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.Scanner;

public class Solution
{

    boolean[] primes;
    int size = 10000001;
    public Solution()
    {
        precomp();
    }

    public void precomp()
    {
        primes = new boolean[size];
        for(int i = 2 ;  i*i < size ; i++)
        {
            if(!primes[i])
            {
                for(int j = i ; j*i < size ; j++)
                    primes[j*i] = true;
            }
        }
    }

    public void tprimeCheck(long[] nums)
    {
        for(int i = 0 ; i < nums.length ; i++)
        {
            if(nums[i] < 4L)
                System.out.println("NO");
            else
            {
                long sqrt = (long)Math.sqrt(nums[i]);
                if( sqrt*sqrt == nums[i] && !primes[(int)sqrt])
                    System.out.println("YES");
                else
                    System.out.println("NO");

            }
        }
    }
    public static void main(String[] args)
    {
        Scanner s = new Scanner(System.in);
        int size = s.nextInt();
        long[] nums = new long[size];
        int i = 0;
        while(size > 0)
        {
            nums[i++] = s.nextLong();
            size--;
        }
        Solution obj = new Solution();
        obj.tprimeCheck(nums);
    }
}