map length (tiers :: [[ Xs Int4 ]])  =  [0,1,1,2,4,8,16,32,64,128,256,512,...]

length (list :: [ Xs Int4 ])  =  Infinity

allUnique (list :: [ Xs Int4 ])  =  True

ratioRepetitions (list :: [ Xs Int4 ])  =  0 % 1

tiers :: [Xs Int4]  =
  [ []
  , [Xs []]
  , [Xs [0]]
  , [ Xs [0,0]
    , Xs [1]
    ]
  , [ Xs [0,0,0]
    , Xs [0,1]
    , Xs [1,0]
    , Xs [-1]
    ]
  , [ Xs [0,0,0,0]
    , Xs [0,0,1]
    , Xs [0,1,0]
    , Xs [0,-1]
    , Xs [1,0,0]
    , Xs [1,1]
    , Xs [-1,0]
    , Xs [7]
    ]
  , [ Xs [0,0,0,0,0]
    , Xs [0,0,0,1]
    , Xs [0,0,1,0]
    , Xs [0,0,-1]
    , Xs [0,1,0,0]
    , Xs [0,1,1]
    , Xs [0,-1,0]
    , Xs [0,7]
    , Xs [1,0,0,0]
    , Xs [1,0,1]
    , Xs [1,1,0]
    , Xs [1,-1]
    , Xs [-1,0,0]
    , Xs [-1,1]
    , Xs [7,0]
    , Xs [-8]
    ]
  , [ Xs [0,0,0,0,0,0]
    , Xs [0,0,0,0,1]
    , Xs [0,0,0,1,0]
    , Xs [0,0,0,-1]
    , Xs [0,0,1,0,0]
    , Xs [0,0,1,1]
    , Xs [0,0,-1,0]
    , Xs [0,0,7]
    , Xs [0,1,0,0,0]
    , Xs [0,1,0,1]
    , Xs [0,1,1,0]
    , Xs [0,1,-1]
    , Xs [0,-1,0,0]
    , Xs [0,-1,1]
    , Xs [0,7,0]
    , Xs [0,-8]
    , Xs [1,0,0,0,0]
    , Xs [1,0,0,1]
    , Xs [1,0,1,0]
    , Xs [1,0,-1]
    , Xs [1,1,0,0]
    , Xs [1,1,1]
    , Xs [1,-1,0]
    , Xs [1,7]
    , Xs [-1,0,0,0]
    , Xs [-1,0,1]
    , Xs [-1,1,0]
    , Xs [-1,-1]
    , Xs [7,0,0]
    , Xs [7,1]
    , Xs [-8,0]
    , Xs [2]
    ]
  , [ Xs [0,0,0,0,0,0,0]
    , Xs [0,0,0,0,0,1]
    , Xs [0,0,0,0,1,0]
    , Xs [0,0,0,0,-1]
    , Xs [0,0,0,1,0,0]
    , Xs [0,0,0,1,1]
    , Xs [0,0,0,-1,0]
    , Xs [0,0,0,7]
    , Xs [0,0,1,0,0,0]
    , Xs [0,0,1,0,1]
    , Xs [0,0,1,1,0]
    , Xs [0,0,1,-1]
    , Xs [0,0,-1,0,0]
    , Xs [0,0,-1,1]
    , Xs [0,0,7,0]
    , Xs [0,0,-8]
    , Xs [0,1,0,0,0,0]
    , Xs [0,1,0,0,1]
    , Xs [0,1,0,1,0]
    , Xs [0,1,0,-1]
    , Xs [0,1,1,0,0]
    , Xs [0,1,1,1]
    , Xs [0,1,-1,0]
    , Xs [0,1,7]
    , Xs [0,-1,0,0,0]
    , Xs [0,-1,0,1]
    , Xs [0,-1,1,0]
    , Xs [0,-1,-1]
    , Xs [0,7,0,0]
    , Xs [0,7,1]
    , Xs [0,-8,0]
    , Xs [0,2]
    , Xs [1,0,0,0,0,0]
    , Xs [1,0,0,0,1]
    , Xs [1,0,0,1,0]
    , Xs [1,0,0,-1]
    , Xs [1,0,1,0,0]
    , Xs [1,0,1,1]
    , Xs [1,0,-1,0]
    , Xs [1,0,7]
    , Xs [1,1,0,0,0]
    , Xs [1,1,0,1]
    , Xs [1,1,1,0]
    , Xs [1,1,-1]
    , Xs [1,-1,0,0]
    , Xs [1,-1,1]
    , Xs [1,7,0]
    , Xs [1,-8]
    , Xs [-1,0,0,0,0]
    , Xs [-1,0,0,1]
    , Xs [-1,0,1,0]
    , Xs [-1,0,-1]
    , Xs [-1,1,0,0]
    , Xs [-1,1,1]
    , Xs [-1,-1,0]
    , Xs [-1,7]
    , Xs [7,0,0,0]
    , Xs [7,0,1]
    , Xs [7,1,0]
    , Xs [7,-1]
    , Xs [-8,0,0]
    , Xs [-8,1]
    , Xs [2,0]
    , Xs [-2]
    ]
  , [ Xs [0,0,0,0,0,0,0,0]
    , Xs [0,0,0,0,0,0,1]
    , Xs [0,0,0,0,0,1,0]
    , Xs [0,0,0,0,0,-1]
    , Xs [0,0,0,0,1,0,0]
    , Xs [0,0,0,0,1,1]
    , Xs [0,0,0,0,-1,0]
