统计学习方法读书笔记10-决策树

文章目录

1.信息增益1.信息熵2.条件熵3.信息增益 2. 信息增益比3.决策树的构建1.ID3算法2.C4.5算法 4.决策树的剪枝5.CART算法6.ID3决策树的创建

1.信息增益

1.信息熵

熵 交叉熵 KL散度

均匀分布时，熵最大，不确定性最大

2.条件熵

P73

3.信息增益

信息增益的概念:表示得知特征X的信息而使得类Y的信息的不确定性减少的程度，倾向与选择取值较多的特征

2. 信息增益比

3.决策树的构建

1.ID3算法

2.C4.5算法

为什么使用信息增益比？ 答：信息增益会导致节点倾向于选取取值较多的特征的问题 另一种答案是知乎上面-大数问题导致的概率是否准确

4.决策树的剪枝

过拟合原因: 1.train太久，early stop 2.模型的复杂度高于数据的复杂度 一种可以降低模型的复杂度，通过减少网络层数 一种可以通过决策树剪枝

5.CART算法

P80~87

6.ID3决策树的创建

#!usr/bin/env python # -*- coding:utf-8 _*- """ @author: liujie @software: PyCharm @file: ID3-DecisionTree.py @time: 2020/10/22 20:47 """ # ID3决策树的创建(未剪枝) import time import numpy as np from tqdm import tqdm def loaddata(filename): """ # 加载mnist数据集 :param filename:文件路径 :return: 返回数据与标签 """ # 存放数据与标签 dataArr = [] labelArr = [] # 打开文件 fr = open(filename) # 遍历文件每一行 for line in tqdm(fr.readlines()): # 对当前行进行处理，并将切割后的字段放到列表中 curLine = line.strip().split(',') # 将每行中除标记外的数据放入数据集中，同时，将字符串类型转换成整型，并进行二值化处理，方便后续运算 dataArr.append([int(int(num) > 128) for num in curLine[1:]]) # 将每行的标签放入数据集中 labelArr.append(int(curLine[0])) # 返回数据与标签 return dataArr, labelArr def majorClass(labelArr): """ 找到当前标签集中占数目最大的标签集 :param labelArr: 标签集 :return: 数目最大的标签 """ # 建立字典，用于不同类别的标签计数 classDict = {} # 遍历所有标签 for i in range(len(labelArr)): # 当这个标签第一次出现时，直接加1是错误的，所以需要判断 if labelArr[i] in classDict.keys(): # 字典中存在该标签，直接加1 classDict[labelArr[i]] += 1 else: # 若字典中不存在该标签，则创建该标签，并设为1 classDict[labelArr[i]] = 1 # 对字典的value进行降值排序 classSort = sorted(classDict.items(), key=lambda x: x[1], reverse=True) # 返回占数最多的标签 return classSort[0][0] def calc_H_D(trainLabelArr): """ 计算数据集的经验熵 :param trainLabelArr: 训练集的标签 :return: 返回经验熵 """ # 初始化H_D H_D = 0 # 利用set得到标签集中不重复的标签(类别) trainLabelSet = set([label for label in trainLabelArr]) # 遍历每一个类别 for i in trainLabelSet: # trainLabelArr[trainLabelArr == i].size：获得为指定标签的样本的大小，即标签为i的样本 # 数量，就是|Ck| # trainLabelArr.size：整个标签集的数量（也就是样本集的数量），即|D| p = (trainLabelArr[trainLabelArr == i].size) / (trainLabelArr.size) # 对经验熵的每一项进行累加求和 H_D += (-1 * p * np.log2(p)) # 返回经验熵 return H_D def calcH_D_A(trainDataArr_DevideByFeature, trainLabelArr): """ 计算经验条件熵 :param trainDataArr_DevideByFeature: 切割后只有feature那列的数组 :param trainLabelArr: 训练标签集 :return: 经验条件熵 """ # 初始化为0 H_D_A = 0 # 将feature那列放入集合中，是为了知道feature那列可供取值的值有哪些 trainDataSet = set([label for label in trainDataArr_DevideByFeature]) # 对于每一个特征取值，遍历计算条件经验熵的每一项 for i in trainDataSet: # 计算H(D/A) H_D_A += trainDataArr_DevideByFeature[ trainDataArr_DevideByFeature == i].size / trainDataArr_DevideByFeature.size * calc_H_D( trainLabelArr[trainDataArr_DevideByFeature == i]) # 返回条件经验熵 return H_D_A def calcBestFeature(trainDataList, trainLabelList): """ 计算信息增益最大的特征 :param trainDataList: 训练数据 :param trainLabelList: 训练数据标签 :return: 返回信息增益最大的特征以及最大信息增益值 """ # 将数据集与标签集转换为数组形式 trainDataArr = np.array(trainDataList) trainLabelArr = np.array(trainLabelList) # 获取当前特征的数目，也就是横轴大小 featureNum = trainDataArr.shape[1] # 初始化最大信息增益 maxG_D_A = -1 # 初始化最大信息增益的特征 maxFeature = -1 # “5.2.2 信息增益”中“算法5.1（信息增益的算法） # 第一步:计算数据集D的经验熵H(D) H_D = calc_H_D(trainLabelArr) # 对每一个特征进行遍历计算 for feature in range(featureNum): # 2.计算条件经验熵H(D|A) # 由于条件经验熵的计算过程中只涉及到标签以及当前特征，为了提高运算速度（全部样本做成的矩阵运算速度太慢，需要剔除不需要的部分） # 将数据集矩阵进行切割 # trainDataArr[:, feature]:在数据集中切割下这么一条 # trainDataArr[:, feature].flat：将这么一条转换成竖着的列表 # np.array(trainDataArr[:, feature].flat)：再转换成一条竖着的矩阵， trainDataArr_DevideByFeature = np.array(trainDataArr[:, feature].flat) # 3.计算信息增益G(D|A) G(D|A) = H(D) - H(D | A) G_D_A = H_D - calcH_D_A(trainDataArr_DevideByFeature, trainLabelArr) # 不断更新信息增益与最大特征 if G_D_A > maxG_D_A: maxG_D_A = G_D_A maxFeature = feature # 返回信息增益最大特征及最大信息增益值 return maxFeature, maxG_D_A def getSubDataArr(trainDataArr, trainLabelArr, A, a): """ 不断更新数据集与标签集 :param trainDataArr: 要更新的数据集 :param trainLabelArr: 要更新的标签集 :param A: 要去除的特征索引 :param a: 当data[A]== a时，说明该行样本时要保留的 :return: 返回新的数据集与标签集 """ # 返回的数据集 retDataArr = [] # 返回的标签集 retLabelArr = [] # 对当前数据的每一个样本进行遍历 for i in range(len(trainDataArr)): # 如果当前样本的特征为指定特征值a if trainDataArr[i][A] == a: # 那么将该样本的第A个特征切割掉，放入返回的数据集中 retDataArr.append(trainDataArr[i][0:A] + trainDataArr[i][A + 1:]) # 将该样本的标签放入返回标签集中 retLabelArr.append(trainLabelArr[i]) # 返回新的数据集和标签集 return retDataArr, retLabelArr # 掌握递归思想 def createTree(*dataSet): """ 递归创建决策树 :param dataSet: (trainDataList,trainLabelList) => 元祖形式 :return: 新的子节点或该叶子节点的值 """ # 设置Epsilon，“5.3.1ID3算法”第4步提到需要将信息增益与阈值Epsilon比较，若小于则直接处理后返回T Epsilon = 0.1 # 从参数中获取trainDataList和trainLabelList # 之所以使用元祖作为参数，是由于后续递归调用时直数据集需要对某个特征进行切割，在函数递归 # 调用上直接将切割函数的返回值放入递归调用中，而函数的返回值形式是元祖的 trainDataList = dataSet[0][0] trainLabelList = dataSet[0][1] # 打印信息：开始一个子节点创建，打印当前特征向量数目及当前剩余样本数目 # print('----', type(trainDataList[0]), type(trainLabelList)) print('start a node', len(trainDataList[0]), len(trainLabelList)) # 将标签放入一个字典中，当前样本有多少类，在字典中就有多少类,相当于去重 classDict = {i for i in trainLabelList} # 如果D中所有实例属于同一类Ck，则置T为单节点数，并将Ck作为该节点的类，返回T if len(classDict) == 1: # 因为所有样本都属于同一类，因此在标签集中随便拿一个标签返回就行 return trainLabelList[0] # 如果A为空集，则置T为单节点树，并将D中实例数最大的类Ck作为该节点的类，返回T # 即已经没有特征可以用来划分，就返回占大多数的类别 if len(trainDataList[0]) == 0: # 返回当前标签集中占数目最大的标签 return majorClass(trainLabelList) # 否则，按式5.10计算A中各特征值的信息增益，选择信息增益最大的特征Ag Ag, EpsilonGet = calcBestFeature(trainDataList, trainLabelList) # 如果Ag的信息增益小于阈值Epsilon,则置T为单节点树，并将D中实例数最大的类Ck作为该节点的类，返回T if EpsilonGet < Epsilon: return majorClass(trainLabelList) # 否则，对Ag的每一可能值ai，依Ag=ai将D分割为若干非空子集Di，将Di中实例数最大的类作为标记，构建子节点，由节点及其子节点构成树T，返回T treeDict = {Ag: {}} # 特征为0时进入0分支,特征值为1时进入1分支 # getSubDataArr(trainDataList, trainLabelList, Ag, 0)：在当前数据集中切割当前feature，返回新的数据集和标签集 treeDict[Ag][0] = createTree(getSubDataArr(trainDataList, trainLabelList, Ag, 0)) treeDict[Ag][1] = createTree(getSubDataArr(trainDataList, trainLabelList, Ag, 1)) # 返回决策树 return treeDict def predict(testDataList, tree): """ 预测标签 :param testDataList: 测试数据集 :param tree: 树 :return: 返回预测结果 """ # 死循环，直到找到一个有效的分类 while True: # 使用下行这种方式读取key和value (key, value), = tree.items() # 如果当前的value是字典，说明还需要遍历下去 if type(tree[key]).__name__ == 'dict': # 获取目前所在节点的feature值，需要在样本中删除该feature # 因为在创建树的过程中，feature的索引值永远是对于当时剩余的feature来设置的 # 所以需要不断地删除已经用掉的特征，保证索引相对位置的一致性 dataVal = testDataList[key] del testDataList[key] # 将tree更新为其子节点的字典 tree = value[dataVal] # 如果当前节点的子节点的值是int，就直接返回该int值 # 例如{403: {0: 7, 1: {297:7}}，dataVal=0 # 此时上一行tree = value[dataVal]，将tree定位到了7，而7不再是一个字典了， # 这里就可以直接返回7了，如果tree = value[1]，那就是一个新的子节点，需要继续遍历下去 if type(tree).__name__ == 'int': # 返回该节点值，也就是分类值 return tree else: # 如果当前value不是字典，那就返回分类值 return value def model_test(testDataList, testLabelList, tree): """ 测试准确率 :param testDataList: 测试数据集 :param testLabelList: 测试标签集 :param tree: 训练生成的树 :return: 返回准确率 """ # 错误次数计数 errorCnt = 0 # 遍历测试集中每一个测试样本 for i in tqdm(range(len(testDataList))): # 判断预测与标签中结果是否一致 if testLabelList[i] != predict(testDataList[i], tree): errorCnt += 1 # 返回准确率 return 1 - errorCnt / len(testDataList) if __name__ == '__main__': start = time.time() # 获取训练集与测试集 trainDataList, trainLabelList = loaddata('data/mnist_train.csv') testDataList, testLabelList = loaddata('data/mnist_test.csv') # 创建决策树 print('start to create tree') tree = createTree((trainDataList, trainLabelList)) print('tree is', tree) # 测试准确率 print('start to test') accur = model_test(testDataList, testLabelList, tree) print('the accur is:', accur) # 结束时间 end = time.time() print('time span:', end - start) tree is {378: {0: {567: {0: {541: {0: {458: {0: {403: {0: {590: {0: {483: {0: {154: {0: {429: {0: 7, 1: {209: {0: {265: {0: {237: {0: {181: {0: {317: {0: {542: {0: {607: {0: 4, 1: {99: {0: 5, 1: 2}}}}, 1: {202: {0: 9, 1: 3}}}}, 1: {261: {0: 5, 1: {158: {0: 9, 1: 8}}}}}}, 1: {480: {0: {155: {0: 9, 1: 3}}, 1: {121: {0: {153: {0: 4, 1: 8}}, 1: 2}}}}}}, 1: {403: {0: {286: {0: {209: {0: 2, 1: 4}}, 1: 5}}, 1: {401: {0: {185: {0: 4, 1: 9}}, 1: {231: {0: 9, 1: 3}}}}}}}}, 1: {403: {0: {204: {0: {98: {0: 5, 1: 2}}, 1: 7}}, 1: {398: {0: {644: {0: {295: {0: {233: {0: 7, 1: 3}}, 1: 7}}, 1: {204: {0: 9, 1: {174: {0: 7, 1: 2}}}}}}, 1: {263: {0: 4, 1: {405: {0: 