Problem: 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.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

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.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in JAVA):

Solution:
import java.util.*;

import javax.lang.model.util.ElementScanner6;

public class T_Primes{
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        Boolean isPrime[] = new Boolean[1000001];
        isPrime[0] = isPrime[1] = false;
        for(int i=2;i<=1000000;i++)
            isPrime[i] = true;
        for(int i=2;i*i<=1000000;i++){
            if(isPrime[i] == true){
                for(int multiple=i*2;multiple<=1000000;multiple+=i)
                    isPrime[multiple] = false;
            }
        }
        int t = sc.nextInt();
        for(int i=0;i<t;i++){
            long n = sc.nextLong();
            long sqr = (long)Math.sqrt(n);
            if(sqr*sqr == n && isPrime[(int)sqr])
                System.out.println("YES");
            else
                System.out.println("NO");        
        }
        sc.close();
    }
}