Given a chess board having \(N \times N\) cells, you need to place N queens on the board in such a way that no queen attacks any other queen.

Input:
The only line of input consists of a single integer denoting N.

Output:
If it is possible to place all the N queens in such a way that no queen attacks another queen, then print "YES" (without quotes) in first line, then print N lines having N integers. The integer in \(i^{th}\) line and \(j^{th}\) column will denote the cell \((i,j)\) of the board and should be 1 if a queen is placed at \((i,j)\) otherwise 0. If there are more than way of placing queens print any of them.

If it is not possible to place all N queens in the desired way, then print "NO" (without quotes).

Constraints:
\(1 \le N \le 10\).