import math
from typing import *


class Fraction:
    """Class for functions with fractions"""
    def __init__(self: "Fraction", a: Any = 0, b: int = 1):
        if isinstance(a, str):
            if a.find("/") != -1:
                self.a, self.b = list(map(int, a.split("/")))
                self.reduce()
            elif a.find(" ") != -1:
                self.a, self.b = list(map(int, a.split()))
                self.reduce()
            else:
                self.a = int(a)
                self.b = 1
                self.reduce()
        elif isinstance(a, int) and isinstance(b, int):
            self.a = a
            self.b = b
            self.reduce()
        elif isinstance(a, Fraction):
            self.a = a.a
            self.b = a.b
            self.reduce()

    def __str__(self) -> str:
        if self.b == 1:
            return str(self.a)
        else:
            return str(self.a) + "/" + str(self.b)

    def reduce(self: "Fraction") -> None:
        gcd = math.gcd(self.a, self.b)
        self.a = self.a // gcd
        self.b = self.b // gcd
        if self.b < 0:
            self.a = -self.a
            self.b = -self.b

    def __lt__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b < other.a * self.b)
        else:
            return(self.a < other * self.b)

    def __le__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b <= other.a * self.b)
        else:
            return(self.a <= other * self.b)

    def __eq__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b == other.a * self.b)
        else:
            return(self.a == other * self.b)

    def __ne__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b != other.a * self.b)
        else:
            return(self.a != other * self.b)

    def __gt__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b > other.a * self.b)
        else:
            return(self.a > other * self.b)

    def __ge__(self: "Fraction", other: Any) -> bool:
        if isinstance(other, Fraction):
            return(self.a * other.b >= other.a * self.b)
        else:
            return(self.a >= other * self.b)

    def __mul__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.a * other.a, self.b * other.b))
        elif isinstance(other, int):
            return(Fraction(self.a * other, self.b))
        elif isinstance(other, float):
            return((self.a * other) / self.b)

    def __rmul__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.a * other.a, self.b * other.b))
        elif isinstance(other, int):
            return(Fraction(self.a * other, self.b))
        elif isinstance(other, float):
            return((self.a * other) / self.b)

    def __imul__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            self.a *= other.a
            self.b *= other.b
            return(Fraction(self.a, self.b))
        elif isinstance(other, int):
            self.a *= other
            return(Fraction(self.a, self.b))
        elif isinstance(other, float):
            return((self.a * other) / self.b)

    def __truediv__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.a * other.b, self.b * other.a))
        elif isinstance(other, int):
            return(Fraction(self.a, self.b * other))
        elif isinstance(other, float):
            return(self.a / (self.b * other))

    def __rtruediv__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.b * other.a, self.a * other.b))
        elif isinstance(other, int):
            return(Fraction(self.b * other, self.a))
        elif isinstance(other, float):
            return((self.b * other) / self.a)

    def __itruediv__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            new_a = self.a * other.b
            new_b = self.b * other.a
            return(Fraction(new_a, new_b))
        elif isinstance(other, int):
            self.b *= other
            return(Fraction(self.a, self.b))
        elif isinstance(other, float):
            return(self.a / (self.b * other))

    def __add__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.a * other.b + other.a * self.b, self.b * other.b))
        elif isinstance(other, int):
            return(Fraction(self.a + self.b * other, self.b))
        elif isinstance(other, float):
            return((self.a / self.b) + other)

    def __radd__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            return(Fraction(self.a * other.b + other.a * self.b, self.b * other.b))
        elif isinstance(other, int):
            return(Fraction(self.a + self.b * other, self.b))
        elif isinstance(other, float):
            return((self.a / self.b) + other)

    def __iadd__(self: "Fraction", other: Any) -> Any:
        if isinstance(other, Fraction):
            new_a = self.a * other.b + other.a * self.b
            new_b = self.b * other.b
            return(Fraction(new_a, new_b))
        elif isinstance(other, int):
            self.a = self.a + self.b * other
            return(Fraction(self.a, self.b))
        elif isinstance(other, float):
            return((self.a / self.b) + other)