python手写代码实现SMO算法

SMO算法

在SMO算法中，每次只调整两个a，其他的a不变，因为有约束
${\sum }_{i=1}^N{a}_i{y}_i=0$，单独拿出两个a，那么有$a_i{y}_i+a_j{y}_j=c$，也就是说，剩下的a有${\sum }_{k\ne i,j}^N{a}_k{y}_k=-c$，所以c的值可以确定，于是根据$a_i$就可以求出$a_j$来，然后优化$a_i$即可，仅有的约束是$a_i\ge 0$。

软间隔支持向量机

约束条件是$y(\omega x+b)\ge 1-\xi$，因为是软间隔，所以不可能所有的点都满足$y(\omega x+b)\ge 1$的条件，所以引入了松弛变量$\xi$。

优化目标函数是最小化$\sum ||\omega ||+C\sum {\xi }_i$，这里的C是惩罚参数。

优化目标函数包含两层含义：

• 使得$\omega$的2范数尽量小
• 使得误分类的点的个数尽量少，即$\xi$求和尽可能小，C是二者的调和参数

分离超平面是$\omega x+b=0$，分类决策函数是$sign(\omega x+b)$。

转化成对偶问题来求解：
$$\frac{1}{2}\sum _{i=1}^N\sum _{j=1}^N{\alpha }_i{\alpha }_j{y}_i{y}_j(x_i{x}_j)-\sum _{i=1}^N{\alpha }_i$$
对偶形式的约束条件是：
$$\begin{gathered} \sum _{i=1}^N{\alpha }_i{y}_i=0 \\ 0\le {\alpha }_i\le C \end{gathered}$$
解得：
$$\begin{gathered} {\omega }^{\ast }=\sum _{i=1}^N{\alpha }_i{y}_i{x}_i \\ {b}^{\ast }=y_j-\sum _{i=1}^N{\alpha }_i{y}_i{x}_i^{\text{T}}{x}_j \end{gathered}$$
这里的 j 是大于0小于C的alpha下标，i属于求和符号，可能会有很多个不等于0的alpha，所以b可能不同，b不一定唯一。

核函数支持向量机

优化目标函数，起始就是把上面的优化目标函数的$(x_i{x}_j)$替换成$K(x_i,x_j)$：
$$\frac{1}{2}\sum _{i=1}^N\sum _{j=1}^N{\alpha }_i{\alpha }_j{y}_i{y}_{j}K(x_i,x_j)-\sum _{i=1}^N{\alpha }_i$$
分类决策函数：${\sum }_{i=1}^N[{\alpha }_i{y}_{i}K(x,x_i)]+b$

SMO支持向量机

假设只优化${\alpha }_0$和${\alpha }_1$，其他的$\alpha$固定。

约束条件：${\alpha }_0{y}_0+{\alpha }_1{y}_1=-\sum _{i=2}^N{\alpha }_i{y}_i,0\le {\alpha }_i\le C$

虽然有两个变量，但是自由度只有1，当确定一个变量后，另一个可以通过约束条件得到，所以只需要算出一个的值就好了。

我们假设只考虑优化${\alpha }_1$

那么$L\le alph{a}_i\le H$

• 如果$y_0\ne y_1$，则$L=max(0,{\alpha }_i-{\alpha }_0),H=min(C,C+{\alpha }_1-{\alpha }_0)$
• 如果$y_0=y_1$，则$L=max(0,{\alpha }_1+{\alpha }_0-C),H=min(C,{\alpha }_1+{\alpha }_0)$

具体推到导可以联立$0\le {\alpha }_0\le C,0\le {\alpha }_1\le C$求得。

为了叙述简单，定义了预测函数g：
$$g(x)=\sum _{i=0}^N[{\alpha }_i{y}_{i}K(x_i,x)]+b$$
E就是预测函数g和真实y之间的差：
$$E_i=g(x_i)-y_i$$

训练算法
$${\alpha }_1={\alpha }_1+\frac{y_1(E_0-E_1)}{K(x_0,x_0)+K(x_1,x_1)-2K(x_0,x_1)}$$
使用H和L来裁剪${\alpha }_1$，可由二次函数在区间内的最小值得到裁剪规则：
$$\begin{gathered} {\alpha }_1=Hif{\alpha }_1>H \\ {\alpha }_1=Lif{\alpha }_1<H \end{gathered}$$
再计算${\alpha }_0$:
$${\alpha }_0={\alpha }_0+y_0{y}_1({\alpha }_1^{old}-{\alpha }_1^{new})$$
变量的选择：首先要找到一个违反KKT条件最严重的$\alpha$，记为${\alpha }_0$

