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;
const int N = 1e5 + 10;
long long a[N], t, n, h = 1;
void lqq() {
  for (long long i = 1; i < 40; i++) {
    a[h++] = a[i - 1] + (1 + i) * i / 2;
  }
}
signed main() {
  lqq();
  cin >> n;
  for (long long i = 1; i <= h - 1; i++) {
    if (a[i] <= n && a[i + 1] > n) {
      cout << i;
      break;
    }
  }
}
