class Model:
    Man = "M"
    Wolf = "W"
    Sheep = "S"
    Cabbage = "C"
    def __init__(self, left, right):
        self.left = set(left)
        self.right = set(right)

    def __eq__(self,other):
        return other.left == self.left and other.right == self.right

    def __repr__(self):
        return "(%s,%s)" % ( repr(self.left), repr(self.right))

    def pretty(self):
        return ",".join(self.left) + " <-> " + ",".join(self.right)

class Simulator:
    def simulate(self, state, stack=[]):
        #stack.append(state)
        stack = stack + [state]
        if state.right == set([Model.Man,Model.Wolf,Model.Sheep,Model.Cabbage]):
            return stack

        nextStates = []
        if Model.Man in state.left:
            for obj in state.left:
                nextStates.append( Model(state.left - set([Model.Man,obj]) , state.right | set([Model.Man,obj]) ) )
        else:
            for obj in state.right:
                nextStates.append( Model(state.left | set([Model.Man, obj]) , state.right - set([Model.Man,obj]) ) )

        nextStates = list(filter(
                lambda s: s not in stack and not(
                    ( (set([Model.Wolf,Model.Sheep]) <= s.left or set([Model.Sheep, Model.Cabbage]) <= s.left) and Model.Man not in s.left ) or
                    ( (set([Model.Wolf,Model.Sheep]) <= s.right or set([Model.Sheep, Model.Cabbage]) <= s.right) and Model.Man not in s.right )
                )
            , nextStates)) #Remove invalid and previous states.
        #print("%s: %s\nstack: %s" % (state,nextStates,stack))

        for s in nextStates:
            m = self.simulate(s,stack)
            if m is not None:
                return m

        return None


if __name__ == "__main__":
    sim = Simulator()
    result = sim.simulate(Model([Model.Man, Model.Wolf, Model.Sheep, Model.Cabbage],[]))
    i = 0
    for state in result:
        print("%d: %s" % (i,state.pretty()))
        i+=1