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The word "levencycle" is inspired by cyclic levenquine challenge.
Definitions
A 1-dup permutation of order \$n\$ is some permutation of \$1, \cdots, n\$ plus one duplicate number in the range.
For example, 1-dup permutations of order 3 include 1, 3, 2, 2 and 3, 2, 1, 3. There are 36 distinct 1-du...