    , Xs [0,0,0,0,7]
    , Xs [0,0,0,1,0,0,0]
    , Xs [0,0,0,1,0,1]
    , Xs [0,0,0,1,1,0]
    , Xs [0,0,0,1,-1]
    , Xs [0,0,0,-1,0,0]
    , Xs [0,0,0,-1,1]
    , Xs [0,0,0,7,0]
    , Xs [0,0,0,-8]
    , Xs [0,0,1,0,0,0,0]
    , Xs [0,0,1,0,0,1]
    , Xs [0,0,1,0,1,0]
    , Xs [0,0,1,0,-1]
    , Xs [0,0,1,1,0,0]
    , Xs [0,0,1,1,1]
    , Xs [0,0,1,-1,0]
    , Xs [0,0,1,7]
    , Xs [0,0,-1,0,0,0]
    , Xs [0,0,-1,0,1]
    , Xs [0,0,-1,1,0]
    , Xs [0,0,-1,-1]
    , Xs [0,0,7,0,0]
    , Xs [0,0,7,1]
    , Xs [0,0,-8,0]
    , Xs [0,0,2]
    , Xs [0,1,0,0,0,0,0]
    , Xs [0,1,0,0,0,1]
    , Xs [0,1,0,0,1,0]
    , Xs [0,1,0,0,-1]
    , Xs [0,1,0,1,0,0]
    , Xs [0,1,0,1,1]
    , Xs [0,1,0,-1,0]
    , Xs [0,1,0,7]
    , Xs [0,1,1,0,0,0]
    , Xs [0,1,1,0,1]
    , Xs [0,1,1,1,0]
    , Xs [0,1,1,-1]
    , Xs [0,1,-1,0,0]
    , Xs [0,1,-1,1]
    , Xs [0,1,7,0]
    , Xs [0,1,-8]
    , Xs [0,-1,0,0,0,0]
    , Xs [0,-1,0,0,1]
    , Xs [0,-1,0,1,0]
    , Xs [0,-1,0,-1]
    , Xs [0,-1,1,0,0]
    , Xs [0,-1,1,1]
    , Xs [0,-1,-1,0]
    , Xs [0,-1,7]
    , Xs [0,7,0,0,0]
    , Xs [0,7,0,1]
    , Xs [0,7,1,0]
    , Xs [0,7,-1]
    , Xs [0,-8,0,0]
    , Xs [0,-8,1]
    , Xs [0,2,0]
    , Xs [0,-2]
    , Xs [1,0,0,0,0,0,0]
    , Xs [1,0,0,0,0,1]
    , Xs [1,0,0,0,1,0]
    , Xs [1,0,0,0,-1]
    , Xs [1,0,0,1,0,0]
    , Xs [1,0,0,1,1]
    , Xs [1,0,0,-1,0]
    , Xs [1,0,0,7]
    , Xs [1,0,1,0,0,0]
    , Xs [1,0,1,0,1]
    , Xs [1,0,1,1,0]
    , Xs [1,0,1,-1]
    , Xs [1,0,-1,0,0]
    , Xs [1,0,-1,1]
    , Xs [1,0,7,0]
    , Xs [1,0,-8]
    , Xs [1,1,0,0,0,0]
    , Xs [1,1,0,0,1]
    , Xs [1,1,0,1,0]
    , Xs [1,1,0,-1]
    , Xs [1,1,1,0,0]
    , Xs [1,1,1,1]
    , Xs [1,1,-1,0]
    , Xs [1,1,7]
    , Xs [1,-1,0,0,0]
    , Xs [1,-1,0,1]
    , Xs [1,-1,1,0]
    , Xs [1,-1,-1]
    , Xs [1,7,0,0]
    , Xs [1,7,1]
    , Xs [1,-8,0]
    , Xs [1,2]
    , Xs [-1,0,0,0,0,0]
    , Xs [-1,0,0,0,1]
    , Xs [-1,0,0,1,0]
    , Xs [-1,0,0,-1]
    , Xs [-1,0,1,0,0]
    , Xs [-1,0,1,1]
    , Xs [-1,0,-1,0]
    , Xs [-1,0,7]
    , Xs [-1,1,0,0,0]
    , Xs [-1,1,0,1]
    , Xs [-1,1,1,0]
    , Xs [-1,1,-1]
    , Xs [-1,-1,0,0]
    , Xs [-1,-1,1]
    , Xs [-1,7,0]
    , Xs [-1,-8]
    , Xs [7,0,0,0,0]
    , Xs [7,0,0,1]
    , Xs [7,0,1,0]
    , Xs [7,0,-1]
    , Xs [7,1,0,0]
    , Xs [7,1,1]
    , Xs [7,-1,0]
    , Xs [7,7]
    , Xs [-8,0,0,0]
    , Xs [-8,0,1]
    , Xs [-8,1,0]
    , Xs [-8,-1]
    , Xs [2,0,0]
    , Xs [2,1]
    , Xs [-2,0]
    , Xs [6]
    ]
  , [ Xs [0,0,0,0,0,0,0,0,0]
    , Xs [0,0,0,0,0,0,0,1]
    , Xs [0,0,0,0,0,0,1,0]
    , Xs [0,0,0,0,0,0,-1]
    , Xs [0,0,0,0,0,1,0,0]
    , Xs [0,0,0,0,0,1,1]
    , Xs [0,0,0,0,0,-1,0]
    , Xs [0,0,0,0,0,7]
    , Xs [0,0,0,0,1,0,0,0]
    , Xs [0,0,0,0,1,0,1]
    , Xs [0,0,0,0,1,1,0]
    , Xs [0,0,0,0,1,-1]
    , Xs [0,0,0,0,-1,0,0]
