




from __future__ import annotations




class     snake_case__							:
				"""simple docstring"""



				def __init__(      self				:     List[str]					,      __lowerCamelCase				:     int							)					->     None:
							a    =			data
							a    =			None
							a    =			None




def 			__magic_name__				( A		:					Node | None   ):  # In Order traversal of the tree






			'''simple docstring'''







			if tree:
						display(tree.left   )
						print(tree.data   )
						display(tree.right   )




def 			__magic_name__				( A		:					Node | None   ):






			'''simple docstring'''







			return 1 + max(depth_of_tree(tree.left   ),  depth_of_tree(tree.right   )   ) if tree else 0




def 			__magic_name__				( A		:					Node   ):






			'''simple docstring'''







			if not tree:
						return True
			if tree.left and tree.right:
						return is_full_binary_tree(tree.left   ) and is_full_binary_tree(tree.right   )
			else:
						return not tree.left and not tree.right




def 			__magic_name__				( ):  # Main function for testing.






			'''simple docstring'''







			a    =			Node(1   )
			a    =			Node(2   )
			a    =			Node(3   )
			a    =			Node(4   )
			a    =			Node(5   )
			a    =			Node(6   )
			a    =			Node(7   )
			a    =			Node(8   )
			a    =			Node(9   )

			print(is_full_binary_tree(A   )   )
			print(depth_of_tree(A   )   )
			print("Tree is: "   )
			display(A   )


if __name__ == "__main__":
		main()








from __future__ import annotations

lowerCamelCase__          =		list[list[int]]

# assigning initial values to the grid
lowerCamelCase__          =		[
    [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
lowerCamelCase__          =		[
    [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  lowerCAmelCase__			(  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  lowerCAmelCase__			(  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  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Matrix | None:
			if location := find_empty_location(SCREAMING_SNAKE_CASE_     ):
						lowerCAmelCase__      ,				lowerCAmelCase__      :      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_     ):
									lowerCAmelCase__      :      Optional[Any]         =		digit

									if sudoku(SCREAMING_SNAKE_CASE_     ) is not None:
												return grid

									lowerCAmelCase__      :      List[Any]         =		0

			return None
def  lowerCAmelCase__			(  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:""")
										lowerCamelCase__          =		sudoku(example_grid)
										if solution is not None:
															print_solution(solution)
										else:
															print("""Cannot find a solution.""")