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.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.util.Map;

/**
 * Created by Ignazio Castrogiovanni on 2019-04-22.
 */
public class HRGraph {

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    int n = scanner.nextInt();

    if (n == 1) {
      System.out.println(1);
    } else {
      int total = 0;

      int level = 1;
      while (total < n) {
        total += cubesPerLevel(level);
        if (total == n) {
          break;
        }
        if (total > n) {
          level--;
          break;
        }
        level++;
      }

      System.out.println(level);
    }
  }

  static int cubesPerLevel(int level) {
    int counter = 0;
    for (int j = level; j > 0 ; j--) {
      counter += j;
    }

    return counter;
  }
}