Permutation Enumeration

For given an integer $n$, print all permutations of $\\{1, 2, ..., n\\}$ in lexicographic order.

Constraints

• $1 \leq n \leq 9$

Input

An integer $n$ is given in a line.

Output

Print each permutation in a line in order. Separate adjacency elements by a space character.

Examples

Input

2

Output

1 2 2 1

Input

3

Output

1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1

inputFormat

Input

An integer $n$ is given in a line.

outputFormat

Output

Print each permutation in a line in order. Separate adjacency elements by a space character.

Examples

Input

2

Output

1 2 2 1

Input

3

Output

1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1

样例

3

1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1

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