Problem L. Lattice Animals ≡

 Author: Roman Elizarov Time limit: 2 sec Input file: lattice.in Memory limit: 64 Mb Output file: lattice.out

Statement

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 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.

Constraints

1 ≤ n ≤ 10, 1 ≤ w, hn.

Sample tests

No. Input file (lattice.in) Output file (lattice.out)
1
5 1 4

0
2
5 2 4
5
3
5 3 4
11
4
5 5 5
12
5
8 3 3
3

0.041s 0.008s 15