Identifier
Identifier
Mp00053: Parking functions to car permutationPermutations
Images
[1] => [1]
[1,1] => [1,2]
[1,2] => [1,2]
[2,1] => [2,1]
[1,1,1] => [1,2,3]
[1,1,2] => [1,2,3]
[1,2,1] => [1,2,3]
[2,1,1] => [2,1,3]
[1,1,3] => [1,2,3]
[1,3,1] => [1,3,2]
[3,1,1] => [2,3,1]
[1,2,2] => [1,2,3]
[2,1,2] => [2,1,3]
[2,2,1] => [3,1,2]
[1,2,3] => [1,2,3]
[1,3,2] => [1,3,2]
[2,1,3] => [2,1,3]
[2,3,1] => [3,1,2]
[3,1,2] => [2,3,1]
[3,2,1] => [3,2,1]
[1,1,1,1] => [1,2,3,4]
[1,1,1,2] => [1,2,3,4]
[1,1,2,1] => [1,2,3,4]
[1,2,1,1] => [1,2,3,4]
[2,1,1,1] => [2,1,3,4]
[1,1,1,3] => [1,2,3,4]
[1,1,3,1] => [1,2,3,4]
[1,3,1,1] => [1,3,2,4]
[3,1,1,1] => [2,3,1,4]
[1,1,1,4] => [1,2,3,4]
[1,1,4,1] => [1,2,4,3]
[1,4,1,1] => [1,3,4,2]
[4,1,1,1] => [2,3,4,1]
[1,1,2,2] => [1,2,3,4]
[1,2,1,2] => [1,2,3,4]
[1,2,2,1] => [1,2,3,4]
[2,1,1,2] => [2,1,3,4]
[2,1,2,1] => [2,1,3,4]
[2,2,1,1] => [3,1,2,4]
[1,1,2,3] => [1,2,3,4]
[1,1,3,2] => [1,2,3,4]
[1,2,1,3] => [1,2,3,4]
[1,2,3,1] => [1,2,3,4]
[1,3,1,2] => [1,3,2,4]
[1,3,2,1] => [1,3,2,4]
[2,1,1,3] => [2,1,3,4]
[2,1,3,1] => [2,1,3,4]
[2,3,1,1] => [3,1,2,4]
[3,1,1,2] => [2,3,1,4]
[3,1,2,1] => [2,3,1,4]
[3,2,1,1] => [3,2,1,4]
[1,1,2,4] => [1,2,3,4]
[1,1,4,2] => [1,2,4,3]
[1,2,1,4] => [1,2,3,4]
[1,2,4,1] => [1,2,4,3]
[1,4,1,2] => [1,3,4,2]
[1,4,2,1] => [1,3,4,2]
[2,1,1,4] => [2,1,3,4]
[2,1,4,1] => [2,1,4,3]
[2,4,1,1] => [3,1,4,2]
[4,1,1,2] => [2,3,4,1]
[4,1,2,1] => [2,3,4,1]
[4,2,1,1] => [3,2,4,1]
[1,1,3,3] => [1,2,3,4]
[1,3,1,3] => [1,3,2,4]
[1,3,3,1] => [1,4,2,3]
[3,1,1,3] => [2,3,1,4]
[3,1,3,1] => [2,4,1,3]
[3,3,1,1] => [3,4,1,2]
[1,1,3,4] => [1,2,3,4]
[1,1,4,3] => [1,2,4,3]
[1,3,1,4] => [1,3,2,4]
[1,3,4,1] => [1,4,2,3]
[1,4,1,3] => [1,3,4,2]
[1,4,3,1] => [1,4,3,2]
[3,1,1,4] => [2,3,1,4]
[3,1,4,1] => [2,4,1,3]
[3,4,1,1] => [3,4,1,2]
[4,1,1,3] => [2,3,4,1]
[4,1,3,1] => [2,4,3,1]
[4,3,1,1] => [3,4,2,1]
[1,2,2,2] => [1,2,3,4]
[2,1,2,2] => [2,1,3,4]
[2,2,1,2] => [3,1,2,4]
[2,2,2,1] => [4,1,2,3]
[1,2,2,3] => [1,2,3,4]
[1,2,3,2] => [1,2,3,4]
[1,3,2,2] => [1,3,2,4]
[2,1,2,3] => [2,1,3,4]
[2,1,3,2] => [2,1,3,4]
[2,2,1,3] => [3,1,2,4]
[2,2,3,1] => [4,1,2,3]
[2,3,1,2] => [3,1,2,4]
[2,3,2,1] => [4,1,2,3]
[3,1,2,2] => [2,3,1,4]
[3,2,1,2] => [3,2,1,4]
[3,2,2,1] => [4,2,1,3]
[1,2,2,4] => [1,2,3,4]
[1,2,4,2] => [1,2,4,3]
[1,4,2,2] => [1,3,4,2]
[2,1,2,4] => [2,1,3,4]
[2,1,4,2] => [2,1,4,3]
[2,2,1,4] => [3,1,2,4]
[2,2,4,1] => [4,1,2,3]
[2,4,1,2] => [3,1,4,2]
[2,4,2,1] => [4,1,3,2]
[4,1,2,2] => [2,3,4,1]
[4,2,1,2] => [3,2,4,1]
[4,2,2,1] => [4,2,3,1]
[1,2,3,3] => [1,2,3,4]
[1,3,2,3] => [1,3,2,4]
[1,3,3,2] => [1,4,2,3]
[2,1,3,3] => [2,1,3,4]
[2,3,1,3] => [3,1,2,4]
[2,3,3,1] => [4,1,2,3]
[3,1,2,3] => [2,3,1,4]
[3,1,3,2] => [2,4,1,3]
[3,2,1,3] => [3,2,1,4]
[3,2,3,1] => [4,2,1,3]
[3,3,1,2] => [3,4,1,2]
[3,3,2,1] => [4,3,1,2]
[1,2,3,4] => [1,2,3,4]
[1,2,4,3] => [1,2,4,3]
[1,3,2,4] => [1,3,2,4]
[1,3,4,2] => [1,4,2,3]
[1,4,2,3] => [1,3,4,2]
[1,4,3,2] => [1,4,3,2]
[2,1,3,4] => [2,1,3,4]
[2,1,4,3] => [2,1,4,3]
[2,3,1,4] => [3,1,2,4]
[2,3,4,1] => [4,1,2,3]
[2,4,1,3] => [3,1,4,2]
[2,4,3,1] => [4,1,3,2]
[3,1,2,4] => [2,3,1,4]
[3,1,4,2] => [2,4,1,3]
[3,2,1,4] => [3,2,1,4]
[3,2,4,1] => [4,2,1,3]
[3,4,1,2] => [3,4,1,2]
[3,4,2,1] => [4,3,1,2]
[4,1,2,3] => [2,3,4,1]
[4,1,3,2] => [2,4,3,1]
[4,2,1,3] => [3,2,4,1]
[4,2,3,1] => [4,2,3,1]
[4,3,1,2] => [3,4,2,1]
[4,3,2,1] => [4,3,2,1]
[1,1,1,1,1] => [1,2,3,4,5]
[1,1,1,1,2] => [1,2,3,4,5]
[1,1,1,2,1] => [1,2,3,4,5]
[1,1,2,1,1] => [1,2,3,4,5]
[1,2,1,1,1] => [1,2,3,4,5]
[2,1,1,1,1] => [2,1,3,4,5]
[1,1,1,1,3] => [1,2,3,4,5]
[1,1,1,3,1] => [1,2,3,4,5]
[1,1,3,1,1] => [1,2,3,4,5]
[1,3,1,1,1] => [1,3,2,4,5]
[3,1,1,1,1] => [2,3,1,4,5]
[1,1,1,1,4] => [1,2,3,4,5]
[1,1,1,4,1] => [1,2,3,4,5]
[1,1,4,1,1] => [1,2,4,3,5]
[1,4,1,1,1] => [1,3,4,2,5]
[4,1,1,1,1] => [2,3,4,1,5]
[1,1,1,1,5] => [1,2,3,4,5]
[1,1,1,5,1] => [1,2,3,5,4]
[1,1,5,1,1] => [1,2,4,5,3]
[1,5,1,1,1] => [1,3,4,5,2]
[5,1,1,1,1] => [2,3,4,5,1]
[1,1,1,2,2] => [1,2,3,4,5]
[1,1,2,1,2] => [1,2,3,4,5]
[1,1,2,2,1] => [1,2,3,4,5]
[1,2,1,1,2] => [1,2,3,4,5]
[1,2,1,2,1] => [1,2,3,4,5]
[1,2,2,1,1] => [1,2,3,4,5]
