From bede2a5ea0316d43f8721ba2e02344ef783dedab Mon Sep 17 00:00:00 2001 From: bushuhui Date: Fri, 5 Nov 2021 16:25:57 +0800 Subject: [PATCH] Improve description of least squares / logistic regression --- 4_logistic_regression/1-Least_squares.ipynb | 167 ++++++++++--------- 4_logistic_regression/2-Logistic_regression.ipynb | 177 +++++++++------------ 4_logistic_regression/PCA.ipynb | 32 ---- 4_logistic_regression/images/least_squares.png | Bin 0 -> 44997 bytes 4_logistic_regression/images/least_squares.xcf | Bin 0 -> 214366 bytes .../images/linear_logistic_regression.png | Bin 0 -> 19669 bytes 4_logistic_regression/images/linear_regression.png | Bin 0 -> 107876 bytes 7 files changed, 157 insertions(+), 219 deletions(-) delete mode 100644 4_logistic_regression/PCA.ipynb create mode 100644 4_logistic_regression/images/least_squares.png create mode 100644 4_logistic_regression/images/least_squares.xcf create mode 100644 4_logistic_regression/images/linear_logistic_regression.png create mode 100644 4_logistic_regression/images/linear_regression.png diff --git a/4_logistic_regression/1-Least_squares.ipynb b/4_logistic_regression/1-Least_squares.ipynb index c6b95e2..e69b769 100644 --- a/4_logistic_regression/1-Least_squares.ipynb +++ b/4_logistic_regression/1-Least_squares.ipynb @@ -4,17 +4,25 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# 最小二乘（Generalized Least Squares）\n", + "# 最小二乘\n", "\n", "## 1. 最小二乘的基本原理\n", "\n", - "最小二乘法（generalized least squares）是一种数学优化技术，它通过最小化误差的平方和找到一组数据的最佳函数匹配。 最小二乘法通常用于曲线拟合、求解模型。很多其他的优化问题也可通过最小化能量或最大化熵用最小二乘形式表达。\n", + "最小二乘法（Least Squares）是一种数学优化技术，它通过最小化误差的平方和找到一组数据的最佳函数匹配， 最小二乘法通常用于曲线拟合、求解模型。很多其他的优化问题也可通过最小化能量或最大化熵用最小二乘形式表达。\n", + "\n", + "![ls_theory](images/least_squares.png)\n", "\n", "最小二乘原理的一般形式为：\n", "$$\n", "L = \\sum (V_{obv} - V_{target}(\\theta))^2\n", "$$\n", - "其中$V_{obv}$是我们观测的多组样本值，$V_{target}$是我们假设拟合函数的输出值，$\\theta$为构造模型的参数。$L$是目标函数，如果通过调整模型参数$\\theta$，使得$L$下降到最小则表明，拟合函数与观测最为接近，也就是找到了最优的模型。\n" + "其中\n", + "* $V_{obv}$是观测的多组样本值\n", + "* $V_{target}$是假设拟合函数的输出值\n", + "* $\\theta$为构造模型的参数\n", + "* $L$是目标函数\n", + "\n", + "如果通过调整模型参数$\\theta$，使得$L$下降到最小则表明，拟合函数与观测最为接近，也就是找到了最优的模型。\n" ] }, { @@ -33,7 +41,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -50,16 +58,16 @@ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", - "# generate data\n", - "data_num = 100\n", + "# 生成数据\n", + "data_num = 50\n", "X = np.random.rand(data_num, 1)*10\n", - "Y = X * 3 + 4 + 8*np.random.randn(data_num,1)\n", + "Y = X * 3 + 4 + 4*np.random.randn(data_num,1)\n", "\n", - "# draw original data\n", + "# 画出数据的分布\n", "plt.scatter(X, Y)\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", - "plt.show()\n" + "plt.show()" ] }, { @@ -74,7 +82,7 @@ "$$\n", "其中$\\mathbf{X}$为自变量，$\\mathbf{Y}$为因变量。\n", "\n", - "我们希望找到一个模型能够解释这些数据，假设我们使用最简单的线性模型来拟合数据：\n", + "我们希望找到一个模型能够解释这些数据，假设使用最简单的线性模型来拟合数据：\n", "$$\n", "y = ax + b\n", "$$\n", @@ -91,7 +99,8 @@ "\\frac{\\partial L}{\\partial a} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i \\\\\n", "\\frac{\\partial L}{\\partial b} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b)\n", "$$\n", - "既当偏微分为0时，误差函数为最小，因此我们可以得到:\n", + "\n", + "即当偏微分为0时，误差函数为最小，因此我们可以得到:\n", "$$\n", "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i = 0 \\\\\n", "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) = 0 \\\\\n", @@ -102,7 +111,8 @@ "a \\sum x_i^2 + b \\sum x_i = \\sum y_i x_i \\\\\n", "a \\sum x_i + b N = \\sum y_i\n", "$$\n", - "通过求解二元一次方程组，我们即可求出模型的最优参数。" + "\n", + "上式中$\\sum x_i^2$, $\\sum x_i$, $\\sum y_i$, $\\sum y_i x_i$都是已知的数据，而参数$a$, $b$是我们想要求得未知参数。