Permutation Matrix

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요약

1부터 2^(2n)까지의 수를 한 번씩 써서 2^n × 2^n 행렬을 만들되, 크기 2^(n-1) × 2^(n-1)인 모든 부분행렬의 합이 같아야 합니다.

문제

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

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

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

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

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 $2^n$ lines, with each line containing $2^n$ space-separated integers.