Squared Frequency
Problem Description
You are now working in a physical laboratory. One day, when you were skimming through your records of experiments, you find that the squared frequency, defined as (P/Q)2, in which Q indicates times of experiments and P means number of experiments in which the expected phenomenon appears, is somehow unreasonable. The squared frequency F (0 < F < 1) is written in decimal form, and rounded to K (K ≤ 9) numbers after the decimal point. You think that Q, i.e. times of experiments, is too small to obtain such a number. Now you need to work out a fraction P/Q, so that rounding (P/Q)2 to K numbers after the decimal point gets exactly F, and minimizes Q.
Input
Input contains no more than 2000 test cases.
Each test case has a single line, which contains a decimal fraction indicating F, the squared frequency.
Output
For each test case, output your answer in a line with the case number, follow the format in sample. You should print a blank after ':'.
If the answer is not unique, output the one with the minimum P.
0.3
0.5
0.50
Case #1: 1/2
Case #2: 5/7
Case #3: 12/17