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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		boolean prime[] = new boolean[(int)1e6 + 1];
		prime[0] = prime[1]  = true;
		for(int i = 2;i <= 1e6;i++) {
			if(!prime[i]) {
				for(int j = i + i;j <= 1e6;j+=i) {
					prime[j] = true;
				}
			}
		}
		int n = sc.nextInt();
		for (int i = 0; i < n; i++) {
			long ai = sc.nextLong();
			double sqrt = Math.sqrt((double)ai);
			if((long)Math.sqrt(ai) == sqrt) {
				if(!prime[(int)sqrt]) {
					System.out.println("YES");
				}else {
					System.out.println("NO");
				}
			}else {
				System.out.println("NO");
			}
		}
		
	}

	private static class Scanner {
		public BufferedReader reader;
		public StringTokenizer st;

		public Scanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			st = null;
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					String line = reader.readLine();
					if (line == null)
						return null;
					st = new StringTokenizer(line);
				} catch (Exception e) {
					throw (new RuntimeException());
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}