



'''simple docstring'''

def 		_snake_case		(					_SCREAMING_SNAKE_CASE     :						int							)			->						bool:







	"""simple docstring"""
	if not isinstance(_SCREAMING_SNAKE_CASE							,		_SCREAMING_SNAKE_CASE							):
		lowerCAmelCase    =	f'Input value of [number={number}] must be an integer'
		raise TypeError(_SCREAMING_SNAKE_CASE							)
	if number < 0 or number % 2 == 1:
		return False
	lowerCAmelCase    =	int(number**0.5							)
	return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
				import doctest

				doctest.testmod()




'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

UpperCAmelCase			=    TypeVar('T', bound=bool)

class __snake_case(      Generic[T]					):


						'''simple docstring'''



						def __init__(					self	,       A_      )	->	None:
							lowerCAmelCase    =	value
							lowerCAmelCase    =	None
							lowerCAmelCase    =	None


						@property
						def 				__snake_case    (					self      )	->	T:
							return self._value




						@staticmethod
						def 				__snake_case    (					A_	,       A_      )	->	RandomizedHeapNode[T] | None:
							if not roota:
								return roota

							if not roota:
								return roota

							if roota.value > roota.value:
								lowerCAmelCase,   lowerCAmelCase    =	roota, roota

							if random.choice([True, False]      ):
								lowerCAmelCase,   lowerCAmelCase    =	roota.right, roota.left

							lowerCAmelCase    =	RandomizedHeapNode.merge(roota.left	,       A_      )

							return roota







class __snake_case(      Generic[T]					):


						'''simple docstring'''



						def __init__(					self	,       A_ = ()      )	->	None:
							lowerCAmelCase    =	None

							if data:
								for item in data:
									self.insert(A_      )


						def 				__snake_case    (					self	,       A_      )	->	None:
							lowerCAmelCase    =	RandomizedHeapNode.merge(self._root	,       RandomizedHeapNode(A_      )      )


						def 				__snake_case    (					self      )	->	T | None:
							lowerCAmelCase    =	self.top()

							if self._root is None:
								return None

							lowerCAmelCase    =	RandomizedHeapNode.merge(self._root.left	,       self._root.right      )

							return result


						def 				__snake_case    (					self      )	->	T:
							if not self._root:
								raise IndexError("""Can't get top element for the empty heap."""      )
							return self._root.value


						def 				__snake_case    (					self      )	->	None:
							lowerCAmelCase    =	None


						def 				__snake_case    (					self      )	->	list[Any]:
							lowerCAmelCase    =	[]
							while self:
								result.append(self.pop()      )

							return result




						def __bool__(					self      )	->	bool:
							return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()