一、算法介绍

邻近算法，或者说K最近邻(kNN，k-NearestNeighbor)分类算法是数据挖掘分类技术中最简单的方法之一。所谓K最近邻，就是k个最近的邻居的意思，说的是每个样本都可以用它最接近的k个邻居来代表。
kNN算法的核心思想是如果一个样本在特征空间中的k个最相邻的样本中的大多数属于某一个类别，则该样本也属于这个类别，并具有这个类别上样本的特性。该方法在确定分类决策上只依据最邻近的一个或者几个样本的类别来决定待分样本所属的类别。 kNN方法在类别决策时，只与极少量的相邻样本有关。由于kNN方法主要靠周围有限的邻近的样本，而不是靠判别类域的方法来确定所属类别的，因此对于类域的交叉或重叠较多的待分样本集来说，kNN方法较其他方法更为适合。

kNN算法的指导思想是“近朱者赤，近墨者黑”，由你的邻居来推断出你的类别。

二 基本概念

1、欧几里得距离
2、曼哈顿距离

三 实现过程

计算步骤：

1. 算距离
2. 找邻居
3. 做分类

本人总结的程序实现流程
1、数据预处理：
对训练数据组集合进行归一化，计算出各参数的最小值，最大值，这样做的目的是了防止某些参数值过大影响距离计算，所以对个参数的数值进行统一。
如训练集合{[2,1],[5,3],[1,2]}进行归于话处理后得出
第一个参数的最大值：5，最小值为：1，相差值：4
归一化后的训练集合为{[0.25,0],[1,1],[0,0.5]}

2、计算测试数据与各点的距离
取出测试数据进行预处理（归一化），计算该个数据到所有训练数据的欧几里得距离。
如测试数据[3，2],预处理后就成为了[0.5, 0.5]
接下来使用欧几里得公式进行距离计算
3、对该个数据到各点的数据距离进行排序
4、过滤出排名前k的点，列出各点的归类
5、计算数量最大归类，测试数据就属于就该分类了。

四、行业应用

客户流失预测、欺诈侦测等（更适合于稀有事件的分类问题）

五、优缺点

1、优点
简单，易于理解，易于实现，无需估计参数，无需训练
适合对稀有事件进行分类（例如当流失率很低时，比如低于0.5%，构造流失预测模型）
特别适合于多分类问题(multi-modal,对象具有多个类别标签)，例如根据基因特征来判断其功能分类，kNN比SVM的表现要好

2、缺点
懒惰算法，对测试样本分类时的计算量大，内存开销大，评分慢
可解释性较差，无法给出决策树那样的规则。

六、常见问题

1、k值设定为多大？
k太小，分类结果易受噪声点影响；k太大，近邻中又可能包含太多的其它类别的点。（对距离加权，可以降低k值设定的影响）
k值通常是采用交叉检验来确定（以k=1为基准）
经验规则：k一般低于训练样本数的平方根

2、类别如何判定最合适？
投票法没有考虑近邻的距离的远近，距离更近的近邻也许更应该决定最终的分类，所以加权投票法更恰当一些。

3、如何选择合适的距离衡量？
高维度对距离衡量的影响：众所周知当变量数越多，欧式距离的区分能力就越差。
变量值域对距离的影响：值域越大的变量常常会在距离计算中占据主导作用，因此应先对变量进行标准化。

4、训练样本是否要一视同仁？
在训练集中，有些样本可能是更值得依赖的。
可以给不同的样本施加不同的权重，加强依赖样本的权重，降低不可信赖样本的影响。

5、性能问题？
kNN是一种懒惰算法，平时不好好学习，考试（对测试样本分类）时才临阵磨枪（临时去找k个近邻）。
懒惰的后果：构造模型很简单，但在对测试样本分类地的系统开销大，因为要扫描全部训练样本并计算距离。
已经有一些方法提高计算的效率，例如压缩训练样本量等。

6、能否大幅减少训练样本量，同时又保持分类精度？
浓缩技术(condensing)
编辑技术(editing)

七、总结

kNN算法因其提出时间较早，随着其他技术的不断更新和完善，kNN算法的诸多不足之处也逐渐显露，因此许多kNN算法的改进算法也应运而生。
针对以上算法的不足，算法的改进方向主要分成了分类效率和分类效果两方面。
分类效率：事先对样本属性进行约简，删除对分类结果影响较小的属性，快速的得出待分类样本的类别。该算法比较适用于样本容量比较大的类域的自动分类，而那些样本容量较小的类域采用这种算法比较容易产生误分。
分类效果：采用权值的方法（和该样本距离小的邻居权值大）来改进，Han等人于2002年尝试利用贪心法，针对文件分类实做可调整权重的k最近邻居法WAkNN (weighted adjusted k nearest neighbor)，以促进分类效果；而Li等人于2004年提出由于不同分类的文件本身有数量上有差异，因此也应该依照训练集合中各种分类的文件数量，选取不同数目的最近邻居，来参与分类。

