#region Imports
import collections
import copy
import functools
import heapq
import itertools
import math
import operator
import re
import sys
import typing
from collections import Counter, defaultdict, deque
from copy import deepcopy
from functools import reduce
from pprint import pprint
#endregion

sys.setrecursionlimit(100000)
T = typing.TypeVar("T")
# Copy a function if you need to modify it.

AIR = "."
WALL = "#"

#region Strings, lists, dicts
def lmap(func, *iterables):
    return list(map(func, *iterables))
def make_grid(*dimensions: typing.List[int], fill=None):
    "Returns a grid such that 'dimensions' is juuust out of bounds."
    if len(dimensions) == 1:
        return [fill for _ in range(dimensions[0])]
    next_down = make_grid(*dimensions[1:], fill=fill)
    return [copy.deepcopy(next_down) for _ in range(dimensions[0])]
def min_max(l):
    return min(l), max(l)
def max_minus_min(l):
    return max(l) - min(l)
def partial_sum(l):
    "out[i] == sum(in[:i])"
    out = [0]
    for i in l:
        out.append(out[-1] + i)
    return out
cum_sum = partial_sum
def list_diff(x):
    return [b-a for a, b in zip(x, x[1:])]
def flatten(l):
    return [i for x in l for i in x]
def every_n(l,n):
    return list(zip(*[iter(l)]*n))
def windows(l, n):
    return list(zip(*[l[i:] for i in range(n)]))

def ints(s: str) -> typing.List[int]:
    assert isinstance(s, str), f"you passed in a {type(s)}!!!"
    return lmap(int, re.findall(r"(?:(?<!\d)-)?\d+", s))  # thanks mserrano!
def positive_ints(s: str) -> typing.List[int]:
    assert isinstance(s, str), f"you passed in a {type(s)}!!!"
    return lmap(int, re.findall(r"\d+", s))  # thanks mserrano!
def floats(s: str) -> typing.List[float]:
    assert isinstance(s, str), f"you passed in a {type(s)}!!!"
    return lmap(float, re.findall(r"-?\d+(?:\.\d+)?", s))
def positive_floats(s: str) -> typing.List[float]:
    assert isinstance(s, str), f"you passed in a {type(s)}!!!"
    return lmap(float, re.findall(r"\d+(?:\.\d+)?", s))
def words(s: str) -> typing.List[str]:
    assert isinstance(s, str), f"you passed in a {type(s)}!!!"
    return re.findall(r"[a-zA-Z]+", s)

def keyvalues(d):
    return list(d.items())  # keep on forgetting this...
def make_hashable(l):
    if isinstance(l, list):
        return tuple(map(make_hashable, l))
    if isinstance(l, dict):
        l = set(l.items())
    if isinstance(l, set):
        return frozenset(map(make_hashable, l))
    return l
def invert_dict(d, single=True):
    out = {}
    if single:
        for k, v in d.items():
            v = make_hashable(v)
            if v in out:
                print("[invert_dict] WARNING WARNING: duplicate key", v)
            out[v] = k
    else:
        for k, v in d.items():
            v = make_hashable(v)
            out.setdefault(v, []).append(k)
    return out
#endregion

#region Algorithms
class RepeatingSequence:
    def __init__(self, generator, to_hashable=lambda x: x):
        """
        generator should yield the things in the sequence.
        to_hashable should be used if things aren't nicely hashable.
        """
        self.index_to_result = []
        self.hashable_to_index = dict()
        for i, result in enumerate(generator):
            self.index_to_result.append(result)
            hashable = to_hashable(result)
            if hashable in self.hashable_to_index:
                break
            else:
                self.hashable_to_index[hashable] = i
        else:
            raise Exception("generator terminated without repeat")
        self.cycle_begin = self.hashable_to_index[hashable]
        self.cycle_end = i
        self.cycle_length = self.cycle_end - self.cycle_begin

        self.first_repeated_result = self.index_to_result[self.cycle_begin]
        self.second_repeated_result = self.index_to_result[self.cycle_end]
    
    def cycle_number(self, index):
        """
        Returns which 0-indexed cycle index appears in.
        cycle_number(cycle_begin) is the first index to return 0,
        cycle_number(cycle_end)   is the first index to return 1,
        and so on.
        """
        if index < self.cycle_begin:
            print("WARNING: Index is before cycle!!")
            return 0
        return (index - self.cycle_begin) // self.cycle_length