KKT条件为：
$$\begin{gathered} if\alpha =0,thenyg(x)\ge 1 \\ if\alpha =C,thenyg(x)\le 1 \\ if0<\alpha <C,thenyg(x)=1 \end{gathered}$$
第二个变量要找到一个能使得$|E_0-E_1|$最大的$\alpha$，记为${\alpha }_1$。

每次优化完两个$\alpha$后，要重新计算b，因为更新了两个$\alpha$，所以会得到两个b：
$$\begin{gathered} b_1=b-E_0-y_{0}K(x_0,x_0)({\alpha }_0^{new}-{\alpha }_0)-y_1({\alpha }_1^{new,clipped}-{\alpha }_1)K(x_0,x_1) \\ {b}_2=b-E_1-y_{0}K(x_0,x_1)({\alpha }_0^{new}-{\alpha }_0)-y_1({\alpha }_1^{new,clipped}-{\alpha }_1)K(x_1,x_1) \end{gathered}$$
如果${\alpha }_0^{new}$和${\alpha }_1^{new}$同时满足$0<alpha<C$，那么$b_1=b_2$

如果${\alpha }_0^{new}$和${\alpha }_0^{new}$都是0或者C，那么$b_1,b_2$都符合KKT条件，选择他的终点作为新的b，即$b=\frac{b_1+b_2}{2}$。

软间隔支持向量机

运行结果

将C调为np.inf就是硬间隔支持向量机了。

之前做发现总是错误率很低，打印预测值发现都是正数或者都是负数，后来打印了支持向量机的下标对应的预测值后，发现全是值为1的向量机，仔细一想，是不是我读入数据没有把0变成-1，修改过后再次查看向量机的预测值，果然出现了-1，再查看预测值，果然有正有负。

使用的核函数是$K(x_i,x_j)=exp(-\frac{||x_i-x_j|{|}_{ord}^2}{2{\sigma }^2})$。

需要调整的参数主要是一个是范式角标ord_opt，即核函数对应的ord，一个是高斯核kernel_opt，即核函数对应的$\sigma$，其他参数对训练结果基本上没有什么影响，保持参数C=200，tolerant =$10^{-6}$不变。

对于data1数据特征比较多，核函数的ord_opt设置较高值比较合适，但是由于数据量太大，训练时间比较长，训练错误率30%大概十几秒钟，但是达到10%左右的错误率需要十几分钟。

对于data2，不断地调整核函数参数，经过多次尝试，选择ord_opt = 3 合适，再通过调节kernel_opt来获取最佳拟合结果。

下面是训练结果和对应参数。

data1

C=200, ord_opt = 3, kernel_opt = 40 error = 31.87%
C=200, ord_opt = 3, kernel_opt = 30 error = 31.54%
C=200, ord_opt = 3, kernel_opt = 20 error = 30.07%
C=200, ord_opt = 3, kernel_opt = 10 error = 25.84%
C=200, ord_opt = 3, kernel_opt = 8 error = 24.39%
C=200, ord_opt = 3, kernel_opt = 5 error = 22.90%

C=200, ord_opt = 10, kernel_opt = 10 error = 33.81%
C=200, ord_opt = 10, kernel_opt = 8 error = 21.81%
C=200, ord_opt = 10, kernel_opt = 6 error = 11.77%
C=200, ord_opt = 10, kernel_opt = 5 error = 10.94%


data2

C=200, ord_opt = 3, kernel_opt = 26 error = 17.97%
C=200, ord_opt = 3, kernel_opt = 18 error = 17.32%
C=200, ord_opt = 3, kernel_opt = 13 error = 7.94%
C=200, ord_opt = 3, kernel_opt = 11 error = 2.73%

代码块展示

import numpy as np

def loadDataSet(filename): #读取数据
    dataMat, labelMat = [], []
    datmat = np.loadtxt(open(filename, "rb"), delimiter=",", skiprows=0)
    for i in range(np.shape(datmat)[0]):
        temp = []
        for j in range(np.shape(datmat)[1]-1):
            temp.append(float(datmat[i,j]))
        dataMat.append(temp)
        labelMat.append(float(datmat[i,-1]))
    return dataMat,labelMat #返回数据特征和数据类别

#########################==========全局变量声明===========##########################
'''在这里选择要打开的文件'''
X,Y = loadDataSet('data1.csv') 