9, 1: 5}}}}}}}}}}, 1: {404: {0: {562: {0: {431: {0: {268: {0: 5, 1: {177: {0: 9, 1: 3}}}}, 1: {345: {0: {426: {0: {234: {0: 9, 1: 8}}, 1: 9}}, 1: {178: {0: 3, 1: 5}}}}}}, 1: {296: {0: {218: {0: 2, 1: 4}}, 1: 8}}}}, 1: {426: {0: {372: {0: {232: {0: 3, 1: {181: {0: 7, 1: 3}}}}, 1: {103: {0: {175: {0: 9, 1: 8}}, 1: 6}}}}, 1: {177: {0: {289: {0: 9, 1: {400: {0: {207: {0: 4, 1: {159: {0: 9, 1: 4}}}}, 1: 9}}}}, 1: {619: {0: {178: {0: 7, 1: 9}}, 1: 3}}}}}}}}}}}}, 1: {512: {0: {508: {0: {512: {0: {321: {0: {478: {0: {481: {0: {642: {0: {183: {0: {613: {0: {375: {0: 4, 1: {154: {0: 1, 1: 4}}}}, 1: {123: {0: 5, 1: {92: {0: 0, 1: 2}}}}}}, 1: {209: {0: {152: {0: 5, 1: 9}}, 1: {211: {0: 3, 1: 7}}}}}}, 1: {560: {0: {239: {0: {240: {0: {587: {0: 5, 1: {375: {0: {204: {0: 5, 1: 9}}, 1: {181: {0: 5, 1: 3}}}}}}, 1: {123: {0: 3, 1: 0}}}}, 1: {157: {0: 3, 1: 5}}}}, 1: {128: {0: 2, 1: 5}}}}}}, 1: {458: {0: {127: {0: 3, 1: 2}}, 1: 8}}}}, 1: {98: {0: 0, 1: 6}}}}, 1: {266: {0: {267: {0: {237: {0: {456: {0: 5, 1: {124: {0: 9, 1: 3}}}}, 1: {369: {0: {126: {0: 3, 1: 1}}, 1: {154: {0: 3, 1: 5}}}}}}, 1: {238: {0: 3, 1: 9}}}}, 1: {402: {0: {286: {0: 3, 1: 9}}, 1: 9}}}}}}, 1: {350: {0: {587: {0: {639: {0: {211: {0: {290: {0: 9, 1: {154: {0: 4, 1: 5}}}}, 1: {615: {0: {177: {0: 8, 1: 3}}, 1: {154: {0: 9, 1: {175: {0: 2, 1: {182: {0: 2, 1: 7}}}}}}}}}}, 1: 3}}, 1: {159: {0: {402: {0: {381: {0: 2, 1: 7}}, 1: 8}}, 1: {123: {0: {124: {0: 5, 1: 6}}, 1: 1}}}}}}, 1: {351: {0: {213: {0: {647: {0: 1, 1: 2}}, 1: 3}}, 1: {613: {0: {151: {0: 9, 1: {148: {0: 2, 1: 7}}}}, 1: 3}}}}}}}}, 1: {459: {0: {294: {0: {431: {0: 0, 1: 9}}, 1: {180: {0: 8, 1: 3}}}}, 1: {72: {0: {122: {0: 8, 1: 2}}, 1: 6}}}}}}, 1: {376: {0: {479: {0: {592: {0: {648: {0: {567: {0: {537: {0: {152: {0: {425: {0: 1, 1: {95: {0: 8, 1: 2}}}}, 1: {180: {0: 7, 1: 2}}}}, 1: {229: {0: {176: {0: 7, 1: {212: {0: 2, 1: 7}}}}, 1: 2}}}}, 1: {563: {0: {124: {0: 8, 1: 9}}, 1: 2}}}}, 1: {151: {0: {154: {0: {618: {0: {151: {0: 9, 1: 3}}, 1: 8}}, 1: {176: {0: 8, 1: 2}}}}, 1: 2}}}}, 1: {383: {0: {534: {0: {213: {0: 2, 1: {152: {0: 8, 1: 3}}}}, 1: 2}}, 1: {93: {0: 5, 1: 8}}}}}}, 1: {298: {0: 6, 1: {99: {0: 9, 1: 4}}}}}}, 1: {431: {0: {155: {0: 1, 1: 5}}, 1: 8}}}}}}}}, 1: {211: {0: {537: {0: {266: {0: {183: {0: {237: {0: {127: {0: {317: {0: {380: {0: 4, 1: {418: {0: {260: {0: 4, 1: 0}}, 1: 6}}}}, 1: {259: {0: {162: {0: 5, 1: 4}}, 1: {230: {0: 9, 1: {230: {0: 0, 1: 7}}}}}}}}, 1: {589: {0: {155: {0: 4, 1: {205: {0: 2, 1: 8}}}}, 1: {455: {0: {99: {0: 5, 1: 0}}, 1: 6}}}}}}, 1: {350: {0: {132: {0: 7, 1: 4}}, 1: 9}}}}, 1: {206: {0: {210: {0: {266: {0: {454: {0: {374: {0: 2, 1: {99: {0: 4, 1: 6}}}}, 1: 4}}, 1: {156: {0: {100: {0: 9, 1: 2}}, 1: 0}}}}, 1: {153: {0: {156: {0: 9, 1: 8}}, 1: {122: {0: 5, 1: 2}}}}}}, 1: {186: {0: 9, 1: {150: {0: 8, 1: 5}}}}}}}}, 1: {487: {0: {458: {0: {354: {0: 5, 1: {154: {0: {199: {0: 0, 1: 7}}, 1: 2}}}}, 1: {264: {0: {104: {0: {160: {0: 3, 1: 4}}, 1: 6}}, 1: {180: {0: {236: {0: 0, 1: 9}}, 1: 7}}}}}}, 1: {211: {0: {439: {0: {537: {0: {260: {0: {160: {0: 9, 1: 4}}, 1: {311: {0: 7, 1: 9}}}}, 1: 7}}, 1: 2}}, 1: {297: {0: 4, 1: 9}}}}}}}}, 1: {269: {0: {244: {0: {293: {0: {245: {0: 6, 1: 4}}, 1: {121: {0: {149: {0: 9, 1: 4}}, 1: 8}}}}, 1: 4}}, 1: {291: {0: {183: {0: {236: {0: {323: {0: 4, 1: 6}}, 1: {175: {0: 0, 1: 9}}}}, 1: {121: {0: 9, 1: 2}}}}, 1: {376: {0: 5, 1: {104: {0: 7, 1: 4}}}}}}}}}}, 1: {407: {0: {378: {0: {432: {0: {448: {0: {433: {0: {515: {0: {378: {0: 5, 1: 9}}, 1: 2}}, 1: {178: {0: 0, 1: {152: {0: 2, 1: 9}}}}}}, 1: {203: {0: {181: {0: 4, 1: 9}}, 1: 0}}}}, 1: {564: {0: {187: {0: 9, 1: 7}}, 1: {211: {0: {101: {0: 8, 1: 6}}, 1: 7}}}}}}, 1: {230: {0: {156: {0: {532: {0: {207: {0: {457: {0: {154: {0: {505: {0: 9, 1: {314: {0: {239: {0: 7, 1: 4}}, 1: 9}}}}, 1: 4}}, 1: {283: {0: 4, 1: {178: {0: 7, 1: 9}}}}}}, 1: {181: {0: {261: {0: 7, 1: 9}}, 1: {500: {0: 9, 1: 2}}}}}}, 1: 2}}, 1: {158: {0: 4, 1: 3}}}}, 1: {211: {0: 3, 1: 7}}}}}}, 1: {589: {0: {346: {0: {230: {0: 9, 1: {312: {0: 7, 1: 9}}}}, 1: {462: {0: {128: {0: {322: {0: 9, 1: 4}}, 1: {71: {0: 4, 1: 6}}}}, 1: {351: {0: {100: {0: 9, 1: 6}}, 1: 4}}}}}}, 1: {373: {0: {381: {0: 2, 1: {180: {0: 8, 1: 7}}}}, 1: {431: {0: 0, 1: {103: {0: 9, 1: 6}}}}}}}}}}}}}}, 1: {425: {0: {322: {0: {458: {0: {481: {0: {384: {0: {451: {0: {395: {0: {151: {0: {324: {0: {324: {0: 5, 1: {149: {0: 0, 1: 3}}}}, 1: {210: {0: {94: {0: 5, 1: 2}}, 1: 3}}}}, 1: {355: {0: 3, 1: 2}}}}, 1: {203: {0: 0, 1: 2}}}}, 1: 0}}, 1: 0}}, 1: {191: {0: {276: {0: 2, 1: 5}}, 1: {245: {0: 5, 1: 8}}}}}}, 1: {537: {0: {404: {0: {433: {0: {124: {0: {481: {0: 5, 1: 6}}, 1: 2}}, 1: {263: {0: 2, 1: {154: {0: {133: {0: 2, 1: 1}}, 1: 3}}}}}}, 1: {268: {0: {535: {0: 3, 1: 1}}, 1: {504: {0: 1, 1: 2}}}}}}, 1: {266: {0: {644: {0: 2, 1: 3}}, 1: {131: {0: 7, 1: {131: {0: 1, 1: 0}}}}}}}}}}, 1: {317: {0: {424: {0: {268: {0: {269: {0: {149: {0: {321: {0: {245: {0: 5, 1: 0}}, 1: {289: {0: 3, 1: {637: {0: 5, 1: {128: {0: 3, 1: 5}}}}}}}}, 1: {234: {0: 3, 1: 5}}}}, 1: {583: {0: {123: {0: {151: {0: 5, 1: 9}}, 1: 3}}, 1: 3}}}}, 1: {219: {0: {419: {0: 3, 1: {96: {0: 0, 1: 3}}}}, 1: 5}}}}, 1: {590: {0: {124: {0: {151: {0: 5, 1: 3}}, 1: 2}}, 1: {107: {0: 0, 1: 6}}}}}}, 1: {301: {0: {125: {0: {242: {0: 5, 1: {157: {0: 5, 1: {155: {0: 1, 1: 3}}}}}}, 1: {260: {0: {133: {0: 3, 1: 5}}, 1: 5}}}}, 1: 0}}}}}}, 1: {512: {0: 0, 1: {103: {0: 2, 1: 6}}}}}}}}, 1: {380: {0: {408: {0: {352: {0: {349: {0: {378: {0: {321: {0: 5, 1: {153: {0: {179: {0: {132: {0: {455: {0: 5, 1: {204: {0: {133: {0: 5, 1: 0}}, 1: 3}}}}, 1: {159: {0: 8, 1: 0}}}}, 1: {233: {0: 3, 1: {180: {0: 5, 1: 8}}}}}}, 1: {235: {0: 3, 1: 5}}}}}}, 1: {647: {0: {318: {0: {260: {0: 2, 1: 4}}, 1: {153: {0: 4, 1: 9}}}}, 1: {183: {0: {209: {0: {123: {0: 4, 1: 3}}, 1: 9}}, 1: {238: {0: 8, 1: 5}}}}}}}}, 1: {179: {0: {319: {0: {507: {0: {188: {0: {244: {0: {529: {0: 3, 1: 6}}, 1: {184: {0: 5, 1: 0}}}}, 1: 5}}, 1: {182: {0: {204: {0: 5, 1: 2}}, 1: {645: {0: 6, 1: 1}}}}}}, 1: {475: {0: {507: {0: {292: {0: {370: {0: {205: {0: 8, 1: 5}}, 1: 5}}, 1: {484: {0: 5, 1: {291: {0: {159: {0: 3, 1: 0}}, 1: 5}}}}}}, 1: {510: {0: {180: {0: {645: {0: 5, 1: 1}}, 1: {99: {0: 1, 1: 4}}}}, 1: 6}}}}, 1: {245: {0: 2, 1: 0}}}}}}, 1: {535: {0: {263: {0: {353: {0: 3, 1: {150: {0: 5, 1: 0}}}}, 1: {209: {0: {155: {0: 1, 1: 8}}, 1: {152: {0: 5, 1: 3}}}}}}, 1: {153: {0: {171: {0: 2, 1: 3}}, 1: {69: {0: 8, 1: 6}}}}}}}}}}, 1: {350: {0: {482: {0: {569: {0: {209: {0: {402: {0: {268: {0: {150: {0: 2, 1: 3}}, 1: {125: {0: 4, 1: 8}}}}, 1: {69: {0: {269: {0: {696: {0: 4, 1: 9}}, 1: 7}}, 1: 2}}}}, 1: {177: {0: {290: {0: {183: {0: 9, 1: 8}}, 1: {210: {0: 4, 1: 9}}}}, 1: {231: {0: 3, 1: 8}}}}}}, 1: {150: {0: {225: {0: 8, 1: 3}}, 1: 3}}}}, 1: {431: {0: {404: {0: {668: {0: 8, 1: 9}}, 1: {160: {0: 7, 1: 4}}}}, 1: {183: {0: 4, 1: {121: {0: 9, 1: 2}}}}}}}}, 1: {377: {0: {328: {0: 3, 1: {199: {0: 5, 1: 3}}}}, 1: {590: {0: {156: {0: 9, 1: 8}}, 1: {127: {0: {158: {0: 1, 1: 5}}, 1: 6}}}}}}}}}}, 1: {588: {0: {154: {0: {209: {0: {236: {0: {559: {0: 4, 1: 8}}, 1: {420: {0: {431: {0: {256: {0: 4, 1: {264: {0: 8, 1: 3}}}}, 1: 9}}, 1: {218: {0: 4, 1: 7}}}}}}, 1: {379: {0: {319: {0: {321: {0: {179: {0: {156: {0: 9, 1: 2}}, 1: 5}}, 1: {202: {0: 4, 1: 7}}}}, 1: 3}}, 1: {535: {0: {317: {0: {430: {0: 5, 1: 9}}, 1: {211: {0: 4, 1: 9}}}}, 1: {325: {0: 8, 1: {122: {0: 9, 1: 2}}}}}}}}}}, 1: {458: {0: {320: {0: {179: {0: 8, 1: 5}}, 1: {130: {0: 3, 1: 5}}}}, 1: {424: {0: {246: {0: 8, 1: 4}}, 1: 2}}}}}}, 1: {347: {0: {559: {0: {516: {0: {157: {0: 8, 1: 9}}, 1: 2}}, 1: 2}}, 1: {328: {0: {210: {0: 3, 1: 5}}, 1: {179: {0: 0, 1: 2}}}}}}}}}}, 1: {211: {0: {155: {0: {237: {0: {182: {0: 4, 1: {482: {0: {258: {0: {208: {0: 3, 1: 9}}, 1: 9}}, 1: {395: {0: 8, 1: {178: {0: 7, 1: 4}}}}}}}}, 1: {234: {0: {212: {0: {207: {0: {104: {0: 4, 1: 2}}, 1: {204: {0: 3, 1: 9}}}}, 1: {185: {0: {316: {0: 9, 1: 4}}, 1: {258: {0: 4, 1: 9}}}}}}, 1: {510: {0: {437: {0: 9, 1: 2}}, 1: {341: {0: 7, 1: {422: {0: 8, 1: 9}}}}}}}}}}, 1: {483: {0: {452: {0: {232: {0: {152: {0: {374: {0: 4, 1: {97: {0: 9, 1: 3}}}}, 1: {206: {0: 3, 1: 5}}}}, 1: {401: {0: {205: {0: 8, 1: 5}}, 1: {260: {0: 9, 1: 5}}}}}}, 1: {588: {0: {155: {0: 4, 1: 8}}, 1: 2}}}}, 1: {102: {0: 8, 1: 2}}}}}}, 1: {484: {0: {235: {0: {423: {0: {152: {0: {615: {0: {455: {0: {148: {0: 9, 1: 5}}, 1: {615: {0: {209: {0: {698: {0: 4, 1: 9}}, 1: {290: {0: {423: {0: 8, 1: 9}}, 1: 4}}}}, 1: {187: {0: 9, 1: 8}}}}}}, 1: {481: {0: {557: {0: 3, 1: 5}}, 1: {129: {0: 9, 1: 8}}}}}}, 1: {370: {0: {449: {0: 3, 1: 2}}, 1: {238: {0: 9, 1: 8}}}}}}, 1: {457: {0: {147: {0: 3, 1: {94: {0: 5, 1: 2}}}}, 1: {701: {0: {150: {0: 4, 1: 2}}, 1: {182: {0: 9, 1: 4}}}}}}}}, 1: {614: {0: {624: {0: 9, 1: {675: {0: {317: {0: {341: {0: 4, 1: 9}}, 1: 4}}, 1: {258: {0: 5, 1: 8}}}}}}, 1: {128: {0: 3, 1: 2}}}}}}, 1: {651: {0: {212: {0: {455: {0: {397: {0: {181: {0: 9, 1: 7}}, 1: {177: {0: 4, 1: 2}}}}, 1: {157: {0: {179: {0: 4, 1: 8}}, 1: {156: {0: 2, 1: 8}}}}}}, 1: {207: {0: {670: {0: {182: {0: {399: {0: 8, 1: {186: {0: 9, 1: 8}}}}, 1: 9}}, 1: {351: {0: {208: {0: 9, 1: 7}}, 1: 9}}}}, 1: {404: {0: 8, 1: 7}}}}}}, 1: 8}}}}}}}}}}, 1: {211: {0: {266: {0: {539: {0: {155: {0: 4, 1: {534: {0: {617: {0: {184: {0: {561: {0: {156: {0: {209: {0: {178: {0: {216: {0: {449: {0: {229: {0: 6, 1: 4}}, 1: 4}}, 1: 5}}, 1: {155: {0: {125: {0: 9, 1: 4}}, 1: {127: {0: 6, 1: 8}}}}}}, 1: 9}}, 1: {212: {0: 5, 1: {154: {0: 9, 1: 3}}}}}}, 1: 6}}, 1: {128: {0: {321: {0: {317: {0: {239: {0: {238: {0: 5, 1: 9}}, 1: {121: {0: 9, 1: {145: {0: 3, 1: 2}}}}}}, 1: {226: {0: 3, 1: 8}}}}, 1: {638: {0: {535: {0: 9, 1: {178: {0: {155: {0: 7, 1: 9}}, 1: 8}}}}, 1: {121: {0: 3, 1: 2}}}}}}, 1: {488: {0: {181: {0: 0, 1: 8}}, 1: {126: {0: 4, 1: 6}}}}}}}}, 1: {287: {0: {647: {0: {370: {0: {666: {0: 2, 1: 3}}, 1: 3}}, 1: {128: {0: 5, 1: 3}}}}, 1: {510: {0: {423: {0: 5, 1: {159: {0: 9, 1: 5}}}}, 1: {152: {0: 2, 1: 8}}}}}}}}, 1: {680: {0: {265: {0: {288: {0: 2, 1: 8}}, 1: 4}}, 1: 8}}}}}}, 1: {620: {0: {590: {0: {296: {0: {271: {0: 6, 1: {205: {0: 4, 1: 8}}}}, 1: {155: {0: {404: {0: {214: {0: {271: {0: 6, 1: 5}}, 1: 4}}, 1: 4}}, 1: {593: {0: {128: {0: 8, 1: 4}}, 1: {125: {0: 0, 1: 2}}}}}}}}, 1: {515: {0: {181: {0: {377: {0: 5, 1: {185: {0: 4, 1: 9}}}}, 1: {179: {0: 2, 1: 8}}}}, 1: {647: {0: {292: {0: 2, 1: 8}}, 1: 8}}}}}}, 1: {156: {0: {485: {0: {374: {0: {98: {0: 5, 1: 2}}, 1: {154: {0: 8, 1: 1}}}}, 1: {210: {0: 4, 1: 9}}}}, 1: {617: {0: {184: {0: {100: {0: {152: {0: 4, 1: 7}}, 1: 6}}, 1: 8}}, 1: {315: {0: 2, 1: {123: {0: 6, 1: 5}}}}}}}}}}}}, 1: {406: {0: {377: {0: {434: {0: {290: {0: {269: {0: {346: {0: {185: {0: {444: {0: {132: {0: 5, 1: 6}}, 1: 2}}, 1: {104: {0: 3, 1: 6}}}}, 1: {188: {0: 3, 1: 8}}}}, 1: 5}}, 1: {490: {0: 5, 1: {202: {0: {179: {0: 9, 1: 0}}, 1: {190: {0: 2, 1: 5}}}}}}}}, 1: {398: {0: {340: {0: {235: {0: 2, 1: {231: {0: 9, 1: 7}}}}, 1: {404: {0: {213: {0: {216: {0: 9, 1: 5}}, 1: 4}}, 1: 9}}}}, 1: {285: {0: {425: {0: 0, 1: 4}}, 1: {297: {0: {176: {0: {186: {0: 3, 1: 8}}, 1: 5}}, 1: 7}}}}}}}}, 1: {484: {0: {373: {0: {480: {0: {147: {0: 9, 1: 3}}, 1: {178: {0: {182: {0: 2, 1: 4}}, 1: 9}}}}, 1: {215: {0: {130: {0: 4, 1: 3}}, 1: 8}}}}, 1: {397: {0: {265: {0: {154: {0: 4, 1: 9}}, 1: {400: {0: 7, 1: {294: {0: 2, 1: {177: {0: 9, 1: 7}}}}}}}}, 1: {297: {0: {206: {0: 4, 1: 9}}, 1: {160: {0: 9, 1: 2}}}}}}}}}}, 1: {397: {0: {258: {0: {504: {0: {297: {0: {263: {0: {482: {0: {177: {0: 9, 1: 7}}, 1: {293: {0: {374: {0: 4, 1: {264: {0: 4, 1: 9}}}}, 1: {215: {0: 4, 1: 7}}}}}}, 1: {613: {0: {368: {0: {365: {0: {153: {0: {210: {0: 7, 1: 4}}, 1: 4}}, 1: 9}}, 1: {456: {0: 9, 1: {265: {0: {237: {0: 7, 1: 5}}, 1: 4}}}}}}, 1: 5}}}}, 1: {163: {0: {591: {0: {284: {0: 9, 1: {236: {0: 7, 1: 9}}}}, 1: {210: {0: {154: {0: 7, 1: 8}}, 1: {212: {0: 9, 1: 3}}}}}}, 1: {161: {0: 4, 1: 8}}}}}}, 1: {347: {0: {313: {0: {161: {0: 2, 1: 8}}, 1: 9}}, 1: 4}}}}, 1: {545: {0: {394: {0: {394: {0: 7, 1: 9}}, 1: 9}}, 1: {238: {0: 2, 1: 3}}}}}}, 1: {236: {0: {353: {0: {396: {0: {457: {0: {205: {0: 9, 1: {128: {0: 4, 1: 3}}}}, 1: {271: {0: 4, 1: 9}}}}, 1: {180: {0: {381: {0: 4, 1: {211: {0: 2, 1: 4}}}}, 1: {154: {0: 9, 1: 8}}}}}}, 1: {274: {0: 9, 1: 8}}}}, 1: {218: {0: {434: {0: {615: {0: 9, 1: 8}}, 1: {514: {0: {181: {0: 7, 1: 4}}, 1: 9}}}}, 1: {238: {0: 4, 1: {213: {0: 5, 1: 8}}}}}}}}}}}}}}, 1: {379: {0: {539: {0: {380: {0: {351: {0: {216: {0: {320: {0: {534: {0: {642: {0: {343: {0: {371: {0: {585: {0: {429: {0: {399: {0: {264: {0: 5, 1: {243: {0: 9, 1: 5}}}}, 1: 9}}, 1: {158: {0: 9, 1: 5}}}}, 1: {206: {0: 2, 1: 9}}}}, 1: {205: {0: {531: {0: 5, 1: 1}}, 1: {151: {0: {178: {0: 7, 1: 9}}, 1: 2}}}}}}, 1: {510: {0: {394: {0: {641: {0: 9, 1: {155: {0: 4, 1: 5}}}}, 1: {101: {0: {208: {0: {211: {0: 9, 1: 5}}, 1: 5}}, 1: 6}}}}, 1: {455: {0: {288: {0: 4, 1: 5}}, 1: {155: {0: {269: {0: 9, 1: 8}}, 1: {152: {0: 4, 1: 9}}}}}}}}}}, 1: {149: {0: 5, 1: {175: {0: 5, 1: 3}}}}}}, 1: {126: {0: 6, 1: 0}}}}, 1: {206: {0: {264: {0: 3, 1: {616: {0: {151: {0: {484: {0: 4, 1: 2}}, 1: 8}}, 1: {558: {0: {671: {0: 5, 1: 9}}, 1: {103: {0: 0, 1: 6}}}}}}}}, 1: {508: {0: 3, 1: {512: {0: {178: {0: 5, 1: 3}}, 1: 2}}}}}}}}, 1: {355: {0: 5, 1: {158: {0: {187: {0: 2, 1: {159: {0: 9, 1: 4}}}}, 1: 0}}}}}}, 1: {371: {0: {209: {0: {293: {0: {429: {0: {185: {0: 2, 1: 9}}, 1: {207: {0: 7, 1: 3}}}}, 1: {450: {0: {93: {0: 7, 1: 2}}, 1: {240: {0: 4, 1: 9}}}}}}, 1: {536: {0: {518: {0: {261: {0: {397: {0: {209: {0: 9, 1: 7}}, 1: 3}}, 1: {616: {0: 9, 1: {207: {0: 9, 1: 3}}}}}}, 1: {149: {0: 2, 1: 8}}}}, 1: {428: {0: 3, 1: {98: {0: 7, 1: 1}}}}}}}}, 1: {430: {0: {266: {0: {185: {0: 2, 1: 8}}, 1: {152: {0: 5, 1: 9}}}}, 1: {209: {0: 4, 1: {448: {0: {155: {0: 9, 1: 3}}, 1: {182: {0: 9, 1: 4}}}}}}}}}}}}, 1: {506: {0: {240: {0: {213: {0: {537: {0: {447: {0: {290: {0: 9, 1: 3}}, 1: 4}}, 1: {702: {0: {187: {0: 4, 1: 9}}, 1: 9}}}}, 1: {458: {0: {209: {0: {184: {0: 5, 1: 9}}, 1: 8}}, 1: 9}}}}, 1: {476: {0: {374: {0: 9, 1: {262: {0: {152: {0: {178: {0: 4, 1: 8}}, 1: 0}}, 1: 9}}}}, 1: {341: {0: {205: {0: {98: {0: {155: {0: 5, 1: 4}}, 1: 2}}, 1: 7}}, 1: 9}}}}}}, 1: {319: {0: {342: {0: {697: {0: 2, 1: 7}}, 1: {183: {0: 8, 1: 9}}}}, 1: {238: {0: {134: {0: 8, 1: 5}}, 1: 4}}}}}}}}, 1: {347: {0: {327: {0: {349: {0: {405: {0: {155: {0: {298: {0: {318: {0: 5, 1: 0}}, 1: 9}}, 1: {95: {0: 6, 1: 2}}}}, 1: {488: {0: {291: {0: {152: {0: 8, 1: 0}}, 1: 9}}, 1: {155: {0: {124: {0: 2, 1: 0}}, 1: 6}}}}}}, 1: {324: {0: {153: {0: {148: {0: 4, 1: 9}}, 1: 2}}, 1: {207: {0: 8, 1: {239: {0: 8, 1: 7}}}}}}}}, 1: {557: {0: {178: {0: {131: {0: 9, 1: 2}}, 1: {153: {0: 8, 1: 3}}}}, 1: 2}}}}, 1: {240: {0: {179: {0: {616: {0: {650: {0: 6, 1: {126: {0: {126: {0: 5, 1: 1}}, 1: 6}}}}, 1: {156: {0: 4, 1: {129: {0: 5, 1: 6}}}}}}, 1: {174: {0: {189: {0: 8, 1: 5}}, 1: 2}}}}, 1: {457: {0: {241: {0: {260: {0: 2, 1: 0}}, 1: 5}}, 1: {373: {0: {154: {0: {181: {0: 4, 1: 9}}, 1: 6}}, 1: 8}}}}}}}}}}, 1: {156: {0: {315: {0: {317: {0: {367: {0: {342: {0: {338: {0: {500: {0: {481: {0: {339: {0: {509: {0: {207: {0: {320: {0: {184: {0: {99: {0: 2, 1: 6}}, 1: 8}}, 1: {155: {0: 3, 1: 4}}}}, 1: {283: {0: 7, 1: 3}}}}, 1: {255: {0: 3, 1: {121: {0: 9, 1: 2}}}}}}, 1: 9}}, 1: {428: {0: {424: {0: {239: {0: 2, 1: 7}}, 1: {557: {0: 3, 1: 7}}}}, 1: {182: {0: {235: {0: {180: {0: {156: {0: 7, 1: 4}}, 1: 9}}, 1: 7}}, 1: {345: {0: {154: {0: {555: {0: {233: {0: 9, 1: 3}}, 1: {202: {0: 9, 1: 7}}}}, 1: {172: {0: 2, 1: 3}}}}, 1: {209: {0: {149: {0: 2, 1: 7}}, 1: {323: {0: 7, 1: 3}}}}}}}}}}}}, 1: {618: {0: {292: {0: 2, 1: 8}}, 1: {181: {0: 7, 1: 3}}}}}}, 1: {673: {0: 9, 1: 3}}}}, 1: {177: {0: {529: {0: 9, 1: 8}}, 1: {158: {0: {177: {0: 4, 1: 7}}, 1: 5}}}}}}, 1: {647: {0: {232: {0: {293: {0: 9, 1: {182: {0: {181: {0: 9, 1: 4}}, 1: 4}}}}, 1: 9}}, 1: {509: {0: 9, 1: {202: {0: 8, 1: {151: {0: 7, 1: 9}}}}}}}}}}, 1: {558: {0: {210: {0: {99: {0: {393: {0: {263: {0: 4, 1: {153: {0: 9, 1: {152: {0: 4, 1: 0}}}}}}, 1: 4}}, 1: 6}}, 1: {537: {0: {644: {0: {421: {0: {482: {0: 9, 1: {321: {0: 4, 1: {184: {0: 9, 1: 4}}}}}}, 1: {701: {0: {454: {0: 