Given a grid of size mxn,
count the number of ways you can go from (0, 0) to end of grid.

You can move down or right only. You don't like taking boring paths, so you move in the same direction continuously at max 2 times. eg: grid [3, 4] : (0, 0) -> (0, 1) -> (0, 2) -> (0, 3) is not valid since you moved right 3 times. (0, 0) -> (0, 1) -> (0, 2) -> (1, 2) -> (1, 3) -> (2, 3) is one of the valid paths.