11.1、关联规则实例
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关联规则
junjun
2016年2月11日
实例一：通过arules包中的Aprior()函数求关联规则、eclat()函数求频繁项集
#1、加载数据并查看library(arules)## Loading required package: Matrix## ## Attaching package: 'arules'## The following objects are masked from 'package:base':## ## %in%, abbreviate, writedata("Groceries")str(Groceries)## Formal class 'transactions' [package "arules"] with 4 slots## ..@ transactionInfo:'data.frame': 9835 obs. of 0 variables## ..@ data :Formal class 'ngCMatrix' [package "Matrix"] with 5 slots## .. .. ..@ i : int [1:43367] 13 60 69 78 14 29 98 24 15 29 ...## .. .. ..@ p : int [1:9836] 0 4 7 8 12 16 21 22 27 28 ...## .. .. ..@ Dim : int [1:2] 169 9835## .. .. ..@ Dimnames:List of 2## .. .. .. ..$ : NULL## .. .. .. ..$ : NULL## .. .. ..@ factors : list()## ..@ itemInfo :'data.frame': 169 obs. of 3 variables:## .. ..$ labels: chr [1:169] "frankfurter" "sausage" "liver loaf" "ham" ...## .. ..$ level2: Factor w/ 55 levels "baby food","bags",..: 44 44 44 44 44 44 44 42 42 41 ...## .. ..$ level1: Factor w/ 10 levels "canned food",..: 6 6 6 6 6 6 6 6 6 6 ...## ..@ itemsetInfo :'data.frame': 9835 obs. of 1 variable:## .. ..$ itemsetID: chr [1:9835] "1" "2" "3" "4" ...summary(Groceries)## transactions as itemMatrix in sparse format with## 9835 rows (elements/itemsets/transactions) and## 169 columns (items) and a density of 0.02609146 ## ## most frequent items:## whole milk other vegetables rolls/buns soda ## 2513 1903 1809 1715 ## yogurt (Other) ## 1372 34055 ## ## element (itemset/transaction) length distribution:## sizes## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55 ## 16 17 18 19 20 21 22 23 24 26 27 28 29 32 ## 46 29 14 14 9 11 4 6 1 1 1 1 3 1 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 2.000 3.000 4.409 6.000 32.000 ## ## includes extended item information - examples:## labels level2 level1## 1 frankfurter sausage meet and sausage## 2 sausage sausage meet and sausage## 3 liver loaf sausage meet and sausagedim(Groceries)## [1] 9835 169#以Groceries数据为例，超市购物的例子，每一行为一个顾客的购买记录，格式为transactions 也就是以稀疏矩阵储存的物品矩阵数据 inspect(Groceries[1:3])## items ## 1 {citrus fruit, ## semi-finished bread,## margarine, ## ready soups} ## 2 {tropical fruit, ## yogurt, ## coffee} ## 3 {whole milk}#2、数据清洗#1）查看某些数据项出现的频率itemFrequency(Groceries[, 1:3])## frankfurter sausage liver loaf ## 0.058973055 0.093950178 0.005083884#2)数据探索itemFrequencyPlot(Groceries, support=0.1)#有8项支持度大于0.1itemFrequencyPlot(Groceries, topN=20)# 画出前20个频率最大的项#3)稀疏矩阵可视化image(Groceries[1:5])image(sample(Groceries, 100))#4)对稀疏矩阵进行转换，把transaction类型转化为data.frame类型df_Gro <- as(Groceries, "data.frame")dim(df_Gro)## [1] 9835 1head(df_Gro, 3)## items## 1 {citrus fruit,semi-finished bread,margarine,ready soups}## 2 {tropical fruit,yogurt,coffee}## 3 {whole milk}#对transactions类型的Groceries数据做处理：aprior()函数求关联规则，eclat()函数求频繁项集#3、创建关联规则：aprior()函数求关联规则rules <- apriori(Groceries, parameter = list(support=0.01, confidence=0.2))## Apriori## ## Parameter specification:## confidence minval smax arem aval originalSupport support minlen maxlen## 0.2 0.1 1 none FALSE TRUE 0.01 1 10## target ext## rules FALSE## ## Algorithmic control:## filter tree heap memopt load sort verbose## 0.1 TRUE TRUE FALSE TRUE 2 TRUE## ## Absolute minimum support count: 98 ## ## set item appearances ...[0 item(s)] done [0.00s].## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].## sorting and recoding items ... [88 item(s)] done [0.00s].## creating transaction tree ... done [0.00s].## checking subsets of size 1 2 3 4 done [0.00s].## writing ... [232 rule(s)] done [0.00s].## creating S4 object ... done [0.00s].summary(rules)## set of 232 rules## ## rule length distribution (lhs + rhs):sizes## 1 2 3 ## 1 151 80 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 2.000 2.000 2.341 3.000 3.000 ## ## summary of quality measures:## support confidence lift ## Min. :0.01007 Min. :0.2006 Min. :0.8991 ## 1st Qu.:0.01200 1st Qu.:0.2470 1st Qu.:1.4432 ## Median :0.01490 Median :0.3170 Median :1.7277 ## Mean :0.02005 Mean :0.3321 Mean :1.7890 ## 3rd Qu.:0.02227 3rd Qu.:0.4033 3rd Qu.:2.0762 ## Max. :0.25552 Max. :0.5862 Max. :3.2950 ## ## mining info:## data ntransactions support confidence## Groceries 9835 0.01 0.2#保存数据到磁盘df_rules <- as(rules, "data.frame")write.csv(df_rules, "F:/R/GeroRules.csv")#直接保存#write(rules, file="F:/R/GeroRules1.csv", sep=",", col.names=NA)#4、按支持度对求得的关联规则子集排序并查看前3条规则inspect(sort(rules)[1:3]) #默认decreasing=T，按支持度排序## lhs rhs support confidence## 1 {} => {whole milk} 0.25551601 0.2555160 ## 151 {other vegetables} => {whole milk} 0.07483477 0.3867578 ## 152 {whole milk} => {other vegetables} 0.07483477 0.2928770 ## lift ## 1 1.000000## 151 1.513634## 152 1.513634inspect(sort(rules, decreasing = F)[1:3])## lhs rhs support confidence lift ## 2 {hard cheese} => {whole milk} 0.01006609 0.4107884 1.607682## 20 {waffles} => {other vegetables} 0.01006609 0.2619048 1.353565## 153 {curd,yogurt} => {whole milk} 0.01006609 0.5823529 2.279125inspect(sort(rules, by="lift")[1:3])## lhs rhs support confidence lift## 1 {citrus fruit, ## other vegetables} => {root vegetables} 0.01037112 0.3591549 3.295045## 2 {other vegetables, ## yogurt} => {whipped/sour cream} 0.01016777 0.2341920 3.267062## 3 {tropical fruit, ## other vegetables} => {root vegetables} 0.01230300 0.3427762 3.144780#5、求所需要的关联规则子集：用subset做规则的筛选,取"右手边"含有whole milk且lift大于1.2的规则sub_rules <- subset(rules, subset=rhs %in% "whole milk" & lift>1.2)berryrules <- subset(Groceries, items %in% "berries")inspect(berryrules[1:3])## items ## 1 {pork, ## berries, ## other vegetables, ## whole milk, ## whipped/sour cream, ## artif. sweetener, ## soda, ## abrasive cleaner} ## 2 {berries, ## yogurt} ## 3 {tropical fruit, ## pip fruit, ## berries, ## whole milk, ## frozen potato products,## rolls/buns, ## pickled vegetables, ## chocolate}class(sub_rules)## [1] "rules"## attr(,"package")## [1] "arules"head(as(sub_rules, "data.frame"))## rules support confidence lift## 2 {hard cheese} => {whole milk} 0.01006609 0.4107884 1.607682## 4 {butter milk} => {whole milk} 0.01159126 0.4145455 1.622385## 5 {ham} => {whole milk} 0.01148958 0.4414062 1.727509## 6 {sliced cheese} => {whole milk} 0.01077783 0.4398340 1.721356## 7 {oil} => {whole milk} 0.01128622 0.4021739 1.573968## 9 {onions} => {whole milk} 0.01209964 0.3901639 1.526965#6、eclat()函数求频繁项集sets <- eclat(Groceries, parameter = list(support=0.05, maxlen=10))## Eclat## ## parameter specification:## tidLists support minlen maxlen target ext## FALSE 0.05 1 10 frequent itemsets FALSE## ## algorithmic control:## sparse sort verbose## 7 -2 TRUE## ## Absolute minimum support count: 491 ## ## create itemset ... ## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].## sorting and recoding items ... [28 item(s)] done [0.00s].## creating sparse bit matrix ... [28 row(s), 9835 column(s)] done [0.00s].## writing ... [31 set(s)] done [0.00s].## Creating S4 object ... done [0.00s].summary(sets)## set of 31 itemsets## ## most frequent items:## whole milk other vegetables yogurt rolls/buns ## 4 2 2 2 ## frankfurter (Other) ## 1 23 ## ## element (itemset/transaction) length distribution:sizes## 1 2 ## 28 3 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.000 1.000 1.000 1.097 1.000 2.000 ## ## summary of quality measures:## support ## Min. :0.05236 ## 1st Qu.:0.05831 ## Median :0.07565 ## Mean :0.09212 ## 3rd Qu.:0.10173 ## Max. :0.25552 ## ## includes transaction ID lists: FALSE ## ## mining info:## data ntransactions support## Groceries 9835 0.05#7、按支持度对求得的频繁项集排序并查看前6条频繁项集：inspect(sort(sets, by="support")[1:6])## items support ## 4 {whole milk} 0.2555160## 5 {other vegetables} 0.1934926## 6 {rolls/buns} 0.1839349## 8 {soda} 0.1743772## 7 {yogurt} 0.1395018## 11 {bottled water} 0.1105236#8、针对transcation数据画频繁项的图itemFrequencyPlot(Groceries, support=0.05, cex.names=0.8)#9、简单介绍一下关联规则的可视化包： #每个画图包背后都有一堆包，像ggplot2 library(arulesViz) #载入需要的程辑包：scatterplot3d #载入需要的程辑包：vcd #载入需要的程辑包：MASS #载入需要的程辑包：grid #载入需要的程辑包：colorspace #载入需要的程辑包：seriation #载入需要的程辑包：cluster #载入需要的程辑包：TSP #载入需要的程辑包：gclus #arulesViz中有很多图形，介绍几个好看的，画图的对象都是ruleslibrary(arulesViz)## Loading required package: grid## ## Attaching package: 'arulesViz'## The following object is masked from 'package:arules':## ## abbreviate## The following object is masked from 'package:base':## ## abbreviateplot(rules, shading="order", control=list(main="Two-key plot"))plot(rules, method="grouped")plot(rules, method="graph")实例二、
购物篮数据，每行表示一个篮子，篮子里用逗号分隔出一个个品牌。 现在采用频繁模式挖掘出品牌关联，主要是频繁二项集。将关联看成一条边，出现次数看作边的权重，这样就得到了一张图，对图进行社区发现，可以看到品牌间是否有关联。 原始数据下载：http://pan.baidu.com/s/1jGHr8iy
