7396번 - Lattice Animals 다국어

문제

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

입력

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

출력

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

제한

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