Minimum flips to make every row and column a palindrome

You are given an N x M grid as a list of strings. Each cell is either "B" (black) or "W" (white).

A row is symmetric if it reads the same left to right as right to left. A column is symmetric if it reads the same top to bottom as bottom to top.

One flip changes a single cell from B to W or from W to B. Return the minimum number of flips needed so that every row and every column is symmetric.

def min_flips(grid: list[str]) -> int: ...

Constraints

• 1 <= N, M <= 1000 (an empty grid returns 0)
• every string has length M and contains only B and W

Example 1

grid = ["BW",
        "WB"]

Output: 2. All four cells must end up the same colour (each is the mirror of the others). Two are black and two are white, so two flips are needed.

Example 2

grid = ["BBWW",
        "WBBW",
        "BWWB"]

Output: 2. Flip (0,3) to B and (0,1) to W. The grid becomes BWWB / WBBW / BWWB, and every row and column is now a palindrome.

Be ready to explain why your answer is the minimum, and to return the resulting grid as well.