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.*;

public class Main 
{
	public static void main(String[] args) throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = Integer.parseInt(br.readLine());
		String[] strs = br.readLine().split(" ");
		br.close();
		boolean[] isComposite = generatePrimes(1000000);
		for(int i = 0; i < n; i++)
		{
			long num = Long.parseLong(strs[i]), sqrt = (long)(Math.sqrt(num));
			pw.println(sqrt*sqrt == num && !isComposite[(int)sqrt] ? "YES" : "NO");
		}
		pw.close();
	}
	public static boolean[] generatePrimes(int max) 
	{
	    boolean[] isComposite = new boolean[max+1];
	    for(int i = 2; i*i <= max; i++) 
	        if(!isComposite[i]) 
	        	for(int j = i; i*j <= max; j++)
	                isComposite[i*j] = true;
	    isComposite[1] = true;
	    return isComposite;
	}
}