from lib import *
import sympy as sp

EXAMPLE = """19, 13, 30 @ -2,  1, -2
18, 19, 22 @ -1, -1, -2
20, 25, 34 @ -2, -2, -4
12, 31, 28 @ -1, -2, -1
20, 19, 15 @  1, -5, -3
"""


def solve1(input: Input):
    if len(input.lines()) == 5:
        lb = 7
        ub = 27
    else:
        lb = 200000000000000
        ub = 400000000000000

    # On paper:
    # (px - sx1) / vx1 = (py - sy1) / vy1
    # (px - sx1) * vy1 = (py - sy1) * vx1
    # (px - sx1) * vy1 - (py - sy1) * vx1 = 0
    res = 0
    eqs = [str_to_ints(l) for l in input.lines()]
    for i, eq1 in enumerate(eqs):
        for eq2 in eqs[:i]:
            sx1, sy1, _, vx1, vy1, _ = eq1
            sx2, sy2, _, vx2, vy2, _ = eq2

            px, py = sp.symbols("px py")
            es = [
                vy1 * (px - sx1) - vx1 * (py - sy1),
                vy2 * (px - sx2) - vx2 * (py - sy2),
            ]
            r = sp.solve(es)
            if not r:
                continue

            x, y = r[px], r[py]
            if lb <= x <= ub and lb <= y < ub:
                t1 = (x - sx1) / vx1
                t2 = (x - sx2) / vx2
                if (t1 > 0 and t2 > 0):
                    res += 1

    return res


def solve2(input: Input):
    eqs = [str_to_ints(l) for l in input.lines()]
    px, py, pz, vxo, vyo, vzo = sp.symbols("px py pz vxo vyo vzo")
    es = []

    # The first six equations are enough to find a solution for my problem set.
    # Might have to be increased depending on input.
    for i, (x, y, z, vx, vy, vz) in enumerate(eqs[:6]):
        t = sp.symbols(f"t{i}")
        es.append(px + vxo * t - x - vx * t)
        es.append(py + vyo * t - y - vy * t)
        es.append(pz + vzo * t - z - vz * t)
    r = sp.solve(es)[0]
    return r[px] + r[py] + r[pz]

def main():
    DAY_INPUT = "i24.txt"
    print("Solution 1:", solve1(Input(EXAMPLE)))
    print("Solution 1:", solve1(Input(DAY_INPUT)))
    print("Example  2:", solve2(Input(EXAMPLE)))
    print("Solution 2:", solve2(Input(DAY_INPUT)))
    return

if __name__ == "__main__":
    main()