通过求解二元一次方程组，我们即可求出模型的最优参数。" ] }, { @@ -121,12 +131,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "a = 2.763945, b = 6.154651\n" + "a = 2.985262, b = 3.577796\n" ] }, { "data": { - "image/png": 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\n", 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5m/uoUSzkFGem++Hbrm9rjwftiSki8XHoEMyeDdnZ0KePs5TrH//opEzmzGEhp/DQgg3sKCjEUl5vvXCtCt5KKYCLSGzt2gWPPeZsCjx0qHOjcsaM8jb3X/wCcFe9tVsphSIiseGvzX30aOjb128liZvqrd1KAVxEosdfm/sttzi7uQfolHRTvbVbKYUiIpHnr8193DinzX3q1KDa3N1Ub+1WmoGLSOREsM3dTfXWoYr2qoUK4CISvo8/dtIk8+eXt7mPHg09eoTVKemWeutQxGLVQgVwkTC4ZV3ouCgpgQULnBuTpbu5jxoFd9wRs93c3fz+V1dFowAuEmduWhc6piq3uZ9xhtMtOWRITNvc3f7+x6KKRjcxRUKUdHXKmzbBnXdCRgbcd5+zPsnChZCX5xyP8Rolbn//q6qWiWQVjWbgIiFKijplf23uN93krAiYfdwad0Ds0hpuf//vu6xNhSsEiHwVjQK4SIgSuk750CF48UUnv/3ZZ+W7ud9+e1mnpD+xTGuE8v7HMmceiyoaBXCREMVihhVzu3Y525FNnep83aGDk++++WZITQ3447G4cVeqpu9/PHLm0a6iUQAXCdGxM6wdBYXUMqZCDtYNN9KCVsM296rEMq1R0xluLD9cYkUBXCQMpf/ww53ZxaUc7uhRZ4ebSZOcNve6dZ0295EjoU1oVxGxTivVZIbr9px5KFSFIhKmcKshSi/tY7Zs6rFt7ldfXd7mvn27czzE4A2RaX9fuHYHueOW0frBN8gdtyxi70MsqkJiTTNwkTCFO7OL2aV9FHdzL1WTtIa/qw4I/2qmKol4z0IBXCRM4aYNon5pX7nN/Ze/dDomw2xzr0owaY2qbijWqX1C1D7MEmFtlcoUwEXCFO7MLip549I294kT4aOPytvc77wTWrUK/XEjpKqrjsrHSkXqw8zLa6v4oxy4SJj6Z6czdkAW6Y3SMEB6ozTGDsgKOlBEdNnUggIYP97pkvz1r2H3bqfNPT8fJkxwRfCGmgdkL+epo0kzcJEICGdmF5FL+02bnN3cZ892blL26uXku/v1c9Vu7qWquupoXDeFouKjCZWnjiYFcBEXCOkDwFpYvtxJk7zxhnMj0rebO506RWOYEVNV2mnM1e2BxMpTR5MCuIjXHDrkVI9MmgTr10OzZvDwwzBiRLVt7m4S6KpDATs4CuAiXuGvzX3mTGdxqSDa3N0m0W4oxoMCuIjbrV9f3uZ++LCT1x41qsZt7pJ4FMBF3Ki0zX3iRFi2zGlzv/XWsNrcJfEogIu4yYEDMGeOU1GyaROkpztt7rfdBiefHO/RicsogEvSceU+itu3O1uU/e1vTi13167Oety//GXE2twl8SiAS1Jx3T6KH33k5LePbXMfPRq6d1d+WwJSJ6YkFVfso1hSAvPmOWuR9OgBb7/tBO2vv4aXX47aGiWSeDQDl6QSaOGoqKZX9u0r3819+3Y480zn68GDY74hsCQGBXBJKtUtHBW19ErlNvfevV3d5i7eoQAuSaW6lQPDWZf7uJn7pWfTv+DfFdvcS3dzd3mbu3iHArgklepauEfPW+f3ZwKtnHfszL1OyWF6rnyXthMXwa5vPNnmLt6hAC5Jp6oW7lDX5R7/Th71Cn5g+Nq3+M3aN2l2sICNzTJ54pf30uHe3/Hkiq18O2mNe0oWJWEogIv4hLQxw/r1jHxhLNd+uYI6R0pYekYXZuZcy79anQvGkPbGpoA5dVfWpYsnBAzgxpgWwN+B5oAFpltrnzbGnAzMAzKBLcCvrLX7ojdUkegKel3uSm3uV6ekMq/jZcw+72q+bpJRdlotYwLm1F1Xly6eEswMvAS4x1r7qTGmAbDGGPMuMARYaq0dZ4x5EHgQeCB6QxWJvmpXyKvc5p6RAePGsaxbP8YuzT9u5h7M9mAx29BYElLARh5r7XfW2k99X/8EbATSgWuBOb7T5gD9ozRGkfjatg3uvx9atIA77oDGjZ0296+/hgceoF+vDn63VEuvInd+bE496hsaS0KrUQ7cGJMJZAMfA82ttd/5/up7nBSLv58ZDgwHaNmyZcgDFXdIqnztRx85aZJXX63Q5r4wtaXzHjz8zwrvgb/3IVBOPZwNjZPqdyF+Bd1Kb4ypD7wKjLLW/njs31lrLU5+/DjW2unW2hxrbU6zZs3CGqzEV2m+dkdBIZbyfO3CtTviPbTIKW1z797daWl/550Kbe4LU1sG/R4Es9lxqBsaJ8XvQgIKagZujEnBCd5zrbULfId3GmNOtdZ+Z4w5FdgVrUGKOyR0vraqNvchQ6B+/bLTavoeBNp1JtQNjRP6dyFBC6YKxQAzgY3W2qeO+atFwGBgnO/P16IyQnGNhMzX/vvfMHlyxTb3KVOcNvcTjr9AjcZ7EMrWYgn5u5AaC2YGngv8FthgjFnnO/YHnMD9sjHmVmAr8KuojFAiKpy8aTj52lgK+Br97eZ+003ONmXnnlvtY7vlPXDLOCS+AgZwa+37QFVrW/aN7HAkmqqrOYbAl/EhNbrEWLV11e2aONUjvt3cDzVuwvN9fsuzbS/hxIzTuO9o04ClVL3bNuP5j7b5PR5LXvhdSPSpEzOJVJU3fez1LygqPhqwmSTUfG0s+XuN9Qp+YM99f4ANbzu7uWdl8ekjExh6+Cz2W98NxCAbaJZ/tbtGx6PFC78LiT4F8CRSVX5038Hi445VdUMslHxtLB37Gtvt+ppbPlnENRudNnf69XMqSvr04c4nl7P/UMX3I5ibgG7KPbv9dyHRpwCeRKrKm1bFizfE0hvWoc2nK7n1k9fouW09B1PqMK/jZbzZ+wZe+t/BZeeFGogTLfesWnJvUwBPIlXlTevUPoGCwuNn4Z4KSgcOwOzZvP3s/1J/+xa+bdCUsb2G8FLHyzjcsBFjB2RVOD3UQJxIuWetw+J9CuBJpKq8KQTuGHStbduc3W18u7nX79aNT26/n3uOnMH2n4ojfkM2kXLPqiX3PgXwJFNd3tRTQenYNndw2txHjYIePegCrKzmR0vTBoXFR6hlDEesJb0GrzlRcs9uyudLaBTABfBIUCopcQL2xInw8cdw0klw993OAlNBrrNTOW1wxNqymbfrX3+EJVo+PxkFvRaKSNzs2wf/8z9w+ulw442wZ4/T5p6f7xyvwSJp1aUNkk2o67CIe2gGLu7173+X7+Z+8CD06VNtm3swlDYol0j5/GSlAC7uYi0sW+Z0Sy5eDCeeGHSbezCUNqjIE6kzqZJSKOIORUUwa5YTpC++2MlxjxnjVJk891xEgjcobSCJRTNwia+dO2HaNOc/X5s7s2bBwIGQmhrxp1PaQBKJArjEx2efOWmSF16Aw4fhqqucNEmfPmCqWjstMoJJG6hDUbxAAVxi5+hRZ/nWiROd5Vzr1oXbboO77oKzz4736MqoQ1G8Qjlwib4DB5xuyTZt4JprnB3dn3zSKQN85hlXBW9QqaF4h2bgEj2V2tzp1g0efxwGDHA2UXAplRqKVyiAS+R9+KGT3z62zX30aGej4Cq4KeesUkPxCqVQJDKKi8t3c+/Z09nN/e67nd3cS49XwW07rKvUULxCM3AJz759ToqktLX9rLOctMngwWW7uQeaXbttVTyVGopXKIBLaPy1uU+bBldeWaHNPZiKDjfmnNWhKF6gFIoEz1pYutSp2W7TBmbMgF/9CtatKz9eaY2SYCo6qsotK+csUj0FcAmscpv7qlVBt7kHM7tWzlkkNEqhSNV27oSpU53UyO7dIbW5B1PRoZyzSGgUwOV4n33mdEu++GJ5m/vo0dC7d43b3IPdukw5Z5GaUwAXR5Ta3APNroOp/3ZTjbiImyRtAFdQ8PHt5s7TT8PmzdCihbPLzbBh0LhxRJ6iqtl1MBUqWpdEpGpJeRPTbY0j0bRw7Q5yxy2j9YNvkDtuWflr3LYN7rsPMjLgzjuhaVOn4eY//3GORyh4VyeYChWtSyJStaScgbutcSRa/M1e501+mS47lpG+7C3npOuvd5ZxraZTMlqCqVBxY424iFskZQBPlqBQ+kFV+0gJV+R9wC2rF5H9XR4/ptaHe+6B3/++RhsCR1owFSpal0SkakmZQkmWxpED3+/mdx/NZ+X/G8ZfXx/PSUU/8fAlv6PHiOec5VzjGLwhuPpv1YiLVC0pZ+DBlrZ5Vl4eTJ7MR3+bRVpxER+06sgfL72d5WfkYM0JpLvkg8pfhUrvts0Y/04eo+etK7u5PHZAlm44i/hhrLUxe7KcnBy7evXqmD1fdRKuCqW0zX3SJKcc8MQT2Xr5ddzV/CI+O7l8pp2WUouxA7Jc+Vor5+zB3eMViRVjzBprbc5xx5M1gCeMoiJnX8lJk2DDBjjlFLj9dvjd76B5c099UOWOW+Y3353eKI0PHuwThxGJuENVATwpUyjhcE1ArNzm3rGj3zZ3L3U4JsvNZZFIUQCvAVc0lRzb5l5cXL6bewht7m6jihORmknKKpRQxa2p5OhRWLTIWXO7Uyd45RWnzT0vr/y4x4M3qOJEpKY0A6+BmF/iHzjgLNc6eXLU2tzdRKsSitSMAngNxOwSf+vW8t3c9+93uiT/8hdnN/fa8f+VRfM+gJdy9iLxFjCFYoyZZYzZZYz5/JhjJxtj3jXGbPL9mXjTQT+ieolvLfzrX84ON2ec4eS5L7/c2eH9ww+d4y4J3smyjoyI2wWTA58NXF7p2IPAUmvtWcBS3/cJr392OmMHZJHeKA2DU94Wdo1ycTG89JIzy87NhXffddrcv/mm/LiLaHEpEfcIOKWz1q40xmRWOnwt0Mv39RxgBfBAJAfmVhG7xN+710mRPPNM+W7uU6bAoEFlu7m7kUr9RNwj1Gvy5tba73xffw80j9B4El9enrP29pw5zm7uffv63c3drVTqJ+IeYUcM67RyVtnOaYwZboxZbYxZvXv37nCfzpushSVLnJrttm1h5kz49a+dmu7S4x4I3qBSPxE3CXUGvtMYc6q19jtjzKnArqpOtNZOB6aD00of4vN5k78290cfLWtz9yKV+om4R6gBfBEwGBjn+/O1iI0oEXz/vZMWObbN/bnn4MYbg97N3c1U6ifiDgEDuDHmRZwblk2NMfnAGJzA/bIx5lZgK/CraA7SM9atc2bbx7a5jx4NvXolRKekiLhLMFUoA6v4q74RHos3HTlSvpv7ihVQrx4MH+7s5n7WWfEenYgksPh3hnhVaZv70087GwG3bAnjx8OttyZkm7uIuI8CeE1t3Qp//SvMmOG0uffoAU884Zo2dxFJHq6POK5Yf9tap5194kRYsMDJZ99wg7OMa7dusR2LiIiPqwN43NffLi6G+fOdG5OrVkGjRnDvvXDHHc7KgCIiceTq7pG4rbuxd6+za/vpp8NNN8G+fU6be36+c1zBW0RcwNUz8Jivu+Gvzf3ZZ+GKKzzTKSkiycPVATwm626U7uY+cSK8+SbUqQM33wwjRzoNOCIiLuXqaWVU190oKnLWJOnYES65BFavhsceg23byo+LiLiYq2fgUVl34/vvnd3cn322Ypv7wIHO7FtExCNcHcAhgutuqM1dRBKM6wN4WI4cgcWLncAdYpu7K+rQRUT8SMwA/tNPMHv28W3uw4Y5tdxBinsduohINVx9E7PGtmxxGm1atHBm2aecAi+/7ATxe++tUfAG7f8oIu7m/Rm4r819x5gn+MXSt7DA8qyLOPGe0Vw06OqwHlr7P4qIm3k3gFdqc6+fWp/pXQfw9879+K5hM9I21WLs2h1hpTq0/6OIuJn3Uih798K4cdC6tdPmXlDAhGvuovuI2TzZawjfNWwGRCbVof0fRcTNvBPA8/Lg9tud/PZDDzmbAy9eDBs3MqXdpRSeePxWZeGmOvpnpzN2QBbpjdIwQHqjNMYOyNINTBFxBW+kUIYOdapKStvcR42CrKyyv45mqkP7P4qIW3ljBt6pU8U292OCNzipjpRaFZtxUmoZpTpEJKF5YwY+cmTgc2yA70VEEow3ZuABjH8nj+KjFSN28VGrem0RSWgJEcBVry0iySghAnhVNytVry0iiSwhArjqtUUkGXnjJmYAUVk3XETE5RIigIPqtUUk+SRECkVEJBkpgIuIeJQCuIiIRymAi4h4lAK4iIhHKYCLiHiUAriIiEcpgIuIeJQCuIiIRymAi4h4lAK4iIhHeWItlIVrd2ihKhGRSlwfwBeu3cFDCzZQWHwEgB0FhTy0YAOAgriIJLWwUijGmMuNMXnGmM3GmAcjNahjjX8nryx4lyosPqLt0kQk6YUcwI0xtYApwBXAOcBAY8w5kRpYKW2XJiLiXzgz8K7AZmvt19baw8BLwLWRGVY5bZcmIuJfOAE8Hdh+zPf5vmMVGGOGG2NWG2NW7969u8ZPou3SRET8i3oZobV2urU2x1qb06xZsxr/fP/sdMYOyCK9URoGSG+UxtgBWbqBKSJJL5wqlB1Ai2O+z/AdizhtlyYicrxwZuCfAGcZY1obY04EbgQWRWZYIiISSMgzcGttiTHmDuAdoBYwy1r7RcRGJiIi1Qqrkcda+ybwZoTGIiIiNaC1UEREPEoBXETEo4y1NnZPZsxuYGvMntBdmgI/xHsQcaTXn9yvH/QehPP6W1lrj6vDjmkAT2bGmNXW2px4jyNe9PqT+/WD3oNovH6lUEREPEoBXETEoxTAY2d6vAcQZ3r9kuzvQcRfv3LgIiIepRm4iIhHKYCLiHiUAniUGWNaGGOWG2O+NMZ8YYwZGe8xxYMxppYxZq0xZnG8xxJrxphGxpj5xpivjDEbjTE94j2mWDLGjPb9v/+5MeZFY0xqvMcUbcaYWcaYXcaYz485drIx5l1jzCbfn43DfR4F8OgrAe6x1p4DdAd+H42t5zxgJLAx3oOIk6eBt621bYFzSaL3wRiTDtwF5FhrO+AsfHdjfEcVE7OByysdexBYaq09C1jq+z4sCuBRZq39zlr7qe/rn3D+8SbV4ubGmAygHzAj3mOJNWPMScCFwEwAa+1ha21BXAcVe7WBNGNMbaAu8G2cxxN11tqVwN5Kh68F5vi+ngP0D/d5FMBjyBiTCWQDH8d5KLE2CbgfOBrnccRDa2A38JwvhTTDGFMv3oOKFWvtDmACsA34Dthvrf1nfEcVN82ttd/5vv4eaB7uAyqAx4gxpj7wKjDKWvtjvMcTK8aYq4Bd1to18R5LnNQGOgPTrLXZwM9E4NLZK3x53mtxPshOA+oZY34T31HFn3Xqt8Ou4VYAjwFjTApO8J5rrV0Q7/HEWC5wjTFmC/AS0McY83x8hxRT+UC+tbb0qms+TkBPFhcD31hrd1tri4EFQM84jyledhpjTgXw/bkr3AdUAI8yY4zByX9utNY+Fe/xxJq19iFrbYa1NhPn5tUya23SzMCstd8D240xbXyH+gJfxnFIsbYN6G6Mqev7t9CXJLqJW8kiYLDv68HAa+E+oAJ49OUCv8WZea7z/XdlvAclMXUnMNcYsx7oBDwR3+HEju/KYz7wKbABJ+YkfEu9MeZF4EOgjTEm3xhzKzAOuMQYswnnymRc2M+jVnoREW/SDFxExKMUwEVEPEoBXETEoxTARUQ8SgFcRMSjFMBFRDxKAVxExKP+P7GcEc+/uVMfAAAAAElFTkSuQmCC\n", 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" ] @@ -148,7 +158,9 @@ "A1 = np.array([[S_X2, S_X], \n", " [S_X, N]])\n", "B1 = np.array([S_XY, S_Y])\n", - "# numpy.linalg模块包含线性代数的函数。使用这个模块，可以计算逆矩阵、求特征值、解线性方程组以及求解行列式等。\n", + "\n", + "# numpy.linalg模块包含线性代数的函数。\n", + "# 使用这个模块，可以计算逆矩阵、求特征值、解线性方程组以及求解行列式等。\n", "coeff = np.linalg.inv(A1).dot(B1)\n", "\n", "print('a = %f, b = %f' % (coeff[0], coeff[1]))\n", @@ -179,21 +191,20 @@ "\n", "梯度下降法的含义是通过当前点的梯度方向寻找到新的迭代点。梯度下降法的基本思想可以类比为一个下山的过程。假设这样一个场景：\n", "* 一个人被困在山上，需要从山上下来(i.e. 找到山的最低点，也就是山谷)。\n", - "* 但此时山上的浓雾很大，导致可视度很低。因此，下山的路径就无法确定，他必须利用自己周围的信息去找到下山的路径。\n", + "* 但此时山上的浓雾很大，导致可视度很低。因此，下山的路径就无法全部确定，他必须利用自己周围的信息去找到下山的路径。\n", "* 这个时候，他就可以利用梯度下降算法来帮助自己下山。\n", " - 具体来说就是，以他当前的所处的位置为基准，寻找这个位置最陡峭的地方，然后朝着山的高度下降的地方走\n", - " - 同理，如果我们的目标是上山，也就是爬到山顶，那么此时应该是朝着最陡峭的方向往上走。\n", " - 然后每走一段距离，都反复采用同一个方法，最后就能成功的抵达山谷。\n", "\n", "\n", - "我们同时可以假设这座山最陡峭的地方是无法通过肉眼立马观察出来的，而是需要一个复杂的工具来测量，同时，这个人此时正好拥有测量出最陡峭方向的能力。所以，此人每走一段距离，都需要一段时间来测量所在位置最陡峭的方向，这是比较耗时的。那么为了在太阳下山之前到达山底，就要尽可能的减少测量方向的次数。这是一个两难的选择，如果测量的频繁，可以保证下山的方向是绝对正确的，但又非常耗时，如果测量的过少，又有偏离轨道的风险。所以需要找到一个合适的测量方向的频率，来确保下山的方向不错误，同时又不至于耗时太多！\n", + "一般情况下，这座山最陡峭的地方是无法通过肉眼立马观察出来的，而是需要一个工具来测量；同时，这个人此时正好拥有测量出最陡峭方向的能力。所以，此人每走一段距离，都需要一段时间来测量所在位置最陡峭的方向，这是比较耗时的。那么为了在太阳下山之前到达山底，就要尽可能的减少测量方向的次数。这是一个两难的选择，如果测量的频繁，可以保证下山的方向是绝对正确的，但又非常耗时；如果测量的过少，又有偏离轨道的风险。所以需要找到一个合适的测量方向的频率，来确保下山的方向不错误，同时又不至于耗时太多！\n", "\n", "\n", "![gradient_descent](images/gradient_descent.png)\n", "\n", - "如上图所示，得到了局部最优解。x,y表示的是$\\theta_0$和$\\theta_1$，z方向表示的是花费函数，很明显出发点不同，最后到达的收敛点可能不一样。当然如果是碗状的，那么收敛点就应该是一样的。\n", + "如上图所示，得到了最优解。$x$,$y$表示的是$\\theta_0$和$\\theta_1$，$z$方向表示的是花费函数，很明显出发点不同，最后到达的收敛点可能不一样。当然如果是碗状的，那么收敛点就应该是一样的。