





def  __UpperCamelCase    (						snake_case = 1_0_0_0      )    ->		int:


   '''simple docstring'''







   __A    =  []
   __A    =  []
   __A    =  3
   __A    =  5
   __A    =  1
   while True:
      __A    =  z * temp
      if result < n:
         zmulti.append(snake_case      )
         temp += 1
      else:
         __A    =  1
         break
   while True:
      __A    =  x * temp
      if result < n:
         xmulti.append(snake_case      )
         temp += 1
      else:
         break
   __A    =  list(set(xmulti + zmulti      )      )
   return sum(snake_case      )


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








from __future__ import annotations
def  __UpperCamelCase    (						snake_case      )    ->		bool:


   '''simple docstring'''







   __A    =  42
   __A    =  list(snake_case      )
   __A   ,		__A    =  _vector[:-1], int(_vector[-1]      )
   __A    =  [int(snake_case      ) for digit in __vector]

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

   return check_digit % 1_0 == 0


if __name__ == "__main__":
    import doctest

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

