{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 逻辑回归 Logistic Regression\n", "\n", "逻辑回归(Logistic Regression, LR)模型其实仅在线性回归的基础上,套用了一个逻辑函数,但也就由于这个逻辑函数,使得逻辑回归模型成为了机器学习领域一颗耀眼的明星,更是计算广告学的核心。本节主要详述逻辑回归模型的基础。\n", "\n", "\n", "## 1. 逻辑回归模型\n", "回归是一种比较容易理解的模型,就相当于$y=f(x)$,表明自变量$x$与因变量$y$的关系。最常见问题有如医生治病时的望、闻、问、切,之后判定病人是否生病或生了什么病,其中的望闻问切就是获取自变量$x$,即特征数据,判断是否生病就相当于获取因变量$y$,即预测分类。\n", "\n", "最简单的回归是线性回归,在此借用Andrew NG的讲义,有如图所示,$X$为数据点——肿瘤的大小,$Y$为观测值——是否是恶性肿瘤。通过构建线性回归模型,如$h_\\theta(x)$所示,构建线性回归模型后,即可以根据肿瘤大小,预测是否为恶性肿瘤$h_\\theta(x)) \\ge 0.5$为恶性,$h_\\theta(x) \\lt 0.5$为良性。\n", "\n", "![LinearRegression](images/fig1.gif)\n", "\n", "然而线性回归的鲁棒性很差,例如在上图的数据集上建立回归,因最右边噪点的存在,使回归模型在训练集上表现都很差。这主要是由于线性回归在整个实数域内敏感度一致,而分类范围,需要在$[0,1]$。\n", "\n", "逻辑回归就是一种减小预测范围,将预测值限定为$[0,1]$间的一种回归模型,其回归方程与回归曲线如图2所示。逻辑曲线在$z=0$时,十分敏感,在$z>>0$或$z<<0$处,都不敏感,将预测值限定为$(0,1)$。\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.figure()\n", "plt.axis([-10,10,0,1])\n", "plt.grid(True)\n", "X=np.arange(-10,10,0.1)\n", "y=1/(1+np.e**(-X))\n", "plt.plot(X,y,'b-')\n", "plt.title(\"Logistic function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 逻辑回归表达式\n", "\n", "这个函数称为Logistic函数(logistic function),也称为Sigmoid函数(sigmoid function)。函数公式如下:\n", "\n", "$$\n", "g(z) = \\frac{1}{1+e^{-z}}\n", "$$\n", "\n", "Logistic函数当z趋近于无穷大时,g(z)趋近于1;当z趋近于无穷小时,g(z)趋近于0。Logistic函数的图形如上图所示。Logistic函数求导时有一个特性,这个特性将在下面的推导中用到,这个特性为:\n", "$$\n", "g'(z) = \\frac{d}{dz} \\frac{1}{1+e^{-z}} \\\\\n", " = \\frac{1}{(1+e^{-z})^2}(e^{-z}) \\\\\n", " = \\frac{1}{(1+e^{-z})} (1 - \\frac{1}{(1+e^{-z})}) \\\\\n", " = g(z)(1-g(z))\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.figure()\n", "plt.axis([-10,10,0,1])\n", "plt.grid(True)\n", "X=np.arange(-10,10,0.1)\n", "y=1/(1+np.e**(-X))\n", "plt.plot(X,y,'b-')\n", "plt.title(\"Logistic function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "逻辑回归本质上是线性回归,只是在特征到结果的映射中加入了一层函数映射,即先把特征线性求和,然后使用函数$g(z)$将做为假设函数来预测。$g(z)$可以将连续值映射到0到1之间。线性回归模型的表达式带入$g(z)$,就得到逻辑回归的表达式:\n", "\n", "$$\n", "h_\\theta(x) = g(\\theta^T x) = \\frac{1}{1+e^{-\\theta^T x}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 逻辑回归的软分类\n", "\n", "现在我们将y的取值$h_\\theta(x)$通过Logistic函数归一化到(0,1)间,$y$的取值有特殊的含义,它表示结果取1的概率,因此对于输入$x$分类结果为类别1和类别0的概率分别为:\n", "\n", "$$\n", "P(y=1|x,\\theta) = h_\\theta(x) \\\\\n", "P(y=0|x,\\theta) = 1 - h_\\theta(x)\n", "$$\n", "\n", "对上面的表达式合并一下就是:\n", "\n", "$$\n", "p(y|x,\\theta) = (h_\\theta(x))^y (1 - h_\\theta(x))^{1-y}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 梯度上升\n", "\n", "得到了逻辑回归的表达式,下一步跟线性回归类似,构建似然函数,然后最大似然估计,最终推导出$\\theta$的迭代更新表达式。只不过这里用的不是梯度下降,而是梯度上升,因为这里是最大化似然函数。\n", "\n", "我们假设训练样本相互独立,那么似然函数表达式为:\n", "![Loss](images/eq_loss.png)\n", "\n", "同样对似然函数取log,转换为:\n", "![LogLoss](images/eq_logloss.png)\n", "\n", "转换后的似然函数对$\\theta$求偏导,在这里我们以只有一个训练样本的情况为例:\n", "![LogLossDiff](images/eq_logloss_diff.png)\n", "\n", "这个求偏导过程中:\n", "* 第一步是对$\\theta$偏导的转化,依据偏导公式:$y=lnx$, $y'=1/x$。\n", "* 第二步是根据g(z)求导的特性g'(z) = g(z)(1 - g(z)) 。\n", "* 第三步就是普通的变换。\n", "\n", "这样我们就得到了梯度上升每次迭代的更新方向,那么$\\theta$的迭代表达式为:(FIXME: `j`)\n", "$$\n", "\\theta_j = \\theta_j + \\alpha(y^i - h_\\theta(x^i)) x_j^i\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.4 示例程序" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "#from __future__ import division\n", "import numpy as np\n", "import sklearn.datasets\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(0)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data = [[ 0.694565 0.42666408]\n", " [ 1.68353008 -0.80016643]\n", " [-0.25046823 0.24392224]\n", " [-1.13337973 -0.6112787 ]\n", " [ 1.76905577 -0.31025439]\n", " [ 2.00225511 -0.18592 ]\n", " [ 0.91169861 0.46995543]\n", " [ 0.88211794 -0.46701178]\n", " [ 0.75006972 0.33995342]\n", " [ 1.30208867 -0.72334923]]\n", "label = [0 1 1 0 1 1 0 1 0 1]\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Original Data')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# load sample data\n", "data, label = sklearn.datasets.make_moons(200, noise=0.30)\n", "\n", "print(\"data = \", data[:10, :])\n", "print(\"label = \", label[:10])\n", "\n", "plt.scatter(data[:,0], data[:,1], c=label)\n", "plt.title(\"Original Data\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def plot_decision_boundary(predict_func, data, label):\n", " \"\"\"画出结果图\n", " Args:\n", " pred_func (callable): 预测函数\n", " data (numpy.ndarray): 训练数据集合\n", " label (numpy.ndarray): 训练数据标签\n", " 散开数据,但是不在原来的数据上做修改\n", " \"\"\"\n", " x_min, x_max = data[:, 0].min() - .5, data[:, 0].max() + .5\n", " y_min, y_max = data[:, 1].min() - .5, data[:, 1].max() + .5\n", " h = 0.01\n", "\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n", "\n", " Z = predict_func(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", "\n", " plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) #画出登高线并填充\n", " plt.scatter(data[:, 0], data[:, 1], c=label, cmap=plt.cm.Spectral)\n", " plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# FIXME: function sample\n", "\n", "\n", "def sigmoid(x):\n", " return 1.0 / (1 + np.exp(-x))\n", "\n", "class Logistic(object):\n", " \"\"\"logistic回归模型\"\"\"\n", " def __init__(self, data, label):\n", " self.data = data\n", " self.label = label\n", "\n", " # FIXME: n -> d\n", " self.data_num, n = np.shape(data)\n", " self.weights = np.ones(n)\n", " self.b = 1\n", "\n", " def train(self, num_iteration=150):\n", " \"\"\"随机梯度上升算法\n", " Args:\n", " data (numpy.ndarray): 训练数据集\n", " labels (numpy.ndarray): 训练标签\n", " num_iteration (int): 迭代次数\n", " \"\"\"\n", " # 学习速率\n", " alpha = 0.01\n", " \n", " for j in range(num_iteration):\n", " data_index = list(range(self.data_num))\n", " for i in range(self.data_num):\n", " rand_index = int(np.random.uniform(0, len(data_index)))\n", " error = self.label[rand_index] - \\\n", " sigmoid(sum(self.data[rand_index] * self.weights + self.b))\n", " self.weights += alpha * error * self.data[rand_index]\n", " self.b += alpha * error\n", " del(data_index[rand_index])\n", "\n", " def predict(self, predict_data):\n", " \"\"\"预测函数\"\"\"\n", " result = list(map(lambda x: 1 if sum(self.weights * x + self.b) > 0 else 0,\n", " predict_data))\n", " return np.array(result)\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "logistic = Logistic(data, label)\n", "logistic.train(200)\n", "plot_decision_boundary(lambda x: logistic.predict(x), data, label)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.如何用sklearn解决逻辑回归问题?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy train = 0.850000\n", "accuracy test = 0.825000\n" ] }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model import LogisticRegression\n", "from sklearn.metrics import confusion_matrix\n", "from sklearn.metrics import accuracy_score\n", "import matplotlib.pyplot as plt\n", "\n", "# calculate train/test data number\n", "N = len(data)\n", "N_train = int(N*0.6)\n", "N_test = N - N_train\n", "\n", "# split train/test data\n", "x_train = data[:N_train, :]\n", "y_train = label[:N_train]\n", "x_test = data[N_train:, :]\n", "y_test = label[N_train:]\n", "\n", "# do logistic regression\n", "lr=LogisticRegression()\n", "lr.fit(x_train,y_train)\n", "\n", "pred_train = lr.predict(x_train)\n", "pred_test = lr.predict(x_test)\n", "\n", "# calculate train/test accuracy\n", "acc_train = accuracy_score(y_train, pred_train)\n", "acc_test = accuracy_score(y_test, pred_test)\n", "print(\"accuracy train = %f\" % acc_train)\n", "print(\"accuracy test = %f\" % acc_test)\n", "\n", "# plot confusion matrix\n", "cm = confusion_matrix(y_test,pred_test)\n", "\n", "plt.matshow(cm)\n", "plt.title(u'Confusion Matrix')\n", "plt.colorbar()\n", "plt.ylabel(u'Groundtruth')\n", "plt.xlabel(u'Predict')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. 多类识别问题" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 加载显示数据" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt \n", "from sklearn.datasets import load_digits\n", "\n", "# load data\n", "digits = load_digits()\n", "\n", "# copied from notebook 02_sklearn_data.ipynb\n", "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", "\n", "# plot the digits: each image is 8x8 pixels\n", "for i in range(64):\n", " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", " ax.imshow(digits.images[i], cmap=plt.cm.binary)\n", " \n", " # label the image with the target value\n", " ax.text(0, 7, str(digits.target[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 可视化特征\n", "\n", "针对机器学习的问题,一个比较好的方法是通过降维的方法将原始的高维特征降到2-3维并可视化处理,通过这样的方法可以对所要处理的数据有一个初步的认识。这里介绍最简单的降维方法主成分分析(Principal Component Analysis, PCA).\n", "\n", "PCA寻求具有最大方差的特征的正交线性组合,因此可以更好地了解数据的结构。在这里,我们将使用Randomized PCA,因为当数据个数$N$比较大时,计算的效率更好。\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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p1x3H2OkjopZPSPFw3i2nx/SKI7arKQhFtJl18EPpNbw7qZ1Svte6DredR+f/jVe3P0XXfjnfaxtJaXEZyl8S4QE3tV2fjibu+f4K6TOiJ28XPMfKmeuoq/Qy/OhBje1+YnHRXWfTY0gur9/zLrvW74m9kJSt5ul2FM/84eV2lwo3RwiFfqN7IYTg0r+dz33nPXpQ1WlOj4NTf3f899p3nJ8vcTH1OD8pNruNCSeNbvfyk84YD8CDlzwZM0/WsiSK+HG9XgAkreo/tEbAF2DftkK69e/C4MP7g6Ddg31CEVxw2xmMmRYukTYsE01p+yFQHarnya1f8l3JRhQhOC5nONf2m0aCFq+E+zkgEXEx9Tg/fwaO79Ni+tjkcw8nb/Uu9m5tVUukwxCK+F6e9rN/epWMrun0GNwVd6IrZouhWKRlp3L+rWfwdeEantz6FaXBWpJUF8PyUkmbF2LYpMFMvfhIXAmuxnV0y+DyJc9Q7K/GkOHv7eO9y1lblc9rh12PIuJRv58Dcc83zs+ejC7pnHDlFL5++btG71fRFNJzUuk2oAtr5m74aQ5EhkMAUso2q9Was+zL1QhFoNm11oXgm2FoFjP2LuOhTZ8RlOHBulrTz4IcH85AOUv/bxXvPPgxTy9/gJTMZADmlGyiMuhtNLwQroTbV1/BsoodTMiI3Xw0zk+HBKz4gFuc/wWuf/xy/vDs1QwY35duA7pw3l9OY+D4vrzz4MdUFdVELKs5tDYVx74vwUCII8+cQOL36MMmLYke0DF1E6G2/sopHQL/X7LZ93Qm92/8uNHwNuJUCJ6fjt8XpLygkn//6ZXGWdvqiqg3I9shAYQsk7y6YixpYcqfIFQTpxUEZjs/HU3c841zUAghmHLhJKZcOAmAkvwyLh/4+6jcWLvTxnm3nI6v2sdnz3/bZtv3g8UyLGa+NvcHb6etXOT6v2RjjvHQ4mB3vYn7b+FQi2VazH5zAYV5xTw85x66udNxqXb8zQywTVGZV7qZZ7bNxJIWI1J7cOuQ0+nuyfjB5xPn4Ai3jj80raPinm+cH8TOdfkNubORhAI6K75ei7e2nrTsZFyJ/3sDTFaaijHajbTF8HrqTWzf1eK5rQB1SyDCL9qyNI8bJtzG1OxhOFUboslcFYFuGayv2oMhTSwkq6t2c8WSf1Ort60fHKdjkVJgSaVdn44mbnx/gZiGyWv3vMtZnS7nBNf5/PnYe9i1oYUUsXayY+1u3nv4U774z7fUVXkbp+f0ysLQowsWFFVh6/I8vnl1LkU7S8Mlu/9jxV9WhgZ6tGesrfCRdOEuXE+Wom4LImIkX+xcm0/J1hJemnAtI1N7oAoFVSgMSO6CJlRMmvSdQxIyDT4vWPljnk6cFjCl0q5PR/ODww5CiG7Aa0AWYS/+eSnl40KINOAdoAewGzhHShkt/Bqnw3not/9m/nuLCfrDr7trZm/g94ffwfNrHyK7x8EJv0gpeezq5/j2zXnoQQNpSR69+jmGHz2Y29/+Iz0Gd6PPyF5sW56H3kQTwbIitR/2V5R93yyFjkbS8rPAcgt8D3VDpmrgbHbT1Zu47ytCBNs+h40Lt3Di4Kk8O/5KgqaOEIIvClbzyJbPopYNWDrb66Lb28f5cQnr+R4ar6AjzLkB3CSlHARMAK4XQgwCbgFmSSn7ArMa/o7zI1NeWMncdxY1Gt796IEQ7z/y6UFvb+nnq5j91gJCfj3CaK6ds5Ebxt+KoRvc99ktHHbaWDS7hmpT6dI3u1F4vDk/B8PbGhIIXJqB1cOBTFYbcoEPHLNteX2bd41UQObYSctJbZzmUG3YFY3eiVkRYYj9OBUbA5Nid82I82Mi/nc9XyllEeGeRUgp64QQm4EuhFtqHN2w2KvAHOD/fuj+4rTO3i0F2J22KD0GQzfZ1mqbnrCX+/nz3/D2Pz+mpqyWfqN7I1TRYjpXVUk1i2Ys58izJnLH238iFAihB3UUVeHMjMs77Jx+KiRgHJ6AOcCJqDWRSSooAkwJugUOAbpEypa9ZqmCdCv47sxm2NTBUfOHJHejb2I2W2oLCFnheIWCwK05OKHLqB/v5OLEJJxq9r/r+TYihOgBjASWAlkNhhmgmHBYItY6VwkhVgghVpSVlXXk4fwq6dInO6YQjqop9BrWvdV1X7vnPZ676TVKdpcR8AVZN28T6+dubnH5UEAnf+MBIXS7044n2YMrwcW4Ew+dIVEbyo81hxYOczQbzJZ2gX50AtIhaOrQSDtoy30k3LKPxIt24Xq4OBzzVcNGFwuM0W6E0bL3bnXS8D7XHa2nh73Byqj5QgieGHMZp3Ydi0dz4FA0jsoaxKsTr8Ojta6fEafjOZTaDh1mfIUQCcAHwB+klLVN58lwAX3MK1ZK+byUcoyUckxmZsv6AnHaR2a3DDpP6o20Rf60NoeNs/50covrBeqDvPfQJ1HC5pZltSjh6PQ4yB0Y+1V54iljaUtdsalouaIqHZIT7HA7OPLMCZz7l1O55qGLsTttmL0cSJvA8ihIm0A/MgH/TdnUvtAdY8iBijQRAhGSiHqJ0CW2BV6cL4YdArXUQDUFMlUjeEJyzItZAmZfJzJFQ5cGVgu1y27Nwfk9DmdYSi6GtFhUto0XdszGZxx8Op4lLSqCdQTM9inPxYmmIyQlhRD9hRBrmnxqhRB/aG2dDsnzFULYCBveN6WUHzZMLhFC5Egpi4QQOUBpR+wrTus8s24JC85JJsHMIGlBOUK30HM9/Pn56+nar3OL65Xkl6G0UHBgd9rCMeRmtsQIGRTvLiUU1LE3SzfbuWZXqy3chIBrH72MBR8tZd+2Qjr3zsbvDbB58baW12nHYF2wPog7yYVm1/jv/R8