*“Given eight identical pearls, except for one that is a little lighter,
how do you find which one is the lightest pearl with only two weighings?”*

This is the last problem that the seven sages put to Beremiz, who solved the problem easily.

Input

Input consists of several cases,
each with a natural number p between 1 and 10^{9}.

Output

For every case, print the minimum number of the weighings to identify with certainty, given p identical pearls, except for one that is a little lighter, which is the lightest pearl. Suppose that the scale can only compare the weight of two groups with the same (arbitrarily large) number of pearls.

Public test cases

**Input**

8 10 1

**Output**

2 3 0

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++ Python