Spiral

Output the square, consisting of NxN cells filled with numbers from 1 to N^2 in a spiral (see examples).

Input

The first line is a single number N (2 ≤ N ≤ 100).

Output

We derive N rows of N numbers, separated by spaces. Not allowed to start a spiral in the other, except in the upper left-hand corner, spinning spiral counterclockwise, or outward.

Examples