E. Mirror Gridtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.  InputThe 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.OutputFor 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}.ExampleInput
5301011001010511100110110101110011110005010001010101010000100100151100100000111111011001111Output
1
0
9
7
6
NoteIn 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.
5301011001010511100110110101110011110005010001010101010000100100151100100000111111011001111
1 0 9 7 6 
['implementation', '*1200']