    , Xs [0,0,0,0,-1,1]
    , Xs [0,0,0,0,7,0]
    , Xs [0,0,0,0,-8]
    , Xs [0,0,0,1,0,0,0,0]
    , Xs [0,0,0,1,0,0,1]
    , Xs [0,0,0,1,0,1,0]
    , Xs [0,0,0,1,0,-1]
    , Xs [0,0,0,1,1,0,0]
    , Xs [0,0,0,1,1,1]
    , Xs [0,0,0,1,-1,0]
    , Xs [0,0,0,1,7]
    , Xs [0,0,0,-1,0,0,0]
    , Xs [0,0,0,-1,0,1]
    , Xs [0,0,0,-1,1,0]
    , Xs [0,0,0,-1,-1]
    , Xs [0,0,0,7,0,0]
    , Xs [0,0,0,7,1]
    , Xs [0,0,0,-8,0]
    , Xs [0,0,0,2]
    , Xs [0,0,1,0,0,0,0,0]
    , Xs [0,0,1,0,0,0,1]
    , Xs [0,0,1,0,0,1,0]
    , Xs [0,0,1,0,0,-1]
    , Xs [0,0,1,0,1,0,0]
    , Xs [0,0,1,0,1,1]
    , Xs [0,0,1,0,-1,0]
    , Xs [0,0,1,0,7]
    , Xs [0,0,1,1,0,0,0]
    , Xs [0,0,1,1,0,1]
    , Xs [0,0,1,1,1,0]
    , Xs [0,0,1,1,-1]
    , Xs [0,0,1,-1,0,0]
    , Xs [0,0,1,-1,1]
    , Xs [0,0,1,7,0]
    , Xs [0,0,1,-8]
    , Xs [0,0,-1,0,0,0,0]
    , Xs [0,0,-1,0,0,1]
    , Xs [0,0,-1,0,1,0]
    , Xs [0,0,-1,0,-1]
    , Xs [0,0,-1,1,0,0]
    , Xs [0,0,-1,1,1]
    , Xs [0,0,-1,-1,0]
    , Xs [0,0,-1,7]
    , Xs [0,0,7,0,0,0]
    , Xs [0,0,7,0,1]
    , Xs [0,0,7,1,0]
    , Xs [0,0,7,-1]
    , Xs [0,0,-8,0,0]
    , Xs [0,0,-8,1]
    , Xs [0,0,2,0]
    , Xs [0,0,-2]
    , Xs [0,1,0,0,0,0,0,0]
    , Xs [0,1,0,0,0,0,1]
    , Xs [0,1,0,0,0,1,0]
    , Xs [0,1,0,0,0,-1]
    , Xs [0,1,0,0,1,0,0]
    , Xs [0,1,0,0,1,1]
    , Xs [0,1,0,0,-1,0]
    , Xs [0,1,0,0,7]
    , Xs [0,1,0,1,0,0,0]
    , Xs [0,1,0,1,0,1]
    , Xs [0,1,0,1,1,0]
    , Xs [0,1,0,1,-1]
    , Xs [0,1,0,-1,0,0]
    , Xs [0,1,0,-1,1]
    , Xs [0,1,0,7,0]
    , Xs [0,1,0,-8]
    , Xs [0,1,1,0,0,0,0]
    , Xs [0,1,1,0,0,1]
    , Xs [0,1,1,0,1,0]
    , Xs [0,1,1,0,-1]
    , Xs [0,1,1,1,0,0]
    , Xs [0,1,1,1,1]
    , Xs [0,1,1,-1,0]
    , Xs [0,1,1,7]
    , Xs [0,1,-1,0,0,0]
    , Xs [0,1,-1,0,1]
    , Xs [0,1,-1,1,0]
    , Xs [0,1,-1,-1]
    , Xs [0,1,7,0,0]
    , Xs [0,1,7,1]
    , Xs [0,1,-8,0]
    , Xs [0,1,2]
    , Xs [0,-1,0,0,0,0,0]
    , Xs [0,-1,0,0,0,1]
    , Xs [0,-1,0,0,1,0]
    , Xs [0,-1,0,0,-1]
    , Xs [0,-1,0,1,0,0]
    , Xs [0,-1,0,1,1]
    , Xs [0,-1,0,-1,0]
    , Xs [0,-1,0,7]
    , Xs [0,-1,1,0,0,0]
    , Xs [0,-1,1,0,1]
    , Xs [0,-1,1,1,0]
    , Xs [0,-1,1,-1]
    , Xs [0,-1,-1,0,0]
    , Xs [0,-1,-1,1]
    , Xs [0,-1,7,0]
    , Xs [0,-1,-8]
    , Xs [0,7,0,0,0,0]
    , Xs [0,7,0,0,1]
    , Xs [0,7,0,1,0]
    , Xs [0,7,0,-1]
    , Xs [0,7,1,0,0]
    , Xs [0,7,1,1]
    , Xs [0,7,-1,0]
    , Xs [0,7,7]
    , Xs [0,-8,0,0,0]
    , Xs [0,-8,0,1]
    , Xs [0,-8,1,0]
    , Xs [0,-8,-1]
    , Xs [0,2,0,0]
    , Xs [0,2,1]
    , Xs [0,-2,0]
    , Xs [0,6]
    , Xs [1,0,0,0,0,0,0,0]
    , Xs [1,0,0,0,0,0,1]
    , Xs [1,0,0,0,0,1,0]
    , Xs [1,0,0,0,0,-1]
    , Xs [1,0,0,0,1,0,0]
    , Xs [1,0,0,0,1,1]
    , Xs [1,0,0,0,-1,0]
    , Xs [1,0,0,0,7]
    , Xs [1,0,0,1,0,0,0]
    , Xs [1,0,0,1,0,1]
    , Xs [1,0,0,1,1,0]
