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## Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

## Goal

Queneau 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 :
1←←←←5
1→→→45
12←←45
12→345
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

`1,2,3,4,5`

And go as follows:

`5,1,4,2,3`

`3,5,2,1,4`

`4,3,1,5,2`

`2,4,5,3,1`

`1,2,3,4,5`

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]
Input
One number N
Output
N lines: the different steps of permutations, as a comma-separated sequence
OR
IMPOSSIBLE if the number is not a Queneau number.
Constraints
2 ≤ N ≤ 30
Example
Input
`3`
Output
```3,1,2
2,3,1
1,2,3```

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