






from __future__ import annotations

UpperCamelCase								=		list[list[int]]

# assigning initial values to the grid
UpperCamelCase								=		[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
UpperCamelCase								=		[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]






def    __magic_name__    (	SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE				)     ->    bool:
							for i in range(9				):
														if grid[row][i] == n or grid[i][column] == n:
																					return False

							for i in range(3				):
														for j in range(3				):
																					if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
																												return False

							return True






def    __magic_name__    (	SCREAMING_SNAKE_CASE				)     ->    tuple[int, int] | None:
							for i in range(9				):
														for j in range(9				):
																					if grid[i][j] == 0:
																												return i, j
							return None






def    __magic_name__    (	SCREAMING_SNAKE_CASE				)     ->    Matrix | None:
							if location := find_empty_location(SCREAMING_SNAKE_CASE				):
														_lowercase							,							_lowercase							:   Any 							=   location
							else:
														# If the location is ``None``, then the grid is solved.
														return grid

							for digit in range(1     ,     10				):
														if is_safe(SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE     ,     SCREAMING_SNAKE_CASE				):
																					_lowercase							:   Optional[Any] 							=   digit

																					if sudoku(SCREAMING_SNAKE_CASE				) is not None:
																												return grid

																					_lowercase							:   List[Any] 							=   0

							return None






def    __magic_name__    (	SCREAMING_SNAKE_CASE				)     ->    None:
							for row in grid:
														for cell in row:
																					print(SCREAMING_SNAKE_CASE     ,     end=' '				)
														print()


if __name__ == "__main__":
							# make a copy of grid so that you can compare with the unmodified grid
							for example_grid in (initial_grid, no_solution):
														print("\nExample grid:\n" + "=" * 20)
														print_solution(example_grid)
														print("\nExample grid solution:")
														UpperCamelCase								=		sudoku(example_grid)
														if solution is not None:
																					print_solution(solution)
														else:
																					print("Cannot find a solution.")







from math import factorial, pi

def 			lowerCamelCase__			(       _a				,      _a = 30):

	if not isinstance(_a				,      (int, float)):
		raise ValueError("maclaurin_sin() requires either an int or float for theta")

	if not isinstance(_a				,      _a) or accuracy <= 0:
		raise ValueError("maclaurin_sin() requires a positive int for accuracy")

	SCREAMING_SNAKE_CASE :   int					  =							float(_a)
	SCREAMING_SNAKE_CASE :   Dict					  =							theta // (2 * pi)
	theta -= 2 * div * pi
	return sum(
	    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1) for r in range(_a))

def 			lowerCamelCase__			(       _a				,      _a = 30):

	if not isinstance(_a				,      (int, float)):
		raise ValueError("maclaurin_cos() requires either an int or float for theta")

	if not isinstance(_a				,      _a) or accuracy <= 0:
		raise ValueError("maclaurin_cos() requires a positive int for accuracy")

	SCREAMING_SNAKE_CASE :   str					  =							float(_a)
	SCREAMING_SNAKE_CASE :   Any					  =							theta // (2 * pi)
	theta -= 2 * div * pi
	return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r) for r in range(_a))


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			print(maclaurin_sin(10))
			print(maclaurin_sin(-10))
			print(maclaurin_sin(10, 15))
			print(maclaurin_sin(-10, 15))

			print(maclaurin_cos(5))
			print(maclaurin_cos(-5))
			print(maclaurin_cos(10, 15))
			print(maclaurin_cos(-10, 15))