from __future__ import division

import math

class Rational(object):

def __init__(self, numer, denom):

if denom!=0:

if denom<0:

self.numer = -numer/math.gcd(abs(numer),abs(denom))

self.denom = -denom/math.gcd(abs(numer),abs(denom))

else:

self.numer = numer/math.gcd(abs(numer),abs(denom))

self.denom = denom/math.gcd(abs(numer),abs(denom))

else:

raise ValueError('ValueError')

def __eq__(self, other):

return self.numer == other.numer and self.denom == other.denom

def __repr__(self):

return '{}/{}'.format(self.numer, self.denom)

def __add__(self, other):

return Rational(int(self.numer*other.denom + self.denom*other.numer),int(self.denom *other.denom))

def __sub__(self, other):

return Rational(int(self.numer*other.denom - self.denom*other.numer),int(self.denom *other.denom))

def __mul__(self, other):

return Rational(int(self.numer*other.numer),int(self.denom *other.denom))

def __truediv__(self, other):

return Rational(int(self.numer*other.denom),int(other.numer*self.denom) )

def __abs__(self):

return Rational( int(abs(self.numer)),int(abs(self.denom)))

def __pow__(self, power):

if type(power) is int:

if power>=0:

return Rational (int(self.numer**power),int(self.denom**power))

else:

return Rational(int(self.denom**abs(power)),int(self.numer**abs(power)))

else:

return Rational(int(self.numer**power),int(self.denom**power))

def __rpow__(self, base):

return (base**self.numer)**(1/self.denom)