12333 - Revenge of Fibonacci

The well-knownFibonacci sequence is defined as following:

F(0)=

F(1) = 1

 

F(n)=

F(n - 1) + F(n - 2)   任意 n>=2

 

Here weregard n as the index of the Fibonacci number F(n).

This sequence hasbeen studied since the publication of Fibonacci book Libber Abaci. So far,many properties of this sequence have been introduced.

You had beeninterested in this sequence, while after reading lots of papers about it. Youthink there's no need to research in it anymore because of the lack of itsunrevealed properties. Yesterday, you decided to study some other sequenceslike Lucas sequence instead.

Fibonacci cameinto your dream last night. ``Stupid human beings. Lots of important propertiesof Fibonacci sequence have not been studied by anyone, for example, from theFibonacci number 347746739…''

You woke up andcouldn't remember the whole number except the first few digits Fibonacci toldyou. You decided to write a program to find this number out in order tocontinue your research on Fibonacci sequence.

Input 

There are multipletest cases. The first line of input contains a single integer T denotingthe number of test cases ( T<=50000).

For each testcase, there is a single line containing one non-empty string made up of at most40 digits. And there won't be any unnecessary leading zeroes.

Output 

For each testcase, output the smallest index of the smallest Fibonacci number whose decimalnotation begins with the given digits. If no Fibonacci number withindex smaller than 100000 satisfy that condition, output `-1' instead -–you think what Fibonacci wants to told you beyond your ability.

Sample Input 

15

1

12

123

1234

12345

9

98

987

9876

98765

89

32

51075176167176176176

347746739

5610

Sample Output 

Case #1: 0

Case #2: 25

Case #3: 226

Case #4: 1628

Case #5: 49516

Case #6: 15

Case #7: 15

Case #8: 15

Case #9: 43764

Case #10: 49750

Case #11: 10

Case #12: 51

Case #13: -1

Case #14: 1233

Case #15: 22374