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

Output

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

Sample Input	Sample Output
5 1 4	0
5 2 4	5
5 3 4	11
5 5 5	12
8 3 3	3