附录一

基于numpy实现的算法程序

# -*- coding: utf-8 -*-
import math
import numpy as np
from collections import Counter
import warnings

## 经典测试
# 流程
#   1、对数据训练数据进行归一化，（防止某些参数值过大影响距离计算）
#   2、按个取出测试数据（归一化），计算该个数据到所有训练数据的欧几里得距离
#   3、对该个数据到各点的数据距离进行排序
#   4、过滤出排名前几名的点，列出各点的归类
#   5、计算最大归类就该分类了。

# k-Nearest Neighbor算法
def k_nearest_neighbors(data, predict, classLabel,  k=5):

    if len(data) >= k:
        warnings.warn("k is too small")

    # 计算predict点到各点的距离
    distances = []
    dataSize = data.shape[0]
    for i in range(dataSize):
        # 了解np.linalg.norm
        features = data[i]
        euclidean_distance = np.linalg.norm(np.array(features)-np.array(predict))
        # print(euclidean_distance)

        distances.append([euclidean_distance, classLabel[i]])
    # print(sorted(distances))
    sorted_distances =[i[1]  for i in sorted(distances)]
    top_nearest = sorted_distances[:k]
    # print(top_nearest)
    group_res = Counter(top_nearest).most_common(1)[0][0]
    # print(Counter(top_nearest).most_common())
    # print(group_res)
    # print(Counter(top_nearest).most_common(1)[0][1])
    confidence = Counter(top_nearest).most_common(1)[0][1]*1.0/k
    # print(group_res)
    return group_res, confidence

def file2Mat(testFileName, parammterNumber):
    fr = open(testFileName)
    lines = fr.readlines()
    lineNums = len(lines)
    resultMat = np.zeros((lineNums, parammterNumber))
    classLabelVector = []
    for i in range(lineNums):
        line = lines[i].strip()
        itemMat = line.split('\t')
        resultMat[i, :] = itemMat[0:parammterNumber]
        classLabelVector.append(itemMat[-1])
    fr.close()
    return resultMat, classLabelVector;

# 为了防止某个属性对结果产生很大的影响，所以有了这个优化，比如:10000,4.5,6.8 10000就对结果基本起了决定作用
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normMat = np.zeros(np.shape(dataSet))
    size = normMat.shape[0]
    normMat = dataSet - np.tile(minVals, (size, 1))
    normMat = normMat / np.tile(ranges, (size, 1))
    return normMat, minVals, ranges

if __name__=='__main__':

    trainigSetFileName=  'data\\datingTrainingSet.txt'
    testFileName = 'data\\datingTestSet.txt'

    # 读取训练数据
    trianingMat, classLabel = file2Mat(trainigSetFileName, 3)
    # 都数据进行归一化的处理
    trianingMat, minVals, ranges = autoNorm(trianingMat)
    # 读取测试数据
    testMat, testLabel = file2Mat(testFileName, 3)

    correct = 0
    total = 0
    testSize = testMat.shape[0]
    print(testSize)
    print(testMat.shape[1])
    testSize = testMat.shape[0]
    for i in range(testSize):
        data = testMat[i]
        # print((data - minVals) / ranges)
        # 你可以调整这个k看看准确率的变化，你也可以使用matplotlib画出k对应的准确率，找到最好的k值
        res,confidence = k_nearest_neighbors(trianingMat, (data - minVals) / ranges, classLabel, k = 5)
        if testLabel[i] == res:
            correct += 1
        total += 1
    #0.641099

    print(correct)  # 准确率
    print(correct/(testSize*1.0))  # 准确率

    print(k_nearest_neighbors(trianingMat, [4,2,1], classLabel, k = 5)) # 预测一条记录

附录二

基于scikit实现的算法程序

# -*- coding: utf-8 -*-
import numpy as np
from sklearn import neighbors, preprocessing
from sklearn.metrics import precision_recall_curve
from sklearn.metrics import classification_report
from sklearn.cross_validation import train_test_split

def file2Mat(testFileName, parammterNumber):
    fr = open(testFileName)
    lines = fr.readlines()
    lineNums = len(lines)
    resultMat = np.zeros((lineNums, parammterNumber))
    classLabelVector = []
    for i in range(lineNums):
        line = lines[i].strip()
        itemMat = line.split('\t')
        resultMat[i, :] = itemMat[0:parammterNumber]
        classLabelVector.append(itemMat[-1])
    fr.close()
    return resultMat, classLabelVector;