RrA8h/DbqnuyGUmdhdbaFB9IAElSUqgOpCs3PXgQl9q9qCVyUzrDViXiHppIfKCd4ZSb2OXWI2mYFEg5B6PhwdZsEblzxMq9OvJ4u7rSIxWp1P5ct/ndjA05TWnxRsJq8umJemnBtuzWBvy1az8ObP6XOCMuDHt95BDcPPJkd3hK21hbS2ZXK2PTe8TLmVghLSv7wsIOUciswAkAIoQIFwEetrdMR2Q4CeBHYLKV8pMmsT4BLgAca/j/jh+4rzgH21tVQHvDRPyUDty3sQQYMnafWLcGvWPgv7E7ZBblghUuAP7UVEa3We4CMLmktCtYMOWIAp/3ueJ7/y+vs3XJAu8HQTV6/5z2WfLaSh+fc09hRGCC7VxZ2l42QP7ZHZnc58CS5SEh2U7KrjJJdpYBoVeymPYN1DredZV+spqqkpjEFTtmn436oBN8/u4Cr4fXRb2GbX4e6N7oCLQJT8sdu0zn/hcnUG0Fe3DGbLwrXIB/sh3LrLkKBhvUNCJ6dijnc3bhqre7ngY0zeHLsZY3TdMvgwY0zqGswvI3TpclObykba/YxJKVbm+e5qnIX965/P6KX3JeFa1hQugWfGcQKCcyASnqii1eOvIoMZ1Kb2/y18iPEfKcAO6SU+a0t1BGe7+HARcB6IcSahmm3ETa67wohrgDygXM6YF+/eqoCfq6e/RHryovRFAXTsrh59JFcMXgMe701KE29JiFABUtK1pQVtbxRwJPkZuJJo5n3/pKoeZ26ZTDhpDGkdErm5mP+SrD+gMEK+kPsWLObFV+vZdzxIxunT7lwEq/c+XaLxldKybIvVjHnnUVNpzYcd1iYHUm7uxrvRwhBTXltRO6xANS8IK6HSgidmQq6xP5lDbZ5B/KVbU4beowOFjm5nThv7NFAOFxwQ//juaH/8TAZis6v5Jwn/oblNTCGupBp0bfT0ortXLjwCa7qcyyHZfbjmmUvsKl6X4shiV3e0gjja0mLFZU7KfHXMCi5K70Tw0MnL+/4LqqJZ8gyKA96CezxECpzgSKptASn5L3KN7+9Go89ujfdr52wqlm73wwyhBBNOxI/L6WM1STzPOCttjbWEdkOC2h58HfKD91+nEiu/e5jVpcVolsWNNilh1bNp1dyGqMyO6ObsY1V96SUNrfdUlPK795eyPVPXM6GBVtiqpr5vQHWzd0YYXyT0hJ5+Lt7uO/8x9i3LVLpzOGyM2raML57e2GLx3LKdcfxydNft3nMzUnvkkrBtuh8WQHYF/uwL/ZFzVPUsMD83ac9SMgfwjIthAgPIN7wVCutgTSBHJOALlt/QGyvK+b2tW9zROYAttcVRRRYNKdHwoFxj5JADdcs/Q9VIR8SiSUtJmb04/4R51NQHz2YBxAqcxIqd4IUYIaPu6JS59ZPv+aJM1uO+f9aCZcXt9v4lkspx7S2gBDCDpwC3NrWxuLaDv9DFHprDxjeJvgNnf9sWMZ/p5/Hqb0H8enOzQTMA56fQ1WxLMlh7/6bHE8Svxs+kclde0VtP2/Nrpj7FUJQtreCtOwUbHYtqsGk3WUnvXNa1Hp9RvbknzPv4MkbXmTVN+swQgbuJDen/+EEzvj9iZyeemnsE5VhBTW704bfe3Ceb2FeyUEtD+G+c6OOGcpTS//Bcze/yu71e+k5LJeL7jqbAeMOKI8V+av47+4FbCjOJ22L4OisQWCTEF1dHUXIMphd0rLqmwASNCe3rfovPjPI8NQeVARrKfRXRvjIi8q28U7+Yoam5FLor4ryoEPFLrCaGRMpmL11J35dx2Vrx8H+qjgoz7c9HA+sklK2eSHGje/PFCkNMHaBkohQswHYWVuJ1cIoVpk/7NHdN3EaTlXjve3rMaUkye6gLhRkScleLCkp9NVx3eyPuXv8FM7rPzxiG136ZlO6pzxq26ZhkpaTymGnjeOpG16Mmq+qCsdccETU9PLCSq4Z9Rd8NfWN8o2GbmCZFu5EF6pNjeqKDKAogm79O3+vRpnfp4jD4bKzb3sRd57yAFUlNSiKwto5mzj8tPxG47ujrpgrZj2Dubwax6PF7FUEa5mHU4J1WzbGaM9B7zfiuIGy4IEkoYXlW2MuF5IGH+xZwqNjLmVu6Sb8ZqjR/KpCQZqxDYlAUB+KG99YdHCF2/m0I+QAcW2HQ4qUJtIsRFreiOmW/0tk6URk5dnIsqlYFRdQ7tvLH+Z+1uj1Zjl8HJO5h/4JlahC4FQ1XtywnDo9yN8mTmXthTey7NzrGJ/VFcOyIoy23zS4f8UcjGYe9G/uPBuHKzIu6HDbOe6yybgTXTjdDh767h5yemXhcDtwehxkdEnjH1/dQXJG9IDO+w9/it/rj9DNDfiCvPevT6iv9XPytbGHAE+8ehpjp4/A5vhpfIMB4/tyy7S/UbyzlIA3QH1tPcH6IM/84WW2Ls9j1/p8fj/uNrSzNuP4RxEiIBH1Vvjjt3D/vQhR+/26a3wfag0/GY5EBjeJDSsIju88goSU2Fmd6R43aW5X1PRfO/uzHTqidbwQwgNMBT5sa1mIe76HDKv+Y6i7H2QAMJG2EaD1AFTwfwQ0yfnU1/DSpn9RG+qOQPK3wQs5o8t2QpaCJiRbvalcvuI4HlxVwSOrF/DatHMYndUFh6qxqqyw8dVUFVbDRSTQLYsiXy3dElMwLYv1FSVYA1L4vzdv5Nk/vkJFQSU2h42Trz2OK+6/oPFQeg3rzqvbn2Tv1kIs0yJ3YJeILIemrJ2zMWYc2eawkb9pH9c8fAlGyODLF2ZjWRaKIjjxqmn87snLEULQb0xvln+1pt2tflrC5oiu+NuPZtc46uyJPH3jS1H93EIBnQ8e/YxlX64mUFPfqn9km19H6MSUAxOkpM1E5+9JliOZ29e8zdrK3Y1fjYXk26L13H3c6dz53jyCuoklQRECu6py74nHxtvat0BHhR2klD4gvb3Lx43vIUAGF0HtXUCT9u368vAHBaIGZAzmlboIWSYXdNvCaZ3zcKomTjVs2AYnVvDQsLlcufI4gsD1cz5h8TnXIIQgy51Ab9dW7h60iF6eGnyGjZd2D+H5XWNIcbhYWVrA1bM+wm/oIAR2ReWZhbcwIqkTdpcdVY2u7BFCkDugbR2CnF5Z7IiR76sHdTK6pKGqKr9/5iqufugSqkqqSe+c1pgvvGdLAWvnbPpBhtfpcXDTC9dimRaPXvMcAW90EcMxFxyBtGTMEIe0JHlrdmOEjNZfTA0J9c1+s9aUe34gu3yl7PaVRQ30BSyd76rW8vW1l/Py0pWs3FNIj/QUrpgwhgHZ8QKmWMR7uP3KkL7niDC8EcQeCc92+tlQC5f12IBbazbgpVockV5AohakznBQGwqQV1NB35QMbhuRxhDlG1xqeJ1Em85VvdYzKiMBCVw88z18+oHUMR9w+awPWXD21bhiGN6D4eybT2HZl6siUtNsDo3Bhw8gq/sBY+B0O8jpGVl9vnVZXrsr3hRVocfQbhRsK2rcl9PjoPeInhxxxniklHz0xBfs2rAn4lgAvvvvAr57e2HMlkIOt4PkzCT2bilo/QA0gTGmIeYrZTgL5UfU5zZa6X5R6K8iKymBW6Ye9eMdwC8ICRjxNkK/Isx9bS/TjN/2XI9L1UjQYhcFSATuBgMrpURrqGoa65mBU4k01i7V4IjUZXy5a13M1umWZfHkmkWsLy8+qNbqzRk4vi9/eeV3JGcm4XA7sDk0xk4fyd0f3Nzmuuld0lp8a29eief0OHjgqzu59+P/Y9KZExg9bTjXP3EF/5p1F5pNw2a38fDce7nm4UvpOTQ3wqjrISOc3ytlRLmzw22nc+8spv5mEs6EloXgpVMQOiYRq6cjbHjLjbAQTwe/4otSHXVbAAItG15NKIxOi85iidM6h0pMPe75Hgpso8EsoCUvtzmbatPY5Uvk/L49WVDenVM6b8WmRBrFipCTkmC4uirbk0iPpAY5Q2NHTDsghEZVoIxQjLzgoGXy361reG/7elKdLl6ZejZ9UtodyorgyLMmcvjp4yjdU05CiofE1Pb1XBsxeTDJ6UkE60MRXqnDbWfokYNYM2s9Ukp6j+jJTS9cS2qnZFKPHcaoY4fF3J7dYeOkq6eybt4mdq2PFpZ3uB2cddPJ7Fizm7oKL5POmsD0y49BCHjrHx9THtQbKwClFlYuM4a70Y9NwhjTUNVmgeehEvz/6NrOX7Z9iBKdxKvzw3erCYGL0gidEZnapyBwqQ4u7nlkB+75V4CMhx1+VYiE65GBmUDrbct1C65dNZXFFZ1BgCK20SfpKE7uUoyFH4UgplQIWgp3bDgaj+bArio8e8xpBwZXbAMgWEBU8FSajM+wsCmSWEVkIcsiZFnUe3XO/+ptlpxzLWoLA2ttoapqVFihLRRF4eE5f+Vv5z7KjjW7UVRBUnoit7x+I8OOHIQeChtDl+fg2hOpWsvn0HdkLy668+yo6U8t+wcv3/EW8z9cilSheooT7zlJYG8qiSaxzanFvcPC40yiNFQbtZ3vhZSom/yIkISGlx7n65VYXewY4w88yI7I7M+fBp5MliulY/b7K+FQiqnHje/3RJrlEPgcaVUh7BPBPq7do8lC645MuA68j9JYphaDF3cNY1FFZwLWgdzM9ZUmZy65gOv75jM8OZ+MhEHsM07mqF4qZ7k8TM3ti1M78LOKhN8hgwtoGmO2cKAIN0PVOzgqYyJzy7rib9xH5EiRBOoNncXFeziic492nV9H0Sk3kycX309FURUhf4jsnp0av2Ob3YbNfvA5q9MuOZoFHy6N0iiWUjJyypCY6yRnJPGHZ6/mD89ejWGZnDL3QbzBusiFgpLEd+q45dXfYQ1O4i+r3/ihSRqNqJv9GMNdhKYmIW0C+5w67B9WRRhfm6LR2Z3aylbitETc8/0fQgYXIquvA2kBQWT9K2Afh0z8G/iegMA3IGzgOhuRcC1CROu0CrULUjhBRpe7AvhNldfzB0YYXggHKjZWh7hueQ4uLZcku8qXxxVwaZd5IJIQ8lzggIi3sA2ixPkUZaW30y+hjGrdSZHfw8CkCmyKxVMjZ/FJYW/e3dePbXVpVOqRuaDCkKh5Pt7Kn0fPS5Lo0jW6kq260suHL89nxbxtpHVK4szLJjHysD5YUlLu95Fod+DSWjeUumXyyc7NzNi5Cadq4/z+wzm6S0+EEKTndJxRGTF5CCdePZVP/z0TaUlUTUFKuOu9m3G42tbT1RSVmwaczG1r3zogjCPBZtN4YM6djOjVF58R7DDDiy4xJiYQvNwFdgFKeHBP3RjZbHOHt+3KvoBuoAiwa/Hbfj+HUkxd/JABlY5mzJgxcsWKFW0veAiRUkeWTgTZ/LXSBcLeYEz3D3ApIFwgMkEGAT1ssO3DwHMJVF1B87ivlPDS7sE8vG0sQUtFtvJKpAqL18Z+yciU0oa0MwE4IPEvKJ7fNC530ievsqmitDHfd+O0l3Gp0R73RwV9uHPj4dSbYUPpLDLo9p4XYUkUE5Bw5hVHcuWfjm9cp7rSy3WnPk5drb8xp9fhsjH6D2P4xL6X2lAAKeHkXgPC1XcxjLBpWVw0811WlxWFU94Al2bjN/1H8Lteo9m4cCuJaQkMPrx/iznFfq8fu9MeFuRpB3u3FrD8qzW4E10cfvq4dseiAc6f9xg76iMVUgVwWGZ/Hh19CR/vXc4/Nn7UMQY4aDUIUzQ7b92CJprNXVxpTM4azEldR9ErITLEk19ZzW2fzmT1vkIEgsN65vL3k6eSldj+c/45IoRY2ZbWQlskD8iSRzx/bruW/eKoJ3/w/poSfwS2gpRBCC1pMJjjEYobGfiiwZA2x98wvakxtcLGuLl3G5oT/sQwrAvLO/PItjEErLZ/mhOyd9EnoYrZpbkELJVJGQVkOvwEq+/jha0ZXDN8KhWBerZXlzM8pZjf5G4mxRbAJmIPB52QvZOXdw8mz5tCwNDo9r4XLRBpQj56eQHjj+jPsHHhUfUPX54fYXgBqlItXgpsRpoHzu+zXVvx6zrPHHNa1H6/27eTlaUFBJsM/vkNnQ8f/IQFnz+P3WFDSklCiocHv7krQpd45TdreeK6FyjJL0XVNKZfPpmrH74kSl8YYKe3hLd2L2SPr5xRaT05+5qjSHO0zwAt/nQF7/5rBuXl1ex4KCHcXqgJElhRsRMIa0B0mEsTkmGPtzla5LQCfyVv7V7Ae3uWcPOgkzi161gAvMEQ5770FjWBYEOVo2ThznzOf+UdZl5/GVorcXzDsnhr5TreXbUe07I4ZegALhk/6hdXohyP+f7MsAJfQ/VfQCiEjaSJVPuDsYnGkY/otQ5yL5G3qJTwuzVTmsRfYy0v6Omp5pqe6zg6cw+LKzrz0q4h5PlSMKXCTX1XcG63rawr+oSxW7bxu2HjuaDbem7quwyHYqAqYFgiqgDLsMCuWLw74TPe3duPhz8cF7NdjmVYfPXe8kbju2L+tqgqtooJTmSzKytoGszat4Nyv48MV6QOwpNrF0UYXgDXplpSPivECFkYDZ2PA94Atx5/H6/lPYUQgrzVu7j79Acbc3dNI8RXL39HXZWP2978fcT2lpZv58+r3kCXJqa02Fizj/f3LOWNw37X5iDV+498yit3vUOwPhhuO2T0jmkQNV1gWRYD3Dm4VTv1Zhtawe0hUQ2nrjUnxviCicS0dB7a9CnHZA3Bodh58Nt51AVDEeXlppRU1/uZl7eLY/r1bnHXv3v3Exbv3kugQZ7zmfnL+HbrDt657LzvPfj6s0P+Qnq4/RKQUseqvhmqbyDszfpAekH6wVhDy4b3h2MhqDVia64KJP0TKhmeXMInh33M6V22k+kMcEL2Lv47/gsGJlYStDQe3j6GGYW9qdHtVAcDPLJqDn/utxS3Fja8AJoSjlYGGzxTn6FRpTuxAKdqcmHuZhLzFYQVfVEKoL7JYFVaZrSmQyhFjWkcbIpKsS9yoKq03suGiuh4Zcp3JYhQdEimuqyWbSvDHuZb//gwSi845A+x8KOlVJVUN1lP8vcNHxKwdMyGAoWQZeDV/TyX923Uvpvi9wUaDS+AsMA2uy4cDmhKwMLzjY+TE37DP3r8Def1u9G2+GNssWWUfSGcT5fivn0f9ncqEXUND6QWOoy0hG6ZvLl9Mcc++RIfrtkYpeEBoJsWeyprWtzGusJiljQxvABBw2BHeSXfbY+tfve/yP6Yb3s+HU3c+DZD1j0GgS8Oyb5VIenliX1DDE4q563xX/D3wYvwaAZaQ56vpkjcmsE9g8Oi5EFL5W+bJrKsKgcA3TQJNZcYJPzWXOBP5M38gdy/aTyTZ5/Lhopw1dnMkh6UTVDZdUkie0/z4M8+EEe1VFicWcinW17CDG7gjEuPwOGK9NTdRWbMlwDDsuiZHDlgt7h4D3Y1+gVM8ZkxXwYVRVBfG07R27O5IGYRiM1hoyT/QDPWimAdVaHogU0TyaKyltsW7d9H8/Q013NlaOv9YQPsNSFkYVvsQ392L6GAjrQkZp4P920FKAXte1ira+pJuGEP9q9qsK3243yrkoSr8xGVRtsrN8NC8vLu2ZT565rIj0qEzQTRcN2oCv2zMlrcxuq9hZgxFOLqQzqvLl3J0t17f1ABzs+JQ2V842GHJkgpwf8mBwbMfnruGLCYa1ZNpXdCDZqw2FibhhCCOwYuJcUeJNkWu8nigMRKFCwsFPQmta0mSvPwJBD2Int6atleN4qvFw9Cq7F4ZN8kbj5zLjetOwo9WYJQCaUp+Hra6DLDiyffILl3gBeumIEUCqEKGNGvC1f88Q+89OgSOnetY/KUPHL6KLyndeWzoq6NpZsuzcbVQ8bhsUV69gk2O2oML9k7OhXnLh9KM+/XNCwGjA/LPA4Y14c9WwqiSoP1oB4RF3Zq9hYNRaKt9TzhtOyUKP1iEZR47irEzLFhdbah7Qkhyozo540usX9UReB3beQ4S4n70RJE8MAxipAE08TxRgWBGw8uRxrCHTC0dD+hEje2dD/OXB+i4YFtlLvpEerBhB6x2xUt2JHPjHWbY3rMACv3FHLNOzPok5HGqxedjbtZyp+UEkvK/4nQhERgxnBOfgp+8cZXSsnmPaXU+AIM6ZFFovvAzbZtXxkvfrWMvIJy+nfN5Irjx9BTObhXxY7EkjA+rZh5R7+DR9MBiSkFq6qy6eoKy06aUqCJGB6JqcUcOLAQ1ITsuFU9wgjvt3dTc238q85Btd/PRn8WF80+mYCnSdhACbdXLzrBw+DKMv5z8UwS7AeMkTTzOXH640w7+XpU/20ITIQwGM8uru/bid8sPZEkRyJXDx3HmX2i82iP6NwDNUaDx9pJmSTNL8deEmg0wJpN5frHL2ssrDjv1tOZ+95i/N4DOcwOt4OTrp5KQsqBuHKC5uSwzH4sKtsWIUbjVG2c1mUcnzSIzx/VpQdZ7sSI48jsms6QSQNZP3cTehMjrKgKSpkJpSZ9RvZkX6CA+rpIvQ5hgrK7bc9XVJiImujsE2GCbZmvRRWQVrepguI00ZKDuLp7EU2SQJydAozt4omZl/7UvMW8sGgFfr1lB8SUkvqQzpaScp6Yu6hRRyJoGPzr2/m8t3oDQcNgUE4n/nrCFIZ1zv4eZ/DTcagG3H7+j6YfQGFFDWfc8ypXPvoe//efz5h2y/O8OnM5AKu27+PSf73NrFXb2VVcycyV27jon++woXhUC1v78b4qKcOf/W95nZx+PJqBRzNJshkc3WkfnZz1LPeewtN5w6k3I9Op/KbKG/mDiC2jJbh4+fEUBzx4DRtm0ziucKEmnMuzN04mJ8WLyx6izqHG3I7pVjAHKnjs4RhracDF5to0QqagzF+JVX8biggiREPTSvz0cpfyTl+Dv3j7MEGmx7zZHarG79UBqF4D4TfDX4KUSE1Q8Kd+VJycg6UJFFXhljdu5PgrDnSm6tInh8cX/p3RU4fhTHDSKTeDK+4/n6sfujhqP3cNPYvBKV1xKDYSNAd2RWN4wgDuW7icWxd+xV+XfMuR7z/Pc+uXRa175zt/YsSUodgcNlyJTtxJLv74/NV8FXybr0Jvc89Hf0aPIZ0pNTCGtq2hK52Cllo9S/f3u+6kCaZPw9GlPsLwAphYfFm0mkCzAcEKXz3PLVjequFtSsg0+WT95sa///ThF7y7ej0Bw0ACG4tKueS199lTWf29zuGnQMp42KHDkVJyw1Mfs7e0OmKk97nPlzAgN4tH3p9LoIknY0lJIGTw8NdTePmSTYQrwvavp0DizVD/Fph7O/xY99skTYAiYle8acLiiU0WiytGkekMNOr5OhSLL4t68sj2ltMPd9WnMGnOuYxLLSLZFkIIhUeGzWdm2TDumLmCrgkJ/PHcxfQUVVyyYRrFodjpV1vr0thQm84j28awtDIHm7AwJYxOLeXpkbNwNLMTAj81BW/x5O/WYhomR549kT+/fH1Erq5pmHz2u7foWeOjvn8illNBqgpGpgN7kR/PuhpcTjvHnH8ER519GEHTYO6+XdSGgkzMyaXn0O488PWdjdsr8Nayrbqc3snpEWlUiTYXz4+/mt3eUor81XR1Z3Dch69Sb0QO2D22egGH5+QyJOOAt5aQ4uH+z2+jqqSamvI6uvTNjqiuy+iSzlFnT2T+h0saMy+EAOwq6kktx1UP7EDFGO5GW11P059fOgShU1LaXj8WClDrRO3aUgm7oCZUj7OJeP6qvYXYVTWm3kdL7I8LF1TXMn/HboLNatVDpsHLS1Zx9wnHHOwZ/GTIDjKsQogU4AVgCGHjcbmUcnFLy/9ijW9eYQXFlXVRbXcCIYO3Zq8mryC6XQ7Apj0+RPrbSO+zYGwD26BwlZrWB0vJgZpbaVkO8ofT2mUwKKmEhRXZ3LHxCB7eNobunlr21SdQHnI3WappebAk1RagWncgUVhaFdbgtStwxJwcqnQ7YLC1upp/7xzCUyO/5Xd9V3PXxsOxmnn6IgjpSxV+/+FpmDZw9BHUDgjvqtawI2KEQgB8tTSGBeZ/sJShRwzkhCuPbZy/b3sRelBHmBLPpsjCFZvDxoipwzn+t8dyxOnj2FBezG++fhdDhjtzmNLiskGjuWXM0RT56rhm9kdsqSpHEwKbqvLg4cczrXvfiG32SOhEj4ROfLF7a0xPPGgafJC3McL47ic1K4XUrBSklJQEatCEQrojHKa4+aXr6Nw3m0+e/or62gBDJw3gyocvZk9GHX9b/yFes/Vrxn9zNu47C1D3hJCqQOiS0OREQickt7peSwgBKSOrkZaCLq2oC8uuqI3HDmFnJcnpiGhn3xSXTYvyiBUhmDqgDwD5lVXYVTXK+BqWZHNJZEHKz4sO9WofB76SUp7V0EjT3drCv1jjW1sfQG2hB1i114/baccXiI7HJbodSGMPGBvC0o+yDhkaj9D6oLhOxJIB8D4CVgX7839/KvonHOhYW6U7qaqONVgksAmDw1ILubHnanql1FClO0izBygOeHgybySfF/cmZNkQSDRhMTq1hBdHz8SuGJzfbSsf7OvH6ppONN6xBnT5CpRQ+G/VhOTNoHmhciysr8mkTrfjVo2IuLI/oPCadzj5f83Fs6aK1JklfPLvryOMb2Kqh1CMlu0Aml3l/i9uB8JVcJd++z7VoUgj9trm1UzIzuVvy2azu7YKU8pwDxBD58a5n/LJyRfTLzXa+wyaRsxXfQvwm7GPB2BzTQF3rn2H4kA1IOmdkM39I86nizuNi+48O0qYZ2X+YurN2IOkTZFJKr7Hc1F2BlHKdMzeDmTGDytmCFkNxjLK8Gpc1+84NEWlsKaWe76YzfwduxGApqoIojXsjYZBzabzpJQs2JFPSZ2XXhlpMT1mm6Iw9Gce8+0Iz1cIkQwcCVwa3qYM0UZe6i825jsoNyvmaK3DpnHMyD6ce9RwnLboZ8/wzpsIVvypIbwgwSqF2nuwqv6INMsRrtPB/TtQuvJjGN7WtHmynfW4lJYNw34Saiz2vdCFv9x+Erf96zhsPkiy6fRLrOafQ+fzm9xN9EmoYtv0F9l83Mu8Oe4LXA15wELAkyNnR+wndT0oeuQ9rJjg2QOqPzxifMXK46jWHdTpNryGRsBUeXPvQL5y9ifUzU319Bz23D0YnxF5PaZlp7bYKDPoC+H3hY3tqrJC/EZ0LLLe0Hl2/TKKfHWYzdsAWSavbV4Vc9uTOveI6gIN4NZsnNCjf8x1KgNernv5cQrn5BOqCRKyTLbUFnLl0ucwrOhrYV3VHp7a+lVUh+HWsHo5MMYn/GDD2xYDk7qwtbqIM//zX+bk7cKUEkNKgoaBIkRU5dv+76rpmUigtM7LrZ98TXZSItMGRIo6Adg1lUvHtzSOcuiREkxLtOsDZAghVjT5XNVkUz2BMuBlIcRqIcQLDT3dWuQX6/m6HDZuOusoHn5/LkHdQMqw4c1OTeTMScNw2DSqvH4+X7qZUJNXpeunLMWhNTdwOgQ/R5Z9C7ZRoK8BfvqsiInpRQxKKmdldTYtBSiEIdE2aBgNXWw378zkhvtP5u1/vYPdZuLWDG7utxwpRYu5+51dPt6a8AW3rZ9EwcpEkjYrEONBhQpaHZgu2FKXzsTZFzApo4BUW4DFFdkUBg8UYEibgpmk4bhkcNRm3Eku