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;

public class TPrimes 
{
    public static void main(String[] args) throws IOException
    {
        int l = 1000000;
        int [] cribaEratostenes = new int[l];
        for (int i = 1; i < l; i++)
        {
            if (cribaEratostenes[i] == 0)
            {
                for (int j = i;j < l;j += (i+1))
                {
                    cribaEratostenes[j] = i+1;
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String linea = br.readLine();
        int n = Integer.parseInt(linea);
        linea = br.readLine();
        String[] resultados = linea.split(" ");
        for (int i = 0;i < n; i++)
        {
            long k = Long.parseLong(resultados[i]);
            long a = (long)Math.sqrt(k);
            int x = (int) a;
            if (cribaEratostenes[x-1] == x && Math.pow(a,2) == k)
            {
                sb.append("YES\n");
            }
            else
            {
                sb.append("NO\n");
            }
        }
        System.out.print(sb.toString());
    }
}