GoalQueneau Numbers were discovered by the French writer and mathematician Raymond Queneau, while member of the OULIPO.
A Queneau Number is a number N such that the sequence [1..N] can go through a series of spiral permutations (or "snail" permutations) and come back to [1..N] in exactly N iterations. The permutation consists in tracing a spiral from the last number of the sequence, spiraling towards the center.
You can visualize it for the sequence 1 2 3 4 5 :
thus [1 2 3 4 5] becomes [5 1 4 2 3]
For instance, 5 being a Queneau Number, the permutations will start from the sequence
And go as follows:
The Nth line is always the same as the initial sequence, or else the number is not a Queneau Number.
Erratum: Actually, a Queneau number should be such that the order of the permutation is exactly N, (i.e the sequence [1..N] cannot become [1..N] again before exactly N spiral permutations).
In this problem, all numbers such that [1..N] is still [1..N] after N spiral permutations are considered valid even if it might take less than N spiral permutations to encounter [1..N]
One number N
N lines: the different steps of permutations, as a comma-separated sequence
IMPOSSIBLE if the number is not a Queneau number.
2 ≤ N ≤ 30
3,1,2 2,3,1 1,2,3
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