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.lang.*;
import java.util.Set;
import java. util. Arrays;

import java.util.Scanner;
public class Codeforces {

    public static void main(String[] args) {
Scanner in= new Scanner (System .in);
int count=0,n=in.nextInt(),x=0;
x+=n;
for (int i=1;n>0;i++){
count+=i;
n-=i;
// System.out.println(count);
}
if (count==x)
    System.out.println("YES");
else
    
    System.out.println("NO");
    }}

  



          
          
          
          
          
          
          
          
          
 