# Mirror Grid solution codeforces-

You are given a square grid with n rows and n columns. Each cell contains either 00 or 11.

## Mirror Grid solution codeforces

In an operation, you can select a cell of the grid and flip it (from 010→1 or 101→0). Find the minimum number of operations you need to obtain a square that remains the same when rotated 00∘9090∘180180∘ and 270270∘.

The picture below shows an example of all rotations of a grid.

Input

The first line contains a single integer t (11001≤t≤100) — the number of test cases.

The first line of each test case contains a single integer n (11001≤n≤100) — the size of the grid.

Then n lines follow, each with n characters ,ai,j (0,10≤ai,j≤1) — the number written in each cell.

## Mirror Grid solution codeforces

For each test case output a single integer  — the minimum number of operations needed to make the square look the same rotated 00∘9090∘180180∘ and 270270∘.

Example
input

Copy
5
3
010
110
010
1
0
5
11100
11011
01011
10011
11000
5
01000
10101
01010
00010
01001
5
11001
00000
11111
10110
01111


## Mirror Grid solution codeforces

output

Copy
1
0
9
7
6

Note

In the first test case, we can perform one operations to make the grid 010111010010111010. Now, all rotations of the square are the same.

In the second test case, all rotations of the square are already the same, so we don’t need any flips.