



from __future__ import annotations

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

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





class    lowerCAmelCase__				(			Generic[T]       ):






						"""simple docstring"""




						def __init__(   self				,							a_     ):
							lowerCamelCase_			:							List[Any]      =       value
							lowerCamelCase_			:							Any      =       None
							lowerCamelCase_			:							List[str]      =       None




						@property
						def 					_UpperCamelCase			(   self     ):
							return self._value




						@staticmethod
						def 					_UpperCamelCase			(   a_				,							a_     ):
							if not roota:
								return roota

							if not roota:
								return roota

							if roota.value > roota.value:
								lowerCamelCase_   ,lowerCamelCase_			:							Dict      =       roota, roota

							lowerCamelCase_			:							Dict      =       roota
							lowerCamelCase_			:							List[str]      =       roota.right
							lowerCamelCase_			:							Any      =       roota.left
							lowerCamelCase_			:							Optional[int]      =       SkewNode.merge(a_				,							a_     )

							return result





class    lowerCAmelCase__				(			Generic[T]       ):






						"""simple docstring"""




						def __init__(   self				,							a_ = ()     ):
							lowerCamelCase_			:							Union[str, Any]      =       None
							if data:
								for item in data:
									self.insert(a_     )




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




						def __iter__(   self     ):
							lowerCamelCase_			:							List[Any]      =       []
							while self:
								result.append(self.pop()     )

							# Pushing items back to the heap not to clear it.
							for item in result:
								self.insert(a_     )

							return iter(a_     )




						def 					_UpperCamelCase			(   self				,							a_     ):
							lowerCamelCase_			:							int      =       SkewNode.merge(self._root				,							SkewNode(a_     )     )




						def 					_UpperCamelCase			(   self     ):
							lowerCamelCase_			:							Dict      =       self.top()
							lowerCamelCase_			:							List[Any]      =       (
							    SkewNode.merge(self._root.left				,							self._root.right     ) if self._root else None
							)

							return result




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




						def 					_UpperCamelCase			(   self     ):
							lowerCamelCase_			:							Optional[int]      =       None


if __name__ == "__main__":
							import doctest

							doctest.testmod()





def     __magic_name__  (      lowerCAmelCase_      ,					lowerCAmelCase_):
	'''simple docstring'''


	lowerCamelCase_			:							Union[str, Any]      =       0
	for ele in arr:
		total_sum += product_sum(lowerCAmelCase_      ,					depth + 1) if isinstance(lowerCAmelCase_      ,					lowerCAmelCase_) else ele
	return total_sum * depth







def     __magic_name__  (      lowerCAmelCase_):
	'''simple docstring'''


	return product_sum(lowerCAmelCase_      ,					1)


if __name__ == "__main__":
							import doctest

							doctest.testmod()