X = np.array(X)
Y = np.array(Y)
Y[Y == 0 ] = -1 # 这个很关键，之前忘记加上了
N, M =np.shape(X)
C = 200 # 超参数C
tol = 10e-6 # 容错率
alpha = np.zeros(N) #alpha系数向量
b = 0 # 偏置系数

'''
在这里设置关键超参数,上面的超参数不用调
data1: ord_opt = 10, kernel_opt = 8, times = 13s, error rate = 33.80%, 正确率越高,耗时越久
data2: ord_opt = 3, kernel_opt = 11, times = 10s, error_rate= 2.73%
''' 
ord_opt = 10 # 核函数,表示几范数
kernel_opt = 10 # 核函数的sigma参数
K = np.zeros((N, N)) # 存放各个向量之间的核函数值
for i in range(N):
    K[i] = np.exp(-np.linalg.norm(X[i]-X,ord = ord_opt, axis = 1)/kernel_opt)
# print(K)

def g(i): # 计算预测值
    return np.sum(alpha*Y*K[:,i])+b 

def E(i): # 计算误差，预测值减去真实值
    return g(i) - Y[i]

def kkt(i): # 检查是否满足KKT条件
    if alpha[i] == 0: # 说明分类分对了
        return Y[i] * g(i) - 1 >= tol
    if alpha[i] == C: # 说明分类分错了
        return Y[i] * g(i) - 1 <= -tol
    if 0 < alpha[i] < C: # 支持向量
        return Y[i] * g(i) - 1 == tol
    return False

def smo():
    #迭代更新alpha

    while True:
        flag = False#判断本次是否找到了更改的变量
        #region 找出两个更新的变量alphai,alphaj
        #选择第一个变量besti
        alpha_0C = (alpha>0) * (alpha<C)
        alpha_index=np.argsort(~alpha_0C)
        b = 0
        for besti in alpha_index:
            bestj = -1
            if kkt(i): # 找到一个不满足kkt条件的下标,即alpha_1
                continue
            maxE_diff=0 # 找到使得|Ei-Ej|最大的下标,即alpha_2
            for j in alpha_index: #开始遍历间隔边上的点和其它点
                if besti==j: #如果是besti，则跳过
                    continue
                E_diff=np.abs(E(besti)-E(j)) #计算E_diff
                if E_diff>maxE_diff: #如果E_diff大于maxE_diff，则更新maxE_diff和bestj
                    bestj=j
                    maxE_diff=E_diff
            #  更新变量alphai、alphaj
            eta = K[besti, besti] + K[bestj, bestj] - 2 * K[besti, bestj] 
            alphaj = alpha[bestj] + Y[bestj] * (E(besti) - E(bestj)) / eta #更新alphaj
            if Y[besti] != Y[bestj]: 
                L = np.max([0, alpha[bestj] - alpha[besti]])
                H = np.min([C, C + alpha[bestj] - alpha[besti]])
            else:
                L = np.max([0, alpha[bestj] + alpha[besti] - C])
                H = np.min([C, alpha[bestj] + alpha[besti]])

            # 修建alpha_j
            if alphaj > H:
                alphaj = H
            elif alphaj < L:
                alphaj = L
            # print('alpha_j changed from %f to %f' % (old, alphaj))
            if np.abs(alphaj - alpha[bestj]) < tol:  # alphaj没有移动足够的值，重新找
                continue

            alphai = alpha[besti] + Y[besti] * Y[bestj] * (alpha[bestj] - alphaj) #根据alphaj更新alphai

            # 更新变量b
            b1_new = -E(besti) - Y[besti] * K[besti, besti] * (alphai - alpha[besti]) - Y[bestj] * K[bestj, besti] * (alphaj - alpha[bestj]) + b
            b2_new = -E(bestj) - Y[besti] * K[besti, bestj] * (alphai - alpha[besti]) - Y[bestj] * K[bestj, bestj] * (alphaj - alpha[bestj]) + b
            if 0 < alphai < C:
                b = b1_new
            elif 0 < alphaj < C:
                b = b2_new
            else:
                b = (b1_new + b2_new) / 2.0
            b = b
            alpha[besti] = alphai
            alpha[bestj] = alphaj

            flag=True

        # 没有找到更改的变量,终止程序
        if not flag:
            break

    return alpha,b


def svm_test():
    alphas,b = smo() 
    sptVecIndex=np.nonzero(alphas>0) #获取支持向量的索引
    sptVec=X[sptVecIndex] #获得支持向量
    sptVeclabel = Y[sptVecIndex] #获得支持向量对应的类别标签
    print('there are %d Support Vectors' % np.shape(sptVec)[0])
    m = np.shape(X)[0]
    errorCount = 0
    for k in range(m):
        kernelEval = np.exp(-np.linalg.norm(X[k]-sptVec,ord = ord_opt, axis = 1)/kernel_opt)
        predict= np.sum(np.multiply(np.multiply(np.mat(kernelEval), sptVeclabel), alphas[sptVecIndex])) + b#计算预测值
        # print(predict)
        if (np.sign(predict)) !=np.sign(Y[k]): errorCount += 1
    print("the training error rate is: %f" % (float(errorCount)/m))

def main():
    svm_test()

main()