    def __getitem__(self, index):
        """
        Gets an item in the sequence.
        If index >= cycle_length, returns the items from the first occurrence
        of the cycle.
        Use first_repeated_result and second_repeated_result if needed.
        """
        if index < 0:
            raise Exception("index can't be negative")
        if index < self.cycle_begin:
            return self.index_to_result[index]
        cycle_offset = (index - self.cycle_begin) % self.cycle_length
        return self.index_to_result[self.cycle_begin + cycle_offset]

def bisect(f, lo=0, hi=None, eps=1e-9):
    """
    Returns a value x such that f(x) is true.
    Based on the values of f at lo and hi.
    Assert that f(lo) != f(hi).
    """
    lo_bool = f(lo)
    if hi is None:
        offset = 1
        while f(lo+offset) == lo_bool:
            offset *= 2
        hi = lo + offset
    else:
        assert f(hi) != lo_bool
    while hi - lo > eps:
        mid = (hi + lo) / 2
        if f(mid) == lo_bool:
            lo = mid
        else:
            hi = mid
    if lo_bool:
        return lo
    else:
        return hi

def binary_search(f, lo=0, hi=None):
    """
    Returns a value x such that f(x) is true.
    Based on the values of f at lo and hi.
    Assert that f(lo) != f(hi).
    """
    lo_bool = f(lo)
    if hi is None:
        offset = 1
        while f(lo+offset) == lo_bool:
            offset *= 2
        hi = lo + offset
    else:
        assert f(hi) != lo_bool
    best_so_far = lo if lo_bool else hi
    while lo <= hi:
        mid = (hi + lo) // 2
        result = f(mid)
        if result:
            best_so_far = mid
        if result == lo_bool:
            lo = mid + 1
        else:
            hi = mid - 1
    return best_so_far

# Graphs
def topsort(out_edges: typing.Dict[T, typing.List[T]]) -> typing.List[T]:
    temp = set()  # type: typing.Set[T]
    seen = set()  # type: typing.Set[T]
    out = []

    def dfs(n):
        nonlocal temp,seen,out
        if n in seen:
            return
        if n in temp:
            raise Exception("not a DAG")
        temp.add(n)
        if n in out_edges:
            for other in out_edges[n]:
                dfs(other)
        temp.remove(n)
        seen.add(n)
        out.append(n)
    
    for n in out_edges:
        dfs(n)
    out.reverse()
    return out


def path_from_parents(parents: typing.Dict[T, T], end: T) -> typing.List[T]:
    out = [end]
    while out[-1] in parents:
        out.append(parents[out[-1]])
    out.reverse()
    return out


def dijkstra(
    from_node: T,
    expand: typing.Callable[[T], typing.Iterable[typing.Tuple[int, T]]],
    to_node: typing.Optional[T] = None,
    heuristic: typing.Optional[typing.Callable[[T], int]] = None,
) -> typing.Tuple[typing.Dict[T, int], typing.Dict[T, T]]:
    """
    expand should return an iterable of (dist, successor node) tuples.
    Returns (distances, parents).
    Use path_from_parents(parents, node) to get a path.
    """
    if heuristic is None:
        heuristic = lambda _: 0
    seen = set()  # type: typing.Set[T]
    g_values = {from_node: 0}  # type: typing.Dict[T, int]
    parents = {}  # type: typing.Dict[T, T]

    # (f, g, n)
    todo = [(0 + heuristic(from_node), 0, from_node)]  # type: typing.List[typing.Tuple[int, int, T]]

    while todo:
        f, g, node = heapq.heappop(todo)

        assert node in g_values
        assert g_values[node] <= g

        if node in seen:
            continue

        assert g_values[node] == g
        if to_node is not None and node == to_node:
            break
        seen.add(node)

        for cost, new_node in expand(node):
            new_g = g + cost
            if new_node not in g_values or new_g < g_values[new_node]:
                parents[new_node] = node
                g_values[new_node] = new_g
                heapq.heappush(todo, (new_g + heuristic(new_node), new_g, new_node))
    
