from typing import Any





class      A							:


   def __init__(self     :						List[str]       ,  __UpperCAmelCase     :						Any		)						->				List[Any]:
         """simple docstring"""



         UpperCAmelCase__								=  data
         UpperCAmelCase__								=  None





   def __repr__(self     :						Union[str, Any]		)						->				str:
         """simple docstring"""



         return f"""Node({self.data})"""





class      A							:


   def __init__(self     :						Dict		)						->				Optional[int]:
         """simple docstring"""



         UpperCAmelCase__								=  None


   def __iter__(self     :						Optional[int]		)						->				Any:
         """simple docstring"""



         UpperCAmelCase__								=  self.head
         while node:
               yield node.data
               UpperCAmelCase__								=  node.next


   def __len__(self     :						Optional[Any]		)						->				int:
         """simple docstring"""



         return sum(1 for _ in self		)


   def __repr__(self     :						Optional[int]		)						->				str:
         """simple docstring"""



         return "->".join([str(UpperCAmelCase__		) for item in self]		)


   def __getitem__(self     :						int       ,  __UpperCAmelCase     :						int		)						->				Any:
         """simple docstring"""



         if not 0 <= index < len(self		):
               raise ValueError("list index out of range."		)
         for i, node in enumerate(self		):
               if i == index:
                     return node
         return None


   def __setitem__(self     :						Tuple       ,  __UpperCAmelCase     :						int       ,  __UpperCAmelCase     :						Any		)						->				None:
         """simple docstring"""



         if not 0 <= index < len(self		):
               raise ValueError("list index out of range."		)
         UpperCAmelCase__								=  self.head
         for _ in range(UpperCAmelCase__		):
               UpperCAmelCase__								=  current.next
         UpperCAmelCase__								=  data


   def 			lowercase_      (self     :						Optional[int]       ,  __UpperCAmelCase     :						Any		)						->				None:
         """simple docstring"""



         self.insert_nth(len(self		)       ,  UpperCAmelCase__		)


   def 			lowercase_      (self     :						Union[str, Any]       ,  __UpperCAmelCase     :						Any		)						->				None:
         """simple docstring"""



         self.insert_nth(0       ,  UpperCAmelCase__		)


   def 			lowercase_      (self     :						Union[str, Any]       ,  __UpperCAmelCase     :						int       ,  __UpperCAmelCase     :						Any		)						->				None:
         """simple docstring"""



         if not 0 <= index <= len(self		):
               raise IndexError("list index out of range"		)
         UpperCAmelCase__								=  Node(UpperCAmelCase__		)
         if self.head is None:
               UpperCAmelCase__								=  new_node
         elif index == 0:
               UpperCAmelCase__								=  self.head  # link new_node to head
               UpperCAmelCase__								=  new_node
         else:
               UpperCAmelCase__								=  self.head
               for _ in range(index - 1		):
                     UpperCAmelCase__								=  temp.next
               UpperCAmelCase__								=  temp.next
               UpperCAmelCase__								=  new_node


   def 			lowercase_      (self     :						str		)						->				None:  # print every node data
         """simple docstring"""



         print(self		)


   def 			lowercase_      (self     :						List[str]		)						->				Any:
         """simple docstring"""



         return self.delete_nth(0		)


   def 			lowercase_      (self     :						Union[str, Any]		)						->				Any:  # delete from tail
         """simple docstring"""



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


   def 			lowercase_      (self     :						str       ,  __UpperCAmelCase     :						int = 0		)						->				Any:
         """simple docstring"""



         if not 0 <= index <= len(self		) - 1:  # test if index is valid
               raise IndexError("List index out of range."		)
         UpperCAmelCase__								=  self.head  # default first node
         if index == 0:
               UpperCAmelCase__								=  self.head.next
         else:
               UpperCAmelCase__								=  self.head
               for _ in range(index - 1		):
                     UpperCAmelCase__								=  temp.next
               UpperCAmelCase__								=  temp.next
               UpperCAmelCase__								=  temp.next.next
         return delete_node.data


   def 			lowercase_      (self     :						Optional[Any]		)						->				bool:
         """simple docstring"""



         return self.head is None





   def 			lowercase_      (self     :						List[str]		)						->				None:
         """simple docstring"""



