Let's assume that we have a pair of numbers ($*a*, *b*$). We can get a new pair ($*a* + *b*, *b*$) or ($*a*, *a* + *b*$) from the given pair in a single step.

Let the initial pair of numbers be (1,1). Your task is to find number $*k*$, that is, the least number of steps needed to transform (1,1) into the pair where at least one number equals $*n*$.

Input

The input contains the only integer $*n*$ ($1 ≤ *n* ≤ 10^{6}$).

Output

Print the only integer $*k*$.

Note

The pair (1,1) can be transformed into a pair containing 5 in three moves: (1,1) $→$ (1,2) $→$ (3,2) $→$ (5,2).