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>
#include <bits/stdc++.h>
using namespace std;
int main() {
  int cc, now, cgsa, fi;
  cin >> cc;
  now = 0;
  fi = 0;
  cgsa = 0;
  while (now < cc) {
    cgsa++;
    fi += cgsa;
    now += fi;
  }
  if (now == cc)
    cout << cgsa;
  else
    cout << cgsa - 1;
  return 0;
}
