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 Primo {
static int[] primos=new int[1000100];
	/**
	 * @param args
	 * @throws IOException 
	 * @throws NumberFormatException 
	 */
	public static void main(String[] args) throws NumberFormatException, IOException {
		primos[0]=0;
		primos[1]=0;
		for(int i=2;i<primos.length;i++){
			primos[i]=1;
		}
		for(int i=2;i<primos.length;i++){
			
			if(primos[i]==1){
				
				for(int j=2*i;j<primos.length;j+=i){
					primos[j]=0;
					
					
					
				}
				
			}
			
		}
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int casos=Integer.parseInt(br.readLine());		
		String pase=br.readLine();
		String[] val=pase.split(" ");
		for (int i=0;i<casos;i++){
		
		long valor=Long.parseLong(val[i]);
		
	    double compa = Math.round(Math.sqrt(valor));
		double compa1 =  Math.sqrt(valor);
		int pos=(int)(compa);
		
		if(compa==compa1 && (primos[pos]==1)){
			
			System.out.println("YES");
			
		}else{
		System.out.println("NO");
		}
		
		}
	}
	
	
	public static boolean primo(double x){
		
		if(x==1 || x==0){
			
		   return false;
		}
		
		if(x==4){
			
			return false;
			
		}
	
		int count=0;
		for(int i=1;i<=Math.sqrt(x);i++){
			if (x%i==0){
				
				count+=1;
				
			}
			if(count>1){
				
				return false;
				
			}
			
		}
		
		
		return true;
		
	}

}