


"""simple docstring"""






from __future__ import annotations

from collections.abc import Iterator
from typing import Any


class     __lowerCamelCase  :

     '''simple docstring'''


     def __init__(      self    ,				__UpperCAmelCase							)       ->							Dict:
          _a    	=				data
          _a    	=				None







class     __lowerCamelCase  :

     '''simple docstring'''


     def __init__(      self							)       ->							List[str]:
          _a    	=				None
          _a    	=				None


     def __iter__(      self							)       ->							Optional[int]:
          _a    	=				self.head
          while self.head:
               yield node.data
               _a    	=				node.next
               if node == self.head:
                    break


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


     def __repr__(      self							)       ->							Optional[Any]:
          return "->".join(str(_lowercase							) for item in iter(self							)							)


     def 							_UpperCAmelCase      (      self    ,				__UpperCAmelCase							)       ->							Tuple:
          self.insert_nth(len(self							)    ,				_lowercase							)


     def 							_UpperCAmelCase      (      self    ,				__UpperCAmelCase							)       ->							Any:
          self.insert_nth(0    ,				_lowercase							)


     def 							_UpperCAmelCase      (      self    ,				__UpperCAmelCase    ,				__UpperCAmelCase							)       ->							str:
          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							)       ->							int:
          return self.delete_nth(0							)


     def 							_UpperCAmelCase      (      self							)       ->							Optional[Any]:
          return self.delete_nth(len(self							) - 1							)


     def 							_UpperCAmelCase      (      self    ,				__UpperCAmelCase = 0							)       ->							Optional[int]:
          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							)       ->							Dict:
          return len(self							) == 0







def       A_   (   ):






     """simple docstring"""

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

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

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

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

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

     assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
   import doctest

   doctest.testmod()



"""simple docstring"""






def       A_   (   _lowerCAmelCase     :					list,     _lowerCAmelCase     :					list,     _lowerCAmelCase     :					int       ):






     """simple docstring"""

     _a    	=				len(_lowerCAmelCase       )
     _a    	=				[[0] * n for i in range(_lowerCAmelCase       )]
     for i in range(_lowerCAmelCase       ):
          _a    	=				y_points[i]

     for i in range(2,     _lowerCAmelCase       ):
          for j in range(_lowerCAmelCase,     _lowerCAmelCase       ):
               _a    	=				(
                   (xa - x_points[j - i + 1]) * q[j][i - 1]
                   - (xa - x_points[j]) * q[j - 1][i - 1]
               ) / (x_points[j] - x_points[j - i + 1])

     return [q[n - 1][n - 1], q]


if __name__ == "__main__":
   import doctest

   doctest.testmod()