#1、加载数据并查看x <- readLines("F:\\R\\Rworkspace\\实验数据/user2items.csv")str(x)## chr [1:475] "6805" "4750,19394,25651,6395,5592" ...#2、数据预处理data <- list()for(n in 1:length(x)) { data[n] <- strsplit(x[n], ",")}data[1]## [[1]]## [1] "6805"data[2]## [[1]]## [1] "4750" "19394" "25651" "6395" "5592"trans <- as(data, "transactions")#3、建模library(arules)frequentsets <- eclat(trans, parameter = list(support=0.004, maxlen=10))## Eclat## ## parameter specification:## tidLists support minlen maxlen target ext## FALSE 0.004 1 10 frequent itemsets FALSE## ## algorithmic control:## sparse sort verbose## 7 -2 TRUE## ## Absolute minimum support count: 1## Warning in eclat(trans, parameter = list(support = 0.004, maxlen = 10)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.## create itemset ... ## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s].## sorting and recoding items ... [520 item(s)] done [0.00s].## creating sparse bit matrix ... [520 row(s), 475 column(s)] done [0.00s].## writing ... [753 set(s)] done [0.00s].## Creating S4 object ... done [0.00s].#查看频繁项集inspect(frequentsets[1:10])## items support ## 1 {13471,7868} 0.004210526## 2 {12688,15217} 0.004210526## 3 {15921,7105} 0.004210526## 4 {18712,26737} 0.004210526## 5 {1282,18180} 0.004210526## 6 {11196,14048} 0.004210526## 7 {26576,6571} 0.004210526## 8 {29078,5598} 0.004210526## 9 {11330,26614} 0.004210526## 10 {7868,9899} 0.004210526inspect(sort(frequentsets, by="support")[1:3])## items support ## 234 {7868} 0.05052632## 237 {27791} 0.04421053## 235 {29099} 0.03789474inspect(sort(frequentsets, by="support", decreasing=F)[1:3])## items support ## 1 {13471,7868} 0.004210526## 2 {12688,15217} 0.004210526## 3 {15921,7105} 0.004210526#4、求关联规则rules <- apriori(trans, parameter = list(support=0.004, confidence=0.001))## Apriori## ## Parameter specification:## confidence minval smax arem aval originalSupport support minlen maxlen## 0.001 0.1 1 none FALSE TRUE 0.004 1 10## target ext## rules FALSE## ## Algorithmic control:## filter tree heap memopt load sort verbose## 0.1 TRUE TRUE FALSE TRUE 2 TRUE## ## Absolute minimum support count: 1## Warning in apriori(trans, parameter = list(support = 0.004, confidence = 0.001)): You chose a very low absolute support count of 1. You might run out of memory! Increase minimum support.## set item appearances ...[0 item(s)] done [0.00s].## set transactions ...[1642 item(s), 475 transaction(s)] done [0.00s].## sorting and recoding items ... [520 item(s)] done [0.00s].## creating transaction tree ... done [0.00s].## checking subsets of size 1 2 3 4 done [0.00s].## writing ... [1026 rule(s)] done [0.00s].## creating S4 object ... done [0.00s].summary(rules)## set of 1026 rules## ## rule length distribution (lhs + rhs):sizes## 1 2 3 4 ## 520 396 90 20 ## ## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 1.00 1.00 1.00 1.62 2.00 4.00 ## ## summary of quality measures:## support confidence lift ## Min. :0.004211 Min. :0.00421 Min. : 1.00 ## 1st Qu.:0.004211 1st Qu.:0.00421 1st Qu.: 1.00 ## Median :0.004211 Median :0.02947 Median : 1.00 ## Mean :0.005836 Mean :0.25990 Mean : 24.92 ## 3rd Qu.:0.006316 3rd Qu.:0.40000 3rd Qu.: 31.67 ## Max. :0.050526 Max. :1.00000 Max. :237.50 ## ## mining info:## data ntransactions support confidence## trans 475 0.004 0.001inspect(rules)## lhs rhs support confidence lift ## 1 {} => {3658} 0.004210526 0.004210526 1.000000## 2 {} => {14294} 0.004210526 0.004210526 1.000000## 3 {} => {7963} 0.004210526 0.004210526 1.000000## 4 {} => {7150} 0.004210526 0.004210526 1.000000## 5 {} => {28438} 0.004210526 0.004210526 1.000000## 6 {} => {5094} 0.004210526 0.004210526 1.000000## 7 {} => {11790} 0.004210526 0.004210526 1.000000## 8 {} => {21899} 0.004210526 0.004210526 1.000000## 9 {} => {11280} 0.004210526 0.004210526 1.000000## 10 {} => {9829} 0.004210526 0.004210526 1.000000## 11 {} => {26722} 0.004210526 0.004210526 1.000000## 12 {} => {4039} 0.004210526 0.004210526 1.000000## 13 {} => {25193} 0.004210526 0.004210526 1.000000## 14 {} => {17237} 0.004210526 0.004210526 1.000000## 15 {} => {9301} 0.004210526 0.004210526 1.000000## 16 {} => {25596} 0.004210526 0.004210526 1.000000## 17 {} => {20902} 0.006315789 0.006315789 1.000000## 18 {} => {13975} 0.004210526 0.004210526 1.000000## 19 {} => {24193} 0.004210526 0.004210526 1.000000## 20 {} => {4808} 0.004210526 0.004210526 1.000000## 21 {} => {22240} 0.004210526 0.004210526 1.000000## 22 {} => {12055} 0.004210526 0.004210526 1.000000## 23 {} => {4960} 0.004210526 0.004210526 1.000000## 24 {} => {14360} 0.004210526 0.004210526 1.000000## 25 {} => {15831} 0.004210526 0.004210526 1.000000## 26 {} => {1481} 0.006315789 0.006315789 1.000000## 27 {} => {3185} 0.004210526 0.004210526 1.000000## 28 {} => {9193} 0.004210526 0.004210526 1.000000## 29 {} => {12453} 0.004210526 0.004210526 1.000000## 30 {} => {12647} 0.004210526 0.004210526 1.000000## 31 {} => {20506} 0.004210526 0.004210526 1.000000## 32 {} => {11857} 0.006315789 0.006315789 1.000000## 33 {} => {5015} 0.004210526 0.004210526 1.000000## 34 {} => {9195} 0.004210526 0.004210526 1.000000## 35 {} => {13390} 0.004210526 0.004210526 1.000000## 36 {} => {24274} 0.004210526 0.004210526 1.000000## 37 {} => {15672} 0.004210526 0.004210526 1.000000## 38 {} => {20578} 0.004210526 0.004210526 1.000000## 39 {} => {11159} 0.004210526 0.004210526 1.000000## 40 {} => {19814} 0.004210526 0.004210526 1.000000## 41 {} => {22094} 0.004210526 0.004210526 1.000000## 42 {} => {12586} 0.004210526 0.004210526 1.000000## 43 {} => {15911} 0.004210526 0.004210526 1.000000## 44 {} => {13998} 0.004210526 0.004210526 1.000000## 45 {} => {24788} 0.004210526 0.004210526 1.000000## 46 {} => {5403} 0.004210526 0.004210526 1.000000## 47 {} => {14159} 0.004210526 0.004210526 1.000000## 48 {} => {13093} 0.004210526 0.004210526 1.000000## 49 {} => {16243} 0.004210526 0.004210526 1.000000## 50 {} => {18575} 0.006315789 0.006315789 1.000000## 51 {} => {17153} 0.006315789 0.006315789 1.000000## 52 {} => {6096} 0.004210526 0.004210526 1.000000## 53 {} => {2891} 0.004210526 0.004210526 1.000000## 54 {} => {8816} 0.004210526 0.004210526 1.000000## 55 {} => {20548} 0.004210526 0.004210526 1.000000## 56 {} => {4691} 0.004210526 0.004210526 1.000000## 57 {} => {16009} 0.004210526 0.004210526 1.000000## 58 {} => {14795} 0.004210526 0.004210526 1.000000## 59 {} => {9220} 0.004210526 0.004210526 1.000000## 60 {} => {20701} 0.004210526 0.004210526 1.000000## 61 {} => {4300} 0.004210526 0.004210526 1.000000## 62 {} => {12063} 0.004210526 0.004210526 1.000000## 63 {} => {13471} 0.004210526 0.004210526 1.000000## 64 {} => {3555} 0.004210526 0.004210526 1.000000## 65 {} => {24459} 0.004210526 0.004210526 1.000000## 66 {} => {25960} 0.004210526 0.004210526 1.000000## 67 {} => {5845} 0.004210526 0.004210526 1.000000## 68 {} => {1533} 0.004210526 0.004210526 1.000000## 69 {} => {1831} 0.004210526 0.004210526 1.000000## 70 {} => {26972} 0.004210526 0.004210526 1.000000## 71 {} => {7936} 0.004210526 0.004210526 1.000000## 72 {} => {2610} 0.004210526 0.004210526 1.000000## 73 {} => {10908} 0.004210526 0.004210526 1.000000## 74 {} => {21392} 0.004210526 0.004210526 1.000000## 75 {} => {11357} 0.004210526 0.004210526 1.000000## 76 {} => {178} 0.004210526 0.004210526 1.000000## 77 {} => {16302} 0.004210526 0.004210526 1.000000## 78 {} => {18281} 0.004210526 0.004210526 1.000000## 79 {} => {614} 0.004210526 0.004210526 1.000000## 80 {} => {28391} 0.004210526 0.004210526 1.000000## 81 {} => {23214} 0.004210526 0.004210526 1.000000## 82 {} => {11578} 0.006315789 0.006315789 1.000000## 83 {} => {8693} 0.004210526 0.004210526 1.000000## 84 {} => {5620} 0.004210526 0.004210526 1.000000## 85 {} => {15217} 0.004210526 0.004210526 1.000000## 86 {} => {11018} 0.004210526 0.004210526 1.000000## 87 {} => {28694} 0.004210526 0.004210526 1.000000## 88 {} => {3135} 0.004210526 0.004210526 1.000000## 89 {} => {8313} 0.004210526 0.004210526 1.000000## 90 {} => {25086} 0.004210526 0.004210526 1.000000## 91 {} => {15089} 0.004210526 0.004210526 1.000000## 92 {} => {23622} 0.004210526 0.004210526 1.000000## 93 {} => {14821} 0.004210526 0.004210526 1.000000## 94 {} => {6447} 0.004210526 0.004210526 1.000000## 95 {} => {21995} 0.004210526 0.004210526 1.000000## 96 {} => {23143} 0.004210526 0.004210526 1.000000## 97 {} => {16500} 0.004210526 0.004210526 1.000000## 98 {} => {599} 0.004210526 0.004210526 1.000000## 99 {} => {28411} 0.004210526 0.004210526 1.000000## 100 {} => {5067} 0.006315789 0.006315789 1.000000## 101 {} => {19540} 0.004210526 0.004210526 1.000000## 102 {} => {22342} 0.004210526 0.004210526 1.000000## 103 {} => {15921} 0.004210526 0.004210526 1.000000## 104 {} => {4172} 0.006315789 0.006315789 1.000000## 105 {} => {28370} 0.004210526 0.004210526 1.000000## 106 {} => {27117} 0.004210526 0.004210526 1.000000## 107 {} => {12790} 0.004210526 0.004210526 1.000000## 108 {} => {26121} 0.004210526 0.004210526 1.000000## 109 {} => {21593} 0.004210526 0.004210526 1.000000## 110 {} => {14446} 0.004210526 0.004210526 1.000000## 111 {} => {360} 