Number of Ways to Paint N × 3 Grid

You have a grid of size n x 3 and you want to paint each cell of the grid with exactly one of the three colors: Red, Yellow, or Green while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).

Given n the count of rows of the grid, provide the count of ways you can paint this grid. As the answer may grow large, the answer must be computed modulo 10^9+ 7.