Statement

You are given a grid A consisting of N rows and M columns, containing only 0s and 1s. You can do the following operations on A: (1) Select a row i (0 < i < N - 1) and invert it (i.e. flip every value in that row, such that each 0 becomes a 1 and each 1 becomes a 0). (2) Select a column j (0 < j < M - 1) and invert it. A binary grid is beautiful if there are no three consecutive equal values in the same row or in the same column. More formally, there is no i, j (0 < i < N - 1, 0 < j < M - 3) such that A_i, j = A_i, j + 1 = A_i, j + 2, and there is no i, j (0 < i < N - 3, 0 < j < M - 1) such that A_i, j = A_i + 1, j = A_i + 2, j. Your task is to decide whether it is possible to make a given grid beautiful, and if so, then report the minimum number of operations to do it.