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 n;
  while (scanf("%d", &n) != EOF) {
    int a[100];
    int i, sum = 1;
    a[0] = 1;
    if (n == 1) {
      printf("%d\n", a[0]);
    } else {
      for (i = 1;; i++) {
        a[i] = a[i - 1] + i + 1;
        sum += a[i];
        if (sum == n) {
          printf("%d\n", i + 1);
          goto drump;
        } else if (sum > n) {
          printf("%d\n", i);
          goto drump;
        }
      }
    drump:;
    }
  }
  return 0;
}
