Pairs of Numbers
Description
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.
The input contains the only integer n (1 ≤ n ≤ 106).
Print the only integer k.
Input
The input contains the only integer n (1 ≤ n ≤ 106).
Output
Print the only integer k.
Samples
5
3
1
0
Note
The pair (1,1) can be transformed into a pair containing 5 in three moves: (1,1) → (1,2) → (3,2) → (5,2).