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.Scanner;

public class CodeForces56 {
  public static int triangulate(int input) {
    return (input*(input + 1))/2;
  }
  public static void main(String argv[]) {
    Scanner scanner = new Scanner(System.in);
    
    int blocks = scanner.nextInt();
    boolean again = true;
    int i = 0;
    
    while(again) {
      if(triangulate(i+1) <= blocks) {
        i++;
        blocks = blocks - triangulate(i);
      } else {
        again = false;
      }
    }
    
    System.out.println(i);
    
    scanner.close();
  }
}