0.004210526 0.004210526 1.000000## 112 {} => {19993} 0.006315789 0.006315789 1.000000## 113 {} => {11776} 0.004210526 0.004210526 1.000000## 114 {} => {20154} 0.004210526 0.004210526 1.000000## 115 {} => {24929} 0.004210526 0.004210526 1.000000## 116 {} => {8630} 0.004210526 0.004210526 1.000000## 117 {} => {21372} 0.004210526 0.004210526 1.000000## 118 {} => {5848} 0.004210526 0.004210526 1.000000## 119 {} => {1392} 0.006315789 0.006315789 1.000000## 120 {} => {4819} 0.004210526 0.004210526 1.000000## 121 {} => {1950} 0.004210526 0.004210526 1.000000## 122 {} => {15018} 0.004210526 0.004210526 1.000000## 123 {} => {1966} 0.004210526 0.004210526 1.000000## 124 {} => {4731} 0.004210526 0.004210526 1.000000## 125 {} => {10866} 0.004210526 0.004210526 1.000000## 126 {} => {22621} 0.004210526 0.004210526 1.000000## 127 {} => {18996} 0.004210526 0.004210526 1.000000## 128 {} => {19217} 0.004210526 0.004210526 1.000000## 129 {} => {22029} 0.004210526 0.004210526 1.000000## 130 {} => {1282} 0.004210526 0.004210526 1.000000## 131 {} => {26737} 0.004210526 0.004210526 1.000000## 132 {} => {27514} 0.004210526 0.004210526 1.000000## 133 {} => {27155} 0.004210526 0.004210526 1.000000## 134 {} => {4775} 0.004210526 0.004210526 1.000000## 135 {} => {4510} 0.004210526 0.004210526 1.000000## 136 {} => {24503} 0.004210526 0.004210526 1.000000## 137 {} => {29078} 0.004210526 0.004210526 1.000000## 138 {} => {21975} 0.004210526 0.004210526 1.000000## 139 {} => {1335} 0.004210526 0.004210526 1.000000## 140 {} => {3190} 0.004210526 0.004210526 1.000000## 141 {} => {21533} 0.004210526 0.004210526 1.000000## 142 {} => {26576} 0.004210526 0.004210526 1.000000## 143 {} => {14048} 0.004210526 0.004210526 1.000000## 144 {} => {20800} 0.006315789 0.006315789 1.000000## 145 {} => {18758} 0.004210526 0.004210526 1.000000## 146 {} => {24886} 0.004210526 0.004210526 1.000000## 147 {} => {27539} 0.004210526 0.004210526 1.000000## 148 {} => {11431} 0.006315789 0.006315789 1.000000## 149 {} => {26619} 0.010526316 0.010526316 1.000000## 150 {} => {26298} 0.004210526 0.004210526 1.000000## 151 {} => {7567} 0.004210526 0.004210526 1.000000## 152 {} => {6621} 0.006315789 0.006315789 1.000000## 153 {} => {17921} 0.004210526 0.004210526 1.000000## 154 {} => {7560} 0.004210526 0.004210526 1.000000## 155 {} => {9881} 0.004210526 0.004210526 1.000000## 156 {} => {22113} 0.004210526 0.004210526 1.000000## 157 {} => {255} 0.004210526 0.004210526 1.000000## 158 {} => {2452} 0.004210526 0.004210526 1.000000## 159 {} => {27637} 0.006315789 0.006315789 1.000000## 160 {} => {11330} 0.006315789 0.006315789 1.000000## 161 {} => {1731} 0.006315789 0.006315789 1.000000## 162 {} => {26180} 0.004210526 0.004210526 1.000000## 163 {} => {2669} 0.004210526 0.004210526 1.000000## 164 {} => {19539} 0.004210526 0.004210526 1.000000## 165 {} => {3068} 0.004210526 0.004210526 1.000000## 166 {} => {14573} 0.004210526 0.004210526 1.000000## 167 {} => {20456} 0.004210526 0.004210526 1.000000## 168 {} => {26394} 0.004210526 0.004210526 1.000000## 169 {} => {19379} 0.004210526 0.004210526 1.000000## 170 {} => {25570} 0.004210526 0.004210526 1.000000## 171 {} => {16818} 0.008421053 0.008421053 1.000000## 172 {} => {5336} 0.004210526 0.004210526 1.000000## 173 {} => {28184} 0.006315789 0.006315789 1.000000## 174 {} => {9899} 0.006315789 0.006315789 1.000000## 175 {} => {17823} 0.004210526 0.004210526 1.000000## 176 {} => {7208} 0.006315789 0.006315789 1.000000## 177 {} => {27346} 0.004210526 0.004210526 1.000000## 178 {} => {8724} 0.004210526 0.004210526 1.000000## 179 {} => {10872} 0.004210526 0.004210526 1.000000## 180 {} => {17732} 0.004210526 0.004210526 1.000000## 181 {} => {6880} 0.004210526 0.004210526 1.000000## 182 {} => {28967} 0.004210526 0.004210526 1.000000## 183 {} => {23549} 0.004210526 0.004210526 1.000000## 184 {} => {14894} 0.004210526 0.004210526 1.000000## 185 {} => {24385} 0.004210526 0.004210526 1.000000## 186 {} => {4578} 0.006315789 0.006315789 1.000000## 187 {} => {22280} 0.006315789 0.006315789 1.000000## 188 {} => {29202} 0.006315789 0.006315789 1.000000## 189 {} => {7070} 0.004210526 0.004210526 1.000000## 190 {} => {16939} 0.008421053 0.008421053 1.000000## 191 {} => {15423} 0.004210526 0.004210526 1.000000## 192 {} => {25381} 0.004210526 0.004210526 1.000000## 193 {} => {953} 0.004210526 0.004210526 1.000000## 194 {} => {7297} 0.004210526 0.004210526 1.000000## 195 {} => {7542} 0.006315789 0.006315789 1.000000## 196 {} => {10948} 0.004210526 0.004210526 1.000000## 197 {} => {12431} 0.004210526 0.004210526 1.000000## 198 {} => {20626} 0.004210526 0.004210526 1.000000## 199 {} => {17087} 0.006315789 0.006315789 1.000000## 200 {} => {21565} 0.004210526 0.004210526 1.000000## 201 {} => {2655} 0.006315789 0.006315789 1.000000## 202 {} => {25733} 0.004210526 0.004210526 1.000000## 203 {} => {28463} 0.004210526 0.004210526 1.000000## 204 {} => {10193} 0.004210526 0.004210526 1.000000## 205 {} => {16768} 0.004210526 0.004210526 1.000000## 206 {} => {19615} 0.004210526 0.004210526 1.000000## 207 {} => {21883} 0.004210526 0.004210526 1.000000## 208 {} => {617} 0.006315789 0.006315789 1.000000## 209 {} => {16952} 0.006315789 0.006315789 1.000000## 210 {} => {11864} 0.004210526 0.004210526 1.000000## 211 {} => {14603} 0.004210526 0.004210526 1.000000## 212 {} => {8719} 0.004210526 0.004210526 1.000000## 213 {} => {9620} 0.006315789 0.006315789 1.000000## 214 {} => {26699} 0.004210526 0.004210526 1.000000## 215 {} => {7997} 0.004210526 0.004210526 1.000000## 216 {} => {6951} 0.006315789 0.006315789 1.000000## 217 {} => {259} 0.004210526 0.004210526 1.000000## 218 {} => {3719} 0.004210526 0.004210526 1.000000## 219 {} => {18697} 0.004210526 0.004210526 1.000000## 220 {} => {23698} 0.004210526 0.004210526 1.000000## 221 {} => {17835} 0.006315789 0.006315789 1.000000## 222 {} => {1917} 0.008421053 0.008421053 1.000000## 223 {} => {3740} 0.006315789 0.006315789 1.000000## 224 {} => {9340} 0.004210526 0.004210526 1.000000## 225 {} => {27437} 0.004210526 0.004210526 1.000000## 226 {} => {3458} 0.008421053 0.008421053 1.000000## 227 {} => {23482} 0.004210526 0.004210526 1.000000## 228 {} => {14292} 0.004210526 0.004210526 1.000000## 229 {} => {13240} 0.004210526 0.004210526 1.000000## 230 {} => {19974} 0.008421053 0.008421053 1.000000## 231 {} => {11734} 0.004210526 0.004210526 1.000000## 232 {} => {9657} 0.006315789 0.006315789 1.000000## 233 {} => {27060} 0.004210526 0.004210526 1.000000## 234 {} => {15065} 0.004210526 0.004210526 1.000000## 235 {} => {1237} 0.004210526 0.004210526 1.000000## 236 {} => {18544} 0.004210526 0.004210526 1.000000## 237 {} => {6246} 0.004210526 0.004210526 1.000000## 238 {} => {619} 0.004210526 0.004210526 1.000000## 239 {} => {3390} 0.004210526 0.004210526 1.000000## 240 {} => {1037} 0.004210526 0.004210526 1.000000## 241 {} => {14596} 0.004210526 0.004210526 1.000000## 242 {} => {504} 0.006315789 0.006315789 1.000000## 243 {} => {7850} 0.004210526 0.004210526 1.000000## 244 {} => {3850} 0.006315789 0.006315789 1.000000## 245 {} => {6148} 0.004210526 0.004210526 1.000000## 246 {} => {21911} 0.004210526 0.004210526 1.000000## 247 {} => {9567} 0.004210526 0.004210526 1.000000## 248 {} => {8943} 0.008421053 0.008421053 1.000000## 249 {} => {9472} 0.006315789 0.006315789 1.000000## 250 {} => {6665} 0.004210526 0.004210526 1.000000## 251 {} => {17512} 0.004210526 0.004210526 1.000000## 252 {} => {24417} 0.004210526 0.004210526 1.000000## 253 {} => {16406} 0.004210526 0.004210526 1.000000## 254 {} => {5086} 0.006315789 0.006315789 1.000000## 255 {} => {15645} 0.004210526 0.004210526 1.000000## 256 {} => {22179} 0.006315789 0.006315789 1.000000## 257 {} => {14661} 0.006315789 0.006315789 1.000000## 258 {} => {24281} 0.004210526 0.004210526 1.000000## 259 {} => {10949} 0.004210526 0.004210526 1.000000## 260 {} => {6672} 0.006315789 0.006315789 1.000000## 261 {} => {6158} 0.004210526 0.004210526 1.000000## 262 {} => {11849} 0.004210526 0.004210526 1.000000## 263 {} => {4750} 0.004210526 0.004210526 1.000000## 264 {} => {14902} 0.006315789 0.006315789 1.000000## 265 {} => {11060} 0.004210526 0.004210526 1.000000## 266 {} => {911} 0.004210526 0.004210526 1.000000## 267 {} => {20661} 0.006315789 0.006315789 1.000000## 268 {} => {1758} 0.004210526 0.004210526 1.000000## 269 {} => {11201} 0.006315789 0.006315789 1.000000## 270 {} => {1293} 0.004210526 0.004210526 1.000000## 271 {} => {18002} 0.008421053 0.008421053 1.000000## 272 {} => {15019} 0.010526316 0.010526316 1.000000## 273 {} => {6839} 0.004210526 0.004210526 1.000000## 274 {} => {15390} 0.004210526 0.004210526 1.000000## 275 {} => {15138} 0.014736842 0.014736842 1.000000## 276 {} => {12271} 0.008421053 0.008421053 1.000000## 277 {} => {4324} 0.004210526 0.004210526 1.000000## 278 {} => {7827} 0.006315789 0.006315789 1.000000## 279 {} => {7680} 0.006315789 0.006315789 1.000000## 280 {} => {2771} 0.004210526 0.004210526 1.000000## 281 {} => {24447} 0.004210526 0.004210526 1.000000## 282 {} => {1803} 0.004210526 0.004210526 1.000000## 283 {} => {5667} 0.004210526 0.004210526 1.000000## 284 {} => {143} 0.006315789 0.006315789 1.000000## 285 {} => {15478} 0.004210526 0.004210526 1.000000## 286 {} => {23013} 0.004210526 0.004210526 1.000000## 287 {} => {15934} 0.010526316 0.010526316 1.000000## 288 {} => {8173} 0.004210526 0.004210526 1.000000## 289 {} => {16624} 0.004210526 0.004210526 1.000000## 290 {} => {8257} 0.006315789 0.006315789 1.000000## 291 {} => {20297} 0.006315789 0.006315789 1.000000## 292 {} => {19772} 0.004210526 0.004210526 1.000000## 293 {} => {7409} 0.008421053 0.008421053 1.000000## 294 {} => {25917} 0.006315789 0.006315789 1.000000## 295 {} => {527} 0.008421053 0.008421053 1.000000## 296 {} => {28662} 0.004210526 0.004210526 1.000000## 297 {} => {16722} 0.006315789 0.006315789 1.000000## 298 {} => {14580} 0.006315789 0.006315789 1.000000## 299 {} => {13554} 0.004210526 0.004210526 1.000000## 300 {} => {3438} 0.006315789 0.006315789 1.000000## 301 {} => {19891} 0.006315789 0.006315789 1.000000## 302 {} => {9906} 0.004210526 0.004210526 1.000000## 303 {} => {12674} 0.006315789 0.006315789 1.000000## 304 {} => {26728} 0.006315789 0.006315789 1.000000## 305 {} => {2257} 0.006315789 0.006315789 1.000000## 306 {} => {5661} 0.006315789 0.006315789 1.000000## 307 {} => {28876} 0.004210526 0.004210526 1.000000## 308 {} => {25372} 0.012631579 0.012631579 1.000000## 309 {} => {2729} 0.006315789 0.006315789 1.000000## 310 {} => {12717} 0.004210526 0.004210526 1.000000## 311 {} => {3324} 0.006315789 0.006315789 1.000000## 312 {} => {10893} 0.010526316 0.010526316 1.000000## 313 {} => {23774} 0.006315789 0.006315789 1.000000## 314 {} => {4059} 0.006315789 0.006315789 1.000000## 315 {} => {12758} 0.004210526 0.004210526 1.000000## 316 {} => {19416} 0.006315789 0.006315789 1.000000## 317 {} => {7613} 0.004210526 0.004210526 1.000000## 318 {} => {20694} 0.006315789 0.006315789 1.000000## 319 {} => {21067} 0.006315789 0.006315789 1.000000## 320 {} => {4220} 0.010526316 0.010526316 1.000000## 321 {} => {5081} 0.006315789 0.006315789 1.000000## 322 {} => {25618} 0.008421053 0.008421053 1.000000## 323 {} => {13039} 0.004210526 0.004210526 1.000000## 324 {} => {7465} 0.006315789 0.006315789 1.000000## 325 {} => {12688} 0.008421053 0.008421053 1.000000## 326 {} => {13265} 0.004210526 0.004210526 1.000000## 327 {} => {28065} 0.006315789 0.006315789 1.000000## 328 {} => {20411} 0.004210526 0.004210526 1.000000## 329 {} => {21983} 0.004210526 0.004210526 1.000000## 330 {} => {2198} 0.008421053 0.008421053 1.000000## 331 {} => {26006} 0.004210526 0.004210526 1.000000## 332 {} => {23475} 0.006315789 0.006315789 1.000000## 333 {} => {12162} 0.006315789 0.006315789 1.000000## 334 {} => {4931} 0.004210526 0.004210526 1.000000## 335 {} => {27052} 0.004210526 0.004210526 1.000000## 336 {} => {16846} 0.004210526 0.004210526 1.000000## 337 {} => {11329} 0.006315789 0.006315789 1.000000## 338 {} => {3047} 0.008421053 0.008421053 1.000000## 339 {} => {949} 0.008421053 0.008421053 1.000000## 340 {} => {24944} 0.006315789 0.006315789 1.000000## 341 {} => {11000} 0.004210526 0.004210526 1.000000## 342 {} => {25488} 0.006315789 0.006315789 1.000000## 343 {} => {18990} 0.006315789 0.006315789 1.000000## 344 {} => {9671} 0.004210526 0.004210526 1.000000## 345 {} => {17945} 0.008421053 0.008421053 1.000000## 346 {} => {28653} 0.004210526 0.004210526 1.000000## 347 {} => {3032} 0.008421053 0.008421053 1.000000## 348 {} => {26114} 0.004210526 0.004210526 1.000000## 349 {} => {27401} 0.004210526 0.004210526 1.000000## 350 {} => {2683} 0.010526316 0.010526316 1.000000## 351 {} => {24907} 0.006315789 0.006315789 1.000000## 352 {} => {239} 0.006315789 0.006315789 1.000000## 353 {} => {19574} 0.004210526 0.004210526 1.000000## 354 {} => {18388} 0.006315789 0.006315789 1.000000## 355 {} => {12541} 0.008421053 0.008421053 1.000000## 356 {} => {20536} 0.006315789 0.006315789 1.000000## 357 {} => {2251} 0.004210526 0.004210526 1.000000## 358 {} => {28481} 0.006315789 0.006315789 1.000000## 359 {} => {7692} 0.004210526 0.004210526 1.000000## 360 {} => {10726} 0.006315789 0.006315789 1.000000## 361 {} => {24172} 0.006315789 0.006315789 1.000000## 362 {} => {1773} 0.006315789 0.006315789 1.000000## 363 {} => {3313} 0.006315789 0.006315789 1.000000## 364 {} => {4479} 0.008421053 0.008421053 1.000000## 365 {} => {23019} 0.004210526 0.004210526 1.000000## 366 {} => {5306} 0.006315789 0.006315789 1.000000## 367 {} => {5598} 0.010526316 0.010526316 1.000000## 368 {} => {12795} 0.004210526 0.004210526 1.000000## 369 {} => {26546} 0.008421053 0.008421053 1.000000## 370 {} => {18829} 0.004210526 0.004210526 1.000000## 371 {} => {5185} 0.012631579 0.012631579 1.000000## 372 {} => {17060} 0.008421053 0.008421053 1.000000## 373 {} => {2999} 0.006315789 0.006315789 1.000000## 374 {} => {3804} 0.006315789 0.006315789 1.000000## 375 {} => {3647} 0.006315789 0.006315789 1.000000## 376 {} => {10840} 0.008421053 0.008421053 1.000000## 377 {} => {554} 0.008421053 0.008421053 1.000000## 378 {} => {24541} 0.008421053 0.008421053 1.000000## 379 {} => {18167} 0.010526316 0.010526316 1.000000## 380 {} => {3181} 0.006315789 0.006315789 1.000000## 381 {} => {23861} 0.012631579 0.012631579 1.000000## 382 {} => {22489} 0.006315789 0.006315789 1.000000## 383 {} => {23656} 0.008421053 0.008421053 1.000000## 384 {} => {3913} 0.004210526 0.004210526 1.000000## 385 {} => {21110} 0.012631579 0.012631579 1.000000## 386 {} => {4078} 0.010526316 0.010526316 1.000000## 387 {} => {25366} 0.006315789 0.006315789 1.000000## 388 {} => {19405} 0.006315789 0.006315789 1.000000## 389 {} => {27205} 0.008421053 0.008421053 1.000000## 390 {} => {17706} 0.008421053 0.008421053 1.000000## 391 {} => {21146} 0.008421053 0.008421053 1.000000## 392 {} => {13020} 0.012631579 0.012631579 1.000000## 393 {} => {24601} 0.014736842 0.014736842 1.000000## 394 {} => {4281} 0.008421053 0.008421053 1.000000## 395 {} => {19166} 0.004210526 0.004210526 1.000000## 396 {} => {1031} 0.008421053 0.008421053 1.000000## 397 {} => {24196} 0.010526316 0.010526316 1.000000## 398 {} => {23779} 0.014736842 0.014736842 1.000000## 399 {} => {2367} 0.016842105 0.016842105 1.000000## 400 {} => {23662} 0.008421053 0.008421053 1.000000## 401 {} => {12352} 0.010526316 0.010526316 1.000000## 402 {} => {23284} 0.010526316 0.010526316 1.000000## 403 {} => {8278} 0.006315789 0.006315789 1.000000## 404 {} => {8628} 0.012631579 0.012631579 1.000000## 405 {} => {21672} 0.008421053 0.008421053 1.000000## 406 {} => {1739} 0.006315789 0.006315789 1.000000## 407 {} => {14942} 0.012631579 0.012631579 1.000000## 408 {} => {12754} 0.012631579 0.012631579 1.000000## 409 {} => {20551} 0.006315789 0.006315789 1.000000## 410 {} => {13592} 0.006315789 0.006315789 1.000000## 411 {} => {21838} 0.008421053 0.008421053 1.000000## 412 {} => {28641} 0.006315789 0.006315789 1.000000## 413 {} => {28985} 0.008421053 0.008421053 1.000000## 414 {} => {7248} 0.010526316 0.010526316 1.000000## 415 {} => {6571} 0.021052632 0.021052632 1.000000## 416 {} => {16331} 0.010526316 0.010526316 1.000000## 417 {} => {13784} 0.008421053 0.008421053 1.000000## 418 {} => {14153} 0.010526316 0.010526316 1.000000## 419 {} => {19394} 0.010526316 0.010526316 1.000000## 420 {} => {12220} 0.014736842 0.014736842 1.000000## 421 {} => {21657} 0.006315789 0.006315789 1.000000## 422 {} => {24869} 0.014736842 0.014736842 1.000000## 423 {} => {23896} 0.006315789 0.006315789 1.000000## 424 {} => {12977} 0.012631579 0.012631579 1.000000## 425 {} => {14482} 0.010526316 0.010526316 1.000000## 426 {} => {18180} 0.012631579 0.012631579 1.000000## 427 {} => {25169} 0.008421053 0.008421053 1.000000## 428 {} => {18075} 0.016842105 0.016842105 1.000000## 429 {} => {19973} 0.010526316 0.010526316 1.000000## 430 {} => {2963} 0.016842105 0.016842105 1.000000## 431 {} => {12068} 0.010526316 0.010526316 1.000000## 432 {} => {16463} 0.018947368 0.018947368 1.000000## 433 {} => {16944} 0.006315789 0.006315789 1.000000## 434 {} => {5053} 0.008421053 0.008421053 1.000000## 435 {} => {21865} 0.014736842 0.014736842 1.000000## 436 {} => {10999} 0.012631579 0.012631579 1.000000## 437 {} => {5043} 0.012631579 0.012631579 1.000000## 438 {} => {530} 0.008421053 0.008421053 1.000000## 439 {} => {27625} 0.010526316 0.010526316 1.000000## 440 {} => {22043} 0.008421053 0.008421053 1.000000## 441 {} => {18741} 0.014736842 0.014736842 1.000000## 442 {} => {16110} 0.012631579 0.012631579 1.000000## 443 {} => {7059} 0.004210526 0.004210526 1.000000## 444 {} => {29547} 0.010526316 0.010526316 1.000000## 445 {} => {5814} 0.004210526 0.004210526 1.000000## 446 {} => {679} 0.014736842 0.014736842 