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.IOException;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.ListIterator;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
 
public class Main{
 
    // public static Scanner input = new Scanner(System.in);
    public static void main(String[] args)
            throws IOException {
 
        Scanner input = new Scanner(System.in);
   //  BufferedReader buffer=new BufferedReader(new InputStreamReader(System.in));
   //  String str;
    //  while((str=buffer.readLine())!=null){
      
int n=input.nextInt();
int i=1;
while(n>0){
    n=n-i;
    
    i++;
}
       
if(n==0)
            System.out.println("YES");
else
            System.out.println("NO");

    }


}