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.Arrays;
import java.util.Scanner;

/**
 * @author Son-Huy TRAN
 * 
 */
public class P230B_TPrimes {

	public static boolean[] primeSieve(int max) {
		if (max == 1) {
			return new boolean[] { false, false };
		}

		boolean[] isPrime = new boolean[max + 1];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] = false;

		for (int i = 2; i * i <= max; i++) {
			if (isPrime[i]) {
				for (int j = i * i; j <= max; j += i) {
					isPrime[j] = false;
				}
			}
		}

		return isPrime;
	}

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		StringBuilder result = new StringBuilder();
		boolean[] isPrime = primeSieve(1000000);
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();

		for (int i = 0; i < n; i++) {
			long number = scanner.nextLong();
			long sqrt = (long) Math.sqrt(number);

			// it must be a square of a prime number
			if (isPrime[(int) sqrt] && sqrt * sqrt == number) {
				result.append("YES\n");
			} else {
				result.append("NO\n");
			}
		}

		scanner.close();
		System.out.println(result.toString().trim());
	}
}