Starting with a positive integer $$M$$ written on the board, Alice plays the following game: in each move, if $$x$$ is the number on the board, she replaces it with $$3x+2$$. Similarly, starting with a positive integer $$N$$ written on the board, Bob plays the following game: in each move, if $$x$$ is the number on the board, he replaces it with $$2x+27$$. Given that Alice and Bob reach the same number after playing $$4$$ moves each, find the smallest value of $$M+N$$.