Calgary Collegiate Programming Competition 2018

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2018-03-17 20:00 CET

Calgary Collegiate Programming Competition 2018

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2018-03-18 00:00 CET
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Problem B
Temperature Confusion

Yraglac has been a bit bored with Calgary lately and decided to move to the United States. After arriving in the strange land, he discovered that the people there use a temperature scale known as Fahrenheit. Celsius and Fahrenheit are related by the following equation:

\[ \left[ ^\circ F \right] = \frac95 \left[ ^\circ C \right] + 32 \]

It is your job to help Yraglac convert Fahrenheit to Celsius. When it comes to temperatures, however, Yraglac is a bit particular. Given a temperature expressed as a fraction in Fahrenheit, he wants to know the exact value in Celsius, expressed as a fraction in lowest terms.

Input

The input consists of a single test case representing a fractional number in Fahrenheit. It will be in the form $a/b$ or $-a/b$ where $a$ and $b$ are integers such that $0 \leq a, b \leq 1\, 000\, 000$ and $b \neq 0$. Note that the input is not guaranteed to be a fraction in lowest terms. You should consider temperatures below absolute zero to be valid.

Output

Output a single line with the exact result of converting the temperature to Celsius, expressed as a fraction in lowest terms (that is, $\gcd (a,b) = 1$).

Sample Input 1 Sample Output 1
32/1
0/1
Sample Input 2 Sample Output 2
33/1
5/9
Sample Input 3 Sample Output 3
-40/1
-40/1
Sample Input 4 Sample Output 4
-84/9
-620/27