cycle groups and sorting

wat.py

class Cmp:
    def __init__(self, value):
        self._value = value

    def __eq__(self, other: 'Cmp'):
        return self._value == other._value

    def __ne__(self, other: 'Cmp'):
        return self._value != other._value

    def __gt__(self, other: 'Cmp'):
        return (
            self._value == 'A' and other._value == 'B'
            or self._value == 'B' and other._value == 'C'
            or self._value == 'C' and other._value == 'A'
        )

    def __ge__(self, other: 'Cmp'):
        return self == other or self > other

    def __lt__(self, other: 'Cmp'):
        return (
            self._value == 'A' and other._value == 'C'
            or self._value == 'B' and other._value == 'A'
            or self._value == 'C' and other._value == 'B'
        )

    def __le__(self, other):
        return self == other or self < other

    def __str__(self):
        return self._value

    def __repr__(self):
        return self._value


x1 = [Cmp('A'), Cmp('B'), Cmp('C')]
x2 = [Cmp('A'), Cmp('C'), Cmp('C')]
x3 = [Cmp('B'), Cmp('A'), Cmp('B')]
x1.sort()
x2.sort()
x3.sort()
print(x1)  # [C, B, A]
print(x2)  # [A, C, C]
print(x3)  # [B, B, A]