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 Solving {
    
private static Scanner in =new Scanner(System.in);
public static HashSet<Integer> get(int n){
    HashSet<Integer> set=new HashSet<Integer>();
    int last=0;
    for(int i=0;i<=n;i++){
        last+=i;
        set.add(last);
    }
    return set;
}
 public static void main(String[] args){
     int n=in.nextInt();
     HashSet<Integer> set=get(500);
     if(set.contains(n))
         System.out.println("YES");
     else
         System.out.println("NO");
     
    
 }
}