You are given an m x n binary matrix grid.

A row or column is considered palindromic if its values read the same forward and backward.

You can flip any number of cells in grid from 0 to 1, or from 1 to 0.

Return the minimum number of cells that need to be flipped to make either all rows palindromic or all columns palindromic.

 

Example 1:

Input: grid = [[1,0,0],[0,0,0],[0,0,1]]

Output: 2

Explanation:

Flipping the highlighted cells makes all the rows palindromic.

Example 2:

Input: grid = [[0,1],[0,1],[0,0]]

Output: 1

Explanation:

Flipping the highlighted cell makes all the columns palindromic.

Example 3:

Input: grid = [[1],[0]]

Output: 0

Explanation:

All rows are already palindromic.

 

Constraints: