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.*;
import java.util.*;
 
public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int N = Integer.parseInt(br.readLine());
        long[] arr = new long[N];
        String[] s = br.readLine().split("\\s");
        for(int i=0;i<arr.length;++i) arr[i] = Long.parseLong(s[i]);
        solve(N,arr);
    }
    
    private static void solve(int N,long[] arr){
        boolean[] primes = new boolean[1000001];
        sieve(primes);
        
        for(int i=0;i<arr.length;++i){
            if(arr[i] % 2 == 1){
                long sq = (long)Math.sqrt(arr[i]);
                if(sq * sq != arr[i] || primes[(int)sq]) System.out.println("NO");
                else System.out.println("YES");
            }else if(arr[i] == 4){
                System.out.println("YES");
            }else{
                System.out.println("NO");
            }
        }   
    }
    
    private static void sieve(boolean[] primes){
       primes[0] = primes[1] = true;
       for(int i=2;i*i<=1000000;++i){
           if(!primes[i]){
               for(int j=i*i;j<=1000000;j+=i){
                primes[j] = true;// doing it in reverse fashion
               }
           }
        }
    } 
}