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# This file is dual licensed under the terms of the Apache License, Version
# 2.0, and the BSD License. See the LICENSE file in the root of this repository
# for complete details.

class InfinityType:
    def __repr__(self) -> str:
        return "Infinity"

def __hash__(self) -> int:
        return hash(repr(self))

def __lt__(self, other: object) -> bool:
        return False

def __le__(self, other: object) -> bool:
        return False

def __eq__(self, other: object) -> bool:
        return isinstance(other, self.__class__)

def __gt__(self, other: object) -> bool:
        return True

def __ge__(self, other: object) -> bool:
        return True

def __neg__(self: object) -> "NegativeInfinityType":
        return NegativeInfinity

Infinity = InfinityType()

class NegativeInfinityType:
    def __repr__(self) -> str:
        return "-Infinity"

def __hash__(self) -> int:
        return hash(repr(self))

def __lt__(self, other: object) -> bool:
        return True

def __le__(self, other: object) -> bool:
        return True

def __eq__(self, other: object) -> bool:
        return isinstance(other, self.__class__)

def __gt__(self, other: object) -> bool:
        return False

def __ge__(self, other: object) -> bool:
        return False

def __neg__(self: object) -> InfinityType:
        return Infinity

NegativeInfinity = NegativeInfinityType()