Chessboard Coloring - Problem Statement

Color an $n \times m$ grid with $2$ colors such that no $2 \times 2$ region is monochromatic. Profile: the coloring of the last row ($2$^$m$ states).

Transition: next row's coloring must differ appropriately. Constraint: for each $2 \times 2$ 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.