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 $*n*$ ($1 ≤ *n* ≤ 10^{4}$) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Note

Illustration to the second sample: