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.Scanner;
public class TriangularNumbers_47A {
    
    public static Scanner in = new Scanner(System.in);
    
    public static void main(String[] args) {
        int n = in.nextInt();
        boolean[] triNum = new boolean[501];
        for (int i = 0; i < Math.sqrt(500*2); i++) 
            triNum[ i*(i+1)/2 ] = true;
    System.out.println(triNum[n] ? "YES" : "NO");
    }
}
