from fractions import Fraction


class Fr(Fraction):
    def __repr__(self):
        return '(%s/%s)' % (self.numerator, self.denominator)


def farey(n, length=False):
    if not length:
        return [Fr(0, 1)] + sorted({Fr(m, k) for k in range(1, n+1) for m in range(1, k+1)})
    else:
        #return 1         +    len({Fr(m, k) for k in range(1, n+1) for m in range(1, k+1)})
        return  (n*(n+3))//2 - sum(farey(n//k, True) for k in range(2, n+1))

if __name__ == '__main__':
    print('Farey sequence for order 1 through 11 (inclusive):')
    for n in range(1, 12):
        print(farey(n))
    print('Number of fractions in the Farey sequence for order 100 through 1,000 (inclusive) by hundreds:')
    print([farey(i, length=True) for i in range(100, 1001, 100)])