A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The n-th triangular number is the number of dots in a triangle with n dots on a side. <image>. You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).

Your task is to find out if a given integer is a triangular number.

Input

The first line contains the single number n (1 ≤ n ≤ 500) — the given integer.

Output

If the given integer is a triangular number output YES, otherwise output NO.

Examples

Input

1


Output

YES


Input

2


Output

NO


Input

3


Output

YES
import java.util.Scanner;
public class Main{
  public static void main(String args[]){
    Scanner sc = new Scanner (System.in);
    int num = sc.nextInt();
    int sum = 0;
    if(num < 0){
      System.out.println("NO");
    }
    for(int i=1;sum <= num; i++){
      sum += i;
      if(sum == num){
        System.out.println("YES");
        break;
      }
    }
    if(sum!=num){
      System.out.println("NO");
    }
  } 
}