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.util.StringTokenizer;
// نورت الكود يا كبير اتفضل

// يا رب Accepted
public class Tprimes {
    private static final boolean[] prime = new boolean[(int) 1e7];

    private static void sieveOfEratosthenes(int n) {
        for (int i = 0; i <= n; i++)
            prime[i] = true;
        for (long p = 2; p * p <= n; p++) {
            if (prime[(int) p]) {
                for (long i = p * p; i <= n; i += p)
                    prime[(int) i] = false;
            }
        }
    }

    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

        sieveOfEratosthenes((int) 1e6);
        long t = in.nextLong();
        while (t-- > 0) {
            long x = in.nextLong();
            double sqrtX = Math.sqrt(x);
            boolean is = (int) sqrtX == sqrtX;
            out.println((prime[(int) sqrtX] && is && x != 1) ? "YES" : "NO");
        }

        out.close();
    }

    private static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}