[Solution] Mirror Grid Codeforces Solution

[Solution] Mirror Grid Codeforces Solution | Solution Codeforces

Mirror Grid solution codeforces – You are given a square grid with 𝑛n rows and 𝑛n columns. Each cell contains either 00 or 11.

[Solution] Mirror Grid solution codeforces

In an operation, you can select a cell of the grid and flip it (from 0→10→1 or 1→01→0). Find the minimum number of operations you need to obtain a square that remains the same when rotated 0∘0∘, 90∘90∘, 180∘180∘ and 270∘270∘.

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

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Mirror Grid solution codeforces

Input

The first line contains a single integer 𝑡t (1≤𝑡≤1001≤t≤100) — the number of test cases.

The first line of each test case contains a single integer 𝑛n (1≤𝑛≤1001≤n≤100) — the size of the grid.

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

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[Solution] 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 0∘0∘, 90∘90∘, 180∘180∘ and 270∘270∘.

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

[Solution] 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.