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.Scanner;


public class tPrimes {
    
    public static boolean isPrime(int x){
        double root = Math.sqrt(x);
        if(x==0 ||x==1) return false;
        //boolean prime = true;
        for(int i = 2; i<=root; i++){
            if(x%i ==0)
                return false;
        }
        return true;
    }
    public static void isTprime(long h){
        double sqrt = Math.sqrt(h);
        if(sqrt==Math.ceil(sqrt)){
            if(isPrime((int)sqrt)){
                System.out.println("YES");
                //System.out.println(h+ " YES");
            }
            else {
                System.out.println("NO");
                //System.out.println(h+ " NO");
            }
            
        }
        else {
            System.out.println("NO");
            //System.out.println(h+ " NO");
        }

    }
    
    public static void main(String[]args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for(int i =0; i<n; i++){
            long h = sc.nextLong();
            isTprime(h);
        }
    
            }

}