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.*;

public class tprime
{
    public static void main (String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] primes = pre();
        
        while (n --> 0)
        {
            long t = in.nextLong();
            long sqrt = (long)Math.sqrt(t);
            
            if (sqrt*sqrt != t || primes[(int)sqrt] == 1)
                System.out.println("NO");
            
            else
                System.out.println("YES");
        }
        
        in.close();
    }
    
    public static int[] pre()
    {
        int[] ret = new int[1000001];
        ret[0] = 1; ret[1] = 1;
        for (int i = 2; i < ret.length; i++)
            if (ret[i] == 0)
                for (int j = 2*i; j < ret.length; j += i)
                    ret[j] = 1;
                    
        return ret;
    }
}