From one to en (2) P53046

Write a program that prints all the permutations of { 1, …, n } with exactly one cycle, for a given n. Assume that the content of the position i of a permutation indicates “the next position to visit”.

For instance, consider the permutation (4,3,2,5,1,7,6). The position 1 has a 4, the position 4 has a 5, and the position 5 has a 1. Therefore, one of the cycles of this permutation is 1 → 4 → 5 → 1. The other two cycles are 2 → 3 → 2 and 6 → 7 → 6. The permutation (3,2,1) has the two cycles 1 → 3 → 1 and 2 → 2. The permutation (3,4,5,6,7,1,2) has only the cycle 1 → 3 → 5 → 7 → 2 → 4 → 6 → 1.

Input

Input consists of a natural number n > 0.

Output

Print all the permutations of { 1, …, n } with only one cycle.

Information about the checker

You can print the solutions to this exercise in any order.

Hint

The judge may accept a program that generates all the permutations and, for each one, checks if it only has one cycle. However, this is not the right solution for this problem.