Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1


Output

1


Input

25


Output

4

Note

Illustration to the second sample: 

<image>
import java.io.*;
import java.util.*;

import static java.lang.Math.max;
import static java.lang.Math.min;


public class Solution {
    static int n;
    public static void main(String[] args) throws IOException {
        //        System.setIn(new FileInputStream("input.txt"));
        //        System.setOut(new PrintStream(new FileOutputStream("output.txt")));
        Scanner sc = new Scanner( System.in );
        n = sc.nextInt();
        int total = 0;
        for ( int i = 1; i <= n+5; i++ ) {
            total += i * (i+1)/2;
            if ( total > n ) {
                System.out.println(i-1);
                return;
            }
        }
        System.out.println(1);
    }
}