# 为了防止某个属性对结果产生很大的影响，所以有了这个优化，比如:10000,4.5,6.8 10000就对结果基本起了决定作用
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normMat = np.zeros(np.shape(dataSet))
    size = normMat.shape[0]
    normMat = dataSet - np.tile(minVals, (size, 1))
    normMat = normMat / np.tile(ranges, (size, 1))
    return normMat, minVals, ranges

if __name__=='__main__':
    trainigSetFileName = 'data\\datingTrainingSet.txt'
    testFileName = 'data\\datingTestSet.txt'

    # 读取训练数据
    trianingMat, classLabel = file2Mat(trainigSetFileName, 3)
    # 都数据进行归一化的处理
    # 都数据进行归一化的处理
    autoNormTrianingMat, minVals, ranges = autoNorm(trianingMat)
    # 读取测试数据
    testMat, testLabel = file2Mat(testFileName, 3)
    autoNormTestMat = []
    for i in range(len(testLabel)):
        autoNormTestMat.append( (testMat[i] - minVals) / ranges)
    # testMat = preprocessing.normalize(testMat)
    print autoNormTestMat
    # ''''' 训练KNN分类器 '''
    clf = neighbors.KNeighborsClassifier(n_neighbors=5, algorithm='kd_tree')
    clf.fit(autoNormTrianingMat, classLabel)

    answer = clf.predict(autoNormTestMat)

    print(np.sum(answer != testLabel))

    # 计算分数
    print(clf.score(autoNormTestMat, testLabel))
    print(np.mean(answer == testLabel))
    print(clf.predict([0.44832535,  0.39805139,  0.56233353]))
    print(clf.predict_proba([0.44832535,  0.39805139,  0.56233353]))
    # '''''准确率与召回率'''
    # precision, recall, thresholds = precision_recall_curve(testLabel, clf.predict(testMat))

附录三

基于tensorflow实现的算法程序

import tensorflow as tf
import numpy as np

def file2Mat(testFileName, parammterNumber):
    fr = open(testFileName)
    lines = fr.readlines()
    lineNums = len(lines)
    resultMat = np.zeros((lineNums, parammterNumber))
    classLabelVector = []
    for i in range(lineNums):
        line = lines[i].strip()
        itemMat = line.split('\t')
        resultMat[i, :] = itemMat[0:parammterNumber]
        classLabelVector.append(itemMat[-1])
    fr.close()
    return resultMat, classLabelVector;

# 为了防止某个属性对结果产生很大的影响，所以有了这个优化，比如:10000,4.5,6.8 10000就对结果基本起了决定作用
def autoNorm(dataSet):
    minVals = dataSet.min(0)
    maxVals = dataSet.max(0)
    ranges = maxVals - minVals
    normMat = np.zeros(np.shape(dataSet))
    size = normMat.shape[0]
    normMat = dataSet - np.tile(minVals, (size, 1))
    normMat = normMat / np.tile(ranges, (size, 1))
    return normMat, minVals, ranges

if __name__=='__main__':

    trainigSetFileName = 'data\\datingTrainingSet.txt'
    testFileName = 'data\\datingTestSet.txt'

    # 读取训练数据
    trianingMat, classLabel = file2Mat(trainigSetFileName, 3)
    # 都数据进行归一化的处理
    # 都数据进行归一化的处理
    autoNormTrianingMat, minVals, ranges = autoNorm(trianingMat)
    # 读取测试数据
    testMat, testLabel = file2Mat(testFileName, 3)
    autoNormTestMat = []
    for i in range(len(testLabel)):
        autoNormTestMat.append((testMat[i] - minVals) / ranges)

## 循环迭代计算每一个测试数据的预测值，并且和真正的值进行对比，并计算精确度。该算法比较经典的是不需要提前训练，直接在测试阶段进行识别。

    traindata_tensor=tf.placeholder('float',[None,3])
    testdata_tensor=tf.placeholder('float',[3])

    distance = tf.sqrt(tf.reduce_sum(tf.pow(tf.add(traindata_tensor, tf.negative(testdata_tensor)), 2), reduction_indices=1))
    pred = tf.arg_min(distance,0)
    test_num=1
    accuracy=0
    init=tf.global_variables_initializer()
    with tf.Session() as sess:
        sess.run(init)
        for i in range(test_num):
            print(sess.run(distance,feed_dict={traindata_tensor:autoNormTrianingMat,testdata_tensor:autoNormTestMat[i]}))
            idx=sess.run(pred,feed_dict={traindata_tensor:autoNormTrianingMat,testdata_tensor:autoNormTestMat[i]})
            print(idx)

            print('test No.%d,the real label %d, the predict label %d'%(i,np.argmax(testLabel[i]),np.argmax(classLabel[idx])))
            if np.argmax(testLabel[i])==np.argmax(classLabel[idx]):
                accuracy+=1
        print("result:%f"%(1.0*accuracy/test_num))

