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.*;

public class Practica_1 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int V[] = new int[500];
        for (int i = 0; i < 500; i++) {
            V[i] = (i * (i + 1)) / 2;
        }
        String rpta = "NO";
        for (int i = 0; i < 500; i++) {
            if (V[i] == n) {
                rpta = "YES";
                break;
            }
            if (V[i] > n) {
                break;
            }
        }
        System.out.println(rpta);
    }
}
