// WARN: Input could contain multiple edges, but not self loops
//
// Returns: (BCC count, indices of BCCs of each vertex)
//
// BCC index starts from 1
pair<int, vector<vector<int>>> vbcc(const vector<vector<int>>& ch) {
    int n = ch.size() - 1;
    vector<vector<int>> c(n + 1);  // a vertex could be contained in multiple vBCCs

    int tm = 0;
    int cnt = 0;

    vector<int> low(n + 1), dfn(n + 1);
    vector<int> stack;
    auto dfs = [&] (auto dfs, int v, int pa) -> void {
        int son = 0;
        low[v] = dfn[v] = ++tm;
        stack.emplace_back(v);
        for (auto&& u : ch[v]) {
            if (u == pa) continue;
            son += 1;
            if (not dfn[u]) {
                dfs(dfs, u, v);
                chmin(low[v], low[u]);
                if (low[u] >= dfn[v]) {
                    cnt += 1;
                    int z;
                    do {
                        z = popback(stack);
                        c[z].emplace_back(cnt);
                    } while (z != u);
                    c[v].emplace_back(cnt);
                }
            }
            chmin(low[v], dfn[u]);
        }
        if (pa == 0 and son == 0) {
            cnt += 1;
            c[v].emplace_back(cnt);
        }
    };
    for (int i = 1; i <= n; ++i) {
        if (not dfn[i]) {
            dfs(dfs, i, 0);
        }
    }
    return { cnt, c };
}