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 Problem6 {
public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int a=sc.nextInt();
	int i=1;
	int temp2=1;
	String ans="NO";
	if(a==1) {
		System.out.println("YES");
	}
	else {
	while(a>=i) {
		int temp=temp2+1;
		i=i+temp;
		temp2++;
		
		if(a==i) {
			ans="YES";
			break;
		}
	}
	System.out.println(ans);
	}
}
}
