You are given an $m imes n$ binary matrix grid.

A row is considered palindromic if it reads the same from left to right as it does from right to left. Similarly, a column is considered palindromic if it reads the same from top to bottom as it does from bottom to top.

A matrix is considered palindromic if every row is palindromic, every column is palindromic, and the total number of $1$’s in the matrix is divisible by $4$.

In one operation, you can flip any element in grid from $0$ to $1$ or from $1$ to $0$.

Return the minimum number of flips required to make grid palindromic.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq m imes n \leq 2 imes 10^5$

• $0 \leq$ grid[i][j] $\leq 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.