import bisect, math
from itertools import combinations
input = open("input", 'r')

points = []
for line in input:
    points.append(tuple((int(cord) for cord in line.split(","))))

# distances = []
# distance_key = lambda d: d[0]
# for i, p in enumerate(points):
#     for j, q in enumerate(points):
#         if i<=j: continue # Avoid duplicates
#         # we'll work with square distances because it won't matter
#         dist = math.dist(*[p,q])
#         bisect.insort(distances, (dist, i, j), key=distance_key)

distances = sorted(combinations(points,2), key=lambda p: math.dist(*p))

circuits = {frozenset([p]) for p in points}

def solution(distances, circuits, pairs=1000, part2=False):
    for i, (p1, p2) in enumerate(distances):
        if not part2 and i >= pairs:
            circuits_by_len = sorted(circuits, key=len, reverse=True)
            return math.prod([len(circuit) for circuit in circuits_by_len[:3]])
        p1_group = [circuit for circuit in circuits if p1 in circuit][0]
        p2_group = [circuit for circuit in circuits if p2 in circuit][0]
        circuits -= {p1_group, p2_group}
        circuits.add(p1_group | p2_group)
        if part2 and len(circuits) == 1:
            return p1[0] * p2[0]
    return None # Impossible!


# print(solution(distances, circuits, points, pairs=10))
print(solution(distances, circuits))
print(solution(distances, circuits, part2=True))