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 t
{
  
  
    
      



   public static void main(String[] args) {

   Scanner sc=new Scanner(System.in);
   
    int a[]=new int[1000001];
   Arrays.fill(a,1);
   a[0]=0;
   a[1]=0;
   for(int i=2;i<=1000;i++){
       if(a[i]==1){
       for(int j=2*i;j<=1000000;j=j+i)
           a[j]=0;
       }
       
   }
   int n=sc.nextInt();
   while(n >0){
       
   
   
   long k=sc.nextLong();
   long sq=(long)Math.sqrt(k);
   if(sq*sq==k && (a[(int)sq]==1) )
      System.out.println("YES");
   else
  System.out.println("NO");
  n--;
   }

   }}