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.Scanner;


public class TPrime {

    /**
     * @param args
     */
    
    static boolean[] s = new boolean[1000001];
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        sieve();
        Scanner sc = new Scanner(System.in);
        Long n = sc.nextLong();
        while(n>0){
            long j = sc.nextLong();
            long k = (long)(Math.sqrt(j));
            if(k*k == j && s[(int)k]){
                    System.out.println("YES");
            }else{
                    System.out.println("NO");
            }
            n--;
        }
    }
    
    public static void sieve(){
        Arrays.fill(s,true);
        s[0]=false;
        s[1]=false;
        for(int i=2; i*i<s.length;i++){
            for(int j=2*i;j<s.length;j+=i){
                s[j]=false;
            }
        }
    }
}