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.