

from __future__ import annotations



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							Union[str, Any]	,       SCREAMING_SNAKE_CASE_:							int	,       SCREAMING_SNAKE_CASE_:							int	,       SCREAMING_SNAKE_CASE_:							Dict      )			->      Union[str, Any]:  # noqa: E741




				'''simple docstring'''





				while r - l > 1:
								A__        =			(l + r) // 2
								if v[m] >= key:
												A__        =			m
								else:
												A__        =			m  # noqa: E741
				return r



def 					lowerCAmelCase__							(	SCREAMING_SNAKE_CASE_:							list[int]      )			->      int:




				'''simple docstring'''





				if len(SCREAMING_SNAKE_CASE_      ) == 0:
								return 0

				A__        =			[0] * len(SCREAMING_SNAKE_CASE_      )
				A__        =			1

				A__        =			v[0]

				for i in range(1	,       len(SCREAMING_SNAKE_CASE_      )      ):
								if v[i] < tail[0]:
												A__        =			v[i]
								elif v[i] > tail[length - 1]:
												A__        =			v[i]
												length += 1
								else:
												A__        =			v[i]

				return length


if __name__ == "__main__":
	import doctest

	doctest.testmod()




from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class 					a__						:
			"""simple docstring"""







			def __init__(    self      ,      lowercase       )  ->						int:
							'''simple docstring'''






							A__        =			data
							A__        =			None

class 					a__						:
			"""simple docstring"""







			def __init__(    self       )  ->						List[Any]:
							'''simple docstring'''






							A__        =			None
							A__        =			None


			def __iter__(    self       )  ->						Iterator[Any]:
							'''simple docstring'''






							A__        =			self.head
							while self.head:
											yield node.data
											A__        =			node.next
											if node == self.head:
															break


			def __len__(    self       )  ->						int:
							'''simple docstring'''






							return sum(1 for _ in self       )


			def __repr__(    self       )  ->						List[Any]:
							'''simple docstring'''






							return "->".join(str(lowercase       ) for item in iter(self       )       )


			def      UpperCamelCase		(    self      ,      lowercase       )  ->						None:
							'''simple docstring'''






							self.insert_nth(len(self       )      ,      lowercase       )


			def      UpperCamelCase		(    self      ,      lowercase       )  ->						None:
							'''simple docstring'''






							self.insert_nth(0      ,      lowercase       )


			def      UpperCamelCase		(    self      ,      lowercase      ,      lowercase       )  ->						None:
							'''simple docstring'''






							if index < 0 or index > len(self       ):
											raise IndexError("list index out of range."       )
							A__        =			Node(lowercase       )
							if self.head is None:
											A__        =			new_node  # first node points itself
											A__        =			A__        =			new_node
							elif index == 0:  # insert at head
											A__        =			self.head
											A__        =			A__        =			new_node
							else:
											A__        =			self.head
											for _ in range(index - 1       ):
															A__        =			temp.next
											A__        =			temp.next
											A__        =			new_node
											if index == len(self       ) - 1:  # insert at tail
															A__        =			new_node


			def      UpperCamelCase		(    self       )  ->						List[Any]:
							'''simple docstring'''






							return self.delete_nth(0       )


			def      UpperCamelCase		(    self       )  ->						Any:
							'''simple docstring'''






							return self.delete_nth(len(self       ) - 1       )


			def      UpperCamelCase		(    self      ,      lowercase = 0       )  ->						Any:
							'''simple docstring'''






							if not 0 <= index < len(self       ):
											raise IndexError("list index out of range."       )
							A__        =			self.head
							if self.head == self.tail:  # just one node
											A__        =			A__        =			None
							elif index == 0:  # delete head node
											A__        =			self.tail.next.next
											A__        =			self.head.next
							else:
											A__        =			self.head
											for _ in range(index - 1       ):
															A__        =			temp.next
											A__        =			temp.next
											A__        =			temp.next.next
											if index == len(self       ) - 1:  # delete at tail
															A__        =			temp
							return delete_node.data


			def      UpperCamelCase		(    self       )  ->						bool:
							'''simple docstring'''






							return len(self       ) == 0



def 					lowerCAmelCase__							(	)			->      None:




				'''simple docstring'''





				A__        =			CircularLinkedList()
				assert len(SCREAMING_SNAKE_CASE_      ) == 0
				assert circular_linked_list.is_empty() is True
				assert str(SCREAMING_SNAKE_CASE_      ) == ""

				try:
								circular_linked_list.delete_front()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_tail()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_nth(-1      )
								raise AssertionError
				except IndexError:
								assert True

				try:
								circular_linked_list.delete_nth(0      )
								raise AssertionError
				except IndexError:
								assert True

				assert circular_linked_list.is_empty() is True
				for i in range(5      ):
								assert len(SCREAMING_SNAKE_CASE_      ) == i
								circular_linked_list.insert_nth(SCREAMING_SNAKE_CASE_	,       i + 1      )
				assert str(SCREAMING_SNAKE_CASE_      ) == "->".join(str(SCREAMING_SNAKE_CASE_      ) for i in range(1	,       6      )      )

				circular_linked_list.insert_tail(6      )
				assert str(SCREAMING_SNAKE_CASE_      ) == "->".join(str(SCREAMING_SNAKE_CASE_      ) for i in range(1	,       7      )      )
				circular_linked_list.insert_head(0      )
				assert str(SCREAMING_SNAKE_CASE_      ) == "->".join(str(SCREAMING_SNAKE_CASE_      ) for i in range(0	,       7      )      )

				assert circular_linked_list.delete_front() == 0
				assert circular_linked_list.delete_tail() == 6
				assert str(SCREAMING_SNAKE_CASE_      ) == "->".join(str(SCREAMING_SNAKE_CASE_      ) for i in range(1	,       6      )      )
				assert circular_linked_list.delete_nth(2      ) == 3

				circular_linked_list.insert_nth(2	,       3      )
				assert str(SCREAMING_SNAKE_CASE_      ) == "->".join(str(SCREAMING_SNAKE_CASE_      ) for i in range(1	,       6      )      )

				assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
	import doctest

	doctest.testmod()