6iq8UdObnmLAaLmVT20oEDNdzZKSfb7YedMZLg+3j5vMP5bPQbdMTClxazaO7daHSTHU2/ZsKeDGKXeiVvtwCYkwIHBJOqHTU6k3Qiwo2xpuJd+ED/YuIWgdurTFlghZBlcufY76Ijv1fg/NVeyEgBSXk3Jf65KnEM58WLp7HwHd4B+nTKNbSjL/XbkWXyjE6G5duG3a0XRJiS7E+TlxENkO5a1oO2jAKOAGKeVSIcTjwC3AnS0s/8s1vgBnThpG3y6ZvP3daipq6zlqWC9OO3wIbmd4kOHO30yld+d0nvxoIcEGr6pzams6rEHQW4yft0hH9VKUwKa6DGIZXoFExSJxF7gKDgxvS6kQCGksWNWdY8aHK8OcqhEzXa0pw5LLudu2nvu+GIU30YGpxahaM8FwyfC7ugWmIfiusBv2KhMjVYNmzpu0q1T3iw6DHXvhkXz23EzqsuyEurmwFQdx765n6KSBjWllY7K6RMXvIZw/fFafITywYm7UPKeqcVSXljs7XDJwFBOyu/FB3gb8hs707v05LCc3KhZsWRa3Tv87vuI6hDzw7Ttfq8Ds58QYqlEaiDbyNSF/izHUQ40uTfSAgj3bjxVUMart0PD6bViyXYa3KZ+s38RTc5dQ4vWR5nZx7wnHcsaI6Aftzw1Jhw247QP2SSmXNvz9PmHj2yIdYnyFEC8BJwGlUsohDdPSgHeAHsBu4BwpZVVH7O9gGNYrh2G9clqcX1rtbTS8AAVVSfTu1HGH2XFNbFUMZSBBM/ZPpgqLa+o38+ma6As+GNIoLm+i/SpkO47JwWsv9EcPmdhqA5gJ9gibL4UkmCZJ2BEibUUANQTBDBVbjYXUBPkXJtL8IaEg6JqUErWnc+46gxfSC6jKVKHBuDkrdZ4+9/LGZVyajQcOn85fFnyJYVkY0sKt2RiWkc1FA0dS4K3lv9vWNqqi2RWVDJeHs/vG1ujdT//UTG4bO7nVZbYs3U5dpTc6EBqS2D+rRg5LYnBy16j1JmcPZlXVTgKtxJAPJa5uPhANxscUeDenIEMH13xOAF2Sk/jbV3MaY76V9X5u/XQmc/J28c9Tj/uZC/F0zICblLJYCLFXCNFfSrkVmAJsam2djor5vgJMbzbtFmCWlLIvMIs2ngKHioG5WbibKGA9PWs8/lDHvRD8cMOrgud6RNZaHCl/arH8eERyKRkePzJWLq3NpF+PCgD8IY0F23MxzTYOTKRRVBD+HhTdwlFchwgZjQnJWk2ItBU1ZM/yY6uV2LyShN0GjioLR5mJrdqkuXiaQ1W5fPDoqF09m7cSX64L6VCRThXLqaJ3dfPEvsh47Sm9BvL5qZdwxeAxnN1nKI8eeRJvHncuNkXljnGT+efh0xmZmUOf5HSuHDKWz0+5hARb2xq9beGrqUfEqNYSEtQ6yfCUHgyKYXyn5wynhycTrXmi7X4OsVMs1LBulKJKhGbh7tV69w2XptEp0YOtQSTEpigkOh14Q6GYg21fb97OxIef4/ONW9lTWR3zzeXnwP48+7Y+7eAG4E0hxDpgBHB/awt3iJWRUs4TQvRoNvlU4OiGf78KzAH+ryP215EcM6IPz3yyiFBlLYZpMW9bT/768bH8+YSFZCTUxVhDEH5m/VRZDhIh7AhhR9oP595Rs7hioU7QUrFQUIWJCljbXDyxazxuzYoYHBOKRedOtQzpW0R9SOPr9X2YubEPPdKr6ZpW28LDwQaynM5d69ixPSxkrgZNXAV1jfZCAEJY2FIlgdpI4yKAbu97qfhNOv5UgaooCOBvE6cyLCMH0/JTWj8X3aoj3TWe97ZvINhswEq3LL7K34ZpWRFlqr2T07l17NFRRyyE4JReAzml18CD/4rbYNDEflElxgA4FQ47fSx3j76ohQISG/8ZfzWfF6zime0z8ep+LECzFBzPleKcWQdDPdSelYg1wIUZW1OpVVSUBu9VYjWoPyfZ3HR1prG5bl9EybNLtWNYZlTLeQgbYdVjhEdSreiHhSbgzBGDeW/1hgjNB5uqUtFKiMKv6/zpwy9waipuu52/nTSVY/u3rKR2KOioPF8p5Rqg3Xq/HSam3mB8P2sSdqiWUqY0/FsAVfv/brbeVcBVALm5uaPz8/M75HgOhmqvn4fem8NXy7diSYlNVRBC8OhFWxmfO59wxogCqJBwI+Xls0nSVmNJCBkalhQku4IH5eWGDIGiSMKaLbGSexoQHkTSvQjXyQDI4FI25f+ZR7cOZVV5FhkECOW5sXwaHkeIsho3WpXEVh/eXlbXOgYOKWF0zwKG55aQleRDt1TsqoFpCdyO5jeiALUHWGWsWubmntsPw9Cb34wSRZF06Rbkr09N4vcXbcRbHTkA6XTZuO7OU+l/bG9qggH6pWbgUDWqA+tYVnwVEokkrND++3nnNCqsNUURgi0X/Qn7D2xh3xHMePpL/vN/bxDy60gpcbgddOvfmccX/h2784DV3FJTwIs7ZrO9rpjeCVlc0ecYBiV3RUrJ8sodrKncTd4Ta9j40mpC/gOZHw6XHccZOey98OAscKLm5MMjb2ZO6SaqQz6GJufS1ZPGlpoCblv79oF0M8AmVByqDa8RO+dYWpC8pwfl1cF2V7kdLE6bxtuXnsvA7E4/eFsdIabu6tNZ9nr4qrYXBDadds//npi6lFKKFrLwpZTPA89DuJPFT3E8zUlJcFFUWRc2njIstwdw05sDuP/i6RzZbyfh0SMb+N/l6hcOp9I3HLddp6Q2PFo8ZVAe95w2G7tmNniFre/TrkkKqxIprUtnxJDrwT4SKs5o1iFDAZzgnNo4xfC9Ra6tgktSNtOv3McNxy7BcXz4ePdUJHPRf84ikK7RfWAlz1z0KXbNxKEZaKpsjD87G7x23RQcMPwaCAcIJyQ/BpXnMmpsKbffs4QnHxpJZWW4TFZVBcMn9OOC64+gNutd/m/dTNZf3Q29PpmUrTrpc+vxKHaGje/FMSePCHeWaMjlt6TBipLrMWRkZsOgtH2sLesW4aUJYGRm50NieBcW7uauxd9S4Kulk8vDbWMnc+r1x9N3dG8+/ffX1JTVcsQZEzj2N5PYHijhsTVfsKW2ALfmoE4PYEoTSVhUfXnFDh4dfQmj03sxLr0P49L7cPqbb0QYXoCgP4ScUYzzot4ErPbHiB8dfQnJdjfH5QzngY0f85+8WeHscxmOizdFl+FQ0KDkrmyq2Re1rW6edD64+kpueP8zFuzIx693fKw6ZJi8snQV/zy1eZTy0HGooiE/pvEtEULkSCmLhBA5QIeVuewXyymuqmNAt050Tv9hqSzlNT427i6OktALhAye+6qGo0f/Hsv3CtQ9CvgprplG0NCoCxyIJ87a1IclO7oyecAuLEthVI8CTh25tVUj3CnJyzVvXM5n404FYEfoORL0O0l37UIIgbANQSQ/hBBOTNPipTcW8MHHWYSMi0hJ9HPlWcuwawdusNz0Gt68+l1enjeK649dSrI7EFNMZz82VYI6GJLuQBjrQc0CxxSEsGMlXAO+5xg3sZjXP/gS01SoqkzFyrkd3aGzo/pO/jKvLxWBHphSBRdUDbdhG5rNg0NPYtiICqi9GsvcB/axCM/VVOlFWDI67/zM3kvZWdOZkOXEb+g4VQ2bovLA4ce1+zfsKD7K28gf53/e+Pcebw3XfPcxd407hssnjGHQhH6N87bXFXHt8hcaB9SCzUITEghYOv/cNIMHR15IV3c6mqLi98ZOU9R9If486GSe2PoVAVMn2IYRvnvoWQxL7Q7AvevfZ17p5ghPNxaaUPnTgBO5b8NHlASqqTdDuFQ7dkXj0TGXIITgibNO4ouNW/nzx191eJzWkpK9VS3rCB8KOirscLD8mMb3E+AS4IGG/8/oiI1Wef1c/8QH5JdUoygC3TCZPrY/d/5m6veWsKsP6igtJPp7AyGk1MH7JPtze7unV7OtJLpqyqlZrN7TmYKqJJbt6sLJI/JQm2k1WBLqAnaSXSEKqxMpqgxhWRZ/fW0m367ejmEeR6pbx+0Icf8lYxmQEvY4n3tlLjM+W00gGPYEK6o9PPraEaQmBRg3pKBx+11T67jz1Oi0q5bxozhGgyNyIEx4rgW1G9L3HFgVCPsI9qTto8J7L7LOZEVpFjUhV9jw7j83oVBjD1CduQKq7qOxDNufjwx8geW5k1hpcmnOeu4e9wFryydRFhjNsPS+nNNvKGnOVqszOxwpJbctnhlz3j9WzOHigaMiig9eyJsdrpRrg92+Mi5e9DSaonJ136mkDc+ibGVR1HL9xvbm5K5jOKHLKMoDtXxRsJrnd8xqFIBvzjPbZmJYJhMz+vFd8UbMdnRSqTdDhCyTNw+/gfllW9haU0BndxrHZg/FrYWdCUUIBudk4bRp1Ic61vtVhaB/VmaHbvOHIBH/28ZXCPEW4cG1DCHEPuBuwkb3XSHEFUA+cE5H7OvOl78kr7CisdwRYObKbQzolsV5k0d8r212zUjG47RHCO1AWHB68vDe4VJieeAivHHqYm56ezpBI5wlkZHg4x9nzWRwl1JMS6HW7+CvM47h4zWTOHPUUvYb7ZChUON3ctHzZ5LkCnJE390cOWAv5933EjsK9w9mSc4dt4zzxq/HMP+LVQbSdjSff5VLoFmVajBk45WPR0UY3/2OSnvizxIN4Tg65jwhBLhObow1ryu9hbLQEiTh72FzZQ5BMzqFKGRabCn+iCN7NY0rmiB9pOhzkC0YCKcWYHz2N6hiPsPTXuKdmWv4bOk6LEJMHZvJNcefhtsRrRC2f8wi1oDXwVLm9zWmqjVHtyyKfHV0SzygtbC1trDdebwBSwdL5+HNn2K/1I5zowBdhmUnNQW7w84NT/0WAFUo7PKV8dKO71o0vABlwVr+telTELTL8O7njytfZfaxdzI5azCTsw6kJlYGvdgVjQSbk+ykhB8klm5XFdLcLirr/YSa3KumlLy1Yi3fbsnjrumTOXZAnw757X4IhyoHo0NSzaSU50spc6SUNillVynli1LKCinlFCllXynlsVLKyra31Dp19QGWb90bYXghHB54e87qiGkbdxdzywufc8mDb/H0jIVU1bU8Iqsogr9efBxOu9aoB+G0a6Qnubls+jhQUiOWn9B7Hw+f9xX9s8uwawb/vvgThnYtwa5ZuOwGWck+HjnvS2ZtGcjO+ttYvaczu8pSeGvpUM5/9hzKvQnsKk/lq/X9uffUr3jhokcY3SMcgzt91CbOHbcBp80kwRlCEELoc7nu3Pkxj724/EDIpUGNsUXD2zRlRkowDIuNJeOjlguZJl/s3sqjqxcwY8cCdlV/SKHvy0bD+9muYSwp6UOsy9aumnRzx/qpLVR9OQMT72HPghR2z0vECEQfqG6GuPaxz3jlmyUUVfopqTR5e9Y+LvzX/XhDuw+ci1mCVXUdsmQwsmQwVtWNSLMi9om3E7fN1mqt02+//YDv9u5o/Lu75/t5cKHeduqe7k7ouCSM/g4cJ2Tx7OoH6T8mnAVgWCZ3rH2boGzbqw5Jo81QQ3OCls7i8u2Nf2+q2cfZ8x/h5Dn/ZNrs+7hu2Yv4TD+XTRiNK0ZloyDswbbWfFMIQYLTye3TjkZpdkFKoNTr408ffcGj3y08qGPvcCRIS7Tr09H8T1W4BUJGi0/JpiI5M1du5a+vzWwsK966t4yPFm7grdsvJDM5tlzi4YN78OatF/LOnDUUlNcwbkAupx8+hARX+FVMun8D9W+y34ud0HsfE3p/huG6kVCNF02NNESqYnHSsLXM3jyBZz87NWp/Uip4g3bWF2Qzofc+HjnvS6Y/cgkXH74Glz3yZhIEOWZcHo++dhi60XQAStK724H83TcXD+O88RtIcIaoCjnY6Uumq8tLlrO+0fDuv1+EAKFIko1bsKzFjTKPlYF6Tv/sDcr99RzZZTm9kjawplzBppgoAgq9KXyzd0hEuGE/ChZJWogpnfbE/I5Xzc/k3ms/xHCNAiTSV8MJ/9xG72MODMBt39WZonIN3TjwOxuGRlFpIm8vu4crJt6PrHuwodVTk+88+C2yciNkfI0Q3++yTrA5GJqezbqK4pjzt1aXc+13M3j8yJM4rkc/ruh9DKsqd7UZm42FzLE1drjwC0F6z/TGeZtqCjBb6CIhJYRKHQSLPUhToCXqOLv5UJ0Hl/q4x1sGnQZSHqjlumUvRDT7XF25i2uWvcA7R/6eVLeLFxYtp6o+QPe0FIZ0zqJbSjLTB/XDr+vc++Vs1hZEf19Bw2RneSVbSspx2Wz4QtGx/pBp8fKSVVw8biQZCa3KIPyo/E+HHX4qMpI9ZCR7KKyITAZXVYWjhjV4DabFP/47OyKEEDJMausDvPjlMm45r2Vd0Z7ZaS3OF4k3IYUd6l8FGQQlDRJvxYYAzUbz1kN2zcJjK6as1IeiCKwY/bAkUF4XvuiEkBzZfzfJrthpQIoicTp1dO8Bo+ewm1xxxgrqQxo7StOYuaEXFx2+mns2TeDtvQOwKyYhS2Vy5l4eHjoHuxp5g2qKJDOxlqrKBaRnHAnA35d9R4G3lh5JRUzL3YBNMWma07y6vFsLbVckue5a3hj3JXZFEL60DEoCbmaV5qLXabx7YzYyNRGEQAiBdLj54q+JXDZkAQmdwvvYV5RJSI++LHVDZcc+E1/pqbhFDTF0t8CqhOAccB4bMUdKSUVgCaX1C7AryXRJPBmXFrvq8fXjzuH4Ga9Q6ItdcBAwDe5bMYfjevRjWGoufROy2VAbW+O5lQTCCBSUiEIMvxlsWQlNguIwGyvRjBobAcWNq7sXRWv/C/TSih1c2HMSH+9bHpUVYWJRHqxlTVU+F48bycXjRra4nXcvP5+lu/dyyevvR52rJSUfrWu1yAu7qrKmoPiQ5v7+ErMdOhwhBH+9eBo3Pv0xhmlhmBYOm0aiy841J00EYF9ZdcxqG8O0mL9hJ7fQflFnKSXLtu5l4+5iOqUkMGXk9TgTbgDpD+ffCoE09sYUQPeHNBbndWbmxm0txs4sS2F4bnjgRVMkHrvO6j05HNE3v7HT8H58ejJlDhe2gEQxwZGgc8q0zZSF3Hz49UC2lWTw8m9n8PqeQby7tz9BSyNohX/e78q68fetE7hvSPQrnl01kco6wmp48FX+NgxpcXjOtgbDG4lCWEeiOQ5hcGmPjXR2+YAUcIzmyQ3VPLVjKCqS5K+rSU1QIirFhKog3Qksf7kbk/9vNwCpSSHsNjPKANs0g+SEOizpb2wCGYUMgLEDOGB8pTRZWXIjFYHlmLIegY28mucYmfkvsjzR10Kyw8mic65hbVkRp332ekzjuaeuGiklNXo9W+sKYx8L4NYcmNIiYOpIEwL7POgVTiRgSw3i7OrDYVeYnDUYTTlgfF/dMTdsEGI4ZEIBLdlAcepISyFhQDVCi9brbYt11fksLt/G3vqKmGGL/aly7aGkztviQyYQQ4muKRaSdE/b3T5+LDpQ2+Gg+Z8yvgBj+nXjnTsu4p05a9hTUsXoft0444ghjb3ZktzhtKxYFFfW8cnijZwyMVL/wLQsCsprcDvsZCSHPdGgbnDlI++yKb+ksb3P39/8ljduvYA+nQ9kOgitGzXmsTitmY3hgpChUOVz8fnaAfj1ph7MgTvKadOZNjiPbmm1jfMW7+jGyt2dGdOjsDE315ICRTiw7KfiyjTxJ6vopoYXjZdWjMKx1kBKwcuXf4jLrvNK/lD8VuRAWNDS+LCgL3cPXIRdjb5N9tWuol+TpsKaMHFpoUht3lobFbuS6JdQydeKIOorFoKjMiuQIoMK19Nc+t1aNlWGswt1wJHoaPhX9Hq78jozySrEY0vhrImnY1of0jN3H756JwuWD2XL9lw0zWJE/314RCvauMIJWp+ISUW+r6kILMOU/oZvWUdKWFN2C8e65qMqscuPh2fmkOVOoLg+Wm0t0xV+8JYH69CEGrNiDGBy1mCO6jSIV3fOZeXSegyfwn4nUy93YtbaGXqEm1sGn8aG6r08u/0bttUWUR3ytWlM7ZkBVLeJsFnEaIHXJn4zxLfF6xme0p3vSjY2psvtHzOwpGRgcpc2tyOlZH7eroM/AMKnmOHxMKJLy9orPzqSRkGhn5r/OeML0C0zhZvPPjrmvLQkNyP7dmHl1r0YzV71pYQH3ppNktvBmh1FVNXVk5Hs5uNFG/EHQhiWpE/ndB6/7jTem7+WDbtLItYPGSaXPPgWCx+7IWJ6Uta/ePh1P6ePXovbrjN7cy9eWTAKv948GyD8IprsCvDHaYs5YfjWxuN6b8VwimuTQUrOf/YcLj18NUO7FbOvKhUl4SqOyn2Yd6/18tbSocxYPZBavwNLKgQb9tGrUxWKgBo9doWUIRWCloZdjTSAQsDmymI8GbVkuTVuGrmGDNfqcCfkBpGbRS8PYO2MXqg2C8tQGNdHZeVxYDkVBALDMhHCxrHzTiHV4capLmVfs9f2mnGJJO+oxVPYzGpLSVFqFg+s/C3vHn8SW6ouYuyIGsAgI62WnE5zWbWhL317VDIm7QiEPpOYRhwVlExwHBUxtcD7aaPhjfwlBFXBVWS4Jsb8vgB+P+Jw7l02OyIDwq6o9ElO45l1SzixZ39kC164Tahc2WcKOa5UXIEkrg5+jBURGxbYpYNTE45me10Rv1/xyoHiirZkNwQoTgM1wfhehnf/LpyqjeM7j+Tfa+ZRvg1QLZxdfChOE6ko+Iy2ReDnbN/FN1t3tLlccxyaSo+0VP597qmHPtshHnboOB644kSuePgddhZFj7oHdIObnv0URRFRRRUAW/aWccLtL+LQYl/V/qDB3LV5HDX8gIdls9mYs30M7y4f0I6jE+imyrGD87AsQchSKQhcS4kxDMFqTAmF1Unc//kBI9K9UxVHXVtBRqLJlUet5K0lw7Bk5PEVlCXi1ExynF7yfKk0v4NTbQEcRL8C+gyVb8t6UunczuC0/9DZsyYiHWzzt11Z92lPTF3FbCgzrtlewylpPRnwxxEsLd7LnH07CTTku5YHWsgqUaBynAvPx75m0wWlh7mw6n28n/dP+qfU0jR+brcbjBuxlcNz3ifF7kZWzI5I+9v/neI8AZF0e9RgmyJaVtQSbVz+5/UbRtA0eGz1QrxGCCklUkoWF+9lZWkhT65ZxNmDRjGnclVEVZomFJ4ddyU5rnCWzNaSspgDaAHdYGNxCR/7Nh1UVZuUYAY0tKTvXwJsFxondRnNun0lFG2wIzwB3H1qGpttBmWQq5e+wJNjL2VMesvx2DdWrDnoUmRFCGZcdRE901PbXvhH58fJZGgPv8hOFskeJ1cePwGXPfaNJyGm4d2PaVnUxxJSaeAfb83muic+5KWvllHl9WOYFqXVMcTAW6A+ZOPKl0/jkhfO5Kh/XMnFT8K7c9a0eExV3gCIcMGBN2iLsKvCkLiLDK6440wuuf0svF+mQIyLqcrr5Pm54/CHNPbbAZ+hsa6mE7NKe6CIMioDyxv0Fg6w+sNeGMFII2XoJpuX7eLMzgNZUryn0fC2ihB4u2tYKkis8H8KFJzkRk/RMKXErmxsTGdrih5U+ezb7xBaV0TqK6D2Iuw32MAxDdFpGUrKwwglLWrdrolnoIromKIQNlKdLQ8khZcRXDpoNKsuuIFbRx+FTWnoh0a4S4bfNJixNZ/bh5xB/8QcMhyJHJs9lLeP+ANDU3Mbt5ObmhIzLctl0+iVnkaetyRqHrTikcmGsEW9FrWMlGD4FerWp1K/M4FYacICwW8bNCfunzkX3bRw5ka2lxcCTEwe2fx59AaaUNc8+bwdZCUm/EwMbwOynZ8O5hfp+QKM6telxXSdH0ppjY/SGh9LNufzytfLeP2WC1Bb8KSbYlcNjh28g6FdS9hbkczn6/pjSjBb8RyEgBF9uoDnSvA+Q5rHj8tmEDI0kBJ3sYEwwUIJdzMugZxvoGgKEb+uZROEMiv4aHcOnV0mIbvGF0W9+Ly4F5qiMiHLTn6tDYvImylQFzuMoSgK1bU+aoMHcfM5FMY8cxSff7sawzCpz7VhOQ48KCr9HnITymlup+xOnZSBT7GsaBUD0/9MYuZXSKsGhAMhYvWxA0vqlNbPwafvIc05lnL/EgQCIVRAMDrrCZR2pqQpQvBl/jYCMQZyTWmRqWXy+uE3xFgzzBG9u5PmcRM0ahtDYQJwaBonDx3AW4sTGnrCNUOC7lXR3Gbj3zTIQCYMqiZmXYUE39YU0FWsgAaKxNW1HtSwhnOC5uSpMZczKKUrIdNke1k5IFFaSFXb6W1dFeCEwf3ZWFiCEeNJoRD7EO86vnX95J8UGR9w63AykxO4bPpYXvpqGbpx8EZYEdCGLQXAG9D55zvfMbJPF1ZsixYr2U+SM8CrV35Amqcej8PAH9K46ugVXPnKqWyPUaocPgaB065x42lHgDsVfK+iEOCwPvl8ub4fakAiYgx0a15I2ga1TbradHLXMKhfOP+2xtRYXNSXr0r6oylwx7jJ5CblsKOmHgVJD82ks2phAcvGFLP82+5YZqRFDGo692y+l5N7epm1twc+vxOpNnxxrfDFvk1cecZO1lUEWVzci9qGzsuaUPCHJmPqr6M0U1oTAlRNUh5YyPyCRSTZBzIy81HWllezq7aKAWmZjMrs3Bg7DBilLCq8EN2qxZJBFGHHpeXQLfFMnFomWe4paMrBlS7blOi8ZggPONnbKGtXFYW3Lj2XOz77hgU78pFSMqJrDvedPI0Eh4PLeh/No1s+jxRdtwShIhehKgfSAC0phKOLH7VBy0MoxHxvNes0aKJCp5e50cudOLr6cGYHCJg692/4iN41A/lo3aaGCjqBNAUiRqpaqr3176l7WkpU7zyAnump3DH9aF5YuIKl+eH7wqlp3HX8MRzT7+clKXmoStx+scYX4Irp4/H6Q7z93eo2vdLmWLL9BnjZ1r1888BVTLvl+Rb3c83kZWQleRuFcFx2A0vCPafN5oLnIiuvs5LqOGP0Zsb1hS6djyO9kxuMHUgZjqce3ncPszf3wjRjGwTFAluTKIhNMTi99wFhcodqcGSXPAamXcyxuUfSLTGZTRX/BCA1mMiTW4azzZvKoMRKzjt/M5sWdaber2EaKlKAVKFgqoethUkk7dLp9V0NoYoAUoOqEQ5Kj3SR5PRTq0ffuH7DjyF3cEL3CqZ3X8ez66dQ5u/EBf0XMDgtnzkzhjJ+6iZsdj0s8h1lyyUF3p3cOPcFakMeJBKbojI4vROvTzsHt83O+vK7CZil7M9PNqWB3yjEb+yjd8rlzTfYLs7vP5y15UXUNys/TrQ7GJSe1eb6mQkenjvvNEJG+Hdv2rz1tK5jqQp6eXXXvMa0xFEZPVml7oJuBoY0MVrIqGiKXVcQ79eRtXQvUlPwjs2mfnA6oKCXOXFmBzCkyfp19ayt2UTIMNHSAhhVToJFLpyd6yNCD4pUuLTX0a3u8/Vla2LarsKaWjonJXHdkRP4varQKcFDTnJSVLXbz4OOOSYhxG6gjvCFZ7QlP/mLNL6WJXn+8yW8MWslIcM4aMPbuJ2DWG3plj1oqoIZo4stwJRBOyMUyCBs3HtmVJHsClDjD78+j8wt5PELP0dVLByaBXITsvwNSLwj3HpAwuSBu/jHZ0fRQmIDlgqBTiCwyHTVcXrvVQzLiPTKNaEwuVtYq8CSOnvq3qO8No2b1k4laIaF2nd4U/iyqAd9smoQOwEhCaYqFJ3gIdDZhqvAIOsjP7phD8to6pC6Osj4MdvJy8igtiqW1yTRLQ1bQ8HH9cMWoym5CPYg0RkwKp/n7j6Nc274hpzc6DxTKeHh1dOoDDrZ/1JrmgZry4p5aNV87hh3JOX+RTQXu5foFPq+ZEjGXbG/tDY4uecA5hbs4vNdW4CwN6sKwQtTzmi3QakO+Xhr90KWlG8n05nEhT2OYGhKLo9t+YIZ+5ZjWhaJdhdndh3HG7sXEJB6o1cm98cdRfi0E/wpuNJN6o0QIDEMk063l1GztQpFD38v9gIvjp3VVJ3SB6vBG7Z0QaDSBg3GXHGa2LN9hIrdCFXiyGrIDBFwbOchnNN9InO37+Kh2fPJr6ymc1ISf5h8GNMHhdXdSupij3XopsnJz72O06ZhWhZdkpP5zwWn0Tn5Z9hMs2Ojk5OllOXtWfAXaXyf/2IJr327Ikoopz0ke5zUB3V0o/3lmhlJHl6duYKg3vI6egteKgKMxgEyyb2nz8IdUV7sR5pF1FbNwmNZaCropkLIVLDsCobTQgvIxroDVbXoOriC35y5hK4JVa0I7CjYRLjU2rTqkdLk1W3j8TcRy7FQCKGwc3wyPfPCXT3stZKkLTqBzjYyFvkRzb5im2Iy5dgNpNXksqOmE6FmOceWFPROPhBHtCshYBsW4fLTrG5VXHHHJ1SVJWEaSuNr9n6CpkqpP5nm3oohLd7P28Ad445s6YSJOfrUToQQPDzpBK4aMpalxXtJdbg4NrcPLq19/cmqQl4uXPgkNaF6dGmyubaAZeV5DEzuwqaagsYux1UhHy/tnBPVbl6I8OF7N6Vi+VUMu527hh2PJ01SrfsIzq3g+d0vNxpeCLd/8qwtp+6wLhiZTixdIEMqQpHIBvF6o8JJwuAqnJ39SD3cFUMokKS5uHvYWczL282N73/WWCyxq7KK//vka4KGyanDBtInI428smhNDUuCJS28wfDvuqO8gvNfeYdvf3c5tp+BOH4jhzDP9xeX7WCYFm98u/J7GV63w8bkEbEFY1qj1udn676yVpeZsXoAgWYdIQxLUBkYgG6GPcSc5DpSPbFyUnXqa77g2Icu5bM1Q1ixqyt2LWzoA5kqwRQFUwt7vAPGVHDhVbPoltia4Q2T5ZkCgKYkYVNS2OGNzhYACOQcOG7FgNQ1QYQhsVdGN91O7epFWoIxnXbTK6kMhxJ+TVcxsSkGF/RfjEM98NuYpoHV7G0hITlAtz6laNp+sfcwQVNlSXFvWnpNDJomirCR5hxL80tboJHtmdbKt9E++qdmcvHAUZzca2C7DS/AG7vmU6PXRxRkBCyd1VW7o7QhmhveRqRAqOEYbX1IZ11hCeMy+jAtZzh5320j4I1Rmi7AkR/OuRYCXC6B0iRN0Qpq+HYkNmxbghQ4cfDv8b/Fpmg8OGt+VJVaQDd4ePYCNhWVMnPzdtqDBIprvRzzxIstesuHioPo4ZYhhFjR5NO8BYYEZgohVsaYF8UvzvP1B0OEDsJrbUp9UGf7vjJEjJtbbdBniHVbBFrxePfz6oKRjMwtYkjXEhQhMS2FGr+LWsdfuf4Ug8c/WkDQ0FBaSNr3hzS8Acm9n0wiPdEgqB9QyNGTVPQkFYFkwvSC8Pt/G/RKvgRNCVfzLS/Zx8w9R+BUdQIxGompgehjUgOSQJaKVhs2wPsP21/tQLVZqIrkd8NnsaGiC+sruuLRgkzIziPbc6AvnmWBqVtojmgjLtDomngGullJSf0sfCE7s/YO5Ku9Q1s8pxEZ4UqpoRn3sKjoAkzLjynrUYUbh5rOgLSb2vxefiwWlm1FbyEk1W4UiT3Tj9anFmEpFKgFmNJCFQpp2alodi2615wAy2PDmWjRLTGVs7tP5NuqYhbsPCB+ZNY4qV3lADU8emt3JtB3evi73FNZHfNQSuq8XPbmBwf9xl7u9XH7pzN54YIzDnLNH5H2+1rlbcRxj5BSFgghOgHfCCG2SCnntbTwL874epwOktwOKutidwtoi017StAUBYdNjQgjfN+48X5CpsZ1r5/M4M6lDMgpp6gmgRW7ujNxcD6ZyQnhY/ZJNhdlMrhzaYRKmj+k8d7ycEm0JaGsNvbP5rDbyMqsxGzhato/iAhQVD+Tfmm/Y37Bbq6c9SEBM5E0Rx2mVNCtA9sXuiR1ZaRHJTXQ3Dp6lpNA0BN+VdUt7BX11PmcLJs3gNzepXTpUc6wjH1R8WYpwQwpGCEVzWHE9NAFCv09E9Fq/w/DqVAuTFZIG5qw0GMoqgngoUnHA+C2dWFy168o8s3Ep+eTZO9HlmdKqwUXB4s0yyD4bbjgw3EMQovuXtyUNHsCO2M1c4mh4SAAm6IhpWz0lKXZoEqXrOOtd6AHbczwbqdiwWu8OOlSjrtsMu89/AlGKHLT2FQyx3bnjcvPIysxgcKaWv6xZ2WMIxTQEBor9/qZuWk70wb1JTspgT0xOk8kOOzUfo8cXwtYvGsvQcPAof1MzE/HNdAsaPh/qRDiI2Ac8OsxvooiuPH0STzw9uw2Qw/Hj+3Pd2vyIjzX/VkzsVTIfjiCjYVZbCw8MDo+d91OFCEaDdCt703juUtnkObxAxJVkczZ0pMPVg6OuUVNEWiaimVJzp88kkxPPoXefVG5slLCpsrODEkPC8EEjbAh+Nuy2Y1FEpXBxP1Lh+2BBckbg2QsCbDfQmgOg7EX55G+vQclJZ0wG6y5tKsEsxMQisXSL4exxBKoNhNPoh93YoDRR22l34g9YSlLES6c+OahERz3l9Vo9ujfKcneG632LyB9qMBVK09lW11aM8MbHoWyC4sXp15At8SUxjmq4qJrYrSUZ0dg1c+A2jsAQblu57vq99DtRzOp6yV098ROG7yw5yQ2VO+NqGSTFlghgWIj/MrfgEO18dioS1hQtoUFZVtxCQe7imvx2uuoqkxsyEsVmCbMyivhPvssbh8/hTvfvYkHLnoCy7AwTBNHipvfvHAFpx03vnFQcOaWvHaV0/7+w8/5OudS/nD0Ydz22TcEmuSiu2waI7pkR3jPB4NERhzD+sJi5uXtxm23ccKg/mQlxZZ9/bFoSafpoLYhhAdQpJR1Df+eBtzb2jq/OOMLcMrEwdT4Ajz2wbyYPqCmKlw6bSzds1KZs24nzUfGddP6SVNiLCkbX30qfImc8eQFjOpRSFaSl40FncivaLkaKMnj4pqTJzJxYHe6ZCRTE8wkv+7biFLioKmyuKgPn+waySOT3gYg2RE25nk1sQTIw7pl5yUUUtvZiz4MynYkk5AeYNyF2+g8vJIFd4zDNNTmqyGlSigQnq4HNQI+JxXFUJyfQcGuDI45I5zylp4YJKmfiS1Gcr/ARjd7Blh5ACytzGGnL4VQDI/3xOxdPDB0Hq7kDKR1IULpeF1YKSVf52/nxU0rqA54mZo+j9/2hKXeDO7fG34LtSjlufzHuajnUVzV99iobRye2Z+r+k7hqS0zMU0JQmLWa9TnJaElh3B29pOUYGNQclfO634YA5O7Miq9FzcOOAGAP6x4la93hBoNb1Ne2LiCvLwqnjjzZN4rfoEtK3cQUmHYqD5ozQa3TMtqV4cKS0qmPfUyUwf04S9TJvH4nEXUBIIIwmlzxbXfL26rCMGILjk4bWHP/q7PZ/HJhs3htDdF4bHvFvHAqcdx/KB+bW+sI5AiZkXo9yAL+Kgh11wD/iul/Kq1FX6RxhfCg2cOuxbT+z1mRB+uO+UwNuWXxLwQBbS7cWB7Ktvai8tuY3jvHMprfHgSe/PFup1trtM1M5mzJg1r/DvZ0Z+Vpb+li+d9uiWGM17sismQ9L1owgAEqnDQP+2PAKQ73ZT5fVHbTXO4eODcxwDIq3qBbdWPNc7buTW7BXeh+fvzgb/1kI1VcwcyacomjupUi1vAiEtX4lQNNodUipoMAiloZLrGgm8xANu8qZgxXw0F6XY/Hs3E8j6O9L8H6R8hlI71nB5ZtYAXNq1oFNjJrx3ER0U9UFP1yAeCNHl913wmdRoYUxHsNz2P5OXPt1GkVyJ1BauhH59e4cJel8xpJ/Tlo5LF3L72bSxpcWKXUdw88GQ0RaW7JwM9VMj+71hRLJJS6rE1vDWs09dwwswtdAl1ZUteHZaUOObM4vdHH8Zvxo4AoE7343NXt7vlkAS+3ZLHN1vyGp0YCTHDEO1BAMlOB/efHB74XLRrD59u2NLoVe+Xgr1lxtdM6t2DBEcLuZQdTQfcvlLKncDwg1nnF5ftsJ+c9NgJ3Q6bSv9unQAY1D2LAd06YdcivYP2/hZDe2Qzsk/bsnvtRVEE5x49gnfvvJjHrjuVCQNzW03/dto1Lp4aHf+/adQVrC0Zgm6pKA2v+Rmueg7vvIMiXzqjs14hxTEEgOuHTYgatXdpNq4dNqHx75L6WY3/3ri1O699Mg3DOPjntqqZ2PakkSBAE1BT5OTxf4zhqSuPYemr/bFMAYTTnZZWPB9uXAr0cNegiWiD4VZ1+iZUA6Cgg1mMrH/toI+rNSoD9Ty/cVmEsllIaniFhhXjgRC0dF7YPjssCxmDPhkZWF4bliHQUoJoSSEQEivJy3tFC/EZQfxmiKBl8HnBah7b8gUA53Sf2GQcQJKa7sVmNxrDOIrNoqZcsnprJX7dIGiY1AaCPDRrPp+s20yJv5qz5j/C+yXzseV4aa9ggdWupdpHVlIC395wBT0adB0+3bAlZnt6VVFYtDO/g/baDg6RtsMv1viOH5BLssfV2JNtP6qqcGoTPd+nfnc6px42GJfj4AZjOqcn8ci1p7Bxd+yWM7HQGhTSbS0opgkhmDCwe+Pft54/hSSPE6c9bOjUkMRZbpBQYuCusbjgyJHkZqbwxEfzeei9OazOK0BKSaLNweQuS3GoMcp0RZDFRQceNpcMHMX1w8bj0Ww4VQ2XpnFM116Myuzc+Fbg1cOv//6Anfc/PxpD2ggliMhxiqYN4lpCQlayH0XAjrxk/nD1Mcyb3ZWqOjujzs1DUSVgYUo/PsvLdl1BYuPwjEKynPVoTUTrhbTQfQqL/5XDC7OHcvHy6Rw99xRuWryTXTVhNbu6UJB3tq3jiTWLmF+wu823GWl5sXz/xaq5E8v3JtLysq68GHuM0mJdqjG9cSlhXtlmps26nxuXvxwly3j9pAm4soMkjajA3bMOd+9akkZUkNwjGJVyFrR03t29hI/Xb6SLO41bRx+DIsDuMBCKFTVQGSxyR71C+3WDp+Yv4fGtX1ITqidg6Tg7+/EMji5g+bE5pm/vCG+2NcfiJ5WZjAvrdCyqovDSzedw20tfsmFXEUIIOqcn8ffLppOWFM6rDekGXyzbzK7iSob2zGb5lr3t+o6TPU4+uudS7n3jG/ztzCc+algvTpowiNV5BWSlJhIMGbzw5dIGQyxQhOCJ60/D0aTstFtmCp/cexmfLt7EwqV5bFmyB9MMD1Y4Dfj0v8t5c9YqDGFhScmHC9Zz/LiBXDRlBAmu2NkeaU4vmypLObnXQADy91ZiLqrnpLJctntq2JBYwdyCXXy3byddPEm8Of1cbEoKpulny45cRIMHGkpVkZqFvdZCWOFBFEWXoCrhlIpmnTyFsPAkBBnUJ6zg9eK/hxIIhEVu+h5ZSKyrO990kuyaRJbxFW+P+4wb105maWUO0hK49xpkf+1nTVYWX3p7IYPhfRX4LWZ++hoPHXE8f1n4FaZl4Td0XJqNwWlZvH7cOThjjLJLswBZcRZY9YT79LmQdY+TzlUYMeQe9aAau9NE4zTJkvI87lz7Do+MvrhxviPRwp3rQ5eA0iSjhdjtoySSu7/+BhWFS4ZOwCad3Lfus+gMEYsWY5cltV4WluVH5A9rbhM1KYRZayf6RCTCqSMDthjzvj8nDo6M4546bBBfbtoWJUlpSYvDeuXyk3AIiyx+scYXICs1kRdvOodqrx/dNCOaZ+qGyW8feY+8wvKDKshw2jUumDySVdv2MXP51natI4CumSlMGdmXKSP7AlDt9eO0a2zdV8awXjmcOnEw9hidYhPdTs49egTvvLAQo4lAkG6Y4XzmcgMzPbxeIGTw1bLNTB7emzrhwqHohAI2EpL9jTdrZSCBbgkpfLcmjy9mb2DVnDxM00JKsLlCTOhdRkWWg81J6ew0K7n+ow+4tMcpyOznsEyxPw8iIr8YKXHvq8dV4MNIcGC6w7KXSnK495xlKqRk1HH2NbPZ7/Rv3ZzG/hvbkaCj2qPDCpYM4dMGUhtcyRUrx7HDl4LNssLVgoZArbMouTARaTtw85hSoV4PcdP8L7Ckj+5J5fh0B/u8aawuL2T6xy8xNqsrlwwcxZCM7Mb1ZO29YFVxoNbUD/gZpD5Mrut08rxJmISzUqQEm3BwSY7Kf4trCFkNGWNRycqSpeXbqQjWke4IZ5LM2Lc8Zjt4FREzRVCagoDf4p4vZ7N8TwETe+by4NhT+Oumd6BpVxIFhM1C6tFeukNTqQ/qYUW0Jsfo6VtL7Zq0xhSzhj2CkMjg90vL89ht+EKx88ybF1eM796Vs0cO5d1V68P5yooCEh454wQ89p8o3kvHZDt8H37Rxnc/KQmReq4VtT7ufeMbNuYXt1vF3mXXsKQkNcHFi18vQxECvYV2Rc2x2zSmjjrw1F+4YRc3Px/2XixL8u2q7RSU1/CHM45EGnsgtByUFHBMQgg7JaW11PiiPSMBaH4ZIQIZ0A0WrNuBWjGSCX12gIA5Xw4lecg+ug0q4avdYxEb1rO3sAqxw48mTI44cR1jJm/C5jCxLIFpKvh1G9tX51C5LIn/PNWFgccMZPDpe2MKT6uKhbvaj6aZaIF6DJ/KYRfv5YoLVkBIY2/ARrU7hIVgm67Q12aRlBwi4A/f4HvXZDD6rDwUV2SYRBE2Ml2Hc9sqN1vq9oTTzBrUvOpzNUqPcmHZY7z6A/VGiEGpZRzZZQv9UkqoCnp4at0UdtdZ7PHW8OmuLTxw+HRO690g/RacT6wifyFMXhzzJRdtmIZXbfB2LYWzux7BdcOnc1rfKs7+5gWCWnVEutiB70alMuRtNL51eiBmBZslw8ppIctsNJDShMAeDyCoC4Z4Z9V6Pt2whR7pKfTrn80ObwlWw5uIEODs5sO/OzHKA/ZqdXhELJEiyB0AZVs1FCEImWa4ECQioyJGInIrtHZPLNtTwIlDDjQcEEJw+3FHc87IIcxtSDWbPrAvaZ6DU5z7wcSN709DeY2P8+57g6q6+nZ/56dMHMSyLXsprqqjqLKu7RWacfKEQQzrFa4Y8gd1/vLC5wSbvWq9O3cth/eaz+jst8MCOgjADmmvUWEmYlky5i3QrKEFihBMSHuSsYdtx+UM72PUgCIWrsnl9UXHMzb9eN4vWIfu03FLOPmyBfQZuhfNFr5pVFWiqiY2m8now3fB4WAZa/nsnnG8/dtJpA2todRzoAzZZjMZNXQbR160hp2LczAshT59TM4atxVNgLCFyHSHqJewJGgj39TwYePU8wO89m8XwYBC8eZUdi/vRPexpdgbDLDASZb7WNy2/szc+0VUYYW0CWoH21u0C05Vx6HpvLn1ME7usYaJOXlcP2wWf19+CpYMdyG+Y/FMju/RD4eqsb/bcizequiDaT+gn4Fq8WnJYo6p6MuY9N4clz2KDwrmY3eFogycALq5D+T+Hp4xgK/2rYsy1JaUnJM6mbfzF6E7AlhBhWChB6M20gOsD+nsLKvimoFjmdCris8KVoUNurRI7QQ2zYsoTsXntTAa9KxVjxE7RKJARV2A0bk9uf7ICby8bjHfbt2Js6sPzaMjTYVgiYtQsRMQaIpCgt1OdSvFFXoMzeP9rN4bu9lo304Z9O0UOz/6pyDu+f4A9pRWMW/9LuyaypSRfUhPajnX85Wvl1NXH2i34e3TJZ2ZK7ZFJJkfDE6bRlmNl5Xb9zG6b1eWbM6PmYURDBl8trSA0acGmzyJfciqq9gZfAY9S2ArCev37kcKCCVFGqUh2aWMG7gdp6NJUrzT4PCRe8j/5mS+XrmboB4eJU9O89J7yL5Gw9u43chwLaoNTrxrGbMeH0FGrzr2+HLYlNcTgGknLGPshHD4ZeTpOxGGwhRPgKZjipoANyA3pzLr21wyejj43SWPsbH4Uxa8twapCL54aDRdzymj//S9IASacizTe9xM0DRaHCiznAJ7mYmeqkaEHuyKzpl9VjAqczeqkPx32wTGZ+8g3ekjx1NNke9A3vSWyjKGZ+aA60Twf0Lz/nB+U+WTip4EZeStErR0XsibzZj03lw3bAKf5W/EkiXAAQ/TJlSu6zsNp3rgFT4plAL1NqQ7FBapC48xEij0MCNvJ3Yri2qvr9XBwYBh8N9l63jxwjO4oX+4qq/YX81uXxndPRlkO1MYcv8Tjcub9VpM706aEKzTWF5XwIx1m9leWUZC/+pwCEOAUC2cnX0odpNgkQtN2qgNhqI31ASnTWuxrVC1P3Zc+5DzS435CiGmA48DKvCClPKBjtz+s58t5tWZK5BSogjBox/M455LpjFtdP+Yyy/ctLvd4QKAnYWV7c75jUVAN5i7bifzN+xiRK/OJLmdMavnJBIrVucNWUNvTzF1h6l45hrYqwi/epvgzwUhFNw2G5aUWJbksqNCaFq092HXTNIT1qKpYdUvaROkZVRjmgq2JkUmlgWKAnpARVElaoNh1mww5cZ1aA6LocHdHG8u5d2nptC924EWOFJCqmbGvJY1Aam6YNOX3bFssPqthzjtoeN5t/M+rHw/wRSFrWlpzFrfD89ugwF7BErXDzn2tFEMTstiXUWMrBIhCKWqOMpNgtnhkIBdMTi++zoOz8lrXOyCfkso8yeR6vTh0Q4YD8OySLSHuxeLxNuQ+mYwd4PUkegIoMJwhvU2YlwCe+vDBSoZLg8zT72SZzcuYmbJKgxRTzdPGtf2m8oRnSL7+jk0DXNnOqEEL1pqEExBqNyF6bVRSF3jbgStvw2XeX2c/eJbnDZ8EH89/hiyXSk4pINvNufhC+2kqQqJWWfDrNdQPQcaboar61SMajuGNHl71XrcPevQlMgHr1DDnZKDBe52tYsyLRlut9TsWhbAsC7ZsVc6lPxImQzt4Uc1viLcs+VpYCqwD1guhPhESrmpI7a/Kb+Y12auiHqFv/vVmYwf0J1kT3SLmfQkN/kl7U+z+SGGN2I7lmRVXkGLRRk2RaJXqixY1Z2Jw/egqgduw0FJXjqlJJB/TA2iVqL6QU8Gp8fGh9MvJG9nObpucsSQnnis9zHqPkdrlmamGwpp6dmcmTOURz+cRyBkUGClNUo2GrrC+iW9yMkqZ+7TQynbmYQQ0GNsCcfcuA5XUgjN0aAT6zCRlsmJlywkrVM4DCMlmJbCf3eOZtTQhVHnZ5pQVRH+PRQd6mr8fPeP+WQXV6AEJVII6ruoWC5BYp5Ove5l5rIKVq5cyOTzctlls6jTY6ToaRDMCV/GozN3ck7fZSTaI70zISQpDh8uVee9sV9REXLxdN5ItvoPo1dyOIQilERI/wj0FUh9O6H6T0BfQ4YWO2tEAAOSOjf+neJwccuoKdzClJjL7ydc3WXHV+lEr4y8PmWzfzs1lU5JieytrI6yD5KwBzxj3WaO6dsLS0r+8MHn4d5rlmw2liHwbU3B0dmHPT0IQqJXOgkUuiO8PsWtx4wLS0ugOC1MX+tSkE5NY0r/3uQkJ/LCohUR81RFcONRLXeKPqT8Eo0vYWGJvIbqD4QQbwOnAh1ifL9cvpWgEf00VhXB/A07OWn8oKh5F08dw6b8kogMB1URaKoSU4+3LQ/kYGlqeLUGQywtUOolixZ2Z82KHLpm1/D4LZ/jchggfVB7N2+OcfL7deewRkhEiiDH6ebhI09gQGYnBmR2atymtE4hVP8QzUumQTB05G9JTu3K4k35LNmST7U3hV17c8hJL+etR6dTU+Yksbga3a+xv8R497JOfHTrRM5/em5E2FAokJLppdCXhFvT2V7TibXl3Um1+9AtBa1ZHqquq3wxo0n7GAn7dpShaIJgViJSU7EFDBz5XoQEV3KQE+9aRkavWixD4R8uhQ93jGB2QbMO0U12kuqsx6XFuB6Ehc1mMUgzSLZZJNt07huygMXBah7dtovxaUcxPv1oVKGCfSzCPhaH61xe2XYug217+U2nrbxeMoBAk9CDQxFcHaOMuC1UReHZc0/lsjc/QEpJyLRajJNqqsofjj6M+76egy8YipJ2BPDrOu+uXs/Cnfkx5zciBaGCBGRxEqEW3vxMv4riNKPa0QtFNlbjtUZOUgKaInixmeEFUITCrooq+h3C2G5LxKjf+Un4sYssugB7m/y9r2Fah9CS+I1sZd6RQ3txzYkTcdg0PE47DpvG8N6duePCqY3FDPtx2DQmDOoekXsL4fs9ye1sq11ZGwcvEV6TxKCCu8TAVhaWVfQH7eQXpvLezCFNFq4ny1HJ22NfZdEpvZl1xm9ZcPbVTMiOkQtp7kNzjUE3NOoDNnx+O4GQE7/jUdIzcqnzBzl38gj+ful00hLdvPXxFD757yRqKz2IapOAcKInuzAS7OGyd1OltsRF4cZIrV+/z04wqLGwqC+mpTCmUz6XDlzAmX1WMj+kUmmBIUGXEAyoPPfkcPK2RWtUBHISkTYVFIHqP9C54YQ7ltOpTw02h4XDY6AoIU7utZIBqbEHbQA2VnSNWXUmpaC6JpPcJrFtp2oywbmevb6tfLTvdf6z819YlkWRbyYLC85nbsGJ9EnqTJXl5KLMrdzcdTVd7V5cis5ITynP9JlP34SUmMchpaRwTwUlBbHfsIZ1yWbBH69iaOfsVgtTdNNiWOds5v7+t1wxcQwOLbYBLK3zojS3mA2M796VY/v35tj+vfnXadN5+7LzSHDYsTdoPqhNHl7BIk+UpyFN0CsdSKNtU7GrspoZ67fEdFZCpsnT85a0uY1Dwq+1yKJBdPgqgNzcg0usnjamHx8tXB+Vp2tZFpOG9GxxvYunjeGsI4eRV1hBepKbLhnJAHgDQZ6esRDTtDAtyfSx/bn1vGNYsGEXj304n33lNWQme7ji+HHkdkrlmU8WsmF37Lbf7UH1Wkh/kOa3VEjX+HZRHy4+eQ0AO0pTeX3RCHaVpzIsdy4XnTQFkRBtZKz6d6D2PgQhbJqFTbODkgUZH+ESiTzy/lzenbsWu01FN8ICK7qhsWdzDooJwm0nmOQ84O6nuXAWe0Hq1Ba76TKkksLd6Xzx+uFUlSVww81fct/Apaw3VCwESoMLYUnBsqCNJCFRTMGjF07DV+uIOFbJ/7N33mF2VdX7/+xTbp3eZzItbdJ7SIEkhBI6hCogICCCKIgoqGABRdGv+kOUogiigvTeaxJIIb33nklmkul95rZT9u+Pe6fcuXeSCQmS4LzPc59kztlnn33uPWedtdd+17tAqiIcYI4YABl5YSZl+8ga1ISqR9/xTtViVsFGdjdlYaN3VAJuR5U/kYUHBjMtbye6Er4nDFtjeWV/+gkN2B/VXgESFZNGO8iu1q0sr/k1Tf53sGQ41CDMClRNIhXJeel7OS+9S8qrSABzCzgmRPW5fWM5v/vh8zTUtCClJLtfKj/781UUDY6u87a7tp615RUxsdF2aIrCyNwsnJrKrtp6rps8jn8tW0X3GY1H15lQ0I9dtfVx+8lPSea3F3SKyEspeeDCc3h25VrqfX7qWtuoiPBvbb9G245k3EWt4WrGNoRqXQTKjo5WRkXz4TOFvmgI+dVlO+wHCrr8nU+3J0BK+TjwOMDEiRMP62sYMyCPi6eN4rWFGwiZFqoiUBSFn1x+CqmJB+cKelyODvpXOy4/eSwXTxtFVX0LqYkevK4wzefUcYM5ddxgpJSs232A2//6JpYtMQ9j4S4etIDskUXZHvN9dslo/vzRiZEXr2Dzfpu31jzFM3ddRVF2pycp7TZovh+iMqVCBIMVbF72CLuC5/DKwvWE2pMzoFPKsp1XqndZbYkY4GCWF70mSEb/ZprrPbzw0BkYQZ2pJ27jvJIqthhqDDtWCAj5NXbsS6C5wkswqMVcpQBspxa1WYkkkeSPrYmkGseiJKWKiwauwpIKac4int+egWGrWNKmJKWSt/aMY31dIZOydiOEZEXVAEqb0rl10DrmVBUyPaMcp2pHrl8iMAEHtu2j3vc6XelmEgtTwh5DZaijW2hAmqCkR21qafJz93X/wNfWScUq31PDj77xOP/55C6crk7Ww6Jde3sMN6iKYGRuNqoiOPWhJ8OcctvqkpkX/m4URTC+OIebp0/iuVXrY/px6RpOXeWJxSuYOag/2UmJnP/Y01QepJKE1eKgdWNa2CJJOJoZbv2Oxfpt8JVlO6wABgsh+hM2ulcAXz+aJ7jzspmcP2U4n67fhVPTmDWhpMOT/TzQVZX8zJSOv1v8QV6ev44PV26lqS1IbdPBaUA9ootsJIC7xuq8v7uZYKfD4NwZW7FswaNzJ9OV4StRaAsY/OX1hfzp5gs6OzTWgYilFDl1ExH6iD897yGkRO9svw47WUPUmbH59EIgVYWMIa1kDmjmw9cnYkRkJC85fTMKEOzhAZW2YPUrg0jO9WHFWyhD0q9/PbvbPCSm+Djl4pUseXAwmaOamfHtjXETFgBURXJyv/bMwi2MSofmUDpZnn5M6/cg9yyZy9t7HOxoDHuaCuGyO3/bPQaFcELI0ye8z7CkOsoMwYTE3dQZCZSHcrBRYuNwAmqtCL2kAxpoJQitOKrp/HfXYlmxtD0zZLJk7iZmnju2Y7vX6UBTVaxucVqHqnLTSSewqmw/K/aWR3n3ATWAK9eH4rSRFigOm10pzaCew2/OO52fv/Mxti0x7LAkasAweHX3SrT0AI+VgdrkpaklnM5+SHwBBun8kUMP3ejLwFfR85VSmkKIW4EPCVPN/iml3HS0zzOkIKtDqexootUf5KrfPktlQ8tBvVwhwvHhg6UpK0GJ3hbWQdD8Mmqqk+gNYlkKhqmgKpIxQyq48NTNBA2VoowGdlRlxvS3Yms3IWslkXgZWrYNTS2O8PQ2TpDaqat866opPP3XBdhm7PGKajPju5vYs7mApVuH4LLC5inDG0QRkKVI6m1J90JAqmZzYHMqimojFGJqV2ouixMu3ckYrYzsQRV4PAESz1fJPW8vqit2HN25xx3nUSDVVYct26hq+5Q/TLuS2QP38uK2Rext2cWWBieGreBrL49kwfUrz+L56S+wy1JQhSRdb6XNrgurqHU7h21DxZ4k/AMbsS2BpkmamvPIHvFYzFhqK5sIBuLoQBgWddXRU+6zhg3mj3MWxrRVhODUkgE8sXhFlOHVUoJ4BjR3cHClBbahULnKw631r/HYhV/jrZuyue6ZV6lqbsWWEndxC3pasKMcvEwI4k5w4N+VxOF4tKoiUIRy0ASKQ0FXFC6f0HMJqC8TX9WwA1LK94D3vujzfBF4ecF6qhsPbnghbBjOmzKc1xdt6FHb13YKREun4W13GEOJgrtv+ZRQk0ZNg5cRA6vJz2ti7taBGKZCbWv88InH1Zn5JKUEbSQoaUjTj+hyNwUNjTfmDQdpI1Fi6tO5nEGmTFyKdvV4nnp2DUYU40OSlN5GcmYL6TlNkGliVyoolmD1hnzyT9lKP81mn6Xgk3QYYDOosPy5EvwNbmr3JGGb0eeUgBnQWP9RDimXtdCk9OP73m0oV23nM1Mlfi5fz9+9EGDJAIuq/sTrlZu4tOB6Hj7lam799C3W122NOcZnqbxfl0dJSjherwpJgaOBFstFoupH7XJ6K6Ty/iNjeL40keIBTTQ1OamvS+GZTz10KZwBwLBxRbg9Dvy+aKqbpqkMHVMQtS0jwcufLzmXH772XkfSjS0lf7r4HCSgdP0OhMTdv6XDiEKYf6sIG0dmkFU7a7j2P69w6dgRNPj82IRpY10Nb/sxenKIUIKJ1do77QanpnLP2aey8UAV727aimHZPSZRQJjBIyVYkVmVriioisL/zT6TBKezx+O+NMijy3aI0GtXAvullOcdrO2XvuB2rKGuuY03Fm+itLKetbv2E4rjDXaHIgTTRhTz2sINPTcSgkCGiuoPe8AIMBIULJfCc8vG8IevfYjbYTJn0wC+9cBsVEVi2YKgGfuQaD4btd7PzHP/AIQNUFZmIjdecw8nD/8FRrAe2wZds3n6zXHMc+bRNs4maasClkRIAdjoms0FZ85jb0sVaeOcDFn+LXbtbiYQNFB1C1W1uPBb83G7DYJ+nYnpu9lgD0UieerNCZx54k5cTpMpTpNyU6HCUmipd/HG7yeyd28/7GyVqlYXmhZCMW0Mt6BmhpuWEh0hoWqzi6x7ffy/Z+bhVcIJAMJUez0LtG2o9ieR4w1X5zVQKPXt4OEd93H74DtoCfUc2zSs6GVOVUi8SoAm00OS6se0VWRAMP+RUVRtC8fWt21Jx+UyOWXWPlqrniAh4VyENqijj4kzhlA4KIvdWysxIrMgp0tn+PhCho8rijpfkz/AlP4FLL7j2ywrLUNKmNK/ALeu4zeMDmFxIEz/iuOeCQX01CDBA1521NTynxVrCETi+VpSrBcf7gy0pGCvjG/74b//aAFBy0RXD/7bzBhUzLQBRTg1jfyUZNaWH8DrdHwppYEOC0fX8/0+sAU4ZIC7z/h2wbayar71p5cxLYugYfW6lJAtJQNyMxhelM3Gg+n7CoHlEVie6Mjikl2FnP7H6zhn9DbeXT+UUE9C5VLiqDdxtkJbt1Xv6poW/vjwKh5Lupzc1N0keoNs3JlNneai9VSQGjSNMnFVKmgtAlw2V5w2jyFFZeFghRrikls+JLnpj6zfvIvS1n/Q2uRg0XtjyC2qZe2iIfhbnRHDLWlqcXH9Ly/il9//kEE5zST4ddY/V8Kbrw7Bn5cEKQIUge2WmEku9OoW9l7jxUhUaHctG8a68PXTKPE2dXibhWrYk+4axgiZKvtaUylIbIjSKDakyos7JvP9sR9jSkF5MJ0Exc8Y73bWVF3FgKQBLK2cRLCbobWlwsDk6GKWQoCKxGc7WNVSzJrSIsznXSRsNjtGMmxEHb/6/SKEkGjacszqJ1C9lyCSfokQgmDAQHdo2JaNEAIpJUWDs7nnkW90xNPXH6jk7jc/pLS+EQFMG1jM7y44g1RPp/iTW9eZ2r+QRRFBcWmJHqME0grvCJoWu2o7qW3SDHugMYdJkFbvGKYy0m8wYtCDh6gKvqy0jD9eeDYp7nDyyLSBRQdtf8zgKBlfIUQ+cC5wP/DDQ7X/yoqpfx7c89SHtAVCHckWvV1Yc2gqq3aU8/OrTo+pitFbBE2d11ePINS9LloEwpR4y00cBymdFTIs6up8bNyZw5J1RbS0ufDldYrvSB38BTahUQGmnbKW4txOAyQE+OwtvPPhSoYMSeCz90awesEQdq4vZNG7Y2hp8GAa7S+FMEWisdnNNqfJPw/kMWnRVTzWPBZ/rjccW26PL4vw/4N5CZhuQdc5vdQEoXSVZXWdrJMS3SJPtVGQqFJiBFRWvTSQP689gwX7hxAwNWwJFW3J/G3DaexsysKSgr2BDBpND5MSduNVgggsxmfupCixBqca9kJVbFyKyW9GLGKcK0D3p04RkK63YSsqo4tqOOny0eG8aMJle37xm8V4vSYej4XDYaEqIczW1yD4CQAP3/s629aXRSQ6w33v3VHFO8+FyyHtLK/mG0+9zM7aekzbxrBtFu4q5eInnuWdDVtp6SJY87MzZ3YEI2VIxfJrMXFzaUGoKlqxrx1GgzM+i0YoWF0y69ReOhi9ga6qVDYde3SyQ6GdbnaoD5AhhFjZ5XNTt67+DPyYeIsvcdDn+UbQ4guwpzI+V/JQ0DWVBLeDkvxMXvrFNVz3hxdo9gXoGv6dMLgfG0sr42bRdaIn90aiRRbrDvdRERZRNkYVFneMe58sdzMONfoesS3BZ8tKWbGqHCPUOS2VdvwXgpSw+P3RLNlRQooeImNpECMtMe7KmLBF3AU/WxG8vWEgFGoMyq4nO6mNkQ6LgSGbxWsy+ed9Uwj5dLRvwutM5PXdE1CFjRVROctLqOez5sH4pZN8Ry0KnZl1qiK5bczHhJry+KymgBQ9wNfytzM4sRFTQqMUVHTzitvqXLQuTOGsc07isssuY1XeGB791ZukpW2LEiDa70/goR3jWFKfR6ZrETeOymPRRxsxu/2+wYDBG08vZsvafbxbsxf/EHfUC8i0bQ40t/Czdz4CBA9cdDanDx3EgIw0sgfYVO1WQEh8OxPxDmlC0e0wE0GRBKvdGA09xFEthbYdyXgGNUcqmAjcDp3fjrmSqWeX0BIIYknJQ58u5sXVGzoU0I4EpmWTn/r5mUbHAWqllLF1uwAhxHlAtZRylRBiZm866zO+EXSv8toV6UkeGlr8PXrCihBMiyR1FGal8t5vb+TdZZtZtHEPWamJfG3GaAbmZfCnV+bz8oJ1hzDAcSAJG9/DOwoAbxk0jei0v+My95Lhao0xvFLC5pXFBAMWwZjU5B6GZSvkDqohf10ajavcKDYYsUlsEQiwJHRRH8OCxO0q83zDWbKiBMNSOW3YLn56/qcYqiQ4uIXr/j2HuX8ZQ+vcQsouTQAVLKkisNEViysGLKMosY5VbcUUO+tQu83lHMLmzJw9XJi7J2q7JsIhjq7G1wioLHt8CLWrMli0dT4pd76FXtjKD56bwlu/MTu+xAN+L+ctuohWU8dCodwPd3z2HknjdNKWx353DbUtLJ+/jcAkT5Th7Yr2WO0dr7/Pp9//FqkeN1ePncCfD6zE8qvIkELrhlRUr4XQbaw2La5wehRanRgbs0jItDl1XD+uGzyDgYlhcZtEV9ho3zJjCh9v3UlTIBg3Vb+3cOsa10wa998renk0cXTCDicBFwghzgFcQJIQ4hkp5dU9HdBnfCNwO3UmDy1k2dZ9UewGp65xyfTRLN2ylw27K2J+J4em8uhtF0elILsc4WMu6VJVGOCHl55MWqKbv769pEcGhaYIbEmnwpkEvcVGi18c4JDQ/JC2Cuonhr2fockVuOLoH1imQvmu7Dg9xIdQbDLyGhg2uoyBgw/w/C0n01zpRWsOYKa4Y73ciJi3tGXHPk+pgtamYEtBW0Q7YO6WAegpzUyaug7FbeEEZt2xlvo7EyhSD9CS4aKyLZnCxHrOKtpArrcJgIne0o4SR11hEk5xjmfzpFQxbAXbEigWLP1PCbs/y2XM7G1MvXYbhsPCMMHfcoAR31IJCfACf9s1hjZLw+oStfNbJsFpblJWB1C6fL1ChMNXVsjEVWPgz3Mge6jh195+zradXDp2JK9+uhc70DXUA1Zb7yOFNhJHcQtBzeC1hSFe/qCMNI+HH50ygwtHD0cIQbrXw7vf+QYvrd7IC6vWs7+xqZe1jTuR4nZx28lT+frEMXH3N/kDvLx2I+vLKxmclc7l40eRlXiMLMAdJbaDlPJu4G6AiOd758EML/QZ3yj86htn8q0/vUR1Y2skJ0IyblA/vnnmCRRlpbJ+d0XMMT+5/BRGFvdeKm/Omp09Gl5FQG56MnqLxb7qRoQArU2iBnt+NXfd05NnnLAPikItDJxeTX/awsamWxKDZaq0NfWcFWiLMAHM6TSQtsCVGmDfJAe3zb+KVGcbYy4tp/kRL3pTEOlQsTyOsDsdcUWFFOTMk9RNhGC6RBESV4MWQ+YPmTqfrB7BpKmdGVuKZnP+z5aTlOOPy/UFELZEjdzN/iYHlVtTcCeHyB7SSL2tkadEv3AMW7Dcl8G7jYXULEmmdZkXdZ2K7jSZeu02dFenBysxcXgkb6/K5fITDrCkLg9TxnqdTocGuU7UAwaWZaM7VDSHhmFYmEGTpN0BmoZ7sBQZNwQTvn6LgGGy4UAV1c2tvay0EllZ654YIWyCPghWpESikIK6lgC/fG8eNa1t3HTSJACSXC6+deJELh4znPP+/h/qff6OmHVvMCIni6si5em7Y39jM5c8+Rz+kEHANPlkx27+tXQ1z137NYbmxPLXvxR8VXm+xxPSkjy8eu+1rNpRzv7aZoYWZHYkbzz/yZq4xzzx3jIuPGnkIaut2rbk3qc/ZMvenrUgRhTl8sDN5/PEfxZSva0+TlnDMNqlFyRgJAvsZI38kIu6yviLHSXF1fz5J++hKTamarMwqEexCWwbQkGNPVtzY451uTQsS9KWFyJrWBUnZe9k7YaB7N2WBx8JXAOhZkAS8z0lpI8MIaSTUKoDJWDjrA6hdGGs6q2CnE9BqjY33/8KD6y8Mi6nNxCKpkGpmiQ5x3/IgHej381rH57A3i2ZJO8P4j5gkZAWJPm+bDILn0MRJqomsXFSYyr8uWw8zaYLe6BAGSBxXm1wlrI6Lq0LYZE1QuWHt85GnEt4YtkNlpD8/qHrWfTiGsp2VzN8XBFnXjqJb577/wBQDEm/DxqoH+PF1y887bed0Z6sJSWqolDX5kM5lHKTYtNvmEWLqzEc1WnT8O9NwPaFvz8JGI3ODsPbjoBp8siCpahCYVBWOtMGFKEqCmleD2/ceBW3vPQW6w/0XrNk8Z59mLaNpsR65b+fs4Amf6AjZBeyLEKWxc/f/ZhXbjiqya6fC4Kjn2QhpfwU+PRQ7fqMbzcIIZhYUsDEkrDB9AVCuJ06O/bXxm1f3dRKwDBxOw7Om/x49XbmrdnZ40s20e3kH3dehq6qXHfZFD76YEOMMlu70TUdYCQqmE5QDRiWno7bUKhpboOAjRLlWEt+9Z25YXlKQAcmOExWB3QCEWZFY00irz0xE2lHPzwup87XL53MKTOGsGjLx7z0ViOLV4+hvjYJLVInLHUdOGuhYaxGMMsVXuATAitBwedR0VttXA3dhLUthZ0ri8lMa6S6LlotTWAzoLCbcllPAhhdsLGuH09uORkrQUFOhlrTQ+LOEP3ea+W3N7aSl38qZ5+/i5xcP+s35jDnpGSaLRc2CmjhBJEAGgtcJQx2VMc9R0Zafx5967fM3bmD25a+i7+LuLhDUZmWW8TYoUWMvTeaYpU1q5iKD3ajWKD5bTKXtmDrrew/Ow07znrZ86vW8++rL+nQ4OgJiUOaaXUZHRKQqtckYWgTLRtSkYaCUMAOxk8nDpoWD37yGQ5NJTPBy3PXXU6610NbyECJY0QPBgk9esoLd5XGXSvZVFFN0DRxxqkk/V9Hn+d77EBKyQufruXxd5bSGgiS6Hbidmgxou0Aboce9wYKGibz1+1ixbYyfEGDjaUV+Huo6urQVH58xSm8t2wrUkqmjezPz+48l/978H3siG+oCAWHQ8XvNxAhG7Uu4rsqsEXUYDkFpCmgKOitNs768P70ZB8pSWGxHcsWLF+fz5J1Bby7aAhpWc0YIY2musSOsaQlt3HNJSsYN7aMRlNBuhu4+9fLqK8V+APpKKoVZi5EoFjg2Q+BNCXsYXWdASgCI1HB0dT9hWCz5INRzLp2MS++fzq2rWBLBaHYqNjMmrqq87eww3qyPVlfKSFkKKypKUIoEhmhhkkHtAxy0DzQSdIOg/1lCfzjr5GYpCppGi2xu/GtJQr7fan87Zqzkc0KBWNrOPm7G0jO8aMIFwOSv4miKMwqGcJ9IsSvl8/DtMO10mbm9+dPM86NO8bvfu9svud/Hs/6ZlS/jT/LQeMoL2ZC/AWziqYW0r0evjllAk8tXx03o8zhtVA8ZhRZVAiQQuLI9hGq9uAZ1ESgLAGrJf55DNvGCNkEG5u59725/OCUk7jsyecOmsEWD7qqEDTD2iDdvV+XpuGLc9+rQvSaR/+F4iusanZc4uUF63n4jUUdWg2NbYFwTSuiX5Iuh8ZVp42PmR5uK6vm239+hVZ/6JBcYU1VuGjaKH7zzJxwP1Ly+xfnccdlJ/Pm87eyas1eVFUwYWwxbb4gT/5nIQs+205rWxApwZ+mhg1vlzEYXgUlBHqrjSUFigKtPgff++15VNUl4A/qgKC2Ipqa4HaGePq3r6BrFg7dJl+CKV/ga99O5uH7LkRKHasHHrLeImJSlyH8hWkeDbvVBGGjKJK0zGayRBWf3D2GnNRqxDiBTFbJz6/G2CNZ/e8BjDl/Dw6vQYpi4yhujVdUPRzjlKCpkiuGLuNSuZIH157RUaNNOsJFNpN2dHv4LRGT8tzRqwVGSEMxYd+qTF78/gyufHg+exdMYdYPJlLZ9jG7Gp8k3VnLU7Mm4tKuJsczkFRXfL4twKSifK65fBqP91uBqoZTvD2RNNyWYGwxyqHZYcHx2085kZF52Ty9fA11bT4A9tU3oqoKEwZnsltvxWd1q9qhgJ4WxJkTIHjAjTPXh69VP6hQjmnbfLJ9N8hwgc6e7lhFiLj3s1PVmPz/HkNTFC4bN5Ifz5rRoRd82biR/HvZmigmha4qzBoyCP0gDKP/Kr4kMfU+4xsHT7y3NEYkp/s9p6mCK2aO5aZzpkRtt23J9//6Js2+niu8doXTofHGZxti6GcPvDyfSUOKmHFSZ8n5YMgkMyMJVVXCC4ICTI+I5dUqglCSgq1JqiwvW/dk8NHiQZRXJWNaPd/whqnidhq0Oy+qCDtWEzJaGDFpN2sXxa+LhwDptCNqjNGej66r/OYn5zF2WD7f+9GzODOWIfYH2bM4G0WVXPKLz0jp14oeEdORNqx6ZSBv/3ISZ/18FfmjavAISVMX7YgoLTglnJmmYmJLk5tGfMqvll9Ip05m/CG7d1j4JijIruO1JbJW4cBpbtqKNZQQpK4J8K9vnobb5eKTk3+PlfU6hu0nZGn4zffQ1fkUJ74K9Gx8AW6dMZXLxo5iaWkZCU4H0wcW8fbGrfz6g0+iPM2wzKdg7rZdnFoygFlDBzFr6KCY/va21nD14u0x26UNRq0b4bCQUuDfm4CaGAqnE9uCnmcQktXlB3o0vElOJ3ecNo0XVq1nZ209UsrwB2gNhV8Apm3z8pqNtIVC/O6CMyPXPYUtVTUsLy1HVRRsKRmUkcavzj14uaX/Jvo832MEUkrqmn2HbOfQNG4+b2qM17u1rIpW/6ENr0NTURTB+ZOH88bijTH7LVvy8aptnDFqEL/903ts21GFZdkoSniBDA6u+icVcDaG76r7HjsVf0A/qOEF8Lg6DW87hIAs3aZwSEVc4yuRSIfkpOkbWTVnDIYZbcyGFWZx0oRw+aBTZgzj6X/WoO4Lp9aWzCwjJa+tw/BC2JiOv3QXeSPqaKrwsmdbGuNH1pCvSg5YYYHIFBv2VXtIyImur6YISHH6yHS3UONPQoQkyZuCYS6R7ByX4rQoTKujVE0laGnYKKi2heFXqQ8mYg+OpEY7oXaqm2CGStHHzfiT32Le3sF8sG8UQUvHowWZ3X8duZ4nGJV5b9RYqltaeW/zdtqCIaYPKmZ0Xg7ZSQnMHj2so80lY0eS5HLx0Pwl7K4NF2q1pWT53nLWlldwYv8C/n7lRXF/q6KETCanD2JRzXZsOl9c0haEqt1IUyC8ITQdFJ8HR+RNqikKPiOE1cXgKEIwubiABp+/w8PuCoeqMue2b5LscnH5+FFsrqxmf2Mz/1mxluV7y6PaBkyTdzdt465ZJ5PsduHQNJ648iK2V9eyvbqWwrQURuVmH3KB+r+KL8n49qUXd4MQgrz0Q4s+h0yLj1bFeh4h0zrojaVrKhdPG8Uts0/irfu+SUFmStySR7Yt2bGnmqtvepLNWys6dGK7JiIJG0S88JyUYfU0wn5OXaMXX+BQQiqS807eEnePJaGptjMu7HQH0R0GqmaSXVDPd3/yOhOSy0hu8SEMO6JdLEkUQa67dDXLK79NadPzzD5vGM56f4fv1X9SJbo7Tt08ATnDGhk0rZK60gT+/rMTKQuqpCkStcrN/Redi+xB7xcpUC0bYUgyGtsY+rUy3IOCCIeN4rbQvQbTb9vA1JnbOSlzJ/0T68j31DNelsEnOlKJDuFIXdBS4sA7xGDegaG8WzoGv+nElgqthpuXd07k3T2lUUOYs3Unsx75Fw/MXcQjC5ZyzdMvc/dbH8ZdlJo1dBC/Pm8SJTmVpHiaOraHLItPd5Yy8Q9/5cp/v8gjC5bS4It+2fx6zBXY1V5sQyAtMJsctG5OjZT8Ecg2J0arRprbzQ1TJ/LPqy/hve9eS2ZiAh49fD94dJ0Ut4v7zj2Nm6dNwt2tZJZTUzlv5BCSXa7IbyMYkZvNGcMGU9lDZQpNUanqJthekpXBeSOHMjov59gzvL39HGX0eb5xcPvF07nn3x8SOMjCg2nZ/Oa5Oew6UMf3L57esX1EUU6PXFSA/Ixkfn5VZ+HF6aP689AbsbquEslH63cg8jX0JhtHS/wMN1e9hT9TjXBmBNgSJDibYgtoHpw0ICjMa8S0BVoX0XVLwt6QyqalAyJbbPoP38+UWZtwJwRJSvXha3Xyr9/OIhR04MWKBMclQhGsWruFYRNLqQ+swq09j+ocQxAHwrRprXNhW6B0c8hFJJKiuCyGnrafbZ/2Y+27xYyZXUqrCkKz8aQGIotx0cfqisnJxjbWvDeQ4feWI5F4R1YR2q+TYPqZNmpbRETHpp+zEUfA4qntJ7FZ0fAW2sg47yhhSho0L+vLhxOyoxuEbI23S/O5Y0IrupqAL2Rw5xvvRxWzDBgmH2zewVnDSzh5UP+O7VJKttY/wP7gM1w9TeHTzSOYu3k0lt35WLYEg6wuO8CmiiqeW7mO12+8iuxIgsJfPllC014X7I3De+uCipZWnlyykvNGDmV/UzMZXi/VLW24NI1pA4v47QVnkOh0UpCaQkVzCw/NX4Ig/ALISUxgddkBvvXc63z7pBM4oSi/o99ReTmUNzbHxIEt2yY/5fhJM/6ywg59nm8cnD6+hN996xwG5aWja0qPxjRkWLz46Vq27OvkROqayi+umhW3vaLAH2+KlvjMz0zhW2dPwaVr4XhfZLuURCpJCEIpCsGUHn4qW+KsM9FabZSAjd5i460wUT5HpujDz57Ern1pGLbAkGHD22DrrFk1gJaGBISQ6JqkdEsO6TlNJKaEp6iblvfHjtDU2nmTAoG0Fd79z0msXzKQUCjEvx4cSHOKl1C6m2B2AnM/nEJL/cFjpapuUTShhs0fF2JbULYmg36j6jsWzIyA2vl9Ef6OT5yyg4tuWo7okibt6BfixFE70BUbTdgRvQPJmPQyTsg+wG3jpnH21DEocR5EqQq++Y3z8ZvRqbM5nkbuHPced014g4/3TWFZxbdYUroeNQ5Vy2cYvLk+umj3vpZX2dv8AkKYuB0hlu4aEmV4uyJoWjT6fPzmg08wLIuQafLsinUH/e6ijjdM/jRvEdc98yobK6qwpSRgmizcVcqj8zsLW14/ZQJL77iZhy49D6eqUt7YTGl9Iwt3lfKt51/n7Y2d+si3TJ/cpbRRGG5d45tTJ+A5BPXymMKX5Pn2Gd8ecPLogbz0i2+w7OHvc9O5U1APkpE0d83OqG1Nbf6odGNhSpw1Jp5ykz8/9BHbdkTLTt5w9iT+/eMruGbWBAqyUmJPEqFsxYvxWh6FYIaGq97GW2XharRRPmfBgTa/g5vvu5Bbfz2bh56bRqPjb3y69Lf8+z8nEgzpSCkwTBUj5GDr6oKOl1JLg7eL4lm38Zkq898Yz5IPRlG2MzNspBUlfE1C58G/XcIvllzEJ3uGYARjb0dpC8yQirQh1Kaz7NkhmEEV1SERCrTUhL3nri9I3WlTMKSObL2xY1uy6keNk0fq1ExO1XYwxp/BTWMnx9X4cLsdXHDqeDLdnSmxbi3EHeM+oDipFjVisesCywhpdyEibwKpSGxNIttrrnVx0z+rncvy6t9jd6m516OUaPt3KeHjrTs58U9/559LVx1WZQmbcDJEd7qk3zB5btU6WruwLpyaxuvrN+MzzA5RdAh78Pd/8AlWJPY1MDOd5677Gif1L8Tr0ClISebuM2Zy28lTez2uYwHC7t3naKMv7NALfPvcqXidDh5587MY4rsQYbpYV2zeW91xkytBiaeqU5Rl3boyvvfj5/jtPRczcVwxEJ5++hr8JPsVWlp7XqyztXBSRefJQSoCJdRl9f8g19G7SJtg+94Mtu/NYM6idQRDJrLbXNwyNT57bxwjJ+8FoN/AGtZ+ZmAE43s7Qb+DdYsHxxhogcBVLShrS+TVXSew7IMSbrn0IxIzO7+DhoCHj0LDabzIxfJPL0M5TeJotBjetJuSlCrSCtrinlNRJPlqPXu3ZGGhkDSojUafB7dm4HUGu7UN8P6qX3FiUiKS4pi+bNvmlZ0bufuEmdz92YcELJPJ2bvQFKtblrDElg3kZe5hQzAH6ZQdXpOnxcGFo4cDsLlpLa+XP81JidEUuGH9yllb2j+agdENEmgOBHnwk8U9tukJPdHINEVlf2MLQ7I7Mz6W7y2PSyvzmyYVzS0dYYVhOVn88+pLDnssxwy+IK+2N+gzvr3EOZOG8ehbn8Vs11SVMyaURG0bkJuGyxGu6eZosAgmK2ERcQFKSGLVW/z5rx/zzBM3YpoWd//qNTZsKicQNPBlqOCOQx+DmFCCoggMr8BdbR3FGrOdCAR7jl20NHg7/j94VBlpmc1UlacRz8Srmo11MAFvCbauUDYohco9WTgTwhlubZaD+5ddQHCAFl4E04FESSBf428bTuPUgk1c0D/+1LtqZxJv/2IKoZCGbQtKRT/ePTmBQKaD/plVXH3Sp+hOk6pAMmquxbj8DWz1ZaCKPAyiwwsB2+Ld0m28cPaVuFSV+5Y9TZ43Wti9HYZtkJLdiKzKpmPFEwimGCQlhfv9uOoNmrcJ9tqZDDqhoiPmff64FeyoyCNo6hjW0X80pZQxXHUA07bIS06M2tYeF+4O25YdYulfBfRMvvvi0Rd26CXSkjz84qpZOHUVlyNcktuhq3z3/KkMyI0uIX7+1BE4NBUBmAnhkAFK2KDaTgVftkppVQP7qxp5/pXlrNuwD3/AQEpwNFmxT4cd1vPtul0AP7nzbLwex0GFd3oDtbsOYy+Qmt3c8X9FlVx+20fkFtXQffC6w+CE0zYxeFQ53Wf0EjCS6FjkErbk5SUTefjtM3jknTP40zPnYChqtAhNJNslLaGViVmlcYVnpATDr+FvcoblGIMKakCSObcVGRDsrs7h9R2T+KylhJ1GNttDOXzmL8FSRI/14/Y2NxIwDc4uHsofTtrKtLydcdtJKSj3pcY80TaSxzctA+DArgbKf5vN4seGE2rTMUPh7z/Z3cZPL3ib608sZPrAIjITvGiH0nfohtykxI4Eh+6IZ3hdmsYlY0Z2SEy246aTTohlPqgqpw8ZeGzWYjsS9LEdjn2cM3kYk4cV8sm6XViWzYzRA8hN66SlVda3sHlfFdkpCfzzzsu556kP2VxaGevFCgglK3z9hifCxTS7WBA1FC4rH0hVw0ZJgt5s42yKZjtIwNcY5JV7ruWyq/920JtDiNgkka7oXu78UNB1hdMv2owinNgySCioEfQ7MUIaZ359MQvfGk/Q70DVbE44bRMnnb0eX6uL0q15hPyJBIMWdkTZq3ZSZ7+2LigfnQAyEltNJ676l6ZYjM4pI8vTHPPVtl9nzpDG2IFLiXdvEG2ySVa/xrCuQxdUyFQENrEBHEltoI0fLXqf/zftRFqNPXG/F9NSKG9KY3dzZoxbI4HlNRvwmbNofDMdafhoqfbw7HdmMvai3fQbVUdTpYfLzr2fS4ae0HHc8tIyvvGfVw757CtCcMnYEfzmvFnc/+GnvLBqfVQduHiGF6AgNZmfnzUzZvvZw0soa2jkrwuXoQqFkGUxfVAx959/xiFGcvyhL8niOEF6kpdLu+n02rbk7n++x9zVYd6vIhTyMpL44SUn8+PH34l6CICwB+xQwDbjx+ACkoSK6H3x/J/lq3dzyewJDCrOZNeemh7HfBjqgL3Cz350HidNvYHyljdo9O3mqedr2LiskJKx+xg2YS9jpu4iGNBxOM0O6UpvUoBv/eINNi8bRW35eXzSspemYrDbZ7CWDBus9jzuztHT/eqlVEhztSKliHlyhICdjVm8v2sURqJAb+ncLyxQgzb98mtQ1NgXjmmrpHp9VDR39ewkKe42WoNuPty7g1tGtyCEGi4zHzUm2F+fwWNzz4I4ssiKsElLaGJBzQeYZW6QYc6ur8HF4n+GY8FOr8p5J+RBF6XFJLcLRYioha94cGgqXxsfLs1+28lT+Wz3XiqbW2gLGbh1DcOy41ar2NfQSEswFDeUcNNJk7j6hHHsrW8gM8FLRoI3ps1XAn1Us+MTUkpu/NNLfLxqe1gEXYbTLPdVN/LwG4uwuhfeCh+EEjq0t3moeFROdgoA11x7Urjbwx/+58Ijf59H0O9mQMr1jM/7NTNH3YSquAj6nGGhEgVcHgMLCEZqrgE4XCajZ6xhyITnOe+8sWHDG0nIQA2HZVxqiAFJ1WS44hP4BTZJHh+mqqHEcVlClsqm+jy2NOex55okujK3pAr+bAdCkXHpg6ZU4sbaUzQ/U/vtJMFh0WpEaynYFuxbncmWjwvZtKEI09TxhExU0dXrtNFVi+KMStY3rWDw0AJEvJJKpiCnX7TexvK95T0K0GiKglNTcWoqN544kdF5nVUq3rzpav7vgjP59kkn8LMzZ3Zwg+P1UdMtIaIrPA6dYTlZPRrekGnScJj6v8cUZB/b4bjDyu1l/PvDlWzfX0NtU/wV910VdfE1syU4mmJ/zcO5fYUQXHHJJEor6/nFQ+8QXzjwi0FtXSvPvLiU79wwE4CignRSkj3s2ZKLZalERB5YVV3M+Ky9Ud+BIiBnwB7KP9wNiUQZuzML13N20QZMqaAJm70t6fxj0wwMW8OSCqZUyExoYULRXgypURrIoMhVixYxwoal4DMdLDwwJMyRdkiahzpI2RjCVsGf68DOheZGNzm5ArVblpwiJDUtnQtPGa4Wbh09hySHHyEklxSvxKt9h9rIC7W5ys1rPzmRQIuOtAWWqZFX0ELgTBfZ+fvYdSATQ2hkJzYxdEAFTs3CqyZyzrdPZuHHG8JVPSKwVcHgGQNITIkWtE9xu9A1FaPby1pXFE4tGciQ7Ay8DgclWelYtt3BMdZVlTOGDeaMYYMBWFZaTkVzSwyDwZbyc9VdC5om973/CW9t2IJEku7x8MtzTuOUkgGHPvhYw1F4bwghXMACwEnYrr4ipbz3YMf0Gd/PgbeWbOL/XpgXI74TDw5d62wnJUpI4qq3UXs4tLsBlYCdraPXmNh2RF5SVbj84hN44OGP2LKnEtFgfkGGt2fy2icLtpKc5Gbhku1s3V4ZSZFWeOGhWXztlrm0KE4SHKGYWnEAFgoVlRtwJQ8gYIc9xDEZ+ziraAMO1cIRSY7on1TL9cMWke1pxJYqFWYS+830DoO9M5hNSKoUOurQhU1ZayrPbD0RnxkRKncoBPorOEJBAsM0cqZXMya7CYQMr38ikEhUVCwp2V6RidmhaSz53piPSXe2Ruld7Gn8O1LaoMD7v5tAa60rSgfZXRZkWtkAVv+rngLhQ1rhF2XL2Qkkfd3PyVlnU9toUX16GgnLGnHWm9gOQVOJm4+zm2n0B9BVhQONzSzfWx6//DugKoJEl4PHFi1HjyyYJjidPH3NpRSnp8a0v2XGFOZs2xkl4uPWNW6eNhm3fvgJEXe9+SFzt+/qCKlVtrRy+2vv8vQ1lzKmX6wo/7GMoxTzDQKnSilbhRA6sEgI8b6UcmlPB/QZ38OEYVn8v5fn98rwQnS81VtudtO17dKupw5EOKZ8/fdOYUBSMqZp8cHcTTz38rKuTf7rqK1v4d/PfkYwZAISISSTz9hAwaBq5r89ln1WJkNO3YmRWoHe7aKFImmoTSQw0EJRwtc+u//qGOqWptiUpFZ2eM5Jto8DNWkYmoKmSlLVNga7qxAyXKm4IKGeO8Z9yO9WnUtDMAGkpGGYkymXVePQYmlhCgoDE4YS3JfIO2/XsXu4B8URFrcpSqwnUQ/ECA1JERYvb6t3UrcnKUaAXlo2q97fFI5HR34ZCTR+mMTpp09h5Jjx/PKzubSkKjSfFS0k71YVrvr3i+yqre947Tk0FSkh0emIeK1hzdyvTxzNv5et6agMAWEe780vvsn737k2Rj9hb30Dlt1JNRNAVmIC108ed7CfOS7q2nzM3baLYLe1jKBh8vdFK/jr5Rccdp9fKo6C8ZXhuEt7/EaPfA7a8xHFfIUQlwkhNgkhbCHExG777hZC7BRCbBNCnHkk5zmWUF7T1Fnc8hAYNzCXYYVZHZ5JTz+FBHrIKgVAURTGDM5j2tTBmJbNkuW7ovb3ENk4KHqjbRKOqcZeazt7ItjxAhJIqbBhyWD6D61g1mUrmDppIwv2D8fqZpwMS2F/Wwo7E9Igor/eT5Vku5tjzhMeQ+R6JAhDsHjeYLZU5FLb6mGY6wCakB0ZZg7Vxq0HOb//2sgBAlBYtntA3EVHC4s9tfv46PtVaPMM1CDYEdlFjxaMSztr/97MkBIReY9F3PBnSKHts6TINcX/8gOG2WF4IfwbBk2rw8A+ctn5PHnVRSy+49usKjuA3+i26AdUNrewq7aelkCQ5kA4e86wLO58/QNClhXVd3VLK6+t20xbKERta1uv47YVzS3oWiydTQKl9Q296uNYgpC9+wAZQoiVXT43RfUjhCqEWAtUAx9LKZfFnq0TR+r5bgQuBv7ebRDDgSuAEUAeMEcIUSKl/JyJr8cOUhLcPRbA7Ir8zGT+fMtFYSbEk++yesd+8FjQFv/YYKqCu9aOazWHDMtldP/wVO6l11b0apwCyMxIoLUtRDBoxCindX/OYshVAlJT/Ewft4c3542IDEugqgq6psRNwAgFdBrrEkjNbGXYoH28tmo6f1l3BlcPWUyOpwmJYH1dAc9tn0rKhAaaQuHpcX7GLiwEWg+vDNsGX4OT1++eQv7N9eTlNaJh4NFCMW1VASPS9qMIG5uwgWgOuDttcTcERSvY6Z3XLgEh2NOcGTcdub2fpGw/7uQQLdW9e4SkBCui43j+qKG8tm5TTMWIg5k+VShUNLdyydgR1LX52NfQGLedQPDD195jd8SID8vJ5PrJ4+NnqxkmD37yGfd/ND/iCXu5//wzmFJccNBrKU5LiZvarArB2OMs5EB8/6In1EopJ/a0M2LfxgohUoDXhRAjpZSxerERHJHxlVJuAeJJxM0GXpBSBoE9QoidwCRgyZGc78uEYVksWL+bPZX1DMxLZ+f+uugbUIZL6qQ4Hdxw/mSuPLPzN/rrbZdQ19zG7n21/PTnrxAKWe2HhPv2CiyPSjAFnA02qio6jOX0M4Zxz3fPRgiBzx+iuaVTC+BQaGj0YZq9u7Pap6NSACrYOgy5chLJjbP42iUGKckekhJdjByWz32/fysutc22FRyusEEpa0ujORSkNpDO/SsvwKkaWLaCKVU0YTIhv5Q5ZV4ClgPdsLENAc7YF0RLjZOFfx/FnmXZpMxqpl9hY1gaIn7dDAAS9CCXDlrB2toitjfmYNoKAVPH44ilhxk1KkhoKdGxdTpc7YDl4M3d45g9YA26YiEEGLaCYak4FANNhTN+tIY3fzEZyxTIHip8tMPldjDz3DEAjMvP45pJ43hq2RpsaaMKBcMO84utOPKiEFa5s2ybz3bv5ZaX3sLowQHwGwbbq2s77q2NB6q45725PXq1TYHOVOvyxmZufuENXr/xavrHiRu3I8Hp5PopE3hqWWeJIwG4dI2bp03q8bhjEe1CUEcTUspGIcQnwFmEHdS4+KJivv2AroHm8si2GERc95sACgsLv6DhHBnqmtu47g8v0NDqxx8ywgpkisAhVKQtMUwLR6ONs8XGFAZPP7GImWMHk5vduYqcnuQlfaSXF/75bZ54agHzFm7Fb5gEUxTMBBVNVUgu8PKL22byl0fmUFPXiiIEiz/eyuz5OwkEw4bjcIob9tbwtkMq0DQUjFQwPfDZk5tZq2iEDAspYcSwPM44dSSXXTiRP/91TseYwuOy6DegGtVrsrElj0U1JaR4AzT5IGjpBK3ORR1FSMZn7mVfSzrrawupfD8fZVisR29YCo/vO4Xq/GTcyQZ5l/lQIneshUq1kUim3oLa5emxpEBBcnK/7UzJ2U1pcwaPbjiN9eUFTCzegyqiaWZ6tknKmY3UNucgHdHm/JP9wylvTeW0/K24tSBraotYXtUfl2ryw/EfkDO8nisf+5Tlz41i+8c5PRo43aEy5dRhjJk8ACklbSGDH5xyEheOHs6CnXtwahqZCR5+/OaHceudQVhc/8QBhVzw2H/i1lhTBKiKgiIEwS76I5Kw/KlT08CI33dXhEyLp5et4d5zTj1ou9tnnkh+chJPLFlJg8/PhIJ+3HnaNArTUg55jmMOR4ftkAkYEcPrBmYBvz/YMYc0vkKIOUBOnF0/k1K++blG2gVSyseBxwEmTpx4TJIFf//CJ1Q2tHR4Jf6QiaYqTB5cwMaFe7D8VsfbU0oIBU1eeGU5P7ilU1qy/cGsrm1h0ZKdqELBrWmoDRbJSR4umT2BEwcXcvP3n8YwIsLpUoIEf6DzoTncbLTDge2C5jDfn7wPQAQlPjrPvX5jOV+79m/889Hr8A734l/biJASzWGRltXE9OtXsbB5CJZU6J9ZR0FaA6pt8dnOQbQY7rAkpWLzzeELSHb6MQwVrQ0C+z18+sY4Tp69BkW1EUJiGipr1w9kd1sW9Je04qC73uMmXz7jvKUka35sKVCE5EAohQJnOO7oVE2EkBQm1LGnOYstFbmMyD3QYXyFAKFD1jca8W/SqPf1w+5mgHc1ZbOjKQcQePUAk7L3kOzwMa98GKNzy7GS+nH3Xf+PGz99EKOHRVhVVVg8ZxM3XfEwm8fpNFohXLrGN6dM4DvTJ6MIgZSSksyVbKmqiTKeEFYZ+9Fp05jz6Ub8viDosS/gvOQkZg0dzH+Wr47ZFzBNzh85lPc2b6OtB+PeDktK9vQibiuE4LLxo7gskthxPEP0MtZ9COQCTwkhVMJraS9JKd852AGHNL5SytMP1SYO9gNdA0f5kW3HHaSUfLp+V8x00LRsVm7YRyoabd1C2aZls3lbWBzG5w/x6BPz+GjeZgzDQlFEjAENHGhjbF4OL726osPw9gZChGvAHUwApzewI6GG2skgDHDWCjBlvNwyHIll3PXAPaTm+mkYlETj6nQKA61c/N25rLAHYNOpf6ypNrYQ3DhuPv0cjVhSQRUWtWYSW/x5ZCS20ai3gEhg1afDKd2ax/CJe1B1i+1riihtyIQzYFhiPT8YvIoxqdU0So2PWvPYGUrERGVF20C8SgC3YtBsufAqIQqcDdgS/rV5Ohvq8jEiq5mlNZlkJ7aQlRSdwCEE5JfUsn19Nn5LDweOAQU7UjdOUJxUw22jP0YREodqETA1UFM5Jf8PpDrS6D8kh52b9setShLwhw1e2cYK1FoH5swUWoMhnli8Aonk1hlTEULw72su5dEFS3lj/WYCpkVhSjKDHInUfrSX115+nYBl4Z7gpa1/rAbyoIx0Zgws4sXV6zG7GViPQ2dmyQCEgJfW9DgLBsKVK04ojDtJBWBnTR3L9paT6nZxaslAXPpxTpiSHC22w3rgsKgjX9Q39xbwnBDiT4QX3AYDy7+gc31psHWBEW8KqAgK88M0op/c8wpbtldgRApkWlbsLx0Mmbz9/lrWbSyP2XcwqKoS92E/XEgVqk4GvVkhZU9YfS2QGVZRc1e10+MknsQA9VVJVJXp6A4Dh24x6rLtLGgroXzb2UwdtKuDedAORYFKI4VCVwOKtFjfVkCNmYiFSlpmG2OT9rD5g5GAoK4yhYXvRO5fzabkvN1cNWYHU9MqKdZNUlVJJlCk7+SZxmLWB8JxyTbbRZvpRFEkJe4KANbWFLGhLj+q8oSNworS/pw9cgNKt3FqDpgxfBsL1gxHTbZASnxWuMozSL41fD4urfO3dmkmimihwfcBqY7r+Nmfr+In1z5OU4MPpCTgD8Usagob3JUhlICN7VLwGyb/XLKam6dNRlMU3LrOnadN587TwpVR5s1Zz4N3vIQZ6ny5Zy4Pvzi6GmDFlFwydgRT+hcyMCON7dW1Hd6zQ1Xpl5zEzMH9WVN+APUgqcqqEHgcDq6cOCb2HpGSn779Me9u2gZINEVBVeby1NWXMjw3K25/xwuOy0oWQoiLhBDlwFTgXSHEhwBSyk3AS8Bm4APgluOV6SCEYMaoATFi6pqqMHPCICZN7I/DEf0O03WVKy+dzPZdVWzfWdlheHuClODzG2RmJB60XXckeJ2fS5GsO1QTMpYKXFUKQgqELcIFJHXCJYqAxJQ2Am0OjFDYmBkhnYDPgbEghSSHHwslwm2NRXsacKPl6TC87XA4LfIv2BeuyRZpJ3SLK77/EbNPWcqA1CqqJKwIaZQa4Wt1KDazE/dT2ZRIfZuHQKuOb4OLcXopKVpYM2Fp1YCYkj/tqGuLnyrrdJuoTRqLZjzP1wu3dnj9/WoaWfXYYOY8OIZ9qzM7jKotA+xvfQuArLwUnvzwTu599BpuvffCmEy1Ll8GarBzdhOyLNqCsayNRxcs5f57Xo4yvBBe1E1f04oIWWBLhCnJahScUjKApXv2ce2kcXxt3CiyEr1kJnj4+sQxvHD95WiKwsWjh8ct1y6AVI+b80cN5fVvXUWaJ9azfn/zdt7fvI2gaRI0LdpCBs2BIDe/+GZcJsXxhOMyvVhK+Trweg/77gfuP5L+jxXcdcWpbN5XRXNbAF/QwOPUSU5w8+OvzSTB6eAvf5vDx59sxrYl2VlJ/PDWMxg0IIs5n27u1YzG5dI5ZfoQvB4n99z/BqFDGGsIT5VvvfFU/vy3OUd+gRDRG+6uviawHYRTc31ObLu7JqRCRWkGo8eWsmtuf+zvKJAYfZeqWOQ76gGoMxKw4rzvM8Y14MwIoq/W8TW6cY1pIqewHqfWySO2ge2mSj/NRheQpIbYVFZIm+UAJOP6lbLdzCbZLkUIefCppCSGeiZtaKhLIGSrXLzoQvYbHiwUMuf7SFwNW818kIIdC/MYNO0Ap/9gXaTWXHsZIxnmY08eiL8tyAM/fTn+qQUYiZ3fo9ehs3reNua9uRohYNZFE9FKknli8Qqym3qIIQck6WtasZ0qSQ02V14zgxl/foKgGdZ1NmyLH5wyjeunjAegJRAkZJoMzEzn52fN5NcffIKmhCVPEfC3y2czqUtttq5YvHsvTy9fw/K95XEX+lqCQTZXVjMyN46a0PGCL+ndcZwHbP47yEj28uavrmfOmu18tHI75TVNZKUksHbXAU4dO4gf3342P7jlDIIhE6/H0UG9Ky7MiLtA1v5bC8Dt0hk2JJeZ04eiqQq33HgqD/19TtzwRFeoqsLWHZX8+Ptncf8D72IYVq9DEG6XjmHamF1XxXvQjVU1myETStm3MRcz1kEDQN+l4mgS7PnPAAZevwshJIpuoyo22Y4msvVwAoUmLBQk3UuBSgmJBT5OG7kJTdiELCVuWrIAKk2VhRWD+KCyP35LJT+ljoL0evwhBx/uHEVjsZdCdz3F6bVsbczD7PbCEEKSntAWNsA2CBVsA6Ql2LaxAOmU7A4kgwJ6vUXaqmCkQnT4pWEGNHYuzGPkWfvoN8KP1ngKt37vYXZvPYDb4+TcK6cwaEQ/HA6dgL/zC5OEwzt14xM66GwuXWNotcZDz73W0XbDilIcJcn4R4Tph0prnOrOQHYVmKEQ51wxib/XbaXeH01BfPCTRczZupN1ByowLRtFUTh7+GB+dc7pnDF0MEv27MOpaZw4oDDMhIiDfy1ZxV/mL45rdNuhIA6rnNExB/nlhR36jG8voSoKb362iQ17KvCHTHZV1LF21wGWTt7Lz75+OrquouvRD/qgAVn0K0iltLSukw0B4ZThBIWSfplce/EUpk0d3BE+OO/sMTzy+FysQ7yOTdPm/Y838r1vn0ZBfhpvvLOGqppm1m4oIxA4+Iq2qipMnTSAeQu2dWxLMAK0OhxIGX0NTqfBhdcsZN6rE1i7qASrS50xodgUDq5k3+bwAo3/gIeUDSbFJ5djSpV0vRWvEuzwMHMdTewIxBJnLKlgt46nxtFAMwYJapBcpTGuKNFvNp/IosoB+O1w9uaBplTSEtooSqujX2oD++rTUFVQPJCT3EhFY0oHEwIBJxTviYr3ShuC+3TK/pJD82kJWKlWxypjwh4jrldkBlX2rujH4KEJ/P7aAwTaIum9bUHeemYxJaPzYw4TQChRxVOchK1DTlICFxcN5r1ffBRlpAP+EMHNdThyk6kf5SFzeUtUTT7NqVFy2kD8uQ6Gjiigf3E2wbf2xYwxaFqsLOtc47Zsm/c3bae21cdT11zKtIFFLNq1l0+272bawKIogXRbSh6Zv4RHFx40QQsIr28c114v9Hm+xzoWby5lQ2kl/i50In/I4J2lm/n6qePpn5MW97iH/u/rzL75MWRj+EG2XIJAmorL6+C3P7uIV15dwf89+D7+gMGo4f34zg0zeyTad0cwZGJZNrqmct1VJ5GW6uWTBVv53YPvETwIA0LTFD5b2i1FuVHBJU2CSWBbKkLYaKrFRWctRFEkM85fy/7dWdRVJWObCqpu4/KEENLdUZvtxLPWM/mUzWh6/Mww1bZJqg9Sn+KOGFaJRNAW0NnfWE5hMlTbGSSqAXIcTXR/KkxbZXFlccTwAghsKdi0P5+C1AY01SYvpSm8R8CEon00ZtZQ3ZKEQzXJS2mM0XgQCtiGArUqWWsaOTAzISyBKSS5GY2g6chuJZBUTdA/YzbL/i4I+ddH/yYBgy