lines = open("input.txt", "r").read().splitlines()


def parse_lines(lines: list) -> (set, set):
    sensors = []
    beacons = []
    for line in lines:
        _, _, sx, sy, _, _, _, _, bx, by = line.split(" ")
        sensors.append((int(sx.split("=")[1][:-1]), int(sy.split("=")[1][:-1])))
        beacons.append((int(bx.split("=")[1][:-1]), int(by.split("=")[1])))
    return sensors, beacons


def manhatten(a, b):
    return abs(a[0] - b[0]) + abs(a[1] - b[1])


def build_search_space(sensors, beacons):
    space = set()
    for sensor, beacon in zip(sensors, beacons):
        space.update(sensor_diamond(sensor, beacon))
    return space


def sensor_diamond(sensor, beacon):
    points = set()
    d = manhatten(sensor, beacon)
    xr = range(d + 2)
    yr = xr[::-1]
    xrneg = range(0, (d + 2) * -1, -1)
    yrneg = xrneg[::-1]
    for x, y, xneg, yneg in zip(xr, yr, xrneg, yrneg):
        points.add((sensor[0] + x, sensor[1] + y))
        points.add((sensor[0] + xneg, sensor[1] + y))
        points.add((sensor[0] + x, sensor[1] + yneg))
        points.add((sensor[0] + xneg, sensor[1] + yneg))
    return points


def search_candidates(sensors, beacons, space):
    candidates = set()
    counter = 0
    for point in space:
        is_candidate = False
        if x_min <= point[0] <= x_max and y_min <= point[1] <= y_max:
            is_candidate = True
            for sensor, beacon in zip(sensors, beacons):
                if manhatten(sensor, point) <= manhatten(sensor, beacon):
                    is_candidate = False
        if is_candidate:
            print("candidate found")
            candidates.add(point)
        counter += 1
        if counter % 100000 == 0:
            print(f"{counter} points searched")
    return candidates


x_min, x_max = 0, 4000000
y_min, y_max = 0, 4000000
sensors, beacons = parse_lines(lines)

space = build_search_space(sensors, beacons)
print("space set up")
candidates = search_candidates(sensors, beacons, space)
print(candidates)
x, y = candidates.pop()
print(x * 4000000 + y)