E. Mirror Grid
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a square grid with $$$n$$$ rows and $$$n$$$ columns. Each cell contains either $$$0$$$ or $$$1$$$.

In an operation, you can select a cell of the grid and flip it (from $$$0 \to 1$$$ or $$$1 \to 0$$$). Find the minimum number of operations you need to obtain a square that remains the same when rotated $$$0^{\circ}$$$, $$$90^{\circ}$$$, $$$180^{\circ}$$$ and $$$270^{\circ}$$$.

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

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 100$$$) — the size of the grid.

Then $$$n$$$ lines follow, each with $$$n$$$ characters $$$a_{i,j}$$$ ($$$0 \leq a_{i,j} \leq 1$$$) — the number written in each cell.

Output

For each test case output a single integer  — the minimum number of operations needed to make the square look the same rotated $$$0^{\circ}$$$, $$$90^{\circ}$$$, $$$180^{\circ}$$$ and $$$270^{\circ}$$$.

Example
Input
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
Output
1
0
9
7
6
Note

In the first test case, we can perform one operations to make the grid $$$\begin{matrix}0 & 1 & 0\\ 1 & 1 & \color{red}{1}\\ 0 & 1 & 0\end{matrix}$$$. 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.