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
//package cf3;

import java.util.*;
import java.io.*;

public class Q2A {

	// main method
	public static void main(String[] args) throws IOException {
		//BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		 Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int c=1;
		while(true){
			int t = c*(c+1)/2;
			if(t==n){
				System.out.println("YES");
				return;
			}else{
				if(t>n){
					System.out.println("NO");
					return;
				}
				c++;
			}
		}
		// end of main
	}

}