         UpperCAmelCase__								=  None
         UpperCAmelCase__								=  self.head

         while current:
               # Store the current node's next node.
               UpperCAmelCase__								=  current.next
               # Make the current node's next point backwards
               UpperCAmelCase__								=  prev
               # Make the previous node be the current node
               UpperCAmelCase__								=  current
               # Make the current node the next node (to progress iteration)
               UpperCAmelCase__								=  next_node
         # Return prev in order to put the head at the end
         UpperCAmelCase__								=  prev




def    lowerCAmelCase_ (     )     ->				Any:







      '''simple docstring'''


      UpperCAmelCase__								=  LinkedList()
      assert linked_list.is_empty() is True
      assert str(UpperCamelCase__							) == ""

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

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

      for i in range(10							):
            assert len(UpperCamelCase__							) == i
            linked_list.insert_nth(UpperCamelCase__,  i + 1							)
      assert str(UpperCamelCase__							) == "->".join(str(UpperCamelCase__							) for i in range(1,  11							)							)

      linked_list.insert_head(0							)
      linked_list.insert_tail(11							)
      assert str(UpperCamelCase__							) == "->".join(str(UpperCamelCase__							) for i in range(0,  12							)							)

      assert linked_list.delete_head() == 0
      assert linked_list.delete_nth(9							) == 10
      assert linked_list.delete_tail() == 11
      assert len(UpperCamelCase__							) == 9
      assert str(UpperCamelCase__							) == "->".join(str(UpperCamelCase__							) for i in range(1,  10							)							)

      assert all(linked_list[i] == i + 1 for i in range(0,  9							)							) is True

      for i in range(0,  9							):
            UpperCAmelCase__								=  -i
      assert all(linked_list[i] == -i for i in range(0,  9							)							) is True

      linked_list.reverse()
      assert str(UpperCamelCase__							) == "->".join(str(UpperCamelCase__							) for i in range(-8,  1							)							)




def    lowerCAmelCase_ (     )     ->				Any:







      '''simple docstring'''


      UpperCAmelCase__								=  [
          -9,
          100,
          Node(77_345_112							),
          """dlrow olleH""",
          7,
          5_555,
          0,
          -192.55555,
          """Hello, world!""",
          77.9,
          Node(10							),
          None,
          None,
          12.20,
      ]
      UpperCAmelCase__								=  LinkedList()

      for i in test_input:
            linked_list.insert_tail(UpperCamelCase__							)

      # Check if it's empty or not
      assert linked_list.is_empty() is False
      assert (
          str(UpperCamelCase__							) == "-9->100->Node(77345112)->dlrow olleH->7->5555->0->"
          "-192.55555->Hello, world!->77.9->Node(10)->None->None->12.2"
      )

      # Delete the head
      UpperCAmelCase__								=  linked_list.delete_head()
      assert result == -9
      assert (
          str(UpperCamelCase__							) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
          "Hello, world!->77.9->Node(10)->None->None->12.2"
      )

      # Delete the tail
      UpperCAmelCase__								=  linked_list.delete_tail()
      assert result == 12.2
      assert (
          str(UpperCamelCase__							) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
          "Hello, world!->77.9->Node(10)->None->None"
      )

      # Delete a node in specific location in linked list
      UpperCAmelCase__								=  linked_list.delete_nth(10							)
      assert result is None
      assert (
          str(UpperCamelCase__							) == "100->Node(77345112)->dlrow olleH->7->5555->0->-192.55555->"
          "Hello, world!->77.9->Node(10)->None"
      )

      # Add a Node instance to its head
      linked_list.insert_head(Node("Hello again, world!"							)							)
      assert (
          str(UpperCamelCase__							)
          == "Node(Hello again, world!)->100->Node(77345112)->dlrow olleH->"
          "7->5555->0->-192.55555->Hello, world!->77.9->Node(10)->None"
      )

      # Add None to its tail
      linked_list.insert_tail(UpperCamelCase__							)
      assert (
          str(UpperCamelCase__							)
          == "Node(Hello again, world!)->100->Node(77345112)->dlrow olleH->"
          "7->5555->0->-192.55555->Hello, world!->77.9->Node(10)->None->None"
      )

