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 static java.lang.Math.*; 

import java.io.*; 
import java.util.*; 
import java.math.*;

public class Main {
	BufferedReader in; 
	PrintWriter out;
	StringTokenizer st; 

	String next() {
		while (st==null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(in.readLine());
			} catch (Exception e) {}
		}
		return st.nextToken(); 
	}

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

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

	double nextDouble() {
		return Double.parseDouble(next());
	}
	public boolean isPrime(long n) {
		for (long i = 2; i * i <= n; i++) {
			if (n % i == 0) return false;
		}
		return true;
	}

	public void run() throws Exception {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		int n = nextInt();

		boolean[] boo = new boolean[1000010];
		Set<Long> set = new HashSet();
		for (int i = 2; i * i < 1000001; i++) {
			if (!boo[i]) {
				for (int j = i * i; j < 1000001; j += i) {
					boo[j] = true;
				}        
			}
		}
		for (long i = 2; i < 1000001; i++) {
			if (!boo[(int)i]) set.add(i * i);
		}
		for (int i = 0; i < n; i++) {
			long k = nextLong();
			if (set.contains(k)) out.println("YES"); else out.println("NO");
		}		        
		out.close(); 
 	}
	
	public static void main(String[] args) throws Exception {
		new Main().run(); 
	}

}