class VendingMachine:
    """A vending machine that vends some product for some price.

    >>> v = VendingMachine('candy', 10)
    >>> v.vend()
    'Nothing left to vend. Please restock.'
    >>> v.add_funds(15)
    'Nothing left to vend. Please restock. Here is your $15.'
    >>> v.restock(2)
    'Current candy stock: 2'
    >>> v.vend()
    'Please add $10 more funds.'
    >>> v.add_funds(7)
    'Current balance: $7'
    >>> v.vend()
    'Please add $3 more funds.'
    >>> v.add_funds(5)
    'Current balance: $12'
    >>> v.vend()
    'Here is your candy and $2 change.'
    >>> v.add_funds(10)
    'Current balance: $10'
    >>> v.vend()
    'Here is your candy.'
    >>> v.add_funds(15)
    'Nothing left to vend. Please restock. Here is your $15.'

    >>> w = VendingMachine('soda', 2)
    >>> w.restock(3)
    'Current soda stock: 3'
    >>> w.restock(3)
    'Current soda stock: 6'
    >>> w.add_funds(2)
    'Current balance: $2'
    >>> w.vend()
    'Here is your soda.'
    """
    def __init__(self, product: str, price: int):
        """Set the product and its price, as well as other instance attributes."""
        self.product = product
        self.price = price
        self.stock = 0
        self.balance = 0
    def restock(self, n: int) -> str:
        """Add n to the stock and return a message about the updated stock level.

        E.g., Current candy stock: 3
        """
        self.stock += n
        return f'Current {self.product} stock: {self.stock}'
    def add_funds(self, n: int) -> str:
        """If the machine is out of stock, return a message informing the user to restock
        (and return their n dollars).

        E.g., Nothing left to vend. Please restock. Here is your $4.

        Otherwise, add n to the balance and return a message about the updated balance.

        E.g., Current balance: $4
        """
        if self.stock == 0:
            return f'Nothing left to vend. Please restock. Here is your ${n}.'
            # Alternatively, we could have:
            # return self.vend() + f' Here is your ${n}.'
        self.balance += n
        return f'Current balance: ${self.balance}'
    def vend(self) -> str:
        """Dispense the product if there is sufficient stock and funds and
        return a message. Update the stock and balance accordingly.

        E.g., Here is your candy and $2 change.

        If not, return a message suggesting how to correct the problem.

        E.g., Nothing left to vend. Please restock.
              Please add $3 more funds.
        """
        if self.stock == 0:
            return 'Nothing left to vend. Please restock.'
        difference = self.price - self.balance
        if difference > 0:
            return f'Please add ${difference} more funds.'
        message = f'Here is your {self.product}'
        if difference != 0:
            message += f' and ${-difference} change'
        self.balance = 0
        self.stock -= 1
        return message + '.'

def cumulative_mul(t: Tree) -> None:
    """Mutates t so that each node's label becomes the product of its own
    label and all labels in the corresponding subtree rooted at t.

    >>> t = Tree(1, [Tree(3, [Tree(5)]), Tree(7)])
    >>> cumulative_mul(t)
    >>> t
    Tree(105, [Tree(15, [Tree(5)]), Tree(7)])
    >>> otherTree = Tree(2, [Tree(1, [Tree(3), Tree(4), Tree(5)]), Tree(6, [Tree(7)])])
    >>> cumulative_mul(otherTree)
    >>> otherTree
    Tree(5040, [Tree(60, [Tree(3), Tree(4), Tree(5)]), Tree(42, [Tree(7)])])
    """
    for b in t.branches:
        cumulative_mul(b)
    total = t.label
    for b in t.branches:
        total *= b.label
    t.label = total

# Alternate solution using only one loop
def cumulative_mul(t: Tree) -> None:
    for b in t.branches:
        cumulative_mul(b)
        t.label *= b.label

def prune_small(t: Tree, n: int) -> None:
    """Prune the tree mutatively, keeping only the n branches
    of each node with the smallest labels.

    >>> t1 = Tree(6)
    >>> prune_small(t1, 2)
    >>> t1
    Tree(6)
    >>> t2 = Tree(6, [Tree(3), Tree(4)])
    >>> prune_small(t2, 1)
    >>> t2
    Tree(6, [Tree(3)])
    >>> t3 = Tree(6, [Tree(1), Tree(3, [Tree(1), Tree(2), Tree(3)]), Tree(5, [Tree(3), Tree(4)])])
    >>> prune_small(t3, 2)
    >>> t3
    Tree(6, [Tree(1), Tree(3, [Tree(1), Tree(2)])])
    """
    while len(t.branches) > n:
        largest = max(t.branches, key=lambda x: x.label)
        t.branches.remove(largest)
    for b in t.branches:
        prune_small(b, n)

class Pet:

    def __init__(self, name: str, owner: str) -> None:
        self.name = name
        self.owner = owner

    def talk(self) -> None:
        print(self.name)

class Cat(Pet):
    """
    >>> my_cat = Cat("Furball", "Me", lives=2)
    >>> my_cat.talk()
    Meow!
    >>> my_cat.name
    'Furball'
    >>> my_cat.lose_life()
    >>> my_cat.is_alive
    True
    >>> my_cat.eat("poison")
    Meow!
    Furball ate a poison!
    >>> my_cat.is_alive
    False
    >>> my_cat.lose_life()
    'Cat is dead x_x'
    """
    def __init__(self, name: str, owner: str, lives: int = 9) -> None:
        assert type(lives) == int and  lives > 0
        Pet.__init__(self, name, owner)
        self.lives = lives
        self.is_alive = True
    def talk(self) -> None:
        """A cat says 'Meow!' when asked to talk."""
        print("Meow!")
    def lose_life(self) -> str | None:
        """A cat can only lose a life if it has at least one
        life. When there are zero lives left, the 'is_alive'
        variable becomes False.
        """
        if not self.is_alive:
            return "Cat is dead x_x"
        self.lives -= 1
        if self.lives == 0:
            self.is_alive = False
    def eat(self, thing: str) -> None:
        self.talk()
        print(f"{self.name} ate a {thing}!")
        if thing == "poison":
            self.is_alive = False