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.*;

public class Solution{
    static Scanner scan = new Scanner(System.in);
    static long MAX = 1000000;
    static boolean[] flag = new boolean[(int)MAX];
    
    static boolean isPerfectSqure(long n){
        double sqrt = Math.sqrt(n);
        
        if(sqrt == (int)Math.sqrt(n)){
            return true;
        }
        else{
            return false;
        }
    }
    
    static void initializeFlag(){
        flag[0] = flag[1] = true;
        
        for(long i = 2; i < MAX; i++){
            if(!flag[(int)i]){
                for(long j = i*i; j < MAX; j+=i){
                    flag[(int)j] = true;
                }
            }
        }
    }
    
    public static void main(String args[]){
        long total = scan.nextLong();
        
        initializeFlag();
        
        for(long i = 0; i < total; i++){
            long number = scan.nextLong();
            
            if(number == 4){
                System.out.println("YES");
            }
            else if(number%2 == 0){
                System.out.println("NO");
            }
            else if(isPerfectSqure(number) && !flag[(int)Math.sqrt(number)]){
                System.out.println("YES");   
            }
            else{
                System.out.println("NO");
            }
        }
    }
    
}