P1866 Numbering

Taro has $N$ rabbits. To make them easier to identify, Taro will assign them numbers. The rabbits expressed their preferences: each rabbit $i$ wants an integer between $1$ and $M_i$ (it can be $1$ or $M_i$). Of course, the numbers assigned to different rabbits must be distinct. Now Taro wants to know how many ways there are to assign the numbers. You only need to output the answer modulo $10^9+7$. If this is impossible, output $0$.

The first line contains an integer $N$. The second line contains $N$ integers $M_i$.

Print a single integer, the total number of ways.

Constraints For all testdata, $1 \le N \le 50$, $1\le M_i\le 1000$. Translated by ChatGPT 5