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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author lw'tn
 */
public class Triangular_number {
    public static void main(String[] args)throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int  i = 1;
        HashSet<Integer> h = new HashSet<Integer>();
        h.add(i);
        int sum = i;
        ++i;
        for (; sum < 600; ++i) {
           sum+=i;
           h.add(sum);
        }
        int l = Integer.parseInt(in.readLine());
        if(h.contains(l)){
            System.out.println("YES");
        }
 else
            System.out.println("NO");

}
}

