Annealing peaceful queens!#2764

Annealing peaceful queens!

2 seconds
64 megabytes
Easy

Arrange queens on a square N \times N board so that no two attack each other — not a simple task. That is why it has been assigned to you.

Input

The input consists of a single line containing the board size (4 \leq N \leq 200).

Output

Print numbers : a_i is the number of the row on which you will place the queen occupying the -th column. The rows are numbered from bottom to top, from to (as on a standard chessboard).

Examples

Example 1

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