    , Xs [1,0,0,1,-1]
    , Xs [1,0,0,-1,0,0]
    , Xs [1,0,0,-1,1]
    , Xs [1,0,0,7,0]
    , Xs [1,0,0,-8]
    , Xs [1,0,1,0,0,0,0]
    , Xs [1,0,1,0,0,1]
    , Xs [1,0,1,0,1,0]
    , Xs [1,0,1,0,-1]
    , Xs [1,0,1,1,0,0]
    , Xs [1,0,1,1,1]
    , Xs [1,0,1,-1,0]
    , Xs [1,0,1,7]
    , Xs [1,0,-1,0,0,0]
    , Xs [1,0,-1,0,1]
    , Xs [1,0,-1,1,0]
    , Xs [1,0,-1,-1]
    , Xs [1,0,7,0,0]
    , Xs [1,0,7,1]
    , Xs [1,0,-8,0]
    , Xs [1,0,2]
    , Xs [1,1,0,0,0,0,0]
    , Xs [1,1,0,0,0,1]
    , Xs [1,1,0,0,1,0]
    , Xs [1,1,0,0,-1]
    , Xs [1,1,0,1,0,0]
    , Xs [1,1,0,1,1]
    , Xs [1,1,0,-1,0]
    , Xs [1,1,0,7]
    , Xs [1,1,1,0,0,0]
    , Xs [1,1,1,0,1]
    , Xs [1,1,1,1,0]
    , Xs [1,1,1,-1]
    , Xs [1,1,-1,0,0]
    , Xs [1,1,-1,1]
    , Xs [1,1,7,0]
    , Xs [1,1,-8]
    , Xs [1,-1,0,0,0,0]
    , Xs [1,-1,0,0,1]
    , Xs [1,-1,0,1,0]
    , Xs [1,-1,0,-1]
    , Xs [1,-1,1,0,0]
    , Xs [1,-1,1,1]
    , Xs [1,-1,-1,0]
    , Xs [1,-1,7]
    , Xs [1,7,0,0,0]
    , Xs [1,7,0,1]
    , Xs [1,7,1,0]
    , Xs [1,7,-1]
    , Xs [1,-8,0,0]
    , Xs [1,-8,1]
    , Xs [1,2,0]
    , Xs [1,-2]
    , Xs [-1,0,0,0,0,0,0]
    , Xs [-1,0,0,0,0,1]
    , Xs [-1,0,0,0,1,0]
    , Xs [-1,0,0,0,-1]
    , Xs [-1,0,0,1,0,0]
    , Xs [-1,0,0,1,1]
    , Xs [-1,0,0,-1,0]
    , Xs [-1,0,0,7]
    , Xs [-1,0,1,0,0,0]
    , Xs [-1,0,1,0,1]
    , Xs [-1,0,1,1,0]
    , Xs [-1,0,1,-1]
    , Xs [-1,0,-1,0,0]
    , Xs [-1,0,-1,1]
    , Xs [-1,0,7,0]
    , Xs [-1,0,-8]
    , Xs [-1,1,0,0,0,0]
    , Xs [-1,1,0,0,1]
    , Xs [-1,1,0,1,0]
    , Xs [-1,1,0,-1]
    , Xs [-1,1,1,0,0]
    , Xs [-1,1,1,1]
    , Xs [-1,1,-1,0]
    , Xs [-1,1,7]
    , Xs [-1,-1,0,0,0]
    , Xs [-1,-1,0,1]
    , Xs [-1,-1,1,0]
    , Xs [-1,-1,-1]
    , Xs [-1,7,0,0]
    , Xs [-1,7,1]
    , Xs [-1,-8,0]
    , Xs [-1,2]
    , Xs [7,0,0,0,0,0]
    , Xs [7,0,0,0,1]
    , Xs [7,0,0,1,0]
    , Xs [7,0,0,-1]
    , Xs [7,0,1,0,0]
    , Xs [7,0,1,1]
    , Xs [7,0,-1,0]
    , Xs [7,0,7]
    , Xs [7,1,0,0,0]
    , Xs [7,1,0,1]
    , Xs [7,1,1,0]
    , Xs [7,1,-1]
    , Xs [7,-1,0,0]
    , Xs [7,-1,1]
    , Xs [7,7,0]
    , Xs [7,-8]
    , Xs [-8,0,0,0,0]
    , Xs [-8,0,0,1]
    , Xs [-8,0,1,0]
    , Xs [-8,0,-1]
    , Xs [-8,1,0,0]
    , Xs [-8,1,1]
    , Xs [-8,-1,0]
    , Xs [-8,7]
    , Xs [2,0,0,0]
    , Xs [2,0,1]
    , Xs [2,1,0]
    , Xs [2,-1]
    , Xs [-2,0,0]
    , Xs [-2,1]
    , Xs [6,0]
    , Xs [-7]
    ]
  , [ Xs [0,0,0,0,0,0,0,0,0,0]
    , Xs [0,0,0,0,0,0,0,0,1]
    , Xs [0,0,0,0,0,0,0,1,0]
    , Xs [0,0,0,0,0,0,0,-1]
    , Xs [0,0,0,0,0,0,1,0,0]
    , Xs [0,0,0,0,0,0,1,1]
    , Xs [0,0,0,0,0,0,-1,0]
    , Xs [0,0,0,0,0,0,7]
    , Xs [0,0,0,0,0,1,0,0,0]
    , Xs [0,0,0,0,0,1,0,1]
    , Xs [0,0,0,0,0,1,1,0]
    , Xs [0,0,0,0,0,1,-1]
    , Xs [0,0,0,0,0,-1,0,0]
    , Xs [0,0,0,0,0,-1,1]
    , Xs [0,0,0,0,0,7,0]
