





'''simple docstring'''


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return number | (1 << position)


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return number & ~(1 << position)


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return number ^ (1 << position)


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return ((number >> position) & 1) == 1


def 	__a(SCREAMING_SNAKE_CASE_  :					int		,       SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    return int((number & (1 << position)) != 0    )


if __name__ == "__main__":
       import doctest

       doctest.testmod()









'''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 []


