On a magical island there are lions, wolves and goats. Wolves can eat goats while lions can eat both wolves and goats. But if a lion eats a wolf, the lion becomes a goat. Likewise if a wolf eats a goat, the wolf becomes a lion. And if a lion eats a goat, the lion becomes a wolf. Initially on the island there are $17$ goats, $55$ wolves and $6$ lions. If they start eating until they no longer possible to eat more, what is the maximum number of animals that they can stay alive?