Permutation Matrix

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.