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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
public class B230 {
    public static void main(String args[]){
        Scanner in = new Scanner(System.in);
        final int n =1000001;
        int i,j,sieve[] = new int[n];
        Arrays.fill(sieve, 1);
        sieve[0]=0;
        sieve[1]=0;
        for(i=4;i<n;i+=2){
            sieve[i]=0;
        }
        int sqrt = (int)Math.sqrt(n);
        for(i=3;i<=sqrt;i+=2){
            if(sieve[i]==1){
                for(j=i*i;j<n;j+=2*i){
                    sieve[j]=0;
                }
            }
        }
        ArrayList<Long> a = new ArrayList<>();
        for(i=2;i<n;i++){
            if(sieve[i]==1){
                long l = ((long)i)*((long)i);
                a.add(l);
            }
        }
        int t = in.nextInt();
        for(i=0;i<t;i++){
            long d = in.nextLong();
            if(Collections.binarySearch(a, d)<0){
                System.out.println("NO");
            }
            else{
                System.out.println("YES");
            }
        }
    }
}