      # Reverse the linked list
      linked_list.reverse()
      assert (
          str(UpperCamelCase__							)
          == "None->None->Node(10)->77.9->Hello, world!->-192.55555->0->5555->"
          "7->dlrow olleH->Node(77345112)->100->Node(Hello again, world!)"
      )




def    lowerCAmelCase_ (     )     ->				Optional[Any]:







      '''simple docstring'''


      from doctest import testmod

      testmod()

      UpperCAmelCase__								=  LinkedList()
      linked_list.insert_head(input("Inserting 1st at head "							).strip()							)
      linked_list.insert_head(input("Inserting 2nd at head "							).strip()							)
      print("\nPrint list:"							)
      linked_list.print_list()
      linked_list.insert_tail(input("\nInserting 1st at tail "							).strip()							)
      linked_list.insert_tail(input("Inserting 2nd at tail "							).strip()							)
      print("\nPrint list:"							)
      linked_list.print_list()
      print("\nDelete head"							)
      linked_list.delete_head()
      print("Delete tail"							)
      linked_list.delete_tail()
      print("\nPrint list:"							)
      linked_list.print_list()
      print("\nReverse linked list"							)
      linked_list.reverse()
      print("\nPrint list:"							)
      linked_list.print_list()
      print("\nString representation of linked list:"							)
      print(UpperCamelCase__							)
      print("\nReading/changing Node data using indexing:"							)
      print(f"""Element at Position 1: {linked_list[1]}"""							)
      UpperCAmelCase__								=  input("Enter New Value: "							).strip()
      print("New list:"							)
      print(UpperCamelCase__							)
      print(f"""length of linked_list is : {len(UpperCamelCase__							)}"""							)


if __name__ == "__main__":
      main()











"""simple docstring"""




import unittest

import numpy as np

def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__ = None     ,   ):



  '''simple docstring'''
  _a  :       List[Any]             =	np.shape(UpperCamelCase__				)
  _a  :       Any             =	np.shape(UpperCamelCase__				)
  _a  :       Union[str, Any]             =	np.shape(UpperCamelCase__				)

  if shape_a[0] != shape_b[0]:
    _a  :       int             =	(
        """Expected the same number of rows for A and B. """
        F"""Instead found A of size {shape_a} and B of size {shape_b}"""
    )
    raise ValueError(UpperCamelCase__				)

  if shape_b[1] != shape_c[1]:
    _a  :       Tuple             =	(
        """Expected the same number of columns for B and C. """
        F"""Instead found B of size {shape_b} and C of size {shape_c}"""
    )
    raise ValueError(UpperCamelCase__				)

  _a  :       int             =	pseudo_inv
  if a_inv is None:
    try:
      _a  :       Optional[int]             =	np.linalg.inv(UpperCamelCase__				)
    except np.linalg.LinAlgError:
      raise ValueError(
          """Input matrix A is not invertible. Cannot compute Schur complement."""				)

  return mat_c - mat_b.T @ a_inv @ mat_b






class        UpperCamelCase			(	unittest.TestCase      ):


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       str             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Tuple             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Optional[int]             =	np.array([[2, 1], [6, 3]]							)

   _a  :       Optional[Any]             =	schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)

   _a  :       Union[str, Any]             =	np.block([[a, b], [b.T, c]]							)

   _a  :       int             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       Union[str, Any]             =	np.linalg.det(UpperCAmelCase__							)
   _a  :       List[Any]             =	np.linalg.det(UpperCAmelCase__							)

   self.assertAlmostEqual(UpperCAmelCase__							,						det_a * det_s							)


 def _lowercase	(     self		:						int							)					->       None:
   _a  :       Optional[int]             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Optional[int]             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       Union[str, Any]             =	np.array([[2, 1], [6, 3]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)







 def _lowercase	(     self		:						List[Any]							)					->       None:
   _a  :       Any             =	np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]							)
   _a  :       Dict             =	np.array([[0, 3], [3, 0], [2, 3]]							)
   _a  :       List[Any]             =	np.array([[2, 1, 3], [6, 3, 5]]							)

   with self.assertRaises(UpperCAmelCase__							):
     schur_complement(UpperCAmelCase__							,						UpperCAmelCase__							,						UpperCAmelCase__							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 unittest.main()

