MINIMUM PATH COLORING

Given a grid of size $N * M$ and some colors for painting the cells in the grid such as $Red(R) , Yellow(Y), Green(G), White(W), Black(B)$ , you have to reach from cell $(1,1)$ to cell $(N, M)$ . You can only do following $operations$ , move $right$ or $down$ . Moving from a cell $(i , j)$ to the right or to the down depends on the the color you assigned to that particular cell , in other words fo