**4 人解决**，25 人已尝试。

**4 份提交通过**，共有 53 份提交。

**9.2** EMB 奖励。

**单点时限: **1.0 sec

**内存限制: **256 MB

**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 squares is called -polyomino.

In this problem you are to find a number of distinct **free** -polyominoes that fit into rectangle . 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 rectangle and 3 different octominoes (8-polyominoes) that fit into rectangle.

The input file consists of a single line with 3 integer numbers , , and (, ).

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

Input

5 1 4

Output

0

Input

5 2 4

Output

5

Input

5 3 4

Output

11

Input

5 5 5

Output

12

Input

8 3 3

Output

3

**4 人解决**，25 人已尝试。

**4 份提交通过**，共有 53 份提交。

**9.2** EMB 奖励。

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