#include <iostream>

using namespace std;

class Rational {
  public:
    Rational(int n=0, int d=1) : n_(n), d_(d) {
      if (d==0) { throw exception();}
      riduci();
    }

    int num() const {return n_;}
    int den() const {return d_;}

    const Rational operator-() const {
      return Rational(-num(), den());
    }

    const Rational inv() const {
      return Rational(den(),num());
    }

  private:
    int n_, d_;

    void riduci() {
      if (n_%d_==0) {
        n_/=d_;
        d_=1;
      }
    }

    friend ostream& operator<<(ostream&, const Rational&);
};

ostream& operator<<(ostream& out , const Rational& r) {
  return out << r.n_ << "/" << r.d_;
}

istream& operator>>(istream& in, Rational& r) {
  int n,d;
  char c = in.peek();
  if (c == '\n' ) {
    r=Rational();
    in.ignore();
    return in;
  }
  in >> n;
  c = in.peek();
  if (c == '\n' ) {
    r=Rational(n);
    in.ignore();
    return in;
  }
  else if (c=='/') {
    in.ignore();
  }
  in >> d;
  if ( d==0 ) {
    cout << "Denominatore == 0! " << endl;
    in.clear();
    throw exception();
  }
  r=Rational(n,d);
  in.ignore();
  return in;
}

const Rational operator*(const Rational& l, const Rational& r) {
  return Rational(l.num()*r.num(), l.den()*r.den());
}

const Rational operator/(const Rational& l, const Rational& r) {
  return l*r.inv();
}

const Rational operator+(const Rational& l, const Rational& r) {
  return Rational(l.num()*r.den()+l.den()*r.num(), l.den()*r.den());
}

const Rational operator-(const Rational& l, const Rational& r) {
  return (l)+(-r);
}

int main() {
  Rational r1(10);
  Rational r2(3,5);

  cout << "r1 " << r1<< endl;
  cout << "r2 " << r2<< endl;

  Rational r3 = r1 * r2;
  cout << "r3 " << r3<< endl;

  Rational r4 = r1 * 3;
  cout << "r4 " << r4<< endl;

  Rational r5 = 3 * r1;
  // r5 = 3.operator*(r1);  ?? 3 e' in int!
  cout << "r5 " << r5<< endl;

  try{ Rational r6(3,0);}
  catch(...){ cout << "Errore nel costruttore!" << endl;}

  Rational r7=-r1;
  cout << "r7 " << r7<< endl;

  Rational r8=r1.inv();
  cout << "r8 " << r8<< endl;

  Rational r9=r1/r7;
  cout << "r9 " << r9<< endl;

  Rational r10;
  std::cin >> r10;
  cout << "r10 " << r10<< endl;


}