pp

#include <iostream>
#include <vector>
#include <sstream>
#include <cctype>
#include <algorithm>
#include <iterator>
#include <cstdlib>
#include <vector>

int nod(int x, int y) {
    if (y == 0)
        return x;
    return nod(y, x % y);
}


class Rational {
public:
    int nom;
    int denom;

    Rational() {
        nom = 0;
        denom = 1;
    }

    Rational(const int &new_n, const int &new_d) {
        if (new_n == 0) {
            nom = 0;
            denom = 1;
         } else {
            nom = new_n;
            denom = new_d;
        }
    }

    const Rational simpl() const {
        Rational ans;
        ans.nom = nom;
        ans.denom = denom;
        if (nom != 0) {
            int tmp = nod(nom, denom);
            ans.nom /= tmp;
            ans.denom /= tmp;
        } else {
            ans.nom = 0;
            ans.denom = 1;
        }
        if (ans.denom < 0) {
            ans.nom *= -1;
            ans.denom *= -1;
            return (ans);
        }
        return ans;
    }

    int numerator() const {
        return simpl().nom;
    }

    int denominator() const {
        return simpl().denom;
    }
};

Rational int_to_rat(const int &n) {
    return Rational(n, 1);
}

const Rational operator+ (const Rational& l, const Rational& right) {
    Rational sum;
    sum.nom = l.nom * right.denom + right.nom * l.denom;
    sum.denom = l.denom * right.denom;
    return sum;
}

const Rational operator+ (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    Rational sum;
    sum.nom = l.nom * r.denom + r.nom * l.denom;
    sum.denom = l.denom * r.denom;
    return sum;
}

const Rational operator- (const Rational& l, const Rational& right) {
    Rational sum;
    sum.nom = l.nom * right.denom - right.nom * l.denom;
    sum.denom = l.denom * right.denom;
    return sum;
}

const Rational operator- (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    Rational sum;
    sum.nom = l.nom * r.denom - r.nom * l.denom;
    sum.denom = l.denom * r.denom;
    return sum;
}

const Rational operator* (const Rational& l, const Rational& right) {
    Rational sum;
    sum.nom = l.nom * right.nom;
    sum.denom = l.denom * right.denom;
    return sum;
}

const Rational operator* (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    Rational sum;
    sum.nom = l.nom * r.nom;
    sum.denom = l.denom * r.denom;
    return sum;
}

const Rational operator/ (const Rational& l, const Rational& right) {
    Rational sum;
    sum.nom = l.nom * right.denom;
    sum.denom = l.denom * right.nom;
    return sum;
}

const Rational operator/ (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    Rational sum;
    sum.nom = l.nom * r.denom;
    sum.denom = l.denom * r.nom;
    return sum;
}

template <typename T>
Rational operator+= (Rational& l, const T& right) {
    Rational ans = Rational(l.nom, l.denom) + right;
    l.nom = ans.nom;
    l.denom = ans.denom;
    return ans;
}

template <typename T>
Rational operator-= (Rational& l, const T& right) {
    Rational ans = Rational(l.nom, l.denom) - right;
    l.nom = ans.nom;
    l.denom = ans.denom;
    return ans;
}

template <typename T>
Rational operator*= (Rational& l, const T& right) {
    Rational ans = Rational(l.nom, l.denom) * right;
    l.nom = ans.nom;
    l.denom = ans.denom;
    return ans;
}

template <typename T>
Rational operator/= (Rational& l, const T& right) {
    Rational ans = Rational(l.nom, l.denom) / right;
    l.nom = ans.nom;
    l.denom = ans.denom;
    return ans;
}

bool operator== (const Rational& l, const Rational& right) {
    return ((l.numerator() == right.numerator()) && (l.denominator() == right.denominator()));
}

bool operator== (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    return ((l.numerator() == r.numerator()) && (l.denominator() == r.denominator()));
}

bool operator== (const int& l, const Rational& right) {
    Rational r = int_to_rat(l);
    return ((right.numerator() == r.numerator()) && (right.denominator() == r.denominator()));
}

bool operator!= (const Rational& l, const Rational& right) {
    return ((l.numerator() != right.numerator()) && (l.denominator() != right.denominator()));
}

bool operator!= (const Rational& l, const int& right) {
    Rational r = int_to_rat(right);
    return ((l.numerator() != r.numerator()) && (l.denominator() != r.denominator()));
}

bool operator!= (const int& l, const Rational& right) {
    Rational r = int_to_rat(l);
    return ((right.numerator() != r.numerator()) && (right.denominator() != r.denominator()));
}

Rational& operator++ (Rational& l) {
    l = l + 1;
    return l;
}

const Rational operator++ (Rational& l, int) {
    l.nom = l.nom + l.denom;
    return Rational(l.nom - l.denom, l.denom);
}

Rational& operator-- (Rational& l) {
    l = l - 1;
    return l;
}

const Rational operator-- (Rational& l, int) {
    l.nom = l.nom - l.denom;
    return Rational(l.nom + l.denom, l.denom);
}
Rational operator- (Rational& l) {
    l.nom = -l.nom;
    return Rational(l.nom, l.denom);
}
Rational operator+ (const Rational& l) {
    return Rational(l.nom, l.denom);
}

const Rational operator+ (const int& right, const Rational& r) {
    Rational l = {right, 1};
    Rational sum;
    sum.nom = l.nom * r.denom + r.nom * l.denom;
    sum.denom = l.denom * r.denom;
    return sum;
}

const Rational operator- (const int& right, const Rational& rr) {
    Rational r = Rational(right, 1);
    return (r - rr);
}
const Rational operator* (const int& right, const Rational& rr) {
    Rational r = Rational(right, 1);
    return (r * rr);
}

const Rational operator/ (const int& right, const Rational& rr) {
    Rational r = Rational(right, 1);
    return (r / rr);
}