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.*;

public class Main 
{
    public static void main(String[] args) throws IOException
    {
        Scanner in = new Scanner(System.in);
//      FastScanner sc = new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        int k = 1;
        while (k * (k + 1) / 2 < n)
            ++k;
        if (k * (k + 1) / 2 == n)
            System.out.print("YES");
        else
            System.out.print("NO");
        System.out.close();
    }
}

class FastScanner
{
    private BufferedReader Reader;
    private StringTokenizer Tokenizer;
    public FastScanner (BufferedReader Reader)
    {
        this.Reader = Reader;
    }
    public String nextToken() throws IOException
    {
        while (Tokenizer == null || !Tokenizer.hasMoreTokens())
            Tokenizer = new StringTokenizer(Reader.readLine());
        return Tokenizer.nextToken();
    }
    public int nextInt() throws NumberFormatException, IOException
    {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws NumberFormatException, IOException
    {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws NumberFormatException, IOException
    {
        return Double.parseDouble(nextToken());
    }
}