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. Input The input file contains several test cases, one per line. This line consists of 3 integer numbers n, w, and h (1 ≤ n ≤ 10, 1 ≤ w, h ≤ n). Output For each one of the test cases, write to the output file a single line with a integer number — the number of distinct free n-polyominoes that fit into rectangle w × h. Sample Input 514 524 534 555 833 Sample Output 0 5 11 12 3