Color an n×m grid with 2 colors such that no 2×2 region is monochromatic. Profile: the coloring of the last row (2^m states).
Transition: next row's coloring must differ appropriately. Constraint: for each 2×2 block involving last row and current row, check it's not monochromatic. DP: dp[row][mask] = ways to color rows 0..row with last row having coloring mask. Enumerate valid next colorings.