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.

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.

Public test cases

**Input**

3

**Output**

(2,3,1) (3,1,2)

**Input**

4

**Output**

(2,3,4,1) (2,4,1,3) (3,4,2,1) (3,1,4,2) (4,3,1,2) (4,1,2,3)

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Codon Python
- User solutions
- C++