    return (g_values, parents)

def a_star(
    from_node: T,
    expand: typing.Callable[[T], typing.Iterable[typing.Tuple[int, T]]],
    to_node: T,
    heuristic: typing.Optional[typing.Callable[[T], int]] = None,
) -> typing.Tuple[int, typing.List[T]]:
    """
    expand should return an iterable of (dist, successor node) tuples.
    Returns (distance, path).
    """
    g_values, parents = dijkstra(from_node, to_node=to_node, expand=expand, heuristic=heuristic)
    if to_node not in g_values:
        raise Exception("couldn't reach to_node")
    return (g_values[to_node], path_from_parents(parents, to_node))


def bfs(
    from_node: T,
    expand: typing.Callable[[T], typing.Iterable[T]],
    to_node: typing.Optional[T] = None
) -> typing.Tuple[typing.Dict[T, int], typing.Dict[T, T]]:
    """
    expand should return an iterable of successor nodes.
    Returns (distances, parents).
    """
    g_values = {from_node: 0}  # type: typing.Tuple[typing.Dict[T, int]]
    parents = {}  # type: typing.Dict[T, T]
    todo = [from_node]  # type: typing.List[T]
    dist = 0

    while todo:
        new_todo = []
        dist += 1
        for node in todo:
            for new_node in expand(node):
                if new_node not in g_values:
                    new_todo.append(new_node)
                    parents[new_node] = node
                    g_values[new_node] = dist
        todo = new_todo
        if to_node is not None and to_node in g_values:
            break
    
    return (g_values, parents)

def bfs_single(
    from_node: T,
    expand: typing.Callable[[T], typing.Iterable[T]],
    to_node: T,
) -> typing.Tuple[int, typing.List[T]]:
    """
    expand should return an iterable of successor nodes.
    Returns (distance, path).
    """
    g_values, parents = bfs(from_node, to_node=to_node, expand=expand)
    if to_node not in g_values:
        raise Exception("couldn't reach to_node")
    return (g_values[to_node], path_from_parents(parents, to_node))

# Distances
BLANK = object()
def hamming_distance(a, b) -> int:
    return sum(i is BLANK or j is BLANK or i != j for i, j in itertools.zip_longest(a, b, fillvalue=BLANK))
def edit_distance(a, b) -> int:
    n = len(a)
    m = len(b)
    dp = [[None] * (m+1) for _ in range(n+1)]
    dp[n][m] = 0
    def aux(i, j):
        assert 0 <= i <= n and 0 <= j <= m
        if dp[i][j] is not None:
            return dp[i][j]
        if i == n:
            dp[i][j] = 1 + aux(i, j+1)
        elif j == m:
            dp[i][j] = 1 + aux(i+1, j)
        else:
            dp[i][j] = min((a[i] != b[j]) + aux(i+1, j+1), 1 + aux(i+1, j), 1 + aux(i, j+1))
        return dp[i][j]
    return aux(0, 0)
#endregion

#region Data Structures
class Linked(typing.Generic[T], typing.Iterable[T]):
    """
    Represents a node in a doubly linked lists.

    Can also be interpreted as a list itself.
    Consider this to be first in the list.
    """
    # item: T
    # forward: "Linked[T]"
    # backward: "Linked[T]"
    def __init__(self, item: T) -> None:
        self.item = item
        self.forward = self
        self.backward = self
    
    @property
    def val(self): return self.item
    @property
    def after(self): return self.forward
    @property
    def before(self): return self.backward

    def _join(self, other: "Linked[T]") -> None:
        self.forward = other
        other.backward = self
    
    def concat(self, other: "Linked[T]") -> None:
        """
        Concatenates other AFTER THE END OF THE LIST,
        i.e. before this current node.
        """
        first_self = self
        last_self = self.backward

        first_other = other
        last_other = other.backward
        # self ++ other
        # consider last_self and first_other
        last_self._join(first_other)
        last_other._join(first_self)
    
    def concat_immediate(self, other: "Linked[T]") -> None:
        """
        Concatenates other IN THE "SECOND" INDEX OF THE LIST
        i.e. after this current node.
        """
        self.forward.concat(other)
    
