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

public class Solution {
    static boolean[] seive(int n){
        boolean [] arr=new boolean[n];
        Arrays.fill(arr, true);
        arr[0]=false;
        int i,j;
        for(i=1;i*i<=n;i++){
            if(arr[i]==true){
               for(j=2;((i+1)*j)<=n;j++){
                   arr[(i+1)*j -1 ]=false;
               }
            }
        }
        return arr;
    }
    public static void main(String[] args) {
        int n;
        Scanner sc=new Scanner(System.in);
        n=sc.nextInt();
        boolean arr[]=seive(1000000);
        
        int i,y;
        long x;
        double d;
       while(n-->0){
           x=sc.nextLong();
           d=Math.sqrt(x);
           y=(int) Math.sqrt(x);
           if((d-(double)y)!=0){ 
               System.out.println("NO");
           continue;
           }
           if(arr[y-1]==true) System.out.println("YES");
           else System.out.println("NO");
       }
        
    }
}