    , Xs [0,0,0,0,0,-8]
    , Xs [0,0,0,0,1,0,0,0,0]
    , Xs [0,0,0,0,1,0,0,1]
    , Xs [0,0,0,0,1,0,1,0]
    , Xs [0,0,0,0,1,0,-1]
    , Xs [0,0,0,0,1,1,0,0]
    , Xs [0,0,0,0,1,1,1]
    , Xs [0,0,0,0,1,-1,0]
    , Xs [0,0,0,0,1,7]
    , Xs [0,0,0,0,-1,0,0,0]
    , Xs [0,0,0,0,-1,0,1]
    , Xs [0,0,0,0,-1,1,0]
    , Xs [0,0,0,0,-1,-1]
    , Xs [0,0,0,0,7,0,0]
    , Xs [0,0,0,0,7,1]
    , Xs [0,0,0,0,-8,0]
    , Xs [0,0,0,0,2]
    , Xs [0,0,0,1,0,0,0,0,0]
    , Xs [0,0,0,1,0,0,0,1]
    , Xs [0,0,0,1,0,0,1,0]
    , Xs [0,0,0,1,0,0,-1]
    , Xs [0,0,0,1,0,1,0,0]
    , Xs [0,0,0,1,0,1,1]
    , Xs [0,0,0,1,0,-1,0]
    , Xs [0,0,0,1,0,7]
    , Xs [0,0,0,1,1,0,0,0]
    , Xs [0,0,0,1,1,0,1]
    , Xs [0,0,0,1,1,1,0]
    , Xs [0,0,0,1,1,-1]
    , Xs [0,0,0,1,-1,0,0]
    , Xs [0,0,0,1,-1,1]
    , Xs [0,0,0,1,7,0]
    , Xs [0,0,0,1,-8]
    , Xs [0,0,0,-1,0,0,0,0]
    , Xs [0,0,0,-1,0,0,1]
    , Xs [0,0,0,-1,0,1,0]
    , Xs [0,0,0,-1,0,-1]
    , Xs [0,0,0,-1,1,0,0]
    , Xs [0,0,0,-1,1,1]
    , Xs [0,0,0,-1,-1,0]
    , Xs [0,0,0,-1,7]
    , Xs [0,0,0,7,0,0,0]
    , Xs [0,0,0,7,0,1]
    , Xs [0,0,0,7,1,0]
    , Xs [0,0,0,7,-1]
    , Xs [0,0,0,-8,0,0]
    , Xs [0,0,0,-8,1]
    , Xs [0,0,0,2,0]
    , Xs [0,0,0,-2]
    , Xs [0,0,1,0,0,0,0,0,0]
    , Xs [0,0,1,0,0,0,0,1]
    , Xs [0,0,1,0,0,0,1,0]
    , Xs [0,0,1,0,0,0,-1]
    , Xs [0,0,1,0,0,1,0,0]
    , Xs [0,0,1,0,0,1,1]
    , Xs [0,0,1,0,0,-1,0]
    , Xs [0,0,1,0,0,7]
    , Xs [0,0,1,0,1,0,0,0]
    , Xs [0,0,1,0,1,0,1]
    , Xs [0,0,1,0,1,1,0]
    , Xs [0,0,1,0,1,-1]
    , Xs [0,0,1,0,-1,0,0]
    , Xs [0,0,1,0,-1,1]
    , Xs [0,0,1,0,7,0]
    , Xs [0,0,1,0,-8]
    , Xs [0,0,1,1,0,0,0,0]
    , Xs [0,0,1,1,0,0,1]
    , Xs [0,0,1,1,0,1,0]
    , Xs [0,0,1,1,0,-1]
    , Xs [0,0,1,1,1,0,0]
    , Xs [0,0,1,1,1,1]
    , Xs [0,0,1,1,-1,0]
    , Xs [0,0,1,1,7]
    , Xs [0,0,1,-1,0,0,0]
    , Xs [0,0,1,-1,0,1]
    , Xs [0,0,1,-1,1,0]
    , Xs [0,0,1,-1,-1]
    , Xs [0,0,1,7,0,0]
    , Xs [0,0,1,7,1]
    , Xs [0,0,1,-8,0]
    , Xs [0,0,1,2]
    , Xs [0,0,-1,0,0,0,0,0]
    , Xs [0,0,-1,0,0,0,1]
    , Xs [0,0,-1,0,0,1,0]
    , Xs [0,0,-1,0,0,-1]
    , Xs [0,0,-1,0,1,0,0]
    , Xs [0,0,-1,0,1,1]
    , Xs [0,0,-1,0,-1,0]
    , Xs [0,0,-1,0,7]
    , Xs [0,0,-1,1,0,0,0]
    , Xs [0,0,-1,1,0,1]
    , Xs [0,0,-1,1,1,0]
    , Xs [0,0,-1,1,-1]
    , Xs [0,0,-1,-1,0,0]
    , Xs [0,0,-1,-1,1]
    , Xs [0,0,-1,7,0]
    , Xs [0,0,-1,-8]
    , Xs [0,0,7,0,0,0,0]
    , Xs [0,0,7,0,0,1]
    , Xs [0,0,7,0,1,0]
    , Xs [0,0,7,0,-1]
    , Xs [0,0,7,1,0,0]
    , Xs [0,0,7,1,1]
    , Xs [0,0,7,-1,0]
    , Xs [0,0,7,7]
    , Xs [0,0,-8,0,0,0]
    , Xs [0,0,-8,0,1]
    , Xs [0,0,-8,1,0]
    , Xs [0,0,-8,-1]
    , Xs [0,0,2,0,0]
    , Xs [0,0,2,1]
    , Xs [0,0,-2,0]
    , Xs [0,0,6]
    , Xs [0,1,0,0,0,0,0,0,0]
    , Xs [0,1,0,0,0,0,0,1]
    , Xs [0,1,0,0,0,0,1,0]