    def append(self, val: T) -> None:
        """
        Appends an item AFTER THE END OF THE LIST,
        i.e. before this current node.
        """
        self.concat(Linked(val))
    
    def append_immediate(self, val: T) -> None:
        """
        Appends an item IN THE "SECOND" INDEX OF THE LIST
        i.e. after this current node.
        """
        self.concat_immediate(Linked(val))
    
    def pop(self, n: int = 1) -> None:
        """
        Pops this node, as well as n others, off from the "parent list"
        into its own list.
        """
        assert n > 0
        first_self = self
        last_self = self.move(n-1)

        first_other = last_self.forward
        last_other = first_self.backward
        
        last_other._join(first_other)
        last_self._join(first_self)
    
    def pop_after(self, after: int, n: int = 1) -> None:
        """
        Pops the node n nodes after this node, as well as n others, into its
        own list.
        Returns the node n nodes after this node (in its new list).
        """
        to_return = self.move(after)
        to_return.pop(n)  # music
        return to_return

    def delete(self) -> None:
        """
        Deletes this node from the "parent list" into its own list.
        """
        self.pop()
    
    def delete_other(self, n: int) -> None:
        """
        Deletes a node n nodes forward, or backwards if n is negative.
        """
        to_delete = self.move(n)
        if to_delete is self:
            raise Exception("can't delete self")
        to_delete.delete()
        del to_delete
    
    def move(self, n: int) -> "Linked[T]":
        """
        Move n nodes forward, or backwards if n is negative.
        """
        out = self
        if n >= 0:
            for _ in range(n):
                out = out.forward
        else:
            for _ in range(-n):
                out = out.backward
        return out
    
    def iterate_nodes_inf(self) -> typing.Iterator["Linked[T]"]:
        cur = self
        while True:
            yield cur
            cur = cur.forward
    
    def iterate_nodes(self, count=1) -> typing.Iterator["Linked[T]"]:
        for node in self.iterate_nodes_inf():
            if node is self:
                count -= 1
                if count < 0:
                    break
            yield node
    
    def iterate_inf(self) -> typing.Iterator[T]:
        return map(lambda node: node.item, self.iterate_nodes_inf())
    
    def iterate(self, count=1) -> typing.Iterator[T]:
        return map(lambda node: node.item, self.iterate_nodes(count))
    
    def to_list(self):
        return list(self.iterate())
    
    def check_correctness(self) -> None:
        assert self.forward.backward is self
        assert self.backward.forward is self
    
    def check_correctness_deep(self) -> None:
        for node in self.iterate_nodes():
            node.check_correctness()
    
    def __iter__(self) -> typing.Iterator[T]:
        return self.iterate()
    
    def __repr__(self) -> str:
        return "Linked({})".format(self.to_list())

    @classmethod
    def from_list(cls, l: typing.Iterable[T]) -> "Linked[T]":
        it = iter(l)
        out = cls(next(it))
        for i in it:
            out.concat(cls(i))
        return out


class UnionFind:
    # n: int
    # parents: List[Optional[int]]
    # ranks: List[int]
    # num_sets: int

    def __init__(self, n: int) -> None:
        self.n = n
        self.parents = [None] * n
        self.ranks = [1] * n
        self.num_sets = n
    
    def find(self, i: int) -> int:
        p = self.parents[i]
        if p is None:
            return i
        p = self.find(p)
        self.parents[i] = p
        return p
    
    def in_same_set(self, i: int, j: int) -> bool:
        return self.find(i) == self.find(j)
    
    def merge(self, i: int, j: int) -> None:
        i = self.find(i)
        j = self.find(j)

        if i == j:
            return
        
        i_rank = self.ranks[i]
        j_rank = self.ranks[j]

        if i_rank < j_rank:
            self.parents[i] = j
        elif i_rank > j_rank:
            self.parents[j] = i
        else:
            self.parents[j] = i
            self.ranks[i] += 1
        self.num_sets -= 1


class Grid(typing.Generic[T]):
    """2D only!!!"""