1.000000## 447 {} => {22359} 0.012631579 0.012631579 1.000000## 448 {} => {251} 0.014736842 0.014736842 1.000000## 449 {} => {25329} 0.010526316 0.010526316 1.000000## 450 {} => {11524} 0.004210526 0.004210526 1.000000## 451 {} => {1461} 0.006315789 0.006315789 1.000000## 452 {} => {28270} 0.016842105 0.016842105 1.000000## 453 {} => {7230} 0.010526316 0.010526316 1.000000## 454 {} => {26614} 0.014736842 0.014736842 1.000000## 455 {} => {18515} 0.004210526 0.004210526 1.000000## 456 {} => {14415} 0.006315789 0.006315789 1.000000## 457 {} => {26288} 0.012631579 0.012631579 1.000000## 458 {} => {22749} 0.012631579 0.012631579 1.000000## 459 {} => {15534} 0.006315789 0.006315789 1.000000## 460 {} => {21071} 0.006315789 0.006315789 1.000000## 461 {} => {29224} 0.006315789 0.006315789 1.000000## 462 {} => {7037} 0.004210526 0.004210526 1.000000## 463 {} => {17061} 0.004210526 0.004210526 1.000000## 464 {} => {11022} 0.006315789 0.006315789 1.000000## 465 {} => {22126} 0.012631579 0.012631579 1.000000## 466 {} => {24669} 0.012631579 0.012631579 1.000000## 467 {} => {8842} 0.006315789 0.006315789 1.000000## 468 {} => {17214} 0.006315789 0.006315789 1.000000## 469 {} => {21092} 0.008421053 0.008421053 1.000000## 470 {} => {16540} 0.018947368 0.018947368 1.000000## 471 {} => {10325} 0.004210526 0.004210526 1.000000## 472 {} => {2128} 0.006315789 0.006315789 1.000000## 473 {} => {29203} 0.018947368 0.018947368 1.000000## 474 {} => {19421} 0.006315789 0.006315789 1.000000## 475 {} => {22313} 0.006315789 0.006315789 1.000000## 476 {} => {11196} 0.031578947 0.031578947 1.000000## 477 {} => {18730} 0.018947368 0.018947368 1.000000## 478 {} => {9563} 0.014736842 0.014736842 1.000000## 479 {} => {1000} 0.006315789 0.006315789 1.000000## 480 {} => {21919} 0.010526316 0.010526316 1.000000## 481 {} => {3151} 0.014736842 0.014736842 1.000000## 482 {} => {26523} 0.010526316 0.010526316 1.000000## 483 {} => {10014} 0.010526316 0.010526316 1.000000## 484 {} => {21336} 0.006315789 0.006315789 1.000000## 485 {} => {7096} 0.014736842 0.014736842 1.000000## 486 {} => {8637} 0.023157895 0.023157895 1.000000## 487 {} => {25651} 0.008421053 0.008421053 1.000000## 488 {} => {11176} 0.021052632 0.021052632 1.000000## 489 {} => {4807} 0.006315789 0.006315789 1.000000## 490 {} => {14065} 0.006315789 0.006315789 1.000000## 491 {} => {22556} 0.008421053 0.008421053 1.000000## 492 {} => {18712} 0.012631579 0.012631579 1.000000## 493 {} => {14917} 0.008421053 0.008421053 1.000000## 494 {} => {17959} 0.008421053 0.008421053 1.000000## 495 {} => {12285} 0.023157895 0.023157895 1.000000## 496 {} => {4571} 0.025263158 0.025263158 1.000000## 497 {} => {15315} 0.016842105 0.016842105 1.000000## 498 {} => {7061} 0.010526316 0.010526316 1.000000## 499 {} => {20979} 0.016842105 0.016842105 1.000000## 500 {} => {7105} 0.025263158 0.025263158 1.000000## 501 {} => {4949} 0.018947368 0.018947368 1.000000## 502 {} => {3228} 0.029473684 0.029473684 1.000000## 503 {} => {11080} 0.031578947 0.031578947 1.000000## 504 {} => {18805} 0.021052632 0.021052632 1.000000## 505 {} => {3627} 0.023157895 0.023157895 1.000000## 506 {} => {23628} 0.021052632 0.021052632 1.000000## 507 {} => {15584} 0.012631579 0.012631579 1.000000## 508 {} => {18024} 0.029473684 0.029473684 1.000000## 509 {} => {4411} 0.012631579 0.012631579 1.000000## 510 {} => {11679} 0.025263158 0.025263158 1.000000## 511 {} => {8689} 0.029473684 0.029473684 1.000000## 512 {} => {23928} 0.016842105 0.016842105 1.000000## 513 {} => {9111} 0.016842105 0.016842105 1.000000## 514 {} => {155} 0.023157895 0.023157895 1.000000## 515 {} => {10702} 0.014736842 0.014736842 1.000000## 516 {} => {14261} 0.023157895 0.023157895 1.000000## 517 {} => {27791} 0.044210526 0.044210526 1.000000## 518 {} => {14020} 0.037894737 0.037894737 1.000000## 519 {} => {29099} 0.037894737 0.037894737 1.000000## 520 {} => {7868} 0.050526316 0.050526316 1.000000## 521 {13471} => {7868} 0.004210526 1.000000000 19.791667## 522 {7868} => {13471} 0.004210526 0.083333333 19.791667## 523 {15217} => {12688} 0.004210526 1.000000000 118.750000## 524 {12688} => {15217} 0.004210526 0.500000000 118.750000## 525 {15921} => {7105} 0.004210526 1.000000000 39.583333## 526 {7105} => {15921} 0.004210526 0.166666667 39.583333## 527 {1282} => {18180} 0.004210526 1.000000000 79.166667## 528 {18180} => {1282} 0.004210526 0.333333333 79.166667## 529 {26737} => {18712} 0.004210526 1.000000000 79.166667## 530 {18712} => {26737} 0.004210526 0.333333333 79.166667## 531 {29078} => {5598} 0.004210526 1.000000000 95.000000## 532 {5598} => {29078} 0.004210526 0.400000000 95.000000## 533 {26576} => {6571} 0.004210526 1.000000000 47.500000## 534 {6571} => {26576} 0.004210526 0.200000000 47.500000## 535 {14048} => {11196} 0.004210526 1.000000000 31.666667## 536 {11196} => {14048} 0.004210526 0.133333333 31.666667## 537 {11330} => {26614} 0.004210526 0.666666667 45.238095## 538 {26614} => {11330} 0.004210526 0.285714286 45.238095## 539 {25570} => {11176} 0.004210526 1.000000000 47.500000## 540 {11176} => {25570} 0.004210526 0.200000000 47.500000## 541 {9899} => {7868} 0.004210526 0.666666667 13.194444## 542 {7868} => {9899} 0.004210526 0.083333333 13.194444## 543 {17087} => {17060} 0.004210526 0.666666667 79.166667## 544 {17060} => {17087} 0.004210526 0.500000000 79.166667## 545 {7680} => {21110} 0.004210526 0.666666667 52.777778## 546 {21110} => {7680} 0.004210526 0.333333333 52.777778## 547 {7680} => {12754} 0.004210526 0.666666667 52.777778## 548 {12754} => {7680} 0.004210526 0.333333333 52.777778## 549 {7680} => {16463} 0.004210526 0.666666667 35.185185## 550 {16463} => {7680} 0.004210526 0.222222222 35.185185## 551 {5667} => {19405} 0.004210526 1.000000000 158.333333## 552 {19405} => {5667} 0.004210526 0.666666667 158.333333## 553 {14580} => {11080} 0.004210526 0.666666667 21.111111## 554 {11080} => {14580} 0.004210526 0.133333333 21.111111## 555 {3438} => {16331} 0.004210526 0.666666667 63.333333## 556 {16331} => {3438} 0.004210526 0.400000000 63.333333## 557 {5661} => {18741} 0.004210526 0.666666667 45.238095## 558 {18741} => {5661} 0.004210526 0.285714286 45.238095## 559 {25372} => {5598} 0.004210526 0.333333333 31.666667## 560 {5598} => {25372} 0.004210526 0.400000000 31.666667## 561 {2729} => {3151} 0.004210526 0.666666667 45.238095## 562 {3151} => {2729} 0.004210526 0.285714286 45.238095## 563 {2729} => {14020} 0.004210526 0.666666667 17.592593## 564 {14020} => {2729} 0.004210526 0.111111111 17.592593## 565 {12717} => {22043} 0.004210526 1.000000000 118.750000## 566 {22043} => {12717} 0.004210526 0.500000000 118.750000## 567 {12717} => {22359} 0.004210526 1.000000000 79.166667## 568 {22359} => {12717} 0.004210526 0.333333333 79.166667## 569 {23774} => {8689} 0.004210526 0.666666667 22.619048## 570 {8689} => {23774} 0.004210526 0.142857143 22.619048## 571 {19416} => {4571} 0.004210526 0.666666667 26.388889## 572 {4571} => {19416} 0.004210526 0.166666667 26.388889## 573 {4220} => {29203} 0.004210526 0.400000000 21.111111## 574 {29203} => {4220} 0.004210526 0.222222222 21.111111## 575 {4220} => {10014} 0.004210526 0.400000000 38.000000## 576 {10014} => {4220} 0.004210526 0.400000000 38.000000## 577 {12688} => {18741} 0.004210526 0.500000000 33.928571## 578 {18741} => {12688} 0.004210526 0.285714286 33.928571## 579 {4931} => {29099} 0.004210526 1.000000000 26.388889## 580 {29099} => {4931} 0.004210526 0.111111111 26.388889## 581 {3047} => {4949} 0.004210526 0.500000000 26.388889## 582 {4949} => {3047} 0.004210526 0.222222222 26.388889## 583 {24944} => {12068} 0.004210526 0.666666667 63.333333## 584 {12068} => {24944} 0.004210526 0.400000000 63.333333## 585 {3032} => {7105} 0.004210526 0.500000000 19.791667## 586 {7105} => {3032} 0.004210526 0.166666667 19.791667## 587 {12541} => {15315} 0.004210526 0.500000000 29.687500## 588 {15315} => {12541} 0.004210526 0.250000000 29.687500## 589 {2251} => {7868} 0.004210526 1.000000000 19.791667## 590 {7868} => {2251} 0.004210526 0.083333333 19.791667## 591 {7692} => {23019} 0.004210526 1.000000000 237.500000## 592 {23019} => {7692} 0.004210526 1.000000000 237.500000## 593 {7692} => {27791} 0.004210526 1.000000000 22.619048## 594 {27791} => {7692} 0.004210526 0.095238095 22.619048## 595 {24172} => {21838} 0.004210526 0.666666667 79.166667## 596 {21838} => {24172} 0.004210526 0.500000000 79.166667## 597 {24172} => {11080} 0.004210526 0.666666667 21.111111## 598 {11080} => {24172} 0.004210526 0.133333333 21.111111## 599 {1773} => {29203} 0.004210526 0.666666667 35.185185## 600 {29203} => {1773} 0.004210526 0.222222222 35.185185## 601 {4479} => {29099} 0.006315789 0.750000000 19.791667## 602 {29099} => {4479} 0.006315789 0.166666667 19.791667## 603 {23019} => {27791} 0.004210526 1.000000000 22.619048## 604 {27791} => {23019} 0.004210526 0.095238095 22.619048## 605 {12795} => {22126} 