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E. Fibonacci Number

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputJohn Doe has a list of all Fibonacci numbers modulo 10^{13}. This list is infinite, it starts with numbers 0 and 1. Each number in the list, apart from the first two, is a sum of previous two modulo 10^{13}. That is, John's list is made from the Fibonacci numbers' list by replacing each number there by the remainder when divided by 10^{13}.

John got interested in number *f* (0 ≤ *f* < 10^{13}) and now wants to find its first occurrence in the list given above. Help John and find the number of the first occurence of number *f* in the list or otherwise state that number *f* does not occur in the list.

The numeration in John's list starts from zero. There, the 0-th position is the number 0, the 1-st position is the number 1, the 2-nd position is the number 1, the 3-rd position is the number 2, the 4-th position is the number 3 and so on. Thus, the beginning of the list looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

Input

The first line contains the single integer *f* (0 ≤ *f* < 10^{13}) — the number, which position in the list we should find.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

Print a single number — the number of the first occurrence of the given number in John's list. If this number doesn't occur in John's list, print -1.

Examples

Input

13

Output

7

Input

377

Output

14

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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