目录
xgboost原理
xgboost和gbdt的区别
xgboost安装
实战
xgboost原理 |
xgboost是一个提升模型,即训练多个分类器,然后将这些分类器串联起来,达到最终的预测效果。每一个基分类器都是一个弱分类器,但是很多串联起来后效果很强大。
工作原理:
每次加入一棵新树是为了让目标函数进一步下降。当然,加入了新树之后obj可以反映当前损失值;那么这棵新树如何分裂呢?可以使用泰勒公式构造一个Gain来决定当前树模型的划分。
xgboost支持自定义损失函数
xgboost和gbdt的区别 |
- 传统GBDT以CART作为基分类器,xgboost还支持线性分类器,这个时候xgboost相当于带L1和L2正则化项的逻辑斯蒂回归(分类问题)或者线性回归(回归问题)。
- 传统GBDT在优化时只用到一阶导数信息,xgboost则对代价函数进行了二阶泰勒展开,同时用到了一阶和二阶导数。顺便提一下,xgboost工具支持自定义代价函数,只要函数可一阶和二阶求导。
- xgboost在代价函数里加入了正则项,用于控制模型的复杂度。正则项里包含了树的叶子节点个数、每个叶子节点上输出的score的L2模的平方和。从Bias-variance tradeoff角度来讲,正则项降低了模型的variance,使学习出来的模型更加简单,防止过拟合,这也是xgboost优于传统GBDT的一个特性。
- 列抽样(column subsampling)。xgboost借鉴了随机森林的做法,支持列抽样,不仅能降低过拟合,还能减少计算,这也是xgboost异于传统gbdt的一个特性。
- 对缺失值的处理。对于特征的值有缺失的样本,xgboost可以自动学习出它的分裂方向
- xgboost工具支持并行。boosting不是一种串行的结构吗?怎么并行的?注意xgboost的并行不是tree粒度的并行,xgboost也是一次迭代完才能进行下一次迭代的(第t次迭代的代价函数里包含了前面t-1次迭代的预测值)。xgboost的并行是在特征粒度上的。我们知道,决策树的学习最耗时的一个步骤就是对特征的值进行排序(因为要确定最佳分割点),xgboost在训练之前,预先对数据进行了排序,然后保存为block结构,后面的迭代中重复地使用这个结构,大大减小计算量。这个block结构也使得并行成为了可能,在进行节点的分裂时,需要计算每个特征的增益,最终选增益最大的那个特征去做分裂,那么各个特征的增益计算就可以开多线程进行。
xgboost安装 |
下载地址:
https://www.lfd.uci.edu/~gohlke/pythonlibs/#xgboost
执行:
pip install xxx.whl
实战 |
# -*- coding: utf-8 -*- import xgboost # First XGBoost model for Pima Indians dataset from numpy import loadtxt from xgboost import XGBClassifier from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score # load data dataset = loadtxt(‘pima-indians-diabetes.csv‘, delimiter=",") # split data into X and y X = dataset[:,0:8] Y = dataset[:,8] # split data into train and test sets seed = 7 test_size = 0.33 X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=test_size, random_state=seed) # fit model no training data model = XGBClassifier() model.fit(X_train, y_train) # make predictions for test data y_pred = model.predict(X_test) predictions = [round(value) for value in y_pred] # evaluate predictions accuracy = accuracy_score(y_test, predictions) print("Accuracy: %.2f%%" % (accuracy * 100.0))
6 148 72 35 0 33.6 0.627 50 1 1 85 66 29 0 26.6 0.351 31 0 8 183 64 0 0 23.3 0.672 32 1 1 89 66 23 94 28.1 0.167 21 0 0 137 40 35 168 43.1 2.288 33 1 5 116 74 0 0 25.6 0.201 30 0 3 78 50 32 88 31 0.248 26 1 10 115 0 0 0 35.3 0.134 29 0 2 197 70 45 543 30.5 0.158 53 1 8 125 96 0 0 0 0.232 54 1 4 110 92 0 0 37.6 0.191 30 0 10 168 74 0 0 38 0.537 34 1 10 139 80 0 0 27.1 1.441 57 0 1 189 60 23 846 30.1 0.398 59 1 5 166 72 19 175 25.8 0.587 51 1 7 100 0 0 0 30 0.484 32 1 0 118 84 47 230 45.8 0.551 31 1 7 107 74 0 0 29.6 0.254 31 1 1 103 30 38 83 43.3 0.183 33 0 1 115 70 30 96 34.6 0.529 32 1 3 126 88 41 235 39.3 0.704 27 0 8 99 84 0 0 35.4 0.388 50 0 7 196 90 0 0 39.8 0.451 41 1 9 119 80 35 0 29 0.263 29 1 11 143 94 33 146 36.6 0.254 51 1 10 125 70 26 115 31.1 0.205 41 1 7 147 76 0 0 39.4 0.257 43 1 1 97 66 15 140 23.2 0.487 22 0 13 145 82 19 110 22.2 0.245 57 0 5 117 92 0 0 34.1 0.337 38 0 5 109 75 26 0 36 0.546 60 0 3 158 76 36 245 31.6 0.851 28 1 3 88 58 11 54 24.8 0.267 22 0 6 92 92 0 0 19.9 0.188 28 0 10 122 78 31 0 27.6 0.512 45 0 4 103 60 33 192 24 0.966 33 0 11 138 76 0 0 33.2 0.42 35 0 9 102 76 37 0 32.9 0.665 46 1 2 90 68 42 0 38.2 