[2,1,1,1,2] => [2,1,3,4,5]
[2,1,1,2,1] => [2,1,3,4,5]
[2,1,2,1,1] => [2,1,3,4,5]
[2,2,1,1,1] => [3,1,2,4,5]
[1,1,1,2,3] => [1,2,3,4,5]
[1,1,1,3,2] => [1,2,3,4,5]
[1,1,2,1,3] => [1,2,3,4,5]
[1,1,2,3,1] => [1,2,3,4,5]
[1,1,3,1,2] => [1,2,3,4,5]
[1,1,3,2,1] => [1,2,3,4,5]
[1,2,1,1,3] => [1,2,3,4,5]
[1,2,1,3,1] => [1,2,3,4,5]
[1,2,3,1,1] => [1,2,3,4,5]
[1,3,1,1,2] => [1,3,2,4,5]
[1,3,1,2,1] => [1,3,2,4,5]
[1,3,2,1,1] => [1,3,2,4,5]
[2,1,1,1,3] => [2,1,3,4,5]
[2,1,1,3,1] => [2,1,3,4,5]
[2,1,3,1,1] => [2,1,3,4,5]
[2,3,1,1,1] => [3,1,2,4,5]
[3,1,1,1,2] => [2,3,1,4,5]
[3,1,1,2,1] => [2,3,1,4,5]
[3,1,2,1,1] => [2,3,1,4,5]
[3,2,1,1,1] => [3,2,1,4,5]
[1,1,1,2,4] => [1,2,3,4,5]
[1,1,1,4,2] => [1,2,3,4,5]
[1,1,2,1,4] => [1,2,3,4,5]
[1,1,2,4,1] => [1,2,3,4,5]
[1,1,4,1,2] => [1,2,4,3,5]
[1,1,4,2,1] => [1,2,4,3,5]
[1,2,1,1,4] => [1,2,3,4,5]
[1,2,1,4,1] => [1,2,3,4,5]
[1,2,4,1,1] => [1,2,4,3,5]
[1,4,1,1,2] => [1,3,4,2,5]
[1,4,1,2,1] => [1,3,4,2,5]
[1,4,2,1,1] => [1,3,4,2,5]
[2,1,1,1,4] => [2,1,3,4,5]
[2,1,1,4,1] => [2,1,3,4,5]
[2,1,4,1,1] => [2,1,4,3,5]
[2,4,1,1,1] => [3,1,4,2,5]
[4,1,1,1,2] => [2,3,4,1,5]
[4,1,1,2,1] => [2,3,4,1,5]
[4,1,2,1,1] => [2,3,4,1,5]
[4,2,1,1,1] => [3,2,4,1,5]
[1,1,1,2,5] => [1,2,3,4,5]
[1,1,1,5,2] => [1,2,3,5,4]
[1,1,2,1,5] => [1,2,3,4,5]
[1,1,2,5,1] => [1,2,3,5,4]
[1,1,5,1,2] => [1,2,4,5,3]
[1,1,5,2,1] => [1,2,4,5,3]
[1,2,1,1,5] => [1,2,3,4,5]
[1,2,1,5,1] => [1,2,3,5,4]
[1,2,5,1,1] => [1,2,4,5,3]
[1,5,1,1,2] => [1,3,4,5,2]
[1,5,1,2,1] => [1,3,4,5,2]
[1,5,2,1,1] => [1,3,4,5,2]
[2,1,1,1,5] => [2,1,3,4,5]
[2,1,1,5,1] => [2,1,3,5,4]
[2,1,5,1,1] => [2,1,4,5,3]
[2,5,1,1,1] => [3,1,4,5,2]
[5,1,1,1,2] => [2,3,4,5,1]
[5,1,1,2,1] => [2,3,4,5,1]
[5,1,2,1,1] => [2,3,4,5,1]
[5,2,1,1,1] => [3,2,4,5,1]
[1,1,1,3,3] => [1,2,3,4,5]
[1,1,3,1,3] => [1,2,3,4,5]
[1,1,3,3,1] => [1,2,3,4,5]
[1,3,1,1,3] => [1,3,2,4,5]
[1,3,1,3,1] => [1,3,2,4,5]
[1,3,3,1,1] => [1,4,2,3,5]
[3,1,1,1,3] => [2,3,1,4,5]
[3,1,1,3,1] => [2,3,1,4,5]
[3,1,3,1,1] => [2,4,1,3,5]
[3,3,1,1,1] => [3,4,1,2,5]
[1,1,1,3,4] => [1,2,3,4,5]
[1,1,1,4,3] => [1,2,3,4,5]
[1,1,3,1,4] => [1,2,3,4,5]
[1,1,3,4,1] => [1,2,3,4,5]
[1,1,4,1,3] => [1,2,4,3,5]
[1,1,4,3,1] => [1,2,4,3,5]
[1,3,1,1,4] => [1,3,2,4,5]
[1,3,1,4,1] => [1,3,2,4,5]
[1,3,4,1,1] => [1,4,2,3,5]
[1,4,1,1,3] => [1,3,4,2,5]
[1,4,1,3,1] => [1,3,4,2,5]
[1,4,3,1,1] => [1,4,3,2,5]
[3,1,1,1,4] => [2,3,1,4,5]
[3,1,1,4,1] => [2,3,1,4,5]
[3,1,4,1,1] => [2,4,1,3,5]
[3,4,1,1,1] => [3,4,1,2,5]
[4,1,1,1,3] => [2,3,4,1,5]
[4,1,1,3,1] => [2,3,4,1,5]
[4,1,3,1,1] => [2,4,3,1,5]
[4,3,1,1,1] => [3,4,2,1,5]
[1,1,1,3,5] => [1,2,3,4,5]
[1,1,1,5,3] => [1,2,3,5,4]
[1,1,3,1,5] => [1,2,3,4,5]
[1,1,3,5,1] => [1,2,3,5,4]
[1,1,5,1,3] => [1,2,4,5,3]
[1,1,5,3,1] => [1,2,4,5,3]
[1,3,1,1,5] => [1,3,2,4,5]
[1,3,1,5,1] => [1,3,2,5,4]
[1,3,5,1,1] => [1,4,2,5,3]
[1,5,1,1,3] => [1,3,4,5,2]
[1,5,1,3,1] => [1,3,4,5,2]
[1,5,3,1,1] => [1,4,3,5,2]
[3,1,1,1,5] => [2,3,1,4,5]
[3,1,1,5,1] => [2,3,1,5,4]
[3,1,5,1,1] => [2,4,1,5,3]
[3,5,1,1,1] => [3,4,1,5,2]
[5,1,1,1,3] => [2,3,4,5,1]
[5,1,1,3,1] => [2,3,4,5,1]
[5,1,3,1,1] => [2,4,3,5,1]
[5,3,1,1,1] => [3,4,2,5,1]
[1,1,1,4,4] => [1,2,3,4,5]
[1,1,4,1,4] => [1,2,4,3,5]
[1,1,4,4,1] => [1,2,5,3,4]
[1,4,1,1,4] => [1,3,4,2,5]
[1,4,1,4,1] => [1,3,5,2,4]
[1,4,4,1,1] => [1,4,5,2,3]
[4,1,1,1,4] => [2,3,4,1,5]
[4,1,1,4,1] => [2,3,5,1,4]
[4,1,4,1,1] => [2,4,5,1,3]
[4,4,1,1,1] => [3,4,5,1,2]
[1,1,1,4,5] => [1,2,3,4,5]
[1,1,1,5,4] => [1,2,3,5,4]
[1,1,4,1,5] => [1,2,4,3,5]
[1,1,4,5,1] => [1,2,5,3,4]
[1,1,5,1,4] => [1,2,4,5,3]
[1,1,5,4,1] => [1,2,5,4,3]
[1,4,1,1,5] => [1,3,4,2,5]
[1,4,1,5,1] => [1,3,5,2,4]
[1,4,5,1,1] => [1,4,5,2,3]
[1,5,1,1,4] => [1,3,4,5,2]
[1,5,1,4,1] => [1,3,5,4,2]
[1,5,4,1,1] => [1,4,5,3,2]
[4,1,1,1,5] => [2,3,4,1,5]
[4,1,1,5,1] => [2,3,5,1,4]
[4,1,5,1,1] => [2,4,5,1,3]
[4,5,1,1,1] => [3,4,5,1,2]
[5,1,1,1,4] => [2,3,4,5,1]
[5,1,1,4,1] => [2,3,5,4,1]
[5,1,4,1,1] => [2,4,5,3,1]
[5,4,1,1,1] => [3,4,5,2,1]
[1,1,2,2,2] => [1,2,3,4,5]
[1,2,1,2,2] => [1,2,3,4,5]
[1,2,2,1,2] => [1,2,3,4,5]
[1,2,2,2,1] => [1,2,3,4,5]
[2,1,1,2,2] => [2,1,3,4,5]
[2,1,2,1,2] => [2,1,3,4,5]
[2,1,2,2,1] => [2,1,3,4,5]
[2,2,1,1,2] => [3,1,2,4,5]
[2,2,1,2,1] => [3,1,2,4,5]
[2,2,2,1,1] => [4,1,2,3,5]
[1,1,2,2,3] => [1,2,3,4,5]
[1,1,2,3,2] => [1,2,3,4,5]
[1,1,3,2,2] => [1,2,3,4,5]
[1,2,1,2,3] => [1,2,3,4,5]
[1,2,1,3,2] => [1,2,3,4,5]
[1,2,2,1,3] => [1,2,3,4,5]
[1,2,2,3,1] => [1,2,3,4,5]
[1,2,3,1,2] => [1,2,3,4,5]
[1,2,3,2,1] => [1,2,3,4,5]
[1,3,1,2,2] => [1,3,2,4,5]
[1,3,2,1,2] => [1,3,2,4,5]
[1,3,2,2,1] => [1,3,2,4,5]
[2,1,1,2,3] => [2,1,3,4,5]
[2,1,1,3,2] => [2,1,3,4,5]
[2,1,2,1,3] => [2,1,3,4,5]
[2,1,2,3,1] => [2,1,3,4,5]
[2,1,3,1,2] => [2,1,3,4,5]
[2,1,3,2,1] => [2,1,3,4,5]
[2,2,1,1,3] => [3,1,2,4,5]
[2,2,1,3,1] => [3,1,2,4,5]
[2,2,3,1,1] => [4,1,2,3,5]
[2,3,1,1,2] => [3,1,2,4,5]
[2,3,1,2,1] => [3,1,2,4,5]
[2,3,2,1,1] => [4,1,2,3,5]
[3,1,1,2,2] => [2,3,1,4,5]
[3,1,2,1,2] => [2,3,1,4,5]
[3,1,2,2,1] => [2,3,1,4,5]
[3,2,1,1,2] => [3,2,1,4,5]
[3,2,1,2,1] => [3,2,1,4,5]
[3,2,2,1,1] => [4,2,1,3,5]
[1,1,2,2,4] => [1,2,3,4,5]
[1,1,2,4,2] => [1,2,3,4,5]
[1,1,4,2,2] => [1,2,4,3,5]
[1,2,1,2,4] => [1,2,3,4,5]
[1,2,1,4,2] => [1,2,3,4,5]
[1,2,2,1,4] => [1,2,3,4,5]
[1,2,2,4,1] => [1,2,3,4,5]
[1,2,4,1,2] => [1,2,4,3,5]
[1,2,4,2,1] => [1,2,4,3,5]
[1,4,1,2,2] => [1,3,4,2,5]
[1,4,2,1,2] => [1,3,4,2,5]
[1,4,2,2,1] => [1,3,4,2,5]
[2,1,1,2,4] => [2,1,3,4,5]
[2,1,1,4,2] => [2,1,3,4,5]
[2,1,2,1,4] => [2,1,3,4,5]
[2,1,2,4,1] => [2,1,3,4,5]
[2,1,4,1,2] => [2,1,4,3,5]
[2,1,4,2,1] => [2,1,4,3,5]
[2,2,1,1,4] => [3,1,2,4,5]
[2,2,1,4,1] => [3,1,2,4,5]
[2,2,4,1,1] => [4,1,2,3,5]
[2,4,1,1,2] => [3,1,4,2,5]
[2,4,1,2,1] => [3,1,4,2,5]
[2,4,2,1,1] => [4,1,3,2,5]
[4,1,1,2,2] => [2,3,4,1,5]
[4,1,2,1,2] => [2,3,4,1,5]
[4,1,2,2,1] => [2,3,4,1,5]
[4,2,1,1,2] => [3,2,4,1,5]
[4,2,1,2,1] => [3,2,4,1,5]
[4,2,2,1,1] => [4,2,3,1,5]
[1,1,2,2,5] => [1,2,3,4,5]
[1,1,2,5,2] => [1,2,3,5,4]
[1,1,5,2,2] => [1,2,4,5,3]
[1,2,1,2,5] => [1,2,3,4,5]
[1,2,1,5,2] => [1,2,3,5,4]
[1,2,2,1,5] => [1,2,3,4,5]
[1,2,2,5,1] => [1,2,3,5,4]
[1,2,5,1,2] => [1,2,4,5,3]
[1,2,5,2,1] => [1,2,4,5,3]
[1,5,1,2,2] => [1,3,4,5,2]
[1,5,2,1,2] => [1,3,4,5,2]
[1,5,2,2,1] => [1,3,4,5,2]
[2,1,1,2,5] => [2,1,3,4,5]
[2,1,1,5,2] => [2,1,3,5,4]
[2,1,2,1,5] => [2,1,3,4,5]
[2,1,2,5,1] => [2,1,3,5,4]
[2,1,5,1,2] => [2,1,4,5,3]
[2,1,5,2,1] => [2,1,4,5,3]
[2,2,1,1,5] => [3,1,2,4,5]
[2,2,1,5,1] => [3,1,2,5,4]
[2,2,5,1,1] => [4,1,2,5,3]
[2,5,1,1,2] => [3,1,4,5,2]
[2,5,1,2,1] => [3,1,4,5,2]
[2,5,2,1,1] => [4,1,3,5,2]
[5,1,1,2,2] => [2,3,4,5,1]
[5,1,2,1,2] => [2,3,4,5,1]
[5,1,2,2,1] => [2,3,4,5,1]
[5,2,1,1,2] => [3,2,4,5,1]
[5,2,1,2,1] => [3,2,4,5,1]
[5,2,2,1,1] => [4,2,3,5,1]
[1,1,2,3,3] => [1,2,3,4,5]
[1,1,3,2,3] => [1,2,3,4,5]
[1,1,3,3,2] => [1,2,3,4,5]
[1,2,1,3,3] => [1,2,3,4,5]
[1,2,3,1,3] => [1,2,3,4,5]
[1,2,3,3,1] => [1,2,3,4,5]
[1,3,1,2,3] => [1,3,2,4,5]
[1,3,1,3,2] => [1,3,2,4,5]
[1,3,2,1,3] => [1,3,2,4,5]
[1,3,2,3,1] => [1,3,2,4,5]
[1,3,3,1,2] => [1,4,2,3,5]
[1,3,3,2,1] => [1,4,2,3,5]
[2,1,1,3,3] => [2,1,3,4,5]
[2,1,3,1,3] => [2,1,3,4,5]
[2,1,3,3,1] => [2,1,3,4,5]
[2,3,1,1,3] => [3,1,2,4,5]
[2,3,1,3,1] => [3,1,2,4,5]
[2,3,3,1,1] => [4,1,2,3,5]
[3,1,1,2,3] => [2,3,1,4,5]
[3,1,1,3,2] => [2,3,1,4,5]
[3,1,2,1,3] => [2,3,1,4,5]
[3,1,2,3,1] => [2,3,1,4,5]
[3,1,3,1,2] => [2,4,1,3,5]
[3,1,3,2,1] => [2,4,1,3,5]
[3,2,1,1,3] => [3,2,1,4,5]
[3,2,1,3,1] => [3,2,1,4,5]
[3,2,3,1,1] => [4,2,1,3,5]
[3,3,1,1,2] => [3,4,1,2,5]
[3,3,1,2,1] => [3,4,1,2,5]
[3,3,2,1,1] => [4,3,1,2,5]
[1,1,2,3,4] => [1,2,3,4,5]
[1,1,2,4,3] => [1,2,3,4,5]
[1,1,3,2,4] => [1,2,3,4,5]
[1,1,3,4,2] => [1,2,3,4,5]
[1,1,4,2,3] => [1,2,4,3,5]
[1,1,4,3,2] => [1,2,4,3,5]
[1,2,1,3,4] => [1,2,3,4,5]
[1,2,1,4,3] => [1,2,3,4,5]
[1,2,3,1,4] => [1,2,3,4,5]
[1,2,3,4,1] => [1,2,3,4,5]
[1,2,4,1,3] => [1,2,4,3,5]
[1,2,4,3,1] => [1,2,4,3,5]
[1,3,1,2,4] => [1,3,2,4,5]
[1,3,1,4,2] => [1,3,2,4,5]
[1,3,2,1,4] => [1,3,2,4,5]
[1,3,2,4,1] => [1,3,2,4,5]
[1,3,4,1,2] => [1,4,2,3,5]
[1,3,4,2,1] => [1,4,2,3,5]
[1,4,1,2,3] => [1,3,4,2,5]
[1,4,1,3,2] => [1,3,4,2,5]
[1,4,2,1,3] => [1,3,4,2,5]
[1,4,2,3,1] => [1,3,4,2,5]
[1,4,3,1,2] => [1,4,3,2,5]
[1,4,3,2,1] => [1,4,3,2,5]
[2,1,1,3,4] => [2,1,3,4,5]
[2,1,1,4,3] => [2,1,3,4,5]
[2,1,3,1,4] => [2,1,3,4,5]