1r9mLGYa14WiW/PuMsxp04CIBnH51LMBBnOmFLkqotaoe6USxJ2ro2lJBEaoLWsYnMzWjG77dYtLYWsVbES3KKC0tK1pQd4Ollq3lg3mcdCmiWbfOHC8/izIgC2u8/ns9zK9cfrCscqoqiCP508Tlx48jHC76IJIveos/49hKLN5XiD8bzKAUrt5X1aHxTEt384w/XcMdjb1Hb3IYQgnSnzu9uOJeHHp3DitWlhCIGff2mcu742UvkZCVxoLLpoOMRQtC/KJ2Lrnq0wwiPGt6Pe++6gD/edxnPvLQ0UhfOjCL/O50aTodOY5M/qj9pKDiaLbJP3k9jRTLFaVWMH76DhAQ/li1wuEy+8eP3KN+RjaxIoyDLx8iSc7npx0HAACGZdFp8wwsQDGm8/fGJ6AUBvGltkSoS4Sy1ZHeA5IIDVNopgKDJ8lAezKC/q7ojQKEAox0GUzIqmVtd1O27sKn3eclKbEFXLLomS6d4/KR4/IRzSGMVki1bsD8pmcpTXOQu8HHWtD28r4wgPbGFwpk17Hs9L+ZaVFXj7AvP5L5b/9NjqEdRRJyUbknJqE4aV0KyG92hEer2onQ4NHKykmnTbVoGeWgb5MEpFYbmZ7G+ogorEi5qZzQcjrCSogj+MHdhTIbcj9/4gPEFebh1jee7VcHojsLUZC4ZO4ILRw8nJ+nwFomPRYijwBj6POgzvr1EaqIbXVViblpVESQnHLyg4OB+Gbx53/XsqazHtGwG5WVQUdUYZXjbETJMhgzOpb6hDcOwsGyJqgosS6LrKoZh4XBoaJrC3rK6jlRlgHUby7nr3ld57M/XMGZUAW2+IHf+/CV27KpG01Qs0+Lkk0pYtnJP3HFKW5AzqJbsYbWUzcvnqVfOwpYCG4GZYjOsZC9fO2EJF44ui3iuj3HqlIv4cGECif0b0Z0H4xsLgiEHaUW1mHTzlESsURzv9DPSadAsBRqQqoRlIH87chGXrE5AKFDdnETQ1JEI9IgimqbYDHYdYFugX7c+Y89hS7Bshd31WYTGaDhCFhePLCUzvZFt/nycSSZ5t9dw4C+RskASsAVX/nQqOflp5BSkUbq9KiazLZ7XC+EU47LdNQwdE87kPPmc0fzrgQ/ifFOCJ++5lsUHypm7fRfJLhen5hRw52vvY+l2XJEKl6YRsizsHopktiNoWmhxsiQlkvc3b2dKcQGaohIkvvF16Rq/u+BMJh6EC3xc4SjxfD8P+oxvL3HelOH864MVcYyvwoxRAw95vBAiqtBmWXk9uqbGGF/TtGlsauPvf7mWF15dTum+WoYPyeXM00aydMVuduyuYsjgHHbtrmb+Z9ujjrUsm917ayjdV0t+XioPPPwRO3dVo2kKRshk0oT+/Pj7Z3PHz19i3Yay2DGqEs1rsvbN4bTVeZAy/JAKQGtQ2biriIq6TM67/LnIgliAW7+xmwNjkrFS6glJFRfxDbBtK5imGpftEA8lzhbcCri7PRnJeoAZxbtotJwo+ZJNB/Koak4mxe1DYJOs+ih0NlBppNJkdVLKHMJJSIan+O22sr7Nw5p9xQRNHRxQO8HD8tBAEnSToV4ndSHwjvUz8G9ltG1wgwVpY2DcyAIe/tUbrFywPcbwOl06yWleaioaY3i+hmGRntVZ8y8lLYHpZ41izhudWWlCCG677yJSUr2ckzqEYVoSv/n+s/yx6lNSDJMEt6BqWjKhtE4anaYoPHnVxby+bjNN/gDZSV5eWbOJgBn9WyhCMCw7k61Vsbocpm3jDxnkJSdi2vENryIEd806+atjeCP4ImhkvUGf8e0lctOS+L8bz+Vn/3wfCE8h3U6dv3x3Ni7H4X+NhfnpGGbsTa5pCoMHZVNcmM5dPzg7at+QwZ2LVd/70XNxp7yaqlJb18qHczexaMmOMG0tQl1btXYv/3h6Id/6xnTu/NmLBLt4zYpukzezBl+TG1+ju8PwdkCC2qrS6nEyp7Q/5wwMx4wXtjWjZ4c1JrcFchnpKY/SWpASAkGNF+bOwJXrxyOCtEknB58sS9pslWQ1NsyjCLCEgh5hQ4zIO0BJZiWasPAoIcZ4yxBAgaOeJn+n8Q3JcNJDsFyn6q8ZWC0qrhEBzJFquKIGIN0SZ7+wz1cXqqI9wUJxSRJP8IXPr7ioXGIx783VMenEQsClN0xn7JRB/PzGfxHssvCp6yqjJvYnMzelY9uqRdtZ+OGG6AsU8Nxf5zHz3DEEfCF+/I3HaW0OtO9Cb5Xkzm1k34XpSF1BUxSmDSxiYmG/DqMopSTd6+WxRcuwbIlp2zg1lZunTWbmoGKu/PdLWN0Ms66onDy4PwlOJ5ePH8XLazZGsRwcqsq/rr7kK2d4gT7P93jAjFEDmPfHm9mwpwJdUxlRlIMSrxaXLXlm3iqenbOaZl+AEcU53HHpyQwr7FwVzstN4YTxxTGhB4eucekFParWdWDC2CK27qiICjsAGIbJoAFZ3PPbN7vo7YYRDJm8N2cFJ5z7Mpd8ZzdzXx1HTUUiyckqV11+CoFhO1m+YxuaotB9GUgQJvj7DJ1djWnALkBjmS8ZI1JMstJIoaXBSYFWT4a7laagm60tOQQ0J7knViIEEcMLPVXJENi4hMGitnQuTDqAowszwZCCLYFkAl0YGapik+dtYICrhkQ10KE1rIlYD1wIcGSZKG5JcK9G62de+q9sYdf1yZgJghkl21G6RESkLTsiIgoqqlC5svAmXn1kdUfKcFe4PE4mTh/C0DGF3P6bi/nrb97GCBpYls2EaSXc+fuvRbV/65klBLv1I21JbWUTpTuq2Ll5f8zvC+EYZdK+EK2D3CS7nPz0jJO7Xafgu9Mnc+3kceypayArwUtWlxpul44bwatrNxGIGFeXrnHJ2BEMzQ5X7rxr1smketz8e+lqmgNBSrIy+PlZp3w1DS99C27HDXRNZfzg+IT0dvzp1fm8tmhDR7WL1Tv2860/vcwzd309amHul3dfwBP/XsA7H6wnEAyzHb7/nVlkd5ma9oSLzh/Pm++tpdnyd+gLu1w6F58/jpRkD35/7Cp6Ymor5167iBp/AwUlBtfdHQ49CFy8tWcvC5YMRpip6EasWZSA5QSPbjAgpQFQQXgxcEEX8Z19vnRWNPdnf2MavpCT8YV7yE9t7BKmFB09OkWIoOxkLijYOITJcM9+mmyNhb4MZnhrMaVAFZI9oQSeayqOuS6XYpCkRfNcK0Kpce270CVJM1vwb3WBLRAhSFseQMw2SHRF9yEUsINglyZx2pTpTMs5jSxXLi+E4usjCAFmZJYx89yxTD9zFFX7G0hM9sTNeGtu8sXtR1EFbS0BdmzYTygObVBYoPptLClpMwyu/PdLvPatq8hOii6S6XU44tLAfn7mKcwaOpi3NmwB4IJRw5jcJclCVRS+O30K350+BSllr9kUxyUkPajff/HoM75HGS2+AK8uXE+wW5Za0DD55/vL+fX1Z3Vsc+gat9x4KrfceHD5vnhITnLz5CPX8cyLS1i8fBdJiW6+dtFETjt5GADDh+SxcUs7z1NyxuXLGDV1J6pmx8yyJAEmZ6/m/b1hFoE7R8FVGU41Du+PQIEkh2TWQAPcl1CuXECb+RAAIb/GnmUF1JWmIoSk/+A6GrLayE5qiStiLoDpniqme2tREOwIJbAh6CJJb2abP5d608tmqTOvNZccLUCj7aDecsb0o2KTqXdWwZASLAQ1ZmLcyIZQQOmiGywsSCw1GJBXFi0mLyGwy0Fwr4PgTidWWwFZN4SFwk89fyzbNpTFeK0AQ0Z36kmpmkpeUUbsIIBQyGRARIzH7Hav2LZk8Ih+/O03b8U9FsCfHn50A4aJYVr8v3kL+eOFZ/fYviuEEEwpLjikaHp72686+mK+XxGU1TShq2qM8bVtyeZ9VUf1XGmpXm67+XRuuzlWeO773z2d2370HCHDYvgJ2xkxeXePNDAAjxYkK7GZRJefZq8Lszqd9gXv9sfP1SL44w1fx5VzFwBv77gfGwvLFKx9fQTBNj0sCgxUbsnCW9WGKI7vVVyatI+J7rqOsMIYVxPDXU0sCuj4LCchqSOA0a5GTvTUogqb1f40FrRlY6B0pAcLJE5hYskwbS1ga6xqK+6oYtEddkDQsiRa28EV1HD4JTgIC8kHBft/n0VgjzOcCWcJnlk6h1kXTSAlLYHTZo/nk3fWsm1DOQFfCEUHhGTI7RZbfGsY7Tihx+/Ztm2Wf7qVP/7kpfCLokvcXygCh0PjOz+7AKdLp7y0tsd+Ahmdj64lJZ/uiM9giYeQZREwDBKdzv8J43ow9PF8v0LITU8iFGchTQii2A6HA9uWvP7ZBl78dC3+kMkpYwZyw9mTSfbGUtwaQ3W8Wv4Um1vWMvIeBUdFEcPSduE4CA0saCksbR0UERu3qS9PZpuSim11S80F5q/ZxaTBYapUmT/8wNfuTsMIaB2GF0BaCr4GD00VCWTkN0XRo5KVECd46tC73PWKAE1CtgIttgsQXJOym+HOJpyRApwZWgVjXI38uW4odqQ/E43PWktwKyGkDQEcRLu8ncncMgS+LU5aV0SHABwW7PthIZ5pjWRdV0/dqyn4dznB6LyekG3yl1+8xr2PfoOAP0RuYTrbd5SSdEILerpJ0sxW2jIs/lP6KKfnzObMnIuizuFrC/LY/W/zyTtr4lLRFFUw4+zRXHTtNEpGhkMAScluauOEHaQKUos2mj2lCHdFyDT57UfzeW3dJixbkpXo5d6zT2Xm4OOw3PvRgpRfWtjhyCWx+hCF1AQ3Z0wcEqNz6tQ1bjj785VYue+Zj3nglfnsPFDH/tomXvx0LVf97ll83bKjglaAB7b9nA1NqzClgSGDBHJ3s8OddpD7S2WLvx8GKrpqoyhgh+J7jZYtqWmqZ3fTv9hW/xB5jjBJsqXGix2vjI4Eu0mL1ELrHEA/3YcZRwFNFWE+b6PPQ6JpM8LZ2GF4ARxCkqkFGOlq7HakwG87CdAziyJNbWG0ex/OhRJVsxFq55gCvhBmyCawOI36l9Nomp8QZXjbr2XFgm0E/CF+dPXfmfPGajyn15J1fR3plzahZ4RfuCEZ5OPK1/Fb0fHce779bz59d12PHGCnU2fCSSUdhhfgkm/OwOmOVmYTuqB1sCfqZebUNL42bmTcfrvip29/zOvrNhM0LUzb5kBTC99/9V3W7a845LFfZRxGAc2e+xCiQAjxiRBic6So8PcPdd4+4/sF4BdXn86lM0bjdmgIISjKTuXB78xmaMHh657ur23ig5Vbo0rVG5ZNfYuPd5Ztjmq7umExAduP7FIR0JImPttBoxW7iCdQKUr8GlVGelSJ9OTcFqQdh8jvUEjr9zzb6h9mV9MTDHKuZrRnH54UP0qc0uxCgaHZ+zk5cQu5eiMqFmATlDZanECbJWF+5QAW7iyBZhdWd7ob4FJsBjtaYrb3DIG0BRt+P4D5Px9N/qg6rv7HvLDyWTdDHQqYyCV5yLYe0mUlrFiwlYryekzDwjMqgOKIbaYKjQP+Tr2F3Vsr2Llpf4+VLgBM06Kl2wLc7GtO5Lwrp+BwangSnOgOjelnjSb9jGI8uo7XoePSNKYUF3Dz9MkH/RbqfX4+3LIjhvsbNEweW/SVk9o+PMhefg4OE7hDSjkcmALcEikk3CP6wg5fAHRV5YeXnsztF8/AtCwcR6D2v7G0MkL9ijZugZDJ8q1lfO3ksR3byv2lhOwg3SFRCch0FBHClgEEGorQGJ/1ZzI909DLr8XoIrfs9Brkj65g/4acDo/WoQucKY0cyNKpaxpAf2cNRc46MnWLEcNK2bsyH9sMpwwDIGx0t8GYAbvRVclobzm2hCojmRojkVrTQaYWouvsOWhpPLlnNJatUhXwRoxv9HWHbEFDl3pwPVUljrp+E4J7nbTVeVmyL4Gtn+RjW/EP8vtCnHLuWD59bx12N2W5hGQ3v7/zRaxIbTyzVkP2DyG6vSMsaZGsp3b8vb+09pC6y0JRGDc1rPlQX9PCyoXb0DSVK759Cld+51Qq9tWTlZtMUqoXKSVr91dQ1tDE0OxMSrLiL+p1RWVTCw5NjUkblkBpXcMhj/8q42jEfKWUFUBF5P8tQogthOtWbu7pmD7j+wVCUQQO5ci+4qyUhLjbNVWhX0Zy1LZcV0EkkyvaAKtCZWr2vXjYRq1/CR49n8KkK0jQiwEYlTyRNY2fIbt4gsUnlJOc00LF5iyskE7GwBqyh9QhVAhJnR2BHEypMMhdQ1FCDWNmb2HH/P40VycggJSCJkpmlCKFAtjYUrC8tT+tlgsLlUfqErgyZS9DHM3YtkJt0M1PNkxnT1sKAJ/WFOC3VDyqEa1uJmBdoPO6e7NeZAcFdiRCYwY1GssT8KQG8dXHioYXD87mhh+dw7rlu2lp9EXpLjTVt0W1bXgvCe9YP6ILe0JFpcDTnwxnJ8WraHB2lHxnd7jcDk4+ZzTFJTm8/ewSnvjDe6hqWDDHvlfyk/93BVNP63SihBCMy89jXH6s7kRPKDxIuffR/eKVaPwfgSQ85eodMoQQK7v8/XikBmUUhBDFhEsKHVQWrs/4HuMYOzCPjGQv+2ubotTONFXhshmjo9pOTDuJ9ypexrBCyMg8SUUl1ZHB0KTxKGIixclXRR1jS5Oh7go2NFkYUqVzKi5ILWgitaCZeLBRKA1mMsBVi0SQkdZEyWWLCBgOas0EUAW2hD3+dAa4aqkIJdNkuWmPdPmkzpMNg1i7eDCWX6dCd2Elyo7TG1LlymXn8bfxH1PoaUEVNqaENSGNcQm72ezL44ARX8yoHe1eseKS9P/Tfsp+lUuo3IER0Mgf2cqeOMZ3z7ZwMsg/3ruD68/4I6Fga4/9B3a4qPpHOlnX1SNUcLhV+ntLuL5/dLivcGAWYyYPZN2yXZ3GXITTdRNTPDic4cdw9Wc7+Mcf38MImXRdZvv9nS/wn0/u6rk6Ri+Q4HRw3eTxPL18TVS5d6eu8Z1pBw9ZfNVxGJ5vrZTyoBlQQogE4FXgdill/Icngr6Y7zEOIQRP/OAyRvbPxaGpuBwamcleHvzObPIzU6LaulQPdwz5DSWJIxEoqEJlTMpkbht8L0r3uXEEOxr+SkPgI1RpErtY1S0mGtSoqU6mucnTsYDXZuuowubExB0McVcwOnEfp6RuQTVNKpqS+c/GaaysLmZPMJPut5tpKFQ1JFPjT0AJKjFxtd1tKZzz2cX86cBgPvW5+DSo0xRJuBjuOYBTxEk/xiZVbSNJ9UfiuqDooLglOd8OU7c0XaFf+rSYxSwIp+bOeXM1vrYgbS2BmP3d0fJZArtuLmDYuvMo+vhcRu24AIcda9R//vDVnP21SXiTXDicGoNH5KPpKs0NbdRUNDHnjdXc+51/x/WQhSJY+smWQ47lUPjBKSdx16yTKUhJJsHpYNrAIl647gqK01MPffBXGe2Mh0N9DgEhhE7Y8D4rpXztUO37PN/jAJkpCfzrzsupbWrDHzLIz0jukZ+Z7sziu4N+ii1tBIfWet3b/By2DGAQv94ZhO+77Vvz2bsnB0WxkVLg9gSZNHkLfo+TNL2lveBvhxsxMbGU1zdORCJ4fvtUzh29LjZE0OVvERSIkEA6ZIeNVhWLzIQWqhQv7zYPZ7ynlExH2BOVQLbexL5QZ7wzR29ghOdAh8cbslVWtxXTZrsQCrgGBJlyw2Y2vzmM/iW5LP90a8y1hoImtRVN6Loazu5y2aiJFma9Bj3EibEE7/91E6Zh8YlnMy/8fR4PPPcdPN5wUkh9TQv/766X2LAiTM3LLUijpqIhKqRhWXb38Hbn92/LGNnJzwMhBFdMGM0VE0YfuvH/EI5GzFeEH7QngS1Syj/15pg+43scISM5fuHHrgjZIRbWfMiK+oVoQmNq+qlMzTg1rucrpcSU4TimRwnSYruJR9WqqkhlX2k2tq1g2+F+WltcrF5ZQt7MBjL1TvaBKRWqQsn4bY2SjANsq+2H2xHCjnisXaFpNukZzdTWJCFQ0GtVLK+N7bVxOUMM6VdBYVp9xwtkra+Q0/TNlK3OZOkzQ2ioSEArMMn4WiOZQ5oY6dkfPkfkElTFZmLCHuY3Dw1fl4D8s6uZPLuFgeaNvPREHEaHx8GoSQNwJ+kMurMNc0gV2CAtqH0hlaa58VO/27PUAr4Q+0vreOXJBXzjtlnYts2Pv/E4lWX1HSWlynbHqoodDLYtmXTykMM6pg+9xNGTlDwJuAbYIIRYG9n2Uynlez0d0Gd8v0KwpMXDO35Fhb8cIyKfWLX/Gba1buCb/X8Q014IQZJjCM2hrQx1H2BFW3xpzNI9OVhWd/qVQnOzl/KWNHIdTeQ5GmkwPaxqLQbARlCSV43XY7C+PL9HDbORY/awfPEwgkENKQVaAJJdfk4fu4ph3goS1QBBW2NXMIsDoWTWLyhiyZ+HYwbDt66xSaf8fiejHtuLSIx+ioQATdqkaW3UmwmAYJeZQz9vGXrWMiZOL2Hlou0dacIOp0Z+cQZTTx3Gy+VPIkbWdlReBsi8qgGjQcO3+uCxVyNk8uk7a/nGbbPYuLKU+prmuLX84sGT4MS2bIIBEyFAd2hcdevpUWpofTh6EIDo/YJbj5BSLuLwdO37jO9XAWU1jfiDBj7PHqoCBzoML4RJ/5ub1lLuKyXfUxxzbH7Sbayq/gmpWhuj3GVs8ud3KXAZySIz4vNehZAYhk5pIJ0cvZE1bUVRZeEVBfqlNuAzdBp8btK8vpjQg8tlMP2U9dTVJuHzOUlK8lGUXs0JiXs6PGWPajDMfQANk8X/GN1heNshQwqiQqDEWbSXAvQuCmdtthPTDlAbWMLdD/6FD15ezvsvLccIWWTnp7B7ayWXTr+Xwof2gBZtMBWXxNEvdEjjC+G48vK6Bbxjv0bOr+tpXuqm4d1k7J44xIDTrXPDj86mcGA2iz7YgO5QOeX8cQwYmnvI87XDMi1CQRO3N1YHow/xIfqEdfpwuCivaeSHj71NWU0jqiKQismAk52kFUYvFEkku9u2RRnfJqOef+7+M+X+UhRRgsBkQoKfa1KLeae6gjoz7A0KJOcX7+SVzcMx7OjbRVEk3gQ/rbaL6lACdpysNUVASVZ1uK8e/AIhICOzc2G4xF0VG6IQkkGuGuY1x49N716QS+HY2pjkDQVJg9kZrlGxUdDwaP1QVYVzr5jCuVdM4fH/e4f3XlxOMGCgZZjYliQeS9C3LnYxrTucLp2iW9t4vvQJbKeJngOp5xgkTvWx9648ZDA2BKQ7NGZffSJnXzYJIQQjJxQf8jxdEQwY/P137zDnzdVYpk1uQRrf++WFjJl8aKH//2l8iZUs+tgOxyks2+amB19hd0UdQcPEFzTw+yVb5gzC3xzt9ahCJUlP6fhbSsmjO37LPt8uTGkQskMEbZsVLYnkJX2P03Ovw6GE+xjmbOamMavJcPtxRsTNFWHj0gzOmbARRQGJYLO/IIon3BVC9I6P244ENT7LQBEST2ZsEglAlZpIm+XA6vICMKWgNJBBqEO2UpKo+lEUjTT32R1VKFqb/bz7wrIO8XOzXkUasQOWNtiBnh8ZTVdxunWKJiRTmbYVW+n0uBUHaMkWSdNjqWuqpnLt7Wdw/Q/P+txCN3/40QvMfXM1RtDEtmz2l9Zy73eeonR75efq738HvWQ6fAHecZ/xPU6xcns5zb4AdrebQtqCis3Racya0BmZNL7j732+XTQYddhEe4mWNFlQ+xFT00/h3KwzULDJ1Xxkuv28eelLfG/CCibnlTN78Daeu+B1TiluV9ISGGiRopjx0RJwsqUim13VmfhCPTMrAHx2nJzd9msZFgor8HSBmm6QfmUTy1sHss2fQ73podpIZF1bETuDXWMRgmbLw8qWfvxx+wP8ctOtbGley/69tWh6l3CALah5NhU72GkIpQUyKKK2dceVN5/Cb5+8gVrlADIOOUFxSbyj/bE7jtD1qqlsYsWC7TGMCCNo8sqTC46o7/8FHA1th8+DIwo7CCH+CJwPhAiXNrheStkY2Xc3cANhAs1tUsoPj2yofeiK+ub4QtzSVrB9XhyKEyklKY50vtX/h2hKp8FrNhpR4nipNjYNoRqEEAzxJqEA1ZYLQyokOkLcMGYdN4xZB0DAVljVXNirsW6tzGZHVU4HBWxzRR6j88soSq+P235nIJtx3r1RoQfTFmyeV0DjwqRw5csIhFuSfWM4885GoSyUQVmo53RbG4Ua0wMYNBr1PLn7QW7IvBujW8WI5vmJWE0qaRc2omVYBHY4qXslBbsp/iMjFGisa8XfFsRuVuMuvUgTQjWxx6uq0sFmkFKybtluls7bjDfBxWmzx/WoCdyOqvJ6HA4tRjvCtiV7dx1dGdOvJI7TmO/HwN1SSlMI8XvgbuAnEUGJK4ARQB4wRwhRIqXsOceyD4eF0QNyOypYdIXboXHT1EuYXJKCIlQynTkxU9lC7wDMOK6ZLhwMSRyFaZvMrd+JiWBTIAVfooYuQh1cXktCUCqs98cn53fVW2jyu9hZlYMdEclpv8/XlxeQndSMS48dR52RyPqWfEq0KtzOEEZAY928QpY9ORRCXbxrReIe5idh9KGTIXqCKQ2W++Yydkq3DDTA3JpM7R9T8LfFVgWJuWYb3nl+KR+/sRojpJHSqCJ0MypuLE1B08fRVDWnW+eCq6ZSMCAL27b5vx8+z4oF2wn4Q6iawiv/WsD3fnkRp88eT0/IH5AZU4gVQNUUho7u3Qvyfxby6LAdPg+OyPhKKT/q8udS4NLI/2cDL0gpg8AeIcROYBKw5EjO14dO9MtI5vypw3lv2Rb8kQfPoavkpidx1glDcR5EzCdZT+PE9NNYWv9JhxCPKjQS9STGpkzhj9vuojpQAQhMS/D9eafQtisFj2py4fjNDB1+gFdbCjF6CDPYkTwJIWB/Y0pUHLYdAkllUzJF6XXhv7s0MVsUti3OZ/HrIxFBgdVhcLv1Ywt86zxIE8TnvJMbP/Xw8n/K0YUDw7A6xuFw6QwZXcCWNXt73ZeUYZ4vQPn9OeTeXo2z0AA7rC9R+VgGZpWO2+PgpDNG4nTrnHr+OIaPKwJg+fxtrFgYNrwAlmljmTYP3/s6U08djjcxVr8ZwlWQz7xkIh+/vqojbi0EOJw6l94w4/N9Mf9L+AqIqX8TeDHy/36EjXE7yiPbYiCEuAm4CaCwsO8tfTj46ZWnMW5QP176dB1twRBnTCjh66eOP6jhbcfF+d+gyDuQ+TXv47f8jE4+gdOyz2de9TvUBquwsZE2bHhnKK21ng5h9T98mE7KxiZGnLmzx74tW2AL0NWD39WS+AtxWpJN8iltJM1oo/z+HKw9B6FNSXDgwuDwvV/fZhfV/05HhsDqVjI06DdYv2x3jGJZb2HWa5Tdk4eWZqK4bEIVOkjBgGG53PX/rqBgQKy86Px313UY765QNZW1S3Zy0hk9a/Z+5+fnk1uQxutPf0Zbs58RE4r51o/PIbvf/3jqcC9wzFLNhBBzgHiyRz+TUr4ZafMzwnqWzx7uACKqQI8DTJw48Ut6Bx2fEEJwzqRhnDNpWI9tbFvS2Oonwe2IkrYUQjAxbRoT06ZFtV/dsLgjJNFQnkxrnSeqooVtqjTuT6