





'''simple docstring'''


from itertools import permutations


def 	__a(SCREAMING_SNAKE_CASE_  :					tuple    ):



    '''simple docstring'''





    if num[3] % 2 != 0:
        return False

    if (num[2] + num[3] + num[4]) % 3 != 0:
        return False

    if num[5] % 5 != 0:
        return False

    _lowerCAmelCase				=      [7, 11, 13, 17]
    for i, test in enumerate(SCREAMING_SNAKE_CASE_    ):
        if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0:
            return False
    return True


def 	__a(SCREAMING_SNAKE_CASE_  :					int = 10    ):



    '''simple docstring'''





    return sum(
        int("".join(map(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    )    )    )
        for num in permutations(range(SCREAMING_SNAKE_CASE_    )    )
        if is_substring_divisible(SCREAMING_SNAKE_CASE_    )    )


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









'''simple docstring'''


def 	__a(SCREAMING_SNAKE_CASE_  :					list[int]		,       SCREAMING_SNAKE_CASE_  :					list[int]		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return not any(
        neighbour == 1 and colored_vertices[i] == color
        for i, neighbour in enumerate(SCREAMING_SNAKE_CASE_    )    )


def 	__a(SCREAMING_SNAKE_CASE_  :					list[list[int]]		,       SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					list[int]		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    if index == len(SCREAMING_SNAKE_CASE_    ):
        return True

    # Recursive Step
    for i in range(SCREAMING_SNAKE_CASE_    ):
        if valid_coloring(graph[index]		,       SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    ):
            # Color current vertex
            _lowerCAmelCase				=      i
            # Validate coloring
            if util_color(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_		,       index + 1    ):
                return True
            # Backtrack
            _lowerCAmelCase				=      -1
    return False





def 	__a(SCREAMING_SNAKE_CASE_  :					list[list[int]]		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    _lowerCAmelCase				=      [-1] * len(SCREAMING_SNAKE_CASE_    )

    if util_color(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_		,       0    ):
        return colored_vertices

    return []


