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;
set<long long> gera_primos(long long n) {
  set<long long> primos;
  vector<bool> crivo(n + 1);
  primos.insert(2);
  for (long long i = 3; i <= n; i += 2) {
    if (crivo[i]) continue;
    primos.insert(i);
    for (long long j = i; j <= n; j += i) {
      crivo[j] = true;
    }
  }
  return primos;
}
struct Link {
  long long from, to, t;
};
struct Node {
  bool visitado = false;
  set<long long> in, out;
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n;
  cin >> n;
  map<long long, long long> d;
  long long ant = 0;
  long long soma = 0;
  for (long long i = 1; i < (long long)1000; i++) {
    long long x = ant + i;
    soma += x;
    if (soma > n) {
      printf("%lld\n", i - 1);
      return 0;
    }
    ant = x;
  }
}
