#!/usr/bin/env python3

import functools
import re
import sys

input_file = sys.argv[1]

with open(input_file) as fd:
    lines = [line.rstrip() for line in fd.readlines()]

coords = tuple[int, int]
prizes: list[coords] = list()
buttons: list[tuple[coords, coords]] = list()

for li, line in enumerate(lines):
    machine = li // 4
    offset = li % 4
    if offset == 0:
        match = re.match(r"^Button A: X\+([0-9]+), Y\+([0-9]+)$", line)
        assert match
        button_a = int(match[1]), int(match[2])
    elif offset == 1:
        match = re.match(r"^Button B: X\+([0-9]+), Y\+([0-9]+)$", line)
        assert match
        button_b = int(match[1]), int(match[2])
        buttons.append((button_a, button_b))
    elif offset == 2:
        match = re.match("^Prize: X=([0-9]+), Y=([0-9]+)$", line)
        assert match
        prize = int(match[1]), int(match[2])
        prizes.append(prize)

assert len(prizes) == len(buttons)

ttoks = 0
for arcade, prize in enumerate(prizes):
    butts = buttons[arcade]
    button_a, button_b = butts

    @functools.lru_cache(4096)
    def fun(x: int, y: int, rem_a: int, rem_b: int) -> int | None:
        if (x, y) == prize:
            return 0
        if x > prize[0] or y > prize[1]:
            return None
        ba = (
            fun(x + button_a[0], y + button_a[1], rem_a - 1, rem_b)
            if rem_a > 0
            else None
        )
        bb = (
            fun(x + button_b[0], y + button_b[1], rem_a, rem_b - 1)
            if rem_b > 0
            else None
        )
        if ba is not None:
            ba += 3
        if bb is not None:
            bb += 1
        if ba is None:
            if bb is None:
                return None
            else:
                return bb
        else:
            if bb is None or ba < bb:
                return ba
            else:
                return bb

    toks = fun(0, 0, 100, 100)
    print(43, arcade, toks)
    if toks is not None:
        ttoks += toks
    # break

print(ttoks)