





from __future__ import annotations

__lowercase       :Optional[int]       =  list[list[int]]

# assigning initial values to the grid
__lowercase       :Matrix       =  [
    [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
__lowercase       :Matrix       =  [
    [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       UpperCAmelCase							(     _lowerCamelCase      :  Matrix			,   _lowerCamelCase      :  int			,   _lowerCamelCase      :  int			,   _lowerCamelCase      :  int     ):





						'''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       UpperCAmelCase							(     _lowerCamelCase      :  Matrix     ):





						'''simple docstring'''


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







def       UpperCAmelCase							(     _lowerCamelCase      :  Matrix     ):





						'''simple docstring'''


						if location := find_empty_location(_lowerCamelCase     ):
												SCREAMING_SNAKE_CASE__     :				Optional[int]   =					location
						else:
												# If the location is ``None``, then the grid is solved.
												return grid

						for digit in range(1			,   10     ):
												if is_safe(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     ):
																		SCREAMING_SNAKE_CASE__     :				Optional[int]   =					digit

																		if sudoku(_lowerCamelCase     ) is not None:
																								return grid

																		SCREAMING_SNAKE_CASE__     :				str   =					0

						return None







def       UpperCAmelCase							(     _lowerCamelCase      :  Matrix     ):





						'''simple docstring'''


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










def       UpperCAmelCase							(     _lowerCamelCase      :  int = 4_000_000     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				Any   =					[0, 1]
						SCREAMING_SNAKE_CASE__     :				List[Any]   =					0
						while fib[i] <= n:
												fib.append(fib[i] + fib[i + 1]     )
												if fib[i + 2] > n:
																		break
												i += 1
						SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					0
						for j in range(len(_lowerCamelCase     ) - 1     ):
												if fib[j] % 2 == 0:
																		total += fib[j]

						return total


if __name__ == "__main__":
				print(f"{solution() = }")