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.nio.*;
import java.util.*;

public class Main
{

    public static void main(String[] args)
    throws Exception
    {

        boolean flag[] = new boolean[1000001];
        Arrays.fill(flag, true);
        flag[1] = false;

        for (int i = 2;i < 1000001;i++)
        {
            if (flag[i])
                if (isPrime(i))
                {
                    for (int j = i+i;j < 1000001;j += i)
                        flag[j] = false;
                }
                else
                    flag[i] = false;

        }


         BufferedReader s  = new BufferedReader(
         new InputStreamReader( System.in));
        int n = Integer.parseInt(s.readLine());
        long num;
        String line[] = s.readLine().split(" ");
        int first;
        
        for (int c = 0;c < n;c++)
        {
            num = Long.parseLong(line[c]);
            first = (int)Math.sqrt(num);
            
            if( first*(long)first == num  && flag[first])
                System.out.println("YES");
            else
                System.out.println("NO");
            
        }//process

    }//main

    public static boolean isPrime(long num)
    {
        if (num == 2 || num == 3 || num == 5 || num == 7)
            return true;

        if (num % 2 == 0)
            return false;

        for (long i = 3;i * i <= num;i += 2)
            if (num % i == 0)
                return false;

        return true;

    }//isPrime

}