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

public class p47a
{
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        System.out.println();
        long n = sc.nextLong();
        if(triangular_check(n)==1) System.out.println("YES");
        else System.out.println("NO");
    }

    public static int triangular_check(long n)
    {
        double a = (Math.sqrt(1+(8*n))-1)/2;
        if((((long)a*((long)a+1))/2)==n) return 1;
        else return 0;
    }
}