Chess Pushing Game

Dave is playing a game with three pawns on a long board. The board can be seen as an (semi-)infinitely long sequence of grid squares numbered starting from 0 with width 3. Thus, the squares on the board can be referred to using (i,j) where i >= 0 and j = 0, 1 or 2. For this problem, the distance between two pawns is the distance along the first coordinate. For example, distance between pawns at (0