9, 1: 4}}, 1: {186: {0: 9, 1: 4}}}}}}, 1: {162: {0: {156: {0: 3, 1: 0}}, 1: 5}}}}, 1: {459: {0: {344: {0: {210: {0: {296: {0: {418: {0: 9, 1: 4}}, 1: 4}}, 1: 9}}, 1: {211: {0: {232: {0: 6, 1: 4}}, 1: {181: {0: 7, 1: 8}}}}}}, 1: {376: {0: 4, 1: {123: {0: 9, 1: 0}}}}}}}}}}, 1: {426: {0: 2, 1: 8}}}}}}, 1: 9}}, 1: {538: {0: {207: {0: {619: {0: {297: {0: 4, 1: {237: {0: 4, 1: {128: {0: 2, 1: 3}}}}}}, 1: {541: {0: {407: {0: {184: {0: 4, 1: 9}}, 1: 4}}, 1: {129: {0: {123: {0: {153: {0: 3, 1: 8}}, 1: 2}}, 1: {100: {0: 5, 1: 6}}}}}}}}, 1: {643: {0: {373: {0: {263: {0: {430: {0: {153: {0: {154: {0: 5, 1: 9}}, 1: 8}}, 1: {402: {0: 2, 1: 9}}}}, 1: 4}}, 1: {376: {0: {100: {0: 5, 1: 2}}, 1: 8}}}}, 1: {324: {0: {259: {0: 5, 1: {151: {0: 8, 1: 9}}}}, 1: 3}}}}}}, 1: {589: {0: {352: {0: {268: {0: 6, 1: 4}}, 1: {488: {0: {482: {0: {129: {0: 9, 1: 2}}, 1: 8}}, 1: {129: {0: 4, 1: {101: {0: 2, 1: 6}}}}}}}}, 1: {343: {0: 2, 1: {214: {0: {129: {0: 8, 1: 2}}, 1: 9}}}}}}}}}}}}}}}}, 1: {242: {0: {653: {0: {295: {0: {243: {0: {267: {0: 6, 1: {339: {0: {289: {0: {260: {0: {235: {0: 2, 1: {176: {0: 2, 1: 7}}}}, 1: {621: {0: {616: {0: {365: {0: 2, 1: 9}}, 1: 8}}, 1: 0}}}}, 1: {347: {0: 6, 1: {266: {0: 4, 1: {154: {0: 7, 1: 0}}}}}}}}, 1: {460: {0: {376: {0: {94: {0: 0, 1: 6}}, 1: 7}}, 1: 9}}}}}}, 1: {185: {0: {128: {0: {593: {0: {210: {0: {371: {0: 4, 1: {154: {0: 5, 1: 2}}}}, 1: {312: {0: {150: {0: {183: {0: 5, 1: 7}}, 1: 8}}, 1: {188: {0: 9, 1: 4}}}}}}, 1: {241: {0: {158: {0: 6, 1: {129: {0: 8, 1: 0}}}}, 1: {96: {0: 4, 1: 8}}}}}}, 1: {407: {0: {287: {0: 2, 1: {127: {0: 8, 1: 6}}}}, 1: 0}}}}, 1: {488: {0: {507: {0: {427: {0: {288: {0: {155: {0: 7, 1: 2}}, 1: {180: {0: 8, 1: 0}}}}, 1: {189: {0: 8, 1: 9}}}}, 1: {350: {0: {130: {0: 0, 1: 6}}, 1: {148: {0: 2, 1: 7}}}}}}, 1: {159: {0: {369: {0: 9, 1: {127: {0: {156: {0: 2, 1: 4}}, 1: 0}}}}, 1: {651: {0: {456: {0: {486: {0: 0, 1: 2}}, 1: 2}}, 1: {128: {0: 9, 1: 6}}}}}}}}}}}}, 1: {487: {0: {239: {0: {481: {0: {595: {0: {298: {0: {377: {0: {243: {0: {146: {0: 0, 1: 5}}, 1: {162: {0: 5, 1: 7}}}}, 1: 9}}, 1: {356: {0: 5, 1: 0}}}}, 1: {566: {0: {126: {0: 8, 1: 5}}, 1: {231: {0: 3, 1: {65: {0: 2, 1: 6}}}}}}}}, 1: {565: {0: {210: {0: 0, 1: {154: {0: 8, 1: 9}}}}, 1: {438: {0: {295: {0: {619: {0: {74: {0: 2, 1: 6}}, 1: {97: {0: 5, 1: 2}}}}, 1: {432: {0: {261: {0: 6, 1: 0}}, 1: {98: {0: 5, 1: 0}}}}}}, 1: 6}}}}}}, 1: {432: {0: {324: {0: {314: {0: {377: {0: {564: {0: 0, 1: 2}}, 1: {210: {0: 2, 1: 3}}}}, 1: {184: {0: 0, 1: 9}}}}, 1: {93: {0: {293: {0: 3, 1: 0}}, 1: 6}}}}, 1: {346: {0: {259: {0: {508: {0: 2, 1: {266: {0: 2, 1: {291: {0: 2, 1: 7}}}}}}, 1: {292: {0: 2, 1: 9}}}}, 1: {129: {0: {127: {0: 3, 1: 0}}, 1: 6}}}}}}}}, 1: {372: {0: {299: {0: {395: {0: {649: {0: 2, 1: {152: {0: 7, 1: 2}}}}, 1: {425: {0: {177: {0: 9, 1: {129: {0: 6, 1: 4}}}}, 1: 2}}}}, 1: {287: {0: {92: {0: 5, 1: 6}}, 1: {242: {0: 2, 1: 7}}}}}}, 1: {482: {0: {240: {0: {262: {0: 5, 1: 7}}, 1: {158: {0: {261: {0: 2, 1: {40: {0: 8, 1: 0}}}}, 1: {104: {0: 4, 1: 6}}}}}}, 1: {377: {0: {562: {0: 4, 1: 6}}, 1: {677: {0: {230: {0: 4, 1: 8}}, 1: 9}}}}}}}}}}}}, 1: {459: {0: {321: {0: {514: {0: {402: {0: {453: {0: {176: {0: {652: {0: {430: {0: {130: {0: 0, 1: 5}}, 1: {185: {0: 9, 1: 8}}}}, 1: 8}}, 1: {204: {0: 3, 1: {127: {0: 2, 1: 5}}}}}}, 1: 0}}, 1: {509: {0: 5, 1: {130: {0: 8, 1: 6}}}}}}, 1: {295: {0: {242: {0: {377: {0: 6, 1: {153: {0: 4, 1: {121: {0: 6, 1: 2}}}}}}, 1: {561: {0: {185: {0: 5, 1: 9}}, 1: {156: {0: {206: {0: 8, 1: 0}}, 1: 6}}}}}}, 1: {234: {0: {128: {0: 2, 1: 5}}, 1: 7}}}}}}, 1: {482: {0: {265: {0: {507: {0: {321: {0: {260: {0: 3, 1: 5}}, 1: 5}}, 1: {343: {0: 9, 1: {123: {0: 6, 1: 5}}}}}}, 1: 3}}, 1: {427: {0: {374: {0: {123: {0: 5, 1: 3}}, 1: {158: {0: 8, 1: 6}}}}, 1: {268: {0: {488: {0: {511: {0: {152: {0: 8, 1: 2}}, 1: 6}}, 1: {459: {0: {318: {0: 0, 1: 6}}, 1: 0}}}}, 1: {150: {0: 0, 1: 8}}}}}}}}}}, 1: {650: {0: {149: {0: {454: {0: {377: {0: {453: {0: {231: {0: {158: {0: 0, 1: 5}}, 1: 8}}, 1: {509: {0: {131: {0: 8, 1: 6}}, 1: 6}}}}, 1: {434: {0: 8, 1: {153: {0: 9, 1: 7}}}}}}, 1: {157: {0: {188: {0: 7, 1: 4}}, 1: {323: {0: 6, 1: 9}}}}}}, 1: {152: {0: {122: {0: 5, 1: 4}}, 1: 2}}}}, 1: {431: {0: {324: {0: {430: {0: {155: {0: 3, 1: 9}}, 1: {573: {0: {176: {0: 8, 1: 2}}, 1: 2}}}}, 1: 2}}, 1: {353: {0: {178: {0: {479: {0: {652: {0: 8, 1: 2}}, 1: {160: {0: {156: {0: 5, 1: 8}}, 1: 6}}}}, 1: {371: {0: 2, 1: {150: {0: 8, 1: 5}}}}}}, 1: 8}}}}}}}}}}, 1: {460: {0: {515: {0: {377: {0: {622: {0: {460: {0: {321: {0: {401: {0: {678: {0: {560: {0: {514: {0: 0, 1: {208: {0: {123: {0: 2, 1: 4}}, 1: 9}}}}, 1: 0}}, 1: {182: {0: 5, 1: {213: {0: 9, 1: 0}}}}}}, 1: {153: {0: {153: {0: 5, 1: 9}}, 1: {153: {0: 1, 1: 8}}}}}}, 1: {243: {0: {316: {0: {93: {0: 8, 1: 6}}, 1: {151: {0: 0, 1: 5}}}}, 1: 5}}}}, 1: {288: {0: {267: {0: {295: {0: 6, 1: {156: {0: 0, 1: 8}}}}, 1: {178: {0: 5, 1: 3}}}}, 1: {233: {0: 9, 1: {178: {0: 7, 1: {94: {0: 5, 1: 4}}}}}}}}}}, 1: 0}}, 1: {484: {0: {352: {0: {245: {0: 8, 1: 5}}, 1: {288: {0: 3, 1: {92: {0: 8, 1: 6}}}}}}, 1: {648: {0: {153: {0: 7, 1: 2}}, 1: 8}}}}}}, 1: {592: {0: {462: {0: {219: {0: {238: {0: {397: {0: {240: {0: 2, 1: {187: {0: {180: {0: 0, 1: 9}}, 1: 3}}}}, 1: {129: {0: 4, 1: 6}}}}, 1: {457: {0: {350: {0: {600: {0: 0, 1: 9}}, 1: 7}}, 1: {230: {0: 8, 1: 2}}}}}}, 1: 5}}, 1: {212: {0: {453: {0: {325: {0: {295: {0: {124: {0: 5, 1: 2}}, 1: {145: {0: 4, 1: 6}}}}, 1: {154: {0: 7, 1: {125: {0: 9, 1: 2}}}}}}, 1: 4}}, 1: {322: {0: {541: {0: {564: {0: {286: {0: {187: {0: 2, 1: 9}}, 1: 9}}, 1: {592: {0: {184: {0: 7, 1: 9}}, 1: 2}}}}, 1: {439: {0: 9, 1: 7}}}}, 1: {679: {0: {231: {0: {242: {0: 4, 1: 5}}, 1: 7}}, 1: {157: {0: 9, 1: 4}}}}}}}}}}, 1: {401: {0: {154: {0: {156: {0: {204: {0: 5, 1: 2}}, 1: {102: {0: {153: {0: 8, 1: 6}}, 1: 4}}}}, 1: {397: {0: 2, 1: {126: {0: 2, 1: 0}}}}}}, 1: {188: {0: {212: {0: {96: {0: {154: {0: 0, 1: 9}}, 1: 2}}, 1: 0}}, 1: {236: {0: 6, 1: {163: {0: 8, 1: 5}}}}}}}}}}}}, 1: {402: {0: {155: {0: {479: {0: {672: {0: {186: {0: {561: {0: {533: {0: {424: {0: {239: {0: 9, 1: 7}}, 1: {68: {0: 9, 1: 6}}}}, 1: {651: {0: {186: {0: 2, 1: 7}}, 1: 9}}}}, 1: {426: {0: {567: {0: {292: {0: {559: {0: {212: {0: 7, 1: 8}}, 1: {694: {0: {343: {0: 2, 1: 0}}, 1: 7}}}}, 1: 7}}, 1: 2}}, 1: {620: {0: {98: {0: {198: {0: 5, 1: 7}}, 1: 2}}, 1: 8}}}}}}, 1: {649: {0: {371: {0: {210: {0: {347: {0: {97: {0: 9, 1: 2}}, 1: 1}}, 1: {538: {0: 7, 1: 2}}}}, 1: {344: {0: 8, 1: {184: {0: 4, 1: {103: {0: 9, 1: 6}}}}}}}}, 1: {134: {0: 8, 1: 6}}}}}}, 1: {297: {0: {670: {0: {235: {0: {159: {0: 9, 1: 1}}, 1: 8}}, 1: {269: {0: {186: {0: 2, 1: 9}}, 1: 7}}}}, 1: 7}}}}, 1: {210: {0: {264: {0: {294: {0: {153: {0: {98: {0: 0, 1: 2}}, 1: 4}}, 1: 4}}, 1: {459: {0: {350: {0: 5, 1: {214: {0: 3, 1: {185: {0: 9, 1: 2}}}}}}, 1: {317: {0: 7, 1: {185: {0: 0, 1: {132: {0: 9, 1: 6}}}}}}}}}}, 1: {314: {0: {349: {0: {452: {0: {129: {0: 9, 1: 2}}, 1: {591: {0: 2, 1: {102: {0: 3, 1: 6}}}}}}, 1: {567: {0: {233: {0: {157: {0: 9, 1: 8}}, 1: 7}}, 1: 2}}}}, 1: {562: {0: {176: {0: 9, 1: 5}}, 1: {206: {0: {257: {0: 9, 1: 8}}, 1: 0}}}}}}}}}}, 1: {398: {0: {151: {0: {350: {0: {398: {0: {127: {0: {94: {0: {126: {0: 7, 1: 6}}, 1: 3}}, 1: 2}}, 1: 8}}, 1: {347: {0: {395: {0: {149: {0: 2, 1: {123: {0: 7, 1: 2}}}}, 1: 8}}, 1: 8}}}}, 1: 2}}, 1: {479: {0: {98: {0: 8, 1: 2}}, 1: {590: {0: {420: {0: 9, 1: 2}}, 1: {157: {0: {126: {0: 4, 1: 0}}, 1: 6}}}}}}}}}}, 1: {480: {0: {455: {0: {649: {0: {482: {0: {236: {0: {72: {0: 6, 1: 2}}, 1: 5}}, 1: {642: {0: {409: {0: 8, 1: {147: {0: {177: {0: 8, 1: 7}}, 1: 3}}}}, 1: {212: {0: {160: {0: 5, 1: {160: {0: 4, 1: 8}}}}, 1: 9}}}}}}, 1: 8}}, 1: {289: {0: {179: {0: {322: {0: {94: {0: 6, 1: 2}}, 1: {183: {0: 4, 1: {100: {0: 7, 1: 2}}}}}}, 1: {511: {0: {175: {0: 8, 1: 3}}, 1: {152: {0: 8, 1: 2}}}}}}, 1: {507: {0: {152: {0: 9, 1: 5}}, 1: 8}}}}}}, 1: {320: {0: {216: {0: {317: {0: 2, 1: {152: {0: 3, 1: 8}}}}, 1: {129: {0: {152: {0: 4, 1: 5}}, 1: 2}}}}, 1: {324: {0: {515: {0: 5, 1: {136: {0: 6, 1: 8}}}}, 1: {211: {0: 4, 1: 0}}}}}}}}}}}}}}}}, 