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.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;

public class TPrime {


    static int N = 1000000;
    public static void main(String[] args) throws IOException {

        boolean isPrime[] = new boolean[N+1];
        isPrime[0] = isPrime[1] = false;

        for (int i=2; i<=N; i++){
            isPrime[i] = true;
        }

        for(int i=2; i*i<=N; i++){

            if(isPrime[i]){

                for ( long  j=i*i; j<=N; j+=i){
                    isPrime[(int)j]=false;
                }
            }
        }


        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        long num = Integer.parseInt(in.readLine());

        StringTokenizer token = new StringTokenizer(in.readLine());

        long Tprime;
        //read number of cases
        for(int i=0; i<num; i++){
            //read the number
            Tprime = Long.parseLong(token.nextToken());


            if((long)Math.sqrt(Tprime)*(long)Math.sqrt(Tprime) == Tprime){
                long s = (long)Math.sqrt(Tprime);
                boolean b = isPrime[(int)Math.sqrt(Tprime)];
                if(b){
                    System.out.println("YES");}
                    else
                        System.out.println("NO");
            }//if
            else
                System.out.println("NO");
        }//for i
    }//main
}//class