    , Xs [0,1,0,0,0,0,-1]
    , Xs [0,1,0,0,0,1,0,0]
    , Xs [0,1,0,0,0,1,1]
    , Xs [0,1,0,0,0,-1,0]
    , Xs [0,1,0,0,0,7]
    , Xs [0,1,0,0,1,0,0,0]
    , Xs [0,1,0,0,1,0,1]
    , Xs [0,1,0,0,1,1,0]
    , Xs [0,1,0,0,1,-1]
    , Xs [0,1,0,0,-1,0,0]
    , Xs [0,1,0,0,-1,1]
    , Xs [0,1,0,0,7,0]
    , Xs [0,1,0,0,-8]
    , Xs [0,1,0,1,0,0,0,0]
    , Xs [0,1,0,1,0,0,1]
    , Xs [0,1,0,1,0,1,0]
    , Xs [0,1,0,1,0,-1]
    , Xs [0,1,0,1,1,0,0]
    , Xs [0,1,0,1,1,1]
    , Xs [0,1,0,1,-1,0]
    , Xs [0,1,0,1,7]
    , Xs [0,1,0,-1,0,0,0]
    , Xs [0,1,0,-1,0,1]
    , Xs [0,1,0,-1,1,0]
    , Xs [0,1,0,-1,-1]
    , Xs [0,1,0,7,0,0]
    , Xs [0,1,0,7,1]
    , Xs [0,1,0,-8,0]
    , Xs [0,1,0,2]
    , Xs [0,1,1,0,0,0,0,0]
    , Xs [0,1,1,0,0,0,1]
    , Xs [0,1,1,0,0,1,0]
    , Xs [0,1,1,0,0,-1]
    , Xs [0,1,1,0,1,0,0]
    , Xs [0,1,1,0,1,1]
    , Xs [0,1,1,0,-1,0]
    , Xs [0,1,1,0,7]
    , Xs [0,1,1,1,0,0,0]
    , Xs [0,1,1,1,0,1]
    , Xs [0,1,1,1,1,0]
    , Xs [0,1,1,1,-1]
    , Xs [0,1,1,-1,0,0]
    , Xs [0,1,1,-1,1]
    , Xs [0,1,1,7,0]
    , Xs [0,1,1,-8]
    , Xs [0,1,-1,0,0,0,0]
    , Xs [0,1,-1,0,0,1]
    , Xs [0,1,-1,0,1,0]
    , Xs [0,1,-1,0,-1]
    , Xs [0,1,-1,1,0,0]
    , Xs [0,1,-1,1,1]
    , Xs [0,1,-1,-1,0]
    , Xs [0,1,-1,7]
    , Xs [0,1,7,0,0,0]
    , Xs [0,1,7,0,1]
    , Xs [0,1,7,1,0]
    , Xs [0,1,7,-1]
    , Xs [0,1,-8,0,0]
    , Xs [0,1,-8,1]
    , Xs [0,1,2,0]
    , Xs [0,1,-2]
    , Xs [0,-1,0,0,0,0,0,0]
    , Xs [0,-1,0,0,0,0,1]
    , Xs [0,-1,0,0,0,1,0]
    , Xs [0,-1,0,0,0,-1]
    , Xs [0,-1,0,0,1,0,0]
    , Xs [0,-1,0,0,1,1]
    , Xs [0,-1,0,0,-1,0]
    , Xs [0,-1,0,0,7]
    , Xs [0,-1,0,1,0,0,0]
    , Xs [0,-1,0,1,0,1]
    , Xs [0,-1,0,1,1,0]
    , Xs [0,-1,0,1,-1]
    , Xs [0,-1,0,-1,0,0]
    , Xs [0,-1,0,-1,1]
    , Xs [0,-1,0,7,0]
    , Xs [0,-1,0,-8]
    , Xs [0,-1,1,0,0,0,0]
    , Xs [0,-1,1,0,0,1]
    , Xs [0,-1,1,0,1,0]
    , Xs [0,-1,1,0,-1]
    , Xs [0,-1,1,1,0,0]
    , Xs [0,-1,1,1,1]
    , Xs [0,-1,1,-1,0]
    , Xs [0,-1,1,7]
    , Xs [0,-1,-1,0,0,0]
    , Xs [0,-1,-1,0,1]
    , Xs [0,-1,-1,1,0]
    , Xs [0,-1,-1,-1]
    , Xs [0,-1,7,0,0]
    , Xs [0,-1,7,1]
    , Xs [0,-1,-8,0]
    , Xs [0,-1,2]
    , Xs [0,7,0,0,0,0,0]
    , Xs [0,7,0,0,0,1]
    , Xs [0,7,0,0,1,0]
    , Xs [0,7,0,0,-1]
    , Xs [0,7,0,1,0,0]
    , Xs [0,7,0,1,1]
    , Xs [0,7,0,-1,0]
    , Xs [0,7,0,7]
    , Xs [0,7,1,0,0,0]
    , Xs [0,7,1,0,1]
    , Xs [0,7,1,1,0]
    , Xs [0,7,1,-1]
    , Xs [0,7,-1,0,0]
    , Xs [0,7,-1,1]
    , Xs [0,7,7,0]
    , Xs [0,7,-8]
    , Xs [0,-8,0,0,0,0]
    , Xs [0,-8,0,0,1]
    , Xs [0,-8,0,1,0]
    , Xs [0,-8,0,-1]
    , Xs [0,-8,1,0,0]
    , Xs [0,-8,1,1]
    , Xs [0,-8,-1,0]
    , Xs [0,-8,7]
    , Xs [0,2,0,0,0]
    , Xs [0,2,0,1]
    , Xs [0,2,1,0]
    , Xs [0,2,-1]
    , Xs [0,-2,0,0]
    , Xs [0,-2,1]
    , Xs [0,6,0]
