#!/usr/bin/env python3

"""
Implementing:
https://www.reddit.com/r/adventofcode/comments/1hd7irq/2024_day_13_an_explanation_of_the_mathematics/
"""

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])
        # prize = prize[0] + 10000000000000, prize[1] + 10000000000000
        prizes.append(prize)

assert len(prizes) == len(buttons)

ttoks = 0
token_a, token_b = 3, 1
for arcade, prize in enumerate(prizes):
    butts = buttons[arcade]
    button_a, button_b = butts

    print(43, prize, button_a, button_b)
    p_x, p_y = prize
    a_x, a_y = button_a
    b_x, b_y = button_b

    denom = a_x * b_y - a_y * b_x
    a = (p_x * b_y - p_y * b_x) / denom
    b = (a_x * p_y - a_y * p_x) / denom

    if not a.is_integer() or not b.is_integer():
        print(76, None)
        continue

    toks = int(a) * token_a + int(b) * token_b
    print(76, toks)
    ttoks += toks

print(ttoks)