exampleCRT <-
structure(list(trial = structure(list(y = c(-4.0451374999326504, 
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-0.43440363025005302, -0.44901599885032401, -0.47334116519446201, 
-0.47794436195026402, -0.47939950992326902, -0.482122594286096, 
-0.48632567331936899, -0.49013818276886301, -0.490562141568812, 
-0.50844356195680995, -0.52404438100281703, -0.52948904165441302, 
-0.55267484064157002, -0.56089979002031098, -0.56640202565791697, 
-0.587370518352476, -0.593184096841194, -0.60932869610909501, 
-0.62903725070982297, -0.62911747375285798, -0.63088647220279603, 
-0.63491018468110705, -0.63546736620198496, -0.65133807429151203, 
-0.65435807395708401, -0.65809829396986796, -0.66430651589038103, 
-0.67261452995718296, 0.17077108731076901, -0.56097838509180098, 
-0.56903039373763098, -0.57201524664359804, -0.57308566732899102, 
-0.58464921717833496, -0.58883814531072598, -0.58884959281947502, 
-0.58996383647381601, -0.59743227103890095, -0.59971523234011503, 
-0.60701245056201203, -0.62102769146178505, -0.62191561735143197, 
-0.62322153197184305, -0.62486549374603895, -0.62810174813463104, 
-0.632072690823824, -0.63217840829151595, -0.63233064086107005, 
-0.63334573267989602, -0.63472949366132003, -0.63605721268401405, 
-0.64220005289460902, -0.64564547113913995, -0.65531765310895895, 
-0.656647867806184, -0.67241673989958195, -0.67622609614505602, 
-0.68686774980628096, -0.698637542405384, -0.70555598647975903, 
-0.70654516394914801, -0.70665803837604602, -0.71321930453666704, 
-0.714227815634215, -0.71671054726212802, -0.71876541288846196, 
-0.73169540558534896, -0.73642873335278303, -0.73650097773456502, 
-0.73755485902874995, -0.74455509252174701, -0.74457098921732601, 
-0.76727232137399104, -0.77236992729630105, -0.78845903580688903, 
-0.82256522336878002, -0.83380939714540903, -0.848434875283266, 
-0.85275225576955205, -0.48147478893386603, -0.48223799220545199, 
-0.49336073871366898, -0.49999204577240203, -0.51390089242668002, 
-0.52415792713848897, -0.53134653004869004, -0.53265565632566403, 
-0.53285975284064202, -0.545460500373393, -0.54903504207050002, 
-0.55235372842243402, -0.56154881484754204, -0.56571792686332101, 
-0.57381890841504701, -0.57403339372624496, -0.60557193324026004, 
-0.60654296971374699, -0.61253182793153405, -0.61395577810290203, 
-0.614924568058132, -0.62324876441485699, -0.62587183401297997, 
-0.62836480205753298, -0.63509749558140305, -0.649684574634385, 
-0.65671014738004996, -0.68406471997931795, -0.73807792971452102, 
-0.749858019945989, -0.77926542274148503), RDT_test_result = c(2L, 
2L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 
1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 
2L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
0L, 2L, 1L, 0L, 1L, 1L, 0L, 2L, 3L, 2L, 2L, 0L, 0L, 0L, 2L, 0L, 
1L, 0L, 5L, 0L, 1L, 0L, 1L, 1L, 2L, 0L, 2L, 0L, 1L, 3L, 0L, 1L, 
0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 3L, 
0L, 0L, 2L, 0L, 1L, 0L, 1L, 1L, 0L, 2L, 0L, 0L, 0L, 1L, 2L, 0L, 
0L, 0L, 0L, 2L, 1L, 0L, 0L, 0L, 1L, 2L, 1L, 0L, 0L, 0L, 1L, 0L, 
