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.*;

public class Main {
    Scanner in;
    PrintWriter out;
    StreamTokenizer ST;
    BufferedReader br;

    int nextInt() throws IOException {
        ST.nextToken();
        return (int) ST.nval;
    }

    double nextDouble() throws IOException {
        ST.nextToken();
        return ST.nval;
    }

    String next() throws IOException {
        ST.nextToken();
        return ST.sval;
    }

    String nextLine() throws IOException {
        return br.readLine();
    }

    void solve() throws IOException {
        int n = nextInt();
        for(int i=1;i<=n;++i)
        {
            if (i*(i+1)/2==n)
            {
                out.println("YES");
                return;
            }
        }
        out.println("NO");
    }

    public void run() throws IOException {
        // br = new BufferedReader(new FileReader(new File("input.txt")));
        br = new BufferedReader(new InputStreamReader(System.in));
        ST = new StreamTokenizer(br);
        in = new Scanner(br);
        out = new PrintWriter(System.out);
        // out = new PrintWriter(new FileWriter(new File("output.txt")));
        solve();
        in.close();
        out.close();
        br.close();
    }

    public static void main(String[] args) throws Exception {
        new Main().run();
    }

}