0.004210526 1.000000000 79.166667## 606 {22126} => {12795} 0.004210526 0.333333333 79.166667## 607 {2999} => {24669} 0.004210526 0.666666667 52.777778## 608 {24669} => {2999} 0.004210526 0.333333333 52.777778## 609 {3647} => {18741} 0.004210526 0.666666667 45.238095## 610 {18741} => {3647} 0.004210526 0.285714286 45.238095## 611 {10840} => {3151} 0.004210526 0.500000000 33.928571## 612 {3151} => {10840} 0.004210526 0.285714286 33.928571## 613 {3913} => {530} 0.004210526 1.000000000 118.750000## 614 {530} => {3913} 0.004210526 0.500000000 118.750000## 615 {3913} => {11679} 0.004210526 1.000000000 39.583333## 616 {11679} => {3913} 0.004210526 0.166666667 39.583333## 617 {21110} => {15534} 0.004210526 0.333333333 52.777778## 618 {15534} => {21110} 0.004210526 0.666666667 52.777778## 619 {21146} => {2963} 0.006315789 0.750000000 44.531250## 620 {2963} => {21146} 0.006315789 0.375000000 44.531250## 621 {21146} => {7096} 0.004210526 0.500000000 33.928571## 622 {7096} => {21146} 0.004210526 0.285714286 33.928571## 623 {24601} => {18024} 0.004210526 0.285714286 9.693878## 624 {18024} => {24601} 0.004210526 0.142857143 9.693878## 625 {2367} => {11679} 0.004210526 0.250000000 9.895833## 626 {11679} => {2367} 0.004210526 0.166666667 9.895833## 627 {12352} => {3627} 0.004210526 0.400000000 17.272727## 628 {3627} => {12352} 0.004210526 0.181818182 17.272727## 629 {8278} => {16331} 0.004210526 0.666666667 63.333333## 630 {16331} => {8278} 0.004210526 0.400000000 63.333333## 631 {8278} => {18024} 0.004210526 0.666666667 22.619048## 632 {18024} => {8278} 0.004210526 0.142857143 22.619048## 633 {8628} => {16463} 0.006315789 0.500000000 26.388889## 634 {16463} => {8628} 0.006315789 0.333333333 26.388889## 635 {8628} => {22359} 0.004210526 0.333333333 26.388889## 636 {22359} => {8628} 0.004210526 0.333333333 26.388889## 637 {1739} => {7096} 0.004210526 0.666666667 45.238095## 638 {7096} => {1739} 0.004210526 0.285714286 45.238095## 639 {14942} => {5043} 0.004210526 0.333333333 26.388889## 640 {5043} => {14942} 0.004210526 0.333333333 26.388889## 641 {14942} => {8637} 0.004210526 0.333333333 14.393939## 642 {8637} => {14942} 0.004210526 0.181818182 14.393939## 643 {13592} => {4949} 0.004210526 0.666666667 35.185185## 644 {4949} => {13592} 0.004210526 0.222222222 35.185185## 645 {21838} => {4571} 0.004210526 0.500000000 19.791667## 646 {4571} => {21838} 0.004210526 0.166666667 19.791667## 647 {21838} => {7105} 0.004210526 0.500000000 19.791667## 648 {7105} => {21838} 0.004210526 0.166666667 19.791667## 649 {21838} => {11080} 0.004210526 0.500000000 15.833333## 650 {11080} => {21838} 0.004210526 0.133333333 15.833333## 651 {21838} => {7868} 0.004210526 0.500000000 9.895833## 652 {7868} => {21838} 0.004210526 0.083333333 9.895833## 653 {28985} => {16463} 0.004210526 0.500000000 26.388889## 654 {16463} => {28985} 0.004210526 0.222222222 26.388889## 655 {28985} => {29203} 0.004210526 0.500000000 26.388889## 656 {29203} => {28985} 0.004210526 0.222222222 26.388889## 657 {7248} => {3151} 0.004210526 0.400000000 27.142857## 658 {3151} => {7248} 0.004210526 0.285714286 27.142857## 659 {16331} => {14261} 0.004210526 0.400000000 17.272727## 660 {14261} => {16331} 0.004210526 0.181818182 17.272727## 661 {16331} => {27791} 0.004210526 0.400000000 9.047619## 662 {27791} => {16331} 0.004210526 0.095238095 9.047619## 663 {12220} => {11080} 0.004210526 0.285714286 9.047619## 664 {11080} => {12220} 0.004210526 0.133333333 9.047619## 665 {21657} => {23628} 0.004210526 0.666666667 31.666667## 666 {23628} => {21657} 0.004210526 0.200000000 31.666667## 667 {24869} => {3228} 0.004210526 0.285714286 9.693878## 668 {3228} => {24869} 0.004210526 0.142857143 9.693878## 669 {23896} => {14261} 0.004210526 0.666666667 28.787879## 670 {14261} => {23896} 0.004210526 0.181818182 28.787879## 671 {12977} => {14020} 0.004210526 0.333333333 8.796296## 672 {14020} => {12977} 0.004210526 0.111111111 8.796296## 673 {18180} => {26614} 0.004210526 0.333333333 22.619048## 674 {26614} => {18180} 0.004210526 0.285714286 22.619048## 675 {18180} => {10014} 0.004210526 0.333333333 31.666667## 676 {10014} => {18180} 0.004210526 0.400000000 31.666667## 677 {18180} => {4411} 0.004210526 0.333333333 26.388889## 678 {4411} => {18180} 0.004210526 0.333333333 26.388889## 679 {25169} => {8637} 0.004210526 0.500000000 21.590909## 680 {8637} => {25169} 0.004210526 0.181818182 21.590909## 681 {18075} => {26523} 0.004210526 0.250000000 23.750000## 682 {26523} => {18075} 0.004210526 0.400000000 23.750000## 683 {18075} => {8689} 0.004210526 0.250000000 8.482143## 684 {8689} => {18075} 0.004210526 0.142857143 8.482143## 685 {19973} => {4571} 0.004210526 0.400000000 15.833333## 686 {4571} => {19973} 0.004210526 0.166666667 15.833333## 687 {12068} => {18024} 0.004210526 0.400000000 13.571429## 688 {18024} => {12068} 0.004210526 0.142857143 13.571429## 689 {16944} => {27791} 0.004210526 0.666666667 15.079365## 690 {27791} => {16944} 0.004210526 0.095238095 15.079365## 691 {5053} => {11679} 0.004210526 0.500000000 19.791667## 692 {11679} => {5053} 0.004210526 0.166666667 19.791667## 693 {21865} => {7105} 0.004210526 0.285714286 11.309524## 694 {7105} => {21865} 0.004210526 0.166666667 11.309524## 695 {10999} => {16110} 0.004210526 0.333333333 26.388889## 696 {16110} => {10999} 0.004210526 0.333333333 26.388889## 697 {10999} => {16540} 0.004210526 0.333333333 17.592593## 698 {16540} => {10999} 0.004210526 0.222222222 17.592593## 699 {10999} => {11679} 0.004210526 0.333333333 13.194444## 700 {11679} => {10999} 0.004210526 0.166666667 13.194444## 701 {530} => {22749} 0.006315789 0.750000000 59.375000## 702 {22749} => {530} 0.006315789 0.500000000 59.375000## 703 {530} => {12285} 0.004210526 0.500000000 21.590909## 704 {12285} => {530} 0.004210526 0.181818182 21.590909## 705 {530} => {23628} 0.004210526 0.500000000 23.750000## 706 {23628} => {530} 0.004210526 0.200000000 23.750000## 707 {530} => {11679} 0.004210526 0.500000000 19.791667## 708 {11679} => {530} 0.004210526 0.166666667 19.791667## 709 {27625} => {18805} 0.004210526 0.400000000 19.000000## 710 {18805} => {27625} 0.004210526 0.200000000 19.000000## 711 {22043} => {22359} 0.004210526 0.500000000 39.583333## 712 {22359} => {22043} 0.004210526 0.333333333 39.583333## 713 {18741} => {14020} 0.004210526 0.285714286 7.539683## 714 {14020} => {18741} 0.004210526 0.111111111 7.539683## 715 {16110} => {16540} 0.004210526 0.333333333 17.592593## 716 {16540} => {16110} 0.004210526 0.222222222 17.592593## 717 {16110} => {11679} 0.004210526 0.333333333 13.194444## 718 {11679} => {16110} 0.004210526 0.166666667 13.194444## 719 {16110} => {14261} 0.004210526 0.333333333 14.393939## 720 {14261} => {16110} 0.004210526 0.181818182 14.393939## 721 {16110} => {14020} 0.004210526 0.333333333 8.796296## 722 {14020} => {16110} 0.004210526 0.111111111 8.796296## 723 {22359} => {29203} 0.004210526 0.333333333 17.592593## 724 {29203} => {22359} 0.004210526 0.222222222 17.592593## 725 {251} => {11176} 0.004210526 0.285714286 13.571429## 726 {11176} => {251} 0.004210526 0.200000000 13.571429## 727 {251} => {4949} 0.004210526 0.285714286 15.079365## 728 {4949} => {251} 0.004210526 0.222222222 15.079365## 729 {251} => {3627} 0.004210526 0.285714286 12.337662## 730 {3627} => {251} 0.004210526 0.181818182 12.337662## 731 {25329} => {7096} 0.004210526 0.400000000 27.142857## 732 {7096} => {25329} 0.004210526 0.285714286 27.142857## 733 {25329} => {27791} 0.004210526 0.400000000 9.047619## 734 {27791} => {25329} 0.004210526 0.095238095 9.047619## 735 {7230} => {14415} 0.004210526 0.400000000 63.333333## 736 {14415} => {7230} 0.004210526 0.666666667 63.333333## 737 {18515} => {8842} 0.004210526 1.000000000 158.333333## 738 {8842} => {18515} 0.004210526 0.666666667 158.333333## 739 {18515} => {10702} 0.004210526 1.000000000 67.857143## 740 {10702} => {18515} 0.004210526 0.285714286 67.857143## 741 {14415} => {21919} 0.004210526 0.666666667 63.333333## 742 {21919} => {14415} 0.004210526 0.400000000 63.333333## 743 {14415} => {23928} 0.004210526 0.666666667 39.583333## 744 {23928} => {14415} 0.004210526 0.250000000 39.583333## 745 {22749} => {12285} 0.004210526 0.333333333 14.393939## 746 {12285} => {22749} 0.004210526 0.181818182 14.393939## 747 {22749} => {23628} 0.004210526 0.333333333 15.833333## 748 {23628} => {22749} 0.004210526 0.200000000 15.833333## 749 {15534} => {21092} 0.004210526 0.666666667 79.166667## 750 {21092} => {15534} 0.004210526 0.500000000 79.166667## 751 {29224} => {15315} 0.004210526 0.666666667 39.583333## 752 {15315} => {29224} 0.004210526 0.250000000 39.583333## 753 {7037} => {21092} 0.004210526 1.000000000 118.750000## 754 {21092} => {7037} 0.004210526 0.500000000 118.750000## 755 {17061} => {14261} 0.004210526 1.000000000 43.181818## 756 {14261} => {17061} 0.004210526 0.181818182 