F008B. Addition of fractions P93090

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

Using the definition

    struct Fraction {
        int num, den;   // always strictly positive
    };

your program must include and use the function

    Fraction addition(const Fraction& x, const Fraction& y);

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.