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.*;
import java.io.*;
import static java.util.Arrays.*;
import static java.lang.Math.*;
import java.math.*;

public class Main {        

    void run() throws IOException {
        int t = nint();
        for (int i = 1; i <= 1000; i++) {
            if (i * (i + 1) / 2 == t) {
                out.println("YES");
                return;
            }
        }
        out.println("NO");
    }

    class pair implements Comparable <pair> {
        int x, y;
        pair(int x, int y) {
            this.x = x;
            this.y = y;            
        }
        public int compareTo (pair p) {
            if (x != p.x) {
                return x - p.x;
            } else {
                return y - p.y;
            }
        }
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        st = new StringTokenizer(" ");
        new Main().run();
        out.close();
    }

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer st;

    String token() throws IOException {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    int nint() throws IOException {
        return Integer.parseInt(token());
    }

    long nlong() throws IOException {
        return Long.parseLong(token());
    }

    double ndouble() throws IOException {
        return Double.parseDouble(token());
    }
}