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.FileInputStream;
import java.io.FileOutputStream;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;


public class TPrime {

    private static final int limit = 1000001;
    
    private static Set<Long> primes;
    
    static {
        initPrimes();
    }
    
    private static void initPrimes(){
        primes = new HashSet<Long>();
        boolean[] p = new boolean[limit];
        for(int i=2;i*i<limit;i++){
            if(!p[i]){
                for(int j=i*i;j<limit;j+=i){
                    p[j]=true;
                }
            }
        }
        
        for(int i=2;i<limit;i++){
            if(!p[i]){
                primes.add((long)i*(long)i);
            }
        }
    }
    
    
    public static String isTPrime(long value){
        
        if(primes.contains(value)){
            return "YES";
        }
        
        return "NO";
    }
    
    /**
     * @param args
     */
    public static void main(String[] args) throws Exception {
        boolean isOnline = System.getProperty("ONLINE_JUDGE") != null;
        InputStream inputStream = isOnline ? System.in : new FileInputStream(
                "input.txt");
        OutputStream outputStream = isOnline ? System.out
                : new FileOutputStream("output.txt");
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n = in.nextInt();
        for(int i=0;i<n;i++){
            out.write(isTPrime(in.nextLong())+"\n");
        }       
        out.close();
        in.close();

    }

}