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.*;

public class Main {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        long[] a = fs.readLongArray(n);
        boolean[] sieve = sieve(1000010);
        for (int i = 0; i<n; i++) {
            double sqrt = Math.sqrt(a[i]);
            long sqrT = Math.round(sqrt);
            if (Math.abs(sqrT-sqrt) < 0.00001 && sieve[(int) sqrT]) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
        }

    }
    public static boolean[] sieve(int n) {
        boolean[] sieve = new boolean[n+1];
        sieve[0] = false; sieve[1] = false;
        for (int i = 2; i< sieve.length; i++) {
            sieve[i] = true;
        }
        for (int i = 2; i*i<n; i++) {
            if (sieve[i] == true) {
                for (int q = i*i; q<=n; q+=i) {
                    sieve[q] = false;
                }
            }

        }
        return sieve;
    }


    public static void arrayPrinter(ArrayList[] a) {
        for (int i = 0; i<a.length; i++) {
            System.out.print(a[i] + " ");
        }
        System.out.println();
    }


    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i<n; i++) {
                a[i] = nextLong();

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

}