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 n, ans, z;
int main() {
  cin >> n;
  int x = 1;
  if (n == 1) {
    cout << 1;
    return 0;
  }
  for (int i = 2;; i++) {
    z += x;
    if (z <= n) {
      ans++;
    } else {
      break;
    }
    x += 1 * i;
  }
  cout << ans;
  return 0;
}
