We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer *t* Т-prime, if *t* has exactly three distinct positive divisors.

You are given an array of *n* positive integers. For each of them determine whether it is Т-prime or not.
The first line contains a single positive integer, *n* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>), showing how many numbers are in the array. The next line contains *n* space-separated integers *x*<sub class="lower-index">*i*</sub> (1 ≤ *x*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">12</sup>).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.
import math

cache = {}

def prime(x):
    if x in cache:
        return cache[x]
    
    for i in range(2, int(math.sqrt(x)) + 1):
        if x % i == 0:
            cache[x] = False
            return False
    
    cache[x] = True
    return True

def main():
    n = int(input())
    
    a = [int(x) for x in input().split()]
    
    ans = []
    for i in a:
        if i == 1:
            ans.append("NO")
            continue
        
        tmp = int(math.sqrt(i))
        if tmp * tmp != i:
            ans.append("NO")
            continue
        
        if prime(tmp):
            ans.append("YES")
        else:
            ans.append("NO")
    
    for result in ans:
        print(result)

if __name__ == "__main__":
    main()
