分数和分数的平方的等式问题利用C语言的办法如何求解,具体一个问题的代码的实现

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.

Sample Input
0.3
0.5
0.50

Sample Output
Case #1: 1/2
Case #2: 5/7
Case #3: 12/17

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