    def __init__(self, grid: typing.List[typing.List[T]]) -> None:
        self.grid = grid
        self.rows = len(self.grid)
        self.cols = len(self.grid[0])
    
    def coords(self) -> typing.List[typing.List[int]]:
        return [[r, c] for r in range(self.rows) for c in range(self.cols)]
    
    def get_row(self, row: int):
        assert 0 <= row < self.rows, f"row {row} is OOB"
    
    def in_bounds(self, row: int, col: int) -> bool:
        return 0 <= row < self.rows and 0 <= col < self.cols
    
    def __contains__(self, coord: typing.Union[typing.Tuple[int, int], typing.List[int]]) -> bool:
        return self.in_bounds(*coord)
    
    def __getitem__(self, coord: typing.Union[typing.Tuple[int, int], typing.List[int]]) -> T:
        return self.grid[coord[0]][coord[1]]
#endregion

#region List/Vector operations
GRID_DELTA = [[-1, 0], [1, 0], [0, -1], [0, 1]]
OCT_DELTA = [[1, 1], [-1, -1], [1, -1], [-1, 1]] + GRID_DELTA
CHAR_TO_DELTA = {
    "U": [-1, 0],
    "R": [0, 1],
    "D": [1, 0],
    "L": [0, -1],
    "N": [-1, 0],
    "E": [0, 1],
    "S": [1, 0],
    "W": [0, -1],
}
DELTA_TO_UDLR = {
    (-1, 0): "U",
    (0, 1): "R",
    (1, 0): "D",
    (0, -1): "L",
}
DELTA_TO_NESW = {
    (-1, 0): "N",
    (0, 1): "E",
    (1, 0): "S",
    (0, -1): "W",
}
def turn_180(drowcol):
    drow, dcol = drowcol
    return [-drow, -dcol]
def turn_right(drowcol):
    # positive dcol -> positive drow
    # positive drow -> negative dcol
    drow, dcol = drowcol
    return [dcol, -drow]
def turn_left(drowcol):
    drow, dcol = drowcol
    return [-dcol, drow]
def dimensions(grid: typing.List) -> typing.List[int]:
    out = []
    while isinstance(grid, list):
        out.append(len(grid))
        grid = grid[0]
    return out
def neighbours(coord, dimensions, deltas) -> typing.List[typing.List[int]]:
    out = []
    for delta in deltas:
        new_coord = padd(coord, delta)
        if all(0 <= c < c_max for c, c_max in zip(new_coord, dimensions)):
            out.append(new_coord)
    return out
def lget(l, i):
    if len(l) == 2: return l[i[0]][i[1]]
    for index in i: l = l[index]
    return l
def lset(l, i, v):
    if len(l) == 2:
        l[i[0]][i[1]] = v
        return
    for index in i[:-1]: l = l[index]
    l[i[-1]] = v
def points_sub_min(points):
    m = [min(p[i] for p in points) for i in range(len(points[0]))]
    return [psub(p, m) for p in points]
def points_to_grid(points, sub_min=True, flip=True):
    if sub_min:
        points = points_sub_min(points)
    if not flip:
        points = [(y, x) for x, y in points]
    grid = make_grid(max(map(snd, points))+1, max(map(fst, points))+1, fill='.')
    for x, y in points:
        grid[y][x] = '#'
    return grid
def print_grid(grid):
    for line in grid:
        print(*line, sep="")
def fst(x):
    return x[0]
def snd(x):
    return x[1]

def padd(x, y):
    return [a+b for a, b in zip(x, y)]
def pneg(v):
    return [-i for i in v]
def psub(x, y):
    return [a-b for a, b in zip(x, y)]
def pmul(m: int, v):
    return [m * i for i in v]
def pdot(x, y):
    return sum(a*b for a, b in zip(x, y))
def pdist1(x, y=None):
    if y is not None: x = psub(x, y)
    return sum(map(abs, x))
def pdist2sq(x, y=None):
    if y is not None: x = psub(x, y)
    return sum(i*i for i in x)
def pdist2(v):
    return math.sqrt(pdist2sq(v))
def pdistinf(x, y=None):
    if y is not None: x = psub(x, y)
    return max(map(abs, x))

def signum(n: int) -> int:
    if n > 0:
        return 1
    elif n == 0:
        return 0
    else:
        return -1
#endregion

