ostream& operator<<(ostream& os, const zrf_Ratio& zrf_Ratio) {    os << zrf_Ratio.num << "/" << zrf_Ratio.den;    return os;}istream& operator>>(istream& in, zrf_Ratio& zrf_Ratio) {    in >> zrf_Ratio.num >> zrf_Ratio.den;    return in;}bool operator==(const zrf_Ratio& zrf_Ratio1, const zrf_Ratio& zrf_Ratio2) {    if (zrf_Ratio1.num == zrf_Ratio2.num &&        zrf_Ratio1.den == zrf_Ratio2.den) {        return 1;    }    return 0;}bool operator<(const zrf_Ratio& zrf_Ratio1, const zrf_Ratio& zrf_Ratio2) {    if (zrf_Ratio1.num * 1.0 / zrf_Ratio1.den <        zrf_Ratio2.num * 1.0 / zrf_Ratio2.den) {        return 1;    }    return 0;}