\n", "\n", - "对于某一个损失函数\n", + "对于最小二乘的损失函数\n", "$$\n", "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2\n", "$$\n", @@ -206,7 +217,7 @@ "\n", "此公式的意义是：$L$是关于$\\theta$的一个函数，我们当前所处的位置为$\\theta_0$点，要从这个点走到L的最小值点，也就是山底。首先我们先确定前进的方向，也就是梯度的反向，然后走一段距离的步长，也就是$\\eta$，走完这个段步长，就到达了$\\theta_1$这个点！\n", "\n", - "我们更新的策略是：\n", + "更新的策略是：\n", "\n", "$$\n", "a^1 = a^0 + 2 \\eta [ y - (ax+b)]*x \\\\\n", @@ -240,21 +251,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "epoch 0: loss = 7670.746142, a = 2.354092, b = 3.762462\n", - "epoch 50: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 100: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 150: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 200: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 250: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 300: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 350: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 400: loss = 8594.865640, a = 1.749804, b = 6.543725\n", - "epoch 450: loss = 8594.865640, a = 1.749804, b = 6.543725\n" + "epoch 0: loss = 961.232595, a = 3.042831, b = 1.277951\n", + "epoch 100: loss = 780.212993, a = 3.110374, b = 3.224871\n", + "epoch 200: loss = 797.359161, a = 2.879130, b = 3.475558\n", + "epoch 300: loss = 845.492885, a = 2.799842, b = 3.518333\n", + "epoch 400: loss = 835.064012, a = 2.813343, b = 3.517065\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -266,12 +272,17 @@ } ], "source": [ + "import random\n", + "\n", "n_epoch = 500 # epoch size\n", - "a, b = 1, 1 # initial parameters\n", - "epsilon = 0.01 # learning rate\n", + "a, b = 1, 1 # initial parameters\n", + "epsilon = 0.001 # learning rate\n", "\n", "for i in range(n_epoch):\n", - " for j in range(N):\n", + " data_idx = list(range(N))\n", + " random.shuffle(data_idx)\n", + " \n", + " for j in data_idx:\n", " a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n", " b = b + epsilon*2*(Y[j] - a*X[j] - b)\n", "\n", @@ -279,7 +290,7 @@ " for j in range(N):\n", " L = L + (Y[j]-a*X[j]-b)**2\n", " \n", - " if i % 50 == 0:\n", + " if i % 100 == 0:\n", " print(\"epoch %4d: loss = %f, a = %f, b = %f\" % (i, L, a, b))\n", " \n", "x_min = np.min(X)\n", @@ -1291,7 +1302,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -1307,24 +1318,23 @@ "import matplotlib.pyplot as plt\n", "import matplotlib.animation as animation\n", "\n", - "n_epoch = 3000 # epoch size\n", + "n_epoch = 300 # epoch size\n", "a, b = 1, 1 # initial parameters\n", - "epsilon = 0.001 # learning rate\n", + "epsilon = 0.0001 # learning rate\n", "\n", "fig = plt.figure()\n", "imgs = []\n", "\n", "for i in range(n_epoch):\n", - " for j in range(N):\n", + " data_idx = list(range(N))\n", + " random.shuffle(data_idx)\n", + " \n", + " for j in data_idx[:10]:\n", " a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n", " b = b + epsilon*2*(Y[j] - a*X[j] - b)\n", "\n", - " L = 0\n", - " for j in range(N):\n", - " L = L + (Y[j]-a*X[j]-b)**2\n", - " #print(\"epoch %4d: loss = %f, a = %f, b = %f\" % (i, L, a, b))\n", - " \n", - " if i % 50 == 0:\n", + "\n", + " if i<80 and i % 5 == 0:\n", " x_min = np.min(X)\n", " x_max = np.max(X)\n", " y_min = a * x_min + b\n", @@ -1375,7 +1385,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -1396,10 +1406,10 @@ "pc = 800\n", "\n", "t = np.linspace(0, 10) \n", - "y = pa*t**2 + pb*t + pc + np.random.randn(np.size(t))*5\n", + "y = pa*t**2 + pb*t + pc + np.random.randn(np.size(t))*15\n", "\n", "\n", - "plt.scatter(t, y)\n", + "plt.plot(t, y)\n", "plt.show()" ] }, @@ -1436,41 +1446,17 @@ "name": "stdout", "output_type": "stream", "text": [ - "epoch 0: loss = 2.60133e+07, a = -4.09558, b = 7.02074, c = 4.32858\n", - "epoch 100: loss = 2.50396e+06, a = -33.1825, b = 282.352, c = 192.658\n", - "epoch 200: loss = 1.94167e+06, a = -35.4465, b = 297.516, c = 270.663\n", - "epoch 300: loss = 1.58138e+06, a = -34.3201, b = 280.422, c = 328.378\n", - "epoch 400: loss = 1.26769e+06, a = -32.8956, b = 261.08, c = 378.356\n", - "epoch 500: loss = 1.01347e+06, a = -31.5673, b = 243.259, c = 422.8\n", - "epoch 600: loss = 810004, a = -30.3731, b = 227.263, c = 462.482\n", - "epoch 700: loss = 647465, a = -29.3051, b = 212.962, c = 497.935\n", - "epoch 800: loss = 517653, a = -28.3507, b = 200.183, c = 529.611\n", - "epoch 900: loss = 413978, a = -27.4979, b = 188.764, c = 557.914\n", - "epoch 1000: loss = 331175, a = -26.736, b = 178.562, c = 583.202\n", - "epoch 1100: loss = 265038, a = -26.0552, b = 169.446, c = 605.798\n", - "epoch 1200: loss = 212210, a = -25.4469, b = 161.301, c = 625.987\n", - "epoch 1300: loss = 170010, a = -24.9033, b = 154.023, c = 644.025\n", - "epoch 1400: loss = 136297, a = -24.4177, b = 147.521, c = 660.143\n", - "epoch 1500: loss = 109363, a = -23.9838, b = 141.711, c = 674.544\n", - "epoch 1600: loss = 87842.3, a = -23.5961, b = 136.519, c = 687.411\n", - "epoch 1700: loss = 70645.3, a = -23.2497, b = 131.881, c = 698.908\n", - "epoch 1800: loss = 56901.8, a = -22.9402, b = 127.737, c = 709.18\n", - "epoch 1900: loss = 45917, a = -22.6637, b = 124.034, c = 718.359\n", - "epoch 2000: loss = 37135.8, a = -22.4166, b = 120.725, c = 726.56\n", - "epoch 2100: loss = 30115.2, a = -22.1958, b = 117.769, c = 733.887\n", - "epoch 2200: loss = 24501.2, a = -21.9985, b = 115.127, c = 740.434\n", - "epoch 2300: loss = 20011, a = -21.8223, b = 112.767, c = 746.284\n", - "epoch 2400: loss = 16419.1, a = -21.6648, b = 110.659, c = 751.511\n", - "epoch 2500: loss = 13544.9, a = -21.5241, b = 108.774, c = 756.181\n", - "epoch 2600: loss = 11244.5, a = -21.3983, b = 107.091, c = 760.354\n", - "epoch 2700: loss = 9402.78, a = -21.286, b = 105.587, c = 764.082\n", - "epoch 2800: loss = 7927.77, a = -21.1856, b = 104.243, c = 767.414\n", - "epoch 2900: loss = 6746.04, a = -21.0959, b = 103.042, c = 770.39\n" + "epoch 0: loss = 2.59199e+07, a = -4.03101, b = 7.0103, c = 4.32798\n", + "epoch 500: loss = 1.03254e+06, a = -31.3488, b = 241.561, c = 424.128\n", + "epoch 1000: loss = 344061, a = -26.488, b = 176.47, c = 585.509\n", + "epoch 1500: loss = 120771, a = -23.7191, b = 139.394, c = 677.407\n", + "epoch 2000: loss = 48363.3, a = -22.1423, b = 118.28, c = 729.741\n", + "epoch 2500: loss = 24884.4, a = -21.2443, b = 106.257, c = 759.543\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1483,7 +1469,7 @@ ], "source": [ "n_epoch = 3000 # epoch size\n", - "a, b, c = 1.0, 1.0, 1.0 # initial parameters\n", + "a, b, c = 1.0, 1.0, 1.0 # initial parameters\n", "epsilon = 0.0001 # learning rate\n", "\n", "N = np.size(t)\n", @@ -1498,15 +1484,15 @@ " for j in range(N):\n", " L = L + (y[j] - a*t[j]**2 - b*t[j] - c)**2\n", " \n", - " if i % 200 == 0:\n", + " if i % 500 == 0:\n", " print(\"epoch %4d: loss = %10g, a = %10g, b = %10g, c = %10g\" % (i, L, a, b, c))\n", " \n", " \n", "y_est = a*t**2 + b*t + c \n", "\n", "\n", - "plt.plot(t, y, 'rx', label='Real data')\n", - "plt.plot(t, y_est, 'go', label='Estimated data')\n", + "plt.plot(t, y, 'r-', label='Real data')\n", + "plt.plot(t, y_est, 'g-x', label='Estimated data')\n", "plt.legend()\n", "plt.show()\n" ] @@ -1529,12 +1515,12 @@ "text": [ "X: (100, 1)\n", "Y: (100, 1)\n", - "a = 3.376138, b = 0.051810\n" + "a = 2.825254, b = 5.366227\n" ] }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -1621,6 +1607,15 @@ "model = model.fit(t[:, np.newaxis], y)\n", "model.named_steps['linear'].coef_\n" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 参考资料\n", + "* [梯度下降法](https://blog.csdn.net/u010402786/article/details/51188876)\n", + "* [如何理解最小二乘法？](https://blog.csdn.net/ccnt_2012/article/details/81127117)\n" + ] } ], "metadata": { diff --git a/4_logistic_regression/2-Logistic_regression.ipynb b/4_logistic_regression/2-Logistic_regression.ipynb index 71f7fb3..c6a1a2f 100644 --- a/4_logistic_regression/2-Logistic_regression.ipynb +++ b/4_logistic_regression/2-Logistic_regression.ipynb @@ -4,21 +4,49 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# 逻辑回归 Logistic Regression\n", + "# 逻辑回归\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", + "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，使得逻辑回归模型能够输出类别的概率。逻辑回归的本质是：假设数据服从这个分布，然后使用极大似然估计做参数的估计。\n", "\n", + "![theory](images/linear_logistic_regression.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. 什么是回归\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", + "一说回归最先想到的是终结者那句：I'll be back\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", + "regress，re表示back，gress等于go，数值go back to mean value，也就是I'll be back 的意思\n", + "\n", + "在数理统计中，回归是确定多种变量相互依赖的定量关系的方法\n", + "\n", + "> 通俗理解：越来越接近期望值的过程，***回归*** 于事物的本质\n", + "\n", + "最简单的回归是线性回归(Linear Regression)，也就是通过最小二乘等方法得到模型的参数。线性回归假设输出变量是若干输出变量的线性组合，并根据这一关系求解线性组合中的最优系数。\n", + "\n", + "通俗理解：输出一个线性函数，例如$y=f(x; \\theta)$，通过寻找最优的参数$\\theta$使得观测数据与模型数据相吻合。\n", + "\n", + "![linear regression](images/linear_regression.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## 2. 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。\n", + "\n", + "以常见的看医举例，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。$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", + "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下图所示。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" ] }, @@ -29,7 +57,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -59,55 +87,25 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 1.1 逻辑回归表达式\n", + "### 2.1 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", + "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", "$$\n", "\n", - "Logistic函数当z趋近于无穷大时，g(z)趋近于1；当z趋近于无穷小时，g(z)趋近于0。Logistic函数的图形如上图所示。Logistic函数求导时有一个特性，这个特性将在下面的推导中用到，这个特性为：\n", + "Logistic函数:\n", + "* 当$z$趋近于无穷大时，$g(z)$趋近于1；\n", + "* 当$z$趋近于无穷小时，$g(z)$趋近于0。\n", + "\n", + "Logistic函数的图形如上图所示。