Problem F
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 |
