from math import inf
from itertools import combinations

from output import ints


def solve(data):
    p1 = 0
    p2 = 0
    A = [tuple(ints(pos)) for pos in data.splitlines()]
    T = inf
    R = 0
    B = 0
    L = inf
    for r, c in A:
        T = min(r, T)
        R = max(c, R)
        B = max(r, B)
        L = min(c, L)
    S = A[0]
    V = set()
    W = set()
    while True:
        V.add(S)
        W.add(S)
        y, x = S
        he = [(r, c) for r, c in A if r == y and (r, c) not in V]
        ve = [(r, c) for r, c in A if c == x and (r, c) not in V]
        if not he and not ve:
            E = A[0]
        elif he and ve:
            E = min(min(he), min(ve))
        elif he and not ve:
            E = min(he)
        else:
            E = min(ve)
        y2, x2 = E
        for r in range(min(y, y2), max(y, y2) + 1):
            for c in range(min(x, x2), max(x, x2) + 1):
                W.add((r, c))
        if E == A[0]:
            break
        S = E
    V = V | W
    for a, b in combinations(A, r=2):
        y1, x1 = a
        y2, x2 = b
        x = abs(x1 - x2) + 1
        y = abs(y1 - y2) + 1
        p1 = max(p1, x * y)
        if _within(W, a, b, T, R, B, L):
            p2 = max(p2, max(p2, x * y))
    return p1, p2


def _within(W, a, b, T, R, B, L):
    y1, x1 = a
    y2, x2 = b
    for r in range(min(y1, y2) + 1, max(y1, y2)):
        for c in range(min(x1, x2) + 1, max(x1, x2)):
            if (r, c) in W:
                continue
            for s, e in [(T, r), (r, B)]:
                z = sum((nr, c) in W for nr in range(s, e))
                if z and z % 2 == 0:
                    return False
            for s, e in [(L, c), (c, R)]:
                z = sum((r, nc) in W for nc in range(s, e))
                if z and z % 2 == 0:
                    return False
    return True


if __name__ == "__main__":
    with open("./input/09.txt", "r") as f:
        inp = f.read().strip()

    p1, p2 = solve(inp)

    print(p1)
    print(p2)

    assert p1 == 4749838800
    assert p2 == 1624057680