0.503 27 1 4 111 72 47 207 37.1 1.39 56 1 3 180 64 25 70 34 0.271 26 0 7 133 84 0 0 40.2 0.696 37 0 7 106 92 18 0 22.7 0.235 48 0 9 171 110 24 240 45.4 0.721 54 1 7 159 64 0 0 27.4 0.294 40 0 0 180 66 39 0 42 1.893 25 1 1 146 56 0 0 29.7 0.564 29 0 2 71 70 27 0 28 0.586 22 0 7 103 66 32 0 39.1 0.344 31 1 7 105 0 0 0 0 0.305 24 0 1 103 80 11 82 19.4 0.491 22 0 1 101 50 15 36 24.2 0.526 26 0 5 88 66 21 23 24.4 0.342 30 0 8 176 90 34 300 33.7 0.467 58 1 7 150 66 42 342 34.7 0.718 42 0 1 73 50 10 0 23 0.248 21 0 7 187 68 39 304 37.7 0.254 41 1 0 100 88 60 110 46.8 0.962 31 0 0 146 82 0 0 40.5 1.781 44 0 0 105 64 41 142 41.5 0.173 22 0 2 84 0 0 0 0 0.304 21 0 8 133 72 0 0 32.9 0.27 39 1 5 44 62 0 0 25 0.587 36 0 2 141 58 34 128 25.4 0.699 24 0 7 114 66 0 0 32.8 0.258 42 1 5 99 74 27 0 29 0.203 32 0 0 109 88 30 0 32.5 0.855 38 1 2 109 92 0 0 42.7 0.845 54 0 1 95 66 13 38 19.6 0.334 25 0 4 146 85 27 100 28.9 0.189 27 0 2 100 66 20 90 32.9 0.867 28 1 5 139 64 35 140 28.6 0.411 26 0 13 126 90 0 0 43.4 0.583 42 1 4 129 86 20 270 35.1 0.231 23 0 1 79 75 30 0 32 0.396 22 0 1 0 48 20 0 24.7 0.14 22 0 7 62 78 0 0 32.6 0.391 41 0 5 95 72 33 0 37.7 0.37 27 0 0 131 0 0 0 43.2 0.27 26 1 2 112 66 22 0 25 0.307 24 0 3 113 44 13 0 22.4 0.14 22 0 2 74 0 0 0 0 0.102 22 0 7 83 78 26 71 29.3 0.767 36 0 0 101 65 28 0 24.6 0.237 22 0 5 137 108 0 0 48.8 0.227 37 1 2 110 74 29 125 32.4 0.698 27 0 13 106 72 54 0 36.6 0.178 45 0 2 100 68 25 71 38.5 0.324 26 0 15 136 70 32 110 37.1 0.153 43 1 1 107 68 19 0 26.5 0.165 24 0 1 80 55 0 0 19.1 0.258 21 0 4 123 80 15 176 32 0.443 34 0 7 81 78 40 48 46.7 0.261 42 0 4 134 72 0 0 23.8 0.277 60 1 2 142 82 18 64 24.7 0.761 21 0 6 144 72 27 228 33.9 0.255 40 0 2 92 62 28 0 31.6 0.13 24 0 1 71 48 18 76 20.4 0.323 22 0 6 93 50 30 64 28.7 0.356 23 0 1 122 90 51 220 49.7 0.325 31 1 1 163 72 0 0 39 1.222 33 1 1 151 60 0 0 26.1 0.179 22 0 0 125 96 0 0 22.5 0.262 21 0 1 81 72 18 40 26.6 0.283 24 0 2 85 65 0 0 39.6 0.93 27 0 1 126 56 29 152 28.7 0.801 21 0 1 96 122 0 0 22.4 0.207 27 0 4 144 58 28 140 29.5 0.287 37 0 3 83 58 31 18 34.3 0.336 25 0 0 95 85 25 36 37.4 0.247 24 1 3 171 72 33 135 33.3 0.199 24 1 8 155 62 26 495 34 0.543 46 1 1 89 76 34 37 31.2 0.192 23 0 4 76 62 0 0 34 0.391 25 0 7 160 54 32 175 30.5 0.588 39 1 4 146 92 0 0 31.2 0.539 61 1 5 124 74 0 0 34 0.22 38 1 5 78 48 0 0 33.7 0.654 25 0 4 97 60 23 0 28.2 0.443 22 0 4 99 76 15 51 23.2 0.223 21 0 0 162 76 56 100 53.2 0.759 25 1 6 111 64 39 0 34.2 0.26 24 0 2 107 74 30 100 33.6 0.404 23 0 5 132 80 0 0 26.8 0.186 69 0 0 113 76 0 0 33.3 0.278 23 1 1 88 30 42 99 55 0.496 26 1 3 120 70 30 135 42.9 0.452 30 0 1 118 58 36 94 33.3 0.261 23 0 1 117 88 24 145 34.5 0.403 40 1 0 105 84 0 0 27.9 0.741 62 1 4 173 70 14 168 29.7 0.361 33 1 9 122 56 0 0 33.3 1.114 33 1 3 170 64 37 225 34.5 0.356 30 1 8 84 74 31 0 38.3 0.457 39 0 2 96 68 13 49 21.1 0.647 26 0 2 125 60 20 140 33.8 0.088 31 0 0 100 70 26 50 30.8 0.597 21 0 0 93 60 25 92 28.7 0.532 22 0 0 129 80 0 0 31.2 0.703 29 0 5 105 72 29 325 36.9 0.159 28 0 3 128 78 0 0 21.1 0.268 55 0 5 106 82 30 0 39.5 0.286 38 0 2 108 52 26 63 32.5 0.318 22 0 10 108 66 0 0 32.4 