Baljit and Harinder go to a local farm to do a corn maze. The map of
the corn maze is given.

Three horizontal paths
intersect with three vertical paths to form a two by two square grid of
paths with nine intersections. The top left corner of the grid has an
entrance labelled Start, and the bottom right corner has an exit
labelled Finish. Also, in the two top squares in the grid, there is a
diagonal path joining the top right corner of the square to the bottom
left corner of the square. In each of the bottom squares in the grid,
there is a diagonal path joining the top left corner of the square to
the bottom right corner of the square. The upwards direction is North.

On the day they arrive, the farm has the restrictions that
they can only travel south, east, or southeast along a path. Using these
restrictions, how many different routes can they take from Start to
Finish?