Your task is to write a program that computes the result of adding a sequence of fractions.

Using the definition

your program must include and use the function

that returns the addition of |x| and |y|,
*without common factors in the numerator and denominator*.

**Input**

The input is a sequence of one or more simplified fractions separated by plus signs, ended with an equal sign. Each fraction consists of its numerator, a bar, and its denominator. Numerators and denominators are natural strictly positive.

**Output**

Your program must print the simplified fraction corresponding to the sum of all the given fractions.

**Observations**

- In order to avoid overflows, use the function |addition()| to accumulate the partial calculations.
- Inefficient calculation of the greatest common divisor will be negatively valued.
- Using vectors is not allowed to solve this problem.

Public test cases

**Input**

1/2 + 1/2 =

**Output**

1/1

**Input**

1/2 + 2/3 + 3/4 + 4/5 + 5/6 =

**Output**

71/20

**Input**

1/10125 + 1/8000 + 1000/999 =

**Output**

4801073/4795200

**Input**

9/4 =

**Output**

9/4

Information

- Author
- Professorat de P1
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++