0.272 42 1 4 154 62 31 284 32.8 0.237 23 0 0 102 75 23 0 0 0.572 21 0 9 57 80 37 0 32.8 0.096 41 0 2 106 64 35 119 30.5 1.4 34 0 5 147 78 0 0 33.7 0.218 65 0 2 90 70 17 0 27.3 0.085 22 0 1 136 74 50 204 37.4 0.399 24 0 4 114 65 0 0 21.9 0.432 37 0 9 156 86 28 155 34.3 1.189 42 1 1 153 82 42 485 40.6 0.687 23 0 8 188 78 0 0 47.9 0.137 43 1 7 152 88 44 0 50 0.337 36 1 2 99 52 15 94 24.6 0.637 21 0 1 109 56 21 135 25.2 0.833 23 0 2 88 74 19 53 29 0.229 22 0 17 163 72 41 114 40.9 0.817 47 1 4 151 90 38 0 29.7 0.294 36 0 7 102 74 40 105 37.2 0.204 45 0 0 114 80 34 285 44.2 0.167 27 0 2 100 64 23 0 29.7 0.368 21 0 0 131 88 0 0 31.6 0.743 32 1 6 104 74 18 156 29.9 0.722 41 1 3 148 66 25 0 32.5 0.256 22 0 4 120 68 0 0 29.6 0.709 34 0 4 110 66 0 0 31.9 0.471 29 0 3 111 90 12 78 28.4 0.495 29 0 6 102 82 0 0 30.8 0.18 36 1 6 134 70 23 130 35.4 0.542 29 1 2 87 0 23 0 28.9 0.773 25 0 1 79 60 42 48 43.5 0.678 23 0 2 75 64 24 55 29.7 0.37 33 0 8 179 72 42 130 32.7 0.719 36 1 6 85 78 0 0 31.2 0.382 42 0 0 129 110 46 130 67.1 0.319 26 1 5 143 78 0 0 45 0.19 47 0 5 130 82 0 0 39.1 0.956 37 1 6 87 80 0 0 23.2 0.084 32 0 0 119 64 18 92 34.9 0.725 23 0 1 0 74 20 23 27.7 0.299 21 0 5 73 60 0 0 26.8 0.268 27 0 4 141 74 0 0 27.6 0.244 40 0 7 194 68 28 0 35.9 0.745 41 1 8 181 68 36 495 30.1 0.615 60 1 1 128 98 41 58 32 1.321 33 1 8 109 76 39 114 27.9 0.64 31 1 5 139 80 35 160 31.6 0.361 25 1 3 111 62 0 0 22.6 0.142 21 0 9 123 70 44 94 33.1 0.374 40 0 7 159 66 0 0 30.4 0.383 36 1 11 135 0 0 0 52.3 0.578 40 1 8 85 55 20 0 24.4 0.136 42 0 5 158 84 41 210 39.4 0.395 29 1 1 105 58 0 0 24.3 0.187 21 0 3 107 62 13 48 22.9 0.678 23 1 4 109 64 44 99 34.8 0.905 26 1 4 148 60 27 318 30.9 0.15 29 1 0 113 80 16 0 31 0.874 21 0 1 138 82 0 0 40.1 0.236 28 0 0 108 68 20 0 27.3 0.787 32 0 2 99 70 16 44 20.4 0.235 27 0 6 103 72 32 190 37.7 0.324 55 0 5 111 72 28 0 23.9 0.407 27 0 8 196 76 29 280 37.5 0.605 57 1 5 162 104 0 0 37.7 0.151 52 1 1 96 64 27 87 33.2 0.289 21 0 7 184 84 33 0 35.5 0.355 41 1 2 81 60 22 0 27.7 0.29 25 0 0 147 85 54 0 42.8 0.375 24 0 7 179 95 31 0 34.2 0.164 60 0 0 140 65 26 130 42.6 0.431 24 1 9 112 82 32 175 34.2 0.26 36 1 12 151 70 40 271 41.8 0.742 38 1 5 109 62 41 129 35.8 0.514 25 1 6 125 68 30 120 30 0.464 32 0 5 85 74 22 0 29 1.224 32 1 5 112 66 0 0 37.8 0.261 41 1 0 177 60 29 478 34.6 1.072 21 1 2 158 90 0 0 31.6 0.805 66 1 7 119 0 0 0 25.2 0.209 37 0 7 142 60 33 190 28.8 0.687 61 0 1 100 66 15 56 23.6 0.666 26 0 1 87 78 27 32 34.6 0.101 22 0 0 101 76 0 0 35.7 0.198 26 0 3 162 52 38 0 37.2 0.652 24 1 4 197 70 39 744 36.7 2.329 31 0 0 117 80 31 53 45.2 0.089 24 0 4 142 86 0 0 44 0.645 22 1 6 134 80 37 370 46.2 0.238 46 1 1 79 80 25 37 25.4 0.583 22 0 4 122 68 0 0 35 0.394 29 0 3 74 68 28 45 29.7 0.293 23 0 4 171 72 0 0 43.6 0.479 26 1 7 181 84 21 192 35.9 0.586 51 1 0 179 90 27 0 44.1 0.686 23 1 9 164 84 21 0 30.8 0.831 32 1 0 104 76 0 0 18.4 0.582 27 0 1 91 64 24 0 29.2 0.192 21 0 4 91 70 32 88 33.1 0.446 22 0 3 139 54 0 0 25.6 0.402 22 1 6 119 50 22 176 27.1 1.318 33 1 2 146 76 35 194 38.2 0.329 29 0 9 184 85 15 0 30 1.213 49 1 10 122 68 0 0 31.2 0.258 41 0 0 165 90 33 680 