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;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.TreeSet;

public class Solution {

    public static Set<Long> getTPrimes(int limit) {
        Set<Long> integers = new TreeSet<Long>();
        boolean[] array = new boolean[limit + 2];
        Arrays.fill(array, 2, array.length, true);
        for (int i = 2; i < array.length; i++) {
            if (array[i]) {
                integers.add((long) i * (long) i);
                for (int j = i * 2; j < array.length; j += i) {
                    array[j] = false;
                }
            }
        }
        return integers;
    }

    public static void main(String[] args) throws IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(
                System.in));
        int n = Integer.valueOf(reader.readLine());
        ArrayList<Long> longs = new ArrayList<Long>();
        long l = Long.MIN_VALUE;
        for (String string : reader.readLine().split(" ")) {
            long m = Long.valueOf(string);
            longs.add(m);
            if (m > l) {
                l = m;
            }
        }
        Set<Long> set = getTPrimes((int) Math.sqrt(l));
        for (Long long1 : longs) {
            System.out.println(set.contains(long1) ? "YES" : "NO");
        }
    }
}