Задача Lattice Animals

Описание

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.

Формат входных данных

The input file consists of a single line with 3 integer numbers n, w, and h (1 ≤ n ≤ 10, 1 ≤ w, h ≤ n).

Формат выходных данных

Write to the output file a single integer number — the number of distinct free n-polyominoes that fit into rectangle w × h.