Week 12: February 8 - 14

You are given a chessboard of size n * n. It is filled with numbers from 1 to n² in the following way: the first ceil(n² / 2) numbers from 1 to ceil(n² / 2) are written in the cells with even sum of coordinates from left to right from top to bottom. The rest n² - ceil(n² / 2) numbers from ceil(n² / 2) + 1 to n² are written in the cells with 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

One integer n (1 ≤ n ≤ 9).

Output

Print the matrix - the chessboard in the given manner. Watch for allignment!

Time limit 1 second

Memory limit 128 MiB

Input example #1

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

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

Week 12: February 8 - 14

Print the chessboard

Input

Output