Shortest Path in Matrix

meta Given an NxM matrix consisting of empty squares, gates (G), and walls (W), you need to fill each empty square with the shortest path length to the nearest gate. Movements are allowed up, down, left, and right. Example Input ['G', 'W', ' ', ' ', 'G'], [' ', 'W', ' ', ' ', ' '], [' ', ' ', ' ', 'W', ' '], ['W', 'G', ' ', ' ', ' ']