Messy Matrix

Time Limit: 10 Seconds Memory Limit: 32768 KB
Special Judge

Polivic likes to play games with his girlfriend, Grace. A game is like this: There is a big picture initially. Cut it into chips (shown in the following figure, all rectangles), then disorder the chips. The goal of the game is to arrange these chips to get the original picture. Grace now asks Polivic to help her to complete this game. "But... it is so boring..." Polivic thinks.

So, instead of solving this problem, Polivic comes up with another method to entertain Grace. He turns over all the chips, and set a positive number (start from 1,continuously) for each chip. Then he arranges these chips again, and compute sums of every row, every column, and two diagonals. Polivic wants Grace to see it's really magic, because there are many many different sums.

Now, Polivic wants you to help him to find such a matrix that the number of different sums are maximized.

Notice

1. The original picture will be cut N times horizontally and N times vertically.

2. All chips are of the same size.

3. We will set the numbers ranged from 1 to N*N.

4. There will be 2*N+2 sums.

5. If there are multiplicate solutions, output any of them.

Input

Each line contains an integer N (1 <= N <= 100).

Output

For each case, output a matrix (N by N).

Print a blank line after each case.

Sample Input

1
2

Sample Output

Submit

Source: ZOJ Monthly, January 2003