




'''simple docstring'''






def       __lowerCAmelCase (   snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__						):

			if start == end:
						return start if lst[start] > item else start + 1
			if start > end:
						return start

			__UpperCamelCase				:      Tuple									=       (start + end) // 2
			if lst[mid] < item:
						return binary_search(SCREAMING_SNAKE_CASE_ ,				SCREAMING_SNAKE_CASE_ ,				mid + 1 ,				SCREAMING_SNAKE_CASE_						)
			elif lst[mid] > item:
						return binary_search(SCREAMING_SNAKE_CASE_ ,				SCREAMING_SNAKE_CASE_ ,				SCREAMING_SNAKE_CASE_ ,				mid - 1						)
			else:
						return mid

def       __lowerCAmelCase (   snake_case__						):
			__UpperCamelCase				:      int									=       len(SCREAMING_SNAKE_CASE_						)

			for index in range(1 ,				SCREAMING_SNAKE_CASE_						):
						__UpperCamelCase				:      List[Any]									=       lst[index]
						__UpperCamelCase				:      List[str]									=       binary_search(SCREAMING_SNAKE_CASE_ ,				SCREAMING_SNAKE_CASE_ ,				0 ,				index - 1						)
						__UpperCamelCase				:      Union[str, Any]									=       lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

			return lst

def       __lowerCAmelCase (   snake_case__ ,				snake_case__						):

			if not left:
						return right

			if not right:
						return left

			if left[0] < right[0]:
						return [left[0], *merge(left[1:] ,				SCREAMING_SNAKE_CASE_						)]

			return [right[0], *merge(SCREAMING_SNAKE_CASE_ ,				right[1:]						)]

def       __lowerCAmelCase (   snake_case__						):
			__UpperCamelCase				:      List[Any]									=       len(SCREAMING_SNAKE_CASE_						)
			__UpperCamelCase				:      List[str]									=       [], []
			__UpperCamelCase				:      Union[str, Any]									=       [lst[0]]
			__UpperCamelCase				:      Optional[Any]									=       []
			__UpperCamelCase				:      int									=       1
			while i < length:
						if lst[i] < lst[i - 1]:
									runs.append(SCREAMING_SNAKE_CASE_						)
									__UpperCamelCase				:      Any									=       [lst[i]]
						else:
									new_run.append(lst[i]						)
						i += 1
			runs.append(SCREAMING_SNAKE_CASE_						)

			for run in runs:
						sorted_runs.append(insertion_sort(SCREAMING_SNAKE_CASE_						)						)
			for run in sorted_runs:
						__UpperCamelCase				:      int									=       merge(SCREAMING_SNAKE_CASE_ ,				SCREAMING_SNAKE_CASE_						)

			return sorted_array

def       __lowerCAmelCase (   ):
			__UpperCamelCase				:      Tuple									=       [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
			__UpperCamelCase				:      List[Any]									=       tim_sort(SCREAMING_SNAKE_CASE_						)
			print(SCREAMING_SNAKE_CASE_						)


if __name__ == "__main__":
				main()





'''simple docstring'''






from __future__ import annotations

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

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



class  A		(			Generic[T]		):




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase      )     ->	None:
							__UpperCamelCase				:      T									=       value
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None
				@property
				def 	a_	(self      )     ->	T:
							return self._value





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

							if not roota:
										return roota

							if roota.value > roota.value:
										__UpperCamelCase		, __UpperCamelCase				:      int									=       roota, roota

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

							__UpperCamelCase				:      Any									=       RandomizedHeapNode.merge(roota.left			,  _UpperCAmelCase      )

							return roota







class  A		(			Generic[T]		):




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase = ()      )     ->	None:
							__UpperCamelCase				:      RandomizedHeapNode[T] | None									=       None

							if data:
										for item in data:
													self.insert(_UpperCAmelCase      )
				def 	a_	(self			,  _UpperCAmelCase      )     ->	None:
							__UpperCamelCase				:      str									=       RandomizedHeapNode.merge(self._root			,  RandomizedHeapNode(_UpperCAmelCase      )      )
				def 	a_	(self      )     ->	T | None:
							__UpperCamelCase				:      Dict									=       self.top()

							if self._root is None:
										return None

							__UpperCamelCase				:      List[str]									=       RandomizedHeapNode.merge(self._root.left			,  self._root.right      )

							return result
				def 	a_	(self      )     ->	T:
							if not self._root:
										raise IndexError("Can't get top element for the empty heap."      )
							return self._root.value
				def 	a_	(self      )     ->	None:
							__UpperCamelCase				:      int									=       None
				def 	a_	(self      )     ->	list[Any]:
							__UpperCamelCase				:      int									=       []
							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()



