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.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    private static boolean isPrime(int a) {
        if(a == 1) {
            return false;
        }
        for(int j = 2; j*j <= a; j++) {
            if(a%j == 0) {
                return false;
            }
        }
        return true;
    }
    public static void main(String[] args) throws IOException {
        //Scanner f = new Scanner(new File("uva.in"));
        //Scanner f = new Scanner(System.in);
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = Integer.parseInt(f.readLine());
        StringTokenizer st = new StringTokenizer(f.readLine());
        for(int i = 0; i < n; i++) {
            long x = Long.parseLong(st.nextToken());
            double sqrt = Math.sqrt(x);
            int floorSqrt = (int) sqrt;
            if(sqrt == floorSqrt && isPrime(floorSqrt)) {
                out.println("YES");
            } else {
                out.println("NO");
            }
        }
        f.close();
        out.close();
    }
}