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 code {
	public static void main(String[] args) {
		Scanner x = new Scanner(System.in);
    int n = x.nextInt();
   StringBuilder s=new StringBuilder();
    while (n-->0) {
      boolean f=true;
      long a=x.nextLong();
      // int count=0;
      double r=Math.sqrt(a);
      if(Math.floor(r)!=Math.ceil(r)){
        // System.out.println("NO");
        s.append("NO\n");
        continue;
      }
      int h=(int)r,i;
      for ( i = 2; i*i <= h; i++)        
        if(h%i==0){
          f=false;
          break;}
      s.append((f && h!=1)?"YES\n":"NO\n");
    }    
  System.out.println(s);    

	}
  }