52.3 0.427 23 0 9 124 70 33 402 35.4 0.282 34 0 1 111 86 19 0 30.1 0.143 23 0 9 106 52 0 0 31.2 0.38 42 0 2 129 84 0 0 28 0.284 27 0 2 90 80 14 55 24.4 0.249 24 0 0 86 68 32 0 35.8 0.238 25 0 12 92 62 7 258 27.6 0.926 44 1 1 113 64 35 0 33.6 0.543 21 1 3 111 56 39 0 30.1 0.557 30 0 2 114 68 22 0 28.7 0.092 25 0 1 193 50 16 375 25.9 0.655 24 0 11 155 76 28 150 33.3 1.353 51 1 3 191 68 15 130 30.9 0.299 34 0 3 141 0 0 0 30 0.761 27 1 4 95 70 32 0 32.1 0.612 24 0 3 142 80 15 0 32.4 0.2 63 0 4 123 62 0 0 32 0.226 35 1 5 96 74 18 67 33.6 0.997 43 0 0 138 0 0 0 36.3 0.933 25 1 2 128 64 42 0 40 1.101 24 0 0 102 52 0 0 25.1 0.078 21 0 2 146 0 0 0 27.5 0.24 28 1 10 101 86 37 0 45.6 1.136 38 1 2 108 62 32 56 25.2 0.128 21 0 3 122 78 0 0 23 0.254 40 0 1 71 78 50 45 33.2 0.422 21 0 13 106 70 0 0 34.2 0.251 52 0 2 100 70 52 57 40.5 0.677 25 0 7 106 60 24 0 26.5 0.296 29 1 0 104 64 23 116 27.8 0.454 23 0 5 114 74 0 0 24.9 0.744 57 0 2 108 62 10 278 25.3 0.881 22 0 0 146 70 0 0 37.9 0.334 28 1 10 129 76 28 122 35.9 0.28 39 0 7 133 88 15 155 32.4 0.262 37 0 7 161 86 0 0 30.4 0.165 47 1 2 108 80 0 0 27 0.259 52 1 7 136 74 26 135 26 0.647 51 0 5 155 84 44 545 38.7 0.619 34 0 1 119 86 39 220 45.6 0.808 29 1 4 96 56 17 49 20.8 0.34 26 0 5 108 72 43 75 36.1 0.263 33 0 0 78 88 29 40 36.9 0.434 21 0 0 107 62 30 74 36.6 0.757 25 1 2 128 78 37 182 43.3 1.224 31 1 1 128 48 45 194 40.5 0.613 24 1 0 161 50 0 0 21.9 0.254 65 0 6 151 62 31 120 35.5 0.692 28 0 2 146 70 38 360 28 0.337 29 1 0 126 84 29 215 30.7 0.52 24 0 14 100 78 25 184 36.6 0.412 46 1 8 112 72 0 0 23.6 0.84 58 0 0 167 0 0 0 32.3 0.839 30 1 2 144 58 33 135 31.6 0.422 25 1 5 77 82 41 42 35.8 0.156 35 0 5 115 98 0 0 52.9 0.209 28 1 3 150 76 0 0 21 0.207 37 0 2 120 76 37 105 39.7 0.215 29 0 10 161 68 23 132 25.5 0.326 47 1 0 137 68 14 148 24.8 0.143 21 0 0 128 68 19 180 30.5 1.391 25 1 2 124 68 28 205 32.9 0.875 30 1 6 80 66 30 0 26.2 0.313 41 0 0 106 70 37 148 39.4 0.605 22 0 2 155 74 17 96 26.6 0.433 27 1 3 113 50 10 85 29.5 0.626 25 0 7 109 80 31 0 35.9 1.127 43 1 2 112 68 22 94 34.1 0.315 26 0 3 99 80 11 64 19.3 0.284 30 0 3 182 74 0 0 30.5 0.345 29 1 3 115 66 39 140 38.1 0.15 28 0 6 194 78 0 0 23.5 0.129 59 1 4 129 60 12 231 27.5 0.527 31 0 3 112 74 30 0 31.6 0.197 25 1 0 124 70 20 0 27.4 0.254 36 1 13 152 90 33 29 26.8 0.731 43 1 2 112 75 32 0 35.7 0.148 21 0 1 157 72 21 168 25.6 0.123 24 0 1 122 64 32 156 35.1 0.692 30 1 10 179 70 0 0 35.1 0.2 37 0 2 102 86 36 120 45.5 0.127 23 1 6 105 70 32 68 30.8 0.122 37 0 8 118 72 19 0 23.1 1.476 46 0 2 87 58 16 52 32.7 0.166 25 0 1 180 0 0 0 43.3 0.282 41 1 12 106 80 0 0 23.6 0.137 44 0 1 95 60 18 58 23.9 0.26 22 0 0 165 76 43 255 47.9 0.259 26 0 0 117 0 0 0 33.8 0.932 44 0 5 115 76 0 0 31.2 0.343 44 1 9 152 78 34 171 34.2 0.893 33 1 7 178 84 0 0 39.9 0.331 41 1 1 130 70 13 105 25.9 0.472 22 0 1 95 74 21 73 25.9 0.673 36 0 1 0 68 35 0 32 0.389 22 0 5 122 86 0 0 34.7 0.29 33 0 8 95 72 0 0 36.8 0.485 57 0 8 126 88 36 108 38.5 0.349 49 0 1 139 46 19 83 28.7 0.654 22 0 3 116 0 0 0 23.5 0.187 23 0 3 99 62 19 74 21.8 0.279 26 0 5 0 80 32 0 41 0.346 37 1 4 92 80 0 0 42.2 0.237 29 0 4 137 84 0 0 