Hermenegilda is training to compete in the International Olympiad in Informatics, but she doesn't have much time left. After pondering for a while about what strategy she should follow, she has decided that the best thing she can do is to stop studying and focus her efforts on becoming a Russian contestant, as this way she is sure to win a medal. To achieve this goal, she travels to the Federal Amusement Park of Kazan, famous for its authentically Russian roller coasters.

An authentically Russian roller coaster is an attraction that consists of $$$2l$$$ segments, placed one after the other. There are only two types of segments: ascending and descending. Each segment measures exactly one Russian unit of length in its horizontal component and one Russian unit of length in its vertical component. That is, each segment advances one Russian unit of length upward or downward and one Russian unit of length horizontally, depending on whether it is an ascending or descending segment. Furthermore, authentically Russian roller coasters have no segments underground and start and end at ground level. Surprisingly, the Federal Amusement Park of Kazan contains all possible authentically Russian roller coasters.

In her effort to become a Russian contestant, Hermenegilda starts her training methodically: she wants to ride all the authentically Russian roller coasters that have a length of $$$2l$$$ Russian units and a height of exactly $$$h$$$ Russian units; that is, their highest point is $$$h$$$ Russian units above ground level. We ask you to tell us how many authentically Russian roller coasters Hermenegilda will need to ride.

$$$1\leq h, l \leq 9, 1\leq t \leq 25 \qquad \qquad \; \; \;$$$ 20 Points

$$$1\leq h, l \leq 13, 1\leq t \leq 9 \qquad \qquad \; \; \;$$$ 20 Points

$$$1\leq h, l \leq 200, 1\leq t \leq 40000 \qquad \, \,$$$ 60 Points