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.

The first line contains integer n (1 \le n \le 104) - the number of cubes given to Vanya.

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

Illustration to the second sample: