


def 			_a (      SCREAMING_SNAKE_CASE = 50     ):


		"""simple docstring"""




		lowercase__            =      [1] * (length + 1)

		for row_length in range(3						,				length + 1     ):
				for block_length in range(3						,				row_length + 1     ):
						for block_start in range(row_length - block_length     ):
								ways_number[row_length] += ways_number[
								    row_length - block_start - block_length - 1
								]

						ways_number[row_length] += 1

		return ways_number[length]


if __name__ == "__main__":
			print(f"""{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')


