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.*;
import java.util.stream.*;

public class Main
{
    public static void main(String arg[]){
        // 入力を読み込む
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        //int a = Integer.parseInt(sc.next());
        //int b = Integer.parseInt(sc.next());
        //String str1 = sc.next();
        //int n = Integer.parseInt(sc.next());
        //List<Integer> x = IntStream.range(1, 101).boxed().collect(Collectors.toList());
        //String str2 = sc.next();
        /*List<String> s = new ArrayList<>();
        for(int i = 0; i < n; ++i){
            s.add(sc.next() + " " + sc.next());
        }*/
        // 判定・表示
        Set<Integer> set = IntStream.range(1, 500).map(i -> i * (i + 1) / 2).boxed().collect(Collectors.toSet());
        System.out.println(set.contains(n) ? "YES" : "NO");
    }
}
