Codeforces Round 806 (Div. 4) |
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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.
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.
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 $$$270^{\circ}$$$.
5301011001010511100110110101110011110005010001010101010000100100151100100000111111011001111
1 0 9 7 6
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.
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