from __future__ import annotations


class Link:
    """A linked list.

    >>> s = Link(1)
    >>> s.first
    1
    >>> s.rest is Link.empty
    True
    >>> s = Link(2, Link(3, Link(4)))
    >>> s.first = 5
    >>> s.rest.first = 6
    >>> s.rest.rest = Link.empty
    >>> s                                    # Displays the contents of repr(s)
    Link(5, Link(6))
    >>> s.rest = Link(7, Link(Link(8, Link(9))))
    >>> s
    Link(5, Link(7, Link(Link(8, Link(9)))))
    >>> print(s)                             # Prints str(s)
    (5 7 (8 9))
    """
    empty = ()

    def __init__(self, first, rest=empty):
        assert rest is Link.empty or isinstance(rest, Link)
        self.first = first
        self.rest = rest

    def __repr__(self):
        if self.rest is not Link.empty:
            rest_repr = ', ' + repr(self.rest)
        else:
            rest_repr = ''
        return 'Link(' + repr(self.first) + rest_repr + ')'

    def __str__(self):
        string = '('
        while self.rest is not Link.empty:
            string += str(self.first) + ' '
            self = self.rest
        return string + str(self.first) + ')'


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 store_digits(n: int):
    """Stores the digits of a positive number n in a linked list.

    >>> s = store_digits(1)
    >>> s
    Link(1)
    >>> store_digits(2345)
    Link(2, Link(3, Link(4, Link(5))))
    >>> store_digits(876)
    Link(8, Link(7, Link(6)))
    >>> store_digits(2450)
    Link(2, Link(4, Link(5, Link(0))))
    >>> store_digits(20105)
    Link(2, Link(0, Link(1, Link(0, Link(5)))))
    >>> # a check for restricted functions
    >>> import inspect, re
    >>> cleaned = re.sub(r"#.*\\n", '', re.sub(r'"{3}[\s\S]*?"{3}', '', inspect.getsource(store_digits)))
    >>> print("Do not use str or reversed!") if any([r in cleaned for r in ["str", "reversed"]]) else None
    """
    result = Link.empty
    while n > 0:
        result = Link(n % 10, result)
        n //= 10
    return result


def deep_map_mut(func, s: Link) -> None:
    """Mutates a deep link s by replacing each item found with the
    result of calling func on the item. Does NOT create new Links (so
    no use of Link's constructor).

    Does not return the modified Link object.

    >>> link1 = Link(3, Link(Link(4), Link(5, Link(6))))
    >>> square = lambda x: x * x
    >>> print(link1)
    (3 (4) 5 6)
    >>> link2 = Link(1, Link(Link(Link(2, Link(3))), Link(4)))
    >>> double = lambda x: x * 2
    >>> print(link2)
    (1 ((2 3)) 4)
    >>> # Disallow the use of making new Links before calling deep_map_mut
    >>> Link.__init__, hold = lambda *args: print("Do not create any new Links."), Link.__init__
    >>> try:
    ...     deep_map_mut(square, link1)
    ...     deep_map_mut(double, link2)
    ... finally:
    ...     Link.__init__ = hold
    >>> print(link1)
    (9 (16) 25 36)
    >>> print(link2)
    (2 ((4 6)) 8)
    """
    if s is Link.empty:
        return None
    elif isinstance(s.first, Link):
        deep_map_mut(func, s.first)
    else:
        s.first = func(s.first)
    deep_map_mut(func, s.rest)


def prune_small(t, n: int):
    """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)


def delete(t, x):
    """Remove all nodes labeled x below the root within Tree t. When a non-leaf
    node is deleted, the deleted node's children become children of its parent.

    The root node will never be removed.

