Bessie the cow is trying to walk from her favorite pasture back to her barn. and the barn in the bottom-right
coner. Bessie wants to get home as soon as possible, so she will only walk down and to the rig ot. There are haybales in some The pasture and farm are on an N xN grid (2< N< 50),with her pasture in the top-left cornel
locations that Bessie cannot walk through; she must walk around them.
Bessie is feeling a little tired today, so she wants to change the direction she walks at most K tin es (1 ≤ K≤3)
How many distinct paths can Bessie walk from her favorite pasture to the barn? Two paths are di stinct if Bessie walks in a square in one path but not in the other.