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.*;
import java.io.*;
public class TPrimes{
	static PrintWriter pw = new PrintWriter(System.out);
	public static void main(String[] args){
		FastReader sc = new FastReader();
		long size = sc.nextLong();
		while(size-->0){
			long input = sc.nextLong();
			double hold = Math.sqrt(input);
			if((long)hold*hold!=input){
				pw.println("NO");
			}else{
				pw.println(hold%1==0&&isPrime((long)hold)?"YES":"NO");
			}
		}
		pw.flush();
		pw.close();
	}
	public static boolean isPrime(long n) 
    { 
 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
  
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (long i = 5; i * i <= n; i += 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
    static class FastReader{
    	BufferedReader br;
    	StringTokenizer st;

    	public FastReader(){
    		br = new BufferedReader(new InputStreamReader(System.in));
    	}
    	String next(){
    		while (st == null|| !st.hasMoreElements()){
    			try{
    				st = new StringTokenizer(br.readLine());
    			}catch(IOException e){
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}
    	 int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
        String nextLine(){
        	String str = "";
        	try{
        		str = br.readLine();
        	}catch(IOException e){
        		e.printStackTrace();
        	}
        	return str;
        }
    }
}