from math import sqrt
from itertools import combinations

from output import ints


def solve(data):
    Di = sorted(
        map(_euclidan_distance, combinations(data.splitlines(), r=2)),
        key=lambda r: r[1],
    )
    C = []
    S = len(data.splitlines())
    IP = 1000
    for i, pq in enumerate(Di, start=1):
        pq, _ = pq
        c = set(pq)
        p, q = pq
        rmq = []
        nothing = False
        for j in C:
            if p in j and q in j:
                nothing = True
                continue
            if p in j or q in j:
                c = c | j
                rmq.append(j)
        C = [e for e in C if e not in rmq]
        if c == pq and nothing:
            continue
        if len(c) == S:
            p2 = ints(p)[0] * ints(q)[0]
            break
        C = [c] + C
        if i == IP:
            a, b, c = sorted(list(map(len, C)), reverse=True)[:3]
            p1 = a * b * c
    return p1, p2


def _euclidan_distance(pq):
    p, q = pq
    p1, p2, p3 = ints(p)
    q1, q2, q3 = ints(q)
    return (p, q), sqrt((p1 - q1) ** 2 + (p2 - q2) ** 2 + (p3 - q3) ** 2)


if __name__ == "__main__":
    with open("./input/08.txt", "r") as f:
        inp = f.read().strip()

    p1, p2 = solve(inp)

    print(p1)
    print(p2)

    assert p1 == 84968
    assert p2 == 8663467782