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.Scanner;


public class Tfactor {
      public static void main(String[] args) {
        
          Scanner in = new Scanner(System.in);
          Long number = in.nextLong();
          long checknumber = 0;
          Long [] lonArr = new Long[number.intValue()];
          int i = 0;
          boolean gurami = true;
          for (int h=0;h<number;h++){
                 
                          checknumber = in.nextLong();
                          
                          if (checknumber == 1 || checknumber == 3 || checknumber == 2){
                              System.out.println("NO");
                              continue;
                        }
                          else if(checknumber == 4){
                              System.out.println("YES");
                              continue;
                          }
                          
                          if (checknumber % 2 == 0){
                              System.out.println("NO");
                          }
                          else{
                              if (isPerfectSquare(checknumber) && isPrime((int)Math.sqrt(checknumber))){
                                  System.out.println("YES");
                              }
                              else {
                                  System.out.println("NO");
                              }
                          }
                  
              
          }
          
    }
      
      
     static boolean isPrime(int n) {
            if (n%2==0) return false;
            for(int i=3;i*i<=n;i+=2) {
                if(n%i==0)
                    return false;
            }
            return true;
        }
      
      
      public final static boolean isPerfectSquare(long n)
      {
          if (n < 0)
              return false;

          switch((int)(n & 0xF))
          {
          case 0: case 1: case 4: case 9:
              long tst = (long)Math.sqrt(n);
              return tst*tst == n;

          default:
              return false;
          }
      }
}