Description

Dogeon (鴿子) likes everything to be rational, just like himself. He thinks that it is irrational that floating-point numbers in C/C++ are not accurate. So he decides to implement a class Rational to represent rational numbers. Since he prefer the class to be over-rational to use, you're asked to help him implement the following functions in an overloaded operator style.

1. Rational(int numerator, int denominator):
   a constructor that takes two integers numerator and denominator to represent the rational number.
2. Rational operator+(Rational const& b) const:
   an overloaded operator + that takes another Rational object b and returns a new Rational object that represents the sum of the two rational numbers.
3. Rational operator-(Rational const& b) const:
   an overloaded operator - that takes another Rational object b and returns a new Rational object that represents the subtraction of the two rational numbers.
4. Rational operator*(Rational const& b) const:
   an overloaded operator * that takes another Rational object b and returns a new Rational object that represents the multiplication of the two rational numbers.
5. Rational operator/(Rational const& b) const:
   an overloaded operator / that takes another Rational object b and returns a new Rational object that represents the division of the two rational numbers.
6. std::ostream& operator<<(std::ostream& os, Rational const& r):
   a friend function that overloads the << operator of std::ostream to output the rational number in the form numerator/denominator.

• This is a partial judge problem. You don't need to handle input. All you need to do is to implement the overloaded operators, the constructor, and the output function.
• This is a work of fiction. Any resemblance to actual persons, living or dead, or actual events is purely coincidental.

Input

The first line of the input contains an integer $N$, the number of expressions to be evaluated.

The next $N$ lines each contain the expression to be evaluated. Each expression contains two rational numbers $\frac{n_{i,1}}{d_{i,1}}, \frac{n_{i,2}}{d_{i,2}}$ and an operator $op_i$, separated by a space. The rational numbers are in the form numerator/denominator and the operator is one of +, -, *, /.

$N$
$n_{1,1}/d_{1,1} \quad op_1 \quad n_{1,2}/d_{1,2}$
$n_{2,1}/d_{2,1} \quad op_2 \quad n_{2,2}/d_{2,2}$
$\vdots$
$n_{N,1}/d_{N,1} \quad op_N \quad n_{N,2}/d_{N,2}$

Constraints

• $1 \leq N \leq 10^5$
• $-10^9 \leq n_{i,1}, d_{i,1}, n_{i,2}, d_{i,2} \leq 10^9$
• It is guaranteed that the denominator of the rational numbers is not 0.
• It is guaranteed that if operator is /, the second rational number is not 0.
• It is guaranteed that the simplest form of the result of each expression has a numerator and a denominator that are both within $[-10^9, 10^9]$.

Output

Each line of the output should contain the result of the corresponding expression in the simplest form $n_{i,3}/d_{i,3}$.

$\frac{n_{i,3}}{d_{i,3}} = (\frac{n_{i,1}}{d_{i,1}} \, \mathrm{op_i} \, \frac{n_{i,2}}{d_{i,2}})$, $d_{i,3} > 0$ and $\mathrm{gcd}(n_{i,3}, d_{i,3}) = 1$.

$n_{1,3}/d_{1,3}$
$n_{2,3}/d_{2,3}$
$\vdots$
$n_{N,3}/d_{N,3}$

Sample Input  Download

Sample Output  Download

Partial Judge Code

14277.cpp

Partial Judge Header

14277.h

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