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.util.* ;
public class QuarentinePractice {
	public static void main(String[] args) {
		
		// Scanner sc = new Scanner(System.in) ;
			FastReader sc = new FastReader() ;
			int n = sc.nextInt() ;
			long arr[] = new long[n] ;
			for(int i = 0 ; i< n ; i++) {
				arr[i] = sc.nextLong() ;
			}
			boolean val[] = sieveofEratosthenes() ;
			
			for(int i = 0 ; i< n ; i++) {
				
				double x = Math.sqrt(arr[i]) ;
				if(x == (int) x && val[(int)x]) {
					System.out.println("YES");
				} else {
					System.out.println("NO");
				}
				
			}
		
	}
	
	
	
	
	
	
	
		

	//	FAST I/O
	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;
        }
	}
	
	
	
	
	
	
        
        
        
	// GCD
	public static int GCD (int a, int b) {
			
			if(b == 0) return a ;
			
			return GCD(b, a%b) ;
		}
	
	
	
	// sieve
	public static boolean [] sieveofEratosthenes() {
			
			boolean isPrime[] = new boolean[10000001] ;
			Arrays.fill(isPrime, true);
			isPrime[0] = false ;
			isPrime[1] = false ;
			
			for(int i = 2 ; i  <= 1000 ; i++) {
				
				for(int j = 2 * i ; j<= 1000001 ; j+= i) {
					isPrime[j] = false ;
				}
			}
			
			return isPrime ;
		}
}