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 ;
import java.*;
import java.math.*;
import java.math.*;
import java.util.*;
public class Hi {
	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		int arr[] = new int[500];
		for(int i=0 ; i<499 ;i++ ) arr[i] = ((i+1)*(i+2))/2;
		
		int x = input.nextInt(); 
		boolean f = false ; 
		for(int i =0 ; i<499;i++) if(arr[i]==x) f=true ; 
		System.out.print(f?"YES":"NO");
	  
	}	    
}   
   

		
		
		
							
	



	

		
	
		
	


			
		
		
			

		
		


