV1/F19cXPz8/Bg4c\nSEpKiq1DKrWiBn6WZ/fL4FS9Xk9AQAD9+/e3dShl7ubNmwwaNAhfX19atmzJgQMH8i9YwnvMdufH\nH39Ujz76qMrMzFRKKXXlyhUbR1T2zp8/r3r37q08PT3VtWvXbB1Omdq2bZvS6/VKKaWmTZumpk2b\nZuOISic7O1t5eXmp2NhYlZmZqfz8/NTJkydtHVaZuXTpkvr111+VUkqlpaWphx56qEIdX47Fixer\n4cOHq/79+9s6lDI3evRo9emnnyqllMrKylI3b97Mt1y5rzl89NFHTJ8+HScnJwDq169v44jK3pQp\nU1i4cKGtw7CIkJAQHBy0/4adOnXiwoULNo6odIoz8LM8ux8Gp164cIHvvvuOZ555xi6fLV0aKSkp\n7N69m3HjxgHg6OhI7dq18y1b7pPDmTNn2LVrF507dyYoKIhDhw7ZOqQytXHjRtzd3Wnbtq2tQ7G4\nzz77jL59+9o6jFLJb+BnYmKiDSOynIo6OPXll19m0aJFxouWiiQ2Npb69eszduxY2rVrx4QJE7hz\n506+ZcvFSKSQkBAuX75s9v7bb79NdnY2N27c4MCBA/z8888MGTKEc+fO2SDKe1fY8c2bN49t27YZ\n3yuPVzIFHd/cuXONbbpvv/02lStXZvjw4dYOr0xV1Nk986qog1M3b95MgwYNCAgIqJBTaGRnZ/PL\nL78QERFBhw4dmDx5MvPnz+ett94yL2y9li7L6NOnj4qOjja+9vLyUsnJyTaMqOwcP35cNWjQQHl6\neipPT0/l6OioHnzwQZWUlGTr0MrU8uXLVdeuXVV6erqtQym14gz8LO+KGpxank2fPl25u7srT09P\n1ahRI1WtWjU1atQoW4dVZi5duqQ8PT2Nr3fv3q369euXb9lynxw+/vhj9eabbyqllIqJiVEeHh42\njshyKuIN6S1btqiWLVuqq1ev2jqUMpGVlaWaNWumYmNjVUZGRoW7IW0wGNSoUaPU5MmTbR2KxUVH\nR6snnnjC1mGUuW7duqmYmBillFKzZs1Sr732Wr7lykWzUmHGjRvHuHHjaNOmDZUrV2bVqlW2Dsli\nKmKTxQsvvEBmZiYhISEAdOnShQ8//NDGUd07R0dHIiIi6N27t3Hgp6+vr63DKjN79+5l9erVtG3b\nloCAAKBiD06tiH9zH3zwASNGjCAzMxMvLy+WL1+ebzkZBCeEEMJMxbsdL4QQotQkOQghhDAjyUEI\nIYQZSQ5CCCHMSHIQQghhRpKDEEIIM5Ic7kGlSpUICAigbdu2DBw4kFu3bpX5PoKCgjh8+HCJ1pk1\naxbbt28v8b42btzIqVOnSr2dsvTwww8XWcbT0zPfKcx37tzJ/v37C1xvy5YtdOjQgVatWtGuXTum\nTp2ab7nNmzcTHh4OwJgxY/jvf/9rVubixYsMHjy4yFjLeoqJ06dP07dvXx566CHat2/P008/zZUr\nV+4pthwFfZ/2LDw8nMWLF5donU2bNt3TVOpHjx5ly5Ytpd4OQFJSkv3PI2a9cXkVR40aNYw/h4aG\nqm2KLwEAAA3ISURBVHfeeafM9xEUFKQOHz5c7PI5017fi9DQUPXll1/e8/q24unpme9UKbNmzSrw\nd3L8+HHl5eVlHCGq1+vVRx99lG/ZoKAgdfnyZaWUUmPGjCnVd5T7/0xJZWVlmbxOT09XzZs3V5s3\nbza+Fx0drX777bd73odS1hmBn/dYSis8PLxEf3/Z2dn3vK/ly5erSZMm3fP6eQ0fPrxEf+PWJjWH\nUurSpQtnz54F4OzZszz++OMEBgbSvXt3YmJijO937tyZtm3bMnPmTGrWrAlAdHS0ycNEJk2axMqV\nK8328fzzz9OhQwdat25tvJIF7Urv9ddfp3379mzYsMF4dXv48GECAgIICAigTZs2xtklP/nkEzp2\n7Ii/vz+DBg0iPT2dffv2sWnTJl599VXatWvHuXPnTK6St2/fTrt27Wjbti3jx48nMzPTuO/w8HDa\nt29P27Ztjcea2xNPPMHx48cBCAgIYM6cOQC8+eab/Oc//wFg0aJFdOzYET8/P5Njy7nSNhgMPP/8\n8/j6+vLYY4/Rr18/kyv4Dz74wCSGuLg4li1bxrvvvktAQAB79uwxiWnhwoXMnDmThx56CAAHBwcm\nTpxoFntCQgKZmZk0bNjQ+N6uXbt4+OGH8fLyMsYQFxdHmzZtALhz5w5DhgyhVatWDBw4kM6dO/PL\nL78Y1585cyb+/v506dLFeJV/9epVBg0aRMeOHenYsSP79u0DtCviUaNG8cgjjxAaGmoS2xdffEHX\nrl3p16+f8b0ePXrQqlUrk3K5Yztx4gSdOnUiICAAPz+/Ip+/vnr1amP5iRMnYjAY0Ov1jBkzhjZt\n2tC2bVuWLFkCwPvvv0+rVq3w8/Nj2LBhZttasWIFAwYMoFevXoSEhHDnzh3GjRtHp06daNeuHd98\n802R31/umteXX37J2LFjzfaT3/9v0Gp9EydOpHPnzrz22musXLmSF154AQB/f3/j30q1atXYvXs3\nP//8M127dqVdu3Y8/PDDnD59mszMTN58803WrVtHQEAA69evZ8WKFcbtxMXFERwcjJ+fH48++igJ\nCQnGfb/00ktm/28ABgwYQGRkZKG/B5uydXYqj3KuArOzs9XAgQPV0qVLlVJKBQcHqzNnziillDpw\n4IAKDg5WSinVr18/tXbtWqWUNhdUzvo7duwwmbtl0qRJauXKlUop05rD9evXjfsLCgpSx48fV0pp\nV3qLFi0yrj9mzBj13//+1yTWV1991Th3Su6rwpkzZ6oPPvgg3/VyXqenpysPDw/jMY0ePVq99957\nxn1HREQopZT68MMP1TPPPGP2Pc2fP18tXbpUpaSkqA4dOqg+ffoopZTq2bOnOn36tPr+++/Vs88+\nq5TSruD79eundu3aZfIdb9iwQfXt21cppdTly5dV3bp1jbEWFEN4eLhavHixWTxKKdWuXTt17Nix\nfD/LLTIy0uQqMTQ0VA0ZMkQppdTJkyeVt7e3Ukqp2NhY1bp1a6WUUosWLVITJ05USin122+/KUdH\nR+PvUKfTGa/0X3vtNfWvf/1LKaXUsGHD1J49e5RSSsXHxytfX1+llFb7CQwMVHfv3jWLbcqUKer9\n998v8hhyxzZp0iS1Zs0apZR29Z7fJIc5NYeTJ0+q/v37G6+yn3/+ebVq1Sp1+PBhFRISYiyfkpKi\nlFLK1dXV+LCtnPdyW758uXJ3d1c3btxQSmmT261evVoppdSNGzfUQw89pG7fvl3o95e75vXll1+q\nMWPGKKVMaw4F/f8ODQ1V/fv3VwaDQSml1IoVK8xqAN98843q3r27ys7OVqmpqcZj/+GHH9Tf//53\n43ovvPCCcZ3c23niiSfUqlWrlFJKffbZZ+qpp54y7ju//zdKKXXu3DnVsWNHs+/LXkjN4R6kp6cT\nEBBA48aNSUhIYOLEidy6dYv9+/czePBg49VWzjTVBw4cMLb95ndlVZR169bRvn172rVrx4kTJzh5\n8qTxs6efftqkrMo1G8q6dev45ZdfmD9/PgDHjx+nW7dutG3bljVr1phsR+WZRUUpRUxMDE2bNsXb\n2xuA0NBQdu3aZSwzcOBAANq1a0dcXJxZ3N26dWPXrl3s3buXfv36cevWLdLT04mNjaV58+Zs27aN\nbdu2ERAQQPv27Tl9+rTZFe2ePXsYMmQIAA0bNqRnz54mnxcUQ97jKanz58/TuHFj42udTsdTTz0F\ngK+vL0lJSWbr7N27l6FDhwLQqlUrk2dwVK5c2Xil3759e2OsUVFRTJo0iYCAAJ588knS0tK4ffs2\nOp2OAQMG8MADD+QbX0mPr2vXrsydO5eFCxcSFxdHlSpVCtzu9u3bOXz4MIGBgQQEBLB9+3ZiY2Np\n1qwZ586d48UXX+T777831oDbtm3L8OHDWbNmDZUqVTLbpk6nIyQkhDp16gCwbds25s+fT0BAAD17\n9iQjI4Pz588X+v0VR0H/v3U6HYMHDy5wnqQzZ87w2muvsX79eipVqmR8jGabNm2YMmWKcTtKm6g0\n320cOHDAON38yJH/397ZhjTVhnH8P1qZmasIssQY6z3P3s4qMjfNZW0QRlCYbT2rjOhDFH2pQGKE\nWDLoBZkfmpGTsFEsbWQWfQoyCoqpZDmCXqxBlmmx1qxozvN8kN3s7GxzPC/Z83T/Pm33ue/rvs51\nrvtc55zrcK4/yB1rKr+ZN29ewnXzq/Cf//DeRJCZmYnu7m58+/YNRqMR169fx/r16zFz5kx0d3en\nLUcsFmN0dJT8j94Gx9LX14czZ87A6/VixowZqKysxPfv38n2rKyshLKfPn2K6upq3Lt3jyyK3bt3\no62tDQqFAhcvXuR9rz7Rwolv4ziO1xY9cU2aNAkjIyOC8atWrYLX68WCBQuwYcMGDA0N4fz581i5\nciXpU1VVhX379iXch6gOsQsyfnGOp0M8DMPA6/WSxy2piJ9rypQpSbeN1x6tVAiMPcqK6spxHB4+\nfMiTHWXatGkJZTEMg7t376ZWPg6TyYSCggK0t7dj48aNaGhoEATaWHbt2oXa2lpBe09PD27fvg2H\nwwG3243GxkbcvHkTHR0duHHjBk6ePIknT54IgkS8n167dg2LFy8WyE9mv1i/i18n6fh3MluGQiFU\nVFTgwoUL5BGi1WpFaWkpPB4P3rx5g5KSkoRj09U9md/Er6dfDXrn8DfIzMyE3W7HsWPHMH36dMhk\nMrS0tAAYO/A9PT0AgIKCAtJ+5coVMl4qlcLn8+HHjx8IBAK4c+eOYI5gMIisrCxIJBIMDAzw3pZI\nhEgkQiAQgMlkQnNzM2bPnk22hUIhzJ07F+FwGJcuXSKOmZ2djWAwKJCzdOlSvH79muRUmpubsXbt\n2rTtM3nyZOTl5eHq1asoLCxEUVERTp8+jeLiYgCA0WiE0+nE8PAwgLEqaoODgzwZWq0Wra2t4DgO\nAwMDaZ0Us7Oz8eXLl4Tbjhw5gtraWjx//hzAWE6joaFB0E8qlSYsUJQKrVYLt9sNAPD5fCTfkgqD\nwQC73U7+P378eNwxZrMZDx48wK1bt0hbR0cHent7k4559eoVZDIZDh48iM2bNyfVTSQSobS0FC0t\nLeRYfPr0CX6/Hx8/fsTIyAi2bNmCmpoadHV1geM4+P1+lJSUwGaz4fPnz+R4Rok/aRqNRt4+Ry+o\nUtkvJycHz549w+joKDweD092VH4y/44nVp89e/agsrKS93ZcMBhEbm4uAPC+WCqRSHh+FSunsLCQ\nrG2Xy0V8PBXv3r2DVCodt99EQYPDXyDW6dRqNRYtWgS32w2Xy4XGxkao1WrI5XKSaKurq8PZs2eh\nVqvx8uVLUrN1/vz52LZtG+RyOSoqKqDRaARzqVQqsCyLZcuWYceOHdDpdOPq19bWBr/fj71794Jl\nWSK3pqYGq1evhk6n431Gevv27Th16hRWrFjBq6KXkZGBpqYmlJeXQ6lUQiwWk+RtrA1EIlHShVhc\nXIycnBxkZGRAp9Ohv78fRUVFAMYqxJnNZqxZswZKpRLl5eXkteCovK1btyIvLw/5+fmwWCzQaDQJ\na97G6rBp0yZ4PB6wLIv79+/z+ikUCtTV1cFkMiE/Px8KhQJ9fX0CeVqtlpdMTrTP8b/379+PwcFB\nMAwDq9UKhmGIrsnsZbfb4fV6oVKpwDAML1Als+nUqVPR3t6O+vp6LFmyBAzDwOFwYM6cOQntAgBu\ntxtyuRwsy6K3txc7d+5M2nf58uU4ceIEDAYDVCoVDAYD3r9/j7dv30Kv14NlWVgsFthsNkQiEVgs\nFiiVSmg0Ghw6dAgSiUQgN3ZfrFYrwuEwlEol5HI5jh8/Pq79bDYbysrKoNVqkZubS+TFyk7m38ns\n7/f70draCqfTSZLSnZ2dOHr0KKqqqqDRaBCJRMhYvV4Pn89HEtKxc9fX16OpqQkqlQoul4sk6xPN\nHeXRo0dpBZEJ4yflNn5rvn79Sn5fvnyZJKso6REKhTiO47ihoSFu4cKFP60Snl6v5/r7+9PuH4lE\nSAL5xYsXnEwm+8df3fw/87vZz2w2c11dXROtRlJozuEn0NnZiQMHDoDjOMyaNQtOp3OiVfpPUVZW\nhkAgQF4nTHSF/G9w+PBhOBwOVFdXp9V/eHgY69atQzgcBsdxOHfuHMRiusTS5Xey34cPHxAIBEjB\npF8RWuyHQqFQKAJozoFCoVAoAmhwoFAoFIoAGhwoFAqFIoAGBwqFQqEIoMGBQqFQKAJocKBQKBSK\ngD8BbXCHXpcNUKMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e0a4e50>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}