

from __future__ import annotations





def  _snake_case		(snake_case_					:     str  )							->		bool:
  __UpperCAmelCase	:  int
  __UpperCAmelCase	:  list[str]		=     list(snake_case_  )
  __UpperCAmelCase,			__UpperCAmelCase	:  Any		=     _vector[:-1], int(_vector[-1]  )
  __UpperCAmelCase	:  list[int]		=     [int(snake_case_  ) for digit in __vector]

  vector.reverse()
  for i, digit in enumerate(snake_case_  ):
    if i & 1 == 0:
      __UpperCAmelCase	:  int		=     digit * 2
      if doubled > 9:
        doubled -= 9
      check_digit += doubled
    else:
      check_digit += digit

  return check_digit % 10 == 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      assert is_luhn('''79927398713''')
      assert not is_luhn('''79927398714''')






def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):
       return n * (2 * n - 1)


def SCREAMING_SNAKE_CASE					(  lowercase_:						int					):
       _UpperCamelCase  :							str	    =	(1 + 24 * n) ** 0.5
       return ((1 + root) / 6) % 1 == 0


def SCREAMING_SNAKE_CASE					(  lowercase_:						int = 144					):
       _UpperCamelCase  :							Optional[Any]	    =	start
       _UpperCamelCase  :							List[str]	    =	hexagonal_num(lowercase_					)
       while not is_pentagonal(lowercase_					):
              n += 1
              _UpperCamelCase  :							Optional[int]	    =	hexagonal_num(lowercase_					)
       return num


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



