from functools import total_ordering

@total_ordering
class Fraction:
    def __init__(self, numerator, denominator):
        numerator / denominator
        self.numerator = numerator
        self.denominator = denominator

    def _reduce(self):
        a = self.numerator
        b = self.denominator
        while b != 0:
            a, b = b, a % b
        self.numerator //= a
        self.denominator //= a
        return self

    def __add__(self, other):
        if type(other) == int:
            other = Fraction(other, 1)
        return Fraction(self.numerator * other.denominator + other.numerator * self.denominator,
                        self.denominator * other.denominator)
    def __sub__(self, other):
        if type(other) == int:
            other = Fraction(other, 1)
        return Fraction(self.numerator * other.denominator - other.numerator * self.denominator,
                        self.denominator * other.denominator)

    def __neg__(self):
        return Fraction(-self.numerator, self.denominator)

    def __float__(self):
        return self.numerator / self.denominator

    def __radd__(self, other):
        return self + other

    def __rsub__(self, other):
        return -self + other

    def __str__(self):
        self._reduce()
        return str(self.numerator) + '/' + str(self.denominator)

    def __eq__(self, other):
        self._reduce()
        other._reduce()
        return self.numerator == other.numerator and self.denominator == other.denominator

    def __lt__(self, other):
        self._reduce()
        other._reduce()
        return self.numerator * other.denominator - self.denominator * other.numerator < 0