0L, 0L, 0L, 1L, 2L, 2L, 2L, 0L, 2L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 
1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L, 2L, 5L, 3L, 
0L, 0L, 0L, 0L, 4L, 1L, 2L, 5L, 2L, 1L, 0L, 1L, 7L, 3L, 0L, 0L, 
0L, 1L, 1L, 3L, 1L, 0L, 1L, 4L, 2L, 0L, 0L, 0L, 0L, 0L, 1L, 3L, 
0L, 2L, 4L, 0L, 0L, 0L, 0L, 0L, 1L, 2L, 1L, 2L, 0L, 4L, 0L, 1L, 
0L, 0L, 0L, 0L, 0L, 0L, 2L, 2L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 3L, 1L, 0L, 0L, 1L, 0L, 
3L, 2L, 1L, 1L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 2L, 0L, 0L, 0L, 2L, 1L, 
0L, 1L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 1L, 3L, 1L, 0L, 1L, 2L, 0L, 
0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 2L, 1L, 0L, 0L, 0L, 1L, 
0L, 2L, 2L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 
1L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 2L, 2L, 0L, 1L, 5L, 0L, 1L, 
1L, 0L, 0L, 2L, 1L, 1L, 1L, 1L, 5L, 0L, 0L, 1L, 0L, 2L, 0L, 1L, 
0L, 0L, 1L, 0L, 0L, 0L, 0L, 2L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 1L, 
2L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 2L, 0L, 2L, 3L, 1L, 
1L, 0L, 0L, 3L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 2L, 1L, 2L, 
0L, 0L, 0L, 1L, 0L, 2L, 2L, 1L, 0L, 0L, 0L, 0L, 4L, 1L, 2L, 0L, 
0L, 0L, 1L, 0L, 1L, 1L, 0L, 3L, 0L, 3L, 0L, 2L, 2L, 1L, 0L, 1L, 
3L, 0L, 0L, 0L, 2L, 0L, 1L, 0L, 0L, 0L, 1L, 2L, 0L, 1L, 0L, 0L, 
1L, 0L, 3L, 0L, 0L, 0L, 0L, 2L, 1L, 0L, 0L, 1L, 1L, 3L, 2L, 2L, 
0L, 1L, 2L, 1L, 0L, 0L, 1L, 3L, 0L, 1L, 1L, 0L, 1L, 0L, 2L, 2L, 
0L, 2L, 1L, 1L, 0L, 0L, 1L, 1L, 4L, 0L, 0L, 1L, 0L, 0L, 0L, 3L, 
0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 
0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 3L, 0L, 0L, 0L, 
2L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 3L, 1L, 1L, 1L, 
3L, 1L, 1L, 1L, 2L, 0L, 1L, 0L, 1L, 0L, 2L, 2L, 1L, 0L, 5L, 1L, 
2L, 1L, 5L, 0L, 2L, 1L, 0L, 2L, 1L, 0L, 0L, 2L, 2L, 3L, 0L, 0L, 
0L, 0L, 0L, 2L, 4L, 6L, 2L, 0L, 3L, 0L, 0L, 2L, 1L, 1L, 0L, 0L, 
0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 3L, 1L, 1L, 
1L, 1L, 0L, 3L, 4L, 6L, 2L, 1L, 0L, 1L, 4L, 0L, 0L, 1L, 2L, 1L, 
0L, 0L, 0L, 0L, 0L, 1L, 5L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 
0L, 0L, 0L, 1L, 0L, 0L, 0L, 2L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 3L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 1L, 0L, 2L, 3L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 
1L, 0L, 0L, 2L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 
1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 2L, 
2L, 2L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 2L, 0L, 1L, 0L, 0L, 
1L, 1L, 3L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 
0L, 2L, 0L, 0L, 0L, 5L, 2L, 1L, 1L, 0L, 0L, 3L, 1L, 2L, 2L, 1L, 
3L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 4L, 0L, 0L, 1L, 1L, 0L, 
0L, 2L, 0L, 0L, 1L, 0L, 0L, 1L, 2L, 1L, 4L, 0L, 3L, 0L, 0L, 1L, 
1L, 1L, 0L, 0L, 3L, 0L, 1L, 0L, 0L, 2L, 3L, 1L, 1L, 2L, 0L, 0L, 
1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 
1L, 0L, 3L, 0L, 0L, 0L, 1L, 3L, 1L, 1L, 0L, 1L, 2L, 0L, 0L, 1L, 
0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 3L, 2L, 1L, 1L, 0L, 0L, 
