

"""simple docstring"""




from __future__ import annotations
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__   ,      UpperCAmelCase__					:  Union[str, Any]					   =					position
 UpperCAmelCase__					:  Dict					   =					[
     (y + 1, x + 2),
     (y - 1, x + 2),
     (y + 1, x - 2),
     (y - 1, x - 2),
     (y + 2, x + 1),
     (y + 2, x - 1),
     (y - 2, x + 1),
     (y - 2, x - 1),
 ]
 UpperCAmelCase__					:  List[str]					   =					[]

 for position in positions:
  UpperCAmelCase__   ,      UpperCAmelCase__					:  Tuple					   =					position
  if 0 <= y_test < n and 0 <= x_test < n:
   permissible_positions.append(__lowerCAmelCase      )

 return permissible_positions
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 return not any(elem == 0 for row in board for elem in row      )
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 if is_complete(__lowerCAmelCase      ):
  return True

 for position in get_valid_pos(__lowerCAmelCase							,    len(__lowerCAmelCase      )      ):
  UpperCAmelCase__   ,      UpperCAmelCase__					:  int					   =					position

  if board[y][x] == 0:
   UpperCAmelCase__					:  int					   =					curr + 1
   if open_knight_tour_helper(__lowerCAmelCase							,    __lowerCAmelCase							,    curr + 1      ):
    return True
   UpperCAmelCase__					:  Optional[Any]					   =					0

 return False
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 UpperCAmelCase__					:  str					   =					[[0 for i in range(__lowerCAmelCase      )] for j in range(__lowerCAmelCase      )]

 for i in range(__lowerCAmelCase      ):
  for j in range(__lowerCAmelCase      ):
   UpperCAmelCase__					:  Union[str, Any]					   =					1
   if open_knight_tour_helper(__lowerCAmelCase							,    (i, j)							,    1      ):
    return board
   UpperCAmelCase__					:  Optional[int]					   =					0

 UpperCAmelCase__					:  Tuple					   =					F"Open Kight Tour cannot be performed on a board of size {n}"
 raise ValueError(__lowerCAmelCase      )


if __name__ == "__main__":
  import doctest

  doctest.testmod()








"""simple docstring"""




__UpperCAmelCase =				'Tobias Carryer'

from time import time







class      __lowercase			:

  def __init__(  self		:			Union[str, Any]					,A		:			Dict					,A		:			Optional[int]					,A		:			Union[str, Any]					,A		:			int=int(time()    )    ):  # noqa: B008






   '''simple docstring'''
   UpperCAmelCase__					:  int					   =					multiplier
   UpperCAmelCase__					:  Union[str, Any]					   =					increment
   UpperCAmelCase__					:  Dict					   =					modulo
   UpperCAmelCase__					:  Tuple					   =					seed




  def    __lowercase       (  self		:			Dict    ):






   '''simple docstring'''
   UpperCAmelCase__					:  Any					   =					(self.multiplier * self.seed + self.increment) % self.modulo
   return self.seed


if __name__ == "__main__":
      # Show the LCG in action.
      __UpperCAmelCase =				LinearCongruentialGenerator(166_4525, 10_1390_4223, 2 << 31)
      while True:
            print(lcg.next_number())





