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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder("");
        
   int[] a= tran(500);
        int n = sc.nextInt();
        int index = Arrays.binarySearch(a, n);
        if(index>=0){System.out.println("YES");}
        else
            System.out.println("NO");
    }
    
    public static int[]tran(int n )
    {
        int[] num = new int[1000];
        for(int i = 0 ; i <=n;++i)
        {
            num[i]=i*(i+1)/2;
        }
        return num;
    }
}
