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 triangularNumbers {
	static int x , y=0;
	
	public static void in(){
		Scanner kb= new Scanner(System.in);
		x = kb.nextInt();
		while(x<=0 || x>=501){
			in();
		}
	}
	static void findNum(){
		int ctr=1 ;
		
		while(y<x){
			y+=ctr;
			ctr++;
		}
	}
	static void display(){
		if (y == x)
			System.out.println("YES");
		else
			System.out.println("NO");
	}
	public static void main(String[]args){
		in();
		findNum();
		display();
		
	}
	
    
    
}