



from __future__ import annotations

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

_lowercase:					Any      =						TypeVar("T", bound=bool)



class       _lowercase				(  Generic[T]      ):





	"""simple docstring"""




	def __init__(self						,			lowerCamelCase_						):
						"""simple docstring"""

						a   	=  value
						a   	=  None
						a   	=  None




	@property
	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						return self._value




	@staticmethod
	def 	UpperCamelCase_			(lowerCamelCase_						,			lowerCamelCase_						):
						"""simple docstring"""

						if not roota:
											return roota

						if not roota:
											return roota

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

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

						a   	=  RandomizedHeapNode.merge(roota.left						,			lowerCamelCase_						)

						return roota




class       _lowercase				(  Generic[T]      ):





	"""simple docstring"""




	def __init__(self						,			lowerCamelCase_ = ()						):
						"""simple docstring"""

						a   	=  None

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




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						a   	=  RandomizedHeapNode.merge(self._root						,			RandomizedHeapNode(lowerCamelCase_						)						)




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						a   	=  self.top()

						if self._root is None:
											return None

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

						return result




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

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




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						a   	=  None




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						a   	=  []
						while self:
											result.append(self.pop()						)

						return result




	def __bool__(self						):
						"""simple docstring"""

						return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()





def        a( A			:       int					,	A			:       int					,	A			:       int			)						->			float:
					"""simple docstring"""





					if common_ratio == 1:
										# Formula for sum if common ratio is 1
										return num_of_terms * first_term

					# Formula for finding sum of n terms of a GeometricProgression
					return (first_term / (1 - common_ratio)) * (1 - common_ratio**num_of_terms)
