# pyright: reportUnknownMemberType=false

from typing import Any, Iterator

import networkx as nx

from ..base import BaseSolver


class Solver(BaseSolver):
    def solve(self, input: str) -> Iterator[Any]:
        components = {
            (p := line.split(": "))[0]: p[1].split() for line in input.splitlines()
        }

        graph: "nx.Graph[str]" = nx.Graph()
        graph.add_edges_from((u, v) for u, vs in components.items() for v in vs)

        cut = nx.minimum_edge_cut(graph)
        graph.remove_edges_from(cut)

        c1, c2 = nx.connected_components(graph)

        # part 1
        yield len(c1) * len(c2)