    >>> t = Tree(3, [Tree(2, [Tree(2), Tree(2)]), Tree(2), Tree(2, [Tree(2, [Tree(2), Tree(2)])])])
    >>> delete(t, 2)
    >>> t
    Tree(3)
    >>> t = Tree(1, [Tree(2, [Tree(4, [Tree(2)]), Tree(5)]), Tree(3, [Tree(6), Tree(2)]), Tree(4)])
    >>> delete(t, 2)
    >>> t
    Tree(1, [Tree(4), Tree(5), Tree(3, [Tree(6)]), Tree(4)])
    >>> t = Tree(1, [Tree(2, [Tree(4), Tree(5)]), Tree(3, [Tree(6), Tree(2)]), Tree(2, [Tree(6),  Tree(2), Tree(7), Tree(8)]), Tree(4)])
    >>> delete(t, 2)
    >>> t
    Tree(1, [Tree(4), Tree(5), Tree(3, [Tree(6)]), Tree(6), Tree(7), Tree(8), Tree(4)])
    """
    new_branches = []
    for b in t.branches:
        delete(b, x)
        if b.label == x:
            new_branches.extend(b.branches)
        else:
            new_branches.append(b)
    t.branches = new_branches


def two_list(vals, counts):
    """
    Returns a linked list according to the two lists that were passed in. Assume
    vals and counts are the same size. Elements in vals represent the value, and the
    corresponding element in counts represents the number of this value desired in the
    final linked list. Assume all elements in counts are greater than 0. Assume both
    lists have at least one element.
    >>> a = [1, 3]
    >>> b = [1, 1]
    >>> c = two_list(a, b)
    >>> c
    Link(1, Link(3))
    >>> a = [1, 3, 2]
    >>> b = [2, 2, 1]
    >>> c = two_list(a, b)
    >>> c
    Link(1, Link(1, Link(3, Link(3, Link(2)))))
    """
    def helper(count, index):
        if count == 0:
            if index + 1 == len(vals):
                return Link.empty
            return Link(vals[index + 1], helper(counts[index + 1] - 1, index + 1))
        return Link(vals[index], helper(count - 1, index))
    return helper(counts[0], 0)

#Iterative solution
def two_list_iterative(vals, counts):
    result = Link(None)
    p = result
    for index in range(len(vals)):
        item = vals[index]
        for _ in range(counts[index]):
            p.rest = Link(item)
            p = p.rest
    return result.rest


class Tree:
    """A tree has a label and a list of branches.

    >>> t = Tree(3, [Tree(2, [Tree(5)]), Tree(4)])
    >>> t.label
    3
    >>> t.branches[0].label
    2
    >>> t.branches[1].is_leaf()
    True
    """
    def __init__(self, label, branches=[]):
        self.label = label
        for branch in branches:
            assert isinstance(branch, Tree)
        self.branches = list(branches)

    def is_leaf(self):
        return not self.branches

    def __repr__(self):
        if self.branches:
            branch_str = ', ' + repr(self.branches)
        else:
            branch_str = ''
        return 'Tree({0}{1})'.format(repr(self.label), branch_str)

    def __str__(self):
        return '\n'.join(self.indented())

    def indented(self):
        lines = []
        for b in self.branches:
            for line in b.indented():
                lines.append('  ' + line)
        return [str(self.label)] + lines


class Link:
    """A linked list.

    >>> s = Link(1)
    >>> s.first
    1
    >>> s.rest is Link.empty
    True
    >>> s = Link(2, Link(3, Link(4)))
    >>> s.first = 5
    >>> s.rest.first = 6
    >>> s.rest.rest = Link.empty
    >>> s                                    # Displays the contents of repr(s)
    Link(5, Link(6))
    >>> s.rest = Link(7, Link(Link(8, Link(9))))
    >>> s
    Link(5, Link(7, Link(Link(8, Link(9)))))
    >>> print(s)                             # Prints str(s)
    (5 7 (8 9))
    """
    empty = ()

    def __init__(self, first, rest=empty):
        assert rest is Link.empty or isinstance(rest, Link)
        self.first = first
        self.rest = rest

    def __repr__(self):
        if self.rest is not Link.empty:
            rest_repr = ', ' + repr(self.rest)
        else:
            rest_repr = ''
        return 'Link(' + repr(self.first) + rest_repr + ')'

    def __str__(self):
        string = '('
        while self.rest is not Link.empty:
            string += str(self.first) + ' '
            self = self.rest
        return string + str(self.first) + ')'