[2,1,3,4,1] => [2,1,3,4,5]
[2,1,4,1,3] => [2,1,4,3,5]
[2,1,4,3,1] => [2,1,4,3,5]
[2,3,1,1,4] => [3,1,2,4,5]
[2,3,1,4,1] => [3,1,2,4,5]
[2,3,4,1,1] => [4,1,2,3,5]
[2,4,1,1,3] => [3,1,4,2,5]
[2,4,1,3,1] => [3,1,4,2,5]
[2,4,3,1,1] => [4,1,3,2,5]
[3,1,1,2,4] => [2,3,1,4,5]
[3,1,1,4,2] => [2,3,1,4,5]
[3,1,2,1,4] => [2,3,1,4,5]
[3,1,2,4,1] => [2,3,1,4,5]
[3,1,4,1,2] => [2,4,1,3,5]
[3,1,4,2,1] => [2,4,1,3,5]
[3,2,1,1,4] => [3,2,1,4,5]
[3,2,1,4,1] => [3,2,1,4,5]
[3,2,4,1,1] => [4,2,1,3,5]
[3,4,1,1,2] => [3,4,1,2,5]
[3,4,1,2,1] => [3,4,1,2,5]
[3,4,2,1,1] => [4,3,1,2,5]
[4,1,1,2,3] => [2,3,4,1,5]
[4,1,1,3,2] => [2,3,4,1,5]
[4,1,2,1,3] => [2,3,4,1,5]
[4,1,2,3,1] => [2,3,4,1,5]
[4,1,3,1,2] => [2,4,3,1,5]
[4,1,3,2,1] => [2,4,3,1,5]
[4,2,1,1,3] => [3,2,4,1,5]
[4,2,1,3,1] => [3,2,4,1,5]
[4,2,3,1,1] => [4,2,3,1,5]
[4,3,1,1,2] => [3,4,2,1,5]
[4,3,1,2,1] => [3,4,2,1,5]
[4,3,2,1,1] => [4,3,2,1,5]
[1,1,2,3,5] => [1,2,3,4,5]
[1,1,2,5,3] => [1,2,3,5,4]
[1,1,3,2,5] => [1,2,3,4,5]
[1,1,3,5,2] => [1,2,3,5,4]
[1,1,5,2,3] => [1,2,4,5,3]
[1,1,5,3,2] => [1,2,4,5,3]
[1,2,1,3,5] => [1,2,3,4,5]
[1,2,1,5,3] => [1,2,3,5,4]
[1,2,3,1,5] => [1,2,3,4,5]
[1,2,3,5,1] => [1,2,3,5,4]
[1,2,5,1,3] => [1,2,4,5,3]
[1,2,5,3,1] => [1,2,4,5,3]
[1,3,1,2,5] => [1,3,2,4,5]
[1,3,1,5,2] => [1,3,2,5,4]
[1,3,2,1,5] => [1,3,2,4,5]
[1,3,2,5,1] => [1,3,2,5,4]
[1,3,5,1,2] => [1,4,2,5,3]
[1,3,5,2,1] => [1,4,2,5,3]
[1,5,1,2,3] => [1,3,4,5,2]
[1,5,1,3,2] => [1,3,4,5,2]
[1,5,2,1,3] => [1,3,4,5,2]
[1,5,2,3,1] => [1,3,4,5,2]
[1,5,3,1,2] => [1,4,3,5,2]
[1,5,3,2,1] => [1,4,3,5,2]
[2,1,1,3,5] => [2,1,3,4,5]
[2,1,1,5,3] => [2,1,3,5,4]
[2,1,3,1,5] => [2,1,3,4,5]
[2,1,3,5,1] => [2,1,3,5,4]
[2,1,5,1,3] => [2,1,4,5,3]
[2,1,5,3,1] => [2,1,4,5,3]
[2,3,1,1,5] => [3,1,2,4,5]
[2,3,1,5,1] => [3,1,2,5,4]
[2,3,5,1,1] => [4,1,2,5,3]
[2,5,1,1,3] => [3,1,4,5,2]
[2,5,1,3,1] => [3,1,4,5,2]
[2,5,3,1,1] => [4,1,3,5,2]
[3,1,1,2,5] => [2,3,1,4,5]
[3,1,1,5,2] => [2,3,1,5,4]
[3,1,2,1,5] => [2,3,1,4,5]
[3,1,2,5,1] => [2,3,1,5,4]
[3,1,5,1,2] => [2,4,1,5,3]
[3,1,5,2,1] => [2,4,1,5,3]
[3,2,1,1,5] => [3,2,1,4,5]
[3,2,1,5,1] => [3,2,1,5,4]
[3,2,5,1,1] => [4,2,1,5,3]
[3,5,1,1,2] => [3,4,1,5,2]
[3,5,1,2,1] => [3,4,1,5,2]
[3,5,2,1,1] => [4,3,1,5,2]
[5,1,1,2,3] => [2,3,4,5,1]
[5,1,1,3,2] => [2,3,4,5,1]
[5,1,2,1,3] => [2,3,4,5,1]
[5,1,2,3,1] => [2,3,4,5,1]
[5,1,3,1,2] => [2,4,3,5,1]
[5,1,3,2,1] => [2,4,3,5,1]
[5,2,1,1,3] => [3,2,4,5,1]
[5,2,1,3,1] => [3,2,4,5,1]
[5,2,3,1,1] => [4,2,3,5,1]
[5,3,1,1,2] => [3,4,2,5,1]
[5,3,1,2,1] => [3,4,2,5,1]
[5,3,2,1,1] => [4,3,2,5,1]
[1,1,2,4,4] => [1,2,3,4,5]
[1,1,4,2,4] => [1,2,4,3,5]
[1,1,4,4,2] => [1,2,5,3,4]
[1,2,1,4,4] => [1,2,3,4,5]
[1,2,4,1,4] => [1,2,4,3,5]
[1,2,4,4,1] => [1,2,5,3,4]
[1,4,1,2,4] => [1,3,4,2,5]
[1,4,1,4,2] => [1,3,5,2,4]
[1,4,2,1,4] => [1,3,4,2,5]
[1,4,2,4,1] => [1,3,5,2,4]
[1,4,4,1,2] => [1,4,5,2,3]
[1,4,4,2,1] => [1,4,5,2,3]
[2,1,1,4,4] => [2,1,3,4,5]
[2,1,4,1,4] => [2,1,4,3,5]
[2,1,4,4,1] => [2,1,5,3,4]
[2,4,1,1,4] => [3,1,4,2,5]
[2,4,1,4,1] => [3,1,5,2,4]
[2,4,4,1,1] => [4,1,5,2,3]
[4,1,1,2,4] => [2,3,4,1,5]
[4,1,1,4,2] => [2,3,5,1,4]
[4,1,2,1,4] => [2,3,4,1,5]
[4,1,2,4,1] => [2,3,5,1,4]
[4,1,4,1,2] => [2,4,5,1,3]
[4,1,4,2,1] => [2,4,5,1,3]
[4,2,1,1,4] => [3,2,4,1,5]
[4,2,1,4,1] => [3,2,5,1,4]
[4,2,4,1,1] => [4,2,5,1,3]
[4,4,1,1,2] => [3,4,5,1,2]
[4,4,1,2,1] => [3,4,5,1,2]
[4,4,2,1,1] => [4,3,5,1,2]
[1,1,2,4,5] => [1,2,3,4,5]
[1,1,2,5,4] => [1,2,3,5,4]
[1,1,4,2,5] => [1,2,4,3,5]
[1,1,4,5,2] => [1,2,5,3,4]
[1,1,5,2,4] => [1,2,4,5,3]
[1,1,5,4,2] => [1,2,5,4,3]
[1,2,1,4,5] => [1,2,3,4,5]
[1,2,1,5,4] => [1,2,3,5,4]
[1,2,4,1,5] => [1,2,4,3,5]
[1,2,4,5,1] => [1,2,5,3,4]
[1,2,5,1,4] => [1,2,4,5,3]
[1,2,5,4,1] => [1,2,5,4,3]
[1,4,1,2,5] => [1,3,4,2,5]
[1,4,1,5,2] => [1,3,5,2,4]
[1,4,2,1,5] => [1,3,4,2,5]
[1,4,2,5,1] => [1,3,5,2,4]
[1,4,5,1,2] => [1,4,5,2,3]
[1,4,5,2,1] => [1,4,5,2,3]
[1,5,1,2,4] => [1,3,4,5,2]
[1,5,1,4,2] => [1,3,5,4,2]
[1,5,2,1,4] => [1,3,4,5,2]
[1,5,2,4,1] => [1,3,5,4,2]
[1,5,4,1,2] => [1,4,5,3,2]
[1,5,4,2,1] => [1,4,5,3,2]
[2,1,1,4,5] => [2,1,3,4,5]
[2,1,1,5,4] => [2,1,3,5,4]
[2,1,4,1,5] => [2,1,4,3,5]
[2,1,4,5,1] => [2,1,5,3,4]