附录四

测试数据
1、datingTestSet.txt

40920   8.326976    0.953952    3
14488   7.153469    1.673904    2
26052   1.441871    0.805124    1
75136   13.147394   0.428964    1
38344   1.669788    0.134296    1
72993   10.141740   1.032955    1
35948   6.830792    1.213192    3
42666   13.276369   0.543880    3
67497   8.631577    0.749278    1
35483   12.273169   1.508053    3
50242   3.723498    0.831917    1
63275   8.385879    1.669485    1
5569    4.875435    0.728658    2
51052   4.680098    0.625224    1
77372   15.299570   0.331351    1
43673   1.889461    0.191283    1
61364   7.516754    1.269164    1
69673   14.239195   0.261333    1
15669   0.000000    1.250185    2
28488   10.528555   1.304844    3
6487    3.540265    0.822483    2
37708   2.991551    0.833920    1
22620   5.297865    0.638306    2
28782   6.593803    0.187108    3
19739   2.816760    1.686209    2
36788   12.458258   0.649617    3
5741    0.000000    1.656418    2
28567   9.968648    0.731232    3
6808    1.364838    0.640103    2
41611   0.230453    1.151996    1
36661   11.865402   0.882810    3
43605   0.120460    1.352013    1
15360   8.545204    1.340429    3
63796   5.856649    0.160006    1
10743   9.665618    0.778626    2
70808   9.778763    1.084103    1
72011   4.932976    0.632026    1
5914    2.216246    0.587095    2
14851   14.305636   0.632317    3
33553   12.591889   0.686581    3
44952   3.424649    1.004504    1
17934   0.000000    0.147573    2
27738   8.533823    0.205324    3
29290   9.829528    0.238620    3
42330   11.492186   0.263499    3
36429   3.570968    0.832254    1
39623   1.771228    0.207612    1
32404   3.513921    0.991854    1
27268   4.398172    0.975024    1
5477    4.276823    1.174874    2
14254   5.946014    1.614244    2
68613   13.798970   0.724375    1
41539   10.393591   1.663724    3
7917    3.007577    0.297302    2
21331   1.031938    0.486174    2
8338    4.751212    0.064693    2
5176    3.692269    1.655113    2
18983   10.448091   0.267652    3
68837   10.585786   0.329557    1
13438   1.604501    0.069064    2
48849   3.679497    0.961466    1
12285   3.795146    0.696694    2
7826    2.531885    1.659173    2
5565    9.733340    0.977746    2
10346   6.093067    1.413798    2
1823    7.712960    1.054927    2
9744    11.470364   0.760461    3
16857   2.886529    0.934416    2
39336   10.054373   1.138351    3
65230   9.972470    0.881876    1
2463    2.335785    1.366145    2
27353   11.375155   1.528626    3
16191   0.000000    0.605619    2
12258   4.126787    0.357501    2
42377   6.319522    1.058602    1
25607   8.680527    0.086955    3
77450   14.856391   1.129823    1
58732   2.454285    0.222380    1
46426   7.292202    0.548607    3
32688   8.745137    0.857348    3
64890   8.579001    0.683048    1
8554    2.507302    0.869177    2
28861   11.415476   1.505466    3
42050   4.838540    1.680892    1
32193   10.339507   0.583646    3
64895   6.573742    1.151433    1
2355    6.539397    0.462065    2
0   2.209159    0.723567    2
70406   11.196378   0.836326    1
57399   4.229595    0.128253    1
41732   9.505944    0.005273    3
11429   8.652725    1.348934    3
75270   17.101108   0.490712    1
5459    7.871839    0.717662    2
73520   8.262131    1.361646    1
40279   9.015635    1.658555    3
21540   9.215351    0.806762    3
17694   6.375007    0.033678    2
22329   2.262014    1.022169    1
46570   5.677110    0.709469    1
42403   11.293017   0.207976    3
33654   6.590043    1.353117    1
9171    4.711960    0.194167    2
28122   8.768099    1.108041    3
34095   11.502519   0.545097    3
1774    4.682812    0.578112    2
40131   12.446578   0.300754    3
13994   12.908384   1.657722    3
77064   12.601108   0.974527    1
