map length (tiers :: [[ Int->Int ]]) = [1,2,5,15,51,188,...] length (list :: [ Int->Int ]) = Infinity allUnique (list :: [ Int->Int ]) = False ratioRepetitions (list :: [ Int->Int ]) = 96 % 131 tiers :: [Int->Int] = [ [ \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... ] , [ \x -> case x of 0 -> 1 1 -> 1 -1 -> 1 2 -> 1 -2 -> 1 3 -> 1 -3 -> 1 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... ] , [ \x -> case x of 0 -> -1 1 -> -1 -1 -> -1 2 -> -1 -2 -> -1 3 -> -1 -3 -> -1 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 1 2 -> 0 -2 -> 1 3 -> 0 -3 -> 1 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... ] , [ \x -> case x of 0 -> 2 1 -> 2 -1 -> 2 2 -> 2 -2 -> 2 3 -> 2 -3 -> 2 4 -> 2 ... , \x -> case x of 0 -> 0 1 -> 0 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-> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 2 1 -> 2 -1 -> 0 2 -> 2 -2 -> 0 3 -> 2 -3 -> 0 4 -> 2 ... , \x -> case x of 0 -> -1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> -1 -1 -> 0 2 -> -1 -2 -> 0 3 -> -1 -3 -> 0 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... ] , [ \x -> case x of 0 -> 3 1 -> 3 -1 -> 3 2 -> 3 -2 -> 3 3 -> 3 -3 -> 3 4 -> 3 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> -2 2 -> 0 -2 -> -2 3 -> 0 -3 -> -2 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 2 3 -> 0 -3 -> 2 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> -1 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 1 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 1 3 -> 0 -3 -> 1 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-> 1 -1 -> 1 2 -> 1 -2 -> 1 3 -> 1 -3 -> 1 4 -> 1 ... , \x -> case x of 0 -> 1 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 1 2 -> 1 -2 -> 1 3 -> 1 -3 -> 1 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 1 2 -> 0 -2 -> 1 3 -> 0 -3 -> 1 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 1 2 -> 0 -2 -> 1 3 -> 0 -3 -> 1 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> -1 -1 -> 1 2 -> -1 -2 -> 1 3 -> -1 -3 -> 1 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> -1 -1 -> 0 2 -> -1 -2 -> 0 3 -> -1 -3 -> 0 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 1 2 -> 0 -2 -> 1 3 -> 0 -3 -> 1 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 1 2 -> 0 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4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> -1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> -1 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 1 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> -1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> -1 -1 -> 0 2 -> -1 -2 -> 0 3 -> -1 -3 -> 0 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> -1 -1 -> 0 2 -> -1 -2 -> 0 3 -> -1 -3 -> 0 4 -> -1 ... , \x -> case x of 0 -> 1 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 1 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 2 -1 -> 0 2 -> 2 -2 -> 0 3 -> 2 -3 -> 0 4 -> 2 ... , \x -> case x of 0 -> 0 1 -> -1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 1 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 1 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> -1 -2 -> 0 3 -> -1 -3 -> 0 4 -> -1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 1 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 1 -3 -> 0 4 -> 1 ... , \x -> case x of 0 -> 0 1 -> 0 -1 -> 0 2 -> 0 -2 -> 0 3 -> 0 -3 -> 0 4 -> 0 ... ] , ... ]