1: {461: {0: {426: {0: {427: {0: {424: {0: {322: {0: {374: {0: {512: {0: {507: {0: {423: {0: {474: {0: {266: {0: {125: {0: {404: {0: {353: {0: {327: {0: {239: {0: 5, 1: {101: {0: {149: {0: 8, 1: 5}}, 1: 1}}}}, 1: 0}}, 1: {182: {0: 8, 1: 2}}}}, 1: {531: {0: {160: {0: {160: {0: 3, 1: 8}}, 1: 5}}, 1: {236: {0: 2, 1: {183: {0: 8, 1: 7}}}}}}}}, 1: {289: {0: {99: {0: {73: {0: 2, 1: 1}}, 1: {97: {0: 6, 1: 5}}}}, 1: 5}}}}, 1: {376: {0: {183: {0: 5, 1: {157: {0: 3, 1: 5}}}}, 1: {294: {0: 3, 1: {99: {0: 8, 1: 1}}}}}}}}, 1: {378: {0: {320: {0: 0, 1: {184: {0: 5, 1: 2}}}}, 1: {324: {0: {97: {0: 5, 1: 6}}, 1: 3}}}}}}, 1: {102: {0: 0, 1: 6}}}}, 1: {593: {0: {179: {0: {352: {0: 1, 1: 8}}, 1: {285: {0: 2, 1: 8}}}}, 1: 2}}}}, 1: {376: {0: 2, 1: {478: {0: {242: {0: {587: {0: {209: {0: 1, 1: 9}}, 1: {124: {0: {99: {0: 7, 1: 3}}, 1: 2}}}}, 1: {216: {0: 3, 1: 5}}}}, 1: {158: {0: 2, 1: 8}}}}}}}}, 1: {479: {0: {451: {0: {127: {0: {642: {0: 5, 1: {298: {0: {301: {0: 5, 1: 8}}, 1: {150: {0: 8, 1: 9}}}}}}, 1: {586: {0: {127: {0: 3, 1: 2}}, 1: {97: {0: 5, 1: 2}}}}}}, 1: {72: {0: 0, 1: 6}}}}, 1: {454: {0: {184: {0: {125: {0: 5, 1: 4}}, 1: {346: {0: 8, 1: 0}}}}, 1: {102: {0: {120: {0: 8, 1: 2}}, 1: 6}}}}}}}}, 1: {268: {0: {266: {0: {268: {0: 5, 1: {271: {0: {344: {0: {155: {0: {98: {0: 9, 1: 3}}, 1: 2}}, 1: 3}}, 1: 5}}}}, 1: {152: {0: {450: {0: {97: {0: {542: {0: {98: {0: 5, 1: {99: {0: 3, 1: 5}}}}, 1: {153: {0: 3, 1: 5}}}}, 1: {96: {0: 0, 1: 3}}}}, 1: {450: {0: {128: {0: 5, 1: 2}}, 1: {560: {0: 0, 1: 6}}}}}}, 1: {427: {0: {234: {0: {258: {0: 3, 1: 5}}, 1: {173: {0: 5, 1: 3}}}}, 1: {97: {0: 8, 1: 1}}}}}}}}, 1: {125: {0: {424: {0: {216: {0: {285: {0: {243: {0: {286: {0: {295: {0: 3, 1: 5}}, 1: {233: {0: {617: {0: {239: {0: 5, 1: 3}}, 1: 3}}, 1: 5}}}}, 1: 5}}, 1: {294: {0: {178: {0: 3, 1: {125: {0: 9, 1: 2}}}}, 1: {149: {0: 5, 1: 9}}}}}}, 1: {352: {0: {127: {0: {270: {0: 5, 1: 3}}, 1: 3}}, 1: 2}}}}, 1: {158: {0: {149: {0: {132: {0: 5, 1: 0}}, 1: {122: {0: 3, 1: 2}}}}, 1: {105: {0: 0, 1: 6}}}}}}, 1: 3}}}}}}, 1: {409: {0: {407: {0: 0, 1: 6}}, 1: {233: {0: {431: {0: 3, 1: {319: {0: 2, 1: {131: {0: 3, 1: 5}}}}}}, 1: {209: {0: {126: {0: 8, 1: 6}}, 1: {292: {0: 9, 1: 0}}}}}}}}}}, 1: {650: {0: {480: {0: {480: {0: {385: {0: {185: {0: {176: {0: 5, 1: 3}}, 1: {346: {0: {239: {0: 2, 1: {159: {0: 9, 1: 3}}}}, 1: 5}}}}, 1: {131: {0: {266: {0: 8, 1: 0}}, 1: {77: {0: 5, 1: 6}}}}}}, 1: {129: {0: {209: {0: {122: {0: 5, 1: {122: {0: 4, 1: 0}}}}, 1: 8}}, 1: {123: {0: 6, 1: 2}}}}}}, 1: {243: {0: {269: {0: {217: {0: {149: {0: {615: {0: {517: {0: 6, 1: {261: {0: {151: {0: 2, 1: 8}}, 1: 6}}}}, 1: {206: {0: {317: {0: {186: {0: {430: {0: 0, 1: 6}}, 1: 0}}, 1: 6}}, 1: {143: {0: 8, 1: 2}}}}}}, 1: {284: {0: 2, 1: 3}}}}, 1: {136: {0: 0, 1: 4}}}}, 1: {372: {0: {343: {0: 2, 1: {94: {0: 0, 1: 6}}}}, 1: {599: {0: 0, 1: {97: {0: {125: {0: 4, 1: 8}}, 1: 0}}}}}}}}, 1: {373: {0: {432: {0: {299: {0: {93: {0: {102: {0: 3, 1: 4}}, 1: 2}}, 1: 0}}, 1: {266: {0: 2, 1: 0}}}}, 1: {327: {0: {588: {0: {237: {0: 4, 1: {185: {0: 5, 1: 9}}}}, 1: {123: {0: {507: {0: {669: {0: 0, 1: 8}}, 1: {431: {0: {160: {0: 5, 1: 6}}, 1: 0}}}}, 1: {100: {0: {121: {0: 8, 1: 4}}, 1: 2}}}}}}, 1: 0}}}}}}}}, 1: {508: {0: {299: {0: {535: {0: {300: {0: 5, 1: {129: {0: 0, 1: 2}}}}, 1: {156: {0: {130: {0: {151: {0: 8, 1: 5}}, 1: 0}}, 1: 3}}}}, 1: {404: {0: {150: {0: 0, 1: 3}}, 1: {150: {0: {129: {0: 5, 1: 8}}, 1: {121: {0: 9, 1: 2}}}}}}}}, 1: 0}}}}}}, 1: {434: {0: 0, 1: {345: {0: {370: {0: {346: {0: {368: {0: {295: {0: 2, 1: 5}}, 1: {150: {0: 5, 1: 9}}}}, 1: {400: {0: {132: {0: 0, 1: 6}}, 1: {159: {0: 5, 1: 4}}}}}}, 1: {400: {0: 6, 1: {175: {0: 8, 1: 2}}}}}}, 1: {243: {0: {268: {0: {449: {0: {155: {0: 0, 1: 5}}, 1: {217: {0: 6, 1: 0}}}}, 1: {242: {0: 0, 1: {128: {0: 9, 1: 4}}}}}}, 1: {354: {0: {218: {0: {187: {0: {124: {0: 9, 1: 7}}, 1: 4}}, 1: 5}}, 1: {589: {0: 9, 1: 0}}}}}}}}}}}}, 1: {347: {0: {345: {0: {346: {0: {343: {0: 2, 1: {213: {0: {504: {0: {425: {0: {463: {0: {154: {0: 8, 1: 3}}, 1: 6}}, 1: {164: {0: 5, 1: 4}}}}, 1: {296: {0: 6, 1: {121: {0: 9, 1: 6}}}}}}, 1: {590: {0: {394: {0: {186: {0: {152: {0: 9, 1: 0}}, 1: 3}}, 1: 8}}, 1: {381: {0: {160: {0: 2, 1: 8}}, 1: {206: {0: 0, 1: 9}}}}}}}}}}, 1: {351: {0: {453: {0: {620: {0: 5, 1: {485: {0: 8, 1: 5}}}}, 1: {265: {0: {236: {0: {247: {0: 6, 1: 5}}, 1: {131: {0: 2, 1: 8}}}}, 1: {507: {0: 5, 1: {95: {0: {101: {0: 8, 1: 6}}, 1: 2}}}}}}}}, 1: {372: {0: {214: {0: 8, 1: 2}}, 1: 8}}}}}}, 1: {452: {0: {510: {0: {378: {0: {407: {0: {478: {0: 5, 1: {127: {0: {104: {0: 5, 1: 8}}, 1: 6}}}}, 1: {127: {0: {240: {0: 8, 1: 3}}, 1: {184: {0: 6, 1: 2}}}}}}, 1: {270: {0: {427: {0: {130: {0: 6, 1: 2}}, 1: {318: {0: 8, 1: 9}}}}, 1: {153: {0: 9, 1: 2}}}}}}, 1: {649: {0: {372: {0: {511: {0: {101: {0: {157: {0: 9, 1: 8}}, 1: 6}}, 1: {210: {0: 8, 1: 2}}}}, 1: {236: {0: {537: {0: {130: {0: 4, 1: 5}}, 1: {290: {0: 2, 1: 8}}}}, 1: {126: {0: 8, 1: 6}}}}}}, 1: 8}}}}, 1: {242: {0: {272: {0: 6, 1: {539: {0: {209: {0: {125: {0: 4, 1: 0}}, 1: {211: {0: 8, 1: 9}}}}, 1: {130: {0: 6, 1: 0}}}}}}, 1: {209: {0: {268: {0: {65: {0: 5, 1: 2}}, 1: 4}}, 1: {258: {0: {124: {0: 9, 1: 2}}, 1: {156: {0: 0, 1: {130: {0: 8, 1: 6}}}}}}}}}}}}}}, 1: {454: {0: {510: {0: {380: {0: {378: {0: {434: {0: 5, 1: {348: {0: {129: {0: 5, 1: 2}}, 1: {104: {0: {157: {0: 3, 1: 8}}, 1: 6}}}}}}, 1: {299: {0: {96: {0: 0, 1: {122: {0: 1, 1: 2}}}}, 1: 8}}}}, 1: {130: {0: {428: {0: {268: {0: {187: {0: 6, 1: 8}}, 1: {181: {0: 7, 1: 5}}}}, 1: {92: {0: 8, 1: 2}}}}, 1: {105: {0: 6, 1: 2}}}}}}, 1: {454: {0: {648: {0: {353: {0: {481: {0: {407: {0: 5, 1: {188: {0: 8, 1: 0}}}}, 1: {488: {0: 8, 1: 6}}}}, 1: {373: {0: {537: {0: {616: {0: 7, 1: {125: {0: {125: {0: 4, 1: 8}}, 1: 3}}}}, 1: 2}}, 1: {435: {0: {323: {0: {595: {0: 8, 1: {128: {0: 2, 1: 8}}}}, 1: {221: {0: 7, 1: 4}}}}, 1: 4}}}}}}, 1: 8}}, 1: {235: {0: {354: {0: 6, 1: {155: {0: {131: {0: 8, 1: 2}}, 1: {153: {0: 6, 1: 0}}}}}}, 1: {329: {0: {155: {0: 4, 1: 2}}, 1: 8}}}}}}}}, 1: {271: {0: {218: {0: 6, 1: {300: {0: {403: {0: {128: {0: 5, 1: 6}}, 1: {245: {0: 6, 1: {164: {0: 8, 1: 4}}}}}}, 1: {396: {0: {208: {0: 2, 1: 8}}, 1: {375: {0: {567: {0: 0, 1: 2}}, 1: 4}}}}}}}}, 1: {380: {0: {351: {0: {508: {0: {271: {0: 0, 1: 5}}, 1: {216: {0: 0, 1: 6}}}}, 1: {129: {0: {424: {0: 9, 1: 4}}, 1: {128: {0: 0, 1: 2}}}}}}, 1: {429: {0: {153: {0: {510: {0: {129: {0: {153: {0: 8, 1: 0}}, 1: 9}}, 1: 0}}, 1: {127: {0: 4, 1: 2}}}}, 1: {343: {0: {214: {0: {182: {0: {161: {0: 2, 1: 4}}, 1: 8}}, 1: 2}}, 1: {184: {0: {131: {0: 8, 1: 4}}, 1: 0}}}}}}}}}}}}}}}}}}, 1: {488: {0: {512: {0: {622: {0: {353: {0: {487: {0: {323: {0: {353: {0: {508: {0: {294: {0: {322: {0: {478: {0: 5, 1: {213: {0: {450: {0: {130: {0: 5, 1: {185: {0: {97: {0: 0, 1: 5}}, 1: 6}}}}, 1: {270: {0: {239: {0: 6, 1: 8}}, 1: 4}}}}, 1: {367: {0: {240: {0: 5, 1: 8}}, 1: {298: {0: 5, 1: 9}}}}}}}}, 1: {342: {0: {558: {0: {643: {0: {368: {0: {420: {0: {343: {0: 3, 1: 9}}, 1: {207: {0: 2, 1: 9}}}}, 1: {402: {0: 9, 1: 4}}}}, 1: 3}}, 1: {154: {0: {262: {0: 5, 1: 3}}, 1: {91: {0: 8, 1: 2}}}}}}, 1: {211: {0: {181: {0: 4, 1: 9}}, 1: {482: {0: {184: {0: {154: {0: 9, 1: 5}}, 1: 8}}, 1: 9}}}}}}}}, 1: {244: {0: {509: {0: {181: {0: {188: {0: {268: {0: {476: {0: {390: {0: {422: {0: 3, 1: {100: {0: {153: {0: 3, 1: 5}}, 1: 6}}}}, 1: {75: {0: {104: {0: 2, 1: 5}}, 1: 6}}}}, 1: 6}}, 1: {310: {0: 5, 1: {235: {0: 8, 1: 0}}}}}}, 1: {188: {0: 0, 1: 5}}}}, 1: 3}}, 1: {559: {0: {266: {0: {200: {0: 1, 1: 3}}, 1: {458: {0: {153: {0: 9, 1: 4}}, 1: 3}}}}, 1: {451: {0: 5, 1: 6}}}}}}, 1: {245: {0: {183: {0: {325: {0: 5, 1: 0}}, 1: {156: {0: {236: {0: 3, 1: 5}}, 1: {152: {0: 0, 1: 8}}}}}}, 1: 5}}}}}}, 1: {427: {0: {455: {0: {150: {0: {212: {0: 5, 1: 8}}, 1: 3}}, 1: {559: {0: {93: {0: {376: {0: 8, 1: 5}}, 1: 2}}, 1: {43: {0: 1, 1: 6}}}}}}, 1: {650: {0: {150: {0: {268: {0: 6, 1: 8}}, 1: 8}}, 1: {343: {0: {158: {0: 8, 1: 6}}, 1: 5}}}}}}}}, 1: {562: {0: {395: {0: {274: {0: {210: {0: {368: {0: {206: {0: 9, 1: 8}}, 1: {432: {0: {322: {0: 4, 1: 9}}, 1: {212: {0: 7, 1: 