11210   3.929456    0.025466    2
6122    9.751503    1.182050    3
15341   3.043767    0.888168    2
44373   4.391522    0.807100    1
28454   11.695276   0.679015    3
63771   7.879742    0.154263    1
9217    5.613163    0.933632    2
69076   9.140172    0.851300    1
24489   4.258644    0.206892    1
16871   6.799831    1.221171    2
39776   8.752758    0.484418    3
5901    1.123033    1.180352    2
40987   10.833248   1.585426    3
7479    3.051618    0.026781    2
38768   5.308409    0.030683    3
4933    1.841792    0.028099    2
32311   2.261978    1.605603    1
26501   11.573696   1.061347    3
37433   8.038764    1.083910    3
23503   10.734007   0.103715    3
68607   9.661909    0.350772    1
27742   9.005850    0.548737    3
11303   0.000000    0.539131    2
0   5.757140    1.062373    2
32729   9.164656    1.624565    3
24619   1.318340    1.436243    1
42414   14.075597   0.695934    3
20210   10.107550   1.308398    3
33225   7.960293    1.219760    3
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3908    0.000000    0.556245    2
2459    0.000000    0.290218    2
32027   10.095799   1.188148    3
12870   0.860695    1.482632    2
9880    1.557564    0.711278    2
72784   10.072779   0.756030    1
17521   0.000000    0.431468    2
50283   7.140817    0.883813    3
33536   11.384548   1.438307    3
9452    3.214568    1.083536    2
37457   11.720655   0.301636    3
17724   6.374475    1.475925    3
43869   5.749684    0.198875    3
264 3.871808    0.552602    2
25736   8.336309    0.636238    3
39584   9.710442    1.503735    3
31246   1.532611    1.433898    1
49567   9.785785    0.984614    3
7052    2.633627    1.097866    2
35493   9.238935    0.494701    3
10986   1.205656    1.398803    2
49508   3.124909    1.670121    1
5734    7.935489    1.585044    2
65479   12.746636   1.560352    1
77268   10.732563   0.545321    1
28490   3.977403    0.766103    1
13546   4.194426    0.450663    2
37166   9.610286    0.142912    3
16381   4.797555    1.260455    2
10848   1.615279    0.093002    2
35405   4.614771    1.027105    1
15917   0.000000    1.369726    2
6131    0.608457    0.512220    2
67432   6.558239    0.667579    1
30354   12.315116   0.197068    3
69696   7.014973    1.494616    1
33481   8.822304    1.194177    3
43075   10.086796   0.570455    3
38343   7.241614    1.661627    3
14318   4.602395    1.511768    2
5367    7.434921    0.079792    2
37894   10.467570   1.595418    3
36172   9.948127    0.003663    3
40123   2.478529    1.568987    1
10976   5.938545    0.878540    2
12705   0.000000    0.948004    2
12495   5.559181    1.357926    2
35681   9.776654    0.535966    3
46202   3.092056    0.490906    1
11505   0.000000    1.623311    2
22834   4.459495    0.538867    1
49901   8.334306    1.646600    3
71932   11.226654   0.384686    1
13279   3.904737    1.597294    2
49112   7.038205    1.211329    3
77129   9.836120    1.054340    1
37447   1.990976    0.378081    1
62397   9.005302    0.485385    1
0   1.772510    1.039873    2
15476   0.458674    0.819560    2
40625   10.003919   0.231658    3
36706   0.520807    1.476008    1
28580   10.678214   1.431837    3
25862   4.425992    1.363842    1
63488   12.035355   0.831222    1
33944   10.606732   1.253858    3
30099   1.568653    0.684264    1
13725   2.545434    0.024271    2
36768   10.264062   0.982593    3
64656   9.866276    0.685218    1
14927   0.142704    0.057455    2
43231   9.853270    1.521432    3
66087   6.596604    1.653574    1
19806   2.602287    1.321481    2
41081   10.411776   0.664168    3
10277   7.083449    0.622589    2
7014    2.080068    1.254441    2
17275   0.522844    1.622458    2
31600   10.362000   1.544827    3

