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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Tprimes {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		int million = 1000000;
        boolean[] isntPrime = new boolean[million + 1];
//        for (int i = 2; i <= 999983; i++) {
//            isPrime[i] = true;
//        }
        for (int i = 2; i*i <= 999983; i++) {
            if (!isntPrime[i]) {
                for (int j = i; i*j <= 999983; j++) {
                    isntPrime[i*j] = true;
                }
            }
        }
        HashSet<Long> preComp = new HashSet<Long>();
        for(long i = 2; i <= 999983; i++){
        	if(!isntPrime[(int) i]){
        		preComp.add(i*i);
        	}
        }
		long n = Long.parseLong(br.readLine());
		String[] longs = br.readLine().split(" ");
		for(long i = 0; i < longs.length; i++){
			long l = Long.parseLong(longs[(int)i]);
			if(preComp.contains(l)){
				out.println("YES");
			}
			else out.println("NO");
		}
		out.flush();
		out.close();
	}

}