al2ktiVrTKVzt0VbK3No38tAbS7CDOBoHhAbuLDZUIcpObehx3e5213FtqKL0zv+Oo6JxkKBlZwFWDZlMVOIBb87KzeQsbmlegCg1b2tg95ewC9e8kIUM9L6ApXovsG2upeCQrfHcfHoceCBvhdjjdOj+8/9K4hhfCdLP26stdISB6QTDeWBWFi6+fzsXXTz/sMf7P41g1vlLK2AJhXSCEuA44DzhNyo6r2A90rc6XH9nWh/8i3lm6mQdfXUBbIIQQgounjeL2S6ajqz0/yKro3NdUkRi3QoW0Bc2VCSRn+WMYEzUtCawtKyTg1ymfWwRtKl4RroNmpZtoI1toDboYmnsgbry3O7QMCy3VxGzQ6Gr8HC4NXdf44f2XUpTaKd94cuZZtJrNbGxaza7WLaxpWBqVdNIVZl10n92RdmET3nF+Cu+roPqpVIK7nREK2uejg3kTXPQf0rN846yLJrDgg/WxhTkFjDtx0Oc6Zx8OAQn0LvnwqOOIqGZCiLOAHwMXSCm7Lr+/BVwhhHAKIfoDg4H/cbn8/y4+27iH3z4/l4ZWPyHTImiYvP7ZBh54ef5Bj5uafipq5J3s8BooahyVLVWSlZxMtjM6ktTsd7Fs9wB8ISeeXTp2i4a0FDDDlZAdjQpFvlbOGrmR/hnxmQ6xJ5PIboI2iiI49YJx/OujH1E0KLY0eoKWxJT0mVxW8E2cqgvRg7FMHBWMm0jRsX9KG4oOruIQhfdW0f/hcsTBWXLRQw9X+MTp1nF7Hfz8L1ehKD0/cqNO6M9F3zgJh1PD6QrHhl0eB794+BoczsM4cR96DYFEyN59jjaOlOf7CJAIfCyEWCuEeAxASrkJeImwivsHwC19TIf/Lh5/b2lU6SEIV794c/Em/KFYKcZ2zMw6G48WzgjLGlQXx8mTKIokb4AfQ4ZQutxCO6uzwlluFuhNoqP0fDtsU6Vyc3ZHnPdQ3HVpQ3CvA6s52vu2bcnuLRWH1Ld1KE5+UHIfAxOGdhhggcCpuNCEzpQri0hI9PRYZaJ7SEJLsvGM9IPaO1dJ1RQKBmQy5ZRhPPr6bQyLLKwdDNfefiZ/f+cH3HTXudz6ywt5dsFPGTulL0vtC4Vt9+5zlHGkbIce50JSyvuB+4+k/z58fhyoi6/jLAQ0tvpxp8X3pFShUeAZwObmNeguk5HnbGPrnEGYkaKaDrfB0Fk7qLH8MRKILUEXEuWghHSrW2HKgyZ0Sah8PD7HdfuGcj56bSVnXHxQbWs2z6ti46OJ1NUMQVEEbS0BnB6N0y8dy423X8CVb/h48e+fMP/99bQ0+pFd3gZNnySSdlEjvnVumhaEK4okTvDj2+ShN66EaViU7aqhen8jyz7Zwi//di1jJg9k15YD/POBD9i+oZzUzESuvPkUTjlvbMdxOflpnHP5/7bA+X8NX2LYoU/b4SuK4UXZLNqwJ4ZFo6nKIaUpJ6aexKam9QhhkZzTyqSr1uJrcCMUiSMxQE8TpnRvG00+N1JVsJ0QkyUsJKkFnYtsPWo9oJDj7Idiaeyq7dnKPXrfm5wwYwipGYlx9//6e/9h8ZzYElr+FoMPn1tD/X4fP//L1Xz3F7P57i9ms2XNXj54ZQXNjT7yizMYObmYf/z7RSqXBzr0GPwb3b0yvF3RTv+6//bn+N2T3+TOq/9OIBLXbW3285d7XqO+poVL+hbLvhR8WWyHvvTi4xTlNY3c/+wcrvjNf7j7yXfZVlYdtf+WC07C6Yh+t7ocGt89/8SDLrgBjE2dQqpWjGl13h6eVD/OpACVzSk9lrwamFmNpkqEgLb+FlKRHeWMhGqhO036Tyo/xJUJri78Duf1uxyhS4p+W4F3YhvxyJiKIuIKokOYthXP8LYjFDRZMX8bVfs7i0cOG1fEtd8/g2lnjGTImELcLic1K2WUEI40xefmhZqGxWO/e4dgoFsFYb/Bs4/MiZso0Yf/Ar4kbYc+z/c4xK4DtVz7hxcIGiaWLdl5oI7563fz4M0XMHlYOK5Ykp/JP++8nIffWMSm0iqyUhK48ZzJzJpQcsj+VaFy1/B7uHbeQ4TEPvymQll9GkFDpySnEqcWf57mdhicXLKNuvoT2OUw8Ux2MMSfjulrxZe8haxhleguExUVp+pGExp+qw1DGggEKhpXFN7IttaNrG1cSsgOoudA7q01tCz1UvVYZsw5e3omXnj800Nep65r7NtV3cGFffkf8/nPwx9jW7LX+ruHi7LdNVGhjXZIoLayibzC9C/kvH3oCUfPsAoh/kmY+VUtpeyZlB1Bn/E9DvHn1xbiDxodDpgtJYGQyW+fn8cbv7quI514aEEWj37v4s91Drfm4OlTb+elHWt5dNPbJLv99C8oIzOx54KSAKluuGvGqQxKiOYeL66dx9yqN/FbfoYmjmJ2/tXowsGi2o/Z3LyGVD2dk7POQRUKL5b9I4oepjggcbKPxg+DBLskXNi2ZPIpQ+OOo6UxvvZFVxiGSb/icEx52/oynn10bozGw+dBRk4SLY2+GA9X11Xy+2fGVEEGsC2blPT4lar78AXi8KoXHwr/JkxCeLo3jfvCDsch1uzcH3fme6CuibbAoXUIeguXpvGNYRN56exrmNx/3yENr0M4GZgwlIHeaIP41v7nea38KepCNbRZraxvWsmC6g/xaF7OyLmQ20t+xbX9b6PYO4itzeux4uhOCF3iHecDVYJmI3TJJT+a0GO891C8WEUVjJkysMPT/Pj1VYSCPbNADge+tiCTTh6K062jqAKnW8flcfCzv1zFVbechtMVvdjpdOmcNnt8R823Pvx3cbSoZlLKBUAvOZR9nu9xiSSPC18cQ6GpSkyc92igyDuIq4pu5oV9T2DKzvMqqGQ5c3GpbiSSKekzmZw+M0rIp8JfxoKaD6I8WUOGmF/zPiekTSPHnR91LpfqiWSnRb9EpAlqskXqWc1oKRYJk9uoLFgKXBh3zFffejpL5m7G1xqIP6uUMOvCTrGagC901MJ6Hq+Lux/8OtvWl7F26S6SUjxMP2s0iclhIfbbf3Mxj//fu7Q2+1EUhTMvnciNPz736Jy8D4ePYzXDrQ/HHq4+fTyPvPlZFI/XqaucP2XEIRfTPi8mpk6jNljF3Kq3UIWGKU0GJgzlm/1vx6X2zLfd2LQaKw49wJYWG5tXxxjfcSlTeHN/nCx1Kah/LQUZUij6vwPoGRaVgfiLd3XVzfz1N2/hawv2+FzZtuSj11Yx/axwJd9pZ45kwfvrMYwjCzs4XTrnXTEFIQRDxxQydEysXsnMc8cy4+zRtDT58Xid6F/AC7MPvYQkSqL0EMgQQqzs8vfjEXmEz4W+X/04xBUzx7G/tolXF27AoamETIvpIwdwx2Unf2HnFEJwdu6lzMw6h8pAOcl6KmmO2AWw7tAUHUUo2N0MsBAKWhwpsgQ9iRsG/JB/7fkz/tZgOLwioOKhTKwmDVRJ/VvJZN9QR6KWHHO8aVj84Iq/UlfdjDzEQ9Xa3ClsPmnmUMadOIjl87fFbasoAvsQ/Wm6yqSZQ7n0hkNTxhRFITn10NWo+/BF47AW3GqllAcnlh8G+ozvMQopwyyGtkCQYYXZUUpliiL40ddO4aZzp7K3qoHc9EQyk/87izVu1UN/76EZE+0YmzKZdw+80OO+eBiWNIbr1Xv59eOPEgwY+Lc4ke3JGZbAv9WJQ3FyRs5FMcd+/MYqmhp82L1YRBkRqZMWCpns2FjOVbfOYuppw3n64Y9pqImOb9u2jCt6A2G+8sBhedz9pysPKXzeh2MQfWGHPrSjrKaR2x59g+qG1rDHJSU/u/I0zpkczSBI9roYPaD3lW2/DKQ60rm84EZeLHsCIRQEAltaXF54IymOnmlV2dnptK51YYS636ISZ7bNWTkXM9Z5En+553Xmv7cWy7RJTvNSW3VojxfCBnPUCf1565nFPPWXsCy1bUuSU73c99h1PPjTV9i9Lbr+Wfsz6nBqUaLr3kQ33/7peX2G93iEBI4SrVAI8Twwk3B4ohy4V0r5ZI/t43EOvyxMnDhRrly58tANv8Kwbcn5v/gnlQ3NUS9kl67xrx9dzpCC+HKExzrazBY2Na0BYETyOLxafJZCV9x3639YuWg7RhdD53Bp/OYf1zFy/ABuu/QRSndUYR5mnFZRBUIIdF3rEC7vCk1Xe+zT7XWiO9SYVGSXx8E/3r+D9KykuMf14ehDCLHqSMMAyc5seWLeVb1q+0Hpg0d8vq7oo5odY1i3+wBNbf6YmVDIsnh5wfrP1adp2cxbu5NH3vyMNz7biO8o0tF6C6+WyKT0GUxKn9Erwwvw4z9czkmzRqI7VBxOjZR0L3f+7jJGTRjIhhV7KC+t7ZXhVRSBqiqomoKmqeEkCtOOa3iBg/YZ8IcIBYyYRAnLtPng5T7hvuMSfRlufQBoagvELR9u25Kapvji5QdDiz/IN//4IhX1zfiCBm6Hzl9eX8i/7ryc4py0ozHkLwwuj4Pv/fJCBg7NYe3SXRQNymbQiDA7Yu+OKiyzd9PFfsUZ3P2nK9m7o4o//OTFQx9wMEgZ1zgbIZP9pXVH1ncf/vs4PLbDUUWf8T3GMLp/LoYZ+3C7HRozRvU/7P7+/s4S9tU0YEQMlT9kEDAM7nnqQ57+yZVHPN4vEk0NbXzvkodpbvQR9BusW7qLd19cxq/+di39ijPQNAWjF058RVk9P772CWwrXBrpSGH2YPQHDDu24+996AF9wjp9AEhL8nDdmSfg7sL9dOoaeenJnDt5+GH39+HKbR2Gtx1Swtayalp8n7/q738Dz/9tHg21rR2VHUzTJug3eODuVxgzZQBJab2japmGha810GOY4XBwsOdUVT5fhYs+fMnoCzv0oR03nzeVkcU5vPDpWlp8AU4fP5hLp4/B9TnI+PFCGF12HsEov3gsnrMp7hS/qaGNbevKaaqPpoMJAUlpXpobfDGMh95Qz3oDTVMx48xMVF35sorg9uFIICVYX06dhz7je4xi2sj+TBvZuzCDZdssWL+bJZv3kpbk4YKpI8hLD6+6nzt5GM/PW0Ooi8FQhGBkcQ6J7mNbS8DtiT8+adnMfXsNZijWo/e1BFBVBdM+8gdK0xSEomCZFrYtcbkdjJhQzIYVu6OoZgCqojB5Zs+FTPtwDKOP59uHz4OQYXLzX15lW3kN/qCBrqo8/dFKfn/juUwfNYCbzpnCym1l7K6sxzAtHJqKx+XgN9ef9WUP/ZA4/6op/OOP70cVlFRVhaFjCynfXRPXA9UdOv2KM9izvQLzCBXKMnNT+PlDVzHnzTWEAgYnzRrJ2KkD+fvv3uGDV1YQCpiAxOHUufi6aR0KaX04ztBnfPvwefDm4k1sLavu0HkwLAvDgp//6wPm/PHbuJ06T/34SlZsL2Prvmry0pM4efSAqDLyxyrOuXwy29aXs+D99aiaipSSzJxk7nrgSl7710I2r9kbE5YwDZPbf3MxT/z+XTav3oumqxghE8u0D5ke3A6hCNIyErnv79eR3z+Tm4bmRe2/+afnM+Ps0Xz67joURXDK+WMZMqqgh976cGxD9rEd+vD58N7yLTGFMiGs8bu5tIoxA/NQFMHkoYVMHhor8nIsQ1EU7vjdZXz9u6exY2M5mTnJDB1biBCC2d84ifdfXh5lfB1OjYnThzBgSC6/++e3qD7QSH1NM4WDsnn8d+/w4avxE3iS07x4E10oqmDQ8H6cev44xp80uMfCmgDDxxUxvBcFMftwjEOCPBoUmM+BPuN7nMPZgwcrpcShfzEKZ/9t5BakkVsQzUnOzEnmgWdv5q+/eYvNq/fi8jg469IT+MbtZ3S0ycpLISsvBYDv3jOb+ppmVizY3rFfUQW3//piZl101JKW+nA84guqWnIo9Bnf4xyXTB/Nhj2VMeXgEz0uhh6nqci9RXFJDn94+qZetXU4NO77+/U01rWxYsFWvIkuxk0dhLtPwPx/G1J+IWXhe4M+43uc4/Txg1m2dR/vLtuCEOFVd01V+Mt3Zx+cZvY/ipR0L7MumvBlD6MPxxL6Ftz68HkghODnV53O1aeNZ/XO/SR7XUwf2f+4WFDrQx+OBcg+z7cPR4LinLRjXquhD3049vDFZK/1BkeUXiyE+LUQYr0QYq0Q4iMhRF5kuxBCPCSE2BnZP/5QffWhD33ow38d7cI6vfkcZRyptsMfpZSjpZRjgXeAeyLbzwYGRz43AX87wvP0oQ996MNRhwSkZfXqc7RxRMZXStnc5U8vdKS3zwaelmEsBVKEEH2ST33oQx+OLUgJ0u7d5xAQQpwlhNgWmfHfdaj2RxzzFULcD3wDaAJOiWzuB5R1aVYe2VZxpOfrQx/60Iejid6UnToUhBAq8Cgwi7C9WyGEeEtKubmnYw7p+Qoh5gghNsb5zAaQUv5MSlkAPAvc+jkGfZMQYqUQYmVNTc3hHt6HPvShD0eGo+P5TgJ2Sil3SylDwAuEIwA94pCer5Ty9F5ewrPAe8C9wH6ga7J7fmRbvP4fBx4HEELUCCH29vJ8PSEDqD3CPr4oHKtjO1bHBX1j+7w4Vsd2NMd1xPndLTR8OEe+0ltFJJcQomuO+uMR+wXxZ/vxy3NHcERhByHEYCnljsifs4Gtkf+/BdwqhHghMoAmKeUhQw5SyswjGU9kTCuPZpG7o4ljdWzH6rigb2yfF8fq2I61cUkpvzR5vyON+f6fEGIIYAN7gZsj298DzgF2Aj7g+iM8Tx/60Ic+HMvo9Wy/HUdkfKWUl/SwXQK3HEnffehDH/pwHGEFMFgI0Z+w0b0C+PrBDvgqZrg9fugmXxqO1bEdq+OCvrF9XhyrYztWx3VEkFKaQohbgQ8BFfinlHLTwY4R8ktKretDH/rQh/9l9FUv7kMf+tCHLwF9xrcPfehDH74EfGWM77Eq8iOE+KMQYmvk3K8LIVK67Ls7Mq5tQogz/5vjipz/MiHEJiGELYSY2G3flzq2yBgOK13zCx7LP4UQ1UKIjV22pQkhPhZC7Ij8m/oljKtACPGJEGJz5Lf8/jE0NpcQYrkQYl1kbL+KbO8vhFgW+V1fFEI4/ttjOyYgpfxKfICkLv+/DXgs8v9zgPf/f3tnD1JlFAbg50VNAluKkKihBKkcgiTCIBoKoiT6gQYhyKiprSkEod2GtsClwSGK/iCb+sNoyoYyEy6W0tBgOoRQBFLxNpz35sclU8p7zrnyPnDg3PMJPtzz3fee7/y8FxCgAxiO7HUQqLd6H9Bn9TbgDdAIbAEmgbrIbtuBrcAzYFehPQe3Ovu/LcAq82lLeH/tA9qBsULbZaDH6j3lvo3stQFot/oa4J31Xw5uAjRZvQEYts/gLaDL2vuB86n6NWVZMSNfzTTJj6o+UtXyL1y+IOz/K3vdVNU5Vf1A2BO9O5aXuZVUdfwPl5K78Q/HNauJqj4HPlc0HwMGrD4AHI/pBKCqU6r6yupfgBLhtFUObqqqX+1lgxUF9gN3UrrlwIoJvhCS/IjIR+AU8+ktF0ryk4KzhFE45OVVSQ5uOTgsRrPOn9z8BDSnlBGRzcBOwggzCzcRqROREWAGeEx4mpktDEhy7Nco1FTwrXaSn2p52d/0Aj/MLRpLcXP+Hw3P0Mn2bYpIE3AXuFDxFJjUTVV/asj3vYnwNLMthUeO1NQhC61ykp9qeYnIGeAIcMA+CMTwWorbAkRxqwGHxZgWkQ2qOmVTWTMpJESkgRB4r6vqvZzcyqjqrIgMAXsIU3/1NvrNsV+jUFMj378hIq2Fl5VJfk7brocOlpjkZxm9DgEXgaOq+q1waRDoEpFGO5LYCryM5bUIObj9Pq5pq+Fd5pUTg0C31buB+7EFRESAa0BJVa9k5ra+vLtHRFYTct2WgCHgZEq3LEi94rdchfDNPwaMAg+AjTq/4nqVMNf0lsKqfiSvCcLc5YiV/sK1XvMaBw4neM9OEObc5oBp4GEububQSVi9nwR6E99fNwg/BvDd3rNzwDrgKfAeeAKsTeC1lzClMFq4xzozcdsBvDa3MeCStbcQvswngNtAY8q+TVX8eLHjOE4CVsy0g+M4Ti3hwddxHCcBHnwdx3ES4MHXcRwnAR58HcdxEuDB13EcJwEefB3HcRLwC74Oh3OvtFA/AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(n_components=2, svd_solver=\"randomized\")\n", "proj = pca.fit_transform(digits.data)\n", "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA的一个缺点是它可能会丢失数据中一些有趣的相互关系。如果想看到非线性的降维与映射\n", "我们可以使用几种流形模块中的方法。在这里,我们将使用[Isomap](https://blog.csdn.net/VictoriaW/article/details/78497316)(串联\n", "等距映射)是一种基于图论的流形降维方法。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.manifold import Isomap\n", "iso = Isomap(n_neighbors=5, n_components=2)\n", "proj = iso.fit_transform(digits.data)\n", "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 示例程序" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1797, 64)\n", "accuracy train = 1.000000, accuracy_test = 0.905556\n", "score_train = 1.000000, score_test = 0.905556\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/bushuhui/anaconda3/envs/dl/lib/python3.7/site-packages/sklearn/linear_model/_logistic.py:765: ConvergenceWarning: lbfgs failed to converge (status=1):\n", "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n", "\n", "Increase the number of iterations (max_iter) or scale the data as shown in:\n", " https://scikit-learn.org/stable/modules/preprocessing.html\n", "Please also refer to the documentation for alternative solver options:\n", " https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n", " extra_warning_msg=_LOGISTIC_SOLVER_CONVERGENCE_MSG)\n" ] } ], "source": [ "from sklearn.datasets import load_digits\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn.metrics import accuracy_score\n", "from sklearn.manifold import Isomap\n", "\n", "import matplotlib.pyplot as plt \n", "\n", "# load digital data\n", "digits, dig_label = load_digits(return_X_y=True)\n", "print(digits.shape)\n", "\n", "feature_trans = False\n", "if feature_trans:\n", " iso = Isomap(n_neighbors=5, n_components=8)\n", " digits = iso.fit_transform(digits)\n", "\n", "# calculate train/test data number\n", "N = len(digits)\n", "N_train = int(N*0.8)\n", "N_test = N - N_train\n", "\n", "# split train/test data\n", "x_train = digits[:N_train, :]\n", "y_train = dig_label[:N_train]\n", "x_test = digits[N_train:, :]\n", "y_test = dig_label[N_train:]\n", "\n", "# FIXME: need to use Isomap to transform data\n", "\n", "# do logistic regression\n", "lr=LogisticRegression()\n", "lr.fit(x_train,y_train)\n", "\n", "pred_train = lr.predict(x_train)\n", "pred_test = lr.predict(x_test)\n", "\n", "# calculate train/test accuracy\n", "acc_train = accuracy_score(y_train, pred_train)\n", "acc_test = accuracy_score(y_test, pred_test)\n", "print(\"accuracy train = %f, accuracy_test = %f\" % (acc_train, acc_test))\n", "\n", "score_train = lr.score(x_train, y_train)\n", "score_test = lr.score(x_test, y_test)\n", "print(\"score_train = %f, score_test = %f\" % (score_train, score_test))\n", "\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "\n", "# plot confusion matrix\n", "cm = confusion_matrix(y_test,pred_test)\n", "\n", "plt.matshow(cm)\n", "plt.title(u'Confusion Matrix')\n", "plt.colorbar()\n", "plt.ylabel(u'Groundtruth')\n", "plt.xlabel(u'Predict')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. 练习 - 如何画出错误分类的数据?\n", "\n", "1. 如何得到错误分类数据的下标?\n", "2. 如何根据下标,将这些错误的数据可视化出来?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "* [逻辑回归模型(Logistic Regression, LR)基础](https://www.cnblogs.com/sparkwen/p/3441197.html)\n", "* [逻辑回归(Logistic Regression)](http://www.cnblogs.com/BYRans/p/4713624.html)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }