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 Main {

    public static void main(String[] args) {
        Scanner write = new Scanner(System.in);
        Main user = new Main();
        int N = write.nextInt();
        long value[] = new long[N];
        for(int i =0;i < N;i++){
            value[i]=write.nextLong();
        }
        int rozmir = (int)Math.pow(10,6);
        boolean Resheto[] = new boolean[rozmir+1];
        for(int i =0;i <= rozmir;i++){
            Resheto[i]=true;
        }
        for(int i = 2; i <= rozmir;i++ ){
            if(Resheto[i]){
                long q = (long)i*i;
                if(q <= rozmir) {
                    for (int j = i * i; j <= rozmir; j += i) {
                        Resheto[j] = false;
                    }
                }
            }
        }
        for(int i =0;i<N;i++){
            if(value[i]==1){
                System.out.println("NO");
            }
            else {
                int a = (int) Math.sqrt(value[i]);
                long q = (long)a*a;
                if (q == value[i]) {
                    if (Resheto[a]){
                        System.out.println("YES");
                    }
                    else {
                        System.out.println("NO");
                    }
                }
                else {
                    System.out.println("NO");
                }
            }
        }
    }

}