0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 2L, 
2L, 0L, 1L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
0L, 0L, 0L, 2L, 1L, 2L, 0L, 1L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 3L, 0L, 0L, 
1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 
0L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
1L, 0L, 0L, 0L, 0L, 0L, 4L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 2L, 3L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 3L, 0L, 1L, 0L, 0L, 0L, 
0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 2L, 
0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), base_denom = c(3L, 
3L, 1L, 4L, 1L, 1L, 2L, 1L, 4L, 3L, 3L, 1L, 4L, 1L, 6L, 1L, 5L, 
4L, 5L, 5L, 4L, 3L, 1L, 1L, 1L, 3L, 4L, 3L, 2L, 1L, 2L, 3L, 4L, 
8L, 3L, 6L, 5L, 3L, 3L, 1L, 2L, 3L, 3L, 6L, 1L, 1L, 4L, 1L, 3L, 
1L, 3L, 3L, 1L, 4L, 2L, 1L, 2L, 4L, 2L, 5L, 1L, 5L, 1L, 3L, 2L, 
3L, 2L, 8L, 2L, 4L, 1L, 4L, 1L, 2L, 4L, 2L, 2L, 4L, 6L, 1L, 5L, 
2L, 3L, 2L, 1L, 1L, 1L, 3L, 2L, 4L, 1L, 3L, 3L, 3L, 5L, 1L, 5L, 
2L, 3L, 4L, 1L, 6L, 2L, 2L, 2L, 1L, 4L, 2L, 3L, 1L, 3L, 4L, 1L, 
1L, 2L, 4L, 4L, 4L, 4L, 3L, 1L, 2L, 4L, 3L, 1L, 7L, 2L, 4L, 1L, 
1L, 4L, 1L, 3L, 3L, 4L, 2L, 1L, 5L, 1L, 2L, 3L, 2L, 5L, 2L, 2L, 
4L, 2L, 2L, 6L, 1L, 1L, 3L, 1L, 1L, 2L, 1L, 1L, 2L, 4L, 5L, 6L, 
1L, 2L, 3L, 1L, 6L, 5L, 6L, 6L, 4L, 2L, 2L, 3L, 9L, 5L, 1L, 2L, 
1L, 1L, 2L, 6L, 3L, 3L, 1L, 5L, 6L, 1L, 2L, 1L, 1L, 1L, 1L, 7L, 
4L, 2L, 5L, 2L, 1L, 1L, 2L, 4L, 4L, 4L, 3L, 5L, 1L, 5L, 3L, 2L, 
3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 4L, 1L, 2L, 4L, 5L, 
1L, 4L, 3L, 1L, 3L, 3L, 3L, 3L, 2L, 3L, 2L, 2L, 4L, 1L, 2L, 3L, 
1L, 1L, 3L, 1L, 3L, 2L, 1L, 2L, 4L, 3L, 7L, 2L, 3L, 2L, 3L, 1L, 
4L, 6L, 4L, 1L, 3L, 1L, 3L, 1L, 4L, 2L, 2L, 1L, 1L, 2L, 1L, 3L, 
1L, 1L, 1L, 1L, 2L, 4L, 4L, 3L, 3L, 1L, 3L, 1L, 1L, 2L, 5L, 3L, 
1L, 2L, 1L, 6L, 2L, 1L, 1L, 3L, 1L, 4L, 3L, 3L, 3L, 8L, 3L, 1L, 
2L, 4L, 2L, 2L, 3L, 5L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 3L, 1L, 
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 5L, 1L, 3L, 2L, 1L, 3L, 1L, 3L, 
6L, 5L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 5L, 4L, 3L, 1L, 1L, 1L, 2L, 
1L, 2L, 3L, 2L, 1L, 5L, 1L, 2L, 1L, 1L, 1L, 2L, 10L, 2L, 2L, 
6L, 1L, 3L, 1L, 3L, 2L, 4L, 2L, 3L, 1L, 1L, 2L, 4L, 1L, 3L, 4L, 
3L, 3L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L, 1L, 2L, 2L, 6L, 2L, 3L, 
3L, 7L, 2L, 2L, 3L, 7L, 1L, 3L, 5L, 2L, 4L, 5L, 2L, 2L, 7L, 2L, 
2L, 5L, 4L, 1L, 5L, 4L, 4L, 2L, 3L, 6L, 1L, 3L, 1L, 1L, 3L, 1L, 
2L, 3L, 3L, 1L, 1L, 3L, 1L, 1L, 3L, 1L, 3L, 2L, 2L, 2L, 3L, 1L, 
3L, 3L, 4L, 4L, 5L, 2L, 1L, 1L, 4L, 3L, 2L, 2L, 4L, 1L, 3L, 4L, 
2L, 1L, 1L, 1L, 4L, 3L, 4L, 1L, 3L, 1L, 4L, 2L, 2L, 3L, 2L, 2L, 
6L, 2L, 1L, 3L, 1L, 1L, 4L, 5L, 2L, 1L, 1L, 2L, 1L, 6L, 1L, 3L, 
5L, 2L, 2L, 4L, 2L, 2L, 1L, 7L, 3L, 1L, 3L, 2L, 5L, 5L, 1L, 4L, 
5L, 4L, 3L, 2L, 3L, 4L, 1L, 4L, 5L, 1L, 2L, 3L, 5L, 1L, 2L, 1L, 
4L, 3L, 2L, 9L, 3L, 3L, 3L, 3L, 5L, 4L, 1L, 3L, 1L, 2L, 6L, 4L, 
4L, 1L, 1L, 4L, 1L, 1L, 3L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 2L, 3L, 
6L, 2L, 4L, 1L, 1L, 2L, 1L, 3L, 4L, 5L, 1L, 1L, 1L, 2L, 1L, 3L, 
