6668: Camels

Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x₁,y₁), (x₂,y₂), ..., (x_n,y_n). The first vertex has a coordinate x₁=1, the second − x₂=2, etc. Coordinates y_i might be any, but should satisfy the following conditions:

• there should be t humps precisely, i.e. such indexes j (2≤j≤n-1), so that y_j-1<y_j>y_j+1,
• there should be precisely t-1 such indexes j (2≤j≤n-1), so that y_j-1>y_j<y_j+1,
• no segment of a polyline should be parallel to the Ox-axis,
• all y_i are integers between 1 and 4.

For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.