#include <iostream>

class Rational {

public:

    Rational() = default;
    Rational(const Rational&) = default;
    Rational(const int num, const int denum = 1);

    Rational& operator=(const Rational&) = default;
    ~Rational() = default;

    int num() const;
    int denum() const;

    bool operator==(Rational& rhs) const;
    bool operator!=(Rational& rhs) const;

    bool operator>(Rational& rhs) const;
    bool operator>=(Rational& rhs) const;

    bool operator<(Rational& rhs) const;
    bool operator<=(Rational& rhs) const;



    Rational& operator+=(const Rational& rhs);
    Rational& operator+=(const int& rhs);

    Rational& operator-=(const Rational& rhs);
    Rational& operator-=(const int& rhs);

    Rational& operator/=(const Rational& rhs);
    Rational& operator/=(const int& rhs);

    Rational& operator*=(const Rational& rhs);
    Rational& operator*=(const int& rhs);

    std::ostream& writeTo(std::ostream& ostr) const;
    std::istream& readFrom(std::istream& ostr);


private:

    int _num {0};
    int _denum {1};

    void normalize();

    int gcd(int a, int b);
};

std::istream operator>>(std::istream istream, Rational& rhs);
std::ostream operator<<(std::ostream istream, Rational& rhs);


Rational operator+(Rational& lhs, Rational& rhs);
Rational operator-(Rational& lhs, Rational& rhs);
Rational operator*(Rational& lhs, Rational& rhs);
Rational operator/(Rational& lhs, Rational& rhs);

Rational operator+(Rational& lhs, int& rhs);
Rational operator-(Rational& lhs, int& rhs);
Rational operator*(Rational& lhs, int& rhs);
Rational operator/(Rational& lhs, int& rhs);

Rational operator+(int& rhs, Rational& lhs);
Rational operator-(int& rhs, Rational& lhs);
Rational operator*(int& rhs, Rational& lhs);
Rational operator/(int& rhs, Rational& lhs);