Problems
Print the chessboard
Print the chessboard
You are given a chessboard of size n \times n. It is filled with numbers from 1 to n^2 in the following way: the first ceil(n^2 / 2) numbers from 1 to ceil(n^2 / 2) are written in the cells with an even sum of coordinates from left to right from top to bottom. The rest of the n^2 - ceil(n^2 / 2) numbers from ceil(n^2 / 2) + 1 to n^2 are written in the cells with an odd sum of coordinates from left to right from top to bottom.
The operation ceil(x / y) means division x by y rounded up.
Input data
One integer n~(1 \le n \le 9).
Output data
Print the matrix — the chessboard in the given manner. Watch for alignment!
Examples
Input example #1
5
Output example #1
1 14 2 15 3 16 4 17 5 18 6 19 7 20 8 21 9 22 10 23 11 24 12 25 13
Input example #2
6
Output example #2
1 19 2 20 3 21 22 4 23 5 24 6 7 25 8 26 9 27 28 10 29 11 30 12 13 31 14 32 15 33 34 16 35 17 36 18