Vanya and Cubes

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:

inputFormat

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

outputFormat

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:

样例

25

4