31.2 0.252 30 0 3 61 82 28 0 34.4 0.243 46 0 1 90 62 12 43 27.2 0.58 24 0 3 90 78 0 0 42.7 0.559 21 0 9 165 88 0 0 30.4 0.302 49 1 1 125 50 40 167 33.3 0.962 28 1 13 129 0 30 0 39.9 0.569 44 1 12 88 74 40 54 35.3 0.378 48 0 1 196 76 36 249 36.5 0.875 29 1 5 189 64 33 325 31.2 0.583 29 1 5 158 70 0 0 29.8 0.207 63 0 5 103 108 37 0 39.2 0.305 65 0 4 146 78 0 0 38.5 0.52 67 1 4 147 74 25 293 34.9 0.385 30 0 5 99 54 28 83 34 0.499 30 0 6 124 72 0 0 27.6 0.368 29 1 0 101 64 17 0 21 0.252 21 0 3 81 86 16 66 27.5 0.306 22 0 1 133 102 28 140 32.8 0.234 45 1 3 173 82 48 465 38.4 2.137 25 1 0 118 64 23 89 0 1.731 21 0 0 84 64 22 66 35.8 0.545 21 0 2 105 58 40 94 34.9 0.225 25 0 2 122 52 43 158 36.2 0.816 28 0 12 140 82 43 325 39.2 0.528 58 1 0 98 82 15 84 25.2 0.299 22 0 1 87 60 37 75 37.2 0.509 22 0 4 156 75 0 0 48.3 0.238 32 1 0 93 100 39 72 43.4 1.021 35 0 1 107 72 30 82 30.8 0.821 24 0 0 105 68 22 0 20 0.236 22 0 1 109 60 8 182 25.4 0.947 21 0 1 90 62 18 59 25.1 1.268 25 0 1 125 70 24 110 24.3 0.221 25 0 1 119 54 13 50 22.3 0.205 24 0 5 116 74 29 0 32.3 0.66 35 1 8 105 100 36 0 43.3 0.239 45 1 5 144 82 26 285 32 0.452 58 1 3 100 68 23 81 31.6 0.949 28 0 1 100 66 29 196 32 0.444 42 0 5 166 76 0 0 45.7 0.34 27 1 1 131 64 14 415 23.7 0.389 21 0 4 116 72 12 87 22.1 0.463 37 0 4 158 78 0 0 32.9 0.803 31 1 2 127 58 24 275 27.7 1.6 25 0 3 96 56 34 115 24.7 0.944 39 0 0 131 66 40 0 34.3 0.196 22 1 3 82 70 0 0 21.1 0.389 25 0 3 193 70 31 0 34.9 0.241 25 1 4 95 64 0 0 32 0.161 31 1 6 137 61 0 0 24.2 0.151 55 0 5 136 84 41 88 35 0.286 35 1 9 72 78 25 0 31.6 0.28 38 0 5 168 64 0 0 32.9 0.135 41 1 2 123 48 32 165 42.1 0.52 26 0 4 115 72 0 0 28.9 0.376 46 1 0 101 62 0 0 21.9 0.336 25 0 8 197 74 0 0 25.9 1.191 39 1 1 172 68 49 579 42.4 0.702 28 1 6 102 90 39 0 35.7 0.674 28 0 1 112 72 30 176 34.4 0.528 25 0 1 143 84 23 310 42.4 1.076 22 0 1 143 74 22 61 26.2 0.256 21 0 0 138 60 35 167 34.6 0.534 21 1 3 173 84 33 474 35.7 0.258 22 1 1 97 68 21 0 27.2 1.095 22 0 4 144 82 32 0 38.5 0.554 37 1 1 83 68 0 0 18.2 0.624 27 0 3 129 64 29 115 26.4 0.219 28 1 1 119 88 41 170 45.3 0.507 26 0 2 94 68 18 76 26 0.561 21 0 0 102 64 46 78 40.6 0.496 21 0 2 115 64 22 0 30.8 0.421 21 0 8 151 78 32 210 42.9 0.516 36 1 4 184 78 39 277 37 0.264 31 1 0 94 0 0 0 0 0.256 25 0 1 181 64 30 180 34.1 0.328 38 1 0 135 94 46 145 40.6 0.284 26 0 1 95 82 25 180 35 0.233 43 1 2 99 0 0 0 22.2 0.108 23 0 3 89 74 16 85 30.4 0.551 38 0 1 80 74 11 60 30 0.527 22 0 2 139 75 0 0 25.6 0.167 29 0 1 90 68 8 0 24.5 1.138 36 0 0 141 0 0 0 42.4 0.205 29 1 12 140 85 33 0 37.4 0.244 41 0 5 147 75 0 0 29.9 0.434 28 0 1 97 70 15 0 18.2 0.147 21 0 6 107 88 0 0 36.8 0.727 31 0 0 189 104 25 0 34.3 0.435 41 1 2 83 66 23 50 32.2 0.497 22 0 4 117 64 27 120 33.2 0.23 24 0 8 108 70 0 0 30.5 0.955 33 1 4 117 62 12 0 29.7 0.38 30 1 0 180 78 63 14 59.4 2.42 25 1 1 100 72 12 70 25.3 0.658 28 0 0 95 80 45 92 36.5 0.33 26 0 0 104 64 37 64 33.6 0.51 22 1 0 120 74 18 63 30.5 0.285 26 0 1 82 64 13 95 21.2 0.415 23 0 2 134 70 0 0 28.9 0.542 23 1 0 91 68 32 210 39.9 0.381 25 0 2 119 0 0 0 19.6 0.832 72 0 2 100 54 28 105 37.8 0.498 24 0 14 175 62 30 0 33.6 0.212 38 1 1 135 54 0 0 26.7 0.687 62 0 5 86 68 28 71 30.2 0.364 24 0 10 148 84 48 237 37.6 1.001 51 1 9 134 74 33 60 25.9 0.46 81 0 9 120 72 22 56 20.8 0.733 48 0 1 71 62 0 0 21.8 0.416 26 0 8 74 70 40 49 35.3 0.705 39 0 5 88 78 30 0 27.6 0.258 37 0 10 115 98 0 0 24 1.022 34 0 0 124 56 13 105 21.8 0.452 21 0 0 74 52 10 36 27.8 0.269 22 0 0 97 64 36 100 36.8 0.6 25 0 8 120 0 0 0 30 0.183 38 1 6 154 78 41 140 46.1 0.571 27 0 1 144 82 40 0 41.3 0.607 28 0 0 137 70 38 0 33.2 0.17 22 0 0 119 66 27 0 38.8 0.259 22 0 7 136 90 0 0 29.9 0.21 50 0 4 114 64 0 0 28.9 0.126 24 0 0 137 84 27 0 27.3 0.231 59 0 2 105 80 45 191 33.7 0.711 29 1 7 114 76 17 110 23.8 0.466 31 0 8 126 74 38 75 25.9 0.162 39 0 4 132 86 31 0 28 0.419 63 0 3 158 70 30 328 35.5 0.344 35 1 0 123 88 37 0 35.2 0.197 29 0 4 85 58 22 49 27.8 0.306 28 0 0 84 82 31 125 38.2 0.233 23 0 0 145 0 0 0 44.2 0.63 31 1 0 135 68 42 250 42.3 0.365 24 1 1 139 62 41 480 40.7 0.536 21 0 0 173 78 32 265 46.5 1.159 58 0 4 99 72 17 0 25.6 0.294 28 0 8 194 80 0 0 26.1 0.551 67 0 2 83 65 28 66 36.8 0.629 24 0 2 89 90 30 0 33.5 0.292 42 0 4 99 68 38 0 32.8 0.145 33 0 4 125 70 18 122 28.9 1.144 45 1 3 80 0 0 0 0 0.174 22 0 6 166 74 0 0 26.6 0.304 66 0 5 110 68 0 0 26 0.292 30 0 2 81 72 15 76 30.1 0.547 25 0 7 195 70 33 145 25.1 0.163 55 1 6 154 74 32 193 29.3 0.839 39 0 2 117 90 19 71 25.2 0.313 21 0 3 84 72 32 0 37.2 0.267 28 0 6 0 68 41 0 39 0.727 41 1 7 94 64 25 79 33.3 0.738 41 0 3 96 78 39 0 37.3 0.238 40 0 10 75 82 0 0 33.3 0.263 38 0 0 180 90 26 90 36.5 0.314 35 1 1 130 60 23 170 28.6 0.692 21 0 2 84 50 23 76 30.4 0.968 21 0 8 120 78 0 0 25 0.409 64 0 12 84 72 31 0 29.7 0.297 46 1 0 139 62 17 210 22.1 0.207 21 0 9 91 68 0 0 24.2 0.2 58 0 2 91 62 0 0 27.3 0.525 22 0 3 99 54 19 86 25.6 0.154 24 0 3 163 70 18 105 31.6 0.268 28 1 9 145 88 34 165 30.3 0.771 53 1 7 125 86 0 0 37.6 0.304 51 0 13 76 60 0 0 32.8 0.18 41 0 6 129 90 7 326 19.6 0.582 60 0 2 68 70 32 66 25 0.187 25 0 3 124 80 33 130 33.2 0.305 26 0 6 114 0 0 0 0 0.189 26 0 9 130 70 0 0 34.2 0.652 45 1 3 125 58 0 0 31.6 0.151 24 0 3 87 60 18 0 21.8 0.444 21 0 1 97 64 19 82 18.2 0.299 21 0 3 116 74 15 105 26.3 0.107 24 0 0 117 66 31 188 30.8 0.493 22 0 0 111 65 0 0 24.6 0.66 31 0 2 122 60 18 106 29.8 0.717 22 0 0 107 76 0 0 45.3 0.686 24 0 1 86 66 52 65 41.3 0.917 29 0 6 91 0 0 0 29.8 0.501 31 0 1 77 56 30 56 33.3 1.251 24 0 4 132 0 0 0 32.9 0.302 23 1 0 105 90 0 0 29.6 0.197 46 0 0 57 60 0 0 21.7 0.735 67 0 0 127 80 37 210 36.3 0.804 23 0 3 129 92 49 155 36.4 0.968 32 1 8 100 74 40 215 39.4 0.661 43 1 3 128 72 25 190 32.4 0.549 27 1 10 90 85 32 0 34.9 0.825 56 1 4 84 90 23 56 39.5 0.159 25 0 1 88 78 29 76 32 0.365 29 0 8 186 90 35 225 34.5 0.423 37 1 5 187 76 27 207 43.6 1.034 53 1 4 131 68 21 166 33.1 0.16 28 0 1 164 82 43 67 32.8 0.341 50 0 4 189 110 31 0 28.5 0.68 37 0 1 116 70 28 0 27.4 0.204 21 0 3 84 68 30 106 31.9 0.591 25 0 6 114 88 0 0 27.8 0.247 66 0 1 88 62 24 44 29.9 0.422 23 0 1 84 64 23 115 36.9 0.471 28 0 7 124 70 33 215 25.5 0.161 37 0 1 97 70 40 0 38.1 0.218 30 0 8 110 76 0 0 27.8 0.237 58 0 11 103 68 40 0 46.2 0.126 42 0 11 85 74 0 0 30.1 0.3 35 0 6 125 76 0 0 33.8 0.121 54 1 0 198 66 32 274 41.3 0.502 28 1 1 87 68 34 77 37.6 0.401 24 0 6 99 60 19 54 26.9 0.497 32 0 0 91 80 0 0 32.4 0.601 27 0 2 95 54 14 88 26.1 0.748 22 0 1 99 72 30 18 38.6 0.412 21 0 6 92 62 32 126 32 0.085 46 0 4 154 72 29 126 31.3 0.338 37 0 0 121 66 30 165 34.3 0.203 33 1 3 78 70 0 0 32.5 0.27 39 0 2 130 96 0 0 22.6 0.268 21 0 3 111 58 31 44 29.5 0.43 22 0 2 98 60 17 120 34.7 0.198 22 0 1 143 86 30 330 30.1 0.892 23 0 1 119 44 47 63 35.5 0.28 25 0 6 108 44 20 130 24 0.813 35 0 2 118 80 0 0 42.9 0.693 21 1 10 133 68 0 0 27 0.245 36 0 2 197 70 99 0 34.7 0.575 62 1 0 151 90 46 0 42.1 0.371 21 1 6 109 60 27 0 25 0.206 27 0 12 121 78 17 0 26.5 0.259 62 0 8 100 76 0 0 38.7 0.19 42 0 8 124 76 24 600 28.7 0.687 52 1 1 93 56 11 0 22.5 0.417 22 0 8 143 66 0 0 34.9 0.129 41 1 6 103 66 0 0 24.3 0.249 29 0 3 176 86 27 156 33.3 1.154 52 1 0 73 0 0 0 21.1 0.342 25 0 11 111 84 40 0 46.8 0.925 45 1 2 112 78 50 140 39.4 0.175 24 0 3 132 80 0 0 34.4 0.402 44 1 2 82 52 22 115 28.5 1.699 25 0 6 123 72 45 230 33.6 0.733 34 0 0 188 82 14 185 32 0.682 22 1 0 67 76 0 0 45.3 0.194 46 0 1 89 24 19 25 27.8 0.559 21 0 1 173 74 0 0 36.8 0.088 38 1 1 109 38 18 120 23.1 0.407 26 0 1 108 88 19 0 27.1 0.4 24 0 6 96 0 0 0 23.7 0.19 28 0 1 124 74 36 0 27.8 0.1 30 0 7 150 78 29 126 35.2 0.692 54 1 4 183 0 0 0 28.4 0.212 36 1 1 124 60 32 0 35.8 0.514 21 0 1 181 78 42 293 40 1.258 22 1 1 92 62 25 41 19.5 0.482 25 0 0 152 82 39 272 41.5 0.27 27 0 1 111 62 13 182 24 0.138 23 0 3 106 54 21 158 30.9 0.292 24 0 3 174 58 22 194 32.9 0.593 36 1 7 168 88 42 321 38.2 0.787 40 1 6 105 80 28 0 32.5 0.878 26 0 11 138 74 26 144 36.1 0.557 50 1 3 106 72 0 0 25.8 0.207 27 0 6 117 96 0 0 28.7 0.157 30 0 2 68 62 13 15 20.1 0.257 23 0 9 112 82 24 0 28.2 1.282 50 1 0 119 0 0 0 32.4 0.141 24 1 2 112 86 42 160 38.4 0.246 28 0 2 92 76 20 0 24.2 1.698 28 0 6 183 94 0 0 40.8 1.461 45 0 0 94 70 27 115 43.5 0.347 21 0 2 108 64 0 0 30.8 0.158 21 0 4 90 88 47 54 37.7 0.362 29 0 0 125 68 0 0 24.7 0.206 21 0 0 132 78 0 0 32.4 0.393 21 0 5 128 80 0 0 34.6 0.144 45 0 4 94 65 22 0 24.7 0.148 21 0 7 114 64 0 0 27.4 0.732 34 1 0 102 78 40 90 34.5 0.238 24 0 2 111 60 0 0 26.2 0.343 23 0 1 128 82 17 183 27.5 0.115 22 0 10 92 62 0 0 25.9 0.167 31 0 13 104 72 0 0 31.2 0.465 38 1 5 104 74 0 0 28.8 0.153 48 0 2 94 76 18 66 31.6 0.649 23 0 7 97 76 32 91 40.9 0.871 32 1 1 100 74 12 46 19.5 0.149 28 0 0 102 86 17 105 29.3 0.695 27 0 4 128 70 0 0 34.3 0.303 24 0 6 147 80 0 0 29.5 0.178 50 1 4 90 0 0 0 28 0.61 31 0 3 103 72 30 152 27.6 0.73 27 0 2 157 74 35 440 39.4 0.134 30 0 1 167 74 17 144 23.4 0.447 33 1 0 179 50 36 159 37.8 0.455 22 1 11 136 84 35 130 28.3 0.26 42 1 0 107 60 25 0 26.4 0.133 23 0 1 91 54 25 100 25.2 0.234 23 0 1 117 60 23 106 33.8 0.466 27 0 5 123 74 40 77 34.1 0.269 28 0 2 120 54 0 0 26.8 0.455 27 0 1 106 70 28 135 34.2 0.142 22 0 2 155 52 27 540 38.7 0.24 25 1 2 101 58 35 90 21.8 0.155 22 0 1 120 80 48 200 38.9 1.162 41 0 11 127 106 0 0 39 0.19 51 0 3 80 82 31 70 34.2 1.292 27 1 10 162 84 0 0 27.7 0.182 54 0 1 199 76 43 0 42.9 1.394 22 1 8 167 106 46 231 37.6 0.165 43 1 9 145 80 46 130 37.9 0.637 40 1 6 