#region Matrices
def matmat(a, b):
    n, k1 = len(a), len(a[0])
    k2, m = len(b), len(b[0])
    assert k1 == k2
    out = [[None] * m for _ in range(n)]
    for i in range(n):
        for j in range(m): out[i][j] = sum(a[i][k] * b[k][j] for k in range(k1))
    return out
def matvec(a, v):
    return [j for i in matmat(a, [[x] for x in v]) for j in i]
def matexp(a, k):
    n = len(a)
    out = [[int(i==j) for j in range(n)] for i in range(n)]
    while k > 0:
        if k % 2 == 1: out = matmat(a, out)
        a = matmat(a, a)
        k //= 2
    return out
#endregion


#region Running
def parse_samples(l):
    samples = [thing.strip("\n") for thing in l]
    while samples and not samples[-1]: samples.pop()
    return samples

def get_actual(day=None, year=None):
    try:
        this_file = __file__
    except NameError:
        this_file = "./utils.py"
    try:
        actual_input = open("./2021/23.input").read()
        return actual_input
    except FileNotFoundError:
        pass
    from pathlib import Path
    cur_folder = Path(this_file).resolve().parent
    input_path = cur_folder.joinpath("input.txt")
    search_path = cur_folder
    try:
        if day is None:
            day = int(search_path.name)
        if year is None:
            year = int(search_path.parent.name)
    except Exception:
        print("Can't get day and year.")
        print("Backup: save 'input.txt' into the same folder as this script.")
        return ""
    
    print("{} day {} input not found.".format(year, day))
    
    # is it time?
    from datetime import datetime, timezone, timedelta
    est = timezone(timedelta(hours=-5))
    unlock_time = datetime(year, 12, day, tzinfo=est)
    cur_time = datetime.now(tz=est)
    delta = unlock_time - cur_time
    if delta.days >= 0:
        print("Remaining time until unlock: {}".format(delta))
        return ""

    while (not list(search_path.glob("*/token.txt"))) and search_path.parent != search_path:
        search_path = search_path.parent
    
    token_files = list(search_path.glob("*/token.txt"))
    if not token_files:
        assert search_path.parent == search_path
        print("Can't find token.txt in a parent directory.")
        print("Backup: save 'input.txt' into the same folder as this script.")
        return ""
    
    with token_files[0].open() as f:
        token = f.read().strip()
    
    # importing requests takes a long time...
    # let's do it without requests.
    import urllib.request
    import urllib.error
    import shutil
    opener = urllib.request.build_opener()
    opener.addheaders = [("Cookie", "session={}".format(token)), ("User-Agent", "python-requests/2.19.1")]
    print("Sending request...")
    url = "https://adventofcode.com/{}/day/{}/input".format(year, day)
    try:
        with opener.open(url) as r:
            with input_path.open(mode="wb") as f:
                shutil.copyfileobj(r, f)
            print("Input saved! First few lines look like:")
            actual = input_path.open().read()
            lines = actual.splitlines()
            for line in lines[:16]:
                print(line[:80] + "…" * (len(line) > 80))
            return actual
    except urllib.error.HTTPError as e:
        status_code = e.getcode()
        if status_code == 400:
            print("Auth failed!")
        elif status_code == 404:
            print("Day is not out yet????")
        else:
            print("Request failed with code {}??".format(status_code))
        return ""

def run_samples_and_actual(samples, do_case):
    samples = parse_samples(samples)
    for sample in samples:
        print("running {}:".format(repr(sample)[:100]))
        print("-"*10)
        do_case(sample, True)
        print("-"*10)
        print("#"*10)

    actual_input = get_actual().strip("\n")

    if actual_input:
        print("!! running actual ({} lines): !!".format(actual_input.count("\n")+1))
        print("-"*10)
        do_case(actual_input, False)
        print("-"*10)
#endregion

import sys; sys.dont_write_bytecode = True; from utils import *

WAITING_ROW = 1
WAITING_COLS = [1, 2, 4, 6, 8, 10, 11]
ROOM_COLS = [3, 5, 7, 9]
COST = {"A": 1, "B": 10, "C": 100, "D": 1000}

def do_case(inp: str, sample=False):
    # READ THE PROBLEM FROM TOP TO BOTTOM OK
    def sprint(*a, **k): sample and print(*a, **k)
    lines: typing.List[str] = inp.splitlines()
    out = 0

