Description

If a matrix satisfies the following conditions, we call it a silver matrix.

1. The dimensions of the matrix are n * n. 2. All its elements belong to the set S = {1, 2, 3, …, 2n - 1}. 3. 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

.

Input

The input contains only an integer K (1 <= K <= 9).

Output

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.

2

1 2 5 6
3 1 7 5
4 6 1 2
7 4 3 1

Source

POJ Monthly--2006.06.25

, Lei Tao