合页损失函数

算法原理

求样本点到超平面的距离：

def get_margin(x,y,w,b):
    w_2 = np.sum(np.multiply(w,w))**0.5 # 表示范式大小
    return y*np.dot(w,x)+b / w_2

合页损失函数：

loss分为两个部分，一个是w越大，loss越大，另一个是预测错误的loss

def get_loss(X,Y,w,b):
    lam = 0.2 # 平衡两个loss的变量
    w_2 = np.sum(np.multiply(w,w))**0.5 # w越大，loss越大
    loss = 0
    for i in range(len(X)):
        pred = Y[i] * (np.dot(X[i],w) + b)
        # 如果分类正确，则这个值至少是1以上，如果小于1，说明分的还不开，如果是负数，就说明分错了，loss更大了
        pred = 1 - pred 
        # 预测正确，则pred是负数，损失为0，否则损失为pred
        relu = np.maximum(pred,0) 
        loss += relu
    return loss + lam * w_2

求w和b的梯度，使用导函数定义求其数值解：

def get_grad(X,Y,w,b):
    epsilon = 1e-8
    loss = get_loss(X,Y,w,b)
    grad_w = np.zeros(len(w))
    for i in range(len(w)): # 对w的每一个元素求偏导
        w[i] += epsilon
        grad_w[i] = (get_loss(X,Y,w,b) - loss) / epsilon
        w[i] -= epsilon
    grad_b = (get_loss(X,Y,w,b+epsilon) - loss) / epsilon

最后训练算法就是常见的梯度下降：

def train(epochs,X,Y,lr=0.003):
    w = np.random.normal(0,0.1,len(X[0]))
    b = 0
    for epoch in range(epochs):
        index = np.random.randint(0,np.shape(X)[0],200)
        grad_w, grad_b = get_grad(np.array(X)[index],np.array(Y)[index],w,b)
        w -= grad_w * lr
        b -= grad_b * lr
	return w, b

代码展示

import numpy as np 
import matplotlib.pyplot as plt

# def get_margin(x,y,w,b): # 获取样本点到分界线的距离
#     w_2 = np.sum(np.multiply(w,w))**0.5
#     return y*np.dot(w,x)+b / w_2

# def get_min_margin(X,Y,w,b): # 找到到分界线上的最小距离
#     w_2 = np.sum(np.multiply(w,w))**0.5
#     _min = np.inf
#     for i in range(len(X)):
#         _margin = get_margin(X[i],Y[i],w,b)
#         if _margin < 0:
#             continue
#         if _margin < _min:
#             _min = _margin
#     return _min / w_2

def get_loss(X,Y,w,b):
    lam = 0.2 # 平衡两个loss的变量
    w_2 = np.sum(np.multiply(w,w))**0.5 # w越大，loss越大
    loss = 0
    for i in range(len(X)):
        pred = Y[i] * (np.dot(X[i],w) + b)
        pred = 1 - pred # 如果分类正确，则这个值至少是1以上，如果小于1，说明分的还不开，如果是负数，就说明分错了，loss更大了
        relu = np.maximum(pred,0) # 预测正确，则pred是负数，损失为0，否则损失为pred
        loss += relu
    return loss + lam * w_2
    
def get_grad(X,Y,w,b): # 暴力求导数
    epsilon = 1e-8
    loss = get_loss(X,Y,w,b)
    grad_w = np.zeros(len(w))
    for i in range(len(w)): # 对w的每一个元素求偏导
        w[i] += epsilon
        grad_w[i] = (get_loss(X,Y,w,b) - loss) / epsilon
        w[i] -= epsilon
    grad_b = (get_loss(X,Y,w,b+epsilon) - loss) / epsilon