[2,1,5,1,4] => [2,1,4,5,3]
[2,1,5,4,1] => [2,1,5,4,3]
[2,4,1,1,5] => [3,1,4,2,5]
[2,4,1,5,1] => [3,1,5,2,4]
[2,4,5,1,1] => [4,1,5,2,3]
[2,5,1,1,4] => [3,1,4,5,2]
[2,5,1,4,1] => [3,1,5,4,2]
[2,5,4,1,1] => [4,1,5,3,2]
[4,1,1,2,5] => [2,3,4,1,5]
[4,1,1,5,2] => [2,3,5,1,4]
[4,1,2,1,5] => [2,3,4,1,5]
[4,1,2,5,1] => [2,3,5,1,4]
[4,1,5,1,2] => [2,4,5,1,3]
[4,1,5,2,1] => [2,4,5,1,3]
[4,2,1,1,5] => [3,2,4,1,5]
[4,2,1,5,1] => [3,2,5,1,4]
[4,2,5,1,1] => [4,2,5,1,3]
[4,5,1,1,2] => [3,4,5,1,2]
[4,5,1,2,1] => [3,4,5,1,2]
[4,5,2,1,1] => [4,3,5,1,2]
[5,1,1,2,4] => [2,3,4,5,1]
[5,1,1,4,2] => [2,3,5,4,1]
[5,1,2,1,4] => [2,3,4,5,1]
[5,1,2,4,1] => [2,3,5,4,1]
[5,1,4,1,2] => [2,4,5,3,1]
[5,1,4,2,1] => [2,4,5,3,1]
[5,2,1,1,4] => [3,2,4,5,1]
[5,2,1,4,1] => [3,2,5,4,1]
[5,2,4,1,1] => [4,2,5,3,1]
[5,4,1,1,2] => [3,4,5,2,1]
[5,4,1,2,1] => [3,4,5,2,1]
[5,4,2,1,1] => [4,3,5,2,1]
[1,1,3,3,3] => [1,2,3,4,5]
[1,3,1,3,3] => [1,3,2,4,5]
[1,3,3,1,3] => [1,4,2,3,5]
[1,3,3,3,1] => [1,5,2,3,4]
[3,1,1,3,3] => [2,3,1,4,5]
[3,1,3,1,3] => [2,4,1,3,5]
[3,1,3,3,1] => [2,5,1,3,4]
[3,3,1,1,3] => [3,4,1,2,5]
[3,3,1,3,1] => [3,5,1,2,4]
[3,3,3,1,1] => [4,5,1,2,3]
[1,1,3,3,4] => [1,2,3,4,5]
[1,1,3,4,3] => [1,2,3,4,5]
[1,1,4,3,3] => [1,2,4,3,5]
[1,3,1,3,4] => [1,3,2,4,5]
[1,3,1,4,3] => [1,3,2,4,5]
[1,3,3,1,4] => [1,4,2,3,5]
[1,3,3,4,1] => [1,5,2,3,4]
[1,3,4,1,3] => [1,4,2,3,5]
[1,3,4,3,1] => [1,5,2,3,4]
[1,4,1,3,3] => [1,3,4,2,5]
[1,4,3,1,3] => [1,4,3,2,5]
[1,4,3,3,1] => [1,5,3,2,4]
[3,1,1,3,4] => [2,3,1,4,5]
[3,1,1,4,3] => [2,3,1,4,5]
[3,1,3,1,4] => [2,4,1,3,5]
[3,1,3,4,1] => [2,5,1,3,4]
[3,1,4,1,3] => [2,4,1,3,5]
[3,1,4,3,1] => [2,5,1,3,4]
[3,3,1,1,4] => [3,4,1,2,5]
[3,3,1,4,1] => [3,5,1,2,4]
[3,3,4,1,1] => [4,5,1,2,3]
[3,4,1,1,3] => [3,4,1,2,5]
[3,4,1,3,1] => [3,5,1,2,4]
[3,4,3,1,1] => [4,5,1,2,3]
[4,1,1,3,3] => [2,3,4,1,5]
[4,1,3,1,3] => [2,4,3,1,5]
[4,1,3,3,1] => [2,5,3,1,4]
[4,3,1,1,3] => [3,4,2,1,5]
[4,3,1,3,1] => [3,5,2,1,4]
[4,3,3,1,1] => [4,5,2,1,3]
[1,1,3,3,5] => [1,2,3,4,5]
[1,1,3,5,3] => [1,2,3,5,4]
[1,1,5,3,3] => [1,2,4,5,3]
[1,3,1,3,5] => [1,3,2,4,5]
[1,3,1,5,3] => [1,3,2,5,4]
[1,3,3,1,5] => [1,4,2,3,5]
[1,3,3,5,1] => [1,5,2,3,4]
[1,3,5,1,3] => [1,4,2,5,3]
[1,3,5,3,1] => [1,5,2,4,3]
[1,5,1,3,3] => [1,3,4,5,2]
[1,5,3,1,3] => [1,4,3,5,2]
[1,5,3,3,1] => [1,5,3,4,2]
[3,1,1,3,5] => [2,3,1,4,5]
[3,1,1,5,3] => [2,3,1,5,4]
[3,1,3,1,5] => [2,4,1,3,5]
[3,1,3,5,1] => [2,5,1,3,4]
[3,1,5,1,3] => [2,4,1,5,3]
[3,1,5,3,1] => [2,5,1,4,3]
[3,3,1,1,5] => [3,4,1,2,5]
[3,3,1,5,1] => [3,5,1,2,4]
[3,3,5,1,1] => [4,5,1,2,3]
[3,5,1,1,3] => [3,4,1,5,2]
[3,5,1,3,1] => [3,5,1,4,2]
[3,5,3,1,1] => [4,5,1,3,2]
[5,1,1,3,3] => [2,3,4,5,1]
[5,1,3,1,3] => [2,4,3,5,1]
[5,1,3,3,1] => [2,5,3,4,1]
[5,3,1,1,3] => [3,4,2,5,1]
[5,3,1,3,1] => [3,5,2,4,1]
[5,3,3,1,1] => [4,5,2,3,1]
[1,1,3,4,4] => [1,2,3,4,5]
[1,1,4,3,4] => [1,2,4,3,5]
[1,1,4,4,3] => [1,2,5,3,4]
[1,3,1,4,4] => [1,3,2,4,5]
[1,3,4,1,4] => [1,4,2,3,5]
[1,3,4,4,1] => [1,5,2,3,4]
[1,4,1,3,4] => [1,3,4,2,5]
[1,4,1,4,3] => [1,3,5,2,4]
[1,4,3,1,4] => [1,4,3,2,5]
[1,4,3,4,1] => [1,5,3,2,4]
[1,4,4,1,3] => [1,4,5,2,3]
[1,4,4,3,1] => [1,5,4,2,3]
[3,1,1,4,4] => [2,3,1,4,5]
[3,1,4,1,4] => [2,4,1,3,5]
[3,1,4,4,1] => [2,5,1,3,4]
[3,4,1,1,4] => [3,4,1,2,5]
[3,4,1,4,1] => [3,5,1,2,4]
[3,4,4,1,1] => [4,5,1,2,3]
[4,1,1,3,4] => [2,3,4,1,5]
[4,1,1,4,3] => [2,3,5,1,4]
[4,1,3,1,4] => [2,4,3,1,5]
[4,1,3,4,1] => [2,5,3,1,4]
[4,1,4,1,3] => [2,4,5,1,3]
[4,1,4,3,1] => [2,5,4,1,3]
[4,3,1,1,4] => [3,4,2,1,5]
[4,3,1,4,1] => [3,5,2,1,4]
[4,3,4,1,1] => [4,5,2,1,3]
[4,4,1,1,3] => [3,4,5,1,2]
[4,4,1,3,1] => [3,5,4,1,2]
[4,4,3,1,1] => [4,5,3,1,2]
[1,1,3,4,5] => [1,2,3,4,5]
[1,1,3,5,4] => [1,2,3,5,4]
[1,1,4,3,5] => [1,2,4,3,5]
[1,1,4,5,3] => [1,2,5,3,4]
[1,1,5,3,4] => [1,2,4,5,3]
[1,1,5,4,3] => [1,2,5,4,3]
[1,3,1,4,5] => [1,3,2,4,5]
[1,3,1,5,4] => [1,3,2,5,4]
[1,3,4,1,5] => [1,4,2,3,5]
[1,3,4,5,1] => [1,5,2,3,4]
[1,3,5,1,4] => [1,4,2,5,3]
[1,3,5,4,1] => [1,5,2,4,3]
[1,4,1,3,5] => [1,3,4,2,5]
[1,4,1,5,3] => [1,3,5,2,4]
[1,4,3,1,5] => [1,4,3,2,5]
[1,4,3,5,1] => [1,5,3,2,4]
[1,4,5,1,3] => [1,4,5,2,3]
[1,4,5,3,1] => [1,5,4,2,3]