    , Xs [0,-7]
    , Xs [1,0,0,0,0,0,0,0,0]
    , Xs [1,0,0,0,0,0,0,1]
    , Xs [1,0,0,0,0,0,1,0]
    , Xs [1,0,0,0,0,0,-1]
    , Xs [1,0,0,0,0,1,0,0]
    , Xs [1,0,0,0,0,1,1]
    , Xs [1,0,0,0,0,-1,0]
    , Xs [1,0,0,0,0,7]
    , Xs [1,0,0,0,1,0,0,0]
    , Xs [1,0,0,0,1,0,1]
    , Xs [1,0,0,0,1,1,0]
    , Xs [1,0,0,0,1,-1]
    , Xs [1,0,0,0,-1,0,0]
    , Xs [1,0,0,0,-1,1]
    , Xs [1,0,0,0,7,0]
    , Xs [1,0,0,0,-8]
    , Xs [1,0,0,1,0,0,0,0]
    , Xs [1,0,0,1,0,0,1]
    , Xs [1,0,0,1,0,1,0]
    , Xs [1,0,0,1,0,-1]
    , Xs [1,0,0,1,1,0,0]
    , Xs [1,0,0,1,1,1]
    , Xs [1,0,0,1,-1,0]
    , Xs [1,0,0,1,7]
    , Xs [1,0,0,-1,0,0,0]
    , Xs [1,0,0,-1,0,1]
    , Xs [1,0,0,-1,1,0]
    , Xs [1,0,0,-1,-1]
    , Xs [1,0,0,7,0,0]
    , Xs [1,0,0,7,1]
    , Xs [1,0,0,-8,0]
    , Xs [1,0,0,2]
    , Xs [1,0,1,0,0,0,0,0]
    , Xs [1,0,1,0,0,0,1]
    , Xs [1,0,1,0,0,1,0]
    , Xs [1,0,1,0,0,-1]
    , Xs [1,0,1,0,1,0,0]
    , Xs [1,0,1,0,1,1]
    , Xs [1,0,1,0,-1,0]
    , Xs [1,0,1,0,7]
    , Xs [1,0,1,1,0,0,0]
    , Xs [1,0,1,1,0,1]
    , Xs [1,0,1,1,1,0]
    , Xs [1,0,1,1,-1]
    , Xs [1,0,1,-1,0,0]
    , Xs [1,0,1,-1,1]
    , Xs [1,0,1,7,0]
    , Xs [1,0,1,-8]
    , Xs [1,0,-1,0,0,0,0]
    , Xs [1,0,-1,0,0,1]
    , Xs [1,0,-1,0,1,0]
    , Xs [1,0,-1,0,-1]
    , Xs [1,0,-1,1,0,0]
    , Xs [1,0,-1,1,1]
    , Xs [1,0,-1,-1,0]
    , Xs [1,0,-1,7]
    , Xs [1,0,7,0,0,0]
    , Xs [1,0,7,0,1]
    , Xs [1,0,7,1,0]
    , Xs [1,0,7,-1]
    , Xs [1,0,-8,0,0]
    , Xs [1,0,-8,1]
    , Xs [1,0,2,0]
    , Xs [1,0,-2]
    , Xs [1,1,0,0,0,0,0,0]
    , Xs [1,1,0,0,0,0,1]
    , Xs [1,1,0,0,0,1,0]
    , Xs [1,1,0,0,0,-1]
    , Xs [1,1,0,0,1,0,0]
    , Xs [1,1,0,0,1,1]
    , Xs [1,1,0,0,-1,0]
    , Xs [1,1,0,0,7]
    , Xs [1,1,0,1,0,0,0]
    , Xs [1,1,0,1,0,1]
    , Xs [1,1,0,1,1,0]
    , Xs [1,1,0,1,-1]
    , Xs [1,1,0,-1,0,0]
    , Xs [1,1,0,-1,1]
    , Xs [1,1,0,7,0]
    , Xs [1,1,0,-8]
    , Xs [1,1,1,0,0,0,0]
    , Xs [1,1,1,0,0,1]
    , Xs [1,1,1,0,1,0]
    , Xs [1,1,1,0,-1]
    , Xs [1,1,1,1,0,0]
    , Xs [1,1,1,1,1]
    , Xs [1,1,1,-1,0]
    , Xs [1,1,1,7]
    , Xs [1,1,-1,0,0,0]
    , Xs [1,1,-1,0,1]
    , Xs [1,1,-1,1,0]
    , Xs [1,1,-1,-1]
    , Xs [1,1,7,0,0]
    , Xs [1,1,7,1]
    , Xs [1,1,-8,0]
    , Xs [1,1,2]
    , Xs [1,-1,0,0,0,0,0]
    , Xs [1,-1,0,0,0,1]
    , Xs [1,-1,0,0,1,0]
    , Xs [1,-1,0,0,-1]
    , Xs [1,-1,0,1,0,0]
    , Xs [1,-1,0,1,1]
    , Xs [1,-1,0,-1,0]
    , Xs [1,-1,0,7]
    , Xs [1,-1,1,0,0,0]
    , Xs [1,-1,1,0,1]
    , Xs [1,-1,1,1,0]
    , Xs [1,-1,1,-1]
    , Xs [1,-1,-1,0,0]
    , Xs [1,-1,-1,1]
    , Xs [1,-1,7,0]
    , Xs [1,-1,-8]
    , Xs [1,7,0,0,0,0]
    , Xs [1,7,0,0,1]
    , Xs [1,7,0,1,0]
    , Xs [1,7,0,-1]
    , Xs [1,7,1,0,0]
    , Xs [1,7,1,1]
    , Xs [1,7,-1,0]
    , Xs [1,7,7]
    , Xs [1,-8,0,0,0]
    , Xs [1,-8,0,1]
    , Xs [1,-8,1,0]
