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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
public class Main {
	public static void main(String[] args) {
                  Scanner sc = new Scanner(System.in);
		    int n = sc.nextInt();
		    boolean flag = false;
		    if(n==1) {
		    	System.out.println("YES");
		    }
		    else {
		    for(int i=2;i<=31;i++) {
		    	int res = (i*(i+1))/2;
		    	if(res == n) {
		    		//System.out.println("inside if i="+i+" ="+ (n*2)%(i*(i+1)));
		    		flag = true;
		    		break;
		    	}
		    }
		    if(flag) System.out.println("YES");
		    else System.out.println("NO");
		    }
}}