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.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

/**
 * Created by Rukshar Alam on 1/10/2018.
 */
public class Tprimes_230B {

    public static Set<Long>setOfPrimes(){
        Set<Long> set = new HashSet<Long>();

        boolean arr[]=new boolean[1000000+1];
        Arrays.fill(arr, true);

        for(int i = 2;i<= 1000000;i++){
            if(arr[i] == true){
                set.add((long)i*(long)i);

                for(int j = 2*i;j<= 1000000; j+= i){
                    arr[j] = false;
                }
            }
        }

        return set;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        Set<Long> set = setOfPrimes();
        for(int t = 0;t<n;t++){
            long number = sc.nextLong();

            if(set.contains(number)){
                System.out.println("YES");
            }
            else System.out.println("NO");
        }

        

    }
}