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:
/**
 *
 * @author Faruk
 */

import java.util.Arrays;
import java.util.Scanner;
import java.util.HashSet;
import java.util.HashMap;
import java.util.ArrayList;


public class tmp {
    public static void main(String [] args){
        Scanner scan = new Scanner(System.in);
        
        int n = scan.nextInt();
        boolean [] arr = new boolean[1000001];
        for(int i=2; i<arr.length; i++)
            for(int j=2*i; j<=1000000; j += i)
                arr[j] = true;
        
        HashSet<Long> set = new HashSet<Long>();
        for(int i=2; i<arr.length; i++)
            if(!arr[i])
                set.add(i*(long)i);
        
        for(int i=0; i< n; i++){
            long x = scan.nextLong();
            if(set.contains(x))
                System.out.println("YES");
            else
                System.out.println("NO");
        }
        
                
                
                
                
                
                
                
                
                


        
        

        
        
        
        






        
        
        
        
    }

    
    
    
    
}