    FINAL_NODE = tuple()

    def expand(node):
        # (weight, node)
        out = []

        # I wrote this line of code first before doing anything else
        # with the problem. It's good to know your search space!
        cur_waitings, cur_rooms = node

        if all(all(chr(ord('A')+i) == x for x in room) for i, room in enumerate(cur_rooms)):
            return [(0, FINAL_NODE)]
        
        def is_blocked(col_1, col_2):
            if col_1 > col_2:
                col_1, col_2 = col_2, col_1
            for blocked_col in range(col_1+1, col_2):
                # This could really be improved...
                if blocked_col in WAITING_COLS and cur_waitings[WAITING_COLS.index(blocked_col)] != "":
                    return True
            return False
        
        # Move from a room to a waiting spot.
        for room_idx, room in enumerate(cur_rooms):
            # The below uses the fact that:
            # - loop variables are still in-scope after the loop is finished, and
            # - you can add an "else" to a for loop which is run if it's not `break`ed from.
            for room_position, to_move in enumerate(room):
                if to_move == "":
                    continue
                to_move_row = 2+room_position
                break
            else:
                continue
            for waiting_idx, waiting_col in enumerate(WAITING_COLS):
                if cur_waitings[waiting_idx] == "":
                    if is_blocked(waiting_col, ROOM_COLS[room_idx]):
                        continue

                    new_waitings = list(cur_waitings)
                    new_rooms = list(map(list, cur_rooms))

                    # To get the cost of moving, I used the Manhattan distance
                    # between the source and destination as it should always work
                    # for this with a single corridor.
                    # If the corridor was expanded, this wouldn't be as simple...
                    cost = pdist1((to_move_row, ROOM_COLS[room_idx]), (WAITING_ROW, waiting_col)) * COST[to_move]
                    new_waitings[waiting_idx] = to_move
                    new_rooms[room_idx][room_position] = ""
                    out.append((cost, (tuple(new_waitings), tuple(map(tuple, new_rooms)))))
        
        # Move from a waiting spot to a room.
        for waiting_idx, waiting_col in enumerate(WAITING_COLS):
            to_move = cur_waitings[waiting_idx]
            if to_move == "":
                continue

            target_room_idx = ord(to_move) - ord('A')
            target_room = cur_rooms[target_room_idx]

            if target_room[0] == "" and all(x == "" or x == to_move for x in target_room[1:]):
                for room_position in range(len(target_room))[::-1]:
                    if target_room[room_position] != "":
                        continue
                    room_row = room_position + 2
                    break
                else:
                    assert False

                room_col = ROOM_COLS[target_room_idx]
                if is_blocked(waiting_col, room_col):
                    continue
                
                cost = pdist1((room_row, room_col), (WAITING_ROW, waiting_col)) * COST[to_move]

                new_waitings = list(cur_waitings)
                new_rooms = list(map(list, cur_rooms))

                new_waitings[waiting_idx] = ""
                new_rooms[target_room_idx][room_position] = to_move
                out.append((cost, (tuple(new_waitings), tuple(map(tuple, new_rooms)))))

        return out
    

    rooms = []
    PART2 = ["DD", "CB", "BA", "AC"]
    for i, room_col in enumerate(ROOM_COLS):
        a, b = [lines[row][room_col] for row in [2, 3]]

        rooms.append(tuple(a+PART2[i]+b))
        # Replace the above with the below for part 1.
        # This also came in handy for testing my generalised part 2 code
        # to make sure that it works with part 1.
        # rooms.append(tuple(a+b))
    rooms = tuple(rooms)
    print(rooms)
    waitings = ("",)*len(WAITING_COLS)

    # "A*" here is actually "Dijkstra, with a target node".
    # My internal implementation also returns a path from start to finish,
    # but I don't use it here.
    out, _ = a_star((waitings, rooms), expand, FINAL_NODE)

    if out:
        print("out:    ", out)
    return  # RETURNED VALUE DOESN'T DO ANYTHING, PRINT THINGS INSTEAD



run_samples_and_actual([
r"""
#############
#...........#
###C#A#B#D###
  #B#A#D#C#
  #########

""",r"""

""",r"""

""",r"""

""",r"""

""",r"""

""",r"""

"""], do_case)