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 TaskB
{

  /**
   * @param args
   */
    int maxN = 1000000;
    boolean isPrime[] = new boolean[maxN + 1];
  
  private boolean isTPrime(long x)
  {
    if (x < 4)
      return false;
    if (x == 4)
      return true;
    double sqrtX = Math.sqrt(x);
    if (sqrtX % 1 != 0)
      return false;
    int IsqrtX = (int)sqrtX;
    return isPrime[IsqrtX];
  }
  
  public static void main(String[] args)
  {
    TaskB solver = new TaskB();
    solver.run();
  }
  
  TaskB()
  {
    for (int i = 0; i <= maxN; i++)
      isPrime[i] = true;
    
    for (int i = 2; i < maxN / 2 + 5; i++)
    {
      if (! isPrime[i])
        continue;
      int num = i * 2;
      while (num <= maxN)
      {
        isPrime[num] = false;
        num += i;
      }
    }
  }
  
  private void run()
  {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    for (int i = 0; i < n; i++)
    {
      long x = sc.nextLong();
      if (isTPrime(x))
        System.out.print("YES\n");
      else
        System.out.print("NO\n");
    }
    sc.close();
  }

}