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.io.*;
public class problem{
	public static void main(String[] args) throws Exception{
		
	//	BufferedReader infile = new BufferedReader(new FileReader("data.txt"));
		BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
		int T=Integer.parseInt(infile.readLine());
		T*=2;
		int num=1;
		while(cal(num)<T){
			num++;
		}	
		if(cal(num)==T){
			System.out.println("YES");
		}
		else{
			System.out.println("NO");
		}
	}
	private static int cal(int num){
		return num*(num-1);
	}
}