# Dead Fraction

To make this tenable, he assumes that the original fraction
is always the simplest one that produces the given sequence of
digits; by *simplest*, he means the the one with
smallest denominator. Also, he assumes that he did not neglect
to write down important digits; no digit from the repeating
portion of the decimal expansion was left unrecorded (even if
this repeating portion was all zeroes).

## Input

There are several test cases. For each test case there is
one line of input of the form “0.*dddd*...” where
*dddd* is a string of $1$ to $9$ digits, not all zero. A line
containing 0 follows the last case.

## Output

For each case, output the original fraction.

Sample Input 1 | Sample Output 1 |
---|---|

0.2... 0.20... 0.474612399... 0 |
2/9 1/5 1186531/2500000 |