If a matrix satisfies the following conditions, we call it a silver matrix.
The dimensions of the matrix are n×n.
All its elements belong to the set S = {1, 2, 3, …, 2n-1}.
For every integer i (1 ≤ i ≤ n), all elements in the i-th row and i-th column make the set {1, 2, 3, …, 2n-1}.
For example, the following 4×4 matrix is a silver matrix:
It is proved that silver matrix with size 2^K×2^K always exists. And it is your job to find a silver matrix with size 2^K×2^K.
The input contains only an integer K (1 ≤ K ≤ 9).
You may output any matrix with size 2^K×2^K. To output a 2^K×2^K matrix, you should output 2^K lines, and in each line output 2^K integers.