4017: Pairs of Numbers
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Description
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputLet'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≤106).
Output
Print the only integer k.
Examples
Input
5
Output
3
Input
1
Output
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).