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.InputStream;
import java.io.InputStreamReader;
import java.io.ObjectInputStream.GetField;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Iterator;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {

	public static TreeSet<Long> getPrimeNumbersInRange() {

		TreeSet<Long> set = new TreeSet<Long>();
		int n = 1000000 + 1;
		boolean[] bs = new boolean[n];
		Arrays.fill(bs, true);
		bs[0] = bs[1] = false;
		for (int i = 2; i < bs.length; i++) {
			if (bs[i]) {
				set.add(i * 1L * i);
				for (int j = i * 2; j < bs.length; j += i) {
					bs[j] = false;
				}
			}
		}

		return set;
	}

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

		BufferedReader reader = new BufferedReader(new InputStreamReader(
				System.in));
		int n = Integer.valueOf(reader.readLine());
		StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
		TreeSet<Long> longs = getPrimeNumbersInRange();
		while (tokenizer.hasMoreTokens()) {
			System.out.println(longs.contains(Long.parseLong(tokenizer
					.nextToken())) ? "YES" : "NO");
		}
	}

}