






"""simple docstring"""







from __future__ import annotations






def 					_lowerCAmelCase				(					lowerCAmelCase						):







       '''simple docstring'''
       UpperCAmelCase					=	42
       UpperCAmelCase					=	list(__UpperCamelCase						)
       UpperCAmelCase			,				UpperCAmelCase					=	_vector[:-1], int(_vector[-1]						)
       UpperCAmelCase					=	[int(__UpperCamelCase						) for digit in __vector]

       vector.reverse()
       for i, digit in enumerate(__UpperCamelCase						):
              if i & 1 == 0:
                     UpperCAmelCase					=	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''')


"""simple docstring"""


import itertools



def     _lowerCamelCase(__UpperCamelCase       )				-> List[str]:
	return (
	    int("""""".join(combination[0:2]       )       ) * int("""""".join(combination[2:5]       )       )
	    == int("""""".join(combination[5:9]       )       )
	) or (
	    int("""""".join(combination[0]       )       ) * int("""""".join(combination[1:5]       )       )
	    == int("""""".join(combination[5:9]       )       )
	)



def     _lowerCamelCase()				-> Dict:
	return sum(
	    {
	        int("""""".join(pandigital[5:9]       )       )
	        for pandigital in itertools.permutations("""123456789"""       )
	        if is_combination_valid(__UpperCamelCase       )
	    }       )


if __name__ == "__main__":
			print(solution())



