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.ArrayList;

/**
 *
 * @author Arles
 */
public class Main {

    static int MAX = 10000000;
    static ArrayList<Integer> primes = new ArrayList<>();
    static boolean sieve[] = new boolean[MAX + 5];
    static ArrayList<Long> primeFactors = new ArrayList<>();

    static void calculateTPrimes() {
        sieve[0] = sieve[1] = true;
        int i;

        for (i = 2; i * i <= MAX; i++) {
            if (!sieve[i]) {
                primes.add(i);
                for (int j = i * i; j <= MAX; j += i) {
                    sieve[j] = true;
                }
            }
        }
        for (; i < MAX; i++) {
            if (!sieve[i]) {
                primes.add(i);
            }
        }
    }

    static boolean binarySearch(int left, int right, long number) {
        if (left > right) {
            return false;
        }
        int mid = (left + right) / 2;
        
       // System.out.println(left + ","+ right + ":" + TPrimes.get(mid) + "num " + number) ;
       long opt = ((long)primes.get(mid)*(long)primes.get(mid));  
       if (opt == number) {
            return true;
        } else if (opt < number) {
            return binarySearch(mid + 1, right, number);
        } else {
            return binarySearch(left, mid - 1, number);
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        calculateTPrimes();

        String[] numbers = br.readLine().split(" ");
       // System.out.println(TPrimes);
        int i = 0;
        while (n > 0) {
            long number = Long.parseLong(numbers[i]);
            if (binarySearch(0, primes.size()-1, number)) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
            i++;
            n--;
        }
    }
}