Leetcode 1931. Painting a Grid With Three Different Colors

Count the number of ways to color an m×n grid with 3 colors so that no two adjacent cells (horizontally or vertically) share a color; with m ≤ 5 and n ≤ 1000, the typical approach is to enumerate valid column colorings (state compression), build transitions between compatible columns, and perform DP or matrix exponentiation across n columns modulo 1e9+7.