2916. Lattice Animals

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 $w\times h$. 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 $2\times 4$ rectangle and 3 different octominoes (8-polyominoes) that fit into $3\times 3$ rectangle.