408808: GYM103328 E Identity Subset

Given a prime number $$$P$$$ and a multiset $$$S$$$ containing $$$P - 1$$$ positive integers, please find out whether there is a non-empty multi-subset $$$S'$$$ of $$$S$$$, such that the product of elements in $$$S'$$$ is $$$1$$$ modulo $$$P$$$. That is,

$$$$$$ \prod_{i \in S'} i \equiv 1 \pmod{P} $$$$$$

.

The first line of the input contains an integer $$$P$$$.

The second line of the input contains $$$P - 1$$$ space-separated integers, which are the elements in $$$S$$$.

• $$$2 \leq P \leq 100000$$$
• It's guaranteed that $$$P$$$ is a prime number
• For each $$$x \in S$$$, $$$1 \leq x \leq 10^9$$$

Output Yes if there exists a multi-subset $$$S'$$$ satisfing the requirement. Output No otherwise.

5
2 2 3 4

Yes

11
2 2 3 3 4 4 5 5 6 6

Yes

3
1 1

Yes