2、datingTrainingSet

40920   8.326976    0.953952    3
14488   7.153469    1.673904    2
26052   1.441871    0.805124    1
75136   13.147394   0.428964    1
38344   1.669788    0.134296    1
72993   10.141740   1.032955    1
35948   6.830792    1.213192    3
42666   13.276369   0.543880    3
67497   8.631577    0.749278    1
35483   12.273169   1.508053    3
50242   3.723498    0.831917    1
63275   8.385879    1.669485    1
5569    4.875435    0.728658    2
51052   4.680098    0.625224    1
77372   15.299570   0.331351    1
43673   1.889461    0.191283    1
61364   7.516754    1.269164    1
69673   14.239195   0.261333    1
15669   0.000000    1.250185    2
28488   10.528555   1.304844    3
6487    3.540265    0.822483    2
37708   2.991551    0.833920    1
22620   5.297865    0.638306    2
28782   6.593803    0.187108    3
19739   2.816760    1.686209    2
36788   12.458258   0.649617    3
5741    0.000000    1.656418    2
28567   9.968648    0.731232    3
6808    1.364838    0.640103    2
41611   0.230453    1.151996    1
36661   11.865402   0.882810    3
43605   0.120460    1.352013    1
15360   8.545204    1.340429    3
63796   5.856649    0.160006    1
10743   9.665618    0.778626    2
70808   9.778763    1.084103    1
72011   4.932976    0.632026    1
5914    2.216246    0.587095    2
14851   14.305636   0.632317    3
33553   12.591889   0.686581    3
44952   3.424649    1.004504    1
17934   0.000000    0.147573    2
27738   8.533823    0.205324    3
29290   9.829528    0.238620    3
42330   11.492186   0.263499    3
36429   3.570968    0.832254    1
39623   1.771228    0.207612    1
32404   3.513921    0.991854    1
27268   4.398172    0.975024    1
5477    4.276823    1.174874    2
14254   5.946014    1.614244    2
68613   13.798970   0.724375    1
41539   10.393591   1.663724    3
7917    3.007577    0.297302    2
21331   1.031938    0.486174    2
8338    4.751212    0.064693    2
5176    3.692269    1.655113    2
18983   10.448091   0.267652    3
68837   10.585786   0.329557    1
13438   1.604501    0.069064    2
48849   3.679497    0.961466    1
12285   3.795146    0.696694    2
7826    2.531885    1.659173    2
5565    9.733340    0.977746    2
10346   6.093067    1.413798    2
1823    7.712960    1.054927    2
9744    11.470364   0.760461    3
16857   2.886529    0.934416    2
39336   10.054373   1.138351    3
65230   9.972470    0.881876    1
2463    2.335785    1.366145    2
27353   11.375155   1.528626    3
16191   0.000000    0.605619    2
12258   4.126787    0.357501    2
42377   6.319522    1.058602    1
25607   8.680527    0.086955    3
77450   14.856391   1.129823    1
58732   2.454285    0.222380    1
46426   7.292202    0.548607    3
32688   8.745137    0.857348    3
64890   8.579001    0.683048    1
8554    2.507302    0.869177    2
28861   11.415476   1.505466    3
42050   4.838540    1.680892    1
32193   10.339507   0.583646    3
64895   6.573742    1.151433    1
2355    6.539397    0.462065    2
0   2.209159    0.723567    2
70406   11.196378   0.836326    1
57399   4.229595    0.128253    1
41732   9.505944    0.005273    3
11429   8.652725    1.348934    3
75270   17.101108   0.490712    1
5459    7.871839    0.717662    2
73520   8.262131    1.361646    1
40279   9.015635    1.658555    3
21540   9.215351    0.806762    3
17694   6.375007    0.033678    2
22329   2.262014    1.022169    1
46570   5.677110    0.709469    1
42403   11.293017   0.207976    3
33654   6.590043    1.353117    1
9171    4.711960    0.194167    2
28122   8.768099    1.108041    3
34095   11.502519   0.545097    3
1774    4.682812    0.578112    2
40131   12.446578   0.300754    3
13994   12.908384   1.657722    3
77064   12.601108   0.974527    1
11210   3.929456    0.025466    2
6122    9.751503    1.182050    3
15341   3.043767    0.888168    2
44373   4.391522    0.807100    1
28454   11.695276   0.679015    3
63771   7.879742    0.154263    1
9217    5.613163    0.933632    2
69076   9.140172    0.851300    1
24489   4.258644    0.206892    1
16871   6.799831    1.221171    2
39776   8.752758    0.484418    3
5901    1.123033    1.180352    2
40987   10.833248   1.585426    3
7479    3.051618    0.026781    2
38768   5.308409    0.030683    3
4933    1.841792    0.028099    2
32311   2.261978    1.605603    1
26501   11.573696   1.061347    3
37433   8.038764    1.083910    3
23503   10.734007   0.103715    3
68607   9.661909    0.350772    1
27742   9.005850    0.548737    3
11303   0.000000    0.539131    2
0   5.757140    1.062373    2
