Description

Kongming excitedly invited Pang Tong to visit. Intending to challenge him, Kongming placed $k$ Wooden Ox and Flowing Horse pieces on a large $n \times n$ tiled grid and painted them in colors. He asked Pang Tong to count how many different valid layout configurations there are.

Input Format

First line: $n, k, h$ ($n \le 20$, $h$ is the number of colors).

The next $h$ lines give the quantity of each color.

Output Format

The total number of valid layouts.

4 4 1
4

24

Hint

No big integer is needed. Moreover, Kongming stipulates that the grid cannot be flipped; that is, if two layouts become the same after a flip, they are still counted as two.

Translated by ChatGPT 5