def parse(filename: str) -> tuple[list[tuple[int, int]], list[tuple[int, ...]]]:
    page_orders = []
    updates = []
    with open(filename) as f:
        first_part = True
        while line := f.readline():
            if first_part and line != "\n":
                page_orders.append(tuple(map(int, line.strip().split("|"))))
            else:
                first_part = False
            if not first_part and line != "\n":
                updates.append(tuple(map(int, filter(lambda x: x != "", line.strip().split(",")))))
    return page_orders, list(map(lambda u: tuple(map(int, u)), updates))


def get_middle_page(update: tuple[int, ...]) -> int:
    return update[int(len(update) / 2)]


def update_is_correct(
    update: tuple[int, ...], not_before: dict[int, list[int]], not_after: dict[int, list[int]]
) -> bool:
    correct = True
    for index, page in enumerate(update[:-1]):
        correct = all(
            map(
                lambda x: x in not_before.get(page, []) and x not in not_after.get(page, []),
                update[index + 1 :],
            )
        )
        if not correct:
            break
    return correct


def condense_page_orders(page_orders: list[tuple[int, int]]) -> tuple[dict[int, list[int]], dict[int, list[int]]]:
    not_before = {}
    not_after = {}
    for item in page_orders:
        if item[0] in not_before:
            not_before[item[0]].append(item[1])
        else:
            not_before[item[0]] = [item[1]]
        if item[1] in not_after:
            not_after[item[1]].append(item[0])
        else:
            not_after[item[1]] = [item[0]]
    return not_before, not_after