





'''simple docstring'''


import math


def 	__a(SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    _lowerCAmelCase				=      0
    _lowerCAmelCase				=      0
    while num > 0:
        _lowerCAmelCase				=      num % 8
        _lowerCAmelCase				=      octal + (remainder * math.floor(math.pow(10		,       SCREAMING_SNAKE_CASE_    )    ))
        counter += 1
        _lowerCAmelCase				=      math.floor(num / 8    )  # basically /= 8 without remainder if any
        # This formatting removes trailing '.0' from `octal`.
    return F'''0o{int(SCREAMING_SNAKE_CASE_    )}'''


def 	__a():



    '''simple docstring'''





    print("\n2 in octal is:"    )
    print(decimal_to_octal(2    )    )  # = 2
    print("\n8 in octal is:"    )
    print(decimal_to_octal(8    )    )  # = 10
    print("\n65 in octal is:"    )
    print(decimal_to_octal(65    )    )  # = 101
    print("\n216 in octal is:"    )
    print(decimal_to_octal(216    )    )  # = 330
    print("\n512 in octal is:"    )
    print(decimal_to_octal(512    )    )  # = 1000
    print("\n"    )


if __name__ == "__main__":
       main()









'''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 []


