
"""simple docstring"""


_lowercase							      = {
    0: '''0''',
    1: '''1''',
    2: '''2''',
    3: '''3''',
    4: '''4''',
    5: '''5''',
    6: '''6''',
    7: '''7''',
    8: '''8''',
    9: '''9''',
    10: '''a''',
    11: '''b''',
    12: '''c''',
    13: '''d''',
    14: '''e''',
    15: '''f''',
}






def 					_snake_case (						snake_case__      :   float   ):
	assert type(__snake_case   ) in (int, float) and decimal == int(__snake_case   )
	A        =      int(__snake_case   )
	A        =      ''
	A        =      False
	if decimal < 0:
		A        =      True
		decimal *= -1
	while decimal > 0:
		A        =      divmod(__snake_case		,					16   )
		A        =      values[remainder] + hexadecimal
	A        =      '0x' + hexadecimal
	if negative:
		A        =      '-' + hexadecimal
	return hexadecimal


if __name__ == "__main__":
		import doctest

		doctest.testmod()







from __future__ import annotations




def      lowercase__      (     __snake_case    :							tuple[int, int]     ,       __snake_case    :							int  ):


					'''simple docstring'''


					UpperCAmelCase_       ,  UpperCAmelCase_    :      Tuple            =						position
					UpperCAmelCase_    :      str            =						[
					    (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_    :      Optional[Any]            =						[]

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

					return permissible_positions




def      lowercase__      (     __snake_case    :							list[list[int]]  ):


					'''simple docstring'''


					return not any(elem == 0 for row in board for elem in row  )




def      lowercase__      (     __snake_case    :							list[list[int]]     ,       __snake_case    :							tuple[int, int]     ,       __snake_case    :							int  ):


					'''simple docstring'''


					if is_complete(__snake_case  ):
										return True

					for position in get_valid_pos(__snake_case     ,       len(__snake_case  )  ):
										UpperCAmelCase_       ,  UpperCAmelCase_    :      Any            =						position

										if board[y][x] == 0:
															UpperCAmelCase_    :      Optional[Any]            =						curr + 1
															if open_knight_tour_helper(__snake_case     ,       __snake_case     ,       curr + 1  ):
																				return True
															UpperCAmelCase_    :      List[Any]            =						0

					return False




def      lowercase__      (     __snake_case    :							int  ):


					'''simple docstring'''


					UpperCAmelCase_    :      str            =						[[0 for i in range(__snake_case  )] for j in range(__snake_case  )]

					for i in range(__snake_case  ):
										for j in range(__snake_case  ):
															UpperCAmelCase_    :      Optional[Any]            =						1
															if open_knight_tour_helper(__snake_case     ,       (i, j)     ,       1  ):
																				return board
															UpperCAmelCase_    :      List[Any]            =						0

					UpperCAmelCase_    :      List[str]            =						F"Open Kight Tour cannot be performed on a board of size {n}"
					raise ValueError(__snake_case  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()






