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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Scanner;

public class A {
    public static void solution(Scanner in, PrintWriter out) {
        int n = in.nextInt();
        boolean ok = false;
        for (int i = 1; i <= 100; i++)
            if (i * (i + 1) == n + n)
                ok = true;
        out.println(ok ? "YES" : "NO");
    }

    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(
                System.in)));
        PrintWriter out = new PrintWriter(new BufferedWriter(
                new OutputStreamWriter(System.out)));
        solution(in, out);
        in.close();
        out.close();
    }
}
