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 codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		int[] arr = new int[1000];
		for(int i =  0;i<=n;i++){
		    arr[i] = i*(i+1)/2;
		}
		int count = 0;
		for(int i = 0;i<=n;i++){
		    if(arr[i]==n){
		        System.out.println("YES");
		        break;
		    }else{
		        count++;
		    }
		}
		if(count==n+1){
		      System.out.println("NO");
		}
	}
}