43.181818## 757 {11022} => {20979} 0.004210526 0.666666667 39.583333## 758 {20979} => {11022} 0.004210526 0.250000000 39.583333## 759 {11022} => {10702} 0.004210526 0.666666667 45.238095## 760 {10702} => {11022} 0.004210526 0.285714286 45.238095## 761 {22126} => {29099} 0.004210526 0.333333333 8.796296## 762 {29099} => {22126} 0.004210526 0.111111111 8.796296## 763 {24669} => {10702} 0.004210526 0.333333333 22.619048## 764 {10702} => {24669} 0.004210526 0.285714286 22.619048## 765 {8842} => {10702} 0.004210526 0.666666667 45.238095## 766 {10702} => {8842} 0.004210526 0.285714286 45.238095## 767 {21092} => {23928} 0.004210526 0.500000000 29.687500## 768 {23928} => {21092} 0.004210526 0.250000000 29.687500## 769 {16540} => {11196} 0.004210526 0.222222222 7.037037## 770 {11196} => {16540} 0.004210526 0.133333333 7.037037## 771 {16540} => {7105} 0.004210526 0.222222222 8.796296## 772 {7105} => {16540} 0.004210526 0.166666667 8.796296## 773 {16540} => {11679} 0.004210526 0.222222222 8.796296## 774 {11679} => {16540} 0.004210526 0.166666667 8.796296## 775 {10325} => {21336} 0.004210526 1.000000000 158.333333## 776 {21336} => {10325} 0.004210526 0.666666667 158.333333## 777 {10325} => {23928} 0.004210526 1.000000000 59.375000## 778 {23928} => {10325} 0.004210526 0.250000000 59.375000## 779 {10325} => {10702} 0.004210526 1.000000000 67.857143## 780 {10702} => {10325} 0.004210526 0.285714286 67.857143## 781 {2128} => {9111} 0.004210526 0.666666667 39.583333## 782 {9111} => {2128} 0.004210526 0.250000000 39.583333## 783 {29203} => {23628} 0.004210526 0.222222222 10.555556## 784 {23628} => {29203} 0.004210526 0.200000000 10.555556## 785 {29203} => {14020} 0.006315789 0.333333333 8.796296## 786 {14020} => {29203} 0.006315789 0.166666667 8.796296## 787 {19421} => {22313} 0.004210526 0.666666667 105.555556## 788 {22313} => {19421} 0.004210526 0.666666667 105.555556## 789 {19421} => {25651} 0.004210526 0.666666667 79.166667## 790 {25651} => {19421} 0.004210526 0.500000000 79.166667## 791 {19421} => {14261} 0.004210526 0.666666667 28.787879## 792 {14261} => {19421} 0.004210526 0.181818182 28.787879## 793 {22313} => {25651} 0.004210526 0.666666667 79.166667## 794 {25651} => {22313} 0.004210526 0.500000000 79.166667## 795 {22313} => {22556} 0.004210526 0.666666667 79.166667## 796 {22556} => {22313} 0.004210526 0.500000000 79.166667## 797 {22313} => {14261} 0.004210526 0.666666667 28.787879## 798 {14261} => {22313} 0.004210526 0.181818182 28.787879## 799 {11196} => {4949} 0.004210526 0.133333333 7.037037## 800 {4949} => {11196} 0.004210526 0.222222222 7.037037## 801 {9563} => {7105} 0.006315789 0.428571429 16.964286## 802 {7105} => {9563} 0.006315789 0.250000000 16.964286## 803 {1000} => {4807} 0.004210526 0.666666667 105.555556## 804 {4807} => {1000} 0.004210526 0.666666667 105.555556## 805 {1000} => {7061} 0.004210526 0.666666667 63.333333## 806 {7061} => {1000} 0.004210526 0.400000000 63.333333## 807 {1000} => {15584} 0.004210526 0.666666667 52.777778## 808 {15584} => {1000} 0.004210526 0.333333333 52.777778## 809 {21919} => {27791} 0.004210526 0.400000000 9.047619## 810 {27791} => {21919} 0.004210526 0.095238095 9.047619## 811 {21919} => {29099} 0.004210526 0.400000000 10.555556## 812 {29099} => {21919} 0.004210526 0.111111111 10.555556## 813 {3151} => {14020} 0.008421053 0.571428571 15.079365## 814 {14020} => {3151} 0.008421053 0.222222222 15.079365## 815 {26523} => {10014} 0.004210526 0.400000000 38.000000## 816 {10014} => {26523} 0.004210526 0.400000000 38.000000## 817 {26523} => {4411} 0.004210526 0.400000000 31.666667## 818 {4411} => {26523} 0.004210526 0.333333333 31.666667## 819 {26523} => {9111} 0.004210526 0.400000000 23.750000## 820 {9111} => {26523} 0.004210526 0.250000000 23.750000## 821 {10014} => {4411} 0.004210526 0.400000000 31.666667## 822 {4411} => {10014} 0.004210526 0.333333333 31.666667## 823 {21336} => {7061} 0.004210526 0.666666667 63.333333## 824 {7061} => {21336} 0.004210526 0.400000000 63.333333## 825 {21336} => {23928} 0.004210526 0.666666667 39.583333## 826 {23928} => {21336} 0.004210526 0.250000000 39.583333## 827 {21336} => {155} 0.004210526 0.666666667 28.787879## 828 {155} => {21336} 0.004210526 0.181818182 28.787879## 829 {21336} => {10702} 0.004210526 0.666666667 45.238095## 830 {10702} => {21336} 0.004210526 0.285714286 45.238095## 831 {7096} => {23628} 0.004210526 0.285714286 13.571429## 832 {23628} => {7096} 0.004210526 0.200000000 13.571429## 833 {7096} => {10702} 0.004210526 0.285714286 19.387755## 834 {10702} => {7096} 0.004210526 0.285714286 19.387755## 835 {8637} => {27791} 0.004210526 0.181818182 4.112554## 836 {27791} => {8637} 0.004210526 0.095238095 4.112554## 837 {8637} => {7868} 0.006315789 0.272727273 5.397727## 838 {7868} => {8637} 0.006315789 0.125000000 5.397727## 839 {25651} => {14261} 0.004210526 0.500000000 21.590909## 840 {14261} => {25651} 0.004210526 0.181818182 21.590909## 841 {11176} => {4949} 0.006315789 0.300000000 15.833333## 842 {4949} => {11176} 0.006315789 0.333333333 15.833333## 843 {11176} => {3627} 0.006315789 0.300000000 12.954545## 844 {3627} => {11176} 0.006315789 0.272727273 12.954545## 845 {11176} => {23628} 0.004210526 0.200000000 9.500000## 846 {23628} => {11176} 0.004210526 0.200000000 9.500000## 847 {4807} => {7061} 0.004210526 0.666666667 63.333333## 848 {7061} => {4807} 0.004210526 0.400000000 63.333333## 849 {4807} => {15584} 0.004210526 0.666666667 52.777778## 850 {15584} => {4807} 0.004210526 0.333333333 52.777778## 851 {14065} => {14917} 0.004210526 0.666666667 79.166667## 852 {14917} => {14065} 0.004210526 0.500000000 79.166667## 853 {14065} => {4411} 0.004210526 0.666666667 52.777778## 854 {4411} => {14065} 0.004210526 0.333333333 52.777778## 855 {22556} => {155} 0.004210526 0.500000000 21.590909## 856 {155} => {22556} 0.004210526 0.181818182 21.590909## 857 {22556} => {14020} 0.004210526 0.500000000 13.194444## 858 {14020} => {22556} 0.004210526 0.111111111 13.194444## 859 {14917} => {4411} 0.004210526 0.500000000 39.583333## 860 {4411} => {14917} 0.004210526 0.333333333 39.583333## 861 {17959} => {9111} 0.004210526 0.500000000 29.687500## 862 {9111} => {17959} 0.004210526 0.250000000 29.687500## 863 {12285} => {23628} 0.004210526 0.181818182 8.636364## 864 {23628} => {12285} 0.004210526 0.200000000 8.636364## 865 {12285} => {11679} 0.004210526 0.181818182 7.196970## 866 {11679} => {12285} 0.004210526 0.166666667 7.196970## 867 {12285} => {14020} 0.006315789 0.272727273 7.196970## 868 {14020} => {12285} 0.006315789 0.166666667 7.196970## 869 {12285} => {7868} 0.004210526 0.181818182 3.598485## 870 {7868} => {12285} 0.004210526 0.083333333 3.598485## 871 {4571} => {3228} 0.004210526 0.166666667 5.654762## 872 {3228} => {4571} 0.004210526 0.142857143 5.654762## 873 {4571} => {29099} 0.004210526 0.166666667 4.398148## 874 {29099} => {4571} 0.004210526 0.111111111 4.398148## 875 {15315} => {9111} 0.004210526 0.250000000 14.843750## 876 {9111} => {15315} 0.004210526 0.250000000 14.843750## 877 {15315} => {14020} 0.004210526 0.250000000 6.597222## 878 {14020} => {15315} 0.004210526 0.111111111 6.597222## 879 {7061} => {15584} 0.004210526 0.400000000 31.666667## 880 {15584} => {7061} 0.004210526 0.333333333 31.666667## 881 {7061} => {155} 0.004210526 0.400000000 17.272727## 882 {155} => {7061} 0.004210526 0.181818182 17.272727## 883 {20979} => {14261} 0.004210526 0.250000000 10.795455## 884 {14261} => {20979} 0.004210526 0.181818182 10.795455## 885 {7105} => {11080} 0.004210526 0.166666667 5.277778## 886 {11080} => {7105} 0.004210526 0.133333333 5.277778## 887 {7105} => {155} 0.004210526 0.166666667 7.196970## 888 {155} => {7105} 0.004210526 0.181818182 7.196970## 889 {7105} => {7868} 0.004210526 0.166666667 3.298611## 890 {7868} => {7105} 0.004210526 0.083333333 3.298611## 891 {4949} => {3627} 0.004210526 0.222222222 9.595960## 892 {3627} => {4949} 0.004210526 0.181818182 9.595960## 893 {4949} => {8689} 0.008421053 0.444444444 15.079365## 894 {8689} => {4949} 0.008421053 0.285714286 15.079365## 895 {3228} => {11679} 0.004210526 0.142857143 5.654762## 896 {11679} => {3228} 0.004210526 0.166666667 5.654762## 897 {18805} => {18024} 0.006315789 0.300000000 10.178571## 898 {18024} => {18805} 0.006315789 0.214285714 10.178571## 899 {18805} => {14261} 0.004210526 0.200000000 8.636364## 900 {14261} => {18805} 0.004210526 0.181818182 8.636364## 901 {23628} => {9111} 0.004210526 0.200000000 11.875000## 902 {9111} => {23628} 0.004210526 0.250000000 11.875000## 903 {15584} => {4411} 0.004210526 0.333333333 26.388889## 904 {4411} => {15584} 0.004210526 0.333333333 26.388889## 905 {15584} => {11679} 0.004210526 0.333333333 13.194444## 906 {11679} => {15584} 0.004210526 0.166666667 13.194444## 907 {18024} => {29099} 0.004210526 0.142857143 3.769841## 908 {29099} => {18024} 0.004210526 0.111111111 3.769841## 909 {8689} => {155} 0.004210526 0.142857143 6.168831## 910 {155} => {8689} 0.004210526 0.181818182 6.168831## 911 {8689} => {14020} 0.006315789 0.214285714 5.654762## 912 {14020} => {8689} 0.006315789 0.166666667 5.654762## 913 {23928} => {10702} 0.004210526 0.250000000 16.964286## 914 {10702} => {23928} 0.004210526 0.285714286 16.964286## 915 {9111} => {29099} 0.004210526 0.250000000 6.597222## 916 {29099} => {9111} 0.004210526 0.111111111 6.597222## 917 {2729,3151} => {14020} 0.004210526 1.000000000 26.388889## 918 {14020,2729} => {3151} 0.004210526 1.000000000 67.857143## 919 {14020,3151} => {2729} 0.004210526 0.500000000 79.166667## 920 {12717,22043} => {22359} 0.004210526 1.000000000 79.166667## 921 {12717,22359} => {22043} 0.004210526 1.000000000 118.750000## 922 {22043,22359} => {12717} 0.004210526 1.000000000 237.500000## 923 {23019,7692} => {27791} 0.004210526 1.000000000 22.619048## 924 {27791,7692} => {23019} 0.004210526 1.000000000 237.500000## 925 {23019,27791} => {7692} 0.004210526 1.000000000 237.500000## 926 {21838,24172} => {11080} 0.004210526 1.000000000 31.666667## 927 {11080,24172} => {21838} 0.004210526 1.000000000 118.750000## 928 {11080,21838} => {24172} 0.004210526 1.000000000 158.333333## 929 {3913,530} => {11679} 0.004210526 1.000000000 39.583333## 930 {11679,3913} => {530} 0.004210526 1.000000000 118.750000## 931 {11679,530} => {3913} 0.004210526 1.000000000 237.500000## 932 {10999,16110} => {16540} 0.004210526 1.000000000 52.777778## 933 {10999,16540} => {16110} 0.004210526 1.000000000 79.166667## 934 {16110,16540} => {10999} 0.004210526 1.000000000 79.166667## 935 {10999,16110} => {11679} 0.004210526 1.000000000 39.583333## 936 {10999,11679} => {16110} 0.004210526 1.000000000 79.166667## 937 {11679,16110} => {10999} 0.004210526 1.000000000 79.166667## 938 {10999,16540} => {11679} 0.004210526 1.000000000 39.583333## 939 {10999,11679} => {16540} 0.004210526 1.000000000 52.777778## 940 {11679,16540} => {10999} 0.004210526 1.000000000 79.166667## 941 {22749,530} => {12285} 0.004210526 0.666666667 28.787879## 942 {12285,530} => {22749} 0.004210526 1.000000000 79.166667## 943 {12285,22749} => {530} 0.004210526 1.000000000 118.750000## 944 {22749,530} => {23628} 0.004210526 0.666666667 31.666667## 945 {23628,530} => {22749} 0.004210526 1.000000000 79.166667## 946 {22749,23628} => {530} 0.004210526 1.000000000 118.750000## 947 {12285,530} => {23628} 0.004210526 1.000000000 47.500000## 948 {23628,530} => {12285} 0.004210526 1.000000000 43.181818## 949 {12285,23628} => {530} 0.004210526 1.000000000 118.750000## 950 {16110,16540} => {11679} 0.004210526 1.000000000 39.583333## 951 {11679,16110} => {16540} 0.004210526 1.000000000 52.777778## 952 {11679,16540} => {16110} 0.004210526 1.000000000 79.166667## 953 {18515,8842} => {10702} 0.004210526 1.000000000 67.857143## 954 {10702,18515} => {8842} 0.004210526 1.000000000 158.333333## 955 {10702,8842} => {18515} 0.004210526 1.000000000 237.500000## 956 {12285,22749} => {23628} 0.004210526 1.000000000 47.500000## 957 {22749,23628} => {12285} 0.004210526 1.000000000 43.181818## 958 {12285,23628} => {22749} 0.004210526 1.000000000 79.166667## 959 {10325,21336} => {23928} 0.004210526 1.000000000 59.375000## 960 {10325,23928} => {21336} 0.004210526 1.000000000 158.333333## 961 {21336,23928} => {10325} 0.004210526 1.000000000 237.500000## 962 {10325,21336} => {10702} 0.004210526 1.000000000 67.857143## 963 {10325,10702} => {21336} 0.004210526 1.000000000 158.333333## 964 {10702,21336} => {10325} 0.004210526 1.000000000 237.500000## 965 {10325,23928} => {10702} 0.004210526 1.000000000 67.857143## 966 {10325,10702} => {23928} 0.004210526 1.000000000 59.375000## 967 {10702,23928} => {10325} 0.004210526 1.000000000 237.500000## 968 {19421,22313} => {25651} 0.004210526 1.000000000 118.750000## 969 {19421,25651} => {22313} 0.004210526 1.000000000 158.333333## 970 {22313,25651} => {19421} 0.004210526 1.000000000 158.333333## 971 {19421,22313} => {14261} 0.004210526 1.000000000 43.181818## 972 {14261,19421} => {22313} 0.004210526 1.000000000 158.333333## 973 {14261,22313} => {19421} 0.004210526 1.000000000 158.333333## 974 {19421,25651} => {14261} 0.004210526 1.000000000 43.181818## 975 {14261,19421} => {25651} 0.004210526 1.000000000 118.750000## 976 {14261,25651} => {19421} 0.004210526 1.000000000 158.333333## 977 {22313,25651} => {14261} 0.004210526 1.000000000 43.181818## 978 {14261,22313} => {25651} 0.004210526 1.000000000 118.750000## 979 {14261,25651} => {22313} 0.004210526 1.000000000 158.333333## 980 {1000,4807} => {7061} 0.004210526 1.000000000 95.000000## 981 {1000,7061} => {4807} 0.004210526 1.000000000 158.333333## 982 {4807,7061} => {1000} 0.004210526 1.000000000 158.333333## 983 {1000,4807} => {15584} 0.004210526 1.000000000 79.166667## 984 {1000,15584} => {4807} 0.004210526 1.000000000 158.333333## 985 {15584,4807} => {1000} 0.004210526 1.000000000 158.333333## 986 {1000,7061} => {15584} 0.004210526 1.000000000 79.166667## 987 {1000,15584} => {7061} 0.004210526 1.000000000 95.000000## 988 {15584,7061} => {1000} 0.004210526 1.000000000 158.333333## 989 {10014,26523} => {4411} 0.004210526 1.000000000 79.166667## 990 {26523,4411} => {10014} 0.004210526 1.000000000 95.000000## 991 {10014,4411} => {26523} 0.004210526 1.000000000 95.000000## 992 {21336,7061} => {155} 0.004210526 1.000000000 43.181818## 993 {155,21336} => {7061} 0.004210526 1.000000000 95.000000## 994 {155,7061} => {21336} 0.004210526 1.000000000 158.333333## 995 {21336,23928} => {10702} 0.004210526 1.000000000 67.857143## 996 {10702,21336} => {23928} 0.004210526 1.000000000 59.375000## 997 {10702,23928} => {21336} 0.004210526 1.000000000 158.333333## 998 {11176,4949} => {3627} 0.004210526 0.666666667 28.787879## 999 {11176,3627} => {4949} 0.004210526 0.666666667 35.185185## 1000 {3627,4949} => {11176} 0.004210526 1.000000000 47.500000## 1001 {4807,7061} => {15584} 0.004210526 1.000000000 79.166667## 1002 {15584,4807} => {7061} 0.004210526 1.000000000 95.000000## 1003 {15584,7061} => {4807} 0.004210526 1.000000000 158.333333## 1004 {14065,14917} => {4411} 0.004210526 1.000000000 79.166667## 1005 {14065,4411} => {14917} 0.004210526 1.000000000 118.750000## 1006 {14917,4411} => {14065} 0.004210526 1.000000000 158.333333## 1007 {10999,16110,16540} => {11679} 0.004210526 1.000000000 39.583333## 1008 {10999,11679,16110} => {16540} 0.004210526 1.000000000 52.777778## 1009 {10999,11679,16540} => {16110} 0.004210526 1.000000000 79.166667## 1010 {11679,16110,16540} => {10999} 0.004210526 1.000000000 79.166667## 1011 {12285,22749,530} => {23628} 0.004210526 1.000000000 47.500000## 1012 {22749,23628,530} => {12285} 0.004210526 1.000000000 43.181818## 1013 {12285,23628,530} => {22749} 0.004210526 1.000000000 79.166667## 1014 {12285,22749,23628} => {530} 0.004210526 1.000000000 118.750000## 1015 {10325,21336,23928} => {10702} 0.004210526 1.000000000 67.857143## 1016 {10325,10702,21336} => {23928} 0.004210526 1.000000000 59.375000## 1017 {10325,10702,23928} => {21336} 0.004210526 1.000000000 158.333333## 1018 {10702,21336,23928} => {10325} 0.004210526 1.000000000 237.500000## 1019 {19421,22313,25651} => {14261} 0.004210526 1.000000000 43.181818## 1020 {14261,19421,22313} => {25651} 0.004210526 1.000000000 118.750000## 1021 {14261,19421,25651} => {22313} 0.004210526 1.000000000 158.333333## 1022 {14261,22313,25651} => {19421} 0.004210526 1.000000000 158.333333## 1023 {1000,4807,7061} => {15584} 0.004210526 1.000000000 79.166667## 1024 {1000,15584,4807} => {7061} 0.004210526 1.000000000 95.000000## 1025 {1000,15584,7061} => {4807} 0.004210526 1.000000000 158.333333## 1026 {15584,4807,7061} => {1000} 0.004210526 1.000000000 158.333333inspect(sort(rules, by="support")[1:3])## lhs rhs support confidence lift## 520 {} => {7868} 0.05052632 0.05052632 1 ## 517 {} => {27791} 0.04421053 0.04421053 1 ## 518 {} => {14020} 0.03789474 0.03789474 1inspect(sort(rules, by="support", decreasing=F)[1:3])## lhs rhs support confidence lift## 1 {} => {3658} 0.004210526 0.004210526 1 ## 2 {} => {14294} 0.004210526 0.004210526 1 ## 3 {} => {7963} 0.004210526 0.004210526 1实例三、分析Titanic数据，其中不同船舱的生存率
#1、加载数据并查看str(Titanic)## table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ...## - attr(*, "dimnames")=List of 4## ..$ Class : chr [1:4] "1st" "2nd" "3rd" "Crew"## ..$ Sex : chr [1:2] "Male" "Female"## ..$ Age : chr [1:2] "Child" "Adult"## ..$ Survived: chr [1:2] "No" "Yes"dim(Titanic)## [1] 4 2 2 2str(Titanic)## table [1:4, 1:2, 1:2, 1:2] 0 0 35 0 0 0 17 0 118 154 ...## - attr(*, "dimnames")=List of 4## ..$ Class : chr [1:4] "1st" "2nd" "3rd" "Crew"## ..$ Sex : chr [1:2] "Male" "Female"## ..$ Age : chr [1:2] "Child" "Adult"## ..$ Survived: chr [1:2] "No" "Yes"str(df)## function (x, df1, df2, ncp, log = FALSE) 0 0
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