32729   9.164656    1.624565    3
24619   1.318340    1.436243    1
42414   14.075597   0.695934    3
20210   10.107550   1.308398    3
33225   7.960293    1.219760    3
54483   6.317292    0.018209    1
18475   12.664194   0.595653    3
33926   2.906644    0.581657    1
43865   2.388241    0.913938    1
26547   6.024471    0.486215    3
44404   7.226764    1.255329    3
16674   4.183997    1.275290    2
8123    11.850211   1.096981    3
42747   11.661797   1.167935    3
56054   3.574967    0.494666    1
10933   0.000000    0.107475    2
18121   7.937657    0.904799    3
11272   3.365027    1.014085    2
16297   0.000000    0.367491    2
28168   13.860672   1.293270    3
40963   10.306714   1.211594    3
31685   7.228002    0.670670    3
55164   4.508740    1.036192    1
17595   0.366328    0.163652    2
1862    3.299444    0.575152    2
57087   0.573287    0.607915    1
63082   9.183738    0.012280    1
51213   7.842646    1.060636    3
6487    4.750964    0.558240    2
4805    11.438702   1.556334    3
30302   8.243063    1.122768    3
68680   7.949017    0.271865    1
17591   7.875477    0.227085    2
74391   9.569087    0.364856    1
37217   7.750103    0.869094    3
42814   0.000000    1.515293    1
14738   3.396030    0.633977    2
19896   11.916091   0.025294    3
14673   0.460758    0.689586    2
32011   13.087566   0.476002    3
58736   4.589016    1.672600    1
54744   8.397217    1.534103    1
29482   5.562772    1.689388    1
27698   10.905159   0.619091    3
11443   1.311441    1.169887    2
56117   10.647170   0.980141    3
39514   0.000000    0.481918    1
26627   8.503025    0.830861    3
16525   0.436880    1.395314    2
24368   6.127867    1.102179    1
22160   12.112492   0.359680    3
6030    1.264968    1.141582    2
6468    6.067568    1.327047    2
22945   8.010964    1.681648    3
18520   3.791084    0.304072    2
34914   11.773195   1.262621    3
6121    8.339588    1.443357    2
38063   2.563092    1.464013    1
23410   5.954216    0.953782    1
35073   9.288374    0.767318    3
52914   3.976796    1.043109    1
16801   8.585227    1.455708    3
9533    1.271946    0.796506    2
16721   0.000000    0.242778    2
5832    0.000000    0.089749    2
44591   11.521298   0.300860    3
10143   1.139447    0.415373    2
21609   5.699090    1.391892    2
23817   2.449378    1.322560    1
15640   0.000000    1.228380    2
8847    3.168365    0.053993    2
50939   10.428610   1.126257    3
28521   2.943070    1.446816    1
32901   10.441348   0.975283    3
42850   12.478764   1.628726    3
13499   5.856902    0.363883    2
40345   2.476420    0.096075    1
43547   1.826637    0.811457    1
70758   4.324451    0.328235    1
19780   1.376085    1.178359    2
44484   5.342462    0.394527    1
54462   11.835521   0.693301    3
20085   12.423687   1.424264    3
42291   12.161273   0.071131    3
47550   8.148360    1.649194    3
11938   1.531067    1.549756    2
40699   3.200912    0.309679    1
70908   8.862691    0.530506    1
73989   6.370551    0.369350    1
11872   2.468841    0.145060    2
48463   11.054212   0.141508    3
15987   2.037080    0.715243    2
70036   13.364030   0.549972    1
32967   10.249135   0.192735    3
63249   10.464252   1.669767    1
42795   9.424574    0.013725    3
14459   4.458902    0.268444    2
19973   0.000000    0.575976    2
5494    9.686082    1.029808    3
67902   13.649402   1.052618    1
25621   13.181148   0.273014    3
27545   3.877472    0.401600    1
58656   1.413952    0.451380    1
7327    4.248986    1.430249    2
64555   8.779183    0.845947    1
8998    4.156252    0.097109    2
11752   5.580018    0.158401    2
76319   15.040440   1.366898    1
27665   12.793870   1.307323    3
67417   3.254877    0.669546    1
21808   10.725607   0.588588    3
15326   8.256473    0.765891    2
20057   8.033892    1.618562    3
79341   10.702532   0.204792    1
15636   5.062996    1.132555    2
35602   10.772286   0.668721    3
28544   1.892354    0.837028    1
57663   1.019966    0.372320    1
78727   15.546043   0.729742    1
68255   11.638205   0.409125    1
14964   3.427886    0.975616    2
21835   11.246174   1.475586    3
7487    0.000000    0.645045    2
8700    0.000000    1.424017    2
26226   8.242553    0.279069    3
65899   8.700060    0.101807    1
6543    0.812344    0.260334    2
46556   2.448235    1.176829    1
71038   13.230078   0.616147    1
47657   0.236133    0.340840    1
19600   11.155826   0.335131    3
37422   11.029636   0.505769    3
1363    2.901181    1.646633    2
26535   3.924594    1.143120    1
