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.*;
import java.util.*;
public class a{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		HashSet<Integer> hs = new HashSet<Integer>();
		for(int i = 0; i < 100; i++){
			hs.add(((i*(i+1))>>1));
		}
		int n = sc.nextInt();
		System.out.println((hs.contains(n)?"YES":"NO"));
	}
}

//n** {{1}}
//n** {{2}}
//n** {{3}}
