Fibonacci numbers is a sequence of numbers F(n), given by the formula:

F(0) = 1, F(1) = 1, F(n) = F(n - 1) + F(n - 2)

Fibonacci number f is given. Find its index n. You must find such index n that F(n) = f.

Input

Fibonacci number f (2 ≤ f ≤ 2·109).

Output

Print the index of Fibonacci number f.