[1,5,1,3,4] => [1,3,4,5,2]
[1,5,1,4,3] => [1,3,5,4,2]
[1,5,3,1,4] => [1,4,3,5,2]
[1,5,3,4,1] => [1,5,3,4,2]
[1,5,4,1,3] => [1,4,5,3,2]
[1,5,4,3,1] => [1,5,4,3,2]
[3,1,1,4,5] => [2,3,1,4,5]
[3,1,1,5,4] => [2,3,1,5,4]
[3,1,4,1,5] => [2,4,1,3,5]
[3,1,4,5,1] => [2,5,1,3,4]
[3,1,5,1,4] => [2,4,1,5,3]
[3,1,5,4,1] => [2,5,1,4,3]
[3,4,1,1,5] => [3,4,1,2,5]
[3,4,1,5,1] => [3,5,1,2,4]
[3,4,5,1,1] => [4,5,1,2,3]
[3,5,1,1,4] => [3,4,1,5,2]
[3,5,1,4,1] => [3,5,1,4,2]
[3,5,4,1,1] => [4,5,1,3,2]
[4,1,1,3,5] => [2,3,4,1,5]
[4,1,1,5,3] => [2,3,5,1,4]
[4,1,3,1,5] => [2,4,3,1,5]
[4,1,3,5,1] => [2,5,3,1,4]
[4,1,5,1,3] => [2,4,5,1,3]
[4,1,5,3,1] => [2,5,4,1,3]
[4,3,1,1,5] => [3,4,2,1,5]
[4,3,1,5,1] => [3,5,2,1,4]
[4,3,5,1,1] => [4,5,2,1,3]
[4,5,1,1,3] => [3,4,5,1,2]
[4,5,1,3,1] => [3,5,4,1,2]
[4,5,3,1,1] => [4,5,3,1,2]
[5,1,1,3,4] => [2,3,4,5,1]
[5,1,1,4,3] => [2,3,5,4,1]
[5,1,3,1,4] => [2,4,3,5,1]
[5,1,3,4,1] => [2,5,3,4,1]
[5,1,4,1,3] => [2,4,5,3,1]
[5,1,4,3,1] => [2,5,4,3,1]
[5,3,1,1,4] => [3,4,2,5,1]
[5,3,1,4,1] => [3,5,2,4,1]
[5,3,4,1,1] => [4,5,2,3,1]
[5,4,1,1,3] => [3,4,5,2,1]
[5,4,1,3,1] => [3,5,4,2,1]
[5,4,3,1,1] => [4,5,3,2,1]
[1,2,2,2,2] => [1,2,3,4,5]
[2,1,2,2,2] => [2,1,3,4,5]
[2,2,1,2,2] => [3,1,2,4,5]
[2,2,2,1,2] => [4,1,2,3,5]
[2,2,2,2,1] => [5,1,2,3,4]
[1,2,2,2,3] => [1,2,3,4,5]
[1,2,2,3,2] => [1,2,3,4,5]
[1,2,3,2,2] => [1,2,3,4,5]
[1,3,2,2,2] => [1,3,2,4,5]
[2,1,2,2,3] => [2,1,3,4,5]
[2,1,2,3,2] => [2,1,3,4,5]
[2,1,3,2,2] => [2,1,3,4,5]
[2,2,1,2,3] => [3,1,2,4,5]
[2,2,1,3,2] => [3,1,2,4,5]
[2,2,2,1,3] => [4,1,2,3,5]
[2,2,2,3,1] => [5,1,2,3,4]
[2,2,3,1,2] => [4,1,2,3,5]
[2,2,3,2,1] => [5,1,2,3,4]
[2,3,1,2,2] => [3,1,2,4,5]
[2,3,2,1,2] => [4,1,2,3,5]
[2,3,2,2,1] => [5,1,2,3,4]
[3,1,2,2,2] => [2,3,1,4,5]
[3,2,1,2,2] => [3,2,1,4,5]
[3,2,2,1,2] => [4,2,1,3,5]
[3,2,2,2,1] => [5,2,1,3,4]
[1,2,2,2,4] => [1,2,3,4,5]
[1,2,2,4,2] => [1,2,3,4,5]
[1,2,4,2,2] => [1,2,4,3,5]
[1,4,2,2,2] => [1,3,4,2,5]
[2,1,2,2,4] => [2,1,3,4,5]
[2,1,2,4,2] => [2,1,3,4,5]
[2,1,4,2,2] => [2,1,4,3,5]
[2,2,1,2,4] => [3,1,2,4,5]
[2,2,1,4,2] => [3,1,2,4,5]
[2,2,2,1,4] => [4,1,2,3,5]
[2,2,2,4,1] => [5,1,2,3,4]
[2,2,4,1,2] => [4,1,2,3,5]
[2,2,4,2,1] => [5,1,2,3,4]
[2,4,1,2,2] => [3,1,4,2,5]
[2,4,2,1,2] => [4,1,3,2,5]
[2,4,2,2,1] => [5,1,3,2,4]
[4,1,2,2,2] => [2,3,4,1,5]
[4,2,1,2,2] => [3,2,4,1,5]
[4,2,2,1,2] => [4,2,3,1,5]
[4,2,2,2,1] => [5,2,3,1,4]
[1,2,2,2,5] => [1,2,3,4,5]
[1,2,2,5,2] => [1,2,3,5,4]
[1,2,5,2,2] => [1,2,4,5,3]
[1,5,2,2,2] => [1,3,4,5,2]
[2,1,2,2,5] => [2,1,3,4,5]
[2,1,2,5,2] => [2,1,3,5,4]
[2,1,5,2,2] => [2,1,4,5,3]
[2,2,1,2,5] => [3,1,2,4,5]
[2,2,1,5,2] => [3,1,2,5,4]
[2,2,2,1,5] => [4,1,2,3,5]
[2,2,2,5,1] => [5,1,2,3,4]
[2,2,5,1,2] => [4,1,2,5,3]
[2,2,5,2,1] => [5,1,2,4,3]
[2,5,1,2,2] => [3,1,4,5,2]
[2,5,2,1,2] => [4,1,3,5,2]
[2,5,2,2,1] => [5,1,3,4,2]
[5,1,2,2,2] => [2,3,4,5,1]
[5,2,1,2,2] => [3,2,4,5,1]
[5,2,2,1,2] => [4,2,3,5,1]
[5,2,2,2,1] => [5,2,3,4,1]
[1,2,2,3,3] => [1,2,3,4,5]
[1,2,3,2,3] => [1,2,3,4,5]
[1,2,3,3,2] => [1,2,3,4,5]
[1,3,2,2,3] => [1,3,2,4,5]
[1,3,2,3,2] => [1,3,2,4,5]
[1,3,3,2,2] => [1,4,2,3,5]
[2,1,2,3,3] => [2,1,3,4,5]
[2,1,3,2,3] => [2,1,3,4,5]
[2,1,3,3,2] => [2,1,3,4,5]
[2,2,1,3,3] => [3,1,2,4,5]
[2,2,3,1,3] => [4,1,2,3,5]
[2,2,3,3,1] => [5,1,2,3,4]
[2,3,1,2,3] => [3,1,2,4,5]
[2,3,1,3,2] => [3,1,2,4,5]
[2,3,2,1,3] => [4,1,2,3,5]
[2,3,2,3,1] => [5,1,2,3,4]
[2,3,3,1,2] => [4,1,2,3,5]
[2,3,3,2,1] => [5,1,2,3,4]
[3,1,2,2,3] => [2,3,1,4,5]
[3,1,2,3,2] => [2,3,1,4,5]
[3,1,3,2,2] => [2,4,1,3,5]
[3,2,1,2,3] => [3,2,1,4,5]
[3,2,1,3,2] => [3,2,1,4,5]
[3,2,2,1,3] => [4,2,1,3,5]
[3,2,2,3,1] => [5,2,1,3,4]
[3,2,3,1,2] => [4,2,1,3,5]
[3,2,3,2,1] => [5,2,1,3,4]
[3,3,1,2,2] => [3,4,1,2,5]
[3,3,2,1,2] => [4,3,1,2,5]
[3,3,2,2,1] => [5,3,1,2,4]
[1,2,2,3,4] => [1,2,3,4,5]
[1,2,2,4,3] => [1,2,3,4,5]
[1,2,3,2,4] => [1,2,3,4,5]
[1,2,3,4,2] => [1,2,3,4,5]
[1,2,4,2,3] => [1,2,4,3,5]
[1,2,4,3,2] => [1,2,4,3,5]
[1,3,2,2,4] => [1,3,2,4,5]
[1,3,2,4,2] => [1,3,2,4,5]
[1,3,4,2,2] => [1,4,2,3,5]
[1,4,2,2,3] => [1,3,4,2,5]
[1,4,2,3,2] => [1,3,4,2,5]
[1,4,3,2,2] => [1,4,3,2,5]
[2,1,2,3,4] => [2,1,3,4,5]