9}}}}}}, 1: {150: {0: 9, 1: 0}}}}, 1: {207: {0: 8, 1: 3}}}}, 1: {492: {0: {679: {0: 4, 1: {216: {0: {208: {0: {155: {0: 4, 1: 9}}, 1: 9}}, 1: 4}}}}, 1: {154: {0: {201: {0: 2, 1: 5}}, 1: 8}}}}}}, 1: {621: {0: {217: {0: 2, 1: {71: {0: 3, 1: 2}}}}, 1: {180: {0: 8, 1: {123: {0: {152: {0: 5, 1: 0}}, 1: 2}}}}}}}}}}, 1: {510: {0: {649: {0: {561: {0: {348: {0: {371: {0: {395: {0: {483: {0: {428: {0: {641: {0: {155: {0: {202: {0: 9, 1: 6}}, 1: 3}}, 1: 3}}, 1: {376: {0: {447: {0: 3, 1: 2}}, 1: {147: {0: 9, 1: 4}}}}}}, 1: {674: {0: {207: {0: {152: {0: 9, 1: 1}}, 1: {209: {0: 3, 1: 7}}}}, 1: {262: {0: 9, 1: 4}}}}}}, 1: {477: {0: {293: {0: {156: {0: 9, 1: 4}}, 1: {173: {0: 4, 1: 5}}}}, 1: 2}}}}, 1: {155: {0: {205: {0: {701: {0: {507: {0: 4, 1: 9}}, 1: {346: {0: 4, 1: 9}}}}, 1: {375: {0: 9, 1: {176: {0: 7, 1: 4}}}}}}, 1: {266: {0: {95: {0: {96: {0: 5, 1: 2}}, 1: 3}}, 1: 4}}}}}}, 1: {317: {0: {484: {0: {291: {0: {314: {0: {274: {0: 3, 1: 7}}, 1: {174: {0: 9, 1: 4}}}}, 1: {242: {0: {95: {0: {171: {0: 9, 1: 3}}, 1: 5}}, 1: 8}}}}, 1: {293: {0: {263: {0: {158: {0: 3, 1: 9}}, 1: {126: {0: 9, 1: 8}}}}, 1: {321: {0: 1, 1: {154: {0: {154: {0: 9, 1: 4}}, 1: 8}}}}}}}}, 1: {591: {0: {208: {0: {153: {0: {182: {0: 7, 1: 9}}, 1: 4}}, 1: 9}}, 1: {127: {0: 3, 1: {98: {0: 8, 1: 1}}}}}}}}}}, 1: {274: {0: {481: {0: {218: {0: {403: {0: {243: {0: {182: {0: 0, 1: 3}}, 1: 5}}, 1: {103: {0: 3, 1: 5}}}}, 1: {274: {0: 5, 1: 0}}}}, 1: {243: {0: {239: {0: 2, 1: {105: {0: {123: {0: 3, 1: 5}}, 1: 6}}}}, 1: {204: {0: 8, 1: 0}}}}}}, 1: {286: {0: 5, 1: 0}}}}}}, 1: {291: {0: 3, 1: {158: {0: {506: {0: {432: {0: {560: {0: {615: {0: 9, 1: {180: {0: 3, 1: 9}}}}, 1: {177: {0: {156: {0: 9, 1: 8}}, 1: 5}}}}, 1: {483: {0: {215: {0: 3, 1: {206: {0: 3, 1: 5}}}}, 1: {204: {0: 9, 1: 3}}}}}}, 1: {185: {0: 5, 1: 8}}}}, 1: {155: {0: 0, 1: 8}}}}}}}}, 1: {650: {0: {404: {0: {595: {0: {516: {0: 1, 1: {70: {0: 3, 1: 2}}}}, 1: {206: {0: 2, 1: {97: {0: 8, 1: 6}}}}}}, 1: {511: {0: {561: {0: 8, 1: {94: {0: 7, 1: 2}}}}, 1: {180: {0: 6, 1: 2}}}}}}, 1: {562: {0: {401: {0: {348: {0: {431: {0: {154: {0: 1, 1: 2}}, 1: 8}}, 1: 8}}, 1: {537: {0: 8, 1: {594: {0: 8, 1: 3}}}}}}, 1: 3}}}}}}}}, 1: {401: {0: {269: {0: {346: {0: {232: {0: 1, 1: {621: {0: {293: {0: {151: {0: 8, 1: 9}}, 1: 2}}, 1: {125: {0: {397: {0: 7, 1: 3}}, 1: {98: {0: 1, 1: 6}}}}}}}}, 1: {292: {0: {209: {0: {536: {0: {121: {0: {127: {0: 5, 1: 2}}, 1: 1}}, 1: 4}}, 1: {644: {0: {184: {0: {151: {0: 9, 1: 8}}, 1: 8}}, 1: {238: {0: {184: {0: 4, 1: 9}}, 1: 5}}}}}}, 1: {347: {0: {156: {0: 5, 1: 4}}, 1: {678: {0: 1, 1: {149: {0: 9, 1: 8}}}}}}}}}}, 1: {401: {0: {649: {0: {211: {0: {93: {0: 5, 1: 6}}, 1: {209: {0: {155: {0: 7, 1: 1}}, 1: 9}}}}, 1: {180: {0: {343: {0: 7, 1: {242: {0: 4, 1: 7}}}}, 1: {155: {0: {177: {0: 1, 1: 3}}, 1: {152: {0: 7, 1: 8}}}}}}}}, 1: {507: {0: {561: {0: {403: {0: {215: {0: 3, 1: {207: {0: {185: {0: 0, 1: 8}}, 1: 3}}}}, 1: {150: {0: 9, 1: 3}}}}, 1: {67: {0: 5, 1: 6}}}}, 1: {239: {0: 8, 1: 1}}}}}}}}, 1: {564: {0: {407: {0: {511: {0: {484: {0: {290: {0: 3, 1: {209: {0: {117: {0: 9, 1: 1}}, 1: 5}}}}, 1: {122: {0: 8, 1: 2}}}}, 1: {178: {0: {321: {0: {215: {0: {209: {0: {210: {0: 4, 1: {423: {0: 9, 1: {211: {0: 4, 1: 9}}}}}}, 1: 9}}, 1: 5}}, 1: {155: {0: {343: {0: {425: {0: {182: {0: {153: {0: 9, 1: 1}}, 1: 1}}, 1: {153: {0: 8, 1: 3}}}}, 1: {210: {0: 4, 1: 9}}}}, 1: 1}}}}, 1: {201: {0: 8, 1: {150: {0: 7, 1: 3}}}}}}}}, 1: {373: {0: {288: {0: {158: {0: 7, 1: 2}}, 1: {124: {0: {144: {0: 4, 1: 1}}, 1: 8}}}}, 1: {240: {0: 4, 1: {263: {0: {209: {0: 4, 1: {181: {0: 3, 1: 7}}}}, 1: {147: {0: 9, 1: 5}}}}}}}}}}, 1: {354: {0: {208: {0: 5, 1: {178: {0: 8, 1: {147: {0: 5, 1: 3}}}}}}, 1: 2}}}}}}}}, 1: {566: {0: {210: {0: {237: {0: {154: {0: {318: {0: {181: {0: {262: {0: 4, 1: {161: {0: {554: {0: {151: {0: 9, 1: 3}}, 1: 3}}, 1: {160: {0: 4, 1: 5}}}}}}, 1: {644: {0: {341: {0: 9, 1: {399: {0: 9, 1: 4}}}}, 1: {284: {0: {267: {0: 5, 1: {178: {0: {153: {0: 8, 1: 4}}, 1: 3}}}}, 1: 9}}}}}}, 1: {399: {0: {205: {0: {313: {0: {234: {0: {157: {0: 7, 1: 1}}, 1: 3}}, 1: {155: {0: 7, 1: 4}}}}, 1: {171: {0: {533: {0: 4, 1: 7}}, 1: {176: {0: 3, 1: 7}}}}}}, 1: {264: {0: {368: {0: {124: {0: {179: {0: 9, 1: 8}}, 1: 3}}, 1: {427: {0: {456: {0: {66: {0: 4, 1: 6}}, 1: 7}}, 1: {151: {0: 4, 1: 9}}}}}}, 1: {674: {0: 9, 1: 4}}}}}}}}, 1: {508: {0: {287: {0: {505: {0: {285: {0: {261: {0: {515: {0: 3, 1: {120: {0: 8, 1: 3}}}}, 1: {400: {0: {213: {0: 5, 1: 3}}, 1: {154: {0: 4, 1: 9}}}}}}, 1: {405: {0: {426: {0: 9, 1: 3}}, 1: {152: {0: 9, 1: 5}}}}}}, 1: {130: {0: 8, 1: 2}}}}, 1: {462: {0: {376: {0: {212: {0: 9, 1: {311: {0: 8, 1: 9}}}}, 1: {182: {0: 4, 1: {266: {0: 5, 1: 9}}}}}}, 1: {152: {0: {177: {0: 6, 1: 3}}, 1: 5}}}}}}, 1: {425: {0: {100: {0: 8, 1: 6}}, 1: 6}}}}}}, 1: {231: {0: {506: {0: 9, 1: {428: {0: {157: {0: {188: {0: 9, 1: 5}}, 1: 1}}, 1: 8}}}}, 1: {485: {0: {618: {0: {228: {0: {231: {0: 7, 1: 9}}, 1: {202: {0: 7, 1: 3}}}}, 1: {207: {0: 5, 1: 3}}}}, 1: {372: {0: 7, 1: {209: {0: {183: {0: 7, 1: 4}}, 1: {127: {0: 9, 1: 8}}}}}}}}}}}}, 1: {178: {0: {644: {0: {155: {0: 9, 1: {459: {0: {429: {0: {100: {0: {152: {0: {292: {0: 5, 1: 3}}, 1: 3}}, 1: 6}}, 1: {232: {0: 8, 1: {178: {0: 3, 1: 9}}}}}}, 1: {178: {0: {421: {0: {238: {0: {535: {0: 4, 1: 9}}, 1: {402: {0: 8, 1: {232: {0: {154: {0: 8, 1: 0}}, 1: 9}}}}}}, 1: {500: {0: 4, 1: 2}}}}, 1: {671: {0: {285: {0: 8, 1: {177: {0: 9, 1: 8}}}}, 1: {286: {0: 3, 1: 9}}}}}}}}}}, 1: {507: {0: {317: {0: {342: {0: {291: {0: 3, 1: {154: {0: {154: {0: 9, 1: 3}}, 1: 5}}}}, 1: 5}}, 1: {271: {0: 5, 1: {154: {0: {154: {0: 3, 1: 9}}, 1: 8}}}}}}, 1: {407: {0: 8, 1: {157: {0: 5, 1: 3}}}}}}}}, 1: {314: {0: {340: {0: {288: {0: 3, 1: {184: {0: {430: {0: {209: {0: 9, 1: 8}}, 1: {226: {0: 3, 1: {151: {0: 9, 1: 3}}}}}}, 1: 5}}}}, 1: {174: {0: 9, 1: 5}}}}, 1: {464: {0: {397: {0: {241: {0: {151: {0: 9, 1: 3}}, 1: 8}}, 1: {322: {0: {177: {0: 9, 1: 5}}, 1: {325: {0: 9, 1: 4}}}}}}, 1: {123: {0: 5, 1: 3}}}}}}}}}}, 1: {482: {0: {485: {0: {297: {0: {347: {0: {480: {0: {479: {0: {370: {0: 3, 1: {154: {0: 5, 1: 3}}}}, 1: {128: {0: 6, 1: 2}}}}, 1: {562: {0: 8, 1: {129: {0: 6, 1: 2}}}}}}, 1: {295: {0: {298: {0: {478: {0: {186: {0: {264: {0: 5, 1: {512: {0: {290: {0: 8, 1: 5}}, 1: 3}}}}, 1: {698: {0: 5, 1: 9}}}}, 1: {154: {0: 5, 1: 8}}}}, 1: {186: {0: 8, 1: 3}}}}, 1: {216: {0: {616: {0: {210: {0: 5, 1: 3}}, 1: 3}}, 1: 5}}}}}}, 1: {323: {0: {403: {0: 5, 1: {565: {0: {510: {0: {124: {0: 3, 1: 8}}, 1: 2}}, 1: {263: {0: 3, 1: 9}}}}}}, 1: {290: {0: 3, 1: {269: {0: 5, 1: {560: {0: 9, 1: {207: {0: 0, 1: 3}}}}}}}}}}}}, 1: {563: {0: {404: {0: 5, 1: 8}}, 1: {278: {0: 6, 1: 5}}}}}}, 1: {652: {0: {298: {0: {486: {0: {216: {0: {434: {0: 6, 1: {263: {0: {101: {0: 5, 1: 3}}, 1: 6}}}}, 1: {100: {0: 8, 1: 5}}}}, 1: {406: {0: 8, 1: 2}}}}, 1: {301: {0: {346: {0: {425: {0: {123: {0: 3, 1: 2}}, 1: 2}}, 1: {453: {0: {505: {0: 2, 1: 3}}, 1: {96: {0: 8, 1: 2}}}}}}, 1: {266: {0: 6, 1: {208: {0: 5, 1: 0}}}}}}}}, 1: {403: {0: {149: {0: {128: {0: 5, 1: 6}}, 1: 3}}, 1: {426: {0: {159: {0: 3, 1: 8}}, 1: 8}}}}}}}}}}}}, 1: {297: {0: {326: {0: {295: {0: {326: {0: {296: {0: 5, 1: {479: {0: {322: {0: {269: {0: {100: {0: {153: {0: 3, 1: 9}}, 1: 2}}, 1: 5}}, 1: {558: {0: 3, 1: {129: {0: {155: {0: 0, 1: 8}}, 1: 3}}}}}}, 1: {405: {0: 8, 1: 3}}}}}}, 1: {449: {0: {478: {0: {427: {0: {186: {0: 5, 1: 9}}, 1: {181: {0: 4, 1: {126: {0: 8, 1: 3}}}}}}, 1: 8}}, 1: {290: {0: {231: {0: 2, 1: 0}}, 1: {266: {0: 8, 1: 0}}}}}}}}, 1: {244: {0: {160: {0: {344: {0: {154: {0: {130: {0: {150: {0: 5, 1: {93: {0: 2, 1: 3}}}}, 1: {157: {0: 1, 1: 8}}}}, 1: {454: {0: {265: {0: 8, 1: 3}}, 1: 1}}}}, 1: 3}}, 1: {451: {0: {238: {0: {158: {0: 1, 1: {238: {0: 5, 1: 3}}}}, 1: {177: {0: {241: {0: 5, 1: 0}}, 1: 3}}}}, 1: {216: {0: 6, 1: {126: {0: 5, 1: 8}}}}}}}}, 1: {380: {0: {204: {0: 5, 1: {180: {0: 0, 1: 3}}}}, 1: {213: {0: 8, 1: 0}}}}}}}}, 1: {481: {0: {317: {0: {423: {0: {506: {0: 3, 1: {454: {0: {158: {0: 9, 1: 3}}, 1: 8}}}}, 1: {128: {0: {477: {0: {301: {0: {210: {0: 5, 1: 3}}, 1: 9}}, 1: {268: {0: 8, 1: 2}}}}, 1: 2}}}}, 1: {299: {0: {404: {0: {297: {0: 5, 1: 3}}, 1: {489: {0: 9, 1: {175: {0: 5, 1: 8}}}}}}, 1: {543: {0: {557: {0: {213: {0: {158: {0: 4, 1: 9}}, 1: 9}}, 1: {154: {0: 8, 1: 3}}}}, 1: {128: {0: 3, 1: {176: {0: 8, 1: 3}}}}}}}}}}, 1: {351: {0: {320: {0: {653: {0: 2, 1: 8}}, 1: {298: {0: 8, 1: 0}}}}, 1: {565: {0: {405: {0: {395: {0: {177: {0: 8, 1: {210: {0: 8, 1: 2}}}}, 1: {126: {0: 5, 1: 8}}}}, 1: {374: {0: 3, 1: {531: {0: {530: {0: {245: {0: 8, 1: 3}}, 1: {148: {0: 8, 1: 3}}}}, 1: 8}}}}}}, 1: {265: {0: {323: {0: 2, 1: {181: {0: 3, 1: {126: {0: 8, 1: 2}}}}}}, 1: {368: {0: {295: {0: {528: {0: 3, 1: 8}}, 1: 2}}, 1: 6}}}}}}}}}}}}, 1: {482: {0: {247: {0: 3, 1: {267: {0: {406: {0: {184: {0: 5, 1: 8}}, 1: 3}}, 1: {328: {0: {343: {0: {209: {0: 5, 1: {184: {0: 3, 1: 5}}}}, 1: 5}}, 1: 0}}}}}}, 1: {650: {0: {154: {0: {372: {0: {563: {0: {407: {0: {456: {0: 8, 1: 6}}, 1: {126: {0: 3, 1: 0}}}}, 1: {319: {0: {96: {0: 2, 1: 6}}, 1: {298: {0: {107: {0: {127: {0: 5, 1: 3}}, 1: 6}}, 1: 0}}}}}}, 1: {164: {0: {103: {0: {104: {0: 0, 1: 6}}, 1: 6}}, 1: 5}}}}, 1: {455: {0: {92: {0: {259: {0: 3, 1: 8}}, 1: 2}}, 1: {291: {0: {297: {0: {370: {0: 2, 1: {95: {0: 3, 1: 2}}}}, 1: {127: {0: 2, 1: 8}}}}, 1: {126: {0: 6, 1: 8}}}}}}}}, 1: {455: {0: {398: {0: {155: {0: {188: {0: {125: {0: 5, 1: 8}}, 1: 3}}, 1: 3}}, 1: {370: {0: {158: {0: 8, 1: 3}}, 1: 0}}}}, 1: {266: {0: {506: {0: {288: {0: 3, 1: 8}}, 1: {482: {0: {463: {0: 8, 1: {589: {0: {402: {0: 3, 1: 8}}, 1: 3}}}}, 1: {124: {0: {150: {0: 8, 1: 3}}, 1: 2}}}}}}, 1: {371: {0: {276: {0: {395: {0: {270: {0: 3, 1: 8}}, 1: 3}}, 1: 5}}, 1: {185: {0: {181: {0: 5, 1: 8}}, 1: {130: {0: {236: {0: 9, 1: 0}}, 1: 3}}}}}}}}}}}}}}}}}}, 1: {653: {0: {269: {0: {270: {0: {293: {0: {425: {0: {426: {0: {427: {0: {394: {0: {174: {0: {539: {0: {262: {0: 5, 1: {315: {0: 5, 1: 8}}}}, 1: {202: {0: {342: {0: {131: {0: 3, 1: 5}}, 1: 5}}, 1: 3}}}}, 1: 3}}, 1: {122: {0: 0, 1: 6}}}}, 1: {535: {0: {450: {0: {402: {0: {99: {0: 2, 1: 1}}, 1: 8}}, 1: {100: {0: {124: {0: 9, 1: 5}}, 1: 6}}}}, 1: {145: {0: 6, 1: 5}}}}}}, 1: {187: {0: {270: {0: {206: {0: 6, 1: {533: {0: {343: {0: {101: {0: 2, 1: 6}}, 1: {154: {0: 3, 1: 8}}}}, 1: {647: {0: 6, 1: {285: {0: 5, 1: {126: {0: 6, 1: 8}}}}}}}}}}, 1: {121: {0: 8, 1: 5}}}}, 1: {562: {0: 8, 1: {431: {0: {533: {0: {104: {0: 8, 1: 6}}, 1: 2}}, 1: 5}}}}}}}}, 1: 6}}, 1: {158: {0: {376: {0: {294: {0: {650: {0: {314: {0: {184: {0: 2, 1: {291: {0: {211: {0: 1, 1: {101: {0: 8, 1: 6}}}}, 1: {259: {0: 2, 1: 4}}}}}}, 1: {393: {0: {98: {0: {123: {0: 2, 1: 9}}, 1: 1}}, 1: {99: {0: 0, 1: 6}}}}}}, 1: {152: {0: {155: {0: 8, 1: 7}}, 1: {126: {0: 3, 1: 2}}}}}}, 1: {567: {0: {156: {0: {198: {0: 5, 1: 2}}, 1: 8}}, 1: {239: {0: 6, 1: 8}}}}}}, 1: {425: {0: {290: {0: {450: {0: {267: {0: {185: {0: 6, 1: 3}}, 1: {180: {0: 3, 1: 8}}}}, 1: {177: {0: 8, 1: 9}}}}, 1: 3}}, 1: {566: {0: {264: {0: {150: {0: {152: {0: 4, 1: 9}}, 1: 2}}, 1: 8}}, 1: {175: {0: 6, 1: 8}}}}}}}}, 1: {616: {0: {454: {0: {236: {0: {76: {0: 3, 1: 6}}, 1: 5}}, 1: {566: {0: {486: {0: {103: {0: {128: {0: 4, 1: 8}}, 1: 1}}, 1: 6}}, 1: 6}}}}, 1: {186: {0: {99: {0: 1, 1: 2}}, 1: 8}}}}}}}}, 1: {158: {0: {183: {0: {242: {0: {568: {0: {155: {0: 5, 1: 8}}, 1: {236: {0: 6, 1: 8}}}}, 1: {377: {0: {456: {0: {106: {0: 1, 1: 8}}, 1: {132: {0: 8, 1: 2}}}}, 1: {208: {0: 4, 1: 9}}}}}}, 1: {477: {0: {314: {0: {566: {0: {398: {0: {202: {0: {179: {0: 7, 1: 8}}, 1: 2}}, 1: 8}}, 1: {120: {0: 2, 1: 3}}}}, 1: 8}}, 1: {208: {0: 2, 1: {184: {0: 6, 1: 3}}}}}}}}, 1: {435: {0: {458: {0: {345: {0: {290: {0: 2, 1: 8}}, 1: {99: {0: 8, 1: 2}}}}, 1: 8}}, 1: {349: {0: {130: {0: 0, 1: 2}}, 1: {288: {0: {125: {0: 3, 1: 8}}, 1: {426: {0: {124: {0: 0, 1: 3}}, 1: 8}}}}}}}}}}}}, 1: {569: {0: {624: {0: {407: {0: {512: {0: {182: {0: {451: {0: {349: {0: {160: {0: 5, 1: 8}}, 1: {598: {0: 1, 1: 2}}}}, 1: {129: {0: {133: {0: 9, 1: 6}}, 1: 2}}}}, 1: {452: {0: 8, 1: {154: {0: {154: {0: 9, 1: 3}}, 1: 2}}}}}}, 1: {271: {0: {132: {0: 2, 1: 1}}, 1: {233: {0: 5, 1: 3}}}}}}, 1: {512: {0: {236: {0: {398: {0: {369: {0: 8, 1: {158: {0: 9, 1: 4}}}}, 1: 4}}, 1: {289: {0: 8, 1: 9}}}}, 1: {153: {0: 5, 1: 4}}}}}}, 1: {347: {0: {406: {0: {459: {0: {590: {0: {149: {0: {212: {0: 0, 1: 8}}, 1: 2}}, 1: 2}}, 1: {324: {0: {92: {0: 6, 1: 2}}, 1: 8}}}}, 1: {120: {0: 8, 1: 3}}}}, 1: {429: {0: {562: {0: {267: {0: 8, 1: {122: {0: {124: {0: 9, 1: 8}}, 1: 3}}}}, 1: 3}}, 1: {352: {0: 8, 1: {151: {0: 4, 1: 0}}}}}}}}}}, 1: {457: {0: {154: {0: {383: {0: {246: {0: {404: {0: {456: {0: {371: {0: 2, 1: {40: {0: {102: {0: 5, 1: 4}}, 1: 6}}}}, 1: 5}}, 1: {452: {0: {105: {0: 3, 1: 5}}, 1: {101: {0: 2, 1: 5}}}}}}, 1: 5}}, 1: {238: {0: 6, 1: 0}}}}, 1: {320: {0: {266: {0: 2, 1: {64: {0: 9, 1: 2}}}}, 1: {425: {0: {287: {0: 3, 1: {152: {0: 8, 1: 9}}}}, 1: {621: {0: 2, 1: {315: {0: 3, 1: {150: {0: 0, 1: 8}}}}}}}}}}}}, 1: {345: {0: {320: {0: {343: {0: 2, 1: {203: {0: 6, 1: 8}}}}, 1: {571: {0: {244: {0: {154: {0: {236: {0: {398: {0: 1, 1: 6}}, 1: 8}}, 1: {265: {0: 8, 1: 2}}}}, 1: {428: {0: {186: {0: 5, 1: 0}}, 1: 8}}}}, 1: {463: {0: 2, 1: {154: {0: 6, 1: 8}}}}}}}}, 1: {353: {0: {205: {0: {424: {0: {589: {0: {123: {0: 6, 1: 4}}, 1: 8}}, 1: {215: {0: 6, 1: {135: {0: 0, 1: 5}}}}}}, 1: {509: {0: 8, 1: {92: {0: 5, 1: 2}}}}}}, 1: {271: {0: {157: {0: 6, 1: 3}}, 1: {177: {0: 0, 1: 3}}}}}}}}}}}}}}, 1: {459: {0: {457: {0: {297: {0: {295: {0: {597: {0: {156: {0: 8, 1: {174: {0: 5, 1: 3}}}}, 1: {327: {0: 5, 1: 3}}}}, 1: {162: {0: {266: {0: 5, 1: 3}}, 1: 5}}}}, 1: {456: {0: {425: {0: {315: {0: {482: {0: {628: {0: 3, 1: 2}}, 1: 8}}, 1: {122: {0: {150: {0: 9, 1: 3}}, 1: 8}}}}, 1: {127: {0: {128: {0: 0, 1: 5}}, 1: 8}}}}, 1: {177: {0: 8, 1: 3}}}}}}, 1: {383: {0: {399: {0: {537: {0: {534: {0: {157: {0: 8, 1: {325: {0: {179: {0: 6, 1: 5}}, 1: 8}}}}, 1: 8}}, 1: {131: {0: 3, 1: 6}}}}, 1: {260: {0: {562: {0: 5, 1: {180: {0: 6, 1: {181: {0: 0, 1: 8}}}}}}, 1: {265: {0: 8, 1: {149: {0: 8, 1: 3}}}}}}}}, 1: {380: {0: {597: {0: 6, 1: 0}}, 1: {566: {0: {185: {0: {121: {0: {124: {0: 8, 1: 5}}, 1: 2}}, 1: 8}}, 1: {130: {0: 0, 1: 3}}}}}}}}}}, 1: 8}}}}}}, 1: {318: {0: {547: {0: {235: {0: {318: {0: {179: {0: 1, 1: {537: {0: {291: {0: {339: {0: {509: {0: {504: {0: 3, 1: {256: {0: 2, 1: 3}}}}, 1: {641: {0: {672: {0: {154: {0: {238: {0: {671: {0: 2, 1: {150: {0: 7, 1: 3}}}}, 1: 7}}, 1: {290: {0: {179: {0: 8, 1: 2}}, 1: {670: {0: 1, 1: 7}}}}}}, 1: {179: {0: 1, 1: 7}}}}, 1: {122: {0: 3, 1: 2}}}}}}, 1: {68: {0: 8, 1: 6}}}}, 1: {149: {0: 1, 1: 7}}}}, 1: {341: {0: {312: {0: {152: {0: {203: {0: {207: {0: 8, 1: {480: {0: 7, 1: {213: {0: 2, 1: 7}}}}}}, 1: {430: {0: 2, 1: {145: {0: {174: {0: 2, 1: 3}}, 1: 7}}}}}}, 1: 2}}, 1: {155: {0: 6, 1: 9}}}}, 1: {180: {0: {69: {0: 4, 1: 6}}, 1: 8}}}}}}}}, 1: {350: {0: {181: {0: {514: {0: {369: {0: {242: {0: {317: {0: {699: {0: {398: {0: {183: {0: 1, 1: {101: {0: 8, 1: 5}}}}, 1: {367: {0: 8, 1: {158: {0: 4, 1: 8}}}}}}, 1: {183: {0: 7, 1: 9}}}}, 1: {185: {0: {476: {0: {290: {0: 4, 1: 1}}, 1: {125: {0: {154: {0: {208: {0: 5, 1: 9}}, 1: 4}}, 1: {121: {0: 1, 1: 2}}}}}}, 1: {345: {0: {158: {0: 8, 1: {315: {0: {212: {0: 8, 1: 5}}, 1: {101: {0: 1, 1: 6}}}}}}, 1: 1}}}}}}, 1: {158: {0: {534: {0: {134: {0: 8, 1: 4}}, 1: {506: {0: {185: {0: 8, 1: 5}}, 1: 5}}}}, 1: 8}}}}, 1: {530: {0: {426: {0: {155: {0: 5, 1: 1}}, 1: {208: {0: {132: {0: {672: {0: 4, 1: 1}}, 1: 6}}, 1: {156: {0: 9, 1: {154: {0: 8, 1: 4}}}}}}}}, 1: {127: {0: 5, 1: 4}}}}}}, 1: {426: {0: {320: {0: 5, 1: {646: {0: {127: {0: 2, 1: 4}}, 1: 8}}}}, 1: {316: {0: {256: {0: 6, 1: 2}}, 1: {448: {0: 8, 1: {106: {0: 0, 1: 6}}}}}}}}}}, 1: {539: {0: {126: {0: {161: {0: 8, 1: 5}}, 1: {345: {0: 6, 1: {99: {0: {124: {0: 4, 1: 1}}, 1: 2}}}}}}, 1: {535: {0: 1, 1: {348: {0: {559: {0: {73: {0: 2, 1: 6}}, 1: 8}}, 1: 1}}}}}}}}, 1: {370: {0: {294: {0: {453: {0: {213: {0: {368: {0: {181: {0: 8, 1: {152: {0: 4, 1: 8}}}}, 1: {126: {0: 4, 1: 3}}}}, 1: {157: {0: {398: {0: 8, 1: {155: {0: 9, 1: 8}}}}, 1: 8}}}}, 1: {458: {0: 8, 1: {153: {0: 6, 1: 8}}}}}}, 1: {156: {0: {479: {0: {212: {0: {186: {0: 7, 1: 4}}, 1: {260: {0: {188: {0: 9, 1: 5}}, 1: 8}}}}, 1: {458: {0: {291: {0: 1, 1: {612: {0: 1, 1: 8}}}}, 1: {103: {0: {182: {0: 7, 1: 2}}, 1: 6}}}}}}, 1: {270: {0: {293: {0: {127: {0: {128: {0: 1, 1: 6}}, 1: 3}}, 1: {264: {0: 8, 1: 1}}}}, 1: 8}}}}}}, 1: {513: {0: {558: {0: {369: {0: {212: {0: {265: {0: {99: {0: 4, 1: 6}}, 1: {210: {0: 9, 1: 4}}}}, 1: {182: {0: 9, 1: 8}}}}, 1: {700: {0: {301: {0: {581: {0: 4, 1: 1}}, 1: {214: {0: 7, 1: 9}}}}, 1: 9}}}}, 1: {265: {0: {186: {0: 5, 1: {105: {0: 2, 1: 1}}}}, 1: {263: {0: {103: {0: 0, 1: 6}}, 1: 8}}}}}}, 1: {295: {0: {188: {0: 6, 1: 2}}, 1: {243: {0: {209: {0: {106: {0: 9, 1: 6}}, 1: 4}}, 1: {263: {0: 3, 1: 0}}}}}}}}}}}}}}, 1: {318: {0: {341: {0: {509: {0: {268: {0: {454: {0: {592: {0: {211: {0: {182: {0: {181: {0: 1, 1: 2}}, 1: 8}}, 1: 7}}, 1: {673: {0: 1, 1: {154: {0: {154: {0: 7, 1: 1}}, 1: 3}}}}}}, 1: {214: {0: {429: {0: {233: {0: {150: {0: 8, 1: 3}}, 1: 2}}, 1: {345: {0: {149: {0: 3, 1: 2}}, 1: 7}}}}, 1: {593: {0: 8, 1: 3}}}}}}, 1: {537: {0: {266: {0: {475: {0: 3, 1: 2}}, 1: {480: {0: {203: {0: 8, 1: 3}}, 1: 7}}}}, 1: {623: {0: {267: {0: {511: {0: {341: {0: 7, 1: {181: {0: 4, 1: 9}}}}, 1: 3}}, 1: {540: {0: 7, 1: 2}}}}, 1: {374: {0: 8, 1: {176: {0: 2, 1: 3}}}}}}}}}}, 1: {155: {0: {238: {0: {322: {0: {125: {0: {372: {0: 2, 1: {258: {0: 2, 1: 7}}}}, 1: 1}}, 1: {348: {0: 8, 1: {98: {0: 2, 1: 6}}}}}}, 1: {624: {0: {531: {0: {428: {0: {232: {0: 7, 1: 2}}, 1: {311: {0: {315: {0: {367: {0: 7, 1: {258: {0: 7, 1: 2}}}}, 1: {178: {0: {155: {0: 8, 1: 1}}, 1: 7}}}}, 1: {177: {0: 2, 1: 9}}}}}}, 1: {459: {0: {156: {0: {175: {0: 7, 1: 2}}, 1: 1}}, 1: 2}}}}, 1: {397: {0: 2, 1: 3}}}}}}, 1: {598: {0: {646: {0: {316: {0: {316: {0: 2, 1: 7}}, 1: 8}}, 1: {232: {0: {233: {0: 2, 1: 8}}, 1: {294: {0: 3, 1: {208: {0: 2, 1: 8}}}}}}}}, 1: 2}}}}}}, 1: {652: {0: {211: {0: {367: {0: {230: {0: 2, 1: 8}}, 1: {99: {0: {209: {0: 4, 1: 9}}, 1: 6}}}}, 1: {189: {0: {560: {0: {406: {0: {702: {0: 9, 1: 7}}, 1: {177: {0: 3, 1: 7}}}}, 1: {182: {0: 9, 1: 8}}}}, 1: 8}}}}, 1: {708: {0: {146: {0: {162: {0: 8, 1: {134: {0: 4, 1: 8}}}}, 1: 5}}, 1: {204: {0: {212: {0: 9, 1: 7}}, 1: {179: {0: 4, 1: 8}}}}}}}}}}, 1: {649: {0: {293: {0: {461: {0: {680: {0: {123: {0: 8, 1: {122: {0: 1, 1: 8}}}}, 1: {149: {0: 1, 1: 4}}}}, 1: {236: {0: {237: {0: 2, 1: 8}}, 1: {97: {0: 3, 1: 6}}}}}}, 1: {233: {0: {480: {0: {235: {0: 8, 1: {213: {0: 1, 1: 8}}}}, 1: {180: {0: 9, 1: {121: {0: {123: {0: 8, 1: 4}}, 1: 2}}}}}}, 1: {593: {0: {205: {0: 9, 1: 2}}, 1: {151: {0: {157: {0: 7, 1: 8}}, 1: {458: {0: 8, 1: 1}}}}}}}}}}, 1: 8}}}}}}, 1: {654: {0: {342: {0: {319: {0: {342: {0: {510: {0: {507: {0: {539: {0: {509: {0: 3, 1: 2}}, 1: {241: {0: 1, 1: {184: {0: {200: {0: 2, 1: 7}}, 1: {123: {0: 3, 1: 6}}}}}}}}, 1: {454: {0: 3, 1: {707: {0: 2, 1: 3}}}}}}, 1: 2}}, 1: {184: {0: {568: {0: {367: {0: {179: {0: {13: {0: 7, 1: 6}}, 1: 8}}, 1: {152: {0: 9, 1: 4}}}}, 1: 6}}, 1: {544: {0: 8, 1: {231: {0: 2, 1: 8}}}}}}}}, 1: {399: {0: {513: {0: {263: {0: {101: {0: 2, 1: 6}}, 1: 8}}, 1: {482: {0: {185: {0: {65: {0: 1, 1: 2}}, 1: 5}}, 1: {378: {0: {72: {0: 2, 1: 6}}, 1: {324: {0: 5, 1: {67: {0: {122: {0: 3, 1: 8}}, 1: 6}}}}}}}}}}, 1: {520: {0: {297: {0: {177: {0: {475: {0: {646: {0: 6, 1: 1}}, 1: {72: {0: {123: {0: 5, 1: 4}}, 1: 6}}}}, 1: 2}}, 1: {508: {0: {122: {0: 8, 1: 3}}, 1: {591: {0: {102: {0: 2, 1: 3}}, 1: {96: {0: 6, 1: 2}}}}}}}}, 1: {203: {0: {283: {0: 2, 1: 8}}, 1: 3}}}}}}}}, 1: {542: {0: {207: {0: {404: {0: 6, 1: 4}}, 1: {405: {0: {235: {0: 8, 1: {100: {0: {150: {0: 0, 1: 3}}, 1: 6}}}}, 1: {155: {0: 9, 1: 8}}}}}}, 1: {238: {0: {186: {0: 6, 1: {124: {0: 9, 1: 2}}}}, 1: {396: {0: {155: {0: 9, 1: 2}}, 1: {90: {0: 8, 1: 6}}}}}}}}}}, 1: {513: {0: {541: {0: {512: {0: {483: {0: 3, 1: {508: {0: {288: {0: 3, 1: 8}}, 1: 8}}}}, 1: {178: {0: 8, 1: {175: {0: 3, 1: 2}}}}}}, 1: {456: {0: {125: {0: {173: {0: 8, 1: 7}}, 1: 1}}, 1: {150: {0: {125: {0: {153: {0: 4, 1: 0}}, 1: 6}}, 1: 2}}}}}}, 1: {490: {0: {343: {0: {595: {0: {153: {0: 3, 1: 8}}, 1: {592: {0: {126: {0: {151: {0: 7, 1: 4}}, 1: {122: {0: 1, 1: 2}}}}, 1: {290: {0: 2, 1: 3}}}}}}, 1: {382: {0: 8, 1: {122: {0: {126: {0: 6, 1: 5}}, 1: 0}}}}}}, 1: {542: {0: {405: {0: {569: {0: 8, 1: 3}}, 1: 8}}, 1: {267: {0: {400: {0: 8, 1: {124: {0: 0, 1: 3}}}}, 1: {205: {0: 1, 1: {123: {0: 3, 1: 2}}}}}}}}}}}}}}}}, 1: {655: {0: {572: {0: {211: {0: {266: {0: {597: {0: {397: {0: {349: {0: {565: {0: {282: {0: 2, 1: 7}}, 1: {318: {0: {123: {0: 4, 1: 8}}, 1: 7}}}}, 1: {402: {0: {396: {0: {185: {0: 7, 1: 8}}, 1: {242: {0: {98: {0: 4, 1: 6}}, 1: {190: {0: 9, 1: 5}}}}}}, 1: {268: {0: {233: {0: {98: {0: 4, 1: 6}}, 1: {184: {0: 2, 1: 9}}}}, 1: 4}}}}}}, 1: {507: {0: 4, 1: {269: {0: {538: {0: {104: {0: 9, 1: 4}}, 1: 6}}, 1: {261: {0: 5, 1: 4}}}}}}}}, 1: {567: {0: {155: {0: 8, 1: 3}}, 1: {184: {0: 6, 1: {98: {0: 9, 1: 8}}}}}}}}, 1: {378: {0: {246: {0: {620: {0: {262: {0: {180: {0: 4, 1: 8}}, 1: 2}}, 1: {453: {0: {340: {0: 1, 1: 7}}, 1: {157: {0: 7, 1: 4}}}}}}, 1: {187: {0: 5, 1: 8}}}}, 1: {505: {0: {264: {0: 4, 1: {263: {0: {376: {0: 9, 1: 4}}, 1: {187: {0: 9, 1: {234: {0: 9, 1: 7}}}}}}}}, 1: {214: {0: {257: {0: 8, 1: 2}}, 1: {210: {0: 0, 1: 5}}}}}}}}}}, 1: {536: {0: {378: {0: {652: {0: {456: {0: {161: {0: 9, 1: 5}}, 1: {454: {0: {212: {0: 8, 1: {182: {0: 8, 1: 9}}}}, 1: {155: {0: 2, 1: 4}}}}}}, 1: {430: {0: 3, 1: 8}}}}, 1: {212: {0: {321: {0: {293: {0: 4, 1: {124: {0: 7, 1: 8}}}}, 1: {234: {0: 8, 1: {671: {0: 9, 1: {183: {0: 9, 1: 4}}}}}}}}, 1: {483: {0: 9, 1: {490: {0: {702: {0: {216: {0: {256: {0: {234: {0: {456: {0: 4, 1: 9}}, 1: 9}}, 1: {184: {0: 9, 1: 7}}}}, 1: {270: {0: 8, 1: 9}}}}, 1: {209: {0: 7, 1: 8}}}}, 1: {234: {0: 4, 1: {213: {0: 9, 1: 2}}}}}}}}}}}}, 1: {489: {0: {532: {0: {370: {0: 8, 1: {185: {0: 4, 1: 7}}}}, 1: {183: {0: 5, 1: 2}}}}, 1: {410: {0: {209: {0: {74: {0: {96: {0: 2, 1: 3}}, 1: 6}}, 1: {652: {0: 2, 1: 9}}}}, 1: {184: {0: 0, 1: 6}}}}}}}}}}, 1: {651: {0: {654: {0: {269: {0: {540: {0: {461: {0: {518: {0: {489: {0: 8, 1: {181: {0: 5, 1: 6}}}}, 1: {615: {0: 6, 1: {101: {0: {101: {0: 8, 1: 1}}, 1: 6}}}}}}, 1: {464: {0: {261: {0: {99: {0: 1, 1: 6}}, 1: 8}}, 1: {258: {0: 4, 1: 2}}}}}}, 1: 6}}, 1: {382: {0: {208: {0: {184: {0: {620: {0: 8, 1: {232: {0: 5, 1: 8}}}}, 1: {156: {0: {236: {0: 9, 1: 4}}, 1: {96: {0: {97: {0: 6, 1: 3}}, 1: 2}}}}}}, 1: {234: {0: 6, 1: 2}}}}, 1: {421: {0: 6, 1: {243: {0: {103: {0: 4, 1: 6}}, 1: 0}}}}}}}}, 1: {542: {0: {321: {0: {210: {0: 4, 1: {300: {0: 9, 1: 4}}}}, 1: {150: {0: {314: {0: {705: {0: 4, 1: 9}}, 1: {201: {0: 7, 1: 4}}}}, 1: {122: {0: 8, 1: 1}}}}}}, 1: {629: {0: {213: {0: {127: {0: 5, 1: 6}}, 1: 4}}, 1: {349: {0: 6, 1: {495: {0: 8, 1: 2}}}}}}}}}}, 1: {372: {0: {704: {0: {522: {0: 8, 1: 2}}, 1: {182: {0: 7, 1: 9}}}}, 1: {591: {0: {185: {0: {406: {0: {234: {0: {163: {0: 8, 1: 4}}, 1: {126: {0: 9, 1: 6}}}}, 1: 4}}, 1: {510: {0: 9, 1: {242: {0: 8, 1: 9}}}}}}, 1: {409: {0: {272: {0: 2, 1: {221: {0: 8, 1: 5}}}}, 1: 0}}}}}}}}}}, 1: {540: {0: {399: {0: {294: {0: {182: {0: {209: {0: {154: {0: {429: {0: {286: {0: 4, 1: 8}}, 1: 4}}, 1: 8}}, 1: {427: {0: {188: {0: 9, 1: 8}}, 1: 8}}}}, 1: 8}}, 1: {374: {0: {486: {0: {565: {0: {429: {0: {183: {0: 5, 1: 8}}, 1: {186: {0: 9, 1: {160: {0: 3, 1: 2}}}}}}, 1: {183: {0: {212: {0: 7, 1: 9}}, 1: 1}}}}, 1: {156: {0: 7, 1: {155: {0: 1, 1: 7}}}}}}, 1: {705: {0: {213: {0: {260: {0: {234: {0: {147: {0: 7, 1: 8}}, 1: 1}}, 1: {228: {0: 8, 1: 7}}}}, 1: 8}}, 1: {182: {0: 9, 1: {180: {0: 3, 1: 8}}}}}}}}}}, 1: {620: {0: {238: {0: {182: {0: {200: {0: {429: {0: 8, 1: 4}}, 1: 7}}, 1: {153: {0: {182: {0: 9, 1: 3}}, 1: {126: {0: 5, 1: 8}}}}}}, 1: {541: {0: {177: {0: 8, 1: 3}}, 1: {465: {0: {405: {0: {426: {0: {153: {0: 1, 1: 4}}, 1: {294: {0: 8, 1: {152: {0: 9, 1: 8}}}}}}, 1: {160: {0: 9, 1: 8}}}}, 1: {202: {0: 4, 1: 3}}}}}}}}, 1: {378: {0: {431: {0: {129: {0: 8, 1: 0}}, 1: 5}}, 1: {538: {0: 8, 1: 3}}}}}}}}, 1: 8}}}}}}}}}} start to test 100%|██████████| 10000/10000 [00:00<00:00, 141222.36it/s] the accur is: 0.8589 time span: 241.9791190624237