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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;
public class Main {
    public static void main(String[]args) throws NumberFormatException, IOException {
        BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter w=new PrintWriter(System.out);
        int n=Integer.parseInt(f.readLine());
        long[]num=new long[n];
        String s=f.readLine();
        StringTokenizer s1=new StringTokenizer(s);
            for(int i=0 ; i<n ; i++){
                while(s1.hasMoreTokens()){
                    num[i]=Long.parseLong(s1.nextToken());
            if(num[i]==1)
                w.println("NO");
            else if(num[i]%Math.sqrt(num[i])==0&&isPrime((int)(Math.sqrt(num[i]))))
               w.println("YES");
            else
                w.println("NO");
            
               }
            }
            w.flush();
            }//end main()
    
    public static boolean isPrime(int i){
        if(i==0)
            return false;
        for(int j=2 ; j<=(int)Math.sqrt(i) ; j++)
            if(i%j==0)
                return false;
        return true;
    }//end isPrime()

}