24700번 - Permutation Matrix 스페셜 저지다국어

문제

You are given a positive integer $n$. Construct such matrix 2ドル^n \times 2^n$ that:

• The matrix contains distinct positive integers from 1ドル$ to 2ドル^{2n}$.
• The sums of elements all each submatrices of size 2ドル^{n-1} \times 2^{n-1}$ are equal.

A submatrix is a contiguous rectangle of elements in the original matrix.

입력

The first line contains an integer $n$ (1ドル \le n \le 10$).

출력

On the very first line, print "YES" if the answer exists, or "NO" if not.

If the answer exists, print any such matrix on the next 2ドル^n$ lines, with each line containing 2ドル^n$ space-separated integers.

제한

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