    , Xs [1,-8,-1]
    , Xs [1,2,0,0]
    , Xs [1,2,1]
    , Xs [1,-2,0]
    , Xs [1,6]
    , Xs [-1,0,0,0,0,0,0,0]
    , Xs [-1,0,0,0,0,0,1]
    , Xs [-1,0,0,0,0,1,0]
    , Xs [-1,0,0,0,0,-1]
    , Xs [-1,0,0,0,1,0,0]
    , Xs [-1,0,0,0,1,1]
    , Xs [-1,0,0,0,-1,0]
    , Xs [-1,0,0,0,7]
    , Xs [-1,0,0,1,0,0,0]
    , Xs [-1,0,0,1,0,1]
    , Xs [-1,0,0,1,1,0]
    , Xs [-1,0,0,1,-1]
    , Xs [-1,0,0,-1,0,0]
    , Xs [-1,0,0,-1,1]
    , Xs [-1,0,0,7,0]
    , Xs [-1,0,0,-8]
    , Xs [-1,0,1,0,0,0,0]
    , Xs [-1,0,1,0,0,1]
    , Xs [-1,0,1,0,1,0]
    , Xs [-1,0,1,0,-1]
    , Xs [-1,0,1,1,0,0]
    , Xs [-1,0,1,1,1]
    , Xs [-1,0,1,-1,0]
    , Xs [-1,0,1,7]
    , Xs [-1,0,-1,0,0,0]
    , Xs [-1,0,-1,0,1]
    , Xs [-1,0,-1,1,0]
    , Xs [-1,0,-1,-1]
    , Xs [-1,0,7,0,0]
    , Xs [-1,0,7,1]
    , Xs [-1,0,-8,0]
    , Xs [-1,0,2]
    , Xs [-1,1,0,0,0,0,0]
    , Xs [-1,1,0,0,0,1]
    , Xs [-1,1,0,0,1,0]
    , Xs [-1,1,0,0,-1]
    , Xs [-1,1,0,1,0,0]
    , Xs [-1,1,0,1,1]
    , Xs [-1,1,0,-1,0]
    , Xs [-1,1,0,7]
    , Xs [-1,1,1,0,0,0]
    , Xs [-1,1,1,0,1]
    , Xs [-1,1,1,1,0]
    , Xs [-1,1,1,-1]
    , Xs [-1,1,-1,0,0]
    , Xs [-1,1,-1,1]
    , Xs [-1,1,7,0]
    , Xs [-1,1,-8]
    , Xs [-1,-1,0,0,0,0]
    , Xs [-1,-1,0,0,1]
    , Xs [-1,-1,0,1,0]
    , Xs [-1,-1,0,-1]
    , Xs [-1,-1,1,0,0]
    , Xs [-1,-1,1,1]
    , Xs [-1,-1,-1,0]
    , Xs [-1,-1,7]
    , Xs [-1,7,0,0,0]
    , Xs [-1,7,0,1]
    , Xs [-1,7,1,0]
    , Xs [-1,7,-1]
    , Xs [-1,-8,0,0]
    , Xs [-1,-8,1]
    , Xs [-1,2,0]
    , Xs [-1,-2]
    , Xs [7,0,0,0,0,0,0]
    , Xs [7,0,0,0,0,1]
    , Xs [7,0,0,0,1,0]
    , Xs [7,0,0,0,-1]
    , Xs [7,0,0,1,0,0]
    , Xs [7,0,0,1,1]
    , Xs [7,0,0,-1,0]
    , Xs [7,0,0,7]
    , Xs [7,0,1,0,0,0]
    , Xs [7,0,1,0,1]
    , Xs [7,0,1,1,0]
    , Xs [7,0,1,-1]
    , Xs [7,0,-1,0,0]
    , Xs [7,0,-1,1]
    , Xs [7,0,7,0]
    , Xs [7,0,-8]
    , Xs [7,1,0,0,0,0]
    , Xs [7,1,0,0,1]
    , Xs [7,1,0,1,0]
    , Xs [7,1,0,-1]
    , Xs [7,1,1,0,0]
    , Xs [7,1,1,1]
    , Xs [7,1,-1,0]
    , Xs [7,1,7]
    , Xs [7,-1,0,0,0]
    , Xs [7,-1,0,1]
    , Xs [7,-1,1,0]
    , Xs [7,-1,-1]
    , Xs [7,7,0,0]
    , Xs [7,7,1]
    , Xs [7,-8,0]
    , Xs [7,2]
    , Xs [-8,0,0,0,0,0]
    , Xs [-8,0,0,0,1]
    , Xs [-8,0,0,1,0]
    , Xs [-8,0,0,-1]
    , Xs [-8,0,1,0,0]
    , Xs [-8,0,1,1]
    , Xs [-8,0,-1,0]
    , Xs [-8,0,7]
    , Xs [-8,1,0,0,0]
    , Xs [-8,1,0,1]
    , Xs [-8,1,1,0]
    , Xs [-8,1,-1]
    , Xs [-8,-1,0,0]
    , Xs [-8,-1,1]
    , Xs [-8,7,0]
    , Xs [-8,-8]
    , Xs [2,0,0,0,0]
    , Xs [2,0,0,1]
    , Xs [2,0,1,0]
    , Xs [2,0,-1]
    , Xs [2,1,0,0]
    , Xs [2,1,1]
    , Xs [2,-1,0]
    , Xs [2,7]
    , Xs [-2,0,0,0]
    , Xs [-2,0,1]
    , Xs [-2,1,0]
    , Xs [-2,-1]
    , Xs [6,0,0]
    , Xs [6,1]
    , Xs [-7,0]
    , Xs [3]
    ]
  , ...
  ]
