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.util.*;
public class Main{
	Scanner in = new Scanner(System.in);
	//var 
	int n;
	int num[];
	int ma;
	public void run(){
		//main
		n = in.nextInt();

		num = new int[n];
		ma = 0;
		for (int i = 0; i < n; i++) {
			long tmp = in.nextLong();
			long dived = (long)Math.sqrt(tmp);
			if (dived * dived == tmp) { num[i] = (int)dived; } else {num[i] = 1;}
			ma = Math.max(ma, num[i]);
		}
		int right = (int)Math.ceil(Math.sqrt(ma));
		boolean istp[] = new boolean[ma + 1];
		Arrays.fill(istp, true);

		istp[0] = false;
		istp[1] = false;
		for (int i = 2; i <= right; i++) {
			if (!istp[i]) { continue; }
			for (int j = i * 2; j <= ma; j += i) {
				istp[j] = false;
			}
		}
		for (int i = 0; i < n; i++) {
			if (istp[num[i]]) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
		}
	}
	public static void main(String[] args) {
		Main m = new Main();
		m.run();
	}
}