Lattice animal is a set of connected sites on a lattice. Lattice animals on a square lattice are especially popular subject of study and are also known as polyominoes. Polyomino is usually represented as a set of sidewise connected squares. Polyomino with n squares is called n-polyomino.
In this problem you are to find a number of distinct free n-polyominoes that fit into rectangle w*h. Free polyominoes can be rotated and flipped over, so that their rotations and mirror images are considered to be the same.
For example, there are 5 different pentominoes (5-polyominoes) that fit into 2*4 rectangle and 3 different octominoes (8-polyominoes) that fit into 3 * 3 rectangle.
The input consists of a single line with 3 integer numbers n, w, and h (1 <= n <= 10, 1 <= w, h <= n).
Write to the output a single integer number -- the number of distinct free n-polyominoes that fit into rectangle w * h.
5 5 5
- Lattice Animals