    return grad_w,grad_b

def train(epochs,X,Y,lr=0.001):
    w = np.random.normal(0,0.1,len(X[0]))
    b = 0
    x, y = [], []
    for epoch in range(epochs):
        index = np.random.randint(0,np.shape(X)[0],200)
        grad_w, grad_b = get_grad(np.array(X)[index],np.array(Y)[index],w,b) # 求梯度
        w -= grad_w * lr # 更新w
        b -= grad_b * lr # 更新b
        loss = get_loss(X,Y,w,b)
        print("epoch:",epoch,"loss:",loss)
        x.append(epoch)
        y.append(loss)
    plt.plot(x,y,'ro')
    plt.show()
    return w, b

def predict(X,w,b):
    X /= np.max(X, axis=0)
    print(np.dot(X,w) + b)
    return np.sign(np.dot(X,w) + b)

def loadDataSet(filename): #读取数据
    dataMat = []
    datmat = np.loadtxt(open(filename, "rb"), delimiter=",", skiprows=0)
    labelMat = datmat[:, -1].tolist() 
    datmat = datmat / np.max(datmat, axis=0)
    for i in range(np.shape(datmat)[0]):
        temp = []
        for j in range(np.shape(datmat)[1]-1):
            temp.append(float(datmat[i,j]))
        dataMat.append(temp)
    return dataMat,labelMat #返回数据特征和数据类别

'''
在这里修改文件路径,以下参数不用修改
lr = 0.01, lam = 0.2
data1: epochs = 1000, times = 190s, error = 11.45%
data2: epochs = 2000, times = 70s, error = 22.53%
'''
dataArr,labelArr = loadDataSet('data2.csv')

labelArr = np.array(labelArr)
labelArr[labelArr == 0] = -1 # 还是老问题，这句忘记写了

'''在这里修改迭代次数epochs'''
w, b = train(2000,dataArr,labelArr)

error = np.mat(np.zeros((np.shape(dataArr)[0],1)))
pred = predict(dataArr,w,b)
print(pred)
error[pred != np.array(labelArr)] = 1
print(np.sum(error)/np.shape(dataArr)[0])

训练过程和结果

超参数设置：

• 泛化系数：$\lambda =0.2$
• 学习率：$\alpha =0.001$
• 批大小：$ batch = 200$

data1 迭代1000次，错误率为11.45%，用时190s

data2 迭代2000次，错误率为22.53%，用时70s

下面是data2的预测结果，证明不是全部蒙的-1

[ 1. -1.  1. -1.  1. -1. -1.  1.  1. -1. -1.  1.  1.  1.  1. -1. -1. -1.
 -1. -1. -1. -1.  1. -1.  1. -1.  1. -1.  1. -1. -1.  1. -1. -1. -1. -1.
  1. -1. -1. -1.  1.  1. -1.  1.  1.  1. -1. -1. -1. -1. -1. -1. -1.  1.
  1. -1.  1. -1.  1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.
  1. -1. -1. -1. -1. -1.  1. -1. -1. -1. -1. -1.  1. -1. -1. -1.  1. -1.
 -1. -1. -1. -1. -1.  1. -1. -1. -1. -1.  1. -1. -1. -1. -1. -1. -1. -1.
 -1. -1.  1.  1. -1. -1.  1. -1. -1. -1. -1. -1.  1. -1. -1. -1. -1. -1.
 -1. -1. -1. -1.  1.  1.  1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.
  1. -1. -1. -1.  1. -1. -1. -1.  1.  1.  1.  1. -1. -1. -1.  1. -1. -1.
 -1. -1. -1. -1. -1. -1. -1. -1. -1.  1. -1. -1. -1.  1. -1.  1.  1.  1.
 -1. -1. -1. -1. -1.  1.  1. -1. -1. -1. -1. -1.  1.  1. -1.  1. -1. -1.
 -1. -1. -1. -1. -1. -1. -1. -1.  1.  1. -1.  1. -1. -1.  1. -1. -1.  1.
 -1. -1. -1. -1.  1.  1. -1.  1. -1. -1. -1.  1.  1. -1.  1.  1. -1. -1.
 -1.  1.  1.  1.  1. -1. -1. -1. -1.  1. -1.  1. -1.  1. -1. -1. -1. -1.
 -1. -1. -1. -1. -1. -1.  1.  1.  1.  1. -1. -1. -1. -1.  1.  1. -1.  1.
  1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.  1. -1.  1. -1. -1.  1. -1.
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0.22526041666666666

data1和data2的合页损失值随着迭代次数的变化曲线分别如下两图所示，可以发现随着迭代次数增大，合页损失值在不断下降。

数据集

data1.csv

由于data1.csv文件量比较大，所以放在了百度网盘里，需要测试的可以提取。
链接：https://pan.baidu.com/s/1Wpgnl18oEMo8M0gBn0fbVA
提取码：9z2s

data2.csv

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