Logistic函数求导时有一个特性，这个特性将在下面的推导中用到，这个特性为：\n", "$$\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", - "$$\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "plt.figure()\n", - "plt.axis([-10,10,0,1])\n", - "plt.grid(True)\n", - "X=np.arange(-10,10,0.1)\n", - "y=1/(1+np.e**(-X))\n", - "plt.plot(X,y,'b-')\n", - "plt.title(\"Logistic function\")\n", - "plt.show()" + "$$" ] }, { @@ -125,7 +123,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 1.2 逻辑回归的软分类\n", + "### 2.2 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", @@ -146,11 +144,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 1.3 梯度上升\n", + "### 2.3 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", + "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", @@ -161,14 +159,15 @@ "\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", + "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：\n", "$$\n", - "\\theta_j = \\theta_j + \\alpha(y^i - h_\\theta(x^i)) x_j^i\n", + "\\theta = \\theta + \\eta (y^i - h_\\theta(x^i)) x_j^i\n", "$$\n", - "\n" + "\n", + "其中$\\eta$是学习速率。" ] }, { @@ -180,7 +179,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -196,33 +195,16 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 3, "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, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, @@ -243,16 +225,13 @@ "# 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, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -281,12 +260,10 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ - "# FIXME: function sample\n", - "\n", "\n", "def sigmoid(x):\n", " return 1.0 / (1 + np.exp(-x))\n", @@ -297,7 +274,7 @@ " self.data = data\n", " self.label = label\n", "\n", - " # FIXME: n -> d\n", + " # parameters\n", " self.data_num, n = np.shape(data)\n", " self.weights = np.ones(n)\n", " self.b = 1\n", @@ -331,7 +308,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -357,12 +334,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 2.如何用sklearn解决逻辑回归问题?" + "## 3. 如何用sklearn解决逻辑回归问题?" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -431,19 +408,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 3. 多类识别问题" + "## 4. 多类识别问题" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### 3.1 加载显示数据" + "### 4.1 加载显示数据" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -481,7 +458,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 3.2 可视化特征\n", + "### 4.2 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", @@ -490,22 +467,22 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 12, + "execution_count": 9, "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", + "image/png": 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\n", 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" ] @@ -536,22 +513,22 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 13, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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" ] @@ -575,12 +552,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 3.3 示例程序" + "### 4.3 示例程序" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -635,8 +612,6 @@ "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", @@ -657,7 +632,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -691,7 +666,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. 练习 - 如何画出错误分类的数据？\n", + "## 5. 深入思考\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？" diff --git a/4_logistic_regression/PCA.ipynb b/4_logistic_regression/PCA.ipynb deleted file mode 100644 index 9fae4a9..0000000 --- a/4_logistic_regression/PCA.ipynb +++ /dev/null @@ -1,32 +0,0 @@ -{ - "cells": [ - { - "cell_type": 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