Is N prime

Given an integer N, decide whether N is prime and print Yes or No. The trailing line of N integers is unused.

Easy2MathNumber theoryBrute forceInterviewNo attempts yetTime limit1sMemory limit256 MB

Problem

You are given an integer NN. Print Yes if NN is prime, and No otherwise.

A prime number is an integer greater than 11 whose only positive divisors are 11 and itself.

Input

The first line contains an integer NN (2N100000)(2 \le N \le 100\,000).

The second line contains NN integers. Each integer is at least 231-2^{31} and strictly less than 2312^{31}.

Output

Print Yes if NN is prime. Print No otherwise.