115 60 39 0 33.7 0.245 40 1 1 112 80 45 132 34.8 0.217 24 0 4 145 82 18 0 32.5 0.235 70 1 10 111 70 27 0 27.5 0.141 40 1 6 98 58 33 190 34 0.43 43 0 9 154 78 30 100 30.9 0.164 45 0 6 165 68 26 168 33.6 0.631 49 0 1 99 58 10 0 25.4 0.551 21 0 10 68 106 23 49 35.5 0.285 47 0 3 123 100 35 240 57.3 0.88 22 0 8 91 82 0 0 35.6 0.587 68 0 6 195 70 0 0 30.9 0.328 31 1 9 156 86 0 0 24.8 0.23 53 1 0 93 60 0 0 35.3 0.263 25 0 3 121 52 0 0 36 0.127 25 1 2 101 58 17 265 24.2 0.614 23 0 2 56 56 28 45 24.2 0.332 22 0 0 162 76 36 0 49.6 0.364 26 1 0 95 64 39 105 44.6 0.366 22 0 4 125 80 0 0 32.3 0.536 27 1 5 136 82 0 0 0 0.64 69 0 2 129 74 26 205 33.2 0.591 25 0 3 130 64 0 0 23.1 0.314 22 0 1 107 50 19 0 28.3 0.181 29 0 1 140 74 26 180 24.1 0.828 23 0 1 144 82 46 180 46.1 0.335 46 1 8 107 80 0 0 24.6 0.856 34 0 13 158 114 0 0 42.3 0.257 44 1 2 121 70 32 95 39.1 0.886 23 0 7 129 68 49 125 38.5 0.439 43 1 2 90 60 0 0 23.5 0.191 25 0 7 142 90 24 480 30.4 0.128 43 1 3 169 74 19 125 29.9 0.268 31 1 0 99 0 0 0 25 0.253 22 0 4 127 88 11 155 34.5 0.598 28 0 4 118 70 0 0 44.5 0.904 26 0 2 122 76 27 200 35.9 0.483 26 0 6 125 78 31 0 27.6 0.565 49 1 1 168 88 29 0 35 0.905 52 1 2 129 0 0 0 38.5 0.304 41 0 4 110 76 20 100 28.4 0.118 27 0 6 80 80 36 0 39.8 0.177 28 0 10 115 0 0 0 0 0.261 30 1 2 127 46 21 335 34.4 0.176 22 0 9 164 78 0 0 32.8 0.148 45 1 2 93 64 32 160 38 0.674 23 1 3 158 64 13 387 31.2 0.295 24 0 5 126 78 27 22 29.6 0.439 40 0 10 129 62 36 0 41.2 0.441 38 1 0 134 58 20 291 26.4 0.352 21 0 3 102 74 0 0 29.5 0.121 32 0 7 187 50 33 392 33.9 0.826 34 1 3 173 78 39 185 33.8 0.97 31 1 10 94 72 18 0 23.1 0.595 56 0 1 108 60 46 178 35.5 0.415 24 0 5 97 76 27 0 35.6 0.378 52 1 4 83 86 19 0 29.3 0.317 34 0 1 114 66 36 200 38.1 0.289 21 0 1 149 68 29 127 29.3 0.349 42 1 5 117 86 30 105 39.1 0.251 42 0 1 111 94 0 0 32.8 0.265 45 0 4 112 78 40 0 39.4 0.236 38 0 1 116 78 29 180 36.1 0.496 25 0 0 141 84 26 0 32.4 0.433 22 0 2 175 88 0 0 22.9 0.326 22 0 2 92 52 0 0 30.1 0.141 22 0 3 130 78 23 79 28.4 0.323 34 1 8 120 86 0 0 28.4 0.259 22 1 2 174 88 37 120 44.5 0.646 24 1 2 106 56 27 165 29 0.426 22 0 2 105 75 0 0 23.3 0.56 53 0 4 95 60 32 0 35.4 0.284 28 0 0 126 86 27 120 27.4 0.515 21 0 8 65 72 23 0 32 0.6 42 0 2 99 60 17 160 36.6 0.453 21 0 1 102 74 0 0 39.5 0.293 42 1 11 120 80 37 150 42.3 0.785 48 1 3 102 44 20 94 30.8 0.4 26 0 1 109 58 18 116 28.5 0.219 22 0 9 140 94 0 0 32.7 0.734 45 1 13 153 88 37 140 40.6 1.174 39 0 12 100 84 33 105 30 0.488 46 0 1 147 94 41 0 49.3 0.358 27 1 1 81 74 41 57 46.3 1.096 32 0 3 187 70 22 200 36.4 0.408 36 1 6 162 62 0 0 24.3 0.178 50 1 4 136 70 0 0 31.2 1.182 22 1 1 121 78 39 74 39 0.261 28 0 3 108 62 24 0 26 0.223 25 0 0 181 88 44 510 43.3 0.222 26 1 8 154 78 32 0 32.4 0.443 45 1 1 128 88 39 110 36.5 1.057 37 1 7 137 90 41 0 32 0.391 39 0 0 123 72 0 0 36.3 0.258 52 1 1 106 76 0 0 37.5 0.197 26 0 6 190 92 0 0 35.5 0.278 66 1 2 88 58 26 16 28.4 0.766 22 0 9 170 74 31 0 44 0.403 43 1 9 89 62 0 0 22.5 0.142 33 0 10 101 76 48 180 32.9 0.171 63 0 2 122 70 27 0 36.8 0.34 27 0 5 121 72 23 112 26.2 0.245 30 0 1 126 60 0 0 30.1 0.349 47 1 1 93 70 31 0 30.4 0.315 23 0