4L, 1L, 4L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 3L, 
2L, 4L, 5L, 3L, 1L, 4L, 1L, 4L, 1L, 1L, 5L, 5L, 2L, 4L, 1L, 1L, 
1L, 4L, 2L, 3L, 1L, 2L, 1L, 1L, 1L, 2L, 4L, 4L, 1L, 5L, 5L, 1L, 
3L, 3L, 1L, 1L, 2L, 4L, 3L, 3L, 3L, 1L, 1L, 2L, 2L, 1L, 1L, 6L, 
3L, 2L, 2L, 8L, 1L, 4L, 3L, 2L, 6L, 2L, 1L, 4L, 3L, 4L, 4L, 5L, 
5L, 1L, 1L, 1L, 5L, 5L, 7L, 4L, 6L, 4L, 1L, 5L, 3L, 6L, 2L, 3L, 
2L, 3L, 2L, 4L, 2L, 3L, 5L, 3L, 1L, 2L, 3L, 2L, 2L, 1L, 3L, 1L, 
3L, 2L, 3L, 4L, 5L, 6L, 11L, 3L, 1L, 2L, 1L, 7L, 1L, 2L, 3L, 
3L, 4L, 2L, 2L, 1L, 9L, 3L, 1L, 9L, 2L, 1L, 3L, 6L, 2L, 1L, 10L, 
1L, 3L, 2L, 2L, 1L, 3L, 1L, 5L, 6L, 7L, 5L, 3L, 3L, 4L, 3L, 1L, 
2L, 1L, 1L, 5L, 1L, 1L, 3L, 5L, 4L, 8L, 2L, 3L, 2L, 2L, 1L, 5L, 
2L, 1L, 3L, 2L, 2L, 1L, 7L, 7L, 3L, 2L, 6L, 1L, 1L, 3L, 2L, 3L, 
4L, 3L, 3L, 1L, 7L, 3L, 1L, 1L, 1L, 5L, 2L, 2L, 2L, 1L, 3L, 1L, 
4L, 5L, 3L, 2L, 2L, 1L, 3L, 3L, 8L, 3L, 1L, 2L, 4L, 1L, 2L, 1L, 
1L, 3L, 5L, 2L, 1L, 5L, 3L, 2L, 2L, 5L, 1L, 2L, 2L, 4L, 1L, 2L, 
1L, 2L, 2L, 3L, 5L, 1L, 4L, 1L, 5L, 1L, 2L, 2L, 1L, 2L, 3L, 1L, 
1L, 2L, 3L, 5L, 1L, 1L, 1L, 6L, 4L, 2L, 2L, 1L, 2L, 3L, 3L, 3L, 
2L, 3L, 4L, 1L, 2L, 3L, 2L, 2L, 1L, 3L, 4L, 3L, 6L, 7L, 3L, 2L, 
2L, 3L, 1L, 3L, 2L, 1L, 4L, 1L, 2L, 10L, 4L, 4L, 6L, 3L, 8L, 
1L, 3L, 2L, 3L, 2L, 2L, 1L, 6L, 1L, 2L, 4L, 1L, 3L, 4L, 1L, 2L, 
5L, 4L, 3L, 5L, 5L, 1L, 1L, 4L, 2L, 1L, 1L, 2L, 3L, 3L, 1L, 5L, 
1L, 3L, 4L, 3L, 2L, 5L, 3L, 1L, 1L, 1L, 6L, 2L, 2L, 1L, 2L, 2L, 
1L, 4L, 3L, 3L, 5L, 3L, 2L, 1L, 2L, 3L, 1L, 4L, 1L, 6L, 4L, 2L, 
2L, 2L, 1L, 3L, 1L, 2L, 3L, 3L, 3L, 5L, 1L, 1L, 3L, 2L, 2L, 2L, 
2L, 4L, 4L, 2L, 5L, 1L, 2L, 4L, 2L, 1L, 1L, 4L, 1L, 1L, 5L, 1L, 
1L, 4L, 3L, 3L, 1L, 1L, 1L, 6L, 3L, 2L, 4L, 2L, 2L, 5L, 1L, 4L, 
2L, 3L, 6L, 4L, 2L, 1L, 7L, 1L, 4L, 2L, 2L, 4L, 2L, 2L, 5L, 2L, 
1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 1L, 4L, 3L, 1L, 1L, 3L, 3L, 
7L, 3L, 3L, 1L, 1L, 2L, 3L, 3L, 1L, 3L, 3L, 2L, 2L, 2L, 1L, 3L, 
1L, 1L, 1L, 5L, 2L, 2L, 5L, 1L, 2L, 1L, 1L, 3L, 4L, 2L, 2L, 1L, 
9L, 2L, 1L, 2L, 4L, 3L, 4L, 3L, 3L, 6L, 2L, 3L, 4L, 1L, 3L, 2L, 
3L, 4L, 5L, 2L, 2L, 1L, 2L, 2L, 4L, 2L, 1L, 7L, 3L, 5L, 2L, 1L, 
1L, 4L, 1L, 2L, 2L, 2L, 6L, 3L, 6L, 3L, 1L, 1L, 4L, 4L, 1L, 4L, 
1L, 3L, 2L, 1L, 3L, 5L, 1L, 2L, 1L, 5L, 2L, 4L, 2L, 5L, 3L, 1L, 
2L, 2L, 2L, 3L, 4L, 2L, 2L, 1L, 1L, 1L, 5L, 5L, 4L, 7L, 1L, 1L, 
3L, 1L, 7L, 1L, 3L, 4L, 1L, 1L, 2L, 1L, 1L, 3L, 5L, 6L, 3L, 1L, 
3L, 2L, 3L, 5L, 1L, 1L, 5L, 5L, 1L, 4L, 2L, 6L, 4L, 3L, 4L, 1L, 
3L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 5L, 3L, 1L, 2L, 2L, 2L, 4L), 
    cluster = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
    11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
    11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
    11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
    11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L, 12L, 
    12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
    12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
    12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 
    12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 13L, 13L, 13L, 
    13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 
    13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 
    13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 
    13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 14L, 
    14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 
    14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 
    14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 
    14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 
    14L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
    15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
    15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
    15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 
    15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
    16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
    16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
    16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 
    16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 
    17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 
    17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 
    17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 
    17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 18L, 
    18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
    18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
    18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 
    18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 19L, 19L, 19L, 
    19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 
    19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 
    19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 
    19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 20L, 
    20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 
    20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 
    20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 
    20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 
    20L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
    21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
    21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
    21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 
    21L, 21L, 21L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
    22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
    22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
    22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 22L, 
    22L, 22L, 22L, 22L, 22L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 
    23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 
    23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 
    23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 
    23L, 23L, 23L, 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 
    24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 
    24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 
    24L, 24L), arm = c("control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
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    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
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    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "intervention", 
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    "intervention", "intervention", "intervention", "intervention", 
    "intervention", "intervention", "intervention", "control", 
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    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
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    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
    "control", "control", "control", "control", "control", "control", 
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    0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0.20000000000000001, 
    0, 1, 0, 0, 0, 0, 0, 0.20000000000000001, 0.20000000000000001, 
    0.5, 0.75, 0, 0, 0, 0.5, 0, 0.33333333333333298, 0, 0, 0, 
    0, 0, 0, 0.25, 0.25, 0, 0.59999999999999998, 0.20000000000000001, 
    1, 0.33333333333333298, 1, 1, 1, 0.5, 0.5, 0, 0.33333333333333298, 
    0, 1, 0, 1, 1, 1, 0, 0.83333333333333304, 0.33333333333333298, 
    1, 0.5, 0.625, 0, 0.5, 0.33333333333333298, 0, 0.33333333333333298, 
    0.5, 0, 0, 0.66666666666666696, 0.5, 0.75, 0, 0, 0, 0, 0, 
    0.40000000000000002, 0.80000000000000004, 0.85714285714285698, 
    0.5, 0, 0.75, 0, 0, 0.66666666666666696, 0.16666666666666699, 
    0.5, 0, 0, 0, 0, 0, 0.5, 0, 0.20000000000000001, 0.33333333333333298, 
    1, 0, 0, 0.5, 0.5, 0, 1, 1, 0.33333333333333298, 0.5, 0.33333333333333298, 
    0, 0.59999999999999998, 0.66666666666666696, 0.54545454545454497, 
    0.66666666666666696, 1, 0, 1, 0.57142857142857095, 0, 0, 
    0.33333333333333298, 0.66666666666666696, 0.25, 0, 0, 0, 
    0, 0, 1, 0.55555555555555602, 0, 0, 0, 0.16666666666666699, 
    0, 0, 0, 0, 0.33333333333333298, 0, 0, 0, 0.33333333333333298, 
    0, 0, 0, 0.28571428571428598, 0, 0, 0.33333333333333298, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0.59999999999999998, 
    0, 0, 0, 0, 0, 0, 0, 0.14285714285714299, 0, 1, 0.5, 0, 0, 
    0, 0, 0, 0.5, 0, 0.33333333333333298, 0, 0, 0.66666666666666696, 
    0, 0, 1, 0.20000000000000001, 0, 0, 0, 1, 0.33333333333333298, 
    0, 0.25, 0.20000000000000001, 0.33333333333333298, 0.5, 0, 
    0, 0.33333333333333298, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0.66666666666666696, 
    0.40000000000000002, 1, 0, 0, 0, 0, 0.5, 0.20000000000000001, 
    0, 0.5, 0.5, 0.5, 0, 0.5, 0, 0, 0.5, 0.33333333333333298, 
    0.59999999999999998, 0, 0.25, 0, 0.20000000000000001, 1, 
    0, 0, 0, 0.5, 0.33333333333333298, 1, 0, 0, 0, 0.40000000000000002, 
    0, 0, 0, 0.83333333333333304, 0.5, 0.5, 0.5, 0, 0, 1, 0.33333333333333298, 
    0.66666666666666696, 1, 0.33333333333333298, 0.75, 0, 0.5, 
    0, 0, 0.5, 0, 0, 0.25, 0.33333333333333298, 0.66666666666666696, 
    0, 0, 0.5, 0.5, 0, 0, 0.66666666666666696, 0, 0, 0.25, 0, 
    0, 0.10000000000000001, 0.5, 0.25, 0.66666666666666696, 0, 
    0.375, 0, 0, 0.5, 0.33333333333333298, 0.5, 0, 0, 0.5, 0, 
    0.5, 0, 0, 0.66666666666666696, 0.75, 1, 0.5, 0.40000000000000002, 
