Problem Description

Sheldon's board has been changed! Someone drew a N * N grid on his board. Although he has no idea who's the bad guy, but as a math geek, he decide to play a game on it. He will fill in the grids with integer 1 to N*N. And the sum of each row, each column and each diagonal are distinct (2N+2 distinct integers in total).

Input

The first line contains a single positive integer T( T <= 200 ), indicates the number of test cases.
For each test case: an integer N (3 <= N <= 200).

Output

For each test case: output the case number as shown and an N * N matrix.
The output must contains N+1 lines, or you maybe get wrong answer because of special judge.
The numbers in each line must be separated by a blankspace or a tab. leading and trailing blankspace will be ignored.

2
3
4

Case #1:
7 5 2
1 4 8
3 6 9
Case #2:
2 8 15 1
5 12 10 16
6 9 4 14
3 7 11 13

Hint

Huge output.
C/C++ user please use printf.

Java user please use PrintWriter. Because of Special Judge, please use .print() method shown as below:
PrintWriter out = new PrintWriter(System.out);
out.print( "Case #" + caseT + ":\n" );
out.close(); // Important!!!