
"""simple docstring"""




from __future__ import annotations

from typing import Any

class __snake_case		:
    def __init__(  self		,snake_case = 6				):



           '''simple docstring'''







           lowercase							:					Node | None	     =				None
           lowercase							:					Node | None	     =				None
           self.create_linked_list(snake_case				)
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case				):



           '''simple docstring'''







           lowercase							:					Tuple	     =				Node()
           lowercase							:					List[Any]	     =				current_node
           lowercase							:					Any	     =				current_node
           lowercase							:					Dict	     =				current_node
           for _ in range(1		,snake_case				):
                  lowercase							:					List[Any]	     =				Node()
                  lowercase							:					Dict	     =				current_node
                  lowercase							:					Union[str, Any]	     =				previous_node
                  lowercase							:					List[Any]	     =				current_node
           lowercase							:					List[str]	     =				self.front
           lowercase							:					List[str]	     =				previous_node
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           return (
               self.front == self.rear
               and self.front is not None
               and self.front.data is None
           )
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           self.check_can_perform_operation()
           return self.front.data if self.front else None
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case				):



           '''simple docstring'''







           if self.rear is None:
                  return

           self.check_is_full()
           if not self.is_empty():
                  lowercase							:					Dict	     =				self.rear.next
           if self.rear:
                  lowercase							:					Optional[int]	     =				data
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           self.check_can_perform_operation()
           if self.rear is None or self.front is None:
                  return None
           if self.front == self.rear:
                  lowercase							:					Optional[int]	     =				self.front.data
                  lowercase							:					List[str]	     =				None
                  return data

           lowercase							:					Dict	     =				self.front
           lowercase							:					List[Any]	     =				old_front.next
           lowercase							:					Union[str, Any]	     =				old_front.data
           lowercase							:					int	     =				None
           return data
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           if self.is_empty():
                  raise Exception("""Empty Queue"""				)
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           if self.rear and self.rear.next == self.front:
                  raise Exception("""Full Queue"""				)






class __snake_case		:
    def __init__(  self				):



           '''simple docstring'''







           lowercase							:					Any | None	     =				None
           lowercase							:					Node | None	     =				None
           lowercase							:					Node | None	     =				None


if __name__ == "__main__":
  import doctest

  doctest.testmod()


from __future__ import annotations

import numpy as np







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   tuple[np.ndarray, np.ndarray]:
       lowercase     ,      lowercase							:					Dict	     =				np.shape(SCREAMING_SNAKE_CASE__    )
       if rows != columns:
              lowercase							:					str	     =				(
                  """'table' has to be of square shaped array but got a """
                  f"{rows}x{columns} array:\n{table}"
              )
              raise ValueError(SCREAMING_SNAKE_CASE__    )

       lowercase							:					Any	     =				np.zeros((rows, columns)    )
       lowercase							:					int	     =				np.zeros((rows, columns)    )
       for i in range(SCREAMING_SNAKE_CASE__    ):
              for j in range(SCREAMING_SNAKE_CASE__    ):
                     lowercase							:					Optional[int]	     =				sum(lower[i][k] * upper[k][j] for k in range(SCREAMING_SNAKE_CASE__    )    )
                     if upper[j][j] == 0:
                            raise ArithmeticError("""No LU decomposition exists"""    )
                     lowercase							:					str	     =				(table[i][j] - total) / upper[j][j]
              lowercase							:					Optional[Any]	     =				1
              for j in range(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    ):
                     lowercase							:					Any	     =				sum(lower[i][k] * upper[k][j] for k in range(SCREAMING_SNAKE_CASE__    )    )
                     lowercase							:					Tuple	     =				table[i][j] - total
       return lower, upper


if __name__ == "__main__":
  import doctest

  doctest.testmod()