47707   2.524806    1.292848    1
38055   3.527474    1.449158    1
6286    3.384281    0.889268    2
10747   0.000000    1.107592    2
44883   11.898890   0.406441    3
56823   3.529892    1.375844    1
68086   11.442677   0.696919    1
70242   10.308145   0.422722    1
11409   8.540529    0.727373    2
67671   7.156949    1.691682    1
61238   0.720675    0.847574    1
17774   0.229405    1.038603    2
53376   3.399331    0.077501    1
30930   6.157239    0.580133    1
28987   1.239698    0.719989    1
13655   6.036854    0.016548    2
7227    5.258665    0.933722    2
40409   12.393001   1.571281    3
13605   9.627613    0.935842    2
26400   11.130453   0.597610    3
13491   8.842595    0.349768    3
30232   10.690010   1.456595    3
43253   5.714718    1.674780    3
55536   3.052505    1.335804    1
8807    0.000000    0.059025    2
25783   9.945307    1.287952    3
22812   2.719723    1.142148    1
77826   11.154055   1.608486    1
38172   2.687918    0.660836    1
31676   10.037847   0.962245    3
74038   12.404762   1.112080    1
44738   10.237305   0.633422    3
17410   4.745392    0.662520    2
5688    4.639461    1.569431    2
36642   3.149310    0.639669    1
29956   13.406875   1.639194    3
60350   6.068668    0.881241    1
23758   9.477022    0.899002    3
25780   3.897620    0.560201    2
11342   5.463615    1.203677    2
36109   3.369267    1.575043    1
14292   5.234562    0.825954    2
11160   0.000000    0.722170    2
23762   12.979069   0.504068    3
39567   5.376564    0.557476    1
25647   13.527910   1.586732    3
14814   2.196889    0.784587    2
73590   10.691748   0.007509    1
35187   1.659242    0.447066    1
49459   8.369667    0.656697    3
31657   13.157197   0.143248    3
6259    8.199667    0.908508    2
33101   4.441669    0.439381    3
27107   9.846492    0.644523    3
17824   0.019540    0.977949    2
43536   8.253774    0.748700    3
67705   6.038620    1.509646    1
35283   6.091587    1.694641    3
71308   8.986820    1.225165    1
31054   11.508473   1.624296    3
52387   8.807734    0.713922    3
40328   0.000000    0.816676    1
34844   8.889202    1.665414    3
11607   3.178117    0.542752    2
64306   7.013795    0.139909    1
32721   9.605014    0.065254    3
33170   1.230540    1.331674    1
37192   10.412811   0.890803    3
13089   0.000000    0.567161    2
66491   9.699991    0.122011    1
15941   0.000000    0.061191    2
4272    4.455293    0.272135    2
48812   3.020977    1.502803    1
28818   8.099278    0.216317    3
35394   1.157764    1.603217    1
71791   10.105396   0.121067    1
40668   11.230148   0.408603    3
39580   9.070058    0.011379    3
11786   0.566460    0.478837    2
19251   0.000000    0.487300    2
56594   8.956369    1.193484    3
54495   1.523057    0.620528    1
11844   2.749006    0.169855    2
45465   9.235393    0.188350    3
31033   10.555573   0.403927    3
16633   6.956372    1.519308    2
13887   0.636281    1.273984    2
52603   3.574737    0.075163    1
72000   9.032486    1.461809    1
68497   5.958993    0.023012    1
35135   2.435300    1.211744    1
26397   10.539731   1.638248    3
7313    7.646702    0.056513    2
91273   20.919349   0.644571    1
24743   1.424726    0.838447    1
31690   6.748663    0.890223    3
15432   2.289167    0.114881    2
58394   5.548377    0.402238    1
33962   6.057227    0.432666    1
31442   10.828595   0.559955    3
31044   11.318160   0.271094    3
29938   13.265311   0.633903    3
9875    0.000000    1.496715    2
51542   6.517133    0.402519    3
11878   4.934374    1.520028    2
69241   10.151738   0.896433    1
37776   2.425781    1.559467    1
68997   9.778962    1.195498    1
67416   12.219950   0.657677    1
59225   7.394151    0.954434    1
29138   8.518535    0.742546    3
5962    2.798700    0.662632    2
10847   0.637930    0.617373    2
70527   10.750490   0.097415    1
9610    0.625382    0.140969    2
64734   10.027968   0.282787    1
25941   9.817347    0.364197    3
2763    0.646828    1.266069    2
55601   3.347111    0.914294    1
31128   11.816892   0.193798    3
5181    0.000000    1.480198    2
69982   10.945666   0.993219    1
52440   10.244706   0.280539    3
57350   2.579801    1.149172    1
57869   2.630410    0.098869    1
56557   11.746200   1.695517    3
42342   8.104232    1.326277    3
15560   12.409743   0.790295    3
34826   12.167844   1.328086    3
8569    3.198408    0.299287    2
77623   16.055513   0.541052    1
78184   7.138659    0.158481    1
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