


'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterator
from typing import Any
class 					lowercase_     :


    def __init__(     self  ,					a    ):
          UpperCamelCase__										=				data
          UpperCamelCase__										=				None

class 					lowercase_     :


    def __init__(     self    ):
          UpperCamelCase__										=				None
          UpperCamelCase__										=				None


    def __iter__(     self    ):
          UpperCamelCase__										=				self.head
          while self.head:
                yield node.data
                UpperCamelCase__										=				node.next
                if node == self.head:
                      break


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


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


    def    __a							(     self  ,					a    ):
          self.insert_nth(len(self    )  ,					a    )


    def    __a							(     self  ,					a    ):
          self.insert_nth(0  ,					a    )


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


    def    __a							(     self    ):
          return self.delete_nth(0    )


    def    __a							(     self    ):
          return self.delete_nth(len(self    ) - 1    )


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


    def    __a							(     self    ):
          return len(self    ) == 0







def _UpperCamelCase       (     )							->		None:


      '''simple docstring'''



      UpperCamelCase__										=				CircularLinkedList()
      assert len(__A    ) == 0
      assert circular_linked_list.is_empty() is True
      assert str(__A    ) == ""

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

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

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

      circular_linked_list.insert_nth(2      ,			3    )
      assert str(__A    ) == "->".join(str(__A    ) 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    a__       (  a__      ,    a__      ,    a__						):




     """simple docstring"""


     if len(a__						) == 0:
          raise ValueError("""find_max() arg is an empty sequence"""						)
     if (
         left >= len(a__						)
         or left < -len(a__						)
         or right >= len(a__						)
         or right < -len(a__						)
     ):
          raise IndexError("""list index out of range"""						)
     if left == right:
          return nums[left]
     __SCREAMING_SNAKE_CASE     =      (left + right) >> 1  # the middle
     __SCREAMING_SNAKE_CASE     =      find_max(a__      ,    a__      ,    a__						)  # find max in range[left, mid]
     __SCREAMING_SNAKE_CASE     =      find_max(a__      ,    mid + 1      ,    a__						)  # find max in range[mid + 1, right]

     return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
  import doctest

  doctest.testmod(verbose=True)