[2,1,2,4,3] => [2,1,3,4,5]
[2,1,3,2,4] => [2,1,3,4,5]
[2,1,3,4,2] => [2,1,3,4,5]
[2,1,4,2,3] => [2,1,4,3,5]
[2,1,4,3,2] => [2,1,4,3,5]
[2,2,1,3,4] => [3,1,2,4,5]
[2,2,1,4,3] => [3,1,2,4,5]
[2,2,3,1,4] => [4,1,2,3,5]
[2,2,3,4,1] => [5,1,2,3,4]
[2,2,4,1,3] => [4,1,2,3,5]
[2,2,4,3,1] => [5,1,2,3,4]
[2,3,1,2,4] => [3,1,2,4,5]
[2,3,1,4,2] => [3,1,2,4,5]
[2,3,2,1,4] => [4,1,2,3,5]
[2,3,2,4,1] => [5,1,2,3,4]
[2,3,4,1,2] => [4,1,2,3,5]
[2,3,4,2,1] => [5,1,2,3,4]
[2,4,1,2,3] => [3,1,4,2,5]
[2,4,1,3,2] => [3,1,4,2,5]
[2,4,2,1,3] => [4,1,3,2,5]
[2,4,2,3,1] => [5,1,3,2,4]
[2,4,3,1,2] => [4,1,3,2,5]
[2,4,3,2,1] => [5,1,3,2,4]
[3,1,2,2,4] => [2,3,1,4,5]
[3,1,2,4,2] => [2,3,1,4,5]
[3,1,4,2,2] => [2,4,1,3,5]
[3,2,1,2,4] => [3,2,1,4,5]
[3,2,1,4,2] => [3,2,1,4,5]
[3,2,2,1,4] => [4,2,1,3,5]
[3,2,2,4,1] => [5,2,1,3,4]
[3,2,4,1,2] => [4,2,1,3,5]
[3,2,4,2,1] => [5,2,1,3,4]
[3,4,1,2,2] => [3,4,1,2,5]
[3,4,2,1,2] => [4,3,1,2,5]
[3,4,2,2,1] => [5,3,1,2,4]
[4,1,2,2,3] => [2,3,4,1,5]
[4,1,2,3,2] => [2,3,4,1,5]
[4,1,3,2,2] => [2,4,3,1,5]
[4,2,1,2,3] => [3,2,4,1,5]
[4,2,1,3,2] => [3,2,4,1,5]
[4,2,2,1,3] => [4,2,3,1,5]
[4,2,2,3,1] => [5,2,3,1,4]
[4,2,3,1,2] => [4,2,3,1,5]
[4,2,3,2,1] => [5,2,3,1,4]
[4,3,1,2,2] => [3,4,2,1,5]
[4,3,2,1,2] => [4,3,2,1,5]
[4,3,2,2,1] => [5,3,2,1,4]
[1,2,2,3,5] => [1,2,3,4,5]
[1,2,2,5,3] => [1,2,3,5,4]
[1,2,3,2,5] => [1,2,3,4,5]
[1,2,3,5,2] => [1,2,3,5,4]
[1,2,5,2,3] => [1,2,4,5,3]
[1,2,5,3,2] => [1,2,4,5,3]
[1,3,2,2,5] => [1,3,2,4,5]
[1,3,2,5,2] => [1,3,2,5,4]
[1,3,5,2,2] => [1,4,2,5,3]
[1,5,2,2,3] => [1,3,4,5,2]
[1,5,2,3,2] => [1,3,4,5,2]
[1,5,3,2,2] => [1,4,3,5,2]
[2,1,2,3,5] => [2,1,3,4,5]
[2,1,2,5,3] => [2,1,3,5,4]
[2,1,3,2,5] => [2,1,3,4,5]
[2,1,3,5,2] => [2,1,3,5,4]
[2,1,5,2,3] => [2,1,4,5,3]
[2,1,5,3,2] => [2,1,4,5,3]
[2,2,1,3,5] => [3,1,2,4,5]
[2,2,1,5,3] => [3,1,2,5,4]
[2,2,3,1,5] => [4,1,2,3,5]
[2,2,3,5,1] => [5,1,2,3,4]
[2,2,5,1,3] => [4,1,2,5,3]
[2,2,5,3,1] => [5,1,2,4,3]
[2,3,1,2,5] => [3,1,2,4,5]
[2,3,1,5,2] => [3,1,2,5,4]
[2,3,2,1,5] => [4,1,2,3,5]
[2,3,2,5,1] => [5,1,2,3,4]
[2,3,5,1,2] => [4,1,2,5,3]
[2,3,5,2,1] => [5,1,2,4,3]
[2,5,1,2,3] => [3,1,4,5,2]
[2,5,1,3,2] => [3,1,4,5,2]
[2,5,2,1,3] => [4,1,3,5,2]
[2,5,2,3,1] => [5,1,3,4,2]
[2,5,3,1,2] => [4,1,3,5,2]
[2,5,3,2,1] => [5,1,3,4,2]
[3,1,2,2,5] => [2,3,1,4,5]
[3,1,2,5,2] => [2,3,1,5,4]
[3,1,5,2,2] => [2,4,1,5,3]
[3,2,1,2,5] => [3,2,1,4,5]
[3,2,1,5,2] => [3,2,1,5,4]
[3,2,2,1,5] => [4,2,1,3,5]
[3,2,2,5,1] => [5,2,1,3,4]
[3,2,5,1,2] => [4,2,1,5,3]
[3,2,5,2,1] => [5,2,1,4,3]
[3,5,1,2,2] => [3,4,1,5,2]
[3,5,2,1,2] => [4,3,1,5,2]
[3,5,2,2,1] => [5,3,1,4,2]
[5,1,2,2,3] => [2,3,4,5,1]
[5,1,2,3,2] => [2,3,4,5,1]
[5,1,3,2,2] => [2,4,3,5,1]
[5,2,1,2,3] => [3,2,4,5,1]
[5,2,1,3,2] => [3,2,4,5,1]
[5,2,2,1,3] => [4,2,3,5,1]
[5,2,2,3,1] => [5,2,3,4,1]
[5,2,3,1,2] => [4,2,3,5,1]
[5,2,3,2,1] => [5,2,3,4,1]
[5,3,1,2,2] => [3,4,2,5,1]
[5,3,2,1,2] => [4,3,2,5,1]
[5,3,2,2,1] => [5,3,2,4,1]
[1,2,2,4,4] => [1,2,3,4,5]
[1,2,4,2,4] => [1,2,4,3,5]
[1,2,4,4,2] => [1,2,5,3,4]
[1,4,2,2,4] => [1,3,4,2,5]
[1,4,2,4,2] => [1,3,5,2,4]
[1,4,4,2,2] => [1,4,5,2,3]
[2,1,2,4,4] => [2,1,3,4,5]
[2,1,4,2,4] => [2,1,4,3,5]
[2,1,4,4,2] => [2,1,5,3,4]
[2,2,1,4,4] => [3,1,2,4,5]
[2,2,4,1,4] => [4,1,2,3,5]
[2,2,4,4,1] => [5,1,2,3,4]
[2,4,1,2,4] => [3,1,4,2,5]
[2,4,1,4,2] => [3,1,5,2,4]
[2,4,2,1,4] => [4,1,3,2,5]
[2,4,2,4,1] => [5,1,3,2,4]
[2,4,4,1,2] => [4,1,5,2,3]
[2,4,4,2,1] => [5,1,4,2,3]
[4,1,2,2,4] => [2,3,4,1,5]
[4,1,2,4,2] => [2,3,5,1,4]
[4,1,4,2,2] => [2,4,5,1,3]
[4,2,1,2,4] => [3,2,4,1,5]
[4,2,1,4,2] => [3,2,5,1,4]
[4,2,2,1,4] => [4,2,3,1,5]
[4,2,2,4,1] => [5,2,3,1,4]
[4,2,4,1,2] => [4,2,5,1,3]
[4,2,4,2,1] => [5,2,4,1,3]
[4,4,1,2,2] => [3,4,5,1,2]
[4,4,2,1,2] => [4,3,5,1,2]
[4,4,2,2,1] => [5,3,4,1,2]
[1,2,2,4,5] => [1,2,3,4,5]
[1,2,2,5,4] => [1,2,3,5,4]
[1,2,4,2,5] => [1,2,4,3,5]
[1,2,4,5,2] => [1,2,5,3,4]
[1,2,5,2,4] => [1,2,4,5,3]
[1,2,5,4,2] => [1,2,5,4,3]
[1,4,2,2,5] => [1,3,4,2,5]
[1,4,2,5,2] => [1,3,5,2,4]
[1,4,5,2,2] => [1,4,5,2,3]
[1,5,2,2,4] => [1,3,4,5,2]
[1,5,2,4,2] => [1,3,5,4,2]
[1,5,4,2,2] => [1,4,5,3,2]
[2,1,2,4,5] => [2,1,3,4,5]
[2,1,2,5,4] => [2,1,3,5,4]
