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.*;
import java.io.*;
public class Solution {

	static Scanner scr=new Scanner(System.in);
	public static void main(String[] args) {
		// TODO Auto-generated method stub
//		int t=scr.nextInt();
//		while(t-->0) {
			solve();
			System.out.println();
//		}
	}
	static void solve() {
		int n=scr.nextInt();
		for(int  i=1;i<=n;i++) {
			if((i)*(i+1)/2==n) {
				System.out.print("YES");
				return;
			}
		}
		System.out.print("NO");
	}
}