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.*;
import java.math.BigInteger;

public class Solution{ 
	
	
	
	 public static void main(String[] args) { 
	     
	     Scanner in = new Scanner(System.in);
	     StringBuilder sb=new StringBuilder();
	     
	     
	     
	     int n,i;
	     
	     n=Integer.parseInt(in.next());
	     
	     for(i=0;i<100;i++){
	    	 if(i*(i+1)/2==n){
	    		 System.out.println("YES");
	    		 return;
	    	 }
	    	 
	     }
	     
	     System.out.println("NO");
	     
	     
	     
	     
	 }
}