




'''simple docstring'''


from __future__ import annotations

from collections.abc import Iterator
from typing import Any





class  __lowercase    :







   def __init__(						self   ,				UpperCamelCase   )					->     Optional[int]:
     __a								=       data
     __a								=       None





class  __lowercase    :







   def __init__(						self   )					->     List[Any]:
     __a								=       None
     __a								=       None







   def __iter__(						self   )					->     Union[str, Any]:
     __a								=       self.head
     while self.head:
       yield node.data
       __a								=       node.next
       if node == self.head:
         break







   def __len__(						self   )					->     Dict:
     return sum(1 for _ in self   )







   def __repr__(						self   )					->     str:
     return "->".join(str(UpperCamelCase   ) for item in iter(self   )   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   )					->     Optional[int]:
     self.insert_nth(len(self   )   ,				UpperCamelCase   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   )					->     Any:
     self.insert_nth(0   ,				UpperCamelCase   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase   ,				UpperCamelCase   )					->     Optional[int]:
     if index < 0 or index > len(self   ):
       raise IndexError('list index out of range.'   )
     __a								=       Node(UpperCamelCase   )
     if self.head is None:
       __a								=       new_node  # first node points itself
       __a								=       new_node
     elif index == 0:  # insert at head
       __a								=       self.head
       __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   )					->     Optional[int]:
     return self.delete_nth(0   )







   def 		UpperCamelCase__      (						self   )					->     str:
     return self.delete_nth(len(self   ) - 1   )







   def 		UpperCamelCase__      (						self   ,				UpperCamelCase = 0   )					->     Tuple:
     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								=       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   )					->     int:
     return len(self   ) == 0


def     SCREAMING_SNAKE_CASE							(   ):
  __a								=       CircularLinkedList()
  assert len(lowercase__      ) == 0
  assert circular_linked_list.is_empty() is True
  assert str(lowercase__      ) == ""

  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(lowercase__      ) == i
    circular_linked_list.insert_nth(lowercase__					,       i + 1      )
  assert str(lowercase__      ) == "->".join(str(lowercase__      ) for i in range(1					,       6      )      )

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

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

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

  assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
  import doctest

  doctest.testmod()









"""simple docstring"""






from __future__ import annotations







def 	_snake_case     (							lowercase__						):  # This function is recursive
				_lowerCamelCase	:     Optional[Any]       =       len(lowercase__						)
				# If the array contains only one element, we return it (it's the stop condition of
				# recursion)
				if array_length <= 1:
								return array
								# Else
				_lowerCamelCase	:     Optional[Any]       =       array[0]
				_lowerCamelCase	:     Optional[int]       =       False
				_lowerCamelCase	:     List[str]       =       1
				_lowerCamelCase	:     list[int]       =       []
				while not is_found and i < array_length:
								if array[i] < pivot:
												_lowerCamelCase	:     Union[str, Any]       =       True
												_lowerCamelCase	:     str       =       [element for element in array[i:] if element >= array[i]]
												_lowerCamelCase	:     str       =       longest_subsequence(lowercase__						)
												if len(lowercase__						) > len(lowercase__						):
																_lowerCamelCase	:     Any       =       temp_array
								else:
												i += 1

				_lowerCamelCase	:     Optional[Any]       =       [element for element in array[1:] if element >= pivot]
				_lowerCamelCase	:     Dict       =       [pivot, *longest_subsequence(lowercase__						)]
				if len(lowercase__						) > len(lowercase__						):
								return temp_array
				else:
								return longest_subseq


if __name__ == "__main__":
			import doctest

			doctest.testmod()