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
In this problem you are to find a number of distinct freen-polyominoes
that fit into rectangle w x 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 x 4 rectangle and
3 different octominoes (8-polyominoes) that fit into 3 x 3 rectangle.
Input file format
The input file consists of a single line with 3 integer numbers n, w, and h
Output file format
Write to the output file a single integer number — the number of distinct
free n-polyominoes that fit into rectangle w x h.