


from __future__ import annotations

__snake_case            =   list[list[int]]

# assigning initial values to the grid
__snake_case            =   [
    [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
__snake_case            =   [
    [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 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		Any       ,  SCREAMING_SNAKE_CASE_   :		List[str]       ,  SCREAMING_SNAKE_CASE_   :		Tuple       ,  SCREAMING_SNAKE_CASE_   :		str	):





			"""simple docstring"""




			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 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		Optional[int]	):





			"""simple docstring"""




			for i in range(9	):
						for j in range(9	):
									if grid[i][j] == 0:
												return i, j
			return None






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		List[str]	):





			"""simple docstring"""




			if location := find_empty_location(__UpperCamelCase	):
						UpperCamelCase  ,  UpperCamelCase         =					location
			else:
						# If the location is ``None``, then the grid is solved.
						return grid

			for digit in range(1       ,  10	):
						if is_safe(__UpperCamelCase       ,  __UpperCamelCase       ,  __UpperCamelCase       ,  __UpperCamelCase	):
									UpperCamelCase         =					digit

									if sudoku(__UpperCamelCase	) is not None:
												return grid

									UpperCamelCase         =					0

			return None






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		Any	):





			"""simple docstring"""




			for row in grid:
						for cell in row:
									print(__UpperCamelCase       ,  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:")
								__snake_case            =   sudoku(example_grid)
								if solution is not None:
												print_solution(solution)
								else:
												print("Cannot find a solution.")








def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int	):





			"""simple docstring"""




			assert (
			    isinstance(SCREAMING_SNAKE_CASE_       ,  SCREAMING_SNAKE_CASE_	) and number_of_steps > 0
			), f'number_of_steps needs to be positive integer, your input {number_of_steps}'
			if number_of_steps == 1:
						return 1
			UpperCamelCase  ,  UpperCamelCase         =					1, 1
			for _ in range(number_of_steps - 1	):
						UpperCamelCase  ,  UpperCamelCase         =					current + previous, current
			return current


if __name__ == "__main__":
			import doctest

			doctest.testmod()