    0, 0, 0.20000000000000001, 0, 0, 0, 0, 0, 0, 0, 0, 0.33333333333333298, 
    0, 0, 0.20000000000000001, 1, 0, 0.25, 0.33333333333333298, 
    0, 0.59999999999999998, 0, 0, 0, 1, 0.5, 0.5, 0.5, 0, 0.5, 
    1, 0, 0, 0.33333333333333298, 0, 0, 0.33333333333333298, 
    0, 0, 0, 0.33333333333333298, 0, 0.25, 0, 0.5, 0.5, 0.5, 
    0.5, 0, 0, 0, 0, 0.5, 0.33333333333333298, 0, 0, 0, 0, 0, 
    0.33333333333333298, 0, 0, 0, 0, 0, 0, 0, 0.40000000000000002, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0.59999999999999998, 0, 0, 0, 
    0.66666666666666696, 0.66666666666666696, 0, 1, 0, 0, 0, 
    0, 0.5, 0, 0, 0, 0, 0.25, 0, 0, 0, 0, 0, 0, 0.28571428571428598, 
    1, 0.5, 0, 0.5, 0, 0, 0, 0.40000000000000002, 0, 0, 0, 0, 
    0, 0, 0, 0, 0.66666666666666696, 0, 0, 0, 0.33333333333333298, 
    0, 0, 0, 0, 0.42857142857142899, 0, 0, 1, 1, 0, 0.33333333333333298, 
    0, 0, 0.33333333333333298, 0.33333333333333298, 0, 0, 0.5, 
    1, 0, 0, 0, 1, 0, 0, 0, 0.40000000000000002, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0.66666666666666696, 
    0, 0, 0, 0, 0, 0, 0, 0, 0.20000000000000001, 0, 0, 0, 0, 
    0.5, 0.25, 0, 1, 0, 0.66666666666666696, 0.59999999999999998, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0.75, 0, 0.25, 
    0, 0, 0, 0, 0.33333333333333298, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.20000000000000001, 
    0, 0.25, 0.14285714285714299, 0, 0, 0.33333333333333298, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.16666666666666699, 
    0, 0, 0, 0.5, 0.66666666666666696, 0, 0, 0, 0, 0.40000000000000002, 
    0, 0, 0, 0.16666666666666699, 0, 0, 0.25, 1, 0.33333333333333298, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), denom = c(1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), num = c(0L, 0L, 
    0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 
    0L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 
    0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
    0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
    0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 
    0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 
    0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 
    0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
    0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 
    0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 
    0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
    0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 
    0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 
    0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 
    1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
    1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
    0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 
    1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 
    1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
    1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
    0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 
    1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
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