


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 			_a (      SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE						,				SCREAMING_SNAKE_CASE     ):


		"""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 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




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


		"""simple docstring"""




		if location := find_empty_location(SCREAMING_SNAKE_CASE     ):
				lowercase__     ,		lowercase__            =      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__            =      digit

						if sudoku(SCREAMING_SNAKE_CASE     ) is not None:
								return grid

						lowercase__            =      0

		return None
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		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.')






def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		return credit_card_number.startswith(('''34''', '''35''', '''37''', '''4''', '''5''', '''6''')     )
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      credit_card_number
		lowercase__            =      0
		lowercase__            =      len(SCREAMING_SNAKE_CASE     ) - 2
		for i in range(SCREAMING_SNAKE_CASE						,				-1						,				-2     ):
				#  double the value of every second digit
				lowercase__            =      int(cc_number[i]     )
				digit *= 2
				# If doubling of a number results in a two digit number
				# i.e greater than 9(e.g., 6 × 2 = 12),
				# then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),
				# to get a single digit number.
				if digit > 9:
						digit %= 10
						digit += 1
				lowercase__            =      cc_number[:i] + str(SCREAMING_SNAKE_CASE     ) + cc_number[i + 1 :]
				total += digit

		# Sum up the remaining digits
		for i in range(len(SCREAMING_SNAKE_CASE     ) - 1						,				-1						,				-2     ):
				total += int(cc_number[i]     )

		return total % 10 == 0
def 			_a (      SCREAMING_SNAKE_CASE     ):


		"""simple docstring"""




		lowercase__            =      f'{credit_card_number} is an invalid credit card number because'
		if not credit_card_number.isdigit():
				print(f'{error_message} it has nonnumerical characters.'     )
				return False

		if not 13 <= len(SCREAMING_SNAKE_CASE     ) <= 16:
				print(f'{error_message} of its length.'     )
				return False

		if not validate_initial_digits(SCREAMING_SNAKE_CASE     ):
				print(f'{error_message} of its first two digits.'     )
				return False

		if not luhn_validation(SCREAMING_SNAKE_CASE     ):
				print(f'{error_message} it fails the Luhn check.'     )
				return False

		print(f'{credit_card_number} is a valid credit card number.'     )
		return True


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			validate_credit_card_number('4111111111111111')
			validate_credit_card_number('32323')


