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 void main(String[] args) {
            
        Scanner t = new Scanner(System.in);
        int c = t.nextInt();
        

        boolean[] rango = new boolean[1500000];
        
        for(int i=0;i<=rango.length-1;i++){
            rango[i]=true;
        }
        
        for(int i=2;i<=rango.length-1;i++){
            for(int j=i;j<=rango.length-1;j+=i){
                if(j==i){
                    continue;
                }
                rango[j]=false;
            }
        }
    
        

        for(int i=0;i<c;i++){
            long a = t.nextLong();
            
            long b = (int) Math.sqrt(a);
            
            if(b*b==a){
                if(rango[(int) b] && (int)b!=1){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
            }else{
                System.out.println("NO");
            }
        }
    }

}