[2,1,4,2,5] => [2,1,4,3,5]
[2,1,4,5,2] => [2,1,5,3,4]
[2,1,5,2,4] => [2,1,4,5,3]
[2,1,5,4,2] => [2,1,5,4,3]
[2,2,1,4,5] => [3,1,2,4,5]
[2,2,1,5,4] => [3,1,2,5,4]
[2,2,4,1,5] => [4,1,2,3,5]
[2,2,4,5,1] => [5,1,2,3,4]
[2,2,5,1,4] => [4,1,2,5,3]
[2,2,5,4,1] => [5,1,2,4,3]
[2,4,1,2,5] => [3,1,4,2,5]
[2,4,1,5,2] => [3,1,5,2,4]
[2,4,2,1,5] => [4,1,3,2,5]
[2,4,2,5,1] => [5,1,3,2,4]
[2,4,5,1,2] => [4,1,5,2,3]
[2,4,5,2,1] => [5,1,4,2,3]
[2,5,1,2,4] => [3,1,4,5,2]
[2,5,1,4,2] => [3,1,5,4,2]
[2,5,2,1,4] => [4,1,3,5,2]
[2,5,2,4,1] => [5,1,3,4,2]
[2,5,4,1,2] => [4,1,5,3,2]
[2,5,4,2,1] => [5,1,4,3,2]
[4,1,2,2,5] => [2,3,4,1,5]
[4,1,2,5,2] => [2,3,5,1,4]
[4,1,5,2,2] => [2,4,5,1,3]
[4,2,1,2,5] => [3,2,4,1,5]
[4,2,1,5,2] => [3,2,5,1,4]
[4,2,2,1,5] => [4,2,3,1,5]
[4,2,2,5,1] => [5,2,3,1,4]
[4,2,5,1,2] => [4,2,5,1,3]
[4,2,5,2,1] => [5,2,4,1,3]
[4,5,1,2,2] => [3,4,5,1,2]
[4,5,2,1,2] => [4,3,5,1,2]
[4,5,2,2,1] => [5,3,4,1,2]
[5,1,2,2,4] => [2,3,4,5,1]
[5,1,2,4,2] => [2,3,5,4,1]
[5,1,4,2,2] => [2,4,5,3,1]
[5,2,1,2,4] => [3,2,4,5,1]
[5,2,1,4,2] => [3,2,5,4,1]
[5,2,2,1,4] => [4,2,3,5,1]
[5,2,2,4,1] => [5,2,3,4,1]
[5,2,4,1,2] => [4,2,5,3,1]
[5,2,4,2,1] => [5,2,4,3,1]
[5,4,1,2,2] => [3,4,5,2,1]
[5,4,2,1,2] => [4,3,5,2,1]
[5,4,2,2,1] => [5,3,4,2,1]
[1,2,3,3,3] => [1,2,3,4,5]
[1,3,2,3,3] => [1,3,2,4,5]
[1,3,3,2,3] => [1,4,2,3,5]
[1,3,3,3,2] => [1,5,2,3,4]
[2,1,3,3,3] => [2,1,3,4,5]
[2,3,1,3,3] => [3,1,2,4,5]
[2,3,3,1,3] => [4,1,2,3,5]
[2,3,3,3,1] => [5,1,2,3,4]
[3,1,2,3,3] => [2,3,1,4,5]
[3,1,3,2,3] => [2,4,1,3,5]
[3,1,3,3,2] => [2,5,1,3,4]
[3,2,1,3,3] => [3,2,1,4,5]
[3,2,3,1,3] => [4,2,1,3,5]
[3,2,3,3,1] => [5,2,1,3,4]
[3,3,1,2,3] => [3,4,1,2,5]
[3,3,1,3,2] => [3,5,1,2,4]
[3,3,2,1,3] => [4,3,1,2,5]
[3,3,2,3,1] => [5,3,1,2,4]
[3,3,3,1,2] => [4,5,1,2,3]
[3,3,3,2,1] => [5,4,1,2,3]
[1,2,3,3,4] => [1,2,3,4,5]
[1,2,3,4,3] => [1,2,3,4,5]
[1,2,4,3,3] => [1,2,4,3,5]
[1,3,2,3,4] => [1,3,2,4,5]
[1,3,2,4,3] => [1,3,2,4,5]
[1,3,3,2,4] => [1,4,2,3,5]
[1,3,3,4,2] => [1,5,2,3,4]
[1,3,4,2,3] => [1,4,2,3,5]
[1,3,4,3,2] => [1,5,2,3,4]
[1,4,2,3,3] => [1,3,4,2,5]
[1,4,3,2,3] => [1,4,3,2,5]
[1,4,3,3,2] => [1,5,3,2,4]
[2,1,3,3,4] => [2,1,3,4,5]
[2,1,3,4,3] => [2,1,3,4,5]
[2,1,4,3,3] => [2,1,4,3,5]
[2,3,1,3,4] => [3,1,2,4,5]
[2,3,1,4,3] => [3,1,2,4,5]
[2,3,3,1,4] => [4,1,2,3,5]
[2,3,3,4,1] => [5,1,2,3,4]
[2,3,4,1,3] => [4,1,2,3,5]
[2,3,4,3,1] => [5,1,2,3,4]
[2,4,1,3,3] => [3,1,4,2,5]
[2,4,3,1,3] => [4,1,3,2,5]
[2,4,3,3,1] => [5,1,3,2,4]
[3,1,2,3,4] => [2,3,1,4,5]
[3,1,2,4,3] => [2,3,1,4,5]
[3,1,3,2,4] => [2,4,1,3,5]
[3,1,3,4,2] => [2,5,1,3,4]
[3,1,4,2,3] => [2,4,1,3,5]
[3,1,4,3,2] => [2,5,1,3,4]
[3,2,1,3,4] => [3,2,1,4,5]
[3,2,1,4,3] => [3,2,1,4,5]
[3,2,3,1,4] => [4,2,1,3,5]
[3,2,3,4,1] => [5,2,1,3,4]
[3,2,4,1,3] => [4,2,1,3,5]
[3,2,4,3,1] => [5,2,1,3,4]
[3,3,1,2,4] => [3,4,1,2,5]
[3,3,1,4,2] => [3,5,1,2,4]
[3,3,2,1,4] => [4,3,1,2,5]
[3,3,2,4,1] => [5,3,1,2,4]
[3,3,4,1,2] => [4,5,1,2,3]
[3,3,4,2,1] => [5,4,1,2,3]
[3,4,1,2,3] => [3,4,1,2,5]
[3,4,1,3,2] => [3,5,1,2,4]
[3,4,2,1,3] => [4,3,1,2,5]
[3,4,2,3,1] => [5,3,1,2,4]
[3,4,3,1,2] => [4,5,1,2,3]
[3,4,3,2,1] => [5,4,1,2,3]
[4,1,2,3,3] => [2,3,4,1,5]
[4,1,3,2,3] => [2,4,3,1,5]
[4,1,3,3,2] => [2,5,3,1,4]
[4,2,1,3,3] => [3,2,4,1,5]
[4,2,3,1,3] => [4,2,3,1,5]
[4,2,3,3,1] => [5,2,3,1,4]
[4,3,1,2,3] => [3,4,2,1,5]
[4,3,1,3,2] => [3,5,2,1,4]
[4,3,2,1,3] => [4,3,2,1,5]
[4,3,2,3,1] => [5,3,2,1,4]
[4,3,3,1,2] => [4,5,2,1,3]
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Description
Maps a parking function to the permutation of cars that correspond to that parking function.
For example, the image $[2, 4, 5, 6, 3, 1, 7]$ means that car 2 takes spots 1, car 4 takes spot 2, and so on.
Properties
surjectiveA map $\phi: A \rightarrow B$ is surjective if for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
Code
def cars_permutation(elt):     # indices are parking spaces, entries are car labels
    out = {}
    for i in range(len(elt)):
        j=0
        while elt[i]+j in out.keys():
            j+=1
        out[elt[i]+j] = i
    return Permutation([out[i+1]+1 for i in range(len(elt))])