(15 points) Consider an n x n table where some cells are marked as forbidden. A frog is placed in the (1,1)-cell (that is lowest and left mostel). At every step, the frog can jump from its current cell (i, j) to any cell (i,,j') that satisfies i,+ j' = i +j+1 provided that the cell is not forbidden. We assume that (1,1) and (n, ) are never forbidden. Design and analyze an efficient algorithm that given the coordinates of the forbidden cells, finds the number of different paths that the frog can take to move from (1, 1) to (n, n)